LMFDB - Embedded newform 425.2.n.c.274.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(49,425)] 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("425.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			274.3
Character	$\chi$	$=$	425.274
Dual form			425.2.n.c.349.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.213325 + 0.213325i) q^{2} +(-0.406032 - 0.980249i) q^{3} +1.90899i q^{4} +(0.295728 + 0.122495i) q^{6} +(-2.31879 - 0.960473i) q^{7} +(-0.833883 - 0.833883i) q^{8} +(1.32529 - 1.32529i) q^{9} +(2.25941 + 0.935880i) q^{11} +(1.87128 - 0.775110i) q^{12} +5.61335 q^{13} +(0.699548 - 0.289762i) q^{14} -3.46219 q^{16} +(3.06205 + 2.76113i) q^{17} +0.565436i q^{18} +(5.04243 + 5.04243i) q^{19} +2.66297i q^{21} +(-0.681636 + 0.282343i) q^{22} +(0.329416 - 0.795280i) q^{23} +(-0.478830 + 1.15600i) q^{24} +(-1.19747 + 1.19747i) q^{26} +(-4.77798 - 1.97910i) q^{27} +(1.83353 - 4.42653i) q^{28} +(1.43561 + 3.46587i) q^{29} +(-2.07626 + 0.860015i) q^{31} +(2.40634 - 2.40634i) q^{32} -2.59479i q^{33} +(-1.24223 + 0.0641935i) q^{34} +(2.52997 + 2.52997i) q^{36} +(1.95382 + 4.71693i) q^{37} -2.15135 q^{38} +(-2.27920 - 5.50249i) q^{39} +(4.72598 - 11.4095i) q^{41} +(-0.568078 - 0.568078i) q^{42} +(1.85272 + 1.85272i) q^{43} +(-1.78658 + 4.31319i) q^{44} +(0.0993804 + 0.239926i) q^{46} -2.30114 q^{47} +(1.40576 + 3.39381i) q^{48} +(-0.495478 - 0.495478i) q^{49} +(1.46330 - 4.12268i) q^{51} +10.7158i q^{52} +(1.96204 - 1.96204i) q^{53} +(1.44145 - 0.597069i) q^{54} +(1.13268 + 2.73452i) q^{56} +(2.89544 - 6.99022i) q^{57} +(-1.04561 - 0.433105i) q^{58} +(5.26206 - 5.26206i) q^{59} +(-0.346822 + 0.837303i) q^{61} +(0.259455 - 0.626380i) q^{62} +(-4.34599 + 1.80017i) q^{63} -5.89773i q^{64} +(0.553532 + 0.553532i) q^{66} -6.69889i q^{67} +(-5.27096 + 5.84541i) q^{68} -0.913326 q^{69} +(0.222439 - 0.0921372i) q^{71} -2.21028 q^{72} +(-5.96591 + 2.47116i) q^{73} +(-1.42304 - 0.589441i) q^{74} +(-9.62592 + 9.62592i) q^{76} +(-4.34022 - 4.34022i) q^{77} +(1.66003 + 0.687606i) q^{78} +(-13.5899 - 5.62912i) q^{79} -0.135560i q^{81} +(1.42577 + 3.44210i) q^{82} +(-9.82767 + 9.82767i) q^{83} -5.08358 q^{84} -0.790460 q^{86} +(2.81451 - 2.81451i) q^{87} +(-1.10367 - 2.66450i) q^{88} +0.395163i q^{89} +(-13.0162 - 5.39148i) q^{91} +(1.51818 + 0.628850i) q^{92} +(1.68606 + 1.68606i) q^{93} +(0.490889 - 0.490889i) q^{94} +(-3.33586 - 1.38176i) q^{96} +(-8.27725 + 3.42855i) q^{97} +0.211396 q^{98} +(4.23471 - 1.75407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.213325	+	0.213325i	−0.150843	+	0.150843i	−0.778495	−	0.627651i	$-0.784016\pi$
$2$	−0.213325	+	0.213325i	−0.150843	+	0.150843i	0.627651	+	0.778495i	$0.284016\pi$
$3$	−0.406032	−	0.980249i	−0.234423	−	0.565947i	0.762265	−	0.647265i	$-0.224087\pi$
$3$	−0.406032	−	0.980249i	−0.234423	−	0.565947i	−0.996688	+	0.0813177i	$0.974087\pi$
$4$			1.90899i			0.954493i
$5$		0			0
$5$		0			0
$6$	0.295728	+	0.122495i	0.120731	+	0.0500082i
$7$	−2.31879	−	0.960473i	−0.876420	−	0.363025i	−0.101312	−	0.994855i	$-0.532304\pi$
$7$	−2.31879	−	0.960473i	−0.876420	−	0.363025i	−0.775107	+	0.631830i	$0.782304\pi$
$8$	−0.833883	−	0.833883i	−0.294822	−	0.294822i
$9$	1.32529	−	1.32529i	0.441765	−	0.441765i
$10$		0			0
$11$	2.25941	+	0.935880i	0.681239	+	0.282179i	0.696345	−	0.717707i	$-0.254808\pi$
$11$	2.25941	+	0.935880i	0.681239	+	0.282179i	−0.0151056	+	0.999886i	$0.504808\pi$
$12$	1.87128	−	0.775110i	0.540192	−	0.223755i
$13$	5.61335			1.55686			0.778432	−	0.627729i	$-0.216015\pi$
$13$	5.61335			1.55686			0.778432	+	0.627729i	$0.216015\pi$
$14$	0.699548	−	0.289762i	0.186962	−	0.0774422i
$15$		0			0
$16$	−3.46219			−0.865549
$17$	3.06205	+	2.76113i	0.742656	+	0.669673i
$17$	3.06205	+	2.76113i	0.742656	+	0.669673i
$18$			0.565436i			0.133275i
$19$	5.04243	+	5.04243i	1.15681	+	1.15681i	0.985157	+	0.171655i	$0.0549113\pi$
$19$	5.04243	+	5.04243i	1.15681	+	1.15681i	0.171655	+	0.985157i	$0.445089\pi$
$20$		0			0
$21$			2.66297i			0.581108i
$22$	−0.681636	+	0.282343i	−0.145325	+	0.0601957i
$23$	0.329416	−	0.795280i	0.0686880	−	0.165827i	−0.885807	−	0.464053i	$-0.846395\pi$
$23$	0.329416	−	0.795280i	0.0686880	−	0.165827i	0.954495	+	0.298226i	$0.0963948\pi$
$24$	−0.478830	+	1.15600i	−0.0977407	+	0.235967i
$25$		0			0
$26$	−1.19747	+	1.19747i	−0.234843	+	0.234843i
$27$	−4.77798	−	1.97910i	−0.919522	−	0.380879i
$28$	1.83353	−	4.42653i	0.346505	−	0.836536i
$29$	1.43561	+	3.46587i	0.266586	+	0.643597i	0.999318	−	0.0369210i	$-0.0117550\pi$
$29$	1.43561	+	3.46587i	0.266586	+	0.643597i	−0.732732	+	0.680518i	$0.761755\pi$
$30$		0			0
$31$	−2.07626	+	0.860015i	−0.372907	+	0.154463i	−0.561263	−	0.827638i	$-0.689684\pi$
$31$	−2.07626	+	0.860015i	−0.372907	+	0.154463i	0.188356	+	0.982101i	$0.439684\pi$
$32$	2.40634	−	2.40634i	0.425385	−	0.425385i
$33$		−	2.59479i		−	0.451694i
$34$	−1.24223	+	0.0641935i	−0.213041	+	0.0110091i
$35$		0			0
$36$	2.52997	+	2.52997i	0.421661	+	0.421661i
$37$	1.95382	+	4.71693i	0.321206	+	0.775459i	0.999184	+	0.0403776i	$0.0128561\pi$
$37$	1.95382	+	4.71693i	0.321206	+	0.775459i	−0.677979	+	0.735081i	$0.737144\pi$
$38$	−2.15135			−0.348995
$39$	−2.27920	−	5.50249i	−0.364965	−	0.881103i
$40$		0			0
$41$	4.72598	−	11.4095i	0.738074	−	1.78187i	0.124518	−	0.992217i	$-0.460262\pi$
$41$	4.72598	−	11.4095i	0.738074	−	1.78187i	0.613556	−	0.789651i	$-0.289738\pi$
$42$	−0.568078	−	0.568078i	−0.0876564	−	0.0876564i
$43$	1.85272	+	1.85272i	0.282536	+	0.282536i	0.834120	−	0.551583i	$-0.185976\pi$
$43$	1.85272	+	1.85272i	0.282536	+	0.282536i	−0.551583	+	0.834120i	$0.685976\pi$
$44$	−1.78658	+	4.31319i	−0.269337	+	0.650238i
$45$		0			0
$46$	0.0993804	+	0.239926i	0.0146528	+	0.0353751i
$47$	−2.30114			−0.335655			−0.167828	−	0.985816i	$-0.553675\pi$
$47$	−2.30114			−0.335655			−0.167828	+	0.985816i	$0.553675\pi$
$48$	1.40576	+	3.39381i	0.202904	+	0.489855i
$49$	−0.495478	−	0.495478i	−0.0707826	−	0.0707826i
$50$		0			0
$51$	1.46330	−	4.12268i	0.204904	−	0.577291i
$52$			10.7158i			1.48602i
$53$	1.96204	−	1.96204i	0.269507	−	0.269507i	−0.559394	−	0.828902i	$-0.688966\pi$
$53$	1.96204	−	1.96204i	0.269507	−	0.269507i	0.828902	+	0.559394i	$0.188966\pi$
$54$	1.44145	−	0.597069i	0.196157	−	0.0812508i
$55$		0			0
$56$	1.13268	+	2.73452i	0.151360	+	0.365416i
$57$	2.89544	−	6.99022i	0.383511	−	0.925877i
$58$	−1.04561	−	0.433105i	−0.137295	−	0.0568695i
$59$	5.26206	−	5.26206i	0.685062	−	0.685062i	−0.276075	−	0.961136i	$-0.589034\pi$
$59$	5.26206	−	5.26206i	0.685062	−	0.685062i	0.961136	+	0.276075i	$0.0890337\pi$
$60$		0			0
$61$	−0.346822	+	0.837303i	−0.0444061	+	0.107206i	−0.944526	−	0.328436i	$-0.893478\pi$
$61$	−0.346822	+	0.837303i	−0.0444061	+	0.107206i	0.900120	+	0.435642i	$0.143478\pi$
$62$	0.259455	−	0.626380i	0.0329508	−	0.0795504i
$63$	−4.34599	+	1.80017i	−0.547543	+	0.226800i
$64$		−	5.89773i		−	0.737216i
$65$		0			0
$66$	0.553532	+	0.553532i	0.0681351	+	0.0681351i
$67$		−	6.69889i		−	0.818399i	−0.912445	−	0.409200i	$-0.865808\pi$
$67$		−	6.69889i		−	0.818399i	0.912445	−	0.409200i	$-0.134192\pi$
$68$	−5.27096	+	5.84541i	−0.639198	+	0.708860i
$69$	−0.913326			−0.109952
$70$		0			0
$71$	0.222439	−	0.0921372i	0.0263986	−	0.0109347i	−0.369445	−	0.929253i	$-0.620452\pi$
$71$	0.222439	−	0.0921372i	0.0263986	−	0.0109347i	0.395844	+	0.918318i	$0.370452\pi$
$72$	−2.21028			−0.260484
$73$	−5.96591	+	2.47116i	−0.698257	+	0.289228i	−0.703436	−	0.710759i	$-0.748352\pi$
$73$	−5.96591	+	2.47116i	−0.698257	+	0.289228i	0.00517825	+	0.999987i	$0.498352\pi$
$74$	−1.42304	−	0.589441i	−0.165425	−	0.0685211i
$75$		0			0
$76$	−9.62592	+	9.62592i	−1.10417	+	1.10417i
$77$	−4.34022	−	4.34022i	−0.494614	−	0.494614i
$78$	1.66003	+	0.687606i	0.187961	+	0.0778560i
$79$	−13.5899	−	5.62912i	−1.52898	−	0.633325i	−0.549615	−	0.835418i	$-0.685226\pi$
$79$	−13.5899	−	5.62912i	−1.52898	−	0.633325i	−0.979366	+	0.202093i	$0.935226\pi$
