LMFDB - Embedded newform 425.2.m.b.376.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(26,425)] 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("425.26"); 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([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,-8,0,0,-24,0,-8,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == 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			376.3
Character	$\chi$	$=$	425.376
Dual form			425.2.m.b.26.3

$q$-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} +(-0.980249 + 0.406032i) q^{3} -1.90899i q^{4} +(0.295728 + 0.122495i) q^{6} +(0.960473 - 2.31879i) q^{7} +(-0.833883 + 0.833883i) q^{8} +(-1.32529 + 1.32529i) q^{9} +(2.25941 + 0.935880i) q^{11} +(0.775110 + 1.87128i) q^{12} -5.61335i q^{13} +(-0.699548 + 0.289762i) q^{14} -3.46219 q^{16} +(-2.76113 + 3.06205i) q^{17} +0.565436 q^{18} +(-5.04243 - 5.04243i) q^{19} +2.66297i q^{21} +(-0.282343 - 0.681636i) q^{22} +(-0.795280 - 0.329416i) q^{23} +(0.478830 - 1.15600i) q^{24} +(-1.19747 + 1.19747i) q^{26} +(1.97910 - 4.77798i) q^{27} +(-4.42653 - 1.83353i) q^{28} +(-1.43561 - 3.46587i) q^{29} +(-2.07626 + 0.860015i) q^{31} +(2.40634 + 2.40634i) q^{32} -2.59479 q^{33} +(1.24223 - 0.0641935i) q^{34} +(2.52997 + 2.52997i) q^{36} +(-4.71693 + 1.95382i) q^{37} +2.15135i 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} -2.30114i q^{47} +(3.39381 - 1.40576i) q^{48} +(0.495478 + 0.495478i) q^{49} +(1.46330 - 4.12268i) q^{51} -10.7158 q^{52} +(-1.96204 - 1.96204i) q^{53} +(-1.44145 + 0.597069i) q^{54} +(1.13268 + 2.73452i) q^{56} +(6.99022 + 2.89544i) q^{57} +(-0.433105 + 1.04561i) q^{58} +(-5.26206 + 5.26206i) q^{59} +(-0.346822 + 0.837303i) q^{61} +(0.626380 + 0.259455i) q^{62} +(1.80017 + 4.34599i) q^{63} +5.89773i q^{64} +(0.553532 + 0.553532i) q^{66} +6.69889 q^{67} +(5.84541 + 5.27096i) q^{68} +0.913326 q^{69} +(0.222439 - 0.0921372i) q^{71} -2.21028i q^{72} +(2.47116 + 5.96591i) q^{73} +(1.42304 + 0.589441i) q^{74} +(-9.62592 + 9.62592i) q^{76} +(4.34022 - 4.34022i) q^{77} +(0.687606 - 1.66003i) q^{78} +(13.5899 + 5.62912i) q^{79} -0.135560i q^{81} +(-3.44210 + 1.42577i) q^{82} +(9.82767 + 9.82767i) q^{83} +5.08358 q^{84} -0.790460 q^{86} +(2.81451 + 2.81451i) q^{87} +(-2.66450 + 1.10367i) q^{88} -0.395163i q^{89} +(-13.0162 - 5.39148i) q^{91} +(-0.628850 + 1.51818i) q^{92} +(1.68606 - 1.68606i) q^{93} +(-0.490889 + 0.490889i) q^{94} +(-3.33586 - 1.38176i) q^{96} +(-3.42855 - 8.27725i) q^{97} -0.211396i q^{98} +(-4.23471 + 1.75407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} - 24 q^{12} - 24 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 32 q^{22} + 16 q^{23} - 8 q^{24} + 16 q^{26} - 24 q^{27} - 48 q^{28} - 8 q^{29} + 16 q^{34} - 24 q^{36} - 24 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 - 24 * q^12 - 24 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 32 * q^22 + 16 * q^23 - 8 * q^24 + 16 * q^26 - 24 * q^27 - 48 * q^28 - 8 * q^29 + 16 * q^34 - 24 * q^36 - 24 * q^37 + 8 * q^39 + 16 * q^41 + 24 * q^42 - 8 * q^43 + 16 * q^44 + 8 * q^46 - 80 * q^48 - 56 * q^51 + 48 * q^52 - 24 * q^53 - 32 * q^54 + 64 * q^56 - 32 * q^57 + 64 * q^58 + 32 * q^59 + 32 * q^61 + 32 * q^62 + 56 * q^63 + 96 * q^66 - 16 * q^67 + 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^76 - 24 * q^77 + 112 * q^78 + 80 * q^82 + 96 * q^83 - 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 - 80 * q^92 - 64 * q^93 + 56 * q^94 - 168 * q^96 + 40 * q^97 - 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	0.627651	−	0.778495i	$-0.284016\pi$
$2$	−0.213325	−	0.213325i	−0.150843	−	0.150843i	−0.778495	+	0.627651i	$0.784016\pi$
$3$	−0.980249	+	0.406032i	−0.565947	+	0.234423i	−0.647265	−	0.762265i	$-0.724087\pi$
$3$	−0.980249	+	0.406032i	−0.565947	+	0.234423i	0.0813177	+	0.996688i	$0.474087\pi$
$4$		−	1.90899i		−	0.954493i
$5$		0			0
$5$		0			0
$6$	0.295728	+	0.122495i	0.120731	+	0.0500082i
$7$	0.960473	−	2.31879i	0.363025	−	0.876420i	−0.631830	−	0.775107i	$-0.717696\pi$
$7$	0.960473	−	2.31879i	0.363025	−	0.876420i	0.994855	−	0.101312i	$-0.0323042\pi$
$8$	−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	$0.504808\pi$
$12$	0.775110	+	1.87128i	0.223755	+	0.540192i
$13$		−	5.61335i		−	1.55686i	−0.627729	−	0.778432i	$-0.716015\pi$
$13$		−	5.61335i		−	1.55686i	0.627729	−	0.778432i	$-0.283985\pi$
$14$	−0.699548	+	0.289762i	−0.186962	+	0.0774422i
$15$		0			0
$16$	−3.46219			−0.865549
$17$	−2.76113	+	3.06205i	−0.669673	+	0.742656i
$17$	−2.76113	+	3.06205i	−0.669673	+	0.742656i
$18$	0.565436			0.133275
$19$	−5.04243	−	5.04243i	−1.15681	−	1.15681i	−0.985157	−	0.171655i	$-0.945089\pi$
$19$	−5.04243	−	5.04243i	−1.15681	−	1.15681i	−0.171655	−	0.985157i	$-0.554911\pi$
$20$		0			0
$21$			2.66297i			0.581108i
$22$	−0.282343	−	0.681636i	−0.0601957	−	0.145325i
$23$	−0.795280	−	0.329416i	−0.165827	−	0.0686880i	0.298226	−	0.954495i	$-0.403605\pi$
$23$	−0.795280	−	0.329416i	−0.165827	−	0.0686880i	−0.464053	+	0.885807i	$0.653605\pi$
$24$	0.478830	−	1.15600i	0.0977407	−	0.235967i
$25$		0			0
$26$	−1.19747	+	1.19747i	−0.234843	+	0.234843i
$27$	1.97910	−	4.77798i	0.380879	−	0.919522i
$28$	−4.42653	−	1.83353i	−0.836536	−	0.346505i
$29$	−1.43561	−	3.46587i	−0.266586	−	0.643597i	0.732732	−	0.680518i	$-0.238245\pi$
$29$	−1.43561	−	3.46587i	−0.266586	−	0.643597i	−0.999318	+	0.0369210i	$0.988245\pi$
$30$		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
$33$	−2.59479			−0.451694
$34$	1.24223	−	0.0641935i	0.213041	−	0.0110091i
$35$		0			0
$36$	2.52997	+	2.52997i	0.421661	+	0.421661i
$37$	−4.71693	+	1.95382i	−0.775459	+	0.321206i	−0.735081	−	0.677979i	$-0.762856\pi$
$37$	−4.71693	+	1.95382i	−0.775459	+	0.321206i	−0.0403776	+	0.999184i	$0.512856\pi$
$38$			2.15135i			0.348995i
$39$	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	−0.551583	−	0.834120i	$-0.685976\pi$
$43$	1.85272	−	1.85272i	0.282536	−	0.282536i	0.834120	+	0.551583i	$0.185976\pi$
$44$	1.78658	−	4.31319i	0.269337	−	0.650238i
$45$		0			0
$46$	0.0993804	+	0.239926i	0.0146528	+	0.0353751i
$47$		−	2.30114i		−	0.335655i	−0.985816	−	0.167828i	$-0.946325\pi$
$47$		−	2.30114i		−	0.335655i	0.985816	−	0.167828i	$-0.0536752\pi$
$48$	3.39381	−	1.40576i	0.489855	−	0.202904i
$49$	0.495478	+	0.495478i	0.0707826	+	0.0707826i
$50$		0			0
$51$	1.46330	−	4.12268i	0.204904	−	0.577291i
$52$	−10.7158			−1.48602
