LMFDB - Embedded newform 608.2.n.a.31.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [608,2,Mod(31,608)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(608, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("608.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.17
Character	$\chi$	$=$	608.31
Dual form			608.2.n.a.255.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12813 + 1.95397i) q^{3} +(0.633877 + 1.09791i) q^{5} +3.90520i q^{7} +(-1.04534 + 1.81059i) q^{9} +O(q^{10})$	\(q+(1.12813 + 1.95397i) q^{3} +(0.633877 + 1.09791i) q^{5} +3.90520i q^{7} +(-1.04534 + 1.81059i) q^{9} +0.217838i q^{11} +(-0.643129 - 0.371310i) q^{13} +(-1.43019 + 2.47716i) q^{15} +(-1.08900 - 1.88620i) q^{17} +(-3.26144 - 2.89189i) q^{19} +(-7.63067 + 4.40557i) q^{21} +(5.85881 + 3.38259i) q^{23} +(1.69640 - 2.93825i) q^{25} +2.05165 q^{27} +(-6.33168 - 3.65559i) q^{29} -1.93711 q^{31} +(-0.425649 + 0.245748i) q^{33} +(-4.28755 + 2.47542i) q^{35} +8.85178i q^{37} -1.67554i q^{39} +(3.88336 - 2.24206i) q^{41} +(4.78192 - 2.76084i) q^{43} -2.65047 q^{45} +(8.44167 + 4.87380i) q^{47} -8.25062 q^{49} +(2.45706 - 4.25575i) q^{51} +(-1.97558 - 1.14060i) q^{53} +(-0.239166 + 0.138082i) q^{55} +(1.97135 - 9.63518i) q^{57} +(0.647162 + 1.12092i) q^{59} +(-0.107459 + 0.186124i) q^{61} +(-7.07071 - 4.08227i) q^{63} -0.941461i q^{65} +(-5.87875 + 10.1823i) q^{67} +15.2639i q^{69} +(-0.00213265 - 0.00369386i) q^{71} +(-4.26155 - 7.38123i) q^{73} +7.65502 q^{75} -0.850700 q^{77} +(-6.23833 - 10.8051i) q^{79} +(5.45055 + 9.44062i) q^{81} +8.83661i q^{83} +(1.38058 - 2.39124i) q^{85} -16.4959i q^{87} +(13.7285 + 7.92616i) q^{89} +(1.45004 - 2.51155i) q^{91} +(-2.18531 - 3.78507i) q^{93} +(1.10767 - 5.41386i) q^{95} +(15.1906 - 8.77029i) q^{97} +(-0.394414 - 0.227715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 16 q^{9}+O(q^{10}) $ 40 * q - 16 * q^9	$ 40 q - 16 q^{9} + 24 q^{13} + 8 q^{17} + 24 q^{21} - 20 q^{25} + 12 q^{33} + 12 q^{41} - 72 q^{49} + 24 q^{53} + 8 q^{57} + 4 q^{73} - 32 q^{77} + 36 q^{81} + 8 q^{85} + 48 q^{89} - 40 q^{93} - 12 q^{97}+O(q^{100}) $ 40 * q - 16 * q^9 + 24 * q^13 + 8 * q^17 + 24 * q^21 - 20 * q^25 + 12 * q^33 + 12 * q^41 - 72 * q^49 + 24 * q^53 + 8 * q^57 + 4 * q^73 - 32 * q^77 + 36 * q^81 + 8 * q^85 + 48 * q^89 - 40 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	1.12813	+	1.95397i	0.651325	+	1.12813i	0.982802	+	0.184664i	$0.0591197\pi$
$3$	1.12813	+	1.95397i	0.651325	+	1.12813i	−0.331477	+	0.943463i	$0.607547\pi$
$4$		0			0
$5$	0.633877	+	1.09791i	0.283479	+	0.490999i	0.972239	−	0.233990i	$-0.0751782\pi$
$5$	0.633877	+	1.09791i	0.283479	+	0.490999i	−0.688761	+	0.724989i	$0.741845\pi$
$6$		0			0
$7$			3.90520i			1.47603i	0.674785	+	0.738014i	$0.264236\pi$
$7$			3.90520i			1.47603i	−0.674785	+	0.738014i	$0.735764\pi$
$8$		0			0
$9$	−1.04534	+	1.81059i	−0.348447	+	0.603529i
$10$		0			0
$11$			0.217838i			0.0656805i	0.999461	+	0.0328402i	$0.0104553\pi$
$11$			0.217838i			0.0656805i	−0.999461	+	0.0328402i	$0.989545\pi$
$12$		0			0
$13$	−0.643129	−	0.371310i	−0.178372	−	0.102983i	0.408156	−	0.912912i	$-0.366172\pi$
$13$	−0.643129	−	0.371310i	−0.178372	−	0.102983i	−0.586527	+	0.809929i	$0.699505\pi$
$14$		0			0
$15$	−1.43019	+	2.47716i	−0.369273	+	0.639600i
$16$		0			0
$17$	−1.08900	−	1.88620i	−0.264121	−	0.457471i	0.703212	−	0.710980i	$-0.251749\pi$
$17$	−1.08900	−	1.88620i	−0.264121	−	0.457471i	−0.967333	+	0.253509i	$0.918415\pi$
$18$		0			0
$19$	−3.26144	−	2.89189i	−0.748226	−	0.663444i
$19$	−3.26144	−	2.89189i	−0.748226	−	0.663444i
$20$		0			0
$21$	−7.63067	+	4.40557i	−1.66515	+	0.961374i
$22$		0			0
$23$	5.85881	+	3.38259i	1.22165	+	0.705318i	0.965269	−	0.261259i	$-0.0841376\pi$
$23$	5.85881	+	3.38259i	1.22165	+	0.705318i	0.256378	+	0.966577i	$0.417471\pi$
$24$		0			0
$25$	1.69640	−	2.93825i	0.339280	−	0.587650i
$26$		0			0
$27$	2.05165			0.394840
$28$		0			0
$29$	−6.33168	−	3.65559i	−1.17576	−	0.678827i	−0.220732	−	0.975334i	$-0.570845\pi$
$29$	−6.33168	−	3.65559i	−1.17576	−	0.678827i	−0.955030	+	0.296508i	$0.904178\pi$
$30$		0			0
$31$	−1.93711			−0.347916			−0.173958	−	0.984753i	$-0.555656\pi$
$31$	−1.93711			−0.347916			−0.173958	+	0.984753i	$0.555656\pi$
$32$		0			0
$33$	−0.425649	+	0.245748i	−0.0740960	+	0.0427793i
$34$		0			0
$35$	−4.28755	+	2.47542i	−0.724729	+	0.418422i
$36$		0			0
$37$			8.85178i			1.45522i	0.685989	+	0.727612i	$0.259370\pi$
$37$			8.85178i			1.45522i	−0.685989	+	0.727612i	$0.740630\pi$
$38$		0			0
$39$		−	1.67554i		−	0.268301i
$40$		0			0
$41$	3.88336	−	2.24206i	0.606479	−	0.350151i	−0.165107	−	0.986276i	$-0.552797\pi$
$41$	3.88336	−	2.24206i	0.606479	−	0.350151i	0.771586	+	0.636125i	$0.219464\pi$
$42$		0			0
$43$	4.78192	−	2.76084i	0.729236	−	0.421024i	−0.0889068	−	0.996040i	$-0.528337\pi$
$43$	4.78192	−	2.76084i	0.729236	−	0.421024i	0.818143	+	0.575015i	$0.195004\pi$
$44$		0			0
$45$	−2.65047			−0.395109
$46$		0			0
$47$	8.44167	+	4.87380i	1.23134	+	0.710917i	0.967310	−	0.253597i	$-0.0816136\pi$
$47$	8.44167	+	4.87380i	1.23134	+	0.710917i	0.264034	+	0.964513i	$0.414947\pi$
$48$		0			0
$49$	−8.25062			−1.17866
$50$		0			0
$51$	2.45706	−	4.25575i	0.344057	−	0.595925i
$52$		0			0
$53$	−1.97558	−	1.14060i	−0.271367	−	0.156674i	0.358142	−	0.933667i	$-0.383410\pi$
$53$	−1.97558	−	1.14060i	−0.271367	−	0.156674i	−0.629509	+	0.776994i	$0.716744\pi$
$54$		0			0
$55$	−0.239166	+	0.138082i	−0.0322491	+	0.0186190i
$56$		0			0
$57$	1.97135	−	9.63518i	0.261112	−	1.27621i
$58$		0			0
$59$	0.647162	+	1.12092i	0.0842533	+	0.145931i	0.905073	−	0.425257i	$-0.139816\pi$
$59$	0.647162	+	1.12092i	0.0842533	+	0.145931i	−0.820819	+	0.571188i	$0.806483\pi$
$60$		0			0
$61$	−0.107459	+	0.186124i	−0.0137587	+	0.0238307i	−0.872823	−	0.488037i	$-0.837713\pi$
$61$	−0.107459	+	0.186124i	−0.0137587	+	0.0238307i	0.859064	+	0.511868i	$0.171046\pi$
$62$		0			0
$63$	−7.07071	−	4.08227i	−0.890825	−	0.514318i
$64$		0			0
$65$		−	0.941461i		−	0.116774i
$66$		0			0
$67$	−5.87875	+	10.1823i	−0.718203	+	1.24396i	0.243508	+	0.969899i	$0.421702\pi$
$67$	−5.87875	+	10.1823i	−0.718203	+	1.24396i	−0.961711	+	0.274065i	$0.911632\pi$
$68$		0			0
$69$			15.2639i			1.83756i
$70$		0			0
$71$	−0.00213265	−	0.00369386i	−0.000253099	−	0.000438381i	0.865899	−	0.500219i	$-0.166747\pi$
$71$	−0.00213265	−	0.00369386i	−0.000253099	−	0.000438381i	−0.866152	+	0.499781i	$0.833414\pi$
$72$		0			0
$73$	−4.26155	−	7.38123i	−0.498777	−	0.863907i	0.501222	−	0.865319i	$-0.332884\pi$
