LMFDB - Embedded newform 925.2.bc.b.599.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(49,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14]))

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

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

chi := DirichletCharacter("925.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bc (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			599.2
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	925.599
Dual form			925.2.bc.b.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.460802 + 1.26604i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(0.141559 - 0.118782i) q^{4} -2.53209 q^{6} +(0.684040 - 0.120615i) q^{7} +(2.54920 + 1.47178i) q^{8} +(-0.407604 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.460802 + 1.26604i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(0.141559 - 0.118782i) q^{4} -2.53209 q^{6} +(0.684040 - 0.120615i) q^{7} +(2.54920 + 1.47178i) q^{8} +(-0.407604 - 0.342020i) q^{9} +(3.20574 - 5.55250i) q^{11} +(0.118782 + 0.326352i) q^{12} +(1.47254 + 1.75490i) q^{13} +(0.467911 + 0.810446i) q^{14} +(-0.624485 + 3.54163i) q^{16} +(-2.49362 + 2.97178i) q^{17} +(0.245188 - 0.673648i) q^{18} +(5.08512 + 1.85083i) q^{19} +(-0.226682 + 1.28558i) q^{21} +(8.50692 + 1.50000i) q^{22} +(5.19615 - 3.00000i) q^{23} +(-4.23783 + 3.55596i) q^{24} +(-1.54323 + 2.67296i) q^{26} +(-4.01676 + 2.31908i) q^{27} +(0.0825054 - 0.0983261i) q^{28} +(-0.979055 + 1.69577i) q^{29} -7.10607 q^{31} +(1.02606 - 0.180922i) q^{32} +(7.74535 + 9.23055i) q^{33} +(-4.91147 - 1.78763i) q^{34} -0.0983261 q^{36} +(-0.300767 - 6.07532i) q^{37} +7.29086i q^{38} +(-4.04576 + 1.47254i) q^{39} +(0.549163 - 0.460802i) q^{41} +(-1.73205 + 0.305407i) q^{42} +2.65270i q^{43} +(-0.205737 - 1.16679i) q^{44} +(6.19253 + 5.19615i) q^{46} +(0.232589 - 0.134285i) q^{47} +(-5.85327 - 3.37939i) q^{48} +(-6.12449 + 2.22913i) q^{49} +(-3.64543 - 6.31407i) q^{51} +(0.416902 + 0.0735111i) q^{52} +(-5.25173 - 0.926022i) q^{53} +(-4.78699 - 4.01676i) q^{54} +(1.92127 + 0.699287i) q^{56} +(-6.53731 + 7.79086i) q^{57} +(-2.59808 - 0.458111i) q^{58} +(-0.358441 + 2.03282i) q^{59} +(-1.67365 + 1.40436i) q^{61} +(-3.27449 - 8.99660i) q^{62} +(-0.320070 - 0.184793i) q^{63} +(4.29813 + 7.44459i) q^{64} +(-8.11721 + 14.0594i) q^{66} +(-0.962858 + 0.169778i) q^{67} +0.716881i q^{68} +(1.95811 + 11.1050i) q^{69} +(6.80453 + 2.47665i) q^{71} +(-0.535685 - 1.47178i) q^{72} -7.17024i q^{73} +(7.55303 - 3.18031i) q^{74} +(0.939693 - 0.342020i) q^{76} +(1.52314 - 4.18479i) q^{77} +(-3.72859 - 4.44356i) q^{78} +(-2.04323 - 11.5878i) q^{79} +(-1.79086 - 10.1565i) q^{81} +(0.836452 + 0.482926i) q^{82} +(-9.01660 + 10.7456i) q^{83} +(0.120615 + 0.208911i) q^{84} +(-3.35844 + 1.22237i) q^{86} +(-2.36549 - 2.81908i) q^{87} +(16.3441 - 9.43629i) q^{88} +(0.486329 - 2.75811i) q^{89} +(1.21894 + 1.02281i) q^{91} +(0.379217 - 1.04189i) q^{92} +(4.56769 - 12.5496i) q^{93} +(0.277189 + 0.232589i) q^{94} +(-0.340022 + 1.92836i) q^{96} +(2.18615 - 1.26217i) q^{97} +(-5.64436 - 6.72668i) q^{98} +(-3.20574 + 1.16679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{4} - 12 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q + 18 * q^4 - 12 * q^6 - 12 * q^9	$ 12 q + 18 q^{4} - 12 q^{6} - 12 q^{9} + 18 q^{11} + 24 q^{14} + 18 q^{16} + 18 q^{19} + 24 q^{21} - 12 q^{24} + 12 q^{26} - 18 q^{29} - 36 q^{31} - 18 q^{34} - 48 q^{36} + 12 q^{39} + 30 q^{41} + 18 q^{44} - 36 q^{46} - 48 q^{49} - 12 q^{51} - 42 q^{54} - 12 q^{56} + 12 q^{59} - 18 q^{61} + 24 q^{64} - 36 q^{66} + 36 q^{69} - 24 q^{71} + 66 q^{74} + 6 q^{79} + 42 q^{81} + 24 q^{84} - 24 q^{86} + 48 q^{89} + 84 q^{91} - 18 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) $ 12 * q + 18 * q^4 - 12 * q^6 - 12 * q^9 + 18 * q^11 + 24 * q^14 + 18 * q^16 + 18 * q^19 + 24 * q^21 - 12 * q^24 + 12 * q^26 - 18 * q^29 - 36 * q^31 - 18 * q^34 - 48 * q^36 + 12 * q^39 + 30 * q^41 + 18 * q^44 - 36 * q^46 - 48 * q^49 - 12 * q^51 - 42 * q^54 - 12 * q^56 + 12 * q^59 - 18 * q^61 + 24 * q^64 - 36 * q^66 + 36 * q^69 - 24 * q^71 + 66 * q^74 + 6 * q^79 + 42 * q^81 + 24 * q^84 - 24 * q^86 + 48 * q^89 + 84 * q^91 - 18 * q^94 + 36 * q^96 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$

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 $

$2$	0.460802	+	1.26604i	0.325837	+	0.895229i	0.989153	+	0.146889i	$0.0469262\pi$
$2$	0.460802	+	1.26604i	0.325837	+	0.895229i	−0.663316	+	0.748339i	$0.730852\pi$
$3$	−0.642788	+	1.76604i	−0.371114	+	1.01963i	0.603818	+	0.797122i	$0.293645\pi$
$3$	−0.642788	+	1.76604i	−0.371114	+	1.01963i	−0.974932	+	0.222504i	$0.928577\pi$
$4$	0.141559	−	0.118782i	0.0707796	−	0.0593912i
$5$		0			0
$5$		0			0
$6$	−2.53209			−1.03372
$7$	0.684040	−	0.120615i	0.258543	−	0.0455881i	−0.0428742	−	0.999080i	$-0.513651\pi$
$7$	0.684040	−	0.120615i	0.258543	−	0.0455881i	0.301417	+	0.953492i	$0.402540\pi$
$8$	2.54920	+	1.47178i	0.901278	+	0.520353i
$9$	−0.407604	−	0.342020i	−0.135868	−	0.114007i
$10$		0			0
$11$	3.20574	−	5.55250i	0.966566	−	1.67414i	0.261219	−	0.965280i	$-0.415876\pi$
$11$	3.20574	−	5.55250i	0.966566	−	1.67414i	0.705347	−	0.708862i	$-0.250791\pi$
$12$	0.118782	+	0.326352i	0.0342895	+	0.0942097i
$13$	1.47254	+	1.75490i	0.408408	+	0.486722i	0.930565	−	0.366128i	$-0.119317\pi$
$13$	1.47254	+	1.75490i	0.408408	+	0.486722i	−0.522156	+	0.852850i	$0.674872\pi$
$14$	0.467911	+	0.810446i	0.125055	+	0.216601i
$15$		0			0
$16$	−0.624485	+	3.54163i	−0.156121	+	0.885408i
$17$	−2.49362	+	2.97178i	−0.604792	+	0.720763i	−0.978376	−	0.206833i	$-0.933684\pi$
$17$	−2.49362	+	2.97178i	−0.604792	+	0.720763i	0.373584	+	0.927596i	$0.378129\pi$
$18$	0.245188	−	0.673648i	0.0577913	−	0.158780i
$19$	5.08512	+	1.85083i	1.16661	+	0.424610i	0.851453	−	0.524430i	$-0.175722\pi$
$19$	5.08512	+	1.85083i	1.16661	+	0.424610i	0.315154	+	0.949041i	$0.397944\pi$
$20$		0			0
$21$	−0.226682	+	1.28558i	−0.0494660	+	0.280536i
$22$	8.50692	+	1.50000i	1.81368	+	0.319801i
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$	−4.23783	+	3.55596i	−0.865043	+	0.725857i
$25$		0			0
$26$	−1.54323	+	2.67296i	−0.302653	+	0.524210i
$27$	−4.01676	+	2.31908i	−0.773026	+	0.446307i
$28$	0.0825054	−	0.0983261i	0.0155920	−	0.0185819i
$29$	−0.979055	+	1.69577i	−0.181806	+	0.314897i	−0.942496	−	0.334219i	$-0.891528\pi$
$29$	−0.979055	+	1.69577i	−0.181806	+	0.314897i	0.760690	+	0.649116i	$0.224861\pi$
$30$		0			0
$31$	−7.10607			−1.27629			−0.638144	−	0.769917i	$-0.720297\pi$
$31$	−7.10607			−1.27629			−0.638144	+	0.769917i	$0.720297\pi$
$32$	1.02606	−	0.180922i	0.181384	−	0.0319828i
$33$	7.74535	+	9.23055i	1.34829	+	1.60683i
$34$	−4.91147	−	1.78763i	−0.842311	−	0.306576i
$35$		0			0
$36$	−0.0983261			−0.0163877
$37$	−0.300767	−	6.07532i	−0.0494459	−	0.998777i
$37$	−0.300767	−	6.07532i	−0.0494459	−	0.998777i
$38$			7.29086i			1.18273i
$39$	−4.04576	+	1.47254i	−0.647840	+	0.235794i
$40$		0			0
$41$	0.549163	−	0.460802i	0.0857649	−	0.0719653i	−0.598897	−	0.800826i	$-0.704394\pi$
$41$	0.549163	−	0.460802i	0.0857649	−	0.0719653i	0.684662	+	0.728861i	$0.259950\pi$
$42$	−1.73205	+	0.305407i	−0.267261	+	0.0471254i
$43$			2.65270i			0.404534i	0.979330	+	0.202267i	$0.0648308\pi$
$43$			2.65270i			0.404534i	−0.979330	+	0.202267i	$0.935169\pi$
$44$	−0.205737	−	1.16679i	−0.0310160	−	0.175901i
$45$		0			0
$46$	6.19253	+	5.19615i	0.913039	+	0.766131i
$47$	0.232589	−	0.134285i	0.0339266	−	0.0195875i	−0.482941	−	0.875653i	$-0.660431\pi$
$47$	0.232589	−	0.134285i	0.0339266	−	0.0195875i	0.516867	+	0.856065i	$0.327098\pi$
$48$	−5.85327	−	3.37939i	−0.844846	−	0.487772i
$49$	−6.12449	+	2.22913i	−0.874926	+	0.318447i
$50$		0			0
$51$	−3.64543	−	6.31407i	−0.510462	−	0.884147i
$52$	0.416902	+	0.0735111i	0.0578139	+	0.0101942i
$53$	−5.25173	−	0.926022i	−0.721381	−	0.127199i	−0.199108	−	0.979977i	$-0.563805\pi$
$53$	−5.25173	−	0.926022i	−0.721381	−	0.127199i	−0.522273	+	0.852779i	$0.674916\pi$
$54$	−4.78699	−	4.01676i	−0.651427	−	0.546612i
$55$		0			0
$56$	1.92127	+	0.699287i	0.256741	+	0.0934461i
$57$	−6.53731	+	7.79086i	−0.865887	+	1.03192i
$58$	−2.59808	−	0.458111i	−0.341144	−	0.0601529i
$59$	−0.358441	+	2.03282i	−0.0466650	+	0.264650i	−0.999210	−	0.0397483i	$-0.987344\pi$
$59$	−0.358441	+	2.03282i	−0.0466650	+	0.264650i	0.952545	+	0.304399i	$0.0984555\pi$
$60$		0			0
$61$	−1.67365	+	1.40436i	−0.214289	+	0.179810i	−0.743614	−	0.668610i	$-0.766890\pi$
$61$	−1.67365	+	1.40436i	−0.214289	+	0.179810i	0.529325	+	0.848419i	$0.322445\pi$
$62$	−3.27449	−	8.99660i	−0.415861	−	1.14257i