$53$	−1.96204	−	1.96204i	−0.269507	−	0.269507i	0.559394	−	0.828902i	$-0.311034\pi$
$53$	−1.96204	−	1.96204i	−0.269507	−	0.269507i	−0.828902	+	0.559394i	$0.811034\pi$
$54$	−1.44145	+	0.597069i	−0.196157	+	0.0812508i
$55$		0			0
$56$	1.13268	+	2.73452i	0.151360	+	0.365416i
$57$	6.99022	+	2.89544i	0.925877	+	0.383511i
$58$	−0.433105	+	1.04561i	−0.0568695	+	0.137295i
$59$	−5.26206	+	5.26206i	−0.685062	+	0.685062i	−0.961136	−	0.276075i	$-0.910966\pi$
$59$	−5.26206	+	5.26206i	−0.685062	+	0.685062i	0.276075	+	0.961136i	$0.410966\pi$
$60$		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	$0.143478\pi$
$62$	0.626380	+	0.259455i	0.0795504	+	0.0329508i
$63$	1.80017	+	4.34599i	0.226800	+	0.547543i
$64$			5.89773i			0.737216i
$65$		0			0
$66$	0.553532	+	0.553532i	0.0681351	+	0.0681351i
$67$	6.69889			0.818399			0.409200	−	0.912445i	$-0.365808\pi$
$67$	6.69889			0.818399			0.409200	+	0.912445i	$0.365808\pi$
$68$	5.84541	+	5.27096i	0.708860	+	0.639198i
$69$	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	$0.370452\pi$
$72$		−	2.21028i		−	0.260484i
$73$	2.47116	+	5.96591i	0.289228	+	0.698257i	0.999987	−	0.00517825i	$-0.00164830\pi$
$73$	2.47116	+	5.96591i	0.289228	+	0.698257i	−0.710759	+	0.703436i	$0.751648\pi$
$74$	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
$78$	0.687606	−	1.66003i	0.0778560	−	0.187961i
$79$	13.5899	+	5.62912i	1.52898	+	0.633325i	0.979366	−	0.202093i	$-0.0647743\pi$
$79$	13.5899	+	5.62912i	1.52898	+	0.633325i	0.549615	+	0.835418i	$0.314774\pi$
$80$		0			0
$81$		−	0.135560i		−	0.0150623i
$82$	−3.44210	+	1.42577i	−0.380117	+	0.157449i
$83$	9.82767	+	9.82767i	1.07873	+	1.07873i	0.996624	+	0.0821031i	$0.0261637\pi$
$83$	9.82767	+	9.82767i	1.07873	+	1.07873i	0.0821031	+	0.996624i	$0.473836\pi$
$84$	5.08358			0.554664
$85$		0			0
$86$	−0.790460			−0.0852375
$87$	2.81451	+	2.81451i	0.301748	+	0.301748i
$88$	−2.66450	+	1.10367i	−0.284037	+	0.117652i
$89$		−	0.395163i		−	0.0418872i	−0.999781	−	0.0209436i	$-0.993333\pi$
$89$		−	0.395163i		−	0.0418872i	0.999781	−	0.0209436i	$-0.00666704\pi$
$90$		0			0
$91$	−13.0162	−	5.39148i	−1.36447	−	0.565181i
$92$	−0.628850	+	1.51818i	−0.0655621	+	0.158281i
$93$	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
$97$	−3.42855	−	8.27725i	−0.348116	−	0.840427i	−0.996842	−	0.0794052i	$-0.974698\pi$
$97$	−3.42855	−	8.27725i	−0.348116	−	0.840427i	0.648726	−	0.761022i	$-0.275302\pi$
$98$		−	0.211396i		−	0.0213542i
$99$	−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	$0.224896\pi$
$102$	−1.19163	+	0.567311i	−0.117989	+	0.0561721i
$103$	14.7746			1.45579			0.727894	−	0.685690i	$-0.240499\pi$
$103$	14.7746			1.45579			0.727894	+	0.685690i	$0.240499\pi$
$104$	4.68088	+	4.68088i	0.458998	+	0.458998i
$105$		0			0
$106$			0.837105i			0.0813068i
$107$	−0.562841	−	1.35882i	−0.0544119	−	0.131362i	0.894336	−	0.447396i	$-0.147649\pi$
$107$	−0.562841	−	1.35882i	−0.0544119	−	0.131362i	−0.948748	+	0.316034i	$0.897649\pi$
$108$	−9.12109	−	3.77808i	−0.877677	−	0.363546i
$109$	3.61166	−	8.71931i	0.345934	−	0.835158i	−0.651157	−	0.758943i	$-0.725716\pi$
$109$	3.61166	−	8.71931i	0.345934	−	0.835158i	0.997091	−	0.0762157i	$-0.0242838\pi$
$110$		0			0
$111$	3.83046	−	3.83046i	0.363571	−	0.363571i
$112$	−3.32535	+	8.02809i	−0.314216	+	0.758584i
$113$	−13.8222	−	5.72534i	−1.30028	−	0.538595i	−0.378249	−	0.925704i	$-0.623474\pi$
$113$	−13.8222	−	5.72534i	−1.30028	−	0.538595i	−0.922034	+	0.387109i	$0.873474\pi$
$114$	−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
$118$	2.24505			0.206674
$119$	4.44825	+	9.34350i	0.407771	+	0.856517i
$120$		0			0
$121$	−3.54909	−	3.54909i	−0.322645	−	0.322645i
$122$	0.252603	−	0.104632i	0.0228696	−	0.00947291i
$123$			13.1031i			1.18146i
$124$	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	$-0.835109\pi$
$127$	−4.21071	+	4.21071i	−0.373640	+	0.373640i	0.495161	+	0.868801i	$0.335109\pi$
$128$	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	$0.933556\pi$
$132$			4.95341i			0.431139i
$133$	−16.5354	+	6.84920i	−1.43380	+	0.593901i
$134$	−1.42904	−	1.42904i	−0.123450	−	0.123450i
$135$		0			0
$136$	−0.250931	−	4.85585i	−0.0215172	−	0.416386i
$137$	−7.25998			−0.620262			−0.310131	−	0.950694i	$-0.600373\pi$
$137$	−7.25998			−0.620262			−0.310131	+	0.950694i	$0.600373\pi$
$138$	−0.194835	−	0.194835i	−0.0165855	−	0.0165855i
$139$	9.60207	−	3.97731i	0.814437	−	0.337351i	0.0637140	−	0.997968i	$-0.479705\pi$
$139$	9.60207	−	3.97731i	0.814437	−	0.337351i	0.750723	+	0.660617i	$0.229705\pi$
$140$		0			0
$141$	0.934336	+	2.25569i	0.0786853	+	0.189963i
$142$	−0.0671069	−	0.0277966i	−0.00563149	−	0.00233264i
$143$	5.25343	−	12.6829i	0.439314	−	1.06060i
$144$	4.58843	−	4.58843i	0.382369	−	0.382369i
$145$		0			0
$146$	0.745517	−	1.79984i	0.0616994	−	0.148956i
$147$	−0.686873	−	0.284512i	−0.0566523	−	0.0234661i
$148$	3.72981	+	9.00455i	0.306588	+	0.740170i
$149$			6.01765i			0.492985i	0.969145	+	0.246492i	$0.0792781\pi$
$149$			6.01765i			0.492985i	−0.969145	+	0.246492i	$0.920722\pi$
$150$		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	$0.610656\pi$
$152$	8.40959			0.682108
$153$	−0.398806	−	7.71743i	−0.0322416	−	0.623917i
$154$	−1.85175			−0.149218
$155$		0			0
$156$	10.5042	−	4.35097i	0.841006	−	0.348356i
$157$		−	13.4073i		−	1.07002i	−0.844847	−	0.535008i	$-0.820309\pi$
$157$		−	13.4073i		−	1.07002i	0.844847	−	0.535008i	$-0.179691\pi$
$158$	−1.69823	−	4.09989i	−0.135104	−	0.326170i
$159$	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
$163$	−0.602777	+	1.45523i	−0.0472132	+	0.113983i	−0.945727	−	0.324963i	$-0.894648\pi$
$163$	−0.602777	+	1.45523i	−0.0472132	+	0.113983i	0.898513	+	0.438946i	$0.144648\pi$
$164$	−21.7806	−	9.02182i	−1.70078	−	0.704486i
$165$		0			0
$166$		−	4.19297i		−	0.325438i
$167$	16.2648	−	6.73711i	1.25861	−	0.521333i	0.349127	−	0.937075i	$-0.386478\pi$
$167$	16.2648	−	6.73711i	1.25861	−	0.521333i	0.909482	+	0.415742i	$0.136478\pi$
$168$	−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
$173$	17.4086	−	7.21087i	1.32355	−	0.548232i	0.394741	−	0.918792i	$-0.370834\pi$
$173$	17.4086	−	7.21087i	1.32355	−	0.548232i	0.928808	+	0.370560i	$0.120834\pi$
$174$		−	1.20081i		−	0.0910333i
$175$		0			0
$176$	−7.82253	−	3.24020i	−0.589646	−	0.244239i
$177$	3.02156	−	7.29469i	0.227114	−	0.548303i
$178$	−0.0842980	+	0.0842980i	−0.00631840	+	0.00631840i
