LMFDB - Embedded newform 400.2.bi.d.303.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			303.7
Character	$\chi$	$=$	400.303
Dual form			400.2.bi.d.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.608022 - 0.0963012i) q^{3} +(-2.10398 - 0.757146i) q^{5} +(-1.38198 - 1.38198i) q^{7} +(-2.49275 + 0.809945i) q^{9} +O(q^{10})$	\(q+(0.608022 - 0.0963012i) q^{3} +(-2.10398 - 0.757146i) q^{5} +(-1.38198 - 1.38198i) q^{7} +(-2.49275 + 0.809945i) q^{9} +(-5.27473 - 1.71386i) q^{11} +(-0.110128 + 0.216137i) q^{13} +(-1.35218 - 0.257745i) q^{15} +(-0.974743 + 6.15428i) q^{17} +(3.29083 - 2.39093i) q^{19} +(-0.973360 - 0.707188i) q^{21} +(-3.85829 - 7.57232i) q^{23} +(3.85346 + 3.18604i) q^{25} +(-3.08316 + 1.57095i) q^{27} +(2.97120 - 4.08950i) q^{29} +(1.96420 + 2.70349i) q^{31} +(-3.37220 - 0.534104i) q^{33} +(1.86130 + 3.95402i) q^{35} +(-7.87958 - 4.01485i) q^{37} +(-0.0461457 + 0.142022i) q^{39} +(2.53683 + 7.80756i) q^{41} +(2.80650 - 2.80650i) q^{43} +(5.85795 + 0.183270i) q^{45} +(-1.06019 - 6.69377i) q^{47} -3.18026i q^{49} +3.83581i q^{51} +(-0.431454 - 2.72409i) q^{53} +(9.80029 + 7.59968i) q^{55} +(1.77065 - 1.77065i) q^{57} +(0.496288 + 1.52742i) q^{59} +(1.00535 - 3.09413i) q^{61} +(4.56426 + 2.32561i) q^{63} +(0.395354 - 0.371366i) q^{65} +(-9.09540 - 1.44057i) q^{67} +(-3.07515 - 4.23258i) q^{69} +(-9.23555 + 12.7116i) q^{71} +(-4.14363 + 2.11129i) q^{73} +(2.64981 + 1.56609i) q^{75} +(4.92105 + 9.65810i) q^{77} +(9.67220 + 7.02726i) q^{79} +(4.63804 - 3.36973i) q^{81} +(1.63523 - 10.3244i) q^{83} +(6.71053 - 12.2105i) q^{85} +(1.41273 - 2.77264i) q^{87} +(-5.96972 - 1.93968i) q^{89} +(0.450892 - 0.146504i) q^{91} +(1.45462 + 1.45462i) q^{93} +(-8.73411 + 2.53882i) q^{95} +(4.71249 - 0.746384i) q^{97} +14.5367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5}+O(q^{10}) $ 80 * q + 4 * q^5	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$-1$

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
$3$	0.608022	−	0.0963012i	0.351042	−	0.0555995i	0.0215763	−	0.999767i	$-0.493132\pi$
$3$	0.608022	−	0.0963012i	0.351042	−	0.0555995i	0.329465	+	0.944168i	$0.393132\pi$
$4$		0			0
$5$	−2.10398	−	0.757146i	−0.940928	−	0.338606i
$5$	−2.10398	−	0.757146i	−0.940928	−	0.338606i
$6$		0			0
$7$	−1.38198	−	1.38198i	−0.522339	−	0.522339i	0.395938	−	0.918277i	$-0.370420\pi$
$7$	−1.38198	−	1.38198i	−0.522339	−	0.522339i	−0.918277	+	0.395938i	$0.870420\pi$
$8$		0			0
$9$	−2.49275	+	0.809945i	−0.830918	+	0.269982i
$10$		0			0
$11$	−5.27473	−	1.71386i	−1.59039	−	0.516750i	−0.625685	−	0.780076i	$-0.715180\pi$
$11$	−5.27473	−	1.71386i	−1.59039	−	0.516750i	−0.964707	+	0.263326i	$0.915180\pi$
$12$		0			0
$13$	−0.110128	+	0.216137i	−0.0305439	+	0.0599457i	−0.905774	−	0.423761i	$-0.860710\pi$
$13$	−0.110128	+	0.216137i	−0.0305439	+	0.0599457i	0.875230	+	0.483706i	$0.160710\pi$
$14$		0			0
$15$	−1.35218	−	0.257745i	−0.349131	−	0.0665496i
$16$		0			0
$17$	−0.974743	+	6.15428i	−0.236410	+	1.49263i	0.528742	+	0.848783i	$0.322664\pi$
$17$	−0.974743	+	6.15428i	−0.236410	+	1.49263i	−0.765152	+	0.643850i	$0.777336\pi$
$18$		0			0
$19$	3.29083	−	2.39093i	0.754967	−	0.548516i	−0.142395	−	0.989810i	$-0.545480\pi$
$19$	3.29083	−	2.39093i	0.754967	−	0.548516i	0.897363	+	0.441294i	$0.145480\pi$
$20$		0			0
$21$	−0.973360	−	0.707188i	−0.212405	−	0.154321i
$22$		0			0
$23$	−3.85829	−	7.57232i	−0.804509	−	1.57894i	−0.815330	−	0.578996i	$-0.803445\pi$
$23$	−3.85829	−	7.57232i	−0.804509	−	1.57894i	0.0108213	−	0.999941i	$-0.496555\pi$
$24$		0			0
$25$	3.85346	+	3.18604i	0.770692	+	0.637208i
$26$		0			0
$27$	−3.08316	+	1.57095i	−0.593355	+	0.302329i
$28$		0			0
$29$	2.97120	−	4.08950i	0.551738	−	0.759402i	−0.438509	−	0.898727i	$-0.644493\pi$
$29$	2.97120	−	4.08950i	0.551738	−	0.759402i	0.990247	+	0.139325i	$0.0444933\pi$
$30$		0			0
$31$	1.96420	+	2.70349i	0.352781	+	0.485561i	0.948120	−	0.317914i	$-0.102982\pi$
$31$	1.96420	+	2.70349i	0.352781	+	0.485561i	−0.595339	+	0.803475i	$0.702982\pi$
$32$		0			0
$33$	−3.37220	−	0.534104i	−0.587025	−	0.0929756i
$34$		0			0
$35$	1.86130	+	3.95402i	0.314617	+	0.668351i
$36$		0			0
$37$	−7.87958	−	4.01485i	−1.29539	−	0.660037i	−0.335936	−	0.941885i	$-0.609053\pi$
$37$	−7.87958	−	4.01485i	−1.29539	−	0.660037i	−0.959459	+	0.281848i	$0.909053\pi$
$38$		0			0
$39$	−0.0461457	+	0.142022i	−0.00738922	+	0.0227417i
$40$		0			0
$41$	2.53683	+	7.80756i	0.396186	+	1.21934i	0.928034	+	0.372496i	$0.121498\pi$
$41$	2.53683	+	7.80756i	0.396186	+	1.21934i	−0.531847	+	0.846840i	$0.678502\pi$
$42$		0			0
$43$	2.80650	−	2.80650i	0.427987	−	0.427987i	−0.459955	−	0.887942i	$-0.652135\pi$
$43$	2.80650	−	2.80650i	0.427987	−	0.427987i	0.887942	+	0.459955i	$0.152135\pi$
$44$		0			0
$45$	5.85795	+	0.183270i	0.873251	+	0.0273203i
$46$		0			0
$47$	−1.06019	−	6.69377i	−0.154644	−	0.976386i	−0.935923	−	0.352204i	$-0.885432\pi$
$47$	−1.06019	−	6.69377i	−0.154644	−	0.976386i	0.781279	−	0.624182i	$-0.214568\pi$
$48$		0			0
$49$		−	3.18026i		−	0.454323i
$50$		0			0
$51$			3.83581i			0.537120i
$52$		0			0
$53$	−0.431454	−	2.72409i	−0.0592647	−	0.374183i	−0.999439	−	0.0334890i	$-0.989338\pi$
$53$	−0.431454	−	2.72409i	−0.0592647	−	0.374183i	0.940174	−	0.340694i	$-0.110662\pi$
$54$		0			0
$55$	9.80029	+	7.59968i	1.32147	+	1.02474i
$56$		0			0
$57$	1.77065	−	1.77065i	0.234528	−	0.234528i
$58$		0			0
$59$	0.496288	+	1.52742i	0.0646112	+	0.198853i	0.978151	−	0.207897i	$-0.0666620\pi$
$59$	0.496288	+	1.52742i	0.0646112	+	0.198853i	−0.913539	+	0.406750i	$0.866662\pi$
$60$		0			0
$61$	1.00535	−	3.09413i	0.128721	−	0.396163i	−0.865839	−	0.500322i	$-0.833215\pi$
$61$	1.00535	−	3.09413i	0.128721	−	0.396163i	0.994561	+	0.104159i	$0.0332150\pi$
$62$		0			0
$63$	4.56426	+	2.32561i	0.575043	+	0.292999i
$64$		0			0
$65$	0.395354	−	0.371366i	0.0490376	−	0.0460623i
$66$		0			0
$67$	−9.09540	−	1.44057i	−1.11118	−	0.175994i	−0.426252	−	0.904604i	$-0.640166\pi$
$67$	−9.09540	−	1.44057i	−1.11118	−	0.175994i	−0.684928	+	0.728611i	$0.740166\pi$
$68$		0			0
$69$	−3.07515	−	4.23258i	−0.370204	−	0.509542i
$70$		0			0
$71$	−9.23555	+	12.7116i	−1.09606	+	1.50859i	−0.255550	+	0.966796i	$0.582257\pi$
$71$	−9.23555	+	12.7116i	−1.09606	+	1.50859i	−0.840508	+	0.541799i	$0.817743\pi$
$72$		0			0
$73$	−4.14363	+	2.11129i	−0.484975	+	0.247107i	−0.679342	−	0.733822i	$-0.737735\pi$
$73$	−4.14363	+	2.11129i	−0.484975	+	0.247107i	0.194367	+	0.980929i	$0.437735\pi$
$74$		0			0
$75$	2.64981	+	1.56609i	0.305973	+	0.180836i
$76$		0			0
$77$	4.92105	+	9.65810i	0.560806	+	1.10064i
$78$		0			0
$79$	9.67220	+	7.02726i	1.08821	+	0.790629i	0.979096	−	0.203401i	$-0.0651994\pi$
$79$	9.67220	+	7.02726i	1.08821	+	0.790629i	0.109112	+	0.994030i	$0.465199\pi$
$80$		0			0
$81$	4.63804	−	3.36973i	0.515338	−	0.374415i
