LMFDB - Embedded newform 19.7.f.a.10.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,7,Mod(2,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, 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:	$4.37102758878$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.4
Character	$\chi$	$=$	19.10
Dual form			19.7.f.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.80629 + 0.847479i) q^{2} +(-21.7309 - 25.8979i) q^{3} +(-37.7581 + 13.7428i) q^{4} +(225.514 + 82.0804i) q^{5} +(126.393 + 106.056i) q^{6} +(-232.429 + 402.578i) q^{7} +(440.331 - 254.225i) q^{8} +(-71.8793 + 407.648i) q^{9} +O(q^{10})$	\(q+(-4.80629 + 0.847479i) q^{2} +(-21.7309 - 25.8979i) q^{3} +(-37.7581 + 13.7428i) q^{4} +(225.514 + 82.0804i) q^{5} +(126.393 + 106.056i) q^{6} +(-232.429 + 402.578i) q^{7} +(440.331 - 254.225i) q^{8} +(-71.8793 + 407.648i) q^{9} +(-1153.45 - 203.384i) q^{10} +(814.887 + 1411.43i) q^{11} +(1176.43 + 679.212i) q^{12} +(-292.948 + 349.122i) q^{13} +(775.943 - 2131.89i) q^{14} +(-2774.92 - 7624.03i) q^{15} +(69.0555 - 57.9444i) q^{16} +(296.531 + 1681.71i) q^{17} -2020.19i q^{18} +(-4210.10 + 5414.88i) q^{19} -9643.00 q^{20} +(15476.8 - 2728.98i) q^{21} +(-5112.74 - 6093.12i) q^{22} +(-1222.80 + 445.064i) q^{23} +(-16152.7 - 5879.11i) q^{24} +(32149.9 + 26977.0i) q^{25} +(1112.12 - 1926.25i) q^{26} +(-9224.44 + 5325.73i) q^{27} +(3243.50 - 18394.8i) q^{28} +(6614.47 + 1166.31i) q^{29} +(19798.3 + 34291.6i) q^{30} +(4653.34 + 2686.61i) q^{31} +(-21199.6 + 25264.7i) q^{32} +(18844.7 - 51775.5i) q^{33} +(-2850.43 - 7831.48i) q^{34} +(-85459.7 + 71709.2i) q^{35} +(-2888.21 - 16379.8i) q^{36} -47458.6i q^{37} +(15646.0 - 29593.5i) q^{38} +15407.6 q^{39} +(120168. - 21188.8i) q^{40} +(30496.4 + 36344.2i) q^{41} +(-72073.4 + 26232.6i) q^{42} +(506.221 + 184.249i) q^{43} +(-50165.5 - 42093.9i) q^{44} +(-49669.7 + 86030.4i) q^{45} +(5499.97 - 3175.41i) q^{46} +(27431.5 - 155571. i) q^{47} +(-3001.28 - 529.207i) q^{48} +(-49221.6 - 85254.3i) q^{49} +(-177384. - 102413. i) q^{50} +(37108.9 - 44224.6i) q^{51} +(6263.25 - 17208.1i) q^{52} +(-8777.68 - 24116.5i) q^{53} +(39821.9 - 33414.6i) q^{54} +(67918.0 + 385182. i) q^{55} +236357. i q^{56} +(231724. - 8637.65i) q^{57} -32779.5 q^{58} +(93697.5 - 16521.4i) q^{59} +(209551. + 249734. i) q^{60} +(37171.1 - 13529.2i) q^{61} +(-24642.1 - 8969.01i) q^{62} +(-147403. - 123686. i) q^{63} +(77595.6 - 134400. i) q^{64} +(-94720.1 + 54686.6i) q^{65} +(-46694.6 + 264819. i) q^{66} +(-414043. - 73006.9i) q^{67} +(-34307.9 - 59423.0i) q^{68} +(38098.9 + 21996.4i) q^{69} +(349972. - 417081. i) q^{70} +(-146173. + 401606. i) q^{71} +(71983.6 + 197773. i) q^{72} +(4128.91 - 3464.56i) q^{73} +(40220.1 + 228100. i) q^{74} -1.41885e6i q^{75} +(84549.6 - 262314. i) q^{76} -757612. q^{77} +(-74053.3 + 13057.6i) q^{78} +(104715. + 124795. i) q^{79} +(20329.1 - 7399.18i) q^{80} +(621942. + 226369. i) q^{81} +(-177376. - 148836. i) q^{82} +(250787. - 434376. i) q^{83} +(-546872. + 315737. i) q^{84} +(-71163.5 + 403588. i) q^{85} +(-2589.19 - 456.545i) q^{86} +(-113534. - 196646. i) q^{87} +(717640. + 414329. i) q^{88} +(-168525. + 200840. i) q^{89} +(165818. - 455581. i) q^{90} +(-72459.4 - 199081. i) q^{91} +(40054.3 - 33609.6i) q^{92} +(-31543.9 - 178894. i) q^{93} +770970. i q^{94} +(-1.39389e6 + 875565. i) q^{95} +1.11499e6 q^{96} +(734952. - 129592. i) q^{97} +(308825. + 368043. i) q^{98} +(-633937. + 230734. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9}+O(q^{10}) $ 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} - 1689 q^{10} + 1677 q^{11} - 9 q^{12} - 10506 q^{13} + 6105 q^{14} + 24138 q^{15} + 23760 q^{16} - 3438 q^{17} - 30918 q^{19} - 76650 q^{20} - 59055 q^{21} + 20490 q^{22} + 42498 q^{23} + 31848 q^{24} + 7914 q^{25} + 109989 q^{26} + 124821 q^{27} - 109476 q^{28} - 27726 q^{29} - 153516 q^{30} - 30789 q^{31} - 114375 q^{32} + 126039 q^{33} + 359796 q^{34} + 160161 q^{35} + 184995 q^{36} - 245244 q^{38} - 390564 q^{39} - 372678 q^{40} - 24708 q^{41} - 244893 q^{42} - 30726 q^{43} - 301419 q^{44} + 293037 q^{45} + 69246 q^{46} - 71454 q^{47} + 1024041 q^{48} - 350346 q^{49} - 104148 q^{50} - 180672 q^{51} + 921801 q^{52} + 822558 q^{53} + 308469 q^{54} + 623517 q^{55} - 17862 q^{57} - 1150644 q^{58} - 463812 q^{59} - 908130 q^{60} - 583698 q^{61} - 429732 q^{62} - 2576043 q^{63} - 328293 q^{64} - 1056789 q^{65} - 1038756 q^{66} + 1120464 q^{67} + 717270 q^{68} + 3771567 q^{69} + 4845345 q^{70} + 94494 q^{71} + 2351634 q^{72} + 950850 q^{73} + 55149 q^{74} - 218814 q^{76} - 343086 q^{77} + 1833471 q^{78} - 4936494 q^{79} - 9642039 q^{80} - 769551 q^{81} - 8627793 q^{82} - 412131 q^{83} - 3125205 q^{84} - 896910 q^{85} + 8878236 q^{86} + 610737 q^{87} + 13604751 q^{88} + 6653022 q^{89} + 3142734 q^{90} + 3409821 q^{91} - 3043740 q^{92} - 816393 q^{93} + 4839186 q^{95} - 5667138 q^{96} - 853656 q^{97} - 17679315 q^{98} - 13991937 q^{99}+O(q^{100}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9 - 1689 * q^10 + 1677 * q^11 - 9 * q^12 - 10506 * q^13 + 6105 * q^14 + 24138 * q^15 + 23760 * q^16 - 3438 * q^17 - 30918 * q^19 - 76650 * q^20 - 59055 * q^21 + 20490 * q^22 + 42498 * q^23 + 31848 * q^24 + 7914 * q^25 + 109989 * q^26 + 124821 * q^27 - 109476 * q^28 - 27726 * q^29 - 153516 * q^30 - 30789 * q^31 - 114375 * q^32 + 126039 * q^33 + 359796 * q^34 + 160161 * q^35 + 184995 * q^36 - 245244 * q^38 - 390564 * q^39 - 372678 * q^40 - 24708 * q^41 - 244893 * q^42 - 30726 * q^43 - 301419 * q^44 + 293037 * q^45 + 69246 * q^46 - 71454 * q^47 + 1024041 * q^48 - 350346 * q^49 - 104148 * q^50 - 180672 * q^51 + 921801 * q^52 + 822558 * q^53 + 308469 * q^54 + 623517 * q^55 - 17862 * q^57 - 1150644 * q^58 - 463812 * q^59 - 908130 * q^60 - 583698 * q^61 - 429732 * q^62 - 2576043 * q^63 - 328293 * q^64 - 1056789 * q^65 - 1038756 * q^66 + 1120464 * q^67 + 717270 * q^68 + 3771567 * q^69 + 4845345 * q^70 + 94494 * q^71 + 2351634 * q^72 + 950850 * q^73 + 55149 * q^74 - 218814 * q^76 - 343086 * q^77 + 1833471 * q^78 - 4936494 * q^79 - 9642039 * q^80 - 769551 * q^81 - 8627793 * q^82 - 412131 * q^83 - 3125205 * q^84 - 896910 * q^85 + 8878236 * q^86 + 610737 * q^87 + 13604751 * q^88 + 6653022 * q^89 + 3142734 * q^90 + 3409821 * q^91 - 3043740 * q^92 - 816393 * q^93 + 4839186 * q^95 - 5667138 * q^96 - 853656 * q^97 - 17679315 * q^98 - 13991937 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−4.80629	+	0.847479i	−0.600786	+	0.105935i	−0.465766	−	0.884908i	$-0.654221\pi$
$2$	−4.80629	+	0.847479i	−0.600786	+	0.105935i	−0.135021	+	0.990843i	$0.543110\pi$
$3$	−21.7309	−	25.8979i	−0.804850	−	0.959182i	0.194916	−	0.980820i	$-0.437556\pi$
$3$	−21.7309	−	25.8979i	−0.804850	−	0.959182i	−0.999766	+	0.0216375i	$0.993112\pi$
$4$	−37.7581	+	13.7428i	−0.589970	+	0.214732i
$5$	225.514	+	82.0804i	1.80411	+	0.656643i	0.997883	+	0.0650403i	$0.0207176\pi$
$5$	225.514	+	82.0804i	1.80411	+	0.656643i	0.806230	+	0.591603i	$0.201505\pi$
$6$	126.393	+	106.056i	0.585154	+	0.491002i
$7$	−232.429	+	402.578i	−0.677634	+	1.17370i	0.298057	+	0.954548i	$0.403661\pi$
$7$	−232.429	+	402.578i	−0.677634	+	1.17370i	−0.975691	+	0.219149i	$0.929672\pi$
$8$	440.331	−	254.225i	0.860021	−	0.496534i
$9$	−71.8793	+	407.648i	−0.0985998	+	0.559187i
$10$	−1153.45	−	203.384i	−1.15345	−	0.203384i
$11$	814.887	+	1411.43i	0.612236	+	1.06042i	0.990863	+	0.134875i	$0.0430633\pi$
$11$	814.887	+	1411.43i	0.612236	+	1.06042i	−0.378626	+	0.925550i	$0.623603\pi$
$12$	1176.43	+	679.212i	0.680804	+	0.393063i
$13$	−292.948	+	349.122i	−0.133340	+	0.158909i	−0.828583	−	0.559866i	$-0.810852\pi$
$13$	−292.948	+	349.122i	−0.133340	+	0.158909i	0.695243	+	0.718775i	$0.255297\pi$
$14$	775.943	−	2131.89i	0.282778	−	0.776926i
$15$	−2774.92	−	7624.03i	−0.822198	−	2.25897i
$16$	69.0555	−	57.9444i	0.0168592	−	0.0141466i
$17$	296.531	+	1681.71i	0.0603563	+	0.342298i	1.00000		0.000143144i	$4.55642e-5\pi$
$17$	296.531	+	1681.71i	0.0603563	+	0.342298i	−0.939644	+	0.342155i	$0.888843\pi$
$18$		−	2020.19i		−	0.346397i
$19$	−4210.10	+	5414.88i	−0.613807	+	0.789457i
$19$	−4210.10	+	5414.88i	−0.613807	+	0.789457i
$20$	−9643.00			−1.20537
$21$	15476.8	−	2728.98i	1.67118	−	0.294675i
$22$	−5112.74	−	6093.12i	−0.480159	−	0.572232i
$23$	−1222.80	+	445.064i	−0.100502	+	0.0365796i	−0.391782	−	0.920058i	$-0.628141\pi$
$23$	−1222.80	+	445.064i	−0.100502	+	0.0365796i	0.291280	+	0.956638i	$0.405919\pi$
$24$	−16152.7	−	5879.11i	−1.16845	−	0.425283i
$25$	32149.9	+	26977.0i	2.05760	+	1.72653i
$26$	1112.12	−	1926.25i	0.0632750	−	0.109596i
$27$	−9224.44	+	5325.73i	−0.468650	+	0.270575i
$28$	3243.50	−	18394.8i	0.147754	−	0.837956i
$29$	6614.47	+	1166.31i	0.271207	+	0.0478211i	0.307598	−	0.951517i	$-0.400475\pi$
$29$	6614.47	+	1166.31i	0.271207	+	0.0478211i	−0.0363907	+	0.999338i	$0.511586\pi$
$30$	19798.3	+	34291.6i	0.733270	+	1.27006i
$31$	4653.34	+	2686.61i	0.156199	+	0.0901818i	0.576062	−	0.817406i	$-0.304589\pi$
$31$	4653.34	+	2686.61i	0.156199	+	0.0901818i	−0.419863	+	0.907588i	$0.637922\pi$
$32$	−21199.6	+	25264.7i	−0.646962	+	0.771019i
$33$	18844.7	−	51775.5i	0.524382	−	1.44073i
$34$	−2850.43	−	7831.48i	−0.0725225	−	0.199254i
$35$	−85459.7	+	71709.2i	−1.99323	+	1.67252i
$36$	−2888.21	−	16379.8i	−0.0619043	−	0.351076i
$37$		−	47458.6i		−	0.936935i	−0.883481	−	0.468468i	$-0.844806\pi$
$37$		−	47458.6i		−	0.936935i	0.883481	−	0.468468i	$-0.155194\pi$
$38$	15646.0	−	29593.5i	0.285136	−	0.539318i
$39$	15407.6			0.259741
$40$	120168.	−	21188.8i	1.87762	−	0.331075i
$41$	30496.4	+	36344.2i	0.442484	+	0.527332i	0.940481	−	0.339847i	$-0.110375\pi$
$41$	30496.4	+	36344.2i	0.442484	+	0.527332i	−0.497997	+	0.867179i	$0.665931\pi$
$42$	−72073.4	+	26232.6i	−0.972808	+	0.354073i
$43$	506.221	+	184.249i	0.00636700	+	0.00231740i	0.345202	−	0.938529i	$-0.387811\pi$
$43$	506.221	+	184.249i	0.00636700	+	0.00231740i	−0.338835	+	0.940846i	$0.610033\pi$
$44$	−50165.5	−	42093.9i	−0.588908	−	0.494153i
$45$	−49669.7	+	86030.4i	−0.545072	+	0.944092i
$46$	5499.97	−	3175.41i	0.0565050	−	0.0326232i
$47$	27431.5	−	155571.i	0.264214	−	1.49843i	−0.507051	−	0.861916i	$-0.669265\pi$
$47$	27431.5	−	155571.i	0.264214	−	1.49843i	0.771265	−	0.636514i	$-0.219624\pi$
$48$	−3001.28	−	529.207i	−0.0271383	−	0.00478522i
$49$	−49221.6	−	85254.3i	−0.418377	−	0.724650i
