LMFDB - Embedded newform 841.2.d.l.778.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			778.4
Character	$\chi$	$=$	841.778
Dual form			841.2.d.l.574.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62259 + 2.03467i) q^{2} +(-0.0977621 - 0.428324i) q^{3} +(-1.06202 + 4.65303i) q^{4} +(1.60887 + 2.01746i) q^{5} +(0.712869 - 0.893909i) q^{6} +(-0.0167182 - 0.0732474i) q^{7} +(-6.50118 + 3.13080i) q^{8} +(2.52900 - 1.21790i) q^{9} +O(q^{10})$	\(q+(1.62259 + 2.03467i) q^{2} +(-0.0977621 - 0.428324i) q^{3} +(-1.06202 + 4.65303i) q^{4} +(1.60887 + 2.01746i) q^{5} +(0.712869 - 0.893909i) q^{6} +(-0.0167182 - 0.0732474i) q^{7} +(-6.50118 + 3.13080i) q^{8} +(2.52900 - 1.21790i) q^{9} +(-1.49432 + 6.54703i) q^{10} +(3.40418 + 1.63937i) q^{11} +2.09683 q^{12} +(-0.793749 - 0.382250i) q^{13} +(0.121907 - 0.152867i) q^{14} +(0.706838 - 0.886347i) q^{15} +(-8.31884 - 4.00614i) q^{16} -3.94108 q^{17} +(6.58158 + 3.16952i) q^{18} +(0.158795 - 0.695725i) q^{19} +(-11.0959 + 5.34353i) q^{20} +(-0.0297392 + 0.0143216i) q^{21} +(2.18804 + 9.58641i) q^{22} +(0.734247 - 0.920717i) q^{23} +(1.97657 + 2.47854i) q^{24} +(-0.369070 + 1.61700i) q^{25} +(-0.510182 - 2.23525i) q^{26} +(-1.59067 - 1.99463i) q^{27} +0.358578 q^{28} +2.95033 q^{30} +(-3.21152 - 4.02711i) q^{31} +(-2.13561 - 9.35673i) q^{32} +(0.369380 - 1.61836i) q^{33} +(-6.39478 - 8.01881i) q^{34} +(0.120876 - 0.151574i) q^{35} +(2.98108 + 13.0610i) q^{36} +(-2.78175 + 1.33962i) q^{37} +(1.67323 - 0.805785i) q^{38} +(-0.0861279 + 0.377351i) q^{39} +(-16.7758 - 8.07880i) q^{40} -6.67122 q^{41} +(-0.0773944 - 0.0372712i) q^{42} +(5.18347 - 6.49987i) q^{43} +(-11.2434 + 14.0987i) q^{44} +(6.52590 + 3.14271i) q^{45} +3.06474 q^{46} +(-9.54310 - 4.59571i) q^{47} +(-0.902658 + 3.95480i) q^{48} +(6.30170 - 3.03474i) q^{49} +(-3.88891 + 1.87280i) q^{50} +(0.385289 + 1.68806i) q^{51} +(2.62160 - 3.28738i) q^{52} +(3.46416 + 4.34391i) q^{53} +(1.47741 - 6.47296i) q^{54} +(2.16953 + 9.50531i) q^{55} +(0.338012 + 0.423853i) q^{56} -0.313519 q^{57} +9.91885 q^{59} +(3.37352 + 4.23026i) q^{60} +(0.793807 + 3.47790i) q^{61} +(2.98286 - 13.0687i) q^{62} +(-0.131489 - 0.164882i) q^{63} +(4.05898 - 5.08980i) q^{64} +(-0.505866 - 2.21634i) q^{65} +(3.89218 - 1.87437i) q^{66} +(-4.45039 + 2.14320i) q^{67} +(4.18553 - 18.3380i) q^{68} +(-0.466146 - 0.224484i) q^{69} +0.504535 q^{70} +(-4.42088 - 2.12899i) q^{71} +(-12.6285 + 15.8356i) q^{72} +(5.55040 - 6.95998i) q^{73} +(-7.23933 - 3.48628i) q^{74} +0.728681 q^{75} +(3.06859 + 1.47775i) q^{76} +(0.0631675 - 0.276755i) q^{77} +(-0.907535 + 0.437046i) q^{78} +(11.8834 - 5.72272i) q^{79} +(-5.30170 - 23.2282i) q^{80} +(4.55153 - 5.70744i) q^{81} +(-10.8247 - 13.5737i) q^{82} +(-3.77983 + 16.5605i) q^{83} +(-0.0350553 - 0.153587i) q^{84} +(-6.34068 - 7.95097i) q^{85} +21.6357 q^{86} -27.2637 q^{88} +(-4.23758 - 5.31376i) q^{89} +(4.19452 + 18.3774i) q^{90} +(-0.0147287 + 0.0645306i) q^{91} +(3.50434 + 4.39430i) q^{92} +(-1.41094 + 1.76927i) q^{93} +(-6.13382 - 26.8740i) q^{94} +(1.65907 - 0.798968i) q^{95} +(-3.79893 + 1.82947i) q^{96} +(-2.54054 + 11.1308i) q^{97} +(16.3998 + 7.89772i) q^{98} +10.6058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} - 12 q^{5} - 22 q^{6} - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 24 * q + 2 * q^4 - 12 * q^5 - 22 * q^6 - 8 * q^7 + 20 * q^9	$ 24 q + 2 q^{4} - 12 q^{5} - 22 q^{6} - 8 q^{7} + 20 q^{9} - 4 q^{13} - 66 q^{16} - 64 q^{20} - 20 q^{22} + 4 q^{23} - 22 q^{24} + 12 q^{25} - 24 q^{28} + 4 q^{30} - 36 q^{33} - 72 q^{34} - 24 q^{35} + 32 q^{36} + 42 q^{38} + 54 q^{42} - 10 q^{45} + 12 q^{49} + 44 q^{51} - 12 q^{52} - 20 q^{53} + 22 q^{54} + 28 q^{57} + 88 q^{59} + 66 q^{62} + 12 q^{63} + 38 q^{64} - 54 q^{65} - 52 q^{67} - 56 q^{71} - 14 q^{74} - 22 q^{78} + 12 q^{80} + 44 q^{81} - 26 q^{82} - 32 q^{83} + 88 q^{86} - 132 q^{88} - 8 q^{91} - 2 q^{92} + 4 q^{93} - 36 q^{94} + 10 q^{96}+O(q^{100}) $ 24 * q + 2 * q^4 - 12 * q^5 - 22 * q^6 - 8 * q^7 + 20 * q^9 - 4 * q^13 - 66 * q^16 - 64 * q^20 - 20 * q^22 + 4 * q^23 - 22 * q^24 + 12 * q^25 - 24 * q^28 + 4 * q^30 - 36 * q^33 - 72 * q^34 - 24 * q^35 + 32 * q^36 + 42 * q^38 + 54 * q^42 - 10 * q^45 + 12 * q^49 + 44 * q^51 - 12 * q^52 - 20 * q^53 + 22 * q^54 + 28 * q^57 + 88 * q^59 + 66 * q^62 + 12 * q^63 + 38 * q^64 - 54 * q^65 - 52 * q^67 - 56 * q^71 - 14 * q^74 - 22 * q^78 + 12 * q^80 + 44 * q^81 - 26 * q^82 - 32 * q^83 + 88 * q^86 - 132 * q^88 - 8 * q^91 - 2 * q^92 + 4 * q^93 - 36 * q^94 + 10 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	1.62259	+	2.03467i	1.14735	+	1.43873i	0.879902	+	0.475156i	$0.157608\pi$
$2$	1.62259	+	2.03467i	1.14735	+	1.43873i	0.267446	+	0.963573i	$0.413820\pi$
$3$	−0.0977621	−	0.428324i	−0.0564430	−	0.247293i	0.938834	−	0.344370i	$-0.111908\pi$
$3$	−0.0977621	−	0.428324i	−0.0564430	−	0.247293i	−0.995277	+	0.0970777i	$0.969050\pi$
$4$	−1.06202	+	4.65303i	−0.531012	+	2.32652i
$5$	1.60887	+	2.01746i	0.719508	+	0.902234i	0.998310	−	0.0581146i	$-0.0185089\pi$
$5$	1.60887	+	2.01746i	0.719508	+	0.902234i	−0.278802	+	0.960348i	$0.589937\pi$
$6$	0.712869	−	0.893909i	0.291027	−	0.364937i
$7$	−0.0167182	−	0.0732474i	−0.00631890	−	0.0276849i	0.971670	−	0.236341i	$-0.0759482\pi$
$7$	−0.0167182	−	0.0732474i	−0.00631890	−	0.0276849i	−0.977989	+	0.208656i	$0.933091\pi$
$8$	−6.50118	+	3.13080i	−2.29852	+	1.10691i
$9$	2.52900	−	1.21790i	0.843001	−	0.405968i
$10$	−1.49432	+	6.54703i	−0.472544	+	2.07035i
$11$	3.40418	+	1.63937i	1.02640	+	0.494288i	0.869816	−	0.493377i	$-0.164238\pi$
$11$	3.40418	+	1.63937i	1.02640	+	0.494288i	0.156584	+	0.987665i	$0.449952\pi$
$12$	2.09683			0.605302
$13$	−0.793749	−	0.382250i	−0.220146	−	0.106017i	0.320560	−	0.947228i	$-0.396129\pi$
$13$	−0.793749	−	0.382250i	−0.220146	−	0.106017i	−0.540707	+	0.841211i	$0.681843\pi$
$14$	0.121907	−	0.152867i	0.0325811	−	0.0408554i
$15$	0.706838	−	0.886347i	0.182505	−	0.228854i
$16$	−8.31884	−	4.00614i	−2.07971	−	1.00154i
$17$	−3.94108			−0.955854			−0.477927	−	0.878400i	$-0.658612\pi$
$17$	−3.94108			−0.955854			−0.477927	+	0.878400i	$0.658612\pi$
$18$	6.58158	+	3.16952i	1.55129	+	0.747063i
$19$	0.158795	−	0.695725i	0.0364300	−	0.159610i	−0.953441	−	0.301579i	$-0.902486\pi$
$19$	0.158795	−	0.695725i	0.0364300	−	0.159610i	0.989871	+	0.141969i	$0.0453434\pi$
$20$	−11.0959	+	5.34353i	−2.48113	+	1.19485i
$21$	−0.0297392	+	0.0143216i	−0.00648962	+	0.00312524i
$22$	2.18804	+	9.58641i	0.466491	+	2.04383i
$23$	0.734247	−	0.920717i	0.153101	−	0.191983i	−0.699366	−	0.714764i	$-0.746534\pi$
$23$	0.734247	−	0.920717i	0.153101	−	0.191983i	0.852467	+	0.522781i	$0.175106\pi$
$24$	1.97657	+	2.47854i	0.403465	+	0.505929i
$25$	−0.369070	+	1.61700i	−0.0738140	+	0.323400i
$26$	−0.510182	−	2.23525i	−0.100055	−	0.438369i
$27$	−1.59067	−	1.99463i	−0.306124	−	0.383867i
$28$	0.358578			0.0677648
$29$		0			0
$29$		0			0
$30$	2.95033			0.538655
$31$	−3.21152	−	4.02711i	−0.576805	−	0.723291i	0.404759	−	0.914423i	$-0.367355\pi$
$31$	−3.21152	−	4.02711i	−0.576805	−	0.723291i	−0.981564	+	0.191132i	$0.938784\pi$
$32$	−2.13561	−	9.35673i	−0.377526	−	1.65405i
$33$	0.369380	−	1.61836i	0.0643008	−	0.281720i
$34$	−6.39478	−	8.01881i	−1.09670	−	1.37521i
$35$	0.120876	−	0.151574i	0.0204318	−	0.0256206i
$36$	2.98108	+	13.0610i	0.496847	+	2.17683i
$37$	−2.78175	+	1.33962i	−0.457316	+	0.220232i	−0.648336	−	0.761354i	$-0.724535\pi$
$37$	−2.78175	+	1.33962i	−0.457316	+	0.220232i	0.191020	+	0.981586i	$0.438821\pi$
$38$	1.67323	−	0.805785i	0.271434	−	0.130716i
$39$	−0.0861279	+	0.377351i	−0.0137915	+	0.0604245i
$40$	−16.7758	−	8.07880i	−2.65249	−	1.27737i
$41$	−6.67122			−1.04187			−0.520935	−	0.853596i	$-0.674417\pi$
$41$	−6.67122			−1.04187			−0.520935	+	0.853596i	$0.674417\pi$
$42$	−0.0773944	−	0.0372712i	−0.0119422	−	0.00575107i
$43$	5.18347	−	6.49987i	0.790472	−	0.991220i	−0.209439	−	0.977822i	$-0.567164\pi$
$43$	5.18347	−	6.49987i	0.790472	−	0.991220i	0.999910	−	0.0133983i	$-0.00426495\pi$
$44$	−11.2434	+	14.0987i	−1.69500	+	2.12546i
$45$	6.52590	+	3.14271i	0.972823	+	0.468487i
$46$	3.06474			0.451871
$47$	−9.54310	−	4.59571i	−1.39200	−	0.670354i	−0.420482	−	0.907301i	$-0.638139\pi$
$47$	−9.54310	−	4.59571i	−1.39200	−	0.670354i	−0.971523	+	0.236947i	$0.923853\pi$
$48$	−0.902658	+	3.95480i	−0.130288	+	0.570827i
$49$	6.30170	−	3.03474i	0.900242	−	0.433534i
$50$	−3.88891	+	1.87280i	−0.549975	+	0.264854i
$51$	0.385289	+	1.68806i	0.0539512	+	0.236376i
$52$	2.62160	−	3.28738i	0.363551	−	0.455878i
$53$	3.46416	+	4.34391i	0.475838	+	0.596683i	0.960590	−	0.277969i	$-0.0896614\pi$
$53$	3.46416	+	4.34391i	0.475838	+	0.596683i	−0.484751	+	0.874652i	$0.661090\pi$
$54$	1.47741	−	6.47296i	0.201050	−	0.880859i
$55$	2.16953	+	9.50531i	0.292539	+	1.28170i
$56$	0.338012	+	0.423853i	0.0451687	+	0.0566398i
$57$	−0.313519			−0.0415267
$58$		0			0
$59$	9.91885			1.29132			0.645662	−	0.763623i	$-0.276582\pi$
$59$	9.91885			1.29132			0.645662	+	0.763623i	$0.276582\pi$
$60$	3.37352	+	4.23026i	0.435520	+	0.546124i
$61$	0.793807	+	3.47790i	0.101637	+	0.445299i	0.999982	+	0.00600904i	$0.00191275\pi$
$61$	0.793807	+	3.47790i	0.101637	+	0.445299i	−0.898345	+	0.439290i	$0.855230\pi$
$62$	2.98286	−	13.0687i	0.378823	−	1.65973i
$63$	−0.131489	−	0.164882i	−0.0165660	−	0.0207731i
$64$	4.05898	−	5.08980i	0.507373	−	0.636226i
$65$	−0.505866	−	2.21634i	−0.0627449	−	0.274904i
$66$	3.89218	−	1.87437i	0.479094	−	0.230720i
$67$	−4.45039	+	2.14320i	−0.543702	+	0.261833i	−0.685513	−	0.728061i	$-0.740422\pi$
