LMFDB - Embedded newform 925.2.y.b.193.12

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 = [68] 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:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.12
Character	$\chi$	$=$	925.193
Dual form			925.2.y.b.532.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25283 - 0.723320i) q^{2} +(0.212077 + 0.791482i) q^{3} +(0.0463849 - 0.0803411i) q^{4} +(0.838191 + 0.838191i) q^{6} +(-0.425785 - 1.58905i) q^{7} +2.75908i q^{8} +(2.01661 - 1.16429i) q^{9} -4.76900i q^{11} +(0.0734257 + 0.0196744i) q^{12} +(5.02850 + 2.90320i) q^{13} +(-1.68283 - 1.68283i) q^{14} +(2.08847 + 3.61733i) q^{16} +(0.725557 + 1.25670i) q^{17} +(1.68431 - 2.91731i) q^{18} +(-0.563197 - 2.10188i) q^{19} +(1.16741 - 0.674003i) q^{21} +(-3.44951 - 5.97473i) q^{22} +4.09430i q^{23} +(-2.18376 + 0.585137i) q^{24} +8.39979 q^{26} +(3.08741 + 3.08741i) q^{27} +(-0.147416 - 0.0395000i) q^{28} +(2.95018 + 2.95018i) q^{29} +(-1.46743 + 1.46743i) q^{31} +(0.454116 + 0.262184i) q^{32} +(3.77458 - 1.01139i) q^{33} +(1.81799 + 1.04962i) q^{34} -0.216022i q^{36} +(6.02617 - 0.827803i) q^{37} +(-2.22592 - 2.22592i) q^{38} +(-1.23141 + 4.59567i) q^{39} +(0.369301 + 0.213216i) q^{41} +(0.975040 - 1.68882i) q^{42} -7.53912i q^{43} +(-0.383146 - 0.221210i) q^{44} +(2.96149 + 5.12945i) q^{46} +(5.55465 - 5.55465i) q^{47} +(-2.42014 + 2.42014i) q^{48} +(3.71838 - 2.14681i) q^{49} +(-0.840783 + 0.840783i) q^{51} +(0.466493 - 0.269330i) q^{52} +(-2.83749 + 10.5896i) q^{53} +(6.10117 + 1.63480i) q^{54} +(4.38432 - 1.17477i) q^{56} +(1.54416 - 0.891520i) q^{57} +(5.82999 + 1.56214i) q^{58} +(-8.06779 - 2.16176i) q^{59} +(-1.52382 - 5.68696i) q^{61} +(-0.777013 + 2.89985i) q^{62} +(-2.70876 - 2.70876i) q^{63} -7.59529 q^{64} +(3.99733 - 3.99733i) q^{66} +(-8.99317 + 2.40971i) q^{67} +0.134620 q^{68} +(-3.24056 + 0.868307i) q^{69} +(-6.20532 + 10.7479i) q^{71} +(3.21236 + 5.56398i) q^{72} +(-2.06563 + 2.06563i) q^{73} +(6.95099 - 5.39595i) q^{74} +(-0.194991 - 0.0522477i) q^{76} +(-7.57818 + 2.03057i) q^{77} +(1.78140 + 6.64828i) q^{78} +(-1.30294 - 4.86264i) q^{79} +(1.70401 - 2.95143i) q^{81} +0.616894 q^{82} +(1.04562 - 3.90229i) q^{83} -0.125054i q^{84} +(-5.45320 - 9.44522i) q^{86} +(-1.70935 + 2.96068i) q^{87} +13.1580 q^{88} +(3.97708 - 14.8427i) q^{89} +(2.47228 - 9.22669i) q^{91} +(0.328940 + 0.189914i) q^{92} +(-1.47265 - 0.850234i) q^{93} +(2.94123 - 10.9768i) q^{94} +(-0.111207 + 0.415028i) q^{96} -17.9332 q^{97} +(3.10566 - 5.37917i) q^{98} +(-5.55249 - 9.61720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

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

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.25283	−	0.723320i	0.885883	−	0.511465i	0.0132894	−	0.999912i	$-0.495770\pi$
$2$	1.25283	−	0.723320i	0.885883	−	0.511465i	0.872594	+	0.488447i	$0.162436\pi$
$3$	0.212077	+	0.791482i	0.122443	+	0.456962i	0.999736	−	0.0229929i	$-0.00731951\pi$
$3$	0.212077	+	0.791482i	0.122443	+	0.456962i	−0.877293	+	0.479955i	$0.840653\pi$
$4$	0.0463849	−	0.0803411i	0.0231925	−	0.0401705i
$5$		0			0
$5$		0			0
$6$	0.838191	+	0.838191i	0.342190	+	0.342190i
$7$	−0.425785	−	1.58905i	−0.160932	−	0.600605i	−0.998524	−	0.0543096i	$-0.982704\pi$
$7$	−0.425785	−	1.58905i	−0.160932	−	0.600605i	0.837592	−	0.546296i	$-0.183962\pi$
$8$			2.75908i			0.975481i
$9$	2.01661	−	1.16429i	0.672203	−	0.388097i
$10$		0			0
$11$		−	4.76900i		−	1.43791i	−0.695059	−	0.718953i	$-0.744622\pi$
$11$		−	4.76900i		−	1.43791i	0.695059	−	0.718953i	$-0.255378\pi$
$12$	0.0734257	+	0.0196744i	0.0211962	+	0.00567950i
$13$	5.02850	+	2.90320i	1.39465	+	0.805204i	0.993826	−	0.110949i	$-0.0353891\pi$
$13$	5.02850	+	2.90320i	1.39465	+	0.805204i	0.400828	+	0.916153i	$0.368722\pi$
$14$	−1.68283	−	1.68283i	−0.449755	−	0.449755i
$15$		0			0
$16$	2.08847	+	3.61733i	0.522117	+	0.904333i
$17$	0.725557	+	1.25670i	0.175973	+	0.304795i	0.940498	−	0.339800i	$-0.110359\pi$
$17$	0.725557	+	1.25670i	0.175973	+	0.304795i	−0.764524	+	0.644595i	$0.777026\pi$
$18$	1.68431	−	2.91731i	0.396995	−	0.687616i
$19$	−0.563197	−	2.10188i	−0.129206	−	0.482204i	0.870748	−	0.491729i	$-0.163635\pi$
$19$	−0.563197	−	2.10188i	−0.129206	−	0.482204i	−0.999955	+	0.00952470i	$0.996968\pi$
$20$		0			0
$21$	1.16741	−	0.674003i	0.254749	−	0.147079i
$22$	−3.44951	−	5.97473i	−0.735438	−	1.27382i
$23$			4.09430i			0.853720i	0.904318	+	0.426860i	$0.140380\pi$
$23$			4.09430i			0.853720i	−0.904318	+	0.426860i	$0.859620\pi$
$24$	−2.18376	+	0.585137i	−0.445758	+	0.119441i
$25$		0			0
$26$	8.39979			1.64733
$27$	3.08741	+	3.08741i	0.594172	+	0.594172i
$28$	−0.147416	−	0.0395000i	−0.0278590	−	0.00746480i
$29$	2.95018	+	2.95018i	0.547834	+	0.547834i	0.925814	−	0.377980i	$-0.123381\pi$
$29$	2.95018	+	2.95018i	0.547834	+	0.547834i	−0.377980	+	0.925814i	$0.623381\pi$
$30$		0			0
$31$	−1.46743	+	1.46743i	−0.263557	+	0.263557i	−0.826498	−	0.562940i	$-0.809670\pi$
$31$	−1.46743	+	1.46743i	−0.263557	+	0.263557i	0.562940	+	0.826498i	$0.309670\pi$
$32$	0.454116	+	0.262184i	0.0802772	+	0.0463481i
$33$	3.77458	−	1.01139i	0.657069	−	0.176061i
$34$	1.81799	+	1.04962i	0.311784	+	0.180008i
$35$		0			0
$36$		−	0.216022i		−	0.0360037i
$37$	6.02617	−	0.827803i	0.990696	−	0.136090i
$37$	6.02617	−	0.827803i	0.990696	−	0.136090i
$38$	−2.22592	−	2.22592i	−0.361092	−	0.361092i
$39$	−1.23141	+	4.59567i	−0.197183	+	0.735896i
$40$		0			0
$41$	0.369301	+	0.213216i	0.0576751	+	0.0332988i	0.528560	−	0.848896i	$-0.322732\pi$
$41$	0.369301	+	0.213216i	0.0576751	+	0.0332988i	−0.470885	+	0.882195i	$0.656065\pi$
$42$	0.975040	−	1.68882i	0.150452	−	0.260590i
$43$		−	7.53912i		−	1.14971i	−0.818257	−	0.574853i	$-0.805059\pi$
$43$		−	7.53912i		−	1.14971i	0.818257	−	0.574853i	$-0.194941\pi$
$44$	−0.383146	−	0.221210i	−0.0577615	−	0.0333486i
$45$		0			0
$46$	2.96149	+	5.12945i	0.436648	+	0.756296i
$47$	5.55465	−	5.55465i	0.810228	−	0.810228i	−0.174440	−	0.984668i	$-0.555811\pi$
$47$	5.55465	−	5.55465i	0.810228	−	0.810228i	0.984668	+	0.174440i	$0.0558114\pi$
$48$	−2.42014	+	2.42014i	−0.349317	+	0.349317i
$49$	3.71838	−	2.14681i	0.531198	−	0.306687i
$50$		0			0
$51$	−0.840783	+	0.840783i	−0.117733	+	0.117733i
$52$	0.466493	−	0.269330i	0.0646909	−	0.0373493i
$53$	−2.83749	+	10.5896i	−0.389759	+	1.45460i	0.440768	+	0.897621i	$0.354706\pi$
$53$	−2.83749	+	10.5896i	−0.389759	+	1.45460i	−0.830527	+	0.556978i	$0.811961\pi$
$54$	6.10117	+	1.63480i	0.830264	+	0.222469i
$55$		0			0
$56$	4.38432	−	1.17477i	0.585879	−	0.156986i
$57$	1.54416	−	0.891520i	0.204529	−	0.118085i
$58$	5.82999	+	1.56214i	0.765515	+	0.205119i
$59$	−8.06779	−	2.16176i	−1.05034	−	0.281437i	−0.307946	−	0.951404i	$-0.599642\pi$
$59$	−8.06779	−	2.16176i	−1.05034	−	0.281437i	−0.742391	+	0.669967i	$0.766308\pi$
$60$		0			0
$61$	−1.52382	−	5.68696i	−0.195105	−	0.728140i	−0.992240	−	0.124339i	$-0.960319\pi$
$61$	−1.52382	−	5.68696i	−0.195105	−	0.728140i	0.797135	−	0.603801i	$-0.206348\pi$
$62$	−0.777013	+	2.89985i	−0.0986807	+	0.368281i
$63$	−2.70876	−	2.70876i	−0.341272	−	0.341272i
$64$	−7.59529			−0.949412
$65$		0			0
$66$	3.99733	−	3.99733i	0.492037	−	0.492037i
$67$	−8.99317	+	2.40971i	−1.09869	+	0.294393i	−0.762231	−	0.647305i	$-0.775896\pi$
$67$	−8.99317	+	2.40971i	−1.09869	+	0.294393i	−0.336460	+	0.941698i	$0.609230\pi$
$68$	0.134620			0.0163250
$69$	−3.24056	+	0.868307i	−0.390118	+	0.104532i
$70$		0			0
$71$	−6.20532	+	10.7479i	−0.736436	+	1.27554i	0.217654	+	0.976026i	$0.430159\pi$
$71$	−6.20532	+	10.7479i	−0.736436	+	1.27554i	−0.954090	+	0.299519i	$0.903174\pi$
$72$	3.21236	+	5.56398i	0.378581	+	0.655721i
$73$	−2.06563	+	2.06563i	−0.241763	+	0.241763i	−0.817579	−	0.575816i	$-0.804684\pi$
$73$	−2.06563	+	2.06563i	−0.241763	+	0.241763i	0.575816	+	0.817579i	$0.304684\pi$
$74$	6.95099	−	5.39595i	0.808036	−	0.627266i
$75$		0			0
$76$	−0.194991	−	0.0522477i	−0.0223670	−	0.00599322i
$77$	−7.57818	+	2.03057i	−0.863614	+	0.231405i
$78$	1.78140	+	6.64828i	0.201704	+	0.752770i
$79$	−1.30294	−	4.86264i	−0.146592	−	0.547089i	−0.999679	−	0.0253210i	$-0.991939\pi$
