LMFDB - Embedded newform 925.2.bb.e.876.5

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			876.5
Character	$\chi$	$=$	925.876
Dual form			925.2.bb.e.151.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.829326 - 0.988352i) q^{2} +(-0.303732 - 0.254862i) q^{3} +(0.0582378 - 0.330283i) q^{4} +0.511558i q^{6} +(-0.177770 + 0.0647030i) q^{7} +(-2.60943 + 1.50656i) q^{8} +(-0.493646 - 2.79960i) q^{9} +(-2.43203 - 4.21239i) q^{11} +(-0.101865 + 0.0854751i) q^{12} +(5.86686 + 1.03449i) q^{13} +(0.211379 + 0.122040i) q^{14} +(3.02277 + 1.10020i) q^{16} +(-3.55082 + 0.626106i) q^{17} +(-2.35760 + 2.80968i) q^{18} +(2.25395 - 2.68616i) q^{19} +(0.0704849 + 0.0256544i) q^{21} +(-2.14639 + 5.89714i) q^{22} +(-2.41225 - 1.39271i) q^{23} +(1.17653 + 0.207454i) q^{24} +(-3.84310 - 6.65645i) q^{26} +(-1.15832 + 2.00626i) q^{27} +(0.0110174 + 0.0624827i) q^{28} +(-6.12379 + 3.53557i) q^{29} -1.01083i q^{31} +(0.641610 + 1.76281i) q^{32} +(-0.334893 + 1.89927i) q^{33} +(3.56360 + 2.99022i) q^{34} -0.953411 q^{36} +(-4.05887 + 4.53051i) q^{37} -4.52413 q^{38} +(-1.51830 - 1.80944i) q^{39} +(-0.0118099 + 0.0669770i) q^{41} +(-0.0330994 - 0.0909397i) q^{42} -9.36105i q^{43} +(-1.53292 + 0.557937i) q^{44} +(0.624051 + 3.53917i) q^{46} +(0.984975 - 1.70603i) q^{47} +(-0.637715 - 1.10455i) q^{48} +(-5.33490 + 4.47651i) q^{49} +(1.23807 + 0.714801i) q^{51} +(0.683346 - 1.87748i) q^{52} +(-5.76016 - 2.09653i) q^{53} +(2.94352 - 0.519022i) q^{54} +(0.366400 - 0.436659i) q^{56} +(-1.36920 + 0.241426i) q^{57} +(8.57301 + 3.12032i) q^{58} +(1.34075 - 3.68368i) q^{59} +(4.72849 + 0.833760i) q^{61} +(-0.999056 + 0.838308i) q^{62} +(0.268898 + 0.465746i) q^{63} +(4.42694 - 7.66768i) q^{64} +(2.15488 - 1.24412i) q^{66} +(-11.6453 + 4.23855i) q^{67} +1.20924i q^{68} +(0.377729 + 1.03780i) q^{69} +(5.85405 + 4.91213i) q^{71} +(5.50589 + 6.56167i) q^{72} -12.9498 q^{73} +(7.84387 + 0.254325i) q^{74} +(-0.755927 - 0.900878i) q^{76} +(0.704896 + 0.591478i) q^{77} +(-0.529199 + 3.00124i) q^{78} +(4.89209 + 13.4409i) q^{79} +(-7.15091 + 2.60272i) q^{81} +(0.0759911 - 0.0438735i) q^{82} +(2.16097 + 12.2554i) q^{83} +(0.0125781 - 0.0217859i) q^{84} +(-9.25201 + 7.76336i) q^{86} +(2.76107 + 0.486852i) q^{87} +(12.6924 + 7.32796i) q^{88} +(3.16477 - 8.69512i) q^{89} +(-1.10989 + 0.195703i) q^{91} +(-0.600474 + 0.715617i) q^{92} +(-0.257622 + 0.307022i) q^{93} +(-2.50302 + 0.441350i) q^{94} +(0.254395 - 0.698945i) q^{96} +(-7.42712 - 4.28805i) q^{97} +(8.84873 + 1.56027i) q^{98} +(-10.5925 + 8.88814i) 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 $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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 $

$2$	−0.829326	−	0.988352i	−0.586422	−	0.698871i	0.388492	−	0.921452i	$-0.372996\pi$
$2$	−0.829326	−	0.988352i	−0.586422	−	0.698871i	−0.974914	+	0.222582i	$0.928552\pi$
$3$	−0.303732	−	0.254862i	−0.175360	−	0.147144i	0.550883	−	0.834582i	$-0.314291\pi$
$3$	−0.303732	−	0.254862i	−0.175360	−	0.147144i	−0.726243	+	0.687438i	$0.758735\pi$
$4$	0.0582378	−	0.330283i	0.0291189	−	0.165142i
$5$		0			0
$5$		0			0
$6$			0.511558i			0.208843i
$7$	−0.177770	+	0.0647030i	−0.0671908	+	0.0244554i	−0.375397	−	0.926864i	$-0.622494\pi$
$7$	−0.177770	+	0.0647030i	−0.0671908	+	0.0244554i	0.308206	+	0.951320i	$0.400271\pi$
$8$	−2.60943	+	1.50656i	−0.922573	+	0.532648i
$9$	−0.493646	−	2.79960i	−0.164549	−	0.933201i
$10$		0			0
$11$	−2.43203	−	4.21239i	−0.733283	−	1.27008i	−0.955472	−	0.295080i	$-0.904654\pi$
$11$	−2.43203	−	4.21239i	−0.733283	−	1.27008i	0.222189	−	0.975004i	$-0.428680\pi$
$12$	−0.101865	+	0.0854751i	−0.0294060	+	0.0246745i
$13$	5.86686	+	1.03449i	1.62717	+	0.286915i	0.911432	−	0.411450i	$-0.134978\pi$
$13$	5.86686	+	1.03449i	1.62717	+	0.286915i	0.715742	+	0.698365i	$0.246089\pi$
$14$	0.211379	+	0.122040i	0.0564934	+	0.0326165i
$15$		0			0
$16$	3.02277	+	1.10020i	0.755693	+	0.275050i
$17$	−3.55082	+	0.626106i	−0.861201	+	0.151853i	−0.586770	−	0.809754i	$-0.699601\pi$
$17$	−3.55082	+	0.626106i	−0.861201	+	0.151853i	−0.274431	+	0.961607i	$0.588490\pi$
$18$	−2.35760	+	2.80968i	−0.555692	+	0.662248i
$19$	2.25395	−	2.68616i	0.517092	−	0.616246i	−0.442799	−	0.896621i	$-0.646014\pi$
$19$	2.25395	−	2.68616i	0.517092	−	0.616246i	0.959891	+	0.280375i	$0.0904588\pi$
$20$		0			0
$21$	0.0704849	+	0.0256544i	0.0153811	+	0.00559825i
$22$	−2.14639	+	5.89714i	−0.457611	+	1.25728i
$23$	−2.41225	−	1.39271i	−0.502989	−	0.290401i	0.226958	−	0.973905i	$-0.427122\pi$
$23$	−2.41225	−	1.39271i	−0.502989	−	0.290401i	−0.729947	+	0.683504i	$0.760455\pi$
$24$	1.17653	+	0.207454i	0.240158	+	0.0423464i
$25$		0			0
$26$	−3.84310	−	6.65645i	−0.753694	−	1.30544i
$27$	−1.15832	+	2.00626i	−0.222918	+	0.386106i
$28$	0.0110174	+	0.0624827i	0.00208209	+	0.0118081i
$29$	−6.12379	+	3.53557i	−1.13716	+	0.656539i	−0.945726	−	0.324966i	$-0.894647\pi$
$29$	−6.12379	+	3.53557i	−1.13716	+	0.656539i	−0.191434	+	0.981506i	$0.561314\pi$
$30$		0			0
$31$		−	1.01083i		−	0.181550i	−0.995871	−	0.0907752i	$-0.971066\pi$
$31$		−	1.01083i		−	0.181550i	0.995871	−	0.0907752i	$-0.0289345\pi$
$32$	0.641610	+	1.76281i	0.113422	+	0.311624i
$33$	−0.334893	+	1.89927i	−0.0582973	+	0.330621i
$34$	3.56360	+	2.99022i	0.611153	+	0.512818i
$35$		0			0
$36$	−0.953411			−0.158902
$37$	−4.05887	+	4.53051i	−0.667275	+	0.744812i
$37$	−4.05887	+	4.53051i	−0.667275	+	0.744812i
$38$	−4.52413			−0.733910
$39$	−1.51830	−	1.80944i	−0.243123	−	0.289743i
$40$		0			0
$41$	−0.0118099	+	0.0669770i	−0.00184439	+	0.0104601i	−0.985716	−	0.168416i	$-0.946135\pi$
$41$	−0.0118099	+	0.0669770i	−0.00184439	+	0.0104601i	0.983872	+	0.178876i	$0.0572460\pi$
$42$	−0.0330994	−	0.0909397i	−0.00510734	−	0.0140323i
$43$		−	9.36105i		−	1.42755i	−0.700377	−	0.713773i	$-0.746985\pi$
$43$		−	9.36105i		−	1.42755i	0.700377	−	0.713773i	$-0.253015\pi$
$44$	−1.53292	+	0.557937i	−0.231096	+	0.0841121i
$45$		0			0
$46$	0.624051	+	3.53917i	0.0920113	+	0.521822i
$47$	0.984975	−	1.70603i	0.143673	−	0.248850i	−0.785204	−	0.619237i	$-0.787442\pi$
$47$	0.984975	−	1.70603i	0.143673	−	0.248850i	0.928877	+	0.370388i	$0.120775\pi$
$48$	−0.637715	−	1.10455i	−0.0920462	−	0.159429i
$49$	−5.33490	+	4.47651i	−0.762128	+	0.639501i
$50$		0			0
$51$	1.23807	+	0.714801i	0.173365	+	0.100092i
$52$	0.683346	−	1.87748i	0.0947631	−	0.260359i
$53$	−5.76016	−	2.09653i	−0.791219	−	0.287980i	−0.0853760	−	0.996349i	$-0.527209\pi$
$53$	−5.76016	−	2.09653i	−0.791219	−	0.287980i	−0.705842	+	0.708369i	$0.749431\pi$
$54$	2.94352	−	0.519022i	0.400562	−	0.0706299i
$55$		0			0
$56$	0.366400	−	0.436659i	0.0489623	−	0.0583510i
$57$	−1.36920	+	0.241426i	−0.181354	+	0.0319777i
$58$	8.57301	+	3.12032i	1.12569	+	0.409718i
$59$	1.34075	−	3.68368i	0.174551	−	0.479574i	−0.821308	−	0.570484i	$-0.806755\pi$
$59$	1.34075	−	3.68368i	0.174551	−	0.479574i	0.995859	+	0.0909104i	$0.0289777\pi$
$60$		0			0
$61$	4.72849	+	0.833760i	0.605421	+	0.106752i	0.467952	−	0.883754i	$-0.344992\pi$
$61$	4.72849	+	0.833760i	0.605421	+	0.106752i	0.137469	+	0.990506i	$0.456103\pi$
$62$	−0.999056	+	0.838308i	−0.126880	+	0.106465i
$63$	0.268898	+	0.465746i	0.0338780	+	0.0586784i
$64$	4.42694	−	7.66768i	0.553367	−	0.958460i
$65$		0			0
$66$	2.15488	−	1.24412i	0.265248	−	0.153141i
$67$	−11.6453	+	4.23855i	−1.42270	+	0.517821i	−0.934830	−	0.355094i	$-0.884449\pi$
$67$	−11.6453	+	4.23855i	−1.42270	+	0.517821i	−0.487871	+	0.872916i	$0.662227\pi$
$68$			1.20924i			0.146642i
$69$	0.377729	+	1.03780i	0.0454733	+	0.124937i
$70$		0			0
$71$	5.85405	+	4.91213i	0.694748	+	0.582962i	0.920274	−	0.391275i	$-0.127966\pi$
$71$	5.85405	+	4.91213i	0.694748	+	0.582962i	−0.225526	+	0.974237i	$0.572410\pi$
$72$	5.50589	+	6.56167i	0.648875	+	0.773300i
$73$	−12.9498			−1.51566			−0.757832	−	0.652450i	$-0.773741\pi$
$73$	−12.9498			−1.51566			−0.757832	+	0.652450i	$0.773741\pi$
$74$	7.84387	+	0.254325i	0.911832	+	0.0295646i
$75$		0			0
$76$	−0.755927	−	0.900878i	−0.0867107	−	0.103338i
$77$	0.704896	+	0.591478i	0.0803304	+	0.0674052i
$78$	−0.529199	+	3.00124i	−0.0599200	+	0.339823i
$79$	4.89209	+	13.4409i	0.550403	+	1.51222i	0.833162	+	0.553029i	$0.186528\pi$
$79$	4.89209	+	13.4409i	0.550403	+	1.51222i	−0.282759	+	0.959191i	$0.591250\pi$
