LMFDB - Embedded newform 58.7.f.b.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [58,7,Mod(3,58)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(58, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("58.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	58.f (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.3431368500$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	58.11
Dual form			58.7.f.b.37.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.33941 + 1.86834i) q^{2} +(5.12154 + 45.4549i) q^{3} +(25.0186 - 19.9517i) q^{4} +(-100.885 + 209.491i) q^{5} +(-112.271 - 233.134i) q^{6} +(-148.380 + 186.062i) q^{7} +(-96.3081 + 153.273i) q^{8} +(-1329.20 + 303.381i) q^{9} +O(q^{10})$	\(q+(-5.33941 + 1.86834i) q^{2} +(5.12154 + 45.4549i) q^{3} +(25.0186 - 19.9517i) q^{4} +(-100.885 + 209.491i) q^{5} +(-112.271 - 233.134i) q^{6} +(-148.380 + 186.062i) q^{7} +(-96.3081 + 153.273i) q^{8} +(-1329.20 + 303.381i) q^{9} +(147.269 - 1307.04i) q^{10} +(987.687 + 1571.90i) q^{11} +(1035.04 + 1035.04i) q^{12} +(2812.48 + 641.930i) q^{13} +(444.632 - 1270.69i) q^{14} +(-10039.1 - 3512.82i) q^{15} +(227.861 - 998.326i) q^{16} +(228.184 - 228.184i) q^{17} +(6530.32 - 4103.27i) q^{18} +(10029.7 + 1130.08i) q^{19} +(1655.68 + 7254.00i) q^{20} +(-9217.38 - 5791.66i) q^{21} +(-8210.50 - 6547.66i) q^{22} +(4243.87 - 2043.74i) q^{23} +(-7460.28 - 3592.68i) q^{24} +(-23966.4 - 30053.0i) q^{25} +(-16216.3 + 1827.14i) q^{26} +(-9584.13 - 27389.9i) q^{27} +7615.44i q^{28} +(-22961.2 + 8222.26i) q^{29} +60165.9 q^{30} +(33815.5 - 11832.6i) q^{31} +(648.568 + 5756.20i) q^{32} +(-66391.9 + 52945.8i) q^{33} +(-792.042 + 1644.69i) q^{34} +(-24009.0 - 49855.1i) q^{35} +(-27201.8 + 34109.9i) q^{36} +(29241.5 - 46537.6i) q^{37} +(-55664.3 + 12705.0i) q^{38} +(-14774.7 + 131129. i) q^{39} +(-22393.3 - 35638.7i) q^{40} +(89582.1 + 89582.1i) q^{41} +(60036.2 + 13702.9i) q^{42} +(6991.86 - 19981.6i) q^{43} +(56072.5 + 19620.6i) q^{44} +(70541.3 - 309062. i) q^{45} +(-18841.3 + 18841.3i) q^{46} +(36682.9 - 23049.4i) q^{47} +(46545.9 + 5244.46i) q^{48} +(13576.7 + 59483.6i) q^{49} +(184116. + 115688. i) q^{50} +(11540.7 + 9203.43i) q^{51} +(83171.9 - 40053.5i) q^{52} +(67637.3 + 32572.4i) q^{53} +(102347. + 128339. i) q^{54} +(-428941. + 48330.0i) q^{55} +(-14228.2 - 40662.0i) q^{56} +461689. i q^{57} +(107237. - 86801.4i) q^{58} -29993.6 q^{59} +(-321250. + 112410. i) q^{60} +(-7275.48 - 64571.6i) q^{61} +(-158448. + 126358. i) q^{62} +(140778. - 292329. i) q^{63} +(-14217.5 - 29522.9i) q^{64} +(-418216. + 524427. i) q^{65} +(255573. - 406742. i) q^{66} +(-140477. + 32062.9i) q^{67} +(1156.19 - 10261.5i) q^{68} +(114633. + 182438. i) q^{69} +(221340. + 221340. i) q^{70} +(11430.4 + 2608.91i) q^{71} +(81512.4 - 232949. i) q^{72} +(-336425. - 117720. i) q^{73} +(-69184.4 + 303116. i) q^{74} +(1.24331e6 - 1.24331e6i) q^{75} +(273477. - 171837. i) q^{76} +(-439023. - 49466.0i) q^{77} +(-166105. - 727754. i) q^{78} +(118829. + 74665.0i) q^{79} +(186152. + 148451. i) q^{80} +(300441. - 144685. i) q^{81} +(-645686. - 310946. i) q^{82} +(-79919.7 - 100216. i) q^{83} +(-346159. + 39002.8i) q^{84} +(24782.0 + 70822.8i) q^{85} +119753. i q^{86} +(-491339. - 1.00159e6i) q^{87} -336052. q^{88} +(1.01266e6 - 354346. i) q^{89} +(200783. + 1.78200e6i) q^{90} +(-536753. + 428047. i) q^{91} +(65399.6 - 135804. i) q^{92} +(711037. + 1.47648e6i) q^{93} +(-152801. + 191607. i) q^{94} +(-1.24860e6 + 1.98713e6i) q^{95} +(-258326. + 58961.2i) q^{96} +(-11479.2 + 101881. i) q^{97} +(-183627. - 292241. i) q^{98} +(-1.78972e6 - 1.78972e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 64 q^{2} - 28 q^{3} - 588 q^{5} - 610 q^{7} + 2048 q^{8}+O(q^{10}) $ 96 * q - 64 * q^2 - 28 * q^3 - 588 * q^5 - 610 * q^7 + 2048 * q^8	\( 96 q - 64 q^{2} - 28 q^{3} - 588 q^{5} - 610 q^{7} + 2048 q^{8} - 1744 q^{10} + 1752 q^{11} + 896 q^{12} - 2608 q^{14} - 3048 q^{15} + 16384 q^{16} - 2144 q^{17} + 24368 q^{18} - 20742 q^{19} + 16064 q^{20} + 80556 q^{21} + 35280 q^{22} + 24730 q^{23} - 17920 q^{24} + 9556 q^{25} - 45072 q^{26} - 196048 q^{27} + 55514 q^{29} + 54464 q^{30} + 130770 q^{31} + 65536 q^{32} + 469616 q^{33} - 65184 q^{34} - 153664 q^{35} + 56960 q^{36} - 361120 q^{37} - 229040 q^{38} + 16520 q^{39} + 19456 q^{40} + 267404 q^{41} - 288064 q^{42} - 104504 q^{43} - 18432 q^{44} + 17462 q^{45} - 12912 q^{46} - 278966 q^{47} + 28672 q^{48} - 59808 q^{49} + 882256 q^{50} + 465150 q^{51} + 125952 q^{52} - 1150130 q^{53} + 31312 q^{54} - 2377762 q^{55} + 83456 q^{56} + 392288 q^{58} - 2028140 q^{59} - 97536 q^{60} + 875164 q^{61} + 404880 q^{62} + 4558036 q^{63} - 731620 q^{65} - 978576 q^{66} - 394170 q^{67} + 68608 q^{68} - 2223748 q^{69} - 1125008 q^{70} - 3274600 q^{71} + 34304 q^{72} + 2623288 q^{73} + 1590592 q^{74} + 3502816 q^{75} + 1044096 q^{76} - 196188 q^{77} + 988064 q^{78} + 854806 q^{79} + 4049800 q^{81} - 3418208 q^{82} - 2509204 q^{83} - 3344768 q^{84} - 4533520 q^{85} + 1785564 q^{87} - 147456 q^{88} + 5032828 q^{89} + 757472 q^{90} + 5996522 q^{91} + 6471360 q^{92} - 1360380 q^{93} + 4358912 q^{94} - 3508130 q^{95} + 6610532 q^{97} - 8015840 q^{98} - 833400 q^{99}+O(q^{100}) \) 96 * q - 64 * q^2 - 28 * q^3 - 588 * q^5 - 610 * q^7 + 2048 * q^8 - 1744 * q^10 + 1752 * q^11 + 896 * q^12 - 2608 * q^14 - 3048 * q^15 + 16384 * q^16 - 2144 * q^17 + 24368 * q^18 - 20742 * q^19 + 16064 * q^20 + 80556 * q^21 + 35280 * q^22 + 24730 * q^23 - 17920 * q^24 + 9556 * q^25 - 45072 * q^26 - 196048 * q^27 + 55514 * q^29 + 54464 * q^30 + 130770 * q^31 + 65536 * q^32 + 469616 * q^33 - 65184 * q^34 - 153664 * q^35 + 56960 * q^36 - 361120 * q^37 - 229040 * q^38 + 16520 * q^39 + 19456 * q^40 + 267404 * q^41 - 288064 * q^42 - 104504 * q^43 - 18432 * q^44 + 17462 * q^45 - 12912 * q^46 - 278966 * q^47 + 28672 * q^48 - 59808 * q^49 + 882256 * q^50 + 465150 * q^51 + 125952 * q^52 - 1150130 * q^53 + 31312 * q^54 - 2377762 * q^55 + 83456 * q^56 + 392288 * q^58 - 2028140 * q^59 - 97536 * q^60 + 875164 * q^61 + 404880 * q^62 + 4558036 * q^63 - 731620 * q^65 - 978576 * q^66 - 394170 * q^67 + 68608 * q^68 - 2223748 * q^69 - 1125008 * q^70 - 3274600 * q^71 + 34304 * q^72 + 2623288 * q^73 + 1590592 * q^74 + 3502816 * q^75 + 1044096 * q^76 - 196188 * q^77 + 988064 * q^78 + 854806 * q^79 + 4049800 * q^81 - 3418208 * q^82 - 2509204 * q^83 - 3344768 * q^84 - 4533520 * q^85 + 1785564 * q^87 - 147456 * q^88 + 5032828 * q^89 + 757472 * q^90 + 5996522 * q^91 + 6471360 * q^92 - 1360380 * q^93 + 4358912 * q^94 - 3508130 * q^95 + 6610532 * q^97 - 8015840 * q^98 - 833400 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{25}{28}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.33941	+	1.86834i	−0.667426	+	0.233543i
$2$	−5.33941	+	1.86834i	−0.667426	+	0.233543i
$3$	5.12154	+	45.4549i	0.189687	+	1.68352i	0.622960	+	0.782254i	$0.285930\pi$
$3$	5.12154	+	45.4549i	0.189687	+	1.68352i	−0.433273	+	0.901263i	$0.642641\pi$
$4$	25.0186	−	19.9517i	0.390916	−	0.311745i
$5$	−100.885	+	209.491i	−0.807083	+	1.67593i	−0.0725375	+	0.997366i	$0.523110\pi$
$5$	−100.885	+	209.491i	−0.807083	+	1.67593i	−0.734545	+	0.678559i	$0.762605\pi$
$6$	−112.271	−	233.134i	−0.519775	−	1.07932i
$7$	−148.380	+	186.062i	−0.432594	+	0.542455i	−0.949574	−	0.313542i	$-0.898484\pi$
$7$	−148.380	+	186.062i	−0.432594	+	0.542455i	0.516981	+	0.855997i	$0.327056\pi$
$8$	−96.3081	+	153.273i	−0.188102	+	0.299362i
$9$	−1329.20	+	303.381i	−1.82332	+	0.416161i
$10$	147.269	−	1307.04i	0.147269	−	1.30704i
$11$	987.687	+	1571.90i	0.742064	+	1.18099i	0.977875	+	0.209189i	$0.0670825\pi$
$11$	987.687	+	1571.90i	0.742064	+	1.18099i	−0.235811	+	0.971799i	$0.575775\pi$
$12$	1035.04	+	1035.04i	0.598979	+	0.598979i
$13$	2812.48	+	641.930i	1.28014	+	0.292185i	0.807919	−	0.589293i	$-0.200594\pi$
$13$	2812.48	+	641.930i	1.28014	+	0.292185i	0.472225	+	0.881478i	$0.343451\pi$
$14$	444.632	−	1270.69i	0.162038	−	0.463078i
$15$	−10039.1	−	3512.82i	−2.97454	−	1.04084i
$16$	227.861	−	998.326i	0.0556302	−	0.243732i
$17$	228.184	−	228.184i	0.0464449	−	0.0464449i	−0.683503	−	0.729948i	$-0.739544\pi$
$17$	228.184	−	228.184i	0.0464449	−	0.0464449i	0.729948	+	0.683503i	$0.239544\pi$
$18$	6530.32	−	4103.27i	1.11974	−	0.703579i
$19$	10029.7	+	1130.08i	1.46228	+	0.164759i	0.806964	−	0.590600i	$-0.201109\pi$
$19$	10029.7	+	1130.08i	1.46228	+	0.164759i	0.655311	+	0.755359i	$0.272538\pi$
$20$	1655.68	+	7254.00i	0.206960	+	0.906750i
$21$	−9217.38	−	5791.66i	−0.995290	−	0.625382i
$22$	−8210.50	−	6547.66i	−0.771084	−	0.614919i
$23$	4243.87	−	2043.74i	0.348801	−	0.167974i	−0.251277	−	0.967915i	$-0.580850\pi$
$23$	4243.87	−	2043.74i	0.348801	−	0.167974i	0.600078	+	0.799941i	$0.295136\pi$
$24$	−7460.28	−	3592.68i	−0.539662	−	0.259887i
$25$	−23966.4	−	30053.0i	−1.53385	−	1.92339i
$26$	−16216.3	+	1827.14i	−0.922640	+	0.103957i
$27$	−9584.13	−	27389.9i	−0.486924	−	1.39155i
$28$			7615.44i			0.346913i
$29$	−22961.2	+	8222.26i	−0.941458	+	0.337130i
$29$	−22961.2	+	8222.26i	−0.941458	+	0.337130i
$30$	60165.9			2.22837
$31$	33815.5	−	11832.6i	1.13509	−	0.397186i	0.303643	−	0.952786i	$-0.401797\pi$
$31$	33815.5	−	11832.6i	1.13509	−	0.397186i	0.831450	+	0.555600i	$0.187511\pi$
$32$	648.568	+	5756.20i	0.0197927	+	0.175665i
$33$	−66391.9	+	52945.8i	−1.84745	+	1.47329i
$34$	−792.042	+	1644.69i	−0.0201517	+	0.0418454i
$35$	−24009.0	−	49855.1i	−0.559976	−	1.16280i
$36$	−27201.8	+	34109.9i	−0.583028	+	0.731094i
$37$	29241.5	−	46537.6i	0.577291	−	0.918753i	−0.422632	−	0.906302i	$-0.638894\pi$
$37$	29241.5	−	46537.6i	0.577291	−	0.918753i	0.999922	−	0.0124516i	$-0.00396358\pi$
$38$	−55664.3	+	12705.0i	−1.01444	+	0.231539i
$39$	−14774.7	+	131129.i	−0.249071	+	2.21057i
$40$	−22393.3	−	35638.7i	−0.349895	−	0.556855i
$41$	89582.1	+	89582.1i	1.29978	+	1.29978i	0.928535	+	0.371244i	$0.121069\pi$
$41$	89582.1	+	89582.1i	1.29978	+	1.29978i	0.371244	+	0.928535i	$0.378931\pi$
$42$	60036.2	+	13702.9i	0.810336	+	0.184954i
$43$	6991.86	−	19981.6i	0.0879401	−	0.251318i	−0.891511	−	0.452998i	$-0.850354\pi$
$43$	6991.86	−	19981.6i	0.0879401	−	0.251318i	0.979451	+	0.201680i	$0.0646401\pi$
$44$	56072.5	+	19620.6i	0.658252	+	0.230332i
$45$	70541.3	−	309062.i	0.774116	−	3.39162i
$46$	−18841.3	+	18841.3i	−0.193570	+	0.193570i
$47$	36682.9	−	23049.4i	0.353322	−	0.222007i	−0.343662	−	0.939093i	$-0.611668\pi$
$47$	36682.9	−	23049.4i	0.353322	−	0.222007i	0.696984	+	0.717086i	$0.254525\pi$
