LMFDB - Embedded newform 325.2.x.c.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(7,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	325.7
Dual form			325.2.x.c.93.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.20489 - 1.27299i) q^{2} +(-0.473014 - 1.76531i) q^{3} +(2.24102 + 3.88157i) q^{4} +(-1.20429 + 4.49446i) q^{6} +(1.77897 + 3.08127i) q^{7} -6.31926i q^{8} +(-0.294506 + 0.170033i) q^{9} +(-1.44584 - 5.39595i) q^{11} +(5.79214 - 5.79214i) q^{12} +(-2.23526 - 2.82906i) q^{13} -9.05848i q^{14} +(-3.56233 + 6.17014i) q^{16} +(-0.522966 - 0.140128i) q^{17} +0.865803 q^{18} +(-3.16517 - 0.848105i) q^{19} +(4.59792 - 4.59792i) q^{21} +(-3.68109 + 13.7380i) q^{22} +(5.62291 - 1.50665i) q^{23} +(-11.1555 + 2.98910i) q^{24} +(1.32713 + 9.08325i) q^{26} +(-3.43743 - 3.43743i) q^{27} +(-7.97344 + 13.8104i) q^{28} +(0.795717 + 0.459408i) q^{29} +(-0.614354 - 0.614354i) q^{31} +(4.76381 - 2.75038i) q^{32} +(-8.84162 + 5.10471i) q^{33} +(0.974699 + 0.974699i) q^{34} +(-1.31999 - 0.762095i) q^{36} +(2.52362 - 4.37103i) q^{37} +(5.89922 + 5.89922i) q^{38} +(-3.93687 + 5.28412i) q^{39} +(-6.34129 + 1.69914i) q^{41} +(-15.9910 + 4.28479i) q^{42} +(1.46927 - 5.48340i) q^{43} +(17.7046 - 17.7046i) q^{44} +(-14.3159 - 3.83592i) q^{46} -10.9051 q^{47} +(12.5772 + 3.37006i) q^{48} +(-2.82949 + 4.90082i) q^{49} +0.989479i q^{51} +(5.97193 - 15.0163i) q^{52} +(1.91524 - 1.91524i) q^{53} +(3.20332 + 11.9550i) q^{54} +(19.4714 - 11.2418i) q^{56} +5.98868i q^{57} +(-1.16965 - 2.02589i) q^{58} +(-0.0766522 + 0.286070i) q^{59} +(1.24398 + 2.15463i) q^{61} +(0.572514 + 2.13665i) q^{62} +(-1.04783 - 0.604968i) q^{63} +0.244439 q^{64} +25.9931 q^{66} +(6.17586 + 3.56563i) q^{67} +(-0.628061 - 2.34396i) q^{68} +(-5.31943 - 9.21352i) q^{69} +(3.36393 - 12.5544i) q^{71} +(1.07448 + 1.86106i) q^{72} +3.87546i q^{73} +(-11.1286 + 6.42509i) q^{74} +(-3.80125 - 14.1865i) q^{76} +(14.0543 - 14.0543i) q^{77} +(15.4070 - 6.63929i) q^{78} -8.77296i q^{79} +(-4.95228 + 8.57759i) q^{81} +(16.1448 + 4.32600i) q^{82} -5.05855 q^{83} +(28.1512 + 7.54310i) q^{84} +(-10.2199 + 10.2199i) q^{86} +(0.434612 - 1.62199i) q^{87} +(-34.0984 + 9.13664i) q^{88} +(0.609451 - 0.163302i) q^{89} +(4.74064 - 11.9203i) q^{91} +(18.4493 + 18.4493i) q^{92} +(-0.793928 + 1.37512i) q^{93} +(24.0445 + 13.8821i) q^{94} +(-7.10863 - 7.10863i) q^{96} +(-2.55465 + 1.47493i) q^{97} +(12.4774 - 7.20384i) q^{98} +(1.34330 + 1.34330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{4} - 12 q^{6} - 24 q^{9} + 8 q^{11} - 32 q^{16} + 24 q^{19} + 32 q^{21} - 56 q^{24} + 76 q^{26} + 36 q^{29} + 8 q^{31} - 44 q^{34} - 60 q^{36} - 44 q^{39} - 52 q^{41} + 80 q^{44} - 60 q^{46}+ \cdots - 208 q^{99}+O(q^{100}) $ 40 * q + 24 * q^4 - 12 * q^6 - 24 * q^9 + 8 * q^11 - 32 * q^16 + 24 * q^19 + 32 * q^21 - 56 * q^24 + 76 * q^26 + 36 * q^29 + 8 * q^31 - 44 * q^34 - 60 * q^36 - 44 * q^39 - 52 * q^41 + 80 * q^44 - 60 * q^46 - 28 * q^49 + 68 * q^54 + 72 * q^56 + 72 * q^59 - 144 * q^64 + 24 * q^66 + 80 * q^69 - 52 * q^71 - 168 * q^74 + 8 * q^76 - 20 * q^81 + 248 * q^84 - 168 * q^86 - 60 * q^89 - 100 * q^91 + 156 * q^94 - 36 * q^96 - 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−2.20489	−	1.27299i	−1.55909	−	0.900142i	−0.997344	−	0.0728338i	$-0.976796\pi$
$2$	−2.20489	−	1.27299i	−1.55909	−	0.900142i	−0.561748	−	0.827308i	$-0.689871\pi$
$3$	−0.473014	−	1.76531i	−0.273095	−	1.01920i	−0.957108	−	0.289733i	$-0.906433\pi$
$3$	−0.473014	−	1.76531i	−0.273095	−	1.01920i	0.684013	−	0.729470i	$-0.260233\pi$
$4$	2.24102	+	3.88157i	1.12051	+	1.94078i
$5$		0			0
$5$		0			0
$6$	−1.20429	+	4.49446i	−0.491648	+	1.83486i
$7$	1.77897	+	3.08127i	0.672389	+	1.16461i	0.977225	+	0.212206i	$0.0680649\pi$
$7$	1.77897	+	3.08127i	0.672389	+	1.16461i	−0.304836	+	0.952405i	$0.598602\pi$
$8$		−	6.31926i		−	2.23420i
$9$	−0.294506	+	0.170033i	−0.0981685	+	0.0566776i
$10$		0			0
$11$	−1.44584	−	5.39595i	−0.435937	−	1.62694i	−0.738814	−	0.673909i	$-0.764614\pi$
$11$	−1.44584	−	5.39595i	−0.435937	−	1.62694i	0.302877	−	0.953030i	$-0.402053\pi$
$12$	5.79214	−	5.79214i	1.67205	−	1.67205i
$13$	−2.23526	−	2.82906i	−0.619950	−	0.784641i
$13$	−2.23526	−	2.82906i	−0.619950	−	0.784641i
$14$		−	9.05848i		−	2.42098i
$15$		0			0
$16$	−3.56233	+	6.17014i	−0.890583	+	1.54253i
$17$	−0.522966	−	0.140128i	−0.126838	−	0.0339861i	0.194842	−	0.980835i	$-0.437581\pi$
$17$	−0.522966	−	0.140128i	−0.126838	−	0.0339861i	−0.321679	+	0.946849i	$0.604247\pi$
$18$	0.865803			0.204072
$19$	−3.16517	−	0.848105i	−0.726140	−	0.194569i	−0.123230	−	0.992378i	$-0.539325\pi$
$19$	−3.16517	−	0.848105i	−0.726140	−	0.194569i	−0.602910	+	0.797809i	$0.705992\pi$
$20$		0			0
$21$	4.59792	−	4.59792i	1.00335	−	1.00335i
$22$	−3.68109	+	13.7380i	−0.784811	+	2.92895i
$23$	5.62291	−	1.50665i	1.17246	−	0.314159i	0.380527	−	0.924770i	$-0.375743\pi$
$23$	5.62291	−	1.50665i	1.17246	−	0.314159i	0.791931	+	0.610610i	$0.209076\pi$
$24$	−11.1555	+	2.98910i	−2.27710	+	0.610147i
$25$		0			0
$26$	1.32713	+	9.08325i	0.260271	+	1.78137i
$27$	−3.43743	−	3.43743i	−0.661533	−	0.661533i
$28$	−7.97344	+	13.8104i	−1.50684	+	2.60992i
$29$	0.795717	+	0.459408i	0.147761	+	0.0853098i	0.572058	−	0.820213i	$-0.306145\pi$
$29$	0.795717	+	0.459408i	0.147761	+	0.0853098i	−0.424297	+	0.905523i	$0.639479\pi$
$30$		0			0
$31$	−0.614354	−	0.614354i	−0.110341	−	0.110341i	0.649781	−	0.760122i	$-0.274861\pi$
$31$	−0.614354	−	0.614354i	−0.110341	−	0.110341i	−0.760122	+	0.649781i	$0.774861\pi$
$32$	4.76381	−	2.75038i	0.842130	−	0.486204i
$33$	−8.84162	+	5.10471i	−1.53913	+	0.888616i
$34$	0.974699	+	0.974699i	0.167159	+	0.167159i
$35$		0			0
$36$	−1.31999	−	0.762095i	−0.219998	−	0.127016i
$37$	2.52362	−	4.37103i	0.414880	−	0.718593i	−0.580536	−	0.814235i	$-0.697157\pi$
$37$	2.52362	−	4.37103i	0.414880	−	0.718593i	0.995416	+	0.0956417i	$0.0304903\pi$
$38$	5.89922	+	5.89922i	0.956980	+	0.956980i
$39$	−3.93687	+	5.28412i	−0.630403	+	0.846136i
$40$		0			0
$41$	−6.34129	+	1.69914i	−0.990343	+	0.265362i	−0.717395	−	0.696667i	$-0.754666\pi$
$41$	−6.34129	+	1.69914i	−0.990343	+	0.265362i	−0.272948	+	0.962029i	$0.587999\pi$
$42$	−15.9910	+	4.28479i	−2.46747	+	0.661157i
$43$	1.46927	−	5.48340i	0.224062	−	0.836211i	−0.758716	−	0.651421i	$-0.774173\pi$
$43$	1.46927	−	5.48340i	0.224062	−	0.836211i	0.982778	−	0.184789i	$-0.0591603\pi$
$44$	17.7046	−	17.7046i	2.66906	−	2.66906i
$45$		0			0
$46$	−14.3159	−	3.83592i	−2.11076	−	0.565576i
$47$	−10.9051			−1.59067			−0.795334	−	0.606171i	$-0.792705\pi$
$47$	−10.9051			−1.59067			−0.795334	+	0.606171i	$0.792705\pi$
$48$	12.5772	+	3.37006i	1.81537	+	0.486427i
$49$	−2.82949	+	4.90082i	−0.404213	+	0.700117i
$50$		0			0
$51$			0.989479i			0.138555i
$52$	5.97193	−	15.0163i	0.828157	−	2.08239i
$53$	1.91524	−	1.91524i	0.263079	−	0.263079i	−0.563225	−	0.826304i	$-0.690439\pi$
$53$	1.91524	−	1.91524i	0.263079	−	0.263079i	0.826304	+	0.563225i	$0.190439\pi$
$54$	3.20332	+	11.9550i	0.435917	+	1.62686i
$55$		0			0
$56$	19.4714	−	11.2418i	2.60197	−	1.50225i
$57$			5.98868i			0.793220i
$58$	−1.16965	−	2.02589i	−0.153582	−	0.266012i
$59$	−0.0766522	+	0.286070i	−0.00997926	+	0.0372431i	−0.970736	−	0.240149i	$-0.922804\pi$
$59$	−0.0766522	+	0.286070i	−0.00997926	+	0.0372431i	0.960757	+	0.277392i	$0.0894702\pi$
$60$		0			0
$61$	1.24398	+	2.15463i	0.159275	+	0.275872i	0.934607	−	0.355681i	$-0.115751\pi$
$61$	1.24398	+	2.15463i	0.159275	+	0.275872i	−0.775333	+	0.631553i	$0.782418\pi$
$62$	0.572514	+	2.13665i	0.0727093	+	0.271355i
$63$	−1.04783	−	0.604968i	−0.132015	−	0.0762188i
$64$	0.244439			0.0305549
$65$		0			0
$66$	25.9931			3.19952
$67$	6.17586	+	3.56563i	0.754501	+	0.435612i	0.827318	−	0.561734i	$-0.189865\pi$
$67$	6.17586	+	3.56563i	0.754501	+	0.435612i	−0.0728167	+	0.997345i	$0.523199\pi$
$68$	−0.628061	−	2.34396i	−0.0761636	−	0.284247i
$69$	−5.31943	−	9.21352i	−0.640384	−	1.10918i
$70$		0			0
$71$	3.36393	−	12.5544i	0.399225	−	1.48993i	−0.415237	−	0.909713i	$-0.636301\pi$
$71$	3.36393	−	12.5544i	0.399225	−	1.48993i	0.814462	−	0.580216i	$-0.197032\pi$
$72$	1.07448	+	1.86106i	0.126629	+	0.219328i