$80$		0			0
$81$	−7.15091	+	2.60272i	−0.794546	+	0.289191i
$82$	0.0759911	−	0.0438735i	0.00839181	−	0.00484502i
$83$	2.16097	+	12.2554i	0.237197	+	1.34521i	0.837938	+	0.545766i	$0.183761\pi$
$83$	2.16097	+	12.2554i	0.237197	+	1.34521i	−0.600741	+	0.799444i	$0.705128\pi$
$84$	0.0125781	−	0.0217859i	0.00137238	−	0.00237704i
$85$		0			0
$86$	−9.25201	+	7.76336i	−0.997670	+	0.837145i
$87$	2.76107	+	0.486852i	0.296018	+	0.0521960i
$88$	12.6924	+	7.32796i	1.35301	+	0.781163i
$89$	3.16477	−	8.69512i	0.335465	−	0.921681i	−0.651199	−	0.758907i	$-0.725734\pi$
$89$	3.16477	−	8.69512i	0.335465	−	0.921681i	0.986663	−	0.162774i	$-0.0520442\pi$
$90$		0			0
$91$	−1.10989	+	0.195703i	−0.116348	+	0.0205152i
$92$	−0.600474	+	0.715617i	−0.0626038	+	0.0746083i
$93$	−0.257622	+	0.307022i	−0.0267141	+	0.0318367i
$94$	−2.50302	+	0.441350i	−0.258167	+	0.0455218i
$95$		0			0
$96$	0.254395	−	0.698945i	0.0259641	−	0.0713357i
$97$	−7.42712	−	4.28805i	−0.754110	−	0.435385i	0.0730673	−	0.997327i	$-0.476721\pi$
$97$	−7.42712	−	4.28805i	−0.754110	−	0.435385i	−0.827177	+	0.561942i	$0.810055\pi$
$98$	8.84873	+	1.56027i	0.893857	+	0.157611i
$99$	−10.5925	+	8.88814i	−1.06458	+	0.893291i
$100$		0			0
$101$	−2.15041	+	3.72462i	−0.213974	+	0.370614i	−0.952955	−	0.303113i	$-0.901974\pi$
$101$	−2.15041	+	3.72462i	−0.213974	+	0.370614i	0.738981	+	0.673727i	$0.235307\pi$
$102$	−0.320290	−	1.81645i	−0.0317134	−	0.179856i
$103$	5.54414	−	3.20091i	0.546281	−	0.315395i	−0.201340	−	0.979521i	$-0.564530\pi$
$103$	5.54414	−	3.20091i	0.546281	−	0.315395i	0.747621	+	0.664126i	$0.231196\pi$
$104$	−16.8677	+	6.13933i	−1.65401	+	0.602011i
$105$		0			0
$106$	2.70494	+	7.43177i	0.262727	+	0.721837i
$107$	1.70761	−	9.68433i	0.165081	−	0.936219i	−0.783900	−	0.620887i	$-0.786773\pi$
$107$	1.70761	−	9.68433i	0.165081	−	0.936219i	0.948981	−	0.315333i	$-0.102116\pi$
$108$	0.595178	+	0.499413i	0.0572710	+	0.0480561i
$109$	−5.21425	−	6.21411i	−0.499435	−	0.595203i	0.456156	−	0.889900i	$-0.349226\pi$
$109$	−5.21425	−	6.21411i	−0.499435	−	0.595203i	−0.955591	+	0.294696i	$0.904781\pi$
$110$		0			0
$111$	2.38747	−	0.341612i	0.226608	−	0.0324244i
$112$	−0.608544			−0.0575020
$113$	−5.46115	−	6.50835i	−0.513742	−	0.612254i	0.445347	−	0.895358i	$-0.353080\pi$
$113$	−5.46115	−	6.50835i	−0.513742	−	0.612254i	−0.959089	+	0.283104i	$0.908636\pi$
$114$	1.37412	+	1.15303i	0.128699	+	0.107991i
$115$		0			0
$116$	0.811104	+	2.22849i	0.0753091	+	0.206910i
$117$		−	16.9356i		−	1.56569i
$118$	−4.75269	+	1.72984i	−0.437521	+	0.159244i
$119$	0.590720	−	0.341052i	0.0541512	−	0.0312642i
$120$		0			0
$121$	−6.32950	+	10.9630i	−0.575409	+	0.996638i
$122$	−3.09741	−	5.36487i	−0.280426	−	0.485713i
$123$	0.0206569	−	0.0173332i	0.00186257	−	0.00156288i
$124$	−0.333860	−	0.0588685i	−0.0299815	−	0.00528655i
$125$		0			0
$126$	0.237316	−	0.652021i	0.0211418	−	0.0580867i
$127$	18.3175	+	6.66702i	1.62541	+	0.591603i	0.984403	−	0.175929i	$-0.0562928\pi$
$127$	18.3175	+	6.66702i	1.62541	+	0.591603i	0.641012	+	0.767531i	$0.278515\pi$
$128$	−7.55486	+	1.33213i	−0.667761	+	0.117744i
$129$	−2.38577	+	2.84325i	−0.210056	+	0.250334i
$130$		0			0
$131$	6.51091	−	1.14805i	0.568860	−	0.100305i	0.118182	−	0.992992i	$-0.462293\pi$
$131$	6.51091	−	1.14805i	0.568860	−	0.100305i	0.450678	+	0.892686i	$0.351182\pi$
$132$	0.607794	+	0.221219i	0.0529016	+	0.0192546i
$133$	−0.226883	+	0.623356i	−0.0196732	+	0.0540518i
$134$	13.8469	+	7.99454i	1.19619	+	0.690623i
$135$		0			0
$136$	8.32236	−	6.98329i	0.713637	−	0.598812i
$137$	1.88778	+	3.26974i	0.161284	+	0.279352i	0.935329	−	0.353778i	$-0.115103\pi$
$137$	1.88778	+	3.26974i	0.161284	+	0.279352i	−0.774045	+	0.633130i	$0.781770\pi$
$138$	0.712454	−	1.23401i	0.0606481	−	0.105046i
$139$	−2.51398	−	14.2575i	−0.213233	−	1.20931i	−0.883946	−	0.467588i	$-0.845123\pi$
$139$	−2.51398	−	14.2575i	−0.213233	−	1.20931i	0.670713	−	0.741717i	$-0.265988\pi$
$140$		0			0
$141$	−0.733970	+	0.267143i	−0.0618114	+	0.0224975i
$142$		−	9.85962i		−	0.827401i
$143$	−9.91069	−	27.2294i	−0.828774	−	2.27704i
$144$	1.58794	−	9.00567i	0.132328	−	0.750472i
$145$		0			0
$146$	10.7396	+	12.7990i	0.888819	+	1.05925i
$147$	2.76127			0.227746
$148$	1.25997	+	1.60442i	0.103569	+	0.131883i
$149$	−0.934593			−0.0765649			−0.0382824	−	0.999267i	$-0.512189\pi$
$149$	−0.934593			−0.0765649			−0.0382824	+	0.999267i	$0.512189\pi$
$150$		0			0
$151$	−13.2126	−	11.0867i	−1.07523	−	0.902223i	−0.0797113	−	0.996818i	$-0.525400\pi$
$151$	−13.2126	−	11.0867i	−1.07523	−	0.902223i	−0.995516	+	0.0945953i	$0.969844\pi$
$152$	−1.83469	+	10.4050i	−0.148813	+	0.843960i
$153$	3.50570	+	9.63183i	0.283419	+	0.778687i
$154$		−	1.18721i		−	0.0956684i
$155$		0			0
$156$	−0.686052	+	0.396092i	−0.0549281	+	0.0317128i
$157$	0.0730161	+	0.414095i	0.00582732	+	0.0330484i	0.987583	−	0.157100i	$-0.0502144\pi$
$157$	0.0730161	+	0.414095i	0.00582732	+	0.0330484i	−0.981755	+	0.190148i	$0.939103\pi$
$158$	9.22721	−	15.9820i	0.734077	−	1.27146i
$159$	1.21522	+	2.10483i	0.0963734	+	0.166924i
$160$		0			0
$161$	0.518939	+	0.0915030i	0.0408981	+	0.00721144i
$162$	8.50284	+	4.90912i	0.668046	+	0.385697i
$163$	2.23369	−	6.13703i	0.174956	−	0.480689i	−0.820958	−	0.570988i	$-0.806560\pi$
$163$	2.23369	−	6.13703i	0.174956	−	0.480689i	0.995915	+	0.0902993i	$0.0287824\pi$
$164$	0.0214336	+	0.00780119i	0.00167368	+	0.000609171i
$165$		0			0
$166$	10.3205	−	12.2996i	0.801030	−	0.954630i
$167$	8.78444	−	10.4689i	0.679760	−	0.810107i	−0.310317	−	0.950633i	$-0.600435\pi$
$167$	8.78444	−	10.4689i	0.679760	−	0.810107i	0.990077	+	0.140526i	$0.0448795\pi$
$168$	−0.222575	+	0.0392460i	−0.0171720	+	0.00302789i
$169$	21.1339	+	7.69210i	1.62568	+	0.591700i
$170$		0			0
$171$	−8.63282	−	4.98416i	−0.660169	−	0.381148i
$172$	−3.09180	−	0.545167i	−0.235747	−	0.0415686i
$173$	0.790269	−	0.663114i	0.0600830	−	0.0504156i	−0.612252	−	0.790663i	$-0.709736\pi$
$173$	0.790269	−	0.663114i	0.0600830	−	0.0504156i	0.672335	+	0.740247i	$0.265292\pi$
$174$	−1.80865	−	3.13267i	−0.137113	−	0.237487i
$175$		0			0
$176$	−2.71699	−	15.4088i	−0.204801	−	1.16148i
$177$	−1.34606	+	0.777147i	−0.101176	+	0.0584139i
$178$	−11.2185	+	4.08319i	−0.840860	+	0.306048i
$179$		−	7.08812i		−	0.529791i	−0.964277	−	0.264896i	$-0.914663\pi$
$179$		−	7.08812i		−	0.529791i	0.964277	−	0.264896i	$-0.0853375\pi$
$180$		0			0
$181$	2.53037	−	14.3505i	0.188081	−	1.06666i	−0.733851	−	0.679310i	$-0.762279\pi$
$181$	2.53037	−	14.3505i	0.188081	−	1.06666i	0.921932	−	0.387351i	$-0.126610\pi$
$182$	1.11388	+	0.934657i	0.0825664	+	0.0692814i
$183$	−1.22370	−	1.45835i	−0.0904586	−	0.107804i
$184$	8.39280			0.618726
$185$		0			0
$186$	0.517098			0.0379155
$187$	11.2731	+	13.4348i	0.824371	+	0.982447i
$188$	−0.506109	−	0.424676i	−0.0369118	−	0.0309727i
$189$	0.0761028	−	0.431601i	0.00553567	−	0.0313943i
$190$		0			0
$191$			21.4074i			1.54899i	0.632583	+	0.774493i	$0.281995\pi$
$191$			21.4074i			1.54899i	−0.632583	+	0.774493i	$0.718005\pi$
$192$	−3.29880	+	1.20067i	−0.238071	+	0.0866506i
$193$	1.17525	−	0.678529i	0.0845961	−	0.0488416i	−0.457105	−	0.889413i	$-0.651114\pi$
$193$	1.17525	−	0.678529i	0.0845961	−	0.0488416i	0.541701	+	0.840571i	$0.317780\pi$
$194$	1.92140	+	10.8968i	0.137948	+	0.782344i
$195$		0			0
$196$	1.16782	+	2.02273i	0.0834159	+	0.144481i
$197$	11.6506	−	9.77603i	0.830072	−	0.696513i	−0.125235	−	0.992127i	$-0.539969\pi$
$197$	11.6506	−	9.77603i	0.830072	−	0.696513i	0.955308	+	0.295614i	$0.0955241\pi$
$198$	17.5692	+	3.09793i	1.24859	+	0.220160i
$199$	−2.55910	−	1.47750i	−0.181410	−	0.104737i	0.406545	−	0.913631i	$-0.366733\pi$
$199$	−2.55910	−	1.47750i	−0.181410	−	0.104737i	−0.587955	+	0.808894i	$0.700067\pi$
$200$		0			0
$201$	4.61730	+	1.68056i	0.325679	+	0.118538i
$202$	5.46463	−	0.963562i	0.384490	−	0.0677960i
$203$	0.859865	−	1.02475i	0.0603507	−	0.0719231i
$204$	0.308189	−	0.367286i	0.0215776	−	0.0257151i
$205$		0			0
$206$	−7.76153	−	2.82497i	−0.540772	−	0.196825i
$207$	−2.70825	+	7.44086i	−0.188236	+	0.517175i
$208$	16.5960	+	9.58172i	1.15073	+	0.664373i
$209$	−16.7968	−	2.96173i	−1.16186	−	0.204867i
$210$		0			0
$211$	−7.03980	−	12.1933i	−0.484640	−	0.839420i	0.515205	−	0.857067i	$-0.327716\pi$
