LMFDB - Embedded newform 961.2.d.j.388.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			388.1
Root			$-0.437016 - 1.34500i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.j.374.1

$q$-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} +(-1.85123 - 1.34500i) q^{3} +(-0.572949 + 1.76336i) q^{4} -2.23607 q^{5} +0.874032 q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.454915 - 1.40008i) q^{8} +(0.690983 + 2.12663i) q^{9} +(0.690983 - 0.502029i) q^{10} +(1.31105 - 4.03499i) q^{11} +(3.43237 - 2.49376i) q^{12} +(-5.55369 - 4.03499i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(4.13948 + 3.00750i) q^{15} +(-2.54508 - 1.84911i) q^{16} +(0.166925 + 0.513743i) q^{17} +(-0.690983 - 0.502029i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(1.28115 - 3.94298i) q^{20} +(1.85123 - 1.34500i) q^{21} +(0.500776 + 1.54123i) q^{22} +(2.12132 + 6.52875i) q^{23} +(-1.04096 + 3.20374i) q^{24} +2.62210 q^{26} +(-0.540182 + 1.66251i) q^{27} +(-1.50000 - 1.08981i) q^{28} +(2.99535 - 2.17625i) q^{29} -1.95440 q^{30} +4.14590 q^{32} +(-7.85410 + 5.70634i) q^{33} +(-0.166925 - 0.121278i) q^{34} +(0.690983 - 2.12663i) q^{35} -4.14590 q^{36} +4.24264 q^{37} +(0.118034 - 0.363271i) q^{38} +(4.85410 + 14.9394i) q^{39} +(1.01722 + 3.13068i) q^{40} +(-6.04508 + 4.39201i) q^{41} +(-0.270091 + 0.831254i) q^{42} +(0.166925 - 0.121278i) q^{43} +(6.36396 + 4.62369i) q^{44} +(-1.54508 - 4.75528i) q^{45} +(-2.12132 - 1.54123i) q^{46} +(-3.00000 - 2.17963i) q^{47} +(2.22449 + 6.84626i) q^{48} +(4.85410 + 3.52671i) q^{49} +(0.381966 - 1.17557i) q^{51} +(10.2971 - 7.48128i) q^{52} +(1.62054 + 4.98752i) q^{53} +(-0.206331 - 0.635021i) q^{54} +(-2.93159 + 9.02251i) q^{55} +1.47214 q^{56} +2.28825 q^{57} +(-0.437016 + 1.34500i) q^{58} +(4.80902 + 3.49396i) q^{59} +(-7.67501 + 5.57622i) q^{60} +4.44897 q^{61} -2.23607 q^{63} +(3.80902 - 2.76741i) q^{64} +(12.4184 + 9.02251i) q^{65} +(1.14590 - 3.52671i) q^{66} +6.00000 q^{67} -1.00155 q^{68} +(4.85410 - 14.9394i) q^{69} +(0.263932 + 0.812299i) q^{70} +(2.30902 + 7.10642i) q^{71} +(2.66312 - 1.93487i) q^{72} +(1.31105 - 4.03499i) q^{73} +(-1.31105 + 0.952532i) q^{74} +(-0.572949 - 1.76336i) q^{76} +(3.43237 + 2.49376i) q^{77} +(-4.85410 - 3.52671i) q^{78} +(-3.43237 - 10.5637i) q^{79} +(5.69098 + 4.13474i) q^{80} +(8.66312 - 6.29412i) q^{81} +(0.881966 - 2.71441i) q^{82} +(-2.55834 + 1.85874i) q^{83} +(1.31105 + 4.03499i) q^{84} +(-0.373256 - 1.14876i) q^{85} +(-0.0243541 + 0.0749541i) q^{86} -8.47214 q^{87} -6.24574 q^{88} +(-1.81182 + 5.57622i) q^{89} +(1.54508 + 1.12257i) q^{90} +(5.55369 - 4.03499i) q^{91} -12.7279 q^{92} +1.41641 q^{94} +(1.80902 - 1.31433i) q^{95} +(-7.67501 - 5.57622i) q^{96} +(-2.16312 + 6.65740i) q^{97} -2.29180 q^{98} +9.48683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 18 q^{4} + 2 q^{7} - 26 q^{8} + 10 q^{9} + 10 q^{10} + 8 q^{14} + 2 q^{16} - 10 q^{18} - 2 q^{19} - 30 q^{20} - 12 q^{28} + 60 q^{32} - 36 q^{33} + 10 q^{35} - 60 q^{36} - 8 q^{38} + 12 q^{39}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 18 * q^4 + 2 * q^7 - 26 * q^8 + 10 * q^9 + 10 * q^10 + 8 * q^14 + 2 * q^16 - 10 * q^18 - 2 * q^19 - 30 * q^20 - 12 * q^28 + 60 * q^32 - 36 * q^33 + 10 * q^35 - 60 * q^36 - 8 * q^38 + 12 * q^39 - 50 * q^40 - 26 * q^41 + 10 * q^45 - 24 * q^47 + 12 * q^49 + 12 * q^51 - 24 * q^56 + 34 * q^59 + 26 * q^64 + 36 * q^66 + 48 * q^67 + 12 * q^69 + 20 * q^70 + 14 * q^71 - 10 * q^72 - 18 * q^76 - 12 * q^78 + 50 * q^80 + 38 * q^81 + 16 * q^82 - 32 * q^87 - 10 * q^90 - 96 * q^94 + 10 * q^95 + 14 * q^97 - 72 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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	−0.691655	−	0.722228i	$-0.743118\pi$
$2$	−0.309017	+	0.224514i	−0.218508	+	0.158755i	0.473147	+	0.880984i	$0.343118\pi$
$3$	−1.85123	−	1.34500i	−1.06881	−	0.776534i	−0.0931103	−	0.995656i	$-0.529681\pi$
$3$	−1.85123	−	1.34500i	−1.06881	−	0.776534i	−0.975698	+	0.219121i	$0.929681\pi$
$4$	−0.572949	+	1.76336i	−0.286475	+	0.881678i
$5$	−2.23607			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$6$	0.874032			0.356822
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	−0.992318	−	0.123716i	$-0.960519\pi$
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	0.875520	+	0.483181i	$0.160519\pi$
$8$	−0.454915	−	1.40008i	−0.160837	−	0.495005i
$9$	0.690983	+	2.12663i	0.230328	+	0.708876i
$10$	0.690983	−	0.502029i	0.218508	−	0.158755i
$11$	1.31105	−	4.03499i	0.395296	−	1.21660i	−0.533435	−	0.845841i	$-0.679099\pi$
$11$	1.31105	−	4.03499i	0.395296	−	1.21660i	0.928731	−	0.370755i	$-0.120901\pi$
$12$	3.43237	−	2.49376i	0.990839	−	0.719887i
$13$	−5.55369	−	4.03499i	−1.54032	−	1.11911i	−0.950137	−	0.311833i	$-0.899057\pi$
$13$	−5.55369	−	4.03499i	−1.54032	−	1.11911i	−0.590179	−	0.807272i	$-0.700943\pi$
$14$	−0.118034	−	0.363271i	−0.0315459	−	0.0970883i
$15$	4.13948	+	3.00750i	1.06881	+	0.776534i
$16$	−2.54508	−	1.84911i	−0.636271	−	0.462278i
$17$	0.166925	+	0.513743i	0.0404853	+	0.124601i	0.969256	−	0.246053i	$-0.0791337\pi$
$17$	0.166925	+	0.513743i	0.0404853	+	0.124601i	−0.928771	+	0.370654i	$0.879134\pi$
$18$	−0.690983	−	0.502029i	−0.162866	−	0.118329i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i	−0.676706	−	0.736253i	$-0.736593\pi$
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i	0.491105	+	0.871100i	$0.336593\pi$
$20$	1.28115	−	3.94298i	0.286475	−	0.881678i
$21$	1.85123	−	1.34500i	0.403971	−	0.293502i
$22$	0.500776	+	1.54123i	0.106766	+	0.328591i
$23$	2.12132	+	6.52875i	0.442326	+	1.36134i	0.885390	+	0.464849i	$0.153891\pi$
$23$	2.12132	+	6.52875i	0.442326	+	1.36134i	−0.443064	+	0.896490i	$0.646109\pi$
$24$	−1.04096	+	3.20374i	−0.212485	+	0.653960i
$25$		0			0
$26$	2.62210			0.514235
$27$	−0.540182	+	1.66251i	−0.103958	+	0.319950i
$28$	−1.50000	−	1.08981i	−0.283473	−	0.205955i
$29$	2.99535	−	2.17625i	0.556223	−	0.404120i	−0.273852	−	0.961772i	$-0.588298\pi$
$29$	2.99535	−	2.17625i	0.556223	−	0.404120i	0.830075	+	0.557652i	$0.188298\pi$
$30$	−1.95440			−0.356822
$31$		0			0
$31$		0			0
$32$	4.14590			0.732898
$33$	−7.85410	+	5.70634i	−1.36722	+	0.993346i
$34$	−0.166925	−	0.121278i	−0.0286274	−	0.0207991i
$35$	0.690983	−	2.12663i	0.116797	−	0.359466i
$36$	−4.14590			−0.690983
$37$	4.24264			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$37$	4.24264			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$38$	0.118034	−	0.363271i	0.0191476	−	0.0589304i
$39$	4.85410	+	14.9394i	0.777278	+	2.39222i
$40$	1.01722	+	3.13068i	0.160837	+	0.495005i
$41$	−6.04508	+	4.39201i	−0.944084	+	0.685917i	−0.949400	−	0.314069i	$-0.898308\pi$
$41$	−6.04508	+	4.39201i	−0.944084	+	0.685917i	0.00531652	+	0.999986i	$0.498308\pi$