$67$	−4.45039	+	2.14320i	−0.543702	+	0.261833i	0.141811	+	0.989894i	$0.454708\pi$
$68$	4.18553	−	18.3380i	0.507570	−	2.22381i
$69$	−0.466146	−	0.224484i	−0.0561174	−	0.0270247i
$70$	0.504535			0.0603035
$71$	−4.42088	−	2.12899i	−0.524662	−	0.252664i	0.152754	−	0.988264i	$-0.451186\pi$
$71$	−4.42088	−	2.12899i	−0.524662	−	0.252664i	−0.677416	+	0.735600i	$0.736900\pi$
$72$	−12.6285	+	15.8356i	−1.48828	+	1.86625i
$73$	5.55040	−	6.95998i	0.649625	−	0.814604i	−0.342544	−	0.939502i	$-0.611289\pi$
$73$	5.55040	−	6.95998i	0.649625	−	0.814604i	0.992170	+	0.124897i	$0.0398602\pi$
$74$	−7.23933	−	3.48628i	−0.841555	−	0.405272i
$75$	0.728681			0.0841408
$76$	3.06859	+	1.47775i	0.351991	+	0.169510i
$77$	0.0631675	−	0.276755i	0.00719860	−	0.0315391i
$78$	−0.907535	+	0.437046i	−0.102758	+	0.0494857i
$79$	11.8834	−	5.72272i	1.33698	−	0.643856i	0.377600	−	0.925969i	$-0.376749\pi$
$79$	11.8834	−	5.72272i	1.33698	−	0.643856i	0.959381	+	0.282112i	$0.0910351\pi$
$80$	−5.30170	−	23.2282i	−0.592748	−	2.59700i
$81$	4.55153	−	5.70744i	0.505726	−	0.634160i
$82$	−10.8247	−	13.5737i	−1.19539	−	1.49897i
$83$	−3.77983	+	16.5605i	−0.414890	+	1.81775i	0.145301	+	0.989387i	$0.453585\pi$
$83$	−3.77983	+	16.5605i	−0.414890	+	1.81775i	−0.560191	+	0.828364i	$0.689272\pi$
$84$	−0.0350553	−	0.153587i	−0.00382485	−	0.0167577i
$85$	−6.34068	−	7.95097i	−0.687744	−	0.862403i
$86$	21.6357			2.33304
$87$		0			0
$88$	−27.2637			−2.90632
$89$	−4.23758	−	5.31376i	−0.449183	−	0.563257i	0.504755	−	0.863263i	$-0.331583\pi$
$89$	−4.23758	−	5.31376i	−0.449183	−	0.563257i	−0.953937	+	0.300006i	$0.903011\pi$
$90$	4.19452	+	18.3774i	0.442141	+	1.93715i
$91$	−0.0147287	+	0.0645306i	−0.00154399	+	0.00676465i
$92$	3.50434	+	4.39430i	0.365352	+	0.458137i
$93$	−1.41094	+	1.76927i	−0.146308	+	0.183464i
$94$	−6.13382	−	26.8740i	−0.632656	−	2.77185i
$95$	1.65907	−	0.798968i	0.170217	−	0.0819724i
$96$	−3.79893	+	1.82947i	−0.387726	+	0.186719i
$97$	−2.54054	+	11.1308i	−0.257953	+	1.13017i	0.665483	+	0.746413i	$0.268226\pi$
$97$	−2.54054	+	11.1308i	−0.257953	+	1.13017i	−0.923436	+	0.383753i	$0.874631\pi$
$98$	16.3998	+	7.89772i	1.65663	+	0.797790i
$99$	10.6058			1.06592
$100$	−7.13200	−	3.43459i	−0.713200	−	0.343459i
$101$	−5.88466	+	7.37913i	−0.585546	+	0.734251i	−0.983048	−	0.183350i	$-0.941306\pi$
$101$	−5.88466	+	7.37913i	−0.585546	+	0.734251i	0.397502	+	0.917601i	$0.369877\pi$
$102$	−2.80948	+	3.52297i	−0.278180	+	0.348826i
$103$	8.27375	+	3.98443i	0.815237	+	0.392597i	0.794558	−	0.607189i	$-0.207703\pi$
$103$	8.27375	+	3.98443i	0.815237	+	0.392597i	0.0206793	+	0.999786i	$0.493417\pi$
$104$	6.35706			0.623361
$105$	−0.0767397	−	0.0369559i	−0.00748903	−	0.00360652i
$106$	−3.21751	+	14.0968i	−0.312512	+	1.36920i
$107$	4.38610	−	2.11223i	0.424020	−	0.204197i	−0.209690	−	0.977768i	$-0.567245\pi$
$107$	4.38610	−	2.11223i	0.424020	−	0.204197i	0.633710	+	0.773571i	$0.281531\pi$
$108$	10.9704	−	5.28308i	1.05563	−	0.508364i
$109$	−0.964457	−	4.22556i	−0.0923782	−	0.404735i	0.907505	−	0.420042i	$-0.137985\pi$
$109$	−0.964457	−	4.22556i	−0.0923782	−	0.404735i	−0.999883	+	0.0153067i	$0.995128\pi$
$110$	−15.8199	+	19.8375i	−1.50837	+	1.89143i
$111$	0.845740	+	1.06052i	0.0802741	+	0.100661i
$112$	−0.154363	+	0.676309i	−0.0145859	+	0.0639052i
$113$	1.00648	+	4.40969i	0.0946819	+	0.414828i	0.999950	−	0.0100126i	$-0.00318716\pi$
$113$	1.00648	+	4.40969i	0.0946819	+	0.414828i	−0.905268	+	0.424841i	$0.860330\pi$
$114$	−0.508715	−	0.637908i	−0.0476455	−	0.0597456i
$115$	3.03881			0.283371
$116$		0			0
$117$	−2.47294			−0.228623
$118$	16.0943	+	20.1816i	1.48160	+	1.85786i
$119$	0.0658880	+	0.288674i	0.00603994	+	0.0264627i
$120$	−1.82030	+	7.97527i	−0.166170	+	0.728040i
$121$	2.04254	+	2.56126i	0.185685	+	0.232842i
$122$	−5.78834	+	7.25835i	−0.524052	+	0.657140i
$123$	0.652193	+	2.85744i	0.0588062	+	0.257647i
$124$	22.1490	−	10.6664i	1.98904	−	0.957870i
$125$	7.76839	−	3.74106i	0.694826	−	0.334611i
$126$	0.122127	−	0.535072i	0.0108799	−	0.0476680i
$127$	5.25952	+	2.53285i	0.466707	+	0.224754i	0.652432	−	0.757848i	$-0.273749\pi$
$127$	5.25952	+	2.53285i	0.466707	+	0.224754i	−0.185725	+	0.982602i	$0.559463\pi$
$128$	−2.25255			−0.199099
$129$	−3.29079	−	1.58476i	−0.289738	−	0.139531i
$130$	3.68871	−	4.62550i	0.323521	−	0.405683i
$131$	4.13025	−	5.17917i	0.360862	−	0.452506i	−0.567947	−	0.823065i	$-0.692262\pi$
$131$	4.13025	−	5.17917i	0.360862	−	0.452506i	0.928809	+	0.370559i	$0.120834\pi$
$132$	7.13799	+	3.43747i	0.621282	+	0.299194i
$133$	−0.0536148			−0.00464899
$134$	−11.5819	−	5.57754i	−1.00052	−	0.481826i
$135$	1.46491	−	6.41820i	0.126080	−	0.552391i
$136$	25.6217	−	12.3388i	2.19704	−	1.05804i
$137$	1.40444	−	0.676341i	0.119989	−	0.0577837i	−0.372926	−	0.927861i	$-0.621646\pi$
$137$	1.40444	−	0.676341i	0.119989	−	0.0577837i	0.492915	+	0.870077i	$0.335931\pi$
$138$	−0.299615	−	1.31270i	−0.0255049	−	0.111744i
$139$	6.63492	−	8.31992i	0.562766	−	0.705686i	−0.416300	−	0.909227i	$-0.636673\pi$
$139$	6.63492	−	8.31992i	0.562766	−	0.705686i	0.979066	+	0.203541i	$0.0652449\pi$
$140$	0.576904	+	0.723415i	0.0487573	+	0.0611397i
$141$	−1.03550	+	4.53682i	−0.0872048	+	0.382069i
$142$	−2.84152	−	12.4495i	−0.238455	−	1.04474i
$143$	−2.07542	−	2.60249i	−0.173555	−	0.217631i
$144$	−25.9175			−2.15979
$145$		0			0
$146$	23.1673			1.91734
$147$	−1.91592	−	2.40248i	−0.158022	−	0.198153i
$148$	−3.27901	−	14.3663i	−0.269533	−	1.18090i
$149$	−1.20885	+	5.29632i	−0.0990329	+	0.433892i	0.900967	+	0.433887i	$0.142858\pi$
$149$	−1.20885	+	5.29632i	−0.0990329	+	0.433892i	−1.00000		4.09823e-6i	$0.999999\pi$
$150$	1.18235	+	1.48262i	0.0965388	+	0.121056i
$151$	11.1242	−	13.9493i	0.905271	−	1.13517i	−0.0850493	−	0.996377i	$-0.527105\pi$
$151$	11.1242	−	13.9493i	0.905271	−	1.13517i	0.990321	−	0.138798i	$-0.0443238\pi$
$152$	1.14583	+	5.02019i	0.0929387	+	0.407191i
$153$	−9.96702	+	4.79986i	−0.805785	+	0.388046i
$154$	0.665600	−	0.320536i	0.0536355	−	0.0258295i
$155$	2.95762	−	12.9582i	0.237562	−	1.04083i
$156$	−1.66436	−	0.801512i	−0.133255	−	0.0641723i
$157$	−9.46360			−0.755278			−0.377639	−	0.925953i	$-0.623264\pi$
$157$	−9.46360			−0.755278			−0.377639	+	0.925953i	$0.623264\pi$
$158$	30.9257	+	14.8930i	2.46032	+	1.18483i
$159$	1.52194	−	1.90845i	0.120698	−	0.151350i
$160$	15.4409	−	19.3622i	1.22071	−	1.53072i
$161$	−0.0797154	−	0.0383889i	−0.00628245	−	0.00302547i
$162$	18.9980			1.49263
$163$	9.42213	+	4.53746i	0.737998	+	0.355401i	0.764824	−	0.644239i	$-0.222826\pi$
$163$	9.42213	+	4.53746i	0.737998	+	0.355401i	−0.0268262	+	0.999640i	$0.508540\pi$
$164$	7.08500	−	31.0414i	0.553246	−	2.42393i
$165$	3.85925	−	1.85852i	0.300442	−	0.144685i
$166$	−39.8283	+	19.1803i	−3.09127	+	1.48868i
$167$	−0.0379256	−	0.166163i	−0.00293477	−	0.0128581i	0.973439	−	0.228945i	$-0.0735276\pi$
$167$	−0.0379256	−	0.166163i	−0.00293477	−	0.0128581i	−0.976374	+	0.216087i	$0.930670\pi$
$168$	0.148502	−	0.186215i	0.0114571	−	0.0143668i
$169$	−7.62144	−	9.55699i	−0.586265	−	0.735153i
$170$	5.88923	−	25.8024i	0.451683	−	1.97895i
$171$	−0.445734	−	1.95289i	−0.0340861	−	0.149341i
$172$	24.7391	+	31.0219i	1.88634	+	2.36539i
$173$	−12.0694			−0.917616			−0.458808	−	0.888535i	$-0.651723\pi$
$173$	−12.0694			−0.917616			−0.458808	+	0.888535i	$0.651723\pi$
$174$		0			0
$175$	0.124611			0.00941973
$176$	−21.7513	−	27.2753i	−1.63957	−	2.05595i
$177$	−0.969687	−	4.24848i	−0.0728861	−	0.319335i
$178$	3.93586	−	17.2441i	0.295005	−	1.29250i
$179$	−1.04424	−	1.30943i	−0.0780501	−	0.0978717i	0.741273	−	0.671203i	$-0.234222\pi$
$179$	−1.04424	−	1.30943i	−0.0780501	−	0.0978717i	−0.819324	+	0.573331i	$0.805651\pi$
$180$	−21.5538	+	27.0276i	−1.60652	+	2.01452i
$181$	3.41851	+	14.9775i	0.254096	+	1.11327i	0.927450	+	0.373947i	$0.121996\pi$
$181$	3.41851	+	14.9775i	0.254096	+	1.11327i	−0.673354	+	0.739320i	$0.735147\pi$
$182$	−0.155197	+	0.0747390i	−0.0115040	+	0.00554002i
$183$	1.41206	−	0.680013i	0.104383	−	0.0502680i
$184$	−1.89089	+	8.28453i	−0.139398	+	0.610744i
$185$	−7.17809	−	3.45678i	−0.527743	−	0.254148i
$186$	−5.88926			−0.431822
$187$	−13.4162	−	6.46089i	−0.981087	−	0.472467i
$188$	31.5190	−	39.5236i	2.29876	−	2.88255i
$189$	−0.119509	+	0.149859i	−0.00869297	+	0.0109006i
$190$	4.31764	+	2.07927i	0.313235	+	0.150846i
$191$	−20.4783			−1.48176			−0.740878	−	0.671640i	$-0.765590\pi$
$191$	−20.4783			−1.48176			−0.740878	+	0.671640i	$0.765590\pi$
$192$	−2.57690	−	1.24097i	−0.185972	−	0.0895592i
$193$	−0.697471	+	3.05582i	−0.0502051	+	0.219963i	−0.993807	−	0.111119i	$-0.964556\pi$
$193$	−0.697471	+	3.05582i	−0.0502051	+	0.219963i	0.943602	+	0.331082i	$0.107414\pi$
$194$	−26.7699	+	12.8917i	−1.92196	+	0.925569i
$195$	−0.899858	+	0.433349i	−0.0644402	+	0.0310327i
$196$	7.42817	+	32.5450i	0.530584	+	2.32464i
$197$	1.77096	−	2.22071i	0.126176	−	0.158219i	−0.714731	−	0.699399i	$-0.753451\pi$
$197$	1.77096	−	2.22071i	0.126176	−	0.158219i	0.840907	+	0.541180i	$0.182022\pi$
$198$	17.2089	+	21.5792i	1.22298	+	1.53357i
$199$	4.25436	−	18.6396i	0.301583	−	1.32132i	−0.566154	−	0.824300i	$-0.691569\pi$
$199$	4.25436	−	18.6396i	0.301583	−	1.32132i	0.867737	−	0.497024i	$-0.165574\pi$
$200$	−2.66312	−	11.6679i	−0.188311	−	0.825045i
$201$	1.35306	+	1.69669i	0.0954376	+	0.119675i
$202$	−24.5625			−1.72821
$203$		0			0
$204$	−8.26378			−0.578580
$205$	−10.7331	−	13.4589i	−0.749633	−	0.940010i
$206$	5.31795	+	23.2995i	0.370519	+	1.62335i
$207$	0.735569	−	3.22274i	0.0511256	−	0.223996i