$211$	−7.03980	−	12.1933i	−0.484640	−	0.839420i	−0.999844	+	0.0176468i	$0.994383\pi$
$212$	−1.02791	+	1.78039i	−0.0705969	+	0.122277i
$213$	−0.526150	−	2.98394i	−0.0360512	−	0.204457i
$214$	−10.9877	+	6.34375i	−0.751103	+	0.433650i
$215$		0			0
$216$		−	6.98028i		−	0.474948i
$217$	0.0654038	+	0.179695i	0.00443990	+	0.0121985i
$218$	−1.81741	+	10.3070i	−0.123090	+	0.698081i
$219$	3.93328	+	3.30042i	0.265787	+	0.223022i
$220$		0			0
$221$	−21.4799			−1.44489
$222$	−2.31762	−	2.07635i	−0.155548	−	0.139355i
$223$	1.05240			0.0704742			0.0352371	−	0.999379i	$-0.488781\pi$
$223$	1.05240			0.0704742			0.0352371	+	0.999379i	$0.488781\pi$
$224$	−0.228118	−	0.271861i	−0.0152418	−	0.0181645i
$225$		0			0
$226$	−1.90347	+	10.7951i	−0.126617	+	0.718079i
$227$	−1.08108	−	2.97024i	−0.0717538	−	0.197142i	0.898632	−	0.438704i	$-0.144562\pi$
$227$	−1.08108	−	2.97024i	−0.0717538	−	0.197142i	−0.970385	+	0.241562i	$0.922340\pi$
$228$			0.466283i			0.0308803i
$229$	23.4029	−	8.51795i	1.54650	−	0.562882i	0.578910	−	0.815391i	$-0.303478\pi$
$229$	23.4029	−	8.51795i	1.54650	−	0.562882i	0.967594	+	0.252510i	$0.0812559\pi$
$230$		0			0
$231$	−0.0633547	−	0.359302i	−0.00416843	−	0.0236403i
$232$	10.6531	−	18.4517i	0.699408	−	1.21141i
$233$	−11.9122	−	20.6326i	−0.780397	−	1.35169i	−0.931711	−	0.363201i	$-0.881684\pi$
$233$	−11.9122	−	20.6326i	−0.780397	−	1.35169i	0.151314	−	0.988486i	$-0.451650\pi$
$234$	−16.7383	+	14.0451i	−1.09422	+	0.918156i
$235$		0			0
$236$	−1.13857	−	0.657356i	−0.0741149	−	0.0427903i
$237$	1.93969	−	5.32924i	0.125996	−	0.346172i
$238$	−0.826979	−	0.300996i	−0.0536051	−	0.0195106i
$239$	−9.23526	+	1.62842i	−0.597379	+	0.105334i	−0.464158	−	0.885752i	$-0.653643\pi$
$239$	−9.23526	+	1.62842i	−0.597379	+	0.105334i	−0.133221	+	0.991086i	$0.542532\pi$
$240$		0			0
$241$	11.2471	−	13.4038i	0.724491	−	0.863415i	−0.270568	−	0.962701i	$-0.587212\pi$
$241$	11.2471	−	13.4038i	0.724491	−	0.863415i	0.995059	+	0.0992862i	$0.0316559\pi$
$242$	16.0845	−	2.83614i	1.03395	−	0.182314i
$243$	9.36607	+	3.40897i	0.600834	+	0.218686i
$244$	0.550754	−	1.51318i	0.0352584	−	0.0968717i
$245$		0			0
$246$	−0.0342626	−	0.00604143i	−0.00218451	−	0.000385187i
$247$	16.0024	−	13.4276i	1.01821	−	0.854379i
$248$	1.52287	+	2.63769i	0.0967024	+	0.167493i
$249$	2.46709	−	4.27312i	0.156345	−	0.270798i
$250$		0			0
$251$	17.5716	−	10.1450i	1.10911	−	0.640346i	0.170513	−	0.985355i	$-0.445458\pi$
$251$	17.5716	−	10.1450i	1.10911	−	0.640346i	0.938599	+	0.345009i	$0.112124\pi$
$252$	0.169488	−	0.0616886i	0.0106767	−	0.00388602i
$253$			13.5485i			0.851785i
$254$	−8.60181	−	23.6333i	−0.539725	−	1.48288i
$255$		0			0
$256$	−5.98288	−	5.02023i	−0.373930	−	0.313764i
$257$	−18.2962	−	21.8046i	−1.14129	−	1.36013i	−0.923254	−	0.384190i	$-0.874481\pi$
$257$	−18.2962	−	21.8046i	−1.14129	−	1.36013i	−0.218032	−	0.975942i	$-0.569964\pi$
$258$	4.78872			0.298133
$259$	0.428409	−	1.06801i	0.0266200	−	0.0663630i
$260$		0			0
$261$	12.9212	+	15.3989i	0.799801	+	0.953166i
$262$	−6.53434	−	5.48296i	−0.403693	−	0.338739i
$263$	2.27693	−	12.9131i	0.140402	−	0.796257i	−0.830543	−	0.556954i	$-0.811970\pi$
$263$	2.27693	−	12.9131i	0.140402	−	0.796257i	0.970945	−	0.239303i	$-0.0769189\pi$
$264$	−1.98748	−	5.46055i	−0.122321	−	0.336073i
$265$		0			0
$266$	0.804255	−	0.292725i	0.0493120	−	0.0179481i
$267$	−3.17730	+	1.83441i	−0.194447	+	0.112264i
$268$	0.721723	+	4.09310i	0.0440863	+	0.250026i
$269$	−0.700788	+	1.21380i	−0.0427278	+	0.0740067i	−0.886598	−	0.462540i	$-0.846938\pi$
$269$	−0.700788	+	1.21380i	−0.0427278	+	0.0740067i	0.843871	+	0.536547i	$0.180271\pi$
$270$		0			0
$271$	12.2350	−	10.2664i	0.743226	−	0.623640i	−0.190476	−	0.981692i	$-0.561003\pi$
$271$	12.2350	−	10.2664i	0.743226	−	0.623640i	0.933702	+	0.358051i	$0.116559\pi$
$272$	−11.4222	−	2.01404i	−0.692571	−	0.122119i
$273$	0.386986	+	0.223426i	0.0234214	+	0.0135224i
$274$	1.66606	−	4.57747i	0.100651	−	0.276535i
$275$		0			0
$276$	0.364767	−	0.0643183i	0.0219564	−	0.00387150i
$277$	−1.11381	+	1.32739i	−0.0669223	+	0.0797549i	−0.798467	−	0.602039i	$-0.794355\pi$
$277$	−1.11381	+	1.32739i	−0.0669223	+	0.0797549i	0.731545	+	0.681794i	$0.238800\pi$
$278$	−12.0065	+	14.3088i	−0.720103	+	0.858185i
$279$	−2.82992	+	0.498992i	−0.169423	+	0.0298739i
$280$		0			0
$281$	3.57639	−	9.82605i	0.213350	−	0.586173i	−0.786142	−	0.618045i	$-0.787925\pi$
$281$	3.57639	−	9.82605i	0.213350	−	0.586173i	0.999492	+	0.0318722i	$0.0101470\pi$
$282$	0.872732	+	0.503872i	0.0519704	+	0.0300051i
$283$	−4.65110	−	0.820115i	−0.276479	−	0.0487508i	0.0336891	−	0.999432i	$-0.489274\pi$
$283$	−4.65110	−	0.820115i	−0.276479	−	0.0487508i	−0.310169	+	0.950682i	$0.600385\pi$
$284$	1.96332	−	1.64742i	0.116502	−	0.0977565i
$285$		0			0
$286$	−18.6931	+	32.3773i	−1.10534	+	1.91451i
$287$	−0.00223418	−	0.0126706i	−0.000131879	−	0.000747925i
$288$	4.61844	−	2.66646i	0.272144	−	0.157123i
$289$	−3.75843	+	1.36796i	−0.221084	+	0.0804680i
$290$		0			0
$291$	1.16300	+	3.19531i	0.0681761	+	0.187312i
$292$	−0.754170	+	4.27711i	−0.0441345	+	0.250299i
$293$	2.06619	+	1.73374i	0.120708	+	0.101286i	0.701144	−	0.713020i	$-0.252673\pi$
$293$	2.06619	+	1.73374i	0.120708	+	0.101286i	−0.580435	+	0.814306i	$0.697118\pi$
$294$	−2.28999	−	2.72911i	−0.133555	−	0.159165i
$295$		0			0
$296$	3.76588	−	17.9370i	0.218887	−	1.04257i
$297$	11.2682			0.653849
$298$	0.775083	+	0.923707i	0.0448993	+	0.0535089i
$299$	−12.7116	−	10.6663i	−0.735131	−	0.616848i
$300$		0			0
$301$	0.605688	+	1.66411i	0.0349113	+	0.0959180i
$302$			22.2532i			1.28053i
$303$	1.60241	−	0.583231i	0.0920563	−	0.0335057i
$304$	9.76848	−	5.63984i	0.560261	−	0.323467i
$305$		0			0
$306$	6.61227	−	11.4528i	0.377998	−	0.654712i
$307$	−6.46425	−	11.1964i	−0.368934	−	0.639012i	0.620465	−	0.784234i	$-0.286944\pi$
$307$	−6.46425	−	11.1964i	−0.368934	−	0.639012i	−0.989399	+	0.145222i	$0.953611\pi$
$308$	0.236407	−	0.198369i	0.0134705	−	0.0113031i
$309$	−2.49973	−	0.440769i	−0.142204	−	0.0250745i
$310$		0			0
$311$	−4.83937	+	13.2961i	−0.274415	+	0.753950i	0.723555	+	0.690267i	$0.242507\pi$
$311$	−4.83937	+	13.2961i	−0.274415	+	0.753950i	−0.997970	+	0.0636831i	$0.979715\pi$
$312$	6.68794	+	2.43421i	0.378630	+	0.137810i
$313$	−8.63725	+	1.52298i	−0.488207	+	0.0860840i	−0.412332	−	0.911033i	$-0.635286\pi$
$313$	−8.63725	+	1.52298i	−0.488207	+	0.0860840i	−0.0758740	+	0.997117i	$0.524175\pi$
$314$	0.348717	−	0.415585i	0.0196793	−	0.0234528i
$315$		0			0
$316$	4.72421	−	0.833005i	0.265758	−	0.0468602i
$317$	−7.62847	−	2.77654i	−0.428458	−	0.155946i	0.118785	−	0.992920i	$-0.462100\pi$
$317$	−7.62847	−	2.77654i	−0.428458	−	0.155946i	−0.547242	+	0.836974i	$0.684322\pi$
$318$	1.07249	−	2.94665i	0.0601425	−	0.165240i
$319$	29.7864	+	17.1972i	1.66772	+	0.962858i
$320$		0			0
$321$	−2.98682	+	2.50624i	−0.166708	+	0.139885i
$322$	−0.339933	−	0.588780i	−0.0189437	−	0.0328115i
$323$	−6.32157	+	10.9493i	−0.351741	+	0.609234i
$324$	0.443181	+	2.51340i	0.0246212	+	0.139634i
$325$		0			0
$326$	−7.91800	+	2.88192i	−0.438538	+	0.159615i
$327$			3.21634i			0.177864i
$328$	−0.0700876	−	0.192564i	−0.00386994	−	0.0106326i
$329$	−0.0647140	+	0.367011i	−0.00356780	+	0.0202340i
$330$		0			0
$331$	−3.56956	−	4.25404i	−0.196201	−	0.233823i	0.658970	−	0.752169i	$-0.270992\pi$
$331$	−3.56956	−	4.25404i	−0.196201	−	0.233823i	−0.855171	+	0.518346i	$0.826548\pi$
$332$	4.17362			0.229057
$333$	14.6873	+	9.12677i	0.804858	+	0.500144i
$334$	−17.6321			−0.964786
$335$		0			0
$336$	0.184835	+	0.155095i	0.0100836	+	0.00846111i
$337$	−1.40048	+	7.94251i	−0.0762890	+	0.432656i	0.922610	+	0.385735i	$0.126052\pi$
$337$	−1.40048	+	7.94251i	−0.0762890	+	0.432656i	−0.998899	+	0.0469213i	$0.985059\pi$
$338$	−9.92437	−	27.2670i	−0.539814	−	1.48313i
$339$			3.36864i			0.182959i
$340$		0			0
$341$	−4.25801	+	2.45836i	−0.230584	+	0.133128i
$342$	2.23332	+	12.6658i	0.120764	+	0.684886i
$343$	1.32087	−	2.28781i	0.0713202	−	0.123530i
$344$	14.1029	+	24.4270i	0.760379	+	1.31702i
$345$		0			0
$346$	−1.31078	−	0.231126i	−0.0704680	−	0.0124254i
$347$	−17.1268	−	9.88814i	−0.919413	−	0.530823i	−0.0359651	−	0.999353i	$-0.511451\pi$
$347$	−17.1268	−	9.88814i	−0.919413	−	0.530823i	−0.883448	+	0.468530i	$0.844784\pi$
$348$	0.321598	−	0.883583i	0.0172395	−	0.0473650i
