LMFDB - Embedded newform 961.2.g.p.732.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,0,-36,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.1
Root			$-1.29195 - 0.575212i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.p.235.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.224514i) q^{2} +(-2.09042 - 0.930713i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(1.11803 - 1.93649i) q^{5} +(0.437016 + 0.756934i) q^{6} +(-0.669131 + 0.743145i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(1.49622 + 1.66172i) q^{9} +(-0.780261 + 0.347395i) q^{10} +(4.14993 + 0.882095i) q^{11} +(-0.443477 + 4.21940i) q^{12} +(0.717560 + 6.82713i) q^{13} +(0.373619 - 0.0794152i) q^{14} +(-4.13948 + 3.00750i) q^{15} +(-2.54508 + 1.84911i) q^{16} +(0.528377 - 0.112310i) q^{17} +(-0.0892780 - 0.849423i) q^{18} +(-0.104528 + 0.994522i) q^{19} +(-4.05530 - 0.861981i) q^{20} +(2.09042 - 0.930713i) q^{21} +(-1.08436 - 1.20430i) q^{22} +(-2.12132 + 6.52875i) q^{23} +(2.25404 - 2.50336i) q^{24} +(1.31105 - 2.27080i) q^{26} +(0.540182 + 1.66251i) q^{27} +(1.69381 + 0.754131i) q^{28} +(-2.99535 - 2.17625i) q^{29} +1.95440 q^{30} +4.14590 q^{32} +(-7.85410 - 5.70634i) q^{33} +(-0.188493 - 0.0839224i) q^{34} +(0.690983 + 2.12663i) q^{35} +(2.07295 - 3.59045i) q^{36} +(2.12132 + 3.67423i) q^{37} +(0.255585 - 0.283856i) q^{38} +(4.85410 - 14.9394i) q^{39} +(2.20264 + 2.44628i) q^{40} +(6.82614 - 3.03919i) q^{41} +(-0.854932 - 0.181721i) q^{42} +(-0.0215675 + 0.205201i) q^{43} +(-0.822251 - 7.82320i) q^{44} +(4.89074 - 1.03956i) q^{45} +(2.12132 - 1.54123i) q^{46} +(-3.00000 + 2.17963i) q^{47} +(7.04128 - 1.49667i) q^{48} +(0.627171 + 5.96713i) q^{49} +(-1.20906 - 0.256993i) q^{51} +(11.6275 - 5.17691i) q^{52} +(-3.50905 - 3.89719i) q^{53} +(0.206331 - 0.635021i) q^{54} +(6.34793 - 7.05009i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.14412 - 1.98168i) q^{57} +(0.437016 + 1.34500i) q^{58} +(-5.43036 - 2.41775i) q^{59} +(7.67501 + 5.57622i) q^{60} -4.44897 q^{61} -2.23607 q^{63} +(3.80902 + 2.76741i) q^{64} +(14.0229 + 6.24341i) q^{65} +(1.14590 + 3.52671i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-0.500776 - 0.867369i) q^{68} +(10.5108 - 11.6735i) q^{69} +(0.263932 - 0.812299i) q^{70} +(4.99983 + 5.55288i) q^{71} +(-3.00721 + 1.33889i) q^{72} +(4.14993 + 0.882095i) q^{73} +(0.169393 - 1.61167i) q^{74} +(1.81359 - 0.385489i) q^{76} +(-3.43237 + 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(-10.8647 + 2.30935i) q^{79} +(0.735299 + 6.99591i) q^{80} +(1.11931 - 10.6495i) q^{81} +(-2.79173 - 0.593401i) q^{82} +(-2.88888 + 1.28621i) q^{83} +(-2.83888 - 3.15290i) q^{84} +(0.373256 - 1.14876i) q^{85} +(0.0527351 - 0.0585683i) q^{86} +(4.23607 + 7.33708i) q^{87} +(-3.12287 + 5.40897i) q^{88} +(1.81182 + 5.57622i) q^{89} +(-1.74472 - 0.776798i) q^{90} +(-5.55369 - 4.03499i) q^{91} +12.7279 q^{92} +1.41641 q^{94} +(1.80902 + 1.31433i) q^{95} +(-8.66665 - 3.85864i) q^{96} +(-2.16312 - 6.65740i) q^{97} +(1.14590 - 1.98475i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 36 q^{4} - 2 q^{7} - 52 q^{8} - 10 q^{9} - 10 q^{10} - 8 q^{14} + 4 q^{16} + 10 q^{18} + 2 q^{19} + 30 q^{20} + 12 q^{28} + 120 q^{32} - 72 q^{33} + 20 q^{35} + 60 q^{36} + 8 q^{38} + 24 q^{39}+ \cdots + 72 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 36 * q^4 - 2 * q^7 - 52 * q^8 - 10 * q^9 - 10 * q^10 - 8 * q^14 + 4 * q^16 + 10 * q^18 + 2 * q^19 + 30 * q^20 + 12 * q^28 + 120 * q^32 - 72 * q^33 + 20 * q^35 + 60 * q^36 + 8 * q^38 + 24 * q^39 + 50 * q^40 + 26 * q^41 - 10 * q^45 - 48 * q^47 - 12 * q^49 - 12 * q^51 + 24 * q^56 - 34 * q^59 + 52 * q^64 + 72 * q^66 - 48 * q^67 - 12 * q^69 + 40 * q^70 - 14 * q^71 + 10 * q^72 + 18 * q^76 - 24 * q^78 - 50 * q^80 - 38 * q^81 - 16 * q^82 + 32 * q^87 + 10 * q^90 - 192 * q^94 + 20 * q^95 + 28 * q^97 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−0.309017	−	0.224514i	−0.218508	−	0.158755i	0.473147	−	0.880984i	$-0.343118\pi$
$2$	−0.309017	−	0.224514i	−0.218508	−	0.158755i	−0.691655	+	0.722228i	$0.743118\pi$
$3$	−2.09042	−	0.930713i	−1.20690	−	0.537348i	−0.298084	−	0.954540i	$-0.596348\pi$
$3$	−2.09042	−	0.930713i	−1.20690	−	0.537348i	−0.908818	+	0.417192i	$0.863014\pi$
$4$	−0.572949	−	1.76336i	−0.286475	−	0.881678i
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i	1.00000			$0$
$6$	0.437016	+	0.756934i	0.178411	+	0.309017i
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	−0.856208	−	0.516632i	$-0.827186\pi$
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	0.603300	+	0.797514i	$0.293852\pi$
$8$	−0.454915	+	1.40008i	−0.160837	+	0.495005i
$9$	1.49622	+	1.66172i	0.498741	+	0.553907i
$10$	−0.780261	+	0.347395i	−0.246740	+	0.109856i
$11$	4.14993	+	0.882095i	1.25125	+	0.265962i	0.785448	−	0.618927i	$-0.212432\pi$
$11$	4.14993	+	0.882095i	1.25125	+	0.265962i	0.465802	+	0.884889i	$0.345766\pi$
$12$	−0.443477	+	4.21940i	−0.128021	+	1.21804i
$13$	0.717560	+	6.82713i	0.199015	+	1.89351i	0.404029	+	0.914746i	$0.367610\pi$
$13$	0.717560	+	6.82713i	0.199015	+	1.89351i	−0.205013	+	0.978759i	$0.565724\pi$
$14$	0.373619	−	0.0794152i	0.0998539	−	0.0212246i
$15$	−4.13948	+	3.00750i	−1.06881	+	0.776534i
$16$	−2.54508	+	1.84911i	−0.636271	+	0.462278i
$17$	0.528377	−	0.112310i	0.128150	−	0.0272392i	−0.143390	−	0.989666i	$-0.545800\pi$
$17$	0.528377	−	0.112310i	0.128150	−	0.0272392i	0.271540	+	0.962427i	$0.412467\pi$
$18$	−0.0892780	−	0.849423i	−0.0210430	−	0.200211i
$19$	−0.104528	+	0.994522i	−0.0239805	+	0.228159i	0.975967	+	0.217918i	$0.0699265\pi$
$19$	−0.104528	+	0.994522i	−0.0239805	+	0.228159i	−0.999948	+	0.0102410i	$0.996740\pi$
$20$	−4.05530	−	0.861981i	−0.906793	−	0.192745i
$21$	2.09042	−	0.930713i	0.456166	−	0.203098i
$22$	−1.08436	−	1.20430i	−0.231185	−	0.256757i
$23$	−2.12132	+	6.52875i	−0.442326	+	1.36134i	0.443064	+	0.896490i	$0.353891\pi$
$23$	−2.12132	+	6.52875i	−0.442326	+	1.36134i	−0.885390	+	0.464849i	$0.846109\pi$
$24$	2.25404	−	2.50336i	0.460104	−	0.510997i
$25$		0			0
$26$	1.31105	−	2.27080i	0.257118	−	0.445341i
$27$	0.540182	+	1.66251i	0.103958	+	0.319950i
$28$	1.69381	+	0.754131i	0.320099	+	0.142517i
$29$	−2.99535	−	2.17625i	−0.556223	−	0.404120i	0.273852	−	0.961772i	$-0.411702\pi$
$29$	−2.99535	−	2.17625i	−0.556223	−	0.404120i	−0.830075	+	0.557652i	$0.811702\pi$
$30$	1.95440			0.356822
$31$		0			0
$31$		0			0
$32$	4.14590			0.732898
$33$	−7.85410	−	5.70634i	−1.36722	−	0.993346i
$34$	−0.188493	−	0.0839224i	−0.0323262	−	0.0143926i
$35$	0.690983	+	2.12663i	0.116797	+	0.359466i
$36$	2.07295	−	3.59045i	0.345492	−	0.598409i
$37$	2.12132	+	3.67423i	0.348743	+	0.604040i	0.986026	−	0.166589i	$-0.0532753\pi$
$37$	2.12132	+	3.67423i	0.348743	+	0.604040i	−0.637284	+	0.770629i	$0.719942\pi$
$38$	0.255585	−	0.283856i	0.0414614	−	0.0460475i
$39$	4.85410	−	14.9394i	0.777278	−	2.39222i
$40$	2.20264	+	2.44628i	0.348268	+	0.386791i
$41$	6.82614	−	3.03919i	1.06606	−	0.474642i	0.202708	−	0.979239i	$-0.435026\pi$
$41$	6.82614	−	3.03919i	1.06606	−	0.474642i	0.863355	+	0.504597i	$0.168359\pi$
$42$	−0.854932	−	0.181721i	−0.131919	−	0.0280402i
$43$	−0.0215675	+	0.205201i	−0.00328901	+	0.0312928i	−0.996043	−	0.0888691i	$-0.971675\pi$
$43$	−0.0215675	+	0.205201i	−0.00328901	+	0.0312928i	0.992754	+	0.120162i	$0.0383414\pi$
$44$	−0.822251	−	7.82320i	−0.123959	−	1.17939i
$45$	4.89074	−	1.03956i	0.729068	−	0.154968i
$46$	2.12132	−	1.54123i	0.312772	−	0.227242i
$47$	−3.00000	+	2.17963i	−0.437595	+	0.317931i	−0.784679	−	0.619903i	$-0.787172\pi$
$47$	−3.00000	+	2.17963i	−0.437595	+	0.317931i	0.347084	+	0.937834i	$0.387172\pi$
$48$	7.04128	−	1.49667i	1.01632	−	0.216026i
$49$	0.627171	+	5.96713i	0.0895958	+	0.852447i
$50$		0			0
$51$	−1.20906	−	0.256993i	−0.169302	−	0.0359862i
$52$	11.6275	−	5.17691i	1.61245	−	0.717909i
$53$	−3.50905	−	3.89719i	−0.482005	−	0.535321i	0.452267	−	0.891883i	$-0.350616\pi$
$53$	−3.50905	−	3.89719i	−0.482005	−	0.535321i	−0.934272	+	0.356562i	$0.883949\pi$
$54$	0.206331	−	0.635021i	0.0280781	−	0.0864155i
$55$	6.34793	−	7.05009i	0.855955	−	0.950634i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$	1.14412	−	1.98168i	0.151543	−	0.262480i
$58$	0.437016	+	1.34500i	0.0573830	+	0.176607i
$59$	−5.43036	−	2.41775i	−0.706973	−	0.314765i	0.0215675	−	0.999767i	$-0.493134\pi$
$59$	−5.43036	−	2.41775i	−0.706973	−	0.314765i	−0.728540	+	0.685003i	$0.759801\pi$
$60$	7.67501	+	5.57622i	0.990839	+	0.719887i
$61$	−4.44897			−0.569632			−0.284816	−	0.958582i	$-0.591933\pi$
$61$	−4.44897			−0.569632			−0.284816	+	0.958582i	$0.591933\pi$
$62$		0			0
$63$	−2.23607			−0.281718
$64$	3.80902	+	2.76741i	0.476127	+	0.345927i
$65$	14.0229	+	6.24341i	1.73933	+	0.774400i
$66$	1.14590	+	3.52671i	0.141050	+	0.434108i
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	−0.500776	−	0.867369i	−0.0607280	−	0.105184i
$69$	10.5108	−	11.6735i	1.26536	−	1.40532i
$70$	0.263932	−	0.812299i	0.0315459	−	0.0970883i
$71$	4.99983	+	5.55288i	0.593371	+	0.659006i	0.962788	−	0.270258i	$-0.0871091\pi$
$71$	4.99983	+	5.55288i	0.593371	+	0.659006i	−0.369417	+	0.929264i	$0.620442\pi$
$72$	−3.00721	+	1.33889i	−0.354403	+	0.157790i
$73$	4.14993	+	0.882095i	0.485712	+	0.103241i	0.444258	−	0.895899i	$-0.353467\pi$
$73$	4.14993	+	0.882095i	0.485712	+	0.103241i	0.0414547	+	0.999140i	$0.486801\pi$
