LMFDB - Embedded newform 925.2.y.c.532.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] 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("925.193"); 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([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (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			532.4
Character	$\chi$	$=$	925.532
Dual form			925.2.y.c.193.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72671 - 0.996919i) q^{2} +(-0.184391 + 0.688157i) q^{3} +(0.987696 + 1.71074i) q^{4} +(1.00443 - 1.00443i) q^{6} +(-0.823709 + 3.07412i) q^{7} +0.0490658i q^{8} +(2.15852 + 1.24622i) q^{9} -2.17335i q^{11} +(-1.35938 + 0.364245i) q^{12} +(2.46782 - 1.42480i) q^{13} +(4.48696 - 4.48696i) q^{14} +(2.02431 - 3.50620i) q^{16} +(-0.754926 + 1.30757i) q^{17} +(-2.48476 - 4.30373i) q^{18} +(0.158906 - 0.593046i) q^{19} +(-1.96360 - 1.13368i) q^{21} +(-2.16666 + 3.75276i) q^{22} +0.334904i q^{23} +(-0.0337650 - 0.00904730i) q^{24} -5.68163 q^{26} +(-2.76691 + 2.76691i) q^{27} +(-6.07260 + 1.62715i) q^{28} +(-3.60210 + 3.60210i) q^{29} +(4.53577 + 4.53577i) q^{31} +(-6.90581 + 3.98707i) q^{32} +(1.49561 + 0.400747i) q^{33} +(2.60708 - 1.50520i) q^{34} +4.92354i q^{36} +(-0.704946 + 6.04178i) q^{37} +(-0.865605 + 0.865605i) q^{38} +(0.525440 + 1.96097i) q^{39} +(1.83132 - 1.05731i) q^{41} +(2.26038 + 3.91509i) q^{42} -7.15520i 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} +(4.87491 + 2.81453i) q^{52} +(0.159478 + 0.595178i) q^{53} +(7.53604 - 2.01928i) q^{54} +(-0.150834 - 0.0404159i) q^{56} +(0.378808 + 0.218705i) q^{57} +(9.81081 - 2.62880i) q^{58} +(-7.80951 + 2.09255i) q^{59} +(-3.57637 + 13.3472i) q^{61} +(-3.31018 - 12.3538i) q^{62} +(-5.60902 + 5.60902i) q^{63} +7.80193 q^{64} +(-2.18298 - 2.18298i) q^{66} +(-0.360748 - 0.0966621i) q^{67} -2.98255 q^{68} +(-0.230467 - 0.0617534i) q^{69} +(4.77717 + 8.27430i) q^{71} +(-0.0611467 + 0.105909i) q^{72} +(11.6826 + 11.6826i) q^{73} +(7.24040 - 9.72965i) q^{74} +(1.17150 - 0.313902i) q^{76} +(6.68116 + 1.79021i) q^{77} +(1.04764 - 3.90986i) q^{78} +(-1.12144 + 4.18528i) q^{79} +(2.34479 + 4.06129i) q^{81} -4.21622 q^{82} +(0.539908 + 2.01496i) q^{83} -4.47894i q^{84} +(-7.13316 + 12.3550i) q^{86} +(-1.81462 - 3.14301i) q^{87} +0.106637 q^{88} +(-0.0491257 - 0.183340i) q^{89} +(2.34724 + 8.76001i) q^{91} +(-0.572934 + 0.330783i) q^{92} +(-3.95768 + 2.28497i) q^{93} +(4.31371 + 16.0990i) q^{94} +(-1.47036 - 5.48747i) q^{96} +7.75205 q^{97} +(3.11910 + 5.40243i) 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 $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.72671	−	0.996919i	−1.22097	−	0.704928i	−0.255847	−	0.966717i	$-0.582354\pi$
$2$	−1.72671	−	0.996919i	−1.22097	−	0.704928i	−0.965125	+	0.261789i	$0.915688\pi$
$3$	−0.184391	+	0.688157i	−0.106458	+	0.397308i	−0.998507	−	0.0546324i	$-0.982601\pi$
$3$	−0.184391	+	0.688157i	−0.106458	+	0.397308i	0.892048	+	0.451940i	$0.149268\pi$
$4$	0.987696	+	1.71074i	0.493848	+	0.855370i
$5$		0			0
$5$		0			0
$6$	1.00443	−	1.00443i	0.410056	−	0.410056i
$7$	−0.823709	+	3.07412i	−0.311333	+	1.16191i	0.616023	+	0.787728i	$0.288743\pi$
$7$	−0.823709	+	3.07412i	−0.311333	+	1.16191i	−0.927356	+	0.374181i	$0.877924\pi$
$8$			0.0490658i			0.0173474i
$9$	2.15852	+	1.24622i	0.719505	+	0.415407i
$10$		0			0
$11$		−	2.17335i		−	0.655290i	−0.944801	−	0.327645i	$-0.893745\pi$
$11$		−	2.17335i		−	0.655290i	0.944801	−	0.327645i	$-0.106255\pi$
$12$	−1.35938	+	0.364245i	−0.392419	+	0.105148i
$13$	2.46782	−	1.42480i	0.684450	−	0.395168i	−0.117079	−	0.993123i	$-0.537353\pi$
$13$	2.46782	−	1.42480i	0.684450	−	0.395168i	0.801530	+	0.597955i	$0.204020\pi$
$14$	4.48696	−	4.48696i	1.19919	−	1.19919i
$15$		0			0
$16$	2.02431	−	3.50620i	0.506076	−	0.876550i
$17$	−0.754926	+	1.30757i	−0.183096	+	0.317132i	−0.942933	−	0.332981i	$-0.891945\pi$
$17$	−0.754926	+	1.30757i	−0.183096	+	0.317132i	0.759837	+	0.650114i	$0.225279\pi$
$18$	−2.48476	−	4.30373i	−0.585664	−	1.01440i
$19$	0.158906	−	0.593046i	0.0364556	−	0.136054i	−0.945300	−	0.326203i	$-0.894231\pi$
$19$	0.158906	−	0.593046i	0.0364556	−	0.136054i	0.981755	+	0.190149i	$0.0608972\pi$
$20$		0			0
$21$	−1.96360	−	1.13368i	−0.428492	−	0.247390i
$22$	−2.16666	+	3.75276i	−0.461933	+	0.800091i
$23$			0.334904i			0.0698323i	0.999390	+	0.0349162i	$0.0111164\pi$
$23$			0.334904i			0.0698323i	−0.999390	+	0.0349162i	$0.988884\pi$
$24$	−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
$28$	−6.07260	+	1.62715i	−1.14761	+	0.307502i
$29$	−3.60210	+	3.60210i	−0.668894	+	0.668894i	−0.957460	−	0.288566i	$-0.906821\pi$
$29$	−3.60210	+	3.60210i	−0.668894	+	0.668894i	0.288566	+	0.957460i	$0.406821\pi$
$30$		0			0
$31$	4.53577	+	4.53577i	0.814648	+	0.814648i	0.985327	−	0.170679i	$-0.0545960\pi$
$31$	4.53577	+	4.53577i	0.814648	+	0.814648i	−0.170679	+	0.985327i	$0.554596\pi$
$32$	−6.90581	+	3.98707i	−1.22079	+	0.704822i
$33$	1.49561	+	0.400747i	0.260352	+	0.0697611i
$34$	2.60708	−	1.50520i	0.447111	−	0.258140i
$35$		0			0
$36$			4.92354i			0.820590i
$37$	−0.704946	+	6.04178i	−0.115892	+	0.993262i
$37$	−0.704946	+	6.04178i	−0.115892	+	0.993262i
$38$	−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	−0.350134	−	0.936699i	$-0.613864\pi$
$41$	1.83132	−	1.05731i	0.286004	−	0.165124i	0.636138	+	0.771575i	$0.280531\pi$
$42$	2.26038	+	3.91509i	0.348784	+	0.604112i
$43$		−	7.15520i		−	1.09116i	−0.838059	−	0.545579i	$-0.816310\pi$
$43$		−	7.15520i		−	1.09116i	0.838059	−	0.545579i	$-0.183690\pi$
$44$	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
$52$	4.87491	+	2.81453i	0.676029	+	0.390305i
$53$	0.159478	+	0.595178i	0.0219059	+	0.0817540i	0.976013	−	0.217710i	$-0.0698588\pi$
$53$	0.159478	+	0.595178i	0.0219059	+	0.0817540i	−0.954108	+	0.299464i	$0.903192\pi$
$54$	7.53604	−	2.01928i	1.02552	−	0.274789i
$55$		0			0
$56$	−0.150834	−	0.0404159i	−0.0201561	−	0.00540080i
$57$	0.378808	+	0.218705i	0.0501744	+	0.0289682i
$58$	9.81081	−	2.62880i	1.28822	−	0.345178i
$59$	−7.80951	+	2.09255i	−1.01671	+	0.272427i	−0.728431	−	0.685119i	$-0.759750\pi$
$59$	−7.80951	+	2.09255i	−1.01671	+	0.272427i	−0.288280	+	0.957546i	$0.593083\pi$
$60$		0			0
$61$	−3.57637	+	13.3472i	−0.457907	+	1.70893i	0.221492	+	0.975162i	$0.428907\pi$
$61$	−3.57637	+	13.3472i	−0.457907	+	1.70893i	−0.679398	+	0.733770i	$0.737759\pi$
$62$	−3.31018	−	12.3538i	−0.420394	−	1.56893i
$63$	−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
$67$	−0.360748	−	0.0966621i	−0.0440723	−	0.0118092i	0.236716	−	0.971579i	$-0.423929\pi$
$67$	−0.360748	−	0.0966621i	−0.0440723	−	0.0118092i	−0.280788	+	0.959770i	$0.590596\pi$
$68$	−2.98255			−0.361687
$69$	−0.230467	−	0.0617534i	−0.0277449	−	0.00743423i
$70$		0			0
$71$	4.77717	+	8.27430i	0.566946	+	0.981979i	0.996866	+	0.0791117i	$0.0252084\pi$
$71$	4.77717	+	8.27430i	0.566946	+	0.981979i	−0.429920	+	0.902867i	$0.641458\pi$
$72$	−0.0611467	+	0.105909i	−0.00720621	+	0.0124815i