$79$	−1.30294	−	4.86264i	−0.146592	−	0.547089i	0.853087	−	0.521768i	$-0.174727\pi$
$80$		0			0
$81$	1.70401	−	2.95143i	0.189334	−	0.327937i
$82$	0.616894			0.0681246
$83$	1.04562	−	3.90229i	0.114771	−	0.428332i	−0.884498	−	0.466543i	$-0.845499\pi$
$83$	1.04562	−	3.90229i	0.114771	−	0.428332i	0.999270	+	0.0382109i	$0.0121659\pi$
$84$		−	0.125054i		−	0.0136445i
$85$		0			0
$86$	−5.45320	−	9.44522i	−0.588034	−	1.01850i
$87$	−1.70935	+	2.96068i	−0.183261	+	0.317418i
$88$	13.1580			1.40265
$89$	3.97708	−	14.8427i	0.421569	−	1.57332i	−0.349733	−	0.936849i	$-0.613728\pi$
$89$	3.97708	−	14.8427i	0.421569	−	1.57332i	0.771302	−	0.636469i	$-0.219606\pi$
$90$		0			0
$91$	2.47228	−	9.22669i	0.259166	−	0.967219i
$92$	0.328940	+	0.189914i	0.0342944	+	0.0197999i
$93$	−1.47265	−	0.850234i	−0.152707	−	0.0881652i
$94$	2.94123	−	10.9768i	0.303364	−	1.13217i
$95$		0			0
$96$	−0.111207	+	0.415028i	−0.0113500	+	0.0423587i
$97$	−17.9332			−1.82084			−0.910418	−	0.413689i	$-0.864240\pi$
$97$	−17.9332			−1.82084			−0.910418	+	0.413689i	$0.864240\pi$
$98$	3.10566	−	5.37917i	0.313719	−	0.543378i
$99$	−5.55249	−	9.61720i	−0.558046	−	0.966565i
$100$		0			0
$101$			6.87214i			0.683803i	0.939736	+	0.341902i	$0.111071\pi$
$101$			6.87214i			0.683803i	−0.939736	+	0.341902i	$0.888929\pi$
$102$	−0.445201	+	1.66151i	−0.0440814	+	0.164514i
$103$	−12.6979			−1.25116			−0.625581	−	0.780159i	$-0.715138\pi$
$103$	−12.6979			−1.25116			−0.625581	+	0.780159i	$0.715138\pi$
$104$	−8.01017	+	13.8740i	−0.785461	+	1.36046i
$105$		0			0
$106$	4.10482	+	15.3194i	0.398696	+	1.48795i
$107$	2.37610	+	8.86771i	0.229706	+	0.857274i	0.980464	+	0.196697i	$0.0630215\pi$
$107$	2.37610	+	8.86771i	0.229706	+	0.857274i	−0.750759	+	0.660577i	$0.770312\pi$
$108$	0.391255	−	0.104836i	0.0376485	−	0.0100879i
$109$	7.90182	+	2.11729i	0.756857	+	0.202799i	0.616557	−	0.787310i	$-0.288527\pi$
$109$	7.90182	+	2.11729i	0.756857	+	0.202799i	0.140299	+	0.990109i	$0.455193\pi$
$110$		0			0
$111$	1.93320	+	4.59405i	0.183492	+	0.436048i
$112$	4.85889	−	4.85889i	0.459122	−	0.459122i
$113$	−3.70539	−	6.41792i	−0.348573	−	0.603747i	0.637423	−	0.770514i	$-0.280000\pi$
$113$	−3.70539	−	6.41792i	−0.348573	−	0.603747i	−0.985996	+	0.166767i	$0.946667\pi$
$114$	1.28971	−	2.23384i	0.120792	−	0.209219i
$115$		0			0
$116$	0.373864	−	0.100177i	0.0347124	−	0.00930117i
$117$	13.5207			1.24999
$118$	−11.6712	+	3.12729i	−1.07442	+	0.287890i
$119$	1.68803	−	1.68803i	0.154742	−	0.154742i
$120$		0			0
$121$	−11.7433			−1.06757
$122$	−6.02257	−	6.02257i	−0.545258	−	0.545258i
$123$	−0.0904365	+	0.337514i	−0.00815438	+	0.0304326i
$124$	0.0498281	+	0.185961i	0.00447470	+	0.0166998i
$125$		0			0
$126$	−5.35291	−	1.43431i	−0.476875	−	0.127778i
$127$	−0.527354	−	0.141304i	−0.0467951	−	0.0125387i	0.235346	−	0.971912i	$-0.424378\pi$
$127$	−0.527354	−	0.141304i	−0.0467951	−	0.0125387i	−0.282141	+	0.959373i	$0.591044\pi$
$128$	−10.4238	+	6.01820i	−0.921345	+	0.531939i
$129$	5.96708	−	1.59887i	0.525372	−	0.140773i
$130$		0			0
$131$	−15.3752	−	4.11977i	−1.34334	−	0.359946i	−0.485666	−	0.874144i	$-0.661423\pi$
$131$	−15.3752	−	4.11977i	−1.34334	−	0.359946i	−0.857671	+	0.514198i	$0.828090\pi$
$132$	0.0938269	−	0.350167i	0.00816658	−	0.0304781i
$133$	−3.10019	+	1.78990i	−0.268821	+	0.155204i
$134$	−9.52390	+	9.52390i	−0.822740	+	0.822740i
$135$		0			0
$136$	−3.46733	+	2.00187i	−0.297322	+	0.171659i
$137$	1.35878	−	1.35878i	0.116088	−	0.116088i	−0.646676	−	0.762765i	$-0.723841\pi$
$137$	1.35878	−	1.35878i	0.116088	−	0.116088i	0.762765	+	0.646676i	$0.223841\pi$
$138$	−3.43180	+	3.43180i	−0.292135	+	0.292135i
$139$	8.69989	+	15.0687i	0.737915	+	1.27811i	0.953432	+	0.301607i	$0.0975230\pi$
$139$	8.69989	+	15.0687i	0.737915	+	1.27811i	−0.215517	+	0.976500i	$0.569144\pi$
$140$		0			0
$141$	5.57442	+	3.21839i	0.469450	+	0.271037i
$142$			17.9537i			1.50664i
$143$	13.8454	−	23.9809i	1.15781	−	2.00538i
$144$	8.42324	+	4.86316i	0.701937	+	0.405263i
$145$		0			0
$146$	−1.09376	+	4.08198i	−0.0905206	+	0.337827i
$147$	2.48775	+	2.48775i	0.205186	+	0.205186i
$148$	0.213017	−	0.522547i	0.0175099	−	0.0429531i
$149$		−	8.07457i		−	0.661495i	−0.943719	−	0.330747i	$-0.892699\pi$
$149$		−	8.07457i		−	0.661495i	0.943719	−	0.330747i	$-0.107301\pi$
$150$		0			0
$151$	−18.1193	−	10.4612i	−1.47453	−	0.851320i	−0.474942	−	0.880017i	$-0.657531\pi$
$151$	−18.1193	−	10.4612i	−1.47453	−	0.851320i	−0.999588	+	0.0286973i	$0.990864\pi$
$152$	5.79924	−	1.55390i	0.470381	−	0.126038i
$153$	2.92633	+	1.68952i	0.236580	+	0.136589i
$154$	−8.02540	+	8.02540i	−0.646706	+	0.646706i
$155$		0			0
$156$	0.312102	+	0.312102i	0.0249882	+	0.0249882i
$157$	−13.3722	−	3.58307i	−1.06722	−	0.285960i	−0.317868	−	0.948135i	$-0.602967\pi$
$157$	−13.3722	−	3.58307i	−1.06722	−	0.285960i	−0.749349	+	0.662175i	$0.769634\pi$
$158$	−5.14960	−	5.14960i	−0.409680	−	0.409680i
$159$	−8.98328			−0.712420
$160$		0			0
$161$	6.50605	−	1.74329i	0.512749	−	0.137391i
$162$		−	4.93018i		−	0.387351i
$163$	−3.13396	−	5.42818i	−0.245471	−	0.425168i	0.716793	−	0.697286i	$-0.245609\pi$
$163$	−3.13396	−	5.42818i	−0.245471	−	0.425168i	−0.962264	+	0.272118i	$0.912276\pi$
$164$	0.0342600	−	0.0197800i	0.00267526	−	0.00154456i
$165$		0			0
$166$	−1.51263	−	5.64522i	−0.117403	−	0.438154i
$167$	1.56860	−	2.71690i	0.121382	−	0.210240i	−0.798931	−	0.601423i	$-0.794601\pi$
$167$	1.56860	−	2.71690i	0.121382	−	0.210240i	0.920313	+	0.391183i	$0.127934\pi$
$168$	1.85963	+	3.22097i	0.143473	+	0.248503i
$169$	10.3572	+	17.9392i	0.796707	+	1.37994i
$170$		0			0
$171$	−3.58294	−	3.58294i	−0.273994	−	0.273994i
$172$	−0.605701	−	0.349702i	−0.0461843	−	0.0266645i
$173$	−4.95158	−	1.32677i	−0.376461	−	0.100873i	0.0656265	−	0.997844i	$-0.479095\pi$
$173$	−4.95158	−	1.32677i	−0.376461	−	0.100873i	−0.442088	+	0.896972i	$0.645762\pi$
$174$			4.94563i			0.374927i
$175$		0			0
$176$	17.2510	−	9.95989i	1.30035	−	0.750755i
$177$		−	6.84398i		−	0.514425i
$178$	−5.75340	−	21.4720i	−0.431236	−	1.60939i
$179$	2.46194	+	2.46194i	0.184014	+	0.184014i	0.793102	−	0.609088i	$-0.208464\pi$
$179$	2.46194	+	2.46194i	0.184014	+	0.184014i	−0.609088	+	0.793102i	$0.708464\pi$
$180$		0			0
$181$	5.87198	−	10.1706i	0.436461	−	0.755972i	−0.560953	−	0.827848i	$-0.689565\pi$
$181$	5.87198	−	10.1706i	0.436461	−	0.755972i	0.997414	+	0.0718755i	$0.0228984\pi$
$182$	−3.57651	−	13.3477i	−0.265108	−	0.989397i
$183$	4.17796	−	2.41215i	0.308844	−	0.178311i
$184$	−11.2965			−0.832788
$185$		0			0
$186$	−2.45997			−0.180374
$187$	5.99320	−	3.46018i	0.438266	−	0.253033i
$188$	−0.188614	−	0.703918i	−0.0137561	−	0.0513385i
$189$	3.59148	−	6.22062i	0.261242	−	0.452484i
$190$		0			0
$191$	15.0489	+	15.0489i	1.08890	+	1.08890i	0.995642	+	0.0932582i	$0.0297282\pi$
$191$	15.0489	+	15.0489i	1.08890	+	1.08890i	0.0932582	+	0.995642i	$0.470272\pi$
$192$	−1.61079	−	6.01154i	−0.116249	−	0.433846i
$193$			12.5994i			0.906924i	0.891276	+	0.453462i	$0.149811\pi$
$193$			12.5994i			0.906924i	−0.891276	+	0.453462i	$0.850189\pi$
$194$	−22.4672	+	12.9714i	−1.61305	+	0.931294i
$195$		0			0
$196$		−	0.398319i		−	0.0284513i
$197$	−5.42726	−	1.45423i	−0.386676	−	0.103610i	0.0602434	−	0.998184i	$-0.480812\pi$
$197$	−5.42726	−	1.45423i	−0.386676	−	0.103610i	−0.446920	+	0.894574i	$0.647479\pi$
$198$	−13.9126	−	8.03246i	−0.988728	−	0.570842i
$199$	−11.5832	−	11.5832i	−0.821108	−	0.821108i	0.165159	−	0.986267i	$-0.447186\pi$
$199$	−11.5832	−	11.5832i	−0.821108	−	0.821108i	−0.986267	+	0.165159i	$0.947186\pi$
$200$		0			0
$201$	−3.81449	−	6.60689i	−0.269053	−	0.466014i
$202$	4.97076	+	8.60961i	0.349741	+	0.605770i
$203$	3.43184	−	5.94413i	0.240868	−	0.417196i
$204$	0.0285497	+	0.106549i	0.00199888	+	0.00745992i
$205$		0			0
$206$	−15.9083	+	9.18465i	−1.10838	+	0.639925i
$207$	4.76695	+	8.25660i	0.331326	+	0.573873i
$208$			24.2530i			1.68164i
$209$	−10.0238	+	2.68588i	−0.693364	+	0.185786i
$210$		0			0
$211$	17.3906			1.19722			0.598609	−	0.801042i	$-0.295720\pi$
$211$	17.3906			1.19722			0.598609	+	0.801042i	$0.295720\pi$