$48$	46545.9	+	5244.46i	0.420879	+	0.0474217i
$49$	13576.7	+	59483.6i	0.115400	+	0.505602i
$50$	184116.	+	115688.i	1.47293	+	0.925501i
$51$	11540.7	+	9203.43i	0.0870008	+	0.0693808i
$52$	83171.9	−	40053.5i	0.591516	−	0.284859i
$53$	67637.3	+	32572.4i	0.454317	+	0.218787i	0.647025	−	0.762469i	$-0.276013\pi$
$53$	67637.3	+	32572.4i	0.454317	+	0.218787i	−0.192708	+	0.981256i	$0.561727\pi$
$54$	102347.	+	128339.i	0.649972	+	0.815039i
$55$	−428941.	+	48330.0i	−2.57815	+	0.290488i
$56$	−14228.2	−	40662.0i	−0.0810190	−	0.231539i
$57$			461689.i			2.49302i
$58$	107237.	−	86801.4i	0.549620	−	0.444880i
$59$	−29993.6			−0.146040			−0.0730200	−	0.997330i	$-0.523264\pi$
$59$	−29993.6			−0.146040			−0.0730200	+	0.997330i	$0.523264\pi$
$60$	−321250.	+	112410.i	−1.48727	+	0.520418i
$61$	−7275.48	−	64571.6i	−0.0320532	−	0.284480i	−0.999506	−	0.0314287i	$-0.989994\pi$
$61$	−7275.48	−	64571.6i	−0.0320532	−	0.284480i	0.967453	−	0.253052i	$-0.0814343\pi$
$62$	−158448.	+	126358.i	−0.664831	+	0.530185i
$63$	140778.	−	292329.i	0.563008	−	1.16910i
$64$	−14217.5	−	29522.9i	−0.0542355	−	0.112621i
$65$	−418216.	+	524427.i	−1.52286	+	1.90961i
$66$	255573.	−	406742.i	0.888962	−	1.41477i
$67$	−140477.	+	32062.9i	−0.467068	+	0.106605i	−0.449577	−	0.893242i	$-0.648425\pi$
$67$	−140477.	+	32062.9i	−0.467068	+	0.106605i	−0.0174914	+	0.999847i	$0.505568\pi$
$68$	1156.19	−	10261.5i	0.00367708	−	0.0326350i
$69$	114633.	+	182438.i	0.348950	+	0.555351i
$70$	221340.	+	221340.i	0.645306	+	0.645306i
$71$	11430.4	+	2608.91i	0.0319363	+	0.00728926i	0.238459	−	0.971153i	$-0.423358\pi$
$71$	11430.4	+	2608.91i	0.0319363	+	0.00728926i	−0.206523	+	0.978442i	$0.566215\pi$
$72$	81512.4	−	232949.i	0.218387	−	0.624113i
$73$	−336425.	−	117720.i	−0.864807	−	0.302609i	−0.138820	−	0.990318i	$-0.544331\pi$
$73$	−336425.	−	117720.i	−0.864807	−	0.302609i	−0.725987	+	0.687709i	$0.758617\pi$
$74$	−69184.4	+	303116.i	−0.170731	+	0.748022i
$75$	1.24331e6	−	1.24331e6i	2.94711	−	2.94711i
$76$	273477.	−	171837.i	0.622989	−	0.391450i
$77$	−439023.	−	49466.0i	−0.961646	−	0.108351i
$78$	−166105.	−	727754.i	−0.350025	−	1.53356i
$79$	118829.	+	74665.0i	0.241013	+	0.151438i	0.647123	−	0.762386i	$-0.275972\pi$
$79$	118829.	+	74665.0i	0.241013	+	0.151438i	−0.406110	+	0.913824i	$0.633115\pi$
$80$	186152.	+	148451.i	0.363578	+	0.289944i
$81$	300441.	−	144685.i	0.565333	−	0.272250i
$82$	−645686.	−	310946.i	−1.17106	−	0.563953i
$83$	−79919.7	−	100216.i	−0.139772	−	0.175268i	0.707019	−	0.707195i	$-0.250040\pi$
$83$	−79919.7	−	100216.i	−0.139772	−	0.175268i	−0.846790	+	0.531927i	$0.821468\pi$
$84$	−346159.	+	39002.8i	−0.584034	+	0.0658048i
$85$	24782.0	+	70822.8i	0.0403533	+	0.115323i
$86$			119753.i			0.188274i
$87$	−491339.	−	1.00159e6i	−0.746146	−	1.52101i
$88$	−336052.			−0.493127
$89$	1.01266e6	−	354346.i	1.43646	−	0.502640i	0.503936	−	0.863741i	$-0.331885\pi$
$89$	1.01266e6	−	354346.i	1.43646	−	0.502640i	0.932527	+	0.361101i	$0.117599\pi$
$90$	200783.	+	1.78200e6i	0.275423	+	2.44445i
$91$	−536753.	+	428047.i	−0.712280	+	0.568024i
$92$	65399.6	−	135804.i	0.0839870	−	0.174401i
$93$	711037.	+	1.47648e6i	0.883981	+	1.83561i
$94$	−152801.	+	191607.i	−0.183968	+	0.230689i
$95$	−1.24860e6	+	1.98713e6i	−1.45630	+	2.31769i
$96$	−258326.	+	58961.2i	−0.291981	+	0.0666427i
$97$	−11479.2	+	101881.i	−0.0125776	+	0.111629i	−0.998432	−	0.0559730i	$-0.982174\pi$
$97$	−11479.2	+	101881.i	−0.0125776	+	0.111629i	0.985855	+	0.167602i	$0.0536025\pi$
$98$	−183627.	−	292241.i	−0.195101	−	0.310501i
$99$	−1.78972e6	−	1.78972e6i	−1.84450	−	1.84450i
$100$	−1.19921e6	−	273713.i	−1.19921	−	0.273713i
$101$	341472.	−	975870.i	0.331429	−	0.947170i	−0.650761	−	0.759282i	$-0.725550\pi$
$101$	341472.	−	975870.i	0.331429	−	0.947170i	0.982191	−	0.187888i	$-0.0601641\pi$
$102$	−78815.9	−	27578.9i	−0.0742700	−	0.0259882i
$103$	−93006.7	+	407489.i	−0.0851143	+	0.372910i	−0.999489	−	0.0319585i	$-0.989826\pi$
$103$	−93006.7	+	407489.i	−0.0851143	+	0.372910i	0.914375	+	0.404868i	$0.132683\pi$
$104$	−369255.	+	369255.i	−0.328267	+	0.328267i
$105$	2.14320e6	−	1.34666e6i	1.85138	−	1.16330i
$106$	−422000.	−	47547.9i	−0.354319	−	0.0399222i
$107$	−334986.	−	1.46767e6i	−0.273448	−	1.19806i	−0.905912	−	0.423466i	$-0.860813\pi$
$107$	−334986.	−	1.46767e6i	−0.273448	−	1.19806i	0.632464	−	0.774590i	$-0.282044\pi$
$108$	−786255.	−	494037.i	−0.624155	−	0.392182i
$109$	827008.	+	659517.i	0.638602	+	0.509268i	0.888424	−	0.459024i	$-0.151801\pi$
$109$	827008.	+	659517.i	0.638602	+	0.509268i	−0.249822	+	0.968292i	$0.580372\pi$
$110$	2.19999e6	−	1.05946e6i	1.65289	−	0.795988i
$111$	2.26513e6	+	1.09083e6i	1.65624	+	0.797603i
$112$	151941.	+	190528.i	0.108148	+	0.135614i
$113$	924497.	−	104166.i	0.640723	−	0.0721921i	0.214375	−	0.976751i	$-0.431229\pi$
$113$	924497.	−	104166.i	0.640723	−	0.0721921i	0.426348	+	0.904559i	$0.359800\pi$
$114$	−862593.	−	2.46515e6i	−0.582226	−	1.66391i
$115$			1.09523e6i			0.720134i
$116$	−410410.	+	663824.i	−0.262932	+	0.425284i
$117$	−3.93309e6			−2.45571
$118$	160148.	−	56038.2i	0.0974710	−	0.0341066i
$119$	8598.55	+	76314.2i	0.00510252	+	0.0452861i
$120$	1.50527e6	−	1.20041e6i	0.871103	−	0.694682i
$121$	−726677.	+	1.50896e6i	−0.410190	+	0.851769i
$122$	159489.	+	331181.i	0.0878314	+	0.182384i
$123$	−3.61315e6	+	4.53075e6i	−1.94165	+	2.43475i
$124$	609938.	−	970711.i	0.319905	−	0.509126i
$125$	5.17169e6	−	1.18040e6i	2.64790	−	0.604367i
$126$	−205503.	+	1.82389e6i	−0.102732	+	0.911773i
$127$	−518939.	−	825887.i	−0.253341	−	0.403190i	0.695705	−	0.718328i	$-0.255092\pi$
$127$	−518939.	−	825887.i	−0.253341	−	0.403190i	−0.949046	+	0.315138i	$0.897949\pi$
$128$	131072.	+	131072.i	0.0625000	+	0.0625000i
$129$	944071.	+	215478.i	0.439780	+	0.100377i
$130$	1.25322e6	−	3.58150e6i	0.570424	−	1.63018i
$131$	871353.	+	304899.i	0.387597	+	0.135626i	0.517041	−	0.855961i	$-0.327034\pi$
$131$	871353.	+	304899.i	0.387597	+	0.135626i	−0.129444	+	0.991587i	$0.541319\pi$
$132$	−604676.	+	2.64926e6i	−0.262906	+	1.15187i
$133$	−1.69848e6	+	1.69848e6i	−0.721946	+	0.721946i
$134$	690159.	−	433655.i	0.286837	−	0.180231i
$135$	6.70482e6	+	755452.i	2.72512	+	0.307047i
$136$	12998.6	+	56950.5i	0.00516748	+	0.0226402i
$137$	−2.52649e6	−	1.58750e6i	−0.982552	−	0.617378i	−0.0579524	−	0.998319i	$-0.518457\pi$
$137$	−2.52649e6	−	1.58750e6i	−0.982552	−	0.617378i	−0.924599	+	0.380941i	$0.875600\pi$
$138$	−952929.	−	759936.i	−0.362596	−	0.289161i
$139$	1.24458e6	−	599358.i	0.463423	−	0.223173i	−0.187578	−	0.982250i	$-0.560064\pi$
$139$	1.24458e6	−	599358.i	0.463423	−	0.223173i	0.651001	+	0.759077i	$0.274349\pi$
$140$	−1.59536e6	−	768287.i	−0.581401	−	0.279988i
$141$	1.23558e6	+	1.54937e6i	0.440773	+	0.552711i
$142$	−65905.7	+	7425.79i	−0.0230175	+	0.00259345i
$143$	1.76880e6	+	5.05495e6i	0.604883	+	1.72866i
$144$			1.39610e6i			0.467552i
$145$	593965.	−	5.63967e6i	0.194830	−	1.84991i
$146$	2.01625e6			0.647867
$147$	−2.63429e6	+	921778.i	−0.829300	+	0.290185i
$148$	−196921.	−	1.74772e6i	−0.0607445	−	0.539123i
$149$	1.79922e6	−	1.43483e6i	0.543907	−	0.433751i	−0.312601	−	0.949884i	$-0.601200\pi$
$149$	1.79922e6	−	1.43483e6i	0.543907	−	0.433751i	0.856508	+	0.516133i	$0.172629\pi$
$150$	−4.31562e6	+	8.96147e6i	−1.27870	+	2.65525i
$151$	−2.44167e6	−	5.07017e6i	−0.709179	−	1.47262i	−0.873809	−	0.486269i	$-0.838357\pi$
$151$	−2.44167e6	−	5.07017e6i	−0.709179	−	1.47262i	0.164630	−	0.986355i	$-0.447357\pi$
$152$	−1.13916e6	+	1.42846e6i	−0.324379	+	0.406759i
$153$	−234075.	+	372529.i	−0.0653553	+	0.104012i
$154$	2.43654e6	−	556125.i	0.667132	−	0.152269i
$155$	−932681.	+	8.27777e6i	−0.250460	+	2.22289i
$156$	2.24660e6	+	3.57544e6i	0.591768	+	0.941793i
$157$	−2.30740e6	−	2.30740e6i	−0.596243	−	0.596243i	0.343068	−	0.939311i	$-0.388534\pi$
$157$	−2.30740e6	−	2.30740e6i	−0.596243	−	0.596243i	−0.939311	+	0.343068i	$0.888534\pi$
$158$	−773975.	−	176655.i	−0.196226	−	0.0447872i
$159$	−1.13417e6	+	3.24127e6i	−0.282154	+	0.806351i
$160$	−1.27130e6	−	444847.i	−0.310376	−	0.108605i
$161$	−249441.	+	1.09287e6i	−0.0597710	+	0.261874i
$162$	−1.33386e6	+	1.33386e6i	−0.313736	+	0.313736i
$163$	996104.	−	625894.i	0.230008	−	0.144523i	−0.412098	−	0.911139i	$-0.635204\pi$
$163$	996104.	−	625894.i	0.230008	−	0.144523i	0.642106	+	0.766616i	$0.278061\pi$
$164$	4.02853e6	+	453907.i	0.913304	+	0.102905i
$165$	−4.39367e6	−	1.92499e7i	−0.978084	−	4.28526i
$166$	613962.	+	385778.i	0.134220	+	0.0843360i
$167$	−4.01378e6	−	3.20089e6i	−0.861796	−	0.687260i	0.0893499	−	0.996000i	$-0.471521\pi$
$167$	−4.01378e6	−	3.20089e6i	−0.861796	−	0.687260i	−0.951146	+	0.308741i	$0.900092\pi$
$168$	1.77542e6	−	854996.i	0.374432	−	0.180317i
$169$	3.14915e6	+	1.51655e6i	0.652430	+	0.314194i
$170$	−264642.	−	331851.i	−0.0538657	−	0.0675455i
$171$	−1.36744e7	+	1.54073e6i	−2.73476	+	0.308133i
$172$	−223739.	−	639410.i	−0.0439701	−	0.125659i
$173$			3.77404e6i			0.728901i	0.931223	+	0.364450i	$0.118743\pi$
$173$			3.77404e6i			0.728901i	−0.931223	+	0.364450i	$0.881257\pi$
$174$	4.49477e6	+	4.42991e6i	0.853218	+	0.840906i
$175$	9.14785e6			1.70689
$176$	1.79432e6	−	627860.i	0.329126	−	0.115166i
$177$	−153613.	−	1.36336e6i	−0.0277019	−	0.245861i
$178$	−4.74498e6	+	3.78399e6i	−0.841345	+	0.670951i
$179$	78563.3	−	163138.i	0.0136981	−	0.0284444i	−0.894008	−	0.448052i	$-0.852118\pi$
$179$	78563.3	−	163138.i	0.0136981	−	0.0284444i	0.907706	+	0.419607i	$0.137832\pi$
$180$	−4.40145e6	−	9.13971e6i	−0.754707	−	1.56716i
$181$	6.23246e6	−	7.81526e6i	1.05105	−	1.31798i	0.104818	−	0.994491i	$-0.466574\pi$
$181$	6.23246e6	−	7.81526e6i	1.05105	−	1.31798i	0.946233	−	0.323485i	$-0.104855\pi$
$182$	2.06621e6	−	3.28835e6i	0.342736	−	0.545462i
$183$	2.89784e6	−	661413.i	0.472847	−	0.107924i
$184$	−95467.9	+	847301.i	−0.0153251	+	0.136014i
$185$	6.79915e6	+	1.08208e7i	1.07384	+	1.70901i
$186$	−6.55509e6	−	6.55509e6i	−1.01868	−	1.01868i
$187$	584055.	+	133307.i	0.0893160	+	0.0203858i
$188$	457882.	−	1.30855e6i	0.0689096	−	0.196932i
$189$	6.51831e6	+	2.28085e6i	0.965494	+	0.337841i
$190$	2.95413e6	−	1.29429e7i	0.430694	−	1.88700i
$191$	−2.02766e6	+	2.02766e6i	−0.291001	+	0.291001i	−0.837476	−	0.546474i	$-0.815970\pi$
$191$	−2.02766e6	+	2.02766e6i	−0.291001	+	0.291001i	0.546474	+	0.837476i	$0.315970\pi$
$192$	1.26915e6	−	797459.i	0.179312	−	0.112669i
$193$	−6.49440e6	−	731743.i	−0.903373	−	0.101786i	−0.351957	−	0.936016i	$-0.614484\pi$
