LMFDB - Embedded newform 925.2.t.c.82.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] 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("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == 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:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.4
Character	$\chi$	$=$	925.82
Dual form			925.2.t.c.643.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996919 - 1.72671i) q^{2} +(-0.688157 + 0.184391i) q^{3} +(-0.987696 + 1.71074i) q^{4} +(1.00443 + 1.00443i) q^{6} +(3.07412 - 0.823709i) q^{7} -0.0490658 q^{8} +(-2.15852 + 1.24622i) q^{9} +2.17335i q^{11} +(0.364245 - 1.35938i) q^{12} +(1.42480 - 2.46782i) q^{13} +(-4.48696 - 4.48696i) q^{14} +(2.02431 + 3.50620i) q^{16} +(1.30757 - 0.754926i) q^{17} +(4.30373 + 2.48476i) q^{18} +(-0.158906 - 0.593046i) q^{19} +(-1.96360 + 1.13368i) q^{21} +(3.75276 - 2.16666i) q^{22} -0.334904 q^{23} +(0.0337650 - 0.00904730i) q^{24} -5.68163 q^{26} +(2.76691 - 2.76691i) q^{27} +(-1.62715 + 6.07260i) q^{28} +(3.60210 + 3.60210i) q^{29} +(4.53577 - 4.53577i) q^{31} +(3.98707 - 6.90581i) q^{32} +(-0.400747 - 1.49561i) q^{33} +(-2.60708 - 1.50520i) q^{34} -4.92354i q^{36} +(6.04178 - 0.704946i) q^{37} +(-0.865605 + 0.865605i) q^{38} +(-0.525440 + 1.96097i) q^{39} +(1.83132 + 1.05731i) q^{41} +(3.91509 + 2.26038i) q^{42} +7.15520 q^{43} +(-3.71804 - 2.14661i) q^{44} +(0.333872 + 0.578284i) q^{46} +(-5.91085 - 5.91085i) q^{47} +(-2.03955 - 2.03955i) q^{48} +(2.70957 - 1.56437i) q^{49} +(-0.760612 + 0.760612i) q^{51} +(2.81453 + 4.87491i) q^{52} +(-0.595178 - 0.159478i) q^{53} +(-7.53604 - 2.01928i) q^{54} +(-0.150834 + 0.0404159i) q^{56} +(0.218705 + 0.378808i) q^{57} +(2.62880 - 9.81081i) q^{58} +(7.80951 + 2.09255i) q^{59} +(-3.57637 - 13.3472i) q^{61} +(-12.3538 - 3.31018i) q^{62} +(-5.60902 + 5.60902i) q^{63} -7.80193 q^{64} +(-2.18298 + 2.18298i) q^{66} +(-0.0966621 - 0.360748i) q^{67} +2.98255i q^{68} +(0.230467 - 0.0617534i) q^{69} +(4.77717 - 8.27430i) q^{71} +(0.105909 - 0.0611467i) q^{72} +(-11.6826 - 11.6826i) q^{73} +(-7.24040 - 9.72965i) q^{74} +(1.17150 + 0.313902i) q^{76} +(1.79021 + 6.68116i) q^{77} +(3.90986 - 1.04764i) q^{78} +(1.12144 + 4.18528i) q^{79} +(2.34479 - 4.06129i) q^{81} -4.21622i q^{82} +(-2.01496 - 0.539908i) q^{83} -4.47894i q^{84} +(-7.13316 - 12.3550i) q^{86} +(-3.14301 - 1.81462i) q^{87} -0.106637i q^{88} +(0.0491257 - 0.183340i) q^{89} +(2.34724 - 8.76001i) q^{91} +(0.330783 - 0.572934i) q^{92} +(-2.28497 + 3.95768i) q^{93} +(-4.31371 + 16.0990i) q^{94} +(-1.47036 + 5.48747i) q^{96} +7.75205i q^{97} +(-5.40243 - 3.11910i) q^{98} +(-2.70847 - 4.69122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 40 q^{4} + 32 q^{14} - 4 q^{16} + 24 q^{19} + 36 q^{21} - 52 q^{24} + 16 q^{26} - 12 q^{29} + 4 q^{31} + 60 q^{34} - 100 q^{39} - 48 q^{41} - 48 q^{44} + 24 q^{46} + 120 q^{49} - 84 q^{51} - 104 q^{54}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q - 40 * q^4 + 32 * q^14 - 4 * q^16 + 24 * q^19 + 36 * q^21 - 52 * q^24 + 16 * q^26 - 12 * q^29 + 4 * q^31 + 60 * q^34 - 100 * q^39 - 48 * q^41 - 48 * q^44 + 24 * q^46 + 120 * q^49 - 84 * q^51 - 104 * q^54 - 68 * q^56 + 28 * q^59 + 68 * q^61 - 48 * q^64 + 4 * q^66 - 28 * q^69 + 48 * q^71 + 48 * q^74 - 152 * q^76 + 92 * q^79 - 16 * q^81 + 20 * q^86 + 8 * q^89 - 12 * q^91 - 56 * q^94 + 252 * q^96 + 24 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.996919	−	1.72671i	−0.704928	−	1.22097i	−0.966717	−	0.255847i	$-0.917646\pi$
$2$	−0.996919	−	1.72671i	−0.704928	−	1.22097i	0.261789	−	0.965125i	$-0.415688\pi$
$3$	−0.688157	+	0.184391i	−0.397308	+	0.106458i	−0.451940	−	0.892048i	$-0.649268\pi$
$3$	−0.688157	+	0.184391i	−0.397308	+	0.106458i	0.0546324	+	0.998507i	$0.482601\pi$
$4$	−0.987696	+	1.71074i	−0.493848	+	0.855370i
$5$		0			0
$5$		0			0
$6$	1.00443	+	1.00443i	0.410056	+	0.410056i
$7$	3.07412	−	0.823709i	1.16191	−	0.311333i	0.374181	−	0.927356i	$-0.377924\pi$
$7$	3.07412	−	0.823709i	1.16191	−	0.311333i	0.787728	+	0.616023i	$0.211257\pi$
$8$	−0.0490658			−0.0173474
$9$	−2.15852	+	1.24622i	−0.719505	+	0.415407i
$10$		0			0
$11$			2.17335i			0.655290i	0.944801	+	0.327645i	$0.106255\pi$
$11$			2.17335i			0.655290i	−0.944801	+	0.327645i	$0.893745\pi$
$12$	0.364245	−	1.35938i	0.105148	−	0.392419i
$13$	1.42480	−	2.46782i	0.395168	−	0.684450i	−0.597955	−	0.801530i	$-0.704020\pi$
$13$	1.42480	−	2.46782i	0.395168	−	0.684450i	0.993123	+	0.117079i	$0.0373532\pi$
$14$	−4.48696	−	4.48696i	−1.19919	−	1.19919i
$15$		0			0
$16$	2.02431	+	3.50620i	0.506076	+	0.876550i
$17$	1.30757	−	0.754926i	0.317132	−	0.183096i	−0.332981	−	0.942933i	$-0.608055\pi$
$17$	1.30757	−	0.754926i	0.317132	−	0.183096i	0.650114	+	0.759837i	$0.274721\pi$
$18$	4.30373	+	2.48476i	1.01440	+	0.585664i
$19$	−0.158906	−	0.593046i	−0.0364556	−	0.136054i	0.945300	−	0.326203i	$-0.105769\pi$
$19$	−0.158906	−	0.593046i	−0.0364556	−	0.136054i	−0.981755	+	0.190149i	$0.939103\pi$
$20$		0			0
$21$	−1.96360	+	1.13368i	−0.428492	+	0.247390i
$22$	3.75276	−	2.16666i	0.800091	−	0.461933i
$23$	−0.334904			−0.0698323			−0.0349162	−	0.999390i	$-0.511116\pi$
$23$	−0.334904			−0.0698323			−0.0349162	+	0.999390i	$0.511116\pi$
$24$	0.0337650	−	0.00904730i	0.00689225	−	0.00184677i
$25$		0			0
$26$	−5.68163			−1.11426
$27$	2.76691	−	2.76691i	0.532491	−	0.532491i
$28$	−1.62715	+	6.07260i	−0.307502	+	1.14761i
$29$	3.60210	+	3.60210i	0.668894	+	0.668894i	0.957460	−	0.288566i	$-0.0931785\pi$
$29$	3.60210	+	3.60210i	0.668894	+	0.668894i	−0.288566	+	0.957460i	$0.593179\pi$
$30$		0			0
$31$	4.53577	−	4.53577i	0.814648	−	0.814648i	−0.170679	−	0.985327i	$-0.554596\pi$
$31$	4.53577	−	4.53577i	0.814648	−	0.814648i	0.985327	+	0.170679i	$0.0545960\pi$
$32$	3.98707	−	6.90581i	0.704822	−	1.22079i
$33$	−0.400747	−	1.49561i	−0.0697611	−	0.260352i
$34$	−2.60708	−	1.50520i	−0.447111	−	0.258140i
$35$		0			0
$36$		−	4.92354i		−	0.820590i
$37$	6.04178	−	0.704946i	0.993262	−	0.115892i
$37$	6.04178	−	0.704946i	0.993262	−	0.115892i
$38$	−0.865605	+	0.865605i	−0.140420	+	0.140420i
$39$	−0.525440	+	1.96097i	−0.0841378	+	0.314006i
$40$		0			0
$41$	1.83132	+	1.05731i	0.286004	+	0.165124i	0.636138	−	0.771575i	$-0.280531\pi$
$41$	1.83132	+	1.05731i	0.286004	+	0.165124i	−0.350134	+	0.936699i	$0.613864\pi$
$42$	3.91509	+	2.26038i	0.604112	+	0.348784i
$43$	7.15520			1.09116			0.545579	−	0.838059i	$-0.316310\pi$
$43$	7.15520			1.09116			0.545579	+	0.838059i	$0.316310\pi$
$44$	−3.71804	−	2.14661i	−0.560515	−	0.323614i
$45$		0			0
$46$	0.333872	+	0.578284i	0.0492268	+	0.0852633i
$47$	−5.91085	−	5.91085i	−0.862187	−	0.862187i	0.129405	−	0.991592i	$-0.458693\pi$
$47$	−5.91085	−	5.91085i	−0.862187	−	0.862187i	−0.991592	+	0.129405i	$0.958693\pi$
$48$	−2.03955	−	2.03955i	−0.294384	−	0.294384i
$49$	2.70957	−	1.56437i	0.387081	−	0.223481i
$50$		0			0
$51$	−0.760612	+	0.760612i	−0.106507	+	0.106507i
$52$	2.81453	+	4.87491i	0.390305	+	0.676029i
$53$	−0.595178	−	0.159478i	−0.0817540	−	0.0219059i	0.217710	−	0.976013i	$-0.430141\pi$
$53$	−0.595178	−	0.159478i	−0.0817540	−	0.0219059i	−0.299464	+	0.954108i	$0.596808\pi$
$54$	−7.53604	−	2.01928i	−1.02552	−	0.274789i
$55$		0			0
$56$	−0.150834	+	0.0404159i	−0.0201561	+	0.00540080i
$57$	0.218705	+	0.378808i	0.0289682	+	0.0501744i
$58$	2.62880	−	9.81081i	0.345178	−	1.28822i
$59$	7.80951	+	2.09255i	1.01671	+	0.272427i	0.728431	−	0.685119i	$-0.240250\pi$
$59$	7.80951	+	2.09255i	1.01671	+	0.272427i	0.288280	+	0.957546i	$0.406917\pi$
$60$		0			0
$61$	−3.57637	−	13.3472i	−0.457907	−	1.70893i	−0.679398	−	0.733770i	$-0.737759\pi$
$61$	−3.57637	−	13.3472i	−0.457907	−	1.70893i	0.221492	−	0.975162i	$-0.428907\pi$
$62$	−12.3538	−	3.31018i	−1.56893	−	0.420394i
$63$	−5.60902	+	5.60902i	−0.706670	+	0.706670i
$64$	−7.80193			−0.975242
$65$		0			0
$66$	−2.18298	+	2.18298i	−0.268706	+	0.268706i
$67$	−0.0966621	−	0.360748i	−0.0118092	−	0.0440723i	0.959770	−	0.280788i	$-0.0905957\pi$
$67$	−0.0966621	−	0.360748i	−0.0118092	−	0.0440723i	−0.971579	+	0.236716i	$0.923929\pi$
$68$			2.98255i			0.361687i
$69$	0.230467	−	0.0617534i	0.0277449	−	0.00743423i
$70$		0			0
$71$	4.77717	−	8.27430i	0.566946	−	0.981979i	−0.429920	−	0.902867i	$-0.641458\pi$