$212$	0.719167	+	0.719167i	0.0493926	+	0.0493926i
$213$	−9.82280	−	2.63201i	−0.673047	−	0.180343i
$214$	9.39103	+	9.39103i	0.641958	+	0.641958i
$215$		0			0
$216$	−8.51839	+	8.51839i	−0.579603	+	0.579603i
$217$	2.95662	+	1.70701i	0.200709	+	0.115879i
$218$	11.4311	−	3.06295i	0.774211	−	0.207449i
$219$	−2.07298	−	1.19683i	−0.140079	−	0.0808746i
$220$		0			0
$221$			8.42576i			0.566778i
$222$	5.74494	+	4.35723i	0.385575	+	0.292438i
$223$	7.72909	+	7.72909i	0.517578	+	0.517578i	0.916838	−	0.399260i	$-0.130733\pi$
$223$	7.72909	+	7.72909i	0.517578	+	0.517578i	−0.399260	+	0.916838i	$0.630733\pi$
$224$	0.223268	−	0.833249i	0.0149177	−	0.0556738i
$225$		0			0
$226$	−9.28442	−	5.36036i	−0.617591	−	0.356566i
$227$	3.31049	−	5.73394i	0.219725	−	0.380575i	−0.734999	−	0.678069i	$-0.762817\pi$
$227$	3.31049	−	5.73394i	0.219725	−	0.380575i	0.954724	+	0.297493i	$0.0961506\pi$
$228$		−	0.165412i		−	0.0109547i
$229$	9.79053	+	5.65257i	0.646977	+	0.373532i	0.787297	−	0.616574i	$-0.211480\pi$
$229$	9.79053	+	5.65257i	0.646977	+	0.373532i	−0.140320	+	0.990106i	$0.544813\pi$
$230$		0			0
$231$	−3.21432	−	5.56736i	−0.211486	−	0.366305i
$232$	−8.13977	+	8.13977i	−0.534402	+	0.534402i
$233$	−10.6730	+	10.6730i	−0.699211	+	0.699211i	−0.964240	−	0.265029i	$-0.914618\pi$
$233$	−10.6730	+	10.6730i	−0.699211	+	0.699211i	0.265029	+	0.964240i	$0.414618\pi$
$234$	16.9391	−	9.77979i	1.10734	−	0.639325i
$235$		0			0
$236$	−0.547902	+	0.547902i	−0.0356654	+	0.0356654i
$237$	3.57237	−	2.06251i	0.232050	−	0.133974i
$238$	0.893825	−	3.33580i	0.0579381	−	0.216228i
$239$	17.2821	+	4.63073i	1.11789	+	0.299537i	0.770028	−	0.638010i	$-0.220242\pi$
$239$	17.2821	+	4.63073i	1.11789	+	0.299537i	0.347859	+	0.937547i	$0.386909\pi$
$240$		0			0
$241$	−27.1013	+	7.26176i	−1.74575	+	0.467771i	−0.983710	−	0.179764i	$-0.942467\pi$
$241$	−27.1013	+	7.26176i	−1.74575	+	0.467771i	−0.762036	+	0.647535i	$0.775800\pi$
$242$	−14.7124	+	8.49418i	−0.945746	+	0.546027i
$243$	15.3498	+	4.11297i	0.984691	+	0.263847i
$244$	−0.527578	−	0.141364i	−0.0337747	−	0.00904991i
$245$		0			0
$246$	0.130829	+	0.488261i	0.00834136	+	0.0311304i
$247$	3.27015	−	12.2044i	0.208075	−	0.776545i
$248$	−4.04874	−	4.04874i	−0.257095	−	0.257095i
$249$	3.31035			0.209785
$250$		0			0
$251$	−1.94654	+	1.94654i	−0.122864	+	0.122864i	−0.765865	−	0.643001i	$-0.777689\pi$
$251$	−1.94654	+	1.94654i	−0.122864	+	0.122864i	0.643001	+	0.765865i	$0.277689\pi$
$252$	−0.343270	+	0.0919790i	−0.0216240	+	0.00579413i
$253$	19.5257			1.22757
$254$	−0.762893	+	0.204416i	−0.0478681	+	0.0128262i
$255$		0			0
$256$	−1.11088	+	1.92410i	−0.0694300	+	0.120256i
$257$	3.13247	+	5.42559i	0.195398	+	0.338439i	0.947031	−	0.321142i	$-0.104067\pi$
$257$	3.13247	+	5.42559i	0.195398	+	0.338439i	−0.751633	+	0.659582i	$0.770734\pi$
$258$	6.31923	−	6.31923i	0.393418	−	0.393418i
$259$	−3.88128	−	9.22343i	−0.241171	−	0.573116i
$260$		0			0
$261$	9.38422	+	2.51449i	0.580869	+	0.155643i
$262$	−22.2424	+	5.95983i	−1.37414	+	0.368200i
$263$	3.92018	+	14.6303i	0.241728	+	0.902143i	0.975000	+	0.222206i	$0.0713259\pi$
$263$	3.92018	+	14.6303i	0.241728	+	0.902143i	−0.733271	+	0.679936i	$0.762007\pi$
$264$	2.79052	+	10.4143i	0.171744	+	0.640959i
$265$		0			0
$266$	−2.58934	+	4.48487i	−0.158763	+	0.274985i
$267$	12.5911			0.770566
$268$	−0.223549	+	0.834296i	−0.0136554	+	0.0509627i
$269$			20.5296i			1.25171i	0.779938	+	0.625856i	$0.215250\pi$
$269$			20.5296i			1.25171i	−0.779938	+	0.625856i	$0.784750\pi$
$270$		0			0
$271$	−6.43197	−	11.1405i	−0.390714	−	0.676737i	0.601830	−	0.798624i	$-0.294439\pi$
$271$	−6.43197	−	11.1405i	−0.390714	−	0.676737i	−0.992544	+	0.121888i	$0.961105\pi$
$272$	−3.03060	+	5.24916i	−0.183757	+	0.318277i
$273$	7.82707			0.473716
$274$	0.719484	−	2.68515i	0.0434656	−	0.162216i
$275$		0			0
$276$	−0.0805527	+	0.300627i	−0.00484870	+	0.0180956i
$277$	−1.07398	−	0.620061i	−0.0645290	−	0.0372559i	0.467388	−	0.884052i	$-0.345195\pi$
$277$	−1.07398	−	0.620061i	−0.0645290	−	0.0372559i	−0.531917	+	0.846796i	$0.678528\pi$
$278$	21.7989	+	12.5856i	1.30741	+	0.754836i
$279$	−1.25072	+	4.66773i	−0.0748784	+	0.279450i
$280$		0			0
$281$	−4.61727	+	17.2319i	−0.275443	+	1.02797i	0.680100	+	0.733119i	$0.261936\pi$
$281$	−4.61727	+	17.2319i	−0.275443	+	1.02797i	−0.955544	+	0.294850i	$0.904730\pi$
$282$	9.31171			0.554504
$283$	8.36334	−	14.4857i	0.497149	−	0.861087i	−0.502846	−	0.864376i	$-0.667714\pi$
$283$	8.36334	−	14.4857i	0.497149	−	0.861087i	0.999995	+	0.00328885i	$0.00104687\pi$
$284$	0.575667	+	0.997084i	0.0341595	+	0.0591661i
$285$		0			0
$286$		−	40.0586i		−	2.36871i
$287$	0.181569	−	0.677623i	0.0107176	−	0.0399988i
$288$	1.22103			0.0719501
$289$	7.44714	−	12.8988i	0.438067	−	0.758754i
$290$		0			0
$291$	−3.80321	−	14.1938i	−0.222948	−	0.832054i
$292$	0.0701407	+	0.261769i	0.00410467	+	0.0153188i
$293$	−19.7965	+	5.30445i	−1.15652	+	0.309889i	−0.785576	−	0.618765i	$-0.787633\pi$
$293$	−19.7965	+	5.30445i	−1.15652	+	0.309889i	−0.370946	+	0.928654i	$0.620967\pi$
$294$	4.91616	+	1.31728i	0.286716	+	0.0768253i
$295$		0			0
$296$	2.28397	+	16.6267i	0.132753	+	0.966406i
$297$	14.7238	−	14.7238i	0.854363	−	0.854363i
$298$	−5.84050	−	10.1160i	−0.338331	−	0.586007i
$299$	−11.8866	+	20.5882i	−0.687419	+	1.19064i
$300$		0			0
$301$	−11.9801	+	3.21005i	−0.690519	+	0.185024i
$302$	−30.2672			−1.74168
$303$	−5.43918	+	1.45742i	−0.312472	+	0.0837268i
$304$	6.42697	−	6.42697i	0.368612	−	0.368612i
$305$		0			0
$306$	4.88825			0.279442
$307$	4.99397	+	4.99397i	0.285021	+	0.285021i	0.835108	−	0.550087i	$-0.185405\pi$
$307$	4.99397	+	4.99397i	0.285021	+	0.285021i	−0.550087	+	0.835108i	$0.685405\pi$
$308$	−0.188375	+	0.703027i	−0.0107337	+	0.0400587i
$309$	−2.69293	−	10.0502i	−0.153196	−	0.571734i
$310$		0			0
$311$	19.0548	+	5.10571i	1.08050	+	0.289518i	0.754800	−	0.655955i	$-0.227734\pi$
$311$	19.0548	+	5.10571i	1.08050	+	0.289518i	0.325698	+	0.945474i	$0.394401\pi$
$312$	−12.6798	−	3.39754i	−0.717853	−	0.192348i
$313$	−17.9617	+	10.3702i	−1.01525	+	0.586156i	−0.912725	−	0.408574i	$-0.866026\pi$
$313$	−17.9617	+	10.3702i	−1.01525	+	0.586156i	−0.102527	+	0.994730i	$0.532693\pi$
$314$	−19.3448	+	5.18341i	−1.09169	+	0.292517i
$315$		0			0
$316$	−0.451106	−	0.120874i	−0.0253767	−	0.00679967i
$317$	−5.35199	+	19.9739i	−0.300597	+	1.12185i	0.636072	+	0.771630i	$0.280558\pi$
$317$	−5.35199	+	19.9739i	−0.300597	+	1.12185i	−0.936669	+	0.350215i	$0.886108\pi$
$318$	−11.2545	+	6.49779i	−0.631121	+	0.364378i
$319$	14.0694	−	14.0694i	0.787735	−	0.787735i
$320$		0			0
$321$	−6.51472	+	3.76127i	−0.363616	+	0.209934i
$322$	6.89000	−	6.89000i	0.383965	−	0.383965i
$323$	2.23280	−	2.23280i	0.124236	−	0.124236i
$324$	−0.158081	−	0.273804i	−0.00878226	−	0.0152113i
$325$		0			0
$326$	−7.85262	−	4.53371i	−0.434917	−	0.251099i
$327$			6.70318i			0.370686i
$328$	−0.588280	+	1.01893i	−0.0324823	+	0.0562610i
$329$	−11.1917	−	6.46153i	−0.617019	−	0.356236i
$330$		0			0
$331$	8.47290	−	31.6213i	0.465713	−	1.73806i	−0.188802	−	0.982015i	$-0.560460\pi$
$331$	8.47290	−	31.6213i	0.465713	−	1.73806i	0.654515	−	0.756049i	$-0.272873\pi$
$332$	−0.265014	−	0.265014i	−0.0145445	−	0.0145445i
$333$	11.1886	−	8.68556i	0.613133	−	0.475966i
$334$		−	4.53841i		−	0.248331i
$335$		0			0
$336$	4.87618	+	2.81526i	0.266018	+	0.153585i
$337$	9.97490	−	2.67277i	0.543368	−	0.145595i	0.0233134	−	0.999728i	$-0.492578\pi$
$337$	9.97490	−	2.67277i	0.543368	−	0.145595i	0.520054	+	0.854133i	$0.325912\pi$
$338$	25.9516	+	14.9831i	1.41158	+	0.814975i
$339$	4.29384	−	4.29384i	0.233209	−	0.233209i
$340$		0			0
$341$	6.99815	+	6.99815i	0.378971	+	0.378971i
$342$	−7.08043	−	1.89719i	−0.382866	−	0.102589i
$343$	−13.1375	−	13.1375i	−0.709358	−	0.709358i
$344$	20.8010			1.12152
$345$		0			0
$346$	−7.16315	+	1.91936i	−0.385093	+	0.103185i
$347$		−	9.81456i		−	0.526873i	−0.964677	−	0.263437i	$-0.915144\pi$
$347$		−	9.81456i		−	0.526873i	0.964677	−	0.263437i	$-0.0848560\pi$
$348$	0.158576	+	0.274662i	0.00850057	+	0.0147234i