$208$	5.07173	+	6.35975i	0.351661	+	0.440969i
$209$	1.68111	−	2.10805i	0.116285	−	0.145817i
$210$	−0.0493244	−	0.216104i	−0.00340371	−	0.0149126i
$211$	16.1215	−	7.76373i	1.10985	−	0.534477i	0.213110	−	0.977028i	$-0.431641\pi$
$211$	16.1215	−	7.76373i	1.10985	−	0.534477i	0.896743	+	0.442551i	$0.145926\pi$
$212$	−23.8914	+	11.5055i	−1.64087	+	0.790200i
$213$	−0.479700	+	2.10170i	−0.0328685	+	0.144006i
$214$	11.4146	+	5.49696i	0.780283	+	0.375765i
$215$	21.4527			1.46306
$216$	16.5860	+	7.98741i	1.12854	+	0.543474i
$217$	−0.241285	+	0.302561i	−0.0163795	+	0.0205392i
$218$	7.03270	−	8.81872i	0.476314	−	0.597279i
$219$	−3.52374	−	1.69695i	−0.238112	−	0.114669i
$220$	−46.5326			−3.13723
$221$	3.12823	+	1.50648i	0.210428	+	0.101337i
$222$	−0.785523	+	3.44160i	−0.0527209	+	0.230985i
$223$	−15.9749	+	7.69313i	−1.06976	+	0.515170i	−0.884030	−	0.467431i	$-0.845180\pi$
$223$	−15.9749	+	7.69313i	−1.06976	+	0.515170i	−0.185731	+	0.982601i	$0.559465\pi$
$224$	−0.649652	+	0.312856i	−0.0434067	+	0.0209036i
$225$	1.03597	+	4.53889i	0.0690648	+	0.302593i
$226$	−7.33914	+	9.20299i	−0.488192	+	0.612174i
$227$	13.8487	+	17.3658i	0.919172	+	1.15261i	0.987919	+	0.154971i	$0.0495285\pi$
$227$	13.8487	+	17.3658i	0.919172	+	1.15261i	−0.0687469	+	0.997634i	$0.521900\pi$
$228$	0.332965	−	1.45882i	0.0220512	−	0.0966125i
$229$	−2.21812	−	9.71820i	−0.146577	−	0.642197i	−0.993821	−	0.110993i	$-0.964597\pi$
$229$	−2.21812	−	9.71820i	−0.146577	−	0.642197i	0.847244	−	0.531204i	$-0.178260\pi$
$230$	4.93076	+	6.18298i	0.325125	+	0.407693i
$231$	−0.124716			−0.00820571
$232$		0			0
$233$	−20.0765			−1.31525			−0.657627	−	0.753344i	$-0.728440\pi$
$233$	−20.0765			−1.31525			−0.657627	+	0.753344i	$0.728440\pi$
$234$	−4.01258	−	5.03161i	−0.262310	−	0.328927i
$235$	−6.08193	−	26.6467i	−0.396741	−	1.73824i
$236$	−10.5341	+	46.1527i	−0.685709	+	3.00429i
$237$	−3.61292	−	4.53045i	−0.234684	−	0.294285i
$238$	−0.480447	+	0.602462i	−0.0311428	+	0.0390518i
$239$	0.262765	+	1.15125i	0.0169968	+	0.0744680i	0.982715	−	0.185125i	$-0.0592689\pi$
$239$	0.262765	+	1.15125i	0.0169968	+	0.0744680i	−0.965718	+	0.259593i	$0.916412\pi$
$240$	−9.43090	+	4.54168i	−0.608762	+	0.293164i
$241$	−10.6595	+	5.13333i	−0.686637	+	0.330667i	−0.744467	−	0.667659i	$-0.767296\pi$
$241$	−10.6595	+	5.13333i	−0.686637	+	0.330667i	0.0578295	+	0.998326i	$0.481582\pi$
$242$	−1.89711	+	8.31177i	−0.121951	+	0.534301i
$243$	−9.78534	−	4.71237i	−0.627730	−	0.302299i
$244$	−17.0258			−1.08997
$245$	16.2610	+	7.83091i	1.03888	+	0.500298i
$246$	−4.75571	+	5.96347i	−0.303213	+	0.380217i
$247$	−0.391984	+	0.491532i	−0.0249413	+	0.0312754i
$248$	33.4868	+	16.1264i	2.12641	+	1.02403i
$249$	7.46278			0.472934
$250$	20.2168	+	9.73589i	1.27862	+	0.615751i
$251$	−1.70562	+	7.47279i	−0.107658	+	0.471679i	0.892144	+	0.451751i	$0.149201\pi$
$251$	−1.70562	+	7.47279i	−0.107658	+	0.471679i	−0.999801	+	0.0199272i	$0.993657\pi$
$252$	0.906844	−	0.436713i	0.0571258	−	0.0275103i
$253$	4.00890	−	1.93059i	0.252038	−	0.121375i
$254$	3.38055	+	14.8112i	0.212115	+	0.929335i
$255$	−2.78571	+	3.49317i	−0.174448	+	0.218751i
$256$	−11.7729	−	14.7628i	−0.735809	−	0.922676i
$257$	−2.53068	+	11.0876i	−0.157860	+	0.691628i	0.832606	+	0.553866i	$0.186848\pi$
$257$	−2.53068	+	11.0876i	−0.157860	+	0.691628i	−0.990465	+	0.137762i	$0.956009\pi$
$258$	−2.11516	−	9.26710i	−0.131684	−	0.576945i
$259$	0.144630	+	0.181360i	0.00898684	+	0.0112691i
$260$	10.8500			0.672886
$261$		0			0
$262$	17.2396			1.06507
$263$	10.4412	+	13.0929i	0.643834	+	0.807342i	0.991477	−	0.130285i	$-0.0415891\pi$
$263$	10.4412	+	13.0929i	0.643834	+	0.807342i	−0.347642	+	0.937627i	$0.613018\pi$
$264$	2.66536	+	11.6777i	0.164042	+	0.718713i
$265$	−3.19029	+	13.9776i	−0.195978	+	0.858635i
$266$	−0.0869951	−	0.109088i	−0.00533401	−	0.00668864i
$267$	−1.86173	+	2.33454i	−0.113936	+	0.142871i
$268$	−5.24594	−	22.9839i	−0.320447	−	1.40397i
$269$	−19.7616	+	9.51667i	−1.20488	+	0.580241i	−0.925064	−	0.379811i	$-0.875989\pi$
$269$	−19.7616	+	9.51667i	−1.20488	+	0.580241i	−0.279820	+	0.960053i	$0.590275\pi$
$270$	15.4359	−	7.43353i	0.939398	−	0.452390i
$271$	−1.45625	+	6.38023i	−0.0884607	+	0.387572i	−0.999705	−	0.0242950i	$-0.992266\pi$
$271$	−1.45625	+	6.38023i	−0.0884607	+	0.387572i	0.911244	+	0.411867i	$0.135123\pi$
$272$	32.7853	+	15.7885i	1.98790	+	0.957321i
$273$	0.0290799			0.00176000
$274$	3.65496	+	1.76014i	0.220804	+	0.106334i
$275$	−3.90724	+	4.89952i	−0.235615	+	0.295452i
$276$	1.53959	−	1.93059i	0.0926725	−	0.116208i
$277$	−19.3957	−	9.34050i	−1.16538	−	0.561216i	−0.251759	−	0.967790i	$-0.581009\pi$
$277$	−19.3957	−	9.34050i	−1.16538	−	0.561216i	−0.913618	+	0.406574i	$0.866723\pi$
$278$	27.6941			1.66098
$279$	−13.0266	−	6.27326i	−0.779880	−	0.375571i
$280$	−0.311289	+	1.36385i	−0.0186031	+	0.0815055i
$281$	7.83586	−	3.77355i	0.467448	−	0.225111i	−0.185306	−	0.982681i	$-0.559328\pi$
$281$	7.83586	−	3.77355i	0.467448	−	0.225111i	0.652754	+	0.757570i	$0.273613\pi$
$282$	−10.9111	+	5.25452i	−0.649748	+	0.312902i
$283$	−4.89294	−	21.4374i	−0.290855	−	1.27432i	−0.883338	−	0.468736i	$-0.844710\pi$
$283$	−4.89294	−	21.4374i	−0.290855	−	1.27432i	0.592484	−	0.805583i	$-0.298147\pi$
$284$	14.6013	−	18.3095i	0.866429	−	1.08647i
$285$	−0.504411	−	0.632512i	−0.0298787	−	0.0374668i
$286$	1.92765	−	8.44558i	0.113984	−	0.499398i
$287$	0.111531	+	0.488650i	0.00658347	+	0.0288441i
$288$	−16.7966	−	21.0622i	−0.989747	−	1.24110i
$289$	−1.46785			−0.0863441
$290$		0			0
$291$	5.01597			0.294042
$292$	26.4904	+	33.2179i	1.55023	+	1.94393i
$293$	−0.495352	−	2.17028i	−0.0289388	−	0.126789i	0.958395	−	0.285445i	$-0.0921412\pi$
$293$	−0.495352	−	2.17028i	−0.0289388	−	0.126789i	−0.987334	+	0.158655i	$0.949284\pi$
$294$	1.77950	−	7.79651i	0.103783	−	0.454702i
$295$	15.9581	+	20.0108i	0.929117	+	1.16508i
$296$	13.8906	−	17.4182i	0.807373	−	1.01241i
$297$	−2.14498	−	9.39778i	−0.124464	−	0.545315i
$298$	−12.7377	+	6.13417i	−0.737877	+	0.355343i
$299$	−0.934752	+	0.450153i	−0.0540581	+	0.0260330i
$300$	−0.773877	+	3.39057i	−0.0446798	+	0.195755i
$301$	−0.562757	−	0.271009i	−0.0324368	−	0.0156207i
$302$	46.4321			2.67187
$303$	3.73595	+	1.79914i	0.214625	+	0.103358i
$304$	−4.10816	+	5.15147i	−0.235619	+	0.295457i
$305$	−5.73937	+	7.19694i	−0.328635	+	0.412096i
$306$	−25.9386	−	12.4914i	−1.48281	−	0.714083i
$307$	13.8760			0.791945			0.395972	−	0.918262i	$-0.370408\pi$
$307$	13.8760			0.791945			0.395972	+	0.918262i	$0.370408\pi$
$308$	1.22066	+	0.587840i	0.0695537	+	0.0334953i
$309$	0.897766	−	3.93337i	0.0510721	−	0.223762i
$310$	31.1646	−	15.0081i	1.77003	−	0.852403i
$311$	−1.27232	+	0.612717i	−0.0721467	+	0.0347440i	−0.469609	−	0.882874i	$-0.655605\pi$
$311$	−1.27232	+	0.612717i	−0.0721467	+	0.0347440i	0.397462	+	0.917618i	$0.369891\pi$
$312$	−0.621479	−	2.72288i	−0.0351843	−	0.154153i
$313$	−17.9245	+	22.4766i	−1.01315	+	1.27046i	−0.0507851	+	0.998710i	$0.516172\pi$
$313$	−17.9245	+	22.4766i	−1.01315	+	1.27046i	−0.962369	+	0.271746i	$0.912399\pi$
$314$	−15.3556	−	19.2553i	−0.866566	−	1.08664i
$315$	0.121094	−	0.530546i	0.00682285	−	0.0298929i
$316$	14.0076	+	61.3713i	0.787989	+	3.45240i
$317$	13.9165	+	17.4507i	0.781626	+	0.980128i	0.999991	+	0.00426075i	$0.00135624\pi$
$317$	13.9165	+	17.4507i	0.781626	+	0.980128i	−0.218365	+	0.975867i	$0.570072\pi$
$318$	6.35255			0.356234
$319$		0			0
$320$	16.7988			0.939083
$321$	−1.33351	−	1.67217i	−0.0744295	−	0.0933316i
$322$	−0.0512370	−	0.224484i	−0.00285533	−	0.0125100i
$323$	−0.625823	+	2.74191i	−0.0348217	+	0.152564i
$324$	21.7231	+	27.2399i	1.20684	+	1.51333i
$325$	0.911047	−	1.14242i	0.0505358	−	0.0633699i
$326$	6.05607	+	26.5334i	0.335415	+	1.46955i
$327$	−1.71562	+	0.826199i	−0.0948740	+	0.0456889i
$328$	43.3708	−	20.8863i	2.39475	−	1.15325i
$329$	−0.177080	+	0.775839i	−0.00976275	+	0.0427734i
$330$	10.0435	+	4.83668i	0.552875	+	0.266251i
$331$	−9.34951			−0.513895			−0.256948	−	0.966425i	$-0.582717\pi$
$331$	−9.34951			−0.513895			−0.256948	+	0.966425i	$0.582717\pi$
$332$	−73.0423	−	35.1753i	−4.00872	−	1.93050i
$333$	−5.40352	+	6.77580i	−0.296111	+	0.371312i
$334$	0.276549	−	0.346781i	0.0151321	−	0.0189750i
$335$	−11.4839	−	5.53035i	−0.627432	−	0.302156i
$336$	0.304770			0.0166266
$337$	−13.9029	−	6.69528i	−0.757339	−	0.364715i	0.0150318	−	0.999887i	$-0.495215\pi$
$337$	−13.9029	−	6.69528i	−0.757339	−	0.364715i	−0.772371	+	0.635172i	$0.780929\pi$
$338$	7.07880	−	31.0142i	0.385036	−	1.68695i
$339$	1.79038	−	0.862200i	0.0972399	−	0.0468283i
$340$	43.7301	−	21.0593i	2.37160	−	1.14210i
$341$	−4.33066	−	18.9739i	−0.234519	−	1.02749i
$342$	3.25023	−	4.07566i	0.175753	−	0.220387i
$343$	−0.655544	−	0.822026i	−0.0353961	−	0.0443853i
$344$	−13.3489	+	58.4852i	−0.719723	+	3.15331i
$345$	−0.297081	−	1.30159i	−0.0159943	−	0.0700755i
$346$	−19.5837	−	24.5572i	−1.05282	−	1.32020i
$347$	−9.39939			−0.504586			−0.252293	−	0.967651i	$-0.581185\pi$
$347$	−9.39939			−0.504586			−0.252293	+	0.967651i	$0.581185\pi$
$348$		0			0
$349$	−24.5072			−1.31184			−0.655921	−	0.754830i	$-0.727720\pi$
$349$	−24.5072			−1.31184			−0.655921	+	0.754830i	$0.727720\pi$
$350$	0.202194	+	0.253543i	0.0108077	+	0.0135524i
$351$	0.500143	+	2.19127i	0.0266957	+	0.116961i
$352$	8.06910	−	35.3530i	0.430085	−	1.88432i
$353$	−15.0557	−	18.8793i	−0.801336	−	1.00484i	−0.999695	−	0.0247144i	$-0.992132\pi$
$353$	−15.0557	−	18.8793i	−0.801336	−	1.00484i	0.198358	−	0.980130i	$-0.436439\pi$
$354$	7.07084	−	8.86655i	0.375811	−	0.471252i