$349$	−5.94041	−	2.16213i	−0.317983	−	0.115736i	0.178098	−	0.984013i	$-0.443006\pi$
$349$	−5.94041	−	2.16213i	−0.317983	−	0.115736i	−0.496080	+	0.868277i	$0.665228\pi$
$350$		0			0
$351$	−8.87114	+	10.5722i	−0.473506	+	0.564303i
$352$	5.86524	−	6.98992i	0.312618	−	0.372564i
$353$	9.34639	−	1.64802i	0.497458	−	0.0877153i	0.0807107	−	0.996738i	$-0.474281\pi$
$353$	9.34639	−	1.64802i	0.497458	−	0.0877153i	0.416748	+	0.909022i	$0.363170\pi$
$354$	1.88441	+	0.685871i	0.100156	+	0.0364536i
$355$		0			0
$356$	−2.68754	−	1.55165i	−0.142440	−	0.0822375i
$357$	−0.266342	−	0.0469632i	−0.0140963	−	0.00248556i
$358$	−7.00556	+	5.87836i	−0.370255	+	0.310681i
$359$	17.1116	+	29.6382i	0.903116	+	1.56424i	0.823426	+	0.567424i	$0.192060\pi$
$359$	17.1116	+	29.6382i	0.903116	+	1.56424i	0.0796904	+	0.996820i	$0.474607\pi$
$360$		0			0
$361$	1.16418	+	6.60242i	0.0612729	+	0.347496i
$362$	−16.2818	+	9.40031i	−0.855753	+	0.494069i
$363$	4.71653	−	1.71668i	0.247553	−	0.0901021i
$364$			0.377974i			0.0198112i
$365$		0			0
$366$	−0.426517	+	2.41890i	−0.0222944	+	0.126438i
$367$	23.4148	+	19.6474i	1.22224	+	1.02558i	0.998704	+	0.0508901i	$0.0162058\pi$
$367$	23.4148	+	19.6474i	1.22224	+	1.02558i	0.223540	+	0.974695i	$0.428239\pi$
$368$	−5.75942	−	6.86381i	−0.300231	−	0.357801i
$369$	0.193339			0.0100648
$370$		0			0
$371$	1.15964			0.0602053
$372$	0.0864008	+	0.102968i	0.00447967	+	0.00533867i
$373$	5.53097	+	4.64103i	0.286383	+	0.240303i	0.774649	−	0.632391i	$-0.217926\pi$
$373$	5.53097	+	4.64103i	0.286383	+	0.240303i	−0.488267	+	0.872694i	$0.662371\pi$
$374$	3.92920	−	22.2836i	0.203174	−	1.15226i
$375$		0			0
$376$			5.93568i			0.306109i
$377$	−39.5849	+	14.4077i	−2.03873	+	0.742036i
$378$	−0.489687	+	0.282721i	−0.0251868	+	0.0145416i
$379$	−1.18565	−	6.72418i	−0.0609030	−	0.345398i	−0.999998	−	0.00174171i	$-0.999446\pi$
$379$	−1.18565	−	6.72418i	−0.0609030	−	0.345398i	0.939095	−	0.343656i	$-0.111666\pi$
$380$		0			0
$381$	−3.86445	−	6.69342i	−0.197982	−	0.342914i
$382$	21.1581	−	17.7537i	1.08254	−	0.908359i
$383$	−30.3978	−	5.35995i	−1.55325	−	0.273880i	−0.669851	−	0.742496i	$-0.733642\pi$
$383$	−30.3978	−	5.35995i	−1.55325	−	0.273880i	−0.883402	+	0.468615i	$0.844753\pi$
$384$	2.63416	+	1.52083i	0.134424	+	0.0776097i
$385$		0			0
$386$	−1.64529	−	0.598836i	−0.0837430	−	0.0304799i
$387$	−26.2072	+	4.62104i	−1.33219	+	0.234901i
$388$	−1.84881	+	2.20333i	−0.0938591	+	0.111857i
$389$	−3.26483	+	3.89087i	−0.165534	+	0.197275i	−0.842434	−	0.538799i	$-0.818878\pi$
$389$	−3.26483	+	3.89087i	−0.165534	+	0.197275i	0.676901	+	0.736074i	$0.263323\pi$
$390$		0			0
$391$	9.43747	+	3.43496i	0.477273	+	0.173713i
$392$	7.17693	−	19.7185i	0.362490	−	0.995932i
$393$	−2.27017	−	1.31068i	−0.114515	−	0.0661151i
$394$	−19.3243	−	3.40740i	−0.973545	−	0.171662i
$395$		0			0
$396$	2.31872	+	4.01614i	0.116520	+	0.201819i
$397$	−19.3050	+	33.4372i	−0.968889	+	1.67817i	−0.270107	+	0.962830i	$0.587059\pi$
$397$	−19.3050	+	33.4372i	−0.968889	+	1.67817i	−0.698782	+	0.715335i	$0.746274\pi$
$398$	0.662041	+	3.75462i	0.0331851	+	0.188202i
$399$	0.227781	−	0.131510i	0.0114033	−	0.00658371i
$400$		0			0
$401$		−	23.2705i		−	1.16207i	−0.813878	−	0.581036i	$-0.802648\pi$
$401$		−	23.2705i		−	1.16207i	0.813878	−	0.581036i	$-0.197352\pi$
$402$	−2.16826	−	5.95725i	−0.108143	−	0.297121i
$403$	1.04569	−	5.93040i	0.0520895	−	0.295414i
$404$	1.10495	+	0.927159i	0.0549731	+	0.0461279i
$405$		0			0
$406$	−1.72592			−0.0856559
$407$	28.9556	+	6.07924i	1.43527	+	0.301337i
$408$	−4.30755			−0.213255
$409$	10.5652	+	12.5912i	0.522418	+	0.622593i	0.961151	−	0.276024i	$-0.0890170\pi$
$409$	10.5652	+	12.5912i	0.522418	+	0.622593i	−0.438733	+	0.898618i	$0.644573\pi$
$410$		0			0
$411$	0.259950	−	1.47425i	0.0128224	−	0.0727193i
$412$	−0.734329	−	2.01755i	−0.0361778	−	0.0993977i
$413$			0.741598i			0.0364917i
$414$	9.60021	−	3.49419i	0.471825	−	0.171730i
$415$		0			0
$416$	1.94064	+	11.0059i	0.0951475	+	0.539609i
$417$	−2.87011	+	4.97118i	−0.140550	+	0.243440i
$418$	11.0028	+	19.0574i	0.538164	+	0.932128i
$419$	−10.3588	+	8.69210i	−0.506063	+	0.424637i	−0.859741	−	0.510730i	$-0.829375\pi$
$419$	−10.3588	+	8.69210i	−0.506063	+	0.424637i	0.353678	+	0.935367i	$0.384931\pi$
$420$		0			0
$421$	16.8939	+	9.75371i	0.823360	+	0.475367i	0.851574	−	0.524235i	$-0.175649\pi$
$421$	16.8939	+	9.75371i	0.823360	+	0.475367i	−0.0282141	+	0.999602i	$0.508982\pi$
$422$	−6.21297	+	17.0700i	−0.302443	+	0.830955i
$423$	−5.26243	−	1.91537i	−0.255868	−	0.0931283i
$424$	18.1893	−	3.20726i	0.883349	−	0.155758i
$425$		0			0
$426$	−2.51284	+	2.99468i	−0.121747	+	0.145093i
$427$	−0.894531	+	0.157730i	−0.0432894	+	0.00763309i
$428$	−3.09912	−	1.12799i	−0.149802	−	0.0545234i
$429$	−3.92954	+	10.7963i	−0.189720	+	0.521251i
$430$		0			0
$431$	−11.3626	−	2.00354i	−0.547319	−	0.0965071i	−0.106850	−	0.994275i	$-0.534077\pi$
$431$	−11.3626	−	2.00354i	−0.547319	−	0.0965071i	−0.440468	+	0.897768i	$0.645188\pi$
$432$	−5.70862	+	4.79010i	−0.274656	+	0.230464i
$433$	−5.20640	−	9.01775i	−0.250204	−	0.433365i	0.713378	−	0.700779i	$-0.247164\pi$
$433$	−5.20640	−	9.01775i	−0.250204	−	0.433365i	−0.963582	+	0.267414i	$0.913831\pi$
$434$	0.123361	−	0.213668i	0.00592153	−	0.0102564i
$435$		0			0
$436$	−2.35608	+	1.36028i	−0.112836	+	0.0651458i
$437$	−9.17814	+	3.34057i	−0.439050	+	0.159801i
$438$		−	6.62459i		−	0.316535i
$439$	−6.68095	−	18.3557i	−0.318864	−	0.876072i	−0.990784	−	0.135449i	$-0.956752\pi$
$439$	−6.68095	−	18.3557i	−0.318864	−	0.876072i	0.671920	−	0.740624i	$-0.265470\pi$
$440$		0			0
$441$	15.1660	+	12.7258i	0.722190	+	0.605990i
$442$	17.8138	+	21.2297i	0.847317	+	1.00979i
$443$	40.1697			1.90852			0.954259	−	0.298981i	$-0.0966467\pi$
$443$	40.1697			1.90852			0.954259	+	0.298981i	$0.0966467\pi$
$444$	0.0262122	−	0.808434i	0.00124397	−	0.0383666i
$445$		0			0
$446$	−0.872786	−	1.04015i	−0.0413276	−	0.0492523i
$447$	0.283866	+	0.238192i	0.0134264	+	0.0112661i
$448$	−0.290855	+	1.64952i	−0.0137416	+	0.0779325i
$449$	−3.46938	−	9.53204i	−0.163730	−	0.449845i	0.830512	−	0.557000i	$-0.188048\pi$
$449$	−3.46938	−	9.53204i	−0.163730	−	0.449845i	−0.994242	+	0.107156i	$0.965826\pi$
$450$		0			0
$451$	0.310855	−	0.113142i	0.0146376	−	0.00532765i
$452$	−2.46764	+	1.42470i	−0.116068	+	0.0670120i
$453$	1.18752	+	6.73478i	0.0557947	+	0.316427i
$454$	−2.03908	+	3.53179i	−0.0956986	+	0.165755i
$455$		0			0
$456$	3.20910	−	2.69275i	0.150280	−	0.126100i
$457$	−10.8301	−	1.90963i	−0.506610	−	0.0893289i	−0.0854990	−	0.996338i	$-0.527248\pi$
$457$	−10.8301	−	1.90963i	−0.506610	−	0.0893289i	−0.421111	+	0.907009i	$0.638360\pi$
$458$	−27.8273	−	16.0661i	−1.30029	−	0.750720i
$459$	2.85685	−	7.84912i	0.133346	−	0.366366i
$460$		0			0
$461$	16.9524	−	2.98916i	0.789551	−	0.139219i	0.235690	−	0.971828i	$-0.424265\pi$
$461$	16.9524	−	2.98916i	0.789551	−	0.139219i	0.553861	+	0.832609i	$0.313154\pi$
$462$	−0.302575	+	0.360595i	−0.0140771	+	0.0167764i
$463$	4.05871	−	4.83698i	0.188624	−	0.224794i	−0.663442	−	0.748228i	$-0.730905\pi$
$463$	4.05871	−	4.83698i	0.188624	−	0.224794i	0.852066	+	0.523434i	$0.175349\pi$
$464$	−22.4006	+	3.94984i	−1.03992	+	0.183367i
$465$		0			0
$466$	−10.5132	+	28.8846i	−0.487012	+	1.33806i
$467$	6.06330	+	3.50065i	0.280576	+	0.161991i	0.633684	−	0.773592i	$-0.281542\pi$
$467$	6.06330	+	3.50065i	0.280576	+	0.161991i	−0.353108	+	0.935583i	$0.614875\pi$
$468$	−5.59353	−	0.986290i	−0.258561	−	0.0455913i
$469$	1.79594	−	1.50697i	0.0829289	−	0.0695856i
$470$		0			0
$471$	0.0833596	−	0.144383i	0.00384101	−	0.00665282i
$472$	2.05107	+	11.6322i	0.0944083	+	0.535416i
$473$	−39.4324	+	22.7663i	−1.81310	+	1.04680i
$474$	−6.87580	+	2.50259i	−0.315816	+	0.114948i
$475$		0			0
$476$	−0.0782415	−	0.214967i	−0.00358620	−	0.00985299i
$477$	−3.02596	+	17.1611i	−0.138549	+	0.785753i
$478$	9.26850	+	7.77719i	0.423931	+	0.355720i
$479$	−12.4628	−	14.8525i	−0.569438	−	0.678630i	0.402077	−	0.915606i	$-0.368288\pi$
$479$	−12.4628	−	14.8525i	−0.569438	−	0.678630i	−0.971516	+	0.236975i	$0.923844\pi$
$480$		0			0
$481$	−28.4996	+	22.3810i	−1.29947	+	1.02049i
$482$	−22.5752			−1.02827
$483$	−0.134298	−	0.160050i	−0.00611077	−	0.00728253i
$484$	3.25228	+	2.72899i	0.147831	+	0.124045i