$73$	−4.26155	−	7.38123i	−0.498777	−	0.863907i	−0.999999	+	0.00141161i	$0.999551\pi$
$74$		0			0
$75$	7.65502			0.883925
$76$		0			0
$77$	−0.850700			−0.0969463
$78$		0			0
$79$	−6.23833	−	10.8051i	−0.701867	−	1.21567i	−0.967810	−	0.251681i	$-0.919017\pi$
$79$	−6.23833	−	10.8051i	−0.701867	−	1.21567i	0.265943	−	0.963989i	$-0.414317\pi$
$80$		0			0
$81$	5.45055	+	9.44062i	0.605616	+	1.04896i
$82$		0			0
$83$			8.83661i			0.969944i	0.874530	+	0.484972i	$0.161170\pi$
$83$			8.83661i			0.969944i	−0.874530	+	0.484972i	$0.838830\pi$
$84$		0			0
$85$	1.38058	−	2.39124i	0.149745	−	0.259367i
$86$		0			0
$87$		−	16.4959i		−	1.76855i
$88$		0			0
$89$	13.7285	+	7.92616i	1.45522	+	0.840171i	0.998770	−	0.0495791i	$-0.0157880\pi$
$89$	13.7285	+	7.92616i	1.45522	+	0.840171i	0.456448	+	0.889750i	$0.349121\pi$
$90$		0			0
$91$	1.45004	−	2.51155i	0.152006	−	0.263282i
$92$		0			0
$93$	−2.18531	−	3.78507i	−0.226606	−	0.392493i
$94$		0			0
$95$	1.10767	−	5.41386i	0.113645	−	0.555450i
$96$		0			0
$97$	15.1906	−	8.77029i	1.54237	−	0.890488i	0.543682	−	0.839291i	$-0.317030\pi$
$97$	15.1906	−	8.77029i	1.54237	−	0.890488i	0.998689	−	0.0511964i	$-0.0163035\pi$
$98$		0			0
$99$	−0.394414	−	0.227715i	−0.0396401	−	0.0228862i
$100$		0			0
$101$	−1.34100	+	2.32268i	−0.133434	+	0.231115i	−0.924998	−	0.379971i	$-0.875934\pi$
$101$	−1.34100	+	2.32268i	−0.133434	+	0.231115i	0.791564	+	0.611086i	$0.209267\pi$
$102$		0			0
$103$	−2.65264			−0.261373			−0.130686	−	0.991424i	$-0.541718\pi$
$103$	−2.65264			−0.261373			−0.130686	+	0.991424i	$0.541718\pi$
$104$		0			0
$105$	−9.67381	−	5.58518i	−0.944067	−	0.545057i
$106$		0			0
$107$	−5.37614			−0.519731			−0.259865	−	0.965645i	$-0.583678\pi$
$107$	−5.37614			−0.519731			−0.259865	+	0.965645i	$0.583678\pi$
$108$		0			0
$109$	16.8361	−	9.72034i	1.61261	−	0.931039i	0.623844	−	0.781549i	$-0.285570\pi$
$109$	16.8361	−	9.72034i	1.61261	−	0.931039i	0.988763	−	0.149491i	$-0.0477635\pi$
$110$		0			0
$111$	−17.2962	+	9.98594i	−1.64168	+	0.947823i
$112$		0			0
$113$			4.80677i			0.452183i	0.974106	+	0.226091i	$0.0725948\pi$
$113$			4.80677i			0.452183i	−0.974106	+	0.226091i	$0.927405\pi$
$114$		0			0
$115$			8.57658i			0.799770i
$116$		0			0
$117$	1.34458	−	0.776293i	0.124306	−	0.0717683i
$118$		0			0
$119$	7.36601	−	4.25277i	0.675241	−	0.389850i
$120$		0			0
$121$	10.9525			0.995686
$122$		0			0
$123$	8.76185	+	5.05866i	0.790029	+	0.456124i
$124$		0			0
$125$	10.6400			0.951671
$126$		0			0
$127$	−4.16404	+	7.21232i	−0.369499	+	0.639990i	−0.989487	−	0.144620i	$-0.953804\pi$
$127$	−4.16404	+	7.21232i	−0.369499	+	0.639990i	0.619989	+	0.784611i	$0.287137\pi$
$128$		0			0
$129$	10.7892	+	6.22916i	0.949938	+	0.548447i
$130$		0			0
$131$	5.72152	−	3.30332i	0.499892	−	0.288613i	−0.228777	−	0.973479i	$-0.573473\pi$
$131$	5.72152	−	3.30332i	0.499892	−	0.288613i	0.728669	+	0.684866i	$0.240139\pi$
$132$		0			0
$133$	11.2934	−	12.7366i	0.979262	−	1.10440i
$134$		0			0
$135$	1.30049	+	2.25252i	0.111929	+	0.193866i
$136$		0			0
$137$	3.55647	−	6.15998i	0.303850	−	0.526283i	−0.673155	−	0.739501i	$-0.735061\pi$
$137$	3.55647	−	6.15998i	0.303850	−	0.526283i	0.977005	+	0.213219i	$0.0683946\pi$
$138$		0			0
$139$	−14.2190	−	8.20933i	−1.20604	−	0.696306i	−0.244147	−	0.969738i	$-0.578508\pi$
$139$	−14.2190	−	8.20933i	−1.20604	−	0.696306i	−0.961891	+	0.273432i	$0.911841\pi$
$140$		0			0
$141$			21.9931i			1.85215i
$142$		0			0
$143$	0.0808854	−	0.140098i	0.00676397	−	0.0117155i
$144$		0			0
$145$		−	9.26879i		−	0.769731i
$146$		0			0
$147$	−9.30775	−	16.1215i	−0.767690	−	1.32968i
$148$		0			0
$149$	−8.77879	−	15.2053i	−0.719187	−	1.24567i	−0.961322	−	0.275425i	$-0.911181\pi$
$149$	−8.77879	−	15.2053i	−0.719187	−	1.24567i	0.242136	−	0.970242i	$-0.422152\pi$
$150$		0			0
$151$	9.54889			0.777078			0.388539	−	0.921432i	$-0.372980\pi$
$151$	9.54889			0.777078			0.388539	+	0.921432i	$0.372980\pi$
$152$		0			0
$153$	4.55351			0.368129
$154$		0			0
$155$	−1.22789	−	2.12677i	−0.0986267	−	0.170826i
$156$		0			0
$157$	−5.84642	−	10.1263i	−0.466595	−	0.808167i	0.532677	−	0.846319i	$-0.321186\pi$
$157$	−5.84642	−	10.1263i	−0.466595	−	0.808167i	−0.999272	+	0.0381521i	$0.987853\pi$
$158$		0			0
$159$		−	5.14697i		−	0.408181i
$160$		0			0
$161$	−13.2097	+	22.8798i	−1.04107	+	1.80318i
$162$		0			0
$163$		−	18.0805i		−	1.41617i	−0.706125	−	0.708087i	$-0.749558\pi$
$163$		−	18.0805i		−	1.41617i	0.706125	−	0.708087i	$-0.250442\pi$
$164$		0			0
$165$	−0.539618	−	0.311549i	−0.0420092	−	0.0242540i
$166$		0			0
$167$	6.30083	−	10.9134i	0.487573	−	0.844501i	−0.512325	−	0.858792i	$-0.671216\pi$
$167$	6.30083	−	10.9134i	0.487573	−	0.844501i	0.999898	+	0.0142904i	$0.00454895\pi$
$168$		0			0
$169$	−6.22426	−	10.7807i	−0.478789	−	0.829287i
$170$		0			0
$171$	8.64533	−	2.88211i	0.661125	−	0.220400i
$172$		0			0
$173$	−4.97163	+	2.87037i	−0.377986	+	0.218230i	−0.676942	−	0.736037i	$-0.736695\pi$
$173$	−4.97163	+	2.87037i	−0.377986	+	0.218230i	0.298956	+	0.954267i	$0.403362\pi$
$174$		0			0
$175$	11.4745	+	6.62479i	0.867388	+	0.500787i
$176$		0			0
$177$	−1.46016	+	2.52907i	−0.109752	+	0.190097i
$178$		0			0
$179$	−25.6536			−1.91744			−0.958721	−	0.284350i	$-0.908222\pi$
$179$	−25.6536			−1.91744			−0.958721	+	0.284350i	$0.908222\pi$
$180$		0			0
$181$	−9.40308	−	5.42887i	−0.698926	−	0.403525i	0.108022	−	0.994149i	$-0.465548\pi$
$181$	−9.40308	−	5.42887i	−0.698926	−	0.403525i	−0.806947	+	0.590624i	$0.798882\pi$
$182$		0			0
$183$	−0.484908			−0.0358455
$184$		0			0
$185$	−9.71844	+	5.61094i	−0.714514	+	0.412525i
$186$		0			0
$187$	0.410886	−	0.237225i	0.0300469	−	0.0173476i
$188$		0			0
$189$			8.01210i			0.582795i
$190$		0			0
$191$		−	2.43930i		−	0.176502i	−0.996098	−	0.0882509i	$-0.971872\pi$
$191$		−	2.43930i		−	0.176502i	0.996098	−	0.0882509i	$-0.0281277\pi$
$192$		0			0
$193$	−4.56803	+	2.63735i	−0.328814	+	0.189841i	−0.655314	−	0.755356i	$-0.727464\pi$
$193$	−4.56803	+	2.63735i	−0.328814	+	0.189841i	0.326500	+	0.945197i	$0.394131\pi$
$194$		0			0
$195$	1.83959	−	1.06209i	0.131736	−	0.0760577i
$196$		0			0
$197$	25.6451			1.82713			0.913567	−	0.406688i	$-0.133316\pi$
$197$	25.6451			1.82713			0.913567	+	0.406688i	$0.133316\pi$
$198$		0			0
$199$	10.0080	+	5.77813i	0.709449	+	0.409600i	0.810857	−	0.585244i	$-0.199001\pi$
$199$	10.0080	+	5.77813i	0.709449	+	0.409600i	−0.101408	+	0.994845i	$0.532335\pi$
$200$		0			0
$201$	−26.5279			−1.87113
$202$		0			0
