LMFDB - Embedded newform 925.2.bb.e.326.6

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			326.6
Character	$\chi$	$=$	925.326
Dual form			925.2.bb.e.576.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.326264 - 0.896403i) q^{2} +(-0.266913 - 0.0971484i) q^{3} +(0.834998 - 0.700647i) q^{4} +0.270958i q^{6} +(-0.0138149 - 0.0783483i) q^{7} +(-2.55275 - 1.47383i) q^{8} +(-2.23633 - 1.87650i) q^{9} +(2.24001 - 3.87981i) q^{11} +(-0.290938 + 0.105893i) q^{12} +(-0.539440 - 0.642880i) q^{13} +(-0.0657244 + 0.0379460i) q^{14} +(-0.109719 + 0.622249i) q^{16} +(-3.04924 + 3.63394i) q^{17} +(-0.952469 + 2.61689i) q^{18} +(-0.698848 + 1.92007i) q^{19} +(-0.00392403 + 0.0222543i) q^{21} +(-4.20871 - 0.742109i) q^{22} +(0.00393731 - 0.00227321i) q^{23} +(0.538182 + 0.641381i) q^{24} +(-0.400280 + 0.693304i) q^{26} +(0.840670 + 1.45608i) q^{27} +(-0.0664299 - 0.0557413i) q^{28} +(0.499013 + 0.288105i) q^{29} -5.06627i q^{31} +(-5.21218 + 0.919048i) q^{32} +(-0.974805 + 0.817959i) q^{33} +(4.25234 + 1.54772i) q^{34} -3.18209 q^{36} +(-4.52888 - 4.06070i) q^{37} +1.94917 q^{38} +(0.0815288 + 0.223999i) q^{39} +(-4.55042 + 3.81825i) q^{41} +(0.0212291 - 0.00374326i) q^{42} -1.01783i q^{43} +(-0.847972 - 4.80909i) q^{44} +(-0.00332232 - 0.00278775i) q^{46} +(-3.97780 - 6.88975i) q^{47} +(0.0897359 - 0.155427i) q^{48} +(6.57190 - 2.39198i) q^{49} +(1.16691 - 0.673718i) q^{51} +(-0.900863 - 0.158846i) q^{52} +(-0.138996 + 0.788285i) q^{53} +(1.03096 - 1.22865i) q^{54} +(-0.0802061 + 0.220365i) q^{56} +(0.373063 - 0.444599i) q^{57} +(0.0954485 - 0.541315i) q^{58} +(-7.84732 - 1.38369i) q^{59} +(-2.86116 - 3.40979i) q^{61} +(-4.54142 + 1.65294i) q^{62} +(-0.116126 + 0.201136i) q^{63} +(3.15623 + 5.46676i) q^{64} +(1.05127 + 0.606948i) q^{66} +(0.563037 + 3.19314i) q^{67} +5.17077i q^{68} +(-0.00127176 + 0.000224245i) q^{69} +(5.63810 + 2.05210i) q^{71} +(2.94314 + 8.08622i) q^{72} +9.38629 q^{73} +(-2.16241 + 5.38456i) q^{74} +(0.761753 + 2.09290i) q^{76} +(-0.334922 - 0.121902i) q^{77} +(0.174193 - 0.146165i) q^{78} +(6.85173 - 1.20814i) q^{79} +(1.43787 + 8.15459i) q^{81} +(4.90733 + 2.83325i) q^{82} +(-10.7389 - 9.01103i) q^{83} +(0.0123158 + 0.0213316i) q^{84} +(-0.912382 + 0.332080i) q^{86} +(-0.105204 - 0.125377i) q^{87} +(-11.4364 + 6.60280i) q^{88} +(-10.5904 - 1.86737i) q^{89} +(-0.0429162 + 0.0511455i) q^{91} +(0.00169493 - 0.00465679i) q^{92} +(-0.492180 + 1.35225i) q^{93} +(-4.87818 + 5.81359i) q^{94} +(1.48048 + 0.261049i) q^{96} +(-6.13702 + 3.54321i) q^{97} +(-4.28835 - 5.11066i) q^{98} +(-12.2899 + 4.47315i) 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 $

$2$	−0.326264	−	0.896403i	−0.230704	−	0.633853i	0.769284	−	0.638907i	$-0.220613\pi$
$2$	−0.326264	−	0.896403i	−0.230704	−	0.633853i	−0.999987	+	0.00505447i	$0.998391\pi$
$3$	−0.266913	−	0.0971484i	−0.154102	−	0.0560886i	0.263817	−	0.964573i	$-0.415018\pi$
$3$	−0.266913	−	0.0971484i	−0.154102	−	0.0560886i	−0.417920	+	0.908484i	$0.637241\pi$
$4$	0.834998	−	0.700647i	0.417499	−	0.350323i
$5$		0			0
$5$		0			0
$6$			0.270958i			0.110618i
$7$	−0.0138149	−	0.0783483i	−0.00522155	−	0.0296129i	0.982086	−	0.188435i	$-0.0603415\pi$
$7$	−0.0138149	−	0.0783483i	−0.00522155	−	0.0296129i	−0.987307	+	0.158822i	$0.949230\pi$
$8$	−2.55275	−	1.47383i	−0.902534	−	0.521078i
$9$	−2.23633	−	1.87650i	−0.745443	−	0.625501i
$10$		0			0
$11$	2.24001	−	3.87981i	0.675389	−	1.16981i	−0.300967	−	0.953635i	$-0.597309\pi$
$11$	2.24001	−	3.87981i	0.675389	−	1.16981i	0.976355	−	0.216173i	$-0.0693574\pi$
$12$	−0.290938	+	0.105893i	−0.0839867	+	0.0305687i
$13$	−0.539440	−	0.642880i	−0.149614	−	0.178303i	0.686032	−	0.727571i	$-0.259351\pi$
$13$	−0.539440	−	0.642880i	−0.149614	−	0.178303i	−0.835646	+	0.549268i	$0.814906\pi$
$14$	−0.0657244	+	0.0379460i	−0.0175656	+	0.0101415i
$15$		0			0
$16$	−0.109719	+	0.622249i	−0.0274298	+	0.155562i
$17$	−3.04924	+	3.63394i	−0.739549	+	0.881360i	−0.996373	−	0.0850980i	$-0.972880\pi$
$17$	−3.04924	+	3.63394i	−0.739549	+	0.881360i	0.256823	+	0.966458i	$0.417324\pi$
$18$	−0.952469	+	2.61689i	−0.224499	+	0.616806i
$19$	−0.698848	+	1.92007i	−0.160327	+	0.440494i	−0.993680	−	0.112246i	$-0.964196\pi$
$19$	−0.698848	+	1.92007i	−0.160327	+	0.440494i	0.833354	+	0.552740i	$0.186418\pi$
$20$		0			0
$21$	−0.00392403	+	0.0222543i	−0.000856293	+	0.00485628i
$22$	−4.20871	−	0.742109i	−0.897300	−	0.158218i
$23$	0.00393731	−	0.00227321i	0.000820986	−	0.000473997i	−0.499589	−	0.866262i	$-0.666516\pi$
$23$	0.00393731	−	0.00227321i	0.000820986	−	0.000473997i	0.500410	+	0.865788i	$0.333182\pi$
$24$	0.538182	+	0.641381i	0.109856	+	0.130921i
$25$		0			0
$26$	−0.400280	+	0.693304i	−0.0785013	+	0.135968i
$27$	0.840670	+	1.45608i	0.161787	+	0.280223i
$28$	−0.0664299	−	0.0557413i	−0.0125541	−	0.0105341i
$29$	0.499013	+	0.288105i	0.0926644	+	0.0534998i	0.545616	−	0.838035i	$-0.316296\pi$
$29$	0.499013	+	0.288105i	0.0926644	+	0.0534998i	−0.452952	+	0.891535i	$0.649629\pi$
$30$		0			0
$31$		−	5.06627i		−	0.909929i	−0.890510	−	0.454965i	$-0.849652\pi$
$31$		−	5.06627i		−	0.909929i	0.890510	−	0.454965i	$-0.150348\pi$
$32$	−5.21218	+	0.919048i	−0.921392	+	0.162466i
$33$	−0.974805	+	0.817959i	−0.169692	+	0.142388i
$34$	4.25234	+	1.54772i	0.729270	+	0.265432i
$35$		0			0
$36$	−3.18209			−0.530349
$37$	−4.52888	−	4.06070i	−0.744543	−	0.667575i
$37$	−4.52888	−	4.06070i	−0.744543	−	0.667575i
$38$	1.94917			0.316196
$39$	0.0815288	+	0.223999i	0.0130551	+	0.0358685i
$40$		0			0
$41$	−4.55042	+	3.81825i	−0.710656	+	0.596311i	−0.924783	−	0.380495i	$-0.875754\pi$
$41$	−4.55042	+	3.81825i	−0.710656	+	0.596311i	0.214127	+	0.976806i	$0.431309\pi$
$42$	0.0212291	−	0.00374326i	0.00327572	−	0.000577597i
$43$		−	1.01783i		−	0.155217i	−0.996984	−	0.0776084i	$-0.975272\pi$
$43$		−	1.01783i		−	0.155217i	0.996984	−	0.0776084i	$-0.0247284\pi$
$44$	−0.847972	−	4.80909i	−0.127837	−	0.724998i
$45$		0			0
$46$	−0.00332232	−	0.00278775i	−0.000489849	−	0.000411032i
$47$	−3.97780	−	6.88975i	−0.580222	−	1.00497i	−0.995453	−	0.0952574i	$-0.969633\pi$
$47$	−3.97780	−	6.88975i	−0.580222	−	1.00497i	0.415231	−	0.909716i	$-0.363701\pi$
$48$	0.0897359	−	0.155427i	0.0129523	−	0.0224340i
$49$	6.57190	−	2.39198i	0.938843	−	0.341711i
$50$		0			0
$51$	1.16691	−	0.673718i	0.163401	−	0.0943393i
$52$	−0.900863	−	0.158846i	−0.124927	−	0.0220280i
$53$	−0.138996	+	0.788285i	−0.0190926	+	0.108279i	−0.992865	−	0.119246i	$-0.961952\pi$
$53$	−0.138996	+	0.788285i	−0.0190926	+	0.108279i	0.973772	+	0.227525i	$0.0730634\pi$
$54$	1.03096	−	1.22865i	0.140296	−	0.167198i
$55$		0			0
$56$	−0.0802061	+	0.220365i	−0.0107180	+	0.0294475i
$57$	0.373063	−	0.444599i	0.0494134	−	0.0588886i
$58$	0.0954485	−	0.541315i	0.0125330	−	0.0710782i
$59$	−7.84732	−	1.38369i	−1.02163	−	0.180142i	−0.362355	−	0.932040i	$-0.618027\pi$
$59$	−7.84732	−	1.38369i	−1.02163	−	0.180142i	−0.659279	+	0.751898i	$0.729138\pi$
$60$		0			0
$61$	−2.86116	−	3.40979i	−0.366333	−	0.436579i	0.551118	−	0.834427i	$-0.314201\pi$
$61$	−2.86116	−	3.40979i	−0.366333	−	0.436579i	−0.917451	+	0.397848i	$0.869757\pi$
$62$	−4.54142	+	1.65294i	−0.576761	+	0.209924i
$63$	−0.116126	+	0.201136i	−0.0146305	+	0.0253408i
$64$	3.15623	+	5.46676i	0.394529	+	0.683345i
$65$		0			0
$66$	1.05127	+	0.606948i	0.129402	+	0.0747102i
$67$	0.563037	+	3.19314i	0.0687859	+	0.390104i	0.999691	+	0.0248440i	$0.00790889\pi$
$67$	0.563037	+	3.19314i	0.0687859	+	0.390104i	−0.930905	+	0.365260i	$0.880980\pi$
$68$			5.17077i			0.627048i
$69$	−0.00127176		0.000224245i	−0.000153102		2.69960e-5i
$70$		0			0
$71$	5.63810	+	2.05210i	0.669119	+	0.243539i	0.654168	−	0.756349i	$-0.273019\pi$
$71$	5.63810	+	2.05210i	0.669119	+	0.243539i	0.0149505	+	0.999888i	$0.495241\pi$
$72$	2.94314	+	8.08622i	0.346853	+	0.952970i
$73$	9.38629			1.09858			0.549291	−	0.835631i	$-0.314898\pi$
$73$	9.38629			1.09858			0.549291	+	0.835631i	$0.314898\pi$
$74$	−2.16241	+	5.38456i	−0.251376	+	0.625943i
$75$		0			0
$76$	0.761753	+	2.09290i	0.0873791	+	0.240072i
$77$	−0.334922	−	0.121902i	−0.0381679	−	0.0138920i
$78$	0.174193	−	0.146165i	0.0197235	−	0.0165500i
$79$	6.85173	−	1.20814i	0.770879	−	0.135927i	0.225644	−	0.974210i	$-0.427551\pi$
$79$	6.85173	−	1.20814i	0.770879	−	0.135927i	0.545235	+	0.838283i	$0.316440\pi$
$80$		0			0