$74$	0.169393	−	1.61167i	0.0196915	−	0.187352i
$75$		0			0
$76$	1.81359	−	0.385489i	0.208033	−	0.0442187i
$77$	−3.43237	+	2.49376i	−0.391155	+	0.284191i
$78$	−4.85410	+	3.52671i	−0.549619	+	0.399321i
$79$	−10.8647	+	2.30935i	−1.22237	+	0.259823i	−0.773512	−	0.633781i	$-0.781502\pi$
$79$	−10.8647	+	2.30935i	−1.22237	+	0.259823i	−0.448857	+	0.893604i	$0.648169\pi$
$80$	0.735299	+	6.99591i	0.0822090	+	0.782166i
$81$	1.11931	−	10.6495i	0.124368	−	1.18328i
$82$	−2.79173	−	0.593401i	−0.308295	−	0.0655302i
$83$	−2.88888	+	1.28621i	−0.317096	+	0.141180i	−0.559112	−	0.829092i	$-0.688858\pi$
$83$	−2.88888	+	1.28621i	−0.317096	+	0.141180i	0.242016	+	0.970272i	$0.422191\pi$
$84$	−2.83888	−	3.15290i	−0.309747	−	0.344009i
$85$	0.373256	−	1.14876i	0.0404853	−	0.124601i
$86$	0.0527351	−	0.0585683i	0.00568658	−	0.00631558i
$87$	4.23607	+	7.33708i	0.454154	+	0.786618i
$88$	−3.12287	+	5.40897i	−0.332899	+	0.576598i
$89$	1.81182	+	5.57622i	0.192053	+	0.591078i	0.999998	+	0.00182083i	$0.000579589\pi$
$89$	1.81182	+	5.57622i	0.192053	+	0.591078i	−0.807945	+	0.589257i	$0.799420\pi$
$90$	−1.74472	−	0.776798i	−0.183909	−	0.0818817i
$91$	−5.55369	−	4.03499i	−0.582185	−	0.422982i
$92$	12.7279			1.32698
$93$		0			0
$94$	1.41641			0.146091
$95$	1.80902	+	1.31433i	0.185601	+	0.134847i
$96$	−8.66665	−	3.85864i	−0.884537	−	0.393821i
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	−0.998792	−	0.0491321i	$-0.984354\pi$
$97$	−2.16312	−	6.65740i	−0.219631	−	0.675956i	0.779161	−	0.626824i	$-0.215646\pi$
$98$	1.14590	−	1.98475i	0.115753	−	0.200490i
$99$	4.74342	+	8.21584i	0.476731	+	0.825723i
$100$		0			0
$101$	−0.690983	+	2.12663i	−0.0687554	+	0.211607i	−0.979531	−	0.201295i	$-0.935485\pi$
$101$	−0.690983	+	2.12663i	−0.0687554	+	0.211607i	0.910775	+	0.412902i	$0.135485\pi$
$102$	0.315921	+	0.350865i	0.0312808	+	0.0347409i
$103$	−2.47407	+	1.10153i	−0.243777	+	0.108537i	−0.524989	−	0.851109i	$-0.675930\pi$
$103$	−2.47407	+	1.10153i	−0.243777	+	0.108537i	0.281211	+	0.959646i	$0.409264\pi$
$104$	−9.88499	−	2.10112i	−0.969303	−	0.206032i
$105$	0.534838	−	5.08864i	0.0521948	−	0.496601i
$106$	0.209381	+	1.99213i	0.0203369	+	0.193493i
$107$	7.30885	−	1.55354i	0.706573	−	0.150187i	0.159410	−	0.987212i	$-0.449041\pi$
$107$	7.30885	−	1.55354i	0.706573	−	0.150187i	0.547164	+	0.837026i	$0.315708\pi$
$108$	2.62210	−	1.90506i	0.252311	−	0.183315i
$109$	11.8992	−	8.64527i	1.13974	−	0.828066i	0.152653	−	0.988280i	$-0.451218\pi$
$109$	11.8992	−	8.64527i	1.13974	−	0.828066i	0.987082	+	0.160214i	$0.0512183\pi$
$110$	−3.54446	+	0.753399i	−0.337951	+	0.0718338i
$111$	−1.01478	−	9.65502i	−0.0963190	−	0.916414i
$112$	0.328836	−	3.12866i	0.0310721	−	0.295631i
$113$	13.9250	+	2.95984i	1.30995	+	0.278439i	0.809395	−	0.587265i	$-0.199795\pi$
$113$	13.9250	+	2.95984i	1.30995	+	0.278439i	0.500557	+	0.865704i	$0.333129\pi$
$114$	−0.798468	+	0.355501i	−0.0747834	+	0.0332957i
$115$	10.2712	+	11.4073i	0.957791	+	1.06373i
$116$	−2.12132	+	6.52875i	−0.196960	+	0.606179i
$117$	−10.2712	+	11.4073i	−0.949570	+	1.05460i
$118$	1.13525	+	1.96632i	0.104509	+	0.181014i
$119$	−0.270091	+	0.467811i	−0.0247592	+	0.0428842i
$120$	−2.32765	−	7.16377i	−0.212485	−	0.653960i
$121$	6.39482	+	2.84716i	0.581347	+	0.258832i
$122$	1.37481	+	0.998856i	0.124469	+	0.0904322i
$123$	−17.0981			−1.54168
$124$		0			0
$125$	11.1803			1.00000
$126$	0.690983	+	0.502029i	0.0615577	+	0.0447243i
$127$	−8.66665	−	3.85864i	−0.769041	−	0.342399i	−0.0155688	−	0.999879i	$-0.504956\pi$
$127$	−8.66665	−	3.85864i	−0.769041	−	0.342399i	−0.753472	+	0.657480i	$0.771623\pi$
$128$	−3.11803	−	9.59632i	−0.275598	−	0.848203i
$129$	0.236068	−	0.408882i	0.0207846	−	0.0360000i
$130$	−2.93159	−	5.07767i	−0.257118	−	0.445341i
$131$	−12.9921	+	14.4292i	−1.13513	+	1.26069i	−0.173949	+	0.984755i	$0.555653\pi$
$131$	−12.9921	+	14.4292i	−1.13513	+	1.26069i	−0.961178	+	0.275931i	$0.911014\pi$
$132$	−5.56231	+	17.1190i	−0.484137	+	1.49002i
$133$	−0.669131	−	0.743145i	−0.0580210	−	0.0644388i
$134$	2.09366	−	0.932157i	0.180865	−	0.0805261i
$135$	3.82337	+	0.812683i	0.329064	+	0.0699446i
$136$	−0.0831232	+	0.790864i	−0.00712775	+	0.0678161i
$137$	0.717560	+	6.82713i	0.0613053	+	0.583281i	0.981452	+	0.191708i	$0.0614025\pi$
$137$	0.717560	+	6.82713i	0.0613053	+	0.583281i	−0.920147	+	0.391574i	$0.871931\pi$
$138$	−5.86889	+	1.24747i	−0.499593	+	0.106192i
$139$	0.810272	−	0.588697i	0.0687264	−	0.0499327i	−0.552892	−	0.833253i	$-0.686476\pi$
$139$	0.810272	−	0.588697i	0.0687264	−	0.0499327i	0.621618	+	0.783321i	$0.286476\pi$
$140$	3.35410	−	2.43690i	0.283473	−	0.205955i
$141$	8.29986	−	1.76419i	0.698974	−	0.148572i
$142$	−0.298335	−	2.83847i	−0.0250357	−	0.238199i
$143$	−3.04435	+	28.9651i	−0.254581	+	2.42218i
$144$	−6.88072	−	1.46254i	−0.573394	−	0.121879i
$145$	−7.56320	+	3.36735i	−0.628089	+	0.279643i
$146$	−1.08436	−	1.20430i	−0.0897419	−	0.0996685i
$147$	4.24264	−	13.0575i	0.349927	−	1.07696i
$148$	5.26357	−	5.84579i	0.432663	−	0.480521i
$149$	−6.70820	−	11.6190i	−0.549557	−	0.951861i	−0.998305	−	0.0582028i	$-0.981463\pi$
$149$	−6.70820	−	11.6190i	−0.549557	−	0.951861i	0.448747	−	0.893659i	$-0.351870\pi$
$150$		0			0
$151$	−0.937792	−	2.88623i	−0.0763164	−	0.234878i	0.905620	−	0.424091i	$-0.139406\pi$
$151$	−0.937792	−	2.88623i	−0.0763164	−	0.234878i	−0.981936	+	0.189213i	$0.939406\pi$
$152$	−1.34486	−	0.598772i	−0.109083	−	0.0485668i
$153$	0.977198	+	0.709976i	0.0790017	+	0.0573981i
$154$	1.62054			0.130587
$155$		0			0
$156$	−29.1246			−2.33184
$157$	3.80902	+	2.76741i	0.303993	+	0.220864i	0.729315	−	0.684179i	$-0.239839\pi$
$157$	3.80902	+	2.76741i	0.303993	+	0.220864i	−0.425322	+	0.905042i	$0.639839\pi$
$158$	3.87585	+	1.72564i	0.308346	+	0.137284i
$159$	3.70820	+	11.4127i	0.294080	+	0.905084i
$160$	4.63525	−	8.02850i	0.366449	−	0.634708i
$161$	−3.43237	−	5.94504i	−0.270509	−	0.468535i
$162$	−2.73686	+	3.03959i	−0.215028	+	0.238813i
$163$	−3.83688	+	11.8087i	−0.300528	+	0.924929i	0.680781	+	0.732487i	$0.261641\pi$
$163$	−3.83688	+	11.8087i	−0.300528	+	0.924929i	−0.981308	+	0.192442i	$0.938359\pi$
$164$	−9.27020	−	10.2956i	−0.723881	−	0.803952i
$165$	−19.8314	+	8.82952i	−1.54387	+	0.687377i
$166$	1.18149	+	0.251133i	0.0917012	+	0.0194917i
$167$	−0.774025	+	7.36435i	−0.0598958	+	0.569871i	0.922882	+	0.385082i	$0.125827\pi$
$167$	−0.774025	+	7.36435i	−0.0598958	+	0.569871i	−0.982778	+	0.184789i	$0.940840\pi$
$168$	0.352115	+	3.35016i	0.0271663	+	0.258470i
$169$	−33.3789	+	7.09491i	−2.56761	+	0.545762i
$170$	−0.373256	+	0.271187i	−0.0286274	+	0.0207991i
$171$	−1.80902	+	1.31433i	−0.138339	+	0.100509i
$172$	0.374199	−	0.0795384i	0.0285324	−	0.00606475i
$173$	−1.88151	−	17.9014i	−0.143049	−	1.36102i	−0.796770	−	0.604282i	$-0.793460\pi$
$173$	−1.88151	−	17.9014i	−0.143049	−	1.36102i	0.653721	−	0.756735i	$-0.273207\pi$
$174$	0.338261	−	3.21834i	0.0256435	−	0.243982i
$175$		0			0
$176$	−12.1930	+	5.42868i	−0.919083	+	0.409202i
$177$	9.10148	+	10.1082i	0.684109	+	0.759780i
$178$	0.692055	−	2.12993i	0.0518717	−	0.159645i
$179$	−10.9941	+	12.2102i	−0.821735	+	0.912630i	−0.997418	−	0.0718172i	$-0.977120\pi$
$179$	−10.9941	+	12.2102i	−0.821735	+	0.912630i	0.175682	+	0.984447i	$0.443787\pi$
$180$	−4.63525	−	8.02850i	−0.345492	−	0.598409i
$181$	9.08922	−	15.7430i	0.675597	−	1.17017i	−0.300698	−	0.953720i	$-0.597219\pi$
$181$	9.08922	−	15.7430i	0.675597	−	1.17017i	0.976294	−	0.216448i	$-0.0694472\pi$
$182$	0.810272	+	2.49376i	0.0600614	+	0.184850i
$183$	9.30020	+	4.14072i	0.687491	+	0.306091i
$184$	−8.17578	−	5.94006i	−0.602727	−	0.437907i
$185$	9.48683			0.697486
$186$		0			0
$187$	2.29180			0.167593
$188$	5.56231	+	4.04125i	0.405673	+	0.294739i
$189$	−1.59694	−	0.711002i	−0.116160	−	0.0517178i
$190$	−0.263932	−	0.812299i	−0.0191476	−	0.0589304i
$191$	−7.11803	+	12.3288i	−0.515043	+	0.892080i	0.484805	+	0.874622i	$0.338891\pi$
$191$	−7.11803	+	12.3288i	−0.515043	+	0.892080i	−0.999848	+	0.0174580i	$0.994443\pi$
$192$	−5.38676	−	9.33015i	−0.388756	−	0.673345i
$193$	−4.87916	+	5.41886i	−0.351210	+	0.390058i	−0.892702	−	0.450648i	$-0.851193\pi$
$193$	−4.87916	+	5.41886i	−0.351210	+	0.390058i	0.541492	+	0.840706i	$0.317860\pi$
$194$	−0.826238	+	2.54290i	−0.0593204	+	0.182569i
$195$	−23.5030	−	26.1027i	−1.68308	−	1.86925i
$196$	10.1628	−	4.52479i	0.725917	−	0.323199i
$197$	−7.24310	−	1.53957i	−0.516050	−	0.109690i	−0.0574773	−	0.998347i	$-0.518306\pi$
$197$	−7.24310	−	1.53957i	−0.516050	−	0.109690i	−0.458572	+	0.888657i	$0.651639\pi$
$198$	0.378774	−	3.60380i	0.0269183	−	0.256111i
$199$	−1.53981	−	14.6503i	−0.109154	−	1.03853i	−0.902773	−	0.430118i	$-0.858472\pi$
$199$	−1.53981	−	14.6503i	−0.109154	−	1.03853i	0.793618	−	0.608416i	$-0.208195\pi$
$200$		0			0
$201$	11.1074	−	8.06998i	0.783454	−	0.569213i
$202$	0.690983	−	0.502029i	0.0486174	−	0.0353226i
$203$	3.62155	−	0.769785i	0.254183	−	0.0540283i
$204$	0.239558	+	2.27924i	0.0167724	+	0.159579i
$205$	1.74648	−	16.6167i	0.121980	−	1.16056i
$206$	1.01184	+	0.215073i	0.0704980	+	0.0149848i
$207$	−14.0229	+	6.24341i	−0.974662	+	0.433947i
$208$	−14.4504	−	16.0488i	−1.00195	−	1.11278i
$209$	−1.31105	+	4.03499i	−0.0906871	+	0.279106i
$210$	−1.30775	+	1.45240i	−0.0902430	+	0.100225i
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	−4.86163	+	8.42060i	−0.333898	+	0.578329i