$71$	4.77717	−	8.27430i	0.566946	−	0.981979i	0.996866	−	0.0791117i	$-0.0252084\pi$
$72$	0.105909	−	0.0611467i	0.0124815	−	0.00720621i
$73$	−11.6826	−	11.6826i	−1.36734	−	1.36734i	−0.864213	−	0.503126i	$-0.832183\pi$
$73$	−11.6826	−	11.6826i	−1.36734	−	1.36734i	−0.503126	−	0.864213i	$-0.667817\pi$
$74$	−7.24040	−	9.72965i	−0.841680	−	1.13105i
$75$		0			0
$76$	1.17150	+	0.313902i	0.134380	+	0.0360070i
$77$	1.79021	+	6.68116i	0.204013	+	0.761388i
$78$	3.90986	−	1.04764i	0.442704	−	0.118622i
$79$	1.12144	+	4.18528i	0.126172	+	0.470881i	0.999879	−	0.0155724i	$-0.00495705\pi$
$79$	1.12144	+	4.18528i	0.126172	+	0.470881i	−0.873707	+	0.486453i	$0.838290\pi$
$80$		0			0
$81$	2.34479	−	4.06129i	0.260532	−	0.451254i
$82$		−	4.21622i		−	0.465603i
$83$	−2.01496	−	0.539908i	−0.221171	−	0.0592626i	0.146532	−	0.989206i	$-0.453189\pi$
$83$	−2.01496	−	0.539908i	−0.221171	−	0.0592626i	−0.367703	+	0.929943i	$0.619856\pi$
$84$		−	4.47894i		−	0.488692i
$85$		0			0
$86$	−7.13316	−	12.3550i	−0.769188	−	1.33227i
$87$	−3.14301	−	1.81462i	−0.336966	−	0.194547i
$88$		−	0.106637i		−	0.0113676i
$89$	0.0491257	−	0.183340i	0.00520732	−	0.0194340i	−0.963273	−	0.268523i	$-0.913464\pi$
$89$	0.0491257	−	0.183340i	0.00520732	−	0.0194340i	0.968481	+	0.249089i	$0.0801312\pi$
$90$		0			0
$91$	2.34724	−	8.76001i	0.246057	−	0.918298i
$92$	0.330783	−	0.572934i	0.0344865	−	0.0597325i
$93$	−2.28497	+	3.95768i	−0.236940	+	0.410392i
$94$	−4.31371	+	16.0990i	−0.444926	+	1.66049i
$95$		0			0
$96$	−1.47036	+	5.48747i	−0.150068	+	0.560062i
$97$			7.75205i			0.787101i	0.919303	+	0.393550i	$0.128753\pi$
$97$			7.75205i			0.787101i	−0.919303	+	0.393550i	$0.871247\pi$
$98$	−5.40243	−	3.11910i	−0.545728	−	0.315076i
$99$	−2.70847	−	4.69122i	−0.272212	−	0.471485i
$100$		0			0
$101$			4.36118i			0.433954i	0.976177	+	0.216977i	$0.0696196\pi$
$101$			4.36118i			0.433954i	−0.976177	+	0.216977i	$0.930380\pi$
$102$	2.07163	+	0.555091i	0.205122	+	0.0549622i
$103$		−	0.120499i		−	0.0118731i	−0.999982	−	0.00593655i	$-0.998110\pi$
$103$		−	0.120499i		−	0.0118731i	0.999982	−	0.00593655i	$-0.00188967\pi$
$104$	−0.0699088	+	0.121086i	−0.00685512	+	0.0118734i
$105$		0			0
$106$	0.317972	+	1.18669i	0.0308842	+	0.115261i
$107$	−9.86809	+	2.64415i	−0.953985	+	0.255619i	−0.702052	−	0.712125i	$-0.747733\pi$
$107$	−9.86809	+	2.64415i	−0.953985	+	0.255619i	−0.251932	+	0.967745i	$0.581066\pi$
$108$	2.00059	+	7.46631i	0.192507	+	0.718446i
$109$	11.9735	+	3.20828i	1.14685	+	0.307297i	0.781702	−	0.623653i	$-0.214352\pi$
$109$	11.9735	+	3.20828i	1.14685	+	0.307297i	0.365147	+	0.930950i	$0.381019\pi$
$110$		0			0
$111$	−4.02771	+	1.59916i	−0.382293	+	0.151786i
$112$	9.11106	+	9.11106i	0.860914	+	0.860914i
$113$	−5.25127	+	3.03182i	−0.493998	+	0.285210i	−0.726232	−	0.687450i	$-0.758730\pi$
$113$	−5.25127	+	3.03182i	−0.493998	+	0.285210i	0.232233	+	0.972660i	$0.425397\pi$
$114$	0.436062	−	0.755282i	0.0408410	−	0.0707387i
$115$		0			0
$116$	−9.72004	+	2.60448i	−0.902483	+	0.241820i
$117$			7.10244i			0.656621i
$118$	−4.17221	−	15.5709i	−0.384083	−	1.43342i
$119$	3.39779	−	3.39779i	0.311475	−	0.311475i
$120$		0			0
$121$	6.27654			0.570594
$122$	−19.4814	+	19.4814i	−1.76377	+	1.76377i
$123$	−1.45519	−	0.389918i	−0.131210	−	0.0351577i
$124$	3.27956	+	12.2395i	0.294513	+	1.09914i
$125$		0			0
$126$	15.2769	+	4.09344i	1.36098	+	0.364673i
$127$	3.40738	−	12.7165i	0.302356	−	1.12841i	−0.632841	−	0.774282i	$-0.718111\pi$
$127$	3.40738	−	12.7165i	0.302356	−	1.12841i	0.935197	−	0.354128i	$-0.115222\pi$
$128$	−0.196248	−	0.339912i	−0.0173461	−	0.0300443i
$129$	−4.92391	+	1.31936i	−0.433526	+	0.116163i
$130$		0			0
$131$	−11.0289	−	2.95518i	−0.963598	−	0.258195i	−0.257475	−	0.966285i	$-0.582891\pi$
$131$	−11.0289	−	2.95518i	−0.963598	−	0.258195i	−0.706122	+	0.708090i	$0.749557\pi$
$132$	2.95441	+	0.791632i	0.257149	+	0.0689028i
$133$	−0.976995	−	1.69220i	−0.0847162	−	0.146733i
$134$	−0.526544	+	0.526544i	−0.0454865	+	0.0454865i
$135$		0			0
$136$	−0.0641569	+	0.0370410i	−0.00550141	+	0.00317624i
$137$	14.8532	+	14.8532i	1.26899	+	1.26899i	0.946610	+	0.322380i	$0.104483\pi$
$137$	14.8532	+	14.8532i	1.26899	+	1.26899i	0.322380	+	0.946610i	$0.395517\pi$
$138$	−0.336387	−	0.336387i	−0.0286352	−	0.0286352i
$139$	2.76488	+	4.78891i	0.234514	+	0.406190i	0.959131	−	0.282961i	$-0.0913168\pi$
$139$	2.76488	+	4.78891i	0.234514	+	0.406190i	−0.724617	+	0.689152i	$0.757983\pi$
$140$		0			0
$141$	5.15751	+	2.97769i	0.434340	+	0.250767i
$142$	−19.0498			−1.59862
$143$	5.36345	+	3.09659i	0.448514	+	0.258950i
$144$	−8.73899	−	5.04546i	−0.728249	−	0.420455i
$145$		0			0
$146$	−8.52587	+	31.8190i	−0.705606	+	2.63336i
$147$	−1.57615	+	1.57615i	−0.129999	+	0.129999i
$148$	−4.76146	+	11.0322i	−0.391389	+	0.906839i
$149$		−	13.7980i		−	1.13038i	−0.824962	−	0.565189i	$-0.808803\pi$
$149$		−	13.7980i		−	1.13038i	0.824962	−	0.565189i	$-0.191197\pi$
$150$		0			0
$151$	1.21576	+	0.701919i	0.0989370	+	0.0571213i	0.548652	−	0.836051i	$-0.315141\pi$
$151$	1.21576	+	0.701919i	0.0989370	+	0.0571213i	−0.449715	+	0.893172i	$0.648474\pi$
$152$	0.00779686	+	0.0290983i	0.000632409	+	0.00236018i
$153$	−1.88161	+	3.25904i	−0.152119	+	0.263478i
$154$	9.75175	−	9.75175i	0.785819	−	0.785819i
$155$		0			0
$156$	−2.83573	−	2.83573i	−0.227040	−	0.227040i
$157$	1.87919	−	7.01323i	0.149976	−	0.559716i	−0.849508	−	0.527576i	$-0.823101\pi$
$157$	1.87919	−	7.01323i	0.149976	−	0.559716i	0.999483	−	0.0321404i	$-0.0102324\pi$
$158$	6.10880	−	6.10880i	0.485990	−	0.485990i
$159$	0.438983			0.0348136
$160$		0			0
$161$	−1.02954	+	0.275864i	−0.0811389	+	0.0217411i
$162$	−9.35024			−0.734625
$163$	−4.40875	+	2.54539i	−0.345320	+	0.199370i	−0.662622	−	0.748954i	$-0.730556\pi$
$163$	−4.40875	+	2.54539i	−0.345320	+	0.199370i	0.317302	+	0.948324i	$0.397223\pi$
$164$	−3.61757	+	2.08860i	−0.282485	+	0.163093i
$165$		0			0
$166$	1.07649	+	4.01751i	0.0835518	+	0.311820i
$167$	4.88520	+	2.82047i	0.378028	+	0.218255i	0.676960	−	0.736020i	$-0.263297\pi$
$167$	4.88520	+	2.82047i	0.378028	+	0.218255i	−0.298932	+	0.954274i	$0.596630\pi$
$168$	0.0963454	−	0.0556250i	0.00743321	−	0.00429157i
$169$	2.43991	+	4.22604i	0.187685	+	0.325080i
$170$		0			0
$171$	1.08207	+	1.08207i	0.0827477	+	0.0827477i
$172$	−7.06716	+	12.2407i	−0.538866	+	0.933343i
$173$	−0.295795	+	1.10392i	−0.0224888	+	0.0839295i	−0.976258	−	0.216610i	$-0.930500\pi$
$173$	−0.295795	+	1.10392i	−0.0224888	+	0.0839295i	0.953769	+	0.300539i	$0.0971667\pi$
$174$			7.23611i			0.548568i
$175$		0			0
$176$	−7.62021	+	4.39953i	−0.574395	+	0.331627i
$177$	−5.76002			−0.432950
$178$	−0.365550	+	0.0979487i	−0.0273991	+	0.00734157i
$179$	11.6801	+	11.6801i	0.873015	+	0.873015i	0.992800	−	0.119785i	$-0.0382206\pi$
$179$	11.6801	+	11.6801i	0.873015	+	0.873015i	−0.119785	+	0.992800i	$0.538221\pi$
$180$		0			0
$181$	12.7282	−	22.0459i	0.946080	−	1.63866i	0.192507	−	0.981296i	$-0.438338\pi$
$181$	12.7282	−	22.0459i	0.946080	−	1.63866i	0.753573	−	0.657364i	$-0.228328\pi$
$182$	−17.4660	+	4.68001i	−1.29467	+	0.346905i
$183$	4.92221	+	8.52551i	0.363860	+	0.630224i
$184$	0.0164323			0.00121141
$185$		0			0
$186$	9.11171			0.668103
$187$	1.64072	+	2.84181i	0.119981	+	0.207814i
$188$	15.9501	−	4.27380i	1.16328	−	0.311699i
$189$	6.22669	−	10.7849i	0.452925	−	0.784489i
$190$		0			0
$191$	12.6423	+	12.6423i	0.914764	+	0.914764i	0.996642	−	0.0818786i	$-0.0260920\pi$
$191$	12.6423	+	12.6423i	0.914764	+	0.914764i	−0.0818786	+	0.996642i	$0.526092\pi$
$192$	5.36896	−	1.43861i	0.387471	−	0.103823i
$193$	19.2629			1.38657			0.693285	−	0.720663i	$-0.256163\pi$
$193$	19.2629			1.38657			0.693285	+	0.720663i	$0.256163\pi$
$194$	13.3856	−	7.72816i	0.961028	−	0.554850i
$195$		0			0
$196$			6.18048i			0.441463i
$197$	4.36604	−	16.2943i	0.311067	−	1.16092i	−0.616528	−	0.787333i	$-0.711461\pi$
$197$	4.36604	−	16.2943i	0.311067	−	1.16092i	0.927595	−	0.373587i	$-0.121872\pi$
$198$	−5.40026	+	9.35352i	−0.383780	+	0.664726i
$199$	12.5591	+	12.5591i	0.890292	+	0.890292i	0.994550	−	0.104259i	$-0.0332469\pi$
$199$	12.5591	+	12.5591i	0.890292	+	0.890292i	−0.104259	+	0.994550i	$0.533247\pi$
$200$		0			0
$201$	0.133037	+	0.230428i	0.00938374	+	0.0162531i
$202$	7.53051	−	4.34774i	0.529845	−	0.305906i
$203$	14.0404	+	8.10623i	0.985443	+	0.568946i
