LMFDB - Embedded newform 750.2.l.b.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	750.107
Dual form			750.2.l.b.743.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(-1.73204 - 0.00452789i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(0.152718 + 0.152718i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.99996 + 0.0156850i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.73204 - 0.00452789i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(0.152718 + 0.152718i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.99996 + 0.0156850i) q^{9} +(-4.88609 + 1.58759i) q^{11} +(-1.01441 - 1.40392i) q^{12} +(-0.674795 - 1.32436i) q^{13} +(-0.0667401 - 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(4.81543 - 0.762690i) q^{17} +(-2.66586 - 1.37593i) q^{18} +(0.283032 - 0.389560i) q^{19} +(-0.263823 - 0.265206i) q^{21} +(5.07429 + 0.803689i) q^{22} +(-1.21389 + 2.38239i) q^{23} +(0.266479 + 1.71143i) q^{24} +1.48636i q^{26} +(-5.19599 - 0.0407506i) q^{27} +(-0.0337860 + 0.213317i) q^{28} +(7.59423 - 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.47012 - 2.72765i) q^{33} +(-4.63684 - 1.50660i) q^{34} +(1.75064 + 2.43624i) q^{36} +(-3.83574 + 1.95441i) q^{37} +(-0.429039 + 0.218606i) q^{38} +(1.16278 + 2.29691i) q^{39} +(-5.95547 - 1.93505i) q^{41} +(0.114667 + 0.356073i) q^{42} +(2.72225 - 2.72225i) q^{43} +(-4.15636 - 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(1.58814 - 10.0271i) q^{47} +(0.539538 - 1.64587i) q^{48} -6.95335i q^{49} +(-8.34400 + 1.29921i) q^{51} +(0.674795 - 1.32436i) q^{52} +(-7.59700 - 1.20325i) q^{53} +(4.61116 + 2.39524i) q^{54} +(0.126947 - 0.174728i) q^{56} +(-0.491987 + 0.673453i) q^{57} +(-9.27141 + 1.46845i) q^{58} +(1.54130 - 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(1.03265 + 2.02668i) q^{62} +(0.455752 + 0.460543i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-8.78526 - 1.41500i) q^{66} +(-2.35050 - 14.8405i) q^{67} +(3.44747 + 3.44747i) q^{68} +(2.11330 - 4.12092i) q^{69} +(7.13100 + 9.81498i) q^{71} +(-0.453805 - 2.96548i) q^{72} +(-8.36209 - 4.26070i) q^{73} +4.30495 q^{74} +0.481522 q^{76} +(-0.988647 - 0.503741i) q^{77} +(0.00673009 - 2.57445i) q^{78} +(-1.28502 - 1.76867i) q^{79} +(8.99951 + 0.0941087i) q^{81} +(4.42787 + 4.42787i) q^{82} +(-0.782253 - 4.93895i) q^{83} +(0.0594848 - 0.369321i) q^{84} +(-3.66142 + 1.18967i) q^{86} +(-13.1785 + 9.52222i) q^{87} +(2.33240 + 4.57759i) q^{88} +(3.38311 + 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(-2.64090 + 0.418278i) q^{92} +(3.18124 + 2.32404i) q^{93} +(-5.96725 + 8.21321i) q^{94} +(-1.22794 + 1.22154i) q^{96} +(9.96799 + 1.57877i) q^{97} +(-3.15676 + 6.19548i) q^{98} +(-14.6830 + 4.68606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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 $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	−1.73204	−	0.00452789i	−0.999997	−	0.00261418i
$3$	−1.73204	−	0.00452789i	−0.999997	−	0.00261418i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	1.54121	+	0.790366i	0.629195	+	0.322666i
$7$	0.152718	+	0.152718i	0.0577219	+	0.0577219i	0.735379	−	0.677657i	$-0.237004\pi$
$7$	0.152718	+	0.152718i	0.0577219	+	0.0577219i	−0.677657	+	0.735379i	$0.737004\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	2.99996	+	0.0156850i	0.999986	+	0.00522833i
$10$		0			0
$11$	−4.88609	+	1.58759i	−1.47321	+	0.478676i	−0.932077	−	0.362259i	$-0.882005\pi$
$11$	−4.88609	+	1.58759i	−1.47321	+	0.478676i	−0.541136	+	0.840935i	$0.682005\pi$
$12$	−1.01441	−	1.40392i	−0.292834	−	0.405275i
$13$	−0.674795	−	1.32436i	−0.187155	−	0.367312i	0.778296	−	0.627897i	$-0.216084\pi$
$13$	−0.674795	−	1.32436i	−0.187155	−	0.367312i	−0.965451	+	0.260586i	$0.916084\pi$
$14$	−0.0667401	−	0.205405i	−0.0178371	−	0.0548968i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	4.81543	−	0.762690i	1.16791	−	0.184979i	0.457793	−	0.889059i	$-0.348640\pi$
$17$	4.81543	−	0.762690i	1.16791	−	0.184979i	0.710121	+	0.704080i	$0.248640\pi$
$18$	−2.66586	−	1.37593i	−0.628350	−	0.324309i
$19$	0.283032	−	0.389560i	0.0649319	−	0.0893711i	−0.775316	−	0.631574i	$-0.782409\pi$
$19$	0.283032	−	0.389560i	0.0649319	−	0.0893711i	0.840248	+	0.542202i	$0.182409\pi$
$20$		0			0
$21$	−0.263823	−	0.265206i	−0.0575708	−	0.0578726i
$22$	5.07429	+	0.803689i	1.08184	+	0.171347i
$23$	−1.21389	+	2.38239i	−0.253114	+	0.496763i	−0.982243	−	0.187612i	$-0.939925\pi$
$23$	−1.21389	+	2.38239i	−0.253114	+	0.496763i	0.729130	+	0.684376i	$0.239925\pi$
$24$	0.266479	+	1.71143i	0.0543949	+	0.349344i
$25$		0			0
$26$			1.48636i			0.291500i
$27$	−5.19599	−	0.0407506i	−0.999969	−	0.00784246i
$28$	−0.0337860	+	0.213317i	−0.00638496	+	0.0403130i
$29$	7.59423	−	5.51753i	1.41021	−	1.02458i	0.416921	−	0.908943i	$-0.363109\pi$
$29$	7.59423	−	5.51753i	1.41021	−	1.02458i	0.993292	−	0.115637i	$-0.0368909\pi$
$30$		0			0
$31$	−1.84019	−	1.33698i	−0.330508	−	0.240128i	0.410138	−	0.912023i	$-0.365480\pi$
$31$	−1.84019	−	1.33698i	−0.330508	−	0.240128i	−0.740646	+	0.671895i	$0.765480\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	8.47012	−	2.72765i	1.47446	−	0.474823i
$34$	−4.63684	−	1.50660i	−0.795211	−	0.258380i
$35$		0			0
$36$	1.75064	+	2.43624i	0.291774	+	0.406040i
$37$	−3.83574	+	1.95441i	−0.630592	+	0.321303i	−0.739912	−	0.672704i	$-0.765133\pi$
$37$	−3.83574	+	1.95441i	−0.630592	+	0.321303i	0.109320	+	0.994007i	$0.465133\pi$
$38$	−0.429039	+	0.218606i	−0.0695994	+	0.0354627i
$39$	1.16278	+	2.29691i	0.186194	+	0.367800i
$40$		0			0
$41$	−5.95547	−	1.93505i	−0.930087	−	0.302204i	−0.195489	−	0.980706i	$-0.562629\pi$
$41$	−5.95547	−	1.93505i	−0.930087	−	0.302204i	−0.734598	+	0.678502i	$0.762629\pi$
$42$	0.114667	+	0.356073i	0.0176935	+	0.0549432i
$43$	2.72225	−	2.72225i	0.415139	−	0.415139i	−0.468385	−	0.883524i	$-0.655164\pi$
$43$	2.72225	−	2.72225i	0.415139	−	0.415139i	0.883524	+	0.468385i	$0.155164\pi$
$44$	−4.15636	−	3.01977i	−0.626595	−	0.455248i
$45$		0			0
$46$	2.16317	−	1.57163i	0.318942	−	0.231725i
$47$	1.58814	−	10.0271i	0.231654	−	1.46260i	−0.548046	−	0.836448i	$-0.684628\pi$
$47$	1.58814	−	10.0271i	0.231654	−	1.46260i	0.779699	−	0.626154i	$-0.215372\pi$
$48$	0.539538	−	1.64587i	0.0778755	−	0.237561i
$49$		−	6.95335i		−	0.993336i
$50$		0			0
$51$	−8.34400	+	1.29921i	−1.16839	+	0.181926i
$52$	0.674795	−	1.32436i	0.0935773	−	0.183656i
$53$	−7.59700	−	1.20325i	−1.04353	−	0.165279i	−0.388939	−	0.921264i	$-0.627158\pi$
$53$	−7.59700	−	1.20325i	−1.04353	−	0.165279i	−0.654589	+	0.755985i	$0.727158\pi$
$54$	4.61116	+	2.39524i	0.627500	+	0.325951i
$55$		0			0
$56$	0.126947	−	0.174728i	0.0169640	−	0.0233490i
$57$	−0.491987	+	0.673453i	−0.0651653	+	0.0892011i
$58$	−9.27141	+	1.46845i	−1.21740	+	0.192817i
$59$	1.54130	−	4.74363i	0.200660	−	0.617569i	−0.799204	−	0.601061i	$-0.794745\pi$
$59$	1.54130	−	4.74363i	0.200660	−	0.617569i	0.999864	−	0.0165081i	$-0.00525494\pi$
$60$		0			0
$61$	−4.21680	−	12.9780i	−0.539906	−	1.66166i	−0.732803	−	0.680440i	$-0.761789\pi$
$61$	−4.21680	−	12.9780i	−0.539906	−	1.66166i	0.192898	−	0.981219i	$-0.438211\pi$
$62$	1.03265	+	2.02668i	0.131146	+	0.257389i
$63$	0.455752	+	0.460543i	0.0574193	+	0.0580229i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	−8.78526	−	1.41500i	−1.08139	−	0.174175i
$67$	−2.35050	−	14.8405i	−0.287159	−	1.81305i	−0.535673	−	0.844425i	$-0.679942\pi$
$67$	−2.35050	−	14.8405i	−0.287159	−	1.81305i	0.248514	−	0.968628i	$-0.420058\pi$
$68$	3.44747	+	3.44747i	0.418067	+	0.418067i
$69$	2.11330	−	4.12092i	0.254411	−	0.496100i
$70$		0			0
$71$	7.13100	+	9.81498i	0.846294	+	1.16482i	0.984667	+	0.174444i	$0.0558128\pi$
$71$	7.13100	+	9.81498i	0.846294	+	1.16482i	−0.138373	+	0.990380i	$0.544187\pi$
$72$	−0.453805	−	2.96548i	−0.0534814	−	0.349485i
$73$	−8.36209	−	4.26070i	−0.978708	−	0.498677i	−0.109963	−	0.993936i	$-0.535073\pi$
$73$	−8.36209	−	4.26070i	−0.978708	−	0.498677i	−0.868745	+	0.495259i	$0.835073\pi$
$74$	4.30495			0.500441
$75$		0			0
$76$	0.481522			0.0552344
$77$	−0.988647	−	0.503741i	−0.112667	−	0.0574066i
$78$	0.00673009	−	2.57445i	0.000762033	−	0.291499i
$79$	−1.28502	−	1.76867i	−0.144576	−	0.198991i	0.730588	−	0.682819i	$-0.239246\pi$
$79$	−1.28502	−	1.76867i	−0.144576	−	0.198991i	−0.875163	+	0.483828i	$0.839246\pi$
$80$		0			0
$81$	8.99951	+	0.0941087i	0.999945	+	0.0104565i
$82$	4.42787	+	4.42787i	0.488976	+	0.488976i