$80$		0			0
$81$		−	0.135560i		−	0.0150623i
$82$	1.42577	+	3.44210i	0.157449	+	0.380117i
$83$	−9.82767	+	9.82767i	−1.07873	+	1.07873i	−0.0821031	+	0.996624i	$0.526164\pi$
$83$	−9.82767	+	9.82767i	−1.07873	+	1.07873i	−0.996624	+	0.0821031i	$0.973836\pi$
$84$	−5.08358			−0.554664
$85$		0			0
$86$	−0.790460			−0.0852375
$87$	2.81451	−	2.81451i	0.301748	−	0.301748i
$88$	−1.10367	−	2.66450i	−0.117652	−	0.284037i
$89$			0.395163i			0.0418872i	0.999781	+	0.0209436i	$0.00666704\pi$
$89$			0.395163i			0.0418872i	−0.999781	+	0.0209436i	$0.993333\pi$
$90$		0			0
$91$	−13.0162	−	5.39148i	−1.36447	−	0.565181i
$92$	1.51818	+	0.628850i	0.158281	+	0.0655621i
$93$	1.68606	+	1.68606i	0.174836	+	0.174836i
$94$	0.490889	−	0.490889i	0.0506314	−	0.0506314i
$95$		0			0
$96$	−3.33586	−	1.38176i	−0.340465	−	0.141025i
$97$	−8.27725	+	3.42855i	−0.840427	+	0.348116i	−0.761022	−	0.648726i	$-0.775302\pi$
$97$	−8.27725	+	3.42855i	−0.840427	+	0.348116i	−0.0794052	+	0.996842i	$0.525302\pi$
$98$	0.211396			0.0213542
$99$	4.23471	−	1.75407i	0.425604	−	0.176291i
$100$		0			0
$101$	15.2882			1.52124			0.760619	−	0.649199i	$-0.224896\pi$
$101$	15.2882			1.52124			0.760619	+	0.649199i	$0.224896\pi$
$102$	0.567311	+	1.19163i	0.0561721	+	0.117989i
$103$			14.7746i			1.45579i	0.685690	+	0.727894i	$0.259501\pi$
$103$			14.7746i			1.45579i	−0.685690	+	0.727894i	$0.740499\pi$
$104$	−4.68088	−	4.68088i	−0.458998	−	0.458998i
$105$		0			0
$106$			0.837105i			0.0813068i
$107$	−1.35882	+	0.562841i	−0.131362	+	0.0544119i	−0.447396	−	0.894336i	$-0.647649\pi$
$107$	−1.35882	+	0.562841i	−0.131362	+	0.0544119i	0.316034	+	0.948748i	$0.397649\pi$
$108$	3.77808	−	9.12109i	0.363546	−	0.877677i
$109$	−3.61166	+	8.71931i	−0.345934	+	0.835158i	0.651157	+	0.758943i	$0.274284\pi$
$109$	−3.61166	+	8.71931i	−0.345934	+	0.835158i	−0.997091	+	0.0762157i	$0.975716\pi$
$110$		0			0
$111$	3.83046	−	3.83046i	0.363571	−	0.363571i
$112$	8.02809	+	3.32535i	0.758584	+	0.314216i
$113$	5.72534	−	13.8222i	0.538595	−	1.30028i	−0.387109	−	0.922034i	$-0.626526\pi$
$113$	5.72534	−	13.8222i	0.538595	−	1.30028i	0.925704	−	0.378249i	$-0.123474\pi$
$114$	0.873517	+	2.10886i	0.0818124	+	0.197513i
$115$		0			0
$116$	−6.61630	+	2.74056i	−0.614308	+	0.254455i
$117$	7.43935	−	7.43935i	0.687768	−	0.687768i
$118$			2.24505i			0.206674i
$119$	−4.44825	−	9.34350i	−0.407771	−	0.856517i
$120$		0			0
$121$	−3.54909	−	3.54909i	−0.322645	−	0.322645i
$122$	−0.104632	−	0.252603i	−0.00947291	−	0.0228696i
$123$	−13.1031			−1.18146
$124$	−1.64176	−	3.96355i	−0.147434	−	0.355937i
$125$		0			0
$126$	0.543087	−	1.31113i	0.0483820	−	0.116804i
$127$	4.21071	+	4.21071i	0.373640	+	0.373640i	0.868801	−	0.495161i	$-0.164891\pi$
$127$	4.21071	+	4.21071i	0.373640	+	0.373640i	−0.495161	+	0.868801i	$0.664891\pi$
$128$	6.07081	+	6.07081i	0.536589	+	0.536589i
$129$	1.06386	−	2.56839i	0.0936677	−	0.226134i
$130$		0			0
$131$	−1.60241	−	3.86856i	−0.140003	−	0.337998i	0.838290	−	0.545225i	$-0.183556\pi$
$131$	−1.60241	−	3.86856i	−0.140003	−	0.337998i	−0.978293	+	0.207228i	$0.933556\pi$
$132$	4.95341			0.431139
$133$	−6.84920	−	16.5354i	−0.593901	−	1.43380i
$134$	1.42904	+	1.42904i	0.123450	+	0.123450i
$135$		0			0
$136$	−0.250931	−	4.85585i	−0.0215172	−	0.416386i
$137$			7.25998i			0.620262i	0.950694	+	0.310131i	$0.100373\pi$
$137$			7.25998i			0.620262i	−0.950694	+	0.310131i	$0.899627\pi$
$138$	0.194835	−	0.194835i	0.0165855	−	0.0165855i
$139$	−9.60207	+	3.97731i	−0.814437	+	0.337351i	−0.750723	−	0.660617i	$-0.770295\pi$
$139$	−9.60207	+	3.97731i	−0.814437	+	0.337351i	−0.0637140	+	0.997968i	$0.520295\pi$
$140$		0			0
$141$	0.934336	+	2.25569i	0.0786853	+	0.189963i
$142$	−0.0277966	+	0.0671069i	−0.00233264	+	0.00563149i
$143$	12.6829	+	5.25343i	1.06060	+	0.439314i
$144$	−4.58843	+	4.58843i	−0.382369	+	0.382369i
$145$		0			0
$146$	0.745517	−	1.79984i	0.0616994	−	0.148956i
$147$	−0.284512	+	0.686873i	−0.0234661	+	0.0566523i
$148$	−9.00455	+	3.72981i	−0.740170	+	0.306588i
$149$		−	6.01765i		−	0.492985i	−0.969145	−	0.246492i	$-0.920722\pi$
$149$		−	6.01765i		−	0.492985i	0.969145	−	0.246492i	$-0.0792781\pi$
$150$		0			0
$151$	7.36684	+	7.36684i	0.599505	+	0.599505i	0.940181	−	0.340676i	$-0.110656\pi$
$151$	7.36684	+	7.36684i	0.599505	+	0.599505i	−0.340676	+	0.940181i	$0.610656\pi$
$152$		−	8.40959i		−	0.682108i
$153$	7.71743	−	0.398806i	0.623917	−	0.0322416i
$154$	1.85175			0.149218
$155$		0			0
$156$	10.5042	−	4.35097i	0.841006	−	0.348356i
$157$	−13.4073			−1.07002			−0.535008	−	0.844847i	$-0.679691\pi$
$157$	−13.4073			−1.07002			−0.535008	+	0.844847i	$0.679691\pi$
$158$	4.09989	−	1.69823i	0.326170	−	0.135104i
$159$	−2.71994	−	1.12664i	−0.215706	−	0.0893482i
$160$		0			0
$161$	−1.52769	+	1.52769i	−0.120399	+	0.120399i
$162$	0.0289184	+	0.0289184i	0.00227204	+	0.00227204i
$163$	−1.45523	−	0.602777i	−0.113983	−	0.0472132i	0.324963	−	0.945727i	$-0.394648\pi$
$163$	−1.45523	−	0.602777i	−0.113983	−	0.0472132i	−0.438946	+	0.898513i	$0.644648\pi$
$164$	21.7806	+	9.02182i	1.70078	+	0.704486i
$165$		0			0
$166$		−	4.19297i		−	0.325438i
$167$	−6.73711	−	16.2648i	−0.521333	−	1.25861i	−0.937075	−	0.349127i	$-0.886478\pi$
$167$	−6.73711	−	16.2648i	−0.521333	−	1.25861i	0.415742	−	0.909482i	$-0.363522\pi$
$168$	2.22061	−	2.22061i	0.171324	−	0.171324i
$169$	18.5098			1.42383
$170$		0			0
$171$	13.3654			1.02208
$172$	−3.53681	+	3.53681i	−0.269679	+	0.269679i
$173$	7.21087	+	17.4086i	0.548232	+	1.32355i	0.918792	+	0.394741i	$0.129166\pi$
$173$	7.21087	+	17.4086i	0.548232	+	1.32355i	−0.370560	+	0.928808i	$0.620834\pi$
$174$			1.20081i			0.0910333i
$175$		0			0
$176$	−7.82253	−	3.24020i	−0.589646	−	0.244239i
$177$	−7.29469	−	3.02156i	−0.548303	−	0.227114i
$178$	−0.0842980	−	0.0842980i	−0.00631840	−	0.00631840i
$179$	−2.34324	+	2.34324i	−0.175142	+	0.175142i	−0.789234	−	0.614092i	$-0.789522\pi$
$179$	−2.34324	+	2.34324i	−0.175142	+	0.175142i	0.614092	+	0.789234i	$0.289522\pi$
$180$		0			0
$181$	−14.6575	−	6.07133i	−1.08948	−	0.451278i	−0.235656	−	0.971836i	$-0.575724\pi$
$181$	−14.6575	−	6.07133i	−1.08948	−	0.451278i	−0.853826	+	0.520558i	$0.825724\pi$
$182$	3.92681	−	1.62654i	0.291075	−	0.120567i
$183$	0.961587			0.0710826
$184$	−0.937865	+	0.388477i	−0.0691404	+	0.0286389i
$185$		0			0
$186$	−0.719356			−0.0527457
$187$	4.33435	+	9.10425i	0.316959	+	0.665769i
$188$		−	4.39284i		−	0.320380i
$189$	9.17824	+	9.17824i	0.667619	+	0.667619i
$190$		0			0
$191$			27.4943i			1.98941i	0.102748	+	0.994707i	$0.467236\pi$
$191$			27.4943i			1.98941i	−0.102748	+	0.994707i	$0.532764\pi$
$192$	−5.78124	+	2.39467i	−0.417225	+	0.172820i
$193$	5.64889	−	13.6376i	0.406616	−	0.981658i	−0.579405	−	0.815040i	$-0.696715\pi$
$193$	5.64889	−	13.6376i	0.406616	−	0.981658i	0.986021	−	0.166619i	$-0.0532849\pi$
$194$	1.03435	−	2.49714i	0.0742618	−	0.179284i
$195$		0			0
$196$	0.945861	−	0.945861i	0.0675615	−	0.0675615i
$197$	−0.347754	−	0.144044i	−0.0247764	−	0.0102627i	0.370261	−	0.928928i	$-0.379268\pi$
$197$	−0.347754	−	0.144044i	−0.0247764	−	0.0102627i	−0.395037	+	0.918665i	$0.629268\pi$
$198$	−0.529181	+	1.27756i	−0.0376072	+	0.0907919i
$199$	−2.88162	−	6.95685i	−0.204273	−	0.493158i	0.788230	−	0.615381i	$-0.210998\pi$
$199$	−2.88162	−	6.95685i	−0.204273	−	0.493158i	−0.992503	+	0.122223i	$0.960998\pi$
$200$		0			0
$201$	−6.56658	+	2.71996i	−0.463171	+	0.191852i
$202$	−3.26136	+	3.26136i	−0.229469	+	0.229469i
$203$		−	9.41549i		−	0.660838i
$204$	7.87014	+	2.79343i	0.551020	+	0.195579i
$205$		0			0
$206$	−3.15180	−	3.15180i	−0.219596	−	0.219596i
$207$	−0.617408	−	1.49055i	−0.0429128	−	0.103601i
$208$	−19.4345			−1.34754
$209$	6.67383	+	16.1120i	0.461638	+	1.11449i
$210$		0			0
$211$	3.32647	−	8.03080i	0.229003	−	0.552863i	−0.767053	−	0.641584i	$-0.778278\pi$
$211$	3.32647	−	8.03080i	0.229003	−	0.552863i	0.996057	+	0.0887204i	$0.0282778\pi$
$212$	3.74551	+	3.74551i	0.257243	+	0.257243i