$204$	−0.549956	−	2.05246i	−0.0385046	−	0.143701i
$205$		0			0
$206$	−0.208067	+	0.120128i	−0.0144967	+	0.00836968i
$207$	0.722896	−	0.417364i	0.0502447	−	0.0290088i
$208$	11.5369			0.799940
$209$	1.28890	−	0.345359i	0.0891549	−	0.0238890i
$210$		0			0
$211$	−3.50233			−0.241110			−0.120555	−	0.992707i	$-0.538467\pi$
$211$	−3.50233			−0.241110			−0.120555	+	0.992707i	$0.538467\pi$
$212$	0.860679	−	0.860679i	0.0591117	−	0.0591117i
$213$	−1.76174	+	6.57489i	−0.120712	+	0.450504i
$214$	14.4034	+	14.4034i	0.984595	+	0.984595i
$215$		0			0
$216$	−0.135760	+	0.135760i	−0.00923732	+	0.00923732i
$217$	10.2074	−	17.6797i	0.692921	−	1.20017i
$218$	−6.39678	−	23.8731i	−0.433245	−	1.61689i
$219$	10.1936	+	5.88528i	0.688819	+	0.397690i
$220$		0			0
$221$		−	4.30246i		−	0.289415i
$222$	6.77660	+	5.36046i	0.454816	+	0.359771i
$223$	11.7322	−	11.7322i	0.785647	−	0.785647i	−0.195131	−	0.980777i	$-0.562513\pi$
$223$	11.7322	−	11.7322i	0.785647	−	0.785647i	0.980777	+	0.195131i	$0.0625131\pi$
$224$	6.56838	−	24.5135i	0.438868	−	1.63788i
$225$		0			0
$226$	10.4702	+	6.04497i	0.696467	+	0.402105i
$227$	−16.3587	−	9.44467i	−1.08576	−	0.626865i	−0.153317	−	0.988177i	$-0.548996\pi$
$227$	−16.3587	−	9.44467i	−1.08576	−	0.626865i	−0.932445	+	0.361312i	$0.882329\pi$
$228$	−0.864056			−0.0572235
$229$	−8.30226	−	4.79331i	−0.548629	−	0.316751i	0.199940	−	0.979808i	$-0.435925\pi$
$229$	−8.30226	−	4.79331i	−0.548629	−	0.316751i	−0.748569	+	0.663057i	$0.769259\pi$
$230$		0			0
$231$	−2.46389	−	4.26759i	−0.162112	−	0.280787i
$232$	−0.176740	−	0.176740i	−0.0116035	−	0.0116035i
$233$	16.8480	+	16.8480i	1.10375	+	1.10375i	0.993954	+	0.109796i	$0.0350197\pi$
$233$	16.8480	+	16.8480i	1.10375	+	1.10375i	0.109796	+	0.993954i	$0.464980\pi$
$234$	12.2639	−	7.08056i	0.801715	−	0.462871i
$235$		0			0
$236$	−11.2932	+	11.2932i	−0.735126	+	0.735126i
$237$	−1.54346	−	2.67335i	−0.100258	−	0.173653i
$238$	−9.25434	−	2.47969i	−0.599870	−	0.160735i
$239$	−24.8308	−	6.65340i	−1.60617	−	0.430373i	−0.659274	−	0.751903i	$-0.729136\pi$
$239$	−24.8308	−	6.65340i	−1.60617	−	0.430373i	−0.946899	+	0.321530i	$0.895803\pi$
$240$		0			0
$241$	−14.6126	+	3.91545i	−0.941283	+	0.252216i	−0.696659	−	0.717402i	$-0.745331\pi$
$241$	−14.6126	+	3.91545i	−0.941283	+	0.252216i	−0.244624	+	0.969618i	$0.578664\pi$
$242$	−6.25720	−	10.8378i	−0.402228	−	0.696680i
$243$	−3.90299	+	14.5662i	−0.250377	+	0.934419i
$244$	26.3659	+	7.06472i	1.68790	+	0.452273i
$245$		0			0
$246$	0.777434	+	2.90142i	0.0495674	+	0.184988i
$247$	−1.68994	−	0.452818i	−0.107528	−	0.0288121i
$248$	−0.222551	+	0.222551i	−0.0141320	+	0.0141320i
$249$	1.48617			0.0941820
$250$		0			0
$251$	−11.1540	+	11.1540i	−0.704037	+	0.704037i	−0.965275	−	0.261238i	$-0.915869\pi$
$251$	−11.1540	+	11.1540i	−0.704037	+	0.704037i	0.261238	+	0.965275i	$0.415869\pi$
$252$	−4.05557	−	15.1356i	−0.255477	−	0.953452i
$253$		−	0.727865i		−	0.0457605i
$254$	−25.3547	+	6.79377i	−1.59090	+	0.426279i
$255$		0			0
$256$	−8.19322	+	14.1911i	−0.512076	+	0.886942i
$257$	−5.15532	+	2.97643i	−0.321580	+	0.185664i	−0.652097	−	0.758136i	$-0.726110\pi$
$257$	−5.15532	+	2.97643i	−0.321580	+	0.185664i	0.330516	+	0.943800i	$0.392777\pi$
$258$	7.18689	+	7.18689i	0.447436	+	0.447436i
$259$	17.9925	−	7.14376i	1.11800	−	0.443891i
$260$		0			0
$261$	−12.2642	−	3.28618i	−0.759135	−	0.203410i
$262$	5.89215	+	21.9898i	0.364018	+	1.35853i
$263$	−7.08485	+	1.89838i	−0.436870	+	0.117059i	−0.470549	−	0.882374i	$-0.655944\pi$
$263$	−7.08485	+	1.89838i	−0.436870	+	0.117059i	0.0336790	+	0.999433i	$0.489278\pi$
$264$	0.0196630	+	0.0733832i	0.00121017	+	0.00451642i
$265$		0			0
$266$	−1.94797	+	3.37398i	−0.119438	+	0.206872i
$267$			0.135225i			0.00827563i
$268$	0.712618	+	0.190945i	0.0435301	+	0.0116638i
$269$			15.0921i			0.920182i	0.887872	+	0.460091i	$0.152183\pi$
$269$			15.0921i			0.920182i	−0.887872	+	0.460091i	$0.847817\pi$
$270$		0			0
$271$	15.1317	+	26.2089i	0.919186	+	1.59208i	0.800654	+	0.599127i	$0.204485\pi$
$271$	15.1317	+	26.2089i	0.919186	+	1.59208i	0.118532	+	0.992950i	$0.462181\pi$
$272$	5.29384	+	3.05640i	0.320986	+	0.185322i
$273$			6.46107i			0.391042i
$274$	10.8398	−	40.4546i	0.654854	−	2.44395i
$275$		0			0
$276$	−0.121987	+	0.455262i	−0.00734276	+	0.0274036i
$277$	7.99538	−	13.8484i	0.480396	−	0.832070i	−0.519351	−	0.854561i	$-0.673826\pi$
$277$	7.99538	−	13.8484i	0.480396	−	0.832070i	0.999747	+	0.0224906i	$0.00715959\pi$
$278$	5.51272	−	9.54832i	0.330631	−	0.572670i
$279$	−4.13796	+	15.4431i	−0.247733	+	0.924553i
$280$		0			0
$281$	−3.07938	+	11.4924i	−0.183701	+	0.685580i	0.811204	+	0.584763i	$0.198812\pi$
$281$	−3.07938	+	11.4924i	−0.183701	+	0.685580i	−0.994905	+	0.100817i	$0.967854\pi$
$282$		−	11.8741i		−	0.707090i
$283$	2.01999	+	1.16624i	0.120076	+	0.0693258i	0.558835	−	0.829279i	$-0.311249\pi$
$283$	2.01999	+	1.16624i	0.120076	+	0.0693258i	−0.438759	+	0.898605i	$0.644582\pi$
$284$	9.43678	+	16.3450i	0.559970	+	0.969896i
$285$		0			0
$286$		−	12.3482i		−	0.730164i
$287$	6.50062	+	1.74184i	0.383719	+	0.102817i
$288$			19.8751i			1.17115i
$289$	−7.36017	+	12.7482i	−0.432951	+	0.749894i
$290$		0			0
$291$	−1.42941	−	5.33463i	−0.0837935	−	0.312721i
$292$	31.5246	−	8.44699i	1.84484	−	0.494323i
$293$	−6.00204	−	22.3999i	−0.350643	−	1.30862i	−0.885879	−	0.463916i	$-0.846444\pi$
$293$	−6.00204	−	22.3999i	−0.350643	−	1.30862i	0.535236	−	0.844702i	$-0.320223\pi$
$294$	4.29286	+	1.15027i	0.250365	+	0.0670850i
$295$		0			0
$296$	−0.296444	+	0.0345887i	−0.0172305	+	0.00201043i
$297$	6.01346	+	6.01346i	0.348936	+	0.348936i
$298$	−23.8252	+	13.7555i	−1.38016	+	0.796835i
$299$	−0.477170	+	0.826484i	−0.0275955	+	0.0477968i
$300$		0			0
$301$	21.9960	−	5.89380i	1.26783	−	0.339713i
$302$		−	2.79902i		−	0.161066i
$303$	−0.804163	−	3.00118i	−0.0461980	−	0.172413i
$304$	1.75766	−	1.75766i	0.100809	−	0.100809i
$305$		0			0
$306$	7.50324			0.428932
$307$	−20.5500	+	20.5500i	−1.17285	+	1.17285i	−0.191323	+	0.981527i	$0.561278\pi$
$307$	−20.5500	+	20.5500i	−1.17285	+	1.17285i	−0.981527	+	0.191323i	$0.938722\pi$
$308$	−13.1979	−	3.53637i	−0.752020	−	0.201503i
$309$	0.0222189	+	0.0829221i	0.00126399	+	0.00471727i
$310$		0			0
$311$	6.27405	+	1.68113i	0.355769	+	0.0953279i	0.432277	−	0.901741i	$-0.357710\pi$
$311$	6.27405	+	1.68113i	0.355769	+	0.0953279i	−0.0765080	+	0.997069i	$0.524377\pi$
$312$	0.0257811	−	0.0962165i	0.00145957	−	0.00544719i
$313$	1.25227	+	2.16900i	0.0707825	+	0.122599i	0.899244	−	0.437446i	$-0.144117\pi$
$313$	1.25227	+	2.16900i	0.0707825	+	0.122599i	−0.828462	+	0.560045i	$0.810784\pi$
$314$	−13.9832	+	3.74680i	−0.789120	+	0.211444i
$315$		0			0
$316$	−8.26757	−	2.21529i	−0.465087	−	0.124620i
$317$	−4.31555	−	1.15635i	−0.242386	−	0.0649470i	0.135581	−	0.990766i	$-0.456710\pi$
$317$	−4.31555	−	1.15635i	−0.242386	−	0.0649470i	−0.377967	+	0.925819i	$0.623377\pi$
$318$	−0.437630	−	0.757998i	−0.0245411	−	0.0425064i
$319$	−7.82864	+	7.82864i	−0.438320	+	0.438320i
$320$		0			0
$321$	6.30324	−	3.63918i	0.351813	−	0.203119i
$322$	1.50270	+	1.50270i	0.0837424	+	0.0837424i
$323$	−0.655487	−	0.655487i	−0.0364723	−	0.0364723i
$324$	4.63187	+	8.02263i	0.257326	+	0.445702i
$325$		0			0
$326$	8.79033	+	5.07510i	0.486851	+	0.281084i
$327$	−8.83120			−0.488366
$328$	−0.0898550	−	0.0518778i	−0.00496141	−	0.00286447i
$329$	−23.0395	−	13.3019i	−1.27021	−	0.733356i
$330$		0			0
$331$	−4.17606	+	15.5853i	−0.229537	+	0.856645i	0.750999	+	0.660304i	$0.229573\pi$
$331$	−4.17606	+	15.5853i	−0.229537	+	0.856645i	−0.980536	+	0.196341i	$0.937094\pi$
$332$	2.91381	−	2.91381i	0.159916	−	0.159916i
$333$	−12.1627	+	9.05101i	−0.666515	+	0.495993i
$334$		−	11.2471i		−	0.615416i
$335$		0			0
$336$	−7.94984	−	4.58984i	−0.433699	−	0.250396i
$337$	9.00391	+	33.6031i	0.490474	+	1.83048i	0.554029	+	0.832497i	$0.313089\pi$
$337$	9.00391	+	33.6031i	0.490474	+	1.83048i	−0.0635550	+	0.997978i	$0.520244\pi$
$338$	4.86478	−	8.42604i	0.264609	−	0.458316i
$339$	3.05466	−	3.05466i	0.165906	−	0.165906i
$340$		0			0
$341$	9.85782	+	9.85782i	0.533831	+	0.533831i
$342$	0.789688	−	2.94715i	0.0427014	−	0.159364i
$343$	−8.71195	+	8.71195i	−0.470401	+	0.470401i
$344$	−0.351075			−0.0189287
$345$		0			0
$346$	2.20104	−	0.589767i	0.118329	−	0.0317061i