$83$	−0.782253	−	4.93895i	−0.0858634	−	0.542120i	−0.992697	−	0.120632i	$-0.961508\pi$
$83$	−0.782253	−	4.93895i	−0.0858634	−	0.542120i	0.906834	−	0.421488i	$-0.138492\pi$
$84$	0.0594848	−	0.369321i	0.00649032	−	0.0402962i
$85$		0			0
$86$	−3.66142	+	1.18967i	−0.394821	+	0.128285i
$87$	−13.1785	+	9.52222i	−1.41289	+	1.02089i
$88$	2.33240	+	4.57759i	0.248634	+	0.487972i
$89$	3.38311	+	10.4121i	0.358609	+	1.10368i	0.953887	+	0.300165i	$0.0970417\pi$
$89$	3.38311	+	10.4121i	0.358609	+	1.10368i	−0.595279	+	0.803519i	$0.702958\pi$
$90$		0			0
$91$	0.0992002	−	0.305307i	0.0103990	−	0.0320048i
$92$	−2.64090	+	0.418278i	−0.275333	+	0.0436085i
$93$	3.18124	+	2.32404i	0.329879	+	0.240991i
$94$	−5.96725	+	8.21321i	−0.615475	+	0.847128i
$95$		0			0
$96$	−1.22794	+	1.22154i	−0.125326	+	0.124673i
$97$	9.96799	+	1.57877i	1.01210	+	0.160300i	0.640390	−	0.768050i	$-0.278773\pi$
$97$	9.96799	+	1.57877i	1.01210	+	0.160300i	0.371706	+	0.928350i	$0.378773\pi$
$98$	−3.15676	+	6.19548i	−0.318881	+	0.625838i
$99$	−14.6830	+	4.68606i	−1.47570	+	0.470967i
$100$		0			0
$101$		−	9.53700i		−	0.948967i	−0.880264	−	0.474483i	$-0.842635\pi$
$101$		−	9.53700i		−	0.948967i	0.880264	−	0.474483i	$-0.157365\pi$
$102$	8.02438	+	2.63049i	0.794533	+	0.260458i
$103$	−1.58215	+	9.98929i	−0.155894	+	0.984274i	0.778400	+	0.627769i	$0.216032\pi$
$103$	−1.58215	+	9.98929i	−0.155894	+	0.984274i	−0.934293	+	0.356505i	$0.883968\pi$
$104$	−1.20249	+	0.873663i	−0.117914	+	0.0856697i
$105$		0			0
$106$	6.22271	+	4.52106i	0.604403	+	0.439125i
$107$	−7.80873	+	7.80873i	−0.754898	+	0.754898i	−0.975389	−	0.220491i	$-0.929234\pi$
$107$	−7.80873	+	7.80873i	−0.754898	+	0.754898i	0.220491	+	0.975389i	$0.429234\pi$
$108$	−3.02116	−	4.22760i	−0.290711	−	0.406801i
$109$	−5.83194	−	1.89491i	−0.558598	−	0.181500i	0.0160921	−	0.999871i	$-0.494877\pi$
$109$	−5.83194	−	1.89491i	−0.558598	−	0.181500i	−0.574690	+	0.818371i	$0.694877\pi$
$110$		0			0
$111$	6.65253	−	3.36776i	0.631430	−	0.319653i
$112$	−0.192436	+	0.0980509i	−0.0181835	+	0.00926494i
$113$	9.78864	−	4.98756i	0.920838	−	0.469190i	0.0717385	−	0.997423i	$-0.477145\pi$
$113$	9.78864	−	4.98756i	0.920838	−	0.469190i	0.849099	+	0.528233i	$0.177145\pi$
$114$	0.744105	−	0.376694i	0.0696918	−	0.0352806i
$115$		0			0
$116$	8.92755	+	2.90074i	0.828902	+	0.269327i
$117$	−2.00359	−	3.98361i	−0.185232	−	0.368285i
$118$	−3.52687	+	3.52687i	−0.324675	+	0.324675i
$119$	0.851879	+	0.618926i	0.0780916	+	0.0567369i
$120$		0			0
$121$	12.4543	−	9.04858i	1.13221	−	0.822598i
$122$	−2.13468	+	13.4778i	−0.193265	+	1.22023i
$123$	10.3064	+	3.37856i	0.929294	+	0.304634i
$124$		−	2.27460i		−	0.204265i
$125$		0			0
$126$	−0.196996	−	0.617253i	−0.0175498	−	0.0549893i
$127$	6.82658	−	13.3979i	0.605761	−	1.18887i	−0.360850	−	0.932624i	$-0.617513\pi$
$127$	6.82658	−	13.3979i	0.605761	−	1.18887i	0.966611	−	0.256249i	$-0.0824868\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	−4.72738	+	4.70273i	−0.416223	+	0.414052i
$130$		0			0
$131$	5.12870	−	7.05905i	0.448097	−	0.616752i	−0.523891	−	0.851785i	$-0.675520\pi$
$131$	5.12870	−	7.05905i	0.448097	−	0.616752i	0.971987	+	0.235034i	$0.0755200\pi$
$132$	7.18533	+	5.24920i	0.625403	+	0.456884i
$133$	0.102717	−	0.0162687i	0.00890667	−	0.00141068i
$134$	−4.64313	+	14.2901i	−0.401105	+	1.23447i
$135$		0			0
$136$	−1.50660	−	4.63684i	−0.129190	−	0.397605i
$137$	1.28180	+	2.51567i	0.109511	+	0.214928i	0.939258	−	0.343212i	$-0.111515\pi$
$137$	1.28180	+	2.51567i	0.109511	+	0.214928i	−0.829747	+	0.558140i	$0.811515\pi$
$138$	−3.75382	+	2.71235i	−0.319546	+	0.230890i
$139$	−6.62014	+	2.15102i	−0.561513	+	0.182447i	−0.576002	−	0.817448i	$-0.695388\pi$
$139$	−6.62014	+	2.15102i	−0.561513	+	0.182447i	0.0144887	+	0.999895i	$0.495388\pi$
$140$		0			0
$141$	−2.79613	+	17.3602i	−0.235476	+	1.46199i
$142$	−1.89786	−	11.9826i	−0.159265	−	1.00556i
$143$	5.39965	+	5.39965i	0.451542	+	0.451542i
$144$	−0.941956	+	2.84828i	−0.0784963	+	0.237357i
$145$		0			0
$146$	5.51636	+	7.59261i	0.456537	+	0.628369i
$147$	−0.0314840	+	12.0435i	−0.00259676	+	0.993333i
$148$	−3.83574	−	1.95441i	−0.315296	−	0.160651i
$149$	−7.72360			−0.632742			−0.316371	−	0.948635i	$-0.602465\pi$
$149$	−7.72360			−0.632742			−0.316371	+	0.948635i	$0.602465\pi$
$150$		0			0
$151$	−14.7868			−1.20333			−0.601667	−	0.798747i	$-0.705497\pi$
$151$	−14.7868			−1.20333			−0.601667	+	0.798747i	$0.705497\pi$
$152$	−0.429039	−	0.218606i	−0.0347997	−	0.0177313i
$153$	14.4581	−	2.21251i	1.16887	−	0.178871i
$154$	0.652197	+	0.897673i	0.0525556	+	0.0723365i
$155$		0			0
$156$	−1.17477	+	2.29080i	−0.0940571	+	0.183411i
$157$	11.5941	+	11.5941i	0.925312	+	0.925312i	0.997398	−	0.0720863i	$-0.0229657\pi$
$157$	11.5941	+	11.5941i	0.925312	+	0.925312i	−0.0720863	+	0.997398i	$0.522966\pi$
$158$	0.341997	+	2.15928i	0.0272078	+	0.171783i
$159$	13.1529	+	2.11847i	1.04309	+	0.168006i
$160$		0			0
$161$	−0.549217	+	0.178451i	−0.0432843	+	0.0140639i
$162$	−7.97590	−	4.16954i	−0.626646	−	0.327590i
$163$	1.84215	+	3.61543i	0.144289	+	0.283182i	0.951829	−	0.306630i	$-0.0992016\pi$
$163$	1.84215	+	3.61543i	0.144289	+	0.283182i	−0.807540	+	0.589813i	$0.799202\pi$
$164$	−1.93505	−	5.95547i	−0.151102	−	0.465044i
$165$		0			0
$166$	−1.54524	+	4.75577i	−0.119934	+	0.369119i
$167$	13.6706	−	2.16520i	1.05786	−	0.167549i	0.396818	−	0.917897i	$-0.370114\pi$
$167$	13.6706	−	2.16520i	1.05786	−	0.167549i	0.661042	+	0.750349i	$0.270114\pi$
$168$	−0.220670	+	0.302062i	−0.0170250	+	0.0233046i
$169$	6.34263	−	8.72988i	0.487894	−	0.671529i
$170$		0			0
$171$	0.855194	−	1.16422i	0.0653983	−	0.0890304i
$172$	3.80244	+	0.602248i	0.289934	+	0.0459210i
$173$	−0.412278	+	0.809140i	−0.0313449	+	0.0615178i	−0.906148	−	0.422961i	$-0.860991\pi$
$173$	−0.412278	+	0.809140i	−0.0313449	+	0.0615178i	0.874803	+	0.484479i	$0.160991\pi$
$174$	16.0652	−	2.50144i	1.21790	−	0.189633i
$175$		0			0
$176$		−	5.13754i		−	0.387257i
$177$	−2.69108	+	8.20921i	−0.202274	+	0.617042i
$178$	1.71264	−	10.8132i	0.128368	−	0.810482i
$179$	−9.58645	+	6.96496i	−0.716525	+	0.520586i	−0.885272	−	0.465074i	$-0.846028\pi$
$179$	−9.58645	+	6.96496i	−0.716525	+	0.520586i	0.168747	+	0.985659i	$0.446028\pi$
$180$		0			0
$181$	13.9076	+	10.1044i	1.03374	+	0.751057i	0.969054	−	0.246848i	$-0.0793949\pi$
$181$	13.9076	+	10.1044i	1.03374	+	0.751057i	0.0646876	+	0.997906i	$0.479395\pi$
$182$	−0.226994	+	0.226994i	−0.0168259	+	0.0168259i
$183$	7.24492	+	22.4975i	0.535560	+	1.66306i
$184$	2.54296	+	0.826257i	0.187469	+	0.0609125i
$185$		0			0
$186$	−1.77942	−	3.51498i	−0.130473	−	0.257731i
$187$	−22.3178	+	11.3715i	−1.63204	+	0.831566i
$188$	9.04558	−	4.60895i	0.659716	−	0.336142i
$189$	−0.787297	−	0.799744i	−0.0572675	−	0.0581728i
$190$		0			0
$191$	4.70151	+	1.52761i	0.340189	+	0.110534i	0.474129	−	0.880455i	$-0.342763\pi$
$191$	4.70151	+	1.52761i	0.340189	+	0.110534i	−0.133940	+	0.990989i	$0.542763\pi$
$192$	1.64867	−	0.530925i	0.118983	−	0.0383162i
$193$	−2.38356	+	2.38356i	−0.171572	+	0.171572i	−0.787670	−	0.616098i	$-0.788713\pi$
$193$	−2.38356	+	2.38356i	−0.171572	+	0.171572i	0.616098	+	0.787670i	$0.288713\pi$
$194$	−8.16479	−	5.93207i	−0.586198	−	0.425898i
$195$		0			0
$196$	5.62538	−	4.08708i	0.401813	−	0.291934i
$197$	−1.14693	+	7.24145i	−0.0817156	+	0.515932i	0.912548	+	0.408970i	$0.134112\pi$
$197$	−1.14693	+	7.24145i	−0.0817156	+	0.515932i	−0.994263	+	0.106961i	$0.965888\pi$
$198$	15.2101	+	2.49062i	1.08093	+	0.177001i
$199$			8.34182i			0.591336i	0.955291	+	0.295668i	$0.0955422\pi$
$199$			8.34182i			0.591336i	−0.955291	+	0.295668i	$0.904458\pi$
$200$		0			0
$201$	4.00398	+	25.7150i	0.282419	+	1.81380i
$202$	−4.32971	+	8.49753i	−0.304637	+	0.597884i
$203$	2.00240	+	0.317149i	0.140541	+	0.0222595i
$204$	−5.95556	−	5.98678i	−0.416973	−	0.419158i
$205$		0			0
$206$	5.94475	−	8.18224i	0.414190	−	0.570084i
$207$	−3.67899	+	7.12804i	−0.255707	+	0.495433i
$208$	1.46807	−	0.232519i	0.101792	−	0.0161223i
$209$	−0.764459	+	2.35276i	−0.0528787	+	0.162744i
$210$		0			0
$211$	1.32487	+	4.07753i	0.0912078	+	0.280709i	0.986247	−	0.165279i	$-0.0528525\pi$
$211$	1.32487	+	4.07753i	0.0912078	+	0.280709i	−0.895039	+	0.445988i	$0.852852\pi$
$212$	−3.49196	−	6.85335i	−0.239828	−	0.470690i
$213$	−12.3068	−	17.0323i	−0.843246	−	1.16703i
$214$	10.5027	−	3.41254i	0.717951	−	0.233276i
$215$		0			0
$216$	0.772583	+	5.13840i	0.0525676	+	0.349624i
