LMFDB - Embedded newform 925.2.bb.e.151.12

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			151.12
Character	$\chi$	$=$	925.151
Dual form			925.2.bb.e.876.12

$q$-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 $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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	$-0.627004\pi$
$2$	0.829326	−	0.988352i	0.586422	−	0.698871i	0.974914	+	0.222582i	$0.0714484\pi$
$3$	0.303732	−	0.254862i	0.175360	−	0.147144i	−0.550883	−	0.834582i	$-0.685709\pi$
$3$	0.303732	−	0.254862i	0.175360	−	0.147144i	0.726243	+	0.687438i	$0.241265\pi$
$4$	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	$-0.377506\pi$
$7$	0.177770	+	0.0647030i	0.0671908	+	0.0244554i	−0.308206	+	0.951320i	$0.599729\pi$
$8$	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	0.222189	+	0.975004i	$0.428680\pi$
$11$	−2.43203	+	4.21239i	−0.733283	+	1.27008i	−0.955472	+	0.295080i	$0.904654\pi$
$12$	0.101865	+	0.0854751i	0.0294060	+	0.0246745i
$13$	−5.86686	+	1.03449i	−1.62717	+	0.286915i	−0.911432	−	0.411450i	$-0.865022\pi$
$13$	−5.86686	+	1.03449i	−1.62717	+	0.286915i	−0.715742	+	0.698365i	$0.753911\pi$
$14$	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	$-0.300399\pi$
$17$	3.55082	+	0.626106i	0.861201	+	0.151853i	0.274431	+	0.961607i	$0.411510\pi$
$18$	2.35760	+	2.80968i	0.555692	+	0.662248i
$19$	2.25395	+	2.68616i	0.517092	+	0.616246i	0.959891	−	0.280375i	$-0.0904588\pi$
$19$	2.25395	+	2.68616i	0.517092	+	0.616246i	−0.442799	+	0.896621i	$0.646014\pi$
$20$		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	$-0.572878\pi$
$23$	2.41225	−	1.39271i	0.502989	−	0.290401i	0.729947	+	0.683504i	$0.239545\pi$
$24$	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	−0.191434	−	0.981506i	$-0.561314\pi$
$29$	−6.12379	−	3.53557i	−1.13716	−	0.656539i	−0.945726	+	0.324966i	$0.894647\pi$
$30$		0			0
$31$			1.01083i			0.181550i	0.995871	+	0.0907752i	$0.0289345\pi$
$31$			1.01083i			0.181550i	−0.995871	+	0.0907752i	$0.971066\pi$
$32$	−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	0.983872	−	0.178876i	$-0.0572460\pi$
$41$	−0.0118099	−	0.0669770i	−0.00184439	−	0.0104601i	−0.985716	+	0.168416i	$0.946135\pi$
$42$	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	$-0.212558\pi$
$47$	−0.984975	−	1.70603i	−0.143673	−	0.248850i	−0.928877	+	0.370388i	$0.879225\pi$
$48$	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	$-0.472791\pi$
$53$	5.76016	−	2.09653i	0.791219	−	0.287980i	0.705842	+	0.708369i	$0.250569\pi$
$54$	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	0.995859	−	0.0909104i	$-0.0289777\pi$
$59$	1.34075	+	3.68368i	0.174551	+	0.479574i	−0.821308	+	0.570484i	$0.806755\pi$
$60$		0			0
$61$	4.72849	−	0.833760i	0.605421	−	0.106752i	0.137469	−	0.990506i	$-0.456103\pi$
$61$	4.72849	−	0.833760i	0.605421	−	0.106752i	0.467952	+	0.883754i	$0.344992\pi$
$62$	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	$-0.115551\pi$
$67$	11.6453	+	4.23855i	1.42270	+	0.517821i	0.487871	+	0.872916i	$0.337773\pi$
$68$			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	−0.225526	−	0.974237i	$-0.572410\pi$
$71$	5.85405	−	4.91213i	0.694748	−	0.582962i	0.920274	+	0.391275i	$0.127966\pi$
$72$	−5.50589	+	6.56167i	−0.648875	+	0.773300i
$73$	12.9498			1.51566			0.757832	−	0.652450i	$-0.226259\pi$
$73$	12.9498			1.51566			0.757832	+	0.652450i	$0.226259\pi$
$74$	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	−0.282759	−	0.959191i	$-0.591250\pi$
$79$	4.89209	−	13.4409i	0.550403	−	1.51222i	0.833162	−	0.553029i	$-0.186528\pi$
$80$		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	0.600741	+	0.799444i	$0.294872\pi$
$83$	−2.16097	+	12.2554i	−0.237197	+	1.34521i	−0.837938	+	0.545766i	$0.816239\pi$
