LMFDB - Embedded newform 961.2.g.p.816.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

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")

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

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			816.2
Root			$0.147826 + 1.40647i$ of defining polynomial
Character	$\chi$	$=$	961.816
Dual form			961.2.g.p.338.2

$q$-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} +(0.239187 + 2.27571i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(1.11803 + 1.93649i) q^{5} +(0.437016 - 0.756934i) q^{6} +(0.978148 + 0.207912i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-2.18720 + 0.464905i) q^{9} +(0.0892780 - 0.849423i) q^{10} +(-2.83888 + 3.15290i) q^{11} +(3.87585 - 1.72564i) q^{12} +(-6.27125 - 2.79214i) q^{13} +(-0.255585 - 0.283856i) q^{14} +(-4.13948 + 3.00750i) q^{15} +(-2.54508 + 1.84911i) q^{16} +(-0.361452 - 0.401433i) q^{17} +(0.780261 + 0.347395i) q^{18} +(0.913545 - 0.406737i) q^{19} +(2.77415 - 3.08100i) q^{20} +(-0.239187 + 2.27571i) q^{21} +(1.58513 - 0.336930i) q^{22} +(-2.12132 + 6.52875i) q^{23} +(-3.29500 - 0.700373i) q^{24} +(1.31105 + 2.27080i) q^{26} +(0.540182 + 1.66251i) q^{27} +(-0.193806 - 1.84395i) q^{28} +(-2.99535 - 2.17625i) q^{29} +1.95440 q^{30} +4.14590 q^{32} +(-7.85410 - 5.70634i) q^{33} +(0.0215675 + 0.205201i) q^{34} +(0.690983 + 2.12663i) q^{35} +(2.07295 + 3.59045i) q^{36} +(2.12132 - 3.67423i) q^{37} +(-0.373619 - 0.0794152i) q^{38} +(4.85410 - 14.9394i) q^{39} +(-3.21986 + 0.684403i) q^{40} +(-0.781051 + 7.43120i) q^{41} +(0.584842 - 0.649532i) q^{42} +(0.188493 - 0.0839224i) q^{43} +(7.18621 + 3.19951i) q^{44} +(-3.34565 - 3.71572i) q^{45} +(2.12132 - 1.54123i) q^{46} +(-3.00000 + 2.17963i) q^{47} +(-4.81680 - 5.34959i) q^{48} +(-5.48127 - 2.44042i) q^{49} +(0.827091 - 0.918578i) q^{51} +(-1.33043 + 12.6582i) q^{52} +(5.12959 - 1.09033i) q^{53} +(0.206331 - 0.635021i) q^{54} +(-9.27952 - 1.97242i) q^{55} +(-0.736068 + 1.27491i) q^{56} +(1.14412 + 1.98168i) q^{57} +(0.437016 + 1.34500i) q^{58} +(0.621346 + 5.91171i) q^{59} +(7.67501 + 5.57622i) q^{60} -4.44897 q^{61} -2.23607 q^{63} +(3.80902 + 2.76741i) q^{64} +(-1.60451 - 15.2659i) q^{65} +(1.14590 + 3.52671i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(-0.500776 + 0.867369i) q^{68} +(-15.3649 - 3.26592i) q^{69} +(0.263932 - 0.812299i) q^{70} +(-7.30885 + 1.55354i) q^{71} +(0.344086 - 3.27376i) q^{72} +(-2.83888 + 3.15290i) q^{73} +(-1.48044 + 0.659135i) q^{74} +(-1.24064 - 1.37787i) q^{76} +(-3.43237 + 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(7.43229 + 8.25439i) q^{79} +(-6.42628 - 2.86117i) q^{80} +(-9.78243 + 4.35542i) q^{81} +(1.90977 - 2.12101i) q^{82} +(0.330548 - 3.14495i) q^{83} +(4.14993 - 0.882095i) q^{84} +(0.373256 - 1.14876i) q^{85} +(-0.0770892 - 0.0163858i) q^{86} +(4.23607 - 7.33708i) q^{87} +(-3.12287 - 5.40897i) q^{88} +(1.81182 + 5.57622i) q^{89} +(0.199632 + 1.89937i) q^{90} +(-5.55369 - 4.03499i) q^{91} +12.7279 q^{92} +1.41641 q^{94} +(1.80902 + 1.31433i) q^{95} +(0.991644 + 9.43486i) 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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	$0.743118\pi$
$3$	0.239187	+	2.27571i	0.138095	+	1.31388i	0.815708	+	0.578464i	$0.196348\pi$
$3$	0.239187	+	2.27571i	0.138095	+	1.31388i	−0.677614	+	0.735418i	$0.736986\pi$
$4$	−0.572949	−	1.76336i	−0.286475	−	0.881678i
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	1.00000			$0$
$5$	1.11803	+	1.93649i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$6$	0.437016	−	0.756934i	0.178411	−	0.309017i
$7$	0.978148	+	0.207912i	0.369705	+	0.0785832i	0.389018	−	0.921230i	$-0.372814\pi$
$7$	0.978148	+	0.207912i	0.369705	+	0.0785832i	−0.0193127	+	0.999813i	$0.506148\pi$
$8$	−0.454915	+	1.40008i	−0.160837	+	0.495005i
$9$	−2.18720	+	0.464905i	−0.729068	+	0.154968i
$10$	0.0892780	−	0.849423i	0.0282322	−	0.268611i
$11$	−2.83888	+	3.15290i	−0.855955	+	0.950634i	−0.999237	−	0.0390478i	$-0.987568\pi$
$11$	−2.83888	+	3.15290i	−0.855955	+	0.950634i	0.143283	+	0.989682i	$0.454234\pi$
$12$	3.87585	−	1.72564i	1.11886	−	0.498149i
$13$	−6.27125	−	2.79214i	−1.73933	−	0.774400i	−0.994208	−	0.107474i	$-0.965724\pi$
$13$	−6.27125	−	2.79214i	−1.73933	−	0.774400i	−0.745124	−	0.666926i	$-0.767610\pi$
$14$	−0.255585	−	0.283856i	−0.0683080	−	0.0758637i
$15$	−4.13948	+	3.00750i	−1.06881	+	0.776534i
$16$	−2.54508	+	1.84911i	−0.636271	+	0.462278i
$17$	−0.361452	−	0.401433i	−0.0876650	−	0.0973618i	0.697716	−	0.716374i	$-0.254200\pi$
$17$	−0.361452	−	0.401433i	−0.0876650	−	0.0973618i	−0.785381	+	0.619012i	$0.787533\pi$
$18$	0.780261	+	0.347395i	0.183909	+	0.0818817i
$19$	0.913545	−	0.406737i	0.209582	−	0.0933118i	−0.299261	−	0.954171i	$-0.596740\pi$
$19$	0.913545	−	0.406737i	0.209582	−	0.0933118i	0.508843	+	0.860859i	$0.330073\pi$
$20$	2.77415	−	3.08100i	0.620318	−	0.688933i
$21$	−0.239187	+	2.27571i	−0.0521948	+	0.496601i
$22$	1.58513	−	0.336930i	0.337951	−	0.0718338i
$23$	−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	$0.846109\pi$
$24$	−3.29500	−	0.700373i	−0.672588	−	0.142963i
$25$		0			0
$26$	1.31105	+	2.27080i	0.257118	+	0.445341i
$27$	0.540182	+	1.66251i	0.103958	+	0.319950i
$28$	−0.193806	−	1.84395i	−0.0366260	−	0.348473i
$29$	−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
$34$	0.0215675	+	0.205201i	0.00369879	+	0.0351916i
$35$	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	−0.637284	−	0.770629i	$-0.719942\pi$
$37$	2.12132	−	3.67423i	0.348743	−	0.604040i	0.986026	+	0.166589i	$0.0532753\pi$
$38$	−0.373619	−	0.0794152i	−0.0606090	−	0.0128828i
$39$	4.85410	−	14.9394i	0.777278	−	2.39222i
$40$	−3.21986	+	0.684403i	−0.509105	+	0.108214i
$41$	−0.781051	+	7.43120i	−0.121980	+	1.16056i	0.746692	+	0.665170i	$0.231641\pi$
$41$	−0.781051	+	7.43120i	−0.121980	+	1.16056i	−0.868671	+	0.495389i	$0.835026\pi$
$42$	0.584842	−	0.649532i	0.0902430	−	0.100225i
$43$	0.188493	−	0.0839224i	0.0287449	−	0.0127980i	−0.392314	−	0.919831i	$-0.628325\pi$
$43$	0.188493	−	0.0839224i	0.0287449	−	0.0127980i	0.421059	+	0.907033i	$0.361659\pi$
$44$	7.18621	+	3.19951i	1.08336	+	0.482344i
$45$	−3.34565	−	3.71572i	−0.498741	−	0.553907i
$46$	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	$0.387172\pi$
$48$	−4.81680	−	5.34959i	−0.695244	−	0.772147i
$49$	−5.48127	−	2.44042i	−0.783039	−	0.348631i
$50$		0			0
$51$	0.827091	−	0.918578i	0.115816	−	0.128627i
$52$	−1.33043	+	12.6582i	−0.184497	+	1.75538i
$53$	5.12959	−	1.09033i	0.704604	−	0.149768i	0.158344	−	0.987384i	$-0.449384\pi$
$53$	5.12959	−	1.09033i	0.704604	−	0.149768i	0.546260	+	0.837616i	$0.316051\pi$
$54$	0.206331	−	0.635021i	0.0280781	−	0.0864155i
$55$	−9.27952	−	1.97242i	−1.25125	−	0.265962i
$56$	−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
$59$	0.621346	+	5.91171i	0.0808923	+	0.769639i	0.957500	+	0.288433i	$0.0931343\pi$
$59$	0.621346	+	5.91171i	0.0808923	+	0.769639i	−0.876608	+	0.481206i	$0.840199\pi$
$60$	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
$65$	−1.60451	−	15.2659i	−0.199015	−	1.89351i
$66$	1.14590	+	3.52671i	0.141050	+	0.434108i
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	−0.500776	+	0.867369i	−0.0607280	+	0.105184i
$69$	−15.3649	−	3.26592i	−1.84972	−	0.393170i
$70$	0.263932	−	0.812299i	0.0315459	−	0.0970883i
