LMFDB - Embedded newform 625.2.e.j.374.4

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)

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")

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);

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			374.4
Character	$\chi$	$=$	625.374
Dual form			625.2.e.j.249.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.294474 - 0.405309i) q^{2} +(-2.94186 - 0.955869i) q^{3} +(0.540474 - 1.66341i) q^{4} +(0.478880 + 1.47384i) q^{6} +0.0237879i q^{7} +(-1.78629 + 0.580400i) q^{8} +(5.31382 + 3.86071i) q^{9} +(-2.89894 + 2.10620i) q^{11} +(-3.18000 + 4.37689i) q^{12} +(-2.21940 + 3.05474i) q^{13} +(0.00964144 - 0.00700492i) q^{14} +(-2.06870 - 1.50300i) q^{16} +(3.44570 - 1.11958i) q^{17} -3.29062i q^{18} +(0.751170 + 2.31186i) q^{19} +(0.0227381 - 0.0699807i) q^{21} +(1.70733 + 0.554744i) q^{22} +(1.00828 + 1.38777i) q^{23} +5.80980 q^{24} +1.89167 q^{26} +(-6.48766 - 8.92950i) q^{27} +(0.0395689 + 0.0128567i) q^{28} +(-1.19198 + 3.66855i) q^{29} +(-1.85713 - 5.71565i) q^{31} +5.03748i q^{32} +(10.5415 - 3.42515i) q^{33} +(-1.46845 - 1.06689i) q^{34} +(9.29391 - 6.75242i) q^{36} +(-0.217074 + 0.298777i) q^{37} +(0.715819 - 0.985240i) q^{38} +(9.44911 - 6.86518i) q^{39} +(6.31761 + 4.59002i) q^{41} +(-0.0350596 + 0.0113915i) q^{42} -0.174574i q^{43} +(1.93667 + 5.96047i) q^{44} +(0.265566 - 0.817327i) q^{46} +(7.42853 + 2.41368i) q^{47} +(4.64916 + 6.39902i) q^{48} +6.99943 q^{49} -11.2070 q^{51} +(3.88175 + 5.34278i) q^{52} +(8.53273 + 2.77245i) q^{53} +(-1.70876 + 5.25902i) q^{54} +(-0.0138065 - 0.0424920i) q^{56} -7.51920i q^{57} +(1.83790 - 0.597171i) q^{58} +(-3.60446 - 2.61879i) q^{59} +(-7.45430 + 5.41587i) q^{61} +(-1.76973 + 2.43582i) q^{62} +(-0.0918382 + 0.126404i) q^{63} +(-2.09566 + 1.52259i) q^{64} +(-4.49246 - 3.26396i) q^{66} +(4.25489 - 1.38250i) q^{67} -6.33671i q^{68} +(-1.63968 - 5.04642i) q^{69} +(-2.99579 + 9.22010i) q^{71} +(-11.7328 - 3.81221i) q^{72} +(-2.32403 - 3.19875i) q^{73} +0.185020 q^{74} +4.25156 q^{76} +(-0.0501021 - 0.0689596i) q^{77} +(-5.56504 - 1.80819i) q^{78} +(2.99236 - 9.20955i) q^{79} +(4.46129 + 13.7304i) q^{81} -3.91223i q^{82} +(-8.51877 + 2.76792i) q^{83} +(-0.104117 - 0.0756454i) q^{84} +(-0.0707566 + 0.0514077i) q^{86} +(7.01330 - 9.65298i) q^{87} +(3.95590 - 5.44483i) q^{88} +(-13.7655 + 10.0012i) q^{89} +(-0.0726659 - 0.0527948i) q^{91} +(2.85338 - 0.927119i) q^{92} +18.5898i q^{93} +(-1.20923 - 3.72161i) q^{94} +(4.81518 - 14.8196i) q^{96} +(2.62908 + 0.854239i) q^{97} +(-2.06115 - 2.83693i) q^{98} -23.5359 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 $

$2$	−0.294474	−	0.405309i	−0.208225	−	0.286597i	0.692113	−	0.721790i	$-0.256680\pi$
$2$	−0.294474	−	0.405309i	−0.208225	−	0.286597i	−0.900337	+	0.435193i	$0.856680\pi$
$3$	−2.94186	−	0.955869i	−1.69848	−	0.551871i	−0.710134	−	0.704066i	$-0.751366\pi$
$3$	−2.94186	−	0.955869i	−1.69848	−	0.551871i	−0.988350	+	0.152195i	$0.951366\pi$
$4$	0.540474	−	1.66341i	0.270237	−	0.831704i
$5$		0			0
$5$		0			0
$6$	0.478880	+	1.47384i	0.195502	+	0.601693i
$7$			0.0237879i			0.00899097i	0.999990	+	0.00449549i	$0.00143096\pi$
$7$			0.0237879i			0.00899097i	−0.999990	+	0.00449549i	$0.998569\pi$
$8$	−1.78629	+	0.580400i	−0.631548	+	0.205202i
$9$	5.31382	+	3.86071i	1.77127	+	1.28690i
$10$		0			0
$11$	−2.89894	+	2.10620i	−0.874063	+	0.635044i	−0.931674	−	0.363295i	$-0.881652\pi$
$11$	−2.89894	+	2.10620i	−0.874063	+	0.635044i	0.0576108	+	0.998339i	$0.481652\pi$
$12$	−3.18000	+	4.37689i	−0.917986	+	1.26350i
$13$	−2.21940	+	3.05474i	−0.615551	+	0.847234i	−0.997020	−	0.0771484i	$-0.975418\pi$
$13$	−2.21940	+	3.05474i	−0.615551	+	0.847234i	0.381468	+	0.924382i	$0.375418\pi$
$14$	0.00964144	−	0.00700492i	0.00257678	−	0.00187214i
$15$		0			0
$16$	−2.06870	−	1.50300i	−0.517175	−	0.375750i
$17$	3.44570	−	1.11958i	0.835706	−	0.271537i	0.140259	−	0.990115i	$-0.455206\pi$
$17$	3.44570	−	1.11958i	0.835706	−	0.271537i	0.695447	+	0.718577i	$0.255206\pi$
$18$		−	3.29062i		−	0.775606i
$19$	0.751170	+	2.31186i	0.172330	+	0.530378i	0.999501	−	0.0315721i	$-0.0100514\pi$
$19$	0.751170	+	2.31186i	0.172330	+	0.530378i	−0.827171	+	0.561950i	$0.810051\pi$
$20$		0			0
$21$	0.0227381	−	0.0699807i	0.00496186	−	0.0152710i
$22$	1.70733	+	0.554744i	0.364003	+	0.118272i
$23$	1.00828	+	1.38777i	0.210240	+	0.289371i	0.901094	−	0.433624i	$-0.142765\pi$
$23$	1.00828	+	1.38777i	0.210240	+	0.289371i	−0.690854	+	0.722994i	$0.742765\pi$
$24$	5.80980			1.18592
$25$		0			0
$26$	1.89167			0.370987
$27$	−6.48766	−	8.92950i	−1.24855	−	1.71848i
$28$	0.0395689	+	0.0128567i	0.00747782	+	0.00242969i
$29$	−1.19198	+	3.66855i	−0.221346	+	0.681232i	0.777296	+	0.629135i	$0.216591\pi$
$29$	−1.19198	+	3.66855i	−0.221346	+	0.681232i	−0.998642	+	0.0520974i	$0.983409\pi$
$30$		0			0
$31$	−1.85713	−	5.71565i	−0.333550	−	1.02656i	−0.967432	−	0.253131i	$-0.918540\pi$
$31$	−1.85713	−	5.71565i	−0.333550	−	1.02656i	0.633882	−	0.773430i	$-0.281460\pi$
$32$			5.03748i			0.890510i
$33$	10.5415	−	3.42515i	1.83505	−	0.596243i
$34$	−1.46845	−	1.06689i	−0.251836	−	0.182970i
$35$		0			0
$36$	9.29391	−	6.75242i	1.54899	−	1.12540i
$37$	−0.217074	+	0.298777i	−0.0356868	+	0.0491186i	−0.826488	−	0.562955i	$-0.809664\pi$
$37$	−0.217074	+	0.298777i	−0.0356868	+	0.0491186i	0.790801	+	0.612074i	$0.209664\pi$
$38$	0.715819	−	0.985240i	0.116121	−	0.159827i
$39$	9.44911	−	6.86518i	1.51307	−	1.09931i
$40$		0			0
$41$	6.31761	+	4.59002i	0.986646	+	0.716840i	0.959184	−	0.282783i	$-0.0912576\pi$
$41$	6.31761	+	4.59002i	0.986646	+	0.716840i	0.0274616	+	0.999623i	$0.491258\pi$
$42$	−0.0350596	+	0.0113915i	−0.00540981	+	0.00175775i
$43$		−	0.174574i		−	0.0266224i	−0.999911	−	0.0133112i	$-0.995763\pi$
$43$		−	0.174574i		−	0.0266224i	0.999911	−	0.0133112i	$-0.00423721\pi$
$44$	1.93667	+	5.96047i	0.291964	+	0.898574i
$45$		0			0
$46$	0.265566	−	0.817327i	0.0391555	−	0.120508i
$47$	7.42853	+	2.41368i	1.08356	+	0.352071i	0.795756	−	0.605618i	$-0.207074\pi$
$47$	7.42853	+	2.41368i	1.08356	+	0.352071i	0.287807	+	0.957689i	$0.407074\pi$
$48$	4.64916	+	6.39902i	0.671049	+	0.923619i
$49$	6.99943			0.999919
$50$		0			0
$51$	−11.2070			−1.56929
$52$	3.88175	+	5.34278i	0.538302	+	0.740910i
$53$	8.53273	+	2.77245i	1.17206	+	0.380826i	0.829412	−	0.558638i	$-0.188676\pi$
$53$	8.53273	+	2.77245i	1.17206	+	0.380826i	0.342649	+	0.939464i	$0.388676\pi$
$54$	−1.70876	+	5.25902i	−0.232533	+	0.715661i
$55$		0			0
$56$	−0.0138065	−	0.0424920i	−0.00184497	−	0.00567823i
$57$		−	7.51920i		−	0.995943i
$58$	1.83790	−	0.597171i	0.241328	−	0.0784124i
$59$	−3.60446	−	2.61879i	−0.469261	−	0.340938i	0.327892	−	0.944715i	$-0.393662\pi$
$59$	−3.60446	−	2.61879i	−0.469261	−	0.340938i	−0.797153	+	0.603777i	$0.793662\pi$
$60$		0			0
$61$	−7.45430	+	5.41587i	−0.954426	+	0.693431i	−0.951850	−	0.306566i	$-0.900820\pi$
$61$	−7.45430	+	5.41587i	−0.954426	+	0.693431i	−0.00257641	+	0.999997i	$0.500820\pi$
$62$	−1.76973	+	2.43582i	−0.224756	+	0.309350i
$63$	−0.0918382	+	0.126404i	−0.0115705	+	0.0159255i
$64$	−2.09566	+	1.52259i	−0.261958	+	0.190324i
$65$		0			0
$66$	−4.49246	−	3.26396i	−0.552983	−	0.401766i
$67$	4.25489	−	1.38250i	0.519817	−	0.168899i	−0.0373451	−	0.999302i	$-0.511890\pi$
$67$	4.25489	−	1.38250i	0.519817	−	0.168899i	0.557162	+	0.830404i	$0.311890\pi$
$68$		−	6.33671i		−	0.768439i
$69$	−1.63968	−	5.04642i	−0.197394	−	0.607517i
$70$		0			0
$71$	−2.99579	+	9.22010i	−0.355535	+	1.09422i	0.600164	+	0.799877i	$0.295102\pi$
$71$	−2.99579	+	9.22010i	−0.355535	+	1.09422i	−0.955699	+	0.294347i	$0.904898\pi$
$72$	−11.7328	−	3.81221i	−1.38272	−	0.449273i
$73$	−2.32403	−	3.19875i	−0.272007	−	0.374385i	0.651059	−	0.759027i	$-0.274325\pi$
$73$	−2.32403	−	3.19875i	−0.272007	−	0.374385i	−0.923066	+	0.384642i	$0.874325\pi$
$74$	0.185020			0.0215081
$75$		0			0
$76$	4.25156			0.487687
$77$	−0.0501021	−	0.0689596i	−0.00570967	−	0.00785868i
$78$	−5.56504	−	1.80819i	−0.630116	−	0.204737i
$79$	2.99236	−	9.20955i	0.336667	−	1.03616i	−0.629228	−	0.777221i	$-0.716629\pi$
$79$	2.99236	−	9.20955i	0.336667	−	1.03616i	0.965895	−	0.258934i	$-0.0833713\pi$
