LMFDB - Embedded newform 952.2.z.c.781.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(373,952)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("952.373"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.z (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [272,-6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$136$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			781.14
Character	$\chi$	$=$	952.781
Dual form			952.2.z.c.373.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36114 - 0.383801i) q^{2} +(1.05412 - 1.82578i) q^{3} +(1.70539 + 1.04481i) q^{4} +(-0.211757 - 0.366775i) q^{5} +(-2.13553 + 2.08057i) q^{6} +(2.37693 + 1.16197i) q^{7} +(-1.92028 - 2.07666i) q^{8} +(-0.722323 - 1.25110i) q^{9} +(0.147463 + 0.580503i) q^{10} +(-1.23105 + 2.13224i) q^{11} +(3.70528 - 2.01233i) q^{12} +1.83577i q^{13} +(-2.78937 - 2.49388i) q^{14} -0.892868 q^{15} +(1.81674 + 3.56363i) q^{16} +(2.27666 + 3.43756i) q^{17} +(0.503008 + 1.98015i) q^{18} +(6.78893 - 3.91959i) q^{19} +(0.0220804 - 0.846742i) q^{20} +(4.62708 - 3.11491i) q^{21} +(2.49398 - 2.42979i) q^{22} +(-3.53329 + 2.03995i) q^{23} +(-5.81573 + 1.31697i) q^{24} +(2.41032 - 4.17479i) q^{25} +(0.704569 - 2.49873i) q^{26} +3.27905 q^{27} +(2.83957 + 4.46507i) q^{28} -1.13811 q^{29} +(1.21532 + 0.342683i) q^{30} +(4.95666 + 2.86173i) q^{31} +(-1.10511 - 5.54786i) q^{32} +(2.59534 + 4.49526i) q^{33} +(-1.77951 - 5.55278i) q^{34} +(-0.0771512 - 1.11786i) q^{35} +(0.0753182 - 2.88831i) q^{36} +(-3.84972 - 6.66792i) q^{37} +(-10.7450 + 2.72951i) q^{38} +(3.35171 + 1.93511i) q^{39} +(-0.355034 + 1.14406i) q^{40} +5.93504i q^{41} +(-7.49360 + 2.46395i) q^{42} -2.67323i q^{43} +(-4.32721 + 2.35009i) q^{44} +(-0.305914 + 0.529859i) q^{45} +(5.59223 - 1.42057i) q^{46} +(3.80805 + 6.59574i) q^{47} +(8.42147 + 0.439511i) q^{48} +(4.29964 + 5.52387i) q^{49} +(-4.88306 + 4.75739i) q^{50} +(8.67610 - 0.533091i) q^{51} +(-1.91803 + 3.13071i) q^{52} +(8.90271 + 5.13998i) q^{53} +(-4.46324 - 1.25850i) q^{54} +1.04273 q^{55} +(-2.15135 - 7.16741i) q^{56} -16.5268i q^{57} +(1.54913 + 0.436808i) q^{58} +(-8.32914 - 4.80883i) q^{59} +(-1.52269 - 0.932878i) q^{60} +(-6.29330 - 10.9003i) q^{61} +(-5.64836 - 5.79758i) q^{62} +(-0.263170 - 3.81310i) q^{63} +(-0.625067 + 7.97554i) q^{64} +(0.673313 - 0.388737i) q^{65} +(-1.80733 - 7.11476i) q^{66} +(3.35335 + 1.93606i) q^{67} +(0.290993 + 8.24108i) q^{68} +8.60137i q^{69} +(-0.324020 + 1.55117i) q^{70} +2.73303i q^{71} +(-1.21105 + 3.90248i) q^{72} +(-0.639595 - 0.369271i) q^{73} +(2.68085 + 10.5535i) q^{74} +(-5.08151 - 8.80144i) q^{75} +(15.6730 + 0.408705i) q^{76} +(-5.40373 + 3.63775i) q^{77} +(-3.81945 - 3.92035i) q^{78} +(-12.6359 + 7.29532i) q^{79} +(0.922341 - 1.42096i) q^{80} +(5.62347 - 9.74013i) q^{81} +(2.27787 - 8.07842i) q^{82} -7.35872i q^{83} +(11.1455 - 0.477730i) q^{84} +(0.778711 - 1.56295i) q^{85} +(-1.02599 + 3.63863i) q^{86} +(-1.19970 + 2.07795i) q^{87} +(6.79190 - 1.53802i) q^{88} +(-6.73261 - 11.6612i) q^{89} +(0.619752 - 0.603802i) q^{90} +(-2.13311 + 4.36350i) q^{91} +(-8.15702 - 0.212710i) q^{92} +(10.4498 - 6.03319i) q^{93} +(-2.65184 - 10.4393i) q^{94} +(-2.87521 - 1.66001i) q^{95} +(-11.2941 - 3.83040i) q^{96} -11.7599i q^{97} +(-3.73233 - 9.16895i) q^{98} +3.55686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 132 q^{9} - 40 q^{15} - 26 q^{16} - 6 q^{17} + 6 q^{18} - 112 q^{25} - 8 q^{26} - 2 q^{30} + 44 q^{32} - 28 q^{33} - 56 q^{34} + 40 q^{36} - 42 q^{38} + 12 q^{42}+ \cdots + 14 q^{98}+O(q^{100}) $ 272 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 132 * q^9 - 40 * q^15 - 26 * q^16 - 6 * q^17 + 6 * q^18 - 112 * q^25 - 8 * q^26 - 2 * q^30 + 44 * q^32 - 28 * q^33 - 56 * q^34 + 40 * q^36 - 42 * q^38 + 12 * q^42 + 28 * q^47 - 60 * q^49 + 72 * q^50 - 38 * q^52 + 232 * q^55 - 6 * q^60 + 40 * q^64 + 48 * q^66 + 32 * q^68 + 86 * q^70 - 36 * q^72 - 148 * q^76 - 168 * q^81 - 34 * q^84 + 22 * q^86 + 16 * q^87 - 72 * q^89 + 62 * q^94 + 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.36114	−	0.383801i	−0.962470	−	0.271388i
$2$	−1.36114	−	0.383801i	−0.962470	−	0.271388i
$3$	1.05412	−	1.82578i	0.608594	−	1.05412i	−0.382878	−	0.923799i	$-0.625067\pi$
$3$	1.05412	−	1.82578i	0.608594	−	1.05412i	0.991472	−	0.130317i	$-0.0415997\pi$
$4$	1.70539	+	1.04481i	0.852697	+	0.522406i
$5$	−0.211757	−	0.366775i	−0.0947008	−	0.164027i	0.814783	−	0.579766i	$-0.196856\pi$
$5$	−0.211757	−	0.366775i	−0.0947008	−	0.164027i	−0.909484	+	0.415740i	$0.863523\pi$
$6$	−2.13553	+	2.08057i	−0.871828	+	0.849390i
$7$	2.37693	+	1.16197i	0.898397	+	0.439185i
$7$	2.37693	+	1.16197i	0.898397	+	0.439185i
$8$	−1.92028	−	2.07666i	−0.678921	−	0.734212i
$9$	−0.722323	−	1.25110i	−0.240774	−	0.417033i
$10$	0.147463	+	0.580503i	0.0466318	+	0.183571i
$11$	−1.23105	+	2.13224i	−0.371175	+	0.642894i	−0.989747	−	0.142834i	$-0.954378\pi$
$11$	−1.23105	+	2.13224i	−0.371175	+	0.642894i	0.618571	+	0.785729i	$0.287712\pi$
$12$	3.70528	−	2.01233i	1.06962	−	0.580909i
$13$			1.83577i			0.509150i	0.967053	+	0.254575i	$0.0819356\pi$
$13$			1.83577i			0.509150i	−0.967053	+	0.254575i	$0.918064\pi$
$14$	−2.78937	−	2.49388i	−0.745491	−	0.666516i
$15$	−0.892868			−0.230537
$16$	1.81674	+	3.56363i	0.454185	+	0.890908i
$17$	2.27666	+	3.43756i	0.552170	+	0.833731i
$17$	2.27666	+	3.43756i	0.552170	+	0.833731i
$18$	0.503008	+	1.98015i	0.118560	+	0.466725i
$19$	6.78893	−	3.91959i	1.55749	−	0.899216i	0.559992	−	0.828498i	$-0.310804\pi$
$19$	6.78893	−	3.91959i	1.55749	−	0.899216i	0.997496	−	0.0707184i	$-0.0225292\pi$
$20$	0.0220804	−	0.846742i	0.00493733	−	0.189337i
$21$	4.62708	−	3.11491i	1.00971	−	0.679730i
$22$	2.49398	−	2.42979i	0.531719	−	0.518034i
$23$	−3.53329	+	2.03995i	−0.736742	+	0.425358i	−0.820884	−	0.571095i	$-0.806519\pi$
$23$	−3.53329	+	2.03995i	−0.736742	+	0.425358i	0.0841413	+	0.996454i	$0.473185\pi$
$24$	−5.81573	+	1.31697i	−1.18713	+	0.268824i
$25$	2.41032	−	4.17479i	0.482064	−	0.834959i
$26$	0.704569	−	2.49873i	0.138177	−	0.490042i
$27$	3.27905			0.631053
$28$	2.83957	+	4.46507i	0.536628	+	0.843819i
$29$	−1.13811			−0.211342			−0.105671	−	0.994401i	$-0.533699\pi$
$29$	−1.13811			−0.211342			−0.105671	+	0.994401i	$0.533699\pi$
$30$	1.21532	+	0.342683i	0.221885	+	0.0625651i
$31$	4.95666	+	2.86173i	0.890242	+	0.513982i	0.874022	−	0.485887i	$-0.161503\pi$
$31$	4.95666	+	2.86173i	0.890242	+	0.513982i	0.0162205	+	0.999868i	$0.494837\pi$
$32$	−1.10511	−	5.54786i	−0.195357	−	0.980732i
$33$	2.59534	+	4.49526i	0.451790	+	0.782524i
$34$	−1.77951	−	5.55278i	−0.305183	−	0.952294i
$35$	−0.0771512	−	1.11786i	−0.0130409	−	0.188952i
$36$	0.0753182	−	2.88831i	0.0125530	−	0.481385i
$37$	−3.84972	−	6.66792i	−0.632891	−	1.09620i	−0.986958	−	0.160979i	$-0.948535\pi$
$37$	−3.84972	−	6.66792i	−0.632891	−	1.09620i	0.354067	−	0.935220i	$-0.384798\pi$
$38$	−10.7450	+	2.72951i	−1.74307	+	0.442785i
$39$	3.35171	+	1.93511i	0.536704	+	0.309866i
$40$	−0.355034	+	1.14406i	−0.0561359	+	0.180891i
$41$			5.93504i			0.926898i	0.886124	+	0.463449i	$0.153388\pi$
$41$			5.93504i			0.926898i	−0.886124	+	0.463449i	$0.846612\pi$
$42$	−7.49360	+	2.46395i	−1.15629	+	0.380196i
$43$		−	2.67323i		−	0.407664i	−0.979006	−	0.203832i	$-0.934660\pi$
$43$		−	2.67323i		−	0.407664i	0.979006	−	0.203832i	$-0.0653396\pi$
$44$	−4.32721	+	2.35009i	−0.652352	+	0.354290i
$45$	−0.305914	+	0.529859i	−0.0456030	+	0.0789868i
$46$	5.59223	−	1.42057i	0.824530	−	0.209452i
$47$	3.80805	+	6.59574i	0.555462	+	0.962088i	0.997867	+	0.0652730i	$0.0207918\pi$
$47$	3.80805	+	6.59574i	0.555462	+	0.962088i	−0.442406	+	0.896815i	$0.645875\pi$
$48$	8.42147	+	0.439511i	1.21553	+	0.0634379i
$49$	4.29964	+	5.52387i	0.614234	+	0.789124i
$50$	−4.88306	+	4.75739i	−0.690569	+	0.672796i
$51$	8.67610	−	0.533091i	1.21490	−	0.0746477i
$52$	−1.91803	+	3.13071i	−0.265983	+	0.434151i
$53$	8.90271	+	5.13998i	1.22288	+	0.706031i	0.965531	−	0.260287i	$-0.0838172\pi$
$53$	8.90271	+	5.13998i	1.22288	+	0.706031i	0.257350	+	0.966318i	$0.417151\pi$
$54$	−4.46324	−	1.25850i	−0.607370	−	0.171260i
$55$	1.04273			0.140602
$56$	−2.15135	−	7.16741i	−0.287486	−	0.957785i
$57$		−	16.5268i		−	2.18903i
$58$	1.54913	+	0.436808i	0.203411	+	0.0573557i
$59$	−8.32914	−	4.80883i	−1.08436	−	0.626057i	−0.152292	−	0.988336i	$-0.548665\pi$
$59$	−8.32914	−	4.80883i	−1.08436	−	0.626057i	−0.932070	+	0.362279i	$0.881999\pi$
$60$	−1.52269	−	0.932878i	−0.196579	−	0.120434i
$61$	−6.29330	−	10.9003i	−0.805774	−	1.39564i	−0.915767	−	0.401709i	$-0.868416\pi$
$61$	−6.29330	−	10.9003i	−0.805774	−	1.39564i	0.109993	−	0.993932i	$-0.464917\pi$
$62$	−5.64836	−	5.79758i	−0.717343	−	0.736293i
$63$	−0.263170	−	3.81310i	−0.0331562	−	0.480406i
$64$	−0.625067	+	7.97554i	−0.0781333	+	0.996943i
$65$	0.673313	−	0.388737i	0.0835142	−	0.0482169i
$66$	−1.80733	−	7.11476i	−0.222467	−	0.875766i
$67$	3.35335	+	1.93606i	0.409677	+	0.236527i	0.690651	−	0.723188i	$-0.257324\pi$
$67$	3.35335	+	1.93606i	0.409677	+	0.236527i	−0.280974	+	0.959715i	$0.590658\pi$
$68$	0.290993	+	8.24108i	0.0352881	+	0.999377i
$69$			8.60137i			1.03548i
$70$	−0.324020	+	1.55117i	−0.0387278	+	0.185400i