$203$	14.2758	−	24.7265i	1.00197	−	1.73546i
$204$		0			0
$205$	4.92315	+	2.84238i	0.343848	+	0.198520i
$206$		0			0
$207$	−12.2489	+	7.07192i	−0.851359	+	0.491532i
$208$		0			0
$209$	0.629961	−	0.710464i	0.0435753	−	0.0491438i
$210$		0			0
$211$	−2.83722	−	4.91421i	−0.195322	−	0.338308i	0.751684	−	0.659524i	$-0.229242\pi$
$211$	−2.83722	−	4.91421i	−0.195322	−	0.338308i	−0.947006	+	0.321215i	$0.895909\pi$
$212$		0			0
$213$	0.00481181	−	0.00833429i	0.000329699	−	0.000571056i
$214$		0			0
$215$	6.06230	+	3.50007i	0.413445	+	0.238703i
$216$		0			0
$217$		−	7.56482i		−	0.513534i
$218$		0			0
$219$	9.61515	−	16.6539i	0.649731	−	1.12537i
$220$		0			0
$221$			1.61743i			0.108800i
$222$		0			0
$223$	−9.85759	−	17.0739i	−0.660113	−	1.14335i	−0.980586	−	0.196092i	$-0.937175\pi$
$223$	−9.85759	−	17.0739i	−0.660113	−	1.14335i	0.320472	−	0.947258i	$-0.396158\pi$
$224$		0			0
$225$	3.54664	+	6.14295i	0.236442	+	0.409530i
$226$		0			0
$227$	7.22236			0.479365			0.239682	−	0.970851i	$-0.422957\pi$
$227$	7.22236			0.479365			0.239682	+	0.970851i	$0.422957\pi$
$228$		0			0
$229$	−10.6162			−0.701540			−0.350770	−	0.936462i	$-0.614080\pi$
$229$	−10.6162			−0.701540			−0.350770	+	0.936462i	$0.614080\pi$
$230$		0			0
$231$	−0.959698	−	1.66225i	−0.0631435	−	0.109368i
$232$		0			0
$233$	12.6438	+	21.8997i	0.828322	+	1.43470i	0.899353	+	0.437223i	$0.144038\pi$
$233$	12.6438	+	21.8997i	0.828322	+	1.43470i	−0.0710309	+	0.997474i	$0.522629\pi$
$234$		0			0
$235$			12.3576i			0.806118i
$236$		0			0
$237$	14.0753	−	24.3791i	0.914287	−	1.58359i
$238$		0			0
$239$			28.1442i			1.82050i	0.414063	+	0.910248i	$0.364109\pi$
$239$			28.1442i			1.82050i	−0.414063	+	0.910248i	$0.635891\pi$
$240$		0			0
$241$	−19.0847	−	11.0186i	−1.22935	−	0.709767i	−0.262459	−	0.964943i	$-0.584533\pi$
$241$	−19.0847	−	11.0186i	−1.22935	−	0.709767i	−0.966895	+	0.255176i	$0.917867\pi$
$242$		0			0
$243$	−9.22035	+	15.9701i	−0.591486	+	1.02448i
$244$		0			0
$245$	−5.22988	−	9.05842i	−0.334125	−	0.578721i
$246$		0			0
$247$	1.02374	+	3.07086i	0.0651389	+	0.195394i
$248$		0			0
$249$	−17.2665	+	9.96882i	−1.09422	+	0.631748i
$250$		0			0
$251$	26.7012	+	15.4159i	1.68536	+	0.973046i	0.957989	+	0.286806i	$0.0925936\pi$
$251$	26.7012	+	15.4159i	1.68536	+	0.973046i	0.727376	+	0.686239i	$0.240740\pi$
$252$		0			0
$253$	−0.736854	+	1.27627i	−0.0463256	+	0.0802383i
$254$		0			0
$255$	6.22990			0.390131
$256$		0			0
$257$	−11.7740	−	6.79771i	−0.734441	−	0.424030i	0.0856038	−	0.996329i	$-0.472718\pi$
$257$	−11.7740	−	6.79771i	−0.734441	−	0.424030i	−0.820045	+	0.572300i	$0.806051\pi$
$258$		0			0
$259$	−34.5680			−2.14795
$260$		0			0
$261$	13.2375	−	7.64269i	0.819383	−	0.473071i
$262$		0			0
$263$	−10.1698	+	5.87151i	−0.627094	+	0.362053i	−0.779626	−	0.626246i	$-0.784591\pi$
$263$	−10.1698	+	5.87151i	−0.627094	+	0.362053i	0.152532	+	0.988299i	$0.451257\pi$
$264$		0			0
$265$		−	2.89200i		−	0.177654i
$266$		0			0
$267$			35.7668i			2.18890i
$268$		0			0
$269$	−15.1394	+	8.74072i	−0.923063	+	0.532931i	−0.884611	−	0.466329i	$-0.845576\pi$
$269$	−15.1394	+	8.74072i	−0.923063	+	0.532931i	−0.0384524	+	0.999260i	$0.512243\pi$
$270$		0			0
$271$	−17.6572	+	10.1944i	−1.07260	+	0.619267i	−0.928891	−	0.370353i	$-0.879237\pi$
$271$	−17.6572	+	10.1944i	−1.07260	+	0.619267i	−0.143710	+	0.989620i	$0.545903\pi$
$272$		0			0
$273$	6.54333			0.396020
$274$		0			0
$275$	0.640061	+	0.369539i	0.0385971	+	0.0222841i
$276$		0			0
$277$	5.88405			0.353538			0.176769	−	0.984252i	$-0.443435\pi$
$277$	5.88405			0.353538			0.176769	+	0.984252i	$0.443435\pi$
$278$		0			0
$279$	2.02495	−	3.50731i	0.121230	−	0.209977i
$280$		0			0
$281$	27.3485	+	15.7897i	1.63148	+	0.941934i	0.983638	+	0.180157i	$0.0576607\pi$
$281$	27.3485	+	15.7897i	1.63148	+	0.941934i	0.647840	+	0.761777i	$0.275673\pi$
$282$		0			0
$283$	−6.22528	+	3.59417i	−0.370054	+	0.213651i	−0.673482	−	0.739203i	$-0.735202\pi$
$283$	−6.22528	+	3.59417i	−0.370054	+	0.213651i	0.303428	+	0.952854i	$0.401869\pi$
$284$		0			0
$285$	11.8281	−	3.94317i	0.700638	−	0.233573i
$286$		0			0
$287$	8.75570	+	15.1653i	0.516832	+	0.895180i
$288$		0			0
$289$	6.12816	−	10.6143i	0.360480	−	0.624370i
$290$		0			0
$291$	34.2738	+	19.7880i	2.00917	+	1.15999i
$292$		0			0
$293$			8.89466i			0.519631i	0.965658	+	0.259816i	$0.0836618\pi$
$293$			8.89466i			0.519631i	−0.965658	+	0.259816i	$0.916338\pi$
$294$		0			0
$295$	−0.820442	+	1.42105i	−0.0477680	+	0.0827366i
$296$		0			0
$297$			0.446926i			0.0259333i
$298$		0			0
$299$	−2.51198	−	4.35087i	−0.145271	−	0.251618i
$300$		0			0
$301$	10.7817	+	18.6744i	0.621444	+	1.07637i
$302$		0			0
$303$	−6.05126			−0.347636
$304$		0			0
$305$	−0.272462			−0.0156012
$306$		0			0
$307$	−0.0789292	−	0.136709i	−0.00450473	−	0.00780242i	0.863764	−	0.503896i	$-0.168101\pi$
$307$	−0.0789292	−	0.136709i	−0.00450473	−	0.00780242i	−0.868269	+	0.496094i	$0.834767\pi$
$308$		0			0
$309$	−2.99252	−	5.18320i	−0.170238	−	0.294862i
$310$		0			0
$311$		−	14.4011i		−	0.816609i	−0.912846	−	0.408304i	$-0.866120\pi$
$311$		−	14.4011i		−	0.816609i	0.912846	−	0.408304i	$-0.133880\pi$
$312$		0			0
$313$	−10.1441	+	17.5701i	−0.573377	+	0.993119i	0.422839	+	0.906205i	$0.361034\pi$
$313$	−10.1441	+	17.5701i	−0.573377	+	0.993119i	−0.996216	+	0.0869136i	$0.972300\pi$
$314$		0			0
$315$		−	10.3506i		−	0.583193i
$316$		0			0
$317$	−22.0881	−	12.7526i	−1.24059	−	0.716255i	−0.271376	−	0.962473i	$-0.587479\pi$
$317$	−22.0881	−	12.7526i	−1.24059	−	0.716255i	−0.969215	+	0.246218i	$0.920812\pi$
$318$		0			0
$319$	0.796326	−	1.37928i	0.0445857	−	0.0772247i
$320$		0			0
$321$	−6.06497	−	10.5048i	−0.338514	−	0.586323i
$322$		0			0
$323$	−1.90298	+	9.30100i	−0.105884	+	0.517522i
$324$		0			0
$325$	−2.18201	+	1.25978i	−0.121036	+	0.0698801i
$326$		0			0
$327$	37.9866	+	21.9316i	2.10066	+	1.21282i
$328$		0			0
$329$	−19.0332	+	32.9664i	−1.04933	+	1.81750i
$330$		0			0
$331$	−0.927477			−0.0509787			−0.0254894	−	0.999675i	$-0.508114\pi$
$331$	−0.927477			−0.0509787			−0.0254894	+	0.999675i	$0.508114\pi$
$332$		0			0
$333$	−16.0269	−	9.25314i	−0.878269	−	0.507069i
$334$		0			0
$335$	−14.9056			−0.814381
$336$		0			0
$337$	5.85422	−	3.37993i	0.318899	−	0.184117i	−0.332002	−	0.943279i	$-0.607724\pi$
$337$	5.85422	−	3.37993i	0.318899	−	0.184117i	0.650902	+	0.759162i	$0.274391\pi$
$338$		0			0
$339$	−9.39230	+	5.42265i	−0.510120	+	0.294518i
$340$		0			0
$341$		−	0.421976i		−	0.0228513i
$342$		0			0
$343$		−	4.88392i		−	0.263707i
