LMFDB - Embedded newform 69.7.h.a.2.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(2,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 2]))

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

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

chi := DirichletCharacter("69.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.h (of order $22$, degree $10$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			2.19
Character	$\chi$	$=$	69.2
Dual form			69.7.h.a.35.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10499 + 3.27543i) q^{2} +(1.61376 + 26.9517i) q^{3} +(20.2891 + 44.4269i) q^{4} +(49.4821 - 168.521i) q^{5} +(-91.6755 - 51.4474i) q^{6} +(211.874 - 244.516i) q^{7} +(-434.874 - 62.5255i) q^{8} +(-723.792 + 86.9871i) q^{9} +O(q^{10})$	\(q+(-2.10499 + 3.27543i) q^{2} +(1.61376 + 26.9517i) q^{3} +(20.2891 + 44.4269i) q^{4} +(49.4821 - 168.521i) q^{5} +(-91.6755 - 51.4474i) q^{6} +(211.874 - 244.516i) q^{7} +(-434.874 - 62.5255i) q^{8} +(-723.792 + 86.9871i) q^{9} +(447.818 + 516.810i) q^{10} +(-1070.39 - 1665.56i) q^{11} +(-1164.64 + 618.521i) q^{12} +(-2618.16 - 3021.52i) q^{13} +(354.901 + 1208.68i) q^{14} +(4621.78 + 1061.68i) q^{15} +(-926.756 + 1069.53i) q^{16} +(1826.47 + 834.120i) q^{17} +(1238.66 - 2553.84i) q^{18} +(-103.560 - 226.766i) q^{19} +(8490.80 - 1220.79i) q^{20} +(6932.04 + 5315.79i) q^{21} +7708.60 q^{22} +(-8970.54 - 8219.81i) q^{23} +(983.389 - 11821.5i) q^{24} +(-12806.1 - 8230.01i) q^{25} +(15408.0 - 2215.33i) q^{26} +(-3512.48 - 19367.1i) q^{27} +(15161.8 + 4451.91i) q^{28} +(8034.31 + 3669.15i) q^{29} +(-13206.3 + 12903.5i) q^{30} +(-1744.35 + 12132.2i) q^{31} +(-9474.17 - 32266.1i) q^{32} +(43162.4 - 31536.7i) q^{33} +(-6576.81 + 4226.66i) q^{34} +(-30722.0 - 47804.3i) q^{35} +(-18549.6 - 30390.9i) q^{36} +(22134.8 - 6499.35i) q^{37} +(960.750 + 138.135i) q^{38} +(77210.0 - 75439.9i) q^{39} +(-32055.3 + 70191.4i) q^{40} +(-29073.0 + 99013.7i) q^{41} +(-32003.4 + 11515.7i) q^{42} +(14084.1 + 97957.1i) q^{43} +(52278.5 - 81347.0i) q^{44} +(-21155.6 + 126278. i) q^{45} +(45806.3 - 12079.8i) q^{46} -108329. i q^{47} +(-30321.3 - 23251.7i) q^{48} +(1845.87 + 12838.3i) q^{49} +(53913.7 - 24621.6i) q^{50} +(-19533.5 + 50572.6i) q^{51} +(81116.6 - 177621. i) q^{52} +(32672.9 + 28311.2i) q^{53} +(70829.2 + 29262.6i) q^{54} +(-333647. + 97967.6i) q^{55} +(-107427. + 93086.1i) q^{56} +(5944.61 - 3157.08i) q^{57} +(-28930.2 + 18592.3i) q^{58} +(-154729. + 134073. i) q^{59} +(46604.6 + 226872. i) q^{60} +(46282.0 - 321898. i) q^{61} +(-36066.5 - 31251.8i) q^{62} +(-132083. + 195409. i) q^{63} +(38724.7 + 11370.6i) q^{64} +(-638740. + 291703. i) q^{65} +(12439.8 + 207760. i) q^{66} +(190513. + 122435. i) q^{67} +98067.9i q^{68} +(207062. - 255036. i) q^{69} +221249. q^{70} +(80303.0 - 124954. i) q^{71} +(320197. + 7426.97i) q^{72} +(71046.7 + 155571. i) q^{73} +(-25305.3 + 86182.0i) q^{74} +(201147. - 358429. i) q^{75} +(7973.36 - 9201.75i) q^{76} +(-634045. - 91161.9i) q^{77} +(84571.8 + 411697. i) q^{78} +(-65479.5 - 75567.4i) q^{79} +(134381. + 209100. i) q^{80} +(516307. - 125921. i) q^{81} +(-263114. - 303650. i) q^{82} +(-161563. - 550234. i) q^{83} +(-95519.3 + 415822. i) q^{84} +(230944. - 266524. i) q^{85} +(-350499. - 160067. i) q^{86} +(-85924.4 + 222460. i) q^{87} +(361346. + 791237. i) q^{88} +(367167. - 52790.6i) q^{89} +(-369083. - 335108. i) q^{90} -1.29353e6 q^{91} +(183177. - 565306. i) q^{92} +(-329800. - 27434.8i) q^{93} +(354824. + 228031. i) q^{94} +(-43339.1 + 6231.22i) q^{95} +(854337. - 307415. i) q^{96} +(479808. + 140884. i) q^{97} +(-45936.6 - 20978.6i) q^{98} +(919623. + 1.11241e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) $ 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$-1$

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 $

$2$	−2.10499	+	3.27543i	−0.263124	+	0.409429i	−0.947527	−	0.319675i	$-0.896426\pi$
$2$	−2.10499	+	3.27543i	−0.263124	+	0.409429i	0.684403	+	0.729104i	$0.260063\pi$
$3$	1.61376	+	26.9517i	0.0597688	+	0.998212i
$3$	1.61376	+	26.9517i	0.0597688	+	0.998212i
$4$	20.2891	+	44.4269i	0.317017	+	0.694171i
$5$	49.4821	−	168.521i	0.395857	−	1.34817i	−0.484889	−	0.874576i	$-0.661140\pi$
$5$	49.4821	−	168.521i	0.395857	−	1.34817i	0.880746	−	0.473589i	$-0.157042\pi$
$6$	−91.6755	−	51.4474i	−0.424424	−	0.238183i
$7$	211.874	−	244.516i	0.617709	−	0.712874i	−0.357561	−	0.933890i	$-0.616392\pi$
$7$	211.874	−	244.516i	0.617709	−	0.712874i	0.975270	+	0.221016i	$0.0709371\pi$
$8$	−434.874	−	62.5255i	−0.849364	−	0.122120i
$9$	−723.792	+	86.9871i	−0.992855	+	0.119324i
$10$	447.818	+	516.810i	0.447818	+	0.516810i
$11$	−1070.39	−	1665.56i	−0.804201	−	1.25136i	−0.964445	−	0.264284i	$-0.914864\pi$
$11$	−1070.39	−	1665.56i	−0.804201	−	1.25136i	0.160244	−	0.987077i	$-0.448772\pi$
$12$	−1164.64	+	618.521i	−0.673982	+	0.357940i
$13$	−2618.16	−	3021.52i	−1.19170	−	1.37529i	−0.909378	−	0.415971i	$-0.863442\pi$
$13$	−2618.16	−	3021.52i	−1.19170	−	1.37529i	−0.282319	−	0.959321i	$-0.591104\pi$
$14$	354.901	+	1208.68i	0.129337	+	0.440482i
$15$	4621.78	+	1061.68i	1.36942	+	0.314571i
$16$	−926.756	+	1069.53i	−0.226259	+	0.261116i
$17$	1826.47	+	834.120i	0.371762	+	0.169778i	0.592530	−	0.805548i	$-0.298129\pi$
$17$	1826.47	+	834.120i	0.371762	+	0.169778i	−0.220768	+	0.975326i	$0.570856\pi$
$18$	1238.66	−	2553.84i	0.212389	−	0.437901i
$19$	−103.560	−	226.766i	−0.0150985	−	0.0330611i	0.901933	−	0.431877i	$-0.142149\pi$
$19$	−103.560	−	226.766i	−0.0150985	−	0.0330611i	−0.917031	+	0.398816i	$0.869421\pi$
$20$	8490.80	−	1220.79i	1.06135	−	0.152599i
$21$	6932.04	+	5315.79i	0.748519	+	0.573997i
$22$	7708.60			0.723948
$23$	−8970.54	−	8219.81i	−0.737285	−	0.675582i
$23$	−8970.54	−	8219.81i	−0.737285	−	0.675582i
$24$	983.389	−	11821.5i	0.0711363	−	0.855144i
$25$	−12806.1	−	8230.01i	−0.819593	−	0.526721i
$26$	15408.0	−	2215.33i	0.876648	−	0.126043i
$27$	−3512.48	−	19367.1i	−0.178452	−	0.983949i
$28$	15161.8	+	4451.91i	0.690681	+	0.202802i
$29$	8034.31	+	3669.15i	0.329424	+	0.150443i	0.573260	−	0.819374i	$-0.305679\pi$
$29$	8034.31	+	3669.15i	0.329424	+	0.150443i	−0.243836	+	0.969816i	$0.578406\pi$
$30$	−13206.3	+	12903.5i	−0.489121	+	0.477907i
$31$	−1744.35	+	12132.2i	−0.0585530	+	0.407245i	0.939374	+	0.342894i	$0.111407\pi$
$31$	−1744.35	+	12132.2i	−0.0585530	+	0.407245i	−0.997927	+	0.0643517i	$0.979502\pi$
$32$	−9474.17	−	32266.1i	−0.289129	−	0.984682i
$33$	43162.4	−	31536.7i	1.20106	−	0.877556i
$34$	−6576.81	+	4226.66i	−0.167332	+	0.107538i
$35$	−30722.0	−	47804.3i	−0.716548	−	1.11497i
$36$	−18549.6	−	30390.9i	−0.397583	−	0.651383i
$37$	22134.8	−	6499.35i	0.436988	−	0.128311i	−0.0558366	−	0.998440i	$-0.517783\pi$
$37$	22134.8	−	6499.35i	0.436988	−	0.128311i	0.492825	+	0.870129i	$0.335964\pi$
$38$	960.750	+	138.135i	0.0175089	+	0.00251740i
$39$	77210.0	−	75439.9i	1.30161	−	1.27177i
$40$	−32055.3	+	70191.4i	−0.500865	+	1.09674i
$41$	−29073.0	+	99013.7i	−0.421831	+	1.43663i	0.425208	+	0.905095i	$0.360201\pi$
$41$	−29073.0	+	99013.7i	−0.421831	+	1.43663i	−0.847040	+	0.531530i	$0.821617\pi$
$42$	−32003.4	+	11515.7i	−0.431964	+	0.155433i
$43$	14084.1	+	97957.1i	0.177143	+	1.23206i	0.863333	+	0.504634i	$0.168373\pi$
$43$	14084.1	+	97957.1i	0.177143	+	1.23206i	−0.686190	+	0.727422i	$0.740718\pi$
$44$	52278.5	−	81347.0i	0.613713	−	0.954956i
$45$	−21155.6	+	126278.i	−0.232161	+	1.38577i
$46$	45806.3	−	12079.8i	0.470600	−	0.124104i
$47$		−	108329.i		−	1.04340i	−0.853129	−	0.521700i	$-0.825298\pi$
$47$		−	108329.i		−	1.04340i	0.853129	−	0.521700i	$-0.174702\pi$
$48$	−30321.3	−	23251.7i	−0.274173	−	0.210248i
$49$	1845.87	+	12838.3i	0.0156897	+	0.109124i
$50$	53913.7	−	24621.6i	0.431309	−	0.196972i
$51$	−19533.5	+	50572.6i	−0.147255	+	0.381245i
$52$	81116.6	−	177621.i	0.576899	−	1.26323i
$53$	32672.9	+	28311.2i	0.219462	+	0.190165i	0.757652	−	0.652658i	$-0.226346\pi$
$53$	32672.9	+	28311.2i	0.219462	+	0.190165i	−0.538190	+	0.842823i	$0.680892\pi$
$54$	70829.2	+	29262.6i	0.449812	+	0.185837i
$55$	−333647.	+	97967.6i	−2.00539	+	0.588836i
$56$	−107427.	+	93086.1i	−0.611716	+	0.530055i
$57$	5944.61	−	3157.08i	0.0320995	−	0.0170475i
$58$	−28930.2	+	18592.3i	−0.148275	+	0.0952905i
$59$	−154729.	+	134073.i	−0.753382	+	0.652809i	−0.944408	−	0.328776i	$-0.893364\pi$
$59$	−154729.	+	134073.i	−0.753382	+	0.652809i	0.191026	+	0.981585i	$0.438818\pi$
$60$	46604.6	+	226872.i	0.215762	+	1.05033i
$61$	46282.0	−	321898.i	0.203902	−	1.41817i	−0.588660	−	0.808381i	$-0.700344\pi$
$61$	46282.0	−	321898.i	0.203902	−	1.41817i	0.792562	−	0.609791i	$-0.208747\pi$
$62$	−36066.5	−	31251.8i	−0.151331	−	0.131129i
$63$	−132083.	+	195409.i	−0.528233	+	0.781488i
$64$	38724.7	+	11370.6i	0.147723	+	0.0433754i
$65$	−638740.	+	291703.i	−2.32586	+	1.06219i
$66$	12439.8	+	207760.i	0.0432695	+	0.722654i
$67$	190513.	+	122435.i	0.633432	+	0.407082i	0.817579	−	0.575817i	$-0.195316\pi$
$67$	190513.	+	122435.i	0.633432	+	0.407082i	−0.184147	+	0.982899i	$0.558952\pi$
$68$			98067.9i			0.311889i
$69$	207062.	−	255036.i	0.630308	−	0.776345i
$70$	221249.			0.645042
$71$	80303.0	−	124954.i	0.224366	−	0.349120i	−0.710761	−	0.703434i	$-0.751649\pi$
$71$	80303.0	−	124954.i	0.224366	−	0.349120i	0.935127	+	0.354314i	$0.115286\pi$
$72$	320197.	+	7426.97i	0.857867	+	0.0198982i
$73$	71046.7	+	155571.i	0.182631	+	0.399907i	0.978699	−	0.205301i	$-0.0658173\pi$
$73$	71046.7	+	155571.i	0.182631	+	0.399907i	−0.796068	+	0.605208i	$0.793090\pi$
$74$	−25305.3	+	86182.0i	−0.0624477	+	0.212677i
$75$	201147.	−	358429.i	0.476793	−	0.849610i
$76$	7973.36	−	9201.75i	0.0181635	−	0.0209618i
$77$	−634045.	−	91161.9i	−1.38883	−	0.199683i
$78$	84571.8	+	411697.i	0.178214	+	0.867548i