$82$		0			0
$83$	1.63523	−	10.3244i	0.179489	−	1.13325i	−0.719244	−	0.694757i	$-0.755512\pi$
$83$	1.63523	−	10.3244i	0.179489	−	1.13325i	0.898734	−	0.438495i	$-0.144488\pi$
$84$		0			0
$85$	6.71053	−	12.2105i	0.727859	−	1.32441i
$86$		0			0
$87$	1.41273	−	2.77264i	0.151460	−	0.297258i
$88$		0			0
$89$	−5.96972	−	1.93968i	−0.632789	−	0.205605i	−0.0249786	−	0.999688i	$-0.507952\pi$
$89$	−5.96972	−	1.93968i	−0.632789	−	0.205605i	−0.607810	+	0.794082i	$0.707952\pi$
$90$		0			0
$91$	0.450892	−	0.146504i	0.0472663	−	0.0153577i
$92$		0			0
$93$	1.45462	+	1.45462i	0.150838	+	0.150838i
$94$		0			0
$95$	−8.73411	+	2.53882i	−0.896101	+	0.260478i
$96$		0			0
$97$	4.71249	−	0.746384i	0.478480	−	0.0757839i	0.0874643	−	0.996168i	$-0.472124\pi$
$97$	4.71249	−	0.746384i	0.478480	−	0.0757839i	0.391016	+	0.920384i	$0.372124\pi$
$98$		0			0
$99$	14.5367			1.46100
$100$		0			0
$101$	−5.93887			−0.590940			−0.295470	−	0.955352i	$-0.595476\pi$
$101$	−5.93887			−0.590940			−0.295470	+	0.955352i	$0.595476\pi$
$102$		0			0
$103$	7.02005	−	1.11187i	0.691706	−	0.109555i	0.199323	−	0.979934i	$-0.436126\pi$
$103$	7.02005	−	1.11187i	0.691706	−	0.109555i	0.492383	+	0.870378i	$0.336126\pi$
$104$		0			0
$105$	1.51249	+	2.22488i	0.147604	+	0.217126i
$106$		0			0
$107$	4.02246	+	4.02246i	0.388866	+	0.388866i	0.874283	−	0.485417i	$-0.161332\pi$
$107$	4.02246	+	4.02246i	0.388866	+	0.388866i	−0.485417	+	0.874283i	$0.661332\pi$
$108$		0			0
$109$	9.07361	−	2.94819i	0.869094	−	0.282386i	0.159672	−	0.987170i	$-0.448956\pi$
$109$	9.07361	−	2.94819i	0.869094	−	0.282386i	0.709422	+	0.704784i	$0.248956\pi$
$110$		0			0
$111$	−5.17759	−	1.68230i	−0.491435	−	0.159677i
$112$		0			0
$113$	−1.16416	+	2.28480i	−0.109515	+	0.214936i	−0.939259	−	0.343208i	$-0.888486\pi$
$113$	−1.16416	+	2.28480i	−0.109515	+	0.214936i	0.829744	+	0.558144i	$0.188486\pi$
$114$		0			0
$115$	2.38441	+	18.8533i	0.222348	+	1.75808i
$116$		0			0
$117$	0.0994614	−	0.627975i	0.00919521	−	0.0580563i
$118$		0			0
$119$	9.85217	−	7.15802i	0.903147	−	0.656175i
$120$		0			0
$121$	15.9863	+	11.6147i	1.45330	+	1.05588i
$122$		0			0
$123$	2.29433	+	4.50287i	0.206872	+	0.406010i
$124$		0			0
$125$	−5.69531	−	9.62099i	−0.509404	−	0.860528i
$126$		0			0
$127$	−9.16965	+	4.67217i	−0.813675	+	0.414588i	−0.810739	−	0.585408i	$-0.800934\pi$
$127$	−9.16965	+	4.67217i	−0.813675	+	0.414588i	−0.00293556	+	0.999996i	$0.500934\pi$
$128$		0			0
$129$	1.43614	−	1.97668i	0.126445	−	0.174037i
$130$		0			0
$131$	1.02092	+	1.40517i	0.0891978	+	0.122770i	0.851284	−	0.524706i	$-0.175825\pi$
$131$	1.02092	+	1.40517i	0.0891978	+	0.122770i	−0.762086	+	0.647476i	$0.775825\pi$
$132$		0			0
$133$	−7.85207	−	1.24365i	−0.680861	−	0.107838i
$134$		0			0
$135$	7.67635	−	0.970843i	0.660675	−	0.0835569i
$136$		0			0
$137$	−1.75454	−	0.893983i	−0.149900	−	0.0763781i	0.377431	−	0.926038i	$-0.376807\pi$
$137$	−1.75454	−	0.893983i	−0.149900	−	0.0763781i	−0.527332	+	0.849660i	$0.676807\pi$
$138$		0			0
$139$	0.413240	−	1.27182i	0.0350505	−	0.107874i	−0.932001	−	0.362457i	$-0.881938\pi$
$139$	0.413240	−	1.27182i	0.0350505	−	0.107874i	0.967051	+	0.254582i	$0.0819380\pi$
$140$		0			0
$141$	−1.28924	−	3.96786i	−0.108573	−	0.334154i
$142$		0			0
$143$	0.951324	−	0.951324i	0.0795537	−	0.0795537i
$144$		0			0
$145$	−9.34769	+	6.35460i	−0.776283	+	0.527721i
$146$		0			0
$147$	−0.306263	−	1.93367i	−0.0252602	−	0.159486i
$148$		0			0
$149$		−	1.78079i		−	0.145888i	−0.997336	−	0.0729441i	$-0.976761\pi$
$149$		−	1.78079i		−	0.145888i	0.997336	−	0.0729441i	$-0.0232395\pi$
$150$		0			0
$151$		−	4.49426i		−	0.365738i	−0.983137	−	0.182869i	$-0.941462\pi$
$151$		−	4.49426i		−	0.365738i	0.983137	−	0.182869i	$-0.0585384\pi$
$152$		0			0
$153$	−2.55484	−	16.1306i	−0.206546	−	1.30408i
$154$		0			0
$155$	−2.08570	−	7.17527i	−0.167527	−	0.576331i
$156$		0			0
$157$	−7.91746	+	7.91746i	−0.631882	+	0.631882i	−0.948540	−	0.316658i	$-0.897439\pi$
$157$	−7.91746	+	7.91746i	−0.631882	+	0.631882i	0.316658	+	0.948540i	$0.397439\pi$
$158$		0			0
$159$	−0.524666	−	1.61476i	−0.0416088	−	0.128059i
$160$		0			0
$161$	−5.13271	+	15.7969i	−0.404515	+	1.24497i
$162$		0			0
$163$	−17.0230	−	8.67364i	−1.33334	−	0.679372i	−0.365472	−	0.930822i	$-0.619092\pi$
$163$	−17.0230	−	8.67364i	−1.33334	−	0.679372i	−0.967870	+	0.251450i	$0.919092\pi$
$164$		0			0
$165$	6.69065	+	3.67699i	0.520866	+	0.286253i
$166$		0			0
$167$	−24.7158	−	3.91459i	−1.91256	−	0.302920i	−0.917147	−	0.398550i	$-0.869514\pi$
$167$	−24.7158	−	3.91459i	−1.91256	−	0.302920i	−0.995417	+	0.0956294i	$0.969514\pi$
$168$		0			0
$169$	7.60662	+	10.4696i	0.585125	+	0.805355i
$170$		0			0
$171$	−6.26670	+	8.62537i	−0.479227	+	0.659599i
$172$		0			0
$173$	1.62937	−	0.830204i	0.123878	−	0.0631192i	−0.390953	−	0.920411i	$-0.627854\pi$
$173$	1.62937	−	0.830204i	0.123878	−	0.0631192i	0.514831	+	0.857291i	$0.327854\pi$
$174$		0			0
$175$	−0.922364	−	9.72845i	−0.0697242	−	0.735401i
$176$		0			0
$177$	0.448846	+	0.880910i	0.0337373	+	0.0662133i
$178$		0			0
$179$	−12.6215	−	9.17002i	−0.943372	−	0.685400i	0.00585814	−	0.999983i	$-0.498135\pi$
$179$	−12.6215	−	9.17002i	−0.943372	−	0.685400i	−0.949230	+	0.314583i	$0.898135\pi$
$180$		0			0
$181$	−0.0662626	+	0.0481426i	−0.00492526	+	0.00357841i	−0.590245	−	0.807224i	$-0.700969\pi$
$181$	−0.0662626	+	0.0481426i	−0.00492526	+	0.00357841i	0.585320	+	0.810802i	$0.300969\pi$
$182$		0			0
$183$	0.313303	−	1.97812i	0.0231600	−	0.146227i
$184$		0			0
$185$	13.5387	+	14.4131i	0.995381	+	1.05968i
$186$		0			0
$187$	15.6891	−	30.7916i	1.14730	−	2.25171i
$188$		0			0
$189$	6.43189	+	2.08985i	0.467851	+	0.152014i
$190$		0			0
$191$	2.29966	−	0.747204i	0.166397	−	0.0540658i	−0.224634	−	0.974443i	$-0.572119\pi$
$191$	2.29966	−	0.747204i	0.166397	−	0.0540658i	0.391031	+	0.920378i	$0.372119\pi$
$192$		0			0
$193$	−7.88387	−	7.88387i	−0.567494	−	0.567494i	0.363932	−	0.931426i	$-0.381434\pi$
$193$	−7.88387	−	7.88387i	−0.567494	−	0.567494i	−0.931426	+	0.363932i	$0.881434\pi$
$194$		0			0
$195$	0.204621	−	0.263872i	0.0146532	−	0.0188963i
$196$		0			0
$197$	−20.4157	+	3.23354i	−1.45456	+	0.230380i	−0.833125	−	0.553085i	$-0.813451\pi$
$197$	−20.4157	+	3.23354i	−1.45456	+	0.230380i	−0.621436	+	0.783465i	$0.713451\pi$
$198$		0			0
$199$	−11.0797			−0.785416			−0.392708	−	0.919663i	$-0.628462\pi$
$199$	−11.0797			−0.785416			−0.392708	+	0.919663i	$0.628462\pi$
$200$		0			0
$201$	−5.66893			−0.399856
$202$		0			0
$203$	−9.75775	+	1.54548i	−0.684860	+	0.108471i
$204$		0			0
$205$	0.574022	−	18.3477i	0.0400915	−	1.28146i
$206$		0			0
$207$	15.7509	+	15.7509i	1.09476	+	1.09476i
$208$		0			0
$209$	−21.4560	+	6.97146i	−1.48414	+	0.482226i
$210$		0			0
$211$	−0.255262	−	0.0829395i	−0.0175729	−	0.00570979i	0.300217	−	0.953871i	$-0.402941\pi$