$217$	−0.0768498	−	0.485210i	−0.00521690	−	0.0329382i
$218$	4.33602	+	4.33602i	0.293672	+	0.293672i
$219$	14.4642	+	7.41758i	0.977401	+	0.501233i
$220$		0			0
$221$	−4.25951	−	5.86271i	−0.286525	−	0.394369i
$222$	−7.45637	−	0.0194923i	−0.500439	−	0.00130824i
$223$	−0.651256	−	0.331831i	−0.0436113	−	0.0222211i	0.432049	−	0.901850i	$-0.357791\pi$
$223$	−0.651256	−	0.331831i	−0.0436113	−	0.0222211i	−0.475660	+	0.879629i	$0.657791\pi$
$224$	0.215976			0.0144305
$225$		0			0
$226$	−10.9860			−0.730781
$227$	−2.94981	−	1.50300i	−0.195786	−	0.0997579i	0.353349	−	0.935492i	$-0.385043\pi$
$227$	−2.94981	−	1.50300i	−0.195786	−	0.0997579i	−0.549135	+	0.835734i	$0.685043\pi$
$228$	−0.834018	−	0.00218028i	−0.0552342	−	0.000144392i
$229$	−6.20224	−	8.53665i	−0.409855	−	0.564117i	0.553328	−	0.832964i	$-0.313358\pi$
$229$	−6.20224	−	8.53665i	−0.409855	−	0.564117i	−0.963183	+	0.268846i	$0.913358\pi$
$230$		0			0
$231$	1.71010	+	0.876978i	0.112516	+	0.0577009i
$232$	−6.63760	−	6.63760i	−0.435780	−	0.435780i
$233$	−1.96935	−	12.4340i	−0.129016	−	0.814577i	−0.964311	−	0.264774i	$-0.914703\pi$
$233$	−1.96935	−	12.4340i	−0.129016	−	0.814577i	0.835294	−	0.549803i	$-0.185297\pi$
$234$	−0.0233136	+	4.45903i	−0.00152406	+	0.291496i
$235$		0			0
$236$	4.74363	−	1.54130i	0.308784	−	0.100330i
$237$	2.21770	+	3.06924i	0.144055	+	0.199369i
$238$	−0.478043	−	0.938212i	−0.0309869	−	0.0608152i
$239$	−3.62951	−	11.1705i	−0.234773	−	0.722558i	−0.997151	−	0.0754263i	$-0.975968\pi$
$239$	−3.62951	−	11.1705i	−0.234773	−	0.722558i	0.762378	−	0.647132i	$-0.224032\pi$
$240$		0			0
$241$	0.375849	−	1.15675i	0.0242106	−	0.0745125i	−0.938221	−	0.346036i	$-0.887527\pi$
$241$	0.375849	−	1.15675i	0.0242106	−	0.0745125i	0.962432	+	0.271524i	$0.0875275\pi$
$242$	−15.2048	+	2.40821i	−0.977403	+	0.154805i
$243$	−15.5871	−	0.203749i	−0.999915	−	0.0130705i
$244$	8.02083	−	11.0397i	0.513481	−	0.706746i
$245$		0			0
$246$	−7.64921	−	7.68931i	−0.487696	−	0.490253i
$247$	−0.706906	−	0.111963i	−0.0449793	−	0.00712403i
$248$	−1.03265	+	2.02668i	−0.0655732	+	0.128695i
$249$	1.33253	+	8.55802i	0.0844459	+	0.542343i
$250$		0			0
$251$		−	22.6123i		−	1.42728i	−0.700515	−	0.713638i	$-0.747046\pi$
$251$		−	22.6123i		−	1.42728i	0.700515	−	0.713638i	$-0.252954\pi$
$252$	−0.104703	+	0.639411i	−0.00659564	+	0.0402791i
$253$	2.14892	−	13.5678i	0.135102	−	0.852998i
$254$	−12.1651	+	8.83843i	−0.763304	+	0.554573i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	2.98436	−	2.98436i	0.186159	−	0.186159i	−0.607874	−	0.794033i	$-0.707978\pi$
$257$	2.98436	−	2.98436i	0.186159	−	0.186159i	0.794033	+	0.607874i	$0.207978\pi$
$258$	6.34713	−	2.04398i	0.395155	−	0.127252i
$259$	−0.884259	−	0.287313i	−0.0549452	−	0.0178528i
$260$		0			0
$261$	22.8689	−	16.4332i	1.41555	−	1.01719i
$262$	−7.77445	+	3.96128i	−0.480307	+	0.244729i
$263$	−2.29146	+	1.16756i	−0.141298	+	0.0719947i	−0.523210	−	0.852204i	$-0.675266\pi$
$263$	−2.29146	+	1.16756i	−0.141298	+	0.0719947i	0.381912	+	0.924199i	$0.375266\pi$
$264$	−4.01909	−	7.93914i	−0.247358	−	0.488621i
$265$		0			0
$266$	−0.0989071	−	0.0321369i	−0.00606438	−	0.00197044i
$267$	−5.81255	−	18.0496i	−0.355722	−	1.10462i
$268$	10.6246	−	10.6246i	0.649002	−	0.649002i
$269$	19.5493	+	14.2034i	1.19194	+	0.865996i	0.993468	−	0.114110i	$-0.0364018\pi$
$269$	19.5493	+	14.2034i	1.19194	+	0.865996i	0.198473	+	0.980106i	$0.436402\pi$
$270$		0			0
$271$	−9.36464	+	6.80381i	−0.568861	+	0.413302i	−0.834691	−	0.550718i	$-0.814354\pi$
$271$	−9.36464	+	6.80381i	−0.568861	+	0.413302i	0.265830	+	0.964020i	$0.414354\pi$
$272$	−0.762690	+	4.81543i	−0.0462448	+	0.291978i
$273$	−0.173202	+	0.528356i	−0.0104826	+	0.0319776i
$274$		−	2.82340i		−	0.170568i
$275$		0			0
$276$	4.57606	−	0.712519i	0.275446	−	0.0428886i
$277$	−3.42126	+	6.71461i	−0.205564	+	0.403442i	−0.970654	−	0.240482i	$-0.922695\pi$
$277$	−3.42126	+	6.71461i	−0.205564	+	0.403442i	0.765090	+	0.643924i	$0.222695\pi$
$278$	6.87513	+	1.08891i	0.412343	+	0.0653087i
$279$	−5.49953	−	4.03974i	−0.329248	−	0.241853i
$280$		0			0
$281$	−13.8790	+	19.1028i	−0.827952	+	1.13958i	0.160349	+	0.987060i	$0.448738\pi$
$281$	−13.8790	+	19.1028i	−0.827952	+	1.13958i	−0.988301	+	0.152517i	$0.951262\pi$
$282$	10.3727	−	14.1986i	0.617687	−	0.845516i
$283$	−9.72347	+	1.54005i	−0.578000	+	0.0915463i	−0.438588	−	0.898688i	$-0.644521\pi$
$283$	−9.72347	+	1.54005i	−0.578000	+	0.0915463i	−0.139412	+	0.990234i	$0.544521\pi$
$284$	−3.74899	+	11.5382i	−0.222462	+	0.684667i
$285$		0			0
$286$	−2.35974	−	7.26252i	−0.139534	−	0.429442i
$287$	−0.613989	−	1.20502i	−0.0362426	−	0.0711302i
$288$	2.13238	−	2.11020i	0.125652	−	0.124345i
$289$	6.43873	−	2.09207i	0.378749	−	0.123063i
$290$		0			0
$291$	−17.2579	−	2.77964i	−1.01167	−	0.162945i
$292$	−1.46814	−	9.26944i	−0.0859161	−	0.542453i
$293$	−3.33944	−	3.33944i	−0.195092	−	0.195092i	0.602800	−	0.797892i	$-0.294052\pi$
$293$	−3.33944	−	3.33944i	−0.195092	−	0.195092i	−0.797892	+	0.602800i	$0.794052\pi$
$294$	5.49570	−	10.7166i	0.320516	−	0.625003i
$295$		0			0
$296$	2.53039	+	3.48278i	0.147076	+	0.202433i
$297$	25.4528	−	8.04999i	1.47692	−	0.467108i
$298$	6.88178	+	3.50644i	0.398651	+	0.203123i
$299$	3.97428			0.229838
$300$		0			0
$301$	0.831472			0.0479252
$302$	13.1751	+	6.71307i	0.758145	+	0.386294i
$303$	−0.0431824	+	16.5185i	−0.00248077	+	0.948964i
$304$	0.283032	+	0.389560i	0.0162330	+	0.0223428i
$305$		0			0
$306$	−13.8867	−	4.59246i	−0.793849	−	0.262534i
$307$	11.8133	+	11.8133i	0.674221	+	0.674221i	0.958686	−	0.284465i	$-0.0918160\pi$
$307$	11.8133	+	11.8133i	0.674221	+	0.674221i	−0.284465	+	0.958686i	$0.591816\pi$
$308$	−0.173577	−	1.09592i	−0.00989048	−	0.0624460i
$309$	2.78558	−	17.2947i	0.158466	−	0.983863i
$310$		0			0
$311$	−28.7239	+	9.33296i	−1.62878	+	0.529224i	−0.973991	−	0.226586i	$-0.927244\pi$
$311$	−28.7239	+	9.33296i	−1.62878	+	0.529224i	−0.654791	+	0.755810i	$0.727244\pi$
$312$	2.08673	−	1.50778i	0.118138	−	0.0853612i
$313$	7.57278	+	14.8624i	0.428039	+	0.840073i	0.999807	+	0.0196580i	$0.00625773\pi$
$313$	7.57278	+	14.8624i	0.428039	+	0.840073i	−0.571768	+	0.820415i	$0.693742\pi$
$314$	−5.06682	−	15.5941i	−0.285937	−	0.880024i
$315$		0			0
$316$	0.675573	−	2.07920i	0.0380040	−	0.116964i
$317$	−10.7129	+	1.69675i	−0.601695	+	0.0952991i	−0.449848	−	0.893105i	$-0.648522\pi$
$317$	−10.7129	+	1.69675i	−0.601695	+	0.0952991i	−0.151847	+	0.988404i	$0.548522\pi$
$318$	−10.7575	−	7.85886i	−0.603253	−	0.440703i
$319$	−28.3466	+	39.0157i	−1.58710	+	2.18446i
$320$		0			0
$321$	13.5604	−	13.4897i	0.756869	−	0.752922i
$322$	0.570371	+	0.0903379i	0.0317855	+	0.00503433i
$323$	1.06581	−	2.09176i	0.0593031	−	0.116389i
$324$	5.21364	+	7.33607i	0.289647	+	0.407559i
$325$		0			0
$326$		−	4.05769i		−	0.224735i
$327$	10.0926	+	3.30848i	0.558122	+	0.182959i
$328$	−0.979584	+	6.18485i	−0.0540885	+	0.341501i
$329$	1.77385	−	1.28878i	0.0977957	−	0.0710527i
$330$		0			0
$331$	−7.79472	−	5.66319i	−0.428436	−	0.311277i	0.352587	−	0.935779i	$-0.385302\pi$
$331$	−7.79472	−	5.66319i	−0.428436	−	0.311277i	−0.781023	+	0.624502i	$0.785302\pi$
$332$	3.53590	−	3.53590i	0.194058	−	0.194058i
$333$	−11.5377	+	5.80298i	−0.632263	+	0.318001i
$334$	−13.1635	−	4.27710i	−0.720277	−	0.234032i
$335$		0			0
$336$	0.333751	−	0.168957i	0.0182076	−	0.00921737i
$337$	25.0858	−	12.7818i	1.36651	−	0.696272i	0.391864	−	0.920023i	$-0.371830\pi$
$337$	25.0858	−	12.7818i	1.36651	−	0.696272i	0.974646	+	0.223752i	$0.0718304\pi$
$338$	−9.61460	+	4.89888i	−0.522965	+	0.266464i
$339$	−16.9769	+	8.59436i	−0.922061	+	0.466782i
$340$		0			0
$341$	11.1139	+	3.61113i	0.601852	+	0.195554i
$342$	−1.29053	+	0.649081i	−0.0697838	+	0.0350983i
$343$	2.13093	−	2.13093i	0.115059	−	0.115059i
$344$	−3.11459	−	2.26288i	−0.167927	−	0.122006i
$345$		0			0
$346$	0.734684	−	0.533779i	0.0394969	−	0.0286962i
$347$	3.02097	−	19.0736i	0.162174	−	1.02393i	−0.763556	−	0.645742i	$-0.776548\pi$
$347$	3.02097	−	19.0736i	0.162174	−	1.02393i	0.925730	−	0.378185i	$-0.123452\pi$
$348$	−15.4498	−	5.06463i	−0.828195	−	0.271493i
$349$		−	14.4119i		−	0.771451i	−0.922614	−	0.385725i	$-0.873951\pi$
$349$		−	14.4119i		−	0.771451i	0.922614	−	0.385725i	$-0.126049\pi$
$350$		0			0
$351$	3.45226	+	6.90887i	0.184268	+	0.368768i
$352$	−2.33240	+	4.57759i	−0.124317	+	0.243986i
$353$	−34.5802	−	5.47696i	−1.84052	−	0.291509i	−0.863448	−	0.504438i	$-0.831700\pi$