$79$	−65479.5	−	75567.4i	−0.132808	−	0.153269i	0.685450	−	0.728120i	$-0.259605\pi$
$79$	−65479.5	−	75567.4i	−0.132808	−	0.153269i	−0.818258	+	0.574851i	$0.805060\pi$
$80$	134381.	+	209100.i	0.262462	+	0.408399i
$81$	516307.	−	125921.i	0.971524	−	0.236943i
$82$	−263114.	−	303650.i	−0.477202	−	0.550721i
$83$	−161563.	−	550234.i	−0.282559	−	0.962306i	−0.971411	−	0.237405i	$-0.923703\pi$
$83$	−161563.	−	550234.i	−0.282559	−	0.962306i	0.688852	−	0.724902i	$-0.258115\pi$
$84$	−95519.3	+	415822.i	−0.161158	+	0.701567i
$85$	230944.	−	266524.i	0.376054	−	0.433989i
$86$	−350499.	−	160067.i	−0.551050	−	0.251656i
$87$	−85924.4	+	222460.i	−0.130484	+	0.337826i
$88$	361346.	+	791237.i	0.530243	+	1.16107i
$89$	367167.	−	52790.6i	0.520827	−	0.0748836i	0.123112	−	0.992393i	$-0.460713\pi$
$89$	367167.	−	52790.6i	0.520827	−	0.0748836i	0.397715	+	0.917509i	$0.369803\pi$
$90$	−369083.	−	335108.i	−0.506287	−	0.459682i
$91$	−1.29353e6			−1.71653
$92$	183177.	−	565306.i	0.235237	−	0.725973i
$93$	−329800.	−	27434.8i	−0.410017	−	0.0341078i
$94$	354824.	+	228031.i	0.427198	+	0.274544i
$95$	−43339.1	+	6231.22i	−0.0505486	+	0.00726779i
$96$	854337.	−	307415.i	0.965641	−	0.347465i
$97$	479808.	+	140884.i	0.525718	+	0.154365i	0.533813	−	0.845603i	$-0.320759\pi$
$97$	479808.	+	140884.i	0.525718	+	0.154365i	−0.00809528	+	0.999967i	$0.502577\pi$
$98$	−45936.6	−	20978.6i	−0.0488069	−	0.0222893i
$99$	919623.	+	1.11241e6i	0.947773	+	1.14646i
$100$	105809.	−	735917.i	0.105809	−	0.735917i
$101$	−439250.	−	1.49595e6i	−0.426332	−	1.45195i	−0.840529	−	0.541766i	$-0.817756\pi$
$101$	−439250.	−	1.49595e6i	−0.426332	−	1.45195i	0.414198	−	0.910187i	$-0.364062\pi$
$102$	−124529.	−	170435.i	−0.117347	−	0.160605i
$103$	−414535.	+	266406.i	−0.379358	+	0.243799i	−0.716398	−	0.697691i	$-0.754211\pi$
$103$	−414535.	+	266406.i	−0.379358	+	0.243799i	0.337040	+	0.941490i	$0.390574\pi$
$104$	949648.	+	1.47768e6i	0.844234	+	1.31365i
$105$	1.23883e6	−	905155.i	1.07015	−	0.781907i
$106$	−161507.	+	47422.9i	−0.135605	+	0.0398172i
$107$	−1.88303e6	−	270739.i	−1.53711	−	0.221003i	−0.678874	−	0.734255i	$-0.737532\pi$
$107$	−1.88303e6	−	270739.i	−1.53711	−	0.221003i	−0.858238	+	0.513252i	$0.828441\pi$
$108$	789154.	−	548989.i	0.626456	−	0.435805i
$109$	950471.	−	2.08124e6i	0.733938	−	1.60710i	−0.0593380	−	0.998238i	$-0.518899\pi$
$109$	950471.	−	2.08124e6i	0.733938	−	1.60710i	0.793276	−	0.608862i	$-0.208374\pi$
$110$	381438.	−	1.29906e6i	0.286580	−	0.976002i
$111$	210889.	+	586081.i	0.154200	+	0.428538i
$112$	65162.2	+	453213.i	0.0463811	+	0.322588i
$113$	696992.	−	1.08454e6i	0.483050	−	0.751641i	−0.511114	−	0.859513i	$-0.670767\pi$
$113$	696992.	−	1.08454e6i	0.483050	−	0.751641i	0.994165	+	0.107872i	$0.0344035\pi$
$114$	−2172.56	+	26116.8i	−0.00146642	+	0.0176281i
$115$	−1.82909e6	+	1.10499e6i	−1.20266	+	0.726548i
$116$			431383.i			0.276369i
$117$	2.15783e6	+	1.95920e6i	1.34729	+	1.22327i
$118$	−113445.	−	789027.i	−0.0690461	−	0.480226i
$119$	590937.	−	269872.i	0.350671	−	0.160146i
$120$	−1.94351e6	−	750675.i	−1.12472	−	0.434418i
$121$	−892425.	+	1.95414e6i	−0.503751	+	1.10306i
$122$	956932.	+	829187.i	0.526989	+	0.456639i
$123$	−2.71551e6	−	623785.i	−1.45927	−	0.335212i
$124$	−574390.	+	168656.i	−0.301260	+	0.0884579i
$125$	53400.5	−	46271.8i	0.0273410	−	0.0236911i
$126$	−362015.	−	843963.i	−0.180973	−	0.421902i
$127$	566172.	−	363856.i	0.276399	−	0.177631i	−0.395096	−	0.918640i	$-0.629289\pi$
$127$	566172.	−	363856.i	0.276399	−	0.177631i	0.671495	+	0.741009i	$0.265652\pi$
$128$	1.50777e6	−	1.30649e6i	0.718961	−	0.622983i
$129$	−2.61739e6	+	537670.i	−1.21927	+	0.250465i
$130$	389090.	−	2.70618e6i	0.177101	−	1.23176i
$131$	−2.90376e6	−	2.51612e6i	−1.29166	−	1.11923i	−0.985939	−	0.167105i	$-0.946558\pi$
$131$	−2.90376e6	−	2.51612e6i	−1.29166	−	1.11923i	−0.305718	−	0.952122i	$-0.598896\pi$
$132$	2.27681e6	+	1.27772e6i	0.989930	+	0.555539i
$133$	−77389.6	−	22723.6i	−0.0328948	−	0.00965880i
$134$	−802057.	+	366287.i	−0.333343	+	0.152232i
$135$	−3.43755e6	−	366398.i	−1.39717	−	0.148920i
$136$	−742130.	−	476938.i	−0.295028	−	0.189603i
$137$			518830.i			0.201773i	0.994898	+	0.100887i	$0.0321679\pi$
$137$			518830.i			0.201773i	−0.994898	+	0.100887i	$0.967832\pi$
$138$	399491.	+	1.21507e6i	0.152009	+	0.462341i
$139$	3.90842e6			1.45531			0.727657	−	0.685941i	$-0.240609\pi$
$139$	3.90842e6			1.45531			0.727657	+	0.685941i	$0.240609\pi$
$140$	1.50048e6	−	2.33479e6i	0.546822	−	0.850871i
$141$	2.91965e6	−	174817.i	1.04153	−	0.0623627i
$142$	240241.	+	526054.i	0.0839038	+	0.183724i
$143$	−2.23007e6	+	7.59491e6i	−0.762623	+	2.59725i
$144$	577742.	−	854735.i	0.193485	−	0.286249i
$145$	1.01588e6	−	1.17239e6i	0.333226	−	0.384564i
$146$	−659114.	−	94766.2i	−0.211788	−	0.0304505i
$147$	−343036.	+	70467.4i	−0.107991	+	0.0221838i
$148$	737840.	+	851513.i	0.227603	+	0.262667i
$149$	2.69778e6	+	4.19783e6i	0.815545	+	1.26901i	0.960139	+	0.279522i	$0.0901760\pi$
$149$	2.69778e6	+	4.19783e6i	0.815545	+	1.26901i	−0.144594	+	0.989491i	$0.546188\pi$
$150$	750597.	+	1.41333e6i	0.222399	+	0.418766i
$151$	3.56397e6	+	4.11304e6i	1.03515	+	1.19463i	0.980580	+	0.196118i	$0.0628335\pi$
$151$	3.56397e6	+	4.11304e6i	1.03515	+	1.19463i	0.0545705	+	0.998510i	$0.482621\pi$
$152$	30857.1	+	105090.i	0.00878668	+	0.0299247i
$153$	−1.39454e6	−	444850.i	−0.389365	−	0.124205i
$154$	1.63325e6	−	1.88488e6i	0.447189	−	0.516084i
$155$	1.95822e6	+	894289.i	0.525855	+	0.240150i
$156$	4.91808e6	+	1.89960e6i	1.29545	+	0.500366i
$157$	−801603.	−	1.75527e6i	−0.207138	−	0.453570i	0.777339	−	0.629082i	$-0.216569\pi$
$157$	−801603.	−	1.75527e6i	−0.207138	−	0.453570i	−0.984477	+	0.175512i	$0.943842\pi$
$158$	385350.	−	55404.9i	0.0976976	−	0.0140468i
$159$	−710309.	+	926277.i	−0.176708	+	0.230436i
$160$	−5.90630e6			−1.44197
$161$	−3.91050e6	+	451875.i	−0.937032	+	0.108278i
$162$	−674377.	+	1.95619e6i	−0.158620	+	0.460115i
$163$	−209325.	−	134525.i	−0.0483346	−	0.0310628i	0.516250	−	0.856438i	$-0.327327\pi$
$163$	−209325.	−	134525.i	−0.0483346	−	0.0310628i	−0.564585	+	0.825375i	$0.690964\pi$
$164$	−4.98874e6	+	717272.i	−1.13099	+	0.162612i
$165$	−3.17882e6	−	8.83427e6i	−0.707643	−	1.96661i
$166$	2.14234e6	+	629049.i	0.468344	+	0.137518i
$167$	1.34791e6	+	615571.i	0.289409	+	0.132169i	0.554830	−	0.831964i	$-0.312783\pi$
$167$	1.34791e6	+	615571.i	0.289409	+	0.132169i	−0.265420	+	0.964133i	$0.585511\pi$
$168$	−2.68219e6	−	2.74513e6i	−0.565669	−	0.578942i
$169$	−1.58788e6	+	1.10439e7i	−0.328971	+	2.28804i
$170$	386845.	+	1.31747e6i	0.0787390	+	0.268160i
$171$	94681.9	+	155123.i	0.0189356	+	0.0310232i
$172$	−4.06618e6	+	2.61318e6i	−0.799100	+	0.513551i
$173$	1.56212e6	+	2.43070e6i	0.301700	+	0.469455i	0.958693	−	0.284442i	$-0.0918082\pi$
$173$	1.56212e6	+	2.43070e6i	0.301700	+	0.469455i	−0.656993	+	0.753897i	$0.728172\pi$
$174$	−547781.	−	749716.i	−0.103982	−	0.142314i
$175$	−4.72566e6	+	1.38758e6i	−0.881756	+	0.258907i
$176$	2.77337e6	+	398750.i	0.508709	+	0.0731413i
$177$	−3.86320e6	−	3.95385e6i	−0.696670	−	0.713017i
$178$	−599971.	+	1.31375e6i	−0.106382	+	0.232945i
$179$	−1.96291e6	+	6.68505e6i	−0.342248	+	1.16559i	0.591095	+	0.806602i	$0.298696\pi$
$179$	−1.96291e6	+	6.68505e6i	−0.342248	+	1.16559i	−0.933343	+	0.358987i	$0.883122\pi$
$180$	−6.03938e6	+	1.62219e6i	−1.03556	+	0.278153i
$181$	−1.57022e6	−	1.09211e7i	−0.264804	−	1.84175i	−0.495357	−	0.868690i	$-0.664963\pi$
$181$	−1.57022e6	−	1.09211e7i	−0.264804	−	1.84175i	0.230553	−	0.973060i	$-0.425946\pi$
$182$	2.72287e6	−	4.23686e6i	0.451661	−	0.702798i
$183$	8.75040e6	+	727914.i	1.42782	+	0.118775i
$184$	3.38711e6	+	4.13547e6i	0.543721	+	0.663852i
$185$		−	4.05176e6i		−	0.639925i
$186$	784087.	−	1.02249e6i	0.121850	−	0.158898i
$187$	−565758.	−	3.93493e6i	−0.0865178	−	0.601745i
$188$	4.81272e6	−	2.19790e6i	0.724298	−	0.330776i
$189$	−5.47976e6	−	3.24452e6i	−0.811663	−	0.480580i
$190$	70818.5	−	155071.i	0.0103249	−	0.0226084i
$191$	−889723.	−	770950.i	−0.127689	−	0.110643i	0.588675	−	0.808370i	$-0.299650\pi$
$191$	−889723.	−	770950.i	−0.127689	−	0.110643i	−0.716364	+	0.697726i	$0.754195\pi$
$192$	−243965.	+	1.06205e6i	−0.0344686	+	0.150051i
$193$	−4.99907e6	+	1.46786e6i	−0.695373	+	0.204180i	−0.610271	−	0.792192i	$-0.708940\pi$
$193$	−4.99907e6	+	1.46786e6i	−0.695373	+	0.204180i	−0.0851014	+	0.996372i	$0.527121\pi$
$194$	−1.47145e6	+	1.27502e6i	−0.201530	+	0.174627i
$195$	−8.89266e6	−	1.67444e7i	−1.19930	−	2.25822i
$196$	−532916.	+	342485.i	−0.0707768	+	0.0454855i
$197$	5.93158e6	−	5.13974e6i	0.775839	−	0.672268i	−0.174092	−	0.984729i	$-0.555699\pi$
$197$	5.93158e6	−	5.13974e6i	0.775839	−	0.672268i	0.949931	+	0.312461i	$0.101153\pi$
$198$	−5.57942e6	+	670549.i	−0.718776	+	0.0863843i
$199$	857827.	−	5.96632e6i	0.108853	−	0.757089i	−0.860150	−	0.510041i	$-0.829630\pi$
$199$	857827.	−	5.96632e6i	0.108853	−	0.757089i	0.969003	−	0.247048i	$-0.0794607\pi$
$200$	5.05448e6	+	4.37973e6i	0.631810	+	0.547466i
$201$	−2.99240e6	+	5.33224e6i	−0.368495	+	0.656631i
$202$	5.82450e6	+	1.71023e6i	0.706650	+	0.207491i
$203$	2.59943e6	−	1.18712e6i	0.310735	−	0.141908i
$204$	−2.64310e6	+	158258.i	−0.311332	+	0.0186412i
$205$	1.52473e7	+	9.79881e6i	1.76982	+	1.13740i
$206$		−	1.91856e6i		−	0.219470i
$207$	7.20782e6	+	5.16911e6i	0.812630	+	0.582780i
$208$	5.65800e6			0.628743
$209$	−266842.	+	415215.i	−0.0292291	+	0.0454814i
$210$	357043.	+	5.96305e6i	0.0385534	+	0.643889i
$211$	−3.12343e6	−	6.83936e6i	−0.332495	−	0.728062i	0.667366	−	0.744730i	$-0.267422\pi$
$211$	−3.12343e6	−	6.83936e6i	−0.332495	−	0.728062i	−0.999861	+	0.0166677i	$0.994694\pi$
$212$	−594876.	+	2.02596e6i	−0.0624337	+	0.212630i
$213$	3.49731e6	+	1.96266e6i	0.361906	+	0.203098i
$214$	4.85055e6	−	5.59783e6i	0.494936	−	0.571187i