$80$		0			0
$81$	4.46129	+	13.7304i	0.495699	+	1.52560i
$82$		−	3.91223i		−	0.432033i
$83$	−8.51877	+	2.76792i	−0.935057	+	0.303818i	−0.736629	−	0.676297i	$-0.763584\pi$
$83$	−8.51877	+	2.76792i	−0.935057	+	0.303818i	−0.198428	+	0.980115i	$0.563584\pi$
$84$	−0.104117	−	0.0756454i	−0.0113601	−	0.00825359i
$85$		0			0
$86$	−0.0707566	+	0.0514077i	−0.00762988	+	0.00554343i
$87$	7.01330	−	9.65298i	0.751905	−	1.03491i
$88$	3.95590	−	5.44483i	0.421700	−	0.580421i
$89$	−13.7655	+	10.0012i	−1.45914	+	1.06013i	−0.475551	+	0.879688i	$0.657751\pi$
$89$	−13.7655	+	10.0012i	−1.45914	+	1.06013i	−0.983586	+	0.180438i	$0.942249\pi$
$90$		0			0
$91$	−0.0726659	−	0.0527948i	−0.00761745	−	0.00553440i
$92$	2.85338	−	0.927119i	0.297485	−	0.0966588i
$93$			18.5898i			1.92767i
$94$	−1.20923	−	3.72161i	−0.124722	−	0.383855i
$95$		0			0
$96$	4.81518	−	14.8196i	0.491447	−	1.51252i
$97$	2.62908	+	0.854239i	0.266942	+	0.0867348i	0.439430	−	0.898277i	$-0.355180\pi$
$97$	2.62908	+	0.854239i	0.266942	+	0.0867348i	−0.172488	+	0.985012i	$0.555180\pi$
$98$	−2.06115	−	2.83693i	−0.208208	−	0.286574i
$99$	−23.5359			−2.36545
$100$		0			0
$101$	10.3526			1.03012			0.515062	−	0.857153i	$-0.327769\pi$
$101$	10.3526			1.03012			0.515062	+	0.857153i	$0.327769\pi$
$102$	3.30016	+	4.54228i	0.326764	+	0.449753i
$103$	−17.3961	−	5.65234i	−1.71409	−	0.556941i	−0.723083	−	0.690761i	$-0.757276\pi$
$103$	−17.3961	−	5.65234i	−1.71409	−	0.556941i	−0.991006	+	0.133820i	$0.957276\pi$
$104$	2.19152	−	6.74479i	0.214896	−	0.661381i
$105$		0			0
$106$	−1.38897	−	4.27481i	−0.134909	−	0.415206i
$107$			15.8786i			1.53504i	0.641023	+	0.767522i	$0.278510\pi$
$107$			15.8786i			1.53504i	−0.641023	+	0.767522i	$0.721490\pi$
$108$	−18.3598	+	5.96546i	−1.76667	+	0.574027i
$109$	4.82262	+	3.50384i	0.461924	+	0.335607i	0.794285	−	0.607545i	$-0.207845\pi$
$109$	4.82262	+	3.50384i	0.461924	+	0.335607i	−0.332362	+	0.943152i	$0.607845\pi$
$110$		0			0
$111$	0.924194	−	0.671466i	0.0877206	−	0.0637327i
$112$	0.0357531	−	0.0492100i	0.00337836	−	0.00464991i
$113$	−1.42732	+	1.96454i	−0.134271	+	0.184808i	−0.870858	−	0.491535i	$-0.836436\pi$
$113$	−1.42732	+	1.96454i	−0.134271	+	0.184808i	0.736587	+	0.676343i	$0.236436\pi$
$114$	−3.04760	+	2.21421i	−0.285434	+	0.207380i
$115$		0			0
$116$	5.45805	+	3.96551i	0.506767	+	0.368188i
$117$	−23.5870	+	7.66387i	−2.18062	+	0.708525i
$118$			2.23209i			0.205480i
$119$	0.0266324	+	0.0819660i	0.00244139	+	0.00751381i
$120$		0			0
$121$	0.568575	−	1.74989i	0.0516886	−	0.159081i
$122$	4.39020	+	1.42646i	0.397470	+	0.129146i
$123$	−14.1981	−	19.5420i	−1.28020	−	1.76204i
$124$	−10.5112			−0.943932
$125$		0			0
$126$	0.0782768			0.00697345
$127$	10.0554	+	13.8401i	0.892274	+	1.22811i	0.972868	+	0.231363i	$0.0743184\pi$
$127$	10.0554	+	13.8401i	0.892274	+	1.22811i	−0.0805937	+	0.996747i	$0.525682\pi$
$128$	10.8161	+	3.51436i	0.956017	+	0.310629i
$129$	−0.166870	+	0.513574i	−0.0146921	+	0.0452177i
$130$		0			0
$131$	1.48005	+	4.55513i	0.129313	+	0.397983i	0.994662	−	0.103186i	$-0.0329035\pi$
$131$	1.48005	+	4.55513i	0.129313	+	0.397983i	−0.865349	+	0.501169i	$0.832904\pi$
$132$		−	19.3861i		−	1.68734i
$133$	−0.0549943	+	0.0178687i	−0.00476861	+	0.00154942i
$134$	−1.81329	−	1.31743i	−0.156645	−	0.113809i
$135$		0			0
$136$	−5.50522	+	3.99977i	−0.472068	+	0.342978i
$137$	7.52974	−	10.3638i	0.643309	−	0.885439i	−0.355478	−	0.934685i	$-0.615682\pi$
$137$	7.52974	−	10.3638i	0.643309	−	0.885439i	0.998787	+	0.0492461i	$0.0156819\pi$
$138$	−1.56251	+	2.15062i	−0.133010	+	0.183073i
$139$	−6.42376	+	4.66713i	−0.544856	+	0.395861i	−0.825885	−	0.563838i	$-0.809324\pi$
$139$	−6.42376	+	4.66713i	−0.544856	+	0.395861i	0.281029	+	0.959699i	$0.409324\pi$
$140$		0			0
$141$	−19.5466	−	14.2014i	−1.64612	−	1.19597i
$142$	4.61917	−	1.50086i	0.387632	−	0.125949i
$143$		−	13.5300i		−	1.13144i
$144$	−5.19004	−	15.9733i	−0.432504	−	1.33111i
$145$		0			0
$146$	−0.612115	+	1.88390i	−0.0506590	+	0.155912i
$147$	−20.5914	−	6.69054i	−1.69835	−	0.551827i
$148$	0.379665	+	0.522564i	0.0312082	+	0.0429545i
$149$	5.62724			0.461002			0.230501	−	0.973072i	$-0.425964\pi$
$149$	5.62724			0.461002			0.230501	+	0.973072i	$0.425964\pi$
$150$		0			0
$151$	−7.36960			−0.599730			−0.299865	−	0.953982i	$-0.596942\pi$
$151$	−7.36960			−0.599730			−0.299865	+	0.953982i	$0.596942\pi$
$152$	−2.68361	−	3.69367i	−0.217670	−	0.299596i
$153$	22.6322	+	7.35365i	1.82971	+	0.594507i
$154$	−0.0131962	+	0.0406137i	−0.00106338	+	0.00327274i
$155$		0			0
$156$	−6.31259	−	19.4282i	−0.505412	−	1.55550i
$157$			8.63091i			0.688822i	0.938819	+	0.344411i	$0.111921\pi$
$157$			8.63091i			0.688822i	−0.938819	+	0.344411i	$0.888079\pi$
$158$	−4.61389	+	1.49914i	−0.367061	+	0.119265i
$159$	−22.4520	−	16.3123i	−1.78056	−	1.29365i
$160$		0			0
$161$	−0.0330122	+	0.0239848i	−0.00260172	+	0.00189026i
$162$	4.25133	−	5.85146i	0.334016	−	0.459734i
$163$	−2.79177	+	3.84254i	−0.218668	+	0.300971i	−0.904232	−	0.427042i	$-0.859556\pi$
$163$	−2.79177	+	3.84254i	−0.218668	+	0.300971i	0.685564	+	0.728012i	$0.259556\pi$
$164$	11.0496	−	8.02798i	0.862826	−	0.626880i
$165$		0			0
$166$	3.63042	+	2.63765i	0.281775	+	0.204722i
$167$	−17.6865	+	5.74670i	−1.36862	+	0.444693i	−0.898913	−	0.438127i	$-0.855642\pi$
$167$	−17.6865	+	5.74670i	−1.36862	+	0.444693i	−0.469711	+	0.882820i	$0.655642\pi$
$168$			0.138203i			0.0106626i
$169$	−0.388497	−	1.19567i	−0.0298844	−	0.0919746i
$170$		0			0
$171$	−4.93386	+	15.1849i	−0.377302	+	1.16122i
$172$	−0.290388	−	0.0943529i	−0.0221419	−	0.00719434i
$173$	9.28447	+	12.7790i	0.705885	+	0.971568i	0.999876	+	0.0157594i	$0.00501657\pi$
$173$	9.28447	+	12.7790i	0.705885	+	0.971568i	−0.293991	+	0.955808i	$0.594983\pi$
$174$	−5.97767			−0.453166
$175$		0			0
$176$	9.16266			0.690661
$177$	8.10060	+	11.1495i	0.608878	+	0.838049i
$178$	8.10715	+	2.63417i	0.607657	+	0.197440i
$179$	−2.89532	+	8.91088i	−0.216407	+	0.666031i	0.782644	+	0.622469i	$0.213870\pi$
$179$	−2.89532	+	8.91088i	−0.216407	+	0.666031i	−0.999051	+	0.0435615i	$0.986130\pi$
$180$		0			0
$181$	−1.80661	−	5.56016i	−0.134284	−	0.413283i	0.861194	−	0.508276i	$-0.169717\pi$
$181$	−1.80661	−	5.56016i	−0.134284	−	0.413283i	−0.995478	+	0.0949930i	$0.969717\pi$
$182$			0.0449988i			0.00333554i
$183$	27.1064	−	8.80740i	2.00376	−	0.651062i
$184$	−2.60654	−	1.89376i	−0.192156	−	0.139610i
$185$		0			0
$186$	7.53462	−	5.47422i	0.552465	−	0.401389i
$187$	−7.63083	+	10.5029i	−0.558022	+	0.768051i
$188$	8.02985	−	11.0521i	0.585637	−	0.806060i
$189$	0.212414	−	0.154328i	0.0154508	−	0.0112257i
$190$		0			0
$191$	17.7132	+	12.8694i	1.28168	+	0.931196i	0.999602	−	0.0281951i	$-0.00897597\pi$
$191$	17.7132	+	12.8694i	1.28168	+	0.931196i	0.282079	+	0.959391i	$0.408976\pi$
$192$	7.62055	−	2.47607i	0.549966	−	0.178695i
$193$			25.2541i			1.81783i	0.416980	+	0.908916i	$0.363089\pi$
$193$			25.2541i			1.81783i	−0.416980	+	0.908916i	$0.636911\pi$
$194$	−0.427965	−	1.31714i	−0.0307261	−	0.0945651i
$195$		0			0
$196$	3.78301	−	11.6429i	0.270215	−	0.831636i
$197$	13.7464	+	4.46648i	0.979391	+	0.318224i	0.754601	−	0.656184i	$-0.227830\pi$
$197$	13.7464	+	4.46648i	0.979391	+	0.318224i	0.224790	+	0.974407i	$0.427830\pi$
$198$	6.93071	+	9.53930i	0.492544	+	0.677929i
$199$	3.77734			0.267768			0.133884	−	0.990997i	$-0.457255\pi$
$199$	3.77734			0.267768			0.133884	+	0.990997i	$0.457255\pi$
$200$		0			0
$201$	−13.8388			−0.976112
$202$	−3.04858	−	4.19601i	−0.214497	−	0.295230i
$203$	−0.0872669	−	0.0283547i	−0.00612494	−	0.00199011i
$204$	−6.05707	+	18.6417i	−0.424079	+	1.30518i
$205$		0			0
$206$	2.83176	+	8.71526i	0.197298	+	0.607221i
$207$			11.2670i			0.783113i
$208$	9.18255	−	2.98359i	0.636695	−	0.206875i
$209$	−7.04685	−	5.11984i	−0.487441	−	0.354147i
$210$		0			0
$211$	15.2909	−	11.1095i	1.05267	−	0.764810i	0.0799522	−	0.996799i	$-0.474523\pi$
$211$	15.2909	−	11.1095i	1.05267	−	0.764810i	0.972718	+	0.231989i	$0.0745232\pi$
$212$	9.22343	−	12.6950i	0.633468	−	0.871894i
$213$	17.6264	−	24.2607i	1.20774	−	1.66231i
$214$	6.43574	−	4.67584i	0.439938	−	0.319634i