$347$	36.0284			1.93411			0.967054	−	0.254572i	$-0.0819345\pi$
$347$	36.0284			1.93411			0.967054	+	0.254572i	$0.0819345\pi$
$348$	6.20868	−	3.58458i	0.332820	−	0.192154i
$349$	17.5896	−	10.1554i	0.941550	−	0.543604i	0.0511041	−	0.998693i	$-0.483726\pi$
$349$	17.5896	−	10.1554i	0.941550	−	0.543604i	0.890446	+	0.455089i	$0.150393\pi$
$350$		0			0
$351$	−2.88595	−	10.7705i	−0.154041	−	0.574887i
$352$	15.0088	+	8.66531i	0.799970	+	0.461863i
$353$	15.4704	−	8.93186i	0.823408	−	0.475395i	−0.0281823	−	0.999603i	$-0.508972\pi$
$353$	15.4704	−	8.93186i	0.823408	−	0.475395i	0.851590	+	0.524208i	$0.175639\pi$
$354$	5.74227	+	9.94591i	0.305198	+	0.528619i
$355$		0			0
$356$	0.265125	+	0.265125i	0.0140516	+	0.0140516i
$357$	−1.71169	+	2.96474i	−0.0905924	+	0.156911i
$358$	8.52411	−	31.8124i	0.450513	−	1.68134i
$359$		−	21.4882i		−	1.13410i	−0.823682	−	0.567051i	$-0.808084\pi$
$359$		−	21.4882i		−	1.13410i	0.823682	−	0.567051i	$-0.191916\pi$
$360$		0			0
$361$	16.1280	−	9.31152i	0.848844	−	0.490080i
$362$	−50.7560			−2.66768
$363$	−4.31925	+	1.15734i	−0.226702	+	0.0607445i
$364$	12.6677	+	12.6677i	0.663970	+	0.663970i
$365$		0			0
$366$	9.81409	−	16.9985i	0.512991	−	0.888526i
$367$	−29.3187	+	7.85591i	−1.53042	+	0.410075i	−0.923156	−	0.384424i	$-0.874400\pi$
$367$	−29.3187	+	7.85591i	−1.53042	+	0.410075i	−0.607265	+	0.794500i	$0.707733\pi$
$368$	−0.677948	−	1.17424i	−0.0353405	−	0.0612115i
$369$	−5.27057			−0.274375
$370$		0			0
$371$	−1.96101			−0.101811
$372$	−4.51370	−	7.81796i	−0.234025	−	0.405343i
$373$	−25.1878	+	6.74904i	−1.30417	+	0.349452i	−0.843027	−	0.537872i	$-0.819228\pi$
$373$	−25.1878	+	6.74904i	−1.30417	+	0.349452i	−0.461146	+	0.887324i	$0.652562\pi$
$374$	3.27133	−	5.66611i	0.169156	−	0.292988i
$375$		0			0
$376$	0.290021	+	0.290021i	0.0149567	+	0.0149567i
$377$	14.0216	−	3.75708i	0.722150	−	0.193499i
$378$	−24.8300			−1.27712
$379$	−24.1459	+	13.9406i	−1.24029	+	0.716082i	−0.969153	−	0.246459i	$-0.920733\pi$
$379$	−24.1459	+	13.9406i	−1.24029	+	0.716082i	−0.271137	+	0.962541i	$0.587400\pi$
$380$		0			0
$381$			9.37927i			0.480514i
$382$	9.22628	−	34.4330i	0.472058	−	1.76174i
$383$	−11.6400	+	20.1610i	−0.594775	+	1.03018i	0.398804	+	0.917036i	$0.369425\pi$
$383$	−11.6400	+	20.1610i	−0.594775	+	1.03018i	−0.993579	+	0.113144i	$0.963908\pi$
$384$	0.197726	+	0.197726i	0.0100902	+	0.0100902i
$385$		0			0
$386$	−19.2035	−	33.2615i	−0.977433	−	1.69296i
$387$	−15.4446	+	8.91695i	−0.785094	+	0.453274i
$388$	−13.2617	−	7.65666i	−0.673262	−	0.388708i
$389$	−6.39722	−	23.8748i	−0.324352	−	1.21050i	−0.914962	−	0.403541i	$-0.867779\pi$
$389$	−6.39722	−	23.8748i	−0.324352	−	1.21050i	0.590610	−	0.806957i	$-0.298887\pi$
$390$		0			0
$391$	−0.437911	+	0.252828i	−0.0221461	+	0.0127861i
$392$	−0.132947	+	0.0767569i	−0.00671483	+	0.00387681i
$393$	8.13451			0.410332
$394$	−32.4882	+	8.70518i	−1.63673	+	0.438561i
$395$		0			0
$396$	10.7006			0.537725
$397$	−1.14631	+	1.14631i	−0.0575316	+	0.0575316i	−0.735287	−	0.677756i	$-0.762953\pi$
$397$	−1.14631	+	1.14631i	−0.0575316	+	0.0575316i	0.677756	+	0.735287i	$0.262953\pi$
$398$	9.16558	−	34.2064i	0.459429	−	1.71461i
$399$	0.984354	+	0.984354i	0.0492793	+	0.0492793i
$400$		0			0
$401$	−5.12856	+	5.12856i	−0.256108	+	0.256108i	−0.823469	−	0.567361i	$-0.807964\pi$
$401$	−5.12856	+	5.12856i	−0.256108	+	0.256108i	0.567361	+	0.823469i	$0.307964\pi$
$402$	0.265255	−	0.459435i	0.0132297	−	0.0229146i
$403$	−4.73091	−	17.6560i	−0.235664	−	0.879509i
$404$	−7.46084	−	4.30752i	−0.371191	−	0.214307i
$405$		0			0
$406$		−	32.3250i		−	1.60426i
$407$	1.53210	+	13.1309i	0.0759431	+	0.650875i
$408$	0.0373200	−	0.0373200i	0.00184762	−	0.00184762i
$409$	−1.06786	+	3.98532i	−0.0528024	+	0.197061i	−0.987289	−	0.158938i	$-0.949193\pi$
$409$	−1.06786	+	3.98532i	−0.0528024	+	0.197061i	0.934486	+	0.356000i	$0.115860\pi$
$410$		0			0
$411$	−12.9601	−	7.48252i	−0.639275	−	0.369085i
$412$	0.206142	+	0.119016i	0.0101559	+	0.00586350i
$413$	25.7310			1.26614
$414$	−1.44134	−	0.832157i	−0.0708379	−	0.0408983i
$415$		0			0
$416$	−11.3615	−	19.6788i	−0.557045	−	0.964831i
$417$	−2.78571	−	2.78571i	−0.136417	−	0.136417i
$418$	−1.88126	−	1.88126i	−0.0920156	−	0.0920156i
$419$	−17.3507	+	10.0174i	−0.847638	+	0.489384i	−0.859853	−	0.510541i	$-0.829445\pi$
$419$	−17.3507	+	10.0174i	−0.847638	+	0.489384i	0.0122153	+	0.999925i	$0.496112\pi$
$420$		0			0
$421$	3.69196	−	3.69196i	0.179935	−	0.179935i	−0.611392	−	0.791328i	$-0.709390\pi$
$421$	3.69196	−	3.69196i	0.179935	−	0.179935i	0.791328	+	0.611392i	$0.209390\pi$
$422$	3.49154	+	6.04753i	0.169966	+	0.294389i
$423$	20.1249	+	5.39245i	0.978506	+	0.262190i
$424$	0.0292029	+	0.00782489i	0.00141822	+	0.000380010i
$425$		0			0
$426$	13.1093	−	3.51262i	0.635146	−	0.170187i
$427$	−21.9884	−	38.0850i	−1.06409	−	1.84306i
$428$	5.22323	−	19.4933i	0.252474	−	0.942246i
$429$	−4.26188	−	1.14197i	−0.205765	−	0.0551347i
$430$		0			0
$431$	−4.73118	−	17.6570i	−0.227893	−	0.850509i	−0.981225	−	0.192868i	$-0.938221\pi$
$431$	−4.73118	−	17.6570i	−0.227893	−	0.850509i	0.753332	−	0.657641i	$-0.228446\pi$
$432$	15.3024	+	4.10026i	0.736237	+	0.197274i
$433$	4.75230	−	4.75230i	0.228381	−	0.228381i	−0.583635	−	0.812016i	$-0.698370\pi$
$433$	4.75230	−	4.75230i	0.228381	−	0.228381i	0.812016	+	0.583635i	$0.198370\pi$
$434$	−40.7037			−1.95384
$435$		0			0
$436$	−17.3146	+	17.3146i	−0.829221	+	0.829221i
$437$	0.0532183	+	0.198614i	0.00254578	+	0.00950098i
$438$		−	23.4686i		−	1.12137i
$439$	−33.2323	+	8.90457i	−1.58609	+	0.424992i	−0.940805	−	0.338948i	$-0.889929\pi$
$439$	−33.2323	+	8.90457i	−1.58609	+	0.424992i	−0.645287	+	0.763940i	$0.723262\pi$
$440$		0			0
$441$	−3.89909	+	6.75343i	−0.185671	+	0.321592i
$442$	−7.42913	+	4.28921i	−0.353368	+	0.204017i
$443$	2.82400	+	2.82400i	0.134172	+	0.134172i	0.771003	−	0.636831i	$-0.219755\pi$
$443$	2.82400	+	2.82400i	0.134172	+	0.134172i	−0.636831	+	0.771003i	$0.719755\pi$
$444$	1.24240	−	8.46984i	0.0589615	−	0.401961i
$445$		0			0
$446$	−31.9542	−	8.56211i	−1.51308	−	0.405428i
$447$	2.54423	+	9.49521i	0.120338	+	0.449108i
$448$	−23.9841	+	6.42652i	−1.13314	+	0.303625i
$449$	−7.10809	−	26.5277i	−0.335451	−	1.25192i	−0.903379	−	0.428843i	$-0.858921\pi$
$449$	−7.10809	−	26.5277i	−0.335451	−	1.25192i	0.567928	−	0.823078i	$-0.307745\pi$
$450$		0			0
$451$	−2.29791	+	3.98010i	−0.108204	+	0.187416i
$452$		−	11.9781i		−	0.563402i
$453$	−0.966061	−	0.258855i	−0.0453895	−	0.0121621i
$454$			37.6623i			1.76758i
$455$		0			0
$456$	−0.0107309	−	0.0185865i	−0.000502522	−	0.000870393i
$457$	−5.87366	−	3.39116i	−0.274758	−	0.158632i	0.356290	−	0.934375i	$-0.384042\pi$
$457$	−5.87366	−	3.39116i	−0.274758	−	0.158632i	−0.631048	+	0.775744i	$0.717375\pi$
$458$			19.1142i			0.893147i
$459$	1.52911	−	5.70673i	0.0713729	−	0.266367i
$460$		0			0
$461$	10.7605	−	40.1588i	0.501168	−	1.87038i	0.00886370	−	0.999961i	$-0.497179\pi$
$461$	10.7605	−	40.1588i	0.501168	−	1.87038i	0.492304	−	0.870423i	$-0.336155\pi$
$462$	−4.91260	+	8.50888i	−0.228555	+	0.395869i
$463$	−9.71266	+	16.8228i	−0.451385	+	0.781822i	−0.998472	−	0.0552533i	$-0.982403\pi$
$463$	−9.71266	+	16.8228i	−0.451385	+	0.781822i	0.547087	+	0.837076i	$0.315737\pi$
$464$	−5.33794	+	19.9215i	−0.247808	+	0.924830i
$465$		0			0
$466$	12.2956	−	45.8878i	0.569583	−	2.12571i
$467$			19.7318i			0.913077i	0.889704	+	0.456538i	$0.150911\pi$
$467$			19.7318i			0.913077i	−0.889704	+	0.456538i	$0.849089\pi$
$468$	−12.1504	−	7.01505i	−0.561653	−	0.324271i
$469$	−0.594302	−	1.02936i	−0.0274423	−	0.0475315i
$470$		0			0
$471$			5.17271i			0.238346i
$472$	−0.383180	−	0.102673i	−0.0176373	−	0.00472589i
$473$			15.5508i			0.715025i
$474$	−3.07741	+	5.33022i	−0.141350	+	0.244825i
$475$		0			0
$476$	2.45675	+	9.16872i	0.112605	+	0.420248i
$477$	1.48345	−	0.397488i	0.0679223	−	0.0181997i
$478$	13.2658	+	49.5087i	0.606764	+	2.26447i
$479$	36.6479	+	9.81978i	1.67449	+	0.448677i	0.966315	−	0.257364i	$-0.0828538\pi$
$479$	36.6479	+	9.81978i	1.67449	+	0.448677i	0.708171	+	0.706041i	$0.249520\pi$
$480$		0			0
$481$	6.86863	−	15.9144i	0.313182	−	0.725635i
$482$	21.3285	+	21.3285i	0.971486	+	0.971486i
$483$	0.657617	−	0.379675i	0.0299226	−	0.0172758i
$484$	−6.19931	+	10.7375i	−0.281787	+	0.488069i