$71$			2.73303i			0.324351i	0.986762	+	0.162176i	$0.0518511\pi$
$71$			2.73303i			0.324351i	−0.986762	+	0.162176i	$0.948149\pi$
$72$	−1.21105	+	3.90248i	−0.142724	+	0.459912i
$73$	−0.639595	−	0.369271i	−0.0748590	−	0.0432198i	0.462103	−	0.886826i	$-0.347095\pi$
$73$	−0.639595	−	0.369271i	−0.0748590	−	0.0432198i	−0.536962	+	0.843606i	$0.680428\pi$
$74$	2.68085	+	10.5535i	0.311643	+	1.22682i
$75$	−5.08151	−	8.80144i	−0.586762	−	1.01630i
$76$	15.6730	+	0.408705i	1.79782	+	0.0468816i
$77$	−5.40373	+	3.63775i	−0.615812	+	0.414560i
$78$	−3.81945	−	3.92035i	−0.432467	−	0.443892i
$79$	−12.6359	+	7.29532i	−1.42165	+	0.820788i	−0.996440	−	0.0843088i	$-0.973132\pi$
$79$	−12.6359	+	7.29532i	−1.42165	+	0.820788i	−0.425206	+	0.905096i	$0.639798\pi$
$80$	0.922341	−	1.42096i	0.103121	−	0.158868i
$81$	5.62347	−	9.74013i	0.624830	−	1.08224i
$82$	2.27787	−	8.07842i	0.251549	−	0.892112i
$83$		−	7.35872i		−	0.807725i	−0.914820	−	0.403862i	$-0.867667\pi$
$83$		−	7.35872i		−	0.807725i	0.914820	−	0.403862i	$-0.132333\pi$
$84$	11.1455	−	0.477730i	1.21607	−	0.0521246i
$85$	0.778711	−	1.56295i	0.0844631	−	0.169526i
$86$	−1.02599	+	3.63863i	−0.110635	+	0.392364i
$87$	−1.19970	+	2.07795i	−0.128622	+	0.222779i
$88$	6.79190	−	1.53802i	0.724019	−	0.163953i
$89$	−6.73261	−	11.6612i	−0.713655	−	1.23609i	−0.963476	−	0.267795i	$-0.913705\pi$
$89$	−6.73261	−	11.6612i	−0.713655	−	1.23609i	0.249821	−	0.968292i	$-0.419628\pi$
$90$	0.619752	−	0.603802i	0.0653276	−	0.0636463i
$91$	−2.13311	+	4.36350i	−0.223611	+	0.457419i
$92$	−8.15702	−	0.212710i	−0.850428	−	0.0221765i
$93$	10.4498	−	6.03319i	1.08359	−	0.625613i
$94$	−2.65184	−	10.4393i	−0.273516	−	1.07673i
$95$	−2.87521	−	1.66001i	−0.294991	−	0.170313i
$96$	−11.2941	−	3.83040i	−1.15270	−	0.390939i
$97$		−	11.7599i		−	1.19404i	−0.802226	−	0.597021i	$-0.796351\pi$
$97$		−	11.7599i		−	1.19404i	0.802226	−	0.597021i	$-0.203649\pi$
$98$	−3.73233	−	9.16895i	−0.377023	−	0.926204i
$99$	3.55686			0.357478
$100$	8.47241	−	4.60134i	0.847241	−	0.460134i
$101$	11.0507	+	6.38013i	1.09959	+	0.634847i	0.936113	−	0.351701i	$-0.114396\pi$
$101$	11.0507	+	6.38013i	1.09959	+	0.634847i	0.163475	+	0.986548i	$0.447730\pi$
$102$	−12.0140	−	2.60428i	−1.18956	−	0.257863i
$103$	0.0717819	+	0.124330i	0.00707288	+	0.0122506i	0.869540	−	0.493862i	$-0.164415\pi$
$103$	0.0717819	+	0.124330i	0.00707288	+	0.0122506i	−0.862467	+	0.506113i	$0.831082\pi$
$104$	3.81227	−	3.52518i	0.373824	−	0.345673i
$105$	−2.12229	−	1.03749i	−0.207114	−	0.101249i
$106$	−10.1451	−	10.4131i	−0.985379	−	1.01141i
$107$	−4.04830	−	7.01186i	−0.391364	−	0.677863i	0.601266	−	0.799049i	$-0.294663\pi$
$107$	−4.04830	−	7.01186i	−0.391364	−	0.677863i	−0.992630	+	0.121187i	$0.961330\pi$
$108$	5.59207	+	3.42599i	0.538097	+	0.329666i
$109$	0.656364	−	1.13686i	0.0628683	−	0.108891i	−0.832878	−	0.553456i	$-0.813309\pi$
$109$	0.656364	−	1.13686i	0.0628683	−	0.108891i	0.895746	+	0.444565i	$0.146642\pi$
$110$	−1.41931	−	0.400202i	−0.135326	−	0.0381578i
$111$	−16.2322			−1.54069
$112$	0.177425	+	10.5815i	0.0167651	+	0.999859i
$113$		−	8.81918i		−	0.829638i	−0.909904	−	0.414819i	$-0.863845\pi$
$113$		−	8.81918i		−	0.829638i	0.909904	−	0.414819i	$-0.136155\pi$
$114$	−6.34301	+	22.4953i	−0.594077	+	2.10688i
$115$	1.49640	+	0.863948i	0.139540	+	0.0805635i
$116$	−1.94093	−	1.18911i	−0.180211	−	0.110406i
$117$	2.29673	−	1.32602i	0.212333	−	0.122590i
$118$	9.49148	+	9.74222i	0.873762	+	0.896844i
$119$	1.41711	+	10.8163i	0.129906	+	0.991526i
$120$	1.71455	+	1.85419i	0.156517	+	0.169263i
$121$	2.46904	+	4.27650i	0.224458	+	0.388773i
$122$	4.38250	+	17.2522i	0.396773	+	1.56194i
$123$	10.8361	+	6.25623i	0.977059	+	0.564105i
$124$	5.46309	+	10.0591i	0.490600	+	0.903338i
$125$	−4.15918			−0.372009
$126$	−1.10526	+	5.29117i	−0.0984645	+	0.471374i
$127$	8.38168			0.743754			0.371877	−	0.928282i	$-0.378714\pi$
$127$	8.38168			0.743754			0.371877	+	0.928282i	$0.378714\pi$
$128$	3.91182	−	10.6159i	0.345759	−	0.938323i
$129$	−4.88074	−	2.81789i	−0.429725	−	0.248102i
$130$	−1.06567	+	0.270707i	−0.0934654	+	0.0237426i
$131$	0.585307	+	1.01378i	0.0511385	+	0.0885744i	0.890462	−	0.455059i	$-0.150382\pi$
$131$	0.585307	+	1.01378i	0.0511385	+	0.0885744i	−0.839323	+	0.543633i	$0.817048\pi$
$132$	−0.270622	+	10.3778i	−0.0235546	+	0.903274i
$133$	20.6913	−	1.42806i	1.79416	−	0.123828i
$134$	−3.82131	−	3.92226i	−0.330111	−	0.338831i
$135$	−0.694363	−	1.20267i	−0.0597612	−	0.103509i
$136$	2.76685	−	11.3289i	0.237255	−	0.971447i
$137$	8.67275	−	15.0216i	0.740963	−	1.28339i	−0.211095	−	0.977466i	$-0.567703\pi$
$137$	8.67275	−	15.0216i	0.740963	−	1.28339i	0.952057	−	0.305920i	$-0.0989639\pi$
$138$	3.30121	−	11.7077i	0.281018	−	0.996621i
$139$	−20.3221			−1.72370			−0.861851	−	0.507161i	$-0.830695\pi$
$139$	−20.3221			−1.72370			−0.861851	+	0.507161i	$0.830695\pi$
$140$	1.03637	−	1.98699i	0.0875897	−	0.167932i
$141$	16.0565			1.35220
$142$	1.04894	−	3.72004i	0.0880251	−	0.312178i
$143$	−3.91430	−	2.25992i	−0.327330	−	0.188984i
$144$	3.14619	−	4.84701i	0.262182	−	0.403918i
$145$	0.241004	+	0.417431i	0.0200143	+	0.0346657i
$146$	0.728851	+	0.748105i	0.0603202	+	0.0619136i
$147$	14.6177	−	2.02740i	1.20565	−	0.167217i
$148$	0.401419	−	15.3937i	0.0329965	−	1.26535i
$149$	−2.58595	+	1.49300i	−0.211849	+	0.122311i	−0.602171	−	0.798367i	$-0.705697\pi$
$149$	−2.58595	+	1.49300i	−0.211849	+	0.122311i	0.390321	+	0.920679i	$0.372364\pi$
$150$	3.53864	+	13.9303i	0.288929	+	1.13740i
$151$	−4.97967	+	8.62505i	−0.405240	+	0.701896i	−0.994349	−	0.106157i	$-0.966145\pi$
$151$	−4.97967	+	8.62505i	−0.405240	+	0.701896i	0.589109	+	0.808053i	$0.299479\pi$
$152$	−21.1763	−	6.57163i	−1.71763	−	0.533029i
$153$	2.65625	−	5.33136i	0.214745	−	0.431015i
$154$	8.75139	−	2.87752i	0.705207	−	0.231877i
$155$		−	2.42397i		−	0.194698i
$156$	3.69417	+	6.80204i	0.295770	+	0.544599i
$157$	3.59725	+	2.07688i	0.287092	+	0.165753i	0.636630	−	0.771170i	$-0.280328\pi$
$157$	3.59725	+	2.07688i	0.287092	+	0.165753i	−0.349538	+	0.936922i	$0.613661\pi$
$158$	19.9991	−	5.08029i	1.59104	−	0.404166i
$159$	18.7690	−	10.8363i	1.48848	−	0.859373i
$160$	−1.80080	+	1.58013i	−0.142366	+	0.124920i
$161$	−10.7688	+	0.743230i	−0.848698	+	0.0585747i
$162$	−11.3926	+	11.0994i	−0.895086	+	0.872049i
$163$	9.13225	+	15.8175i	0.715293	+	1.23892i	0.962847	+	0.270049i	$0.0870400\pi$
$163$	9.13225	+	15.8175i	0.715293	+	1.23892i	−0.247554	+	0.968874i	$0.579627\pi$
$164$	−6.20100	+	10.1216i	−0.484217	+	0.790363i
$165$	1.09916	−	1.90381i	0.0855698	−	0.148211i
$166$	−2.82428	+	10.0162i	−0.219207	+	0.777411i
$167$			12.3442i			0.955222i	0.878571	+	0.477611i	$0.158497\pi$
$167$			12.3442i			0.955222i	−0.878571	+	0.477611i	$0.841503\pi$
$168$	−15.3539	−	3.62739i	−1.18458	−	0.279859i
$169$	9.62996			0.740766
$170$	−1.65979	+	1.82852i	−0.127300	+	0.140241i
$171$	−9.80761	−	5.66242i	−0.750006	−	0.433016i
$172$	2.79302	−	4.55891i	0.212966	−	0.347614i
$173$	5.71630	+	9.90091i	0.434602	+	0.752753i	0.997263	−	0.0739350i	$-0.0235557\pi$
$173$	5.71630	+	9.90091i	0.434602	+	0.752753i	−0.562661	+	0.826688i	$0.690222\pi$
$174$	2.43048	−	2.36793i	0.184254	−	0.179512i
$175$	10.5802	−	7.12248i	0.799785	−	0.538409i
$176$	−9.83501	−	0.513282i	−0.741341	−	0.0386901i
$177$	−17.5598	+	10.1381i	−1.31987	+	0.762029i
$178$	4.68843	+	18.4565i	0.351412	+	1.38337i
$179$	−5.51975	−	3.18683i	−0.412566	−	0.238195i	0.279326	−	0.960196i	$-0.409889\pi$
$179$	−5.51975	−	3.18683i	−0.412566	−	0.238195i	−0.691892	+	0.722001i	$0.743222\pi$
$180$	−1.07531	+	0.583996i	−0.0801487	+	0.0435285i
$181$	−13.4657			−1.00090			−0.500449	−	0.865766i	$-0.666832\pi$
$181$	−13.4657			−1.00090			−0.500449	+	0.865766i	$0.666832\pi$
$182$	4.57818	−	5.12064i	0.339357	−	0.379567i
$183$	−26.5355			−1.96156
$184$	11.0212	+	3.42020i	0.812493	+	0.252140i
$185$	−1.63041	+	2.82396i	−0.119870	+	0.207622i
$186$	−16.5392	+	4.20137i	−1.21271	+	0.308059i
$187$	−10.1324	+	0.622570i	−0.740953	+	0.0455268i
$188$	−0.397074	+	15.2270i	−0.0289596	+	1.11055i
$189$	7.79408	+	3.81017i	0.566936	+	0.277149i
$190$	3.27645	+	3.36301i	0.237699	+	0.243978i
$191$	−12.9302	−	22.3958i	−0.935596	−	1.62050i	−0.773568	−	0.633714i	$-0.781530\pi$
$191$	−12.9302	−	22.3958i	−0.935596	−	1.62050i	−0.162028	−	0.986786i	$-0.551804\pi$
$192$	13.9027	+	9.54839i	1.00334	+	0.689096i
$193$	8.56195	+	4.94325i	0.616303	+	0.355823i	0.775428	−	0.631436i	$-0.217534\pi$
$193$	8.56195	+	4.94325i	0.616303	+	0.355823i	−0.159125	+	0.987258i	$0.550867\pi$
$194$	−4.51348	+	16.0069i	−0.324049	+	1.14923i
$195$		−	1.63910i		−	0.117378i
$196$	1.56117	+	13.9127i	0.111512	+	0.993763i
$197$	7.75491			0.552515			0.276257	−	0.961084i	$-0.410906\pi$
$197$	7.75491			0.552515			0.276257	+	0.961084i	$0.410906\pi$
$198$	−4.84138	−	1.36513i	−0.344062	−	0.0970152i
$199$	−12.1735	−	7.02837i	−0.862956	−	0.498228i	0.00204497	−	0.999998i	$-0.499349\pi$
$199$	−12.1735	−	7.02837i	−0.862956	−	0.498228i	−0.865001	+	0.501770i	$0.832682\pi$
$200$	−13.2981	+	3.01134i	−0.940319	+	0.212934i
$201$	7.06964	−	4.08166i	0.498654	−	0.287898i
$202$	−12.5928	−	12.9255i	−0.886030	−	0.909436i
$203$	−2.70522	−	1.32246i	−0.189869	−	0.0928182i