$215$		0			0
$216$	16.7715	+	12.1852i	1.14116	+	0.829099i
$217$	0.135963	−	0.0441771i	0.00922978	−	0.00299894i
$218$		−	2.98644i		−	0.202267i
$219$	3.77938	+	11.6317i	0.255387	+	0.786000i
$220$		0			0
$221$	−4.22738	+	13.0105i	−0.284364	+	0.875183i
$222$	−0.544302	−	0.176855i	−0.0365312	−	0.0118697i
$223$	−6.67464	−	9.18686i	−0.446967	−	0.615197i	0.524775	−	0.851241i	$-0.324149\pi$
$223$	−6.67464	−	9.18686i	−0.446967	−	0.615197i	−0.971743	+	0.236043i	$0.924149\pi$
$224$	−0.119831			−0.00800655
$225$		0			0
$226$	1.21655			0.0809239
$227$	−6.58183	−	9.05912i	−0.436852	−	0.601275i	0.532657	−	0.846331i	$-0.321194\pi$
$227$	−6.58183	−	9.05912i	−0.436852	−	0.601275i	−0.969509	+	0.245056i	$0.921194\pi$
$228$	−12.5075	−	4.06393i	−0.828329	−	0.269140i
$229$	−2.98192	+	9.17740i	−0.197051	+	0.606459i	0.802896	+	0.596119i	$0.203291\pi$
$229$	−2.98192	+	9.17740i	−0.197051	+	0.606459i	−0.999947	+	0.0103402i	$0.996709\pi$
$230$		0			0
$231$	0.0814771	+	0.250761i	0.00536080	+	0.0164988i
$232$		−	7.24491i		−	0.475651i
$233$	−14.7662	+	4.79782i	−0.967363	+	0.314315i	−0.749751	−	0.661720i	$-0.769827\pi$
$233$	−14.7662	+	4.79782i	−0.967363	+	0.314315i	−0.217612	+	0.976035i	$0.569827\pi$
$234$	10.0520	+	7.30320i	0.657119	+	0.477425i
$235$		0			0
$236$	−6.30423	+	4.58029i	−0.410371	+	0.298152i
$237$	−17.6062	+	24.2329i	−1.14365	+	1.57410i
$238$	0.0253790	−	0.0349312i	0.00164508	−	0.00226425i
$239$	11.5966	−	8.42544i	0.750123	−	0.544996i	−0.145742	−	0.989323i	$-0.546557\pi$
$239$	11.5966	−	8.42544i	0.750123	−	0.544996i	0.895865	+	0.444326i	$0.146557\pi$
$240$		0			0
$241$	−20.4773	−	14.8777i	−1.31906	−	0.958354i	−0.999943	−	0.0106385i	$-0.996614\pi$
$241$	−20.4773	−	14.8777i	−1.31906	−	0.958354i	−0.319117	−	0.947715i	$-0.603386\pi$
$242$	−0.876678	+	0.284850i	−0.0563550	+	0.0183109i
$243$		−	11.5450i		−	0.740613i
$244$	4.97994	+	15.3267i	0.318808	+	0.981190i
$245$		0			0
$246$	−3.73958	+	11.5092i	−0.238427	+	0.733802i
$247$	−8.72930	−	2.83632i	−0.555432	−	0.180471i
$248$	6.63473	+	9.13192i	0.421305	+	0.579877i
$249$	27.7068			1.75585
$250$		0			0
$251$	4.23698			0.267436			0.133718	−	0.991019i	$-0.457308\pi$
$251$	4.23698			0.267436			0.133718	+	0.991019i	$0.457308\pi$
$252$	0.160626	+	0.221083i	0.0101185	+	0.0139269i
$253$	−5.84587	−	1.89944i	−0.367526	−	0.119417i
$254$	2.64845	−	8.15110i	0.166179	−	0.511445i
$255$		0			0
$256$	−0.159715	−	0.491553i	−0.00998220	−	0.0307221i
$257$		−	20.4007i		−	1.27256i	−0.771458	−	0.636281i	$-0.780472\pi$
$257$		−	20.4007i		−	1.27256i	0.771458	−	0.636281i	$-0.219528\pi$
$258$	0.257295	−	0.0836003i	0.0160185	−	0.00520472i
$259$	−0.00710727	−	0.00516373i	−0.000441624	−	0.000320859i
$260$		0			0
$261$	−20.4972	+	14.8921i	−1.26874	+	0.921796i
$262$	1.41040	−	1.94125i	0.0871346	−	0.119931i
$263$	−16.8505	+	23.1927i	−1.03905	+	1.43012i	−0.141113	+	0.989994i	$0.545068\pi$
$263$	−16.8505	+	23.1927i	−1.03905	+	1.43012i	−0.897934	+	0.440131i	$0.854932\pi$
$264$	−16.8423	+	12.2366i	−1.03657	+	0.753112i
$265$		0			0
$266$	0.0234368	+	0.0170278i	0.00143700	+	0.00104404i
$267$	50.0560	−	16.2642i	3.06338	−	0.995351i
$268$		−	7.82481i		−	0.477977i
$269$	−2.45561	−	7.55759i	−0.149721	−	0.460794i	0.847867	−	0.530209i	$-0.177887\pi$
$269$	−2.45561	−	7.55759i	−0.149721	−	0.460794i	−0.997588	+	0.0694152i	$0.977887\pi$
$270$		0			0
$271$	2.95262	−	9.08722i	0.179359	−	0.552009i	−0.820447	−	0.571723i	$-0.806275\pi$
$271$	2.95262	−	9.08722i	0.179359	−	0.552009i	0.999806	+	0.0197133i	$0.00627535\pi$
$272$	−8.81085	−	2.86282i	−0.534236	−	0.173584i
$273$	0.163308	+	0.224774i	0.00988385	+	0.0136040i
$274$	−6.41785			−0.387717
$275$		0			0
$276$	−9.28045			−0.558618
$277$	−10.1043	−	13.9073i	−0.607107	−	0.835612i	0.389228	−	0.921141i	$-0.372742\pi$
$277$	−10.1043	−	13.9073i	−0.607107	−	0.835612i	−0.996336	+	0.0855297i	$0.972742\pi$
$278$	3.78326	+	1.22926i	0.226905	+	0.0737259i
$279$	12.1981	−	37.5417i	0.730278	−	2.24757i
$280$		0			0
$281$	8.41089	+	25.8861i	0.501752	+	1.54423i	0.806164	+	0.591692i	$0.201540\pi$
$281$	8.41089	+	25.8861i	0.501752	+	1.54423i	−0.304412	+	0.952540i	$0.598460\pi$
$282$			12.1043i			0.720803i
$283$	−3.30874	+	1.07507i	−0.196684	+	0.0639065i	−0.405703	−	0.914005i	$-0.632973\pi$
$283$	−3.30874	+	1.07507i	−0.196684	+	0.0639065i	0.209018	+	0.977912i	$0.432973\pi$
$284$	13.7176	+	9.96644i	0.813991	+	0.591399i
$285$		0			0
$286$	−5.48384	+	3.98424i	−0.324266	+	0.235593i
$287$	−0.109187	+	0.150283i	−0.00644509	+	0.00887090i
$288$	−19.4483	+	26.7683i	−1.14600	+	1.57734i
$289$	−3.13386	+	2.27688i	−0.184345	+	0.133934i
$290$		0			0
$291$	−6.91784	−	5.02611i	−0.405531	−	0.294636i
$292$	−6.57689	+	2.13696i	−0.384883	+	0.125056i
$293$		−	23.4941i		−	1.37254i	−0.727346	−	0.686271i	$-0.759246\pi$
$293$		−	23.4941i		−	1.37254i	0.727346	−	0.686271i	$-0.240754\pi$
$294$	3.35189	+	10.3161i	0.195486	+	0.601645i
$295$		0			0
$296$	0.214347	−	0.659691i	0.0124586	−	0.0383438i
$297$	37.6147	+	12.2218i	2.18263	+	0.709178i
$298$	−1.65708	−	2.28077i	−0.0959919	−	0.132122i
$299$	−6.47706			−0.374578
$300$		0			0
$301$	0.00415276			0.000239361
$302$	2.17016	+	2.98696i	0.124879	+	0.171881i
$303$	−30.4560	−	9.89574i	−1.74965	−	0.568496i
$304$	1.92078	−	5.91156i	0.110164	−	0.339051i
$305$		0			0
$306$	−3.68410	−	11.3385i	−0.210606	−	0.648179i
$307$			1.11253i			0.0634952i	0.999496	+	0.0317476i	$0.0101073\pi$
$307$			1.11253i			0.0634952i	−0.999496	+	0.0317476i	$0.989893\pi$
$308$	−0.141787	+	0.0460693i	−0.00807905	+	0.00262504i
$309$	45.7740	+	33.2568i	2.60399	+	1.89191i
$310$		0			0
$311$	11.9354	−	8.67154i	0.676792	−	0.491718i	−0.195500	−	0.980704i	$-0.562633\pi$
$311$	11.9354	−	8.67154i	0.676792	−	0.491718i	0.872292	+	0.488986i	$0.162633\pi$
$312$	−12.8943	+	17.7474i	−0.729994	+	1.00475i
$313$	−2.90856	+	4.00329i	−0.164402	+	0.226279i	−0.883268	−	0.468869i	$-0.844661\pi$
$313$	−2.90856	+	4.00329i	−0.164402	+	0.226279i	0.718866	+	0.695149i	$0.244661\pi$
$314$	3.49819	−	2.54158i	0.197414	−	0.143430i
$315$		0			0
$316$	−13.7019	−	9.95504i	−0.770794	−	0.560015i
$317$	−21.5752	+	7.01020i	−1.21178	+	0.393732i	−0.844083	−	0.536212i	$-0.819855\pi$
$317$	−21.5752	+	7.01020i	−1.21178	+	0.393732i	−0.367700	+	0.929944i	$0.619855\pi$
$318$			13.9036i			0.779673i
$319$	−4.27122	−	13.1455i	−0.239142	−	0.736004i
$320$		0			0
$321$	15.1779	−	46.7127i	0.847146	−	2.60725i
$322$	0.0194425	+	0.00631724i	0.00108349	+	0.000352046i
$323$	5.17662	+	7.12501i	0.288035	+	0.396446i
$324$	25.2505			1.40281
$325$		0			0
$326$	2.37952			0.131789
$327$	−10.8383	−	14.9176i	−0.599358	−	0.824946i
$328$	−13.9491	−	4.53234i	−0.770211	−	0.250257i
$329$	−0.0574162	+	0.176709i	−0.00316546	+	0.00974228i
$330$		0			0
$331$	0.535397	+	1.64778i	0.0294281	+	0.0905702i	0.964692	−	0.263381i	$-0.0848378\pi$
$331$	0.535397	+	1.64778i	0.0294281	+	0.0905702i	−0.935264	+	0.353952i	$0.884838\pi$
$332$			15.6662i			0.859793i
$333$	−2.30698	+	0.749584i	−0.126422	+	0.0410770i
$334$	7.53741	+	5.47625i	0.412429	+	0.299647i
$335$		0			0
$336$	−0.152219	+	0.110594i	−0.00830423	+	0.00603338i
$337$	8.21786	−	11.3109i	0.447655	−	0.616144i	−0.524237	−	0.851573i	$-0.675649\pi$
$337$	8.21786	−	11.3109i	0.447655	−	0.616144i	0.971892	+	0.235428i	$0.0756493\pi$
$338$	−0.370214	+	0.509555i	−0.0201370	+	0.0277161i
$339$	6.07682	−	4.41507i	0.330048	−	0.239794i
$340$		0			0
$341$	17.4220	+	12.6578i	0.943455	+	0.685460i
$342$	7.60746	−	2.47181i	0.411364	−	0.133660i
$343$			0.333017i			0.0179812i
$344$	0.101323	+	0.311840i	0.00546297	+	0.0168133i
$345$		0			0
$346$	2.44540	−	7.52616i	0.131465	−	0.404609i
$347$	4.83301	+	1.57034i	0.259450	+	0.0843003i	0.435854	−	0.900018i	$-0.356447\pi$
$347$	4.83301	+	1.57034i	0.259450	+	0.0843003i	−0.176404	+	0.984318i	$0.556447\pi$
$348$	−12.2663	−	16.8832i	−0.657544	−	0.905032i
$349$	8.88643			0.475680			0.237840	−	0.971304i	$-0.423561\pi$
$349$	8.88643			0.475680			0.237840	+	0.971304i	$0.423561\pi$
$350$		0			0
$351$	41.6761			2.22450
$352$	−10.6100	−	14.6034i	−0.565513	−	0.778362i
$353$	−8.95362	−	2.90921i	−0.476553	−	0.154842i	0.0608848	−	0.998145i	$-0.480608\pi$
