LMFDB - Embedded newform 625.2.e.j.374.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [625,2,Mod(124,625)] 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("625.124"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(625, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,6,0,14,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			374.3
Character	$\chi$	$=$	625.374
Dual form			625.2.e.j.249.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.989484 - 1.36191i) q^{2} +(0.675574 + 0.219507i) q^{3} +(-0.257680 + 0.793058i) q^{4} +(-0.369521 - 1.13727i) q^{6} -4.59110i q^{7} +(-1.86699 + 0.606623i) q^{8} +(-2.01883 - 1.46677i) q^{9} +(-3.16713 + 2.30105i) q^{11} +(-0.348164 + 0.479206i) q^{12} +(0.336765 - 0.463518i) q^{13} +(-6.25266 + 4.54282i) q^{14} +(4.02276 + 2.92270i) q^{16} +(0.221226 - 0.0718808i) q^{17} +4.20081i q^{18} +(1.71507 + 5.27846i) q^{19} +(1.00778 - 3.10163i) q^{21} +(6.26765 + 2.03648i) q^{22} +(-2.89935 - 3.99061i) q^{23} -1.39445 q^{24} -0.964492 q^{26} +(-2.29449 - 3.15809i) q^{27} +(3.64101 + 1.18304i) q^{28} +(-1.27643 + 3.92845i) q^{29} +(-1.08011 - 3.32424i) q^{31} -4.44444i q^{32} +(-2.64473 + 0.859324i) q^{33} +(-0.316795 - 0.230165i) q^{34} +(1.68345 - 1.22310i) q^{36} +(-3.18373 + 4.38203i) q^{37} +(5.49173 - 7.55872i) q^{38} +(0.329255 - 0.239218i) q^{39} +(-8.43214 - 6.12630i) q^{41} +(-5.22132 + 1.69651i) q^{42} -1.38833i q^{43} +(-1.00876 - 3.10465i) q^{44} +(-2.56598 + 7.89729i) q^{46} +(0.875370 + 0.284425i) q^{47} +(2.07611 + 2.85753i) q^{48} -14.0782 q^{49} +0.165233 q^{51} +(0.280819 + 0.386514i) q^{52} +(-1.17092 - 0.380455i) q^{53} +(-2.03067 + 6.24976i) q^{54} +(2.78507 + 8.57157i) q^{56} +3.94246i q^{57} +(6.61320 - 2.14876i) q^{58} +(3.64689 + 2.64962i) q^{59} +(9.43214 - 6.85285i) q^{61} +(-3.45856 + 4.76029i) q^{62} +(-6.73409 + 9.26868i) q^{63} +(1.99259 - 1.44770i) q^{64} +(3.78724 + 2.75159i) q^{66} +(2.80987 - 0.912982i) q^{67} +0.193968i q^{68} +(-1.08276 - 3.33238i) q^{69} +(0.990558 - 3.04862i) q^{71} +(4.65893 + 1.51378i) q^{72} +(-6.04961 - 8.32657i) q^{73} +9.11816 q^{74} -4.62806 q^{76} +(10.5644 + 14.5406i) q^{77} +(-0.651586 - 0.211713i) q^{78} +(2.97123 - 9.14449i) q^{79} +(1.45651 + 4.48267i) q^{81} +17.5457i q^{82} +(-9.97030 + 3.23955i) q^{83} +(2.20009 + 1.59846i) q^{84} +(-1.89077 + 1.37373i) q^{86} +(-1.72465 + 2.37377i) q^{87} +(4.51714 - 6.21731i) q^{88} +(5.87207 - 4.26631i) q^{89} +(-2.12806 - 1.54612i) q^{91} +(3.91189 - 1.27105i) q^{92} -2.48286i q^{93} +(-0.478804 - 1.47361i) q^{94} +(0.975587 - 3.00255i) q^{96} +(-7.91252 - 2.57093i) q^{97} +(13.9302 + 19.1733i) q^{98} +9.76903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} + 14 q^{6} + 24 q^{9} - 6 q^{11} + 2 q^{14} + 2 q^{16} - 20 q^{19} + 14 q^{21} - 20 q^{24} + 44 q^{26} - 16 q^{31} + 12 q^{34} + 2 q^{36} - 2 q^{39} - 16 q^{41} + 62 q^{44} + 84 q^{46} + 16 q^{49}+ \cdots + 88 q^{99}+O(q^{100}) $ 32 * q + 6 * q^4 + 14 * q^6 + 24 * q^9 - 6 * q^11 + 2 * q^14 + 2 * q^16 - 20 * q^19 + 14 * q^21 - 20 * q^24 + 44 * q^26 - 16 * q^31 + 12 * q^34 + 2 * q^36 - 2 * q^39 - 16 * q^41 + 62 * q^44 + 84 * q^46 + 16 * q^49 - 56 * q^51 - 100 * q^54 + 70 * q^56 + 30 * q^59 + 34 * q^61 - 74 * q^64 + 88 * q^66 + 18 * q^69 - 26 * q^71 + 72 * q^74 - 40 * q^76 + 110 * q^79 - 38 * q^81 - 118 * q^84 + 14 * q^86 - 56 * q^91 - 8 * q^94 - 86 * q^96 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.989484	−	1.36191i	−0.699671	−	0.963014i	−0.999958	−	0.00916528i	$-0.997083\pi$
$2$	−0.989484	−	1.36191i	−0.699671	−	0.963014i	0.300287	−	0.953849i	$-0.402917\pi$
$3$	0.675574	+	0.219507i	0.390043	+	0.126733i	0.497472	−	0.867480i	$-0.334262\pi$
$3$	0.675574	+	0.219507i	0.390043	+	0.126733i	−0.107429	+	0.994213i	$0.534262\pi$
$4$	−0.257680	+	0.793058i	−0.128840	+	0.396529i
$5$		0			0
$5$		0			0
$6$	−0.369521	−	1.13727i	−0.150856	−	0.464288i
$7$		−	4.59110i		−	1.73527i	−0.497198	−	0.867637i	$-0.665638\pi$
$7$		−	4.59110i		−	1.73527i	0.497198	−	0.867637i	$-0.334362\pi$
$8$	−1.86699	+	0.606623i	−0.660082	+	0.214474i
$9$	−2.01883	−	1.46677i	−0.672945	−	0.488923i
$10$		0			0
$11$	−3.16713	+	2.30105i	−0.954926	+	0.693794i	−0.951967	−	0.306201i	$-0.900942\pi$
$11$	−3.16713	+	2.30105i	−0.954926	+	0.693794i	−0.00295900	+	0.999996i	$0.500942\pi$
$12$	−0.348164	+	0.479206i	−0.100506	+	0.138335i
$13$	0.336765	−	0.463518i	0.0934019	−	0.128557i	−0.759758	−	0.650205i	$-0.774683\pi$
$13$	0.336765	−	0.463518i	0.0934019	−	0.128557i	0.853160	+	0.521649i	$0.174683\pi$
$14$	−6.25266	+	4.54282i	−1.67109	+	1.21412i
$15$		0			0
$16$	4.02276	+	2.92270i	1.00569	+	0.730676i
$17$	0.221226	−	0.0718808i	0.0536553	−	0.0174337i	−0.282066	−	0.959395i	$-0.591020\pi$
$17$	0.221226	−	0.0718808i	0.0536553	−	0.0174337i	0.335722	+	0.941961i	$0.391020\pi$
$18$			4.20081i			0.990140i
$19$	1.71507	+	5.27846i	0.393465	+	1.21096i	0.930151	+	0.367178i	$0.119676\pi$
$19$	1.71507	+	5.27846i	0.393465	+	1.21096i	−0.536685	+	0.843782i	$0.680324\pi$
$20$		0			0
$21$	1.00778	−	3.10163i	0.219916	−	0.676831i
$22$	6.26765	+	2.03648i	1.33627	+	0.434179i
$23$	−2.89935	−	3.99061i	−0.604556	−	0.832100i	0.391560	−	0.920153i	$-0.371936\pi$
$23$	−2.89935	−	3.99061i	−0.604556	−	0.832100i	−0.996116	+	0.0880529i	$0.971936\pi$
$24$	−1.39445			−0.284641
$25$		0			0
$26$	−0.964492			−0.189152
$27$	−2.29449	−	3.15809i	−0.441574	−	0.607775i
$28$	3.64101	+	1.18304i	0.688086	+	0.223573i
$29$	−1.27643	+	3.92845i	−0.237028	+	0.729496i	0.759818	+	0.650135i	$0.225288\pi$
$29$	−1.27643	+	3.92845i	−0.237028	+	0.729496i	−0.996846	+	0.0793604i	$0.974712\pi$
$30$		0			0
$31$	−1.08011	−	3.32424i	−0.193994	−	0.597051i	−0.999987	−	0.00512633i	$-0.998368\pi$
$31$	−1.08011	−	3.32424i	−0.193994	−	0.597051i	0.805993	−	0.591925i	$-0.201632\pi$
$32$		−	4.44444i		−	0.785674i
$33$	−2.64473	+	0.859324i	−0.460388	+	0.149589i
$34$	−0.316795	−	0.230165i	−0.0543299	−	0.0394730i
$35$		0			0
$36$	1.68345	−	1.22310i	0.280574	−	0.203849i
$37$	−3.18373	+	4.38203i	−0.523402	+	0.720401i	−0.986107	−	0.166112i	$-0.946879\pi$
$37$	−3.18373	+	4.38203i	−0.523402	+	0.720401i	0.462705	+	0.886512i	$0.346879\pi$
$38$	5.49173	−	7.55872i	0.890876	−	1.22619i
$39$	0.329255	−	0.239218i	0.0527230	−	0.0383055i
$40$		0			0
$41$	−8.43214	−	6.12630i	−1.31688	−	0.956768i	−0.999965	−	0.00831339i	$-0.997354\pi$
$41$	−8.43214	−	6.12630i	−1.31688	−	0.956768i	−0.316913	−	0.948455i	$-0.602646\pi$
$42$	−5.22132	+	1.69651i	−0.805666	+	0.261777i
$43$		−	1.38833i		−	0.211718i	−0.994381	−	0.105859i	$-0.966241\pi$
$43$		−	1.38833i		−	0.211718i	0.994381	−	0.105859i	$-0.0337592\pi$
$44$	−1.00876	−	3.10465i	−0.152077	−	0.468044i
$45$		0			0
$46$	−2.56598	+	7.89729i	−0.378334	+	1.16439i
$47$	0.875370	+	0.284425i	0.127686	+	0.0414876i	0.372163	−	0.928167i	$-0.378616\pi$
$47$	0.875370	+	0.284425i	0.127686	+	0.0414876i	−0.244477	+	0.969655i	$0.578616\pi$
$48$	2.07611	+	2.85753i	0.299661	+	0.412448i
$49$	−14.0782			−2.01118
$50$		0			0
$51$	0.165233			0.0231373
$52$	0.280819	+	0.386514i	0.0389425	+	0.0535998i
$53$	−1.17092	−	0.380455i	−0.160838	−	0.0522595i	0.227491	−	0.973780i	$-0.426948\pi$
$53$	−1.17092	−	0.380455i	−0.160838	−	0.0522595i	−0.388329	+	0.921521i	$0.626948\pi$
$54$	−2.03067	+	6.24976i	−0.276339	+	0.850485i
$55$		0			0
$56$	2.78507	+	8.57157i	0.372171	+	1.14542i
$57$			3.94246i			0.522191i
$58$	6.61320	−	2.14876i	0.868356	−	0.282146i
$59$	3.64689	+	2.64962i	0.474785	+	0.344951i	0.799303	−	0.600928i	$-0.205202\pi$
$59$	3.64689	+	2.64962i	0.474785	+	0.344951i	−0.324518	+	0.945879i	$0.605202\pi$
$60$		0			0
$61$	9.43214	−	6.85285i	1.20766	−	0.877417i	0.212645	−	0.977129i	$-0.431792\pi$
$61$	9.43214	−	6.85285i	1.20766	−	0.877417i	0.995016	+	0.0997121i	$0.0317922\pi$
$62$	−3.45856	+	4.76029i	−0.439237	+	0.604558i
$63$	−6.73409	+	9.26868i	−0.848416	+	1.16774i
$64$	1.99259	−	1.44770i	0.249074	−	0.180963i
$65$		0			0
$66$	3.78724	+	2.75159i	0.466177	+	0.338697i
$67$	2.80987	−	0.912982i	0.343280	−	0.111539i	−0.132303	−	0.991209i	$-0.542237\pi$
$67$	2.80987	−	0.912982i	0.343280	−	0.111539i	0.475583	+	0.879671i	$0.342237\pi$
$68$			0.193968i			0.0235220i
$69$	−1.08276	−	3.33238i	−0.130348	−	0.401171i
$70$		0			0
$71$	0.990558	−	3.04862i	0.117558	−	0.361805i	−0.874914	−	0.484278i	$-0.839082\pi$