$213$	−0.180635	−	0.180635i	−0.0123769	−	0.0123769i
$214$	0.169802	−	0.409938i	0.0116074	−	0.0280228i
$215$		0			0
$216$	2.33394	+	5.63462i	0.158804	+	0.383387i
$217$	5.64043			0.382897
$218$	−1.08959	−	2.63050i	−0.0737963	−	0.178160i
$219$	4.84471	+	4.84471i	0.327375	+	0.327375i
$220$		0			0
$221$	17.1884	+	15.4992i	1.15622	+	1.04259i
$222$			1.63426i			0.109684i
$223$	4.57010	−	4.57010i	0.306037	−	0.306037i	−0.537333	−	0.843370i	$-0.680568\pi$
$223$	4.57010	−	4.57010i	0.306037	−	0.306037i	0.843370	+	0.537333i	$0.180568\pi$
$224$	−7.89101	+	3.26856i	−0.527241	+	0.218390i
$225$		0			0
$226$	1.72726	+	4.16997i	0.114896	+	0.277382i
$227$	−1.17124	+	2.82763i	−0.0777381	+	0.187676i	−0.957971	−	0.286866i	$-0.907386\pi$
$227$	−1.17124	+	2.82763i	−0.0777381	+	0.187676i	0.880233	+	0.474543i	$0.157386\pi$
$228$	13.3442	+	5.52736i	0.883743	+	0.366058i
$229$	−5.34518	+	5.34518i	−0.353219	+	0.353219i	−0.861306	−	0.508087i	$-0.830353\pi$
$229$	−5.34518	+	5.34518i	−0.353219	+	0.353219i	0.508087	+	0.861306i	$0.330353\pi$
$230$		0			0
$231$	−2.49222	+	6.01676i	−0.163976	+	0.395874i
$232$	1.69300	−	4.08727i	0.111151	−	0.268342i
$233$	20.6467	−	8.55214i	1.35261	−	0.560270i	0.415593	−	0.909551i	$-0.363574\pi$
$233$	20.6467	−	8.55214i	1.35261	−	0.560270i	0.937018	+	0.349281i	$0.113574\pi$
$234$			3.17400i			0.207491i
$235$		0			0
$236$	10.0452	+	10.0452i	0.653886	+	0.653886i
$237$			15.6071i			1.01379i
$238$	2.94212	+	1.04428i	0.190709	+	0.0676904i
$239$	3.45981			0.223797			0.111898	−	0.993720i	$-0.464307\pi$
$239$	3.45981			0.223797			0.111898	+	0.993720i	$0.464307\pi$
$240$		0			0
$241$	−16.6541	+	6.89834i	−1.07278	+	0.444361i	−0.847972	−	0.530042i	$-0.822176\pi$
$241$	−16.6541	+	6.89834i	−1.07278	+	0.444361i	−0.224810	+	0.974403i	$0.572176\pi$
$242$	1.51422			0.0973376
$243$	−14.4668	+	5.99235i	−0.928047	+	0.384410i
$244$	−1.59840	−	0.662079i	−0.102327	−	0.0423853i
$245$		0			0
$246$	2.79521	−	2.79521i	0.178216	−	0.178216i
$247$	28.3049	+	28.3049i	1.80100	+	1.80100i
$248$	2.44851	+	1.01421i	0.155481	+	0.0644022i
$249$	13.6239	+	5.64321i	0.863381	+	0.357624i
$250$		0			0
$251$		−	24.0478i		−	1.51788i	−0.651159	−	0.758941i	$-0.725717\pi$
$251$		−	24.0478i		−	1.51788i	0.651159	−	0.758941i	$-0.274283\pi$
$252$	−3.43649	−	8.29643i	−0.216479	−	0.522626i
$253$	1.48857	−	1.48857i	0.0935859	−	0.0935859i
$254$	−1.79650			−0.112722
$255$		0			0
$256$	9.20534			0.575334
$257$	10.4664	−	10.4664i	0.652873	−	0.652873i	−0.300811	−	0.953684i	$-0.597257\pi$
$257$	10.4664	−	10.4664i	0.652873	−	0.652873i	0.953684	+	0.300811i	$0.0972573\pi$
$258$	0.320953	+	0.774848i	0.0199816	+	0.0482399i
$259$		−	12.8142i		−	0.796233i
$260$		0			0
$261$	6.49591	+	2.69070i	0.402087	+	0.166550i
$262$	1.16709	+	0.483426i	0.0721032	+	0.0298661i
$263$	−17.3357	−	17.3357i	−1.06896	−	1.06896i	−0.997439	−	0.0715243i	$-0.977214\pi$
$263$	−17.3357	−	17.3357i	−1.06896	−	1.06896i	−0.0715243	−	0.997439i	$-0.522786\pi$
$264$	−2.16375	+	2.16375i	−0.133170	+	0.133170i
$265$		0			0
$266$	4.98852	+	2.06631i	0.305866	+	0.126694i
$267$	0.387358	−	0.160449i	0.0237059	−	0.00981932i
$268$	12.7881			0.781156
$269$	−6.09269	+	2.52367i	−0.371478	+	0.153871i	−0.560609	−	0.828081i	$-0.689433\pi$
$269$	−6.09269	+	2.52367i	−0.371478	+	0.153871i	0.189131	+	0.981952i	$0.439433\pi$
$270$		0			0
$271$	−26.1956			−1.59127			−0.795634	−	0.605778i	$-0.792862\pi$
$271$	−26.1956			−1.59127			−0.795634	+	0.605778i	$0.792862\pi$
$272$	−10.6014	−	9.55957i	−0.642805	−	0.579634i
$273$			14.9482i			0.904707i
$274$	−1.54873	−	1.54873i	−0.0935624	−	0.0935624i
$275$		0			0
$276$		−	1.74353i		−	0.104948i
$277$	−8.83695	+	3.66038i	−0.530961	+	0.219931i	−0.632024	−	0.774949i	$-0.717776\pi$
$277$	−8.83695	+	3.66038i	−0.530961	+	0.219931i	0.101063	+	0.994880i	$0.467776\pi$
$278$	1.19990	−	2.89682i	0.0719653	−	0.173740i
$279$	−1.61188	+	3.89143i	−0.0965009	+	0.232974i
$280$		0			0
$281$	8.78037	−	8.78037i	0.523793	−	0.523793i	−0.394922	−	0.918715i	$-0.629228\pi$
$281$	8.78037	−	8.78037i	0.523793	−	0.523793i	0.918715	+	0.394922i	$0.129228\pi$
$282$	−0.680511	−	0.281877i	−0.0405238	−	0.0167855i
$283$	6.44566	−	15.5612i	0.383155	−	0.925017i	−0.608197	−	0.793786i	$-0.708107\pi$
$283$	6.44566	−	15.5612i	0.383155	−	0.925017i	0.991352	−	0.131231i	$-0.0418930\pi$
$284$	0.175889	+	0.424633i	0.0104371	+	0.0251973i
$285$		0			0
$286$	−3.82626	+	1.58489i	−0.226252	+	0.0937165i
$287$	−21.9171	+	21.9171i	−1.29372	+	1.29372i
$288$		−	6.37822i		−	0.375840i
$289$	1.75231	+	16.9094i	0.103077	+	0.994673i
$290$		0			0
$291$	6.72166	+	6.72166i	0.394031	+	0.394031i
$292$	−4.71741	−	11.3888i	−0.276066	−	0.666482i
$293$	−20.8806			−1.21986			−0.609930	−	0.792456i	$-0.708802\pi$
$293$	−20.8806			−1.21986			−0.609930	+	0.792456i	$0.708802\pi$
$294$	−0.0858335	−	0.207220i	−0.00500591	−	0.0120853i
$295$		0			0
$296$	2.30412	−	5.56263i	0.133924	−	0.323321i
$297$	−8.94323	−	8.94323i	−0.518939	−	0.518939i
$298$	1.28371	+	1.28371i	0.0743635	+	0.0743635i
$299$	1.84913	−	4.46419i	0.106938	−	0.258171i
$300$		0			0
$301$	−2.51657	−	6.07554i	−0.145053	−	0.350188i
$302$	−3.14306			−0.180863
$303$	−6.20752	−	14.9863i	−0.356613	−	0.860940i
$304$	−17.4579	−	17.4579i	−1.00128	−	1.00128i
$305$		0			0
$306$	−1.56124	+	1.73139i	−0.0892504	+	0.0989772i
$307$		−	29.9529i		−	1.70950i	−0.519038	−	0.854751i	$-0.673710\pi$
$307$		−	29.9529i		−	1.70950i	0.519038	−	0.854751i	$-0.326290\pi$
$308$	8.28541	−	8.28541i	0.472105	−	0.472105i
$309$	14.4828	−	5.99898i	0.823899	−	0.341270i
$310$		0			0
$311$	0.0804873	+	0.194314i	0.00456402	+	0.0110185i	0.926145	−	0.377167i	$-0.123102\pi$
$311$	0.0804873	+	0.194314i	0.00456402	+	0.0110185i	−0.921581	+	0.388186i	$0.873102\pi$
$312$	−2.68784	+	6.48902i	−0.152169	+	0.367369i
$313$	29.9561	+	12.4082i	1.69322	+	0.701354i	0.999816	−	0.0191979i	$-0.00611125\pi$
$313$	29.9561	+	12.4082i	1.69322	+	0.701354i	0.693402	+	0.720551i	$0.256111\pi$
$314$	2.86010	−	2.86010i	0.161405	−	0.161405i
$315$		0			0
$316$	10.7459	−	25.9429i	0.604504	−	1.45940i
$317$	12.7966	−	30.8937i	0.718728	−	1.73516i	0.0417842	−	0.999127i	$-0.486696\pi$
$317$	12.7966	−	30.8937i	0.718728	−	1.73516i	0.676943	−	0.736035i	$-0.263304\pi$
$318$	0.820571	−	0.339892i	0.0460154	−	0.0190602i
$319$			9.17441i			0.513668i
$320$		0			0
$321$	1.10345	+	1.10345i	0.0615886	+	0.0615886i
$322$		−	0.651789i		−	0.0363228i
$323$	1.51736	+	29.3630i	0.0844283	+	1.63380i
$324$	0.258783			0.0143768
$325$		0			0
$326$	0.439025	−	0.181850i	0.0243153	−	0.0100717i
$327$	10.0135			0.553750
$328$	−13.4551	+	5.57330i	−0.742935	+	0.307734i
$329$	5.33585	+	2.21018i	0.294175	+	0.121851i
$330$		0			0
$331$	0.626030	−	0.626030i	0.0344097	−	0.0344097i	−0.689693	−	0.724102i	$-0.742254\pi$
$331$	0.626030	−	0.626030i	0.0344097	−	0.0344097i	0.724102	+	0.689693i	$0.242254\pi$
$332$	−18.7609	−	18.7609i	−1.02964	−	1.02964i
$333$	8.84071	+	3.66194i	0.484468	+	0.200673i
$334$	4.90688	+	2.03250i	0.268493	+	0.111213i
$335$		0			0
$336$		−	9.21973i		−	0.502977i
$337$	6.56551	+	15.8506i	0.357646	+	0.863434i	0.995630	+	0.0933847i	$0.0297687\pi$
$337$	6.56551	+	15.8506i	0.357646	+	0.863434i	−0.637984	+	0.770050i	$0.720231\pi$
$338$	−3.94859	+	3.94859i	−0.214775	+	0.214775i
$339$	−15.8739			−0.862150
$340$		0			0
$341$	−5.49600			−0.297625
$342$	−2.85117	+	2.85117i	−0.154174	+	0.154174i
$343$	7.39633	+	17.8563i	0.399364	+	0.964151i
$344$		−	3.08990i		−	0.166596i
$345$		0			0
$346$	−5.25194	−	2.17542i	−0.282346	−	0.116951i
$347$	28.5572	+	11.8288i	1.53303	+	0.635003i	0.980150	−	0.198257i	$-0.0635281\pi$
$347$	28.5572	+	11.8288i	1.53303	+	0.635003i	0.552882	+	0.833260i	$0.313528\pi$
$348$	5.37287	+	5.37287i	0.288016	+	0.288016i
$349$	−2.38415	+	2.38415i	−0.127621	+	0.127621i	−0.768032	−	0.640411i	$-0.778764\pi$
$349$	−2.38415	+	2.38415i	−0.127621	+	0.127621i	0.640411	+	0.768032i	$0.278764\pi$
$350$		0			0