$215$	1.72047e7	+	2.47366e6i	1.73114	+	0.248900i
$216$	316551.	+	8.64186e6i	0.0314111	+	0.857523i
$217$	2.59694e6	+	2.99703e6i	0.254146	+	0.293300i
$218$	4.81623e6	+	7.49420e6i	0.464877	+	0.723362i
$219$	−4.07824e6	+	2.16589e6i	−0.388276	+	0.206207i
$220$	−1.11218e7	−	1.28352e7i	−1.04450	−	1.20541i
$221$	−2.26168e6	−	7.70256e6i	−0.209534	−	0.713606i
$222$	−2.36359e6	−	542945.i	−0.216030	−	0.0496246i
$223$	7.01501e6	−	8.09576e6i	0.632578	−	0.730033i	−0.345467	−	0.938431i	$-0.612279\pi$
$223$	7.01501e6	−	8.09576e6i	0.632578	−	0.730033i	0.978044	+	0.208398i	$0.0668248\pi$
$224$	−9.89689e6	−	4.51976e6i	−0.880552	−	0.402134i
$225$	9.98489e6	+	4.84284e6i	0.876588	+	0.425160i
$226$	2.08518e6	+	4.56590e6i	0.180641	+	0.395550i
$227$	1.87817e7	−	2.70041e6i	1.60568	−	0.230862i	0.719597	−	0.694392i	$-0.244327\pi$
$227$	1.87817e7	−	2.70041e6i	1.60568	−	0.230862i	0.886081	+	0.463531i	$0.153418\pi$
$228$	260870.	+	200046.i	0.0220100	+	0.0168782i
$229$	−1.91098e7			−1.59129			−0.795647	−	0.605761i	$-0.792869\pi$
$229$	−1.91098e7			−1.59129			−0.795647	+	0.605761i	$0.792869\pi$
$230$	230905.	−	8.31705e6i	0.0189780	−	0.683574i
$231$	1.43378e6	−	1.72357e7i	0.116318	−	1.39828i
$232$	−3.26450e6	−	2.09797e6i	−0.261428	−	0.168010i
$233$	1.93309e7	−	2.77936e6i	1.52821	−	0.219724i	0.673642	−	0.739058i	$-0.264729\pi$
$233$	1.93309e7	−	2.77936e6i	1.52821	−	0.219724i	0.854572	+	0.519334i	$0.173820\pi$
$234$	−1.09595e7	+	2.94373e6i	−0.855345	+	0.229748i
$235$	−1.82557e7	−	5.36034e6i	−1.40668	−	0.413037i
$236$	−9.09577e6	−	4.15390e6i	−0.691996	−	0.316024i
$237$	1.93100e6	−	1.88673e6i	0.145057	−	0.141731i
$238$	−359971.	+	2.50365e6i	−0.0267016	+	0.185713i
$239$	−1.72443e6	−	5.87286e6i	−0.126314	−	0.430185i	0.871916	−	0.489655i	$-0.162877\pi$
$239$	−1.72443e6	−	5.87286e6i	−0.126314	−	0.430185i	−0.998230	+	0.0594696i	$0.981059\pi$
$240$	−5.41876e6	+	3.95923e6i	−0.391982	+	0.286402i
$241$	2.43684e6	−	1.56606e6i	0.174091	−	0.111881i	−0.450693	−	0.892679i	$-0.648823\pi$
$241$	2.43684e6	−	1.56606e6i	0.174091	−	0.111881i	0.624784	+	0.780797i	$0.285187\pi$
$242$	−4.52210e6	−	7.03653e6i	−0.319076	−	0.496492i
$243$	4.22699e6	+	1.37122e7i	0.294586	+	0.955625i
$244$	1.52400e7	−	4.47486e6i	1.04909	−	0.308042i
$245$	2.25486e6	+	324200.i	0.153328	+	0.0220452i
$246$	7.75928e6	−	7.58139e6i	0.521214	−	0.509265i
$247$	−414039.	+	906618.i	−0.0274758	+	0.0601636i
$248$	1.51715e6	−	5.16693e6i	0.0994656	−	0.338749i
$249$	1.45690e7	−	5.24236e6i	0.943698	−	0.339569i
$250$	39152.4	+	272311.i	0.00250576	+	0.0174279i
$251$	−1.05510e7	+	1.64176e7i	−0.667224	+	1.03822i	0.328379	+	0.944546i	$0.393498\pi$
$251$	−1.05510e7	+	1.64176e7i	−0.667224	+	1.03822i	−0.995603	+	0.0936748i	$0.970139\pi$
$252$	−1.13613e7	−	1.90337e6i	−0.709945	−	0.118939i
$253$	−4.08861e6	+	2.37394e7i	−0.252472	+	1.46591i
$254$			2.62037e6i			0.159905i
$255$	7.55596e6	+	5.79424e6i	0.455690	+	0.349442i
$256$	1.47308e6	+	1.02455e7i	0.0878022	+	0.610678i
$257$	−2.91625e7	+	1.33181e7i	−1.71801	+	0.784589i	−0.722349	+	0.691529i	$0.756937\pi$
$257$	−2.91625e7	+	1.33181e7i	−1.71801	+	0.784589i	−0.995661	+	0.0930595i	$0.970335\pi$
$258$	3.74847e6	−	9.70486e6i	0.218271	−	0.565106i
$259$	3.10059e6	−	6.78934e6i	0.178462	−	0.390776i
$260$	−2.59189e7	−	2.24589e7i	−1.47468	−	1.27781i
$261$	−6.13433e6	−	1.95682e6i	−0.345021	−	0.110060i
$262$	1.43538e7	−	4.21465e6i	0.798110	−	0.234346i
$263$	−7.69166e6	+	6.66486e6i	−0.422817	+	0.366373i	−0.840126	−	0.542392i	$-0.817519\pi$
$263$	−7.69166e6	+	6.66486e6i	−0.422817	+	0.366373i	0.417309	+	0.908765i	$0.362973\pi$
$264$	−2.07421e7	+	1.10158e7i	−1.12730	+	0.598691i
$265$	6.38774e6	−	4.10515e6i	0.343249	−	0.220593i
$266$	237334.	−	205651.i	0.0126100	−	0.0109266i
$267$	2.01532e6	+	9.81058e6i	0.105879	+	0.515420i
$268$	−1.57409e6	+	1.09480e7i	−0.0817757	+	0.568762i
$269$	1.05006e7	+	9.09884e6i	0.539459	+	0.467444i	0.881462	−	0.472255i	$-0.156560\pi$
$269$	1.05006e7	+	9.09884e6i	0.539459	+	0.467444i	−0.342003	+	0.939699i	$0.611105\pi$
$270$	8.43614e6	−	1.04882e7i	0.428600	−	0.532856i
$271$	−1.27181e7	−	3.73437e6i	−0.639020	−	0.187633i	−0.0538568	−	0.998549i	$-0.517151\pi$
$271$	−1.27181e7	−	3.73437e6i	−0.639020	−	0.187633i	−0.585163	+	0.810915i	$0.698970\pi$
$272$	−2.58481e6	+	1.18044e6i	−0.128446	+	0.0586595i
$273$	−2.08744e6	−	3.48628e7i	−0.102595	−	1.71346i
$274$	−1.69939e6	−	1.09213e6i	−0.0826118	−	0.0530914i
$275$			3.01388e7i			1.44920i
$276$	1.55316e7	+	4.02466e6i	0.738735	+	0.191426i
$277$	−7.24869e6			−0.341052			−0.170526	−	0.985353i	$-0.554547\pi$
$277$	−7.24869e6			−0.341052			−0.170526	+	0.985353i	$0.554547\pi$
$278$	−8.22720e6	+	1.28018e7i	−0.382928	+	0.595848i
$279$	207200.	−	8.93295e6i	0.00954061	−	0.411322i
$280$	1.03712e7	+	2.27098e7i	0.472450	+	1.03452i
$281$	5.05205e6	−	1.72057e7i	0.227693	−	0.775450i	−0.763819	−	0.645431i	$-0.776678\pi$
$281$	5.05205e6	−	1.72057e7i	0.227693	−	0.775450i	0.991511	−	0.130019i	$-0.0415039\pi$
$282$	−5.57324e6	+	9.93111e6i	−0.248520	+	0.442843i
$283$	4.74335e6	−	5.47411e6i	0.209279	−	0.241521i	−0.641400	−	0.767207i	$-0.721646\pi$
$283$	4.74335e6	−	5.47411e6i	0.209279	−	0.241521i	0.850679	+	0.525686i	$0.176191\pi$
$284$	7.18059e6	+	1.03241e6i	0.313477	+	0.0450711i
$285$	−237881.	−	1.15801e6i	−0.0102760	−	0.0500239i
$286$	−2.01823e7	−	2.32917e7i	−0.862727	−	0.995640i
$287$	1.80506e7	+	2.80873e7i	0.763564	+	1.18813i
$288$	9.66405e6	+	2.25298e7i	0.404559	+	0.943147i
$289$	−1.31665e7	−	1.51950e7i	−0.545478	−	0.629515i
$290$	1.70166e6	+	5.79532e6i	0.0697716	+	0.237620i
$291$	−3.02279e6	+	1.31590e7i	−0.122667	+	0.534004i
$292$	−5.47005e6	+	6.31277e6i	−0.219706	+	0.253555i
$293$	1.12511e7	+	5.13823e6i	0.447295	+	0.204273i	0.626311	−	0.779573i	$-0.284564\pi$
$293$	1.12511e7	+	5.13823e6i	0.447295	+	0.204273i	−0.179016	+	0.983846i	$0.557291\pi$
$294$	491278.	−	1.27193e6i	0.0193324	−	0.0500518i
$295$	1.49378e7	+	3.27092e7i	0.581863	+	1.27410i
$296$	−1.00322e7	+	1.44241e6i	−0.386831	+	0.0556179i
$297$	−2.84973e7	+	2.65806e7i	−1.08776	+	1.01460i
$298$	−1.94285e7			−0.734160
$299$	−1.34998e6	+	4.86254e7i	−0.0505025	+	1.81907i
$300$	2.00050e7	+	1.66414e6i	0.740926	+	0.0616349i
$301$	2.69361e7	+	1.73108e7i	0.987724	+	0.634772i
$302$	−2.09741e7	+	3.01563e6i	−0.761488	+	0.109485i
$303$	3.96096e7	−	1.42526e7i	1.42388	−	0.512351i
$304$	338509.	+	99395.1i	0.0120489	+	0.00353789i
$305$	−5.19564e7	−	2.37277e7i	−1.83121	−	0.836288i
$306$	4.39257e6	−	3.63132e6i	0.153304	−	0.126736i
$307$	4.13432e6	−	2.87548e7i	0.142886	−	0.993791i	−0.784619	−	0.619979i	$-0.787141\pi$
$307$	4.13432e6	−	2.87548e7i	0.142886	−	0.993791i	0.927504	−	0.373813i	$-0.121950\pi$
$308$	−8.81415e6	−	3.00182e7i	−0.301667	−	1.02738i
$309$	−7.84905e6	−	1.07425e7i	−0.266037	−	0.364109i
$310$	−7.05122e6	+	4.53154e6i	−0.236690	+	0.152111i
$311$	−2.60650e7	−	4.05579e7i	−0.866516	−	1.34833i	−0.936460	−	0.350775i	$-0.885918\pi$
$311$	−2.60650e7	−	4.05579e7i	−0.866516	−	1.34833i	0.0699436	−	0.997551i	$-0.477718\pi$
$312$	−3.82936e7	+	2.79793e7i	−1.26085	+	0.921240i
$313$	3.72658e7	−	1.09422e7i	1.21528	−	0.356840i	0.389606	−	0.920982i	$-0.372611\pi$
$313$	3.72658e7	−	1.09422e7i	1.21528	−	0.356840i	0.825678	+	0.564142i	$0.190793\pi$
$314$	7.43663e6	+	1.06923e6i	0.240208	+	0.0345367i
$315$	2.63947e7	+	3.19280e7i	0.844471	+	1.02150i
$316$	2.02871e6	−	4.44225e6i	0.0642922	−	0.140780i
$317$	−174323.	+	593691.i	−0.00547240	+	0.0186373i	−0.962184	−	0.272401i	$-0.912182\pi$
$317$	−174323.	+	593691.i	−0.00547240	+	0.0186373i	0.956712	+	0.291038i	$0.0940006\pi$
$318$	−1.53876e6	−	4.27638e6i	−0.0478509	−	0.132983i
$319$	−2.48867e6	−	1.73091e7i	−0.0766646	−	0.533214i
$320$	3.83236e6	−	5.96327e6i	0.116954	−	0.181984i
$321$	4.25812e6	−	5.11878e7i	0.128737	−	1.54757i
$322$	6.75149e6	−	1.37598e7i	0.202224	−	0.412139i
$323$		−	500562.i		−	0.0148542i
$324$	1.60697e7	+	2.03831e7i	0.472468	+	0.599288i
$325$	8.66141e6	+	6.02414e7i	0.252312	+	1.75487i
$326$	881254.	−	402455.i	0.0254360	−	0.0116162i
$327$	5.76269e7	+	2.22582e7i	1.64809	+	0.636571i
$328$	1.88340e7	−	4.12407e7i	0.533729	−	1.16870i
$329$	−2.64881e7	−	2.29521e7i	−0.743813	−	0.644517i
$330$	3.56274e7	+	8.18405e6i	0.991386	+	0.227733i
$331$	−5.29142e7	+	1.55370e7i	−1.45911	+	0.428433i	−0.912543	−	0.408982i	$-0.865884\pi$
$331$	−5.29142e7	+	1.55370e7i	−1.45911	+	0.428433i	−0.546567	+	0.837415i	$0.684066\pi$
$332$	2.11672e7	−	1.83415e7i	0.578429	−	0.501212i
$333$	−1.54556e7	+	6.62961e6i	−0.418555	+	0.179538i
$334$	−4.85361e6	+	3.11922e6i	−0.130264	+	0.0837158i
$335$	3.00599e7	−	2.60470e7i	0.799563	−	0.692825i
$336$	−1.21097e7	+	2.48761e6i	−0.319239	+	0.0655789i
$337$	−758119.	+	5.27283e6i	−0.0198083	+	0.137770i	−0.997326	−	0.0730848i	$-0.976716\pi$
$337$	−758119.	+	5.27283e6i	−0.0198083	+	0.137770i	0.977517	+	0.210855i	$0.0676247\pi$
$338$	−3.28312e7	−	2.84484e7i	−0.850230	−	0.736729i
$339$	3.03550e7	+	1.70350e7i	0.779169	+	0.437262i
$340$	1.65265e7	+	4.85261e6i	0.420478	+	0.123464i
$341$	2.20741e7	−	1.00809e7i	0.556699	−	0.254236i
$342$	−707399.	−	16408.1i	−0.0176842	−	0.000410185i
$343$	3.55520e7	+	2.28479e7i	0.881011	+	0.566191i
$344$		−	4.34796e7i		−	1.06810i
$345$	−3.27331e7	−	4.75139e7i	−0.797130	−	1.15708i
$346$	−1.12499e7			−0.271593
$347$	−4.65646e6	+	7.24559e6i	−0.111447	+	0.173415i	−0.892497	−	0.451054i	$-0.851048\pi$
$347$	−4.65646e6	+	7.24559e6i	−0.111447	+	0.173415i	0.781050	+	0.624469i	$0.214684\pi$
$348$	−1.16265e7	+	696148.i	−0.275875	+	0.0165182i
$349$	−1.93927e7	−	4.24641e7i	−0.456207	−	0.998954i	−0.988336	−	0.152290i	$-0.951335\pi$
$349$	−1.93927e7	−	4.24641e7i	−0.456207	−	0.998954i	0.532129	−	0.846663i	$-0.321392\pi$
$350$	5.40256e6	−	1.83994e7i	0.126007	−	0.429141i
$351$	−4.93217e7	+	6.13190e7i	−1.14056	+	1.41799i