$211$	−0.255262	−	0.0829395i	−0.0175729	−	0.00570979i	−0.317790	+	0.948161i	$0.602941\pi$
$212$		0			0
$213$	−4.39127	+	8.61835i	−0.300885	+	0.590520i
$214$		0			0
$215$	−8.02974	+	3.77989i	−0.547624	+	0.257786i
$216$		0			0
$217$	1.02168	−	6.45065i	0.0693563	−	0.437899i
$218$		0			0
$219$	−2.31610	+	1.68274i	−0.156507	+	0.113709i
$220$		0			0
$221$	−1.22283	−	0.888434i	−0.0822561	−	0.0597626i
$222$		0			0
$223$	−2.86545	−	5.62377i	−0.191885	−	0.376596i	0.774940	−	0.632035i	$-0.217780\pi$
$223$	−2.86545	−	5.62377i	−0.191885	−	0.376596i	−0.966825	+	0.255439i	$0.917780\pi$
$224$		0			0
$225$	−12.1862	−	4.82092i	−0.812416	−	0.321394i
$226$		0			0
$227$	−14.1090	+	7.18890i	−0.936447	+	0.477144i	−0.854476	−	0.519491i	$-0.826122\pi$
$227$	−14.1090	+	7.18890i	−0.936447	+	0.477144i	−0.0819714	+	0.996635i	$0.526122\pi$
$228$		0			0
$229$	4.49909	−	6.19246i	0.297308	−	0.409209i	−0.634063	−	0.773282i	$-0.718614\pi$
$229$	4.49909	−	6.19246i	0.297308	−	0.409209i	0.931371	+	0.364072i	$0.118614\pi$
$230$		0			0
$231$	3.92219	+	5.39843i	0.258061	+	0.355191i
$232$		0			0
$233$	4.94301	+	0.782896i	0.323828	+	0.0512892i	0.316232	−	0.948682i	$-0.397582\pi$
$233$	4.94301	+	0.782896i	0.323828	+	0.0512892i	0.00759562	+	0.999971i	$0.497582\pi$
$234$		0			0
$235$	−2.83754	+	14.8863i	−0.185101	+	0.971073i
$236$		0			0
$237$	6.55764	+	3.34128i	0.425965	+	0.217040i
$238$		0			0
$239$	1.42217	−	4.37697i	0.0919922	−	0.283123i	−0.894466	−	0.447136i	$-0.852444\pi$
$239$	1.42217	−	4.37697i	0.0919922	−	0.283123i	0.986458	+	0.164013i	$0.0524440\pi$
$240$		0			0
$241$	−7.75089	−	23.8548i	−0.499279	−	1.53662i	−0.810181	−	0.586180i	$-0.800631\pi$
$241$	−7.75089	−	23.8548i	−0.499279	−	1.53662i	0.310902	−	0.950442i	$-0.399369\pi$
$242$		0			0
$243$	9.83596	−	9.83596i	0.630977	−	0.630977i
$244$		0			0
$245$	−2.40792	+	6.69121i	−0.153837	+	0.427486i
$246$		0			0
$247$	0.154358	+	0.974578i	0.00982156	+	0.0620109i
$248$		0			0
$249$		−	6.43494i		−	0.407798i
$250$		0			0
$251$		−	22.4500i		−	1.41703i	−0.705695	−	0.708515i	$-0.749365\pi$
$251$		−	22.4500i		−	1.41703i	0.705695	−	0.708515i	$-0.250635\pi$
$252$		0			0
$253$	7.37352	+	46.5546i	0.463569	+	2.92686i
$254$		0			0
$255$	2.90426	−	8.07046i	0.181872	−	0.505392i
$256$		0			0
$257$	20.9029	−	20.9029i	1.30389	−	1.30389i	0.378135	−	0.925751i	$-0.376566\pi$
$257$	20.9029	−	20.9029i	1.30389	−	1.30389i	0.925751	−	0.378135i	$-0.123434\pi$
$258$		0			0
$259$	5.34098	+	16.4379i	0.331873	+	1.02140i
$260$		0			0
$261$	−4.09419	+	12.6006i	−0.253424	+	0.779959i
$262$		0			0
$263$	10.8744	+	5.54077i	0.670543	+	0.341659i	0.755896	−	0.654692i	$-0.227202\pi$
$263$	10.8744	+	5.54077i	0.670543	+	0.341659i	−0.0853526	+	0.996351i	$0.527202\pi$
$264$		0			0
$265$	−1.15476	+	6.05811i	−0.0709366	+	0.372146i
$266$		0			0
$267$	−3.81651	−	0.604476i	−0.233567	−	0.0369933i
$268$		0			0
$269$	5.56033	+	7.65314i	0.339019	+	0.466620i	0.944155	−	0.329502i	$-0.106881\pi$
$269$	5.56033	+	7.65314i	0.339019	+	0.466620i	−0.605135	+	0.796123i	$0.706881\pi$
$270$		0			0
$271$	8.95493	−	12.3254i	0.543973	−	0.748715i	−0.445206	−	0.895428i	$-0.646869\pi$
$271$	8.95493	−	12.3254i	0.543973	−	0.748715i	0.989179	+	0.146713i	$0.0468695\pi$
$272$		0			0
$273$	0.260044	−	0.132499i	0.0157385	−	0.00801919i
$274$		0			0
$275$	−14.8655	−	23.4098i	−0.896426	−	1.41166i
$276$		0			0
$277$	4.50555	+	8.84264i	0.270712	+	0.531303i	0.985840	−	0.167692i	$-0.0536313\pi$
$277$	4.50555	+	8.84264i	0.270712	+	0.531303i	−0.715127	+	0.698994i	$0.753631\pi$
$278$		0			0
$279$	−7.08594	−	5.14824i	−0.424224	−	0.308217i
$280$		0			0
$281$	14.0071	−	10.1768i	0.835596	−	0.607096i	−0.0855408	−	0.996335i	$-0.527262\pi$
$281$	14.0071	−	10.1768i	0.835596	−	0.607096i	0.921137	+	0.389238i	$0.127262\pi$
$282$		0			0
$283$	−2.62782	+	16.5914i	−0.156208	+	0.986258i	0.777672	+	0.628671i	$0.216401\pi$
$283$	−2.62782	+	16.5914i	−0.156208	+	0.986258i	−0.933880	+	0.357588i	$0.883599\pi$
$284$		0			0
$285$	−5.06604	+	2.38477i	−0.300086	+	0.141261i
$286$		0			0
$287$	7.28404	−	14.2957i	0.429964	−	0.843851i
$288$		0			0
$289$	−20.7571	−	6.74439i	−1.22101	−	0.396729i
$290$		0			0
$291$	2.79342	−	0.907636i	0.163753	−	0.0532066i
$292$		0			0
$293$	−1.94789	−	1.94789i	−0.113797	−	0.113797i	0.647915	−	0.761712i	$-0.275641\pi$
$293$	−1.94789	−	1.94789i	−0.113797	−	0.113797i	−0.761712	+	0.647915i	$0.775641\pi$
$294$		0			0
$295$	0.112298	−	3.58942i	0.00653823	−	0.208984i
$296$		0			0
$297$	18.9553	−	3.00222i	1.09990	−	0.174206i
$298$		0			0
$299$	2.06157			0.119223
$300$		0			0
$301$	−7.75705			−0.447109
$302$		0			0
$303$	−3.61096	+	0.571921i	−0.207444	+	0.0328560i
$304$		0			0
$305$	−4.45794	+	5.74880i	−0.255261	+	0.329175i
$306$		0			0
$307$	19.9476	+	19.9476i	1.13847	+	1.13847i	0.988724	+	0.149748i	$0.0478463\pi$
$307$	19.9476	+	19.9476i	1.13847	+	1.13847i	0.149748	+	0.988724i	$0.452154\pi$
$308$		0			0
$309$	4.16127	−	1.35208i	0.236726	−	0.0769170i
$310$		0			0
$311$	−21.2038	−	6.88952i	−1.20235	−	0.390669i	−0.361728	−	0.932284i	$-0.617813\pi$
$311$	−21.2038	−	6.88952i	−1.20235	−	0.390669i	−0.840627	+	0.541615i	$0.817813\pi$
$312$		0			0
$313$	12.2631	−	24.0676i	0.693150	−	1.36038i	−0.228953	−	0.973438i	$-0.573530\pi$
$313$	12.2631	−	24.0676i	0.693150	−	1.36038i	0.922102	−	0.386946i	$-0.126470\pi$
$314$		0			0
$315$	−7.84229	−	8.34884i	−0.441863	−	0.470404i
$316$		0			0
$317$	−1.63653	+	10.3326i	−0.0919166	+	0.580338i	0.898144	+	0.439700i	$0.144915\pi$
$317$	−1.63653	+	10.3326i	−0.0919166	+	0.580338i	−0.990061	+	0.140638i	$0.955085\pi$
$318$		0			0
$319$	−22.6811	+	16.4788i	−1.26990	+	0.922636i
$320$		0			0
$321$	2.83311	+	2.05838i	0.158129	+	0.114887i
$322$		0			0
$323$	11.5067	+	22.5832i	0.640251	+	1.25656i
$324$		0			0
$325$	−1.11299	+	0.482007i	−0.0617378	+	0.0267369i
$326$		0			0
$327$	5.23304	−	2.66636i	0.289388	−	0.147450i
$328$		0			0
$329$	−7.78549	+	10.7158i	−0.429228	+	0.590782i
$330$		0			0
$331$	17.8173	+	24.5234i	0.979326	+	1.34793i	0.937192	+	0.348814i	$0.113416\pi$
$331$	17.8173	+	24.5234i	0.979326	+	1.34793i	0.0421337	+	0.999112i	$0.486584\pi$
$332$		0			0
$333$	22.8936	+	3.62600i	1.25456	+	0.198703i
$334$		0			0
$335$	18.0458	+	9.91748i	0.985948	+	0.541850i
$336$		0			0
$337$	−27.1843	−	13.8511i	−1.48082	−	0.754517i	−0.487858	−	0.872923i	$-0.662222\pi$
$337$	−27.1843	−	13.8511i	−1.48082	−	0.754517i	−0.992965	+	0.118405i	$0.962222\pi$
$338$		0			0
$339$	−0.487808	+	1.50132i	−0.0264941	+	0.0815404i
$340$		0			0
$341$	−5.72721	−	17.6265i	−0.310146	−	0.954531i
$342$		0			0
$343$	−14.0689	+	14.0689i	−0.759650	+	0.759650i
$344$		0			0
$345$	3.26537	+	11.2336i	0.175802	+	0.604796i
$346$		0			0
$347$	3.43298	+	21.6750i	0.184292	+	1.16357i	0.890302	+	0.455371i	$0.150493\pi$