$353$	−34.5802	−	5.47696i	−1.84052	−	0.291509i	−0.977068	+	0.212929i	$0.931700\pi$
$354$	6.12467	−	6.09273i	0.325523	−	0.323825i
$355$		0			0
$356$	−6.43505	+	8.85709i	−0.341057	+	0.469425i
$357$	−1.47269	−	1.07586i	−0.0779430	−	0.0569408i
$358$	11.7036	−	1.85367i	0.618555	−	0.0979695i
$359$	10.6846	−	32.8840i	0.563914	−	1.73555i	−0.107242	−	0.994233i	$-0.534202\pi$
$359$	10.6846	−	32.8840i	0.563914	−	1.73555i	0.671156	−	0.741316i	$-0.265798\pi$
$360$		0			0
$361$	5.79967	+	17.8496i	0.305246	+	0.939450i
$362$	−7.80442	−	15.3170i	−0.410191	−	0.805045i
$363$	−21.6124	+	15.6161i	−1.13436	+	0.819635i
$364$	0.305307	−	0.0992002i	0.0160024	−	0.00519950i
$365$		0			0
$366$	3.75839	−	23.3346i	0.196454	−	1.21972i
$367$	−0.505240	−	3.18996i	−0.0263733	−	0.166514i	0.970986	−	0.239135i	$-0.0768638\pi$
$367$	−0.505240	−	3.18996i	−0.0263733	−	0.166514i	−0.997360	+	0.0726205i	$0.976864\pi$
$368$	−1.89068	−	1.89068i	−0.0985584	−	0.0985584i
$369$	−17.8358	−	5.89848i	−0.928495	−	0.307062i
$370$		0			0
$371$	−0.976440	−	1.34395i	−0.0506942	−	0.0697746i
$372$	−0.0102991	+	3.93971i	−0.000533985	+	0.204265i
$373$	−9.65408	−	4.91900i	−0.499869	−	0.254696i	0.185829	−	0.982582i	$-0.440503\pi$
$373$	−9.65408	−	4.91900i	−0.499869	−	0.254696i	−0.685698	+	0.727886i	$0.740503\pi$
$374$	25.0479			1.29519
$375$		0			0
$376$	−10.1521			−0.523554
$377$	−12.4317	−	6.33429i	−0.640268	−	0.326233i
$378$	0.338411	+	1.07000i	0.0174060	+	0.0550350i
$379$	19.6854	+	27.0946i	1.01117	+	1.39176i	0.918213	+	0.396087i	$0.129632\pi$
$379$	19.6854	+	27.0946i	1.01117	+	1.39176i	0.0929573	+	0.995670i	$0.470368\pi$
$380$		0			0
$381$	−11.8846	+	23.1749i	−0.608867	+	1.18729i
$382$	−3.49555	−	3.49555i	−0.178848	−	0.178848i
$383$	−2.54182	−	16.0484i	−0.129881	−	0.820034i	−0.963503	−	0.267699i	$-0.913737\pi$
$383$	−2.54182	−	16.0484i	−0.129881	−	0.820034i	0.833622	−	0.552335i	$-0.186263\pi$
$384$	−1.71001	−	0.275424i	−0.0872637	−	0.0140552i
$385$		0			0
$386$	3.20588	−	1.04165i	0.163175	−	0.0530187i
$387$	8.20933	−	8.12394i	0.417304	−	0.412963i
$388$	4.58178	+	8.99225i	0.232605	+	0.456512i
$389$	0.804900	+	2.47723i	0.0408101	+	0.125600i	0.969386	−	0.245542i	$-0.0789660\pi$
$389$	0.804900	+	2.47723i	0.0408101	+	0.125600i	−0.928576	+	0.371143i	$0.878966\pi$
$390$		0			0
$391$	−4.02838	+	12.3981i	−0.203724	+	0.626998i
$392$	−6.86775	+	1.08774i	−0.346874	+	0.0549394i
$393$	−8.91510	+	12.2034i	−0.449707	+	0.615578i
$394$	4.30947	−	5.93148i	0.217108	−	0.298824i
$395$		0			0
$396$	−12.4215	−	9.12439i	−0.624206	−	0.458518i
$397$	−1.86357	−	0.295160i	−0.0935298	−	0.0148137i	0.109494	−	0.993987i	$-0.465077\pi$
$397$	−1.86357	−	0.295160i	−0.0935298	−	0.0148137i	−0.203024	+	0.979174i	$0.565077\pi$
$398$	3.78711	−	7.43262i	0.189831	−	0.372563i
$399$	−0.177984	+	0.0277131i	−0.00891032	+	0.00138739i
$400$		0			0
$401$		−	7.16880i		−	0.357993i	−0.983850	−	0.178996i	$-0.942715\pi$
$401$		−	7.16880i		−	0.357993i	0.983850	−	0.178996i	$-0.0572850\pi$
$402$	8.10681	−	24.7300i	0.404331	−	1.23342i
$403$	−0.528887	+	3.33926i	−0.0263458	+	0.166341i
$404$	7.71559	−	5.60571i	0.383865	−	0.278894i
$405$		0			0
$406$	−1.64017	−	1.19165i	−0.0814002	−	0.0591407i
$407$	15.6390	−	15.6390i	0.775197	−	0.775197i
$408$	2.58850	+	8.03803i	0.128150	+	0.397942i
$409$	15.2838	+	4.96600i	0.755734	+	0.245553i	0.661447	−	0.749992i	$-0.269943\pi$
$409$	15.2838	+	4.96600i	0.755734	+	0.245553i	0.0942874	+	0.995545i	$0.469943\pi$
$410$		0			0
$411$	−2.20874	−	4.36305i	−0.108949	−	0.215214i
$412$	−9.01147	+	4.59157i	−0.443963	+	0.226211i
$413$	0.959822	−	0.489054i	0.0472297	−	0.0240648i
$414$	6.51407	−	4.68091i	0.320149	−	0.230054i
$415$		0			0
$416$	−1.41362	−	0.459312i	−0.0693083	−	0.0225196i
$417$	11.4761	−	3.69568i	0.561988	−	0.180978i
$418$	1.74927	−	1.74927i	0.0855596	−	0.0855596i
$419$	−1.81333	−	1.31746i	−0.0885872	−	0.0643624i	0.542610	−	0.839985i	$-0.317436\pi$
$419$	−1.81333	−	1.31746i	−0.0885872	−	0.0643624i	−0.631197	+	0.775622i	$0.717436\pi$
$420$		0			0
$421$	2.09500	−	1.52210i	0.102104	−	0.0741828i	−0.535562	−	0.844496i	$-0.679900\pi$
$421$	2.09500	−	1.52210i	0.102104	−	0.0741828i	0.637666	+	0.770313i	$0.279900\pi$
$422$	0.670692	−	4.23458i	0.0326488	−	0.206136i
$423$	4.92162	−	30.0560i	0.239297	−	1.46137i
$424$			7.69169i			0.373542i
$425$		0			0
$426$	3.23292	+	20.7630i	0.156636	+	1.00597i
$427$	1.33799	−	2.62595i	0.0647498	−	0.127079i
$428$	−10.9072	−	1.72754i	−0.527222	−	0.0835037i
$429$	−9.32799	−	9.37689i	−0.450360	−	0.452721i
$430$		0			0
$431$	0.661426	−	0.910375i	0.0318598	−	0.0438512i	−0.792790	−	0.609495i	$-0.791372\pi$
$431$	0.661426	−	0.910375i	0.0318598	−	0.0438512i	0.824650	+	0.565644i	$0.191372\pi$
$432$	1.64441	−	4.92909i	0.0791165	−	0.237151i
$433$	−20.2750	+	3.21125i	−0.974355	+	0.154323i	−0.623258	−	0.782016i	$-0.714191\pi$
$433$	−20.2750	+	3.21125i	−0.974355	+	0.154323i	−0.351097	+	0.936339i	$0.614191\pi$
$434$	−0.151807	+	0.467215i	−0.00728698	+	0.0224270i
$435$		0			0
$436$	−1.89491	−	5.83194i	−0.0907498	−	0.279299i
$437$	0.584515	+	1.14718i	0.0279611	+	0.0548768i
$438$	−9.52020	−	13.1757i	−0.454893	−	0.629561i
$439$	22.3736	−	7.26963i	1.06783	−	0.346960i	0.278191	−	0.960526i	$-0.410265\pi$
$439$	22.3736	−	7.26963i	1.06783	−	0.346960i	0.789644	+	0.613565i	$0.210265\pi$
$440$		0			0
$441$	0.109063	−	20.8598i	0.00519350	−	0.993323i
$442$	1.13363	+	7.15749i	0.0539215	+	0.340447i
$443$	−13.6168	−	13.6168i	−0.646952	−	0.646952i	0.305303	−	0.952255i	$-0.401242\pi$
$443$	−13.6168	−	13.6168i	−0.646952	−	0.646952i	−0.952255	+	0.305303i	$0.901242\pi$
$444$	6.63483	+	3.40249i	0.314875	+	0.161475i
$445$		0			0
$446$	0.429625	+	0.591328i	0.0203433	+	0.0280002i
$447$	13.3776	+	0.0349716i	0.632740	+	0.00165410i
$448$	−0.192436	−	0.0980509i	−0.00909173	−	0.00463247i
$449$	−19.2184			−0.906973			−0.453487	−	0.891263i	$-0.649820\pi$
$449$	−19.2184			−0.906973			−0.453487	+	0.891263i	$0.649820\pi$
$450$		0			0
$451$	32.1710			1.51487
$452$	9.78864	+	4.98756i	0.460419	+	0.234595i
$453$	25.6114	+	0.0669530i	1.20333	+	0.00314573i
$454$	1.94595	+	2.67837i	0.0913281	+	0.125702i
$455$		0			0
$456$	0.742126	+	0.380579i	0.0347532	+	0.0178222i
$457$	−15.9563	−	15.9563i	−0.746405	−	0.746405i	0.227397	−	0.973802i	$-0.426979\pi$
$457$	−15.9563	−	15.9563i	−0.746405	−	0.746405i	−0.973802	+	0.227397i	$0.926979\pi$
$458$	1.65068	+	10.4220i	0.0771311	+	0.486986i
$459$	−25.0520	+	3.76670i	−1.16933	+	0.175814i
$460$		0			0
$461$	−15.2184	+	4.94475i	−0.708790	+	0.230300i	−0.641156	−	0.767410i	$-0.721545\pi$
$461$	−15.2184	+	4.94475i	−0.708790	+	0.230300i	−0.0676337	+	0.997710i	$0.521545\pi$
$462$	−1.12557	−	1.55776i	−0.0523663	−	0.0724737i
$463$	2.81092	+	5.51675i	0.130635	+	0.256385i	0.947054	−	0.321075i	$-0.104044\pi$
$463$	2.81092	+	5.51675i	0.130635	+	0.256385i	−0.816419	+	0.577460i	$0.804044\pi$
$464$	2.90074	+	8.92755i	0.134663	+	0.414451i
$465$		0			0
$466$	−3.89021	+	11.9728i	−0.180210	+	0.554630i
$467$	22.9270	−	3.63127i	1.06093	−	0.168035i	0.398509	−	0.917164i	$-0.369528\pi$
$467$	22.9270	−	3.63127i	1.06093	−	0.168035i	0.662424	+	0.749129i	$0.269528\pi$
$468$	2.04513	−	3.96244i	0.0945362	−	0.183164i
$469$	1.90744	−	2.62537i	0.0880775	−	0.121228i
$470$		0			0
$471$	−20.0291	−	20.1340i	−0.922890	−	0.927728i
$472$	−4.92635	−	0.780256i	−0.226753	−	0.0359142i
$473$	−8.97936	+	17.6230i	−0.412871	+	0.810305i
$474$	−0.582577	−	3.74153i	−0.0267587	−	0.171854i
$475$		0			0
$476$			1.05298i			0.0482633i
$477$	−22.7718	−	3.72885i	−1.04265	−	0.170732i
$478$	−1.83738	+	11.6007i	−0.0840396	+	0.530605i
$479$	18.1330	−	13.1744i	0.828519	−	0.601954i	−0.0906212	−	0.995885i	$-0.528885\pi$
$479$	18.1330	−	13.1744i	0.828519	−	0.601954i	0.919140	+	0.393931i	$0.128885\pi$
$480$		0			0
$481$	5.17668	+	3.76108i	0.236036	+	0.171491i
$482$	−0.860035	+	0.860035i	−0.0391735	+	0.0391735i
$483$	0.952076	−	0.306599i	0.0433210	−	0.0139507i
$484$	14.6409	+	4.75712i	0.665496	+	0.216233i
$485$		0			0
$486$	13.7957	+	7.25795i	0.625787	+	0.329227i
$487$	−18.8976	+	9.62881i	−0.856332	+	0.436323i	−0.826303	−	0.563226i	$-0.809560\pi$
$487$	−18.8976	+	9.62881i	−0.856332	+	0.436323i	−0.0300294	+	0.999549i	$0.509560\pi$
$488$	−12.1585	+	6.19509i	−0.550391	+	0.280438i
$489$	−3.17432	−	6.27042i	−0.143548	−	0.283558i
$490$		0			0
$491$	29.6177	+	9.62339i	1.33663	+	0.434297i	0.888174	−	0.459507i	$-0.151974\pi$
$491$	29.6177	+	9.62339i	1.33663	+	0.434297i	0.448456	+	0.893805i	$0.351974\pi$