$81$	1.43787	+	8.15459i	0.159764	+	0.906065i
$82$	4.90733	+	2.83325i	0.541924	+	0.312880i
$83$	−10.7389	−	9.01103i	−1.17875	−	0.989089i	−0.999986	−	0.00519711i	$-0.998346\pi$
$83$	−10.7389	−	9.01103i	−1.17875	−	0.989089i	−0.178764	−	0.983892i	$-0.557210\pi$
$84$	0.0123158	+	0.0213316i	0.00134377	+	0.00232747i
$85$		0			0
$86$	−0.912382	+	0.332080i	−0.0983847	+	0.0358091i
$87$	−0.105204	−	0.125377i	−0.0112791	−	0.0134419i
$88$	−11.4364	+	6.60280i	−1.21912	+	0.703861i
$89$	−10.5904	−	1.86737i	−1.12258	−	0.197941i	−0.418607	−	0.908167i	$-0.637482\pi$
$89$	−10.5904	−	1.86737i	−1.12258	−	0.197941i	−0.703974	+	0.710226i	$0.748593\pi$
$90$		0			0
$91$	−0.0429162	+	0.0511455i	−0.00449884	+	0.00536151i
$92$	0.00169493	−	0.00465679i	0.000176709	−	0.000485504i
$93$	−0.492180	+	1.35225i	−0.0510367	+	0.140222i
$94$	−4.87818	+	5.81359i	−0.503146	+	0.599626i
$95$		0			0
$96$	1.48048	+	0.261049i	0.151101	+	0.0266432i
$97$	−6.13702	+	3.54321i	−0.623120	+	0.359759i	−0.778083	−	0.628162i	$-0.783808\pi$
$97$	−6.13702	+	3.54321i	−0.623120	+	0.359759i	0.154962	+	0.987920i	$0.450474\pi$
$98$	−4.28835	−	5.11066i	−0.433189	−	0.516254i
$99$	−12.2899	+	4.47315i	−1.23518	+	0.449568i
$100$		0			0
$101$	3.69395	+	6.39812i	0.367562	+	0.636636i	0.989184	−	0.146681i	$-0.0468592\pi$
$101$	3.69395	+	6.39812i	0.367562	+	0.636636i	−0.621622	+	0.783318i	$0.713526\pi$
$102$	−0.984645	−	0.826215i	−0.0974944	−	0.0818075i
$103$	9.21085	+	5.31788i	0.907572	+	0.523987i	0.879649	−	0.475623i	$-0.157777\pi$
$103$	9.21085	+	5.31788i	0.907572	+	0.523987i	0.0279226	+	0.999610i	$0.491111\pi$
$104$	0.429560	+	2.43616i	0.0421218	+	0.238885i
$105$		0			0
$106$	0.751971	−	0.132593i	0.0730379	−	0.0128785i
$107$	8.83539	−	7.41377i	0.854149	−	0.716716i	−0.106550	−	0.994307i	$-0.533980\pi$
$107$	8.83539	−	7.41377i	0.854149	−	0.716716i	0.960699	+	0.277591i	$0.0895360\pi$
$108$	1.72216	+	0.626814i	0.165715	+	0.0603152i
$109$	−3.70141	−	10.1695i	−0.354531	−	0.974066i	−0.980895	−	0.194535i	$-0.937680\pi$
$109$	−3.70141	−	10.1695i	−0.354531	−	0.974066i	0.626365	−	0.779530i	$-0.284542\pi$
$110$		0			0
$111$	0.814326	+	1.52383i	0.0772924	+	0.144635i
$112$	0.0502679			0.00474987
$113$	−6.18933	−	17.0050i	−0.582243	−	1.59970i	−0.784338	−	0.620334i	$-0.786997\pi$
$113$	−6.18933	−	17.0050i	−0.582243	−	1.59970i	0.202095	−	0.979366i	$-0.435225\pi$
$114$	−0.520258	−	0.189358i	−0.0487266	−	0.0177350i
$115$		0			0
$116$	0.618535	−	0.109064i	0.0574295	−	0.0101264i
$117$			2.44995i			0.226498i
$118$	1.31995	+	7.48582i	0.121511	+	0.689125i
$119$	0.326838	+	0.188700i	0.0299612	+	0.0172981i
$120$		0			0
$121$	−4.53529	−	7.85536i	−0.412299	−	0.714123i
$122$	−2.12306	+	3.67724i	−0.192213	+	0.332922i
$123$	1.58550	−	0.577076i	0.142960	−	0.0520332i
$124$	−3.54967	−	4.23033i	−0.318769	−	0.379895i
$125$		0			0
$126$	0.218187	+	0.0384723i	0.0194376	+	0.00342738i
$127$	1.54564	−	8.76576i	0.137153	−	0.777835i	−0.836183	−	0.548451i	$-0.815218\pi$
$127$	1.54564	−	8.76576i	0.137153	−	0.777835i	0.973336	−	0.229384i	$-0.0736712\pi$
$128$	−2.93336	+	3.49585i	−0.259275	+	0.308992i
$129$	−0.0988801	+	0.271671i	−0.00870591	+	0.0239193i
$130$		0			0
$131$	−13.7521	+	16.3891i	−1.20152	+	1.43192i	−0.328317	+	0.944567i	$0.606482\pi$
$131$	−13.7521	+	16.3891i	−1.20152	+	1.43192i	−0.873206	+	0.487352i	$0.837963\pi$
$132$	−0.240860	+	1.36599i	−0.0209642	+	0.118894i
$133$	0.160089	+	0.0282279i	0.0138814	+	0.00244767i
$134$	2.67864	−	1.54652i	0.231400	−	0.133599i
$135$		0			0
$136$	13.1398	−	4.78249i	1.12673	−	0.410095i
$137$	10.2571	−	17.7659i	0.876327	−	1.51784i	0.0209840	−	0.999780i	$-0.493320\pi$
$137$	10.2571	−	17.7659i	0.876327	−	1.51784i	0.855343	−	0.518063i	$-0.173347\pi$
$138$	0.000615943		0.00106685i	5.24326e−5		9.08159e-5i
$139$	16.1848	+	13.5807i	1.37278	+	1.15190i	0.971799	+	0.235810i	$0.0757743\pi$
$139$	16.1848	+	13.5807i	1.37278	+	1.15190i	0.400979	+	0.916087i	$0.368670\pi$
$140$		0			0
$141$	0.392398	+	2.22540i	0.0330459	+	0.187413i
$142$		−	5.72354i		−	0.480308i
$143$	−3.70260	+	0.652869i	−0.309627	+	0.0545956i
$144$	1.41302	−	1.18566i	0.117752	−	0.0988054i
$145$		0			0
$146$	−3.06241	−	8.41391i	−0.253447	−	0.696340i
$147$	−1.98650			−0.163844
$148$	−6.62672	−	0.217533i	−0.544713	−	0.0178811i
$149$	15.0751			1.23500			0.617501	−	0.786570i	$-0.288145\pi$
$149$	15.0751			1.23500			0.617501	+	0.786570i	$0.288145\pi$
$150$		0			0
$151$	−9.99530	−	3.63799i	−0.813406	−	0.296056i	−0.0983759	−	0.995149i	$-0.531365\pi$
$151$	−9.99530	−	3.63799i	−0.813406	−	0.296056i	−0.715030	+	0.699094i	$0.753587\pi$
$152$	4.61384	−	3.87148i	0.374232	−	0.314018i
$153$	13.6382	−	2.40478i	1.10258	−	0.194415i
$154$			0.339997i			0.0273978i
$155$		0			0
$156$	0.225020	+	0.129916i	0.0180160	+	0.0104016i
$157$	13.7743	+	11.5580i	1.09931	+	0.922432i	0.997379	−	0.0723591i	$-0.0230528\pi$
$157$	13.7743	+	11.5580i	1.09931	+	0.922432i	0.101933	+	0.994791i	$0.467497\pi$
$158$	−3.31846	−	5.74774i	−0.264002	−	0.457265i
$159$	0.113680	−	0.196900i	0.00901545	−	0.0156152i
$160$		0			0
$161$	−0.000232496	0	0.000277077i	−1.83232e−5	0	2.18368e-5i
$162$	6.84067	−	3.94947i	0.537454	−	0.310299i
$163$	22.3930	+	3.94850i	1.75396	+	0.309270i	0.955984	−	0.293420i	$-0.0947935\pi$
$163$	22.3930	+	3.94850i	1.75396	+	0.309270i	0.797975	+	0.602690i	$0.205905\pi$
$164$	−1.12434	+	6.37647i	−0.0877965	+	0.497918i
$165$		0			0
$166$	−4.57379	+	12.5664i	−0.354995	+	0.975341i
$167$	−5.07057	+	13.9313i	−0.392372	+	1.07803i	0.573543	+	0.819176i	$0.305569\pi$
$167$	−5.07057	+	13.9313i	−0.392372	+	1.07803i	−0.965915	+	0.258859i	$0.916654\pi$
$168$	0.0428161	−	0.0510263i	0.00330334	−	0.00393676i
$169$	2.13513	−	12.1089i	0.164241	−	0.931455i
$170$		0			0
$171$	5.16587	−	2.98252i	0.395044	−	0.228079i
$172$	−0.713136	−	0.849882i	−0.0543761	−	0.0648029i
$173$	21.1475	−	7.69707i	1.60782	−	0.585198i	0.626811	−	0.779171i	$-0.284360\pi$
$173$	21.1475	−	7.69707i	1.60782	−	0.585198i	0.981007	+	0.193974i	$0.0621376\pi$
$174$	−0.0780643	+	0.135211i	−0.00591804	+	0.0102503i
$175$		0			0
$176$	2.16844	+	1.81953i	0.163452	+	0.137153i
$177$	1.96013	+	1.13168i	0.147332	+	0.0850623i
$178$	1.78135	+	10.1025i	0.133518	+	0.757217i
$179$		−	10.0280i		−	0.749526i	−0.927121	−	0.374763i	$-0.877724\pi$
$179$		−	10.0280i		−	0.749526i	0.927121	−	0.374763i	$-0.122276\pi$
$180$		0			0
$181$	−6.29551	+	5.28256i	−0.467942	+	0.392650i	−0.846043	−	0.533114i	$-0.821022\pi$
$181$	−6.29551	+	5.28256i	−0.467942	+	0.392650i	0.378101	+	0.925764i	$0.376577\pi$
$182$	0.0598490	+	0.0217833i	0.00443631	+	0.00161468i
$183$	0.432424	+	1.18807i	0.0319657	+	0.0878250i
$184$	−0.0134013			−0.000987958
$185$		0			0
$186$	1.37275			0.100655
$187$	7.26868	+	19.9705i	0.531539	+	1.46039i
$188$	−8.14873	−	2.96590i	−0.594308	−	0.216310i
$189$	0.102468	−	0.0859807i	0.00745344	−	0.00625418i
$190$		0			0
$191$		−	22.0191i		−	1.59324i	−0.604478	−	0.796622i	$-0.706618\pi$
$191$		−	22.0191i		−	1.59324i	0.604478	−	0.796622i	$-0.293382\pi$
$192$	−0.311353	−	1.76577i	−0.0224700	−	0.127434i
$193$	−5.10229	−	2.94581i	−0.367271	−	0.212044i	0.304995	−	0.952354i	$-0.401345\pi$
$193$	−5.10229	−	2.94581i	−0.367271	−	0.212044i	−0.672265	+	0.740310i	$0.734679\pi$
$194$	5.17844	+	4.34523i	0.371790	+	0.311969i
$195$		0			0
$196$	3.81159	−	6.60187i	0.272257	−	0.471562i
$197$	6.28009	−	2.28577i	0.447438	−	0.162854i	−0.108467	−	0.994100i	$-0.534594\pi$
$197$	6.28009	−	2.28577i	0.447438	−	0.162854i	0.555905	+	0.831246i	$0.312372\pi$
$198$	8.01949	+	9.55726i	0.569921	+	0.679205i
$199$	9.14409	−	5.27934i	0.648207	−	0.374243i	−0.139562	−	0.990213i	$-0.544569\pi$
$199$	9.14409	−	5.27934i	0.648207	−	0.374243i	0.787769	+	0.615971i	$0.211236\pi$
$200$		0			0
$201$	0.159927	−	0.906989i	0.0112804	−	0.0639741i
$202$	4.53009	−	5.39875i	0.318736	−	0.379855i
$203$	0.0156787	−	0.0430769i	0.00110043	−	0.00302341i
$204$	0.502332	−	1.38015i	0.0351703	−	0.0966296i
$205$		0			0
$206$	1.76180	−	9.99167i	0.122750	−	0.696153i
$207$	−0.0130708	−	0.00230474i	−0.000908484	−	0.000160190i
$208$	0.459218	−	0.265130i	0.0318410	−	0.0183834i
$209$	5.88408	+	7.01237i	0.407010	+	0.485056i
$210$		0			0
$211$	5.33976	−	9.24874i	0.367605	−	0.636710i	−0.621586	−	0.783346i	$-0.713511\pi$
$211$	5.33976	−	9.24874i	0.367605	−	0.636710i	0.989190	+	0.146636i	$0.0468447\pi$