$347$	3.43298	+	21.6750i	0.184292	+	1.16357i	−0.706010	+	0.708202i	$0.749507\pi$
$348$		0			0
$349$			17.6597i			0.945304i	0.881249	+	0.472652i	$0.156703\pi$
$349$			17.6597i			0.945304i	−0.881249	+	0.472652i	$0.843297\pi$
$350$		0			0
$351$		−	0.839392i		−	0.0448034i
$352$		0			0
$353$	−2.84105	−	17.9377i	−0.151214	−	0.954728i	−0.940276	−	0.340414i	$-0.889433\pi$
$353$	−2.84105	−	17.9377i	−0.151214	−	0.954728i	0.789062	−	0.614314i	$-0.210567\pi$
$354$		0			0
$355$	29.0560	−	19.7524i	1.54213	−	1.04835i
$356$		0			0
$357$	5.30101	−	5.30101i	0.280559	−	0.280559i
$358$		0			0
$359$	−2.79654	−	8.60687i	−0.147596	−	0.454253i	0.849740	−	0.527202i	$-0.176759\pi$
$359$	−2.79654	−	8.60687i	−0.147596	−	0.454253i	−0.997336	+	0.0729491i	$0.976759\pi$
$360$		0			0
$361$	−0.758308	+	2.33383i	−0.0399109	+	0.122833i
$362$		0			0
$363$	10.8385	+	5.52250i	0.568875	+	0.289856i
$364$		0			0
$365$	10.3167	−	1.30477i	0.539999	−	0.0682947i
$366$		0			0
$367$	9.13198	+	1.44636i	0.476686	+	0.0754996i	0.390154	−	0.920750i	$-0.372422\pi$
$367$	9.13198	+	1.44636i	0.476686	+	0.0754996i	0.0865314	+	0.996249i	$0.472422\pi$
$368$		0			0
$369$	−12.6474	−	17.4076i	−0.658397	−	0.906205i
$370$		0			0
$371$	−3.16838	+	4.36090i	−0.164494	+	0.226407i
$372$		0			0
$373$	18.9566	−	9.65886i	0.981535	−	0.500117i	0.111850	−	0.993725i	$-0.464322\pi$
$373$	18.9566	−	9.65886i	0.981535	−	0.500117i	0.869684	+	0.493608i	$0.164322\pi$
$374$		0			0
$375$	−4.38938	−	5.30131i	−0.226667	−	0.273758i
$376$		0			0
$377$	0.556684	+	1.09255i	0.0286707	+	0.0562694i
$378$		0			0
$379$	−1.18561	−	0.861395i	−0.0609006	−	0.0442469i	0.556918	−	0.830567i	$-0.311984\pi$
$379$	−1.18561	−	0.861395i	−0.0609006	−	0.0442469i	−0.617819	+	0.786320i	$0.711984\pi$
$380$		0			0
$381$	−5.12541	+	3.72383i	−0.262583	+	0.190777i
$382$		0			0
$383$	−0.735091	+	4.64118i	−0.0375614	+	0.237153i	−0.999325	−	0.0367263i	$-0.988307\pi$
$383$	−0.735091	+	4.64118i	−0.0375614	+	0.237153i	0.961764	+	0.273880i	$0.0883070\pi$
$384$		0			0
$385$	−3.04120	−	24.0464i	−0.154994	−	1.22552i
$386$		0			0
$387$	−4.72280	+	9.26901i	−0.240073	+	0.471170i
$388$		0			0
$389$	30.1518	+	9.79690i	1.52876	+	0.496723i	0.948248	−	0.317532i	$-0.102854\pi$
$389$	30.1518	+	9.79690i	1.52876	+	0.496723i	0.580508	+	0.814255i	$0.302854\pi$
$390$		0			0
$391$	50.3630	−	16.3639i	2.54697	−	0.827560i
$392$		0			0
$393$	0.756059	+	0.756059i	0.0381381	+	0.0381381i
$394$		0			0
$395$	−15.0294	−	22.1085i	−0.756213	−	1.11240i
$396$		0			0
$397$	0.271809	−	0.0430504i	0.0136417	−	0.00216064i	−0.149610	−	0.988745i	$-0.547802\pi$
$397$	0.271809	−	0.0430504i	0.0136417	−	0.00216064i	0.163252	+	0.986584i	$0.447802\pi$
$398$		0			0
$399$	−4.89399			−0.245006
$400$		0			0
$401$	22.4178			1.11949			0.559747	−	0.828664i	$-0.310898\pi$
$401$	22.4178			1.11949			0.559747	+	0.828664i	$0.310898\pi$
$402$		0			0
$403$	−0.800637	+	0.126809i	−0.0398826	+	0.00631678i
$404$		0			0
$405$	−12.3097	+	3.57818i	−0.611675	+	0.177801i
$406$		0			0
$407$	34.6818	+	34.6818i	1.71911	+	1.71911i
$408$		0			0
$409$	33.7949	−	10.9806i	1.67105	−	0.542957i	0.687907	−	0.725799i	$-0.258530\pi$
$409$	33.7949	−	10.9806i	1.67105	−	0.542957i	0.983142	+	0.182842i	$0.0585296\pi$
$410$		0			0
$411$	−1.15289	−	0.374597i	−0.0568679	−	0.0184775i
$412$		0			0
$413$	1.42500	−	2.79672i	0.0701197	−	0.137618i
$414$		0			0
$415$	−11.2576	+	20.4843i	−0.552612	+	1.00553i
$416$		0			0
$417$	0.128781	−	0.813090i	0.00630643	−	0.0398172i
$418$		0			0
$419$	−1.85956	+	1.35105i	−0.0908453	+	0.0660030i	−0.632281	−	0.774739i	$-0.717881\pi$
$419$	−1.85956	+	1.35105i	−0.0908453	+	0.0660030i	0.541435	+	0.840742i	$0.317881\pi$
$420$		0			0
$421$	−27.2084	−	19.7681i	−1.32606	−	0.963438i	−0.999835	−	0.0181445i	$-0.994224\pi$
$421$	−27.2084	−	19.7681i	−1.32606	−	0.963438i	−0.326223	−	0.945293i	$-0.605776\pi$
$422$		0			0
$423$	8.06437	+	15.8272i	0.392103	+	0.769546i
$424$		0			0
$425$	−23.3639	+	20.6097i	−1.13332	+	0.999718i
$426$		0			0
$427$	−5.66540	+	2.88666i	−0.274168	+	0.139695i
$428$		0			0
$429$	0.486812	−	0.670039i	0.0235035	−	0.0323498i
$430$		0			0
$431$	5.08316	+	6.99637i	0.244847	+	0.337003i	0.913698	−	0.406393i	$-0.133214\pi$
$431$	5.08316	+	6.99637i	0.244847	+	0.337003i	−0.668851	+	0.743396i	$0.733214\pi$
$432$		0			0
$433$	4.90998	+	0.777665i	0.235959	+	0.0373722i	0.273294	−	0.961931i	$-0.411887\pi$
$433$	4.90998	+	0.777665i	0.235959	+	0.0373722i	−0.0373350	+	0.999303i	$0.511887\pi$
$434$		0			0
$435$	−5.07164	+	4.76393i	−0.243167	+	0.228413i
$436$		0			0
$437$	−30.8018	−	15.6943i	−1.47345	−	0.750761i
$438$		0			0
$439$	−6.03790	+	18.5827i	−0.288173	+	0.886906i	0.697256	+	0.716822i	$0.254404\pi$
$439$	−6.03790	+	18.5827i	−0.288173	+	0.886906i	−0.985430	+	0.170084i	$0.945596\pi$
$440$		0			0
$441$	2.57584	+	7.92761i	0.122659	+	0.377505i
$442$		0			0
$443$	−17.0562	+	17.0562i	−0.810362	+	0.810362i	−0.984688	−	0.174326i	$-0.944225\pi$
$443$	−17.0562	+	17.0562i	−0.810362	+	0.810362i	0.174326	+	0.984688i	$0.444225\pi$
$444$		0			0
$445$	11.0915	+	8.60099i	0.525790	+	0.407726i
$446$		0			0
$447$	−0.171493	−	1.08276i	−0.00811132	−	0.0512129i
$448$		0			0
$449$			7.97342i			0.376289i	0.982141	+	0.188144i	$0.0602473\pi$
$449$			7.97342i			0.376289i	−0.982141	+	0.188144i	$0.939753\pi$
$450$		0			0
$451$		−	45.5306i		−	2.14395i
$452$		0			0
$453$	−0.432803	−	2.73261i	−0.0203348	−	0.128389i
$454$		0			0
$455$	−1.05959	−	0.0331501i	−0.0496744	−	0.00155410i
$456$		0			0
$457$	19.5360	−	19.5360i	0.913857	−	0.913857i	−0.0827158	−	0.996573i	$-0.526359\pi$
$457$	19.5360	−	19.5360i	0.913857	−	0.913857i	0.996573	+	0.0827158i	$0.0263594\pi$
$458$		0			0
$459$	−6.66278	−	20.5059i	−0.310992	−	0.957135i
$460$		0			0
$461$	5.40979	−	16.6496i	0.251959	−	0.775450i	−0.742455	−	0.669896i	$-0.766339\pi$
$461$	5.40979	−	16.6496i	0.251959	−	0.775450i	0.994414	−	0.105554i	$-0.0336615\pi$
$462$		0			0
$463$	−22.8406	−	11.6379i	−1.06149	−	0.540858i	−0.166088	−	0.986111i	$-0.553114\pi$
$463$	−22.8406	−	11.6379i	−1.06149	−	0.540858i	−0.895405	+	0.445253i	$0.853114\pi$
$464$		0			0
$465$	−1.95914	−	4.16186i	−0.0908528	−	0.193002i
$466$		0			0
$467$	25.5032	+	4.03932i	1.18015	+	0.186917i	0.715523	−	0.698589i	$-0.246189\pi$
$467$	25.5032	+	4.03932i	1.18015	+	0.186917i	0.464627	+	0.885507i	$0.346189\pi$
$468$		0			0
$469$	10.5788	+	14.5605i	0.488485	+	0.672342i
$470$		0			0
$471$	−4.05153	+	5.57645i	−0.186684	+	0.256949i
$472$		0			0
$473$	−19.6135	+	9.99357i	−0.901829	+	0.459505i
$474$		0			0
$475$	20.2987	+	1.27136i	0.931366	+	0.0583341i
$476$		0			0
$477$	3.28187	+	6.44103i	0.150266	+	0.294915i
$478$		0			0
$479$	5.89989	+	4.28652i	0.269573	+	0.195856i	0.714357	−	0.699782i	$-0.246719\pi$
$479$	5.89989	+	4.28652i	0.269573	+	0.195856i	−0.444784	+	0.895638i	$0.646719\pi$