$204$	15.3532	+	8.15576i	1.07494	+	0.571018i
$205$	2.17682	−	1.25679i	0.152036	−	0.0877780i
$206$	−0.0499872	−	0.196780i	−0.00348277	−	0.0137103i
$207$	5.10436	+	2.94700i	0.354777	+	0.204831i
$208$	−6.54200	+	3.33511i	−0.453606	+	0.231248i
$209$			19.3008i			1.33507i
$210$	2.49054	+	2.22670i	0.171863	+	0.153657i
$211$	−10.0513			−0.691959			−0.345980	−	0.938242i	$-0.612453\pi$
$211$	−10.0513			−0.691959			−0.345980	+	0.938242i	$0.612453\pi$
$212$	9.81232	+	18.0674i	0.673913	+	1.24087i
$213$	4.98993	+	2.88093i	0.341904	+	0.197398i
$214$	2.81914	+	11.0979i	0.192712	+	0.758634i
$215$	−0.980472	+	0.566076i	−0.0668677	+	0.0386061i
$216$	−6.29668	−	6.80948i	−0.428435	−	0.463327i
$217$	8.45640	+	12.5616i	0.574058	+	0.852740i
$218$	−1.32973	+	1.29551i	−0.0900606	+	0.0877427i
$219$	−1.34842	+	0.778508i	−0.0911175	+	0.0526067i
$220$	1.77827	+	1.08946i	0.119891	+	0.0734514i
$221$	−6.31057	+	4.17941i	−0.424495	+	0.281138i
$222$	22.0943	+	6.22994i	1.48287	+	0.418126i
$223$	−17.7002			−1.18529			−0.592646	−	0.805463i	$-0.701917\pi$
$223$	−17.7002			−1.18529			−0.592646	+	0.805463i	$0.701917\pi$
$224$	3.81969	−	14.4710i	0.255214	−	0.966885i
$225$	−6.96411			−0.464274
$226$	−3.38481	+	12.0041i	−0.225154	+	0.798502i
$227$	−3.35391	+	5.80914i	−0.222607	+	0.385566i	−0.955599	−	0.294671i	$-0.904790\pi$
$227$	−3.35391	+	5.80914i	−0.222607	+	0.385566i	0.732992	+	0.680237i	$0.238123\pi$
$228$	17.2674	−	28.1848i	1.14356	−	1.86658i
$229$	−25.7626	+	14.8741i	−1.70244	+	0.982906i	−0.759168	+	0.650895i	$0.774394\pi$
$229$	−25.7626	+	14.8741i	−1.70244	+	0.982906i	−0.943276	+	0.332011i	$0.892273\pi$
$230$	−1.70523	−	1.75027i	−0.112439	−	0.115410i
$231$	0.945580	+	13.7006i	0.0622146	+	0.901436i
$232$	2.18549	+	2.36348i	0.143485	+	0.155170i
$233$	−11.6749	+	6.74052i	−0.764850	+	0.441586i	−0.831034	−	0.556221i	$-0.812251\pi$
$233$	−11.6749	+	6.74052i	−0.764850	+	0.441586i	0.0661845	+	0.997807i	$0.478917\pi$
$234$	−3.63509	+	0.923407i	−0.237633	+	0.0603650i
$235$	1.61277	−	2.79339i	0.105205	−	0.182221i
$236$	−9.18015	−	16.9033i	−0.597577	−	1.10031i
$237$			30.7605i			1.99811i
$238$	2.22241	−	15.2663i	0.144058	−	0.989569i
$239$	−16.1765			−1.04637			−0.523185	−	0.852219i	$-0.675256\pi$
$239$	−16.1765			−1.04637			−0.523185	+	0.852219i	$0.675256\pi$
$240$	−1.62211	−	3.18185i	−0.104707	−	0.205388i
$241$	21.3721	+	12.3392i	1.37670	+	0.794838i	0.991761	−	0.128104i	$-0.0408892\pi$
$241$	21.3721	+	12.3392i	1.37670	+	0.794838i	0.384939	+	0.922942i	$0.374223\pi$
$242$	−1.71938	−	6.76852i	−0.110526	−	0.435097i
$243$	−6.93701	−	12.0152i	−0.445009	−	0.770779i
$244$	0.656216	−	25.1646i	0.0420099	−	1.61100i
$245$	1.11553	−	2.74672i	0.0712689	−	0.175481i
$246$	−12.3483	−	12.6745i	−0.787298	−	0.808096i
$247$	7.19546	+	12.4629i	0.457836	+	0.792996i
$248$	−3.57531	−	15.7886i	−0.227033	−	1.00258i
$249$	−13.4354	−	7.75695i	−0.851436	−	0.491577i
$250$	5.66122	+	1.59630i	0.358047	+	0.100959i
$251$			28.2407i			1.78254i	0.453477	+	0.891268i	$0.350183\pi$
$251$			28.2407i			1.78254i	−0.453477	+	0.891268i	$0.649817\pi$
$252$	3.53517	−	6.77781i	0.222695	−	0.426962i
$253$		−	10.0451i		−	0.631530i
$254$	−11.4086	−	3.21690i	−0.715841	−	0.201846i
$255$	−2.03275	−	3.06929i	−0.127296	−	0.192206i
$256$	−9.39892	+	12.9484i	−0.587433	+	0.809273i
$257$	−6.45876	−	11.1869i	−0.402886	−	0.697820i	0.591186	−	0.806535i	$-0.298660\pi$
$257$	−6.45876	−	11.1869i	−0.402886	−	0.697820i	−0.994073	+	0.108715i	$0.965326\pi$
$258$	5.56185	+	5.70877i	0.346266	+	0.355413i
$259$	−1.40260	−	20.3225i	−0.0871533	−	1.26278i
$260$	1.55442	+	0.0405345i	0.0964011	+	0.00251384i
$261$	0.822085	+	1.42389i	0.0508858	+	0.0881368i
$262$	−0.407593	−	1.60454i	−0.0251812	−	0.0991286i
$263$	10.4510	−	18.1016i	0.644436	−	1.11620i	−0.339996	−	0.940427i	$-0.610426\pi$
$263$	10.4510	−	18.1016i	0.644436	−	1.11620i	0.984432	−	0.175768i	$-0.0562410\pi$
$264$	4.35137	−	14.0218i	0.267808	−	0.862981i
$265$		−	4.35372i		−	0.267447i
$266$	−28.7118	−	5.99756i	−1.76044	−	0.367734i
$267$	−28.3878			−1.73731
$268$	3.69596	+	6.80535i	0.225767	+	0.415703i
$269$	7.88535	−	13.6578i	0.480778	−	0.832732i	−0.518979	−	0.854787i	$-0.673688\pi$
$269$	7.88535	−	13.6578i	0.480778	−	0.832732i	0.999757	+	0.0220552i	$0.00702097\pi$
$270$	0.483537	+	1.90350i	0.0294272	+	0.115843i
$271$	8.20990	+	14.2200i	0.498716	+	0.863802i	0.999999	−	0.00148196i	$-0.000471722\pi$
$271$	8.20990	+	14.2200i	0.498716	+	0.863802i	−0.501283	+	0.865283i	$0.667138\pi$
$272$	−8.11411	+	14.3583i	−0.491990	+	0.870601i
$273$	5.71826	+	8.49424i	0.346085	+	0.514095i
$274$	−17.5701	+	17.1179i	−1.06145	+	1.03413i
$275$	5.93444	+	10.2787i	0.357860	+	0.619832i
$276$	−8.98681	+	14.6687i	−0.540942	+	0.882953i
$277$	−8.69488	+	15.0600i	−0.522425	+	0.904866i	0.477235	+	0.878776i	$0.341639\pi$
$277$	−8.69488	+	15.0600i	−0.522425	+	0.904866i	−0.999660	+	0.0260904i	$0.991694\pi$
$278$	27.6613	+	7.79965i	1.65901	+	0.467792i
$279$		−	8.26837i		−	0.495014i
$280$	−2.17326	+	2.30681i	−0.129877	+	0.137858i
$281$	17.2744			1.03050			0.515251	−	0.857039i	$-0.327699\pi$
$281$	17.2744			1.03050			0.515251	+	0.857039i	$0.327699\pi$
$282$	−21.8552	−	6.16251i	−1.30146	−	0.366972i
$283$	−4.82135	+	8.35082i	−0.286599	+	0.496405i	−0.972996	−	0.230823i	$-0.925858\pi$
$283$	−4.82135	+	8.35082i	−0.286599	+	0.496405i	0.686396	+	0.727228i	$0.259192\pi$
$284$	−2.85550	+	4.66090i	−0.169443	+	0.276573i
$285$	−6.06162	+	3.49968i	−0.359059	+	0.207303i
$286$	4.46054	+	4.57837i	0.263757	+	0.270725i
$287$	−6.89636	+	14.1072i	−0.407079	+	0.832722i
$288$	−6.14268	+	5.38995i	−0.361961	+	0.317606i
$289$	−6.63367	+	15.6523i	−0.390216	+	0.920723i
$290$	−0.167829	−	0.660678i	−0.00985527	−	0.0387964i
$291$	−21.4711	−	12.3964i	−1.25866	−	0.726687i
$292$	−0.704944	−	1.29801i	−0.0412537	−	0.0759602i
$293$		−	23.7118i		−	1.38526i	−0.721293	−	0.692630i	$-0.756452\pi$
$293$		−	23.7118i		−	1.38526i	0.721293	−	0.692630i	$-0.243548\pi$
$294$	−20.6748	−	2.85071i	−1.20578	−	0.166257i
$295$			4.07322i			0.237152i
$296$	−6.45448	+	20.7988i	−0.375159	+	1.20891i
$297$	−4.03667	+	6.99172i	−0.234231	+	0.405700i
$298$	4.09285	−	1.03969i	0.237092	−	0.0602275i
$299$	−3.74487	−	6.48630i	−0.216571	−	0.375113i
$300$	0.529860	−	20.3191i	0.0305915	−	1.17313i
$301$	3.10622	−	6.35409i	0.179040	−	0.366244i
$302$	10.0883	−	9.82868i	0.580518	−	0.565577i
$303$	23.2975	−	13.4508i	1.33841	−	0.772729i
$304$	26.3017	+	17.0724i	1.50851	+	0.979168i
$305$	−2.66530	+	4.61644i	−0.152615	+	0.264337i
$306$	−5.66171	+	6.23724i	−0.323658	+	0.356559i
$307$			1.47081i			0.0839433i	0.999119	+	0.0419717i	$0.0133639\pi$
$307$			1.47081i			0.0839433i	−0.999119	+	0.0419717i	$0.986636\pi$
$308$	−13.0162	+	0.557917i	−0.741669	+	0.0317902i
$309$	0.302666			0.0172181
$310$	−0.930321	+	3.29936i	−0.0528387	+	0.187391i
$311$	0.748263	+	0.432010i	0.0424301	+	0.0244970i	0.521065	−	0.853517i	$-0.325535\pi$
$311$	0.748263	+	0.432010i	0.0424301	+	0.0244970i	−0.478635	+	0.878014i	$0.658868\pi$
$312$	−2.41764	−	10.6763i	−0.136872	−	0.604429i
$313$	−16.8585	+	9.73327i	−0.952900	+	0.550157i	−0.893981	−	0.448106i	$-0.852099\pi$
$313$	−16.8585	+	9.73327i	−0.952900	+	0.550157i	−0.0589193	+	0.998263i	$0.518765\pi$
$314$	−4.09925	−	4.20754i	−0.231334	−	0.237445i
$315$	−1.34282	+	0.903977i	−0.0756594	+	0.0509333i
$316$	−29.1714	−	0.760699i	−1.64102	−	0.0427927i
$317$	10.1002	+	17.4940i	0.567283	+	0.982563i	0.996833	+	0.0795202i	$0.0253388\pi$
$317$	10.1002	+	17.4940i	0.567283	+	0.982563i	−0.429550	+	0.903043i	$0.641328\pi$
$318$	−29.7062	+	7.54613i	−1.66584	+	0.423166i
$319$	1.40107	−	2.42673i	0.0784450	−	0.135871i
$320$	3.05759	−	1.45962i	0.170924	−	0.0815953i
$321$	−17.0695			−0.952728
$322$	14.9430	+	3.12142i	0.832743	+	0.173950i
$323$	28.9299	+	14.4138i	1.60970	+	0.802006i
$324$	19.7668	−	10.7353i	1.09816	−	0.596406i
$325$	7.66395	+	4.42478i	0.425119	+	0.245443i
$326$	−6.35948	−	25.0348i	−0.352219	−	1.38655i
$327$	−1.38377	−	2.39676i	−0.0765226	−	0.132541i
$328$	12.3251	−	11.3969i	0.680539	−	0.629290i
$329$	1.38742	+	20.1025i	0.0764908	+	1.10829i
$330$	−2.22680	+	2.16949i	−0.122581	+	0.119426i
$331$	−3.34686	+	1.93231i	−0.183960	+	0.106209i	−0.589152	−	0.808022i	$-0.700538\pi$
$331$	−3.34686	+	1.93231i	−0.183960	+	0.106209i	0.405192	+	0.914232i	$0.367205\pi$
$332$	7.68848	−	12.5495i	0.421960	−	0.688745i
$333$	−5.56149	+	9.63278i	−0.304768	+	0.527873i
$334$	4.73771	−	16.8022i	0.259236	−	0.919373i
$335$		−	1.63990i		−	0.0895971i
$336$	19.5066	+	10.8302i	1.06417	+	0.590837i
$337$			4.31350i			0.234972i	0.993075	+	0.117486i	$0.0374835\pi$
$337$			4.31350i			0.234972i	−0.993075	+	0.117486i	$0.962517\pi$
$338$	−13.1077	−	3.69598i	−0.712965	−	0.201035i
$339$	−16.1019	−	9.29644i	−0.874535	−	0.504913i
$340$	2.96100	−	1.85184i	0.160583	−	0.100430i
$341$	−12.2038	+	7.04585i	−0.660872	+	0.381554i
$342$	11.1763	+	11.4715i	0.604343	+	0.620308i
$343$	3.80137	+	18.1259i	0.205254	+	0.978709i
$344$	−5.55140	+	5.13334i	−0.299311	+	0.276771i
$345$	3.15476	−	1.82140i	0.169847	−	0.0980610i
$346$	−3.98069	−	15.6704i	−0.214003	−	0.842448i
$347$	2.61968	−	4.53743i	0.140632	−	0.243582i	−0.787103	−	0.616822i	$-0.788420\pi$