$50$	−177384.	−	102413.i	−1.41908	−	0.819304i
$51$	37108.9	−	44224.6i	0.279748	−	0.333391i
$52$	6263.25	−	17208.1i	0.0445440	−	0.122384i
$53$	−8777.68	−	24116.5i	−0.0589593	−	0.161989i	0.906716	−	0.421742i	$-0.138581\pi$
$53$	−8777.68	−	24116.5i	−0.0589593	−	0.161989i	−0.965675	+	0.259753i	$0.916359\pi$
$54$	39821.9	−	33414.6i	0.252895	−	0.212204i
$55$	67918.0	+	385182.i	0.408223	+	2.31515i
$56$			236357.i			1.34587i
$57$	231724.	−	8637.65i	1.25125	−	0.0466414i
$58$	−32779.5			−0.168003
$59$	93697.5	−	16521.4i	0.456218	−	0.0804435i	0.0591830	−	0.998247i	$-0.481150\pi$
$59$	93697.5	−	16521.4i	0.456218	−	0.0804435i	0.397034	+	0.917804i	$0.370039\pi$
$60$	209551.	+	249734.i	0.970145	+	1.15617i
$61$	37171.1	−	13529.2i	0.163763	−	0.0596048i	−0.258838	−	0.965921i	$-0.583340\pi$
$61$	37171.1	−	13529.2i	0.163763	−	0.0596048i	0.422601	+	0.906316i	$0.361117\pi$
$62$	−24642.1	−	8969.01i	−0.103396	−	0.0376330i
$63$	−147403.	−	123686.i	−0.589502	−	0.494651i
$64$	77595.6	−	134400.i	0.296004	−	0.512694i
$65$	−94720.1	+	54686.6i	−0.344907	+	0.199132i
$66$	−46694.6	+	264819.i	−0.162418	+	0.921121i
$67$	−414043.	−	73006.9i	−1.37664	−	0.242739i	−0.564131	−	0.825685i	$-0.690789\pi$
$67$	−414043.	−	73006.9i	−1.37664	−	0.242739i	−0.812511	+	0.582946i	$0.801900\pi$
$68$	−34307.9	−	59423.0i	−0.109111	−	0.188985i
$69$	38098.9	+	21996.4i	0.115975	+	0.0669583i
$70$	349972.	−	417081.i	1.02033	−	1.21598i
$71$	−146173.	+	401606.i	−0.408405	+	1.12208i	0.549624	+	0.835412i	$0.314771\pi$
$71$	−146173.	+	401606.i	−0.408405	+	1.12208i	−0.958029	+	0.286672i	$0.907451\pi$
$72$	71983.6	+	197773.i	0.192857	+	0.529871i
$73$	4128.91	−	3464.56i	0.0106137	−	0.00890595i	−0.637465	−	0.770479i	$-0.720017\pi$
$73$	4128.91	−	3464.56i	0.0106137	−	0.00890595i	0.648079	+	0.761573i	$0.275573\pi$
$74$	40220.1	+	228100.i	0.0992541	+	0.562898i
$75$		−	1.41885e6i		−	3.36321i
$76$	84549.6	−	262314.i	0.192606	−	0.597560i
$77$	−757612.			−1.65949
$78$	−74053.3	+	13057.6i	−0.156049	+	0.0275156i
$79$	104715.	+	124795.i	0.212387	+	0.253113i	0.861712	−	0.507398i	$-0.169393\pi$
$79$	104715.	+	124795.i	0.212387	+	0.253113i	−0.649324	+	0.760512i	$0.724948\pi$
$80$	20329.1	−	7399.18i	0.0397052	−	0.0144515i
$81$	621942.	+	226369.i	1.17029	+	0.425952i
$82$	−177376.	−	148836.i	−0.321701	−	0.269939i
$83$	250787.	−	434376.i	0.438603	−	0.759682i	−0.558979	−	0.829182i	$-0.688807\pi$
$83$	250787.	−	434376.i	0.438603	−	0.759682i	0.997582	+	0.0694996i	$0.0221402\pi$
$84$	−546872.	+	315737.i	−0.922673	+	0.532705i
$85$	−71163.5	+	403588.i	−0.115878	+	0.657176i
$86$	−2589.19	−	456.545i	−0.00407070	−	0.000717774i
$87$	−113534.	−	196646.i	−0.172412	−	0.298626i
$88$	717640.	+	414329.i	1.05307	+	0.607992i
$89$	−168525.	+	200840.i	−0.239053	+	0.284892i	−0.872211	−	0.489131i	$-0.837314\pi$
$89$	−168525.	+	200840.i	−0.239053	+	0.284892i	0.633157	+	0.774023i	$0.281759\pi$
$90$	165818.	−	455581.i	0.227459	−	0.624940i
$91$	−72459.4	−	199081.i	−0.0961547	−	0.264183i
$92$	40054.3	−	33609.6i	0.0514382	−	0.0431618i
$93$	−31543.9	−	178894.i	−0.0392163	−	0.222407i
$94$			770970.i			0.928226i
$95$	−1.39389e6	+	875565.i	−1.62577	+	1.02122i
$96$	1.11499e6			1.26025
$97$	734952.	−	129592.i	0.805274	−	0.141992i	0.244165	−	0.969734i	$-0.421486\pi$
$97$	734952.	−	129592.i	0.805274	−	0.141992i	0.561109	+	0.827742i	$0.310375\pi$
$98$	308825.	+	368043.i	0.328121	+	0.391039i
$99$	−633937.	+	230734.i	−0.653342	+	0.237797i
$100$	−1.58466e6	−	576769.i	−1.58466	−	0.576769i
$101$	−466017.	−	391035.i	−0.452312	−	0.379535i	0.387981	−	0.921667i	$-0.373173\pi$
$101$	−466017.	−	391035.i	−0.452312	−	0.379535i	−0.840293	+	0.542133i	$0.817617\pi$
$102$	−140877.	+	244006.i	−0.132751	+	0.229932i
$103$	460909.	−	266106.i	0.421797	−	0.243525i	−0.274049	−	0.961716i	$-0.588363\pi$
$103$	460909.	−	266106.i	0.421797	−	0.243525i	0.695846	+	0.718191i	$0.255030\pi$
$104$	−40238.6	+	228204.i	−0.0357719	+	0.202873i
$105$	3.71424e6	+	654920.i	3.20850	+	0.565745i
$106$	62626.3	+	108472.i	0.0525823	+	0.0910751i
$107$	1.60265e6	+	925290.i	1.30824	+	0.755312i	0.981802	−	0.189907i	$-0.0608187\pi$
$107$	1.60265e6	+	925290.i	1.30824	+	0.755312i	0.326437	+	0.945219i	$0.394152\pi$
$108$	275107.	−	327860.i	0.218389	−	0.260266i
$109$	−452512.	+	1.24327e6i	−0.349422	+	0.960029i	0.633131	+	0.774045i	$0.281770\pi$
$109$	−452512.	+	1.24327e6i	−0.349422	+	0.960029i	−0.982553	+	0.185984i	$0.940453\pi$
$110$	−652868.	−	1.79374e6i	−0.490509	−	1.34766i
$111$	−1.22908e6	+	1.03132e6i	−0.898692	+	0.754092i
$112$	7276.69	+	41268.2i	0.00517941	+	0.0293739i
$113$		−	2.56242e6i		−	1.77589i	−0.459952	−	0.887944i	$-0.652133\pi$
$113$		−	2.56242e6i		−	1.77589i	0.459952	−	0.887944i	$-0.347867\pi$
$114$	−1.10641e6	+	237896.i	−0.746796	+	0.160573i
$115$	−312290.			−0.205336
$116$	−265778.	+	46863.8i	−0.170273	+	0.0300237i
$117$	−121262.	−	144514.i	−0.0757124	−	0.0902305i
$118$	−436336.	+	158813.i	−0.265568	+	0.0966587i
$119$	−745941.	−	271501.i	−0.442653	−	0.161113i
$120$	−3.16010e6	−	2.65164e6i	−1.82876	−	1.53451i
$121$	−442300.	+	766086.i	−0.249667	+	0.432436i
$122$	−167189.	+	96526.8i	−0.0920723	+	0.0531580i
$123$	278524.	−	1.57959e6i	0.149674	−	0.848846i
$124$	−212623.	−	37491.1i	−0.111518	−	0.0196636i
$125$	3.16108e6	+	5.47515e6i	1.61847	+	2.80328i
$126$	813284.	+	469550.i	0.406566	+	0.234731i
$127$	1.73856e6	−	2.07193e6i	0.848745	−	1.01150i	−0.150991	−	0.988535i	$-0.548246\pi$
$127$	1.73856e6	−	2.07193e6i	0.848745	−	1.01150i	0.999736	−	0.0229602i	$-0.00730910\pi$
$128$	462879.	−	1.27175e6i	0.220718	−	0.606418i
$129$	−6228.98	−	17114.0i	−0.00290167	−	0.00797227i
$130$	408906.	−	343113.i	0.186120	−	0.156174i
$131$	−241787.	−	1.37124e6i	−0.107552	−	0.609959i	−0.990170	−	0.139868i	$-0.955332\pi$
$131$	−241787.	−	1.37124e6i	−0.107552	−	0.609959i	0.882618	−	0.470091i	$-0.155779\pi$
$132$			2.21392e6i			0.962589i
$133$	−1.20137e6	−	2.95347e6i	−0.510646	−	1.25539i
$134$	2.05188e6			0.852782
$135$	−2.51738e6	+	443882.i	−1.02317	+	0.180412i
$136$	558104.	+	665123.i	0.221870	+	0.264414i
$137$	−1.12380e6	+	409031.i	−0.437047	+	0.159072i	−0.551167	−	0.834395i	$-0.685817\pi$
$137$	−1.12380e6	+	409031.i	−0.437047	+	0.159072i	0.114120	+	0.993467i	$0.463595\pi$
$138$	−201756.	−	73433.2i	−0.0767696	−	0.0279418i
$139$	628180.	+	527105.i	0.233905	+	0.196270i	0.752205	−	0.658929i	$-0.228990\pi$
$139$	628180.	+	527105.i	0.233905	+	0.196270i	−0.518300	+	0.855199i	$0.673435\pi$
$140$	2.24131e6	−	3.88206e6i	0.816803	−	1.41475i
$141$	−4.62509e6	+	2.67030e6i	−1.64992	+	0.952582i
$142$	362196.	−	2.05412e6i	0.126497	−	0.717397i
$143$	−731480.	−	128980.i	−0.250146	−	0.0441075i
$144$	18657.2	+	32315.3i	0.00624828	+	0.0108223i
$145$	1.39592e6	+	805937.i	0.457886	+	0.264361i
$146$	−16908.6	+	20150.9i	−0.00543311	+	0.00647493i
$147$	−1.13828e6	+	3.12739e6i	−0.358341	+	0.984534i
$148$	652215.	+	1.79195e6i	0.201190	+	0.552764i
$149$	1.80580e6	−	1.51525e6i	0.545898	−	0.458063i	−0.327651	−	0.944799i	$-0.606257\pi$
$149$	1.80580e6	−	1.51525e6i	0.545898	−	0.458063i	0.873549	+	0.486736i	$0.161813\pi$
$150$	1.20245e6	+	6.81942e6i	0.356281	+	2.02057i
$151$		−	2.90204e6i		−	0.842893i	−0.906853	−	0.421447i	$-0.861523\pi$
$151$		−	2.90204e6i		−	0.842893i	0.906853	−	0.421447i	$-0.138477\pi$
$152$	−477237.	+	3.45465e6i	−0.135895	+	0.983725i
$153$	−706859.			−0.197360
$154$	3.64130e6	−	642060.i	0.996999	−	0.175798i
$155$	828875.	+	987815.i	0.222584	+	0.265265i
$156$	−581761.	+	211744.i	−0.153240	+	0.0557746i
$157$	5.72215e6	+	2.08269e6i	1.47863	+	0.538178i	0.950430	−	0.310940i	$-0.100644\pi$
$157$	5.72215e6	+	2.08269e6i	1.47863	+	0.538178i	0.528203	+	0.849118i	$0.322866\pi$
$158$	−609053.	−	511056.i	−0.154413	−	0.129568i
$159$	−433820.	+	751397.i	−0.107924	+	0.186930i
$160$	−6.85455e6	+	3.95748e6i	−1.67348	+	0.966181i
$161$	105041.	−	595720.i	0.0251700	−	0.142746i
$162$	−3.18108e6	−	560910.i	−0.748220	−	0.131931i
$163$	−2.40788e6	−	4.17058e6i	−0.555997	−	0.963016i	−0.997825	−	0.0659157i	$-0.979003\pi$
$163$	−2.40788e6	−	4.17058e6i	−0.555997	−	0.963016i	0.441828	−	0.897100i	$-0.354330\pi$
$164$	−1.65096e6	−	953182.i	−0.374287	−	0.216095i
$165$	8.49950e6	−	1.01293e7i	1.89209	−	2.25490i
$166$	−837232.	+	2.30028e6i	−0.183030	+	0.502870i
$167$	671236.	+	1.84420e6i	0.144120	+	0.395968i	0.990659	−	0.136359i	$-0.0435401\pi$
$167$	671236.	+	1.84420e6i	0.144120	+	0.395968i	−0.846539	+	0.532327i	$0.821318\pi$
$168$	6.12115e6	−	5.13626e6i	1.29094	−	1.08323i
$169$	802099.	+	4.54893e6i	0.166176	+	0.942430i
$170$		−	2.00007e6i		−	0.407098i
$171$	−1.90474e6	−	2.10545e6i	−0.380933	−	0.421073i
$172$	−21646.1			−0.00425396
$173$	2.92123e6	−	515091.i	0.564192	−	0.0994823i	0.115724	−	0.993281i	$-0.463081\pi$
$173$	2.92123e6	−	515091.i	0.564192	−	0.0994823i	0.448468	+	0.893799i	$0.351970\pi$
$174$	712329.	+	848920.i	0.135217	+	0.161146i
$175$	−1.83329e7	+	6.67264e6i	−3.42072	+	1.24504i
$176$	138057.	+	50248.5i	0.0253232	+	0.00921690i
$177$	−2.46400e6	−	2.06755e6i	−0.444346	−	0.372851i
$178$	639773.	−	1.10812e6i	0.113440	−	0.196484i
$179$	5.56587e6	−	3.21345e6i	0.970451	−	0.560290i	0.0710773	−	0.997471i	$-0.477356\pi$
$179$	5.56587e6	−	3.21345e6i	0.970451	−	0.560290i	0.899374	+	0.437181i	$0.144023\pi$
$180$	693132.	−	3.93095e6i	0.118850	−	0.674030i
$181$	−8.04191e6	−	1.41801e6i	−1.35620	−	0.239135i	−0.552174	−	0.833729i	$-0.686202\pi$
$181$	−8.04191e6	−	1.41801e6i	−1.35620	−	0.239135i	−0.804026	+	0.594594i	$0.797313\pi$
$182$	516978.	+	895432.i	0.0857546	+	0.148531i
$183$	−1.15814e6	−	668652.i	−0.188976	−	0.109106i
$184$	−425292.	+	506843.i	−0.0682706	+	0.0813617i
$185$	3.89542e6	−	1.07026e7i	0.615232	−	1.69034i
$186$	303218.	+	833085.i	0.0471212	+	0.129465i
$187$	−2.13197e6	+	1.78893e6i	−0.326029	+	0.273571i
$188$	1.10223e6	+	6.25107e6i	0.165882	+	0.940764i
$189$		−	4.95141e6i		−	0.733405i
$190$	5.95743e6	−	5.38952e6i	0.868556	−	0.785758i
$191$	−1.59370e6			−0.228721			−0.114361	−	0.993439i	$-0.536482\pi$
$191$	−1.59370e6			−0.228721			−0.114361	+	0.993439i	$0.536482\pi$
$192$	−5.16690e6	+	911063.i	−0.730005	+	0.128720i
$193$	−907427.	−	1.08143e6i	−0.126223	−	0.150427i	0.699231	−	0.714895i	$-0.253526\pi$
$193$	−907427.	−	1.08143e6i	−0.126223	−	0.150427i	−0.825455	+	0.564468i	$0.809081\pi$
$194$	−3.42257e6	+	1.24571e6i	−0.468756	+	0.170613i