$213$	−5.28360	−	16.2612i	−0.362026	−	1.11420i
$214$	−2.60735	−	1.16087i	−0.178235	−	0.0793553i
$215$	0.373256	+	0.271187i	0.0254559	+	0.0184948i
$216$	−2.57339			−0.175097
$217$		0			0
$218$	−5.61803			−0.380501
$219$	−7.85410	−	5.70634i	−0.530731	−	0.385599i
$220$	−16.0689	−	7.15432i	−1.08336	−	0.482344i
$221$	1.14590	+	3.52671i	0.0770814	+	0.237232i
$222$	−1.85410	+	3.21140i	−0.124439	+	0.215535i
$223$	−10.9010	−	18.8812i	−0.729988	−	1.26438i	−0.956888	−	0.290458i	$-0.906192\pi$
$223$	−10.9010	−	18.8812i	−0.729988	−	1.26438i	0.226900	−	0.973918i	$-0.427141\pi$
$224$	−2.77415	+	3.08100i	−0.185356	+	0.205858i
$225$		0			0
$226$	−3.63853	−	4.04099i	−0.242031	−	0.268803i
$227$	14.3502	−	6.38910i	0.952453	−	0.424060i	0.129127	−	0.991628i	$-0.458782\pi$
$227$	14.3502	−	6.38910i	0.952453	−	0.424060i	0.823326	+	0.567568i	$0.192116\pi$
$228$	−4.14993	−	0.882095i	−0.274836	−	0.0584181i
$229$	0.443477	−	4.21940i	0.0293058	−	0.278826i	−0.970049	−	0.242909i	$-0.921898\pi$
$229$	0.443477	−	4.21940i	0.0293058	−	0.278826i	0.999355	−	0.0359165i	$-0.0114350\pi$
$230$	−0.612870	−	5.83107i	−0.0404114	−	0.384489i
$231$	9.49606	−	2.01845i	0.624795	−	0.132804i
$232$	4.40957	−	3.20374i	0.289502	−	0.210336i
$233$	3.66312	−	2.66141i	0.239979	−	0.174355i	−0.461295	−	0.887247i	$-0.652615\pi$
$233$	3.66312	−	2.66141i	0.239979	−	0.174355i	0.701274	+	0.712892i	$0.252615\pi$
$234$	5.73506	−	1.21902i	0.374913	−	0.0796901i
$235$	0.866729	+	8.24637i	0.0565391	+	0.537934i
$236$	−1.15204	+	10.9609i	−0.0749913	+	0.713494i
$237$	24.8610	+	5.28437i	1.61490	+	0.343257i
$238$	0.188493	−	0.0839224i	0.0122182	−	0.00543988i
$239$	10.9413	+	12.1516i	0.707736	+	0.786021i	0.984588	−	0.174892i	$-0.0559577\pi$
$239$	10.9413	+	12.1516i	0.707736	+	0.786021i	−0.276851	+	0.960913i	$0.589291\pi$
$240$	4.97410	−	15.3087i	0.321077	−	0.988173i
$241$	−9.85698	+	10.9473i	−0.634944	+	0.705177i	−0.971648	−	0.236434i	$-0.924021\pi$
$241$	−9.85698	+	10.9473i	−0.634944	+	0.705177i	0.336704	+	0.941611i	$0.390688\pi$
$242$	−1.33688	−	2.31555i	−0.0859380	−	0.148849i
$243$	−9.62940	+	16.6786i	−0.617727	+	1.06993i
$244$	2.54903	+	7.84512i	0.163185	+	0.502232i
$245$	12.2565	+	5.45694i	0.783039	+	0.348631i
$246$	5.28360	+	3.83876i	0.336870	+	0.244750i
$247$	−6.86474			−0.436793
$248$		0			0
$249$	7.23607			0.458567
$250$	−3.45492	−	2.51014i	−0.218508	−	0.158755i
$251$	21.7026	+	9.66263i	1.36986	+	0.609900i	0.954076	−	0.299564i	$-0.0968413\pi$
$251$	21.7026	+	9.66263i	1.36986	+	0.609900i	0.415782	+	0.909464i	$0.363508\pi$
$252$	1.28115	+	3.94298i	0.0807050	+	0.248385i
$253$	−14.5623	+	25.2227i	−0.915524	+	1.58573i
$254$	1.81182	+	3.13817i	0.113684	+	0.196906i
$255$	−1.84943	+	2.05400i	−0.115816	+	0.128627i
$256$	1.71885	−	5.29007i	0.107428	−	0.330629i
$257$	16.0218	+	17.7941i	0.999415	+	1.10996i	0.993934	+	0.109978i	$0.0350781\pi$
$257$	16.0218	+	17.7941i	0.999415	+	1.10996i	0.00548123	+	0.999985i	$0.498255\pi$
$258$	−0.164749	+	0.0733508i	−0.0102568	+	0.00456662i
$259$	−4.14993	−	0.882095i	−0.257864	−	0.0548107i
$260$	2.97493	−	28.3046i	0.184497	−	1.75538i
$261$	−0.865386	−	8.23360i	−0.0535660	−	0.509647i
$262$	7.25434	−	1.54196i	0.448175	−	0.0952625i
$263$	2.18508	−	1.58755i	0.134738	−	0.0978928i	−0.518375	−	0.855153i	$-0.673463\pi$
$263$	2.18508	−	1.58755i	0.134738	−	0.0978928i	0.653113	+	0.757261i	$0.273463\pi$
$264$	11.5623	−	8.40051i	0.711611	−	0.517015i
$265$	−11.4701	+	2.43805i	−0.704604	+	0.149768i
$266$	0.0399263	+	0.379874i	0.00244804	+	0.0232915i
$267$	1.40240	−	13.3429i	0.0858253	−	0.816573i
$268$	10.8815	+	2.31294i	0.664694	+	0.141285i
$269$	−13.5295	+	6.02370i	−0.824906	+	0.367272i	−0.775375	−	0.631501i	$-0.782439\pi$
$269$	−13.5295	+	6.02370i	−0.824906	+	0.367272i	−0.0495306	+	0.998773i	$0.515773\pi$
$270$	−0.999029	−	1.10953i	−0.0607990	−	0.0675241i
$271$	8.67656	−	26.7037i	0.527064	−	1.62213i	−0.233135	−	0.972444i	$-0.574899\pi$
$271$	8.67656	−	26.7037i	0.527064	−	1.62213i	0.760199	−	0.649690i	$-0.225101\pi$
$272$	−1.13709	+	1.26287i	−0.0689463	+	0.0765726i
$273$	7.85410	+	13.6037i	0.475352	+	0.823334i
$274$	1.31105	−	2.27080i	0.0792033	−	0.137184i
$275$		0			0
$276$	−26.6067	−	11.8460i	−1.60153	−	0.713048i
$277$	15.8508	+	11.5163i	0.952382	+	0.691946i	0.951369	−	0.308054i	$-0.0996776\pi$
$277$	15.8508	+	11.5163i	0.952382	+	0.691946i	0.00101288	+	0.999999i	$0.499678\pi$
$278$	−0.382559			−0.0229443
$279$		0			0
$280$	−3.29180			−0.196722
$281$	25.3713	+	18.4333i	1.51353	+	1.09964i	0.964582	+	0.263782i	$0.0849699\pi$
$281$	25.3713	+	18.4333i	1.51353	+	1.09964i	0.548944	+	0.835859i	$0.315030\pi$
$282$	−2.96088	−	1.31827i	−0.176318	−	0.0785018i
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	0.886961	+	0.461844i	$0.152812\pi$
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	−0.446101	+	0.894982i	$0.647188\pi$
$284$	6.92705	−	11.9980i	0.411045	−	0.711951i
$285$	−2.55834	−	4.43117i	−0.151543	−	0.262480i
$286$	7.44382	−	8.26720i	0.440162	−	0.488850i
$287$	−2.30902	+	7.10642i	−0.136297	+	0.419479i
$288$	6.20318	+	6.88933i	0.365526	+	0.405958i
$289$	−15.2637	+	6.79584i	−0.897865	+	0.399755i
$290$	3.09317	+	0.657474i	0.181637	+	0.0386082i
$291$	−1.67431	+	15.9300i	−0.0981496	+	0.933832i
$292$	−0.822251	−	7.82320i	−0.0481186	−	0.457818i
$293$	15.3649	−	3.26592i	0.897629	−	0.190797i	0.264081	−	0.964500i	$-0.414931\pi$
$293$	15.3649	−	3.26592i	0.897629	−	0.190797i	0.633548	+	0.773703i	$0.281598\pi$
$294$	−4.24264	+	3.08246i	−0.247436	+	0.179773i
$295$	−10.7533	+	7.81272i	−0.626081	+	0.454874i
$296$	−6.10926	+	1.29856i	−0.355093	+	0.0754775i
$297$	0.775226	+	7.37578i	0.0449832	+	0.427986i
$298$	−0.535668	+	5.09654i	−0.0310304	+	0.295235i
$299$	−46.0948	−	9.79776i	−2.66573	−	0.566619i
$300$		0			0
$301$	−0.138062	−	0.153334i	−0.00795778	−	0.00883801i
$302$	−0.358205	+	1.10244i	−0.0206124	+	0.0634383i
$303$	3.42372	−	3.80243i	0.196688	−	0.218444i
$304$	−1.57295	−	2.72443i	−0.0902148	−	0.156257i
$305$	−4.97410	+	8.61540i	−0.284816	+	0.493316i
$306$	−0.142571	−	0.438789i	−0.00815025	−	0.0250839i
$307$	−14.7306	−	6.55847i	−0.840718	−	0.374312i	−0.0592393	−	0.998244i	$-0.518867\pi$
$307$	−14.7306	−	6.55847i	−0.840718	−	0.374312i	−0.781479	+	0.623932i	$0.785534\pi$
$308$	6.36396	+	4.62369i	0.362620	+	0.263459i
$309$	6.19704			0.352537
$310$		0			0
$311$	16.5279			0.937209			0.468605	−	0.883408i	$-0.344757\pi$
$311$	16.5279			0.937209			0.468605	+	0.883408i	$0.344757\pi$
$312$	18.7082	+	13.5923i	1.05914	+	0.769513i
$313$	19.1907	+	8.54426i	1.08472	+	0.482950i	0.869661	−	0.493650i	$-0.164337\pi$
$313$	19.1907	+	8.54426i	1.08472	+	0.482950i	0.215064	+	0.976600i	$0.431004\pi$
$314$	−0.555728	−	1.71036i	−0.0313616	−	0.0965209i
$315$	−2.50000	+	4.33013i	−0.140859	+	0.243975i
$316$	10.2971	+	17.8351i	0.579257	+	1.00330i
$317$	14.5629	−	16.1738i	0.817935	−	0.908408i	−0.179219	−	0.983809i	$-0.557357\pi$
$317$	14.5629	−	16.1738i	0.817935	−	0.908408i	0.997153	+	0.0754008i	$0.0240236\pi$
$318$	1.41641	−	4.35926i	0.0794282	−	0.244455i
$319$	−10.5108	−	11.6735i	−0.588494	−	0.653589i
$320$	9.61768	−	4.28207i	0.537645	−	0.239375i
$321$	−16.7244	−	3.55489i	−0.933468	−	0.198415i
$322$	−0.274084	+	2.60773i	−0.0152741	+	0.145323i
$323$	0.0564643	+	0.537222i	0.00314176	+	0.0298919i
$324$	−19.4202	+	4.12790i	−1.07890	+	0.229328i
$325$		0			0
$326$	3.83688	−	2.78766i	0.212505	−	0.154394i
$327$	−32.9205	+	6.99747i	−1.82051	+	0.386961i
$328$	1.14981	+	10.9397i	0.0634878	+	0.604046i
$329$	0.387613	−	3.68789i	0.0213698	−	0.203320i
$330$	8.11060	+	1.72396i	0.446474	+	0.0949009i
$331$	23.4161	−	10.4255i	1.28706	−	0.573037i	0.354842	−	0.934926i	$-0.384535\pi$
$331$	23.4161	−	10.4255i	1.28706	−	0.573037i	0.932221	+	0.361889i	$0.117868\pi$
$332$	3.92324	+	4.35720i	0.215316	+	0.239132i
$333$	−2.93159	+	9.02251i	−0.160650	+	0.494431i
$334$	1.89259	−	2.10193i	0.103558	−	0.115013i
$335$	6.70820	+	11.6190i	0.366508	+	0.634811i
$336$	−3.59929	+	6.23416i	−0.196358	+	0.340101i
$337$	1.81182	+	5.57622i	0.0986963	+	0.303756i	0.988199	−	0.153173i	$-0.0489492\pi$
$337$	1.81182	+	5.57622i	0.0986963	+	0.303756i	−0.889503	+	0.456929i	$0.848949\pi$
$338$	11.9076	+	5.30159i	0.647686	+	0.288368i
$339$	−26.3542	−	19.1475i	−1.43137	−	1.03995i
$340$	−2.23954			−0.121456
$341$		0			0
$342$	0.854102			0.0461845
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$	−0.277487	−	0.123545i	−0.0149611	−	0.00666111i
$345$	−10.8541	−	33.4055i	−0.584365	−	1.79849i
$346$	−3.43769	+	5.95426i	−0.184812	+	0.320103i
$347$	12.9192	+	22.3767i	0.693539	+	1.20124i	0.970671	+	0.240413i	$0.0772829\pi$
$347$	12.9192	+	22.3767i	0.693539	+	1.20124i	−0.277132	+	0.960832i	$0.589384\pi$
$348$	10.5108	−	11.6735i	0.563440	−	0.625764i
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	−0.889090	−	0.457733i	$-0.848662\pi$
$349$	1.85410	−	5.70634i	0.0992478	−	0.305453i	0.988337	+	0.152280i	$0.0486615\pi$
$350$		0			0
$351$	−10.9625	+	4.88084i	−0.585137	+	0.260520i
$352$	17.2052	+	3.65707i	0.917039	+	0.194923i
$353$	1.66098	−	15.8032i	0.0884049	−	0.841117i	−0.857021	−	0.515281i	$-0.827688\pi$
$353$	1.66098	−	15.8032i	0.0884049	−	0.841117i	0.945426	−	0.325836i	$-0.105646\pi$
$354$	−0.543076	−	5.16702i	−0.0288642	−	0.274624i
$355$	16.3431	−	3.47383i	0.867401	−	0.184372i