$71$	−7.30885	+	1.55354i	−0.867401	+	0.184372i	−0.620058	−	0.784556i	$-0.712891\pi$
$71$	−7.30885	+	1.55354i	−0.867401	+	0.184372i	−0.247343	+	0.968928i	$0.579558\pi$
$72$	0.344086	−	3.27376i	0.0405510	−	0.385817i
$73$	−2.83888	+	3.15290i	−0.332266	+	0.369019i	−0.886008	−	0.463669i	$-0.846533\pi$
$73$	−2.83888	+	3.15290i	−0.332266	+	0.369019i	0.553742	+	0.832688i	$0.313199\pi$
$74$	−1.48044	+	0.659135i	−0.172098	+	0.0766229i
$75$		0			0
$76$	−1.24064	−	1.37787i	−0.142311	−	0.158052i
$77$	−3.43237	+	2.49376i	−0.391155	+	0.284191i
$78$	−4.85410	+	3.52671i	−0.549619	+	0.399321i
$79$	7.43229	+	8.25439i	0.836198	+	0.928691i	0.998312	−	0.0580805i	$-0.0184980\pi$
$79$	7.43229	+	8.25439i	0.836198	+	0.928691i	−0.162114	+	0.986772i	$0.551831\pi$
$80$	−6.42628	−	2.86117i	−0.718480	−	0.319888i
$81$	−9.78243	+	4.35542i	−1.08694	+	0.483935i
$82$	1.90977	−	2.12101i	0.210898	−	0.234226i
$83$	0.330548	−	3.14495i	0.0362824	−	0.345204i	−0.961288	−	0.275544i	$-0.911142\pi$
$83$	0.330548	−	3.14495i	0.0362824	−	0.345204i	0.997571	−	0.0696596i	$-0.0221913\pi$
$84$	4.14993	−	0.882095i	0.452794	−	0.0962444i
$85$	0.373256	−	1.14876i	0.0404853	−	0.124601i
$86$	−0.0770892	−	0.0163858i	−0.00831274	−	0.00176693i
$87$	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	$0.799420\pi$
$90$	0.199632	+	1.89937i	0.0210430	+	0.200211i
$91$	−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
$96$	0.991644	+	9.43486i	0.101209	+	0.962942i
$97$	−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	$0.135485\pi$
$102$	−0.461819	+	0.0981626i	−0.0457269	+	0.00971954i
$103$	0.283084	−	2.69337i	0.0278931	−	0.265385i	−0.971683	−	0.236287i	$-0.924070\pi$
$103$	0.283084	−	2.69337i	0.0278931	−	0.265385i	0.999577	−	0.0290988i	$-0.00926376\pi$
$104$	6.76212	−	7.51009i	0.663080	−	0.736425i
$105$	−4.67431	+	2.08114i	−0.456166	+	0.203098i
$106$	−1.82993	−	0.814735i	−0.177738	−	0.0791341i
$107$	−4.99983	−	5.55288i	−0.483352	−	0.536817i	0.451304	−	0.892370i	$-0.350959\pi$
$107$	−4.99983	−	5.55288i	−0.483352	−	0.536817i	−0.934656	+	0.355553i	$0.884292\pi$
$108$	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	$0.0512183\pi$
$110$	2.42469	+	2.69290i	0.231185	+	0.256757i
$111$	8.86889	+	3.94868i	0.841797	+	0.374792i
$112$	−2.87392	+	1.27955i	−0.271560	+	0.120906i
$113$	−9.52579	+	10.5795i	−0.896111	+	0.995232i	0.103889	+	0.994589i	$0.466871\pi$
$113$	−9.52579	+	10.5795i	−0.896111	+	0.995232i	−1.00000		0.000643002i	$0.999795\pi$
$114$	0.0913612	−	0.869244i	0.00855676	−	0.0814122i
$115$	−15.0146	+	3.19145i	−1.40012	+	0.297604i
$116$	−2.12132	+	6.52875i	−0.196960	+	0.606179i
$117$	15.0146	+	3.19145i	1.38810	+	0.295049i
$118$	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
$121$	−0.731699	−	6.96165i	−0.0665181	−	0.632878i
$122$	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
$127$	0.991644	+	9.43486i	0.0879942	+	0.837209i	0.946130	+	0.323786i	$0.104956\pi$
$127$	0.991644	+	9.43486i	0.0879942	+	0.837209i	−0.858136	+	0.513422i	$0.828377\pi$
$128$	−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
$131$	18.9921	+	4.03690i	1.65935	+	0.352705i	0.939797	−	0.341733i	$-0.111014\pi$
$131$	18.9921	+	4.03690i	1.65935	+	0.352705i	0.719552	+	0.694439i	$0.244347\pi$
$132$	−5.56231	+	17.1190i	−0.484137	+	1.49002i
$133$	0.978148	−	0.207912i	0.0848162	−	0.0180282i
$134$	−0.239558	+	2.27924i	−0.0206947	+	0.196896i
$135$	−2.61549	+	2.90480i	−0.225106	+	0.250005i
$136$	0.726470	−	0.323445i	0.0622943	−	0.0277352i
$137$	−6.27125	−	2.79214i	−0.535789	−	0.238549i	0.120961	−	0.992657i	$-0.461403\pi$
$137$	−6.27125	−	2.79214i	−0.535789	−	0.238549i	−0.656750	+	0.754109i	$0.728069\pi$
$138$	4.01478	+	4.45887i	0.341761	+	0.379564i
$139$	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
$141$	−5.67776	−	6.30579i	−0.478154	−	0.531044i
$142$	2.60735	+	1.16087i	0.218804	+	0.0974179i
$143$	26.6067	−	11.8460i	2.22496	−	0.990616i
$144$	4.70696	−	5.22761i	0.392247	−	0.435634i
$145$	0.865386	−	8.23360i	0.0718664	−	0.683763i
$146$	1.58513	−	0.336930i	0.131186	−	0.0278845i
$147$	4.24264	−	13.0575i	0.349927	−	1.07696i
$148$	−7.69439	−	1.63549i	−0.632475	−	0.134437i
$149$	−6.70820	+	11.6190i	−0.549557	+	0.951861i	0.448747	+	0.893659i	$0.351870\pi$
$149$	−6.70820	+	11.6190i	−0.549557	+	0.951861i	−0.998305	+	0.0582028i	$0.981463\pi$
$150$		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	$0.939406\pi$
$152$	0.153880	+	1.46407i	0.0124813	+	0.118752i
$153$	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	$0.639839\pi$
$158$	−0.443477	−	4.21940i	−0.0352811	−	0.335677i
$159$	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
$162$	4.00079	+	0.850394i	0.314332	+	0.0668133i
$163$	−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	$0.938359\pi$
$164$	13.5514	−	2.88043i	1.05818	−	0.224924i
$165$	2.26913	−	21.5893i	0.176651	−	1.68072i
$166$	−0.808231	+	0.897632i	−0.0627309	+	0.0696697i
$167$	6.76473	−	3.01185i	0.523470	−	0.233064i	−0.127951	−	0.991781i	$-0.540840\pi$
$167$	6.76473	−	3.01185i	0.523470	−	0.233064i	0.651421	+	0.758716i	$0.274173\pi$
$168$	−3.07738	−	1.37014i	−0.237425	−	0.105708i
$169$	22.8338	+	25.3595i	1.75645	+	1.95073i
$170$	−0.373256	+	0.271187i	−0.0286274	+	0.0207991i
$171$	−1.80902	+	1.31433i	−0.138339	+	0.100509i
$172$	−0.255982	−	0.284296i	−0.0195184	−	0.0216774i
$173$	16.4438	+	7.32126i	1.25020	+	0.556625i	0.921709	−	0.387882i	$-0.126793\pi$
$173$	16.4438	+	7.32126i	1.25020	+	0.556625i	0.328491	+	0.944507i	$0.393460\pi$
$174$	−2.95630	+	1.31623i	−0.224116	+	0.0997829i
$175$		0			0
$176$	1.39513	−	13.2738i	0.105162	−	1.00055i
$177$	−13.3047	+	2.82801i	−1.00004	+	0.212566i
$178$	0.692055	−	2.12993i	0.0518717	−	0.159645i
$179$	16.0713	+	3.41607i	1.20123	+	0.255329i	0.764715	−	0.644369i	$-0.222880\pi$
$179$	16.0713	+	3.41607i	1.20123	+	0.255329i	0.436513	+	0.899698i	$0.356213\pi$
$180$	−4.63525	+	8.02850i	−0.345492	+	0.598409i
$181$	9.08922	+	15.7430i	0.675597	+	1.17017i	0.976294	+	0.216448i	$0.0694472\pi$
$181$	9.08922	+	15.7430i	0.675597	+	1.17017i	−0.300698	+	0.953720i	$0.597219\pi$
$182$	0.810272	+	2.49376i	0.0600614	+	0.184850i
$183$	−1.06414	−	10.1246i	−0.0786631	−	0.748430i
$184$	−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
$189$	0.182722	+	1.73849i	0.0132911	+	0.126456i
$190$	−0.263932	−	0.812299i	−0.0191476	−	0.0589304i
$191$	−7.11803	−	12.3288i	−0.515043	−	0.892080i	−0.999848	−	0.0174580i	$-0.994443\pi$
$191$	−7.11803	−	12.3288i	−0.515043	−	0.892080i	0.484805	−	0.874622i	$-0.338891\pi$
$192$	−5.38676	+	9.33015i	−0.388756	+	0.673345i
$193$	7.13245	+	1.51605i	0.513405	+	0.109128i	0.457327	−	0.889299i	$-0.348807\pi$
$193$	7.13245	+	1.51605i	0.513405	+	0.109128i	0.0560784	+	0.998426i	$0.482140\pi$
$194$	−0.826238	+	2.54290i	−0.0593204	+	0.182569i
$195$	34.3571	−	7.30282i	2.46036	−	0.522966i
$196$	−1.16284	+	11.0637i	−0.0830599	+	0.790262i
$197$	4.95486	−	5.50293i	0.353019	−	0.392067i	−0.540313	−	0.841464i	$-0.681694\pi$
$197$	4.95486	−	5.50293i	0.353019	−	0.392067i	0.893332	+	0.449397i	$0.148361\pi$
$198$	−3.31037	+	1.47387i	−0.235258	+	0.104743i
$199$	13.4575	+	5.99165i	0.953974	+	0.424737i	0.823880	−	0.566765i	$-0.191805\pi$
$199$	13.4575	+	5.99165i	0.953974	+	0.424737i	0.130095	+	0.991502i	$0.458472\pi$
$200$		0			0
$201$	11.1074	−	8.06998i	0.783454	−	0.569213i