$73$			3.87546i			0.453588i	0.973943	+	0.226794i	$0.0728244\pi$
$73$			3.87546i			0.453588i	−0.973943	+	0.226794i	$0.927176\pi$
$74$	−11.1286	+	6.42509i	−1.29367	+	0.746902i
$75$		0			0
$76$	−3.80125	−	14.1865i	−0.436033	−	1.62730i
$77$	14.0543	−	14.0543i	1.60163	−	1.60163i
$78$	15.4070	−	6.63929i	1.74450	−	0.751752i
$79$		−	8.77296i		−	0.987035i	−0.869736	−	0.493517i	$-0.835711\pi$
$79$		−	8.77296i		−	0.987035i	0.869736	−	0.493517i	$-0.164289\pi$
$80$		0			0
$81$	−4.95228	+	8.57759i	−0.550253	+	0.953066i
$82$	16.1448	+	4.32600i	1.78290	+	0.477726i
$83$	−5.05855			−0.555248			−0.277624	−	0.960690i	$-0.589547\pi$
$83$	−5.05855			−0.555248			−0.277624	+	0.960690i	$0.589547\pi$
$84$	28.1512	+	7.54310i	3.07155	+	0.823019i
$85$		0			0
$86$	−10.2199	+	10.2199i	−1.10204	+	1.10204i
$87$	0.434612	−	1.62199i	0.0465953	−	0.173896i
$88$	−34.0984	+	9.13664i	−3.63490	+	0.973969i
$89$	0.609451	−	0.163302i	0.0646017	−	0.0173100i	−0.226373	−	0.974041i	$-0.572687\pi$
$89$	0.609451	−	0.163302i	0.0646017	−	0.0173100i	0.290975	+	0.956731i	$0.406020\pi$
$90$		0			0
$91$	4.74064	−	11.9203i	0.496954	−	1.24958i
$92$	18.4493	+	18.4493i	1.92347	+	1.92347i
$93$	−0.793928	+	1.37512i	−0.0823265	+	0.142594i
$94$	24.0445	+	13.8821i	2.48000	+	1.43183i
$95$		0			0
$96$	−7.10863	−	7.10863i	−0.725521	−	0.725521i
$97$	−2.55465	+	1.47493i	−0.259385	+	0.149756i	−0.624054	−	0.781381i	$-0.714515\pi$
$97$	−2.55465	+	1.47493i	−0.259385	+	0.149756i	0.364669	+	0.931137i	$0.381182\pi$
$98$	12.4774	−	7.20384i	1.26041	−	0.727698i
$99$	1.34330	+	1.34330i	0.135006	+	0.135006i
$100$		0			0
$101$	10.0555	+	5.80554i	1.00056	+	0.577673i	0.908413	−	0.418073i	$-0.137294\pi$
$101$	10.0555	+	5.80554i	1.00056	+	0.577673i	0.0921450	+	0.995746i	$0.470628\pi$
$102$	1.25960	−	2.18169i	0.124719	−	0.216020i
$103$	4.94517	+	4.94517i	0.487263	+	0.487263i	0.907441	−	0.420179i	$-0.138033\pi$
$103$	4.94517	+	4.94517i	0.487263	+	0.487263i	−0.420179	+	0.907441i	$0.638033\pi$
$104$	−17.8776	+	14.1252i	−1.75304	+	1.38509i
$105$		0			0
$106$	−6.66099	+	1.78481i	−0.646973	+	0.173356i
$107$	−0.547587	+	0.146725i	−0.0529372	+	0.0141845i	−0.285190	−	0.958471i	$-0.592057\pi$
$107$	−0.547587	+	0.146725i	−0.0529372	+	0.0141845i	0.232253	+	0.972655i	$0.425390\pi$
$108$	5.63925	−	21.0460i	0.542637	−	2.02515i
$109$	−7.63903	+	7.63903i	−0.731686	+	0.731686i	−0.970954	−	0.239267i	$-0.923093\pi$
$109$	−7.63903	+	7.63903i	−0.731686	+	0.731686i	0.239267	+	0.970954i	$0.423093\pi$
$110$		0			0
$111$	−8.90993	−	2.38741i	−0.845693	−	0.226603i
$112$	−25.3492			−2.39527
$113$	2.44331	+	0.654684i	0.229847	+	0.0615874i	0.371904	−	0.928271i	$-0.378705\pi$
$113$	2.44331	+	0.654684i	0.229847	+	0.0615874i	−0.142057	+	0.989858i	$0.545372\pi$
$114$	7.62355	−	13.2044i	0.714011	−	1.23670i
$115$		0			0
$116$			4.11817i			0.382363i
$117$	1.13933	+	0.453107i	0.105331	+	0.0418897i
$118$	0.533174	−	0.533174i	0.0490827	−	0.0490827i
$119$	−0.498568	−	1.86068i	−0.0457037	−	0.170569i
$120$		0			0
$121$	−17.4995	+	10.1033i	−1.59086	+	0.918486i
$122$		−	6.33429i		−	0.573480i
$123$	5.99903	+	10.3906i	0.540915	+	0.936892i
$124$	1.00787	−	3.76144i	0.0905098	−	0.337787i
$125$		0			0
$126$	1.54024	+	2.66777i	0.137215	+	0.237664i
$127$	−3.19516	−	11.9245i	−0.283525	−	1.05813i	−0.949910	−	0.312522i	$-0.898826\pi$
$127$	−3.19516	−	11.9245i	−0.283525	−	1.05813i	0.666385	−	0.745607i	$-0.267841\pi$
$128$	−10.0666	−	5.81194i	−0.889768	−	0.513708i
$129$	−10.3749			−0.913459
$130$		0			0
$131$	1.00566			0.0878646			0.0439323	−	0.999035i	$-0.486011\pi$
$131$	1.00566			0.0878646			0.0439323	+	0.999035i	$0.486011\pi$
$132$	−39.6286	−	22.8796i	−3.44923	−	1.99141i
$133$	−3.01751	−	11.2615i	−0.261651	−	0.976496i
$134$	−9.07806	−	15.7237i	−0.784225	−	1.35832i
$135$		0			0
$136$	−0.885507	+	3.30476i	−0.0759316	+	0.283381i
$137$	4.45219	+	7.71142i	0.380376	+	0.658831i	0.991116	−	0.133000i	$-0.0424611\pi$
$137$	4.45219	+	7.71142i	0.380376	+	0.658831i	−0.610740	+	0.791831i	$0.709128\pi$
$138$			27.0864i			2.30575i
$139$	14.4284	−	8.33023i	1.22380	−	0.706561i	0.258073	−	0.966125i	$-0.416912\pi$
$139$	14.4284	−	8.33023i	1.22380	−	0.706561i	0.965726	+	0.259565i	$0.0835791\pi$
$140$		0			0
$141$	5.15825	+	19.2509i	0.434403	+	1.62121i
$142$	−23.3987	+	23.3987i	−1.96358	+	1.96358i
$143$	−12.0336	+	16.1517i	−1.00630	+	1.35068i
$144$		−	2.42285i		−	0.201904i
$145$		0			0
$146$	4.93343	−	8.54495i	0.408293	−	0.707185i
$147$	9.98986	+	2.67677i	0.823949	+	0.220777i
$148$	22.6219			1.85951
$149$	5.96188	+	1.59748i	0.488416	+	0.130871i	0.494619	−	0.869110i	$-0.335308\pi$
$149$	5.96188	+	1.59748i	0.488416	+	0.130871i	−0.00620243	+	0.999981i	$0.501974\pi$
$150$		0			0
$151$	−1.74107	+	1.74107i	−0.141687	+	0.141687i	−0.774392	−	0.632706i	$-0.781944\pi$
$151$	−1.74107	+	1.74107i	−0.141687	+	0.141687i	0.632706	+	0.774392i	$0.281944\pi$
$152$	−5.35940	+	20.0015i	−0.434705	+	1.62234i
$153$	0.177843	−	0.0476528i	0.0143777	−	0.00385250i
$154$	−48.8791	+	13.0971i	−3.93879	+	1.05540i
$155$		0			0
$156$	−29.3333	−	3.43938i	−2.34854	−	0.275371i
$157$	4.01877	+	4.01877i	0.320732	+	0.320732i	0.849048	−	0.528316i	$-0.177176\pi$
$157$	4.01877	+	4.01877i	0.320732	+	0.320732i	−0.528316	+	0.849048i	$0.677176\pi$
$158$	−11.1679	+	19.3434i	−0.888472	+	1.53888i
$159$	−4.28694	−	2.47507i	−0.339976	−	0.196285i
$160$		0			0
$161$	14.6454	+	14.6454i	1.15422	+	1.15422i
$162$	21.8384	−	12.6084i	1.71579	−	0.990612i
$163$	20.1892	−	11.6562i	1.58134	−	0.912986i	0.586673	−	0.809824i	$-0.300437\pi$
$163$	20.1892	−	11.6562i	1.58134	−	0.912986i	0.994665	−	0.103162i	$-0.0328959\pi$
$164$	−20.8063	−	20.8063i	−1.62470	−	1.62470i
$165$		0			0
$166$	11.1535	+	6.43950i	0.865683	+	0.499802i
$167$	10.3506	−	17.9278i	0.800956	−	1.38730i	−0.118031	−	0.993010i	$-0.537658\pi$
$167$	10.3506	−	17.9278i	0.800956	−	1.38730i	0.918987	−	0.394287i	$-0.129008\pi$
$168$	−29.0555	−	29.0555i	−2.24168	−	2.24168i
$169$	−3.00720	+	12.6474i	−0.231323	+	0.972877i
$170$		0			0
$171$	1.07637	−	0.288411i	0.0823118	−	0.0220554i
$172$	24.5769	−	6.58535i	1.87397	−	0.502128i
$173$	−2.48803	+	9.28545i	−0.189161	+	0.705960i	0.804540	+	0.593899i	$0.202412\pi$
$173$	−2.48803	+	9.28545i	−0.189161	+	0.705960i	−0.993701	+	0.112061i	$0.964255\pi$
$174$	−3.02306	+	3.02306i	−0.229178	+	0.229178i
$175$		0			0
$176$	38.4443	+	10.3011i	2.89785	+	0.776476i
$177$	0.541260			0.0406836
$178$	−1.55166	−	0.415765i	−0.116301	−	0.0311629i
$179$	8.68658	−	15.0456i	0.649266	−	1.12456i	−0.334033	−	0.942561i	$-0.608410\pi$
$179$	8.68658	−	15.0456i	0.649266	−	1.12456i	0.983299	−	0.182000i	$-0.0582570\pi$
$180$		0			0
$181$		−	10.7285i		−	0.797446i	−0.917071	−	0.398723i	$-0.869453\pi$
$181$		−	10.7285i		−	0.797446i	0.917071	−	0.398723i	$-0.130547\pi$
$182$	−25.6270	+	20.2481i	−1.89960	+	1.50089i
$183$	3.21518	−	3.21518i	0.237673	−	0.237673i
$184$	−9.52095	−	35.5327i	−0.701894	−	2.61950i
$185$		0			0
$186$	3.50105	−	2.02133i	0.256709	−	0.148211i
$187$			3.02450i			0.221173i
$188$	−24.4385	−	42.3288i	−1.78236	−	3.08714i
$189$	4.47656	−	16.7067i	0.325621	−	1.21524i
$190$		0			0
$191$	2.72984	+	4.72822i	0.197524	+	0.342122i	0.947725	−	0.319088i	$-0.103377\pi$
$191$	2.72984	+	4.72822i	0.197524	+	0.342122i	−0.750201	+	0.661210i	$0.770043\pi$
$192$	−0.115623	−	0.431512i	−0.00834439	−	0.0311417i
$193$	19.2652	+	11.1228i	1.38674	+	0.800636i	0.992947	−	0.118563i	$-0.0378287\pi$
$193$	19.2652	+	11.1228i	1.38674	+	0.800636i	0.393795	+	0.919198i	$0.371162\pi$
$194$	7.51028			0.539207
$195$		0			0
$196$	−25.3638			−1.81170
$197$	−9.19967	−	5.31143i	−0.655450	−	0.378424i	0.135091	−	0.990833i	$-0.456867\pi$
$197$	−9.19967	−	5.31143i	−0.655450	−	0.378424i	−0.790541	+	0.612409i	$0.790201\pi$
$198$	−1.25181	−	4.67183i	−0.0889624	−	0.332012i
$199$	11.4195	+	19.7791i	0.809504	+	1.40210i	0.913208	+	0.407494i	$0.133597\pi$
$199$	11.4195	+	19.7791i	0.809504	+	1.40210i	−0.103704	+	0.994608i	$0.533070\pi$
$200$		0			0
$201$	3.37319	−	12.5889i	0.237926	−	0.887953i
$202$	−14.7808	−	25.6011i	−1.03998	−	1.80129i
$203$			3.26909i			0.229445i
$204$	−3.84073	+	2.21745i	−0.268905	+	0.155252i
$205$		0			0
$206$	−4.60839	−	17.1987i	−0.321082	−	1.19829i