$351$	−26.8205	−	11.1094i	−1.43157	−	0.592976i
$352$	7.68896	−	3.18487i	0.409823	−	0.169754i
$353$	−23.7918			−1.26631			−0.633155	−	0.774025i	$-0.718240\pi$
$353$	−23.7918			−1.26631			−0.633155	+	0.774025i	$0.718240\pi$
$354$	2.20071	−	0.911565i	0.116967	−	0.0484491i
$355$		0			0
$356$	−0.754360			−0.0399810
$357$	−7.35282	+	8.15416i	−0.389152	+	0.431564i
$358$		−	0.999743i		−	0.0528381i
$359$	−22.4244	−	22.4244i	−1.18351	−	1.18351i	−0.978827	−	0.204688i	$-0.934382\pi$
$359$	−22.4244	−	22.4244i	−1.18351	−	1.18351i	−0.204688	−	0.978827i	$-0.565618\pi$
$360$		0			0
$361$			31.8521i			1.67643i
$362$	4.42197	−	1.83164i	0.232414	−	0.0962689i
$363$	−2.03795	+	4.92004i	−0.106964	+	0.258235i
$364$	10.2923	−	24.8477i	0.539461	−	1.30237i
$365$		0			0
$366$	−0.205130	+	0.205130i	−0.0107223	+	0.0107223i
$367$	−4.17304	−	1.72853i	−0.217831	−	0.0902286i	0.271099	−	0.962551i	$-0.412613\pi$
$367$	−4.17304	−	1.72853i	−0.217831	−	0.0902286i	−0.488930	+	0.872323i	$0.662613\pi$
$368$	−1.14050	+	2.75341i	−0.0594528	+	0.143532i
$369$	−8.85767	−	21.3843i	−0.461112	−	1.11322i
$370$		0			0
$371$	−6.43405	+	2.66507i	−0.334039	+	0.138364i
$372$	−3.21866	+	3.21866i	−0.166880	+	0.166880i
$373$			5.12748i			0.265491i	0.991150	+	0.132745i	$0.0423792\pi$
$373$			5.12748i			0.265491i	−0.991150	+	0.132745i	$0.957621\pi$
$374$	−2.86679	−	1.01754i	−0.148238	−	0.0526156i
$375$		0			0
$376$	1.91888	+	1.91888i	0.0989586	+	0.0989586i
$377$	8.05860	+	19.4552i	0.415039	+	1.00199i
$378$	−3.91589			−0.201412
$379$	−2.11629	−	5.10917i	−0.108706	−	0.262441i	0.860160	−	0.510024i	$-0.170364\pi$
$379$	−2.11629	−	5.10917i	−0.108706	−	0.262441i	−0.968867	+	0.247584i	$0.920364\pi$
$380$		0			0
$381$	2.41786	−	5.83722i	0.123871	−	0.299050i
$382$	−5.86521	−	5.86521i	−0.300090	−	0.300090i
$383$	−14.4493	−	14.4493i	−0.738326	−	0.738326i	0.233928	−	0.972254i	$-0.424842\pi$
$383$	−14.4493	−	14.4493i	−0.738326	−	0.738326i	−0.972254	+	0.233928i	$0.924842\pi$
$384$	3.48596	−	8.41585i	0.177892	−	0.429469i
$385$		0			0
$386$	1.70420	+	4.11429i	0.0867413	+	0.209412i
$387$	4.91079			0.249629
$388$	−6.54505	−	15.8011i	−0.332274	−	0.802181i
$389$	3.66726	+	3.66726i	0.185937	+	0.185937i	0.793937	−	0.608000i	$-0.208028\pi$
$389$	3.66726	+	3.66726i	0.185937	+	0.185937i	−0.608000	+	0.793937i	$0.708028\pi$
$390$		0			0
$391$	3.20456	−	1.52563i	0.162062	−	0.0771543i
$392$			0.826343i			0.0417366i
$393$	−3.14152	+	3.14152i	−0.158469	+	0.158469i
$394$	0.104913	−	0.0434563i	0.00528543	−	0.00218930i
$395$		0			0
$396$	3.34850	+	8.08399i	0.168268	+	0.406236i
$397$	2.36251	−	5.70360i	0.118571	−	0.286255i	−0.853440	−	0.521191i	$-0.825488\pi$
$397$	2.36251	−	5.70360i	0.118571	−	0.286255i	0.972011	+	0.234936i	$0.0754879\pi$
$398$	2.09879	+	0.869348i	0.105203	+	0.0435765i
$399$	−13.4278	+	13.4278i	−0.672233	+	0.672233i
$400$		0			0
$401$	−3.63413	+	8.77356i	−0.181480	+	0.438131i	−0.988272	−	0.152705i	$-0.951202\pi$
$401$	−3.63413	+	8.77356i	−0.181480	+	0.438131i	0.806792	+	0.590835i	$0.201202\pi$
$402$	0.820577	−	1.98105i	0.0409267	−	0.0988058i
$403$	−11.6548	+	4.82757i	−0.580566	+	0.240478i
$404$			29.1850i			1.45201i
$405$		0			0
$406$	2.00856	+	2.00856i	0.0996831	+	0.0996831i
$407$			12.4860i			0.618910i
$408$	−4.65806	+	2.21761i	−0.230608	+	0.109788i
$409$	−14.3886			−0.711469			−0.355734	−	0.934587i	$-0.615769\pi$
$409$	−14.3886			−0.711469			−0.355734	+	0.934587i	$0.615769\pi$
$410$		0			0
$411$	7.11659	−	2.94779i	0.351035	−	0.145404i
$412$	−28.2046			−1.38954
$413$	−17.2557	+	7.14753i	−0.849096	+	0.351707i
$414$	0.449680	+	0.186264i	0.0221006	+	0.00915436i
$415$		0			0
$416$	13.5076	−	13.5076i	0.662266	−	0.662266i
$417$	7.79750	+	7.79750i	0.381845	+	0.381845i
$418$	−4.86079	−	2.01340i	−0.237749	−	0.0984789i
$419$	−19.6078	−	8.12181i	−0.957903	−	0.396776i	−0.151707	−	0.988425i	$-0.548477\pi$
$419$	−19.6078	−	8.12181i	−0.957903	−	0.396776i	−0.806196	+	0.591649i	$0.798477\pi$
$420$		0			0
$421$			20.1672i			0.982887i	0.870909	+	0.491444i	$0.163531\pi$
$421$			20.1672i			0.982887i	−0.870909	+	0.491444i	$0.836469\pi$
$422$	1.00355	+	2.42279i	0.0488521	+	0.117939i
$423$	−3.04968	+	3.04968i	−0.148281	+	0.148281i
$424$	−3.27223			−0.158914
$425$		0			0
$426$	0.0770678			0.00373395
$427$	1.60842	−	1.60842i	0.0778367	−	0.0778367i
$428$	−1.07446	−	2.59397i	−0.0519358	−	0.125384i
$429$		−	14.5655i		−	0.703227i
$430$		0			0
$431$	−18.4485	−	7.64163i	−0.888635	−	0.368085i	−0.108795	−	0.994064i	$-0.534699\pi$
$431$	−18.4485	−	7.64163i	−0.888635	−	0.368085i	−0.779839	+	0.625980i	$0.784699\pi$
$432$	16.5423	+	6.85204i	0.795891	+	0.329669i
$433$	−12.8860	−	12.8860i	−0.619263	−	0.619263i	0.326080	−	0.945342i	$-0.394272\pi$
$433$	−12.8860	−	12.8860i	−0.619263	−	0.619263i	−0.945342	+	0.326080i	$0.894272\pi$
$434$	−1.20324	+	1.20324i	−0.0577575	+	0.0577575i
$435$		0			0
$436$	−16.6450	−	6.89460i	−0.797152	−	0.330191i
$437$	5.67120	−	2.34909i	0.271290	−	0.112372i
$438$	−2.06699			−0.0987648
$439$	−13.6117	+	5.63815i	−0.649651	+	0.269094i	−0.683077	−	0.730347i	$-0.739358\pi$
$439$	−13.6117	+	5.63815i	−0.649651	+	0.269094i	0.0334251	+	0.999441i	$0.489358\pi$
$440$		0			0
$441$	−1.31331			−0.0625386
$442$	−6.97307	+	0.360341i	−0.331675	+	0.0171397i
$443$			23.3335i			1.10861i	0.832314	+	0.554305i	$0.187016\pi$
$443$			23.3335i			1.10861i	−0.832314	+	0.554305i	$0.812984\pi$
$444$	7.31228	+	7.31228i	0.347026	+	0.347026i
$445$		0			0
$446$			1.94983i			0.0923272i
$447$	−5.89879	+	2.44336i	−0.279003	+	0.115567i
$448$	−5.66461	+	13.6756i	−0.267628	+	0.646110i
$449$	0.655009	−	1.58133i	0.0309118	−	0.0746277i	−0.907670	−	0.419685i	$-0.862141\pi$
$449$	0.655009	−	1.58133i	0.0309118	−	0.0746277i	0.938582	+	0.345057i	$0.112141\pi$
$450$		0			0
$451$	21.3559	−	21.3559i	1.00561	−	1.00561i
$452$	26.3864	+	10.9296i	1.24111	+	0.514085i
$453$	4.23016	−	10.2125i	0.198750	−	0.479826i
$454$	−0.353348	−	0.853058i	−0.0165835	−	0.0400360i
$455$		0			0
$456$	−8.24349	+	3.41457i	−0.386037	+	0.159902i
$457$	−9.34572	+	9.34572i	−0.437174	+	0.437174i	−0.891060	−	0.453886i	$-0.850037\pi$
$457$	−9.34572	+	9.34572i	−0.437174	+	0.437174i	0.453886	+	0.891060i	$0.350037\pi$
$458$		−	2.28052i		−	0.106562i
$459$	−9.16585	−	19.2527i	−0.427825	−	0.898641i
$460$		0			0
$461$	−20.7116	−	20.7116i	−0.964634	−	0.964634i	0.0347616	−	0.999396i	$-0.488933\pi$
$461$	−20.7116	−	20.7116i	−0.964634	−	0.964634i	−0.999396	+	0.0347616i	$0.988933\pi$
$462$	−0.751871	−	1.81518i	−0.0349802	−	0.0844497i
$463$	9.80371			0.455617			0.227808	−	0.973706i	$-0.426844\pi$
$463$	9.80371			0.455617			0.227808	+	0.973706i	$0.426844\pi$
$464$	−4.97037	−	11.9995i	−0.230744	−	0.557064i
$465$		0			0
$466$	−2.58007	+	6.22884i	−0.119519	+	0.288545i
$467$	−9.67459	−	9.67459i	−0.447687	−	0.447687i	0.446898	−	0.894585i	$-0.352529\pi$
$467$	−9.67459	−	9.67459i	−0.447687	−	0.447687i	−0.894585	+	0.446898i	$0.852529\pi$
$468$	14.2016	+	14.2016i	0.656469	+	0.656469i
$469$	−6.43410	+	15.5333i	−0.297099	+	0.717261i
$470$		0			0
$471$	5.44378	+	13.1424i	0.250836	+	0.605572i
$472$	−8.77589			−0.403943
$473$	2.45213	+	5.91997i	0.112749	+	0.272201i
$474$	−3.32938	−	3.32938i	−0.152923	−	0.152923i
$475$		0			0
$476$	17.8366	−	8.49165i	0.817539	−	0.389214i
$477$		−	5.20057i		−	0.238118i
$478$	−0.738063	+	0.738063i	−0.0337582	+	0.0337582i
$479$	10.1719	−	4.21334i	0.464766	−	0.192513i	−0.137997	−	0.990433i	$-0.544066\pi$
$479$	10.1719	−	4.21334i	0.464766	−	0.192513i	0.602763	+	0.797920i	$0.294066\pi$
$480$		0			0
$481$	10.9675	+	26.4778i	0.500074	+	1.20728i
$482$	2.08114	−	5.02431i	0.0947932	−	0.228851i
$483$	2.11781	+	0.877226i	0.0963637	+	0.0399151i
$484$	6.77516	−	6.77516i	0.307962	−	0.307962i
$485$		0			0
$486$	1.80781	−	4.36445i	0.0820041	−	0.197975i
$487$	−3.86290	+	9.32586i	−0.175045	+	0.422595i	−0.986915	−	0.161243i	$-0.948450\pi$
$487$	−3.86290	+	9.32586i	−0.175045	+	0.422595i	0.811870	+	0.583838i	$0.198450\pi$