$202$	0.690983	−	0.502029i	0.0486174	−	0.0353226i
$203$	−2.47743	−	2.75146i	−0.173881	−	0.193115i
$204$	−2.09366	−	0.932157i	−0.146586	−	0.0652641i
$205$	−15.2637	+	6.79584i	−1.06606	+	0.474642i
$206$	−0.692177	+	0.768740i	−0.0482262	+	0.0535607i
$207$	1.60451	−	15.2659i	0.111521	−	1.06106i
$208$	21.1238	−	4.49001i	1.46467	−	0.311326i
$209$	−1.31105	+	4.03499i	−0.0906871	+	0.279106i
$210$	1.91169	+	0.406342i	0.131919	+	0.0280402i
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	−4.86163	−	8.42060i	−0.333898	−	0.578329i
$213$	−5.28360	−	16.2612i	−0.362026	−	1.11420i
$214$	0.298335	+	2.83847i	0.0203938	+	0.194034i
$215$	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
$220$	1.83861	+	17.4932i	0.123959	+	1.17939i
$221$	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	0.226900	+	0.973918i	$0.427141\pi$
$223$	−10.9010	+	18.8812i	−0.729988	+	1.26438i	−0.956888	+	0.290458i	$0.906192\pi$
$224$	4.05530	+	0.861981i	0.270956	+	0.0575935i
$225$		0			0
$226$	5.31887	−	1.13056i	0.353806	−	0.0752037i
$227$	−1.64195	+	15.6222i	−0.108980	+	1.03688i	0.794211	+	0.607641i	$0.207884\pi$
$227$	−1.64195	+	15.6222i	−0.108980	+	1.03688i	−0.903192	+	0.429237i	$0.858782\pi$
$228$	2.83888	−	3.15290i	0.188009	−	0.208806i
$229$	−3.87585	+	1.72564i	−0.256123	+	0.114033i	−0.530782	−	0.847508i	$-0.678102\pi$
$229$	−3.87585	+	1.72564i	−0.256123	+	0.114033i	0.274659	+	0.961542i	$0.411435\pi$
$230$	5.35629	+	2.38477i	0.353183	+	0.157247i
$231$	−6.49606	−	7.21460i	−0.427409	−	0.474686i
$232$	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	$0.252615\pi$
$234$	−3.92324	−	4.35720i	−0.256470	−	0.284839i
$235$	−7.57493	−	3.37258i	−0.494134	−	0.220003i
$236$	10.0684	−	4.48276i	0.655400	−	0.291803i
$237$	−17.0069	+	18.8881i	−1.10472	+	1.22691i
$238$	−0.0215675	+	0.205201i	−0.00139801	+	0.0133012i
$239$	−15.9942	+	3.39968i	−1.03458	+	0.219907i	−0.693749	−	0.720217i	$-0.744042\pi$
$239$	−15.9942	+	3.39968i	−1.03458	+	0.219907i	−0.340833	+	0.940124i	$0.610709\pi$
$240$	4.97410	−	15.3087i	0.321077	−	0.988173i
$241$	14.4091	+	3.06275i	0.928173	+	0.197289i	0.647107	−	0.762399i	$-0.275979\pi$
$241$	14.4091	+	3.06275i	0.928173	+	0.197289i	0.281066	+	0.959688i	$0.409312\pi$
$242$	−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
$245$	−1.40240	−	13.3429i	−0.0895958	−	0.852447i
$246$	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
$251$	−2.48323	−	23.6263i	−0.156740	−	1.49128i	−0.736468	−	0.676472i	$-0.763508\pi$
$251$	−2.48323	−	23.6263i	−0.156740	−	1.49128i	0.579728	−	0.814810i	$-0.303159\pi$
$252$	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
$255$	2.70353	+	0.574654i	0.169302	+	0.0359862i
$256$	1.71885	−	5.29007i	0.107428	−	0.330629i
$257$	−23.4210	+	4.97829i	−1.46096	+	0.310537i	−0.868753	−	0.495246i	$-0.835078\pi$
$257$	−23.4210	+	4.97829i	−1.46096	+	0.310537i	−0.592211	+	0.805783i	$0.701745\pi$
$258$	0.0188507	−	0.179352i	0.00117359	−	0.0111660i
$259$	2.83888	−	3.15290i	0.176399	−	0.195911i
$260$	−26.0000	+	11.5759i	−1.61245	+	0.717909i
$261$	7.56320	+	3.36735i	0.468150	+	0.208434i
$262$	−4.96255	−	5.51147i	−0.306587	−	0.340499i
$263$	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
$265$	7.84647	+	8.71439i	0.482005	+	0.535321i
$266$	−0.348943	−	0.155360i	−0.0213951	−	0.00952571i
$267$	−12.2565	+	5.45694i	−0.750086	+	0.333960i
$268$	−7.44382	+	8.26720i	−0.454704	+	0.504999i
$269$	1.54805	−	14.7287i	0.0943862	−	0.898025i	−0.840197	−	0.542281i	$-0.817561\pi$
$269$	1.54805	−	14.7287i	0.0943862	−	0.898025i	0.934583	−	0.355744i	$-0.115773\pi$
$270$	1.46040	−	0.310417i	0.0888770	−	0.0188914i
$271$	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	$-0.225101\pi$
$272$	1.66222	+	0.353316i	0.100787	+	0.0214229i
$273$	7.85410	−	13.6037i	0.475352	−	0.823334i
$274$	1.31105	+	2.27080i	0.0792033	+	0.137184i
$275$		0			0
$276$	3.04435	+	28.9651i	0.183248	+	1.74349i
$277$	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	$0.315030\pi$
$282$	0.338786	+	3.22333i	0.0201744	+	0.191947i
$283$	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
$286$	−10.8815	−	2.31294i	−0.643437	−	0.136767i
$287$	−2.30902	+	7.10642i	−0.136297	+	0.419479i
$288$	−9.06793	+	1.92745i	−0.534333	+	0.113576i
$289$	1.74648	−	16.6167i	0.102734	−	0.977451i
$290$	−2.11598	+	2.35003i	−0.124254	+	0.137999i
$291$	14.6329	−	6.51499i	0.857797	−	0.381916i
$292$	7.18621	+	3.19951i	0.420541	+	0.187237i
$293$	−10.5108	−	11.6735i	−0.614050	−	0.681971i	0.353273	−	0.935520i	$-0.385069\pi$
$293$	−10.5108	−	11.6735i	−0.614050	−	0.681971i	−0.967323	+	0.253549i	$0.918402\pi$
$294$	−4.24264	+	3.08246i	−0.247436	+	0.179773i
$295$	−10.7533	+	7.81272i	−0.626081	+	0.454874i
$296$	4.17922	+	4.64149i	0.242912	+	0.269781i
$297$	−6.77523	−	3.01652i	−0.393138	−	0.175037i
$298$	4.68157	−	2.08437i	0.271196	−	0.120744i
$299$	31.5325	−	35.0204i	1.82357	−	2.02528i
$300$		0			0
$301$	0.201822	−	0.0428986i	0.0116328	−	0.00247264i
$302$	−0.358205	+	1.10244i	−0.0206124	+	0.0634383i
$303$	−5.00486	−	1.06382i	−0.287522	−	0.0611146i
$304$	−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
$307$	1.68548	+	16.0363i	0.0961955	+	0.915239i	0.931080	+	0.364814i	$0.118867\pi$
$307$	1.68548	+	16.0363i	0.0961955	+	0.915239i	−0.834885	+	0.550425i	$0.814466\pi$
$308$	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
$313$	−2.19582	−	20.8918i	−0.124115	−	1.18087i	−0.862344	−	0.506324i	$-0.831004\pi$
$313$	−2.19582	−	20.8918i	−0.124115	−	1.18087i	0.738229	−	0.674550i	$-0.235663\pi$
$314$	−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
$317$	−21.2883	−	4.52498i	−1.19567	−	0.254148i	−0.433278	−	0.901260i	$-0.642643\pi$
$317$	−21.2883	−	4.52498i	−1.19567	−	0.254148i	−0.762395	+	0.647113i	$0.775976\pi$
$318$	1.41641	−	4.35926i	0.0794282	−	0.244455i
$319$	15.3649	−	3.26592i	0.860272	−	0.182856i
$320$	−1.10046	+	10.4702i	−0.0615177	+	0.585301i
$321$	11.4409	−	12.7064i	0.638566	−	0.709199i
$322$	2.39540	−	1.06650i	0.133491	−	0.0594339i
$323$	−0.493480	−	0.219712i	−0.0274580	−	0.0122251i
$324$	13.2850	+	14.7545i	0.738055	+	0.819693i
$325$		0			0
$326$	3.83688	−	2.78766i	0.212505	−	0.154394i
$327$	22.5202	+	25.0113i	1.24537	+	1.38313i
$328$	−10.0490	−	4.47410i	−0.554863	−	0.247041i
$329$	−3.38761	+	1.50826i	−0.186765	+	0.0831532i
$330$	−5.54829	+	6.16201i	−0.305424	+	0.339207i
$331$	−2.67928	+	25.4917i	−0.147267	+	1.40115i	0.632249	+	0.774765i	$0.282132\pi$
$331$	−2.67928	+	25.4917i	−0.147267	+	1.40115i	−0.779516	+	0.626383i	$0.784535\pi$
$332$	−5.73506	+	1.21902i	−0.314752	+	0.0669027i
$333$	−2.93159	+	9.02251i	−0.160650	+	0.494431i
$334$	−2.76662	−	0.588063i	−0.151383	−	0.0321774i
$335$	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	$0.848949\pi$
$338$	−1.36247	−	12.9630i	−0.0741086	−	0.705096i
$339$	−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
$344$	0.0317502	+	0.302083i	0.00171186	+	0.0162872i
$345$	−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	−0.277132	−	0.960832i	$-0.589384\pi$
$347$	12.9192	−	22.3767i	0.693539	−	1.20124i	0.970671	−	0.240413i	$-0.0772829\pi$
$348$	−15.3649	−	3.26592i	−0.823647	−	0.175072i
$349$	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
$351$	1.25434	−	11.9343i	0.0669518	−	0.637004i
$352$	−11.7697	+	13.0716i	−0.627328	+	0.696718i