$347$	2.61968	−	4.53743i	0.140632	−	0.243582i	0.927735	+	0.373240i	$0.121753\pi$
$348$	−4.21703	+	2.29025i	−0.226057	+	0.122771i
$349$		−	8.06632i		−	0.431780i	−0.976418	−	0.215890i	$-0.930735\pi$
$349$		−	8.06632i		−	0.431780i	0.976418	−	0.215890i	$-0.0692653\pi$
$350$	−17.1347	+	5.63401i	−0.915887	+	0.301151i
$351$			6.01957i			0.321301i
$352$	13.1898	+	4.47333i	0.703019	+	0.238429i
$353$	14.7925	−	25.6213i	0.787324	−	1.36368i	−0.140278	−	0.990112i	$-0.544799\pi$
$353$	14.7925	−	25.6213i	0.787324	−	1.36368i	0.927601	−	0.373572i	$-0.121867\pi$
$354$	27.7923	−	7.05996i	1.47714	−	0.375232i
$355$	1.00241	−	0.578740i	0.0532022	−	0.0307163i
$356$	0.702024	−	26.9213i	0.0372072	−	1.42682i
$357$	21.2420	+	8.81428i	1.12424	+	0.466501i
$358$	6.29004	+	6.45620i	0.332439	+	0.341221i
$359$	0.108648	+	0.188183i	0.00573421	+	0.00993194i	0.868878	−	0.495026i	$-0.164841\pi$
$359$	0.108648	+	0.188183i	0.00573421	+	0.00993194i	−0.863144	+	0.504958i	$0.831508\pi$
$360$	1.68778	−	0.382196i	0.0889538	−	0.0201435i
$361$	21.2264	−	36.7652i	1.11718	−	1.93501i
$362$	18.3287	+	5.16814i	0.963334	+	0.271632i
$363$	10.4106			0.546415
$364$	−8.19683	+	5.21279i	−0.429631	+	0.273224i
$365$			0.312783i			0.0163718i
$366$	36.1184	+	10.1843i	1.88794	+	0.532343i
$367$	5.77016	+	3.33140i	0.301200	+	0.173898i	0.642982	−	0.765881i	$-0.277697\pi$
$367$	5.77016	+	3.33140i	0.301200	+	0.173898i	−0.341782	+	0.939779i	$0.611030\pi$
$368$	−13.6887	−	8.88530i	−0.713572	−	0.463178i
$369$	7.42533	−	4.28702i	0.386547	−	0.223173i
$370$	3.30306	−	3.21805i	0.171718	−	0.167298i
$371$	15.1886	+	22.5621i	0.788555	+	1.17137i
$372$	24.1246	+	0.629094i	1.25080	+	0.0326170i
$373$	1.71008	−	0.987315i	0.0885446	−	0.0511212i	−0.455074	−	0.890454i	$-0.650387\pi$
$373$	1.71008	−	0.987315i	0.0885446	−	0.0511212i	0.543619	+	0.839332i	$0.317054\pi$
$374$	14.0305	+	3.04141i	0.725501	+	0.157268i
$375$	−4.38426	+	7.59377i	−0.226402	+	0.392140i
$376$	6.38462	−	20.5737i	0.329262	−	1.06101i
$377$		−	2.08931i		−	0.107605i
$378$	−9.14648	−	8.17754i	−0.470444	−	0.420607i
$379$	−2.21241			−0.113644			−0.0568220	−	0.998384i	$-0.518097\pi$
$379$	−2.21241			−0.113644			−0.0568220	+	0.998384i	$0.518097\pi$
$380$	−3.16898	−	5.83502i	−0.162565	−	0.299330i
$381$	8.83527	−	15.3031i	0.452645	−	0.784003i
$382$	9.00428	+	35.4463i	0.460699	+	1.81359i
$383$	9.13044	+	15.8144i	0.466544	+	0.808078i	0.999270	−	0.0382102i	$-0.0121656\pi$
$383$	9.13044	+	15.8144i	0.466544	+	0.808078i	−0.532726	+	0.846288i	$0.678832\pi$
$384$	−15.2588	−	18.3325i	−0.778675	−	0.935529i
$385$	2.47851	+	1.21163i	0.126317	+	0.0617504i
$386$	−9.75678	−	10.0145i	−0.496607	−	0.509726i
$387$	−3.34448	+	1.93093i	−0.170009	+	0.0981549i
$388$	12.2869	−	20.0553i	0.623774	−	1.01816i
$389$	−16.9092	−	9.76251i	−0.857328	−	0.494979i	0.00578837	−	0.999983i	$-0.498157\pi$
$389$	−16.9092	−	9.76251i	−0.857328	−	0.494979i	−0.863117	+	0.505004i	$0.831491\pi$
$390$	−0.629087	+	2.23104i	−0.0318550	+	0.112973i
$391$	−15.0565	−	7.50165i	−0.761442	−	0.379375i
$392$	3.21472	−	19.5363i	0.162368	−	0.986730i
$393$	2.46793			0.124490
$394$	−10.5555	−	2.97634i	−0.531779	−	0.149946i
$395$	5.35148	+	3.08968i	0.269262	+	0.155458i
$396$	6.06585	+	3.71625i	0.304820	+	0.186748i
$397$	−2.92554	−	5.06719i	−0.146829	−	0.254315i	0.783225	−	0.621738i	$-0.213573\pi$
$397$	−2.92554	−	5.06719i	−0.146829	−	0.254315i	−0.930054	+	0.367424i	$0.880240\pi$
$398$	13.8723	+	14.2388i	0.695356	+	0.713725i
$399$	19.2037	−	39.2832i	0.961389	−	1.96662i
$400$	19.2563	+	1.00498i	0.962817	+	0.0502488i
$401$	−6.39779	+	3.69377i	−0.319490	+	0.184458i	−0.651165	−	0.758936i	$-0.725720\pi$
$401$	−6.39779	+	3.69377i	−0.319490	+	0.184458i	0.331675	+	0.943394i	$0.392386\pi$
$402$	−11.1893	+	2.84237i	−0.558071	+	0.141764i
$403$	−5.25347	+	9.09927i	−0.261694	+	0.453267i
$404$	12.1798	+	22.4266i	0.605967	+	1.11576i
$405$	−4.76324			−0.236687
$406$	3.17462	+	2.83831i	0.157554	+	0.140863i
$407$	18.9568			0.939653
$408$	−17.7676	−	16.9937i	−0.879626	−	0.841312i
$409$	12.7168	−	22.0262i	0.628806	−	1.08912i	−0.358986	−	0.933343i	$-0.616877\pi$
$409$	12.7168	−	22.0262i	0.628806	−	1.08912i	0.987792	−	0.155781i	$-0.0497893\pi$
$410$	−3.44531	+	0.875198i	−0.170152	+	0.0432229i
$411$	−18.2842	−	31.6691i	−0.901892	−	1.56212i
$412$	−0.00748485	+	0.287030i	−0.000368752	+	0.0141409i
$413$	−14.2101	−	21.1085i	−0.699233	−	1.03868i
$414$	−5.81667	−	5.97033i	−0.285874	−	0.293426i
$415$	−2.69899	+	1.55826i	−0.132488	+	0.0764922i
$416$	10.1846	−	2.02872i	0.499340	−	0.0994663i
$417$	−21.4219	+	37.1038i	−1.04904	+	1.81698i
$418$	7.40768	−	26.2711i	0.362321	−	1.28496i
$419$	−17.3809			−0.849114			−0.424557	−	0.905401i	$-0.639570\pi$
$419$	−17.3809			−0.849114			−0.424557	+	0.905401i	$0.639570\pi$
$420$	−2.53536	−	3.98672i	−0.123713	−	0.194532i
$421$		−	36.8475i		−	1.79584i	−0.440163	−	0.897918i	$-0.645079\pi$
$421$		−	36.8475i		−	1.79584i	0.440163	−	0.897918i	$-0.354921\pi$
$422$	13.6812	+	3.85769i	0.665990	+	0.187789i
$423$	5.50129	−	9.52851i	0.267482	−	0.463292i
$424$	−6.42166	−	28.3581i	−0.311864	−	1.37719i
$425$	19.8386	−	1.21895i	0.962312	−	0.0591279i
$426$	−5.68627	−	5.83649i	−0.275501	−	0.282779i
$427$	−2.29289	−	33.2220i	−0.110961	−	1.60772i
$428$	0.422125	−	16.1877i	0.0204042	−	0.782462i
$429$	−8.25225	+	4.76444i	−0.398422	+	0.230029i
$430$	1.55182	−	0.394202i	0.0748353	−	0.0190101i
$431$	10.2389	+	5.91141i	0.493188	+	0.284742i	0.725896	−	0.687804i	$-0.241425\pi$
$431$	10.2389	+	5.91141i	0.493188	+	0.284742i	−0.232708	+	0.972547i	$0.574759\pi$
$432$	5.95717	+	11.6853i	0.286615	+	0.562210i
$433$	−14.6168			−0.702440			−0.351220	−	0.936293i	$-0.614233\pi$
$433$	−14.6168			−0.702440			−0.351220	+	0.936293i	$0.614233\pi$
$434$	−6.68916	−	20.3437i	−0.321090	−	0.976529i
$435$	1.01618			0.0487223
$436$	2.30716	−	1.25301i	0.110493	−	0.0600084i
$437$	−15.9915	+	27.6981i	−0.764979	+	1.32498i
$438$	2.13417	−	0.542134i	0.101975	−	0.0259042i
$439$	5.36428	−	3.09707i	0.256023	−	0.147815i	−0.366496	−	0.930420i	$-0.619443\pi$
$439$	5.36428	−	3.09707i	0.256023	−	0.147815i	0.622519	+	0.782605i	$0.286109\pi$
$440$	−2.00234	−	2.16541i	−0.0954578	−	0.103232i
$441$	3.80519	−	9.36929i	0.181199	−	0.446157i
$442$	10.1936	−	3.26676i	0.484861	−	0.155384i
$443$	−13.6550	+	7.88370i	−0.648767	+	0.374566i	−0.787984	−	0.615696i	$-0.788875\pi$
$443$	−13.6550	+	7.88370i	−0.648767	+	0.374566i	0.139216	+	0.990262i	$0.455542\pi$
$444$	−27.6823	−	16.9596i	−1.31375	−	0.804868i
$445$	−2.85136	+	4.93870i	−0.135167	+	0.234117i
$446$	24.0924	+	6.79334i	1.14081	+	0.321674i
$447$			6.29518i			0.297752i
$448$	−10.7531	+	18.2310i	−0.508037	+	0.861335i
$449$		−	38.1388i		−	1.79988i	−0.436014	−	0.899940i	$-0.643610\pi$
$449$		−	38.1388i		−	1.79988i	0.436014	−	0.899940i	$-0.356390\pi$
$450$	9.47912	+	2.67283i	0.446850	+	0.125998i
$451$	−12.6549	−	7.30633i	−0.595898	−	0.344042i
$452$	9.21438	−	15.0402i	0.433408	−	0.707430i
$453$	10.4983	+	18.1836i	0.493254	+	0.854340i
$454$	6.79469	−	6.61981i	0.318890	−	0.310683i
$455$	2.05212	−	0.141632i	0.0962050	−	0.00663980i
$456$	−34.3207	+	31.7361i	−1.60721	+	1.48618i
$457$	19.4725	+	33.7274i	0.910886	+	1.57770i	0.812816	+	0.582521i	$0.197933\pi$
$457$	19.4725	+	33.7274i	0.910886	+	1.57770i	0.0980697	+	0.995180i	$0.468733\pi$
$458$	40.7752	−	10.3579i	1.90530	−	0.483995i
$459$	7.46527	+	11.2719i	0.348449	+	0.526129i
$460$	1.64929	+	3.03683i	0.0768986	+	0.141593i
$461$			6.88009i			0.320438i	0.987082	+	0.160219i	$0.0512200\pi$
$461$			6.88009i			0.320438i	−0.987082	+	0.160219i	$0.948780\pi$
$462$	3.97125	−	19.0114i	0.184759	−	0.884490i
$463$	7.88175			0.366296			0.183148	−	0.983085i	$-0.441371\pi$
$463$	7.88175			0.366296			0.183148	+	0.983085i	$0.441371\pi$
$464$	−2.06765	−	4.05581i	−0.0959884	−	0.188286i
$465$	−4.42564	−	2.55514i	−0.205234	−	0.118492i
$466$	18.4782	−	4.69394i	0.855986	−	0.217442i
$467$	−6.52301	+	3.76606i	−0.301849	+	0.174273i	−0.643273	−	0.765637i	$-0.722424\pi$
$467$	−6.52301	+	3.76606i	−0.301849	+	0.174273i	0.341424	+	0.939909i	$0.389091\pi$
$468$	5.30227	+	0.138267i	0.245097	+	0.00639138i
$469$	5.72104	+	8.49838i	0.264173	+	0.392419i
$470$	−3.26731	+	3.18321i	−0.150710	+	0.146831i
$471$	7.58385	−	4.37854i	0.349445	−	0.201752i
$472$	6.00794	+	26.5311i	0.276538	+	1.22119i
$473$	5.69996	+	3.29088i	0.262085	+	0.151315i
$474$	11.8059	−	41.8692i	0.542262	−	1.92312i
$475$		−	37.7899i		−	1.73392i
$476$	−8.88424	+	19.9266i	−0.407208	+	0.913335i
$477$		−	14.8509i		−	0.679977i
$478$	22.0184	+	6.20854i	1.00710	+	0.283972i
$479$	−26.3598	−	15.2188i	−1.20441	−	0.695366i	−0.242876	−	0.970057i	$-0.578091\pi$
$479$	−26.3598	−	15.2188i	−1.20441	−	0.695366i	−0.961532	+	0.274692i	$0.911424\pi$
$480$	0.986716	+	4.95350i	0.0450372	+	0.226095i
$481$	12.2407	−	7.06720i	0.558130	−	0.322237i
$482$	−24.3546	−	24.9980i	−1.10932	−	1.13863i
$483$	−9.99456	+	20.4449i	−0.454768	+	0.930275i
$484$	−0.257452	+	9.87279i	−0.0117024	+	0.448763i
$485$	−4.31325	+	2.49026i	−0.195855	+	0.113077i
$486$	4.83077	+	19.0168i	0.219128	+	0.862621i
$487$	−12.8045	−	7.39267i	−0.580226	−	0.334994i	0.180997	−	0.983484i	$-0.442068\pi$