$212$	0.436248	+	0.755604i	0.0299616	+	0.0518951i
$213$	−1.30552	−	1.09546i	−0.0894530	−	0.0750600i
$214$	−9.52840	−	5.50122i	−0.651348	−	0.376056i
$215$		0			0
$216$		−	4.95603i		−	0.337215i
$217$	−0.396934	+	0.0699901i	−0.0269456	+	0.00475124i
$218$	−7.90838	+	6.63592i	−0.535623	+	0.449441i
$219$	−2.50532	−	0.911863i	−0.169294	−	0.0616180i
$220$		0			0
$221$	3.98107			0.267796
$222$	1.10028	−	1.22713i	0.0738458	−	0.0823599i
$223$	14.5288			0.972917			0.486459	−	0.873704i	$-0.338288\pi$
$223$	14.5288			0.972917			0.486459	+	0.873704i	$0.338288\pi$
$224$	0.144012	+	0.395669i	0.00962218	+	0.0264367i
$225$		0			0
$226$	−13.2240	+	11.0963i	−0.879649	+	0.738113i
$227$	22.3876	−	3.94753i	1.48591	−	0.262007i	0.628976	−	0.777425i	$-0.283474\pi$
$227$	22.3876	−	3.94753i	1.48591	−	0.262007i	0.856939	+	0.515418i	$0.172363\pi$
$228$		−	0.632625i		−	0.0418966i
$229$	−0.748417	−	4.24448i	−0.0494568	−	0.280483i	0.950043	−	0.312120i	$-0.101039\pi$
$229$	−0.748417	−	4.24448i	−0.0494568	−	0.280483i	−0.999499	+	0.0316367i	$0.989928\pi$
$230$		0			0
$231$	0.0775525	+	0.0650743i	0.00510258	+	0.00428157i
$232$	−0.849237	−	1.47092i	−0.0557552	−	0.0965708i
$233$	2.79779	−	4.84592i	0.183289	−	0.317467i	−0.759709	−	0.650263i	$-0.774659\pi$
$233$	2.79779	−	4.84592i	0.183289	−	0.317467i	0.942999	+	0.332796i	$0.107992\pi$
$234$	2.19614	−	0.799331i	0.143566	−	0.0522539i
$235$		0			0
$236$	−7.52198	+	4.34282i	−0.489639	+	0.282693i
$237$	−1.94618	−	0.343165i	−0.126418	−	0.0222909i
$238$	0.0625158	−	0.354545i	0.00405230	−	0.0229817i
$239$	−13.5730	+	16.1757i	−0.877966	+	1.04632i	0.120595	+	0.992702i	$0.461520\pi$
$239$	−13.5730	+	16.1757i	−0.877966	+	1.04632i	−0.998562	+	0.0536175i	$0.982925\pi$
$240$		0			0
$241$	2.32326	−	6.38312i	0.149655	−	0.411173i	−0.842100	−	0.539321i	$-0.818681\pi$
$241$	2.32326	−	6.38312i	0.149655	−	0.411173i	0.991755	+	0.128148i	$0.0409033\pi$
$242$	−5.56187	+	6.62837i	−0.357530	+	0.426088i
$243$	1.28430	−	7.28364i	0.0823881	−	0.467246i
$244$	−4.77812	−	0.842511i	−0.305888	−	0.0539362i
$245$		0			0
$246$	−1.03459	−	1.23297i	−0.0659628	−	0.0786114i
$247$	1.61136	−	0.586487i	0.102528	−	0.0373173i
$248$	−7.46683	+	12.9329i	−0.474144	+	0.821242i
$249$	1.99095	+	3.44843i	0.126171	+	0.218535i
$250$		0			0
$251$	4.04419	+	2.33491i	0.255267	+	0.147379i	0.622174	−	0.782879i	$-0.286250\pi$
$251$	4.04419	+	2.33491i	0.255267	+	0.147379i	−0.366907	+	0.930258i	$0.619583\pi$
$252$	0.0439604	+	0.249312i	0.00276924	+	0.0157052i
$253$		−	0.0203680i		−	0.00128053i
$254$	−8.36194	+	1.47444i	−0.524675	+	0.0925144i
$255$		0			0
$256$	15.9543	+	5.80689i	0.997144	+	0.362931i
$257$	−5.75524	−	15.8124i	−0.359002	−	0.986350i	−0.979376	−	0.202044i	$-0.935241\pi$
$257$	−5.75524	−	15.8124i	−0.359002	−	0.986350i	0.620374	−	0.784306i	$-0.286981\pi$
$258$	0.275788			0.0171698
$259$	−0.255583	+	0.410928i	−0.0158811	+	0.0255338i
$260$		0			0
$261$	−0.575327	−	1.58070i	−0.0356118	−	0.0978427i
$262$	19.1780	+	6.98023i	1.18482	+	0.431240i
$263$	−19.3334	+	16.2226i	−1.19215	+	1.00033i	−0.192329	+	0.981331i	$0.561604\pi$
$263$	−19.3334	+	16.2226i	−1.19215	+	1.00033i	−0.999819	+	0.0190003i	$0.993952\pi$
$264$	3.69397	−	0.651346i	0.227348	−	0.0400876i
$265$		0			0
$266$	−0.0269276	−	0.152714i	−0.00165103	−	0.00936348i
$267$	2.64530	+	1.52727i	0.161890	+	0.0934672i
$268$	2.70740	+	2.27178i	0.165381	+	0.138771i
$269$	−8.30018	−	14.3763i	−0.506071	−	0.876541i	−0.999975	−	0.00702440i	$-0.997764\pi$
$269$	−8.30018	−	14.3763i	−0.506071	−	0.876541i	0.493904	−	0.869516i	$-0.335569\pi$
$270$		0			0
$271$	3.10033	−	1.12843i	0.188331	−	0.0685470i	−0.246133	−	0.969236i	$-0.579160\pi$
$271$	3.10033	−	1.12843i	0.188331	−	0.0685470i	0.434464	+	0.900689i	$0.356938\pi$
$272$	−1.92666	−	2.29610i	−0.116821	−	0.139221i
$273$	0.0164236	−	0.00948217i	0.000994001	−	0.000573887i
$274$	−19.2719	−	3.39816i	−1.16426	−	0.205291i
$275$		0			0
$276$	−0.000904799		0.00107830i	−5.44625e−5		6.49059e-5i
$277$	5.93054	−	16.2940i	0.356332	−	0.979013i	−0.623960	−	0.781456i	$-0.714477\pi$
$277$	5.93054	−	16.2940i	0.356332	−	0.979013i	0.980291	−	0.197557i	$-0.0633006\pi$
$278$	6.89323	−	18.9390i	0.413429	−	1.13589i
$279$	−9.50687	+	11.3298i	−0.569162	+	0.678300i
$280$		0			0
$281$	18.8706	+	3.32740i	1.12573	+	0.198496i	0.705354	−	0.708855i	$-0.250788\pi$
$281$	18.8706	+	3.32740i	1.12573	+	0.198496i	0.420374	+	0.907351i	$0.361899\pi$
$282$	1.86683	−	1.07782i	0.111168	−	0.0641830i
$283$	−0.388913	−	0.463488i	−0.0231185	−	0.0275515i	0.754361	−	0.656459i	$-0.227947\pi$
$283$	−0.388913	−	0.463488i	−0.0231185	−	0.0275515i	−0.777480	+	0.628908i	$0.783502\pi$
$284$	6.14560	−	2.23681i	0.364674	−	0.132730i
$285$		0			0
$286$	1.79326	+	3.10602i	0.106038	+	0.183663i
$287$	0.362017	+	0.303768i	0.0213692	+	0.0179309i
$288$	13.3807	+	7.72538i	0.788468	+	0.455222i
$289$	−0.955655	−	5.41979i	−0.0562150	−	0.318811i
$290$		0			0
$291$	1.98227	−	0.349527i	0.116203	−	0.0204897i
$292$	7.83754	−	6.57647i	0.458657	−	0.384859i
$293$	−14.4365	−	5.25445i	−0.843388	−	0.306968i	−0.116046	−	0.993244i	$-0.537022\pi$
$293$	−14.4365	−	5.25445i	−0.843388	−	0.306968i	−0.727341	+	0.686276i	$0.759244\pi$
$294$	0.648125	+	1.78071i	0.0377994	+	0.103853i
$295$		0			0
$296$	5.57631	+	17.0408i	0.324117	+	0.990474i
$297$	7.53244			0.437076
$298$	−4.91847	−	13.5134i	−0.284919	−	0.782809i
$299$	−0.00358534	−	0.00130496i	−0.000207346	−	7.54677e-5i
$300$		0			0
$301$	−0.0797449	+	0.0140612i	−0.00459642	+	0.000810472i
$302$			10.1468i			0.583881i
$303$	−0.364398	−	2.06660i	−0.0209341	−	0.118723i
$304$	−1.11808	−	0.645526i	−0.0641265	−	0.0370234i
$305$		0			0
$306$	−6.60531	−	11.4407i	−0.377601	−	0.654023i
$307$	−14.7246	+	25.5038i	−0.840378	+	1.45558i	0.0491975	+	0.998789i	$0.484334\pi$
$307$	−14.7246	+	25.5038i	−0.840378	+	1.45558i	−0.889575	+	0.456788i	$0.849000\pi$
$308$	−0.365069	+	0.132874i	−0.0208018	+	0.00757122i
$309$	−1.94187	−	2.31423i	−0.110469	−	0.131652i
$310$		0			0
$311$	2.29988	+	0.405531i	0.130414	+	0.0229956i	0.238474	−	0.971149i	$-0.423353\pi$
$311$	2.29988	+	0.405531i	0.130414	+	0.0229956i	−0.108060	+	0.994144i	$0.534464\pi$
$312$	0.122013	−	0.691973i	0.00690765	−	0.0391752i
$313$	2.19805	−	2.61953i	0.124241	−	0.148065i	−0.700338	−	0.713811i	$-0.746967\pi$
$313$	2.19805	−	2.61953i	0.124241	−	0.148065i	0.824579	+	0.565746i	$0.191412\pi$
$314$	5.86660	−	16.1183i	0.331071	−	0.909611i
$315$		0			0
$316$	4.87469	−	5.80944i	0.274223	−	0.326806i
$317$	1.67589	−	9.50445i	0.0941274	−	0.533823i	−0.900884	−	0.434060i	$-0.857080\pi$
$317$	1.67589	−	9.50445i	0.0941274	−	0.533823i	0.995011	−	0.0997628i	$-0.0318084\pi$
$318$	−0.213592	−	0.0376620i	−0.0119776	−	0.00211198i
$319$	2.23559	−	1.29072i	0.125169	−	0.0722663i
$320$		0			0
$321$	−3.07852	+	1.12049i	−0.171826	+	0.0625395i
$322$	−0.000172518	0	0.000298810i	−9.61406e−6	0	1.66520e-5i
$323$	−4.84646	−	8.39432i	−0.269665	−	0.467073i
$324$	6.91411	+	5.80162i	0.384117	+	0.322312i
$325$		0			0
$326$	−3.76660	−	21.3615i	−0.208613	−	1.18310i
$327$			3.07397i			0.169991i
$328$	17.2435	−	3.04050i	0.952116	−	0.167884i
$329$	−0.484847	+	0.406835i	−0.0267305	+	0.0224295i
$330$		0			0
$331$	3.72850	+	10.2440i	0.204937	+	0.563059i	0.998997	−	0.0447803i	$-0.0142588\pi$
$331$	3.72850	+	10.2440i	0.204937	+	0.563059i	−0.794060	+	0.607839i	$0.792037\pi$
$332$	−15.2805			−0.838628
$333$	2.50815	+	17.5795i	0.137446	+	0.963351i
$334$	14.1424			0.773837
$335$		0			0
$336$	−0.0134171	−	0.00488344i	−0.000731965	−	0.000266414i
$337$	22.7726	−	19.1085i	1.24050	−	1.04091i	0.243019	−	0.970021i	$-0.421862\pi$
$337$	22.7726	−	19.1085i	1.24050	−	1.04091i	0.997484	−	0.0708850i	$-0.0225823\pi$
$338$	−11.5511	+	2.03677i	−0.628296	+	0.110786i
$339$			5.14015i			0.279175i
$340$		0			0
$341$	−19.6562	−	11.3485i	−1.06444	−	0.614556i
$342$	−4.35897	−	3.65761i	−0.235706	−	0.197781i
$343$	−0.556647	−	0.964140i	−0.0300561	−	0.0520587i
$344$	−1.50010	+	2.59826i	−0.0808802	+	0.140089i
$345$		0			0
$346$	−13.7994	−	16.4454i	−0.741859	−	0.884113i
$347$	−18.5136	+	10.6888i	−0.993863	+	0.573807i	−0.906427	−	0.422363i	$-0.861201\pi$
$347$	−18.5136	+	10.6888i	−0.993863	+	0.573807i	−0.0874362	+	0.996170i	$0.527867\pi$
$348$	−0.175690	−	0.0309789i	−0.00941799	−	0.00166065i
$349$	−1.56915	+	8.89911i	−0.0839948	+	0.476358i	0.913574	+	0.406672i	$0.133311\pi$