$353$	−8.95362	−	2.90921i	−0.476553	−	0.154842i	−0.537438	+	0.843303i	$0.680608\pi$
$354$	2.13358	−	6.56649i	0.113399	−	0.349005i
$355$		0			0
$356$	9.19620	+	28.3030i	0.487397	+	1.50005i
$357$		−	0.266590i		−	0.0141094i
$358$	4.46426	−	1.45053i	0.235943	−	0.0766627i
$359$	7.37418	+	5.35765i	0.389194	+	0.282766i	0.765125	−	0.643882i	$-0.222677\pi$
$359$	7.37418	+	5.35765i	0.389194	+	0.282766i	−0.375931	+	0.926648i	$0.622677\pi$
$360$		0			0
$361$	10.5909	−	7.69472i	0.557414	−	0.404985i
$362$	−1.72158	+	2.36956i	−0.0904844	+	0.124541i
$363$	−3.34534	+	4.60446i	−0.175585	+	0.241672i
$364$	−0.127093	+	0.0923387i	−0.00666150	+	0.00483986i
$365$		0			0
$366$	−11.5519	−	8.39291i	−0.603825	−	0.438705i
$367$	17.0034	−	5.52474i	0.887570	−	0.288389i	0.170473	−	0.985362i	$-0.445471\pi$
$367$	17.0034	−	5.52474i	0.887570	−	0.288389i	0.717097	+	0.696974i	$0.245471\pi$
$368$		−	4.38633i		−	0.228653i
$369$	15.8499	+	48.7810i	0.825113	+	2.53944i
$370$		0			0
$371$	−0.0659507	+	0.202976i	−0.00342399	+	0.0105380i
$372$	30.9224	+	10.0473i	1.60325	+	0.520929i
$373$	−1.80682	−	2.48687i	−0.0935536	−	0.128765i	0.759674	−	0.650304i	$-0.225358\pi$
$373$	−1.80682	−	2.48687i	−0.0935536	−	0.128765i	−0.853228	+	0.521538i	$0.825358\pi$
$374$	6.50402			0.336315
$375$		0			0
$376$	−14.6704			−0.756567
$377$	−8.56098	−	11.7832i	−0.440913	−	0.606865i
$378$	−0.125101	−	0.0406477i	−0.00643449	−	0.00209069i
$379$	−7.90670	+	24.3343i	−0.406140	+	1.24997i	0.513799	+	0.857910i	$0.328238\pi$
$379$	−7.90670	+	24.3343i	−0.406140	+	1.24997i	−0.919939	+	0.392060i	$0.871762\pi$
$380$		0			0
$381$	−16.3523	−	50.3273i	−0.837755	−	2.57835i
$382$		−	10.9690i		−	0.561224i
$383$	−2.11638	+	0.687652i	−0.108142	+	0.0351374i	−0.362588	−	0.931950i	$-0.618107\pi$
$383$	−2.11638	+	0.687652i	−0.108142	+	0.0351374i	0.254446	+	0.967087i	$0.418107\pi$
$384$	−28.4602	−	20.6776i	−1.45235	−	1.05520i
$385$		0			0
$386$	10.2357	−	7.43669i	0.520985	−	0.378517i
$387$	0.673982	−	0.927657i	0.0342604	−	0.0471554i
$388$	2.84189	−	3.91153i	0.144275	−	0.198578i
$389$	3.75718	−	2.72975i	0.190496	−	0.138404i	−0.488449	−	0.872592i	$-0.662437\pi$
$389$	3.75718	−	2.72975i	0.190496	−	0.138404i	0.678946	+	0.734189i	$0.262437\pi$
$390$		0			0
$391$	5.02794	+	3.65301i	0.254274	+	0.184741i
$392$	−12.5030	+	4.06247i	−0.631497	+	0.205186i
$393$		−	14.8153i		−	0.747333i
$394$	−2.23766	−	6.88681i	−0.112732	−	0.346952i
$395$		0			0
$396$	−12.7205	+	39.1497i	−0.639230	+	1.96735i
$397$	−36.0880	−	11.7257i	−1.81121	−	0.588497i	−0.999993	−	0.00374665i	$-0.998807\pi$
$397$	−36.0880	−	11.7257i	−1.81121	−	0.588497i	−0.811214	−	0.584750i	$-0.801193\pi$
$398$	−1.11233	−	1.53099i	−0.0557560	−	0.0767415i
$399$	0.178866			0.00895449
$400$		0			0
$401$	−16.7187			−0.834890			−0.417445	−	0.908702i	$-0.637074\pi$
$401$	−16.7187			−0.834890			−0.417445	+	0.908702i	$0.637074\pi$
$402$	4.07516	+	5.60898i	0.203251	+	0.279751i
$403$	21.5816	+	7.01227i	1.07505	+	0.349306i
$404$	5.59532	−	17.2206i	0.278377	−	0.856757i
$405$		0			0
$406$	0.0142054	+	0.0437198i	0.000705004	+	0.00216978i
$407$		−	1.32334i		−	0.0655955i
$408$	20.0188	−	6.50452i	0.991081	−	0.322022i
$409$	0.382772	+	0.278100i	0.0189268	+	0.0137512i	0.597208	−	0.802086i	$-0.296277\pi$
$409$	0.382772	+	0.278100i	0.0189268	+	0.0137512i	−0.578282	+	0.815837i	$0.696277\pi$
$410$		0			0
$411$	−32.0579	+	23.2914i	−1.58130	+	1.14888i
$412$	−18.8043	+	25.8819i	−0.926420	+	1.27511i
$413$	0.0622955	−	0.0857424i	0.00306536	−	0.00421911i
$414$	4.56663	−	3.31785i	0.224438	−	0.163064i
$415$		0			0
$416$	−15.3882	−	11.1802i	−0.754470	−	0.548154i
$417$	23.3590	−	7.58979i	1.14389	−	0.371674i
$418$			4.36381i			0.213441i
$419$	−7.48898	−	23.0487i	−0.365861	−	1.12600i	−0.949440	−	0.313947i	$-0.898349\pi$
$419$	−7.48898	−	23.0487i	−0.365861	−	1.12600i	0.583580	−	0.812056i	$-0.301651\pi$
$420$		0			0
$421$	−9.68711	+	29.8139i	−0.472121	+	1.45304i	0.377680	+	0.925936i	$0.376722\pi$
$421$	−9.68711	+	29.8139i	−0.472121	+	1.45304i	−0.849801	+	0.527103i	$0.823278\pi$
$422$	−9.00556	−	2.92609i	−0.438384	−	0.142440i
$423$	30.1553	+	41.5052i	1.46620	+	2.01805i
$424$	−16.8510			−0.818359
$425$		0			0
$426$	−15.0236			−0.727895
$427$	−0.128832	−	0.177322i	−0.00623462	−	0.00858122i
$428$	26.4126	+	8.58197i	1.27670	+	0.414825i
$429$	−12.9329	+	39.8035i	−0.624408	+	1.92173i
$430$		0			0
$431$	−0.618239	−	1.90275i	−0.0297795	−	0.0916520i	0.935062	−	0.354484i	$-0.115343\pi$
$431$	−0.618239	−	1.90275i	−0.0297795	−	0.0916520i	−0.964842	+	0.262832i	$0.915343\pi$
$432$			28.2234i			1.35790i
$433$	6.72637	−	2.18553i	0.323249	−	0.105030i	−0.142898	−	0.989737i	$-0.545642\pi$
$433$	6.72637	−	2.18553i	0.323249	−	0.105030i	0.466147	+	0.884708i	$0.345642\pi$
$434$	−0.0579430	−	0.0420981i	−0.00278135	−	0.00202077i
$435$		0			0
$436$	8.43482	−	6.12825i	0.403954	−	0.293490i
$437$	−2.45096	+	3.37345i	−0.117245	+	0.161374i
$438$	3.60152	−	4.95706i	0.172087	−	0.236858i
$439$	10.4865	−	7.61889i	0.500493	−	0.363630i	−0.308712	−	0.951156i	$-0.599898\pi$
$439$	10.4865	−	7.61889i	0.500493	−	0.363630i	0.809205	+	0.587526i	$0.199898\pi$
$440$		0			0
$441$	37.1937	+	27.0228i	1.77113	+	1.28680i
$442$	6.51814	−	2.11787i	0.310036	−	0.100737i
$443$		−	21.8687i		−	1.03901i	−0.854467	−	0.519506i	$-0.826116\pi$
$443$		−	21.8687i		−	1.03901i	0.854467	−	0.519506i	$-0.173884\pi$
$444$	−0.617419	−	1.90022i	−0.0293014	−	0.0901804i
$445$		0			0
$446$	−1.75801	+	5.41058i	−0.0832440	+	0.256199i
$447$	−16.5546	−	5.37890i	−0.783004	−	0.254413i
$448$	−0.0362191	−	0.0498514i	−0.00171119	−	0.00235526i
$449$	−0.399626			−0.0188595			−0.00942976	−	0.999956i	$-0.503002\pi$
$449$	−0.399626			−0.0188595			−0.00942976	+	0.999956i	$0.503002\pi$
$450$		0			0
$451$	−27.9819			−1.31762
$452$	2.49640	+	3.43600i	0.117421	+	0.161616i
$453$	21.6803	+	7.04437i	1.01863	+	0.330973i
$454$	−1.73356	+	5.33535i	−0.0813600	+	0.250400i
$455$		0			0
$456$	4.36415	+	13.4315i	0.204370	+	0.628986i
$457$		−	35.2247i		−	1.64774i	−0.566777	−	0.823872i	$-0.691810\pi$
$457$		−	35.2247i		−	1.64774i	0.566777	−	0.823872i	$-0.308190\pi$
$458$	4.59778	−	1.49391i	0.214840	−	0.0698058i
$459$	−32.3518	−	23.5050i	−1.51005	−	1.09712i
$460$		0			0
$461$	12.9131	−	9.38194i	0.601425	−	0.436961i	−0.244960	−	0.969533i	$-0.578775\pi$
$461$	12.9131	−	9.38194i	0.601425	−	0.436961i	0.846384	+	0.532573i	$0.178775\pi$
$462$	0.0776427	−	0.106866i	0.00361226	−	0.00497185i
$463$	17.9175	−	24.6614i	0.832699	−	1.14611i	−0.154716	−	0.987959i	$-0.549446\pi$
$463$	17.9175	−	24.6614i	0.832699	−	1.14611i	0.987415	−	0.158153i	$-0.0505538\pi$
$464$	7.97968	−	5.79757i	0.370447	−	0.269146i
$465$		0			0
$466$	6.29285	+	4.57202i	0.291511	+	0.211795i
$467$	−6.32127	+	2.05390i	−0.292513	+	0.0950434i	−0.451598	−	0.892222i	$-0.649146\pi$
$467$	−6.32127	+	2.05390i	−0.292513	+	0.0950434i	0.159084	+	0.987265i	$0.449146\pi$
$468$			43.3769i			2.00510i
$469$	0.0328867	+	0.101215i	0.00151857	+	0.00467366i
$470$		0			0
$471$	8.25002	−	25.3910i	0.380141	−	1.16995i
$472$	7.95855	+	2.58589i	0.366322	+	0.119025i
$473$	0.367689	+	0.506081i	0.0169064	+	0.0232696i
$474$	15.0064			0.689267
$475$		0			0
$476$	0.150737			0.00690902
$477$	34.6377	+	47.6747i	1.58595	+	2.18288i
$478$	−6.82981	−	2.21914i	−0.312388	−	0.101501i
$479$	−6.87278	+	21.1522i	−0.314025	+	0.966471i	0.662128	+	0.749390i	$0.269653\pi$
$479$	−6.87278	+	21.1522i	−0.314025	+	0.966471i	−0.976154	+	0.217080i	$0.930347\pi$
$480$		0			0
$481$	−0.430912	−	1.32621i	−0.0196479	−	0.0604700i
$482$			12.6807i			0.577591i
$483$	0.120044	−	0.0390045i	0.00546217	−	0.00177477i
$484$	−2.60349	−	1.89154i	−0.118340	−	0.0859792i
$485$		0			0
$486$	−4.67930	+	3.39971i	−0.212257	+	0.154214i
$487$	5.98665	−	8.23992i	0.271281	−	0.373386i	−0.651541	−	0.758614i	$-0.725877\pi$
$487$	5.98665	−	8.23992i	0.271281	−	0.373386i	0.922822	+	0.385227i	$0.125877\pi$
$488$	10.1722	−	14.0008i	0.460472	−	0.633785i
$489$	11.8860	−	8.63565i	0.537501	−	0.390518i
$490$		0			0
$491$	−5.37191	−	3.90292i	−0.242431	−	0.176136i	0.459935	−	0.887953i	$-0.347873\pi$
$491$	−5.37191	−	3.90292i	−0.242431	−	0.176136i	−0.702366	+	0.711816i	$0.747873\pi$