$487$	−12.8045	−	7.39267i	−0.580226	−	0.334994i	−0.761223	+	0.648490i	$0.775401\pi$
$488$	−10.5514	+	34.0007i	−0.477640	+	1.53914i
$489$	38.5058			1.74129
$490$	−2.57259	+	3.31052i	−0.116218	+	0.149554i
$491$			43.0996i			1.94506i	0.232782	+	0.972529i	$0.425217\pi$
$491$			43.0996i			1.94506i	−0.232782	+	0.972529i	$0.574783\pi$
$492$	11.9433	+	21.9910i	0.538443	+	0.991432i
$493$	−2.59109	−	3.91233i	−0.116697	−	0.176203i
$494$	−5.01075	−	19.7254i	−0.225444	−	0.887486i
$495$	−0.753191	−	1.30457i	−0.0338534	−	0.0586359i
$496$	−1.19319	+	22.8627i	−0.0535758	+	1.02657i
$497$	−3.17571	+	6.49624i	−0.142450	+	0.291396i
$498$	15.3104	+	15.7148i	0.686074	+	0.704197i
$499$	−0.799145	−	1.38416i	−0.0357747	−	0.0619635i	0.847584	−	0.530662i	$-0.178057\pi$
$499$	−0.799145	−	1.38416i	−0.0357747	−	0.0619635i	−0.883358	+	0.468698i	$0.844723\pi$
$500$	−7.09305	−	4.34556i	−0.317211	−	0.194339i
$501$	22.5378	+	13.0122i	1.00692	+	0.581343i
$502$	10.8388	−	38.4395i	0.483759	−	1.71564i
$503$		−	26.2670i		−	1.17119i	−0.810605	−	0.585593i	$-0.800862\pi$
$503$		−	26.2670i		−	1.17119i	0.810605	−	0.585593i	$-0.199138\pi$
$504$	−7.41318	+	7.86873i	−0.330209	+	0.350501i
$505$		−	5.40416i		−	0.240482i
$506$	−3.85532	+	13.6728i	−0.171390	+	0.607829i
$507$	10.1511	−	17.5822i	0.450826	−	0.780854i
$508$	14.2941	+	8.75728i	0.634197	+	0.388541i
$509$	1.98334	−	1.14508i	0.0879099	−	0.0507548i	−0.455401	−	0.890287i	$-0.650504\pi$
$509$	1.98334	−	1.14508i	0.0879099	−	0.0507548i	0.543311	+	0.839532i	$0.317171\pi$
$510$	1.58886	+	4.95790i	0.0703560	+	0.219539i
$511$	−1.09119	−	1.62092i	−0.0482716	−	0.0717055i
$512$	17.7628	−	14.0172i	0.785013	−	0.619479i
$513$	22.2612	−	12.8525i	0.982858	−	0.567453i
$514$	4.49773	+	17.7058i	0.198386	+	0.780969i
$515$	0.0304007	−	0.0526555i	0.00133961	−	0.00232028i
$516$	−5.37941	−	9.90507i	−0.236815	−	0.436046i
$517$	−18.7516			−0.824695
$518$	−5.89065	+	28.2000i	−0.258820	+	1.23904i
$519$	24.1026			1.05799
$520$	−2.10022	−	0.651761i	−0.0921009	−	0.0285816i
$521$	−2.01588	−	1.16387i	−0.0883172	−	0.0509900i	0.455191	−	0.890394i	$-0.349571\pi$
$521$	−2.01588	−	1.16387i	−0.0883172	−	0.0509900i	−0.543508	+	0.839404i	$0.682904\pi$
$522$	−0.572480	−	2.25363i	−0.0250568	−	0.0986388i
$523$	3.90183	−	2.25273i	0.170615	−	0.0985048i	−0.412261	−	0.911066i	$-0.635261\pi$
$523$	3.90183	−	2.25273i	0.170615	−	0.0985048i	0.582876	+	0.812561i	$0.301927\pi$
$524$	−0.0610312	+	2.34043i	−0.00266616	+	0.102242i
$525$	−1.85139	−	26.8250i	−0.0808011	−	1.17074i
$526$	−21.1727	+	20.6277i	−0.923172	+	0.899412i
$527$	1.44724	+	23.5540i	0.0630428	+	1.02603i
$528$	−11.3044	+	17.4155i	−0.491960	+	0.757914i
$529$	−3.17723	+	5.50312i	−0.138140	+	0.239266i
$530$	−1.67096	+	5.92601i	−0.0725818	+	0.257409i
$531$			13.8941i			0.602953i
$532$	36.7789	+	19.1831i	1.59457	+	0.831694i
$533$	−10.8954			−0.471931
$534$	38.6397	+	10.8953i	1.67210	+	0.471484i
$535$	−1.71452	+	2.96963i	−0.0741250	+	0.128388i
$536$	−2.41882	−	10.6815i	−0.104477	−	0.461372i
$537$	−11.6369	+	6.71858i	−0.502170	+	0.289928i
$538$	−15.9749	+	15.5638i	−0.688728	+	0.671002i
$539$	−17.0713	+	2.36770i	−0.735312	+	0.101984i
$540$	0.0724027	−	2.77651i	0.00311572	−	0.119482i
$541$	9.87121	+	17.0974i	0.424396	+	0.735076i	0.996364	−	0.0852001i	$-0.0271529\pi$
$541$	9.87121	+	17.0974i	0.424396	+	0.735076i	−0.571967	+	0.820276i	$0.693820\pi$
$542$	−5.71718	−	22.5063i	−0.245574	−	0.966729i
$543$	−14.1944	+	24.5854i	−0.609141	+	1.05506i
$544$	16.5552	−	16.4294i	0.709796	−	0.704407i
$545$	−0.555960			−0.0238147
$546$	−4.52324	−	13.7565i	−0.193577	−	0.588724i
$547$	36.4050			1.55657			0.778284	−	0.627913i	$-0.216091\pi$
$547$	36.4050			1.55657			0.778284	+	0.627913i	$0.216091\pi$
$548$	30.4852	−	16.5564i	1.30226	−	0.707256i
$549$	−9.09159	+	15.7471i	−0.388019	+	0.672069i
$550$	−4.13260	−	16.2684i	−0.176215	−	0.693688i
$551$	−7.72657	+	4.46094i	−0.329163	+	0.190042i
$552$	17.8622	−	16.5170i	0.760264	−	0.703011i
$553$	−38.5116	+	2.65796i	−1.63768	+	0.113028i
$554$	17.6150	−	17.1616i	0.748388	−	0.729127i
$555$	3.43729	+	5.95357i	0.145905	+	0.252715i
$556$	−34.6573	−	21.2328i	−1.46980	−	0.900472i
$557$	−8.04793	−	4.64648i	−0.341002	−	0.196878i	0.319713	−	0.947514i	$-0.396413\pi$
$557$	−8.04793	−	4.64648i	−0.341002	−	0.196878i	−0.660715	+	0.750637i	$0.729747\pi$
$558$	−3.17341	+	11.2544i	−0.134341	+	0.476436i
$559$	4.90743			0.207562
$560$	3.84346	−	2.30579i	0.162416	−	0.0974374i
$561$	−9.54403	+	19.1558i	−0.402949	+	0.808758i
$562$	−23.5128	−	6.62992i	−0.991828	−	0.279666i
$563$	−1.36346	−	0.787195i	−0.0574630	−	0.0331763i	0.470993	−	0.882137i	$-0.343896\pi$
$563$	−1.36346	−	0.787195i	−0.0574630	−	0.0331763i	−0.528456	+	0.848961i	$0.677229\pi$
$564$	27.3827	+	16.7760i	1.15302	+	0.706399i
$565$	−3.23465	+	1.86753i	−0.136083	+	0.0785674i
$566$	9.76757	−	9.51619i	0.410562	−	0.399995i
$567$	24.6844	−	16.6173i	1.03665	−	0.697863i
$568$	5.67559	−	5.24818i	0.238142	−	0.220209i
$569$	−15.5046	−	26.8547i	−0.649985	−	1.12581i	−0.983126	−	0.182930i	$-0.941442\pi$
$569$	−15.5046	−	26.8547i	−0.649985	−	1.12581i	0.333141	−	0.942877i	$-0.391892\pi$
$570$	9.59388	−	2.43709i	0.401843	−	0.102079i
$571$	−19.4680	+	33.7196i	−0.814711	+	1.41112i	0.0948235	+	0.995494i	$0.469771\pi$
$571$	−19.4680	+	33.7196i	−0.814711	+	1.41112i	−0.909535	+	0.415628i	$0.863562\pi$
$572$	−4.31423	−	7.94376i	−0.180387	−	0.332145i
$573$	−54.5197			−2.27759
$574$	14.8013	−	16.5550i	0.617793	−	0.690994i
$575$			19.6677i			0.820199i
$576$	10.4297	−	4.97890i	0.434571	−	0.207454i
$577$	−21.6000	+	37.4123i	−0.899220	+	1.55749i	−0.0707259	+	0.997496i	$0.522532\pi$
$577$	−21.6000	+	37.4123i	−0.899220	+	1.55749i	−0.828494	+	0.559998i	$0.810802\pi$
$578$	15.0367	−	18.7589i	0.625444	−	0.780269i
$579$	18.0506	−	10.4215i	0.750157	−	0.433103i
$580$	−0.0251300	+	0.963687i	−0.00104347	+	0.0400149i
$581$	8.55064	−	17.4912i	0.354740	−	0.725657i
$582$	24.4674	+	25.1138i	1.01421	+	1.04100i
$583$	−21.9194	+	12.6551i	−0.907807	+	0.524122i
$584$	0.461350	+	2.03733i	0.0190908	+	0.0843052i
$585$	−0.972699	−	0.561588i	−0.0402161	−	0.0232188i
$586$	−9.10061	+	32.2751i	−0.375943	+	1.33327i
$587$			6.13869i			0.253371i	0.991943	+	0.126685i	$0.0404339\pi$
$587$			6.13869i			0.253371i	−0.991943	+	0.126685i	$0.959566\pi$
$588$	27.0472	+	11.8152i	1.11541	+	0.487252i
$589$	44.8672			1.84872
$590$	1.56331	−	5.54422i	0.0643603	−	0.228252i
$591$	8.17458	−	14.1588i	0.336257	−	0.582415i
$592$	16.7681	−	25.8329i	0.689163	−	1.06172i
$593$	−7.77637	−	13.4691i	−0.319337	−	0.553108i	0.661013	−	0.750375i	$-0.270127\pi$
$593$	−7.77637	−	13.4691i	−0.319337	−	0.553108i	−0.980350	+	0.197266i	$0.936794\pi$
$594$	8.17789	−	7.96741i	0.335543	−	0.326907i
$595$	3.66705	−	2.81019i	0.150334	−	0.115206i
$596$	−5.96997	−	0.155678i	−0.244539	−	0.00637683i
$597$	−25.6646	+	14.8174i	−1.05038	+	0.606438i
$598$	2.60784	+	10.2660i	0.106642	+	0.419810i
$599$	−0.245820	+	0.425773i	−0.0100439	+	0.0173966i	−0.871004	−	0.491276i	$-0.836530\pi$
$599$	−0.245820	+	0.425773i	−0.0100439	+	0.0173966i	0.860960	+	0.508673i	$0.169864\pi$
$600$	−8.51971	+	27.4538i	−0.347816	+	1.12080i
$601$		−	20.5768i		−	0.839344i	−0.907676	−	0.419672i	$-0.862145\pi$
$601$		−	20.5768i		−	0.839344i	0.907676	−	0.419672i	$-0.137855\pi$
$602$	−6.66670	+	7.45663i	−0.271714	+	0.303909i
$603$		−	5.59383i		−	0.227798i
$604$	−17.5038	+	9.50628i	−0.712222	+	0.386805i
$605$	1.04567	−	1.81116i	0.0425127	−	0.0736341i
$606$	−36.8735	+	9.36682i	−1.49788	+	0.380501i
$607$	−16.0120	+	9.24451i	−0.649906	+	0.375223i	−0.788420	−	0.615137i	$-0.789101\pi$
$607$	−16.0120	+	9.24451i	−0.649906	+	0.375223i	0.138514	+	0.990360i	$0.455767\pi$
$608$	−29.2479	−	33.3325i	−1.18616	−	1.35181i
$609$	−5.26613	+	3.54512i	−0.213395	+	0.143656i
$610$	5.39964	−	5.26067i	0.218625	−	0.212998i
$611$	−12.1083	+	6.99070i	−0.489847	+	0.282814i
$612$	10.1002	−	6.31678i	0.408277	−	0.255341i
$613$	−19.2978	−	11.1416i	−0.779433	−	0.450006i	0.0567966	−	0.998386i	$-0.481911\pi$
$613$	−19.2978	−	11.1416i	−0.779433	−	0.450006i	−0.836229	+	0.548380i	$0.815245\pi$
$614$	0.564496	−	2.00197i	0.0227812	−	0.0807929i
$615$		−	5.29921i		−	0.213685i
$616$	17.9310	+	4.23624i	0.722462	+	0.170683i
$617$		−	22.5377i		−	0.907333i	−0.891172	−	0.453666i	$-0.850116\pi$
$617$		−	22.5377i		−	0.907333i	0.891172	−	0.453666i	$-0.149884\pi$
$618$	−0.411970	−	0.116163i	−0.0165719	−	0.00467277i
$619$	4.79505	−	8.30528i	0.192729	−	0.333817i	−0.753424	−	0.657535i	$-0.771599\pi$
$619$	4.79505	−	8.30528i	0.192729	−	0.333817i	0.946154	+	0.323717i	$0.104933\pi$
$620$	2.53259	−	4.13382i	0.101711	−	0.166018i
$621$	−11.5858	+	6.68909i	−0.464924	+	0.268424i
$622$	−0.852684	−	0.875209i	−0.0341895	−	0.0350927i
$623$	−2.45294	−	35.5411i	−0.0982751	−	1.42392i
$624$	−0.806840	+	15.4599i	−0.0322994	+	0.618890i
$625$	−11.1709	−	19.3485i	−0.446834	−	0.773939i
$626$	26.6824	−	6.77802i	1.06644	−	0.270904i
$627$	35.2392	+	20.3453i	1.40732	+	0.812514i
$628$	3.96479	+	7.30034i	0.158212	+	0.291315i
$629$	14.1569	−	28.4142i	0.564472	−	1.13295i
$630$	2.17471	−	0.715061i	0.0866426	−	0.0284887i
$631$	9.78563			0.389560			0.194780	−	0.980847i	$-0.437601\pi$
