LMFDB - Embedded newform 925.2.bb.e.326.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			326.15
Character	$\chi$	$=$	925.326
Dual form			925.2.bb.e.576.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.768352 + 2.11103i) q^{2} +(1.65672 + 0.602996i) q^{3} +(-2.33399 + 1.95845i) q^{4} +3.96069i q^{6} +(0.185690 + 1.05310i) q^{7} +(-2.03660 - 1.17583i) q^{8} +(0.0829802 + 0.0696287i) q^{9} +(-0.107723 + 0.186582i) q^{11} +(-5.04770 + 1.83721i) q^{12} +(3.81491 + 4.54644i) q^{13} +(-2.08045 + 1.20115i) q^{14} +(-0.140756 + 0.798269i) q^{16} +(2.80586 - 3.34390i) q^{17} +(-0.0832301 + 0.228673i) q^{18} +(-1.34424 + 3.69328i) q^{19} +(-0.327380 + 1.85667i) q^{21} +(-0.476650 - 0.0840463i) q^{22} +(-2.75237 + 1.58908i) q^{23} +(-2.66505 - 3.17608i) q^{24} +(-6.66646 + 11.5467i) q^{26} +(-2.54908 - 4.41513i) q^{27} +(-2.49585 - 2.09427i) q^{28} +(-3.22377 - 1.86124i) q^{29} -2.43489i q^{31} +(-6.42519 + 1.13293i) q^{32} +(-0.290976 + 0.244158i) q^{33} +(9.21496 + 3.35397i) q^{34} -0.330039 q^{36} +(-3.68154 - 4.84213i) q^{37} -8.82947 q^{38} +(3.57876 + 9.83255i) q^{39} +(1.58232 - 1.32773i) q^{41} +(-4.17102 + 0.735463i) q^{42} -9.40443i q^{43} +(-0.113987 - 0.646452i) q^{44} +(-5.46938 - 4.58935i) q^{46} +(5.39131 + 9.33803i) q^{47} +(-0.714547 + 1.23763i) q^{48} +(5.50330 - 2.00304i) q^{49} +(6.66489 - 3.84797i) q^{51} +(-17.8079 - 3.14002i) q^{52} +(1.08310 - 6.14257i) q^{53} +(7.36188 - 8.77355i) q^{54} +(0.860094 - 2.36309i) q^{56} +(-4.45407 + 5.30815i) q^{57} +(1.45215 - 8.23556i) q^{58} +(2.70230 + 0.476488i) q^{59} +(5.71443 + 6.81019i) q^{61} +(5.14012 - 1.87085i) q^{62} +(-0.0579175 + 0.100316i) q^{63} +(-6.51787 - 11.2893i) q^{64} +(-0.738996 - 0.426660i) q^{66} +(1.59627 + 9.05289i) q^{67} +13.2998i q^{68} +(-5.51811 + 0.972991i) q^{69} +(-1.81248 - 0.659688i) q^{71} +(-0.0871258 - 0.239376i) q^{72} -0.242447 q^{73} +(7.39317 - 11.4923i) q^{74} +(-4.09565 - 11.2527i) q^{76} +(-0.216494 - 0.0787973i) q^{77} +(-18.0071 + 15.1097i) q^{78} +(-1.58386 + 0.279276i) q^{79} +(-1.61723 - 9.17175i) q^{81} +(4.01865 + 2.32017i) q^{82} +(-1.09454 - 0.918429i) q^{83} +(-2.87208 - 4.97460i) q^{84} +(19.8530 - 7.22591i) q^{86} +(-4.21856 - 5.02748i) q^{87} +(0.438779 - 0.253329i) q^{88} +(9.15190 + 1.61373i) q^{89} +(-4.07947 + 4.86173i) q^{91} +(3.31186 - 9.09926i) q^{92} +(1.46823 - 4.03393i) q^{93} +(-15.5704 + 18.5561i) q^{94} +(-11.3279 - 1.99741i) q^{96} +(13.9866 - 8.07516i) q^{97} +(8.45694 + 10.0786i) q^{98} +(-0.0219304 + 0.00798202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	0.768352	+	2.11103i	0.543307	+	1.49272i	0.842588	+	0.538558i	$0.181031\pi$
$2$	0.768352	+	2.11103i	0.543307	+	1.49272i	−0.299282	+	0.954165i	$0.596747\pi$
$3$	1.65672	+	0.602996i	0.956507	+	0.348140i	0.772664	−	0.634815i	$-0.218924\pi$
$3$	1.65672	+	0.602996i	0.956507	+	0.348140i	0.183843	+	0.982956i	$0.441146\pi$
$4$	−2.33399	+	1.95845i	−1.16699	+	0.979225i
$5$		0			0
$5$		0			0
$6$			3.96069i			1.61695i
$7$	0.185690	+	1.05310i	0.0701844	+	0.398035i	0.999581	+	0.0289524i	$0.00921711\pi$
$7$	0.185690	+	1.05310i	0.0701844	+	0.398035i	−0.929396	+	0.369083i	$0.879672\pi$
$8$	−2.03660	−	1.17583i	−0.720046	−	0.415719i
$9$	0.0829802	+	0.0696287i	0.0276601	+	0.0232096i
$10$		0			0
$11$	−0.107723	+	0.186582i	−0.0324798	+	0.0562567i	−0.881808	−	0.471608i	$-0.843674\pi$
$11$	−0.107723	+	0.186582i	−0.0324798	+	0.0562567i	0.849329	+	0.527865i	$0.177007\pi$
$12$	−5.04770	+	1.83721i	−1.45715	+	0.530358i
$13$	3.81491	+	4.54644i	1.05807	+	1.26095i	0.964145	+	0.265375i	$0.0854958\pi$
$13$	3.81491	+	4.54644i	1.05807	+	1.26095i	0.0939215	+	0.995580i	$0.470060\pi$
$14$	−2.08045	+	1.20115i	−0.556025	+	0.321021i
$15$		0			0
$16$	−0.140756	+	0.798269i	−0.0351891	+	0.199567i
$17$	2.80586	−	3.34390i	0.680522	−	0.811015i	−0.309653	−	0.950850i	$-0.600213\pi$
$17$	2.80586	−	3.34390i	0.680522	−	0.811015i	0.990175	+	0.139835i	$0.0446573\pi$
$18$	−0.0832301	+	0.228673i	−0.0196175	+	0.0538987i
$19$	−1.34424	+	3.69328i	−0.308391	+	0.847297i	0.684580	+	0.728938i	$0.259986\pi$
$19$	−1.34424	+	3.69328i	−0.308391	+	0.847297i	−0.992971	+	0.118359i	$0.962237\pi$
$20$		0			0
$21$	−0.327380	+	1.85667i	−0.0714402	+	0.405158i
$22$	−0.476650	−	0.0840463i	−0.101622	−	0.0179187i
$23$	−2.75237	+	1.58908i	−0.573908	+	0.331346i	−0.758709	−	0.651430i	$-0.774169\pi$
$23$	−2.75237	+	1.58908i	−0.573908	+	0.331346i	0.184801	+	0.982776i	$0.440836\pi$
$24$	−2.66505	−	3.17608i	−0.544001	−	0.648315i
$25$		0			0
$26$	−6.66646	+	11.5467i	−1.30740	+	2.26449i
$27$	−2.54908	−	4.41513i	−0.490570	−	0.849692i
$28$	−2.49585	−	2.09427i	−0.471671	−	0.395779i
$29$	−3.22377	−	1.86124i	−0.598639	−	0.345624i	0.169867	−	0.985467i	$-0.445666\pi$
$29$	−3.22377	−	1.86124i	−0.598639	−	0.345624i	−0.768506	+	0.639843i	$0.779000\pi$
$30$		0			0
$31$		−	2.43489i		−	0.437319i	−0.975801	−	0.218660i	$-0.929832\pi$
$31$		−	2.43489i		−	0.437319i	0.975801	−	0.218660i	$-0.0701684\pi$
$32$	−6.42519	+	1.13293i	−1.13582	+	0.200276i
$33$	−0.290976	+	0.244158i	−0.0506524	+	0.0425024i
$34$	9.21496	+	3.35397i	1.58035	+	0.575201i
$35$		0			0
$36$	−0.330039			−0.0550065
$37$	−3.68154	−	4.84213i	−0.605241	−	0.796042i
$37$	−3.68154	−	4.84213i	−0.605241	−	0.796042i
$38$	−8.82947			−1.43233
$39$	3.57876	+	9.83255i	0.573059	+	1.57447i
$40$		0			0
$41$	1.58232	−	1.32773i	0.247117	−	0.207356i	−0.510813	−	0.859692i	$-0.670655\pi$
$41$	1.58232	−	1.32773i	0.247117	−	0.207356i	0.757930	+	0.652336i	$0.226211\pi$
$42$	−4.17102	+	0.735463i	−0.643602	+	0.113484i
$43$		−	9.40443i		−	1.43416i	−0.696989	−	0.717081i	$-0.745478\pi$
$43$		−	9.40443i		−	1.43416i	0.696989	−	0.717081i	$-0.254522\pi$
$44$	−0.113987	−	0.646452i	−0.0171842	−	0.0974564i
$45$		0			0
$46$	−5.46938	−	4.58935i	−0.806416	−	0.676663i
$47$	5.39131	+	9.33803i	0.786404	+	1.36209i	0.928157	+	0.372190i	$0.121393\pi$
$47$	5.39131	+	9.33803i	0.786404	+	1.36209i	−0.141753	+	0.989902i	$0.545274\pi$
$48$	−0.714547	+	1.23763i	−0.103136	+	0.178637i
$49$	5.50330	−	2.00304i	0.786186	−	0.286148i
$50$		0			0
$51$	6.66489	−	3.84797i	0.933271	−	0.538824i
$52$	−17.8079	−	3.14002i	−2.46952	−	0.435442i
$53$	1.08310	−	6.14257i	0.148775	−	0.843747i	−0.815483	−	0.578781i	$-0.803528\pi$
$53$	1.08310	−	6.14257i	0.148775	−	0.843747i	0.964258	−	0.264965i	$-0.0853605\pi$
$54$	7.36188	−	8.77355i	1.00182	−	1.19393i
$55$		0			0
$56$	0.860094	−	2.36309i	0.114935	−	0.315781i
$57$	−4.45407	+	5.30815i	−0.589956	+	0.703082i
$58$	1.45215	−	8.23556i	0.190677	−	1.08138i
$59$	2.70230	+	0.476488i	0.351809	+	0.0620335i	0.346760	−	0.937954i	$-0.387282\pi$
$59$	2.70230	+	0.476488i	0.351809	+	0.0620335i	0.00504903	+	0.999987i	$0.498393\pi$
$60$		0			0
$61$	5.71443	+	6.81019i	0.731657	+	0.871955i	0.995708	−	0.0925536i	$-0.0295029\pi$
$61$	5.71443	+	6.81019i	0.731657	+	0.871955i	−0.264050	+	0.964509i	$0.585059\pi$
$62$	5.14012	−	1.87085i	0.652796	−	0.237598i
$63$	−0.0579175	+	0.100316i	−0.00729692	+	0.0126386i
$64$	−6.51787	−	11.2893i	−0.814734	−	1.41116i
$65$		0			0
$66$	−0.738996	−	0.426660i	−0.0909642	−	0.0525182i
$67$	1.59627	+	9.05289i	0.195015	+	1.10599i	0.912397	+	0.409306i	$0.134229\pi$
$67$	1.59627	+	9.05289i	0.195015	+	1.10599i	−0.717382	+	0.696680i	$0.754660\pi$
$68$			13.2998i			1.61283i
$69$	−5.51811	+	0.972991i	−0.664302	+	0.117134i
$70$		0			0
$71$	−1.81248	−	0.659688i	−0.215102	−	0.0782906i	0.232222	−	0.972663i	$-0.425400\pi$
$71$	−1.81248	−	0.659688i	−0.215102	−	0.0782906i	−0.447323	+	0.894372i	$0.647623\pi$
$72$	−0.0871258	−	0.239376i	−0.0102679	−	0.0282108i
$73$	−0.242447			−0.0283763			−0.0141882	−	0.999899i	$-0.504516\pi$
$73$	−0.242447			−0.0283763			−0.0141882	+	0.999899i	$0.504516\pi$
$74$	7.39317	−	11.4923i	0.859438	−	1.33595i
$75$		0			0
$76$	−4.09565	−	11.2527i	−0.469804	−	1.29077i
$77$	−0.216494	−	0.0787973i	−0.0246718	−	0.00897978i
$78$	−18.0071	+	15.1097i	−2.03890	+	1.71084i
$79$	−1.58386	+	0.279276i	−0.178198	+	0.0314210i	−0.262035	−	0.965058i	$-0.584394\pi$
$79$	−1.58386	+	0.279276i	−0.178198	+	0.0314210i	0.0838372	+	0.996479i	$0.473282\pi$
$80$		0			0
$81$	−1.61723	−	9.17175i	−0.179692	−	1.01908i