$73$	11.6826	+	11.6826i	1.36734	+	1.36734i	0.864213	+	0.503126i	$0.167817\pi$
$73$	11.6826	+	11.6826i	1.36734	+	1.36734i	0.503126	+	0.864213i	$0.332183\pi$
$74$	7.24040	−	9.72965i	0.841680	−	1.13105i
$75$		0			0
$76$	1.17150	−	0.313902i	0.134380	−	0.0360070i
$77$	6.68116	+	1.79021i	0.761388	+	0.204013i
$78$	1.04764	−	3.90986i	0.118622	−	0.442704i
$79$	−1.12144	+	4.18528i	−0.126172	+	0.470881i	−0.999879	−	0.0155724i	$-0.995043\pi$
$79$	−1.12144	+	4.18528i	−0.126172	+	0.470881i	0.873707	+	0.486453i	$0.161710\pi$
$80$		0			0
$81$	2.34479	+	4.06129i	0.260532	+	0.451254i
$82$	−4.21622			−0.465603
$83$	0.539908	+	2.01496i	0.0592626	+	0.221171i	0.989206	−	0.146532i	$-0.0468110\pi$
$83$	0.539908	+	2.01496i	0.0592626	+	0.221171i	−0.929943	+	0.367703i	$0.880144\pi$
$84$		−	4.47894i		−	0.488692i
$85$		0			0
$86$	−7.13316	+	12.3550i	−0.769188	+	1.33227i
$87$	−1.81462	−	3.14301i	−0.194547	−	0.336966i
$88$	0.106637			0.0113676
$89$	−0.0491257	−	0.183340i	−0.00520732	−	0.0194340i	0.963273	−	0.268523i	$-0.0865355\pi$
$89$	−0.0491257	−	0.183340i	−0.00520732	−	0.0194340i	−0.968481	+	0.249089i	$0.919869\pi$
$90$		0			0
$91$	2.34724	+	8.76001i	0.246057	+	0.918298i
$92$	−0.572934	+	0.330783i	−0.0597325	+	0.0344865i
$93$	−3.95768	+	2.28497i	−0.410392	+	0.236940i
$94$	4.31371	+	16.0990i	0.444926	+	1.66049i
$95$		0			0
$96$	−1.47036	−	5.48747i	−0.150068	−	0.560062i
$97$	7.75205			0.787101			0.393550	−	0.919303i	$-0.371247\pi$
$97$	7.75205			0.787101			0.393550	+	0.919303i	$0.371247\pi$
$98$	3.11910	+	5.40243i	0.315076	+	0.545728i
$99$	2.70847	−	4.69122i	0.272212	−	0.471485i
$100$		0			0
$101$		−	4.36118i		−	0.433954i	−0.976177	−	0.216977i	$-0.930380\pi$
$101$		−	4.36118i		−	0.433954i	0.976177	−	0.216977i	$-0.0696196\pi$
$102$	0.555091	+	2.07163i	0.0549622	+	0.205122i
$103$	0.120499			0.0118731			0.00593655	−	0.999982i	$-0.498110\pi$
$103$	0.120499			0.0118731			0.00593655	+	0.999982i	$0.498110\pi$
$104$	0.0699088	+	0.121086i	0.00685512	+	0.0118734i
$105$		0			0
$106$	0.317972	−	1.18669i	0.0308842	−	0.115261i
$107$	2.64415	−	9.86809i	0.255619	−	0.953985i	−0.712125	−	0.702052i	$-0.752267\pi$
$107$	2.64415	−	9.86809i	0.255619	−	0.953985i	0.967745	−	0.251932i	$-0.0810661\pi$
$108$	−7.46631	−	2.00059i	−0.718446	−	0.192507i
$109$	−11.9735	+	3.20828i	−1.14685	+	0.307297i	−0.781702	−	0.623653i	$-0.785648\pi$
$109$	−11.9735	+	3.20828i	−1.14685	+	0.307297i	−0.365147	+	0.930950i	$0.618981\pi$
$110$		0			0
$111$	−4.02771	−	1.59916i	−0.382293	−	0.151786i
$112$	9.11106	+	9.11106i	0.860914	+	0.860914i
$113$	−3.03182	+	5.25127i	−0.285210	+	0.493998i	−0.972660	−	0.232233i	$-0.925397\pi$
$113$	−3.03182	+	5.25127i	−0.285210	+	0.493998i	0.687450	+	0.726232i	$0.258730\pi$
$114$	−0.436062	−	0.755282i	−0.0408410	−	0.0707387i
$115$		0			0
$116$	−9.72004	−	2.60448i	−0.902483	−	0.241820i
$117$	7.10244			0.656621
$118$	15.5709	+	4.17221i	1.43342	+	0.384083i
$119$	−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
$123$	0.389918	+	1.45519i	0.0351577	+	0.131210i
$124$	−3.27956	+	12.2395i	−0.294513	+	1.09914i
$125$		0			0
$126$	15.2769	−	4.09344i	1.36098	−	0.364673i
$127$	−12.7165	+	3.40738i	−1.12841	+	0.302356i	−0.774282	−	0.632841i	$-0.781889\pi$
$127$	−12.7165	+	3.40738i	−1.12841	+	0.302356i	−0.354128	+	0.935197i	$0.615222\pi$
$128$	0.339912	+	0.196248i	0.0300443	+	0.0173461i
$129$	4.92391	+	1.31936i	0.433526	+	0.116163i
$130$		0			0
$131$	−11.0289	+	2.95518i	−0.963598	+	0.258195i	−0.706122	−	0.708090i	$-0.749557\pi$
$131$	−11.0289	+	2.95518i	−0.963598	+	0.258195i	−0.257475	+	0.966285i	$0.582891\pi$
$132$	0.791632	+	2.95441i	0.0689028	+	0.257149i
$133$	1.69220	+	0.976995i	0.146733	+	0.0847162i
$134$	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	$-0.908683\pi$
$139$	−2.76488	+	4.78891i	−0.234514	+	0.406190i	0.724617	+	0.689152i	$0.242017\pi$
$140$		0			0
$141$	5.15751	−	2.97769i	0.434340	−	0.250767i
$142$		−	19.0498i		−	1.59862i
$143$	−3.09659	−	5.36345i	−0.258950	−	0.448514i
$144$	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
$148$	−11.0322	+	4.76146i	−0.906839	+	0.391389i
$149$		−	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	−0.449715	−	0.893172i	$-0.648474\pi$
$151$	1.21576	−	0.701919i	0.0989370	−	0.0571213i	0.548652	+	0.836051i	$0.315141\pi$
$152$	0.0290983	+	0.00779686i	0.00236018	+	0.000632409i
$153$	−3.25904	+	1.88161i	−0.263478	+	0.152119i
$154$	−9.75175	−	9.75175i	−0.785819	−	0.785819i
$155$		0			0
$156$	−2.83573	+	2.83573i	−0.227040	+	0.227040i
$157$	−7.01323	+	1.87919i	−0.559716	+	0.149976i	−0.527576	−	0.849508i	$-0.676899\pi$
$157$	−7.01323	+	1.87919i	−0.559716	+	0.149976i	−0.0321404	+	0.999483i	$0.510232\pi$
$158$	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
$162$		−	9.35024i		−	0.734625i
$163$	−2.54539	+	4.40875i	−0.199370	+	0.345320i	−0.948324	−	0.317302i	$-0.897223\pi$
$163$	−2.54539	+	4.40875i	−0.199370	+	0.345320i	0.748954	+	0.662622i	$0.230556\pi$
$164$	3.61757	+	2.08860i	0.282485	+	0.163093i
$165$		0			0
$166$	1.07649	−	4.01751i	0.0835518	−	0.311820i
$167$	2.82047	+	4.88520i	0.218255	+	0.378028i	0.954274	−	0.298932i	$-0.0966303\pi$
$167$	2.82047	+	4.88520i	0.218255	+	0.378028i	−0.736020	+	0.676960i	$0.763297\pi$
$168$	0.0556250	−	0.0963454i	0.00429157	−	0.00743321i
$169$	−2.43991	+	4.22604i	−0.187685	+	0.325080i
$170$		0			0
$171$	1.08207	−	1.08207i	0.0827477	−	0.0827477i
$172$	12.2407	−	7.06716i	0.933343	−	0.538866i
$173$	−1.10392	+	0.295795i	−0.0839295	+	0.0224888i	−0.300539	−	0.953769i	$-0.597167\pi$
$173$	−1.10392	+	0.295795i	−0.0839295	+	0.0224888i	0.216610	+	0.976258i	$0.430500\pi$
$174$			7.23611i			0.548568i
$175$		0			0
$176$	−7.62021	−	4.39953i	−0.574395	−	0.331627i
$177$		−	5.76002i		−	0.432950i
$178$	−0.0979487	+	0.365550i	−0.00734157	+	0.0273991i
$179$	−11.6801	+	11.6801i	−0.873015	+	0.873015i	−0.992800	−	0.119785i	$-0.961779\pi$
$179$	−11.6801	+	11.6801i	−0.873015	+	0.873015i	0.119785	+	0.992800i	$0.461779\pi$
$180$		0			0
$181$	12.7282	+	22.0459i	0.946080	+	1.63866i	0.753573	+	0.657364i	$0.228328\pi$
$181$	12.7282	+	22.0459i	0.946080	+	1.63866i	0.192507	+	0.981296i	$0.438338\pi$
$182$	4.68001	−	17.4660i	0.346905	−	1.29467i
$183$	−8.52551	−	4.92221i	−0.630224	−	0.363860i
$184$	−0.0164323			−0.00121141
$185$		0			0
$186$	9.11171			0.668103
$187$	2.84181	+	1.64072i	0.207814	+	0.119981i
$188$	4.27380	−	15.9501i	0.311699	−	1.16328i
$189$	−6.22669	−	10.7849i	−0.452925	−	0.784489i
$190$		0			0
$191$	12.6423	−	12.6423i	0.914764	−	0.914764i	−0.0818786	−	0.996642i	$-0.526092\pi$
$191$	12.6423	−	12.6423i	0.914764	−	0.914764i	0.996642	+	0.0818786i	$0.0260920\pi$
$192$	−1.43861	+	5.36896i	−0.103823	+	0.387471i
$193$		−	19.2629i		−	1.38657i	−0.720663	−	0.693285i	$-0.756163\pi$
$193$		−	19.2629i		−	1.38657i	0.720663	−	0.693285i	$-0.243837\pi$
$194$	−13.3856	−	7.72816i	−0.961028	−	0.554850i
$195$		0			0
$196$		−	6.18048i		−	0.441463i
$197$	−16.2943	+	4.36604i	−1.16092	+	0.311067i	−0.787333	−	0.616528i	$-0.788539\pi$