$353$	−14.5164	+	6.46313i	−0.772631	+	0.343998i	−0.754895	−	0.655845i	$-0.772312\pi$
$353$	−14.5164	+	6.46313i	−0.772631	+	0.343998i	−0.0177357	+	0.999843i	$0.505646\pi$
$354$	4.74631	+	2.11319i	0.252264	+	0.112315i
$355$	−11.1800	−	12.4166i	−0.593371	−	0.659006i
$356$	8.79478	−	6.38978i	0.466122	−	0.338658i
$357$	1.00000	−	0.726543i	0.0529256	−	0.0384527i
$358$	−4.19936	−	4.66386i	−0.221943	−	0.246493i
$359$	8.91980	+	3.97135i	0.470769	+	0.209600i	0.628388	−	0.777900i	$-0.283715\pi$
$359$	8.91980	+	3.97135i	0.470769	+	0.209600i	−0.157619	+	0.987500i	$0.550382\pi$
$360$	6.72432	−	2.99386i	0.354403	−	0.157790i
$361$	−12.0444	+	13.3766i	−0.633913	+	0.704032i
$362$	0.725798	−	6.90551i	0.0381471	−	0.362946i
$363$	15.6677	−	3.33027i	0.822341	−	0.174794i
$364$	−3.93314	+	12.1050i	−0.206153	+	0.634473i
$365$	−9.27952	−	1.97242i	−0.485712	−	0.103241i
$366$	−1.94427	+	3.36758i	−0.101629	+	0.176026i
$367$	−6.15763	−	10.6653i	−0.321426	−	0.556726i	0.659357	−	0.751830i	$-0.270829\pi$
$367$	−6.15763	−	10.6653i	−0.321426	−	0.556726i	−0.980782	+	0.195105i	$0.937495\pi$
$368$	−6.67346	−	20.5388i	−0.347878	−	1.07066i
$369$	−1.74648	−	16.6167i	−0.0909183	−	0.865030i
$370$	−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
$375$	2.67419	+	25.4432i	0.138095	+	1.31388i
$376$	−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
$379$	18.9921	+	4.03690i	0.975559	+	0.207362i	0.667995	−	0.744166i	$-0.267153\pi$
$379$	18.9921	+	4.03690i	0.975559	+	0.207362i	0.307564	+	0.951527i	$0.400486\pi$
$380$	1.28115	−	3.94298i	0.0657218	−	0.202271i
$381$	−21.2338	+	4.51339i	−1.08784	+	0.231228i
$382$	−0.568394	+	5.40791i	−0.0290816	+	0.276693i
$383$	12.7486	−	14.1587i	0.651423	−	0.723478i	−0.323449	−	0.946246i	$-0.604842\pi$
$383$	12.7486	−	14.1587i	0.651423	−	0.723478i	0.974872	+	0.222767i	$0.0715090\pi$
$384$	21.0927	−	9.39106i	1.07638	−	0.479235i
$385$	−8.66665	−	3.85864i	−0.441694	−	0.196655i
$386$	−1.86367	−	2.06982i	−0.0948585	−	0.105351i
$387$	−0.373256	+	0.271187i	−0.0189737	+	0.0137852i
$388$	−10.5000	+	7.62870i	−0.533057	+	0.387288i
$389$	−22.6056	−	25.1060i	−1.14615	−	1.27293i	−0.956713	−	0.291033i	$-0.906001\pi$
$389$	−22.6056	−	25.1060i	−1.14615	−	1.27293i	−0.189435	−	0.981893i	$-0.560666\pi$
$390$	−12.2565	−	5.45694i	−0.620632	−	0.276323i
$391$	3.38761	−	1.50826i	0.171319	−	0.0762761i
$392$	5.91031	−	6.56406i	0.298516	−	0.331535i
$393$	−4.64415	+	44.1861i	−0.234266	+	2.22889i
$394$	−2.76662	+	0.588063i	−0.139380	+	0.0296262i
$395$	−7.67501	+	23.6212i	−0.386172	+	1.18851i
$396$	−17.2052	−	3.65707i	−0.864593	−	0.183775i
$397$	−0.645898	+	1.11873i	−0.0324167	+	0.0561474i	−0.881779	−	0.471664i	$-0.843654\pi$
$397$	−0.645898	+	1.11873i	−0.0324167	+	0.0561474i	0.849362	+	0.527811i	$0.176987\pi$
$398$	−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
$406$	0.147826	+	1.40647i	0.00733646	+	0.0698018i
$407$	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	−0.996787	−	0.0800961i	$-0.974477\pi$
$409$	−8.67656	+	15.0282i	−0.429028	+	0.743099i	0.567759	+	0.823195i	$0.307811\pi$
$410$	6.24250	+	1.32689i	0.308295	+	0.0655302i
$411$	4.85410	−	14.9394i	0.239435	−	0.736906i
$412$	−4.91156	+	1.04398i	−0.241975	+	0.0514334i
$413$	−0.621346	+	5.91171i	−0.0305744	+	0.290896i
$414$	−3.92324	+	4.35720i	−0.192817	+	0.214144i
$415$	6.45974	−	2.87606i	0.317096	−	0.141180i
$416$	−26.0000	−	11.5759i	−1.27475	−	0.567557i
$417$	1.53351	+	1.70314i	0.0750964	+	0.0834029i
$418$	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	$0.149905\pi$
$420$	6.34793	+	7.05009i	0.309747	+	0.344009i
$421$	−0.380408	−	0.169368i	−0.0185399	−	0.00825451i	0.397446	−	0.917626i	$-0.369897\pi$
$421$	−0.380408	−	0.169368i	−0.0185399	−	0.00825451i	−0.415986	+	0.909371i	$0.636563\pi$
$422$	−1.74472	+	0.776798i	−0.0849315	+	0.0378139i
$423$	5.54829	−	6.16201i	0.269767	−	0.299607i
$424$	−0.806977	+	7.67787i	−0.0391903	+	0.372870i
$425$		0			0
$426$	−2.01815	+	6.21124i	−0.0977799	+	0.300936i
$427$	−4.35175	−	0.924993i	−0.210596	−	0.0447636i
$428$	−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
$431$	0.0116503	+	0.110846i	0.000561177	+	0.00533925i	0.994799	−	0.101858i	$-0.0324789\pi$
$431$	0.0116503	+	0.110846i	0.000561177	+	0.00533925i	−0.994238	+	0.107198i	$0.965812\pi$
$432$	−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
$437$	0.717560	+	6.82713i	0.0343256	+	0.326586i
$438$	1.14590	+	3.52671i	0.0547531	+	0.168513i
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$	6.98295	−	12.0948i	0.332899	−	0.576598i
$441$	13.1232	+	2.78943i	0.624916	+	0.132830i
$442$	0.437694	−	1.34708i	0.0208190	−	0.0640742i
$443$	−23.4210	+	4.97829i	−1.11277	+	0.236526i	−0.727384	−	0.686231i	$-0.759264\pi$
$443$	−23.4210	+	4.97829i	−1.11277	+	0.236526i	−0.385383	+	0.922757i	$0.625931\pi$
$444$	1.88151	−	17.9014i	0.0892926	−	0.849563i
$445$	−8.77262	+	9.74299i	−0.415862	+	0.461862i
$446$	7.60769	−	3.38716i	0.360235	−	0.160387i
$447$	−28.0459	−	12.4868i	−1.32652	−	0.590607i
$448$	3.15040	+	3.49888i	0.148843	+	0.165306i
$449$	−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
$451$	−21.2125	−	23.5589i	−0.998858	−	1.10934i
$452$	24.1131	+	10.7359i	1.13419	+	0.504973i
$453$	6.34391	−	2.82449i	0.298063	−	0.132706i
$454$	4.01478	−	4.45887i	0.188423	−	0.209265i
$455$	1.60451	−	15.2659i	0.0752208	−	0.715678i
$456$	−3.29500	+	0.700373i	−0.154302	+	0.0327980i
$457$	−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	$0.185245\pi$
$458$	1.58513	+	0.336930i	0.0740683	+	0.0157437i
$459$	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	$0.535554\pi$
$462$	0.387613	+	3.68789i	0.0180334	+	0.171576i
$463$	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	$0.817959\pi$
$468$	−2.97493	−	28.3046i	−0.137516	−	1.30838i
$469$	−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
$472$	−8.55955	−	1.81939i	−0.393985	−	0.0837442i
$473$	−0.270510	+	0.832544i	−0.0124381	+	0.0382804i
$474$	9.49606	−	2.01845i	0.436168	−	0.0927104i
$475$		0			0
$476$	−0.670169	+	0.744298i	−0.0307171	+	0.0341148i
$477$	−10.7126	+	4.76954i	−0.490495	+	0.218382i
$478$	5.70577	+	2.54037i	0.260976	+	0.116194i
$479$	17.0442	+	18.9295i	0.778769	+	0.864910i	0.993741	−	0.111710i	$-0.0356327\pi$
$479$	17.0442	+	18.9295i	0.778769	+	0.864910i	−0.214972	+	0.976620i	$0.568966\pi$
$480$	−17.1618	+	12.4688i	−0.783327	+	0.569121i
$481$	−23.5623	+	17.1190i	−1.07435	+	0.780560i
$482$	−3.76503	−	4.18149i	−0.171492	−	0.190462i
$483$	−14.3502	−	6.38910i	−0.652955	−	0.290714i
$484$	−11.8566	+	5.27892i	−0.538938	+	0.239951i
$485$	10.4736	−	11.6321i	0.475579	−	0.528184i
$486$	−0.768933	+	7.31591i	−0.0348795	+	0.331857i
$487$	18.1848	−	3.86531i	0.824034	−	0.175154i	0.223450	−	0.974715i	$-0.428268\pi$
$487$	18.1848	−	3.86531i	0.824034	−	0.175154i	0.600584	+	0.799562i	$0.294935\pi$
$488$	2.02390	−	6.22894i	0.0916178	−	0.281971i
$489$	−27.7909	−	5.90714i	−1.25675	−	0.267130i
$490$	−2.56231	+	4.43804i	−0.115753	+	0.200490i
$491$	−4.78282	−	8.28409i	−0.215846	−	0.373856i	0.737688	−	0.675142i	$-0.235917\pi$
$491$	−4.78282	−	8.28409i	−0.215846	−	0.373856i	−0.953534	+	0.301286i	$0.902584\pi$
$492$	9.79633	+	30.1500i	0.441653	+	1.35927i
$493$	0.209057	+	1.98904i	0.00941545	+	0.0895820i
$494$	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
$499$	1.92173	+	18.2841i	0.0860286	+	0.818507i	0.949428	+	0.313986i	$0.101664\pi$