$356$	8.79478	−	6.38978i	0.466122	−	0.338658i
$357$	1.00000	−	0.726543i	0.0529256	−	0.0384527i
$358$	6.13870	−	1.30482i	0.324441	−	0.0689620i
$359$	−1.02061	−	9.71044i	−0.0538657	−	0.512498i	−0.987875	−	0.155250i	$-0.950382\pi$
$359$	−1.02061	−	9.71044i	−0.0538657	−	0.512498i	0.934010	−	0.357248i	$-0.116285\pi$
$360$	−0.769401	+	7.32036i	−0.0405510	+	0.385817i
$361$	17.6067	+	3.74241i	0.926666	+	0.196969i
$362$	−6.34325	+	2.82420i	−0.333394	+	0.148436i
$363$	−10.7179	−	11.9035i	−0.562546	−	0.624771i
$364$	−3.93314	+	12.1050i	−0.206153	+	0.634473i
$365$	6.34793	−	7.05009i	0.332266	−	0.369019i
$366$	−1.94427	−	3.36758i	−0.101629	−	0.176026i
$367$	−6.15763	+	10.6653i	−0.321426	+	0.556726i	−0.980782	−	0.195105i	$-0.937495\pi$
$367$	−6.15763	+	10.6653i	−0.321426	+	0.556726i	0.659357	+	0.751830i	$0.270829\pi$
$368$	−6.67346	−	20.5388i	−0.347878	−	1.07066i
$369$	15.2637	+	6.79584i	0.794597	+	0.353777i
$370$	−2.93159	−	2.12993i	−0.152406	−	0.110730i
$371$	5.24419			0.272265
$372$		0			0
$373$	−22.7082			−1.17579			−0.587893	−	0.808939i	$-0.700042\pi$
$373$	−22.7082			−1.17579			−0.587893	+	0.808939i	$0.700042\pi$
$374$	−0.708204	−	0.514540i	−0.0366204	−	0.0266062i
$375$	−23.3716	−	10.4057i	−1.20690	−	0.537348i
$376$	−1.68692	−	5.19180i	−0.0869961	−	0.267747i
$377$	12.7082	−	22.0113i	0.654506	−	1.13364i
$378$	0.333851	+	0.578246i	0.0171714	+	0.0297418i
$379$	−12.9921	+	14.4292i	−0.667360	+	0.741178i	−0.977829	−	0.209405i	$-0.932847\pi$
$379$	−12.9921	+	14.4292i	−0.667360	+	0.741178i	0.310469	+	0.950584i	$0.399514\pi$
$380$	1.28115	−	3.94298i	0.0657218	−	0.202271i
$381$	14.5256	+	16.1323i	0.744170	+	0.826485i
$382$	4.96758	−	2.21171i	0.254164	−	0.113161i
$383$	−18.6361	−	3.96123i	−0.952262	−	0.202410i	−0.294514	−	0.955647i	$-0.595158\pi$
$383$	−18.6361	−	3.96123i	−0.952262	−	0.202410i	−0.657748	+	0.753238i	$0.728491\pi$
$384$	−2.41344	+	22.9623i	−0.123160	+	1.17179i
$385$	0.991644	+	9.43486i	0.0505389	+	0.480845i
$386$	2.72435	−	0.579079i	0.138666	−	0.0294744i
$387$	−0.373256	+	0.271187i	−0.0189737	+	0.0137852i
$388$	−10.5000	+	7.62870i	−0.533057	+	0.387288i
$389$	33.0453	−	7.02399i	1.67546	−	0.356130i	0.730399	−	0.683021i	$-0.239334\pi$
$389$	33.0453	−	7.02399i	1.67546	−	0.356130i	0.945062	+	0.326891i	$0.106001\pi$
$390$	1.40240	+	13.3429i	0.0710131	+	0.675645i
$391$	−0.387613	+	3.68789i	−0.0196024	+	0.186505i
$392$	−8.63980	−	1.83645i	−0.436376	−	0.0927545i
$393$	40.5884	−	18.0711i	2.04741	−	0.911567i
$394$	1.89259	+	2.10193i	0.0953472	+	0.105894i
$395$	−7.67501	+	23.6212i	−0.386172	+	1.18851i
$396$	11.7697	−	13.0716i	0.591450	−	0.656872i
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	0.849362	−	0.527811i	$-0.176987\pi$
$397$	−0.645898	−	1.11873i	−0.0324167	−	0.0561474i	−0.881779	+	0.471664i	$0.843654\pi$
$398$	−2.81338	+	4.87291i	−0.141022	+	0.244257i
$399$	0.707107	+	2.17625i	0.0353996	+	0.108949i
$400$		0			0
$401$	−2.99535	−	2.17625i	−0.149581	−	0.108677i	0.510478	−	0.859891i	$-0.329469\pi$
$401$	−2.99535	−	2.17625i	−0.149581	−	0.108677i	−0.660059	+	0.751214i	$0.729469\pi$
$402$	−5.24419			−0.261557
$403$		0			0
$404$	4.14590			0.206266
$405$	−19.3713	−	14.0741i	−0.962569	−	0.699347i
$406$	−1.29195	−	0.575212i	−0.0641183	−	0.0285473i
$407$	5.56231	+	17.1190i	0.275713	+	0.848558i
$408$	0.909830	−	1.57587i	0.0450433	−	0.0780173i
$409$	−8.67656	−	15.0282i	−0.429028	−	0.743099i	0.567759	−	0.823195i	$-0.307811\pi$
$409$	−8.67656	−	15.0282i	−0.429028	−	0.743099i	−0.996787	+	0.0800961i	$0.974477\pi$
$410$	−4.27037	+	4.74273i	−0.210898	+	0.234226i
$411$	4.85410	−	14.9394i	0.239435	−	0.736906i
$412$	3.35990	+	3.73154i	0.165530	+	0.183840i
$413$	5.43036	−	2.41775i	0.267211	−	0.118970i
$414$	5.73506	+	1.21902i	0.281863	+	0.0599118i
$415$	−0.739128	+	7.03233i	−0.0362824	+	0.345204i
$416$	2.97493	+	28.3046i	0.145858	+	1.38775i
$417$	−2.24171	+	0.476491i	−0.109777	+	0.0233339i
$418$	1.31105	−	0.952532i	0.0641255	−	0.0465899i
$419$	15.0451	−	10.9309i	0.735000	−	0.534009i	−0.156141	−	0.987735i	$-0.549905\pi$
$419$	15.0451	−	10.9309i	0.735000	−	0.534009i	0.891141	+	0.453726i	$0.149905\pi$
$420$	−9.27952	+	1.97242i	−0.452794	+	0.0962444i
$421$	0.0435265	+	0.414127i	0.00212135	+	0.0201833i	0.995531	−	0.0944314i	$-0.0301033\pi$
$421$	0.0435265	+	0.414127i	0.00212135	+	0.0201833i	−0.993410	+	0.114615i	$0.963437\pi$
$422$	0.199632	−	1.89937i	0.00971791	−	0.0924598i
$423$	−8.11060	−	1.72396i	−0.394351	−	0.0838219i
$424$	7.05272	−	3.14007i	0.342510	−	0.152495i
$425$		0			0
$426$	−2.01815	+	6.21124i	−0.0977799	+	0.300936i
$427$	2.97694	−	3.30623i	0.144064	−	0.160000i
$428$	−6.92705	−	11.9980i	−0.334832	−	0.579945i
$429$	33.3221	−	57.7156i	1.60881	−	2.78654i
$430$	−0.0544574	−	0.167602i	−0.00262617	−	0.00808251i
$431$	−0.101820	−	0.0453333i	−0.00490451	−	0.00218363i	0.404283	−	0.914634i	$-0.367521\pi$
$431$	−0.101820	−	0.0453333i	−0.00490451	−	0.00218363i	−0.409187	+	0.912450i	$0.634188\pi$
$432$	−4.44897	−	3.23237i	−0.214051	−	0.155517i
$433$	−21.5958			−1.03783			−0.518913	−	0.854827i	$-0.673663\pi$
$433$	−21.5958			−1.03783			−0.518913	+	0.854827i	$0.673663\pi$
$434$		0			0
$435$	18.9443			0.908308
$436$	−22.0623	−	16.0292i	−1.05659	−	0.767660i
$437$	−6.27125	−	2.79214i	−0.299995	−	0.133566i
$438$	1.14590	+	3.52671i	0.0547531	+	0.168513i
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	6.98295	+	12.0948i	0.332899	+	0.576598i
$441$	−8.97733	+	9.97033i	−0.427492	+	0.474778i
$442$	0.437694	−	1.34708i	0.0208190	−	0.0640742i
$443$	16.0218	+	17.7941i	0.761221	+	0.845421i	0.991822	−	0.127627i	$-0.0407360\pi$
$443$	16.0218	+	17.7941i	0.761221	+	0.845421i	−0.230601	+	0.973048i	$0.574069\pi$
$444$	−16.4438	+	7.32126i	−0.780389	+	0.347452i
$445$	12.8240	+	2.72582i	0.607915	+	0.129216i
$446$	−0.870477	+	8.28204i	−0.0412183	+	0.392166i
$447$	3.20903	+	30.5319i	0.151782	+	1.44411i
$448$	−4.60532	+	0.978891i	−0.217581	+	0.0462482i
$449$	−34.1324	+	24.7986i	−1.61081	+	1.17032i	−0.749915	+	0.661535i	$0.769905\pi$
$449$	−34.1324	+	24.7986i	−1.61081	+	1.17032i	−0.860893	+	0.508786i	$0.830095\pi$
$450$		0			0
$451$	31.0088	−	6.59113i	1.46015	−	0.310364i
$452$	−2.75904	−	26.2505i	−0.129774	−	1.23472i
$453$	−0.725874	+	6.90623i	−0.0341045	+	0.324483i
$454$	−5.86889	−	1.24747i	−0.275440	−	0.0585467i
$455$	−14.0229	+	6.24341i	−0.657406	+	0.292696i
$456$	2.25404	+	2.50336i	0.105555	+	0.117231i
$457$	−3.49613	+	10.7600i	−0.163542	+	0.503330i	−0.998926	−	0.0463365i	$-0.985245\pi$
$457$	−3.49613	+	10.7600i	−0.163542	+	0.503330i	0.835384	+	0.549667i	$0.185245\pi$
$458$	−1.08436	+	1.20430i	−0.0506686	+	0.0562732i
$459$	0.472136	+	0.817763i	0.0220374	+	0.0381699i
$460$	14.2302	−	24.6475i	0.663489	−	1.14920i
$461$	12.0846	+	37.1925i	0.562835	+	1.73223i	0.674299	+	0.738459i	$0.264446\pi$
$461$	12.0846	+	37.1925i	0.562835	+	1.73223i	−0.111464	+	0.993768i	$0.535554\pi$
$462$	−3.38761	−	1.50826i	−0.157606	−	0.0701707i
$463$	12.2515	+	8.90124i	0.569376	+	0.413676i	0.834878	−	0.550435i	$-0.185538\pi$
$463$	12.2515	+	8.90124i	0.569376	+	0.413676i	−0.265503	+	0.964110i	$0.585538\pi$
$464$	11.6476			0.540724
$465$		0			0
$466$	−1.72949			−0.0801171
$467$	−12.6631	−	9.20029i	−0.585979	−	0.425739i	0.254895	−	0.966969i	$-0.417959\pi$
$467$	−12.6631	−	9.20029i	−0.585979	−	0.425739i	−0.840875	+	0.541230i	$0.817959\pi$
$468$	26.0000	+	11.5759i	1.20185	+	0.535097i
$469$	−1.85410	−	5.70634i	−0.0856145	−	0.263494i
$470$	1.58359	−	2.74286i	0.0730457	−	0.126519i
$471$	−5.38676	−	9.33015i	−0.248209	−	0.429911i
$472$	5.85541	−	6.50309i	0.269517	−	0.299329i
$473$	−0.270510	+	0.832544i	−0.0124381	+	0.0382804i
$474$	−6.49606	−	7.21460i	−0.298374	−	0.331378i
$475$		0			0
$476$	0.979665	+	0.208234i	0.0449029	+	0.00954440i
$477$	1.22574	−	11.6621i	0.0561228	−	0.533972i
$478$	−0.652858	−	6.21153i	−0.0298610	−	0.284109i
$479$	−24.9155	+	5.29595i	−1.13842	+	0.241978i	−0.738292	−	0.674481i	$-0.764367\pi$
$479$	−24.9155	+	5.29595i	−1.13842	+	0.241978i	−0.400127	+	0.916460i	$0.631034\pi$
$480$	−17.1618	+	12.4688i	−0.783327	+	0.569121i
$481$	−23.5623	+	17.1190i	−1.07435	+	0.780560i
$482$	5.50379	−	1.16987i	0.250691	−	0.0532860i
$483$	1.64195	+	15.6222i	0.0747115	+	0.710833i
$484$	1.35665	−	12.9076i	0.0616657	−	0.586710i
$485$	−15.3104	−	3.25433i	−0.695211	−	0.147772i
$486$	6.72023	−	2.99204i	0.304836	−	0.135722i
$487$	−12.4399	−	13.8159i	−0.563705	−	0.626058i	0.392149	−	0.919902i	$-0.371732\pi$
$487$	−12.4399	−	13.8159i	−0.563705	−	0.626058i	−0.955853	+	0.293844i	$0.905065\pi$
$488$	2.02390	−	6.22894i	0.0916178	−	0.281971i
$489$	19.0112	−	21.1141i	0.859716	−	0.954811i
$490$	−2.56231	−	4.43804i	−0.115753	−	0.200490i
$491$	−4.78282	+	8.28409i	−0.215846	+	0.373856i	−0.953534	−	0.301286i	$-0.902584\pi$
$491$	−4.78282	+	8.28409i	−0.215846	+	0.373856i	0.737688	+	0.675142i	$0.235917\pi$
$492$	9.79633	+	30.1500i	0.441653	+	1.35927i
$493$	−1.82709	−	0.813473i	−0.0822880	−	0.0366370i
$494$	2.12132	+	1.54123i	0.0954427	+	0.0693432i
$495$	21.2132			0.953463
$496$		0			0
$497$	−7.47214			−0.335171
$498$	−2.23607	−	1.62460i	−0.100201	−	0.0728000i
$499$	−16.7953	−	7.47776i	−0.751862	−	0.334751i	−0.00522878	−	0.999986i	$-0.501664\pi$
$499$	−16.7953	−	7.47776i	−0.751862	−	0.334751i	−0.746633	+	0.665236i	$0.768331\pi$
$500$	−6.40576	−	19.7149i	−0.286475	−	0.881678i