$349$	−11.0564	+	6.38340i	−0.591834	+	0.341696i	−0.765822	−	0.643052i	$-0.777668\pi$
$349$	−11.0564	+	6.38340i	−0.591834	+	0.341696i	0.173988	+	0.984748i	$0.444335\pi$
$350$		0			0
$351$	6.56164	+	24.4884i	0.350235	+	1.30709i
$352$	1.25036	−	2.16568i	0.0666442	−	0.115431i
$353$	1.70337	+	2.95032i	0.0906610	+	0.157030i	0.907789	−	0.419426i	$-0.137769\pi$
$353$	1.70337	+	2.95032i	0.0906610	+	0.157030i	−0.817128	+	0.576456i	$0.804435\pi$
$354$	−4.95039	−	8.57432i	−0.263110	−	0.455720i
$355$		0			0
$356$	−1.00800	−	1.00800i	−0.0534238	−	0.0534238i
$357$	1.69404	+	0.978054i	0.0896581	+	0.0517641i
$358$	4.86517	+	1.30362i	0.257132	+	0.0688983i
$359$			4.52436i			0.238787i	0.992847	+	0.119393i	$0.0380949\pi$
$359$			4.52436i			0.238787i	−0.992847	+	0.119393i	$0.961905\pi$
$360$		0			0
$361$	12.3538	−	7.13246i	0.650199	−	0.375393i
$362$		−	16.9893i		−	0.892937i
$363$	−2.49049	−	9.29463i	−0.130717	−	0.487841i
$364$	−0.626605	−	0.626605i	−0.0328430	−	0.0328430i
$365$		0			0
$366$	3.48951	−	6.04401i	0.182400	−	0.315925i
$367$	2.79712	+	10.4390i	0.146009	+	0.544912i	0.999708	+	0.0241463i	$0.00768676\pi$
$367$	2.79712	+	10.4390i	0.146009	+	0.544912i	−0.853700	+	0.520766i	$0.825647\pi$
$368$	−14.8104	+	8.55081i	−0.772047	+	0.445742i
$369$	0.992981			0.0516925
$370$		0			0
$371$	18.0357			0.936364
$372$	−0.136617	+	0.0788761i	−0.00708328	+	0.00408954i
$373$	−5.06699	−	18.9102i	−0.262359	−	0.979135i	−0.963847	−	0.266455i	$-0.914148\pi$
$373$	−5.06699	−	18.9102i	−0.262359	−	0.979135i	0.701489	−	0.712680i	$-0.252519\pi$
$374$	5.00563	−	8.67001i	0.258835	−	0.448316i
$375$		0			0
$376$	15.3257	+	15.3257i	0.790362	+	0.790362i
$377$	6.27000	+	23.3999i	0.322921	+	1.20516i
$378$		−	10.3912i		−	0.534463i
$379$	−4.24970	+	2.45356i	−0.218292	+	0.126031i	−0.605159	−	0.796104i	$-0.706891\pi$
$379$	−4.24970	+	2.45356i	−0.218292	+	0.126031i	0.386867	+	0.922136i	$0.373557\pi$
$380$		0			0
$381$		−	0.447359i		−	0.0229189i
$382$	29.7389	+	7.96850i	1.52157	+	0.407704i
$383$	5.61179	+	3.23997i	0.286749	+	0.165555i	0.636475	−	0.771298i	$-0.280392\pi$
$383$	5.61179	+	3.23997i	0.286749	+	0.165555i	−0.349726	+	0.936852i	$0.613725\pi$
$384$	−6.97395	−	6.97395i	−0.355888	−	0.355888i
$385$		0			0
$386$	9.11340	+	15.7849i	0.463860	+	0.803429i
$387$	−8.77772	−	15.2035i	−0.446197	−	0.772835i
$388$	−0.831829	+	1.44077i	−0.0422297	+	0.0731440i
$389$	−2.23101	−	8.32624i	−0.113117	−	0.422157i	0.886022	−	0.463642i	$-0.153458\pi$
$389$	−2.23101	−	8.32624i	−0.113117	−	0.422157i	−0.999139	+	0.0414853i	$0.986791\pi$
$390$		0			0
$391$	−5.14531	+	2.97065i	−0.260209	+	0.150232i
$392$	5.92322	+	10.2593i	0.299168	+	0.518173i
$393$		−	13.0429i		−	0.657928i
$394$	−7.85130	+	2.10375i	−0.395543	+	0.105985i
$395$		0			0
$396$	−1.03021			−0.0517699
$397$	−0.770578	−	0.770578i	−0.0386742	−	0.0386742i	0.687505	−	0.726179i	$-0.258706\pi$
$397$	−0.770578	−	0.770578i	−0.0386742	−	0.0386742i	−0.726179	+	0.687505i	$0.758706\pi$
$398$	−22.8900	−	6.13337i	−1.14737	−	0.307438i
$399$	−2.07415	−	2.07415i	−0.103837	−	0.103837i
$400$		0			0
$401$	−17.3804	+	17.3804i	−0.867936	+	0.867936i	−0.992244	−	0.124308i	$-0.960329\pi$
$401$	−17.3804	+	17.3804i	−0.867936	+	0.867936i	0.124308	+	0.992244i	$0.460329\pi$
$402$	−9.55780	−	5.51820i	−0.476700	−	0.275223i
$403$	−11.6392	+	3.11871i	−0.579789	+	0.155354i
$404$	0.552115	+	0.318764i	0.0274687	+	0.0158591i
$405$		0			0
$406$		−	9.92929i		−	0.492783i
$407$	−3.94779	−	28.7388i	−0.195685	−	1.42453i
$408$	−2.31978	−	2.31978i	−0.114846	−	0.114846i
$409$	2.48177	−	9.26208i	0.122715	−	0.457980i	−0.877033	−	0.480431i	$-0.840480\pi$
$409$	2.48177	−	9.26208i	0.122715	−	0.457980i	0.999748	+	0.0224508i	$0.00714691\pi$
$410$		0			0
$411$	1.36362	+	0.787285i	0.0672623	+	0.0388339i
$412$	−0.588991	+	1.02016i	−0.0290175	+	0.0502598i
$413$			13.7406i			0.676130i
$414$	11.9443	+	6.89606i	0.587032	+	0.338923i
$415$		0			0
$416$	1.52235	+	2.63679i	0.0746393	+	0.129279i
$417$	−10.0815	+	10.0815i	−0.493695	+	0.493695i
$418$	−10.6154	+	10.6154i	−0.519216	+	0.519216i
$419$	−14.2802	+	8.24465i	−0.697631	+	0.402778i	−0.806465	−	0.591282i	$-0.798622\pi$
$419$	−14.2802	+	8.24465i	−0.697631	+	0.402778i	0.108833	+	0.994060i	$0.465289\pi$
$420$		0			0
$421$	0.456713	−	0.456713i	0.0222588	−	0.0222588i	−0.695890	−	0.718149i	$-0.744990\pi$
$421$	0.456713	−	0.456713i	0.0222588	−	0.0222588i	0.718149	+	0.695890i	$0.244990\pi$
$422$	21.7874	−	12.5790i	1.06059	−	0.612335i
$423$	4.73433	−	17.6688i	0.230191	−	0.859085i
$424$	−29.2176	−	7.82884i	−1.41893	−	0.380202i
$425$		0			0
$426$	−14.2101	+	3.80758i	−0.688480	+	0.184478i
$427$	−8.38805	+	4.84284i	−0.405926	+	0.234362i
$428$	0.822656	+	0.220430i	0.0397646	+	0.0106549i
$429$	21.9167	+	5.87257i	1.05815	+	0.283530i
$430$		0			0
$431$	−3.57129	−	13.3283i	−0.172023	−	0.641999i	−0.997040	−	0.0768905i	$-0.975501\pi$
$431$	−3.57129	−	13.3283i	−0.172023	−	0.641999i	0.825016	−	0.565109i	$-0.191166\pi$
$432$	−4.72022	+	17.6161i	−0.227102	+	0.847556i
$433$	16.0407	+	16.0407i	0.770868	+	0.770868i	0.978258	−	0.207391i	$-0.0664971\pi$
$433$	16.0407	+	16.0407i	0.770868	+	0.770868i	−0.207391	+	0.978258i	$0.566497\pi$
$434$	4.93885			0.237073
$435$		0			0
$436$	0.536630	−	0.536630i	0.0256999	−	0.0256999i
$437$	8.60572	−	2.30589i	0.411667	−	0.110306i
$438$	−3.46278			−0.165458
$439$	−10.9533	+	2.93493i	−0.522774	+	0.140077i	−0.510549	−	0.859849i	$-0.670558\pi$
$439$	−10.9533	+	2.93493i	−0.522774	+	0.140077i	−0.0122243	+	0.999925i	$0.503891\pi$
$440$		0			0
$441$	4.99902	−	8.65855i	0.238048	−	0.412312i
$442$	6.09452	+	10.5560i	0.289887	+	0.502099i
$443$	−18.6448	+	18.6448i	−0.885840	+	0.885840i	−0.994120	−	0.108280i	$-0.965466\pi$
$443$	−18.6448	+	18.6448i	−0.885840	+	0.885840i	0.108280	+	0.994120i	$0.465466\pi$
$444$	0.458762	+	0.0577790i	0.0217719	+	0.00274207i
$445$		0			0
$446$	15.2738	+	4.09261i	0.723237	+	0.193791i
$447$	6.39088	−	1.71243i	0.302278	−	0.0809952i
$448$	3.23396	+	12.0693i	0.152790	+	0.570222i
$449$	−9.44296	−	35.2416i	−0.445641	−	1.66315i	−0.714239	−	0.699902i	$-0.753227\pi$
$449$	−9.44296	−	35.2416i	−0.445641	−	1.66315i	0.268598	−	0.963252i	$-0.413440\pi$
$450$		0			0
$451$	1.01683	−	1.76120i	0.0478805	−	0.0829314i
$452$	−0.687496			−0.0323371
$453$	4.43716	−	16.5597i	0.208476	−	0.778043i
$454$		−	9.57819i		−	0.449527i
$455$		0			0
$456$	2.45977	+	4.26045i	0.115189	+	0.199514i
$457$	20.6281	−	35.7289i	0.964941	−	1.67133i	0.255168	−	0.966897i	$-0.417869\pi$
$457$	20.6281	−	35.7289i	0.964941	−	1.67133i	0.709773	−	0.704430i	$-0.248797\pi$
$458$	16.3545			0.764194
$459$	−1.63986	+	6.12004i	−0.0765420	+	0.285659i
$460$		0			0
$461$	7.84179	−	29.2660i	0.365229	−	1.36305i	−0.501882	−	0.864936i	$-0.667359\pi$
$461$	7.84179	−	29.2660i	0.365229	−	1.36305i	0.867111	−	0.498115i	$-0.165974\pi$
$462$	−8.05397	−	4.64996i	−0.374705	−	0.216336i
$463$	−3.67480	−	2.12165i	−0.170783	−	0.0986013i	0.412172	−	0.911106i	$-0.364770\pi$
$463$	−3.67480	−	2.12165i	−0.170783	−	0.0986013i	−0.582955	+	0.812505i	$0.698104\pi$
$464$	−4.51042	+	16.8331i	−0.209391	+	0.781458i
$465$		0			0
$466$	−5.65143	+	21.0914i	−0.261797	+	0.977041i
$467$	−9.79517			−0.453266			−0.226633	−	0.973980i	$-0.572772\pi$
$467$	−9.79517			−0.453266			−0.226633	+	0.973980i	$0.572772\pi$
$468$	0.627156	−	1.08627i	0.0289903	−	0.0502127i
$469$	7.65832	+	13.2646i	0.353628	+	0.612502i
$470$		0			0
$471$		−	11.3437i		−	0.522692i
$472$	5.96446	−	22.2597i	0.274537	−	1.02458i
$473$	−35.9540			−1.65317
$474$	2.98371	−	5.16793i	0.137046	−	0.237371i
$475$		0			0
$476$	−0.0573190	−	0.213917i	−0.00262721	−	0.00980489i
$477$	6.60731	+	24.6588i	0.302528	+	1.12905i
$478$	25.0010	−	6.69901i	1.14352	−	0.306405i
$479$	29.0918	+	7.79512i	1.32924	+	0.356168i	0.852431	−	0.522840i	$-0.175127\pi$
$479$	29.0918	+	7.79512i	1.32924	+	0.356168i	0.476807	+	0.879008i	$0.341794\pi$
$480$		0			0
$481$	32.7059	+	13.3326i	1.49126	+	0.607914i
$482$	−28.7006	+	28.7006i	−1.30728	+	1.30728i
$483$	2.75957	+	4.77971i	0.125565	+	0.217484i
$484$	−0.544713	+	0.943471i	−0.0247597	+	0.0428850i