$71$	0.990558	−	3.04862i	0.117558	−	0.361805i	0.992472	+	0.122473i	$0.0390824\pi$
$72$	4.65893	+	1.51378i	0.549060	+	0.178400i
$73$	−6.04961	−	8.32657i	−0.708053	−	0.974551i	−0.999837	−	0.0180667i	$-0.994249\pi$
$73$	−6.04961	−	8.32657i	−0.708053	−	0.974551i	0.291784	−	0.956484i	$-0.405751\pi$
$74$	9.11816			1.05996
$75$		0			0
$76$	−4.62806			−0.530875
$77$	10.5644	+	14.5406i	1.20392	+	1.65706i
$78$	−0.651586	−	0.211713i	−0.0737775	−	0.0239718i
$79$	2.97123	−	9.14449i	0.334289	−	1.02884i	−0.632782	−	0.774330i	$-0.718087\pi$
$79$	2.97123	−	9.14449i	0.334289	−	1.02884i	0.967071	−	0.254506i	$-0.0819129\pi$
$80$		0			0
$81$	1.45651	+	4.48267i	0.161834	+	0.498074i
$82$			17.5457i			1.93759i
$83$	−9.97030	+	3.23955i	−1.09438	+	0.355587i	−0.799939	−	0.600082i	$-0.795135\pi$
$83$	−9.97030	+	3.23955i	−1.09438	+	0.355587i	−0.294445	+	0.955669i	$0.595135\pi$
$84$	2.20009	+	1.59846i	0.240049	+	0.174406i
$85$		0			0
$86$	−1.89077	+	1.37373i	−0.203887	+	0.148133i
$87$	−1.72465	+	2.37377i	−0.184902	+	0.254495i
$88$	4.51714	−	6.21731i	0.481529	−	0.662768i
$89$	5.87207	−	4.26631i	0.622438	−	0.452228i	−0.231334	−	0.972874i	$-0.574309\pi$
$89$	5.87207	−	4.26631i	0.622438	−	0.452228i	0.853772	+	0.520646i	$0.174309\pi$
$90$		0			0
$91$	−2.12806	−	1.54612i	−0.223081	−	0.162078i
$92$	3.91189	−	1.27105i	0.407843	−	0.132516i
$93$		−	2.48286i		−	0.257461i
$94$	−0.478804	−	1.47361i	−0.0493848	−	0.151991i
$95$		0			0
$96$	0.975587	−	3.00255i	0.0995704	−	0.306446i
$97$	−7.91252	−	2.57093i	−0.803394	−	0.261039i	−0.121597	−	0.992580i	$-0.538801\pi$
$97$	−7.91252	−	2.57093i	−0.803394	−	0.261039i	−0.681797	+	0.731541i	$0.738801\pi$
$98$	13.9302	+	19.1733i	1.40716	+	1.93679i
$99$	9.76903			0.981824
$100$		0			0
$101$	−3.56513			−0.354744			−0.177372	−	0.984144i	$-0.556760\pi$
$101$	−3.56513			−0.354744			−0.177372	+	0.984144i	$0.556760\pi$
$102$	−0.163495	−	0.225032i	−0.0161885	−	0.0222815i
$103$	0.379779	+	0.123398i	0.0374207	+	0.0121587i	0.327668	−	0.944793i	$-0.393737\pi$
$103$	0.379779	+	0.123398i	0.0374207	+	0.0121587i	−0.290247	+	0.956952i	$0.593737\pi$
$104$	−0.347558	+	1.06967i	−0.0340809	+	0.104890i
$105$		0			0
$106$	0.640462	+	1.97114i	0.0622071	+	0.191454i
$107$		−	1.64372i		−	0.158904i	−0.996839	−	0.0794522i	$-0.974683\pi$
$107$		−	1.64372i		−	0.158904i	0.996839	−	0.0794522i	$-0.0253171\pi$
$108$	3.09579	−	1.00588i	0.297893	−	0.0967913i
$109$	0.0606078	+	0.0440342i	0.00580518	+	0.00421771i	0.590684	−	0.806903i	$-0.298858\pi$
$109$	0.0606078	+	0.0440342i	0.00580518	+	0.00421771i	−0.584879	+	0.811121i	$0.698858\pi$
$110$		0			0
$111$	−3.11273	+	2.26153i	−0.295447	+	0.214655i
$112$	13.4184	−	18.4689i	1.26792	−	1.74515i
$113$	−8.30708	+	11.4337i	−0.781464	+	1.07559i	0.213655	+	0.976909i	$0.431463\pi$
$113$	−8.30708	+	11.4337i	−0.781464	+	1.07559i	−0.995119	+	0.0986840i	$0.968537\pi$
$114$	5.36926	−	3.90100i	0.502878	−	0.365362i
$115$		0			0
$116$	−2.78658	−	2.02457i	−0.258728	−	0.187977i
$117$	−1.35975	+	0.441808i	−0.125709	+	0.0408452i
$118$		−	7.58848i		−	0.698576i
$119$	−0.330012	−	1.01567i	−0.0302522	−	0.0931066i
$120$		0			0
$121$	1.33667	−	4.11386i	0.121516	−	0.373987i
$122$	−18.6659	−	6.06492i	−1.68993	−	0.549092i
$123$	−4.35176	−	5.98969i	−0.392385	−	0.540072i
$124$	2.91464			0.261742
$125$		0			0
$126$	19.2864			1.71817
$127$	−6.94318	−	9.55647i	−0.616108	−	0.848000i	0.380955	−	0.924594i	$-0.375595\pi$
$127$	−6.94318	−	9.55647i	−0.616108	−	0.848000i	−0.997062	+	0.0765941i	$0.975595\pi$
$128$	−12.3971	−	4.02807i	−1.09576	−	0.356034i
$129$	0.304748	−	0.937917i	0.0268315	−	0.0825790i
$130$		0			0
$131$	−5.17210	−	15.9181i	−0.451888	−	1.39077i	−0.874750	−	0.484575i	$-0.838974\pi$
$131$	−5.17210	−	15.9181i	−0.451888	−	1.39077i	0.422862	−	0.906194i	$-0.361026\pi$
$132$		−	2.31885i		−	0.201830i
$133$	24.2339	−	7.87408i	2.10135	−	0.682770i
$134$	−4.02372	−	2.92340i	−0.347596	−	0.252544i
$135$		0			0
$136$	−0.369424	+	0.268402i	−0.0316778	+	0.0230153i
$137$	6.12598	−	8.43168i	0.523378	−	0.720367i	−0.462726	−	0.886502i	$-0.653128\pi$
$137$	6.12598	−	8.43168i	0.523378	−	0.720367i	0.986103	+	0.166134i	$0.0531285\pi$
$138$	−3.46702	+	4.77195i	−0.295133	+	0.406215i
$139$	5.38800	−	3.91461i	0.457004	−	0.332033i	−0.335351	−	0.942093i	$-0.608855\pi$
$139$	5.38800	−	3.91461i	0.457004	−	0.332033i	0.792355	+	0.610060i	$0.208855\pi$
$140$		0			0
$141$	0.528944	+	0.384300i	0.0445451	+	0.0323639i
$142$	−5.13208	+	1.66752i	−0.430675	+	0.139935i
$143$			2.24294i			0.187564i
$144$	−3.83435	−	11.8009i	−0.319529	−	0.983409i
$145$		0			0
$146$	−5.35403	+	16.4780i	−0.443103	+	1.36373i
$147$	−9.51089	−	3.09027i	−0.784445	−	0.254882i
$148$	−2.65482	−	3.65404i	−0.218225	−	0.300360i
$149$	12.0316			0.985667			0.492834	−	0.870124i	$-0.335961\pi$
$149$	12.0316			0.985667			0.492834	+	0.870124i	$0.335961\pi$
$150$		0			0
$151$	−1.54218			−0.125501			−0.0627505	−	0.998029i	$-0.519987\pi$
$151$	−1.54218			−0.125501			−0.0627505	+	0.998029i	$0.519987\pi$
$152$	−6.40407	−	8.81445i	−0.519439	−	0.714946i
$153$	−0.552052	−	0.179373i	−0.0446308	−	0.0145014i
$154$	9.34970	−	28.7754i	0.753420	−	2.31879i
$155$		0			0
$156$	0.104871	+	0.322760i	0.00839641	+	0.0258415i
$157$		−	9.82482i		−	0.784106i	−0.919943	−	0.392053i	$-0.871765\pi$
$157$		−	9.82482i		−	0.784106i	0.919943	−	0.392053i	$-0.128235\pi$
$158$	−15.3939	+	5.00179i	−1.22468	+	0.397921i
$159$	−0.707530	−	0.514051i	−0.0561108	−	0.0407669i
$160$		0			0
$161$	−18.3213	+	13.3112i	−1.44392	+	1.04907i
$162$	4.66379	−	6.41915i	0.366422	−	0.504336i
$163$	3.28047	−	4.51518i	0.256946	−	0.353656i	−0.660982	−	0.750401i	$-0.729860\pi$
$163$	3.28047	−	4.51518i	0.256946	−	0.353656i	0.917929	+	0.396745i	$0.129860\pi$
$164$	7.03131	−	5.10854i	0.549053	−	0.398910i
$165$		0			0
$166$	14.2774	+	10.3732i	1.10814	+	0.805113i
$167$	20.7908	−	6.75534i	1.60884	−	0.522744i	0.639568	−	0.768735i	$-0.279113\pi$
$167$	20.7908	−	6.75534i	1.60884	−	0.522744i	0.969272	+	0.245991i	$0.0791133\pi$
$168$			6.40207i			0.493930i
$169$	3.91578	+	12.0515i	0.301214	+	0.927042i
$170$		0			0
$171$	4.27982	−	13.1719i	0.327286	−	1.00728i
$172$	1.10102	+	0.357744i	0.0839522	+	0.0272777i
$173$	13.7768	+	18.9622i	1.04743	+	1.44167i	0.891013	+	0.453977i	$0.149995\pi$
$173$	13.7768	+	18.9622i	1.04743	+	1.44167i	0.156420	+	0.987691i	$0.450005\pi$
$174$	4.93937			0.374453
$175$		0			0
$176$	−19.4659			−1.46730
$177$	1.88213	+	2.59053i	0.141470	+	0.194716i
$178$	−11.6206	−	3.77577i	−0.871004	−	0.283006i
$179$	1.95259	−	6.00947i	0.145944	−	0.449169i	−0.851187	−	0.524862i	$-0.824117\pi$
$179$	1.95259	−	6.00947i	0.145944	−	0.449169i	0.997131	+	0.0756932i	$0.0241170\pi$
$180$		0			0
$181$	−4.12158	−	12.6849i	−0.306355	−	0.942863i	−0.979168	−	0.203051i	$-0.934914\pi$
$181$	−4.12158	−	12.6849i	−0.306355	−	0.942863i	0.672813	−	0.739812i	$-0.265086\pi$
$182$			4.42808i			0.328231i
$183$	7.87636	−	2.55918i	0.582237	−	0.189180i
$184$	7.83387	+	5.69164i	0.577520	+	0.419593i
$185$		0			0
$186$	−3.38143	+	2.45675i	−0.247938	+	0.180138i
$187$	−0.535251	+	0.736710i	−0.0391414	+	0.0538736i
$188$	−0.451131	+	0.620928i	−0.0329021	+	0.0452859i
$189$	−14.4991	+	10.5342i	−1.05466	+	0.766253i
$190$		0			0
$191$	2.24974	+	1.63453i	0.162785	+	0.118270i	0.666196	−	0.745777i	$-0.267922\pi$
$191$	2.24974	+	1.63453i	0.162785	+	0.118270i	−0.503410	+	0.864047i	$0.667922\pi$
$192$	1.66393	−	0.540642i	0.120084	−	0.0390175i
$193$		−	22.5667i		−	1.62438i	−0.583391	−	0.812192i	$-0.698274\pi$
$193$		−	22.5667i		−	1.62438i	0.583391	−	0.812192i	$-0.301726\pi$
$194$	4.32793	+	13.3200i	0.310728	+	0.956321i
$195$		0			0
$196$	3.62768	−	11.1649i	0.259120	−	0.797490i
$197$	1.20957	+	0.393014i	0.0861786	+	0.0280011i	0.351789	−	0.936079i	$-0.385573\pi$
$197$	1.20957	+	0.393014i	0.0861786	+	0.0280011i	−0.265610	+	0.964080i	$0.585573\pi$
$198$	−9.66629	−	13.3045i	−0.686954	−	0.945511i
$199$	8.62648			0.611515			0.305757	−	0.952109i	$-0.401090\pi$
$199$	8.62648			0.611515			0.305757	+	0.952109i	$0.401090\pi$
$200$		0			0
$201$	2.09868			0.148030
$202$	3.52764	+	4.85538i	0.248204	+	0.341623i
$203$	18.0359	+	5.86023i	1.26588	+	0.411308i
$204$	−0.0425773	+	0.131039i	−0.00298101	+	0.00917459i
$205$		0			0
$206$	−0.207729	−	0.639324i	−0.0144732	−	0.0445438i