$352$	−4.36001e7	+	5.03171e7i	−0.999675	+	1.15369i
$353$	−6.65411e7	−	9.56717e6i	−1.51275	−	0.217500i	−0.664574	−	0.747222i	$-0.731387\pi$
$353$	−6.65411e7	−	9.56717e6i	−1.51275	−	0.217500i	−0.848171	+	0.529722i	$0.822296\pi$
$354$	2.10826e7	−	4.33083e6i	0.475241	−	0.0976251i
$355$	−1.70837e7	−	1.97157e7i	−0.381855	−	0.440684i
$356$	9.79480e6	+	1.52410e7i	0.217093	+	0.337803i
$357$	8.22714e6	+	1.54913e7i	0.180819	+	0.340473i
$358$	−1.77645e7	−	2.05013e7i	−0.387172	−	0.446821i
$359$	1.83247e7	+	6.24081e7i	0.396053	+	1.34883i	0.880515	+	0.474019i	$0.157197\pi$
$359$	1.83247e7	+	6.24081e7i	0.396053	+	1.34883i	−0.484462	+	0.874812i	$0.660985\pi$
$360$	1.70956e7	−	5.35924e7i	0.366419	−	1.14867i
$361$	3.07678e7	−	3.55079e7i	0.653996	−	0.754751i
$362$	3.90766e7	+	1.78457e7i	0.823742	+	0.376190i
$363$	−5.41076e7	−	2.08989e7i	−1.13120	−	0.436922i
$364$	−2.62445e7	−	5.74675e7i	−0.544170	−	1.19157i
$365$	2.97324e7	−	4.27487e6i	0.611437	−	0.0879113i
$366$	−2.08038e7	+	2.71291e7i	−0.424325	+	0.553340i
$367$	4.87185e7			0.985588			0.492794	−	0.870146i	$-0.335976\pi$
$367$	4.87185e7			0.985588			0.492794	+	0.870146i	$0.335976\pi$
$368$	1.71049e7	−	1.97654e6i	0.343223	−	0.0396608i
$369$	1.24299e7	−	7.41942e7i	0.247394	−	1.47670i
$370$	1.32713e7	+	8.52893e6i	0.262004	+	0.168380i
$371$	1.38451e7	−	1.99062e6i	0.271127	−	0.0389822i
$372$	−5.47250e6	−	1.52086e7i	−0.106306	−	0.295434i
$373$	4.52832e7	+	1.32963e7i	0.872591	+	0.256216i	0.687217	−	0.726452i	$-0.258832\pi$
$373$	4.52832e7	+	1.32963e7i	0.872591	+	0.256216i	0.185374	+	0.982668i	$0.440650\pi$
$374$	1.40795e7	+	6.42990e6i	0.269137	+	0.122911i
$375$	1.33328e6	+	1.36456e6i	0.0252829	+	0.0258762i
$376$	−6.77332e6	+	4.71094e7i	−0.127420	+	0.886226i
$377$	−9.94871e6	−	3.38822e7i	−0.185670	−	0.632336i
$378$	2.21621e7	−	1.11189e7i	0.410331	−	0.205866i
$379$	−4.06895e7	+	2.61496e7i	−0.747421	+	0.480338i	−0.858077	−	0.513521i	$-0.828341\pi$
$379$	−4.06895e7	+	2.61496e7i	−0.747421	+	0.480338i	0.110656	+	0.993859i	$0.464705\pi$
$380$	−1.15615e6	−	1.79900e6i	−0.0210699	−	0.0327854i
$381$	1.07202e7	+	1.46721e7i	0.193834	+	0.265288i
$382$	4.39805e6	−	1.29138e6i	0.0788988	−	0.0231668i
$383$	3.79771e7	+	5.46028e6i	0.675967	+	0.0971893i	0.471745	−	0.881735i	$-0.343624\pi$
$383$	3.79771e7	+	5.46028e6i	0.675967	+	0.0971893i	0.204222	+	0.978925i	$0.434534\pi$
$384$	3.76454e7	+	3.85287e7i	0.664841	+	0.680441i
$385$	−4.67365e7	+	1.02339e8i	−0.818982	+	1.79332i
$386$	5.71514e6	−	1.94640e7i	0.0993721	−	0.338430i
$387$	−1.87150e7	−	6.96754e7i	−0.322891	−	1.20212i
$388$	3.47582e6	+	2.41748e7i	0.0595061	+	0.413874i
$389$	1.98632e7	−	3.09078e7i	0.337443	−	0.525072i	−0.630517	−	0.776175i	$-0.717157\pi$
$389$	1.98632e7	−	3.09078e7i	0.337443	−	0.525072i	0.967960	+	0.251104i	$0.0807935\pi$
$390$	7.35642e7	+	6.11953e6i	1.24015	+	0.103163i
$391$	−9.52811e6	−	2.24957e7i	−0.159396	−	0.376331i
$392$		−	5.69847e6i		−	0.0946020i
$393$	6.31279e7	−	8.23218e7i	1.04003	−	1.35624i
$394$	4.34895e6	+	3.02476e7i	0.0711043	+	0.494541i
$395$	−1.59747e7	+	7.29542e6i	−0.259204	+	0.118375i
$396$	−3.07626e7	+	6.34258e7i	−0.495379	+	1.02136i
$397$	1.10826e7	−	2.42675e7i	0.177121	−	0.387841i	−0.800161	−	0.599786i	$-0.795252\pi$
$397$	1.10826e7	−	2.42675e7i	0.177121	−	0.387841i	0.977282	+	0.211945i	$0.0679797\pi$
$398$	1.77366e7	+	1.53688e7i	0.281333	+	0.243776i
$399$	487553.	−	2.12245e6i	0.00767544	−	0.0334133i
$400$	2.06704e7	−	6.06939e6i	0.322976	−	0.0948342i
$401$	−9.08269e7	+	7.87020e7i	−1.40858	+	1.22054i	−0.466777	+	0.884375i	$0.654585\pi$
$401$	−9.08269e7	+	7.87020e7i	−1.40858	+	1.22054i	−0.941803	+	0.336166i	$0.890870\pi$
$402$	−1.11664e7	−	2.10257e7i	−0.171884	−	0.323648i
$403$	4.12248e7	−	2.64935e7i	0.629858	−	0.404785i
$404$	5.75484e7	−	4.98660e7i	0.872749	−	0.756241i
$405$	4.32770e6	−	9.32393e7i	0.0651466	−	1.40357i
$406$	−1.58345e6	+	1.10131e7i	−0.0236606	+	0.164563i
$407$	−3.45179e7	−	2.99100e7i	−0.511990	−	0.443642i
$408$	1.16567e7	−	2.07714e7i	0.171631	−	0.305833i
$409$	4.18504e6	+	1.22884e6i	0.0611688	+	0.0179608i	0.312174	−	0.950025i	$-0.398943\pi$
$409$	4.18504e6	+	1.22884e6i	0.0611688	+	0.0179608i	−0.251005	+	0.967986i	$0.580761\pi$
$410$	−6.41907e7	+	2.93149e7i	−0.931366	+	0.425341i
$411$	−1.39834e7	+	837266.i	−0.201412	+	0.0120597i
$412$	−2.02461e7	−	1.30114e7i	−0.289501	−	0.186051i
$413$			6.62403e7i			0.940312i
$414$	−3.21035e7	+	1.27278e7i	−0.452429	+	0.179371i
$415$	−1.00720e8			−1.40920
$416$	−7.26875e7	+	1.13104e8i	−1.00967	+	1.57108i
$417$	6.30724e6	+	1.05339e8i	0.0869824	+	1.45271i
$418$	−798306.	−	1.74805e6i	−0.0109305	−	0.0239345i
$419$	5.79844e6	−	1.97477e7i	0.0788259	−	0.268456i	−0.910645	−	0.413190i	$-0.864414\pi$
$419$	5.79844e6	−	1.97477e7i	0.0788259	−	0.268456i	0.989471	+	0.144734i	$0.0462326\pi$
$420$	6.53480e7	+	3.66727e7i	0.882033	+	0.494989i
$421$	5.10762e7	−	5.89450e7i	0.684498	−	0.789953i	−0.302073	−	0.953285i	$-0.597679\pi$
$421$	5.10762e7	−	5.89450e7i	0.684498	−	0.789953i	0.986571	+	0.163332i	$0.0522242\pi$
$422$	2.89767e7	+	4.16622e6i	0.385577	+	0.0554376i
$423$	9.42322e6	+	7.84075e7i	0.124502	+	1.03594i
$424$	−1.24384e7	−	1.43547e7i	−0.163180	−	0.188320i
$425$	−1.65252e7	−	2.57137e7i	−0.215268	−	0.334964i
$426$	−1.37904e7	+	7.32383e6i	−0.178380	+	0.0947347i
$427$	−6.89032e7	−	7.95186e7i	−0.885026	−	1.02137i
$428$	−2.61769e7	−	8.91502e7i	−0.333877	−	1.13708i
$429$	−2.08295e8	−	4.78478e7i	−2.63819	−	0.606025i
$430$	−4.43181e7	+	5.11458e7i	−0.557411	+	0.643287i
$431$	−6.11694e7	−	2.79351e7i	−0.764016	−	0.348914i	−0.00500089	−	0.999987i	$-0.501592\pi$
$431$	−6.11694e7	−	2.79351e7i	−0.764016	−	0.348914i	−0.759015	+	0.651073i	$0.774319\pi$
$432$	2.39689e7	+	1.41918e7i	0.297302	+	0.176030i
$433$	−2.22776e7	−	4.87811e7i	−0.274413	−	0.600881i	0.721377	−	0.692542i	$-0.243509\pi$
$433$	−2.22776e7	−	4.87811e7i	−0.274413	−	0.600881i	−0.995790	+	0.0916617i	$0.970782\pi$
$434$	−1.52831e7	+	2.19738e6i	−0.186957	+	0.0268804i
$435$	3.32373e7	+	2.54878e7i	0.403793	+	0.309646i
$436$	1.11747e8			1.34827
$437$	−934978.	+	2.88546e6i	−0.0112036	+	0.0345757i
$438$	1.49046e6	−	1.79172e7i	0.0177378	−	0.213230i
$439$	1.79374e6	+	1.15277e6i	0.0212015	+	0.0136254i	0.551199	−	0.834374i	$-0.314171\pi$
$439$	1.79374e6	+	1.15277e6i	0.0212015	+	0.0136254i	−0.529997	+	0.847999i	$0.677807\pi$
$440$	1.51220e8	−	2.17421e7i	1.77522	−	0.255237i
$441$	−2.45280e6	−	9.13171e6i	−0.0285987	−	0.106472i
$442$	2.99900e7	+	8.80587e6i	0.347304	+	0.101978i
$443$	3.48371e7	+	1.59096e7i	0.400710	+	0.182998i	0.605568	−	0.795793i	$-0.292946\pi$
$443$	3.48371e7	+	1.59096e7i	0.400710	+	0.182998i	−0.204858	+	0.978792i	$0.565673\pi$
$444$	−2.17591e7	+	2.12602e7i	−0.248594	+	0.242895i
$445$	9.27188e6	−	6.44873e7i	0.105217	−	0.731804i
$446$	1.17505e7	+	4.00187e7i	0.132450	+	0.451085i
$447$	−1.08785e8	+	7.94842e7i	−1.21800	+	0.889935i
$448$	1.09850e7	−	7.05966e6i	0.122171	−	0.0785145i
$449$	1.69412e7	+	2.63610e7i	0.187156	+	0.291221i	0.922134	−	0.386870i	$-0.126444\pi$
$449$	1.69412e7	+	2.63610e7i	0.187156	+	0.291221i	−0.734978	+	0.678091i	$0.762807\pi$
$450$	−3.68805e7	+	2.25107e7i	−0.404724	+	0.247031i
$451$	1.96033e8	−	5.75605e7i	2.13697	−	0.627472i
$452$	6.23241e7	+	8.96086e6i	0.674902	+	0.0970363i
$453$	−1.05102e8	+	1.02693e8i	−1.13062	+	1.10470i
$454$	−3.06904e7	+	6.72027e7i	−0.327971	+	0.718156i
$455$	−6.40066e7	+	2.17986e8i	−0.679501	+	2.31417i
$456$	−2.78256e6	+	1.00124e6i	−0.0293460	+	0.0105595i
$457$	−2.62228e6	−	1.82384e7i	−0.0274745	−	0.191090i	0.971462	−	0.237195i	$-0.0762281\pi$
$457$	−2.62228e6	−	1.82384e7i	−0.0274745	−	0.191090i	−0.998937	+	0.0461055i	$0.985319\pi$
$458$	4.02260e7	−	6.25929e7i	0.418708	−	0.651522i
$459$	9.73903e6	−	3.83031e7i	0.100711	−	0.396092i
$460$	−8.62018e7	−	5.88416e7i	−0.885611	−	0.604520i
$461$			1.45676e8i			1.48691i	0.668784	+	0.743457i	$0.266815\pi$
$461$			1.45676e8i			1.48691i	−0.668784	+	0.743457i	$0.733185\pi$
$462$	5.34363e7	+	4.09773e7i	0.541889	+	0.415544i
$463$	8.81084e6	+	6.12808e7i	0.0887717	+	0.617421i	0.984835	+	0.173494i	$0.0555058\pi$
$463$	8.81084e6	+	6.12808e7i	0.0887717	+	0.617421i	−0.896063	+	0.443927i	$0.853585\pi$
$464$	−1.13701e7	+	5.19256e6i	−0.113818	+	0.0519789i
$465$	−2.09425e7	+	5.42206e7i	−0.208291	+	0.539269i
$466$	−3.15878e7	+	6.91676e7i	−0.312148	+	0.683510i
$467$	4.20407e7	+	3.64285e7i	0.412781	+	0.357677i	0.836358	−	0.548183i	$-0.184680\pi$
$467$	4.20407e7	+	3.64285e7i	0.412781	+	0.357677i	−0.423577	+	0.905860i	$0.639226\pi$
$468$	−4.32608e7	+	1.35616e8i	−0.422043	+	1.32304i
$469$	7.03021e7	−	2.06426e7i	0.681475	−	0.200099i
$470$	5.59855e7	−	4.85117e7i	0.539239	−	0.467254i
$471$	4.60139e7	−	2.44372e7i	0.440379	−	0.233877i
$472$	7.56705e7	−	4.86305e7i	0.719616	−	0.462469i
$473$	1.48078e8	−	1.28310e8i	1.39929	−	1.21249i
$474$	2.11512e6	+	1.02964e7i	0.0198609	+	0.0966834i
$475$	−540074.	+	3.75630e6i	−0.00503933	+	0.0350493i
$476$	2.39792e7	+	2.07781e7i	0.222338	+	0.192657i
$477$	−2.61110e7	−	1.76493e7i	−0.240585	−	0.162619i
$478$	2.28660e7	+	6.71408e6i	0.209367	+	0.0614756i
$479$	−1.62338e8	+	7.41374e7i	−1.47711	+	0.674576i	−0.981058	−	0.193714i	$-0.937947\pi$
$479$	−1.62338e8	+	7.41374e7i	−1.47711	+	0.674576i	−0.496057	+	0.868290i	$0.665219\pi$
$480$	−9.53133e6	−	1.59185e8i	−0.0861847	−	1.43939i
$481$	−7.75902e7	−	4.98642e7i	−0.697223	−	0.448078i
$482$			1.12783e7i			0.100717i
$483$	−1.84894e7	−	1.04666e8i	−0.164090	−	0.928886i
$484$	−1.04923e8			−0.925410
$485$	4.74839e7	−	7.38864e7i	0.416218	−	0.647648i
$486$	−5.38111e7	−	1.50188e7i	−0.468773	−	0.130836i
$487$	6.31927e7	+	1.38373e8i	0.547116	+	1.19802i	0.958115	+	0.286382i	$0.0924527\pi$
$487$	6.31927e7	+	1.38373e8i	0.547116	+	1.19802i	−0.410999	+	0.911636i	$0.634820\pi$
$488$	−4.02537e7	+	1.37091e8i	−0.346375	+	1.17964i