$179$	2.34324	−	2.34324i	0.175142	−	0.175142i	−0.614092	−	0.789234i	$-0.710478\pi$
$179$	2.34324	−	2.34324i	0.175142	−	0.175142i	0.789234	+	0.614092i	$0.210478\pi$
$180$		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	$0.825724\pi$
$182$	1.62654	+	3.92681i	0.120567	+	0.291075i
$183$		−	0.961587i		−	0.0710826i
$184$	0.937865	−	0.388477i	0.0691404	−	0.0286389i
$185$		0			0
$186$	−0.719356			−0.0527457
$187$	−9.10425	+	4.33435i	−0.665769	+	0.316959i
$188$	−4.39284			−0.320380
$189$	−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	$0.532764\pi$
$192$	−2.39467	−	5.78124i	−0.172820	−	0.417225i
$193$	−13.6376	−	5.64889i	−0.981658	−	0.406616i	−0.166619	−	0.986021i	$-0.553285\pi$
$193$	−13.6376	−	5.64889i	−0.981658	−	0.406616i	−0.815040	+	0.579405i	$0.803285\pi$
$194$	−1.03435	+	2.49714i	−0.0742618	+	0.179284i
$195$		0			0
$196$	0.945861	−	0.945861i	0.0675615	−	0.0675615i
$197$	0.144044	−	0.347754i	0.0102627	−	0.0247764i	−0.918665	−	0.395037i	$-0.870732\pi$
$197$	0.144044	−	0.347754i	0.0102627	−	0.0247764i	0.928928	+	0.370261i	$0.120732\pi$
$198$	1.27756	+	0.529181i	0.0907919	+	0.0376072i
$199$	2.88162	+	6.95685i	0.204273	+	0.493158i	0.992503	−	0.122223i	$-0.0390022\pi$
$199$	2.88162	+	6.95685i	0.204273	+	0.493158i	−0.788230	+	0.615381i	$0.789002\pi$
$200$		0			0
$201$	−6.56658	+	2.71996i	−0.463171	+	0.191852i
$202$	−3.26136	−	3.26136i	−0.229469	−	0.229469i
$203$	−9.41549			−0.660838
$204$	−7.87014	−	2.79343i	−0.551020	−	0.195579i
$205$		0			0
$206$	−3.15180	−	3.15180i	−0.219596	−	0.219596i
$207$	1.49055	−	0.617408i	0.103601	−	0.0429128i
$208$			19.4345i			1.34754i
$209$	−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
$217$			5.64043i			0.382897i
$218$	−2.63050	+	1.08959i	−0.178160	+	0.0737963i
$219$	−4.84471	−	4.84471i	−0.327375	−	0.327375i
$220$		0			0
$221$	17.1884	+	15.4992i	1.15622	+	1.04259i
$222$	−1.63426			−0.109684
$223$	−4.57010	−	4.57010i	−0.306037	−	0.306037i	0.537333	−	0.843370i	$-0.319432\pi$
$223$	−4.57010	−	4.57010i	−0.306037	−	0.306037i	−0.843370	+	0.537333i	$0.819432\pi$
$224$	7.89101	−	3.26856i	0.527241	−	0.218390i
$225$		0			0
$226$	1.72726	+	4.16997i	0.114896	+	0.277382i
$227$	−2.82763	−	1.17124i	−0.187676	−	0.0777381i	0.286866	−	0.957971i	$-0.407386\pi$
$227$	−2.82763	−	1.17124i	−0.187676	−	0.0777381i	−0.474543	+	0.880233i	$0.657386\pi$
$228$	5.52736	−	13.3442i	0.366058	−	0.883743i
$229$	5.34518	−	5.34518i	0.353219	−	0.353219i	−0.508087	−	0.861306i	$-0.669647\pi$
$229$	5.34518	−	5.34518i	0.353219	−	0.353219i	0.861306	+	0.508087i	$0.169647\pi$
$230$		0			0
$231$	−2.49222	+	6.01676i	−0.163976	+	0.395874i
$232$	4.08727	+	1.69300i	0.268342	+	0.111151i
$233$	−8.55214	−	20.6467i	−0.560270	−	1.35261i	−0.909551	−	0.415593i	$-0.863574\pi$
$233$	−8.55214	−	20.6467i	−0.560270	−	1.35261i	0.349281	−	0.937018i	$-0.386426\pi$
$234$		−	3.17400i		−	0.207491i
$235$		0			0
$236$	10.0452	+	10.0452i	0.653886	+	0.653886i
$237$	−15.6071			−1.01379
$238$	1.04428	−	2.94212i	0.0676904	−	0.190709i
$239$	−3.45981			−0.223797			−0.111898	−	0.993720i	$-0.535693\pi$
$239$	−3.45981			−0.223797			−0.111898	+	0.993720i	$0.535693\pi$
$240$		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	$0.572176\pi$
$242$			1.51422i			0.0973376i
$243$	5.99235	+	14.4668i	0.384410	+	0.928047i
$244$	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
$248$	1.01421	−	2.44851i	0.0644022	−	0.155481i
$249$	−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	$-0.274283\pi$
$252$	8.29643	−	3.43649i	0.522626	−	0.216479i
$253$	−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	0.953684	−	0.300811i	$-0.0972573\pi$
$257$	10.4664	+	10.4664i	0.652873	+	0.652873i	−0.300811	+	0.953684i	$0.597257\pi$
$258$	0.774848	−	0.320953i	0.0482399	−	0.0199816i
$259$			12.8142i			0.796233i
$260$		0			0
$261$	6.49591	+	2.69070i	0.402087	+	0.166550i
$262$	−0.483426	+	1.16709i	−0.0298661	+	0.0721032i
$263$	−17.3357	+	17.3357i	−1.06896	+	1.06896i	−0.0715243	+	0.997439i	$0.522786\pi$
$263$	−17.3357	+	17.3357i	−1.06896	+	1.06896i	−0.997439	+	0.0715243i	$0.977214\pi$
$264$	2.16375	−	2.16375i	0.133170	−	0.133170i
$265$		0			0
$266$	4.98852	+	2.06631i	0.305866	+	0.126694i
$267$	0.160449	+	0.387358i	0.00981932	+	0.0237059i
$268$		−	12.7881i		−	0.781156i
$269$	6.09269	−	2.52367i	0.371478	−	0.153871i	−0.189131	−	0.981952i	$-0.560567\pi$
$269$	6.09269	−	2.52367i	0.371478	−	0.153871i	0.560609	+	0.828081i	$0.310567\pi$
$270$		0			0
$271$	−26.1956			−1.59127			−0.795634	−	0.605778i	$-0.792862\pi$
$271$	−26.1956			−1.59127			−0.795634	+	0.605778i	$0.792862\pi$
$272$	9.55957	−	10.6014i	0.579634	−	0.642805i
$273$	14.9482			0.904707
$274$	1.54873	+	1.54873i	0.0935624	+	0.0935624i
$275$		0			0
$276$		−	1.74353i		−	0.104948i
$277$	−3.66038	−	8.83695i	−0.219931	−	0.530961i	0.774949	−	0.632024i	$-0.217776\pi$
$277$	−3.66038	−	8.83695i	−0.219931	−	0.530961i	−0.994880	+	0.101063i	$0.967776\pi$
$278$	−2.89682	−	1.19990i	−0.173740	−	0.0719653i
$279$	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	$0.129228\pi$
$282$	0.281877	−	0.680511i	0.0167855	−	0.0405238i
$283$	−15.5612	−	6.44566i	−0.925017	−	0.383155i	−0.131231	−	0.991352i	$-0.541893\pi$
$283$	−15.5612	−	6.44566i	−0.925017	−	0.383155i	−0.793786	+	0.608197i	$0.791893\pi$
$284$	−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
$288$	−6.37822			−0.375840
$289$	−1.75231	−	16.9094i	−0.103077	−	0.994673i
$290$		0			0
$291$	6.72166	+	6.72166i	0.394031	+	0.394031i
$292$	11.3888	−	4.71741i	0.666482	−	0.276066i
$293$			20.8806i			1.21986i	0.792456	+	0.609930i	$0.208802\pi$
$293$			20.8806i			1.21986i	−0.792456	+	0.609930i	$0.791198\pi$
$294$	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
$302$		−	3.14306i		−	0.180863i
$303$	−14.9863	+	6.20752i	−0.860940	+	0.356613i
$304$	17.4579	+	17.4579i	1.00128	+	1.00128i
$305$		0			0
$306$	−1.56124	+	1.73139i	−0.0892504	+	0.0989772i
$307$	29.9529			1.70950			0.854751	−	0.519038i	$-0.173710\pi$
$307$	29.9529			1.70950			0.854751	+	0.519038i	$0.173710\pi$
$308$	−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	$0.873102\pi$
$312$	−6.48902	−	2.68784i	−0.367369	−	0.152169i
$313$	12.4082	−	29.9561i	0.701354	−	1.69322i	−0.0191979	−	0.999816i	$-0.506111\pi$
$313$	12.4082	−	29.9561i	0.701354	−	1.69322i	0.720551	−	0.693402i	$-0.243889\pi$
$314$	−2.86010	+	2.86010i	−0.161405	+	0.161405i
$315$		0			0
