LMFDB - Embedded newform 425.2.j.a.149.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(149,425)] 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("425.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [12,-4,-2] 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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 119x^{8} + 364x^{6} + 519x^{4} + 278x^{2} + 1 $ x^12 + 18x^10 + 119x^8 + 364x^6 + 519x^4 + 278*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.4
Root			$-0.0601793i$ of defining polynomial
Character	$\chi$	$=$	425.149
Dual form			425.2.j.a.174.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.0601793 q^{2} +(0.294708 - 0.294708i) q^{3} -1.99638 q^{4} +(0.0177353 - 0.0177353i) q^{6} +(0.900793 + 0.900793i) q^{7} -0.240499 q^{8} +2.82629i q^{9} +(2.24864 - 2.24864i) q^{11} +(-0.588349 + 0.588349i) q^{12} +4.23326i q^{13} +(0.0542091 + 0.0542091i) q^{14} +3.97828 q^{16} +(1.29364 + 3.91491i) q^{17} +0.170084i q^{18} -4.76249i q^{19} +0.530942 q^{21} +(0.135322 - 0.135322i) q^{22} +(5.13512 + 5.13512i) q^{23} +(-0.0708771 + 0.0708771i) q^{24} +0.254754i q^{26} +(1.71706 + 1.71706i) q^{27} +(-1.79832 - 1.79832i) q^{28} +(1.35382 + 1.35382i) q^{29} +(1.64149 + 1.64149i) q^{31} +0.720409 q^{32} -1.32539i q^{33} +(0.0778504 + 0.235596i) q^{34} -5.64235i q^{36} +(-3.84759 + 3.84759i) q^{37} -0.286603i q^{38} +(1.24758 + 1.24758i) q^{39} +(0.0814719 - 0.0814719i) q^{41} +0.0319517 q^{42} +0.562791 q^{43} +(-4.48914 + 4.48914i) q^{44} +(0.309028 + 0.309028i) q^{46} -5.01576i q^{47} +(1.17243 - 1.17243i) q^{48} -5.37714i q^{49} +(1.53500 + 0.772509i) q^{51} -8.45118i q^{52} -7.75525 q^{53} +(0.103331 + 0.103331i) q^{54} +(-0.216640 - 0.216640i) q^{56} +(-1.40355 - 1.40355i) q^{57} +(0.0814719 + 0.0814719i) q^{58} +2.01596i q^{59} +(-7.03868 + 7.03868i) q^{61} +(0.0987837 + 0.0987837i) q^{62} +(-2.54591 + 2.54591i) q^{63} -7.91321 q^{64} -0.0797608i q^{66} +3.64576i q^{67} +(-2.58260 - 7.81564i) q^{68} +3.02672 q^{69} +(-6.92188 - 6.92188i) q^{71} -0.679721i q^{72} +(10.2527 - 10.2527i) q^{73} +(-0.231545 + 0.231545i) q^{74} +9.50774i q^{76} +4.05112 q^{77} +(0.0750782 + 0.0750782i) q^{78} +(5.78193 - 5.78193i) q^{79} -7.46682 q^{81} +(0.00490292 - 0.00490292i) q^{82} -4.38162 q^{83} -1.05996 q^{84} +0.0338684 q^{86} +0.797964 q^{87} +(-0.540797 + 0.540797i) q^{88} +13.8492 q^{89} +(-3.81329 + 3.81329i) q^{91} +(-10.2516 - 10.2516i) q^{92} +0.967522 q^{93} -0.301845i q^{94} +(0.212310 - 0.212310i) q^{96} +(9.15882 - 9.15882i) q^{97} -0.323593i q^{98} +(6.35533 + 6.35533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 2 q^{3} + 12 q^{4} + 6 q^{6} - 12 q^{8} - 4 q^{11} + 4 q^{12} - 14 q^{14} + 4 q^{16} + 10 q^{17} + 8 q^{21} - 10 q^{22} - 12 q^{23} + 8 q^{24} + 22 q^{27} + 34 q^{28} + 6 q^{29} - 6 q^{31}+ \cdots - 30 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - 2 * q^3 + 12 * q^4 + 6 * q^6 - 12 * q^8 - 4 * q^11 + 4 * q^12 - 14 * q^14 + 4 * q^16 + 10 * q^17 + 8 * q^21 - 10 * q^22 - 12 * q^23 + 8 * q^24 + 22 * q^27 + 34 * q^28 + 6 * q^29 - 6 * q^31 - 48 * q^32 - 30 * q^34 - 18 * q^37 - 16 * q^39 + 6 * q^41 + 56 * q^42 - 16 * q^43 - 32 * q^44 + 30 * q^46 - 10 * q^48 - 40 * q^51 + 48 * q^53 - 16 * q^54 - 56 * q^56 - 18 * q^57 + 6 * q^58 - 8 * q^61 - 22 * q^62 - 30 * q^63 + 44 * q^64 + 18 * q^68 + 72 * q^69 - 20 * q^71 - 18 * q^73 + 26 * q^74 + 24 * q^77 - 38 * q^78 + 14 * q^79 - 8 * q^81 + 10 * q^82 + 52 * q^83 - 36 * q^84 + 84 * q^86 - 48 * q^87 + 66 * q^88 + 24 * q^89 + 12 * q^91 - 32 * q^92 - 60 * q^93 + 22 * q^96 + 52 * q^97 - 30 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.0601793			0.0425532			0.0212766	−	0.999774i	$-0.493227\pi$
$2$	0.0601793			0.0425532			0.0212766	+	0.999774i	$0.493227\pi$
$3$	0.294708	−	0.294708i	0.170150	−	0.170150i	−0.616895	−	0.787045i	$-0.711610\pi$
$3$	0.294708	−	0.294708i	0.170150	−	0.170150i	0.787045	+	0.616895i	$0.211610\pi$
$4$	−1.99638			−0.998189
$5$		0			0
$5$		0			0
$6$	0.0177353	−	0.0177353i	0.00724042	−	0.00724042i
$7$	0.900793	+	0.900793i	0.340468	+	0.340468i	0.856543	−	0.516075i	$-0.172608\pi$
$7$	0.900793	+	0.900793i	0.340468	+	0.340468i	−0.516075	+	0.856543i	$0.672608\pi$
$8$	−0.240499			−0.0850293
$9$			2.82629i			0.942098i
$10$		0			0
$11$	2.24864	−	2.24864i	0.677991	−	0.677991i	−0.281554	−	0.959545i	$-0.590850\pi$
$11$	2.24864	−	2.24864i	0.677991	−	0.677991i	0.959545	+	0.281554i	$0.0908499\pi$
$12$	−0.588349	+	0.588349i	−0.169842	+	0.169842i
$13$			4.23326i			1.17409i	0.809553	+	0.587047i	$0.199710\pi$
$13$			4.23326i			1.17409i	−0.809553	+	0.587047i	$0.800290\pi$
$14$	0.0542091	+	0.0542091i	0.0144880	+	0.0144880i
$15$		0			0
$16$	3.97828			0.994571
$17$	1.29364	+	3.91491i	0.313754	+	0.949504i
$17$	1.29364	+	3.91491i	0.313754	+	0.949504i
$18$			0.170084i			0.0400893i
$19$		−	4.76249i		−	1.09259i	−0.837593	−	0.546295i	$-0.816038\pi$
$19$		−	4.76249i		−	1.09259i	0.837593	−	0.546295i	$-0.183962\pi$
$20$		0			0
$21$	0.530942			0.115861
$22$	0.135322	−	0.135322i	0.0288507	−	0.0288507i
$23$	5.13512	+	5.13512i	1.07075	+	1.07075i	0.997299	+	0.0734466i	$0.0233998\pi$
$23$	5.13512	+	5.13512i	1.07075	+	1.07075i	0.0734466	+	0.997299i	$0.476600\pi$
$24$	−0.0708771	+	0.0708771i	−0.0144677	+	0.0144677i
$25$		0			0
$26$			0.254754i			0.0499614i
$27$	1.71706	+	1.71706i	0.330448	+	0.330448i
$28$	−1.79832	−	1.79832i	−0.339851	−	0.339851i
$29$	1.35382	+	1.35382i	0.251398	+	0.251398i	0.821544	−	0.570146i	$-0.193113\pi$
$29$	1.35382	+	1.35382i	0.251398	+	0.251398i	−0.570146	+	0.821544i	$0.693113\pi$
$30$		0			0
$31$	1.64149	+	1.64149i	0.294820	+	0.294820i	0.838981	−	0.544161i	$-0.183152\pi$
$31$	1.64149	+	1.64149i	0.294820	+	0.294820i	−0.544161	+	0.838981i	$0.683152\pi$
$32$	0.720409			0.127351
$33$		−	1.32539i		−	0.230720i
$34$	0.0778504	+	0.235596i	0.0133512	+	0.0404044i
$35$		0			0
$36$		−	5.64235i		−	0.940392i
$37$	−3.84759	+	3.84759i	−0.632539	+	0.632539i	−0.948704	−	0.316165i	$-0.897605\pi$
$37$	−3.84759	+	3.84759i	−0.632539	+	0.632539i	0.316165	+	0.948704i	$0.397605\pi$
$38$		−	0.286603i		−	0.0464932i
$39$	1.24758	+	1.24758i	0.199772	+	0.199772i
$40$		0			0
$41$	0.0814719	−	0.0814719i	0.0127238	−	0.0127238i	−0.700716	−	0.713440i	$-0.747136\pi$
$41$	0.0814719	−	0.0814719i	0.0127238	−	0.0127238i	0.713440	+	0.700716i	$0.247136\pi$
$42$	0.0319517			0.00493026
$43$	0.562791			0.0858249			0.0429124	−	0.999079i	$-0.486336\pi$
$43$	0.562791			0.0858249			0.0429124	+	0.999079i	$0.486336\pi$
$44$	−4.48914	+	4.48914i	−0.676764	+	0.676764i
$45$		0			0
$46$	0.309028	+	0.309028i	0.0455636	+	0.0455636i
$47$		−	5.01576i		−	0.731624i	−0.930689	−	0.365812i	$-0.880791\pi$
$47$		−	5.01576i		−	0.731624i	0.930689	−	0.365812i	$-0.119209\pi$
$48$	1.17243	−	1.17243i	0.169226	−	0.169226i
$49$		−	5.37714i		−	0.768164i
$50$		0			0
$51$	1.53500	+	0.772509i	0.214943	+	0.108173i
$52$		−	8.45118i		−	1.17197i
$53$	−7.75525			−1.06527			−0.532633	−	0.846346i	$-0.678797\pi$
$53$	−7.75525			−1.06527			−0.532633	+	0.846346i	$0.678797\pi$
$54$	0.103331	+	0.103331i	0.0140616	+	0.0140616i
$55$		0			0
$56$	−0.216640	−	0.216640i	−0.0289497	−	0.0289497i
$57$	−1.40355	−	1.40355i	−0.185904	−	0.185904i
$58$	0.0814719	+	0.0814719i	0.0106978	+	0.0106978i
$59$			2.01596i			0.262456i	0.991352	+	0.131228i	$0.0418919\pi$
$59$			2.01596i			0.262456i	−0.991352	+	0.131228i	$0.958108\pi$
$60$		0			0
$61$	−7.03868	+	7.03868i	−0.901211	+	0.901211i	−0.995541	−	0.0943302i	$-0.969929\pi$
$61$	−7.03868	+	7.03868i	−0.901211	+	0.901211i	0.0943302	+	0.995541i	$0.469929\pi$
$62$	0.0987837	+	0.0987837i	0.0125455	+	0.0125455i