$84$	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	0.986663	+	0.162774i	$0.0520442\pi$
$89$	3.16477	+	8.69512i	0.335465	+	0.921681i	−0.651199	+	0.758907i	$0.725734\pi$
$90$		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	$-0.523279\pi$
$97$	7.42712	−	4.28805i	0.754110	−	0.435385i	0.827177	+	0.561942i	$0.189945\pi$
$98$	−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	0.738981	−	0.673727i	$-0.235307\pi$
$101$	−2.15041	−	3.72462i	−0.213974	−	0.370614i	−0.952955	+	0.303113i	$0.901974\pi$
$102$	0.320290	−	1.81645i	0.0317134	−	0.179856i
$103$	−5.54414	−	3.20091i	−0.546281	−	0.315395i	0.201340	−	0.979521i	$-0.435470\pi$
$103$	−5.54414	−	3.20091i	−0.546281	−	0.315395i	−0.747621	+	0.664126i	$0.768804\pi$
$104$	−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	−0.948981	−	0.315333i	$-0.897884\pi$
$107$	−1.70761	−	9.68433i	−0.165081	−	0.936219i	0.783900	−	0.620887i	$-0.213227\pi$
$108$	−0.595178	+	0.499413i	−0.0572710	+	0.0480561i
$109$	−5.21425	+	6.21411i	−0.499435	+	0.595203i	−0.955591	−	0.294696i	$-0.904781\pi$
$109$	−5.21425	+	6.21411i	−0.499435	+	0.595203i	0.456156	+	0.889900i	$0.349226\pi$
$110$		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	$-0.646920\pi$
$113$	5.46115	−	6.50835i	0.513742	−	0.612254i	0.959089	+	0.283104i	$0.0913641\pi$
$114$	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	$-0.943707\pi$
$127$	−18.3175	+	6.66702i	−1.62541	+	0.591603i	−0.641012	+	0.767531i	$0.721485\pi$
$128$	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	0.450678	−	0.892686i	$-0.351182\pi$
$131$	6.51091	+	1.14805i	0.568860	+	0.100305i	0.118182	+	0.992992i	$0.462293\pi$
$132$	−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	$-0.884897\pi$
$137$	−1.88778	+	3.26974i	−0.161284	+	0.279352i	0.774045	+	0.633130i	$0.218230\pi$
$138$	−0.712454	−	1.23401i	−0.0606481	−	0.105046i
$139$	−2.51398	+	14.2575i	−0.213233	+	1.20931i	0.670713	+	0.741717i	$0.265988\pi$
$139$	−2.51398	+	14.2575i	−0.213233	+	1.20931i	−0.883946	+	0.467588i	$0.845123\pi$
$140$		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	−0.995516	−	0.0945953i	$-0.969844\pi$
$151$	−13.2126	+	11.0867i	−1.07523	+	0.902223i	−0.0797113	+	0.996818i	$0.525400\pi$
$152$	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	$-0.949786\pi$
$157$	−0.0730161	+	0.414095i	−0.00582732	+	0.0330484i	0.981755	+	0.190148i	$0.0608968\pi$
$158$	−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	$-0.193440\pi$
$163$	−2.23369	−	6.13703i	−0.174956	−	0.480689i	−0.995915	+	0.0902993i	$0.971218\pi$
$164$	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	$-0.399565\pi$
$167$	−8.78444	−	10.4689i	−0.679760	−	0.810107i	−0.990077	+	0.140526i	$0.955120\pi$
$168$	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	$-0.290264\pi$
$173$	−0.790269	−	0.663114i	−0.0600830	−	0.0504156i	−0.672335	+	0.740247i	$0.734708\pi$
$174$	−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	$0.0853375\pi$
$179$			7.08812i			0.529791i	−0.964277	+	0.264896i	$0.914663\pi$
$180$		0			0
$181$	2.53037	+	14.3505i	0.188081	+	1.06666i	0.921932	+	0.387351i	$0.126610\pi$
$181$	2.53037	+	14.3505i	0.188081	+	1.06666i	−0.733851	+	0.679310i	$0.762279\pi$
$182$	−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	$-0.718005\pi$
$191$		−	21.4074i		−	1.54899i	0.632583	−	0.774493i	$-0.281995\pi$
$192$	3.29880	+	1.20067i	0.238071	+	0.0866506i
$193$	−1.17525	−	0.678529i	−0.0845961	−	0.0488416i	0.457105	−	0.889413i	$-0.348886\pi$
$193$	−1.17525	−	0.678529i	−0.0845961	−	0.0488416i	−0.541701	+	0.840571i	$0.682220\pi$
$194$	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	$-0.460031\pi$