$485$		0			0
$486$	29.0426	−	7.78193i	1.31740	−	0.352995i
$487$			29.1168i			1.31941i	0.751526	+	0.659703i	$0.229318\pi$
$487$			29.1168i			1.31941i	−0.751526	+	0.659703i	$0.770682\pi$
$488$	0.175477	+	0.654890i	0.00794348	+	0.0296455i
$489$	2.56456	−	2.56456i	0.115974	−	0.115974i
$490$		0			0
$491$	−32.9750			−1.48814			−0.744070	−	0.668102i	$-0.767107\pi$
$491$	−32.9750			−1.48814			−0.744070	+	0.668102i	$0.767107\pi$
$492$	2.10434	−	2.10434i	0.0948709	−	0.0948709i
$493$	7.42932	+	1.99068i	0.334600	+	0.0896558i
$494$	0.902846	+	3.36947i	0.0406210	+	0.151600i
$495$		0			0
$496$	25.0851	+	6.72153i	1.12635	+	0.301806i
$497$	7.86999	−	29.3712i	0.353017	−	1.31748i
$498$	−1.48159	−	2.56619i	−0.0663916	−	0.114994i
$499$	4.27129	−	1.14449i	0.191209	−	0.0512344i	−0.161944	−	0.986800i	$-0.551776\pi$
$499$	4.27129	−	1.14449i	0.191209	−	0.0512344i	0.353153	+	0.935566i	$0.385110\pi$
$500$		0			0
$501$	−3.88186	−	1.04014i	−0.173429	−	0.0464701i
$502$	30.3795	+	8.14017i	1.35590	+	0.363314i
$503$	−14.7057	−	25.4710i	−0.655694	−	1.13570i	−0.981719	−	0.190335i	$-0.939043\pi$
$503$	−14.7057	−	25.4710i	−0.655694	−	1.13570i	0.326025	−	0.945361i	$-0.394291\pi$
$504$	0.275211	−	0.275211i	0.0122589	−	0.0122589i
$505$		0			0
$506$	−1.25681	+	0.725622i	−0.0558722	+	0.0322578i
$507$	−2.45828	−	2.45828i	−0.109176	−	0.109176i
$508$	18.3892	+	18.3892i	0.815889	+	0.815889i
$509$	−21.2253	−	36.7633i	−0.940794	−	1.62950i	−0.763962	−	0.645261i	$-0.776748\pi$
$509$	−21.2253	−	36.7633i	−0.940794	−	1.62950i	−0.176832	−	0.984241i	$-0.556585\pi$
$510$		0			0
$511$	−45.5366	−	26.2906i	−2.01442	−	1.16303i
$512$	31.8869			1.40922
$513$	−2.08058	−	1.20122i	−0.0918599	−	0.0530353i
$514$	10.2789	+	5.93451i	0.453382	+	0.261760i
$515$		0			0
$516$	2.60625	−	9.72664i	0.114734	−	0.428191i
$517$	12.8464	−	12.8464i	0.564983	−	0.564983i
$518$	−30.2723	−	23.9462i	−1.33009	−	1.05213i
$519$		−	0.814213i		−	0.0357400i
$520$		0			0
$521$	9.27032	+	5.35222i	0.406140	+	0.234485i	0.689130	−	0.724638i	$-0.257993\pi$
$521$	9.27032	+	5.35222i	0.406140	+	0.234485i	−0.282990	+	0.959123i	$0.591326\pi$
$522$	6.55212	+	24.4528i	0.286779	+	1.07027i
$523$	0.928801	−	1.60873i	0.0406137	−	0.0703449i	−0.845004	−	0.534760i	$-0.820402\pi$
$523$	0.928801	−	1.60873i	0.0406137	−	0.0703449i	0.885618	+	0.464415i	$0.153735\pi$
$524$	15.9487	−	15.9487i	0.696723	−	0.696723i
$525$		0			0
$526$	10.3410	+	10.3410i	0.450888	+	0.450888i
$527$	2.50667	−	9.35500i	0.109192	−	0.407510i
$528$	4.43267	−	4.43267i	0.192907	−	0.192907i
$529$	−22.8878			−0.995123
$530$		0			0
$531$	−19.4647	+	5.21556i	−0.844697	+	0.226336i
$532$	3.85989			0.167348
$533$	5.21851	−	3.01291i	0.226039	−	0.130504i
$534$	0.233495	−	0.134808i	0.0101043	−	0.00583373i
$535$		0			0
$536$	0.00474280	+	0.0177004i	0.000204858	+	0.000764539i
$537$	−10.1915	−	5.88406i	−0.439795	−	0.253916i
$538$	26.0598	−	15.0456i	1.12352	−	0.648662i
$539$	3.39992	+	5.88884i	0.146445	+	0.253650i
$540$		0			0
$541$	18.3486	+	18.3486i	0.788870	+	0.788870i	0.981309	−	0.192439i	$-0.0616399\pi$
$541$	18.3486	+	18.3486i	0.788870	+	0.788870i	−0.192439	+	0.981309i	$0.561640\pi$
$542$	30.1702	−	52.2563i	1.29592	−	2.24460i
$543$	−4.69394	+	17.5180i	−0.201436	+	0.751770i
$544$		−	12.0398i		−	0.516201i
$545$		0			0
$546$	11.1564	−	6.44117i	0.477451	−	0.275657i
$547$	−38.0204			−1.62563			−0.812817	−	0.582518i	$-0.802067\pi$
$547$	−38.0204			−1.62563			−0.812817	+	0.582518i	$0.802067\pi$
$548$	−40.0803	+	10.7395i	−1.71214	+	0.458768i
$549$	24.3532	+	24.3532i	1.03937	+	1.03937i
$550$		0			0
$551$	1.56382	−	2.70861i	0.0666208	−	0.115391i
$552$	−0.0113080	+	0.00302998i	−0.000481302	+	0.000128964i
$553$	6.89491	+	11.9423i	0.293201	+	0.507840i
$554$	−31.8830			−1.35458
$555$		0			0
$556$	−10.9234			−0.463257
$557$	14.4598	+	25.0451i	0.612681	+	1.06119i	0.990787	+	0.135432i	$0.0432421\pi$
$557$	14.4598	+	25.0451i	0.612681	+	1.06119i	−0.378106	+	0.925762i	$0.623425\pi$
$558$	30.7910	−	8.25043i	1.30349	−	0.349269i
$559$	10.1947	−	17.6578i	0.431190	−	0.746844i
$560$		0			0
$561$	−1.65308	−	1.65308i	−0.0697930	−	0.0697930i
$562$	22.9140	−	6.13979i	0.966570	−	0.258992i
$563$	−21.7412			−0.916284			−0.458142	−	0.888879i	$-0.651485\pi$
$563$	−21.7412			−0.916284			−0.458142	+	0.888879i	$0.651485\pi$
$564$	−10.1881	+	5.88210i	−0.428996	+	0.247681i
$565$		0			0
$566$		−	4.65059i		−	0.195479i
$567$	3.86284	−	14.4163i	0.162224	−	0.605429i
$568$	−0.234395	+	0.405985i	−0.00983502	+	0.0170347i
$569$	−17.8811	−	17.8811i	−0.749613	−	0.749613i	0.224793	−	0.974406i	$-0.427829\pi$
$569$	−17.8811	−	17.8811i	−0.749613	−	0.749613i	−0.974406	+	0.224793i	$0.927829\pi$
$570$		0			0
$571$	−1.01988	−	1.76649i	−0.0426808	−	0.0739253i	0.843896	−	0.536507i	$-0.180257\pi$
$571$	−1.01988	−	1.76649i	−0.0426808	−	0.0739253i	−0.886577	+	0.462582i	$0.846923\pi$
$572$	−10.5949	+	6.11697i	−0.442995	+	0.255763i
$573$	−11.0310	−	6.36876i	−0.460827	−	0.266059i
$574$	−3.47294	−	12.9612i	−0.144958	−	0.540989i
$575$		0			0
$576$	16.8406	−	9.72292i	0.701692	−	0.405122i
$577$	−19.2382	+	11.1072i	−0.800897	+	0.462398i	−0.843785	−	0.536682i	$-0.819677\pi$
$577$	−19.2382	+	11.1072i	−0.800897	+	0.462398i	0.0428880	+	0.999080i	$0.486344\pi$
$578$	29.3500			1.22080
$579$	−13.2559	+	3.55190i	−0.550896	+	0.147612i
$580$		0			0
$581$	−6.63898			−0.275431
$582$	−7.78637	+	7.78637i	−0.322756	+	0.322756i
$583$	0.346601	−	1.29353i	0.0143547	−	0.0535726i
$584$	0.573213	+	0.573213i	0.0237197	+	0.0237197i
$585$		0			0
$586$	−32.6947	+	32.6947i	−1.35061	+	1.35061i
$587$	9.53161	−	16.5092i	0.393412	−	0.681409i	−0.599485	−	0.800386i	$-0.704628\pi$
$587$	9.53161	−	16.5092i	0.393412	−	0.681409i	0.992897	+	0.118977i	$0.0379614\pi$
$588$	−1.13963	−	4.25314i	−0.0469974	−	0.175397i
$589$	−3.41068	−	1.96916i	−0.140535	−	0.0811377i
$590$		0			0
$591$			12.0181i			0.494358i
$592$	14.7021	+	19.7567i	0.604252	+	0.811993i
$593$	13.1075	−	13.1075i	0.538261	−	0.538261i	−0.384757	−	0.923018i	$-0.625715\pi$
$593$	13.1075	−	13.1075i	0.538261	−	0.538261i	0.923018	+	0.384757i	$0.125715\pi$
$594$	4.38860	−	16.3785i	0.180066	−	0.672017i
$595$		0			0
$596$	23.6048	+	13.6282i	0.966890	+	0.558234i
$597$	−10.9584	−	6.32686i	−0.448499	−	0.258941i
$598$	1.90280			0.0778113
$599$	10.4679	+	6.04367i	0.427709	+	0.246938i	0.698370	−	0.715737i	$-0.253909\pi$
$599$	10.4679	+	6.04367i	0.427709	+	0.246938i	−0.270661	+	0.962675i	$0.587242\pi$
$600$		0			0
$601$	0.320993	+	0.555976i	0.0130936	+	0.0226787i	0.872498	−	0.488618i	$-0.162499\pi$
$601$	0.320993	+	0.555976i	0.0130936	+	0.0226787i	−0.859404	+	0.511297i	$0.829165\pi$
$602$	−32.1051	−	32.1051i	−1.30851	−	1.30851i
$603$	0.658217	+	0.658217i	0.0268047	+	0.0268047i
$604$	−2.40160	+	1.38656i	−0.0977197	+	0.0564185i
$605$		0			0
$606$	−4.38049	+	4.38049i	−0.177945	+	0.177945i
$607$	−18.6984	−	32.3865i	−0.758943	−	1.31453i	−0.943390	−	0.331685i	$-0.892383\pi$
$607$	−18.6984	−	32.3865i	−0.758943	−	1.31453i	0.184447	−	0.982842i	$-0.440950\pi$
$608$	−4.72904	−	1.26714i	−0.191788	−	0.0513894i
$609$	−11.1567	−	2.98944i	−0.452093	−	0.121138i
$610$		0			0
$611$	−23.0087	+	6.16516i	−0.930832	+	0.249416i
$612$	−3.71691	−	6.43788i	−0.150247	−	0.260236i
$613$	8.63260	−	32.2173i	0.348668	−	1.30125i	−0.539601	−	0.841921i	$-0.681425\pi$
$613$	8.63260	−	32.2173i	0.348668	−	1.30125i	0.888269	−	0.459324i	$-0.151908\pi$
$614$	55.9707	+	14.9973i	2.25879	+	0.605242i
$615$		0			0
$616$	−0.0878380	−	0.327816i	−0.00353910	−	0.0132081i
$617$	8.56459	+	2.29488i	0.344798	+	0.0923882i	0.427062	−	0.904222i	$-0.359549\pi$
$617$	8.56459	+	2.29488i	0.344798	+	0.0923882i	−0.0822645	+	0.996611i	$0.526215\pi$
$618$	0.121032	−	0.121032i	0.00486864	−	0.00486864i
$619$	−16.0269			−0.644174			−0.322087	−	0.946710i	$-0.604384\pi$
$619$	−16.0269			−0.644174			−0.322087	+	0.946710i	$0.604384\pi$
$620$		0			0
$621$	−0.926648	+	0.926648i	−0.0371851	+	0.0371851i
$622$	−3.35189	−	12.5094i	−0.134399	−	0.501583i
$623$		−	0.604074i		−	0.0242017i
$624$	−7.93921	+	2.12730i	−0.317823	+	0.0851603i
$625$		0			0
$626$	2.49682	−	4.32463i	0.0997932	−	0.172847i
$627$	−0.823284	+	0.475323i	−0.0328788	+	0.0189826i
$628$	10.1417	+	10.1417i	0.404699	+	0.404699i
$629$	7.36786	−	5.48286i	0.293776	−	0.218616i
$630$		0			0
