LMFDB - Embedded newform 51.7.f.a.38.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,7,Mod(38,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.38"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	51.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7327582646$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.4
Character	$\chi$	$=$	51.38
Dual form			51.7.f.a.47.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-13.3013 q^{2} +(20.6191 - 17.4313i) q^{3} +112.924 q^{4} +(-135.530 - 135.530i) q^{5} +(-274.261 + 231.859i) q^{6} +(-104.927 - 104.927i) q^{7} -650.746 q^{8} +(121.297 - 718.838i) q^{9} +(1802.72 + 1802.72i) q^{10} +(1501.87 - 1501.87i) q^{11} +(2328.39 - 1968.41i) q^{12} -345.349 q^{13} +(1395.66 + 1395.66i) q^{14} +(-5156.99 - 432.043i) q^{15} +1428.63 q^{16} +(-1074.43 + 4794.08i) q^{17} +(-1613.41 + 9561.45i) q^{18} -5520.56i q^{19} +(-15304.6 - 15304.6i) q^{20} +(-3992.52 - 334.486i) q^{21} +(-19976.7 + 19976.7i) q^{22} +(-6694.40 + 6694.40i) q^{23} +(-13417.8 + 11343.4i) q^{24} +21111.9i q^{25} +4593.57 q^{26} +(-10029.3 - 16936.2i) q^{27} +(-11848.7 - 11848.7i) q^{28} +(-9650.00 - 9650.00i) q^{29} +(68594.5 + 5746.72i) q^{30} +(-33846.8 + 33846.8i) q^{31} +22645.2 q^{32} +(4787.65 - 57146.8i) q^{33} +(14291.2 - 63767.3i) q^{34} +28441.6i q^{35} +(13697.3 - 81173.8i) q^{36} +(4151.72 - 4151.72i) q^{37} +73430.4i q^{38} +(-7120.79 + 6019.89i) q^{39} +(88195.7 + 88195.7i) q^{40} +(-32509.6 + 32509.6i) q^{41} +(53105.6 + 4449.09i) q^{42} +126669. i q^{43} +(169596. - 169596. i) q^{44} +(-113864. + 80984.8i) q^{45} +(89044.0 - 89044.0i) q^{46} -80864.4i q^{47} +(29457.1 - 24902.9i) q^{48} -95629.6i q^{49} -280815. i q^{50} +(61413.4 + 117578. i) q^{51} -38998.0 q^{52} +158022. q^{53} +(133402. + 225273. i) q^{54} -407097. q^{55} +(68280.8 + 68280.8i) q^{56} +(-96230.7 - 113829. i) q^{57} +(128357. + 128357. i) q^{58} -235108. q^{59} +(-582346. - 48787.9i) q^{60} +(-2436.73 - 2436.73i) q^{61} +(450206. - 450206. i) q^{62} +(-88152.9 + 62698.2i) q^{63} -392641. q^{64} +(46805.2 + 46805.2i) q^{65} +(-63681.8 + 760124. i) q^{66} +482859. q^{67} +(-121328. + 541364. i) q^{68} +(-21340.4 + 254725. i) q^{69} -378309. i q^{70} +(-260550. - 260550. i) q^{71} +(-78933.7 + 467781. i) q^{72} +(473132. - 473132. i) q^{73} +(-55223.2 + 55223.2i) q^{74} +(368008. + 435309. i) q^{75} -623401. i q^{76} -315173. q^{77} +(94715.5 - 80072.1i) q^{78} +(156534. + 156534. i) q^{79} +(-193622. - 193622. i) q^{80} +(-502015. - 174386. i) q^{81} +(432419. - 432419. i) q^{82} +315758. q^{83} +(-450850. - 37771.4i) q^{84} +(795360. - 504125. i) q^{85} -1.68485e6i q^{86} +(-367187. - 30762.3i) q^{87} +(-977334. + 977334. i) q^{88} +1.05421e6i q^{89} +(1.51453e6 - 1.07720e6i) q^{90} +(36236.4 + 36236.4i) q^{91} +(-755956. + 755956. i) q^{92} +(-107897. + 1.28789e6i) q^{93} +1.07560e6i q^{94} +(-748202. + 748202. i) q^{95} +(466924. - 394735. i) q^{96} +(426698. - 426698. i) q^{97} +1.27199e6i q^{98} +(-897427. - 1.26177e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) $ 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−13.3013			−1.66266			−0.831329	−	0.555781i	$-0.812419\pi$
$2$	−13.3013			−1.66266			−0.831329	+	0.555781i	$0.812419\pi$
$3$	20.6191	−	17.4313i	0.763672	−	0.645605i
$3$	20.6191	−	17.4313i	0.763672	−	0.645605i
$4$	112.924			1.76443
$5$	−135.530	−	135.530i	−1.08424	−	1.08424i	−0.996109	−	0.0881331i	$-0.971910\pi$
$5$	−135.530	−	135.530i	−1.08424	−	1.08424i	−0.0881331	−	0.996109i	$-0.528090\pi$
$6$	−274.261	+	231.859i	−1.26972	+	1.07342i
$7$	−104.927	−	104.927i	−0.305910	−	0.305910i	0.537411	−	0.843321i	$-0.319402\pi$
$7$	−104.927	−	104.927i	−0.305910	−	0.305910i	−0.843321	+	0.537411i	$0.819402\pi$
$8$	−650.746			−1.27099
$9$	121.297	−	718.838i	0.166389	−	0.986060i
$10$	1802.72	+	1802.72i	1.80272	+	1.80272i
$11$	1501.87	−	1501.87i	1.12838	−	1.12838i	0.137934	−	0.990441i	$-0.455954\pi$
$11$	1501.87	−	1501.87i	1.12838	−	1.12838i	0.990441	−	0.137934i	$-0.0440461\pi$
$12$	2328.39	−	1968.41i	1.34745	−	1.13913i
$13$	−345.349			−0.157191			−0.0785955	−	0.996907i	$-0.525044\pi$
$13$	−345.349			−0.157191			−0.0785955	+	0.996907i	$0.525044\pi$
$14$	1395.66	+	1395.66i	0.508623	+	0.508623i
$15$	−5156.99	−	432.043i	−1.52800	−	0.128013i
$16$	1428.63			0.348786
$17$	−1074.43	+	4794.08i	−0.218690	+	0.975794i
$17$	−1074.43	+	4794.08i	−0.218690	+	0.975794i
$18$	−1613.41	+	9561.45i	−0.276647	+	1.63948i
$19$		−	5520.56i		−	0.804863i	−0.915450	−	0.402432i	$-0.868165\pi$
$19$		−	5520.56i		−	0.804863i	0.915450	−	0.402432i	$-0.131835\pi$
$20$	−15304.6	−	15304.6i	−1.91307	−	1.91307i
$21$	−3992.52	−	334.486i	−0.431111	−	0.0361177i
$22$	−19976.7	+	19976.7i	−1.87610	+	1.87610i
$23$	−6694.40	+	6694.40i	−0.550210	+	0.550210i	−0.926501	−	0.376292i	$-0.877199\pi$
$23$	−6694.40	+	6694.40i	−0.550210	+	0.550210i	0.376292	+	0.926501i	$0.377199\pi$
$24$	−13417.8	+	11343.4i	−0.970617	+	0.820556i
$25$			21111.9i			1.35116i
$26$	4593.57			0.261355
$27$	−10029.3	−	16936.2i	−0.509539	−	0.860447i
$28$	−11848.7	−	11848.7i	−0.539757	−	0.539757i
$29$	−9650.00	−	9650.00i	−0.395670	−	0.395670i	0.481033	−	0.876703i	$-0.340262\pi$
$29$	−9650.00	−	9650.00i	−0.395670	−	0.395670i	−0.876703	+	0.481033i	$0.840262\pi$
$30$	68594.5	+	5746.72i	2.54054	+	0.212841i
$31$	−33846.8	+	33846.8i	−1.13614	+	1.13614i	−0.147008	+	0.989135i	$0.546964\pi$
$31$	−33846.8	+	33846.8i	−1.13614	+	1.13614i	−0.989135	+	0.147008i	$0.953036\pi$
$32$	22645.2			0.691075
$33$	4787.65	−	57146.8i	0.133223	−	1.59019i
$34$	14291.2	−	63767.3i	0.363607	−	1.62241i
$35$			28441.6i			0.663360i
$36$	13697.3	−	81173.8i	0.293581	−	1.73984i
$37$	4151.72	−	4151.72i	0.0819640	−	0.0819640i	−0.664936	−	0.746900i	$-0.731541\pi$
$37$	4151.72	−	4151.72i	0.0819640	−	0.0819640i	0.746900	+	0.664936i	$0.231541\pi$
$38$			73430.4i			1.33821i
$39$	−7120.79	+	6019.89i	−0.120042	+	0.101483i
$40$	88195.7	+	88195.7i	1.37806	+	1.37806i
$41$	−32509.6	+	32509.6i	−0.471694	+	0.471694i	−0.902462	−	0.430769i	$-0.858242\pi$
$41$	−32509.6	+	32509.6i	−0.471694	+	0.471694i	0.430769	+	0.902462i	$0.358242\pi$
$42$	53105.6	+	4449.09i	0.716791	+	0.0600514i
$43$			126669.i			1.59318i	0.604521	+	0.796589i	$0.293364\pi$
$43$			126669.i			1.59318i	−0.604521	+	0.796589i	$0.706636\pi$
$44$	169596.	−	169596.i	1.99094	−	1.99094i
$45$	−113864.	+	80984.8i	−1.24953	+	0.888722i
$46$	89044.0	−	89044.0i	0.914810	−	0.914810i
$47$		−	80864.4i		−	0.778867i	−0.921054	−	0.389434i	$-0.872671\pi$
$47$		−	80864.4i		−	0.778867i	0.921054	−	0.389434i	$-0.127329\pi$
$48$	29457.1	−	24902.9i	0.266358	−	0.225178i
$49$		−	95629.6i		−	0.812839i
$50$		−	280815.i		−	2.24652i
$51$	61413.4	+	117578.i	0.462970	+	0.886374i
$52$	−38998.0			−0.277353
$53$	158022.			1.06143			0.530714	−	0.847551i	$-0.321924\pi$
$53$	158022.			1.06143			0.530714	+	0.847551i	$0.321924\pi$
$54$	133402.	+	225273.i	0.847189	+	1.43063i
$55$	−407097.			−2.44686
$56$	68280.8	+	68280.8i	0.388807	+	0.388807i
$57$	−96230.7	−	113829.i	−0.519624	−	0.614651i
$58$	128357.	+	128357.i	0.657864	+	0.657864i
$59$	−235108.			−1.14475			−0.572377	−	0.819991i	$-0.693979\pi$
$59$	−235108.			−1.14475			−0.572377	+	0.819991i	$0.693979\pi$
$60$	−582346.	−	48787.9i	−2.69604	−	0.225870i
$61$	−2436.73	−	2436.73i	−0.0107354	−	0.0107354i	0.701719	−	0.712454i	$-0.252416\pi$
$61$	−2436.73	−	2436.73i	−0.0107354	−	0.0107354i	−0.712454	+	0.701719i	$0.752416\pi$
$62$	450206.	−	450206.i	1.88902	−	1.88902i
$63$	−88152.9	+	62698.2i	−0.352545	+	0.250746i
$64$	−392641.			−1.49781
$65$	46805.2	+	46805.2i	0.170433	+	0.170433i
$66$	−63681.8	+	760124.i	−0.221505	+	2.64395i
$67$	482859.			1.60545			0.802723	−	0.596352i	$-0.203384\pi$
$67$	482859.			1.60545			0.802723	+	0.596352i	$0.203384\pi$
$68$	−121328.	+	541364.i	−0.385864	+	1.72172i
$69$	−21340.4	+	254725.i	−0.0649614	+	0.775397i
$70$		−	378309.i		−	1.10294i
$71$	−260550.	−	260550.i	−0.727976	−	0.727976i	0.242241	−	0.970216i	$-0.422118\pi$
$71$	−260550.	−	260550.i	−0.727976	−	0.727976i	−0.970216	+	0.242241i	$0.922118\pi$
$72$	−78933.7	+	467781.i	−0.211478	+	1.25327i
$73$	473132.	−	473132.i	1.21622	−	1.21622i	0.247280	−	0.968944i	$-0.420463\pi$
$73$	473132.	−	473132.i	1.21622	−	1.21622i	0.968944	−	0.247280i	$-0.0795366\pi$
$74$	−55223.2	+	55223.2i	−0.136278	+	0.136278i
$75$	368008.	+	435309.i	0.872316	+	1.03184i
$76$		−	623401.i		−	1.42013i
$77$	−315173.			−0.690362
$78$	94715.5	−	80072.1i	0.199589	−	0.168732i
$79$	156534.	+	156534.i	0.317488	+	0.317488i	0.847802	−	0.530313i	$-0.177926\pi$
$79$	156534.	+	156534.i	0.317488	+	0.317488i	−0.530313	+	0.847802i	$0.677926\pi$
$80$	−193622.	−	193622.i	−0.378168	−	0.378168i
$81$	−502015.	−	174386.i	−0.944630	−	0.328138i
$82$	432419.	−	432419.i	0.784265	−	0.784265i
$83$	315758.			0.552229			0.276115	−	0.961125i	$-0.410953\pi$