$197$	−11.6506	−	9.77603i	−0.830072	−	0.696513i	−0.955308	+	0.295614i	$0.904476\pi$
$198$	−17.5692	+	3.09793i	−1.24859	+	0.220160i
$199$	−2.55910	+	1.47750i	−0.181410	+	0.104737i	−0.587955	−	0.808894i	$-0.700067\pi$
$199$	−2.55910	+	1.47750i	−0.181410	+	0.104737i	0.406545	+	0.913631i	$0.366733\pi$
$200$		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	−0.999844	−	0.0176468i	$-0.994383\pi$
$211$	−7.03980	+	12.1933i	−0.484640	+	0.839420i	0.515205	+	0.857067i	$0.327716\pi$
$212$	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	$-0.511219\pi$
$223$	−1.05240			−0.0704742			−0.0352371	+	0.999379i	$0.511219\pi$
$224$	−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	$-0.855438\pi$
$227$	1.08108	−	2.97024i	0.0717538	−	0.197142i	0.970385	+	0.241562i	$0.0776598\pi$
$228$			0.466283i			0.0308803i
$229$	23.4029	+	8.51795i	1.54650	+	0.562882i	0.967594	−	0.252510i	$-0.0812559\pi$
$229$	23.4029	+	8.51795i	1.54650	+	0.562882i	0.578910	+	0.815391i	$0.303478\pi$
$230$		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	−0.151314	−	0.988486i	$-0.548350\pi$
$233$	11.9122	−	20.6326i	0.780397	−	1.35169i	0.931711	−	0.363201i	$-0.118316\pi$
$234$	−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	−0.133221	−	0.991086i	$-0.542532\pi$
$239$	−9.23526	−	1.62842i	−0.597379	−	0.105334i	−0.464158	+	0.885752i	$0.653643\pi$
$240$		0			0
$241$	11.2471	+	13.4038i	0.724491	+	0.863415i	0.995059	−	0.0992862i	$-0.0316559\pi$
$241$	11.2471	+	13.4038i	0.724491	+	0.863415i	−0.270568	+	0.962701i	$0.587212\pi$
$242$	−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	0.938599	−	0.345009i	$-0.112124\pi$
$251$	17.5716	+	10.1450i	1.10911	+	0.640346i	0.170513	+	0.985355i	$0.445458\pi$
$252$	−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	0.218032	−	0.975942i	$-0.430036\pi$
$257$	18.2962	−	21.8046i	1.14129	−	1.36013i	0.923254	−	0.384190i	$-0.125519\pi$
$258$	−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	−0.970945	−	0.239303i	$-0.923081\pi$
$263$	−2.27693	−	12.9131i	−0.140402	−	0.796257i	0.830543	−	0.556954i	$-0.188030\pi$
$264$	−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	0.843871	−	0.536547i	$-0.180271\pi$
$269$	−0.700788	−	1.21380i	−0.0427278	−	0.0740067i	−0.886598	+	0.462540i	$0.846938\pi$
$270$		0			0
$271$	12.2350	+	10.2664i	0.743226	+	0.623640i	0.933702	−	0.358051i	$-0.116559\pi$
$271$	12.2350	+	10.2664i	0.743226	+	0.623640i	−0.190476	+	0.981692i	$0.561003\pi$
$272$	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	$-0.205645\pi$
$277$	1.11381	+	1.32739i	0.0669223	+	0.0797549i	−0.731545	+	0.681794i	$0.761200\pi$
$278$	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	0.999492	−	0.0318722i	$-0.0101470\pi$
$281$	3.57639	+	9.82605i	0.213350	+	0.586173i	−0.786142	+	0.618045i	$0.787925\pi$
$282$	−0.872732	+	0.503872i	−0.0519704	+	0.0300051i
$283$	4.65110	−	0.820115i	0.276479	−	0.0487508i	−0.0336891	−	0.999432i	$-0.510726\pi$
$283$	4.65110	−	0.820115i	0.276479	−	0.0487508i	0.310169	+	0.950682i	$0.399615\pi$
$284$	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	$-0.747327\pi$
$293$	−2.06619	+	1.73374i	−0.120708	+	0.101286i	0.580435	+	0.814306i	$0.302882\pi$
$294$	−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	$-0.713056\pi$
$307$	6.46425	−	11.1964i	0.368934	−	0.639012i	0.989399	+	0.145222i	$0.0463895\pi$
$308$	−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	−0.997970	−	0.0636831i	$-0.979715\pi$
$311$	−4.83937	−	13.2961i	−0.274415	−	0.753950i	0.723555	−	0.690267i	$-0.242507\pi$
$312$	−6.68794	+	2.43421i	−0.378630	+	0.137810i
$313$	8.63725	+	1.52298i	0.488207	+	0.0860840i	0.412332	−	0.911033i	$-0.364714\pi$
$313$	8.63725	+	1.52298i	0.488207	+	0.0860840i	0.0758740	+	0.997117i	$0.475825\pi$