$82$	4.01865	+	2.32017i	0.443785	+	0.256219i
$83$	−1.09454	−	0.918429i	−0.120142	−	0.100811i	0.580737	−	0.814091i	$-0.302764\pi$
$83$	−1.09454	−	0.918429i	−0.120142	−	0.100811i	−0.700879	+	0.713280i	$0.747209\pi$
$84$	−2.87208	−	4.97460i	−0.313370	−	0.542773i
$85$		0			0
$86$	19.8530	−	7.22591i	2.14081	−	0.779190i
$87$	−4.21856	−	5.02748i	−0.452277	−	0.539002i
$88$	0.438779	−	0.253329i	0.0467740	−	0.0270050i
$89$	9.15190	+	1.61373i	0.970100	+	0.171055i	0.636175	−	0.771545i	$-0.280516\pi$
$89$	9.15190	+	1.61373i	0.970100	+	0.171055i	0.333925	+	0.942600i	$0.391627\pi$
$90$		0			0
$91$	−4.07947	+	4.86173i	−0.427645	+	0.509647i
$92$	3.31186	−	9.09926i	0.345285	−	0.948664i
$93$	1.46823	−	4.03393i	0.152248	−	0.418299i
$94$	−15.5704	+	18.5561i	−1.60597	+	1.91392i
$95$		0			0
$96$	−11.3279	−	1.99741i	−1.15615	−	0.203860i
$97$	13.9866	−	8.07516i	1.42012	−	0.819908i	0.423814	−	0.905749i	$-0.360691\pi$
$97$	13.9866	−	8.07516i	1.42012	−	0.819908i	0.996309	+	0.0858406i	$0.0273576\pi$
$98$	8.45694	+	10.0786i	0.854280	+	1.01809i
$99$	−0.0219304	+	0.00798202i	−0.00220409	+	0.000802223i
$100$		0			0
$101$	−2.43044	−	4.20965i	−0.241838	−	0.418876i	0.719400	−	0.694596i	$-0.244417\pi$
$101$	−2.43044	−	4.20965i	−0.241838	−	0.418876i	−0.961238	+	0.275720i	$0.911084\pi$
$102$	13.2442	+	11.1132i	1.31137	+	1.10037i
$103$	10.9775	+	6.33785i	1.08164	+	0.624487i	0.931339	−	0.364152i	$-0.118641\pi$
$103$	10.9775	+	6.33785i	1.08164	+	0.624487i	0.150304	+	0.988640i	$0.451975\pi$
$104$	−2.42361	−	13.7450i	−0.237654	−	1.34780i
$105$		0			0
$106$	13.7993	−	2.43320i	1.34031	−	0.236333i
$107$	−3.23884	+	2.71771i	−0.313111	+	0.262731i	−0.785776	−	0.618511i	$-0.787736\pi$
$107$	−3.23884	+	2.71771i	−0.313111	+	0.262731i	0.472666	+	0.881242i	$0.343292\pi$
$108$	14.5963	+	5.31263i	1.40453	+	0.511208i
$109$	4.70871	+	12.9371i	0.451013	+	1.23915i	0.932012	+	0.362426i	$0.118051\pi$
$109$	4.70871	+	12.9371i	0.451013	+	1.23915i	−0.481000	+	0.876721i	$0.659726\pi$
$110$		0			0
$111$	−3.17949	−	10.2420i	−0.301783	−	0.972129i
$112$	−0.866797			−0.0819046
$113$	−6.07741	−	16.6975i	−0.571714	−	1.57077i	−0.801794	−	0.597601i	$-0.796121\pi$
$113$	−6.07741	−	16.6975i	−0.571714	−	1.57077i	0.230079	−	0.973172i	$-0.426101\pi$
$114$	−14.6280	−	5.32414i	−1.37003	−	0.498652i
$115$		0			0
$116$	11.1694	−	1.96947i	1.03705	−	0.182860i
$117$			0.642892i			0.0594354i
$118$	1.07044	+	6.07074i	0.0985416	+	0.558857i
$119$	4.04249	+	2.33393i	0.370575	+	0.213951i
$120$		0			0
$121$	5.47679	+	9.48608i	0.497890	+	0.862371i
$122$	−9.98581	+	17.2959i	−0.904073	+	1.56590i
$123$	3.42208	−	1.24553i	0.308558	−	0.112306i
$124$	4.76861	+	5.68301i	0.428234	+	0.510349i
$125$		0			0
$126$	−0.256271	−	0.0451875i	−0.0228304	−	0.00402562i
$127$	3.15246	−	17.8785i	0.279735	−	1.58646i	−0.443770	−	0.896141i	$-0.646359\pi$
$127$	3.15246	−	17.8785i	0.279735	−	1.58646i	0.723506	−	0.690318i	$-0.242529\pi$
$128$	10.4365	−	12.4377i	0.922466	−	1.09935i
$129$	5.67084	−	15.5805i	0.499290	−	1.37179i
$130$		0			0
$131$	12.9124	−	15.3884i	1.12816	−	1.34449i	0.196779	−	0.980448i	$-0.436952\pi$
$131$	12.9124	−	15.3884i	1.12816	−	1.34449i	0.931382	−	0.364042i	$-0.118604\pi$
$132$	0.200964	−	1.13972i	0.0174917	−	0.0992002i
$133$	−4.13902	−	0.729820i	−0.358898	−	0.0632835i
$134$	−17.8844	+	10.3256i	−1.54498	+	0.891994i
$135$		0			0
$136$	−9.64628	+	3.51096i	−0.827161	+	0.301062i
$137$	−5.06566	+	8.77397i	−0.432788	+	0.749611i	−0.997112	−	0.0759422i	$-0.975804\pi$
$137$	−5.06566	+	8.77397i	−0.432788	+	0.749611i	0.564324	+	0.825553i	$0.309137\pi$
$138$	−6.29386	−	10.9013i	−0.535769	−	0.927979i
$139$	−2.00041	−	1.67855i	−0.169673	−	0.142372i	0.553997	−	0.832519i	$-0.313102\pi$
$139$	−2.00041	−	1.67855i	−0.169673	−	0.142372i	−0.723670	+	0.690146i	$0.757546\pi$
$140$		0			0
$141$	3.30109	+	18.7214i	0.278002	+	1.57663i
$142$		−	4.33307i		−	0.363623i
$143$	−1.25924	+	0.222038i	−0.105303	+	0.0185678i
$144$	−0.0672624	+	0.0564399i	−0.00560520	+	0.00470332i
$145$		0			0
$146$	−0.186285	−	0.511813i	−0.0154170	−	0.0423580i
$147$	10.3253			0.851613
$148$	18.0757	+	4.09138i	1.48582	+	0.336309i
$149$	4.83367			0.395990			0.197995	−	0.980203i	$-0.436557\pi$
$149$	4.83367			0.395990			0.197995	+	0.980203i	$0.436557\pi$
$150$		0			0
$151$	−17.3991	−	6.33275i	−1.41592	−	0.515352i	−0.483056	−	0.875589i	$-0.660473\pi$
$151$	−17.3991	−	6.33275i	−1.41592	−	0.515352i	−0.932860	+	0.360238i	$0.882696\pi$
$152$	7.08036	−	5.94113i	0.574293	−	0.481889i
$153$	0.465663	−	0.0821089i	0.0376466	−	0.00663811i
$154$		−	0.517569i		−	0.0417069i
$155$		0			0
$156$	−27.6093	−	15.9403i	−2.21052	−	1.27624i
$157$	−15.4165	−	12.9359i	−1.23037	−	1.03240i	−0.998215	−	0.0597210i	$-0.980979\pi$
$157$	−15.4165	−	12.9359i	−1.23037	−	1.03240i	−0.232152	−	0.972680i	$-0.574577\pi$
$158$	−1.80652	−	3.12898i	−0.143719	−	0.248928i
$159$	5.49834	−	9.52340i	0.436047	−	0.755255i
$160$		0			0
$161$	−2.18455	−	2.60345i	−0.172167	−	0.205180i
$162$	18.1192	−	10.4611i	1.42358	−	0.821905i
$163$	−13.2114	−	2.32952i	−1.03479	−	0.182462i	−0.369645	−	0.929173i	$-0.620521\pi$
$163$	−13.2114	−	2.32952i	−1.03479	−	0.182462i	−0.665149	+	0.746711i	$0.731632\pi$
$164$	−1.09284	+	6.19779i	−0.0853363	+	0.483966i
$165$		0			0
$166$	1.09784	−	3.01628i	0.0852087	−	0.234109i
$167$	0.760502	−	2.08946i	0.0588494	−	0.161687i	−0.906784	−	0.421596i	$-0.861470\pi$
$167$	0.760502	−	2.08946i	0.0588494	−	0.161687i	0.965633	+	0.259908i	$0.0836923\pi$
$168$	2.84987	−	3.39634i	0.219872	−	0.262033i
$169$	−3.85910	+	21.8860i	−0.296854	+	1.68354i
$170$		0			0
$171$	−0.368704	+	0.212871i	−0.0281955	+	0.0162787i
$172$	18.4181	+	21.9498i	1.40437	+	1.67366i
$173$	20.3734	−	7.41530i	1.54896	−	0.563775i	0.580786	−	0.814056i	$-0.302745\pi$
$173$	20.3734	−	7.41530i	1.54896	−	0.563775i	0.968173	+	0.250281i	$0.0805230\pi$
$174$	7.37182	−	12.7684i	0.558856	−	0.967967i
$175$		0			0
$176$	−0.133780	−	0.112255i	−0.0100841	−	0.00846154i
$177$	4.18963	+	2.41888i	0.314912	+	0.181814i
$178$	3.62525	+	20.5598i	0.271724	+	1.54102i
$179$		−	24.0775i		−	1.79964i	−0.436264	−	0.899819i	$-0.643699\pi$
$179$		−	24.0775i		−	1.79964i	0.436264	−	0.899819i	$-0.356301\pi$
$180$		0			0
$181$	−17.5075	+	14.6905i	−1.30132	+	1.09194i	−0.311408	+	0.950276i	$0.600801\pi$
$181$	−17.5075	+	14.6905i	−1.30132	+	1.09194i	−0.989915	+	0.141663i	$0.954755\pi$
$182$	−13.3977	−	4.87637i	−0.993105	−	0.361461i
$183$	5.36068	+	14.7283i	0.396273	+	1.08875i
$184$	7.47395			0.550987
$185$		0			0
$186$	9.64385			0.707122
$187$	0.321656	+	0.883741i	0.0235218	+	0.0646256i
$188$	−30.8713	−	11.2362i	−2.25152	−	0.819487i
$189$	4.17625	−	3.50429i	0.303777	−	0.254899i
$190$		0			0
$191$			7.86944i			0.569412i	0.958615	+	0.284706i	$0.0918961\pi$
$191$			7.86944i			0.569412i	−0.958615	+	0.284706i	$0.908104\pi$
$192$	−3.99089	−	22.6334i	−0.288017	−	1.63343i
$193$	−2.89039	−	1.66877i	−0.208055	−	0.120121i	0.392352	−	0.919815i	$-0.371661\pi$
$193$	−2.89039	−	1.66877i	−0.208055	−	0.120121i	−0.600407	+	0.799694i	$0.704995\pi$
$194$	27.7935	+	23.3215i	1.99546	+	1.67439i
$195$		0			0
$196$	−8.92180	+	15.4530i	−0.637271	+	1.10379i
$197$	11.6510	−	4.24063i	0.830101	−	0.302132i	0.108201	−	0.994129i	$-0.465491\pi$
$197$	11.6510	−	4.24063i	0.830101	−	0.302132i	0.721901	+	0.691997i	$0.243269\pi$
$198$	−0.0337005	−	0.0401627i	−0.00239499	−	0.00285424i
$199$	−18.9318	+	10.9303i	−1.34204	+	0.774826i	−0.987106	−	0.160066i	$-0.948829\pi$
$199$	−18.9318	+	10.9303i	−1.34204	+	0.774826i	−0.354932	+	0.934892i	$0.615496\pi$
$200$		0			0
$201$	−2.81429	+	15.9606i	−0.198505	+	1.12578i
$202$	7.01926	−	8.36523i	0.493874	−	0.588576i
$203$	1.36146	−	3.74058i	0.0955556	−	0.262537i
$204$	−8.01971	+	22.0340i	−0.561492	+	1.54269i
$205$		0			0
$206$	−4.94482	+	28.0435i	−0.344522	+	1.95388i
$207$	−0.339037	−	0.0597815i	−0.0235647	−	0.00415510i
$208$	−4.16625	+	2.40539i	−0.288878	+	0.166784i
$209$	−0.544295	−	0.648665i	−0.0376497	−	0.0448691i
$210$		0			0
$211$	−3.86743	+	6.69859i	−0.266245	+	0.461150i	−0.967889	−	0.251378i	$-0.919116\pi$
$211$	−3.86743	+	6.69859i	−0.266245	+	0.461150i	0.701644	+	0.712528i	$0.252450\pi$
$212$	9.50196	+	16.4579i	0.652598	+	1.13033i