$349$	−1.56915	+	8.89911i	−0.0839948	+	0.476358i	−0.997569	+	0.0696862i	$0.977800\pi$
$350$		0			0
$351$	0.482595	−	1.32592i	0.0257590	−	0.0707723i
$352$	−8.10961	+	22.2810i	−0.432243	+	1.18758i
$353$	13.4451	−	16.0232i	0.715609	−	0.852830i	−0.278587	−	0.960411i	$-0.589866\pi$
$353$	13.4451	−	16.0232i	0.715609	−	0.852830i	0.994196	+	0.107581i	$0.0343105\pi$
$354$	0.374923	−	2.12629i	0.0199269	−	0.113011i
$355$		0			0
$356$	−10.1513	+	5.86088i	−0.538020	+	0.310626i
$357$	−0.0689054	−	0.0821183i	−0.00364686	−	0.00434616i
$358$	−8.98911	+	3.27177i	−0.475089	+	0.172918i
$359$	1.20188	−	2.08172i	0.0634328	−	0.109869i	−0.832565	−	0.553927i	$-0.813128\pi$
$359$	1.20188	−	2.08172i	0.0634328	−	0.109869i	0.895998	+	0.444059i	$0.146462\pi$
$360$		0			0
$361$	11.3566	+	9.52929i	0.597714	+	0.501542i
$362$	6.78931	+	3.91981i	0.356838	+	0.206021i
$363$	0.447393	+	2.53729i	0.0234821	+	0.133173i
$364$			0.0727755i			0.00381447i
$365$		0			0
$366$	0.923910	−	0.775252i	0.0482935	−	0.0405231i
$367$	−13.6333	−	4.96213i	−0.711655	−	0.259021i	−0.0392761	−	0.999228i	$-0.512505\pi$
$367$	−13.6333	−	4.96213i	−0.711655	−	0.259021i	−0.672379	+	0.740207i	$0.734727\pi$
$368$	0.000982502		0.00269940i	5.12165e−5		0.000140716i
$369$	17.3412			0.902746
$370$		0			0
$371$	0.0636810			0.00330615
$372$	0.536482	+	1.47397i	0.0278153	+	0.0764220i
$373$	−30.6899	−	11.1702i	−1.58907	−	0.578372i	−0.611915	−	0.790923i	$-0.709601\pi$
$373$	−30.6899	−	11.1702i	−1.58907	−	0.578372i	−0.977150	+	0.212551i	$0.931823\pi$
$374$	15.5302	−	13.0313i	0.803045	−	0.673835i
$375$		0			0
$376$			23.4504i			1.20936i
$377$	−0.0839705	−	0.476221i	−0.00432470	−	0.0245266i
$378$	−0.110505	−	0.0638001i	−0.00568377	−	0.00328152i
$379$	−5.35493	−	4.49332i	−0.275064	−	0.230806i	0.494811	−	0.869001i	$-0.335237\pi$
$379$	−5.35493	−	4.49332i	−0.275064	−	0.230806i	−0.769875	+	0.638194i	$0.779682\pi$
$380$		0			0
$381$	−1.26413	+	2.18954i	−0.0647634	+	0.112173i
$382$	−19.7380	+	7.18403i	−1.00988	+	0.367567i
$383$	14.2017	+	16.9250i	0.725675	+	0.864826i	0.995169	−	0.0981762i	$-0.0313009\pi$
$383$	14.2017	+	16.9250i	0.725675	+	0.864826i	−0.269494	+	0.963002i	$0.586856\pi$
$384$	1.12257	−	0.648116i	0.0572859	−	0.0330740i
$385$		0			0
$386$	−0.975938	+	5.53482i	−0.0496739	+	0.281715i
$387$	−1.90995	+	2.27619i	−0.0970883	+	0.115705i
$388$	−2.64186	+	7.25846i	−0.134120	+	0.368492i
$389$	−11.8837	+	32.6501i	−0.602525	+	1.65542i	0.143614	+	0.989634i	$0.454128\pi$
$389$	−11.8837	+	32.6501i	−0.602525	+	1.65542i	−0.746139	+	0.665790i	$0.768094\pi$
$390$		0			0
$391$	−0.00374510	+	0.0212395i	−0.000189398	+	0.00107413i
$392$	−20.3018	−	3.57976i	−1.02540	−	0.180805i
$393$	5.26277	−	3.03846i	0.265472	−	0.153270i
$394$	−4.09794	−	4.88373i	−0.206451	−	0.246039i
$395$		0			0
$396$	−7.12793	+	12.3459i	−0.358192	+	0.620406i
$397$	−16.5516	−	28.6683i	−0.830702	−	1.43882i	−0.897482	−	0.441051i	$-0.854606\pi$
$397$	−16.5516	−	28.6683i	−0.830702	−	1.43882i	0.0667799	−	0.997768i	$-0.478727\pi$
$398$	−7.71581	−	6.47433i	−0.386759	−	0.324529i
$399$	−0.0399874	−	0.0230868i	−0.00200188	−	0.00115578i
$400$		0			0
$401$			9.52924i			0.475868i	0.971281	+	0.237934i	$0.0764701\pi$
$401$			9.52924i			0.475868i	−0.971281	+	0.237934i	$0.923530\pi$
$402$	−0.865206	+	0.152559i	−0.0431526	+	0.00760896i
$403$	−3.25700	+	2.73295i	−0.162243	+	0.136138i
$404$	7.56726	+	2.75426i	0.376485	+	0.137029i
$405$		0			0
$406$	−0.0437297			−0.00217027
$407$	−25.8995	+	8.47518i	−1.28379	+	0.420099i
$408$	−3.97179			−0.196633
$409$	5.48437	+	15.0682i	0.271185	+	0.745074i	0.998285	+	0.0585427i	$0.0186454\pi$
$409$	5.48437	+	15.0682i	0.271185	+	0.745074i	−0.727100	+	0.686531i	$0.759132\pi$
$410$		0			0
$411$	−4.46369	+	3.74548i	−0.220178	+	0.184751i
$412$	11.4170	−	2.01312i	0.562475	−	0.0991795i
$413$			0.633940i			0.0311941i
$414$	0.00219856	+	0.0124687i	0.000108053	+	0.000612802i
$415$		0			0
$416$	3.40250	+	2.85503i	0.166821	+	0.139980i
$417$	−3.00060	−	5.19719i	−0.146940	−	0.254507i
$418$	4.36615	−	7.56240i	0.213555	−	0.369889i
$419$	4.35092	−	1.58361i	0.212557	−	0.0773643i	−0.233547	−	0.972345i	$-0.575033\pi$
$419$	4.35092	−	1.58361i	0.212557	−	0.0773643i	0.446104	+	0.894981i	$0.352811\pi$
$420$		0			0
$421$	7.17774	−	4.14407i	0.349822	−	0.201970i	−0.314785	−	0.949163i	$-0.601932\pi$
$421$	7.17774	−	4.14407i	0.349822	−	0.201970i	0.664607	+	0.747193i	$0.268599\pi$
$422$	−10.0328	−	1.76905i	−0.488388	−	0.0861160i
$423$	−4.03297	+	22.8721i	−0.196090	+	1.11208i
$424$	1.51662	−	1.80744i	0.0736537	−	0.0877770i
$425$		0			0
$426$	−0.556032	+	1.52769i	−0.0269399	+	0.0740166i
$427$	−0.227625	+	0.271273i	−0.0110155	+	0.0131278i
$428$	2.18310	−	12.3810i	0.105524	−	0.598457i
$429$	1.05170	+	0.185443i	0.0507765	+	0.00895326i
$430$		0			0
$431$	−0.202710	−	0.241581i	−0.00976422	−	0.0116365i	0.761140	−	0.648587i	$-0.224640\pi$
$431$	−0.202710	−	0.241581i	−0.00976422	−	0.0116365i	−0.770904	+	0.636951i	$0.780195\pi$
$432$	−0.998284	+	0.363346i	−0.0480300	+	0.0174815i
$433$	4.56186	−	7.90137i	0.219229	−	0.379716i	−0.735343	−	0.677695i	$-0.762979\pi$
$433$	4.56186	−	7.90137i	0.219229	−	0.379716i	0.954572	+	0.297979i	$0.0963125\pi$
$434$	0.192245	+	0.332977i	0.00922804	+	0.0159834i
$435$		0			0
$436$	−10.2159	−	5.89817i	−0.489254	−	0.282471i
$437$	0.00161313	+	0.00914854i	7.71667e−5	+	0.000437634i
$438$			2.54329i			0.121523i
$439$	19.7260	−	3.47823i	0.941473	−	0.166007i	0.318211	−	0.948020i	$-0.396918\pi$
$439$	19.7260	−	3.47823i	0.941473	−	0.166007i	0.623262	+	0.782013i	$0.285807\pi$
$440$		0			0
$441$	−19.1855	−	6.98294i	−0.913594	−	0.332521i
$442$	−1.29888	−	3.56864i	−0.0617814	−	0.169743i
$443$	−25.8163			−1.22657			−0.613284	−	0.789862i	$-0.710152\pi$
$443$	−25.8163			−1.22657			−0.613284	+	0.789862i	$0.710152\pi$
$444$	1.74762	+	0.701837i	0.0829386	+	0.0333077i
$445$		0			0
$446$	−4.74021	−	13.0236i	−0.224456	−	0.616686i
$447$	−4.02374	−	1.46452i	−0.190317	−	0.0692695i
$448$	0.384708	−	0.322808i	0.0181757	−	0.0152513i
$449$	−25.1893	+	4.44155i	−1.18876	+	0.209610i	−0.732832	−	0.680409i	$-0.761802\pi$
$449$	−25.1893	+	4.44155i	−1.18876	+	0.209610i	−0.455923	+	0.890019i	$0.650691\pi$
$450$		0			0
$451$	4.62112	+	26.2077i	0.217600	+	1.23407i
$452$	−17.0826	−	9.86264i	−0.803498	−	0.463900i
$453$	2.31445	+	1.94205i	0.108742	+	0.0912457i
$454$	−10.8428	−	18.7803i	−0.508880	−	0.881405i
$455$		0			0
$456$	−1.60760	+	0.585119i	−0.0752829	+	0.0274007i
$457$	−2.26391	−	2.69802i	−0.105901	−	0.126208i	0.710490	−	0.703707i	$-0.248473\pi$
$457$	−2.26391	−	2.69802i	−0.105901	−	0.126208i	−0.816391	+	0.577499i	$0.804029\pi$
$458$	−3.56059	+	2.05571i	−0.166375	+	0.0960569i
$459$	−7.85473	−	1.38500i	−0.366627	−	0.0646463i
$460$		0			0
$461$	−6.74610	+	8.03969i	−0.314197	+	0.374446i	−0.899912	−	0.436072i	$-0.856369\pi$
$461$	−6.74610	+	8.03969i	−0.314197	+	0.374446i	0.585715	+	0.810517i	$0.300814\pi$
$462$	0.0330302	−	0.0907497i	0.00153670	−	0.00422206i
$463$	−4.07686	+	11.2011i	−0.189468	+	0.520558i	−0.997661	−	0.0683595i	$-0.978224\pi$
$463$	−4.07686	+	11.2011i	−0.189468	+	0.520558i	0.808193	+	0.588918i	$0.200446\pi$
$464$	−0.234024	+	0.278899i	−0.0108643	+	0.0129476i
$465$		0			0
$466$	−5.25672	−	0.926901i	−0.243513	−	0.0429379i
$467$	−1.15024	+	0.664094i	−0.0532270	+	0.0307306i	−0.526377	−	0.850251i	$-0.676450\pi$
$467$	−1.15024	+	0.664094i	−0.0532270	+	0.0307306i	0.473150	+	0.880982i	$0.343117\pi$
$468$	1.71655	+	2.04570i	0.0793475	+	0.0945627i
$469$	0.242399	−	0.0882259i	0.0111929	−	0.00407390i
$470$		0			0
$471$	−2.55370	−	4.42315i	−0.117668	−	0.203808i
$472$	17.9929	+	15.0979i	0.828192	+	0.694936i
$473$	−3.94897	−	2.27994i	−0.181574	−	0.104832i
$474$	0.327356	+	1.85653i	0.0150360	+	0.0852732i
$475$		0			0
$476$	0.405121	−	0.0714338i	0.0185687	−	0.00327416i
$477$	1.79006	−	1.50204i	0.0819612	−	0.0687736i
$478$	18.9283	+	6.88936i	0.865763	+	0.315112i
$479$	13.6672	+	37.5504i	0.624472	+	1.71572i	0.695767	+	0.718268i	$0.255065\pi$
$479$	13.6672	+	37.5504i	0.624472	+	1.71572i	−0.0712949	+	0.997455i	$0.522713\pi$
$480$		0			0
$481$	−0.167483	+	5.10203i	−0.00763655	+	0.232632i
$482$	−6.47985			−0.295149
$483$	3.51385e−5	0	9.65421e-5i	1.59886e−6	0	4.39282e-6i
$484$	−9.29079	−	3.38157i	−0.422309	−	0.153708i
$485$		0			0
$486$	−6.94811	+	1.22514i	−0.315172	+	0.0555734i