$195$	3.47463e6	+	1.26466e6i	0.468602	+	0.170557i
$196$	3.03015e6	+	2.54260e6i	0.402435	+	0.337683i
$197$	−6.00132e6	+	1.03946e7i	−0.784961	+	1.35959i	0.144061	+	0.989569i	$0.453984\pi$
$197$	−6.00132e6	+	1.03946e7i	−0.784961	+	1.35959i	−0.929022	+	0.370024i	$0.879349\pi$
$198$	2.85135e6	−	1.64623e6i	0.367328	−	0.212077i
$199$	507836.	−	2.88008e6i	0.0644413	−	0.365465i	−0.935486	−	0.353365i	$-0.885037\pi$
$199$	507836.	−	2.88008e6i	0.0644413	−	0.365465i	0.999927	−	0.0120997i	$-0.00385153\pi$
$200$	2.10148e7	+	3.70548e6i	2.62686	+	0.463186i
$201$	7.10681e6	+	1.23094e7i	0.875158	+	1.51582i
$202$	2.57121e6	+	1.48449e6i	0.311949	+	0.180104i
$203$	−2.00692e6	+	2.39176e6i	−0.239907	+	0.285910i
$204$	−793390.	+	2.17982e6i	−0.0934536	+	0.256762i
$205$	3.89422e6	+	1.06993e7i	0.452022	+	1.24192i
$206$	−1.98974e6	+	1.66959e6i	−0.227612	+	0.190989i
$207$	−93535.1	−	530464.i	−0.0105454	−	0.0598060i
$208$			41083.5i			0.00456539i
$209$	−1.10735e7	−	1.52972e6i	−1.21295	−	0.167561i
$210$	−1.84067e7			−1.98755
$211$	9.72718e6	−	1.71516e6i	1.03548	−	0.182582i	0.370023	−	0.929023i	$-0.379350\pi$
$211$	9.72718e6	−	1.71516e6i	1.03548	−	0.182582i	0.665452	+	0.746440i	$0.268239\pi$
$212$	662857.	+	789962.i	0.0695685	+	0.0829085i
$213$	1.35772e7	−	4.94171e6i	1.40499	−	0.511374i
$214$	−8.48696e6	−	3.08900e6i	−0.865986	−	0.315193i
$215$	99036.7	+	83101.7i	0.00996508	+	0.00836169i
$216$	−2.70787e6	+	4.69017e6i	−0.268700	+	0.465401i
$217$	−2.16314e6	+	1.24889e6i	−0.211692	+	0.122221i
$218$	1.12126e6	−	6.35899e6i	0.108228	−	0.613789i
$219$	−179450.	−	31641.9i	−0.0170849	−	0.00301252i
$220$	−7.85795e6	−	1.36104e7i	−0.737974	−	1.27821i
$221$	−673990.	−	389128.i	−0.0624420	−	0.0360509i
$222$	5.03329e6	−	5.99844e6i	0.460037	−	0.548251i
$223$	2.95366e6	−	8.11511e6i	0.266346	−	0.731778i	−0.732360	−	0.680917i	$-0.761581\pi$
$223$	2.95366e6	−	8.11511e6i	0.266346	−	0.731778i	0.998706	−	0.0508610i	$-0.0161965\pi$
$224$	−5.24363e6	−	1.44068e7i	−0.466539	−	1.28181i
$225$	−1.33080e7	+	1.11668e7i	−1.16833	+	0.980346i
$226$	2.17160e6	+	1.23158e7i	0.188128	+	1.06693i
$227$			6.25563e6i			0.534803i	0.963585	+	0.267401i	$0.0861650\pi$
$227$			6.25563e6i			0.534803i	−0.963585	+	0.267401i	$0.913835\pi$
$228$	−8.63074e6	+	3.51068e6i	−0.728188	+	0.296201i
$229$	1.74781e7			1.45542			0.727708	−	0.685887i	$-0.240585\pi$
$229$	1.74781e7			1.45542			0.727708	+	0.685887i	$0.240585\pi$
$230$	1.50096e6	−	264659.i	0.123363	−	0.0217522i
$231$	1.64636e7	+	1.96206e7i	1.33564	+	1.59175i
$232$	3.20906e6	−	1.16800e6i	0.256989	−	0.0935362i
$233$	−1.63682e7	−	5.95754e6i	−1.29400	−	0.470976i	−0.398960	−	0.916968i	$-0.630629\pi$
$233$	−1.63682e7	−	5.95754e6i	−1.29400	−	0.470976i	−0.895037	+	0.445992i	$0.852851\pi$
$234$	705293.	+	591811.i	0.0550455	+	0.0461887i
$235$	1.89555e7	−	3.28320e7i	1.46060	−	2.52984i
$236$	−3.31079e6	+	1.91149e6i	−0.251881	+	0.145424i
$237$	956365.	−	5.42381e6i	0.0718420	−	0.407436i
$238$	3.81530e6	+	672741.i	0.283008	+	0.0499019i
$239$	9.32617e6	+	1.61534e7i	0.683140	+	1.18323i	0.974017	+	0.226473i	$0.0727194\pi$
$239$	9.32617e6	+	1.61534e7i	0.683140	+	1.18323i	−0.290878	+	0.956760i	$0.593947\pi$
$240$	−633393.	−	365690.i	−0.0458184	−	0.0264533i
$241$	−1.75202e7	+	2.08797e7i	−1.25166	+	1.49167i	−0.451044	+	0.892502i	$0.648948\pi$
$241$	−1.75202e7	+	2.08797e7i	−1.25166	+	1.49167i	−0.800619	+	0.599173i	$0.795496\pi$
$242$	1.47658e6	−	4.05687e6i	0.104186	−	0.286250i
$243$	−4.99716e6	−	1.37296e7i	−0.348261	−	0.956838i
$244$	−1.21758e6	+	1.02167e6i	−0.0838162	+	0.0703302i
$245$	−4.10245e6	−	2.32662e7i	−0.278962	−	1.58207i
$246$			7.82801e6i			0.525831i
$247$	−657114.	−	3.05612e6i	−0.0436064	−	0.202805i
$248$	2.73201e6			0.179113
$249$	−1.66993e7	+	2.94453e6i	−1.08168	+	0.190730i
$250$	−1.98332e7	−	2.36362e7i	−1.26932	−	1.51272i
$251$	−364436.	+	132644.i	−0.0230462	+	0.00838814i	−0.353518	−	0.935428i	$-0.615015\pi$
$251$	−364436.	+	132644.i	−0.0230462	+	0.00838814i	0.330471	+	0.943816i	$0.392792\pi$
$252$	7.26546e6	+	2.64441e6i	0.454006	+	0.165245i
$253$	−1.62462e6	−	1.36322e6i	−0.100321	−	0.0841790i
$254$	−6.60009e6	+	1.14317e7i	−0.402762	+	0.697604i
$255$	1.19985e7	−	6.92737e6i	0.723616	−	0.417780i
$256$	−2.87167e6	+	1.62860e7i	−0.171165	+	0.970723i
$257$	−2.34677e7	−	4.13799e6i	−1.38252	−	0.243776i	−0.567579	−	0.823319i	$-0.692120\pi$
$257$	−2.34677e7	−	4.13799e6i	−1.38252	−	0.243776i	−0.814942	+	0.579543i	$0.803231\pi$
$258$	44442.1	+	76975.9i	0.00258783	+	0.00448225i
$259$	1.91058e7	+	1.10307e7i	1.09968	+	0.634899i
$260$	2.82490e6	−	3.36659e6i	0.160725	−	0.191544i
$261$	−950886.	+	2.61254e6i	−0.0534819	+	0.146940i
$262$	2.32420e6	+	6.38569e6i	0.129232	+	0.355062i
$263$	1.58894e6	−	1.33328e6i	0.0873455	−	0.0732916i	−0.598069	−	0.801444i	$-0.704065\pi$
$263$	1.58894e6	−	1.33328e6i	0.0873455	−	0.0732916i	0.685415	+	0.728153i	$0.259621\pi$
$264$	−4.86471e6	−	2.75891e7i	−0.264390	−	1.49943i
$265$		−	6.15908e6i		−	0.330962i
$266$	8.27712e6	+	1.31771e7i	0.439779	+	0.700124i
$267$	8.86355e6			0.465666
$268$	1.66368e7	−	2.93352e6i	0.864302	−	0.152400i
$269$	4.42372e6	+	5.27198e6i	0.227264	+	0.270843i	0.867612	−	0.497243i	$-0.165654\pi$
$269$	4.42372e6	+	5.27198e6i	0.227264	+	0.270843i	−0.640348	+	0.768085i	$0.721210\pi$
$270$	1.17231e7	−	4.26685e6i	0.595594	−	0.216779i
$271$	1.78615e7	+	6.50105e6i	0.897449	+	0.326645i	0.749230	−	0.662310i	$-0.230424\pi$
$271$	1.78615e7	+	6.50105e6i	0.897449	+	0.326645i	0.148219	+	0.988955i	$0.452646\pi$
$272$	117923.	+	98948.9i	0.00585991	+	0.00491705i
$273$	−3.58116e6	+	6.20276e6i	−0.176010	+	0.304857i
$274$	5.05468e6	−	2.91832e6i	0.245721	−	0.141867i
$275$	−1.18775e7	+	6.73604e7i	−0.571118	+	3.23897i
$276$	−1.74084e6	−	306956.i	−0.0828000	−	0.0145999i
$277$	−9.60466e6	−	1.66358e7i	−0.451900	−	0.782714i	0.546604	−	0.837391i	$-0.315920\pi$
$277$	−9.60466e6	−	1.66358e7i	−0.451900	−	0.782714i	−0.998504	+	0.0546772i	$0.982587\pi$
$278$	−3.46593e6	−	2.00105e6i	−0.161319	−	0.0931374i
$279$	−1.42967e6	+	1.70381e6i	−0.0658298	+	0.0784529i
$280$	−1.94003e7	+	5.33018e7i	−0.883758	+	2.42811i
$281$	−1.10453e7	−	3.03467e7i	−0.497803	−	1.36770i	−0.893393	−	0.449276i	$-0.851682\pi$
$281$	−1.10453e7	−	3.03467e7i	−0.497803	−	1.36770i	0.395590	−	0.918427i	$-0.370540\pi$
$282$	1.99665e7	−	1.67539e7i	0.890338	−	0.747082i
$283$	−295851.	−	1.67785e6i	−0.0130531	−	0.0740278i	0.977585	−	0.210539i	$-0.0675220\pi$
$283$	−295851.	−	1.67785e6i	−0.0130531	−	0.0740278i	−0.990638	+	0.136512i	$0.956411\pi$
$284$		−	1.71727e7i		−	0.749694i
$285$	5.29659e7	+	1.70721e7i	2.28803	+	0.737482i
$286$	3.62501e6			0.154957
$287$	−2.17196e7	+	3.82976e6i	−0.918770	+	0.162004i
$288$	−8.77530e6	−	1.04580e7i	−0.367354	−	0.437795i
$289$	1.99417e7	−	7.25818e6i	0.826168	−	0.300700i
$290$	−7.39223e6	−	2.69055e6i	−0.303097	−	0.110318i
$291$	−1.93274e7	−	1.62176e7i	−0.784320	−	0.658123i
$292$	−108287.	+	187558.i	−0.00434938	+	0.00753334i
$293$	−3.21691e7	+	1.85729e7i	−1.27890	+	0.738373i	−0.976646	−	0.214855i	$-0.931072\pi$
$293$	−3.21691e7	+	1.85729e7i	−1.27890	+	0.738373i	−0.302254	+	0.953228i	$0.597739\pi$
$294$	2.82050e6	−	1.59958e7i	0.110990	−	0.629455i
$295$	2.24862e7	+	3.96492e6i	0.875890	+	0.154443i
$296$	−1.20652e7	−	2.08975e7i	−0.465220	−	0.805784i
$297$	−1.50338e7	−	8.67974e6i	−0.573849	−	0.331312i
$298$	−7.39508e6	+	8.81311e6i	−0.279443	+	0.333028i
$299$	202836.	−	557289.i	0.00758809	−	0.0208481i
$300$	1.94990e7	+	5.35732e7i	0.722187	+	1.98419i
$301$	−191835.	+	160969.i	−0.00703442	+	0.00590258i
$302$	2.45942e6	+	1.39480e7i	0.0892918	+	0.506399i
$303$			2.05664e7i			0.739318i
$304$	23031.9	+	617879.i	0.000819800	+	0.0219929i
$305$	9.49307e6			0.334586
$306$	3.39737e6	−	599048.i	0.118571	−	0.0209073i
$307$	−2.03251e7	−	2.42225e7i	−0.702453	−	0.837151i	0.290349	−	0.956921i	$-0.406229\pi$
$307$	−2.03251e7	−	2.42225e7i	−0.702453	−	0.837151i	−0.992802	+	0.119770i	$0.961784\pi$
$308$	2.86060e7	−	1.04117e7i	0.979050	−	0.356345i
$309$	−1.69076e7	−	6.15386e6i	−0.573068	−	0.208580i
$310$	−4.82097e6	−	4.04527e6i	−0.161826	−	0.135788i
$311$	−1.32863e6	+	2.30125e6i	−0.0441695	+	0.0765039i	−0.887265	−	0.461260i	$-0.847398\pi$
$311$	−1.32863e6	+	2.30125e6i	−0.0441695	+	0.0765039i	0.843095	+	0.537764i	$0.180731\pi$
$312$	6.78444e6	−	3.91700e6i	0.223383	−	0.128970i
$313$	6.64085e6	−	3.76621e7i	0.216566	−	1.22821i	−0.661602	−	0.749855i	$-0.730123\pi$
$313$	6.64085e6	−	3.76621e7i	0.216566	−	1.22821i	0.878168	−	0.478352i	$-0.158766\pi$
$314$	−2.92674e7	−	5.16063e6i	−0.945354	−	0.166691i
$315$	−2.30893e7	−	3.99918e7i	−0.738719	−	1.27950i
$316$	−5.66888e6	−	3.27293e6i	−0.179654	−	0.103723i
$317$	−2.22023e6	+	2.64596e6i	−0.0696979	+	0.0830627i	−0.799767	−	0.600311i	$-0.795044\pi$
$317$	−2.22023e6	+	2.64596e6i	−0.0696979	+	0.0830627i	0.730069	+	0.683374i	$0.239488\pi$
$318$	1.44827e6	−	3.97909e6i	0.0450369	−	0.123738i
$319$	3.74388e6	+	1.02862e7i	0.115332	+	0.316872i
$320$	2.85305e7	−	2.39399e7i	0.870681	−	0.730588i
$321$	−1.08640e7	−	6.16127e7i	−0.328453	−	1.86275i
$322$			2.95222e6i			0.0884263i
$323$	−1.03547e7	−	5.47448e6i	−0.307276	−	0.162456i
$324$	−2.65943e7			−0.781905
$325$	−1.88365e7	+	3.32139e6i	−0.548720	+	0.0967542i
$326$	1.51075e7	+	1.80044e7i	0.436053	+	0.519667i
$327$	4.20315e7	−	1.52982e7i	1.20208	−	0.437520i
$328$	2.26681e7	+	8.25053e6i	0.642384	+	0.233809i
$329$	5.62538e7	+	4.72026e7i	1.57966	+	1.32549i
$330$	−3.22667e7	+	5.58876e7i	−0.897869	+	1.55515i
$331$	4.59394e7	−	2.65231e7i	1.26678	−	0.731376i	0.292403	−	0.956295i	$-0.405545\pi$
$331$	4.59394e7	−	2.65231e7i	1.26678	−	0.731376i	0.974377	+	0.224920i	$0.0722120\pi$
$332$	−3.49969e6	+	1.98478e7i	−0.0956348	+	0.542372i
$333$	1.93464e7	+	3.41129e6i	0.523922	+	0.0923816i
$334$	−4.78908e6	−	8.29493e6i	−0.128532	−	0.222625i
$335$	−8.73800e7	−	5.04489e7i	−2.32422	−	1.34189i
$336$	910631.	−	1.08525e6i	0.0240063	−	0.0286095i
$337$	−1.22415e7	+	3.36332e7i	−0.319848	+	0.878776i	0.670714	+	0.741716i	$0.265988\pi$
$337$	−1.22415e7	+	3.36332e7i	−0.319848	+	0.878776i	−0.990563	+	0.137060i	$0.956235\pi$
$338$	−7.71024e6	−	2.11837e7i	−0.199672	−	0.548595i
$339$	−6.63614e7	+	5.56839e7i	−1.70340	+	1.42932i
$340$	−2.85945e6	−	1.62167e7i	−0.0727520	−	0.412597i
$341$			8.75712e6i			0.220850i
$342$	1.09391e7	+	8.50520e6i	0.273466	+	0.212621i
$343$	−8.92796e6			−0.221243