$480$		0			0
$481$	1.73552	−	1.26093i	0.0791328	−	0.0574933i
$482$		0			0
$483$	−1.59954	+	10.0991i	−0.0727818	+	0.459526i
$484$		0			0
$485$	−10.4801	−	1.99766i	−0.475877	−	0.0907091i
$486$		0			0
$487$	14.4111	−	28.2835i	0.653031	−	1.28165i	−0.292547	−	0.956251i	$-0.594503\pi$
$487$	14.4111	−	28.2835i	0.653031	−	1.28165i	0.945578	−	0.325395i	$-0.105497\pi$
$488$		0			0
$489$	−11.1856	−	3.63443i	−0.505831	−	0.164355i
$490$		0			0
$491$	15.6064	−	5.07082i	0.704306	−	0.228843i	0.0651005	−	0.997879i	$-0.479263\pi$
$491$	15.6064	−	5.07082i	0.704306	−	0.228843i	0.639206	+	0.769036i	$0.279263\pi$
$492$		0			0
$493$	22.2718	+	22.2718i	1.00307	+	1.00307i
$494$		0			0
$495$	−30.5850	−	11.0064i	−1.37469	−	0.494702i
$496$		0			0
$497$	30.3306	−	4.80389i	1.36051	−	0.215484i
$498$		0			0
$499$	−40.5715			−1.81623			−0.908115	−	0.418722i	$-0.862478\pi$
$499$	−40.5715			−1.81623			−0.908115	+	0.418722i	$0.862478\pi$
$500$		0			0
$501$	−15.4047			−0.688232
$502$		0			0
$503$	−0.483896	+	0.0766417i	−0.0215759	+	0.00341728i	−0.167213	−	0.985921i	$-0.553477\pi$
$503$	−0.483896	+	0.0766417i	−0.0215759	+	0.00341728i	0.145637	+	0.989338i	$0.453477\pi$
$504$		0			0
$505$	12.4953	+	4.49659i	0.556032	+	0.200096i
$506$		0			0
$507$	5.63323	+	5.63323i	0.250180	+	0.250180i
$508$		0			0
$509$	−31.2911	+	10.1671i	−1.38695	+	0.450648i	−0.904949	−	0.425521i	$-0.860091\pi$
$509$	−31.2911	+	10.1671i	−1.38695	+	0.450648i	−0.482004	+	0.876169i	$0.660091\pi$
$510$		0			0
$511$	8.64417	+	2.80866i	0.382395	+	0.124248i
$512$		0			0
$513$	−6.39013	+	12.5413i	−0.282131	+	0.553714i
$514$		0			0
$515$	−15.6119	−	2.97586i	−0.687942	−	0.131132i
$516$		0			0
$517$	−5.88000	+	37.1249i	−0.258602	+	1.63275i
$518$		0			0
$519$	0.910741	−	0.661692i	0.0399771	−	0.0290451i
$520$		0			0
$521$	14.2215	+	10.3325i	0.623054	+	0.452675i	0.853987	−	0.520294i	$-0.174178\pi$
$521$	14.2215	+	10.3325i	0.623054	+	0.452675i	−0.230933	+	0.972970i	$0.574178\pi$
$522$		0			0
$523$	−13.4016	−	26.3021i	−0.586011	−	1.15011i	−0.973596	−	0.228278i	$-0.926690\pi$
$523$	−13.4016	−	26.3021i	−0.586011	−	1.15011i	0.387585	−	0.921834i	$-0.373310\pi$
$524$		0			0
$525$	−1.49768	−	5.82628i	−0.0653640	−	0.254280i
$526$		0			0
$527$	−18.5526	+	9.45303i	−0.808165	+	0.411780i
$528$		0			0
$529$	−28.9346	+	39.8250i	−1.25802	+	1.73152i
$530$		0			0
$531$	−2.47425	−	3.40551i	−0.107373	−	0.147787i
$532$		0			0
$533$	−1.96688	−	0.311523i	−0.0851951	−	0.0134936i
$534$		0			0
$535$	−5.41759	−	11.5088i	−0.234223	−	0.497568i
$536$		0			0
$537$	−8.55720	−	4.36011i	−0.369271	−	0.188153i
$538$		0			0
$539$	−5.45054	+	16.7750i	−0.234771	+	0.722552i
$540$		0			0
$541$	−4.54176	−	13.9781i	−0.195266	−	0.600966i	−0.999973	−	0.00729474i	$-0.997678\pi$
$541$	−4.54176	−	13.9781i	−0.195266	−	0.600966i	0.804708	−	0.593671i	$-0.202322\pi$
$542$		0			0
$543$	−0.0356529	+	0.0356529i	−0.00153001	+	0.00153001i
$544$		0			0
$545$	−21.3229	−	0.667103i	−0.913372	−	0.0285756i
$546$		0			0
$547$	−5.51566	−	34.8245i	−0.235833	−	1.48899i	−0.766959	−	0.641696i	$-0.778231\pi$
$547$	−5.51566	−	34.8245i	−0.235833	−	1.48899i	0.531127	−	0.847292i	$-0.321769\pi$
$548$		0			0
$549$			8.52719i			0.363931i
$550$		0			0
$551$		−	20.5618i		−	0.875960i
$552$		0			0
$553$	−3.65525	−	23.0783i	−0.155437	−	0.981390i
$554$		0			0
$555$	9.61980	+	7.45972i	0.408338	+	0.316647i
$556$		0			0
$557$	28.1833	−	28.1833i	1.19416	−	1.19416i	0.218277	−	0.975887i	$-0.429956\pi$
$557$	28.1833	−	28.1833i	1.19416	−	1.19416i	0.975887	−	0.218277i	$-0.0700435\pi$
$558$		0			0
$559$	0.297517	+	0.915662i	0.0125836	+	0.0387284i
$560$		0			0
$561$	6.57405	−	20.2329i	0.277557	−	0.854232i
$562$		0			0
$563$	27.8784	+	14.2047i	1.17493	+	0.598658i	0.928801	−	0.370578i	$-0.120840\pi$
$563$	27.8784	+	14.2047i	1.17493	+	0.598658i	0.246132	+	0.969236i	$0.420840\pi$
$564$		0			0
$565$	4.17930	−	3.92573i	0.175824	−	0.165157i
$566$		0			0
$567$	−11.0666	−	1.75277i	−0.464753	−	0.0736096i
$568$		0			0
$569$	−1.41163	−	1.94294i	−0.0591785	−	0.0814522i	0.778402	−	0.627766i	$-0.216031\pi$
$569$	−1.41163	−	1.94294i	−0.0591785	−	0.0814522i	−0.837581	+	0.546314i	$0.816031\pi$
$570$		0			0
$571$	−12.0020	+	16.5193i	−0.502266	+	0.691310i	−0.982591	−	0.185780i	$-0.940519\pi$
$571$	−12.0020	+	16.5193i	−0.502266	+	0.691310i	0.480325	+	0.877091i	$0.340519\pi$
$572$		0			0
$573$	1.32629	−	0.675776i	0.0554064	−	0.0282310i
$574$		0			0
$575$	9.25793	−	41.4723i	0.386083	−	1.72951i
$576$		0			0
$577$	2.62322	+	5.14836i	0.109206	+	0.214329i	0.939142	−	0.343530i	$-0.111623\pi$
$577$	2.62322	+	5.14836i	0.109206	+	0.214329i	−0.829936	+	0.557859i	$0.811623\pi$
$578$		0			0
$579$	−5.55279	−	4.03434i	−0.230766	−	0.167661i
$580$		0			0
$581$	−16.5280	+	12.0083i	−0.685696	+	0.498187i
$582$		0			0
$583$	−2.39292	+	15.1083i	−0.0991046	+	0.625722i
$584$		0			0
$585$	−0.684733	+	1.24594i	−0.0283102	+	0.0515132i
$586$		0			0
$587$	10.4669	−	20.5424i	0.432013	−	0.847874i	−0.567683	−	0.823247i	$-0.692160\pi$
$587$	10.4669	−	20.5424i	0.432013	−	0.847874i	0.999697	−	0.0246269i	$-0.00783979\pi$
$588$		0			0
$589$	12.9277	+	4.20046i	0.532676	+	0.173077i
$590$		0			0
$591$	−12.1018	+	3.93212i	−0.497802	+	0.161746i
$592$		0			0
$593$	15.1048	+	15.1048i	0.620278	+	0.620278i	0.945602	−	0.325324i	$-0.105474\pi$
$593$	15.1048	+	15.1048i	0.620278	+	0.620278i	−0.325324	+	0.945602i	$0.605474\pi$
$594$		0			0
$595$	−26.1484	+	7.60080i	−1.07198	+	0.311602i
$596$		0			0
$597$	−6.73667	+	1.06698i	−0.275714	+	0.0436688i
$598$		0			0
$599$	−4.43366			−0.181154			−0.0905772	−	0.995889i	$-0.528871\pi$
$599$	−4.43366			−0.181154			−0.0905772	+	0.995889i	$0.528871\pi$
$600$		0			0
$601$	−32.0467			−1.30721			−0.653606	−	0.756835i	$-0.726745\pi$
$601$	−32.0467			−1.30721			−0.653606	+	0.756835i	$0.726745\pi$
$602$		0			0
$603$	23.8394	−	3.77579i	0.970814	−	0.153762i
$604$		0			0
$605$	−24.8408	−	36.5411i	−1.00992	−	1.48561i
$606$		0			0
$607$	−2.49396	−	2.49396i	−0.101227	−	0.101227i	0.654680	−	0.755906i	$-0.272803\pi$
$607$	−2.49396	−	2.49396i	−0.101227	−	0.101227i	−0.755906	+	0.654680i	$0.772803\pi$
$608$		0			0
$609$	−5.78409	+	1.87937i	−0.234383	+	0.0761557i
$610$		0			0
$611$	1.56353	+	0.508022i	0.0632537	+	0.0205524i
$612$		0			0
$613$	−10.2952	+	20.2054i	−0.415818	+	0.816088i	0.584172	+	0.811630i	$0.301419\pi$
$613$	−10.2952	+	20.2054i	−0.415818	+	0.816088i	−0.999990	+	0.00445848i	$0.998581\pi$
$614$		0			0
$615$	−1.41789	−	11.2111i	−0.0571747	−	0.452074i
$616$		0			0
$617$	−0.130313	+	0.822763i	−0.00524620	+	0.0331232i	−0.990173	−	0.139851i	$-0.955338\pi$
$617$	−0.130313	+	0.822763i	−0.00524620	+	0.0331232i	0.984926	+	0.172974i	$0.0553377\pi$
$618$		0			0
$619$	−5.35809	+	3.89288i	−0.215360	+	0.156468i	−0.690235	−	0.723585i	$-0.742493\pi$