$83$	315758.			0.552229			0.276115	+	0.961125i	$0.410953\pi$
$84$	−450850.	−	37771.4i	−0.760666	−	0.0637273i
$85$	795360.	−	504125.i	1.29511	−	0.820884i
$86$		−	1.68485e6i		−	2.64891i
$87$	−367187.	−	30762.3i	−0.557608	−	0.0467154i
$88$	−977334.	+	977334.i	−1.43415	+	1.43415i
$89$			1.05421e6i			1.49540i	0.664036	+	0.747700i	$0.268842\pi$
$89$			1.05421e6i			1.49540i	−0.664036	+	0.747700i	$0.731158\pi$
$90$	1.51453e6	−	1.07720e6i	2.07755	−	1.47764i
$91$	36236.4	+	36236.4i	0.0480863	+	0.0480863i
$92$	−755956.	+	755956.i	−0.970807	+	0.970807i
$93$	−107897.	+	1.28789e6i	−0.134141	+	1.60114i
$94$			1.07560e6i			1.29499i
$95$	−748202.	+	748202.i	−0.872667	+	0.872667i
$96$	466924.	−	394735.i	0.527755	−	0.446162i
$97$	426698.	−	426698.i	0.467525	−	0.467525i	−0.433587	−	0.901112i	$-0.642752\pi$
$97$	426698.	−	426698.i	0.467525	−	0.467525i	0.901112	+	0.433587i	$0.142752\pi$
$98$			1.27199e6i			1.35147i
$99$	−897427.	−	1.26177e6i	−0.924897	−	1.30039i
$100$			2.38403e6i			2.38403i
$101$		−	919907.i		−	0.892852i	−0.894820	−	0.446426i	$-0.852697\pi$
$101$		−	919907.i		−	0.892852i	0.894820	−	0.446426i	$-0.147303\pi$
$102$	−816876.	−	1.56394e6i	−0.769761	−	1.47374i
$103$	−2.03693e6			−1.86408			−0.932042	−	0.362351i	$-0.881974\pi$
$103$	−2.03693e6			−1.86408			−0.932042	+	0.362351i	$0.881974\pi$
$104$	224734.			0.199788
$105$	495774.	+	586440.i	0.428269	+	0.506589i
$106$	−2.10190e6			−1.76479
$107$	−687318.	−	687318.i	−0.561056	−	0.561056i	0.368551	−	0.929607i	$-0.379854\pi$
$107$	−687318.	−	687318.i	−0.561056	−	0.561056i	−0.929607	+	0.368551i	$0.879854\pi$
$108$	−1.13254e6	−	1.91250e6i	−0.899047	−	1.51820i
$109$	−233695.	−	233695.i	−0.180456	−	0.180456i	0.611099	−	0.791554i	$-0.290728\pi$
$109$	−233695.	−	233695.i	−0.180456	−	0.180456i	−0.791554	+	0.611099i	$0.790728\pi$
$110$	5.41490e6			4.06830
$111$	13234.9	−	157975.i	0.00967722	−	0.115510i
$112$	−149902.	−	149902.i	−0.106697	−	0.106697i
$113$	−139762.	+	139762.i	−0.0968622	+	0.0968622i	−0.753877	−	0.657015i	$-0.771819\pi$
$113$	−139762.	+	139762.i	−0.0968622	+	0.0968622i	0.657015	+	0.753877i	$0.271819\pi$
$114$	1.27999e6	+	1.51407e6i	0.863957	+	1.02195i
$115$	1.81459e6			1.19312
$116$	−1.08971e6	−	1.08971e6i	−0.698133	−	0.698133i
$117$	−41889.9	+	248250.i	−0.0261548	+	0.155000i
$118$	3.12724e6			1.90333
$119$	615765.	−	390292.i	0.365404	−	0.231605i
$120$	3.35589e6	+	281150.i	1.94206	+	0.162703i
$121$		−	2.73965e6i		−	1.54646i
$122$	32411.6	+	32411.6i	0.0178493	+	0.0178493i
$123$	−103634.	+	1.23700e6i	−0.0556913	+	0.664747i
$124$	−3.82211e6	+	3.82211e6i	−2.00465	+	2.00465i
$125$	743639.	−	743639.i	0.380743	−	0.380743i
$126$	1.17254e6	−	833965.i	0.586162	−	0.416904i
$127$		−	266887.i		−	0.130291i	−0.997876	−	0.0651457i	$-0.979249\pi$
$127$		−	266887.i		−	0.130291i	0.997876	−	0.0651457i	$-0.0207512\pi$
$128$	3.77334e6			1.79927
$129$	2.20801e6	+	2.61180e6i	1.02856	+	1.21666i
$130$	−622568.	−	622568.i	−0.283372	−	0.283372i
$131$	−1.76438e6	−	1.76438e6i	−0.784836	−	0.784836i	0.195806	−	0.980643i	$-0.437268\pi$
$131$	−1.76438e6	−	1.76438e6i	−0.784836	−	0.784836i	−0.980643	+	0.195806i	$0.937268\pi$
$132$	540639.	−	6.45322e6i	0.235064	−	2.80579i
$133$	−579256.	+	579256.i	−0.246215	+	0.246215i
$134$	−6.42263e6			−2.66931
$135$	−936098.	+	3.65463e6i	−0.380469	+	1.48540i
$136$	699178.	−	3.11972e6i	0.277953	−	1.24022i
$137$			1.13956e6i			0.443175i	0.975140	+	0.221588i	$0.0711239\pi$
$137$			1.13956e6i			0.443175i	−0.975140	+	0.221588i	$0.928876\pi$
$138$	283854.	−	3.38816e6i	0.108009	−	1.28922i
$139$	975288.	−	975288.i	0.363152	−	0.363152i	−0.501820	−	0.864972i	$-0.667336\pi$
$139$	975288.	−	975288.i	0.363152	−	0.363152i	0.864972	+	0.501820i	$0.167336\pi$
$140$			3.21172e6i			1.17045i
$141$	−1.40957e6	−	1.66735e6i	−0.502841	−	0.594799i
$142$	3.46565e6	+	3.46565e6i	1.21037	+	1.21037i
$143$	−518668.	+	518668.i	−0.177370	+	0.177370i
$144$	173289.	−	1.02695e6i	0.0580340	−	0.343924i
$145$			2.61573e6i			0.858004i
$146$	−6.29325e6	+	6.29325e6i	−2.02216	+	2.02216i
$147$	−1.66695e6	−	1.97180e6i	−0.524773	−	0.620742i
$148$	468828.	−	468828.i	0.144620	−	0.144620i
$149$			381220.i			0.115244i	0.998338	+	0.0576218i	$0.0183518\pi$
$149$			381220.i			0.115244i	−0.998338	+	0.0576218i	$0.981648\pi$
$150$	−4.89497e6	−	5.79016e6i	−1.45036	−	1.71560i
$151$		−	2.47171e6i		−	0.717905i	−0.933356	−	0.358952i	$-0.883134\pi$
$151$		−	2.47171e6i		−	0.717905i	0.933356	−	0.358952i	$-0.116866\pi$
$152$			3.59248e6i			1.02297i
$153$	3.31584e6	+	1.35385e6i	0.925804	+	0.378003i
$154$	4.19220e6			1.14784
$155$	9.17454e6			2.46371
$156$	−804105.	+	679787.i	−0.211806	+	0.179060i
$157$	−3.04437e6			−0.786681			−0.393341	−	0.919393i	$-0.628681\pi$
$157$	−3.04437e6			−0.786681			−0.393341	+	0.919393i	$0.628681\pi$
$158$	−2.08210e6	−	2.08210e6i	−0.527874	−	0.527874i
$159$	3.25828e6	−	2.75454e6i	0.810583	−	0.685264i
$160$	−3.06910e6	−	3.06910e6i	−0.749293	−	0.749293i
$161$	1.40485e6			0.336629
$162$	6.67743e6	+	2.31956e6i	1.57060	+	0.545582i
$163$	1.60098e6	+	1.60098e6i	0.369677	+	0.369677i	0.867359	−	0.497682i	$-0.165816\pi$
$163$	1.60098e6	+	1.60098e6i	0.369677	+	0.369677i	−0.497682	+	0.867359i	$0.665816\pi$
$164$	−3.67110e6	+	3.67110e6i	−0.832271	+	0.832271i
$165$	−8.39398e6	+	7.09624e6i	−1.86860	+	1.57971i
$166$	−4.19998e6			−0.918169
$167$	−5.82721e6	−	5.82721e6i	−1.25116	−	1.25116i	−0.955202	−	0.295953i	$-0.904363\pi$
$167$	−5.82721e6	−	5.82721e6i	−1.25116	−	1.25116i	−0.295953	−	0.955202i	$-0.595637\pi$
$168$	2.59812e6	+	217665.i	0.547937	+	0.0459052i
$169$	−4.70754e6			−0.975291
$170$	−1.05793e7	+	6.70550e6i	−2.15333	+	1.36485i
$171$	−3.96839e6	−	669629.i	−0.793644	−	0.133920i
$172$			1.43039e7i			2.81105i
$173$	3.32262e6	+	3.32262e6i	0.641714	+	0.641714i	0.950977	−	0.309262i	$-0.100082\pi$
$173$	3.32262e6	+	3.32262e6i	0.641714	+	0.641714i	−0.309262	+	0.950977i	$0.600082\pi$
$174$	4.88405e6	+	409177.i	0.927112	+	0.0776718i
$175$	2.21521e6	−	2.21521e6i	0.413333	−	0.413333i
$176$	2.14561e6	−	2.14561e6i	0.393562	−	0.393562i
$177$	−4.84773e6	+	4.09825e6i	−0.874216	+	0.739059i
$178$		−	1.40223e7i		−	2.48634i
$179$	4.19649e6			0.731690			0.365845	−	0.930676i	$-0.380780\pi$
$179$	4.19649e6			0.731690			0.365845	+	0.930676i	$0.380780\pi$
$180$	−1.28579e7	+	9.14510e6i	−2.20472	+	1.56809i
$181$	−3.32108e6	−	3.32108e6i	−0.560071	−	0.560071i	0.369257	−	0.929327i	$-0.379612\pi$
$181$	−3.32108e6	−	3.32108e6i	−0.560071	−	0.560071i	−0.929327	+	0.369257i	$0.879612\pi$
$182$	−481990.	−	481990.i	−0.0799510	−	0.0799510i
$183$	−92718.7	−	7767.80i	−0.0151291	−	0.00126749i
$184$	4.35635e6	−	4.35635e6i	0.699309	−	0.699309i
$185$	−1.12537e6			−0.177738
$186$	1.43517e6	−	1.71305e7i	0.223030	−	2.66215i
$187$	5.58642e6	+	8.81371e6i	0.854297	+	1.34783i
$188$		−	9.13149e6i		−	1.37426i
$189$	−724723.	+	2.82940e6i	−0.107346	+	0.419092i
$190$	9.95204e6	−	9.95204e6i	1.45095	−	1.45095i
$191$			2.90301e6i			0.416629i	0.978062	+	0.208314i	$0.0667977\pi$
$191$			2.90301e6i			0.416629i	−0.978062	+	0.208314i	$0.933202\pi$
$192$	−8.09593e6	+	6.84426e6i	−1.14383	+	0.966992i
$193$	−4.47678e6	−	4.47678e6i	−0.622721	−	0.622721i	0.323505	−	0.946226i	$-0.395139\pi$
$193$	−4.47678e6	−	4.47678e6i	−0.622721	−	0.622721i	−0.946226	+	0.323505i	$0.895139\pi$
$194$	−5.67562e6	+	5.67562e6i	−0.777335	+	0.777335i
$195$	1.78096e6	+	149206.i	0.240187	+	0.0201225i
$196$		−	1.07988e7i		−	1.43420i
$197$	2.49928e6	−	2.49928e6i	0.326901	−	0.326901i	−0.524506	−	0.851407i	$-0.675750\pi$
$197$	2.49928e6	−	2.49928e6i	0.326901	−	0.326901i	0.851407	+	0.524506i	$0.175750\pi$
$198$	1.19369e7	+	1.67832e7i	1.53779	+	2.16211i
$199$	5.28030e6	−	5.28030e6i	0.670038	−	0.670038i	−0.287687	−	0.957725i	$-0.592886\pi$
$199$	5.28030e6	−	5.28030e6i	0.670038	−	0.670038i	0.957725	+	0.287687i	$0.0928861\pi$
$200$		−	1.37385e7i		−	1.71731i
$201$	9.95613e6	−	8.41688e6i	1.22603	−	1.03648i
$202$			1.22359e7i			1.48451i
$203$			2.02509e6i			0.242079i
$204$	6.93502e6	+	1.32774e7i	0.816879	+	1.56395i
$205$	8.81206e6			1.02286
$206$	2.70938e7			3.09933
$207$	4.00018e6	+	5.62420e6i	0.450991	+	0.634088i
$208$	−493375.			−0.0548260
$209$	−8.29115e6	−	8.29115e6i	−0.908188	−	0.908188i
$210$	−6.59443e6	−	7.80040e6i	−0.712064	−	0.842285i
$211$	−5.03475e6	−	5.03475e6i	−0.535958	−	0.535958i	0.386381	−	0.922339i	$-0.373725\pi$
$211$	−5.03475e6	−	5.03475e6i	−0.535958	−	0.535958i	−0.922339	+	0.386381i	$0.873725\pi$
$212$	1.78444e7			1.87282
$213$	−9.91407e6	−	830583.i	−1.02592	−	0.0859496i
$214$	9.14219e6	+	9.14219e6i	0.932844	+	0.932844i
$215$	1.71674e7	−	1.71674e7i	1.72739	−	1.72739i
$216$	6.52650e6	+	1.10211e7i	0.647618	+	1.09362i
$217$	7.10290e6			0.695115
$218$	3.10844e6	+	3.10844e6i	0.300036	+	0.300036i
$219$	1.50825e6	−	1.80029e7i	0.143595	−	1.71400i
$220$	−4.59708e7			−4.31732
$221$	371052.	−	1.65563e6i	0.0343762	−	0.153386i
$222$	−176040.	+	2.10127e6i	−0.0160899	+	0.192054i