$316$	10.7459	−	25.9429i	0.604504	−	1.45940i
$317$	30.8937	+	12.7966i	1.73516	+	0.718728i	0.999127	+	0.0417842i	$0.0133042\pi$
$317$	30.8937	+	12.7966i	1.73516	+	0.718728i	0.736035	+	0.676943i	$0.236696\pi$
$318$	−0.339892	−	0.820571i	−0.0190602	−	0.0460154i
$319$		−	9.17441i		−	0.513668i
$320$		0			0
$321$	1.10345	+	1.10345i	0.0615886	+	0.0615886i
$322$	0.651789			0.0363228
$323$	29.3630	−	1.51736i	1.63380	−	0.0844283i
$324$	−0.258783			−0.0143768
$325$		0			0
$326$	0.439025	−	0.181850i	0.0243153	−	0.0100717i
$327$			10.0135i			0.553750i
$328$	5.57330	+	13.4551i	0.307734	+	0.742935i
$329$	−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
$333$	3.66194	−	8.84071i	0.200673	−	0.484468i
$334$	−4.90688	−	2.03250i	−0.268493	−	0.111213i
$335$		0			0
$336$		−	9.21973i		−	0.502977i
$337$	−15.8506	+	6.56551i	−0.863434	+	0.357646i	−0.770050	−	0.637984i	$-0.779769\pi$
$337$	−15.8506	+	6.56551i	−0.863434	+	0.357646i	−0.0933847	+	0.995630i	$0.529769\pi$
$338$	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
$343$	17.8563	−	7.39633i	0.964151	−	0.399364i
$344$			3.08990i			0.166596i
$345$		0			0
$346$	−5.25194	−	2.17542i	−0.282346	−	0.116951i
$347$	−11.8288	+	28.5572i	−0.635003	+	1.53303i	0.198257	+	0.980150i	$0.436472\pi$
$347$	−11.8288	+	28.5572i	−0.635003	+	1.53303i	−0.833260	+	0.552882i	$0.813528\pi$
$348$	5.37287	−	5.37287i	0.288016	−	0.288016i
$349$	2.38415	−	2.38415i	0.127621	−	0.127621i	−0.640411	−	0.768032i	$-0.721236\pi$
$349$	2.38415	−	2.38415i	0.127621	−	0.127621i	0.768032	+	0.640411i	$0.221236\pi$
$350$		0			0
$351$	−26.8205	−	11.1094i	−1.43157	−	0.592976i
$352$	3.18487	+	7.68896i	0.169754	+	0.409823i
$353$			23.7918i			1.26631i	0.774025	+	0.633155i	$0.218240\pi$
$353$			23.7918i			1.26631i	−0.774025	+	0.633155i	$0.781760\pi$
$354$	−2.20071	+	0.911565i	−0.116967	+	0.0484491i
$355$		0			0
$356$	−0.754360			−0.0399810
$357$	−8.15416	−	7.35282i	−0.431564	−	0.389152i
$358$	−0.999743			−0.0528381
$359$	22.4244	+	22.4244i	1.18351	+	1.18351i	0.978827	+	0.204688i	$0.0656178\pi$
$359$	22.4244	+	22.4244i	1.18351	+	1.18351i	0.204688	+	0.978827i	$0.434382\pi$
$360$		0			0
$361$			31.8521i			1.67643i
$362$	1.83164	+	4.42197i	0.0962689	+	0.232414i
$363$	4.92004	+	2.03795i	0.258235	+	0.106964i
$364$	−10.2923	+	24.8477i	−0.539461	+	1.30237i
$365$		0			0
$366$	−0.205130	+	0.205130i	−0.0107223	+	0.0107223i
$367$	1.72853	−	4.17304i	0.0902286	−	0.217831i	−0.872323	−	0.488930i	$-0.837387\pi$
$367$	1.72853	−	4.17304i	0.0902286	−	0.217831i	0.962551	+	0.271099i	$0.0873872\pi$
$368$	2.75341	+	1.14050i	0.143532	+	0.0594528i
$369$	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
$373$	5.12748			0.265491			0.132745	−	0.991150i	$-0.457621\pi$
$373$	5.12748			0.265491			0.132745	+	0.991150i	$0.457621\pi$
$374$	2.86679	+	1.01754i	0.148238	+	0.0526156i
$375$		0			0
$376$	1.91888	+	1.91888i	0.0989586	+	0.0989586i
$377$	−19.4552	+	8.05860i	−1.00199	+	0.415039i
$378$			3.91589i			0.201412i
$379$	2.11629	+	5.10917i	0.108706	+	0.262441i	0.968867	−	0.247584i	$-0.0796365\pi$
$379$	2.11629	+	5.10917i	0.108706	+	0.262441i	−0.860160	+	0.510024i	$0.829636\pi$
$380$		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	−0.972254	−	0.233928i	$-0.924842\pi$
$383$	−14.4493	+	14.4493i	−0.738326	+	0.738326i	0.233928	+	0.972254i	$0.424842\pi$
$384$	−3.48596	+	8.41585i	−0.177892	+	0.429469i
$385$		0			0
$386$	1.70420	+	4.11429i	0.0867413	+	0.209412i
$387$			4.91079i			0.249629i
$388$	−15.8011	+	6.54505i	−0.802181	+	0.332274i
$389$	−3.66726	−	3.66726i	−0.185937	−	0.185937i	0.608000	−	0.793937i	$-0.291972\pi$
$389$	−3.66726	−	3.66726i	−0.185937	−	0.185937i	−0.793937	+	0.608000i	$0.791972\pi$
$390$		0			0
$391$	3.20456	−	1.52563i	0.162062	−	0.0771543i
$392$	−0.826343			−0.0417366
$393$	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
$397$	5.70360	+	2.36251i	0.286255	+	0.118571i	0.521191	−	0.853440i	$-0.325488\pi$
$397$	5.70360	+	2.36251i	0.286255	+	0.118571i	−0.234936	+	0.972011i	$0.575488\pi$
$398$	0.869348	−	2.09879i	0.0435765	−	0.105203i
$399$	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	$0.201202\pi$
$402$	1.98105	+	0.820577i	0.0988058	+	0.0409267i
$403$	4.82757	+	11.6548i	0.240478	+	0.580566i
$404$		−	29.1850i		−	1.45201i
$405$		0			0
$406$	2.00856	+	2.00856i	0.0996831	+	0.0996831i
$407$	−12.4860			−0.618910
$408$	2.21761	+	4.65806i	0.109788	+	0.230608i
$409$	14.3886			0.711469			0.355734	−	0.934587i	$-0.384231\pi$
$409$	14.3886			0.711469			0.355734	+	0.934587i	$0.384231\pi$
$410$		0			0
$411$	7.11659	−	2.94779i	0.351035	−	0.145404i
$412$		−	28.2046i		−	1.38954i
$413$	7.14753	+	17.2557i	0.351707	+	0.849096i
$414$	−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
$418$	−2.01340	+	4.86079i	−0.0984789	+	0.237749i
$419$	19.6078	+	8.12181i	0.957903	+	0.396776i	0.806196	−	0.591649i	$-0.201523\pi$
$419$	19.6078	+	8.12181i	0.957903	+	0.396776i	0.151707	+	0.988425i	$0.451523\pi$
$420$		0			0
$421$			20.1672i			0.982887i	0.870909	+	0.491444i	$0.163531\pi$
$421$			20.1672i			0.982887i	−0.870909	+	0.491444i	$0.836469\pi$
$422$	−2.42279	+	1.00355i	−0.117939	+	0.0488521i
$423$	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
$428$	−2.59397	+	1.07446i	−0.125384	+	0.0519358i
$429$			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	$0.784699\pi$
$432$	−6.85204	+	16.5423i	−0.329669	+	0.795891i
$433$	−12.8860	+	12.8860i	−0.619263	+	0.619263i	−0.945342	−	0.326080i	$-0.894272\pi$
$433$	−12.8860	+	12.8860i	−0.619263	+	0.619263i	0.326080	+	0.945342i	$0.394272\pi$
$434$	1.20324	−	1.20324i	0.0577575	−	0.0577575i
$435$		0			0
$436$	−16.6450	−	6.89460i	−0.797152	−	0.330191i
$437$	2.34909	+	5.67120i	0.112372	+	0.271290i
$438$			2.06699i			0.0987648i
$439$	13.6117	−	5.63815i	0.649651	−	0.269094i	−0.0334251	−	0.999441i	$-0.510642\pi$
$439$	13.6117	−	5.63815i	0.649651	−	0.269094i	0.683077	+	0.730347i	$0.260642\pi$
$440$		0			0
$441$	−1.31331			−0.0625386
$442$	−0.360341	−	6.97307i	−0.0171397	−	0.331675i
$443$	23.3335			1.10861			0.554305	−	0.832314i	$-0.312984\pi$
$443$	23.3335			1.10861			0.554305	+	0.832314i	$0.312984\pi$
$444$	−7.31228	−	7.31228i	−0.347026	−	0.347026i
$445$		0			0
$446$			1.94983i			0.0923272i
$447$	−2.44336	−	5.89879i	−0.115567	−	0.279003i
$448$	13.6756	+	5.66461i	0.646110	+	0.267628i
$449$	−0.655009	+	1.58133i	−0.0309118	+	0.0746277i	−0.938582	−	0.345057i	$-0.887859\pi$