$63$	−0.320070	−	0.184793i	−0.0403250	−	0.0232817i
$64$	4.29813	+	7.44459i	0.537267	+	0.930573i
$65$		0			0
$66$	−8.11721	+	14.0594i	−0.999160	+	1.73060i
$67$	−0.962858	+	0.169778i	−0.117632	+	0.0207417i	−0.232154	−	0.972679i	$-0.574577\pi$
$67$	−0.962858	+	0.169778i	−0.117632	+	0.0207417i	0.114522	+	0.993421i	$0.463466\pi$
$68$			0.716881i			0.0869346i
$69$	1.95811	+	11.1050i	0.235729	+	1.33688i
$70$		0			0
$71$	6.80453	+	2.47665i	0.807549	+	0.293924i	0.712611	−	0.701559i	$-0.247512\pi$
$71$	6.80453	+	2.47665i	0.807549	+	0.293924i	0.0949381	+	0.995483i	$0.469735\pi$
$72$	−0.535685	−	1.47178i	−0.0631310	−	0.173451i
$73$		−	7.17024i		−	0.839214i	−0.907706	−	0.419607i	$-0.862168\pi$
$73$		−	7.17024i		−	0.839214i	0.907706	−	0.419607i	$-0.137832\pi$
$74$	7.55303	−	3.18031i	0.878022	−	0.369703i
$75$		0			0
$76$	0.939693	−	0.342020i	0.107790	−	0.0392324i
$77$	1.52314	−	4.18479i	0.173578	−	0.476901i
$78$	−3.72859	−	4.44356i	−0.422180	−	0.503134i
$79$	−2.04323	−	11.5878i	−0.229882	−	1.30372i	−0.853129	−	0.521699i	$-0.825298\pi$
$79$	−2.04323	−	11.5878i	−0.229882	−	1.30372i	0.623248	−	0.782025i	$-0.285813\pi$
$80$		0			0
$81$	−1.79086	−	10.1565i	−0.198984	−	1.12850i
$82$	0.836452	+	0.482926i	0.0923707	+	0.0533302i
$83$	−9.01660	+	10.7456i	−0.989701	+	1.17948i	−0.00594199	+	0.999982i	$0.501891\pi$
$83$	−9.01660	+	10.7456i	−0.989701	+	1.17948i	−0.983759	+	0.179497i	$0.942553\pi$
$84$	0.120615	+	0.208911i	0.0131601	+	0.0227940i
$85$		0			0
$86$	−3.35844	+	1.22237i	−0.362150	+	0.131812i
$87$	−2.36549	−	2.81908i	−0.253607	−	0.302237i
$88$	16.3441	−	9.43629i	1.74229	−	1.00591i
$89$	0.486329	−	2.75811i	0.0515508	−	0.292359i	−0.948123	−	0.317904i	$-0.897021\pi$
$89$	0.486329	−	2.75811i	0.0515508	−	0.292359i	0.999674	+	0.0255449i	$0.00813209\pi$
$90$		0			0
$91$	1.21894	+	1.02281i	0.127780	+	0.107220i
$92$	0.379217	−	1.04189i	0.0395361	−	0.108624i
$93$	4.56769	−	12.5496i	0.473648	−	1.30134i
$94$	0.277189	+	0.232589i	0.0285898	+	0.0239897i
$95$		0			0
$96$	−0.340022	+	1.92836i	−0.0347034	+	0.196813i
$97$	2.18615	−	1.26217i	0.221970	−	0.128154i	−0.384892	−	0.922962i	$-0.625761\pi$
$97$	2.18615	−	1.26217i	0.221970	−	0.128154i	0.606862	+	0.794807i	$0.292428\pi$
$98$	−5.64436	−	6.72668i	−0.570166	−	0.679497i
$99$	−3.20574	+	1.16679i	−0.322189	+	0.117267i
$100$		0			0
$101$	3.38666	+	5.86587i	0.336985	+	0.583675i	0.983864	−	0.178917i	$-0.0572594\pi$
$101$	3.38666	+	5.86587i	0.336985	+	0.583675i	−0.646879	+	0.762593i	$0.723926\pi$
$102$	6.31407	−	7.52481i	0.625186	−	0.745068i
$103$	−8.51363	−	4.91534i	−0.838873	−	0.484323i	0.0180083	−	0.999838i	$-0.494267\pi$
$103$	−8.51363	−	4.91534i	−0.838873	−	0.484323i	−0.856881	+	0.515515i	$0.827601\pi$
$104$	1.17096	+	6.64084i	0.114822	+	0.651188i
$105$		0			0
$106$	−1.24763	−	7.07564i	−0.121180	−	0.687247i
$107$	−2.99070	−	3.56418i	−0.289122	−	0.344562i	0.601859	−	0.798602i	$-0.294427\pi$
$107$	−2.99070	−	3.56418i	−0.289122	−	0.344562i	−0.890981	+	0.454040i	$0.849982\pi$
$108$	−0.293144	+	0.805407i	−0.0282078	+	0.0775004i
$109$	−2.87939	+	1.04801i	−0.275795	+	0.100381i	−0.476215	−	0.879329i	$-0.657992\pi$
$109$	−2.87939	+	1.04801i	−0.275795	+	0.100381i	0.200420	+	0.979710i	$0.435769\pi$
$110$		0			0
$111$	10.9226	+	3.37397i	1.03673	+	0.320243i
$112$			2.49794i			0.236033i
$113$	5.37316	+	14.7626i	0.505465	+	1.38875i	0.885870	+	0.463933i	$0.153562\pi$
$113$	5.37316	+	14.7626i	0.505465	+	1.38875i	−0.380406	+	0.924820i	$0.624216\pi$
$114$	−12.8760	−	4.68647i	−1.20595	−	0.438929i
$115$		0			0
$116$	0.0628336	+	0.356347i	0.00583395	+	0.0330860i
$117$		−	1.21894i		−	0.112691i
$118$	−2.73881	+	0.482926i	−0.252128	+	0.0444569i
$119$	−1.34730	+	2.33359i	−0.123506	+	0.213919i
$120$		0			0
$121$	−15.0535	−	26.0734i	−1.36850	−	2.37031i
$122$	−2.54920	−	1.47178i	−0.230794	−	0.133249i
$123$	0.460802	+	1.26604i	0.0415492	+	0.114155i
$124$	−1.00593	+	0.844075i	−0.0903352	+	0.0758002i
$125$		0			0
$126$	0.0864665	−	0.490376i	0.00770305	−	0.0436861i
$127$	−13.5278	−	2.38532i	−1.20040	−	0.211662i	−0.462527	−	0.886605i	$-0.653057\pi$
$127$	−13.5278	−	2.38532i	−1.20040	−	0.211662i	−0.737870	+	0.674943i	$0.764168\pi$
$128$	−6.10516	+	7.27584i	−0.539625	+	0.643100i
$129$	−4.68479	−	1.70513i	−0.412473	−	0.150128i
$130$		0			0
$131$	7.40033	+	6.20961i	0.646570	+	0.542536i	0.906028	−	0.423218i	$-0.139100\pi$
$131$	7.40033	+	6.20961i	0.646570	+	0.542536i	−0.259458	+	0.965754i	$0.583544\pi$
$132$	2.19285	+	0.386659i	0.190863	+	0.0336544i
$133$	3.70167	+	0.652704i	0.320975	+	0.0565966i
$134$	−0.658633	−	1.14079i	−0.0568973	−	0.0985489i
$135$		0			0
$136$	−10.7306	+	3.90560i	−0.920137	+	0.334903i
$137$	4.65020	+	2.68479i	0.397293	+	0.229377i	0.685315	−	0.728246i	$-0.259664\pi$
$137$	4.65020	+	2.68479i	0.397293	+	0.229377i	−0.288022	+	0.957624i	$0.592998\pi$
$138$	−13.1571	+	7.59627i	−1.12001	+	0.646637i
$139$	0.699807	+	0.587208i	0.0593569	+	0.0498063i	0.671983	−	0.740566i	$-0.265443\pi$
$139$	0.699807	+	0.587208i	0.0593569	+	0.0498063i	−0.612627	+	0.790372i	$0.709887\pi$
$140$		0			0
$141$	0.0876485	+	0.497079i	0.00738134	+	0.0418616i
$142$			9.75608i			0.818712i
$143$	14.4646	−	2.55051i	1.20959	−	0.213284i
$144$	1.46585	−	1.23000i	0.122154	−	0.102500i
$145$		0			0
$146$	9.07785	−	3.30407i	0.751288	−	0.273446i
$147$		−	12.2490i		−	1.01028i
$148$	−0.764217	−	0.824292i	−0.0628183	−	0.0677564i
$149$	3.89899			0.319417			0.159709	−	0.987164i	$-0.448945\pi$
$149$	3.89899			0.319417			0.159709	+	0.987164i	$0.448945\pi$
$150$		0			0
$151$	1.56031	+	0.567905i	0.126976	+	0.0462155i	0.404727	−	0.914438i	$-0.367367\pi$
$151$	1.56031	+	0.567905i	0.126976	+	0.0462155i	−0.277751	+	0.960653i	$0.589589\pi$
$152$	10.2390	+	12.2023i	0.830490	+	0.989740i
$153$	2.03282	−	0.358441i	0.164344	−	0.0289782i
$154$	6.00000			0.483494
$155$		0			0
$156$	−0.397804	+	0.689016i	−0.0318498	+	0.0551654i
$157$	4.39506	−	5.23783i	0.350764	−	0.418024i	−0.561597	−	0.827411i	$-0.689813\pi$
$157$	4.39506	−	5.23783i	0.350764	−	0.418024i	0.912361	+	0.409387i	$0.134257\pi$
$158$	13.7291	−	7.92649i	1.09223	−	0.630598i
$159$	5.01114	−	8.67956i	0.397410	−	0.688334i
$160$		0			0
$161$	3.19253	−	2.67885i	0.251607	−	0.211123i
$162$	12.0333	−	6.94743i	0.945426	−	0.545842i
$163$	11.0149	+	1.94222i	0.862751	+	0.152126i	0.587478	−	0.809240i	$-0.300121\pi$
$163$	11.0149	+	1.94222i	0.862751	+	0.152126i	0.275273	+	0.961366i	$0.411232\pi$
$164$	0.0230039	−	0.130462i	0.00179630	−	0.0101874i
$165$		0			0
$166$	−17.7592	−	6.46383i	−1.37838	−	0.501691i
$167$	−2.66036	+	7.30928i	−0.205865	+	0.565609i	−0.999060	−	0.0433592i	$-0.986194\pi$
$167$	−2.66036	+	7.30928i	−0.205865	+	0.565609i	0.793195	+	0.608968i	$0.208416\pi$
$168$	−2.46994	+	2.94356i	−0.190560	+	0.227101i
$169$	1.34611	−	7.63419i	0.103547	−	0.587246i
$170$		0			0
$171$	−1.43969	−	2.49362i	−0.110096	−	0.190692i
$172$	0.315094	+	0.375515i	0.0240257	+	0.0286327i
$173$	−5.70583	−	15.6766i	−0.433806	−	1.19187i	−0.943458	−	0.331492i	$-0.892448\pi$
$173$	−5.70583	−	15.6766i	−0.433806	−	1.19187i	0.509652	−	0.860381i	$-0.329774\pi$
$174$	2.47906	−	4.29385i	0.187937	−	0.325516i
$175$		0			0
$176$	17.6630	+	14.8210i	1.33140	+	1.11717i
$177$	−3.35965	−	1.93969i	−0.252526	−	0.145796i
$178$	3.71599	−	0.655230i	0.278525	−	0.0491116i
$179$	4.94087			0.369298			0.184649	−	0.982805i	$-0.440885\pi$
$179$	4.94087			0.369298			0.184649	+	0.982805i	$0.440885\pi$
$180$		0			0
$181$	18.4834	−	15.5094i	1.37386	−	1.15281i	0.402437	−	0.915447i	$-0.368163\pi$
$181$	18.4834	−	15.5094i	1.37386	−	1.15281i	0.971422	−	0.237358i	$-0.0762814\pi$
$182$	−0.733235	+	2.01455i	−0.0543510	+	0.149328i
$183$	−1.40436	−	3.85844i	−0.103813	−	0.285224i
$184$	17.6614			1.30201
$185$		0			0
$186$	17.9932			1.31932
$187$	8.50692	+	23.3726i	0.622088	+	1.70917i
$188$	0.0169744	−	0.0466368i	0.00123799	−	0.00340134i
$189$	−2.46791	+	2.07082i	−0.179514	+	0.150630i
$190$		0			0
$191$	17.2267			1.24648			0.623239	−	0.782031i	$-0.285816\pi$
$191$	17.2267			1.24648			0.623239	+	0.782031i	$0.285816\pi$
$192$	−15.9103	+	2.80541i	−1.14822	+	0.202463i
$193$	−9.42182	−	5.43969i	−0.678198	−	0.391558i	0.120978	−	0.992655i	$-0.461397\pi$
$193$	−9.42182	−	5.43969i	−0.678198	−	0.391558i	−0.799176	+	0.601098i	$0.794730\pi$
$194$	2.60535	+	2.18615i	0.187053	+	0.156956i
$195$		0			0
$196$	−0.602196	+	1.04303i	−0.0430140	+	0.0745025i
$197$	−1.16009	−	3.18732i	−0.0826529	−	0.227087i	0.891481	−	0.453058i	$-0.149667\pi$
$197$	−1.16009	−	3.18732i	−0.0826529	−	0.227087i	−0.974134	+	0.225971i	$0.927445\pi$
$198$	−2.95442	−	3.52094i	−0.209962	−	0.250223i
$199$	6.90033	+	11.9517i	0.489151	+	0.847235i	0.999922	−	0.0124819i	$-0.00397321\pi$