$355$	−2.81748	−	12.3442i	−0.149536	−	0.655162i
$356$	29.2255	−	14.0743i	1.54895	−	0.745934i
$357$	0.117205	−	0.0564428i	0.00620313	−	0.00298727i
$358$	0.969889	−	4.24936i	0.0512602	−	0.224586i
$359$	−13.7354	−	6.61463i	−0.724928	−	0.349107i	0.0347593	−	0.999396i	$-0.488934\pi$
$359$	−13.7354	−	6.61463i	−0.724928	−	0.349107i	−0.759687	+	0.650289i	$0.774648\pi$
$360$	−52.2653			−2.75462
$361$	16.6596	+	8.02284i	0.876821	+	0.422255i
$362$	−24.9273	+	31.2579i	−1.31015	+	1.64288i
$363$	0.897365	−	1.12526i	0.0470994	−	0.0590608i
$364$	−0.284621	−	0.137066i	−0.0149182	−	0.00718422i
$365$	22.9713			1.20237
$366$	3.67480	+	1.76969i	0.192085	+	0.0925033i
$367$	−2.84872	+	12.4811i	−0.148702	+	0.651506i	0.844545	+	0.535485i	$0.179871\pi$
$367$	−2.84872	+	12.4811i	−0.148702	+	0.651506i	−0.993247	+	0.116021i	$0.962986\pi$
$368$	−9.79660	+	4.71780i	−0.510683	+	0.245932i
$369$	−16.8715	+	8.12491i	−0.878297	+	0.422966i
$370$	−4.61371	−	20.2140i	−0.239855	−	1.05088i
$371$	0.260266	−	0.326363i	0.0135123	−	0.0169439i
$372$	−6.73400	−	8.44417i	−0.349142	−	0.437810i
$373$	0.00435576	−	0.0190838i	0.000225533	−	0.000988124i	−0.974815	−	0.223015i	$-0.928410\pi$
$373$	0.00435576	−	0.0190838i	0.000225533	−	0.000988124i	0.975041	+	0.222027i	$0.0712673\pi$
$374$	−8.62324	−	37.7809i	−0.445897	−	1.95360i
$375$	−2.36184	−	2.96165i	−0.121965	−	0.152939i
$376$	76.4297			3.94156
$377$		0			0
$378$	−0.498827			−0.0256569
$379$	3.26442	+	4.09345i	0.167682	+	0.210267i	0.858572	−	0.512694i	$-0.171352\pi$
$379$	3.26442	+	4.09345i	0.167682	+	0.210267i	−0.690890	+	0.722960i	$0.742781\pi$
$380$	1.95565	+	8.56825i	0.100323	+	0.439542i
$381$	0.570698	−	2.50039i	0.0292378	−	0.128099i
$382$	−33.2279	−	41.6665i	−1.70009	−	2.13184i
$383$	−0.171362	+	0.214881i	−0.00875620	+	0.0109799i	−0.786190	−	0.617984i	$-0.787949\pi$
$383$	−0.171362	+	0.214881i	−0.00875620	+	0.0109799i	0.777434	+	0.628964i	$0.216521\pi$
$384$	0.220214	+	0.964821i	0.0112378	+	0.0492358i
$385$	0.659969	−	0.317824i	0.0336351	−	0.0161978i
$386$	−7.34930	+	3.53924i	−0.374069	+	0.180142i
$387$	5.19280	−	22.7511i	0.263965	−	1.15651i
$388$	−49.0941	−	23.6425i	−2.49237	−	1.20026i
$389$	7.53699			0.382140			0.191070	−	0.981576i	$-0.438804\pi$
$389$	7.53699			0.382140			0.191070	+	0.981576i	$0.438804\pi$
$390$	−2.34183	−	1.12776i	−0.118583	−	0.0571065i
$391$	−2.89373	+	3.62862i	−0.146342	+	0.183507i
$392$	−31.4673	+	39.4588i	−1.58934	+	1.99297i
$393$	−2.62214	−	1.26276i	−0.132270	−	0.0636977i
$394$	7.39197			0.372402
$395$	30.6641	+	14.7670i	1.54288	+	0.743010i
$396$	−11.2636	+	49.3490i	−0.566017	+	2.47988i
$397$	−15.0772	+	7.26080i	−0.756703	+	0.364409i	−0.772124	−	0.635472i	$-0.780805\pi$
$397$	−15.0772	+	7.26080i	−0.756703	+	0.364409i	0.0154209	+	0.999881i	$0.495091\pi$
$398$	44.8284	−	21.5882i	2.24705	−	1.08212i
$399$	0.00524149	+	0.0229645i	0.000262403	+	0.00114966i
$400$	9.54817	−	11.9730i	0.477408	−	0.598651i
$401$	−5.02376	−	6.29959i	−0.250874	−	0.314587i	0.640408	−	0.768035i	$-0.278765\pi$
$401$	−5.02376	−	6.29959i	−0.250874	−	0.314587i	−0.891283	+	0.453448i	$0.850194\pi$
$402$	−1.25672	+	5.50607i	−0.0626797	+	0.274618i
$403$	1.00978	+	4.42412i	0.0503005	+	0.220381i
$404$	−28.0857	−	35.2183i	−1.39731	−	1.75218i
$405$	18.8373			0.936034
$406$		0			0
$407$	−11.6657			−0.578247
$408$	−7.78982	−	9.76812i	−0.385653	−	0.483594i
$409$	−2.11475	−	9.26533i	−0.104568	−	0.458141i	−0.999918	−	0.0127792i	$-0.995932\pi$
$409$	−2.11475	−	9.26533i	−0.104568	−	0.458141i	0.895351	−	0.445362i	$-0.146925\pi$
$410$	9.96892	−	43.6767i	0.492330	−	2.15704i
$411$	−0.426994	−	0.535433i	−0.0210620	−	0.0264110i
$412$	−27.3266	+	34.2665i	−1.34628	+	1.68819i
$413$	−0.165826	−	0.726530i	−0.00815975	−	0.0357502i
$414$	7.75073	−	3.73256i	0.380928	−	0.183445i
$415$	−39.4913	+	19.0180i	−1.93855	+	0.933558i
$416$	−1.88146	+	8.24323i	−0.0922464	+	0.404158i
$417$	−4.21226	−	2.02852i	−0.206275	−	0.0993370i
$418$	7.01695			0.343210
$419$	−20.9457	−	10.0869i	−1.02327	−	0.492779i	−0.154496	−	0.987993i	$-0.549375\pi$
$419$	−20.9457	−	10.0869i	−1.02327	−	0.492779i	−0.868771	+	0.495214i	$0.835089\pi$
$420$	0.253456	−	0.317824i	0.0123674	−	0.0155082i
$421$	−10.8819	+	13.6455i	−0.530351	+	0.665040i	−0.972771	−	0.231769i	$-0.925549\pi$
$421$	−10.8819	+	13.6455i	−0.530351	+	0.665040i	0.442420	+	0.896808i	$0.354120\pi$
$422$	41.9554	+	20.2046i	2.04236	+	0.983546i
$423$	−29.7317			−1.44560
$424$	−36.1211	−	17.3950i	−1.75419	−	0.844775i
$425$	1.45454	−	6.37274i	0.0705553	−	0.309123i
$426$	−5.05463	+	2.43418i	−0.244898	+	0.117936i
$427$	0.241476	−	0.116289i	0.0116858	−	0.00562760i
$428$	5.17015	+	22.6519i	0.249909	+	1.09492i
$429$	−0.911812	+	1.14338i	−0.0440227	+	0.0552027i
$430$	34.8091	+	43.6492i	1.67864	+	2.10495i
$431$	7.29534	−	31.9630i	0.351404	−	1.53960i	−0.422537	−	0.906345i	$-0.638861\pi$
$431$	7.29534	−	31.9630i	0.351404	−	1.53960i	0.773942	−	0.633257i	$-0.218282\pi$
$432$	5.24172	+	22.9655i	0.252192	+	1.10493i
$433$	3.13046	+	3.92547i	0.150440	+	0.188646i	0.851341	−	0.524613i	$-0.175790\pi$
$433$	3.13046	+	3.92547i	0.150440	+	0.188646i	−0.700901	+	0.713259i	$0.747218\pi$
$434$	−1.00712			−0.0483433
$435$		0			0
$436$	20.6859			0.990677
$437$	−0.523971	−	0.657039i	−0.0250649	−	0.0314304i
$438$	−2.26488	−	9.92311i	−0.108220	−	0.474144i
$439$	4.75507	−	20.8333i	0.226947	−	0.994320i	−0.725166	−	0.688574i	$-0.758237\pi$
$439$	4.75507	−	20.8333i	0.226947	−	0.994320i	0.952113	−	0.305746i	$-0.0989059\pi$
$440$	−43.8637	−	55.0034i	−2.09112	−	2.62218i
$441$	12.2410	−	15.3497i	0.582904	−	0.730939i
$442$	2.01067	+	8.80932i	0.0956379	+	0.419017i
$443$	35.8848	−	17.2812i	1.70494	−	0.821056i	0.712036	−	0.702143i	$-0.247773\pi$
$443$	35.8848	−	17.2812i	1.70494	−	0.821056i	0.992905	−	0.118913i	$-0.0379410\pi$
$444$	−5.83285	+	2.80895i	−0.276815	+	0.133307i
$445$	3.90257	−	17.0983i	0.184999	−	0.810535i
$446$	−41.5738	−	20.0209i	−1.96858	−	0.948017i
$447$	2.38672			0.112888
$448$	−0.440674	−	0.212217i	−0.0208199	−	0.0100263i
$449$	6.18914	−	7.76093i	0.292084	−	0.366261i	−0.614040	−	0.789275i	$-0.710456\pi$
$449$	6.18914	−	7.76093i	0.292084	−	0.366261i	0.906123	+	0.423014i	$0.139028\pi$
$450$	−7.55418	+	9.47264i	−0.356107	+	0.446545i
$451$	−22.7101	−	10.9366i	−1.06937	−	0.514984i
$452$	−21.5873			−1.01538
$453$	−7.06232	−	3.40103i	−0.331817	−	0.159794i
$454$	−12.8627	+	56.3552i	−0.603676	+	2.64488i
$455$	−0.153884	+	0.0741067i	−0.00721420	+	0.00347418i
$456$	2.03825	−	0.981568i	0.0954497	−	0.0459661i
$457$	−3.25424	−	14.2578i	−0.152227	−	0.666951i	−0.992235	−	0.124377i	$-0.960307\pi$
$457$	−3.25424	−	14.2578i	−0.152227	−	0.666951i	0.840008	−	0.542574i	$-0.182550\pi$
$458$	16.1742	−	20.2818i	0.755772	−	0.947708i
$459$	6.26895	+	7.86102i	0.292610	+	0.366921i
$460$	−3.22729	+	14.1397i	−0.150473	+	0.659266i
$461$	−4.19502	−	18.3796i	−0.195382	−	0.856023i	−0.973642	−	0.228081i	$-0.926755\pi$
$461$	−4.19502	−	18.3796i	−0.195382	−	0.856023i	0.778260	−	0.627942i	$-0.216102\pi$
$462$	−0.202363	−	0.253756i	−0.00941480	−	0.0118058i
$463$	−35.4987			−1.64977			−0.824883	−	0.565304i	$-0.808759\pi$
$463$	−35.4987			−1.64977			−0.824883	+	0.565304i	$0.808759\pi$
$464$		0			0
$465$	−5.83944			−0.270798
$466$	−32.5760	−	40.8490i	−1.50905	−	1.89229i
$467$	−1.35023	−	5.91573i	−0.0624810	−	0.273747i	0.934031	−	0.357191i	$-0.116265\pi$
$467$	−1.35023	−	5.91573i	−0.0624810	−	0.273747i	−0.996513	+	0.0834434i	$0.973408\pi$
$468$	2.62632	−	11.5067i	0.121402	−	0.531895i
$469$	0.231386	+	0.290149i	0.0106844	+	0.0133978i
$470$	44.3487	−	55.6115i	2.04565	−	2.56517i
$471$	0.925181	+	4.05348i	0.0426301	+	0.186775i
$472$	−64.4842	+	31.0540i	−2.96813	+	1.42937i
$473$	28.3011	−	13.6291i	1.30129	−	0.626667i
$474$	3.35568	−	14.7022i	0.154131	−	0.675294i
$475$	1.06638	+	0.513542i	0.0489289	+	0.0235629i
$476$	−1.41319			−0.0647732
$477$	14.0513	+	6.76676i	0.643366	+	0.309829i
$478$	−1.91605	+	2.40265i	−0.0876379	+	0.109894i
$479$	2.19412	−	2.75134i	0.100252	−	0.125712i	−0.729175	−	0.684328i	$-0.760096\pi$
$479$	2.19412	−	2.75134i	0.100252	−	0.125712i	0.829427	+	0.558616i	$0.188667\pi$
$480$	−9.80284	−	4.72080i	−0.447436	−	0.215474i
$481$	2.72008			0.124025
$482$	−27.7407	−	13.3592i	−1.26355	−	0.608495i
$483$	−0.00864974	+	0.0378970i	−0.000393577	+	0.00172437i
$484$	−14.0868	+	6.78386i	−0.640311	+	0.308357i
$485$	−26.5434	+	12.7826i	−1.20527	+	0.580429i
$486$	−6.28952	−	27.5562i	−0.285299	−	1.24997i
$487$	4.91151	−	6.15884i	0.222562	−	0.279083i	−0.657997	−	0.753020i	$-0.728596\pi$
$487$	4.91151	−	6.15884i	0.222562	−	0.279083i	0.880559	+	0.473937i	$0.157168\pi$
$488$	−16.0493	−	20.1252i	−0.726517	−	0.911024i
$489$	1.02237	−	4.47931i	0.0462333	−	0.202561i
$490$	10.4518	+	45.7922i	0.472163	+	2.06868i
$491$	13.6110	+	17.0676i	0.614254	+	0.770250i	0.987523	−	0.157473i	$-0.0503346\pi$
$491$	13.6110	+	17.0676i	0.614254	+	0.770250i	−0.373269	+	0.927723i	$0.621763\pi$
$492$	−13.9884			−0.630646
$493$		0			0
$494$	−1.63614			−0.0736132
$495$	17.0633	+	21.3967i	0.766938	+	0.961710i
$496$	10.5829	+	46.3667i	0.475186	+	2.08193i
$497$	−0.0820332	+	0.359411i	−0.00367969	+	0.0161218i
$498$	12.1091	+	15.1843i	0.542620	+	0.680424i
$499$	−18.4625	+	23.1512i	−0.826493	+	1.03639i	0.172189	+	0.985064i	$0.444916\pi$
$499$	−18.4625	+	23.1512i	−0.826493	+	1.03639i	−0.998682	+	0.0513255i	$0.983655\pi$
$500$	9.15705	+	40.1197i	0.409516	+	1.79421i
$501$	−0.0674639	+	0.0324889i	−0.00301406	+	0.00145150i
$502$	−17.9722	+	8.65495i	−0.802138	+	0.386289i