$499$	1.92173	+	18.2841i	0.0860286	+	0.818507i	−0.863399	+	0.504521i	$0.831669\pi$
$500$	−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
$503$	−2.82542	−	0.600562i	−0.125979	−	0.0267777i	0.144490	−	0.989506i	$-0.453846\pi$
$503$	−2.82542	−	0.600562i	−0.125979	−	0.0267777i	−0.270470	+	0.962728i	$0.587179\pi$
$504$	1.01722	−	3.13068i	0.0453106	−	0.139452i
$505$	−4.89074	+	1.03956i	−0.217635	+	0.0462597i
$506$	−1.16284	+	11.0637i	−0.0516945	+	0.491840i
$507$	−52.2494	+	58.0288i	−2.32048	+	2.57715i
$508$	16.0689	−	7.15432i	0.712940	−	0.317421i
$509$	4.36933	+	1.94535i	0.193667	+	0.0862261i	0.501279	−	0.865286i	$-0.332863\pi$
$509$	4.36933	+	1.94535i	0.193667	+	0.0862261i	−0.307612	+	0.951512i	$0.599530\pi$
$510$	−0.706420	−	0.784559i	−0.0312808	−	0.0347409i
$511$	−3.43237	+	2.49376i	−0.151839	+	0.110318i
$512$	−18.0451	+	13.1105i	−0.797488	+	0.579409i
$513$	1.16968	+	1.29906i	0.0516428	+	0.0573551i
$514$	8.35519	+	3.71997i	0.368532	+	0.164081i
$515$	5.53218	−	2.46309i	0.243777	−	0.108537i
$516$	0.585749	−	0.650540i	0.0257862	−	0.0286384i
$517$	1.64450	−	15.6464i	0.0723251	−	0.688128i
$518$	−1.58513	+	0.336930i	−0.0696467	+	0.0148039i
$519$	−12.7279	+	39.1725i	−0.558694	+	1.71948i
$520$	22.1035	+	4.69825i	0.969303	+	0.206032i
$521$	−6.70820	+	11.6190i	−0.293892	+	0.509035i	−0.974726	−	0.223402i	$-0.928284\pi$
$521$	−6.70820	+	11.6190i	−0.293892	+	0.509035i	0.680835	+	0.732437i	$0.261617\pi$
$522$	−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	$-0.319321\pi$
$524$	−3.76302	−	35.8028i	−0.164388	−	1.56405i
$525$		0			0
$526$	−1.03165			−0.0449823
$527$		0			0
$528$	30.5410			1.32913
$529$	−19.5172	−	14.1801i	−0.848575	−	0.616526i
$530$	−0.468191	−	4.45454i	−0.0203369	−	0.193493i
$531$	−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
$534$	5.01263	+	1.06547i	0.216918	+	0.0461073i
$535$	5.16312	−	15.8904i	0.223221	−	0.687004i
$536$	8.63980	−	1.83645i	0.373182	−	0.0793224i
$537$	−3.92993	+	37.3908i	−0.169589	+	1.61353i
$538$	−3.78517	+	4.20386i	−0.163190	+	0.181241i
$539$	23.2551	−	10.3538i	1.00167	−	0.445971i
$540$	6.62073	+	2.94774i	0.284911	+	0.126851i
$541$	−18.6238	−	20.6838i	−0.800699	−	0.889267i	0.195104	−	0.980782i	$-0.437495\pi$
$541$	−18.6238	−	20.6838i	−0.800699	−	0.889267i	−0.995804	+	0.0915159i	$0.970829\pi$
$542$	−8.67656	+	6.30389i	−0.372690	+	0.270775i
$543$	−33.6525	+	24.4500i	−1.44417	+	1.04925i
$544$	−1.49854	−	1.66430i	−0.0642495	−	0.0713563i
$545$	30.0452	+	13.3770i	1.28699	+	0.573007i
$546$	−5.48127	+	2.44042i	−0.234577	+	0.104440i
$547$	−16.3378	+	18.1449i	−0.698552	+	0.775821i	−0.983145	−	0.182827i	$-0.941475\pi$
$547$	−16.3378	+	18.1449i	−0.698552	+	0.775821i	0.284593	+	0.958649i	$0.408142\pi$
$548$	−1.33043	+	12.6582i	−0.0568332	+	0.540731i
$549$	9.73081	−	2.06835i	0.415301	−	0.0882749i
$550$		0			0
$551$	−3.62155	−	0.769785i	−0.154283	−	0.0327939i
$552$	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
$555$	2.26913	+	21.5893i	0.0963190	+	0.916414i
$556$	−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
$561$	0.548167	+	5.21546i	0.0231436	+	0.220197i
$562$	−3.70163	−	11.3924i	−0.156144	−	0.480561i
$563$	−7.11803	−	12.3288i	−0.299989	−	0.519597i	0.676144	−	0.736770i	$-0.263650\pi$
$563$	−7.11803	−	12.3288i	−0.299989	−	0.519597i	−0.976133	+	0.217173i	$0.930316\pi$
$564$	−7.86629	+	13.6248i	−0.331230	+	0.573708i
$565$	−31.1372	−	6.61841i	−1.30995	−	0.278439i
$566$	2.83282	−	8.71851i	0.119072	−	0.366466i
$567$	−10.4742	+	2.22636i	−0.439875	+	0.0934984i
$568$	1.14981	−	10.9397i	0.0482451	−	0.459021i
$569$	20.5423	−	22.8146i	0.861179	−	0.956437i	−0.138244	−	0.990398i	$-0.544146\pi$
$569$	20.5423	−	22.8146i	0.861179	−	0.956437i	0.999423	+	0.0339616i	$0.0108124\pi$
$570$	1.78543	−	0.794924i	0.0747834	−	0.0332957i
$571$	−6.27125	−	2.79214i	−0.262444	−	0.116847i	0.271297	−	0.962496i	$-0.412547\pi$
$571$	−6.27125	−	2.79214i	−0.262444	−	0.116847i	−0.533741	+	0.845648i	$0.679214\pi$
$572$	−36.1331	−	40.1298i	−1.51080	−	1.67791i
$573$	26.3542	−	19.1475i	1.10096	−	0.799897i
$574$	2.30902	−	1.67760i	0.0963765	−	0.0700216i
$575$		0			0
$576$	−9.61768	−	4.28207i	−0.400737	−	0.178420i
$577$	−27.4064	+	12.2021i	−1.14094	+	0.507980i	−0.888156	−	0.459542i	$-0.848013\pi$
$577$	−27.4064	+	12.2021i	−1.14094	+	0.507980i	−0.252786	+	0.967522i	$0.581347\pi$
$578$	−4.27037	+	4.74273i	−0.177624	+	0.197271i
$579$	−1.74410	+	16.5940i	−0.0724824	+	0.689624i
$580$	−15.0146	+	3.19145i	−0.623447	+	0.132518i
$581$	0.977198	−	3.00750i	0.0405410	−	0.124772i
$582$	−5.98453	−	1.27205i	−0.248067	−	0.0527282i
$583$	−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
$586$	0.627171	+	5.96713i	0.0259082	+	0.246500i
$587$	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
$592$	1.39513	+	13.2738i	0.0573396	+	0.545550i
$593$	−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
$596$	24.3318	+	5.17188i	0.996669	+	0.211849i
$597$	−10.4164	+	32.0584i	−0.426315	+	1.31206i
$598$	−17.6067	+	3.74241i	−0.719990	+	0.153039i
$599$	−2.50286	+	23.8131i	−0.102264	+	0.972977i	0.816280	+	0.577657i	$0.196033\pi$
$599$	−2.50286	+	23.8131i	−0.102264	+	0.972977i	−0.918544	+	0.395320i	$0.870634\pi$
$600$		0			0
$601$	−7.94018	+	3.53520i	−0.323887	+	0.144204i	−0.562238	−	0.826975i	$-0.690060\pi$
$601$	−7.94018	+	3.53520i	−0.323887	+	0.144204i	0.238352	+	0.971179i	$0.423393\pi$
$602$	−0.0719978	−	0.0320555i	−0.00293441	−	0.00130648i
$603$	8.97733	+	9.97033i	0.365585	+	0.406023i
$604$	−4.55214	+	3.30732i	−0.185224	+	0.134573i
$605$	12.6631	−	9.20029i	0.514829	−	0.374045i
$606$	1.30775	+	1.45240i	0.0531235	+	0.0589997i
$607$	−22.9525	−	10.2191i	−0.931612	−	0.414780i	−0.115915	−	0.993259i	$-0.536980\pi$
$607$	−22.9525	−	10.2191i	−0.931612	−	0.414780i	−0.815697	+	0.578479i	$0.803647\pi$
$608$	3.78747	−	1.68629i	0.153602	−	0.0683880i
$609$	5.66897	−	6.29602i	0.229718	−	0.255128i
$610$	−0.397195	+	3.77906i	−0.0160820	+	0.153010i
$611$	24.8996	−	5.29257i	1.00733	−	0.214114i
$612$	0.692055	−	2.12993i	0.0279747	−	0.0860972i
$613$	−36.5421	−	7.76726i	−1.47592	−	0.313717i	−0.601495	−	0.798877i	$-0.705428\pi$
$613$	−36.5421	−	7.76726i	−1.47592	−	0.313717i	−0.874425	+	0.485160i	$0.838761\pi$
$614$	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
$617$	4.92586	+	46.8665i	0.198308	+	1.88677i	0.413949	+	0.910300i	$0.364149\pi$
$617$	4.92586	+	46.8665i	0.198308	+	1.88677i	−0.215641	+	0.976473i	$0.569184\pi$
$618$	−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
$623$	0.612870	+	5.83107i	0.0245541	+	0.233617i
$624$	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
$627$	−9.49606	−	2.01845i	−0.379236	−	0.0806091i
$628$	2.69756	−	8.30224i	0.107644	−	0.331295i
$629$	−2.24171	+	0.476491i	−0.0893830	+	0.0189989i
$630$	−0.199632	+	1.89937i	−0.00795351	+	0.0756726i
$631$	3.11501	−	3.45956i	0.124006	−	0.137723i	−0.677944	−	0.735113i	$-0.737129\pi$
$631$	3.11501	−	3.45956i	0.124006	−	0.137723i	0.801951	+	0.597390i	$0.203796\pi$
$632$	−14.9379	+	6.65078i	−0.594198	+	0.264554i
$633$	10.4521	+	4.65357i	0.415433	+	0.184963i
$634$	5.56254	+	6.17782i	0.220917	+	0.245353i
$635$	−17.1618	+	12.4688i	−0.681047	+	0.494810i
$636$	18.0000	−	13.0778i	0.713746	−	0.518567i
$637$	27.5604	+	30.6090i	1.09198	+	1.21277i
$638$	−5.48127	−	2.44042i	−0.217006	−	0.0966171i