$488$	0.987423	−	0.409004i	0.0446985	−	0.0185147i
$489$			1.67124i			0.0755760i
$490$		0			0
$491$	−12.0793	−	12.0793i	−0.545132	−	0.545132i	0.379897	−	0.925029i	$-0.375959\pi$
$491$	−12.0793	−	12.0793i	−0.545132	−	0.545132i	−0.925029	+	0.379897i	$0.875959\pi$
$492$		−	25.0136i		−	1.12770i
$493$	−5.17382	+	14.5766i	−0.233017	+	0.656497i
$494$	−12.0763			−0.543338
$495$		0			0
$496$	7.18841	−	2.97754i	0.322769	−	0.133695i
$497$	−0.604284			−0.0271059
$498$	−4.11016	+	1.70248i	−0.184180	+	0.0762901i
$499$	28.9724	+	12.0008i	1.29698	+	0.537227i	0.921059	−	0.389424i	$-0.127326\pi$
$499$	28.9724	+	12.0008i	1.29698	+	0.537227i	0.375923	+	0.926651i	$0.377326\pi$
$500$		0			0
$501$	−13.2081	+	13.2081i	−0.590094	+	0.590094i
$502$	5.12999	+	5.12999i	0.228963	+	0.228963i
$503$	8.01498	+	3.31991i	0.357370	+	0.148028i	0.554143	−	0.832422i	$-0.313046\pi$
$503$	8.01498	+	3.31991i	0.357370	+	0.148028i	−0.196773	+	0.980449i	$0.563046\pi$
$504$	5.12518	+	2.12292i	0.228293	+	0.0945623i
$505$		0			0
$506$			0.635099i			0.0282336i
$507$	−7.51556	−	18.1442i	−0.333778	−	0.805811i
$508$	−8.03817	+	8.03817i	−0.356636	+	0.356636i
$509$	14.1196			0.625840			0.312920	−	0.949780i	$-0.398693\pi$
$509$	14.1196			0.625840			0.312920	+	0.949780i	$0.398693\pi$
$510$		0			0
$511$	16.2072			0.716963
$512$	−14.1053	+	14.1053i	−0.623374	+	0.623374i
$513$	−14.1131	−	34.0721i	−0.623109	−	1.50432i
$514$			4.46546i			0.196963i
$515$		0			0
$516$	4.90301	+	2.03089i	0.215843	+	0.0894051i
$517$	−5.19922	−	2.15359i	−0.228662	−	0.0947147i
$518$	2.73358	+	2.73358i	0.120106	+	0.120106i
$519$	14.1369	−	14.1369i	0.620541	−	0.620541i
$520$		0			0
$521$	−16.2808	−	6.74373i	−0.713275	−	0.295448i	−0.00361608	−	0.999993i	$-0.501151\pi$
$521$	−16.2808	−	6.74373i	−0.713275	−	0.295448i	−0.709659	+	0.704545i	$0.751151\pi$
$522$	−1.95973	+	0.811747i	−0.0857751	+	0.0355292i
$523$	26.3853			1.15375			0.576875	−	0.816833i	$-0.304272\pi$
$523$	26.3853			1.15375			0.576875	+	0.816833i	$0.304272\pi$
$524$	7.38502	−	3.05898i	0.322616	−	0.133632i
$525$		0			0
$526$	7.39626			0.322492
$527$	−8.73223	−	3.09942i	−0.380382	−	0.135013i
$528$			8.98366i			0.390963i
$529$	15.7395	+	15.7395i	0.684326	+	0.684326i
$530$		0			0
$531$		−	13.9476i		−	0.605272i
$532$	31.5659	−	13.0750i	1.36856	−	0.566874i
$533$	26.5286	−	64.0457i	1.14908	−	2.77413i
$534$	−0.0484053	+	0.116861i	−0.00209470	+	0.00505706i
$535$		0			0
$536$	−5.58609	+	5.58609i	−0.241282	+	0.241282i
$537$	3.24839	+	1.34553i	0.140178	+	0.0580638i
$538$	0.761359	−	1.83808i	0.0328245	−	0.0792454i
$539$	−0.655783	−	1.58320i	−0.0282466	−	0.0681932i
$540$		0			0
$541$	−4.07266	+	1.68695i	−0.175097	+	0.0725277i	−0.468510	−	0.883458i	$-0.655209\pi$
$541$	−4.07266	+	1.68695i	−0.175097	+	0.0725277i	0.293413	+	0.955986i	$0.405209\pi$
$542$	5.58816	−	5.58816i	0.240032	−	0.240032i
$543$			16.8331i			0.722379i
$544$	14.0125	−	0.724113i	0.600783	−	0.0310461i
$545$		0			0
$546$	−3.18882	−	3.18882i	−0.136469	−	0.136469i
$547$	−8.67306	−	20.9386i	−0.370833	−	0.895271i	−0.993610	−	0.112871i	$-0.963995\pi$
$547$	−8.67306	−	20.9386i	−0.370833	−	0.895271i	0.622776	−	0.782400i	$-0.286005\pi$
$548$	−13.8592			−0.592035
$549$	0.650032	+	1.56932i	0.0277427	+	0.0669768i
$550$		0			0
$551$	−10.2374	+	24.7154i	−0.436130	+	1.05291i
$552$	0.761607	+	0.761607i	0.0324162	+	0.0324162i
$553$	26.1055	+	26.1055i	1.11012	+	1.11012i
$554$	1.10429	−	2.66599i	0.0469167	−	0.113267i
$555$		0			0
$556$	−7.59262	−	18.3302i	−0.321999	−	0.777374i
$557$	11.4954			0.487076			0.243538	−	0.969891i	$-0.421692\pi$
$557$	11.4954			0.487076			0.243538	+	0.969891i	$0.421692\pi$
$558$	−0.486284	−	1.17399i	−0.0205860	−	0.0496991i
$559$	10.4000	+	10.4000i	0.439871	+	0.439871i
$560$		0			0
$561$	7.16455	−	7.94537i	0.302487	−	0.335454i
$562$			3.74614i			0.158021i
$563$	9.57715	−	9.57715i	0.403629	−	0.403629i	−0.475881	−	0.879510i	$-0.657871\pi$
$563$	9.57715	−	9.57715i	0.403629	−	0.403629i	0.879510	+	0.475881i	$0.157871\pi$
$564$	−4.30607	+	1.78363i	−0.181318	+	0.0751045i
$565$		0			0
$566$	1.94457	+	4.69461i	0.0817364	+	0.197329i
$567$	−0.130202	+	0.314336i	−0.00546797	+	0.0132009i
$568$	−0.262320	−	0.108656i	−0.0110067	−	0.00455912i
$569$	11.2263	−	11.2263i	0.470632	−	0.470632i	−0.431487	−	0.902119i	$-0.642011\pi$
$569$	11.2263	−	11.2263i	0.470632	−	0.470632i	0.902119	+	0.431487i	$0.142011\pi$
$570$		0			0
$571$	1.35486	−	3.27093i	0.0566993	−	0.136884i	−0.892991	−	0.450074i	$-0.851398\pi$
$571$	1.35486	−	3.27093i	0.0566993	−	0.136884i	0.949691	+	0.313190i	$0.101398\pi$
$572$	−10.0287	+	24.2115i	−0.419322	+	1.01233i
$573$	26.9512	−	11.1636i	1.12590	−	0.466364i
$574$		−	9.35092i		−	0.390300i
$575$		0			0
$576$	−7.81622	−	7.81622i	−0.325676	−	0.325676i
$577$			18.5078i			0.770492i	0.922814	+	0.385246i	$0.125883\pi$
$577$			18.5078i			0.770492i	−0.922814	+	0.385246i	$0.874117\pi$
$578$	−3.98101	−	3.23339i	−0.165588	−	0.134491i
$579$	−15.6619			−0.650887
$580$		0			0
$581$	32.2275	−	13.3491i	1.33702	−	0.553813i
$582$	−2.86779			−0.118874
$583$	6.26931	−	2.59683i	0.259648	−	0.107550i
$584$	7.03554	+	2.91422i	0.291133	+	0.120591i
$585$		0			0
$586$	4.45436	−	4.45436i	0.184008	−	0.184008i
$587$	−9.70579	−	9.70579i	−0.400601	−	0.400601i	0.477844	−	0.878445i	$-0.341418\pi$
$587$	−9.70579	−	9.70579i	−0.400601	−	0.400601i	−0.878445	+	0.477844i	$0.841418\pi$
$588$	−1.31123	−	0.543129i	−0.0540742	−	0.0223983i
$589$	−14.8059	−	6.13282i	−0.610068	−	0.252699i
$590$		0			0
$591$			0.399372i			0.0164280i
$592$	−6.76450	−	16.3309i	−0.278019	−	0.671197i
$593$	−14.3711	+	14.3711i	−0.590150	+	0.590150i	−0.937672	−	0.347522i	$-0.887023\pi$
$593$	−14.3711	+	14.3711i	−0.590150	+	0.590150i	0.347522	+	0.937672i	$0.387023\pi$
$594$	3.81563			0.156557
$595$		0			0
$596$	11.4876			0.470550
$597$	−5.64942	+	5.64942i	−0.231215	+	0.231215i
$598$	0.557858	+	1.34679i	0.0228125	+	0.0550742i
$599$			26.7277i			1.09206i	0.837764	+	0.546032i	$0.183862\pi$
$599$			26.7277i			1.09206i	−0.837764	+	0.546032i	$0.816138\pi$
$600$		0			0
$601$	25.5537	+	10.5847i	1.04236	+	0.431758i	0.837157	−	0.546962i	$-0.184216\pi$
$601$	25.5537	+	10.5847i	1.04236	+	0.431758i	0.205199	+	0.978720i	$0.434216\pi$
$602$	1.83291	+	0.759216i	0.0747038	+	0.0309433i
$603$	−8.87800	−	8.87800i	−0.361540	−	0.361540i
$604$	−14.0632	+	14.0632i	−0.572223	+	0.572223i
$605$		0			0
$606$	4.52117	+	1.87273i	0.183660	+	0.0760744i
$607$	21.8207	−	9.03844i	0.885676	−	0.366859i	0.106981	−	0.994261i	$-0.465882\pi$
$607$	21.8207	−	9.03844i	0.885676	−	0.366859i	0.778696	+	0.627402i	$0.215882\pi$
$608$	24.2676			0.984180
$609$	−9.22953	+	3.82300i	−0.373999	+	0.154916i
$610$		0			0
$611$	−12.9171			−0.522570
$612$	0.761315	+	14.7325i	0.0307744	+	0.595524i
$613$		−	12.0396i		−	0.486275i	−0.969992	−	0.243137i	$-0.921823\pi$
$613$		−	12.0396i		−	0.486275i	0.969992	−	0.243137i	$-0.0781766\pi$
$614$	6.38969	+	6.38969i	0.257867	+	0.257867i
$615$		0			0
$616$			7.23847i			0.291646i
$617$	−14.3643	+	5.94989i	−0.578285	+	0.239534i	−0.652602	−	0.757701i	$-0.726322\pi$
$617$	−14.3643	+	5.94989i	−0.578285	+	0.239534i	0.0743165	+	0.997235i	$0.476322\pi$
$618$	−1.80981	+	4.36928i	−0.0728014	+	0.175758i
$619$	−12.8172	+	30.9434i	−0.515166	+	1.24372i	0.425676	+	0.904876i	$0.360036\pi$
$619$	−12.8172	+	30.9434i	−0.515166	+	1.24372i	−0.940842	+	0.338845i	$0.889964\pi$
$620$		0			0
$621$	−3.14788	+	3.14788i	−0.126320	+	0.126320i
$622$	−0.0586218	−	0.0242820i	−0.00235052	−	0.000973618i
$623$	0.379543	−	0.916299i	0.0152061	−	0.0367107i
$624$	7.89105	+	19.0507i	0.315895	+	0.762637i
$625$		0			0
$626$	−9.03735	+	3.74339i	−0.361205	+	0.149616i
$627$	13.0840	−	13.0840i	0.522525	−	0.522525i
$628$		−	25.5942i		−	1.02132i
$629$	−7.04138	+	19.8382i	−0.280758	+	0.791002i
$630$		0			0
$631$	−0.385100	−	0.385100i	−0.0153306	−	0.0153306i	0.699400	−	0.714731i	$-0.253451\pi$