$213$	−2.60498	−	2.18584i	−0.178490	−	0.149771i
$214$	−8.22574	−	4.74913i	−0.562300	−	0.324644i
$215$		0			0
$216$			11.9891i			0.815757i
$217$	2.56419	−	0.452136i	0.174068	−	0.0306930i
$218$	−23.6926	+	19.8804i	−1.60466	+	1.34647i
$219$	−0.401667	−	0.146195i	−0.0271421	−	0.00987893i
$220$		0			0
$221$	25.9070			1.74269
$222$	19.1782	−	14.5815i	1.28716	−	0.978643i
$223$	13.9333			0.933043			0.466521	−	0.884510i	$-0.345507\pi$
$223$	13.9333			0.933043			0.466521	+	0.884510i	$0.345507\pi$
$224$	−2.38619	−	6.55601i	−0.159434	−	0.438042i
$225$		0			0
$226$	30.5794	−	25.6592i	2.03411	−	1.70682i
$227$	−8.81677	+	1.55463i	−0.585189	+	0.103185i	−0.458402	−	0.888745i	$-0.651578\pi$
$227$	−8.81677	+	1.55463i	−0.585189	+	0.103185i	−0.126788	+	0.991930i	$0.540467\pi$
$228$		−	21.1122i		−	1.39819i
$229$	2.12898	+	12.0740i	0.140687	+	0.797874i	0.970730	+	0.240175i	$0.0772048\pi$
$229$	2.12898	+	12.0740i	0.140687	+	0.797874i	−0.830043	+	0.557700i	$0.811684\pi$
$230$		0			0
$231$	−0.311155	−	0.261090i	−0.0204725	−	0.0171785i
$232$	4.37701	+	7.58121i	0.287365	+	0.497731i
$233$	4.78901	−	8.29480i	0.313738	−	0.543410i	−0.665430	−	0.746460i	$-0.731752\pi$
$233$	4.78901	−	8.29480i	0.313738	−	0.543410i	0.979168	+	0.203050i	$0.0650852\pi$
$234$	−1.35716	+	0.493967i	−0.0887205	+	0.0322916i
$235$		0			0
$236$	−7.24031	+	4.18020i	−0.471304	+	0.272108i
$237$	−2.79241	−	0.492376i	−0.181386	−	0.0319833i
$238$	−1.82095	+	10.3271i	−0.118034	+	0.669406i
$239$	−8.99415	+	10.7188i	−0.581783	+	0.693342i	−0.974004	−	0.226529i	$-0.927262\pi$
$239$	−8.99415	+	10.7188i	−0.581783	+	0.693342i	0.392221	+	0.919871i	$0.371707\pi$
$240$		0			0
$241$	−3.48870	+	9.58512i	−0.224727	+	0.617432i	−0.999897	−	0.0143200i	$-0.995442\pi$
$241$	−3.48870	+	9.58512i	−0.224727	+	0.617432i	0.775171	+	0.631752i	$0.217664\pi$
$242$	−15.8173	+	18.8503i	−1.01677	+	1.21174i
$243$	0.195386	−	1.10809i	0.0125340	−	0.0710839i
$244$	−26.6748	−	4.70349i	−1.70768	−	0.301110i
$245$		0			0
$246$	5.25872	+	6.26709i	0.335283	+	0.399575i
$247$	−21.9194	+	7.97803i	−1.39470	+	0.507630i
$248$	−2.86302	+	4.95889i	−0.181802	+	0.314890i
$249$	−1.25954	−	2.18158i	−0.0798200	−	0.138252i
$250$		0			0
$251$	8.91571	+	5.14749i	0.562754	+	0.324906i	0.754250	−	0.656587i	$-0.228001\pi$
$251$	8.91571	+	5.14749i	0.562754	+	0.324906i	−0.191496	+	0.981493i	$0.561334\pi$
$252$	−0.0612851	−	0.347565i	−0.00386060	−	0.0218945i
$253$		−	0.684724i		−	0.0430483i
$254$	40.1642	−	7.08203i	2.52013	−	0.444366i
$255$		0			0
$256$	9.77616	+	3.55823i	0.611010	+	0.222389i
$257$	1.95008	+	5.35780i	0.121643	+	0.334210i	0.985536	−	0.169464i	$-0.0542035\pi$
$257$	1.95008	+	5.35780i	0.121643	+	0.334210i	−0.863894	+	0.503674i	$0.831981\pi$
$258$	37.2481			2.31897
$259$	4.41564	−	4.77618i	0.274374	−	0.296777i
$260$		0			0
$261$	−0.137913	−	0.378913i	−0.00853661	−	0.0234541i
$262$	42.4066	+	15.4347i	2.61989	+	0.953561i
$263$	6.07190	−	5.09493i	0.374409	−	0.314167i	−0.436094	−	0.899901i	$-0.643638\pi$
$263$	6.07190	−	5.09493i	0.374409	−	0.314167i	0.810503	+	0.585735i	$0.199194\pi$
$264$	0.879690	−	0.155113i	0.0541412	−	0.00954655i
$265$		0			0
$266$	−1.63955	−	9.29834i	−0.100527	−	0.570118i
$267$	14.1891	+	8.19206i	0.868356	+	0.501346i
$268$	−21.4553	−	18.0031i	−1.31059	−	1.09972i
$269$	−3.95925	−	6.85763i	−0.241400	−	0.418117i	0.719713	−	0.694271i	$-0.244273\pi$
$269$	−3.95925	−	6.85763i	−0.241400	−	0.418117i	−0.961113	+	0.276154i	$0.910940\pi$
$270$		0			0
$271$	−26.1809	+	9.52907i	−1.59038	+	0.578850i	−0.977427	−	0.211273i	$-0.932239\pi$
$271$	−26.1809	+	9.52907i	−1.59038	+	0.578850i	−0.612949	+	0.790122i	$0.710017\pi$
$272$	2.27439	+	2.71051i	0.137905	+	0.164349i
$273$	−9.69014	+	5.59461i	−0.586474	+	0.338601i
$274$	−22.4143	−	3.95225i	−1.35410	−	0.238764i
$275$		0			0
$276$	10.9736	−	13.0779i	0.660536	−	0.787196i
$277$	6.28754	−	17.2749i	0.377782	−	1.03795i	−0.594492	−	0.804102i	$-0.702647\pi$
$277$	6.28754	−	17.2749i	0.377782	−	1.03795i	0.972274	−	0.233845i	$-0.0751310\pi$
$278$	2.00644	−	5.51264i	0.120338	−	0.330626i
$279$	0.169538	−	0.202048i	0.0101500	−	0.0120963i
$280$		0			0
$281$	−31.3753	−	5.53231i	−1.87169	−	0.330030i	−0.881774	−	0.471673i	$-0.843650\pi$
$281$	−31.3753	−	5.53231i	−1.87169	−	0.330030i	−0.989918	+	0.141643i	$0.954761\pi$
$282$	−36.9851	+	21.3534i	−2.20243	+	1.27157i
$283$	−9.57476	−	11.4107i	−0.569160	−	0.678299i	0.402298	−	0.915509i	$-0.368211\pi$
$283$	−9.57476	−	11.4107i	−0.569160	−	0.678299i	−0.971458	+	0.237210i	$0.923767\pi$
$284$	5.52227	−	2.00994i	0.327687	−	0.119268i
$285$		0			0
$286$	−1.43627	−	2.48769i	−0.0849284	−	0.147100i
$287$	1.69205	+	1.41980i	0.0998787	+	0.0838082i
$288$	−0.612048	−	0.353366i	−0.0360653	−	0.0208223i
$289$	−0.356766	−	2.02332i	−0.0209862	−	0.119019i
$290$		0			0
$291$	28.0411	−	4.94441i	1.64380	−	0.289846i
$292$	0.565869	−	0.474821i	0.0331150	−	0.0277868i
$293$	2.92410	+	1.06429i	0.170828	+	0.0621762i	0.426018	−	0.904715i	$-0.359916\pi$
$293$	2.92410	+	1.06429i	0.170828	+	0.0621762i	−0.255190	+	0.966891i	$0.582138\pi$
$294$	7.93343	+	21.7969i	0.462687	+	1.27122i
$295$		0			0
$296$	1.80429	+	14.1903i	0.104872	+	0.824797i
$297$	1.09838			0.0637345
$298$	3.71396	+	10.2040i	0.215144	+	0.591103i
$299$	−17.7247	−	6.45126i	−1.02505	−	0.373086i
$300$		0			0
$301$	9.90384	−	1.74631i	0.570848	−	0.100656i
$302$		−	41.5957i		−	2.39356i
$303$	−1.48816	−	8.43976i	−0.0854924	−	0.484852i
$304$	−2.75902	−	1.59292i	−0.158241	−	0.0913603i
$305$		0			0
$306$	0.531127	+	0.919938i	0.0303625	+	0.0525894i
$307$	−2.65714	+	4.60231i	−0.151651	+	0.262667i	−0.931835	−	0.362883i	$-0.881792\pi$
$307$	−2.65714	+	4.60231i	−0.151651	+	0.262667i	0.780183	+	0.625551i	$0.215126\pi$
$308$	0.659615	−	0.240080i	0.0375850	−	0.0136798i
$309$	14.3649	+	17.1194i	0.817191	+	0.973890i
$310$		0			0
$311$	0.572034	+	0.100865i	0.0324370	+	0.00571953i	0.189843	−	0.981814i	$-0.439202\pi$
$311$	0.572034	+	0.100865i	0.0324370	+	0.00571953i	−0.157406	+	0.987534i	$0.550313\pi$
$312$	4.27292	−	24.2330i	0.241907	−	1.37192i
$313$	4.73086	−	5.63802i	0.267404	−	0.318679i	−0.615588	−	0.788068i	$-0.711081\pi$
$313$	4.73086	−	5.63802i	0.267404	−	0.318679i	0.882992	+	0.469389i	$0.155526\pi$
$314$	15.4629	−	42.4839i	0.872621	−	2.39751i
$315$		0			0
$316$	3.14975	−	3.75373i	0.177187	−	0.211164i
$317$	3.94755	−	22.3877i	0.221717	−	1.25742i	−0.647146	−	0.762366i	$-0.724038\pi$
$317$	3.94755	−	22.3877i	0.221717	−	1.25742i	0.868863	−	0.495052i	$-0.164851\pi$
$318$	24.3288	+	4.28983i	1.36429	+	0.240562i
$319$	0.694551	−	0.400999i	0.0388874	−	0.0224516i
$320$		0			0
$321$	−7.00462	+	2.54947i	−0.390960	+	0.142298i
$322$	3.81745	−	6.61201i	0.212738	−	0.368473i
$323$	8.57819	+	14.8579i	0.477303	+	0.826714i
$324$	21.7370	+	18.2395i	1.20761	+	1.01331i
$325$		0			0
$326$	−5.23329	−	29.6795i	−0.289845	−	1.64379i
$327$			24.2724i			1.34227i
$328$	−4.78373	+	0.843501i	−0.264137	+	0.0465746i
$329$	−8.83279	+	7.41159i	−0.486968	+	0.408614i
$330$		0			0
$331$	0.923369	+	2.53693i	0.0507529	+	0.139443i	0.962479	−	0.271356i	$-0.0874721\pi$
$331$	0.923369	+	2.53693i	0.0507529	+	0.139443i	−0.911726	+	0.410799i	$0.865250\pi$
$332$	4.35334			0.238921
$333$	0.0316565	−	0.658142i	0.00173476	−	0.0360660i
$334$	4.99525			0.273328
$335$		0			0
$336$	−1.43604	−	0.522675i	−0.0783423	−	0.0285143i
$337$	−12.7103	+	10.6652i	−0.692374	+	0.580971i	−0.919593	−	0.392873i	$-0.871481\pi$
$337$	−12.7103	+	10.6652i	−0.692374	+	0.580971i	0.227218	+	0.973844i	$0.427037\pi$
$338$	−49.1672	+	8.66950i	−2.67434	+	0.471559i
$339$		−	31.3278i		−	1.70149i
$340$		0			0
$341$	0.454308	+	0.262295i	0.0246021	+	0.0142041i
$342$	−0.732672	−	0.614785i	−0.0396184	−	0.0332437i
$343$	6.87404	+	11.9062i	0.371163	+	0.642873i
$344$	−11.0580	+	19.1531i	−0.596208	+	1.03266i
$345$		0			0
$346$	31.3078	+	37.3112i	1.68312	+	2.00586i
$347$	18.7298	−	10.8137i	1.00547	−	0.580509i	0.0956085	−	0.995419i	$-0.469520\pi$
$347$	18.7298	−	10.8137i	1.00547	−	0.580509i	0.909862	+	0.414910i	$0.136187\pi$
$348$	19.6921	+	3.47225i	1.05561	+	0.186132i
$349$	4.48589	−	25.4408i	0.240124	−	1.36181i	−0.591424	−	0.806361i	$-0.701434\pi$