$197$	−16.2943	+	4.36604i	−1.16092	+	0.311067i	−0.373587	+	0.927595i	$0.621872\pi$
$198$	−9.35352	+	5.40026i	−0.664726	+	0.383780i
$199$	−12.5591	+	12.5591i	−0.890292	+	0.890292i	−0.994550	−	0.104259i	$-0.966753\pi$
$199$	−12.5591	+	12.5591i	−0.890292	+	0.890292i	0.104259	+	0.994550i	$0.466753\pi$
$200$		0			0
$201$	0.133037	−	0.230428i	0.00938374	−	0.0162531i
$202$	−4.34774	+	7.53051i	−0.305906	+	0.529845i
$203$	−8.10623	−	14.0404i	−0.568946	−	0.985443i
$204$	0.549956	−	2.05246i	0.0385046	−	0.143701i
$205$		0			0
$206$	−0.208067	−	0.120128i	−0.0144967	−	0.00836968i
$207$	−0.417364	+	0.722896i	−0.0290088	+	0.0502447i
$208$		−	11.5369i		−	0.799940i
$209$	−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
$213$	−6.57489	+	1.76174i	−0.450504	+	0.120712i
$214$	−14.4034	+	14.4034i	−0.984595	+	0.984595i
$215$		0			0
$216$	−0.135760	−	0.135760i	−0.00923732	−	0.00923732i
$217$	−17.6797	+	10.2074i	−1.20017	+	0.692921i
$218$	23.8731	+	6.39678i	1.61689	+	0.433245i
$219$	−10.1936	+	5.88528i	−0.688819	+	0.397690i
$220$		0			0
$221$			4.30246i			0.289415i
$222$	5.36046	+	6.77660i	0.359771	+	0.454816i
$223$	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
$227$	−9.44467	−	16.3587i	−0.626865	−	1.08576i	−0.988177	−	0.153317i	$-0.951004\pi$
$227$	−9.44467	−	16.3587i	−0.626865	−	1.08576i	0.361312	−	0.932445i	$-0.382329\pi$
$228$			0.864056i			0.0572235i
$229$	8.30226	−	4.79331i	0.548629	−	0.316751i	−0.199940	−	0.979808i	$-0.564075\pi$
$229$	8.30226	−	4.79331i	0.548629	−	0.316751i	0.748569	+	0.663057i	$0.230741\pi$
$230$		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	$-0.964980\pi$
$233$	−16.8480	−	16.8480i	−1.10375	−	1.10375i	−0.109796	−	0.993954i	$-0.535020\pi$
$234$	−12.2639	−	7.08056i	−0.801715	−	0.462871i
$235$		0			0
$236$	−11.2932	−	11.2932i	−0.735126	−	0.735126i
$237$	−2.67335	−	1.54346i	−0.173653	−	0.100258i
$238$	2.47969	+	9.25434i	0.160735	+	0.599870i
$239$	24.8308	−	6.65340i	1.60617	−	0.430373i	0.659274	−	0.751903i	$-0.270864\pi$
$239$	24.8308	−	6.65340i	1.60617	−	0.430373i	0.946899	+	0.321530i	$0.104197\pi$
$240$		0			0
$241$	−14.6126	−	3.91545i	−0.941283	−	0.252216i	−0.244624	−	0.969618i	$-0.578664\pi$
$241$	−14.6126	−	3.91545i	−0.941283	−	0.252216i	−0.696659	+	0.717402i	$0.745331\pi$
$242$	−10.8378	−	6.25720i	−0.696680	−	0.402228i
$243$	−14.5662	+	3.90299i	−0.934419	+	0.250377i
$244$	−26.3659	+	7.06472i	−1.68790	+	0.452273i
$245$		0			0
$246$	0.777434	−	2.90142i	0.0495674	−	0.184988i
$247$	−0.452818	−	1.68994i	−0.0288121	−	0.107528i
$248$	−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	0.261238	−	0.965275i	$-0.415869\pi$
$251$	−11.1540	−	11.1540i	−0.704037	−	0.704037i	−0.965275	+	0.261238i	$0.915869\pi$
$252$	−15.1356	−	4.05557i	−0.953452	−	0.255477i
$253$	0.727865			0.0457605
$254$	25.3547	+	6.79377i	1.59090	+	0.426279i
$255$		0			0
$256$	−8.19322	−	14.1911i	−0.512076	−	0.886942i
$257$	2.97643	−	5.15532i	0.185664	−	0.321580i	−0.758136	−	0.652097i	$-0.773890\pi$
$257$	2.97643	−	5.15532i	0.185664	−	0.321580i	0.943800	+	0.330516i	$0.107223\pi$
$258$	−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
$262$	21.9898	+	5.89215i	1.35853	+	0.364018i
$263$	−1.89838	+	7.08485i	−0.117059	+	0.436870i	−0.999433	−	0.0336790i	$-0.989278\pi$
$263$	−1.89838	+	7.08485i	−0.117059	+	0.436870i	0.882374	+	0.470549i	$0.155944\pi$
$264$	−0.0196630	+	0.0733832i	−0.00121017	+	0.00451642i
$265$		0			0
$266$	−1.94797	−	3.37398i	−0.119438	−	0.206872i
$267$	0.135225			0.00827563
$268$	−0.190945	−	0.712618i	−0.0116638	−	0.0435301i
$269$			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	0.118532	−	0.992950i	$-0.462181\pi$
$271$	15.1317	−	26.2089i	0.919186	−	1.59208i	0.800654	−	0.599127i	$-0.204485\pi$
$272$	3.05640	+	5.29384i	0.185322	+	0.320986i
$273$	−6.46107			−0.391042
$274$	−10.8398	−	40.4546i	−0.654854	−	2.44395i
$275$		0			0
$276$	−0.121987	−	0.455262i	−0.00734276	−	0.0274036i
$277$	−13.8484	+	7.99538i	−0.832070	+	0.480396i	−0.854561	−	0.519351i	$-0.826174\pi$
$277$	−13.8484	+	7.99538i	−0.832070	+	0.480396i	0.0224906	+	0.999747i	$0.492840\pi$
$278$	9.54832	−	5.51272i	0.572670	−	0.330631i
$279$	4.13796	+	15.4431i	0.247733	+	0.924553i
$280$		0			0
$281$	−3.07938	−	11.4924i	−0.183701	−	0.685580i	−0.994905	−	0.100817i	$-0.967854\pi$
$281$	−3.07938	−	11.4924i	−0.183701	−	0.685580i	0.811204	−	0.584763i	$-0.198812\pi$
$282$	−11.8741			−0.707090
$283$	−1.16624	−	2.01999i	−0.0693258	−	0.120076i	0.829279	−	0.558835i	$-0.188751\pi$
$283$	−1.16624	−	2.01999i	−0.0693258	−	0.120076i	−0.898605	+	0.438759i	$0.855418\pi$
$284$	−9.43678	+	16.3450i	−0.559970	+	0.969896i
$285$		0			0
$286$			12.3482i			0.730164i
$287$	1.74184	+	6.50062i	0.102817	+	0.383719i
$288$	−19.8751			−1.17115
$289$	7.36017	+	12.7482i	0.432951	+	0.749894i
$290$		0			0
$291$	−1.42941	+	5.33463i	−0.0837935	+	0.312721i
$292$	−8.44699	+	31.5246i	−0.494323	+	1.84484i
$293$	22.3999	+	6.00204i	1.30862	+	0.350643i	0.844702	−	0.535236i	$-0.179777\pi$
$293$	22.3999	+	6.00204i	1.30862	+	0.350643i	0.463916	+	0.885879i	$0.346444\pi$
$294$	−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
$298$	−13.7555	+	23.8252i	−0.796835	+	1.38016i
$299$	0.477170	+	0.826484i	0.0275955	+	0.0477968i
$300$		0			0
$301$	21.9960	+	5.89380i	1.26783	+	0.339713i
$302$	−2.79902			−0.161066
$303$	3.00118	+	0.804163i	0.172413	+	0.0461980i
$304$	−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	$-0.438722\pi$
$307$	20.5500	−	20.5500i	1.17285	−	1.17285i	0.981527	−	0.191323i	$-0.0612779\pi$
$308$	3.53637	+	13.1979i	0.201503	+	0.752020i
$309$	−0.0222189	+	0.0829221i	−0.00126399	+	0.00471727i
$310$		0			0
$311$	6.27405	−	1.68113i	0.355769	−	0.0953279i	−0.0765080	−	0.997069i	$-0.524377\pi$
$311$	6.27405	−	1.68113i	0.355769	−	0.0953279i	0.432277	+	0.901741i	$0.357710\pi$
$312$	−0.0962165	+	0.0257811i	−0.00544719	+	0.00145957i
$313$	−2.16900	−	1.25227i	−0.122599	−	0.0707825i	0.437446	−	0.899244i	$-0.355883\pi$
$313$	−2.16900	−	1.25227i	−0.122599	−	0.0707825i	−0.560045	+	0.828462i	$0.689216\pi$
$314$	13.9832	+	3.74680i	0.789120	+	0.211444i
$315$		0			0
$316$	−8.26757	+	2.21529i	−0.465087	+	0.124620i
$317$	−1.15635	−	4.31555i	−0.0649470	−	0.242386i	0.925819	−	0.377967i	$-0.123377\pi$
$317$	−1.15635	−	4.31555i	−0.0649470	−	0.242386i	−0.990766	+	0.135581i	$0.956710\pi$
$318$	0.757998	+	0.437630i	0.0425064	+	0.0245411i
$319$	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
$327$		−	8.83120i		−	0.488366i
$328$	0.0518778	+	0.0898550i	0.00286447	+	0.00496141i
$329$	23.0395	−	13.3019i	1.27021	−	0.733356i
$330$		0			0
$331$	−4.17606	−	15.5853i	−0.229537	−	0.856645i	−0.980536	−	0.196341i	$-0.937094\pi$
$331$	−4.17606	−	15.5853i	−0.229537	−	0.856645i	0.750999	−	0.660304i	$-0.229573\pi$
$332$	−2.91381	+	2.91381i	−0.159916	+	0.159916i
$333$	−9.05101	+	12.1627i	−0.495993	+	0.666515i
$334$		−	11.2471i		−	0.615416i
$335$		0			0