$492$	3.32462	+	10.3239i	0.149886	+	0.465437i
$493$	32.3613	−	32.3613i	1.45748	−	1.45748i
$494$	0.579028	+	0.420688i	0.0260517	+	0.0189277i
$495$		0			0
$496$	1.84019	−	1.33698i	0.0826270	−	0.0600320i
$497$	−0.409892	+	2.58795i	−0.0183862	+	0.116086i
$498$	2.69796	−	8.23021i	0.120899	−	0.368805i
$499$		−	1.25659i		−	0.0562528i	−0.999604	−	0.0281264i	$-0.991046\pi$
$499$		−	1.25659i		−	0.0562528i	0.999604	−	0.0281264i	$-0.00895410\pi$
$500$		0			0
$501$	−23.6878	+	3.68833i	−1.05829	+	0.164783i
$502$	−10.2658	+	20.1477i	−0.458184	+	0.899236i
$503$	25.9752	+	4.11407i	1.15818	+	0.183437i	0.705815	−	0.708397i	$-0.250581\pi$
$503$	25.9752	+	4.11407i	1.15818	+	0.183437i	0.452363	+	0.891834i	$0.350581\pi$
$504$	0.383577	−	0.522186i	0.0170859	−	0.0232600i
$505$		0			0
$506$	−8.07434	+	11.1134i	−0.358948	+	0.494050i
$507$	−11.0252	+	15.0918i	−0.489648	+	0.670251i
$508$	14.8517	−	2.35228i	0.658938	−	0.104366i
$509$	5.31690	−	16.3637i	0.235668	−	0.725310i	−0.761365	−	0.648324i	$-0.775470\pi$
$509$	5.31690	−	16.3637i	0.235668	−	0.725310i	0.997032	−	0.0769863i	$-0.0245298\pi$
$510$		0			0
$511$	−0.626355	−	1.92772i	−0.0277083	−	0.0852775i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−1.48651	+	2.01262i	−0.0656308	+	0.0888591i
$514$	−4.01395	+	1.30421i	−0.177048	+	0.0575263i
$515$		0			0
$516$	−6.58328	−	1.06034i	−0.289813	−	0.0466788i
$517$	8.15912	+	51.5147i	0.358838	+	2.26561i
$518$	0.657443	+	0.657443i	0.0288864	+	0.0288864i
$519$	0.717747	−	1.39960i	0.0315056	−	0.0614357i
$520$		0			0
$521$	−7.91212	−	10.8901i	−0.346636	−	0.477104i	0.599729	−	0.800203i	$-0.295275\pi$
$521$	−7.91212	−	10.8901i	−0.346636	−	0.477104i	−0.946365	+	0.323099i	$0.895275\pi$
$522$	−27.8369	+	4.25986i	−1.21839	+	0.186449i
$523$	22.9585	+	11.6979i	1.00390	+	0.511514i	0.877046	−	0.480407i	$-0.159511\pi$
$523$	22.9585	+	11.6979i	1.00390	+	0.511514i	0.126858	+	0.991921i	$0.459511\pi$
$524$	8.72546			0.381174
$525$		0			0
$526$	2.57177			0.112134
$527$	−9.88101	−	5.03463i	−0.430424	−	0.219312i
$528$	−0.0232622	+	8.89846i	−0.00101236	+	0.387256i
$529$	9.31679	+	12.8235i	0.405078	+	0.557542i
$530$		0			0
$531$	4.69824	−	14.2065i	0.203886	−	0.616511i
$532$	0.0735370	+	0.0735370i	0.00318823	+	0.00318823i
$533$	1.45602	+	9.19295i	0.0630672	+	0.398191i
$534$	−3.01533	+	18.7212i	−0.130486	+	0.810144i
$535$		0			0
$536$	−14.2901	+	4.64313i	−0.617237	+	0.200553i
$537$	16.6357	−	12.0202i	0.717883	−	0.518711i
$538$	−10.9703	−	21.5305i	−0.472965	−	0.928246i
$539$	11.0391	+	33.9747i	0.475486	+	1.46340i
$540$		0			0
$541$	−6.47364	+	19.9238i	−0.278323	+	0.856591i	0.709998	+	0.704204i	$0.248696\pi$
$541$	−6.47364	+	19.9238i	−0.278323	+	0.856591i	−0.988321	+	0.152387i	$0.951304\pi$
$542$	11.4328	−	1.81078i	0.491082	−	0.0777797i
$543$	−24.0428	−	17.5643i	−1.03177	−	0.753757i
$544$	2.86572	−	3.94433i	0.122867	−	0.169112i
$545$		0			0
$546$	0.394192	−	0.392137i	0.0168699	−	0.0167819i
$547$	−43.0967	−	6.82585i	−1.84268	−	0.291852i	−0.864974	−	0.501817i	$-0.832665\pi$
$547$	−43.0967	−	6.82585i	−1.84268	−	0.291852i	−0.977709	+	0.209965i	$0.932665\pi$
$548$	−1.28180	+	2.51567i	−0.0547557	+	0.107464i
$549$	−12.4467	−	38.9995i	−0.531211	−	1.66446i
$550$		0			0
$551$		−	4.52004i		−	0.192560i
$552$	−4.40077	−	1.44263i	−0.187309	−	0.0614023i
$553$	0.0738630	−	0.466353i	0.00314098	−	0.0198313i
$554$	6.09674	−	4.42954i	0.259025	−	0.188193i
$555$		0			0
$556$	−5.63143	−	4.09147i	−0.238826	−	0.173517i
$557$	−20.7979	+	20.7979i	−0.881236	+	0.881236i	−0.993660	−	0.112424i	$-0.964139\pi$
$557$	−20.7979	+	20.7979i	−0.881236	+	0.881236i	0.112424	+	0.993660i	$0.464139\pi$
$558$	3.06611	+	6.09617i	0.129799	+	0.258071i
$559$	−5.44220	−	1.76828i	−0.230181	−	0.0747902i
$560$		0			0
$561$	38.7070	−	19.5949i	1.63421	−	0.827297i
$562$	21.0388	−	10.7198i	0.887467	−	0.452187i
$563$	14.0139	−	7.14045i	0.590616	−	0.300934i	−0.133022	−	0.991113i	$-0.542468\pi$
$563$	14.0139	−	7.14045i	0.590616	−	0.300934i	0.723639	+	0.690179i	$0.242468\pi$
$564$	−15.6882	+	7.94195i	−0.660593	+	0.334417i
$565$		0			0
$566$	9.36284	+	3.04217i	0.393550	+	0.127872i
$567$	1.36001	+	1.38876i	0.0571152	+	0.0583223i
$568$	8.57861	−	8.57861i	0.359950	−	0.359950i
$569$	3.20445	+	2.32817i	0.134338	+	0.0976021i	0.652925	−	0.757423i	$-0.273542\pi$
$569$	3.20445	+	2.32817i	0.134338	+	0.0976021i	−0.518587	+	0.855025i	$0.673542\pi$
$570$		0			0
$571$	−31.7943	+	23.0999i	−1.33055	+	0.966702i	−0.330815	+	0.943696i	$0.607324\pi$
$571$	−31.7943	+	23.0999i	−1.33055	+	0.966702i	−0.999735	+	0.0230060i	$0.992676\pi$
$572$	−1.19457	+	7.54225i	−0.0499477	+	0.315357i
$573$	−8.13631	−	2.66718i	−0.339899	−	0.111423i
$574$			1.35243i			0.0564492i
$575$		0			0
$576$	−2.85798	+	0.912121i	−0.119082	+	0.0380050i
$577$	8.56788	−	16.8154i	0.356685	−	0.700034i	−0.641036	−	0.767511i	$-0.721495\pi$
$577$	8.56788	−	16.8154i	0.356685	−	0.700034i	0.997721	+	0.0674769i	$0.0214949\pi$
$578$	−6.68673	−	1.05907i	−0.278131	−	0.0440517i
$579$	4.13922	−	4.11763i	0.172020	−	0.171123i
$580$		0			0
$581$	0.634802	−	0.873729i	0.0263360	−	0.0362484i
$582$	14.1149	+	10.3116i	0.585083	+	0.427429i
$583$	39.0299	−	6.18173i	1.61645	−	0.256021i
$584$	−2.90012	+	8.92565i	−0.120008	+	0.369346i
$585$		0			0
$586$	1.45939	+	4.49153i	0.0602867	+	0.185543i
$587$	2.11434	+	4.14963i	0.0872683	+	0.171274i	0.930516	−	0.366252i	$-0.119359\pi$
$587$	2.11434	+	4.14963i	0.0872683	+	0.171274i	−0.843247	+	0.537526i	$0.819359\pi$
$588$	−9.76192	+	7.05353i	−0.402575	+	0.290883i
$589$	−1.04166	+	0.338457i	−0.0429210	+	0.0139459i
$590$		0			0
$591$	2.01933	−	12.5373i	0.0830640	−	0.515716i
$592$	−0.673443	−	4.25195i	−0.0276783	−	0.174754i
$593$	32.4687	+	32.4687i	1.33333	+	1.33333i	0.902371	+	0.430960i	$0.141825\pi$
$593$	32.4687	+	32.4687i	1.33333	+	1.33333i	0.430960	+	0.902371i	$0.358175\pi$
$594$	−26.3332	−	4.38274i	−1.08047	−	0.179826i
$595$		0			0
$596$	−4.53982	−	6.24853i	−0.185958	−	0.255950i
$597$	0.0377708	−	14.4484i	0.00154586	−	0.591334i
$598$	−3.54111	−	1.80428i	−0.144807	−	0.0737826i
$599$	−18.2921			−0.747393			−0.373697	−	0.927551i	$-0.621910\pi$
$599$	−18.2921			−0.747393			−0.373697	+	0.927551i	$0.621910\pi$
$600$		0			0
$601$	−0.981781			−0.0400477			−0.0200238	−	0.999800i	$-0.506374\pi$
$601$	−0.981781			−0.0400477			−0.0200238	+	0.999800i	$0.506374\pi$
$602$	−0.740847	−	0.377480i	−0.0301947	−	0.0153850i
$603$	−6.81864	−	44.5577i	−0.277676	−	1.81453i
$604$	−8.69147	−	11.9628i	−0.353651	−	0.486759i
$605$		0			0
$606$	7.53772	−	14.6985i	0.306199	−	0.597086i
$607$	2.39455	+	2.39455i	0.0971917	+	0.0971917i	0.754031	−	0.656839i	$-0.228107\pi$
$607$	2.39455	+	2.39455i	0.0971917	+	0.0971917i	−0.656839	+	0.754031i	$0.728107\pi$
$608$	−0.0753267	−	0.475594i	−0.00305490	−	0.0192879i
$609$	−3.46681	−	0.558383i	−0.140482	−	0.0226268i
$610$		0			0
$611$	−14.3512	+	4.66298i	−0.580586	+	0.188644i
$612$	10.2882	+	10.3963i	0.415875	+	0.420247i
$613$	−6.24017	−	12.2470i	−0.252038	−	0.494653i	0.729973	−	0.683476i	$-0.239533\pi$
$613$	−6.24017	−	12.2470i	−0.252038	−	0.494653i	−0.982011	+	0.188823i	$0.939533\pi$
$614$	−5.16261	−	15.8889i	−0.208346	−	0.641223i
$615$		0			0
$616$	−0.342880	+	1.05528i	−0.0138150	+	0.0425183i
$617$	−10.1292	+	1.60431i	−0.407787	+	0.0645872i	−0.356959	−	0.934120i	$-0.616186\pi$
$617$	−10.1292	+	1.60431i	−0.407787	+	0.0645872i	−0.0508287	+	0.998707i	$0.516186\pi$
$618$	−10.3336	+	14.1451i	−0.415679	+	0.568999i
$619$	27.3325	−	37.6199i	1.09859	−	1.51207i	0.261338	−	0.965247i	$-0.415836\pi$
$619$	27.3325	−	37.6199i	1.09859	−	1.51207i	0.837247	−	0.546825i	$-0.184164\pi$
$620$		0			0
$621$	6.40445	−	12.3294i	0.257002	−	0.494763i
$622$	29.8303	+	4.72465i	1.19608	+	0.189441i
$623$	−1.07346	+	2.10678i	−0.0430072	+	0.0844063i
$624$	−2.54381	+	0.396086i	−0.101834	+	0.0158561i
$625$		0			0
$626$		−	16.6805i		−	0.666686i
$627$	1.33473	−	4.07163i	0.0533040	−	0.162605i
$628$	−2.56499	+	16.1947i	−0.102354	+	0.646239i
$629$	−16.9802	+	12.3368i	−0.677043	+	0.491900i
$630$		0			0
$631$	−20.6748	−	15.0211i	−0.823051	−	0.597981i	0.0945340	−	0.995522i	$-0.469864\pi$
$631$	−20.6748	−	15.0211i	−0.823051	−	0.597981i	−0.917585	+	0.397540i	$0.869864\pi$
$632$	−1.54588	+	1.54588i	−0.0614917	+	0.0614917i
$633$	−2.27627	−	7.06846i	−0.0904736	−	0.280946i
$634$	10.3155	+	3.35172i	0.409683	+	0.133114i
$635$		0			0
$636$	6.01719	+	11.8861i	0.238597	+	0.471315i