$193$	−6.49440e6	−	731743.i	−0.903373	−	0.101786i	−0.551416	+	0.834231i	$0.685912\pi$
$194$	−129056.	−	565432.i	−0.0176756	−	0.0774418i
$195$	−2.59797e7	−	1.63241e7i	−3.50373	−	2.20154i
$196$	1.52647e6	+	1.21732e6i	0.202731	+	0.161672i
$197$	6.92579e6	−	3.33529e6i	0.905880	−	0.436249i	0.0778711	−	0.996963i	$-0.475188\pi$
$197$	6.92579e6	−	3.33529e6i	0.905880	−	0.436249i	0.828009	+	0.560714i	$0.189473\pi$
$198$	1.28998e7	+	6.21223e6i	1.66184	+	0.800299i
$199$	−6.53049e6	−	8.18897e6i	−0.828679	−	1.03913i	−0.998559	−	0.0536656i	$-0.982909\pi$
$199$	−6.53049e6	−	8.18897e6i	−0.828679	−	1.03913i	0.169880	−	0.985465i	$-0.445662\pi$
$200$	6.91448e6	−	779075.i	0.864311	−	0.0973844i
$201$	−2.17688e6	−	6.22115e6i	−0.268068	−	0.766095i
$202$			5.84856e6i			0.709569i
$203$	1.87713e6	−	5.49223e6i	0.224391	−	0.656539i
$204$	472357.			0.0556391
$205$	−2.78041e7	+	9.72909e6i	−3.22736	+	1.12930i
$206$	−264727.	−	2.34952e6i	−0.0302829	−	0.268768i
$207$	−5.02091e6	+	4.00405e6i	−0.566072	+	0.451427i
$208$	1.28171e6	−	2.66150e6i	0.142430	−	0.295758i
$209$	8.12988e6	+	1.68819e7i	0.890524	+	1.84919i
$210$	−8.92739e6	+	1.11946e7i	−0.963977	+	1.20879i
$211$	−4.04841e6	+	6.44300e6i	−0.430960	+	0.685868i	−0.989649	−	0.143509i	$-0.954162\pi$
$211$	−4.04841e6	+	6.44300e6i	−0.430960	+	0.685868i	0.558689	+	0.829377i	$0.311304\pi$
$212$	2.34206e6	−	534561.i	0.245805	−	0.0561035i
$213$	−60046.6	+	532928.i	−0.00621369	+	0.0551480i
$214$	4.53074e6	+	7.21062e6i	0.462304	+	0.735752i
$215$	3.48058e6	+	3.48058e6i	0.350216	+	0.350216i
$216$	5.12117e6	+	1.16887e6i	0.508168	+	0.115986i
$217$	−2.81595e6	+	8.04751e6i	−0.275578	+	0.787557i
$218$	−5.64793e6	−	1.97630e6i	−0.545155	−	0.190758i
$219$	3.62794e6	−	1.58951e7i	0.345405	−	1.51332i
$220$	−9.76723e6	+	9.76723e6i	−0.917283	+	0.917283i
$221$	788240.	−	495284.i	0.0730267	−	0.0458857i
$222$	−1.41325e7	−	1.59235e6i	−1.29169	−	0.145539i
$223$	−836826.	−	3.66637e6i	−0.0754606	−	0.330615i	0.923081	−	0.384606i	$-0.125663\pi$
$223$	−836826.	−	3.66637e6i	−0.0754606	−	0.330615i	−0.998541	+	0.0539916i	$0.982806\pi$
$224$	−1.16724e6	−	733428.i	−0.103853	−	0.0652550i
$225$	4.09737e7	+	3.26754e7i	3.59714	+	2.86862i
$226$	−4.74165e6	+	2.28346e6i	−0.410775	+	0.197819i
$227$	−9.26556e6	−	4.46206e6i	−0.792126	−	0.381468i	−0.00635069	−	0.999980i	$-0.502022\pi$
$227$	−9.26556e6	−	4.46206e6i	−0.792126	−	0.381468i	−0.785775	+	0.618512i	$0.787736\pi$
$228$	9.21147e6	+	1.15508e7i	0.777185	+	0.974560i
$229$	1.30634e7	−	1.47190e6i	1.08781	−	0.122566i	0.450199	−	0.892928i	$-0.351353\pi$
$229$	1.30634e7	−	1.47190e6i	1.08781	−	0.122566i	0.637607	+	0.770362i	$0.279925\pi$
$230$	−2.04627e6	−	5.84790e6i	−0.168182	−	0.480636i
$231$		−	2.02091e7i		−	1.63950i
$232$	951097.	−	4.31122e6i	0.0761660	−	0.345252i
$233$	2.11939e7			1.67550			0.837748	−	0.546058i	$-0.183872\pi$
$233$	2.11939e7			1.67550			0.837748	+	0.546058i	$0.183872\pi$
$234$	2.10004e7	−	7.34836e6i	1.63900	−	0.573512i
$235$	1.12787e6	+	1.00101e7i	0.0869068	+	0.771319i
$236$	−750397.	+	598422.i	−0.0570893	+	0.0455272i
$237$	−2.78531e6	+	5.78375e6i	−0.209232	+	0.434475i
$238$	−188492.	−	391408.i	−0.0139818	−	0.0290335i
$239$	−1.06997e7	+	1.34170e7i	−0.783749	+	0.982791i	0.216230	+	0.976342i	$0.430624\pi$
$239$	−1.06997e7	+	1.34170e7i	−0.783749	+	0.982791i	−0.999979	+	0.00644812i	$0.997947\pi$
$240$	−5.79446e6	+	9.22183e6i	−0.419160	+	0.667089i
$241$	1.07092e7	−	2.44430e6i	0.765077	−	0.174624i	0.177863	−	0.984055i	$-0.443082\pi$
$241$	1.07092e7	−	2.44430e6i	0.765077	−	0.174624i	0.587214	+	0.809431i	$0.300225\pi$
$242$	1.06077e6	−	9.41464e6i	0.0748475	−	0.664290i
$243$	−3.13941e6	−	4.99635e6i	−0.218791	−	0.348204i
$244$	−1.47033e6	−	1.47033e6i	−0.101215	−	0.101215i
$245$	−1.38310e7	−	3.15682e6i	−0.940489	−	0.214661i
$246$	1.08271e7	−	3.09421e7i	0.727290	−	2.07847i
$247$	2.74830e7	+	9.61672e6i	1.82378	+	0.638170i
$248$	−1.44309e6	+	6.32260e6i	−0.0946104	+	0.414515i
$249$	4.14600e6	−	4.14600e6i	0.268554	−	0.268554i
$250$	−2.54084e7	+	1.59651e7i	−1.62614	+	1.02177i
$251$	−1.77373e6	−	199851.i	−0.112167	−	0.0126382i	0.0557025	−	0.998447i	$-0.482260\pi$
$251$	−1.77373e6	−	199851.i	−0.112167	−	0.0126382i	−0.167870	+	0.985809i	$0.553689\pi$
$252$	−2.31038e6	−	1.01224e7i	−0.144372	−	0.632533i
$253$	7.40416e6	+	4.65234e6i	0.457208	+	0.287283i
$254$	4.31387e6	+	3.44020e6i	0.263248	+	0.209934i
$255$	−3.09232e6	+	1.48918e6i	−0.186494	+	0.0898107i
$256$	−944734.	−	454960.i	−0.0563106	−	0.0271177i
$257$	−6.44028e6	−	8.07585e6i	−0.379407	−	0.475761i	0.555060	−	0.831810i	$-0.312695\pi$
$257$	−6.44028e6	−	8.07585e6i	−0.379407	−	0.475761i	−0.934467	+	0.356049i	$0.884124\pi$
$258$	−5.44337e6	+	613320.i	−0.316963	+	0.0357131i
$259$	4.32004e6	+	1.23460e7i	0.248650	+	0.710601i
$260$			2.14645e7i			1.22124i
$261$	2.80256e7	−	1.78950e7i	1.57628	−	1.00649i
$262$	−5.22216e6			−0.290367
$263$	1.52641e7	−	5.34114e6i	0.839082	−	0.293607i	0.123681	−	0.992322i	$-0.460530\pi$
$263$	1.52641e7	−	5.34114e6i	0.839082	−	0.293607i	0.715400	+	0.698715i	$0.246244\pi$
$264$	−1.72110e6	−	1.52752e7i	−0.0935396	−	0.830187i
$265$	−1.36472e7	+	1.08833e7i	−0.733342	+	0.584821i
$266$	5.89553e6	−	1.22422e7i	0.313240	−	0.650450i
$267$	2.12932e7	+	4.42157e7i	1.11868	+	2.32297i
$268$	−2.87482e6	+	3.60492e6i	−0.149351	+	0.187280i
$269$	−1.09644e7	+	1.74497e7i	−0.563284	+	0.896462i	−0.999995	−	0.00314001i	$-0.999001\pi$
$269$	−1.09644e7	+	1.74497e7i	−0.563284	+	0.896462i	0.436711	+	0.899602i	$0.356143\pi$
$270$	−3.72112e7	+	8.49322e6i	−1.89053	+	0.431500i
$271$	2.00002e6	−	1.77507e7i	0.100491	−	0.891883i	−0.837786	−	0.545999i	$-0.816150\pi$
$271$	2.00002e6	−	1.77507e7i	0.100491	−	0.891883i	0.938277	−	0.345884i	$-0.112421\pi$
$272$	−175808.	−	279796.i	−0.00873637	−	0.0139039i
$273$	−2.22058e7	−	2.22058e7i	−1.09139	−	1.09139i
$274$	1.64559e7	+	3.75596e6i	0.799965	+	0.182587i
$275$	2.35688e7	−	6.73557e7i	1.13328	−	3.23874i
$276$	6.50790e6	+	2.27721e6i	0.309538	+	0.108312i
$277$	4.40963e6	−	1.93198e7i	0.207473	−	0.909000i	−0.758768	−	0.651361i	$-0.774198\pi$
$277$	4.40963e6	−	1.93198e7i	0.207473	−	0.909000i	0.966241	−	0.257639i	$-0.0829446\pi$
$278$	−5.52551e6	+	5.52551e6i	−0.257181	+	0.257181i
$279$	−4.13578e7	+	2.59868e7i	−1.90434	+	1.19658i
$280$	9.95372e6	+	1.12151e6i	0.453431	+	0.0510894i
$281$	8.73244e6	+	3.82593e7i	0.393565	+	1.72432i	0.651934	+	0.758275i	$0.273958\pi$
$281$	8.73244e6	+	3.82593e7i	0.393565	+	1.72432i	−0.258369	+	0.966046i	$0.583185\pi$
$282$	−9.49204e6	−	5.96424e6i	−0.423265	−	0.265955i
$283$	1.96561e7	+	1.56752e7i	0.867238	+	0.691599i	0.952427	−	0.304766i	$-0.0985782\pi$
$283$	1.96561e7	+	1.56752e7i	0.867238	+	0.691599i	−0.0851896	+	0.996365i	$0.527150\pi$
$284$	338024.	−	162784.i	0.0147568	−	0.00710650i
$285$	−9.67196e7	−	4.65777e7i	−4.17811	−	2.01207i
$286$	−1.88887e7	−	2.36857e7i	−0.807429	−	1.01248i
$287$	−2.99600e7	+	3.37568e6i	−1.26735	+	0.142796i
$288$	−2.60840e6	−	7.45437e6i	−0.109193	−	0.312057i
$289$			2.40334e7i			0.995686i
$290$	7.36540e6	+	3.12222e7i	0.301997	+	1.28018i
$291$	−4.68979e6			−0.190316
$292$	−1.07656e7	+	3.76704e6i	−0.432403	+	0.151304i
$293$	2.26459e6	+	2.00988e7i	0.0900297	+	0.799036i	0.954877	+	0.297001i	$0.0959865\pi$
$293$	2.26459e6	+	2.00988e7i	0.0900297	+	0.799036i	−0.864847	+	0.502035i	$0.832585\pi$
$294$	1.23434e7	−	9.84350e6i	0.485726	−	0.387354i
$295$	3.02591e6	−	6.28337e6i	0.117866	−	0.244752i
$296$	4.31678e6	+	8.96390e6i	0.166451	+	0.345638i
$297$	3.35879e7	−	4.21179e7i	1.28207	−	1.60767i
$298$	−6.92601e6	+	1.10227e7i	−0.261718	+	0.416523i
$299$	1.32477e7	−	3.02371e6i	0.495596	−	0.113116i
$300$	6.29977e6	−	5.59120e7i	0.233325	−	2.07082i
$301$	2.68037e6	+	4.26578e6i	0.0982867	+	0.156422i
$302$	2.25099e7	+	2.25099e7i	0.817245	+	0.817245i
$303$	4.61070e7	+	1.05236e7i	1.65744	+	0.378301i
$304$	3.41358e6	−	9.75546e6i	0.121504	−	0.347238i
$305$	1.42611e7	+	4.99019e6i	0.502637	+	0.175880i
$306$	553813.	−	2.42641e6i	0.0193285	−	0.0846839i
$307$	−3.22234e7	+	3.22234e7i	−1.11367	+	1.11367i	−0.121020	+	0.992650i	$0.538617\pi$
$307$	−3.22234e7	+	3.22234e7i	−1.11367	+	1.11367i	−0.992650	+	0.121020i	$0.961383\pi$
$308$	−1.19707e7	+	7.52167e6i	−0.409700	+	0.257432i
$309$	−1.89987e7	−	2.14064e6i	−0.643945	−	0.0725552i
$310$	−1.04857e7	−	4.59410e7i	−0.351977	−	1.54211i
$311$	−3.65204e7	−	2.29473e7i	−1.21410	−	0.762869i	−0.236150	−	0.971717i	$-0.575886\pi$
$311$	−3.65204e7	−	2.29473e7i	−1.21410	−	0.762869i	−0.977948	+	0.208848i	$0.933029\pi$
$312$	−1.86756e7	−	1.48933e7i	−0.614910	−	0.490374i
$313$	1.63741e7	−	7.88534e6i	0.533979	−	0.257151i	−0.147406	−	0.989076i	$-0.547092\pi$
$313$	1.63741e7	−	7.88534e6i	0.533979	−	0.257151i	0.681385	+	0.731925i	$0.261378\pi$
$314$	1.66311e7	+	8.00914e6i	0.537197	+	0.258700i
$315$	4.70378e7	+	5.89835e7i	1.50493	+	1.88712i
$316$	4.46262e6	−	502817.i	0.141426	−	0.0159349i
$317$	−1.16812e7	−	3.33828e7i	−0.366698	−	1.04796i	−0.968435	−	0.249267i	$-0.919810\pi$
$317$	−1.16812e7	−	3.33828e7i	−0.366698	−	1.04796i	0.601737	−	0.798694i	$-0.294475\pi$
$318$		−	1.94255e7i		−	0.604075i
$319$	−3.56030e7	−	2.79716e7i	−1.09677	−	0.861679i
$320$	7.61912e6			0.232517
$321$	6.49972e7	−	2.27435e7i	1.96508	−	0.687610i
$322$	−709990.	−	6.30134e6i	−0.0212659	−	0.188740i
$323$	2.54649e6	−	2.03076e6i	0.0755675	−	0.0602630i
$324$	4.62991e6	−	9.61412e6i	0.136125	−	0.282666i
$325$	−4.81132e7	−	9.99081e7i	−1.40157	−	2.91039i
$326$	−4.14923e6	+	5.20297e6i	−0.119761	+	0.150175i
$327$	−2.57427e7	+	4.09693e7i	−0.736226	+	1.17170i
$328$	−2.23580e7	+	5.10308e6i	−0.633596	+	0.144614i
$329$	−1.15438e6	+	1.02454e7i	−0.0324160	+	0.287700i
$330$	5.94251e7	+	9.45745e7i	1.65359	+	2.63167i
$331$	3.15827e7	+	3.15827e7i	0.870894	+	0.870894i	0.992570	−	0.121676i	$-0.0388268\pi$
$331$	3.15827e7	+	3.15827e7i	0.870894	+	0.870894i	−0.121676	+	0.992570i	$0.538827\pi$
$332$	−3.99896e6	−	912736.i	−0.109278	−	0.0249420i
$333$	−2.47492e7	+	7.07291e7i	−0.670236	+	1.91543i
$334$	2.74116e7	+	9.59173e6i	0.735690	+	0.257429i
$335$	7.45517e6	−	3.26632e7i	0.198300	−	0.868810i
$336$	−7.88226e6	+	7.88226e6i	−0.207794	+	0.207794i
$337$	−3.45426e7	+	2.17045e7i	−0.902536	+	0.567101i	−0.901443	−	0.432898i	$-0.857491\pi$
$337$	−3.45426e7	+	2.17045e7i	−0.902536	+	0.567101i	−0.00109363	+	0.999999i	$0.500348\pi$
$338$	−1.96481e7	−	2.21381e6i	−0.508827	−	0.0573310i
$339$	9.46970e6	+	4.14895e7i	0.243073	+	1.06497i
$340$	2.03304e6	+	1.27745e6i	0.0517261	+	0.0325017i