$344$		0			0
$345$	−16.7584	+	9.67547i	−0.902242	+	0.520910i
$346$		0			0
$347$	−3.42889	+	1.97967i	−0.184072	+	0.106274i	−0.589205	−	0.807984i	$-0.700559\pi$
$347$	−3.42889	+	1.97967i	−0.184072	+	0.106274i	0.405132	+	0.914258i	$0.367225\pi$
$348$		0			0
$349$	2.45852			0.131601			0.0658007	−	0.997833i	$-0.479040\pi$
$349$	2.45852			0.131601			0.0658007	+	0.997833i	$0.479040\pi$
$350$		0			0
$351$	−1.31947	−	0.761798i	−0.0704283	−	0.0406618i
$352$		0			0
$353$	−28.6524			−1.52501			−0.762506	−	0.646981i	$-0.776031\pi$
$353$	−28.6524			−1.52501			−0.762506	+	0.646981i	$0.776031\pi$
$354$		0			0
$355$	0.00270368	−	0.00468291i	0.000143496	−	0.000248543i
$356$		0			0
$357$	16.6196	+	9.59532i	0.879602	+	0.507838i
$358$		0			0
$359$	11.2848	−	6.51531i	0.595591	−	0.343865i	−0.171714	−	0.985147i	$-0.554931\pi$
$359$	11.2848	−	6.51531i	0.595591	−	0.343865i	0.767305	+	0.641282i	$0.221597\pi$
$360$		0			0
$361$	2.27399	+	18.8634i	0.119684	+	0.992812i
$362$		0			0
$363$	12.3559	+	21.4010i	0.648515	+	1.12326i
$364$		0			0
$365$	5.40260	−	9.35758i	0.282785	−	0.489798i
$366$		0			0
$367$	−20.6479	−	11.9211i	−1.07781	−	0.622274i	−0.147506	−	0.989061i	$-0.547125\pi$
$367$	−20.6479	−	11.9211i	−1.07781	−	0.622274i	−0.930305	+	0.366787i	$0.880458\pi$
$368$		0			0
$369$			9.37488i			0.488037i
$370$		0			0
$371$	4.45428	−	7.71504i	0.231255	−	0.400545i
$372$		0			0
$373$		−	18.6963i		−	0.968058i	−0.875052	−	0.484029i	$-0.839173\pi$
$373$		−	18.6963i		−	0.968058i	0.875052	−	0.484029i	$-0.160827\pi$
$374$		0			0
$375$	12.0033	+	20.7903i	0.619847	+	1.07361i
$376$		0			0
$377$	2.71472	+	4.70203i	0.139815	+	0.242167i
$378$		0			0
$379$	−24.2023			−1.24319			−0.621594	−	0.783339i	$-0.713515\pi$
$379$	−24.2023			−1.24319			−0.621594	+	0.783339i	$0.713515\pi$
$380$		0			0
$381$	−18.7903			−0.962654
$382$		0			0
$383$	−12.2949	−	21.2953i	−0.628239	−	1.08814i	−0.987905	−	0.155060i	$-0.950443\pi$
$383$	−12.2949	−	21.2953i	−0.628239	−	1.08814i	0.359666	−	0.933081i	$-0.382890\pi$
$384$		0			0
$385$	−0.539239	−	0.933990i	−0.0274822	−	0.0476005i
$386$		0			0
$387$			11.5441i			0.586819i
$388$		0			0
$389$	4.01729	−	6.95816i	0.203685	−	0.352793i	−0.746028	−	0.665915i	$-0.768042\pi$
$389$	4.01729	−	6.95816i	0.203685	−	0.352793i	0.949713	+	0.313122i	$0.101375\pi$
$390$		0			0
$391$		−	14.7345i		−	0.745158i
$392$		0			0
$393$	12.9092	+	7.45314i	0.651183	+	0.375961i
$394$		0			0
$395$	7.90868	−	13.6982i	0.397929	−	0.689233i
$396$		0			0
$397$	9.25422	+	16.0288i	0.464456	+	0.804461i	0.999177	−	0.0405675i	$-0.0129166\pi$
$397$	9.25422	+	16.0288i	0.464456	+	0.804461i	−0.534721	+	0.845029i	$0.679583\pi$
$398$		0			0
$399$	37.6274	+	7.69852i	1.88372	+	0.385408i
$400$		0			0
$401$	21.5039	−	12.4153i	1.07386	−	0.619991i	0.144623	−	0.989487i	$-0.453803\pi$
$401$	21.5039	−	12.4153i	1.07386	−	0.619991i	0.929232	+	0.369496i	$0.120470\pi$
$402$		0			0
$403$	1.24581	+	0.719270i	0.0620584	+	0.0358294i
$404$		0			0
$405$	−6.90995	+	11.9684i	−0.343358	+	0.594714i
$406$		0			0
$407$	−1.92825			−0.0955799
$408$		0			0
$409$	−27.1866	−	15.6962i	−1.34429	−	0.776126i	−0.356856	−	0.934159i	$-0.616151\pi$
$409$	−27.1866	−	15.6962i	−1.34429	−	0.776126i	−0.987434	+	0.158033i	$0.949485\pi$
$410$		0			0
$411$	16.0486			0.791619
$412$		0			0
$413$	−4.37741	+	2.52730i	−0.215398	+	0.124360i
$414$		0			0
$415$	−9.70178	+	5.60133i	−0.476242	+	0.274958i
$416$		0			0
$417$		−	37.0447i		−	1.81409i
$418$		0			0
$419$			11.0311i			0.538904i	0.963014	+	0.269452i	$0.0868425\pi$
$419$			11.0311i			0.538904i	−0.963014	+	0.269452i	$0.913157\pi$
$420$		0			0
$421$	−3.43100	+	1.98089i	−0.167217	+	0.0965425i	−0.581273	−	0.813709i	$-0.697445\pi$
$421$	−3.43100	+	1.98089i	−0.167217	+	0.0965425i	0.414056	+	0.910251i	$0.364112\pi$
$422$		0			0
$423$	−17.6489	+	10.1896i	−0.858117	+	0.495434i
$424$		0			0
$425$	−7.38951			−0.358444
$426$		0			0
$427$	−0.726852	−	0.419648i	−0.0351748	−	0.0203082i
$428$		0			0
$429$	0.364996			0.0176222
$430$		0			0
$431$	−5.37130	+	9.30337i	−0.258726	+	0.448127i	−0.965901	−	0.258912i	$-0.916636\pi$
$431$	−5.37130	+	9.30337i	−0.258726	+	0.448127i	0.707175	+	0.707039i	$0.249969\pi$
$432$		0			0
$433$	−7.72991	−	4.46287i	−0.371476	−	0.214472i	0.302627	−	0.953109i	$-0.402136\pi$
$433$	−7.72991	−	4.46287i	−0.371476	−	0.214472i	−0.674103	+	0.738637i	$0.735470\pi$
$434$		0			0
$435$	18.1110	−	10.4564i	0.868355	−	0.501345i
$436$		0			0
$437$	−9.32611	−	27.9751i	−0.446128	−	1.33823i
$438$		0			0
$439$	−8.64135	−	14.9673i	−0.412429	−	0.714348i	0.582726	−	0.812669i	$-0.301986\pi$
$439$	−8.64135	−	14.9673i	−0.412429	−	0.714348i	−0.995155	+	0.0983208i	$0.968653\pi$
$440$		0			0
$441$	8.62472	−	14.9385i	0.410701	−	0.711355i
$442$		0			0
$443$	3.66258	+	2.11459i	0.174014	+	0.100467i	0.584477	−	0.811410i	$-0.301300\pi$
$443$	3.66258	+	2.11459i	0.174014	+	0.100467i	−0.410463	+	0.911877i	$0.634633\pi$
$444$		0			0
$445$			20.0968i			0.952682i
$446$		0			0
$447$	19.8072	−	34.3070i	0.936848	−	1.62267i
$448$		0			0
$449$			12.6511i			0.597043i	0.954403	+	0.298522i	$0.0964935\pi$
$449$			12.6511i			0.597043i	−0.954403	+	0.298522i	$0.903507\pi$
$450$		0			0
$451$	0.488405	+	0.845942i	0.0229981	+	0.0398338i
$452$		0			0
$453$	10.7724	+	18.6583i	0.506130	+	0.876643i
$454$		0			0
$455$	3.67660			0.172362
$456$		0			0
$457$	13.7169			0.641652			0.320826	−	0.947138i	$-0.396040\pi$
$457$	13.7169			0.641652			0.320826	+	0.947138i	$0.396040\pi$
$458$		0			0
$459$	−2.23424	−	3.86982i	−0.104286	−	0.180628i
$460$		0			0
$461$	−5.74794	−	9.95573i	−0.267708	−	0.463685i	0.700561	−	0.713592i	$-0.252933\pi$
$461$	−5.74794	−	9.95573i	−0.267708	−	0.463685i	−0.968270	+	0.249908i	$0.919600\pi$
$462$		0			0
$463$			10.7485i			0.499527i	0.968307	+	0.249764i	$0.0803530\pi$
$463$			10.7485i			0.499527i	−0.968307	+	0.249764i	$0.919647\pi$
$464$		0			0
$465$	2.77044	−	4.79854i	0.128476	−	0.222527i
$466$		0			0
$467$		−	1.34155i		−	0.0620797i	−0.999518	−	0.0310398i	$-0.990118\pi$
$467$		−	1.34155i		−	0.0620797i	0.999518	−	0.0310398i	$-0.00988187\pi$
$468$		0			0
$469$	−39.7639	−	22.9577i	−1.83613	−	1.06009i
$470$		0			0
$471$	13.1910	−	22.8475i	0.607810	−	1.05276i
$472$		0			0
$473$	0.601415	+	1.04168i	0.0276531	+	0.0478966i
$474$		0			0
$475$	−14.0298	+	4.67713i	−0.643731	+	0.214602i
$476$		0			0
$477$	4.13031	−	2.38464i	0.189114	−	0.109185i
$478$		0			0
$479$	−16.1455	−	9.32160i	−0.737706	−	0.425915i	0.0835289	−	0.996505i	$-0.473381\pi$