$637$	−9.20875	+	4.69209i	−0.364864	+	0.185907i
$638$	42.9697	−	21.8942i	1.70119	−	0.866798i
$639$	21.2388	+	29.5564i	0.840193	+	1.16923i
$640$		0			0
$641$	−0.702023	−	0.228101i	−0.0277282	−	0.00900945i	0.295120	−	0.955460i	$-0.404640\pi$
$641$	−0.702023	−	0.228101i	−0.0277282	−	0.00900945i	−0.322848	+	0.946451i	$0.604640\pi$
$642$	−18.2066	+	5.86312i	−0.718558	+	0.231399i
$643$	−17.1573	+	17.1573i	−0.676616	+	0.676616i	−0.959233	−	0.282617i	$-0.908797\pi$
$643$	−17.1573	+	17.1573i	−0.676616	+	0.676616i	0.282617	+	0.959233i	$0.408797\pi$
$644$	−0.467192	−	0.339435i	−0.0184099	−	0.0133756i
$645$		0			0
$646$	−1.89928	+	1.37991i	−0.0747262	+	0.0542918i
$647$	−0.943217	+	5.95524i	−0.0370817	+	0.234125i	−0.999267	−	0.0382696i	$-0.987815\pi$
$647$	−0.943217	+	5.95524i	−0.0370817	+	0.234125i	0.962186	+	0.272394i	$0.0878154\pi$
$648$	−1.31488	−	8.90343i	−0.0516535	−	0.349760i
$649$			25.6248i			1.00586i
$650$		0			0
$651$	0.130910	+	0.840754i	0.00513078	+	0.0329517i
$652$	−1.84215	+	3.61543i	−0.0721443	+	0.141591i
$653$	−9.97451	−	1.57981i	−0.390333	−	0.0618226i	−0.0418163	−	0.999125i	$-0.513314\pi$
$653$	−9.97451	−	1.57981i	−0.390333	−	0.0618226i	−0.348516	+	0.937303i	$0.613314\pi$
$654$	−7.49055	−	7.52982i	−0.292904	−	0.294439i
$655$		0			0
$656$	3.68068	−	5.06602i	0.143706	−	0.197795i
$657$	−25.0191	−	12.9131i	−0.976087	−	0.503787i
$658$	−2.16561	+	0.342999i	−0.0844242	+	0.0133715i
$659$	−3.59331	+	11.0591i	−0.139975	+	0.430800i	−0.996331	−	0.0855871i	$-0.972723\pi$
$659$	−3.59331	+	11.0591i	−0.139975	+	0.430800i	0.856355	+	0.516387i	$0.172723\pi$
$660$		0			0
$661$	12.8291	+	39.4838i	0.498993	+	1.53574i	0.810641	+	0.585544i	$0.199119\pi$
$661$	12.8291	+	39.4838i	0.498993	+	1.53574i	−0.311648	+	0.950197i	$0.600881\pi$
$662$	4.37411	+	8.58467i	0.170005	+	0.333653i
$663$	7.35111	+	10.1738i	0.285494	+	0.395116i
$664$	−4.75577	+	1.54524i	−0.184560	+	0.0599671i
$665$		0			0
$666$	12.9147	+	0.0675232i	0.500434	+	0.00261647i
$667$	3.92637	+	24.7901i	0.152030	+	0.959877i
$668$	9.78704	+	9.78704i	0.378672	+	0.378672i
$669$	1.12650	+	0.577696i	0.0435531	+	0.0223350i
$670$		0			0
$671$	41.2074	+	56.7171i	1.59079	+	2.18954i
$672$	−0.374079		0.000977913i	−0.0144304		3.77238e-5i
$673$	23.9046	+	12.1800i	0.921454	+	0.469504i	0.849313	−	0.527890i	$-0.177017\pi$
$673$	23.9046	+	12.1800i	0.921454	+	0.469504i	0.0721411	+	0.997394i	$0.477017\pi$
$674$	−28.1544			−1.08447
$675$		0			0
$676$	10.7907			0.415028
$677$	19.6621	+	10.0184i	0.755677	+	0.385037i	0.788988	−	0.614408i	$-0.210605\pi$
$677$	19.6621	+	10.0184i	0.755677	+	0.385037i	−0.0333112	+	0.999445i	$0.510605\pi$
$678$	19.0283	+	0.0497436i	0.730779	+	0.00191039i
$679$	1.28118	+	1.76340i	0.0491673	+	0.0676729i
$680$		0			0
$681$	5.10240	+	2.61663i	0.195524	+	0.100269i
$682$	−8.26315	−	8.26315i	−0.316413	−	0.316413i
$683$	3.06282	+	19.3379i	0.117196	+	0.739944i	0.974376	+	0.224927i	$0.0722144\pi$
$683$	3.06282	+	19.3379i	0.117196	+	0.739944i	−0.857180	+	0.515017i	$0.827786\pi$
$684$	1.44455	+	0.00755268i	0.0552336	+	0.000288784i
$685$		0			0
$686$	−2.86609	+	0.931249i	−0.109428	+	0.0355552i
$687$	10.7039	+	14.8139i	0.408379	+	0.565187i
$688$	1.74779	+	3.43023i	0.0666339	+	0.130776i
$689$	3.53289	+	10.8731i	0.134592	+	0.414232i
$690$		0			0
$691$	12.6136	−	38.8206i	0.479843	−	1.47681i	−0.359469	−	0.933157i	$-0.617042\pi$
$691$	12.6136	−	38.8206i	0.479843	−	1.47681i	0.839313	−	0.543649i	$-0.182958\pi$
$692$	−0.896939	+	0.142061i	−0.0340965	+	0.00540036i
$693$	−2.95800	−	1.52671i	−0.112365	−	0.0579949i
$694$	−11.3510	+	15.6232i	−0.430876	+	0.593050i
$695$		0			0
$696$	11.4666	+	11.5267i	0.434639	+	0.436917i
$697$	−30.1540	−	4.77592i	−1.14216	−	0.180901i
$698$	−6.54286	+	12.8411i	−0.247651	+	0.486042i
$699$	3.35470	+	21.5451i	0.126886	+	0.814912i
$700$		0			0
$701$		−	1.34594i		−	0.0508356i	−0.999677	−	0.0254178i	$-0.991908\pi$
$701$		−	1.34594i		−	0.0508356i	0.999677	−	0.0254178i	$-0.00809161\pi$
$702$	0.0605703	−	7.72314i	0.00228608	−	0.291491i
$703$	−0.324278	+	2.04741i	−0.0122304	+	0.0772195i
$704$	4.15636	−	3.01977i	0.156649	−	0.113812i
$705$		0			0
$706$	28.3247	+	20.5791i	1.06601	+	0.774503i
$707$	1.45647	−	1.45647i	0.0547762	−	0.0547762i
$708$	−8.22317	+	2.64812i	−0.309046	+	0.0995225i
$709$	−5.99345	−	1.94739i	−0.225089	−	0.0731358i	0.194301	−	0.980942i	$-0.437756\pi$
$709$	−5.99345	−	1.94739i	−0.225089	−	0.0731358i	−0.419390	+	0.907806i	$0.637756\pi$
$710$		0			0
$711$	−3.82725	−	5.32610i	−0.143533	−	0.199744i
$712$	9.75471	−	4.97027i	0.365573	−	0.186269i
$713$	5.41900	−	2.76112i	0.202943	−	0.103405i
$714$	0.823744	+	1.62719i	0.0308278	+	0.0608960i
$715$		0			0
$716$	−11.2695	−	3.66170i	−0.421163	−	0.136844i
$717$	6.23589	+	19.3642i	0.232884	+	0.723170i
$718$	−24.4491	+	24.4491i	−0.912432	+	0.912432i
$719$	−15.2779	−	11.1001i	−0.569770	−	0.413962i	0.265251	−	0.964179i	$-0.414545\pi$
$719$	−15.2779	−	11.1001i	−0.569770	−	0.413962i	−0.835022	+	0.550217i	$0.814545\pi$
$720$		0			0
$721$	−1.76717	+	1.28392i	−0.0658127	+	0.0478157i
$722$	2.93598	−	18.5371i	0.109266	−	0.689878i
$723$	−0.656225	+	2.00183i	−0.0244053	+	0.0744490i
$724$			17.1907i			0.638888i
$725$		0			0
$726$	26.3463	−	4.10228i	0.977805	−	0.152250i
$727$	5.62601	−	11.0417i	0.208657	−	0.409513i	−0.762832	−	0.646597i	$-0.776192\pi$
$727$	5.62601	−	11.0417i	0.208657	−	0.409513i	0.971489	+	0.237084i	$0.0761916\pi$
$728$	−0.317066	−	0.0502184i	−0.0117513	−	0.00186122i
$729$	26.9967	+	0.423480i	0.999877	+	0.0156844i
$730$		0			0
$731$	11.0326	−	15.1850i	0.408055	−	0.561639i
$732$	−13.9424	+	19.0850i	−0.515327	+	0.705401i
$733$	−9.27418	+	1.46889i	−0.342550	+	0.0542545i	−0.325339	−	0.945597i	$-0.605478\pi$
$733$	−9.27418	+	1.46889i	−0.342550	+	0.0542545i	−0.0172103	+	0.999852i	$0.505478\pi$
$734$	−0.998039	+	3.07165i	−0.0368383	+	0.113377i
$735$		0			0
$736$	0.826257	+	2.54296i	0.0304562	+	0.0937346i
$737$	35.0454	+	68.7804i	1.29091	+	2.53356i
$738$	13.2140	+	13.3529i	0.486413	+	0.491526i
$739$	−18.0916	+	5.87832i	−0.665511	+	0.216238i	−0.622241	−	0.782826i	$-0.713778\pi$
$739$	−18.0916	+	5.87832i	−0.665511	+	0.216238i	−0.0432699	+	0.999063i	$0.513778\pi$
$740$		0			0
$741$	1.22389	+	0.197126i	0.0449606	+	0.00724159i
$742$	0.259872	+	1.64077i	0.00954019	+	0.0602344i
$743$	23.1938	+	23.1938i	0.850899	+	0.850899i	0.990244	−	0.139345i	$-0.0444997\pi$
$743$	23.1938	+	23.1938i	0.850899	+	0.850899i	−0.139345	+	0.990244i	$0.544500\pi$
$744$	1.79777	−	3.50563i	0.0659094	−	0.128523i
$745$		0			0
$746$	6.36867	+	8.76572i	0.233174	+	0.320936i
$747$	−2.26926	−	14.8289i	−0.0830278	−	0.542562i
$748$	−22.3178	−	11.3715i	−0.816020	−	0.415783i
$749$	−2.38506			−0.0871483
$750$		0			0
$751$	35.1267			1.28179			0.640895	−	0.767628i	$-0.278563\pi$
$751$	35.1267			1.28179			0.640895	+	0.767628i	$0.278563\pi$
$752$	9.04558	+	4.60895i	0.329858	+	0.168071i
$753$	−0.102386	+	39.1655i	−0.00373115	+	1.42727i
$754$	8.20106	+	11.2878i	0.298665	+	0.411077i
$755$		0			0
$756$	0.184245	−	1.10701i	0.00670092	−	0.0402617i
$757$	−20.0652	−	20.0652i	−0.729283	−	0.729283i	0.241194	−	0.970477i	$-0.422461\pi$
$757$	−20.0652	−	20.0652i	−0.729283	−	0.729283i	−0.970477	+	0.241194i	$0.922461\pi$
$758$	−5.23911	−	33.0785i	−0.190293	−	1.20146i
$759$	−3.78346	+	23.4902i	−0.137331	+	0.852642i
$760$		0			0
$761$	30.4666	−	9.89919i	1.10441	−	0.358845i	0.300613	−	0.953746i	$-0.402809\pi$
$761$	30.4666	−	9.89919i	1.10441	−	0.358845i	0.803799	+	0.594901i	$0.202809\pi$
$762$	21.1104	−	15.2535i	0.764751	−	0.552575i
$763$	−0.601254	−	1.18003i	−0.0217669	−	0.0427199i
$764$	1.52761	+	4.70151i	0.0552671	+	0.170095i
$765$		0			0
$766$	−5.02104	+	15.4532i	−0.181418	+	0.558346i
$767$	−7.32235	+	1.15975i	−0.264395	+	0.0418760i
$768$	1.39859	+	1.02173i	0.0504674	+	0.0368686i
$769$	−8.74366	+	12.0346i	−0.315305	+	0.433980i	−0.937026	−	0.349259i	$-0.886433\pi$
$769$	−8.74366	+	12.0346i	−0.315305	+	0.433980i	0.621722	+	0.783238i	$0.286433\pi$
$770$		0			0
$771$	−5.18256	+	5.15553i	−0.186645	+	0.185672i
$772$	−3.32936	−	0.527318i	−0.119826	−	0.0189786i
$773$	−10.0990	+	19.8204i	−0.363235	+	0.712889i	−0.998220	−	0.0596354i	$-0.981006\pi$
$773$	−10.0990	+	19.8204i	−0.363235	+	0.712889i	0.634985	+	0.772524i	$0.281006\pi$
$774$	−11.0028	+	3.51152i	−0.395486	+	0.126219i
$775$		0			0
$776$		−	10.0922i		−	0.362290i
$777$	1.53028	+	0.501643i	0.0548983	+	0.0179964i