$42$	−0.270091	+	0.831254i	−0.0416759	+	0.128265i
$43$	0.166925	−	0.121278i	0.0254559	−	0.0184948i	−0.574985	−	0.818164i	$-0.694992\pi$
$43$	0.166925	−	0.121278i	0.0254559	−	0.0184948i	0.600440	+	0.799669i	$0.294992\pi$
$44$	6.36396	+	4.62369i	0.959403	+	0.697047i
$45$	−1.54508	−	4.75528i	−0.230328	−	0.708876i
$46$	−2.12132	−	1.54123i	−0.312772	−	0.227242i
$47$	−3.00000	−	2.17963i	−0.437595	−	0.317931i	0.347084	−	0.937834i	$-0.387172\pi$
$47$	−3.00000	−	2.17963i	−0.437595	−	0.317931i	−0.784679	+	0.619903i	$0.787172\pi$
$48$	2.22449	+	6.84626i	0.321077	+	0.988173i
$49$	4.85410	+	3.52671i	0.693443	+	0.503816i
$50$		0			0
$51$	0.381966	−	1.17557i	0.0534859	−	0.164613i
$52$	10.2971	−	7.48128i	1.42795	−	1.03747i
$53$	1.62054	+	4.98752i	0.222599	+	0.685089i	0.998526	+	0.0542670i	$0.0172822\pi$
$53$	1.62054	+	4.98752i	0.222599	+	0.685089i	−0.775928	+	0.630822i	$0.782718\pi$
$54$	−0.206331	−	0.635021i	−0.0280781	−	0.0864155i
$55$	−2.93159	+	9.02251i	−0.395296	+	1.21660i
$56$	1.47214			0.196722
$57$	2.28825			0.303086
$58$	−0.437016	+	1.34500i	−0.0573830	+	0.176607i
$59$	4.80902	+	3.49396i	0.626081	+	0.454874i	0.855040	−	0.518562i	$-0.173532\pi$
$59$	4.80902	+	3.49396i	0.626081	+	0.454874i	−0.228960	+	0.973436i	$0.573532\pi$
$60$	−7.67501	+	5.57622i	−0.990839	+	0.719887i
$61$	4.44897			0.569632			0.284816	−	0.958582i	$-0.408067\pi$
$61$	4.44897			0.569632			0.284816	+	0.958582i	$0.408067\pi$
$62$		0			0
$63$	−2.23607			−0.281718
$64$	3.80902	−	2.76741i	0.476127	−	0.345927i
$65$	12.4184	+	9.02251i	1.54032	+	1.11911i
$66$	1.14590	−	3.52671i	0.141050	−	0.434108i
$67$	6.00000			0.733017			0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000			0.733017			0.366508	+	0.930415i	$0.380553\pi$
$68$	−1.00155			−0.121456
$69$	4.85410	−	14.9394i	0.584365	−	1.79849i
$70$	0.263932	+	0.812299i	0.0315459	+	0.0970883i
$71$	2.30902	+	7.10642i	0.274030	+	0.843377i	0.989474	+	0.144708i	$0.0462242\pi$
$71$	2.30902	+	7.10642i	0.274030	+	0.843377i	−0.715445	+	0.698670i	$0.753776\pi$
$72$	2.66312	−	1.93487i	0.313852	−	0.228027i
$73$	1.31105	−	4.03499i	0.153447	−	0.472260i	−0.844554	−	0.535471i	$-0.820134\pi$
$73$	1.31105	−	4.03499i	0.153447	−	0.472260i	0.998000	+	0.0632110i	$0.0201341\pi$
$74$	−1.31105	+	0.952532i	−0.152406	+	0.110730i
$75$		0			0
$76$	−0.572949	−	1.76336i	−0.0657218	−	0.202271i
$77$	3.43237	+	2.49376i	0.391155	+	0.284191i
$78$	−4.85410	−	3.52671i	−0.549619	−	0.399321i
$79$	−3.43237	−	10.5637i	−0.386172	−	1.18851i	−0.935627	−	0.352991i	$-0.885165\pi$
$79$	−3.43237	−	10.5637i	−0.386172	−	1.18851i	0.549455	−	0.835523i	$-0.314835\pi$
$80$	5.69098	+	4.13474i	0.636271	+	0.462278i
$81$	8.66312	−	6.29412i	0.962569	−	0.699347i
$82$	0.881966	−	2.71441i	0.0973969	−	0.299757i
$83$	−2.55834	+	1.85874i	−0.280814	+	0.204023i	−0.719272	−	0.694728i	$-0.755525\pi$
$83$	−2.55834	+	1.85874i	−0.280814	+	0.204023i	0.438458	+	0.898751i	$0.355525\pi$
$84$	1.31105	+	4.03499i	0.143047	+	0.440254i
$85$	−0.373256	−	1.14876i	−0.0404853	−	0.124601i
$86$	−0.0243541	+	0.0749541i	−0.00262617	+	0.00808251i
$87$	−8.47214			−0.908308
$88$	−6.24574			−0.665799
$89$	−1.81182	+	5.57622i	−0.192053	+	0.591078i	0.807945	+	0.589257i	$0.200580\pi$
$89$	−1.81182	+	5.57622i	−0.192053	+	0.591078i	−0.999998	+	0.00182083i	$0.999420\pi$
$90$	1.54508	+	1.12257i	0.162866	+	0.118329i
$91$	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
$96$	−7.67501	−	5.57622i	−0.783327	−	0.569121i
$97$	−2.16312	+	6.65740i	−0.219631	+	0.675956i	0.779161	+	0.626824i	$0.215646\pi$
$97$	−2.16312	+	6.65740i	−0.219631	+	0.675956i	−0.998792	+	0.0491321i	$0.984354\pi$
$98$	−2.29180			−0.231506
$99$	9.48683			0.953463
$100$		0			0
$101$	−0.690983	−	2.12663i	−0.0687554	−	0.211607i	0.910775	−	0.412902i	$-0.135485\pi$
$101$	−0.690983	−	2.12663i	−0.0687554	−	0.211607i	−0.979531	+	0.201295i	$0.935485\pi$
$102$	0.145898	+	0.449028i	0.0144461	+	0.0444604i
$103$	2.19098	−	1.59184i	0.215884	−	0.156849i	−0.474588	−	0.880208i	$-0.657403\pi$
$103$	2.19098	−	1.59184i	0.215884	−	0.156849i	0.690472	+	0.723359i	$0.257403\pi$
$104$	−3.12287	+	9.61121i	−0.306223	+	0.942457i
$105$	−4.13948	+	3.00750i	−0.403971	+	0.293502i
$106$	−1.62054	−	1.17739i	−0.157401	−	0.114359i
$107$	−2.30902	−	7.10642i	−0.223221	−	0.687004i	−0.998467	−	0.0553447i	$-0.982374\pi$
$107$	−2.30902	−	7.10642i	−0.223221	−	0.687004i	0.775246	−	0.631659i	$-0.217626\pi$
$108$	−2.62210	−	1.90506i	−0.252311	−	0.183315i
$109$	11.8992	+	8.64527i	1.13974	+	0.828066i	0.987082	−	0.160214i	$-0.0512183\pi$
$109$	11.8992	+	8.64527i	1.13974	+	0.828066i	0.152653	+	0.988280i	$0.451218\pi$
$110$	−1.11977	−	3.44629i	−0.106766	−	0.328591i
$111$	−7.85410	−	5.70634i	−0.745478	−	0.541622i
$112$	2.54508	−	1.84911i	0.240488	−	0.174725i
$113$	−4.39919	+	13.5393i	−0.413841	+	1.27367i	0.499443	+	0.866347i	$0.333538\pi$
$113$	−4.39919	+	13.5393i	−0.413841	+	1.27367i	−0.913284	+	0.407324i	$0.866462\pi$
$114$	−0.707107	+	0.513743i	−0.0662266	+	0.0481165i
$115$	−4.74342	−	14.5987i	−0.442326	−	1.36134i
$116$	2.12132	+	6.52875i	0.196960	+	0.606179i
$117$	4.74342	−	14.5987i	0.438529	−	1.34965i
$118$	−2.27051			−0.209017
$119$	−0.540182			−0.0495184
$120$	2.32765	−	7.16377i	0.212485	−	0.653960i
$121$	−5.66312	−	4.11450i	−0.514829	−	0.374045i
$122$	−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
$127$	−7.67501	−	5.57622i	−0.681047	−	0.494810i	0.192658	−	0.981266i	$-0.438289\pi$
$127$	−7.67501	−	5.57622i	−0.681047	−	0.494810i	−0.873705	+	0.486456i	$0.838289\pi$
$128$	−3.11803	+	9.59632i	−0.275598	+	0.848203i
$129$	−0.472136			−0.0415693
$130$	−5.86319			−0.514235
$131$	−6.00000	+	18.4661i	−0.524222	+	1.61339i	0.241626	+	0.970369i	$0.422319\pi$
$131$	−6.00000	+	18.4661i	−0.524222	+	1.61339i	−0.765848	+	0.643021i	$0.777681\pi$
$132$	−5.56231	−	17.1190i	−0.484137	−	1.49002i
$133$	−0.309017	−	0.951057i	−0.0267952	−	0.0824671i
$134$	−1.85410	+	1.34708i	−0.160170	+	0.116370i
$135$	1.20788	−	3.71748i	0.103958	−	0.319950i
$136$	0.643347	−	0.467419i	0.0551666	−	0.0400808i
$137$	−5.55369	−	4.03499i	−0.474484	−	0.344733i	0.324702	−	0.945816i	$-0.394736\pi$
$137$	−5.55369	−	4.03499i	−0.474484	−	0.344733i	−0.799186	+	0.601084i	$0.794736\pi$
$138$	1.85410	+	5.70634i	0.157832	+	0.485756i
$139$	−0.810272	−	0.588697i	−0.0687264	−	0.0499327i	0.552892	−	0.833253i	$-0.313524\pi$
$139$	−0.810272	−	0.588697i	−0.0687264	−	0.0499327i	−0.621618	+	0.783321i	$0.713524\pi$
$140$	3.35410	+	2.43690i	0.283473	+	0.205955i
$141$	2.62210	+	8.06998i	0.220820	+	0.679615i
$142$	−2.30902	−	1.67760i	−0.193768	−	0.140781i
$143$	−23.5623	+	17.1190i	−1.97038	+	1.43156i
$144$	2.17376	−	6.69015i	0.181147	−	0.557513i
$145$	−6.69781	+	4.86624i	−0.556223	+	0.404120i