$479$	−16.1455	−	9.32160i	−0.737706	−	0.425915i	−0.821235	+	0.570591i	$0.806714\pi$
$480$		0			0
$481$	3.28676	−	5.69284i	0.149863	−	0.259571i
$482$		0			0
$483$	−59.6088			−2.71230
$484$		0			0
$485$	19.2579	+	11.1186i	0.874458	+	0.504868i
$486$		0			0
$487$	−35.0199			−1.58690			−0.793451	−	0.608635i	$-0.791717\pi$
$487$	−35.0199			−1.58690			−0.793451	+	0.608635i	$0.791717\pi$
$488$		0			0
$489$	35.3288	−	20.3971i	1.59763	−	0.922390i
$490$		0			0
$491$	19.1284	−	11.0438i	0.863251	−	0.498398i	−0.00184853	−	0.999998i	$-0.500588\pi$
$491$	19.1284	−	11.0438i	0.863251	−	0.498398i	0.865100	+	0.501600i	$0.167255\pi$
$492$		0			0
$493$			15.9238i			0.717170i
$494$		0			0
$495$		−	0.577373i		−	0.0259510i
$496$		0			0
$497$	0.0144253	−	0.00832844i	0.000647062	−	0.000373582i
$498$		0			0
$499$	15.5812	−	8.99583i	0.697512	−	0.402709i	−0.108908	−	0.994052i	$-0.534735\pi$
$499$	15.5812	−	8.99583i	0.697512	−	0.402709i	0.806420	+	0.591343i	$0.201402\pi$
$500$		0			0
$501$	28.4326			1.27027
$502$		0			0
$503$	−14.7564	−	8.51963i	−0.657957	−	0.379872i	0.133541	−	0.991043i	$-0.457365\pi$
$503$	−14.7564	−	8.51963i	−0.657957	−	0.379872i	−0.791498	+	0.611172i	$0.790699\pi$
$504$		0			0
$505$	−3.40011			−0.151303
$506$		0			0
$507$	14.0435	−	24.3241i	0.623694	−	1.08027i
$508$		0			0
$509$	−4.93890	−	2.85148i	−0.218913	−	0.126389i	0.386534	−	0.922275i	$-0.373672\pi$
$509$	−4.93890	−	2.85148i	−0.218913	−	0.126389i	−0.605447	+	0.795886i	$0.707006\pi$
$510$		0			0
$511$	28.8252	−	16.6422i	1.27515	−	0.736209i
$512$		0			0
$513$	−6.69133	−	5.93313i	−0.295429	−	0.261954i
$514$		0			0
$515$	−1.68145	−	2.91236i	−0.0740935	−	0.128334i
$516$		0			0
$517$	−1.06170	+	1.83891i	−0.0466934	+	0.0808753i
$518$		0			0
$519$	−11.2173	−	6.47628i	−0.492383	−	0.284277i
$520$		0			0
$521$			29.6859i			1.30056i	0.759693	+	0.650282i	$0.225349\pi$
$521$			29.6859i			1.30056i	−0.759693	+	0.650282i	$0.774651\pi$
$522$		0			0
$523$	12.8491	−	22.2553i	0.561853	−	0.973158i	−0.435482	−	0.900197i	$-0.643422\pi$
$523$	12.8491	−	22.2553i	0.561853	−	0.973158i	0.997335	−	0.0729601i	$-0.0232446\pi$
$524$		0			0
$525$			29.8944i			1.30470i
$526$		0			0
$527$	2.10952	+	3.65379i	0.0918919	+	0.159162i
$528$		0			0
$529$	11.3838	+	19.7173i	0.494947	+	0.857273i
$530$		0			0
$531$	−2.70602			−0.117431
$532$		0			0
$533$	−3.33000			−0.144238
$534$		0			0
$535$	−3.40781	−	5.90250i	−0.147333	−	0.255187i
$536$		0			0
$537$	−28.9405	−	50.1265i	−1.24888	−	2.16312i
$538$		0			0
$539$		−	1.79729i		−	0.0774150i
$540$		0			0
$541$	−0.155834	+	0.269913i	−0.00669983	+	0.0116044i	−0.869356	−	0.494187i	$-0.835466\pi$
$541$	−0.155834	+	0.269913i	−0.00669983	+	0.0116044i	0.862656	+	0.505791i	$0.168799\pi$
$542$		0			0
$543$		−	24.4978i		−	1.05130i
$544$		0			0
$545$	21.3441	+	12.3230i	0.914279	+	0.527859i
$546$		0			0
$547$	1.80528	−	3.12684i	0.0771884	−	0.133694i	−0.824847	−	0.565355i	$-0.808739\pi$
$547$	1.80528	−	3.12684i	0.0771884	−	0.133694i	0.902036	+	0.431661i	$0.142072\pi$
$548$		0			0
$549$	−0.224662	−	0.389126i	−0.00958835	−	0.0166075i
$550$		0			0
$551$	10.0788	+	30.2330i	0.429372	+	1.28797i
$552$		0			0
$553$	42.1962	−	24.3620i	1.79436	−	1.03598i
$554$		0			0
$555$	−21.9273	−	12.6597i	−0.930761	−	0.537375i
$556$		0			0
$557$	8.74248	−	15.1424i	0.370431	−	0.641605i	−0.619201	−	0.785233i	$-0.712543\pi$
$557$	8.74248	−	15.1424i	0.370431	−	0.641605i	0.989632	+	0.143628i	$0.0458767\pi$
$558$		0			0
$559$	−4.10052			−0.173433
$560$		0			0
$561$	0.927063	+	0.535240i	0.0391406	+	0.0225979i
$562$		0			0
$563$	23.1594			0.976054			0.488027	−	0.872828i	$-0.337717\pi$
$563$	23.1594			0.976054			0.488027	+	0.872828i	$0.337717\pi$
$564$		0			0
$565$	−5.27739	+	3.04690i	−0.222021	+	0.128184i
$566$		0			0
$567$	−36.8676	+	21.2855i	−1.54829	+	0.893907i
$568$		0			0
$569$		−	6.99015i		−	0.293042i	−0.989208	−	0.146521i	$-0.953192\pi$
$569$		−	6.99015i		−	0.293042i	0.989208	−	0.146521i	$-0.0468076\pi$
$570$		0			0
$571$			26.4141i			1.10539i	0.833382	+	0.552697i	$0.186401\pi$
$571$			26.4141i			1.10539i	−0.833382	+	0.552697i	$0.813599\pi$
$572$		0			0
$573$	4.76634	−	2.75185i	0.199117	−	0.114960i
$574$		0			0
$575$	19.8778	−	11.4764i	0.828960	−	0.478600i
$576$		0			0
$577$	18.1234			0.754489			0.377244	−	0.926114i	$-0.376872\pi$
$577$	18.1234			0.754489			0.377244	+	0.926114i	$0.376872\pi$
$578$		0			0
$579$	−10.3066	−	5.95054i	−0.428329	−	0.247296i
$580$		0			0
$581$	−34.5088			−1.43166
$582$		0			0
$583$	0.248466	−	0.430355i	0.0102904	−	0.0178235i
$584$		0			0
$585$	1.70460	+	0.984149i	0.0704764	+	0.0406895i
$586$		0			0
$587$	−27.7754	+	16.0361i	−1.14641	+	0.661882i	−0.948011	−	0.318238i	$-0.896909\pi$
$587$	−27.7754	+	16.0361i	−1.14641	+	0.661882i	−0.198403	+	0.980120i	$0.563576\pi$
$588$		0			0
$589$	6.31778	+	5.60191i	0.260320	+	0.230823i
$590$		0			0
$591$	28.9309	+	50.1098i	1.19006	+	2.06124i
$592$		0			0
$593$	8.08437	−	14.0025i	0.331985	−	0.575015i	−0.650916	−	0.759150i	$-0.725615\pi$
$593$	8.08437	−	14.0025i	0.331985	−	0.575015i	0.982901	+	0.184135i	$0.0589482\pi$
$594$		0			0
$595$	9.33829	+	5.39146i	0.382832	+	0.221028i
$596$		0			0
$597$			26.0738i			1.06713i
$598$		0			0
$599$	9.47143	−	16.4050i	0.386992	−	0.670290i	−0.605051	−	0.796186i	$-0.706847\pi$
$599$	9.47143	−	16.4050i	0.386992	−	0.670290i	0.992043	+	0.125897i	$0.0401808\pi$
$600$		0			0
$601$			12.2176i			0.498366i	0.968456	+	0.249183i	$0.0801620\pi$
$601$			12.2176i			0.498366i	−0.968456	+	0.249183i	$0.919838\pi$
$602$		0			0
$603$	−12.2906	−	21.2879i	−0.500512	−	0.866912i
$604$		0			0
$605$	6.94257	+	12.0249i	0.282256	+	0.488881i
$606$		0			0
$607$	−19.3781			−0.786531			−0.393266	−	0.919425i	$-0.628655\pi$
$607$	−19.3781			−0.786531			−0.393266	+	0.919425i	$0.628655\pi$
$608$		0			0
$609$	64.4199			2.61042
$610$		0			0
$611$	−3.61938	−	6.26896i	−0.146425	−	0.253615i
$612$		0			0
$613$	14.2177	+	24.6258i	0.574248	+	0.994627i	0.996123	+	0.0879727i	$0.0280388\pi$
$613$	14.2177	+	24.6258i	0.574248	+	0.994627i	−0.421875	+	0.906654i	$0.638628\pi$
$614$		0			0
$615$			12.8263i			0.517205i
$616$		0			0
$617$	21.4156	−	37.0929i	0.862158	−	1.49330i	−0.00768271	−	0.999970i	$-0.502446\pi$
$617$	21.4156	−	37.0929i	0.862158	−	1.49330i	0.869841	−	0.493332i	$-0.164221\pi$
$618$		0			0
$619$		−	23.1600i		−	0.930879i	−0.885080	−	0.465439i	$-0.845896\pi$
$619$		−	23.1600i		−	0.930879i	0.885080	−	0.465439i	$-0.154104\pi$
$620$		0			0
$621$	12.0202	+	6.93987i	0.482355	+	0.278488i