$207$			12.3091i			0.855538i
$208$	2.70945	−	0.880354i	0.187867	−	0.0610415i
$209$	−17.5779	−	12.7711i	−1.21589	−	0.883394i
$210$		0			0
$211$	17.0149	−	12.3621i	1.17136	−	0.851039i	0.180185	−	0.983633i	$-0.442330\pi$
$211$	17.0149	−	12.3621i	1.17136	−	0.851039i	0.991171	+	0.132593i	$0.0423305\pi$
$212$	0.603445	−	0.830571i	0.0414448	−	0.0570439i
$213$	1.33839	−	1.84214i	0.0917050	−	0.126221i
$214$	−2.23859	+	1.62643i	−0.153027	+	0.111181i
$215$		0			0
$216$	6.19957	+	4.50425i	0.421827	+	0.306475i
$217$	−15.2619	+	4.95890i	−1.03605	+	0.336632i
$218$		−	0.126113i		−	0.00854148i
$219$	−2.25921	−	6.95314i	−0.152663	−	0.469850i
$220$		0			0
$221$	0.0411833	−	0.126749i	0.00277029	−	0.00852608i
$222$	6.15999	+	2.00150i	0.413432	+	0.134332i
$223$	−3.72384	−	5.12542i	−0.249367	−	0.343224i	0.665923	−	0.746021i	$-0.268038\pi$
$223$	−3.72384	−	5.12542i	−0.249367	−	0.343224i	−0.915289	+	0.402797i	$0.868038\pi$
$224$	−20.4049			−1.36336
$225$		0			0
$226$	23.7914			1.58258
$227$	6.61988	+	9.11148i	0.439377	+	0.604750i	0.970073	−	0.242812i	$-0.0780697\pi$
$227$	6.61988	+	9.11148i	0.439377	+	0.604750i	−0.530697	+	0.847562i	$0.678070\pi$
$228$	−3.12660	−	1.01589i	−0.207064	−	0.0672792i
$229$	−4.64788	+	14.3047i	−0.307140	+	0.945281i	0.671729	+	0.740797i	$0.265552\pi$
$229$	−4.64788	+	14.3047i	−0.307140	+	0.945281i	−0.978870	+	0.204484i	$0.934448\pi$
$230$		0			0
$231$	3.94525	+	12.1422i	0.259578	+	0.798900i
$232$		−	8.10872i		−	0.532363i
$233$	−7.44438	+	2.41883i	−0.487698	+	0.158463i	−0.542536	−	0.840033i	$-0.682536\pi$
$233$	−7.44438	+	2.41883i	−0.487698	+	0.158463i	0.0548381	+	0.998495i	$0.482536\pi$
$234$	1.94715	+	1.41469i	0.127289	+	0.0924810i
$235$		0			0
$236$	−3.04103	+	2.20944i	−0.197954	+	0.143822i
$237$	4.01456	−	5.52557i	0.260774	−	0.358925i
$238$	−1.05671	+	1.45444i	−0.0684964	+	0.0942772i
$239$	7.06988	−	5.13657i	0.457313	−	0.332257i	−0.335163	−	0.942160i	$-0.608792\pi$
$239$	7.06988	−	5.13657i	0.457313	−	0.332257i	0.792476	+	0.609903i	$0.208792\pi$
$240$		0			0
$241$	0.486132	+	0.353195i	0.0313145	+	0.0227513i	0.603332	−	0.797490i	$-0.293839\pi$
$241$	0.486132	+	0.353195i	0.0313145	+	0.0227513i	−0.572018	+	0.820241i	$0.693839\pi$
$242$	−6.92531	+	2.25017i	−0.445176	+	0.144646i
$243$			15.0589i			0.966031i
$244$	3.00423	+	9.24607i	0.192326	+	0.591919i
$245$		0			0
$246$	−3.85140	+	11.8534i	−0.245556	+	0.755745i
$247$	3.02423	+	0.982634i	0.192427	+	0.0625235i
$248$	4.03312	+	5.55112i	0.256104	+	0.352496i
$249$	−7.44678			−0.471921
$250$		0			0
$251$	−14.1908			−0.895712			−0.447856	−	0.894106i	$-0.647812\pi$
$251$	−14.1908			−0.895712			−0.447856	+	0.894106i	$0.647812\pi$
$252$	−5.61536	−	7.72888i	−0.353734	−	0.486873i
$253$	18.3652	+	5.96722i	1.15461	+	0.375156i
$254$	−6.14486	+	18.9119i	−0.385563	+	1.18664i
$255$		0			0
$256$	5.25868	+	16.1846i	0.328668	+	1.01153i
$257$		−	17.6859i		−	1.10322i	−0.834103	−	0.551609i	$-0.814014\pi$
$257$		−	17.6859i		−	1.10322i	0.834103	−	0.551609i	$-0.185986\pi$
$258$	−1.57890	+	0.513015i	−0.0982980	+	0.0319389i
$259$	20.1183	+	14.6168i	1.25009	+	0.908245i
$260$		0			0
$261$	8.33904	−	6.05867i	0.516174	−	0.375022i
$262$	−16.5612	+	22.7946i	−1.02316	+	1.40825i
$263$	14.3036	−	19.6873i	0.882000	−	1.21397i	−0.0938630	−	0.995585i	$-0.529922\pi$
$263$	14.3036	−	19.6873i	0.882000	−	1.21397i	0.975863	−	0.218384i	$-0.0700784\pi$
$264$	4.41641	−	3.20871i	0.271811	−	0.197482i
$265$		0			0
$266$	−34.7029	−	25.2131i	−2.12777	−	1.54591i
$267$	4.90350	−	1.59324i	0.300090	−	0.0975050i
$268$			2.46365i			0.150491i
$269$	−9.26490	−	28.5144i	−0.564891	−	1.73856i	−0.668275	−	0.743915i	$-0.732967\pi$
$269$	−9.26490	−	28.5144i	−0.564891	−	1.73856i	0.103384	−	0.994642i	$-0.467033\pi$
$270$		0			0
$271$	−8.55920	+	26.3425i	−0.519934	+	1.60019i	0.254187	+	0.967155i	$0.418192\pi$
$271$	−8.55920	+	26.3425i	−0.519934	+	1.60019i	−0.774121	+	0.633038i	$0.781808\pi$
$272$	1.10003	+	0.357420i	0.0666989	+	0.0216718i
$273$	−1.09827	−	1.51165i	−0.0664706	−	0.0914889i
$274$	−17.5447			−1.05992
$275$		0			0
$276$	2.92177			0.175870
$277$	−1.34842	−	1.85594i	−0.0810189	−	0.111513i	0.766584	−	0.642144i	$-0.221955\pi$
$277$	−1.34842	−	1.85594i	−0.0810189	−	0.111513i	−0.847603	+	0.530631i	$0.821955\pi$
$278$	−10.6627	−	3.46451i	−0.639505	−	0.207788i
$279$	−2.69533	+	8.29536i	−0.161365	+	0.496630i
$280$		0			0
$281$	−0.500078	−	1.53908i	−0.0298321	−	0.0918139i	0.935032	−	0.354564i	$-0.115371\pi$
$281$	−0.500078	−	1.53908i	−0.0298321	−	0.0918139i	−0.964864	+	0.262750i	$0.915371\pi$
$282$		−	1.10063i		−	0.0655416i
$283$	−12.3563	+	4.01481i	−0.734506	+	0.238656i	−0.652301	−	0.757960i	$-0.726196\pi$
$283$	−12.3563	+	4.01481i	−0.734506	+	0.238656i	−0.0822051	+	0.996615i	$0.526196\pi$
$284$	2.16249	+	1.57114i	0.128320	+	0.0932300i
$285$		0			0
$286$	3.05467	−	2.21935i	0.180627	−	0.131233i
$287$	−28.1265	+	38.7128i	−1.66025	+	2.28514i
$288$	−6.51897	+	8.97259i	−0.384134	+	0.528715i
$289$	−13.7095	+	9.96055i	−0.806442	+	0.585914i
$290$		0			0
$291$	−4.78115	−	3.47371i	−0.280276	−	0.203632i
$292$	8.16231	−	2.65210i	0.477663	−	0.155202i
$293$			11.7009i			0.683572i	0.939778	+	0.341786i	$0.111032\pi$
$293$			11.7009i			0.683572i	−0.939778	+	0.341786i	$0.888968\pi$
$294$	5.20220	+	16.0107i	0.303398	+	0.933765i
$295$		0			0
$296$	3.28576	−	10.1125i	0.190981	−	0.587780i
$297$	14.5339	+	4.72235i	0.843342	+	0.274018i
$298$	−11.9051	−	16.3859i	−0.689642	−	0.949211i
$299$	−2.82612			−0.163439
$300$		0			0
$301$	−6.37395			−0.367388
$302$	1.52596	+	2.10031i	0.0878094	+	0.120859i
$303$	−2.40851	−	0.782572i	−0.138365	−	0.0449576i
$304$	−8.52804	+	26.2466i	−0.489116	+	1.50535i
$305$		0			0
$306$	0.301958	+	0.929330i	0.0172618	+	0.0531263i
$307$			26.5673i			1.51628i	0.652094	+	0.758138i	$0.273891\pi$
$307$			26.5673i			1.51628i	−0.652094	+	0.758138i	$0.726109\pi$
$308$	−14.2538	+	4.63134i	−0.812185	+	0.263895i
$309$	0.229482	+	0.166728i	0.0130548	+	0.00948485i
$310$		0			0
$311$	10.9145	−	7.92981i	0.618902	−	0.449658i	−0.233636	−	0.972324i	$-0.575062\pi$
$311$	10.9145	−	7.92981i	0.618902	−	0.449658i	0.852538	+	0.522666i	$0.175062\pi$
$312$	−0.469603	+	0.646353i	−0.0265860	+	0.0365925i
$313$	−9.98904	+	13.7487i	−0.564614	+	0.777124i	−0.991904	−	0.126990i	$-0.959468\pi$
$313$	−9.98904	+	13.7487i	−0.564614	+	0.777124i	0.427290	+	0.904115i	$0.359468\pi$
$314$	−13.3805	+	9.72150i	−0.755105	+	0.548616i
$315$		0			0
$316$	6.48649	+	4.71271i	0.364893	+	0.265111i
$317$	−15.9738	+	5.19021i	−0.897180	+	0.291511i	−0.721072	−	0.692860i	$-0.756351\pi$
$317$	−15.9738	+	5.19021i	−0.897180	+	0.291511i	−0.176107	+	0.984371i	$0.556351\pi$
$318$			1.47224i			0.0825588i
$319$	−4.99696	−	15.3791i	−0.279776	−	0.861063i
$320$		0			0
$321$	0.360808	−	1.11045i	0.0201384	−	0.0619795i
$322$	36.2573	+	11.7807i	2.02054	+	0.656513i
$323$	0.758839	+	1.04445i	0.0422230	+	0.0581149i
$324$	−3.93033			−0.218351
$325$		0			0
$326$	−9.39524			−0.520354
$327$	0.0312793	+	0.0430522i	0.00172975	+	0.00238079i
$328$	19.4591	+	6.32265i	1.07445	+	0.349110i
$329$	1.30582	−	4.01891i	0.0719924	−	0.221570i
$330$		0			0
$331$	3.96604	+	12.2062i	0.217994	+	0.670915i	0.998928	+	0.0463015i	$0.0147435\pi$
$331$	3.96604	+	12.2062i	0.217994	+	0.670915i	−0.780934	+	0.624614i	$0.785257\pi$
$332$		−	8.74180i		−	0.479768i
$333$	12.8548	−	4.17679i	0.704441	−	0.228887i
$334$	−29.7723	−	21.6308i	−1.62907	−	1.18359i
$335$		0			0
$336$	13.1192	−	9.53166i	0.715711	−	0.519995i
$337$	12.4831	−	17.1815i	0.679997	−	0.935935i	−0.319937	−	0.947439i	$-0.603662\pi$
$337$	12.4831	−	17.1815i	0.679997	−	0.935935i	0.999934	+	0.0115037i	$0.00366181\pi$
$338$	12.5385	−	17.2577i	0.682003	−	0.938697i
$339$	−8.12183	+	5.90085i	−0.441117	+	0.320490i
$340$		0			0
$341$	11.0701	+	8.04291i	0.599480	+	0.435548i
$342$	−22.1738	+	7.20470i	−1.19902	+	0.389586i
$343$			32.4969i			1.75467i
$344$	0.842191	+	2.59200i	0.0454079	+	0.139751i
$345$		0			0
$346$	12.1928	−	37.5255i	0.655488	−	2.01739i
$347$	27.2270	+	8.84658i	1.46162	+	0.474909i	0.928565	−	0.371171i	$-0.121044\pi$
$347$	27.2270	+	8.84658i	1.46162	+	0.474909i	0.533056	+	0.846080i	$0.321044\pi$
$348$	−1.43813	−	1.97942i	−0.0770920	−	0.106108i
$349$	−19.9124			−1.06588			−0.532942	−	0.846152i	$-0.678914\pi$