$489$	3.28788e6	−	5.85876e6i	0.0281183	−	0.0501048i
$490$	−5.80836e6	+	6.70321e6i	−0.0493703	+	0.0569763i
$491$	−3.88053e6	−	557936.i	−0.0327828	−	0.00471346i	0.125904	−	0.992042i	$-0.459817\pi$
$491$	−3.88053e6	−	557936.i	−0.0327828	−	0.00471346i	−0.158687	+	0.987329i	$0.550726\pi$
$492$	−2.73823e7	−	1.33298e8i	−0.229919	−	1.11925i
$493$	1.16139e7	+	1.34032e7i	0.0969254	+	0.111858i
$494$	−2.09802e6	−	3.26458e6i	−0.0174032	−	0.0270799i
$495$	2.32969e8	−	9.99311e7i	1.92080	−	0.823920i
$496$	−1.13592e7	−	1.31093e7i	−0.0930903	−	0.107432i
$497$	−1.35391e7	−	4.61098e7i	−0.110286	−	0.375599i
$498$	−1.34967e7	+	5.87550e7i	−0.109280	+	0.475726i
$499$	−3.16160e7	+	3.64868e7i	−0.254452	+	0.293653i	−0.868576	−	0.495557i	$-0.834964\pi$
$499$	−3.16160e7	+	3.64868e7i	−0.254452	+	0.293653i	0.614124	+	0.789210i	$0.289510\pi$
$500$	3.13916e6	+	1.43361e6i	0.0251133	+	0.0114688i
$501$	−1.44155e7	+	3.73220e7i	−0.114635	+	0.296791i
$502$	−3.15652e7	−	6.91180e7i	−0.249515	−	0.546362i
$503$	1.62296e8	−	2.33346e7i	1.27527	−	0.183357i	0.528786	−	0.848755i	$-0.322647\pi$
$503$	1.62296e8	−	2.33346e7i	1.27527	−	0.183357i	0.746488	+	0.665399i	$0.231738\pi$
$504$	6.96575e7	−	7.67197e7i	0.544097	−	0.599260i
$505$	−2.73833e8			−2.12624
$506$	−6.91503e7	−	6.33632e7i	−0.533756	−	0.489087i
$507$	−3.00216e8	−	2.49738e7i	−2.30361	−	0.191629i
$508$	2.76521e7	+	1.77709e7i	0.210930	+	0.135556i
$509$	−9.03377e7	+	1.29886e7i	−0.685040	+	0.0984939i	−0.476042	−	0.879422i	$-0.657929\pi$
$509$	−9.03377e7	+	1.29886e7i	−0.685040	+	0.0984939i	−0.208997	+	0.977916i	$0.567020\pi$
$510$	−3.48839e7	+	1.25522e7i	−0.262975	+	0.0946258i
$511$	5.30924e7	+	1.55893e7i	0.397896	+	0.116833i
$512$	7.94865e7	+	3.63003e7i	0.592221	+	0.270458i
$513$	−4.02803e6	+	2.80217e6i	−0.0298360	+	0.0207559i
$514$	1.77644e7	−	1.23554e8i	0.130816	−	0.909847i
$515$	2.43828e7	+	8.30401e7i	0.178509	+	0.607947i
$516$	−7.69914e7	−	1.05374e8i	−0.560394	−	0.766977i
$517$	−1.80428e8	+	1.15954e8i	−1.30567	+	0.839103i
$518$	1.57113e7	+	2.44473e7i	0.113038	+	0.175890i
$519$	−6.29908e7	+	4.60244e7i	−0.450583	+	0.329220i
$520$	2.96010e8	−	8.69165e7i	2.10522	−	0.618148i
$521$	8.66675e7	+	1.24609e7i	0.612834	+	0.0881123i	0.441741	−	0.897143i	$-0.354361\pi$
$521$	8.66675e7	+	1.24609e7i	0.612834	+	0.0881123i	0.171093	+	0.985255i	$0.445270\pi$
$522$	1.93221e7	−	1.59735e7i	0.135845	−	0.112302i
$523$	−3.98228e7	+	8.71998e7i	−0.278373	+	0.609551i	−0.996241	−	0.0866280i	$-0.972391\pi$
$523$	−3.98228e7	+	8.71998e7i	−0.278373	+	0.609551i	0.717868	+	0.696179i	$0.245118\pi$
$524$	5.28690e7	−	1.80055e8i	0.367457	−	1.25144i
$525$	−4.50237e7	−	1.25125e8i	−0.311145	−	0.864705i
$526$	−5.63941e6	−	3.92230e7i	−0.0387504	−	0.269515i
$527$	−1.33058e7	+	2.07042e7i	−0.0909092	+	0.141457i
$528$	−6.27146e6	+	7.53905e7i	−0.0426056	+	0.512171i
$529$	1.29054e7	+	1.47472e8i	0.0871775	+	0.996193i
$530$			2.95639e7i			0.198580i
$531$	1.00329e8	−	1.10500e8i	0.670103	−	0.738041i
$532$	−560624.	−	3.89922e6i	−0.00372337	−	0.0258966i
$533$	3.75289e8	−	1.71389e8i	2.47847	−	1.13188i
$534$	−3.63761e7	−	1.40502e7i	−0.238887	−	0.0922695i
$535$	−1.38801e8	+	3.03932e8i	−0.906426	+	1.98480i
$536$	−7.51939e7	−	6.51559e7i	−0.488302	−	0.423116i
$537$	−1.83341e8	−	4.21157e7i	−1.18396	−	0.271970i
$538$	−5.19064e7	+	1.52411e7i	−0.333330	+	0.0978744i
$539$	1.94072e7	−	1.68165e7i	0.123936	−	0.107391i
$540$	−5.34669e7	−	1.60154e8i	−0.339550	−	1.01708i
$541$	5.72344e7	−	3.67823e7i	0.361464	−	0.232299i	−0.347285	−	0.937760i	$-0.612896\pi$
$541$	5.72344e7	−	3.67823e7i	0.361464	−	0.232299i	0.708749	+	0.705461i	$0.249260\pi$
$542$	3.90032e7	−	3.37965e7i	0.244964	−	0.212263i
$543$	2.91808e8	−	5.99441e7i	1.82263	−	0.374409i
$544$	9.60950e6	−	6.68355e7i	0.0596903	−	0.415155i
$545$	−3.03701e8	−	2.63158e8i	−1.87610	−	1.62565i
$546$	1.18585e8	+	6.65487e7i	0.728537	+	0.408848i
$547$	2.71599e8	+	7.97487e7i	1.65946	+	0.487261i	0.971212	−	0.238216i	$-0.0765627\pi$
$547$	2.71599e8	+	7.97487e7i	1.65946	+	0.487261i	0.688246	+	0.725477i	$0.258381\pi$
$548$	−2.30500e7	+	1.05266e7i	−0.140065	+	0.0639655i
$549$	−5.49751e6	+	2.37013e8i	−0.0332238	+	1.43237i
$550$	−9.87175e7	−	6.34419e7i	−0.593343	−	0.381319i
$551$		−	2.20189e6i		−	0.0131625i
$552$	−1.05992e8	+	9.79622e7i	−0.630168	+	0.582426i
$553$	−3.23508e7			−0.191298
$554$	1.52584e7	−	2.37426e7i	0.0897390	−	0.139637i
$555$	1.09202e8	−	6.53856e6i	0.638781	−	0.0382475i
$556$	7.92983e7	+	1.73639e8i	0.461360	+	1.01024i
$557$	3.29751e7	−	1.12303e8i	0.190819	−	0.649869i	−0.807389	−	0.590020i	$-0.799120\pi$
$557$	3.29751e7	−	1.12303e8i	0.190819	−	0.649869i	0.998207	−	0.0598489i	$-0.0190619\pi$
$558$	2.88231e7	+	1.94825e7i	0.165897	+	0.112135i
$559$	2.59105e8	−	2.99023e8i	1.48334	−	1.71186i
$560$	7.96001e7	+	1.14448e7i	0.453262	+	0.0651693i
$561$	1.05140e8	−	2.15982e7i	0.595498	−	0.122329i
$562$	4.57216e7	+	5.27655e7i	0.257580	+	0.297263i
$563$	7.90553e7	+	1.23012e8i	0.443002	+	0.689325i	0.988909	−	0.148521i	$-0.0474512\pi$
$563$	7.90553e7	+	1.23012e8i	0.443002	+	0.689325i	−0.545907	+	0.837846i	$0.683815\pi$
$564$	6.70036e7	+	1.26164e8i	0.373475	+	0.703233i
$565$	−1.48279e8	−	1.71123e8i	−0.822117	−	0.948774i
$566$	7.94538e6	+	2.70595e7i	0.0438193	+	0.149235i
$567$	7.86025e7	−	1.52925e8i	0.431209	−	0.838936i
$568$	−4.27345e7	+	4.93182e7i	−0.233203	+	0.269130i
$569$	4.09588e7	+	1.87053e7i	0.222336	+	0.101538i	0.523469	−	0.852045i	$-0.324638\pi$
$569$	4.09588e7	+	1.87053e7i	0.222336	+	0.101538i	−0.301133	+	0.953582i	$0.597365\pi$
$570$	4.29372e6	+	1.65844e6i	0.0231851	+	0.00895517i
$571$	−3.73880e7	−	8.18684e7i	−0.200828	−	0.439752i	0.782244	−	0.622972i	$-0.214075\pi$
$571$	−3.73880e7	−	8.18684e7i	−0.200828	−	0.439752i	−0.983072	+	0.183220i	$0.941348\pi$
$572$	−3.82665e8	+	5.50189e7i	−2.04470	+	0.293984i
$573$	1.93426e7	−	2.52237e7i	0.102814	−	0.134074i
$574$	−1.29994e8			−0.687366
$575$	4.72290e7	+	1.79092e8i	0.248431	+	0.942046i
$576$	−2.90177e7	−	4.86139e6i	−0.151843	−	0.0254386i
$577$	6.74765e7	+	4.33645e7i	0.351257	+	0.225739i	0.704356	−	0.709847i	$-0.251236\pi$
$577$	6.74765e7	+	4.33645e7i	0.351257	+	0.225739i	−0.353099	+	0.935586i	$0.614872\pi$
$578$	7.74855e7	−	1.11407e7i	0.401270	−	0.0576939i
$579$	−4.76287e7	−	1.32365e8i	−0.245376	−	0.681926i
$580$	7.26970e7	+	2.13458e7i	0.372591	+	0.109403i
$581$	−1.68772e8	−	7.70756e7i	−0.860542	−	0.392996i
$582$	−3.67385e7	−	3.76006e7i	−0.186360	−	0.190733i
$583$	1.21813e7	−	8.47227e7i	0.0614735	−	0.427557i
$584$	−2.11693e7	−	7.20959e7i	−0.106284	−	0.361969i
$585$	4.36940e8	−	2.66694e8i	2.18250	−	1.33213i
$586$	−4.05135e7	+	2.60364e7i	−0.201329	+	0.129386i
$587$	−2.01002e7	−	3.12766e7i	−0.0993773	−	0.154634i	0.788004	−	0.615670i	$-0.211114\pi$
$587$	−2.01002e7	−	3.12766e7i	−0.0993773	−	0.154634i	−0.887382	+	0.461036i	$0.847478\pi$
$588$	−1.00906e7	−	1.38103e7i	−0.0496344	−	0.0679317i
$589$	2.93182e6	−	860861.i	0.0143480	−	0.00421296i
$590$	−1.38581e8	−	1.99249e7i	−0.674756	−	0.0970153i
$591$	1.48097e8	+	1.51572e8i	0.717437	+	0.734271i
$592$	−1.35622e7	+	2.96972e7i	−0.0653682	+	0.143136i
$593$	7.26074e7	−	2.47278e8i	0.348190	−	1.18583i	−0.580279	−	0.814418i	$-0.697056\pi$
$593$	7.26074e7	−	2.47278e8i	0.348190	−	1.18583i	0.928469	−	0.371409i	$-0.121125\pi$
$594$	−2.70763e7	−	1.49293e8i	−0.129190	−	0.712328i
$595$	−1.62382e7	−	1.12939e8i	−0.0770879	−	0.536158i
$596$	−1.31761e8	+	2.05024e8i	−0.622370	+	0.968427i
$597$	1.62187e8	+	1.34917e7i	0.762242	+	0.0634081i
$598$	−1.56427e8	−	1.06778e8i	−0.731492	−	0.499318i
$599$		−	9.01788e7i		−	0.419589i	−0.977746	−	0.209794i	$-0.932721\pi$
$599$		−	9.01788e7i		−	0.419589i	0.977746	−	0.209794i	$-0.0672795\pi$
$600$	−1.09885e8	+	1.43295e8i	−0.508725	+	0.663402i
$601$	4.82764e7	+	3.35769e8i	0.222388	+	1.54674i	0.728967	+	0.684548i	$0.240001\pi$
$601$	4.82764e7	+	3.35769e8i	0.222388	+	1.54674i	−0.506580	+	0.862193i	$0.669090\pi$
$602$	−1.13401e8	+	5.17884e7i	−0.519788	+	0.237379i
$603$	−1.48542e8	−	7.20454e7i	−0.677481	−	0.328590i
$604$	−1.10420e8	+	2.41786e8i	−0.501115	+	1.09729i
$605$	2.85154e8	+	2.47087e8i	1.28769	+	1.11579i
$606$	−3.66942e7	+	1.59740e8i	−0.164885	+	0.717788i
$607$	−2.51615e8	+	7.38808e7i	−1.12505	+	0.330343i	−0.790759	−	0.612128i	$-0.790314\pi$
$607$	−2.51615e8	+	7.38808e7i	−1.12505	+	0.330343i	−0.334287	+	0.942471i	$0.608495\pi$
$608$	−6.33569e6	+	5.48991e6i	−0.0281892	+	0.0244261i
$609$	3.61897e7	+	6.81433e7i	0.160226	+	0.301697i
$610$	1.87086e8	−	1.20233e8i	0.824237	−	0.529705i
$611$	−3.27317e8	+	2.83622e8i	−1.43498	+	1.24342i
$612$	−8.53064e6	−	7.09807e7i	−0.0372158	−	0.309661i
$613$	4.47765e7	−	3.11427e8i	0.194388	−	1.35200i	−0.625837	−	0.779954i	$-0.715242\pi$
$613$	4.47765e7	−	3.11427e8i	0.194388	−	1.35200i	0.820225	−	0.572042i	$-0.193848\pi$
$614$	8.54817e7	+	7.40703e7i	0.369290	+	0.319992i
$615$	−2.39490e8	+	4.26753e8i	−1.02958	+	1.83464i
$616$	2.70030e8	+	7.92879e7i	1.15523	+	0.339207i
$617$	2.59240e7	−	1.18391e7i	0.110369	−	0.0504038i	−0.359465	−	0.933158i	$-0.617041\pi$
$617$	2.59240e7	−	1.18391e7i	0.110369	−	0.0504038i	0.469834	+	0.882755i	$0.344314\pi$
$618$	5.17086e7	−	3.09610e6i	0.219077	−	0.0131174i
$619$	5.99599e7	+	3.85339e7i	0.252807	+	0.162469i	0.660906	−	0.750468i	$-0.270172\pi$
$619$	5.99599e7	+	3.85339e7i	0.252807	+	0.162469i	−0.408099	+	0.912937i	$0.633808\pi$
$620$			1.05142e8i			0.441165i
$621$	−1.27685e8	+	2.02605e8i	−0.533168	+	0.846009i
$622$	1.87711e8			0.780045
$623$	6.48850e7	−	1.00963e8i	0.268337	−	0.417540i
$624$	9.13064e6	+	1.52493e8i	0.0375792	+	0.627619i
$625$	−1.03964e8	−	2.27649e8i	−0.425836	−	0.932450i
$626$	−4.26037e7	+	1.45095e8i	−0.173670	+	0.591465i
$627$	−1.16214e7	−	6.52180e6i	−0.0471471	−	0.0264585i
$628$	6.17173e7	−	7.12256e7i	0.249188	−	0.287579i