$336$	−7.94984	+	4.58984i	−0.433699	+	0.250396i
$337$	33.6031	+	9.00391i	1.83048	+	0.490474i	0.997978	−	0.0635550i	$-0.0202438\pi$
$337$	33.6031	+	9.00391i	1.83048	+	0.490474i	0.832497	+	0.554029i	$0.186911\pi$
$338$	8.42604	−	4.86478i	0.458316	−	0.264609i
$339$	−3.05466	−	3.05466i	−0.165906	−	0.165906i
$340$		0			0
$341$	9.85782	−	9.85782i	0.533831	−	0.533831i
$342$	−2.94715	+	0.789688i	−0.159364	+	0.0427014i
$343$	−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
$347$			36.0284i			1.93411i	0.254572	+	0.967054i	$0.418066\pi$
$347$			36.0284i			1.93411i	−0.254572	+	0.967054i	$0.581934\pi$
$348$	3.58458	−	6.20868i	0.192154	−	0.332820i
$349$	−17.5896	−	10.1554i	−0.941550	−	0.543604i	−0.0511041	−	0.998693i	$-0.516274\pi$
$349$	−17.5896	−	10.1554i	−0.941550	−	0.543604i	−0.890446	+	0.455089i	$0.849607\pi$
$350$		0			0
$351$	−2.88595	+	10.7705i	−0.154041	+	0.574887i
$352$	8.66531	+	15.0088i	0.461863	+	0.799970i
$353$	8.93186	−	15.4704i	0.475395	−	0.823408i	−0.524208	−	0.851590i	$-0.675639\pi$
$353$	8.93186	−	15.4704i	0.475395	−	0.823408i	0.999603	+	0.0281823i	$0.00897190\pi$
$354$	−5.74227	+	9.94591i	−0.305198	+	0.528619i
$355$		0			0
$356$	0.265125	−	0.265125i	0.0140516	−	0.0140516i
$357$	2.96474	−	1.71169i	0.156911	−	0.0905924i
$358$	31.8124	−	8.52411i	1.68134	−	0.450513i
$359$		−	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
$362$		−	50.7560i		−	2.66768i
$363$	−1.15734	+	4.31925i	−0.0607445	+	0.226702i
$364$	−12.6677	+	12.6677i	−0.663970	+	0.663970i
$365$		0			0
$366$	9.81409	+	16.9985i	0.512991	+	0.888526i
$367$	7.85591	−	29.3187i	0.410075	−	1.53042i	−0.384424	−	0.923156i	$-0.625600\pi$
$367$	7.85591	−	29.3187i	0.410075	−	1.53042i	0.794500	−	0.607265i	$-0.207733\pi$
$368$	1.17424	+	0.677948i	0.0612115	+	0.0353405i
$369$	5.27057			0.274375
$370$		0			0
$371$	−1.96101			−0.101811
$372$	−7.81796	−	4.51370i	−0.405343	−	0.234025i
$373$	−6.74904	+	25.1878i	−0.349452	+	1.30417i	0.537872	+	0.843027i	$0.319228\pi$
$373$	−6.74904	+	25.1878i	−0.349452	+	1.30417i	−0.887324	+	0.461146i	$0.847438\pi$
$374$	−3.27133	−	5.66611i	−0.169156	−	0.292988i
$375$		0			0
$376$	0.290021	−	0.290021i	0.0149567	−	0.0149567i
$377$	−3.75708	+	14.0216i	−0.193499	+	0.722150i
$378$			24.8300i			1.27712i
$379$	24.1459	+	13.9406i	1.24029	+	0.716082i	0.969153	−	0.246459i	$-0.0792670\pi$
$379$	24.1459	+	13.9406i	1.24029	+	0.716082i	0.271137	+	0.962541i	$0.412600\pi$
$380$		0			0
$381$		−	9.37927i		−	0.480514i
$382$	−34.4330	+	9.22628i	−1.76174	+	0.472058i
$383$	−20.1610	+	11.6400i	−1.03018	+	0.594775i	−0.917036	−	0.398804i	$-0.869425\pi$
$383$	−20.1610	+	11.6400i	−1.03018	+	0.594775i	−0.113144	+	0.993579i	$0.536092\pi$
$384$	−0.197726	+	0.197726i	−0.0100902	+	0.0100902i
$385$		0			0
$386$	−19.2035	+	33.2615i	−0.977433	+	1.69296i
$387$	8.91695	−	15.4446i	0.453274	−	0.785094i
$388$	7.65666	+	13.2617i	0.388708	+	0.673262i
$389$	6.39722	−	23.8748i	0.324352	−	1.21050i	−0.590610	−	0.806957i	$-0.701113\pi$
$389$	6.39722	−	23.8748i	0.324352	−	1.21050i	0.914962	−	0.403541i	$-0.132221\pi$
$390$		0			0
$391$	−0.437911	−	0.252828i	−0.0221461	−	0.0127861i
$392$	0.0767569	−	0.132947i	0.00387681	−	0.00671483i
$393$		−	8.13451i		−	0.410332i
$394$	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	−0.677756	−	0.735287i	$-0.737047\pi$
$397$	1.14631	−	1.14631i	0.0575316	−	0.0575316i	0.735287	+	0.677756i	$0.237047\pi$
$398$	34.2064	−	9.16558i	1.71461	−	0.459429i
$399$	−0.984354	+	0.984354i	−0.0492793	+	0.0492793i
$400$		0			0
$401$	−5.12856	−	5.12856i	−0.256108	−	0.256108i	0.567361	−	0.823469i	$-0.307964\pi$
$401$	−5.12856	−	5.12856i	−0.256108	−	0.256108i	−0.823469	+	0.567361i	$0.807964\pi$
$402$	−0.459435	+	0.265255i	−0.0229146	+	0.0132297i
$403$	17.6560	+	4.73091i	0.879509	+	0.235664i
$404$	7.46084	−	4.30752i	0.371191	−	0.214307i
$405$		0			0
$406$			32.3250i			1.60426i
$407$	13.1309	+	1.53210i	0.650875	+	0.0759431i
$408$	0.0373200	−	0.0373200i	0.00184762	−	0.00184762i
$409$	1.06786	+	3.98532i	0.0528024	+	0.197061i	0.987289	−	0.158938i	$-0.0508071\pi$
$409$	1.06786	+	3.98532i	0.0528024	+	0.197061i	−0.934486	+	0.356000i	$0.884140\pi$
$410$		0			0
$411$	−12.9601	+	7.48252i	−0.639275	+	0.369085i
$412$	0.119016	+	0.206142i	0.00586350	+	0.0101559i
$413$		−	25.7310i		−	1.26614i
$414$	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	$-0.170555\pi$
$419$	17.3507	+	10.0174i	0.847638	+	0.489384i	−0.0122153	+	0.999925i	$0.503888\pi$
$420$		0			0
$421$	3.69196	+	3.69196i	0.179935	+	0.179935i	0.791328	−	0.611392i	$-0.209390\pi$
$421$	3.69196	+	3.69196i	0.179935	+	0.179935i	−0.611392	+	0.791328i	$0.709390\pi$
$422$	6.04753	+	3.49154i	0.294389	+	0.169966i
$423$	−5.39245	−	20.1249i	−0.262190	−	0.978506i
$424$	−0.0292029	+	0.00782489i	−0.00141822	+	0.000380010i
$425$		0			0
$426$	13.1093	+	3.51262i	0.635146	+	0.170187i
$427$	−38.0850	−	21.9884i	−1.84306	−	1.06409i
$428$	19.4933	−	5.22323i	0.942246	−	0.252474i
$429$	4.26188	−	1.14197i	0.205765	−	0.0551347i
$430$		0			0
$431$	−4.73118	+	17.6570i	−0.227893	+	0.850509i	0.753332	+	0.657641i	$0.228446\pi$
$431$	−4.73118	+	17.6570i	−0.227893	+	0.850509i	−0.981225	+	0.192868i	$0.938221\pi$
$432$	4.10026	+	15.3024i	0.197274	+	0.736237i
$433$	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
$437$	0.198614	+	0.0532183i	0.00950098	+	0.00254578i
$438$	23.4686			1.12137
$439$	33.2323	+	8.90457i	1.58609	+	0.424992i	0.940805	−	0.338948i	$-0.110071\pi$
$439$	33.2323	+	8.90457i	1.58609	+	0.424992i	0.645287	+	0.763940i	$0.276738\pi$
$440$		0			0
$441$	−3.89909	−	6.75343i	−0.185671	−	0.321592i
$442$	4.28921	−	7.42913i	0.204017	−	0.353368i
$443$	−2.82400	−	2.82400i	−0.134172	−	0.134172i	0.636831	−	0.771003i	$-0.280245\pi$
$443$	−2.82400	−	2.82400i	−0.134172	−	0.134172i	−0.771003	+	0.636831i	$0.780245\pi$
$444$	−1.24240	−	8.46984i	−0.0589615	−	0.401961i
$445$		0			0
$446$	−31.9542	+	8.56211i	−1.51308	+	0.405428i
$447$	9.49521	+	2.54423i	0.449108	+	0.120338i
$448$	−6.42652	+	23.9841i	−0.303625	+	1.13314i
$449$	7.10809	−	26.5277i	0.335451	−	1.25192i	−0.567928	−	0.823078i	$-0.692255\pi$
$449$	7.10809	−	26.5277i	0.335451	−	1.25192i	0.903379	−	0.428843i	$-0.141079\pi$
$450$		0			0
$451$	−2.29791	−	3.98010i	−0.108204	−	0.187416i
$452$	−11.9781			−0.563402
$453$	0.258855	+	0.966061i	0.0121621	+	0.0453895i
$454$			37.6623i			1.76758i
$455$		0			0
$456$	−0.0107309	+	0.0185865i	−0.000502522	+	0.000870393i
$457$	−3.39116	−	5.87366i	−0.158632	−	0.274758i	0.775744	−	0.631048i	$-0.217375\pi$
$457$	−3.39116	−	5.87366i	−0.158632	−	0.274758i	−0.934375	+	0.356290i	$0.884042\pi$
$458$	−19.1142			−0.893147
$459$	−1.52911	−	5.70673i	−0.0713729	−	0.266367i
$460$		0			0
$461$	10.7605	+	40.1588i	0.501168	+	1.87038i	0.492304	+	0.870423i	$0.336155\pi$
$461$	10.7605	+	40.1588i	0.501168	+	1.87038i	0.00886370	+	0.999961i	$0.497179\pi$
$462$	8.50888	−	4.91260i	0.395869	−	0.228555i
$463$	−16.8228	+	9.71266i	−0.781822	+	0.451385i	−0.837076	−	0.547087i	$-0.815737\pi$