$619$	−5.35809	+	3.89288i	−0.215360	+	0.156468i	0.474876	+	0.880053i	$0.342493\pi$
$620$		0			0
$621$	23.7915	+	17.2855i	0.954719	+	0.693644i
$622$		0			0
$623$	5.56943	+	10.9306i	0.223135	+	0.437926i
$624$		0			0
$625$	4.69832	+	24.5545i	0.187933	+	0.982182i
$626$		0			0
$627$	−12.3743	+	6.30504i	−0.494183	+	0.251799i
$628$		0			0
$629$	32.3891	−	44.5797i	1.29144	−	1.77751i
$630$		0			0
$631$	−6.07267	−	8.35832i	−0.241749	−	0.332739i	0.670851	−	0.741592i	$-0.265929\pi$
$631$	−6.07267	−	8.35832i	−0.241749	−	0.332739i	−0.912600	+	0.408853i	$0.865929\pi$
$632$		0			0
$633$	−0.163192	−	0.0258470i	−0.00648629	−	0.00102733i
$634$		0			0
$635$	22.8303	−	2.88739i	0.905991	−	0.114583i
$636$		0			0
$637$	0.687374	+	0.350235i	0.0272348	+	0.0138768i
$638$		0			0
$639$	12.7262	−	39.1673i	0.503441	−	1.54943i
$640$		0			0
$641$	5.89660	+	18.1479i	0.232902	+	0.716797i	0.997393	+	0.0721631i	$0.0229902\pi$
$641$	5.89660	+	18.1479i	0.232902	+	0.716797i	−0.764491	+	0.644634i	$0.777010\pi$
$642$		0			0
$643$	−21.9124	+	21.9124i	−0.864140	+	0.864140i	−0.991816	−	0.127676i	$-0.959248\pi$
$643$	−21.9124	+	21.9124i	−0.864140	+	0.864140i	0.127676	+	0.991816i	$0.459248\pi$
$644$		0			0
$645$	−4.51825	+	3.07153i	−0.177906	+	0.120941i
$646$		0			0
$647$	5.44670	+	34.3891i	0.214132	+	1.35198i	0.827183	+	0.561932i	$0.189942\pi$
$647$	5.44670	+	34.3891i	0.214132	+	1.35198i	−0.613051	+	0.790043i	$0.710058\pi$
$648$		0			0
$649$		−	8.90729i		−	0.349642i
$650$		0			0
$651$		−	4.02052i		−	0.157577i
$652$		0			0
$653$	2.69065	+	16.9881i	0.105293	+	0.664795i	0.982722	+	0.185088i	$0.0592569\pi$
$653$	2.69065	+	16.9881i	0.105293	+	0.664795i	−0.877429	+	0.479707i	$0.840743\pi$
$654$		0			0
$655$	−1.08407	−	3.72943i	−0.0423580	−	0.145721i
$656$		0			0
$657$	8.61902	−	8.61902i	0.336260	−	0.336260i
$658$		0			0
$659$	−6.04315	−	18.5989i	−0.235408	−	0.724510i	−0.997067	−	0.0765325i	$-0.975615\pi$
$659$	−6.04315	−	18.5989i	−0.235408	−	0.724510i	0.761660	−	0.647977i	$-0.224385\pi$
$660$		0			0
$661$	−7.63854	+	23.5090i	−0.297105	+	0.914394i	0.685402	+	0.728165i	$0.259627\pi$
$661$	−7.63854	+	23.5090i	−0.297105	+	0.914394i	−0.982506	+	0.186229i	$0.940373\pi$
$662$		0			0
$663$	−0.829062	−	0.422428i	−0.0321981	−	0.0164057i
$664$		0			0
$665$	15.5790	+	8.56176i	0.604126	+	0.332011i
$666$		0			0
$667$	−42.4308	−	6.72037i	−1.64293	−	0.260214i
$668$		0			0
$669$	−2.28383	−	3.14343i	−0.0882982	−	0.121532i
$670$		0			0
$671$	−10.6059	+	14.5977i	−0.409434	+	0.563538i
$672$		0			0
$673$	−10.9211	+	5.56458i	−0.420977	+	0.214499i	−0.651629	−	0.758538i	$-0.725914\pi$
$673$	−10.9211	+	5.56458i	−0.420977	+	0.214499i	0.230652	+	0.973036i	$0.425914\pi$
$674$		0			0
$675$	−16.8860	−	3.76948i	−0.649941	−	0.145087i
$676$		0			0
$677$	−11.3111	−	22.1992i	−0.434719	−	0.853185i	−0.999607	−	0.0280174i	$-0.991081\pi$
$677$	−11.3111	−	22.1992i	−0.434719	−	0.853185i	0.564888	−	0.825168i	$-0.308919\pi$
$678$		0			0
$679$	−7.54405	−	5.48107i	−0.289514	−	0.210344i
$680$		0			0
$681$	−7.88628	+	5.72972i	−0.302203	+	0.219563i
$682$		0			0
$683$	4.79285	−	30.2608i	0.183393	−	1.15790i	−0.708519	−	0.705691i	$-0.750637\pi$
$683$	4.79285	−	30.2608i	0.183393	−	1.15790i	0.891913	−	0.452208i	$-0.149363\pi$
$684$		0			0
$685$	3.01464	+	3.20936i	0.115184	+	0.122624i
$686$		0			0
$687$	2.13920	−	4.19842i	0.0816156	−	0.160180i
$688$		0			0
$689$	0.636293	+	0.206744i	0.0242408	+	0.00787632i
$690$		0			0
$691$	30.0322	−	9.75806i	1.14248	−	0.371214i	0.324174	−	0.945998i	$-0.394914\pi$
$691$	30.0322	−	9.75806i	1.14248	−	0.371214i	0.818306	+	0.574783i	$0.194914\pi$
$692$		0			0
$693$	−20.0895	−	20.0895i	−0.763136	−	0.763136i
$694$		0			0
$695$	−1.83240	+	2.36300i	−0.0695070	+	0.0896338i
$696$		0			0
$697$	−50.5227	+	8.00201i	−1.91368	+	0.303098i
$698$		0			0
$699$	3.08085			0.116529
$700$		0			0
$701$	−35.1688			−1.32831			−0.664154	−	0.747596i	$-0.731208\pi$
$701$	−35.1688			−1.32831			−0.664154	+	0.747596i	$0.731208\pi$
$702$		0			0
$703$	−35.5295	+	5.62732i	−1.34002	+	0.212239i
$704$		0			0
$705$	−0.291722	+	9.32443i	−0.0109869	+	0.351178i
$706$		0			0
$707$	8.20740	+	8.20740i	0.308671	+	0.308671i
$708$		0			0
$709$	3.81710	−	1.24025i	0.143354	−	0.0465786i	−0.236461	−	0.971641i	$-0.575988\pi$
$709$	3.81710	−	1.24025i	0.143354	−	0.0465786i	0.379815	+	0.925062i	$0.375988\pi$
$710$		0			0
$711$	−29.8021	−	9.68329i	−1.11767	−	0.363152i
$712$		0			0
$713$	12.8932	−	25.3044i	0.482855	−	0.947656i
$714$		0			0
$715$	−2.72186	+	1.28128i	−0.101792	+	0.0479170i
$716$		0			0
$717$	0.443200	−	2.79825i	0.0165516	−	0.104503i
$718$		0			0
$719$	18.5453	−	13.4739i	0.691622	−	0.502493i	−0.185571	−	0.982631i	$-0.559413\pi$
$719$	18.5453	−	13.4739i	0.691622	−	0.502493i	0.877193	+	0.480138i	$0.159413\pi$
$720$		0			0
$721$	−11.2381	−	8.16499i	−0.418530	−	0.304080i
$722$		0			0
$723$	−7.00995	−	13.7578i	−0.260703	−	0.511658i
$724$		0			0
$725$	24.4787	−	6.29239i	0.909116	−	0.233693i
$726$		0			0
$727$	−2.48871	+	1.26806i	−0.0923013	+	0.0470299i	−0.499532	−	0.866296i	$-0.666495\pi$
$727$	−2.48871	+	1.26806i	−0.0923013	+	0.0470299i	0.407230	+	0.913325i	$0.366495\pi$
$728$		0			0
$729$	−5.07594	+	6.98643i	−0.187998	+	0.258757i
$730$		0			0
$731$	14.5364	+	20.0076i	0.537647	+	0.740007i
$732$		0			0
$733$	−47.0203	−	7.44728i	−1.73673	−	0.275072i	−0.793831	−	0.608138i	$-0.791917\pi$
$733$	−47.0203	−	7.44728i	−1.73673	−	0.275072i	−0.942903	+	0.333067i	$0.891917\pi$
$734$		0			0
$735$	−0.819698	+	4.30029i	−0.0302350	+	0.158618i
$736$		0			0
$737$	45.5069	+	23.1869i	1.67627	+	0.854101i
$738$		0			0
$739$	−5.84094	+	17.9766i	−0.214862	+	0.661279i	0.784301	+	0.620381i	$0.213022\pi$
$739$	−5.84094	+	17.9766i	−0.214862	+	0.661279i	−0.999163	+	0.0408981i	$0.986978\pi$
$740$		0			0
$741$	0.187706	+	0.577700i	0.00689555	+	0.0212223i
$742$		0			0
$743$	20.7346	−	20.7346i	0.760679	−	0.760679i	−0.215766	−	0.976445i	$-0.569225\pi$
$743$	20.7346	−	20.7346i	0.760679	−	0.760679i	0.976445	+	0.215766i	$0.0692248\pi$
$744$		0			0
$745$	−1.34832	+	3.74675i	−0.0493986	+	0.137270i
$746$		0			0
$747$	4.28599	+	27.0607i	0.156816	+	0.990098i
$748$		0			0
$749$		−	11.1179i		−	0.406240i
$750$		0			0
$751$			14.2893i			0.521425i	0.965417	+	0.260712i	$0.0839574\pi$
$751$			14.2893i			0.521425i	−0.965417	+	0.260712i	$0.916043\pi$
$752$		0			0
$753$	−2.16196	−	13.6501i	−0.0787862	−	0.497437i
$754$		0			0
$755$	−3.40281	+	9.45583i	−0.123841	+	0.344133i
$756$		0			0
$757$	−8.80688	+	8.80688i	−0.320091	+	0.320091i	−0.848802	−	0.528711i	$-0.822676\pi$
$757$	−8.80688	+	8.80688i	−0.320091	+	0.320091i	0.528711	+	0.848802i	$0.322676\pi$
$758$		0			0
$759$	8.96652	+	27.5961i	0.325464	+	1.00168i
$760$		0			0