$344$	269746.	−	47563.4i	0.00662642	−	0.00116842i
$345$	6.78636e6	+	8.08767e6i	0.165265	+	0.196955i
$346$	−1.36037e7	+	4.95136e6i	−0.328420	+	0.119535i
$347$	5.28703e7	+	1.92432e7i	1.26539	+	0.460563i	0.885573	−	0.464500i	$-0.153766\pi$
$347$	5.28703e7	+	1.92432e7i	1.26539	+	0.460563i	0.379814	+	0.925063i	$0.375988\pi$
$348$	6.98928e6	+	5.86470e6i	0.165842	+	0.139158i
$349$	2.57758e7	−	4.46450e7i	0.606367	−	1.05026i	−0.385466	−	0.922722i	$-0.625959\pi$
$349$	2.57758e7	−	4.46450e7i	0.606367	−	1.05026i	0.991834	−	0.127537i	$-0.0407073\pi$
$350$	8.24584e7	−	4.76074e7i	1.92323	−	1.11038i
$351$	842953.	−	4.78062e6i	0.0194931	−	0.110551i
$352$	−5.29346e7	−	9.33380e6i	−1.21370	−	0.214008i
$353$	2.24798e7	+	3.89362e7i	0.511057	+	0.885176i	0.999918	+	0.0128145i	$0.00407910\pi$
$353$	2.24798e7	+	3.89362e7i	0.511057	+	0.885176i	−0.488861	+	0.872362i	$0.662588\pi$
$354$	1.35949e7	+	7.84903e6i	0.306455	+	0.176932i
$355$	−6.59280e7	+	7.85699e7i	−1.47362	+	1.75619i
$356$	3.60307e6	−	9.89936e6i	0.0798588	−	0.219410i
$357$	9.17871e6	+	2.52183e7i	0.201733	+	0.554257i
$358$	−2.40278e7	+	2.01618e7i	−0.523680	+	0.439419i
$359$	5.98760e6	+	3.39573e7i	0.129410	+	0.733923i	0.978590	+	0.205819i	$0.0659858\pi$
$359$	5.98760e6	+	3.39573e7i	0.129410	+	0.733923i	−0.849180	+	0.528104i	$0.822903\pi$
$360$			5.05091e7i			1.08259i
$361$	−1.15960e7	−	4.55944e7i	−0.246483	−	0.969147i
$362$	3.98535e7			0.840119
$363$	2.94516e7	−	5.19312e6i	0.615729	−	0.108570i
$364$	5.47186e6	+	6.52111e6i	0.113457	+	0.135213i
$365$	1.21550e6	−	442405.i	0.0249963	−	0.00909792i
$366$	6.13302e6	+	2.23224e6i	0.125093	+	0.0455300i
$367$	4.37404e7	+	3.67026e7i	0.884881	+	0.742503i	0.967177	−	0.254105i	$-0.0817808\pi$
$367$	4.37404e7	+	3.67026e7i	0.884881	+	0.742503i	−0.0822957	+	0.996608i	$0.526225\pi$
$368$	−58652.3	+	101589.i	−0.00117691	+	0.00203846i
$369$	−1.70077e7	+	9.81940e6i	−0.338506	+	0.195437i
$370$	−9.65231e6	+	5.47410e7i	−0.190558	+	1.08071i
$371$	1.17490e7	+	2.07166e6i	0.230079	+	0.0405692i
$372$	3.64955e6	+	6.32121e6i	0.0708942	+	0.122792i
$373$	4.13947e7	+	2.38992e7i	0.797661	+	0.460530i	0.842652	−	0.538458i	$-0.180993\pi$
$373$	4.13947e7	+	2.38992e7i	0.797661	+	0.460530i	−0.0449919	+	0.998987i	$0.514326\pi$
$374$	8.73077e6	−	1.04049e7i	0.166893	−	0.198895i
$375$	7.31018e7	−	2.00846e8i	1.38623	−	3.80863i
$376$	−2.74713e7	−	7.54767e7i	−0.516791	−	1.41987i
$377$	−2.34488e6	+	1.96759e6i	−0.0437620	+	0.0367206i
$378$	4.19622e6	+	2.37979e7i	0.0776931	+	0.440620i
$379$			7.93716e7i			1.45797i	0.684532	+	0.728983i	$0.260007\pi$
$379$			7.93716e7i			1.45797i	−0.684532	+	0.728983i	$0.739993\pi$
$380$	4.05980e7	−	5.22157e7i	0.739867	−	0.951591i
$381$	−9.14391e7			−1.65332
$382$	7.65979e6	−	1.35063e6i	0.137413	−	0.0242296i
$383$	−3.12434e7	−	3.72344e7i	−0.556111	−	0.662748i	0.412607	−	0.910909i	$-0.364618\pi$
$383$	−3.12434e7	−	3.72344e7i	−0.556111	−	0.662748i	−0.968719	+	0.248161i	$0.920174\pi$
$384$	−4.29945e7	+	1.56487e7i	−0.759310	+	0.276366i
$385$	−1.70852e8	−	6.21851e7i	−2.99391	−	1.08969i
$386$	5.27784e6	+	4.42864e6i	0.0917687	+	0.0770031i
$387$	−111496.	+	193116.i	−0.00192365	+	0.00333185i
$388$	−2.59694e7	+	1.49935e7i	−0.444598	+	0.256689i
$389$	1.63687e7	−	9.28313e7i	0.278077	−	1.57705i	−0.450940	−	0.892554i	$-0.648911\pi$
$389$	1.63687e7	−	9.28313e7i	0.278077	−	1.57705i	0.729016	−	0.684496i	$-0.239978\pi$
$390$	−1.77718e7	−	3.13366e6i	−0.299598	−	0.0528272i
$391$	−1.11107e6	−	1.92442e6i	−0.0185870	−	0.0321937i
$392$	−4.33476e7	−	2.50267e7i	−0.719626	−	0.415476i
$393$	−3.02581e7	+	3.60602e7i	−0.498499	+	0.594088i
$394$	2.00349e7	−	5.50455e7i	0.327566	−	0.899980i
$395$	1.33715e7	+	3.67380e7i	0.216965	+	0.596108i
$396$	2.07653e7	−	1.74242e7i	0.334390	−	0.280587i
$397$	4.49545e6	+	2.54950e7i	0.0718459	+	0.407458i	0.999427	+	0.0338373i	$0.0107728\pi$
$397$	4.49545e6	+	2.54950e7i	0.0718459	+	0.407458i	−0.927581	+	0.373621i	$0.878116\pi$
$398$			1.42729e7i			0.226393i
$399$	−5.03819e7	+	9.52945e7i	−0.793150	+	1.50020i
$400$	3.78330e6			0.0591140
$401$	3.94647e7	−	6.95868e6i	0.612034	−	0.107918i	0.140965	−	0.990015i	$-0.454980\pi$
$401$	3.94647e7	−	6.95868e6i	0.612034	−	0.107918i	0.471069	+	0.882097i	$0.343868\pi$
$402$	−4.45893e7	−	5.31395e7i	−0.686361	−	0.817974i
$403$	−2.30114e6	+	837547.i	−0.0351583	+	0.0127966i
$404$	2.29699e7	+	8.36035e6i	0.348349	+	0.126789i
$405$	1.21676e8	+	1.02099e8i	1.83164	+	1.53693i
$406$	7.61889e6	−	1.31963e7i	0.113845	−	0.197185i
$407$	6.69842e7	−	3.86734e7i	0.993549	−	0.573626i
$408$	5.09717e6	−	2.89075e7i	0.0750497	−	0.425628i
$409$	4.19905e7	+	7.40406e6i	0.613735	+	0.108218i	0.471870	−	0.881668i	$-0.343579\pi$
$409$	4.19905e7	+	7.40406e6i	0.613735	+	0.108218i	0.141865	+	0.989886i	$0.454690\pi$
$410$	−2.77842e7	−	4.81237e7i	−0.403131	−	0.698244i
$411$	3.50144e7	+	2.02155e7i	0.504337	+	0.291179i
$412$	−1.37460e7	+	1.63819e7i	−0.196555	+	0.234246i
$413$	−1.51268e7	+	4.15606e7i	−0.214732	+	0.589972i
$414$	899114.	+	2.47029e6i	0.0126711	+	0.0348135i
$415$	9.22098e7	−	7.73732e7i	1.29013	−	1.08255i
$416$	−2.61009e6	−	1.48025e7i	−0.0362556	−	0.205616i
$417$		−	2.77230e7i		−	0.382325i
$418$	5.45187e7	−	2.03222e6i	0.746477	−	0.0278254i
$419$	2.15719e7			0.293256			0.146628	−	0.989192i	$-0.453158\pi$
$419$	2.15719e7			0.293256			0.146628	+	0.989192i	$0.453158\pi$
$420$	−1.49243e8	+	2.63156e7i	−2.01440	+	0.355194i
$421$	−3.16086e7	−	3.76697e7i	−0.423603	−	0.504831i	0.511462	−	0.859306i	$-0.329104\pi$
$421$	−3.16086e7	−	3.76697e7i	−0.423603	−	0.504831i	−0.935065	+	0.354475i	$0.884660\pi$
$422$	−4.52981e7	+	1.64872e7i	−0.602758	+	0.219386i
$423$	6.14466e7	+	2.23647e7i	0.811852	+	0.295490i
$424$	−9.99610e6	−	8.38773e6i	−0.131139	−	0.110039i
$425$	−3.58340e7	+	6.20664e7i	−0.466798	+	0.808518i
$426$	−6.10682e7	+	3.52577e7i	−0.789926	+	0.456064i
$427$	−3.19307e6	+	1.81088e7i	−0.0410134	+	0.232598i
$428$	−7.32291e7	−	1.29123e7i	−0.934011	−	0.164691i
$429$	1.25554e7	+	2.17467e7i	0.159023	+	0.275436i
$430$	−546426.	−	315479.i	−0.00687268	−	0.00396794i
$431$	−9.58884e6	+	1.14275e7i	−0.119766	+	0.142732i	−0.822596	−	0.568626i	$-0.807475\pi$
$431$	−9.58884e6	+	1.14275e7i	−0.119766	+	0.142732i	0.702830	+	0.711358i	$0.251920\pi$
$432$	−328402.	+	902276.i	−0.00407337	+	0.0111915i
$433$	3.32766e7	+	9.14267e7i	0.409897	+	1.12618i	0.957245	+	0.289278i	$0.0934153\pi$
$433$	3.32766e7	+	9.14267e7i	0.409897	+	1.12618i	−0.547348	+	0.836905i	$0.684362\pi$
$434$	9.33827e6	−	7.83574e6i	0.114234	−	0.0958541i
$435$	−9.46264e6	−	5.36653e7i	−0.114959	−	0.651967i
$436$		−	5.31622e7i		−	0.641421i
$437$	2.73815e6	−	8.49510e6i	0.0328106	−	0.101794i
$438$	889305.			0.0105835
$439$	7.16489e7	−	1.26336e7i	0.846868	−	0.149326i	0.266657	−	0.963792i	$-0.414081\pi$
$439$	7.16489e7	−	1.26336e7i	0.846868	−	0.149326i	0.580212	+	0.814466i	$0.302970\pi$
$440$	1.27829e8	+	1.52341e8i	1.50063	+	1.78838i
$441$	3.82917e7	−	1.39370e7i	0.446467	−	0.162501i
$442$	3.56917e6	+	1.29907e6i	0.0413334	+	0.0150441i
$443$	−7.42825e7	−	6.23304e7i	−0.854428	−	0.716950i	0.106332	−	0.994331i	$-0.466089\pi$
$443$	−7.42825e7	−	6.23304e7i	−0.854428	−	0.716950i	−0.960760	+	0.277380i	$0.910534\pi$
$444$	3.22344e7	−	5.58317e7i	0.368274	−	0.637869i
$445$	−5.44898e7	+	3.14597e7i	−0.618351	+	0.357005i
$446$	−7.31876e6	+	4.15067e7i	−0.0824960	+	0.467858i
$447$	−7.84836e7	−	1.38388e7i	−0.878732	−	0.154944i
$448$	3.60709e7	+	6.24766e7i	0.401165	+	0.694838i
$449$	−2.43188e7	−	1.40405e7i	−0.268660	−	0.155111i	0.359618	−	0.933099i	$-0.382907\pi$
$449$	−2.43188e7	−	1.40405e7i	−0.268660	−	0.155111i	−0.628279	+	0.777988i	$0.716240\pi$
$450$	5.44987e7	−	6.49490e7i	0.598065	−	0.712746i
$451$	−2.64460e7	+	7.26599e7i	−0.288291	+	0.792073i
$452$	3.52149e7	+	9.67523e7i	0.381339	+	1.04772i
$453$	−7.51568e7	+	6.30640e7i	−0.808488	+	0.678402i
$454$	−5.30152e6	−	3.00664e7i	−0.0566543	−	0.321302i
$455$		−	5.08430e7i		−	0.539755i
$456$	9.98392e7	−	6.27134e7i	1.05295	−	0.661403i
$457$	1.41535e8			1.48291			0.741455	−	0.671003i	$-0.234136\pi$
$457$	1.41535e8			1.48291			0.741455	+	0.671003i	$0.234136\pi$
$458$	−8.40048e7	+	1.48123e7i	−0.874395	+	0.154179i
$459$	−1.16917e7	−	1.39336e7i	−0.120903	−	0.144087i
$460$	1.17915e7	−	4.29175e6i	0.121142	−	0.0440921i
$461$	9.21191e7	+	3.35286e7i	0.940258	+	0.342226i	0.766268	−	0.642521i	$-0.222112\pi$
$461$	9.21191e7	+	3.35286e7i	0.940258	+	0.342226i	0.173990	+	0.984747i	$0.444334\pi$
$462$	−9.57570e7	−	8.03496e7i	−0.971056	−	0.814813i
$463$	−7.67100e7	+	1.32866e8i	−0.772875	+	1.33866i	0.163107	+	0.986608i	$0.447849\pi$
$463$	−7.67100e7	+	1.32866e8i	−0.772875	+	1.33866i	−0.935981	+	0.352050i	$0.885485\pi$
$464$	524346.	−	302731.i	0.00524885	−	0.00303043i
$465$	7.57012e6	−	4.29323e7i	0.0752912	−	0.426998i
$466$	8.37192e7	+	1.47620e7i	0.827308	+	0.145877i
$467$	−2.61864e7	−	4.53562e7i	−0.257114	−	0.445335i	0.708354	−	0.705858i	$-0.249438\pi$
$467$	−2.61864e7	−	4.53562e7i	−0.257114	−	0.445335i	−0.965468	+	0.260523i	$0.916105\pi$
$468$	6.56466e6	+	3.79011e6i	0.0640434	+	0.0369755i
$469$	1.25626e8	−	1.49716e8i	1.21776	−	1.45127i
$470$	−6.32815e7	+	1.73864e8i	−0.609513	+	1.67462i
$471$	−7.04103e7	−	1.93451e8i	−0.673866	−	1.85143i
$472$	3.70578e7	−	3.10951e7i	0.352414	−	0.295710i
$473$	152459.	+	864636.i	0.00144068	+	0.00817052i
$474$			2.68789e7i			0.252393i
$475$	−2.81432e8	+	6.05123e7i	−2.62598	+	0.564628i
$476$	3.18965e7			0.295748
$477$	1.04620e7	−	1.84473e6i	0.0963957	−	0.0169972i
$478$	−5.85140e7	−	6.97342e7i	−0.535767	−	0.638502i
$479$	−1.12365e8	+	4.08975e7i	−1.02241	+	0.372126i	−0.798185	−	0.602412i	$-0.794206\pi$
$479$	−1.12365e8	+	4.08975e7i	−1.02241	+	0.372126i	−0.224222	+	0.974538i	$0.571984\pi$
$480$	2.51446e8	+	9.15190e7i	2.27364	+	0.827537i
$481$	1.65688e7	+	1.39029e7i	0.148887	+	0.124931i
$482$	6.65120e7	−	1.15202e8i	0.593962	−	1.02877i
$483$	−1.77105e7	+	1.02252e7i	−0.157178	+	0.0907465i
$484$	6.17222e6	−	3.50044e7i	0.0544384	−	0.308736i
$485$	1.76379e8	+	3.11004e7i	1.54604	+	0.272609i
$486$	3.56533e7	+	6.17534e7i	0.310593	+	0.537962i
$487$	−1.61918e8	−	9.34834e7i	−1.40187	−	0.809371i	−0.407287	−	0.913300i	$-0.633525\pi$
$487$	−1.61918e8	−	9.34834e7i	−1.40187	−	0.809371i	−0.994585	+	0.103930i	$0.966858\pi$
$488$	1.29281e7	−	1.54071e7i	0.111244	−	0.132575i
$489$	−5.56837e7	+	1.52990e8i	−0.476213	+	1.30839i