$63$	−2.54591	+	2.54591i	−0.320754	+	0.320754i
$64$	−7.91321			−0.989152
$65$		0			0
$66$		−	0.0797608i		−	0.00981788i
$67$			3.64576i			0.445400i	0.974887	+	0.222700i	$0.0714870\pi$
$67$			3.64576i			0.445400i	−0.974887	+	0.222700i	$0.928513\pi$
$68$	−2.58260	−	7.81564i	−0.313186	−	0.947785i
$69$	3.02672			0.364375
$70$		0			0
$71$	−6.92188	−	6.92188i	−0.821476	−	0.821476i	0.164844	−	0.986320i	$-0.447288\pi$
$71$	−6.92188	−	6.92188i	−0.821476	−	0.821476i	−0.986320	+	0.164844i	$0.947288\pi$
$72$		−	0.679721i		−	0.0801059i
$73$	10.2527	−	10.2527i	1.19999	−	1.19999i	0.225825	−	0.974168i	$-0.427492\pi$
$73$	10.2527	−	10.2527i	1.19999	−	1.19999i	0.974168	−	0.225825i	$-0.0725076\pi$
$74$	−0.231545	+	0.231545i	−0.0269166	+	0.0269166i
$75$		0			0
$76$			9.50774i			1.09061i
$77$	4.05112			0.461668
$78$	0.0750782	+	0.0750782i	0.00850093	+	0.00850093i
$79$	5.78193	−	5.78193i	0.650518	−	0.650518i	−0.302599	−	0.953118i	$-0.597854\pi$
$79$	5.78193	−	5.78193i	0.650518	−	0.650518i	0.953118	+	0.302599i	$0.0978544\pi$
$80$		0			0
$81$	−7.46682			−0.829647
$82$	0.00490292	−	0.00490292i	0.000541437	−	0.000541437i
$83$	−4.38162			−0.480946			−0.240473	−	0.970656i	$-0.577303\pi$
$83$	−4.38162			−0.480946			−0.240473	+	0.970656i	$0.577303\pi$
$84$	−1.05996			−0.115651
$85$		0			0
$86$	0.0338684			0.00365212
$87$	0.797964			0.0855507
$88$	−0.540797	+	0.540797i	−0.0576491	+	0.0576491i
$89$	13.8492			1.46801			0.734006	−	0.679143i	$-0.237648\pi$
$89$	13.8492			1.46801			0.734006	+	0.679143i	$0.237648\pi$
$90$		0			0
$91$	−3.81329	+	3.81329i	−0.399741	+	0.399741i
$92$	−10.2516	−	10.2516i	−1.06881	−	1.06881i
$93$	0.967522			0.100327
$94$		−	0.301845i		−	0.0311329i
$95$		0			0
$96$	0.212310	−	0.212310i	0.0216688	−	0.0216688i
$97$	9.15882	−	9.15882i	0.929937	−	0.929937i	−0.0677639	−	0.997701i	$-0.521586\pi$
$97$	9.15882	−	9.15882i	0.929937	−	0.929937i	0.997701	+	0.0677639i	$0.0215865\pi$
$98$		−	0.323593i		−	0.0326878i
$99$	6.35533	+	6.35533i	0.638734	+	0.638734i
$100$		0			0
$101$	−12.0395			−1.19798			−0.598989	−	0.800757i	$-0.704431\pi$
$101$	−12.0395			−1.19798			−0.598989	+	0.800757i	$0.704431\pi$
$102$	0.0923753	+	0.0464890i	0.00914652	+	0.00460310i
$103$			6.06868i			0.597965i	0.954259	+	0.298982i	$0.0966472\pi$
$103$			6.06868i			0.597965i	−0.954259	+	0.298982i	$0.903353\pi$
$104$		−	1.01809i		−	0.0998324i
$105$		0			0
$106$	−0.466705			−0.0453304
$107$	−11.9571	+	11.9571i	−1.15594	+	1.15594i	−0.170601	+	0.985340i	$0.554571\pi$
$107$	−11.9571	+	11.9571i	−1.15594	+	1.15594i	−0.985340	+	0.170601i	$0.945429\pi$
$108$	−3.42790	−	3.42790i	−0.329849	−	0.329849i
$109$	6.38396	−	6.38396i	0.611473	−	0.611473i	−0.331857	−	0.943330i	$-0.607675\pi$
$109$	6.38396	−	6.38396i	0.611473	−	0.611473i	0.943330	+	0.331857i	$0.107675\pi$
$110$		0			0
$111$			2.26783i			0.215253i
$112$	3.58361	+	3.58361i	0.338619	+	0.338619i
$113$	−3.62958	−	3.62958i	−0.341443	−	0.341443i	0.515467	−	0.856909i	$-0.327619\pi$
$113$	−3.62958	−	3.62958i	−0.341443	−	0.341443i	−0.856909	+	0.515467i	$0.827619\pi$
$114$	−0.0844644	−	0.0844644i	−0.00791081	−	0.00791081i
$115$		0			0
$116$	−2.70274	−	2.70274i	−0.250943	−	0.250943i
$117$	−11.9644			−1.10611
$118$			0.121319i			0.0111683i
$119$	−2.36122	+	4.69182i	−0.216452	+	0.430099i
$120$		0			0
$121$			0.887212i			0.0806556i
$122$	−0.423583	+	0.423583i	−0.0383494	+	0.0383494i
$123$		−	0.0480209i		−	0.00432990i
$124$	−3.27704	−	3.27704i	−0.294287	−	0.294287i
$125$		0			0
$126$	−0.153211	+	0.153211i	−0.0136491	+	0.0136491i
$127$	17.4817			1.55125			0.775626	−	0.631193i	$-0.217434\pi$
$127$	17.4817			1.55125			0.775626	+	0.631193i	$0.217434\pi$
$128$	−1.91703			−0.169443
$129$	0.165859	−	0.165859i	0.0146031	−	0.0146031i
$130$		0			0
$131$	7.39051	+	7.39051i	0.645712	+	0.645712i	0.951954	−	0.306242i	$-0.0990715\pi$
$131$	7.39051	+	7.39051i	0.645712	+	0.645712i	−0.306242	+	0.951954i	$0.599072\pi$
$132$			2.64597i			0.230302i
$133$	4.29002	−	4.29002i	0.371992	−	0.371992i
$134$			0.219399i			0.0189532i
$135$		0			0
$136$	−0.311120	−	0.941532i	−0.0266783	−	0.0807357i
$137$		−	16.3203i		−	1.39434i	−0.716908	−	0.697168i	$-0.754443\pi$
$137$		−	16.3203i		−	1.39434i	0.716908	−	0.697168i	$-0.245557\pi$
$138$	0.182146			0.0155053
$139$	−15.8001	−	15.8001i	−1.34015	−	1.34015i	−0.895908	−	0.444240i	$-0.853474\pi$
$139$	−15.8001	−	15.8001i	−1.34015	−	1.34015i	−0.444240	−	0.895908i	$-0.646526\pi$
$140$		0			0
$141$	−1.47819	−	1.47819i	−0.124486	−	0.124486i
$142$	−0.416554	−	0.416554i	−0.0349564	−	0.0349564i
$143$	9.51908	+	9.51908i	0.796026	+	0.796026i
$144$			11.2438i			0.936983i
$145$		0			0
$146$	0.617003	−	0.617003i	0.0510635	−	0.0510635i
$147$	−1.58469	−	1.58469i	−0.130703	−	0.130703i
$148$	7.68124	−	7.68124i	0.631394	−	0.631394i
$149$	2.33253			0.191088			0.0955441	−	0.995425i	$-0.469541\pi$
$149$	2.33253			0.191088			0.0955441	+	0.995425i	$0.469541\pi$
$150$		0			0
$151$		−	14.0599i		−	1.14418i	−0.820192	−	0.572088i	$-0.806133\pi$
$151$		−	14.0599i		−	1.14418i	0.820192	−	0.572088i	$-0.193867\pi$
$152$			1.14538i			0.0929022i
$153$	−11.0647	+	3.65621i	−0.894526	+	0.295587i
$154$	0.243794			0.0196454
$155$		0			0
$156$	−2.49063	−	2.49063i	−0.199410	−	0.199410i
$157$		−	11.3114i		−	0.902750i	−0.892334	−	0.451375i	$-0.850934\pi$
$157$		−	11.3114i		−	0.902750i	0.892334	−	0.451375i	$-0.149066\pi$
$158$	0.347953	−	0.347953i	0.0276816	−	0.0276816i
$159$	−2.28554	+	2.28554i	−0.181255	+	0.181255i
$160$		0			0
$161$			9.25135i			0.729109i
$162$	−0.449348			−0.0353041
$163$	−7.34754	−	7.34754i	−0.575504	−	0.575504i	0.358157	−	0.933661i	$-0.383405\pi$
$163$	−7.34754	−	7.34754i	−0.575504	−	0.575504i	−0.933661	+	0.358157i	$0.883405\pi$
$164$	−0.162649	+	0.162649i	−0.0127007	+	0.0127007i
$165$		0			0
$166$	−0.263683			−0.0204658
$167$	−13.4849	+	13.4849i	−1.04349	+	1.04349i	−0.0444820	+	0.999010i	$0.514164\pi$
$167$	−13.4849	+	13.4849i	−1.04349	+	1.04349i	−0.999010	+	0.0444820i	$0.985836\pi$
$168$	−0.127691			−0.00985158
$169$	−4.92046			−0.378497
$170$		0			0
$171$	13.4602			1.02933
$172$	−1.12354			−0.0856694
$173$	1.44947	−	1.44947i	0.110201	−	0.110201i	−0.649856	−	0.760057i	$-0.725171\pi$
$173$	1.44947	−	1.44947i	0.110201	−	0.110201i	0.760057	+	0.649856i	$0.225171\pi$
$174$	0.0480209			0.00364045
$175$		0			0
$176$	8.94574	−	8.94574i	0.674310	−	0.674310i
$177$	0.594120	+	0.594120i	0.0446568	+	0.0446568i
$178$	0.833435			0.0624686
$179$			16.3180i			1.21966i	0.792531	+	0.609831i	$0.208763\pi$
$179$			16.3180i			1.21966i	−0.792531	+	0.609831i	$0.791237\pi$
$180$		0			0
$181$	5.23176	−	5.23176i	0.388873	−	0.388873i	−0.485412	−	0.874285i	$-0.661330\pi$
$181$	5.23176	−	5.23176i	0.388873	−	0.388873i	0.874285	+	0.485412i	$0.161330\pi$
$182$	−0.229481	+	0.229481i	−0.0170103	+	0.0170103i
$183$			4.14871i			0.306682i
$184$	−1.23499	−	1.23499i	−0.0910448	−	0.0910448i
$185$		0			0
$186$	0.0582248			0.00426925
$187$	11.7122	+	5.89429i	0.856478	+	0.431033i
$188$			10.0134i			0.730299i
$189$			3.09342i			0.225014i
$190$		0			0
$191$	19.6307			1.42042			0.710212	−	0.703987i	$-0.248599\pi$
$191$	19.6307			1.42042			0.710212	+	0.703987i	$0.248599\pi$
$192$	−2.33209	+	2.33209i	−0.168304	+	0.168304i
$193$	1.37554	+	1.37554i	0.0990133	+	0.0990133i	0.754878	−	0.655865i	$-0.227696\pi$
$193$	1.37554	+	1.37554i	0.0990133	+	0.0990133i	−0.655865	+	0.754878i	$0.727696\pi$
$194$	0.551171	−	0.551171i	0.0395718	−	0.0395718i
$195$		0			0
$196$			10.7348i			0.766773i
$197$	18.4793	+	18.4793i	1.31659	+	1.31659i	0.916454	+	0.400140i	$0.131039\pi$
$197$	18.4793	+	18.4793i	1.31659	+	1.31659i	0.400140	+	0.916454i	$0.368961\pi$