$223$			1.63070e7i			1.47048i	0.677807	+	0.735240i	$0.262931\pi$
$223$			1.63070e7i			1.47048i	−0.677807	+	0.735240i	$0.737069\pi$
$224$	−2.37609e6	−	2.37609e6i	−0.211407	−	0.211407i
$225$	1.51760e7	+	2.56081e6i	1.33233	+	0.224818i
$226$	1.85901e6	−	1.85901e6i	0.161049	−	0.161049i
$227$	1.05446e7	−	1.05446e7i	0.901471	−	0.901471i	−0.0940929	−	0.995563i	$-0.529995\pi$
$227$	1.05446e7	−	1.05446e7i	0.901471	−	0.901471i	0.995563	+	0.0940929i	$0.0299951\pi$
$228$	−1.08667e7	−	1.28540e7i	−0.916840	−	1.08451i
$229$			7.58496e6i			0.631607i	0.948825	+	0.315804i	$0.102274\pi$
$229$			7.58496e6i			0.631607i	−0.948825	+	0.315804i	$0.897726\pi$
$230$	−2.41363e7			−1.98375
$231$	−6.49859e6	+	5.49389e6i	−0.527210	+	0.445701i
$232$	6.27969e6	+	6.27969e6i	0.502892	+	0.502892i
$233$	−31630.0	−	31630.0i	−0.00250053	−	0.00250053i	0.705855	−	0.708356i	$-0.250563\pi$
$233$	−31630.0	−	31630.0i	−0.00250053	−	0.00250053i	−0.708356	+	0.705855i	$0.750563\pi$
$234$	557188.	−	3.30204e6i	0.0434865	−	0.257712i
$235$	−1.09596e7	+	1.09596e7i	−0.844481	+	0.844481i
$236$	−2.65493e7			−2.01984
$237$	5.95619e6	+	498999.i	0.447429	+	0.0374848i
$238$	−8.19045e6	+	5.19138e6i	−0.607543	+	0.385081i
$239$			7.93949e6i			0.581566i	0.956789	+	0.290783i	$0.0939157\pi$
$239$			7.93949e6i			0.581566i	−0.956789	+	0.290783i	$0.906084\pi$
$240$	−7.36742e6	−	617229.i	−0.532944	−	0.0446491i
$241$	1.65164e7	−	1.65164e7i	1.17995	−	1.17995i	0.200196	−	0.979756i	$-0.435842\pi$
$241$	1.65164e7	−	1.65164e7i	1.17995	−	1.17995i	0.979756	−	0.200196i	$-0.0641579\pi$
$242$			3.64408e7i			2.57124i
$243$	−1.33909e7	+	5.15510e6i	−0.933235	+	0.359268i
$244$	−275164.	−	275164.i	−0.0189418	−	0.0189418i
$245$	−1.29607e7	+	1.29607e7i	−0.881314	+	0.881314i
$246$	1.37846e6	−	1.64537e7i	0.0925955	−	1.10525i
$247$			1.90652e6i			0.126517i
$248$	2.20257e7	−	2.20257e7i	1.44402	−	1.44402i
$249$	6.51065e6	−	5.50408e6i	0.421722	−	0.356522i
$250$	−9.89133e6	+	9.89133e6i	−0.633045	+	0.633045i
$251$		−	1.23919e7i		−	0.783639i	−0.920042	−	0.391819i	$-0.871846\pi$
$251$		−	1.23919e7i		−	0.783639i	0.920042	−	0.391819i	$-0.128154\pi$
$252$	−9.95454e6	+	7.08010e6i	−0.622042	+	0.442423i
$253$			2.01082e7i			1.24169i
$254$			3.54993e6i			0.216630i
$255$	7.61205e6	−	2.42588e7i	0.459072	−	1.46302i
$256$	−2.50611e7			−1.49376
$257$	−2.32193e7			−1.36789			−0.683944	−	0.729535i	$-0.739737\pi$
$257$	−2.32193e7			−1.36789			−0.683944	+	0.729535i	$0.739737\pi$
$258$	−2.93693e7	−	3.47402e7i	−1.71015	−	2.02290i
$259$	−871256.			−0.0501472
$260$	5.28541e6	+	5.28541e6i	0.300717	+	0.300717i
$261$	−8.10730e6	+	5.76627e6i	−0.455989	+	0.324320i
$262$	2.34685e7	+	2.34685e7i	1.30491	+	1.30491i
$263$	9.24163e6			0.508021			0.254010	−	0.967202i	$-0.418250\pi$
$263$	9.24163e6			0.508021			0.254010	+	0.967202i	$0.418250\pi$
$264$	−3.11554e6	+	3.71880e7i	−0.169325	+	2.02112i
$265$	−2.14168e7	−	2.14168e7i	−1.15085	−	1.15085i
$266$	7.70483e6	−	7.70483e6i	0.409372	−	0.409372i
$267$	1.83763e7	+	2.17369e7i	0.965438	+	1.14200i
$268$	5.45262e7			2.83270
$269$	−1.72811e7	−	1.72811e7i	−0.887801	−	0.887801i	0.106511	−	0.994312i	$-0.466032\pi$
$269$	−1.72811e7	−	1.72811e7i	−0.887801	−	0.887801i	−0.994312	+	0.106511i	$0.966032\pi$
$270$	1.24513e7	−	4.86112e7i	0.632591	−	2.46971i
$271$	−1.14854e7			−0.577083			−0.288541	−	0.957467i	$-0.593170\pi$
$271$	−1.14854e7			−0.577083			−0.288541	+	0.957467i	$0.593170\pi$
$272$	−1.53496e6	+	6.84895e6i	−0.0762762	+	0.340343i
$273$	1.37881e6	+	115514.i	0.0677668	+	0.00567738i
$274$		−	1.51576e7i		−	0.736849i
$275$	3.17073e7	+	3.17073e7i	1.52462	+	1.52462i
$276$	−2.40984e6	+	2.87645e7i	−0.114620	+	1.36814i
$277$	−8.23566e6	+	8.23566e6i	−0.387489	+	0.387489i	−0.873791	−	0.486302i	$-0.838346\pi$
$277$	−8.23566e6	+	8.23566e6i	−0.387489	+	0.387489i	0.486302	+	0.873791i	$0.338346\pi$
$278$	−1.29726e7	+	1.29726e7i	−0.603797	+	0.603797i
$279$	2.02249e7	+	2.84359e7i	0.931265	+	1.30935i
$280$		−	1.85082e7i		−	0.843122i
$281$	−5.12027e6			−0.230767			−0.115384	−	0.993321i	$-0.536810\pi$
$281$	−5.12027e6			−0.230767			−0.115384	+	0.993321i	$0.536810\pi$
$282$	1.87491e7	+	2.21779e7i	0.836052	+	0.988947i
$283$	−943702.	−	943702.i	−0.0416366	−	0.0416366i	0.685982	−	0.727619i	$-0.259373\pi$
$283$	−943702.	−	943702.i	−0.0416366	−	0.0416366i	−0.727619	+	0.685982i	$0.759373\pi$
$284$	−2.94223e7	−	2.94223e7i	−1.28446	−	1.28446i
$285$	−2.38512e6	+	2.84695e7i	−0.103033	+	1.22983i
$286$	6.89894e6	−	6.89894e6i	0.294906	−	0.294906i
$287$	6.82227e6			0.288591
$288$	2.74680e6	−	1.62782e7i	0.114987	−	0.681442i
$289$	−2.18288e7	−	1.03018e7i	−0.904349	−	0.426794i
$290$		−	3.47925e7i		−	1.42657i
$291$	1.36023e6	−	1.62360e7i	0.0551992	−	0.658873i
$292$	5.34277e7	−	5.34277e7i	2.14594	−	2.14594i
$293$		−	4.16615e7i		−	1.65627i	−0.560526	−	0.828137i	$-0.689401\pi$
$293$		−	4.16615e7i		−	1.65627i	0.560526	−	0.828137i	$-0.310599\pi$
$294$	2.21726e7	+	2.62274e7i	0.872517	+	1.03208i
$295$	3.18643e7	+	3.18643e7i	1.24119	+	1.24119i
$296$	−2.70172e6	+	2.70172e6i	−0.104175	+	0.104175i
$297$	−4.04985e7	−	1.03733e7i	−1.54586	−	0.395956i
$298$		−	5.07071e6i		−	0.191611i
$299$	2.31190e6	−	2.31190e6i	0.0864880	−	0.0864880i
$300$	4.15568e7	+	4.91566e7i	1.53914	+	1.82062i
$301$	1.32910e7	−	1.32910e7i	0.487369	−	0.487369i
$302$			3.28769e7i			1.19363i
$303$	−1.60352e7	−	1.89677e7i	−0.576430	−	0.681846i
$304$		−	7.88682e6i		−	0.280725i
$305$			660501.i			0.0232795i
$306$	−4.41049e7	−	1.80079e7i	−1.53930	−	0.628490i
$307$	6.62935e6			0.229116			0.114558	−	0.993417i	$-0.463455\pi$
$307$	6.62935e6			0.229116			0.114558	+	0.993417i	$0.463455\pi$
$308$	−3.55905e7			−1.21810
$309$	−4.19998e7	+	3.55065e7i	−1.42355	+	1.20346i
$310$	−1.22033e8			−4.09630
$311$	1.32942e7	+	1.32942e7i	0.441959	+	0.441959i	0.892670	−	0.450711i	$-0.148829\pi$
$311$	1.32942e7	+	1.32942e7i	0.441959	+	0.441959i	−0.450711	+	0.892670i	$0.648829\pi$
$312$	4.63382e6	−	3.91742e6i	0.152572	−	0.128984i
$313$	3.78211e6	+	3.78211e6i	0.123339	+	0.123339i	0.766082	−	0.642743i	$-0.222204\pi$
$313$	3.78211e6	+	3.78211e6i	0.123339	+	0.123339i	−0.642743	+	0.766082i	$0.722204\pi$
$314$	4.04940e7			1.30798
$315$	2.04449e7	+	3.44988e6i	0.654113	+	0.110376i
$316$	1.76764e7	+	1.76764e7i	0.560186	+	0.560186i
$317$	−9.06045e6	+	9.06045e6i	−0.284428	+	0.284428i	−0.834872	−	0.550444i	$-0.814458\pi$
$317$	−9.06045e6	+	9.06045e6i	−0.284428	+	0.284428i	0.550444	+	0.834872i	$0.314458\pi$
$318$	−4.33393e7	+	3.66389e7i	−1.34772	+	1.13936i
$319$	−2.89860e7			−0.892929
$320$	5.32148e7	+	5.32148e7i	1.62399	+	1.62399i
$321$	−2.61528e7	−	2.19103e6i	−0.790683	−	0.0662420i
$322$	−1.86862e7			−0.559699
$323$	2.64660e7	+	5.93143e6i	0.785381	+	0.176016i
$324$	−5.66893e7	−	1.96923e7i	−1.66673	−	0.578977i
$325$		−	7.29096e6i		−	0.212390i
$326$	−2.12950e7	−	2.12950e7i	−0.614646	−	0.614646i
$327$	−8.89222e6	−	744974.i	−0.254312	−	0.0213058i
$328$	2.11555e7	−	2.11555e7i	0.599517	−	0.599517i
$329$	−8.48486e6	+	8.48486e6i	−0.238263	+	0.238263i
$330$	1.11651e8	−	9.43890e7i	3.10684	−	2.62651i
$331$		−	6.15210e7i		−	1.69644i	−0.529642	−	0.848221i	$-0.677674\pi$
$331$		−	6.15210e7i		−	1.69644i	0.529642	−	0.848221i	$-0.322326\pi$
$332$	3.56565e7			0.974371
$333$	−2.48082e6	−	3.48801e6i	−0.0671836	−	0.0944594i
$334$	7.75093e7	+	7.75093e7i	2.08024	+	2.08024i
$335$	−6.54420e7	−	6.54420e7i	−1.74069	−	1.74069i
$336$	−5.70383e6	−	477856.i	−0.150366	−	0.0125974i
$337$	−2.79093e7	+	2.79093e7i	−0.729222	+	0.729222i	−0.970465	−	0.241243i	$-0.922445\pi$
$337$	−2.79093e7	+	2.79093e7i	−0.729222	+	0.729222i	0.241243	+	0.970465i	$0.422445\pi$
$338$	6.26163e7			1.62158
$339$	−445534.	+	5.31802e6i	−0.0114362	+	0.136506i
$340$	8.98149e7	−	5.69276e7i	2.28513	−	1.44839i
$341$			1.01667e8i			2.56399i
$342$	5.27846e7	+	8.90691e6i	1.31956	+	0.222663i
$343$	−2.23787e7	+	2.23787e7i	−0.554565	+	0.554565i
$344$		−	8.24292e7i		−	2.02491i
$345$	3.74152e7	−	3.16307e7i	0.911152	−	0.770284i
$346$	−4.41950e7	−	4.41950e7i	−1.06695	−	1.06695i
$347$	1.55564e7	−	1.55564e7i	0.372323	−	0.372323i	−0.496000	−	0.868323i	$-0.665198\pi$
$347$	1.55564e7	−	1.55564e7i	0.372323	−	0.372323i	0.868323	+	0.496000i	$0.165198\pi$
$348$	−4.14641e7	−	3.47378e6i	−0.983862	−	0.0824262i
$349$			5.51355e7i			1.29704i	0.761196	+	0.648522i	$0.224613\pi$
$349$			5.51355e7i			1.29704i	−0.761196	+	0.648522i	$0.775387\pi$
$350$	−2.94651e7	+	2.94651e7i	−0.687232	+	0.687232i
$351$	3.46359e6	+	5.84889e6i	0.0800950	+	0.135255i
$352$	3.40100e7	−	3.40100e7i	0.779793	−	0.779793i
$353$			3.30729e6i			0.0751880i	0.999293	+	0.0375940i	$0.0119694\pi$
$353$			3.30729e6i			0.0751880i	−0.999293	+	0.0375940i	$0.988031\pi$
$354$	6.44810e7	−	5.45119e7i	1.45352	−	1.22880i
$355$			7.06249e7i			1.57860i
$356$			1.19045e8i			2.63853i
$357$	5.89322e6	−	1.87811e7i	0.129523	−	0.412777i
$358$	−5.58186e7			−1.21655