$639$	15.2637	−	6.79584i	0.603823	−	0.268839i
$640$	15.0971	−	16.7671i	0.596766	−	0.662776i
$641$	−0.886953	+	8.43880i	−0.0350326	+	0.333312i	0.962943	+	0.269707i	$0.0869267\pi$
$641$	−0.886953	+	8.43880i	−0.0350326	+	0.333312i	−0.997975	+	0.0636059i	$0.979740\pi$
$642$	−6.38817	+	1.35785i	−0.252121	+	0.0535900i
$643$	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	$-0.0542758\pi$
$644$	12.4498	+	2.64628i	0.490590	+	0.104278i
$645$	−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	$-0.222723\pi$
$648$	−1.64778	−	15.6776i	−0.0647309	−	0.615873i
$649$	−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	$0.658449\pi$
$654$	−1.34376	−	12.7850i	−0.0525452	−	0.499934i
$655$	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
$658$	1.38546	+	0.294488i	0.0540107	+	0.0114803i
$659$	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	$-0.270955\pi$
$660$	−39.3697	+	8.36828i	−1.53246	+	0.325735i
$661$	4.79083	−	45.5817i	0.186342	−	1.77292i	−0.357671	−	0.933848i	$-0.616429\pi$
$661$	4.79083	−	45.5817i	0.186342	−	1.77292i	0.544013	−	0.839077i	$-0.316904\pi$
$662$	6.55118	−	7.27582i	0.254619	−	0.282783i
$663$	−7.75169	+	3.45127i	−0.301051	+	0.134036i
$664$	4.25283	+	1.89348i	0.165042	+	0.0734814i
$665$	1.49622	+	1.66172i	0.0580210	+	0.0644388i
$666$	2.93159	−	2.12993i	0.113597	−	0.0825330i
$667$	20.5623	−	14.9394i	0.796176	−	0.578455i
$668$	−9.18681	−	10.2030i	−0.355448	−	0.394765i
$669$	−45.5755	−	20.2915i	−1.76205	−	0.784515i
$670$	−4.68157	+	2.08437i	−0.180865	+	0.0805261i
$671$	12.6301	−	14.0271i	0.487580	−	0.541512i
$672$	−0.991644	+	9.43486i	−0.0382535	+	0.363958i
$673$	−7.29075	+	1.54970i	−0.281038	+	0.0597364i	−0.346274	−	0.938133i	$-0.612553\pi$
$673$	−7.29075	+	1.54970i	−0.281038	+	0.0597364i	0.0652363	+	0.997870i	$0.479220\pi$
$674$	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	0.586981	−	0.809601i	$-0.300317\pi$
$677$	−10.6066	−	18.3712i	−0.407645	−	0.706062i	−0.994625	+	0.103540i	$0.966983\pi$
$678$	3.84503	+	11.8338i	0.147668	+	0.454474i
$679$	−0.731699	−	6.96165i	−0.0280800	−	0.267164i
$680$	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
$685$	−1.60451	−	15.2659i	−0.0613053	−	0.583281i
$686$	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
$689$	−35.2133	−	7.48482i	−1.34152	−	0.285149i
$690$	−4.14590	+	12.7598i	−0.157832	+	0.485756i
$691$	21.1119	−	4.48748i	0.803136	−	0.170712i	0.211985	−	0.977273i	$-0.432007\pi$
$691$	21.1119	−	4.48748i	0.803136	−	0.170712i	0.591151	+	0.806561i	$0.298674\pi$
$692$	3.48852	−	33.1910i	0.132613	−	1.26173i
$693$	6.34793	−	7.05009i	0.241138	−	0.267811i
$694$	−9.01614	+	4.01424i	−0.342248	+	0.152379i
$695$	2.04592	+	0.910902i	0.0776061	+	0.0345525i
$696$	8.34549	+	9.26860i	0.316335	+	0.351326i
$697$	3.26544	−	2.37248i	0.123687	−	0.0898642i
$698$	−1.85410	+	1.34708i	−0.0701788	+	0.0509879i
$699$	6.93277	+	7.69962i	0.262222	+	0.291226i
$700$		0			0
$701$	25.2618	−	11.2473i	0.954125	−	0.424804i	0.130190	−	0.991489i	$-0.458441\pi$
$701$	25.2618	−	11.2473i	0.954125	−	0.424804i	0.823934	+	0.566685i	$0.191774\pi$
$702$	−3.06702	+	3.40627i	−0.115757	+	0.128561i
$703$	0.443477	−	4.21940i	0.0167260	−	0.159138i
$704$	−19.5387	+	4.15308i	−0.736393	+	0.156525i
$705$	5.86319	−	18.0450i	0.220820	−	0.679615i
$706$	5.93688	+	1.26192i	0.223438	+	0.0474931i
$707$	−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	$0.995461\pi$
$710$	0.667097	+	6.34700i	0.0250357	+	0.238199i
$711$	−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
$716$	−3.18431	−	30.2967i	−0.119003	−	1.13224i
$717$	−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	−0.938338	−	0.345720i	$-0.887635\pi$
$719$	−4.55214	+	7.88453i	−0.169766	+	0.294043i	0.768571	+	0.639764i	$0.220968\pi$
$720$	15.3858	+	3.27034i	0.573394	+	0.121879i
$721$	0.836881	−	2.57565i	0.0311671	−	0.0959224i
$722$	6.72514	−	1.42947i	0.250284	−	0.0531995i
$723$	−3.52347	+	33.5235i	−0.131039	+	1.24675i
$724$	22.5528	−	25.0475i	0.838170	−	0.930882i
$725$		0			0
$726$	−5.58928	−	2.48851i	−0.207437	−	0.0923571i
$727$	−2.39789	−	2.66313i	−0.0889329	−	0.0987699i	0.697036	−	0.717036i	$-0.254502\pi$
$727$	−2.39789	−	2.66313i	−0.0889329	−	0.0987699i	−0.785969	+	0.618267i	$0.787835\pi$
$728$	8.17578	−	5.94006i	0.303015	−	0.220153i
$729$	9.66312	−	7.02067i	0.357893	−	0.260025i
$730$	2.42469	+	2.69290i	0.0897419	+	0.0996685i
$731$	−0.101820	−	0.0453333i	−0.00376596	−	0.00167671i
$732$	−17.2435	+	7.67731i	−0.637339	+	0.283762i
$733$	8.30820	−	9.22719i	0.306870	−	0.340814i	−0.569908	−	0.821708i	$-0.693021\pi$
$733$	8.30820	−	9.22719i	0.306870	−	0.340814i	0.876779	+	0.480894i	$0.159688\pi$
$734$	−0.491703	+	4.67824i	−0.0181491	+	0.172677i
$735$	30.0292	−	6.38290i	1.10764	−	0.235437i
$736$	−8.79478	+	27.0675i	−0.324180	+	0.997723i
$737$	24.8996	+	5.29257i	0.917188	+	0.194954i
$738$	−3.19098	+	5.52694i	−0.117462	+	0.203450i
$739$	−12.8311	−	22.2241i	−0.471999	−	0.817527i	0.527488	−	0.849563i	$-0.323134\pi$
$739$	−12.8311	−	22.2241i	−0.471999	−	0.817527i	−0.999487	+	0.0320362i	$0.989801\pi$
$740$	−5.43547	−	16.7287i	−0.199812	−	0.614958i
$741$	−1.64195	−	15.6222i	−0.0603187	−	0.573894i
$742$	−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
$747$	0.739128	+	7.03233i	0.0270433	+	0.257300i
$748$	−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
$751$	−28.8955	−	6.14192i	−1.05441	−	0.224122i	−0.352078	−	0.935971i	$-0.614525\pi$
$751$	−28.8955	−	6.14192i	−1.05441	−	0.224122i	−0.702333	+	0.711849i	$0.747858\pi$
$752$	3.60488	−	11.0947i	0.131456	−	0.404581i
$753$	53.1728	−	11.3022i	1.93772	−	0.411876i
$754$	1.01478	−	9.65502i	0.0369562	−	0.351615i
$755$	4.54067	−	5.04293i	0.165252	−	0.183531i
$756$	2.96088	−	1.31827i	0.107686	−	0.0479450i
$757$	17.5218	+	7.80121i	0.636841	+	0.283540i	0.699650	−	0.714486i	$-0.253339\pi$
$757$	17.5218	+	7.80121i	0.636841	+	0.283540i	−0.0628093	+	0.998026i	$0.520006\pi$
$758$	−4.96255	−	5.51147i	−0.180248	−	0.200185i
$759$	53.9163	−	39.1725i	1.95704	−	1.42187i
$760$	−2.66312	+	1.93487i	−0.0966015	+	0.0701851i
$761$	−1.49854	−	1.66430i	−0.0543221	−	0.0603309i	0.715371	−	0.698745i	$-0.246258\pi$
$761$	−1.49854	−	1.66430i	−0.0543221	−	0.0603309i	−0.769693	+	0.638414i	$0.779591\pi$
$762$	7.57493	+	3.37258i	0.274411	+	0.122176i
$763$	13.4366	−	5.98237i	0.486438	−	0.216576i
$764$	−17.6618	+	19.6154i	−0.638981	+	0.709660i
$765$	−0.282322	+	2.68611i	−0.0102074	+	0.0971166i
$766$	−7.11837	+	1.51306i	−0.257197	+	0.0546689i
$767$	12.6097	−	38.8087i	0.455310	−	1.40130i
$768$	12.4498	+	2.64628i	0.449243	+	0.0954895i
$769$	−6.93769	+	12.0164i	−0.250180	+	0.433324i	−0.963575	−	0.267438i	$-0.913823\pi$
$769$	−6.93769	+	12.0164i	−0.250180	+	0.433324i	0.713395	+	0.700762i	$0.247156\pi$
$770$	1.81182	+	3.13817i	0.0652936	+	0.113092i
$771$	−16.9312	−	52.1087i	−0.609761	−	1.87665i
$772$	−1.41320	−	13.4457i	−0.0508621	−	0.483920i
$773$	−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
$778$	1.34885	+	12.8335i	0.0483586	+	0.460102i
$779$	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
$782$	−1.38546	−	0.294488i	−0.0495438	−	0.0105309i
$783$	2.00000	−	6.15537i	0.0714742	−	0.219975i
$784$	18.4629	−	3.92441i	0.659390	−	0.140158i
$785$	−1.10046	+	10.4702i	−0.0392772	+	0.373697i
$786$	11.3555	−	12.6116i	0.405038	−	0.449840i