$146$	0.500776	+	1.54123i	0.0414445	+	0.127553i
$147$	−4.24264	−	13.0575i	−0.349927	−	1.07696i
$148$	−2.43082	+	7.48128i	−0.199812	+	0.614958i
$149$	13.4164			1.09911			0.549557	−	0.835456i	$-0.314796\pi$
$149$	13.4164			1.09911			0.549557	+	0.835456i	$0.314796\pi$
$150$		0			0
$151$	0.937792	−	2.88623i	0.0763164	−	0.234878i	−0.905620	−	0.424091i	$-0.860594\pi$
$151$	0.937792	−	2.88623i	0.0763164	−	0.234878i	0.981936	+	0.189213i	$0.0605937\pi$
$152$	1.19098	+	0.865300i	0.0966015	+	0.0701851i
$153$	−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	−0.425322	−	0.905042i	$-0.639839\pi$
$157$	3.80902	−	2.76741i	0.303993	−	0.220864i	0.729315	+	0.684179i	$0.239839\pi$
$158$	3.43237	+	2.49376i	0.273065	+	0.198393i
$159$	3.70820	−	11.4127i	0.294080	−	0.905084i
$160$	−9.27051			−0.732898
$161$	−6.86474			−0.541017
$162$	−1.26393	+	3.88998i	−0.0993039	+	0.305626i
$163$	−3.83688	−	11.8087i	−0.300528	−	0.924929i	−0.981308	−	0.192442i	$-0.938359\pi$
$163$	−3.83688	−	11.8087i	−0.300528	−	0.924929i	0.680781	−	0.732487i	$-0.261641\pi$
$164$	−4.28115	−	13.1760i	−0.334302	−	1.02888i
$165$	17.5623	−	12.7598i	1.36722	−	0.993346i
$166$	0.373256	−	1.14876i	0.0289703	−	0.0891614i
$167$	5.99070	−	4.35250i	0.463575	−	0.336807i	−0.331357	−	0.943505i	$-0.607507\pi$
$167$	5.99070	−	4.35250i	0.463575	−	0.336807i	0.794932	+	0.606699i	$0.207507\pi$
$168$	−2.72526	−	1.98002i	−0.210258	−	0.152762i
$169$	10.5451	+	32.4544i	0.811160	+	2.49649i
$170$	0.373256	+	0.271187i	0.0286274	+	0.0207991i
$171$	−1.80902	−	1.31433i	−0.138339	−	0.100509i
$172$	0.118217	+	0.363835i	0.00901397	+	0.0277422i
$173$	−14.5623	−	10.5801i	−1.10715	−	0.804393i	−0.124939	−	0.992164i	$-0.539873\pi$
$173$	−14.5623	−	10.5801i	−1.10715	−	0.804393i	−0.982213	+	0.187772i	$0.939873\pi$
$174$	2.61803	−	1.90211i	0.198473	−	0.144199i
$175$		0			0
$176$	−10.7979	+	7.84512i	−0.813921	+	0.591348i
$177$	−4.20323	−	12.9362i	−0.315934	−	0.972346i
$178$	−0.692055	−	2.12993i	−0.0518717	−	0.159645i
$179$	5.07727	−	15.6262i	0.379493	−	1.16796i	−0.560904	−	0.827881i	$-0.689546\pi$
$179$	5.07727	−	15.6262i	0.379493	−	1.16796i	0.940397	−	0.340078i	$-0.110454\pi$
$180$	9.27051			0.690983
$181$	18.1784			1.35119			0.675597	−	0.737271i	$-0.263886\pi$
$181$	18.1784			1.35119			0.675597	+	0.737271i	$0.263886\pi$
$182$	−0.810272	+	2.49376i	−0.0600614	+	0.184850i
$183$	−8.23607	−	5.98385i	−0.608828	−	0.442339i
$184$	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
$189$	−1.41421	−	1.02749i	−0.102869	−	0.0747386i
$190$	−0.263932	+	0.812299i	−0.0191476	+	0.0589304i
$191$	14.2361			1.03009			0.515043	−	0.857164i	$-0.327776\pi$
$191$	14.2361			1.03009			0.515043	+	0.857164i	$0.327776\pi$
$192$	−10.7735			−0.777512
$193$	−2.25329	+	6.93491i	−0.162195	+	0.499186i	−0.998819	−	0.0485928i	$-0.984526\pi$
$193$	−2.25329	+	6.93491i	−0.162195	+	0.499186i	0.836623	+	0.547779i	$0.184526\pi$
$194$	−0.826238	−	2.54290i	−0.0593204	−	0.182569i
$195$	−10.8541	−	33.4055i	−0.777278	−	2.39222i
$196$	−9.00000	+	6.53888i	−0.642857	+	0.467063i
$197$	−2.28825	+	7.04250i	−0.163031	+	0.501757i	−0.998886	−	0.0471932i	$-0.984972\pi$
$197$	−2.28825	+	7.04250i	−0.163031	+	0.501757i	0.835855	+	0.548950i	$0.184972\pi$
$198$	−2.93159	+	2.12993i	−0.208339	+	0.151367i
$199$	11.9176	+	8.65868i	0.844820	+	0.613798i	0.923713	−	0.383086i	$-0.125139\pi$
$199$	11.9176	+	8.65868i	0.844820	+	0.613798i	−0.0788931	+	0.996883i	$0.525139\pi$
$200$		0			0
$201$	−11.1074	−	8.06998i	−0.783454	−	0.569213i
$202$	0.690983	+	0.502029i	0.0486174	+	0.0353226i
$203$	1.14412	+	3.52125i	0.0803017	+	0.247143i
$204$	1.85410	+	1.34708i	0.129813	+	0.0943147i
$205$	13.5172	−	9.82084i	0.944084	−	0.685917i
$206$	−0.319660	+	0.983813i	−0.0222718	+	0.0685455i
$207$	−12.4184	+	9.02251i	−0.863140	+	0.627108i
$208$	6.67346	+	20.5388i	0.462721	+	1.42411i
$209$	1.31105	+	4.03499i	0.0906871	+	0.279106i
$210$	0.603941	−	1.85874i	0.0416759	−	0.128265i
$211$	−5.00000			−0.344214			−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000			−0.344214			−0.172107	+	0.985078i	$0.555058\pi$
$212$	−9.72327			−0.667797
$213$	5.28360	−	16.2612i	0.362026	−	1.11420i
$214$	2.30902	+	1.67760i	0.157841	+	0.114678i
$215$	−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
$220$	−14.2302	−	10.3389i	−0.959403	−	0.697047i
$221$	1.14590	−	3.52671i	0.0770814	−	0.237232i
$222$	3.70820			0.248878
$223$	−21.8021			−1.45998			−0.729988	−	0.683460i	$-0.760474\pi$
$223$	−21.8021			−1.45998			−0.729988	+	0.683460i	$0.760474\pi$
$224$	−1.28115	+	3.94298i	−0.0856006	+	0.263452i
$225$		0			0
$226$	−1.68034	−	5.17155i	−0.111775	−	0.344007i
$227$	−12.7082	+	9.23305i	−0.843473	+	0.612819i	−0.923339	−	0.383987i	$-0.874551\pi$
$227$	−12.7082	+	9.23305i	−0.843473	+	0.612819i	0.0798656	+	0.996806i	$0.474551\pi$
$228$	−1.31105	+	4.03499i	−0.0868263	+	0.267224i
$229$	−3.43237	+	2.49376i	−0.226817	+	0.164792i	−0.695390	−	0.718632i	$-0.744768\pi$
$229$	−3.43237	+	2.49376i	−0.226817	+	0.164792i	0.468573	+	0.883425i	$0.344768\pi$
$230$	4.74342	+	3.44629i	0.312772	+	0.227242i
$231$	−3.00000	−	9.23305i	−0.197386	−	0.607490i
$232$	−4.40957	−	3.20374i	−0.289502	−	0.210336i
$233$	3.66312	+	2.66141i	0.239979	+	0.174355i	0.701274	−	0.712892i	$-0.252615\pi$
$233$	3.66312	+	2.66141i	0.239979	+	0.174355i	−0.461295	+	0.887247i	$0.652615\pi$
$234$	1.81182	+	5.57622i	0.118443	+	0.364529i
$235$	6.70820	+	4.87380i	0.437595	+	0.317931i
$236$	−8.91641	+	6.47815i	−0.580409	+	0.421692i
$237$	−7.85410	+	24.1724i	−0.510179	+	1.57017i
$238$	0.166925	−	0.121278i	0.0108202	−	0.00786130i
$239$	−5.05291	−	15.5513i	−0.326846	−	1.00593i	−0.970601	−	0.240696i	$-0.922624\pi$
$239$	−5.05291	−	15.5513i	−0.326846	−	1.00593i	0.643755	−	0.765232i	$-0.277376\pi$
$240$	−4.97410	−	15.3087i	−0.321077	−	0.988173i
$241$	4.55214	−	14.0100i	0.293229	−	0.902466i	−0.690582	−	0.723254i	$-0.742645\pi$
$241$	4.55214	−	14.0100i	0.293229	−	0.902466i	0.983811	−	0.179211i	$-0.0573546\pi$
$242$	2.67376			0.171876
$243$	−19.2588			−1.23545
$244$	−2.54903	+	7.84512i	−0.163185	+	0.502232i
$245$	−10.8541	−	7.88597i	−0.693443	−	0.503816i
$246$	−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
$251$	19.2194	+	13.9637i	1.21312	+	0.881382i	0.995510	−	0.0946545i	$-0.0301746\pi$
$251$	19.2194	+	13.9637i	1.21312	+	0.881382i	0.217608	+	0.976036i	$0.430175\pi$
$252$	1.28115	−	3.94298i	0.0807050	−	0.248385i
$253$	29.1246			1.83105
$254$	3.62365			0.227368
$255$	−0.854102	+	2.62866i	−0.0534859	+	0.164613i
$256$	1.71885	+	5.29007i	0.107428	+	0.330629i
$257$	7.39919	+	22.7724i	0.461549	+	1.42050i	0.863272	+	0.504739i	$0.168411\pi$
$257$	7.39919	+	22.7724i	0.461549	+	1.42050i	−0.401723	+	0.915761i	$0.631589\pi$