$778$	0.407467	−	2.57264i	0.0146084	−	0.0922337i
$779$	−2.43940	+	1.77233i	−0.0874006	+	0.0635003i
$780$		0			0
$781$	−50.4249	−	36.6358i	−1.80435	−	1.31093i
$782$	9.21792	−	9.21792i	0.329632	−	0.329632i
$783$	−39.6844	+	28.3596i	−1.41820	+	1.01349i
$784$	6.61303	+	2.14870i	0.236180	+	0.0767395i
$785$		0			0
$786$	13.4836	−	6.82591i	0.480945	−	0.243472i
$787$	45.7145	−	23.2927i	1.62955	−	0.830295i	0.631035	−	0.775755i	$-0.282631\pi$
$787$	45.7145	−	23.2927i	1.62955	−	0.830295i	0.998512	−	0.0545406i	$-0.0173694\pi$
$788$	−6.53260	+	3.32853i	−0.232714	+	0.118574i
$789$	3.97420	−	2.01189i	0.141485	−	0.0716251i
$790$		0			0
$791$	2.25659	+	0.733210i	0.0802351	+	0.0260700i
$792$	6.92529	+	13.7692i	0.246080	+	0.489265i
$793$	−14.3420	+	14.3420i	−0.509301	+	0.509301i
$794$	1.52645	+	1.10903i	0.0541717	+	0.0393580i
$795$		0			0
$796$	−6.74867	+	4.90320i	−0.239200	+	0.173789i
$797$	0.485494	−	3.06529i	0.0171971	−	0.108578i	−0.977597	−	0.210487i	$-0.932495\pi$
$797$	0.485494	−	3.06529i	0.0171971	−	0.108578i	0.994794	+	0.101909i	$0.0324950\pi$
$798$	0.171166	+	0.0561103i	0.00605921	+	0.00198628i
$799$		−	49.4961i		−	1.75105i
$800$		0			0
$801$	9.98587	+	31.2890i	0.352833	+	1.10554i
$802$	−3.25457	+	6.38745i	−0.114923	+	0.225549i
$803$	47.6222	+	7.54261i	1.68055	+	0.266173i
$804$	−18.4504	+	18.3542i	−0.650696	+	0.647303i
$805$		0			0
$806$	1.98724	−	2.73520i	0.0699974	−	0.0963431i
$807$	−33.7959	−	24.6894i	−1.18967	−	0.869109i
$808$	−9.41958	+	1.49192i	−0.331380	+	0.0524854i
$809$	−4.71934	+	14.5246i	−0.165923	+	0.510659i	−0.999103	−	0.0423432i	$-0.986518\pi$
$809$	−4.71934	+	14.5246i	−0.165923	+	0.510659i	0.833180	+	0.553002i	$0.186518\pi$
$810$		0			0
$811$	1.02202	+	3.14544i	0.0358879	+	0.110451i	0.967396	−	0.253270i	$-0.0815060\pi$
$811$	1.02202	+	3.14544i	0.0358879	+	0.110451i	−0.931508	+	0.363721i	$0.881506\pi$
$812$	0.920402	+	1.80639i	0.0322998	+	0.0633919i
$813$	16.2508	−	11.7421i	0.569940	−	0.411814i
$814$	−21.0344	+	6.83450i	−0.737256	+	0.239549i
$815$		0			0
$816$	1.34282	−	8.33709i	0.0470080	−	0.291857i
$817$	−0.289996	−	1.83096i	−0.0101457	−	0.0640572i
$818$	−11.3634	−	11.3634i	−0.397313	−	0.397313i
$819$	0.302385	−	0.914352i	0.0105662	−	0.0319500i
$820$		0			0
$821$	−18.3359	−	25.2372i	−0.639927	−	0.880784i	0.358685	−	0.933459i	$-0.383225\pi$
$821$	−18.3359	−	25.2372i	−0.639927	−	0.880784i	−0.998612	+	0.0526750i	$0.983225\pi$
$822$	−0.0127840	+	4.89026i	−0.000445895	+	0.170567i
$823$	−13.9035	−	7.08420i	−0.484647	−	0.246940i	0.194555	−	0.980892i	$-0.437674\pi$
$823$	−13.9035	−	7.08420i	−0.484647	−	0.246940i	−0.679202	+	0.733952i	$0.737674\pi$
$824$	10.1138			0.352331
$825$		0			0
$826$	−1.07723			−0.0374817
$827$	3.23908	+	1.65039i	0.112634	+	0.0573898i	0.509400	−	0.860530i	$-0.329868\pi$
$827$	3.23908	+	1.65039i	0.112634	+	0.0573898i	−0.396766	+	0.917920i	$0.629868\pi$
$828$	−7.92916	+	1.21339i	−0.275557	+	0.0421684i
$829$	−14.6691	−	20.1903i	−0.509480	−	0.701239i	0.474351	−	0.880336i	$-0.342683\pi$
$829$	−14.6691	−	20.1903i	−0.509480	−	0.701239i	−0.983832	+	0.179096i	$0.942683\pi$
$830$		0			0
$831$	5.95618	−	11.6145i	0.206618	−	0.402903i
$832$	1.05102	+	1.05102i	0.0364375	+	0.0364375i
$833$	−5.30325	−	33.4834i	−0.183747	−	1.16013i
$834$	−11.9031	−	1.91718i	−0.412171	−	0.0663864i
$835$		0			0
$836$	−2.35276	+	0.764459i	−0.0813720	+	0.0264394i
$837$	9.50714	+	7.02191i	0.328615	+	0.242713i
$838$	1.01758	+	1.99711i	0.0351516	+	0.0689889i
$839$	−5.55073	−	17.0834i	−0.191632	−	0.589784i	−0.999999	−	0.00110507i	$-0.999648\pi$
$839$	−5.55073	−	17.0834i	−0.191632	−	0.589784i	0.808367	−	0.588679i	$-0.200352\pi$
$840$		0			0
$841$	18.2677	−	56.2221i	0.629920	−	1.93869i
$842$	−2.55767	+	0.405096i	−0.0881433	+	0.0139605i
$843$	24.1255	−	33.0241i	0.830928	−	1.13741i
$844$	−2.52005	+	3.46855i	−0.0867437	+	0.119392i
$845$		0			0
$846$	−18.0303	+	24.5457i	−0.619895	+	0.843899i
$847$	3.28387	+	0.520114i	0.112835	+	0.0178713i
$848$	3.49196	−	6.85335i	0.119914	−	0.235345i
$849$	16.8485	−	2.62340i	0.578238	−	0.0900350i
$850$		0			0
$851$		−	11.5107i		−	0.394581i
$852$	6.54566	−	19.9677i	0.224251	−	0.684083i
$853$	4.94081	−	31.1950i	0.169170	−	1.06810i	−0.746270	−	0.665643i	$-0.768157\pi$
$853$	4.94081	−	31.1950i	0.169170	−	1.06810i	0.915440	−	0.402454i	$-0.131843\pi$
$854$	−2.38431	+	1.73230i	−0.0815894	+	0.0592782i
$855$		0			0
$856$	8.93414	+	6.49104i	0.305363	+	0.221859i
$857$	−8.57240	+	8.57240i	−0.292828	+	0.292828i	−0.838196	−	0.545369i	$-0.816390\pi$
$857$	−8.57240	+	8.57240i	−0.292828	+	0.292828i	0.545369	+	0.838196i	$0.316390\pi$
$858$	4.05428	+	12.5897i	0.138411	+	0.429805i
$859$	1.99366	+	0.647780i	0.0680228	+	0.0221020i	0.342831	−	0.939397i	$-0.388614\pi$
$859$	1.99366	+	0.647780i	0.0680228	+	0.0221020i	−0.274808	+	0.961499i	$0.588614\pi$
$860$		0			0
$861$	1.05800	+	2.08993i	0.0360566	+	0.0712247i
$862$	−1.00264	+	0.510869i	−0.0341500	+	0.0174003i
$863$	−25.5918	+	13.0397i	−0.871155	+	0.443876i	−0.831622	−	0.555343i	$-0.812587\pi$
$863$	−25.5918	+	13.0397i	−0.871155	+	0.443876i	−0.0395333	+	0.999218i	$0.512587\pi$
$864$	−3.70294	+	3.64531i	−0.125976	+	0.124016i
$865$		0			0
$866$	19.5231	+	6.34342i	0.663420	+	0.215558i
$867$	−11.1616	+	3.59441i	−0.379069	+	0.122072i
$868$	0.347372	−	0.347372i	0.0117906	−	0.0117906i
$869$	9.08664	+	6.60183i	0.308243	+	0.223952i
$870$		0			0
$871$	−18.0680	+	13.1272i	−0.612212	+	0.444798i
$872$	−0.959266	+	6.05656i	−0.0324848	+	0.205101i
$873$	29.8788	+	4.89261i	1.01124	+	0.165590i
$874$		−	1.28751i		−	0.0435505i
$875$		0			0
$876$	2.50091	+	16.0617i	0.0844978	+	0.542676i
$877$	−7.83550	+	15.3780i	−0.264586	+	0.519279i	−0.984631	−	0.174648i	$-0.944121\pi$
$877$	−7.83550	+	15.3780i	−0.264586	+	0.519279i	0.720045	+	0.693927i	$0.244121\pi$
$878$	−23.2354	−	3.68012i	−0.784156	−	0.124198i
$879$	5.76893	+	5.79917i	0.194581	+	0.195601i
$880$		0			0
$881$	11.5046	−	15.8347i	0.387600	−	0.533485i	−0.569978	−	0.821660i	$-0.693048\pi$
$881$	11.5046	−	15.8347i	0.387600	−	0.533485i	0.957578	+	0.288175i	$0.0930484\pi$
$882$	−9.56732	+	18.5367i	−0.322148	+	0.624163i
$883$	−13.3245	+	2.11040i	−0.448406	+	0.0710206i	−0.376554	−	0.926395i	$-0.622891\pi$
$883$	−13.3245	+	2.11040i	−0.448406	+	0.0710206i	−0.0718524	+	0.997415i	$0.522891\pi$
$884$	2.23936	−	6.89203i	0.0753177	−	0.231804i
$885$		0			0
$886$	5.95075	+	18.3145i	0.199919	+	0.615288i
$887$	−23.7996	−	46.7094i	−0.799114	−	1.56835i	−0.822597	−	0.568624i	$-0.807476\pi$
$887$	−23.7996	−	46.7094i	−0.799114	−	1.56835i	0.0234837	−	0.999724i	$-0.492524\pi$
$888$	−4.36698	−	6.04379i	−0.146546	−	0.202816i
$889$	3.08864	−	1.00356i	0.103590	−	0.0336583i
$890$		0			0
$891$	−44.1219	+	13.8277i	−1.47814	+	0.463245i
$892$	−0.114341	−	0.721923i	−0.00382843	−	0.0241718i
$893$	−3.45666	−	3.45666i	−0.115673	−	0.115673i
$894$	−11.9037	−	6.10448i	−0.398119	−	0.204164i
$895$		0			0
$896$	0.126947	+	0.174728i	0.00424101	+	0.00583725i
$897$	−6.88362	−	0.0179951i	−0.229838	−	0.000600838i
$898$	17.1237	+	8.72498i	0.571426	+	0.291156i
$899$	−21.3516			−0.712117
$900$		0			0
$901$	−37.5005			−1.24932
$902$	−28.6646	−	14.6053i	−0.954427	−	0.486305i
$903$	−1.44015	−	0.00376481i	−0.0479251	−	0.000125285i
$904$	−6.45744	−	8.88790i	−0.214771	−	0.295607i
$905$		0			0
$906$	−22.7896	−	11.6870i	−0.757132	−	0.388275i
$907$	−7.30011	−	7.30011i	−0.242396	−	0.242396i	0.575445	−	0.817841i	$-0.304829\pi$
$907$	−7.30011	−	7.30011i	−0.242396	−	0.242396i	−0.817841	+	0.575445i	$0.804829\pi$
$908$	−0.517900	−	3.26989i	−0.0171871	−	0.108515i
$909$	0.149588	−	28.6106i	0.00496152	−	0.948954i
$910$		0			0
$911$	−26.9954	+	8.77133i	−0.894397	+	0.290607i	−0.719922	−	0.694055i	$-0.755823\pi$
$911$	−26.9954	+	8.77133i	−0.894397	+	0.290607i	−0.174474	+	0.984662i	$0.555823\pi$
$912$	−0.488460	−	0.676016i	−0.0161745	−	0.0223851i
$913$	11.6632	+	22.8903i	0.385995	+	0.757557i
$914$	6.97317	+	21.4612i	0.230652	+	0.709874i
$915$		0			0
$916$	3.26071	−	10.0354i	0.107737	−	0.331580i
$917$	1.86129	−	0.294799i	0.0614651	−	0.00973511i
$918$	24.0316	+	8.01723i	0.793160	+	0.264608i
$919$	4.27526	−	5.88440i	0.141028	−	0.194108i	−0.732660	−	0.680594i	$-0.761722\pi$
$919$	4.27526	−	5.88440i	0.141028	−	0.194108i	0.873688	+	0.486486i	$0.161722\pi$
$920$		0			0
$921$	−20.4077	−	20.5147i	−0.672457	−	0.675982i
$922$	15.8045	+	2.50319i	0.520494	+	0.0824382i
$923$	8.18661	−	16.0671i	0.269466	−	0.528856i