$198$	0.382459	+	0.382459i	0.0271802	+	0.0271802i
$199$	1.79715	+	1.79715i	0.127397	+	0.127397i	0.767930	−	0.640533i	$-0.221287\pi$
$199$	1.79715	+	1.79715i	0.127397	+	0.127397i	−0.640533	+	0.767930i	$0.721287\pi$
$200$		0			0
$201$	1.07443	+	1.07443i	0.0757848	+	0.0757848i
$202$	−0.724531			−0.0509778
$203$			2.43902i			0.171186i
$204$	−3.06444	−	1.54222i	−0.214554	−	0.107977i
$205$		0			0
$206$			0.365209i			0.0254453i
$207$	−14.5133	+	14.5133i	−1.00875	+	1.00875i
$208$			16.8411i			1.16772i
$209$	−10.7091	−	10.7091i	−0.740767	−	0.740767i
$210$		0			0
$211$	10.9560	−	10.9560i	0.754240	−	0.754240i	−0.221028	−	0.975268i	$-0.570941\pi$
$211$	10.9560	−	10.9560i	0.754240	−	0.754240i	0.975268	+	0.221028i	$0.0709411\pi$
$212$	15.4824			1.06334
$213$	−4.07987			−0.279548
$214$	−0.719572	+	0.719572i	−0.0491890	+	0.0491890i
$215$		0			0
$216$	−0.412951	−	0.412951i	−0.0280977	−	0.0280977i
$217$			2.95729i			0.200754i
$218$	0.384182	−	0.384182i	0.0260201	−	0.0260201i
$219$		−	6.04313i		−	0.408357i
$220$		0			0
$221$	−16.5728	+	5.47631i	−1.11481	+	0.368377i
$222$			0.136476i			0.00915970i
$223$	25.3456			1.69726			0.848632	−	0.528984i	$-0.177427\pi$
$223$	25.3456			1.69726			0.848632	+	0.528984i	$0.177427\pi$
$224$	0.648939	+	0.648939i	0.0433591	+	0.0433591i
$225$		0			0
$226$	−0.218426	−	0.218426i	−0.0145295	−	0.0145295i
$227$	−1.05058	−	1.05058i	−0.0697291	−	0.0697291i	0.671382	−	0.741111i	$-0.265701\pi$
$227$	−1.05058	−	1.05058i	−0.0697291	−	0.0697291i	−0.741111	+	0.671382i	$0.765701\pi$
$228$	2.80201	+	2.80201i	0.185568	+	0.185568i
$229$			11.7431i			0.776008i	0.921658	+	0.388004i	$0.126835\pi$
$229$			11.7431i			0.776008i	−0.921658	+	0.388004i	$0.873165\pi$
$230$		0			0
$231$	1.19390	−	1.19390i	0.0785528	−	0.0785528i
$232$	−0.325593	−	0.325593i	−0.0213762	−	0.0213762i
$233$	−12.4941	+	12.4941i	−0.818515	+	0.818515i	−0.985893	−	0.167378i	$-0.946470\pi$
$233$	−12.4941	+	12.4941i	−0.818515	+	0.818515i	0.167378	+	0.985893i	$0.446470\pi$
$234$	−0.720011			−0.0470686
$235$		0			0
$236$		−	4.02462i		−	0.261980i
$237$		−	3.40797i		−	0.221371i
$238$	−0.142096	+	0.282350i	−0.00921074	+	0.0183021i
$239$	12.3555			0.799213			0.399606	−	0.916687i	$-0.369147\pi$
$239$	12.3555			0.799213			0.399606	+	0.916687i	$0.369147\pi$
$240$		0			0
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	0.355091	−	0.934832i	$-0.384450\pi$
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	−0.934832	+	0.355091i	$0.884450\pi$
$242$			0.0533918i			0.00343215i
$243$	−7.35170	+	7.35170i	−0.471612	+	0.471612i
$244$	14.0519	−	14.0519i	0.899579	−	0.899579i
$245$		0			0
$246$		−	0.00288986i		−	0.000184251i
$247$	20.1609			1.28280
$248$	−0.394777	−	0.394777i	−0.0250684	−	0.0250684i
$249$	−1.29130	+	1.29130i	−0.0818329	+	0.0818329i
$250$		0			0
$251$	21.4164			1.35179			0.675894	−	0.736998i	$-0.263758\pi$
$251$	21.4164			1.35179			0.675894	+	0.736998i	$0.263758\pi$
$252$	5.08259	−	5.08259i	0.320173	−	0.320173i
$253$	23.0941			1.45191
$254$	1.05204			0.0660107
$255$		0			0
$256$	15.7111			0.981941
$257$	−18.5145			−1.15490			−0.577450	−	0.816426i	$-0.695952\pi$
$257$	−18.5145			−1.15490			−0.577450	+	0.816426i	$0.695952\pi$
$258$	0.00998129	−	0.00998129i	0.000621408	−	0.000621408i
$259$	−6.93176			−0.430718
$260$		0			0
$261$	−3.82629	+	3.82629i	−0.236842	+	0.236842i
$262$	0.444756	+	0.444756i	0.0274771	+	0.0274771i
$263$	−15.9953			−0.986314			−0.493157	−	0.869940i	$-0.664157\pi$
$263$	−15.9953			−0.986314			−0.493157	+	0.869940i	$0.664157\pi$
$264$			0.318755i			0.0196180i
$265$		0			0
$266$	0.258170	−	0.258170i	0.0158294	−	0.0158294i
$267$	4.08147	−	4.08147i	0.249782	−	0.249782i
$268$		−	7.27831i		−	0.444593i
$269$	−11.1688	−	11.1688i	−0.680975	−	0.680975i	0.279245	−	0.960220i	$-0.409916\pi$
$269$	−11.1688	−	11.1688i	−0.680975	−	0.680975i	−0.960220	+	0.279245i	$0.909916\pi$
$270$		0			0
$271$	12.3067			0.747577			0.373788	−	0.927514i	$-0.378059\pi$
$271$	12.3067			0.747577			0.373788	+	0.927514i	$0.378059\pi$
$272$	5.14647	+	15.5746i	0.312051	+	0.944349i
$273$			2.24761i			0.136032i
$274$		−	0.982143i		−	0.0593334i
$275$		0			0
$276$	−6.04248			−0.363715
$277$	−10.3628	+	10.3628i	−0.622640	+	0.622640i	−0.946206	−	0.323566i	$-0.895118\pi$
$277$	−10.3628	+	10.3628i	−0.622640	+	0.622640i	0.323566	+	0.946206i	$0.395118\pi$
$278$	−0.950839	−	0.950839i	−0.0570275	−	0.0570275i
$279$	−4.63934	+	4.63934i	−0.277750	+	0.277750i
$280$		0			0
$281$			0.269035i			0.0160493i	0.999968	+	0.00802465i	$0.00255435\pi$
$281$			0.269035i			0.0160493i	−0.999968	+	0.00802465i	$0.997446\pi$
$282$	−0.0889562	−	0.0889562i	−0.00529726	−	0.00529726i
$283$	5.76819	+	5.76819i	0.342884	+	0.342884i	0.857450	−	0.514567i	$-0.172047\pi$
$283$	5.76819	+	5.76819i	0.342884	+	0.342884i	−0.514567	+	0.857450i	$0.672047\pi$
$284$	13.8187	+	13.8187i	0.819988	+	0.819988i
$285$		0			0
$286$	0.572851	+	0.572851i	0.0338734	+	0.0338734i
$287$	0.146779			0.00866407
$288$			2.03609i			0.119978i
$289$	−13.6530	+	10.1290i	−0.803117	+	0.595822i
$290$		0			0
$291$		−	5.39836i		−	0.316457i
$292$	−20.4684	+	20.4684i	−1.19782	+	1.19782i
$293$		−	14.1503i		−	0.826668i	−0.910579	−	0.413334i	$-0.864364\pi$
$293$		−	14.1503i		−	0.826668i	0.910579	−	0.413334i	$-0.135636\pi$
$294$	−0.0953654	−	0.0953654i	−0.00556183	−	0.00556183i
$295$		0			0
$296$	0.925341	−	0.925341i	0.0537844	−	0.0537844i
$297$	7.72209			0.448081
$298$	0.140370			0.00813141
$299$	−21.7383	+	21.7383i	−1.25716	+	1.25716i
$300$		0			0
$301$	0.506958	+	0.506958i	0.0292206	+	0.0292206i
$302$		−	0.846113i		−	0.0486883i
$303$	−3.54815	+	3.54815i	−0.203836	+	0.203836i
$304$		−	18.9466i		−	1.08666i
$305$		0			0
$306$	−0.665864	+	0.220028i	−0.0380649	+	0.0125782i
$307$		−	31.1618i		−	1.77850i	−0.457424	−	0.889249i	$-0.651228\pi$
$307$		−	31.1618i		−	1.77850i	0.457424	−	0.889249i	$-0.348772\pi$
$308$	−8.08757			−0.460832
$309$	1.78849	+	1.78849i	0.101744	+	0.101744i
$310$		0			0
$311$	−9.69400	−	9.69400i	−0.549697	−	0.549697i	0.376656	−	0.926353i	$-0.377074\pi$
$311$	−9.69400	−	9.69400i	−0.549697	−	0.549697i	−0.926353	+	0.376656i	$0.877074\pi$
$312$	−0.300041	−	0.300041i	−0.0169865	−	0.0169865i
$313$	−11.5603	−	11.5603i	−0.653424	−	0.653424i	0.300392	−	0.953816i	$-0.402883\pi$
$313$	−11.5603	−	11.5603i	−0.653424	−	0.653424i	−0.953816	+	0.300392i	$0.902883\pi$
$314$		−	0.680713i		−	0.0384149i
$315$		0			0
$316$	−11.5429	+	11.5429i	−0.649340	+	0.649340i
$317$	−21.7775	−	21.7775i	−1.22315	−	1.22315i	−0.966507	−	0.256640i	$-0.917384\pi$
$317$	−21.7775	−	21.7775i	−1.22315	−	1.22315i	−0.256640	−	0.966507i	$-0.582616\pi$
$318$	−0.137542	+	0.137542i	−0.00771297	+	0.00771297i
$319$	6.08852			0.340891
$320$		0			0
$321$			7.04774i			0.393366i
$322$			0.556740i			0.0310259i
$323$	18.6447	−	6.16096i	1.03742	−	0.342805i
$324$	14.9066			0.828144
$325$		0			0
$326$	−0.442170	−	0.442170i	−0.0244895	−	0.0244895i
$327$		−	3.76281i		−	0.208084i
$328$	−0.0195939	+	0.0195939i	−0.00108189	+	0.00108189i
$329$	4.51816	−	4.51816i	0.249094	−	0.249094i
$330$		0			0
$331$			0.792939i			0.0435839i	0.999763	+	0.0217919i	$0.00693714\pi$
$331$			0.792939i			0.0435839i	−0.999763	+	0.0217919i	$0.993063\pi$
$332$	8.74738			0.480075
$333$	−10.8744	−	10.8744i	−0.595914	−	0.595914i
$334$	−0.811511	+	0.811511i	−0.0444039	+	0.0444039i
$335$		0			0
$336$	2.11224			0.115232
$337$	18.0622	−	18.0622i	0.983912	−	0.983912i	−0.0159607	−	0.999873i	$-0.505081\pi$
$337$	18.0622	−	18.0622i	0.983912	−	0.983912i	0.999873	+	0.0159607i	$0.00508066\pi$
$338$	−0.296110			−0.0161062
$339$	−2.13934			−0.116193
$340$		0			0
$341$	7.38225			0.399771