$341$	5.19987e7	+	4.14676e7i	1.31138	+	1.04579i
$342$	7.01345e7	−	3.37750e7i	1.75329	−	0.844339i
$343$	−3.83079e7	−	1.84481e7i	−0.949304	−	0.457161i
$344$	2.38927e6	+	2.99605e6i	0.0586936	+	0.0735994i
$345$	−4.97838e7	+	5.60929e6i	−1.21236	+	0.136600i
$346$	−7.05119e6	−	2.01512e7i	−0.170229	−	0.486488i
$347$		−	5.93599e7i		−	1.42071i	−0.703845	−	0.710354i	$-0.748535\pi$
$347$		−	5.93599e7i		−	1.42071i	0.703845	−	0.710354i	$-0.251465\pi$
$348$	−3.22760e7	−	1.52554e7i	−0.765848	−	0.361980i
$349$	7.41389e7			1.74409			0.872046	−	0.489423i	$-0.162793\pi$
$349$	7.41389e7			1.74409			0.872046	+	0.489423i	$0.162793\pi$
$350$	−4.88441e7	+	1.70913e7i	−1.13922	+	0.398631i
$351$	−9.37278e6	−	8.31857e7i	−0.216744	−	1.92366i
$352$	−8.40755e6	+	6.70480e6i	−0.192771	+	0.153730i
$353$	−2.96149e7	+	6.14959e7i	−0.673264	+	1.39805i	0.231796	+	0.972764i	$0.425540\pi$
$353$	−2.96149e7	+	6.14959e7i	−0.673264	+	1.39805i	−0.905060	+	0.425283i	$0.860175\pi$
$354$	3.36742e6	+	6.99251e6i	0.0759079	+	0.157624i
$355$	−1.69970e6	+	2.13135e6i	−0.0379915	+	0.0476399i
$356$	1.82656e7	−	2.90695e7i	0.404841	−	0.644300i
$357$	−3.42482e6	+	781693.i	−0.0752720	+	0.0171803i
$358$	−114684.	+	1.01785e6i	−0.00249950	+	0.0221836i
$359$	−3.17268e7	−	5.04928e7i	−0.685713	−	1.09131i	−0.990317	−	0.138827i	$-0.955667\pi$
$359$	−3.17268e7	−	5.04928e7i	−0.685713	−	1.09131i	0.304604	−	0.952479i	$-0.401476\pi$
$360$	4.05772e7	+	4.05772e7i	0.869711	+	0.869711i
$361$	5.34524e7	+	1.22002e7i	1.13618	+	0.259325i
$362$	−1.86761e7	+	5.33732e7i	−0.393696	+	1.12512i
$363$	−7.23114e7	−	2.53029e7i	−1.51177	−	0.528993i
$364$	−4.88858e6	+	2.14183e7i	−0.101363	+	0.444099i
$365$	5.86016e7	−	5.86016e7i	1.20512	−	1.20512i
$366$	−1.42370e7	+	8.94570e6i	−0.290386	+	0.182461i
$367$	6.76535e7	+	7.62272e6i	1.36865	+	0.154210i	0.765509	−	0.643425i	$-0.222487\pi$
$367$	6.76535e7	+	7.62272e6i	1.36865	+	0.154210i	0.603140	+	0.797635i	$0.293916\pi$
$368$	−1.07330e6	−	4.70245e6i	−0.0215367	−	0.0943585i
$369$	−1.46250e8	−	9.18950e7i	−2.91083	−	1.82900i
$370$	−5.65204e7	−	4.50735e7i	−1.11583	−	0.889849i
$371$	−1.60965e7	+	7.75166e6i	−0.315217	+	0.151800i
$372$	4.72475e7	+	2.27532e7i	0.917803	+	0.441991i
$373$	9.57053e6	+	1.20011e7i	0.184421	+	0.231256i	0.865444	−	0.501005i	$-0.167036\pi$
$373$	9.57053e6	+	1.20011e7i	0.184421	+	0.231256i	−0.681024	+	0.732262i	$0.738465\pi$
$374$	−3.36757e6	+	379434.i	−0.0643728	+	0.00725307i
$375$	8.01422e7	+	2.29033e8i	1.51973	+	4.34315i
$376$			7.84237e6i			0.147531i
$377$	−6.98561e7	+	8.38543e6i	−1.30371	+	0.156495i
$378$	−3.90653e7			−0.723296
$379$	6.10125e7	−	2.13492e7i	1.12073	−	0.392160i	0.294589	−	0.955624i	$-0.404817\pi$
$379$	6.10125e7	−	2.13492e7i	1.12073	−	0.392160i	0.826141	+	0.563463i	$0.190531\pi$
$380$	8.40842e6	+	7.46268e7i	0.153237	+	1.36002i
$381$	3.48829e7	−	2.78182e7i	0.630721	−	0.502984i
$382$	7.03815e6	−	1.46149e7i	0.126261	−	0.262183i
$383$	6.57918e6	+	1.36618e7i	0.117105	+	0.243171i	0.951280	−	0.308329i	$-0.0997698\pi$
$383$	6.57918e6	+	1.36618e7i	0.117105	+	0.243171i	−0.834175	+	0.551500i	$0.814056\pi$
$384$	−5.28658e6	+	6.62916e6i	−0.0933644	+	0.117075i
$385$	5.46537e7	−	8.69808e7i	0.957717	−	1.52420i
$386$	3.60434e7	−	8.22667e6i	0.626706	−	0.143042i
$387$	−3.23154e6	+	2.86807e7i	−0.0557540	+	0.494831i
$388$	1.74550e6	+	2.77796e6i	0.0298831	+	0.0475587i
$389$	−1.04412e7	−	1.04412e7i	−0.177380	−	0.177380i	0.612833	−	0.790212i	$-0.290030\pi$
$389$	−1.04412e7	−	1.04412e7i	−0.177380	−	0.177380i	−0.790212	+	0.612833i	$0.790030\pi$
$390$	1.69215e8	+	3.86223e7i	2.85263	+	0.651095i
$391$	502034.	−	1.43473e6i	0.00839852	−	0.0240016i
$392$	−1.04248e7	−	3.64780e6i	−0.173065	−	0.0605581i
$393$	−9.39652e6	+	4.11688e7i	−0.154807	+	0.678252i
$394$	−3.07482e7	+	3.07482e7i	−0.502726	+	0.502726i
$395$	−2.76297e7	+	1.73609e7i	−0.448317	+	0.281696i
$396$	−8.04841e7	−	9.06838e6i	−1.29606	−	0.146031i
$397$	−3.11666e6	−	1.36550e7i	−0.0498102	−	0.218233i	0.943897	−	0.330239i	$-0.107129\pi$
$397$	−3.11666e6	−	1.36550e7i	−0.0498102	−	0.218233i	−0.993707	+	0.112007i	$0.964272\pi$
$398$	5.01687e7	+	3.15231e7i	0.795763	+	0.500011i
$399$	−8.59029e7	−	6.85053e7i	−1.35235	−	1.07846i
$400$	−3.54637e7	+	1.70784e7i	−0.554120	+	0.266850i
$401$	−5.64150e6	−	2.71681e6i	−0.0874907	−	0.0421333i	0.389627	−	0.920973i	$-0.372604\pi$
$401$	−5.64150e6	−	2.71681e6i	−0.0874907	−	0.0421333i	−0.477117	+	0.878840i	$0.658318\pi$
$402$	2.32465e7	+	2.91501e7i	0.357832	+	0.448707i
$403$	1.02701e8	−	1.15716e7i	1.56913	−	0.176799i
$404$	−1.09271e7	−	3.12278e7i	−0.165715	−	0.473585i
$405$			7.75362e7i			1.16718i
$406$	238611.	+	3.28324e7i	0.00356543	+	0.490596i
$407$	1.02034e8			1.51342
$408$	−2.52211e6	+	882524.i	−0.0371350	+	0.0129941i
$409$	1.11850e7	+	9.92692e7i	0.163480	+	1.45092i	0.760834	+	0.648947i	$0.224790\pi$
$409$	1.11850e7	+	9.92692e7i	0.163480	+	1.45092i	−0.597354	+	0.801978i	$0.703781\pi$
$410$	1.30280e8	−	1.03895e8i	1.89029	−	1.50745i
$411$	5.92201e7	−	1.22972e8i	0.852989	−	1.77125i
$412$	5.80319e6	+	1.20504e7i	0.0829803	+	0.172310i
$413$	4.45043e6	−	5.58067e6i	0.0631760	−	0.0792202i
$414$	1.93278e7	−	3.07600e7i	0.272384	−	0.433496i
$415$	2.90571e7	−	6.63208e6i	0.406544	−	0.0927910i
$416$	−1.87099e6	+	1.66055e7i	−0.0259891	+	0.230660i
$417$	3.36179e7	+	5.35026e7i	0.463621	+	0.737848i
$418$	−7.49499e7	−	7.49499e7i	−1.02622	−	1.02622i
$419$	−1.14443e8	−	2.61208e7i	−1.55577	−	0.355094i	−0.643749	−	0.765237i	$-0.722622\pi$
$419$	−1.14443e8	−	2.61208e7i	−1.55577	−	0.355094i	−0.912021	+	0.410143i	$0.865479\pi$
$420$	2.67517e7	−	7.64520e7i	0.361080	−	1.03191i
$421$	−1.35092e8	−	4.72708e7i	−1.81044	−	0.633500i	−0.998781	−	0.0493656i	$-0.984280\pi$
$421$	−1.35092e8	−	4.72708e7i	−1.81044	−	0.633500i	−0.811657	−	0.584134i	$-0.801434\pi$
$422$	9.57838e6	−	4.19656e7i	0.127454	−	0.558414i
$423$	−4.17662e7	+	4.17662e7i	−0.551828	+	0.551828i
$424$	−1.15065e7	+	7.23002e6i	−0.150954	+	0.0948509i
$425$	−1.23264e7	−	1.38885e6i	−0.160571	−	0.0180920i
$426$	−675078.	−	2.95771e6i	−0.00873223	−	0.0382584i
$427$	1.30939e7	+	8.22743e6i	0.168184	+	0.105677i
$428$	−3.76634e7	−	3.00355e7i	−0.480383	−	0.383093i
$429$	−2.20713e8	+	1.06290e8i	−2.79548	+	1.34623i
$430$	−2.50871e7	−	1.20813e7i	−0.315534	−	0.151953i
$431$	−5.58052e7	−	6.99775e7i	−0.697016	−	0.874031i	0.299780	−	0.954008i	$-0.403087\pi$
$431$	−5.58052e7	−	6.99775e7i	−0.697016	−	0.874031i	−0.996797	+	0.0799773i	$0.974515\pi$
$432$	−2.95279e7	+	3.32699e6i	−0.366253	+	0.0412668i
$433$	−2.27464e7	−	6.50053e7i	−0.280187	−	0.800729i	−0.994859	−	0.101269i	$-0.967710\pi$
$433$	−2.27464e7	−	6.50053e7i	−0.280187	−	0.800729i	0.714672	−	0.699460i	$-0.246576\pi$
$434$		−	4.82301e7i		−	0.589996i
$435$	2.59393e8	−	1.88515e6i	3.15130	−	0.0229022i
$436$	3.38490e7			0.408401
$437$	4.48745e7	−	1.57023e7i	0.537719	−	0.188156i
$438$	1.03263e7	+	9.16485e7i	0.122892	+	1.09069i
$439$	−9.58719e6	+	7.64553e6i	−0.113318	+	0.0903679i	−0.678509	−	0.734592i	$-0.737374\pi$
$439$	−9.58719e6	+	7.64553e6i	−0.113318	+	0.0903679i	0.565192	+	0.824960i	$0.308802\pi$
$440$	3.39027e7	−	7.03998e7i	0.397994	−	0.826444i
$441$	−3.60924e7	−	7.49466e7i	−0.420823	−	0.873849i
$442$	−3.28338e6	+	4.11723e6i	−0.0380237	+	0.0476802i
$443$	−7.42364e7	+	1.18147e8i	−0.853898	+	1.35897i	0.0782654	+	0.996933i	$0.475062\pi$
$443$	−7.42364e7	+	1.18147e8i	−0.853898	+	1.35897i	−0.932163	+	0.362038i	$0.882081\pi$
$444$	7.84341e7	−	1.79021e7i	0.896099	−	0.204529i
$445$	−2.79307e7	+	2.47891e8i	−0.316958	+	2.81308i
$446$	1.13182e7	+	1.80128e7i	0.127577	+	0.203038i
$447$	7.44348e7	+	7.44348e7i	0.833400	+	0.833400i
$448$	7.60269e6	+	1.73527e6i	0.0845539	+	0.0192989i
$449$	−22717.7	+	64923.5i	−0.000250972	+	0.000717237i	−0.944009	−	0.329920i	$-0.892978\pi$
$449$	−22717.7	+	64923.5i	−0.000250972	+	0.000717237i	0.943758	+	0.330638i	$0.107264\pi$
$450$	−2.79824e8	−	9.79147e7i	−3.07077	−	1.07451i
$451$	−5.23346e7	+	2.29293e8i	−0.570505	+	2.49954i
$452$	2.10513e7	−	2.10513e7i	0.227963	−	0.227963i
$453$	2.17959e8	−	1.36953e8i	2.34467	−	1.47325i
$454$	5.78093e7	+	6.51354e6i	0.617775	+	0.0696065i
$455$	−3.55212e7	−	1.55628e8i	−0.377097	−	1.65217i
$456$	−7.07647e7	−	4.44644e7i	−0.746315	−	0.468941i
$457$	6.54501e7	+	5.21947e7i	0.685744	+	0.546862i	0.903207	−	0.429206i	$-0.141207\pi$
$457$	6.54501e7	+	5.21947e7i	0.685744	+	0.546862i	−0.217463	+	0.976069i	$0.569778\pi$
$458$	−6.70011e7	+	3.22660e7i	−0.697406	+	0.335853i
$459$	−8.43687e6	−	4.06298e6i	−0.0872455	−	0.0420152i
$460$	2.18517e7	+	2.74012e7i	0.224498	+	0.281512i
$461$	2.29090e7	−	2.58122e6i	0.233831	−	0.0263465i	0.00572881	−	0.999984i	$-0.498176\pi$
$461$	2.29090e7	−	2.58122e6i	0.233831	−	0.0263465i	0.228102	+	0.973637i	$0.426748\pi$
$462$	3.77575e7	+	1.07905e8i	0.382893	+	1.09424i
$463$		−	1.40759e8i		−	1.41818i	−0.705117	−	0.709091i	$-0.749105\pi$
$463$		−	1.40759e8i		−	1.41818i	0.705117	−	0.709091i	$-0.250895\pi$
$464$	2.97652e6	+	2.47963e7i	0.0297958	+	0.248218i
$465$	−3.81043e8			−3.78979
$466$	−1.13163e8	+	3.95974e7i	−1.11827	+	0.391299i
$467$	2.03773e7	+	1.80854e8i	0.200077	+	1.77573i	0.546313	+	0.837581i	$0.316031\pi$
$467$	2.03773e7	+	1.80854e8i	0.200077	+	1.77573i	−0.346237	+	0.938147i	$0.612541\pi$
$468$	−9.84005e7	+	7.84718e7i	−0.959975	+	0.765554i
$469$	1.48782e7	−	3.08949e7i	0.144222	−	0.299480i
$470$	−2.47244e7	−	5.13407e7i	−0.238140	−	0.494502i
$471$	9.30652e7	−	1.16700e8i	0.890686	−	1.11688i
$472$	2.88862e6	−	4.59722e6i	0.0274704	−	0.0437189i
$473$	3.83147e7	−	8.74508e6i	0.362061	−	0.0826381i
$474$	4.06589e6	−	3.60857e7i	0.0381786	−	0.338845i
$475$	−2.06415e8	−	3.28508e8i	−1.92602	−	3.06524i
$476$	1.73772e6	+	1.73772e6i	0.0161124	+	0.0161124i
$477$	−9.97853e7	−	2.27753e7i	−0.919415	−	0.209850i
$478$	3.20625e7	−	9.16294e7i	0.293571	−	0.838979i
$479$	−3.16944e7	−	1.10904e7i	−0.288387	−	0.100911i	0.182209	−	0.983260i	$-0.441675\pi$
$479$	−3.16944e7	−	1.10904e7i	−0.288387	−	0.100911i	−0.470596	+	0.882349i	$0.655961\pi$
$480$	1.37095e7	−	6.00652e7i	0.123965	−	0.543124i
$481$	1.12115e8	−	1.12115e8i	1.00746	−	1.00746i
$482$	−5.26140e7	+	3.30595e7i	−0.469851	+	0.295227i
$483$	−5.09540e7	−	5.74113e6i	−0.452206	−	0.0509514i
$484$	1.19258e7	+	5.22505e7i	0.105185	+	0.460845i
$485$	−2.01851e7	−	1.26831e7i	−0.176931	−	0.111173i
$486$	2.60975e7	+	2.08121e7i	0.227348	+	0.181304i
$487$	8.79458e7	−	4.23524e7i	0.761427	−	0.366684i	−0.0125307	−	0.999921i	$-0.503989\pi$
$487$	8.79458e7	−	4.23524e7i	0.761427	−	0.366684i	0.773957	+	0.633238i	$0.218274\pi$