$207$	−1.39980	+	1.39980i	−0.0972927	+	0.0972927i
$208$	25.4185	−	3.71382i	1.76245	−	0.257507i
$209$			18.3053i			1.26621i
$210$		0			0
$211$	−10.2452	+	17.7453i	−0.705311	+	1.22163i	0.261268	+	0.965266i	$0.415859\pi$
$211$	−10.2452	+	17.7453i	−0.705311	+	1.22163i	−0.966579	+	0.256369i	$0.917474\pi$
$212$	11.7263	+	3.14204i	0.805363	+	0.215796i
$213$	−23.7536			−1.62757
$214$	1.39415	+	0.373561i	0.0953020	+	0.0255361i
$215$		0			0
$216$	−21.7220	+	21.7220i	−1.47799	+	1.47799i
$217$	0.800072	−	2.98591i	0.0543124	−	0.202697i
$218$	26.5676	−	7.11878i	1.79939	−	0.482145i
$219$	6.84138	−	1.83314i	0.462298	−	0.123872i
$220$		0			0
$221$	0.772534	+	1.79273i	0.0519662	+	0.120592i
$222$	16.6063	+	16.6063i	1.11454	+	1.11454i
$223$	9.38179	−	16.2497i	0.628251	−	1.08816i	−0.359651	−	0.933087i	$-0.617104\pi$
$223$	9.38179	−	16.2497i	0.628251	−	1.08816i	0.987903	−	0.155076i	$-0.0495623\pi$
$224$	16.9494	+	9.78572i	1.13248	+	0.653836i
$225$		0			0
$226$	−4.55382	−	4.55382i	−0.302916	−	0.302916i
$227$	−15.4463	+	8.91793i	−1.02521	+	0.591904i	−0.915608	−	0.402072i	$-0.868290\pi$
$227$	−15.4463	+	8.91793i	−1.02521	+	0.591904i	−0.109599	+	0.993976i	$0.534957\pi$
$228$	−23.2455	+	13.4208i	−1.53947	+	0.888812i
$229$	17.9844	+	17.9844i	1.18844	+	1.18844i	0.977498	+	0.210944i	$0.0676539\pi$
$229$	17.9844	+	17.9844i	1.18844	+	1.18844i	0.210944	+	0.977498i	$0.432346\pi$
$230$		0			0
$231$	−31.4580	−	18.1623i	−2.06979	−	1.19499i
$232$	2.90312	−	5.02835i	0.190599	−	0.330127i
$233$	2.78064	+	2.78064i	0.182166	+	0.182166i	0.792299	−	0.610133i	$-0.208884\pi$
$233$	2.78064	+	2.78064i	0.182166	+	0.182166i	−0.610133	+	0.792299i	$0.708884\pi$
$234$	−1.93530	−	2.44941i	−0.126514	−	0.160123i
$235$		0			0
$236$	−1.28218	+	0.343559i	−0.0834627	+	0.0223638i
$237$	−15.4870	+	4.14973i	−1.00599	+	0.269554i
$238$	−1.26935	+	4.73727i	−0.0822797	+	0.307072i
$239$	0.237179	−	0.237179i	0.0153418	−	0.0153418i	−0.699394	−	0.714736i	$-0.746547\pi$
$239$	0.237179	−	0.237179i	0.0153418	−	0.0153418i	0.714736	+	0.699394i	$0.246547\pi$
$240$		0			0
$241$	20.4856	+	5.48909i	1.31959	+	0.353583i	0.848825	−	0.528675i	$-0.177311\pi$
$241$	20.4856	+	5.48909i	1.31959	+	0.353583i	0.470766	+	0.882258i	$0.343977\pi$
$242$	51.4460			3.30707
$243$	3.39778	+	0.910433i	0.217968	+	0.0584043i
$244$	−5.57556	+	9.65716i	−0.356939	+	0.618236i
$245$		0			0
$246$		−	30.5469i		−	1.94760i
$247$	4.67564	+	10.8502i	0.297504	+	0.690382i
$248$	−3.88226	+	3.88226i	−0.246524	+	0.246524i
$249$	2.39276	+	8.92992i	0.151635	+	0.565910i
$250$		0			0
$251$	−10.0366	+	5.79465i	−0.633507	+	0.365755i	−0.782109	−	0.623142i	$-0.785856\pi$
$251$	−10.0366	+	5.79465i	−0.633507	+	0.365755i	0.148602	+	0.988897i	$0.452523\pi$
$252$		−	5.42299i		−	0.341616i
$253$	−16.2597	−	28.1626i	−1.02224	−	1.77056i
$254$	−8.13485	+	30.3597i	−0.510426	+	1.90493i
$255$		0			0
$256$	14.5527	+	25.2060i	0.909542	+	1.57537i
$257$	5.44551	+	20.3229i	0.339681	+	1.26771i	0.898704	+	0.438556i	$0.144510\pi$
$257$	5.44551	+	20.3229i	0.339681	+	1.26771i	−0.559023	+	0.829152i	$0.688824\pi$
$258$	22.8755	+	13.2072i	1.42417	+	0.822243i
$259$	17.9578			1.11584
$260$		0			0
$261$	−0.312458			−0.0193406
$262$	−2.21736	−	1.28019i	−0.136989	−	0.0790907i
$263$	1.48177	+	5.53006i	0.0913701	+	0.340998i	0.996444	−	0.0842561i	$-0.0268514\pi$
$263$	1.48177	+	5.53006i	0.0913701	+	0.340998i	−0.905074	+	0.425254i	$0.860185\pi$
$264$	32.2580	+	55.8725i	1.98534	+	3.43872i
$265$		0			0
$266$	−7.68254	+	28.6716i	−0.471047	+	1.75797i
$267$	−0.576558	−	0.998627i	−0.0352848	−	0.0611150i
$268$			31.9627i			1.95243i
$269$	−8.60187	+	4.96629i	−0.524465	+	0.302800i	−0.738760	−	0.673969i	$-0.764588\pi$
$269$	−8.60187	+	4.96629i	−0.524465	+	0.302800i	0.214294	+	0.976769i	$0.431255\pi$
$270$		0			0
$271$	2.57752	+	9.61945i	0.156573	+	0.584340i	0.998965	+	0.0454748i	$0.0144801\pi$
$271$	2.57752	+	9.61945i	0.156573	+	0.584340i	−0.842392	+	0.538865i	$0.818853\pi$
$272$	2.72759	−	2.72759i	0.165384	−	0.165384i
$273$	−23.2854	−	2.73025i	−1.40930	−	0.165242i
$274$		−	22.6704i		−	1.36957i
$275$		0			0
$276$	23.8419	−	41.2955i	1.43512	−	2.48569i
$277$	−6.44661	−	1.72737i	−0.387340	−	0.103787i	0.0598935	−	0.998205i	$-0.480924\pi$
$277$	−6.44661	−	1.72737i	−0.387340	−	0.103787i	−0.447233	+	0.894417i	$0.647591\pi$
$278$	−42.4173			−2.54402
$279$	0.285391	+	0.0764703i	0.0170859	+	0.00457815i
$280$		0			0
$281$	10.2459	−	10.2459i	0.611217	−	0.611217i	−0.332047	−	0.943263i	$-0.607739\pi$
$281$	10.2459	−	10.2459i	0.611217	−	0.611217i	0.943263	+	0.332047i	$0.107739\pi$
$282$	13.1328	−	49.0124i	0.782049	−	2.91865i
$283$	−4.20616	+	1.12704i	−0.250030	+	0.0669953i	−0.381657	−	0.924304i	$-0.624646\pi$
$283$	−4.20616	+	1.12704i	−0.250030	+	0.0669953i	0.131627	+	0.991299i	$0.457980\pi$
$284$	56.2693	−	15.0773i	3.33897	−	0.894674i
$285$		0			0
$286$	47.0939	−	20.2940i	2.78472	−	1.20001i
$287$	−16.5165	−	16.5165i	−0.974938	−	0.974938i
$288$	−0.935311	+	1.62001i	−0.0551137	+	0.0954598i
$289$	−14.4686	−	8.35344i	−0.851093	−	0.491379i
$290$		0			0
$291$	3.81208	+	3.81208i	0.223468	+	0.223468i
$292$	−15.0428	+	8.68499i	−0.880316	+	0.508251i
$293$	9.00804	−	5.20079i	0.526255	−	0.303834i	−0.213235	−	0.977001i	$-0.568400\pi$
$293$	9.00804	−	5.20079i	0.526255	−	0.303834i	0.739490	+	0.673167i	$0.235067\pi$
$294$	−18.6190	−	18.6190i	−1.08588	−	1.08588i
$295$		0			0
$296$	−27.6217	−	15.9474i	−1.60548	−	0.926923i
$297$	−13.5782	+	23.5181i	−0.787887	+	1.36466i
$298$	−11.1117	−	11.1117i	−0.643684	−	0.643684i
$299$	−16.8311	−	12.5398i	−0.973368	−	0.725196i
$300$		0			0
$301$	19.5096	−	5.22759i	1.12452	−	0.301313i
$302$	6.05525	−	1.62250i	0.348440	−	0.0933643i
$303$	5.49220	−	20.4972i	0.315519	−	1.17753i
$304$	16.5083	−	16.5083i	0.946817	−	0.946817i
$305$		0			0
$306$	−0.452785	−	0.121323i	−0.0258840	−	0.00693560i
$307$	8.32839			0.475326			0.237663	−	0.971348i	$-0.423619\pi$
$307$	8.32839			0.475326			0.237663	+	0.971348i	$0.423619\pi$
$308$	86.0485	+	23.0566i	4.90307	+	1.31377i
$309$	6.39064	−	11.0689i	0.363551	−	0.629688i
$310$		0			0
$311$		−	28.0328i		−	1.58960i	−0.606873	−	0.794799i	$-0.707576\pi$
$311$		−	28.0328i		−	1.58960i	0.606873	−	0.794799i	$-0.292424\pi$
$312$	33.3917	+	24.8781i	1.89044	+	1.40845i
$313$	7.96555	−	7.96555i	0.450240	−	0.450240i	−0.445194	−	0.895434i	$-0.646865\pi$
$313$	7.96555	−	7.96555i	0.450240	−	0.450240i	0.895434	+	0.445194i	$0.146865\pi$
$314$	−3.74507	−	13.9768i	−0.211347	−	0.788756i
$315$		0			0
$316$	34.0528	−	19.6604i	1.91562	−	1.10598i
$317$			8.97791i			0.504249i	0.967695	+	0.252125i	$0.0811293\pi$
$317$			8.97791i			0.504249i	−0.967695	+	0.252125i	$0.918871\pi$
$318$	6.30148	+	10.9145i	0.353370	+	0.612054i
$319$	1.32846	−	4.95788i	0.0743794	−	0.277588i
$320$		0			0
$321$	0.518032	+	0.897258i	0.0289137	+	0.0500800i
$322$	−13.6480	−	50.9351i	−0.760574	−	2.83850i
$323$	1.53643	+	0.887059i	0.0854894	+	0.0493573i
$324$	−44.3927			−2.46626
$325$		0			0
$326$	−59.3532			−3.28727
$327$	17.0986	+	9.87190i	0.945556	+	0.545917i
$328$	10.7373	+	40.0723i	0.592870	+	2.21262i
$329$	−19.3998	−	33.6015i	−1.06955	−	1.85251i
$330$		0			0
$331$	6.85543	−	25.5848i	0.376808	−	1.40627i	−0.473876	−	0.880591i	$-0.657146\pi$
$331$	6.85543	−	25.5848i	0.376808	−	1.40627i	0.850685	−	0.525676i	$-0.176188\pi$
$332$	−11.3363	−	19.6351i	−0.622162	−	1.07762i
$333$			1.71639i			0.0940576i
$334$	−45.6440	+	26.3526i	−2.49753	+	1.44195i
$335$		0			0
$336$	11.9905	+	44.7492i	0.654135	+	2.44127i
$337$	−7.90748	+	7.90748i	−0.430748	+	0.430748i	−0.888883	−	0.458135i	$-0.848518\pi$
$337$	−7.90748	+	7.90748i	−0.430748	+	0.430748i	0.458135	+	0.888883i	$0.348518\pi$
$338$	22.7306	−	24.0580i	1.23638	−	1.30858i
$339$		−	4.62288i		−	0.251080i
$340$		0			0
$341$	−2.42676	+	4.20328i	−0.131417	+	0.227620i
$342$	−2.74041	−	0.734292i	−0.148185	−	0.0397059i
$343$	4.77129			0.257625
$344$	−34.6511	−	9.28472i	−1.86826	−	0.500599i
$345$		0			0
$346$	17.3062	−	17.3062i	0.930384	−	0.930384i
$347$	−9.09230	+	33.9329i	−0.488100	+	1.82161i	0.0775746	+	0.996987i	$0.475282\pi$
$347$	−9.09230	+	33.9329i	−0.488100	+	1.82161i	−0.565675	+	0.824628i	$0.691384\pi$