$314$	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	$-0.537900\pi$
$317$	7.62847	−	2.77654i	0.428458	−	0.155946i	0.547242	+	0.836974i	$0.315678\pi$
$318$	−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	−0.855171	−	0.518346i	$-0.826548\pi$
$331$	−3.56956	+	4.25404i	−0.196201	+	0.233823i	0.658970	+	0.752169i	$0.270992\pi$
$332$	−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	0.998899	+	0.0469213i	$0.0149410\pi$
$337$	1.40048	+	7.94251i	0.0762890	+	0.432656i	−0.922610	+	0.385735i	$0.873948\pi$
$338$	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	$-0.488549\pi$
$347$	17.1268	−	9.88814i	0.919413	−	0.530823i	0.883448	+	0.468530i	$0.155216\pi$
$348$	−0.321598	−	0.883583i	−0.0172395	−	0.0473650i
$349$	−5.94041	+	2.16213i	−0.317983	+	0.115736i	−0.496080	−	0.868277i	$-0.665228\pi$
$349$	−5.94041	+	2.16213i	−0.317983	+	0.115736i	0.178098	+	0.984013i	$0.443006\pi$
$350$		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	$-0.525719\pi$
$353$	−9.34639	−	1.64802i	−0.497458	−	0.0877153i	−0.416748	+	0.909022i	$0.636830\pi$
$354$	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	0.0796904	−	0.996820i	$-0.474607\pi$
$359$	17.1116	−	29.6382i	0.903116	−	1.56424i	0.823426	−	0.567424i	$-0.192060\pi$
$360$		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	−0.223540	+	0.974695i	$0.571761\pi$
$367$	−23.4148	+	19.6474i	−1.22224	+	1.02558i	−0.998704	+	0.0508901i	$0.983794\pi$
$368$	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	$-0.782074\pi$
$373$	−5.53097	+	4.64103i	−0.286383	+	0.240303i	0.488267	+	0.872694i	$0.337629\pi$
$374$	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	0.939095	+	0.343656i	$0.111666\pi$
$379$	−1.18565	+	6.72418i	−0.0609030	+	0.345398i	−0.999998	+	0.00174171i	$0.999446\pi$
$380$		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	$-0.266358\pi$
$383$	30.3978	−	5.35995i	1.55325	−	0.273880i	0.883402	+	0.468615i	$0.155247\pi$
$384$	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	0.676901	−	0.736074i	$-0.263323\pi$
$389$	−3.26483	−	3.89087i	−0.165534	−	0.197275i	−0.842434	+	0.538799i	$0.818878\pi$
$390$		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	0.698782	+	0.715335i	$0.253726\pi$
$397$	19.3050	+	33.4372i	0.968889	+	1.67817i	0.270107	+	0.962830i	$0.412941\pi$
$398$	−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	$0.197352\pi$
$401$			23.2705i			1.16207i	−0.813878	+	0.581036i	$0.802648\pi$
$402$	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	−0.438733	−	0.898618i	$-0.644573\pi$
$409$	10.5652	−	12.5912i	0.522418	−	0.622593i	0.961151	+	0.276024i	$0.0890170\pi$
$410$		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	0.353678	−	0.935367i	$-0.384931\pi$
$419$	−10.3588	−	8.69210i	−0.506063	−	0.424637i	−0.859741	+	0.510730i	$0.829375\pi$
$420$		0			0
$421$	16.8939	−	9.75371i	0.823360	−	0.475367i	−0.0282141	−	0.999602i	$-0.508982\pi$
$421$	16.8939	−	9.75371i	0.823360	−	0.475367i	0.851574	+	0.524235i	$0.175649\pi$
$422$	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	−0.440468	−	0.897768i	$-0.645188\pi$
$431$	−11.3626	+	2.00354i	−0.547319	+	0.0965071i	−0.106850	+	0.994275i	$0.534077\pi$
$432$	5.70862	+	4.79010i	0.274656	+	0.230464i
$433$	5.20640	−	9.01775i	0.250204	−	0.433365i	−0.713378	−	0.700779i	$-0.752836\pi$
$433$	5.20640	−	9.01775i	0.250204	−	0.433365i	0.963582	+	0.267414i	$0.0861691\pi$
$434$	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	0.671920	+	0.740624i	$0.265470\pi$
$439$	−6.68095	+	18.3557i	−0.318864	+	0.876072i	−0.990784	+	0.135449i	$0.956752\pi$
$440$		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	$-0.903353\pi$
$443$	−40.1697			−1.90852			−0.954259	+	0.298981i	$0.903353\pi$