$463$	−16.8228	+	9.71266i	−0.781822	+	0.451385i	0.0552533	+	0.998472i	$0.482403\pi$
$464$	5.33794	+	19.9215i	0.247808	+	0.924830i
$465$		0			0
$466$	12.2956	+	45.8878i	0.569583	+	2.12571i
$467$	19.7318			0.913077			0.456538	−	0.889704i	$-0.349089\pi$
$467$	19.7318			0.913077			0.456538	+	0.889704i	$0.349089\pi$
$468$	7.01505	+	12.1504i	0.324271	+	0.561653i
$469$	0.594302	−	1.02936i	0.0274423	−	0.0475315i
$470$		0			0
$471$		−	5.17271i		−	0.238346i
$472$	−0.102673	−	0.383180i	−0.00472589	−	0.0176373i
$473$	−15.5508			−0.715025
$474$	3.07741	+	5.33022i	0.141350	+	0.244825i
$475$		0			0
$476$	2.45675	−	9.16872i	0.112605	−	0.420248i
$477$	−0.397488	+	1.48345i	−0.0181997	+	0.0679223i
$478$	−49.5087	−	13.2658i	−2.26447	−	0.606764i
$479$	−36.6479	+	9.81978i	−1.67449	+	0.448677i	−0.966315	−	0.257364i	$-0.917146\pi$
$479$	−36.6479	+	9.81978i	−1.67449	+	0.448677i	−0.708171	+	0.706041i	$0.750480\pi$
$480$		0			0
$481$	6.86863	+	15.9144i	0.313182	+	0.725635i
$482$	21.3285	+	21.3285i	0.971486	+	0.971486i
$483$	0.379675	−	0.657617i	0.0172758	−	0.0299226i
$484$	6.19931	+	10.7375i	0.281787	+	0.488069i
$485$		0			0
$486$	29.0426	+	7.78193i	1.31740	+	0.352995i
$487$	29.1168			1.31941			0.659703	−	0.751526i	$-0.270682\pi$
$487$	29.1168			1.31941			0.659703	+	0.751526i	$0.270682\pi$
$488$	−0.654890	−	0.175477i	−0.0296455	−	0.00794348i
$489$	−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
$493$	−1.99068	−	7.42932i	−0.0896558	−	0.334600i
$494$	−0.902846	+	3.36947i	−0.0406210	+	0.151600i
$495$		0			0
$496$	25.0851	−	6.72153i	1.12635	−	0.301806i
$497$	−29.3712	+	7.86999i	−1.31748	+	0.353017i
$498$	2.56619	+	1.48159i	0.114994	+	0.0663916i
$499$	−4.27129	−	1.14449i	−0.191209	−	0.0512344i	0.161944	−	0.986800i	$-0.448224\pi$
$499$	−4.27129	−	1.14449i	−0.191209	−	0.0512344i	−0.353153	+	0.935566i	$0.614890\pi$
$500$		0			0
$501$	−3.88186	+	1.04014i	−0.173429	+	0.0464701i
$502$	8.14017	+	30.3795i	0.363314	+	1.35590i
$503$	25.4710	+	14.7057i	1.13570	+	0.655694i	0.945361	−	0.326025i	$-0.105709\pi$
$503$	25.4710	+	14.7057i	1.13570	+	0.655694i	0.190335	+	0.981719i	$0.439043\pi$
$504$	−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	0.176832	−	0.984241i	$-0.443415\pi$
$509$	21.2253	−	36.7633i	0.940794	−	1.62950i	0.763962	−	0.645261i	$-0.223252\pi$
$510$		0			0
$511$	−45.5366	+	26.2906i	−2.01442	+	1.16303i
$512$			31.8869i			1.40922i
$513$	1.20122	+	2.08058i	0.0530353	+	0.0918599i
$514$	−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
$518$	23.9462	+	30.2723i	1.05213	+	1.33009i
$519$		−	0.814213i		−	0.0357400i
$520$		0			0
$521$	9.27032	−	5.35222i	0.406140	−	0.234485i	−0.282990	−	0.959123i	$-0.591326\pi$
$521$	9.27032	−	5.35222i	0.406140	−	0.234485i	0.689130	+	0.724638i	$0.257993\pi$
$522$	24.4528	+	6.55212i	1.07027	+	0.286779i
$523$	1.60873	−	0.928801i	0.0703449	−	0.0406137i	−0.464415	−	0.885618i	$-0.653735\pi$
$523$	1.60873	−	0.928801i	0.0703449	−	0.0406137i	0.534760	+	0.845004i	$0.320402\pi$
$524$	−15.9487	−	15.9487i	−0.696723	−	0.696723i
$525$		0			0
$526$	10.3410	−	10.3410i	0.450888	−	0.450888i
$527$	−9.35500	+	2.50667i	−0.407510	+	0.109192i
$528$	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
$532$			3.85989i			0.167348i
$533$	3.01291	−	5.21851i	0.130504	−	0.226039i
$534$	−0.233495	−	0.134808i	−0.0101043	−	0.00583373i
$535$		0			0
$536$	0.00474280	−	0.0177004i	0.000204858	−	0.000764539i
$537$	−5.88406	−	10.1915i	−0.253916	−	0.439795i
$538$	15.0456	−	26.0598i	0.648662	−	1.12352i
$539$	−3.39992	+	5.88884i	−0.146445	+	0.253650i
$540$		0			0
$541$	18.3486	−	18.3486i	0.788870	−	0.788870i	−0.192439	−	0.981309i	$-0.561640\pi$
$541$	18.3486	−	18.3486i	0.788870	−	0.788870i	0.981309	+	0.192439i	$0.0616399\pi$
$542$	−52.2563	+	30.1702i	−2.24460	+	1.29592i
$543$	−17.5180	+	4.69394i	−0.751770	+	0.201436i
$544$		−	12.0398i		−	0.516201i
$545$		0			0
$546$	11.1564	+	6.44117i	0.477451	+	0.275657i
$547$		−	38.0204i		−	1.62563i	−0.582518	−	0.812817i	$-0.697933\pi$
$547$		−	38.0204i		−	1.62563i	0.582518	−	0.812817i	$-0.302067\pi$
$548$	−10.7395	+	40.0803i	−0.458768	+	1.71214i
$549$	−24.3532	+	24.3532i	−1.03937	+	1.03937i
$550$		0			0
$551$	1.56382	+	2.70861i	0.0666208	+	0.115391i
$552$	0.00302998	−	0.0113080i	0.000128964	−	0.000481302i
$553$	−11.9423	−	6.89491i	−0.507840	−	0.293201i
$554$	31.8830			1.35458
$555$		0			0
$556$	−10.9234			−0.463257
$557$	25.0451	+	14.4598i	1.06119	+	0.612681i	0.925762	−	0.378106i	$-0.123425\pi$
$557$	25.0451	+	14.4598i	1.06119	+	0.612681i	0.135432	+	0.990787i	$0.456758\pi$
$558$	8.25043	−	30.7910i	0.349269	−	1.30349i
$559$	−10.1947	−	17.6578i	−0.431190	−	0.746844i
$560$		0			0
$561$	−1.65308	+	1.65308i	−0.0697930	+	0.0697930i
$562$	−6.13979	+	22.9140i	−0.258992	+	0.966570i
$563$			21.7412i			0.916284i	0.888879	+	0.458142i	$0.151485\pi$
$563$			21.7412i			0.916284i	−0.888879	+	0.458142i	$0.848515\pi$
$564$	10.1881	+	5.88210i	0.428996	+	0.247681i
$565$		0			0
$566$			4.65059i			0.195479i
$567$	−14.4163	+	3.86284i	−0.605429	+	0.162224i
$568$	−0.405985	+	0.234395i	−0.0170347	+	0.00983502i
$569$	17.8811	−	17.8811i	0.749613	−	0.749613i	−0.224793	−	0.974406i	$-0.572171\pi$
$569$	17.8811	−	17.8811i	0.749613	−	0.749613i	0.974406	+	0.224793i	$0.0721707\pi$
$570$		0			0
$571$	−1.01988	+	1.76649i	−0.0426808	+	0.0739253i	−0.886577	−	0.462582i	$-0.846923\pi$
$571$	−1.01988	+	1.76649i	−0.0426808	+	0.0739253i	0.843896	+	0.536507i	$0.180257\pi$
$572$	6.11697	−	10.5949i	0.255763	−	0.442995i
$573$	6.36876	+	11.0310i	0.266059	+	0.460827i
$574$	3.47294	−	12.9612i	0.144958	−	0.540989i
$575$		0			0
$576$	16.8406	+	9.72292i	0.701692	+	0.405122i
$577$	11.1072	−	19.2382i	0.462398	−	0.800897i	−0.536682	−	0.843785i	$-0.680323\pi$
$577$	11.1072	−	19.2382i	0.462398	−	0.800897i	0.999080	+	0.0428880i	$0.0136559\pi$
$578$		−	29.3500i		−	1.22080i
$579$	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
$583$	1.29353	−	0.346601i	0.0535726	−	0.0143547i
$584$	−0.573213	+	0.573213i	−0.0237197	+	0.0237197i
$585$		0			0
$586$	−32.6947	−	32.6947i	−1.35061	−	1.35061i
$587$	−16.5092	+	9.53161i	−0.681409	+	0.393412i	−0.800386	−	0.599485i	$-0.795372\pi$
$587$	−16.5092	+	9.53161i	−0.681409	+	0.393412i	0.118977	+	0.992897i	$0.462039\pi$
$588$	4.25314	+	1.13963i	0.175397	+	0.0469974i
$589$	3.41068	−	1.96916i	0.140535	−	0.0811377i
$590$		0			0
$591$		−	12.0181i		−	0.494358i
$592$	19.7567	+	14.7021i	0.811993	+	0.604252i
$593$	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
$597$	−6.32686	−	10.9584i	−0.258941	−	0.448499i
$598$		−	1.90280i		−	0.0778113i
$599$	−10.4679	+	6.04367i	−0.427709	+	0.246938i	−0.698370	−	0.715737i	$-0.746091\pi$
$599$	−10.4679	+	6.04367i	−0.427709	+	0.246938i	0.270661	+	0.962675i	$0.412758\pi$
$600$		0			0
$601$	0.320993	−	0.555976i	0.0130936	−	0.0226787i	−0.859404	−	0.511297i	$-0.829165\pi$
$601$	0.320993	−	0.555976i	0.0130936	−	0.0226787i	0.872498	+	0.488618i	$0.162499\pi$