$631$	23.2525	+	6.23050i	0.925669	+	0.248032i	0.690007	−	0.723803i	$-0.257607\pi$
$631$	23.2525	+	6.23050i	0.925669	+	0.248032i	0.235662	+	0.971835i	$0.424274\pi$
$632$	−0.0550244	−	0.205354i	−0.00218875	−	0.00816854i
$633$	2.41016	−	0.645799i	0.0957951	−	0.0256682i
$634$	2.30557	+	8.60452i	0.0915660	+	0.341729i
$635$		0			0
$636$	−0.433581	+	0.750985i	−0.0171926	+	0.0297785i
$637$		−	8.91563i		−	0.353250i
$638$	21.3224	+	5.71331i	0.844160	+	0.226192i
$639$			23.8136i			0.942052i
$640$		0			0
$641$	9.86299	+	17.0832i	0.389565	+	0.674746i	0.992391	−	0.123127i	$-0.0392922\pi$
$641$	9.86299	+	17.0832i	0.389565	+	0.674746i	−0.602826	+	0.797872i	$0.705959\pi$
$642$	−12.5677	−	7.25594i	−0.496006	−	0.286369i
$643$			2.09981i			0.0828085i	0.999142	+	0.0414043i	$0.0131832\pi$
$643$			2.09981i			0.0828085i	−0.999142	+	0.0414043i	$0.986817\pi$
$644$	0.544939	−	2.03374i	0.0214736	−	0.0801405i
$645$		0			0
$646$	−0.478371	+	1.78531i	−0.0188213	+	0.0702419i
$647$	−9.75517	+	16.8964i	−0.383515	+	0.664268i	−0.991562	−	0.129633i	$-0.958620\pi$
$647$	−9.75517	+	16.8964i	−0.383515	+	0.664268i	0.608047	+	0.793901i	$0.291953\pi$
$648$	−0.115049	+	0.199270i	−0.00451954	+	0.00782807i
$649$	−4.54785	+	16.9728i	−0.178519	+	0.666241i
$650$		0			0
$651$	−3.76430	+	14.0485i	−0.147534	+	0.550606i
$652$		−	10.0563i		−	0.393835i
$653$	4.60233	+	2.65715i	0.180103	+	0.103983i	0.587341	−	0.809340i	$-0.300175\pi$
$653$	4.60233	+	2.65715i	0.180103	+	0.103983i	−0.407238	+	0.913322i	$0.633508\pi$
$654$	8.80399	+	15.2490i	0.344263	+	0.596281i
$655$		0			0
$656$			8.56129i			0.334262i
$657$	39.7760	+	10.6579i	1.55181	+	0.415806i
$658$			53.0436i			2.06785i
$659$	1.89214	−	3.27728i	0.0737073	−	0.127665i	−0.826816	−	0.562472i	$-0.809850\pi$
$659$	1.89214	−	3.27728i	0.0737073	−	0.127665i	0.900523	+	0.434808i	$0.143184\pi$
$660$		0			0
$661$	5.01853	+	18.7294i	0.195198	+	0.728490i	0.992215	+	0.124533i	$0.0397433\pi$
$661$	5.01853	+	18.7294i	0.195198	+	0.728490i	−0.797017	+	0.603957i	$0.793590\pi$
$662$	31.0745	−	8.32640i	1.20775	−	0.323615i
$663$	0.793337	+	2.96077i	0.0308106	+	0.114987i
$664$	0.0988658	+	0.0264910i	0.00383674	+	0.00102805i
$665$		0			0
$666$	27.7538	+	11.9785i	1.07544	+	0.464156i
$667$	−1.20636	−	1.20636i	−0.0467104	−	0.0467104i
$668$	−9.65018	+	5.57154i	−0.373377	+	0.215569i
$669$	−5.91029	+	10.2369i	−0.228505	+	0.395782i
$670$		0			0
$671$	29.0081	−	7.77271i	1.11985	−	0.300062i
$672$			18.0803i			0.697463i
$673$	−0.282562	−	1.05454i	−0.0108920	−	0.0406494i	0.960266	−	0.279086i	$-0.0900316\pi$
$673$	−0.282562	−	1.05454i	−0.0108920	−	0.0406494i	−0.971158	+	0.238437i	$0.923365\pi$
$674$	49.0467	−	49.0467i	1.88921	−	1.88921i
$675$		0			0
$676$	−9.63954			−0.370751
$677$	2.41626	−	2.41626i	0.0928643	−	0.0928643i	−0.659149	−	0.752013i	$-0.729083\pi$
$677$	2.41626	−	2.41626i	0.0928643	−	0.0928643i	0.752013	+	0.659149i	$0.229083\pi$
$678$	−8.31978	−	2.22928i	−0.319519	−	0.0856149i
$679$	6.38543	+	23.8307i	0.245050	+	0.914540i
$680$		0			0
$681$	12.9988	+	3.48303i	0.498117	+	0.133470i
$682$	7.19419	−	26.8491i	0.275480	−	1.02811i
$683$	−11.4434	−	19.8205i	−0.437869	−	0.758411i	0.559656	−	0.828725i	$-0.310933\pi$
$683$	−11.4434	−	19.8205i	−0.437869	−	0.758411i	−0.997525	+	0.0703137i	$0.977600\pi$
$684$	−2.91989	+	0.782381i	−0.111645	+	0.0299151i
$685$		0			0
$686$	23.7282	+	6.35794i	0.905945	+	0.242747i
$687$	6.59711	+	1.76769i	0.251695	+	0.0674416i
$688$	14.4843	+	25.0876i	0.552209	+	0.956455i
$689$	−1.24157	+	1.24157i	−0.0473001	+	0.0473001i
$690$		0			0
$691$	15.4346	−	8.91116i	0.587159	−	0.338996i	−0.176814	−	0.984244i	$-0.556579\pi$
$691$	15.4346	−	8.91116i	0.587159	−	0.338996i	0.763973	+	0.645248i	$0.223246\pi$
$692$	−1.59636	−	1.59636i	−0.0606847	−	0.0606847i
$693$	−12.1904	−	12.1904i	−0.463074	−	0.463074i
$694$	−35.9174	−	62.2108i	−1.36341	−	2.36149i
$695$		0			0
$696$	0.154214	+	0.0890356i	0.00584548	+	0.00337489i
$697$	3.19277			0.120935
$698$	−35.0708	−	20.2482i	−1.32745	−	0.766404i
$699$	−14.7007	−	8.48746i	−0.556032	−	0.321025i
$700$		0			0
$701$	−6.42467	+	23.9772i	−0.242656	+	0.905606i	0.731890	+	0.681422i	$0.238638\pi$
$701$	−6.42467	+	23.9772i	−0.242656	+	0.905606i	−0.974547	+	0.224184i	$0.928028\pi$
$702$	−15.7205	+	15.7205i	−0.593333	+	0.593333i
$703$	−1.37814	−	3.47103i	−0.0519776	−	0.130912i
$704$		−	16.9564i		−	0.639067i
$705$		0			0
$706$	−30.8455	−	17.8087i	−1.16089	−	0.670239i
$707$	3.59234	+	13.4068i	0.135104	+	0.504215i
$708$	5.68915	−	9.85389i	0.213811	−	0.370332i
$709$	27.9093	−	27.9093i	1.04815	−	1.04815i	0.0493742	−	0.998780i	$-0.484277\pi$
$709$	27.9093	−	27.9093i	1.04815	−	1.04815i	0.998780	−	0.0493742i	$-0.0157227\pi$
$710$		0			0
$711$	−7.63643	−	7.63643i	−0.286388	−	0.286388i
$712$	−0.00241039	+	0.00899570i	−9.03332e−5	+	0.000337128i
$713$	−1.51905	+	1.51905i	−0.0568888	+	0.0568888i
$714$	6.82568			0.255445
$715$		0			0
$716$	−31.5181	+	8.44525i	−1.17789	+	0.315614i
$717$	18.3144			0.683962
$718$	−37.1040	+	21.4220i	−1.38471	+	0.799461i
$719$	−3.76115	+	2.17150i	−0.140267	+	0.0809833i	−0.568491	−	0.822689i	$-0.692473\pi$
$719$	−3.76115	+	2.17150i	−0.140267	+	0.0809833i	0.428224	+	0.903673i	$0.359139\pi$
$720$		0			0
$721$	−0.0992559	−	0.370428i	−0.00369648	−	0.0137955i
$722$	−32.1567	−	18.5657i	−1.19675	−	0.690943i
$723$	9.33382	−	5.38889i	0.347129	−	0.200415i
$724$	25.1432	+	43.5493i	0.934440	+	1.61850i
$725$		0			0
$726$	6.30433	+	6.30433i	0.233976	+	0.233976i
$727$	5.83294	−	10.1029i	0.216332	−	0.374698i	−0.737352	−	0.675509i	$-0.763924\pi$
$727$	5.83294	−	10.1029i	0.216332	−	0.374698i	0.953684	+	0.300811i	$0.0972574\pi$
$728$	−0.115169	+	0.429817i	−0.00426845	+	0.0159301i
$729$			3.32523i			0.123157i
$730$		0			0
$731$	9.35593	−	5.40165i	0.346041	−	0.199787i
$732$	−19.4466			−0.718766
$733$	9.61910	−	2.57743i	0.355290	−	0.0951996i	−0.0767595	−	0.997050i	$-0.524457\pi$
$733$	9.61910	−	2.57743i	0.355290	−	0.0951996i	0.432049	+	0.901850i	$0.357791\pi$
$734$	42.7932	+	42.7932i	1.57953	+	1.57953i
$735$		0			0
$736$	−1.33529	+	2.31279i	−0.0492193	+	0.0852504i
$737$	0.784032	−	0.210081i	0.0288802	−	0.00773842i
$738$	5.25433	+	9.10077i	0.193415	+	0.335004i
$739$	24.0193			0.883563			0.441782	−	0.897123i	$-0.354347\pi$
$739$	24.0193			0.883563			0.441782	+	0.897123i	$0.354347\pi$
$740$		0			0
$741$	1.24644			0.0457892
$742$	1.95497	+	3.38611i	0.0717693	+	0.124308i
$743$	−33.7511	+	9.04359i	−1.23821	+	0.331777i	−0.817771	−	0.575544i	$-0.804790\pi$
$743$	−33.7511	+	9.04359i	−1.23821	+	0.331777i	−0.420438	+	0.907321i	$0.638124\pi$
$744$	0.112114	−	0.194187i	0.00411029	−	0.00711922i
$745$		0			0
$746$	36.7638	+	36.7638i	1.34602	+	1.34602i
$747$	5.02218	−	1.34569i	0.183752	−	0.0492362i
$748$	−6.48213			−0.237010
$749$	−28.1577	+	16.2569i	−1.02886	+	0.594013i
$750$		0			0
$751$			49.1968i			1.79522i	0.440793	+	0.897609i	$0.354697\pi$
$751$			49.1968i			1.79522i	−0.440793	+	0.897609i	$0.645303\pi$
$752$	8.75926	−	32.6900i	0.319417	−	1.19208i
$753$	5.61903	−	9.73245i	0.204769	−	0.354670i
$754$	−20.4658	−	20.4658i	−0.745321	−	0.745321i
$755$		0			0
$756$	12.3001	+	21.3045i	0.447352	+	0.774836i
$757$	−1.93838	+	1.11912i	−0.0704516	+	0.0406752i	−0.534812	−	0.844971i	$-0.679618\pi$
$757$	−1.93838	+	1.11912i	−0.0704516	+	0.0406752i	0.464360	+	0.885646i	$0.346284\pi$
$758$	48.1430	+	27.7954i	1.74863	+	1.00957i
$759$	0.134212	+	0.500886i	0.00487158	+	0.0181810i
$760$		0			0
$761$	−35.8171	+	20.6790i	−1.29837	+	0.749614i	−0.980122	−	0.198394i	$-0.936427\pi$
$761$	−35.8171	+	20.6790i	−1.29837	+	0.749614i	−0.318247	+	0.948008i	$0.603094\pi$
$762$	16.1953	−	9.35037i	0.586695	−	0.338728i
$763$	39.4506			1.42821
$764$	−34.1144	+	9.14092i	−1.23422	+	0.330707i
$765$		0			0
$766$	46.4164			1.67709
$767$	16.2910	−	16.2910i	0.588234	−	0.588234i
$768$	3.02152	−	11.2765i	0.109030	−	0.406904i
$769$	−0.953352	−	0.953352i	−0.0343788	−	0.0343788i	0.689708	−	0.724087i	$-0.257739\pi$
$769$	−0.953352	−	0.953352i	−0.0343788	−	0.0343788i	−0.724087	+	0.689708i	$0.757739\pi$
$770$		0			0
$771$	2.99885	−	2.99885i	0.108001	−	0.108001i
$772$	−19.0258	+	32.9537i	−0.684755	+	1.18603i
$773$	−7.85273	−	29.3068i	−0.282443	−	1.05409i	−0.950688	−	0.310150i	$-0.899621\pi$
$773$	−7.85273	−	29.3068i	−0.282443	−	1.05409i	0.668244	−	0.743942i	$-0.267046\pi$