$348$	7.26986	−	1.94795i	0.389705	−	0.104421i
$349$	14.6583	−	3.92769i	0.784643	−	0.210244i	0.155812	−	0.987787i	$-0.450201\pi$
$349$	14.6583	−	3.92769i	0.784643	−	0.210244i	0.628831	+	0.777542i	$0.283534\pi$
$350$		0			0
$351$	−2.04115	+	17.4082i	−0.108948	+	0.929184i
$352$	−21.7286	−	21.7286i	−1.15814	−	1.15814i
$353$	−15.2374	+	26.3920i	−0.811007	+	1.40471i	0.101153	+	0.994871i	$0.467747\pi$
$353$	−15.2374	+	26.3920i	−0.811007	+	1.40471i	−0.912160	+	0.409835i	$0.865586\pi$
$354$	−1.19342	−	0.689020i	−0.0634294	−	0.0366210i
$355$		0			0
$356$	1.99966	+	1.99966i	0.105982	+	0.105982i
$357$	−3.04885	+	1.76026i	−0.161363	+	0.0931627i
$358$	−38.3059	+	22.1159i	−2.02453	+	1.16886i
$359$	24.2548	+	24.2548i	1.28012	+	1.28012i	0.940598	+	0.339523i	$0.110266\pi$
$359$	24.2548	+	24.2548i	1.28012	+	1.28012i	0.339523	+	0.940598i	$0.389734\pi$
$360$		0			0
$361$	−7.15546	−	4.13120i	−0.376603	−	0.217432i
$362$	−13.6574	+	23.6553i	−0.717815	+	1.24329i
$363$	26.1130	+	26.1130i	1.37058	+	1.37058i
$364$	56.8933	−	8.31251i	2.98202	−	0.435694i
$365$		0			0
$366$	−11.1820	+	2.99621i	−0.584493	+	0.156614i
$367$	6.18372	−	1.65692i	0.322787	−	0.0864906i	−0.0937869	−	0.995592i	$-0.529897\pi$
$367$	6.18372	−	1.65692i	0.322787	−	0.0864906i	0.416574	+	0.909102i	$0.363231\pi$
$368$	−10.7344	+	40.0613i	−0.559570	+	2.08834i
$369$	1.57863	−	1.57863i	0.0821804	−	0.0821804i
$370$		0			0
$371$	9.30855	+	2.49422i	0.483276	+	0.129493i
$372$	−7.11685			−0.368991
$373$	−34.2706	−	9.18277i	−1.77446	−	0.475466i	−0.784906	−	0.619614i	$-0.787289\pi$
$373$	−34.2706	−	9.18277i	−1.77446	−	0.475466i	−0.989556	+	0.144148i	$0.953956\pi$
$374$	3.85016	−	6.66868i	0.199087	−	0.344829i
$375$		0			0
$376$			68.9120i			3.55387i
$377$	−0.478944	−	3.27803i	−0.0246669	−	0.168827i
$378$	−31.1379	+	31.1379i	−1.60156	+	1.60156i
$379$	−8.72914	−	32.5776i	−0.448386	−	1.67340i	−0.706838	−	0.707375i	$-0.749879\pi$
$379$	−8.72914	−	32.5776i	−0.448386	−	1.67340i	0.258452	−	0.966024i	$-0.416788\pi$
$380$		0			0
$381$	−19.5391	+	11.2809i	−1.00102	+	0.577939i
$382$		−	13.9003i		−	0.711199i
$383$	12.2034	+	21.1370i	0.623567	+	1.08005i	0.988816	+	0.149140i	$0.0476505\pi$
$383$	12.2034	+	21.1370i	0.623567	+	1.08005i	−0.365249	+	0.930910i	$0.619016\pi$
$384$	−5.49825	+	20.5198i	−0.280582	+	1.04714i
$385$		0			0
$386$	−28.3185	−	49.0490i	−1.44137	−	2.49653i
$387$	0.499649	+	1.86472i	0.0253986	+	0.0947889i
$388$	−11.4500	−	6.61069i	−0.581288	−	0.335607i
$389$	−2.40141			−0.121756			−0.0608782	−	0.998145i	$-0.519390\pi$
$389$	−2.40141			−0.121756			−0.0608782	+	0.998145i	$0.519390\pi$
$390$		0			0
$391$	−3.15171			−0.159389
$392$	30.9696	+	17.8803i	1.56420	+	0.903091i
$393$	−0.475689	−	1.77530i	−0.0239954	−	0.0895519i
$394$	13.5228	+	23.4222i	0.681271	+	1.18000i
$395$		0			0
$396$	−2.20374	+	8.22445i	−0.110742	+	0.413294i
$397$	−12.5294	−	21.7016i	−0.628834	−	1.08917i	−0.987786	−	0.155816i	$-0.950199\pi$
$397$	−12.5294	−	21.7016i	−0.628834	−	1.08917i	0.358953	−	0.933356i	$-0.383134\pi$
$398$		−	58.1476i		−	2.91467i
$399$	−18.4527	+	10.6537i	−0.923792	+	0.533352i
$400$		0			0
$401$	−2.48638	−	9.27930i	−0.124164	−	0.463386i	0.875644	−	0.482956i	$-0.160437\pi$
$401$	−2.48638	−	9.27930i	−0.124164	−	0.463386i	−0.999808	+	0.0195699i	$0.993770\pi$
$402$	−23.4631	+	23.4631i	−1.17023	+	1.17023i
$403$	−0.364804	+	3.11129i	−0.0181722	+	0.154984i
$404$			52.0414i			2.58916i
$405$		0			0
$406$	4.16154	−	7.20799i	0.206534	−	0.357727i
$407$	−27.2346	−	7.29748i	−1.34997	−	0.361723i
$408$	6.25278			0.309559
$409$	−15.1555	−	4.06090i	−0.749391	−	0.200799i	−0.136143	−	0.990689i	$-0.543471\pi$
$409$	−15.1555	−	4.06090i	−0.749391	−	0.200799i	−0.613248	+	0.789891i	$0.710137\pi$
$410$		0			0
$411$	11.5071	−	11.5071i	0.567604	−	0.567604i
$412$	−8.11277	+	30.2773i	−0.399688	+	1.49165i
$413$	−1.01782	+	0.272724i	−0.0500837	+	0.0134199i
$414$	4.86833	−	1.30447i	0.239266	−	0.0641110i
$415$		0			0
$416$	−18.4294	−	7.32928i	−0.903574	−	0.359347i
$417$	−21.5303	−	21.5303i	−1.05434	−	1.05434i
$418$	23.3025	−	40.3612i	1.13976	−	1.97413i
$419$	10.9632	+	6.32959i	0.535586	+	0.309221i	0.743288	−	0.668971i	$-0.233265\pi$
$419$	10.9632	+	6.32959i	0.535586	+	0.309221i	−0.207702	+	0.978192i	$0.566598\pi$
$420$		0			0
$421$	7.29559	+	7.29559i	0.355565	+	0.355565i	0.862175	−	0.506610i	$-0.169102\pi$
$421$	7.29559	+	7.29559i	0.355565	+	0.355565i	−0.506610	+	0.862175i	$0.669102\pi$
$422$	45.1792	−	26.0842i	2.19929	−	1.26976i
$423$	3.21161	−	1.85422i	0.156154	−	0.0901553i
$424$	−12.1029	−	12.1029i	−0.587770	−	0.587770i
$425$		0			0
$426$	52.3740	+	30.2381i	2.53753	+	1.46504i
$427$	−4.42600	+	7.66606i	−0.214189	+	0.370987i
$428$	−1.79668	−	1.79668i	−0.0868458	−	0.0868458i
$429$	34.2049	+	13.6031i	1.65143	+	0.656766i
$430$		0			0
$431$	−5.98197	+	1.60286i	−0.288141	+	0.0772073i	−0.399995	−	0.916517i	$-0.630988\pi$
$431$	−5.98197	+	1.60286i	−0.288141	+	0.0772073i	0.111853	+	0.993725i	$0.464321\pi$
$432$	33.4546	−	8.96414i	1.60959	−	0.431288i
$433$	10.1428	−	37.8533i	0.487431	−	1.81912i	−0.0814270	−	0.996679i	$-0.525948\pi$
$433$	10.1428	−	37.8533i	0.487431	−	1.81912i	0.568857	−	0.822436i	$-0.307386\pi$
$434$	−5.56511	+	5.56511i	−0.267134	+	0.267134i
$435$		0			0
$436$	−46.7707	−	12.5322i	−2.23991	−	0.600182i
$437$	−19.0753			−0.912495
$438$	−17.4181	−	4.66716i	−0.832268	−	0.223005i
$439$	−10.9109	+	18.8983i	−0.520750	+	0.901966i	0.478959	+	0.877837i	$0.341014\pi$
$439$	−10.9109	+	18.8983i	−0.520750	+	0.901966i	−0.999709	+	0.0241284i	$0.992319\pi$
$440$		0			0
$441$		−	1.92442i		−	0.0916392i
$442$	0.578777	−	4.93619i	0.0275296	−	0.234791i
$443$	−14.4160	+	14.4160i	−0.684925	+	0.684925i	−0.961106	−	0.276180i	$-0.910931\pi$
$443$	−14.4160	+	14.4160i	−0.684925	+	0.684925i	0.276180	+	0.961106i	$0.410931\pi$
$444$	−10.7005	−	39.9348i	−0.507823	−	1.89522i
$445$		0			0
$446$	−41.3716	+	23.8859i	−1.95900	+	1.13103i
$447$		−	11.2802i		−	0.533536i
$448$	0.434851	+	0.753184i	0.0205448	+	0.0355846i
$449$	1.00906	−	3.76587i	0.0476206	−	0.177722i	−0.938019	−	0.346583i	$-0.887342\pi$
$449$	1.00906	−	3.76587i	0.0476206	−	0.177722i	0.985640	+	0.168860i	$0.0540087\pi$
$450$		0			0
$451$	18.3370	+	31.7606i	0.863454	+	1.49555i
$452$	2.93432	+	10.9510i	0.138019	+	0.515094i
$453$	3.89709	+	2.24998i	0.183101	+	0.105713i
$454$	45.4098			2.13119
$455$		0			0
$456$	37.8440			1.77221
$457$	−5.19983	−	3.00212i	−0.243238	−	0.140433i	0.373426	−	0.927660i	$-0.378183\pi$
$457$	−5.19983	−	3.00212i	−0.243238	−	0.140433i	−0.616664	+	0.787227i	$0.711516\pi$
$458$	−16.7596	−	62.5476i	−0.783124	−	2.92266i
$459$	1.31598	+	2.27934i	0.0614245	+	0.106390i
$460$		0			0
$461$	−4.10333	+	15.3138i	−0.191111	+	0.713237i	0.802128	+	0.597152i	$0.203701\pi$
$461$	−4.10333	+	15.3138i	−0.191111	+	0.713237i	−0.993239	+	0.116085i	$0.962966\pi$
$462$	46.2410	+	80.0917i	2.15132	+	3.72620i
$463$			12.0148i			0.558373i	0.960237	+	0.279187i	$0.0900648\pi$
$463$			12.0148i			0.558373i	−0.960237	+	0.279187i	$0.909935\pi$
$464$	−5.66922	+	3.27312i	−0.263187	+	0.151951i
$465$		0			0
$466$	−2.59127	−	9.67075i	−0.120038	−	0.447989i
$467$	15.3736	−	15.3736i	0.711403	−	0.711403i	−0.255426	−	0.966829i	$-0.582216\pi$
$467$	15.3736	−	15.3736i	0.711403	−	0.711403i	0.966829	+	0.255426i	$0.0822156\pi$
$468$	0.794503	+	5.43781i	0.0367259	+	0.251363i
$469$			25.3727i			1.17160i
$470$		0			0
$471$	5.19344	−	8.99530i	0.239301	−	0.414482i
$472$	1.80775	+	0.484385i	0.0832084	+	0.0222956i
$473$	−31.7125			−1.45814
$474$	39.4297	+	10.5652i	1.81107	+	0.485274i
$475$		0			0
$476$	6.10506	−	6.10506i	0.279825	−	0.279825i
$477$	−0.238396	+	0.889704i	−0.0109154	+	0.0407368i
$478$	−0.824880	+	0.221026i	−0.0377291	+	0.0101095i
$479$	0.0161350	−	0.00432337i	0.000737228	−	0.000197540i	−0.258450	−	0.966025i	$-0.583212\pi$
$479$	0.0161350	−	0.00432337i	0.000737228	−	0.000197540i	0.259188	+	0.965827i	$0.416545\pi$
$480$		0			0
$481$	−18.0069	+	2.63093i	−0.821042	+	0.119960i
$482$	−38.1808	−	38.1808i	−1.73909	−	1.73909i
$483$	18.9262	−	32.7812i	0.861174	−	1.49160i
$484$	−78.4336	−	45.2837i	−3.56516	−	2.05835i
$485$		0			0