$501$	8.47214	−	14.6742i	0.378507	−	0.655594i
$502$	−4.53709	−	7.85846i	−0.202500	−	0.350740i
$503$	1.93281	−	2.14661i	0.0861799	−	0.0957124i	−0.698512	−	0.715598i	$-0.746154\pi$
$503$	1.93281	−	2.14661i	0.0861799	−	0.0957124i	0.784692	+	0.619886i	$0.212821\pi$
$504$	1.01722	−	3.13068i	0.0453106	−	0.139452i
$505$	3.34565	+	3.71572i	0.148880	+	0.165348i
$506$	10.1628	−	4.52479i	0.451793	−	0.201151i
$507$	76.3791	+	16.2349i	3.39212	+	0.721017i
$508$	−1.83861	+	17.4932i	−0.0815751	+	0.776135i
$509$	−0.499941	−	4.75662i	−0.0221595	−	0.210834i	−0.999999	−	0.00147718i	$-0.999530\pi$
$509$	−0.499941	−	4.75662i	−0.0221595	−	0.210834i	0.977839	−	0.209356i	$-0.0671369\pi$
$510$	1.03266	−	0.219498i	0.0457269	−	0.00971954i
$511$	−3.43237	+	2.49376i	−0.151839	+	0.110318i
$512$	−18.0451	+	13.1105i	−0.797488	+	0.579409i
$513$	−1.70986	+	0.363443i	−0.0754924	+	0.0160464i
$514$	−0.956007	−	9.09580i	−0.0421676	−	0.401198i
$515$	−0.632996	+	6.02255i	−0.0278931	+	0.265385i
$516$	−0.856259	−	0.182003i	−0.0376947	−	0.00801225i
$517$	−14.3724	+	6.39902i	−0.632098	+	0.281428i
$518$	1.08436	+	1.20430i	0.0476439	+	0.0529139i
$519$	−12.7279	+	39.1725i	−0.558694	+	1.71948i
$520$	−15.1206	+	16.7931i	−0.663080	+	0.736425i
$521$	−6.70820	−	11.6190i	−0.293892	−	0.509035i	0.680835	−	0.732437i	$-0.261617\pi$
$521$	−6.70820	−	11.6190i	−0.293892	−	0.509035i	−0.974726	+	0.223402i	$0.928284\pi$
$522$	−1.58114	+	2.73861i	−0.0692046	+	0.119866i
$523$	−8.98606	−	27.6562i	−0.392933	−	1.20932i	−0.930560	−	0.366140i	$-0.880679\pi$
$523$	−8.98606	−	27.6562i	−0.392933	−	1.20932i	0.537627	−	0.843183i	$-0.319321\pi$
$524$	32.8876	+	14.6425i	1.43670	+	0.639661i
$525$		0			0
$526$	−1.03165			−0.0449823
$527$		0			0
$528$	30.5410			1.32913
$529$	−19.5172	−	14.1801i	−0.848575	−	0.616526i
$530$	4.09184	+	1.82180i	0.177738	+	0.0791341i
$531$	−4.10739	−	12.6412i	−0.178246	−	0.548583i
$532$	−0.927051	+	1.60570i	−0.0401928	+	0.0696159i
$533$	25.6471	+	44.4221i	1.11090	+	1.92414i
$534$	−3.42903	+	3.80833i	−0.148389	+	0.164803i
$535$	5.16312	−	15.8904i	0.223221	−	0.687004i
$536$	−5.91031	−	6.56406i	−0.255286	−	0.283524i
$537$	34.3463	−	15.2920i	1.48215	−	0.659897i
$538$	5.53324	+	1.17613i	0.238555	+	0.0507064i
$539$	−2.66086	+	25.3164i	−0.114611	+	1.09045i
$540$	−0.757549	−	7.20759i	−0.0325997	−	0.310165i
$541$	27.2246	−	5.78677i	1.17048	−	0.248793i	0.418647	−	0.908149i	$-0.362505\pi$
$541$	27.2246	−	5.78677i	1.17048	−	0.248793i	0.751830	+	0.659357i	$0.229171\pi$
$542$	−8.67656	+	6.30389i	−0.372690	+	0.270775i
$543$	−33.6525	+	24.4500i	−1.44417	+	1.04925i
$544$	2.19060	−	0.465626i	0.0939211	−	0.0199636i
$545$	−3.43779	−	32.7084i	−0.147259	−	1.40107i
$546$	0.627171	−	5.96713i	0.0268404	−	0.255370i
$547$	23.8829	+	5.07646i	1.02116	+	0.217054i	0.687918	−	0.725789i	$-0.258525\pi$
$547$	23.8829	+	5.07646i	1.02116	+	0.217054i	0.333239	+	0.942842i	$0.391858\pi$
$548$	11.6275	−	5.17691i	0.496704	−	0.221147i
$549$	−6.65665	−	7.39296i	−0.284099	−	0.315524i
$550$		0			0
$551$	2.47743	−	2.75146i	0.105542	−	0.117216i
$552$	11.5623	+	20.0265i	0.492124	+	0.852384i
$553$	5.55369	−	9.61927i	0.236167	−	0.409053i
$554$	−2.31260	−	7.11745i	−0.0982529	−	0.302391i
$555$	−19.8314	−	8.82952i	−0.841797	−	0.374792i
$556$	−1.50233	−	1.09150i	−0.0637129	−	0.0462901i
$557$	23.2951			0.987046			0.493523	−	0.869733i	$-0.335709\pi$
$557$	23.2951			0.987046			0.493523	+	0.869733i	$0.335709\pi$
$558$		0			0
$559$	−1.41641			−0.0599077
$560$	−5.69098	−	4.13474i	−0.240488	−	0.174725i
$561$	−4.79081	−	2.13301i	−0.202268	−	0.0900555i
$562$	−3.70163	−	11.3924i	−0.156144	−	0.480561i
$563$	−7.11803	+	12.3288i	−0.299989	+	0.519597i	−0.976133	−	0.217173i	$-0.930316\pi$
$563$	−7.11803	+	12.3288i	−0.299989	+	0.519597i	0.676144	+	0.736770i	$0.263650\pi$
$564$	−7.86629	−	13.6248i	−0.331230	−	0.573708i
$565$	21.3003	−	23.6564i	0.896111	−	0.995232i
$566$	2.83282	−	8.71851i	0.119072	−	0.366466i
$567$	7.16519	+	7.95775i	0.300910	+	0.334194i
$568$	−10.0490	+	4.47410i	−0.421647	+	0.187729i
$569$	−30.0292	−	6.38290i	−1.25889	−	0.267585i	−0.470300	−	0.882507i	$-0.655854\pi$
$569$	−30.0292	−	6.38290i	−1.25889	−	0.267585i	−0.788588	+	0.614922i	$0.789188\pi$
$570$	−0.204290	+	1.94369i	−0.00855676	+	0.0814122i
$571$	0.717560	+	6.82713i	0.0300290	+	0.285707i	0.999223	+	0.0394088i	$0.0125475\pi$
$571$	0.717560	+	6.82713i	0.0300290	+	0.285707i	−0.969194	+	0.246298i	$0.920786\pi$
$572$	52.8200	−	11.2272i	2.20851	−	0.469434i
$573$	26.3542	−	19.1475i	1.10096	−	0.799897i
$574$	2.30902	−	1.67760i	0.0963765	−	0.0700216i
$575$		0			0
$576$	1.10046	+	10.4702i	0.0458526	+	0.436258i
$577$	3.13585	−	29.8357i	0.130547	−	1.24207i	−0.711506	−	0.702680i	$-0.751987\pi$
$577$	3.13585	−	29.8357i	0.130547	−	1.24207i	0.842053	−	0.539395i	$-0.181347\pi$
$578$	6.24250	+	1.32689i	0.259654	+	0.0551912i
$579$	15.2429	−	6.78657i	0.633473	−	0.282040i
$580$	10.2712	+	11.4073i	0.426487	+	0.473662i
$581$	0.977198	−	3.00750i	0.0405410	−	0.124772i
$582$	4.09389	−	4.54673i	0.169697	−	0.188468i
$583$	−11.1246	−	19.2684i	−0.460734	−	0.798015i
$584$	−3.12287	+	5.40897i	−0.129225	+	0.223825i
$585$	10.6066	+	32.6438i	0.438529	+	1.34965i
$586$	−5.48127	−	2.44042i	−0.226429	−	0.100813i
$587$	33.3221	+	24.2099i	1.37535	+	0.999251i	0.997298	+	0.0734679i	$0.0234066\pi$
$587$	33.3221	+	24.2099i	1.37535	+	0.999251i	0.378054	+	0.925784i	$0.376593\pi$
$588$	−25.4558			−1.04978
$589$		0			0
$590$	5.07701			0.209017
$591$	13.7082	+	9.95959i	0.563880	+	0.409683i
$592$	−12.1930	−	5.42868i	−0.501130	−	0.223117i
$593$	−5.30902	−	16.3395i	−0.218015	−	0.670982i	−0.998926	−	0.0463389i	$-0.985245\pi$
$593$	−5.30902	−	16.3395i	−0.218015	−	0.670982i	0.780911	−	0.624643i	$-0.214755\pi$
$594$	1.41641	−	2.45329i	0.0581159	−	0.100660i
$595$	0.603941	+	1.04606i	0.0247592	+	0.0428842i
$596$	−16.6449	+	18.4860i	−0.681801	+	0.757217i
$597$	−10.4164	+	32.0584i	−0.426315	+	1.31206i
$598$	12.0444	+	13.3766i	0.492530	+	0.547010i
$599$	21.8742	−	9.73901i	0.893755	−	0.397925i	0.0921260	−	0.995747i	$-0.470634\pi$
$599$	21.8742	−	9.73901i	0.893755	−	0.397925i	0.801629	+	0.597822i	$0.203967\pi$
$600$		0			0
$601$	0.908521	−	8.64400i	0.0370593	−	0.352596i	−0.960241	−	0.279171i	$-0.909940\pi$
$601$	0.908521	−	8.64400i	0.0370593	−	0.352596i	0.997301	−	0.0734250i	$-0.0233930\pi$
$602$	0.00823804	+	0.0783797i	0.000335757	+	0.00319452i
$603$	−13.1232	+	2.78943i	−0.534419	+	0.113594i
$604$	−4.55214	+	3.30732i	−0.185224	+	0.134573i
$605$	12.6631	−	9.20029i	0.514829	−	0.374045i
$606$	−1.91169	+	0.406342i	−0.0776570	+	0.0165065i
$607$	2.62624	+	24.9870i	0.106596	+	1.01419i	0.908826	+	0.417175i	$0.136980\pi$
$607$	2.62624	+	24.9870i	0.106596	+	1.01419i	−0.802230	+	0.597015i	$0.796353\pi$
$608$	−0.433364	+	4.12319i	−0.0175752	+	0.167217i
$609$	−8.28700	−	1.76146i	−0.335806	−	0.0713778i
$610$	3.47136	−	1.54555i	0.140551	−	0.0625774i
$611$	−17.0333	−	18.9174i	−0.689093	−	0.765315i
$612$	0.692055	−	2.12993i	0.0279747	−	0.0860972i
$613$	24.9977	−	27.7627i	1.00965	−	1.12133i	0.0170518	−	0.999855i	$-0.494572\pi$
$613$	24.9977	−	27.7627i	1.00965	−	1.12133i	0.992595	−	0.121472i	$-0.0387613\pi$
$614$	3.07953	+	5.33390i	0.124280	+	0.215259i
$615$	−19.1162	+	33.1103i	−0.770841	+	1.33514i
$616$	−1.93004	−	5.94006i	−0.0777636	−	0.239332i
$617$	−43.0505	−	19.1673i	−1.73315	−	0.771647i	−0.995318	−	0.0966594i	$-0.969184\pi$
$617$	−43.0505	−	19.1673i	−1.73315	−	0.771647i	−0.737829	−	0.674987i	$-0.764149\pi$
$618$	−1.91499	−	1.39132i	−0.0770322	−	0.0559671i
$619$	21.5958			0.868007			0.434003	−	0.900911i	$-0.357101\pi$
$619$	21.5958			0.868007			0.434003	+	0.900911i	$0.357101\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	−5.10739	−	3.71074i	−0.204788	−	0.148787i
$623$	−5.35629	−	2.38477i	−0.214595	−	0.0955439i
$624$	15.2705	+	46.9978i	0.611310	+	1.88142i
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	−4.01196	−	6.94891i	−0.160350	−	0.277734i
$627$	6.49606	−	7.21460i	0.259428	−	0.288123i
$628$	2.69756	−	8.30224i	0.107644	−	0.331295i
$629$	1.53351	+	1.70314i	0.0611451	+	0.0679085i
$630$	1.74472	−	0.776798i	0.0695112	−	0.0309484i
$631$	−4.55357	−	0.967892i	−0.181275	−	0.0385312i	0.116380	−	0.993205i	$-0.462871\pi$
$631$	−4.55357	−	0.967892i	−0.181275	−	0.0385312i	−0.297655	+	0.954674i	$0.596204\pi$
$632$	1.70920	−	16.2620i	0.0679885	−	0.646867i
$633$	−1.19593	−	11.3786i	−0.0475341	−	0.452257i
$634$	−8.13142	+	1.72839i	−0.322940	+	0.0686430i
$635$	−17.1618	+	12.4688i	−0.681047	+	0.494810i
$636$	18.0000	−	13.0778i	0.713746	−	0.518567i
$637$	−40.2884	+	8.56355i	−1.59628	+	0.339300i
$638$	0.627171	+	5.96713i	0.0248299	+	0.236241i
$639$	−1.74648	+	16.6167i	−0.0690898	+	0.657345i
$640$	−22.0693	−	4.69097i	−0.872364	−	0.185427i
$641$	7.75169	−	3.45127i	0.306173	−	0.136317i	−0.247898	−	0.968786i	$-0.579740\pi$
$641$	7.75169	−	3.45127i	0.306173	−	0.136317i	0.554072	+	0.832469i	$0.313073\pi$
$642$	4.37002	+	4.85339i	0.172471	+	0.191548i
$643$	7.30175	−	22.4725i	0.287953	−	0.886228i	−0.697545	−	0.716541i	$-0.745724\pi$
$643$	7.30175	−	22.4725i	0.287953	−	0.886228i	0.985498	−	0.169687i	$-0.0542758\pi$
$644$	−8.51664	+	9.45869i	−0.335603	+	0.372725i
$645$	−0.527864	−	0.914287i	−0.0207846	−	0.0360000i
$646$	0.103165	−	0.178688i	0.00405899	−	0.00703038i
$647$	−5.91189	−	18.1949i	−0.232421	−	0.715317i	−0.997453	−	0.0713252i	$-0.977277\pi$