$629$	4.58497e7	+	6.59219e6i	0.184240	+	0.0264897i
$630$	−1.60138e8	+	1.92458e7i	−0.640433	+	0.0769689i
$631$	−1.77246e8	−	2.04553e8i	−0.705485	−	0.814173i	0.283998	−	0.958825i	$-0.408339\pi$
$631$	−1.77246e8	−	2.04553e8i	−0.705485	−	0.814173i	−0.989483	+	0.144652i	$0.953794\pi$
$632$	2.37505e7	+	3.69565e7i	0.0940851	+	0.146399i
$633$	1.79292e8	−	9.52190e7i	0.706887	−	0.375416i
$634$	−1.57764e6	−	1.82070e6i	−0.00619072	−	0.00714448i
$635$	−3.33019e7	−	1.13416e8i	−0.130061	−	0.442948i
$636$	−5.55632e7	−	1.27635e7i	−0.215981	−	0.0496135i
$637$	3.39584e7	−	3.91901e7i	0.131380	−	0.151621i
$638$	6.19333e7	+	2.82840e7i	0.238486	+	0.108913i
$639$	−4.72532e7	+	9.74259e7i	−0.181104	+	0.373398i
$640$	−1.45563e8	−	3.18739e8i	−0.555279	−	1.21589i
$641$	7.86418e7	−	1.13070e7i	0.298593	−	0.0429312i	0.00860980	−	0.999963i	$-0.497259\pi$
$641$	7.86418e7	−	1.13070e7i	0.298593	−	0.0429312i	0.289983	+	0.957032i	$0.406350\pi$
$642$	1.58699e8	+	1.21697e8i	0.599748	+	0.459912i
$643$	1.71913e8			0.646660			0.323330	−	0.946286i	$-0.395198\pi$
$643$	1.71913e8			0.646660			0.323330	+	0.946286i	$0.395198\pi$
$644$	−9.94159e7	−	1.64563e8i	−0.372219	−	0.616135i
$645$	−3.89053e7	+	4.67689e8i	−0.144987	+	1.74292i
$646$	1.63956e6	+	1.05368e6i	0.00608176	+	0.00390851i
$647$	−3.16600e8	+	4.55202e7i	−1.16896	+	0.168070i	−0.699333	−	0.714796i	$-0.746519\pi$
$647$	−3.16600e8	+	4.55202e7i	−1.16896	+	0.168070i	−0.469623	+	0.882867i	$0.655610\pi$
$648$	−2.32402e8	+	2.24775e7i	−0.854113	+	0.0826080i
$649$	3.88928e8	+	1.14199e8i	1.42277	+	0.417763i
$650$	−2.15549e8	−	9.84379e7i	−0.784885	−	0.358445i
$651$	−7.65843e7	+	7.48286e7i	−0.277586	+	0.271222i
$652$	1.72952e6	−	1.20291e7i	0.00623996	−	0.0433999i
$653$	−5.06091e7	−	1.72359e8i	−0.181756	−	0.619005i	−0.999082	−	0.0428295i	$-0.986363\pi$
$653$	−5.06091e7	−	1.72359e8i	−0.181756	−	0.619005i	0.817326	−	0.576175i	$-0.195455\pi$
$654$	−1.94209e8	+	1.41900e8i	−0.694284	+	0.507280i
$655$	−5.67703e8	+	3.64841e8i	−2.02021	+	1.29831i
$656$	−7.89548e7	−	1.22856e8i	−0.279684	−	0.435196i
$657$	−6.49556e7	−	1.06421e8i	−0.229045	−	0.375257i
$658$	1.30935e8	−	3.84461e7i	0.459599	−	0.134950i
$659$	−4.66698e7	−	6.71010e6i	−0.163072	−	0.0234462i	0.0602952	−	0.998181i	$-0.480796\pi$
$659$	−4.66698e7	−	6.71010e6i	−0.163072	−	0.0234462i	−0.223367	+	0.974734i	$0.571705\pi$
$660$	3.27984e8	−	3.20465e8i	1.14083	−	1.11467i
$661$	−5.52204e7	+	1.20916e8i	−0.191203	+	0.418677i	−0.980818	−	0.194926i	$-0.937553\pi$
$661$	−5.52204e7	+	1.20916e8i	−0.191203	+	0.418677i	0.789615	+	0.613603i	$0.210280\pi$
$662$	6.04935e7	−	2.06022e8i	0.208514	−	0.710133i
$663$	2.03948e8	−	7.33862e7i	0.699806	−	0.251810i
$664$	3.58561e7	+	2.49385e8i	0.122478	+	0.851854i
$665$	−7.65881e6	+	1.19173e7i	−0.0260433	+	0.0405242i
$666$	1.08190e7	−	6.45790e7i	0.0366241	−	0.218609i
$667$	−4.19124e7	−	9.89547e7i	−0.141243	−	0.333472i
$668$			7.23730e7i			0.242799i
$669$	2.29515e8	+	1.76002e8i	0.766537	+	0.587814i
$670$	2.20395e7	+	1.53288e8i	0.0732785	+	0.509663i
$671$	−5.85681e8	+	2.67472e8i	−1.93862	+	0.885340i
$672$	1.05844e8	−	2.74032e8i	0.348786	−	0.903013i
$673$	3.51335e7	−	7.69315e7i	0.115259	−	0.252382i	−0.843207	−	0.537589i	$-0.819335\pi$
$673$	3.51335e7	−	7.69315e7i	0.115259	−	0.252382i	0.958466	+	0.285207i	$0.0920623\pi$
$674$	−1.56750e7	−	1.35824e7i	−0.0511950	−	0.0443607i
$675$	−1.14410e8	+	2.76925e8i	−0.372008	+	0.900432i
$676$	−5.22865e8	+	1.53527e8i	−1.69258	+	0.496986i
$677$	−1.13518e7	+	9.83636e6i	−0.0365845	+	0.0317007i	−0.672961	−	0.739678i	$-0.734978\pi$
$677$	−1.13518e7	+	9.83636e6i	−0.0365845	+	0.0317007i	0.636377	+	0.771378i	$0.280432\pi$
$678$	−1.19694e8	+	6.35674e7i	−0.384046	+	0.203960i
$679$	1.36107e8	−	8.74710e7i	0.434783	−	0.279418i
$680$	−1.17096e8	+	1.01464e8i	−0.372405	+	0.322691i
$681$	1.03090e8	+	5.01843e8i	0.326418	+	1.58901i
$682$	−1.34465e7	+	9.35226e7i	−0.0423894	+	0.294824i
$683$	2.80958e8	+	2.43451e8i	0.881819	+	0.764100i	0.972774	−	0.231755i	$-0.0744467\pi$
$683$	2.80958e8	+	2.43451e8i	0.881819	+	0.764100i	−0.0909556	+	0.995855i	$0.528992\pi$
$684$	−4.97062e6	+	7.35373e6i	−0.0155325	+	0.0229794i
$685$	8.74336e7	+	2.56728e7i	0.272024	+	0.0798733i
$686$	−1.49673e8	+	6.83535e7i	−0.463630	+	0.211733i
$687$	−3.08386e7	−	5.15043e8i	−0.0951097	−	1.58845i
$688$	−1.17821e8	−	7.57189e7i	−0.361790	−	0.232509i
$689$		−	1.72845e8i		−	0.528443i
$690$	2.24531e8	−	7.19841e6i	0.683487	−	0.0219124i
$691$	−1.93760e8			−0.587260			−0.293630	−	0.955919i	$-0.594863\pi$
$691$	−1.93760e8			−0.587260			−0.293630	+	0.955919i	$0.594863\pi$
$692$	−7.62948e7	+	1.18717e8i	−0.230238	+	0.358257i
$693$	4.66846e8	+	1.08285e7i	1.40273	+	0.0325363i
$694$	−1.39306e7	−	3.05038e7i	−0.0416766	−	0.0912591i
$695$	1.93397e8	−	6.58650e8i	0.576097	−	1.96201i
$696$	5.12757e7	−	9.13695e7i	0.152084	−	0.271003i
$697$	−1.35690e8	+	1.56595e8i	−0.400729	+	0.462465i
$698$	1.79910e8	+	2.58671e7i	0.529040	+	0.0760644i
$699$	1.06104e8	+	5.16516e8i	0.310671	+	1.51235i
$700$	−1.57525e8	−	1.81794e8i	−0.459257	−	0.530011i
$701$	3.26249e7	+	5.07653e7i	0.0947098	+	0.147371i	0.885375	−	0.464877i	$-0.153902\pi$
$701$	3.26249e7	+	5.07653e7i	0.0947098	+	0.147371i	−0.790665	+	0.612249i	$0.790265\pi$
$702$	−9.70246e7	−	2.90626e8i	−0.280460	−	0.840084i
$703$	−3.76612e6	−	4.34633e6i	−0.0108400	−	0.0125100i
$704$	−2.25121e7	−	7.66693e7i	−0.0645207	−	0.219737i
$705$	1.15010e8	−	5.00672e8i	0.328223	−	1.42885i
$706$	1.71405e8	−	1.97812e8i	0.487091	−	0.562132i
$707$	−4.58849e8	−	2.09549e8i	−1.29841	−	0.592963i
$708$	9.72764e7	−	2.51850e8i	0.274099	−	0.709647i
$709$	−2.48295e8	−	5.43691e8i	−0.696674	−	1.52550i	−0.843958	−	0.536409i	$-0.819781\pi$
$709$	−2.48295e8	−	5.43691e8i	−0.696674	−	1.52550i	0.147284	−	0.989094i	$-0.452947\pi$
$710$	1.00539e8	−	1.44553e7i	0.280904	−	0.0403879i
$711$	5.39669e7	+	4.89992e7i	0.150148	+	0.136326i
$712$	−1.62972e8			−0.451516
$713$	1.15373e8	−	9.44946e7i	0.318298	−	0.260698i
$714$	−6.80587e7	−	5.66155e6i	−0.186977	−	0.0155540i
$715$	1.16955e9	+	7.51625e8i	3.19964	+	2.05628i
$716$	−3.36822e8	+	4.84277e7i	−0.917616	+	0.131933i
$717$	1.55501e8	−	5.59536e7i	0.421867	−	0.151800i
$718$	−2.42987e8	−	7.13473e7i	−0.656462	−	0.192754i
$719$	3.90680e8	+	1.78418e8i	1.05108	+	0.480011i	0.864607	−	0.502449i	$-0.167568\pi$
$719$	3.90680e8	+	1.78418e8i	1.05108	+	0.480011i	0.186471	+	0.982460i	$0.440295\pi$
$720$	−1.15453e8	−	1.39656e8i	−0.309319	−	0.374163i
$721$	−2.26889e7	+	1.57805e8i	−0.0605352	+	0.421032i
$722$	5.15378e7	+	1.75522e8i	0.136935	+	0.466358i
$723$	4.61406e7	+	6.31499e7i	0.122087	+	0.167093i
$724$	4.53332e8	−	2.91339e8i	1.19454	−	0.767685i
$725$	−7.26914e7	−	1.13110e8i	−0.190752	−	0.296816i
$726$	1.82349e8	−	1.33234e8i	0.476534	−	0.348180i
$727$	−1.80924e8	+	5.31242e7i	−0.470862	+	0.138258i	−0.508551	−	0.861032i	$-0.669819\pi$
$727$	−1.80924e8	+	5.31242e7i	−0.470862	+	0.138258i	0.0376886	+	0.999290i	$0.488001\pi$
$728$	5.62522e8	+	8.08785e7i	1.45796	+	0.209623i
$729$	−3.62746e8	+	1.36053e8i	−0.936310	+	0.351176i
$730$	−4.85844e7	+	1.06385e8i	−0.124890	+	0.273471i
$731$	−5.59838e7	+	1.90663e8i	−0.143321	+	0.488107i
$732$	1.45199e8	+	4.03522e8i	0.370194	+	1.02881i
$733$	−5.97059e7	−	4.15264e8i	−0.151602	−	1.05442i	−0.913535	−	0.406760i	$-0.866659\pi$
$733$	−5.97059e7	−	4.15264e8i	−0.151602	−	1.05442i	0.761933	−	0.647656i	$-0.224251\pi$
$734$	−1.02552e8	+	1.59574e8i	−0.259332	+	0.403528i
$735$	−5.09896e6	+	6.12956e7i	−0.0128416	+	0.154372i
$736$	−1.80232e8	+	3.67320e8i	−0.452063	+	0.921321i
$737$		−	4.48365e8i		−	1.12003i
$738$	2.16853e8	+	1.96892e8i	0.539507	+	0.489844i
$739$	7.77282e7	+	5.40611e8i	0.192595	+	1.33953i	0.825107	+	0.564977i	$0.191115\pi$
$739$	7.77282e7	+	5.40611e8i	0.192595	+	1.33953i	−0.632511	+	0.774551i	$0.717976\pi$
$740$	1.80007e8	−	8.22067e7i	0.444217	−	0.202867i
$741$	−2.51031e7	−	9.69600e6i	−0.0616982	−	0.0238308i
$742$	−2.26236e7	+	4.95388e7i	−0.0553797	+	0.121265i
$743$	−6.37295e7	−	5.52220e7i	−0.155373	−	0.134631i	0.573705	−	0.819062i	$-0.305505\pi$
$743$	−6.37295e7	−	5.52220e7i	−0.155373	−	0.134631i	−0.729078	+	0.684431i	$0.760051\pi$
$744$	1.41706e8	+	3.25516e7i	0.344088	+	0.0790412i
$745$	8.40913e8	−	2.46914e8i	2.03368	−	0.597142i
$746$	−1.38872e8	+	1.20333e8i	−0.334502	+	0.289847i
$747$	1.64801e8	+	3.84201e8i	0.395366	+	0.921715i
$748$	1.63338e8	−	1.04971e8i	0.390286	−	0.250822i
$749$	−4.65165e8	+	4.03068e8i	−1.10704	+	0.959252i
$750$	−7.27608e6	+	1.49467e6i	−0.0172470	+	0.00354292i
$751$	5.45251e7	−	3.79230e8i	0.128729	−	0.895330i	−0.818439	−	0.574593i	$-0.805160\pi$
$751$	5.45251e7	−	3.79230e8i	0.128729	−	0.895330i	0.947168	−	0.320737i	$-0.103931\pi$
$752$	1.15861e8	+	1.00394e8i	0.272449	+	0.236078i
$753$	−4.59511e8	−	2.57873e8i	−1.07624	−	0.603978i
$754$	1.31921e8	+	3.87354e7i	0.307751	+	0.0903638i
$755$	8.69486e8	−	3.97081e8i	2.02033	−	0.922653i
$756$	3.29649e7	−	3.09277e8i	0.0762933	−	0.715785i
$757$	3.25688e8	+	2.09307e8i	0.750783	+	0.482499i	0.859221	−	0.511604i	$-0.170949\pi$
$757$	3.25688e8	+	2.09307e8i	0.750783	+	0.482499i	−0.108438	+	0.994103i	$0.534585\pi$
$758$		−	1.88321e8i		−	0.432404i
$759$	−6.46416e8	−	7.18854e7i	−1.47838	−	0.164405i
$760$	1.92367e7			0.0438217
$761$	1.24501e8	−	1.93728e8i	0.282501	−	0.439581i	−0.670784	−	0.741653i	$-0.734042\pi$
$761$	1.24501e8	−	1.93728e8i	0.282501	−	0.439581i	0.953285	+	0.302072i	$0.0976784\pi$
$762$	−7.06235e7	+	4.22864e6i	−0.159619	+	0.00955732i
$763$	−3.07516e8	−	6.73366e8i	−0.692300	−	1.51593i
$764$	1.61992e7	−	5.51695e7i	0.0363257	−	0.123714i
$765$	−1.43971e8	+	2.12997e8i	−0.321582	+	0.475761i
$766$	−9.78263e7	+	1.12898e8i	−0.217655	+	0.251188i
$767$	8.10209e8	+	1.16490e8i	1.79561	+	0.258169i
$768$	−2.73756e8	+	5.62357e7i	−0.604338	+	0.124145i