$490$	3.94352e7	+	1.08347e8i	0.335193	+	0.920937i
$491$	1.42496e8	−	1.19568e8i	1.20381	−	1.01012i	0.204296	−	0.978909i	$-0.434510\pi$
$491$	1.42496e8	−	1.19568e8i	1.20381	−	1.01012i	0.999513	−	0.0312060i	$-0.00993480\pi$
$492$	1.11915e7	+	6.34700e7i	0.0939706	+	0.532934i
$493$			1.14695e7i			0.0957198i
$494$	5.74828e6	+	1.41317e7i	0.0476823	+	0.117223i
$495$	−1.61901e8			−1.33485
$496$	477012.	−	84110.2i	0.00390917	−	0.000689292i
$497$	−1.27703e8	−	1.52191e8i	−1.04024	−	1.23971i
$498$	7.77662e7	−	2.83046e7i	0.629655	−	0.229176i
$499$	−1.83133e8	−	6.66550e7i	−1.47389	−	0.536452i	−0.524737	−	0.851265i	$-0.675836\pi$
$499$	−1.83133e8	−	6.66550e7i	−1.47389	−	0.536452i	−0.949154	+	0.314812i	$0.898058\pi$
$500$	−1.94600e8	−	1.63289e8i	−1.55680	−	1.30631i
$501$	3.31745e7	−	5.74599e7i	0.263810	−	0.456932i
$502$	1.63917e6	−	946377.i	0.0129573	−	0.00748088i
$503$	−1.72836e7	+	9.80202e7i	−0.135810	+	0.770214i	0.838483	+	0.544928i	$0.183443\pi$
$503$	−1.72836e7	+	9.80202e7i	−0.135810	+	0.770214i	−0.974293	+	0.225286i	$0.927668\pi$
$504$	−9.63503e7	−	1.69892e7i	−0.752595	−	0.132703i
$505$	−7.29972e7	−	1.26435e8i	−0.566803	−	0.981731i
$506$	8.96370e6	+	5.17519e6i	0.0691888	+	0.0399462i
$507$	1.00377e8	−	1.19625e8i	0.770216	−	0.917907i
$508$	−3.71704e7	+	1.02125e8i	−0.283535	+	0.779005i
$509$	−2.76932e7	−	7.60863e7i	−0.210000	−	0.576970i	0.789315	−	0.613989i	$-0.210436\pi$
$509$	−2.76932e7	−	7.60863e7i	−0.210000	−	0.576970i	−0.999315	+	0.0370189i	$0.988214\pi$
$510$	−5.17977e7	+	4.34635e7i	−0.390481	+	0.327653i
$511$	435082.	+	2.46747e6i	0.00326068	+	0.0184922i
$512$			5.90648e6i			0.0440067i
$513$	9.99759e6	−	7.23711e7i	0.0740531	−	0.536060i
$514$	1.16300e8			0.856424
$515$	1.25784e8	−	2.21790e7i	0.920878	−	0.162376i
$516$	470389.	+	560588.i	0.00342380	+	0.00408032i
$517$	2.41931e8	−	8.80557e7i	1.75073	−	0.637215i
$518$	−1.01176e8	−	3.68252e7i	−0.727930	−	0.264945i
$519$	−7.68208e7	−	6.44603e7i	−0.549511	−	0.461095i
$520$	−2.78054e7	+	4.81605e7i	−0.197752	+	0.342516i
$521$	−1.96718e8	+	1.13575e8i	−1.39102	+	0.803103i	−0.993428	−	0.114461i	$-0.963486\pi$
$521$	−1.96718e8	+	1.13575e8i	−1.39102	+	0.803103i	−0.397587	+	0.917564i	$0.630152\pi$
$522$	2.35616e6	−	1.33625e7i	0.0165651	−	0.0939454i
$523$	1.98066e8	+	3.49243e7i	1.38454	+	0.244131i	0.815774	−	0.578371i	$-0.196312\pi$
$523$	1.98066e8	+	3.49243e7i	1.38454	+	0.244131i	0.568762	+	0.822502i	$0.307423\pi$
$524$	2.79742e7	+	4.84527e7i	0.194430	+	0.336763i
$525$	5.71199e8	+	3.29782e8i	3.94738	+	2.27902i
$526$	−6.50699e6	+	7.75473e6i	−0.0447119	+	0.0532855i
$527$	−3.13823e6	+	8.62222e6i	−0.0214414	+	0.0589098i
$528$	−1.69877e6	−	4.66733e6i	−0.0115407	−	0.0317078i
$529$	−1.12105e8	+	9.40672e7i	−0.757282	+	0.635435i
$530$	5.21969e6	+	2.96023e7i	0.0350604	+	0.198838i
$531$			3.93831e7i			0.263043i
$532$	8.59503e7	+	9.50072e7i	0.570837	+	0.630989i
$533$	−2.16225e7			−0.142798
$534$	−4.26008e7	+	7.51168e6i	−0.279766	+	0.0493302i
$535$	2.85472e8	+	3.40212e8i	1.86424	+	2.22171i
$536$	−2.00876e8	+	7.31129e7i	−1.30447	+	0.474788i
$537$	−2.04173e8	−	7.43130e7i	−1.31849	−	0.479890i
$538$	−2.57296e7	−	2.15897e7i	−0.165229	−	0.138643i
$539$	8.02200e7	−	1.38945e8i	0.512291	−	0.887314i
$540$	8.89513e7	−	5.13561e7i	0.564899	−	0.326145i
$541$	3.54575e6	−	2.01089e7i	0.0223932	−	0.126998i	−0.971562	−	0.236786i	$-0.923906\pi$
$541$	3.54575e6	−	2.01089e7i	0.0223932	−	0.126998i	0.993955	+	0.109788i	$0.0350171\pi$
$542$	−9.13571e7	−	1.61087e7i	−0.573778	−	0.101173i
$543$	1.38035e8	+	2.39083e8i	0.862163	+	1.49331i
$544$	−4.87743e7	−	2.81598e7i	−0.302966	−	0.174918i
$545$	−2.04096e8	+	2.43232e8i	−1.26079	+	1.50256i
$546$	1.19554e7	−	3.28472e7i	0.0734491	−	0.201800i
$547$	−8.17421e7	−	2.24584e8i	−0.499440	−	1.37220i	−0.891817	−	0.452396i	$-0.850569\pi$
$547$	−8.17421e7	−	2.24584e8i	−0.499440	−	1.37220i	0.392377	−	0.919805i	$-0.371653\pi$
$548$	3.68114e7	−	3.08885e7i	0.223687	−	0.187696i
$549$	2.84330e6	+	1.61252e7i	0.0171833	+	0.0974511i
$550$		−	3.33820e8i		−	2.00643i
$551$	−3.41630e7	+	3.09063e7i	−0.204221	+	0.184753i
$552$	2.23682e7			0.132988
$553$	−7.45784e7	+	1.31502e7i	−0.440999	+	0.0777601i
$554$	6.02612e7	+	7.18165e7i	0.354412	+	0.422372i
$555$	−3.61826e8	+	1.31694e8i	−2.11651	+	0.770347i
$556$	−3.09628e7	−	1.12695e7i	−0.180142	−	0.0655664i
$557$	4.98120e7	+	4.17972e7i	0.288249	+	0.241870i	0.775433	−	0.631430i	$-0.217532\pi$
$557$	4.98120e7	+	4.17972e7i	0.288249	+	0.241870i	−0.487184	+	0.873299i	$0.661976\pi$
$558$	5.42745e6	−	9.40063e6i	0.0312387	−	0.0541071i
$559$	−212622.	+	122758.i	−0.00121723	+	0.000702769i
$560$	−1.74631e6	+	9.90382e6i	−0.00994392	+	0.0563948i
$561$	9.26593e7	+	1.63383e7i	0.524808	+	0.0925378i
$562$	7.88050e7	+	1.36494e8i	0.443961	+	0.768963i
$563$	1.56608e8	+	9.04177e7i	0.877584	+	0.506674i	0.869861	−	0.493297i	$-0.164208\pi$
$563$	1.56608e8	+	9.04177e7i	0.877584	+	0.506674i	0.00772312	+	0.999970i	$0.497542\pi$
$564$	1.37937e8	−	1.64387e8i	0.768854	−	0.916285i
$565$	2.10325e8	−	5.77862e8i	1.16612	−	3.20390i
$566$	2.84389e6	+	7.81353e6i	0.0156843	+	0.0430921i
$567$	−2.35688e8	+	1.97766e8i	−1.29297	+	1.08493i
$568$	3.77341e7	+	2.14001e8i	0.205915	+	1.16780i
$569$		−	3.38287e8i		−	1.83632i	−0.396208	−	0.918161i	$-0.629674\pi$
$569$		−	3.38287e8i		−	1.83632i	0.396208	−	0.918161i	$-0.370326\pi$
$570$	−2.69038e8	−	3.71658e7i	−1.45274	−	0.200687i
$571$	−5.94377e7			−0.319267			−0.159633	−	0.987176i	$-0.551031\pi$
$571$	−5.94377e7			−0.319267			−0.159633	+	0.987176i	$0.551031\pi$
$572$	2.93918e7	−	5.18257e6i	0.157050	−	0.0276922i
$573$	3.46326e7	+	4.12736e7i	0.184086	+	0.219386i
$574$	1.01145e8	−	3.68139e7i	0.534823	−	0.194660i
$575$	−5.13195e7	−	1.86788e7i	−0.269947	−	0.0982529i
$576$	4.92101e7	+	4.12922e7i	0.257506	+	0.216073i
$577$	−2.08271e7	+	3.60737e7i	−0.108418	+	0.187786i	−0.915130	−	0.403160i	$-0.867912\pi$
$577$	−2.08271e7	+	3.60737e7i	−0.108418	+	0.187786i	0.806711	+	0.590946i	$0.201245\pi$
$578$	−8.96944e7	+	5.17851e7i	−0.464496	+	0.268177i
$579$	−8.28753e6	+	4.70009e7i	−0.0426962	+	0.242142i
$580$	−6.37833e7	−	1.12467e7i	−0.326906	−	0.0576423i
$581$	1.16580e8	+	2.01923e8i	0.594424	+	1.02957i
$582$	1.06637e8	+	6.15669e7i	0.540927	+	0.312304i
$583$	2.68858e7	−	3.20412e7i	0.135680	−	0.161698i
$584$	937306.	−	2.57523e6i	0.00470590	−	0.0129294i
$585$	−1.54845e7	−	4.25432e7i	−0.0773444	−	0.212502i
$586$	1.38874e8	−	1.16529e8i	0.690126	−	0.579085i
$587$	−1.79255e7	−	1.01661e8i	−0.0886251	−	0.502618i	−0.996515	−	0.0834100i	$-0.973419\pi$
$587$	−1.79255e7	−	1.01661e8i	−0.0886251	−	0.502618i	0.907890	−	0.419208i	$-0.137692\pi$
$588$		−	1.33728e8i		−	0.657793i
$589$	−3.41387e7	+	1.38864e7i	−0.167071	+	0.0679585i
$590$	−1.11435e8			−0.542584
$591$	3.99613e8	−	7.04625e7i	1.93587	−	0.341347i
$592$	−2.74996e6	−	3.27728e6i	−0.0132544	−	0.0157960i
$593$	−9.56750e7	+	3.48228e7i	−0.458812	+	0.166994i	−0.561077	−	0.827763i	$-0.689613\pi$
$593$	−9.56750e7	+	3.48228e7i	−0.458812	+	0.166994i	0.102266	+	0.994757i	$0.467391\pi$
$594$	7.96125e7	+	2.89766e7i	0.379859	+	0.138257i
$595$	−1.45935e8	−	1.22454e8i	−0.692803	−	0.581331i
$596$	−4.73599e7	+	8.20298e7i	−0.223703	+	0.387465i
$597$	−8.56239e7	+	4.94350e7i	−0.402413	+	0.232333i
$598$	−502601.	+	2.85039e6i	−0.00235028	+	0.0133291i
$599$	5.79890e7	+	1.02250e7i	0.269814	+	0.0475756i	0.306918	−	0.951736i	$-0.400702\pi$
$599$	5.79890e7	+	1.02250e7i	0.269814	+	0.0475756i	−0.0371039	+	0.999311i	$0.511813\pi$
$600$	−3.60708e8	−	6.24765e8i	−1.66994	−	2.89243i
$601$	−3.36881e8	−	1.94498e8i	−1.55186	−	0.895967i	−0.997991	−	0.0633629i	$-0.979817\pi$
$601$	−3.36881e8	−	1.94498e8i	−1.55186	−	0.895967i	−0.553869	−	0.832604i	$-0.686849\pi$
$602$	785598.	−	936239.i	0.00360090	−	0.00429138i
$603$	5.95222e7	−	1.63536e8i	0.271473	−	0.745867i
$604$	3.98822e7	+	1.09576e8i	0.180996	+	0.497282i
$605$	−1.62625e8	+	1.36459e8i	−0.734383	+	0.616220i
$606$	−1.74296e7	−	9.88483e7i	−0.0783196	−	0.444172i
$607$			2.74255e8i			1.22627i	0.789976	+	0.613137i	$0.210093\pi$
$607$			2.74255e8i			1.22627i	−0.789976	+	0.613137i	$0.789907\pi$
$608$	−4.75530e7	−	2.21161e8i	−0.211577	−	0.984004i
$609$	1.05554e8			0.467328
$610$	−4.56265e7	+	8.04518e6i	−0.201015	+	0.0354443i
$611$	4.62775e7	+	5.51513e7i	0.202883	+	0.241787i
$612$	2.66897e7	−	9.71424e6i	0.116436	−	0.0423794i
$613$	−1.03921e8	−	3.78240e7i	−0.451149	−	0.164205i	0.106445	−	0.994319i	$-0.466053\pi$
$613$	−1.03921e8	−	3.78240e7i	−0.451149	−	0.164205i	−0.557594	+	0.830114i	$0.688275\pi$
$614$	1.18216e8	+	9.91953e7i	0.510708	+	0.428535i
$615$	1.92464e8	−	3.33358e8i	0.827418	−	1.43313i
$616$	−3.33600e8	+	1.92604e8i	−1.42720	+	0.823992i
$617$	2.79603e6	−	1.58571e7i	0.0119038	−	0.0675099i	−0.978277	−	0.207301i	$-0.933532\pi$
$617$	2.79603e6	−	1.58571e7i	0.0119038	−	0.0675099i	0.990181	+	0.139791i	$0.0446431\pi$
$618$	8.64780e7	+	1.52484e7i	0.366387	+	0.0646040i
$619$	1.62916e8	+	2.82180e8i	0.686899	+	1.18974i	0.972836	+	0.231496i	$0.0743620\pi$
$619$	1.62916e8	+	2.82180e8i	0.686899	+	1.18974i	−0.285936	+	0.958249i	$0.592305\pi$
$620$	−4.48721e7	−	2.59069e7i	−0.188279	−	0.108703i
$621$	8.90939e6	−	1.06178e7i	0.0372026	−	0.0443363i
$622$	4.43552e6	−	1.21865e7i	0.0184320	−	0.0506416i
$623$	−4.16839e7	−	1.14526e8i	−0.172387	−	0.473629i
$624$	1.06398e6	−	892784.i	0.00437904	−	0.00367445i
$625$	1.49594e8	+	8.48387e8i	0.612735	+	3.47499i
$626$			1.86643e8i			0.760832i
$627$	2.01020e8	+	3.20022e8i	0.815523	+	1.29831i
$628$	−2.44680e8			−0.987913
$629$	7.98115e7	−	1.40729e7i	0.320711	−	0.0565500i
$630$	1.44866e8	+	1.72645e8i	0.579356	+	0.690449i
$631$	−1.41774e8	+	5.16015e7i	−0.564298	+	0.205388i	−0.608388	−	0.793640i	$-0.708184\pi$
$631$	−1.41774e8	+	5.16015e7i	−0.564298	+	0.205388i	0.0440896	+	0.999028i	$0.485961\pi$
$632$	7.78353e7	+	2.83297e7i	0.308337	+	0.112225i
$633$	−2.55800e8	−	2.14642e8i	−1.00853	−	0.846258i
$634$	8.42866e6	−	1.45989e7i	0.0330743	−	0.0572864i
$635$	5.62133e8	−	3.24548e8i	2.19542	−	1.26753i
$636$	6.05388e6	−	3.43333e7i	0.0235322	−	0.133458i
$637$	4.41836e7	+	7.79075e6i	0.170940	+	0.0301412i
$638$	−2.67116e7	−	4.62658e7i	−0.102858	−	0.178155i
$639$	−1.53207e8	−	8.84541e7i	−0.587187	−	0.339012i
$640$	2.08772e8	−	2.48804e8i	0.796400	−	0.949113i
$641$	−6.81689e7	+	1.87292e8i	−0.258828	+	0.711125i	0.740412	+	0.672153i	$0.234630\pi$