$487$			23.3742i			1.05919i	0.848252	+	0.529593i	$0.177655\pi$
$487$			23.3742i			1.05919i	−0.848252	+	0.529593i	$0.822345\pi$
$488$	2.27836	+	12.9212i	0.103136	+	0.584916i
$489$	−5.59340	−	3.22935i	−0.252943	−	0.146036i
$490$		0			0
$491$	1.94286	+	3.36513i	0.0876800	+	0.151866i	0.906530	−	0.422141i	$-0.138721\pi$
$491$	1.94286	+	3.36513i	0.0876800	+	0.151866i	−0.818850	+	0.574007i	$0.805388\pi$
$492$	0.919565	−	1.59273i	0.0414572	−	0.0718060i
$493$	−2.56857	+	0.934882i	−0.115682	+	0.0421050i
$494$	−1.05146	−	1.25308i	−0.0473073	−	0.0563787i
$495$		0			0
$496$	3.15248	+	0.555867i	0.141551	+	0.0249592i
$497$	0.0828886	−	0.470085i	0.00371806	−	0.0210862i
$498$	2.44161	−	2.90980i	0.109411	−	0.130391i
$499$	9.60639	−	26.3933i	0.430041	−	1.18153i	−0.515746	−	0.856741i	$-0.672485\pi$
$499$	9.60639	−	26.3933i	0.430041	−	1.18153i	0.945787	−	0.324787i	$-0.105293\pi$
$500$		0			0
$501$	2.70680	−	3.22584i	0.120931	−	0.144120i
$502$	0.773551	−	4.38703i	0.0345253	−	0.195803i
$503$	11.7381	+	2.06975i	0.523378	+	0.0922856i	0.429094	−	0.903260i	$-0.358833\pi$
$503$	11.7381	+	2.06975i	0.523378	+	0.0922856i	0.0942836	+	0.995545i	$0.469944\pi$
$504$	0.592882	−	0.342301i	0.0264091	−	0.0152473i
$505$		0			0
$506$	−0.0182580	+	0.00664536i	−0.000811666	+	0.000295422i
$507$	−1.74625	+	3.02460i	−0.0775539	+	0.134327i
$508$	−4.85109	−	8.40234i	−0.215232	−	0.372793i
$509$	−12.1400	−	10.1867i	−0.538097	−	0.451517i	0.332790	−	0.943001i	$-0.392010\pi$
$509$	−12.1400	−	10.1867i	−0.538097	−	0.451517i	−0.870886	+	0.491484i	$0.836454\pi$
$510$		0			0
$511$	−0.129671	−	0.735400i	−0.00573630	−	0.0325322i
$512$		−	7.06906i		−	0.312411i
$513$	−3.38328	+	0.596564i	−0.149376	+	0.0263389i
$514$	−12.2966	+	10.3180i	−0.542378	+	0.455109i
$515$		0			0
$516$	0.107781	+	0.296125i	0.00474477	+	0.0130362i
$517$	−35.6412			−1.56750
$518$	0.451745	+	0.0950341i	0.0198485	+	0.00417556i
$519$	−6.39231			−0.280591
$520$		0			0
$521$	−2.75061	−	1.00114i	−0.120507	−	0.0438608i	0.281063	−	0.959689i	$-0.409313\pi$
$521$	−2.75061	−	1.00114i	−0.120507	−	0.0438608i	−0.401570	+	0.915829i	$0.631535\pi$
$522$	−1.22923	+	1.03145i	−0.0538021	+	0.0451453i
$523$	14.4547	−	2.54875i	0.632060	−	0.111449i	0.151566	−	0.988447i	$-0.451568\pi$
$523$	14.4547	−	2.54875i	0.632060	−	0.111449i	0.480494	+	0.876998i	$0.340457\pi$
$524$			23.3202i			1.01875i
$525$		0			0
$526$	20.8498	+	12.0377i	0.909096	+	0.524867i
$527$	18.4105	+	15.4483i	0.801976	+	0.672937i
$528$	−0.402019	−	0.696317i	−0.0174956	−	0.0303033i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	14.9527	+	17.8199i	0.648891	+	0.773319i
$532$	0.153451	−	0.0885953i	0.00665297	−	0.00384109i
$533$	4.90935	+	0.865652i	0.212648	+	0.0374955i
$534$	0.505980	−	2.86955i	0.0218959	−	0.124178i
$535$		0			0
$536$	3.26886	−	8.98112i	0.141193	−	0.387925i
$537$	−0.974201	+	2.67660i	−0.0420399	+	0.115504i
$538$	−10.1789	+	12.1308i	−0.438846	+	0.522996i
$539$	5.44071	−	30.8558i	0.234348	−	1.32905i
$540$		0			0
$541$	35.5976	−	20.5523i	1.53046	−	0.883611i	0.531119	−	0.847297i	$-0.321772\pi$
$541$	35.5976	−	20.5523i	1.53046	−	0.883611i	0.999340	−	0.0363140i	$-0.0115617\pi$
$542$	−2.02305	−	2.41098i	−0.0868974	−	0.103560i
$543$	2.19355	−	0.798386i	0.0941341	−	0.0342620i
$544$	12.5534	−	21.7432i	0.538223	−	0.932230i
$545$		0			0
$546$	−0.0138583	−	0.0116285i	−0.000593079	−	0.000497653i
$547$	6.83527	+	3.94634i	0.292255	+	0.168734i	0.638958	−	0.769241i	$-0.279366\pi$
$547$	6.83527	+	3.94634i	0.292255	+	0.168734i	−0.346703	+	0.937975i	$0.612699\pi$
$548$	−3.88292	−	22.0211i	−0.165870	−	0.940695i
$549$			12.9944i			0.554587i
$550$		0			0
$551$	−0.901916	+	0.756797i	−0.0384229	+	0.0322406i
$552$	0.00357698	+	0.00130192i	0.000152247	+	5.54132e-5i
$553$	−0.189312	−	0.520130i	−0.00805037	−	0.0221182i
$554$	−16.5409			−0.702757
$555$		0			0
$556$	23.0295			0.976670
$557$	8.29054	+	22.7781i	0.351281	+	0.965137i	0.981959	+	0.189093i	$0.0605547\pi$
$557$	8.29054	+	22.7781i	0.351281	+	0.965137i	−0.630678	+	0.776045i	$0.717223\pi$
$558$	13.2579	+	4.82547i	0.561250	+	0.204278i
$559$	−0.654339	+	0.549056i	−0.0276756	+	0.0232226i
$560$		0			0
$561$		−	6.03654i		−	0.254863i
$562$	−3.17412	−	18.0013i	−0.133892	−	0.759340i
$563$	−30.4693	−	17.5915i	−1.28413	−	0.741391i	−0.306527	−	0.951862i	$-0.599167\pi$
$563$	−30.4693	−	17.5915i	−1.28413	−	0.741391i	−0.977600	+	0.210471i	$0.932500\pi$
$564$	1.88687	+	1.58327i	0.0794516	+	0.0666678i
$565$		0			0
$566$	−0.288584	+	0.499842i	−0.0121301	+	0.0210099i
$567$	0.619034	−	0.225310i	0.0259970	−	0.00946213i
$568$	−11.3682	−	13.5481i	−0.477000	−	0.568466i
$569$	27.2904	−	15.7561i	1.14407	−	0.660531i	0.196638	−	0.980476i	$-0.436998\pi$
$569$	27.2904	−	15.7561i	1.14407	−	0.660531i	0.947436	+	0.319945i	$0.103664\pi$
$570$		0			0
$571$	−2.32777	+	13.2014i	−0.0974141	+	0.552463i	0.896567	+	0.442909i	$0.146053\pi$
$571$	−2.32777	+	13.2014i	−0.0974141	+	0.552463i	−0.993981	+	0.109554i	$0.965058\pi$
$572$	−2.63424	+	3.13936i	−0.110143	+	0.131263i
$573$	−2.13912	+	5.87718i	−0.0893629	+	0.245523i
$574$	0.154186	−	0.423622i	0.00643559	−	0.0176817i
$575$		0			0
$576$	3.20001	−	18.1481i	0.133334	−	0.756173i
$577$	−1.03944	−	0.183282i	−0.0432726	−	0.00763013i	0.151970	−	0.988385i	$-0.451438\pi$
$577$	−1.03944	−	0.183282i	−0.0432726	−	0.00763013i	−0.195243	+	0.980755i	$0.562549\pi$
$578$	−4.54652	+	2.62493i	−0.189110	+	0.109183i
$579$	1.07569	+	1.28195i	0.0447040	+	0.0532761i
$580$		0			0
$581$	−0.557641	+	0.965863i	−0.0231349	+	0.0400708i
$582$	−0.960061	−	1.66287i	−0.0397958	−	0.0689284i
$583$	2.74705	+	2.30505i	0.113771	+	0.0954652i
$584$	−23.9609	−	13.8338i	−0.991508	−	0.572447i
$585$		0			0
$586$			14.6552i			0.605402i
$587$	7.74311	−	1.36532i	0.319592	−	0.0563528i	−0.0115508	−	0.999933i	$-0.503677\pi$
$587$	7.74311	−	1.36532i	0.319592	−	0.0563528i	0.331143	+	0.943581i	$0.392566\pi$
$588$	−1.65873	+	1.39184i	−0.0684047	+	0.0573983i
$589$	9.72759	+	3.54055i	0.400818	+	0.145886i
$590$		0			0
$591$	−1.89830			−0.0780855
$592$	3.02367	−	2.37255i	0.124272	−	0.0975113i
$593$	−28.8879			−1.18628			−0.593142	−	0.805098i	$-0.702113\pi$
$593$	−28.8879			−1.18628			−0.593142	+	0.805098i	$0.702113\pi$
$594$	−2.45757	−	6.75211i	−0.100835	−	0.277042i
$595$		0			0
$596$	12.5877	−	10.5623i	0.515612	−	0.432650i
$597$	−2.95356	+	0.520792i	−0.120881	+	0.0213146i
$598$			0.00363968i			0.000148837i
$599$	7.63439	+	43.2968i	0.311933	+	1.76906i	0.588927	+	0.808187i	$0.299551\pi$
$599$	7.63439	+	43.2968i	0.311933	+	1.76906i	−0.276994	+	0.960872i	$0.589338\pi$
$600$		0			0
$601$	−16.3655	−	13.7323i	−0.667563	−	0.560152i	0.244780	−	0.969579i	$-0.421284\pi$
$601$	−16.3655	−	13.7323i	−0.667563	−	0.560152i	−0.912343	+	0.409427i	$0.865729\pi$
$602$	0.0386224	+	0.0668959i	0.00157413	+	0.00272647i
$603$	4.73280	−	8.19745i	0.192735	−	0.333826i
$604$	−10.8950	+	3.96546i	−0.443311	+	0.161352i
$605$		0			0
$606$	−1.73362	+	1.00091i	−0.0704235	+	0.0406590i
$607$	−20.8955	−	3.68445i	−0.848124	−	0.149547i	−0.267337	−	0.963603i	$-0.586144\pi$
$607$	−20.8955	−	3.68445i	−0.848124	−	0.149547i	−0.580787	+	0.814056i	$0.697255\pi$
$608$	1.87789	−	10.6500i	0.0761583	−	0.431915i
$609$	−0.00836971	+	0.00997463i	−0.000339158	+	0.000404192i
$610$		0			0
$611$	−2.28350	+	6.27385i	−0.0923803	+	0.253813i
$612$	9.70297	−	11.5635i	0.392219	−	0.467429i
$613$	−5.03066	+	28.5303i	−0.203187	+	1.15233i	0.697081	+	0.716992i	$0.254482\pi$
$613$	−5.03066	+	28.5303i	−0.203187	+	1.15233i	−0.900268	+	0.435336i	$0.856630\pi$
$614$	27.6658	+	4.87822i	1.11650	+	0.196869i
$615$		0			0
$616$	0.675310	+	0.804804i	0.0272090	+	0.0324265i
$617$	−24.4424	+	8.89630i	−0.984014	+	0.358152i	−0.783399	−	0.621519i	$-0.786516\pi$
$617$	−24.4424	+	8.89630i	−0.984014	+	0.358152i	−0.200614	+	0.979670i	$0.564294\pi$
$618$	−1.44092	+	2.49575i	−0.0579624	+	0.100394i
$619$	−20.5919	−	35.6662i	−0.827658	−	1.43355i	−0.899871	−	0.436156i	$-0.856340\pi$
$619$	−20.5919	−	35.6662i	−0.827658	−	1.43355i	0.0722132	−	0.997389i	$-0.476994\pi$
$620$		0			0
$621$	0.00661996	+	0.00382204i	0.000265650	+	0.000153373i
$622$	−0.386849	−	2.19393i	−0.0155112	−	0.0879686i
$623$			0.855538i			0.0342764i
$624$	−0.148328	+	0.0261543i	−0.00593788	+	0.00104701i
$625$		0			0
$626$	−3.06530	−	1.11568i	−0.122514	−	0.0445915i