$449$	−0.655009	+	1.58133i	−0.0309118	+	0.0746277i	0.907670	+	0.419685i	$0.137859\pi$
$450$		0			0
$451$	21.3559	−	21.3559i	1.00561	−	1.00561i
$452$	−10.9296	+	26.3864i	−0.514085	+	1.24111i
$453$	−10.2125	−	4.23016i	−0.479826	−	0.198750i
$454$	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	0.453886	−	0.891060i	$-0.350037\pi$
$457$	−9.34572	−	9.34572i	−0.437174	−	0.437174i	−0.891060	+	0.453886i	$0.850037\pi$
$458$	−2.28052			−0.106562
$459$	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	$0.988933\pi$
$462$	1.81518	−	0.751871i	0.0844497	−	0.0349802i
$463$		−	9.80371i		−	0.455617i	−0.973706	−	0.227808i	$-0.926844\pi$
$463$		−	9.80371i		−	0.455617i	0.973706	−	0.227808i	$-0.0731560\pi$
$464$	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	$-0.647471\pi$
$467$	9.67459	−	9.67459i	0.447687	−	0.447687i	0.894585	+	0.446898i	$0.147471\pi$
$468$	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
$472$		−	8.77589i		−	0.403943i
$473$	5.91997	−	2.45213i	0.272201	−	0.112749i
$474$	3.32938	+	3.32938i	0.152923	+	0.152923i
$475$		0			0
$476$	17.8366	−	8.49165i	0.817539	−	0.389214i
$477$	5.20057			0.238118
$478$	0.738063	+	0.738063i	0.0337582	+	0.0337582i
$479$	−10.1719	+	4.21334i	−0.464766	+	0.192513i	−0.602763	−	0.797920i	$-0.705934\pi$
$479$	−10.1719	+	4.21334i	−0.464766	+	0.192513i	0.137997	+	0.990433i	$0.455934\pi$
$480$		0			0
$481$	10.9675	+	26.4778i	0.500074	+	1.20728i
$482$	5.02431	+	2.08114i	0.228851	+	0.0947932i
$483$	0.877226	−	2.11781i	0.0399151	−	0.0963637i
$484$	−6.77516	+	6.77516i	−0.307962	+	0.307962i
$485$		0			0
$486$	1.80781	−	4.36445i	0.0820041	−	0.197975i
$487$	−9.32586	−	3.86290i	−0.422595	−	0.175045i	0.161243	−	0.986915i	$-0.448450\pi$
$487$	−9.32586	−	3.86290i	−0.422595	−	0.175045i	−0.583838	+	0.811870i	$0.698450\pi$
$488$	−0.409004	−	0.987423i	−0.0185147	−	0.0446985i
$489$		−	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	$0.875959\pi$
$492$	25.0136			1.12770
$493$	14.5766	+	5.17382i	0.656497	+	0.233017i
$494$	12.0763			0.543338
$495$		0			0
$496$	7.18841	−	2.97754i	0.322769	−	0.133695i
$497$		−	0.604284i		−	0.0271059i
$498$	1.70248	+	4.11016i	0.0762901	+	0.184180i
$499$	−28.9724	−	12.0008i	−1.29698	−	0.537227i	−0.375923	−	0.926651i	$-0.622674\pi$
$499$	−28.9724	−	12.0008i	−1.29698	−	0.537227i	−0.921059	+	0.389424i	$0.872674\pi$
$500$		0			0
$501$	−13.2081	+	13.2081i	−0.590094	+	0.590094i
$502$	−5.12999	+	5.12999i	−0.228963	+	0.228963i
$503$	3.31991	−	8.01498i	0.148028	−	0.357370i	−0.832422	−	0.554143i	$-0.813046\pi$
$503$	3.31991	−	8.01498i	0.148028	−	0.357370i	0.980449	+	0.196773i	$0.0630461\pi$
$504$	−5.12518	−	2.12292i	−0.228293	−	0.0945623i
$505$		0			0
$506$			0.635099i			0.0282336i
$507$	18.1442	−	7.51556i	0.805811	−	0.333778i
$508$	8.03817	+	8.03817i	0.356636	+	0.356636i
$509$	−14.1196			−0.625840			−0.312920	−	0.949780i	$-0.601307\pi$
$509$	−14.1196			−0.625840			−0.312920	+	0.949780i	$0.601307\pi$
$510$		0			0
$511$	16.2072			0.716963
$512$	−14.1053	−	14.1053i	−0.623374	−	0.623374i
$513$	−34.0721	+	14.1131i	−1.50432	+	0.623109i
$514$		−	4.46546i		−	0.196963i
$515$		0			0
$516$	4.90301	+	2.03089i	0.215843	+	0.0894051i
$517$	2.15359	−	5.19922i	0.0947147	−	0.228662i
$518$	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	$0.751151\pi$
$522$	−0.811747	−	1.95973i	−0.0355292	−	0.0857751i
$523$		−	26.3853i		−	1.15375i	−0.816833	−	0.576875i	$-0.804272\pi$
$523$		−	26.3853i		−	1.15375i	0.816833	−	0.576875i	$-0.195728\pi$
$524$	−7.38502	+	3.05898i	−0.322616	+	0.133632i
$525$		0			0
$526$	7.39626			0.322492
$527$	3.09942	−	8.73223i	0.135013	−	0.380382i
$528$	8.98366			0.390963
$529$	−15.7395	−	15.7395i	−0.684326	−	0.684326i
$530$		0			0
$531$		−	13.9476i		−	0.605272i
$532$	13.0750	+	31.5659i	0.566874	+	1.36856i
$533$	−64.0457	−	26.5286i	−2.77413	−	1.14908i
$534$	0.0484053	−	0.116861i	0.00209470	−	0.00505706i
$535$		0			0
$536$	−5.58609	+	5.58609i	−0.241282	+	0.241282i
$537$	−1.34553	+	3.24839i	−0.0580638	+	0.140178i
$538$	−1.83808	−	0.761359i	−0.0792454	−	0.0328245i
$539$	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
$543$	16.8331			0.722379
$544$	−14.0125	+	0.724113i	−0.600783	+	0.0310461i
$545$		0			0
$546$	−3.18882	−	3.18882i	−0.136469	−	0.136469i
$547$	20.9386	−	8.67306i	0.895271	−	0.370833i	0.112871	−	0.993610i	$-0.463995\pi$
$547$	20.9386	−	8.67306i	0.895271	−	0.370833i	0.782400	+	0.622776i	$0.213995\pi$
$548$			13.8592i			0.592035i
$549$	−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
$557$			11.4954i			0.487076i	0.969891	+	0.243538i	$0.0783080\pi$
$557$			11.4954i			0.487076i	−0.969891	+	0.243538i	$0.921692\pi$
$558$	−1.17399	+	0.486284i	−0.0496991	+	0.0205860i
$559$	−10.4000	−	10.4000i	−0.439871	−	0.439871i
$560$		0			0
$561$	7.16455	−	7.94537i	0.302487	−	0.335454i
$562$	−3.74614			−0.158021
$563$	−9.57715	−	9.57715i	−0.403629	−	0.403629i	0.475881	−	0.879510i	$-0.342129\pi$
$563$	−9.57715	−	9.57715i	−0.403629	−	0.403629i	−0.879510	+	0.475881i	$0.842129\pi$
$564$	4.30607	−	1.78363i	0.181318	−	0.0751045i
$565$		0			0
$566$	1.94457	+	4.69461i	0.0817364	+	0.197329i
$567$	−0.314336	−	0.130202i	−0.0132009	−	0.00546797i
$568$	−0.108656	+	0.262320i	−0.00455912	+	0.0110067i
$569$	−11.2263	+	11.2263i	−0.470632	+	0.470632i	−0.902119	−	0.431487i	$-0.857989\pi$
$569$	−11.2263	+	11.2263i	−0.470632	+	0.470632i	0.431487	+	0.902119i	$0.357989\pi$
$570$		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	$0.101398\pi$
$572$	−24.2115	−	10.0287i	−1.01233	−	0.419322i
$573$	−11.1636	−	26.9512i	−0.466364	−	1.12590i
$574$			9.35092i			0.390300i
$575$		0			0
$576$	−7.81622	−	7.81622i	−0.325676	−	0.325676i
$577$	−18.5078			−0.770492			−0.385246	−	0.922814i	$-0.625883\pi$
$577$	−18.5078			−0.770492			−0.385246	+	0.922814i	$0.625883\pi$
$578$	−3.23339	+	3.98101i	−0.134491	+	0.165588i
$579$	15.6619			0.650887
$580$		0			0
$581$	32.2275	−	13.3491i	1.33702	−	0.553813i
$582$		−	2.86779i		−	0.118874i
$583$	−2.59683	−	6.26931i	−0.107550	−	0.259648i
$584$	−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	$-0.658582\pi$
$587$	9.70579	−	9.70579i	0.400601	−	0.400601i	0.878445	+	0.477844i	$0.158582\pi$
$588$	−0.543129	+	1.31123i	−0.0223983	+	0.0540742i
$589$	14.8059	+	6.13282i	0.610068	+	0.252699i
$590$		0			0
$591$			0.399372i			0.0164280i
$592$	16.3309	−	6.76450i	0.671197	−	0.278019i