$641$	−6.81689e7	+	1.87292e8i	−0.258828	+	0.711125i	−0.999240	+	0.0389718i	$0.987592\pi$
$642$	1.04431e8	+	2.86922e8i	0.394661	+	1.08432i
$643$	1.98958e7	−	1.66945e7i	0.0748390	−	0.0627974i	−0.604601	−	0.796529i	$-0.706667\pi$
$643$	1.98958e7	−	1.66945e7i	0.0748390	−	0.0627974i	0.679440	+	0.733731i	$0.262223\pi$
$644$	4.22070e6	+	2.39368e7i	0.0158026	+	0.0896208i
$645$		−	4.37072e6i		−	0.0162882i
$646$	5.44071e7	+	1.75366e7i	0.201817	+	0.0650500i
$647$	−6.47574e7			−0.239098			−0.119549	−	0.992828i	$-0.538145\pi$
$647$	−6.47574e7			−0.239098			−0.119549	+	0.992828i	$0.538145\pi$
$648$	3.31409e8	−	5.84364e7i	1.21798	−	0.214762i
$649$	9.96716e7	+	1.18784e8i	0.364617	+	0.434534i
$650$	8.77191e7	−	3.19271e7i	0.319414	−	0.116257i
$651$	7.93506e7	+	2.88813e7i	0.287612	+	0.104682i
$652$	1.48233e8	+	1.24382e8i	0.534812	+	0.448760i
$653$	−1.45435e8	+	2.51901e8i	−0.522311	+	0.904669i	0.477352	+	0.878712i	$0.341597\pi$
$653$	−1.45435e8	+	2.51901e8i	−0.522311	+	0.904669i	−0.999663	+	0.0259566i	$0.991737\pi$
$654$	−1.89051e8	+	1.09149e8i	−0.675842	+	0.390198i
$655$	5.80258e7	−	3.29081e8i	0.206489	−	1.17106i
$656$	4.21189e6	+	742670.i	0.0149199	+	0.00263078i
$657$	1.11554e6	+	1.93217e6i	0.00393358	+	0.00681317i
$658$	−3.10375e8	−	1.79195e8i	−1.08946	−	0.628998i
$659$	3.98006e7	−	4.74325e7i	0.139070	−	0.165737i	−0.692014	−	0.721884i	$-0.743276\pi$
$659$	3.98006e7	−	4.74325e7i	0.139070	−	0.165737i	0.831084	+	0.556147i	$0.187721\pi$
$660$	−1.81720e8	+	4.99271e8i	−0.632077	+	1.73662i
$661$	−6.77420e7	−	1.86120e8i	−0.234560	−	0.644448i	−1.00000		0.000940097i	$-0.999701\pi$
$661$	−6.77420e7	−	1.86120e8i	−0.234560	−	0.644448i	0.765440	−	0.643507i	$-0.222521\pi$
$662$	−1.98320e8	+	1.66410e8i	−0.683586	+	0.573597i
$663$	4.56882e6	+	2.59111e7i	0.0156770	+	0.0889088i
$664$		−	2.55026e8i		−	0.871124i
$665$	−2.85031e7	−	7.64657e8i	−0.0969230	−	2.60017i
$666$	−9.58753e7			−0.324552
$667$	−8.60727e6	+	1.51769e6i	−0.0290060	+	0.00511454i
$668$	−5.06892e7	−	6.04090e7i	−0.170054	−	0.202662i
$669$	−2.74350e8	+	9.98553e7i	−0.916277	+	0.333498i
$670$	4.62728e8	+	1.68419e8i	1.53851	+	0.559974i
$671$	4.93856e7	+	4.14394e7i	0.163468	+	0.137166i
$672$	−2.59156e8	+	4.48872e8i	−0.853992	+	1.47916i
$673$	1.91069e8	−	1.10314e8i	0.626822	−	0.361896i	−0.152698	−	0.988273i	$-0.548796\pi$
$673$	1.91069e8	−	1.10314e8i	0.626822	−	0.361896i	0.779520	+	0.626377i	$0.215463\pi$
$674$	3.03327e7	−	1.72025e8i	0.0990675	−	0.561840i
$675$	−4.40238e8	−	7.76258e7i	−1.43145	−	0.252403i
$676$	−9.28009e7	−	1.60736e8i	−0.300408	−	0.520323i
$677$	4.73057e8	+	2.73119e8i	1.52457	+	0.880210i	0.999576	+	0.0291034i	$0.00926522\pi$
$677$	4.73057e8	+	2.73119e8i	1.52457	+	0.880210i	0.524993	+	0.851107i	$0.324068\pi$
$678$	2.71762e8	−	3.23873e8i	0.871965	−	1.03917i
$679$	−1.18653e8	+	3.25996e8i	−0.379026	+	1.04137i
$680$	7.12668e7	+	1.95804e8i	0.226653	+	0.622723i
$681$	1.62008e8	−	1.35941e8i	0.512974	−	0.430436i
$682$	−7.42147e6	−	4.20893e7i	−0.0233958	−	0.132684i
$683$		−	1.03373e8i		−	0.324449i	−0.986754	−	0.162224i	$-0.948133\pi$
$683$		−	1.03373e8i		−	0.324449i	0.986754	−	0.162224i	$-0.0518668\pi$
$684$	1.00854e8	+	5.33214e7i	0.315157	+	0.166622i
$685$	−2.87007e8			−0.892936
$686$	4.29104e7	−	7.56625e6i	0.132920	−	0.0234374i
$687$	−3.79815e8	−	4.52646e8i	−1.17139	−	1.39601i
$688$	45633.6	−	16609.3i	0.000140126	−	5.10017e-5i
$689$	1.09910e7	+	4.00040e6i	0.0336031	+	0.0122305i
$690$	−3.94714e7	−	3.31204e7i	−0.120153	−	0.100820i
$691$	−6.96582e7	+	1.20652e8i	−0.211124	+	0.365678i	−0.952067	−	0.305891i	$-0.901046\pi$
$691$	−6.96582e7	+	1.20652e8i	−0.211124	+	0.365678i	0.740942	+	0.671569i	$0.234379\pi$
$692$	−1.03221e8	+	5.95948e7i	−0.311495	+	0.179841i
$693$	5.44566e7	−	3.08839e8i	0.163625	−	0.927966i
$694$	−2.70418e8	−	4.76821e7i	−0.809017	−	0.142652i
$695$	9.83983e7	+	1.70431e8i	0.293112	+	0.507684i
$696$	−9.99847e7	−	5.77262e7i	−0.296555	−	0.171216i
$697$	−5.20773e7	+	6.20633e7i	−0.153798	+	0.183289i
$698$	−8.60503e7	+	2.36421e8i	−0.253038	+	0.695217i
$699$	2.01408e8	+	5.53365e8i	0.589720	+	1.62024i
$700$	6.00515e8	−	5.03892e8i	1.75077	−	1.46907i
$701$	−6.49276e7	−	3.68222e8i	−0.188484	−	1.06895i	−0.921396	−	0.388624i	$-0.872951\pi$
$701$	−6.49276e7	−	3.68222e8i	−0.188484	−	1.06895i	0.732912	−	0.680323i	$-0.238161\pi$
$702$			2.36915e7i			0.0684826i
$703$	2.56983e8	+	1.99805e8i	0.739670	+	0.575097i
$704$	2.52927e8			0.724897
$705$	−1.26220e9	+	2.22560e8i	−3.60215	+	0.635156i
$706$	−1.41042e8	−	1.68088e8i	−0.400807	−	0.477663i
$707$	2.65738e8	−	9.67207e7i	0.751961	−	0.273691i
$708$	1.21450e8	+	4.42042e7i	0.342214	+	0.124556i
$709$	4.07116e7	+	3.41611e7i	0.114230	+	0.0958503i	0.698113	−	0.715987i	$-0.254023\pi$
$709$	4.07116e7	+	3.41611e7i	0.114230	+	0.0958503i	−0.583884	+	0.811837i	$0.698468\pi$
$710$	2.50283e8	−	4.33503e8i	0.699288	−	1.21120i
$711$	−5.83991e7	+	3.37168e7i	−0.162479	+	0.0938074i
$712$	−2.31481e7	+	1.31280e8i	−0.0641321	+	0.363711i
$713$	−6.88583e6	−	1.21416e6i	−0.0189971	−	0.00334970i
$714$	−6.54875e7	−	1.13428e8i	−0.179914	−	0.311619i
$715$	−1.54372e8	−	8.91268e7i	−0.422329	−	0.243832i
$716$	−1.65995e8	+	1.97825e8i	−0.452225	+	0.538941i
$717$	2.15673e8	−	5.92557e8i	0.585111	−	1.60758i
$718$	−5.75563e7	−	1.58135e8i	−0.155496	−	0.427222i
$719$	−6.92179e7	+	5.80807e7i	−0.186222	+	0.156259i	−0.731133	−	0.682235i	$-0.761008\pi$
$719$	−6.92179e7	+	5.80807e7i	−0.186222	+	0.156259i	0.544911	+	0.838494i	$0.316564\pi$
$720$	1.55502e6	+	8.81895e6i	0.00416618	+	0.0236276i
$721$			2.47403e8i			0.660083i
$722$	9.43741e7	+	2.09313e8i	0.250750	+	0.556139i
$723$	9.21472e8			2.43819
$724$	3.23135e8	−	5.69774e7i	0.851467	−	0.150137i
$725$	1.81191e8	+	2.15935e8i	0.475470	+	0.566643i
$726$	−1.37152e8	+	4.99193e7i	−0.358420	+	0.130454i
$727$	−2.18981e8	−	7.97025e7i	−0.569905	−	0.207429i	0.0409631	−	0.999161i	$-0.486957\pi$
$727$	−2.18981e8	−	7.97025e7i	−0.569905	−	0.207429i	−0.610869	+	0.791732i	$0.709180\pi$
$728$	−8.25174e7	−	6.92403e7i	−0.213871	−	0.179459i
$729$	−5.72769e6	+	9.92064e6i	−0.0147842	+	0.0256069i
$730$	−5.46711e6	+	3.15644e6i	−0.0140537	+	0.00811389i
$731$	−159744.	+	905952.i	−0.000408952	+	0.00231928i
$732$	5.29183e7	+	9.33093e6i	0.134919	+	0.0237898i
$733$	−9.37911e7	−	1.62451e8i	−0.238150	−	0.412487i	0.722034	−	0.691858i	$-0.243207\pi$
$733$	−9.37911e7	−	1.62451e8i	−0.238150	−	0.412487i	−0.960183	+	0.279371i	$0.909874\pi$
$734$	−2.41334e8	−	1.39334e8i	−0.610282	−	0.352346i
$735$	−5.13395e8	+	6.11841e8i	−1.29297	+	1.54091i
$736$	1.46786e7	−	4.03290e7i	0.0368171	−	0.101154i
$737$	−2.34354e8	−	6.43883e8i	−0.585424	−	1.60844i
$738$	7.34222e7	−	6.16086e7i	0.182666	−	0.153275i
$739$	−5.89576e7	−	3.34365e8i	−0.146085	−	0.828491i	−0.966489	−	0.256707i	$-0.917363\pi$
$739$	−5.89576e7	−	3.34365e8i	−0.146085	−	0.828491i	0.820404	−	0.571784i	$-0.193749\pi$
$740$			4.57643e8i			1.12936i
$741$	−6.48675e7	+	8.34303e7i	−0.159431	+	0.205054i
$742$	−5.82246e7			−0.142526
$743$	3.03822e8	−	5.35720e7i	0.740717	−	0.130608i	0.209458	−	0.977818i	$-0.432830\pi$
$743$	3.03822e8	−	5.35720e7i	0.740717	−	0.130608i	0.531259	+	0.847209i	$0.321719\pi$
$744$	−5.93692e7	−	7.07534e7i	−0.144159	−	0.171802i
$745$	5.31606e8	−	1.93489e8i	1.28565	−	0.467937i
$746$	−2.19209e8	−	7.97856e7i	−0.528010	−	0.192180i
$747$	1.59046e8	+	1.33455e8i	0.381558	+	0.320166i
$748$	5.59141e7	−	9.68460e7i	0.133603	−	0.231407i
$749$	−7.45003e8	+	4.30128e8i	−1.77301	+	1.02365i
$750$	−1.81136e8	+	1.02727e9i	−0.429360	+	2.43502i
$751$	2.89346e7	+	5.10195e6i	0.0683121	+	0.0120453i	0.207700	−	0.978193i	$-0.433402\pi$
$751$	2.89346e7	+	5.10195e6i	0.0683121	+	0.0120453i	−0.139388	+	0.990238i	$0.544513\pi$
$752$	−7.12021e6	−	1.23326e7i	−0.0167432	−	0.0290001i
$753$	1.13547e7	+	6.55566e6i	0.0265945	+	0.0153544i
$754$	9.60269e6	−	1.14440e7i	0.0224016	−	0.0266972i
$755$	2.38201e8	−	6.54451e8i	0.553480	−	1.52067i
$756$	6.80464e7	+	1.86956e8i	0.157485	+	0.432687i
$757$	−2.02499e8	+	1.69917e8i	−0.466804	+	0.391695i	−0.845627	−	0.533774i	$-0.820773\pi$
$757$	−2.02499e8	+	1.69917e8i	−0.466804	+	0.391695i	0.378823	+	0.925469i	$0.376329\pi$
$758$	−6.72657e7	−	3.81483e8i	−0.154449	−	0.875926i
$759$			7.16983e7i			0.163977i
$760$	−3.91183e8	+	7.39901e8i	−0.891126	+	1.68552i
$761$	8.27395e7			0.187741			0.0938705	−	0.995584i	$-0.470076\pi$
$761$	8.27395e7			0.187741			0.0938705	+	0.995584i	$0.470076\pi$
$762$	4.39483e8	−	7.74927e7i	0.993293	−	0.175144i
$763$	−3.95335e8	−	4.71142e8i	−0.890003	−	1.06066i
$764$	6.01751e7	−	2.19020e7i	0.134939	−	0.0491137i
$765$	−1.59407e8	−	5.80193e7i	−0.356059	−	0.129595i
$766$	1.81720e8	+	1.52481e8i	0.404312	+	0.339258i
$767$	−2.16805e7	+	3.75518e7i	−0.0480490	+	0.0832232i
$768$	4.84178e8	−	2.79541e8i	1.06886	−	0.617108i
$769$	−7.95333e7	+	4.51055e8i	−0.174892	+	0.991861i	0.763377	+	0.645954i	$0.223540\pi$
$769$	−7.95333e7	+	4.51055e8i	−0.174892	+	0.991861i	−0.938269	+	0.345908i	$0.887571\pi$
$770$	8.73866e8	+	1.54086e8i	1.91413	+	0.337514i
$771$	4.02810e8	+	6.97688e8i	0.878896	+	1.52229i
$772$	4.91246e7	+	2.83621e7i	0.106769	+	0.0616434i
$773$	7.35052e7	−	8.76000e7i	0.159140	−	0.189656i	−0.680582	−	0.732671i	$-0.738273\pi$
$773$	7.35052e7	−	8.76000e7i	0.159140	−	0.189656i	0.839722	+	0.543016i	$0.182718\pi$
$774$	372219.	−	1.02266e6i	0.000802741	−	0.00220551i
$775$	7.71280e7	+	2.11907e8i	0.165694	+	0.455241i
$776$	2.90677e8	−	2.43907e8i	0.622049	−	0.521961i
$777$	−1.29514e8	−	7.34508e8i	−0.276091	−	1.56579i
$778$			4.60046e8i			0.976929i
$779$	−3.25193e8	+	1.21218e7i	−0.687905	+	0.0256421i
$780$	−1.48575e8			−0.313085
$781$	−6.85951e8	+	1.20952e8i	−1.43993	+	0.253898i
$782$	6.97102e6	+	8.30774e6i	0.0145773	+	0.0173725i
$783$	−6.72262e7	+	2.44683e7i	−0.140040	+	0.0509705i
$784$	−8.33903e6	−	3.03516e6i	−0.0173048	−	0.00629845i
$785$	1.11948e9	+	9.39353e8i	2.31423	+	1.94187i
$786$	1.14869e8	−	1.98959e8i	0.236557	−	0.409728i
$787$	3.18128e8	−	1.83671e8i	0.652647	−	0.376806i	−0.136823	−	0.990596i	$-0.543689\pi$
$787$	3.18128e8	−	1.83671e8i	0.652647	−	0.376806i	0.789469	+	0.613790i	$0.210356\pi$
$788$	8.37475e7	−	4.74955e8i	0.171156	−	0.970676i
$789$	−6.90584e7	−	1.21769e7i	−0.140600	−	0.0247916i
$790$	−9.54023e7	−	1.65242e8i	−0.193498	−	0.335149i
$791$	1.03158e9	+	5.95580e8i	2.08435	+	1.20340i
$792$	−2.20484e8	+	2.62762e8i	−0.443814	+	0.528917i