$761$	−12.3054	+	37.8723i	−0.446072	+	1.37287i	0.435232	+	0.900318i	$0.356666\pi$
$761$	−12.3054	+	37.8723i	−0.446072	+	1.37287i	−0.881304	+	0.472550i	$0.843334\pi$
$762$		0			0
$763$	−16.6139	−	8.46520i	−0.601463	−	0.306461i
$764$		0			0
$765$	−6.83789	+	35.8728i	−0.247224	+	1.29698i
$766$		0			0
$767$	−0.384787	−	0.0609443i	−0.0138939	−	0.00220057i
$768$		0			0
$769$	6.14739	+	8.46116i	0.221681	+	0.305117i	0.905343	−	0.424681i	$-0.139614\pi$
$769$	6.14739	+	8.46116i	0.221681	+	0.305117i	−0.683662	+	0.729799i	$0.739614\pi$
$770$		0			0
$771$	10.6964	−	14.7224i	0.385223	−	0.530213i
$772$		0			0
$773$	39.8265	−	20.2926i	1.43246	−	0.729875i	0.446179	−	0.894944i	$-0.352785\pi$
$773$	39.8265	−	20.2926i	1.43246	−	0.729875i	0.986282	+	0.165069i	$0.0527846\pi$
$774$		0			0
$775$	−1.04445	+	16.6758i	−0.0375179	+	0.599012i
$776$		0			0
$777$	4.83042	+	9.48023i	0.173290	+	0.340101i
$778$		0			0
$779$	27.0156	+	19.6280i	0.967933	+	0.703245i
$780$		0			0
$781$	70.5011	−	51.2221i	2.52273	−	1.83287i
$782$		0			0
$783$	−2.73628	+	17.2762i	−0.0977867	+	0.617401i
$784$		0			0
$785$	22.6528	−	10.6635i	0.808515	−	0.380597i
$786$		0			0
$787$	14.1275	−	27.7268i	0.503591	−	0.988352i	−0.489610	−	0.871941i	$-0.662861\pi$
$787$	14.1275	−	27.7268i	0.503591	−	0.988352i	0.993201	−	0.116411i	$-0.0371390\pi$
$788$		0			0
$789$	7.14544	+	2.32170i	0.254385	+	0.0826546i
$790$		0			0
$791$	4.76639	−	1.54870i	0.169473	−	0.0550653i
$792$		0			0
$793$	0.558042	+	0.558042i	0.0198167	+	0.0198167i
$794$		0			0
$795$	−0.118719	+	3.79467i	−0.00421053	+	0.134583i
$796$		0			0
$797$	5.28045	−	0.836341i	0.187043	−	0.0296247i	−0.0622101	−	0.998063i	$-0.519815\pi$
$797$	5.28045	−	0.836341i	0.187043	−	0.0296247i	0.249253	+	0.968438i	$0.419815\pi$
$798$		0			0
$799$	42.2287			1.49395
$800$		0			0
$801$	16.4521			0.581305
$802$		0			0
$803$	25.4750	−	4.03484i	0.898993	−	0.142387i
$804$		0			0
$805$	22.7597	−	29.3501i	0.802173	−	1.03445i
$806$		0			0
$807$	4.11781	+	4.11781i	0.144954	+	0.144954i
$808$		0			0
$809$	13.9087	−	4.51920i	0.489002	−	0.158886i	−0.0541295	−	0.998534i	$-0.517238\pi$
$809$	13.9087	−	4.51920i	0.489002	−	0.158886i	0.543132	+	0.839647i	$0.317238\pi$
$810$		0			0
$811$	−21.5817	−	7.01231i	−0.757834	−	0.246235i	−0.0954855	−	0.995431i	$-0.530440\pi$
$811$	−21.5817	−	7.01231i	−0.757834	−	0.246235i	−0.662349	+	0.749195i	$0.730440\pi$
$812$		0			0
$813$	4.25784	−	8.35648i	0.149329	−	0.293075i
$814$		0			0
$815$	29.2488	+	31.1380i	1.02454	+	1.09072i
$816$		0			0
$817$	2.52557	−	15.9458i	0.0883585	−	0.557874i
$818$		0			0
$819$	−1.00530	+	0.730395i	−0.0351281	+	0.0255220i
$820$		0			0
$821$	13.9024	+	10.1007i	0.485195	+	0.352515i	0.803334	−	0.595529i	$-0.203058\pi$
$821$	13.9024	+	10.1007i	0.485195	+	0.352515i	−0.318138	+	0.948044i	$0.603058\pi$
$822$		0			0
$823$	−7.25314	−	14.2351i	−0.252829	−	0.496204i	0.729353	−	0.684137i	$-0.239821\pi$
$823$	−7.25314	−	14.2351i	−0.252829	−	0.496204i	−0.982182	+	0.187933i	$0.939821\pi$
$824$		0			0
$825$	−11.2930	−	12.8021i	−0.393171	−	0.445712i
$826$		0			0
$827$	−4.34475	+	2.21376i	−0.151082	+	0.0769799i	−0.527897	−	0.849309i	$-0.677019\pi$
$827$	−4.34475	+	2.21376i	−0.151082	+	0.0769799i	0.376815	+	0.926288i	$0.377019\pi$
$828$		0			0
$829$	−14.6868	+	20.2147i	−0.510095	+	0.702085i	−0.983935	−	0.178526i	$-0.942867\pi$
$829$	−14.6868	+	20.2147i	−0.510095	+	0.702085i	0.473841	+	0.880611i	$0.342867\pi$
$830$		0			0
$831$	3.59103	+	4.94263i	0.124571	+	0.171458i
$832$		0			0
$833$	19.5722	+	3.09994i	0.678138	+	0.107406i
$834$		0			0
$835$	49.0376	+	26.9497i	1.69701	+	0.932632i
$836$		0			0
$837$	−10.3030	−	5.24963i	−0.356123	−	0.181454i
$838$		0			0
$839$	4.39453	−	13.5250i	0.151716	−	0.466934i	−0.846097	−	0.533028i	$-0.821054\pi$
$839$	4.39453	−	13.5250i	0.151716	−	0.466934i	0.997813	+	0.0660945i	$0.0210539\pi$
$840$		0			0
$841$	1.06547	+	3.27919i	0.0367405	+	0.113076i
$842$		0			0
$843$	7.53661	−	7.53661i	0.259575	−	0.259575i
$844$		0			0
$845$	−8.07715	−	27.7872i	−0.277862	−	0.955908i
$846$		0			0
$847$	−6.04142	−	38.1440i	−0.207586	−	1.31064i
$848$		0			0
$849$			10.3410i			0.354903i
$850$		0			0
$851$			75.1571i			2.57635i
$852$		0			0
$853$	3.72656	+	23.5286i	0.127595	+	0.805604i	0.965617	+	0.259968i	$0.0837120\pi$
$853$	3.72656	+	23.5286i	0.127595	+	0.805604i	−0.838022	+	0.545636i	$0.816288\pi$
$854$		0			0
$855$	19.7157	−	13.4028i	0.674262	−	0.458366i
$856$		0			0
$857$	−29.2311	+	29.2311i	−0.998514	+	0.998514i	−0.999999	−	0.00148469i	$-0.999527\pi$
$857$	−29.2311	+	29.2311i	−0.998514	+	0.998514i	0.00148469	+	0.999999i	$0.499527\pi$
$858$		0			0
$859$	2.15809	+	6.64192i	0.0736331	+	0.226619i	0.981099	−	0.193506i	$-0.0619860\pi$
$859$	2.15809	+	6.64192i	0.0736331	+	0.226619i	−0.907466	+	0.420126i	$0.861986\pi$
$860$		0			0
$861$	3.05216	−	9.39359i	0.104017	−	0.320133i
$862$		0			0
$863$	35.0318	+	17.8496i	1.19249	+	0.607606i	0.933606	−	0.358301i	$-0.116644\pi$
$863$	35.0318	+	17.8496i	1.19249	+	0.607606i	0.258889	+	0.965907i	$0.416644\pi$
$864$		0			0
$865$	−4.05674	+	0.513064i	−0.137933	+	0.0174447i
$866$		0			0
$867$	−13.2703	−	2.10180i	−0.450682	−	0.0713810i
$868$		0			0
$869$	−38.9745	−	53.6438i	−1.32212	−	1.81974i
$870$		0			0
$871$	1.31302	−	1.80721i	0.0444898	−	0.0612350i
$872$		0			0
$873$	−11.1425	+	5.67740i	−0.377118	+	0.192151i
$874$		0			0
$875$	−5.42522	+	21.1668i	−0.183406	+	0.715569i
$876$		0			0
$877$	7.75307	+	15.2163i	0.261803	+	0.513816i	0.984066	−	0.177801i	$-0.0568984\pi$
$877$	7.75307	+	15.2163i	0.261803	+	0.513816i	−0.722264	+	0.691618i	$0.756898\pi$
$878$		0			0
$879$	−1.37194	−	0.996776i	−0.0462745	−	0.0336204i
$880$		0			0
$881$	28.5877	−	20.7702i	0.963145	−	0.699766i	0.00926621	−	0.999957i	$-0.497050\pi$
$881$	28.5877	−	20.7702i	0.963145	−	0.699766i	0.953879	+	0.300191i	$0.0970504\pi$
$882$		0			0
$883$	0.332584	−	2.09986i	0.0111924	−	0.0706658i	−0.981460	−	0.191667i	$-0.938611\pi$
$883$	0.332584	−	2.09986i	0.0111924	−	0.0706658i	0.992652	+	0.121001i	$0.0386106\pi$
$884$		0			0
$885$	−0.277386	−	2.19326i	−0.00932422	−	0.0737256i
$886$		0			0
$887$	9.35262	−	18.3556i	0.314030	−	0.616319i	−0.679005	−	0.734133i	$-0.737589\pi$
$887$	9.35262	−	18.3556i	0.314030	−	0.616319i	0.993036	+	0.117814i	$0.0375887\pi$
$888$		0			0
$889$	19.1291	+	6.21542i	0.641570	+	0.208459i
$890$		0			0
$891$	−30.2397	+	9.82547i	−1.01307	+	0.329166i
$892$		0			0
$893$	−19.4932	−	19.4932i	−0.652315	−	0.652315i
$894$		0			0
$895$	19.6122	+	28.8498i	0.655565	+	0.964343i
$896$		0			0
$897$	1.25348	−	0.198531i	0.0418524	−	0.00662877i
$898$		0			0
$899$	16.8919			0.563378
$900$		0			0
$901$	17.1854			0.572528
$902$		0			0
$903$	−4.71645	+	0.747013i	−0.156954	+	0.0248590i
$904$		0			0
$905$	0.175866	−	0.0511206i	0.00584598	−	0.00169931i
$906$		0			0