$593$	14.3711	+	14.3711i	0.590150	+	0.590150i	0.937672	−	0.347522i	$-0.112977\pi$
$593$	14.3711	+	14.3711i	0.590150	+	0.590150i	−0.347522	+	0.937672i	$0.612977\pi$
$594$	−3.81563			−0.156557
$595$		0			0
$596$	11.4876			0.470550
$597$	−5.64942	−	5.64942i	−0.231215	−	0.231215i
$598$	1.34679	−	0.557858i	0.0550742	−	0.0228125i
$599$		−	26.7277i		−	1.09206i	−0.837764	−	0.546032i	$-0.816138\pi$
$599$		−	26.7277i		−	1.09206i	0.837764	−	0.546032i	$-0.183862\pi$
$600$		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	$0.434216\pi$
$602$	−0.759216	+	1.83291i	−0.0309433	+	0.0747038i
$603$	−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
$607$	9.03844	+	21.8207i	0.366859	+	0.885676i	0.994261	+	0.106981i	$0.0341183\pi$
$607$	9.03844	+	21.8207i	0.366859	+	0.885676i	−0.627402	+	0.778696i	$0.715882\pi$
$608$		−	24.2676i		−	0.984180i
$609$	9.22953	−	3.82300i	0.373999	−	0.154916i
$610$		0			0
$611$	−12.9171			−0.522570
$612$	−14.7325	+	0.761315i	−0.595524	+	0.0307744i
$613$	−12.0396			−0.486275			−0.243137	−	0.969992i	$-0.578177\pi$
$613$	−12.0396			−0.486275			−0.243137	+	0.969992i	$0.578177\pi$
$614$	−6.38969	−	6.38969i	−0.257867	−	0.257867i
$615$		0			0
$616$			7.23847i			0.291646i
$617$	−5.94989	−	14.3643i	−0.239534	−	0.578285i	0.757701	−	0.652602i	$-0.226322\pi$
$617$	−5.94989	−	14.3643i	−0.239534	−	0.578285i	−0.997235	+	0.0743165i	$0.976322\pi$
$618$	4.36928	+	1.80981i	0.175758	+	0.0728014i
$619$	12.8172	−	30.9434i	0.515166	−	1.24372i	−0.425676	−	0.904876i	$-0.639964\pi$
$619$	12.8172	−	30.9434i	0.515166	−	1.24372i	0.940842	−	0.338845i	$-0.110036\pi$
$620$		0			0
$621$	−3.14788	+	3.14788i	−0.126320	+	0.126320i
$622$	0.0242820	−	0.0586218i	0.000973618	−	0.00235052i
$623$	−0.916299	−	0.379543i	−0.0367107	−	0.0152061i
$624$	−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
$628$	−25.5942			−1.02132
$629$	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	$0.753451\pi$
$632$	−16.0264	+	6.63836i	−0.637496	+	0.264060i
$633$			9.22284i			0.366575i
$634$	−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	$0.796093\pi$
$642$		−	0.470786i		−	0.0185805i
$643$	−35.4438	+	14.6813i	−1.39777	+	0.578975i	−0.949171	−	0.314760i	$-0.898076\pi$
$643$	−35.4438	+	14.6813i	−1.39777	+	0.578975i	−0.448597	+	0.893734i	$0.648076\pi$
$644$	2.91634	+	2.91634i	0.114920	+	0.114920i
$645$		0			0
$646$	−6.58754	−	5.94016i	−0.259183	−	0.233712i
$647$	−19.6602			−0.772923			−0.386462	−	0.922305i	$-0.626303\pi$
$647$	−19.6602			−0.772923			−0.386462	+	0.922305i	$0.626303\pi$
$648$	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
$652$	2.77802	+	1.15069i	0.108796	+	0.0450646i
$653$	−11.9119	+	28.7578i	−0.466147	+	1.12538i	0.499684	+	0.866208i	$0.333449\pi$
$653$	−11.9119	+	28.7578i	−0.466147	+	1.12538i	−0.965831	+	0.259171i	$0.916551\pi$
$654$	2.13614	−	2.13614i	0.0835296	−	0.0835296i
$655$		0			0
$656$	−16.3623	+	39.5020i	−0.638839	+	1.54229i
$657$	−11.1816	−	4.63158i	−0.436236	−	0.180695i
$658$	0.666782	+	1.60975i	0.0259939	+	0.0627548i
$659$			4.15956i			0.162033i	0.996713	+	0.0810167i	$0.0258167\pi$
$659$			4.15956i			0.162033i	−0.996713	+	0.0810167i	$0.974183\pi$
$660$		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	$0.707404\pi$
$662$	−0.267095			−0.0103810
$663$	−23.1421	−	8.21405i	−0.898764	−	0.319007i
$664$	−16.3903			−0.636066
$665$		0			0
$666$	−2.66713	+	1.10476i	−0.103349	+	0.0428086i
$667$			3.22925i			0.125037i
$668$	−12.8610	−	31.0493i	−0.497608	−	1.20133i
$669$	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
$673$	6.61298	−	15.9651i	0.254912	−	0.615411i	−0.743676	−	0.668540i	$-0.766919\pi$
$673$	6.61298	−	15.9651i	0.254912	−	0.615411i	0.998588	+	0.0531290i	$0.0169194\pi$
$674$	4.78190	+	1.98073i	0.184192	+	0.0762948i
$675$		0			0
$676$			35.3348i			1.35903i
$677$	−7.51469	+	3.11269i	−0.288813	+	0.119630i	−0.522386	−	0.852709i	$-0.674958\pi$
$677$	−7.51469	+	3.11269i	−0.288813	+	0.119630i	0.233573	+	0.972339i	$0.424958\pi$
$678$	−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
$683$	26.9190	−	11.1502i	1.03003	−	0.426652i	0.197306	−	0.980342i	$-0.436781\pi$
$683$	26.9190	−	11.1502i	1.03003	−	0.426652i	0.832723	+	0.553690i	$0.186781\pi$
$684$		−	25.5143i		−	0.975566i
$685$		0			0
$686$	−5.38702	−	2.23138i	−0.205677	−	0.0851943i
$687$	−3.06929	+	7.40992i	−0.117101	+	0.282706i
$688$	−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	$0.373198\pi$
$692$	−13.7654	−	33.2327i	−0.523283	−	1.26332i
$693$			11.5041i			0.437006i
$694$	8.61534	−	3.56859i	0.327034	−	0.135462i
$695$		0			0
$696$	−4.69395			−0.177924
$697$	21.8875	+	45.9744i	0.829048	+	1.74140i
$698$	−1.01720			−0.0385015
$699$	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	$0.910820\pi$
$702$	3.35156	+	8.09139i	0.126497	+	0.305390i
$703$	33.6368	+	13.9328i	1.26863	+	0.525486i
$704$	−5.51956	+	13.3254i	−0.208026	+	0.502220i
$705$		0			0
$706$	5.07538	−	5.07538i	0.191014	−	0.191014i
$707$	14.6840	−	35.4502i	0.552247	−	1.33324i
$708$	−13.9255	−	5.76812i	−0.523351	−	0.216779i
$709$	−10.8526	−	26.2006i	−0.407579	−	0.983983i	−0.985773	−	0.168083i	$-0.946242\pi$
$709$	−10.8526	−	26.2006i	−0.407579	−	0.983983i	0.578194	−	0.815899i	$-0.303758\pi$
$710$		0			0
$711$	−25.4708	+	10.5504i	−0.955231	+	0.395670i
$712$	0.329520	+	0.329520i	0.0123493	+	0.0123493i
$713$	1.93451			0.0724480
$714$	0.170946	+	3.30802i	0.00639748	+	0.123800i
$715$		0			0
$716$	−4.47321	−	4.47321i	−0.167172	−	0.167172i
$717$	3.39148	−	1.40480i	0.126657	−	0.0524631i
$718$		−	9.56736i		−	0.357051i
$719$	−4.83536	−	11.6736i	−0.180329	−	0.435352i	0.807706	−	0.589586i	$-0.200709\pi$
$719$	−4.83536	−	11.6736i	−0.180329	−	0.435352i	−0.988034	+	0.154234i	$0.950709\pi$
$720$		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
$727$		−	15.0242i		−	0.557218i	−0.960405	−	0.278609i	$-0.910127\pi$
$727$		−	15.0242i		−	0.557218i	0.960405	−	0.278609i	$-0.0898734\pi$
$728$	15.3498	−	6.35811i	0.568903	−	0.235647i
$729$	−11.4604	−	11.4604i	−0.424460	−	0.424460i
$730$		0			0
$731$	0.557517	+	10.7887i	0.0206205	+	0.399035i
$732$	−1.83566			−0.0678478
$733$	1.24931	+	1.24931i	0.0461442	+	0.0461442i	0.729802	−	0.683658i	$-0.239612\pi$
$733$	1.24931	+	1.24931i	0.0461442	+	0.0461442i	−0.683658	+	0.729802i	$0.739612\pi$
$734$	−1.25895	+	0.521475i	−0.0464688	+	0.0192480i
$735$		0			0
$736$	−1.12103	−	2.70640i	−0.0413216	−	0.0997592i