$793$	−6.16587e6	+	1.69406e7i	−0.0123645	+	0.0339710i
$794$	−4.32129e7	−	1.18726e8i	−0.0863281	−	0.237184i
$795$	−1.59507e8	+	1.33843e8i	−0.317453	+	0.266375i
$796$	2.04055e7	+	1.15726e8i	0.0404584	+	0.229451i
$797$			1.24373e8i			0.245670i	0.992427	+	0.122835i	$0.0391985\pi$
$797$			1.24373e8i			0.245670i	−0.992427	+	0.122835i	$0.960801\pi$
$798$	1.61390e8	−	5.00711e8i	0.317591	−	0.985322i
$799$	2.69760e8			0.528856
$800$	−1.36313e9	+	2.40357e8i	−2.66237	+	0.469448i
$801$	−6.97586e7	−	8.31351e7i	−0.135738	−	0.161766i
$802$	−1.83781e8	+	6.68909e7i	−0.356269	+	0.129671i
$803$	8.25456e6	+	3.00442e6i	0.0159422	+	0.00580248i
$804$	−4.37505e8	−	3.67110e8i	−0.841812	−	0.706364i
$805$	7.25852e7	−	1.25721e8i	0.139143	−	0.241002i
$806$	1.03502e7	−	5.97567e6i	0.0197670	−	0.0114125i
$807$	4.04018e7	−	2.29130e8i	0.0768742	−	0.435975i
$808$	−3.04613e8	−	5.37115e7i	−0.577450	−	0.101820i
$809$	8.56509e6	+	1.48352e7i	0.0161766	+	0.0280186i	0.874000	−	0.485925i	$-0.161517\pi$
$809$	8.56509e6	+	1.48352e7i	0.0161766	+	0.0280186i	−0.857824	+	0.513944i	$0.828184\pi$
$810$	−6.71338e8	−	3.87597e8i	−1.26324	−	0.729333i
$811$	−3.90005e8	+	4.64790e8i	−0.731153	+	0.871354i	−0.995663	−	0.0930288i	$-0.970345\pi$
$811$	−3.90005e8	+	4.64790e8i	−0.731153	+	0.871354i	0.264511	+	0.964383i	$0.414790\pi$
$812$	4.29081e7	−	1.17889e8i	0.0801440	−	0.220194i
$813$	−2.19783e8	−	6.03850e8i	−0.409000	−	1.12372i
$814$	−2.89171e8	+	2.42643e8i	−0.536144	+	0.449878i
$815$	−2.00689e8	−	1.13816e9i	−0.370724	−	2.10248i
$816$		−	5.20421e6i		−	0.00957821i
$817$	−3.12893e6	+	1.96542e6i	−0.00573759	+	0.00360404i
$818$	−2.08093e8			−0.380188
$819$	8.63630e7	−	1.52281e7i	0.157209	−	0.0277201i
$820$	−2.94077e8	−	3.50467e8i	−0.533359	−	0.635633i
$821$	−2.10723e8	+	7.66967e7i	−0.380787	+	0.138595i	−0.525320	−	0.850905i	$-0.676054\pi$
$821$	−2.10723e8	+	7.66967e7i	−0.380787	+	0.138595i	0.144533	+	0.989500i	$0.453832\pi$
$822$	−1.85421e8	−	6.74879e7i	−0.333845	−	0.121510i
$823$	−5.70894e8	−	4.79037e8i	−1.02413	−	0.859349i	−0.0339909	−	0.999422i	$-0.510822\pi$
$823$	−5.70894e8	−	4.79037e8i	−1.02413	−	0.859349i	−0.990141	+	0.140073i	$0.955266\pi$
$824$	1.35302e8	−	2.34349e8i	0.241836	−	0.418873i
$825$	2.00260e9	−	1.15620e9i	3.56643	−	2.05908i
$826$	3.74822e7	−	2.12572e8i	0.0665097	−	0.377195i
$827$	−2.50261e8	−	4.41277e7i	−0.442462	−	0.0780180i	−0.0520210	−	0.998646i	$-0.516566\pi$
$827$	−2.50261e8	−	4.41277e7i	−0.442462	−	0.0780180i	−0.390441	+	0.920628i	$0.627677\pi$
$828$	1.08218e7	+	1.87439e7i	0.0190637	+	0.0330193i
$829$	3.08924e8	+	1.78357e8i	0.542236	+	0.313060i	0.745985	−	0.665963i	$-0.231979\pi$
$829$	3.08924e8	+	1.78357e8i	0.542236	+	0.313060i	−0.203749	+	0.979023i	$0.565313\pi$
$830$	−3.77615e8	+	4.50024e8i	−0.660412	+	0.787049i
$831$	−2.22113e8	+	6.10251e8i	−0.387054	+	1.06342i
$832$	2.41904e7	+	6.64625e7i	0.0420023	+	0.115400i
$833$	1.28777e8	−	1.08057e8i	0.222794	−	0.186947i
$834$	2.34947e7	+	1.33245e8i	0.0405016	+	0.229696i
$835$			4.70989e8i			0.809006i
$836$	4.39135e8	−	9.44211e7i	0.751588	−	0.161603i
$837$	−5.72326e7			−0.0976039
$838$	−1.03681e8	+	1.82817e7i	−0.176184	+	0.0310660i
$839$	5.61362e6	+	6.69006e6i	0.00950512	+	0.0113278i	0.770776	−	0.637106i	$-0.219869\pi$
$839$	5.61362e6	+	6.69006e6i	0.00950512	+	0.0113278i	−0.761271	+	0.648434i	$0.775424\pi$
$840$	1.80199e9	−	6.55871e8i	3.04029	−	1.10657i
$841$	−5.16560e8	−	1.88013e8i	−0.868426	−	0.316081i
$842$	1.83845e8	+	1.54264e8i	0.307974	+	0.258421i
$843$	−5.45891e8	+	9.45511e8i	−0.911220	+	1.57828i
$844$	−3.43709e8	+	1.98440e8i	−0.571693	+	0.330067i
$845$	−1.92493e8	+	1.09168e9i	−0.319040	+	1.80937i
$846$	−3.14284e8	−	5.54167e7i	−0.519052	−	0.0915229i
$847$	−2.05606e8	−	3.56121e8i	−0.338366	−	0.586066i
$848$	−2.00356e6	−	1.15676e6i	−0.00328561	−	0.00189695i
$849$	−3.70238e7	+	4.41233e7i	−0.0605004	+	0.0721015i
$850$	1.19629e8	−	3.28678e8i	0.194796	−	0.535197i
$851$	2.11221e7	+	5.80325e7i	0.0342727	+	0.0941635i
$852$	−4.44738e8	+	3.73179e8i	−0.719093	+	0.603391i
$853$	−1.80753e7	−	1.02510e8i	−0.0291232	−	0.165166i	0.966777	−	0.255620i	$-0.0822794\pi$
$853$	−1.80753e7	−	1.02510e8i	−0.0291232	−	0.165166i	−0.995901	+	0.0904536i	$0.971168\pi$
$854$		−	8.97423e7i		−	0.144087i
$855$	−2.56730e8	−	6.31152e8i	−0.410751	−	1.00980i
$856$	9.40928e8			1.50015
$857$	4.14179e8	−	7.30309e7i	0.658030	−	0.116028i	0.165344	−	0.986236i	$-0.447126\pi$
$857$	4.14179e8	−	7.30309e7i	0.658030	−	0.116028i	0.492685	+	0.870208i	$0.336015\pi$
$858$	−7.87749e7	−	9.38803e7i	−0.124717	−	0.148632i
$859$	9.16566e8	−	3.33603e8i	1.44605	−	0.526320i	0.504567	−	0.863373i	$-0.331652\pi$
$859$	9.16566e8	−	3.33603e8i	1.44605	−	0.526320i	0.941486	+	0.337052i	$0.109430\pi$
$860$	−4.88149e6	−	1.77672e6i	−0.00767462	−	0.00279333i
$861$	5.71171e8	+	4.79269e8i	0.894863	+	0.750879i
$862$	3.64022e7	−	6.30504e7i	0.0568336	−	0.0984388i
$863$	4.18345e7	−	2.41532e7i	0.0650882	−	0.0375787i	−0.467103	−	0.884203i	$-0.654702\pi$
$863$	4.18345e7	−	2.41532e7i	0.0650882	−	0.0375787i	0.532191	+	0.846624i	$0.321369\pi$
$864$	6.10015e7	−	3.45957e8i	0.0945800	−	0.536390i
$865$	7.01056e8	+	1.23615e8i	1.08319	+	0.190996i
$866$	−2.37419e8	−	4.11222e8i	−0.365563	−	0.633173i
$867$	−6.21323e8	−	3.58721e8i	−0.953367	−	0.550427i
$868$	6.45127e7	−	7.68833e7i	0.0986475	−	0.117564i
$869$	−9.08074e7	+	2.49491e8i	−0.138376	+	0.380186i
$870$	9.09604e7	+	2.49912e8i	0.138132	+	0.379515i
$871$	1.46782e8	−	1.23164e8i	0.222135	−	0.186393i
$872$	1.16815e8	+	6.62488e8i	0.176176	+	0.999146i
$873$			3.08916e8i			0.464299i
$874$	−5.96095e6	+	4.31505e7i	−0.00892855	+	0.0646325i
$875$	−2.93890e9			−4.38693
$876$	7.21054e6	−	1.27141e6i	0.0107264	−	0.00189136i
$877$	−2.39332e7	−	2.85225e7i	−0.0354815	−	0.0422852i	0.748012	−	0.663685i	$-0.231009\pi$
$877$	−2.39332e7	−	2.85225e7i	−0.0354815	−	0.0422852i	−0.783493	+	0.621400i	$0.786564\pi$
$878$	−3.33659e8	+	1.21442e8i	−0.492968	+	0.179426i
$879$	1.18006e9	+	4.29508e8i	1.73756	+	0.632419i
$880$	2.70093e7	+	2.26635e7i	0.0396337	+	0.0332567i
$881$	−4.88084e8	+	8.45386e8i	−0.713784	+	1.23631i	0.249643	+	0.968338i	$0.419687\pi$
$881$	−4.88084e8	+	8.45386e8i	−0.713784	+	1.23631i	−0.963427	+	0.267972i	$0.913647\pi$
$882$	−1.72230e8	+	9.94369e7i	−0.251017	+	0.144925i
$883$	1.05582e8	−	5.98788e8i	0.153359	−	0.869743i	−0.806912	−	0.590672i	$-0.798863\pi$
$883$	1.05582e8	−	5.98788e8i	0.153359	−	0.869743i	0.960271	−	0.279070i	$-0.0900263\pi$
$884$	3.07963e7	+	5.43022e6i	0.0445802	+	0.00786069i
$885$	−3.85963e8	−	6.68507e8i	−0.556821	−	0.964442i
$886$	4.09847e8	+	2.36625e8i	0.589279	+	0.340220i
$887$	−5.94927e8	+	7.09006e8i	−0.852497	+	1.01597i	0.147142	+	0.989115i	$0.452992\pi$
$887$	−5.94927e8	+	7.09006e8i	−0.852497	+	1.01597i	−0.999639	+	0.0268510i	$0.991452\pi$
$888$	−2.79014e8	+	7.66585e8i	−0.398462	+	1.09477i
$889$	4.30024e8	+	1.18148e9i	0.612050	+	1.68159i
$890$	2.35232e8	−	1.97384e8i	0.333678	−	0.279989i
$891$	1.87310e8	+	1.06229e9i	0.264807	+	1.50179i
$892$			3.47003e8i			0.488920i
$893$	7.26912e8	+	8.03509e8i	1.02077	+	1.12833i
$894$	3.88943e8			0.544344
$895$	1.51894e9	−	2.67831e8i	2.11871	−	0.373586i
$896$	4.04393e8	+	4.81936e8i	0.562185	+	0.669986i
$897$	−1.88404e7	+	6.85736e6i	−0.0261044	+	0.00950123i
$898$	1.28782e8	+	4.68729e7i	0.177839	+	0.0647282i
$899$	2.76459e7	+	2.31977e7i	0.0380498	+	0.0319276i
$900$	3.49023e8	−	6.04525e8i	0.478769	−	0.829253i
$901$	3.79541e7	−	2.19128e7i	0.0518900	−	0.0299587i
$902$	6.55296e7	−	3.71637e8i	0.0892931	−	0.506407i
$903$	8.33751e6	+	1.47013e6i	0.0113233	+	0.00199660i
$904$	−6.51433e8	−	1.12831e9i	−0.881788	−	1.52730i
$905$	−1.69717e9	−	9.79864e8i	−2.28971	−	1.32196i
$906$	3.07780e8	−	3.66798e8i	0.413862	−	0.493222i
$907$	−2.00925e8	+	5.52038e8i	−0.269286	+	0.739856i	0.729172	+	0.684331i	$0.239906\pi$
$907$	−2.00925e8	+	5.52038e8i	−0.269286	+	0.739856i	−0.998457	+	0.0555253i	$0.982317\pi$
$908$	−8.59701e7	−	2.36201e8i	−0.114839	−	0.315518i
$909$	1.92901e8	−	1.61864e8i	0.256829	−	0.215505i
$910$	4.30883e7	+	2.44366e8i	0.0571789	+	0.324277i
$911$		−	1.25998e9i		−	1.66652i	−0.552885	−	0.833258i	$-0.686473\pi$
$911$		−	1.25998e9i		−	1.66652i	0.552885	−	0.833258i	$-0.313527\pi$
$912$	1.55013e7	−	1.40236e7i	0.0204354	−	0.0184873i
$913$	8.17453e8			1.07411
$914$	−6.80257e8	+	1.19948e8i	−0.890912	+	0.157092i
$915$	−2.06293e8	−	2.45851e8i	−0.269291	−	0.320929i
$916$	−6.59939e8	+	2.40198e8i	−0.858653	+	0.312524i
$917$	6.08231e8	+	2.21378e8i	0.788788	+	0.287095i
$918$	6.80020e7	+	5.70604e7i	0.0879009	+	0.0737576i
$919$	3.54717e8	−	6.14388e8i	0.457020	−	0.791582i	−0.541782	−	0.840519i	$-0.682250\pi$
$919$	3.54717e8	−	6.14388e8i	0.457020	−	0.791582i	0.998802	+	0.0489370i	$0.0155833\pi$
$920$	−1.37511e8	+	7.93921e7i	−0.176593	+	0.101956i
$921$	−1.85629e8	+	1.05276e9i	−0.237611	+	1.34756i
$922$	−4.71166e8	−	8.30793e7i	−0.601148	−	0.105999i
$923$	−9.73886e7	−	1.68682e8i	−0.123852	−	0.214518i
$924$	−8.91277e8	−	5.14579e8i	−1.12979	−	0.652283i
$925$	1.28029e9	−	1.52579e9i	1.61764	−	1.92783i
$926$	2.56090e8	−	7.03601e8i	0.322522	−	0.886122i
$927$	7.53477e7	+	2.07016e8i	0.0945868	+	0.259875i
$928$	−1.69691e8	+	1.42387e8i	−0.212331	+	0.178167i
$929$	−1.70793e8	−	9.68616e8i	−0.213022	−	1.20811i	−0.884307	−	0.466906i	$-0.845369\pi$
$929$	−1.70793e8	−	9.68616e8i	−0.213022	−	1.20811i	0.671285	−	0.741199i	$-0.265743\pi$
$930$			2.12761e8i			0.264510i
$931$	6.68870e8	+	9.23999e7i	0.828882	+	0.114504i
$932$	6.99906e8			0.864553
$933$	8.84701e7	−	1.55997e7i	0.108931	−	0.0192075i
$934$	1.64298e8	+	1.95803e8i	0.201647	+	0.240314i
$935$	−6.27625e8	+	2.28437e8i	−0.767830	+	0.279467i
$936$	−9.01346e7	−	3.28063e7i	−0.109917	−	0.0400064i
$937$	5.69967e7	+	4.78259e7i	0.0692836	+	0.0581359i	0.676772	−	0.736193i	$-0.263378\pi$
$937$	5.69967e7	+	4.78259e7i	0.0692836	+	0.0581359i	−0.607488	+	0.794329i	$0.707823\pi$
$938$	−4.76916e8	+	8.26043e8i	−0.577875	+	1.00091i
$939$	−1.11968e9	+	6.46449e8i	−1.35238	+	0.780796i
$940$	−2.64521e8	+	1.50018e9i	−0.318476	+	1.80617i
$941$	−1.37020e9	−	2.41603e8i	−1.64443	−	0.289957i	−0.726638	−	0.687021i	$-0.758918\pi$
$941$	−1.37020e9	−	2.41603e8i	−1.64443	−	0.289957i	−0.917791	+	0.397064i	$0.870029\pi$
$942$	5.02358e8	+	8.70109e8i	0.600980	+	1.04093i
$943$	−5.34667e7	−	3.08690e7i	−0.0637599	−	0.0368118i
$944$	5.51300e6	−	6.57014e6i	0.00655348	−	0.00781014i