$485$		0			0
$486$	−4.39826	−	12.0841i	−0.199509	−	0.548147i
$487$		−	23.2062i		−	1.05157i	−0.850617	−	0.525786i	$-0.823771\pi$
$487$		−	23.2062i		−	1.05157i	0.850617	−	0.525786i	$-0.176229\pi$
$488$	−13.5948	+	4.94809i	−0.615406	+	0.223990i
$489$	−2.24254	+	1.29473i	−0.101411	+	0.0585497i
$490$		0			0
$491$	−7.16276	+	12.4063i	−0.323251	+	0.559887i	−0.981157	−	0.193213i	$-0.938109\pi$
$491$	−7.16276	+	12.4063i	−0.323251	+	0.559887i	0.657906	+	0.753100i	$0.271442\pi$
$492$	−0.00452185	−	0.00783208i	−0.000203861	−	0.000353097i
$493$	19.5309	−	16.3883i	0.879626	−	0.738094i
$494$	−26.5424	−	4.68015i	−1.19420	−	0.210570i
$495$		0			0
$496$	1.11211	−	3.05551i	0.0499354	−	0.137196i
$497$	−1.35850	−	0.494455i	−0.0609372	−	0.0221793i
$498$	−6.26937	+	1.10546i	−0.280937	+	0.0495368i
$499$	7.88222	−	9.39367i	0.352857	−	0.420518i	−0.560196	−	0.828360i	$-0.689274\pi$
$499$	7.88222	−	9.39367i	0.352857	−	0.420518i	0.913053	+	0.407842i	$0.133719\pi$
$500$		0			0
$501$	−5.33624	+	0.940923i	−0.238405	+	0.0420373i
$502$	−24.5994	−	8.95347i	−1.09793	−	0.399613i
$503$	−4.78894	+	13.1575i	−0.213528	+	0.586665i	−0.999501	−	0.0315972i	$-0.989941\pi$
$503$	−4.78894	+	13.1575i	−0.213528	+	0.586665i	0.785972	+	0.618262i	$0.212163\pi$
$504$	−1.40334	−	0.810220i	−0.0625099	−	0.0360901i
$505$		0			0
$506$	13.3907	−	11.2361i	0.595287	−	0.499505i
$507$	−4.45862	−	7.72256i	−0.198014	−	0.342971i
$508$	3.26878	−	5.66169i	0.145028	−	0.251197i
$509$	6.85758	+	38.8913i	0.303957	+	1.72383i	0.628374	+	0.777912i	$0.283721\pi$
$509$	6.85758	+	38.8913i	0.303957	+	1.72383i	−0.324417	+	0.945914i	$0.605168\pi$
$510$		0			0
$511$	2.30209	−	0.837894i	0.101839	−	0.0370662i
$512$			25.4194i			1.12339i
$513$	2.77835	+	7.63344i	0.122667	+	0.337025i
$514$	−6.37708	+	36.1662i	−0.281281	+	1.59522i
$515$		0			0
$516$	0.800136	+	0.953565i	0.0352240	+	0.0419784i
$517$	−9.58194			−0.421413
$518$	−1.41086	+	0.462311i	−0.0619897	+	0.0203128i
$519$	−0.409033			−0.0179545
$520$		0			0
$521$	9.63053	+	8.08098i	0.421921	+	0.354034i	0.828893	−	0.559407i	$-0.188971\pi$
$521$	9.63053	+	8.08098i	0.421921	+	0.354034i	−0.406972	+	0.913441i	$0.633415\pi$
$522$	4.50363	−	25.5414i	0.197119	−	1.11791i
$523$	10.4396	+	28.6826i	0.456492	+	1.25420i	0.928080	+	0.372382i	$0.121459\pi$
$523$	10.4396	+	28.6826i	0.456492	+	1.25420i	−0.471588	+	0.881819i	$0.656319\pi$
$524$		−	2.21730i		−	0.0968633i
$525$		0			0
$526$	−14.6510	+	8.45878i	−0.638815	+	0.368820i
$527$	0.632887	+	3.58928i	0.0275690	+	0.156351i
$528$	−3.10188	+	5.37261i	−0.134992	+	0.233813i
$529$	−7.62069	−	13.1994i	−0.331335	−	0.573888i
$530$		0			0
$531$	−10.9747	−	1.93513i	−0.476261	−	0.0839777i
$532$	0.192671	+	0.111238i	0.00835334	+	0.00482280i
$533$	−0.138574	+	0.380728i	−0.00600229	+	0.0164911i
$534$	4.44806	+	1.61896i	0.192486	+	0.0700593i
$535$		0			0
$536$	24.0020	−	28.6045i	1.03673	−	1.23553i
$537$	−1.80649	+	2.15289i	−0.0779558	+	0.0929041i
$538$	1.78084	−	0.314011i	0.0767776	−	0.0135380i
$539$	31.8314	+	11.5857i	1.37108	+	0.499031i
$540$		0			0
$541$	4.64371	+	2.68105i	0.199649	+	0.115267i	0.596492	−	0.802619i	$-0.296561\pi$
$541$	4.64371	+	2.68105i	0.199649	+	0.115267i	−0.396843	+	0.917887i	$0.629894\pi$
$542$	−20.2937	−	3.57832i	−0.871688	−	0.153702i
$543$	−4.42594	+	3.71380i	−0.189935	+	0.159375i
$544$	−3.38195	−	5.85771i	−0.145000	−	0.251147i
$545$		0			0
$546$	−0.100113	−	0.567771i	−0.00428446	−	0.0242984i
$547$	5.94736	−	3.43371i	0.254291	−	0.146815i	−0.367437	−	0.930049i	$-0.619765\pi$
$547$	5.94736	−	3.43371i	0.254291	−	0.146815i	0.621727	+	0.783234i	$0.286431\pi$
$548$	1.18988	−	0.433081i	0.0508291	−	0.0185003i
$549$		−	13.6495i		−	0.582545i
$550$		0			0
$551$	−4.30563	+	24.4185i	−0.183426	+	1.04026i
$552$	−2.54917	−	2.13900i	−0.108500	−	0.0910421i
$553$	−1.73933	−	2.07286i	−0.0739640	−	0.0881469i
$554$	2.23564			0.0949830
$555$		0			0
$556$	−4.85542			−0.205916
$557$	20.4606	+	24.3839i	0.866942	+	1.03318i	0.999120	+	0.0419547i	$0.0133585\pi$
$557$	20.4606	+	24.3839i	0.866942	+	1.03318i	−0.132178	+	0.991226i	$0.542197\pi$
$558$	2.84011	+	2.38313i	0.120231	+	0.100886i
$559$	9.68387	−	54.9199i	0.409584	−	2.32287i
$560$		0			0
$561$		−	6.95365i		−	0.293583i
$562$	−12.6776	+	4.61427i	−0.534772	+	0.194641i
$563$	23.9805	−	13.8451i	1.01066	−	0.583503i	0.0992728	−	0.995060i	$-0.468348\pi$
$563$	23.9805	−	13.8451i	1.01066	−	0.583503i	0.911384	+	0.411557i	$0.135015\pi$
$564$	0.0454881	+	0.257976i	0.00191539	+	0.0108627i
$565$		0			0
$566$	3.04672	+	5.27707i	0.128063	+	0.221812i
$567$	1.10282	−	0.925372i	0.0463139	−	0.0388620i
$568$	−22.6761	−	3.99841i	−0.951469	−	0.167770i
$569$	35.8180	+	20.6795i	1.50157	+	0.866930i	0.999998	+	0.00181213i	$0.000576819\pi$
$569$	35.8180	+	20.6795i	1.50157	+	0.866930i	0.501569	+	0.865118i	$0.332757\pi$
$570$		0			0
$571$	38.7418	+	14.1009i	1.62129	+	0.590102i	0.983628	−	0.180211i	$-0.0576781\pi$
$571$	38.7418	+	14.1009i	1.62129	+	0.590102i	0.637665	+	0.770314i	$0.279900\pi$
$572$	−9.57059	+	1.68755i	−0.400167	+	0.0705602i
$573$	5.45593	−	6.50212i	0.227925	−	0.271630i
$574$	−0.0106702	+	0.0127163i	−0.000445366	+	0.000530766i
$575$		0			0
$576$	−23.6518	−	8.60855i	−0.985492	−	0.358690i
$577$	−6.05420	+	16.6338i	−0.252040	+	0.692473i	0.747560	+	0.664194i	$0.231225\pi$
$577$	−6.05420	+	16.6338i	−0.252040	+	0.692473i	−0.999600	+	0.0282794i	$0.990997\pi$
$578$	4.46899	+	2.58017i	0.185885	+	0.107321i
$579$	−0.529892	−	0.0934342i	−0.0220215	−	0.00388299i
$580$		0			0
$581$	−1.17712	−	2.03883i	−0.0488351	−	0.0845849i
$582$	2.19359	−	3.79940i	0.0909270	−	0.157490i
$583$	5.17746	+	29.3628i	0.214429	+	1.21608i
$584$	33.7917	−	19.5096i	1.39831	−	0.807315i
$585$		0			0
$586$		−	3.47997i		−	0.143756i
$587$	−8.53967	−	23.4626i	−0.352470	−	0.968403i	−0.981574	−	0.191082i	$-0.938800\pi$
$587$	−8.53967	−	23.4626i	−0.352470	−	0.968403i	0.629104	−	0.777321i	$-0.283422\pi$
$588$	0.160810	−	0.912001i	0.00663171	−	0.0376103i
$589$	−2.71525	−	2.27836i	−0.111880	−	0.0938783i
$590$		0			0
$591$	−6.03021			−0.248050
$592$	−17.2535	+	9.22913i	−0.709115	+	0.379315i
$593$	24.7820			1.01768			0.508838	−	0.860862i	$-0.330075\pi$
$593$	24.7820			1.01768			0.508838	+	0.860862i	$0.330075\pi$
$594$	−9.34504	−	11.1370i	−0.383431	−	0.456956i
$595$		0			0
$596$	−0.0544287	+	0.308680i	−0.00222949	+	0.0126440i
$597$	0.400724	+	1.10098i	0.0164006	+	0.0450602i
$598$			21.4094i			0.875494i
$599$	−0.772242	+	0.281073i	−0.0315529	+	0.0114843i	−0.357748	−	0.933818i	$-0.616455\pi$
$599$	−0.772242	+	0.281073i	−0.0315529	+	0.0114843i	0.326195	+	0.945302i	$0.394233\pi$
$600$		0			0
$601$	−7.20863	−	40.8822i	−0.294046	−	1.66762i	−0.671053	−	0.741409i	$-0.734158\pi$
$601$	−7.20863	−	40.8822i	−0.294046	−	1.66762i	0.377007	−	0.926210i	$-0.376953\pi$
$602$	1.14242	−	1.97873i	0.0465615	−	0.0806469i
$603$	17.6149	+	30.5099i	0.717335	+	1.24246i
$604$	−4.43122	+	3.71824i	−0.180304	+	0.151293i
$605$		0			0
$606$	−1.90536	−	1.10006i	−0.0774000	−	0.0446869i
$607$	11.7617	−	32.3151i	0.477394	−	1.31163i	−0.434304	−	0.900766i	$-0.643006\pi$
$607$	11.7617	−	32.3151i	0.477394	−	1.31163i	0.911698	−	0.410862i	$-0.134772\pi$
$608$	6.18134	+	2.24982i	0.250686	+	0.0912424i
$609$	−0.522337	+	0.0921022i	−0.0211662	+	0.00373217i
$610$		0			0
$611$	7.54357	−	8.99008i	0.305180	−	0.363700i
$612$	3.38539	−	0.596936i	0.136846	−	0.0241297i
$613$	−40.0883	−	14.5909i	−1.61915	−	0.589322i	−0.635930	−	0.771747i	$-0.719383\pi$
$613$	−40.0883	−	14.5909i	−1.61915	−	0.589322i	−0.983220	+	0.182425i	$0.941605\pi$
$614$	−5.70502	+	15.6744i	−0.230236	+	0.632568i
$615$		0			0
$616$	−2.73047	−	0.481456i	−0.110014	−	0.0193984i
$617$	18.8824	−	15.8442i	0.760178	−	0.637865i	−0.177995	−	0.984031i	$-0.556961\pi$
$617$	18.8824	−	15.8442i	0.760178	−	0.637865i	0.938173	+	0.346167i	$0.112517\pi$
$618$	1.63745	+	2.83615i	0.0658680	+	0.114087i
$619$	−24.4719	+	42.3866i	−0.983609	+	1.70366i	−0.335650	+	0.941987i	$0.608956\pi$
$619$	−24.4719	+	42.3866i	−0.983609	+	1.70366i	−0.647960	+	0.761675i	$0.724378\pi$
$620$		0			0
$621$	5.58831	−	3.22641i	0.224251	−	0.129471i
$622$	17.1546	−	6.24376i	0.687837	−	0.250352i
$623$			1.75050i			0.0701324i
$624$	−2.59874	−	7.13997i	−0.104033	−	0.285828i
$625$		0			0