$349$	−19.9124			−1.06588			−0.532942	+	0.846152i	$0.678914\pi$
$350$		0			0
$351$	−2.23654			−0.119377
$352$	10.2269	+	14.0761i	0.545096	+	0.750260i
$353$	−23.4831	−	7.63011i	−1.24988	−	0.406110i	−0.392000	−	0.919965i	$-0.628217\pi$
$353$	−23.4831	−	7.63011i	−1.24988	−	0.406110i	−0.857877	+	0.513855i	$0.828217\pi$
$354$	1.66573	−	5.12658i	0.0885324	−	0.272475i
$355$		0			0
$356$	1.87031	+	5.75624i	0.0991265	+	0.305080i
$357$		−	0.758602i		−	0.0401495i
$358$	−10.1164	+	3.28702i	−0.534668	+	0.173724i
$359$	17.3947	+	12.6380i	0.918058	+	0.667008i	0.943040	−	0.332679i	$-0.107953\pi$
$359$	17.3947	+	12.6380i	0.918058	+	0.667008i	−0.0249816	+	0.999688i	$0.507953\pi$
$360$		0			0
$361$	−9.54930	+	6.93797i	−0.502595	+	0.365156i
$362$	−13.1975	+	18.1647i	−0.693643	+	0.954718i
$363$	1.80604	−	2.48581i	0.0947927	−	0.130471i
$364$	1.77452	−	1.28927i	0.0930103	−	0.0675760i
$365$		0			0
$366$	−11.2789	−	8.19460i	−0.589557	−	0.428338i
$367$	1.08785	−	0.353463i	0.0567852	−	0.0184506i	−0.280487	−	0.959858i	$-0.590496\pi$
$367$	1.08785	−	0.353463i	0.0567852	−	0.0184506i	0.337272	+	0.941407i	$0.390496\pi$
$368$		−	24.5272i		−	1.27857i
$369$	8.03721	+	24.7360i	0.418400	+	1.28770i
$370$		0			0
$371$	−1.74671	+	5.37581i	−0.0906845	+	0.279098i
$372$	1.96905	+	0.639784i	0.102091	+	0.0331713i
$373$	6.78275	+	9.33566i	0.351198	+	0.483382i	0.947670	−	0.319251i	$-0.103431\pi$
$373$	6.78275	+	9.33566i	0.351198	+	0.483382i	−0.596472	+	0.802634i	$0.703431\pi$
$374$	1.53295			0.0792671
$375$		0			0
$376$	−1.80685			−0.0931812
$377$	1.39105	+	1.91462i	0.0716427	+	0.0986077i
$378$	28.6933	+	9.32302i	1.47582	+	0.479524i
$379$	−6.52188	+	20.0723i	−0.335007	+	1.03104i	0.631712	+	0.775203i	$0.282352\pi$
$379$	−6.52188	+	20.0723i	−0.335007	+	1.03104i	−0.966719	+	0.255841i	$0.917648\pi$
$380$		0			0
$381$	−2.59292	−	7.98018i	−0.132839	−	0.408837i
$382$		−	4.68127i		−	0.239515i
$383$	−0.816129	+	0.265176i	−0.0417022	+	0.0135499i	−0.329794	−	0.944053i	$-0.606979\pi$
$383$	−0.816129	+	0.265176i	−0.0417022	+	0.0135499i	0.288092	+	0.957603i	$0.406979\pi$
$384$	−7.49097	−	5.44251i	−0.382272	−	0.277737i
$385$		0			0
$386$	−30.7337	+	22.3293i	−1.56430	+	1.13653i
$387$	−2.03635	+	2.80280i	−0.103514	+	0.142474i
$388$	4.07780	−	5.61260i	0.207019	−	0.284937i
$389$	−27.4537	+	19.9463i	−1.39196	+	1.01132i	−0.396310	+	0.918117i	$0.629710\pi$
$389$	−27.4537	+	19.9463i	−1.39196	+	1.01132i	−0.995647	+	0.0931998i	$0.970290\pi$
$390$		0			0
$391$	−0.928260	−	0.674421i	−0.0469442	−	0.0341069i
$392$	26.2840	−	8.54019i	1.32754	−	0.431345i
$393$		−	11.8891i		−	0.599728i
$394$	−0.661604	−	2.03621i	−0.0333311	−	0.102583i
$395$		0			0
$396$	−2.51728	+	7.74740i	−0.126498	+	0.389322i
$397$	−25.5155	−	8.29049i	−1.28059	−	0.416088i	−0.411800	−	0.911274i	$-0.635100\pi$
$397$	−25.5155	−	8.29049i	−1.28059	−	0.416088i	−0.868787	+	0.495186i	$0.835100\pi$
$398$	−8.53576	−	11.7485i	−0.427859	−	0.588897i
$399$	18.1002			0.906145
$400$		0			0
$401$	3.79757			0.189642			0.0948208	−	0.995494i	$-0.469772\pi$
$401$	3.79757			0.189642			0.0948208	+	0.995494i	$0.469772\pi$
$402$	−2.07661	−	2.85821i	−0.103572	−	0.142555i
$403$	−1.90459	−	0.618838i	−0.0948743	−	0.0308265i
$404$	0.918663	−	2.82736i	0.0457052	−	0.140666i
$405$		0			0
$406$	−9.86518	−	30.3619i	−0.489601	−	1.50684i
$407$		−	21.2044i		−	1.05106i
$408$	−0.308489	+	0.100234i	−0.0152725	+	0.00496234i
$409$	−11.4681	−	8.33207i	−0.567062	−	0.411994i	0.266975	−	0.963703i	$-0.413976\pi$
$409$	−11.4681	−	8.33207i	−0.567062	−	0.411994i	−0.834037	+	0.551709i	$0.813976\pi$
$410$		0			0
$411$	5.98936	−	4.35153i	0.295434	−	0.214645i
$412$	−0.195723	+	0.269389i	−0.00964257	+	0.0132719i
$413$	12.1647	−	16.7432i	0.598585	−	0.823881i
$414$	16.7638	−	12.1796i	0.823896	−	0.598595i
$415$		0			0
$416$	−2.06008	−	1.49673i	−0.101004	−	0.0733834i
$417$	4.49928	−	1.46190i	0.220331	−	0.0715897i
$418$			36.5762i			1.78900i
$419$	6.05576	+	18.6377i	0.295843	+	0.910512i	0.982937	+	0.183943i	$0.0588862\pi$
$419$	6.05576	+	18.6377i	0.295843	+	0.910512i	−0.687094	+	0.726569i	$0.741114\pi$
$420$		0			0
$421$	−7.96770	+	24.5221i	−0.388322	+	1.19513i	0.545720	+	0.837968i	$0.316256\pi$
$421$	−7.96770	+	24.5221i	−0.388322	+	1.19513i	−0.934042	+	0.357164i	$0.883744\pi$
$422$	−33.6720	−	10.9407i	−1.63913	−	0.532584i
$423$	−1.35004	−	1.85817i	−0.0656412	−	0.0903474i
$424$	2.41689			0.117375
$425$		0			0
$426$	−3.83313			−0.185716
$427$	−31.4621	−	43.3039i	−1.52256	−	2.09562i
$428$	1.30356	+	0.423554i	0.0630102	+	0.0204732i
$429$	−0.492341	+	1.51527i	−0.0237704	+	0.0731579i
$430$		0			0
$431$	2.91259	+	8.96402i	0.140294	+	0.431782i	0.996376	−	0.0850590i	$-0.0271079\pi$
$431$	2.91259	+	8.96402i	0.140294	+	0.431782i	−0.856081	+	0.516841i	$0.827108\pi$
$432$		−	19.4103i		−	0.933881i
$433$	−1.66588	+	0.541277i	−0.0800571	+	0.0260121i	−0.348772	−	0.937208i	$-0.613401\pi$
$433$	−1.66588	+	0.541277i	−0.0800571	+	0.0260121i	0.268715	+	0.963220i	$0.413401\pi$
$434$	21.8550	+	15.8786i	1.04907	+	0.762197i
$435$		0			0
$436$	−0.0505391	+	0.0367188i	−0.00242038	+	0.00175851i
$437$	16.0917	−	22.1483i	0.769769	−	1.05950i
$438$	−7.23408	+	9.95686i	−0.345658	+	0.475757i
$439$	22.7197	−	16.5068i	1.08435	−	0.787827i	0.105914	−	0.994375i	$-0.466223\pi$
$439$	22.7197	−	16.5068i	1.08435	−	0.787827i	0.978436	+	0.206549i	$0.0662232\pi$
$440$		0			0
$441$	28.4216	+	20.6495i	1.35341	+	0.983311i
$442$	−0.213371	+	0.0693285i	−0.0101490	+	0.00329762i
$443$		−	29.9110i		−	1.42111i	−0.703640	−	0.710557i	$-0.748443\pi$
$443$		−	29.9110i		−	1.42111i	0.703640	−	0.710557i	$-0.251557\pi$
$444$	−0.991436	−	3.05133i	−0.0470515	−	0.144810i
$445$		0			0
$446$	−3.29568	+	10.1430i	−0.156055	+	0.480287i
$447$	8.12823	+	2.64102i	0.384452	+	0.124916i
$448$	−6.64656	−	9.14821i	−0.314021	−	0.432212i
$449$	−6.29974			−0.297303			−0.148652	−	0.988890i	$-0.547493\pi$
$449$	−6.29974			−0.297303			−0.148652	+	0.988890i	$0.547493\pi$
$450$		0			0
$451$	40.8026			1.92132
$452$	−6.92703	−	9.53424i	−0.325820	−	0.448453i
$453$	−1.04186	−	0.338520i	−0.0489508	−	0.0159051i
$454$	5.85873	−	18.0313i	0.274964	−	0.846252i
$455$		0			0
$456$	−2.39159	−	7.36055i	−0.111996	−	0.344689i
$457$		−	19.1809i		−	0.897243i	−0.893722	−	0.448622i	$-0.851915\pi$
$457$		−	19.1809i		−	0.897243i	0.893722	−	0.448622i	$-0.148085\pi$
$458$	24.0807	−	7.82429i	1.12522	−	0.365605i
$459$	−0.734607	−	0.533724i	−0.0342885	−	0.0249121i
$460$		0			0
$461$	−5.72064	+	4.15629i	−0.266437	+	0.193578i	−0.712980	−	0.701184i	$-0.752655\pi$
$461$	−5.72064	+	4.15629i	−0.266437	+	0.193578i	0.446543	+	0.894762i	$0.352655\pi$
$462$	12.6328	−	17.3876i	0.587732	−	0.808944i
$463$	−5.65356	+	7.78146i	−0.262743	+	0.361635i	−0.919923	−	0.392099i	$-0.871749\pi$
$463$	−5.65356	+	7.78146i	−0.262743	+	0.361635i	0.657180	+	0.753734i	$0.271749\pi$
$464$	−16.6165	+	12.0726i	−0.771401	+	0.560456i
$465$		0			0
$466$	10.6603	+	7.74517i	0.493830	+	0.358788i
$467$	−18.2812	+	5.93992i	−0.845953	+	0.274867i	−0.699750	−	0.714388i	$-0.746705\pi$
$467$	−18.2812	+	5.93992i	−0.845953	+	0.274867i	−0.146203	+	0.989255i	$0.546705\pi$
$468$		−	1.19220i		−	0.0551096i
$469$	−4.19160	−	12.9004i	−0.193550	−	0.595686i
$470$		0			0
$471$	2.15662	−	6.63739i	0.0993717	−	0.305835i
$472$	−8.41605	−	2.73454i	−0.387380	−	0.125867i
$473$	3.19462	+	4.39701i	0.146889	+	0.202175i
$474$	−11.4977			−0.528105
$475$		0			0
$476$	0.890525			0.0408172
$477$	1.80585	+	2.48554i	0.0826843	+	0.113805i
$478$	−13.9911	−	4.54598i	−0.639937	−	0.207928i
$479$	11.7425	−	36.1398i	0.536529	−	1.65127i	−0.203792	−	0.979014i	$-0.565327\pi$
$479$	11.7425	−	36.1398i	0.536529	−	1.65127i	0.740321	−	0.672253i	$-0.234673\pi$
$480$		0			0
$481$	0.958977	+	2.95143i	0.0437256	+	0.134574i
$482$		−	1.01155i		−	0.0460747i
$483$	−15.2993	+	4.97104i	−0.696142	+	0.226190i
$484$	2.91809	+	2.12012i	0.132641	+	0.0963691i
$485$		0			0
$486$	20.5089	−	14.9006i	0.930302	−	0.675904i
$487$	9.84481	−	13.5502i	0.446111	−	0.614019i	−0.525445	−	0.850827i	$-0.676101\pi$
$487$	9.84481	−	13.5502i	0.446111	−	0.614019i	0.971556	+	0.236808i	$0.0761013\pi$
$488$	−13.4527	+	18.5160i	−0.608973	+	0.838180i
$489$	3.20732	−	2.33025i	0.145040	−	0.105378i
$490$		0			0
$491$	7.24115	+	5.26100i	0.326789	+	0.237426i	0.739067	−	0.673632i	$-0.235267\pi$