$342$	0.810026			0.0438012
$343$	11.1492	−	11.1492i	0.602002	−	0.602002i
$344$	−0.135351			−0.00729763
$345$		0			0
$346$	0.0872281	−	0.0872281i	0.00468941	−	0.00468941i
$347$	−19.1514	−	19.1514i	−1.02810	−	1.02810i	−0.999594	−	0.0285081i	$-0.990924\pi$
$347$	−19.1514	−	19.1514i	−1.02810	−	1.02810i	−0.0285081	−	0.999594i	$-0.509076\pi$
$348$	−1.59304			−0.0853958
$349$		−	9.63831i		−	0.515927i	−0.966155	−	0.257964i	$-0.916949\pi$
$349$		−	9.63831i		−	0.515927i	0.966155	−	0.257964i	$-0.0830514\pi$
$350$		0			0
$351$	−7.26874	+	7.26874i	−0.387977	+	0.387977i
$352$	1.61994	−	1.61994i	0.0863432	−	0.0863432i
$353$		−	15.9003i		−	0.846288i	−0.906062	−	0.423144i	$-0.860926\pi$
$353$		−	15.9003i		−	0.846288i	0.906062	−	0.423144i	$-0.139074\pi$
$354$	0.0357537	+	0.0357537i	0.00190029	+	0.00190029i
$355$		0			0
$356$	−27.6482			−1.46535
$357$	0.686848	+	2.07859i	0.0363519	+	0.110011i
$358$			0.982004i			0.0519005i
$359$		−	12.6719i		−	0.668799i	−0.942431	−	0.334400i	$-0.891467\pi$
$359$		−	12.6719i		−	0.668799i	0.942431	−	0.334400i	$-0.108533\pi$
$360$		0			0
$361$	−3.68134			−0.193755
$362$	0.314843	−	0.314843i	0.0165478	−	0.0165478i
$363$	0.261469	+	0.261469i	0.0137235	+	0.0137235i
$364$	7.61276	−	7.61276i	0.399017	−	0.399017i
$365$		0			0
$366$			0.249667i			0.0130503i
$367$	16.3592	+	16.3592i	0.853941	+	0.853941i	0.990616	−	0.136675i	$-0.0436415\pi$
$367$	16.3592	+	16.3592i	0.853941	+	0.853941i	−0.136675	+	0.990616i	$0.543642\pi$
$368$	20.4289	+	20.4289i	1.06493	+	1.06493i
$369$	0.230264	+	0.230264i	0.0119870	+	0.0119870i
$370$		0			0
$371$	−6.98587	−	6.98587i	−0.362688	−	0.362688i
$372$	−1.93154			−0.100146
$373$		−	21.1325i		−	1.09420i	−0.837067	−	0.547100i	$-0.815732\pi$
$373$		−	21.1325i		−	1.09420i	0.837067	−	0.547100i	$-0.184268\pi$
$374$	0.704830	+	0.354714i	0.0364459	+	0.0183418i
$375$		0			0
$376$			1.20629i			0.0622095i
$377$	−5.73107	+	5.73107i	−0.295165	+	0.295165i
$378$			0.186160i			0.00957504i
$379$	−13.1729	−	13.1729i	−0.676646	−	0.676646i	0.282593	−	0.959240i	$-0.408805\pi$
$379$	−13.1729	−	13.1729i	−0.676646	−	0.676646i	−0.959240	+	0.282593i	$0.908805\pi$
$380$		0			0
$381$	5.15201	−	5.15201i	0.263945	−	0.263945i
$382$	1.18136			0.0604436
$383$	−32.5035			−1.66085			−0.830425	−	0.557131i	$-0.811902\pi$
$383$	−32.5035			−1.66085			−0.830425	+	0.557131i	$0.811902\pi$
$384$	−0.564964	+	0.564964i	−0.0288307	+	0.0288307i
$385$		0			0
$386$	0.0827788	+	0.0827788i	0.00421333	+	0.00421333i
$387$			1.59061i			0.0808554i
$388$	−18.2845	+	18.2845i	−0.928254	+	0.928254i
$389$			27.7344i			1.40619i	0.711096	+	0.703095i	$0.248199\pi$
$389$			27.7344i			1.40619i	−0.711096	+	0.703095i	$0.751801\pi$
$390$		0			0
$391$	−13.4605	+	26.7465i	−0.680727	+	1.35263i
$392$			1.29320i			0.0653164i
$393$	4.35609			0.219736
$394$	1.11207	+	1.11207i	0.0560253	+	0.0560253i
$395$		0			0
$396$	−12.6876	−	12.6876i	−0.637578	−	0.637578i
$397$	−9.44969	−	9.44969i	−0.474267	−	0.474267i	0.429026	−	0.903292i	$-0.358857\pi$
$397$	−9.44969	−	9.44969i	−0.474267	−	0.474267i	−0.903292	+	0.429026i	$0.858857\pi$
$398$	0.108151	+	0.108151i	0.00542114	+	0.00542114i
$399$		−	2.52861i		−	0.126589i
$400$		0			0
$401$	−26.9567	+	26.9567i	−1.34615	+	1.34615i	−0.456355	+	0.889798i	$0.650845\pi$
$401$	−26.9567	+	26.9567i	−1.34615	+	1.34615i	−0.889798	+	0.456355i	$0.849155\pi$
$402$	0.0646587	+	0.0646587i	0.00322488	+	0.00322488i
$403$	−6.94885	+	6.94885i	−0.346147	+	0.346147i
$404$	24.0355			1.19581
$405$		0			0
$406$			0.146779i			0.00728450i
$407$			17.3037i			0.857712i
$408$	−0.369167	−	0.185788i	−0.0182765	−	0.00919786i
$409$	27.6899			1.36918			0.684590	−	0.728929i	$-0.259981\pi$
$409$	27.6899			1.36918			0.684590	+	0.728929i	$0.259981\pi$
$410$		0			0
$411$	−4.80972	−	4.80972i	−0.237246	−	0.237246i
$412$		−	12.1154i		−	0.596882i
$413$	−1.81596	+	1.81596i	−0.0893577	+	0.0893577i
$414$	−0.873403	+	0.873403i	−0.0429254	+	0.0429254i
$415$		0			0
$416$			3.04967i			0.149523i
$417$	−9.31284			−0.456052
$418$	−0.644469	−	0.644469i	−0.0315220	−	0.0315220i
$419$	−4.32322	+	4.32322i	−0.211203	+	0.211203i	−0.804779	−	0.593575i	$-0.797716\pi$
$419$	−4.32322	+	4.32322i	−0.211203	+	0.211203i	0.593575	+	0.804779i	$0.297716\pi$
$420$		0			0
$421$	−17.3965			−0.847851			−0.423926	−	0.905697i	$-0.639348\pi$
$421$	−17.3965			−0.847851			−0.423926	+	0.905697i	$0.639348\pi$
$422$	0.659322	−	0.659322i	0.0320953	−	0.0320953i
$423$	14.1760			0.689261
$424$	1.86513			0.0905788
$425$		0			0
$426$	−0.245524			−0.0118957
$427$	−12.6808			−0.613666
$428$	23.8710	−	23.8710i	1.15385	−	1.15385i
$429$	5.61070			0.270887
$430$		0			0
$431$	8.29991	−	8.29991i	0.399793	−	0.399793i	−0.478367	−	0.878160i	$-0.658771\pi$
$431$	8.29991	−	8.29991i	0.399793	−	0.399793i	0.878160	+	0.478367i	$0.158771\pi$
$432$	6.83094	+	6.83094i	0.328654	+	0.328654i
$433$	−23.3059			−1.12001			−0.560006	−	0.828489i	$-0.689201\pi$
$433$	−23.3059			−1.12001			−0.560006	+	0.828489i	$0.689201\pi$
$434$			0.177967i			0.00854271i
$435$		0			0
$436$	−12.7448	+	12.7448i	−0.610366	+	0.610366i
$437$	24.4560	−	24.4560i	1.16989	−	1.16989i
$438$		−	0.363671i		−	0.0173769i
$439$	4.25782	+	4.25782i	0.203215	+	0.203215i	0.801376	−	0.598161i	$-0.204102\pi$
$439$	4.25782	+	4.25782i	0.203215	+	0.203215i	−0.598161	+	0.801376i	$0.704102\pi$
$440$		0			0
$441$	15.1974			0.723685
$442$	−0.997339	+	0.329561i	−0.0474386	+	0.0156756i
$443$		−	12.6102i		−	0.599130i	−0.954076	−	0.299565i	$-0.903158\pi$
$443$		−	12.6102i		−	0.599130i	0.954076	−	0.299565i	$-0.0968416\pi$
$444$		−	4.52745i		−	0.214863i
$445$		0			0
$446$	1.52528			0.0722240
$447$	0.687415	−	0.687415i	0.0325136	−	0.0325136i
$448$	−7.12817	−	7.12817i	−0.336774	−	0.336774i
$449$	23.2014	−	23.2014i	1.09494	−	1.09494i	0.0999508	−	0.994992i	$-0.468131\pi$
$449$	23.2014	−	23.2014i	1.09494	−	1.09494i	0.994992	−	0.0999508i	$-0.0318685\pi$
$450$		0			0
$451$		−	0.366403i		−	0.0172532i
$452$	7.24602	+	7.24602i	0.340824	+	0.340824i
$453$	−4.14356	−	4.14356i	−0.194682	−	0.194682i
$454$	−0.0632229	−	0.0632229i	−0.00296720	−	0.00296720i
$455$		0			0
$456$	0.337552	+	0.337552i	0.0158073	+	0.0158073i
$457$	−38.1782			−1.78590			−0.892951	−	0.450154i	$-0.851369\pi$
$457$	−38.1782			−1.78590			−0.892951	+	0.450154i	$0.851369\pi$
$458$			0.706693i			0.0330216i
$459$	−4.50086	+	8.94337i	−0.210082	+	0.417441i
$460$		0			0
$461$			3.75572i			0.174921i	0.996168	+	0.0874606i	$0.0278752\pi$
$461$			3.75572i			0.174921i	−0.996168	+	0.0874606i	$0.972125\pi$
$462$	0.0718480	−	0.0718480i	0.00334267	−	0.00334267i
$463$			2.87858i			0.133779i	0.997760	+	0.0668895i	$0.0213075\pi$
$463$			2.87858i			0.133779i	−0.997760	+	0.0668895i	$0.978692\pi$
$464$	5.38588	+	5.38588i	0.250033	+	0.250033i
$465$		0			0
$466$	−0.751885	+	0.751885i	−0.0348304	+	0.0348304i
$467$	19.5036			0.902519			0.451259	−	0.892393i	$-0.350975\pi$
$467$	19.5036			0.902519			0.451259	+	0.892393i	$0.350975\pi$
$468$	23.8855			1.10411
$469$	−3.28407	+	3.28407i	−0.151644	+	0.151644i
$470$		0			0
$471$	−3.33357	−	3.33357i	−0.153603	−	0.153603i
$472$		−	0.484837i		−	0.0223164i
$473$	1.26552	−	1.26552i	0.0581885	−	0.0581885i
$474$		−	0.205089i		−	0.00942005i
$475$		0			0
$476$	4.71388	−	9.36665i	0.216060	−	0.429320i
$477$		−	21.9186i		−	1.00358i
$478$	0.743547			0.0340090
$479$	−21.9512	−	21.9512i	−1.00298	−	1.00298i	−0.999996	−	0.00298006i	$-0.999051\pi$
$479$	−21.9512	−	21.9512i	−1.00298	−	1.00298i	−0.00298006	−	0.999996i	$-0.500949\pi$
$480$		0			0
$481$	−16.2878	−	16.2878i	−0.742661	−	0.742661i
$482$	−0.541614	−	0.541614i	−0.0246698	−	0.0246698i
$483$	2.72645	+	2.72645i	0.124058	+	0.124058i