$602$	−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
$607$	−32.3865	−	18.6984i	−1.31453	−	0.758943i	−0.331685	−	0.943390i	$-0.607617\pi$
$607$	−32.3865	−	18.6984i	−1.31453	−	0.758943i	−0.982842	+	0.184447i	$0.940950\pi$
$608$	1.26714	+	4.72904i	0.0513894	+	0.191788i
$609$	11.1567	−	2.98944i	0.452093	−	0.121138i
$610$		0			0
$611$	−23.0087	−	6.16516i	−0.930832	−	0.249416i
$612$	−6.43788	−	3.71691i	−0.260236	−	0.150247i
$613$	32.2173	−	8.63260i	1.30125	−	0.348668i	0.459324	−	0.888269i	$-0.348092\pi$
$613$	32.2173	−	8.63260i	1.30125	−	0.348668i	0.841921	+	0.539601i	$0.181425\pi$
$614$	−55.9707	+	14.9973i	−2.25879	+	0.605242i
$615$		0			0
$616$	−0.0878380	+	0.327816i	−0.00353910	+	0.0132081i
$617$	2.29488	+	8.56459i	0.0923882	+	0.344798i	0.996611	−	0.0822645i	$-0.0262152\pi$
$617$	2.29488	+	8.56459i	0.0923882	+	0.344798i	−0.904222	+	0.427062i	$0.859549\pi$
$618$	0.121032	−	0.121032i	0.00486864	−	0.00486864i
$619$	16.0269			0.644174			0.322087	−	0.946710i	$-0.395616\pi$
$619$	16.0269			0.644174			0.322087	+	0.946710i	$0.395616\pi$
$620$		0			0
$621$	−0.926648	−	0.926648i	−0.0371851	−	0.0371851i
$622$	−12.5094	−	3.35189i	−0.501583	−	0.134399i
$623$	0.604074			0.0242017
$624$	7.93921	+	2.12730i	0.317823	+	0.0851603i
$625$		0			0
$626$	2.49682	+	4.32463i	0.0997932	+	0.172847i
$627$	0.475323	−	0.823284i	0.0189826	−	0.0328788i
$628$	−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	0.235662	−	0.971835i	$-0.424274\pi$
$631$	23.2525	−	6.23050i	0.925669	−	0.248032i	0.690007	+	0.723803i	$0.257607\pi$
$632$	−0.205354	−	0.0550244i	−0.00816854	−	0.00218875i
$633$	0.645799	−	2.41016i	0.0256682	−	0.0957951i
$634$	−2.30557	+	8.60452i	−0.0915660	+	0.341729i
$635$		0			0
$636$	−0.433581	−	0.750985i	−0.0171926	−	0.0297785i
$637$	−8.91563			−0.353250
$638$	−5.71331	−	21.3224i	−0.226192	−	0.844160i
$639$			23.8136i			0.942052i
$640$		0			0
$641$	9.86299	−	17.0832i	0.389565	−	0.674746i	−0.602826	−	0.797872i	$-0.705959\pi$
$641$	9.86299	−	17.0832i	0.389565	−	0.674746i	0.992391	+	0.123127i	$0.0392922\pi$
$642$	−7.25594	−	12.5677i	−0.286369	−	0.496006i
$643$	−2.09981			−0.0828085			−0.0414043	−	0.999142i	$-0.513183\pi$
$643$	−2.09981			−0.0828085			−0.0414043	+	0.999142i	$0.513183\pi$
$644$	−0.544939	−	2.03374i	−0.0214736	−	0.0801405i
$645$		0			0
$646$	−0.478371	−	1.78531i	−0.0188213	−	0.0702419i
$647$	16.8964	−	9.75517i	0.664268	−	0.383515i	−0.129633	−	0.991562i	$-0.541380\pi$
$647$	16.8964	−	9.75517i	0.664268	−	0.383515i	0.793901	+	0.608047i	$0.208047\pi$
$648$	−0.199270	+	0.115049i	−0.00782807	+	0.00451954i
$649$	4.54785	+	16.9728i	0.178519	+	0.666241i
$650$		0			0
$651$	−3.76430	−	14.0485i	−0.147534	−	0.550606i
$652$	−10.0563			−0.393835
$653$	−2.65715	−	4.60233i	−0.103983	−	0.180103i	0.809340	−	0.587341i	$-0.199825\pi$
$653$	−2.65715	−	4.60233i	−0.103983	−	0.180103i	−0.913322	+	0.407238i	$0.866492\pi$
$654$	−8.80399	+	15.2490i	−0.344263	+	0.596281i
$655$		0			0
$656$		−	8.56129i		−	0.334262i
$657$	10.6579	+	39.7760i	0.415806	+	1.55181i
$658$	−53.0436			−2.06785
$659$	−1.89214	−	3.27728i	−0.0737073	−	0.127665i	0.826816	−	0.562472i	$-0.190150\pi$
$659$	−1.89214	−	3.27728i	−0.0737073	−	0.127665i	−0.900523	+	0.434808i	$0.856816\pi$
$660$		0			0
$661$	5.01853	−	18.7294i	0.195198	−	0.728490i	−0.797017	−	0.603957i	$-0.793590\pi$
$661$	5.01853	−	18.7294i	0.195198	−	0.728490i	0.992215	−	0.124533i	$-0.0397433\pi$
$662$	−8.32640	+	31.0745i	−0.323615	+	1.20775i
$663$	−2.96077	−	0.793337i	−0.114987	−	0.0308106i
$664$	−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
$668$	−5.57154	+	9.65018i	−0.215569	+	0.373377i
$669$	5.91029	+	10.2369i	0.228505	+	0.395782i
$670$		0			0
$671$	29.0081	+	7.77271i	1.11985	+	0.300062i
$672$	18.0803			0.697463
$673$	1.05454	+	0.282562i	0.0406494	+	0.0108920i	0.279086	−	0.960266i	$-0.409968\pi$
$673$	1.05454	+	0.282562i	0.0406494	+	0.0108920i	−0.238437	+	0.971158i	$0.576635\pi$
$674$	−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	−0.752013	−	0.659149i	$-0.770917\pi$
$677$	−2.41626	+	2.41626i	−0.0928643	+	0.0928643i	0.659149	+	0.752013i	$0.270917\pi$
$678$	2.22928	+	8.31978i	0.0856149	+	0.319519i
$679$	−6.38543	+	23.8307i	−0.245050	+	0.914540i
$680$		0			0
$681$	12.9988	−	3.48303i	0.498117	−	0.133470i
$682$	−26.8491	+	7.19419i	−1.02811	+	0.275480i
$683$	19.8205	+	11.4434i	0.758411	+	0.437869i	0.828725	−	0.559656i	$-0.189067\pi$
$683$	19.8205	+	11.4434i	0.758411	+	0.437869i	−0.0703137	+	0.997525i	$0.522400\pi$
$684$	2.91989	+	0.782381i	0.111645	+	0.0299151i
$685$		0			0
$686$	23.7282	−	6.35794i	0.905945	−	0.242747i
$687$	1.76769	+	6.59711i	0.0674416	+	0.251695i
$688$	−25.0876	−	14.4843i	−0.956455	−	0.552209i
$689$	1.24157	+	1.24157i	0.0473001	+	0.0473001i
$690$		0			0
$691$	15.4346	+	8.91116i	0.587159	+	0.338996i	0.763973	−	0.645248i	$-0.223246\pi$
$691$	15.4346	+	8.91116i	0.587159	+	0.338996i	−0.176814	+	0.984244i	$0.556579\pi$
$692$	−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
$697$			3.19277i			0.120935i
$698$	20.2482	+	35.0708i	0.766404	+	1.32745i
$699$	14.7007	−	8.48746i	0.556032	−	0.321025i
$700$		0			0
$701$	−6.42467	−	23.9772i	−0.242656	−	0.905606i	−0.974547	−	0.224184i	$-0.928028\pi$
$701$	−6.42467	−	23.9772i	−0.242656	−	0.905606i	0.731890	−	0.681422i	$-0.238638\pi$
$702$	15.7205	−	15.7205i	0.593333	−	0.593333i
$703$	3.47103	+	1.37814i	0.130912	+	0.0519776i
$704$		−	16.9564i		−	0.639067i
$705$		0			0
$706$	−30.8455	+	17.8087i	−1.16089	+	0.670239i
$707$	13.4068	+	3.59234i	0.504215	+	0.135104i
$708$	9.85389	−	5.68915i	0.370332	−	0.213811i
$709$	−27.9093	−	27.9093i	−1.04815	−	1.04815i	−0.998780	−	0.0493742i	$-0.984277\pi$
$709$	−27.9093	−	27.9093i	−1.04815	−	1.04815i	−0.0493742	−	0.998780i	$-0.515723\pi$
$710$		0			0
$711$	−7.63643	+	7.63643i	−0.286388	+	0.286388i
$712$	0.00899570	−	0.00241039i	0.000337128	−	9.03332e-5i
$713$	−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
$717$			18.3144i			0.683962i
$718$	−21.4220	+	37.1040i	−0.799461	+	1.38471i
$719$	3.76115	+	2.17150i	0.140267	+	0.0809833i	0.568491	−	0.822689i	$-0.307527\pi$
$719$	3.76115	+	2.17150i	0.140267	+	0.0809833i	−0.428224	+	0.903673i	$0.640861\pi$
$720$		0			0
$721$	−0.0992559	+	0.370428i	−0.00369648	+	0.0137955i
$722$	−18.5657	−	32.1567i	−0.690943	−	1.19675i
$723$	5.38889	−	9.33382i	0.200415	−	0.347129i
$724$	−25.1432	+	43.5493i	−0.934440	+	1.61850i
$725$		0			0
$726$	6.30433	−	6.30433i	0.233976	−	0.233976i
$727$	−10.1029	+	5.83294i	−0.374698	+	0.216332i	−0.675509	−	0.737352i	$-0.736076\pi$
$727$	−10.1029	+	5.83294i	−0.374698	+	0.216332i	0.300811	+	0.953684i	$0.402743\pi$
$728$	−0.429817	+	0.115169i	−0.0159301	+	0.00426845i
$729$			3.32523i			0.123157i
$730$		0			0
$731$	9.35593	+	5.40165i	0.346041	+	0.199787i
$732$		−	19.4466i		−	0.718766i
$733$	2.57743	−	9.61910i	0.0951996	−	0.355290i	−0.901850	−	0.432049i	$-0.857791\pi$
$733$	2.57743	−	9.61910i	0.0951996	−	0.355290i	0.997050	+	0.0767595i	$0.0244574\pi$