$491$	7.24115	+	5.26100i	0.326789	+	0.237426i	−0.412278	+	0.911058i	$0.635267\pi$
$492$	5.87153	−	1.90778i	0.264709	−	0.0860092i
$493$			0.960829i			0.0432736i
$494$	−1.65418	−	5.09103i	−0.0744249	−	0.229056i
$495$		0			0
$496$	5.37075	−	16.5295i	0.241154	−	0.742194i
$497$	−13.9965	−	4.54775i	−0.627831	−	0.203995i
$498$	7.36847	+	10.1418i	0.330189	+	0.454466i
$499$	36.3310			1.62640			0.813200	−	0.581985i	$-0.197724\pi$
$499$	36.3310			1.62640			0.813200	+	0.581985i	$0.197724\pi$
$500$		0			0
$501$	15.5286			0.693765
$502$	14.0415	+	19.3265i	0.626704	+	0.862583i
$503$	11.6928	+	3.79921i	0.521354	+	0.169398i	0.557860	−	0.829935i	$-0.311623\pi$
$503$	11.6928	+	3.79921i	0.521354	+	0.169398i	−0.0365056	+	0.999333i	$0.511623\pi$
$504$	6.94991	−	21.3896i	0.309574	−	0.952770i
$505$		0			0
$506$	−10.0453	−	30.9162i	−0.446567	−	1.37439i
$507$			9.00125i			0.399759i
$508$	9.36795	−	3.04383i	0.415636	−	0.135048i
$509$	−25.1841	−	18.2973i	−1.11626	−	0.811013i	−0.132625	−	0.991166i	$-0.542341\pi$
$509$	−25.1841	−	18.2973i	−1.11626	−	0.811013i	−0.983639	+	0.180153i	$0.942341\pi$
$510$		0			0
$511$	−38.2281	+	27.7744i	−1.69111	+	1.22867i
$512$	1.51482	−	2.08496i	0.0669460	−	0.0921433i
$513$	12.7346	−	17.5277i	0.562248	−	0.773868i
$514$	−24.0866	+	17.4999i	−1.06241	+	0.771889i
$515$		0			0
$516$	0.665295	+	0.483365i	0.0292880	+	0.0212790i
$517$	−3.42689	+	1.11346i	−0.150714	+	0.0489701i
$518$		−	41.8624i		−	1.83933i
$519$	5.14493	+	15.8345i	0.225837	+	0.695056i
$520$		0			0
$521$	5.01130	−	15.4232i	0.219549	−	0.675702i	−0.779250	−	0.626713i	$-0.784400\pi$
$521$	5.01130	−	15.4232i	0.219549	−	0.675702i	0.998799	−	0.0489896i	$-0.0156001\pi$
$522$	−16.5027	−	5.36205i	−0.722303	−	0.234691i
$523$	17.9822	+	24.7504i	0.786307	+	1.08226i	0.994558	+	0.104183i	$0.0332229\pi$
$523$	17.9822	+	24.7504i	0.786307	+	1.08226i	−0.208251	+	0.978075i	$0.566777\pi$
$524$	13.9567			0.609701
$525$		0			0
$526$	−40.9655			−1.78618
$527$	−0.477898	−	0.657770i	−0.0208176	−	0.0286529i
$528$	−13.1507	−	4.27291i	−0.572309	−	0.185954i
$529$	−0.411359	+	1.26603i	−0.0178852	+	0.0550449i
$530$		0			0
$531$	−3.47608	−	10.6983i	−0.150849	−	0.464266i
$532$			21.2479i			0.921214i
$533$	−5.67930	+	1.84532i	−0.245998	+	0.0799295i
$534$	−7.02179	−	5.10163i	−0.303863	−	0.220769i
$535$		0			0
$536$	−4.69218	+	3.40907i	−0.202671	+	0.147249i
$537$	2.63824	−	3.63123i	0.113849	−	0.156699i
$538$	−29.6666	+	40.8325i	−1.27902	+	1.76041i
$539$	44.5876	−	32.3948i	1.92052	−	1.39534i
$540$		0			0
$541$	−14.8062	−	10.7573i	−0.636567	−	0.462493i	0.222102	−	0.975023i	$-0.428708\pi$
$541$	−14.8062	−	10.7573i	−0.636567	−	0.462493i	−0.858669	+	0.512530i	$0.828708\pi$
$542$	44.3452	−	14.4086i	1.90479	−	0.618904i
$543$		−	9.47432i		−	0.406582i
$544$	−0.319470	−	0.983228i	−0.0136972	−	0.0421555i
$545$		0			0
$546$	−0.971996	+	2.99150i	−0.0415976	+	0.128024i
$547$	6.23515	+	2.02592i	0.266596	+	0.0866223i	0.439265	−	0.898358i	$-0.355239\pi$
$547$	6.23515	+	2.02592i	0.266596	+	0.0866223i	−0.172669	+	0.984980i	$0.555239\pi$
$548$	5.10827	+	7.03093i	0.218214	+	0.300346i
$549$	−29.0935			−1.24168
$550$		0			0
$551$	−22.9254			−0.976653
$552$	4.04300	+	5.56471i	0.172081	+	0.236850i
$553$	−41.9833	−	13.6412i	−1.78531	−	0.580083i
$554$	−1.19338	+	3.67285i	−0.0507020	+	0.156045i
$555$		0			0
$556$	1.71613	+	5.28171i	0.0727802	+	0.223994i
$557$			35.5383i			1.50581i	0.658131	+	0.752904i	$0.271347\pi$
$557$			35.5383i			1.50581i	−0.658131	+	0.752904i	$0.728653\pi$
$558$	13.9645	−	4.53734i	0.591164	−	0.192081i
$559$	−0.643514	−	0.467540i	−0.0272177	−	0.0197748i
$560$		0			0
$561$	−0.523315	+	0.380210i	−0.0220944	+	0.0160525i
$562$	−1.60127	+	2.20396i	−0.0675454	+	0.0929682i
$563$	22.4816	−	30.9432i	0.947486	−	1.30410i	−0.00514973	−	0.999987i	$-0.501639\pi$
$563$	22.4816	−	30.9432i	0.947486	−	1.30410i	0.952635	−	0.304115i	$-0.0983608\pi$
$564$	−0.441070	+	0.320456i	−0.0185724	+	0.0134936i
$565$		0			0
$566$	17.6942	+	12.8556i	0.743741	+	0.540360i
$567$	20.5804	−	6.68697i	0.864295	−	0.280826i
$568$			6.29266i			0.264034i
$569$	−2.33585	−	7.18901i	−0.0979240	−	0.301379i	0.890081	−	0.455803i	$-0.150648\pi$
$569$	−2.33585	−	7.18901i	−0.0979240	−	0.301379i	−0.988005	+	0.154424i	$0.950648\pi$
$570$		0			0
$571$	7.11549	−	21.8992i	0.297774	−	0.916454i	−0.684501	−	0.729011i	$-0.739980\pi$
$571$	7.11549	−	21.8992i	0.297774	−	0.916454i	0.982276	−	0.187443i	$-0.0600199\pi$
$572$	−1.77878	−	0.577960i	−0.0743745	−	0.0241657i
$573$	1.16107	+	1.59808i	0.0485045	+	0.0667607i
$574$	80.5540			3.36226
$575$		0			0
$576$	−6.14617			−0.256090
$577$	13.1175	+	18.0546i	0.546087	+	0.751624i	0.989475	−	0.144706i	$-0.0462235\pi$
$577$	13.1175	+	18.0546i	0.546087	+	0.751624i	−0.443388	+	0.896330i	$0.646223\pi$
$578$	27.1307	+	8.81529i	1.12849	+	0.366668i
$579$	4.95354	−	15.2454i	0.205862	−	0.633579i
$580$		0			0
$581$	14.8731	+	45.7747i	0.617040	+	1.89905i
$582$			9.94866i			0.412385i
$583$	4.58390	−	1.48940i	0.189846	−	0.0616846i
$584$	16.3457	+	11.8758i	0.676389	+	0.491425i
$585$		0			0
$586$	15.9355	−	11.5778i	0.658290	−	0.478276i
$587$	12.3897	−	17.0530i	0.511378	−	0.703851i	−0.472773	−	0.881184i	$-0.656747\pi$
$587$	12.3897	−	17.0530i	0.511378	−	0.703851i	0.984151	+	0.177333i	$0.0567471\pi$
$588$	4.90153	−	6.74638i	0.202136	−	0.278216i
$589$	15.6944	−	11.4026i	0.646676	−	0.469838i
$590$		0			0
$591$	0.730887	+	0.531020i	0.0300647	+	0.0218433i
$592$	−25.6147	+	8.32273i	−1.05276	+	0.342062i
$593$			34.3547i			1.41078i	0.708819	+	0.705390i	$0.249228\pi$
$593$			34.3547i			1.41078i	−0.708819	+	0.705390i	$0.750772\pi$
$594$	−7.94965	−	24.4665i	−0.326178	−	1.00387i
$595$		0			0
$596$	−3.10030	+	9.54175i	−0.126993	+	0.390846i
$597$	5.82782	+	1.89357i	0.238517	+	0.0774988i
$598$	2.79640	+	3.84891i	0.114353	+	0.157394i
$599$	−0.498231			−0.0203572			−0.0101786	−	0.999948i	$-0.503240\pi$
$599$	−0.498231			−0.0203572			−0.0101786	+	0.999948i	$0.503240\pi$
$600$		0			0
$601$	27.8635			1.13657			0.568287	−	0.822830i	$-0.307606\pi$
$601$	27.8635			1.13657			0.568287	+	0.822830i	$0.307606\pi$
$602$	6.30692	+	8.68073i	0.257051	+	0.353800i
$603$	−7.01180	−	2.27827i	−0.285543	−	0.0927784i
$604$	0.397390	−	1.22304i	0.0161696	−	0.0497648i
$605$		0			0
$606$	1.31739	+	4.05451i	0.0535153	+	0.164703i
$607$			14.1000i			0.572303i	0.958184	+	0.286152i	$0.0923761\pi$
$607$			14.1000i			0.572303i	−0.958184	+	0.286152i	$0.907624\pi$
$608$	23.4598	−	7.62255i	0.951420	−	0.309135i
$609$	10.8982	+	7.91804i	0.441619	+	0.320855i
$610$		0			0
$611$	0.426630	−	0.309965i	0.0172596	−	0.0125398i
$612$	0.284506	−	0.391588i	0.0115005	−	0.0158290i
$613$	−18.7067	+	25.7475i	−0.755556	+	1.03993i	0.242015	+	0.970272i	$0.422192\pi$
$613$	−18.7067	+	25.7475i	−0.755556	+	1.03993i	−0.997571	+	0.0696606i	$0.977808\pi$
$614$	36.1822	−	26.2879i	1.46020	−	1.06089i
$615$		0			0
$616$	−28.5443	−	20.7387i	−1.15008	−	0.835585i
$617$	−32.3038	+	10.4961i	−1.30050	+	0.422559i	−0.875756	−	0.482753i	$-0.839637\pi$
$617$	−32.3038	+	10.4961i	−1.30050	+	0.422559i	−0.424746	+	0.905312i	$0.639637\pi$
$618$		−	0.477508i		−	0.0192082i
$619$	−0.348700	−	1.07319i	−0.0140155	−	0.0431351i	0.943804	−	0.330505i	$-0.107219\pi$
$619$	−0.348700	−	1.07319i	−0.0140155	−	0.0431351i	−0.957820	+	0.287370i	$0.907219\pi$
$620$		0			0
$621$	−5.95019	+	18.3128i	−0.238773	+	0.734868i
$622$	−21.5993	−	7.01805i	−0.866055	−	0.281398i
$623$	−19.5871	−	26.9593i	−0.784739	−	1.08010i
$624$	2.02368			0.0810119
$625$		0			0
$626$	28.6085			1.14343
$627$	−9.07181	−	12.4863i	−0.362293	−	0.498654i
$628$	7.79165	+	2.53166i	0.310921	+	0.101024i
$629$	−0.389341	+	1.19827i	−0.0155240	+	0.0477781i
$630$		0			0
$631$	10.1296	+	31.1758i	0.403254	+	1.24109i	0.922345	+	0.386368i	$0.126271\pi$
$631$	10.1296	+	31.1758i	0.403254	+	1.24109i	−0.519091	+	0.854719i	$0.673729\pi$
$632$			18.8751i			0.750813i
$633$	14.2084	−	4.61659i	0.564733	−	0.183493i
$634$	22.8744	+	16.6193i	0.908460	+	0.660035i
$635$		0			0
$636$	0.589988	−	0.428652i	0.0233946	−	0.0169971i
$637$	−4.74106	+	6.52551i	−0.187848	+	0.258550i
$638$	−16.0005	+	22.0227i	−0.633464	+	0.871889i
$639$	−6.47140	+	4.70175i	−0.256005	+	0.185998i
$640$		0			0
$641$	−24.6043	−	17.8761i	−0.971812	−	0.706063i	−0.0159485	−	0.999873i	$-0.505077\pi$