$626$	8.66834	+	7.27360i	0.346457	+	0.290712i
$627$	4.34690	+	5.18044i	0.173599	+	0.206887i
$628$	0.141021			0.00562734
$629$	11.5758	−	18.6283i	0.461556	−	0.742761i
$630$		0			0
$631$	−11.8495	−	14.1216i	−0.471720	−	0.562174i	0.476751	−	0.879038i	$-0.341814\pi$
$631$	−11.8495	−	14.1216i	−0.471720	−	0.562174i	−0.948471	+	0.316865i	$0.897370\pi$
$632$	−33.0150	−	27.7029i	−1.31327	−	1.10196i
$633$	−0.969387	+	5.49767i	−0.0385297	+	0.218513i
$634$	3.58229	+	9.84227i	0.142271	+	0.390886i
$635$		0			0
$636$	0.765961	−	0.278787i	0.0303723	−	0.0110546i
$637$	−35.9300	+	20.7442i	−1.42360	+	0.821914i
$638$	−7.70577	−	43.7016i	−0.305074	−	1.73016i
$639$	10.8622	−	18.8139i	0.429702	−	0.744265i
$640$		0			0
$641$	−15.2402	+	12.7881i	−0.601952	+	0.505098i	−0.892072	−	0.451892i	$-0.850749\pi$
$641$	−15.2402	+	12.7881i	−0.601952	+	0.505098i	0.290120	+	0.956990i	$0.406305\pi$
$642$	4.95409	+	0.873541i	0.195523	+	0.0344759i
$643$	−12.5163	−	7.22627i	−0.493593	−	0.284976i	0.232471	−	0.972603i	$-0.425319\pi$
$643$	−12.5163	−	7.22627i	−0.493593	−	0.284976i	−0.726064	+	0.687627i	$0.758652\pi$
$644$	0.0604438	−	0.166068i	0.00238182	−	0.00654399i
$645$		0			0
$646$	16.0644	−	2.83258i	0.632045	−	0.111447i
$647$	15.8662	−	18.9086i	0.623764	−	0.743373i	−0.357949	−	0.933741i	$-0.616524\pi$
$647$	15.8662	−	18.9086i	0.623764	−	0.743373i	0.981713	+	0.190368i	$0.0609682\pi$
$648$	14.7387	−	17.5649i	0.578990	−	0.690013i
$649$	−18.7778	+	3.31104i	−0.737094	+	0.129970i
$650$		0			0
$651$	0.0259322	−	0.0712482i	0.00101636	−	0.00279244i
$652$	−1.89687	−	1.09516i	−0.0742872	−	0.0428897i
$653$	−32.3099	−	5.69712i	−1.26439	−	0.222945i	−0.499048	−	0.866574i	$-0.666317\pi$
$653$	−32.3099	−	5.69712i	−1.26439	−	0.222945i	−0.765338	+	0.643629i	$0.777428\pi$
$654$	3.17888	−	2.66739i	0.124304	−	0.104303i
$655$		0			0
$656$	−0.109386	+	0.189463i	−0.00427083	+	0.00739729i
$657$	6.39263	+	36.2544i	0.249400	+	1.41442i
$658$	0.416406	−	0.240412i	0.0162332	−	0.00937223i
$659$	6.92927	−	2.52205i	0.269926	−	0.0982451i	−0.203511	−	0.979073i	$-0.565235\pi$
$659$	6.92927	−	2.52205i	0.269926	−	0.0982451i	0.473437	+	0.880828i	$0.343013\pi$
$660$		0			0
$661$	1.79433	+	4.92989i	0.0697915	+	0.191750i	0.969685	−	0.244360i	$-0.0785779\pi$
$661$	1.79433	+	4.92989i	0.0697915	+	0.191750i	−0.899893	+	0.436111i	$0.856356\pi$
$662$	−1.24416	+	7.05597i	−0.0483555	+	0.274238i
$663$	6.52414	+	5.47440i	0.253376	+	0.212608i
$664$	−24.1024	−	28.7241i	−0.935354	−	1.11471i
$665$		0			0
$666$	−3.16009	−	22.0853i	−0.122451	−	0.855787i
$667$	19.6962			0.762638
$668$	−2.94611	−	3.51104i	−0.113988	−	0.135846i
$669$	−0.319649	−	0.268217i	−0.0123583	−	0.0103699i
$670$		0			0
$671$	−7.98768	−	21.9460i	−0.308361	−	0.847215i
$672$			0.140712i			0.00542807i
$673$	−6.48615	+	2.36077i	−0.250023	+	0.0910009i	−0.463991	−	0.885840i	$-0.653583\pi$
$673$	−6.48615	+	2.36077i	−0.250023	+	0.0910009i	0.213969	+	0.976841i	$0.431361\pi$
$674$	9.01145	−	5.20277i	0.347108	−	0.200403i
$675$		0			0
$676$	3.77136	−	6.53219i	0.145052	−	0.251238i
$677$	−0.576422	−	0.998393i	−0.0221537	−	0.0383714i	0.854736	−	0.519063i	$-0.173719\pi$
$677$	−0.576422	−	0.998393i	−0.0221537	−	0.0383714i	−0.876890	+	0.480692i	$0.840386\pi$
$678$	3.32940	−	2.79370i	0.127865	−	0.107291i
$679$	1.59777	+	0.281730i	0.0613168	+	0.0108118i
$680$		0			0
$681$	−0.428642	+	1.17768i	−0.0164256	+	0.0451290i
$682$	5.96101	+	2.16963i	0.228259	+	0.0830794i
$683$	9.98262	−	1.76021i	0.381974	−	0.0673524i	0.0206357	−	0.999787i	$-0.493431\pi$
$683$	9.98262	−	1.76021i	0.381974	−	0.0673524i	0.361339	+	0.932435i	$0.382320\pi$
$684$	−2.14894	+	2.56101i	−0.0821669	+	0.0979226i
$685$		0			0
$686$	−3.35659	+	0.591858i	−0.128155	+	0.0225972i
$687$	−9.27911	−	3.37732i	−0.354020	−	0.128853i
$688$	10.2990	−	28.2963i	0.392646	−	1.07879i
$689$	−31.6252	−	18.2588i	−1.20482	−	0.695606i
$690$		0			0
$691$	3.46669	−	2.90890i	0.131879	−	0.110660i	−0.574462	−	0.818531i	$-0.694789\pi$
$691$	3.46669	−	2.90890i	0.131879	−	0.110660i	0.706341	+	0.707871i	$0.250344\pi$
$692$	−0.172992	−	0.299631i	−0.00657617	−	0.0113903i
$693$	1.30794	−	2.26541i	0.0496844	−	0.0860558i
$694$	4.43070	+	25.1278i	0.168187	+	0.953837i
$695$		0			0
$696$	−7.93830	+	2.88931i	−0.300901	+	0.109519i
$697$		−	0.245218i		−	0.00928829i
$698$	2.78959	+	7.66433i	0.105587	+	0.290099i
$699$	−1.64033	+	9.30276i	−0.0620429	+	0.351863i
$700$		0			0
$701$	0.0244893	+	0.0291852i	0.000924948	+	0.00110231i	0.766507	−	0.642236i	$-0.221993\pi$
$701$	0.0244893	+	0.0291852i	0.000924948	+	0.00110231i	−0.765582	+	0.643339i	$0.777549\pi$
$702$	17.8061			0.672049
$703$	3.02116	+	21.1143i	0.113945	+	0.796342i
$704$	−43.0657			−1.62310
$705$		0			0
$706$	−9.38003	−	7.87078i	−0.353022	−	0.296221i
$707$	0.141285	−	0.801265i	0.00531356	−	0.0301347i
$708$	0.178287	+	0.489839i	0.00670044	+	0.0184093i
$709$			33.0614i			1.24165i	0.783951	+	0.620823i	$0.213202\pi$
$709$			33.0614i			1.24165i	−0.783951	+	0.620823i	$0.786798\pi$
$710$		0			0
$711$	35.2142	−	20.3310i	1.32064	−	0.762470i
$712$	4.84145	+	27.4572i	0.181441	+	1.02900i
$713$	−1.40780	+	2.43838i	−0.0527224	+	0.0913179i
$714$	0.174468	+	0.302187i	0.00652930	+	0.0113091i
$715$		0			0
$716$	−2.34109	−	0.412797i	−0.0874905	−	0.0154269i
$717$	3.22007	+	1.85911i	0.120256	+	0.0694297i
$718$	15.1019	−	41.4920i	0.563596	−	1.54847i
$719$	5.52050	+	2.00930i	0.205880	+	0.0749341i	0.442902	−	0.896570i	$-0.353949\pi$
$719$	5.52050	+	2.00930i	0.205880	+	0.0749341i	−0.237022	+	0.971504i	$0.576171\pi$
$720$		0			0
$721$	−0.778474	+	0.927750i	−0.0289919	+	0.0345512i
$722$	5.56003	−	6.62618i	0.206923	−	0.246601i
$723$	−6.83223	+	1.20471i	−0.254093	+	0.0448035i
$724$	−4.59235	−	1.67148i	−0.170673	−	0.0621200i
$725$		0			0
$726$	−5.60822	−	3.23791i	−0.208141	−	0.120170i
$727$	41.4281	+	7.30490i	1.53648	+	0.270924i	0.876887	−	0.480696i	$-0.159616\pi$
$727$	41.4281	+	7.30490i	1.53648	+	0.270924i	0.659597	+	0.751620i	$0.270727\pi$
$728$	2.60133	−	2.18278i	0.0964119	−	0.0808992i
$729$	9.43880	+	16.3485i	0.349585	+	0.605499i
$730$		0			0
$731$	5.86101	+	33.2394i	0.216777	+	1.22940i
$732$	−0.552934	+	0.319237i	−0.0204370	+	0.0117993i
$733$	−20.2905	+	7.38515i	−0.749448	+	0.272777i	−0.688373	−	0.725356i	$-0.741675\pi$
$733$	−20.2905	+	7.38515i	−0.749448	+	0.272777i	−0.0610745	+	0.998133i	$0.519453\pi$
$734$		−	39.4362i		−	1.45562i
$735$		0			0
$736$	0.907365	−	5.14592i	0.0334459	−	0.189681i
$737$	46.1761	+	38.7464i	1.70092	+	1.42724i
$738$	−0.160341	−	0.191087i	−0.00590224	−	0.00703401i
$739$	−17.1769			−0.631862			−0.315931	−	0.948782i	$-0.602317\pi$
$739$	−17.1769			−0.631862			−0.315931	+	0.948782i	$0.602317\pi$
$740$		0			0
$741$	−8.28263			−0.304270
$742$	−0.961716	−	1.14613i	−0.0353057	−	0.0420757i
$743$	−30.7730	−	25.8216i	−1.12895	−	0.947303i	−0.129930	−	0.991523i	$-0.541475\pi$
$743$	−30.7730	−	25.8216i	−1.12895	−	0.947303i	−0.999022	+	0.0442206i	$0.985920\pi$
$744$	0.209701	−	1.18927i	0.00768801	−	0.0436009i
$745$		0			0
$746$		−	9.31547i		−	0.341064i
$747$	33.2436	−	12.0997i	1.21632	−	0.442705i
$748$	5.09380	−	2.94090i	0.186248	−	0.107530i
$749$	0.323044	+	1.83207i	0.0118038	+	0.0669424i
$750$		0			0
$751$	−18.3737	−	31.8241i	−0.670465	−	1.16128i	−0.977772	−	0.209669i	$-0.932761\pi$
$751$	−18.3737	−	31.8241i	−0.670465	−	1.16128i	0.307308	−	0.951610i	$-0.400572\pi$
$752$	4.85432	−	4.07326i	0.177019	−	0.148536i
$753$	−7.92265	−	1.39698i	−0.288717	−	0.0509087i
$754$	47.0687	+	27.1751i	1.71414	+	0.989660i
$755$		0			0
$756$	−0.138118	−	0.0502710i	−0.00502332	−	0.00182834i
$757$	−40.3317	+	7.11156i	−1.46588	+	0.258474i	−0.848920	−	0.528521i	$-0.822747\pi$
$757$	−40.3317	+	7.11156i	−1.46588	+	0.258474i	−0.616959	+	0.786995i	$0.711636\pi$
$758$	−5.66257	+	6.74838i	−0.205674	+	0.245112i
$759$	3.45299	−	4.11511i	0.125335	−	0.149369i
$760$		0			0
$761$	−23.4132	−	8.52171i	−0.848728	−	0.308912i	−0.119207	−	0.992869i	$-0.538035\pi$
$761$	−23.4132	−	8.52171i	−0.848728	−	0.308912i	−0.729522	+	0.683958i	$0.760257\pi$
$762$	−3.41057	+	9.37046i	−0.123552	+	0.339456i
$763$	1.32901	+	0.767304i	0.0481134	+	0.0277783i
$764$	7.07051	+	1.24672i	0.255802	+	0.0451048i
$765$		0			0
$766$	19.9121	+	34.4888i	0.719455	+	1.24613i
$767$	11.6767	−	20.2246i	0.421621	−	0.730269i