$484$		−	1.77121i		−	0.0805096i
$485$		0			0
$486$	−0.442420	+	0.442420i	−0.0200686	+	0.0200686i
$487$	13.3233	+	13.3233i	0.603738	+	0.603738i	0.941303	−	0.337564i	$-0.109603\pi$
$487$	13.3233	+	13.3233i	0.603738	+	0.603738i	−0.337564	+	0.941303i	$0.609603\pi$
$488$	1.69280	−	1.69280i	0.0766293	−	0.0766293i
$489$	−4.33076			−0.195844
$490$		0			0
$491$			10.7005i			0.482906i	0.970413	+	0.241453i	$0.0776239\pi$
$491$			10.7005i			0.482906i	−0.970413	+	0.241453i	$0.922376\pi$
$492$			0.0958679i			0.00432206i
$493$	−3.54872	+	7.05144i	−0.159826	+	0.317581i
$494$	1.21327			0.0545874
$495$		0			0
$496$	6.53032	+	6.53032i	0.293220	+	0.293220i
$497$		−	12.4704i		−	0.559372i
$498$	−0.0777096	+	0.0777096i	−0.00348225	+	0.00348225i
$499$	−22.9732	+	22.9732i	−1.02842	+	1.02842i	−0.0288371	+	0.999584i	$0.509180\pi$
$499$	−22.9732	+	22.9732i	−1.02842	+	1.02842i	−0.999584	+	0.0288371i	$0.990820\pi$
$500$		0			0
$501$			7.94822i			0.355100i
$502$	1.28882			0.0575229
$503$	1.24757	+	1.24757i	0.0556265	+	0.0556265i	0.734373	−	0.678746i	$-0.237476\pi$
$503$	1.24757	+	1.24757i	0.0556265	+	0.0556265i	−0.678746	+	0.734373i	$0.737476\pi$
$504$	0.612288	−	0.612288i	0.0272735	−	0.0272735i
$505$		0			0
$506$	1.38979			0.0617835
$507$	−1.45010	+	1.45010i	−0.0644012	+	0.0644012i
$508$	−34.9001			−1.54844
$509$	−3.00023			−0.132983			−0.0664914	−	0.997787i	$-0.521181\pi$
$509$	−3.00023			−0.132983			−0.0664914	+	0.997787i	$0.521181\pi$
$510$		0			0
$511$	18.4712			0.817117
$512$	4.77954			0.211228
$513$	8.17747	−	8.17747i	0.361044	−	0.361044i
$514$	−1.11419			−0.0491447
$515$		0			0
$516$	−0.331118	+	0.331118i	−0.0145766	+	0.0145766i
$517$	−11.2787	−	11.2787i	−0.496035	−	0.496035i
$518$	−0.417148			−0.0183284
$519$		−	0.854342i		−	0.0375014i
$520$		0			0
$521$	15.9121	−	15.9121i	0.697121	−	0.697121i	−0.266668	−	0.963789i	$-0.585923\pi$
$521$	15.9121	−	15.9121i	0.697121	−	0.697121i	0.963789	+	0.266668i	$0.0859226\pi$
$522$	−0.230264	+	0.230264i	−0.0100784	+	0.0100784i
$523$			0.441113i			0.0192885i	0.999953	+	0.00964426i	$0.00306991\pi$
$523$			0.441113i			0.0192885i	−0.999953	+	0.00964426i	$0.996930\pi$
$524$	−14.7543	−	14.7543i	−0.644543	−	0.644543i
$525$		0			0
$526$	−0.962587			−0.0419708
$527$	−4.30278	+	8.54978i	−0.187432	+	0.372434i
$528$		−	5.27277i		−	0.229468i
$529$			29.7388i			1.29299i
$530$		0			0
$531$	−5.69770			−0.247259
$532$	−8.56450	+	8.56450i	−0.371318	+	0.371318i
$533$	0.344892	+	0.344892i	0.0149389	+	0.0149389i
$534$	0.245620	−	0.245620i	0.0106290	−	0.0106290i
$535$		0			0
$536$		−	0.876801i		−	0.0378721i
$537$	4.80904	+	4.80904i	0.207525	+	0.207525i
$538$	−0.672132	−	0.672132i	−0.0289777	−	0.0289777i
$539$	−12.0913	−	12.0913i	−0.520808	−	0.520808i
$540$		0			0
$541$	−9.19175	−	9.19175i	−0.395184	−	0.395184i	0.481346	−	0.876531i	$-0.340148\pi$
$541$	−9.19175	−	9.19175i	−0.395184	−	0.395184i	−0.876531	+	0.481346i	$0.840148\pi$
$542$	0.740606			0.0318118
$543$		−	3.08368i		−	0.132334i
$544$	0.931950	+	2.82033i	0.0399570	+	0.120921i
$545$		0			0
$546$			0.135260i			0.00578858i
$547$	−4.06711	+	4.06711i	−0.173897	+	0.173897i	−0.788689	−	0.614792i	$-0.789240\pi$
$547$	−4.06711	+	4.06711i	−0.173897	+	0.173897i	0.614792	+	0.788689i	$0.289240\pi$
$548$			32.5815i			1.39181i
$549$	−19.8934	−	19.8934i	−0.849029	−	0.849029i
$550$		0			0
$551$	6.44756	−	6.44756i	0.274675	−	0.274675i
$552$	−0.727924			−0.0309825
$553$	10.4166			0.442961
$554$	−0.623625	+	0.623625i	−0.0264953	+	0.0264953i
$555$		0			0
$556$	31.5430	+	31.5430i	1.33772	+	1.33772i
$557$			16.8695i			0.714782i	0.933955	+	0.357391i	$0.116334\pi$
$557$			16.8695i			0.714782i	−0.933955	+	0.357391i	$0.883666\pi$
$558$	−0.279192	+	0.279192i	−0.0118191	+	0.0118191i
$559$			2.38244i			0.100766i
$560$		0			0
$561$	5.18877	−	1.71457i	0.219070	−	0.0723894i
$562$			0.0161904i			0.000682949i
$563$	6.74798			0.284394			0.142197	−	0.989838i	$-0.454583\pi$
$563$	6.74798			0.284394			0.142197	+	0.989838i	$0.454583\pi$
$564$	2.95102	+	2.95102i	0.124260	+	0.124260i
$565$		0			0
$566$	0.347126	+	0.347126i	0.0145908	+	0.0145908i
$567$	−6.72606	−	6.72606i	−0.282468	−	0.282468i
$568$	1.66471	+	1.66471i	0.0698495	+	0.0698495i
$569$			17.7358i			0.743523i	0.928328	+	0.371761i	$0.121246\pi$
$569$			17.7358i			0.743523i	−0.928328	+	0.371761i	$0.878754\pi$
$570$		0			0
$571$	26.9615	−	26.9615i	1.12830	−	1.12830i	0.137851	−	0.990453i	$-0.455981\pi$
$571$	26.9615	−	26.9615i	1.12830	−	1.12830i	0.990453	−	0.137851i	$-0.0440194\pi$
$572$	−19.0037	−	19.0037i	−0.794584	−	0.794584i
$573$	5.78532	−	5.78532i	0.241685	−	0.241685i
$574$	0.00883303			0.000368684
$575$		0			0
$576$		−	22.3651i		−	0.931878i
$577$			12.9541i			0.539285i	0.962960	+	0.269643i	$0.0869056\pi$
$577$			12.9541i			0.539285i	−0.962960	+	0.269643i	$0.913094\pi$
$578$	−0.821627	+	0.609554i	−0.0341752	+	0.0253541i
$579$	0.810764			0.0336942
$580$		0			0
$581$	−3.94694	−	3.94694i	−0.163746	−	0.163746i
$582$		−	0.324869i		−	0.0134663i
$583$	−17.4388	+	17.4388i	−0.722241	+	0.722241i
$584$	−2.46578	+	2.46578i	−0.102035	+	0.102035i
$585$		0			0
$586$		−	0.851554i		−	0.0351774i
$587$	43.4517			1.79344			0.896722	−	0.442594i	$-0.145942\pi$
$587$	43.4517			1.79344			0.896722	+	0.442594i	$0.145942\pi$
$588$	3.16364	+	3.16364i	0.130466	+	0.130466i
$589$	7.81759	−	7.81759i	0.322118	−	0.322118i
$590$		0			0
$591$	10.8920			0.448037
$592$	−15.3068	+	15.3068i	−0.629105	+	0.629105i
$593$	20.8552			0.856419			0.428209	−	0.903680i	$-0.359145\pi$
$593$	20.8552			0.856419			0.428209	+	0.903680i	$0.359145\pi$
$594$	0.464710			0.0190673
$595$		0			0
$596$	−4.65661			−0.190742
$597$	1.05927			0.0433531
$598$	−1.30819	+	1.30819i	−0.0534960	+	0.0534960i
$599$	33.9126			1.38563			0.692816	−	0.721115i	$-0.256370\pi$
$599$	33.9126			1.38563			0.692816	+	0.721115i	$0.256370\pi$
$600$		0			0
$601$	13.1613	−	13.1613i	0.536860	−	0.536860i	−0.385745	−	0.922605i	$-0.626056\pi$
$601$	13.1613	−	13.1613i	0.536860	−	0.536860i	0.922605	+	0.385745i	$0.126056\pi$
$602$	0.0305084	+	0.0305084i	0.00124343	+	0.00124343i
$603$	−10.3040			−0.419610
$604$			28.0688i			1.14210i
$605$		0			0
$606$	−0.213525	+	0.213525i	−0.00867387	+	0.00867387i
$607$	−17.1393	+	17.1393i	−0.695661	+	0.695661i	−0.963472	−	0.267811i	$-0.913700\pi$
$607$	−17.1393	+	17.1393i	−0.695661	+	0.695661i	0.267811	+	0.963472i	$0.413700\pi$
$608$		−	3.43094i		−	0.139143i
$609$	0.718800	+	0.718800i	0.0291273	+	0.0291273i
$610$		0			0
$611$	21.2330			0.858995
$612$	22.0893	−	7.29918i	0.892906	−	0.295052i
$613$			33.3708i			1.34784i	0.738806	+	0.673918i	$0.235390\pi$
$613$			33.3708i			1.34784i	−0.738806	+	0.673918i	$0.764610\pi$
$614$		−	1.87529i		−	0.0756807i
$615$		0			0
$616$	−0.974292			−0.0392553
$617$	−2.71740	+	2.71740i	−0.109399	+	0.109399i	−0.759687	−	0.650289i	$-0.774648\pi$
$617$	−2.71740	+	2.71740i	−0.109399	+	0.109399i	0.650289	+	0.759687i	$0.274648\pi$
$618$	0.107630	+	0.107630i	0.00432951	+	0.00432951i
$619$	−10.8425	+	10.8425i	−0.435796	+	0.435796i	−0.890594	−	0.454799i	$-0.849711\pi$
$619$	−10.8425	+	10.8425i	−0.435796	+	0.435796i	0.454799	+	0.890594i	$0.349711\pi$
$620$		0			0
$621$			17.6346i			0.707651i
$622$	−0.583378	−	0.583378i	−0.0233913	−	0.0233913i
$623$	12.4753	+	12.4753i	0.499811	+	0.499811i
$624$	4.96321	+	4.96321i	0.198687	+	0.198687i
$625$		0			0
$626$	−0.695688	−	0.695688i	−0.0278053	−	0.0278053i
$627$	−6.31215			−0.252083
$628$			22.5819i			0.901115i
$629$	−20.0403	−	10.0855i	−0.799061	−	0.402137i
$630$		0			0
$631$			5.30984i			0.211381i	0.994399	+	0.105691i	$0.0337053\pi$
$631$			5.30984i			0.211381i	−0.994399	+	0.105691i	$0.966295\pi$