$199$	6.90033	+	11.9517i	0.489151	+	0.847235i	−0.510771	+	0.859717i	$0.670640\pi$
$200$		0			0
$201$	0.319078	−	1.80958i	0.0225060	−	0.127638i
$202$	−5.86587	+	6.99067i	−0.412721	+	0.491862i
$203$	−0.465178	+	1.27807i	−0.0326491	+	0.0897027i
$204$	−1.26604	−	0.460802i	−0.0886408	−	0.0322626i
$205$		0			0
$206$	2.29994	−	13.0436i	0.160245	−	0.908793i
$207$	−3.14403	−	0.554378i	−0.218525	−	0.0385319i
$208$	−7.13479	+	4.11927i	−0.494708	+	0.285620i
$209$	26.5783	−	22.3019i	1.83846	−	1.54265i
$210$		0			0
$211$	−4.10607	+	7.11192i	−0.282673	+	0.489605i	−0.972042	−	0.234806i	$-0.924555\pi$
$211$	−4.10607	+	7.11192i	−0.282673	+	0.489605i	0.689369	+	0.724410i	$0.257888\pi$
$212$	−0.853427	+	0.492726i	−0.0586136	+	0.0338406i
$213$	−8.74774	+	10.4251i	−0.599385	+	0.714319i
$214$	3.13429	−	5.42874i	0.214255	−	0.371101i
$215$		0			0
$216$	−13.6527			−0.928949
$217$	−4.86084	+	0.857097i	−0.329975	+	0.0581835i
$218$	−2.65366	−	3.16250i	−0.179728	−	0.214192i
$219$	12.6630	+	4.60894i	0.855684	+	0.311444i
$220$		0			0
$221$	−8.88713			−0.597813
$222$	0.761570	+	15.3833i	0.0511132	+	1.03246i
$223$			10.7537i			0.720122i	0.932929	+	0.360061i	$0.117244\pi$
$223$			10.7537i			0.720122i	−0.932929	+	0.360061i	$0.882756\pi$
$224$	0.680045	−	0.247516i	0.0454374	−	0.0165379i
$225$		0			0
$226$	−16.2142	+	13.6053i	−1.07855	+	0.905013i
$227$	0.914901	−	0.161322i	0.0607241	−	0.0107073i	−0.143204	−	0.989693i	$-0.545740\pi$
$227$	0.914901	−	0.161322i	0.0607241	−	0.0107073i	0.203928	+	0.978986i	$0.434629\pi$
$228$			1.87939i			0.124465i
$229$	−4.60994	−	26.1443i	−0.304633	−	1.72766i	−0.625226	−	0.780444i	$-0.714993\pi$
$229$	−4.60994	−	26.1443i	−0.304633	−	1.72766i	0.320593	−	0.947217i	$-0.396118\pi$
$230$		0			0
$231$	6.41147	+	5.37987i	0.421844	+	0.353969i
$232$	−4.99162	+	2.88191i	−0.327716	+	0.189207i
$233$	−3.50038	−	2.02094i	−0.229317	−	0.132396i	0.380940	−	0.924600i	$-0.375601\pi$
$233$	−3.50038	−	2.02094i	−0.229317	−	0.132396i	−0.610257	+	0.792203i	$0.708934\pi$
$234$	1.54323	−	0.561691i	0.100884	−	0.0367189i
$235$		0			0
$236$	0.190722	+	0.330341i	0.0124150	+	0.0215034i
$237$	21.7778	+	3.84002i	1.41462	+	0.249436i
$238$	−3.57526	−	0.630415i	−0.231750	−	0.0408637i
$239$	11.7246	+	9.83813i	0.758403	+	0.636375i	0.937711	−	0.347418i	$-0.112941\pi$
$239$	11.7246	+	9.83813i	0.758403	+	0.636375i	−0.179308	+	0.983793i	$0.557386\pi$
$240$		0			0
$241$	−25.2866	−	9.20356i	−1.62885	−	0.592854i	−0.643812	−	0.765183i	$-0.722648\pi$
$241$	−25.2866	−	9.20356i	−1.62885	−	0.592854i	−0.985039	+	0.172330i	$0.944871\pi$
$242$	26.0734	−	31.0731i	1.67606	−	1.99745i
$243$	5.38484	+	0.949493i	0.345438	+	0.0609100i
$244$	−0.0701076	+	0.397600i	−0.00448818	+	0.0254537i
$245$		0			0
$246$	−1.39053	+	1.16679i	−0.0886569	+	0.0743920i
$247$	4.24000	+	11.6493i	0.269785	+	0.741227i
$248$	−18.1148	−	10.4586i	−1.15029	−	0.664120i
$249$	−13.1814	−	22.8308i	−0.835337	−	1.44685i
$250$		0			0
$251$	11.6630	−	20.2009i	0.736160	−	1.27507i	−0.218052	−	0.975937i	$-0.569970\pi$
$251$	11.6630	−	20.2009i	0.736160	−	1.27507i	0.954212	−	0.299130i	$-0.0966963\pi$
$252$	−0.0672590	+	0.0118596i	−0.00423692	+	0.000747083i
$253$		−	38.4688i		−	2.41852i
$254$	−3.21373	−	18.2259i	−0.201647	−	1.14360i
$255$		0			0
$256$	4.13088	+	1.50352i	0.258180	+	0.0939699i
$257$	−1.01936	−	2.80066i	−0.0635857	−	0.174700i	0.903831	−	0.427889i	$-0.140743\pi$
$257$	−1.01936	−	2.80066i	−0.0635857	−	0.174700i	−0.967417	+	0.253189i	$0.918521\pi$
$258$		−	6.71688i		−	0.418175i
$259$	−0.938511	−	4.11949i	−0.0583162	−	0.255973i
$260$		0			0
$261$	0.979055	−	0.356347i	0.0606020	−	0.0220573i
$262$	−4.45156	+	12.2306i	−0.275018	+	0.755606i
$263$	8.51130	+	10.1434i	0.524829	+	0.625467i	0.961716	−	0.274050i	$-0.0883633\pi$
$263$	8.51130	+	10.1434i	0.524829	+	0.625467i	−0.436886	+	0.899517i	$0.643919\pi$
$264$	6.15910	+	34.9300i	0.379066	+	2.14979i
$265$		0			0
$266$	0.879385	+	4.98724i	0.0539186	+	0.305787i
$267$	4.55834	+	2.63176i	0.278966	+	0.161061i
$268$	−0.116135	+	0.138404i	−0.00709406	+	0.00845438i
$269$	−11.4572	−	19.8445i	−0.698560	−	1.20994i	−0.968966	−	0.247195i	$-0.920491\pi$
$269$	−11.4572	−	19.8445i	−0.698560	−	1.20994i	0.270406	−	0.962746i	$-0.412842\pi$
$270$		0			0
$271$	−20.5865	+	7.49286i	−1.25054	+	0.455159i	−0.880584	−	0.473891i	$-0.842849\pi$
$271$	−20.5865	+	7.49286i	−1.25054	+	0.455159i	−0.369955	+	0.929050i	$0.620627\pi$
$272$	−8.96773	−	10.6873i	−0.543748	−	0.648014i
$273$	−2.58985	+	1.49525i	−0.156745	+	0.0904968i
$274$	−1.25624	+	7.12452i	−0.0758925	+	0.430408i
$275$		0			0
$276$	1.59627	+	1.33943i	0.0960840	+	0.0806240i
$277$	3.84505	−	10.5642i	0.231026	−	0.634740i	−0.768963	−	0.639293i	$-0.779227\pi$
$277$	3.84505	−	10.5642i	0.231026	−	0.634740i	0.999990	+	0.00455313i	$0.00144931\pi$
$278$	−0.420959	+	1.15657i	−0.0252474	+	0.0693667i
$279$	2.89646	+	2.43042i	0.173406	+	0.145505i
$280$		0			0
$281$	0.698463	−	3.96118i	0.0416668	−	0.236304i	−0.956861	−	0.290546i	$-0.906163\pi$
$281$	0.698463	−	3.96118i	0.0416668	−	0.236304i	0.998528	+	0.0542418i	$0.0172742\pi$
$282$	−0.588936	+	0.340022i	−0.0350706	+	0.0202480i
$283$	−13.9582	−	16.6348i	−0.829730	−	0.988833i	−0.999994	−	0.00343496i	$-0.998907\pi$
$283$	−13.9582	−	16.6348i	−0.829730	−	0.988833i	0.170264	−	0.985398i	$-0.445538\pi$
$284$	1.25743	−	0.457666i	0.0746145	−	0.0271575i
$285$		0			0
$286$	9.89440	+	17.1376i	0.585068	+	1.01337i
$287$	0.320070	−	0.381445i	0.0188931	−	0.0225160i
$288$	−0.480105	−	0.277189i	−0.0282905	−	0.0163335i
$289$	0.338678	+	1.92074i	0.0199222	+	0.112985i
$290$		0			0
$291$	0.823826	+	4.67215i	0.0482935	+	0.273886i
$292$	−0.851698	−	1.01501i	−0.0498419	−	0.0593992i
$293$	−7.87268	+	21.6300i	−0.459927	+	1.26364i	0.465613	+	0.884988i	$0.345834\pi$
$293$	−7.87268	+	21.6300i	−0.459927	+	1.26364i	−0.925540	+	0.378650i	$0.876388\pi$
$294$	15.5077	−	5.64436i	0.904430	−	0.329186i
$295$		0			0
$296$	8.17483	−	15.9299i	0.475152	−	0.925905i
$297$			29.7374i			1.72554i
$298$	1.79666	+	4.93629i	0.104078	+	0.285952i
$299$	12.9162	+	4.70112i	0.746964	+	0.271873i
$300$		0			0
$301$	0.319955	+	1.81456i	0.0184419	+	0.104589i
$302$			2.23711i			0.128731i
$303$	−12.5363	+	2.21048i	−0.720191	+	0.126989i
$304$	−9.73055	+	16.8538i	−0.558085	+	0.966632i
$305$		0			0
$306$	1.39053	+	2.40847i	0.0794913	+	0.137683i
$307$	−5.91912	−	3.41740i	−0.337822	−	0.195042i	0.321487	−	0.946914i	$-0.395818\pi$
$307$	−5.91912	−	3.41740i	−0.337822	−	0.195042i	−0.659308	+	0.751873i	$0.729151\pi$
$308$	−0.281465	−	0.773318i	−0.0160380	−	0.0440639i
$309$	14.1532	−	11.8759i	0.805146	−	0.675597i
$310$		0			0
$311$	−0.267389	+	1.51644i	−0.0151622	+	0.0859892i	−0.991450	−	0.130488i	$-0.958346\pi$
$311$	−0.267389	+	1.51644i	−0.0151622	+	0.0859892i	0.976288	+	0.216477i	$0.0694567\pi$
$312$	−12.4807	−	2.20068i	−0.706581	−	0.124589i
$313$	14.0501	−	16.7442i	0.794157	−	0.946439i	−0.205323	−	0.978694i	$-0.565824\pi$
$313$	14.0501	−	16.7442i	0.794157	−	0.946439i	0.999480	+	0.0322549i	$0.0102688\pi$
$314$	8.65657	+	3.15074i	0.488519	+	0.177806i
$315$		0			0
$316$	−1.66566	−	1.39765i	−0.0937006	−	0.0786242i
$317$	−26.8216	−	4.72937i	−1.50645	−	0.265628i	−0.641359	−	0.767241i	$-0.721629\pi$
$317$	−26.8216	−	4.72937i	−1.50645	−	0.265628i	−0.865092	+	0.501613i	$0.832740\pi$
$318$	13.2979	+	2.34477i	0.745707	+	0.131488i
$319$	6.27719	+	10.8724i	0.351455	+	0.608738i
$320$		0			0
$321$	8.21688	−	2.99070i	0.458622	−	0.166925i
$322$	4.86267	+	2.80747i	0.270986	+	0.156454i
$323$	−18.1806	+	10.4966i	−1.01160	+	0.584046i
$324$	−1.45992	−	1.22502i	−0.0811068	−	0.0680567i
$325$		0			0
$326$	2.61674	+	14.8403i	0.144928	+	0.821928i
$327$		−	5.75877i		−	0.318461i
$328$	2.07813	−	0.366430i	0.114745	−	0.0202327i
$329$	0.142903	−	0.119910i	0.00787852	−	0.00661087i
$330$		0			0
$331$	−14.1912	+	5.16517i	−0.780018	+	0.283903i	−0.701180	−	0.712984i	$-0.747343\pi$
$331$	−14.1912	+	5.16517i	−0.780018	+	0.283903i	−0.0788380	+	0.996887i	$0.525121\pi$
$332$			2.59215i			0.142263i
$333$	−1.95529	+	2.57919i	−0.107149	+	0.141339i
$334$	−10.4798			−0.573428
$335$		0			0
$336$	−4.41147	−	1.60565i	−0.240666	−	0.0875951i
$337$	−8.98530	−	10.7083i	−0.489460	−	0.583316i	0.463620	−	0.886034i	$-0.346550\pi$
$337$	−8.98530	−	10.7083i	−0.489460	−	0.583316i	−0.953080	+	0.302718i	$0.902106\pi$
$338$	10.2855	−	1.81361i	0.559459	−	0.0986476i
$339$	−29.5253			−1.60359
$340$		0			0
$341$	−22.7802	+	39.4564i	−1.23362	+	2.13669i
$342$	2.49362	−	2.97178i	0.134840	−	0.160696i
$343$	−8.13127	+	4.69459i	−0.439047	+	0.253484i
$344$	−3.90420	+	6.76227i	−0.210500	+	0.364597i
$345$		0			0