$258$	0.145898	−	0.106001i	0.00908321	−	0.00659934i
$259$	−1.31105	+	4.03499i	−0.0814646	+	0.250722i
$260$	−23.0250	+	16.7287i	−1.42795	+	1.03747i
$261$	6.69781	+	4.86624i	0.414584	+	0.301213i
$262$	−2.29180	−	7.05342i	−0.141588	−	0.435762i
$263$	−2.18508	−	1.58755i	−0.134738	−	0.0978928i	0.518375	−	0.855153i	$-0.326537\pi$
$263$	−2.18508	−	1.58755i	−0.134738	−	0.0978928i	−0.653113	+	0.757261i	$0.726537\pi$
$264$	11.5623	+	8.40051i	0.711611	+	0.517015i
$265$	−3.62365	−	11.1524i	−0.222599	−	0.685089i
$266$	0.309017	+	0.224514i	0.0189470	+	0.0137658i
$267$	10.8541	−	7.88597i	0.664260	−	0.482613i
$268$	−3.43769	+	10.5801i	−0.209991	+	0.646285i
$269$	−11.9814	+	8.70500i	−0.730519	+	0.530753i	−0.889728	−	0.456492i	$-0.849106\pi$
$269$	−11.9814	+	8.70500i	−0.730519	+	0.530753i	0.159208	+	0.987245i	$0.449106\pi$
$270$	0.461370	+	1.41995i	0.0280781	+	0.0864155i
$271$	−8.67656	−	26.7037i	−0.527064	−	1.62213i	−0.760199	−	0.649690i	$-0.774899\pi$
$271$	−8.67656	−	26.7037i	−0.527064	−	1.62213i	0.233135	−	0.972444i	$-0.425101\pi$
$272$	0.525130	−	1.61618i	0.0318407	−	0.0979955i
$273$	−15.7082			−0.950704
$274$	2.62210			0.158407
$275$		0			0
$276$	23.5623	+	17.1190i	1.41828	+	1.03044i
$277$	−15.8508	+	11.5163i	−0.952382	+	0.691946i	−0.951369	−	0.308054i	$-0.900322\pi$
$277$	−15.8508	+	11.5163i	−0.952382	+	0.691946i	−0.00101288	+	0.999999i	$0.500322\pi$
$278$	0.382559			0.0229443
$279$		0			0
$280$	−3.29180			−0.196722
$281$	25.3713	−	18.4333i	1.51353	−	1.09964i	0.548944	−	0.835859i	$-0.315030\pi$
$281$	25.3713	−	18.4333i	1.51353	−	1.09964i	0.964582	−	0.263782i	$-0.0849699\pi$
$282$	−2.62210	−	1.90506i	−0.156144	−	0.113445i
$283$	7.41641	−	22.8254i	0.440860	−	1.35683i	−0.446101	−	0.894982i	$-0.647188\pi$
$283$	7.41641	−	22.8254i	0.440860	−	1.35683i	0.886961	−	0.461844i	$-0.152812\pi$
$284$	−13.8541			−0.822090
$285$	−5.11667			−0.303086
$286$	3.43769	−	10.5801i	0.203275	−	0.625616i
$287$	−2.30902	−	7.10642i	−0.136297	−	0.419479i
$288$	2.86475	+	8.81678i	0.168807	+	0.519534i
$289$	13.5172	−	9.82084i	0.795131	−	0.577696i
$290$	0.977198	−	3.00750i	0.0573830	−	0.176607i
$291$	12.9586	−	9.41498i	0.759647	−	0.551916i
$292$	6.36396	+	4.62369i	0.372423	+	0.270581i
$293$	−4.85410	−	14.9394i	−0.283580	−	0.872768i	−0.986821	−	0.161817i	$-0.948265\pi$
$293$	−4.85410	−	14.9394i	−0.283580	−	0.872768i	0.703241	−	0.710951i	$-0.251735\pi$
$294$	4.24264	+	3.08246i	0.247436	+	0.179773i
$295$	−10.7533	−	7.81272i	−0.626081	−	0.454874i
$296$	−1.93004	−	5.94006i	−0.112181	−	0.345259i
$297$	6.00000	+	4.35926i	0.348155	+	0.252950i
$298$	−4.14590	+	3.01217i	−0.240165	+	0.174490i
$299$	14.5623	−	44.8182i	0.842160	−	2.59190i
$300$		0			0
$301$	0.0637598	+	0.196232i	0.00367505	+	0.0113106i
$302$	0.358205	+	1.10244i	0.0206124	+	0.0634383i
$303$	−1.58114	+	4.86624i	−0.0908341	+	0.279558i
$304$	3.14590			0.180430
$305$	−9.94820			−0.569632
$306$	0.142571	−	0.438789i	0.00815025	−	0.0250839i
$307$	13.0451	+	9.47781i	0.744522	+	0.540927i	0.894124	−	0.447819i	$-0.147799\pi$
$307$	13.0451	+	9.47781i	0.744522	+	0.540927i	−0.149602	+	0.988746i	$0.547799\pi$
$308$	−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
$313$	16.9949	+	12.3475i	0.960609	+	0.697924i	0.953292	−	0.302050i	$-0.0976708\pi$
$313$	16.9949	+	12.3475i	0.960609	+	0.697924i	0.00731728	+	0.999973i	$0.497671\pi$
$314$	−0.555728	+	1.71036i	−0.0313616	+	0.0965209i
$315$	5.00000			0.281718
$316$	20.5942			1.15851
$317$	6.72542	−	20.6987i	0.377737	−	1.16256i	−0.563876	−	0.825860i	$-0.690690\pi$
$317$	6.72542	−	20.6987i	0.377737	−	1.16256i	0.941613	−	0.336697i	$-0.109310\pi$
$318$	1.41641	+	4.35926i	0.0794282	+	0.244455i
$319$	−4.85410	−	14.9394i	−0.271778	−	0.836445i
$320$	−8.51722	+	6.18812i	−0.476127	+	0.345927i
$321$	−5.28360	+	16.2612i	−0.294902	+	0.907614i
$322$	2.12132	−	1.54123i	0.118217	−	0.0858894i
$323$	−0.437016	−	0.317511i	−0.0243162	−	0.0176668i
$324$	6.13525	+	18.8824i	0.340847	+	1.04902i
$325$		0			0
$326$	3.83688	+	2.78766i	0.212505	+	0.154394i
$327$	−10.4003	−	32.0087i	−0.575136	−	1.77009i
$328$	8.89919	+	6.46564i	0.491375	+	0.357005i
$329$	3.00000	−	2.17963i	0.165395	−	0.120167i
$330$	−2.56231	+	7.88597i	−0.141050	+	0.434108i
$331$	20.7368	−	15.0662i	1.13980	−	0.828111i	0.152706	−	0.988272i	$-0.451201\pi$
$331$	20.7368	−	15.0662i	1.13980	−	0.828111i	0.987091	+	0.160161i	$0.0512013\pi$
$332$	−1.81182	−	5.57622i	−0.0994368	−	0.306035i
$333$	2.93159	+	9.02251i	0.160650	+	0.494431i
$334$	−0.874032	+	2.68999i	−0.0478249	+	0.147190i
$335$	−13.4164			−0.733017
$336$	−7.19859			−0.392715
$337$	−1.81182	+	5.57622i	−0.0986963	+	0.303756i	−0.988199	−	0.153173i	$-0.951051\pi$
$337$	−1.81182	+	5.57622i	−0.0986963	+	0.303756i	0.889503	+	0.456929i	$0.151051\pi$
$338$	−10.5451	−	7.66145i	−0.573577	−	0.416728i
$339$	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
$344$	−0.245737	−	0.178538i	−0.0132492	−	0.00962613i
$345$	−10.8541	+	33.4055i	−0.584365	+	1.79849i
$346$	6.87539			0.369623
$347$	25.8384			1.38708			0.693539	−	0.720419i	$-0.256050\pi$
$347$	25.8384			1.38708			0.693539	+	0.720419i	$0.256050\pi$
$348$	4.85410	−	14.9394i	0.260207	−	0.800835i
$349$	1.85410	+	5.70634i	0.0992478	+	0.305453i	0.988337	−	0.152280i	$-0.0486615\pi$
$349$	1.85410	+	5.70634i	0.0992478	+	0.305453i	−0.889090	+	0.457733i	$0.848662\pi$
$350$		0			0
$351$	9.70820	−	7.05342i	0.518186	−	0.376484i
$352$	5.43547	−	16.7287i	0.289712	−	0.891641i
$353$	−12.8554	+	9.34003i	−0.684226	+	0.497119i	−0.874757	−	0.484562i	$-0.838979\pi$
$353$	−12.8554	+	9.34003i	−0.684226	+	0.497119i	0.190531	+	0.981681i	$0.438979\pi$
$354$	4.20323	+	3.05383i	0.223399	+	0.162309i
$355$	−5.16312	−	15.8904i	−0.274030	−	0.843377i
$356$	−8.79478	−	6.38978i	−0.466122	−	0.338658i
$357$	1.00000	+	0.726543i	0.0529256	+	0.0384527i
$358$	1.93934	+	5.96869i	0.102497	+	0.315455i
$359$	−7.89919	−	5.73910i	−0.416903	−	0.302898i	0.359487	−	0.933150i	$-0.382952\pi$
$359$	−7.89919	−	5.73910i	−0.416903	−	0.302898i	−0.776391	+	0.630252i	$0.782952\pi$
$360$	−5.95492	+	4.32650i	−0.313852	+	0.228027i
$361$	−5.56231	+	17.1190i	−0.292753	+	0.901001i
$362$	−5.61745	+	4.08132i	−0.295247	+	0.214509i
$363$	4.94975	+	15.2338i	0.259794	+	0.799565i
$364$	3.93314	+	12.1050i	0.206153	+	0.634473i
$365$	−2.93159	+	9.02251i	−0.153447	+	0.472260i
$366$	3.88854			0.203257
$367$	−12.3153			−0.642851			−0.321426	−	0.946935i	$-0.604162\pi$
$367$	−12.3153			−0.642851			−0.321426	+	0.946935i	$0.604162\pi$
$368$	6.67346	−	20.5388i	0.347878	−	1.07066i
$369$	−13.5172	−	9.82084i	−0.703678	−	0.511252i
$370$	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
$375$	−20.6974	−	15.0375i	−1.06881	−	0.776534i
$376$	−1.68692	+	5.19180i	−0.0869961	+	0.267747i