$349$	4.48589	−	25.4408i	0.240124	−	1.36181i	0.831548	−	0.555452i	$-0.187455\pi$
$350$		0			0
$351$	10.3486	−	28.4326i	0.552368	−	1.51762i
$352$	0.480758	−	1.32087i	0.0256245	−	0.0704027i
$353$	−16.0676	+	19.1486i	−0.855191	+	1.01918i	0.144369	+	0.989524i	$0.453885\pi$
$353$	−16.0676	+	19.1486i	−0.855191	+	1.01918i	−0.999560	+	0.0296534i	$0.990560\pi$
$354$	−1.88722	+	10.7030i	−0.100305	+	0.568857i
$355$		0			0
$356$	−24.5208	+	14.1571i	−1.29960	+	0.750326i
$357$	5.28992	+	6.30428i	0.279972	+	0.333658i
$358$	50.8283	−	18.5000i	2.68636	−	0.977755i
$359$	−8.51899	+	14.7553i	−0.449615	+	0.778756i	−0.998361	−	0.0572333i	$-0.981772\pi$
$359$	−8.51899	+	14.7553i	−0.449615	+	0.778756i	0.548746	+	0.835989i	$0.315105\pi$
$360$		0			0
$361$	2.72151	+	2.28362i	0.143238	+	0.120191i
$362$	−44.4641	−	25.6713i	−2.33698	−	1.34926i
$363$	3.35343	+	19.0183i	0.176010	+	0.998200i
$364$		−	19.3367i		−	1.01352i
$365$		0			0
$366$	−26.9731	+	22.6331i	−1.40991	+	1.18305i
$367$	28.5453	+	10.3896i	1.49005	+	0.542334i	0.953463	−	0.301511i	$-0.0974909\pi$
$367$	28.5453	+	10.3896i	1.49005	+	0.542334i	0.536588	+	0.843845i	$0.319713\pi$
$368$	−0.881100	−	2.42080i	−0.0459305	−	0.126193i
$369$	0.223749			0.0116479
$370$		0			0
$371$	6.66988			0.346283
$372$	4.47341	+	12.2906i	0.231936	+	0.637238i
$373$	7.09136	+	2.58104i	0.367177	+	0.133641i	0.519018	−	0.854764i	$-0.326298\pi$
$373$	7.09136	+	2.58104i	0.367177	+	0.133641i	−0.151841	+	0.988405i	$0.548520\pi$
$374$	−1.61846	+	1.35805i	−0.0836885	+	0.0702230i
$375$		0			0
$376$		−	25.3571i		−	1.30769i
$377$	−3.83637	−	21.7572i	−0.197583	−	1.12055i
$378$	10.6065	+	6.12365i	0.545538	+	0.314967i
$379$	−8.62568	−	7.23780i	−0.443071	−	0.371781i	0.393786	−	0.919202i	$-0.371165\pi$
$379$	−8.62568	−	7.23780i	−0.443071	−	0.371781i	−0.836857	+	0.547421i	$0.815610\pi$
$380$		0			0
$381$	16.0034	−	27.7187i	0.819879	−	1.42007i
$382$	−16.6126	+	6.04649i	−0.849975	+	0.309366i
$383$	−5.11110	−	6.09117i	−0.261165	−	0.311244i	0.619488	−	0.785006i	$-0.287340\pi$
$383$	−5.11110	−	6.09117i	−0.261165	−	0.311244i	−0.880653	+	0.473762i	$0.842896\pi$
$384$	24.7903	−	14.3127i	1.26507	−	0.730391i
$385$		0			0
$386$	1.30198	−	7.38391i	0.0662691	−	0.375831i
$387$	0.654818	−	0.780382i	0.0332863	−	0.0396691i
$388$	−16.8298	+	46.2394i	−0.854401	+	2.34745i
$389$	−0.893872	+	2.45589i	−0.0453211	+	0.124519i	−0.960288	−	0.279009i	$-0.909994\pi$
$389$	−0.893872	+	2.45589i	−0.0453211	+	0.124519i	0.914967	+	0.403528i	$0.132216\pi$
$390$		0			0
$391$	−2.40905	+	13.6624i	−0.121831	+	0.690936i
$392$	−13.5633	−	2.39157i	−0.685048	−	0.120792i
$393$	30.6714	−	17.7081i	1.54717	−	0.893256i
$394$	17.9042	+	21.3374i	0.901999	+	1.07496i
$395$		0			0
$396$	0.0355530	−	0.0615795i	0.00178660	−	0.00309449i
$397$	9.97122	+	17.2707i	0.500441	+	0.866790i	1.00000		0.000509692i	$0.000162240\pi$
$397$	9.97122	+	17.2707i	0.500441	+	0.866790i	−0.499559	+	0.866280i	$0.666504\pi$
$398$	−37.6204	−	31.5672i	−1.88574	−	1.58232i
$399$	−6.41711	−	3.70492i	−0.321257	−	0.185478i
$400$		0			0
$401$		−	25.8893i		−	1.29285i	−0.762978	−	0.646424i	$-0.776264\pi$
$401$		−	25.8893i		−	1.29285i	0.762978	−	0.646424i	$-0.223736\pi$
$402$	−35.8557	+	6.32233i	−1.78832	+	0.315329i
$403$	11.0701	−	9.28889i	0.551440	−	0.462713i
$404$	13.9170	+	5.06538i	0.692398	+	0.252012i
$405$		0			0
$406$	8.94254			0.443811
$407$	1.30005	−	0.165299i	0.0644409	−	0.00819358i
$408$	−18.0983			−0.895998
$409$	−2.11638	−	5.81471i	−0.104648	−	0.287519i	0.876307	−	0.481753i	$-0.160000\pi$
$409$	−2.11638	−	5.81471i	−0.104648	−	0.287519i	−0.980955	+	0.194235i	$0.937778\pi$
$410$		0			0
$411$	−13.6830	+	11.4814i	−0.674935	+	0.566338i
$412$	−38.0337	+	6.70637i	−1.87379	+	0.330399i
$413$			2.93428i			0.144386i
$414$	−0.134300	−	0.761651i	−0.00660047	−	0.0374331i
$415$		0			0
$416$	−29.6623	−	24.8897i	−1.45432	−	1.22032i
$417$	−2.30197	−	3.98712i	−0.112728	−	0.195250i
$418$	0.951141	−	1.64743i	0.0465218	−	0.0805782i
$419$	11.0784	−	4.03222i	0.541217	−	0.196987i	−0.0569227	−	0.998379i	$-0.518129\pi$
$419$	11.0784	−	4.03222i	0.541217	−	0.196987i	0.598140	+	0.801392i	$0.295907\pi$
$420$		0			0
$421$	3.44467	−	1.98878i	0.167883	−	0.0969273i	−0.413704	−	0.910411i	$-0.635765\pi$
$421$	3.44467	−	1.98878i	0.167883	−	0.0969273i	0.581587	+	0.813484i	$0.302432\pi$
$422$	−17.1125	−	3.01739i	−0.833021	−	0.146884i
$423$	−0.202822	+	1.15026i	−0.00986155	+	0.0559277i
$424$	−9.42846	+	11.2364i	−0.457886	+	0.545688i
$425$		0			0
$426$	2.61282	−	7.17868i	0.126592	−	0.347808i
$427$	−6.11071	+	7.28247i	−0.295718	+	0.352423i
$428$	2.23692	−	12.6862i	0.108126	−	0.613212i
$429$	−2.22010	−	0.391463i	−0.107187	−	0.0189000i
$430$		0			0
$431$	−21.4691	−	25.5859i	−1.03413	−	1.23243i	−0.972152	−	0.234351i	$-0.924704\pi$
$431$	−21.4691	−	25.5859i	−1.03413	−	1.23243i	−0.0619778	−	0.998078i	$-0.519741\pi$
$432$	3.88326	−	1.41339i	0.186833	−	0.0680018i
$433$	−4.29277	+	7.43530i	−0.206298	+	0.357318i	−0.950545	−	0.310586i	$-0.899475\pi$
$433$	−4.29277	+	7.43530i	−0.206298	+	0.357318i	0.744248	+	0.667904i	$0.232808\pi$
$434$	2.92467	+	5.06568i	0.140389	+	0.243160i
$435$		0			0
$436$	−36.3267	−	20.9732i	−1.73973	−	1.00443i
$437$	−2.16906	−	12.3014i	−0.103760	−	0.588454i
$438$		−	0.960260i		−	0.0458830i
$439$	−5.27817	+	0.930683i	−0.251913	+	0.0444191i	−0.298179	−	0.954510i	$-0.596379\pi$
$439$	−5.27817	+	0.930683i	−0.251913	+	0.0444191i	0.0462654	+	0.998929i	$0.485268\pi$
$440$		0			0
$441$	0.596134	+	0.216975i	0.0283873	+	0.0103322i
$442$	19.9057	+	54.6903i	0.946815	+	2.60135i
$443$	−4.57823			−0.217518			−0.108759	−	0.994068i	$-0.534688\pi$
$443$	−4.57823			−0.217518			−0.108759	+	0.994068i	$0.534688\pi$
$444$	27.4793	+	17.6779i	1.30411	+	0.838955i
$445$		0			0
$446$	10.7057	+	29.4136i	0.506928	+	1.39277i
$447$	8.00804	+	2.91469i	0.378767	+	0.137860i
$448$	10.6785	−	8.96031i	0.504511	−	0.423335i
$449$	−12.4229	+	2.19049i	−0.586273	+	0.103376i	−0.458914	−	0.888481i	$-0.651761\pi$
$449$	−12.4229	+	2.19049i	−0.586273	+	0.103376i	−0.127359	+	0.991857i	$0.540650\pi$
$450$		0			0
$451$	0.0772772	+	0.438261i	0.00363884	+	0.0206369i
$452$	46.8859	+	27.0696i	2.20533	+	1.27325i
$453$	−25.0068	−	20.9832i	−1.17492	−	0.985875i
$454$	−10.0563	−	17.4179i	−0.471963	−	0.817465i
$455$		0			0
$456$	15.3126	−	5.57335i	0.717080	−	0.260996i
$457$	−19.5331	−	23.2787i	−0.913721	−	1.08893i	−0.995731	−	0.0922987i	$-0.970579\pi$
$457$	−19.5331	−	23.2787i	−0.913721	−	1.08893i	0.0820104	−	0.996631i	$-0.473866\pi$
$458$	−23.8528	+	13.7714i	−1.11457	+	0.643497i
$459$	−21.9161	−	3.86440i	−1.02296	−	0.180375i
$460$		0			0
$461$	0.471380	−	0.561769i	0.0219544	−	0.0261642i	−0.754956	−	0.655776i	$-0.772342\pi$
$461$	0.471380	−	0.561769i	0.0219544	−	0.0261642i	0.776910	+	0.629612i	$0.216786\pi$
$462$	0.312092	−	0.857466i	0.0145198	−	0.0398929i
$463$	−3.08487	+	8.47560i	−0.143366	+	0.393894i	−0.990505	−	0.137477i	$-0.956101\pi$
$463$	−3.08487	+	8.47560i	−0.143366	+	0.393894i	0.847139	+	0.531371i	$0.178323\pi$
$464$	1.93954	−	2.31145i	0.0900409	−	0.107307i
$465$		0			0
$466$	21.1902	+	3.73640i	0.981617	+	0.173086i
$467$	−26.1582	+	15.1024i	−1.21046	+	0.698857i	−0.962859	−	0.270006i	$-0.912974\pi$
$467$	−26.1582	+	15.1024i	−1.21046	+	0.698857i	−0.247598	+	0.968863i	$0.579641\pi$
$468$	−1.25907	−	1.50050i	−0.0582006	−	0.0693608i
$469$	−9.23721	+	3.36207i	−0.426535	+	0.155246i
$470$		0			0
$471$	−17.7404	−	30.7273i	−0.817435	−	1.41584i
$472$	−4.94323	−	4.14786i	−0.227530	−	0.190921i
$473$	1.75470	+	1.01308i	0.0806813	+	0.0465814i
$474$	−1.10613	−	6.27317i	−0.0508062	−	0.288136i
$475$		0			0
$476$	−14.0060	+	2.46964i	−0.641965	+	0.113196i
$477$	0.517575	−	0.434297i	0.0236981	−	0.0198851i
$478$	−29.5384	−	10.7511i	−1.35105	−	0.491744i
$479$	2.04419	+	5.61637i	0.0934014	+	0.256618i	0.977592	−	0.210508i	$-0.0675117\pi$
$479$	2.04419	+	5.61637i	0.0934014	+	0.256618i	−0.884191	+	0.467126i	$0.845289\pi$
$480$		0			0
$481$	7.96971	−	35.2102i	0.363387	−	1.60545i
$482$	−22.9150			−1.04375
$483$	−2.04932	−	5.63046i	−0.0932473	−	0.256195i
$484$	−31.3608	−	11.4144i	−1.42549	−	0.518836i
$485$		0			0
$486$	2.48933	−	0.438936i	0.112918	−	0.0199105i