$359$	−6.32439e6			−0.136689			−0.0683447	−	0.997662i	$-0.521772\pi$
$359$	−6.32439e6			−0.136689			−0.0683447	+	0.997662i	$0.521772\pi$
$360$	7.40963e7	−	5.27005e7i	1.58814	−	1.12955i
$361$	1.65693e7			0.352195
$362$	4.41745e7	+	4.41745e7i	0.931206	+	0.931206i
$363$	−4.77558e7	−	5.64892e7i	−0.998403	−	1.18099i
$364$	4.09195e6	+	4.09195e6i	0.0848449	+	0.0848449i
$365$	−1.28247e8			−2.63736
$366$	1.23328e6	+	103322.i	0.0251546	+	0.00210740i
$367$	−4.04974e7	−	4.04974e7i	−0.819273	−	0.819273i	0.166730	−	0.986003i	$-0.446679\pi$
$367$	−4.04974e7	−	4.04974e7i	−0.819273	−	0.819273i	−0.986003	+	0.166730i	$0.946679\pi$
$368$	−9.56381e6	+	9.56381e6i	−0.191905	+	0.191905i
$369$	1.94258e7	+	2.73124e7i	0.386634	+	0.543603i
$370$	1.49688e7			0.295517
$371$	−1.65808e7	−	1.65808e7i	−0.324701	−	0.324701i
$372$	−1.21841e7	+	1.45433e8i	−0.236682	+	2.82510i
$373$	−3.27729e7			−0.631523			−0.315761	−	0.948839i	$-0.602260\pi$
$373$	−3.27729e7			−0.631523			−0.315761	+	0.948839i	$0.602260\pi$
$374$	−7.43065e7	−	1.17234e8i	−1.42040	−	2.24098i
$375$	2.37057e6	−	2.82958e7i	0.0449530	−	0.536572i
$376$			5.26221e7i			0.989931i
$377$	3.33261e6	+	3.33261e6i	0.0621958	+	0.0621958i
$378$	9.63974e6	−	3.76346e7i	0.178480	−	0.696807i
$379$	3.91359e7	−	3.91359e7i	0.718883	−	0.718883i	−0.249494	−	0.968376i	$-0.580264\pi$
$379$	3.91359e7	−	3.91359e7i	0.718883	−	0.718883i	0.968376	+	0.249494i	$0.0802642\pi$
$380$	−8.44897e7	+	8.44897e7i	−1.53976	+	1.53976i
$381$	−4.65219e6	−	5.50297e6i	−0.0841167	−	0.0994998i
$382$		−	3.86138e7i		−	0.692711i
$383$	7.29630e7			1.29869			0.649347	−	0.760493i	$-0.275042\pi$
$383$	7.29630e7			1.29869			0.649347	+	0.760493i	$0.275042\pi$
$384$	7.78029e7	−	6.57743e7i	1.37405	−	1.16162i
$385$	4.27155e7	+	4.27155e7i	0.748519	+	0.748519i
$386$	5.95468e7	+	5.95468e7i	1.03537	+	1.03537i
$387$	9.10543e7	+	1.53646e7i	1.57097	+	0.265087i
$388$	4.81842e7	−	4.81842e7i	0.824916	−	0.824916i
$389$	3.98119e7			0.676338			0.338169	−	0.941085i	$-0.390192\pi$
$389$	3.98119e7			0.676338			0.338169	+	0.941085i	$0.390192\pi$
$390$	−2.36890e7	−	1.98462e6i	−0.399349	−	0.0334568i
$391$	−2.49008e7	−	3.92861e7i	−0.416566	−	0.657217i
$392$			6.22306e7i			1.03311i
$393$	−6.71356e7	−	5.62450e6i	−1.10605	−	0.0926630i
$394$	−3.32436e7	+	3.32436e7i	−0.543525	+	0.543525i
$395$		−	4.24302e7i		−	0.688468i
$396$	−1.01341e8	−	1.42484e8i	−1.63192	−	2.29446i
$397$	7.78726e7	+	7.78726e7i	1.24455	+	1.24455i	0.958092	+	0.286460i	$0.0924784\pi$
$397$	7.78726e7	+	7.78726e7i	1.24455	+	1.24455i	0.286460	+	0.958092i	$0.407522\pi$
$398$	−7.02347e7	+	7.02347e7i	−1.11404	+	1.11404i
$399$	−1.84655e6	+	2.20409e7i	−0.0290698	+	0.346986i
$400$			3.01610e7i			0.471266i
$401$	6.99797e7	−	6.99797e7i	1.08527	−	1.08527i	0.0892654	−	0.996008i	$-0.471548\pi$
$401$	6.99797e7	−	6.99797e7i	1.08527	−	1.08527i	0.996008	−	0.0892654i	$-0.0284519\pi$
$402$	−1.32429e8	+	1.11955e8i	−2.03848	+	1.72332i
$403$	1.16890e7	−	1.16890e7i	0.178592	−	0.178592i
$404$		−	1.03879e8i		−	1.57538i
$405$	4.44036e7	+	9.16728e7i	0.668426	+	1.37999i
$406$		−	2.69363e7i		−	0.402494i
$407$		−	1.24707e7i		−	0.184972i
$408$	−3.99645e7	−	7.65136e7i	−0.588429	−	1.12657i
$409$	1.70450e7			0.249130			0.124565	−	0.992211i	$-0.460246\pi$
$409$	1.70450e7			0.249130			0.124565	+	0.992211i	$0.460246\pi$
$410$	−1.17212e8			−1.70067
$411$	1.98641e7	+	2.34968e7i	0.286116	+	0.338441i
$412$	−2.30018e8			−3.28905
$413$	2.46692e7	+	2.46692e7i	0.350191	+	0.350191i
$414$	−5.32074e7	−	7.48090e7i	−0.749844	−	1.05427i
$415$	−4.27947e7	−	4.27947e7i	−0.598750	−	0.598750i
$416$	−7.82048e6			−0.108631
$417$	3.10902e6	−	3.71102e7i	0.0428761	−	0.511781i
$418$	1.10283e8	+	1.10283e8i	1.51001	+	1.51001i
$419$	1.82362e6	−	1.82362e6i	0.0247909	−	0.0247909i	−0.694603	−	0.719394i	$-0.744420\pi$
$419$	1.82362e6	−	1.82362e6i	0.0247909	−	0.0247909i	0.719394	+	0.694603i	$0.244420\pi$
$420$	5.59846e7	+	6.62230e7i	0.755650	+	0.893842i
$421$	−2.93342e7			−0.393123			−0.196561	−	0.980492i	$-0.562977\pi$
$421$	−2.93342e7			−0.393123			−0.196561	+	0.980492i	$0.562977\pi$
$422$	6.69685e7	+	6.69685e7i	0.891114	+	0.891114i
$423$	−5.81284e7	−	9.80862e6i	−0.768010	−	0.129595i
$424$	−1.02832e8			−1.34906
$425$	−1.01212e8	−	2.26832e7i	−1.31845	−	0.295486i
$426$	1.31870e8	+	1.10478e7i	1.70575	+	0.142905i
$427$			511357.i			0.00656812i
$428$	−7.76144e7	−	7.76144e7i	−0.989945	−	0.989945i
$429$	−1.65341e6	+	1.97356e7i	−0.0209415	+	0.249964i
$430$	−2.28349e8	+	2.28349e8i	−2.87206	+	2.87206i
$431$	5.13954e7	−	5.13954e7i	0.641937	−	0.641937i	−0.309094	−	0.951031i	$-0.600026\pi$
$431$	5.13954e7	−	5.13954e7i	0.641937	−	0.641937i	0.951031	+	0.309094i	$0.100026\pi$
$432$	−1.43281e7	−	2.41955e7i	−0.177720	−	0.300112i
$433$			4.13922e7i			0.509865i	0.966959	+	0.254932i	$0.0820532\pi$
$433$			4.13922e7i			0.509865i	−0.966959	+	0.254932i	$0.917947\pi$
$434$	−9.44775e7			−1.15574
$435$	4.55957e7	+	5.39341e7i	0.553932	+	0.655233i
$436$	−2.63897e7	−	2.63897e7i	−0.318402	−	0.318402i
$437$	3.69568e7	+	3.69568e7i	0.442844	+	0.442844i
$438$	−2.00616e7	+	2.39461e8i	−0.238750	+	2.84979i
$439$	9.65946e7	−	9.65946e7i	1.14172	−	1.14172i	0.153583	−	0.988136i	$-0.450919\pi$
$439$	9.65946e7	−	9.65946e7i	1.14172	−	1.14172i	0.988136	−	0.153583i	$-0.0490812\pi$
$440$	2.64917e8			3.10993
$441$	−6.87422e7	−	1.15996e7i	−0.801508	−	0.135247i
$442$	−4.93546e6	+	2.20219e7i	−0.0571558	+	0.255029i
$443$			3.60393e7i			0.414539i	0.978284	+	0.207269i	$0.0664577\pi$
$443$			3.60393e7i			0.414539i	−0.978284	+	0.207269i	$0.933542\pi$
$444$	1.49453e6	−	1.78391e7i	0.0170748	−	0.203809i
$445$	1.42877e8	−	1.42877e8i	1.62138	−	1.62138i
$446$		−	2.16904e8i		−	2.44491i
$447$	6.64517e6	+	7.86042e6i	0.0744018	+	0.0880082i
$448$	4.11987e7	+	4.11987e7i	0.458194	+	0.458194i
$449$	−5.37994e7	+	5.37994e7i	−0.594345	+	0.594345i	−0.938802	−	0.344457i	$-0.888063\pi$
$449$	−5.37994e7	+	5.37994e7i	−0.594345	+	0.594345i	0.344457	+	0.938802i	$0.388063\pi$
$450$	−2.01860e8	−	3.40621e7i	−2.21520	−	0.373795i
$451$			9.76502e7i			1.06449i
$452$	−1.57825e7	+	1.57825e7i	−0.170907	+	0.170907i
$453$	−4.30852e7	−	5.09645e7i	−0.463483	−	0.548244i
$454$	−1.40256e8	+	1.40256e8i	−1.49884	+	1.49884i
$455$		−	9.82226e6i		−	0.104274i
$456$	6.26217e7	+	7.40738e7i	0.660435	+	0.781214i
$457$		−	8.18376e7i		−	0.857441i	−0.903437	−	0.428720i	$-0.858965\pi$
$457$		−	8.18376e7i		−	0.857441i	0.903437	−	0.428720i	$-0.141035\pi$
$458$		−	1.00890e8i		−	1.05015i
$459$	9.19691e7	−	2.98844e7i	0.951051	−	0.309034i
$460$	2.04910e8			2.10518
$461$	3.33395e7			0.340295			0.170148	−	0.985419i	$-0.445576\pi$
$461$	3.33395e7			0.340295			0.170148	+	0.985419i	$0.445576\pi$
$462$	8.64395e7	−	7.30756e7i	0.876569	−	0.741048i
$463$	1.39418e8			1.40467			0.702336	−	0.711846i	$-0.252140\pi$
$463$	1.39418e8			1.40467			0.702336	+	0.711846i	$0.252140\pi$
$464$	−1.37863e7	−	1.37863e7i	−0.138004	−	0.138004i
$465$	1.89171e8	−	1.59924e8i	1.88146	−	1.59058i
$466$	420719.	+	420719.i	0.00415752	+	0.00415752i
$467$	1.72859e8			1.69724			0.848618	−	0.529006i	$-0.177435\pi$
$467$	1.72859e8			1.69724			0.848618	+	0.529006i	$0.177435\pi$
$468$	−4.73035e6	+	2.80333e7i	−0.0461483	+	0.273487i
$469$	−5.06650e7	−	5.06650e7i	−0.491122	−	0.491122i
$470$	1.45776e8	−	1.45776e8i	1.40408	−	1.40408i
$471$	−6.27723e7	+	5.30675e7i	−0.600766	+	0.507885i
$472$	1.52996e8			1.45497
$473$	1.90240e8	+	1.90240e8i	1.79770	+	1.79770i
$474$	−7.92249e7	−	6.63732e6i	−0.743921	−	0.0623243i
$475$	1.16549e8			1.08750
$476$	6.95343e7	−	4.40732e7i	0.644731	−	0.408652i
$477$	1.91677e7	−	1.13592e8i	0.176610	−	1.04663i
$478$		−	1.05605e8i		−	0.966945i
$479$	−5.79786e7	−	5.79786e7i	−0.527547	−	0.527547i	0.392293	−	0.919840i	$-0.371682\pi$
$479$	−5.79786e7	−	5.79786e7i	−0.527547	−	0.527547i	−0.919840	+	0.392293i	$0.871682\pi$
$480$	−1.16781e8	−	9.78369e6i	−1.05596	−	0.0884665i
$481$	−1.43379e6	+	1.43379e6i	−0.0128840	+	0.0128840i
$482$	−2.19689e8	+	2.19689e8i	−1.96186	+	1.96186i
$483$	2.89667e7	−	2.44884e7i	0.257074	−	0.217329i
$484$		−	3.09371e8i		−	2.72863i
$485$	−1.15661e8			−1.01382
$486$	1.78116e8	−	6.85693e7i	1.55165	−	0.597339i
$487$	−1.57839e8	−	1.57839e8i	−1.36656	−	1.36656i	−0.865296	−	0.501261i	$-0.832870\pi$
$487$	−1.57839e8	−	1.57839e8i	−1.36656	−	1.36656i	−0.501261	−	0.865296i	$-0.667130\pi$
$488$	1.58569e6	+	1.58569e6i	0.0136445	+	0.0136445i
$489$	6.09179e7	+	5.10359e6i	0.520977	+	0.0436465i
$490$	1.72394e8	−	1.72394e8i	1.46532	−	1.46532i
$491$	−7.53381e7			−0.636459			−0.318229	−	0.948014i	$-0.603088\pi$
$491$	−7.53381e7			−0.636459			−0.318229	+	0.948014i	$0.603088\pi$
$492$	−1.17027e7	+	1.39687e8i	−0.0982634	+	1.17290i
$493$	5.66310e7	−	3.58946e7i	0.472622	−	0.299563i
$494$		−	2.53591e7i		−	0.210355i
$495$	−4.93797e7	+	2.92637e8i	−0.407130	+	2.41275i
$496$	−4.83546e7	+	4.83546e7i	−0.396271	+	0.396271i
$497$			5.46776e7i			0.445390i