$488$	1.05978e7	+	5.10363e6i	0.0911919	+	0.0439157i
$489$	3.35516e7	+	4.20723e7i	0.286937	+	0.359807i
$490$	7.97472e7	−	8.98535e6i	0.677840	−	0.0763742i
$491$	−5.31403e7	−	1.51866e8i	−0.448931	−	1.28297i	−0.916861	−	0.399205i	$-0.869286\pi$
$491$	−5.31403e7	−	1.51866e8i	−0.448931	−	1.28297i	0.467931	−	0.883765i	$-0.345000\pi$
$492$			1.85441e8i			1.55708i
$493$	−3.36319e6	+	7.11557e6i	−0.0280680	+	0.0593839i
$494$	−1.64710e8			−1.36628
$495$	5.55485e8	−	1.94373e8i	4.57991	−	1.60258i
$496$	−4.10751e6	−	3.64551e7i	−0.0336615	−	0.298754i
$497$	−2.18145e6	+	1.73965e6i	−0.0177696	+	0.0141707i
$498$	−1.43911e7	+	2.98834e7i	−0.116521	+	0.241959i
$499$	1.03226e8	+	2.14351e8i	0.830781	+	1.72513i	0.675627	+	0.737244i	$0.263873\pi$
$499$	1.03226e8	+	2.14351e8i	0.830781	+	1.72513i	0.155154	+	0.987890i	$0.450413\pi$
$500$	1.05837e8	−	1.32716e8i	0.846699	−	1.06173i
$501$	1.24939e8	−	1.98840e8i	0.993542	−	1.58121i
$502$	9.84404e6	−	2.24684e6i	0.0778148	−	0.0177607i
$503$	−3.15105e6	+	2.79663e7i	−0.0247600	+	0.219751i	−0.999999	−	0.00140226i	$-0.999554\pi$
$503$	−3.15105e6	+	2.79663e7i	−0.0247600	+	0.219751i	0.975239	+	0.221154i	$0.0709822\pi$
$504$	3.12482e7	+	4.97313e7i	0.244081	+	0.388453i
$505$	1.69986e8	+	1.69986e8i	1.31989	+	1.31989i
$506$	−4.82260e7	−	1.10073e7i	−0.372246	−	0.0849626i
$507$	−5.28063e7	+	1.50912e8i	−0.405193	+	1.15797i
$508$	−2.94610e7	−	1.03088e7i	−0.224727	−	0.0786355i
$509$	−2.68360e7	+	1.17576e8i	−0.203500	+	0.891593i	0.765285	+	0.643691i	$0.222598\pi$
$509$	−2.68360e7	+	1.17576e8i	−0.203500	+	0.891593i	−0.968785	+	0.247901i	$0.920259\pi$
$510$	1.37289e7	−	1.37289e7i	0.103496	−	0.103496i
$511$	7.18218e7	−	4.51286e7i	0.538262	−	0.338212i
$512$	5.89434e6	+	664133.i	0.0439163	+	0.00494818i
$513$	−6.51736e7	−	2.85544e8i	−0.482747	−	2.11505i
$514$	4.94757e7	+	3.10877e7i	0.364337	+	0.228928i
$515$	−7.59821e7	−	6.05937e7i	−0.556275	−	0.443614i
$516$	2.79185e7	−	1.34448e7i	0.203209	−	0.0978602i
$517$	7.24625e7	+	3.48961e7i	0.524375	+	0.252526i
$518$	−4.61330e7	−	5.78489e7i	−0.331911	−	0.416204i
$519$	−1.71549e8	+	1.93289e7i	−1.22712	+	0.138263i
$520$	−4.01031e7	−	1.14608e8i	−0.285212	−	0.815088i
$521$		−	9.60013e7i		−	0.678834i	−0.940636	−	0.339417i	$-0.889770\pi$
$521$		−	9.60013e7i		−	0.678834i	0.940636	−	0.339417i	$-0.110230\pi$
$522$	−1.16206e8	+	1.47910e8i	−0.816991	+	1.03989i
$523$	−1.24350e8			−0.869239			−0.434619	−	0.900614i	$-0.643117\pi$
$523$	−1.24350e8			−0.869239			−0.434619	+	0.900614i	$0.643117\pi$
$524$	2.78833e7	−	9.75678e6i	0.193798	−	0.0678130i
$525$	4.68511e7	+	4.15815e8i	0.323774	+	2.87357i
$526$	−7.15223e7	+	5.70371e7i	−0.491455	+	0.391923i
$527$	5.01616e6	−	1.04162e7i	0.0342720	−	0.0711666i
$528$	3.77290e7	+	7.83451e7i	0.256315	+	0.532243i
$529$	−7.84653e7	+	9.83924e7i	−0.530043	+	0.664652i
$530$	5.25344e7	−	8.36081e7i	0.352871	−	0.561592i
$531$	3.98674e7	−	9.09948e6i	0.266278	−	0.0607761i
$532$	−8.60606e6	+	7.63809e7i	−0.0571570	+	0.507283i
$533$	1.94442e8	+	3.09453e8i	1.28413	+	2.04368i
$534$	−1.96303e8	−	1.96303e8i	−1.28915	−	1.28915i
$535$	3.41258e8	+	7.78900e7i	2.22855	+	0.508651i
$536$	8.61466e6	−	2.46193e7i	0.0559427	−	0.159875i
$537$	7.81781e6	+	2.73557e6i	0.0504850	+	0.0176655i
$538$	2.59414e7	−	1.13656e8i	0.166589	−	0.729873i
$539$	−8.00924e7	+	8.00924e7i	−0.511476	+	0.511476i
$540$	1.82818e8	−	1.14872e8i	1.16101	−	0.729513i
$541$	−1.88007e8	−	2.11833e7i	−1.18736	−	0.133783i	−0.503894	−	0.863766i	$-0.668100\pi$
$541$	−1.88007e8	−	2.11833e7i	−1.18736	−	0.133783i	−0.683466	+	0.729982i	$0.739528\pi$
$542$	2.24854e7	+	9.85151e7i	0.141222	+	0.618735i
$543$	3.87162e8	+	2.43270e8i	2.41821	+	1.51946i
$544$	1.46146e6	+	1.16548e6i	0.00907802	+	0.00723948i
$545$	−2.21596e8	+	1.06715e8i	−1.36890	+	0.659227i
$546$	1.60054e8	+	7.70780e7i	0.983307	+	0.473536i
$547$	−6.98411e6	−	8.75780e6i	−0.0426726	−	0.0535098i	0.760037	−	0.649880i	$-0.225181\pi$
$547$	−6.98411e6	−	8.75780e6i	−0.0426726	−	0.0535098i	−0.802710	+	0.596370i	$0.796609\pi$
$548$	−9.48824e7	+	1.06907e7i	−0.576559	+	0.0649626i
$549$	2.92604e7	+	8.36213e7i	0.176833	+	0.505359i
$550$			4.03674e8i			2.42629i
$551$	−2.39587e8	+	5.65191e7i	−1.43222	+	0.337863i
$552$	−3.90030e7			−0.231889
$553$	−3.15241e7	+	1.10308e7i	−0.186409	+	0.0652274i
$554$	1.25512e7	+	1.11395e8i	0.0738171	+	0.655145i
$555$	−4.57036e8	+	3.64474e8i	−2.67345	+	2.13200i
$556$	1.91794e7	−	3.98265e7i	0.111586	−	0.231712i
$557$	−4.10578e7	−	8.52574e7i	−0.237591	−	0.493363i	0.747745	−	0.663986i	$-0.231136\pi$
$557$	−4.10578e7	−	8.52574e7i	−0.237591	−	0.493363i	−0.985336	+	0.170622i	$0.945422\pi$
$558$	1.72274e8	−	2.16025e8i	0.991557	−	1.24337i
$559$	3.24912e7	−	5.17095e7i	0.186008	−	0.296029i
$560$	−5.52424e7	+	1.26087e7i	−0.314563	+	0.0717971i
$561$	−3.06819e6	+	2.72309e7i	−0.0173778	+	0.154232i
$562$	−1.18108e8	−	1.87967e8i	−0.665378	−	1.05894i
$563$	−5.81904e7	−	5.81904e7i	−0.326081	−	0.326081i	0.525013	−	0.851094i	$-0.324060\pi$
$563$	−5.81904e7	−	5.81904e7i	−0.326081	−	0.326081i	−0.851094	+	0.525013i	$0.824060\pi$
$564$	6.18251e7	+	1.41112e7i	0.344610	+	0.0786550i
$565$	−7.14465e7	+	2.04182e8i	−0.396128	+	1.13207i
$566$	−1.34239e8	−	4.69721e7i	−0.740335	−	0.259054i
$567$	−1.76590e7	+	7.73690e7i	−0.0968760	+	0.424442i
$568$	−1.50071e6	+	1.50071e6i	−0.00818941	+	0.00818941i
$569$	−1.12236e8	+	7.05225e7i	−0.609249	+	0.382817i	−0.801033	−	0.598620i	$-0.795716\pi$
$569$	−1.12236e8	+	7.05225e7i	−0.609249	+	0.382817i	0.191783	+	0.981437i	$0.438573\pi$
$570$	6.03449e8	+	6.79923e7i	3.25849	+	0.367143i
$571$	−2.76682e7	−	1.21222e8i	−0.148618	−	0.651139i	−0.993270	−	0.115823i	$-0.963050\pi$
$571$	−2.76682e7	−	1.21222e8i	−0.148618	−	0.651139i	0.844652	−	0.535316i	$-0.179808\pi$
$572$	1.45108e8	+	9.11772e7i	0.775358	+	0.487190i
$573$	−1.02552e8	−	8.17824e7i	−0.545105	−	0.434706i
$574$	1.53662e8	−	7.39996e7i	0.812513	−	0.391286i
$575$	−1.63131e8	−	7.85597e7i	−0.858089	−	0.413234i
$576$	2.78546e7	+	3.49286e7i	0.145757	+	0.182774i
$577$	−1.33161e8	+	1.50037e7i	−0.693188	+	0.0781035i	−0.451527	−	0.892257i	$-0.649121\pi$
$577$	−1.33161e8	+	1.50037e7i	−0.693188	+	0.0781035i	−0.241661	+	0.970361i	$0.577692\pi$
$578$	−4.49026e7	−	1.28324e8i	−0.232535	−	0.664547i
$579$		−	2.98950e8i		−	1.54015i
$580$	−9.76606e7	−	1.52947e8i	−0.500536	−	0.783894i
$581$	3.05049e7			0.155540
$582$	2.50407e7	−	8.76213e6i	0.127022	−	0.0444468i
$583$	1.56041e7	+	1.38490e8i	0.0787468	+	0.698897i
$584$	5.04438e7	−	4.02276e7i	0.253261	−	0.201969i
$585$	3.96792e8	−	8.23946e8i	1.98196	−	4.11558i
$586$	−4.96429e7	−	1.03084e8i	−0.246697	−	0.512272i
$587$	1.05159e8	−	1.31866e8i	0.519917	−	0.651955i	−0.450674	−	0.892688i	$-0.648816\pi$
$587$	1.05159e8	−	1.31866e8i	0.519917	−	0.651955i	0.970591	+	0.240733i	$0.0773879\pi$
$588$	−4.75153e7	+	7.56201e7i	−0.233723	+	0.371968i
$589$	3.52533e8	−	8.04634e7i	1.72526	−	0.393779i
$590$	−4.41711e6	+	3.92029e7i	−0.0215071	+	0.190881i
$591$	1.87076e8	+	2.97730e8i	0.906266	+	1.44231i
$592$	−3.97967e7	−	3.97967e7i	−0.191815	−	0.191815i
$593$	−1.58362e8	−	3.61451e7i	−0.759429	−	0.173335i	−0.174765	−	0.984610i	$-0.555917\pi$
$593$	−1.58362e8	−	3.61451e7i	−0.759429	−	0.173335i	−0.584664	+	0.811275i	$0.698774\pi$
$594$	−1.00649e8	+	2.87638e8i	−0.480231	+	1.37242i
$595$	−1.68546e7	−	5.89767e6i	−0.0800142	−	0.0279982i
$596$	1.63867e7	−	7.17948e7i	0.0774021	−	0.339121i
$597$	3.38783e8	−	3.38783e8i	1.59220	−	1.59220i
$598$	−6.50857e7	+	4.08961e7i	−0.304356	+	0.191240i
$599$	6.94745e7	+	7.82789e6i	0.323255	+	0.0364221i	0.272101	−	0.962269i	$-0.412282\pi$
$599$	6.94745e7	+	7.82789e6i	0.323255	+	0.0364221i	0.0511538	+	0.998691i	$0.483710\pi$
$600$	7.08256e7	+	3.10307e8i	0.327897	+	1.43661i
$601$	1.07834e8	+	6.77569e7i	0.496746	+	0.312126i	0.757001	−	0.653414i	$-0.226664\pi$
$601$	1.07834e8	+	6.77569e7i	0.496746	+	0.312126i	−0.260255	+	0.965540i	$0.583807\pi$
$602$	−2.22815e7	−	1.77689e7i	−0.102130	−	0.0814463i
$603$	1.76994e8	−	8.52360e7i	0.807249	−	0.388751i
$604$	−1.62246e8	−	7.81334e7i	−0.736312	−	0.354589i
$605$	−2.42802e8	−	3.04464e8i	−1.09644	−	1.37490i
$606$	−2.65846e8	+	2.99536e7i	−1.19457	+	0.134596i
$607$	−2.08818e6	−	5.96768e6i	−0.00933689	−	0.0266833i	0.939121	−	0.343588i	$-0.111642\pi$
$607$	−2.08818e6	−	5.96768e6i	−0.00933689	−	0.0266833i	−0.948457	+	0.316904i	$0.897357\pi$
$608$			5.84661e7i			0.260132i
$609$	2.59263e8	+	5.71960e7i	1.14786	+	0.253229i
$610$	−8.54695e7			−0.376549
$611$	1.17966e8	−	4.12781e7i	0.517170	−	0.180966i
$612$	1.57633e6	+	1.39903e7i	0.00687691	+	0.0610343i
$613$	−1.82803e8	+	1.45780e8i	−0.793599	+	0.632874i	−0.934021	−	0.357218i	$-0.883725\pi$
$613$	−1.82803e8	+	1.45780e8i	−0.793599	+	0.632874i	0.140422	+	0.990092i	$0.455154\pi$
$614$	1.11850e8	−	2.32258e8i	0.483203	−	1.00338i
$615$	−5.84635e8	−	1.21401e9i	−2.51339	−	5.21911i
$616$	4.98633e7	−	6.25266e7i	0.213324	−	0.267499i
$617$	−7.59928e7	+	1.20942e8i	−0.323532	+	0.514898i	−0.968402	−	0.249394i	$-0.919768\pi$
$617$	−7.59928e7	+	1.20942e8i	−0.323532	+	0.514898i	0.644870	+	0.764292i	$0.276911\pi$
$618$	1.05441e8	−	2.40663e7i	0.446731	−	0.101963i
$619$	1.29683e7	−	1.15097e8i	0.0546778	−	0.485279i	−0.936295	−	0.351215i	$-0.885769\pi$
$619$	1.29683e7	−	1.15097e8i	0.0546778	−	0.485279i	0.990973	−	0.134064i	$-0.0428028\pi$
$620$	1.41821e8	+	2.25707e8i	0.595067	+	0.947043i
$621$	−9.66515e7	−	9.66515e7i	−0.403584	−	0.403584i
$622$	2.37871e8	+	5.42924e7i	0.988484	+	0.225615i
$623$	−8.43281e7	+	2.40996e8i	−0.348745	+	0.996656i
$624$	1.27543e8	+	4.46291e7i	0.524930	+	0.183681i
$625$	−1.40815e8	+	6.16952e8i	−0.576779	+	2.52704i
$626$	−7.26955e7	+	7.26955e7i	−0.296336	+	0.296336i
$627$	−7.25727e8	+	4.56005e8i	−2.94422	+	1.84998i
$628$	−1.03764e8	−	1.16914e7i	−0.418957	−	0.0472051i
$629$	−3.94669e6	−	1.72916e7i	−0.0158592	−	0.0694836i
$630$	−3.61355e8	−	2.27055e8i	−1.44515	−	0.908048i
$631$	4.96645e7	+	3.96061e7i	0.197678	+	0.157643i	0.717326	−	0.696737i	$-0.245366\pi$
$631$	4.96645e7	+	3.96061e7i	0.197678	+	0.157643i	−0.519649	+	0.854380i	$0.673937\pi$
$632$	−2.28883e7	+	1.10224e7i	−0.0906699	+	0.0436643i
$633$	−3.13600e8	−	1.51022e8i	−1.23642	−	0.595428i
$634$	1.24741e8	+	1.56420e8i	0.489487	+	0.613798i
$635$	2.25369e8	−	2.53930e7i	0.880183	−	0.0991728i
$636$	3.62934e7	+	1.03721e8i	0.141077	+	0.403175i
$637$			1.76012e8i			0.680962i
$638$	2.42360e8	+	8.28333e7i	0.933251	+	0.318965i
$639$	−1.59847e7			−0.0612636