$622$		0			0
$623$	−30.9533	+	53.6126i	−1.24012	+	2.14794i
$624$		0			0
$625$	−1.73754	−	3.00950i	−0.0695015	−	0.120380i
$626$		0			0
$627$	2.09891	+	0.429434i	0.0838222	+	0.0171499i
$628$		0			0
$629$	16.6963	−	9.63959i	0.665723	−	0.384356i
$630$		0			0
$631$	23.5116	+	13.5744i	0.935982	+	0.540389i	0.888698	−	0.458492i	$-0.151610\pi$
$631$	23.5116	+	13.5744i	0.935982	+	0.540389i	0.0472834	+	0.998882i	$0.484944\pi$
$632$		0			0
$633$	6.40149	−	11.0877i	0.254437	−	0.440697i
$634$		0			0
$635$	−10.5580			−0.418980
$636$		0			0
$637$	5.30621	+	3.06354i	0.210240	+	0.121382i
$638$		0			0
$639$	0.00891740			0.000352767
$640$		0			0
$641$	−36.6586	+	21.1649i	−1.44793	+	0.835963i	−0.998358	−	0.0572818i	$-0.981757\pi$
$641$	−36.6586	+	21.1649i	−1.44793	+	0.835963i	−0.449572	+	0.893244i	$0.648423\pi$
$642$		0			0
$643$	24.4456	−	14.1137i	0.964040	−	0.556589i	0.0666257	−	0.997778i	$-0.478777\pi$
$643$	24.4456	−	14.1137i	0.964040	−	0.556589i	0.897414	+	0.441189i	$0.145443\pi$
$644$		0			0
$645$			15.7941i			0.621892i
$646$		0			0
$647$		−	35.4972i		−	1.39554i	−0.716322	−	0.697770i	$-0.754176\pi$
$647$		−	35.4972i		−	1.39554i	0.716322	−	0.697770i	$-0.245824\pi$
$648$		0			0
$649$	−0.244178	+	0.140976i	−0.00958482	+	0.00553380i
$650$		0			0
$651$	14.7815	−	8.53408i	0.579331	−	0.334477i
$652$		0			0
$653$	8.13074			0.318181			0.159090	−	0.987264i	$-0.449144\pi$
$653$	8.13074			0.318181			0.159090	+	0.987264i	$0.449144\pi$
$654$		0			0
$655$	7.25348	+	4.18780i	0.283417	+	0.163631i
$656$		0			0
$657$	17.8191			0.695190
$658$		0			0
$659$	−9.25286	+	16.0264i	−0.360440	+	0.624301i	−0.988033	−	0.154241i	$-0.950707\pi$
$659$	−9.25286	+	16.0264i	−0.360440	+	0.624301i	0.627593	+	0.778542i	$0.284040\pi$
$660$		0			0
$661$	−13.9409	−	8.04877i	−0.542237	−	0.313061i	0.203748	−	0.979023i	$-0.434688\pi$
$661$	−13.9409	−	8.04877i	−0.542237	−	0.313061i	−0.745985	+	0.665963i	$0.768021\pi$
$662$		0			0
$663$	−3.16041	+	1.82466i	−0.122740	+	0.0708641i
$664$		0			0
$665$	21.1422	+	4.32568i	0.819861	+	0.167743i
$666$		0			0
$667$	−24.7307	−	42.8349i	−0.957577	−	1.65857i
$668$		0			0
$669$	22.2412	−	38.5230i	0.859896	−	1.48938i
$670$		0			0
$671$	−0.0405448	−	0.0234085i	−0.00156521	−	0.000903677i
$672$		0			0
$673$		−	27.4220i		−	1.05704i	−0.848920	−	0.528521i	$-0.822747\pi$
$673$		−	27.4220i		−	1.05704i	0.848920	−	0.528521i	$-0.177253\pi$
$674$		0			0
$675$	3.48041	−	6.02825i	0.133961	−	0.232028i
$676$		0			0
$677$		−	2.07017i		−	0.0795631i	−0.999208	−	0.0397815i	$-0.987334\pi$
$677$		−	2.07017i		−	0.0795631i	0.999208	−	0.0397815i	$-0.0126662\pi$
$678$		0			0
$679$	34.2498	+	59.3223i	1.31439	+	2.27658i
$680$		0			0
$681$	8.14774	+	14.1123i	0.312222	+	0.540784i
$682$		0			0
$683$	−9.19233			−0.351735			−0.175867	−	0.984414i	$-0.556273\pi$
$683$	−9.19233			−0.351735			−0.175867	+	0.984414i	$0.556273\pi$
$684$		0			0
$685$	9.01746			0.344539
$686$		0			0
$687$	−11.9764	−	20.7438i	−0.456930	−	0.791426i
$688$		0			0
$689$	0.847034	+	1.46711i	0.0322694	+	0.0558923i
$690$		0			0
$691$			20.7211i			0.788268i	0.919053	+	0.394134i	$0.128955\pi$
$691$			20.7211i			0.788268i	−0.919053	+	0.394134i	$0.871045\pi$
$692$		0			0
$693$	0.889273	−	1.54027i	0.0337807	−	0.0585098i
$694$		0			0
$695$		−	20.8148i		−	0.789552i
$696$		0			0
$697$	−8.45796	−	4.88320i	−0.320368	−	0.184965i
$698$		0			0
$699$	−28.5276	+	49.4113i	−1.07901	+	1.86891i
$700$		0			0
$701$	5.15141	+	8.92251i	0.194566	+	0.336999i	0.946758	−	0.321945i	$-0.104337\pi$
$701$	5.15141	+	8.92251i	0.194566	+	0.336999i	−0.752192	+	0.658944i	$0.771003\pi$
$702$		0			0
$703$	25.5984	−	28.8696i	0.965460	−	1.08884i
$704$		0			0
$705$	−24.1463	+	13.9409i	−0.909404	+	0.525045i
$706$		0			0
$707$	−9.07052	−	5.23687i	−0.341132	−	0.196953i
$708$		0			0
$709$	17.5512	−	30.3996i	0.659150	−	1.14168i	−0.321686	−	0.946846i	$-0.604250\pi$
$709$	17.5512	−	30.3996i	0.659150	−	1.14168i	0.980836	−	0.194834i	$-0.0624170\pi$
$710$		0			0
$711$	26.0848			0.978255
$712$		0			0
$713$	−11.3492	−	6.55245i	−0.425030	−	0.245391i
$714$		0			0
$715$	0.205086			0.00766977
$716$		0			0
$717$	−54.9930	+	31.7502i	−2.05375	+	1.18573i
$718$		0			0
$719$	−17.9397	+	10.3575i	−0.669036	+	0.386268i	−0.795711	−	0.605676i	$-0.792903\pi$
$719$	−17.9397	+	10.3575i	−0.669036	+	0.386268i	0.126675	+	0.991944i	$0.459569\pi$
$720$		0			0
$721$		−	10.3591i		−	0.385794i
$722$		0			0
$723$		−	49.7213i		−	1.84916i
$724$		0			0
$725$	−21.4821	+	12.4027i	−0.797825	+	0.460625i
$726$		0			0
$727$	−22.5952	+	13.0454i	−0.838011	+	0.483826i	−0.856588	−	0.516001i	$-0.827420\pi$
$727$	−22.5952	+	13.0454i	−0.838011	+	0.483826i	0.0185764	+	0.999827i	$0.494087\pi$
$728$		0			0
$729$	−8.90362			−0.329764
$730$		0			0
$731$	−10.4150	−	6.01311i	−0.385213	−	0.222403i
$732$		0			0
$733$	−37.8290			−1.39724			−0.698622	−	0.715491i	$-0.746203\pi$
$733$	−37.8290			−1.39724			−0.698622	+	0.715491i	$0.746203\pi$
$734$		0			0
$735$	11.7999	−	20.4381i	0.435247	−	0.753870i
$736$		0			0
$737$	−2.21808	−	1.28061i	−0.0817042	−	0.0471719i
$738$		0			0
$739$	35.3389	−	20.4029i	1.29996	−	0.750533i	0.319565	−	0.947564i	$-0.396463\pi$
$739$	35.3389	−	20.4029i	1.29996	−	0.750533i	0.980397	+	0.197031i	$0.0631299\pi$
$740$		0			0
$741$	−4.84548	+	5.46468i	−0.178003	+	0.200750i
$742$		0			0
$743$	−1.68505	−	2.91859i	−0.0618185	−	0.107073i	0.833460	−	0.552580i	$-0.186357\pi$
$743$	−1.68505	−	2.91859i	−0.0618185	−	0.107073i	−0.895278	+	0.445507i	$0.853023\pi$
$744$		0			0
$745$	11.1294	−	19.2766i	0.407748	−	0.706240i
$746$		0			0
$747$	−15.9994	−	9.23728i	−0.585389	−	0.337974i
$748$		0			0
$749$		−	20.9949i		−	0.767138i
$750$		0			0
$751$	13.7071	−	23.7414i	0.500178	−	0.866334i	−0.499822	−	0.866128i	$-0.666601\pi$
$751$	13.7071	−	23.7414i	0.500178	−	0.866334i	1.00000		0.000206003i	$-6.55727e-5\pi$
$752$		0			0
$753$			69.5646i			2.53507i
$754$		0			0
$755$	6.05282	+	10.4838i	0.220285	+	0.381545i
$756$		0			0
$757$	21.3688	+	37.0119i	0.776664	+	1.34522i	0.933854	+	0.357653i	$0.116423\pi$
$757$	21.3688	+	37.0119i	0.776664	+	1.34522i	−0.157190	+	0.987568i	$0.550244\pi$
$758$		0			0
$759$	−3.32506			−0.120692
$760$		0			0
$761$	−4.92781			−0.178633			−0.0893165	−	0.996003i	$-0.528468\pi$
$761$	−4.92781			−0.178633			−0.0893165	+	0.996003i	$0.528468\pi$
$762$		0			0
$763$	37.9599	+	65.7485i	1.37424	+	2.38025i
$764$		0			0
$765$	2.88637	+	4.99933i	0.104357	+	0.180751i
$766$		0			0
$767$		−	0.961192i		−	0.0347066i
$768$		0			0