$631$	−0.385100	−	0.385100i	−0.0153306	−	0.0153306i	−0.714731	+	0.699400i	$0.753451\pi$
$632$	6.63836	+	16.0264i	0.264060	+	0.637496i
$633$	−9.22284			−0.366575
$634$	3.86056	+	9.32021i	0.153322	+	0.370153i
$635$		0			0
$636$	2.15074	−	5.19233i	0.0852822	−	0.205889i
$637$	−2.78130	−	2.78130i	−0.110199	−	0.110199i
$638$	−1.95713	−	1.95713i	−0.0774835	−	0.0774835i
$639$	0.172688	−	0.416906i	0.00683144	−	0.0164926i
$640$		0			0
$641$	4.75450	+	11.4784i	0.187792	+	0.453369i	0.989534	−	0.144301i	$-0.0460933\pi$
$641$	4.75450	+	11.4784i	0.187792	+	0.453369i	−0.801742	+	0.597670i	$0.796093\pi$
$642$	−0.470786			−0.0185805
$643$	−14.6813	−	35.4438i	−0.578975	−	1.39777i	−0.893734	−	0.448597i	$-0.851924\pi$
$643$	−14.6813	−	35.4438i	−0.578975	−	1.39777i	0.314760	−	0.949171i	$-0.398076\pi$
$644$	−2.91634	−	2.91634i	−0.114920	−	0.114920i
$645$		0			0
$646$	−6.58754	−	5.94016i	−0.259183	−	0.233712i
$647$			19.6602i			0.772923i	0.922305	+	0.386462i	$0.126303\pi$
$647$			19.6602i			0.772923i	−0.922305	+	0.386462i	$0.873697\pi$
$648$	−0.113041	+	0.113041i	−0.00444069	+	0.00444069i
$649$	16.8138	−	6.96452i	0.660001	−	0.273381i
$650$		0			0
$651$	−2.29020	−	5.52902i	−0.0897599	−	0.216700i
$652$	1.15069	−	2.77802i	0.0450646	−	0.108796i
$653$	−28.7578	−	11.9119i	−1.12538	−	0.466147i	−0.259171	−	0.965831i	$-0.583449\pi$
$653$	−28.7578	−	11.9119i	−1.12538	−	0.466147i	−0.866208	+	0.499684i	$0.833449\pi$
$654$	−2.13614	+	2.13614i	−0.0835296	+	0.0835296i
$655$		0			0
$656$	−16.3623	+	39.5020i	−0.638839	+	1.54229i
$657$	−4.63158	+	11.1816i	−0.180695	+	0.436236i
$658$	−1.60975	+	0.666782i	−0.0627548	+	0.0259939i
$659$		−	4.15956i		−	0.162033i	−0.996713	−	0.0810167i	$-0.974183\pi$
$659$		−	4.15956i		−	0.162033i	0.996713	−	0.0810167i	$-0.0258167\pi$
$660$		0			0
$661$	4.85106	+	4.85106i	0.188685	+	0.188685i	0.795127	−	0.606443i	$-0.207404\pi$
$661$	4.85106	+	4.85106i	0.188685	+	0.188685i	−0.606443	+	0.795127i	$0.707404\pi$
$662$			0.267095i			0.0103810i
$663$	8.21405	−	23.1421i	0.319007	−	0.898764i
$664$	16.3903			0.636066
$665$		0			0
$666$	−2.66713	+	1.10476i	−0.103349	+	0.0428086i
$667$	3.22925			0.125037
$668$	31.0493	−	12.8610i	1.20133	−	0.497608i
$669$	−6.33545	−	2.62423i	−0.244943	−	0.101459i
$670$		0			0
$671$	−1.56723	+	1.56723i	−0.0605023	+	0.0605023i
$672$	6.40801	+	6.40801i	0.247195	+	0.247195i
$673$	15.9651	+	6.61298i	0.615411	+	0.254912i	0.668540	−	0.743676i	$-0.266919\pi$
$673$	15.9651	+	6.61298i	0.615411	+	0.254912i	−0.0531290	+	0.998588i	$0.516919\pi$
$674$	−4.78190	−	1.98073i	−0.184192	−	0.0762948i
$675$		0			0
$676$			35.3348i			1.35903i
$677$	3.11269	+	7.51469i	0.119630	+	0.288813i	0.972339	−	0.233573i	$-0.0750419\pi$
$677$	3.11269	+	7.51469i	0.119630	+	0.288813i	−0.852709	+	0.522386i	$0.825042\pi$
$678$	3.38629	−	3.38629i	0.130050	−	0.130050i
$679$	22.4862			0.862942
$680$		0			0
$681$	3.24734			0.124438
$682$	1.17243	−	1.17243i	0.0448948	−	0.0448948i
$683$	11.1502	+	26.9190i	0.426652	+	1.03003i	0.980342	+	0.197306i	$0.0632191\pi$
$683$	11.1502	+	26.9190i	0.426652	+	1.03003i	−0.553690	+	0.832723i	$0.686781\pi$
$684$			25.5143i			0.975566i
$685$		0			0
$686$	−5.38702	−	2.23138i	−0.205677	−	0.0851943i
$687$	7.40992	+	3.06929i	0.282706	+	0.117101i
$688$	−6.41446	−	6.41446i	−0.244549	−	0.244549i
$689$	11.0136	−	11.0136i	0.419587	−	0.419587i
$690$		0			0
$691$	34.5393	+	14.3066i	1.31394	+	0.544250i	0.926031	−	0.377448i	$-0.123198\pi$
$691$	34.5393	+	14.3066i	1.31394	+	0.544250i	0.387906	+	0.921699i	$0.373198\pi$
$692$	−33.2327	+	13.7654i	−1.26332	+	0.523283i
$693$	−11.5041			−0.437006
$694$	−8.61534	+	3.56859i	−0.327034	+	0.135462i
$695$		0			0
$696$	−4.69395			−0.177924
$697$	45.9744	−	21.8875i	1.74140	−	0.829048i
$698$		−	1.01720i		−	0.0385015i
$699$	−16.7665	−	16.7665i	−0.634166	−	0.634166i
$700$		0			0
$701$			14.6423i			0.553031i	0.961009	+	0.276515i	$0.0891797\pi$
$701$			14.6423i			0.553031i	−0.961009	+	0.276515i	$0.910820\pi$
$702$	8.09139	−	3.35156i	0.305390	−	0.126497i
$703$	−13.9328	+	33.6368i	−0.525486	+	1.26863i
$704$	5.51956	−	13.3254i	0.208026	−	0.502220i
$705$		0			0
$706$	5.07538	−	5.07538i	0.191014	−	0.191014i
$707$	−35.4502	−	14.6840i	−1.33324	−	0.552247i
$708$	5.76812	−	13.9255i	0.216779	−	0.523351i
$709$	10.8526	+	26.2006i	0.407579	+	0.983983i	0.985773	+	0.168083i	$0.0537578\pi$
$709$	10.8526	+	26.2006i	0.407579	+	0.983983i	−0.578194	+	0.815899i	$0.696242\pi$
$710$		0			0
$711$	−25.4708	+	10.5504i	−0.955231	+	0.395670i
$712$	0.329520	−	0.329520i	0.0123493	−	0.0123493i
$713$			1.93451i			0.0724480i
$714$	−0.170946	−	3.30802i	−0.00639748	−	0.123800i
$715$		0			0
$716$	−4.47321	−	4.47321i	−0.167172	−	0.167172i
$717$	−1.40480	−	3.39148i	−0.0524631	−	0.126657i
$718$	9.56736			0.357051
$719$	4.83536	+	11.6736i	0.180329	+	0.435352i	0.988034	−	0.154234i	$-0.0492910\pi$
$719$	4.83536	+	11.6736i	0.180329	+	0.435352i	−0.807706	+	0.589586i	$0.799291\pi$
$720$		0			0
$721$	14.1906	−	34.2593i	0.528487	−	1.27588i
$722$	−6.79485	−	6.79485i	−0.252878	−	0.252878i
$723$	13.5242	+	13.5242i	0.502969	+	0.502969i
$724$	11.5901	−	27.9809i	0.430742	−	1.03990i
$725$		0			0
$726$	−0.614822	−	1.48431i	−0.0228182	−	0.0550879i
$727$	−15.0242			−0.557218			−0.278609	−	0.960405i	$-0.589873\pi$
$727$	−15.0242			−0.557218			−0.278609	+	0.960405i	$0.589873\pi$
$728$	6.35811	+	15.3498i	0.235647	+	0.568903i
$729$	11.4604	+	11.4604i	0.424460	+	0.424460i
$730$		0			0
$731$	0.557517	+	10.7887i	0.0206205	+	0.399035i
$732$			1.83566i			0.0678478i
$733$	−1.24931	+	1.24931i	−0.0461442	+	0.0461442i	−0.729802	−	0.683658i	$-0.760388\pi$
$733$	−1.24931	+	1.24931i	−0.0461442	+	0.0461442i	0.683658	+	0.729802i	$0.260388\pi$
$734$	1.25895	−	0.521475i	0.0464688	−	0.0192480i
$735$		0			0
$736$	−1.12103	−	2.70640i	−0.0413216	−	0.0997592i
$737$	6.26935	−	15.1356i	0.230935	−	0.557526i
$738$	6.45136	+	2.67224i	0.237478	+	0.0983665i
$739$	13.9406	−	13.9406i	0.512812	−	0.512812i	−0.402575	−	0.915387i	$-0.631885\pi$
$739$	13.9406	−	13.9406i	0.512812	−	0.512812i	0.915387	+	0.402575i	$0.131885\pi$
$740$		0			0
$741$	16.2532	−	39.2386i	0.597075	−	1.44147i
$742$	0.804017	−	1.94107i	0.0295164	−	0.0712589i
$743$	−26.2027	+	10.8535i	−0.961282	+	0.398176i	−0.807460	−	0.589922i	$-0.799158\pi$
$743$	−26.2027	+	10.8535i	−0.961282	+	0.398176i	−0.153822	+	0.988099i	$0.549158\pi$
$744$		−	2.81195i		−	0.103091i
$745$		0			0
$746$	−1.09382	−	1.09382i	−0.0400475	−	0.0400475i
$747$			26.0491i			0.953087i
$748$	−17.3799	+	8.27422i	−0.635472	+	0.302535i
$749$	3.69141			0.134881
$750$		0			0
$751$	16.5853	−	6.86987i	0.605207	−	0.250685i	−0.0589704	−	0.998260i	$-0.518782\pi$
$751$	16.5853	−	6.86987i	0.605207	−	0.250685i	0.664178	+	0.747575i	$0.268782\pi$
$752$	7.96698			0.290526
$753$	−23.5728	+	9.76418i	−0.859041	+	0.355826i
$754$	−5.86937	−	2.43117i	−0.213750	−	0.0885381i
$755$		0			0
$756$	−17.5211	+	17.5211i	−0.637237	+	0.637237i
$757$	−31.0649	−	31.0649i	−1.12907	−	1.12907i	−0.990328	−	0.138743i	$-0.955694\pi$
$757$	−31.0649	−	31.0649i	−1.12907	−	1.12907i	−0.138743	−	0.990328i	$-0.544306\pi$
$758$	1.54137	+	0.638456i	0.0559851	+	0.0231898i
$759$	−2.06358	−	0.854764i	−0.0749033	−	0.0310260i
$760$		0			0
$761$		−	13.2781i		−	0.481331i	−0.970608	−	0.240666i	$-0.922634\pi$
$761$		−	13.2781i		−	0.481331i	0.970608	−	0.240666i	$-0.0773657\pi$
$762$	0.729435	+	1.76101i	0.0264247	+	0.0637948i
$763$	16.7493	−	16.7493i	0.606367	−	0.606367i
$764$	−52.4861			−1.89888
$765$		0			0
$766$	6.16480			0.222743
$767$	29.5378	−	29.5378i	1.06655	−	1.06655i
$768$	−3.73767	−	9.02353i	−0.134871	−	0.325609i
$769$		−	24.8906i		−	0.897578i	−0.893638	−	0.448789i	$-0.851856\pi$
$769$		−	24.8906i		−	0.897578i	0.893638	−	0.448789i	$-0.148144\pi$
$770$		0			0
$771$	−14.5093	−	6.00995i	−0.522540	−	0.216443i
$772$	26.0340	+	10.7836i	0.936985	+	0.388112i
$773$	37.9750	+	37.9750i	1.36587	+	1.36587i	0.866242	+	0.499624i	$0.166529\pi$