$640$	−4.06816e7	+	1.42351e7i	−0.155188	+	0.0543026i
$641$	−3.68894e7	−	3.27402e8i	−0.140064	−	1.24310i	−0.845362	−	0.534194i	$-0.820615\pi$
$641$	−3.68894e7	−	3.27402e8i	−0.140064	−	1.24310i	0.705298	−	0.708911i	$-0.250813\pi$
$642$	−3.04554e8	+	2.42874e8i	−1.15096	+	0.917858i
$643$	7.08912e7	−	1.47207e8i	0.266661	−	0.553727i	−0.724044	−	0.689753i	$-0.757719\pi$
$643$	7.08912e7	−	1.47207e8i	0.266661	−	0.553727i	0.990705	+	0.136026i	$0.0434332\pi$
$644$	1.55640e7	+	3.23189e7i	0.0582724	+	0.121004i
$645$	−1.40384e8	+	1.76035e8i	−0.523163	+	0.656026i
$646$	−9.80262e6	+	1.56008e7i	−0.0363617	+	0.0578694i
$647$	2.44530e8	−	5.58124e7i	0.902858	−	0.206071i	0.254200	−	0.967152i	$-0.418188\pi$
$647$	2.44530e8	−	5.58124e7i	0.902858	−	0.206071i	0.648658	+	0.761080i	$0.275331\pi$
$648$	−6.75857e6	+	5.99840e7i	−0.0248388	+	0.220450i
$649$	−2.96243e7	−	4.71467e7i	−0.108371	−	0.172472i
$650$	4.43558e8	+	4.43558e8i	1.61514	+	1.61514i
$651$	−3.80221e8	−	8.67830e7i	−1.37814	−	0.314551i
$652$	1.24335e7	−	3.55329e7i	0.0448592	−	0.128200i
$653$	−5.58093e7	−	1.95285e7i	−0.200432	−	0.0701342i	0.228196	−	0.973615i	$-0.426717\pi$
$653$	−5.58093e7	−	1.95285e7i	−0.200432	−	0.0701342i	−0.428628	+	0.903481i	$0.641003\pi$
$654$	6.09064e7	−	2.66848e8i	0.217736	−	0.953962i
$655$	−1.51780e8	+	1.51780e8i	−0.540122	+	0.540122i
$656$	1.09844e8	−	6.90199e7i	0.389105	−	0.244491i
$657$	4.82889e8	+	5.44086e7i	1.70275	+	0.191854i
$658$	−1.29782e7	−	5.68610e7i	−0.0455549	−	0.199589i
$659$	−1.11871e8	−	7.02935e7i	−0.390897	−	0.245617i	0.322215	−	0.946666i	$-0.395572\pi$
$659$	−1.11871e8	−	7.02935e7i	−0.390897	−	0.245617i	−0.713113	+	0.701049i	$0.752715\pi$
$660$	−4.93992e8	−	3.93946e8i	−1.71826	−	1.37026i
$661$	8.78493e7	−	4.23060e7i	0.304182	−	0.146486i	−0.275566	−	0.961282i	$-0.588865\pi$
$661$	8.78493e7	−	4.23060e7i	0.304182	−	0.146486i	0.579748	+	0.814796i	$0.303151\pi$
$662$	−2.27640e8	−	1.09626e8i	−0.784649	−	0.377867i
$663$	2.65501e7	+	3.32928e7i	0.0911016	+	0.114238i
$664$	2.30574e7	−	2.59794e6i	0.0787600	−	0.00887412i
$665$	−1.84463e8	−	5.27166e8i	−0.627257	−	1.79260i
$666$		−	4.23891e8i		−	1.43493i
$667$	−8.06402e7	+	8.18209e7i	−0.271753	+	0.275732i
$668$	−1.64282e8			−0.551139
$669$	1.62369e8	−	5.68153e7i	0.542281	−	0.189752i
$670$	2.12198e7	+	1.88331e8i	0.0705534	+	0.626178i
$671$	9.43139e7	−	7.52129e7i	0.312182	−	0.248957i
$672$	2.73599e7	−	5.68133e7i	0.0901584	−	0.187216i
$673$	7.04400e7	+	1.46270e8i	0.231086	+	0.479855i	0.983978	−	0.178289i	$-0.0570561\pi$
$673$	7.04400e7	+	1.46270e8i	0.231086	+	0.479855i	−0.752892	+	0.658144i	$0.771342\pi$
$674$	1.43885e8	−	1.80427e8i	0.469934	−	0.589279i
$675$	−5.93449e8	+	9.44469e8i	−1.92962	+	3.07098i
$676$	1.09045e8	−	2.48889e7i	0.352993	−	0.0805684i
$677$	1.16138e7	−	1.03075e8i	0.0374290	−	0.332192i	−0.961018	−	0.276485i	$-0.910830\pi$
$677$	1.16138e7	−	1.03075e8i	0.0374290	−	0.332192i	0.998447	−	0.0557065i	$-0.0177411\pi$
$678$	−1.28079e8	−	2.03837e8i	−0.410950	−	0.654023i
$679$	−1.72529e7	−	1.72529e7i	−0.0551130	−	0.0551130i
$680$	−1.32420e7	−	3.02239e6i	−0.0421139	−	0.00961222i
$681$	1.55369e8	−	4.44018e8i	0.491951	−	1.40592i
$682$	−3.55118e8	−	1.24261e8i	−1.11949	−	0.391726i
$683$	7.38764e7	−	3.23674e8i	0.231869	−	1.01589i	−0.716218	−	0.697877i	$-0.754128\pi$
$683$	7.38764e7	−	3.23674e8i	0.231869	−	1.01589i	0.948087	−	0.318010i	$-0.103014\pi$
$684$	−3.11374e8	+	3.11374e8i	−0.973002	+	0.973002i
$685$	5.87451e8	−	3.69120e8i	1.82768	−	1.14841i
$686$	2.39009e8	+	2.69298e7i	0.740357	+	0.0834182i
$687$	1.33810e8	+	5.86260e8i	0.412685	+	1.80809i
$688$	−1.83550e7	−	1.15332e7i	−0.0563622	−	0.0354147i
$689$	1.69319e8	+	1.35028e8i	0.517665	+	0.412824i
$690$	2.55336e8	−	1.22963e8i	0.777257	−	0.374307i
$691$	2.44117e8	+	1.17561e8i	0.739884	+	0.356310i	0.765563	−	0.643361i	$-0.222460\pi$
$691$	2.44117e8	+	1.17561e8i	0.739884	+	0.356310i	−0.0256789	+	0.999670i	$0.508175\pi$
$692$	7.52984e7	+	9.44213e7i	0.227231	+	0.284939i
$693$	5.98556e8	−	6.74411e7i	1.79848	−	0.202640i
$694$	1.10905e8	+	3.16947e8i	0.331796	+	0.948218i
$695$			3.21194e8i			0.956782i
$696$	2.00837e8	+	2.11520e7i	0.595685	+	0.0627370i
$697$	4.08824e7			0.120736
$698$	−3.95858e8	+	1.38517e8i	−1.16405	+	0.407320i
$699$	1.08545e8	+	9.63368e8i	0.317819	+	2.82072i
$700$	2.28867e8	−	1.82515e8i	0.667249	−	0.532114i
$701$	−2.29372e7	+	4.76295e7i	−0.0665864	+	0.138268i	−0.931606	−	0.363470i	$-0.881592\pi$
$701$	−2.29372e7	+	4.76295e7i	−0.0665864	+	0.138268i	0.865019	+	0.501739i	$0.167306\pi$
$702$	2.05464e8	+	4.26651e8i	0.593916	+	1.23328i
$703$	3.45876e8	−	4.33715e8i	0.995531	−	1.24836i
$704$	3.23645e7	−	5.15079e7i	0.0927580	−	0.147624i
$705$	−4.49231e8	+	1.02534e8i	−1.28204	+	0.292618i
$706$	4.32306e7	−	3.83682e8i	0.122851	−	1.09033i
$707$	1.30905e8	+	2.08334e8i	0.370423	+	0.589525i
$708$	−3.10444e7	−	3.10444e7i	−0.0874749	−	0.0874749i
$709$	1.42589e8	+	3.25449e7i	0.400079	+	0.0913155i	0.417826	−	0.908527i	$-0.362792\pi$
$709$	1.42589e8	+	3.25449e7i	0.400079	+	0.0913155i	−0.0177468	+	0.999843i	$0.505649\pi$
$710$	5.09329e6	−	1.45558e7i	0.0142306	−	0.0406687i
$711$	−1.80599e8	−	6.31943e7i	−0.502466	−	0.175820i
$712$	−4.32157e7	+	1.89341e8i	−0.119730	+	0.524570i
$713$	1.19326e8	−	1.19326e8i	0.329205	−	0.329205i
$714$	1.68261e7	−	1.05725e7i	0.0462262	−	0.0290458i
$715$	−1.23741e9	−	1.39423e8i	−3.38529	−	0.381430i
$716$	−1.28934e6	−	5.64896e6i	−0.00351260	−	0.0153897i
$717$	−6.64667e8	−	4.17638e8i	−1.80321	−	1.13303i
$718$	2.63740e8	+	2.10326e8i	0.712529	+	0.568223i
$719$	−8.14604e7	+	3.92293e7i	−0.219159	+	0.105542i	−0.540242	−	0.841509i	$-0.681667\pi$
$719$	−8.14604e7	+	3.92293e7i	−0.219159	+	0.105542i	0.321083	+	0.947051i	$0.395953\pi$
$720$	−2.92471e8	−	1.40846e8i	−0.783582	−	0.377353i
$721$	−6.20180e7	−	7.77681e7i	−0.165467	−	0.207489i
$722$	−3.08198e8	+	3.47256e7i	−0.818877	+	0.0922653i
$723$	1.65953e8	+	4.74267e8i	0.439107	+	1.25490i
$724$		−	3.19875e8i		−	0.842878i
$725$	7.97402e8	+	4.92995e8i	2.09249	+	1.29368i
$726$	4.33375e8			1.13254
$727$	−1.19280e8	+	4.17380e7i	−0.310431	+	0.108625i	−0.480998	−	0.876721i	$-0.659726\pi$
$727$	−1.19280e8	+	4.17380e7i	−0.310431	+	0.108625i	0.170567	+	0.985346i	$0.445440\pi$
$728$	−1.39145e7	−	1.23494e8i	−0.0360639	−	0.320076i
$729$	4.01090e8	−	3.19859e8i	1.03528	−	0.825611i
$730$	−2.03410e8	+	4.22385e8i	−0.522882	+	1.08578i
$731$	−2.96404e6	−	6.15490e6i	−0.00758809	−	0.0157568i
$732$	5.93036e7	−	7.43644e7i	0.151199	−	0.189597i
$733$	−1.07614e8	+	1.71266e8i	−0.273247	+	0.434870i	−0.954953	−	0.296756i	$-0.904095\pi$
$733$	−1.07614e8	+	1.71266e8i	−0.273247	+	0.434870i	0.681706	+	0.731626i	$0.261238\pi$
$734$	−3.75472e8	+	8.56990e7i	−0.949487	+	0.216714i
$735$	7.26575e7	−	6.44853e8i	0.182986	−	1.62405i
$736$	1.45166e7	+	2.31030e7i	0.0364109	+	0.0579476i
$737$	−1.89147e8	−	1.89147e8i	−0.472494	−	0.472494i
$738$	9.52580e8	+	2.17420e8i	2.36991	+	0.540917i
$739$	2.50676e8	−	7.16389e8i	0.621124	−	1.77507i	−0.0106790	−	0.999943i	$-0.503399\pi$
$739$	2.50676e8	−	7.16389e8i	0.621124	−	1.77507i	0.631803	−	0.775129i	$-0.282315\pi$
$740$	3.85998e8	+	1.35067e8i	0.952555	+	0.333313i
$741$	−2.96372e8	+	1.29849e9i	−0.728421	+	3.19142i
$742$	7.14630e7	−	7.14630e7i	0.174932	−	0.174932i
$743$	2.20256e8	−	1.38396e8i	0.536983	−	0.337409i	−0.236085	−	0.971733i	$-0.575864\pi$
$743$	2.20256e8	−	1.38396e8i	0.536983	−	0.337409i	0.773068	+	0.634324i	$0.218721\pi$
$744$	−2.94784e8	−	3.32142e7i	−0.715790	−	0.0806501i
$745$	1.19068e8	+	5.21672e8i	0.287957	+	1.26162i
$746$	−7.35231e7	−	4.61976e7i	−0.177095	−	0.111276i
$747$	1.36633e8	+	1.08961e8i	0.327788	+	0.261402i
$748$	1.72719e7	−	8.31773e6i	0.0412702	−	0.0198747i
$749$	3.22783e8	+	1.55444e8i	0.768184	+	0.369938i
$750$	−8.55824e8	−	1.07317e9i	−2.02862	−	2.54381i
$751$	7.18548e8	−	8.09609e7i	1.69643	−	0.191142i	0.789886	−	0.613254i	$-0.210140\pi$
$751$	7.18548e8	−	8.09609e7i	1.69643	−	0.191142i	0.906543	+	0.422113i	$0.138711\pi$
$752$	−1.46522e7	−	4.18736e7i	−0.0344548	−	0.0984661i
$753$		−	8.16481e7i		−	0.191232i
$754$	3.57323e8	−	1.75288e8i	0.833580	−	0.408920i
$755$	1.30848e9			3.04037
$756$	2.08586e8	−	7.29873e7i	0.482747	−	0.168920i
$757$	−8.54597e7	−	7.58475e8i	−0.197003	−	1.74845i	−0.570934	−	0.820996i	$-0.693419\pi$
$757$	−8.54597e7	−	7.58475e8i	−0.197003	−	1.74845i	0.373931	−	0.927457i	$-0.378010\pi$
$758$	−2.85883e8	+	2.27984e8i	−0.656419	+	0.523476i
$759$	−1.73551e8	+	3.60383e8i	−0.396919	+	0.824211i
$760$	−1.84324e8	−	3.82753e8i	−0.419896	−	0.871923i
$761$	−1.10795e8	+	1.38932e8i	−0.251400	+	0.315245i	−0.891478	−	0.453065i	$-0.850331\pi$
$761$	−1.10795e8	+	1.38932e8i	−0.251400	+	0.315245i	0.640078	+	0.768310i	$0.278902\pi$
$762$	−1.34280e8	+	2.13706e8i	−0.303492	+	0.483005i
$763$	−2.45422e8	+	5.60160e7i	−0.552510	+	0.126107i
$764$	−1.02740e7	+	9.11844e7i	−0.0230388	+	0.204475i
$765$	−5.44265e7	−	8.66192e7i	−0.121570	−	0.193477i
$766$	−6.06539e7	−	6.06539e7i	−0.134950	−	0.134950i
$767$	−8.43562e7	−	1.92538e7i	−0.186952	−	0.0426707i
$768$	1.58417e7	−	4.52729e7i	0.0349718	−	0.0999436i
$769$	−2.59505e8	−	9.08046e7i	−0.570645	−	0.199677i	0.0295050	−	0.999565i	$-0.490607\pi$
$769$	−2.59505e8	−	9.08046e7i	−0.570645	−	0.199677i	−0.600150	+	0.799887i	$0.704893\pi$
$770$	−1.29309e8	+	5.66538e8i	−0.283240	+	1.24096i
$771$	3.34103e8	−	3.34103e8i	0.728984	−	0.728984i
$772$	−1.77080e8	+	1.11267e8i	−0.384874	+	0.241832i
$773$	−2.12289e8	−	2.39192e7i	−0.459609	−	0.0517855i	−0.120875	−	0.992668i	$-0.538570\pi$
$773$	−2.12289e8	−	2.39192e7i	−0.459609	−	0.0517855i	−0.338734	+	0.940882i	$0.609999\pi$
$774$	−3.63308e7	−	1.59176e8i	−0.0783524	−	0.343284i
$775$	−1.16604e9	−	7.32673e8i	−2.50501	−	1.57400i
$776$	−1.45101e7	−	1.15714e7i	−0.0310518	−	0.0247630i
$777$	−5.39060e8	+	2.59598e8i	−1.14914	+	0.553398i
$778$	7.52579e7	+	3.62423e7i	0.159813	+	0.0769621i
$779$	7.97251e8	+	9.99721e8i	1.68649	+	2.11479i
$780$	−9.75669e8	+	1.09932e8i	−2.05598	+	0.231653i
$781$	7.18870e6	+	2.05441e7i	0.0150903	+	0.0431255i
$782$			8.59858e6i			0.0179807i
$783$	4.45270e8	+	5.50102e8i	0.927551	+	1.14593i
$784$	6.24777e7			0.129651
$785$	7.16161e8	−	2.50596e8i	1.48048	−	0.518041i
$786$	−2.67455e7	−	2.37373e8i	−0.0550787	−	0.488837i
$787$	−5.28669e8	+	4.21600e8i	−1.08458	+	0.864921i	−0.991418	−	0.130731i	$-0.958268\pi$
$787$	−5.28669e8	+	4.21600e8i	−1.08458	+	0.864921i	−0.0931582	+	0.995651i	$0.529696\pi$
$788$	1.06729e8	−	2.21625e8i	0.218124	−	0.452940i
$789$	3.20957e8	+	6.66474e8i	0.653455	+	1.35691i