$503$	3.13213	−	13.7228i	0.139655	−	0.611868i	−0.855856	−	0.517215i	$-0.826969\pi$
$503$	3.13213	−	13.7228i	0.139655	−	0.611868i	0.995510	−	0.0946528i	$-0.0301741\pi$
$504$	1.37104	+	0.660260i	0.0610712	+	0.0294103i
$505$	−24.3547			−1.08377
$506$	10.4329	+	5.02423i	0.463800	+	0.223354i
$507$	−3.34840	+	4.19876i	−0.148707	+	0.186473i
$508$	−17.3712	+	21.7828i	−0.770721	+	0.966454i
$509$	25.3311	+	12.1988i	1.12278	+	0.540702i	0.900750	−	0.434338i	$-0.143018\pi$
$509$	25.3311	+	12.1988i	1.12278	+	0.540702i	0.222029	+	0.975040i	$0.428732\pi$
$510$	−11.6275			−0.514875
$511$	−0.602593	−	0.290194i	−0.0266572	−	0.0128374i
$512$	9.93223	−	43.5160i	0.438947	−	1.92315i
$513$	−1.64031	+	0.789929i	−0.0724213	+	0.0348762i
$514$	−26.6660	+	12.8417i	−1.17619	+	0.566421i
$515$	5.27296	+	23.1024i	0.232354	+	1.01801i
$516$	10.8689	−	13.6291i	0.478474	−	0.599988i
$517$	−24.9524	−	31.2893i	−1.09740	−	1.37610i
$518$	−0.134332	+	0.588547i	−0.00590221	+	0.0258593i
$519$	1.17993	+	5.16959i	0.0517930	+	0.226920i
$520$	10.2277	+	12.8251i	0.448513	+	0.562417i
$521$	30.6374			1.34225			0.671125	−	0.741344i	$-0.265811\pi$
$521$	30.6374			1.34225			0.671125	+	0.741344i	$0.265811\pi$
$522$		0			0
$523$	31.1728			1.36309			0.681546	−	0.731775i	$-0.261308\pi$
$523$	31.1728			1.36309			0.681546	+	0.731775i	$0.261308\pi$
$524$	19.7124	+	24.7186i	0.861141	+	1.07984i
$525$	−0.0121823	−	0.0533740i	−0.000531677	−	0.00232943i
$526$	−9.69782	+	42.4889i	−0.422845	+	1.85261i
$527$	12.6569	+	15.8712i	0.551341	+	0.691360i
$528$	−9.55619	+	11.9831i	−0.415880	+	0.521497i
$529$	4.80938	+	21.0713i	0.209104	+	0.916142i
$530$	−33.6163	+	16.1887i	−1.46020	+	0.703194i
$531$	25.0848	−	12.0802i	1.08859	−	0.524236i
$532$	0.0569402	−	0.249471i	0.00246867	−	0.0108160i
$533$	5.29528	+	2.55007i	0.229364	+	0.110456i
$534$	−7.77085			−0.336278
$535$	11.3180	+	5.45046i	0.489319	+	0.235644i
$536$	22.2229	−	27.8666i	0.959883	−	1.20365i
$537$	−0.458775	+	0.575285i	−0.0197976	+	0.0248254i
$538$	−51.4283	−	24.7666i	−2.21723	−	1.06776i
$539$	26.4272			1.13830
$540$	28.3083	+	13.6326i	1.21820	+	0.586653i
$541$	4.97933	−	21.8159i	0.214078	−	0.937937i	−0.747685	−	0.664054i	$-0.768835\pi$
$541$	4.97933	−	21.8159i	0.214078	−	0.937937i	0.961763	−	0.273883i	$-0.0883082\pi$
$542$	−15.3446	+	7.38955i	−0.659106	+	0.317409i
$543$	6.08100	−	2.92846i	0.260961	−	0.125672i
$544$	8.41663	+	36.8757i	0.360860	+	1.58103i
$545$	6.97320	−	8.74412i	0.298699	−	0.374557i
$546$	0.0471849	+	0.0591680i	0.00201933	+	0.00253216i
$547$	2.73618	−	11.9880i	0.116991	−	0.512570i	−0.882144	−	0.470980i	$-0.843900\pi$
$547$	2.73618	−	11.9880i	0.116991	−	0.512570i	0.999135	−	0.0415902i	$-0.0132424\pi$
$548$	1.65549	+	7.25318i	0.0707191	+	0.309841i
$549$	6.24328	+	7.82883i	0.266457	+	0.334126i
$550$	−16.3088			−0.695408
$551$		0			0
$552$	3.73332			0.158901
$553$	−0.617843	−	0.774751i	−0.0262734	−	0.0329457i
$554$	−12.4666	−	54.6198i	−0.529655	−	2.32057i
$555$	−0.778878	+	3.41249i	−0.0330615	+	0.144852i
$556$	31.6664	+	39.7084i	1.34296	+	1.68401i
$557$	3.74571	−	4.69697i	0.158711	−	0.199017i	−0.696118	−	0.717928i	$-0.745091\pi$
$557$	3.74571	−	4.69697i	0.158711	−	0.199017i	0.854829	+	0.518911i	$0.173662\pi$
$558$	−8.37282	−	36.6837i	−0.354450	−	1.55295i
$559$	−6.59895	+	3.17788i	−0.279106	+	0.134410i
$560$	−1.61277	+	0.776671i	−0.0681521	+	0.0328203i
$561$	−1.45576	+	6.37809i	−0.0614621	+	0.269283i
$562$	20.3923	+	9.82044i	0.860199	+	0.414250i
$563$	28.0097			1.18047			0.590233	−	0.807233i	$-0.299036\pi$
$563$	28.0097			1.18047			0.590233	+	0.807233i	$0.299036\pi$
$564$	−20.0103	−	9.63643i	−0.842584	−	0.405767i
$565$	−7.27705	+	9.12514i	−0.306148	+	0.383897i
$566$	35.6787	−	44.7396i	1.49969	−	1.88055i
$567$	−0.494149	−	0.237969i	−0.0207523	−	0.00999378i
$568$	35.4064			1.48562
$569$	31.2424	+	15.0455i	1.30975	+	0.630742i	0.952861	−	0.303406i	$-0.0981238\pi$
$569$	31.2424	+	15.0455i	1.30975	+	0.630742i	0.356887	+	0.934148i	$0.383838\pi$
$570$	0.468497	−	2.05262i	0.0196232	−	0.0859748i
$571$	−3.94460	+	1.89962i	−0.165077	+	0.0794967i	−0.514597	−	0.857432i	$-0.672059\pi$
$571$	−3.94460	+	1.89962i	−0.165077	+	0.0794967i	0.349521	+	0.936929i	$0.386344\pi$
$572$	14.3136	−	6.89308i	0.598483	−	0.288214i
$573$	2.00200	+	8.77133i	0.0836347	+	0.366427i
$574$	−0.813271	+	1.01981i	−0.0339453	+	0.0425660i
$575$	1.21781	+	1.52709i	0.0507862	+	0.0636839i
$576$	4.06629	−	17.8156i	0.169429	−	0.742316i
$577$	−9.98044	−	43.7271i	−0.415491	−	1.82038i	−0.557079	−	0.830459i	$-0.688078\pi$
$577$	−9.98044	−	43.7271i	−0.415491	−	1.82038i	0.141588	−	0.989926i	$-0.454779\pi$
$578$	−2.38172	−	2.98659i	−0.0990667	−	0.124226i
$579$	1.37707			0.0572289
$580$		0			0
$581$	1.27621			0.0529459
$582$	8.13889	+	10.2058i	0.337368	+	0.423046i
$583$	4.67134	+	20.4665i	0.193467	+	0.847636i
$584$	−14.2938	+	62.6253i	−0.591483	+	2.59145i
$585$	−3.97863	−	4.98904i	−0.164496	−	0.206272i
$586$	3.61205	−	4.52936i	0.149212	−	0.187106i
$587$	−1.42586	−	6.24712i	−0.0588517	−	0.257846i	0.936940	−	0.349490i	$-0.113645\pi$
$587$	−1.42586	−	6.24712i	−0.0588517	−	0.257846i	−0.995792	+	0.0916436i	$0.970788\pi$
$588$	13.2136	−	6.36333i	0.544919	−	0.262419i
$589$	−3.31173	+	1.59485i	−0.136458	+	0.0657145i
$590$	−14.8219	+	64.9390i	−0.610208	+	2.67349i
$591$	−1.12432	−	0.541443i	−0.0462482	−	0.0222720i
$592$	28.5076			1.17166
$593$	1.27716	+	0.615047i	0.0524466	+	0.0252570i	0.459923	−	0.887959i	$-0.347877\pi$
$593$	1.27716	+	0.615047i	0.0524466	+	0.0252570i	−0.407477	+	0.913216i	$0.633591\pi$
$594$	15.6409	−	19.6131i	0.641756	−	0.804736i
$595$	−0.476383	+	0.597365i	−0.0195298	+	0.0244896i
$596$	−23.3601	−	11.2496i	−0.956868	−	0.460803i
$597$	−8.39968			−0.343776
$598$	−2.43263	−	1.17150i	−0.0994778	−	0.0479060i
$599$	−8.28976	+	36.3198i	−0.338710	+	1.48399i	0.463045	+	0.886335i	$0.346757\pi$
$599$	−8.28976	+	36.3198i	−0.338710	+	1.48399i	−0.801755	+	0.597652i	$0.796100\pi$
$600$	−4.73729	+	2.28136i	−0.193399	+	0.0931360i
$601$	22.8102	−	10.9848i	0.930448	−	0.448080i	0.0936583	−	0.995604i	$-0.470144\pi$
$601$	22.8102	−	10.9848i	0.930448	−	0.448080i	0.836790	+	0.547524i	$0.184430\pi$
$602$	−0.361712	−	1.58476i	−0.0147423	−	0.0645901i
$603$	−8.64485	+	10.8403i	−0.352046	+	0.441451i
$604$	53.0922	+	66.5755i	2.16029	+	2.70892i
$605$	−1.88106	+	8.24145i	−0.0764759	+	0.335063i
$606$	2.40128	+	10.5207i	0.0975454	+	0.427374i
$607$	−18.5971	−	23.3200i	−0.754831	−	0.946529i	0.244904	−	0.969547i	$-0.421244\pi$
$607$	−18.5971	−	23.3200i	−0.754831	−	0.946529i	−0.999735	+	0.0230188i	$0.992672\pi$
$608$	−6.84883			−0.277757
$609$		0			0
$610$	−23.9561			−0.969953
$611$	5.81812	+	7.29569i	0.235376	+	0.295152i
$612$	−11.7487	−	51.4744i	−0.474913	−	2.08073i
$613$	−7.02909	+	30.7965i	−0.283902	+	1.24386i	0.608841	+	0.793292i	$0.291635\pi$
$613$	−7.02909	+	30.7965i	−0.283902	+	1.24386i	−0.892743	+	0.450565i	$0.851222\pi$
$614$	22.5151	+	28.2331i	0.908636	+	1.13939i
$615$	−4.71547	+	5.91302i	−0.190146	+	0.238436i
$616$	0.455802	+	1.99700i	0.0183648	+	0.0804613i
$617$	−17.3659	+	8.36295i	−0.699123	+	0.336680i	−0.749457	−	0.662053i	$-0.769686\pi$
$617$	−17.3659	+	8.36295i	−0.699123	+	0.336680i	0.0503345	+	0.998732i	$0.483971\pi$
$618$	9.45982	−	4.55561i	0.380530	−	0.183253i
$619$	−9.99377	+	43.7856i	−0.401683	+	1.75989i	0.218898	+	0.975748i	$0.429754\pi$
$619$	−9.99377	+	43.7856i	−0.401683	+	1.75989i	−0.620581	+	0.784142i	$0.713103\pi$
$620$	57.1538	+	27.5238i	2.29535	+	1.10538i
$621$	−3.00443			−0.120564
$622$	−3.31114	−	1.59456i	−0.132765	−	0.0639360i
$623$	−0.318374	+	0.399228i	−0.0127554	+	0.0159947i
$624$	2.22821	−	2.79408i	0.0891997	−	0.111853i
$625$	27.5174	+	13.2517i	1.10070	+	0.530067i
$626$	−74.8168			−2.99028
$627$	−1.06728	−	0.513974i	−0.0426229	−	0.0205261i
$628$	10.0506	−	44.0344i	0.401062	−	1.75717i
$629$	10.9631	−	5.27955i	0.437128	−	0.210510i
$630$	1.27597	−	0.614475i	0.0508359	−	0.0244813i
$631$	8.48287	+	37.1659i	0.337698	+	1.47955i	0.803843	+	0.594842i	$0.202785\pi$
$631$	8.48287	+	37.1659i	0.337698	+	1.47955i	−0.466145	+	0.884708i	$0.654357\pi$
$632$	−59.3391	+	74.4089i	−2.36038	+	2.95983i
$633$	−4.90146	−	6.14624i	−0.194816	−	0.244291i
$634$	−12.9256	+	56.6308i	−0.513341	+	2.24910i
$635$	3.35195	+	14.6859i	0.133018	+	0.582791i
$636$	7.26374	+	9.10845i	0.288026	+	0.361173i
$637$	−6.16199			−0.244147
$638$		0			0
$639$	−13.7733			−0.544864
$640$	−3.62406	−	4.54442i	−0.143253	−	0.179634i
$641$	8.22778	+	36.0483i	0.324978	+	1.42382i	0.828573	+	0.559881i	$0.189153\pi$
$641$	8.22778	+	36.0483i	0.324978	+	1.42382i	−0.503595	+	0.863940i	$0.667990\pi$
$642$	1.23857	−	5.42652i	0.0488824	−	0.214168i
$643$	−10.6531	−	13.3586i	−0.420118	−	0.526811i	0.526065	−	0.850444i	$-0.323667\pi$
$643$	−10.6531	−	13.3586i	−0.420118	−	0.526811i	−0.946182	+	0.323634i	$0.895096\pi$
$644$	0.263285	−	0.330148i	0.0103749	−	0.0130097i
$645$	−2.09726	−	9.18870i	−0.0825796	−	0.361805i
$646$	−6.59434	+	3.17567i	−0.259451	+	0.124945i
$647$	−5.58002	+	2.68719i	−0.219373	+	0.105644i	−0.540343	−	0.841445i	$-0.681705\pi$
$647$	−5.58002	+	2.68719i	−0.219373	+	0.105644i	0.320970	+	0.947089i	$0.395991\pi$
$648$	−11.7215	+	51.3551i	−0.460462	+	2.01742i
$649$	33.7655	+	16.2606i	1.32541	+	0.638286i
$650$	3.80270			0.149154
$651$	0.153183	+	0.0737689i	0.00600370	+	0.00289123i
$652$	−31.1195	+	39.0226i	−1.21873	+	1.52824i
$653$	−9.82526	+	12.3205i	−0.384492	+	0.482138i	−0.935984	−	0.352042i	$-0.885487\pi$
$653$	−9.82526	+	12.3205i	−0.384492	+	0.482138i	0.551492	+	0.834180i	$0.314059\pi$