$924$	0.295681	+	1.89897i	0.00972720	+	0.0624717i
$925$		0			0
$926$		−	6.19159i		−	0.203468i
$927$	−4.90306	+	29.9427i	−0.161038	+	0.983446i
$928$	1.46845	−	9.27141i	0.0482041	−	0.304349i
$929$	−5.66314	+	4.11451i	−0.185802	+	0.134993i	−0.676798	−	0.736169i	$-0.736633\pi$
$929$	−5.66314	+	4.11451i	−0.185802	+	0.134993i	0.490996	+	0.871162i	$0.336633\pi$
$930$		0			0
$931$	−2.70875	−	1.96802i	−0.0887756	−	0.0644992i
$932$	8.90175	−	8.90175i	0.291586	−	0.291586i
$933$	49.7933	−	16.0350i	1.63016	−	0.524964i
$934$	−22.0766	−	7.17313i	−0.722369	−	0.234712i
$935$		0			0
$936$	−3.62114	+	2.60209i	−0.118361	+	0.0850521i
$937$	35.4943	−	18.0852i	1.15955	−	0.590819i	0.235040	−	0.971986i	$-0.424478\pi$
$937$	35.4943	−	18.0852i	1.15955	−	0.590819i	0.924506	+	0.381167i	$0.124478\pi$
$938$	−2.89144	+	1.47326i	−0.0944088	+	0.0481037i
$939$	−13.0491	−	25.7767i	−0.425841	−	0.841189i
$940$		0			0
$941$	−0.912873	−	0.296610i	−0.0297588	−	0.00966922i	0.294100	−	0.955775i	$-0.404980\pi$
$941$	−0.912873	−	0.296610i	−0.0297588	−	0.00966922i	−0.323859	+	0.946106i	$0.604980\pi$
$942$	8.70535	+	27.0326i	0.283636	+	0.880769i
$943$	11.8393	−	11.8393i	0.385542	−	0.385542i
$944$	4.03518	+	2.93173i	0.131334	+	0.0954196i
$945$		0			0
$946$	16.0013	−	11.6256i	0.520248	−	0.377982i
$947$	−5.95470	+	37.5965i	−0.193502	+	1.22172i	0.679378	+	0.733788i	$0.262250\pi$
$947$	−5.95470	+	37.5965i	−0.193502	+	1.22172i	−0.872880	+	0.487935i	$0.837750\pi$
$948$	−1.17954	+	3.59821i	−0.0383096	+	0.116864i
$949$			13.9495i			0.452820i
$950$		0			0
$951$	18.5629	−	2.89034i	0.601942	−	0.0937258i
$952$	0.478043	−	0.938212i	0.0154935	−	0.0304076i
$953$	−56.6214	−	8.96795i	−1.83415	−	0.290500i	−0.858986	−	0.511999i	$-0.828905\pi$
$953$	−56.6214	−	8.96795i	−1.83415	−	0.290500i	−0.975161	+	0.221499i	$0.928905\pi$
$954$	18.5970	+	13.6606i	0.602099	+	0.442279i
$955$		0			0
$956$	6.90374	−	9.50218i	0.223283	−	0.307322i
$957$	49.2742	−	67.4486i	1.59281	−	2.18030i
$958$	−22.1377	+	3.50627i	−0.715236	+	0.113282i
$959$	−0.188434	+	0.579941i	−0.00608486	+	0.0187273i
$960$		0			0
$961$	−7.98073	−	24.5622i	−0.257443	−	0.792328i
$962$	−2.90496	−	5.70131i	−0.0936598	−	0.183818i
$963$	−23.5483	+	23.3034i	−0.758835	+	0.750941i
$964$	1.15675	−	0.375849i	0.0372563	−	0.0121053i
$965$		0			0
$966$	−0.987499	−	0.159052i	−0.0317723	−	0.00511741i
$967$	6.91329	+	43.6488i	0.222316	+	1.40365i	0.806118	+	0.591755i	$0.201565\pi$
$967$	6.91329	+	43.6488i	0.222316	+	1.40365i	−0.583802	+	0.811896i	$0.698435\pi$
$968$	−10.8855	−	10.8855i	−0.349872	−	0.349872i
$969$	−1.85550	+	3.61820i	−0.0596071	+	0.116233i
$970$		0			0
$971$	32.4405	+	44.6505i	1.04107	+	1.43290i	0.896306	+	0.443437i	$0.146241\pi$
$971$	32.4405	+	44.6505i	1.04107	+	1.43290i	0.144760	+	0.989467i	$0.453759\pi$
$972$	−8.99705	−	12.7300i	−0.288580	−	0.408315i
$973$	−1.33951	−	0.682516i	−0.0429428	−	0.0218804i
$974$	21.2093			0.679589
$975$		0			0
$976$	13.6458			0.436793
$977$	−29.4915	−	15.0267i	−0.943516	−	0.480746i	−0.0866240	−	0.996241i	$-0.527608\pi$
$977$	−29.4915	−	15.0267i	−0.943516	−	0.480746i	−0.856892	+	0.515496i	$0.827608\pi$
$978$	−0.0183728	+	7.02810i	−0.000587496	+	0.224734i
$979$	−33.0604	−	45.5037i	−1.05661	−	1.45430i
$980$		0			0
$981$	−17.4658	−	5.77613i	−0.557642	−	0.184418i
$982$	−22.0207	−	22.0207i	−0.702708	−	0.702708i
$983$	3.05030	+	19.2588i	0.0972894	+	0.614261i	0.987367	+	0.158451i	$0.0506501\pi$
$983$	3.05030	+	19.2588i	0.0972894	+	0.614261i	−0.890077	+	0.455809i	$0.849350\pi$
$984$	1.72469	−	10.7080i	0.0549811	−	0.341359i
$985$		0			0
$986$	−43.5259	+	14.1424i	−1.38615	+	0.450386i
$987$	−3.07823	+	2.22419i	−0.0979811	+	0.0707968i
$988$	−0.324929	−	0.637709i	−0.0103374	−	0.0202882i
$989$	3.18096	+	9.78998i	0.101149	+	0.311303i
$990$		0			0
$991$	10.9360	−	33.6576i	0.347394	−	1.06917i	−0.612896	−	0.790164i	$-0.709995\pi$
$991$	10.9360	−	33.6576i	0.347394	−	1.06917i	0.960290	−	0.279005i	$-0.0900046\pi$
$992$	−2.24660	+	0.355826i	−0.0713295	+	0.0112975i
$993$	13.4752	+	9.84420i	0.427621	+	0.312396i
$994$	1.54012	−	2.11980i	0.0488497	−	0.0672359i
$995$		0			0
$996$	−6.14034	+	6.10832i	−0.194564	+	0.193550i
$997$	−45.5136	−	7.20864i	−1.44143	−	0.228300i	−0.613750	−	0.789501i	$-0.710340\pi$
$997$	−45.5136	−	7.20864i	−1.44143	−	0.228300i	−0.827680	+	0.561201i	$0.810340\pi$
$998$	−0.570481	+	1.11963i	−0.0180583	+	0.0354414i
$999$	20.0101	−	9.99878i	0.633093	−	0.316347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.b.107.1		80
3.2	odd	2	inner	750.2.l.b.107.10		80
5.2	odd	4		750.2.l.c.143.8		80
5.3	odd	4		750.2.l.a.143.3		80
5.4	even	2		150.2.l.a.17.10	yes	80
15.2	even	4		750.2.l.c.143.4		80
15.8	even	4		750.2.l.a.143.7		80
15.14	odd	2		150.2.l.a.17.1	✓	80
25.3	odd	20	inner	750.2.l.b.743.10		80
25.4	even	10		750.2.l.c.257.4		80
25.21	even	5		750.2.l.a.257.7		80
25.22	odd	20		150.2.l.a.53.1	yes	80
75.29	odd	10		750.2.l.c.257.8		80
75.47	even	20		150.2.l.a.53.10	yes	80
75.53	even	20	inner	750.2.l.b.743.1		80
75.71	odd	10		750.2.l.a.257.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.1	✓	80	15.14	odd	2
150.2.l.a.17.10	yes	80	5.4	even	2
150.2.l.a.53.1	yes	80	25.22	odd	20
150.2.l.a.53.10	yes	80	75.47	even	20
750.2.l.a.143.3		80	5.3	odd	4
750.2.l.a.143.7		80	15.8	even	4
750.2.l.a.257.3		80	75.71	odd	10
750.2.l.a.257.7		80	25.21	even	5
750.2.l.b.107.1		80	1.1	even	1	trivial
750.2.l.b.107.10		80	3.2	odd	2	inner
750.2.l.b.743.1		80	75.53	even	20	inner
750.2.l.b.743.10		80	25.3	odd	20	inner
750.2.l.c.143.4		80	15.2	even	4
750.2.l.c.143.8		80	5.2	odd	4
750.2.l.c.257.4		80	25.4	even	10
750.2.l.c.257.8		80	75.29	odd	10

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.73204 - 0.00452789i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(0.152718 + 0.152718i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.99996 + 0.0156850i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-1.73204 - 0.00452789i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.54121 + 0.790366i) q^{6} +(0.152718 + 0.152718i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.99996 + 0.0156850i) q^{9} +(-4.88609 + 1.58759i) q^{11} +(-1.01441 - 1.40392i) q^{12} +(-0.674795 - 1.32436i) q^{13} +(-0.0667401 - 0.205405i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(4.81543 - 0.762690i) q^{17} +(-2.66586 - 1.37593i) q^{18} +(0.283032 - 0.389560i) q^{19} +(-0.263823 - 0.265206i) q^{21} +(5.07429 + 0.803689i) q^{22} +(-1.21389 + 2.38239i) q^{23} +(0.266479 + 1.71143i) q^{24} +1.48636i q^{26} +(-5.19599 - 0.0407506i) q^{27} +(-0.0337860 + 0.213317i) q^{28} +(7.59423 - 5.51753i) q^{29} +(-1.84019 - 1.33698i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.47012 - 2.72765i) q^{33} +(-4.63684 - 1.50660i) q^{34} +(1.75064 + 2.43624i) q^{36} +(-3.83574 + 1.95441i) q^{37} +(-0.429039 + 0.218606i) q^{38} +(1.16278 + 2.29691i) q^{39} +(-5.95547 - 1.93505i) q^{41} +(0.114667 + 0.356073i) q^{42} +(2.72225 - 2.72225i) q^{43} +(-4.15636 - 3.01977i) q^{44} +(2.16317 - 1.57163i) q^{46} +(1.58814 - 10.0271i) q^{47} +(0.539538 - 1.64587i) q^{48} -6.95335i q^{49} +(-8.34400 + 1.29921i) q^{51} +(0.674795 - 1.32436i) q^{52} +(-7.59700 - 1.20325i) q^{53} +(4.61116 + 2.39524i) q^{54} +(0.126947 - 0.174728i) q^{56} +(-0.491987 + 0.673453i) q^{57} +(-9.27141 + 1.46845i) q^{58} +(1.54130 - 4.74363i) q^{59} +(-4.21680 - 12.9780i) q^{61} +(1.03265 + 2.02668i) q^{62} +(0.455752 + 0.460543i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-8.78526 - 1.41500i) q^{66} +(-2.35050 - 14.8405i) q^{67} +(3.44747 + 3.44747i) q^{68} +(2.11330 - 4.12092i) q^{69} +(7.13100 + 9.81498i) q^{71} +(-0.453805 - 2.96548i) q^{72} +(-8.36209 - 4.26070i) q^{73} +4.30495 q^{74} +0.481522 q^{76} +(-0.988647 - 0.503741i) q^{77} +(0.00673009 - 2.57445i) q^{78} +(-1.28502 - 1.76867i) q^{79} +(8.99951 + 0.0941087i) q^{81} +(4.42787 + 4.42787i) q^{82} +(-0.782253 - 4.93895i) q^{83} +(0.0594848 - 0.369321i) q^{84} +(-3.66142 + 1.18967i) q^{86} +(-13.1785 + 9.52222i) q^{87} +(2.33240 + 4.57759i) q^{88} +(3.38311 + 10.4121i) q^{89} +(0.0992002 - 0.305307i) q^{91} +(-2.64090 + 0.418278i) q^{92} +(3.18124 + 2.32404i) q^{93} +(-5.96725 + 8.21321i) q^{94} +(-1.22794 + 1.22154i) q^{96} +(9.96799 + 1.57877i) q^{97} +(-3.15676 + 6.19548i) q^{98} +(-14.6830 + 4.68606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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