$498$	−8.65998e7	+	7.32112e7i	−0.701179	+	0.592774i
$499$	−9.54717e7	−	9.54717e7i	−0.768375	−	0.768375i	0.209445	−	0.977820i	$-0.432834\pi$
$499$	−9.54717e7	−	9.54717e7i	−0.768375	−	0.768375i	−0.977820	+	0.209445i	$0.932834\pi$
$500$	8.39743e7	−	8.39743e7i	0.671795	−	0.671795i
$501$	−2.21728e8	−	1.85760e7i	−1.76322	−	0.147720i
$502$			1.64828e8i			1.30292i
$503$	−8.24541e7	+	8.24541e7i	−0.647900	+	0.647900i	−0.952485	−	0.304585i	$-0.901482\pi$
$503$	−8.24541e7	+	8.24541e7i	−0.647900	+	0.647900i	0.304585	+	0.952485i	$0.401482\pi$
$504$	5.73651e7	−	4.08006e7i	0.448081	−	0.318694i
$505$	−1.24675e8	+	1.24675e8i	−0.968068	+	0.968068i
$506$		−	2.67465e8i		−	2.06450i
$507$	−9.70655e7	+	8.20588e7i	−0.744802	+	0.629653i
$508$		−	3.01378e7i		−	0.229890i
$509$		−	1.77130e8i		−	1.34320i	−0.740916	−	0.671598i	$-0.765608\pi$
$509$		−	1.77130e8i		−	1.34320i	0.740916	−	0.671598i	$-0.234392\pi$
$510$	−1.01250e8	+	3.22673e8i	−0.763280	+	2.43249i
$511$	−9.92886e7			−0.744109
$512$	9.18506e7			0.684340
$513$	−9.34972e7	+	5.53671e7i	−0.692543	+	0.410109i
$514$	3.08846e8			2.27433
$515$	2.76066e8	+	2.76066e8i	2.02112	+	2.02112i
$516$	2.49336e8	+	2.94934e8i	1.81483	+	2.14672i
$517$	−1.21448e8	−	1.21448e8i	−0.878855	−	0.878855i
$518$	1.15888e7			0.0833776
$519$	1.26427e8	+	1.05918e7i	0.904353	+	0.0757651i
$520$	−3.04583e7	−	3.04583e7i	−0.216618	−	0.216618i
$521$	−5.10822e7	+	5.10822e7i	−0.361208	+	0.361208i	−0.864257	−	0.503050i	$-0.832211\pi$
$521$	−5.10822e7	+	5.10822e7i	−0.361208	+	0.361208i	0.503050	+	0.864257i	$0.332211\pi$
$522$	1.07837e8	−	7.66986e7i	0.758154	−	0.539232i
$523$	−1.36671e8			−0.955372			−0.477686	−	0.878531i	$-0.658524\pi$
$523$	−1.36671e8			−0.955372			−0.477686	+	0.878531i	$0.658524\pi$
$524$	−1.99241e8	−	1.99241e8i	−1.38479	−	1.38479i
$525$	7.06164e6	−	8.42897e7i	0.0488009	−	0.582501i
$526$	−1.22925e8			−0.844665
$527$	−1.25898e8	−	1.98630e8i	−0.860179	−	1.35711i
$528$	6.83977e6	−	8.16415e7i	0.0464665	−	0.554637i
$529$			5.84059e7i			0.394539i
$530$	2.84870e8	+	2.84870e8i	1.91346	+	1.91346i
$531$	−2.85180e7	+	1.69005e8i	−0.190474	+	1.12880i
$532$	−6.54116e7	+	6.54116e7i	−0.434430	+	0.434430i
$533$	1.12271e7	−	1.12271e7i	0.0741460	−	0.0741460i
$534$	−2.44428e8	−	2.89129e8i	−1.60519	−	1.89875i
$535$			1.86305e8i			1.21664i
$536$	−3.14218e8			−2.04050
$537$	8.65280e7	−	7.31505e7i	0.558771	−	0.472383i
$538$	2.29861e8	+	2.29861e8i	1.47611	+	1.47611i
$539$	−1.43623e8	−	1.43623e8i	−0.917187	−	0.917187i
$540$	−1.05708e8	+	4.12694e8i	−0.671312	+	2.62088i
$541$	−1.31120e7	+	1.31120e7i	−0.0828088	+	0.0828088i	−0.747298	−	0.664489i	$-0.768649\pi$
$541$	−1.31120e7	+	1.31120e7i	−0.0828088	+	0.0828088i	0.664489	+	0.747298i	$0.268649\pi$
$542$	1.52770e8			0.959491
$543$	−1.26368e8	−	1.05869e7i	−0.789295	−	0.0661257i
$544$	−2.43306e7	+	1.08563e8i	−0.151132	+	0.674347i
$545$			6.33456e7i			0.391315i
$546$	−1.83399e7	−	1.53649e6i	−0.112673	−	0.00943955i
$547$	−1.54290e7	+	1.54290e7i	−0.0942708	+	0.0942708i	−0.752669	−	0.658399i	$-0.771234\pi$
$547$	−1.54290e7	+	1.54290e7i	−0.0942708	+	0.0942708i	0.658399	+	0.752669i	$0.271234\pi$
$548$			1.28683e8i			0.781953i
$549$	−2.04718e6	+	1.45604e6i	−0.0123720	+	0.00879949i
$550$	−4.21747e8	−	4.21747e8i	−2.53492	−	2.53492i
$551$	−5.32734e7	+	5.32734e7i	−0.318460	+	0.318460i
$552$	1.38872e7	−	1.65761e8i	0.0825651	−	0.985520i
$553$		−	3.28493e7i		−	0.194245i
$554$	1.09545e8	−	1.09545e8i	0.644261	−	0.644261i
$555$	−2.32041e7	+	1.96167e7i	−0.135733	+	0.114748i
$556$	1.10133e8	−	1.10133e8i	0.640757	−	0.640757i
$557$		−	1.22033e8i		−	0.706172i	−0.935591	−	0.353086i	$-0.885132\pi$
$557$		−	1.22033e8i		−	0.706172i	0.935591	−	0.353086i	$-0.114868\pi$
$558$	−2.69016e8	−	3.78234e8i	−1.54837	−	2.17700i
$559$		−	4.37449e7i		−	0.250433i
$560$			4.06324e7i			0.231371i
$561$	2.68822e8	+	8.43524e7i	1.52257	+	0.477759i
$562$	6.81061e7			0.383687
$563$	3.86818e7			0.216761			0.108381	−	0.994109i	$-0.465434\pi$
$563$	3.86818e7			0.216761			0.108381	+	0.994109i	$0.465434\pi$
$564$	−1.59174e8	−	1.88283e8i	−0.887228	−	1.04948i
$565$	3.78840e7			0.210044
$566$	1.25524e7	+	1.25524e7i	0.0692275	+	0.0692275i
$567$	3.43771e7	+	7.09728e7i	0.188591	+	0.389352i
$568$	1.69552e8	+	1.69552e8i	0.925248	+	0.925248i
$569$	9.37720e7			0.509022			0.254511	−	0.967070i	$-0.418086\pi$
$569$	9.37720e7			0.509022			0.254511	+	0.967070i	$0.418086\pi$
$570$	3.17251e7	−	3.78680e8i	0.171308	−	2.04478i
$571$	1.70551e8	+	1.70551e8i	0.916107	+	0.916107i	0.996744	−	0.0806365i	$-0.0256953\pi$
$571$	1.70551e8	+	1.70551e8i	0.916107	+	0.916107i	−0.0806365	+	0.996744i	$0.525695\pi$
$572$	−5.85699e7	+	5.85699e7i	−0.312958	+	0.312958i
$573$	5.06034e7	+	5.98576e7i	0.268978	+	0.318167i
$574$	−9.07448e7			−0.479828
$575$	−1.41331e8	−	1.41331e8i	−0.743421	−	0.743421i
$576$	−4.76263e7	+	2.82246e8i	−0.249218	+	1.47693i
$577$	−1.12078e8			−0.583435			−0.291717	−	0.956505i	$-0.594227\pi$
$577$	−1.12078e8			−0.583435			−0.291717	+	0.956505i	$0.594227\pi$
$578$	2.90350e8	+	1.37026e8i	1.50362	+	0.709612i
$579$	−1.70343e8	−	1.42711e7i	−0.877586	−	0.0735226i
$580$			2.95378e8i			1.51389i
$581$	−3.31315e7	−	3.31315e7i	−0.168932	−	0.168932i
$582$	−1.80927e7	+	2.15960e8i	−0.0917773	+	1.09548i
$583$	2.37329e8	−	2.37329e8i	1.19769	−	1.19769i
$584$	−3.07888e8	+	3.07888e8i	−1.54581	+	1.54581i
$585$	3.93227e7	−	2.79680e7i	0.196415	−	0.139699i
$586$			5.54150e8i			2.75382i
$587$	1.65927e8			0.820359			0.410180	−	0.912005i	$-0.365466\pi$
$587$	1.65927e8			0.820359			0.410180	+	0.912005i	$0.365466\pi$
$588$	−1.88238e8	−	2.22663e8i	−0.925925	−	1.09526i
$589$	1.86853e8	+	1.86853e8i	0.914440	+	0.914440i
$590$	−4.23835e8	−	4.23835e8i	−2.06367	−	2.06367i
$591$	7.96721e6	−	9.50989e7i	0.0385961	−	0.460694i
$592$	5.93127e6	−	5.93127e6i	0.0285879	−	0.0285879i
$593$	−3.74030e8			−1.79367			−0.896834	−	0.442367i	$-0.854139\pi$
$593$	−3.74030e8			−1.79367			−0.896834	+	0.442367i	$0.854139\pi$
$594$	5.38682e8	+	1.37978e8i	2.57023	+	0.658340i
$595$	−1.36351e8	−	3.05584e7i	−0.647303	−	0.145071i
$596$			4.30487e7i			0.203339i
$597$	1.68325e7	−	2.00918e8i	0.0791092	−	0.944269i
$598$	−3.07512e7	+	3.07512e7i	−0.143800	+	0.143800i
$599$			6.67935e7i			0.310780i	0.987853	+	0.155390i	$0.0496635\pi$
$599$			6.67935e7i			0.310780i	−0.987853	+	0.155390i	$0.950337\pi$
$600$	−2.39480e8	−	2.83275e8i	−1.10870	−	1.31146i
$601$	−3.15340e7	−	3.15340e7i	−0.145263	−	0.145263i	0.630735	−	0.775998i	$-0.282754\pi$
$601$	−3.15340e7	−	3.15340e7i	−0.145263	−	0.145263i	−0.775998	+	0.630735i	$0.782754\pi$
$602$	−1.76787e8	+	1.76787e8i	−0.810327	+	0.810327i
$603$	5.85695e7	−	3.47097e8i	0.267128	−	1.58307i
$604$		−	2.79115e8i		−	1.26669i
$605$	−3.71306e8	+	3.71306e8i	−1.67674	+	1.67674i
$606$	2.13288e8	+	2.52294e8i	0.958406	+	1.13368i
$607$	2.02901e7	−	2.02901e7i	0.0907232	−	0.0907232i	−0.660289	−	0.751012i	$-0.729566\pi$
$607$	2.02901e7	−	2.02901e7i	0.0907232	−	0.0907232i	0.751012	+	0.660289i	$0.229566\pi$
$608$		−	1.25014e8i		−	0.556221i
$609$	3.53000e7	+	4.17556e7i	0.156287	+	0.184869i
$610$		−	8.78549e6i		−	0.0387059i
$611$			2.79264e7i			0.122431i
$612$	3.74437e8	+	1.52881e8i	1.63352	+	0.666960i
$613$	−1.63950e7			−0.0711754			−0.0355877	−	0.999367i	$-0.511330\pi$
$613$	−1.63950e7			−0.0711754			−0.0355877	+	0.999367i	$0.511330\pi$
$614$	−8.81787e7			−0.380942
$615$	1.81697e8	−	1.53606e8i	0.781129	−	0.660363i
$616$	2.05097e8			0.877441
$617$	2.09034e8	+	2.09034e8i	0.889940	+	0.889940i	0.994517	−	0.104576i	$-0.0333487\pi$
$617$	2.09034e8	+	2.09034e8i	0.889940	+	0.889940i	−0.104576	+	0.994517i	$0.533349\pi$
$618$	5.58651e8	−	4.72281e8i	2.36687	−	2.00094i
$619$	7.71872e7	+	7.71872e7i	0.325442	+	0.325442i	0.850850	−	0.525408i	$-0.176087\pi$
$619$	7.71872e7	+	7.71872e7i	0.325442	+	0.325442i	−0.525408	+	0.850850i	$0.676087\pi$
$620$	1.03602e9			4.34704
$621$	1.80517e8	+	4.62377e7i	0.753780	+	0.193073i
$622$	−1.76830e8	−	1.76830e8i	−0.734827	−	0.734827i
$623$	1.10615e8	−	1.10615e8i	0.457458	−	0.457458i
$624$	−1.01730e7	+	8.60018e6i	−0.0418691	+	0.0353960i
$625$	1.28302e8			0.525526
$626$	−5.03069e7	−	5.03069e7i	−0.205071	−	0.205071i
$627$	−3.15482e8	−	2.64305e7i	−1.27989	−	0.107227i
$628$	−3.43782e8			−1.38805
$629$	1.54430e7	+	2.43644e7i	0.0620553	+	0.0979048i
$630$	−2.71943e8	−	4.58878e7i	−1.08757	−	0.183517i
$631$		−	1.30044e8i		−	0.517608i	−0.965930	−	0.258804i	$-0.916672\pi$
$631$		−	1.30044e8i		−	0.517608i	0.965930	−	0.258804i	$-0.0833284\pi$
$632$	−1.01864e8	−	1.01864e8i	−0.403524	−	0.403524i
$633$	−1.91575e8	−	1.60498e7i	−0.755313	−	0.0632787i
$634$	1.20515e8	−	1.20515e8i	0.472906	−	0.472906i
$635$	−3.61712e7	+	3.61712e7i	−0.141267	+	0.141267i
$636$	3.67937e8	−	3.11052e8i	1.43022	−	1.20910i
$637$			3.30256e7i			0.127771i
$638$	3.85551e8			1.48463
$639$	−2.18898e8	+	1.55689e8i	−0.838955	+	0.596701i
$640$	−5.11401e8	−	5.11401e8i	−1.95084	−	1.95084i