$632$	−1.39055	+	1.39055i	−0.0553131	+	0.0553131i
$633$		−	6.45763i		−	0.256668i
$634$	−1.31056	−	1.31056i	−0.0520488	−	0.0520488i
$635$		0			0
$636$	4.56280	−	4.56280i	0.180927	−	0.180927i
$637$	22.7628			0.901896
$638$	0.366403			0.0145060
$639$	19.5633	−	19.5633i	0.773911	−	0.773911i
$640$		0			0
$641$	−12.0435	−	12.0435i	−0.475689	−	0.475689i	0.428061	−	0.903750i	$-0.359197\pi$
$641$	−12.0435	−	12.0435i	−0.475689	−	0.475689i	−0.903750	+	0.428061i	$0.859197\pi$
$642$			0.424128i			0.0167390i
$643$	23.5197	−	23.5197i	0.927528	−	0.927528i	−0.0700181	−	0.997546i	$-0.522306\pi$
$643$	23.5197	−	23.5197i	0.927528	−	0.927528i	0.997546	+	0.0700181i	$0.0223057\pi$
$644$		−	18.4692i		−	0.727788i
$645$		0			0
$646$	1.12203	−	0.370762i	0.0441455	−	0.0145874i
$647$			24.1907i			0.951033i	0.879707	+	0.475517i	$0.157739\pi$
$647$			24.1907i			0.951033i	−0.879707	+	0.475517i	$0.842261\pi$
$648$	1.79576			0.0705443
$649$	4.53317	+	4.53317i	0.177943	+	0.177943i
$650$		0			0
$651$	0.871537	+	0.871537i	0.0341582	+	0.0341582i
$652$	14.6685	+	14.6685i	0.574462	+	0.574462i
$653$	2.03577	+	2.03577i	0.0796657	+	0.0796657i	0.745817	−	0.666151i	$-0.232059\pi$
$653$	2.03577	+	2.03577i	0.0796657	+	0.0796657i	−0.666151	+	0.745817i	$0.732059\pi$
$654$		−	0.226443i		−	0.00885464i
$655$		0			0
$656$	0.324118	−	0.324118i	0.0126547	−	0.0126547i
$657$	28.9773	+	28.9773i	1.13051	+	1.13051i
$658$	0.271900	−	0.271900i	0.0105998	−	0.0105998i
$659$	−24.3591			−0.948895			−0.474447	−	0.880284i	$-0.657352\pi$
$659$	−24.3591			−0.948895			−0.474447	+	0.880284i	$0.657352\pi$
$660$		0			0
$661$			3.36043i			0.130706i	0.997862	+	0.0653529i	$0.0208173\pi$
$661$			3.36043i			0.130706i	−0.997862	+	0.0653529i	$0.979183\pi$
$662$			0.0477185i			0.00185463i
$663$	−3.27023	+	6.49806i	−0.127005	+	0.252364i
$664$	1.05378			0.0408945
$665$		0			0
$666$	−0.654414	−	0.654414i	−0.0253580	−	0.0253580i
$667$			13.9040i			0.538367i
$668$	26.9209	−	26.9209i	1.04160	−	1.04160i
$669$	7.46954	−	7.46954i	0.288789	−	0.288789i
$670$		0			0
$671$			31.6550i			1.22203i
$672$	0.382495			0.0147551
$673$	−5.01831	−	5.01831i	−0.193441	−	0.193441i	0.603740	−	0.797181i	$-0.293677\pi$
$673$	−5.01831	−	5.01831i	−0.193441	−	0.193441i	−0.797181	+	0.603740i	$0.793677\pi$
$674$	1.08697	−	1.08697i	0.0418686	−	0.0418686i
$675$		0			0
$676$	9.82309			0.377811
$677$	−10.0170	+	10.0170i	−0.384986	+	0.384986i	−0.872895	−	0.487909i	$-0.837760\pi$
$677$	−10.0170	+	10.0170i	−0.384986	+	0.384986i	0.487909	+	0.872895i	$0.337760\pi$
$678$	−0.128744			−0.00494437
$679$	16.5004			0.633227
$680$		0			0
$681$	−0.619226			−0.0237288
$682$	0.444259			0.0170115
$683$	−33.0280	+	33.0280i	−1.26378	+	1.26378i	−0.314536	+	0.949246i	$0.601849\pi$
$683$	−33.0280	+	33.0280i	−1.26378	+	1.26378i	−0.949246	+	0.314536i	$0.898151\pi$
$684$	−26.8717			−1.02746
$685$		0			0
$686$	0.670953	−	0.670953i	0.0256171	−	0.0256171i
$687$	3.46080	+	3.46080i	0.132038	+	0.132038i
$688$	2.23894			0.0853589
$689$		−	32.8300i		−	1.25072i
$690$		0			0
$691$	12.6534	−	12.6534i	0.481357	−	0.481357i	−0.424208	−	0.905565i	$-0.639447\pi$
$691$	12.6534	−	12.6534i	0.481357	−	0.481357i	0.905565	+	0.424208i	$0.139447\pi$
$692$	−2.89369	+	2.89369i	−0.110002	+	0.110002i
$693$			11.4497i			0.434937i
$694$	−1.15252	−	1.15252i	−0.0437490	−	0.0437490i
$695$		0			0
$696$	−0.191910			−0.00727432
$697$	0.424350	+	0.213560i	0.0160734	+	0.00808915i
$698$		−	0.580027i		−	0.0219543i
$699$			7.36422i			0.278540i
$700$		0			0
$701$	38.7447			1.46337			0.731683	−	0.681645i	$-0.238735\pi$
$701$	38.7447			1.46337			0.731683	+	0.681645i	$0.238735\pi$
$702$	−0.437428	+	0.437428i	−0.0165096	+	0.0165096i
$703$	18.3241	+	18.3241i	0.691107	+	0.691107i
$704$	−17.7940	+	17.7940i	−0.670636	+	0.670636i
$705$		0			0
$706$		−	0.956869i		−	0.0360122i
$707$	−10.8451	−	10.8451i	−0.407873	−	0.407873i
$708$	−1.18609	−	1.18609i	−0.0445759	−	0.0445759i
$709$	11.7213	+	11.7213i	0.440202	+	0.440202i	0.892080	−	0.451878i	$-0.149246\pi$
$709$	11.7213	+	11.7213i	0.440202	+	0.440202i	−0.451878	+	0.892080i	$0.649246\pi$
$710$		0			0
$711$	16.3414	+	16.3414i	0.612852	+	0.612852i
$712$	−3.33072			−0.124824
$713$			16.8585i			0.631356i
$714$	0.0413340	+	0.125088i	0.00154689	+	0.00468130i
$715$		0			0
$716$		−	32.5768i		−	1.21745i
$717$	3.64128	−	3.64128i	0.135986	−	0.135986i
$718$		−	0.762588i		−	0.0284595i
$719$	32.5474	+	32.5474i	1.21381	+	1.21381i	0.969763	+	0.244049i	$0.0784758\pi$
$719$	32.5474	+	32.5474i	1.21381	+	1.21381i	0.244049	+	0.969763i	$0.421524\pi$
$720$		0			0
$721$	−5.46662	+	5.46662i	−0.203588	+	0.203588i
$722$	−0.221541			−0.00824488
$723$	−5.30475			−0.197286
$724$	−10.4446	+	10.4446i	−0.388169	+	0.388169i
$725$		0			0
$726$	0.0157350	+	0.0157350i	0.000583980	+	0.000583980i
$727$		−	18.1923i		−	0.674715i	−0.941377	−	0.337357i	$-0.890467\pi$
$727$		−	18.1923i		−	0.674715i	0.941377	−	0.337357i	$-0.109533\pi$
$728$	0.917092	−	0.917092i	0.0339897	−	0.0339897i
$729$		−	18.0672i		−	0.669157i
$730$		0			0
$731$	0.728050	+	2.20327i	0.0269279	+	0.0814911i
$732$		−	8.28240i		−	0.306126i
$733$	−9.02248			−0.333253			−0.166626	−	0.986020i	$-0.553287\pi$
$733$	−9.02248			−0.333253			−0.166626	+	0.986020i	$0.553287\pi$
$734$	0.984483	+	0.984483i	0.0363379	+	0.0363379i
$735$		0			0
$736$	3.69938	+	3.69938i	0.136361	+	0.136361i
$737$	8.19800	+	8.19800i	0.301977	+	0.301977i
$738$	0.0138571	+	0.0138571i	0.000510087	+	0.000510087i
$739$			28.2213i			1.03814i	0.854733	+	0.519068i	$0.173721\pi$
$739$			28.2213i			1.03814i	−0.854733	+	0.519068i	$0.826279\pi$
$740$		0			0
$741$	5.94157	−	5.94157i	0.218269	−	0.218269i
$742$	−0.420405	−	0.420405i	−0.0154335	−	0.0154335i
$743$	−22.1541	+	22.1541i	−0.812757	+	0.812757i	−0.985046	−	0.172290i	$-0.944883\pi$
$743$	−22.1541	+	22.1541i	−0.812757	+	0.812757i	0.172290	+	0.985046i	$0.444883\pi$
$744$	−0.232688			−0.00853076
$745$		0			0
$746$		−	1.27174i		−	0.0465617i
$747$		−	12.3838i		−	0.453098i
$748$	−23.3819	−	11.7672i	−0.854927	−	0.430253i
$749$	−21.5418			−0.787121
$750$		0			0
$751$	−26.0910	−	26.0910i	−0.952075	−	0.952075i	0.0468280	−	0.998903i	$-0.485089\pi$
$751$	−26.0910	−	26.0910i	−0.952075	−	0.952075i	−0.998903	+	0.0468280i	$0.985089\pi$
$752$		−	19.9541i		−	0.727652i
$753$	6.31158	−	6.31158i	0.230007	−	0.230007i
$754$	−0.344892	+	0.344892i	−0.0125602	+	0.0125602i
$755$		0			0
$756$		−	6.17565i		−	0.224606i
$757$	−28.0818			−1.02065			−0.510325	−	0.859981i	$-0.670475\pi$
$757$	−28.0818			−1.02065			−0.510325	+	0.859981i	$0.670475\pi$
$758$	−0.792735	−	0.792735i	−0.0287934	−	0.0287934i
$759$	6.80602	−	6.80602i	0.247043	−	0.247043i
$760$		0			0
$761$	−22.1562			−0.803161			−0.401581	−	0.915824i	$-0.631539\pi$
$761$	−22.1562			−0.803161			−0.401581	+	0.915824i	$0.631539\pi$
$762$	0.310044	−	0.310044i	0.0112317	−	0.0112317i
$763$	11.5013			0.416373
$764$	−39.1902			−1.41785
$765$		0			0
$766$	−1.95603			−0.0706744
$767$	−8.53408			−0.308148
$768$	4.63018	−	4.63018i	0.167077	−	0.167077i
$769$	0.921771			0.0332399			0.0166200	−	0.999862i	$-0.494709\pi$
$769$	0.921771			0.0332399			0.0166200	+	0.999862i	$0.494709\pi$
$770$		0			0
$771$	−5.45637	+	5.45637i	−0.196506	+	0.196506i
$772$	−2.74609	−	2.74609i	−0.0988340	−	0.0988340i
$773$	37.8535			1.36150			0.680748	−	0.732518i	$-0.261655\pi$
$773$	37.8535			1.36150			0.680748	+	0.732518i	$0.261655\pi$
$774$			0.0957220i			0.00344066i
$775$		0			0
$776$	−2.20269	+	2.20269i	−0.0790719	+	0.0790719i
$777$	−2.04285	+	2.04285i	−0.0732867	+	0.0732867i
$778$			1.66904i			0.0598379i
$779$	−0.388010	−	0.388010i	−0.0139019	−	0.0139019i