$631$	9.78563			0.389560			0.194780	+	0.980847i	$0.437601\pi$
$632$	39.4143	+	12.2314i	1.56782	+	0.486539i
$633$	−10.5952	+	18.3515i	−0.421122	+	0.729406i
$634$	−7.03353	−	27.6883i	−0.279337	−	1.09964i
$635$	−1.77488	−	3.07419i	−0.0704341	−	0.121995i
$636$	43.3304	+	1.12992i	1.71816	+	0.0448044i
$637$	−10.1405	+	7.89313i	−0.401783	+	0.312737i
$638$	−2.83843	+	2.76538i	−0.112375	+	0.109482i
$639$	3.41930	−	1.97413i	0.135265	−	0.0780955i
$640$	−4.72200	+	0.813242i	−0.186654	+	0.0321462i
$641$	−10.3975	−	6.00298i	−0.410675	−	0.237103i	0.280405	−	0.959882i	$-0.409531\pi$
$641$	−10.3975	−	6.00298i	−0.410675	−	0.237103i	−0.691080	+	0.722779i	$0.742865\pi$
$642$	23.2340	+	6.55130i	0.916972	+	0.258559i
$643$	2.10922			0.0831796			0.0415898	−	0.999135i	$-0.486758\pi$
$643$	2.10922			0.0831796			0.0415898	+	0.999135i	$0.486758\pi$
$644$	−19.1415	−	9.98383i	−0.754282	−	0.393418i
$645$			2.38684i			0.0939817i
$646$	−33.8456	−	30.7225i	−1.33164	−	1.20876i
$647$	−7.37496	+	12.7738i	−0.289940	+	0.502190i	−0.973795	−	0.227427i	$-0.926969\pi$
$647$	−7.37496	+	12.7738i	−0.289940	+	0.502190i	0.683855	+	0.729618i	$0.260302\pi$
$648$	−31.0256	+	7.02571i	−1.21880	+	0.275996i
$649$	20.5072	−	11.8398i	0.804977	−	0.464753i
$650$	−8.73346	−	8.96417i	−0.342554	−	0.351604i
$651$	31.8489	−	2.19812i	1.24826	−	0.0861511i
$652$	−0.952240	+	36.5166i	−0.0372926	+	1.43010i
$653$	−18.7506	−	32.4770i	−0.733769	−	1.27092i	−0.955261	−	0.295763i	$-0.904426\pi$
$653$	−18.7506	−	32.4770i	−0.733769	−	1.27092i	0.221493	−	0.975162i	$-0.428907\pi$
$654$	0.963623	+	3.79341i	0.0376807	+	0.148334i
$655$	0.247886	−	0.429351i	0.00968571	−	0.0167761i
$656$	−21.1503	+	10.7824i	−0.825781	+	0.420983i
$657$			1.06693i			0.0416249i
$658$	5.82689	−	27.8948i	0.227156	−	1.08745i
$659$		−	7.67997i		−	0.299169i	−0.988749	−	0.149585i	$-0.952206\pi$
$659$		−	7.67997i		−	0.299169i	0.988749	−	0.149585i	$-0.0477936\pi$
$660$	3.86363	−	2.09832i	0.150391	−	0.0816771i
$661$	1.04777	+	0.604929i	0.0407534	+	0.0235290i	0.520238	−	0.854021i	$-0.325843\pi$
$661$	1.04777	+	0.604929i	0.0407534	+	0.0235290i	−0.479485	+	0.877550i	$0.659176\pi$
$662$	5.29715	−	1.34561i	0.205880	−	0.0522987i
$663$	0.978631	+	15.9273i	0.0380069	+	0.618566i
$664$	−15.2816	+	14.1308i	−0.593041	+	0.548381i
$665$	−4.90531	−	7.28665i	−0.190220	−	0.282564i
$666$	11.2670	−	10.9770i	0.436588	−	0.425352i
$667$	4.02128	−	2.32169i	0.155705	−	0.0898962i
$668$	−12.8974	+	21.0517i	−0.499014	+	0.814515i
$669$	−18.6581	+	32.3167i	−0.721362	+	1.24944i
$670$	−0.629393	+	2.23213i	−0.0243156	+	0.0862345i
$671$	30.9894			1.19633
$672$	−22.3945	−	22.2281i	−0.863887	−	0.857466i
$673$			16.9855i			0.654742i	0.944896	+	0.327371i	$0.106163\pi$
$673$			16.9855i			0.654742i	−0.944896	+	0.327371i	$0.893837\pi$
$674$	1.65553	−	5.87128i	0.0637685	−	0.226153i
$675$	7.90355	−	13.6893i	0.304208	−	0.526903i
$676$	16.4229	+	10.0615i	0.631649	+	0.386980i
$677$	−22.3212	−	38.6614i	−0.857873	−	1.48588i	−0.873954	−	0.486009i	$-0.838452\pi$
$677$	−22.3212	−	38.6614i	−0.857873	−	1.48588i	0.0160810	−	0.999871i	$-0.494881\pi$
$678$	18.3489	+	18.8337i	0.704687	+	0.723302i
$679$	13.6647	−	27.9526i	0.524405	−	1.07272i
$680$	−4.74106	+	1.38417i	−0.181811	+	0.0530806i
$681$	7.07082	+	12.2470i	0.270955	+	0.469307i
$682$	19.3152	−	4.90656i	0.739618	−	0.187882i
$683$	10.4724	−	18.1388i	0.400716	−	0.694061i	−0.593096	−	0.805131i	$-0.702095\pi$
$683$	10.4724	−	18.1388i	0.400716	−	0.694061i	0.993812	+	0.111071i	$0.0354280\pi$
$684$	−10.8097	−	19.9038i	−0.413318	−	0.761040i
$685$	−7.34607			−0.280679
$686$	1.78256	−	26.1309i	0.0680586	−	0.997681i
$687$			62.7160i			2.39276i
$688$	9.52640	−	4.85656i	0.363191	−	0.185155i
$689$	−9.43582	+	16.3433i	−0.359476	+	0.622631i
$690$	−4.99312	+	1.26838i	−0.190085	+	0.0482864i
$691$	−6.47175	−	11.2094i	−0.246197	−	0.426426i	0.716270	−	0.697823i	$-0.245848\pi$
$691$	−6.47175	−	11.2094i	−0.246197	−	0.426426i	−0.962468	+	0.271397i	$0.912514\pi$
$692$	−0.596051	+	22.8574i	−0.0226585	+	0.868908i
$693$	8.45442	+	4.13298i	0.321157	+	0.156999i
$694$	−5.30722	+	5.17063i	−0.201459	+	0.196274i
$695$	4.30336	+	7.45365i	0.163236	+	0.282733i
$696$	6.61896	−	1.49885i	0.250891	−	0.0568139i
$697$	−20.4021	+	13.5121i	−0.772784	+	0.511806i
$698$	−3.09586	+	10.9794i	−0.117180	+	0.415576i
$699$			28.4212i			1.07499i
$700$	25.4850	−	1.09237i	0.963243	−	0.0412876i
$701$			24.8210i			0.937476i	0.883337	+	0.468738i	$0.155291\pi$
$701$			24.8210i			0.937476i	−0.883337	+	0.468738i	$0.844709\pi$
$702$	2.31032	−	8.19347i	0.0871972	−	0.309243i
$703$	−52.2710	−	30.1787i	−1.97144	−	1.13821i
$704$	−16.2363	−	11.1511i	−0.611928	−	0.420272i
$705$	−3.40009	−	5.88913i	−0.128055	−	0.221797i
$706$	−29.9681	+	29.1968i	−1.12786	+	1.09884i
$707$	18.8533	+	28.0058i	0.709051	+	1.05327i
$708$	−40.5388	−	1.05713i	−1.52354	−	0.0397292i
$709$	−21.7671	−	37.7017i	−0.817481	−	1.41592i	−0.907533	−	0.419982i	$-0.862036\pi$
$709$	−21.7671	−	37.7017i	−0.817481	−	1.41592i	0.0900515	−	0.995937i	$-0.471297\pi$
$710$	−1.58653	+	0.403020i	−0.0595416	+	0.0151251i
$711$	18.2544	+	10.5392i	0.684592	+	0.395249i
$712$	−11.2880	+	36.3741i	−0.423034	+	1.36318i
$713$	−23.3511			−0.874506
$714$	−25.5303	−	20.1501i	−0.955449	−	0.754100i
$715$			1.91422i			0.0715877i
$716$	−6.08372	−	11.2019i	−0.227359	−	0.418635i
$717$	−17.0519	+	29.5347i	−0.636815	+	1.10300i
$718$	−0.0756597	−	0.297843i	−0.00282359	−	0.0111154i
$719$	−38.0279	+	21.9554i	−1.41820	+	0.818799i	−0.996141	−	0.0877680i	$-0.972027\pi$
$719$	−38.0279	+	21.9554i	−1.41820	+	0.818799i	−0.422061	+	0.906567i	$0.638693\pi$
$720$	−2.44399	−	0.127550i	−0.0910821	−	0.00475351i
$721$	0.0261528	+	0.378932i	0.000973983	+	0.0141122i
$722$	−43.0026	+	41.8959i	−1.60039	+	1.55920i
$723$	45.0574	−	26.0139i	1.67570	−	0.967468i
$724$	−22.9643	−	14.0691i	−0.853462	−	0.522875i
$725$	−2.74321	+	4.75138i	−0.101880	+	0.176462i
$726$	−14.1703	−	3.99560i	−0.525908	−	0.148291i
$727$	−39.0818			−1.44946			−0.724731	−	0.689032i	$-0.758036\pi$
$727$	−39.0818			−1.44946			−0.724731	+	0.689032i	$0.758036\pi$
$728$	13.1577	−	3.94937i	0.487657	−	0.146373i
$729$	4.49115			0.166339
$730$	0.120046	−	0.425741i	0.00444311	−	0.0157574i
$731$	9.18939	−	6.08603i	0.339882	−	0.225100i
$732$	−45.2534	−	27.7246i	−1.67262	−	1.02473i
$733$	13.0324	−	7.52423i	0.481361	−	0.277914i	−0.239622	−	0.970866i	$-0.577024\pi$
$733$	13.0324	−	7.52423i	0.481361	−	0.277914i	0.720984	+	0.692952i	$0.243690\pi$
$734$	−6.57539	−	6.74909i	−0.242702	−	0.249114i
$735$	−3.83901	−	4.93208i	−0.141604	−	0.181923i
$736$	15.2220	+	17.3478i	0.561091	+	0.639450i
$737$	−8.25627	+	4.76676i	−0.304124	+	0.175586i
$738$	−11.7523	+	2.98538i	−0.432607	+	0.109893i
$739$	14.9340	+	8.62216i	0.549357	+	0.317171i	0.748862	−	0.662725i	$-0.230600\pi$
$739$	14.9340	+	8.62216i	0.549357	+	0.317171i	−0.199506	+	0.979897i	$0.563934\pi$
$740$	−5.73101	+	3.11249i	−0.210676	+	0.114417i
$741$	30.3394			1.11455
$742$	−12.0145	−	36.5396i	−0.441066	−	1.34141i
$743$		−	6.40885i		−	0.235118i	−0.993066	−	0.117559i	$-0.962493\pi$
$743$		−	6.40885i		−	0.235118i	0.993066	−	0.117559i	$-0.0375069\pi$
$744$	−32.5954	−	10.1153i	−1.19501	−	0.370845i
$745$	1.09519	+	0.632307i	0.0401246	+	0.0231659i
$746$	−2.70659	+	0.687543i	−0.0990952	+	0.0251727i
$747$	−9.20650	+	5.31538i	−0.336848	+	0.194479i
$748$	−17.9302	−	9.52470i	−0.655592	−	0.348258i
$749$	−1.47495	−	21.3708i	−0.0538935	−	0.780871i
$750$	8.88208	−	8.65348i	0.324328	−	0.315981i
$751$	31.9612	−	18.4528i	1.16628	−	0.673352i	0.213479	−	0.976948i	$-0.431521\pi$
$751$	31.9612	−	18.4528i	1.16628	−	0.673352i	0.952801	+	0.303596i	$0.0981872\pi$
$752$	−16.5866	+	25.5532i	−0.604849	+	0.931831i
$753$	51.5614	+	29.7690i	1.87900	+	1.08484i
$754$	−0.801879	+	2.84384i	−0.0292027	+	0.103567i
$755$	4.21793			0.153506
$756$	9.31108	+	14.6412i	0.338641	+	0.532495i
$757$		−	17.6840i		−	0.642736i	−0.946954	−	0.321368i	$-0.895857\pi$
$757$		−	17.6840i		−	0.642736i	0.946954	−	0.321368i	$-0.104143\pi$
$758$	3.01140	+	0.849125i	0.109379	+	0.0308416i
$759$	−18.3402	−	10.5887i	−0.665706	−	0.384346i
$760$	2.07394	+	9.15852i	0.0752296	+	0.332215i
$761$	−8.42432	−	14.5913i	−0.305381	−	0.528936i	0.671965	−	0.740583i	$-0.265451\pi$
$761$	−8.42432	−	14.5913i	−0.305381	−	0.528936i	−0.977346	+	0.211647i	$0.932117\pi$
$762$	−17.8994	+	17.4387i	−0.648426	+	0.631738i
$763$	2.88113	−	1.93956i	0.104304	−	0.0702166i
$764$	1.34826	−	51.7032i	0.0487783	−	1.87056i
$765$	−2.51789	+	0.154708i	−0.0910344	+	0.00559348i
$766$	−6.35822	−	25.0298i	−0.229732	−	0.904365i
$767$	8.82790	−	15.2904i	0.318757	−	0.552103i
$768$	13.7334	+	30.8095i	0.495560	+	1.11174i
$769$	−10.6661			−0.384630			−0.192315	−	0.981333i	$-0.561600\pi$
$769$	−10.6661			−0.384630			−0.192315	+	0.981333i	$0.561600\pi$
$770$	−2.90857	−	2.60045i	−0.104818	−	0.0937137i
$771$	−27.2331			−0.980778
$772$	9.43674	+	17.3758i	0.339636	+	0.625369i
$773$	20.9514	+	12.0963i	0.753569	+	0.435073i	0.826982	−	0.562228i	$-0.190056\pi$
$773$	20.9514	+	12.0963i	0.753569	+	0.435073i	−0.0734131	+	0.997302i	$0.523389\pi$
$774$	5.29339	−	1.34466i	0.190267	−	0.0483327i