$485$		0			0
$486$	22.2057	−	5.94999i	1.00727	−	0.269897i
$487$	8.80800			0.399129			0.199564	−	0.979885i	$-0.436047\pi$
$487$	8.80800			0.399129			0.199564	+	0.979885i	$0.436047\pi$
$488$	15.6908	−	4.20433i	0.710287	−	0.190321i
$489$	3.63166	−	3.63166i	0.164230	−	0.164230i
$490$		0			0
$491$	−37.2665			−1.68181			−0.840907	−	0.541179i	$-0.817978\pi$
$491$	−37.2665			−1.68181			−0.840907	+	0.541179i	$0.817978\pi$
$492$	0.0229213	+	0.0229213i	0.00103337	+	0.00103337i
$493$	−1.56697	+	5.84801i	−0.0705728	+	0.263381i
$494$	−4.73073	−	17.6553i	−0.212846	−	0.794351i
$495$		0			0
$496$	−8.37284	−	2.24349i	−0.375951	−	0.100736i
$497$	19.7212	+	5.28427i	0.884615	+	0.237032i
$498$	4.14729	−	2.39444i	0.185845	−	0.107297i
$499$	−3.52008	+	0.943201i	−0.157580	+	0.0422235i	−0.336747	−	0.941595i	$-0.609327\pi$
$499$	−3.52008	+	0.943201i	−0.157580	+	0.0422235i	0.179166	+	0.983819i	$0.442660\pi$
$500$		0			0
$501$	2.48305	+	0.665330i	0.110934	+	0.0297248i
$502$	−1.03071	+	3.84664i	−0.0460026	+	0.171684i
$503$	21.1433	−	12.2071i	0.942732	−	0.544287i	0.0519165	−	0.998651i	$-0.483467\pi$
$503$	21.1433	−	12.2071i	0.942732	−	0.544287i	0.890816	+	0.454365i	$0.150134\pi$
$504$	7.47367	−	7.47367i	0.332904	−	0.332904i
$505$		0			0
$506$	24.4623	−	14.1233i	1.08748	−	0.627859i
$507$	−12.0020	+	12.0020i	−0.533029	+	0.533029i
$508$	−0.0358138	+	0.0358138i	−0.00158898	+	0.00158898i
$509$	−21.1376	−	36.6113i	−0.936906	−	1.62277i	−0.771199	−	0.636595i	$-0.780343\pi$
$509$	−21.1376	−	36.6113i	−0.936906	−	1.62277i	−0.165708	−	0.986175i	$-0.552991\pi$
$510$		0			0
$511$	4.16190	+	2.40287i	0.184112	+	0.106297i
$512$		−	20.8587i		−	0.921833i
$513$	4.75054	−	8.22817i	0.209741	−	0.363283i
$514$	7.84888	+	4.53155i	0.346199	+	0.199878i
$515$		0			0
$516$	0.148327	−	0.553565i	0.00652975	−	0.0243694i
$517$	−26.4901	−	26.4901i	−1.16503	−	1.16503i
$518$	−11.5341	−	8.74797i	−0.506778	−	0.384364i
$519$		−	4.20046i		−	0.184380i
$520$		0			0
$521$	20.8093	+	12.0143i	0.911672	+	0.526354i	0.880969	−	0.473174i	$-0.156892\pi$
$521$	20.8093	+	12.0143i	0.911672	+	0.526354i	0.0307035	+	0.999529i	$0.490225\pi$
$522$	13.5756	−	3.63757i	0.594188	−	0.159212i
$523$	−12.8269	−	7.40563i	−0.560882	−	0.323825i	0.192617	−	0.981274i	$-0.438302\pi$
$523$	−12.8269	−	7.40563i	−0.560882	−	0.323825i	−0.753500	+	0.657448i	$0.771636\pi$
$524$	−1.04416	+	1.04416i	−0.0456145	+	0.0456145i
$525$		0			0
$526$	15.4937	+	15.4937i	0.675557	+	0.675557i
$527$	−2.90882	−	0.779415i	−0.126710	−	0.0339518i
$528$	11.5416	+	11.5416i	0.502285	+	0.502285i
$529$	6.23672			0.271162
$530$		0			0
$531$	−18.7865	+	5.03383i	−0.815265	+	0.218449i
$532$			0.332097i			0.0143982i
$533$	1.23802	+	2.14431i	0.0536246	+	0.0928805i
$534$	15.7745	−	9.10743i	0.682631	−	0.394117i
$535$		0			0
$536$	−6.64859	−	24.8129i	−0.287175	−	1.07175i
$537$	−1.42646	+	2.47071i	−0.0615564	+	0.106619i
$538$	14.8495	+	25.7201i	0.640207	+	1.10887i
$539$	−10.2381	−	17.7330i	−0.440987	−	0.763813i
$540$		0			0
$541$	11.8805	+	11.8805i	0.510784	+	0.510784i	0.914767	−	0.403983i	$-0.132374\pi$
$541$	11.8805	+	11.8805i	0.510784	+	0.510784i	−0.403983	+	0.914767i	$0.632374\pi$
$542$	−16.1163	−	9.30474i	−0.692254	−	0.399673i
$543$	9.29514	+	2.49062i	0.398892	+	0.106883i
$544$			0.760918i			0.0326241i
$545$		0			0
$546$	9.80597	−	5.66148i	0.419657	−	0.242289i
$547$			17.4832i			0.747526i	0.927524	+	0.373763i	$0.121933\pi$
$547$			17.4832i			0.747526i	−0.927524	+	0.373763i	$0.878067\pi$
$548$	−0.0461389	−	0.172193i	−0.00197096	−	0.00735571i
$549$	−9.69421	−	9.69421i	−0.413739	−	0.413739i
$550$		0			0
$551$	4.53939	−	7.86245i	0.193384	−	0.334952i
$552$	−2.39572	−	8.94097i	−0.101969	−	0.380553i
$553$	−7.17221	+	4.14088i	−0.304993	+	0.176088i
$554$	−1.79401			−0.0762202
$555$		0			0
$556$	1.61418			0.0684563
$557$	27.2299	−	15.7212i	1.15377	−	0.666129i	0.203967	−	0.978978i	$-0.434617\pi$
$557$	27.2299	−	15.7212i	1.15377	−	0.666129i	0.949803	+	0.312849i	$0.101283\pi$
$558$	1.80934	+	6.75253i	0.0765953	+	0.285858i
$559$	21.8876	−	37.9105i	0.925747	−	1.60344i
$560$		0			0
$561$	4.00969	+	4.00969i	0.169289	+	0.169289i
$562$	6.67954	+	24.9284i	0.281759	+	1.05154i
$563$			17.3599i			0.731633i	0.930687	+	0.365816i	$0.119210\pi$
$563$			17.3599i			0.731633i	−0.930687	+	0.365816i	$0.880790\pi$
$564$	0.517138	−	0.298570i	0.0217754	−	0.0125720i
$565$		0			0
$566$		−	24.1975i		−	1.01710i
$567$	−5.41552	−	1.45108i	−0.227430	−	0.0609398i
$568$	−29.6544	−	17.1210i	−1.24427	−	0.718380i
$569$	13.2625	+	13.2625i	0.555994	+	0.555994i	0.928165	−	0.372170i	$-0.121386\pi$
$569$	13.2625	+	13.2625i	0.555994	+	0.555994i	−0.372170	+	0.928165i	$0.621386\pi$
$570$		0			0
$571$	−13.5109	−	23.4016i	−0.565415	−	0.979327i	−0.997011	−	0.0772604i	$-0.975383\pi$
$571$	−13.5109	−	23.4016i	−0.565415	−	0.979327i	0.431596	−	0.902067i	$-0.357951\pi$
$572$	−1.28443	−	2.22470i	−0.0537048	−	0.0930195i
$573$	−8.71941	+	15.1025i	−0.364259	+	0.630914i
$574$	−0.262664	−	0.980277i	−0.0109634	−	0.0409160i
$575$		0			0
$576$	−15.3167	+	8.84312i	−0.638197	+	0.368463i
$577$	12.6946	+	21.9876i	0.528482	+	0.915357i	0.999449	+	0.0332064i	$0.0105719\pi$
$577$	12.6946	+	21.9876i	0.528482	+	0.915357i	−0.470967	+	0.882151i	$0.656095\pi$
$578$		−	21.5467i		−	0.896223i
$579$	−9.97220	+	2.67204i	−0.414430	+	0.111046i
$580$		0			0
$581$	−6.64615			−0.275729
$582$	−15.0314	−	15.0314i	−0.623072	−	0.623072i
$583$	50.5020	+	13.5320i	2.09158	+	0.560436i
$584$	−5.69922	−	5.69922i	−0.235836	−	0.235836i
$585$		0			0
$586$	−20.9648	+	20.9648i	−0.866046	+	0.866046i
$587$	−36.6636	−	21.1677i	−1.51327	−	0.873686i	−0.999879	−	0.0155295i	$-0.995057\pi$
$587$	−36.6636	−	21.1677i	−1.51327	−	0.873686i	−0.513389	−	0.858156i	$-0.671610\pi$
$588$	0.315262	−	0.0844742i	0.0130012	−	0.00348366i
$589$	3.91080	+	2.25790i	0.161142	+	0.0930352i
$590$		0			0
$591$		−	4.60399i		−	0.189383i
$592$	15.5799	+	20.0698i	0.640330	+	0.824864i
$593$	22.5131	+	22.5131i	0.924503	+	0.924503i	0.997344	−	0.0728403i	$-0.0232063\pi$
$593$	22.5131	+	22.5131i	0.924503	+	0.924503i	−0.0728403	+	0.997344i	$0.523206\pi$
$594$	7.79637	−	29.0965i	0.319889	−	1.19384i
$595$		0			0
$596$	−0.648720	−	0.374539i	−0.0265726	−	0.0153417i
$597$	6.71134	−	11.6244i	0.274677	−	0.475754i
$598$			34.3912i			1.40636i
$599$	−13.9673	−	8.06402i	−0.570688	−	0.329487i	0.186736	−	0.982410i	$-0.440209\pi$
$599$	−13.9673	−	8.06402i	−0.570688	−	0.329487i	−0.757424	+	0.652923i	$0.773542\pi$
$600$		0			0
$601$	12.0579	+	20.8849i	0.491852	+	0.851912i	0.999956	−	0.00938333i	$-0.00298685\pi$
$601$	12.0579	+	20.8849i	0.491852	+	0.851912i	−0.508104	+	0.861296i	$0.669654\pi$
$602$	−12.6871	+	12.6871i	−0.517086	+	0.517086i
$603$	−15.3301	+	15.3301i	−0.624290	+	0.624290i
$604$	−1.68093	+	0.970484i	−0.0683960	+	0.0394884i
$605$		0			0
$606$	−5.76017	+	5.76017i	−0.233991	+	0.233991i
$607$	−4.09934	+	2.36675i	−0.166387	+	0.0960635i	−0.580881	−	0.813988i	$-0.697292\pi$
$607$	−4.09934	+	2.36675i	−0.166387	+	0.0960635i	0.414494	+	0.910052i	$0.363959\pi$
$608$	0.295323	−	1.10216i	0.0119769	−	0.0446984i
$609$	5.43249	+	1.45563i	0.220136	+	0.0589851i
$610$		0			0
$611$	44.0578	−	11.8053i	1.78239	−	0.477589i
$612$	0.271475	−	0.156736i	0.0109737	−	0.00633568i
$613$	19.9102	+	5.33493i	0.804167	+	0.215476i	0.637413	−	0.770523i	$-0.280005\pi$
$613$	19.9102	+	5.33493i	0.804167	+	0.215476i	0.166754	+	0.985999i	$0.446671\pi$
$614$	9.86883	+	2.64434i	0.398273	+	0.106717i
$615$		0			0
$616$	−5.60249	−	20.9088i	−0.225731	−	0.842439i
$617$	−3.95109	+	14.7457i	−0.159065	+	0.593638i	0.839658	+	0.543115i	$0.182755\pi$
$617$	−3.95109	+	14.7457i	−0.159065	+	0.593638i	−0.998723	+	0.0505225i	$0.983911\pi$
$618$	−10.6433	−	10.6433i	−0.428135	−	0.428135i
$619$	6.80631			0.273569			0.136784	−	0.990601i	$-0.456323\pi$
$619$	6.80631			0.273569			0.136784	+	0.990601i	$0.456323\pi$
$620$		0			0
$621$	−12.6408	+	12.6408i	−0.507256	+	0.507256i
$622$	27.5654	−	7.38613i	1.10527	−	0.296157i
$623$	−25.2791			−1.01279
$624$	−19.1958	+	5.14350i	−0.768447	+	0.205905i
$625$		0			0