$768$	0.537729	+	3.04961i	0.0194036	+	0.110043i
$769$	−26.8863	+	15.5228i	−0.969545	+	0.559767i	−0.899097	−	0.437749i	$-0.855776\pi$
$769$	−26.8863	+	15.5228i	−0.969545	+	0.559767i	−0.0704473	+	0.997516i	$0.522443\pi$
$770$		0			0
$771$			11.2858i			0.406447i
$772$	−0.155663	−	0.427680i	−0.00560243	−	0.0153926i
$773$	3.01653	−	17.1076i	0.108497	−	0.615317i	−0.881269	−	0.472616i	$-0.843310\pi$
$773$	3.01653	−	17.1076i	0.108497	−	0.615317i	0.989766	−	0.142702i	$-0.0455790\pi$
$774$	26.3015	+	22.0696i	0.945390	+	0.793276i
$775$		0			0
$776$	25.8407			0.927628
$777$	−0.402317	+	0.215205i	−0.0144330	+	0.00772042i
$778$	6.55316			0.234942
$779$	0.153292	+	0.182686i	0.00549225	+	0.00654541i
$780$		0			0
$781$	6.45462	−	36.6060i	0.230964	−	1.30986i
$782$	−4.43179	−	12.1762i	−0.158480	−	0.435422i
$783$		−	16.3813i		−	0.585418i
$784$	−21.0512	+	7.66201i	−0.751829	+	0.273643i
$785$		0			0
$786$	0.587293	+	3.33071i	0.0209481	+	0.118802i
$787$	−6.73845	+	11.6713i	−0.240200	+	0.416038i	−0.960771	−	0.277343i	$-0.910546\pi$
$787$	−6.73845	+	11.6713i	−0.240200	+	0.416038i	0.720571	+	0.693381i	$0.243880\pi$
$788$	−2.55035	−	4.41734i	−0.0908525	−	0.157361i
$789$	−3.98264	+	3.34183i	−0.141786	+	0.118972i
$790$		0			0
$791$	1.39194	+	0.803637i	0.0494917	+	0.0285740i
$792$	14.2498	−	39.1511i	0.506346	−	1.39117i
$793$	26.8789	+	9.78311i	0.954496	+	0.347408i
$794$	49.0579	−	8.65022i	1.74100	−	0.306985i
$795$		0			0
$796$	−0.637030	+	0.759182i	−0.0225789	+	0.0269085i
$797$	−2.17019	+	0.382662i	−0.0768720	+	0.0135546i	−0.211952	−	0.977280i	$-0.567982\pi$
$797$	−2.17019	+	0.382662i	−0.0768720	+	0.0135546i	0.135080	+	0.990835i	$0.456871\pi$
$798$	−0.318883	−	0.116064i	−0.0112883	−	0.00410861i
$799$	−2.42932	+	6.67450i	−0.0859432	+	0.236127i
$800$		0			0
$801$	−25.9052	−	4.56778i	−0.915314	−	0.161395i
$802$	−22.9994	+	19.2988i	−0.812138	+	0.681464i
$803$	31.4943	+	54.5498i	1.11141	+	1.92502i
$804$	0.823963	−	1.42715i	0.0290589	−	0.0503315i
$805$		0			0
$806$	−6.72854	+	3.88472i	−0.237003	+	0.136834i
$807$	0.522203	−	0.190066i	0.0183824	−	0.00669065i
$808$		−	12.9589i		−	0.455891i
$809$	−12.7393	−	35.0009i	−0.447889	−	1.23057i	−0.934191	−	0.356774i	$-0.883877\pi$
$809$	−12.7393	−	35.0009i	−0.447889	−	1.23057i	0.486302	−	0.873791i	$-0.338346\pi$
$810$		0			0
$811$	−13.1584	−	11.0412i	−0.462054	−	0.387710i	0.381832	−	0.924232i	$-0.375293\pi$
$811$	−13.1584	−	11.0412i	−0.462054	−	0.387710i	−0.843886	+	0.536522i	$0.819738\pi$
$812$	−0.288380	−	0.343678i	−0.0101202	−	0.0120607i
$813$	−6.33269			−0.222097
$814$	−18.0052	−	33.6600i	−0.631081	−	1.17978i
$815$		0			0
$816$	2.95598	+	3.52280i	0.103480	+	0.123323i
$817$	−25.1452	−	21.0993i	−0.879720	−	0.738173i
$818$	3.68248	−	20.8844i	0.128755	−	0.730205i
$819$	1.09578	+	3.01064i	0.0382897	+	0.105200i
$820$		0			0
$821$	2.01451	−	0.733221i	0.0703068	−	0.0255896i	−0.306627	−	0.951830i	$-0.599201\pi$
$821$	2.01451	−	0.733221i	0.0703068	−	0.0255896i	0.376934	+	0.926240i	$0.376978\pi$
$822$	−1.67266	+	0.965710i	−0.0583407	+	0.0336830i
$823$	−6.16074	−	34.9393i	−0.214750	−	1.21791i	−0.881340	−	0.472483i	$-0.843358\pi$
$823$	−6.16074	−	34.9393i	−0.214750	−	1.21791i	0.666590	−	0.745425i	$-0.267753\pi$
$824$	−9.64470	+	16.7051i	−0.335989	+	0.581950i
$825$		0			0
$826$	0.732961	−	0.615027i	0.0255030	−	0.0213995i
$827$	−0.537183	−	0.0947198i	−0.0186797	−	0.00329373i	0.164301	−	0.986410i	$-0.447463\pi$
$827$	−0.537183	−	0.0947198i	−0.0186797	−	0.00329373i	−0.182980	+	0.983117i	$0.558574\pi$
$828$	2.29987	+	1.32783i	0.0799259	+	0.0461452i
$829$	4.25980	−	11.7037i	0.147949	−	0.406487i	−0.843475	−	0.537168i	$-0.819494\pi$
$829$	4.25980	−	11.7037i	0.147949	−	0.406487i	0.991424	+	0.130681i	$0.0417164\pi$
$830$		0			0
$831$	0.676600	−	0.119303i	0.0234710	−	0.00413857i
$832$	33.9043	−	40.4056i	1.17542	−	1.40081i
$833$	16.1405	−	19.2355i	0.559235	−	0.666471i
$834$	7.29354	−	1.28605i	0.252555	−	0.0445322i
$835$		0			0
$836$	−1.95642	+	5.37522i	−0.0676642	+	0.185906i
$837$	2.02799	+	1.17086i	0.0700977	+	0.0404709i
$838$	17.1817	+	3.02960i	0.593533	+	0.104656i
$839$	14.2158	−	11.9285i	0.490784	−	0.411817i	−0.363523	−	0.931585i	$-0.618426\pi$
$839$	14.2158	−	11.9285i	0.490784	−	0.411817i	0.854307	+	0.519769i	$0.173982\pi$
$840$		0			0
$841$	10.5005	−	18.1875i	0.362087	−	0.627154i
$842$	−4.37047	−	24.7862i	−0.150616	−	0.854187i
$843$	−3.59055	+	2.07301i	−0.123665	+	0.0713981i
$844$	−4.43722	+	1.61502i	−0.152735	+	0.0555911i
$845$		0			0
$846$	2.47121	+	6.78960i	0.0849620	+	0.233431i
$847$	0.415856	−	2.35843i	0.0142890	−	0.0810368i
$848$	−15.1050	−	12.6746i	−0.518709	−	0.435249i
$849$	1.20367	+	1.43448i	0.0413100	+	0.0492314i
$850$		0			0
$851$	16.1007	−	5.27589i	0.551926	−	0.180855i
$852$	−1.01619			−0.0348140
$853$	33.4196	+	39.8279i	1.14427	+	1.36368i	0.921299	+	0.388856i	$0.127130\pi$
$853$	33.4196	+	39.8279i	1.14427	+	1.36368i	0.222967	+	0.974826i	$0.428426\pi$
$854$	0.897750	+	0.753302i	0.0307204	+	0.0257775i
$855$		0			0
$856$	10.1341	+	27.8432i	0.346376	+	0.951660i
$857$		−	36.2095i		−	1.23689i	−0.785826	−	0.618447i	$-0.787762\pi$
$857$		−	36.2095i		−	1.23689i	0.785826	−	0.618447i	$-0.212238\pi$
$858$	13.9294	−	5.06990i	0.475543	−	0.173083i
$859$	−1.81511	+	1.04795i	−0.0619308	+	0.0357557i	−0.530646	−	0.847594i	$-0.678050\pi$
$859$	−1.81511	+	1.04795i	−0.0619308	+	0.0357557i	0.468715	+	0.883350i	$0.344717\pi$
$860$		0			0
$861$	−0.00255067	+	0.00441789i	−8.69266e−5	+	0.000150561i
$862$	7.44312	+	12.8919i	0.253514	+	0.439099i
$863$	−12.8856	+	10.8123i	−0.438631	+	0.368055i	−0.835197	−	0.549951i	$-0.814646\pi$
$863$	−12.8856	+	10.8123i	−0.438631	+	0.368055i	0.396566	+	0.918006i	$0.370202\pi$
$864$	−4.27985	−	0.754653i	−0.145604	−	0.0256738i
$865$		0			0
$866$	−4.59491	+	12.6244i	−0.156141	+	0.428995i
$867$	1.49020	+	0.542387i	0.0506097	+	0.0184204i
$868$	0.0631593	−	0.0111367i	0.00214377	−	0.000378004i
$869$	44.7207	−	53.2960i	1.51704	−	1.80794i
$870$		0			0
$871$	−72.7062	+	12.8201i	−2.46355	+	0.434391i
$872$	22.9681	+	8.35971i	0.777799	+	0.283096i
$873$	−8.33847	+	22.9098i	−0.282215	+	0.775378i
$874$	10.9133	+	6.30082i	0.369149	+	0.213128i
$875$		0			0
$876$	1.31914	−	1.10689i	0.0445696	−	0.0373983i
$877$	−9.11730	−	15.7916i	−0.307869	−	0.533245i	0.670027	−	0.742337i	$-0.266283\pi$
$877$	−9.11730	−	15.7916i	−0.307869	−	0.533245i	−0.977896	+	0.209092i	$0.932949\pi$
$878$	−12.6013	+	21.8260i	−0.425272	+	0.736593i
$879$	−0.185705	−	1.05319i	−0.00626369	−	0.0355231i
$880$		0			0
$881$	−1.95511	+	0.711602i	−0.0658694	+	0.0239745i	−0.374745	−	0.927128i	$-0.622270\pi$
$881$	−1.95511	+	0.711602i	−0.0658694	+	0.0239745i	0.308875	+	0.951103i	$0.400047\pi$
$882$		−	25.5432i		−	0.860083i
$883$	9.43951	+	25.9348i	0.317665	+	0.872777i	0.991051	+	0.133486i	$0.0426170\pi$
$883$	9.43951	+	25.9348i	0.317665	+	0.872777i	−0.673386	+	0.739291i	$0.735161\pi$
$884$	−1.25094	+	7.09445i	−0.0420737	+	0.238612i
$885$		0			0
$886$	−33.3137	−	39.7018i	−1.11920	−	1.33381i
$887$	42.4786			1.42629			0.713146	−	0.701015i	$-0.247270\pi$
$887$	42.4786			1.42629			0.713146	+	0.701015i	$0.247270\pi$
$888$	−5.71527	+	4.48826i	−0.191792	+	0.150616i
$889$	−3.68768			−0.123681
$890$		0			0
$891$	28.3549	+	23.7926i	0.949924	+	0.797081i
$892$	0.0612897	−	0.347591i	0.00205213	−	0.0116382i
$893$	−2.36257	−	6.49110i	−0.0790603	−	0.217216i
$894$		−	0.478099i		−	0.0159900i
$895$		0			0
$896$	1.25684	−	0.725634i	0.0419879	−	0.0242417i
$897$	1.14249	+	6.47940i	0.0381467	+	0.216341i
$898$	−6.54377	+	11.3341i	−0.218368	+	0.378225i
$899$	3.57386	+	6.19011i	0.119195	+	0.206452i
$900$		0			0
$901$	21.7660	+	3.83793i	0.725129	+	0.127860i
$902$	−0.369625	−	0.213403i	−0.0123072	−	0.00710554i
$903$	0.240152	−	0.659812i	0.00799176	−	0.0219572i
$904$	24.0557	+	8.75556i	0.800080	+	0.291205i
$905$		0			0
$906$	5.67149	−	6.75902i	0.188423	−	0.224553i
$907$	29.6303	−	35.3120i	0.983858	−	1.17252i	−0.00114797	−	0.999999i	$-0.500365\pi$
$907$	29.6303	−	35.3120i	0.983858	−	1.17252i	0.985006	−	0.172518i	$-0.0551901\pi$
$908$	−1.04398	+	0.184082i	−0.0346457	+	0.00610897i
$909$	11.4890	+	4.18166i	0.381067	+	0.138697i
$910$		0			0
$911$	26.5045	+	15.3024i	0.878132	+	0.506990i	0.870042	−	0.492977i	$-0.164091\pi$