$907$	9.76592	+	9.76592i	0.324272	+	0.324272i	0.850403	−	0.526131i	$-0.176358\pi$
$907$	9.76592	+	9.76592i	0.324272	+	0.324272i	−0.526131	+	0.850403i	$0.676358\pi$
$908$		0			0
$909$	14.8041	−	4.81016i	0.491022	−	0.159543i
$910$		0			0
$911$	0.295698	+	0.0960782i	0.00979693	+	0.00318321i	0.313911	−	0.949452i	$-0.398361\pi$
$911$	0.295698	+	0.0960782i	0.00979693	+	0.00318321i	−0.304114	+	0.952636i	$0.598361\pi$
$912$		0			0
$913$	−26.3200	+	51.6560i	−0.871066	+	1.70956i
$914$		0			0
$915$	−2.15691	+	3.92470i	−0.0713051	+	0.129747i
$916$		0			0
$917$	0.531032	−	3.35280i	0.0175362	−	0.110719i
$918$		0			0
$919$	−31.8583	+	23.1464i	−1.05091	+	0.763530i	−0.972385	−	0.233382i	$-0.925021\pi$
$919$	−31.8583	+	23.1464i	−1.05091	+	0.763530i	−0.0785242	+	0.996912i	$0.525021\pi$
$920$		0			0
$921$	14.0496	+	10.2076i	0.462950	+	0.336353i
$922$		0			0
$923$	−1.73037	−	3.39605i	−0.0569560	−	0.111782i
$924$		0			0
$925$	−17.5722	−	40.5757i	−0.577770	−	1.33412i
$926$		0			0
$927$	−16.5987	+	8.45746i	−0.545173	+	0.277779i
$928$		0			0
$929$	5.11727	−	7.04331i	0.167892	−	0.231084i	−0.716778	−	0.697302i	$-0.754384\pi$
$929$	5.11727	−	7.04331i	0.167892	−	0.231084i	0.884670	+	0.466218i	$0.154384\pi$
$930$		0			0
$931$	−7.60377	−	10.4657i	−0.249204	−	0.342999i
$932$		0			0
$933$	−13.5558	−	2.14703i	−0.443798	−	0.0702906i
$934$		0			0
$935$	−56.3233	+	52.9060i	−1.84197	+	1.73021i
$936$		0			0
$937$	−11.9655	−	6.09671i	−0.390895	−	0.199171i	0.247486	−	0.968891i	$-0.420396\pi$
$937$	−11.9655	−	6.09671i	−0.390895	−	0.199171i	−0.638381	+	0.769721i	$0.720396\pi$
$938$		0			0
$939$	5.13847	−	15.8146i	0.167688	−	0.516090i
$940$		0			0
$941$	−5.79856	−	17.8461i	−0.189028	−	0.581767i	0.810967	−	0.585092i	$-0.198942\pi$
$941$	−5.79856	−	17.8461i	−0.189028	−	0.581767i	−0.999994	+	0.00332483i	$0.998942\pi$
$942$		0			0
$943$	49.3335	−	49.3335i	1.60652	−	1.60652i
$944$		0			0
$945$	−11.9502	−	9.26687i	−0.388742	−	0.301451i
$946$		0			0
$947$	−1.41576	−	8.93875i	−0.0460060	−	0.290470i	0.953949	−	0.299969i	$-0.0969764\pi$
$947$	−1.41576	−	8.93875i	−0.0460060	−	0.290470i	−0.999955	+	0.00949874i	$0.996976\pi$
$948$		0			0
$949$		−	1.12810i		−	0.0366198i
$950$		0			0
$951$			6.44007i			0.208833i
$952$		0			0
$953$	−2.61027	−	16.4806i	−0.0845550	−	0.533859i	−0.993212	−	0.116316i	$-0.962891\pi$
$953$	−2.61027	−	16.4806i	−0.0845550	−	0.533859i	0.908657	−	0.417543i	$-0.137109\pi$
$954$		0			0
$955$	−5.40418	−	0.169074i	−0.174875	−	0.00547110i
$956$		0			0
$957$	−12.2037	+	12.2037i	−0.394489	+	0.394489i
$958$		0			0
$959$	1.18927	+	3.66021i	0.0384036	+	0.118194i
$960$		0			0
$961$	6.12876	−	18.8624i	0.197702	−	0.608464i
$962$		0			0
$963$	−13.2850	−	6.76904i	−0.428103	−	0.218129i
$964$		0			0
$965$	10.6183	+	22.5567i	0.341814	+	0.726127i
$966$		0			0
$967$	−25.3150	−	4.00950i	−0.814075	−	0.128937i	−0.264505	−	0.964384i	$-0.585209\pi$
$967$	−25.3150	−	4.00950i	−0.814075	−	0.128937i	−0.549570	+	0.835448i	$0.685209\pi$
$968$		0			0
$969$	9.17113	+	12.6230i	0.294619	+	0.405508i
$970$		0			0
$971$	−1.23355	+	1.69783i	−0.0395865	+	0.0544861i	−0.828351	−	0.560209i	$-0.810721\pi$
$971$	−1.23355	+	1.69783i	−0.0395865	+	0.0544861i	0.788765	+	0.614695i	$0.210721\pi$
$972$		0			0
$973$	−2.32872	+	1.18654i	−0.0746553	+	0.0380388i
$974$		0			0
$975$	−0.630307	+	0.400253i	−0.0201860	+	0.0128184i
$976$		0			0
$977$	11.5134	+	22.5963i	0.368345	+	0.722918i	0.998568	−	0.0534961i	$-0.0170365\pi$
$977$	11.5134	+	22.5963i	0.368345	+	0.722918i	−0.630223	+	0.776414i	$0.717036\pi$
$978$		0			0
$979$	28.1643	+	20.4626i	0.900135	+	0.653987i
$980$		0			0
$981$	−20.2304	+	14.6982i	−0.645906	+	0.469278i
$982$		0			0
$983$	5.34152	−	33.7250i	0.170368	−	1.07566i	−0.743228	−	0.669038i	$-0.766706\pi$
$983$	5.34152	−	33.7250i	0.170368	−	1.07566i	0.913596	−	0.406623i	$-0.133294\pi$
$984$		0			0
$985$	45.4026	+	8.65440i	1.44665	+	0.275752i
$986$		0			0
$987$	−3.70180	+	7.26520i	−0.117830	+	0.231254i
$988$		0			0
$989$	−32.0800	−	10.4234i	−1.02008	−	0.331445i
$990$		0			0
$991$	−19.2828	+	6.26537i	−0.612539	+	0.199026i	−0.598825	−	0.800880i	$-0.704366\pi$
$991$	−19.2828	+	6.26537i	−0.612539	+	0.199026i	−0.0137143	+	0.999906i	$0.504366\pi$
$992$		0			0
$993$	13.1949	+	13.1949i	0.418728	+	0.418728i
$994$		0			0
$995$	23.3114	+	8.38892i	0.739020	+	0.265947i
$996$		0			0
$997$	−1.57690	+	0.249757i	−0.0499410	+	0.00790987i	−0.181355	−	0.983418i	$-0.558048\pi$
$997$	−1.57690	+	0.249757i	−0.0499410	+	0.00790987i	0.131414	+	0.991328i	$0.458048\pi$
$998$		0			0
$999$	30.6011			0.968178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.303.7	yes	80
4.3	odd	2	inner	400.2.bi.d.303.4	✓	80
25.17	odd	20	inner	400.2.bi.d.367.4	yes	80
100.67	even	20	inner	400.2.bi.d.367.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.303.4	✓	80	4.3	odd	2	inner
400.2.bi.d.303.7	yes	80	1.1	even	1	trivial
400.2.bi.d.367.4	yes	80	25.17	odd	20	inner
400.2.bi.d.367.7	yes	80	100.67	even	20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.608022 - 0.0963012i) q^{3} +(-2.10398 - 0.757146i) q^{5} +(-1.38198 - 1.38198i) q^{7} +(-2.49275 + 0.809945i) q^{9} +O(q^{10})\)	\(q+(0.608022 - 0.0963012i) q^{3} +(-2.10398 - 0.757146i) q^{5} +(-1.38198 - 1.38198i) q^{7} +(-2.49275 + 0.809945i) q^{9} +(-5.27473 - 1.71386i) q^{11} +(-0.110128 + 0.216137i) q^{13} +(-1.35218 - 0.257745i) q^{15} +(-0.974743 + 6.15428i) q^{17} +(3.29083 - 2.39093i) q^{19} +(-0.973360 - 0.707188i) q^{21} +(-3.85829 - 7.57232i) q^{23} +(3.85346 + 3.18604i) q^{25} +(-3.08316 + 1.57095i) q^{27} +(2.97120 - 4.08950i) q^{29} +(1.96420 + 2.70349i) q^{31} +(-3.37220 - 0.534104i) q^{33} +(1.86130 + 3.95402i) q^{35} +(-7.87958 - 4.01485i) q^{37} +(-0.0461457 + 0.142022i) q^{39} +(2.53683 + 7.80756i) q^{41} +(2.80650 - 2.80650i) q^{43} +(5.85795 + 0.183270i) q^{45} +(-1.06019 - 6.69377i) q^{47} -3.18026i q^{49} +3.83581i q^{51} +(-0.431454 - 2.72409i) q^{53} +(9.80029 + 7.59968i) q^{55} +(1.77065 - 1.77065i) q^{57} +(0.496288 + 1.52742i) q^{59} +(1.00535 - 3.09413i) q^{61} +(4.56426 + 2.32561i) q^{63} +(0.395354 - 0.371366i) q^{65} +(-9.09540 - 1.44057i) q^{67} +(-3.07515 - 4.23258i) q^{69} +(-9.23555 + 12.7116i) q^{71} +(-4.14363 + 2.11129i) q^{73} +(2.64981 + 1.56609i) q^{75} +(4.92105 + 9.65810i) q^{77} +(9.67220 + 7.02726i) q^{79} +(4.63804 - 3.36973i) q^{81} +(1.63523 - 10.3244i) q^{83} +(6.71053 - 12.2105i) q^{85} +(1.41273 - 2.77264i) q^{87} +(-5.96972 - 1.93968i) q^{89} +(0.450892 - 0.146504i) q^{91} +(1.45462 + 1.45462i) q^{93} +(-8.73411 + 2.53882i) q^{95} +(4.71249 - 0.746384i) q^{97} +14.5367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5}+O(q^{10}) \) 80 * q + 4 * q^5	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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