$775$	23.8942	−	13.7953i	0.858307	−	0.495544i
$776$	−24.4215	+	22.5824i	−0.876679	+	0.810660i
$777$	−38.5829	−	18.8614i	−1.38416	−	0.676650i
$778$	19.2688	+	19.7779i	0.690822	+	0.709071i
$779$	23.2630	+	40.2926i	0.833482	+	1.44363i
$780$	1.71255	−	2.79531i	0.0613191	−	0.100088i
$781$	−5.82748	−	3.36450i	−0.208524	−	0.120391i
$782$	17.6149	+	15.9895i	0.629907	+	0.571783i
$783$	−3.73193			−0.133368
$784$	−11.8737	+	25.3577i	−0.424061	+	0.905634i
$785$		−	1.75917i		−	0.0627876i
$786$	−3.35919	−	0.947191i	−0.119818	−	0.0337852i
$787$	26.2970	−	45.5477i	0.937386	−	1.62360i	0.167064	−	0.985946i	$-0.446571\pi$
$787$	26.2970	−	45.5477i	0.937386	−	1.62360i	0.770322	−	0.637655i	$-0.220095\pi$
$788$	13.2252	+	8.10242i	0.471128	+	0.288637i
$789$	−22.0331	−	38.1625i	−0.784400	−	1.35862i
$790$	−6.09828	−	6.25937i	−0.216967	−	0.222699i
$791$	10.2476	−	20.9626i	0.364364	−	0.745344i
$792$	−6.83016	−	7.38640i	−0.242699	−	0.262464i
$793$	20.0104	−	11.5530i	0.710591	−	0.410260i
$794$	2.03728	+	8.01997i	0.0723003	+	0.284618i
$795$	−7.94895	−	4.58933i	−0.281920	−	0.162767i
$796$	−13.4173	−	24.7051i	−0.475563	−	0.875651i
$797$			28.8089i			1.02046i	0.860037	+	0.510231i	$0.170440\pi$
$797$			28.8089i			1.02046i	−0.860037	+	0.510231i	$0.829560\pi$
$798$	−41.2159	+	46.0995i	−1.45903	+	1.63190i
$799$	−14.0036	+	28.1067i	−0.495413	+	0.994342i
$800$	−25.8248	−	8.75850i	−0.913045	−	0.309660i
$801$	−9.72623	+	16.8463i	−0.343660	+	0.595236i
$802$	10.1259	−	2.57225i	0.357560	−	0.0908293i
$803$	1.57475	−	0.909180i	0.0555716	−	0.0320843i
$804$	16.3211	+	0.425603i	0.575600	+	0.0150099i
$805$	2.55296	+	3.79233i	0.0899802	+	0.133662i
$806$	10.6430	−	10.3691i	0.374884	−	0.365235i
$807$	−16.6241	−	28.7939i	−0.585198	−	1.01359i
$808$	−7.97105	−	35.2002i	−0.280421	−	1.23834i
$809$	−6.23711	−	3.60100i	−0.219285	−	0.126604i	0.386334	−	0.922359i	$-0.373741\pi$
$809$	−6.23711	−	3.60100i	−0.219285	−	0.126604i	−0.605619	+	0.795755i	$0.707074\pi$
$810$	6.48343	+	1.82814i	0.227805	+	0.0642341i
$811$	−25.1130			−0.881835			−0.440918	−	0.897548i	$-0.645347\pi$
$811$	−25.1130			−0.881835			−0.440918	+	0.897548i	$0.645347\pi$
$812$	−3.23175	−	5.08175i	−0.113412	−	0.178335i
$813$	34.6168			1.21406
$814$	−25.8028	−	7.27563i	−0.904388	−	0.255011i
$815$	3.86764	−	6.69895i	0.135478	−	0.234654i
$816$	17.6620	+	29.9499i	0.618292	+	1.04846i
$817$	−10.4780	−	18.1484i	−0.366578	−	0.634931i
$818$	−25.7630	+	25.0999i	−0.900782	+	0.877599i
$819$	6.99997	−	0.483118i	0.244599	−	0.0168815i
$820$	5.02545	+	0.131048i	0.175496	+	0.00457640i
$821$	−17.0274	−	29.4923i	−0.594261	−	1.02929i	−0.993651	−	0.112509i	$-0.964111\pi$
$821$	−17.0274	−	29.4923i	−0.594261	−	1.02929i	0.399390	−	0.916781i	$-0.369222\pi$
$822$	12.7327	+	50.1235i	0.444102	+	1.74826i
$823$	18.1551	+	10.4818i	0.632846	+	0.365374i	0.781853	−	0.623462i	$-0.214275\pi$
$823$	18.1551	+	10.4818i	0.632846	+	0.365374i	−0.149007	+	0.988836i	$0.547608\pi$
$824$	0.120350	−	0.387815i	0.00419260	−	0.0135102i
$825$	25.0224			0.871167
$826$	11.2404	+	34.1855i	0.391105	+	1.18946i
$827$	34.3158			1.19328			0.596638	−	0.802510i	$-0.296503\pi$
$827$	34.3158			1.19328			0.596638	+	0.802510i	$0.296503\pi$
$828$	5.62588	+	10.3589i	0.195513	+	0.359996i
$829$	−30.2382	−	17.4580i	−1.05022	−	0.606343i	−0.127507	−	0.991838i	$-0.540697\pi$
$829$	−30.2382	−	17.4580i	−1.05022	−	0.606343i	−0.922710	+	0.385495i	$0.874031\pi$
$830$	4.27176	−	1.08514i	0.148275	−	0.0376657i
$831$	18.3308	+	31.7499i	0.635890	+	1.10139i
$832$	−14.6412	−	1.14748i	−0.507594	−	0.0397816i
$833$	−9.19985	+	27.3562i	−0.318756	+	0.947837i
$834$	43.3987	−	42.2817i	1.50277	−	1.46410i
$835$	4.52754	−	2.61397i	0.156682	−	0.0904603i
$836$	−20.1657	+	32.9155i	−0.697447	+	1.13841i
$837$	16.2531	+	9.38375i	0.561790	+	0.324350i
$838$	23.6578	+	6.67081i	0.817247	+	0.230439i
$839$		−	10.1881i		−	0.351732i	−0.984414	−	0.175866i	$-0.943728\pi$
$839$		−	10.1881i		−	0.351732i	0.984414	−	0.175866i	$-0.0562725\pi$
$840$	1.92087	+	6.39955i	0.0662762	+	0.220805i
$841$	−27.7047			−0.955334
$842$	−14.1421	+	50.1545i	−0.487368	+	1.72844i
$843$	18.2092	−	31.5393i	0.627158	−	1.08627i
$844$	−17.1414	−	10.5017i	−0.590032	−	0.361483i
$845$	−2.03921	−	3.53202i	−0.0701511	−	0.121505i
$846$	−11.1451	+	10.8582i	−0.383175	+	0.373313i
$847$	0.899564	+	13.0339i	0.0309094	+	0.447850i
$848$	−2.14310	+	41.0640i	−0.0735944	+	1.41014i
$849$	10.1645	+	17.6055i	0.348846	+	0.604218i
$850$	−27.4709	−	5.95489i	−0.942243	−	0.204251i
$851$	27.2044	+	15.7065i	0.932555	+	0.538411i
$852$	5.49976	+	10.1267i	0.188419	+	0.346934i
$853$	−20.6453			−0.706882			−0.353441	−	0.935457i	$-0.614988\pi$
$853$	−20.6453			−0.706882			−0.353441	+	0.935457i	$0.614988\pi$
$854$	−9.62968	+	46.0997i	−0.329521	+	1.57750i
$855$			4.79624i			0.164028i
$856$	−6.78742	+	21.8717i	−0.231989	+	0.747559i
$857$	20.5097	+	11.8413i	0.700600	+	0.404491i	0.807571	−	0.589771i	$-0.200782\pi$
$857$	20.5097	+	11.8413i	0.700600	+	0.404491i	−0.106971	+	0.994262i	$0.534115\pi$
$858$	13.0610	−	3.31784i	0.445897	−	0.113269i
$859$	−27.5587	+	15.9110i	−0.940289	+	0.542876i	−0.890051	−	0.455861i	$-0.849331\pi$
$859$	−27.5587	+	15.9110i	−0.940289	+	0.542876i	−0.0502382	+	0.998737i	$0.515998\pi$
$860$	−2.26353	−	0.0590260i	−0.0771859	−	0.00201277i
$861$	18.4871	+	27.4619i	0.630040	+	0.935899i
$862$	−11.6677	−	11.9759i	−0.397403	−	0.407901i
$863$	−2.06599	−	3.57839i	−0.0703270	−	0.121810i	0.828718	−	0.559667i	$-0.189071\pi$
$863$	−2.06599	−	3.57839i	−0.0703270	−	0.121810i	−0.899045	+	0.437857i	$0.855738\pi$
$864$	−3.62370	−	18.1917i	−0.123281	−	0.618894i
$865$	2.42094	−	4.19318i	0.0823143	−	0.142573i
$866$	19.8955	+	5.60995i	0.676077	+	0.190634i
$867$	21.5850	+	28.6110i	0.733067	+	0.971680i
$868$	1.29695	+	30.2579i	0.0440213	+	1.02702i
$869$		−	35.9236i		−	1.21862i
$870$	−1.38317	−	0.390012i	−0.0468937	−	0.0132226i
$871$	−3.55415	+	6.15597i	−0.120428	+	0.208587i
$872$	−3.62127	+	0.820032i	−0.122632	+	0.0277698i
$873$	−14.7129	+	8.49448i	−0.497955	+	0.287495i
$874$	32.3972	−	31.5634i	1.09585	−	1.06765i
$875$	−9.88611	−	4.83286i	−0.334211	−	0.163380i
$876$	−3.11298	−	0.0811768i	−0.105178	−	0.00274271i
$877$	−7.08946	−	12.2793i	−0.239394	−	0.414643i	0.721146	−	0.692783i	$-0.243615\pi$
$877$	−7.08946	−	12.2793i	−0.239394	−	0.414643i	−0.960541	+	0.278140i	$0.910282\pi$
$878$	−8.49019	+	2.15673i	−0.286530	+	0.0727860i
$879$	−43.2926	−	24.9950i	−1.46022	−	0.843061i
$880$	1.89438	+	3.71592i	0.0638594	+	0.125264i
$881$			46.0646i			1.55196i	0.630760	+	0.775978i	$0.282743\pi$
$881$			46.0646i			1.55196i	−0.630760	+	0.775978i	$0.717257\pi$
$882$	−8.77533	+	11.2925i	−0.295481	+	0.380237i
$883$		−	27.2693i		−	0.917683i	−0.888518	−	0.458842i	$-0.848265\pi$
$883$		−	27.2693i		−	0.917683i	0.888518	−	0.458842i	$-0.151735\pi$
$884$	−15.1287	+	0.534196i	−0.508833	+	0.0179669i
$885$	7.43682	+	4.29365i	0.249986	+	0.144329i
$886$	21.6121	−	5.49002i	0.726072	−	0.184441i
$887$	0.305780	−	0.176542i	0.0102671	−	0.00592771i	−0.494858	−	0.868974i	$-0.664780\pi$
$887$	0.305780	−	0.176542i	0.0102671	−	0.00592771i	0.505125	+	0.863046i	$0.331446\pi$
$888$	31.1704	+	33.7089i	1.04601	+	1.13120i
$889$	19.9227	+	9.73929i	0.668186	+	0.326645i
$890$	5.77657	−	5.62790i	0.193631	−	0.188648i
$891$	13.8455	+	23.9812i	0.463843	+	0.803399i
$892$	−30.1858	−	18.4934i	−1.01070	−	0.619204i
$893$	51.7053	+	29.8520i	1.73025	+	0.998961i
$894$	2.41609	−	8.56861i	0.0808063	−	0.286577i
$895$			2.69934i			0.0902290i
$896$	21.6336	−	20.6879i	0.722726	−	0.691134i
$897$	−15.7901			−0.527217
$898$	−14.6377	+	51.9121i	−0.488466	+	1.73233i
$899$	−5.64124	−	3.25697i	−0.188146	−	0.108626i
$900$	−11.8766	−	7.27618i	−0.395885	−	0.242539i
$901$	2.59941	+	42.3056i	0.0865988	+	1.40940i
$902$	14.4209	+	14.8019i	0.480165	+	0.492849i
$903$	−8.32687	−	12.3692i	−0.277101	−	0.411622i
$904$	−18.3145	+	16.9353i	−0.609130	+	0.563259i
$905$	2.85146	+	4.93888i	0.0947858	+	0.164174i
$906$	−7.31077	−	28.7797i	−0.242884	−	0.956140i
$907$	−21.0698	+	36.4940i	−0.699611	+	1.21176i	0.268990	+	0.963143i	$0.413310\pi$
$907$	−21.0698	+	36.4940i	−0.699611	+	1.21176i	−0.968601	+	0.248619i	$0.920023\pi$
$908$	−11.7892	+	6.40267i	−0.391238	+	0.212480i
$909$		−	18.4341i		−	0.611419i
$910$	−2.84758	−	0.594826i	−0.0943964	−	0.0197183i
$911$		−	26.5892i		−	0.880939i	−0.897768	−	0.440469i	$-0.854812\pi$
$911$		−	26.5892i		−	0.880939i	0.897768	−	0.440469i	$-0.145188\pi$
$912$	58.8955	−	30.0249i	1.95023	−	0.994225i
$913$	15.6906	+	9.05895i	0.519282	+	0.299807i
$914$	−13.5602	−	53.3812i	−0.448531	−	1.76569i
$915$	5.61908	+	9.73253i	0.185761	+	0.321748i
$916$	−59.4761	−	1.55095i	−1.96514	−	0.0512449i
$917$	0.213249	+	3.08980i	0.00704211	+	0.102034i
$918$	−5.83509	−	18.2078i	−0.192587	−	0.600948i
$919$	−4.24178	−	7.34698i	−0.139923	−	0.242354i	0.787544	−	0.616258i	$-0.211352\pi$
$919$	−4.24178	−	7.34698i	−0.139923	−	0.242354i	−0.927467	+	0.373904i	$0.878019\pi$
$920$	−1.07938	−	4.76654i	−0.0355860	−	0.157148i
$921$	2.68537	+	1.55040i	0.0884860	+	0.0510874i
$922$	2.64058	−	9.36475i	0.0869629	−	0.308412i
$923$	−5.01721			−0.165144
$924$	−12.7020	+	24.3530i	−0.417865	+	0.801153i