$627$	−0.889296	−	2.44332i	−0.0355151	−	0.0975769i
$628$	19.5996			0.782111
$629$	28.5660	−	4.07563i	1.13900	−	0.162506i
$630$		0			0
$631$	−12.7116	−	34.9248i	−0.506040	−	1.39033i	−0.885290	−	0.465039i	$-0.846040\pi$
$631$	−12.7116	−	34.9248i	−0.506040	−	1.39033i	0.379251	−	0.925294i	$-0.376182\pi$
$632$	−19.2714	−	7.01420i	−0.766573	−	0.279010i
$633$	−2.32375	+	1.94986i	−0.0923609	+	0.0775000i
$634$	−9.06660	+	1.59869i	−0.360081	+	0.0634920i
$635$		0			0
$636$	−0.0430346	−	0.244061i	−0.00170643	−	0.00967766i
$637$	−5.08290	−	2.93461i	−0.201392	−	0.116274i
$638$	−1.88640	−	1.58287i	−0.0746831	−	0.0626666i
$639$	−8.75787	−	15.1691i	−0.346456	−	0.600079i
$640$		0			0
$641$	17.7377	−	6.45598i	0.700595	−	0.254996i	0.0329303	−	0.999458i	$-0.489516\pi$
$641$	17.7377	−	6.45598i	0.700595	−	0.254996i	0.667665	+	0.744462i	$0.267294\pi$
$642$	2.00882	+	2.39402i	0.0792817	+	0.0944843i
$643$	−13.6913	+	7.90467i	−0.539932	+	0.311730i	−0.745051	−	0.667007i	$-0.767575\pi$
$643$	−13.6913	+	7.90467i	−0.539932	+	0.311730i	0.205119	+	0.978737i	$0.434242\pi$
$644$	−0.000388267	0	6.84619e-5i	−1.52999e−5	0	2.69778e-6i
$645$		0			0
$646$	−5.94347	+	7.08315i	−0.233843	+	0.278683i
$647$	−7.57072	+	20.8004i	−0.297636	+	0.817747i	0.697258	+	0.716820i	$0.254403\pi$
$647$	−7.57072	+	20.8004i	−0.297636	+	0.817747i	−0.994894	+	0.100927i	$0.967819\pi$
$648$	8.34796	−	22.9358i	0.327939	−	0.901004i
$649$	−22.9466	+	27.3466i	−0.900731	+	1.07345i
$650$		0			0
$651$	0.112746	+	0.0198802i	0.00441887	+	0.000779166i
$652$	21.4647	−	12.3926i	0.840621	−	0.485333i
$653$	−7.95869	−	9.48480i	−0.311448	−	0.371169i	0.587501	−	0.809224i	$-0.300112\pi$
$653$	−7.95869	−	9.48480i	−0.311448	−	0.371169i	−0.898948	+	0.438055i	$0.855668\pi$
$654$	2.75552	−	1.00293i	0.107749	−	0.0392175i
$655$		0			0
$656$	−1.87663	−	3.25043i	−0.0732703	−	0.126908i
$657$	−20.9908	−	17.6134i	−0.818931	−	0.687164i
$658$	0.522877	+	0.301883i	0.0203839	+	0.0117686i
$659$	−8.18785	−	46.4356i	−0.318953	−	1.80887i	−0.549143	−	0.835728i	$-0.685046\pi$
$659$	−8.18785	−	46.4356i	−0.318953	−	1.80887i	0.230190	−	0.973146i	$-0.426065\pi$
$660$		0			0
$661$	−16.8898	+	2.97813i	−0.656937	+	0.115836i	−0.492173	−	0.870497i	$-0.663797\pi$
$661$	−16.8898	+	2.97813i	−0.656937	+	0.115836i	−0.164764	+	0.986333i	$0.552686\pi$
$662$	7.96624	−	6.68447i	0.309617	−	0.259799i
$663$	−1.06260	−	0.386754i	−0.0412679	−	0.0150203i
$664$	14.1331	+	38.8303i	0.548470	+	1.50691i
$665$		0			0
$666$	14.9400	−	7.98387i	0.578914	−	0.309369i
$667$	0.00261969			0.000101435
$668$	5.52698	+	15.1853i	0.213845	+	0.587535i
$669$	−3.87791	−	1.41144i	−0.149929	−	0.0545696i
$670$		0			0
$671$	−19.6384	+	3.46277i	−0.758131	+	0.133679i
$672$		−	0.119600i		−	0.00461366i
$673$	3.51443	+	19.9313i	0.135471	+	0.768297i	0.974530	+	0.224256i	$0.0719952\pi$
$673$	3.51443	+	19.9313i	0.135471	+	0.768297i	−0.839059	+	0.544041i	$0.816894\pi$
$674$	−24.5588	−	14.1790i	−0.945970	−	0.546156i
$675$		0			0
$676$	−6.70124	−	11.6069i	−0.257740	−	0.446419i
$677$	12.4453	−	21.5559i	0.478312	−	0.828461i	−0.521379	−	0.853326i	$-0.674582\pi$
$677$	12.4453	−	21.5559i	0.478312	−	0.828461i	0.999691	+	0.0248643i	$0.00791537\pi$
$678$	4.60765	−	1.67705i	0.176956	−	0.0644066i
$679$	0.362387	+	0.431876i	0.0139071	+	0.0165739i
$680$		0			0
$681$	−6.35903	−	1.12127i	−0.243678	−	0.0429671i
$682$	−3.75973	+	21.3225i	−0.143967	+	0.816480i
$683$	−7.44681	+	8.87476i	−0.284944	+	0.339583i	−0.889463	−	0.457008i	$-0.848921\pi$
$683$	−7.44681	+	8.87476i	−0.284944	+	0.339583i	0.604518	+	0.796591i	$0.293366\pi$
$684$	2.22380	−	6.10984i	0.0850291	−	0.233616i
$685$		0			0
$686$	−0.682645	+	0.813545i	−0.0260635	+	0.0310613i
$687$	−0.212583	+	1.20562i	−0.00811053	+	0.0459971i
$688$	0.633340	+	0.111675i	0.0241459	+	0.00425757i
$689$	0.581752	−	0.335875i	0.0221630	−	0.0127958i
$690$		0			0
$691$	0.0158943	−	0.00578507i	0.000604649	−	0.000220074i	−0.341718	−	0.939803i	$-0.611009\pi$
$691$	0.0158943	−	0.00578507i	0.000604649	−	0.000220074i	0.342322	+	0.939583i	$0.388786\pi$
$692$	12.2652	−	21.2440i	0.466254	−	0.807575i
$693$	0.520247	+	0.901094i	0.0197626	+	0.0342297i
$694$	15.6218	+	13.1083i	0.592997	+	0.497584i
$695$		0			0
$696$	0.0837747	+	0.475110i	0.00317547	+	0.0180090i
$697$		−	28.1787i		−	1.06735i
$698$	8.48915	−	1.49687i	0.321319	−	0.0566572i
$699$	−1.21754	+	1.02164i	−0.0460516	+	0.0386419i
$700$		0			0
$701$	1.50535	+	4.13593i	0.0568565	+	0.156212i	0.964869	−	0.262731i	$-0.0846231\pi$
$701$	1.50535	+	4.13593i	0.0568565	+	0.156212i	−0.908013	+	0.418943i	$0.862401\pi$
$702$	−1.34601			−0.0508020
$703$	10.9618	−	5.85795i	0.413433	−	0.220937i
$704$	28.2800			1.06584
$705$		0			0
$706$	−18.7499	−	6.82441i	−0.705663	−	0.256840i
$707$	0.450250	−	0.377804i	0.0169334	−	0.0142088i
$708$	2.42961	−	0.428406i	0.0913104	−	0.0161005i
$709$			32.9793i			1.23856i	0.785169	+	0.619281i	$0.212576\pi$
$709$			32.9793i			1.23856i	−0.785169	+	0.619281i	$0.787424\pi$
$710$		0			0
$711$	−17.5898	−	10.1555i	−0.659669	−	0.380860i
$712$	24.2825	+	20.3754i	0.910024	+	0.763601i
$713$	−0.0115167	−	0.0199475i	−0.000431303	−	0.000747040i
$714$	−0.0511297	+	0.0885593i	−0.00191348	+	0.00331425i
$715$		0			0
$716$	−7.02606	−	8.37333i	−0.262576	−	0.312926i
$717$	5.19426	−	2.99891i	0.193983	−	0.111996i
$718$	−2.25819	−	0.398180i	−0.0842749	−	0.0148599i
$719$	2.37186	−	13.4515i	0.0884554	−	0.501655i	−0.908102	−	0.418749i	$-0.862469\pi$
$719$	2.37186	−	13.4515i	0.0884554	−	0.501655i	0.996557	−	0.0829063i	$-0.0264202\pi$
$720$		0			0
$721$	0.289400	−	0.795120i	0.0107778	−	0.0296118i
$722$	4.83685	−	13.2891i	0.180009	−	0.494570i
$723$	−1.24022	+	1.47804i	−0.0461242	+	0.0549687i
$724$	−1.55553	+	8.82186i	−0.0578109	+	0.327862i
$725$		0			0
$726$	2.12847	−	1.22887i	0.0789949	−	0.0456077i
$727$	26.6882	+	31.8057i	0.989809	+	1.17961i	0.983735	+	0.179627i	$0.0574892\pi$
$727$	26.6882	+	31.8057i	0.989809	+	1.17961i	0.00607473	+	0.999982i	$0.498066\pi$
$728$	0.184934	−	0.0673106i	0.00685412	−	0.00249470i
$729$	11.3702	−	19.6937i	0.421118	−	0.729398i
$730$		0			0
$731$	3.69872	+	3.10359i	0.136802	+	0.114791i
$732$	1.19349	+	0.689064i	0.0441128	+	0.0254685i
$733$	−2.61901	−	14.8531i	−0.0967353	−	0.548613i	−0.994202	−	0.107531i	$-0.965706\pi$
$733$	−2.61901	−	14.8531i	−0.0967353	−	0.548613i	0.897466	−	0.441083i	$-0.145405\pi$
$734$			13.8399i			0.510842i
$735$		0			0
$736$	−0.0184328	+	0.0154670i	−0.000679442	+	0.000570119i
$737$	13.6500	+	4.96819i	0.502804	+	0.183006i
$738$	−5.65781	−	15.5447i	−0.208267	−	0.572208i
$739$	21.3018			0.783601			0.391801	−	0.920050i	$-0.371852\pi$
$739$	21.3018			0.783601			0.391801	+	0.920050i	$0.371852\pi$
$740$		0			0
$741$	−0.487069			−0.0178929
$742$	−0.0207768	−	0.0570839i	−0.000762741	−	0.00209561i
$743$	8.77491	+	3.19381i	0.321920	+	0.117169i	0.497925	−	0.867220i	$-0.334095\pi$
$743$	8.77491	+	3.19381i	0.321920	+	0.117169i	−0.176005	+	0.984389i	$0.556318\pi$
$744$	3.24941	−	2.72658i	0.119129	−	0.0999612i
$745$		0			0
$746$			31.1550i			1.14067i
$747$	7.10655	+	40.3033i	0.260015	+	1.47462i
$748$	20.0616	+	11.5826i	0.733526	+	0.423501i
$749$	−0.702916	−	0.589817i	−0.0256840	−	0.0215514i
$750$		0			0
$751$	−18.5706	+	32.1652i	−0.677651	+	1.17373i	0.298036	+	0.954555i	$0.403669\pi$
$751$	−18.5706	+	32.1652i	−0.677651	+	1.17373i	−0.975687	+	0.219171i	$0.929665\pi$
$752$	4.72358	−	1.71924i	0.172251	−	0.0626943i
$753$	−0.852614	−	1.01611i	−0.0310710	−	0.0370290i
$754$	−0.399489	+	0.230645i	−0.0145485	+	0.00839960i
$755$		0			0
$756$	0.0253183	−	0.143587i	0.000920819	−	0.00522223i
$757$	−21.4087	+	25.5138i	−0.778111	+	0.927317i	−0.998847	−	0.0480171i	$-0.984710\pi$
$757$	−21.4087	+	25.5138i	−0.778111	+	0.927317i	0.220736	+	0.975334i	$0.429154\pi$
$758$	−2.28071	+	6.26619i	−0.0828390	+	0.227598i
$759$	−0.00197872	+	0.00543649i	−7.18231e−5	+	0.000197332i
$760$		0			0
$761$	3.84248	−	21.7918i	0.139290	−	0.789951i	−0.832486	−	0.554045i	$-0.813083\pi$
$761$	3.84248	−	21.7918i	0.139290	−	0.789951i	0.971776	−	0.235905i	$-0.0758055\pi$
$762$	2.37515	+	0.418803i	0.0860426	+	0.0151716i
$763$	−0.745632	+	0.430491i	−0.0269937	+	0.0155848i
$764$	−15.4276	−	18.3859i	−0.558150	−	0.665178i
$765$		0			0
$766$	10.5381	−	18.2525i	0.380757	−	0.659490i
$767$	3.34361	+	5.79130i	0.120731	+	0.209112i
$768$	−3.69428	−	3.09987i	−0.133306	−	0.111857i