$773$	37.9750	+	37.9750i	1.36587	+	1.36587i	0.499624	+	0.866242i	$0.333471\pi$
$774$	−1.04759	+	1.04759i	−0.0376549	+	0.0376549i
$775$		0			0
$776$	9.76127	+	4.04325i	0.350409	+	0.145144i
$777$	−12.5611	+	5.20296i	−0.450626	+	0.186655i
$778$	−1.56463			−0.0560949
$779$	81.3621	−	33.7013i	2.91510	−	1.20747i
$780$		0			0
$781$	0.588811			0.0210693
$782$	−0.358158	+	1.00907i	−0.0128077	+	0.0360841i
$783$		−	19.4011i		−	0.693339i
$784$	1.71544	+	1.71544i	0.0612658	+	0.0612658i
$785$		0			0
$786$		−	1.34033i		−	0.0478079i
$787$	−47.5592	+	19.6997i	−1.69530	+	0.702217i	−0.999866	−	0.0163714i	$-0.994789\pi$
$787$	−47.5592	+	19.6997i	−1.69530	+	0.702217i	−0.695436	+	0.718588i	$0.744789\pi$
$788$	0.274979	−	0.663857i	0.00979571	−	0.0236489i
$789$	−9.95443	+	24.0321i	−0.354387	+	0.855566i
$790$		0			0
$791$	−26.5517	+	26.5517i	−0.944070	+	0.944070i
$792$	−4.99394	−	2.06856i	−0.177452	−	0.0735031i
$793$	−1.94684	+	4.70008i	−0.0691342	+	0.166905i
$794$	0.712737	+	1.72070i	0.0252941	+	0.0610654i
$795$		0			0
$796$	13.2805	−	5.50097i	0.470716	−	0.194977i
$797$	−13.3772	+	13.3772i	−0.473846	+	0.473846i	−0.903157	−	0.429311i	$-0.858756\pi$
$797$	−13.3772	+	13.3772i	−0.473846	+	0.473846i	0.429311	+	0.903157i	$0.358756\pi$
$798$		−	5.72898i		−	0.202804i
$799$	−7.04620	−	6.35374i	−0.249276	−	0.224779i
$800$		0			0
$801$	0.523707	+	0.523707i	0.0185043	+	0.0185043i
$802$	−1.09637	−	2.64687i	−0.0387141	−	0.0934642i
$803$	−15.7922			−0.557294
$804$	−5.19237	−	12.5355i	−0.183121	−	0.442093i
$805$		0			0
$806$	1.45641	−	3.51609i	0.0513000	−	0.123849i
$807$	4.94766	+	4.94766i	0.174166	+	0.174166i
$808$	−12.7486	−	12.7486i	−0.448495	−	0.448495i
$809$	−11.5703	+	27.9333i	−0.406791	+	0.982081i	0.579185	+	0.815196i	$0.303371\pi$
$809$	−11.5703	+	27.9333i	−0.406791	+	0.982081i	−0.985976	+	0.166885i	$0.946629\pi$
$810$		0			0
$811$	−6.57121	−	15.8643i	−0.230746	−	0.557071i	0.765519	−	0.643413i	$-0.222482\pi$
$811$	−6.57121	−	15.8643i	−0.230746	−	0.557071i	−0.996266	+	0.0863422i	$0.972482\pi$
$812$	17.9740			0.630765
$813$	10.6362	+	25.6782i	0.373030	+	0.900573i
$814$	−2.66358	−	2.66358i	−0.0933586	−	0.0933586i
$815$		0			0
$816$	−5.06624	+	14.2735i	−0.177354	+	0.499673i
$817$			18.6844i			0.653683i
$818$	3.06944	−	3.06944i	0.107320	−	0.107320i
$819$	−24.3956	+	10.1050i	−0.852450	+	0.353096i
$820$		0			0
$821$	−16.7555	−	40.4514i	−0.584771	−	1.41176i	−0.888443	−	0.458986i	$-0.848213\pi$
$821$	−16.7555	−	40.4514i	−0.584771	−	1.41176i	0.303672	−	0.952777i	$-0.401787\pi$
$822$	−0.889309	+	2.14698i	−0.0310182	+	0.0748846i
$823$	−23.3460	−	9.67025i	−0.813792	−	0.337084i	−0.0633260	−	0.997993i	$-0.520171\pi$
$823$	−23.3460	−	9.67025i	−0.813792	−	0.337084i	−0.750466	+	0.660909i	$0.770171\pi$
$824$	12.3203	−	12.3203i	0.429199	−	0.429199i
$825$		0			0
$826$	2.15632	−	5.20581i	0.0750278	−	0.181133i
$827$	8.44496	−	20.3879i	0.293660	−	0.708958i	−0.706339	−	0.707874i	$-0.749655\pi$
$827$	8.44496	−	20.3879i	0.293660	−	0.708958i	0.999999	−	0.00108492i	$-0.000345340\pi$
$828$	2.84544	−	1.17862i	0.0988860	−	0.0409599i
$829$		−	20.9555i		−	0.727816i	−0.931435	−	0.363908i	$-0.881442\pi$
$829$		−	20.9555i		−	0.727816i	0.931435	−	0.363908i	$-0.118558\pi$
$830$		0			0
$831$	7.17617	+	7.17617i	0.248939	+	0.248939i
$832$		−	33.1060i		−	1.14774i
$833$	−0.149099	−	2.88526i	−0.00516597	−	0.0999684i
$834$	−3.32680			−0.115198
$835$		0			0
$836$	−30.7576	+	12.7402i	−1.06378	+	0.440630i
$837$	11.6224			0.401728
$838$	5.91541	−	2.45024i	0.204344	−	0.0846422i
$839$	−18.6855	−	7.73980i	−0.645096	−	0.267207i	0.0360558	−	0.999350i	$-0.488521\pi$
$839$	−18.6855	−	7.73980i	−0.645096	−	0.267207i	−0.681152	+	0.732142i	$0.738521\pi$
$840$		0			0
$841$	10.5548	−	10.5548i	0.363958	−	0.363958i
$842$	−4.30216	−	4.30216i	−0.148262	−	0.148262i
$843$	−12.1721	−	5.04183i	−0.419228	−	0.173650i
$844$	15.3307	+	6.35018i	0.527704	+	0.218582i
$845$		0			0
$846$		−	1.30115i		−	0.0447343i
$847$	4.82078	+	11.6384i	0.165644	+	0.399900i
$848$	−6.79298	+	6.79298i	−0.233272	+	0.233272i
$849$	−17.8710			−0.613331
$850$		0			0
$851$	4.39490			0.150655
$852$	0.344829	−	0.344829i	0.0118137	−	0.0118137i
$853$	−4.39863	−	10.6192i	−0.150606	−	0.363595i	0.830513	−	0.556999i	$-0.188047\pi$
$853$	−4.39863	−	10.6192i	−0.150606	−	0.363595i	−0.981119	+	0.193404i	$0.938047\pi$
$854$			0.686230i			0.0234823i
$855$		0			0
$856$	1.60244	+	0.663753i	0.0547703	+	0.0226866i
$857$	−25.9484	−	10.7482i	−0.886380	−	0.367151i	−0.107412	−	0.994215i	$-0.534256\pi$
$857$	−25.9484	−	10.7482i	−0.886380	−	0.367151i	−0.778968	+	0.627064i	$0.784256\pi$
$858$	3.10717	+	3.10717i	0.106077	+	0.106077i
$859$	2.22749	−	2.22749i	0.0760011	−	0.0760011i	−0.668084	−	0.744086i	$-0.732885\pi$
$859$	2.22749	−	2.22749i	0.0760011	−	0.0760011i	0.744086	+	0.668084i	$0.232885\pi$
$860$		0			0
$861$	30.3833	+	12.5852i	1.03546	+	0.428901i
$862$	5.56568	−	2.30538i	0.189568	−	0.0785216i
$863$	34.5368			1.17565			0.587823	−	0.808989i	$-0.299985\pi$
$863$	34.5368			1.17565			0.587823	+	0.808989i	$0.299985\pi$
$864$	−16.2598	+	6.73504i	−0.553171	+	0.229131i
$865$		0			0
$866$	5.49781			0.186823
$867$	15.8640	−	8.58348i	0.538769	−	0.291510i
$868$			10.7675i			0.365473i
$869$	−25.4370	−	25.4370i	−0.862892	−	0.862892i
$870$		0			0
$871$		−	37.6032i		−	1.27414i
$872$	10.2826	−	4.25919i	0.348212	−	0.144234i
$873$	−6.42595	+	15.5136i	−0.217486	+	0.525057i
$874$	−0.708688	+	1.71093i	−0.0239717	+	0.0578729i
$875$		0			0
$876$	−9.24848	+	9.24848i	−0.312477	+	0.312477i
$877$	−14.6203	−	6.05591i	−0.493691	−	0.204493i	0.121926	−	0.992539i	$-0.461093\pi$
$877$	−14.6203	−	6.05591i	−0.493691	−	0.204493i	−0.615617	+	0.788046i	$0.711093\pi$
$878$	1.70096	−	4.10647i	0.0574045	−	0.138587i
$879$	8.47821	+	20.4682i	0.285963	+	0.690376i
$880$		0			0
$881$	29.1623	−	12.0794i	0.982504	−	0.406967i	0.167152	−	0.985931i	$-0.446543\pi$
$881$	29.1623	−	12.0794i	0.982504	−	0.406967i	0.815353	+	0.578965i	$0.196543\pi$
$882$	0.280162	−	0.280162i	0.00943353	−	0.00943353i
$883$			20.2779i			0.682406i	0.939990	+	0.341203i	$0.110834\pi$
$883$			20.2779i			0.682406i	−0.939990	+	0.341203i	$0.889166\pi$
$884$	−29.5878	+	32.8124i	−0.995144	+	1.10360i
$885$		0			0
$886$	−4.97762	−	4.97762i	−0.167226	−	0.167226i
$887$	18.6899	+	45.1215i	0.627547	+	1.51503i	0.842662	+	0.538443i	$0.180987\pi$
$887$	18.6899	+	45.1215i	0.627547	+	1.51503i	−0.215115	+	0.976589i	$0.569013\pi$
$888$	−6.38831			−0.214378
$889$	−5.71946	−	13.8080i	−0.191825	−	0.463106i
$890$		0			0
$891$	0.126868	−	0.306287i	0.00425024	−	0.0102610i
$892$	8.72426	+	8.72426i	0.292110	+	0.292110i
$893$	−11.6033	−	11.6033i	−0.388290	−	0.388290i
$894$	0.737129	−	1.77959i	0.0246533	−	0.0595183i
$895$		0			0
$896$	−8.24607	−	19.9078i	−0.275482	−	0.665072i
$897$	−5.12682			−0.171180
$898$	0.197608	+	0.477067i	0.00659425	+	0.0159199i
$899$	−5.96141	−	5.96141i	−0.198824	−	0.198824i
$900$		0			0
$901$	11.4253	−	0.590416i	0.380633	−	0.0196696i
$902$			9.11148i			0.303379i
$903$	−4.93373	+	4.93373i	−0.164184	+	0.164184i
$904$	−16.3004	+	6.75183i	−0.542142	+	0.224563i
$905$		0			0
$906$	1.27618	+	3.08098i	0.0423984	+	0.102359i
$907$	15.9603	−	38.5317i	0.529955	−	1.27942i	−0.401598	−	0.915816i	$-0.631545\pi$
$907$	15.9603	−	38.5317i	0.529955	−	1.27942i	0.931552	−	0.363608i	$-0.118455\pi$
$908$	−5.39790	−	2.23588i	−0.179136	−	0.0742004i
$909$	20.2614	−	20.2614i	0.672029	−	0.672029i
$910$		0			0
$911$	2.44973	−	5.91417i	0.0811632	−	0.195945i	−0.878088	−	0.478498i	$-0.841181\pi$
$911$	2.44973	−	5.91417i	0.0811632	−	0.195945i	0.959252	+	0.282553i	$0.0911813\pi$
$912$	−10.0246	+	24.2015i	−0.331947	+	0.801392i
$913$	−31.4023	+	13.0073i	−1.03926	+	0.430478i
$914$		−	3.98735i		−	0.131890i
$915$		0			0
$916$	−10.2039	−	10.2039i	−0.337145	−	0.337145i
$917$			10.5094i			0.347052i
$918$	6.06239	+	2.15178i	0.200089	+	0.0710195i
$919$	23.6812			0.781170			0.390585	−	0.920567i	$-0.372273\pi$