$346$	17.2181	−	14.4477i	0.925649	−	0.776712i
$347$	3.31077	−	1.91147i	0.177731	−	0.102613i	−0.408495	−	0.912761i	$-0.633946\pi$
$347$	3.31077	−	1.91147i	0.177731	−	0.102613i	0.586226	+	0.810147i	$0.300613\pi$
$348$	−0.669713	−	0.118089i	−0.0359004	−	0.00633021i
$349$	−3.08630	+	17.5033i	−0.165206	+	0.936930i	0.783646	+	0.621208i	$0.213358\pi$
$349$	−3.08630	+	17.5033i	−0.165206	+	0.936930i	−0.948852	+	0.315722i	$0.897753\pi$
$350$		0			0
$351$	−9.98457	−	3.63409i	−0.532937	−	0.193973i
$352$	2.28471	−	6.27719i	0.121775	−	0.334575i
$353$	−3.01000	+	3.58718i	−0.160206	+	0.190926i	−0.840176	−	0.542314i	$-0.817548\pi$
$353$	−3.01000	+	3.58718i	−0.160206	+	0.190926i	0.679970	+	0.733240i	$0.261993\pi$
$354$	0.907604	−	5.14728i	0.0482386	−	0.273575i
$355$		0			0
$356$	−0.258770	−	0.448204i	−0.0137148	−	0.0237547i
$357$	−3.25519	−	3.87939i	−0.172283	−	0.205319i
$358$	2.27677	+	6.25537i	0.120331	+	0.330606i
$359$	−8.81908	+	15.2751i	−0.465453	+	0.806188i	−0.999222	−	0.0394420i	$-0.987442\pi$
$359$	−8.81908	+	15.2751i	−0.465453	+	0.806188i	0.533769	+	0.845630i	$0.320775\pi$
$360$		0			0
$361$	7.87804	+	6.61046i	0.414634	+	0.347919i
$362$	28.1528	+	16.2540i	1.47968	+	0.854292i
$363$	55.7230	−	9.82547i	2.92470	−	0.515704i
$364$	0.294045			0.0154121
$365$		0			0
$366$	4.23783	−	3.55596i	0.221515	−	0.185873i
$367$	4.84386	−	13.3084i	0.252848	−	0.694693i	−0.746716	−	0.665143i	$-0.768370\pi$
$367$	4.84386	−	13.3084i	0.252848	−	0.694693i	0.999563	−	0.0295496i	$-0.00940730\pi$
$368$	7.37997	+	20.2763i	0.384708	+	1.05698i
$369$	−0.381445			−0.0198572
$370$		0			0
$371$	−3.70409			−0.192307
$372$	−0.844075	−	2.31908i	−0.0437633	−	0.120239i
$373$	−6.51363	+	17.8960i	−0.337263	+	0.926622i	0.648904	+	0.760870i	$0.275227\pi$
$373$	−6.51363	+	17.8960i	−0.337263	+	0.926622i	−0.986167	+	0.165752i	$0.946995\pi$
$374$	−25.6707	+	21.5403i	−1.32740	+	1.11382i
$375$		0			0
$376$	0.790555			0.0407697
$377$	−4.41761	+	0.778943i	−0.227518	+	0.0401176i
$378$	−3.75897	−	2.17024i	−0.193341	−	0.111625i
$379$	−11.5608	−	9.70064i	−0.593837	−	0.498288i	0.295621	−	0.955305i	$-0.404473\pi$
$379$	−11.5608	−	9.70064i	−0.593837	−	0.498288i	−0.889458	+	0.457017i	$0.848918\pi$
$380$		0			0
$381$	12.9081	−	22.3574i	0.661300	−	1.14541i
$382$	7.93810	+	21.8097i	0.406148	+	1.11588i
$383$	−6.60224	−	7.86824i	−0.337359	−	0.402048i	0.570518	−	0.821285i	$-0.306742\pi$
$383$	−6.60224	−	7.86824i	−0.337359	−	0.402048i	−0.907877	+	0.419236i	$0.862298\pi$
$384$	−8.92514	−	15.4588i	−0.455459	−	0.788879i
$385$		0			0
$386$	2.54529	−	14.4351i	0.129552	−	0.734726i
$387$	0.907278	−	1.08125i	0.0461195	−	0.0549631i
$388$	0.159546	−	0.438348i	0.00809971	−	0.0222538i
$389$	−21.6789	−	7.89046i	−1.09916	−	0.400062i	−0.272155	−	0.962254i	$-0.587736\pi$
$389$	−21.6789	−	7.89046i	−1.09916	−	0.400062i	−0.827007	+	0.562191i	$0.809958\pi$
$390$		0			0
$391$	−4.04189	+	22.9227i	−0.204407	+	1.15925i
$392$	−18.8933	−	3.33140i	−0.954257	−	0.168261i
$393$	−15.7233	+	9.07785i	−0.793135	+	0.457917i
$394$	3.50072	−	2.93745i	0.176363	−	0.147987i
$395$		0			0
$396$	−0.315207	+	0.545955i	−0.0158398	+	0.0274353i
$397$	17.3375	−	10.0098i	0.870143	−	0.502377i	0.00274745	−	0.999996i	$-0.499125\pi$
$397$	17.3375	−	10.0098i	0.870143	−	0.502377i	0.867396	+	0.497619i	$0.165792\pi$
$398$	−11.9517	+	14.2435i	−0.599086	+	0.713963i
$399$	−3.53209	+	6.11776i	−0.176826	+	0.306271i
$400$		0			0
$401$	15.1753			0.757818			0.378909	−	0.925434i	$-0.376299\pi$
$401$	15.1753			0.757818			0.378909	+	0.925434i	$0.376299\pi$
$402$	2.43804	−	0.429892i	0.121598	−	0.0214411i
$403$	−10.4639	−	12.4704i	−0.521246	−	0.621197i
$404$	1.17617	+	0.428092i	0.0585169	+	0.0212984i
$405$		0			0
$406$	−1.83244			−0.0909427
$407$	−34.6974	−	17.8059i	−1.71989	−	0.882604i
$408$		−	21.4611i		−	1.06248i
$409$	3.31016	−	1.20480i	0.163677	−	0.0595734i	−0.258882	−	0.965909i	$-0.583354\pi$
$409$	3.31016	−	1.20480i	0.163677	−	0.0595734i	0.422559	+	0.906335i	$0.361132\pi$
$410$		0			0
$411$	−7.73055	+	6.48670i	−0.381320	+	0.319965i
$412$	−1.78904	+	0.315456i	−0.0881396	+	0.0155414i
$413$			1.43376i			0.0705509i
$414$	−0.746911	−	4.23594i	−0.0367087	−	0.208185i
$415$		0			0
$416$	1.82841	+	1.53422i	0.0896452	+	0.0752213i
$417$	−1.48686	+	0.858441i	−0.0728120	+	0.0420380i
$418$	40.4825	+	23.3726i	1.98006	+	1.14319i
$419$	−5.24510	+	1.90906i	−0.256240	+	0.0932637i	−0.466946	−	0.884286i	$-0.654646\pi$
$419$	−5.24510	+	1.90906i	−0.256240	+	0.0932637i	0.210706	+	0.977549i	$0.432424\pi$
$420$		0			0
$421$	−5.20099	−	9.00838i	−0.253481	−	0.439041i	0.711001	−	0.703191i	$-0.248242\pi$
$421$	−5.20099	−	9.00838i	−0.253481	−	0.439041i	−0.964482	+	0.264149i	$0.914909\pi$
$422$	−10.8961	−	1.92127i	−0.530413	−	0.0935262i
$423$	−0.140732	−	0.0248149i	−0.00684265	−	0.00120654i
$424$	−12.0248	−	10.0900i	−0.583977	−	0.490015i
$425$		0			0
$426$	−17.2297	−	6.27109i	−0.834780	−	0.303835i
$427$	−0.975457	+	1.16250i	−0.0472057	+	0.0562575i
$428$	−0.846723	−	0.149300i	−0.0409279	−	0.00721669i
$429$	−4.79339	+	27.1846i	−0.231427	+	1.31249i
$430$		0			0
$431$	23.6648	−	19.8571i	1.13989	−	0.956483i	0.140457	−	0.990087i	$-0.455143\pi$
$431$	23.6648	−	19.8571i	1.13989	−	0.956483i	0.999435	+	0.0336034i	$0.0106983\pi$
$432$	−5.70491	−	15.6741i	−0.274478	−	0.754121i
$433$	11.5354	+	6.65998i	0.554357	+	0.320058i	0.750877	−	0.660442i	$-0.229631\pi$
$433$	11.5354	+	6.65998i	0.554357	+	0.320058i	−0.196521	+	0.980500i	$0.562964\pi$
$434$	−3.32501	−	5.75908i	−0.159605	−	0.276445i
$435$		0			0
$436$	−0.283119	+	0.490376i	−0.0135589	+	0.0234847i
$437$	31.9756	−	5.63816i	1.52960	−	0.269710i
$438$			18.1557i			0.867513i
$439$	4.35962	+	24.7246i	0.208073	+	1.18004i	0.892530	+	0.450989i	$0.148929\pi$
$439$	4.35962	+	24.7246i	0.208073	+	1.18004i	−0.684456	+	0.729054i	$0.739960\pi$
$440$		0			0
$441$	3.25877	+	1.18610i	0.155180	+	0.0564807i
$442$	−4.09521	−	11.2515i	−0.194789	−	0.535179i
$443$		−	28.8384i		−	1.37016i	−0.728470	−	0.685078i	$-0.759768\pi$
$443$		−	28.8384i		−	1.37016i	0.728470	−	0.685078i	$-0.240232\pi$
$444$	1.94697	−	0.819797i	0.0923989	−	0.0389058i
$445$		0			0
$446$	−13.6147	+	4.95534i	−0.644674	+	0.234642i
$447$	−2.50622	+	6.88578i	−0.118540	+	0.325686i
$448$	3.83802	+	4.57398i	0.181330	+	0.216100i
$449$	2.62877	+	14.9085i	0.124059	+	0.703574i	0.981862	+	0.189596i	$0.0607178\pi$
$449$	2.62877	+	14.9085i	0.124059	+	0.703574i	−0.857803	+	0.513978i	$0.828171\pi$
$450$		0			0
$451$	−0.798133	−	4.52644i	−0.0375826	−	0.213142i
$452$	2.51416	+	1.45155i	0.118256	+	0.0682753i
$453$	−2.00589	+	2.39053i	−0.0942451	+	0.112317i
$454$	0.625829	+	1.08397i	0.0293716	+	0.0508731i
$455$		0			0
$456$	−28.1313	+	10.2390i	−1.31737	+	0.479484i
$457$	−19.2397	−	22.9290i	−0.899997	−	1.07257i	−0.997009	−	0.0772909i	$-0.975373\pi$
$457$	−19.2397	−	22.9290i	−0.899997	−	1.07257i	0.0970121	−	0.995283i	$-0.469071\pi$
$458$	30.9755	−	17.8837i	1.44739	−	0.835651i
$459$	3.12449	−	17.7198i	0.145838	−	0.827091i
$460$		0			0
$461$	−29.6826	−	24.9066i	−1.38246	−	1.16002i	−0.968294	−	0.249814i	$-0.919630\pi$
$461$	−29.6826	−	24.9066i	−1.38246	−	1.16002i	−0.414161	−	0.910203i	$-0.635925\pi$
$462$	−3.85673	+	10.5963i	−0.179431	+	0.492983i
$463$	2.47929	−	6.81180i	0.115223	−	0.316571i	−0.868654	−	0.495419i	$-0.835015\pi$
$463$	2.47929	−	6.81180i	0.115223	−	0.316571i	0.983877	+	0.178847i	$0.0572368\pi$
$464$	−5.39440	−	4.52644i	−0.250429	−	0.210135i
$465$		0			0
$466$	0.945622	−	5.36289i	0.0438051	−	0.248431i
$467$	4.35970	−	2.51707i	0.201743	−	0.116476i	−0.395725	−	0.918369i	$-0.629507\pi$
$467$	4.35970	−	2.51707i	0.201743	−	0.116476i	0.597468	+	0.801893i	$0.296173\pi$
$468$	−0.144789	−	0.172552i	−0.00669286	−	0.00797624i
$469$	−0.638156	+	0.232270i	−0.0294673	+	0.0107252i
$470$		0			0
$471$	6.42514	+	11.1287i	0.296055	+	0.512782i
$472$	−3.90560	+	4.65451i	−0.179770	+	0.214241i
$473$	14.7291	+	8.50387i	0.677246	+	0.391008i
$474$	5.17365	+	29.3412i	0.237634	+	1.34769i
$475$		0			0
$476$	0.0864665	+	0.490376i	0.00396318	+	0.0224763i
$477$	1.82391	+	2.17365i	0.0835110	+	0.0995245i
$478$	−7.05277	+	19.3773i	−0.322586	+	0.886298i
$479$	2.69119	−	0.979513i	0.122964	−	0.0447551i	−0.279806	−	0.960057i	$-0.590270\pi$
$479$	2.69119	−	0.979513i	0.122964	−	0.0447551i	0.402769	+	0.915302i	$0.368048\pi$
$480$		0			0
$481$	10.2187	−	9.47395i	0.465932	−	0.431975i
$482$		−	36.2550i		−	1.65137i
$483$	2.67885	+	7.36009i	0.121892	+	0.334896i
$484$	−5.22803	−	1.90285i	−0.237638	−	0.0864930i
$485$		0			0
$486$	1.27925	+	7.25498i	0.0580279	+	0.329092i
$487$			14.4439i			0.654514i	0.944935	+	0.327257i	$0.106124\pi$