$486$	−6.33276	−	6.33276i	−0.287260	−	0.287260i
$487$	25.0150	−	14.4424i	1.13354	−	0.654448i	0.188715	−	0.982032i	$-0.439568\pi$
$487$	25.0150	−	14.4424i	1.13354	−	0.654448i	0.944822	+	0.327584i	$0.106234\pi$
$488$	13.6157	−	7.86101i	0.616353	−	0.355851i
$489$	−30.1266	−	30.1266i	−1.36237	−	1.36237i
$490$		0			0
$491$	−23.4886	−	13.5611i	−1.06003	−	0.612006i	−0.134586	−	0.990902i	$-0.542970\pi$
$491$	−23.4886	−	13.5611i	−1.06003	−	0.612006i	−0.925439	+	0.378896i	$0.876304\pi$
$492$	−26.8880	+	46.5713i	−1.21220	+	2.09960i
$493$	−0.351757	−	0.351757i	−0.0158423	−	0.0158423i
$494$	3.50296	−	29.8756i	0.157606	−	1.34417i
$495$		0			0
$496$	5.97918	−	1.60212i	0.268473	−	0.0719371i
$497$	44.6678	−	11.9687i	2.00362	−	0.536869i
$498$	6.09194	−	22.7354i	0.272987	−	1.01880i
$499$	−22.8802	+	22.8802i	−1.02426	+	1.02426i	−0.0245604	+	0.999698i	$0.507819\pi$
$499$	−22.8802	+	22.8802i	−1.02426	+	1.02426i	−0.999698	+	0.0245604i	$0.992181\pi$
$500$		0			0
$501$	−36.5442	−	9.79199i	−1.63267	−	0.437474i
$502$	29.5062			1.31693
$503$	−12.8789	−	3.45088i	−0.574240	−	0.153867i	−0.0399996	−	0.999200i	$-0.512736\pi$
$503$	−12.8789	−	3.45088i	−0.574240	−	0.153867i	−0.534241	+	0.845333i	$0.679402\pi$
$504$	−3.82295	+	6.62154i	−0.170288	+	0.294947i
$505$		0			0
$506$			82.7937i			3.68063i
$507$	23.7490	−	0.673744i	1.05473	−	0.0299220i
$508$	39.1254	−	39.1254i	1.73591	−	1.73591i
$509$	1.36731	+	5.10285i	0.0606047	+	0.226180i	0.989585	−	0.143949i	$-0.0459801\pi$
$509$	1.36731	+	5.10285i	0.0606047	+	0.226180i	−0.928980	+	0.370129i	$0.879313\pi$
$510$		0			0
$511$	−11.9413	+	6.89433i	−0.528253	+	0.304987i
$512$		−	50.8541i		−	2.24745i
$513$	7.96474	+	13.7953i	0.351652	+	0.609079i
$514$	13.8642	−	51.7418i	0.611523	−	2.28224i
$515$		0			0
$516$	−23.2504	−	40.2709i	−1.02354	−	1.77283i
$517$	15.7670	+	58.8432i	0.693431	+	2.58792i
$518$	−39.5949	−	22.8601i	−1.73970	−	1.00442i
$519$	17.5686			0.771175
$520$		0			0
$521$	36.2307			1.58730			0.793648	−	0.608378i	$-0.208179\pi$
$521$	36.2307			1.58730			0.793648	+	0.608378i	$0.208179\pi$
$522$	0.688934	+	0.397756i	0.0301538	+	0.0174093i
$523$	5.39989	+	20.1527i	0.236121	+	0.881214i	0.977640	+	0.210283i	$0.0674386\pi$
$523$	5.39989	+	20.1527i	0.236121	+	0.881214i	−0.741520	+	0.670931i	$0.765895\pi$
$524$	2.25370	+	3.90352i	0.0984534	+	0.170526i
$525$		0			0
$526$	3.77258	−	14.0795i	0.164492	−	0.613893i
$527$	0.235198	+	0.407374i	0.0102454	+	0.0177455i
$528$		−	72.7387i		−	3.16555i
$529$	9.42855	−	5.44358i	0.409937	−	0.236677i
$530$		0			0
$531$	−0.0260668	−	0.0972825i	−0.00113120	−	0.00422170i
$532$	36.9500	−	36.9500i	1.60199	−	1.60199i
$533$	18.9814	+	14.1419i	0.822177	+	0.612553i
$534$			2.93582i			0.127045i
$535$		0			0
$536$	22.5322	−	39.0269i	0.973242	−	1.68570i
$537$	−30.6690	−	8.21775i	−1.32347	−	0.354622i
$538$	25.2882			1.09025
$539$	30.5355	+	8.18197i	1.31526	+	0.352423i
$540$		0			0
$541$	31.3852	−	31.3852i	1.34936	−	1.34936i	0.462998	−	0.886359i	$-0.346774\pi$
$541$	31.3852	−	31.3852i	1.34936	−	1.34936i	0.886359	−	0.462998i	$-0.153226\pi$
$542$	6.56234	−	24.4910i	0.281877	−	1.05198i
$543$	−18.9392	+	5.07475i	−0.812760	+	0.217778i
$544$	−2.87671	+	0.770813i	−0.123338	+	0.0330483i
$545$		0			0
$546$	47.8661	+	35.6621i	2.04848	+	1.52619i
$547$	2.86933	+	2.86933i	0.122684	+	0.122684i	0.765783	−	0.643099i	$-0.222352\pi$
$547$	2.86933	+	2.86933i	0.122684	+	0.122684i	−0.643099	+	0.765783i	$0.722352\pi$
$548$	−19.9549	+	34.5630i	−0.852433	+	1.47646i
$549$	−0.732716	−	0.423034i	−0.0312716	−	0.0180546i
$550$		0			0
$551$	−2.12896	−	2.12896i	−0.0906966	−	0.0906966i
$552$	−58.2227	+	33.6149i	−2.47812	+	1.43074i
$553$	27.0319	−	15.6069i	1.14951	−	0.663671i
$554$	12.0151	+	12.0151i	0.510475	+	0.510475i
$555$		0			0
$556$	64.6687	+	37.3365i	2.74256	+	1.58342i
$557$	7.71063	−	13.3552i	0.326710	−	0.565878i	−0.655147	−	0.755501i	$-0.727393\pi$
$557$	7.71063	−	13.3552i	0.326710	−	0.565878i	0.981857	+	0.189623i	$0.0607267\pi$
$558$	−0.531909	−	0.531909i	−0.0225175	−	0.0225175i
$559$	−18.7971	+	8.10017i	−0.795033	+	0.342601i
$560$		0			0
$561$	5.33918	−	1.43063i	0.225420	−	0.0604012i
$562$	−35.6339	+	9.54807i	−1.50312	+	0.402761i
$563$	0.0909534	−	0.339443i	0.00383323	−	0.0143058i	−0.963983	−	0.265965i	$-0.914309\pi$
$563$	0.0909534	−	0.339443i	0.00383323	−	0.0143058i	0.967816	+	0.251659i	$0.0809762\pi$
$564$	−63.1637	+	63.1637i	−2.65967	+	2.65967i
$565$		0			0
$566$	10.7088	+	2.86942i	0.450125	+	0.120611i
$567$	−35.2399			−1.47993
$568$	−79.3344	−	21.2576i	−3.32880	−	0.891948i
$569$	−13.0602	+	22.6210i	−0.547513	+	0.948320i	0.450931	+	0.892559i	$0.351092\pi$
$569$	−13.0602	+	22.6210i	−0.547513	+	0.948320i	−0.998444	+	0.0557615i	$0.982241\pi$
$570$		0			0
$571$			7.08928i			0.296677i	0.988937	+	0.148339i	$0.0473925\pi$
$571$			7.08928i			0.296677i	−0.988937	+	0.148339i	$0.952607\pi$
$572$	−89.6617	−	10.5130i	−3.74894	−	0.439570i
$573$	7.05552	−	7.05552i	0.294749	−	0.294749i
$574$	15.3917	+	57.4425i	0.642436	+	2.39760i
$575$		0			0
$576$	−0.0719888	+	0.0415627i	−0.00299953	+	0.00173178i
$577$		−	1.22910i		−	0.0511681i	−0.999673	−	0.0255841i	$-0.991855\pi$
$577$		−	1.22910i		−	0.0511681i	0.999673	−	0.0255841i	$-0.00814455\pi$
$578$	21.2677	+	36.8368i	0.884621	+	1.53221i
$579$	10.5225	−	39.2704i	0.437298	−	1.63202i
$580$		0			0
$581$	−8.99902	−	15.5868i	−0.373342	−	0.646648i
$582$	−3.55247	−	13.2580i	−0.147254	−	0.549561i
$583$	−13.1037	−	7.56542i	−0.542699	−	0.313328i
$584$	24.4900			1.01340
$585$		0			0
$586$	−26.4823			−1.09397
$587$	16.8844	+	9.74820i	0.696893	+	0.402351i	0.806189	−	0.591658i	$-0.201526\pi$
$587$	16.8844	+	9.74820i	0.696893	+	0.402351i	−0.109296	+	0.994009i	$0.534860\pi$
$588$	11.9974	+	44.7750i	0.494766	+	1.84649i
$589$	1.42350	+	2.46557i	0.0586542	+	0.101592i
$590$		0			0
$591$	−5.02476	+	18.7527i	−0.206691	+	0.771382i
$592$	17.9799	+	31.1421i	0.738970	+	1.27993i
$593$			8.09052i			0.332238i	0.986106	+	0.166119i	$0.0531236\pi$
$593$			8.09052i			0.332238i	−0.986106	+	0.166119i	$0.946876\pi$
$594$	59.8769	−	34.5699i	2.45678	−	1.41842i
$595$		0			0
$596$	7.15999	+	26.7214i	0.293285	+	1.09455i
$597$	29.5147	−	29.5147i	1.20796	−	1.20796i
$598$	21.1476	+	49.0748i	0.864791	+	2.00682i
$599$		−	19.1900i		−	0.784082i	−0.919948	−	0.392041i	$-0.871769\pi$
$599$		−	19.1900i		−	0.784082i	0.919948	−	0.392041i	$-0.128231\pi$
$600$		0			0
$601$	−12.1043	+	20.9652i	−0.493743	+	0.855189i	−0.999974	−	0.00720945i	$-0.997705\pi$
$601$	−12.1043	+	20.9652i	−0.493743	+	0.855189i	0.506231	+	0.862398i	$0.331038\pi$
$602$	−49.6713	−	13.3094i	−2.02445	−	0.542450i
$603$	−2.42510			−0.0987577
$604$	−10.6599	−	2.85631i	−0.433744	−	0.116221i
$605$		0			0
$606$	−38.2024	+	38.2024i	−1.55187	+	1.55187i
$607$	8.51656	−	31.7842i	0.345677	−	1.29008i	−0.546143	−	0.837692i	$-0.683905\pi$
$607$	8.51656	−	31.7842i	0.345677	−	1.29008i	0.891820	−	0.452391i	$-0.149429\pi$
$608$	−17.4109	+	4.66523i	−0.706104	+	0.189200i
$609$	5.77097	−	1.54633i	0.233851	−	0.0626603i
$610$		0			0
$611$	24.3757	+	30.8512i	0.986136	+	1.24810i
$612$	0.583517	+	0.583517i	0.0235873	+	0.0235873i
$613$	−15.1843	+	26.3000i	−0.613287	+	1.06225i	0.377395	+	0.926052i	$0.376820\pi$
$613$	−15.1843	+	26.3000i	−0.613287	+	1.06225i	−0.990682	+	0.136193i	$0.956513\pi$
$614$	−18.3632	−	10.6020i	−0.741078	−	0.427861i
$615$		0			0
$616$	−88.8126	−	88.8126i	−3.57836	−	3.57836i
$617$	10.3576	−	5.97999i	0.416983	−	0.240745i	−0.276803	−	0.960927i	$-0.589275\pi$
$617$	10.3576	−	5.97999i	0.416983	−	0.240745i	0.693786	+	0.720182i	$0.255942\pi$
$618$	−28.1813	+	16.2705i	−1.13362	+	0.654495i
$619$	−16.0012	−	16.0012i	−0.643142	−	0.643142i	0.308185	−	0.951326i	$-0.400278\pi$
$619$	−16.0012	−	16.0012i	−0.643142	−	0.643142i	−0.951326	+	0.308185i	$0.900278\pi$
$620$		0			0
$621$	−24.5074	−	14.1493i	−0.983447	−	0.567793i
$622$	−35.6856	+	61.8093i	−1.43086	+	2.47833i
$623$	1.58738	+	1.58738i	0.0635969	+	0.0635969i
$624$	−18.5793	−	43.1148i	−0.743768	−	1.72597i
$625$		0			0
$626$	−27.7033	+	7.42307i	−1.10724	+	0.296685i
$627$	32.3146	−	8.65867i	1.29052	−	0.345794i
$628$	−6.59296	+	24.6053i	−0.263088	+	0.981857i