$774$	30.7941	+	17.7790i	1.10687	+	0.639052i
$775$		0			0
$776$		−	0.380360i		−	0.0136541i
$777$	−11.0644	+	8.23369i	−0.396934	+	0.295382i
$778$	−34.8474	+	34.8474i	−1.24934	+	1.24934i
$779$	0.336027	−	1.25407i	0.0120394	−	0.0449317i
$780$		0			0
$781$	17.9830	+	10.3825i	0.643481	+	0.371514i
$782$	0.873123	+	0.504098i	0.0312228	+	0.0180265i
$783$	19.9334			0.712360
$784$	10.9700	+	6.33352i	0.391785	+	0.226197i
$785$		0			0
$786$	−8.10945	−	14.0460i	−0.289255	−	0.501004i
$787$	−29.1860	−	29.1860i	−1.04037	−	1.04037i	−0.999150	−	0.0412185i	$-0.986876\pi$
$787$	−29.1860	−	29.1860i	−1.04037	−	1.04037i	−0.0412185	−	0.999150i	$-0.513124\pi$
$788$	23.5629	+	23.5629i	0.839395	+	0.839395i
$789$	4.52545	−	2.61277i	0.161110	−	0.0930170i
$790$		0			0
$791$	−13.6457	+	13.6457i	−0.485186	+	0.485186i
$792$	0.132893	+	0.230178i	0.00472216	+	0.00817902i
$793$	−38.0341	−	10.1912i	−1.35063	−	0.361900i
$794$	3.12212	+	0.836570i	0.110800	+	0.0296888i
$795$		0			0
$796$	−33.8899	+	9.08078i	−1.20120	+	0.321860i
$797$	21.6932	+	37.5737i	0.768412	+	1.33093i	0.938424	+	0.345486i	$0.112286\pi$
$797$	21.6932	+	37.5737i	0.768412	+	1.33093i	−0.170012	+	0.985442i	$0.554381\pi$
$798$	0.718377	−	2.68102i	0.0254303	−	0.0949071i
$799$	−12.1911	−	3.26660i	−0.431290	−	0.115564i
$800$		0			0
$801$	0.122443	+	0.456963i	0.00432631	+	0.0161460i
$802$	13.9683	+	3.74280i	0.493239	+	0.132163i
$803$	25.3903	−	25.3903i	0.896004	−	0.896004i
$804$	−0.525602			−0.0185366
$805$		0			0
$806$	−25.7706	+	25.7706i	−0.907729	+	0.907729i
$807$	−2.78285	−	10.3857i	−0.0979610	−	0.365595i
$808$		−	0.213985i		−	0.00752795i
$809$	31.3117	−	8.38994i	1.10086	−	0.294975i	0.337745	−	0.941238i	$-0.390336\pi$
$809$	31.3117	−	8.38994i	1.10086	−	0.294975i	0.763115	+	0.646263i	$0.223669\pi$
$810$		0			0
$811$	−8.19451	+	14.1933i	−0.287748	+	0.498394i	−0.973272	−	0.229656i	$-0.926240\pi$
$811$	−8.19451	+	14.1933i	−0.287748	+	0.498394i	0.685524	+	0.728050i	$0.259573\pi$
$812$	−27.7353	+	16.0130i	−0.973318	+	0.561945i
$813$	−15.2457	−	15.2457i	−0.534690	−	0.534690i
$814$	21.1460	−	15.7359i	0.741165	−	0.551545i
$815$		0			0
$816$	−4.20657	−	1.12715i	−0.147259	−	0.0394581i
$817$	−1.13701	−	4.24336i	−0.0397788	−	0.148456i
$818$	7.94607	−	2.12914i	0.277828	−	0.0744438i
$819$	5.85034	+	21.8338i	0.204428	+	0.762934i
$820$		0			0
$821$	1.40290	−	2.42990i	0.0489617	−	0.0848042i	−0.840506	−	0.541802i	$-0.817742\pi$
$821$	1.40290	−	2.42990i	0.0489617	−	0.0848042i	0.889468	+	0.456998i	$0.151075\pi$
$822$			29.8379i			1.04071i
$823$	−2.87916	−	0.771469i	−0.100361	−	0.0268917i	0.208289	−	0.978067i	$-0.433211\pi$
$823$	−2.87916	−	0.771469i	−0.100361	−	0.0268917i	−0.308650	+	0.951176i	$0.599877\pi$
$824$			0.00591236i			0.000205967i
$825$		0			0
$826$	−25.6518	−	44.4302i	−0.892539	−	1.54592i
$827$	5.45795	+	3.15115i	0.189792	+	0.109576i	0.591885	−	0.806022i	$-0.298384\pi$
$827$	5.45795	+	3.15115i	0.189792	+	0.109576i	−0.402093	+	0.915599i	$0.631717\pi$
$828$			1.64891i			0.0573037i
$829$	6.63332	−	24.7559i	0.230385	−	0.859808i	−0.749790	−	0.661675i	$-0.769846\pi$
$829$	6.63332	−	24.7559i	0.230385	−	0.859808i	0.980175	−	0.198132i	$-0.0634876\pi$
$830$		0			0
$831$	−2.94856	+	11.0042i	−0.102284	+	0.381730i
$832$	−11.1162	+	19.2538i	−0.385384	+	0.667505i
$833$	2.36196	−	4.09104i	0.0818372	−	0.141746i
$834$	−2.03300	+	7.58725i	−0.0703969	+	0.262725i
$835$		0			0
$836$	−0.682220	+	2.54608i	−0.0235951	+	0.0880579i
$837$		−	25.1001i		−	0.867586i
$838$	34.5945	+	19.9732i	1.19505	+	0.689961i
$839$	13.2861	+	23.0123i	0.458688	+	0.794472i	0.998892	−	0.0470627i	$-0.0149861\pi$
$839$	13.2861	+	23.0123i	0.458688	+	0.794472i	−0.540203	+	0.841534i	$0.681653\pi$
$840$		0			0
$841$		−	3.04970i		−	0.105162i
$842$	−10.0556	−	2.69438i	−0.346537	−	0.0928544i
$843$		−	8.47640i		−	0.291943i
$844$	3.45924	−	5.99158i	0.119072	−	0.206239i
$845$		0			0
$846$	−10.7517	−	40.1258i	−0.369650	−	1.37955i
$847$	19.2949	−	5.17004i	0.662979	−	0.177645i
$848$	−0.645663	−	2.40965i	−0.0221721	−	0.0827476i
$849$	−1.60511	−	0.430089i	−0.0550874	−	0.0147606i
$850$		0			0
$851$	−2.02342	+	0.236089i	−0.0693618	+	0.00809303i
$852$	−9.50786	−	9.50786i	−0.325734	−	0.325734i
$853$	−5.51510	+	3.18415i	−0.188833	+	0.109023i	−0.591436	−	0.806352i	$-0.701439\pi$
$853$	−5.51510	+	3.18415i	−0.188833	+	0.109023i	0.402603	+	0.915375i	$0.368106\pi$
$854$	−43.8413	+	75.9354i	−1.50022	+	2.59845i
$855$		0			0
$856$	0.484186	−	0.129737i	0.0165491	−	0.00443432i
$857$			56.2325i			1.92086i	0.278515	+	0.960432i	$0.410158\pi$
$857$			56.2325i			1.92086i	−0.278515	+	0.960432i	$0.589842\pi$
$858$	2.27690	+	8.49750i	0.0777320	+	0.290100i
$859$	27.5622	−	27.5622i	0.940410	−	0.940410i	−0.0579119	−	0.998322i	$-0.518444\pi$
$859$	27.5622	−	27.5622i	0.940410	−	0.940410i	0.998322	+	0.0579119i	$0.0184443\pi$
$860$		0			0
$861$	−4.79463			−0.163400
$862$	−25.7720	+	25.7720i	−0.877799	+	0.877799i
$863$	−34.7055	−	9.29932i	−1.18139	−	0.316552i	−0.385912	−	0.922535i	$-0.626113\pi$
$863$	−34.7055	−	9.29932i	−1.18139	−	0.316552i	−0.795478	+	0.605983i	$0.792780\pi$
$864$	−8.07588	−	30.1396i	−0.274747	−	1.02537i
$865$		0			0
$866$	−12.9435	−	3.46820i	−0.439839	−	0.117854i
$867$	2.71430	−	10.1299i	0.0921826	−	0.344030i
$868$	20.1635	+	34.9243i	0.684395	+	1.18541i
$869$	−9.09609	+	2.43729i	−0.308564	+	0.0826794i
$870$		0			0
$871$	−1.02798	−	0.275448i	−0.0348319	−	0.00933319i
$872$	−0.587487	−	0.157417i	−0.0198948	−	0.00533080i
$873$	−9.66075	−	16.7329i	−0.326967	−	0.566323i
$874$	0.289895	−	0.289895i	0.00980583	−	0.00980583i
$875$		0			0
$876$	−20.1363	+	11.6257i	−0.680344	+	0.392797i
$877$	14.8201	+	14.8201i	0.500441	+	0.500441i	0.911575	−	0.411134i	$-0.134867\pi$
$877$	14.8201	+	14.8201i	0.500441	+	0.500441i	−0.411134	+	0.911575i	$0.634867\pi$
$878$	48.5056	+	48.5056i	1.63698	+	1.63698i
$879$	8.26070	+	14.3080i	0.278627	+	0.482595i
$880$		0			0
$881$	−21.8096	−	12.5918i	−0.734783	−	0.424227i	0.0853866	−	0.996348i	$-0.472787\pi$
$881$	−21.8096	−	12.5918i	−0.734783	−	0.424227i	−0.820169	+	0.572121i	$0.806121\pi$
$882$	15.5483			0.523539
$883$	42.6439	+	24.6204i	1.43508	+	0.828544i	0.997502	−	0.0706369i	$-0.0225032\pi$
$883$	42.6439	+	24.6204i	1.43508	+	0.828544i	0.437578	+	0.899181i	$0.355836\pi$
$884$	7.36039	+	4.24953i	0.247557	+	0.142927i
$885$		0			0
$886$	2.06094	−	7.69155i	0.0692388	−	0.258403i
$887$	−10.7898	+	10.7898i	−0.362286	+	0.362286i	−0.864654	−	0.502368i	$-0.832462\pi$
$887$	−10.7898	+	10.7898i	−0.362286	+	0.362286i	0.502368	+	0.864654i	$0.332462\pi$
$888$	0.197623	−	0.0784642i	0.00663178	−	0.00263309i
$889$		−	41.8989i		−	1.40524i
$890$		0			0
$891$	8.82661	+	5.09604i	0.295702	+	0.170724i
$892$	8.48290	+	31.6586i	0.284028	+	1.06001i
$893$	−2.56614	+	4.44468i	−0.0858725	+	0.148736i
$894$	13.8591	−	13.8591i	0.463518	−	0.463518i
$895$		0			0
$896$	−0.883280	−	0.883280i	−0.0295083	−	0.0295083i
$897$	0.175972	−	0.656737i	0.00587554	−	0.0219278i
$898$	−38.7196	+	38.7196i	−1.29209	+	1.29209i
$899$	32.6766			1.08983
$900$		0			0
$901$	−0.898631	+	0.240787i	−0.0299377	+	0.00802179i
$902$	9.16333			0.305105
$903$	−14.0499	+	8.11173i	−0.467552	+	0.269942i
$904$	0.257658	−	0.148759i	0.00856957	−	0.00494765i
$905$		0			0
$906$	0.516116	+	1.92617i	0.0171468	+	0.0639927i
$907$	−8.21945	−	4.74550i	−0.272923	−	0.157572i	0.357292	−	0.933993i	$-0.383700\pi$
$907$	−8.21945	−	4.74550i	−0.272923	−	0.157572i	−0.630215	+	0.776421i	$0.717033\pi$
$908$	32.3147	−	18.6569i	1.07240	−	0.619152i
$909$	−5.43499	−	9.41367i	−0.180267	−	0.312232i
$910$		0			0
$911$	−10.6794	−	10.6794i	−0.353825	−	0.353825i	0.507706	−	0.861531i	$-0.330494\pi$
$911$	−10.6794	−	10.6794i	−0.353825	−	0.353825i	−0.861531	+	0.507706i	$0.830494\pi$
$912$	−0.885452	+	1.53365i	−0.0293202	+	0.0507841i
$913$	1.17341	−	4.37923i	0.0388342	−	0.144931i
$914$			13.5228i			0.447296i
$915$		0			0
$916$	16.4002	−	9.46867i	0.541879	−	0.312854i
$917$	−36.3384			−1.20000
$918$	−11.3783	+	3.04881i	−0.375540	+	0.100626i
$919$	2.76311	+	2.76311i	0.0911467	+	0.0911467i	0.751210	−	0.660063i	$-0.229471\pi$
$919$	2.76311	+	2.76311i	0.0911467	+	0.0911467i	−0.660063	+	0.751210i	$0.729471\pi$
$920$		0			0
$921$	10.3524	−	17.9309i	0.341123	−	0.590842i