$769$	−2.27226e8	−	2.62233e8i	−0.499666	−	0.576645i	0.448757	−	0.893654i	$-0.351867\pi$
$769$	−2.27226e8	−	2.62233e8i	−0.499666	−	0.576645i	−0.948423	+	0.317009i	$0.897322\pi$
$770$	−2.36824e8	−	3.68505e8i	−0.518744	−	0.807181i
$771$	−4.06006e8	−	7.64488e8i	−0.885869	−	1.66804i
$772$	−1.66639e8	−	1.92312e8i	−0.362181	−	0.417979i
$773$	1.58089e7	+	5.38403e7i	0.0342266	+	0.116565i	0.974835	−	0.222930i	$-0.0715620\pi$
$773$	1.58089e7	+	5.38403e7i	0.0342266	+	0.116565i	−0.940608	+	0.339495i	$0.889744\pi$
$774$	2.67612e8	+	8.53666e7i	0.577142	+	0.184105i
$775$	1.22187e8	−	1.41011e8i	0.262494	−	0.302934i
$776$	−1.99847e8	−	9.12673e7i	−0.427675	−	0.195312i
$777$	1.87988e8	+	7.26099e7i	0.400744	+	0.154786i
$778$	5.94244e7	+	1.30121e8i	0.126190	+	0.276318i
$779$	2.54637e7	−	3.66113e6i	0.0538654	−	0.00774467i
$780$	5.63479e8	−	7.34803e8i	1.18739	−	1.54841i
$781$	−2.94074e8			−0.617310
$782$	9.37398e7	+	1.61447e7i	0.196022	+	0.0337605i
$783$	4.28403e7	−	1.68489e8i	0.0892415	−	0.350983i
$784$	−1.54417e7	−	9.92377e6i	−0.0320440	−	0.0205934i
$785$	−3.35464e8	+	4.82324e7i	−0.693484	+	0.0997080i
$786$	1.36756e8	+	3.80058e8i	0.281629	+	0.782677i
$787$	−5.25944e8	−	1.54431e8i	−1.07898	−	0.316819i	−0.306512	−	0.951867i	$-0.599162\pi$
$787$	−5.25944e8	−	1.54431e8i	−1.07898	−	0.316819i	−0.772473	+	0.635048i	$0.780980\pi$
$788$	3.48689e8	+	1.59241e8i	0.712623	+	0.325444i
$789$	−1.92042e8	−	1.96548e8i	−0.390989	−	0.400164i
$790$	9.73105e6	−	6.76809e7i	0.0197369	−	0.137273i
$791$	−1.17513e8	−	4.00212e8i	−0.237441	−	0.808649i
$792$	−3.30366e8	−	5.41258e8i	−0.664998	−	1.08950i
$793$	−1.09379e9	+	7.02939e8i	−2.19339	+	1.40961i
$794$	5.61578e7	+	8.73832e7i	0.112189	+	0.174569i
$795$	1.20949e8	+	1.65536e8i	0.240714	+	0.329451i
$796$	2.82470e8	−	8.29406e7i	0.560058	−	0.164448i
$797$	−6.50537e8	−	9.35331e7i	−1.28498	−	0.184752i	−0.534231	−	0.845338i	$-0.679399\pi$
$797$	−6.50537e8	−	9.35331e7i	−1.28498	−	0.184752i	−0.750750	+	0.660586i	$0.770308\pi$
$798$	5.92566e6	+	6.06470e6i	0.0116608	+	0.0119344i
$799$	9.03593e7	−	1.97859e8i	0.177146	−	0.387897i
$800$	−1.44222e8	+	4.91176e8i	−0.281684	+	0.959329i
$801$	−2.61160e8	+	7.01481e7i	−0.508170	+	0.136496i
$802$	−6.65930e7	−	4.63164e8i	−0.129094	−	0.897867i
$803$	1.83065e8	−	2.84854e8i	0.353556	−	0.550144i
$804$	−2.97608e8	−	2.47569e7i	−0.572633	−	0.0476352i
$805$	−1.17350e8	+	6.81360e8i	−0.224954	+	1.30614i
$806$			1.90798e8i			0.364391i
$807$	−2.28284e8	+	2.97693e8i	−0.434365	+	0.566433i
$808$	9.74837e7	+	6.78014e8i	0.184798	+	1.28530i
$809$	−2.76624e8	+	1.26330e8i	−0.522449	+	0.238595i	−0.659141	−	0.752019i	$-0.729080\pi$
$809$	−2.76624e8	+	1.26330e8i	−0.522449	+	0.238595i	0.136692	+	0.990614i	$0.456353\pi$
$810$	2.96289e8	+	2.10443e8i	0.557521	+	0.395986i
$811$	1.20632e8	−	2.64147e8i	0.226152	−	0.495204i	−0.762209	−	0.647331i	$-0.775885\pi$
$811$	1.20632e8	−	2.64147e8i	0.226152	−	0.495204i	0.988361	+	0.152127i	$0.0486124\pi$
$812$	1.05480e8	+	9.13990e7i	0.197016	+	0.170716i
$813$	8.01239e7	−	3.48801e8i	0.149104	−	0.649092i
$814$	1.70628e8	−	5.01009e7i	0.316357	−	0.0928907i
$815$	−3.30281e7	+	2.86190e7i	−0.0610113	+	0.0528666i
$816$	−3.59862e7	−	6.77601e7i	−0.0662317	−	0.124711i
$817$	2.07548e7	−	1.33383e7i	0.0380585	−	0.0244587i
$818$	−1.28345e7	+	1.11211e7i	−0.0234486	+	0.0203184i
$819$	9.36245e8	−	1.12520e8i	1.70427	−	0.204823i
$820$	−1.25978e8	+	8.76198e8i	−0.228483	+	1.58913i
$821$	−3.18797e8	−	2.76239e8i	−0.576082	−	0.499178i	0.317391	−	0.948295i	$-0.397193\pi$
$821$	−3.18797e8	−	2.76239e8i	−0.576082	−	0.499178i	−0.893473	+	0.449117i	$0.851739\pi$
$822$	2.66925e7	−	4.75640e7i	0.0480588	−	0.0856373i
$823$	−6.74062e8	−	1.97922e8i	−1.20921	−	0.355055i	−0.385840	−	0.922566i	$-0.626088\pi$
$823$	−6.74062e8	−	1.97922e8i	−1.20921	−	0.355055i	−0.823366	+	0.567511i	$0.807906\pi$
$824$	1.96928e8	−	8.99339e7i	0.351986	−	0.160747i
$825$	−8.12292e8	+	4.86366e7i	−1.44661	+	0.0866167i
$826$	−2.16966e8	−	1.39435e8i	−0.384991	−	0.247419i
$827$			4.42455e8i			0.782263i	0.920335	+	0.391132i	$0.127916\pi$
$827$			4.42455e8i			0.782263i	−0.920335	+	0.391132i	$0.872084\pi$
$828$	−8.34073e7	+	4.25098e8i	−0.146931	+	0.748855i
$829$	3.05957e8			0.537028			0.268514	−	0.963276i	$-0.413467\pi$
$829$	3.05957e8			0.537028			0.268514	+	0.963276i	$0.413467\pi$
$830$	2.12016e8	−	3.29903e8i	0.370795	−	0.576968i
$831$	−1.16976e7	−	1.95365e8i	−0.0203843	−	0.340442i
$832$	−6.70309e7	−	1.46777e8i	−0.116387	−	0.254852i
$833$	−7.33728e6	+	2.49885e7i	−0.0126940	+	0.0432320i
$834$	−3.58307e8	−	2.01078e8i	−0.617670	−	0.346631i
$835$	1.70434e8	−	1.96691e8i	0.292750	−	0.337852i
$836$	−2.38607e7	−	3.43065e6i	−0.0408380	−	0.00587162i
$837$	2.41093e8	−	8.83123e6i	0.411157	−	0.0150607i
$838$	5.24765e7	+	6.05611e7i	0.0891729	+	0.102911i
$839$	−1.91795e8	−	2.98440e8i	−0.324752	−	0.505325i	0.640038	−	0.768343i	$-0.278918\pi$
$839$	−1.91795e8	−	2.98440e8i	−0.324752	−	0.505325i	−0.964791	+	0.263018i	$0.915282\pi$
$840$	−5.95331e8	+	3.16170e8i	−1.00443	+	0.533437i
$841$	−3.38439e8	−	3.90579e8i	−0.568974	−	0.656631i
$842$	8.55555e7	+	2.91375e8i	0.143322	+	0.488109i
$843$	4.71877e8	+	1.08396e8i	0.787672	+	0.180938i
$844$	2.40480e8	−	2.77529e8i	0.399993	−	0.461616i
$845$	1.78256e9	+	8.14068e8i	2.95443	+	1.34924i
$846$	−2.76654e8	−	1.34182e8i	−0.456906	−	0.221607i
$847$	2.88736e8	+	6.32244e8i	0.475172	+	1.04048i
$848$	−6.05595e7	+	8.70714e6i	−0.0993104	+	0.0142787i
$849$	1.55191e8	+	1.19008e8i	0.253597	+	0.194469i
$850$	1.19009e8			0.193786
$851$	−2.51984e8	−	1.23641e8i	−0.408869	−	0.200619i
$852$	−1.62376e7	+	1.95195e8i	−0.0262544	+	0.315610i
$853$	4.74338e8	+	3.04839e8i	0.764260	+	0.491160i	0.863776	−	0.503876i	$-0.168093\pi$
$853$	4.74338e8	+	3.04839e8i	0.764260	+	0.491160i	−0.0995160	+	0.995036i	$0.531729\pi$
$854$	4.05498e8	−	5.83019e7i	0.651052	−	0.0936071i
$855$	3.08264e7	−	8.28005e6i	0.0493202	−	0.0132475i
$856$	8.01953e8	+	2.35475e8i	1.27858	+	0.375425i
$857$	9.64454e8	+	4.40451e8i	1.53228	+	0.699770i	0.990084	−	0.140480i	$-0.0448645\pi$
$857$	9.64454e8	+	4.40451e8i	1.53228	+	0.699770i	0.542199	+	0.840250i	$0.317592\pi$
$858$	5.95181e8	−	5.81536e8i	0.942296	−	0.920693i
$859$	−1.52759e8	+	1.06246e9i	−0.241005	+	1.67623i	0.406102	+	0.913828i	$0.366888\pi$
$859$	−1.52759e8	+	1.06246e9i	−0.241005	+	1.67623i	−0.647107	+	0.762399i	$0.724021\pi$
$860$	2.39171e8	+	8.14541e8i	0.376022	+	1.28061i
$861$	−7.27871e8	+	5.31820e8i	−1.14037	+	0.833212i
$862$	2.20261e8	−	1.41553e8i	0.343887	−	0.221003i
$863$	−4.51888e8	−	7.03152e8i	−0.703070	−	1.09400i	−0.990675	−	0.136249i	$-0.956495\pi$
$863$	−4.51888e8	−	7.03152e8i	−0.703070	−	1.09400i	0.287604	−	0.957749i	$-0.407141\pi$
$864$	−5.91621e8	+	2.96821e8i	−0.917281	+	0.460207i
$865$	4.86921e8	−	1.42973e8i	0.752333	−	0.220905i
$866$	2.06673e8	+	2.97152e7i	0.318223	+	0.0457535i
$867$	3.88283e8	−	3.79381e8i	0.595787	−	0.582128i
$868$	−8.04593e7	+	1.76181e8i	−0.123032	+	0.269402i
$869$	−5.57734e7	+	1.89947e8i	−0.0849901	+	0.289450i
$870$	−1.53448e8	+	5.52149e7i	−0.233025	+	0.0838492i
$871$	−1.28853e8	−	8.96193e8i	−0.195003	−	1.35627i
$872$	−5.43466e8	+	8.45650e8i	−0.819640	+	1.27538i
$873$	−3.59536e8	−	6.02338e7i	−0.540381	−	0.0905311i
$874$	−7.48300e6	−	9.13633e6i	−0.0112084	−	0.0136848i
$875$		−	2.28610e7i		−	0.0341249i
$876$	−1.78968e8	−	1.37240e8i	−0.266233	−	0.204159i
$877$	3.18334e7	+	2.21406e8i	0.0471937	+	0.328239i	0.999717	+	0.0237747i	$0.00756845\pi$
$877$	3.18334e7	+	2.21406e8i	0.0471937	+	0.328239i	−0.952524	+	0.304465i	$0.901522\pi$
$878$	−7.55162e6	+	3.44871e6i	−0.0111572	+	0.00509534i
$879$	−1.20327e8	+	3.11530e8i	−0.177173	+	0.458704i
$880$	2.04430e8	−	4.47638e8i	0.299982	−	0.656870i
$881$	6.33187e8	+	5.48659e8i	0.925985	+	0.802371i	0.980576	−	0.196138i	$-0.0628401\pi$
$881$	6.33187e8	+	5.48659e8i	0.925985	+	0.802371i	−0.0545911	+	0.998509i	$0.517386\pi$
$882$	3.50734e7	+	1.11882e7i	0.0511178	+	0.0163063i
$883$	−2.47147e8	+	7.25689e7i	−0.358982	+	0.105407i	−0.456250	−	0.889852i	$-0.650808\pi$
$883$	−2.47147e8	+	7.25689e7i	−0.358982	+	0.105407i	0.0972679	+	0.995258i	$0.468990\pi$
$884$	2.96314e8	−	2.56757e8i	0.428939	−	0.371677i
$885$	−8.57464e8	+	4.55384e8i	−1.23705	+	0.656974i
$886$	−1.25443e8	+	8.06170e7i	−0.180361	+	0.115911i
$887$	−8.94050e7	+	7.74699e7i	−0.128112	+	0.111010i	−0.716560	−	0.697525i	$-0.754285\pi$
$887$	−8.94050e7	+	7.74699e7i	−0.128112	+	0.111010i	0.588448	+	0.808535i	$0.299739\pi$
$888$	−5.50651e7	−	2.68058e8i	−0.0786389	−	0.382815i
$889$	3.09885e7	−	2.15530e8i	0.0441057	−	0.306762i
$890$	1.91707e8	+	1.66115e8i	0.271936	+	0.235634i
$891$	−7.62381e8	−	7.25157e8i	−1.07780	−	1.02518i
$892$	5.01998e8	+	1.47400e8i	0.707306	+	0.207684i
$893$	−2.45653e7	+	1.12186e7i	−0.0344959	+	0.0157537i
$894$	−3.13529e7	−	5.23632e8i	−0.0438799	−	0.732848i
$895$	1.02944e9	+	6.61581e8i	1.43593	+	0.922813i
$896$		−	6.45486e8i		−	0.897351i
$897$	−1.31272e9	+	4.20853e7i	−1.81884	+	0.0583114i
$898$	−1.22005e8			−0.168480
$899$	−5.85297e7	+	9.10739e7i	−0.0805558	+	0.125347i
$900$	−1.25683e7	+	5.41855e8i	−0.0172405	+	0.743285i
$901$	3.60610e7	+	7.89626e7i	0.0493019	+	0.107956i
$902$	−2.24112e8	+	7.63257e8i	−0.305384	+	1.04004i
$903$	−4.23088e8	+	7.53911e8i	−0.574602	+	1.02390i
$904$	−3.70915e8	+	4.28059e8i	−0.502076	+	0.579427i
$905$	−1.91813e9	−	2.75785e8i	−2.58781	−	0.372070i
$906$	−1.15123e8	−	5.60423e8i	−0.154803	−	0.753583i
$907$	−1.12855e8	−	1.30242e8i	−0.151252	−	0.174554i	0.675067	−	0.737756i	$-0.264115\pi$
$907$	−1.12855e8	−	1.30242e8i	−0.151252	−	0.174554i	−0.826319	+	0.563202i	$0.809569\pi$
$908$	5.01035e8	+	7.79626e8i	0.669285	+	1.04143i
$909$	4.48054e8	+	1.04455e9i	0.596538	+	1.39071i
$910$	−5.79266e8	−	6.68509e8i	−0.768695	−	0.887121i