$911$	26.5045	+	15.3024i	0.878132	+	0.506990i	0.00809016	+	0.999967i	$0.497425\pi$
$912$	−4.40438	−	0.776611i	−0.145844	−	0.0257162i
$913$	46.3692	−	38.9084i	1.53460	−	1.28768i
$914$	7.09427	+	12.2876i	0.234658	+	0.406439i
$915$		0			0
$916$	−1.45040	−	8.22564i	−0.0479226	−	0.271783i
$917$	−1.08316	+	0.625364i	−0.0357692	+	0.0206513i
$918$	−10.1270	+	3.68591i	−0.334239	+	0.121653i
$919$		−	5.91058i		−	0.194972i	−0.995237	−	0.0974860i	$-0.968920\pi$
$919$		−	5.91058i		−	0.194972i	0.995237	−	0.0974860i	$-0.0310801\pi$
$920$		0			0
$921$	−0.890134	+	5.04820i	−0.0293309	+	0.166344i
$922$	−17.0134	−	14.2759i	−0.560306	−	0.470152i
$923$	29.2633	+	34.8747i	0.963215	+	1.14791i
$924$	−0.122361			−0.00402538
$925$		0			0
$926$	−8.14664			−0.267715
$927$	−11.6981	−	13.9413i	−0.384217	−	0.457892i
$928$	−10.1616	−	8.52662i	−0.333572	−	0.279900i
$929$	−1.78034	+	10.0968i	−0.0584111	+	0.331266i	−0.999985	−	0.00554174i	$-0.998236\pi$
$929$	−1.78034	+	10.0968i	−0.0584111	+	0.331266i	0.941574	+	0.336807i	$0.109347\pi$
$930$		0			0
$931$			24.4202i			0.800339i
$932$	−7.50835	+	2.73281i	−0.245944	+	0.0895163i
$933$	4.85853	−	2.80507i	0.159061	−	0.0918340i
$934$	−1.56858	−	8.89586i	−0.0513255	−	0.291081i
$935$		0			0
$936$	25.5143	+	44.1921i	0.833962	+	1.44447i
$937$	10.7261	−	9.00024i	0.350405	−	0.294025i	−0.450547	−	0.892753i	$-0.648771\pi$
$937$	10.7261	−	9.00024i	0.350405	−	0.294025i	0.800953	+	0.598727i	$0.204327\pi$
$938$	−2.97884	−	0.525250i	−0.0972627	−	0.0171500i
$939$	3.01156	+	1.73873i	0.0982787	+	0.0567412i
$940$		0			0
$941$	3.88489	+	1.41398i	0.126644	+	0.0460945i	0.404565	−	0.914509i	$-0.367423\pi$
$941$	3.88489	+	1.41398i	0.126644	+	0.0460945i	−0.277921	+	0.960604i	$0.589645\pi$
$942$	−0.211833	+	0.0373520i	−0.00690191	+	0.00121699i
$943$	0.121768	−	0.145118i	0.00396532	−	0.00472568i
$944$	8.10555	−	9.65982i	0.263813	−	0.314400i
$945$		0			0
$946$	55.2034	+	20.0924i	1.79482	+	0.653261i
$947$	−0.702056	+	1.92888i	−0.0228137	+	0.0626802i	−0.950577	−	0.310490i	$-0.899507\pi$
$947$	−0.702056	+	1.92888i	−0.0228137	+	0.0626802i	0.927763	+	0.373170i	$0.121729\pi$
$948$	−1.64720	−	0.951009i	−0.0534984	−	0.0308873i
$949$	−75.9749	−	13.3964i	−2.46625	−	0.434866i
$950$		0			0
$951$	1.60938	+	2.78753i	0.0521877	+	0.0903918i
$952$	−1.02763	+	1.77990i	−0.0333056	+	0.0576870i
$953$	0.194825	+	1.10491i	0.00631099	+	0.0357914i	0.987801	−	0.155724i	$-0.0497710\pi$
$953$	0.194825	+	1.10491i	0.00631099	+	0.0357914i	−0.981490	+	0.191515i	$0.938660\pi$
$954$	19.4707	−	11.2414i	0.630388	−	0.363955i
$955$		0			0
$956$			3.14509i			0.101719i
$957$	−4.66419	−	12.8148i	−0.150772	−	0.414243i
$958$	−4.34385	+	24.6352i	−0.140343	+	0.795928i
$959$	−0.547153	−	0.459116i	−0.0176685	−	0.0148256i
$960$		0			0
$961$	29.9782			0.967039
$962$	45.7558	+	9.60646i	1.47523	+	0.309725i
$963$	−27.9552			−0.900845
$964$	−3.77204	−	4.49534i	−0.121489	−	0.144785i
$965$		0			0
$966$	−0.0468091	+	0.265467i	−0.00150606	+	0.00854128i
$967$	−13.0114	−	35.7485i	−0.418418	−	1.14960i	−0.952600	−	0.304225i	$-0.901602\pi$
$967$	−13.0114	−	35.7485i	−0.418418	−	1.14960i	0.534182	−	0.845370i	$-0.320620\pi$
$968$		−	38.1430i		−	1.22596i
$969$	4.71062	−	1.71452i	0.151327	−	0.0550785i
$970$		0			0
$971$	4.23837	+	24.0370i	0.136016	+	0.771384i	0.974147	+	0.225915i	$0.0725372\pi$
$971$	4.23837	+	24.0370i	0.136016	+	0.771384i	−0.838131	+	0.545469i	$0.816352\pi$
$972$	1.67139	−	2.89492i	0.0536097	−	0.0928548i
$973$	1.36941	+	2.37189i	0.0439014	+	0.0760395i
$974$	−22.9359	+	19.2455i	−0.734913	+	0.616665i
$975$		0			0
$976$	13.3758	+	7.72254i	0.428150	+	0.247192i
$977$	0.812913	−	2.23346i	0.0260074	−	0.0714547i	−0.926009	−	0.377500i	$-0.876784\pi$
$977$	0.812913	−	2.23346i	0.0260074	−	0.0714547i	0.952017	+	0.306045i	$0.0990060\pi$
$978$	3.13944	+	1.14266i	0.100388	+	0.0365384i
$979$	−44.3241	+	7.81553i	−1.41660	+	0.249785i
$980$		0			0
$981$	−14.8230	+	17.6654i	−0.473263	+	0.564013i
$982$	18.2020	−	3.20951i	0.580850	−	0.102420i
$983$	20.5658	+	7.48536i	0.655949	+	0.238746i	0.648486	−	0.761226i	$-0.275402\pi$
$983$	20.5658	+	7.48536i	0.655949	+	0.238746i	0.00746235	+	0.999972i	$0.497625\pi$
$984$	−0.0277893	+	0.0763506i	−0.000885892	+	0.00243397i
$985$		0			0
$986$	−32.3949	−	5.71209i	−1.03166	−	0.181910i
$987$	0.113193	−	0.0949801i	0.00360297	−	0.00302325i
$988$	−3.50297	−	6.06732i	−0.111444	−	0.193027i
$989$	−13.0373	+	22.5812i	−0.414561	+	0.718040i
$990$		0			0
$991$	−9.88916	+	5.70951i	−0.314139	+	0.181369i	−0.648777	−	0.760978i	$-0.724719\pi$
$991$	−9.88916	+	5.70951i	−0.314139	+	0.181369i	0.334638	+	0.942347i	$0.391386\pi$
$992$	1.78190	−	0.648559i	0.0565754	−	0.0205918i
$993$			2.20183i			0.0698731i
$994$	0.637947	+	1.75275i	0.0202345	+	0.0555937i
$995$		0			0
$996$	−1.26766	−	1.06369i	−0.0401674	−	0.0337045i
$997$	12.8706	+	15.3386i	0.407616	+	0.485777i	0.930326	−	0.366733i	$-0.119524\pi$
$997$	12.8706	+	15.3386i	0.407616	+	0.485777i	−0.522711	+	0.852510i	$0.675079\pi$
$998$	−15.8212			−0.500811
$999$	−4.38794	−	13.3909i	−0.138828	−	0.423671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.876.5		96
5.2	odd	4		185.2.v.a.99.12	yes	96
5.3	odd	4		185.2.v.a.99.5	✓	96
5.4	even	2	inner	925.2.bb.e.876.12		96
37.3	even	18	inner	925.2.bb.e.151.5		96
185.3	odd	36		185.2.v.a.114.12	yes	96
185.77	odd	36		185.2.v.a.114.5	yes	96
185.114	even	18	inner	925.2.bb.e.151.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.99.5	✓	96	5.3	odd	4
185.2.v.a.99.12	yes	96	5.2	odd	4
185.2.v.a.114.5	yes	96	185.77	odd	36
185.2.v.a.114.12	yes	96	185.3	odd	36
925.2.bb.e.151.5		96	37.3	even	18	inner
925.2.bb.e.151.12		96	185.114	even	18	inner
925.2.bb.e.876.5		96	1.1	even	1	trivial
925.2.bb.e.876.12		96	5.4	even	2	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+(-0.829326 - 0.988352i) q^{2} +(-0.303732 - 0.254862i) q^{3} +(0.0582378 - 0.330283i) q^{4} +0.511558i q^{6} +(-0.177770 + 0.0647030i) q^{7} +(-2.60943 + 1.50656i) q^{8} +(-0.493646 - 2.79960i) q^{9} +(-2.43203 - 4.21239i) q^{11} +(-0.101865 + 0.0854751i) q^{12} +(5.86686 + 1.03449i) q^{13} +(0.211379 + 0.122040i) q^{14} +(3.02277 + 1.10020i) q^{16} +(-3.55082 + 0.626106i) q^{17} +(-2.35760 + 2.80968i) q^{18} +(2.25395 - 2.68616i) q^{19} +(0.0704849 + 0.0256544i) q^{21} +(-2.14639 + 5.89714i) q^{22} +(-2.41225 - 1.39271i) q^{23} +(1.17653 + 0.207454i) q^{24} +(-3.84310 - 6.65645i) q^{26} +(-1.15832 + 2.00626i) q^{27} +(0.0110174 + 0.0624827i) q^{28} +(-6.12379 + 3.53557i) q^{29} -1.01083i q^{31} +(0.641610 + 1.76281i) q^{32} +(-0.334893 + 1.89927i) q^{33} +(3.56360 + 2.99022i) q^{34} -0.953411 q^{36} +(-4.05887 + 4.53051i) q^{37} -4.52413 q^{38} +(-1.51830 - 1.80944i) q^{39} +(-0.0118099 + 0.0669770i) q^{41} +(-0.0330994 - 0.0909397i) q^{42} -9.36105i q^{43} +(-1.53292 + 0.557937i) q^{44} +(0.624051 + 3.53917i) q^{46} +(0.984975 - 1.70603i) q^{47} +(-0.637715 - 1.10455i) q^{48} +(-5.33490 + 4.47651i) q^{49} +(1.23807 + 0.714801i) q^{51} +(0.683346 - 1.87748i) q^{52} +(-5.76016 - 2.09653i) q^{53} +(2.94352 - 0.519022i) q^{54} +(0.366400 - 0.436659i) q^{56} +(-1.36920 + 0.241426i) q^{57} +(8.57301 + 3.12032i) q^{58} +(1.34075 - 3.68368i) q^{59} +(4.72849 + 0.833760i) q^{61} +(-0.999056 + 0.838308i) q^{62} +(0.268898 + 0.465746i) q^{63} +(4.42694 - 7.66768i) q^{64} +(2.15488 - 1.24412i) q^{66} +(-11.6453 + 4.23855i) q^{67} +1.20924i q^{68} +(0.377729 + 1.03780i) q^{69} +(5.85405 + 4.91213i) q^{71} +(5.50589 + 6.56167i) q^{72} -12.9498 q^{73} +(7.84387 + 0.254325i) q^{74} +(-0.755927 - 0.900878i) q^{76} +(0.704896 + 0.591478i) q^{77} +(-0.529199 + 3.00124i) q^{78} +(4.89209 + 13.4409i) q^{79} +(-7.15091 + 2.60272i) q^{81} +(0.0759911 - 0.0438735i) q^{82} +(2.16097 + 12.2554i) q^{83} +(0.0125781 - 0.0217859i) q^{84} +(-9.25201 + 7.76336i) q^{86} +(2.76107 + 0.486852i) q^{87} +(12.6924 + 7.32796i) q^{88} +(3.16477 - 8.69512i) q^{89} +(-1.10989 + 0.195703i) q^{91} +(-0.600474 + 0.715617i) q^{92} +(-0.257622 + 0.307022i) q^{93} +(-2.50302 + 0.441350i) q^{94} +(0.254395 - 0.698945i) q^{96} +(-7.42712 - 4.28805i) q^{97} +(8.84873 + 1.56027i) q^{98} +(-10.5925 + 8.88814i) 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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