$626$	−15.0019	+	25.9841i	−0.599597	+	1.03853i
$627$	−4.25166	−	7.36408i	−0.169795	−	0.294093i
$628$	−0.908136	+	0.908136i	−0.0362386	+	0.0362386i
$629$	5.41263	+	6.97248i	0.215816	+	0.278011i
$630$		0			0
$631$	24.9840	+	6.69444i	0.994597	+	0.266501i	0.719180	−	0.694824i	$-0.244518\pi$
$631$	24.9840	+	6.69444i	0.994597	+	0.266501i	0.275416	+	0.961325i	$0.411184\pi$
$632$	13.4164	−	3.59491i	0.533675	−	0.142998i
$633$	3.68814	+	13.7643i	0.146591	+	0.547083i
$634$	7.74240	+	28.8950i	0.307490	+	1.14757i
$635$		0			0
$636$	−0.416689	+	0.721726i	−0.0165228	+	0.0286183i
$637$	24.9305			0.987783
$638$	7.44984	−	27.8032i	0.294942	−	1.10074i
$639$			28.8992i			1.14323i
$640$		0			0
$641$	17.3223	+	30.0031i	0.684190	+	1.18505i	0.973691	+	0.227874i	$0.0731773\pi$
$641$	17.3223	+	30.0031i	0.684190	+	1.18505i	−0.289501	+	0.957178i	$0.593489\pi$
$642$	−5.44121	+	9.42446i	−0.214748	+	0.371954i
$643$	−22.9695			−0.905827			−0.452913	−	0.891555i	$-0.649615\pi$
$643$	−22.9695			−0.905827			−0.452913	+	0.891555i	$0.649615\pi$
$644$	0.161725	−	0.603566i	0.00637285	−	0.0237838i
$645$		0			0
$646$	1.18228	−	4.41235i	0.0465164	−	0.173601i
$647$	−12.3356	−	7.12196i	−0.484962	−	0.279993i	0.237520	−	0.971383i	$-0.423666\pi$
$647$	−12.3356	−	7.12196i	−0.484962	−	0.279993i	−0.722482	+	0.691389i	$0.756999\pi$
$648$	8.14323	+	4.70149i	0.319896	+	0.184692i
$649$	−10.3094	+	38.4753i	−0.404680	+	1.51029i
$650$		0			0
$651$	−0.724034	+	2.70213i	−0.0283771	+	0.105905i
$652$	−0.581474			−0.0227723
$653$	−5.21666	+	9.03552i	−0.204144	+	0.353587i	−0.949860	−	0.312677i	$-0.898774\pi$
$653$	−5.21666	+	9.03552i	−0.204144	+	0.353587i	0.745716	+	0.666264i	$0.232108\pi$
$654$	4.84854	+	8.39792i	0.189593	+	0.328385i
$655$		0			0
$656$			1.78118i			0.0695434i
$657$	−1.76057	+	6.57055i	−0.0686865	+	0.256341i
$658$	−18.6950			−0.728808
$659$	−9.90312	+	17.1527i	−0.385771	+	0.668174i	−0.991876	−	0.127210i	$-0.959398\pi$
$659$	−9.90312	+	17.1527i	−0.385771	+	0.668174i	0.606105	+	0.795385i	$0.292731\pi$
$660$		0			0
$661$	−5.73632	−	21.4082i	−0.223117	−	0.832683i	−0.983150	−	0.182799i	$-0.941484\pi$
$661$	−5.73632	−	21.4082i	−0.223117	−	0.832683i	0.760033	−	0.649884i	$-0.225183\pi$
$662$	−12.2572	−	45.7447i	−0.476391	−	1.77792i
$663$	−6.66884	+	1.78691i	−0.258996	+	0.0693978i
$664$	10.7667	+	2.88494i	0.417830	+	0.111957i
$665$		0			0
$666$	7.73498	−	18.9745i	0.299724	−	0.735246i
$667$	−12.0789	+	12.0789i	−0.467697	+	0.467697i
$668$	−0.145519	−	0.252047i	−0.00563031	−	0.00975198i
$669$	−4.47828	+	7.75660i	−0.173140	+	0.299888i
$670$		0			0
$671$	−27.1211	+	7.26707i	−1.04700	+	0.280542i
$672$	0.706852			0.0272674
$673$	47.2502	−	12.6606i	1.82136	−	0.488032i	0.824404	−	0.566001i	$-0.191510\pi$
$673$	47.2502	−	12.6606i	1.82136	−	0.488032i	0.996956	+	0.0779695i	$0.0248437\pi$
$674$	10.5636	−	10.5636i	0.406893	−	0.406893i
$675$		0			0
$676$	1.92167			0.0739104
$677$	−8.62241	−	8.62241i	−0.331386	−	0.331386i	0.521727	−	0.853113i	$-0.325288\pi$
$677$	−8.62241	−	8.62241i	−0.331386	−	0.331386i	−0.853113	+	0.521727i	$0.825288\pi$
$678$	2.27362	−	8.48527i	0.0873179	−	0.325875i
$679$	7.63567	+	28.4967i	0.293030	+	1.09360i
$680$		0			0
$681$	5.24039	+	1.40416i	0.200812	+	0.0538075i
$682$	13.8294	+	3.70557i	0.529554	+	0.141894i
$683$	13.8168	−	7.97715i	0.528686	−	0.305237i	−0.211795	−	0.977314i	$-0.567931\pi$
$683$	13.8168	−	7.97715i	0.528686	−	0.305237i	0.740481	+	0.672077i	$0.234598\pi$
$684$	−0.454052	+	0.121663i	−0.0173611	+	0.00465190i
$685$		0			0
$686$	−25.9616	−	6.95640i	−0.991220	−	0.265597i
$687$	−2.39756	+	8.94781i	−0.0914726	+	0.341380i
$688$	27.2715	−	15.7452i	1.03972	−	0.600280i
$689$	−45.0122	+	45.0122i	−1.71483	+	1.71483i
$690$		0			0
$691$	−16.8398	+	9.72247i	−0.640617	+	0.369860i	−0.784852	−	0.619683i	$-0.787261\pi$
$691$	−16.8398	+	9.72247i	−0.640617	+	0.369860i	0.144235	+	0.989543i	$0.453928\pi$
$692$	−0.336273	+	0.336273i	−0.0127832	+	0.0127832i
$693$	−12.9181	+	12.9181i	−0.490716	+	0.490716i
$694$	−7.09907	−	12.2960i	−0.269477	−	0.466748i
$695$		0			0
$696$	−8.16874	−	4.71623i	−0.309635	−	0.178768i
$697$			0.618801i			0.0234388i
$698$	−9.23449	+	15.9946i	−0.349531	+	0.605405i
$699$	−10.7110	−	6.18399i	−0.405127	−	0.233900i
$700$		0			0
$701$	−11.0896	+	41.3868i	−0.418847	+	1.56316i	0.358155	+	0.933662i	$0.383406\pi$
$701$	−11.0896	+	41.3868i	−0.418847	+	1.56316i	−0.777003	+	0.629497i	$0.783261\pi$
$702$	25.9336	+	25.9336i	0.978799	+	0.978799i
$703$	−5.13386	−	12.2001i	−0.193627	−	0.460134i
$704$			36.2219i			1.36517i
$705$		0			0
$706$	4.26805	+	2.46416i	0.160630	+	0.0927399i
$707$	10.9202	−	2.92605i	0.410696	−	0.110046i
$708$	−0.549852	−	0.317457i	−0.0206647	−	0.0119308i
$709$	11.6125	−	11.6125i	0.436116	−	0.436116i	−0.454586	−	0.890703i	$-0.650213\pi$
$709$	11.6125	−	11.6125i	0.436116	−	0.436116i	0.890703	+	0.454586i	$0.150213\pi$
$710$		0			0
$711$	−8.28904	−	8.28904i	−0.310863	−	0.310863i
$712$	40.9520	+	10.9731i	1.53474	+	0.411233i
$713$	−6.00808	−	6.00808i	−0.225004	−	0.225004i
$714$	2.82979			0.105902
$715$		0			0
$716$	0.311992	−	0.0835981i	0.0116597	−	0.00312421i
$717$			14.6606i			0.547509i
$718$	3.27256	+	5.66824i	0.122131	+	0.211537i
$719$	−28.4138	+	16.4047i	−1.05966	+	0.611794i	−0.925337	−	0.379144i	$-0.876218\pi$
$719$	−28.4138	+	16.4047i	−1.05966	+	0.611794i	−0.134320	+	0.990938i	$0.542885\pi$
$720$		0			0
$721$	5.40658	+	20.1776i	0.201352	+	0.751454i
$722$	10.3181	−	17.8715i	0.384000	−	0.665108i
$723$	−11.4951	−	19.9101i	−0.427508	−	0.740465i
$724$	−0.544743	−	0.943522i	−0.0202452	−	0.0350657i
$725$		0			0
$726$	−9.84315	−	9.84315i	−0.365313	−	0.365313i
$727$	−34.1431	−	19.7125i	−1.26630	−	0.731097i	−0.292011	−	0.956415i	$-0.594324\pi$
$727$	−34.1431	−	19.7125i	−1.26630	−	0.731097i	−0.974285	+	0.225318i	$0.927658\pi$
$728$	25.4571	+	6.82122i	0.943504	+	0.252811i
$729$			2.79732i			0.103604i
$730$		0			0
$731$	9.47442	−	5.47006i	0.350424	−	0.202317i
$732$		−	0.447549i		−	0.0165419i
$733$	−10.9468	−	40.8538i	−0.404328	−	1.50897i	−0.805293	−	0.592878i	$-0.797992\pi$
$733$	−10.9468	−	40.8538i	−0.404328	−	1.50897i	0.400965	−	0.916093i	$-0.368675\pi$
$734$	11.0551	+	11.0551i	0.408050	+	0.408050i
$735$		0			0
$736$	−1.07346	+	1.85929i	−0.0395683	+	0.0685343i
$737$	11.4919	+	42.8884i	0.423310	+	1.57981i
$738$	1.24403	−	0.718244i	0.0457935	−	0.0264389i
$739$	32.4999			1.19553			0.597764	−	0.801672i	$-0.296056\pi$
$739$	32.4999			1.19553			0.597764	+	0.801672i	$0.296056\pi$
$740$		0			0
$741$	10.3531			0.380329
$742$	22.5956	−	13.0456i	0.829509	−	0.478917i
$743$	2.97059	+	11.0864i	0.108980	+	0.406720i	0.998766	−	0.0496580i	$-0.0158131\pi$
$743$	2.97059	+	11.0864i	0.108980	+	0.406720i	−0.889786	+	0.456378i	$0.849146\pi$
$744$	2.34586	−	4.06315i	0.0860035	−	0.148962i
$745$		0			0
$746$	−20.0262	−	20.0262i	−0.733212	−	0.733212i
$747$	−2.43480	−	9.08680i	−0.0890847	−	0.332469i
$748$		−	0.642000i		−	0.0234739i
$749$	13.0795	−	7.55148i	0.477916	−	0.275925i
$750$		0			0
$751$		−	35.5418i		−	1.29694i	−0.761240	−	0.648470i	$-0.775409\pi$
$751$		−	35.5418i		−	1.29694i	0.761240	−	0.648470i	$-0.224591\pi$
$752$	31.6937	+	8.49230i	1.15575	+	0.309682i
$753$	−1.95346	−	1.12783i	−0.0711882	−	0.0411005i
$754$	24.7809	+	24.7809i	0.902466	+	0.902466i
$755$		0			0
$756$	−0.333181	−	0.577086i	−0.0121177	−	0.0209884i
$757$	−18.3273	−	31.7438i	−0.666117	−	1.15375i	−0.978981	−	0.203951i	$-0.934622\pi$
$757$	−18.3273	−	31.7438i	−0.666117	−	1.15375i	0.312864	−	0.949798i	$-0.398712\pi$
$758$	−3.54943	+	6.14778i	−0.128921	+	0.223298i
$759$	4.14095	+	15.4542i	0.150307	+	0.560953i
$760$		0			0
$761$	18.5429	−	10.7058i	0.672180	−	0.388083i	−0.124722	−	0.992192i	$-0.539804\pi$
$761$	18.5429	−	10.7058i	0.672180	−	0.388083i	0.796902	+	0.604109i	$0.206471\pi$
$762$	−0.323584	−	0.560464i	−0.0117222	−	0.0203035i
$763$		−	13.4579i		−	0.487209i
$764$	1.90709	−	0.511002i	0.0689960	−	0.0184874i
$765$		0			0
$766$	9.37414			0.338701
$767$	−34.2929	−	34.2929i	−1.23824	−	1.23824i
$768$	−1.75848	−	0.471184i	−0.0634538	−	0.0170024i