$790$	1.15090e8	−	1.44319e8i	0.233430	−	0.292712i
$791$	−1.17795e8	+	1.87470e8i	−0.238012	+	0.378793i
$792$	4.46680e8	−	1.01952e8i	0.899127	−	0.205220i
$793$	2.09883e7	−	1.86277e8i	0.0420880	−	0.373542i
$794$	4.21533e7	+	6.70866e7i	0.0842112	+	0.134021i
$795$	−5.64595e8	−	5.64595e8i	−1.12366	−	1.12366i
$796$	−3.26767e8	−	7.45825e7i	−0.647887	−	0.147876i
$797$	−2.50064e8	+	7.14643e8i	−0.493943	+	1.41161i	0.379731	+	0.925097i	$0.376017\pi$
$797$	−2.50064e8	+	7.14643e8i	−0.493943	+	1.41161i	−0.873674	+	0.486512i	$0.838269\pi$
$798$	5.86662e8	+	2.05282e8i	1.15446	+	0.403964i
$799$	3.11095e6	−	1.36300e7i	0.00609892	−	0.0267211i
$800$	1.57447e8	−	1.57447e8i	0.307514	−	0.307514i
$801$	−1.23853e9	+	7.78219e8i	−2.40995	+	1.51427i
$802$	3.51982e7	+	3.96589e6i	0.0682335	+	0.00768807i
$803$	−1.47239e8	−	6.45095e8i	−0.284364	−	1.24588i
$804$	−1.78585e8	−	1.12212e8i	−0.343618	−	0.215910i
$805$	−2.03782e8	−	1.62510e8i	−0.390641	−	0.311525i
$806$	−5.26744e8	+	2.53667e8i	−1.00599	+	0.484460i
$807$	−8.49331e8	−	4.09016e8i	−1.61606	−	0.778252i
$808$	1.16688e8	+	1.46323e8i	0.221204	+	0.277382i
$809$	−2.37691e8	+	2.67813e7i	−0.448917	+	0.0505808i	−0.333529	−	0.942740i	$-0.608240\pi$
$809$	−2.37691e8	+	2.67813e7i	−0.448917	+	0.0505808i	−0.115388	+	0.993321i	$0.536811\pi$
$810$	−1.44864e8	−	4.13997e8i	−0.272587	−	0.779009i
$811$		−	6.52681e7i		−	0.122360i	−0.998127	−	0.0611798i	$-0.980514\pi$
$811$		−	6.52681e7i		−	0.122360i	0.998127	−	0.0611798i	$-0.0194863\pi$
$812$	−6.26161e7	−	1.74860e8i	−0.116955	−	0.326604i
$813$	8.17101e8			1.52056
$814$	−5.44800e8	+	1.90634e8i	−1.01010	+	0.353449i
$815$	3.06265e7	+	2.71818e8i	0.0565751	+	0.502118i
$816$	1.18177e7	−	9.42431e6i	0.0217502	−	0.0173452i
$817$	9.27073e7	−	1.92509e8i	0.170000	−	0.353008i
$818$	−2.45190e8	−	5.09142e8i	−0.447963	−	0.930206i
$819$	5.83591e8	−	7.31800e8i	1.06232	−	1.33211i
$820$	−5.01509e8	+	7.98147e8i	−0.909573	+	1.44758i
$821$	3.33393e8	−	7.60947e7i	0.602458	−	0.137507i	0.0895960	−	0.995978i	$-0.471442\pi$
$821$	3.33393e8	−	7.60947e7i	0.602458	−	0.137507i	0.512862	+	0.858471i	$0.328585\pi$
$822$	−8.64472e7	+	7.67240e8i	−0.155645	+	1.38139i
$823$	−5.11664e7	−	8.14308e7i	−0.0917879	−	0.146080i	0.797674	−	0.603089i	$-0.206064\pi$
$823$	−5.11664e7	−	8.14308e7i	−0.0917879	−	0.146080i	−0.889462	+	0.457009i	$0.848921\pi$
$824$	−5.34999e7	−	5.34999e7i	−0.0956250	−	0.0956250i
$825$	3.18236e9	+	7.26352e8i	5.66744	+	1.29356i
$826$	−1.33361e7	+	3.81124e7i	−0.0236640	+	0.0676279i
$827$	−6.74357e8	−	2.35968e8i	−1.19227	−	0.417192i	−0.340063	−	0.940403i	$-0.610449\pi$
$827$	−6.74357e8	−	2.35968e8i	−1.19227	−	0.417192i	−0.852204	+	0.523210i	$0.824734\pi$
$828$	−4.57289e7	+	2.00351e8i	−0.0805563	+	0.352940i
$829$	1.91422e8	−	1.91422e8i	0.335992	−	0.335992i	−0.518864	−	0.854857i	$-0.673645\pi$
$829$	1.91422e8	−	1.91422e8i	0.335992	−	0.335992i	0.854857	+	0.518864i	$0.173645\pi$
$830$	−1.42757e8	+	8.96999e7i	−0.249667	+	0.156876i
$831$	9.00766e8	+	1.01492e8i	1.56967	+	0.176860i
$832$	−2.10348e7	−	9.21593e7i	−0.0365231	−	0.160018i
$833$	1.66712e7	+	1.04752e7i	0.0288424	+	0.0181229i
$834$	−2.79461e8	−	2.22863e8i	−0.481752	−	0.384184i
$835$	1.07549e9	−	5.17928e8i	1.84734	−	0.889631i
$836$	5.40220e8	+	2.60156e8i	0.924596	+	0.445262i
$837$	−6.48185e8	−	8.12798e8i	−1.10541	−	1.38614i
$838$	6.59858e8	−	7.43482e7i	1.12129	−	0.126339i
$839$	−1.07129e7	−	3.06157e7i	−0.0181393	−	0.0518392i	0.934458	−	0.356074i	$-0.115885\pi$
$839$	−1.07129e7	−	3.06157e7i	−0.0181393	−	0.0518392i	−0.952597	+	0.304235i	$0.901599\pi$
$840$			4.58190e8i			0.773050i
$841$	4.59612e8	−	3.77586e8i	0.772687	−	0.634787i
$842$	8.09630e8			1.35628
$843$	−1.69435e9	+	5.92879e8i	−2.82827	+	0.989654i
$844$	2.72632e7	+	2.41967e8i	0.0453470	+	0.402466i
$845$	−6.35407e8	+	5.06720e8i	−1.05313	+	0.839843i
$846$	1.44973e8	−	3.01040e8i	0.239429	−	0.497180i
$847$	−1.72936e8	−	3.59106e8i	−0.284601	−	0.590980i
$848$	4.79298e7	−	6.01021e7i	0.0785992	−	0.0985603i
$849$	−6.11847e8	+	9.73748e8i	−0.999815	+	1.59120i
$850$	6.84103e7	−	1.56142e7i	0.111395	−	0.0254251i
$851$	2.89864e7	−	2.57261e8i	0.0470333	−	0.417432i
$852$	9.13053e6	+	1.45311e7i	0.0147631	+	0.0234953i
$853$	−4.84308e8	−	4.84308e8i	−0.780323	−	0.780323i	0.199563	−	0.979885i	$-0.436048\pi$
$853$	−4.84308e8	−	4.84308e8i	−0.780323	−	0.780323i	−0.979885	+	0.199563i	$0.936048\pi$
$854$	−8.52852e7	−	1.94658e7i	−0.136930	−	0.0312535i
$855$	1.05678e9	−	3.02009e9i	1.69077	−	4.83194i
$856$	2.57217e8	+	9.00040e7i	0.410089	+	0.143496i
$857$	2.23476e8	−	9.79114e8i	0.355050	−	1.55557i	−0.410295	−	0.911953i	$-0.634574\pi$
$857$	2.23476e8	−	9.79114e8i	0.355050	−	1.55557i	0.765344	−	0.643621i	$-0.222569\pi$
$858$	9.79893e8	−	9.79893e8i	1.55138	−	1.55138i
$859$	−2.22064e8	+	1.39532e8i	−0.350347	+	0.220138i	−0.695695	−	0.718337i	$-0.744904\pi$
$859$	−2.22064e8	+	1.39532e8i	−0.350347	+	0.220138i	0.345348	+	0.938475i	$0.387761\pi$
$860$	1.56523e8	+	1.76359e7i	0.246083	+	0.0277269i
$861$	−3.06883e8	−	1.34454e9i	−0.480799	−	2.10652i
$862$	4.28709e8	+	2.69376e8i	0.669331	+	0.420568i
$863$	−2.16886e8	−	1.72961e8i	−0.337442	−	0.269101i	0.440078	−	0.897960i	$-0.354951\pi$
$863$	−2.16886e8	−	1.72961e8i	−0.337442	−	0.269101i	−0.777519	+	0.628859i	$0.783522\pi$
$864$	1.51445e8	−	7.29323e7i	0.234809	−	0.113078i
$865$	−7.90626e8	−	3.80746e8i	−1.22158	−	0.588283i
$866$	2.42904e8	+	3.04592e8i	0.374008	+	0.468992i
$867$	−1.09244e9	+	1.23088e8i	−1.67625	+	0.188868i
$868$	9.01102e7	+	2.57520e8i	0.137789	+	0.393779i
$869$			2.60532e8i			0.397010i
$870$	−1.38148e9	+	4.94700e8i	−2.09791	+	0.751249i
$871$	−4.15670e8			−0.629063
$872$	−1.80734e8	+	6.32415e7i	−0.272578	+	0.0953790i
$873$	−1.56506e7	−	1.38903e8i	−0.0235228	−	0.208770i
$874$	−2.10266e8	+	1.67682e8i	−0.314945	+	0.251161i
$875$	−5.47745e8	+	1.13740e9i	−0.817625	+	1.69782i
$876$	−2.26367e8	−	4.70056e8i	−0.336745	−	0.699258i
$877$	−1.13713e8	+	1.42591e8i	−0.168582	+	0.211395i	−0.858945	−	0.512068i	$-0.828879\pi$
$877$	−1.13713e8	+	1.42591e8i	−0.168582	+	0.211395i	0.690363	+	0.723463i	$0.257451\pi$
$878$	3.69055e7	−	5.87348e7i	0.0545265	−	0.0867784i
$879$	−9.01989e8	+	2.05873e8i	−1.32811	+	0.303133i
$880$	−4.94899e7	+	4.39235e8i	−0.0726221	+	0.644539i
$881$	5.03786e8	+	8.01770e8i	0.736746	+	1.17253i	0.979305	+	0.202389i	$0.0648704\pi$
$881$	5.03786e8	+	8.01770e8i	0.736746	+	1.17253i	−0.242559	+	0.970137i	$0.577987\pi$
$882$	3.32738e8	+	3.32738e8i	0.484950	+	0.484950i
$883$	−8.00982e8	−	1.82819e8i	−1.16343	−	0.265546i	−0.403147	−	0.915135i	$-0.632084\pi$
$883$	−8.00982e8	−	1.82819e8i	−1.16343	−	0.265546i	−0.760285	+	0.649590i	$0.774941\pi$
$884$	9.83892e6	−	2.81180e7i	0.0142426	−	0.0407032i
$885$	3.01108e8	+	1.05362e8i	0.434402	+	0.152004i
$886$	1.75641e8	−	7.69532e8i	0.252536	−	1.10643i
$887$	1.38878e8	−	1.38878e8i	0.199004	−	0.199004i	−0.600569	−	0.799573i	$-0.705059\pi$
$887$	1.38878e8	−	1.38878e8i	0.199004	−	0.199004i	0.799573	+	0.600569i	$0.205059\pi$
$888$	−3.85345e8	+	2.42128e8i	−0.550314	+	0.345785i
$889$	2.30666e8	+	2.59899e7i	0.328306	+	0.0369912i
$890$	−3.14012e8	−	1.37578e9i	−0.445427	−	1.95154i
$891$	5.24171e8	+	3.29359e8i	0.741037	+	0.465625i
$892$	−9.40865e7	−	7.50315e7i	−0.132566	−	0.105718i
$893$	3.93968e8	−	1.89725e8i	0.553231	−	0.266422i
$894$	−5.36507e8	−	2.58368e8i	−0.750867	−	0.361599i
$895$	2.62501e7	+	3.29166e7i	0.0366152	+	0.0459140i
$896$	−4.38360e7	+	4.93913e6i	−0.0609406	+	0.00686635i
$897$	2.05291e8	+	5.86688e8i	0.284441	+	0.812887i
$898$		−	389098.i		−	0.000537316i
$899$	−6.79156e8	+	5.49731e8i	−0.934739	+	0.756608i
$900$	1.67703e9			2.30046
$901$	2.28662e7	−	8.00124e6i	0.0312623	−	0.0109391i
$902$	−1.48961e8	−	1.32207e9i	−0.202980	−	1.80150i
$903$	−1.80173e8	+	1.43683e8i	−0.244696	+	0.195139i
$904$	−7.30707e7	+	1.51733e8i	−0.0989095	+	0.205388i
$905$	1.00846e9	+	2.09409e9i	1.36054	+	2.82520i
$906$	−9.07900e8	+	1.13847e9i	−1.22082	+	1.53087i
$907$	−1.26408e8	+	2.01177e8i	−0.169415	+	0.269622i	−0.920631	−	0.390434i	$-0.872325\pi$
$907$	−1.26408e8	+	2.01177e8i	−0.169415	+	0.269622i	0.751216	+	0.660056i	$0.229468\pi$
$908$	−3.20837e8	+	7.32290e7i	−0.428575	+	0.0978195i
$909$	−1.57823e8	+	1.40072e9i	−0.210126	+	1.86492i
$910$	4.80429e8	+	7.64599e8i	0.637537	+	1.01463i
$911$	−4.48231e8	−	4.48231e8i	−0.592853	−	0.592853i	0.345548	−	0.938401i	$-0.387693\pi$
$911$	−4.48231e8	−	4.48231e8i	−0.592853	−	0.592853i	−0.938401	+	0.345548i	$0.887693\pi$
$912$	4.60917e8	+	1.05201e8i	0.607628	+	0.138687i
$913$	7.85936e7	−	2.24607e8i	0.103270	−	0.295129i
$914$	−4.46983e8	−	1.56406e8i	−0.585399	−	0.204840i
$915$	−1.53790e8	+	6.73797e8i	−0.200754	+	0.879561i
$916$	2.97462e8	−	2.97462e8i	0.387031	−	0.387031i
$917$	−1.86021e8	+	1.16885e8i	−0.241243	+	0.151583i
$918$	5.26389e7	+	5.93098e6i	0.0680423	+	0.00766653i
$919$	1.49765e8	+	6.56164e8i	0.192959	+	0.845407i	0.975004	+	0.222186i	$0.0713192\pi$
$919$	1.49765e8	+	6.56164e8i	0.192959	+	0.845407i	−0.782046	+	0.623221i	$0.785824\pi$
$920$	−1.67870e8	−	1.05480e8i	−0.215581	−	0.135458i
$921$	−1.62975e9	−	1.29968e9i	−2.08613	−	1.66363i
$922$	−1.17498e8	+	5.65839e7i	−0.149912	+	0.0721939i
$923$	3.04729e7	+	1.46750e7i	0.0387533	+	0.0186626i
$924$	−4.03206e8	−	5.05604e8i	−0.511106	−	0.640906i
$925$	−2.09941e9	+	2.36547e8i	−2.65260	+	0.298876i
$926$	2.62985e8	+	7.51568e8i	0.331206	+	0.946532i
$927$		−	5.69850e8i		−	0.715355i
$928$	−6.22208e7	−	1.26837e8i	−0.0778560	−	0.158709i
$929$	9.58263e8			1.19519			0.597596	−	0.801797i	$-0.296123\pi$
$929$	9.58263e8			1.19519			0.597596	+	0.801797i	$0.296123\pi$
$930$	2.03454e9	−	7.11917e8i	2.52940	−	0.885076i
$931$	6.89500e7	+	6.11948e8i	0.0854447	+	0.758343i
$932$	5.30242e8	−	4.22854e8i	0.654977	−	0.522327i
$933$	8.56026e8	−	1.77756e9i	1.05400	−	2.18866i
$934$	−4.46699e8	−	9.27580e8i	−0.548244	−	1.13844i
$935$	−8.68492e7	+	1.08905e8i	−0.106250	+	0.133234i
$936$	3.78789e8	−	6.02839e8i	0.461923	−	0.735146i
$937$	−3.78342e8	+	8.63540e7i	−0.459902	+	0.104970i	−0.446194	−	0.894936i	$-0.647221\pi$
$937$	−3.78342e8	+	8.63540e7i	−0.459902	+	0.104970i	−0.0137084	+	0.999906i	$0.504364\pi$
$938$	−2.17186e7	+	1.92758e8i	−0.0263162	+	0.233563i
$939$	4.42288e8	+	7.03898e8i	0.534206	+	0.850184i
$940$	2.27936e8	+	2.27936e8i	0.274428	+	0.274428i
$941$	−1.43399e9	−	3.27298e8i	−1.72098	−	0.392803i	−0.755886	−	0.654703i	$-0.772794\pi$
$941$	−1.43399e9	−	3.27298e8i	−1.72098	−	0.392803i	−0.965095	+	0.261901i	$0.915651\pi$