$769$	−0.919212	−	0.530707i	−0.0331476	−	0.0191378i	0.483335	−	0.875436i	$-0.339425\pi$
$769$	−0.919212	−	0.530707i	−0.0331476	−	0.0191378i	−0.516482	+	0.856298i	$0.672759\pi$
$770$		0			0
$771$			4.77965i			0.172135i
$772$	−6.32437	+	1.11516i	−0.227619	+	0.0401354i
$773$	8.53732	−	7.16366i	0.307066	−	0.257659i	−0.476212	−	0.879330i	$-0.657991\pi$
$773$	8.53732	−	7.16366i	0.307066	−	0.257659i	0.783278	+	0.621672i	$0.213546\pi$
$774$	2.66354	+	0.969447i	0.0957388	+	0.0348461i
$775$		0			0
$776$	20.8884			0.749850
$777$	0.108139	−	0.0848526i	0.00387948	−	0.00304407i
$778$	33.1448			1.18830
$779$	−4.15126	−	11.4055i	−0.148734	−	0.408644i
$780$		0			0
$781$	20.5912	−	17.2780i	0.736809	−	0.618257i
$782$	0.0202611	−	0.00357257i	0.000724534	−	0.000127755i
$783$			0.968806i			0.0346223i
$784$	0.767340	+	4.35180i	0.0274050	+	0.155422i
$785$		0			0
$786$	−4.44074	−	3.72623i	−0.158396	−	0.132910i
$787$	−18.4614	−	31.9760i	−0.658077	−	1.13982i	−0.981113	−	0.193436i	$-0.938037\pi$
$787$	−18.4614	−	31.9760i	−0.658077	−	1.13982i	0.323036	−	0.946387i	$-0.395296\pi$
$788$	3.64235	−	6.30873i	0.129753	−	0.224739i
$789$	6.73634	−	2.45183i	0.239820	−	0.0872873i
$790$		0			0
$791$	−1.24681	+	0.719846i	−0.0443315	+	0.0255948i
$792$	37.9657	+	6.69437i	1.34905	+	0.237874i
$793$	−0.648664	+	3.67876i	−0.0230347	+	0.130636i
$794$	−20.2981	+	24.1904i	−0.720353	+	0.858484i
$795$		0			0
$796$	3.93634	−	10.8150i	0.139520	−	0.383328i
$797$	32.7040	−	38.9751i	1.15843	−	1.38057i	0.247053	−	0.969002i	$-0.420538\pi$
$797$	32.7040	−	38.9751i	1.15843	−	1.38057i	0.911380	−	0.411565i	$-0.135018\pi$
$798$	−0.00764858	+	0.0433773i	−0.000270757	+	0.00153554i
$799$	37.1662	+	6.55341i	1.31485	+	0.231843i
$800$		0			0
$801$	20.1795	+	24.0490i	0.713007	+	0.849729i
$802$	8.54205	−	3.10905i	0.301630	−	0.109784i
$803$	21.0254	−	36.4171i	0.741970	−	1.28513i
$804$	−0.501940	−	0.869386i	−0.0177021	−	0.0306609i
$805$		0			0
$806$	3.51247	+	2.02792i	0.123721	+	0.0714306i
$807$	0.818788	+	4.64358i	0.0288227	+	0.163462i
$808$		−	21.7771i		−	0.766115i
$809$	12.0988	−	2.13335i	0.425373	−	0.0750047i	0.0431362	−	0.999069i	$-0.486265\pi$
$809$	12.0988	−	2.13335i	0.425373	−	0.0750047i	0.382237	+	0.924064i	$0.375154\pi$
$810$		0			0
$811$	−17.9533	−	6.53447i	−0.630426	−	0.229456i	0.00699079	−	0.999976i	$-0.497775\pi$
$811$	−17.9533	−	6.53447i	−0.630426	−	0.229456i	−0.637417	+	0.770519i	$0.719997\pi$
$812$	−0.0170900	−	0.0469544i	−0.000599742	−	0.00164778i
$813$	−0.937142			−0.0328670
$814$	16.0473	+	20.4512i	0.562456	+	0.716815i
$815$		0			0
$816$	0.291187	+	0.800030i	0.0101936	+	0.0280067i
$817$	1.95429	+	0.711305i	0.0683721	+	0.0248854i
$818$	11.7178	−	9.83242i	0.409704	−	0.343783i
$819$	0.191949	−	0.0338459i	0.00670725	−	0.00118267i
$820$		0			0
$821$	−5.18433	−	29.4018i	−0.180934	−	1.02613i	−0.931069	−	0.364844i	$-0.881122\pi$
$821$	−5.18433	−	29.4018i	−0.180934	−	1.02613i	0.750134	−	0.661286i	$-0.229989\pi$
$822$	4.81381	+	2.77925i	0.167901	+	0.0969375i
$823$	27.7400	+	23.2766i	0.966955	+	0.811371i	0.982070	−	0.188514i	$-0.0603672\pi$
$823$	27.7400	+	23.2766i	0.966955	+	0.811371i	−0.0151157	+	0.999886i	$0.504812\pi$
$824$	−15.6753	−	27.1505i	−0.546076	−	0.945832i
$825$		0			0
$826$	0.568266	−	0.206832i	0.0197725	−	0.00719660i
$827$	10.0600	+	11.9890i	0.349819	+	0.416898i	0.912048	−	0.410084i	$-0.134500\pi$
$827$	10.0600	+	11.9890i	0.349819	+	0.416898i	−0.562229	+	0.826982i	$0.690056\pi$
$828$	−0.0125289	+	0.00723356i	−0.000435409	+	0.000251384i
$829$	−35.2290	−	6.21182i	−1.22355	−	0.215745i	−0.475699	−	0.879608i	$-0.657805\pi$
$829$	−35.2290	−	6.21182i	−1.22355	−	0.215745i	−0.747854	+	0.663863i	$0.768916\pi$
$830$		0			0
$831$	−3.16588	+	3.77294i	−0.109823	+	0.130882i
$832$	1.81187	−	4.97807i	0.0628152	−	0.172583i
$833$	−11.3470	+	31.1756i	−0.393150	+	1.08017i
$834$	−3.67979	+	4.38540i	−0.127421	+	0.151854i
$835$		0			0
$836$	9.82639	+	1.73266i	0.339853	+	0.0599252i
$837$	7.37692	−	4.25906i	0.254983	−	0.147215i
$838$	−2.83910	−	3.38351i	−0.0980752	−	0.116881i
$839$	−11.7973	+	4.29388i	−0.407289	+	0.148241i	−0.537537	−	0.843240i	$-0.680645\pi$
$839$	−11.7973	+	4.29388i	−0.407289	+	0.148241i	0.130248	+	0.991482i	$0.458423\pi$
$840$		0			0
$841$	−14.3340	−	24.8272i	−0.494276	−	0.856110i
$842$	−6.05660	−	5.08209i	−0.208724	−	0.175140i
$843$	−4.71357	−	2.72138i	−0.162344	−	0.0937293i
$844$	−2.02141	−	11.4640i	−0.0695797	−	0.394606i
$845$		0			0
$846$	21.8184	−	3.84718i	0.750133	−	0.132269i
$847$	−0.552799	+	0.463853i	−0.0189944	+	0.0159382i
$848$	−0.475259	−	0.172980i	−0.0163205	−	0.00594016i
$849$	0.0587787	+	0.161493i	0.00201728	+	0.00554243i
$850$		0			0
$851$	−0.0270624	−	0.00569316i	−0.000927688	−	0.000195159i
$852$	−1.85764			−0.0636418
$853$	7.27082	+	19.9764i	0.248948	+	0.683979i	0.999726	+	0.0234241i	$0.00745681\pi$
$853$	7.27082	+	19.9764i	0.248948	+	0.683979i	−0.750778	+	0.660555i	$0.770321\pi$
$854$	0.317435	+	0.115537i	0.0108624	+	0.00395360i
$855$		0			0
$856$	−33.4812	+	5.90364i	−1.14436	+	0.201782i
$857$		−	11.6284i		−	0.397217i	−0.980079	−	0.198609i	$-0.936358\pi$
$857$		−	11.6284i		−	0.397217i	0.980079	−	0.198609i	$-0.0636423\pi$
$858$	−0.176900	−	1.00325i	−0.00603926	−	0.0342504i
$859$	−5.34045	−	3.08331i	−0.182214	−	0.105201i	0.406119	−	0.913820i	$-0.366882\pi$
$859$	−5.34045	−	3.08331i	−0.182214	−	0.105201i	−0.588332	+	0.808619i	$0.700215\pi$
$860$		0			0
$861$	−0.0671165	−	0.116249i	−0.00228732	−	0.00396176i
$862$	−0.150417	+	0.260530i	−0.00512322	+	0.00887367i
$863$	−29.2167	+	10.6340i	−0.994548	+	0.361986i	−0.787480	−	0.616341i	$-0.788614\pi$
$863$	−29.2167	+	10.6340i	−0.994548	+	0.361986i	−0.207068	+	0.978327i	$0.566392\pi$
$864$	−5.71994	−	6.81675i	−0.194596	−	0.231911i
$865$		0			0
$866$	−8.57119	−	1.51133i	−0.291261	−	0.0513571i
$867$	−0.271447	+	1.53945i	−0.00921882	+	0.0522825i
$868$	−0.282400	+	0.336552i	−0.00958530	+	0.0114233i
$869$	10.6606	−	29.2897i	0.361635	−	0.993584i
$870$		0			0
$871$	1.74908	−	2.08447i	0.0592653	−	0.0706297i
$872$	−5.53941	+	31.4156i	−0.187588	+	1.06387i
$873$	20.3733	+	3.59235i	0.689530	+	0.121583i
$874$	0.00767447	−	0.00443086i	0.000259593	−	0.000149876i
$875$		0			0
$876$	−2.73083	+	0.993942i	−0.0922663	+	0.0335822i
$877$	7.23472	−	12.5309i	0.244299	−	0.423138i	−0.717635	−	0.696419i	$-0.754776\pi$
$877$	7.23472	−	12.5309i	0.244299	−	0.423138i	0.961934	+	0.273281i	$0.0881088\pi$
$878$	−9.55380	−	16.5477i	−0.322425	−	0.558457i
$879$	3.34282	+	2.80496i	0.112751	+	0.0946089i
$880$		0			0
$881$	6.21884	+	35.2688i	0.209518	+	1.18824i	0.890170	+	0.455629i	$0.150585\pi$
$881$	6.21884	+	35.2688i	0.209518	+	1.18824i	−0.680652	+	0.732607i	$0.738303\pi$
$882$			19.4762i			0.655798i
$883$	−17.4875	+	3.08352i	−0.588502	+	0.103769i	−0.459967	−	0.887936i	$-0.652139\pi$
$883$	−17.4875	+	3.08352i	−0.588502	+	0.103769i	−0.128535	+	0.991705i	$0.541028\pi$
$884$	3.32418	−	2.78932i	0.111804	−	0.0938150i
$885$		0			0
$886$	8.42293	+	23.1418i	0.282974	+	0.777464i
$887$	33.9486			1.13988			0.569942	−	0.821685i	$-0.306966\pi$
$887$	33.9486			1.13988			0.569942	+	0.821685i	$0.306966\pi$
$888$	0.167092	−	5.09013i	0.00560725	−	0.170814i
$889$	−0.708135			−0.0237501
$890$		0			0
$891$	34.8591	+	12.6877i	1.16782	+	0.425053i
$892$	12.1315	−	10.1795i	0.406192	−	0.340836i
$893$	16.0087	−	2.82276i	0.535710	−	0.0944601i
$894$			4.08472i			0.136613i
$895$		0			0
$896$	0.314418	+	0.181529i	0.0105040	+	0.00606447i
$897$	0.000830200	0	0.000696621i	2.77196e−5	0	2.32595e-5i
$898$	12.1998	+	21.1306i	0.407112	+	0.705138i
$899$	1.45962	−	2.52813i	0.0486810	−	0.0843180i
$900$		0			0
$901$	−2.44075	−	2.90877i	−0.0813132	−	0.0969053i
$902$	21.9850	−	12.6930i	0.732019	−	0.422631i
$903$	0.0226510	+	0.00399397i	0.000753777	+	0.000132911i
$904$	−9.26275	+	52.5317i	−0.308075	+	1.74718i
$905$		0			0
$906$	0.985742	−	2.70830i	0.0327491	−	0.0899774i
$907$	−8.80699	+	24.1970i	−0.292431	+	0.803449i	0.703278	+	0.710915i	$0.251719\pi$
$907$	−8.80699	+	24.1970i	−0.292431	+	0.803449i	−0.995710	+	0.0925339i	$0.970503\pi$
$908$	15.9277	−	18.9819i	0.528581	−	0.629938i
$909$	3.74519	−	21.2400i	0.124220	−	0.704486i
$910$		0			0
$911$	20.1765	−	11.6489i	0.668477	−	0.385946i	−0.127022	−	0.991900i	$-0.540542\pi$
$911$	20.1765	−	11.6489i	0.668477	−	0.385946i	0.795499	+	0.605954i	$0.207209\pi$