$780$		0			0
$781$	−31.1297			−1.11391
$782$	−0.810043	+	1.60958i	−0.0289671	+	0.0575586i
$783$			4.64917i			0.166148i
$784$		−	21.3918i		−	0.763993i
$785$		0			0
$786$	0.262146			0.00935045
$787$	0.116710	−	0.116710i	0.00416026	−	0.00416026i	−0.705024	−	0.709184i	$-0.749064\pi$
$787$	0.116710	−	0.116710i	0.00416026	−	0.00416026i	0.709184	+	0.705024i	$0.249064\pi$
$788$	−36.8916	−	36.8916i	−1.31421	−	1.31421i
$789$	−4.71395	+	4.71395i	−0.167821	+	0.167821i
$790$		0			0
$791$		−	6.53901i		−	0.232500i
$792$	−1.52845	−	1.52845i	−0.0543111	−	0.0543111i
$793$	−29.7965	−	29.7965i	−1.05811	−	1.05811i
$794$	−0.568676	−	0.568676i	−0.0201815	−	0.0201815i
$795$		0			0
$796$	−3.58780	−	3.58780i	−0.127166	−	0.127166i
$797$	38.6997			1.37081			0.685407	−	0.728160i	$-0.259624\pi$
$797$	38.6997			1.37081			0.685407	+	0.728160i	$0.259624\pi$
$798$		−	0.152170i		−	0.00538675i
$799$	19.6362	−	6.48859i	0.694680	−	0.229550i
$800$		0			0
$801$			39.1419i			1.38301i
$802$	−1.62223	+	1.62223i	−0.0572831	+	0.0572831i
$803$		−	46.1095i		−	1.62717i
$804$	−2.14498	−	2.14498i	−0.0756475	−	0.0756475i
$805$		0			0
$806$	−0.418177	+	0.418177i	−0.0147297	+	0.0147297i
$807$	−6.58309			−0.231736
$808$	2.89550			0.101863
$809$	−14.6123	+	14.6123i	−0.513741	+	0.513741i	−0.915670	−	0.401930i	$-0.868340\pi$
$809$	−14.6123	+	14.6123i	−0.513741	+	0.513741i	0.401930	+	0.915670i	$0.368340\pi$
$810$		0			0
$811$	−24.8273	−	24.8273i	−0.871805	−	0.871805i	0.120864	−	0.992669i	$-0.461433\pi$
$811$	−24.8273	−	24.8273i	−0.871805	−	0.871805i	−0.992669	+	0.120864i	$0.961433\pi$
$812$		−	4.86921i		−	0.170876i
$813$	3.62688	−	3.62688i	0.127200	−	0.127200i
$814$			1.04132i			0.0364984i
$815$		0			0
$816$	6.10667	+	3.07326i	0.213776	+	0.107586i
$817$		−	2.68029i		−	0.0937715i
$818$	1.66636			0.0582629
$819$	−10.7775	−	10.7775i	−0.376595	−	0.376595i
$820$		0			0
$821$	34.0467	+	34.0467i	1.18824	+	1.18824i	0.977554	+	0.210683i	$0.0675687\pi$
$821$	34.0467	+	34.0467i	1.18824	+	1.18824i	0.210683	+	0.977554i	$0.432431\pi$
$822$	−0.289446	−	0.289446i	−0.0100956	−	0.0100956i
$823$	8.39703	+	8.39703i	0.292702	+	0.292702i	0.838147	−	0.545445i	$-0.183639\pi$
$823$	8.39703	+	8.39703i	0.292702	+	0.292702i	−0.545445	+	0.838147i	$0.683639\pi$
$824$		−	1.45951i		−	0.0508445i
$825$		0			0
$826$	−0.109283	+	0.109283i	−0.00380245	+	0.00380245i
$827$	−17.5744	−	17.5744i	−0.611122	−	0.611122i	0.332116	−	0.943238i	$-0.392237\pi$
$827$	−17.5744	−	17.5744i	−0.611122	−	0.611122i	−0.943238	+	0.332116i	$0.892237\pi$
$828$	28.9741	−	28.9741i	1.00692	−	1.00692i
$829$	22.4093			0.778307			0.389154	−	0.921173i	$-0.372768\pi$
$829$	22.4093			0.778307			0.389154	+	0.921173i	$0.372768\pi$
$830$		0			0
$831$			6.10800i			0.211884i
$832$		−	33.4987i		−	1.16136i
$833$	21.0510	−	6.95609i	0.729375	−	0.241014i
$834$	−0.560440			−0.0194065
$835$		0			0
$836$	21.3795	+	21.3795i	0.739426	+	0.739426i
$837$			5.63707i			0.194846i
$838$	−0.260169	+	0.260169i	−0.00898737	+	0.00898737i
$839$	30.9672	−	30.9672i	1.06911	−	1.06911i	0.0716773	−	0.997428i	$-0.477165\pi$
$839$	30.9672	−	30.9672i	1.06911	−	1.06911i	0.997428	−	0.0716773i	$-0.0228352\pi$
$840$		0			0
$841$		−	25.3343i		−	0.873598i
$842$	−1.04691			−0.0360788
$843$	0.0792869	+	0.0792869i	0.00273079	+	0.00273079i
$844$	−21.8723	+	21.8723i	−0.752874	+	0.752874i
$845$		0			0
$846$	0.853102			0.0293303
$847$	−0.799194	+	0.799194i	−0.0274606	+	0.0274606i
$848$	−30.8526			−1.05948
$849$	3.39987			0.116683
$850$		0			0
$851$	−39.5156			−1.35458
$852$	8.14496			0.279042
$853$	−24.5706	+	24.5706i	−0.841281	+	0.841281i	−0.989026	−	0.147744i	$-0.952799\pi$
$853$	−24.5706	+	24.5706i	−0.841281	+	0.841281i	0.147744	+	0.989026i	$0.452799\pi$
$854$	−0.763121			−0.0261134
$855$		0			0
$856$	2.87568	−	2.87568i	0.0982888	−	0.0982888i
$857$	−2.16478	−	2.16478i	−0.0739476	−	0.0739476i	0.669166	−	0.743113i	$-0.266652\pi$
$857$	−2.16478	−	2.16478i	−0.0739476	−	0.0739476i	−0.743113	+	0.669166i	$0.766652\pi$
$858$	0.337648			0.0115271
$859$			14.1387i			0.482405i	0.970475	+	0.241202i	$0.0775417\pi$
$859$			14.1387i			0.482405i	−0.970475	+	0.241202i	$0.922458\pi$
$860$		0			0
$861$	0.0432569	−	0.0432569i	0.00147419	−	0.00147419i
$862$	0.499483	−	0.499483i	0.0170125	−	0.0170125i
$863$			13.4091i			0.456452i	0.973608	+	0.228226i	$0.0732925\pi$
$863$			13.4091i			0.456452i	−0.973608	+	0.228226i	$0.926708\pi$
$864$	1.23698	+	1.23698i	0.0420830	+	0.0420830i
$865$		0			0
$866$	−1.40253			−0.0476601
$867$	−1.03856	+	7.00874i	−0.0352713	+	0.238029i
$868$		−	5.90386i		−	0.200390i
$869$		−	26.0030i		−	0.882092i
$870$		0			0
$871$	−15.4334			−0.522941
$872$	−1.53534	+	1.53534i	−0.0519931	+	0.0519931i
$873$	25.8855	+	25.8855i	0.876092	+	0.876092i
$874$	1.47174	−	1.47174i	0.0497824	−	0.0497824i
$875$		0			0
$876$			12.0644i			0.407618i
$877$	−3.94729	−	3.94729i	−0.133290	−	0.133290i	0.637314	−	0.770604i	$-0.280045\pi$
$877$	−3.94729	−	3.94729i	−0.133290	−	0.133290i	−0.770604	+	0.637314i	$0.780045\pi$
$878$	0.256232	+	0.256232i	0.00864742	+	0.00864742i
$879$	−4.17021	−	4.17021i	−0.140658	−	0.140658i
$880$		0			0
$881$	10.5800	+	10.5800i	0.356448	+	0.356448i	0.862502	−	0.506054i	$-0.168896\pi$
$881$	10.5800	+	10.5800i	0.356448	+	0.356448i	−0.506054	+	0.862502i	$0.668896\pi$
$882$	0.914568			0.0307951
$883$		−	17.3722i		−	0.584620i	−0.956324	−	0.292310i	$-0.905576\pi$
$883$		−	17.3722i		−	0.584620i	0.956324	−	0.292310i	$-0.0944239\pi$
$884$	33.0856	−	10.9328i	1.11279	−	0.367710i
$885$		0			0
$886$		−	0.758875i		−	0.0254949i
$887$	15.1642	−	15.1642i	0.509164	−	0.509164i	−0.405106	−	0.914270i	$-0.632765\pi$
$887$	15.1642	−	15.1642i	0.509164	−	0.509164i	0.914270	+	0.405106i	$0.132765\pi$
$888$		−	0.545411i		−	0.0183028i
$889$	15.7474	+	15.7474i	0.528151	+	0.528151i
$890$		0			0
$891$	−16.7902	+	16.7902i	−0.562493	+	0.562493i
$892$	−50.5993			−1.69419
$893$	−23.8875			−0.799366
$894$	0.0413681	−	0.0413681i	0.00138356	−	0.00138356i
$895$		0			0
$896$	−1.72685	−	1.72685i	−0.0576899	−	0.0576899i
$897$			12.8129i			0.427810i
$898$	1.39625	−	1.39625i	0.0465933	−	0.0465933i
$899$			4.44457i			0.148235i
$900$		0			0
$901$	−10.0325	−	30.3611i	−0.334231	−	1.01147i
$902$		−	0.0220498i		−	0.000734179i
$903$	0.298810			0.00994376
$904$	0.872912	+	0.872912i	0.0290326	+	0.0290326i
$905$		0			0
$906$	−0.249357	−	0.249357i	−0.00828432	−	0.00828432i
$907$	−21.8367	−	21.8367i	−0.725076	−	0.725076i	0.244558	−	0.969635i	$-0.421357\pi$
$907$	−21.8367	−	21.8367i	−0.725076	−	0.725076i	−0.969635	+	0.244558i	$0.921357\pi$
$908$	2.09735	+	2.09735i	0.0696029	+	0.0696029i
$909$		−	34.0273i		−	1.12861i
$910$		0			0
$911$	−32.0459	+	32.0459i	−1.06173	+	1.06173i	−0.0637617	+	0.997965i	$0.520310\pi$
$911$	−32.0459	+	32.0459i	−1.06173	+	1.06173i	−0.997965	+	0.0637617i	$0.979690\pi$
$912$	−5.58370	−	5.58370i	−0.184895	−	0.184895i
$913$	−9.85271	+	9.85271i	−0.326077	+	0.326077i
$914$	−2.29754			−0.0759958
$915$		0			0
$916$		−	23.4437i		−	0.774603i
$917$			13.3146i			0.439688i
$918$	−0.270859	+	0.538206i	−0.00893967	+	0.0177634i
$919$	4.76737			0.157261			0.0786305	−	0.996904i	$-0.474945\pi$
$919$	4.76737			0.157261			0.0786305	+	0.996904i	$0.474945\pi$
$920$		0			0
$921$	−9.18364	−	9.18364i	−0.302611	−	0.302611i
$922$			0.226016i			0.00744346i
$923$	29.3021	−	29.3021i	0.964490	−	0.964490i
$924$	−2.38347	+	2.38347i	−0.0784106	+	0.0784106i
$925$		0			0
$926$			0.173231i			0.00569272i
$927$	−17.1519			−0.563341
$928$	0.975304	+	0.975304i	0.0320159	+	0.0320159i
$929$	20.0545	−	20.0545i	0.657968	−	0.657968i	−0.296931	−	0.954899i	$-0.595963\pi$