$945$	4.06414e8	−	1.11661e9i	0.481585	−	1.32314i
$946$	−1.46552e6	−	4.02649e6i	−0.00173109	−	0.00475612i
$947$	6.19995e8	−	5.20238e8i	0.730026	−	0.612564i	−0.200113	−	0.979773i	$-0.564131\pi$
$947$	6.19995e8	−	5.20238e8i	0.730026	−	0.612564i	0.930139	+	0.367208i	$0.119686\pi$
$948$	3.84280e7	+	2.17936e8i	0.0451048	+	0.255802i
$949$			2.45643e6i			0.00287413i
$950$	1.30136e9	−	5.29347e8i	1.51784	−	0.617404i
$951$	1.16773e8			0.135769
$952$	−3.97483e8	+	7.00871e7i	−0.460689	+	0.0812320i
$953$	7.79672e8	+	9.29177e8i	0.900811	+	1.07354i	0.996940	+	0.0781754i	$0.0249094\pi$
$953$	7.79672e8	+	9.29177e8i	0.900811	+	1.07354i	−0.0961290	+	0.995369i	$0.530646\pi$
$954$	−4.87199e7	+	1.77326e7i	−0.0561127	+	0.0204233i
$955$	−3.59402e8	−	1.30812e8i	−0.412639	−	0.150188i
$956$	−5.74132e8	−	4.81754e8i	−0.657110	−	0.551381i
$957$	1.85034e8	−	3.20488e8i	0.211113	−	0.365659i
$958$	5.05399e8	−	2.91792e8i	0.574827	−	0.331877i
$959$	9.65371e7	−	5.47489e8i	0.109456	−	0.620754i
$960$	−1.23999e9	−	2.18643e8i	−1.40153	−	0.247128i
$961$	−4.29316e8	−	7.43597e8i	−0.483734	−	0.837853i
$962$	−9.14171e7	−	5.27797e7i	−0.102684	−	0.0592846i
$963$	−4.92389e8	+	5.86807e8i	−0.551353	+	0.657077i
$964$	3.74582e8	−	1.02916e9i	0.418135	−	1.14882i
$965$	−1.15873e8	−	3.18359e8i	−0.128944	−	0.354271i
$966$	7.64564e7	−	6.41546e7i	0.0848169	−	0.0711699i
$967$	−1.80746e8	−	1.02506e9i	−0.199890	−	1.13363i	−0.905281	−	0.424812i	$-0.860340\pi$
$967$	−1.80746e8	−	1.02506e9i	−0.199890	−	1.13363i	0.705392	−	0.708818i	$-0.250771\pi$
$968$			4.49775e8i			0.495872i
$969$	8.32392e7	+	3.87130e8i	0.0914864	+	0.425487i
$970$	−8.74085e8			−0.957720
$971$	4.29355e8	−	7.57069e7i	0.468985	−	0.0826947i	0.0658387	−	0.997830i	$-0.479028\pi$
$971$	4.29355e8	−	7.57069e7i	0.468985	−	0.0826947i	0.403146	+	0.915136i	$0.367917\pi$
$972$	3.77366e8	+	4.49728e8i	0.410927	+	0.489724i
$973$	−3.58208e8	+	1.30377e8i	−0.388863	+	0.141535i
$974$	8.57450e8	+	3.12086e8i	0.927966	+	0.337752i
$975$	4.95353e8	+	4.15650e8i	0.534442	+	0.448450i
$976$	1.78293e6	−	3.08812e6i	0.00191771	−	0.00332158i
$977$	−2.46218e8	+	1.42154e8i	−0.264020	+	0.152432i	−0.626167	−	0.779689i	$-0.715377\pi$
$977$	−2.46218e8	+	1.42154e8i	−0.264020	+	0.152432i	0.362147	+	0.932121i	$0.382044\pi$
$978$	1.37977e8	−	7.82504e8i	0.147499	−	0.836508i
$979$	−4.20800e8	−	7.41984e7i	−0.448464	−	0.0790763i
$980$	4.74644e8	+	8.22107e8i	0.504301	+	0.873475i
$981$	−4.74288e8	−	2.73830e8i	−0.502383	−	0.290051i
$982$	−5.83545e8	+	6.95441e8i	−0.616225	+	0.734389i
$983$	−3.19754e8	+	8.78517e8i	−0.336632	+	0.924889i	0.649711	+	0.760182i	$0.274890\pi$
$983$	−3.19754e8	+	8.78517e8i	−0.336632	+	0.924889i	−0.986343	+	0.164707i	$0.947332\pi$
$984$	−2.78928e8	−	7.66350e8i	−0.292757	−	0.804344i
$985$	−2.20657e9	+	1.85154e9i	−2.30893	+	1.93742i
$986$	−9.72012e6	−	5.51255e7i	−0.0101401	−	0.0575072i
$987$		−	2.48261e9i		−	2.58201i
$988$	6.68111e7	+	1.06363e8i	0.0692752	+	0.110286i
$989$	−701012.			−0.000724664
$990$	7.78141e8	−	1.37207e8i	0.801960	−	0.141407i
$991$	−9.95107e8	−	1.18592e9i	−1.02247	−	1.21853i	−0.975584	−	0.219627i	$-0.929516\pi$
$991$	−9.95107e8	−	1.18592e9i	−1.02247	−	1.21853i	−0.0468816	−	0.998900i	$-0.514928\pi$
$992$	−1.66525e8	+	6.06103e7i	−0.170587	+	0.0620886i
$993$	−1.68520e9	−	6.13362e8i	−1.72109	−	0.626425i
$994$	7.42757e8	+	6.23247e8i	0.756289	+	0.634602i
$995$	3.50922e8	−	6.07815e8i	0.356239	−	0.617024i
$996$	5.90067e8	−	3.40675e8i	0.597205	−	0.344796i
$997$	3.47535e7	−	1.97097e8i	0.0350682	−	0.198881i	−0.962240	−	0.272201i	$-0.912248\pi$
$997$	3.47535e7	−	1.97097e8i	0.0350682	−	0.198881i	0.997308	+	0.0733199i	$0.0233594\pi$
$998$	9.36680e8	+	1.65162e8i	0.942323	+	0.166157i
$999$	2.52752e8	+	4.37779e8i	0.253512	+	0.439095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.7.f.a.10.4	yes	54
19.2	odd	18	inner	19.7.f.a.2.4	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.7.f.a.2.4	✓	54	19.2	odd	18	inner
19.7.f.a.10.4	yes	54	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.80629 + 0.847479i) q^{2} +(-21.7309 - 25.8979i) q^{3} +(-37.7581 + 13.7428i) q^{4} +(225.514 + 82.0804i) q^{5} +(126.393 + 106.056i) q^{6} +(-232.429 + 402.578i) q^{7} +(440.331 - 254.225i) q^{8} +(-71.8793 + 407.648i) q^{9} +O(q^{10})\)	\(q+(-4.80629 + 0.847479i) q^{2} +(-21.7309 - 25.8979i) q^{3} +(-37.7581 + 13.7428i) q^{4} +(225.514 + 82.0804i) q^{5} +(126.393 + 106.056i) q^{6} +(-232.429 + 402.578i) q^{7} +(440.331 - 254.225i) q^{8} +(-71.8793 + 407.648i) q^{9} +(-1153.45 - 203.384i) q^{10} +(814.887 + 1411.43i) q^{11} +(1176.43 + 679.212i) q^{12} +(-292.948 + 349.122i) q^{13} +(775.943 - 2131.89i) q^{14} +(-2774.92 - 7624.03i) q^{15} +(69.0555 - 57.9444i) q^{16} +(296.531 + 1681.71i) q^{17} -2020.19i q^{18} +(-4210.10 + 5414.88i) q^{19} -9643.00 q^{20} +(15476.8 - 2728.98i) q^{21} +(-5112.74 - 6093.12i) q^{22} +(-1222.80 + 445.064i) q^{23} +(-16152.7 - 5879.11i) q^{24} +(32149.9 + 26977.0i) q^{25} +(1112.12 - 1926.25i) q^{26} +(-9224.44 + 5325.73i) q^{27} +(3243.50 - 18394.8i) q^{28} +(6614.47 + 1166.31i) q^{29} +(19798.3 + 34291.6i) q^{30} +(4653.34 + 2686.61i) q^{31} +(-21199.6 + 25264.7i) q^{32} +(18844.7 - 51775.5i) q^{33} +(-2850.43 - 7831.48i) q^{34} +(-85459.7 + 71709.2i) q^{35} +(-2888.21 - 16379.8i) q^{36} -47458.6i q^{37} +(15646.0 - 29593.5i) q^{38} +15407.6 q^{39} +(120168. - 21188.8i) q^{40} +(30496.4 + 36344.2i) q^{41} +(-72073.4 + 26232.6i) q^{42} +(506.221 + 184.249i) q^{43} +(-50165.5 - 42093.9i) q^{44} +(-49669.7 + 86030.4i) q^{45} +(5499.97 - 3175.41i) q^{46} +(27431.5 - 155571. i) q^{47} +(-3001.28 - 529.207i) q^{48} +(-49221.6 - 85254.3i) q^{49} +(-177384. - 102413. i) q^{50} +(37108.9 - 44224.6i) q^{51} +(6263.25 - 17208.1i) q^{52} +(-8777.68 - 24116.5i) q^{53} +(39821.9 - 33414.6i) q^{54} +(67918.0 + 385182. i) q^{55} +236357. i q^{56} +(231724. - 8637.65i) q^{57} -32779.5 q^{58} +(93697.5 - 16521.4i) q^{59} +(209551. + 249734. i) q^{60} +(37171.1 - 13529.2i) q^{61} +(-24642.1 - 8969.01i) q^{62} +(-147403. - 123686. i) q^{63} +(77595.6 - 134400. i) q^{64} +(-94720.1 + 54686.6i) q^{65} +(-46694.6 + 264819. i) q^{66} +(-414043. - 73006.9i) q^{67} +(-34307.9 - 59423.0i) q^{68} +(38098.9 + 21996.4i) q^{69} +(349972. - 417081. i) q^{70} +(-146173. + 401606. i) q^{71} +(71983.6 + 197773. i) q^{72} +(4128.91 - 3464.56i) q^{73} +(40220.1 + 228100. i) q^{74} -1.41885e6i q^{75} +(84549.6 - 262314. i) q^{76} -757612. q^{77} +(-74053.3 + 13057.6i) q^{78} +(104715. + 124795. i) q^{79} +(20329.1 - 7399.18i) q^{80} +(621942. + 226369. i) q^{81} +(-177376. - 148836. i) q^{82} +(250787. - 434376. i) q^{83} +(-546872. + 315737. i) q^{84} +(-71163.5 + 403588. i) q^{85} +(-2589.19 - 456.545i) q^{86} +(-113534. - 196646. i) q^{87} +(717640. + 414329. i) q^{88} +(-168525. + 200840. i) q^{89} +(165818. - 455581. i) q^{90} +(-72459.4 - 199081. i) q^{91} +(40054.3 - 33609.6i) q^{92} +(-31543.9 - 178894. i) q^{93} +770970. i q^{94} +(-1.39389e6 + 875565. i) q^{95} +1.11499e6 q^{96} +(734952. - 129592. i) q^{97} +(308825. + 368043. i) q^{98} +(-633937. + 230734. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9}+O(q^{10}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9	\( 54 q - 6 q^{2} - 36 q^{3} + 192 q^{4} - 6 q^{5} + 720 q^{6} - 219 q^{7} - 9 q^{8} - 2076 q^{9} - 1689 q^{10} + 1677 q^{11} - 9 q^{12} - 10506 q^{13} + 6105 q^{14} + 24138 q^{15} + 23760 q^{16} - 3438 q^{17} - 30918 q^{19} - 76650 q^{20} - 59055 q^{21} + 20490 q^{22} + 42498 q^{23} + 31848 q^{24} + 7914 q^{25} + 109989 q^{26} + 124821 q^{27} - 109476 q^{28} - 27726 q^{29} - 153516 q^{30} - 30789 q^{31} - 114375 q^{32} + 126039 q^{33} + 359796 q^{34} + 160161 q^{35} + 184995 q^{36} - 245244 q^{38} - 390564 q^{39} - 372678 q^{40} - 24708 q^{41} - 244893 q^{42} - 30726 q^{43} - 301419 q^{44} + 293037 q^{45} + 69246 q^{46} - 71454 q^{47} + 1024041 q^{48} - 350346 q^{49} - 104148 q^{50} - 180672 q^{51} + 921801 q^{52} + 822558 q^{53} + 308469 q^{54} + 623517 q^{55} - 17862 q^{57} - 1150644 q^{58} - 463812 q^{59} - 908130 q^{60} - 583698 q^{61} - 429732 q^{62} - 2576043 q^{63} - 328293 q^{64} - 1056789 q^{65} - 1038756 q^{66} + 1120464 q^{67} + 717270 q^{68} + 3771567 q^{69} + 4845345 q^{70} + 94494 q^{71} + 2351634 q^{72} + 950850 q^{73} + 55149 q^{74} - 218814 q^{76} - 343086 q^{77} + 1833471 q^{78} - 4936494 q^{79} - 9642039 q^{80} - 769551 q^{81} - 8627793 q^{82} - 412131 q^{83} - 3125205 q^{84} - 896910 q^{85} + 8878236 q^{86} + 610737 q^{87} + 13604751 q^{88} + 6653022 q^{89} + 3142734 q^{90} + 3409821 q^{91} - 3043740 q^{92} - 816393 q^{93} + 4839186 q^{95} - 5667138 q^{96} - 853656 q^{97} - 17679315 q^{98} - 13991937 q^{99}+O(q^{100}) \) 54 * q - 6 * q^2 - 36 * q^3 + 192 * q^4 - 6 * q^5 + 720 * q^6 - 219 * q^7 - 9 * q^8 - 2076 * q^9 - 1689 * q^10 + 1677 * q^11 - 9 * q^12 - 10506 * q^13 + 6105 * q^14 + 24138 * q^15 + 23760 * q^16 - 3438 * q^17 - 30918 * q^19 - 76650 * q^20 - 59055 * q^21 + 20490 * q^22 + 42498 * q^23 + 31848 * q^24 + 7914 * q^25 + 109989 * q^26 + 124821 * q^27 - 109476 * q^28 - 27726 * q^29 - 153516 * q^30 - 30789 * q^31 - 114375 * q^32 + 126039 * q^33 + 359796 * q^34 + 160161 * q^35 + 184995 * q^36 - 245244 * q^38 - 390564 * q^39 - 372678 * q^40 - 24708 * q^41 - 244893 * q^42 - 30726 * q^43 - 301419 * q^44 + 293037 * q^45 + 69246 * q^46 - 71454 * q^47 + 1024041 * q^48 - 350346 * q^49 - 104148 * q^50 - 180672 * q^51 + 921801 * q^52 + 822558 * q^53 + 308469 * q^54 + 623517 * q^55 - 17862 * q^57 - 1150644 * q^58 - 463812 * q^59 - 908130 * q^60 - 583698 * q^61 - 429732 * q^62 - 2576043 * q^63 - 328293 * q^64 - 1056789 * q^65 - 1038756 * q^66 + 1120464 * q^67 + 717270 * q^68 + 3771567 * q^69 + 4845345 * q^70 + 94494 * q^71 + 2351634 * q^72 + 950850 * q^73 + 55149 * q^74 - 218814 * q^76 - 343086 * q^77 + 1833471 * q^78 - 4936494 * q^79 - 9642039 * q^80 - 769551 * q^81 - 8627793 * q^82 - 412131 * q^83 - 3125205 * q^84 - 896910 * q^85 + 8878236 * q^86 + 610737 * q^87 + 13604751 * q^88 + 6653022 * q^89 + 3142734 * q^90 + 3409821 * q^91 - 3043740 * q^92 - 816393 * q^93 + 4839186 * q^95 - 5667138 * q^96 - 853656 * q^97 - 17679315 * q^98 - 13991937 * q^99

Introduction

L-functions

Modular forms

Varieties

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