$922$	−80.0702	+	21.4548i	−2.63697	+	0.706575i
$923$	−13.6130	−	23.5784i	−0.448077	−	0.776092i
$924$	9.73431			0.320235
$925$		0			0
$926$	38.7309			1.27278
$927$	0.150168	+	0.260098i	0.00493216	+	0.00854275i
$928$	39.2373	−	10.5136i	1.28803	−	0.345126i
$929$	19.5842	−	33.9209i	0.642538	−	1.11291i	−0.342326	−	0.939581i	$-0.611215\pi$
$929$	19.5842	−	33.9209i	0.642538	−	1.11291i	0.984864	−	0.173328i	$-0.0554520\pi$
$930$		0			0
$931$	−1.35831	−	1.35831i	−0.0445168	−	0.0445168i
$932$	−45.4633	+	12.1818i	−1.48920	+	0.399030i
$933$	−4.62752			−0.151498
$934$	34.0711	−	19.6710i	1.11484	−	0.643654i
$935$		0			0
$936$		−	0.348487i		−	0.0113906i
$937$	−1.63216	+	6.09129i	−0.0533202	+	0.198994i	−0.987448	−	0.157945i	$-0.949513\pi$
$937$	−1.63216	+	6.09129i	−0.0533202	+	0.198994i	0.934128	+	0.356939i	$0.116180\pi$
$938$	−1.18494	+	2.05238i	−0.0386898	+	0.0670126i
$939$	−1.26170	−	1.26170i	−0.0411741	−	0.0411741i
$940$		0			0
$941$	−22.4635	−	38.9080i	−0.732290	−	1.26836i	−0.955902	−	0.293686i	$-0.905118\pi$
$941$	−22.4635	−	38.9080i	−0.732290	−	1.26836i	0.223612	−	0.974678i	$-0.428215\pi$
$942$	8.93180	−	5.15677i	0.291014	−	0.168017i
$943$	−0.613316	−	0.354098i	−0.0199723	−	0.0115310i
$944$	8.47193	+	31.6177i	0.275738	+	1.02907i
$945$		0			0
$946$	26.8517	−	15.5029i	0.873026	−	0.504042i
$947$	−29.2790	+	16.9042i	−0.951439	+	0.549313i	−0.893528	−	0.449008i	$-0.851777\pi$
$947$	−29.2790	+	16.9042i	−0.951439	+	0.549313i	−0.0579110	+	0.998322i	$0.518444\pi$
$948$	6.09787			0.198050
$949$	−45.4757	+	12.1852i	−1.47620	+	0.395548i
$950$		0			0
$951$	3.18300			0.103216
$952$	−0.166715	+	0.166715i	−0.00540328	+	0.00540328i
$953$	−8.06792	+	30.1099i	−0.261345	+	0.975354i	0.703104	+	0.711087i	$0.251797\pi$
$953$	−8.06792	+	30.1099i	−0.261345	+	0.975354i	−0.964449	+	0.264267i	$0.914870\pi$
$954$	−2.16522	−	2.16522i	−0.0701017	−	0.0701017i
$955$		0			0
$956$	35.9075	−	35.9075i	1.16133	−	1.16133i
$957$	3.94381	−	6.83087i	0.127485	−	0.220811i
$958$	−19.5791	−	73.0700i	−0.632570	−	2.36079i
$959$	57.8951	+	33.4258i	1.86953	+	1.07937i
$960$		0			0
$961$		−	10.1464i		−	0.327302i
$962$	−34.3271	+	4.00524i	−1.10675	+	0.129134i
$963$	18.0052	−	18.0052i	0.580211	−	0.580211i
$964$	7.73454	−	28.8657i	0.249113	−	0.929701i
$965$		0			0
$966$	−1.31118	−	0.757011i	−0.0421866	−	0.0243564i
$967$	−6.50246	−	3.75420i	−0.209105	−	0.120727i	0.391790	−	0.920054i	$-0.371856\pi$
$967$	−6.50246	−	3.75420i	−0.209105	−	0.120727i	−0.600895	+	0.799328i	$0.705189\pi$
$968$	−0.307963			−0.00989831
$969$	0.571944	+	0.330212i	0.0183735	+	0.0106079i
$970$		0			0
$971$	10.7517	+	18.6225i	0.345038	+	0.597623i	0.985361	−	0.170483i	$-0.0545328\pi$
$971$	10.7517	+	18.6225i	0.345038	+	0.597623i	−0.640323	+	0.768106i	$0.721199\pi$
$972$	−21.0639	−	21.0639i	−0.675626	−	0.675626i
$973$	12.4443	+	12.4443i	0.398945	+	0.398945i
$974$	50.2763	−	29.0271i	1.61096	−	0.930087i
$975$		0			0
$976$	39.5582	−	39.5582i	1.26623	−	1.26623i
$977$	22.6200	+	39.1789i	0.723677	+	1.25344i	0.959516	+	0.281653i	$0.0908826\pi$
$977$	22.6200	+	39.1789i	0.723677	+	1.25344i	−0.235840	+	0.971792i	$0.575784\pi$
$978$	−6.98493	−	1.87161i	−0.223354	−	0.0598474i
$979$	0.398462	+	0.106768i	0.0127349	+	0.00341230i
$980$		0			0
$981$	−29.8431	+	7.99643i	−0.952817	+	0.255306i
$982$	32.8734	+	56.9384i	1.04903	+	1.81698i
$983$	12.0061	−	44.8074i	0.382936	−	1.42913i	−0.458460	−	0.888715i	$-0.651599\pi$
$983$	12.0061	−	44.8074i	0.382936	−	1.42913i	0.841396	−	0.540420i	$-0.181735\pi$
$984$	0.0714002	+	0.0191316i	0.00227616	+	0.000609894i
$985$		0			0
$986$	−3.96910	−	14.8129i	−0.126402	−	0.471738i
$987$	18.3076	+	4.90550i	0.582736	+	0.156144i
$988$	2.44380	−	2.44380i	0.0777477	−	0.0777477i
$989$	−2.39631			−0.0761981
$990$		0			0
$991$	4.97517	−	4.97517i	0.158042	−	0.158042i	−0.623657	−	0.781698i	$-0.714354\pi$
$991$	4.97517	−	4.97517i	0.158042	−	0.158042i	0.781698	+	0.623657i	$0.214354\pi$
$992$	−13.2387	−	49.4076i	−0.420330	−	1.56869i
$993$		−	11.4952i		−	0.364788i
$994$	−58.5615	+	15.6915i	−1.85746	+	0.497704i
$995$		0			0
$996$	−1.46788	+	2.54244i	−0.0465116	+	0.0805604i
$997$	−35.2584	+	20.3564i	−1.11664	+	0.644694i	−0.940542	−	0.339678i	$-0.889682\pi$
$997$	−35.2584	+	20.3564i	−1.11664	+	0.644694i	−0.176101	+	0.984372i	$0.556349\pi$
$998$	−6.23434	−	6.23434i	−0.197345	−	0.197345i
$999$	14.7665	−	18.6675i	0.467192	−	0.590615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.t.c.82.4	✓	96
5.2	odd	4		925.2.y.c.193.21	yes	96
5.3	odd	4		925.2.y.c.193.4	yes	96
5.4	even	2	inner	925.2.t.c.82.21	yes	96
37.14	odd	12		925.2.y.c.532.4	yes	96
185.14	odd	12		925.2.y.c.532.21	yes	96
185.88	even	12	inner	925.2.t.c.643.4	yes	96
185.162	even	12	inner	925.2.t.c.643.21	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.t.c.82.4	✓	96	1.1	even	1	trivial
925.2.t.c.82.21	yes	96	5.4	even	2	inner
925.2.t.c.643.4	yes	96	185.88	even	12	inner
925.2.t.c.643.21	yes	96	185.162	even	12	inner
925.2.y.c.193.4	yes	96	5.3	odd	4
925.2.y.c.193.21	yes	96	5.2	odd	4
925.2.y.c.532.4	yes	96	37.14	odd	12
925.2.y.c.532.21	yes	96	185.14	odd	12

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.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996919 - 1.72671i) q^{2} +(-0.688157 + 0.184391i) q^{3} +(-0.987696 + 1.71074i) q^{4} +(1.00443 + 1.00443i) q^{6} +(3.07412 - 0.823709i) q^{7} -0.0490658 q^{8} +(-2.15852 + 1.24622i) q^{9} +2.17335i q^{11} +(0.364245 - 1.35938i) q^{12} +(1.42480 - 2.46782i) q^{13} +(-4.48696 - 4.48696i) q^{14} +(2.02431 + 3.50620i) q^{16} +(1.30757 - 0.754926i) q^{17} +(4.30373 + 2.48476i) q^{18} +(-0.158906 - 0.593046i) q^{19} +(-1.96360 + 1.13368i) q^{21} +(3.75276 - 2.16666i) q^{22} -0.334904 q^{23} +(0.0337650 - 0.00904730i) q^{24} -5.68163 q^{26} +(2.76691 - 2.76691i) q^{27} +(-1.62715 + 6.07260i) q^{28} +(3.60210 + 3.60210i) q^{29} +(4.53577 - 4.53577i) q^{31} +(3.98707 - 6.90581i) q^{32} +(-0.400747 - 1.49561i) q^{33} +(-2.60708 - 1.50520i) q^{34} -4.92354i q^{36} +(6.04178 - 0.704946i) q^{37} +(-0.865605 + 0.865605i) q^{38} +(-0.525440 + 1.96097i) q^{39} +(1.83132 + 1.05731i) q^{41} +(3.91509 + 2.26038i) q^{42} +7.15520 q^{43} +(-3.71804 - 2.14661i) q^{44} +(0.333872 + 0.578284i) q^{46} +(-5.91085 - 5.91085i) q^{47} +(-2.03955 - 2.03955i) q^{48} +(2.70957 - 1.56437i) q^{49} +(-0.760612 + 0.760612i) q^{51} +(2.81453 + 4.87491i) q^{52} +(-0.595178 - 0.159478i) q^{53} +(-7.53604 - 2.01928i) q^{54} +(-0.150834 + 0.0404159i) q^{56} +(0.218705 + 0.378808i) q^{57} +(2.62880 - 9.81081i) q^{58} +(7.80951 + 2.09255i) q^{59} +(-3.57637 - 13.3472i) q^{61} +(-12.3538 - 3.31018i) q^{62} +(-5.60902 + 5.60902i) q^{63} -7.80193 q^{64} +(-2.18298 + 2.18298i) q^{66} +(-0.0966621 - 0.360748i) q^{67} +2.98255i q^{68} +(0.230467 - 0.0617534i) q^{69} +(4.77717 - 8.27430i) q^{71} +(0.105909 - 0.0611467i) q^{72} +(-11.6826 - 11.6826i) q^{73} +(-7.24040 - 9.72965i) q^{74} +(1.17150 + 0.313902i) q^{76} +(1.79021 + 6.68116i) q^{77} +(3.90986 - 1.04764i) q^{78} +(1.12144 + 4.18528i) q^{79} +(2.34479 - 4.06129i) q^{81} -4.21622i q^{82} +(-2.01496 - 0.539908i) q^{83} -4.47894i q^{84} +(-7.13316 - 12.3550i) q^{86} +(-3.14301 - 1.81462i) q^{87} -0.106637i q^{88} +(0.0491257 - 0.183340i) q^{89} +(2.34724 - 8.76001i) q^{91} +(0.330783 - 0.572934i) q^{92} +(-2.28497 + 3.95768i) q^{93} +(-4.31371 + 16.0990i) q^{94} +(-1.47036 + 5.48747i) q^{96} +7.75205i q^{97} +(-5.40243 - 3.11910i) q^{98} +(-2.70847 - 4.69122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 40 q^{4} + 32 q^{14} - 4 q^{16} + 24 q^{19} + 36 q^{21} - 52 q^{24} + 16 q^{26} - 12 q^{29} + 4 q^{31} + 60 q^{34} - 100 q^{39} - 48 q^{41} - 48 q^{44} + 24 q^{46} + 120 q^{49} - 84 q^{51} - 104 q^{54}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q - 40 * q^4 + 32 * q^14 - 4 * q^16 + 24 * q^19 + 36 * q^21 - 52 * q^24 + 16 * q^26 - 12 * q^29 + 4 * q^31 + 60 * q^34 - 100 * q^39 - 48 * q^41 - 48 * q^44 + 24 * q^46 + 120 * q^49 - 84 * q^51 - 104 * q^54 - 68 * q^56 + 28 * q^59 + 68 * q^61 - 48 * q^64 + 4 * q^66 - 28 * q^69 + 48 * q^71 + 48 * q^74 - 152 * q^76 + 92 * q^79 - 16 * q^81 + 20 * q^86 + 8 * q^89 - 12 * q^91 - 56 * q^94 + 252 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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