$641$	1.15711e8	+	1.15711e8i	0.439339	+	0.439339i	0.891790	−	0.452450i	$-0.149450\pi$
$641$	1.15711e8	+	1.15711e8i	0.439339	+	0.439339i	−0.452450	+	0.891790i	$0.649450\pi$
$642$	3.47865e8	+	2.91435e7i	1.31464	+	0.110138i
$643$	−8.43569e7	+	8.43569e7i	−0.317313	+	0.317313i	−0.847734	−	0.530421i	$-0.822034\pi$
$643$	−8.43569e7	+	8.43569e7i	−0.317313	+	0.317313i	0.530421	+	0.847734i	$0.322034\pi$
$644$	1.58640e8			0.593958
$645$	5.47264e7	−	6.53229e8i	0.203947	−	2.43437i
$646$	−3.52031e8	−	7.88955e7i	−1.30582	−	0.292654i
$647$			4.39837e8i			1.62397i	0.583676	+	0.811987i	$0.301614\pi$
$647$			4.39837e8i			1.62397i	−0.583676	+	0.811987i	$0.698386\pi$
$648$	3.26684e8	+	1.13481e8i	1.20061	+	0.417060i
$649$	−3.53102e8	+	3.53102e8i	−1.29171	+	1.29171i
$650$			9.69790e7i			0.353132i
$651$	1.46456e8	−	1.23813e8i	0.530839	−	0.448769i
$652$	1.80788e8	+	1.80788e8i	0.652269	+	0.652269i
$653$	−9.51860e7	+	9.51860e7i	−0.341848	+	0.341848i	−0.857062	−	0.515213i	$-0.827713\pi$
$653$	−9.51860e7	+	9.51860e7i	−0.341848	+	0.341848i	0.515213	+	0.857062i	$0.327713\pi$
$654$	1.18278e8	+	9.90910e6i	0.422834	+	0.0354243i
$655$			4.78255e8i			1.70190i
$656$	−4.64441e7	+	4.64441e7i	−0.164520	+	0.164520i
$657$	−2.82715e8	−	3.97495e8i	−0.996904	−	1.40164i
$658$	1.12859e8	−	1.12859e8i	0.396150	−	0.396150i
$659$		−	6.89218e7i		−	0.240824i	−0.992724	−	0.120412i	$-0.961578\pi$
$659$		−	6.89218e7i		−	0.240824i	0.992724	−	0.120412i	$-0.0384216\pi$
$660$	−9.47879e8	+	8.01333e8i	−3.29702	+	2.78728i
$661$		−	1.11917e8i		−	0.387516i	−0.981049	−	0.193758i	$-0.937932\pi$
$661$		−	1.11917e8i		−	0.387516i	0.981049	−	0.193758i	$-0.0620677\pi$
$662$			8.18306e8i			2.82060i
$663$	−2.12090e7	−	4.06055e7i	−0.0727747	−	0.139330i
$664$	−2.05478e8			−0.701877
$665$	1.57013e8			0.533914
$666$	3.29981e7	+	4.63949e7i	0.111703	+	0.157054i
$667$	1.29202e8			0.435403
$668$	−6.58030e8	−	6.58030e8i	−2.20758	−	2.20758i
$669$	2.84253e8	+	3.36236e8i	0.949349	+	1.12296i
$670$	8.70461e8	+	8.70461e8i	2.89418	+	2.89418i
$671$	−7.31929e6			−0.0242271
$672$	−9.04113e7	−	7.57450e6i	−0.297930	−	0.0249601i
$673$	1.56977e8	+	1.56977e8i	0.514981	+	0.514981i	0.916048	−	0.401068i	$-0.131361\pi$
$673$	1.56977e8	+	1.56977e8i	0.514981	+	0.514981i	−0.401068	+	0.916048i	$0.631361\pi$
$674$	3.71229e8	−	3.71229e8i	1.21245	−	1.21245i
$675$	3.57555e8	−	2.11737e8i	1.16260	−	0.688469i
$676$	−5.31593e8			−1.72083
$677$	−1.99197e8	−	1.99197e8i	−0.641972	−	0.641972i	0.309068	−	0.951040i	$-0.399983\pi$
$677$	−1.99197e8	−	1.99197e8i	−0.641972	−	0.641972i	−0.951040	+	0.309068i	$0.899983\pi$
$678$	5.92616e6	−	7.07363e7i	0.0190145	−	0.226962i
$679$	−8.95443e7			−0.286041
$680$	−5.17577e8	+	3.28057e8i	−1.64607	+	1.04333i
$681$	3.36140e7	−	4.01226e8i	0.106434	−	1.27042i
$682$		−	1.35230e9i		−	4.26304i
$683$	−3.16717e7	−	3.16717e7i	−0.0994051	−	0.0994051i	0.655655	−	0.755060i	$-0.272392\pi$
$683$	−3.16717e7	−	3.16717e7i	−0.0994051	−	0.0994051i	−0.755060	+	0.655655i	$0.772392\pi$
$684$	−4.48124e8	−	7.56169e7i	−1.40033	−	0.236293i
$685$	1.54445e8	−	1.54445e8i	0.480509	−	0.480509i
$686$	2.97665e8	−	2.97665e8i	0.922052	−	0.922052i
$687$	1.32216e8	+	1.56395e8i	0.407769	+	0.482340i
$688$			1.80963e8i			0.555678i
$689$	−5.45728e7			−0.166847
$690$	−4.97670e8	+	4.20728e8i	−1.51493	+	1.28072i
$691$	5.25388e7	+	5.25388e7i	0.159238	+	0.159238i	0.782229	−	0.622991i	$-0.214083\pi$
$691$	5.25388e7	+	5.25388e7i	0.159238	+	0.159238i	−0.622991	+	0.782229i	$0.714083\pi$
$692$	3.75202e8	+	3.75202e8i	1.13226	+	1.13226i
$693$	−3.82296e7	+	2.26558e8i	−0.114868	+	0.680738i
$694$	−2.06919e8	+	2.06919e8i	−0.619046	+	0.619046i
$695$	−2.64362e8			−0.787489
$696$	2.38945e8	+	2.00184e7i	0.708713	+	0.0593747i
$697$	−1.20924e8	−	1.90783e8i	−0.357121	−	0.563431i
$698$		−	7.33371e8i		−	2.15654i
$699$	−1.20354e6	−	100830.i	−0.00352393	−	0.000295229i
$700$	2.50149e8	−	2.50149e8i	0.729298	−	0.729298i
$701$			4.02608e8i			1.16877i	0.811477	+	0.584384i	$0.198664\pi$
$701$			4.02608e8i			1.16877i	−0.811477	+	0.584384i	$0.801336\pi$
$702$	−4.60701e7	−	7.77976e7i	−0.133171	−	0.224882i
$703$	−2.29198e7	−	2.29198e7i	−0.0659698	−	0.0659698i
$704$	−5.89695e8	+	5.89695e8i	−1.69009	+	1.69009i
$705$	−3.49369e7	+	4.17017e8i	−0.0997050	+	1.19011i
$706$		−	4.39912e7i		−	0.125012i
$707$	−9.65231e7	+	9.65231e7i	−0.273132	+	0.273132i
$708$	−5.47423e8	+	4.62790e8i	−1.54249	+	1.30402i
$709$	6.65820e7	−	6.65820e7i	0.186818	−	0.186818i	−0.607501	−	0.794319i	$-0.707828\pi$
$709$	6.65820e7	−	6.65820e7i	0.186818	−	0.186818i	0.794319	+	0.607501i	$0.207828\pi$
$710$		−	9.39401e8i		−	2.62468i
$711$	1.31510e8	−	9.35355e7i	0.365889	−	0.260236i
$712$		−	6.86023e8i		−	1.90064i
$713$		−	4.53169e8i		−	1.25023i
$714$	−7.83873e7	+	2.49812e8i	−0.215353	+	0.686308i
$715$	1.40590e8			0.384625
$716$	4.73883e8			1.29102
$717$	1.38396e8	+	1.63705e8i	0.375462	+	0.444125i
$718$	8.41223e7			0.227268
$719$	2.04482e8	+	2.04482e8i	0.550135	+	0.550135i	0.926480	−	0.376345i	$-0.122819\pi$
$719$	2.04482e8	+	2.04482e8i	0.550135	+	0.550135i	−0.376345	+	0.926480i	$0.622819\pi$
$720$	−1.62669e8	+	1.15697e8i	−0.435820	+	0.309974i
$721$	2.13729e8	+	2.13729e8i	0.570241	+	0.570241i
$722$	−2.20393e8			−0.585580
$723$	5.26510e7	−	6.28457e8i	0.139313	−	1.66288i
$724$	−3.75028e8	−	3.75028e8i	−0.988207	−	0.988207i
$725$	2.03730e8	−	2.03730e8i	0.534614	−	0.534614i
$726$	6.35212e8	+	7.51378e8i	1.66000	+	1.96358i
$727$	2.20498e8			0.573853			0.286927	−	0.957953i	$-0.407366\pi$
$727$	2.20498e8			0.573853			0.286927	+	0.957953i	$0.407366\pi$
$728$	−2.35807e7	−	2.35807e7i	−0.0611170	−	0.0611170i
$729$	−1.86248e8	+	3.39715e8i	−0.480740	+	0.876863i
$730$	1.70585e9			4.38503
$731$	−6.07260e8	−	1.36096e8i	−1.55461	−	0.348413i
$732$	−1.04701e7	−	877168.i	−0.0266943	−	0.00223640i
$733$		−	2.25500e8i		−	0.572579i	−0.958143	−	0.286289i	$-0.907578\pi$
$733$		−	2.25500e8i		−	0.572579i	0.958143	−	0.286289i	$-0.0924219\pi$
$734$	5.38666e8	+	5.38666e8i	1.36217	+	1.36217i
$735$	−4.13161e7	+	4.93161e8i	−0.104054	+	1.24201i
$736$	−1.51596e8	+	1.51596e8i	−0.380236	+	0.380236i
$737$	7.25190e8	−	7.25190e8i	1.81155	−	1.81155i
$738$	−2.58388e8	−	3.63290e8i	−0.642840	−	0.903825i
$739$			1.08366e8i			0.268511i	0.990947	+	0.134255i	$0.0428642\pi$
$739$			1.08366e8i			0.268511i	−0.990947	+	0.134255i	$0.957136\pi$
$740$	−1.27081e8			−0.313606
$741$	3.32331e7	+	3.93107e7i	0.0816802	+	0.0966177i
$742$	2.20546e8	+	2.20546e8i	0.539867	+	0.539867i
$743$	−3.05319e8	−	3.05319e8i	−0.744366	−	0.744366i	0.229049	−	0.973415i	$-0.426438\pi$
$743$	−3.05319e8	−	3.05319e8i	−0.744366	−	0.744366i	−0.973415	+	0.229049i	$0.926438\pi$
$744$	7.02135e7	−	8.38088e8i	0.170491	−	2.03503i
$745$	5.16668e7	−	5.16668e7i	0.124952	−	0.124952i
$746$	4.35921e8			1.05001
$747$	3.83005e7	−	2.26979e8i	0.0918847	−	0.544532i
$748$	6.30839e8	+	9.95276e8i	1.50735	+	2.37815i
$749$			1.44236e8i			0.343265i
$750$	−3.15316e7	+	3.76370e8i	−0.0747415	+	0.892136i
$751$	−2.47566e8	+	2.47566e8i	−0.584483	+	0.584483i	−0.936132	−	0.351649i	$-0.885621\pi$
$751$	−2.47566e8	+	2.47566e8i	−0.584483	+	0.584483i	0.351649	+	0.936132i	$0.385621\pi$
$752$		−	1.15525e8i		−	0.271658i
$753$	−2.16007e8	−	2.55510e8i	−0.505921	−	0.598443i
$754$	−4.43280e7	−	4.43280e7i	−0.103410	−	0.103410i
$755$	−3.34992e8	+	3.34992e8i	−0.778382	+	0.778382i
$756$	−8.18384e7	+	3.19506e8i	−0.189405	+	0.739459i
$757$		−	1.26629e8i		−	0.291908i	−0.989291	−	0.145954i	$-0.953375\pi$
$757$		−	1.26629e8i		−	0.291908i	0.989291	−	0.145954i	$-0.0466252\pi$
$758$	−5.20557e8	+	5.20557e8i	−1.19526	+	1.19526i
$759$	3.50513e8	+	4.14614e8i	0.801638	+	0.948240i
$760$	4.86889e8	−	4.86889e8i	1.10915	−	1.10915i
$761$			4.90419e8i			1.11279i	0.830918	+	0.556395i	$0.187816\pi$
$761$			4.90419e8i			1.11279i	−0.830918	+	0.556395i	$0.812184\pi$
$762$	6.18800e7	+	7.31965e7i	0.139857	+	0.165434i
$763$			4.90419e7i			0.110406i
$764$			3.27819e8i			0.735113i
$765$	−2.65909e8	−	6.32884e8i	−0.593949	−	1.41364i
$766$	−9.70501e8			−2.15928
$767$	8.11944e7			0.179945
$768$	−5.16738e8	+	4.36848e8i	−1.14074	+	0.964377i
$769$	−1.85749e8			−0.408457			−0.204229	−	0.978923i	$-0.565469\pi$
$769$	−1.85749e8			−0.408457			−0.204229	+	0.978923i	$0.565469\pi$
$770$	−5.68170e8	−	5.68170e8i	−1.24453	−	1.24453i
$771$	−4.78762e8	+	4.04744e8i	−1.04462	+	0.883115i
$772$	−5.05534e8	−	5.05534e8i	−1.09875	−	1.09875i
$773$	1.41072e7			0.0305423			0.0152712	−	0.999883i	$-0.495139\pi$
$773$	1.41072e7			0.0305423			0.0152712	+	0.999883i	$0.495139\pi$
$774$	−1.21114e9	−	2.04368e8i	−2.61198	−	0.440748i
$775$	−7.14571e8	−	7.14571e8i	−1.53511	−	1.53511i
$776$	−2.77672e8	+	2.77672e8i	−0.594219	+	0.594219i
$777$	−1.79645e7	+	1.51872e7i	−0.0382960	+	0.0323753i
$778$	−5.29548e8			−1.12452
$779$	1.79471e8	+	1.79471e8i	0.379649	+	0.379649i
$780$	2.01112e8	+	1.68488e7i	0.423794	+	0.0355047i