$737$	15.1356	+	6.26935i	0.557526	+	0.230935i
$738$	2.67224	−	6.45136i	0.0983665	−	0.237478i
$739$	−13.9406	+	13.9406i	−0.512812	+	0.512812i	−0.915387	−	0.402575i	$-0.868115\pi$
$739$	−13.9406	+	13.9406i	−0.512812	+	0.512812i	0.402575	+	0.915387i	$0.368115\pi$
$740$		0			0
$741$	16.2532	−	39.2386i	0.597075	−	1.44147i
$742$	1.94107	+	0.804017i	0.0712589	+	0.0295164i
$743$	10.8535	+	26.2027i	0.398176	+	0.961282i	0.988099	+	0.153822i	$0.0491583\pi$
$743$	10.8535	+	26.2027i	0.398176	+	0.961282i	−0.589922	+	0.807460i	$0.700842\pi$
$744$			2.81195i			0.103091i
$745$		0			0
$746$	−1.09382	−	1.09382i	−0.0400475	−	0.0400475i
$747$	−26.0491			−0.953087
$748$	8.27422	+	17.3799i	0.302535	+	0.635472i
$749$	−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	$0.268782\pi$
$752$			7.96698i			0.290526i
$753$	9.76418	+	23.5728i	0.355826	+	0.859041i
$754$	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	0.138743	−	0.990328i	$-0.455694\pi$
$757$	31.0649	−	31.0649i	1.12907	−	1.12907i	0.990328	−	0.138743i	$-0.0443062\pi$
$758$	0.638456	−	1.54137i	0.0231898	−	0.0559851i
$759$	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	$-0.0773657\pi$
$762$	−1.76101	+	0.729435i	−0.0637948	+	0.0264247i
$763$	−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
$768$	−9.02353	+	3.73767i	−0.325609	+	0.134871i
$769$			24.8906i			0.897578i	0.893638	+	0.448789i	$0.148144\pi$
$769$			24.8906i			0.897578i	−0.893638	+	0.448789i	$0.851856\pi$
$770$		0			0
$771$	−14.5093	−	6.00995i	−0.522540	−	0.216443i
$772$	−10.7836	+	26.0340i	−0.388112	+	0.936985i
$773$	37.9750	−	37.9750i	1.36587	−	1.36587i	0.499624	−	0.866242i	$-0.333471\pi$
$773$	37.9750	−	37.9750i	1.36587	−	1.36587i	0.866242	−	0.499624i	$-0.166529\pi$
$774$	1.04759	−	1.04759i	0.0376549	−	0.0376549i
$775$		0			0
$776$	9.76127	+	4.04325i	0.350409	+	0.145144i
$777$	−5.20296	−	12.5611i	−0.186655	−	0.450626i
$778$			1.56463i			0.0560949i
$779$	−81.3621	+	33.7013i	−2.91510	+	1.20747i
$780$		0			0
$781$	0.588811			0.0210693
$782$	−1.00907	−	0.358158i	−0.0360841	−	0.0128077i
$783$	−19.4011			−0.693339
$784$	−1.71544	−	1.71544i	−0.0612658	−	0.0612658i
$785$		0			0
$786$		−	1.34033i		−	0.0478079i
$787$	−19.6997	−	47.5592i	−0.702217	−	1.69530i	−0.718588	−	0.695436i	$-0.755211\pi$
$787$	−19.6997	−	47.5592i	−0.702217	−	1.69530i	0.0163714	−	0.999866i	$-0.494789\pi$
$788$	−0.663857	−	0.274979i	−0.0236489	−	0.00979571i
$789$	9.95443	−	24.0321i	0.354387	−	0.855566i
$790$		0			0
$791$	−26.5517	+	26.5517i	−0.944070	+	0.944070i
$792$	2.06856	−	4.99394i	0.0735031	−	0.177452i
$793$	4.70008	+	1.94684i	0.166905	+	0.0691342i
$794$	−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	0.429311	−	0.903157i	$-0.358756\pi$
$797$	−13.3772	−	13.3772i	−0.473846	−	0.473846i	−0.903157	+	0.429311i	$0.858756\pi$
$798$	−5.72898			−0.202804
$799$	7.04620	+	6.35374i	0.249276	+	0.224779i
$800$		0			0
$801$	0.523707	+	0.523707i	0.0185043	+	0.0185043i
$802$	2.64687	−	1.09637i	0.0934642	−	0.0387141i
$803$			15.7922i			0.557294i
$804$	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	$-0.696629\pi$
$809$	11.5703	−	27.9333i	0.406791	−	0.982081i	0.985976	−	0.166885i	$-0.0533709\pi$
$810$		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	$0.972482\pi$
$812$			17.9740i			0.630765i
$813$	25.6782	−	10.6362i	0.900573	−	0.373030i
$814$	2.66358	+	2.66358i	0.0933586	+	0.0933586i
$815$		0			0
$816$	−5.06624	+	14.2735i	−0.177354	+	0.499673i
$817$	−18.6844			−0.653683
$818$	−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	$-0.401787\pi$
$822$	−2.14698	−	0.889309i	−0.0748846	−	0.0310182i
$823$	−9.67025	+	23.3460i	−0.337084	+	0.813792i	0.660909	+	0.750466i	$0.270171\pi$
$823$	−9.67025	+	23.3460i	−0.337084	+	0.813792i	−0.997993	+	0.0633260i	$0.979829\pi$
$824$	−12.3203	+	12.3203i	−0.429199	+	0.429199i
$825$		0			0
$826$	2.15632	−	5.20581i	0.0750278	−	0.181133i
$827$	20.3879	+	8.44496i	0.708958	+	0.293660i	0.707874	−	0.706339i	$-0.249655\pi$
$827$	20.3879	+	8.44496i	0.708958	+	0.293660i	0.00108492	+	0.999999i	$0.499655\pi$
$828$	−1.17862	−	2.84544i	−0.0409599	−	0.0988860i
$829$			20.9555i			0.727816i	0.931435	+	0.363908i	$0.118558\pi$
$829$			20.9555i			0.727816i	−0.931435	+	0.363908i	$0.881442\pi$
$830$		0			0
$831$	7.17617	+	7.17617i	0.248939	+	0.248939i
$832$	33.1060			1.14774
$833$	−2.88526	+	0.149099i	−0.0999684	+	0.00516597i
$834$	3.32680			0.115198
$835$		0			0
$836$	−30.7576	+	12.7402i	−1.06378	+	0.440630i
$837$			11.6224i			0.401728i
$838$	−2.45024	−	5.91541i	−0.0846422	−	0.204344i
$839$	18.6855	+	7.73980i	0.645096	+	0.267207i	0.681152	−	0.732142i	$-0.261479\pi$
$839$	18.6855	+	7.73980i	0.645096	+	0.267207i	−0.0360558	+	0.999350i	$0.511479\pi$
$840$		0			0
$841$	10.5548	−	10.5548i	0.363958	−	0.363958i
$842$	4.30216	−	4.30216i	0.148262	−	0.148262i
$843$	−5.04183	+	12.1721i	−0.173650	+	0.419228i
$844$	−15.3307	−	6.35018i	−0.527704	−	0.218582i
$845$		0			0
$846$		−	1.30115i		−	0.0447343i
$847$	−11.6384	+	4.82078i	−0.399900	+	0.165644i
$848$	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
$853$	−10.6192	+	4.39863i	−0.363595	+	0.150606i	−0.556999	−	0.830513i	$-0.688047\pi$
$853$	−10.6192	+	4.39863i	−0.363595	+	0.150606i	0.193404	+	0.981119i	$0.438047\pi$
$854$		−	0.686230i		−	0.0234823i
$855$		0			0
$856$	1.60244	+	0.663753i	0.0547703	+	0.0226866i
$857$	10.7482	−	25.9484i	0.367151	−	0.886380i	−0.627064	−	0.778968i	$-0.715744\pi$
$857$	10.7482	−	25.9484i	0.367151	−	0.886380i	0.994215	−	0.107412i	$-0.0342565\pi$
$858$	3.10717	−	3.10717i	0.106077	−	0.106077i
$859$	−2.22749	+	2.22749i	−0.0760011	+	0.0760011i	−0.744086	−	0.668084i	$-0.767115\pi$
$859$	−2.22749	+	2.22749i	−0.0760011	+	0.0760011i	0.668084	+	0.744086i	$0.267115\pi$
$860$		0			0
$861$	30.3833	+	12.5852i	1.03546	+	0.428901i
$862$	2.30538	+	5.56568i	0.0785216	+	0.189568i
$863$		−	34.5368i		−	1.17565i	−0.808989	−	0.587823i	$-0.799985\pi$
$863$		−	34.5368i		−	1.17565i	0.808989	−	0.587823i	$-0.200015\pi$
$864$	16.2598	−	6.73504i	0.553171	−	0.229131i
$865$		0			0
$866$	5.49781			0.186823
$867$	8.58348	+	15.8640i	0.291510	+	0.538769i
$868$	10.7675			0.365473
$869$	25.4370	+	25.4370i	0.862892	+	0.862892i
$870$		0			0
$871$		−	37.6032i		−	1.27414i
$872$	4.25919	+	10.2826i	0.144234	+	0.348212i
$873$	15.5136	+	6.42595i	0.525057	+	0.217486i
$874$	0.708688	−	1.71093i	0.0239717	−	0.0578729i
$875$		0			0
$876$	−9.24848	+	9.24848i	−0.312477	+	0.312477i