$492$	−40.1800	+	13.0553i	−1.81145	+	0.588577i
$493$			13.9752i			0.629413i
$494$	1.42097	+	4.37329i	0.0639323	+	0.196763i
$495$		0			0
$496$	−4.74877	+	14.6152i	−0.213226	+	0.656243i
$497$	−0.219327	−	0.0712635i	−0.00983814	−	0.00319660i
$498$	−8.15894	−	11.2298i	−0.365611	−	0.503220i
$499$	−1.08397			−0.0485253			−0.0242626	−	0.999706i	$-0.507724\pi$
$499$	−1.08397			−0.0485253			−0.0242626	+	0.999706i	$0.507724\pi$
$500$		0			0
$501$	57.5244			2.57000
$502$	−1.24768	−	1.71729i	−0.0556867	−	0.0766462i
$503$	1.88882	+	0.613716i	0.0842184	+	0.0273642i	0.350823	−	0.936442i	$-0.385902\pi$
$503$	1.88882	+	0.613716i	0.0842184	+	0.0273642i	−0.266605	+	0.963806i	$0.585902\pi$
$504$	0.0906843	−	0.279097i	0.00403940	−	0.0124320i
$505$		0			0
$506$	0.951598	+	2.92872i	0.0423037	+	0.130197i
$507$			3.88885i			0.172710i
$508$	28.4564	−	9.24604i	1.26255	−	0.410227i
$509$	1.86814	+	1.35729i	0.0828040	+	0.0601607i	0.628417	−	0.777877i	$-0.283703\pi$
$509$	1.86814	+	1.35729i	0.0828040	+	0.0601607i	−0.545613	+	0.838037i	$0.683703\pi$
$510$		0			0
$511$	0.0760914	−	0.0552836i	0.00336608	−	0.00244560i
$512$	13.2172	−	18.1920i	0.584125	−	0.803979i
$513$	15.7705	−	21.7062i	0.696283	−	0.958351i
$514$	−8.26859	+	6.00748i	−0.364712	+	0.264979i
$515$		0			0
$516$	0.764094	+	0.555147i	0.0336373	+	0.0244390i
$517$	−26.6186	+	8.64889i	−1.17068	+	0.380378i
$518$			0.00440122i			0.000193379i
$519$	−15.0986	−	46.4687i	−0.662755	−	2.03975i
$520$		0			0
$521$	−3.41302	+	10.5042i	−0.149527	+	0.460197i	−0.997565	−	0.0697382i	$-0.977784\pi$
$521$	−3.41302	+	10.5042i	−0.149527	+	0.460197i	0.848038	+	0.529935i	$0.177784\pi$
$522$	12.0718	+	3.92236i	0.528368	+	0.171677i
$523$	15.2839	+	21.0365i	0.668318	+	0.919861i	0.999721	−	0.0236286i	$-0.00752191\pi$
$523$	15.2839	+	21.0365i	0.668318	+	0.919861i	−0.331403	+	0.943489i	$0.607522\pi$
$524$	8.37696			0.365949
$525$		0			0
$526$	14.3623			0.626224
$527$	−12.7982	−	17.6152i	−0.557499	−	0.767332i
$528$	−26.9553	−	8.75830i	−1.17308	−	0.381156i
$529$	6.19810	−	19.0758i	0.269482	−	0.829382i
$530$		0			0
$531$	−9.04302	−	27.8316i	−0.392434	−	1.20779i
$532$			0.101136i			0.00438478i
$533$	−28.0426	+	9.11161i	−1.21466	+	0.394667i
$534$	−21.3322	−	15.4988i	−0.923135	−	0.670697i
$535$		0			0
$536$	−6.79805	+	4.93907i	−0.293631	+	0.213336i
$537$	17.0353	−	23.4470i	0.735126	−	1.01181i
$538$	−2.34004	+	3.22079i	−0.100886	+	0.138858i
$539$	−20.2909	+	14.7422i	−0.873993	+	0.634993i
$540$		0			0
$541$	0.0147558	+	0.0107207i	0.000634400	+	0.000460919i	0.588102	−	0.808786i	$-0.299875\pi$
$541$	0.0147558	+	0.0107207i	0.000634400	+	0.000460919i	−0.587468	+	0.809247i	$0.699875\pi$
$542$	−4.55260	+	1.47923i	−0.195551	+	0.0635384i
$543$			18.0841i			0.776063i
$544$	5.63985	+	17.3577i	0.241807	+	0.744205i
$545$		0			0
$546$	0.0430130	−	0.132380i	0.00184079	−	0.00566536i
$547$	−9.47298	−	3.07796i	−0.405035	−	0.131604i	0.0994121	−	0.995046i	$-0.468304\pi$
$547$	−9.47298	−	3.07796i	−0.405035	−	0.131604i	−0.504447	+	0.863442i	$0.668304\pi$
$548$	−13.1696	−	18.1264i	−0.562577	−	0.774320i
$549$	−60.5199			−2.58293
$550$		0			0
$551$	−9.37656			−0.399455
$552$	5.85788	+	8.06268i	0.249328	+	0.343171i
$553$	0.219076	+	0.0711820i	0.00931604	+	0.00302697i
$554$	−2.66132	+	8.19071i	−0.113069	+	0.347990i
$555$		0			0
$556$	4.29147	+	13.2078i	0.181999	+	0.560135i
$557$		−	34.9291i		−	1.47999i	−0.672611	−	0.739996i	$-0.734827\pi$
$557$		−	34.9291i		−	1.47999i	0.672611	−	0.739996i	$-0.265173\pi$
$558$	−18.8080	+	6.11109i	−0.796207	+	0.258703i
$559$	0.533280	+	0.387451i	0.0225554	+	0.0163874i
$560$		0			0
$561$	32.4883	−	23.6041i	1.37166	−	0.996567i
$562$	8.01506	−	11.0318i	0.338095	−	0.465348i
$563$	−9.28343	+	12.7775i	−0.391250	+	0.538509i	−0.958521	−	0.285022i	$-0.907999\pi$
$563$	−9.28343	+	12.7775i	−0.391250	+	0.538509i	0.567271	+	0.823531i	$0.307999\pi$
$564$	−34.1871	+	24.8384i	−1.43954	+	1.04588i
$565$		0			0
$566$	1.41008	+	1.02448i	0.0592699	+	0.0430621i
$567$	−0.326618	+	0.106125i	−0.0137167	+	0.00445681i
$568$		−	18.2085i		−	0.764012i
$569$	4.49944	+	13.8479i	0.188627	+	0.580533i	0.999992	−	0.00400651i	$-0.00127532\pi$
$569$	4.49944	+	13.8479i	0.188627	+	0.580533i	−0.811365	+	0.584539i	$0.801275\pi$
$570$		0			0
$571$	8.53315	−	26.2623i	0.357101	−	1.09904i	−0.597680	−	0.801735i	$-0.703911\pi$
$571$	8.53315	−	26.2623i	0.357101	−	1.09904i	0.954781	−	0.297309i	$-0.0960892\pi$
$572$	−22.5059	−	7.31263i	−0.941021	−	0.305756i
$573$	−39.8083	−	54.7914i	−1.66302	−	2.28895i
$574$	0.0930636			0.00388440
$575$		0			0
$576$	−17.0142			−0.708927
$577$	15.9595	+	21.9664i	0.664405	+	0.914475i	0.999617	−	0.0276679i	$-0.00880810\pi$
$577$	15.9595	+	21.9664i	0.664405	+	0.914475i	−0.335212	+	0.942143i	$0.608808\pi$
$578$	1.84568	+	0.599698i	0.0767702	+	0.0249442i
$579$	24.1396	−	74.2941i	1.00321	−	3.08756i
$580$		0			0
$581$	−0.0658429	−	0.202644i	−0.00273162	−	0.00840707i
$582$			4.28392i			0.177574i
$583$	−30.5752	+	9.93449i	−1.26630	+	0.411445i
$584$	6.00793	+	4.36502i	0.248610	+	0.180626i
$585$		0			0
$586$	−9.52239	+	6.91842i	−0.393366	+	0.285797i
$587$	−6.29145	+	8.65944i	−0.259676	+	0.357413i	−0.918871	−	0.394559i	$-0.870897\pi$
$587$	−6.29145	+	8.65944i	−0.259676	+	0.357413i	0.659195	+	0.751972i	$0.270897\pi$
$588$	−22.2582	+	30.6358i	−0.917912	+	1.26340i
$589$	11.8188	−	8.58685i	0.486984	−	0.353815i
$590$		0			0
$591$	−36.1707	−	26.2795i	−1.48786	−	1.08100i
$592$	0.898122	−	0.291818i	0.0369126	−	0.0119936i
$593$			3.84629i			0.157948i	0.996877	+	0.0789740i	$0.0251644\pi$
$593$			3.84629i			0.157948i	−0.996877	+	0.0789740i	$0.974836\pi$
$594$	−6.12297	−	18.8446i	−0.251229	−	0.773202i
$595$		0			0
$596$	3.04138	−	9.36039i	0.124580	−	0.383417i
$597$	−11.1124	−	3.61064i	−0.454801	−	0.147774i
$598$	1.90733	+	2.62521i	0.0779964	+	0.107353i
$599$	−46.1423			−1.88532			−0.942662	−	0.333750i	$-0.891686\pi$
$599$	−46.1423			−1.88532			−0.942662	+	0.333750i	$0.891686\pi$
$600$		0			0
$601$	−13.3119			−0.543005			−0.271503	−	0.962438i	$-0.587521\pi$
$601$	−13.3119			−0.543005			−0.271503	+	0.962438i	$0.587521\pi$
$602$	−0.00122288	−	0.00168315i	−4.98408e−5	−	6.86000e-5i
$603$	27.9471	+	9.08057i	1.13809	+	0.369789i
$604$	−3.98308	+	12.2586i	−0.162069	+	0.498797i
$605$		0			0
$606$	4.95766	+	15.2581i	0.201391	+	0.619818i
$607$			34.0838i			1.38342i	0.722176	+	0.691709i	$0.243142\pi$
$607$			34.0838i			1.38342i	−0.722176	+	0.691709i	$0.756858\pi$
$608$	−11.6460	+	3.78401i	−0.472307	+	0.153462i
$609$	0.229624	+	0.166832i	0.00930483	+	0.00676035i
$610$		0			0
$611$	−23.8600	+	17.3353i	−0.965274	+	0.701313i
$612$	24.4642	−	33.6721i	0.988908	−	1.36111i
$613$	−14.9773	+	20.6145i	−0.604928	+	0.832612i	−0.996148	−	0.0876853i	$-0.972053\pi$
$613$	−14.9773	+	20.6145i	−0.604928	+	0.832612i	0.391220	+	0.920297i	$0.372053\pi$
$614$	0.450916	−	0.327610i	0.0181975	−	0.0132213i
$615$		0			0
$616$	0.129521	+	0.0941025i	0.00521855	+	0.00379150i
$617$	25.6265	−	8.32657i	1.03169	−	0.335215i	0.256229	−	0.966616i	$-0.417520\pi$
$617$	25.6265	−	8.32657i	1.03169	−	0.335215i	0.775456	+	0.631401i	$0.217520\pi$
$618$		−	28.3459i		−	1.14024i
$619$	−12.1533	−	37.4040i	−0.488482	−	1.50339i	−0.826873	−	0.562389i	$-0.809882\pi$
$619$	−12.1533	−	37.4040i	−0.488482	−	1.50339i	0.338391	−	0.941006i	$-0.390118\pi$
$620$		0			0
$621$	5.85077	−	18.0068i	0.234783	−	0.722589i
$622$	−7.02931	−	2.28396i	−0.281849	−	0.0915784i
$623$	−0.237907	−	0.327451i	−0.00953156	−	0.0131191i
$624$	−29.8657			−1.19559
$625$		0			0
$626$	2.47906			0.0990833
$627$	15.8370	+	21.7977i	0.632468	+	0.870517i
$628$	14.3567	+	4.66478i	0.572896	+	0.186145i
$629$	−0.413469	+	1.27253i	−0.0164861	+	0.0507390i
$630$		0			0
$631$	3.47469	+	10.6940i	0.138325	+	0.425722i	0.996092	−	0.0883169i	$-0.0281488\pi$
$631$	3.47469	+	10.6940i	0.138325	+	0.425722i	−0.857767	+	0.514039i	$0.828149\pi$
$632$			18.1877i			0.723467i
$633$	−55.6030	+	18.0665i	−2.21002	+	0.718080i
$634$	9.19463	+	6.68029i	0.365166	+	0.265308i
$635$		0			0
$636$	−39.2688	+	28.5304i	−1.55711	+	1.13131i
$637$	−15.5346	+	21.3815i	−0.615501	+	0.847165i