$647$	−5.91189	−	18.1949i	−0.232421	−	0.715317i	0.765033	−	0.643992i	$-0.222723\pi$
$648$	14.4011	+	6.41177i	0.565727	+	0.251878i
$649$	−20.4029	−	14.8236i	−0.800885	−	0.581877i
$650$		0			0
$651$		0			0
$652$	23.0213			0.901583
$653$	5.38197	+	3.91023i	0.210613	+	0.153019i	0.688091	−	0.725625i	$-0.258449\pi$
$653$	5.38197	+	3.91023i	0.210613	+	0.153019i	−0.477478	+	0.878644i	$0.658449\pi$
$654$	11.7440	+	5.22878i	0.459228	+	0.204461i
$655$	13.4164	+	41.2915i	0.524222	+	1.61339i
$656$	−11.7533	+	20.3573i	−0.458889	+	0.794819i
$657$	4.74342	+	8.21584i	0.185058	+	0.320530i
$658$	−0.947762	+	1.05260i	−0.0369476	+	0.0410345i
$659$	14.5795	−	44.8712i	0.567938	−	1.74793i	−0.0911197	−	0.995840i	$-0.529045\pi$
$659$	14.5795	−	44.8712i	0.567938	−	1.74793i	0.659057	−	0.752093i	$-0.270955\pi$
$660$	26.9320	+	29.9110i	1.04833	+	1.16428i
$661$	−41.8704	+	18.6419i	−1.62857	+	0.725085i	−0.998668	−	0.0515909i	$-0.983571\pi$
$661$	−41.8704	+	18.6419i	−1.62857	+	0.725085i	−0.629900	+	0.776676i	$0.716904\pi$
$662$	−9.57663	−	2.03558i	−0.372206	−	0.0791149i
$663$	0.886953	−	8.43880i	0.0344464	−	0.327736i
$664$	−0.486612	−	4.62980i	−0.0188842	−	0.179671i
$665$	−2.18720	+	0.464905i	−0.0848162	+	0.0180282i
$666$	2.93159	−	2.12993i	0.113597	−	0.0825330i
$667$	20.5623	−	14.9394i	0.796176	−	0.578455i
$668$	13.4295	−	2.85452i	0.519601	−	0.110445i
$669$	5.21477	+	49.6152i	0.201615	+	1.91824i
$670$	0.535668	−	5.09654i	0.0206947	−	0.196896i
$671$	−18.4629	−	3.92441i	−0.712753	−	0.151500i
$672$	8.66665	−	3.85864i	0.334323	−	0.148850i
$673$	4.98745	+	5.53912i	0.192252	+	0.213518i	0.831562	−	0.555431i	$-0.187447\pi$
$673$	4.98745	+	5.53912i	0.192252	+	0.213518i	−0.639310	+	0.768949i	$0.720780\pi$
$674$	0.692055	−	2.12993i	0.0266570	−	0.0820417i
$675$		0			0
$676$	31.6353	+	54.7939i	1.21674	+	2.10746i
$677$	−10.6066	+	18.3712i	−0.407645	+	0.706062i	−0.994625	−	0.103540i	$-0.966983\pi$
$677$	−10.6066	+	18.3712i	−0.407645	+	0.706062i	0.586981	+	0.809601i	$0.300317\pi$
$678$	3.84503	+	11.8338i	0.147668	+	0.454474i
$679$	6.39482	+	2.84716i	0.245411	+	0.109264i
$680$	1.43857	+	1.04518i	0.0551666	+	0.0400808i
$681$	−35.9442			−1.37739
$682$		0			0
$683$	−18.8197			−0.720114			−0.360057	−	0.932930i	$-0.617243\pi$
$683$	−18.8197			−0.720114			−0.360057	+	0.932930i	$0.617243\pi$
$684$	3.35410	+	2.43690i	0.128247	+	0.0931771i
$685$	14.0229	+	6.24341i	0.535789	+	0.238549i
$686$	1.53444	+	4.72253i	0.0585853	+	0.180307i
$687$	−4.85410	+	8.40755i	−0.185196	+	0.320768i
$688$	−0.324548	−	0.562134i	−0.0123733	−	0.0214312i
$689$	24.0887	−	26.7532i	0.917706	−	1.01922i
$690$	−4.14590	+	12.7598i	−0.157832	+	0.485756i
$691$	−14.4422	−	16.0397i	−0.549409	−	0.610180i	0.402927	−	0.915232i	$-0.367993\pi$
$691$	−14.4422	−	16.0397i	−0.549409	−	0.610180i	−0.952336	+	0.305052i	$0.901326\pi$
$692$	−30.4885	+	13.5744i	−1.15900	+	0.516020i
$693$	−9.27952	−	1.97242i	−0.352500	−	0.0749262i
$694$	1.03163	−	9.81533i	0.0391602	−	0.372585i
$695$	−0.234095	−	2.22727i	−0.00887975	−	0.0844851i
$696$	−12.1996	+	2.59310i	−0.462424	+	0.0982913i
$697$	3.26544	−	2.37248i	0.123687	−	0.0898642i
$698$	−1.85410	+	1.34708i	−0.0701788	+	0.0509879i
$699$	−10.1345	+	2.15414i	−0.383320	+	0.0814772i
$700$		0			0
$701$	−2.89047	+	27.5010i	−0.109172	+	1.03870i	0.793559	+	0.608493i	$0.208226\pi$
$701$	−2.89047	+	27.5010i	−0.109172	+	1.03870i	−0.902731	+	0.430205i	$0.858441\pi$
$702$	4.48343	+	0.952982i	0.169216	+	0.0359680i
$703$	−3.87585	+	1.72564i	−0.146180	+	0.0650836i
$704$	13.3660	+	14.8445i	0.503751	+	0.559472i
$705$	5.86319	−	18.0450i	0.220820	−	0.679615i
$706$	−4.06130	+	4.51053i	−0.152849	+	0.169756i
$707$	−1.11803	−	1.93649i	−0.0420480	−	0.0728293i
$708$	12.6097	−	21.8406i	0.473902	−	0.820822i
$709$	−4.86163	−	14.9626i	−0.182582	−	0.561931i	0.817316	−	0.576190i	$-0.195461\pi$
$709$	−4.86163	−	14.9626i	−0.182582	−	0.561931i	−0.999898	+	0.0142588i	$0.995461\pi$
$710$	−5.83022	−	2.59578i	−0.218804	−	0.0974179i
$711$	−20.0934	−	14.5987i	−0.753563	−	0.547495i
$712$	−8.63141			−0.323476
$713$		0			0
$714$	−0.472136			−0.0176692
$715$	52.6869	+	38.2793i	1.97038	+	1.43156i
$716$	27.8299	+	12.3907i	1.04005	+	0.463061i
$717$	−11.5623	−	35.5851i	−0.431802	−	1.32895i
$718$	−1.86475	+	3.22983i	−0.0695917	+	0.120536i
$719$	−4.55214	−	7.88453i	−0.169766	−	0.294043i	0.768571	−	0.639764i	$-0.220968\pi$
$719$	−4.55214	−	7.88453i	−0.169766	−	0.294043i	−0.938338	+	0.345720i	$0.887635\pi$
$720$	−10.5251	+	11.6893i	−0.392247	+	0.435634i
$721$	0.836881	−	2.57565i	0.0311671	−	0.0959224i
$722$	−4.60053	−	5.10941i	−0.171214	−	0.190153i
$723$	30.7940	−	13.7104i	1.14524	−	0.509894i
$724$	−32.9682	−	7.00760i	−1.22525	−	0.260435i
$725$		0			0
$726$	0.639529	+	6.08471i	0.0237351	+	0.225825i
$727$	3.50528	−	0.745071i	0.130004	−	0.0276331i	−0.142450	−	0.989802i	$-0.545498\pi$
$727$	3.50528	−	0.745071i	0.130004	−	0.0276331i	0.272454	+	0.962169i	$0.412165\pi$
$728$	8.17578	−	5.94006i	0.303015	−	0.220153i
$729$	9.66312	−	7.02067i	0.357893	−	0.260025i
$730$	−3.54446	+	0.753399i	−0.131186	+	0.0278845i
$731$	0.0116503	+	0.110846i	0.000430904	+	0.00409977i
$732$	1.97302	−	18.7720i	0.0729247	−	0.693833i
$733$	−12.1451	−	2.58152i	−0.448589	−	0.0953505i	−0.0219226	−	0.999760i	$-0.506979\pi$
$733$	−12.1451	−	2.58152i	−0.448589	−	0.0953505i	−0.426666	+	0.904409i	$0.640312\pi$
$734$	4.29733	−	1.91329i	0.158617	−	0.0706210i
$735$	−20.5423	−	22.8146i	−0.757715	−	0.841528i
$736$	−8.79478	+	27.0675i	−0.324180	+	0.997723i
$737$	−17.0333	+	18.9174i	−0.627429	+	0.696831i
$738$	−3.19098	−	5.52694i	−0.117462	−	0.203450i
$739$	−12.8311	+	22.2241i	−0.471999	+	0.817527i	−0.999487	−	0.0320362i	$-0.989801\pi$
$739$	−12.8311	+	22.2241i	−0.471999	+	0.817527i	0.527488	+	0.849563i	$0.323134\pi$
$740$	−5.43547	−	16.7287i	−0.199812	−	0.614958i
$741$	14.3502	+	6.38910i	0.527166	+	0.234710i
$742$	−1.62054	−	1.17739i	−0.0594921	−	0.0432235i
$743$	1.69936			0.0623433			0.0311717	−	0.999514i	$-0.490076\pi$
$743$	1.69936			0.0623433			0.0311717	+	0.999514i	$0.490076\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	7.01722	+	5.09831i	0.256919	+	0.186662i
$747$	−6.45974	−	2.87606i	−0.236350	−	0.105230i
$748$	−1.31308	−	4.04125i	−0.0480110	−	0.147763i
$749$	−3.73607	+	6.47106i	−0.136513	+	0.236447i
$750$	4.88599	+	8.46278i	0.178411	+	0.309017i
$751$	19.7668	−	21.9533i	0.721301	−	0.801086i	−0.265313	−	0.964162i	$-0.585475\pi$
$751$	19.7668	−	21.9533i	0.721301	−	0.801086i	0.986613	+	0.163077i	$0.0521418\pi$
$752$	3.60488	−	11.0947i	0.131456	−	0.404581i
$753$	−36.3744	−	40.3979i	−1.32556	−	1.47218i
$754$	−8.86889	+	3.94868i	−0.322986	+	0.143803i
$755$	−6.63764	−	1.41087i	−0.241568	−	0.0513469i
$756$	−0.338786	+	3.22333i	−0.0123215	+	0.117232i
$757$	−2.00486	−	19.0749i	−0.0728677	−	0.693290i	−0.968588	−	0.248672i	$-0.920006\pi$
$757$	−2.00486	−	19.0749i	−0.0728677	−	0.693290i	0.895720	−	0.444618i	$-0.146661\pi$
$758$	7.25434	−	1.54196i	0.263490	−	0.0560064i
$759$	53.9163	−	39.1725i	1.95704	−	1.42187i
$760$	−2.66312	+	1.93487i	−0.0966015	+	0.0701851i
$761$	2.19060	−	0.465626i	0.0794091	−	0.0168789i	−0.168036	−	0.985781i	$-0.553742\pi$
$761$	2.19060	−	0.465626i	0.0794091	−	0.0168789i	0.247445	+	0.968902i	$0.420409\pi$
$762$	−0.866729	−	8.24637i	−0.0313983	−	0.298735i
$763$	−1.53743	+	14.6276i	−0.0556586	+	0.529556i
$764$	25.8183	+	5.48785i	0.934074	+	0.198544i
$765$	2.46740	−	1.09856i	0.0892091	−	0.0397185i
$766$	4.86953	+	5.40816i	0.175943	+	0.195405i
$767$	12.6097	−	38.8087i	0.455310	−	1.40130i
$768$	−8.51664	+	9.45869i	−0.307318	+	0.341311i
$769$	−6.93769	−	12.0164i	−0.250180	−	0.433324i	0.713395	−	0.700762i	$-0.247156\pi$
$769$	−6.93769	−	12.0164i	−0.250180	−	0.433324i	−0.963575	+	0.267438i	$0.913823\pi$
$770$	1.81182	−	3.13817i	0.0652936	−	0.113092i
$771$	−16.9312	−	52.1087i	−0.609761	−	1.87665i
$772$	12.3509	+	5.49897i	0.444518	+	0.197912i
$773$	−21.8415	−	15.8688i	−0.785584	−	0.570760i	0.121066	−	0.992645i	$-0.461369\pi$
$773$	−21.8415	−	15.8688i	−0.785584	−	0.570760i	−0.906650	+	0.421884i	$0.861369\pi$
$774$	0.176228			0.00633437
$775$		0			0
$776$	10.3050			0.369926
$777$	7.85410	+	5.70634i	0.281764	+	0.204714i
$778$	−11.7885	−	5.24859i	−0.422639	−	0.188171i
$779$	2.30902	+	7.10642i	0.0827291	+	0.254614i
$780$	−32.5623	+	56.3996i	−1.16592	+	2.01943i
$781$	15.8508	+	27.4544i	0.567186	+	0.982395i
$782$	0.947762	−	1.05260i	0.0338919	−	0.0376408i
$783$	2.00000	−	6.15537i	0.0714742	−	0.219975i
$784$	−12.6301	−	14.0271i	−0.451075	−	0.500970i
$785$	9.61768	−	4.28207i	0.343270	−	0.152834i
$786$	−16.5997	−	3.52838i	−0.592092	−	0.125853i
$787$	−0.951656	+	9.05440i	−0.0339229	+	0.322755i	0.964380	+	0.264520i	$0.0852137\pi$
$787$	−0.951656	+	9.05440i	−0.0339229	+	0.322755i	−0.998303	+	0.0582341i	$0.981453\pi$
$788$	1.43512	+	13.6543i	0.0511241	+	0.486413i
$789$	−6.04528	+	1.28496i	−0.215218	+	0.0457460i
$790$	7.67501	−	5.57622i	0.273065	−	0.198393i
$791$	−11.5172	+	8.36775i	−0.409505	+	0.297523i
$792$	−13.6607	+	2.90368i	−0.485413	+	0.103178i
$793$	−3.19241	−	30.3737i	−0.113366	−	1.07860i
$794$	−0.0515767	+	0.490719i	−0.00183039	+	0.0174150i
$795$	26.2465	+	5.57886i	0.930866	+	0.197862i
$796$	−24.9515	+	11.1091i	−0.884383	+	0.393753i
$797$	−3.50905	−	3.89719i	−0.124297	−	0.138046i	0.677784	−	0.735261i	$-0.262940\pi$