$781$	−7.82625e8			−1.64286
$782$	3.31213e8	+	5.22555e8i	0.692606	+	1.09273i
$783$	−6.66518e7	+	2.60216e8i	−0.138844	+	0.542063i
$784$		−	1.36619e8i		−	0.283507i
$785$	4.12605e8	+	4.12605e8i	0.852953	+	0.852953i
$786$	8.92989e8	+	7.48130e7i	1.83899	+	0.154067i
$787$	−6.06000e8	+	6.06000e8i	−1.24322	+	1.24322i	−0.284564	+	0.958657i	$0.591849\pi$
$787$	−6.06000e8	+	6.06000e8i	−1.24322	+	1.24322i	−0.958657	+	0.284564i	$0.908151\pi$
$788$	2.82228e8	−	2.82228e8i	0.576795	−	0.576795i
$789$	1.90554e8	−	1.61094e8i	0.387961	−	0.327981i
$790$			5.64375e8i			1.14469i
$791$	2.93297e7			0.0592622
$792$	5.83997e8	+	8.21092e8i	1.17553	+	1.65279i
$793$	841521.	+	841521.i	0.00168751	+	0.00168751i
$794$	−1.03580e9	−	1.03580e9i	−2.06926	−	2.06926i
$795$	−8.14919e8	−	6.82725e7i	−1.62186	−	0.135876i
$796$	5.96271e8	−	5.96271e8i	1.18224	−	1.18224i
$797$	−7.75366e8			−1.53155			−0.765776	−	0.643107i	$-0.777645\pi$
$797$	−7.75366e8			−1.53155			−0.765776	+	0.643107i	$0.777645\pi$
$798$	2.45615e7	−	2.93172e8i	0.0483332	−	0.576919i
$799$	3.87670e8	+	8.68828e7i	0.760014	+	0.170331i
$800$			4.78082e8i			0.933754i
$801$	7.57807e8	+	1.27873e8i	1.47456	+	0.248818i
$802$	−9.30819e8	+	9.30819e8i	−1.80444	+	1.80444i
$803$		−	1.42116e9i		−	2.74471i
$804$	1.12428e9	−	9.50464e8i	2.16325	−	1.82881i
$805$	−1.90399e8	−	1.90399e8i	−0.364987	−	0.364987i
$806$	−1.55478e8	+	1.55478e8i	−0.296937	+	0.296937i
$807$	−6.57556e8	−	5.50888e7i	−1.25116	−	0.104820i
$808$			5.98625e8i			1.13480i
$809$	3.55721e8	−	3.55721e8i	0.671838	−	0.671838i	−0.286302	−	0.958140i	$-0.592426\pi$
$809$	3.55721e8	−	3.55721e8i	0.671838	−	0.671838i	0.958140	+	0.286302i	$0.0924260\pi$
$810$	−5.90624e8	−	1.21936e9i	−1.11136	−	2.29445i
$811$	2.98190e8	−	2.98190e8i	0.559024	−	0.559024i	−0.370006	−	0.929030i	$-0.620644\pi$
$811$	2.98190e8	−	2.98190e8i	0.559024	−	0.559024i	0.929030	+	0.370006i	$0.120644\pi$
$812$			2.28681e8i			0.427131i
$813$	−2.36819e8	+	2.00206e8i	−0.440702	+	0.372567i
$814$			1.65876e8i			0.307546i
$815$		−	4.33962e8i		−	0.801638i
$816$	8.77369e7	+	1.67976e8i	0.161477	+	0.309155i
$817$	6.99282e8			1.28229
$818$	−2.26719e8			−0.414218
$819$	3.04435e7	−	2.16527e7i	0.0554170	−	0.0394149i
$820$	9.95090e8			1.80477
$821$	1.59698e8	+	1.59698e8i	0.288582	+	0.288582i	0.836519	−	0.547938i	$-0.184587\pi$
$821$	1.59698e8	+	1.59698e8i	0.288582	+	0.288582i	−0.547938	+	0.836519i	$0.684587\pi$
$822$	−2.64217e8	−	3.12536e8i	−0.475713	−	0.562711i
$823$	−1.19495e8	−	1.19495e8i	−0.214364	−	0.214364i	0.591755	−	0.806118i	$-0.298435\pi$
$823$	−1.19495e8	−	1.19495e8i	−0.214364	−	0.214364i	−0.806118	+	0.591755i	$0.798435\pi$
$824$	1.32553e9			2.36923
$825$	1.20648e9	+	1.01076e8i	2.14861	+	0.180006i
$826$	−3.28132e8	−	3.28132e8i	−0.582248	−	0.582248i
$827$	3.62764e8	−	3.62764e8i	0.641368	−	0.641368i	−0.309523	−	0.950892i	$-0.600170\pi$
$827$	3.62764e8	−	3.62764e8i	0.641368	−	0.641368i	0.950892	+	0.309523i	$0.100170\pi$
$828$	4.51714e8	+	6.35105e8i	0.795743	+	1.11881i
$829$	−5.46257e8			−0.958812			−0.479406	−	0.877593i	$-0.659148\pi$
$829$	−5.46257e8			−0.958812			−0.479406	+	0.877593i	$0.659148\pi$
$830$	5.69224e8	+	5.69224e8i	0.995517	+	0.995517i
$831$	−2.62536e7	+	3.13371e8i	−0.0457495	+	0.546079i
$832$	1.35598e8			0.235442
$833$	4.58456e8	+	1.02747e8i	0.793163	+	0.177760i
$834$	−4.13539e7	+	4.93612e8i	−0.0712883	+	0.850918i
$835$			1.57953e9i			2.71311i
$836$	−9.36266e8	−	9.36266e8i	−1.60244	−	1.60244i
$837$	9.12695e8	+	2.33778e8i	1.55650	+	0.398682i
$838$	−2.42564e7	+	2.42564e7i	−0.0412188	+	0.0412188i
$839$	7.68753e7	−	7.68753e7i	0.130167	−	0.130167i	−0.639022	−	0.769189i	$-0.720661\pi$
$839$	7.68753e7	−	7.68753e7i	0.130167	−	0.130167i	0.769189	+	0.639022i	$0.220661\pi$
$840$	−3.22623e8	−	3.81623e8i	−0.544324	−	0.643869i
$841$		−	4.08578e8i		−	0.686890i
$842$	3.90182e8			0.653628
$843$	−1.05576e8	+	8.92532e7i	−0.176230	+	0.148985i
$844$	−5.68542e8	−	5.68542e8i	−0.945661	−	0.945661i
$845$	6.38014e8	+	6.38014e8i	1.05745	+	1.05745i
$846$	7.73181e8	+	1.30467e8i	1.27694	+	0.215472i
$847$	−2.87463e8	+	2.87463e8i	−0.473078	+	0.473078i
$848$	2.25755e8			0.370212
$849$	−3.59083e7	−	3.00833e6i	−0.0586775	−	0.00491590i
$850$	1.34625e9	+	3.01715e8i	2.19214	+	0.491292i
$851$			5.55866e7i			0.0901948i
$852$	−1.11953e9	−	9.37924e7i	−1.81016	−	0.151652i
$853$	1.36879e8	−	1.36879e8i	0.220541	−	0.220541i	−0.588185	−	0.808726i	$-0.700157\pi$
$853$	1.36879e8	−	1.36879e8i	0.220541	−	0.220541i	0.808726	+	0.588185i	$0.200157\pi$
$854$		−	6.80170e6i		−	0.0109205i
$855$	4.47081e8	+	6.28591e8i	0.715300	+	1.00570i
$856$	4.47269e8	+	4.47269e8i	0.713095	+	0.713095i
$857$	3.00423e8	−	3.00423e8i	0.477299	−	0.477299i	−0.426968	−	0.904267i	$-0.640418\pi$
$857$	3.00423e8	−	3.00423e8i	0.477299	−	0.477299i	0.904267	+	0.426968i	$0.140418\pi$
$858$	2.19924e7	−	2.62508e8i	0.0348186	−	0.415605i
$859$		−	2.42092e8i		−	0.381945i	−0.981595	−	0.190972i	$-0.938836\pi$
$859$		−	2.42092e8i		−	0.381945i	0.981595	−	0.190972i	$-0.0611641\pi$
$860$	1.93861e9	−	1.93861e9i	3.04786	−	3.04786i
$861$	1.40669e8	−	1.18921e8i	0.220389	−	0.186316i
$862$	−6.83624e8	+	6.83624e8i	−1.06732	+	1.06732i
$863$			7.15732e8i			1.11357i	0.830656	+	0.556786i	$0.187966\pi$
$863$			7.15732e8i			1.11357i	−0.830656	+	0.556786i	$0.812034\pi$
$864$	−2.27114e8	−	3.83523e8i	−0.352130	−	0.594634i
$865$		−	9.00630e8i		−	1.39155i
$866$		−	5.50569e8i		−	0.847730i
$867$	−6.29664e8	+	1.68091e8i	−0.966166	+	0.257922i
$868$	8.02085e8			1.22648
$869$	4.70187e8			0.716492
$870$	−6.06480e8	−	7.17392e8i	−0.920999	−	1.08943i
$871$	−1.66755e8			−0.252362
$872$	1.52076e8	+	1.52076e8i	0.229357	+	0.229357i
$873$	−2.54969e8	−	3.58484e8i	−0.383217	−	0.538799i
$874$	−4.91572e8	−	4.91572e8i	−0.736297	−	0.736297i
$875$	−1.56056e8			−0.232946
$876$	1.70317e8	−	2.03295e9i	0.253364	−	3.02423i
$877$	4.71422e8	+	4.71422e8i	0.698893	+	0.698893i	0.964172	−	0.265278i	$-0.0854639\pi$
$877$	4.71422e8	+	4.71422e8i	0.698893	+	0.698893i	−0.265278	+	0.964172i	$0.585464\pi$
$878$	−1.28483e9	+	1.28483e9i	−1.89829	+	1.89829i
$879$	−7.26215e8	−	8.59024e8i	−1.06930	−	1.26485i
$880$	−5.81590e8			−0.853432
$881$	−5.72951e8	−	5.72951e8i	−0.837896	−	0.837896i	0.150686	−	0.988582i	$-0.451852\pi$
$881$	−5.72951e8	−	5.72951e8i	−0.837896	−	0.837896i	−0.988582	+	0.150686i	$0.951852\pi$
$882$	9.14358e8	+	1.54290e8i	1.33263	+	0.224870i
$883$	8.25770e8			1.19944			0.599718	−	0.800211i	$-0.295279\pi$
$883$	8.25770e8			1.19944			0.599718	+	0.800211i	$0.295279\pi$
$884$	4.19005e7	−	1.86959e8i	0.0606544	−	0.270639i
$885$	1.21245e9	+	1.01577e8i	1.74918	+	0.146543i
$886$		−	4.79368e8i		−	0.689236i
$887$	1.64991e8	+	1.64991e8i	0.236422	+	0.236422i	0.815367	−	0.578945i	$-0.196535\pi$
$887$	1.64991e8	+	1.64991e8i	0.236422	+	0.236422i	−0.578945	+	0.815367i	$0.696535\pi$
$888$	−8.61253e6	+	1.02802e8i	−0.0122996	+	0.146812i
$889$	−2.80036e7	+	2.80036e7i	−0.0398574	+	0.0398574i
$890$	−1.90045e9	+	1.90045e9i	−2.69579	+	2.69579i
$891$	−1.01586e9	+	4.92055e8i	−1.43616	+	0.695634i
$892$			1.84144e9i			2.59456i
$893$	−4.46416e8			−0.626882
$894$	−8.83892e7	−	1.04554e8i	−0.123705	−	0.146328i
$895$	−5.68752e8	−	5.68752e8i	−0.793329	−	0.793329i
$896$	−3.95925e8	−	3.95925e8i	−0.550413	−	0.550413i
$897$	7.36988e6	−	8.79690e7i	0.0102113	−	0.121886i
$898$	7.15600e8	−	7.15600e8i	0.988192	−	0.988192i
$899$	6.53244e8			0.899076
$900$	1.71373e9	+	2.89176e8i	2.35080	+	0.396675i
$901$	−1.69783e8	+	7.57571e8i	−0.232124	+	1.03574i
$902$		−	1.29887e9i		−	1.76989i
$903$	4.23690e7	−	5.05728e8i	0.0575420	−	0.686837i
$904$	9.09496e7	−	9.09496e7i	0.123111	−	0.123111i
$905$			9.00212e8i			1.21450i
$906$	5.73088e8	+	6.77893e8i	0.770614	+	0.911541i
$907$	3.52819e8	+	3.52819e8i	0.472858	+	0.472858i	0.902838	−	0.429980i	$-0.141480\pi$
$907$	3.52819e8	+	3.52819e8i	0.472858	+	0.472858i	−0.429980	+	0.902838i	$0.641480\pi$
$908$	1.19073e9	−	1.19073e9i	1.59058	−	1.59058i
$909$	−6.61264e8	−	1.11582e8i	−0.880406	−	0.148560i
$910$			1.30648e8i			0.173372i
$911$	8.29042e7	−	8.29042e7i	0.109653	−	0.109653i	−0.650151	−	0.759805i	$-0.725295\pi$
$911$	8.29042e7	−	8.29042e7i	0.109653	−	0.109653i	0.759805	+	0.650151i	$0.225295\pi$
$912$	−1.37478e8	−	1.62619e8i	−0.181238	−	0.214382i
$913$	4.74226e8	−	4.74226e8i	0.623122	−	0.623122i
$914$			1.08854e9i			1.42563i
$915$	1.15134e7	+	1.36190e7i	0.0150294	+	0.0177779i
$916$			8.56521e8i			1.11443i
$917$			3.70263e8i			0.480178i
$918$	−1.22331e9	+	3.97500e8i	−1.58127	+	0.513817i
$919$	1.03025e9			1.32738			0.663689	−	0.748009i	$-0.268990\pi$
$919$	1.03025e9			1.32738			0.663689	+	0.748009i	$0.268990\pi$
$920$	−1.18083e9			−1.51644
$921$	1.36691e8	−	1.15558e8i	0.174970	−	0.147919i
$922$	−4.43457e8			−0.565795
$923$	8.99808e7	+	8.99808e7i	0.114431	+	0.114431i
$924$	−7.33845e8	+	6.20389e8i	−0.930225	+	0.786409i
$925$	8.76507e7	+	8.76507e7i	0.110747	+	0.110747i