$487$			29.8839i			1.35417i	0.735905	+	0.677085i	$0.236757\pi$
$487$			29.8839i			1.35417i	−0.735905	+	0.677085i	$0.763243\pi$
$488$	−3.63036	−	20.5888i	−0.164339	−	0.932012i
$489$	−20.4828	−	11.8258i	−0.926265	−	0.534779i
$490$		0			0
$491$	16.9739	+	29.3996i	0.766019	+	1.32678i	0.939706	+	0.341984i	$0.111099\pi$
$491$	16.9739	+	29.3996i	0.766019	+	1.32678i	−0.173686	+	0.984801i	$0.555568\pi$
$492$	−5.54777	+	9.60903i	−0.250113	+	0.433208i
$493$	−15.2693	+	5.55756i	−0.687693	+	0.250300i
$494$	−33.6837	−	40.1427i	−1.51550	−	1.80610i
$495$		0			0
$496$	1.94370	+	0.342726i	0.0872746	+	0.0153889i
$497$	0.358160	−	2.03122i	0.0160657	−	0.0911129i
$498$	3.63762	−	4.33514i	0.163006	−	0.194262i
$499$	−2.06033	+	5.66070i	−0.0922328	+	0.253408i	−0.977228	−	0.212193i	$-0.931939\pi$
$499$	−2.06033	+	5.66070i	−0.0922328	+	0.253408i	0.884995	+	0.465601i	$0.154162\pi$
$500$		0			0
$501$	2.51988	−	3.00307i	0.112580	−	0.134167i
$502$	−4.01609	+	22.7764i	−0.179247	+	1.01656i
$503$	−21.4165	−	3.77631i	−0.954915	−	0.168377i	−0.325583	−	0.945514i	$-0.605560\pi$
$503$	−21.4165	−	3.77631i	−0.954915	−	0.168377i	−0.629332	+	0.777136i	$0.716672\pi$
$504$	0.235909	−	0.136202i	0.0105082	−	0.00606694i
$505$		0			0
$506$	1.44547	−	0.526109i	0.0642591	−	0.0233884i
$507$	−19.5906	+	33.9320i	−0.870051	+	1.50697i
$508$	27.6563	+	47.9021i	1.22705	+	2.12531i
$509$	−8.04713	−	6.75234i	−0.356683	−	0.299292i	0.446784	−	0.894642i	$-0.352569\pi$
$509$	−8.04713	−	6.75234i	−0.356683	−	0.299292i	−0.803467	+	0.595349i	$0.797014\pi$
$510$		0			0
$511$	−0.0450201	−	0.255322i	−0.00199157	−	0.0112948i
$512$		−	9.10093i		−	0.402208i
$513$	19.7329	−	3.47944i	0.871229	−	0.153621i
$514$	−9.81212	+	8.23335i	−0.432794	+	0.363157i
$515$		0			0
$516$	17.2780	+	47.4708i	0.760619	+	2.08978i
$517$	−2.32308			−0.102169
$518$	13.4754	+	5.65176i	0.592076	+	0.248324i
$519$	38.2244			1.67786
$520$		0			0
$521$	−6.94857	−	2.52907i	−0.304423	−	0.110801i	0.185292	−	0.982683i	$-0.440677\pi$
$521$	−6.94857	−	2.52907i	−0.304423	−	0.110801i	−0.489715	+	0.871883i	$0.662899\pi$
$522$	0.693931	−	0.582277i	0.0303725	−	0.0254856i
$523$	−21.4232	+	3.77748i	−0.936770	+	0.165178i	−0.621135	−	0.783703i	$-0.713328\pi$
$523$	−21.4232	+	3.77748i	−0.936770	+	0.165178i	−0.315634	+	0.948881i	$0.602217\pi$
$524$			61.2046i			2.67374i
$525$		0			0
$526$	15.4209	+	8.90326i	0.672383	+	0.388200i
$527$	−8.14202	−	6.83197i	−0.354672	−	0.297605i
$528$	−0.153947	−	0.266644i	−0.00669968	−	0.0116042i
$529$	−6.44965	+	11.1711i	−0.280420	+	0.485701i
$530$		0			0
$531$	0.191060	+	0.227697i	0.00829130	+	0.00988119i
$532$	11.0897	−	6.40266i	0.480801	−	0.277591i
$533$	12.0728	+	2.12877i	0.522933	+	0.0922072i
$534$	−6.39148	+	36.2479i	−0.276586	+	1.56860i
$535$		0			0
$536$	7.39371	−	20.3140i	0.319359	−	0.877433i
$537$	14.5187	−	39.8897i	0.626526	−	1.72137i
$538$	11.4345	−	13.6272i	0.492978	−	0.587509i
$539$	−0.219103	+	1.24259i	−0.00943743	+	0.0535223i
$540$		0			0
$541$	−6.97183	+	4.02519i	−0.299742	+	0.173056i	−0.642327	−	0.766431i	$-0.722031\pi$
$541$	−6.97183	+	4.02519i	−0.299742	+	0.173056i	0.342585	+	0.939487i	$0.388698\pi$
$542$	−40.2323	−	47.9469i	−1.72812	−	2.05950i
$543$	−37.8634	+	13.7811i	−1.62487	+	0.591405i
$544$	−14.2398	+	24.6640i	−0.610526	+	1.05746i
$545$		0			0
$546$	−19.2558	−	16.1575i	−0.824073	−	0.691479i
$547$	−32.1952	−	18.5879i	−1.37657	−	0.794761i	−0.384821	−	0.922991i	$-0.625737\pi$
$547$	−32.1952	−	18.5879i	−1.37657	−	0.794761i	−0.991744	+	0.128231i	$0.959070\pi$
$548$	−5.36020	−	30.3992i	−0.228976	−	1.29859i
$549$			0.962999i			0.0410998i
$550$		0			0
$551$	11.2076	−	9.40432i	0.477461	−	0.400637i
$552$	12.3822	+	4.50677i	0.527023	+	0.191821i
$553$	−0.588213	−	1.61610i	−0.0250134	−	0.0687237i
$554$	41.2988			1.75462
$555$		0			0
$556$	7.95629			0.337422
$557$	−6.80811	−	18.7051i	−0.288469	−	0.792561i	−0.996281	−	0.0861609i	$-0.972540\pi$
$557$	−6.80811	−	18.7051i	−0.288469	−	0.792561i	0.707813	−	0.706400i	$-0.249682\pi$
$558$	0.556793	+	0.202656i	0.0235709	+	0.00857912i
$559$	42.7567	−	35.8771i	1.80841	−	1.51744i
$560$		0			0
$561$			1.65807i			0.0700037i
$562$	−12.4284	−	70.4848i	−0.524260	−	2.97322i
$563$	−14.7629	−	8.52338i	−0.622183	−	0.359218i	0.155535	−	0.987830i	$-0.450290\pi$
$563$	−14.7629	−	8.52338i	−0.622183	−	0.359218i	−0.777719	+	0.628613i	$0.783623\pi$
$564$	−44.3697	−	37.2306i	−1.86830	−	1.56769i
$565$		0			0
$566$	16.7316	−	28.9801i	0.703283	−	1.21812i
$567$	9.35849	−	3.40621i	0.393020	−	0.143047i
$568$	2.91561	+	3.47469i	0.122336	+	0.145795i
$569$	−3.44480	+	1.98886i	−0.144413	+	0.0833771i	−0.570466	−	0.821321i	$-0.693237\pi$
$569$	−3.44480	+	1.98886i	−0.144413	+	0.0833771i	0.426052	+	0.904699i	$0.359904\pi$
$570$		0			0
$571$	−0.648539	+	3.67805i	−0.0271405	+	0.153921i	−0.995366	−	0.0961564i	$-0.969345\pi$
$571$	−0.648539	+	3.67805i	−0.0271405	+	0.153921i	0.968226	+	0.250078i	$0.0804562\pi$
$572$	2.50420	−	2.98440i	0.104706	−	0.124784i
$573$	−4.74524	+	13.0374i	−0.198235	+	0.544647i
$574$	−1.69715	+	4.66288i	−0.0708376	+	0.194625i
$575$		0			0
$576$	0.245204	−	1.39062i	0.0102168	−	0.0579425i
$577$	−21.9209	−	3.86525i	−0.912580	−	0.160912i	−0.302405	−	0.953179i	$-0.597790\pi$
$577$	−21.9209	−	3.86525i	−0.912580	−	0.160912i	−0.610174	+	0.792267i	$0.708901\pi$
$578$	3.99717	−	2.30777i	0.166260	−	0.0959904i
$579$	−3.78231	−	4.50758i	−0.157187	−	0.187329i
$580$		0			0
$581$	0.763954	−	1.32321i	0.0316942	−	0.0548959i
$582$	31.9833	+	55.3966i	1.32575	+	2.29626i
$583$	1.02942	+	0.863786i	0.0426342	+	0.0357744i
$584$	0.493768	+	0.285077i	0.0204323	+	0.0117966i
$585$		0			0
$586$			6.99061i			0.288779i
$587$	31.6724	−	5.58469i	1.30726	−	0.230505i	0.523743	−	0.851876i	$-0.324535\pi$
$587$	31.6724	−	5.58469i	1.30726	−	0.230505i	0.783516	+	0.621371i	$0.213424\pi$
$588$	−24.0990	+	20.2215i	−0.993827	+	0.833920i
$589$	8.99273	+	3.27309i	0.370539	+	0.134865i
$590$		0			0
$591$	21.8596			0.899182
$592$	4.38353	−	2.25730i	0.180162	−	0.0927744i
$593$	−22.2448			−0.913486			−0.456743	−	0.889599i	$-0.650984\pi$
$593$	−22.2448			−0.913486			−0.456743	+	0.889599i	$0.650984\pi$
$594$	0.843943	+	2.31871i	0.0346274	+	0.0951380i
$595$		0			0
$596$	−11.2817	+	9.46650i	−0.462118	+	0.387763i
$597$	−37.9555	+	6.69259i	−1.55342	+	0.273909i
$598$		−	42.3742i		−	1.73281i
$599$	−5.99975	−	34.0263i	−0.245143	−	1.39028i	−0.820160	−	0.572134i	$-0.806116\pi$
$599$	−5.99975	−	34.0263i	−0.245143	−	1.39028i	0.575017	−	0.818141i	$-0.304995\pi$
$600$		0			0
$601$	−6.43803	−	5.40215i	−0.262613	−	0.220358i	0.501968	−	0.864886i	$-0.332609\pi$
$601$	−6.43803	−	5.40215i	−0.262613	−	0.220358i	−0.764581	+	0.644528i	$0.777054\pi$
$602$	11.2961	+	19.5655i	0.460397	+	0.797430i
$603$	−0.497882	+	0.862357i	−0.0202753	+	0.0351179i
$604$	53.0116	−	19.2946i	2.15701	−	0.785088i
$605$		0			0
$606$	16.6732	−	9.62625i	0.677300	−	0.391040i
$607$	−20.5090	−	3.61629i	−0.832434	−	0.146781i	−0.258840	−	0.965920i	$-0.583340\pi$
$607$	−20.5090	−	3.61629i	−0.832434	−	0.146781i	−0.573594	+	0.819140i	$0.694451\pi$
$608$	4.45278	−	25.2530i	0.180584	−	1.02414i
$609$	4.51111	−	5.37613i	0.182799	−	0.217852i
$610$		0			0
$611$	−21.8874	+	60.1351i	−0.885468	+	2.43280i
$612$	−0.926045	+	1.10362i	−0.0374332	+	0.0446111i
$613$	−4.08244	+	23.1527i	−0.164888	+	0.935128i	0.784291	+	0.620393i	$0.213027\pi$
$613$	−4.08244	+	23.1527i	−0.164888	+	0.935128i	−0.949180	+	0.314735i	$0.898084\pi$
$614$	−11.7572	−	2.07311i	−0.474483	−	0.0836641i
$615$		0			0
$616$	0.348259	+	0.415038i	0.0140317	+	0.0167224i
$617$	22.9503	−	8.35321i	0.923942	−	0.336288i	0.164137	−	0.986438i	$-0.447516\pi$
$617$	22.9503	−	8.35321i	0.923942	−	0.336288i	0.759806	+	0.650150i	$0.225294\pi$
$618$	−25.1023	+	43.4785i	−1.00976	+	1.74896i
$619$	−2.39506	−	4.14836i	−0.0962655	−	0.166737i	0.813871	−	0.581046i	$-0.197356\pi$
$619$	−2.39506	−	4.14836i	−0.0962655	−	0.166737i	−0.910136	+	0.414309i	$0.864023\pi$
$620$		0			0
$621$	14.0320	+	8.10137i	0.563084	+	0.325097i
$622$	0.226594	+	1.28508i	0.00908560	+	0.0515270i
$623$			9.93755i			0.398139i
$624$	−8.35275	+	1.47282i	−0.334378	+	0.0589598i
$625$		0			0
$626$	15.5370	+	5.65500i	0.620982	+	0.226019i