$797$	−3.50905	−	3.89719i	−0.124297	−	0.138046i	−0.802081	+	0.597215i	$0.796274\pi$
$798$	0.270091	−	0.831254i	0.00956111	−	0.0294261i
$799$	−1.34034	+	1.48860i	−0.0474177	+	0.0526627i
$800$		0			0
$801$	−6.55524	+	11.3540i	−0.231618	+	0.401174i
$802$	0.437016	+	1.34500i	0.0154316	+	0.0474935i
$803$	16.4438	+	7.32126i	0.580290	+	0.258362i
$804$	−20.5942	−	14.9626i	−0.726302	−	0.527689i
$805$	−15.3500			−0.541017
$806$		0			0
$807$	33.8885			1.19293
$808$	−2.66312	−	1.93487i	−0.0936882	−	0.0680685i
$809$	20.1502	+	8.97144i	0.708443	+	0.315419i	0.729138	−	0.684367i	$-0.239921\pi$
$809$	20.1502	+	8.97144i	0.708443	+	0.315419i	−0.0206950	+	0.999786i	$0.506588\pi$
$810$	2.82624	+	8.69827i	0.0993039	+	0.305626i
$811$	21.7082	−	37.5997i	0.762278	−	1.32030i	−0.179396	−	0.983777i	$-0.557414\pi$
$811$	21.7082	−	37.5997i	0.762278	−	1.32030i	0.941674	−	0.336527i	$-0.109252\pi$
$812$	−3.43237	−	5.94504i	−0.120453	−	0.208630i
$813$	−42.9911	+	47.7465i	−1.50776	+	1.67454i
$814$	2.12461	−	6.53888i	0.0744676	−	0.229188i
$815$	18.5777	+	20.6326i	0.650748	+	0.722729i
$816$	3.55236	−	1.58161i	0.124358	−	0.0553675i
$817$	−0.201822	−	0.0428986i	−0.00706086	−	0.00150083i
$818$	−0.692846	+	6.59199i	−0.0242248	+	0.230484i
$819$	−1.60451	−	15.2659i	−0.0560663	−	0.533435i
$820$	−30.3018	+	6.44084i	−1.05818	+	0.224924i
$821$	11.6082	−	8.43382i	0.405127	−	0.294342i	−0.366499	−	0.930419i	$-0.619444\pi$
$821$	11.6082	−	8.43382i	0.405127	−	0.294342i	0.771626	+	0.636076i	$0.219444\pi$
$822$	−4.85410	+	3.52671i	−0.169306	+	0.123008i
$823$	14.6109	−	3.10565i	0.509305	−	0.108256i	0.0539105	−	0.998546i	$-0.482831\pi$
$823$	14.6109	−	3.10565i	0.509305	−	0.108256i	0.455395	+	0.890290i	$0.349498\pi$
$824$	−0.416739	−	3.96500i	−0.0145178	−	0.138127i
$825$		0			0
$826$	−2.22089	−	0.472066i	−0.0772748	−	0.0164253i
$827$	−43.8987	+	19.5450i	−1.52651	+	0.679646i	−0.986761	−	0.162181i	$-0.948147\pi$
$827$	−43.8987	+	19.5450i	−1.52651	+	0.679646i	−0.539748	+	0.841827i	$0.681480\pi$
$828$	19.0438	+	21.1503i	0.661817	+	0.735023i
$829$	1.80252	−	5.54759i	0.0626042	−	0.192676i	−0.914863	−	0.403765i	$-0.867701\pi$
$829$	1.80252	−	5.54759i	0.0626042	−	0.192676i	0.977467	+	0.211090i	$0.0677012\pi$
$830$	1.80726	−	2.00717i	0.0627309	−	0.0696697i
$831$	−22.4164	−	38.8264i	−0.777617	−	1.34687i
$832$	−16.1603	+	27.9904i	−0.560257	+	0.970394i
$833$	1.00155	+	3.08246i	0.0347017	+	0.106801i
$834$	0.799707	+	0.356052i	0.0276916	+	0.0123291i
$835$	13.3956	+	9.73249i	0.463575	+	0.336807i
$836$	7.86629			0.272061
$837$		0			0
$838$	−7.10333			−0.245380
$839$	−6.00000	−	4.35926i	−0.207143	−	0.150498i	0.479377	−	0.877609i	$-0.340863\pi$
$839$	−6.00000	−	4.35926i	−0.207143	−	0.150498i	−0.686520	+	0.727111i	$0.740863\pi$
$840$	6.88122	+	3.06372i	0.237425	+	0.105708i
$841$	−4.72542	−	14.5434i	−0.162946	−	0.501495i
$842$	0.0795268	−	0.137745i	0.00274068	−	0.00474699i
$843$	−35.8805	−	62.1468i	−1.23579	−	2.14045i
$844$	6.20318	−	6.88933i	0.213522	−	0.237141i
$845$	−23.5795	+	72.5703i	−0.811160	+	2.49649i
$846$	2.11926	+	2.35368i	0.0728617	+	0.0809211i
$847$	−6.39482	+	2.84716i	−0.219729	+	0.0978295i
$848$	16.1372	+	3.43006i	0.554153	+	0.117789i
$849$	5.74048	−	54.6170i	0.197013	−	1.87445i
$850$		0			0
$851$	−28.4882	+	6.05535i	−0.976562	+	0.207575i
$852$	−25.6471	+	18.6337i	−0.878656	+	0.638381i
$853$	36.9787	−	26.8666i	1.26613	−	0.919895i	0.267086	−	0.963673i	$-0.413939\pi$
$853$	36.9787	−	26.8666i	1.26613	−	0.919895i	0.999041	+	0.0437776i	$0.0139393\pi$
$854$	−1.66222	+	0.353316i	−0.0568800	+	0.0120902i
$855$	0.522642	+	4.97261i	0.0178740	+	0.170060i
$856$	−1.14981	+	10.9397i	−0.0392998	+	0.373913i
$857$	5.86889	+	1.24747i	0.200477	+	0.0426128i	0.307056	−	0.951692i	$-0.400656\pi$
$857$	5.86889	+	1.24747i	0.200477	+	0.0426128i	−0.106578	+	0.994304i	$0.533990\pi$
$858$	−23.2551	+	10.3538i	−0.793915	+	0.353474i
$859$	2.44484	+	2.71527i	0.0834167	+	0.0926437i	0.783408	−	0.621508i	$-0.213480\pi$
$859$	2.44484	+	2.71527i	0.0834167	+	0.0926437i	−0.699991	+	0.714151i	$0.746813\pi$
$860$	0.264342	−	0.813560i	0.00901397	−	0.0277422i
$861$	11.4409	−	12.7064i	0.389903	−	0.433031i
$862$	0.0212862	+	0.0368688i	0.000725012	+	0.00125576i
$863$	17.6626	−	30.5926i	0.601243	−	1.04138i	−0.391391	−	0.920225i	$-0.628006\pi$
$863$	17.6626	−	30.5926i	0.601243	−	1.04138i	0.992633	−	0.121158i	$-0.0386608\pi$
$864$	2.23954	+	6.89259i	0.0761906	+	0.234491i
$865$	−36.7695	−	16.3708i	−1.25020	−	0.556625i
$866$	6.67346	+	4.84855i	0.226773	+	0.164760i
$867$	38.2325			1.29844
$868$		0			0
$869$	−47.1246			−1.59859
$870$	−5.85410	−	4.25325i	−0.198473	−	0.144199i
$871$	−37.6275	−	16.7528i	−1.27496	−	0.567648i
$872$	6.69098	+	20.5927i	0.226585	+	0.697358i
$873$	7.82624	−	13.5554i	0.264878	−	0.458782i
$874$	1.31105	+	2.27080i	0.0443469	+	0.0768110i
$875$	−7.48111	+	8.30861i	−0.252908	+	0.280882i
$876$	−5.56231	+	17.1190i	−0.187933	+	0.578398i
$877$	−10.2322	−	11.3640i	−0.345517	−	0.383736i	0.545191	−	0.838312i	$-0.316457\pi$
$877$	−10.2322	−	11.3640i	−0.345517	−	0.383736i	−0.890708	+	0.454576i	$0.849791\pi$
$878$	−8.72358	+	3.88399i	−0.294407	+	0.131078i
$879$	−35.1588	−	7.47323i	−1.18588	−	0.252066i
$880$	−3.11961	+	29.6811i	−0.105162	+	1.00055i
$881$	−5.19232	−	49.4016i	−0.174934	−	1.66438i	−0.632014	−	0.774957i	$-0.717772\pi$
$881$	−5.19232	−	49.4016i	−0.174934	−	1.66438i	0.457081	−	0.889425i	$-0.348895\pi$
$882$	5.01263	−	1.06547i	0.168784	−	0.0358761i
$883$	−27.4589	+	19.9501i	−0.924067	+	0.671374i	−0.944533	−	0.328416i	$-0.893485\pi$
$883$	−27.4589	+	19.9501i	−0.924067	+	0.671374i	0.0204659	+	0.999791i	$0.493485\pi$
$884$	5.56231	−	4.04125i	0.187081	−	0.135922i
$885$	29.7503	−	6.32361i	1.00004	−	0.212566i
$886$	−0.956007	−	9.09580i	−0.0321177	−	0.305579i
$887$	2.02374	−	19.2546i	0.0679506	−	0.646507i	−0.906546	−	0.422106i	$-0.861291\pi$
$887$	2.02374	−	19.2546i	0.0679506	−	0.646507i	0.974497	−	0.224401i	$-0.0720424\pi$
$888$	13.9795	+	2.97143i	0.469121	+	0.0997147i
$889$	8.66665	−	3.85864i	0.290670	−	0.129415i
$890$	−3.35084	−	3.72149i	−0.112321	−	0.124745i
$891$	14.0390	−	43.2075i	0.470323	−	1.44751i
$892$	−27.0485	+	30.0404i	−0.905650	+	1.00583i
$893$	−1.85410	−	3.21140i	−0.0620452	−	0.107465i
$894$	5.86319	−	10.1553i	0.196094	−	0.339645i
$895$	11.3531	+	34.9413i	0.379493	+	1.16796i
$896$	9.21783	+	4.10404i	0.307946	+	0.137106i
$897$	87.2385	+	63.3825i	2.91281	+	2.11628i
$898$	16.1151			0.537769
$899$		0			0
$900$		0			0
$901$	−2.29180	−	1.66509i	−0.0763508	−	0.0554721i
$902$	−11.0621	−	4.92515i	−0.368326	−	0.163989i
$903$	0.145898	+	0.449028i	0.00485518	+	0.0149427i
$904$	−10.4787	+	18.1497i	−0.348517	+	0.603649i
$905$	−20.3241	−	35.2024i	−0.675597	−	1.17017i
$906$	1.77485	−	1.97117i	0.0589655	−	0.0654879i
$907$	−17.1631	+	52.8226i	−0.569892	+	1.75395i	0.0830564	+	0.996545i	$0.473532\pi$
$907$	−17.1631	+	52.8226i	−0.569892	+	1.75395i	−0.652948	+	0.757402i	$0.726468\pi$
$908$	−19.4882	−	21.6438i	−0.646738	−	0.718275i
$909$	−4.56773	+	2.03368i	−0.151502	+	0.0674530i
$910$	5.73506	+	1.21902i	0.190115	+	0.0404103i
$911$	1.48335	−	14.1131i	0.0491455	−	0.467588i	−0.942078	−	0.335393i	$-0.891131\pi$
$911$	1.48335	−	14.1131i	0.0491455	−	0.467588i	0.991224	−	0.132195i	$-0.0422025\pi$
$912$	0.752457	+	7.15915i	0.0249164	+	0.237063i
$913$	−13.1232	+	2.78943i	−0.434315	+	0.0923166i
$914$	3.49613	−	2.54009i	0.115642	−	0.0840186i
$915$	18.4164	−	13.3803i	0.608828	−	0.442339i
$916$	−7.69439	+	1.63549i	−0.254230	+	0.0540382i
$917$	−2.02957	−	19.3100i	−0.0670222	−	0.637674i
$918$	0.0377013	−	0.358704i	0.00124433	−	0.0118390i
$919$	−24.0047	−	5.10236i	−0.791843	−	0.168311i	−0.205803	−	0.978593i	$-0.565981\pi$
$919$	−24.0047	−	5.10236i	−0.791843	−	0.168311i	−0.586040	+	0.810282i	$0.699314\pi$
$920$	−20.6437	+	9.19116i	−0.680602	+	0.303023i
$921$	24.6890	+	27.4199i	0.813529	+	0.903515i
$922$	4.61590	−	14.2063i	0.152016	−	0.467859i
$923$	−34.3226	+	38.1191i	−1.12974	+	1.25470i
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$		0			0
$926$	−1.78747	−	5.50127i	−0.0587399	−	0.180783i
$927$	−5.53218	−	2.46309i	−0.181701	−	0.0808984i
$928$	−12.4184	−	9.02251i	−0.407655	−	0.296179i
$929$	−23.2951			−0.764288			−0.382144	−	0.924103i	$-0.624814\pi$
$929$	−23.2951			−0.764288			−0.382144	+	0.924103i	$0.624814\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	−6.79180	−	4.93453i	−0.222473	−	0.161636i
$933$	−34.5501	−	15.3827i	−1.13112	−	0.503607i
$934$	1.84752	+	5.68609i	0.0604528	+	0.186055i
$935$	2.56231	−	4.43804i	0.0837964	−	0.145140i
$936$	−11.2987	−	19.5698i	−0.369308	−	0.639660i
$937$	−37.6381	+	41.8013i	−1.22958	+	1.36559i	−0.321439	+	0.946930i	$0.604167\pi$
$937$	−37.6381	+	41.8013i	−1.22958	+	1.36559i	−0.908143	+	0.418659i	$0.862500\pi$
$938$	−0.708204	+	2.17963i	−0.0231237	+	0.0711674i
$939$	−32.1644	−	35.7221i	−1.04964	−	1.16575i
$940$	14.0447	−	6.25310i	0.458088	−	0.203954i
$941$	49.7221	+	10.5687i	1.62089	+	0.344531i	0.926859	−	0.375411i	$-0.122498\pi$
$941$	49.7221	+	10.5687i	1.62089	+	0.344531i	0.694034	+	0.719942i	$0.255832\pi$
$942$	−0.430147	+	4.09258i	−0.0140150	+	0.133343i
$943$	5.36171	+	51.0133i	0.174601	+	1.66122i
$944$	18.2914	−	3.88796i	0.595335	−	0.126542i
$945$	−3.16228	+	2.29753i	−0.102869	+	0.0747386i