$912$	0.235719	+	0.280919i	0.00780544	+	0.00930216i
$913$	−59.0164	+	21.4802i	−1.95316	+	0.710891i
$914$	−1.67988	+	2.90964i	−0.0555656	+	0.0962424i
$915$		0			0
$916$	−3.59881	−	3.01976i	−0.118908	−	0.0997757i
$917$	1.47404	+	0.851037i	0.0486770	+	0.0281037i
$918$	1.32120	+	7.49288i	0.0436060	+	0.247302i
$919$			5.85605i			0.193173i	0.995325	+	0.0965866i	$0.0307925\pi$
$919$			5.85605i			0.193173i	−0.995325	+	0.0965866i	$0.969208\pi$
$920$		0			0
$921$	6.40784	−	5.37682i	0.211146	−	0.177172i
$922$	9.40782	+	3.42417i	0.309830	+	0.112769i
$923$	−1.72216	−	4.73160i	−0.0566857	−	0.155743i
$924$	0.110350			0.00363026
$925$		0			0
$926$	11.3708			0.373668
$927$	−10.6195	−	29.1767i	−0.348789	−	0.958289i
$928$	−2.86573	−	1.04304i	−0.0940721	−	0.0342395i
$929$	−7.91261	+	6.63947i	−0.259604	+	0.217834i	−0.763295	−	0.646050i	$-0.776420\pi$
$929$	−7.91261	+	6.63947i	−0.259604	+	0.217834i	0.503690	+	0.863884i	$0.331975\pi$
$930$		0			0
$931$			14.2901i			0.468340i
$932$	−1.05912	−	6.00660i	−0.0346928	−	0.196753i
$933$	−0.574471	−	0.331671i	−0.0188074	−	0.0108584i
$934$	0.970580	+	0.814413i	0.0317583	+	0.0266484i
$935$		0			0
$936$	3.61082	−	6.25412i	0.118023	−	0.204422i
$937$	45.5732	−	16.5873i	1.48881	−	0.541884i	0.535676	−	0.844424i	$-0.320057\pi$
$937$	45.5732	−	16.5873i	1.48881	−	0.541884i	0.953137	+	0.302540i	$0.0978346\pi$
$938$	−0.158172	−	0.188502i	−0.00516450	−	0.00615481i
$939$	−0.841171	+	0.485650i	−0.0274506	+	0.0158486i
$940$		0			0
$941$	−3.34738	+	18.9839i	−0.109122	+	0.618859i	0.880372	+	0.474283i	$0.157293\pi$
$941$	−3.34738	+	18.9839i	−0.109122	+	0.618859i	−0.989494	+	0.144576i	$0.953818\pi$
$942$	−3.13174	+	3.73226i	−0.102038	+	0.121604i
$943$	−0.00923673	+	0.0253777i	−0.000300789	+	0.000826412i
$944$	1.72200	−	4.73117i	0.0560465	−	0.153986i
$945$		0			0
$946$	−0.755338	+	4.28373i	−0.0245581	+	0.139276i
$947$	11.3425	+	1.99999i	0.368582	+	0.0649910i	0.354872	−	0.934915i	$-0.384525\pi$
$947$	11.3425	+	1.99999i	0.368582	+	0.0649910i	0.0137104	+	0.999906i	$0.495636\pi$
$948$	−1.86550	+	1.07704i	−0.0605885	+	0.0349808i
$949$	−5.06334	−	6.03426i	−0.164363	−	0.195880i
$950$		0			0
$951$	−1.37066	+	2.37405i	−0.0444467	+	0.0769839i
$952$	−0.556224	−	0.963409i	−0.0180273	−	0.0312243i
$953$	15.9845	+	13.4126i	0.517790	+	0.434477i	0.863860	−	0.503731i	$-0.168040\pi$
$953$	15.9845	+	13.4126i	0.517790	+	0.434477i	−0.346071	+	0.938208i	$0.612484\pi$
$954$	−1.93046	−	1.11455i	−0.0625011	−	0.0360850i
$955$		0			0
$956$			23.0166i			0.744409i
$957$	−0.722098	+	0.127325i	−0.0233421	+	0.00411585i
$958$	29.2012	−	24.5027i	0.943448	−	0.791647i
$959$	−1.53363	−	0.558195i	−0.0495234	−	0.0180251i
$960$		0			0
$961$	5.33289			0.172029
$962$	4.62812	−	1.51448i	0.149216	−	0.0488287i
$963$	−33.6708			−1.08503
$964$	−2.53239	−	6.95768i	−0.0815627	−	0.224092i
$965$		0			0
$966$	7.50763e−5	0	6.29965e-5i	2.41554e−6	0	2.02688e-6i
$967$	28.0911	−	4.95322i	0.903349	−	0.159285i	0.297367	−	0.954763i	$-0.403892\pi$
$967$	28.0911	−	4.95322i	0.903349	−	0.159285i	0.605982	+	0.795479i	$0.292780\pi$
$968$			26.7370i			0.859361i
$969$	0.478089	+	2.71138i	0.0153584	+	0.0871021i
$970$		0			0
$971$	32.7310	+	27.4646i	1.05039	+	0.881380i	0.993134	−	0.116980i	$-0.0373213\pi$
$971$	32.7310	+	27.4646i	1.05039	+	0.881380i	0.0572532	+	0.998360i	$0.481766\pi$
$972$	−4.03087	−	6.98167i	−0.129290	−	0.223937i
$973$	0.840430	−	1.45567i	0.0269430	−	0.0466666i
$974$	20.9527	−	7.62617i	0.671369	−	0.244358i
$975$		0			0
$976$	2.43566	−	1.40623i	0.0779637	−	0.0450123i
$977$	39.0748	+	6.88994i	1.25011	+	0.220429i	0.759245	−	0.650805i	$-0.225568\pi$
$977$	39.0748	+	6.88994i	1.25011	+	0.220429i	0.490869	+	0.871234i	$0.336679\pi$
$978$	−1.06988	+	6.06757i	−0.0342109	+	0.194019i
$979$	−30.9677	+	36.9058i	−0.989731	+	1.17952i
$980$		0			0
$981$	−10.8056	+	29.6881i	−0.344996	+	0.947870i
$982$	2.38263	−	2.83951i	0.0760327	−	0.0906123i
$983$	−4.65015	+	26.3723i	−0.148317	+	0.841146i	0.816327	+	0.577590i	$0.196007\pi$
$983$	−4.65015	+	26.3723i	−0.148317	+	0.841146i	−0.964644	+	0.263556i	$0.915104\pi$
$984$	−4.89791	−	0.863633i	−0.156140	−	0.0275316i
$985$		0			0
$986$	1.67606	+	1.99745i	0.0533767	+	0.0636119i
$987$	0.168935	−	0.0614874i	0.00537727	−	0.00195717i
$988$	0.934562	−	1.61871i	0.0297324	−	0.0514980i
$989$	−0.00231373	−	0.00400750i	−7.35723e−5	−	0.000127431i
$990$		0			0
$991$	−21.3558	−	12.3298i	−0.678390	−	0.391669i	0.120858	−	0.992670i	$-0.461435\pi$
$991$	−21.3558	−	12.3298i	−0.678390	−	0.391669i	−0.799248	+	0.601001i	$0.794769\pi$
$992$	4.65615	+	26.4063i	0.147833	+	0.838402i
$993$		−	3.09646i		−	0.0982633i
$994$	−0.448429	+	0.0790702i	−0.0142233	+	0.00250795i
$995$		0			0
$996$	4.07857	+	1.48448i	0.129234	+	0.0470375i
$997$	−12.7608	−	35.0601i	−0.404140	−	1.11036i	−0.960222	−	0.279237i	$-0.909918\pi$
$997$	−12.7608	−	35.0601i	−0.404140	−	1.11036i	0.556083	−	0.831127i	$-0.312304\pi$
$998$	−26.7933			−0.848127
$999$	2.10542	−	10.0081i	0.0666127	−	0.316643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.326.6		96
5.2	odd	4		185.2.v.a.104.11	yes	96
5.3	odd	4		185.2.v.a.104.6	✓	96
5.4	even	2	inner	925.2.bb.e.326.11		96
37.21	even	18	inner	925.2.bb.e.576.6		96
185.58	odd	36		185.2.v.a.169.11	yes	96
185.132	odd	36		185.2.v.a.169.6	yes	96
185.169	even	18	inner	925.2.bb.e.576.11		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.104.6	✓	96	5.3	odd	4
185.2.v.a.104.11	yes	96	5.2	odd	4
185.2.v.a.169.6	yes	96	185.132	odd	36
185.2.v.a.169.11	yes	96	185.58	odd	36
925.2.bb.e.326.6		96	1.1	even	1	trivial
925.2.bb.e.326.11		96	5.4	even	2	inner
925.2.bb.e.576.6		96	37.21	even	18	inner
925.2.bb.e.576.11		96	185.169	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+(-0.326264 - 0.896403i) q^{2} +(-0.266913 - 0.0971484i) q^{3} +(0.834998 - 0.700647i) q^{4} +0.270958i q^{6} +(-0.0138149 - 0.0783483i) q^{7} +(-2.55275 - 1.47383i) q^{8} +(-2.23633 - 1.87650i) q^{9} +(2.24001 - 3.87981i) q^{11} +(-0.290938 + 0.105893i) q^{12} +(-0.539440 - 0.642880i) q^{13} +(-0.0657244 + 0.0379460i) q^{14} +(-0.109719 + 0.622249i) q^{16} +(-3.04924 + 3.63394i) q^{17} +(-0.952469 + 2.61689i) q^{18} +(-0.698848 + 1.92007i) q^{19} +(-0.00392403 + 0.0222543i) q^{21} +(-4.20871 - 0.742109i) q^{22} +(0.00393731 - 0.00227321i) q^{23} +(0.538182 + 0.641381i) q^{24} +(-0.400280 + 0.693304i) q^{26} +(0.840670 + 1.45608i) q^{27} +(-0.0664299 - 0.0557413i) q^{28} +(0.499013 + 0.288105i) q^{29} -5.06627i q^{31} +(-5.21218 + 0.919048i) q^{32} +(-0.974805 + 0.817959i) q^{33} +(4.25234 + 1.54772i) q^{34} -3.18209 q^{36} +(-4.52888 - 4.06070i) q^{37} +1.94917 q^{38} +(0.0815288 + 0.223999i) q^{39} +(-4.55042 + 3.81825i) q^{41} +(0.0212291 - 0.00374326i) q^{42} -1.01783i q^{43} +(-0.847972 - 4.80909i) q^{44} +(-0.00332232 - 0.00278775i) q^{46} +(-3.97780 - 6.88975i) q^{47} +(0.0897359 - 0.155427i) q^{48} +(6.57190 - 2.39198i) q^{49} +(1.16691 - 0.673718i) q^{51} +(-0.900863 - 0.158846i) q^{52} +(-0.138996 + 0.788285i) q^{53} +(1.03096 - 1.22865i) q^{54} +(-0.0802061 + 0.220365i) q^{56} +(0.373063 - 0.444599i) q^{57} +(0.0954485 - 0.541315i) q^{58} +(-7.84732 - 1.38369i) q^{59} +(-2.86116 - 3.40979i) q^{61} +(-4.54142 + 1.65294i) q^{62} +(-0.116126 + 0.201136i) q^{63} +(3.15623 + 5.46676i) q^{64} +(1.05127 + 0.606948i) q^{66} +(0.563037 + 3.19314i) q^{67} +5.17077i q^{68} +(-0.00127176 + 0.000224245i) q^{69} +(5.63810 + 2.05210i) q^{71} +(2.94314 + 8.08622i) q^{72} +9.38629 q^{73} +(-2.16241 + 5.38456i) q^{74} +(0.761753 + 2.09290i) q^{76} +(-0.334922 - 0.121902i) q^{77} +(0.174193 - 0.146165i) q^{78} +(6.85173 - 1.20814i) q^{79} +(1.43787 + 8.15459i) q^{81} +(4.90733 + 2.83325i) q^{82} +(-10.7389 - 9.01103i) q^{83} +(0.0123158 + 0.0213316i) q^{84} +(-0.912382 + 0.332080i) q^{86} +(-0.105204 - 0.125377i) q^{87} +(-11.4364 + 6.60280i) q^{88} +(-10.5904 - 1.86737i) q^{89} +(-0.0429162 + 0.0511455i) q^{91} +(0.00169493 - 0.00465679i) q^{92} +(-0.492180 + 1.35225i) q^{93} +(-4.87818 + 5.81359i) q^{94} +(1.48048 + 0.261049i) q^{96} +(-6.13702 + 3.54321i) q^{97} +(-4.28835 - 5.11066i) q^{98} +(-12.2899 + 4.47315i) 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

Fields

Representations

Groups

Database

Properties

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