$787$	8.31717	−	3.70304i	0.296475	−	0.131999i	−0.253109	−	0.967438i	$-0.581453\pi$
$787$	8.31717	−	3.70304i	0.296475	−	0.131999i	0.549584	+	0.835439i	$0.314786\pi$
$788$	−12.5425	−	5.58428i	−0.446808	−	0.198932i
$789$	4.13545	+	4.59289i	0.147226	+	0.163511i
$790$	7.67501	−	5.57622i	0.273065	−	0.198393i
$791$	−11.5172	+	8.36775i	−0.409505	+	0.297523i
$792$	9.34502	+	10.3787i	0.332061	+	0.368791i
$793$	27.9006	+	12.4222i	0.990780	+	0.441124i
$794$	0.450764	−	0.200693i	0.0159970	−	0.00712232i
$795$	−17.9547	+	19.9407i	−0.636786	+	0.707223i
$796$	2.85497	−	27.1632i	0.101192	−	0.962774i
$797$	5.12959	−	1.09033i	0.181700	−	0.0386214i	−0.116163	−	0.993230i	$-0.537060\pi$
$797$	5.12959	−	1.09033i	0.181700	−	0.0386214i	0.297863	+	0.954609i	$0.403726\pi$
$798$	0.270091	−	0.831254i	0.00956111	−	0.0294261i
$799$	1.95933	+	0.416469i	0.0693161	+	0.0147336i
$800$		0			0
$801$	−6.55524	−	11.3540i	−0.231618	−	0.401174i
$802$	0.437016	+	1.34500i	0.0154316	+	0.0474935i
$803$	−1.88151	−	17.9014i	−0.0663971	−	0.631726i
$804$	−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
$809$	−2.30560	−	21.9363i	−0.0810605	−	0.771239i	−0.957248	−	0.289269i	$-0.906588\pi$
$809$	−2.30560	−	21.9363i	−0.0810605	−	0.771239i	0.876187	−	0.481971i	$-0.160079\pi$
$810$	2.82624	+	8.69827i	0.0993039	+	0.305626i
$811$	21.7082	+	37.5997i	0.762278	+	1.32030i	0.941674	+	0.336527i	$0.109252\pi$
$811$	21.7082	+	37.5997i	0.762278	+	1.32030i	−0.179396	+	0.983777i	$0.557414\pi$
$812$	−3.43237	+	5.94504i	−0.120453	+	0.208630i
$813$	62.8452	+	13.3582i	2.20408	+	0.468491i
$814$	2.12461	−	6.53888i	0.0744676	−	0.229188i
$815$	−27.1572	+	5.77245i	−0.951276	+	0.202200i
$816$	−0.406464	+	3.86724i	−0.0142291	+	0.135381i
$817$	0.138062	−	0.153334i	0.00483019	−	0.00536447i
$818$	6.05526	−	2.69597i	0.211717	−	0.0942625i
$819$	14.0229	+	6.24341i	0.490001	+	0.218163i
$820$	20.7288	+	23.0217i	0.723881	+	0.803952i
$821$	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
$823$	−9.99504	−	11.1006i	−0.348405	−	0.386943i	0.543316	−	0.839528i	$-0.317169\pi$
$823$	−9.99504	−	11.1006i	−0.348405	−	0.386943i	−0.891721	+	0.452585i	$0.850502\pi$
$824$	3.64216	+	1.62160i	0.126881	+	0.0564910i
$825$		0			0
$826$	1.51927	−	1.68732i	0.0528621	−	0.0587093i
$827$	5.02292	−	47.7899i	0.174664	−	1.66182i	−0.459169	−	0.888349i	$-0.651853\pi$
$827$	5.02292	−	47.7899i	0.174664	−	1.66182i	0.633834	−	0.773470i	$-0.281480\pi$
$828$	−27.8386	+	5.91727i	−0.967457	+	0.205639i
$829$	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	$0.0677012\pi$
$830$	−2.64189	−	0.561550i	−0.0917012	−	0.0194917i
$831$	−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
$834$	−0.0915030	−	0.870593i	−0.00316849	−	0.0301462i
$835$	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	$0.740863\pi$
$840$	−0.787354	−	7.49117i	−0.0271663	−	0.258470i
$841$	−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
$844$	−9.06793	−	1.92745i	−0.312131	−	0.0663455i
$845$	−23.5795	+	72.5703i	−0.811160	+	2.49649i
$846$	−3.09797	+	0.658495i	−0.106511	+	0.0226395i
$847$	0.731699	−	6.96165i	0.0251415	−	0.239205i
$848$	−11.0391	+	12.2602i	−0.379085	+	0.421016i
$849$	−50.1700	+	22.3371i	−1.72183	+	0.766608i
$850$		0			0
$851$	19.4882	+	21.6438i	0.668046	+	0.741940i
$852$	−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	$0.0139393\pi$
$854$	1.13709	+	1.26287i	0.0389105	+	0.0432144i
$855$	−4.56773	−	2.03368i	−0.156213	−	0.0695505i
$856$	10.0490	−	4.47410i	0.343468	−	0.152922i
$857$	−4.01478	+	4.45887i	−0.137142	+	0.152312i	−0.807804	−	0.589452i	$-0.799344\pi$
$857$	−4.01478	+	4.45887i	−0.137142	+	0.152312i	0.670661	+	0.741764i	$0.266010\pi$
$858$	2.66086	−	25.3164i	0.0908403	−	0.864287i
$859$	−3.57391	+	0.759658i	−0.121940	+	0.0259192i	−0.268477	−	0.963286i	$-0.586520\pi$
$859$	−3.57391	+	0.759658i	−0.121940	+	0.0259192i	0.146537	+	0.989205i	$0.453187\pi$
$860$	0.264342	−	0.813560i	0.00901397	−	0.0277422i
$861$	−16.7244	−	3.55489i	−0.569968	−	0.121150i
$862$	0.0212862	−	0.0368688i	0.000725012	−	0.00125576i
$863$	17.6626	+	30.5926i	0.601243	+	1.04138i	0.992633	+	0.121158i	$0.0386608\pi$
$863$	17.6626	+	30.5926i	0.601243	+	1.04138i	−0.391391	+	0.920225i	$0.628006\pi$
$864$	2.23954	+	6.89259i	0.0761906	+	0.234491i
$865$	4.20719	+	40.0287i	0.143049	+	1.36102i
$866$	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
$871$	4.30536	+	40.9628i	0.145882	+	1.38797i
$872$	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
$875$	10.9360	+	2.32452i	0.369705	+	0.0785832i
$876$	−5.56231	+	17.1190i	−0.187933	+	0.578398i
$877$	14.9576	−	3.17934i	0.505083	−	0.107359i	0.0516791	−	0.998664i	$-0.483543\pi$
$877$	14.9576	−	3.17934i	0.505083	−	0.107359i	0.453404	+	0.891305i	$0.350209\pi$
$878$	0.998158	−	9.49684i	0.0336862	−	0.320503i
$879$	24.0514	−	26.7118i	0.811233	−	0.900966i
$880$	27.2644	−	12.1389i	0.919083	−	0.409202i
$881$	45.3792	+	20.2041i	1.52886	+	0.680694i	0.987139	−	0.159862i	$-0.0511050\pi$
$881$	45.3792	+	20.2041i	1.52886	+	0.680694i	0.541724	+	0.840556i	$0.317772\pi$
$882$	−3.42903	−	3.80833i	−0.115462	−	0.128233i
$883$	−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
$885$	−20.3515	−	22.6027i	−0.684109	−	0.759780i
$886$	8.35519	+	3.71997i	0.280698	+	0.124975i
$887$	−17.6869	+	7.87470i	−0.593867	+	0.264406i	−0.681585	−	0.731739i	$-0.738709\pi$
$887$	−17.6869	+	7.87470i	−0.593867	+	0.264406i	0.0877185	+	0.996145i	$0.472042\pi$
$888$	−9.56308	+	10.6209i	−0.320916	+	0.356413i
$889$	−0.991644	+	9.43486i	−0.0332587	+	0.316435i
$890$	4.89833	−	1.04117i	0.164192	−	0.0349001i
$891$	14.0390	−	43.2075i	0.470323	−	1.44751i
$892$	39.5400	+	8.40448i	1.32390	+	0.281403i
$893$	−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
$896$	−1.05471	−	10.0349i	−0.0352354	−	0.335242i
$897$	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
$902$	1.26573	+	12.0426i	0.0421441	+	0.400975i
$903$	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
$906$	−2.59451	−	0.551481i	−0.0861969	−	0.0183217i
$907$	−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	$0.726468\pi$
$908$	28.4882	−	6.05535i	0.945413	−	0.200954i
$909$	0.522642	−	4.97261i	0.0173350	−	0.164931i
$910$	−3.92324	+	4.35720i	−0.130054	+	0.144440i
$911$	−12.9640	+	5.77194i	−0.429516	+	0.191233i	−0.610096	−	0.792327i	$-0.708869\pi$
$911$	−12.9640	+	5.77194i	−0.429516	+	0.191233i	0.180580	+	0.983560i	$0.442202\pi$
$912$	−6.57624	−	2.92793i	−0.217761	−	0.0969534i
$913$	8.97733	+	9.97033i	0.297106	+	0.329970i
$914$	3.49613	−	2.54009i	0.115642	−	0.0840186i
$915$	18.4164	−	13.3803i	0.608828	−	0.442339i
$916$	5.26357	+	5.84579i	0.173913	+	0.193150i
$917$	17.7378	+	7.89736i	0.585753	+	0.260794i
$918$	−0.329497	+	0.146702i	−0.0108750	+	0.00484188i
$919$	16.4211	−	18.2375i	0.541684	−	0.601601i	−0.408705	−	0.912667i	$-0.634019\pi$
$919$	16.4211	−	18.2375i	0.541684	−	0.601601i	0.950388	+	0.311066i	$0.100686\pi$
$920$	2.36206	−	22.4735i	0.0778749	−	0.740930i
$921$	−36.0908	+	7.67133i	−1.18923	+	0.252779i
$922$	4.61590	−	14.2063i	0.152016	−	0.467859i
$923$	50.1733	+	10.6647i	1.65148	+	0.351032i
$924$	−9.00000	+	15.5885i	−0.296078	+	0.512823i
$925$		0			0
$926$	−1.78747	−	5.50127i	−0.0587399	−	0.180783i
$927$	0.632996	+	6.02255i	0.0207903	+	0.197807i
$928$	−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
$933$	3.95325	+	37.6126i	0.129423	+	1.23138i