$946$	0.270510	−	0.196537i	0.00879503	−	0.00638997i
$947$	2.19060	−	0.465626i	0.0711849	−	0.0151308i	−0.172182	−	0.985065i	$-0.555082\pi$
$947$	2.19060	−	0.465626i	0.0711849	−	0.0151308i	0.243366	+	0.969934i	$0.421748\pi$
$948$	−4.92586	−	46.8665i	−0.159985	−	1.52215i
$949$	−3.04435	+	28.9651i	−0.0988238	+	0.940246i
$950$		0			0
$951$	−45.4957	+	20.2560i	−1.47530	+	0.656845i
$952$	−0.532106	−	0.590964i	−0.0172457	−	0.0191533i
$953$	−16.5185	+	50.8387i	−0.535087	+	1.64683i	0.208375	+	0.978049i	$0.433182\pi$
$953$	−16.5185	+	50.8387i	−0.535087	+	1.64683i	−0.743462	+	0.668778i	$0.766818\pi$
$954$	−2.99709	+	3.32860i	−0.0970342	+	0.107767i
$955$	15.9164	+	27.5680i	0.515043	+	0.892080i
$956$	15.1587	−	26.2557i	0.490269	−	0.849170i
$957$	11.1074	+	34.1850i	0.359051	+	1.10504i
$958$	8.88833	+	3.95734i	0.287169	+	0.127856i
$959$	−5.55369	−	4.03499i	−0.179338	−	0.130297i
$960$	−24.0903			−0.777512
$961$		0			0
$962$	11.1246			0.358672
$963$	13.5172	+	9.82084i	0.435586	+	0.316472i
$964$	24.9515	+	11.1091i	0.803634	+	0.357801i
$965$	5.03851	+	15.5069i	0.162195	+	0.499186i
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	−6.45207	−	11.1753i	−0.207485	−	0.359374i	0.743437	−	0.668806i	$-0.233194\pi$
$967$	−6.45207	−	11.1753i	−0.207485	−	0.359374i	−0.950922	+	0.309432i	$0.899861\pi$
$968$	−6.89536	+	7.65807i	−0.221625	+	0.246140i
$969$	0.381966	−	1.17557i	0.0122705	−	0.0377648i
$970$	4.00054	+	4.44305i	0.128450	+	0.142658i
$971$	16.5456	−	7.36659i	0.530975	−	0.236405i	−0.123695	−	0.992320i	$-0.539474\pi$
$971$	16.5456	−	7.36659i	0.530975	−	0.236405i	0.654670	+	0.755915i	$0.272808\pi$
$972$	34.9275	+	7.42407i	1.12030	+	0.238127i
$973$	−0.104691	+	0.996065i	−0.00335623	+	0.0319324i
$974$	0.742275	+	7.06227i	0.0237840	+	0.226290i
$975$		0			0
$976$	11.3230	−	8.22665i	0.362441	−	0.263329i
$977$	−34.3713	+	24.9722i	−1.09964	+	0.798932i	−0.981000	−	0.194006i	$-0.937852\pi$
$977$	−34.3713	+	24.9722i	−1.09964	+	0.798932i	−0.118636	+	0.992938i	$0.537852\pi$
$978$	−10.6152	+	2.25633i	−0.339436	+	0.0721494i
$979$	2.60019	+	24.7391i	0.0831023	+	0.790666i
$980$	2.60019	−	24.7391i	0.0830599	−	0.790262i
$981$	32.1699	+	6.83791i	1.02710	+	0.218318i
$982$	3.33787	−	1.48611i	0.106516	−	0.0474238i
$983$	2.01051	+	2.23289i	0.0641252	+	0.0712182i	0.774354	−	0.632753i	$-0.218075\pi$
$983$	2.01051	+	2.23289i	0.0641252	+	0.0712182i	−0.710229	+	0.703971i	$0.751408\pi$
$984$	7.77817	−	23.9388i	0.247959	−	0.763140i
$985$	−11.0794	+	12.3049i	−0.353019	+	0.392067i
$986$	0.381966	+	0.661585i	0.0121643	+	0.0210691i
$987$	−4.24264	+	7.34847i	−0.135045	+	0.233904i
$988$	3.93314	+	12.1050i	0.125130	+	0.385111i
$989$	−1.29395	−	0.576105i	−0.0411453	−	0.0183191i
$990$	−6.55524	−	4.76266i	−0.208339	−	0.151367i
$991$	4.44897			0.141326			0.0706631	−	0.997500i	$-0.477488\pi$
$991$	4.44897			0.141326			0.0706631	+	0.997500i	$0.477488\pi$
$992$		0			0
$993$	−58.6525			−1.86128
$994$	2.30902	+	1.67760i	0.0732376	+	0.0532102i
$995$	−30.0918	−	13.3977i	−0.953974	−	0.424737i
$996$	−4.14590	−	12.7598i	−0.131368	−	0.404309i
$997$	−24.3328	+	42.1457i	−0.770628	+	1.33477i	0.166591	+	0.986026i	$0.446724\pi$
$997$	−24.3328	+	42.1457i	−0.770628	+	1.33477i	−0.937219	+	0.348741i	$0.886609\pi$
$998$	3.51118	+	6.08154i	0.111144	+	0.192508i
$999$	−4.96255	+	5.51147i	−0.157008	+	0.174375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.p.732.1		16
31.2	even	5		961.2.g.i.448.1		16
31.3	odd	30		961.2.d.j.388.1		8
31.4	even	5		961.2.c.h.521.2		8
31.5	even	3	inner	961.2.g.p.816.2		16
31.6	odd	6		961.2.d.j.374.1		8
31.7	even	15		961.2.a.h.1.1	✓	4
31.8	even	5		961.2.g.i.844.2		16
31.9	even	15		961.2.g.i.547.1		16
31.10	even	15		961.2.g.i.846.2		16
31.11	odd	30		961.2.c.h.439.1		8
31.12	odd	30		961.2.d.h.628.2		8
31.13	odd	30	inner	961.2.g.p.235.2		16
31.14	even	15		961.2.d.h.531.1		8
31.15	odd	10	inner	961.2.g.p.338.1		16
31.16	even	5	inner	961.2.g.p.338.2		16
31.17	odd	30		961.2.d.h.531.2		8
31.18	even	15	inner	961.2.g.p.235.1		16
31.19	even	15		961.2.d.h.628.1		8
31.20	even	15		961.2.c.h.439.2		8
31.21	odd	30		961.2.g.i.846.1		16
31.22	odd	30		961.2.g.i.547.2		16
31.23	odd	10		961.2.g.i.844.1		16
31.24	odd	30		961.2.a.h.1.2	yes	4
31.25	even	3		961.2.d.j.374.2		8
31.26	odd	6	inner	961.2.g.p.816.1		16
31.27	odd	10		961.2.c.h.521.1		8
31.28	even	15		961.2.d.j.388.2		8
31.29	odd	10		961.2.g.i.448.2		16
31.30	odd	2	inner	961.2.g.p.732.2		16
93.38	odd	30		8649.2.a.r.1.4		4
93.86	even	30		8649.2.a.r.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.1	✓	4	31.7	even	15
961.2.a.h.1.2	yes	4	31.24	odd	30
961.2.c.h.439.1		8	31.11	odd	30
961.2.c.h.439.2		8	31.20	even	15
961.2.c.h.521.1		8	31.27	odd	10
961.2.c.h.521.2		8	31.4	even	5
961.2.d.h.531.1		8	31.14	even	15
961.2.d.h.531.2		8	31.17	odd	30
961.2.d.h.628.1		8	31.19	even	15
961.2.d.h.628.2		8	31.12	odd	30
961.2.d.j.374.1		8	31.6	odd	6
961.2.d.j.374.2		8	31.25	even	3
961.2.d.j.388.1		8	31.3	odd	30
961.2.d.j.388.2		8	31.28	even	15
961.2.g.i.448.1		16	31.2	even	5
961.2.g.i.448.2		16	31.29	odd	10
961.2.g.i.547.1		16	31.9	even	15
961.2.g.i.547.2		16	31.22	odd	30
961.2.g.i.844.1		16	31.23	odd	10
961.2.g.i.844.2		16	31.8	even	5
961.2.g.i.846.1		16	31.21	odd	30
961.2.g.i.846.2		16	31.10	even	15
961.2.g.p.235.1		16	31.18	even	15	inner
961.2.g.p.235.2		16	31.13	odd	30	inner
961.2.g.p.338.1		16	31.15	odd	10	inner
961.2.g.p.338.2		16	31.16	even	5	inner
961.2.g.p.732.1		16	1.1	even	1	trivial
961.2.g.p.732.2		16	31.30	odd	2	inner
961.2.g.p.816.1		16	31.26	odd	6	inner
961.2.g.p.816.2		16	31.5	even	3	inner
8649.2.a.r.1.3		4	93.86	even	30
8649.2.a.r.1.4		4	93.38	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.224514i) q^{2} +(-2.09042 - 0.930713i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(1.11803 - 1.93649i) q^{5} +(0.437016 + 0.756934i) q^{6} +(-0.669131 + 0.743145i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(1.49622 + 1.66172i) q^{9} +(-0.780261 + 0.347395i) q^{10} +(4.14993 + 0.882095i) q^{11} +(-0.443477 + 4.21940i) q^{12} +(0.717560 + 6.82713i) q^{13} +(0.373619 - 0.0794152i) q^{14} +(-4.13948 + 3.00750i) q^{15} +(-2.54508 + 1.84911i) q^{16} +(0.528377 - 0.112310i) q^{17} +(-0.0892780 - 0.849423i) q^{18} +(-0.104528 + 0.994522i) q^{19} +(-4.05530 - 0.861981i) q^{20} +(2.09042 - 0.930713i) q^{21} +(-1.08436 - 1.20430i) q^{22} +(-2.12132 + 6.52875i) q^{23} +(2.25404 - 2.50336i) q^{24} +(1.31105 - 2.27080i) q^{26} +(0.540182 + 1.66251i) q^{27} +(1.69381 + 0.754131i) q^{28} +(-2.99535 - 2.17625i) q^{29} +1.95440 q^{30} +4.14590 q^{32} +(-7.85410 - 5.70634i) q^{33} +(-0.188493 - 0.0839224i) q^{34} +(0.690983 + 2.12663i) q^{35} +(2.07295 - 3.59045i) q^{36} +(2.12132 + 3.67423i) q^{37} +(0.255585 - 0.283856i) q^{38} +(4.85410 - 14.9394i) q^{39} +(2.20264 + 2.44628i) q^{40} +(6.82614 - 3.03919i) q^{41} +(-0.854932 - 0.181721i) q^{42} +(-0.0215675 + 0.205201i) q^{43} +(-0.822251 - 7.82320i) q^{44} +(4.89074 - 1.03956i) q^{45} +(2.12132 - 1.54123i) q^{46} +(-3.00000 + 2.17963i) q^{47} +(7.04128 - 1.49667i) q^{48} +(0.627171 + 5.96713i) q^{49} +(-1.20906 - 0.256993i) q^{51} +(11.6275 - 5.17691i) q^{52} +(-3.50905 - 3.89719i) q^{53} +(0.206331 - 0.635021i) q^{54} +(6.34793 - 7.05009i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(1.14412 - 1.98168i) q^{57} +(0.437016 + 1.34500i) q^{58} +(-5.43036 - 2.41775i) q^{59} +(7.67501 + 5.57622i) q^{60} -4.44897 q^{61} -2.23607 q^{63} +(3.80902 + 2.76741i) q^{64} +(14.0229 + 6.24341i) q^{65} +(1.14590 + 3.52671i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(-0.500776 - 0.867369i) q^{68} +(10.5108 - 11.6735i) q^{69} +(0.263932 - 0.812299i) q^{70} +(4.99983 + 5.55288i) q^{71} +(-3.00721 + 1.33889i) q^{72} +(4.14993 + 0.882095i) q^{73} +(0.169393 - 1.61167i) q^{74} +(1.81359 - 0.385489i) q^{76} +(-3.43237 + 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(-10.8647 + 2.30935i) q^{79} +(0.735299 + 6.99591i) q^{80} +(1.11931 - 10.6495i) q^{81} +(-2.79173 - 0.593401i) q^{82} +(-2.88888 + 1.28621i) q^{83} +(-2.83888 - 3.15290i) q^{84} +(0.373256 - 1.14876i) q^{85} +(0.0527351 - 0.0585683i) q^{86} +(4.23607 + 7.33708i) q^{87} +(-3.12287 + 5.40897i) q^{88} +(1.81182 + 5.57622i) q^{89} +(-1.74472 - 0.776798i) q^{90} +(-5.55369 - 4.03499i) q^{91} +12.7279 q^{92} +1.41641 q^{94} +(1.80902 + 1.31433i) q^{95} +(-8.66665 - 3.85864i) q^{96} +(-2.16312 - 6.65740i) q^{97} +(1.14590 - 1.98475i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 36 q^{4} - 2 q^{7} - 52 q^{8} - 10 q^{9} - 10 q^{10} - 8 q^{14} + 4 q^{16} + 10 q^{18} + 2 q^{19} + 30 q^{20} + 12 q^{28} + 120 q^{32} - 72 q^{33} + 20 q^{35} + 60 q^{36} + 8 q^{38} + 24 q^{39}+ \cdots + 72 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 36 * q^4 - 2 * q^7 - 52 * q^8 - 10 * q^9 - 10 * q^10 - 8 * q^14 + 4 * q^16 + 10 * q^18 + 2 * q^19 + 30 * q^20 + 12 * q^28 + 120 * q^32 - 72 * q^33 + 20 * q^35 + 60 * q^36 + 8 * q^38 + 24 * q^39 + 50 * q^40 + 26 * q^41 - 10 * q^45 - 48 * q^47 - 12 * q^49 - 12 * q^51 + 24 * q^56 - 34 * q^59 + 52 * q^64 + 72 * q^66 - 48 * q^67 - 12 * q^69 + 40 * q^70 - 14 * q^71 + 10 * q^72 + 18 * q^76 - 24 * q^78 - 50 * q^80 - 38 * q^81 - 16 * q^82 + 32 * q^87 + 10 * q^90 - 192 * q^94 + 20 * q^95 + 28 * q^97 + 72 * q^98

Introduction

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