$877$	6.05591	−	14.6203i	0.204493	−	0.493691i	−0.788046	−	0.615617i	$-0.788907\pi$
$877$	6.05591	−	14.6203i	0.204493	−	0.493691i	0.992539	+	0.121926i	$0.0389070\pi$
$878$	−4.10647	−	1.70096i	−0.138587	−	0.0574045i
$879$	−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
$883$	20.2779			0.682406			0.341203	−	0.939990i	$-0.389166\pi$
$883$	20.2779			0.682406			0.341203	+	0.939990i	$0.389166\pi$
$884$	29.5878	−	32.8124i	0.995144	−	1.10360i
$885$		0			0
$886$	−4.97762	−	4.97762i	−0.167226	−	0.167226i
$887$	−45.1215	+	18.6899i	−1.51503	+	0.627547i	−0.976589	−	0.215115i	$-0.930987\pi$
$887$	−45.1215	+	18.6899i	−1.51503	+	0.627547i	−0.538443	+	0.842662i	$0.680987\pi$
$888$			6.38831i			0.214378i
$889$	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
$897$		−	5.12682i		−	0.171180i
$898$	0.477067	−	0.197608i	0.0159199	−	0.00659425i
$899$	5.96141	+	5.96141i	0.198824	+	0.198824i
$900$		0			0
$901$	11.4253	−	0.590416i	0.380633	−	0.0196696i
$902$	−9.11148			−0.303379
$903$	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
$907$	38.5317	+	15.9603i	1.27942	+	0.529955i	0.915816	−	0.401598i	$-0.131545\pi$
$907$	38.5317	+	15.9603i	1.27942	+	0.529955i	0.363608	+	0.931552i	$0.381545\pi$
$908$	−2.23588	+	5.39790i	−0.0742004	+	0.179136i
$909$	−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	$0.0911813\pi$
$912$	−24.2015	−	10.0246i	−0.801392	−	0.331947i
$913$	13.0073	+	31.4023i	0.430478	+	1.03926i
$914$			3.98735i			0.131890i
$915$		0			0
$916$	−10.2039	−	10.2039i	−0.337145	−	0.337145i
$917$	−10.5094			−0.347052
$918$	2.15178	−	6.06239i	0.0710195	−	0.200089i
$919$	−23.6812			−0.781170			−0.390585	−	0.920567i	$-0.627727\pi$
$919$	−23.6812			−0.781170			−0.390585	+	0.920567i	$0.627727\pi$
$920$		0			0
$921$	−29.3613	+	12.1618i	−0.967488	+	0.400746i
$922$			8.83658i			0.291017i
$923$	−0.517199	−	1.24863i	−0.0170238	−	0.0410991i
$924$	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
$928$	4.88550	−	11.7946i	0.160374	−	0.387178i
$929$	50.7164	+	21.0074i	1.66395	+	0.689232i	0.998369	−	0.0570920i	$-0.0181828\pi$
$929$	50.7164	+	21.0074i	1.66395	+	0.689232i	0.665583	+	0.746324i	$0.268183\pi$
$930$		0			0
$931$		−	4.99683i		−	0.163764i
$932$	−39.4142	+	16.3259i	−1.29106	+	0.534773i
$933$	−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	0.624530	−	0.781001i	$-0.285291\pi$
$937$	−4.78966	−	4.78966i	−0.156471	−	0.156471i	−0.781001	+	0.624530i	$0.785291\pi$
$938$	−4.68619	+	1.94108i	−0.153010	+	0.0633786i
$939$			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	$0.759840\pi$
$942$	1.64232	−	3.96490i	0.0535096	−	0.129184i
$943$	−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
$947$	−9.37621	−	22.6362i	−0.304686	−	0.735577i	−0.999860	−	0.0167354i	$-0.994673\pi$
$947$	−9.37621	−	22.6362i	−0.304686	−	0.735577i	0.695174	−	0.718841i	$-0.255327\pi$
$948$			29.7937i			0.967654i
$949$	33.4888	−	13.8715i	1.08709	−	0.450288i
$950$		0			0
$951$	−35.4793			−1.15050
$952$	−11.5007	−	4.08206i	−0.372740	−	0.132300i
$953$	−30.3936			−0.984545			−0.492272	−	0.870441i	$-0.663834\pi$
$953$	−30.3936			−0.984545			−0.492272	+	0.870441i	$0.663834\pi$
$954$	−1.10941	−	1.10941i	−0.0359185	−	0.0359185i
$955$		0			0
$956$			6.60473i			0.213612i
$957$	3.72511	+	8.99320i	0.120416	+	0.290709i
$958$	3.06873	+	1.27111i	0.0991462	+	0.0410677i
$959$	−6.97302	+	16.8344i	−0.225171	+	0.543610i
$960$		0			0
$961$	−18.3491	+	18.3491i	−0.591906	+	0.591906i
$962$	3.30874	−	7.98801i	0.106678	−	0.257544i
$963$	2.54677	+	1.05491i	0.0820684	+	0.0339939i
$964$	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	1.00000		0.000584066i	$-0.000185914\pi$
$967$	31.0785	+	31.0785i	0.999416	+	0.999416i	−0.000584066		1.00000i	$0.500186\pi$
$968$	5.91906			0.190246
$969$	−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	$0.511875\pi$
$972$	27.6169	−	11.4393i	0.885814	−	0.366916i
$973$		−	26.0853i		−	0.836255i
$974$	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	$-0.873933\pi$
$977$	−16.7792	+	16.7792i	−0.536813	+	0.536813i	0.385778	+	0.922591i	$0.373933\pi$
$978$	−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
$982$			5.15363i			0.164459i
$983$	25.9264	−	10.7391i	0.826925	−	0.342524i	0.0712405	−	0.997459i	$-0.477304\pi$
$983$	25.9264	−	10.7391i	0.826925	−	0.342524i	0.755685	+	0.654935i	$0.227304\pi$
$984$	−10.9264	−	10.9264i	−0.348322	−	0.348322i
$985$		0			0
$986$	−2.00585	−	4.21325i	−0.0638791	−	0.134177i
$987$	6.12786			0.195052
$988$	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	$0.624807\pi$
$992$	−7.06567	−	2.92670i	−0.224335	−	0.0929227i
$993$	−0.359477	+	0.867854i	−0.0114076	+	0.0275405i
$994$	−0.128909	+	0.128909i	−0.00408874	+	0.00408874i
$995$		0			0
$996$	−10.7728	+	26.0079i	−0.341349	+	0.824090i
$997$	18.9837	+	7.86332i	0.601221	+	0.249034i	0.662470	−	0.749089i	$-0.269508\pi$
$997$	18.9837	+	7.86332i	0.601221	+	0.249034i	−0.0612487	+	0.998123i	$0.519508\pi$
$998$	3.62047	+	8.74058i	0.114604	+	0.276678i
$999$			26.4042i			0.835392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.b.376.3		24
5.2	odd	4		425.2.n.f.274.4		24
5.3	odd	4		425.2.n.c.274.3		24
5.4	even	2		85.2.l.a.36.4	yes	24
15.14	odd	2		765.2.be.b.631.3		24
17.3	odd	16		7225.2.a.bs.1.6		12
17.9	even	8	inner	425.2.m.b.26.3		24
17.14	odd	16		7225.2.a.bq.1.6		12
85.9	even	8		85.2.l.a.26.4	✓	24
85.14	odd	16		1445.2.a.q.1.7		12
85.29	odd	16		1445.2.d.j.866.11		24
85.39	odd	16		1445.2.d.j.866.12		24
85.43	odd	8		425.2.n.f.349.4		24
85.54	odd	16		1445.2.a.p.1.7		12
85.77	odd	8		425.2.n.c.349.3		24
255.179	odd	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	85.9	even	8
85.2.l.a.36.4	yes	24	5.4	even	2
425.2.m.b.26.3		24	17.9	even	8	inner
425.2.m.b.376.3		24	1.1	even	1	trivial
425.2.n.c.274.3		24	5.3	odd	4
425.2.n.c.349.3		24	85.77	odd	8
425.2.n.f.274.4		24	5.2	odd	4
425.2.n.f.349.4		24	85.43	odd	8
765.2.be.b.451.3		24	255.179	odd	8
765.2.be.b.631.3		24	15.14	odd	2
1445.2.a.p.1.7		12	85.54	odd	16
1445.2.a.q.1.7		12	85.14	odd	16
1445.2.d.j.866.11		24	85.29	odd	16
1445.2.d.j.866.12		24	85.39	odd	16
7225.2.a.bq.1.6		12	17.14	odd	16
7225.2.a.bs.1.6		12	17.3	odd	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.m (of order \(8\), degree \(4\), minimal)

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

Introduction

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