$627$	−0.510601	−	1.40286i	−0.0203914	−	0.0560250i
$628$	61.3162			2.44678
$629$	−26.5215	−	1.27568i	−1.05748	−	0.0508646i
$630$		0			0
$631$	13.3898	+	36.7882i	0.533041	+	1.46452i	0.855434	+	0.517911i	$0.173290\pi$
$631$	13.3898	+	36.7882i	0.533041	+	1.46452i	−0.322394	+	0.946606i	$0.604488\pi$
$632$	3.55406	+	1.29357i	0.141373	+	0.0514555i
$633$	−10.4465	+	8.76563i	−0.415210	+	0.348402i
$634$	50.2942	−	8.86822i	1.99744	−	0.352202i
$635$		0			0
$636$	5.81804	+	32.9957i	0.230700	+	1.30837i
$637$	30.1013	+	17.3790i	1.19266	+	0.688581i
$638$	1.38018	+	1.15811i	0.0546419	+	0.0458500i
$639$	−0.104467	−	0.180942i	−0.00413264	−	0.00715794i
$640$		0			0
$641$	1.51477	−	0.551331i	0.0598298	−	0.0217763i	−0.311932	−	0.950104i	$-0.600976\pi$
$641$	1.51477	−	0.551331i	0.0598298	−	0.0217763i	0.371762	+	0.928328i	$0.378754\pi$
$642$	−10.7640	−	12.8281i	−0.424822	−	0.506284i
$643$	33.2448	−	19.1939i	1.31105	−	0.756933i	0.328776	−	0.944408i	$-0.393364\pi$
$643$	33.2448	−	19.1939i	1.31105	−	0.756933i	0.982269	+	0.187475i	$0.0600304\pi$
$644$	10.1974	+	1.79808i	0.401835	+	0.0708544i
$645$		0			0
$646$	−24.7743	+	29.5249i	−0.974732	+	1.16164i
$647$	−6.80192	+	18.6881i	−0.267411	+	0.734706i	0.731207	+	0.682156i	$0.238957\pi$
$647$	−6.80192	+	18.6881i	−0.267411	+	0.734706i	−0.998618	+	0.0525507i	$0.983265\pi$
$648$	−7.49078	+	20.5807i	−0.294266	+	0.808488i
$649$	−0.380005	+	0.452873i	−0.0149165	+	0.0177768i
$650$		0			0
$651$	4.52078	+	0.797135i	0.177183	+	0.0312422i
$652$	35.3974	−	20.4367i	1.38627	−	0.800363i
$653$	7.20132	+	8.58220i	0.281809	+	0.335847i	0.888317	−	0.459230i	$-0.151875\pi$
$653$	7.20132	+	8.58220i	0.281809	+	0.335847i	−0.606508	+	0.795077i	$0.707430\pi$
$654$	−51.2398	+	18.6498i	−2.00363	+	0.729263i
$655$		0			0
$656$	0.837160	+	1.45000i	0.0326856	+	0.0566132i
$657$	−0.0201183	−	0.0168813i	−0.000784891	−	0.000658602i
$658$	−22.4328	−	12.9516i	−0.874521	−	0.504905i
$659$	4.49748	+	25.5065i	0.175197	+	0.993591i	0.937916	+	0.346861i	$0.112753\pi$
$659$	4.49748	+	25.5065i	0.175197	+	0.993591i	−0.762720	+	0.646729i	$0.776136\pi$
$660$		0			0
$661$	10.5830	−	1.86606i	0.411630	−	0.0725815i	0.0360014	−	0.999352i	$-0.488538\pi$
$661$	10.5830	−	1.86606i	0.411630	−	0.0725815i	0.375629	+	0.926770i	$0.377427\pi$
$662$	−4.64607	+	3.89852i	−0.180575	+	0.151520i
$663$	42.9206	+	15.6218i	1.66690	+	0.606701i
$664$	1.14922	+	3.15747i	0.0445985	+	0.122533i
$665$		0			0
$666$	1.41368	−	0.438857i	0.0547790	−	0.0170054i
$667$	11.8307			0.458085
$668$	2.31710	+	6.36619i	0.0896514	+	0.246315i
$669$	23.0836	+	8.40173i	0.892462	+	0.324830i
$670$		0			0
$671$	−1.88624	+	0.332595i	−0.0728175	+	0.0128397i
$672$		−	12.3003i		−	0.474495i
$673$	−8.41500	−	47.7238i	−0.324374	−	1.83962i	−0.514037	−	0.857768i	$-0.671850\pi$
$673$	−8.41500	−	47.7238i	−0.324374	−	1.83962i	0.189662	−	0.981849i	$-0.439261\pi$
$674$	−32.2806	−	18.6372i	−1.24340	−	0.717878i
$675$		0			0
$676$	−33.8556	−	58.6396i	−1.30214	−	2.25537i
$677$	1.56590	−	2.71222i	0.0601825	−	0.104239i	−0.834364	−	0.551213i	$-0.814165\pi$
$677$	1.56590	−	2.71222i	0.0601825	−	0.104239i	0.894547	+	0.446974i	$0.147498\pi$
$678$	66.1339	−	24.0708i	2.53986	−	0.924432i
$679$	11.1012	+	13.2298i	0.426023	+	0.507715i
$680$		0			0
$681$	−15.5443	−	2.74089i	−0.595661	−	0.105031i
$682$	−0.204644	+	1.16059i	−0.00783621	+	0.0444413i
$683$	−8.64110	+	10.2981i	−0.330642	+	0.394044i	−0.905596	−	0.424142i	$-0.860576\pi$
$683$	−8.64110	+	10.2981i	−0.330642	+	0.394044i	0.574953	+	0.818186i	$0.305020\pi$
$684$	0.443653	−	1.21893i	0.0169635	−	0.0466069i
$685$		0			0
$686$	−19.8526	+	23.6594i	−0.757976	+	0.903321i
$687$	−3.75348	+	21.2870i	−0.143204	+	0.812151i
$688$	7.50727	+	1.32373i	0.286212	+	0.0504669i
$689$	32.0587	−	18.5091i	1.22134	−	0.705141i
$690$		0			0
$691$	2.94793	−	1.07296i	0.112145	−	0.0408173i	−0.285338	−	0.958427i	$-0.592106\pi$
$691$	2.94793	−	1.07296i	0.112145	−	0.0408173i	0.397483	+	0.917610i	$0.369884\pi$
$692$	−33.0287	+	57.2075i	−1.25556	+	2.17470i
$693$	−0.0124782	−	0.0216128i	−0.000474006	−	0.000821002i
$694$	37.2191	+	31.2305i	1.41282	+	1.18549i
$695$		0			0
$696$	2.68004	+	15.1993i	0.101587	+	0.576127i
$697$		−	9.01654i		−	0.341526i
$698$	57.1529	−	10.0776i	2.16327	−	0.381443i
$699$	12.9358	−	10.8544i	0.489276	−	0.410551i
$700$		0			0
$701$	0.814874	+	2.23885i	0.0307774	+	0.0845601i	0.954130	−	0.299394i	$-0.0967844\pi$
$701$	0.814874	+	2.23885i	0.0307774	+	0.0845601i	−0.923352	+	0.383954i	$0.874562\pi$
$702$	67.9733			2.56549
$703$	22.8323	−	7.08795i	0.861135	−	0.267327i
$704$	2.80851			0.105850
$705$		0			0
$706$	−52.7688	−	19.2063i	−1.98598	−	0.722838i
$707$	3.98189	−	3.34120i	0.149754	−	0.125659i
$708$	−14.5158	+	2.55953i	−0.545538	+	0.0961930i
$709$			34.7951i			1.30676i	0.757031	+	0.653379i	$0.226649\pi$
$709$			34.7951i			1.30676i	−0.757031	+	0.653379i	$0.773351\pi$
$710$		0			0
$711$	−0.150874	−	0.0871073i	−0.00565823	−	0.00326678i
$712$	−16.7413	−	14.0476i	−0.627406	−	0.526456i
$713$	3.86923	+	6.70171i	0.144904	+	0.250981i
$714$	−9.24400	+	16.0111i	−0.345948	+	0.599199i
$715$		0			0
$716$	47.1546	+	56.1966i	1.76225	+	2.10017i
$717$	−21.3642	+	12.3346i	−0.797860	+	0.460645i
$718$	−37.6945	−	6.64655i	−1.40675	−	0.248047i
$719$	−5.17805	+	29.3662i	−0.193109	+	1.09517i	0.721978	+	0.691916i	$0.243233\pi$
$719$	−5.17805	+	29.3662i	−0.193109	+	1.09517i	−0.915087	+	0.403258i	$0.867878\pi$
$720$		0			0
$721$	−4.63600	+	12.7373i	−0.172654	+	0.474362i
$722$	−2.72971	+	7.49982i	−0.101589	+	0.279114i
$723$	−11.5596	+	13.7762i	−0.429906	+	0.512342i
$724$	12.0916	−	68.5751i	0.449382	−	2.54857i
$725$		0			0
$726$	−37.5715	+	21.6919i	−1.39441	+	0.805062i
$727$	13.1297	+	15.6474i	0.486955	+	0.580331i	0.952440	−	0.304725i	$-0.0985645\pi$
$727$	13.1297	+	15.6474i	0.486955	+	0.580331i	−0.465485	+	0.885056i	$0.654120\pi$
$728$	14.0248	−	5.10461i	0.519794	−	0.189190i
$729$	−12.9780	+	22.4785i	−0.480666	+	0.832538i
$730$		0			0
$731$	−31.4475	−	26.3876i	−1.16313	−	0.975979i
$732$	−41.3565	−	23.8772i	−1.52858	−	0.882526i
$733$	−0.0589184	−	0.334143i	−0.00217620	−	0.0123419i	0.983700	−	0.179816i	$-0.0575501\pi$
$733$	−0.0589184	−	0.334143i	−0.00217620	−	0.0123419i	−0.985877	+	0.167474i	$0.946439\pi$
$734$			68.2427i			2.51889i
$735$		0			0
$736$	15.8841	−	13.3284i	0.585497	−	0.491291i
$737$	−1.86107	−	0.677373i	−0.0685533	−	0.0249513i
$738$	0.171918	+	0.472341i	0.00632839	+	0.0173871i
$739$	4.56934			0.168086			0.0840429	−	0.996462i	$-0.473217\pi$
$739$	4.56934			0.168086			0.0840429	+	0.996462i	$0.473217\pi$
$740$		0			0
$741$	−41.1251			−1.51077
$742$	5.12481	+	14.0803i	0.188138	+	0.516904i
$743$	14.4209	+	5.24877i	0.529051	+	0.192559i	0.592714	−	0.805413i	$-0.298056\pi$
$743$	14.4209	+	5.24877i	0.529051	+	0.192559i	−0.0636636	+	0.997971i	$0.520278\pi$
$744$	−7.73341	+	6.48910i	−0.283521	+	0.237902i
$745$		0			0
$746$			16.9532i			0.620701i
$747$	−0.0268763	−	0.152423i	−0.000983351	−	0.00557686i
$748$	−2.48150	−	1.43270i	−0.0907328	−	0.0523846i
$749$	−3.46345	−	2.90618i	−0.126552	−	0.106190i
$750$		0			0
$751$	−8.58344	+	14.8670i	−0.313214	+	0.542503i	−0.979056	−	0.203590i	$-0.934739\pi$
$751$	−8.58344	+	14.8670i	−0.313214	+	0.542503i	0.665842	+	0.746093i	$0.268072\pi$
$752$	−8.21312	+	2.98933i	−0.299502	+	0.109010i
$753$	11.6669	+	13.9041i	0.425166	+	0.506693i
$754$	42.9823	−	24.8158i	1.56532	−	0.903739i
$755$		0			0
$756$	−2.88435	+	16.3579i	−0.104903	+	0.594932i
$757$	1.96009	−	2.33594i	0.0712406	−	0.0849012i	−0.729247	−	0.684251i	$-0.760129\pi$
$757$	1.96009	−	2.33594i	0.0712406	−	0.0849012i	0.800488	+	0.599349i	$0.204574\pi$
$758$	8.65166	−	23.7702i	0.314242	−	0.863374i
$759$	0.412886	−	1.13440i	0.0149868	−	0.0411760i
$760$		0			0
$761$	2.00329	−	11.3612i	0.0726193	−	0.411844i	−0.926728	−	0.375732i	$-0.877391\pi$
$761$	2.00329	−	11.3612i	0.0726193	−	0.411844i	0.999348	−	0.0361126i	$-0.0114975\pi$
$762$	70.8112	+	12.4859i	2.56522	+	0.452317i
$763$	−12.7497	+	7.36105i	−0.461570	+	0.266488i
$764$	−15.4119	−	18.3672i	−0.557583	−	0.664501i
$765$		0			0
$766$	8.93152	−	15.4698i	0.322709	−	0.558948i
$767$	8.14271	+	14.1036i	0.294016	+	0.509251i