$641$	−24.6043	−	17.8761i	−0.971812	−	0.706063i	−0.955864	+	0.293810i	$0.905077\pi$
$642$	−1.86935	+	0.607388i	−0.0737773	+	0.0239717i
$643$			1.06932i			0.0421700i	0.999778	+	0.0210850i	$0.00671206\pi$
$643$			1.06932i			0.0421700i	−0.999778	+	0.0210850i	$0.993288\pi$
$644$	−5.83552	−	17.9599i	−0.229952	−	0.707719i
$645$		0			0
$646$	0.671589	−	2.06694i	0.0264233	−	0.0813226i
$647$	−29.0719	−	9.44602i	−1.14293	−	0.371362i	−0.324456	−	0.945901i	$-0.605181\pi$
$647$	−29.0719	−	9.44602i	−1.14293	−	0.371362i	−0.818477	+	0.574539i	$0.805181\pi$
$648$	−5.43858	−	7.48556i	−0.213648	−	0.294061i
$649$	−17.6471			−0.692709
$650$		0			0
$651$	−11.3991			−0.446765
$652$	2.73549	+	3.76508i	0.107130	+	0.147452i
$653$	−31.7179	−	10.3058i	−1.24122	−	0.403296i	−0.386451	−	0.922310i	$-0.626299\pi$
$653$	−31.7179	−	10.3058i	−1.24122	−	0.403296i	−0.854766	+	0.519014i	$0.826299\pi$
$654$	0.0276828	−	0.0851989i	0.00108248	−	0.00333154i
$655$		0			0
$656$	−16.0151	−	49.2893i	−0.625283	−	1.92442i
$657$			25.6833i			1.00200i
$658$	−6.76548	+	2.19824i	−0.263746	+	0.0856962i
$659$	−8.18325	−	5.94548i	−0.318774	−	0.231603i	0.416878	−	0.908962i	$-0.363124\pi$
$659$	−8.18325	−	5.94548i	−0.318774	−	0.231603i	−0.735652	+	0.677360i	$0.763124\pi$
$660$		0			0
$661$	24.9487	−	18.1263i	0.970392	−	0.705031i	0.0148510	−	0.999890i	$-0.495273\pi$
$661$	24.9487	−	18.1263i	0.970392	−	0.705031i	0.955541	+	0.294859i	$0.0952726\pi$
$662$	12.6994	−	17.4793i	0.493577	−	0.679350i
$663$	0.0556448	−	0.0765885i	0.00216106	−	0.00297445i
$664$	16.6493	−	12.0964i	0.646119	−	0.469433i
$665$		0			0
$666$	−18.4081	−	13.3742i	−0.713298	−	0.518241i
$667$	19.3778	−	6.29621i	0.750310	−	0.243790i
$668$			18.2290i			0.705302i
$669$	−1.39066	−	4.28001i	−0.0537660	−	0.165475i
$670$		0			0
$671$	−14.1040	+	43.4077i	−0.544480	+	1.67574i
$672$	−13.7850	−	4.47902i	−0.531768	−	0.172782i
$673$	18.1185	+	24.9379i	0.698415	+	0.961286i	0.999969	+	0.00783693i	$0.00249460\pi$
$673$	18.1185	+	24.9379i	0.698415	+	0.961286i	−0.301554	+	0.953449i	$0.597505\pi$
$674$	−35.7514			−1.37709
$675$		0			0
$676$	−10.5666			−0.406407
$677$	24.2474	+	33.3736i	0.931902	+	1.28265i	0.959113	+	0.283023i	$0.0913374\pi$
$677$	24.2474	+	33.3736i	0.931902	+	1.28265i	−0.0272110	+	0.999630i	$0.508663\pi$
$678$	16.0728	+	5.22238i	0.617273	+	0.200564i
$679$	−11.8034	+	36.3272i	−0.452974	+	1.39411i
$680$		0			0
$681$	2.47218	+	7.60859i	0.0947342	+	0.291562i
$682$		−	23.0348i		−	0.882048i
$683$	−21.2575	+	6.90698i	−0.813395	+	0.264288i	−0.686035	−	0.727568i	$-0.740650\pi$
$683$	−21.2575	+	6.90698i	−0.813395	+	0.264288i	−0.127360	+	0.991857i	$0.540650\pi$
$684$	9.34329	+	6.78830i	0.357250	+	0.259557i
$685$		0			0
$686$	44.2578	−	32.1552i	1.68977	−	1.22769i
$687$	−6.27997	+	8.64364i	−0.239596	+	0.329775i
$688$	4.05767	−	5.58490i	0.154697	−	0.212922i
$689$	−0.570673	+	0.414618i	−0.0217409	+	0.0157957i
$690$		0			0
$691$	−7.43406	−	5.40116i	−0.282805	−	0.205470i	0.437335	−	0.899299i	$-0.355922\pi$
$691$	−7.43406	−	5.40116i	−0.282805	−	0.205470i	−0.720140	+	0.693829i	$0.755922\pi$
$692$	−18.5881	+	6.03965i	−0.706614	+	0.229593i
$693$		−	44.8506i		−	1.70373i
$694$	−14.8924	−	45.8342i	−0.565309	−	1.73984i
$695$		0			0
$696$	1.77992	−	5.47804i	0.0674678	−	0.207644i
$697$	−2.30577	−	0.749192i	−0.0873374	−	0.0283777i
$698$	19.7030	+	27.1188i	0.745768	+	1.02646i
$699$	−5.56018			−0.210305
$700$		0			0
$701$	−35.9929			−1.35943			−0.679717	−	0.733475i	$-0.737897\pi$
$701$	−35.9929			−1.35943			−0.679717	+	0.733475i	$0.737897\pi$
$702$	2.21302	+	3.04595i	0.0835249	+	0.114962i
$703$	−28.5907	−	9.28967i	−1.07832	−	0.350366i
$704$	−2.97956	+	9.17014i	−0.112296	+	0.345613i
$705$		0			0
$706$	12.8446	+	39.5316i	0.483413	+	1.48779i
$707$			16.3679i			0.615578i
$708$	−2.53943	+	0.825111i	−0.0954376	+	0.0310096i
$709$	16.3795	+	11.9004i	0.615144	+	0.446928i	0.851222	−	0.524806i	$-0.175862\pi$
$709$	16.3795	+	11.9004i	0.615144	+	0.446928i	−0.236078	+	0.971734i	$0.575862\pi$
$710$		0			0
$711$	−19.4113	+	14.1031i	−0.727980	+	0.528908i
$712$	−8.37508	+	11.5273i	−0.313870	+	0.432004i
$713$	−10.1341	+	13.9484i	−0.379526	+	0.522373i
$714$	−1.03315	+	0.750625i	−0.0386645	+	0.0280914i
$715$		0			0
$716$	4.26271	+	3.09704i	0.159305	+	0.115742i
$717$	5.90374	−	1.91824i	0.220479	−	0.0716381i
$718$		−	36.1951i		−	1.35079i
$719$	11.4418	+	35.2143i	0.426708	+	1.31327i	0.901349	+	0.433093i	$0.142578\pi$
$719$	11.4418	+	35.2143i	0.426708	+	1.31327i	−0.474641	+	0.880180i	$0.657422\pi$
$720$		0			0
$721$	0.566531	−	1.74360i	0.0210987	−	0.0649352i
$722$	18.8977	+	6.14025i	0.703301	+	0.228516i
$723$	0.250889	+	0.345319i	0.00933066	+	0.0128425i
$724$	11.1219			0.413343
$725$		0			0
$726$	−5.17249			−0.191969
$727$	−7.09986	−	9.77211i	−0.263319	−	0.362428i	0.656801	−	0.754064i	$-0.271909\pi$
$727$	−7.09986	−	9.77211i	−0.263319	−	0.362428i	−0.920120	+	0.391636i	$0.871909\pi$
$728$	4.91099	+	1.59568i	0.182013	+	0.0591397i
$729$	1.06397	−	3.27458i	0.0394065	−	0.121281i
$730$		0			0
$731$	−0.0997940	−	0.307134i	−0.00369102	−	0.0113598i
$732$			6.90586i			0.255248i
$733$	−42.4282	+	13.7858i	−1.56712	+	0.509188i	−0.958698	−	0.284425i	$-0.908197\pi$
$733$	−42.4282	+	13.7858i	−1.56712	+	0.509188i	−0.608422	+	0.793614i	$0.708197\pi$
$734$	−1.55779	−	1.13180i	−0.0574992	−	0.0417756i
$735$		0			0
$736$	−17.7360	+	12.8860i	−0.653759	+	0.474984i
$737$	−6.79840	+	9.35720i	−0.250422	+	0.344677i
$738$	25.7354	−	35.4218i	0.947335	−	1.30389i
$739$	−11.8491	+	8.60890i	−0.435877	+	0.316683i	−0.783995	−	0.620768i	$-0.786821\pi$
$739$	−11.8491	+	8.60890i	−0.435877	+	0.316683i	0.348117	+	0.937451i	$0.386821\pi$
$740$		0			0
$741$	1.82740	+	1.32768i	0.0671312	+	0.0487737i
$742$	9.04970	−	2.94043i	0.332225	−	0.107946i
$743$			24.4397i			0.896604i	0.893882	+	0.448302i	$0.147971\pi$
$743$			24.4397i			0.896604i	−0.893882	+	0.448302i	$0.852029\pi$
$744$	1.50616	+	4.63549i	0.0552186	+	0.169945i
$745$		0			0
$746$	6.00288	−	18.4750i	0.219781	−	0.676417i
$747$	24.8801	+	8.08402i	0.910314	+	0.295779i
$748$	−0.446330	−	0.614321i	−0.0163194	−	0.0224618i
$749$	−7.54648			−0.275743
$750$		0			0
$751$	31.2863			1.14165			0.570826	−	0.821071i	$-0.306623\pi$
$751$	31.2863			1.14165			0.570826	+	0.821071i	$0.306623\pi$
$752$	2.69011	+	3.70262i	0.0980982	+	0.135021i
$753$	−9.58690	−	3.11497i	−0.349366	−	0.113516i
$754$	1.23111	−	3.78896i	0.0448343	−	0.137986i
$755$		0			0
$756$	−4.61812	−	14.2131i	−0.167959	−	0.516926i
$757$			11.3251i			0.411617i	0.978592	+	0.205808i	$0.0659824\pi$
$757$			11.3251i			0.411617i	−0.978592	+	0.205808i	$0.934018\pi$
$758$	33.7899	−	10.9790i	1.22730	−	0.398775i
$759$	11.0972	+	8.06260i	0.402803	+	0.292654i
$760$		0			0
$761$	33.4397	−	24.2954i	1.21219	−	0.880707i	0.216761	−	0.976225i	$-0.430451\pi$
$761$	33.4397	−	24.2954i	1.21219	−	0.880707i	0.995428	+	0.0955176i	$0.0304506\pi$
$762$	−8.30262	+	11.4276i	−0.300772	+	0.413977i
$763$	0.202165	−	0.278257i	0.00731888	−	0.0100736i
$764$	−1.87599	+	1.36299i	−0.0678709	+	0.0493111i
$765$		0			0
$766$	1.16869	+	0.849104i	0.0422266	+	0.0306794i
$767$	2.45629	−	0.798097i	0.0886915	−	0.0288176i
$768$			12.0882i			0.436195i
$769$	−6.99895	−	21.5406i	−0.252389	−	0.776773i	−0.994333	−	0.106311i	$-0.966096\pi$
$769$	−6.99895	−	21.5406i	−0.252389	−	0.776773i	0.741944	−	0.670462i	$-0.233904\pi$
$770$		0			0
$771$	3.88219	−	11.9481i	0.139814	−	0.430302i
$772$	17.8967	+	5.81498i	0.644115	+	0.209286i
$773$	−9.90659	−	13.6353i	−0.356315	−	0.490426i	0.592802	−	0.805348i	$-0.298022\pi$
$773$	−9.90659	−	13.6353i	−0.356315	−	0.490426i	−0.949118	+	0.314922i	$0.898022\pi$
$774$	5.83210			0.209630
$775$		0			0
$776$	16.3322			0.586292
$777$	10.3829	+	14.2909i	0.372485	+	0.512682i
$778$	54.3300	+	17.6529i	1.94782	+	0.632886i
$779$	17.8757	−	55.0157i	0.640463	−	1.97114i
$780$		0			0
$781$	3.87782	+	11.9347i	0.138759	+	0.427058i
$782$			1.93153i			0.0690715i
$783$	15.3352	−	4.98270i	0.548035	−	0.178067i
$784$	−56.6333	−	41.1465i	−2.02262	−	1.46952i
$785$		0			0
$786$	−16.1919	+	11.7641i	−0.577547	+	0.419612i
$787$	−11.8196	+	16.2683i	−0.421323	+	0.579902i	−0.965934	−	0.258787i	$-0.916677\pi$
$787$	−11.8196	+	16.2683i	−0.421323	+	0.579902i	0.544611	+	0.838689i	$0.316677\pi$