$919$	23.6812			0.781170			0.390585	+	0.920567i	$0.372273\pi$
$920$		0			0
$921$	−29.3613	+	12.1618i	−0.967488	+	0.400746i
$922$	8.83658			0.291017
$923$	1.24863	−	0.517199i	0.0410991	−	0.0170238i
$924$	−11.4859	−	4.75762i	−0.377859	−	0.156514i
$925$		0			0
$926$	−2.09137	+	2.09137i	−0.0687268	+	0.0687268i
$927$	19.5807	+	19.5807i	0.643116	+	0.643116i
$928$	11.7946	+	4.88550i	0.387178	+	0.160374i
$929$	−50.7164	−	21.0074i	−1.66395	−	0.689232i	−0.665583	−	0.746324i	$-0.731817\pi$
$929$	−50.7164	−	21.0074i	−1.66395	−	0.689232i	−0.998369	+	0.0570920i	$0.981817\pi$
$930$		0			0
$931$		−	4.99683i		−	0.163764i
$932$	16.3259	+	39.4142i	0.534773	+	1.29106i
$933$	0.157795	−	0.157795i	0.00516598	−	0.00516598i
$934$	4.12766			0.135061
$935$		0			0
$936$	−12.4071			−0.405539
$937$	−4.78966	+	4.78966i	−0.156471	+	0.156471i	−0.781001	−	0.624530i	$-0.785291\pi$
$937$	−4.78966	+	4.78966i	−0.156471	+	0.156471i	0.624530	+	0.781001i	$0.285291\pi$
$938$	−1.94108	−	4.68619i	−0.0633786	−	0.153010i
$939$		−	34.4025i		−	1.12268i
$940$		0			0
$941$	−23.2992	−	9.65084i	−0.759532	−	0.314608i	−0.0309078	−	0.999522i	$-0.509840\pi$
$941$	−23.2992	−	9.65084i	−0.759532	−	0.314608i	−0.728624	+	0.684914i	$0.759840\pi$
$942$	−3.96490	−	1.64232i	−0.129184	−	0.0535096i
$943$	−7.51696	−	7.51696i	−0.244786	−	0.244786i
$944$	−18.2183	+	18.2183i	−0.592954	+	0.592954i
$945$		0			0
$946$	−1.78598	−	0.739776i	−0.0580671	−	0.0240522i
$947$	−22.6362	+	9.37621i	−0.735577	+	0.304686i	−0.718841	−	0.695174i	$-0.755327\pi$
$947$	−22.6362	+	9.37621i	−0.735577	+	0.304686i	−0.0167354	+	0.999860i	$0.505327\pi$
$948$	−29.7937			−0.967654
$949$	−33.4888	+	13.8715i	−1.08709	+	0.450288i
$950$		0			0
$951$	−35.4793			−1.15050
$952$	−4.08206	+	11.5007i	−0.132300	+	0.372740i
$953$		−	30.3936i		−	0.984545i	−0.870441	−	0.492272i	$-0.836166\pi$
$953$		−	30.3936i		−	0.984545i	0.870441	−	0.492272i	$-0.163834\pi$
$954$	1.10941	+	1.10941i	0.0359185	+	0.0359185i
$955$		0			0
$956$			6.60473i			0.213612i
$957$	8.99320	−	3.72511i	0.290709	−	0.120416i
$958$	−1.27111	+	3.06873i	−0.0410677	+	0.0991462i
$959$	6.97302	−	16.8344i	0.225171	−	0.543610i
$960$		0			0
$961$	−18.3491	+	18.3491i	−0.591906	+	0.591906i
$962$	−7.98801	−	3.30874i	−0.257544	−	0.106678i
$963$	−1.05491	+	2.54677i	−0.0339939	+	0.0820684i
$964$	−13.1688	−	31.7923i	−0.424139	−	1.02396i
$965$		0			0
$966$	−0.638915	+	0.264647i	−0.0205568	+	0.00851489i
$967$	31.0785	−	31.0785i	0.999416	−	0.999416i	−0.000584066	−	1.00000i	$-0.500186\pi$
$967$	31.0785	−	31.0785i	0.999416	−	0.999416i	1.00000		0.000584066i	$0.000185914\pi$
$968$			5.91906i			0.190246i
$969$	28.1669	−	13.4097i	0.904852	−	0.430782i
$970$		0			0
$971$	29.9769	+	29.9769i	0.962005	+	0.962005i	0.999304	−	0.0372988i	$-0.0118753\pi$
$971$	29.9769	+	29.9769i	0.962005	+	0.962005i	−0.0372988	+	0.999304i	$0.511875\pi$
$972$	−11.4393	−	27.6169i	−0.366916	−	0.885814i
$973$	26.0853			0.836255
$974$	−1.16538	−	2.81349i	−0.0373413	−	0.0901500i
$975$		0			0
$976$	1.20077	−	2.89891i	0.0384356	−	0.0927918i
$977$	16.7792	+	16.7792i	0.536813	+	0.536813i	0.922591	−	0.385778i	$-0.126067\pi$
$977$	16.7792	+	16.7792i	0.536813	+	0.536813i	−0.385778	+	0.922591i	$0.626067\pi$
$978$	−0.356517	−	0.356517i	−0.0114001	−	0.0114001i
$979$	−0.369825	+	0.892837i	−0.0118197	+	0.0285352i
$980$		0			0
$981$	6.76915	+	16.3422i	0.216122	+	0.521765i
$982$	5.15363			0.164459
$983$	10.7391	+	25.9264i	0.342524	+	0.826925i	0.997459	+	0.0712405i	$0.0226958\pi$
$983$	10.7391	+	25.9264i	0.342524	+	0.826925i	−0.654935	+	0.755685i	$0.727304\pi$
$984$	10.9264	+	10.9264i	0.348322	+	0.348322i
$985$		0			0
$986$	−2.00585	−	4.21325i	−0.0638791	−	0.134177i
$987$		−	6.12786i		−	0.195052i
$988$	−54.0337	+	54.0337i	−1.71904	+	1.71904i
$989$	2.08374	−	0.863114i	0.0662591	−	0.0274454i
$990$		0			0
$991$	17.0472	+	41.1557i	0.541523	+	1.30735i	0.923648	+	0.383242i	$0.125193\pi$
$991$	17.0472	+	41.1557i	0.541523	+	1.30735i	−0.382124	+	0.924111i	$0.624807\pi$
$992$	−2.92670	+	7.06567i	−0.0929227	+	0.224335i
$993$	−0.867854	−	0.359477i	−0.0275405	−	0.0114076i
$994$	0.128909	−	0.128909i	0.00408874	−	0.00408874i
$995$		0			0
$996$	−10.7728	+	26.0079i	−0.341349	+	0.824090i
$997$	7.86332	−	18.9837i	0.249034	−	0.601221i	−0.749089	−	0.662470i	$-0.769508\pi$
$997$	7.86332	−	18.9837i	0.249034	−	0.601221i	0.998123	+	0.0612487i	$0.0195083\pi$
$998$	−8.74058	+	3.62047i	−0.276678	+	0.114604i
$999$		−	26.4042i		−	0.835392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.c.274.3		24
5.2	odd	4		425.2.m.b.376.3		24
5.3	odd	4		85.2.l.a.36.4	yes	24
5.4	even	2		425.2.n.f.274.4		24
15.8	even	4		765.2.be.b.631.3		24
17.9	even	8		425.2.n.f.349.4		24
85.3	even	16		1445.2.a.p.1.7		12
85.9	even	8	inner	425.2.n.c.349.3		24
85.37	even	16		7225.2.a.bs.1.6		12
85.43	odd	8		85.2.l.a.26.4	✓	24
85.48	even	16		1445.2.a.q.1.7		12
85.63	even	16		1445.2.d.j.866.11		24
85.73	even	16		1445.2.d.j.866.12		24
85.77	odd	8		425.2.m.b.26.3		24
85.82	even	16		7225.2.a.bq.1.6		12
255.128	even	8		765.2.be.b.451.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.4	✓	24	85.43	odd	8
85.2.l.a.36.4	yes	24	5.3	odd	4
425.2.m.b.26.3		24	85.77	odd	8
425.2.m.b.376.3		24	5.2	odd	4
425.2.n.c.274.3		24	1.1	even	1	trivial
425.2.n.c.349.3		24	85.9	even	8	inner
425.2.n.f.274.4		24	5.4	even	2
425.2.n.f.349.4		24	17.9	even	8
765.2.be.b.451.3		24	255.128	even	8
765.2.be.b.631.3		24	15.8	even	4
1445.2.a.p.1.7		12	85.3	even	16
1445.2.a.q.1.7		12	85.48	even	16
1445.2.d.j.866.11		24	85.63	even	16
1445.2.d.j.866.12		24	85.73	even	16
7225.2.a.bq.1.6		12	85.82	even	16
7225.2.a.bs.1.6		12	85.37	even	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.213325 + 0.213325i) q^{2} +(-0.406032 - 0.980249i) q^{3} +1.90899i q^{4} +(0.295728 + 0.122495i) q^{6} +(-2.31879 - 0.960473i) q^{7} +(-0.833883 - 0.833883i) q^{8} +(1.32529 - 1.32529i) q^{9} +(2.25941 + 0.935880i) q^{11} +(1.87128 - 0.775110i) q^{12} +5.61335 q^{13} +(0.699548 - 0.289762i) q^{14} -3.46219 q^{16} +(3.06205 + 2.76113i) q^{17} +0.565436i q^{18} +(5.04243 + 5.04243i) q^{19} +2.66297i q^{21} +(-0.681636 + 0.282343i) q^{22} +(0.329416 - 0.795280i) q^{23} +(-0.478830 + 1.15600i) q^{24} +(-1.19747 + 1.19747i) q^{26} +(-4.77798 - 1.97910i) q^{27} +(1.83353 - 4.42653i) q^{28} +(1.43561 + 3.46587i) q^{29} +(-2.07626 + 0.860015i) q^{31} +(2.40634 - 2.40634i) q^{32} -2.59479i q^{33} +(-1.24223 + 0.0641935i) q^{34} +(2.52997 + 2.52997i) q^{36} +(1.95382 + 4.71693i) q^{37} -2.15135 q^{38} +(-2.27920 - 5.50249i) q^{39} +(4.72598 - 11.4095i) q^{41} +(-0.568078 - 0.568078i) q^{42} +(1.85272 + 1.85272i) q^{43} +(-1.78658 + 4.31319i) q^{44} +(0.0993804 + 0.239926i) q^{46} -2.30114 q^{47} +(1.40576 + 3.39381i) q^{48} +(-0.495478 - 0.495478i) q^{49} +(1.46330 - 4.12268i) q^{51} +10.7158i q^{52} +(1.96204 - 1.96204i) q^{53} +(1.44145 - 0.597069i) q^{54} +(1.13268 + 2.73452i) q^{56} +(2.89544 - 6.99022i) q^{57} +(-1.04561 - 0.433105i) q^{58} +(5.26206 - 5.26206i) q^{59} +(-0.346822 + 0.837303i) q^{61} +(0.259455 - 0.626380i) q^{62} +(-4.34599 + 1.80017i) q^{63} -5.89773i q^{64} +(0.553532 + 0.553532i) q^{66} -6.69889i q^{67} +(-5.27096 + 5.84541i) q^{68} -0.913326 q^{69} +(0.222439 - 0.0921372i) q^{71} -2.21028 q^{72} +(-5.96591 + 2.47116i) q^{73} +(-1.42304 - 0.589441i) q^{74} +(-9.62592 + 9.62592i) q^{76} +(-4.34022 - 4.34022i) q^{77} +(1.66003 + 0.687606i) q^{78} +(-13.5899 - 5.62912i) q^{79} -0.135560i q^{81} +(1.42577 + 3.44210i) q^{82} +(-9.82767 + 9.82767i) q^{83} -5.08358 q^{84} -0.790460 q^{86} +(2.81451 - 2.81451i) q^{87} +(-1.10367 - 2.66450i) q^{88} +0.395163i q^{89} +(-13.0162 - 5.39148i) q^{91} +(1.51818 + 0.628850i) q^{92} +(1.68606 + 1.68606i) q^{93} +(0.490889 - 0.490889i) q^{94} +(-3.33586 - 1.38176i) q^{96} +(-8.27725 + 3.42855i) q^{97} +0.211396 q^{98} +(4.23471 - 1.75407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more