$942$	−2.78878e8	+	7.96987e8i	−0.333627	+	0.953451i
$943$	5.63257e8	+	1.97092e8i	0.671694	+	0.235036i
$944$	−6.83437e6	+	2.99434e7i	−0.00812424	+	0.0355946i
$945$	−1.13542e9	+	1.13542e9i	−1.34543	+	1.34543i
$946$	−1.88239e8	+	1.18279e8i	−0.222350	+	0.139712i
$947$	1.42048e9	+	1.60049e8i	1.67257	+	0.188453i	0.896761	−	0.442515i	$-0.145914\pi$
$947$	1.42048e9	+	1.60049e8i	1.67257	+	0.188453i	0.775809	+	0.630968i	$0.217342\pi$
$948$	4.57110e7	+	2.00273e8i	0.0536532	+	0.235070i
$949$	−8.70619e8	−	5.47046e8i	−1.01866	−	0.640067i
$950$	1.71590e9	+	1.36838e9i	2.00134	+	1.59602i
$951$	1.45759e9	−	7.01938e8i	1.69470	−	0.816126i
$952$	−1.25251e7	−	6.03175e6i	−0.0145167	−	0.00699089i
$953$	−6.91332e7	−	8.66902e7i	−0.0798744	−	0.100159i	0.740289	−	0.672289i	$-0.234689\pi$
$953$	−6.91332e7	−	8.66902e7i	−0.0798744	−	0.100159i	−0.820163	+	0.572130i	$0.806117\pi$
$954$	5.75347e8	−	6.48260e7i	0.662651	−	0.0746628i
$955$	−2.20215e8	−	6.29337e8i	−0.252834	−	0.722559i
$956$			5.49151e8i			0.628518i
$957$	1.08911e9	−	1.76159e9i	1.24261	−	2.00988i
$958$	1.89950e8			0.216044
$959$	6.70252e8	−	2.34531e8i	0.759946	−	0.265917i
$960$	3.90216e7	+	3.46327e8i	0.0441054	+	0.391446i
$961$	3.09603e8	−	2.46900e8i	0.348847	−	0.278196i
$962$	−3.89159e8	+	8.08097e8i	−0.437121	+	0.907692i
$963$	8.90527e8	+	1.84920e9i	0.997167	+	2.07064i
$964$	2.19161e8	−	2.74819e8i	0.244643	−	0.306772i
$965$	8.08483e8	−	1.28669e9i	0.899682	−	1.43184i
$966$	2.82791e8	−	6.45451e7i	0.313714	−	0.0716031i
$967$	1.42053e8	−	1.26076e9i	0.157098	−	1.39429i	−0.629586	−	0.776931i	$-0.716776\pi$
$967$	1.42053e8	−	1.26076e9i	0.157098	−	1.39429i	0.786685	−	0.617355i	$-0.211796\pi$
$968$	−1.61299e8	−	2.56705e8i	−0.177830	−	0.283015i
$969$	1.05350e8	+	1.05350e8i	0.115788	+	0.115788i
$970$	1.31473e8	+	3.00078e7i	0.144052	+	0.0328790i
$971$	−4.09349e8	+	1.16985e9i	−0.447133	+	1.27783i	0.471202	+	0.882025i	$0.343820\pi$
$971$	−4.09349e8	+	1.16985e9i	−0.447133	+	1.27783i	−0.918334	+	0.395806i	$0.870465\pi$
$972$	−1.78229e8	−	6.23651e7i	−0.194080	−	0.0679115i
$973$	−7.31524e7	+	3.20502e8i	−0.0794127	+	0.347930i
$974$	−3.90450e8	+	3.90450e8i	−0.422560	+	0.422560i
$975$	4.29490e9	−	2.69867e9i	4.63382	−	2.91162i
$976$	−6.61214e7	−	7.45009e6i	−0.0711201	−	0.00801331i
$977$	2.19616e8	+	9.62200e8i	0.235494	+	1.03177i	0.945001	+	0.327068i	$0.106061\pi$
$977$	2.19616e8	+	9.62200e8i	0.235494	+	1.03177i	−0.709506	+	0.704699i	$0.751082\pi$
$978$	−2.57751e8	−	1.61956e8i	−0.275539	−	0.173133i
$979$	1.55719e9	+	1.24182e9i	1.65956	+	1.32345i
$980$	−4.09015e8	+	1.96971e8i	−0.434571	+	0.209279i
$981$	−1.29934e9	−	6.25730e8i	−1.37631	−	0.662797i
$982$	5.67476e8	+	7.11592e8i	0.599257	+	0.751444i
$983$	−1.70000e9	+	1.91544e8i	−1.78973	+	0.201654i	−0.943547	−	0.331239i	$-0.892533\pi$
$983$	−1.70000e9	+	1.91544e8i	−1.78973	+	0.201654i	−0.846183	+	0.532893i	$0.821105\pi$
$984$	−3.46468e8	−	9.90148e8i	−0.363645	−	1.03924i
$985$			1.78737e9i			1.87028i
$986$	4.66317e6	−	4.42765e7i	0.00486463	−	0.0461894i
$987$	−4.71615e8			−0.490497
$988$	8.79456e8	−	3.07735e8i	0.911892	−	0.319085i
$989$	−1.11646e7	−	9.90887e7i	−0.0115413	−	0.102432i
$990$	−2.60281e9	+	2.07567e9i	−2.68248	+	2.13921i
$991$	−3.81081e8	+	7.91323e8i	−0.391558	+	0.813079i	0.608255	+	0.793742i	$0.291870\pi$
$991$	−3.81081e8	+	7.91323e8i	−0.391558	+	0.813079i	−0.999813	+	0.0193374i	$0.993844\pi$
$992$	9.00423e7	+	1.86975e8i	0.0922383	+	0.191535i
$993$	−1.27384e9	+	1.59734e9i	−1.30097	+	1.63136i
$994$	8.39741e6	−	1.33644e7i	0.00855039	−	0.0136079i
$995$	2.37434e9	−	5.41928e8i	2.41032	−	0.550139i
$996$	2.10075e7	−	1.86447e8i	0.0212617	−	0.188702i
$997$	5.16520e8	+	8.22037e8i	0.521197	+	0.829480i	0.998794	−	0.0490987i	$-0.0156349\pi$
$997$	5.16520e8	+	8.22037e8i	0.521197	+	0.829480i	−0.477597	+	0.878579i	$0.658492\pi$
$998$	−9.51644e8	−	9.51644e8i	−0.957377	−	0.957377i
$999$	−1.55491e9	−	3.54899e8i	−1.55959	−	0.355966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.7.f.b.11.7	✓	96
29.8	odd	28	inner	58.7.f.b.37.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.7.f.b.11.7	✓	96	1.1	even	1	trivial
58.7.f.b.37.7	yes	96	29.8	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	58.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.33941 + 1.86834i) q^{2} +(5.12154 + 45.4549i) q^{3} +(25.0186 - 19.9517i) q^{4} +(-100.885 + 209.491i) q^{5} +(-112.271 - 233.134i) q^{6} +(-148.380 + 186.062i) q^{7} +(-96.3081 + 153.273i) q^{8} +(-1329.20 + 303.381i) q^{9} +O(q^{10})\)	\(q+(-5.33941 + 1.86834i) q^{2} +(5.12154 + 45.4549i) q^{3} +(25.0186 - 19.9517i) q^{4} +(-100.885 + 209.491i) q^{5} +(-112.271 - 233.134i) q^{6} +(-148.380 + 186.062i) q^{7} +(-96.3081 + 153.273i) q^{8} +(-1329.20 + 303.381i) q^{9} +(147.269 - 1307.04i) q^{10} +(987.687 + 1571.90i) q^{11} +(1035.04 + 1035.04i) q^{12} +(2812.48 + 641.930i) q^{13} +(444.632 - 1270.69i) q^{14} +(-10039.1 - 3512.82i) q^{15} +(227.861 - 998.326i) q^{16} +(228.184 - 228.184i) q^{17} +(6530.32 - 4103.27i) q^{18} +(10029.7 + 1130.08i) q^{19} +(1655.68 + 7254.00i) q^{20} +(-9217.38 - 5791.66i) q^{21} +(-8210.50 - 6547.66i) q^{22} +(4243.87 - 2043.74i) q^{23} +(-7460.28 - 3592.68i) q^{24} +(-23966.4 - 30053.0i) q^{25} +(-16216.3 + 1827.14i) q^{26} +(-9584.13 - 27389.9i) q^{27} +7615.44i q^{28} +(-22961.2 + 8222.26i) q^{29} +60165.9 q^{30} +(33815.5 - 11832.6i) q^{31} +(648.568 + 5756.20i) q^{32} +(-66391.9 + 52945.8i) q^{33} +(-792.042 + 1644.69i) q^{34} +(-24009.0 - 49855.1i) q^{35} +(-27201.8 + 34109.9i) q^{36} +(29241.5 - 46537.6i) q^{37} +(-55664.3 + 12705.0i) q^{38} +(-14774.7 + 131129. i) q^{39} +(-22393.3 - 35638.7i) q^{40} +(89582.1 + 89582.1i) q^{41} +(60036.2 + 13702.9i) q^{42} +(6991.86 - 19981.6i) q^{43} +(56072.5 + 19620.6i) q^{44} +(70541.3 - 309062. i) q^{45} +(-18841.3 + 18841.3i) q^{46} +(36682.9 - 23049.4i) q^{47} +(46545.9 + 5244.46i) q^{48} +(13576.7 + 59483.6i) q^{49} +(184116. + 115688. i) q^{50} +(11540.7 + 9203.43i) q^{51} +(83171.9 - 40053.5i) q^{52} +(67637.3 + 32572.4i) q^{53} +(102347. + 128339. i) q^{54} +(-428941. + 48330.0i) q^{55} +(-14228.2 - 40662.0i) q^{56} +461689. i q^{57} +(107237. - 86801.4i) q^{58} -29993.6 q^{59} +(-321250. + 112410. i) q^{60} +(-7275.48 - 64571.6i) q^{61} +(-158448. + 126358. i) q^{62} +(140778. - 292329. i) q^{63} +(-14217.5 - 29522.9i) q^{64} +(-418216. + 524427. i) q^{65} +(255573. - 406742. i) q^{66} +(-140477. + 32062.9i) q^{67} +(1156.19 - 10261.5i) q^{68} +(114633. + 182438. i) q^{69} +(221340. + 221340. i) q^{70} +(11430.4 + 2608.91i) q^{71} +(81512.4 - 232949. i) q^{72} +(-336425. - 117720. i) q^{73} +(-69184.4 + 303116. i) q^{74} +(1.24331e6 - 1.24331e6i) q^{75} +(273477. - 171837. i) q^{76} +(-439023. - 49466.0i) q^{77} +(-166105. - 727754. i) q^{78} +(118829. + 74665.0i) q^{79} +(186152. + 148451. i) q^{80} +(300441. - 144685. i) q^{81} +(-645686. - 310946. i) q^{82} +(-79919.7 - 100216. i) q^{83} +(-346159. + 39002.8i) q^{84} +(24782.0 + 70822.8i) q^{85} +119753. i q^{86} +(-491339. - 1.00159e6i) q^{87} -336052. q^{88} +(1.01266e6 - 354346. i) q^{89} +(200783. + 1.78200e6i) q^{90} +(-536753. + 428047. i) q^{91} +(65399.6 - 135804. i) q^{92} +(711037. + 1.47648e6i) q^{93} +(-152801. + 191607. i) q^{94} +(-1.24860e6 + 1.98713e6i) q^{95} +(-258326. + 58961.2i) q^{96} +(-11479.2 + 101881. i) q^{97} +(-183627. - 292241. i) q^{98} +(-1.78972e6 - 1.78972e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 64 q^{2} - 28 q^{3} - 588 q^{5} - 610 q^{7} + 2048 q^{8}+O(q^{10}) \) 96 * q - 64 * q^2 - 28 * q^3 - 588 * q^5 - 610 * q^7 + 2048 * q^8	\( 96 q - 64 q^{2} - 28 q^{3} - 588 q^{5} - 610 q^{7} + 2048 q^{8} - 1744 q^{10} + 1752 q^{11} + 896 q^{12} - 2608 q^{14} - 3048 q^{15} + 16384 q^{16} - 2144 q^{17} + 24368 q^{18} - 20742 q^{19} + 16064 q^{20} + 80556 q^{21} + 35280 q^{22} + 24730 q^{23} - 17920 q^{24} + 9556 q^{25} - 45072 q^{26} - 196048 q^{27} + 55514 q^{29} + 54464 q^{30} + 130770 q^{31} + 65536 q^{32} + 469616 q^{33} - 65184 q^{34} - 153664 q^{35} + 56960 q^{36} - 361120 q^{37} - 229040 q^{38} + 16520 q^{39} + 19456 q^{40} + 267404 q^{41} - 288064 q^{42} - 104504 q^{43} - 18432 q^{44} + 17462 q^{45} - 12912 q^{46} - 278966 q^{47} + 28672 q^{48} - 59808 q^{49} + 882256 q^{50} + 465150 q^{51} + 125952 q^{52} - 1150130 q^{53} + 31312 q^{54} - 2377762 q^{55} + 83456 q^{56} + 392288 q^{58} - 2028140 q^{59} - 97536 q^{60} + 875164 q^{61} + 404880 q^{62} + 4558036 q^{63} - 731620 q^{65} - 978576 q^{66} - 394170 q^{67} + 68608 q^{68} - 2223748 q^{69} - 1125008 q^{70} - 3274600 q^{71} + 34304 q^{72} + 2623288 q^{73} + 1590592 q^{74} + 3502816 q^{75} + 1044096 q^{76} - 196188 q^{77} + 988064 q^{78} + 854806 q^{79} + 4049800 q^{81} - 3418208 q^{82} - 2509204 q^{83} - 3344768 q^{84} - 4533520 q^{85} + 1785564 q^{87} - 147456 q^{88} + 5032828 q^{89} + 757472 q^{90} + 5996522 q^{91} + 6471360 q^{92} - 1360380 q^{93} + 4358912 q^{94} - 3508130 q^{95} + 6610532 q^{97} - 8015840 q^{98} - 833400 q^{99}+O(q^{100}) \) 96 * q - 64 * q^2 - 28 * q^3 - 588 * q^5 - 610 * q^7 + 2048 * q^8 - 1744 * q^10 + 1752 * q^11 + 896 * q^12 - 2608 * q^14 - 3048 * q^15 + 16384 * q^16 - 2144 * q^17 + 24368 * q^18 - 20742 * q^19 + 16064 * q^20 + 80556 * q^21 + 35280 * q^22 + 24730 * q^23 - 17920 * q^24 + 9556 * q^25 - 45072 * q^26 - 196048 * q^27 + 55514 * q^29 + 54464 * q^30 + 130770 * q^31 + 65536 * q^32 + 469616 * q^33 - 65184 * q^34 - 153664 * q^35 + 56960 * q^36 - 361120 * q^37 - 229040 * q^38 + 16520 * q^39 + 19456 * q^40 + 267404 * q^41 - 288064 * q^42 - 104504 * q^43 - 18432 * q^44 + 17462 * q^45 - 12912 * q^46 - 278966 * q^47 + 28672 * q^48 - 59808 * q^49 + 882256 * q^50 + 465150 * q^51 + 125952 * q^52 - 1150130 * q^53 + 31312 * q^54 - 2377762 * q^55 + 83456 * q^56 + 392288 * q^58 - 2028140 * q^59 - 97536 * q^60 + 875164 * q^61 + 404880 * q^62 + 4558036 * q^63 - 731620 * q^65 - 978576 * q^66 - 394170 * q^67 + 68608 * q^68 - 2223748 * q^69 - 1125008 * q^70 - 3274600 * q^71 + 34304 * q^72 + 2623288 * q^73 + 1590592 * q^74 + 3502816 * q^75 + 1044096 * q^76 - 196188 * q^77 + 988064 * q^78 + 854806 * q^79 + 4049800 * q^81 - 3418208 * q^82 - 2509204 * q^83 - 3344768 * q^84 - 4533520 * q^85 + 1785564 * q^87 - 147456 * q^88 + 5032828 * q^89 + 757472 * q^90 + 5996522 * q^91 + 6471360 * q^92 - 1360380 * q^93 + 4358912 * q^94 - 3508130 * q^95 + 6610532 * q^97 - 8015840 * q^98 - 833400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more