$444$	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	−0.994242	−	0.107156i	$-0.965826\pi$
$449$	−3.46938	+	9.53204i	−0.163730	+	0.449845i	0.830512	+	0.557000i	$0.188048\pi$
$450$		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	$-0.472752\pi$
$457$	10.8301	−	1.90963i	0.506610	−	0.0893289i	0.421111	+	0.907009i	$0.361640\pi$
$458$	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	0.553861	−	0.832609i	$-0.313154\pi$
$461$	16.9524	+	2.98916i	0.789551	+	0.139219i	0.235690	+	0.971828i	$0.424265\pi$
$462$	0.302575	+	0.360595i	0.0140771	+	0.0167764i
$463$	−4.05871	−	4.83698i	−0.188624	−	0.224794i	0.663442	−	0.748228i	$-0.269095\pi$
$463$	−4.05871	−	4.83698i	−0.188624	−	0.224794i	−0.852066	+	0.523434i	$0.824651\pi$
$464$	−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	$-0.718458\pi$
$467$	−6.06330	+	3.50065i	−0.280576	+	0.161991i	0.353108	+	0.935583i	$0.385125\pi$
$468$	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	−0.971516	−	0.236975i	$-0.923844\pi$
$479$	−12.4628	+	14.8525i	−0.569438	+	0.678630i	0.402077	+	0.915606i	$0.368288\pi$
$480$		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	0.657906	−	0.753100i	$-0.271442\pi$
$491$	−7.16276	−	12.4063i	−0.323251	−	0.559887i	−0.981157	+	0.193213i	$0.938109\pi$
$492$	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	0.913053	−	0.407842i	$-0.133719\pi$
$499$	7.88222	+	9.39367i	0.352857	+	0.420518i	−0.560196	+	0.828360i	$0.689274\pi$
$500$		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	$-0.0100594\pi$
$503$	4.78894	+	13.1575i	0.213528	+	0.586665i	−0.785972	+	0.618262i	$0.787837\pi$
$504$	−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	−0.324417	−	0.945914i	$-0.605168\pi$
$509$	6.85758	−	38.8913i	0.303957	−	1.72383i	0.628374	−	0.777912i	$-0.283721\pi$
$510$		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	−0.406972	−	0.913441i	$-0.633415\pi$
$521$	9.63053	−	8.08098i	0.421921	−	0.354034i	0.828893	+	0.559407i	$0.188971\pi$
$522$	−4.50363	−	25.5414i	−0.197119	−	1.11791i
$523$	−10.4396	+	28.6826i	−0.456492	+	1.25420i	0.471588	+	0.881819i	$0.343681\pi$
$523$	−10.4396	+	28.6826i	−0.456492	+	1.25420i	−0.928080	+	0.372382i	$0.878541\pi$
$524$			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	−0.396843	−	0.917887i	$-0.629894\pi$
$541$	4.64371	−	2.68105i	0.199649	−	0.115267i	0.596492	+	0.802619i	$0.296561\pi$
$542$	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	$-0.380235\pi$
$547$	−5.94736	−	3.43371i	−0.254291	−	0.146815i	−0.621727	+	0.783234i	$0.713569\pi$
$548$	−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	0.132178	+	0.991226i	$0.457803\pi$
$557$	−20.4606	+	24.3839i	−0.866942	+	1.03318i	−0.999120	+	0.0419547i	$0.986641\pi$
$558$	−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	$-0.531652\pi$
$563$	−23.9805	−	13.8451i	−1.01066	−	0.583503i	−0.911384	+	0.411557i	$0.864985\pi$
$564$	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	0.501569	−	0.865118i	$-0.332757\pi$
$569$	35.8180	−	20.6795i	1.50157	−	0.866930i	0.999998	−	0.00181213i	$-0.000576819\pi$
$570$		0			0
$571$	38.7418	−	14.1009i	1.62129	−	0.590102i	0.637665	−	0.770314i	$-0.279900\pi$
$571$	38.7418	−	14.1009i	1.62129	−	0.590102i	0.983628	+	0.180211i	$0.0576781\pi$
$572$	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	0.999600	+	0.0282794i	$0.00900281\pi$
$577$	6.05420	+	16.6338i	0.252040	+	0.692473i	−0.747560	+	0.664194i	$0.768775\pi$
$578$	−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	−0.629104	−	0.777321i	$-0.716578\pi$
$587$	8.53967	−	23.4626i	0.352470	−	0.968403i	0.981574	−	0.191082i	$-0.0611997\pi$
$588$	−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	$-0.669925\pi$