$638$	−4.07021	+	5.60216i	−0.161141	+	0.221792i
$639$	−51.5152	+	37.4280i	−2.03791	+	1.48063i
$640$		0			0
$641$	−14.1394	−	10.2729i	−0.558473	−	0.405755i	0.272427	−	0.962177i	$-0.412174\pi$
$641$	−14.1394	−	10.2729i	−0.558473	−	0.405755i	−0.830900	+	0.556422i	$0.812174\pi$
$642$	−23.4026	+	7.60395i	−0.923625	+	0.300104i
$643$			8.72320i			0.344009i	0.985096	+	0.172005i	$0.0550244\pi$
$643$			8.72320i			0.344009i	−0.985096	+	0.172005i	$0.944976\pi$
$644$	0.0220542	+	0.0678758i	0.000869057	+	0.00267468i
$645$		0			0
$646$	1.36345	−	4.19626i	0.0536441	−	0.165100i
$647$	23.8386	+	7.74562i	0.937191	+	0.304512i	0.737500	−	0.675347i	$-0.236006\pi$
$647$	23.8386	+	7.74562i	0.937191	+	0.304512i	0.199691	+	0.979859i	$0.436006\pi$
$648$	−15.9383	−	21.9372i	−0.626115	−	0.861773i
$649$	15.9648			0.626674
$650$		0			0
$651$	−0.442212			−0.0173317
$652$	4.88283	+	6.72063i	0.191226	+	0.263200i
$653$	−28.5105	−	9.26362i	−1.11570	−	0.362514i	−0.307576	−	0.951523i	$-0.599518\pi$
$653$	−28.5105	−	9.26362i	−1.11570	−	0.362514i	−0.808126	+	0.589010i	$0.799518\pi$
$654$	−2.85465	+	8.78570i	−0.111626	+	0.343548i
$655$		0			0
$656$	−6.17046	−	18.9907i	−0.240916	−	0.741464i
$657$		−	25.9699i		−	1.01318i
$658$	0.0885293	−	0.0287649i	0.00345123	−	0.00112137i
$659$	−3.53218	−	2.56628i	−0.137594	−	0.0999680i	0.516859	−	0.856071i	$-0.327101\pi$
$659$	−3.53218	−	2.56628i	−0.137594	−	0.0999680i	−0.654453	+	0.756102i	$0.727101\pi$
$660$		0			0
$661$	15.7377	−	11.4341i	0.612125	−	0.444735i	−0.238037	−	0.971256i	$-0.576504\pi$
$661$	15.7377	−	11.4341i	0.612125	−	0.444735i	0.850162	+	0.526521i	$0.176504\pi$
$662$	0.510200	−	0.702230i	0.0198295	−	0.0272929i
$663$	24.8727	−	34.2344i	0.965977	−	1.32955i
$664$	13.6105	−	9.88859i	0.528189	−	0.383752i
$665$		0			0
$666$	0.983160	+	0.714308i	0.0380967	+	0.0276789i
$667$	−6.29296	+	2.04471i	−0.243664	+	0.0791714i
$668$			32.5258i			1.25846i
$669$	10.8544	+	33.4065i	0.419657	+	1.29157i
$670$		0			0
$671$	10.2027	−	31.4006i	0.393869	−	1.21221i
$672$	0.352526	+	0.114543i	0.0135990	+	0.00441858i
$673$	−21.2940	−	29.3087i	−0.820823	−	1.12977i	−0.989562	−	0.144105i	$-0.953970\pi$
$673$	−21.2940	−	29.3087i	−0.820823	−	1.12977i	0.168740	−	0.985661i	$-0.446030\pi$
$674$	−7.00436			−0.269798
$675$		0			0
$676$	−2.19886			−0.0845715
$677$	−1.19936	−	1.65077i	−0.0460950	−	0.0634443i	0.785347	−	0.619055i	$-0.212484\pi$
$677$	−1.19936	−	1.65077i	−0.0460950	−	0.0634443i	−0.831442	+	0.555611i	$0.812484\pi$
$678$	−3.57893	−	1.16287i	−0.137448	−	0.0446596i
$679$	−0.0203205	+	0.0625402i	−0.000779831	+	0.00240007i
$680$		0			0
$681$	10.7035	+	32.9420i	0.410160	+	1.26234i
$682$		−	10.7887i		−	0.413121i
$683$	15.1318	−	4.91662i	0.579003	−	0.188129i	−0.00485110	−	0.999988i	$-0.501544\pi$
$683$	15.1318	−	4.91662i	0.579003	−	0.188129i	0.583854	+	0.811859i	$0.301544\pi$
$684$	22.5920	+	16.4140i	0.863826	+	0.627607i
$685$		0			0
$686$	0.134975	−	0.0980649i	0.00515336	−	0.00374413i
$687$	17.5448	−	24.1483i	0.669375	−	0.921316i
$688$	−0.262385	+	0.361142i	−0.0100033	+	0.0137684i
$689$	−27.4067	+	19.9121i	−1.04411	+	0.758591i
$690$		0			0
$691$	3.15651	+	2.29334i	0.120079	+	0.0872427i	0.646204	−	0.763165i	$-0.276356\pi$
$691$	3.15651	+	2.29334i	0.120079	+	0.0872427i	−0.526125	+	0.850407i	$0.676356\pi$
$692$	26.2747	−	8.53715i	0.998812	−	0.324534i
$693$		−	0.559869i		−	0.0212677i
$694$	−0.786724	−	2.42129i	−0.0298636	−	0.0919108i
$695$		0			0
$696$	−6.92518	+	21.3135i	−0.262498	+	0.807887i
$697$	26.9075	+	8.74278i	1.01919	+	0.331156i
$698$	−2.61683	−	3.60175i	−0.0990483	−	0.136328i
$699$	48.0261			1.81651
$700$		0			0
$701$	30.3587			1.14663			0.573316	−	0.819335i	$-0.305657\pi$
$701$	30.3587			1.14663			0.573316	+	0.819335i	$0.305657\pi$
$702$	−12.2725	−	16.8917i	−0.463197	−	0.637536i
$703$	−0.853791	−	0.277413i	−0.0322013	−	0.0104628i
$704$	2.86832	−	8.82779i	0.108104	−	0.332710i
$705$		0			0
$706$	1.45748	+	4.48567i	0.0548531	+	0.168820i
$707$			0.246267i			0.00926181i
$708$	22.9243	−	7.44857i	0.861550	−	0.279934i
$709$	−39.2921	−	28.5474i	−1.47565	−	1.07212i	−0.978928	−	0.204206i	$-0.934539\pi$
$709$	−39.2921	−	28.5474i	−1.47565	−	1.07212i	−0.496717	−	0.867912i	$-0.665461\pi$
$710$		0			0
$711$	51.4563	−	37.3852i	1.92976	−	1.40205i
$712$	18.7844	−	25.8545i	0.703975	−	0.968939i
$713$	6.05953	−	8.34023i	0.226931	−	0.312344i
$714$	−0.108051	+	0.0785038i	−0.00404371	+	0.00293793i
$715$		0			0
$716$	13.2576	+	9.63220i	0.495459	+	0.359972i
$717$	−42.1693	+	13.7016i	−1.57484	+	0.511697i
$718$		−	4.56651i		−	0.170421i
$719$	−1.47166	−	4.52929i	−0.0548835	−	0.168914i	0.919857	−	0.392253i	$-0.128304\pi$
$719$	−1.47166	−	4.52929i	−0.0548835	−	0.168914i	−0.974741	+	0.223339i	$0.928304\pi$
$720$		0			0
$721$	0.134457	−	0.413816i	0.00500744	−	0.0154113i
$722$	−6.23747	−	2.02668i	−0.232135	−	0.0754251i
$723$	46.0204	+	63.3416i	1.71152	+	2.35570i
$724$	−10.2252			−0.380018
$725$		0			0
$726$	2.85135			0.105823
$727$	1.99078	+	2.74007i	0.0738338	+	0.101624i	0.844337	−	0.535813i	$-0.179995\pi$
$727$	1.99078	+	2.74007i	0.0738338	+	0.101624i	−0.770503	+	0.637437i	$0.779995\pi$
$728$	0.160444	+	0.0521315i	0.00594646	+	0.00193212i
$729$	2.34834	−	7.22745i	0.0869756	−	0.267683i
$730$		0			0
$731$	−0.195450	−	0.601532i	−0.00722897	−	0.0222485i
$732$		−	49.8491i		−	1.84248i
$733$	14.6472	−	4.75915i	0.541005	−	0.175783i	−0.0257516	−	0.999668i	$-0.508198\pi$
$733$	14.6472	−	4.75915i	0.541005	−	0.175783i	0.566757	+	0.823885i	$0.308198\pi$
$734$	−7.24628	−	5.26473i	−0.267465	−	0.194325i
$735$		0			0
$736$	−6.99089	+	5.07918i	−0.257688	+	0.187221i
$737$	−9.42285	+	12.9694i	−0.347095	+	0.477735i
$738$	15.1040	−	20.7888i	0.555985	−	0.765248i
$739$	8.07775	−	5.86883i	0.297145	−	0.215888i	−0.429216	−	0.903202i	$-0.641210\pi$
$739$	8.07775	−	5.86883i	0.297145	−	0.215888i	0.726361	+	0.687314i	$0.241210\pi$
$740$		0			0
$741$	22.9692	+	16.6881i	0.843796	+	0.613054i
$742$	0.101689	−	0.0330406i	0.00373311	−	0.00121296i
$743$			41.4419i			1.52036i	0.649715	+	0.760178i	$0.274888\pi$
$743$			41.4419i			1.52036i	−0.649715	+	0.760178i	$0.725112\pi$
$744$	−10.7895	−	33.2068i	−0.395563	−	1.21742i
$745$		0			0
$746$	−0.475891	+	1.46464i	−0.0174236	+	0.0536243i
$747$	−55.9533	−	18.1803i	−2.04723	−	0.665184i
$748$	13.3464	+	18.3697i	0.487993	+	0.671665i
$749$	−0.377719			−0.0138015
$750$		0			0
$751$	21.1036			0.770082			0.385041	−	0.922900i	$-0.374187\pi$
$751$	21.1036			0.770082			0.385041	+	0.922900i	$0.374187\pi$
$752$	−11.7396	−	16.1582i	−0.428101	−	0.589230i
$753$	−12.4646	−	4.05000i	−0.454236	−	0.147590i
$754$	−2.25484	+	6.93968i	−0.0821164	+	0.252728i
$755$		0			0
$756$	−0.141906	−	0.436741i	−0.00516106	−	0.0158841i
$757$			40.7168i			1.47988i	0.672675	+	0.739938i	$0.265145\pi$
$757$			40.7168i			1.47988i	−0.672675	+	0.739938i	$0.734855\pi$
$758$	12.1912	−	3.96117i	0.442806	−	0.143876i
$759$	15.3821	+	11.1758i	0.558336	+	0.405655i
$760$		0			0
$761$	4.10708	−	2.98397i	0.148882	−	0.108169i	−0.510851	−	0.859669i	$-0.670670\pi$
$761$	4.10708	−	2.98397i	0.148882	−	0.108169i	0.659733	+	0.751500i	$0.270670\pi$
$762$	−15.5828	+	21.4478i	−0.564504	+	0.776973i
$763$	−0.0833489	+	0.114720i	−0.00301743	+	0.00415314i
$764$	30.9805	−	22.5087i	1.12084	−	0.814335i
$765$		0			0
$766$	0.901929	+	0.655290i	0.0325880	+	0.0236766i
$767$	15.9995	−	5.19855i	0.577708	−	0.187709i
$768$			1.59875i			0.0576899i
$769$	14.4523	+	44.4797i	0.521164	+	1.60398i	0.771779	+	0.635891i	$0.219367\pi$
$769$	14.4523	+	44.4797i	0.521164	+	1.60398i	−0.250615	+	0.968087i	$0.580633\pi$
$770$		0			0
$771$	−19.5004	+	60.0161i	−0.702290	+	2.16143i
$772$	42.0079	+	13.6492i	1.51190	+	0.491245i
$773$	11.2231	+	15.4472i	0.403665	+	0.555598i	0.961659	−	0.274248i	$-0.0884288\pi$
$773$	11.2231	+	15.4472i	0.403665	+	0.555598i	−0.557994	+	0.829845i	$0.688429\pi$
$774$	−0.574458			−0.0206485
$775$		0			0
$776$	−5.19209			−0.186385
$777$	0.0159727	+	0.0219846i	0.000573019	+	0.000788693i
$778$	−2.21278	−	0.718977i	−0.0793321	−	0.0257766i
$779$	−5.86589	+	18.0533i	−0.210167	+	0.646828i
$780$		0			0
$781$	−10.7348	−	33.0383i	−0.384121	−	1.18220i