$926$	−1.85443e9			−2.33549
$927$	−2.47075e8	+	1.46423e9i	−0.310162	+	1.83810i
$928$	−2.18526e8	−	2.18526e8i	−0.273438	−	0.273438i
$929$	7.32076e8	−	7.32076e8i	0.913081	−	0.913081i	−0.0834327	−	0.996513i	$-0.526588\pi$
$929$	7.32076e8	−	7.32076e8i	0.913081	−	0.913081i	0.996513	+	0.0834327i	$0.0265884\pi$
$930$	−2.51621e9	+	2.12720e9i	−3.12823	+	2.64459i
$931$	−5.27929e8			−0.654224
$932$	−3.57177e6	−	3.57177e6i	−0.00441201	−	0.00441201i
$933$	5.05852e8	+	4.23793e7i	0.622842	+	0.0521806i
$934$	−2.29925e9			−2.82192
$935$	4.37396e8	−	1.95165e9i	0.535106	−	2.38764i
$936$	2.72596e7	−	1.61547e8i	0.0332424	−	0.197003i
$937$		−	9.76902e8i		−	1.18750i	−0.804651	−	0.593748i	$-0.797648\pi$
$937$		−	9.76902e8i		−	1.18750i	0.804651	−	0.593748i	$-0.202352\pi$
$938$	6.73908e8	+	6.73908e8i	0.816567	+	0.816567i
$939$	1.43911e8	+	1.20566e7i	0.173819	+	0.0145623i
$940$	−1.23759e9	+	1.23759e9i	−1.49003	+	1.49003i
$941$	7.76495e8	−	7.76495e8i	0.931901	−	0.931901i	−0.0659234	−	0.997825i	$-0.520999\pi$
$941$	7.76495e8	−	7.76495e8i	0.931901	−	0.931901i	0.997825	+	0.0659234i	$0.0209993\pi$
$942$	8.34951e8	−	7.05864e8i	0.998869	−	0.844440i
$943$		−	4.35264e8i		−	0.519061i
$944$	−3.35882e8			−0.399274
$945$	4.81692e8	−	2.85248e8i	0.570787	−	0.338008i
$946$	−2.53043e9	−	2.53043e9i	−2.98896	−	2.98896i
$947$	−4.65235e8	−	4.65235e8i	−0.547800	−	0.547800i	0.378004	−	0.925804i	$-0.376611\pi$
$947$	−4.65235e8	−	4.65235e8i	−0.547800	−	0.547800i	−0.925804	+	0.378004i	$0.876611\pi$
$948$	6.72595e8	+	5.63488e7i	0.789457	+	0.0661393i
$949$	−1.63395e8	+	1.63395e8i	−0.191179	+	0.191179i
$950$	−1.55025e9			−1.80814
$951$	−2.88829e7	+	3.44754e8i	−0.0335814	+	0.400837i
$952$	−4.00706e8	+	2.53981e8i	−0.464424	+	0.294368i
$953$			5.52054e8i			0.637827i	0.947784	+	0.318914i	$0.103318\pi$
$953$			5.52054e8i			0.637827i	−0.947784	+	0.318914i	$0.896682\pi$
$954$	−2.54954e8	+	1.51092e9i	−0.293641	+	1.74019i
$955$	3.93446e8	−	3.93446e8i	0.451726	−	0.451726i
$956$			8.96556e8i			1.02613i
$957$	−5.97667e8	+	5.05265e8i	−0.681904	+	0.576479i
$958$	7.71188e8	+	7.71188e8i	0.877130	+	0.877130i
$959$	1.19571e8	−	1.19571e8i	0.135572	−	0.135572i
$960$	2.02485e9	+	1.69638e8i	2.28865	+	0.191739i
$961$		−	1.40371e9i		−	1.58164i
$962$	1.90713e7	−	1.90713e7i	0.0214217	−	0.0214217i
$963$	−5.77440e8	+	4.10700e8i	−0.646588	+	0.459882i
$964$	1.86509e9	−	1.86509e9i	2.08194	−	2.08194i
$965$			1.21348e9i			1.35036i
$966$	−3.85294e8	+	3.25726e8i	−0.427426	+	0.361344i
$967$		−	1.18919e9i		−	1.31514i	−0.753394	−	0.657569i	$-0.771585\pi$
$967$		−	1.18919e9i		−	1.31514i	0.753394	−	0.657569i	$-0.228415\pi$
$968$			1.78282e9i			1.96553i
$969$	6.49098e8	−	3.39036e8i	0.713410	−	0.372628i
$970$	1.53844e9			1.68564
$971$	−1.52938e9			−1.67054			−0.835271	−	0.549839i	$-0.814689\pi$
$971$	−1.52938e9			−1.67054			−0.835271	+	0.549839i	$0.814689\pi$
$972$	−1.51215e9	+	5.82132e8i	−1.64663	+	0.633903i
$973$	−2.04668e8			−0.222183
$974$	2.09946e9	+	2.09946e9i	2.27212	+	2.27212i
$975$	−1.27091e8	−	1.50333e8i	−0.137120	−	0.162196i
$976$	−3.48118e6	−	3.48118e6i	−0.00374435	−	0.00374435i
$977$	−9.20805e8			−0.987379			−0.493689	−	0.869638i	$-0.664352\pi$
$977$	−9.20805e8			−0.987379			−0.493689	+	0.869638i	$0.664352\pi$
$978$	−8.10285e8	−	6.78842e7i	−0.866206	−	0.0725692i
$979$	1.58329e9	+	1.58329e9i	1.68737	+	1.68737i
$980$	−1.46357e9	+	1.46357e9i	−1.55502	+	1.55502i
$981$	−1.96336e8	+	1.39643e8i	−0.207966	+	0.147915i
$982$	1.00209e9			1.05821
$983$	1.05438e9	+	1.05438e9i	1.11003	+	1.11003i	0.993145	+	0.116887i	$0.0372914\pi$
$983$	1.05438e9	+	1.05438e9i	1.11003	+	1.11003i	0.116887	+	0.993145i	$0.462709\pi$
$984$	6.74394e7	−	8.04976e8i	0.0707829	−	0.844885i
$985$	−6.77457e8			−0.708880
$986$	−7.53264e8	+	4.77444e8i	−0.785808	+	0.498071i
$987$	−2.70480e7	+	3.22853e8i	−0.0281309	+	0.335779i
$988$			2.15291e8i			0.223231i
$989$	−8.47972e8	−	8.47972e8i	−0.876582	−	0.876582i
$990$	6.56813e8	−	3.89244e9i	0.676918	−	4.01159i
$991$	7.39565e8	−	7.39565e8i	0.759899	−	0.759899i	−0.216405	−	0.976304i	$-0.569433\pi$
$991$	7.39565e8	−	7.39565e8i	0.759899	−	0.759899i	0.976304	+	0.216405i	$0.0694332\pi$
$992$	−7.66467e8	+	7.66467e8i	−0.785161	+	0.785161i
$993$	−1.07239e9	−	1.26851e9i	−1.09523	−	1.29552i
$994$		−	7.27281e8i		−	0.740530i
$995$	−1.43128e9			−1.45297
$996$	7.35206e8	−	6.21540e8i	0.744099	−	0.629059i
$997$	1.11079e8	+	1.11079e8i	0.112084	+	0.112084i	0.760925	−	0.648840i	$-0.224746\pi$
$997$	1.11079e8	+	1.11079e8i	0.112084	+	0.112084i	−0.648840	+	0.760925i	$0.724746\pi$
$998$	1.26989e9	+	1.26989e9i	1.27754	+	1.27754i
$999$	−1.11953e8	−	2.86757e7i	−0.112290	−	0.0287619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.7.f.a.38.4	✓	68
3.2	odd	2	inner	51.7.f.a.38.31	yes	68
17.13	even	4	inner	51.7.f.a.47.31	yes	68
51.47	odd	4	inner	51.7.f.a.47.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.7.f.a.38.4	✓	68	1.1	even	1	trivial
51.7.f.a.38.31	yes	68	3.2	odd	2	inner
51.7.f.a.47.4	yes	68	51.47	odd	4	inner
51.7.f.a.47.31	yes	68	17.13	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	51.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-13.3013 q^{2} +(20.6191 - 17.4313i) q^{3} +112.924 q^{4} +(-135.530 - 135.530i) q^{5} +(-274.261 + 231.859i) q^{6} +(-104.927 - 104.927i) q^{7} -650.746 q^{8} +(121.297 - 718.838i) q^{9} +(1802.72 + 1802.72i) q^{10} +(1501.87 - 1501.87i) q^{11} +(2328.39 - 1968.41i) q^{12} -345.349 q^{13} +(1395.66 + 1395.66i) q^{14} +(-5156.99 - 432.043i) q^{15} +1428.63 q^{16} +(-1074.43 + 4794.08i) q^{17} +(-1613.41 + 9561.45i) q^{18} -5520.56i q^{19} +(-15304.6 - 15304.6i) q^{20} +(-3992.52 - 334.486i) q^{21} +(-19976.7 + 19976.7i) q^{22} +(-6694.40 + 6694.40i) q^{23} +(-13417.8 + 11343.4i) q^{24} +21111.9i q^{25} +4593.57 q^{26} +(-10029.3 - 16936.2i) q^{27} +(-11848.7 - 11848.7i) q^{28} +(-9650.00 - 9650.00i) q^{29} +(68594.5 + 5746.72i) q^{30} +(-33846.8 + 33846.8i) q^{31} +22645.2 q^{32} +(4787.65 - 57146.8i) q^{33} +(14291.2 - 63767.3i) q^{34} +28441.6i q^{35} +(13697.3 - 81173.8i) q^{36} +(4151.72 - 4151.72i) q^{37} +73430.4i q^{38} +(-7120.79 + 6019.89i) q^{39} +(88195.7 + 88195.7i) q^{40} +(-32509.6 + 32509.6i) q^{41} +(53105.6 + 4449.09i) q^{42} +126669. i q^{43} +(169596. - 169596. i) q^{44} +(-113864. + 80984.8i) q^{45} +(89044.0 - 89044.0i) q^{46} -80864.4i q^{47} +(29457.1 - 24902.9i) q^{48} -95629.6i q^{49} -280815. i q^{50} +(61413.4 + 117578. i) q^{51} -38998.0 q^{52} +158022. q^{53} +(133402. + 225273. i) q^{54} -407097. q^{55} +(68280.8 + 68280.8i) q^{56} +(-96230.7 - 113829. i) q^{57} +(128357. + 128357. i) q^{58} -235108. q^{59} +(-582346. - 48787.9i) q^{60} +(-2436.73 - 2436.73i) q^{61} +(450206. - 450206. i) q^{62} +(-88152.9 + 62698.2i) q^{63} -392641. q^{64} +(46805.2 + 46805.2i) q^{65} +(-63681.8 + 760124. i) q^{66} +482859. q^{67} +(-121328. + 541364. i) q^{68} +(-21340.4 + 254725. i) q^{69} -378309. i q^{70} +(-260550. - 260550. i) q^{71} +(-78933.7 + 467781. i) q^{72} +(473132. - 473132. i) q^{73} +(-55223.2 + 55223.2i) q^{74} +(368008. + 435309. i) q^{75} -623401. i q^{76} -315173. q^{77} +(94715.5 - 80072.1i) q^{78} +(156534. + 156534. i) q^{79} +(-193622. - 193622. i) q^{80} +(-502015. - 174386. i) q^{81} +(432419. - 432419. i) q^{82} +315758. q^{83} +(-450850. - 37771.4i) q^{84} +(795360. - 504125. i) q^{85} -1.68485e6i q^{86} +(-367187. - 30762.3i) q^{87} +(-977334. + 977334. i) q^{88} +1.05421e6i q^{89} +(1.51453e6 - 1.07720e6i) q^{90} +(36236.4 + 36236.4i) q^{91} +(-755956. + 755956. i) q^{92} +(-107897. + 1.28789e6i) q^{93} +1.07560e6i q^{94} +(-748202. + 748202. i) q^{95} +(466924. - 394735. i) q^{96} +(426698. - 426698. i) q^{97} +1.27199e6i q^{98} +(-897427. - 1.26177e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 18 q^{3} + 2040 q^{4} - 290 q^{6} - 4 q^{7} - 4256 q^{10} + 4182 q^{12} - 1832 q^{13} + 54976 q^{16} + 10940 q^{18} - 1604 q^{21} + 19576 q^{22} + 15110 q^{24} + 37314 q^{27} - 63120 q^{28} + 51360 q^{30}+ \cdots + 203004 q^{99}+O(q^{100}) \) 68 * q + 18 * q^3 + 2040 * q^4 - 290 * q^6 - 4 * q^7 - 4256 * q^10 + 4182 * q^12 - 1832 * q^13 + 54976 * q^16 + 10940 * q^18 - 1604 * q^21 + 19576 * q^22 + 15110 * q^24 + 37314 * q^27 - 63120 * q^28 + 51360 * q^30 - 88660 * q^31 - 128604 * q^33 + 80200 * q^34 + 335180 * q^37 + 31460 * q^39 - 286828 * q^40 + 45484 * q^45 - 85244 * q^46 + 111922 * q^48 - 590566 * q^51 - 904320 * q^52 - 1215638 * q^54 - 731624 * q^55 + 753144 * q^57 - 328292 * q^58 + 751532 * q^61 + 88664 * q^63 + 870368 * q^64 + 174232 * q^67 + 1420428 * q^69 + 1158660 * q^72 + 2397332 * q^73 + 1415042 * q^75 - 1868044 * q^78 - 1438708 * q^79 - 2973932 * q^81 - 617036 * q^82 + 4901976 * q^84 + 2375468 * q^85 + 521156 * q^88 - 3185088 * q^90 + 1741672 * q^91 + 4082570 * q^96 + 2753300 * q^97 + 203004 * q^99

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