$929$	20.0545	−	20.0545i	0.657968	−	0.657968i	0.954899	+	0.296931i	$0.0959632\pi$
$930$		0			0
$931$	−25.6086			−0.839289
$932$	24.9429	−	24.9429i	0.817033	−	0.817033i
$933$	−5.71381			−0.187062
$934$	1.17371			0.0384050
$935$		0			0
$936$	2.87743			0.0940519
$937$	24.1392			0.788595			0.394297	−	0.918983i	$-0.370988\pi$
$937$	24.1392			0.788595			0.394297	+	0.918983i	$0.370988\pi$
$938$	−0.197633	+	0.197633i	−0.00645295	+	0.00645295i
$939$	−6.81380			−0.222360
$940$		0			0
$941$	−41.1168	+	41.1168i	−1.34037	+	1.34037i	−0.444678	+	0.895691i	$0.646682\pi$
$941$	−41.1168	+	41.1168i	−1.34037	+	1.34037i	−0.895691	+	0.444678i	$0.853318\pi$
$942$	−0.200612	−	0.200612i	−0.00653629	−	0.00653629i
$943$	0.836736			0.0272479
$944$			8.02006i			0.261031i
$945$		0			0
$946$	0.0761579	−	0.0761579i	0.00247611	−	0.00247611i
$947$	4.09293	−	4.09293i	0.133002	−	0.133002i	−0.637471	−	0.770474i	$-0.720020\pi$
$947$	4.09293	−	4.09293i	0.133002	−	0.133002i	0.770474	+	0.637471i	$0.220020\pi$
$948$			6.80359i			0.220970i
$949$	43.4025	+	43.4025i	1.40890	+	1.40890i
$950$		0			0
$951$	−12.8360			−0.416237
$952$	0.567871	−	1.12838i	0.0184048	−	0.0365710i
$953$			18.4069i			0.596258i	0.954526	+	0.298129i	$0.0963625\pi$
$953$			18.4069i			0.596258i	−0.954526	+	0.298129i	$0.903637\pi$
$954$		−	1.31905i		−	0.0427057i
$955$		0			0
$956$	−24.6663			−0.797766
$957$	1.79434	−	1.79434i	0.0580026	−	0.0580026i
$958$	−1.32101	−	1.32101i	−0.0426798	−	0.0426798i
$959$	14.7012	−	14.7012i	0.474726	−	0.474726i
$960$		0			0
$961$		−	25.6110i		−	0.826162i
$962$	−0.980189	−	0.980189i	−0.0316026	−	0.0316026i
$963$	−33.7944	−	33.7944i	−1.08901	−	1.08901i
$964$	17.9674	+	17.9674i	0.578691	+	0.578691i
$965$		0			0
$966$	0.164076	+	0.164076i	0.00527905	+	0.00527905i
$967$	19.0245			0.611786			0.305893	−	0.952066i	$-0.401045\pi$
$967$	19.0245			0.611786			0.305893	+	0.952066i	$0.401045\pi$
$968$		−	0.213374i		−	0.00685809i
$969$	3.67907	−	7.31044i	0.118189	−	0.234845i
$970$		0			0
$971$		−	25.9469i		−	0.832676i	−0.909210	−	0.416338i	$-0.863313\pi$
$971$		−	25.9469i		−	0.832676i	0.909210	−	0.416338i	$-0.136687\pi$
$972$	14.6768	−	14.6768i	0.470758	−	0.470758i
$973$		−	28.4652i		−	0.912554i
$974$	0.801789	+	0.801789i	0.0256910	+	0.0256910i
$975$		0			0
$976$	−28.0019	+	28.0019i	−0.896318	+	0.896318i
$977$	−32.8611			−1.05132			−0.525660	−	0.850694i	$-0.676182\pi$
$977$	−32.8611			−1.05132			−0.525660	+	0.850694i	$0.676182\pi$
$978$	−0.260622			−0.00833378
$979$	31.1419	−	31.1419i	0.995299	−	0.995299i
$980$		0			0
$981$	18.0430	+	18.0430i	0.576067	+	0.576067i
$982$			0.643947i			0.0205492i
$983$	16.6750	−	16.6750i	0.531851	−	0.531851i	−0.389272	−	0.921123i	$-0.627273\pi$
$983$	16.6750	−	16.6750i	0.531851	−	0.531851i	0.921123	+	0.389272i	$0.127273\pi$
$984$			0.0115490i			0.000368168i
$985$		0			0
$986$	−0.213560	+	0.424350i	−0.00680112	+	0.0135141i
$987$		−	2.66308i		−	0.0847667i
$988$	−40.2487			−1.28048
$989$	2.89000	+	2.89000i	0.0918966	+	0.0918966i
$990$		0			0
$991$	−4.05359	−	4.05359i	−0.128767	−	0.128767i	0.639786	−	0.768553i	$-0.279023\pi$
$991$	−4.05359	−	4.05359i	−0.128767	−	0.128767i	−0.768553	+	0.639786i	$0.779023\pi$
$992$	1.18254	+	1.18254i	0.0375458	+	0.0375458i
$993$	0.233686	+	0.233686i	0.00741579	+	0.00741579i
$994$		−	0.750457i		−	0.0238031i
$995$		0			0
$996$	2.57793	−	2.57793i	0.0816847	−	0.0816847i
$997$	18.1702	+	18.1702i	0.575455	+	0.575455i	0.933648	−	0.358193i	$-0.116607\pi$
$997$	18.1702	+	18.1702i	0.575455	+	0.575455i	−0.358193	+	0.933648i	$0.616607\pi$
$998$	−1.38251	+	1.38251i	−0.0437626	+	0.0437626i
$999$	−13.2131			−0.418042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.j.a.149.4		12
5.2	odd	4		425.2.e.e.251.4	yes	12
5.3	odd	4		425.2.e.c.251.3	✓	12
5.4	even	2		425.2.j.d.149.3		12
17.4	even	4		425.2.j.d.174.3		12
85.2	odd	8		7225.2.a.br.1.5		12
85.4	even	4	inner	425.2.j.a.174.4		12
85.32	odd	8		7225.2.a.br.1.6		12
85.38	odd	4		425.2.e.c.276.4	yes	12
85.53	odd	8		7225.2.a.bm.1.8		12
85.72	odd	4		425.2.e.e.276.3	yes	12
85.83	odd	8		7225.2.a.bm.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.e.c.251.3	✓	12	5.3	odd	4
425.2.e.c.276.4	yes	12	85.38	odd	4
425.2.e.e.251.4	yes	12	5.2	odd	4
425.2.e.e.276.3	yes	12	85.72	odd	4
425.2.j.a.149.4		12	1.1	even	1	trivial
425.2.j.a.174.4		12	85.4	even	4	inner
425.2.j.d.149.3		12	5.4	even	2
425.2.j.d.174.3		12	17.4	even	4
7225.2.a.bm.1.7		12	85.83	odd	8
7225.2.a.bm.1.8		12	85.53	odd	8
7225.2.a.br.1.5		12	85.2	odd	8
7225.2.a.br.1.6		12	85.32	odd	8

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.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.0601793 q^{2} +(0.294708 - 0.294708i) q^{3} -1.99638 q^{4} +(0.0177353 - 0.0177353i) q^{6} +(0.900793 + 0.900793i) q^{7} -0.240499 q^{8} +2.82629i q^{9} +(2.24864 - 2.24864i) q^{11} +(-0.588349 + 0.588349i) q^{12} +4.23326i q^{13} +(0.0542091 + 0.0542091i) q^{14} +3.97828 q^{16} +(1.29364 + 3.91491i) q^{17} +0.170084i q^{18} -4.76249i q^{19} +0.530942 q^{21} +(0.135322 - 0.135322i) q^{22} +(5.13512 + 5.13512i) q^{23} +(-0.0708771 + 0.0708771i) q^{24} +0.254754i q^{26} +(1.71706 + 1.71706i) q^{27} +(-1.79832 - 1.79832i) q^{28} +(1.35382 + 1.35382i) q^{29} +(1.64149 + 1.64149i) q^{31} +0.720409 q^{32} -1.32539i q^{33} +(0.0778504 + 0.235596i) q^{34} -5.64235i q^{36} +(-3.84759 + 3.84759i) q^{37} -0.286603i q^{38} +(1.24758 + 1.24758i) q^{39} +(0.0814719 - 0.0814719i) q^{41} +0.0319517 q^{42} +0.562791 q^{43} +(-4.48914 + 4.48914i) q^{44} +(0.309028 + 0.309028i) q^{46} -5.01576i q^{47} +(1.17243 - 1.17243i) q^{48} -5.37714i q^{49} +(1.53500 + 0.772509i) q^{51} -8.45118i q^{52} -7.75525 q^{53} +(0.103331 + 0.103331i) q^{54} +(-0.216640 - 0.216640i) q^{56} +(-1.40355 - 1.40355i) q^{57} +(0.0814719 + 0.0814719i) q^{58} +2.01596i q^{59} +(-7.03868 + 7.03868i) q^{61} +(0.0987837 + 0.0987837i) q^{62} +(-2.54591 + 2.54591i) q^{63} -7.91321 q^{64} -0.0797608i q^{66} +3.64576i q^{67} +(-2.58260 - 7.81564i) q^{68} +3.02672 q^{69} +(-6.92188 - 6.92188i) q^{71} -0.679721i q^{72} +(10.2527 - 10.2527i) q^{73} +(-0.231545 + 0.231545i) q^{74} +9.50774i q^{76} +4.05112 q^{77} +(0.0750782 + 0.0750782i) q^{78} +(5.78193 - 5.78193i) q^{79} -7.46682 q^{81} +(0.00490292 - 0.00490292i) q^{82} -4.38162 q^{83} -1.05996 q^{84} +0.0338684 q^{86} +0.797964 q^{87} +(-0.540797 + 0.540797i) q^{88} +13.8492 q^{89} +(-3.81329 + 3.81329i) q^{91} +(-10.2516 - 10.2516i) q^{92} +0.967522 q^{93} -0.301845i q^{94} +(0.212310 - 0.212310i) q^{96} +(9.15882 - 9.15882i) q^{97} -0.323593i q^{98} +(6.35533 + 6.35533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 2 q^{3} + 12 q^{4} + 6 q^{6} - 12 q^{8} - 4 q^{11} + 4 q^{12} - 14 q^{14} + 4 q^{16} + 10 q^{17} + 8 q^{21} - 10 q^{22} - 12 q^{23} + 8 q^{24} + 22 q^{27} + 34 q^{28} + 6 q^{29} - 6 q^{31}+ \cdots - 30 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 2 * q^3 + 12 * q^4 + 6 * q^6 - 12 * q^8 - 4 * q^11 + 4 * q^12 - 14 * q^14 + 4 * q^16 + 10 * q^17 + 8 * q^21 - 10 * q^22 - 12 * q^23 + 8 * q^24 + 22 * q^27 + 34 * q^28 + 6 * q^29 - 6 * q^31 - 48 * q^32 - 30 * q^34 - 18 * q^37 - 16 * q^39 + 6 * q^41 + 56 * q^42 - 16 * q^43 - 32 * q^44 + 30 * q^46 - 10 * q^48 - 40 * q^51 + 48 * q^53 - 16 * q^54 - 56 * q^56 - 18 * q^57 + 6 * q^58 - 8 * q^61 - 22 * q^62 - 30 * q^63 + 44 * q^64 + 18 * q^68 + 72 * q^69 - 20 * q^71 - 18 * q^73 + 26 * q^74 + 24 * q^77 - 38 * q^78 + 14 * q^79 - 8 * q^81 + 10 * q^82 + 52 * q^83 - 36 * q^84 + 84 * q^86 - 48 * q^87 + 66 * q^88 + 24 * q^89 + 12 * q^91 - 32 * q^92 - 60 * q^93 + 22 * q^96 + 52 * q^97 - 30 * q^99

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