$734$	−42.7932	+	42.7932i	−1.57953	+	1.57953i
$735$		0			0
$736$	−1.33529	−	2.31279i	−0.0492193	−	0.0852504i
$737$	−0.210081	+	0.784032i	−0.00773842	+	0.0288802i
$738$	−9.10077	−	5.25433i	−0.335004	−	0.193415i
$739$	−24.0193			−0.883563			−0.441782	−	0.897123i	$-0.645653\pi$
$739$	−24.0193			−0.883563			−0.441782	+	0.897123i	$0.645653\pi$
$740$		0			0
$741$	1.24644			0.0457892
$742$	3.38611	+	1.95497i	0.124308	+	0.0717693i
$743$	−9.04359	+	33.7511i	−0.331777	+	1.23821i	0.575544	+	0.817771i	$0.304790\pi$
$743$	−9.04359	+	33.7511i	−0.331777	+	1.23821i	−0.907321	+	0.420438i	$0.861876\pi$
$744$	−0.112114	−	0.194187i	−0.00411029	−	0.00711922i
$745$		0			0
$746$	36.7638	−	36.7638i	1.34602	−	1.34602i
$747$	−1.34569	+	5.02218i	−0.0492362	+	0.183752i
$748$			6.48213i			0.237010i
$749$	28.1577	+	16.2569i	1.02886	+	0.594013i
$750$		0			0
$751$		−	49.1968i		−	1.79522i	−0.440793	−	0.897609i	$-0.645303\pi$
$751$		−	49.1968i		−	1.79522i	0.440793	−	0.897609i	$-0.354697\pi$
$752$	−32.6900	+	8.75926i	−1.19208	+	0.319417i
$753$	9.73245	−	5.61903i	0.354670	−	0.204769i
$754$	20.4658	−	20.4658i	0.745321	−	0.745321i
$755$		0			0
$756$	12.3001	−	21.3045i	0.447352	−	0.774836i
$757$	1.11912	−	1.93838i	0.0406752	−	0.0704516i	−0.844971	−	0.534812i	$-0.820382\pi$
$757$	1.11912	−	1.93838i	0.0406752	−	0.0704516i	0.885646	+	0.464360i	$0.153716\pi$
$758$	−27.7954	−	48.1430i	−1.00957	−	1.74863i
$759$	−0.134212	+	0.500886i	−0.00487158	+	0.0181810i
$760$		0			0
$761$	−35.8171	−	20.6790i	−1.29837	−	0.749614i	−0.318247	−	0.948008i	$-0.603094\pi$
$761$	−35.8171	−	20.6790i	−1.29837	−	0.749614i	−0.980122	+	0.198394i	$0.936427\pi$
$762$	−9.35037	+	16.1953i	−0.338728	+	0.586695i
$763$		−	39.4506i		−	1.42821i
$764$	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
$768$	11.2765	−	3.02152i	0.406904	−	0.109030i
$769$	0.953352	−	0.953352i	0.0343788	−	0.0343788i	−0.689708	−	0.724087i	$-0.742261\pi$
$769$	0.953352	−	0.953352i	0.0343788	−	0.0343788i	0.724087	+	0.689708i	$0.242261\pi$
$770$		0			0
$771$	2.99885	+	2.99885i	0.108001	+	0.108001i
$772$	32.9537	−	19.0258i	1.18603	−	0.684755i
$773$	29.3068	+	7.85273i	1.05409	+	0.282443i	0.743942	−	0.668244i	$-0.232954\pi$
$773$	29.3068	+	7.85273i	1.05409	+	0.282443i	0.310150	+	0.950688i	$0.399621\pi$
$774$	−30.7941	+	17.7790i	−1.10687	+	0.639052i
$775$		0			0
$776$			0.380360i			0.0136541i
$777$	8.23369	−	11.0644i	0.295382	−	0.396934i
$778$	−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
$782$	0.504098	+	0.873123i	0.0180265	+	0.0312228i
$783$		−	19.9334i		−	0.712360i
$784$	−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
$792$	0.230178	+	0.132893i	0.00817902	+	0.00472216i
$793$	10.1912	+	38.0341i	0.361900	+	1.35063i
$794$	−3.12212	+	0.836570i	−0.110800	+	0.0296888i
$795$		0			0
$796$	−33.8899	−	9.08078i	−1.20120	−	0.321860i
$797$	37.5737	+	21.6932i	1.33093	+	0.768412i	0.985442	−	0.170012i	$-0.0543808\pi$
$797$	37.5737	+	21.6932i	1.33093	+	0.768412i	0.345486	+	0.938424i	$0.387714\pi$
$798$	2.68102	−	0.718377i	0.0949071	−	0.0254303i
$799$	12.1911	−	3.26660i	0.431290	−	0.115564i
$800$		0			0
$801$	0.122443	−	0.456963i	0.00432631	−	0.0161460i
$802$	3.74280	+	13.9683i	0.132163	+	0.493239i
$803$	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
$807$	−10.3857	−	2.78285i	−0.365595	−	0.0979610i
$808$	0.213985			0.00752795
$809$	−31.3117	−	8.38994i	−1.10086	−	0.294975i	−0.337745	−	0.941238i	$-0.609664\pi$
$809$	−31.3117	−	8.38994i	−1.10086	−	0.294975i	−0.763115	+	0.646263i	$0.776331\pi$
$810$		0			0
$811$	−8.19451	−	14.1933i	−0.287748	−	0.498394i	0.685524	−	0.728050i	$-0.259573\pi$
$811$	−8.19451	−	14.1933i	−0.287748	−	0.498394i	−0.973272	+	0.229656i	$0.926240\pi$
$812$	16.0130	−	27.7353i	0.561945	−	0.973318i
$813$	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
$817$	−4.24336	−	1.13701i	−0.148456	−	0.0397788i
$818$	2.12914	−	7.94607i	0.0744438	−	0.277828i
$819$	−5.85034	+	21.8338i	−0.204428	+	0.762934i
$820$		0			0
$821$	1.40290	+	2.42990i	0.0489617	+	0.0848042i	0.889468	−	0.456998i	$-0.151075\pi$
$821$	1.40290	+	2.42990i	0.0489617	+	0.0848042i	−0.840506	+	0.541802i	$0.817742\pi$
$822$	29.8379			1.04071
$823$	0.771469	+	2.87916i	0.0268917	+	0.100361i	0.978067	−	0.208289i	$-0.0667894\pi$
$823$	0.771469	+	2.87916i	0.0268917	+	0.100361i	−0.951176	+	0.308650i	$0.900123\pi$
$824$			0.00591236i			0.000205967i
$825$		0			0
$826$	−25.6518	+	44.4302i	−0.892539	+	1.54592i
$827$	3.15115	+	5.45795i	0.109576	+	0.189792i	0.915599	−	0.402093i	$-0.131717\pi$
$827$	3.15115	+	5.45795i	0.109576	+	0.189792i	−0.806022	+	0.591885i	$0.798384\pi$
$828$	−1.64891			−0.0573037
$829$	−6.63332	−	24.7559i	−0.230385	−	0.859808i	−0.980175	−	0.198132i	$-0.936512\pi$
$829$	−6.63332	−	24.7559i	−0.230385	−	0.859808i	0.749790	−	0.661675i	$-0.230154\pi$
$830$		0			0
$831$	−2.94856	−	11.0042i	−0.102284	−	0.381730i
$832$	19.2538	−	11.1162i	0.667505	−	0.385384i
$833$	4.09104	−	2.36196i	0.141746	−	0.0818372i
$834$	2.03300	+	7.58725i	0.0703969	+	0.262725i
$835$		0			0
$836$	−0.682220	−	2.54608i	−0.0235951	−	0.0880579i
$837$	−25.1001			−0.867586
$838$	−19.9732	−	34.5945i	−0.689961	−	1.19505i
$839$	−13.2861	+	23.0123i	−0.458688	+	0.794472i	−0.998892	−	0.0470627i	$-0.985014\pi$
$839$	−13.2861	+	23.0123i	−0.458688	+	0.794472i	0.540203	+	0.841534i	$0.318347\pi$
$840$		0			0
$841$			3.04970i			0.105162i
$842$	−2.69438	−	10.0556i	−0.0928544	−	0.346537i
$843$	8.47640			0.291943
$844$	−3.45924	−	5.99158i	−0.119072	−	0.206239i
$845$		0			0
$846$	−10.7517	+	40.1258i	−0.369650	+	1.37955i
$847$	−5.17004	+	19.2949i	−0.177645	+	0.662979i
$848$	2.40965	+	0.645663i	0.0827476	+	0.0221721i
$849$	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
$853$	−3.18415	+	5.51510i	−0.109023	+	0.188833i	−0.915375	−	0.402603i	$-0.868106\pi$
$853$	−3.18415	+	5.51510i	−0.109023	+	0.188833i	0.806352	+	0.591436i	$0.201439\pi$
$854$	43.8413	+	75.9354i	1.50022	+	2.59845i
$855$		0			0
$856$	0.484186	+	0.129737i	0.0165491	+	0.00443432i
$857$	56.2325			1.92086			0.960432	−	0.278515i	$-0.0898421\pi$
$857$	56.2325			1.92086			0.960432	+	0.278515i	$0.0898421\pi$
$858$	−8.49750	−	2.27690i	−0.290100	−	0.0777320i
$859$	−27.5622	−	27.5622i	−0.940410	−	0.940410i	0.0579119	−	0.998322i	$-0.481556\pi$
$859$	−27.5622	−	27.5622i	−0.940410	−	0.940410i	−0.998322	+	0.0579119i	$0.981556\pi$
$860$		0			0
$861$	−4.79463			−0.163400
$862$	25.7720	−	25.7720i	0.877799	−	0.877799i
$863$	9.29932	+	34.7055i	0.316552	+	1.18139i	0.922535	+	0.385912i	$0.126113\pi$
$863$	9.29932	+	34.7055i	0.316552	+	1.18139i	−0.605983	+	0.795478i	$0.707220\pi$
$864$	8.07588	−	30.1396i	0.274747	−	1.02537i
$865$		0			0
$866$	−12.9435	+	3.46820i	−0.439839	+	0.117854i
$867$	−10.1299	+	2.71430i	−0.344030	+	0.0921826i
$868$	−34.9243	−	20.1635i	−1.18541	−	0.684395i
$869$	9.09609	+	2.43729i	0.308564	+	0.0826794i
$870$		0			0
$871$	−1.02798	+	0.275448i	−0.0348319	+	0.00933319i
$872$	−0.157417	−	0.587487i	−0.00533080	−	0.0198948i