$593$	−24.7820			−1.01768			−0.508838	+	0.860862i	$0.669925\pi$
$594$	−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	0.326195	−	0.945302i	$-0.394233\pi$
$599$	−0.772242	−	0.281073i	−0.0315529	−	0.0114843i	−0.357748	+	0.933818i	$0.616455\pi$
$600$		0			0
$601$	−7.20863	+	40.8822i	−0.294046	+	1.66762i	0.377007	+	0.926210i	$0.376953\pi$
$601$	−7.20863	+	40.8822i	−0.294046	+	1.66762i	−0.671053	+	0.741409i	$0.734158\pi$
$602$	−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	−0.911698	−	0.410862i	$-0.865228\pi$
$607$	−11.7617	−	32.3151i	−0.477394	−	1.31163i	0.434304	−	0.900766i	$-0.356994\pi$
$608$	−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	$-0.280617\pi$
$613$	40.0883	−	14.5909i	1.61915	−	0.589322i	0.983220	+	0.182425i	$0.0583946\pi$
$614$	−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	$-0.443039\pi$
$617$	−18.8824	−	15.8442i	−0.760178	−	0.637865i	−0.938173	+	0.346167i	$0.887483\pi$
$618$	−1.63745	+	2.83615i	−0.0658680	+	0.114087i
$619$	−24.4719	−	42.3866i	−0.983609	−	1.70366i	−0.647960	−	0.761675i	$-0.724378\pi$
$619$	−24.4719	−	42.3866i	−0.983609	−	1.70366i	−0.335650	−	0.941987i	$-0.608956\pi$
$620$		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	−0.948471	−	0.316865i	$-0.897370\pi$
$631$	−11.8495	+	14.1216i	−0.471720	+	0.562174i	0.476751	+	0.879038i	$0.341814\pi$
$632$	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	0.290120	−	0.956990i	$-0.406305\pi$
$641$	−15.2402	−	12.7881i	−0.601952	−	0.505098i	−0.892072	+	0.451892i	$0.850749\pi$
$642$	−4.95409	+	0.873541i	−0.195523	+	0.0344759i
$643$	12.5163	−	7.22627i	0.493593	−	0.284976i	−0.232471	−	0.972603i	$-0.574681\pi$
$643$	12.5163	−	7.22627i	0.493593	−	0.284976i	0.726064	+	0.687627i	$0.241348\pi$
$644$	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	$-0.383476\pi$
$647$	−15.8662	−	18.9086i	−0.623764	−	0.743373i	−0.981713	+	0.190368i	$0.939032\pi$
$648$	−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	$-0.333683\pi$
$653$	32.3099	−	5.69712i	1.26439	−	0.222945i	0.765338	+	0.643629i	$0.222572\pi$
$654$	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	0.473437	−	0.880828i	$-0.343013\pi$
$659$	6.92927	+	2.52205i	0.269926	+	0.0982451i	−0.203511	+	0.979073i	$0.565235\pi$
$660$		0			0
$661$	1.79433	−	4.92989i	0.0697915	−	0.191750i	−0.899893	−	0.436111i	$-0.856356\pi$
$661$	1.79433	−	4.92989i	0.0697915	−	0.191750i	0.969685	+	0.244360i	$0.0785779\pi$
$662$	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	$-0.346417\pi$
$673$	6.48615	+	2.36077i	0.250023	+	0.0910009i	−0.213969	+	0.976841i	$0.568639\pi$
$674$	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	$-0.826281\pi$
$677$	0.576422	−	0.998393i	0.0221537	−	0.0383714i	0.876890	+	0.480692i	$0.159614\pi$
$678$	−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	$-0.506569\pi$
$683$	−9.98262	−	1.76021i	−0.381974	−	0.0673524i	−0.361339	+	0.932435i	$0.617680\pi$
$684$	−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	0.706341	−	0.707871i	$-0.250344\pi$
$691$	3.46669	+	2.90890i	0.131879	+	0.110660i	−0.574462	+	0.818531i	$0.694789\pi$
$692$	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	−0.765582	−	0.643339i	$-0.777549\pi$
$701$	0.0244893	−	0.0291852i	0.000924948	−	0.00110231i	0.766507	+	0.642236i	$0.221993\pi$
$702$	−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	$-0.786798\pi$
$709$		−	33.0614i		−	1.24165i	0.783951	−	0.620823i	$-0.213202\pi$
$710$		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	−0.237022	−	0.971504i	$-0.576171\pi$
$719$	5.52050	−	2.00930i	0.205880	−	0.0749341i	0.442902	+	0.896570i	$0.353949\pi$
$720$		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	$-0.840384\pi$