$769$	−23.2703	−	23.2703i	−0.839147	−	0.839147i	0.149599	−	0.988747i	$-0.452202\pi$
$769$	−23.2703	−	23.2703i	−0.839147	−	0.839147i	−0.988747	+	0.149599i	$0.952202\pi$
$770$		0			0
$771$	−3.62993	+	3.62993i	−0.130729	+	0.130729i
$772$	1.01225	+	0.584422i	0.0364316	+	0.0210338i
$773$	33.5748	−	8.99634i	1.20760	−	0.323576i	0.401781	−	0.915736i	$-0.368391\pi$
$773$	33.5748	−	8.99634i	1.20760	−	0.323576i	0.805821	+	0.592160i	$0.201725\pi$
$774$	−21.9939	−	12.6982i	−0.790556	−	0.456428i
$775$		0			0
$776$		−	49.4790i		−	1.77619i
$777$	6.47705	−	5.02804i	0.232363	−	0.180380i
$778$	−8.81761	−	8.81761i	−0.316127	−	0.316127i
$779$	0.240165	−	0.896309i	0.00860481	−	0.0321136i
$780$		0			0
$781$	51.2568	+	29.5931i	1.83411	+	1.05893i
$782$	−4.29746	+	7.44341i	−0.153677	+	0.266176i
$783$			18.2168i			0.651015i
$784$	15.5314	+	8.96708i	0.554695	+	0.320253i
$785$		0			0
$786$	−9.43420	−	16.3405i	−0.336507	−	0.582847i
$787$	1.73887	−	1.73887i	0.0619839	−	0.0619839i	−0.675435	−	0.737419i	$-0.736044\pi$
$787$	1.73887	−	1.73887i	0.0619839	−	0.0619839i	0.737419	+	0.675435i	$0.236044\pi$
$788$	−0.368577	+	0.368577i	−0.0131300	+	0.0131300i
$789$	−10.7482	+	6.20550i	−0.382647	+	0.220922i
$790$		0			0
$791$	−8.62071	+	8.62071i	−0.306517	+	0.306517i
$792$	26.5346	−	15.3198i	0.942866	−	0.544364i
$793$	8.84790	−	33.0208i	0.314198	−	1.17260i
$794$	−1.52278	−	0.408027i	−0.0540413	−	0.0144803i
$795$		0			0
$796$	−1.46789	+	0.393319i	−0.0520279	+	0.0139408i
$797$	−27.1461	+	15.6728i	−0.961566	+	0.555160i	−0.896655	−	0.442731i	$-0.854010\pi$
$797$	−27.1461	+	15.6728i	−0.961566	+	0.555160i	−0.0649113	+	0.997891i	$0.520676\pi$
$798$	−4.09883	−	1.09828i	−0.145097	−	0.0388786i
$799$	11.0107	+	2.95032i	0.389532	+	0.104375i
$800$		0			0
$801$	−9.26094	−	34.5623i	−0.327219	−	1.22120i
$802$	−9.20305	+	34.3462i	−0.324971	+	1.21281i
$803$	9.85096	+	9.85096i	0.347633	+	0.347633i
$804$	−0.707740			−0.0249601
$805$		0			0
$806$	−12.3261	+	12.3261i	−0.434167	+	0.434167i
$807$	−16.2488	+	4.35386i	−0.571986	+	0.153263i
$808$	−18.9608			−0.667037
$809$	0.121396	−	0.0325280i	0.00426806	−	0.00114362i	−0.256684	−	0.966495i	$-0.582630\pi$
$809$	0.121396	−	0.0325280i	0.00426806	−	0.00114362i	0.260952	+	0.965352i	$0.415963\pi$
$810$		0			0
$811$	−7.32474	+	12.6868i	−0.257207	+	0.445495i	−0.965492	−	0.260431i	$-0.916135\pi$
$811$	−7.32474	+	12.6868i	−0.257207	+	0.445495i	0.708286	+	0.705926i	$0.249469\pi$
$812$	−0.318372	−	0.551436i	−0.0111727	−	0.0193516i
$813$	7.45343	−	7.45343i	0.261403	−	0.261403i
$814$	−25.7332	−	33.1492i	−0.901950	−	1.16188i
$815$		0			0
$816$	−4.79733	−	1.28544i	−0.167940	−	0.0449995i
$817$	−15.8463	+	4.24601i	−0.554393	+	0.148549i
$818$	−3.59022	−	13.3989i	−0.125529	−	0.468482i
$819$	−5.75691	−	21.4851i	−0.201163	−	0.750749i
$820$		0			0
$821$	−7.54707	+	13.0719i	−0.263394	+	0.456213i	−0.967142	−	0.254238i	$-0.918175\pi$
$821$	−7.54707	+	13.0719i	−0.263394	+	0.456213i	0.703747	+	0.710450i	$0.251509\pi$
$822$	2.27784			0.0794487
$823$	4.09584	−	15.2859i	0.142772	−	0.532832i	−0.857073	−	0.515196i	$-0.827719\pi$
$823$	4.09584	−	15.2859i	0.142772	−	0.532832i	0.999844	−	0.0176363i	$-0.00561411\pi$
$824$		−	35.0345i		−	1.22048i
$825$		0			0
$826$	9.93885	+	17.2146i	0.345817	+	0.598972i
$827$	−11.5992	+	20.0903i	−0.403343	+	0.698610i	−0.994127	−	0.108220i	$-0.965485\pi$
$827$	−11.5992	+	20.0903i	−0.403343	+	0.698610i	0.590784	+	0.806829i	$0.298818\pi$
$828$	0.884458			0.0307371
$829$	6.63771	−	24.7723i	0.230537	−	0.860377i	−0.749573	−	0.661922i	$-0.769741\pi$
$829$	6.63771	−	24.7723i	0.230537	−	0.860377i	0.980110	−	0.198455i	$-0.0635924\pi$
$830$		0			0
$831$	0.263001	−	0.981534i	0.00912342	−	0.0340491i
$832$	−38.1929	−	22.0507i	−1.32410	−	0.764470i
$833$	5.39580	+	3.11527i	0.186953	+	0.107938i
$834$	−5.33824	+	19.9226i	−0.184848	+	0.689863i
$835$		0			0
$836$	−0.249169	+	0.929911i	−0.00861769	+	0.0321616i
$837$	−9.06108			−0.313197
$838$	−11.9270	+	20.6583i	−0.412013	+	0.713628i
$839$	28.4964	+	49.3573i	0.983806	+	1.70400i	0.647125	+	0.762384i	$0.275971\pi$
$839$	28.4964	+	49.3573i	0.983806	+	1.70400i	0.336681	+	0.941619i	$0.390696\pi$
$840$		0			0
$841$		−	11.5929i		−	0.399755i
$842$	0.241833	−	0.902532i	0.00833410	−	0.0311033i
$843$	−14.6180			−0.503469
$844$	0.806661	−	1.39718i	0.0277664	−	0.0480929i
$845$		0			0
$846$	−6.84888	−	25.5604i	−0.235469	−	0.878783i
$847$	5.00013	+	18.6607i	0.171807	+	0.641191i
$848$	−44.2322	+	11.8520i	−1.51894	+	0.406999i
$849$	13.2389	+	3.54735i	0.454357	+	0.121745i
$850$		0			0
$851$	3.38927	+	24.6729i	0.116183	+	0.845778i
$852$	−0.667089	+	0.667089i	−0.0228541	+	0.0228541i
$853$	12.2105	+	21.1492i	0.418079	+	0.724135i	0.995746	−	0.0921378i	$-0.0293700\pi$
$853$	12.2105	+	21.1492i	0.418079	+	0.724135i	−0.577667	+	0.816273i	$0.696037\pi$
$854$	−7.00586	+	12.1345i	−0.239735	+	0.415234i
$855$		0			0
$856$	−24.4667	+	6.55583i	−0.836254	+	0.224074i
$857$	−23.7142			−0.810060			−0.405030	−	0.914303i	$-0.632739\pi$
$857$	−23.7142			−0.810060			−0.405030	+	0.914303i	$0.632739\pi$
$858$	31.7056	−	8.49550i	1.08241	−	0.290032i
$859$	−1.55152	+	1.55152i	−0.0529373	+	0.0529373i	−0.733080	−	0.680143i	$-0.761918\pi$
$859$	−1.55152	+	1.55152i	−0.0529373	+	0.0529373i	0.680143	+	0.733080i	$0.261918\pi$
$860$		0			0
$861$	0.574833			0.0195903
$862$	−14.1148	−	14.1148i	−0.480753	−	0.480753i
$863$	10.4349	−	38.9434i	0.355207	−	1.32565i	−0.525018	−	0.851091i	$-0.675941\pi$
$863$	10.4349	−	38.9434i	0.355207	−	1.32565i	0.880224	−	0.474558i	$-0.157392\pi$
$864$	0.592573	+	2.21151i	0.0201597	+	0.0752372i
$865$		0			0
$866$	31.6988	+	8.49368i	1.07717	+	0.288627i
$867$	11.7886	+	3.15873i	0.400360	+	0.107276i
$868$	0.274286	−	0.158359i	0.00930986	−	0.00537505i
$869$	−23.1899	+	6.21371i	−0.786663	+	0.210786i
$870$		0			0
$871$	−52.2180	−	13.9918i	−1.76934	−	0.474094i
$872$	−5.84175	+	21.8017i	−0.197827	+	0.738299i
$873$	−36.1642	+	20.8794i	−1.22397	+	0.706660i
$874$	9.11358	−	9.11358i	0.308271	−	0.308271i
$875$		0			0
$876$	−0.192310	+	0.111030i	−0.00649755	+	0.00375136i
$877$	−5.84034	+	5.84034i	−0.197214	+	0.197214i	−0.798805	−	0.601590i	$-0.794534\pi$
$877$	−5.84034	+	5.84034i	−0.197214	+	0.197214i	0.601590	+	0.798805i	$0.294534\pi$
$878$	−11.5997	+	11.5997i	−0.391472	+	0.391472i
$879$	−8.39676	−	14.5436i	−0.283216	−	0.490544i
$880$		0			0
$881$	−32.5692	−	18.8038i	−1.09728	−	0.633517i	−0.161777	−	0.986827i	$-0.551723\pi$
$881$	−32.5692	−	18.8038i	−1.09728	−	0.633517i	−0.935506	+	0.353311i	$0.885056\pi$
$882$		−	14.4636i		−	0.487014i
$883$	−11.9594	+	20.7143i	−0.402466	+	0.697091i	−0.994023	−	0.109172i	$-0.965180\pi$
$883$	−11.9594	+	20.7143i	−0.402466	+	0.697091i	0.591557	+	0.806263i	$0.298513\pi$
$884$	0.676934	+	0.390828i	0.0227678	+	0.0131450i
$885$		0			0
$886$	−9.87255	+	36.8448i	−0.331675	+	1.23783i
$887$	21.5121	+	21.5121i	0.722305	+	0.722305i	0.969074	−	0.246769i	$-0.0793690\pi$
$887$	21.5121	+	21.5121i	0.722305	+	0.722305i	−0.246769	+	0.969074i	$0.579369\pi$
$888$	−12.6753	+	5.33386i	−0.425356	+	0.178993i
$889$			0.898159i			0.0301233i
$890$		0			0
$891$	−14.0754	−	8.12641i	−0.471542	−	0.272245i
$892$	0.979477	−	0.262450i	0.0327953	−	0.00878748i
$893$	−14.8035	−	8.54683i	−0.495382	−	0.286009i
$894$	6.76804	−	6.76804i	0.226357	−	0.226357i
$895$		0			0
$896$	14.0015	+	14.0015i	0.467759	+	0.467759i
$897$	−18.8160	−	5.04174i	−0.628249	−	0.168339i
$898$	−37.3214	−	37.3214i	−1.24543	−	1.24543i
$899$	−8.65834			−0.288772
$900$		0			0
$901$	−15.3668	+	4.11751i	−0.511941	+	0.137174i
$902$		−	2.94197i		−	0.0979567i
$903$	−5.08139	−	8.80122i	−0.169098	−	0.292886i
$904$	17.7075	−	10.2234i	0.588944	−	0.340027i
$905$		0			0
$906$	−6.41898	−	23.9559i	−0.213256	−	0.795883i
$907$	15.3447	−	26.5778i	0.509512	−	0.882500i	−0.490428	−	0.871482i	$-0.663159\pi$
$907$	15.3447	−	26.5778i	0.509512	−	0.882500i	0.999939	−	0.0110183i	$-0.00350730\pi$
$908$	−0.307114	−	0.531937i	−0.0101919	−	0.0176530i
$909$	8.00116	+	13.8584i	0.265382	+	0.459655i
$910$		0			0
$911$	−2.31494	−	2.31494i	−0.0766975	−	0.0766975i	0.667717	−	0.744415i	$-0.267271\pi$