$873$	16.7329	+	9.66075i	0.566323	+	0.326967i
$874$	−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	−0.820169	−	0.572121i	$-0.806121\pi$
$881$	−21.8096	+	12.5918i	−0.734783	+	0.424227i	0.0853866	+	0.996348i	$0.472787\pi$
$882$			15.5483i			0.523539i
$883$	−24.6204	−	42.6439i	−0.828544	−	1.43508i	−0.899181	−	0.437578i	$-0.855836\pi$
$883$	−24.6204	−	42.6439i	−0.828544	−	1.43508i	0.0706369	−	0.997502i	$-0.477497\pi$
$884$	−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	−0.502368	−	0.864654i	$-0.667538\pi$
$887$	10.7898	−	10.7898i	0.362286	−	0.362286i	0.864654	+	0.502368i	$0.167538\pi$
$888$	0.0784642	−	0.197623i	0.00263309	−	0.00663178i
$889$		−	41.8989i		−	1.40524i
$890$		0			0
$891$	8.82661	−	5.09604i	0.295702	−	0.170724i
$892$	31.6586	+	8.48290i	1.06001	+	0.284028i
$893$	−4.44468	+	2.56614i	−0.148736	+	0.0858725i
$894$	−13.8591	−	13.8591i	−0.463518	−	0.463518i
$895$		0			0
$896$	−0.883280	+	0.883280i	−0.0295083	+	0.0295083i
$897$	−0.656737	+	0.175972i	−0.0219278	+	0.00587554i
$898$	−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
$902$			9.16333i			0.305105i
$903$	−8.11173	+	14.0499i	−0.269942	+	0.467552i
$904$	−0.257658	−	0.148759i	−0.00856957	−	0.00494765i
$905$		0			0
$906$	0.516116	−	1.92617i	0.0171468	−	0.0639927i
$907$	−4.74550	−	8.21945i	−0.157572	−	0.272923i	0.776421	−	0.630215i	$-0.217033\pi$
$907$	−4.74550	−	8.21945i	−0.157572	−	0.272923i	−0.933993	+	0.357292i	$0.883700\pi$
$908$	18.6569	−	32.3147i	0.619152	−	1.07240i
$909$	5.43499	−	9.41367i	0.180267	−	0.312232i
$910$		0			0
$911$	−10.6794	+	10.6794i	−0.353825	+	0.353825i	−0.861531	−	0.507706i	$-0.830494\pi$
$911$	−10.6794	+	10.6794i	−0.353825	+	0.353825i	0.507706	+	0.861531i	$0.330494\pi$
$912$	1.53365	−	0.885452i	0.0507841	−	0.0293202i
$913$	4.37923	−	1.17341i	0.144931	−	0.0388342i
$914$			13.5228i			0.447296i
$915$		0			0
$916$	16.4002	+	9.46867i	0.541879	+	0.312854i
$917$		−	36.3384i		−	1.20000i
$918$	−3.04881	+	11.3783i	−0.100626	+	0.375540i
$919$	−2.76311	+	2.76311i	−0.0911467	+	0.0911467i	−0.751210	−	0.660063i	$-0.770529\pi$
$919$	−2.76311	+	2.76311i	−0.0911467	+	0.0911467i	0.660063	+	0.751210i	$0.270529\pi$
$920$		0			0
$921$	10.3524	+	17.9309i	0.341123	+	0.590842i
$922$	21.4548	−	80.0702i	0.706575	−	2.63697i
$923$	23.5784	+	13.6130i	0.776092	+	0.448077i
$924$	−9.73431			−0.320235
$925$		0			0
$926$	38.7309			1.27278
$927$	0.260098	+	0.150168i	0.00854275	+	0.00493216i
$928$	10.5136	−	39.2373i	0.345126	−	1.28803i
$929$	−19.5842	−	33.9209i	−0.642538	−	1.11291i	−0.984864	−	0.173328i	$-0.944548\pi$
$929$	−19.5842	−	33.9209i	−0.642538	−	1.11291i	0.342326	−	0.939581i	$-0.388785\pi$
$930$		0			0
$931$	−1.35831	+	1.35831i	−0.0445168	+	0.0445168i
$932$	12.1818	−	45.4633i	0.399030	−	1.48920i
$933$			4.62752i			0.151498i
$934$	−34.0711	−	19.6710i	−1.11484	−	0.643654i
$935$		0			0
$936$			0.348487i			0.0113906i
$937$	6.09129	−	1.63216i	0.198994	−	0.0533202i	−0.157945	−	0.987448i	$-0.550487\pi$
$937$	6.09129	−	1.63216i	0.198994	−	0.0533202i	0.356939	+	0.934128i	$0.383820\pi$
$938$	−2.05238	+	1.18494i	−0.0670126	+	0.0386898i
$939$	1.26170	−	1.26170i	0.0411741	−	0.0411741i
$940$		0			0
$941$	−22.4635	+	38.9080i	−0.732290	+	1.26836i	0.223612	+	0.974678i	$0.428215\pi$
$941$	−22.4635	+	38.9080i	−0.732290	+	1.26836i	−0.955902	+	0.293686i	$0.905118\pi$
$942$	−5.15677	+	8.93180i	−0.168017	+	0.291014i
$943$	0.354098	+	0.613316i	0.0115310	+	0.0199723i
$944$	−8.47193	+	31.6177i	−0.275738	+	1.02907i
$945$		0			0
$946$	26.8517	+	15.5029i	0.873026	+	0.504042i
$947$	16.9042	−	29.2790i	0.549313	−	0.951439i	−0.449008	−	0.893528i	$-0.648223\pi$
$947$	16.9042	−	29.2790i	0.549313	−	0.951439i	0.998322	−	0.0579110i	$-0.0184440\pi$
$948$		−	6.09787i		−	0.198050i
$949$	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
$953$	−30.1099	+	8.06792i	−0.975354	+	0.261345i	−0.711087	−	0.703104i	$-0.751797\pi$
$953$	−30.1099	+	8.06792i	−0.975354	+	0.261345i	−0.264267	+	0.964449i	$0.585130\pi$
$954$	2.16522	−	2.16522i	0.0701017	−	0.0701017i
$955$		0			0
$956$	35.9075	+	35.9075i	1.16133	+	1.16133i
$957$	−6.83087	+	3.94381i	−0.220811	+	0.127485i
$958$	73.0700	+	19.5791i	2.36079	+	0.632570i
$959$	−57.8951	+	33.4258i	−1.86953	+	1.07937i
$960$		0			0
$961$			10.1464i			0.327302i
$962$	4.00524	−	34.3271i	0.129134	−	1.10675i
$963$	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
$967$	−3.75420	−	6.50246i	−0.120727	−	0.209105i	0.799328	−	0.600895i	$-0.205189\pi$
$967$	−3.75420	−	6.50246i	−0.120727	−	0.209105i	−0.920054	+	0.391790i	$0.871856\pi$
$968$			0.307963i			0.00989831i
$969$	−0.571944	+	0.330212i	−0.0183735	+	0.0106079i
$970$		0			0
$971$	10.7517	−	18.6225i	0.345038	−	0.597623i	−0.640323	−	0.768106i	$-0.721199\pi$
$971$	10.7517	−	18.6225i	0.345038	−	0.597623i	0.985361	+	0.170483i	$0.0545328\pi$
$972$	−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
$977$	39.1789	+	22.6200i	1.25344	+	0.723677i	0.971792	−	0.235840i	$-0.0757841\pi$
$977$	39.1789	+	22.6200i	1.25344	+	0.723677i	0.281653	+	0.959516i	$0.409117\pi$
$978$	1.87161	+	6.98493i	0.0598474	+	0.223354i
$979$	−0.398462	+	0.106768i	−0.0127349	+	0.00341230i
$980$		0			0
$981$	−29.8431	−	7.99643i	−0.952817	−	0.255306i
$982$	56.9384	+	32.8734i	1.81698	+	1.04903i
$983$	44.8074	−	12.0061i	1.42913	−	0.382936i	0.540420	−	0.841396i	$-0.318265\pi$
$983$	44.8074	−	12.0061i	1.42913	−	0.382936i	0.888715	+	0.458460i	$0.151599\pi$
$984$	−0.0714002	+	0.0191316i	−0.00227616	+	0.000609894i
$985$		0			0
$986$	−3.96910	+	14.8129i	−0.126402	+	0.471738i
$987$	4.90550	+	18.3076i	0.156144	+	0.582736i
$988$	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	0.781698	−	0.623657i	$-0.214354\pi$
$991$	4.97517	+	4.97517i	0.158042	+	0.158042i	−0.623657	+	0.781698i	$0.714354\pi$
$992$	−49.4076	−	13.2387i	−1.56869	−	0.420330i
$993$	11.4952			0.364788
$994$	58.5615	+	15.6915i	1.85746	+	0.497704i
$995$		0			0
$996$	−1.46788	−	2.54244i	−0.0465116	−	0.0805604i
$997$	20.3564	−	35.2584i	0.644694	−	1.11664i	−0.339678	−	0.940542i	$-0.610318\pi$
$997$	20.3564	−	35.2584i	0.644694	−	1.11664i	0.984372	−	0.176101i	$-0.0563487\pi$
$998$	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.y.c.532.4	yes	96
5.2	odd	4		925.2.t.c.643.21	yes	96
5.3	odd	4		925.2.t.c.643.4	yes	96
5.4	even	2	inner	925.2.y.c.532.21	yes	96
37.8	odd	12		925.2.t.c.82.4	✓	96
185.8	even	12	inner	925.2.y.c.193.4	yes	96
185.82	even	12	inner	925.2.y.c.193.21	yes	96
185.119	odd	12		925.2.t.c.82.21	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.t.c.82.4	✓	96	37.8	odd	12
925.2.t.c.82.21	yes	96	185.119	odd	12
925.2.t.c.643.4	yes	96	5.3	odd	4
925.2.t.c.643.21	yes	96	5.2	odd	4
925.2.y.c.193.4	yes	96	185.8	even	12	inner
925.2.y.c.193.21	yes	96	185.82	even	12	inner
925.2.y.c.532.4	yes	96	1.1	even	1	trivial
925.2.y.c.532.21	yes	96	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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