$788$	−0.623366	+	0.857990i	−0.0222065	+	0.0305646i
$789$	13.9847	−	10.1605i	0.497867	−	0.361722i
$790$		0			0
$791$	52.4934	+	38.1387i	1.86645	+	1.35605i
$792$	−18.2387	+	5.92612i	−0.648085	+	0.210576i
$793$		−	6.67976i		−	0.237205i
$794$	13.9563	+	42.9531i	0.495291	+	1.52435i
$795$		0			0
$796$	−2.22287	+	6.84130i	−0.0787876	+	0.242483i
$797$	51.5213	+	16.7403i	1.82498	+	0.592971i	0.999597	+	0.0283955i	$0.00903979\pi$
$797$	51.5213	+	16.7403i	1.82498	+	0.592971i	0.825381	+	0.564576i	$0.190960\pi$
$798$	−17.9099	−	24.6508i	−0.634003	−	0.872631i
$799$	0.214100			0.00757430
$800$		0			0
$801$	−18.1124			−0.639971
$802$	−3.75763	−	5.17194i	−0.132687	−	0.182627i
$803$	38.3198	+	12.4508i	1.35228	+	0.439381i
$804$	−0.540788	+	1.66438i	−0.0190721	+	0.0586980i
$805$		0			0
$806$	1.04176	+	3.20620i	0.0366944	+	0.112934i
$807$		−	21.2973i		−	0.749701i
$808$	6.65608	−	2.16269i	0.234160	−	0.0760832i
$809$	12.4076	+	9.01462i	0.436227	+	0.316937i	0.784134	−	0.620592i	$-0.213108\pi$
$809$	12.4076	+	9.01462i	0.436227	+	0.316937i	−0.347907	+	0.937529i	$0.613108\pi$
$810$		0			0
$811$	−9.35757	+	6.79868i	−0.328589	+	0.238734i	−0.739832	−	0.672792i	$-0.765095\pi$
$811$	−9.35757	+	6.79868i	−0.328589	+	0.238734i	0.411243	+	0.911526i	$0.365095\pi$
$812$	−9.29501	+	12.7935i	−0.326191	+	0.448963i
$813$	−11.5647	+	15.9175i	−0.405593	+	0.558251i
$814$	−28.8784	+	20.9814i	−1.01219	+	0.735397i
$815$		0			0
$816$	0.664693	+	0.482927i	0.0232689	+	0.0169058i
$817$	7.32822	−	2.38108i	0.256382	−	0.0833036i
$818$			23.8630i			0.834349i
$819$	2.02839	+	6.24274i	0.0708776	+	0.218139i
$820$		0			0
$821$	10.3111	−	31.7344i	0.359861	−	1.10754i	−0.593276	−	0.804999i	$-0.702166\pi$
$821$	10.3111	−	31.7344i	0.359861	−	1.10754i	0.953137	−	0.302539i	$-0.0978343\pi$
$822$	−11.8528	−	3.85119i	−0.413412	−	0.134326i
$823$	−17.6230	−	24.2560i	−0.614300	−	0.845511i	0.382623	−	0.923905i	$-0.375021\pi$
$823$	−17.6230	−	24.2560i	−0.614300	−	0.845511i	−0.996922	+	0.0783937i	$0.975021\pi$
$824$	−0.783901			−0.0273085
$825$		0			0
$826$	−34.8395			−1.21222
$827$	−14.5318	−	20.0013i	−0.505320	−	0.695514i	0.477801	−	0.878468i	$-0.341434\pi$
$827$	−14.5318	−	20.0013i	−0.505320	−	0.695514i	−0.983121	+	0.182954i	$0.941434\pi$
$828$	−9.76179	−	3.17180i	−0.339246	−	0.110228i
$829$	0.0653280	−	0.201059i	0.00226893	−	0.00698306i	−0.949916	−	0.312506i	$-0.898831\pi$
$829$	0.0653280	−	0.201059i	0.00226893	−	0.00698306i	0.952185	+	0.305523i	$0.0988314\pi$
$830$		0			0
$831$	−0.503566	−	1.54982i	−0.0174685	−	0.0537625i
$832$		−	1.41114i		−	0.0489225i
$833$	−3.11448	+	1.01195i	−0.107910	+	0.0350622i
$834$	−6.44294	−	4.68107i	−0.223101	−	0.162092i
$835$		0			0
$836$	14.6577	−	10.6494i	0.506946	−	0.368318i
$837$	−8.01995	+	11.0385i	−0.277210	+	0.381547i
$838$	19.3908	−	26.6891i	0.669843	−	0.921960i
$839$	−4.46346	+	3.24290i	−0.154096	+	0.111957i	−0.662162	−	0.749361i	$-0.730361\pi$
$839$	−4.46346	+	3.24290i	−0.154096	+	0.111957i	0.508066	+	0.861318i	$0.330361\pi$
$840$		0			0
$841$	9.65802	+	7.01696i	0.333035	+	0.241964i
$842$	41.2807	−	13.4129i	1.42263	−	0.462239i
$843$		−	1.14953i		−	0.0395920i
$844$	5.41942	+	16.6793i	0.186544	+	0.574124i
$845$		0			0
$846$	−1.19482	+	3.67726i	−0.0410786	+	0.126427i
$847$	−18.8872	−	6.13681i	−0.648970	−	0.210863i
$848$	−3.59837	−	4.95273i	−0.123568	−	0.170077i
$849$	−9.22888			−0.316734
$850$		0			0
$851$	26.7177			0.915871
$852$	1.11604	+	1.53610i	0.0382350	+	0.0526260i
$853$	1.46411	+	0.475718i	0.0501302	+	0.0162883i	0.333975	−	0.942582i	$-0.391610\pi$
$853$	1.46411	+	0.475718i	0.0501302	+	0.0162883i	−0.283845	+	0.958870i	$0.591610\pi$
$854$	−27.8447	+	85.6971i	−0.952825	+	2.93249i
$855$		0			0
$856$	0.997118	+	3.06881i	0.0340808	+	0.104890i
$857$		−	45.3407i		−	1.54881i	−0.632691	−	0.774404i	$-0.718050\pi$
$857$		−	45.3407i		−	1.54881i	0.632691	−	0.774404i	$-0.281950\pi$
$858$	2.55082	−	0.828811i	0.0870835	−	0.0282952i
$859$	−17.6337	−	12.8116i	−0.601654	−	0.437127i	0.244812	−	0.969571i	$-0.421274\pi$
$859$	−17.6337	−	12.8116i	−0.601654	−	0.437127i	−0.846465	+	0.532444i	$0.821274\pi$
$860$		0			0
$861$	−27.4993	+	19.9794i	−0.937173	+	0.680896i
$862$	9.32621	−	12.8364i	0.317652	−	0.437211i
$863$	7.51669	−	10.3458i	0.255871	−	0.352176i	−0.661685	−	0.749782i	$-0.730159\pi$
$863$	7.51669	−	10.3458i	0.255871	−	0.352176i	0.917557	+	0.397605i	$0.130159\pi$
$864$	−14.0360	+	10.1977i	−0.477513	+	0.346933i
$865$		0			0
$866$	2.38553	+	1.73319i	0.0810637	+	0.0588962i
$867$	−11.4482	+	3.71975i	−0.388801	+	0.126329i
$868$		−	13.3814i		−	0.454194i
$869$	11.6317	+	35.7988i	0.394579	+	1.21439i
$870$		0			0
$871$	0.523084	−	1.60989i	0.0177240	−	0.0545489i
$872$	−0.139867	−	0.0454454i	−0.00473648	−	0.00153898i
$873$	12.2031	+	16.7961i	0.413012	+	0.568463i
$874$	−46.0863			−1.55889
$875$		0			0
$876$	6.09640			0.205978
$877$	−5.61535	−	7.72887i	−0.189617	−	0.260985i	0.703615	−	0.710581i	$-0.251568\pi$
$877$	−5.61535	−	7.72887i	−0.189617	−	0.260985i	−0.893232	+	0.449596i	$0.851568\pi$
$878$	−44.9615	−	14.6089i	−1.51738	−	0.493025i
$879$	−2.56843	+	7.90481i	−0.0866309	+	0.266622i
$880$		0			0
$881$	−12.0929	−	37.2180i	−0.407419	−	1.25391i	−0.918859	−	0.394587i	$-0.870888\pi$
$881$	−12.0929	−	37.2180i	−0.407419	−	1.25391i	0.511440	−	0.859319i	$-0.329112\pi$
$882$		−	59.1400i		−	1.99135i
$883$	−33.3111	+	10.8234i	−1.12101	+	0.364238i	−0.810152	−	0.586220i	$-0.800616\pi$
$883$	−33.3111	+	10.8234i	−1.12101	+	0.364238i	−0.310856	+	0.950457i	$0.600616\pi$
$884$	0.0899074	+	0.0653215i	0.00302391	+	0.00219700i
$885$		0			0
$886$	−40.7360	+	29.5964i	−1.36855	+	0.994312i
$887$	21.3036	−	29.3219i	0.715304	−	0.984531i	−0.284363	−	0.958717i	$-0.591782\pi$
$887$	21.3036	−	29.3219i	0.715304	−	0.984531i	0.999667	−	0.0258147i	$-0.00821798\pi$
$888$	4.43955	−	6.11052i	0.148982	−	0.205056i
$889$	−43.8747	+	31.8769i	−1.47151	+	1.06912i
$890$		0			0
$891$	−14.9278	−	10.8457i	−0.500100	−	0.363344i
$892$	5.02432	−	1.63250i	0.168227	−	0.0546601i
$893$			5.10841i			0.170946i
$894$	−4.44593	−	13.6832i	−0.148694	−	0.457633i
$895$		0			0
$896$	−18.4933	+	56.9164i	−0.617817	+	1.90144i
$897$	−1.90925	−	0.620353i	−0.0637480	−	0.0207130i
$898$	6.23349	+	8.57967i	0.208014	+	0.286307i
$899$	14.4378			0.481528
$900$		0			0
$901$	−0.286386			−0.00954089
$902$	−40.3735	−	55.5694i	−1.34429	−	1.85026i
$903$	−4.30607	−	1.39913i	−0.143297	−	0.0465601i
$904$	8.57332	−	26.3860i	0.285144	−	0.877584i
$905$		0			0
$906$	0.569869	+	1.75388i	0.0189326	+	0.0582686i
$907$		−	40.8532i		−	1.35651i	−0.734827	−	0.678255i	$-0.762737\pi$
$907$		−	40.8532i		−	1.35651i	0.734827	−	0.678255i	$-0.237263\pi$
$908$	−8.93174	+	2.90210i	−0.296410	+	0.0963095i
$909$	7.19741	+	5.22922i	0.238723	+	0.173442i
$910$		0			0
$911$	−10.3124	+	7.49237i	−0.341664	+	0.248233i	−0.745364	−	0.666658i	$-0.767724\pi$
$911$	−10.3124	+	7.49237i	−0.341664	+	0.248233i	0.403700	+	0.914892i	$0.367724\pi$
$912$	−11.5226	+	15.8595i	−0.381553	+	0.525162i
$913$	24.1229	−	33.2023i	0.798351	−	1.09884i
$914$	−26.1226	+	18.9792i	−0.864058	+	0.627775i
$915$		0			0
$916$	−10.1468	−	7.37207i	−0.335259	−	0.243580i
$917$	−73.0815	+	23.7456i	−2.41337	+	0.784150i
$918$			1.52858i			0.0504506i
$919$	−2.98883	−	9.19868i	−0.0985924	−	0.303436i	0.889581	−	0.456778i	$-0.150997\pi$
$919$	−2.98883	−	9.19868i	−0.0985924	−	0.303436i	−0.988173	+	0.153341i	$0.950997\pi$
$920$		0			0
$921$	−5.83172	+	17.9482i	−0.192162	+	0.591413i
$922$	11.3210	+	3.67840i	0.372836	+	0.121142i
$923$	−1.07951	−	1.48581i	−0.0355323	−	0.0489061i
$924$	−10.6461			−0.350231
$925$		0			0
$926$	16.1917			0.532094
$927$	−0.585715	−	0.806167i	−0.0192374	−	0.0264780i
$928$	17.4598	+	5.67303i	0.573146	+	0.186226i
$929$	−3.37431	+	10.3850i	−0.110707	+	0.340722i	−0.991028	−	0.133658i	$-0.957328\pi$
$929$	−3.37431	+	10.3850i	−0.110707	+	0.340722i	0.880320	+	0.474380i	$0.157328\pi$
$930$		0			0
$931$	−24.1452	−	74.3113i	−0.791328	−	2.43546i
$932$		−	6.52711i		−	0.213803i
$933$	9.11417	−	2.96137i	0.298384	−	0.0969510i
$934$	26.1786	+	19.0199i	0.856589	+	0.622349i
$935$		0			0
$936$	2.27063	−	1.64971i	0.0742178	−	0.0539224i
$937$	9.37319	−	12.9011i	0.306209	−	0.421460i	−0.627985	−	0.778225i	$-0.716120\pi$
$937$	9.37319	−	12.9011i	0.306209	−	0.421460i	0.934194	+	0.356765i	$0.116120\pi$