$487$			14.4439i			0.654514i	−0.944935	+	0.327257i	$0.893876\pi$
$488$	−6.33337	+	1.11674i	−0.286698	+	0.0505526i
$489$	−10.5103	+	18.2043i	−0.475291	+	0.823228i
$490$		0			0
$491$	17.1887	+	29.7716i	0.775713	+	1.34358i	0.934393	+	0.356245i	$0.115943\pi$
$491$	17.1887	+	29.7716i	0.775713	+	1.34358i	−0.158679	+	0.987330i	$0.550724\pi$
$492$	0.215615	+	0.124485i	0.00972066	+	0.00561222i
$493$	−2.59808	−	7.13816i	−0.117011	−	0.321486i
$494$	−12.7947	+	10.7361i	−0.575662	+	0.483038i
$495$		0			0
$496$	4.43763	−	25.1671i	0.199256	−	1.13003i
$497$	4.95329	+	0.873399i	0.222186	+	0.0391773i
$498$	22.8308	−	27.2087i	1.02307	−	1.21925i
$499$	−37.9800	−	13.8236i	−1.70022	−	0.618829i	−0.704368	−	0.709835i	$-0.748769\pi$
$499$	−37.9800	−	13.8236i	−1.70022	−	0.618829i	−0.995850	+	0.0910068i	$0.970992\pi$
$500$		0			0
$501$	−11.1985	−	9.39663i	−0.500310	−	0.419810i
$502$	30.9495	+	5.45723i	1.38134	+	0.243568i
$503$	14.3023	+	2.52188i	0.637707	+	0.112445i	0.483148	−	0.875539i	$-0.339493\pi$
$503$	14.3023	+	2.52188i	0.637707	+	0.112445i	0.154559	+	0.987984i	$0.450604\pi$
$504$	−0.543948	−	0.942146i	−0.0242294	−	0.0419665i
$505$		0			0
$506$	48.7033	−	17.7265i	2.16512	−	0.788041i
$507$	12.6171	+	7.28446i	0.560343	+	0.323514i
$508$	−2.19832	+	1.26920i	−0.0975346	+	0.0563116i
$509$	−16.5726	−	13.9061i	−0.734569	−	0.616377i	0.196804	−	0.980443i	$-0.436944\pi$
$509$	−16.5726	−	13.9061i	−0.734569	−	0.616377i	−0.931373	+	0.364066i	$0.881388\pi$
$510$		0			0
$511$	−0.864837	−	4.90474i	−0.0382582	−	0.216973i
$512$			24.9186i			1.10126i
$513$	−24.7179	+	4.35844i	−1.09132	+	0.192430i
$514$	3.07604	−	2.58110i	0.135678	−	0.113848i
$515$		0			0
$516$	−0.865715	+	0.315094i	−0.0381110	+	0.0138713i
$517$		−	1.72193i		−	0.0757306i
$518$	4.78299	−	3.08647i	0.210152	−	0.135612i
$519$	31.3533			1.37626
$520$		0			0
$521$	21.6018	+	7.86241i	0.946391	+	0.344458i	0.768687	−	0.639626i	$-0.220911\pi$
$521$	21.6018	+	7.86241i	0.946391	+	0.344458i	0.177705	+	0.984084i	$0.443133\pi$
$522$	0.902302	+	1.07532i	0.0394927	+	0.0470656i
$523$	12.9532	−	2.28400i	0.566403	−	0.0998722i	0.116888	−	0.993145i	$-0.462708\pi$
$523$	12.9532	−	2.28400i	0.566403	−	0.0998722i	0.449515	+	0.893273i	$0.351597\pi$
$524$	1.78518			0.0779859
$525$		0			0
$526$	−8.91993	+	15.4498i	−0.388927	+	0.673642i
$527$	17.7198	−	21.1177i	0.771888	−	0.919901i
$528$	−37.5281	+	21.6668i	−1.63320	+	0.942928i
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	0.841367	−	0.705990i	0.0365122	−	0.0306374i
$532$	0.601535	−	0.347296i	0.0260798	−	0.0150572i
$533$	1.61732	+	0.285178i	0.0700541	+	0.0123524i
$534$	−1.23143	+	6.98378i	−0.0532892	+	0.302218i
$535$		0			0
$536$	−2.70439	−	0.984319i	−0.116812	−	0.0425161i
$537$	−3.17593	+	8.72580i	−0.137052	+	0.376546i
$538$	19.8445	−	23.6498i	0.855558	−	1.01961i
$539$	−7.25624	+	41.1522i	−0.312549	+	1.77255i
$540$		0			0
$541$	17.5988	+	30.4820i	0.756631	+	1.31052i	0.944559	+	0.328341i	$0.106489\pi$
$541$	17.5988	+	30.4820i	0.756631	+	1.31052i	−0.187928	+	0.982183i	$0.560177\pi$
$542$	−18.9726	−	22.6107i	−0.814943	−	0.971211i
$543$	15.5094	+	42.6117i	0.665572	+	1.82865i
$544$	−2.02094	+	3.50038i	−0.0866473	+	0.150077i
$545$		0			0
$546$	−3.08647	−	2.58985i	−0.132089	−	0.110835i
$547$	−21.3100	−	12.3033i	−0.911151	−	0.526053i	−0.0303496	−	0.999539i	$-0.509662\pi$
$547$	−21.3100	−	12.3033i	−0.911151	−	0.526053i	−0.880801	+	0.473486i	$0.842995\pi$
$548$	0.977185	−	0.172304i	0.0417433	−	0.00736046i
$549$	1.16250			0.0496145
$550$		0			0
$551$	−8.11721	+	6.81115i	−0.345805	+	0.290165i
$552$	−11.3525	+	31.1908i	−0.483195	+	1.32757i
$553$	−2.79531	−	7.68004i	−0.118869	−	0.326589i
$554$	15.1465			0.643514
$555$		0			0
$556$	0.168814			0.00715932
$557$	−2.58548	−	7.10354i	−0.109550	−	0.300987i	0.872788	−	0.488099i	$-0.162309\pi$
$557$	−2.58548	−	7.10354i	−0.109550	−	0.300987i	−0.982339	+	0.187112i	$0.940087\pi$
$558$	−1.74232	+	4.78699i	−0.0737584	+	0.202649i
$559$	−4.65523	+	3.90620i	−0.196895	+	0.165215i
$560$		0			0
$561$	−46.7452			−1.97358
$562$	5.33688	−	0.941037i	0.225123	−	0.0396952i
$563$	2.26978	+	1.31046i	0.0956599	+	0.0552293i	0.547067	−	0.837089i	$-0.315744\pi$
$563$	2.26978	+	1.31046i	0.0956599	+	0.0552293i	−0.451407	+	0.892318i	$0.649078\pi$
$564$	0.0714517	+	0.0599551i	0.00300866	+	0.00252457i
$565$		0			0
$566$	14.6284	−	25.3371i	0.614876	−	1.06500i
$567$	−2.45004	−	6.73143i	−0.102892	−	0.282693i
$568$	13.7010	+	16.3282i	0.574882	+	0.685118i
$569$	8.19728	+	14.1981i	0.343648	+	0.595216i	0.985107	−	0.171941i	$-0.0550040\pi$
$569$	8.19728	+	14.1981i	0.343648	+	0.595216i	−0.641459	+	0.767157i	$0.721671\pi$
$570$		0			0
$571$	−4.94444	+	28.0413i	−0.206918	+	1.17349i	0.687474	+	0.726209i	$0.258720\pi$
$571$	−4.94444	+	28.0413i	−0.206918	+	1.17349i	−0.894392	+	0.447283i	$0.852392\pi$
$572$	1.74465	−	2.07919i	0.0729475	−	0.0869354i
$573$	−11.0731	+	30.4231i	−0.462585	+	1.27094i
$574$	0.630415	+	0.229452i	0.0263130	+	0.00957715i
$575$		0			0
$576$	0.794263	−	4.50449i	0.0330943	−	0.187687i
$577$	24.0389	+	4.23870i	1.00075	+	0.176460i	0.649939	−	0.759986i	$-0.274794\pi$
$577$	24.0389	+	4.23870i	1.00075	+	0.176460i	0.350812	+	0.936446i	$0.385905\pi$
$578$	−2.27568	+	1.31386i	−0.0946557	+	0.0546495i
$579$	15.6630	−	13.1428i	0.650931	−	0.546196i
$580$		0			0
$581$	−4.87164	+	8.43794i	−0.202110	+	0.350065i
$582$	−5.53553	+	3.19594i	−0.229455	+	0.132476i
$583$	−21.9774	+	26.1917i	−0.910211	+	1.08475i
$584$	10.5530	−	18.2784i	0.436688	−	0.756365i
$585$		0			0
$586$	−31.0123			−1.28111
$587$	−36.0152	+	6.35045i	−1.48651	+	0.262111i	−0.857175	−	0.515026i	$-0.827782\pi$
$587$	−36.0152	+	6.35045i	−1.48651	+	0.262111i	−0.629332	+	0.777137i	$0.716671\pi$
$588$	−1.45496	−	1.73396i	−0.0600016	−	0.0715071i
$589$	−36.1352	−	13.1521i	−1.48893	−	0.541925i
$590$		0			0
$591$	6.37464			0.262218
$592$	21.7044	+	2.72874i	0.892044	+	0.112151i
$593$		−	22.2344i		−	0.913058i	−0.889708	−	0.456529i	$-0.849092\pi$
$593$		−	22.2344i		−	0.913058i	0.889708	−	0.456529i	$-0.150908\pi$
$594$	−37.6489	+	13.7031i	−1.54475	+	0.562244i
$595$		0			0
$596$	0.551938	−	0.463131i	0.0226082	−	0.0189706i
$597$	−25.5427	+	4.50387i	−1.04539	+	0.184331i
$598$			18.5188i			0.757290i
$599$	0.0346151	+	0.196312i	0.00141433	+	0.00802109i	0.985507	−	0.169636i	$-0.0542593\pi$
$599$	0.0346151	+	0.196312i	0.00141433	+	0.00802109i	−0.984092	+	0.177657i	$0.943148\pi$
$600$		0			0
$601$	6.14337	+	5.15490i	0.250593	+	0.210273i	0.759428	−	0.650592i	$-0.225479\pi$
$601$	6.14337	+	5.15490i	0.250593	+	0.210273i	−0.508834	+	0.860864i	$0.669923\pi$
$602$	−2.14987	+	1.24123i	−0.0876223	+	0.0505887i
$603$	0.450532	+	0.260115i	0.0183471	+	0.0105927i
$604$	0.288333	−	0.104945i	0.0117321	−	0.00427014i
$605$		0			0
$606$	−8.57532	−	14.8529i	−0.348349	−	0.603358i
$607$	−0.412846	−	0.0727959i	−0.0167569	−	0.00295469i	0.165263	−	0.986249i	$-0.447153\pi$
$607$	−0.412846	−	0.0727959i	−0.0167569	−	0.00295469i	−0.182020	+	0.983295i	$0.558264\pi$
$608$	5.55250	+	0.979055i	0.225184	+	0.0397059i
$609$	−1.95811	−	1.64305i	−0.0793467	−	0.0665798i
$610$		0			0
$611$	0.578153	+	0.210430i	0.0233896	+	0.00851311i
$612$	0.245188	−	0.292204i	0.00991113	−	0.0118116i
$613$	−1.85175	−	0.326514i	−0.0747916	−	0.0131878i	0.136127	−	0.990691i	$-0.456534\pi$
$613$	−1.85175	−	0.326514i	−0.0747916	−	0.0131878i	−0.210919	+	0.977504i	$0.567646\pi$
$614$	1.59904	−	9.06861i	0.0645321	−	0.365979i
$615$		0			0
$616$	10.0419	−	8.42615i	0.404599	−	0.339499i
$617$	5.91241	+	16.2442i	0.238025	+	0.653968i	0.999980	+	0.00633794i	$0.00201744\pi$
$617$	5.91241	+	16.2442i	0.238025	+	0.653968i	−0.761955	+	0.647630i	$0.775760\pi$
$618$	21.5573	+	12.4461i	0.867160	+	0.500655i
$619$	19.9204	+	34.5031i	0.800668	+	1.38680i	0.919177	+	0.393845i	$0.128855\pi$
$619$	19.9204	+	34.5031i	0.800668	+	1.38680i	−0.118508	+	0.992953i	$0.537811\pi$
$620$		0			0
$621$	−13.9145	+	24.1006i	−0.558368	+	0.967122i
$622$	−2.04309	+	0.360252i	−0.0819204	+	0.0144448i
$623$		−	1.94532i		−	0.0779375i
$624$	−2.68866	−	15.2482i	−0.107633	−	0.610415i
$625$		0			0
$626$	27.6732	+	10.0722i	1.10605	+	0.402567i
$627$	22.3019	+	61.2738i	0.890650	+	2.44704i
$628$		−	1.26352i		−	0.0504199i
$629$	18.8045	+	14.2557i	0.749786	+	0.568413i
$630$		0			0
$631$	1.14883	−	0.418141i	0.0457343	−	0.0166459i	−0.319052	−	0.947737i	$-0.603364\pi$
$631$	1.14883	−	0.418141i	0.0457343	−	0.0166459i	0.364786	+	0.931091i	$0.381142\pi$
$632$	11.8460	−	32.5467i	0.471210	−	1.29464i
$633$	−9.92063	−	11.8229i	−0.394310	−	0.469920i
$634$	−6.37186	−	36.1366i	−0.253059	−	1.43517i
$635$		0			0
$636$	−0.321604	−	1.82391i	−0.0127524	−	0.0723226i