$377$	−25.4164			−1.30901
$378$	0.667701			0.0343428
$379$	−6.00000	+	18.4661i	−0.308199	+	0.948540i	0.670265	+	0.742122i	$0.266181\pi$
$379$	−6.00000	+	18.4661i	−0.308199	+	0.948540i	−0.978464	+	0.206418i	$0.933819\pi$
$380$	1.28115	+	3.94298i	0.0657218	+	0.202271i
$381$	6.70820	+	20.6457i	0.343672	+	1.05771i
$382$	−4.39919	+	3.19620i	−0.225082	+	0.163532i
$383$	−5.88754	+	18.1200i	−0.300839	+	0.925888i	0.680358	+	0.732880i	$0.261824\pi$
$383$	−5.88754	+	18.1200i	−0.300839	+	0.925888i	−0.981197	+	0.193008i	$0.938176\pi$
$384$	18.6792	−	13.5712i	0.953220	−	0.692555i
$385$	−7.67501	−	5.57622i	−0.391155	−	0.284191i
$386$	−0.860680	−	2.64890i	−0.0438074	−	0.134825i
$387$	0.373256	+	0.271187i	0.0189737	+	0.0137852i
$388$	−10.5000	−	7.62870i	−0.533057	−	0.387288i
$389$	10.4397	+	32.1300i	0.529313	+	1.62906i	0.755627	+	0.655002i	$0.227332\pi$
$389$	10.4397	+	32.1300i	0.529313	+	1.62906i	−0.226314	+	0.974054i	$0.572668\pi$
$390$	10.8541	+	7.88597i	0.549619	+	0.399321i
$391$	−3.00000	+	2.17963i	−0.151717	+	0.110229i
$392$	2.72949	−	8.40051i	0.137860	−	0.424290i
$393$	35.9442	−	26.1150i	1.81315	−	1.31733i
$394$	−0.874032	−	2.68999i	−0.0440331	−	0.135520i
$395$	7.67501	+	23.6212i	0.386172	+	1.18851i
$396$	−5.43547	+	16.7287i	−0.273143	+	0.840647i
$397$	1.29180			0.0648334			0.0324167	−	0.999474i	$-0.489680\pi$
$397$	1.29180			0.0648334			0.0324167	+	0.999474i	$0.489680\pi$
$398$	−5.62675			−0.282044
$399$	−0.707107	+	2.17625i	−0.0353996	+	0.108949i
$400$		0			0
$401$	2.99535	−	2.17625i	0.149581	−	0.108677i	−0.510478	−	0.859891i	$-0.670531\pi$
$401$	2.99535	−	2.17625i	0.149581	−	0.108677i	0.660059	+	0.751214i	$0.270531\pi$
$402$	5.24419			0.261557
$403$		0			0
$404$	4.14590			0.206266
$405$	−19.3713	+	14.0741i	−0.962569	+	0.699347i
$406$	−1.14412	−	0.831254i	−0.0567819	−	0.0412544i
$407$	5.56231	−	17.1190i	0.275713	−	0.848558i
$408$	−1.81966			−0.0900866
$409$	−17.3531			−0.858057			−0.429028	−	0.903291i	$-0.641144\pi$
$409$	−17.3531			−0.858057			−0.429028	+	0.903291i	$0.641144\pi$
$410$	−1.97214	+	6.06961i	−0.0973969	+	0.299757i
$411$	4.85410	+	14.9394i	0.239435	+	0.736906i
$412$	1.55166	+	4.77553i	0.0764449	+	0.235273i
$413$	−4.80902	+	3.49396i	−0.236636	+	0.171926i
$414$	1.81182	−	5.57622i	0.0890463	−	0.274056i
$415$	5.72061	−	4.15627i	0.280814	−	0.204023i
$416$	−23.0250	−	16.7287i	−1.12889	−	0.820190i
$417$	0.708204	+	2.17963i	0.0346809	+	0.106737i
$418$	−1.31105	−	0.952532i	−0.0641255	−	0.0465899i
$419$	15.0451	+	10.9309i	0.735000	+	0.534009i	0.891141	−	0.453726i	$-0.149905\pi$
$419$	15.0451	+	10.9309i	0.735000	+	0.534009i	−0.156141	+	0.987735i	$0.549905\pi$
$420$	−2.93159	−	9.02251i	−0.143047	−	0.440254i
$421$	0.336881	+	0.244758i	0.0164186	+	0.0119288i	0.595964	−	0.803011i	$-0.296770\pi$
$421$	0.336881	+	0.244758i	0.0164186	+	0.0119288i	−0.579546	+	0.814940i	$0.696770\pi$
$422$	1.54508	−	1.12257i	0.0752136	−	0.0546458i
$423$	2.56231	−	7.88597i	0.124584	−	0.383429i
$424$	6.24574	−	4.53780i	0.303320	−	0.220375i
$425$		0			0
$426$	2.01815	+	6.21124i	0.0977799	+	0.300936i
$427$	−1.37481	+	4.23122i	−0.0665316	+	0.204763i
$428$	13.8541			0.669663
$429$	66.6443			3.21762
$430$	0.0544574	−	0.167602i	0.00262617	−	0.00808251i
$431$	0.0901699	+	0.0655123i	0.00434333	+	0.00315562i	0.589955	−	0.807436i	$-0.299146\pi$
$431$	0.0901699	+	0.0655123i	0.00434333	+	0.00315562i	−0.585611	+	0.810592i	$0.699146\pi$
$432$	4.44897	−	3.23237i	0.214051	−	0.155517i
$433$	21.5958			1.03783			0.518913	−	0.854827i	$-0.326337\pi$
$433$	21.5958			1.03783			0.518913	+	0.854827i	$0.326337\pi$
$434$		0			0
$435$	18.9443			0.908308
$436$	−22.0623	+	16.0292i	−1.05659	+	0.767660i
$437$	−5.55369	−	4.03499i	−0.265669	−	0.193020i
$438$	1.14590	−	3.52671i	0.0547531	−	0.168513i
$439$	−25.0000			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$440$	13.9659			0.665799
$441$	−4.14590	+	12.7598i	−0.197424	+	0.607608i
$442$	0.437694	+	1.34708i	0.0208190	+	0.0640742i
$443$	7.39919	+	22.7724i	0.351546	+	1.08195i	0.957985	+	0.286817i	$0.0925973\pi$
$443$	7.39919	+	22.7724i	0.351546	+	1.08195i	−0.606439	+	0.795130i	$0.707403\pi$
$444$	14.5623	−	10.5801i	0.691096	−	0.502111i
$445$	4.05136	−	12.4688i	0.192053	−	0.591078i
$446$	6.73722	−	4.89487i	0.319016	−	0.231779i
$447$	−24.8369	−	18.0450i	−1.17474	−	0.853501i
$448$	1.45492	+	4.47777i	0.0687383	+	0.211555i
$449$	34.1324	+	24.7986i	1.61081	+	1.17032i	0.860893	+	0.508786i	$0.169905\pi$
$449$	34.1324	+	24.7986i	1.61081	+	1.17032i	0.749915	+	0.661535i	$0.230095\pi$
$450$		0			0
$451$	9.79633	+	30.1500i	0.461291	+	1.41971i
$452$	−21.3541	−	15.5147i	−1.00441	−	0.729748i
$453$	−5.61803	+	4.08174i	−0.263958	+	0.191777i
$454$	1.85410	−	5.70634i	0.0870173	−	0.267812i
$455$	−12.4184	+	9.02251i	−0.582185	+	0.422982i
$456$	−1.04096	−	3.20374i	−0.0487473	−	0.150029i
$457$	3.49613	+	10.7600i	0.163542	+	0.503330i	0.998926	−	0.0463365i	$-0.0147546\pi$
$457$	3.49613	+	10.7600i	0.163542	+	0.503330i	−0.835384	+	0.549667i	$0.814755\pi$
$458$	0.500776	−	1.54123i	0.0233997	−	0.0720169i
$459$	−0.944272			−0.0440748
$460$	28.4605			1.32698
$461$	−12.0846	+	37.1925i	−0.562835	+	1.73223i	0.111464	+	0.993768i	$0.464446\pi$
$461$	−12.0846	+	37.1925i	−0.562835	+	1.73223i	−0.674299	+	0.738459i	$0.735554\pi$
$462$	3.00000	+	2.17963i	0.139573	+	0.101405i
$463$	−12.2515	+	8.90124i	−0.569376	+	0.413676i	−0.834878	−	0.550435i	$-0.814462\pi$
$463$	−12.2515	+	8.90124i	−0.569376	+	0.413676i	0.265503	+	0.964110i	$0.414462\pi$
$464$	−11.6476			−0.540724
$465$		0			0
$466$	−1.72949			−0.0801171
$467$	−12.6631	+	9.20029i	−0.585979	+	0.425739i	−0.840875	−	0.541230i	$-0.817959\pi$
$467$	−12.6631	+	9.20029i	−0.585979	+	0.425739i	0.254895	+	0.966969i	$0.417959\pi$
$468$	23.0250	+	16.7287i	1.06433	+	0.773283i
$469$	−1.85410	+	5.70634i	−0.0856145	+	0.263494i
$470$	−3.16718			−0.146091
$471$	−10.7735			−0.496418
$472$	2.70414	−	8.32248i	0.124468	−	0.383073i
$473$	−0.270510	−	0.832544i	−0.0124381	−	0.0382804i
$474$	−3.00000	−	9.23305i	−0.137795	−	0.424088i
$475$		0			0
$476$	0.309496	−	0.952532i	0.0141857	−	0.0436592i
$477$	−9.48683	+	6.89259i	−0.434372	+	0.315590i
$478$	5.05291	+	3.67116i	0.231115	+	0.167915i
$479$	7.87132	+	24.2254i	0.359650	+	1.10689i	0.953264	+	0.302139i	$0.0977006\pi$
$479$	7.87132	+	24.2254i	0.359650	+	1.10689i	−0.593614	+	0.804750i	$0.702299\pi$
$480$	17.1618	+	12.4688i	0.783327	+	0.569121i
$481$	−23.5623	−	17.1190i	−1.07435	−	0.780560i
$482$	1.73876	+	5.35136i	0.0791984	+	0.243748i
$483$	12.7082	+	9.23305i	0.578243	+	0.420118i
$484$	10.5000	−	7.62870i	0.477273	−	0.346759i
$485$	4.83688	−	14.8864i	0.219631	−	0.675956i
$486$	5.95130	−	4.32387i	0.269956	−	0.196135i