$925$	−37.1162			−1.22037
$926$	−10.7281	−	3.02502i	−0.352549	−	0.0994083i
$927$	0.103699	−	0.179613i	0.00340593	−	0.00589925i
$928$	1.25774	+	6.31409i	0.0412873	+	0.207270i
$929$	−39.8189	+	22.9894i	−1.30642	+	0.754259i	−0.981496	−	0.191482i	$-0.938670\pi$
$929$	−39.8189	+	22.9894i	−1.30642	+	0.754259i	−0.324919	+	0.945742i	$0.605337\pi$
$930$	5.04324	+	5.17647i	0.165374	+	0.169743i
$931$	50.8413	+	20.6484i	1.66626	+	0.676723i
$932$	−26.9529	−	0.702849i	−0.882872	−	0.0230226i
$933$	1.57751	−	0.910778i	0.0516455	−	0.0298175i
$934$	10.3241	−	2.62259i	0.337816	−	0.0858139i
$935$	2.37395	+	3.58447i	0.0776364	+	0.117225i
$936$	−7.16405	−	2.22321i	−0.234164	−	0.0726680i
$937$	28.4955			0.930908			0.465454	−	0.885072i	$-0.345891\pi$
$937$	28.4955			0.930908			0.465454	+	0.885072i	$0.345891\pi$
$938$	−4.52544	−	13.7632i	−0.147761	−	0.449385i
$939$			41.0400i			1.33929i
$940$	5.66897	−	3.07880i	0.184902	−	0.100419i
$941$	9.80524	−	16.9832i	0.319642	−	0.553635i	−0.660772	−	0.750587i	$-0.729771\pi$
$941$	9.80524	−	16.9832i	0.319642	−	0.553635i	0.980413	+	0.196952i	$0.0631042\pi$
$942$	−12.0032	+	3.04911i	−0.391084	+	0.0993453i
$943$	−12.1072	−	20.9702i	−0.394264	−	0.682885i
$944$	2.00503	−	38.4184i	0.0652581	−	1.25041i
$945$	−0.252983	−	3.66550i	−0.00822952	−	0.119239i
$946$	−6.49540	−	6.66699i	−0.211184	−	0.216762i
$947$	3.19582	+	5.53532i	0.103850	+	0.179874i	0.913268	−	0.407360i	$-0.133550\pi$
$947$	3.19582	+	5.53532i	0.103850	+	0.179874i	−0.809418	+	0.587233i	$0.800217\pi$
$948$	−32.1389	+	52.4587i	−1.04382	+	1.70378i
$949$	0.677895	−	1.17415i	0.0220054	−	0.0381145i
$950$	−14.5038	+	51.4372i	−0.470564	+	1.66884i
$951$	42.5871			1.38098
$952$	19.7405	−	23.7131i	0.639794	−	0.768546i
$953$	2.45636			0.0795694			0.0397847	−	0.999208i	$-0.487333\pi$
$953$	2.45636			0.0795694			0.0397847	+	0.999208i	$0.487333\pi$
$954$	−5.69979	+	20.2141i	−0.184538	+	0.654457i
$955$	−5.47613	+	9.48493i	−0.177203	+	0.306925i
$956$	−27.5873	−	16.9014i	−0.892236	−	0.546629i
$957$	−2.95379	−	5.11611i	−0.0954824	−	0.165380i
$958$	30.0383	+	30.8318i	0.970493	+	0.996131i
$959$	38.0693	−	25.6280i	1.22932	−	0.827570i
$960$	0.558102	−	7.12110i	0.0180127	−	0.229833i
$961$	0.878978	+	1.52243i	0.0283541	+	0.0491108i
$962$	−19.3737	+	4.92143i	−0.624635	+	0.158673i
$963$	−5.84836	+	10.1297i	−0.188461	+	0.326424i
$964$	23.5558	+	43.3730i	0.758680	+	1.39695i
$965$		−	4.18707i		−	0.134787i
$966$	21.4507	−	23.9924i	0.690166	−	0.771943i
$967$	3.52496			0.113355			0.0566775	−	0.998393i	$-0.481949\pi$
$967$	3.52496			0.113355			0.0566775	+	0.998393i	$0.481949\pi$
$968$	4.13961	−	13.3394i	0.133052	−	0.428745i
$969$	56.8120	−	37.6259i	1.82506	−	1.20872i
$970$	6.82669	−	1.73415i	0.219192	−	0.0556803i
$971$	−18.3086	+	10.5705i	−0.587552	+	0.339223i	−0.764129	−	0.645064i	$-0.776831\pi$
$971$	−18.3086	+	10.5705i	−0.587552	+	0.339223i	0.176577	+	0.984287i	$0.443497\pi$
$972$	0.723337	−	27.7386i	0.0232011	−	0.889716i
$973$	−48.3044	−	23.6138i	−1.54857	−	0.757023i
$974$	14.5914	+	14.9768i	0.467537	+	0.479888i
$975$	16.1574	−	9.32847i	0.517451	−	0.298750i
$976$	27.4114	−	42.2300i	0.877418	−	1.35175i
$977$	−19.7686	+	34.2402i	−0.632453	+	1.09544i	0.354595	+	0.935020i	$0.384619\pi$
$977$	−19.7686	+	34.2402i	−0.632453	+	1.09544i	−0.987049	+	0.160422i	$0.948715\pi$
$978$	−52.4117	−	14.7786i	−1.67594	−	0.472566i
$979$	33.1527			1.05956
$980$	4.77223	−	3.51871i	0.152443	−	0.112401i
$981$	−1.89643			−0.0605483
$982$	16.5417	−	58.6645i	0.527865	−	1.87206i
$983$	23.3043	+	13.4547i	0.743292	+	0.429140i	0.823265	−	0.567657i	$-0.192150\pi$
$983$	23.3043	+	13.4547i	0.743292	+	0.429140i	−0.0799733	+	0.996797i	$0.525484\pi$
$984$	−7.81625	−	34.5166i	−0.249173	−	1.10035i
$985$	−1.64216	−	2.84430i	−0.0523236	−	0.0906271i
$986$	2.02528	+	6.31969i	0.0644980	+	0.201260i
$987$	38.1653	+	18.6573i	1.21482	+	0.593867i
$988$	−0.750287	+	28.7721i	−0.0238698	+	0.915362i
$989$	5.45325	+	9.44530i	0.173403	+	0.300343i
$990$	0.524504	+	2.06477i	0.0166698	+	0.0656227i
$991$	45.9132	+	26.5080i	1.45848	+	0.842055i	0.998937	−	0.0460995i	$-0.0146791\pi$
$991$	45.9132	+	26.5080i	1.45848	+	0.842055i	0.459545	+	0.888154i	$0.348012\pi$
$992$	10.3988	−	30.6614i	0.330163	−	0.973499i
$993$			8.14751i			0.258553i
$994$	6.81584	−	7.62344i	0.216185	−	0.241801i
$995$			5.95324i			0.188730i
$996$	−14.8082	−	27.2662i	−0.469214	−	0.863961i
$997$	−15.3591	+	26.6028i	−0.486428	+	0.842518i	−0.999878	−	0.0156016i	$-0.995034\pi$
$997$	−15.3591	+	26.6028i	−0.486428	+	0.842518i	0.513450	+	0.858119i	$0.328367\pi$
$998$	0.556506	+	2.19075i	0.0176159	+	0.0693469i
$999$	−12.6234	−	21.8644i	−0.399388	−	0.691760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.z.c.781.14	yes	272
7.2	even	3	inner	952.2.z.c.373.80	yes	272
8.5	even	2	inner	952.2.z.c.781.79	yes	272
17.16	even	2	inner	952.2.z.c.781.13	yes	272
56.37	even	6	inner	952.2.z.c.373.13	✓	272
119.16	even	6	inner	952.2.z.c.373.79	yes	272
136.101	even	2	inner	952.2.z.c.781.80	yes	272
952.373	even	6	inner	952.2.z.c.373.14	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.z.c.373.13	✓	272	56.37	even	6	inner
952.2.z.c.373.14	yes	272	952.373	even	6	inner
952.2.z.c.373.79	yes	272	119.16	even	6	inner
952.2.z.c.373.80	yes	272	7.2	even	3	inner
952.2.z.c.781.13	yes	272	17.16	even	2	inner
952.2.z.c.781.14	yes	272	1.1	even	1	trivial
952.2.z.c.781.79	yes	272	8.5	even	2	inner
952.2.z.c.781.80	yes	272	136.101	even	2	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:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36114 - 0.383801i) q^{2} +(1.05412 - 1.82578i) q^{3} +(1.70539 + 1.04481i) q^{4} +(-0.211757 - 0.366775i) q^{5} +(-2.13553 + 2.08057i) q^{6} +(2.37693 + 1.16197i) q^{7} +(-1.92028 - 2.07666i) q^{8} +(-0.722323 - 1.25110i) q^{9} +(0.147463 + 0.580503i) q^{10} +(-1.23105 + 2.13224i) q^{11} +(3.70528 - 2.01233i) q^{12} +1.83577i q^{13} +(-2.78937 - 2.49388i) q^{14} -0.892868 q^{15} +(1.81674 + 3.56363i) q^{16} +(2.27666 + 3.43756i) q^{17} +(0.503008 + 1.98015i) q^{18} +(6.78893 - 3.91959i) q^{19} +(0.0220804 - 0.846742i) q^{20} +(4.62708 - 3.11491i) q^{21} +(2.49398 - 2.42979i) q^{22} +(-3.53329 + 2.03995i) q^{23} +(-5.81573 + 1.31697i) q^{24} +(2.41032 - 4.17479i) q^{25} +(0.704569 - 2.49873i) q^{26} +3.27905 q^{27} +(2.83957 + 4.46507i) q^{28} -1.13811 q^{29} +(1.21532 + 0.342683i) q^{30} +(4.95666 + 2.86173i) q^{31} +(-1.10511 - 5.54786i) q^{32} +(2.59534 + 4.49526i) q^{33} +(-1.77951 - 5.55278i) q^{34} +(-0.0771512 - 1.11786i) q^{35} +(0.0753182 - 2.88831i) q^{36} +(-3.84972 - 6.66792i) q^{37} +(-10.7450 + 2.72951i) q^{38} +(3.35171 + 1.93511i) q^{39} +(-0.355034 + 1.14406i) q^{40} +5.93504i q^{41} +(-7.49360 + 2.46395i) q^{42} -2.67323i q^{43} +(-4.32721 + 2.35009i) q^{44} +(-0.305914 + 0.529859i) q^{45} +(5.59223 - 1.42057i) q^{46} +(3.80805 + 6.59574i) q^{47} +(8.42147 + 0.439511i) q^{48} +(4.29964 + 5.52387i) q^{49} +(-4.88306 + 4.75739i) q^{50} +(8.67610 - 0.533091i) q^{51} +(-1.91803 + 3.13071i) q^{52} +(8.90271 + 5.13998i) q^{53} +(-4.46324 - 1.25850i) q^{54} +1.04273 q^{55} +(-2.15135 - 7.16741i) q^{56} -16.5268i q^{57} +(1.54913 + 0.436808i) q^{58} +(-8.32914 - 4.80883i) q^{59} +(-1.52269 - 0.932878i) q^{60} +(-6.29330 - 10.9003i) q^{61} +(-5.64836 - 5.79758i) q^{62} +(-0.263170 - 3.81310i) q^{63} +(-0.625067 + 7.97554i) q^{64} +(0.673313 - 0.388737i) q^{65} +(-1.80733 - 7.11476i) q^{66} +(3.35335 + 1.93606i) q^{67} +(0.290993 + 8.24108i) q^{68} +8.60137i q^{69} +(-0.324020 + 1.55117i) q^{70} +2.73303i q^{71} +(-1.21105 + 3.90248i) q^{72} +(-0.639595 - 0.369271i) q^{73} +(2.68085 + 10.5535i) q^{74} +(-5.08151 - 8.80144i) q^{75} +(15.6730 + 0.408705i) q^{76} +(-5.40373 + 3.63775i) q^{77} +(-3.81945 - 3.92035i) q^{78} +(-12.6359 + 7.29532i) q^{79} +(0.922341 - 1.42096i) q^{80} +(5.62347 - 9.74013i) q^{81} +(2.27787 - 8.07842i) q^{82} -7.35872i q^{83} +(11.1455 - 0.477730i) q^{84} +(0.778711 - 1.56295i) q^{85} +(-1.02599 + 3.63863i) q^{86} +(-1.19970 + 2.07795i) q^{87} +(6.79190 - 1.53802i) q^{88} +(-6.73261 - 11.6612i) q^{89} +(0.619752 - 0.603802i) q^{90} +(-2.13311 + 4.36350i) q^{91} +(-8.15702 - 0.212710i) q^{92} +(10.4498 - 6.03319i) q^{93} +(-2.65184 - 10.4393i) q^{94} +(-2.87521 - 1.66001i) q^{95} +(-11.2941 - 3.83040i) q^{96} -11.7599i q^{97} +(-3.73233 - 9.16895i) q^{98} +3.55686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 132 q^{9} - 40 q^{15} - 26 q^{16} - 6 q^{17} + 6 q^{18} - 112 q^{25} - 8 q^{26} - 2 q^{30} + 44 q^{32} - 28 q^{33} - 56 q^{34} + 40 q^{36} - 42 q^{38} + 12 q^{42}+ \cdots + 14 q^{98}+O(q^{100}) \) 272 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 132 * q^9 - 40 * q^15 - 26 * q^16 - 6 * q^17 + 6 * q^18 - 112 * q^25 - 8 * q^26 - 2 * q^30 + 44 * q^32 - 28 * q^33 - 56 * q^34 + 40 * q^36 - 42 * q^38 + 12 * q^42 + 28 * q^47 - 60 * q^49 + 72 * q^50 - 38 * q^52 + 232 * q^55 - 6 * q^60 + 40 * q^64 + 48 * q^66 + 32 * q^68 + 86 * q^70 - 36 * q^72 - 148 * q^76 - 168 * q^81 - 34 * q^84 + 22 * q^86 + 16 * q^87 - 72 * q^89 + 62 * q^94 + 14 * q^98

Introduction

L-functions

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