$782$		−	3.11359i		−	0.111342i
$783$	40.4915	−	13.1565i	1.44705	−	0.470174i
$784$	−14.4797	−	10.5201i	−0.517133	−	0.375719i
$785$		0			0
$786$	−6.00477	+	4.36272i	−0.214183	+	0.155613i
$787$	−2.36591	+	3.25640i	−0.0843357	+	0.116078i	−0.849100	−	0.528232i	$-0.822855\pi$
$787$	−2.36591	+	3.25640i	−0.0843357	+	0.116078i	0.764765	+	0.644310i	$0.222855\pi$
$788$	14.8592	−	20.4519i	0.529335	−	0.728568i
$789$	71.7410	−	52.1229i	2.55405	−	1.85562i
$790$		0			0
$791$	−0.0467322	−	0.0339529i	−0.00166161	−	0.00120723i
$792$	42.0419	−	13.6602i	1.49389	−	0.485395i
$793$		−	34.7910i		−	1.23546i
$794$	5.87446	+	18.0797i	0.208477	+	0.641625i
$795$		0			0
$796$	2.04155	−	6.28325i	0.0723609	−	0.222704i
$797$	−15.2023	−	4.93953i	−0.538493	−	0.174967i	0.0271283	−	0.999632i	$-0.491364\pi$
$797$	−15.2023	−	4.93953i	−0.538493	−	0.174967i	−0.565622	+	0.824665i	$0.691364\pi$
$798$	−0.0526714	−	0.0724959i	−0.00186455	−	0.00256633i
$799$	28.2988			1.00114
$800$		0			0
$801$	−111.759			−3.94881
$802$	4.92321	+	6.77622i	0.173845	+	0.239277i
$803$	13.4744	+	4.37810i	0.475502	+	0.154500i
$804$	−7.47950	+	23.0195i	−0.263782	+	0.811836i
$805$		0			0
$806$	−3.51307	−	10.8121i	−0.123743	−	0.380841i
$807$			24.5806i			0.865279i
$808$	−18.4927	+	6.00866i	−0.650573	+	0.211384i
$809$	−23.6245	−	17.1642i	−0.830594	−	0.603462i	0.0891332	−	0.996020i	$-0.471590\pi$
$809$	−23.6245	−	17.1642i	−0.830594	−	0.603462i	−0.919727	+	0.392558i	$0.871590\pi$
$810$		0			0
$811$	−5.75792	+	4.18338i	−0.202188	+	0.146898i	−0.684272	−	0.729227i	$-0.739880\pi$
$811$	−5.75792	+	4.18338i	−0.202188	+	0.146898i	0.482084	+	0.876125i	$0.339880\pi$
$812$	−0.0943310	+	0.129835i	−0.00331037	+	0.00455633i
$813$	−17.3724	+	23.9110i	−0.609276	+	0.838597i
$814$	−0.536361	+	0.389689i	−0.0187994	+	0.0136586i
$815$		0			0
$816$	23.1838	+	16.8440i	0.811597	+	0.589659i
$817$	0.403592	−	0.131135i	0.0141199	−	0.00458784i
$818$		−	0.237034i		−	0.00828770i
$819$	−0.182307	−	0.561084i	−0.00637033	−	0.0196059i
$820$		0			0
$821$	−10.0749	+	31.0074i	−0.351617	+	1.08217i	0.606327	+	0.795215i	$0.292642\pi$
$821$	−10.0749	+	31.0074i	−0.351617	+	1.08217i	−0.957945	+	0.286952i	$0.907358\pi$
$822$	18.8804	+	6.13462i	0.658531	+	0.213970i
$823$	15.9502	+	21.9536i	0.555989	+	0.765253i	0.990810	−	0.135264i	$-0.0431882\pi$
$823$	15.9502	+	21.9536i	0.555989	+	0.765253i	−0.434821	+	0.900517i	$0.643188\pi$
$824$	34.3551			1.19681
$825$		0			0
$826$	−0.0530966			−0.00184747
$827$	32.2243	+	44.3529i	1.12055	+	1.54230i	0.804886	+	0.593429i	$0.202226\pi$
$827$	32.2243	+	44.3529i	1.12055	+	1.54230i	0.315662	+	0.948872i	$0.397774\pi$
$828$	18.7417	+	6.08954i	0.651318	+	0.211626i
$829$	−0.145846	+	0.448869i	−0.00506545	+	0.0155899i	−0.953557	−	0.301212i	$-0.902609\pi$
$829$	−0.145846	+	0.448869i	−0.00506545	+	0.0155899i	0.948492	+	0.316802i	$0.102609\pi$
$830$		0			0
$831$	16.4318	+	50.5719i	0.570013	+	1.75432i
$832$		−	9.78095i		−	0.339093i
$833$	24.1180	−	7.83641i	0.835639	−	0.271515i
$834$	−9.95482	−	7.23260i	−0.344707	−	0.250444i
$835$		0			0
$836$	−12.3250	+	8.95464i	−0.426269	+	0.309703i
$837$	−38.9895	+	53.6644i	−1.34767	+	1.85491i
$838$	−7.13653	+	9.82260i	−0.246528	+	0.339316i
$839$	−31.1259	+	22.6143i	−1.07458	+	0.780731i	−0.976731	−	0.214470i	$-0.931198\pi$
$839$	−31.1259	+	22.6143i	−1.07458	+	0.780731i	−0.0978532	+	0.995201i	$0.531198\pi$
$840$		0			0
$841$	11.4241	+	8.30008i	0.393934	+	0.286210i
$842$	14.9364	−	4.85314i	0.514743	−	0.167250i
$843$		−	84.1929i		−	2.89976i
$844$	−10.2153	−	31.4394i	−0.351625	−	1.08219i
$845$		0			0
$846$	7.94248	−	24.4444i	0.273068	−	0.840417i
$847$	0.0416263	+	0.0135252i	0.00143030	+	0.000464731i
$848$	−13.4847	−	18.5601i	−0.463065	−	0.637355i
$849$	10.7615			0.369333
$850$		0			0
$851$	−0.633505			−0.0217163
$852$	−30.8288	−	42.4321i	−1.05618	−	1.45370i
$853$	34.0993	+	11.0795i	1.16754	+	0.379356i	0.827723	−	0.561136i	$-0.189636\pi$
$853$	34.0993	+	11.0795i	1.16754	+	0.379356i	0.339815	+	0.940492i	$0.389636\pi$
$854$	−0.0339325	+	0.104434i	−0.00116115	+	0.00357364i
$855$		0			0
$856$	−9.21595	−	28.3638i	−0.314995	−	0.969454i
$857$			0.386299i			0.0131957i	0.999978	+	0.00659786i	$0.00210018\pi$
$857$			0.386299i			0.0131957i	−0.999978	+	0.00659786i	$0.997900\pi$
$858$	19.9411	−	6.47926i	0.680779	−	0.221198i
$859$	18.0321	+	13.1011i	0.615247	+	0.447003i	0.851258	−	0.524747i	$-0.175840\pi$
$859$	18.0321	+	13.1011i	0.615247	+	0.447003i	−0.236011	+	0.971750i	$0.575840\pi$
$860$		0			0
$861$	0.464863	−	0.337743i	0.0158425	−	0.0115102i
$862$	−0.589144	+	0.810887i	−0.0200663	+	0.0276189i
$863$	−5.46528	+	7.52231i	−0.186040	+	0.256062i	−0.891842	−	0.452347i	$-0.850587\pi$
$863$	−5.46528	+	7.52231i	−0.186040	+	0.256062i	0.705802	+	0.708409i	$0.250587\pi$
$864$	44.9822	−	32.6815i	1.53033	−	1.11185i
$865$		0			0
$866$	−2.86656	−	2.08268i	−0.0974096	−	0.0707722i
$867$	11.3958	−	3.70272i	0.387021	−	0.125751i
$868$		−	0.250039i		−	0.00848686i
$869$	10.7225	+	33.0005i	0.363736	+	1.11946i
$870$		0			0
$871$	−5.22013	+	16.0659i	−0.176877	+	0.544373i
$872$	−10.6482	−	3.45982i	−0.360594	−	0.117164i
$873$	10.6725	+	14.6894i	0.361208	+	0.497160i
$874$	2.08903			0.0706626
$875$		0			0
$876$	21.3910			0.722734
$877$	−17.1508	−	23.6060i	−0.579140	−	0.797118i	0.414461	−	0.910067i	$-0.363970\pi$
$877$	−17.1508	−	23.6060i	−0.579140	−	0.797118i	−0.993601	+	0.112949i	$0.963970\pi$
$878$	−6.17601	−	2.00671i	−0.208430	−	0.0677230i
$879$	−22.4573	+	69.1165i	−0.757467	+	2.33124i
$880$		0			0
$881$	−12.3835	−	38.1124i	−0.417210	−	1.28404i	−0.910260	−	0.414038i	$-0.864118\pi$
$881$	−12.3835	−	38.1124i	−0.417210	−	1.28404i	0.493050	−	0.870001i	$-0.335882\pi$
$882$		−	23.0325i		−	0.775543i
$883$	29.3248	−	9.52820i	0.986858	−	0.320650i	0.229256	−	0.973366i	$-0.426371\pi$
$883$	29.3248	−	9.52820i	0.986858	−	0.320650i	0.757602	+	0.652717i	$0.226371\pi$
$884$	19.3570	+	14.0637i	0.651047	+	0.473014i
$885$		0			0
$886$	−8.86357	+	6.43976i	−0.297777	+	0.216348i
$887$	−22.6608	+	31.1899i	−0.760875	+	1.04725i	0.236266	+	0.971688i	$0.424076\pi$
$887$	−22.6608	+	31.1899i	−0.760875	+	1.04725i	−0.997141	+	0.0755658i	$0.975924\pi$
$888$	−1.26116	+	1.73583i	−0.0423216	+	0.0582507i
$889$	−0.329226	+	0.239197i	−0.0110419	+	0.00802241i
$890$		0			0
$891$	−41.8521	−	30.4073i	−1.40210	−	1.01868i
$892$	−18.8889	+	6.13739i	−0.632449	+	0.205495i
$893$			18.9868i			0.635370i
$894$	2.69477	+	8.29366i	0.0901267	+	0.277382i
$895$		0			0
$896$	−0.0835993	+	0.257292i	−0.00279286	+	0.00859553i
$897$	19.0546	+	6.19122i	0.636215	+	0.206719i
$898$	0.117680	+	0.161972i	0.00392702	+	0.00540508i
$899$	23.1818			0.773156
$900$		0			0
$901$	32.5052			1.08291
$902$	8.23994	+	11.3413i	0.274360	+	0.377624i
$903$	−0.0122168	−	0.00396949i	−0.000406551	−	0.000132096i
$904$	1.40939	−	4.33765i	0.0468755	−	0.144268i
$905$		0			0
$906$	−3.52916	−	10.8616i	−0.117248	−	0.360853i
$907$		−	4.77670i		−	0.158608i	−0.996850	−	0.0793038i	$-0.974730\pi$
$907$		−	4.77670i		−	0.158608i	0.996850	−	0.0793038i	$-0.0252697\pi$
$908$	−18.6263	+	6.05205i	−0.618136	+	0.200844i
$909$	55.0119	+	39.9685i	1.82463	+	1.32567i
$910$		0			0
$911$	9.33054	−	6.77904i	0.309135	−	0.224600i	−0.422390	−	0.906414i	$-0.638809\pi$
$911$	9.33054	−	6.77904i	0.309135	−	0.224600i	0.731525	+	0.681814i	$0.238809\pi$
$912$	−11.3014	+	15.5550i	−0.374225	+	0.515077i
$913$	18.8656	−	25.9663i	0.624361	−	0.859359i
$914$	−14.2769	+	10.3728i	−0.472238	+	0.343101i
$915$		0			0
$916$	13.6541	+	9.92028i	0.451144	+	0.327775i
$917$	−0.108357	+	0.0352073i	−0.00357826	+	0.00116265i
$918$			20.0341i			0.661224i
$919$	12.7707	+	39.3041i	0.421266	+	1.29652i	0.906525	+	0.422153i	$0.138726\pi$
$919$	12.7707	+	39.3041i	0.421266	+	1.29652i	−0.485258	+	0.874371i	$0.661274\pi$
$920$		0			0
$921$	1.06343	−	3.27290i	0.0350411	−	0.107846i
$922$	−7.60517	−	2.47107i	−0.250463	−	0.0813803i
$923$	−21.5162	−	29.6145i	−0.708213	−	0.974772i
$924$	0.461153			0.0151708
$925$		0			0
$926$	−15.2717			−0.501860
$927$	−70.6176	−	97.1968i	−2.31939	−	3.19236i
$928$	−18.4802	−	6.00460i	−0.606644	−	0.197111i
$929$	4.14621	−	12.7607i	0.136033	−	0.418666i	−0.859716	−	0.510772i	$-0.829360\pi$