$654$	−4.46480	−	2.15013i	−0.174587	−	0.0840769i
$655$	17.0938			0.667909
$656$	55.4968	+	26.7259i	2.16679	+	1.04347i
$657$	5.56039	−	24.3617i	0.216932	−	0.950439i
$658$	−1.86591	+	0.898573i	−0.0727406	+	0.0350300i
$659$	−14.9657	+	7.20709i	−0.582980	+	0.280749i	−0.702039	−	0.712139i	$-0.747727\pi$
$659$	−14.9657	+	7.20709i	−0.582980	+	0.280749i	0.119058	+	0.992887i	$0.462012\pi$
$660$	4.54912	+	19.9310i	0.177074	+	0.775814i
$661$	−24.9646	+	31.3046i	−0.971011	+	1.21761i	0.00502177	+	0.999987i	$0.498402\pi$
$661$	−24.9646	+	31.3046i	−0.971011	+	1.21761i	−0.976033	+	0.217622i	$0.930170\pi$
$662$	−15.1705	−	19.0232i	−0.589617	−	0.739356i
$663$	0.339437	−	1.48717i	0.0131827	−	0.0577570i
$664$	−27.2743	−	119.497i	−1.05845	−	4.63737i
$665$	−0.0862591	−	0.108166i	−0.00334498	−	0.00419448i
$666$	−22.5542			−0.873959
$667$		0			0
$668$	0.813440			0.0314729
$669$	4.85689	+	6.09035i	0.187778	+	0.235466i
$670$	−7.38127	−	32.3395i	−0.285163	−	1.24938i
$671$	−2.99929	+	13.1407i	−0.115786	+	0.507292i
$672$	0.197515	+	0.247676i	0.00761931	+	0.00955431i
$673$	−8.24529	+	10.3393i	−0.317833	+	0.398550i	−0.914926	−	0.403622i	$-0.867751\pi$
$673$	−8.24529	+	10.3393i	−0.317833	+	0.398550i	0.597093	+	0.802172i	$0.296322\pi$
$674$	−8.93608	−	39.1515i	−0.344205	−	1.50806i
$675$	3.81239	−	1.83595i	0.146739	−	0.0706658i
$676$	52.5631	−	25.3131i	2.02166	−	0.973580i
$677$	−5.29824	+	23.2131i	−0.203628	+	0.892152i	0.765077	+	0.643938i	$0.222701\pi$
$677$	−5.29824	+	23.2131i	−0.203628	+	0.892152i	−0.968705	+	0.248214i	$0.920157\pi$
$678$	4.65935	+	2.24382i	0.178941	+	0.0861735i
$679$	0.857779			0.0329185
$680$	66.1149	+	31.8392i	2.53539	+	1.22098i
$681$	6.08428	−	7.62945i	0.233150	−	0.292361i
$682$	31.5787	−	39.5984i	1.20921	−	1.51630i
$683$	−25.9180	−	12.4814i	−0.991723	−	0.477589i	−0.133601	−	0.991035i	$-0.542654\pi$
$683$	−25.9180	−	12.4814i	−0.991723	−	0.477589i	−0.858122	+	0.513446i	$0.828368\pi$
$684$	9.56022			0.365544
$685$	3.62404	+	1.74525i	0.138468	+	0.0666825i
$686$	0.608869	−	2.66763i	0.0232467	−	0.101851i
$687$	−3.94569	+	1.90014i	−0.150537	+	0.0724949i
$688$	−69.1598	+	33.3056i	−2.63669	+	1.26977i
$689$	−1.08921	−	4.77215i	−0.0414957	−	0.181804i
$690$	2.16627	−	2.71642i	0.0824686	−	0.103412i
$691$	16.9038	+	21.1967i	0.643050	+	0.806360i	0.991381	−	0.131012i	$-0.0418227\pi$
$691$	16.9038	+	21.1967i	0.643050	+	0.806360i	−0.348330	+	0.937372i	$0.613251\pi$
$692$	12.8180	−	56.1591i	0.487265	−	2.13485i
$693$	−0.177310	−	0.776845i	−0.00673545	−	0.0295099i
$694$	−15.2514	−	19.1246i	−0.578935	−	0.725962i
$695$	27.4598			1.04161
$696$		0			0
$697$	26.2919			0.995875
$698$	−39.7653	−	49.8641i	−1.50514	−	1.88738i
$699$	1.96272	+	8.59923i	0.0742368	+	0.325253i
$700$	−0.132340	+	0.579820i	−0.00500199	+	0.0219151i
$701$	−15.2827	−	19.1639i	−0.577219	−	0.723810i	0.404416	−	0.914575i	$-0.367475\pi$
$701$	−15.2827	−	19.1639i	−0.577219	−	0.723810i	−0.981636	+	0.190765i	$0.938903\pi$
$702$	−3.64698	+	4.57317i	−0.137646	+	0.172603i
$703$	0.490280	+	2.14806i	0.0184912	+	0.0810154i
$704$	22.1616	−	10.6725i	0.835246	−	0.402233i
$705$	−10.8188	+	5.21007i	−0.407460	+	0.196223i
$706$	13.9838	−	61.2669i	0.526286	−	2.30581i
$707$	0.638883	+	0.307670i	0.0240277	+	0.0115711i
$708$	20.7981			0.781641
$709$	−14.9484	−	7.19875i	−0.561397	−	0.270355i	0.131590	−	0.991304i	$-0.457992\pi$
$709$	−14.9484	−	7.19875i	−0.561397	−	0.270355i	−0.692988	+	0.720950i	$0.743706\pi$
$710$	20.5447	−	25.7623i	0.771030	−	0.966841i
$711$	23.0833	−	28.9456i	0.865692	−	1.08554i
$712$	44.1856	+	21.2787i	1.65593	+	0.797452i
$713$	−6.06588			−0.227169
$714$	0.305018	+	0.146889i	0.0114150	+	0.00549718i
$715$	1.91134	−	8.37413i	0.0714801	−	0.313175i
$716$	7.20184	−	3.46823i	0.269146	−	0.129614i
$717$	0.467418	−	0.225097i	0.0174560	−	0.00840638i
$718$	−8.82843	−	38.6799i	−0.329474	−	1.44352i
$719$	25.2525	−	31.6656i	0.941758	−	1.18093i	−0.0415791	−	0.999135i	$-0.513239\pi$
$719$	25.2525	−	31.6656i	0.941758	−	1.18093i	0.983337	−	0.181792i	$-0.0581897\pi$
$720$	−41.6978	−	52.2874i	−1.55398	−	1.94863i
$721$	0.153526	−	0.672643i	0.00571762	−	0.0250505i
$722$	10.7079	+	46.9146i	0.398508	+	1.74598i
$723$	3.24082	+	4.06386i	0.120527	+	0.151137i
$724$	−73.3212			−2.72496
$725$		0			0
$726$	3.74559			0.139012
$727$	19.7832	+	24.8074i	0.733719	+	0.920054i	0.999027	−	0.0441095i	$-0.0140451\pi$
$727$	19.7832	+	24.8074i	0.733719	+	0.920054i	−0.265308	+	0.964164i	$0.585474\pi$
$728$	−0.106279	−	0.465638i	−0.00393896	−	0.0172577i
$729$	3.81148	−	16.6992i	0.141166	−	0.618489i
$730$	37.2731	+	46.7390i	1.37954	+	1.72989i
$731$	−20.4285	+	25.6165i	−0.755575	+	0.947461i
$732$	1.66448	+	7.29255i	0.0615209	+	0.269541i
$733$	1.34189	−	0.646221i	0.0495639	−	0.0238687i	−0.408938	−	0.912562i	$-0.634101\pi$
$733$	1.34189	−	0.646221i	0.0495639	−	0.0238687i	0.458502	+	0.888694i	$0.348386\pi$
$734$	−30.0171	+	14.4555i	−1.10795	+	0.533562i
$735$	1.76445	−	7.73056i	0.0650827	−	0.285146i
$736$	−10.1830	−	4.90386i	−0.375349	−	0.180759i
$737$	−18.6634			−0.687476
$738$	−43.9072	−	21.1446i	−1.61625	−	0.778343i
$739$	22.8974	−	28.7125i	0.842295	−	1.05620i	−0.155366	−	0.987857i	$-0.549656\pi$
$739$	22.8974	−	28.7125i	0.842295	−	1.05620i	0.997662	−	0.0683478i	$-0.0217728\pi$
$740$	23.7078	−	29.7287i	0.871517	−	1.09285i
$741$	0.248856	+	0.119843i	0.00914195	+	0.00440253i
$742$	1.08635			0.0398810
$743$	−28.0883	−	13.5266i	−1.03046	−	0.496244i	−0.159294	−	0.987231i	$-0.550922\pi$
$743$	−28.0883	−	13.5266i	−1.03046	−	0.496244i	−0.871167	+	0.490987i	$0.836636\pi$
$744$	3.63357	−	15.9197i	0.133213	−	0.583645i
$745$	−12.6300	+	6.08228i	−0.462727	+	0.222837i
$746$	0.0458969	−	0.0221028i	0.00168041	−	0.000809241i
$747$	10.6099	+	46.4850i	0.388196	+	1.70080i
$748$	44.3110	−	55.5642i	1.62017	−	2.03163i
$749$	−0.228043	−	0.285957i	−0.00833253	−	0.0104487i
$750$	2.19368	−	9.61112i	0.0801017	−	0.350949i
$751$	10.0802	+	44.1642i	0.367831	+	1.61157i	0.732725	+	0.680525i	$0.238248\pi$
$751$	10.0802	+	44.1642i	0.367831	+	1.61157i	−0.364894	+	0.931049i	$0.618895\pi$
$752$	60.9764	+	76.4620i	2.22358	+	2.78828i
$753$	3.36752			0.122719
$754$		0			0
$755$	46.0393			1.67554
$756$	−0.570378	−	0.715231i	−0.0207444	−	0.0260127i
$757$	4.20260	+	18.4128i	0.152746	+	0.669225i	0.992080	+	0.125608i	$0.0400883\pi$
$757$	4.20260	+	18.4128i	0.152746	+	0.669225i	−0.839334	+	0.543617i	$0.817055\pi$
$758$	−3.03199	+	13.2840i	−0.110127	+	0.482498i
$759$	−1.21883	−	1.52837i	−0.0442409	−	0.0554763i
$760$	−8.28453	+	10.3885i	−0.300511	+	0.376829i
$761$	−3.87786	−	16.9900i	−0.140572	−	0.615888i	−0.995302	−	0.0968150i	$-0.969134\pi$
$761$	−3.87786	−	16.9900i	−0.140572	−	0.615888i	0.854730	−	0.519073i	$-0.173723\pi$
$762$	6.01348	−	2.89594i	0.217846	−	0.104909i
$763$	−0.293387	+	0.141288i	−0.0106213	+	0.00511497i
$764$	21.7484	−	95.2860i	0.786830	−	3.44733i
$765$	−25.7191	−	12.3857i	−0.929877	−	0.447805i
$766$	−0.715264			−0.0258435
$767$	−7.87308	−	3.79147i	−0.284280	−	0.136902i
$768$	−5.17231	+	6.48587i	−0.186640	+	0.234039i
$769$	−17.0194	+	21.3417i	−0.613737	+	0.769602i	−0.987448	−	0.157943i	$-0.949514\pi$
$769$	−17.0194	+	21.3417i	−0.613737	+	0.769602i	0.373711	+	0.927545i	$0.378085\pi$
$770$	1.71753	+	0.827118i	0.0618954	+	0.0298073i
$771$	4.99650			0.179945
$772$	−13.4781	−	6.49071i	−0.485087	−	0.233606i
$773$	−1.31238	+	5.74991i	−0.0472030	+	0.206810i	−0.993030	−	0.117861i	$-0.962396\pi$
$773$	−1.31238	+	5.74991i	−0.0472030	+	0.206810i	0.945827	+	0.324671i	$0.105253\pi$
$774$	54.7169	−	26.3503i	1.96676	−	0.947140i
$775$	7.69712	−	3.70674i	0.276489	−	0.133150i
$776$	−18.3320	−	80.3176i	−0.658079	−	2.88323i
$777$	0.0635414	−	0.0796783i	0.00227953	−	0.00285844i
$778$	12.2295	+	15.3353i	0.438448	+	0.549796i
$779$	−1.05935	+	4.64134i	−0.0379553	+	0.166293i
$780$	−1.06071	−	4.64729i	−0.0379797	−	0.166400i
$781$	−11.5593	−	14.4949i	−0.413624	−	0.518668i
$782$	−12.0784			−0.431923
$783$		0			0
$784$	−64.5804			−2.30644
$785$	−15.2257	−	19.0924i	−0.543428	−	0.681437i
$786$	−1.68538	−	7.38414i	−0.0601156	−	0.263383i
$787$	9.74589	−	42.6995i	0.347404	−	1.52207i	−0.435648	−	0.900117i	$-0.643481\pi$
$787$	9.74589	−	42.6995i	0.347404	−	1.52207i	0.783051	−	0.621957i	$-0.213662\pi$
$788$	8.45225	+	10.5988i	0.301099	+	0.377566i
$789$	4.58724	−	5.75222i	0.163310	−	0.204784i
$790$	19.7093	+	86.3522i	0.701226	+	3.07227i
$791$	0.306171	−	0.147444i	0.0108862	−	0.00524252i
$792$	−68.9501	+	33.2046i	−2.45003	+	1.17987i
$793$	0.699340	−	3.06401i	0.0248343	−	0.108806i
$794$	−39.2375	−	18.8958i	−1.39249	−	0.670586i
$795$	6.29881			0.223396
$796$	82.2122	+	39.5913i	2.91394	+	1.40328i
$797$	22.8625	−	28.6687i	0.809832	−	1.01550i	−0.189602	−	0.981861i	$-0.560720\pi$
$797$	22.8625	−	28.6687i	0.809832	−	1.01550i	0.999434	−	0.0336361i	$-0.0107087\pi$
$798$	−0.0382203	+	0.0479268i	−0.00135298	+	0.00169659i
$799$	37.6102	+	18.1121i	1.33055	+	0.640760i
$800$	15.9180			0.562787
$801$	−17.1885	−	8.27754i	−0.607326	−	0.292473i
$802$	4.66607	−	20.4434i	0.164765	−	0.721880i
$803$	30.3045	−	14.5939i	1.06942	−	0.515007i
$804$	−9.33172	+	4.49392i	−0.329104	+	0.158488i
$805$	−0.0508036	−	0.222585i	−0.00179059	−	0.00784509i
$806$	−7.36316	+	9.23311i	−0.259356	+	0.325223i
$807$	6.00814	+	7.53398i	0.211497	+	0.265208i
$808$	15.1546	−	66.3968i	0.533138	−	2.33583i
$809$	4.17728	+	18.3019i	0.146865	+	0.643459i	0.993745	+	0.111674i	$0.0356214\pi$
$809$	4.17728	+	18.3019i	0.146865	+	0.643459i	−0.846879	+	0.531785i	$0.821521\pi$