$637$	−12.9304	−	7.46538i	−0.512322	−	0.295789i
$638$	−10.8724	+	12.9572i	−0.430443	+	0.512982i
$639$	−1.92649	−	3.33678i	−0.0762107	−	0.132001i
$640$		0			0
$641$	−32.0171	+	11.6533i	−1.26460	+	0.460277i	−0.885310	−	0.465001i	$-0.846054\pi$
$641$	−32.0171	+	11.6533i	−1.26460	+	0.460277i	−0.379290	+	0.925278i	$0.623832\pi$
$642$	7.57272	+	9.02481i	0.298871	+	0.356181i
$643$	−1.23292	+	0.711829i	−0.0486218	+	0.0280718i	−0.524114	−	0.851648i	$-0.675603\pi$
$643$	−1.23292	+	0.711829i	−0.0486218	+	0.0280718i	0.475492	+	0.879720i	$0.342270\pi$
$644$	0.133732	−	0.758433i	0.00526979	−	0.0298865i
$645$		0			0
$646$	−21.6668	−	18.1806i	−0.852470	−	0.715308i
$647$	5.46145	−	15.0052i	0.214712	−	0.589916i	−0.784845	−	0.619692i	$-0.787257\pi$
$647$	5.46145	−	15.0052i	0.214712	−	0.589916i	0.999557	+	0.0297766i	$0.00947957\pi$
$648$	10.3828	−	28.5266i	0.407877	−	1.12063i
$649$	10.1382	+	8.50692i	0.397957	+	0.333926i
$650$		0			0
$651$	1.61081	−	9.13538i	0.0631328	−	0.358044i
$652$	1.78996	−	1.03343i	0.0701002	−	0.0404724i
$653$	−0.0836332	−	0.0996702i	−0.00327282	−	0.00390040i	0.764406	−	0.644736i	$-0.223033\pi$
$653$	−0.0836332	−	0.0996702i	−0.00327282	−	0.00390040i	−0.767678	+	0.640835i	$0.778588\pi$
$654$	7.29086	−	2.65366i	0.285095	−	0.103766i
$655$		0			0
$656$	1.28905	+	2.23270i	0.0503289	+	0.0871722i
$657$	−2.45237	+	2.92262i	−0.0956760	+	0.114022i
$658$	0.217662	+	0.125667i	0.00848535	+	0.00489902i
$659$	4.27925	+	24.2688i	0.166696	+	0.945379i	0.947299	+	0.320352i	$0.103801\pi$
$659$	4.27925	+	24.2688i	0.166696	+	0.945379i	−0.780603	+	0.625027i	$0.785088\pi$
$660$		0			0
$661$	5.06402	+	28.7195i	0.196967	+	1.11706i	0.909589	+	0.415509i	$0.136397\pi$
$661$	5.06402	+	28.7195i	0.196967	+	1.11706i	−0.712622	+	0.701549i	$0.752492\pi$
$662$	−13.0787	−	15.5866i	−0.508317	−	0.605789i
$663$	5.71253	−	15.6951i	0.221856	−	0.609546i
$664$	−38.8002	+	14.1221i	−1.50574	+	0.548045i
$665$		0			0
$666$	−4.16637	−	1.28698i	−0.161444	−	0.0498696i
$667$			11.7487i			0.454910i
$668$	0.491615	+	1.35070i	0.0190211	+	0.0522601i
$669$	−18.9915	−	6.91236i	−0.734256	−	0.267247i
$670$		0			0
$671$	2.43242	+	13.7949i	0.0939025	+	0.532547i
$672$			1.36009i			0.0524666i
$673$	−46.1924	+	8.14496i	−1.78059	+	0.313965i	−0.964523	−	0.263999i	$-0.914959\pi$
$673$	−46.1924	+	8.14496i	−1.78059	+	0.313965i	−0.816062	+	0.577964i	$0.803847\pi$
$674$	9.41669	−	16.3102i	0.362717	−	0.628245i
$675$		0			0
$676$	−0.716252	−	1.24059i	−0.0275482	−	0.0477148i
$677$	33.4439	+	19.3089i	1.28535	+	0.742100i	0.977822	−	0.209437i	$-0.0671632\pi$
$677$	33.4439	+	19.3089i	1.28535	+	0.742100i	0.307533	+	0.951537i	$0.400497\pi$
$678$	−13.6053	−	37.3803i	−0.522509	−	1.43558i
$679$	1.34318	−	1.12706i	0.0515464	−	0.0432526i
$680$		0			0
$681$	−0.303186	+	1.71945i	−0.0116181	+	0.0658895i
$682$	−60.4508	−	10.6591i	−2.31478	−	0.408158i
$683$	9.12106	−	10.8701i	0.349008	−	0.415931i	−0.562771	−	0.826613i	$-0.690265\pi$
$683$	9.12106	−	10.8701i	0.349008	−	0.415931i	0.911779	+	0.410682i	$0.134709\pi$
$684$	−0.500000	−	0.181985i	−0.0191180	−	0.00695837i
$685$		0			0
$686$	−9.69047	−	8.13127i	−0.369984	−	0.310453i
$687$	49.1351	+	8.66385i	1.87462	+	0.330546i
$688$	−9.39490	−	1.65657i	−0.358177	−	0.0631563i
$689$	−6.10829	−	10.5799i	−0.232707	−	0.403061i
$690$		0			0
$691$	2.53936	−	0.924252i	0.0966019	−	0.0351602i	−0.293267	−	0.956031i	$-0.594743\pi$
$691$	2.53936	−	0.924252i	0.0966019	−	0.0351602i	0.389869	+	0.920870i	$0.372520\pi$
$692$	−2.66982	−	1.54142i	−0.101491	−	0.0585961i
$693$	−2.05212	+	1.18479i	−0.0779536	+	0.0450065i
$694$	3.94562	+	3.31077i	0.149774	+	0.125675i
$695$		0			0
$696$	−1.88103	−	10.6679i	−0.0713004	−	0.404365i
$697$			2.78106i			0.105340i
$698$	−23.5821	+	4.15817i	−0.892597	+	0.157389i
$699$	5.81908	−	4.88279i	0.220098	−	0.184684i
$700$		0			0
$701$	7.82800	−	2.84916i	0.295660	−	0.107611i	−0.189932	−	0.981797i	$-0.560827\pi$
$701$	7.82800	−	2.84916i	0.295660	−	0.107611i	0.485591	+	0.874186i	$0.338604\pi$
$702$		−	14.3155i		−	0.540304i
$703$	9.71497	−	31.4504i	0.366407	−	1.18618i
$704$	55.1147			2.07721
$705$		0			0
$706$	−5.92855	−	2.15782i	−0.223124	−	0.0812104i
$707$	3.02412	+	3.60401i	0.113734	+	0.135543i
$708$	−0.705990	+	0.124485i	−0.0265327	+	0.00467844i
$709$	6.95399			0.261163			0.130581	−	0.991438i	$-0.458316\pi$
$709$	6.95399			0.261163			0.130581	+	0.991438i	$0.458316\pi$
$710$		0			0
$711$	−3.13041	+	5.42204i	−0.117400	+	0.203342i
$712$	5.29909	−	6.31521i	0.198592	−	0.236672i
$713$	−36.9242	+	21.3182i	−1.38282	+	0.798373i
$714$	3.41147	−	5.90885i	0.127671	−	0.221133i
$715$		0			0
$716$	0.699427	−	0.586889i	0.0261388	−	0.0219331i
$717$	−24.9110	+	14.3824i	−0.930319	+	0.537120i
$718$	−23.4028	−	4.12654i	−0.873385	−	0.154001i
$719$	7.11112	−	40.3292i	0.265200	−	1.50402i	−0.503265	−	0.864132i	$-0.667868\pi$
$719$	7.11112	−	40.3292i	0.265200	−	1.50402i	0.768465	−	0.639892i	$-0.221021\pi$
$720$		0			0
$721$	−6.41653	−	2.33542i	−0.238964	−	0.0869758i
$722$	−4.73892	+	13.0201i	−0.176364	+	0.484557i
$723$	32.5078	−	38.7413i	1.20898	−	1.44080i
$724$	0.774252	−	4.39100i	0.0287749	−	0.163190i
$725$		0			0
$726$	38.1168	+	66.0202i	1.41465	+	2.45024i
$727$	6.61219	+	7.88010i	0.245233	+	0.292257i	0.874594	−	0.484856i	$-0.161128\pi$
$727$	6.61219	+	7.88010i	0.245233	+	0.292257i	−0.629362	+	0.777113i	$0.716684\pi$
$728$	1.60197	+	4.40137i	0.0593729	+	0.163126i
$729$	10.3316	−	17.8948i	0.382651	−	0.662770i
$730$		0			0
$731$	−7.88326	−	6.61484i	−0.291573	−	0.244659i
$732$	−0.657115	−	0.379385i	−0.0242877	−	0.0140225i
$733$	−17.5142	+	3.08822i	−0.646901	+	0.114066i	−0.487465	−	0.873142i	$-0.662078\pi$
$733$	−17.5142	+	3.08822i	−0.646901	+	0.114066i	−0.159435	+	0.987208i	$0.550967\pi$
$734$	19.0811			0.704296
$735$		0			0
$736$	4.78880	−	4.01828i	0.176518	−	0.148116i
$737$	−2.14398	+	5.89053i	−0.0789744	+	0.216980i
$738$	−0.175771	−	0.482926i	−0.00647021	−	0.0177767i
$739$	38.0651			1.40025			0.700124	−	0.714021i	$-0.253128\pi$
$739$	38.0651			1.40025			0.700124	+	0.714021i	$0.253128\pi$
$740$		0			0
$741$	−23.2986			−0.855895
$742$	−1.70685	−	4.68954i	−0.0626605	−	0.172158i
$743$	5.87024	−	16.1284i	0.215358	−	0.591692i	−0.784227	−	0.620473i	$-0.786940\pi$
$743$	5.87024	−	16.1284i	0.215358	−	0.591692i	0.999586	+	0.0287815i	$0.00916269\pi$
$744$	30.1143	−	25.2689i	1.10404	−	0.926402i
$745$		0			0
$746$	−25.6587			−0.939431
$747$	7.35040	−	1.29607i	0.268937	−	0.0474209i
$748$	3.98048	+	2.29813i	0.145541	+	0.0840281i
$749$	−2.47565	−	2.07732i	−0.0904584	−	0.0759036i
$750$		0			0
$751$	16.1702	−	28.0077i	0.590061	−	1.02201i	−0.404163	−	0.914687i	$-0.632437\pi$
$751$	16.1702	−	28.0077i	0.590061	−	1.02201i	0.994224	−	0.107328i	$-0.0342295\pi$
$752$	0.330341	+	0.907604i	0.0120463	+	0.0330969i
$753$	28.1788	+	33.5822i	1.02689	+	1.22380i
$754$	−3.02182	−	5.23395i	−0.110048	−	0.190609i
$755$		0			0
$756$	−0.103378	+	0.586289i	−0.00375984	+	0.0213231i
$757$	−5.97053	+	7.11540i	−0.217003	+	0.258614i	−0.863554	−	0.504257i	$-0.831766\pi$
$757$	−5.97053	+	7.11540i	−0.217003	+	0.258614i	0.646551	+	0.762871i	$0.276211\pi$
$758$	6.95421	−	19.1065i	0.252588	−	0.693981i
$759$	67.9377	+	24.7273i	2.46598	+	0.897544i
$760$		0			0
$761$	2.18685	−	12.4023i	0.0792733	−	0.449581i	−0.919173	−	0.393855i	$-0.871141\pi$
$761$	2.18685	−	12.4023i	0.0792733	−	0.449581i	0.998446	−	0.0557267i	$-0.0177476\pi$
$762$	34.2536	+	6.03983i	1.24088	+	0.218800i
$763$	−1.84321	+	1.06418i	−0.0667287	+	0.0385258i
$764$	2.43860	−	2.04623i	0.0882253	−	0.0740298i
$765$		0			0
$766$	6.91921	−	11.9844i	0.250001	−	0.433015i
$767$	−4.09521	+	2.36437i	−0.147869	+	0.0853725i
$768$	−5.31056	+	6.32888i	−0.191628	+	0.228374i
$769$	1.92602	−	3.33597i	0.0694541	−	0.120298i	−0.829207	−	0.558942i	$-0.811208\pi$
$769$	1.92602	−	3.33597i	0.0694541	−	0.120298i	0.898661	+	0.438644i	$0.144541\pi$
$770$		0			0
$771$	5.60132			0.201727
$772$	−1.97989	+	0.349107i	−0.0712577	+	0.0125646i
$773$	25.3134	+	30.1673i	0.910459	+	1.08504i	0.996057	+	0.0887129i	$0.0282754\pi$
$773$	25.3134	+	30.1673i	0.910459	+	1.08504i	−0.0855984	+	0.996330i	$0.527280\pi$
$774$	1.78699	+	0.650411i	0.0642320	+	0.0233785i
$775$		0			0
$776$	7.43058			0.266742
$777$	7.87846	+	0.990505i	0.282638	+	0.0355342i
$778$		−	31.0823i		−	1.11436i
$779$	3.64543	−	1.32683i	0.130611	−	0.0475385i
$780$		0			0
$781$	35.5651	−	29.8427i	1.27262	−	1.06785i
$782$	−30.8837	+	5.44562i	−1.10440	+	0.194735i
$783$		−	9.08202i		−	0.324565i
$784$	−4.07011	−	23.0827i	−0.145361	−	0.824383i
$785$		0			0
$786$	−18.7383	−	15.7233i	−0.668373	−	0.560831i