$929$	4.14621	−	12.7607i	0.136033	−	0.418666i	0.995749	+	0.0921056i	$0.0293597\pi$
$930$		0			0
$931$	5.25776	+	16.1817i	0.172316	+	0.530335i
$932$			27.1552i			0.889499i
$933$	−43.4010	+	14.1018i	−1.42089	+	0.461674i
$934$	2.69392	+	1.95724i	0.0881476	+	0.0640430i
$935$		0			0
$936$	37.6850	−	27.3798i	1.23177	−	0.894936i
$937$	24.6828	−	33.9729i	0.806351	−	1.10985i	−0.185525	−	0.982640i	$-0.559398\pi$
$937$	24.6828	−	33.9729i	0.806351	−	1.10985i	0.991876	−	0.127208i	$-0.0406015\pi$
$938$	0.0313390	−	0.0431344i	0.00102325	−	0.00140839i
$939$	12.3832	−	8.99692i	0.404111	−	0.293603i
$940$		0			0
$941$	−32.4064	−	23.5446i	−1.05642	−	0.767532i	−0.0829949	−	0.996550i	$-0.526449\pi$
$941$	−32.4064	−	23.5446i	−1.05642	−	0.767532i	−0.973422	+	0.229018i	$0.926449\pi$
$942$	−12.7206	+	4.13317i	−0.414460	+	0.134666i
$943$			13.3954i			0.436215i
$944$	3.52050	+	10.8350i	0.114583	+	0.352649i
$945$		0			0
$946$	0.0968441	−	0.298056i	0.00314867	−	0.00969062i
$947$	41.8228	+	13.5890i	1.35906	+	0.441585i	0.895728	−	0.444602i	$-0.146655\pi$
$947$	41.8228	+	13.5890i	1.35906	+	0.441585i	0.463329	+	0.886186i	$0.346655\pi$
$948$	30.7935	+	42.3836i	1.00013	+	1.37656i
$949$	14.9293			0.484625
$950$		0			0
$951$	70.1721			2.27549
$952$	−0.0951461	−	0.130957i	−0.00308370	−	0.00424435i
$953$	−38.6292	−	12.5514i	−1.25132	−	0.406579i	−0.392928	−	0.919569i	$-0.628538\pi$
$953$	−38.6292	−	12.5514i	−1.25132	−	0.406579i	−0.858395	+	0.512990i	$0.828538\pi$
$954$	9.12308	−	28.0779i	0.295371	−	0.909057i
$955$		0			0
$956$	−7.74726	−	23.8436i	−0.250564	−	0.771158i
$957$			42.7548i			1.38207i
$958$	10.5970	−	3.44319i	0.342375	−	0.111244i
$959$	0.246533	+	0.179116i	0.00796095	+	0.00578397i
$960$		0			0
$961$	−4.14019	+	3.00803i	−0.133555	+	0.0970331i
$962$	−0.410633	+	0.565188i	−0.0132393	+	0.0182224i
$963$	−61.3028	+	84.3760i	−1.97545	+	2.71898i
$964$	−35.8150	+	26.0212i	−1.15352	+	0.838085i
$965$		0			0
$966$	−0.0511586	−	0.0371689i	−0.00164600	−	0.00119589i
$967$	15.2171	−	4.94432i	0.489348	−	0.158999i	−0.0539419	−	0.998544i	$-0.517179\pi$
$967$	15.2171	−	4.94432i	0.489348	−	0.158999i	0.543290	+	0.839545i	$0.317179\pi$
$968$			3.45581i			0.111074i
$969$	−8.41833	−	25.9090i	−0.270436	−	0.832315i
$970$		0			0
$971$	17.1567	−	52.8028i	0.550583	−	1.69452i	−0.156747	−	0.987639i	$-0.550101\pi$
$971$	17.1567	−	52.8028i	0.550583	−	1.69452i	0.707331	−	0.706883i	$-0.249899\pi$
$972$	−19.2041	−	6.23978i	−0.615971	−	0.200141i
$973$	−0.111021	−	0.152808i	−0.00355917	−	0.00489878i
$974$	−5.10263			−0.163499
$975$		0			0
$976$	23.5608			0.754162
$977$	−3.71797	−	5.11734i	−0.118948	−	0.163718i	0.745391	−	0.666628i	$-0.232263\pi$
$977$	−3.71797	−	5.11734i	−0.118948	−	0.163718i	−0.864339	+	0.502909i	$0.832263\pi$
$978$	−7.00021	−	2.27451i	−0.223842	−	0.0727307i
$979$	18.8407	−	57.9858i	0.602152	−	1.85323i
$980$		0			0
$981$	12.0992	+	37.2375i	0.386298	+	1.18890i
$982$			3.32659i			0.106156i
$983$	46.2615	−	15.0313i	1.47551	−	0.479423i	0.542743	−	0.839899i	$-0.317386\pi$
$983$	46.2615	−	15.0313i	1.47551	−	0.479423i	0.932768	+	0.360476i	$0.117386\pi$
$984$	36.7041	+	26.6671i	1.17008	+	0.850115i
$985$		0			0
$986$	5.66429	−	4.11535i	0.180388	−	0.131059i
$987$	0.337821	−	0.464971i	0.0107530	−	0.0148002i
$988$	−9.43591	+	12.9874i	−0.300196	+	0.413185i
$989$	0.242270	−	0.176019i	0.00770373	−	0.00559709i
$990$		0			0
$991$	35.7394	+	25.9662i	1.13530	+	0.824842i	0.986457	−	0.164019i	$-0.0524458\pi$
$991$	35.7394	+	25.9662i	1.13530	+	0.824842i	0.148841	+	0.988861i	$0.452446\pi$
$992$	28.7925	−	9.35525i	0.914163	−	0.297029i
$993$		−	5.35931i		−	0.170073i
$994$	0.0357023	+	0.109880i	0.00113241	+	0.00348519i
$995$		0			0
$996$	14.9748	−	46.0877i	0.474495	−	1.46035i
$997$	38.2574	+	12.4306i	1.21162	+	0.393681i	0.844025	−	0.536304i	$-0.180180\pi$
$997$	38.2574	+	12.4306i	1.21162	+	0.393681i	0.367599	+	0.929984i	$0.380180\pi$
$998$	0.319202	+	0.439344i	0.0101042	+	0.0139072i
$999$	4.07623			0.128966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.e.j.374.4		32
5.2	odd	4		625.2.d.q.251.2		16
5.3	odd	4		625.2.d.m.251.3		16
5.4	even	2	inner	625.2.e.j.374.5		32
25.2	odd	20		625.2.d.p.126.3		16
25.3	odd	20		625.2.a.g.1.4	yes	8
25.4	even	10		625.2.b.d.624.7		16
25.6	even	5		625.2.e.k.124.5		32
25.8	odd	20		625.2.d.n.501.2		16
25.9	even	10	inner	625.2.e.j.249.4		32
25.11	even	5		625.2.e.k.499.4		32
25.12	odd	20		625.2.d.q.376.2		16
25.13	odd	20		625.2.d.m.376.3		16
25.14	even	10		625.2.e.k.499.5		32
25.16	even	5	inner	625.2.e.j.249.5		32
25.17	odd	20		625.2.d.p.501.3		16
25.19	even	10		625.2.e.k.124.4		32
25.21	even	5		625.2.b.d.624.10		16
25.22	odd	20		625.2.a.e.1.5	✓	8
25.23	odd	20		625.2.d.n.126.2		16
75.47	even	20		5625.2.a.be.1.4		8
75.53	even	20		5625.2.a.s.1.5		8
100.3	even	20		10000.2.a.be.1.1		8
100.47	even	20		10000.2.a.bn.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.5	✓	8	25.22	odd	20
625.2.a.g.1.4	yes	8	25.3	odd	20
625.2.b.d.624.7		16	25.4	even	10
625.2.b.d.624.10		16	25.21	even	5
625.2.d.m.251.3		16	5.3	odd	4
625.2.d.m.376.3		16	25.13	odd	20
625.2.d.n.126.2		16	25.23	odd	20
625.2.d.n.501.2		16	25.8	odd	20
625.2.d.p.126.3		16	25.2	odd	20
625.2.d.p.501.3		16	25.17	odd	20
625.2.d.q.251.2		16	5.2	odd	4
625.2.d.q.376.2		16	25.12	odd	20
625.2.e.j.249.4		32	25.9	even	10	inner
625.2.e.j.249.5		32	25.16	even	5	inner
625.2.e.j.374.4		32	1.1	even	1	trivial
625.2.e.j.374.5		32	5.4	even	2	inner
625.2.e.k.124.4		32	25.19	even	10
625.2.e.k.124.5		32	25.6	even	5
625.2.e.k.499.4		32	25.11	even	5
625.2.e.k.499.5		32	25.14	even	10
5625.2.a.s.1.5		8	75.53	even	20
5625.2.a.be.1.4		8	75.47	even	20
10000.2.a.be.1.1		8	100.3	even	20
10000.2.a.bn.1.8		8	100.47	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+(-0.294474 - 0.405309i) q^{2} +(-2.94186 - 0.955869i) q^{3} +(0.540474 - 1.66341i) q^{4} +(0.478880 + 1.47384i) q^{6} +0.0237879i q^{7} +(-1.78629 + 0.580400i) q^{8} +(5.31382 + 3.86071i) q^{9} +(-2.89894 + 2.10620i) q^{11} +(-3.18000 + 4.37689i) q^{12} +(-2.21940 + 3.05474i) q^{13} +(0.00964144 - 0.00700492i) q^{14} +(-2.06870 - 1.50300i) q^{16} +(3.44570 - 1.11958i) q^{17} -3.29062i q^{18} +(0.751170 + 2.31186i) q^{19} +(0.0227381 - 0.0699807i) q^{21} +(1.70733 + 0.554744i) q^{22} +(1.00828 + 1.38777i) q^{23} +5.80980 q^{24} +1.89167 q^{26} +(-6.48766 - 8.92950i) q^{27} +(0.0395689 + 0.0128567i) q^{28} +(-1.19198 + 3.66855i) q^{29} +(-1.85713 - 5.71565i) q^{31} +5.03748i q^{32} +(10.5415 - 3.42515i) q^{33} +(-1.46845 - 1.06689i) q^{34} +(9.29391 - 6.75242i) q^{36} +(-0.217074 + 0.298777i) q^{37} +(0.715819 - 0.985240i) q^{38} +(9.44911 - 6.86518i) q^{39} +(6.31761 + 4.59002i) q^{41} +(-0.0350596 + 0.0113915i) q^{42} -0.174574i q^{43} +(1.93667 + 5.96047i) q^{44} +(0.265566 - 0.817327i) q^{46} +(7.42853 + 2.41368i) q^{47} +(4.64916 + 6.39902i) q^{48} +6.99943 q^{49} -11.2070 q^{51} +(3.88175 + 5.34278i) q^{52} +(8.53273 + 2.77245i) q^{53} +(-1.70876 + 5.25902i) q^{54} +(-0.0138065 - 0.0424920i) q^{56} -7.51920i q^{57} +(1.83790 - 0.597171i) q^{58} +(-3.60446 - 2.61879i) q^{59} +(-7.45430 + 5.41587i) q^{61} +(-1.76973 + 2.43582i) q^{62} +(-0.0918382 + 0.126404i) q^{63} +(-2.09566 + 1.52259i) q^{64} +(-4.49246 - 3.26396i) q^{66} +(4.25489 - 1.38250i) q^{67} -6.33671i q^{68} +(-1.63968 - 5.04642i) q^{69} +(-2.99579 + 9.22010i) q^{71} +(-11.7328 - 3.81221i) q^{72} +(-2.32403 - 3.19875i) q^{73} +0.185020 q^{74} +4.25156 q^{76} +(-0.0501021 - 0.0689596i) q^{77} +(-5.56504 - 1.80819i) q^{78} +(2.99236 - 9.20955i) q^{79} +(4.46129 + 13.7304i) q^{81} -3.91223i q^{82} +(-8.51877 + 2.76792i) q^{83} +(-0.104117 - 0.0756454i) q^{84} +(-0.0707566 + 0.0514077i) q^{86} +(7.01330 - 9.65298i) q^{87} +(3.95590 - 5.44483i) q^{88} +(-13.7655 + 10.0012i) q^{89} +(-0.0726659 - 0.0527948i) q^{91} +(2.85338 - 0.927119i) q^{92} +18.5898i q^{93} +(-1.20923 - 3.72161i) q^{94} +(4.81518 - 14.8196i) q^{96} +(2.62908 + 0.854239i) q^{97} +(-2.06115 - 2.83693i) q^{98} -23.5359 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

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