$629$	−1.93227	+	1.93227i	−0.0770446	+	0.0770446i
$630$		0			0
$631$	−20.3559	−	5.45435i	−0.810356	−	0.217134i	−0.170230	−	0.985404i	$-0.554451\pi$
$631$	−20.3559	−	5.45435i	−0.810356	−	0.217134i	−0.640126	+	0.768270i	$0.721118\pi$
$632$	−55.4386			−2.20523
$633$	36.1721	+	9.69228i	1.43771	+	0.385233i
$634$	11.4288	−	19.7953i	0.453896	−	0.786171i
$635$		0			0
$636$		−	22.1867i		−	0.879761i
$637$	20.1894	−	2.94981i	0.799932	−	0.116876i
$638$	−9.24045	+	9.24045i	−0.365833	+	0.365833i
$639$	1.14396	+	4.26931i	0.0452543	+	0.168891i
$640$		0			0
$641$	23.3129	−	13.4597i	0.920804	−	0.531627i	0.0369127	−	0.999318i	$-0.488248\pi$
$641$	23.3129	−	13.4597i	0.920804	−	0.531627i	0.883892	+	0.467692i	$0.154914\pi$
$642$		−	2.63781i		−	0.104106i
$643$	−7.56614	−	13.1049i	−0.298380	−	0.516809i	0.677386	−	0.735628i	$-0.263113\pi$
$643$	−7.56614	−	13.1049i	−0.298380	−	0.516809i	−0.975765	+	0.218819i	$0.929779\pi$
$644$	−24.0265	+	89.6679i	−0.946775	+	3.53341i
$645$		0			0
$646$	−2.25844	−	3.91174i	−0.0888572	−	0.153905i
$647$	−0.308952	−	1.15302i	−0.0121462	−	0.0453301i	0.959587	−	0.281413i	$-0.0908030\pi$
$647$	−0.308952	−	1.15302i	−0.0121462	−	0.0453301i	−0.971733	+	0.236083i	$0.924136\pi$
$648$	54.2041	+	31.2947i	2.12934	+	1.22937i
$649$	1.65444			0.0649426
$650$		0			0
$651$	−5.64950			−0.221422
$652$	90.4888	+	52.2437i	3.54382	+	2.04602i
$653$	−6.13430	−	22.8935i	−0.240054	−	0.895893i	−0.975805	−	0.218641i	$-0.929838\pi$
$653$	−6.13430	−	22.8935i	−0.240054	−	0.895893i	0.735751	−	0.677252i	$-0.236829\pi$
$654$	−25.1337	−	43.5329i	−0.982806	−	1.70227i
$655$		0			0
$656$	12.1058	−	45.1795i	0.472653	−	1.76396i
$657$	−0.658955	−	1.14134i	−0.0257083	−	0.0445280i
$658$			98.7834i			3.85098i
$659$	−17.8428	+	10.3015i	−0.695056	+	0.401291i	−0.805503	−	0.592591i	$-0.798105\pi$
$659$	−17.8428	+	10.3015i	−0.695056	+	0.401291i	0.110447	+	0.993882i	$0.464772\pi$
$660$		0			0
$661$	7.86806	+	29.3640i	0.306032	+	1.14213i	0.932053	+	0.362321i	$0.118016\pi$
$661$	7.86806	+	29.3640i	0.306032	+	1.14213i	−0.626021	+	0.779806i	$0.715318\pi$
$662$	−47.6847	+	47.6847i	−1.85332	+	1.85332i
$663$	2.79930	−	2.21175i	0.108716	−	0.0858971i
$664$			31.9663i			1.24053i
$665$		0			0
$666$	2.18495	−	3.78445i	0.0846652	−	0.146644i
$667$	5.16642	+	1.38434i	0.200044	+	0.0536018i
$668$	92.7841			3.58992
$669$	−33.1236	−	8.87543i	−1.28063	−	0.343144i
$670$		0			0
$671$	9.82768	−	9.82768i	0.379393	−	0.379393i
$672$	9.25756	−	34.5497i	0.357118	−	1.33278i
$673$	22.1033	−	5.92256i	0.852019	−	0.228298i	0.193722	−	0.981056i	$-0.437944\pi$
$673$	22.1033	−	5.92256i	0.852019	−	0.228298i	0.658297	+	0.752759i	$0.271277\pi$
$674$	27.5013	−	7.36895i	1.05931	−	0.283841i
$675$		0			0
$676$	−55.8310	+	16.6705i	−2.14734	+	0.641172i
$677$	15.8670	+	15.8670i	0.609820	+	0.609820i	0.942899	−	0.333079i	$-0.108088\pi$
$677$	15.8670	+	15.8670i	0.609820	+	0.609820i	−0.333079	+	0.942899i	$0.608088\pi$
$678$	−5.88490	+	10.1929i	−0.226008	+	0.391457i
$679$	−9.08929	−	5.24770i	−0.348815	−	0.201388i
$680$		0			0
$681$	23.0492	+	23.0492i	0.883248	+	0.883248i
$682$	10.7015	−	6.17851i	0.409781	−	0.236587i
$683$	2.91771	−	1.68454i	0.111643	−	0.0644573i	−0.443139	−	0.896453i	$-0.646135\pi$
$683$	2.91771	−	1.68454i	0.111643	−	0.0644573i	0.554782	+	0.831996i	$0.312802\pi$
$684$	3.53165	+	3.53165i	0.135036	+	0.135036i
$685$		0			0
$686$	−10.5202	−	6.07381i	−0.401661	−	0.231899i
$687$	23.2412	−	40.2549i	0.886707	−	1.53582i
$688$	28.5993	+	28.5993i	1.09034	+	1.09034i
$689$	−9.69942	−	1.13727i	−0.369518	−	0.0433267i
$690$		0			0
$691$	−6.49607	+	1.74062i	−0.247122	+	0.0662162i	−0.380254	−	0.924882i	$-0.624163\pi$
$691$	−6.49607	+	1.74062i	−0.247122	+	0.0662162i	0.133132	+	0.991098i	$0.457497\pi$
$692$	−41.6179	+	11.1515i	−1.58207	+	0.423915i
$693$	−1.74937	+	6.52875i	−0.0664532	+	0.248007i
$694$	63.2439	−	63.2439i	2.40071	−	2.40071i
$695$		0			0
$696$	−10.2498	−	2.74643i	−0.388518	−	0.104103i
$697$	3.55437			0.134632
$698$	−37.3199	−	9.99985i	−1.41258	−	0.378500i
$699$	3.59342	−	6.22398i	0.135916	−	0.235413i
$700$		0			0
$701$		−	16.0006i		−	0.604333i	−0.953255	−	0.302166i	$-0.902290\pi$
$701$		−	16.0006i		−	0.604333i	0.953255	−	0.302166i	$-0.0977099\pi$
$702$	26.6611	−	35.7849i	1.00626	−	1.35061i
$703$	−11.6948	+	11.6948i	−0.441076	+	0.441076i
$704$	−0.353420	−	1.31898i	−0.0133200	−	0.0497110i
$705$		0			0
$706$	67.1937	−	38.7943i	2.52887	−	1.46004i
$707$			41.3116i			1.55368i
$708$	1.21298	+	2.10094i	0.0455864	+	0.0789580i
$709$	−2.26954	+	8.47006i	−0.0852345	+	0.318100i	−0.995359	−	0.0962364i	$-0.969320\pi$
$709$	−2.26954	+	8.47006i	−0.0852345	+	0.318100i	0.910124	+	0.414336i	$0.135986\pi$
$710$		0			0
$711$	1.49169	+	2.58368i	0.0559428	+	0.0968958i
$712$	−1.03195	−	3.85128i	−0.0386739	−	0.144333i
$713$	−4.38008	−	2.52884i	−0.164035	−	0.0947057i
$714$	8.96318			0.335439
$715$		0			0
$716$	77.8674			2.91004
$717$	−0.530883	−	0.306506i	−0.0198262	−	0.0114467i
$718$	−22.6030	−	84.3554i	−0.843535	−	3.14812i
$719$	−4.30110	−	7.44972i	−0.160404	−	0.277828i	0.774610	−	0.632440i	$-0.217946\pi$
$719$	−4.30110	−	7.44972i	−0.160404	−	0.277828i	−0.935014	+	0.354612i	$0.884613\pi$
$720$		0			0
$721$	−6.44009	+	24.0348i	−0.239842	+	0.895101i
$722$	10.5180	+	18.2177i	0.391439	+	0.677993i
$723$		−	38.7598i		−	1.44149i
$724$	41.6436	−	24.0429i	1.54767	−	0.893548i
$725$		0			0
$726$	−24.3346	−	90.8181i	−0.903143	−	3.37058i
$727$	−11.6303	+	11.6303i	−0.431344	+	0.431344i	−0.889085	−	0.457742i	$-0.848659\pi$
$727$	−11.6303	+	11.6303i	−0.431344	+	0.431344i	0.457742	+	0.889085i	$0.348659\pi$
$728$	−75.3274	−	29.9574i	−2.79182	−	1.11029i
$729$			23.2849i			0.862402i
$730$		0			0
$731$	−1.53676	+	2.66174i	−0.0568391	+	0.0984481i
$732$	19.6852	+	5.27464i	0.727586	+	0.194956i
$733$	−15.5743			−0.575248			−0.287624	−	0.957743i	$-0.592865\pi$
$733$	−15.5743			−0.575248			−0.287624	+	0.957743i	$0.592865\pi$
$734$	−15.7437	−	4.21850i	−0.581109	−	0.155708i
$735$		0			0
$736$	22.6426	−	22.6426i	0.834617	−	0.834617i
$737$	10.3107	−	38.4799i	0.379798	−	1.41743i
$738$	−5.49031	+	1.47112i	−0.202101	+	0.0541528i
$739$	17.2629	−	4.62558i	0.635026	−	0.170155i	0.0730764	−	0.997326i	$-0.476718\pi$
$739$	17.2629	−	4.62558i	0.635026	−	0.170155i	0.561949	+	0.827172i	$0.310052\pi$
$740$		0			0
$741$	16.9424	−	13.3863i	0.622393	−	0.491757i
$742$	−17.3492	−	17.3492i	−0.636909	−	0.636909i
$743$	−0.457869	+	0.793052i	−0.0167976	+	0.0290943i	−0.874302	−	0.485382i	$-0.838680\pi$
$743$	−0.457869	+	0.793052i	−0.0167976	+	0.0290943i	0.857504	+	0.514477i	$0.172014\pi$
$744$	8.68977	+	5.01704i	0.318582	+	0.183934i
$745$		0			0
$746$	63.8732	+	63.8732i	2.33856	+	2.33856i
$747$	1.48977	−	0.860120i	0.0545079	−	0.0314701i
$748$	−11.7398	+	6.77797i	−0.429249	+	0.247827i
$749$	−1.42624	−	1.42624i	−0.0521138	−	0.0521138i
$750$		0			0
$751$	−21.2043	−	12.2423i	−0.773755	−	0.446728i	0.0604575	−	0.998171i	$-0.480744\pi$
$751$	−21.2043	−	12.2423i	−0.773755	−	0.446728i	−0.834212	+	0.551443i	$0.814077\pi$
$752$	38.8475	−	67.2858i	1.41662	−	2.45366i
$753$	14.9768	+	14.9768i	0.545786	+	0.545786i
$754$	−3.11689	+	7.83739i	−0.113511	+	0.285421i
$755$		0			0
$756$	74.8804	−	20.0641i	2.72337	−	0.729726i
$757$	7.69750	−	2.06254i	0.279771	−	0.0749643i	−0.116205	−	0.993225i	$-0.537073\pi$
$757$	7.69750	−	2.06254i	0.279771	−	0.0749643i	0.395976	+	0.918261i	$0.370406\pi$
$758$	−22.2243	+	82.9422i	−0.807222	+	3.01259i
$759$	−42.0246	+	42.0246i	−1.52540	+	1.52540i
$760$		0			0
$761$	19.1063	+	5.11951i	0.692602	+	0.185582i	0.587914	−	0.808923i	$-0.299949\pi$
$761$	19.1063	+	5.11951i	0.692602	+	0.185582i	0.104687	+	0.994505i	$0.466616\pi$
$762$	57.4421			2.08091
$763$	−37.1275	−	9.94830i	−1.34411	−	0.360152i
$764$	−12.2353	+	21.1921i	−0.442656	+	0.766703i
$765$		0			0
$766$		−	62.1396i		−	2.24520i
$767$	0.980647	−	0.422587i	0.0354091	−	0.0152587i
$768$	37.6128	−	37.6128i	1.35723	−	1.35723i
$769$	6.03319	+	22.5162i	0.217563	+	0.811954i	0.985249	+	0.171128i	$0.0547413\pi$
$769$	6.03319	+	22.5162i	0.217563	+	0.811954i	−0.767686	+	0.640826i	$0.778592\pi$
$770$		0			0
$771$	33.3005	−	19.2260i	1.19929	−	0.692408i
$772$			99.7057i			3.58849i