$787$	−33.6611	+	19.4342i	−1.19989	+	0.692755i	−0.960530	−	0.278176i	$-0.910270\pi$
$787$	−33.6611	+	19.4342i	−1.19989	+	0.692755i	−0.239358	+	0.970931i	$0.576937\pi$
$788$	−0.542819	−	0.313396i	−0.0193371	−	0.0111643i
$789$	−23.3846	+	8.51130i	−0.832514	+	0.303010i
$790$		0			0
$791$	5.45605	+	9.45016i	0.193995	+	0.336009i
$792$	−9.88933	−	1.74376i	−0.351402	−	0.0619617i
$793$	−4.92901	−	0.869118i	−0.175034	−	0.0308633i
$794$	20.6620	+	17.3375i	0.733267	+	0.615284i
$795$		0			0
$796$	2.39646	+	0.872240i	0.0849403	+	0.0309157i
$797$	15.9404	−	18.9971i	0.564639	−	0.672911i	−0.405882	−	0.913925i	$-0.633036\pi$
$797$	15.9404	−	18.9971i	0.564639	−	0.672911i	0.970521	+	0.241015i	$0.0774802\pi$
$798$	−9.37295	−	1.65270i	−0.331799	−	0.0585051i
$799$	−0.180922	+	1.02606i	−0.00640057	+	0.0362994i
$800$		0			0
$801$	−1.14156	+	0.957882i	−0.0403350	+	0.0338451i
$802$	6.99281	+	19.2126i	0.246925	+	0.678421i
$803$	−39.8128	−	22.9859i	−1.40496	−	0.811155i
$804$	−0.169778	−	0.294064i	−0.00598760	−	0.0103708i
$805$		0			0
$806$	10.9663	−	18.9942i	0.386272	−	0.669043i
$807$	42.4109	−	7.47818i	1.49293	−	0.263244i
$808$			19.9377i			0.701405i
$809$	2.95858	+	16.7789i	0.104018	+	0.589916i	0.991608	+	0.129281i	$0.0412670\pi$
$809$	2.95858	+	16.7789i	0.104018	+	0.589916i	−0.887590	+	0.460634i	$0.847622\pi$
$810$		0			0
$811$	15.5722	+	5.66783i	0.546815	+	0.199024i	0.600631	−	0.799527i	$-0.294916\pi$
$811$	15.5722	+	5.66783i	0.546815	+	0.199024i	−0.0538160	+	0.998551i	$0.517138\pi$
$812$	0.0859614	+	0.236177i	0.00301665	+	0.00828819i
$813$		−	41.1729i		−	1.44400i
$814$	6.55438	−	52.1334i	0.229731	−	1.82728i
$815$		0			0
$816$	24.6386	−	8.96773i	0.862524	−	0.313933i
$817$	−4.90971	+	13.4893i	−0.171769	+	0.471932i
$818$	3.05066	+	3.63563i	0.106664	+	0.127117i
$819$	−0.147022	−	0.833805i	−0.00513737	−	0.0291355i
$820$		0			0
$821$	−0.429892	−	2.43804i	−0.0150033	−	0.0850882i	0.976387	−	0.216030i	$-0.0693110\pi$
$821$	−0.429892	−	2.43804i	−0.0150033	−	0.0850882i	−0.991390	+	0.130942i	$0.958200\pi$
$822$	−11.7747	−	6.79813i	−0.410690	−	0.237112i
$823$	20.2085	−	24.0835i	0.704423	−	0.839499i	−0.288596	−	0.957451i	$-0.593188\pi$
$823$	20.2085	−	24.0835i	0.704423	−	0.839499i	0.993019	+	0.117952i	$0.0376329\pi$
$824$	−14.4686	−	25.0604i	−0.504038	−	0.873020i
$825$		0			0
$826$	−1.81521	+	0.660681i	−0.0631591	+	0.0229880i
$827$	16.0434	+	19.1197i	0.557882	+	0.664858i	0.969097	−	0.246680i	$-0.0793397\pi$
$827$	16.0434	+	19.1197i	0.557882	+	0.664858i	−0.411214	+	0.911539i	$0.634895\pi$
$828$	−0.510917	+	0.294978i	−0.0177556	+	0.0102512i
$829$	3.05674	−	17.3356i	0.106165	−	0.602092i	−0.884584	−	0.466382i	$-0.845557\pi$
$829$	3.05674	−	17.3356i	0.106165	−	0.602092i	0.990749	−	0.135710i	$-0.0433316\pi$
$830$		0			0
$831$	16.1853	+	13.5810i	0.561460	+	0.471121i
$832$	−6.73535	+	18.5052i	−0.233506	+	0.641553i
$833$	8.64766	−	23.7592i	0.299623	−	0.823209i
$834$	−1.77197	−	1.48686i	−0.0613584	−	0.0514859i
$835$		0			0
$836$	1.11334	−	6.31407i	0.0385057	−	0.218377i
$837$	28.5434	−	16.4795i	0.986603	−	0.569616i
$838$	−4.83391	−	5.76083i	−0.166985	−	0.199005i
$839$	−33.9244	+	12.3475i	−1.17120	+	0.426282i	−0.853086	−	0.521770i	$-0.825272\pi$
$839$	−33.9244	+	12.3475i	−1.17120	+	0.426282i	−0.318115	+	0.948052i	$0.603050\pi$
$840$		0			0
$841$	12.5829	+	21.7942i	0.433893	+	0.751525i
$842$	9.00838	−	10.7358i	0.310449	−	0.369979i
$843$	6.54666	+	3.77972i	0.225479	+	0.130180i
$844$	0.263518	+	1.49449i	0.00907067	+	0.0514423i
$845$		0			0
$846$	−0.0334331	−	0.189608i	−0.00114945	−	0.00651887i
$847$	−13.4420	−	16.0196i	−0.461874	−	0.550440i
$848$	6.55926	−	18.0214i	0.225246	−	0.618858i
$849$	38.3499	−	13.9582i	1.31616	−	0.479045i
$850$		0			0
$851$	−19.7888	−	30.6660i	−0.678351	−	1.05122i
$852$			2.51485i			0.0861574i
$853$	5.67951	+	15.6043i	0.194463	+	0.534281i	0.998152	−	0.0607676i	$-0.0193548\pi$
$853$	5.67951	+	15.6043i	0.194463	+	0.534281i	−0.803689	+	0.595049i	$0.797133\pi$
$854$	−1.92127	−	0.699287i	−0.0657447	−	0.0239291i
$855$		0			0
$856$	−2.37820	−	13.4875i	−0.0812853	−	0.460992i
$857$		−	37.6255i		−	1.28526i	−0.766176	−	0.642631i	$-0.777843\pi$
$857$		−	37.6255i		−	1.28526i	0.766176	−	0.642631i	$-0.222157\pi$
$858$	−36.6258	+	6.45811i	−1.25038	+	0.220476i
$859$	−16.6866	+	28.9020i	−0.569340	+	0.986125i	0.427292	+	0.904114i	$0.359468\pi$
$859$	−16.6866	+	28.9020i	−0.569340	+	0.986125i	−0.996631	+	0.0820113i	$0.973866\pi$
$860$		0			0
$861$	0.467911	+	0.810446i	0.0159464	+	0.0276199i
$862$	36.0448	+	20.8105i	1.22769	+	0.708807i
$863$	11.0924	+	30.4761i	0.377590	+	1.03742i	0.972353	+	0.233518i	$0.0750237\pi$
$863$	11.0924	+	30.4761i	0.377590	+	1.03742i	−0.594763	+	0.803901i	$0.702754\pi$
$864$	−3.70187	+	3.10623i	−0.125940	+	0.105676i
$865$		0			0
$866$	−3.11628	+	17.6733i	−0.105895	+	0.600563i
$867$	−3.60981	−	0.636507i	−0.122596	−	0.0216169i
$868$	−0.586289	+	0.698711i	−0.0198999	+	0.0237158i
$869$	−70.8911	−	25.8022i	−2.40481	−	0.875281i
$870$		0			0
$871$	−1.71579	−	1.43972i	−0.0581372	−	0.0487829i
$872$	−8.88257	−	1.56624i	−0.300802	−	0.0530395i
$873$	−1.32277	−	0.233240i	−0.0447690	−	0.00789399i
$874$	21.8726	+	37.8844i	0.739851	+	1.28146i
$875$		0			0
$876$	2.34002	−	0.851698i	0.0790620	−	0.0287762i
$877$	−31.5557	−	18.2187i	−1.06556	−	0.615202i	−0.138595	−	0.990349i	$-0.544259\pi$
$877$	−31.5557	−	18.2187i	−1.06556	−	0.615202i	−0.926965	+	0.375148i	$0.877592\pi$
$878$	−29.2936	+	16.9127i	−0.988610	+	0.570774i
$879$	−33.1391	−	27.8070i	−1.11775	−	0.937907i
$880$		0			0
$881$	6.79396	+	38.5305i	0.228894	+	1.29812i	0.855099	+	0.518465i	$0.173496\pi$
$881$	6.79396	+	38.5305i	0.228894	+	1.29812i	−0.626205	+	0.779659i	$0.715393\pi$
$882$			4.67230i			0.157325i
$883$	−41.9793	+	7.40208i	−1.41272	+	0.249100i	−0.827358	−	0.561675i	$-0.810157\pi$
$883$	−41.9793	+	7.40208i	−1.41272	+	0.249100i	−0.585358	+	0.810775i	$0.699046\pi$
$884$	−1.25806	+	1.05563i	−0.0423130	+	0.0355048i
$885$		0			0
$886$	36.5107	−	13.2888i	1.22660	−	0.446447i
$887$		−	24.6973i		−	0.829254i	−0.909992	−	0.414627i	$-0.863912\pi$
$887$		−	24.6973i		−	0.829254i	0.909992	−	0.414627i	$-0.136088\pi$
$888$	22.8782	+	24.6766i	0.767742	+	0.828094i
$889$	−9.54126			−0.320004
$890$		0			0
$891$	−62.1348	−	22.6152i	−2.08159	−	0.757638i
$892$	1.27735	+	1.52229i	0.0427689	+	0.0509700i
$893$	1.43128	−	0.252374i	0.0478961	−	0.00844537i
$894$	−9.87258			−0.330188
$895$		0			0
$896$	−3.29860	+	5.71334i	−0.110198	+	0.190869i
$897$	−16.6048	+	19.7888i	−0.554417	+	0.660729i
$898$	−17.6634	+	10.1980i	−0.589437	+	0.340312i
$899$	6.95723	−	12.0503i	0.232037	−	0.401899i
$900$		0			0
$901$	15.8478	−	13.2979i	0.527966	−	0.443016i
$902$	5.36289	−	3.09627i	0.178565	−	0.103094i
$903$	−3.41025	−	0.601319i	−0.113486	−	0.0200106i
$904$	−8.03012	+	45.5410i	−0.267078	+	1.51467i
$905$		0			0
$906$	−3.95084	−	1.43799i	−0.131258	−	0.0477739i
$907$	3.40944	−	9.36736i	0.113209	−	0.311038i	−0.870130	−	0.492823i	$-0.835965\pi$
$907$	3.40944	−	9.36736i	0.113209	−	0.311038i	0.983338	+	0.181785i	$0.0581873\pi$
$908$	0.110351	−	0.131511i	0.00366211	−	0.00436434i
$909$	0.625829	−	3.54925i	0.0207574	−	0.117721i
$910$		0			0
$911$	8.91834	+	15.4470i	0.295478	+	0.511782i	0.975096	−	0.221784i	$-0.0711879\pi$
$911$	8.91834	+	15.4470i	0.295478	+	0.511782i	−0.679618	+	0.733566i	$0.737855\pi$
$912$	−23.5099	−	28.0180i	−0.778491	−	0.927769i
$913$	30.7599	+	84.5121i	1.01800	+	2.79694i
$914$	20.1634	−	34.9241i	0.666947	−	1.15519i
$915$		0			0
$916$	−3.75806	−	3.15338i	−0.124170	−	0.104191i
$917$	5.81109	+	3.35504i	0.191899	+	0.110793i
$918$	23.8739	−	4.20961i	0.787955	−	0.138938i
$919$	33.5689			1.10734			0.553668	−	0.832737i	$-0.313228\pi$
$919$	33.5689			1.10734			0.553668	+	0.832737i	$0.313228\pi$
$920$		0			0
$921$	9.84002	−	8.25676i	0.324240	−	0.272069i
$922$	17.8551	−	49.0565i	0.588027	−	1.61559i
$923$	5.67365	+	15.5882i	0.186750	+	0.513093i
$924$	1.54664			0.0508806
$925$		0			0
$926$	9.76651			0.320947
$927$	1.78904	+	4.91534i	0.0587598	+	0.161441i
$928$	−0.697767	+	1.91710i	−0.0229053	+	0.0629319i
$929$	−7.69434	+	6.45632i	−0.252443	+	0.211825i	−0.760224	−	0.649662i	$-0.774911\pi$
$929$	−7.69434	+	6.45632i	−0.252443	+	0.211825i	0.507780	+	0.861487i	$0.330466\pi$
$930$		0			0
$931$	−35.2695			−1.15591
$932$	−0.735564	+	0.129700i	−0.0240942	+	0.00424846i
$933$	−2.50622	−	1.44697i	−0.0820499	−	0.0473716i
$934$	5.19569	+	4.35970i	0.170008	+	0.142654i
$935$		0			0
$936$	1.79401	−	3.10732i	0.0586392	−	0.101566i
$937$	19.2137	+	52.7893i	0.627685	+	1.72455i	0.687345	+	0.726331i	$0.258776\pi$
$937$	19.2137	+	52.7893i	0.627685	+	1.72455i	−0.0596597	+	0.998219i	$0.519002\pi$