$768$	14.0507	+	11.7900i	0.507013	+	0.425434i
$769$	−27.7964	−	16.0483i	−1.00236	−	0.578715i	−0.0934169	−	0.995627i	$-0.529779\pi$
$769$	−27.7964	−	16.0483i	−1.00236	−	0.578715i	−0.908947	+	0.416912i	$0.863112\pi$
$770$		0			0
$771$			10.0523i			0.362023i
$772$	10.0144	−	1.76580i	0.360424	−	0.0635525i
$773$	12.6857	−	10.6446i	0.456273	−	0.382859i	−0.385484	−	0.922714i	$-0.625966\pi$
$773$	12.6857	−	10.6446i	0.456273	−	0.382859i	0.841758	+	0.539856i	$0.181521\pi$
$774$	2.15054	+	0.782732i	0.0772996	+	0.0281347i
$775$		0			0
$776$	−37.9801			−1.36341
$777$	10.1955	−	5.25017i	0.365761	−	0.188349i
$778$	−5.87127			−0.210495
$779$	2.77664	+	7.62875i	0.0994833	+	0.273328i
$780$		0			0
$781$	0.318333	−	0.267113i	0.0113908	−	0.00955805i
$782$	−30.6927	+	5.41194i	−1.09757	+	0.193531i
$783$			18.9778i			0.678212i
$784$	0.824339	+	4.67506i	0.0294407	+	0.166966i
$785$		0			0
$786$	60.9487	+	51.1421i	2.17397	+	1.82418i
$787$	25.0585	+	43.4026i	0.893240	+	1.54714i	0.835968	+	0.548778i	$0.184907\pi$
$787$	25.0585	+	43.4026i	0.893240	+	1.54714i	0.0572717	+	0.998359i	$0.481760\pi$
$788$	−18.8883	+	32.7155i	−0.672868	+	1.16544i
$789$	13.1317	−	4.77953i	0.467499	−	0.170156i
$790$		0			0
$791$	16.4557	−	9.50071i	0.585098	−	0.337806i
$792$	0.0540489	+	0.00953028i	0.00192054	+	0.000338644i
$793$	−9.16205	+	51.9606i	−0.325354	+	1.84517i
$794$	−28.7975	+	34.3195i	−1.02198	+	1.21795i
$795$		0			0
$796$	22.7802	−	62.5880i	0.807422	−	2.21837i
$797$	4.10771	−	4.89537i	0.145502	−	0.173403i	−0.688371	−	0.725359i	$-0.741674\pi$
$797$	4.10771	−	4.89537i	0.145502	−	0.173403i	0.833873	+	0.551956i	$0.186118\pi$
$798$	2.89060	−	16.3934i	0.102326	−	0.580320i
$799$	46.3527	+	8.17324i	1.63984	+	0.289148i
$800$		0			0
$801$	0.647065	+	0.771142i	0.0228629	+	0.0272470i
$802$	54.6530	−	19.8921i	1.92986	−	0.702413i
$803$	0.0261173	−	0.0452364i	0.000921658	−	0.00159636i
$804$	−24.6896	−	42.7636i	−0.870734	−	1.50816i
$805$		0			0
$806$	28.1148	+	16.2321i	0.990303	+	0.571751i
$807$	−2.42425	−	13.7486i	−0.0853375	−	0.483973i
$808$			11.4312i			0.402147i
$809$	34.4240	−	6.06987i	1.21028	−	0.213405i	0.468144	−	0.883652i	$-0.344923\pi$
$809$	34.4240	−	6.06987i	1.21028	−	0.213405i	0.742138	+	0.670247i	$0.233812\pi$
$810$		0			0
$811$	24.0701	+	8.76081i	0.845216	+	0.307634i	0.728088	−	0.685483i	$-0.240409\pi$
$811$	24.0701	+	8.76081i	0.845216	+	0.307634i	0.117128	+	0.993117i	$0.462631\pi$
$812$	4.14810	+	11.3968i	0.145570	+	0.399950i
$813$	−49.1204			−1.72273
$814$	1.34784	+	2.61743i	0.0472419	+	0.0917407i
$815$		0			0
$816$	2.13359	+	5.86200i	0.0746907	+	0.205211i
$817$	34.7332	+	12.6419i	1.21516	+	0.442283i
$818$	10.6489	−	8.93548i	0.372330	−	0.312422i
$819$	−0.677031	+	0.119379i	−0.0236574	+	0.00417143i
$820$		0			0
$821$	−1.57030	−	8.90559i	−0.0548037	−	0.310807i	0.945067	−	0.326876i	$-0.105996\pi$
$821$	−1.57030	−	8.90559i	−0.0548037	−	0.310807i	−0.999871	+	0.0160689i	$0.994885\pi$
$822$	−34.7510	−	20.0635i	−1.21208	−	0.699796i
$823$	12.7322	+	10.6836i	0.443818	+	0.372407i	0.837136	−	0.546995i	$-0.184228\pi$
$823$	12.7322	+	10.6836i	0.443818	+	0.372407i	−0.393318	+	0.919402i	$0.628673\pi$
$824$	−14.9045	−	25.8153i	−0.519222	−	0.899319i
$825$		0			0
$826$	−6.19434	+	2.25456i	−0.215529	+	0.0784461i
$827$	−7.29936	−	8.69904i	−0.253824	−	0.302495i	0.624053	−	0.781382i	$-0.285485\pi$
$827$	−7.29936	−	8.69904i	−0.253824	−	0.302495i	−0.877877	+	0.478887i	$0.841040\pi$
$828$	0.908389	−	0.524458i	0.0315687	−	0.0182262i
$829$	−27.3466	−	4.82194i	−0.949787	−	0.167473i	−0.322769	−	0.946478i	$-0.604614\pi$
$829$	−27.3466	−	4.82194i	−0.949787	−	0.167473i	−0.627018	+	0.779005i	$0.715725\pi$
$830$		0			0
$831$	20.8334	−	24.8283i	0.722702	−	0.861283i
$832$	26.4609	−	72.7008i	0.917367	−	2.52045i
$833$	8.74356	−	24.0227i	0.302947	−	0.832339i
$834$	6.64821	−	7.92303i	0.230209	−	0.274352i
$835$		0			0
$836$	2.54076	+	0.448004i	0.0878739	+	0.0154945i
$837$	−10.7504	+	6.20672i	−0.371587	+	0.214536i
$838$	17.0243	+	20.2887i	0.588094	+	0.700863i
$839$	−14.3458	+	5.22145i	−0.495272	+	0.180264i	−0.577566	−	0.816344i	$-0.695998\pi$
$839$	−14.3458	+	5.22145i	−0.495272	+	0.180264i	0.0822941	+	0.996608i	$0.473775\pi$
$840$		0			0
$841$	−7.57154	−	13.1143i	−0.261088	−	0.452217i
$842$	6.84510	+	5.74372i	0.235898	+	0.197942i
$843$	−48.6440	−	28.0847i	−1.67539	−	0.967287i
$844$	−4.09230	−	23.2086i	−0.140863	−	0.798873i
$845$		0			0
$846$	−2.58408	+	0.455642i	−0.0888423	+	0.0156653i
$847$	−8.97283	+	7.52910i	−0.308310	+	0.258703i
$848$	4.75097	+	1.72921i	0.163149	+	0.0593814i
$849$	−8.98204	−	24.6780i	−0.308263	−	0.846945i
$850$		0			0
$851$	17.8275	+	7.47707i	0.611118	+	0.256311i
$852$	10.3608			0.354957
$853$	−10.6321	−	29.2114i	−0.364036	−	1.00018i	−0.977588	−	0.210526i	$-0.932482\pi$
$853$	−10.6321	−	29.2114i	−0.364036	−	1.00018i	0.613552	−	0.789654i	$-0.289740\pi$
$854$	−20.0687	−	7.30440i	−0.686736	−	0.249951i
$855$		0			0
$856$	9.79179	−	1.72656i	0.334677	−	0.0590125i
$857$		−	17.7963i		−	0.607909i	−0.952687	−	0.303955i	$-0.901693\pi$
$857$		−	17.7963i		−	0.607909i	0.952687	−	0.303955i	$-0.0983071\pi$
$858$	−0.879426	−	4.98747i	−0.0300231	−	0.170269i
$859$	−29.7351	−	17.1675i	−1.01455	−	0.585749i	−0.102028	−	0.994782i	$-0.532533\pi$
$859$	−29.7351	−	17.1675i	−1.01455	−	0.585749i	−0.912520	+	0.409032i	$0.865866\pi$
$860$		0			0
$861$	1.94712	+	3.37251i	0.0663577	+	0.114935i
$862$	37.5167	−	64.9808i	1.27782	−	2.21326i
$863$	26.9153	−	9.79638i	0.916209	−	0.333473i	0.159480	−	0.987201i	$-0.449018\pi$
$863$	26.9153	−	9.79638i	0.916209	−	0.333473i	0.756729	+	0.653728i	$0.226796\pi$
$864$	21.3803	+	25.4801i	0.727374	+	0.866851i
$865$		0			0
$866$	−18.9945	−	3.34924i	−0.645459	−	0.113812i
$867$	0.628994	−	3.56720i	0.0213618	−	0.121149i
$868$	−5.09930	+	6.07711i	−0.173082	+	0.206271i
$869$	0.118510	−	0.325604i	0.00402019	−	0.0110454i
$870$		0			0
$871$	−35.0688	+	41.7933i	−1.18826	+	1.41611i
$872$	5.62205	−	31.8843i	0.190387	−	1.07974i
$873$	1.72287	+	0.303789i	0.0583104	+	0.0102817i
$874$	24.3019	−	14.0307i	0.822026	−	0.474597i
$875$		0			0
$876$	1.22380	−	0.445427i	0.0413484	−	0.0150496i
$877$	−3.76685	+	6.52438i	−0.127198	+	0.220313i	−0.922590	−	0.385782i	$-0.873932\pi$
$877$	−3.76685	+	6.52438i	−0.127198	+	0.220313i	0.795392	+	0.606095i	$0.207265\pi$
$878$	−6.02019	−	10.4273i	−0.203171	−	0.351903i
$879$	4.20265	+	3.52644i	0.141752	+	0.118944i
$880$		0			0
$881$	−2.73507	−	15.5114i	−0.0921469	−	0.522591i	−0.995584	−	0.0938712i	$-0.970076\pi$
$881$	−2.73507	−	15.5114i	−0.0921469	−	0.522591i	0.903437	−	0.428720i	$-0.141035\pi$
$882$			1.42517i			0.0479880i
$883$	−38.6978	+	6.82347i	−1.30229	+	0.229628i	−0.781417	−	0.624009i	$-0.785503\pi$
$883$	−38.6978	+	6.82347i	−1.30229	+	0.229628i	−0.520868	+	0.853637i	$0.674392\pi$
$884$	−60.4666	+	50.7375i	−2.03371	+	1.70649i
$885$		0			0
$886$	−3.51769	−	9.66477i	−0.118179	−	0.324694i
$887$	26.5275			0.890706			0.445353	−	0.895355i	$-0.353078\pi$
$887$	26.5275			0.890706			0.445353	+	0.895355i	$0.353078\pi$
$888$	−5.56753	+	24.5974i	−0.186834	+	0.825435i
$889$	19.4133			0.651100
$890$		0			0
$891$	1.88550	+	0.686266i	0.0631666	+	0.0229908i
$892$	−32.5202	+	27.2877i	−1.08886	+	0.913659i
$893$	−41.7352	+	7.35904i	−1.39662	+	0.246261i
$894$			19.1447i			0.640295i
$895$		0			0
$896$	15.0362	+	8.68115i	0.502324	+	0.290017i
$897$	−25.4747	−	21.3758i	−0.850577	−	0.713719i
$898$	−14.1693	−	24.5420i	−0.472837	−	0.818978i
$899$	−4.53192	+	7.84952i	−0.151148	+	0.261796i
$900$		0			0
$901$	−17.5011	−	20.8570i	−0.583046	−	0.694847i
$902$	−0.865805	+	0.499873i	−0.0288281	+	0.0166439i
$903$	17.4609	+	3.07883i	0.581062	+	0.102457i
$904$	−7.25624	+	41.1522i	−0.241339	+	1.36870i
$905$		0			0
$906$	25.0821	−	68.9124i	0.833296	−	2.28946i
$907$	−7.73188	+	21.2432i	−0.256733	+	0.705368i	0.742631	+	0.669701i	$0.233578\pi$
$907$	−7.73188	+	21.2432i	−0.256733	+	0.705368i	−0.999364	+	0.0356669i	$0.988644\pi$
$908$	17.5336	−	20.8957i	0.581872	−	0.693448i
$909$	0.0914338	−	0.518547i	0.00303267	−	0.0171991i
$910$		0			0
$911$	33.8325	−	19.5332i	1.12092	−	0.647165i	0.179286	−	0.983797i	$-0.442621\pi$