$769$	0.168207	−	0.291343i	0.00606569	−	0.0105061i	−0.862977	−	0.505244i	$-0.831403\pi$
$769$	0.168207	−	0.291343i	0.00606569	−	0.0105061i	0.869042	+	0.494738i	$0.164736\pi$
$770$		0			0
$771$		−	30.6747i		−	1.10472i
$772$		0			0
$773$	−38.8751	−	22.4446i	−1.39824	−	0.807275i	−0.404033	−	0.914744i	$-0.632392\pi$
$773$	−38.8751	−	22.4446i	−1.39824	−	0.807275i	−0.994208	+	0.107469i	$0.965725\pi$
$774$		0			0
$775$	−3.28612	+	5.69172i	−0.118041	+	0.204453i
$776$		0			0
$777$	−38.9971	−	67.5450i	−1.39901	−	2.42316i
$778$		0			0
$779$	−19.1491	−	3.91789i	−0.686089	−	0.140373i
$780$		0			0
$781$	0.000804662	0	0.000464572i	2.87931e−5	0	1.66237e-5i
$782$		0			0
$783$	−12.9904	−	7.49999i	−0.464238	−	0.268028i
$784$		0			0
$785$	7.41183	−	12.8377i	0.264540	−	0.458196i
$786$		0			0
$787$	−11.3755			−0.405494			−0.202747	−	0.979231i	$-0.564987\pi$
$787$	−11.3755			−0.405494			−0.202747	+	0.979231i	$0.564987\pi$
$788$		0			0
$789$	−22.9455	−	13.2476i	−0.816883	−	0.471628i
$790$		0			0
$791$	−18.7714			−0.667435
$792$		0			0
$793$	0.138220	−	0.0798011i	0.00490832	−	0.00283382i
$794$		0			0
$795$	5.65090	−	3.26255i	0.200417	−	0.115711i
$796$		0			0
$797$			5.62042i			0.199085i	0.995033	+	0.0995427i	$0.0317380\pi$
$797$			5.62042i			0.199085i	−0.995033	+	0.0995427i	$0.968262\pi$
$798$		0			0
$799$		−	21.2303i		−	0.751073i
$800$		0			0
$801$	−28.7020	+	16.5711i	−1.01413	+	0.585511i
$802$		0			0
$803$	1.60791	−	0.928326i	0.0567419	−	0.0327599i
$804$		0			0
$805$	−33.4933			−1.18048
$806$		0			0
$807$	−34.1583	−	19.7213i	−1.20243	−	0.694222i
$808$		0			0
$809$	28.8659			1.01487			0.507435	−	0.861690i	$-0.330594\pi$
$809$	28.8659			1.01487			0.507435	+	0.861690i	$0.330594\pi$
$810$		0			0
$811$	1.29192	−	2.23767i	0.0453654	−	0.0785752i	−0.842451	−	0.538773i	$-0.818888\pi$
$811$	1.29192	−	2.23767i	0.0453654	−	0.0785752i	0.887817	+	0.460198i	$0.152221\pi$
$812$		0			0
$813$	−39.8392	−	23.0012i	−1.39722	−	0.806687i
$814$		0			0
$815$	19.8507	−	11.4608i	0.695341	−	0.401455i
$816$		0			0
$817$	−23.5800	−	4.82444i	−0.824959	−	0.168786i
$818$		0			0
$819$	3.03158	+	5.25085i	0.105932	+	0.183480i
$820$		0			0
$821$	−4.01381	+	6.95213i	−0.140083	+	0.242631i	−0.927528	−	0.373754i	$-0.878070\pi$
$821$	−4.01381	+	6.95213i	−0.140083	+	0.242631i	0.787445	+	0.616385i	$0.211404\pi$
$822$		0			0
$823$	−21.9449	−	12.6699i	−0.764951	−	0.441645i	0.0661194	−	0.997812i	$-0.478938\pi$
$823$	−21.9449	−	12.6699i	−0.764951	−	0.441645i	−0.831071	+	0.556167i	$0.812272\pi$
$824$		0			0
$825$			1.66755i			0.0580566i
$826$		0			0
$827$	25.3632	−	43.9303i	0.881963	−	1.52761i	0.0328085	−	0.999462i	$-0.489555\pi$
$827$	25.3632	−	43.9303i	0.881963	−	1.52761i	0.849155	−	0.528144i	$-0.177112\pi$
$828$		0			0
$829$		−	14.9155i		−	0.518037i	−0.965872	−	0.259019i	$-0.916601\pi$
$829$		−	14.9155i		−	0.518037i	0.965872	−	0.259019i	$-0.0833991\pi$
$830$		0			0
$831$	6.63795	+	11.4973i	0.230268	+	0.398836i
$832$		0			0
$833$	8.98492	+	15.5623i	0.311309	+	0.539203i
$834$		0			0
$835$	15.9758			0.552866
$836$		0			0
$837$	−3.97427			−0.137371
$838$		0			0
$839$	−18.2327	−	31.5799i	−0.629461	−	1.09026i	−0.987660	−	0.156613i	$-0.949942\pi$
$839$	−18.2327	−	31.5799i	−0.629461	−	1.09026i	0.358199	−	0.933645i	$-0.383391\pi$
$840$		0			0
$841$	12.2267	+	21.1773i	0.421612	+	0.730253i
$842$		0			0
$843$			71.2511i			2.45402i
$844$		0			0
$845$	7.89083	−	13.6673i	0.271453	−	0.470170i
$846$		0			0
$847$			42.7719i			1.46966i
$848$		0			0
$849$	−14.0458	−	8.10935i	−0.482051	−	0.278312i
$850$		0			0
$851$	−29.9419	+	51.8609i	−1.02640	+	1.77777i
$852$		0			0
$853$	25.8516	+	44.7763i	0.885141	+	1.53311i	0.845551	+	0.533894i	$0.179272\pi$
$853$	25.8516	+	44.7763i	0.885141	+	1.53311i	0.0395900	+	0.999216i	$0.487395\pi$
$854$		0			0
$855$	8.64436	+	7.66487i	0.295631	+	0.262133i
$856$		0			0
$857$	−22.8712	+	13.2047i	−0.781265	+	0.451063i	−0.836878	−	0.547389i	$-0.815622\pi$
$857$	−22.8712	+	13.2047i	−0.781265	+	0.451063i	0.0556137	+	0.998452i	$0.482288\pi$
$858$		0			0
$859$	36.8741	+	21.2893i	1.25813	+	0.726381i	0.972710	−	0.232022i	$-0.0745342\pi$
$859$	36.8741	+	21.2893i	1.25813	+	0.726381i	0.285418	+	0.958403i	$0.407868\pi$
$860$		0			0
$861$	−19.7551	+	34.2168i	−0.673251	+	1.16611i
$862$		0			0
$863$	18.4520			0.628112			0.314056	−	0.949404i	$-0.398312\pi$
$863$	18.4520			0.628112			0.314056	+	0.949404i	$0.398312\pi$
$864$		0			0
$865$	−6.30280	−	3.63892i	−0.214302	−	0.123727i
$866$		0			0
$867$	27.6534			0.939158
$868$		0			0
$869$	2.35376	−	1.35894i	0.0798458	−	0.0460990i
$870$		0			0
$871$	7.56158	−	4.36568i	0.256214	−	0.147925i
$872$		0			0
$873$			36.6718i			1.24115i
$874$		0			0
$875$			41.5514i			1.40469i
$876$		0			0
$877$	9.49019	−	5.47916i	0.320461	−	0.185018i	−0.331137	−	0.943583i	$-0.607432\pi$
$877$	9.49019	−	5.47916i	0.320461	−	0.185018i	0.651598	+	0.758564i	$0.274099\pi$
$878$		0			0
$879$	−17.3799	+	10.0343i	−0.586210	+	0.338449i
$880$		0			0
$881$	−5.45935			−0.183930			−0.0919652	−	0.995762i	$-0.529315\pi$
$881$	−5.45935			−0.183930			−0.0919652	+	0.995762i	$0.529315\pi$
$882$		0			0
$883$	26.1706	+	15.1096i	0.880711	+	0.508479i	0.870893	−	0.491473i	$-0.163541\pi$
$883$	26.1706	+	15.1096i	0.880711	+	0.508479i	0.00981855	+	0.999952i	$0.496875\pi$
$884$		0			0
$885$	−3.70225			−0.124450
$886$		0			0
$887$	4.06623	−	7.04291i	0.136531	−	0.236478i	−0.789651	−	0.613557i	$-0.789738\pi$
$887$	4.06623	−	7.04291i	0.136531	−	0.236478i	0.926181	+	0.377079i	$0.123071\pi$
$888$		0			0
$889$	−28.1656	−	16.2614i	−0.944644	−	0.545390i
$890$		0			0
$891$	−2.05652	+	1.18733i	−0.0688961	+	0.0397772i
$892$		0			0
$893$	−13.4375	−	40.3079i	−0.449670	−	1.34885i
$894$		0			0
$895$	−16.2612	−	28.1653i	−0.543553	−	0.941462i
$896$		0			0
$897$	5.66766	−	9.81668i	0.189238	−	0.327769i
$898$		0			0
$899$	12.2652	+	7.08130i	0.409066	+	0.236175i
$900$		0			0
$901$			4.96846i			0.165523i
$902$		0			0
$903$	−24.3261	+	42.1341i	−0.809524	+	1.40214i
$904$		0			0
$905$		−	13.7650i		−	0.457563i
$906$		0			0
$907$	29.1930	+	50.5638i	0.969338	+	1.67894i	0.697480	+	0.716605i	$0.254305\pi$
$907$	29.1930	+	50.5638i	0.969338	+	1.67894i	0.271858	+	0.962337i	$0.412362\pi$
$908$		0			0
$909$	−2.80360	−	4.85598i	−0.0929896	−	0.161063i
$910$		0			0
$911$	46.1510			1.52905			0.764525	−	0.644594i	$-0.222974\pi$
$911$	46.1510			1.52905			0.764525	+	0.644594i	$0.222974\pi$
$912$		0			0
$913$	−1.92495			−0.0637064
$914$		0			0
$915$	−0.307372	−	0.532385i	−0.0101614	−	0.0176001i