$773$	10.3043	+	17.8476i	0.370620	+	0.641932i	0.989661	−	0.143426i	$-0.0458120\pi$
$773$	10.3043	+	17.8476i	0.370620	+	0.641932i	−0.619041	+	0.785358i	$0.712479\pi$
$774$	1.27210	−	4.74754i	0.0457247	−	0.170647i
$775$		0			0
$776$	9.32044	+	16.1435i	0.334584	+	0.579517i
$777$	−8.49427	−	31.7011i	−0.304730	−	1.13727i
$778$	5.29484	+	3.05698i	0.189829	+	0.109598i
$779$	21.5123			0.770759
$780$		0			0
$781$	−72.6064			−2.59806
$782$	6.94918	+	4.01211i	0.248502	+	0.143473i
$783$	−1.15604	−	4.31440i	−0.0413135	−	0.154184i
$784$	−20.1591	−	34.9167i	−0.719970	−	1.24702i
$785$		0			0
$786$	−1.21110	+	4.51988i	−0.0431985	+	0.161219i
$787$	−23.0726	−	39.9629i	−0.822449	−	1.42452i	−0.903854	−	0.427842i	$-0.859274\pi$
$787$	−23.0726	−	39.9629i	−0.822449	−	1.42452i	0.0814049	−	0.996681i	$-0.474059\pi$
$788$		−	47.6122i		−	1.69611i
$789$	9.06137	−	5.23159i	0.322593	−	0.186249i
$790$		0			0
$791$	2.32933	+	8.69317i	0.0828214	+	0.309094i
$792$	8.48864	−	8.48864i	0.301631	−	0.301631i
$793$	3.31497	−	8.33545i	0.117718	−	0.296001i
$794$			63.7995i			2.26416i
$795$		0			0
$796$	−51.1826	+	88.6508i	−1.81412	+	3.14214i
$797$	32.1175	+	8.60586i	1.13766	+	0.304835i	0.778010	−	0.628252i	$-0.216229\pi$
$797$	32.1175	+	8.60586i	1.13766	+	0.304835i	0.359650	+	0.933087i	$0.382896\pi$
$798$	54.2483			1.92037
$799$	5.70298	+	1.52811i	0.201757	+	0.0540606i
$800$		0			0
$801$	−0.151720	+	0.151720i	−0.00536077	+	0.00536077i
$802$	−6.33030	+	23.6250i	−0.223531	+	0.834227i
$803$	20.9117	−	5.60329i	0.737960	−	0.197736i
$804$	56.4241	−	15.1188i	1.98992	−	0.533199i
$805$		0			0
$806$	4.76500	−	6.39565i	0.167840	−	0.225277i
$807$	12.8358	+	12.8358i	0.451843	+	0.451843i
$808$	36.6867	−	63.5433i	1.29063	−	2.23544i
$809$	40.0177	+	23.1042i	1.40695	+	0.812301i	0.995093	−	0.0989485i	$-0.0315479\pi$
$809$	40.0177	+	23.1042i	1.40695	+	0.812301i	0.411854	+	0.911250i	$0.364881\pi$
$810$		0			0
$811$	−22.7481	−	22.7481i	−0.798792	−	0.798792i	0.184113	−	0.982905i	$-0.441059\pi$
$811$	−22.7481	−	22.7481i	−0.798792	−	0.798792i	−0.982905	+	0.184113i	$0.941059\pi$
$812$	−12.6892	+	7.32612i	−0.445304	+	0.257096i
$813$	15.7621	−	9.10026i	0.552801	−	0.319160i
$814$	50.7596	+	50.7596i	1.77912	+	1.77912i
$815$		0			0
$816$	−6.10522	−	3.52485i	−0.213726	−	0.123395i
$817$	−9.30100	+	16.1098i	−0.325401	+	0.563611i
$818$	28.2467	+	28.2467i	0.987622	+	0.987622i
$819$	0.630694	+	4.31665i	0.0220382	+	0.150836i
$820$		0			0
$821$	25.6010	−	6.85976i	0.893480	−	0.239407i	0.217266	−	0.976112i	$-0.430286\pi$
$821$	25.6010	−	6.85976i	0.893480	−	0.239407i	0.676214	+	0.736705i	$0.263619\pi$
$822$	−40.0204	+	10.7234i	−1.39587	+	0.374022i
$823$	−3.18945	+	11.9032i	−0.111177	+	0.414919i	−0.998973	−	0.0453193i	$-0.985569\pi$
$823$	−3.18945	+	11.9032i	−0.111177	+	0.414919i	0.887795	+	0.460239i	$0.152236\pi$
$824$	31.2499	−	31.2499i	1.08864	−	1.08864i
$825$		0			0
$826$	2.59136	+	0.694352i	0.0901649	+	0.0241596i
$827$	−34.6546			−1.20506			−0.602529	−	0.798097i	$-0.705840\pi$
$827$	−34.6546			−1.20506			−0.602529	+	0.798097i	$0.705840\pi$
$828$	−8.57039	−	2.29643i	−0.297842	−	0.0798065i
$829$	20.9069	−	36.2119i	0.726128	−	1.25769i	−0.232380	−	0.972625i	$-0.574651\pi$
$829$	20.9069	−	36.2119i	0.726128	−	1.25769i	0.958508	−	0.285066i	$-0.0920155\pi$
$830$		0			0
$831$			12.1973i			0.423121i
$832$	−0.546386	−	0.691535i	−0.0189425	−	0.0239747i
$833$	2.16647	−	2.16647i	0.0750637	−	0.0750637i
$834$	20.0640	+	74.8797i	0.694758	+	2.59287i
$835$		0			0
$836$	−71.0533	+	41.0227i	−2.45743	+	1.41880i
$837$			4.22359i			0.145989i
$838$	−16.1151	−	27.9121i	−0.556685	−	0.964207i
$839$	−8.40611	+	31.3720i	−0.290211	+	1.08308i	0.654735	+	0.755858i	$0.272780\pi$
$839$	−8.40611	+	31.3720i	−0.290211	+	1.08308i	−0.944947	+	0.327225i	$0.893887\pi$
$840$		0			0
$841$	−14.0779	−	24.3836i	−0.485444	−	0.840814i
$842$	−6.79873	−	25.3732i	−0.234300	−	0.874418i
$843$	−22.9336	−	13.2407i	−0.789874	−	0.456034i
$844$	−91.8393			−3.16124
$845$		0			0
$846$	−9.44165			−0.324610
$847$	−62.2623	−	35.9471i	−2.13936	−	1.23516i
$848$	4.99459	+	18.6401i	0.171515	+	0.640102i
$849$	3.97914	+	6.89207i	0.136564	+	0.236535i
$850$		0			0
$851$	7.60443	−	28.3801i	0.260677	−	0.972859i
$852$	−53.2323	−	92.2011i	−1.82371	−	3.15876i
$853$			26.3352i			0.901700i	0.892600	+	0.450850i	$0.148879\pi$
$853$			26.3352i			0.901700i	−0.892600	+	0.450850i	$0.851121\pi$
$854$	19.5177	−	11.2685i	0.667881	−	0.385601i
$855$		0			0
$856$	0.927196	+	3.46034i	0.0316909	+	0.118272i
$857$	6.68096	−	6.68096i	0.228217	−	0.228217i	−0.583730	−	0.811948i	$-0.698407\pi$
$857$	6.68096	−	6.68096i	0.228217	−	0.228217i	0.811948	+	0.583730i	$0.198407\pi$
$858$	−58.1013	−	73.5360i	−1.98355	−	2.51048i
$859$		−	53.3535i		−	1.82040i	−0.414172	−	0.910199i	$-0.635929\pi$
$859$		−	53.3535i		−	1.82040i	0.414172	−	0.910199i	$-0.364071\pi$
$860$		0			0
$861$	−21.3442	+	36.9693i	−0.727410	+	1.25991i
$862$	15.2300	+	4.08087i	0.518737	+	0.138995i
$863$	5.83375			0.198583			0.0992916	−	0.995058i	$-0.468342\pi$
$863$	5.83375			0.198583			0.0992916	+	0.995058i	$0.468342\pi$
$864$	−25.8295	−	6.92099i	−0.878737	−	0.235457i
$865$		0			0
$866$	−70.5507	+	70.5507i	−2.39741	+	2.39741i
$867$	−7.90258	+	29.4928i	−0.268386	+	1.00163i
$868$	13.3830	−	3.58596i	0.454248	−	0.121715i
$869$	−47.3384	+	12.6843i	−1.60585	+	0.430285i
$870$		0			0
$871$	−3.71726	−	25.4420i	−0.125955	−	0.862070i
$872$	48.2730	+	48.2730i	1.63473	+	1.63473i
$873$	0.501571	−	0.868747i	0.0169756	−	0.0294026i
$874$	42.0589	+	24.2827i	1.42266	+	0.821375i
$875$		0			0
$876$	22.4472	+	22.4472i	0.758420	+	0.758420i
$877$	−22.5558	+	13.0226i	−0.761655	+	0.439742i	−0.829890	−	0.557928i	$-0.811597\pi$
$877$	−22.5558	+	13.0226i	−0.761655	+	0.439742i	0.0682348	+	0.997669i	$0.478263\pi$
$878$	48.1148	−	27.7791i	1.62380	−	0.937499i
$879$	−13.4419	−	13.4419i	−0.453386	−	0.453386i
$880$		0			0
$881$	−29.7404	−	17.1706i	−1.00198	−	0.578494i	−0.0931468	−	0.995652i	$-0.529693\pi$
$881$	−29.7404	−	17.1706i	−1.00198	−	0.578494i	−0.908834	+	0.417159i	$0.863026\pi$
$882$	−2.44978	+	4.24314i	−0.0824884	+	0.142874i
$883$	−6.01885	−	6.01885i	−0.202550	−	0.202550i	0.598541	−	0.801092i	$-0.295747\pi$
$883$	−6.01885	−	6.01885i	−0.202550	−	0.202550i	−0.801092	+	0.598541i	$0.795747\pi$
$884$	−5.22732	+	7.01618i	−0.175814	+	0.235980i
$885$		0			0
$886$	50.1372	−	13.4342i	1.68439	−	0.451331i
$887$	−30.0112	+	8.04148i	−1.00768	+	0.270006i	−0.724659	−	0.689108i	$-0.758003\pi$
$887$	−30.0112	+	8.04148i	−1.00768	+	0.270006i	−0.283019	+	0.959114i	$0.591336\pi$
$888$	−15.0867	+	56.3042i	−0.506275	+	1.88945i
$889$	31.0586	−	31.0586i	1.04167	−	1.04167i
$890$		0			0
$891$	53.4444	+	14.3204i	1.79046	+	0.479751i
$892$	84.0993			2.81585
$893$	34.5164	+	9.24865i	1.15505	+	0.309494i
$894$	−14.3596	+	24.8716i	−0.480258	+	0.831831i
$895$		0			0
$896$		−	41.3571i		−	1.38164i
$897$	−14.1753	+	35.6436i	−0.473300	+	1.19011i
$898$	−7.01880	+	7.01880i	−0.234220	+	0.234220i
$899$	−0.206613	−	0.771091i	−0.00689093	−	0.0257173i
$900$		0			0
$901$	−1.26999	+	0.733227i	−0.0423094	+	0.0244273i
$902$		−	93.3714i		−	3.10893i
$903$	−18.4567	−	31.9679i	−0.614199	−	1.06382i
$904$	4.13712	−	15.4399i	0.137598	−	0.513524i
$905$		0			0
$906$	−5.72843	−	9.92193i	−0.190314	−	0.329634i
$907$	13.1112	+	48.9315i	0.435349	+	1.62474i	0.740230	+	0.672354i	$0.234717\pi$
$907$	13.1112	+	48.9315i	0.435349	+	1.62474i	−0.304881	+	0.952390i	$0.598617\pi$
$908$	−69.2311	−	39.9706i	−2.29751	−	1.32647i
$909$	−3.94853			−0.130964
$910$		0			0
$911$	13.7580			0.455822			0.227911	−	0.973682i	$-0.426811\pi$
$911$	13.7580			0.455822			0.227911	+	0.973682i	$0.426811\pi$
$912$	−36.9510	−	21.3336i	−1.22357	−	0.706428i
$913$	7.31385	+	27.2957i	0.242053	+	0.903355i
$914$	7.64336	+	13.2387i	0.252820	+	0.437897i
$915$		0			0
$916$	−29.5042	+	110.111i	−0.974846	+	3.63817i
$917$	1.78904	+	3.09870i	0.0590792	+	0.102328i
$918$		−	6.70091i		−	0.221163i
$919$	−30.1005	+	17.3785i	−0.992922	+	0.573264i	−0.906147	−	0.422964i	$-0.860990\pi$
$919$	−30.1005	+	17.3785i	−0.992922	+	0.573264i	−0.0867759	+	0.996228i	$0.527656\pi$
$920$		0			0