$727$	−41.4281	+	7.30490i	−1.53648	+	0.270924i	−0.659597	+	0.751620i	$0.729273\pi$
$728$	−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	$-0.258325\pi$
$733$	20.2905	+	7.38515i	0.749448	+	0.272777i	0.0610745	+	0.998133i	$0.480547\pi$
$734$			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	$-0.458525\pi$
$743$	30.7730	−	25.8216i	1.12895	−	0.947303i	0.999022	+	0.0442206i	$0.0140804\pi$
$744$	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	0.307308	+	0.951610i	$0.400572\pi$
$751$	−18.3737	+	31.8241i	−0.670465	+	1.16128i	−0.977772	+	0.209669i	$0.932761\pi$
$752$	−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	$-0.177253\pi$
$757$	40.3317	+	7.11156i	1.46588	+	0.258474i	0.616959	+	0.786995i	$0.288364\pi$
$758$	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	−0.729522	−	0.683958i	$-0.760257\pi$
$761$	−23.4132	+	8.52171i	−0.848728	+	0.308912i	−0.119207	+	0.992869i	$0.538035\pi$
$762$	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	−0.0704473	−	0.997516i	$-0.522443\pi$
$769$	−26.8863	−	15.5228i	−0.969545	−	0.559767i	−0.899097	+	0.437749i	$0.855776\pi$
$770$		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	−0.989766	−	0.142702i	$-0.954421\pi$
$773$	−3.01653	−	17.1076i	−0.108497	−	0.615317i	0.881269	−	0.472616i	$-0.156690\pi$
$774$	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	$-0.0894537\pi$
$787$	6.73845	+	11.6713i	0.240200	+	0.416038i	−0.720571	+	0.693381i	$0.756120\pi$
$788$	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	$-0.432018\pi$
$797$	2.17019	+	0.382662i	0.0768720	+	0.0135546i	−0.135080	+	0.990835i	$0.543129\pi$
$798$	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	0.486302	+	0.873791i	$0.338346\pi$
$809$	−12.7393	+	35.0009i	−0.447889	+	1.23057i	−0.934191	+	0.356774i	$0.883877\pi$
$810$		0			0
$811$	−13.1584	+	11.0412i	−0.462054	+	0.387710i	−0.843886	−	0.536522i	$-0.819738\pi$
$811$	−13.1584	+	11.0412i	−0.462054	+	0.387710i	0.381832	+	0.924232i	$0.375293\pi$
$812$	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	0.376934	−	0.926240i	$-0.376978\pi$
$821$	2.01451	+	0.733221i	0.0703068	+	0.0255896i	−0.306627	+	0.951830i	$0.599201\pi$
$822$	1.67266	+	0.965710i	0.0583407	+	0.0336830i
$823$	6.16074	−	34.9393i	0.214750	−	1.21791i	−0.666590	−	0.745425i	$-0.732247\pi$
$823$	6.16074	−	34.9393i	0.214750	−	1.21791i	0.881340	−	0.472483i	$-0.156642\pi$
$824$	−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	$-0.552537\pi$
$827$	0.537183	−	0.0947198i	0.0186797	−	0.00329373i	0.182980	+	0.983117i	$0.441426\pi$
$828$	−2.29987	+	1.32783i	−0.0799259	+	0.0461452i
$829$	4.25980	+	11.7037i	0.147949	+	0.406487i	0.991424	−	0.130681i	$-0.0417164\pi$
$829$	4.25980	+	11.7037i	0.147949	+	0.406487i	−0.843475	+	0.537168i	$0.819494\pi$
$830$		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	0.854307	−	0.519769i	$-0.173982\pi$
$839$	14.2158	+	11.9285i	0.490784	+	0.411817i	−0.363523	+	0.931585i	$0.618426\pi$
$840$		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	−0.222967	+	0.974826i	$0.571574\pi$
$853$	−33.4196	+	39.8279i	−1.14427	+	1.36368i	−0.921299	+	0.388856i	$0.872870\pi$
$854$	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	0.468715	−	0.883350i	$-0.344717\pi$
$859$	−1.81511	−	1.04795i	−0.0619308	−	0.0357557i	−0.530646	+	0.847594i	$0.678050\pi$
$860$		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	$-0.185354\pi$
$863$	12.8856	+	10.8123i	0.438631	+	0.368055i	−0.396566	+	0.918006i	$0.629798\pi$
$864$	−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	$-0.733717\pi$
$877$	9.11730	−	15.7916i	0.307869	−	0.533245i	0.977896	+	0.209092i	$0.0670507\pi$
$878$	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	0.308875	−	0.951103i	$-0.400047\pi$