$916$		0			0
$917$	12.9001	+	22.3437i	0.426000	+	0.737854i
$918$		0			0
$919$			6.22961i			0.205496i	0.994707	+	0.102748i	$0.0327635\pi$
$919$			6.22961i			0.205496i	−0.994707	+	0.102748i	$0.967237\pi$
$920$		0			0
$921$	0.178084	−	0.308451i	0.00586808	−	0.0101638i
$922$		0			0
$923$			0.00316750i			0.000104260i
$924$		0			0
$925$	26.0088	+	15.0162i	0.855163	+	0.493728i
$926$		0			0
$927$	2.77292	−	4.80284i	0.0910746	−	0.157746i
$928$		0			0
$929$	14.8487	+	25.7187i	0.487170	+	0.843804i	0.999891	−	0.0147518i	$-0.00469581\pi$
$929$	14.8487	+	25.7187i	0.487170	+	0.843804i	−0.512721	+	0.858555i	$0.671362\pi$
$930$		0			0
$931$	26.9089	+	23.8598i	0.881904	+	0.781975i
$932$		0			0
$933$	28.1393	−	16.2462i	0.921238	−	0.531877i
$934$		0			0
$935$	0.520902	+	0.300743i	0.0170353	+	0.00983535i
$936$		0			0
$937$	9.08395	−	15.7339i	0.296760	−	0.514003i	−0.678633	−	0.734478i	$-0.737427\pi$
$937$	9.08395	−	15.7339i	0.296760	−	0.514003i	0.975393	+	0.220475i	$0.0707606\pi$
$938$		0			0
$939$	−45.7753			−1.49382
$940$		0			0
$941$	34.8828	+	20.1396i	1.13715	+	0.656532i	0.945723	−	0.324975i	$-0.105356\pi$
$941$	34.8828	+	20.1396i	1.13715	+	0.656532i	0.191424	+	0.981507i	$0.438689\pi$
$942$		0			0
$943$	30.3358			0.987870
$944$		0			0
$945$	−8.79655	+	5.07869i	−0.286152	+	0.165210i
$946$		0			0
$947$	−9.11864	+	5.26465i	−0.296316	+	0.171078i	−0.640787	−	0.767719i	$-0.721392\pi$
$947$	−9.11864	+	5.26465i	−0.296316	+	0.171078i	0.344471	+	0.938797i	$0.388058\pi$
$948$		0			0
$949$			6.32944i			0.205462i
$950$		0			0
$951$		−	57.5461i		−	1.86606i
$952$		0			0
$953$	10.4513	−	6.03405i	0.338550	−	0.195462i	−0.321081	−	0.947052i	$-0.604046\pi$
$953$	10.4513	−	6.03405i	0.338550	−	0.195462i	0.659631	+	0.751590i	$0.270713\pi$
$954$		0			0
$955$	2.67813	−	1.54622i	0.0866623	−	0.0500345i
$956$		0			0
$957$	3.59343			0.116159
$958$		0			0
$959$	24.0560	+	13.8887i	0.776809	+	0.448491i
$960$		0			0
$961$	−27.2476			−0.878955
$962$		0			0
$963$	5.61990	−	9.73396i	0.181099	−	0.313672i
$964$		0			0
$965$	−5.79114	−	3.34352i	−0.186423	−	0.107632i
$966$		0			0
$967$	−48.7914	+	28.1697i	−1.56902	+	0.905877i	−0.572742	+	0.819736i	$0.694120\pi$
$967$	−48.7914	+	28.1697i	−1.56902	+	0.905877i	−0.996283	+	0.0861411i	$0.972546\pi$
$968$		0			0
$969$	−20.3207	+	6.77435i	−0.652795	+	0.217623i
$970$		0			0
$971$	4.55015	+	7.88108i	0.146021	+	0.252916i	0.929753	−	0.368183i	$-0.120020\pi$
$971$	4.55015	+	7.88108i	0.146021	+	0.252916i	−0.783732	+	0.621099i	$0.786687\pi$
$972$		0			0
$973$	32.0591	−	55.5280i	1.02777	−	1.78015i
$974$		0			0
$975$	−4.92316	−	2.84239i	−0.157667	−	0.0910293i
$976$		0			0
$977$			30.0902i			0.962671i	0.876536	+	0.481336i	$0.159848\pi$
$977$			30.0902i			0.962671i	−0.876536	+	0.481336i	$0.840152\pi$
$978$		0			0
$979$	−1.72661	+	2.99058i	−0.0551828	+	0.0955795i
$980$		0			0
$981$			40.6443i			1.29767i
$982$		0			0
$983$	20.3831	+	35.3045i	0.650119	+	1.12604i	0.983094	+	0.183104i	$0.0586144\pi$
$983$	20.3831	+	35.3045i	0.650119	+	1.12604i	−0.332974	+	0.942936i	$0.608052\pi$
$984$		0			0
$985$	16.2558	+	28.1559i	0.517953	+	0.897121i
$986$		0			0
$987$	−85.8874			−2.73383
$988$		0			0
$989$	37.3551			1.18782
$990$		0			0
$991$	2.69921	+	4.67517i	0.0857432	+	0.148512i	0.905708	−	0.423903i	$-0.139340\pi$
$991$	2.69921	+	4.67517i	0.0857432	+	0.148512i	−0.819964	+	0.572414i	$0.806007\pi$
$992$		0			0
$993$	−1.04631	−	1.81227i	−0.0332037	−	0.0575105i
$994$		0			0
$995$			14.6505i			0.464452i
$996$		0			0
$997$	−25.7167	+	44.5427i	−0.814457	+	1.41068i	0.0952596	+	0.995452i	$0.469632\pi$
$997$	−25.7167	+	44.5427i	−0.814457	+	1.41068i	−0.909717	+	0.415229i	$0.863701\pi$
$998$		0			0
$999$			18.1607i			0.574580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.n.a.31.17	yes	40
4.3	odd	2	inner	608.2.n.a.31.4	✓	40
8.3	odd	2		1216.2.n.g.639.17		40
8.5	even	2		1216.2.n.g.639.4		40
19.8	odd	6	inner	608.2.n.a.255.4	yes	40
76.27	even	6	inner	608.2.n.a.255.17	yes	40
152.27	even	6		1216.2.n.g.255.4		40
152.141	odd	6		1216.2.n.g.255.17		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.n.a.31.4	✓	40	4.3	odd	2	inner
608.2.n.a.31.17	yes	40	1.1	even	1	trivial
608.2.n.a.255.4	yes	40	19.8	odd	6	inner
608.2.n.a.255.17	yes	40	76.27	even	6	inner
1216.2.n.g.255.4		40	152.27	even	6
1216.2.n.g.255.17		40	152.141	odd	6
1216.2.n.g.639.4		40	8.5	even	2
1216.2.n.g.639.17		40	8.3	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12813 + 1.95397i) q^{3} +(0.633877 + 1.09791i) q^{5} +3.90520i q^{7} +(-1.04534 + 1.81059i) q^{9} +O(q^{10})\)	\(q+(1.12813 + 1.95397i) q^{3} +(0.633877 + 1.09791i) q^{5} +3.90520i q^{7} +(-1.04534 + 1.81059i) q^{9} +0.217838i q^{11} +(-0.643129 - 0.371310i) q^{13} +(-1.43019 + 2.47716i) q^{15} +(-1.08900 - 1.88620i) q^{17} +(-3.26144 - 2.89189i) q^{19} +(-7.63067 + 4.40557i) q^{21} +(5.85881 + 3.38259i) q^{23} +(1.69640 - 2.93825i) q^{25} +2.05165 q^{27} +(-6.33168 - 3.65559i) q^{29} -1.93711 q^{31} +(-0.425649 + 0.245748i) q^{33} +(-4.28755 + 2.47542i) q^{35} +8.85178i q^{37} -1.67554i q^{39} +(3.88336 - 2.24206i) q^{41} +(4.78192 - 2.76084i) q^{43} -2.65047 q^{45} +(8.44167 + 4.87380i) q^{47} -8.25062 q^{49} +(2.45706 - 4.25575i) q^{51} +(-1.97558 - 1.14060i) q^{53} +(-0.239166 + 0.138082i) q^{55} +(1.97135 - 9.63518i) q^{57} +(0.647162 + 1.12092i) q^{59} +(-0.107459 + 0.186124i) q^{61} +(-7.07071 - 4.08227i) q^{63} -0.941461i q^{65} +(-5.87875 + 10.1823i) q^{67} +15.2639i q^{69} +(-0.00213265 - 0.00369386i) q^{71} +(-4.26155 - 7.38123i) q^{73} +7.65502 q^{75} -0.850700 q^{77} +(-6.23833 - 10.8051i) q^{79} +(5.45055 + 9.44062i) q^{81} +8.83661i q^{83} +(1.38058 - 2.39124i) q^{85} -16.4959i q^{87} +(13.7285 + 7.92616i) q^{89} +(1.45004 - 2.51155i) q^{91} +(-2.18531 - 3.78507i) q^{93} +(1.10767 - 5.41386i) q^{95} +(15.1906 - 8.77029i) q^{97} +(-0.394414 - 0.227715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 16 q^{9}+O(q^{10}) \) 40 * q - 16 * q^9	\( 40 q - 16 q^{9} + 24 q^{13} + 8 q^{17} + 24 q^{21} - 20 q^{25} + 12 q^{33} + 12 q^{41} - 72 q^{49} + 24 q^{53} + 8 q^{57} + 4 q^{73} - 32 q^{77} + 36 q^{81} + 8 q^{85} + 48 q^{89} - 40 q^{93} - 12 q^{97}+O(q^{100}) \) 40 * q - 16 * q^9 + 24 * q^13 + 8 * q^17 + 24 * q^21 - 20 * q^25 + 12 * q^33 + 12 * q^41 - 72 * q^49 + 24 * q^53 + 8 * q^57 + 4 * q^73 - 32 * q^77 + 36 * q^81 + 8 * q^85 + 48 * q^89 - 40 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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