$810$	30.5653	+	38.3277i	1.07396	+	1.34670i
$811$	−33.9249			−1.19127			−0.595633	−	0.803257i	$-0.703099\pi$
$811$	−33.9249			−1.19127			−0.595633	+	0.803257i	$0.703099\pi$
$812$		0			0
$813$	2.87517			0.100837
$814$	−18.9287	−	23.7358i	−0.663451	−	0.831941i
$815$	6.00483	+	26.3089i	0.210340	+	0.921561i
$816$	3.55745	−	15.5862i	0.124536	−	0.545627i
$817$	−3.69901	−	4.63841i	−0.129412	−	0.162277i
$818$	15.4205	−	19.3367i	0.539165	−	0.676092i
$819$	0.0413432	+	0.181136i	0.00144465	+	0.00632941i
$820$	74.0235	−	35.6479i	2.58501	−	1.24488i
$821$	11.2785	−	5.43142i	0.393621	−	0.189558i	−0.226595	−	0.973989i	$-0.572759\pi$
$821$	11.2785	−	5.43142i	0.393621	−	0.189558i	0.620216	+	0.784431i	$0.287045\pi$
$822$	0.396592	−	1.73758i	0.0138327	−	0.0606051i
$823$	24.9400	+	12.0105i	0.869355	+	0.418659i	0.814725	−	0.579847i	$-0.196888\pi$
$823$	24.9400	+	12.0105i	0.869355	+	0.418659i	0.0546298	+	0.998507i	$0.482602\pi$
$824$	−66.2636			−2.30840
$825$	2.48056	+	1.19458i	0.0863620	+	0.0415898i
$826$	1.20918	−	1.51626i	0.0420727	−	0.0527576i
$827$	−18.4239	+	23.1028i	−0.640662	+	0.803364i	−0.991086	−	0.133227i	$-0.957466\pi$
$827$	−18.4239	+	23.1028i	−0.640662	+	0.803364i	0.350424	+	0.936591i	$0.386038\pi$
$828$	14.2143	+	6.84525i	0.493981	+	0.237889i
$829$	1.28760			0.0447203			0.0223601	−	0.999750i	$-0.492882\pi$
$829$	1.28760			0.0447203			0.0223601	+	0.999750i	$0.492882\pi$
$830$	−102.774	−	49.4933i	−3.56733	−	1.71794i
$831$	−2.10459	+	9.22080i	−0.0730073	+	0.319866i
$832$	−5.16739	+	2.48848i	−0.179147	+	0.0862727i
$833$	−24.8355	+	11.9602i	−0.860500	+	0.414395i
$834$	−2.70743	−	11.8620i	−0.0937506	−	0.410748i
$835$	0.274209	−	0.343848i	0.00948941	−	0.0118993i
$836$	8.02344	+	10.0611i	0.277497	+	0.347970i
$837$	−2.92416	+	12.8116i	−0.101074	+	0.442833i
$838$	−13.4629	−	58.9847i	−0.465067	−	2.03759i
$839$	10.1948	+	12.7839i	0.351963	+	0.441348i	0.926024	−	0.377465i	$-0.123204\pi$
$839$	10.1948	+	12.7839i	0.351963	+	0.441348i	−0.574061	+	0.818813i	$0.694633\pi$
$840$	0.614600			0.0212057
$841$		0			0
$842$	−45.4209			−1.56531
$843$	−2.38235	−	2.98737i	−0.0820525	−	0.102891i
$844$	19.0034	+	83.2594i	0.654124	+	2.86591i
$845$	7.01891	−	30.7519i	0.241458	−	1.05790i
$846$	−48.2424	−	60.4941i	−1.65861	−	2.07983i
$847$	0.153458	−	0.192430i	0.00527288	−	0.00661198i
$848$	−11.4154	−	50.0142i	−0.392007	−	1.71750i
$849$	−8.70378	+	4.19152i	−0.298713	+	0.143853i
$850$	15.3265	−	7.38087i	0.525696	−	0.253162i
$851$	−0.809080	+	3.54481i	−0.0277349	+	0.121515i
$852$	−9.26984	−	4.46412i	−0.317579	−	0.152938i
$853$	−51.4321			−1.76100			−0.880501	−	0.474045i	$-0.842793\pi$
$853$	−51.4321			−1.76100			−0.880501	+	0.474045i	$0.842793\pi$
$854$	0.628426	+	0.302634i	0.0215043	+	0.0103559i
$855$	3.22274	−	4.04118i	0.110215	−	0.138206i
$856$	−21.9018	+	27.4640i	−0.748589	+	0.938701i
$857$	17.5024	+	8.42873i	0.597872	+	0.287920i	0.708241	−	0.705971i	$-0.249489\pi$
$857$	17.5024	+	8.42873i	0.597872	+	0.287920i	−0.110369	+	0.993891i	$0.535203\pi$
$858$	−3.80589			−0.129931
$859$	21.5528	+	10.3793i	0.735372	+	0.354137i	0.763795	−	0.645459i	$-0.223334\pi$
$859$	21.5528	+	10.3793i	0.735372	+	0.354137i	−0.0284225	+	0.999596i	$0.509048\pi$
$860$	−22.7833	+	99.8202i	−0.776904	+	3.40384i
$861$	0.198397	−	0.0955428i	0.00676134	−	0.00325609i
$862$	76.8715	−	37.0194i	2.61825	−	1.26088i
$863$	6.32763	+	27.7232i	0.215395	+	0.943708i	0.960832	+	0.277132i	$0.0893838\pi$
$863$	6.32763	+	27.7232i	0.215395	+	0.943708i	−0.745437	+	0.666576i	$0.767759\pi$
$864$	−15.2662	+	19.1432i	−0.519367	+	0.651265i
$865$	−19.4180	−	24.3494i	−0.660232	−	0.827904i
$866$	−2.90757	+	12.7389i	−0.0988032	+	0.432885i
$867$	0.143500	+	0.628714i	0.00487351	+	0.0213523i
$868$	−1.15158	−	1.44403i	−0.0390871	−	0.0490137i
$869$	49.8347			1.69053
$870$		0			0
$871$	4.35173			0.147453
$872$	19.4995	+	24.4516i	0.660337	+	0.828036i
$873$	7.13126	+	31.2441i	0.241356	+	1.05745i
$874$	0.486664	−	2.13222i	0.0164617	−	0.0721232i
$875$	−0.403897	−	0.506471i	−0.0136542	−	0.0171218i
$876$	11.6382	−	14.5939i	0.393220	−	0.493082i
$877$	0.825788	+	3.61802i	0.0278849	+	0.122172i	0.986955	−	0.160998i	$-0.0514712\pi$
$877$	0.825788	+	3.61802i	0.0278849	+	0.122172i	−0.959070	+	0.283170i	$0.908614\pi$
$878$	50.1045	−	24.1291i	1.69094	−	0.814316i
$879$	−0.881156	+	0.424342i	−0.0297206	+	0.0143127i
$880$	20.0317	−	87.7646i	0.675268	−	2.95854i
$881$	10.7449	+	5.17448i	0.362006	+	0.174333i	0.606041	−	0.795434i	$-0.292757\pi$
$881$	10.7449	+	5.17448i	0.362006	+	0.174333i	−0.244035	+	0.969766i	$0.578471\pi$
$882$	51.0938			1.72042
$883$	−5.31499	−	2.55957i	−0.178864	−	0.0861363i	0.342309	−	0.939587i	$-0.388791\pi$
$883$	−5.31499	−	2.55957i	−0.178864	−	0.0861363i	−0.521173	+	0.853451i	$0.674505\pi$
$884$	−10.3319	+	12.9559i	−0.347501	+	0.435753i
$885$	7.01102	−	8.79154i	0.235673	−	0.295524i
$886$	93.3882	+	44.9734i	3.13744	+	1.51091i
$887$	−24.5541			−0.824445			−0.412223	−	0.911083i	$-0.635247\pi$
$887$	−24.5541			−0.824445			−0.412223	+	0.911083i	$0.635247\pi$
$888$	−8.81860	−	4.24682i	−0.295933	−	0.142514i
$889$	0.0975948	−	0.427591i	0.00327322	−	0.0143409i
$890$	41.1216	−	19.8031i	1.37840	−	0.663802i
$891$	24.8508	−	11.9675i	0.832534	−	0.400927i
$892$	−18.8306	−	82.5022i	−0.630495	−	2.76238i
$893$	−4.71275	+	5.90960i	−0.157706	+	0.197757i
$894$	3.87268	+	4.85618i	0.129522	+	0.162415i
$895$	0.961684	−	4.21341i	0.0321455	−	0.140839i
$896$	0.0376587	+	0.164994i	0.00125809	+	0.00551205i
$897$	0.284194	+	0.356368i	0.00948897	+	0.0118988i
$898$	25.8334			0.862072
$899$		0			0
$900$	−22.2198			−0.740661
$901$	−13.6525	−	17.1197i	−0.454832	−	0.570341i
$902$	−14.5969	−	63.9531i	−0.486023	−	2.12940i
$903$	−0.0610634	+	0.267536i	−0.00203206	+	0.00890305i
$904$	−20.3492	−	25.5171i	−0.676804	−	0.848685i
$905$	−24.7165	+	30.9935i	−0.821603	+	1.03026i
$906$	−4.53930	−	19.8880i	−0.150808	−	0.660734i
$907$	36.2334	−	17.4491i	1.20311	−	0.579387i	0.278549	−	0.960422i	$-0.410147\pi$
$907$	36.2334	−	17.4491i	1.20311	−	0.579387i	0.924561	+	0.381035i	$0.124432\pi$
$908$	−95.5111	+	45.9957i	−3.16965	+	1.52642i
$909$	−5.89525	+	25.8288i	−0.195533	+	0.856687i
$910$	−0.400474	−	0.192858i	−0.0132756	−	0.00639319i
$911$	−13.5344			−0.448415			−0.224208	−	0.974541i	$-0.571979\pi$
$911$	−13.5344			−0.448415			−0.224208	+	0.974541i	$0.571979\pi$
$912$	2.60812	+	1.25600i	0.0863634	+	0.0415904i
$913$	−40.0160	+	50.1784i	−1.32433	+	1.66066i
$914$	23.7295	−	29.7559i	0.784903	−	0.984238i
$915$	3.64371	+	1.75472i	0.120457	+	0.0580093i
$916$	47.5748			1.57191
$917$	−0.448411	−	0.215943i	−0.0148078	−	0.00713108i
$918$	−5.82261	+	25.5105i	−0.192175	+	0.841972i
$919$	−49.6547	+	23.9124i	−1.63796	+	0.788798i	−0.638134	+	0.769925i	$0.720293\pi$
$919$	−49.6547	+	23.9124i	−1.63796	+	0.788798i	−0.999822	+	0.0188726i	$0.993992\pi$
$920$	−19.7559	+	9.51393i	−0.651332	+	0.313665i
$921$	−1.35655	−	5.94342i	−0.0446997	−	0.195842i
$922$	30.5896	−	38.3581i	1.00741	−	1.26326i
$923$	2.69527	+	3.37976i	0.0887159	+	0.111246i
$924$	0.132451	−	0.580307i	0.00435733	−	0.0190907i
$925$	−1.13951	−	4.99250i	−0.0374667	−	0.164152i
$926$	−57.6000	−	72.2282i	−1.89285	−	2.37356i
$927$	25.7770			0.846627
$928$		0			0
$929$	4.05714			0.133111			0.0665553	−	0.997783i	$-0.478799\pi$
$929$	4.05714			0.133111			0.0665553	+	0.997783i	$0.478799\pi$
$930$	−9.47504	−	11.8813i	−0.310699	−	0.389604i
$931$	−1.11067	−	4.86615i	−0.0364006	−	0.159482i
$932$	21.3217	−	93.4165i	0.698415	−	3.05996i
$933$	0.386826	+	0.485064i	0.0126641	+	0.0158803i
$934$	9.84568	−	12.3461i	0.322161	−	0.403977i
$935$	−8.55028	−	37.4612i	−0.279624	−	1.22511i
$936$	16.0770	−	7.74228i	0.525494	−	0.253064i
$937$	27.1988	−	13.0983i	0.888547	−	0.427902i	0.0668080	−	0.997766i	$-0.478718\pi$
$937$	27.1988	−	13.0983i	0.888547	−	0.427902i	0.821739	+	0.569864i	$0.193004\pi$
$938$	−0.214912	+	0.941589i	−0.00701711	+	0.0307440i
$939$	11.3796	+	5.48014i	0.371360	+	0.178837i
$940$	130.447			4.25471
$941$	7.55014	+	3.63595i	0.246127	+	0.118529i	0.552881	−	0.833260i	$-0.313528\pi$
$941$	7.55014	+	3.63595i	0.246127	+	0.118529i	−0.306753	+	0.951789i	$0.599243\pi$
$942$	−6.74631	+	8.45960i	−0.219807	+	0.275629i
$943$	−4.89833	+	6.14231i	−0.159511	+	0.200021i
$944$	−82.5133	−	39.7363i	−2.68558	−	1.29331i
$945$	−0.494607			−0.0160896
$946$	73.6520	+	35.4689i	2.39463	+	1.15319i
$947$	0.406294	−	1.78009i	0.0132028	−	0.0578452i	−0.967897	−	0.251346i	$-0.919127\pi$
$947$	0.406294	−	1.78009i	0.0132028	−	0.0578452i	0.981100	+	0.193500i	$0.0619841\pi$
$948$	24.9174	−	11.9996i	0.809278	−	0.389728i
$949$	−7.06608	+	3.40284i	−0.229375	+	0.110461i
$950$	0.685416	+	3.00300i	0.0222378	+	0.0974303i
$951$	6.11404	−	7.66676i	0.198261	−	0.248612i
$952$	−1.33213	−	1.67044i	−0.0431747	−	0.0541393i
$953$	−10.4339	+	45.7137i	−0.337986	+	1.48081i	0.465265	+	0.885171i	$0.345959\pi$
$953$	−10.4339	+	45.7137i	−0.337986	+	1.48081i	−0.803251	+	0.595641i	$0.796898\pi$
$954$	9.03149	+	39.5695i	0.292405	+	1.28111i
$955$	−32.9468	−	41.3140i	−1.06613	−	1.33689i
$956$	−5.63585			−0.182276
$957$		0			0
$958$	9.15823			0.295889
$959$	−0.0730200	−	0.0915641i	−0.00235794	−	0.00295676i
$960$	−1.64229	−	7.19533i	−0.0530046	−	0.232228i
$961$	0.994340	−	4.35649i	0.0320755	−	0.140532i
$962$	4.41359	+	5.53446i	0.142300	+	0.178438i
$963$	8.51996	−	10.6837i	0.274552	−	0.344277i
$964$	−12.5649	−	55.0506i	−0.404690	−	1.77306i
$965$	−7.28712	+	3.50929i	−0.234581	+	0.112968i
$966$	−0.0911428	+	0.0438921i	−0.00293247	+	0.00141220i