$911$	−2.34695e8	−	7.99297e8i	−0.310419	−	1.05719i	−0.955968	−	0.293471i	$-0.905190\pi$
$911$	−2.34695e8	−	7.99297e8i	−0.310419	−	1.05719i	0.645549	−	0.763719i	$-0.276629\pi$
$912$	−2.13260e6	+	9.28380e6i	−0.00281141	+	0.0122389i
$913$	−7.43513e8	+	8.58060e8i	−0.976959	+	1.12747i
$914$	6.52584e7	+	2.98025e7i	0.0854668	+	0.0390314i
$915$	5.55657e8	−	1.43860e9i	0.725343	−	1.87792i
$916$	−3.87721e8	−	8.48991e8i	−0.504467	−	1.10463i
$917$	−1.23046e9	+	1.76914e8i	−1.59574	+	0.229432i
$918$	1.04959e8	+	1.12527e8i	0.135672	+	0.145455i
$919$	−2.15541e7			−0.0277705			−0.0138852	−	0.999904i	$-0.504420\pi$
$919$	−2.15541e7			−0.0277705			−0.0138852	+	0.999904i	$0.504420\pi$
$920$	8.64514e8	−	3.66166e8i	1.11022	−	0.470235i
$921$	7.81663e8	+	6.50237e7i	1.00055	+	0.0832325i
$922$	−4.77153e8	−	3.06647e8i	−0.608786	−	0.391243i
$923$	−5.87796e8	+	8.45123e7i	−0.747518	+	0.107477i
$924$	7.94820e8	−	2.85999e8i	1.00752	−	0.362534i
$925$	−3.36951e8	−	9.89376e7i	−0.425737	−	0.125008i
$926$	−2.19268e8	−	1.00136e8i	−0.276148	−	0.126113i
$927$	2.76863e8	−	2.28881e8i	0.347557	−	0.287324i
$928$	4.22705e7	−	2.93998e8i	0.0528924	−	0.367875i
$929$	5.47748e7	+	1.86546e8i	0.0683178	+	0.232669i	0.986573	−	0.163320i	$-0.0522202\pi$
$929$	5.47748e7	+	1.86546e8i	0.0683178	+	0.232669i	−0.918255	+	0.395989i	$0.870402\pi$
$930$	−1.33512e8	−	1.82730e8i	−0.165986	−	0.227175i
$931$	2.72013e6	−	1.74812e6i	0.00337086	−	0.00216632i
$932$	5.15685e8	+	8.02421e8i	0.636996	+	0.991185i
$933$	1.05104e9	−	7.67948e8i	1.29412	−	0.945555i
$934$	−2.07814e8	+	6.10198e7i	−0.255056	+	0.0748911i
$935$	−6.91112e8	−	9.93669e7i	−0.845500	−	0.121565i
$936$	−8.15886e8	−	9.86926e8i	−0.994952	−	1.20353i
$937$	−4.85806e8	+	1.06377e9i	−0.590533	+	1.29309i	0.344587	+	0.938754i	$0.388019\pi$
$937$	−4.85806e8	+	1.06377e9i	−0.590533	+	1.29309i	−0.935120	+	0.354332i	$0.884708\pi$
$938$	−8.03721e7	+	2.73722e8i	−0.0973861	+	0.331667i
$939$	3.55050e8	+	9.86720e8i	0.428838	+	1.19178i
$940$	−1.32247e8	−	9.19799e8i	−0.159222	−	1.10741i
$941$	2.22543e8	−	3.46284e8i	0.267082	−	0.415588i	−0.681645	−	0.731683i	$-0.738735\pi$
$941$	2.22543e8	−	3.46284e8i	0.267082	−	0.415588i	0.948728	+	0.316095i	$0.102372\pi$
$942$	−1.68166e7	+	2.02155e8i	−0.0201180	+	0.241843i
$943$	1.07467e9	−	6.49231e8i	1.28157	−	0.774220i
$944$		−	2.89741e8i		−	0.344424i
$945$	−8.17919e8	+	7.62906e8i	−0.969204	+	0.904015i
$946$	1.08569e8	+	7.55112e8i	0.128242	+	0.891945i
$947$	3.28597e7	−	1.50065e7i	0.0386913	−	0.0176697i	−0.395975	−	0.918261i	$-0.629593\pi$
$947$	3.28597e7	−	1.50065e7i	0.0386913	−	0.0176697i	0.434667	+	0.900591i	$0.356866\pi$
$948$	1.23000e8	+	4.75084e7i	0.144371	+	0.0557630i
$949$	2.84047e8	−	6.21977e8i	0.332347	−	0.727739i
$950$	−1.11667e7	−	9.67596e6i	−0.0130242	−	0.0112856i
$951$	−1.62823e7	−	3.74024e6i	−0.0189310	−	0.00434869i
$952$	−2.73857e8	+	8.04117e7i	−0.317405	+	0.0931984i
$953$	9.77035e8	−	8.46605e8i	1.12884	−	0.978143i	0.128928	−	0.991654i	$-0.458846\pi$
$953$	9.77035e8	−	8.46605e8i	1.12884	−	0.978143i	0.999909	+	0.0135109i	$0.00430079\pi$
$954$	1.12773e8	−	4.83733e7i	0.129885	−	0.0557136i
$955$	−1.73946e8	+	1.11789e8i	−0.199712	+	0.128347i
$956$	2.25926e8	−	1.95766e8i	0.258578	−	0.224059i
$957$	4.62493e8	−	9.50065e7i	0.527679	−	0.108397i
$958$	9.88888e7	−	6.87786e8i	0.112474	−	0.782271i
$959$	1.26862e8	+	1.09927e8i	0.143839	+	0.124637i
$960$	1.66905e8	+	9.36654e7i	0.188649	+	0.105868i
$961$	7.07405e8	+	2.07713e8i	0.797073	+	0.234042i
$962$	3.26653e8	−	1.49178e8i	0.366912	−	0.167563i
$963$	1.38647e9	+	3.21592e7i	1.55250	+	0.0360102i
$964$	1.19017e8	+	7.64874e7i	0.132855	+	0.0853805i
$965$			9.15080e8i			1.01830i
$966$	3.81745e8	+	1.59759e8i	0.423489	+	0.177229i
$967$	−1.29284e8			−0.142977			−0.0714884	−	0.997441i	$-0.522775\pi$
$967$	−1.29284e8			−0.142977			−0.0714884	+	0.997441i	$0.522775\pi$
$968$	5.10276e8	−	7.94006e8i	0.562574	−	0.875382i
$969$	1.34910e7	−	807786.i	0.0148277	−	0.000887820i
$970$	1.42057e8	+	3.11060e8i	0.155649	+	0.340823i
$971$	1.42584e8	−	4.85596e8i	0.155744	−	0.530417i	−0.844240	−	0.535965i	$-0.819948\pi$
$971$	1.42584e8	−	4.85596e8i	0.155744	−	0.530417i	0.999985	+	0.00554828i	$0.00176608\pi$
$972$	−5.23428e8	+	4.66000e8i	−0.569978	+	0.507442i
$973$	8.28094e8	−	9.55671e8i	0.898961	−	1.03746i
$974$	−5.86250e8	−	8.42901e7i	−0.634463	−	0.0912220i
$975$	−1.60963e9	+	3.30655e8i	−1.73665	+	0.356748i
$976$	3.01389e8	+	3.47821e8i	0.324173	+	0.374116i
$977$	−3.51957e7	−	5.47655e7i	−0.0377403	−	0.0587251i	0.821871	−	0.569674i	$-0.192931\pi$
$977$	−3.51957e7	−	5.47655e7i	−0.0377403	−	0.0587251i	−0.859611	+	0.510949i	$0.829294\pi$
$978$	1.22690e7	+	2.31019e7i	0.0131157	+	0.0246962i
$979$	−4.80938e8	−	5.55032e8i	−0.512556	−	0.591521i
$980$	3.13459e7	+	1.06754e8i	0.0333045	+	0.113425i
$981$	−5.06902e8	+	1.58906e9i	−0.536929	+	1.68319i
$982$	9.99596e6	−	1.15360e7i	0.0105558	−	0.0121820i
$983$	1.48412e8	+	6.77773e7i	0.156245	+	0.0713549i	0.492003	−	0.870594i	$-0.336265\pi$
$983$	1.48412e8	+	6.77773e7i	0.156245	+	0.0713549i	−0.335757	+	0.941949i	$0.608992\pi$
$984$	1.14190e9	+	4.41056e8i	1.19851	+	0.462923i
$985$	−5.72646e8	−	1.25392e9i	−0.599207	−	1.31208i
$986$	−6.83483e7	+	9.82700e6i	−0.0713012	+	0.0102516i
$987$	5.75853e8	−	7.50940e8i	0.598908	−	0.781005i
$988$	−4.86787e7			−0.0504741
$989$	6.78847e8	−	9.94497e8i	0.701751	−	1.02805i
$990$	−1.63080e8	+	9.73428e8i	−0.168072	+	1.00322i
$991$	−9.75002e8	−	6.26596e8i	−1.00181	−	0.643823i	−0.0665475	−	0.997783i	$-0.521198\pi$
$991$	−9.75002e8	−	6.26596e8i	−1.00181	−	0.643823i	−0.935260	+	0.353960i	$0.884835\pi$
$992$	4.07986e8	−	5.86595e7i	0.417936	−	0.0600902i
$993$	−5.04140e8	−	1.40106e9i	−0.514877	−	1.43089i
$994$	1.79529e8	+	5.27146e7i	0.182800	+	0.0536749i
$995$	−9.63001e8	−	4.39788e8i	−0.977592	−	0.446451i
$996$	5.28494e8	+	5.40895e8i	0.534887	+	0.547438i
$997$	3.30993e7	−	2.30210e8i	0.0333989	−	0.232295i	−0.966284	−	0.257479i	$-0.917108\pi$
$997$	3.30993e7	−	2.30210e8i	0.0333989	−	0.232295i	0.999683	+	0.0251843i	$0.00801725\pi$
$998$	−5.29587e7	−	1.80361e8i	−0.0532777	−	0.181447i
$999$	−2.03621e8	−	4.05856e8i	−0.204233	−	0.407076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.h.a.2.19	✓	460
3.2	odd	2	inner	69.7.h.a.2.28	yes	460
23.12	even	11	inner	69.7.h.a.35.28	yes	460
69.35	odd	22	inner	69.7.h.a.35.19	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.h.a.2.19	✓	460	1.1	even	1	trivial
69.7.h.a.2.28	yes	460	3.2	odd	2	inner
69.7.h.a.35.19	yes	460	69.35	odd	22	inner
69.7.h.a.35.28	yes	460	23.12	even	11	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10499 + 3.27543i) q^{2} +(1.61376 + 26.9517i) q^{3} +(20.2891 + 44.4269i) q^{4} +(49.4821 - 168.521i) q^{5} +(-91.6755 - 51.4474i) q^{6} +(211.874 - 244.516i) q^{7} +(-434.874 - 62.5255i) q^{8} +(-723.792 + 86.9871i) q^{9} +O(q^{10})\)	\(q+(-2.10499 + 3.27543i) q^{2} +(1.61376 + 26.9517i) q^{3} +(20.2891 + 44.4269i) q^{4} +(49.4821 - 168.521i) q^{5} +(-91.6755 - 51.4474i) q^{6} +(211.874 - 244.516i) q^{7} +(-434.874 - 62.5255i) q^{8} +(-723.792 + 86.9871i) q^{9} +(447.818 + 516.810i) q^{10} +(-1070.39 - 1665.56i) q^{11} +(-1164.64 + 618.521i) q^{12} +(-2618.16 - 3021.52i) q^{13} +(354.901 + 1208.68i) q^{14} +(4621.78 + 1061.68i) q^{15} +(-926.756 + 1069.53i) q^{16} +(1826.47 + 834.120i) q^{17} +(1238.66 - 2553.84i) q^{18} +(-103.560 - 226.766i) q^{19} +(8490.80 - 1220.79i) q^{20} +(6932.04 + 5315.79i) q^{21} +7708.60 q^{22} +(-8970.54 - 8219.81i) q^{23} +(983.389 - 11821.5i) q^{24} +(-12806.1 - 8230.01i) q^{25} +(15408.0 - 2215.33i) q^{26} +(-3512.48 - 19367.1i) q^{27} +(15161.8 + 4451.91i) q^{28} +(8034.31 + 3669.15i) q^{29} +(-13206.3 + 12903.5i) q^{30} +(-1744.35 + 12132.2i) q^{31} +(-9474.17 - 32266.1i) q^{32} +(43162.4 - 31536.7i) q^{33} +(-6576.81 + 4226.66i) q^{34} +(-30722.0 - 47804.3i) q^{35} +(-18549.6 - 30390.9i) q^{36} +(22134.8 - 6499.35i) q^{37} +(960.750 + 138.135i) q^{38} +(77210.0 - 75439.9i) q^{39} +(-32055.3 + 70191.4i) q^{40} +(-29073.0 + 99013.7i) q^{41} +(-32003.4 + 11515.7i) q^{42} +(14084.1 + 97957.1i) q^{43} +(52278.5 - 81347.0i) q^{44} +(-21155.6 + 126278. i) q^{45} +(45806.3 - 12079.8i) q^{46} -108329. i q^{47} +(-30321.3 - 23251.7i) q^{48} +(1845.87 + 12838.3i) q^{49} +(53913.7 - 24621.6i) q^{50} +(-19533.5 + 50572.6i) q^{51} +(81116.6 - 177621. i) q^{52} +(32672.9 + 28311.2i) q^{53} +(70829.2 + 29262.6i) q^{54} +(-333647. + 97967.6i) q^{55} +(-107427. + 93086.1i) q^{56} +(5944.61 - 3157.08i) q^{57} +(-28930.2 + 18592.3i) q^{58} +(-154729. + 134073. i) q^{59} +(46604.6 + 226872. i) q^{60} +(46282.0 - 321898. i) q^{61} +(-36066.5 - 31251.8i) q^{62} +(-132083. + 195409. i) q^{63} +(38724.7 + 11370.6i) q^{64} +(-638740. + 291703. i) q^{65} +(12439.8 + 207760. i) q^{66} +(190513. + 122435. i) q^{67} +98067.9i q^{68} +(207062. - 255036. i) q^{69} +221249. q^{70} +(80303.0 - 124954. i) q^{71} +(320197. + 7426.97i) q^{72} +(71046.7 + 155571. i) q^{73} +(-25305.3 + 86182.0i) q^{74} +(201147. - 358429. i) q^{75} +(7973.36 - 9201.75i) q^{76} +(-634045. - 91161.9i) q^{77} +(84571.8 + 411697. i) q^{78} +(-65479.5 - 75567.4i) q^{79} +(134381. + 209100. i) q^{80} +(516307. - 125921. i) q^{81} +(-263114. - 303650. i) q^{82} +(-161563. - 550234. i) q^{83} +(-95519.3 + 415822. i) q^{84} +(230944. - 266524. i) q^{85} +(-350499. - 160067. i) q^{86} +(-85924.4 + 222460. i) q^{87} +(361346. + 791237. i) q^{88} +(367167. - 52790.6i) q^{89} +(-369083. - 335108. i) q^{90} -1.29353e6 q^{91} +(183177. - 565306. i) q^{92} +(-329800. - 27434.8i) q^{93} +(354824. + 228031. i) q^{94} +(-43339.1 + 6231.22i) q^{95} +(854337. - 307415. i) q^{96} +(479808. + 140884. i) q^{97} +(-45936.6 - 20978.6i) q^{98} +(919623. + 1.11241e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more