$487$	5.74497	+	17.6812i	0.260329	+	0.801211i	0.992733	+	0.120340i	$0.0383986\pi$
$487$	5.74497	+	17.6812i	0.260329	+	0.801211i	−0.732403	+	0.680871i	$0.761601\pi$
$488$	−2.02390	−	6.22894i	−0.0916178	−	0.281971i
$489$	−8.77973	+	27.0212i	−0.397033	+	1.22194i
$490$	5.12461			0.231506
$491$	−9.56564			−0.431691			−0.215846	−	0.976427i	$-0.569251\pi$
$491$	−9.56564			−0.431691			−0.215846	+	0.976427i	$0.569251\pi$
$492$	−9.79633	+	30.1500i	−0.441653	+	1.35927i
$493$	1.61803	+	1.17557i	0.0728726	+	0.0529450i
$494$	−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
$499$	−14.8736	−	10.8063i	−0.665834	−	0.483756i	0.202794	−	0.979221i	$-0.434998\pi$
$499$	−14.8736	−	10.8063i	−0.665834	−	0.483756i	−0.868628	+	0.495465i	$0.834998\pi$
$500$	−6.40576	+	19.7149i	−0.286475	+	0.881678i
$501$	−16.9443			−0.757014
$502$	−9.07417			−0.405000
$503$	0.892609	−	2.74717i	0.0397995	−	0.122490i	−0.929183	−	0.369621i	$-0.879488\pi$
$503$	0.892609	−	2.74717i	0.0397995	−	0.122490i	0.968982	+	0.247130i	$0.0794876\pi$
$504$	1.01722	+	3.13068i	0.0453106	+	0.139452i
$505$	1.54508	+	4.75528i	0.0687554	+	0.211607i
$506$	−9.00000	+	6.53888i	−0.400099	+	0.290689i
$507$	24.1297	−	74.2637i	1.07164	−	3.29817i
$508$	14.2302	−	10.3389i	0.631365	−	0.458714i
$509$	3.86938	+	2.81127i	0.171507	+	0.124607i	0.670228	−	0.742156i	$-0.266196\pi$
$509$	3.86938	+	2.81127i	0.171507	+	0.124607i	−0.498720	+	0.866763i	$0.666196\pi$
$510$	−0.326238	−	1.00406i	−0.0144461	−	0.0444604i
$511$	3.43237	+	2.49376i	0.151839	+	0.110318i
$512$	−18.0451	−	13.1105i	−0.797488	−	0.579409i
$513$	−0.540182	−	1.66251i	−0.0238496	−	0.0734015i
$514$	−7.39919	−	5.37582i	−0.326364	−	0.237117i
$515$	−4.89919	+	3.55947i	−0.215884	+	0.156849i
$516$	0.270510	−	0.832544i	0.0119085	−	0.0366507i
$517$	−12.7279	+	9.24738i	−0.559773	+	0.406699i
$518$	−0.500776	−	1.54123i	−0.0220028	−	0.0677177i
$519$	12.7279	+	39.1725i	0.558694	+	1.71948i
$520$	6.98295	−	21.4913i	0.306223	−	0.942457i
$521$	13.4164			0.587784			0.293892	−	0.955839i	$-0.405049\pi$
$521$	13.4164			0.587784			0.293892	+	0.955839i	$0.405049\pi$
$522$	−3.16228			−0.138409
$523$	8.98606	−	27.6562i	0.392933	−	1.20932i	−0.537627	−	0.843183i	$-0.680679\pi$
$523$	8.98606	−	27.6562i	0.392933	−	1.20932i	0.930560	−	0.366140i	$-0.119321\pi$
$524$	−29.1246	−	21.1603i	−1.27231	−	0.924391i
$525$		0			0
$526$	1.03165			0.0449823
$527$		0			0
$528$	30.5410			1.32913
$529$	−19.5172	+	14.1801i	−0.848575	+	0.616526i
$530$	3.62365	+	2.63273i	0.157401	+	0.114359i
$531$	−4.10739	+	12.6412i	−0.178246	+	0.548583i
$532$	1.85410			0.0803855
$533$	51.2942			2.22180
$534$	−1.58359	+	4.87380i	−0.0685287	+	0.210910i
$535$	5.16312	+	15.8904i	0.223221	+	0.687004i
$536$	−2.72949	−	8.40051i	−0.117896	−	0.362847i
$537$	−30.4164	+	22.0988i	−1.31256	+	0.953634i
$538$	1.74806	−	5.37999i	0.0753644	−	0.231948i
$539$	20.5942	−	14.9626i	0.887055	−	0.644484i
$540$	5.86319	+	4.25985i	0.252311	+	0.183315i
$541$	−8.60081	−	26.4706i	−0.369778	−	1.13806i	−0.946935	−	0.321426i	$-0.895838\pi$
$541$	−8.60081	−	26.4706i	−0.369778	−	1.13806i	0.577157	−	0.816633i	$-0.304162\pi$
$542$	8.67656	+	6.30389i	0.372690	+	0.270775i
$543$	−33.6525	−	24.4500i	−1.44417	−	1.04925i
$544$	0.692055	+	2.12993i	0.0296716	+	0.0913199i
$545$	−26.6074	−	19.3314i	−1.13974	−	0.828066i
$546$	4.85410	−	3.52671i	0.207736	−	0.150929i
$547$	−7.54508	+	23.2214i	−0.322605	+	0.992875i	0.649906	+	0.760015i	$0.274808\pi$
$547$	−7.54508	+	23.2214i	−0.322605	+	0.992875i	−0.972510	+	0.232860i	$0.925192\pi$
$548$	10.2971	−	7.48128i	0.439871	−	0.319585i
$549$	3.07416	+	9.46130i	0.131202	+	0.403799i
$550$		0			0
$551$	−1.14412	+	3.52125i	−0.0487413	+	0.150010i
$552$	−23.1246			−0.984249
$553$	11.1074			0.472334
$554$	2.31260	−	7.11745i	0.0982529	−	0.302391i
$555$	17.5623	+	12.7598i	0.745478	+	0.541622i
$556$	1.50233	−	1.09150i	0.0637129	−	0.0462901i
$557$	−23.2951			−0.987046			−0.493523	−	0.869733i	$-0.664291\pi$
$557$	−23.2951			−0.987046			−0.493523	+	0.869733i	$0.664291\pi$
$558$		0			0
$559$	−1.41641			−0.0599077
$560$	−5.69098	+	4.13474i	−0.240488	+	0.174725i
$561$	−4.24264	−	3.08246i	−0.179124	−	0.130142i
$562$	−3.70163	+	11.3924i	−0.156144	+	0.480561i
$563$	14.2361			0.599979			0.299989	−	0.953943i	$-0.403017\pi$
$563$	14.2361			0.599979			0.299989	+	0.953943i	$0.403017\pi$
$564$	−15.7326			−0.662461
$565$	9.83688	−	30.2748i	0.413841	−	1.27367i
$566$	2.83282	+	8.71851i	0.119072	+	0.366466i
$567$	3.30902	+	10.1841i	0.138966	+	0.427692i
$568$	8.89919	−	6.46564i	0.373402	−	0.271292i
$569$	−9.48683	+	29.1975i	−0.397709	+	1.22402i	0.529123	+	0.848545i	$0.322521\pi$
$569$	−9.48683	+	29.1975i	−0.397709	+	1.22402i	−0.926832	+	0.375477i	$0.877479\pi$
$570$	1.58114	−	1.14876i	0.0662266	−	0.0481165i
$571$	−5.55369	−	4.03499i	−0.232415	−	0.168859i	0.465483	−	0.885057i	$-0.345881\pi$
$571$	−5.55369	−	4.03499i	−0.232415	−	0.168859i	−0.697897	+	0.716198i	$0.745881\pi$
$572$	−16.6869	−	51.3571i	−0.697715	−	2.14735i
$573$	−26.3542	−	19.1475i	−1.10096	−	0.799897i
$574$	2.30902	+	1.67760i	0.0963765	+	0.0700216i
$575$		0			0
$576$	8.51722	+	6.18812i	0.354884	+	0.257838i
$577$	24.2705	−	17.6336i	1.01039	−	0.734095i	0.0461028	−	0.998937i	$-0.485320\pi$
$577$	24.2705	−	17.6336i	1.01039	−	0.734095i	0.964292	+	0.264842i	$0.0853198\pi$
$578$	−1.97214	+	6.06961i	−0.0820300	+	0.252463i
$579$	13.4988	−	9.80744i	0.560991	−	0.407583i
$580$	−4.74342	−	14.5987i	−0.196960	−	0.606179i
$581$	−0.977198	−	3.00750i	−0.0405410	−	0.124772i
$582$	−1.89064	+	5.81878i	−0.0783694	+	0.241196i
$583$	22.2492			0.921469
$584$	−6.24574			−0.258451
$585$	−10.6066	+	32.6438i	−0.438529	+	1.34965i
$586$	4.85410	+	3.52671i	0.200521	+	0.145687i
$587$	−33.3221	+	24.2099i	−1.37535	+	0.999251i	−0.378054	+	0.925784i	$0.623407\pi$
$587$	−33.3221	+	24.2099i	−1.37535	+	0.999251i	−0.997298	+	0.0734679i	$0.976593\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	5.07701			0.209017
$591$	13.7082	−	9.95959i	0.563880	−	0.409683i
$592$	−10.7979	−	7.84512i	−0.443790	−	0.322432i
$593$	−5.30902	+	16.3395i	−0.218015	+	0.670982i	0.780911	+	0.624643i	$0.214755\pi$
$593$	−5.30902	+	16.3395i	−0.218015	+	0.670982i	−0.998926	+	0.0463389i	$0.985245\pi$
$594$	−2.83282			−0.116232
$595$	1.20788			0.0495184
$596$	−7.68692	+	23.6579i	−0.314868	+	0.969065i
$597$	−10.4164	−	32.0584i	−0.426315	−	1.31206i
$598$	5.56231	+	17.1190i	0.227460	+	0.700049i
$599$	−19.3713	+	14.0741i	−0.791491	+	0.575052i	−0.908406	−	0.418090i	$-0.862700\pi$
$599$	−19.3713	+	14.0741i	−0.791491	+	0.575052i	0.116915	+	0.993142i	$0.462700\pi$
$600$		0			0
$601$	−7.03166	+	5.10880i	−0.286827	+	0.208392i	−0.721890	−	0.692008i	$-0.756726\pi$
$601$	−7.03166	+	5.10880i	−0.286827	+	0.208392i	0.435062	+	0.900400i	$0.356726\pi$