$967$	4.48559	−	19.6526i	0.144247	−	0.631986i	−0.850174	−	0.526501i	$-0.823503\pi$
$967$	4.48559	−	19.6526i	0.144247	−	0.631986i	0.994421	−	0.105485i	$-0.0336394\pi$
$968$	−21.2977	−	10.2564i	−0.684534	−	0.329654i
$969$	1.23561			0.0396934
$970$	−69.0776	−	33.2660i	−2.21795	−	1.06811i
$971$	10.5487	−	13.2276i	0.338523	−	0.424495i	−0.583209	−	0.812322i	$-0.698203\pi$
$971$	10.5487	−	13.2276i	0.338523	−	0.424495i	0.921732	+	0.387828i	$0.126774\pi$
$972$	32.3191	−	40.5269i	1.03664	−	1.29990i
$973$	−0.720337	−	0.346896i	−0.0230929	−	0.0111210i
$974$	20.5006			0.656881
$975$	−0.578390	−	0.278538i	−0.0185233	−	0.00892035i
$976$	7.32939	−	32.1122i	0.234608	−	1.02789i
$977$	0.933678	−	0.449636i	0.0298710	−	0.0143851i	−0.418889	−	0.908038i	$-0.637580\pi$
$977$	0.933678	−	0.449636i	0.0298710	−	0.0143851i	0.448760	+	0.893653i	$0.351866\pi$
$978$	10.7728	−	5.18791i	0.344477	−	0.165891i
$979$	−5.71429	−	25.0359i	−0.182629	−	0.800152i
$980$	−53.7071	+	67.3466i	−1.71561	+	2.15131i
$981$	−7.58544	−	9.51184i	−0.242184	−	0.303690i
$982$	−12.6419	+	55.3876i	−0.403418	+	1.76749i
$983$	−3.61165	−	15.8237i	−0.115194	−	0.504697i	−0.999300	−	0.0374107i	$-0.988089\pi$
$983$	−3.61165	−	15.8237i	−0.115194	−	0.504697i	0.884106	−	0.467286i	$-0.154768\pi$
$984$	−13.1861	−	16.5349i	−0.420358	−	0.527112i
$985$	7.32943			0.233535
$986$		0			0
$987$	0.349622			0.0111286
$988$	−1.87082	−	2.34593i	−0.0595186	−	0.0746340i
$989$	−2.17859	−	9.54501i	−0.0692750	−	0.303514i
$990$	−15.8484	+	69.4363i	−0.503695	+	2.20683i
$991$	23.1578	+	29.0389i	0.735631	+	0.922452i	0.999109	−	0.0422134i	$-0.0134409\pi$
$991$	23.1578	+	29.0389i	0.735631	+	0.922452i	−0.263478	+	0.964666i	$0.584870\pi$
$992$	−30.8221	+	38.6496i	−0.978601	+	1.22713i
$993$	0.914027	+	4.00462i	0.0290058	+	0.127083i
$994$	−0.864389	+	0.416268i	−0.0274168	+	0.0132032i
$995$	44.4492	−	21.4056i	1.40913	−	0.678603i
$996$	−7.92565	+	34.7245i	−0.251134	+	1.10029i
$997$	32.5585	+	15.6793i	1.03114	+	0.496569i	0.871391	−	0.490589i	$-0.163218\pi$
$997$	32.5585	+	15.6793i	1.03114	+	0.496569i	0.159746	+	0.987158i	$0.448933\pi$
$998$	−77.0621			−2.43936
$999$	7.09688	+	3.41768i	0.224535	+	0.108131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.d.l.778.4		24
29.2	odd	28		841.2.e.i.270.2		12
29.3	odd	28		29.2.e.a.13.1	yes	12
29.4	even	14		841.2.d.k.645.4		24
29.5	even	14		841.2.d.m.571.4		24
29.6	even	14	inner	841.2.d.l.574.1		24
29.7	even	7		841.2.d.m.190.1		24
29.8	odd	28		841.2.b.e.840.12		12
29.9	even	14		841.2.a.k.1.1		12
29.10	odd	28		841.2.e.f.196.2		12
29.11	odd	28		841.2.e.f.236.2		12
29.12	odd	4		841.2.e.a.63.1		12
29.13	even	14		841.2.d.k.605.4		24
29.14	odd	28		841.2.e.a.267.1		12
29.15	odd	28		841.2.e.h.267.2		12
29.16	even	7		841.2.d.k.605.1		24
29.17	odd	4		841.2.e.h.63.2		12
29.18	odd	28		841.2.e.e.236.1		12
29.19	odd	28		841.2.e.e.196.1		12
29.20	even	7		841.2.a.k.1.12		12
29.21	odd	28		841.2.b.e.840.1		12
29.22	even	14		841.2.d.m.190.4		24
29.23	even	7	inner	841.2.d.l.574.4		24
29.24	even	7		841.2.d.m.571.1		24
29.25	even	7		841.2.d.k.645.1		24
29.26	odd	28		841.2.e.i.651.2		12
29.27	odd	28		29.2.e.a.9.1	✓	12
29.28	even	2	inner	841.2.d.l.778.1		24
87.20	odd	14		7569.2.a.bp.1.1		12
87.32	even	28		261.2.o.a.100.2		12
87.38	odd	14		7569.2.a.bp.1.12		12
87.56	even	28		261.2.o.a.154.2		12
116.3	even	28		464.2.y.d.129.1		12
116.27	even	28		464.2.y.d.241.1		12
145.3	even	28		725.2.p.a.274.4		24
145.27	even	28		725.2.p.a.299.4		24
145.32	even	28		725.2.p.a.274.1		24
145.114	odd	28		725.2.q.a.676.2		12
145.119	odd	28		725.2.q.a.651.2		12
145.143	even	28		725.2.p.a.299.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.9.1	✓	12	29.27	odd	28
29.2.e.a.13.1	yes	12	29.3	odd	28
261.2.o.a.100.2		12	87.32	even	28
261.2.o.a.154.2		12	87.56	even	28
464.2.y.d.129.1		12	116.3	even	28
464.2.y.d.241.1		12	116.27	even	28
725.2.p.a.274.1		24	145.32	even	28
725.2.p.a.274.4		24	145.3	even	28
725.2.p.a.299.1		24	145.143	even	28
725.2.p.a.299.4		24	145.27	even	28
725.2.q.a.651.2		12	145.119	odd	28
725.2.q.a.676.2		12	145.114	odd	28
841.2.a.k.1.1		12	29.9	even	14
841.2.a.k.1.12		12	29.20	even	7
841.2.b.e.840.1		12	29.21	odd	28
841.2.b.e.840.12		12	29.8	odd	28
841.2.d.k.605.1		24	29.16	even	7
841.2.d.k.605.4		24	29.13	even	14
841.2.d.k.645.1		24	29.25	even	7
841.2.d.k.645.4		24	29.4	even	14
841.2.d.l.574.1		24	29.6	even	14	inner
841.2.d.l.574.4		24	29.23	even	7	inner
841.2.d.l.778.1		24	29.28	even	2	inner
841.2.d.l.778.4		24	1.1	even	1	trivial
841.2.d.m.190.1		24	29.7	even	7
841.2.d.m.190.4		24	29.22	even	14
841.2.d.m.571.1		24	29.24	even	7
841.2.d.m.571.4		24	29.5	even	14
841.2.e.a.63.1		12	29.12	odd	4
841.2.e.a.267.1		12	29.14	odd	28
841.2.e.e.196.1		12	29.19	odd	28
841.2.e.e.236.1		12	29.18	odd	28
841.2.e.f.196.2		12	29.10	odd	28
841.2.e.f.236.2		12	29.11	odd	28
841.2.e.h.63.2		12	29.17	odd	4
841.2.e.h.267.2		12	29.15	odd	28
841.2.e.i.270.2		12	29.2	odd	28
841.2.e.i.651.2		12	29.26	odd	28
7569.2.a.bp.1.1		12	87.20	odd	14
7569.2.a.bp.1.12		12	87.38	odd	14

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62259 + 2.03467i) q^{2} +(-0.0977621 - 0.428324i) q^{3} +(-1.06202 + 4.65303i) q^{4} +(1.60887 + 2.01746i) q^{5} +(0.712869 - 0.893909i) q^{6} +(-0.0167182 - 0.0732474i) q^{7} +(-6.50118 + 3.13080i) q^{8} +(2.52900 - 1.21790i) q^{9} +O(q^{10})\)	\(q+(1.62259 + 2.03467i) q^{2} +(-0.0977621 - 0.428324i) q^{3} +(-1.06202 + 4.65303i) q^{4} +(1.60887 + 2.01746i) q^{5} +(0.712869 - 0.893909i) q^{6} +(-0.0167182 - 0.0732474i) q^{7} +(-6.50118 + 3.13080i) q^{8} +(2.52900 - 1.21790i) q^{9} +(-1.49432 + 6.54703i) q^{10} +(3.40418 + 1.63937i) q^{11} +2.09683 q^{12} +(-0.793749 - 0.382250i) q^{13} +(0.121907 - 0.152867i) q^{14} +(0.706838 - 0.886347i) q^{15} +(-8.31884 - 4.00614i) q^{16} -3.94108 q^{17} +(6.58158 + 3.16952i) q^{18} +(0.158795 - 0.695725i) q^{19} +(-11.0959 + 5.34353i) q^{20} +(-0.0297392 + 0.0143216i) q^{21} +(2.18804 + 9.58641i) q^{22} +(0.734247 - 0.920717i) q^{23} +(1.97657 + 2.47854i) q^{24} +(-0.369070 + 1.61700i) q^{25} +(-0.510182 - 2.23525i) q^{26} +(-1.59067 - 1.99463i) q^{27} +0.358578 q^{28} +2.95033 q^{30} +(-3.21152 - 4.02711i) q^{31} +(-2.13561 - 9.35673i) q^{32} +(0.369380 - 1.61836i) q^{33} +(-6.39478 - 8.01881i) q^{34} +(0.120876 - 0.151574i) q^{35} +(2.98108 + 13.0610i) q^{36} +(-2.78175 + 1.33962i) q^{37} +(1.67323 - 0.805785i) q^{38} +(-0.0861279 + 0.377351i) q^{39} +(-16.7758 - 8.07880i) q^{40} -6.67122 q^{41} +(-0.0773944 - 0.0372712i) q^{42} +(5.18347 - 6.49987i) q^{43} +(-11.2434 + 14.0987i) q^{44} +(6.52590 + 3.14271i) q^{45} +3.06474 q^{46} +(-9.54310 - 4.59571i) q^{47} +(-0.902658 + 3.95480i) q^{48} +(6.30170 - 3.03474i) q^{49} +(-3.88891 + 1.87280i) q^{50} +(0.385289 + 1.68806i) q^{51} +(2.62160 - 3.28738i) q^{52} +(3.46416 + 4.34391i) q^{53} +(1.47741 - 6.47296i) q^{54} +(2.16953 + 9.50531i) q^{55} +(0.338012 + 0.423853i) q^{56} -0.313519 q^{57} +9.91885 q^{59} +(3.37352 + 4.23026i) q^{60} +(0.793807 + 3.47790i) q^{61} +(2.98286 - 13.0687i) q^{62} +(-0.131489 - 0.164882i) q^{63} +(4.05898 - 5.08980i) q^{64} +(-0.505866 - 2.21634i) q^{65} +(3.89218 - 1.87437i) q^{66} +(-4.45039 + 2.14320i) q^{67} +(4.18553 - 18.3380i) q^{68} +(-0.466146 - 0.224484i) q^{69} +0.504535 q^{70} +(-4.42088 - 2.12899i) q^{71} +(-12.6285 + 15.8356i) q^{72} +(5.55040 - 6.95998i) q^{73} +(-7.23933 - 3.48628i) q^{74} +0.728681 q^{75} +(3.06859 + 1.47775i) q^{76} +(0.0631675 - 0.276755i) q^{77} +(-0.907535 + 0.437046i) q^{78} +(11.8834 - 5.72272i) q^{79} +(-5.30170 - 23.2282i) q^{80} +(4.55153 - 5.70744i) q^{81} +(-10.8247 - 13.5737i) q^{82} +(-3.77983 + 16.5605i) q^{83} +(-0.0350553 - 0.153587i) q^{84} +(-6.34068 - 7.95097i) q^{85} +21.6357 q^{86} -27.2637 q^{88} +(-4.23758 - 5.31376i) q^{89} +(4.19452 + 18.3774i) q^{90} +(-0.0147287 + 0.0645306i) q^{91} +(3.50434 + 4.39430i) q^{92} +(-1.41094 + 1.76927i) q^{93} +(-6.13382 - 26.8740i) q^{94} +(1.65907 - 0.798968i) q^{95} +(-3.79893 + 1.82947i) q^{96} +(-2.54054 + 11.1308i) q^{97} +(16.3998 + 7.89772i) q^{98} +10.6058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} - 12 q^{5} - 22 q^{6} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 24 * q + 2 * q^4 - 12 * q^5 - 22 * q^6 - 8 * q^7 + 20 * q^9	\( 24 q + 2 q^{4} - 12 q^{5} - 22 q^{6} - 8 q^{7} + 20 q^{9} - 4 q^{13} - 66 q^{16} - 64 q^{20} - 20 q^{22} + 4 q^{23} - 22 q^{24} + 12 q^{25} - 24 q^{28} + 4 q^{30} - 36 q^{33} - 72 q^{34} - 24 q^{35} + 32 q^{36} + 42 q^{38} + 54 q^{42} - 10 q^{45} + 12 q^{49} + 44 q^{51} - 12 q^{52} - 20 q^{53} + 22 q^{54} + 28 q^{57} + 88 q^{59} + 66 q^{62} + 12 q^{63} + 38 q^{64} - 54 q^{65} - 52 q^{67} - 56 q^{71} - 14 q^{74} - 22 q^{78} + 12 q^{80} + 44 q^{81} - 26 q^{82} - 32 q^{83} + 88 q^{86} - 132 q^{88} - 8 q^{91} - 2 q^{92} + 4 q^{93} - 36 q^{94} + 10 q^{96}+O(q^{100}) \) 24 * q + 2 * q^4 - 12 * q^5 - 22 * q^6 - 8 * q^7 + 20 * q^9 - 4 * q^13 - 66 * q^16 - 64 * q^20 - 20 * q^22 + 4 * q^23 - 22 * q^24 + 12 * q^25 - 24 * q^28 + 4 * q^30 - 36 * q^33 - 72 * q^34 - 24 * q^35 + 32 * q^36 + 42 * q^38 + 54 * q^42 - 10 * q^45 + 12 * q^49 + 44 * q^51 - 12 * q^52 - 20 * q^53 + 22 * q^54 + 28 * q^57 + 88 * q^59 + 66 * q^62 + 12 * q^63 + 38 * q^64 - 54 * q^65 - 52 * q^67 - 56 * q^71 - 14 * q^74 - 22 * q^78 + 12 * q^80 + 44 * q^81 - 26 * q^82 - 32 * q^83 + 88 * q^86 - 132 * q^88 - 8 * q^91 - 2 * q^92 + 4 * q^93 - 36 * q^94 + 10 * q^96

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