$934$	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
$937$	55.0200	+	11.6949i	1.79743	+	0.382055i	0.980785	−	0.195091i	$-0.0625002\pi$
$937$	55.0200	+	11.6949i	1.79743	+	0.382055i	0.816641	+	0.577146i	$0.195833\pi$
$938$	−0.708204	+	2.17963i	−0.0231237	+	0.0711674i
$939$	47.0185	−	9.99408i	1.53439	−	0.326145i
$940$	−1.60700	+	15.2896i	−0.0524147	+	0.498692i
$941$	−34.0138	+	37.7762i	−1.10882	+	1.23147i	−0.138314	+	0.990388i	$0.544168\pi$
$941$	−34.0138	+	37.7762i	−1.10882	+	1.23147i	−0.970505	+	0.241080i	$0.922498\pi$
$942$	3.75935	−	1.67377i	0.122486	−	0.0545344i
$943$	−46.8596	−	20.8632i	−1.52596	−	0.679401i
$944$	−12.5128	−	13.8969i	−0.407257	−	0.452304i
$945$	−3.16228	+	2.29753i	−0.102869	+	0.0747386i
$946$	0.270510	−	0.196537i	0.00879503	−	0.00638997i
$947$	−1.49854	−	1.66430i	−0.0486961	−	0.0540825i	0.718305	−	0.695729i	$-0.244918\pi$
$947$	−1.49854	−	1.66430i	−0.0486961	−	0.0540825i	−0.767001	+	0.641646i	$0.778252\pi$
$948$	43.0505	+	19.1673i	1.39821	+	0.622525i
$949$	26.6067	−	11.8460i	0.863689	−	0.384539i
$950$		0			0
$951$	5.20565	−	49.5284i	0.168805	−	1.60607i
$952$	0.777843	−	0.165336i	0.0252100	−	0.00535856i
$953$	−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	$0.766818\pi$
$954$	4.38120	+	0.931252i	0.141846	+	0.0301504i
$955$	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
$958$	−1.01701	−	9.67619i	−0.0328581	−	0.312624i
$959$	−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
$964$	−2.85497	−	27.1632i	−0.0919523	−	0.874868i
$965$	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	−0.950922	−	0.309432i	$-0.899861\pi$
$967$	−6.45207	+	11.1753i	−0.207485	+	0.359374i	0.743437	+	0.668806i	$0.233194\pi$
$968$	10.0798	+	2.14252i	0.323976	+	0.0688632i
$969$	0.381966	−	1.17557i	0.0122705	−	0.0377648i
$970$	−5.84806	+	1.24304i	−0.187770	+	0.0399118i
$971$	−1.89316	+	18.0122i	−0.0607545	+	0.578040i	0.921222	+	0.389037i	$0.127192\pi$
$971$	−1.89316	+	18.0122i	−0.0607545	+	0.578040i	−0.981977	+	0.189003i	$0.939474\pi$
$972$	−23.8932	+	26.5361i	−0.766374	+	0.851145i
$973$	0.914963	−	0.407368i	0.0293324	−	0.0130596i
$974$	−6.48724	−	2.88831i	−0.207865	−	0.0925473i
$975$		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	$0.537852\pi$
$978$	7.26163	+	8.06486i	0.232201	+	0.257886i
$979$	−22.7248	−	10.1177i	−0.726288	−	0.323364i
$980$	−22.7248	+	10.1177i	−0.725917	+	0.323199i
$981$	−22.0067	+	24.4410i	−0.702621	+	0.780340i
$982$	−0.381921	+	3.63374i	−0.0121876	+	0.115957i
$983$	−2.93900	+	0.624703i	−0.0937394	+	0.0199249i	−0.254543	−	0.967062i	$-0.581925\pi$
$983$	−2.93900	+	0.624703i	−0.0937394	+	0.0199249i	0.160803	+	0.986986i	$0.448592\pi$
$984$	7.77817	−	23.9388i	0.247959	−	0.763140i
$985$	16.1961	+	3.44258i	0.516050	+	0.109690i
$986$	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
$989$	0.148055	+	1.40865i	0.00470787	+	0.0447924i
$990$	−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
$995$	3.44312	+	32.7591i	0.109154	+	1.03853i
$996$	−4.14590	−	12.7598i	−0.131368	−	0.404309i
$997$	−24.3328	−	42.1457i	−0.770628	−	1.33477i	−0.937219	−	0.348741i	$-0.886609\pi$
$997$	−24.3328	−	42.1457i	−0.770628	−	1.33477i	0.166591	−	0.986026i	$-0.446724\pi$
$998$	3.51118	−	6.08154i	0.111144	−	0.192508i
$999$	7.25434	+	1.54196i	0.229517	+	0.0487854i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.1	✓	4	31.20	even	15
961.2.a.h.1.2	yes	4	31.11	odd	30
961.2.c.h.439.1		8	31.27	odd	10
961.2.c.h.439.2		8	31.4	even	5
961.2.c.h.521.1		8	31.24	odd	30
961.2.c.h.521.2		8	31.7	even	15
961.2.d.h.531.1		8	31.9	even	15
961.2.d.h.531.2		8	31.22	odd	30
961.2.d.h.628.1		8	31.10	even	15
961.2.d.h.628.2		8	31.21	odd	30
961.2.d.j.374.1		8	31.26	odd	6
961.2.d.j.374.2		8	31.5	even	3
961.2.d.j.388.1		8	31.13	odd	30
961.2.d.j.388.2		8	31.18	even	15
961.2.g.i.448.1		16	31.19	even	15
961.2.g.i.448.2		16	31.12	odd	30
961.2.g.i.547.1		16	31.8	even	5
961.2.g.i.547.2		16	31.23	odd	10
961.2.g.i.844.1		16	31.17	odd	30
961.2.g.i.844.2		16	31.14	even	15
961.2.g.i.846.1		16	31.29	odd	10
961.2.g.i.846.2		16	31.2	even	5
961.2.g.p.235.1		16	31.16	even	5	inner
961.2.g.p.235.2		16	31.15	odd	10	inner
961.2.g.p.338.1		16	31.3	odd	30	inner
961.2.g.p.338.2		16	31.28	even	15	inner
961.2.g.p.732.1		16	31.25	even	3	inner
961.2.g.p.732.2		16	31.6	odd	6	inner
961.2.g.p.816.1		16	31.30	odd	2	inner
961.2.g.p.816.2		16	1.1	even	1	trivial
8649.2.a.r.1.3		4	93.11	even	30
8649.2.a.r.1.4		4	93.20	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 $\F_{q}$

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} +(0.239187 + 2.27571i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(1.11803 + 1.93649i) q^{5} +(0.437016 - 0.756934i) q^{6} +(0.978148 + 0.207912i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-2.18720 + 0.464905i) q^{9} +(0.0892780 - 0.849423i) q^{10} +(-2.83888 + 3.15290i) q^{11} +(3.87585 - 1.72564i) q^{12} +(-6.27125 - 2.79214i) q^{13} +(-0.255585 - 0.283856i) q^{14} +(-4.13948 + 3.00750i) q^{15} +(-2.54508 + 1.84911i) q^{16} +(-0.361452 - 0.401433i) q^{17} +(0.780261 + 0.347395i) q^{18} +(0.913545 - 0.406737i) q^{19} +(2.77415 - 3.08100i) q^{20} +(-0.239187 + 2.27571i) q^{21} +(1.58513 - 0.336930i) q^{22} +(-2.12132 + 6.52875i) q^{23} +(-3.29500 - 0.700373i) q^{24} +(1.31105 + 2.27080i) q^{26} +(0.540182 + 1.66251i) q^{27} +(-0.193806 - 1.84395i) q^{28} +(-2.99535 - 2.17625i) q^{29} +1.95440 q^{30} +4.14590 q^{32} +(-7.85410 - 5.70634i) q^{33} +(0.0215675 + 0.205201i) q^{34} +(0.690983 + 2.12663i) q^{35} +(2.07295 + 3.59045i) q^{36} +(2.12132 - 3.67423i) q^{37} +(-0.373619 - 0.0794152i) q^{38} +(4.85410 - 14.9394i) q^{39} +(-3.21986 + 0.684403i) q^{40} +(-0.781051 + 7.43120i) q^{41} +(0.584842 - 0.649532i) q^{42} +(0.188493 - 0.0839224i) q^{43} +(7.18621 + 3.19951i) q^{44} +(-3.34565 - 3.71572i) q^{45} +(2.12132 - 1.54123i) q^{46} +(-3.00000 + 2.17963i) q^{47} +(-4.81680 - 5.34959i) q^{48} +(-5.48127 - 2.44042i) q^{49} +(0.827091 - 0.918578i) q^{51} +(-1.33043 + 12.6582i) q^{52} +(5.12959 - 1.09033i) q^{53} +(0.206331 - 0.635021i) q^{54} +(-9.27952 - 1.97242i) q^{55} +(-0.736068 + 1.27491i) q^{56} +(1.14412 + 1.98168i) q^{57} +(0.437016 + 1.34500i) q^{58} +(0.621346 + 5.91171i) q^{59} +(7.67501 + 5.57622i) q^{60} -4.44897 q^{61} -2.23607 q^{63} +(3.80902 + 2.76741i) q^{64} +(-1.60451 - 15.2659i) q^{65} +(1.14590 + 3.52671i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(-0.500776 + 0.867369i) q^{68} +(-15.3649 - 3.26592i) q^{69} +(0.263932 - 0.812299i) q^{70} +(-7.30885 + 1.55354i) q^{71} +(0.344086 - 3.27376i) q^{72} +(-2.83888 + 3.15290i) q^{73} +(-1.48044 + 0.659135i) q^{74} +(-1.24064 - 1.37787i) q^{76} +(-3.43237 + 2.49376i) q^{77} +(-4.85410 + 3.52671i) q^{78} +(7.43229 + 8.25439i) q^{79} +(-6.42628 - 2.86117i) q^{80} +(-9.78243 + 4.35542i) q^{81} +(1.90977 - 2.12101i) q^{82} +(0.330548 - 3.14495i) q^{83} +(4.14993 - 0.882095i) q^{84} +(0.373256 - 1.14876i) q^{85} +(-0.0770892 - 0.0163858i) q^{86} +(4.23607 - 7.33708i) q^{87} +(-3.12287 - 5.40897i) q^{88} +(1.81182 + 5.57622i) q^{89} +(0.199632 + 1.89937i) q^{90} +(-5.55369 - 4.03499i) q^{91} +12.7279 q^{92} +1.41641 q^{94} +(1.80902 + 1.31433i) q^{95} +(0.991644 + 9.43486i) 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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