$911$	−2.31494	−	2.31494i	−0.0766975	−	0.0766975i	−0.744415	+	0.667717i	$0.767271\pi$
$912$	6.44985	+	3.72382i	0.213576	+	0.123308i
$913$	−18.6100	−	4.98654i	−0.615902	−	0.165030i
$914$		−	59.6829i		−	1.97413i
$915$		0			0
$916$	0.908266	−	0.524388i	0.0300100	−	0.0173263i
$917$			26.1861i			0.864742i
$918$	2.37229	+	8.85349i	0.0782971	+	0.292209i
$919$	19.7684	+	19.7684i	0.652098	+	0.652098i	0.953498	−	0.301400i	$-0.0974538\pi$
$919$	19.7684	+	19.7684i	0.652098	+	0.652098i	−0.301400	+	0.953498i	$0.597454\pi$
$920$		0			0
$921$	−2.89353	+	5.01175i	−0.0953452	+	0.165143i
$922$	−11.3443	−	42.3373i	−0.373603	−	1.39431i
$923$	−62.4069	+	36.0306i	−2.05415	+	1.18596i
$924$	−0.596383			−0.0196196
$925$		0			0
$926$	−6.13852			−0.201724
$927$	−25.6067	+	14.7840i	−0.841034	+	0.485571i
$928$	0.566234	+	2.11322i	0.0185876	+	0.0693697i
$929$	−9.70159	+	16.8036i	−0.318299	+	0.551310i	−0.980133	−	0.198340i	$-0.936445\pi$
$929$	−9.70159	+	16.8036i	−0.318299	+	0.551310i	0.661834	+	0.749650i	$0.269778\pi$
$930$		0			0
$931$	−6.60652	−	6.60652i	−0.216520	−	0.216520i
$932$	0.362414	+	1.35255i	0.0118713	+	0.0443041i
$933$			16.1643i			0.529196i
$934$	−12.2717	+	7.08504i	−0.401541	+	0.231830i
$935$		0			0
$936$			37.3046i			1.21934i
$937$	19.7492	+	5.29178i	0.645178	+	0.172875i	0.566548	−	0.824029i	$-0.308279\pi$
$937$	19.7492	+	5.29178i	0.645178	+	0.172875i	0.0786302	+	0.996904i	$0.474945\pi$
$938$	19.1891	+	11.0788i	0.626547	+	0.361737i
$939$	−12.0171	−	12.0171i	−0.392162	−	0.392162i
$940$		0			0
$941$	0.662999	+	1.14835i	0.0216131	+	0.0374351i	0.876630	−	0.481166i	$-0.159786\pi$
$941$	0.662999	+	1.14835i	0.0216131	+	0.0374351i	−0.855017	+	0.518601i	$0.826453\pi$
$942$	−8.20516	−	14.2118i	−0.267339	−	0.463044i
$943$	−0.872970	+	1.51203i	−0.0284278	+	0.0492384i
$944$	−9.02952	−	33.6986i	−0.293886	−	1.09680i
$945$		0			0
$946$	−45.0442	+	26.0063i	−1.46451	+	0.845537i
$947$	7.29012	+	12.6269i	0.236897	+	0.410318i	0.959822	−	0.280608i	$-0.0905362\pi$
$947$	7.29012	+	12.6269i	0.236897	+	0.410318i	−0.722925	+	0.690926i	$0.757203\pi$
$948$		−	0.382677i		−	0.0124288i
$949$	−16.3839	+	4.39006i	−0.531845	+	0.142507i
$950$		0			0
$951$	−16.9440			−0.549447
$952$	4.65741	+	4.65741i	0.150948	+	0.150948i
$953$	−23.9459	−	6.41629i	−0.775684	−	0.207844i	−0.150803	−	0.988564i	$-0.548186\pi$
$953$	−23.9459	−	6.41629i	−0.775684	−	0.207844i	−0.624881	+	0.780720i	$0.714853\pi$
$954$	26.1141	+	26.1141i	0.845474	+	0.845474i
$955$		0			0
$956$	1.17367	−	1.17367i	0.0379591	−	0.0379591i
$957$	14.1195	+	8.15188i	0.456418	+	0.263513i
$958$	42.0854	−	11.2767i	1.35972	−	0.364335i
$959$	−2.73772	−	1.58062i	−0.0884057	−	0.0510410i
$960$		0			0
$961$			26.6933i			0.861075i
$962$	50.6186	−	6.95337i	1.63201	−	0.224186i
$963$	15.1162	+	15.1162i	0.487114	+	0.487114i
$964$	−0.673673	+	2.51418i	−0.0216975	+	0.0809763i
$965$		0			0
$966$	6.91453	+	3.99210i	0.222471	+	0.128444i
$967$	−16.6321	+	28.8077i	−0.534853	+	0.926393i	0.464317	+	0.885669i	$0.346300\pi$
$967$	−16.6321	+	28.8077i	−0.534853	+	0.926393i	−0.999170	+	0.0407238i	$0.987034\pi$
$968$		−	32.4007i		−	1.04140i
$969$	2.24075	+	1.29370i	0.0719832	+	0.0415595i
$970$		0			0
$971$	−6.82047	−	11.8134i	−0.218879	−	0.379110i	0.735586	−	0.677431i	$-0.236907\pi$
$971$	−6.82047	−	11.8134i	−0.218879	−	0.379110i	−0.954466	+	0.298321i	$0.903573\pi$
$972$	1.04244	−	1.04244i	0.0334363	−	0.0334363i
$973$	20.2406	−	20.2406i	0.648884	−	0.648884i
$974$	11.0349	−	6.37101i	0.353581	−	0.204140i
$975$		0			0
$976$	17.3892	−	17.3892i	0.556614	−	0.556614i
$977$	6.38040	−	3.68372i	0.204127	−	0.117853i	−0.394452	−	0.918917i	$-0.629066\pi$
$977$	6.38040	−	3.68372i	0.204127	−	0.117853i	0.598579	+	0.801064i	$0.295732\pi$
$978$	1.92299	−	7.17671i	0.0614905	−	0.229486i
$979$	−70.7846	−	18.9667i	−2.26228	−	0.606177i
$980$		0			0
$981$	18.4000	−	4.93027i	0.587467	−	0.157411i
$982$	−46.6885	+	26.9556i	−1.48989	+	0.860189i
$983$	37.1014	+	9.94128i	1.18335	+	0.317078i	0.796254	−	0.604962i	$-0.206812\pi$
$983$	37.1014	+	9.94128i	1.18335	+	0.317078i	0.387095	+	0.922040i	$0.373478\pi$
$984$	−0.931226	−	0.249521i	−0.0296864	−	0.00795445i
$985$		0			0
$986$	2.26684	+	8.45998i	0.0721910	+	0.269421i
$987$	2.74069	−	10.2284i	0.0872370	−	0.325573i
$988$	−0.828826	−	0.828826i	−0.0263685	−	0.0263685i
$989$	30.8674			0.981527
$990$		0			0
$991$	−10.4917	+	10.4917i	−0.333278	+	0.333278i	−0.853830	−	0.520552i	$-0.825726\pi$
$991$	−10.4917	+	10.4917i	−0.333278	+	0.333278i	0.520552	+	0.853830i	$0.325726\pi$
$992$	−1.05112	+	0.281646i	−0.0333730	+	0.00894228i
$993$	26.8246			0.851253
$994$	28.5294	−	7.64444i	0.904899	−	0.242467i
$995$		0			0
$996$	0.153550	−	0.265957i	0.00486542	−	0.00842716i
$997$	−12.3915	−	21.4627i	−0.392443	−	0.679731i	0.600328	−	0.799754i	$-0.295037\pi$
$997$	−12.3915	−	21.4627i	−0.392443	−	0.679731i	−0.992771	+	0.120023i	$0.961703\pi$
$998$	−3.72781	+	3.72781i	−0.118002	+	0.118002i
$999$	21.1610	+	16.0495i	0.669505	+	0.507783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.193.12		68
5.2	odd	4		925.2.t.b.82.12		68
5.3	odd	4		185.2.p.a.82.6	✓	68
5.4	even	2		185.2.u.a.8.6	yes	68
37.14	odd	12		925.2.t.b.643.12		68
185.14	odd	12		185.2.p.a.88.6	yes	68
185.88	even	12		185.2.u.a.162.6	yes	68
185.162	even	12	inner	925.2.y.b.532.12		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.6	✓	68	5.3	odd	4
185.2.p.a.88.6	yes	68	185.14	odd	12
185.2.u.a.8.6	yes	68	5.4	even	2
185.2.u.a.162.6	yes	68	185.88	even	12
925.2.t.b.82.12		68	5.2	odd	4
925.2.t.b.643.12		68	37.14	odd	12
925.2.y.b.193.12		68	1.1	even	1	trivial
925.2.y.b.532.12		68	185.162	even	12	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+(1.25283 - 0.723320i) q^{2} +(0.212077 + 0.791482i) q^{3} +(0.0463849 - 0.0803411i) q^{4} +(0.838191 + 0.838191i) q^{6} +(-0.425785 - 1.58905i) q^{7} +2.75908i q^{8} +(2.01661 - 1.16429i) q^{9} -4.76900i q^{11} +(0.0734257 + 0.0196744i) q^{12} +(5.02850 + 2.90320i) q^{13} +(-1.68283 - 1.68283i) q^{14} +(2.08847 + 3.61733i) q^{16} +(0.725557 + 1.25670i) q^{17} +(1.68431 - 2.91731i) q^{18} +(-0.563197 - 2.10188i) q^{19} +(1.16741 - 0.674003i) q^{21} +(-3.44951 - 5.97473i) q^{22} +4.09430i q^{23} +(-2.18376 + 0.585137i) q^{24} +8.39979 q^{26} +(3.08741 + 3.08741i) q^{27} +(-0.147416 - 0.0395000i) q^{28} +(2.95018 + 2.95018i) q^{29} +(-1.46743 + 1.46743i) q^{31} +(0.454116 + 0.262184i) q^{32} +(3.77458 - 1.01139i) q^{33} +(1.81799 + 1.04962i) q^{34} -0.216022i q^{36} +(6.02617 - 0.827803i) q^{37} +(-2.22592 - 2.22592i) q^{38} +(-1.23141 + 4.59567i) q^{39} +(0.369301 + 0.213216i) q^{41} +(0.975040 - 1.68882i) q^{42} -7.53912i q^{43} +(-0.383146 - 0.221210i) q^{44} +(2.96149 + 5.12945i) q^{46} +(5.55465 - 5.55465i) q^{47} +(-2.42014 + 2.42014i) q^{48} +(3.71838 - 2.14681i) q^{49} +(-0.840783 + 0.840783i) q^{51} +(0.466493 - 0.269330i) q^{52} +(-2.83749 + 10.5896i) q^{53} +(6.10117 + 1.63480i) q^{54} +(4.38432 - 1.17477i) q^{56} +(1.54416 - 0.891520i) q^{57} +(5.82999 + 1.56214i) q^{58} +(-8.06779 - 2.16176i) q^{59} +(-1.52382 - 5.68696i) q^{61} +(-0.777013 + 2.89985i) q^{62} +(-2.70876 - 2.70876i) q^{63} -7.59529 q^{64} +(3.99733 - 3.99733i) q^{66} +(-8.99317 + 2.40971i) q^{67} +0.134620 q^{68} +(-3.24056 + 0.868307i) q^{69} +(-6.20532 + 10.7479i) q^{71} +(3.21236 + 5.56398i) q^{72} +(-2.06563 + 2.06563i) q^{73} +(6.95099 - 5.39595i) q^{74} +(-0.194991 - 0.0522477i) q^{76} +(-7.57818 + 2.03057i) q^{77} +(1.78140 + 6.64828i) q^{78} +(-1.30294 - 4.86264i) q^{79} +(1.70401 - 2.95143i) q^{81} +0.616894 q^{82} +(1.04562 - 3.90229i) q^{83} -0.125054i q^{84} +(-5.45320 - 9.44522i) q^{86} +(-1.70935 + 2.96068i) q^{87} +13.1580 q^{88} +(3.97708 - 14.8427i) q^{89} +(2.47228 - 9.22669i) q^{91} +(0.328940 + 0.189914i) q^{92} +(-1.47265 - 0.850234i) q^{93} +(2.94123 - 10.9768i) q^{94} +(-0.111207 + 0.415028i) q^{96} -17.9332 q^{97} +(3.10566 - 5.37917i) q^{98} +(-5.55249 - 9.61720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

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