$938$	−13.4216	+	18.4733i	−0.438232	+	0.603175i
$939$	−9.76628	+	7.09562i	−0.318710	+	0.231557i
$940$		0			0
$941$	−4.79505	−	3.48381i	−0.156314	−	0.113569i	0.506879	−	0.862017i	$-0.330799\pi$
$941$	−4.79505	−	3.48381i	−0.156314	−	0.113569i	−0.663193	+	0.748448i	$0.730799\pi$
$942$	−11.1734	+	3.63047i	−0.364051	+	0.118287i
$943$			51.4117i			1.67419i
$944$	6.92649	+	21.3176i	0.225438	+	0.693827i
$945$		0			0
$946$	2.82730	−	8.70154i	0.0919235	−	0.282912i
$947$	−0.941910	−	0.306045i	−0.0306080	−	0.00994513i	0.293673	−	0.955906i	$-0.405122\pi$
$947$	−0.941910	−	0.306045i	−0.0306080	−	0.00994513i	−0.324281	+	0.945961i	$0.605122\pi$
$948$	3.34763	+	4.60761i	0.108726	+	0.149648i
$949$	−5.89681			−0.191418
$950$		0			0
$951$	−11.9308			−0.386882
$952$	1.23226	+	1.69606i	0.0399379	+	0.0549697i
$953$	50.9759	+	16.5631i	1.65127	+	0.536531i	0.979015	−	0.203787i	$-0.0653250\pi$
$953$	50.9759	+	16.5631i	1.65127	+	0.536531i	0.672257	+	0.740318i	$0.265325\pi$
$954$	1.59822	−	4.91881i	0.0517442	−	0.159252i
$955$		0			0
$956$	2.25183	+	6.93042i	0.0728294	+	0.224146i
$957$		−	11.4866i		−	0.371308i
$958$	−60.8380	+	19.7675i	−1.96559	+	0.638658i
$959$	−38.7107	−	28.1250i	−1.25003	−	0.908203i
$960$		0			0
$961$	15.1956	−	11.0402i	0.490180	−	0.356137i
$962$	3.07068	−	4.22643i	0.0990027	−	0.136266i
$963$	−2.41096	+	3.31840i	−0.0776920	+	0.106934i
$964$	−0.405371	+	0.294519i	−0.0130561	+	0.00948582i
$965$		0			0
$966$	21.9085	+	15.9175i	0.704895	+	0.512136i
$967$	28.2796	−	9.18861i	0.909412	−	0.295486i	0.183296	−	0.983058i	$-0.441323\pi$
$967$	28.2796	−	9.18861i	0.909412	−	0.295486i	0.726116	+	0.687572i	$0.241323\pi$
$968$			8.49141i			0.272924i
$969$	0.283387	+	0.872176i	0.00910370	+	0.0280183i
$970$		0			0
$971$	18.7316	−	57.6498i	0.601125	−	1.85007i	0.0796154	−	0.996826i	$-0.474631\pi$
$971$	18.7316	−	57.6498i	0.601125	−	1.85007i	0.521509	−	0.853246i	$-0.325369\pi$
$972$	−11.9426	−	3.88039i	−0.383059	−	0.124463i
$973$	−17.9724	−	24.7369i	−0.576168	−	0.793027i
$974$	−28.1954			−0.903440
$975$		0			0
$976$	57.9720			1.85564
$977$	−26.1641	−	36.0117i	−0.837062	−	1.15212i	−0.986567	−	0.163356i	$-0.947768\pi$
$977$	−26.1641	−	36.0117i	−0.837062	−	1.15212i	0.149505	−	0.988761i	$-0.452232\pi$
$978$	−6.34718	−	2.06232i	−0.202960	−	0.0659458i
$979$	−8.78060	+	27.0239i	−0.280629	+	0.863688i
$980$		0			0
$981$	−0.0577692	−	0.177795i	−0.00184443	−	0.00567657i
$982$		−	15.0675i		−	0.480822i
$983$	36.3685	−	11.8168i	1.15997	−	0.376898i	0.335082	−	0.942189i	$-0.391236\pi$
$983$	36.3685	−	11.8168i	1.15997	−	0.376898i	0.824892	+	0.565291i	$0.191236\pi$
$984$	11.7582	+	8.54283i	0.374838	+	0.272336i
$985$		0			0
$986$	1.30856	−	0.950724i	0.0416730	−	0.0302772i
$987$	1.76436	−	2.42844i	0.0561602	−	0.0772979i
$988$	−1.55857	+	2.14519i	−0.0495847	+	0.0682475i
$989$	−5.54027	+	4.02524i	−0.176170	+	0.127995i
$990$		0			0
$991$	−18.3713	−	13.3475i	−0.583584	−	0.423998i	0.256431	−	0.966563i	$-0.417453\pi$
$991$	−18.3713	−	13.3475i	−0.583584	−	0.423998i	−0.840014	+	0.542564i	$0.817453\pi$
$992$	−14.7744	+	4.80049i	−0.469087	+	0.152416i
$993$			9.11678i			0.289312i
$994$	7.65574	+	23.5619i	0.242825	+	0.747339i
$995$		0			0
$996$	1.91889	−	5.90573i	0.0608023	−	0.187130i
$997$	19.6188	+	6.37453i	0.621333	+	0.201883i	0.602732	−	0.797944i	$-0.294079\pi$
$997$	19.6188	+	6.37453i	0.621333	+	0.201883i	0.0186012	+	0.999827i	$0.494079\pi$
$998$	−35.9490	−	49.4795i	−1.13794	−	1.56625i
$999$	21.1439			0.668962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.j.374.3		32
5.2	odd	4		625.2.d.m.251.4		16
5.3	odd	4		625.2.d.q.251.1		16
5.4	even	2	inner	625.2.e.j.374.6		32
25.2	odd	20		625.2.d.n.126.1		16
25.3	odd	20		625.2.a.e.1.7	✓	8
25.4	even	10		625.2.b.d.624.5		16
25.6	even	5		625.2.e.k.124.6		32
25.8	odd	20		625.2.d.p.501.4		16
25.9	even	10	inner	625.2.e.j.249.3		32
25.11	even	5		625.2.e.k.499.3		32
25.12	odd	20		625.2.d.m.376.4		16
25.13	odd	20		625.2.d.q.376.1		16
25.14	even	10		625.2.e.k.499.6		32
25.16	even	5	inner	625.2.e.j.249.6		32
25.17	odd	20		625.2.d.n.501.1		16
25.19	even	10		625.2.e.k.124.3		32
25.21	even	5		625.2.b.d.624.12		16
25.22	odd	20		625.2.a.g.1.2	yes	8
25.23	odd	20		625.2.d.p.126.4		16
75.47	even	20		5625.2.a.s.1.7		8
75.53	even	20		5625.2.a.be.1.2		8
100.3	even	20		10000.2.a.bn.1.4		8
100.47	even	20		10000.2.a.be.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.7	✓	8	25.3	odd	20
625.2.a.g.1.2	yes	8	25.22	odd	20
625.2.b.d.624.5		16	25.4	even	10
625.2.b.d.624.12		16	25.21	even	5
625.2.d.m.251.4		16	5.2	odd	4
625.2.d.m.376.4		16	25.12	odd	20
625.2.d.n.126.1		16	25.2	odd	20
625.2.d.n.501.1		16	25.17	odd	20
625.2.d.p.126.4		16	25.23	odd	20
625.2.d.p.501.4		16	25.8	odd	20
625.2.d.q.251.1		16	5.3	odd	4
625.2.d.q.376.1		16	25.13	odd	20
625.2.e.j.249.3		32	25.9	even	10	inner
625.2.e.j.249.6		32	25.16	even	5	inner
625.2.e.j.374.3		32	1.1	even	1	trivial
625.2.e.j.374.6		32	5.4	even	2	inner
625.2.e.k.124.3		32	25.19	even	10
625.2.e.k.124.6		32	25.6	even	5
625.2.e.k.499.3		32	25.11	even	5
625.2.e.k.499.6		32	25.14	even	10
5625.2.a.s.1.7		8	75.47	even	20
5625.2.a.be.1.2		8	75.53	even	20
10000.2.a.be.1.5		8	100.47	even	20
10000.2.a.bn.1.4		8	100.3	even	20

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.989484 - 1.36191i) q^{2} +(0.675574 + 0.219507i) q^{3} +(-0.257680 + 0.793058i) q^{4} +(-0.369521 - 1.13727i) q^{6} -4.59110i q^{7} +(-1.86699 + 0.606623i) q^{8} +(-2.01883 - 1.46677i) q^{9} +(-3.16713 + 2.30105i) q^{11} +(-0.348164 + 0.479206i) q^{12} +(0.336765 - 0.463518i) q^{13} +(-6.25266 + 4.54282i) q^{14} +(4.02276 + 2.92270i) q^{16} +(0.221226 - 0.0718808i) q^{17} +4.20081i q^{18} +(1.71507 + 5.27846i) q^{19} +(1.00778 - 3.10163i) q^{21} +(6.26765 + 2.03648i) q^{22} +(-2.89935 - 3.99061i) q^{23} -1.39445 q^{24} -0.964492 q^{26} +(-2.29449 - 3.15809i) q^{27} +(3.64101 + 1.18304i) q^{28} +(-1.27643 + 3.92845i) q^{29} +(-1.08011 - 3.32424i) q^{31} -4.44444i q^{32} +(-2.64473 + 0.859324i) q^{33} +(-0.316795 - 0.230165i) q^{34} +(1.68345 - 1.22310i) q^{36} +(-3.18373 + 4.38203i) q^{37} +(5.49173 - 7.55872i) q^{38} +(0.329255 - 0.239218i) q^{39} +(-8.43214 - 6.12630i) q^{41} +(-5.22132 + 1.69651i) q^{42} -1.38833i q^{43} +(-1.00876 - 3.10465i) q^{44} +(-2.56598 + 7.89729i) q^{46} +(0.875370 + 0.284425i) q^{47} +(2.07611 + 2.85753i) q^{48} -14.0782 q^{49} +0.165233 q^{51} +(0.280819 + 0.386514i) q^{52} +(-1.17092 - 0.380455i) q^{53} +(-2.03067 + 6.24976i) q^{54} +(2.78507 + 8.57157i) q^{56} +3.94246i q^{57} +(6.61320 - 2.14876i) q^{58} +(3.64689 + 2.64962i) q^{59} +(9.43214 - 6.85285i) q^{61} +(-3.45856 + 4.76029i) q^{62} +(-6.73409 + 9.26868i) q^{63} +(1.99259 - 1.44770i) q^{64} +(3.78724 + 2.75159i) q^{66} +(2.80987 - 0.912982i) q^{67} +0.193968i q^{68} +(-1.08276 - 3.33238i) q^{69} +(0.990558 - 3.04862i) q^{71} +(4.65893 + 1.51378i) q^{72} +(-6.04961 - 8.32657i) q^{73} +9.11816 q^{74} -4.62806 q^{76} +(10.5644 + 14.5406i) q^{77} +(-0.651586 - 0.211713i) q^{78} +(2.97123 - 9.14449i) q^{79} +(1.45651 + 4.48267i) q^{81} +17.5457i q^{82} +(-9.97030 + 3.23955i) q^{83} +(2.20009 + 1.59846i) q^{84} +(-1.89077 + 1.37373i) q^{86} +(-1.72465 + 2.37377i) q^{87} +(4.51714 - 6.21731i) q^{88} +(5.87207 - 4.26631i) q^{89} +(-2.12806 - 1.54612i) q^{91} +(3.91189 - 1.27105i) q^{92} -2.48286i q^{93} +(-0.478804 - 1.47361i) q^{94} +(0.975587 - 3.00255i) q^{96} +(-7.91252 - 2.57093i) q^{97} +(13.9302 + 19.1733i) q^{98} +9.76903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} + 14 q^{6} + 24 q^{9} - 6 q^{11} + 2 q^{14} + 2 q^{16} - 20 q^{19} + 14 q^{21} - 20 q^{24} + 44 q^{26} - 16 q^{31} + 12 q^{34} + 2 q^{36} - 2 q^{39} - 16 q^{41} + 62 q^{44} + 84 q^{46} + 16 q^{49}+ \cdots + 88 q^{99}+O(q^{100}) \) 32 * q + 6 * q^4 + 14 * q^6 + 24 * q^9 - 6 * q^11 + 2 * q^14 + 2 * q^16 - 20 * q^19 + 14 * q^21 - 20 * q^24 + 44 * q^26 - 16 * q^31 + 12 * q^34 + 2 * q^36 - 2 * q^39 - 16 * q^41 + 62 * q^44 + 84 * q^46 + 16 * q^49 - 56 * q^51 - 100 * q^54 + 70 * q^56 + 30 * q^59 + 34 * q^61 - 74 * q^64 + 88 * q^66 + 18 * q^69 - 26 * q^71 + 72 * q^74 - 40 * q^76 + 110 * q^79 - 38 * q^81 - 118 * q^84 + 14 * q^86 - 56 * q^91 - 8 * q^94 - 86 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more