$602$	−0.0637598	−	0.0463242i	−0.00259865	−	0.00188803i
$603$	4.14590	+	12.7598i	0.168834	+	0.519618i
$604$	4.55214	+	3.30732i	0.185224	+	0.134573i
$605$	12.6631	+	9.20029i	0.514829	+	0.374045i
$606$	−0.603941	−	1.85874i	−0.0245334	−	0.0755062i
$607$	20.3262	+	14.7679i	0.825017	+	0.599410i	0.918145	−	0.396244i	$-0.129687\pi$
$607$	20.3262	+	14.7679i	0.825017	+	0.599410i	−0.0931285	+	0.995654i	$0.529687\pi$
$608$	−3.35410	+	2.43690i	−0.136027	+	0.0988293i
$609$	2.61803	−	8.05748i	0.106088	−	0.326506i
$610$	3.07416	−	2.23351i	0.124469	−	0.0904322i
$611$	7.86629	+	24.2099i	0.318236	+	0.979430i
$612$	−0.692055	−	2.12993i	−0.0279747	−	0.0860972i
$613$	−11.5444	+	35.5300i	−0.466274	+	1.43504i	0.391100	+	0.920348i	$0.372095\pi$
$613$	−11.5444	+	35.5300i	−0.466274	+	1.43504i	−0.857374	+	0.514695i	$0.827905\pi$
$614$	−6.15905			−0.248559
$615$	−38.2325			−1.54168
$616$	1.93004	−	5.94006i	0.0777636	−	0.239332i
$617$	38.1246	+	27.6992i	1.53484	+	1.11513i	0.953471	+	0.301485i	$0.0974824\pi$
$617$	38.1246	+	27.6992i	1.53484	+	1.11513i	0.581368	+	0.813641i	$0.302518\pi$
$618$	1.91499	−	1.39132i	0.0770322	−	0.0559671i
$619$	−21.5958			−0.868007			−0.434003	−	0.900911i	$-0.642899\pi$
$619$	−21.5958			−0.868007			−0.434003	+	0.900911i	$0.642899\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	−5.10739	+	3.71074i	−0.204788	+	0.148787i
$623$	−4.74342	−	3.44629i	−0.190041	−	0.138073i
$624$	15.2705	−	46.9978i	0.611310	−	1.88142i
$625$	−25.0000			−1.00000
$626$	−8.02391			−0.320700
$627$	3.00000	−	9.23305i	0.119808	−	0.368733i
$628$	2.69756	+	8.30224i	0.107644	+	0.331295i
$629$	0.708204	+	2.17963i	0.0282379	+	0.0869074i
$630$	−1.54508	+	1.12257i	−0.0615577	+	0.0447243i
$631$	−1.43857	+	4.42746i	−0.0572685	+	0.176254i	−0.975599	−	0.219560i	$-0.929538\pi$
$631$	−1.43857	+	4.42746i	−0.0572685	+	0.176254i	0.918330	+	0.395815i	$0.129538\pi$
$632$	−13.2287	+	9.61121i	−0.526209	+	0.382313i
$633$	9.25615	+	6.72499i	0.367899	+	0.267294i
$634$	2.56888	+	7.90621i	0.102023	+	0.313996i
$635$	17.1618	+	12.4688i	0.681047	+	0.494810i
$636$	18.0000	+	13.0778i	0.713746	+	0.518567i
$637$	−12.7279	−	39.1725i	−0.504299	−	1.55207i
$638$	4.85410	+	3.52671i	0.192176	+	0.139624i
$639$	−13.5172	+	9.82084i	−0.534733	+	0.388506i
$640$	6.97214	−	21.4580i	0.275598	−	0.848203i
$641$	6.86474	−	4.98752i	0.271141	−	0.196995i	−0.443903	−	0.896075i	$-0.646407\pi$
$641$	6.86474	−	4.98752i	0.271141	−	0.196995i	0.715044	+	0.699079i	$0.246407\pi$
$642$	−2.01815	−	6.21124i	−0.0796502	−	0.245138i
$643$	−7.30175	−	22.4725i	−0.287953	−	0.886228i	−0.985498	−	0.169687i	$-0.945724\pi$
$643$	−7.30175	−	22.4725i	−0.287953	−	0.886228i	0.697545	−	0.716541i	$-0.254276\pi$
$644$	3.93314	−	12.1050i	0.154988	−	0.477003i
$645$	1.05573			0.0415693
$646$	0.206331			0.00811798
$647$	5.91189	−	18.1949i	0.232421	−	0.715317i	−0.765033	−	0.643992i	$-0.777277\pi$
$647$	5.91189	−	18.1949i	0.232421	−	0.715317i	0.997453	−	0.0713252i	$-0.0227228\pi$
$648$	−12.7533	−	9.26581i	−0.500997	−	0.363995i
$649$	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	−0.477478	−	0.878644i	$-0.658449\pi$
$653$	5.38197	−	3.91023i	0.210613	−	0.153019i	0.688091	+	0.725625i	$0.258449\pi$
$654$	10.4003	+	7.55624i	0.406683	+	0.295472i
$655$	13.4164	−	41.2915i	0.524222	−	1.61339i
$656$	23.5066			0.917778
$657$	9.48683			0.370117
$658$	−0.437694	+	1.34708i	−0.0170631	+	0.0525148i
$659$	14.5795	+	44.8712i	0.567938	+	1.74793i	0.659057	+	0.752093i	$0.270955\pi$
$659$	14.5795	+	44.8712i	0.567938	+	1.74793i	−0.0911197	+	0.995840i	$0.529045\pi$
$660$	12.4377	+	38.2793i	0.484137	+	1.49002i
$661$	37.0795	−	26.9399i	1.44223	−	1.04784i	0.454655	−	0.890668i	$-0.349763\pi$
$661$	37.0795	−	26.9399i	1.44223	−	1.04784i	0.987571	−	0.157171i	$-0.0502375\pi$
$662$	−3.02546	+	9.31140i	−0.117588	+	0.361898i
$663$	−6.86474	+	4.98752i	−0.266604	+	0.193699i
$664$	3.76622	+	2.73632i	0.146158	+	0.106190i
$665$	0.690983	+	2.12663i	0.0267952	+	0.0824671i
$666$	−2.93159	−	2.12993i	−0.113597	−	0.0825330i
$667$	20.5623	+	14.9394i	0.796176	+	0.578455i
$668$	4.24264	+	13.0575i	0.164153	+	0.505210i
$669$	40.3607	+	29.3238i	1.56043	+	1.13372i
$670$	4.14590	−	3.01217i	0.160170	−	0.116370i
$671$	5.83282	−	17.9516i	0.225173	−	0.693012i
$672$	7.67501	−	5.57622i	0.296070	−	0.215107i
$673$	−2.30330	−	7.08882i	−0.0887856	−	0.273254i	0.896799	−	0.442439i	$-0.145887\pi$
$673$	−2.30330	−	7.08882i	−0.0887856	−	0.273254i	−0.985584	+	0.169185i	$0.945887\pi$
$674$	−0.692055	−	2.12993i	−0.0266570	−	0.0820417i
$675$		0			0
$676$	−63.2705			−2.43348
$677$	−21.2132			−0.815290			−0.407645	−	0.913141i	$-0.633650\pi$
$677$	−21.2132			−0.815290			−0.407645	+	0.913141i	$0.633650\pi$
$678$	−3.84503	+	11.8338i	−0.147668	+	0.454474i
$679$	−5.66312	−	4.11450i	−0.217331	−	0.157900i
$680$	−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
$685$	12.4184	+	9.02251i	0.474484	+	0.344733i
$686$	1.53444	−	4.72253i	0.0585853	−	0.180307i
$687$	9.70820			0.370391
$688$	−0.649096			−0.0247466
$689$	11.1246	−	34.2380i	0.423814	−	1.30437i
$690$	−4.14590	−	12.7598i	−0.157832	−	0.485756i
$691$	−6.66970	−	20.5272i	−0.253727	−	0.780892i	−0.994078	−	0.108671i	$-0.965340\pi$
$691$	−6.66970	−	20.5272i	−0.253727	−	0.780892i	0.740351	−	0.672221i	$-0.234660\pi$
$692$	27.0000	−	19.6166i	1.02639	−	0.745713i
$693$	−2.93159	+	9.02251i	−0.111362	+	0.342737i
$694$	−7.98451	+	5.80108i	−0.303088	+	0.220206i
$695$	1.81182	+	1.31637i	0.0687264	+	0.0499327i
$696$	3.85410	+	11.8617i	0.146089	+	0.449617i
$697$	−3.26544	−	2.37248i	−0.123687	−	0.0898642i
$698$	−1.85410	−	1.34708i	−0.0701788	−	0.0509879i
$699$	−3.20168	−	9.85377i	−0.121099	−	0.372704i
$700$		0			0
$701$	−22.3713	+	16.2537i	−0.844953	+	0.613894i	−0.923750	−	0.382996i	$-0.874892\pi$
$701$	−22.3713	+	16.2537i	−0.844953	+	0.613894i	0.0787967	+	0.996891i	$0.474892\pi$
$702$	−1.41641	+	4.35926i	−0.0534589	+	0.164529i
$703$	−3.43237	+	2.49376i	−0.129454	+	0.0940540i
$704$	−6.17268	−	18.9976i	−0.232642	−	0.715998i
$705$	−5.86319	−	18.0450i	−0.220820	−	0.679615i
$706$	1.87558	−	5.77245i	0.0705885	−	0.217249i
$707$	2.23607			0.0840960
$708$	25.2194			0.947803
$709$	4.86163	−	14.9626i	0.182582	−	0.561931i	−0.817316	−	0.576190i	$-0.804539\pi$
$709$	4.86163	−	14.9626i	0.182582	−	0.561931i	0.999898	+	0.0142588i	$0.00453887\pi$
$710$	5.16312	+	3.75123i	0.193768	+	0.140781i
$711$	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
$716$	24.6456	+	17.9061i	0.921048	+	0.669181i
$717$	−11.5623	+	35.5851i	−0.431802	+	1.32895i
$718$	3.72949			0.139183
$719$	−9.10427			−0.339532			−0.169766	−	0.985484i	$-0.554301\pi$
$719$	−9.10427			−0.339532			−0.169766	+	0.985484i	$0.554301\pi$