$911$	33.8325	−	19.5332i	1.12092	−	0.647165i	0.941636	+	0.336632i	$0.109288\pi$
$912$	−3.61040	−	4.30270i	−0.119552	−	0.142477i
$913$	0.289271	−	0.105286i	0.00957346	−	0.00348445i
$914$	34.1336	−	59.1212i	1.12904	−	1.95555i
$915$		0			0
$916$	−28.6154	−	24.0112i	−0.945479	−	0.793351i
$917$	18.6033	+	10.7406i	0.614334	+	0.354686i
$918$	−8.68142	−	49.2348i	−0.286529	−	1.62499i
$919$			20.5177i			0.676815i	0.941000	+	0.338408i	$0.109888\pi$
$919$			20.5177i			0.676815i	−0.941000	+	0.338408i	$0.890112\pi$
$920$		0			0
$921$	−7.17731	+	6.02248i	−0.236500	+	0.198447i
$922$	1.54810	+	0.563461i	0.0509838	+	0.0185566i
$923$	−3.91522	−	10.7570i	−0.128871	−	0.354070i
$924$	1.23756			0.0407129
$925$		0			0
$926$	−20.2625			−0.665867
$927$	0.469618	+	1.29026i	0.0154243	+	0.0423778i
$928$	22.8220	+	8.30652i	0.749168	+	0.272675i
$929$	−3.64896	+	3.06184i	−0.119719	+	0.100456i	−0.700682	−	0.713474i	$-0.747121\pi$
$929$	−3.64896	+	3.06184i	−0.119719	+	0.100456i	0.580963	+	0.813930i	$0.302676\pi$
$930$		0			0
$931$			23.0178i			0.754379i
$932$	5.06746	+	28.7390i	0.165990	+	0.941377i
$933$	0.886878	+	0.512039i	0.0290351	+	0.0167634i
$934$	−51.9804	−	43.6167i	−1.70085	−	1.42718i
$935$		0			0
$936$	0.755932	−	1.30931i	0.0247084	−	0.0427962i
$937$	−22.4066	+	8.15535i	−0.731993	+	0.266424i	−0.681008	−	0.732276i	$-0.738458\pi$
$937$	−22.4066	+	8.15535i	−0.731993	+	0.266424i	−0.0509848	+	0.998699i	$0.516236\pi$
$938$	−14.1949	−	16.9168i	−0.463478	−	0.552352i
$939$	11.2374	−	6.48792i	0.366719	−	0.211725i
$940$		0			0
$941$	−4.24043	+	24.0487i	−0.138234	+	0.783965i	0.834319	+	0.551283i	$0.185861\pi$
$941$	−4.24043	+	24.0487i	−0.138234	+	0.783965i	−0.972553	+	0.232683i	$0.925250\pi$
$942$	51.2353	−	61.0599i	1.66934	−	1.98944i
$943$	−2.24527	+	6.16882i	−0.0731160	+	0.200884i
$944$	−0.760732	+	2.09009i	−0.0247597	+	0.0680267i
$945$		0			0
$946$	−0.790408	+	4.48263i	−0.0256984	+	0.145743i
$947$	1.41799	+	0.250030i	0.0460785	+	0.00812489i	0.196640	−	0.980476i	$-0.436997\pi$
$947$	1.41799	+	0.250030i	0.0460785	+	0.00812489i	−0.150561	+	0.988601i	$0.548108\pi$
$948$	7.48174	−	4.31958i	0.242996	−	0.140294i
$949$	−0.924915	−	1.10227i	−0.0300240	−	0.0357812i
$950$		0			0
$951$	20.0397	−	34.7098i	0.649831	−	1.12554i
$952$	−5.48862	−	9.50657i	−0.177887	−	0.308110i
$953$	20.6848	+	17.3566i	0.670047	+	0.562237i	0.913079	−	0.407782i	$-0.133698\pi$
$953$	20.6848	+	17.3566i	0.670047	+	0.562237i	−0.243032	+	0.970018i	$0.578142\pi$
$954$	1.31449	+	0.758923i	0.0425583	+	0.0245710i
$955$		0			0
$956$		−	42.6322i		−	1.37882i
$957$	1.39248	−	0.245531i	0.0450124	−	0.00793690i
$958$	−10.2857	+	8.63069i	−0.332314	+	0.278845i
$959$	−10.1805	−	3.70541i	−0.328747	−	0.119654i
$960$		0			0
$961$	25.0713			0.808752
$962$	80.4533	−	10.2295i	2.59392	−	0.329814i
$963$	−0.457991			−0.0147585
$964$	−10.6294	−	29.2040i	−0.342350	−	0.940598i
$965$		0			0
$966$	10.3115	−	8.65234i	0.331766	−	0.278385i
$967$	−57.3879	+	10.1190i	−1.84547	+	0.325406i	−0.983409	−	0.181400i	$-0.941937\pi$
$967$	−57.3879	+	10.1190i	−1.84547	+	0.325406i	−0.862060	+	0.506806i	$0.830826\pi$
$968$		−	25.7591i		−	0.827929i
$969$	5.25241	+	29.7879i	0.168732	+	0.956926i
$970$		0			0
$971$	−29.8320	−	25.0320i	−0.957353	−	0.803315i	0.0231674	−	0.999732i	$-0.492625\pi$
$971$	−29.8320	−	25.0320i	−0.957353	−	0.803315i	−0.980520	+	0.196417i	$0.937069\pi$
$972$	1.71411	+	2.96892i	0.0549800	+	0.0952281i
$973$	1.39622	−	2.41833i	0.0447609	−	0.0775281i
$974$	−63.0858	+	22.9614i	−2.02140	+	0.735730i
$975$		0			0
$976$	−6.24071	+	3.60307i	−0.199760	+	0.115332i
$977$	−4.24774	−	0.748992i	−0.135897	−	0.0239624i	0.105286	−	0.994442i	$-0.466424\pi$
$977$	−4.24774	−	0.748992i	−0.135897	−	0.0239624i	−0.241183	+	0.970480i	$0.577535\pi$
$978$	9.22652	−	52.3262i	0.295031	−	1.67321i
$979$	−1.28697	+	1.53375i	−0.0411317	+	0.0490188i
$980$		0			0
$981$	−0.510061	+	1.40138i	−0.0162850	+	0.0447427i
$982$	−49.0215	+	58.4215i	−1.56434	+	1.86431i
$983$	−6.29543	+	35.7032i	−0.200793	+	1.13875i	0.703131	+	0.711061i	$0.251785\pi$
$983$	−6.29543	+	35.7032i	−0.200793	+	1.13875i	−0.903924	+	0.427694i	$0.859326\pi$
$984$	−8.43393	−	1.48713i	−0.268864	−	0.0474080i
$985$		0			0
$986$	−23.4643	−	27.9637i	−0.747257	−	0.890546i
$987$	−19.1026	+	6.95278i	−0.608043	+	0.221310i
$988$	35.5352	−	61.5488i	1.13052	−	1.95813i
$989$	14.9444	+	25.8844i	0.475204	+	0.823077i
$990$		0			0
$991$	−3.80747	−	2.19825i	−0.120948	−	0.0698296i	0.438305	−	0.898826i	$-0.355579\pi$
$991$	−3.80747	−	2.19825i	−0.120948	−	0.0698296i	−0.559254	+	0.828997i	$0.688912\pi$
$992$	2.75857	+	15.6446i	0.0875846	+	0.496717i
$993$			4.75978i			0.151047i
$994$	4.56317	−	0.804609i	0.144735	−	0.0255207i
$995$		0			0
$996$	7.21227	+	2.62505i	0.228529	+	0.0831779i
$997$	−16.7124	−	45.9168i	−0.529286	−	1.45420i	−0.859914	−	0.510440i	$-0.829483\pi$
$997$	−16.7124	−	45.9168i	−0.529286	−	1.45420i	0.330628	−	0.943761i	$-0.392740\pi$
$998$	−13.5330			−0.428378
$999$	−11.9941	+	28.5974i	−0.379477	+	0.904783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.326.15		96
5.2	odd	4		185.2.v.a.104.2	✓	96
5.3	odd	4		185.2.v.a.104.15	yes	96
5.4	even	2	inner	925.2.bb.e.326.2		96
37.21	even	18	inner	925.2.bb.e.576.15		96
185.58	odd	36		185.2.v.a.169.2	yes	96
185.132	odd	36		185.2.v.a.169.15	yes	96
185.169	even	18	inner	925.2.bb.e.576.2		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.2	✓	96	5.2	odd	4
185.2.v.a.104.15	yes	96	5.3	odd	4
185.2.v.a.169.2	yes	96	185.58	odd	36
185.2.v.a.169.15	yes	96	185.132	odd	36
925.2.bb.e.326.2		96	5.4	even	2	inner
925.2.bb.e.326.15		96	1.1	even	1	trivial
925.2.bb.e.576.2		96	185.169	even	18	inner
925.2.bb.e.576.15		96	37.21	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.768352 + 2.11103i) q^{2} +(1.65672 + 0.602996i) q^{3} +(-2.33399 + 1.95845i) q^{4} +3.96069i q^{6} +(0.185690 + 1.05310i) q^{7} +(-2.03660 - 1.17583i) q^{8} +(0.0829802 + 0.0696287i) q^{9} +(-0.107723 + 0.186582i) q^{11} +(-5.04770 + 1.83721i) q^{12} +(3.81491 + 4.54644i) q^{13} +(-2.08045 + 1.20115i) q^{14} +(-0.140756 + 0.798269i) q^{16} +(2.80586 - 3.34390i) q^{17} +(-0.0832301 + 0.228673i) q^{18} +(-1.34424 + 3.69328i) q^{19} +(-0.327380 + 1.85667i) q^{21} +(-0.476650 - 0.0840463i) q^{22} +(-2.75237 + 1.58908i) q^{23} +(-2.66505 - 3.17608i) q^{24} +(-6.66646 + 11.5467i) q^{26} +(-2.54908 - 4.41513i) q^{27} +(-2.49585 - 2.09427i) q^{28} +(-3.22377 - 1.86124i) q^{29} -2.43489i q^{31} +(-6.42519 + 1.13293i) q^{32} +(-0.290976 + 0.244158i) q^{33} +(9.21496 + 3.35397i) q^{34} -0.330039 q^{36} +(-3.68154 - 4.84213i) q^{37} -8.82947 q^{38} +(3.57876 + 9.83255i) q^{39} +(1.58232 - 1.32773i) q^{41} +(-4.17102 + 0.735463i) q^{42} -9.40443i q^{43} +(-0.113987 - 0.646452i) q^{44} +(-5.46938 - 4.58935i) q^{46} +(5.39131 + 9.33803i) q^{47} +(-0.714547 + 1.23763i) q^{48} +(5.50330 - 2.00304i) q^{49} +(6.66489 - 3.84797i) q^{51} +(-17.8079 - 3.14002i) q^{52} +(1.08310 - 6.14257i) q^{53} +(7.36188 - 8.77355i) q^{54} +(0.860094 - 2.36309i) q^{56} +(-4.45407 + 5.30815i) q^{57} +(1.45215 - 8.23556i) q^{58} +(2.70230 + 0.476488i) q^{59} +(5.71443 + 6.81019i) q^{61} +(5.14012 - 1.87085i) q^{62} +(-0.0579175 + 0.100316i) q^{63} +(-6.51787 - 11.2893i) q^{64} +(-0.738996 - 0.426660i) q^{66} +(1.59627 + 9.05289i) q^{67} +13.2998i q^{68} +(-5.51811 + 0.972991i) q^{69} +(-1.81248 - 0.659688i) q^{71} +(-0.0871258 - 0.239376i) q^{72} -0.242447 q^{73} +(7.39317 - 11.4923i) q^{74} +(-4.09565 - 11.2527i) q^{76} +(-0.216494 - 0.0787973i) q^{77} +(-18.0071 + 15.1097i) q^{78} +(-1.58386 + 0.279276i) q^{79} +(-1.61723 - 9.17175i) q^{81} +(4.01865 + 2.32017i) q^{82} +(-1.09454 - 0.918429i) q^{83} +(-2.87208 - 4.97460i) q^{84} +(19.8530 - 7.22591i) q^{86} +(-4.21856 - 5.02748i) q^{87} +(0.438779 - 0.253329i) q^{88} +(9.15190 + 1.61373i) q^{89} +(-4.07947 + 4.86173i) q^{91} +(3.31186 - 9.09926i) q^{92} +(1.46823 - 4.03393i) q^{93} +(-15.5704 + 18.5561i) q^{94} +(-11.3279 - 1.99741i) q^{96} +(13.9866 - 8.07516i) q^{97} +(8.45694 + 10.0786i) q^{98} +(-0.0219304 + 0.00798202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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