$881$	−1.95511	−	0.711602i	−0.0658694	−	0.0239745i	−0.374745	+	0.927128i	$0.622270\pi$
$882$		−	25.5432i		−	0.860083i
$883$	−9.43951	+	25.9348i	−0.317665	+	0.872777i	0.673386	+	0.739291i	$0.264839\pi$
$883$	−9.43951	+	25.9348i	−0.317665	+	0.872777i	−0.991051	+	0.133486i	$0.957383\pi$
$884$	−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	$-0.752730\pi$
$887$	−42.4786			−1.42629			−0.713146	+	0.701015i	$0.752730\pi$
$888$	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	−0.985006	−	0.172518i	$-0.944810\pi$
$907$	−29.6303	−	35.3120i	−0.983858	−	1.17252i	0.00114797	−	0.999999i	$-0.499635\pi$
$908$	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	0.00809016	−	0.999967i	$-0.497425\pi$
$911$	26.5045	−	15.3024i	0.878132	−	0.506990i	0.870042	+	0.492977i	$0.164091\pi$
$912$	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	$0.0310801\pi$
$919$			5.91058i			0.194972i	−0.995237	+	0.0974860i	$0.968920\pi$
$920$		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	0.941574	−	0.336807i	$-0.109347\pi$
$929$	−1.78034	−	10.0968i	−0.0584111	−	0.331266i	−0.999985	+	0.00554174i	$0.998236\pi$
$930$		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	$-0.351229\pi$
$937$	−10.7261	−	9.00024i	−0.350405	−	0.294025i	−0.800953	+	0.598727i	$0.795673\pi$
$938$	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	−0.277921	−	0.960604i	$-0.589645\pi$
$941$	3.88489	−	1.41398i	0.126644	−	0.0460945i	0.404565	+	0.914509i	$0.367423\pi$
$942$	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	$-0.100493\pi$
$947$	0.702056	+	1.92888i	0.0228137	+	0.0626802i	−0.927763	+	0.373170i	$0.878271\pi$
$948$	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	$-0.950229\pi$
$953$	−0.194825	+	1.10491i	−0.00631099	+	0.0357914i	0.981490	+	0.191515i	$0.0613401\pi$
$954$	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	−0.534182	−	0.845370i	$-0.679380\pi$
$967$	13.0114	−	35.7485i	0.418418	−	1.14960i	0.952600	−	0.304225i	$-0.0983976\pi$
$968$		−	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	−0.838131	−	0.545469i	$-0.816352\pi$
$971$	4.23837	−	24.0370i	0.136016	−	0.771384i	0.974147	−	0.225915i	$-0.0725372\pi$
$972$	−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	$-0.123216\pi$
$977$	−0.812913	−	2.23346i	−0.0260074	−	0.0714547i	−0.952017	+	0.306045i	$0.900994\pi$
$978$	−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	$-0.724598\pi$
$983$	−20.5658	+	7.48536i	−0.655949	+	0.238746i	−0.00746235	+	0.999972i	$0.502375\pi$
$984$	−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	0.334638	−	0.942347i	$-0.391386\pi$
$991$	−9.88916	−	5.70951i	−0.314139	−	0.181369i	−0.648777	+	0.760978i	$0.724719\pi$
$992$	−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	$-0.880476\pi$
$997$	−12.8706	+	15.3386i	−0.407616	+	0.485777i	0.522711	+	0.852510i	$0.324921\pi$
$998$	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.151.12		96
5.2	odd	4		185.2.v.a.114.12	yes	96
5.3	odd	4		185.2.v.a.114.5	yes	96
5.4	even	2	inner	925.2.bb.e.151.5		96
37.25	even	18	inner	925.2.bb.e.876.12		96
185.62	odd	36		185.2.v.a.99.5	✓	96
185.99	even	18	inner	925.2.bb.e.876.5		96
185.173	odd	36		185.2.v.a.99.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.99.5	✓	96	185.62	odd	36
185.2.v.a.99.12	yes	96	185.173	odd	36
185.2.v.a.114.5	yes	96	5.3	odd	4
185.2.v.a.114.12	yes	96	5.2	odd	4
925.2.bb.e.151.5		96	5.4	even	2	inner
925.2.bb.e.151.12		96	1.1	even	1	trivial
925.2.bb.e.876.5		96	185.99	even	18	inner
925.2.bb.e.876.12		96	37.25	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.829326 - 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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