$921$	−3.93944	−	14.7022i	−0.129809	−	0.484454i
$922$	28.5418	−	28.5418i	0.939974	−	0.939974i
$923$	−43.0364	+	18.5455i	−1.41656	+	0.610434i
$924$		−	162.809i		−	5.35601i
$925$		0			0
$926$	15.2947	−	26.4912i	0.502615	−	0.870555i
$927$	−2.29722	−	0.615539i	−0.0754507	−	0.0202170i
$928$	5.05419			0.165912
$929$	−16.6081	−	4.45014i	−0.544895	−	0.146004i	−0.0241374	−	0.999709i	$-0.507684\pi$
$929$	−16.6081	−	4.45014i	−0.544895	−	0.146004i	−0.520758	+	0.853704i	$0.674351\pi$
$930$		0			0
$931$	13.1122	−	13.1122i	0.429736	−	0.429736i
$932$	−4.56177	+	17.0247i	−0.149426	+	0.557664i
$933$	−49.4867	+	13.2599i	−1.62012	+	0.434110i
$934$	−53.4674	+	14.3266i	−1.74951	+	0.468779i
$935$		0			0
$936$	2.86330	−	7.19973i	0.0935899	−	0.235331i
$937$	7.99008	+	7.99008i	0.261025	+	0.261025i	0.825470	−	0.564446i	$-0.190910\pi$
$937$	7.99008	+	7.99008i	0.261025	+	0.261025i	−0.564446	+	0.825470i	$0.690910\pi$
$938$	32.2992	−	55.9439i	1.05461	−	1.82663i
$939$	−17.8295	−	10.2939i	−0.581844	−	0.335928i
$940$		0			0
$941$	−33.6480	−	33.6480i	−1.09689	−	1.09689i	−0.994772	−	0.102122i	$-0.967437\pi$
$941$	−33.6480	−	33.6480i	−1.09689	−	1.09689i	−0.102122	−	0.994772i	$-0.532563\pi$
$942$	−22.9019	+	13.2224i	−0.746185	+	0.430810i
$943$	−33.0965	+	19.1083i	−1.07777	+	0.622251i
$944$	−1.49203	−	1.49203i	−0.0485614	−	0.0485614i
$945$		0			0
$946$	69.9225	+	40.3698i	2.27338	+	1.31253i
$947$	5.85058	−	10.1335i	0.190118	−	0.329294i	−0.755171	−	0.655528i	$-0.772446\pi$
$947$	5.85058	−	10.1335i	0.190118	−	0.329294i	0.945289	+	0.326233i	$0.105780\pi$
$948$	−50.8142	−	50.8142i	−1.65037	−	1.65037i
$949$	10.9639	−	8.66266i	0.355904	−	0.281202i
$950$		0			0
$951$	15.8488	−	4.24667i	0.513933	−	0.137708i
$952$	−11.7581	+	3.15059i	−0.381084	+	0.102111i
$953$	11.5252	−	43.0128i	0.373339	−	1.39332i	−0.482417	−	0.875942i	$-0.660241\pi$
$953$	11.5252	−	43.0128i	0.373339	−	1.39332i	0.855756	−	0.517379i	$-0.173092\pi$
$954$	1.65822	−	1.65822i	0.0536870	−	0.0536870i
$955$		0			0
$956$	1.45215	+	0.389102i	0.0469659	+	0.0125845i
$957$	−9.38058			−0.303231
$958$	−0.0410796	−	0.0110072i	−0.00132722	−	0.000355628i
$959$	−15.8407	+	27.4368i	−0.511521	+	0.885981i
$960$		0			0
$961$		−	30.2451i		−	0.975650i
$962$	43.0523	+	17.1217i	1.38806	+	0.552026i
$963$	0.136319	−	0.136319i	0.00439282	−	0.00439282i
$964$	24.6024	+	91.8173i	0.792389	+	2.95724i
$965$		0			0
$966$	−83.4605	+	48.1860i	−2.68530	+	1.55036i
$967$			5.16153i			0.165984i	0.996550	+	0.0829918i	$0.0264475\pi$
$967$			5.16153i			0.165984i	−0.996550	+	0.0829918i	$0.973552\pi$
$968$	63.8457	+	110.584i	2.05208	+	3.55430i
$969$	0.839183	−	3.13187i	0.0269584	−	0.100610i
$970$		0			0
$971$	28.4769	+	49.3235i	0.913868	+	1.58287i	0.808550	+	0.588427i	$0.200253\pi$
$971$	28.4769	+	49.3235i	0.913868	+	1.58287i	0.105318	+	0.994439i	$0.466414\pi$
$972$	4.08060	+	15.2290i	0.130885	+	0.488471i
$973$	51.3354	+	29.6385i	1.64574	+	0.950167i
$974$	−73.5404			−2.35639
$975$		0			0
$976$	−17.7258			−0.567390
$977$	−6.05123	−	3.49368i	−0.193596	−	0.111773i	0.400069	−	0.916485i	$-0.368986\pi$
$977$	−6.05123	−	3.49368i	−0.193596	−	0.111773i	−0.593665	+	0.804712i	$0.702320\pi$
$978$	28.0749	+	104.777i	0.897735	+	3.35039i
$979$	−1.76234	−	3.05246i	−0.0563246	−	0.0975570i
$980$		0			0
$981$	0.950850	−	3.54862i	0.0303583	−	0.113299i
$982$	34.5265	+	59.8016i	1.10178	+	1.90835i
$983$		−	42.2337i		−	1.34705i	−0.739166	−	0.673523i	$-0.764780\pi$
$983$		−	42.2337i		−	1.34705i	0.739166	−	0.673523i	$-0.235220\pi$
$984$	65.6611	−	37.9095i	2.09320	−	1.20851i
$985$		0			0
$986$	0.327801	+	1.22337i	0.0104393	+	0.0389600i
$987$	−50.1407	+	50.1407i	−1.59600	+	1.59600i
$988$	−31.6376	+	42.4644i	−1.00653	+	1.35097i
$989$		−	33.0464i		−	1.05081i
$990$		0			0
$991$	3.29979	−	5.71540i	0.104821	−	0.181556i	−0.808844	−	0.588023i	$-0.799906\pi$
$991$	3.29979	−	5.71540i	0.104821	−	0.181556i	0.913665	+	0.406468i	$0.133240\pi$
$992$	−4.61637	−	1.23695i	−0.146570	−	0.0392733i
$993$	−48.4078			−1.53618
$994$	−113.724	−	30.4721i	−3.60709	−	0.966517i
$995$		0			0
$996$	−29.2998	+	29.2998i	−0.928401	+	0.928401i
$997$	2.72446	−	10.1678i	0.0862846	−	0.322018i	−0.909270	−	0.416207i	$-0.863359\pi$
$997$	2.72446	−	10.1678i	0.0862846	−	0.322018i	0.995554	+	0.0941888i	$0.0300257\pi$
$998$	79.5747	−	21.3220i	2.51889	−	0.674935i
$999$	−23.6998	+	6.35035i	−0.749830	+	0.200916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.x.c.7.1	yes	40
5.2	odd	4		325.2.s.c.293.10	yes	40
5.3	odd	4		325.2.s.c.293.1	yes	40
5.4	even	2	inner	325.2.x.c.7.10	yes	40
13.2	odd	12		325.2.s.c.132.1	✓	40
65.2	even	12	inner	325.2.x.c.93.10	yes	40
65.28	even	12	inner	325.2.x.c.93.1	yes	40
65.54	odd	12		325.2.s.c.132.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.132.1	✓	40	13.2	odd	12
325.2.s.c.132.10	yes	40	65.54	odd	12
325.2.s.c.293.1	yes	40	5.3	odd	4
325.2.s.c.293.10	yes	40	5.2	odd	4
325.2.x.c.7.1	yes	40	1.1	even	1	trivial
325.2.x.c.7.10	yes	40	5.4	even	2	inner
325.2.x.c.93.1	yes	40	65.28	even	12	inner
325.2.x.c.93.10	yes	40	65.2	even	12	inner

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.20489 - 1.27299i) q^{2} +(-0.473014 - 1.76531i) q^{3} +(2.24102 + 3.88157i) q^{4} +(-1.20429 + 4.49446i) q^{6} +(1.77897 + 3.08127i) q^{7} -6.31926i q^{8} +(-0.294506 + 0.170033i) q^{9} +(-1.44584 - 5.39595i) q^{11} +(5.79214 - 5.79214i) q^{12} +(-2.23526 - 2.82906i) q^{13} -9.05848i q^{14} +(-3.56233 + 6.17014i) q^{16} +(-0.522966 - 0.140128i) q^{17} +0.865803 q^{18} +(-3.16517 - 0.848105i) q^{19} +(4.59792 - 4.59792i) q^{21} +(-3.68109 + 13.7380i) q^{22} +(5.62291 - 1.50665i) q^{23} +(-11.1555 + 2.98910i) q^{24} +(1.32713 + 9.08325i) q^{26} +(-3.43743 - 3.43743i) q^{27} +(-7.97344 + 13.8104i) q^{28} +(0.795717 + 0.459408i) q^{29} +(-0.614354 - 0.614354i) q^{31} +(4.76381 - 2.75038i) q^{32} +(-8.84162 + 5.10471i) q^{33} +(0.974699 + 0.974699i) q^{34} +(-1.31999 - 0.762095i) q^{36} +(2.52362 - 4.37103i) q^{37} +(5.89922 + 5.89922i) q^{38} +(-3.93687 + 5.28412i) q^{39} +(-6.34129 + 1.69914i) q^{41} +(-15.9910 + 4.28479i) q^{42} +(1.46927 - 5.48340i) q^{43} +(17.7046 - 17.7046i) q^{44} +(-14.3159 - 3.83592i) q^{46} -10.9051 q^{47} +(12.5772 + 3.37006i) q^{48} +(-2.82949 + 4.90082i) q^{49} +0.989479i q^{51} +(5.97193 - 15.0163i) q^{52} +(1.91524 - 1.91524i) q^{53} +(3.20332 + 11.9550i) q^{54} +(19.4714 - 11.2418i) q^{56} +5.98868i q^{57} +(-1.16965 - 2.02589i) q^{58} +(-0.0766522 + 0.286070i) q^{59} +(1.24398 + 2.15463i) q^{61} +(0.572514 + 2.13665i) q^{62} +(-1.04783 - 0.604968i) q^{63} +0.244439 q^{64} +25.9931 q^{66} +(6.17586 + 3.56563i) q^{67} +(-0.628061 - 2.34396i) q^{68} +(-5.31943 - 9.21352i) q^{69} +(3.36393 - 12.5544i) q^{71} +(1.07448 + 1.86106i) q^{72} +3.87546i q^{73} +(-11.1286 + 6.42509i) q^{74} +(-3.80125 - 14.1865i) q^{76} +(14.0543 - 14.0543i) q^{77} +(15.4070 - 6.63929i) q^{78} -8.77296i q^{79} +(-4.95228 + 8.57759i) q^{81} +(16.1448 + 4.32600i) q^{82} -5.05855 q^{83} +(28.1512 + 7.54310i) q^{84} +(-10.2199 + 10.2199i) q^{86} +(0.434612 - 1.62199i) q^{87} +(-34.0984 + 9.13664i) q^{88} +(0.609451 - 0.163302i) q^{89} +(4.74064 - 11.9203i) q^{91} +(18.4493 + 18.4493i) q^{92} +(-0.793928 + 1.37512i) q^{93} +(24.0445 + 13.8821i) q^{94} +(-7.10863 - 7.10863i) q^{96} +(-2.55465 + 1.47493i) q^{97} +(12.4774 - 7.20384i) q^{98} +(1.34330 + 1.34330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{4} - 12 q^{6} - 24 q^{9} + 8 q^{11} - 32 q^{16} + 24 q^{19} + 32 q^{21} - 56 q^{24} + 76 q^{26} + 36 q^{29} + 8 q^{31} - 44 q^{34} - 60 q^{36} - 44 q^{39} - 52 q^{41} + 80 q^{44} - 60 q^{46}+ \cdots - 208 q^{99}+O(q^{100}) \) 40 * q + 24 * q^4 - 12 * q^6 - 24 * q^9 + 8 * q^11 - 32 * q^16 + 24 * q^19 + 32 * q^21 - 56 * q^24 + 76 * q^26 + 36 * q^29 + 8 * q^31 - 44 * q^34 - 60 * q^36 - 44 * q^39 - 52 * q^41 + 80 * q^44 - 60 * q^46 - 28 * q^49 + 68 * q^54 + 72 * q^56 + 72 * q^59 - 144 * q^64 + 24 * q^66 + 80 * q^69 - 52 * q^71 - 168 * q^74 + 8 * q^76 - 20 * q^81 + 248 * q^84 - 168 * q^86 - 60 * q^89 - 100 * q^91 + 156 * q^94 - 36 * q^96 - 208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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