$938$	−0.588127	−	0.700903i	−0.0192030	−	0.0228853i
$939$	20.5398	+	35.5760i	0.670292	+	1.16098i
$940$		0			0
$941$	4.44238	−	25.1940i	0.144817	−	0.821301i	−0.822696	−	0.568481i	$-0.807531\pi$
$941$	4.44238	−	25.1940i	0.144817	−	0.821301i	0.967514	−	0.252819i	$-0.0813578\pi$
$942$	−11.1287	+	13.2626i	−0.362592	+	0.432120i
$943$	1.47113	−	4.04189i	0.0479065	−	0.131622i
$944$	−6.97565	−	2.53893i	−0.227038	−	0.0826351i
$945$		0			0
$946$	−3.97906	+	22.5663i	−0.129370	+	0.733695i
$947$	−25.3095	−	4.46275i	−0.822449	−	0.145020i	−0.253440	−	0.967351i	$-0.581562\pi$
$947$	−25.3095	−	4.46275i	−0.822449	−	0.145020i	−0.569009	+	0.822331i	$0.692673\pi$
$948$	3.53898	−	2.04323i	0.114941	−	0.0663611i
$949$	12.5831	−	10.5584i	0.408464	−	0.342742i
$950$		0			0
$951$	25.5929	−	44.3281i	0.829905	−	1.43744i
$952$	−6.86906	+	3.96585i	−0.222627	+	0.128534i
$953$	−2.63873	+	3.14471i	−0.0854768	+	0.101867i	−0.807088	−	0.590432i	$-0.798958\pi$
$953$	−2.63873	+	3.14471i	−0.0854768	+	0.101867i	0.721611	+	0.692299i	$0.243402\pi$
$954$	−1.91147	+	3.31077i	−0.0618863	+	0.107190i
$955$		0			0
$956$	2.82832			0.0914746
$957$	−23.2361	+	4.09714i	−0.751115	+	0.132442i
$958$	2.48021	+	2.95580i	0.0801321	+	0.0954977i
$959$	3.50475	+	1.27562i	0.113174	+	0.0411920i
$960$		0			0
$961$	19.4962			0.628909
$962$	16.7032	+	8.57170i	0.538534	+	0.276363i
$963$			2.47565i			0.0797768i
$964$	−4.67277	+	1.70075i	−0.150500	+	0.0547775i
$965$		0			0
$966$	−8.08378	+	6.78310i	−0.260091	+	0.218243i
$967$	56.6253	−	9.98457i	1.82095	−	0.321082i	0.844291	−	0.535885i	$-0.180022\pi$
$967$	56.6253	−	9.98457i	1.82095	−	0.321082i	0.976657	+	0.214803i	$0.0689110\pi$
$968$		−	88.6219i		−	2.84841i
$969$	−6.85117	−	38.8549i	−0.220091	−	1.24820i
$970$		0			0
$971$	−4.91329	−	4.12274i	−0.157675	−	0.132305i	0.560537	−	0.828129i	$-0.310595\pi$
$971$	−4.91329	−	4.12274i	−0.157675	−	0.132305i	−0.718212	+	0.695824i	$0.755039\pi$
$972$	0.875057	−	0.505215i	0.0280675	−	0.0162048i
$973$	0.549522	+	0.317267i	0.0176169	+	0.0101711i
$974$	−18.2866	+	6.65577i	−0.585940	+	0.213265i
$975$		0			0
$976$	−3.92855	−	6.80445i	−0.125750	−	0.217805i
$977$	46.0157	+	8.11381i	1.47217	+	0.259584i	0.851445	−	0.524443i	$-0.175726\pi$
$977$	46.0157	+	8.11381i	1.47217	+	0.259584i	0.620727	+	0.784027i	$0.286838\pi$
$978$	−27.8906	−	4.91787i	−0.891844	−	0.157256i
$979$	−13.7554	−	11.5421i	−0.439623	−	0.368888i
$980$		0			0
$981$	1.53209	+	0.557635i	0.0489158	+	0.0178039i
$982$	−29.7716	+	35.4805i	−0.950051	+	1.13223i
$983$	43.5709	+	7.68273i	1.38970	+	0.245041i	0.817903	−	0.575356i	$-0.195136\pi$
$983$	43.5709	+	7.68273i	1.38970	+	0.245041i	0.571794	+	0.820397i	$0.306248\pi$
$984$	−0.688663	+	3.90560i	−0.0219538	+	0.124506i
$985$		0			0
$986$	7.84002	−	6.57856i	0.249677	−	0.209504i
$987$	0.119910	+	0.329451i	0.00381679	+	0.0104865i
$988$	1.98394	+	1.14543i	0.0631176	+	0.0364410i
$989$	7.95811	+	13.7839i	0.253053	+	0.438301i
$990$		0			0
$991$	16.7010	−	28.9270i	0.530524	−	0.918895i	−0.468841	−	0.883282i	$-0.655328\pi$
$991$	16.7010	−	28.9270i	0.530524	−	0.918895i	0.999366	−	0.0356128i	$-0.0113383\pi$
$992$	−7.29125	+	1.28564i	−0.231498	+	0.0408193i
$993$		−	28.3824i		−	0.900688i
$994$	1.17673	+	6.67355i	0.0373235	+	0.211672i
$995$		0			0
$996$	−4.57785	−	1.66620i	−0.145055	−	0.0527956i
$997$	−21.0406	−	57.8085i	−0.666361	−	1.83081i	−0.545440	−	0.838150i	$-0.683637\pi$
$997$	−21.0406	−	57.8085i	−0.666361	−	1.83081i	−0.120922	−	0.992662i	$-0.538585\pi$
$998$		−	54.4543i		−	1.72372i
$999$	15.2973	+	23.7056i	0.483984	+	0.750012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bc.b.599.2		12
5.2	odd	4		925.2.p.a.451.1		6
5.3	odd	4		37.2.f.b.7.1	✓	6
5.4	even	2	inner	925.2.bc.b.599.1		12
15.8	even	4		333.2.x.a.118.1		6
20.3	even	4		592.2.bc.c.81.1		6
37.16	even	9	inner	925.2.bc.b.349.1		12
185.13	even	36		1369.2.b.e.1368.5		6
185.33	odd	36		1369.2.a.i.1.2		3
185.53	odd	36		37.2.f.b.16.1	yes	6
185.78	odd	36		1369.2.a.l.1.2		3
185.98	even	36		1369.2.b.e.1368.2		6
185.127	odd	36		925.2.p.a.201.1		6
185.164	even	18	inner	925.2.bc.b.349.2		12
555.53	even	36		333.2.x.a.127.1		6
740.423	even	36		592.2.bc.c.497.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.f.b.7.1	✓	6	5.3	odd	4
37.2.f.b.16.1	yes	6	185.53	odd	36
333.2.x.a.118.1		6	15.8	even	4
333.2.x.a.127.1		6	555.53	even	36
592.2.bc.c.81.1		6	20.3	even	4
592.2.bc.c.497.1		6	740.423	even	36
925.2.p.a.201.1		6	185.127	odd	36
925.2.p.a.451.1		6	5.2	odd	4
925.2.bc.b.349.1		12	37.16	even	9	inner
925.2.bc.b.349.2		12	185.164	even	18	inner
925.2.bc.b.599.1		12	5.4	even	2	inner
925.2.bc.b.599.2		12	1.1	even	1	trivial
1369.2.a.i.1.2		3	185.33	odd	36
1369.2.a.l.1.2		3	185.78	odd	36
1369.2.b.e.1368.2		6	185.98	even	36
1369.2.b.e.1368.5		6	185.13	even	36

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.460802 + 1.26604i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(0.141559 - 0.118782i) q^{4} -2.53209 q^{6} +(0.684040 - 0.120615i) q^{7} +(2.54920 + 1.47178i) q^{8} +(-0.407604 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.460802 + 1.26604i) q^{2} +(-0.642788 + 1.76604i) q^{3} +(0.141559 - 0.118782i) q^{4} -2.53209 q^{6} +(0.684040 - 0.120615i) q^{7} +(2.54920 + 1.47178i) q^{8} +(-0.407604 - 0.342020i) q^{9} +(3.20574 - 5.55250i) q^{11} +(0.118782 + 0.326352i) q^{12} +(1.47254 + 1.75490i) q^{13} +(0.467911 + 0.810446i) q^{14} +(-0.624485 + 3.54163i) q^{16} +(-2.49362 + 2.97178i) q^{17} +(0.245188 - 0.673648i) q^{18} +(5.08512 + 1.85083i) q^{19} +(-0.226682 + 1.28558i) q^{21} +(8.50692 + 1.50000i) q^{22} +(5.19615 - 3.00000i) q^{23} +(-4.23783 + 3.55596i) q^{24} +(-1.54323 + 2.67296i) q^{26} +(-4.01676 + 2.31908i) q^{27} +(0.0825054 - 0.0983261i) q^{28} +(-0.979055 + 1.69577i) q^{29} -7.10607 q^{31} +(1.02606 - 0.180922i) q^{32} +(7.74535 + 9.23055i) q^{33} +(-4.91147 - 1.78763i) q^{34} -0.0983261 q^{36} +(-0.300767 - 6.07532i) q^{37} +7.29086i q^{38} +(-4.04576 + 1.47254i) q^{39} +(0.549163 - 0.460802i) q^{41} +(-1.73205 + 0.305407i) q^{42} +2.65270i q^{43} +(-0.205737 - 1.16679i) q^{44} +(6.19253 + 5.19615i) q^{46} +(0.232589 - 0.134285i) q^{47} +(-5.85327 - 3.37939i) q^{48} +(-6.12449 + 2.22913i) q^{49} +(-3.64543 - 6.31407i) q^{51} +(0.416902 + 0.0735111i) q^{52} +(-5.25173 - 0.926022i) q^{53} +(-4.78699 - 4.01676i) q^{54} +(1.92127 + 0.699287i) q^{56} +(-6.53731 + 7.79086i) q^{57} +(-2.59808 - 0.458111i) q^{58} +(-0.358441 + 2.03282i) q^{59} +(-1.67365 + 1.40436i) q^{61} +(-3.27449 - 8.99660i) q^{62} +(-0.320070 - 0.184793i) q^{63} +(4.29813 + 7.44459i) q^{64} +(-8.11721 + 14.0594i) q^{66} +(-0.962858 + 0.169778i) q^{67} +0.716881i q^{68} +(1.95811 + 11.1050i) q^{69} +(6.80453 + 2.47665i) q^{71} +(-0.535685 - 1.47178i) q^{72} -7.17024i q^{73} +(7.55303 - 3.18031i) q^{74} +(0.939693 - 0.342020i) q^{76} +(1.52314 - 4.18479i) q^{77} +(-3.72859 - 4.44356i) q^{78} +(-2.04323 - 11.5878i) q^{79} +(-1.79086 - 10.1565i) q^{81} +(0.836452 + 0.482926i) q^{82} +(-9.01660 + 10.7456i) q^{83} +(0.120615 + 0.208911i) q^{84} +(-3.35844 + 1.22237i) q^{86} +(-2.36549 - 2.81908i) q^{87} +(16.3441 - 9.43629i) q^{88} +(0.486329 - 2.75811i) q^{89} +(1.21894 + 1.02281i) q^{91} +(0.379217 - 1.04189i) q^{92} +(4.56769 - 12.5496i) q^{93} +(0.277189 + 0.232589i) q^{94} +(-0.340022 + 1.92836i) q^{96} +(2.18615 - 1.26217i) q^{97} +(-5.64436 - 6.72668i) q^{98} +(-3.20574 + 1.16679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{4} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q + 18 * q^4 - 12 * q^6 - 12 * q^9	\( 12 q + 18 q^{4} - 12 q^{6} - 12 q^{9} + 18 q^{11} + 24 q^{14} + 18 q^{16} + 18 q^{19} + 24 q^{21} - 12 q^{24} + 12 q^{26} - 18 q^{29} - 36 q^{31} - 18 q^{34} - 48 q^{36} + 12 q^{39} + 30 q^{41} + 18 q^{44} - 36 q^{46} - 48 q^{49} - 12 q^{51} - 42 q^{54} - 12 q^{56} + 12 q^{59} - 18 q^{61} + 24 q^{64} - 36 q^{66} + 36 q^{69} - 24 q^{71} + 66 q^{74} + 6 q^{79} + 42 q^{81} + 24 q^{84} - 24 q^{86} + 48 q^{89} + 84 q^{91} - 18 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) \) 12 * q + 18 * q^4 - 12 * q^6 - 12 * q^9 + 18 * q^11 + 24 * q^14 + 18 * q^16 + 18 * q^19 + 24 * q^21 - 12 * q^24 + 12 * q^26 - 18 * q^29 - 36 * q^31 - 18 * q^34 - 48 * q^36 + 12 * q^39 + 30 * q^41 + 18 * q^44 - 36 * q^46 - 48 * q^49 - 12 * q^51 - 42 * q^54 - 12 * q^56 + 12 * q^59 - 18 * q^61 + 24 * q^64 - 36 * q^66 + 36 * q^69 - 24 * q^71 + 66 * q^74 + 6 * q^79 + 42 * q^81 + 24 * q^84 - 24 * q^86 + 48 * q^89 + 84 * q^91 - 18 * q^94 + 36 * q^96 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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