$720$	−4.86068	+	14.9596i	−0.181147	+	0.557513i
$721$	0.836881	+	2.57565i	0.0311671	+	0.0959224i
$722$	−2.12461	−	6.53888i	−0.0790699	−	0.243352i
$723$	−27.2705	+	19.8132i	−1.01420	+	0.736860i
$724$	−10.4153	+	32.0551i	−0.387082	+	1.19132i
$725$		0			0
$726$	−4.94975	−	3.59620i	−0.183702	−	0.133468i
$727$	−1.10739	−	3.40820i	−0.0410709	−	0.126403i	0.928419	−	0.371535i	$-0.121169\pi$
$727$	−1.10739	−	3.40820i	−0.0410709	−	0.126403i	−0.969490	+	0.245132i	$0.921169\pi$
$728$	−8.17578	−	5.94006i	−0.303015	−	0.220153i
$729$	9.66312	+	7.02067i	0.357893	+	0.260025i
$730$	−1.11977	−	3.44629i	−0.0414445	−	0.127553i
$731$	0.0901699	+	0.0655123i	0.00333506	+	0.00242306i
$732$	15.2705	−	11.0947i	0.564414	−	0.410071i
$733$	3.83688	−	11.8087i	0.141718	−	0.436164i	−0.854856	−	0.518865i	$-0.826355\pi$
$733$	3.83688	−	11.8087i	0.141718	−	0.436164i	0.996574	+	0.0827009i	$0.0263546\pi$
$734$	3.80562	−	2.76495i	0.140468	−	0.102056i
$735$	9.48683	+	29.1975i	0.349927	+	1.07696i
$736$	8.79478	+	27.0675i	0.324180	+	0.997723i
$737$	7.86629	−	24.2099i	0.289758	−	0.891785i
$738$	6.38197			0.234923
$739$	−25.6622			−0.943998			−0.471999	−	0.881599i	$-0.656467\pi$
$739$	−25.6622			−0.943998			−0.471999	+	0.881599i	$0.656467\pi$
$740$	5.43547	−	16.7287i	0.199812	−	0.614958i
$741$	−12.7082	−	9.23305i	−0.466848	−	0.339185i
$742$	1.62054	−	1.17739i	0.0594921	−	0.0432235i
$743$	−1.69936			−0.0623433			−0.0311717	−	0.999514i	$-0.509924\pi$
$743$	−1.69936			−0.0623433			−0.0311717	+	0.999514i	$0.509924\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	7.01722	−	5.09831i	0.256919	−	0.186662i
$747$	−5.72061	−	4.15627i	−0.209306	−	0.152070i
$748$	−1.31308	+	4.04125i	−0.0480110	+	0.147763i
$749$	7.47214			0.273026
$750$	9.77198			0.356822
$751$	9.12868	−	28.0952i	0.333110	−	1.02521i	−0.634535	−	0.772894i	$-0.718808\pi$
$751$	9.12868	−	28.0952i	0.333110	−	1.02521i	0.967645	−	0.252314i	$-0.0811915\pi$
$752$	3.60488	+	11.0947i	0.131456	+	0.404581i
$753$	−16.7984	−	51.7001i	−0.612167	−	1.88406i
$754$	7.85410	−	5.70634i	0.286030	−	0.207813i
$755$	−2.09697	+	6.45380i	−0.0763164	+	0.234878i
$756$	2.62210	−	1.90506i	0.0953647	−	0.0692865i
$757$	15.5169	+	11.2737i	0.563973	+	0.409750i	0.832911	−	0.553407i	$-0.186673\pi$
$757$	15.5169	+	11.2737i	0.563973	+	0.409750i	−0.268938	+	0.963158i	$0.586673\pi$
$758$	−2.29180	−	7.05342i	−0.0832418	−	0.256192i
$759$	−53.9163	−	39.1725i	−1.95704	−	1.42187i
$760$	−2.66312	−	1.93487i	−0.0966015	−	0.0701851i
$761$	0.692055	+	2.12993i	0.0250870	+	0.0772098i	0.962816	−	0.270157i	$-0.0870757\pi$
$761$	0.692055	+	2.12993i	0.0250870	+	0.0772098i	−0.937729	+	0.347367i	$0.887076\pi$
$762$	−6.70820	−	4.87380i	−0.243013	−	0.176559i
$763$	−11.8992	+	8.64527i	−0.430779	+	0.312980i
$764$	−8.15654	+	25.1033i	−0.295093	+	0.908204i
$765$	2.18508	−	1.58755i	0.0790017	−	0.0573981i
$766$	−2.24884	−	6.92122i	−0.0812539	−	0.250074i
$767$	−12.6097	−	38.8087i	−0.455310	−	1.40130i
$768$	3.93314	−	12.1050i	0.141925	−	0.436801i
$769$	13.8754			0.500359			0.250180	−	0.968199i	$-0.419510\pi$
$769$	13.8754			0.500359			0.250180	+	0.968199i	$0.419510\pi$
$770$	3.62365			0.130587
$771$	16.9312	−	52.1087i	0.609761	−	1.87665i

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.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.224514i) q^{2} +(-1.85123 - 1.34500i) q^{3} +(-0.572949 + 1.76336i) q^{4} -2.23607 q^{5} +0.874032 q^{6} +(-0.309017 + 0.951057i) q^{7} +(-0.454915 - 1.40008i) q^{8} +(0.690983 + 2.12663i) q^{9} +(0.690983 - 0.502029i) q^{10} +(1.31105 - 4.03499i) q^{11} +(3.43237 - 2.49376i) q^{12} +(-5.55369 - 4.03499i) q^{13} +(-0.118034 - 0.363271i) q^{14} +(4.13948 + 3.00750i) q^{15} +(-2.54508 - 1.84911i) q^{16} +(0.166925 + 0.513743i) q^{17} +(-0.690983 - 0.502029i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(1.28115 - 3.94298i) q^{20} +(1.85123 - 1.34500i) q^{21} +(0.500776 + 1.54123i) q^{22} +(2.12132 + 6.52875i) q^{23} +(-1.04096 + 3.20374i) q^{24} +2.62210 q^{26} +(-0.540182 + 1.66251i) q^{27} +(-1.50000 - 1.08981i) q^{28} +(2.99535 - 2.17625i) q^{29} -1.95440 q^{30} +4.14590 q^{32} +(-7.85410 + 5.70634i) q^{33} +(-0.166925 - 0.121278i) q^{34} +(0.690983 - 2.12663i) q^{35} -4.14590 q^{36} +4.24264 q^{37} +(0.118034 - 0.363271i) q^{38} +(4.85410 + 14.9394i) q^{39} +(1.01722 + 3.13068i) q^{40} +(-6.04508 + 4.39201i) q^{41} +(-0.270091 + 0.831254i) q^{42} +(0.166925 - 0.121278i) q^{43} +(6.36396 + 4.62369i) q^{44} +(-1.54508 - 4.75528i) q^{45} +(-2.12132 - 1.54123i) q^{46} +(-3.00000 - 2.17963i) q^{47} +(2.22449 + 6.84626i) q^{48} +(4.85410 + 3.52671i) q^{49} +(0.381966 - 1.17557i) q^{51} +(10.2971 - 7.48128i) q^{52} +(1.62054 + 4.98752i) q^{53} +(-0.206331 - 0.635021i) q^{54} +(-2.93159 + 9.02251i) q^{55} +1.47214 q^{56} +2.28825 q^{57} +(-0.437016 + 1.34500i) q^{58} +(4.80902 + 3.49396i) q^{59} +(-7.67501 + 5.57622i) q^{60} +4.44897 q^{61} -2.23607 q^{63} +(3.80902 - 2.76741i) q^{64} +(12.4184 + 9.02251i) q^{65} +(1.14590 - 3.52671i) q^{66} +6.00000 q^{67} -1.00155 q^{68} +(4.85410 - 14.9394i) q^{69} +(0.263932 + 0.812299i) q^{70} +(2.30902 + 7.10642i) q^{71} +(2.66312 - 1.93487i) q^{72} +(1.31105 - 4.03499i) q^{73} +(-1.31105 + 0.952532i) q^{74} +(-0.572949 - 1.76336i) q^{76} +(3.43237 + 2.49376i) q^{77} +(-4.85410 - 3.52671i) q^{78} +(-3.43237 - 10.5637i) q^{79} +(5.69098 + 4.13474i) q^{80} +(8.66312 - 6.29412i) q^{81} +(0.881966 - 2.71441i) q^{82} +(-2.55834 + 1.85874i) q^{83} +(1.31105 + 4.03499i) q^{84} +(-0.373256 - 1.14876i) q^{85} +(-0.0243541 + 0.0749541i) q^{86} -8.47214 q^{87} -6.24574 q^{88} +(-1.81182 + 5.57622i) q^{89} +(1.54508 + 1.12257i) q^{90} +(5.55369 - 4.03499i) q^{91} -12.7279 q^{92} +1.41641 q^{94} +(1.80902 - 1.31433i) q^{95} +(-7.67501 - 5.57622i) q^{96} +(-2.16312 + 6.65740i) q^{97} -2.29180 q^{98} +9.48683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 18 q^{4} + 2 q^{7} - 26 q^{8} + 10 q^{9} + 10 q^{10} + 8 q^{14} + 2 q^{16} - 10 q^{18} - 2 q^{19} - 30 q^{20} - 12 q^{28} + 60 q^{32} - 36 q^{33} + 10 q^{35} - 60 q^{36} - 8 q^{38} + 12 q^{39}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 18 * q^4 + 2 * q^7 - 26 * q^8 + 10 * q^9 + 10 * q^10 + 8 * q^14 + 2 * q^16 - 10 * q^18 - 2 * q^19 - 30 * q^20 - 12 * q^28 + 60 * q^32 - 36 * q^33 + 10 * q^35 - 60 * q^36 - 8 * q^38 + 12 * q^39 - 50 * q^40 - 26 * q^41 + 10 * q^45 - 24 * q^47 + 12 * q^49 + 12 * q^51 - 24 * q^56 + 34 * q^59 + 26 * q^64 + 36 * q^66 + 48 * q^67 + 12 * q^69 + 20 * q^70 + 14 * q^71 - 10 * q^72 - 18 * q^76 - 12 * q^78 + 50 * q^80 + 38 * q^81 + 16 * q^82 - 32 * q^87 - 10 * q^90 - 96 * q^94 + 10 * q^95 + 14 * q^97 - 72 * q^98

Introduction

L-functions

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