LMFDB - Embedded newform 1148.2.n.e.57.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.5
Character	$\chi$	$=$	1148.57
Dual form			1148.2.n.e.141.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26837 q^{3} +(1.20758 + 0.877362i) q^{5} +(-0.309017 - 0.951057i) q^{7} +2.14552 q^{9} +O(q^{10})$	\(q+2.26837 q^{3} +(1.20758 + 0.877362i) q^{5} +(-0.309017 - 0.951057i) q^{7} +2.14552 q^{9} +(3.91994 - 2.84801i) q^{11} +(-0.142146 + 0.437481i) q^{13} +(2.73925 + 1.99018i) q^{15} +(1.61984 - 1.17688i) q^{17} +(0.659977 + 2.03120i) q^{19} +(-0.700966 - 2.15735i) q^{21} +(-1.05167 + 3.23671i) q^{23} +(-0.856588 - 2.63631i) q^{25} -1.93829 q^{27} +(1.34241 + 0.975318i) q^{29} +(3.63564 - 2.64145i) q^{31} +(8.89190 - 6.46034i) q^{33} +(0.461256 - 1.41960i) q^{35} +(-0.968975 - 0.704002i) q^{37} +(-0.322440 + 0.992369i) q^{39} +(1.88733 - 6.11866i) q^{41} +(-2.34385 + 7.21362i) q^{43} +(2.59089 + 1.88239i) q^{45} +(-2.75545 + 8.48040i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(3.67440 - 2.66961i) q^{51} +(7.81908 + 5.68089i) q^{53} +7.23240 q^{55} +(1.49707 + 4.60752i) q^{57} +(1.89193 - 5.82277i) q^{59} +(1.05462 + 3.24578i) q^{61} +(-0.663001 - 2.04051i) q^{63} +(-0.555482 + 0.403581i) q^{65} +(-6.57143 - 4.77442i) q^{67} +(-2.38558 + 7.34207i) q^{69} +(-0.586448 + 0.426080i) q^{71} -3.52188 q^{73} +(-1.94306 - 5.98012i) q^{75} +(-3.91994 - 2.84801i) q^{77} -7.17021 q^{79} -10.8333 q^{81} -6.91274 q^{83} +2.98865 q^{85} +(3.04509 + 2.21239i) q^{87} +(1.92909 + 5.93712i) q^{89} +0.459994 q^{91} +(8.24699 - 5.99179i) q^{93} +(-0.985118 + 3.03188i) q^{95} +(2.29899 + 1.67031i) q^{97} +(8.41030 - 6.11044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.26837			1.30965			0.654823	−	0.755782i	$-0.272743\pi$
$3$	2.26837			1.30965			0.654823	+	0.755782i	$0.272743\pi$
$4$		0			0
$5$	1.20758	+	0.877362i	0.540048	+	0.392368i	0.824103	−	0.566440i	$-0.191680\pi$
$5$	1.20758	+	0.877362i	0.540048	+	0.392368i	−0.284055	+	0.958808i	$0.591680\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$		0			0
$9$	2.14552			0.715172
$10$		0			0
$11$	3.91994	−	2.84801i	1.18191	−	0.858706i	0.189522	−	0.981876i	$-0.439306\pi$
$11$	3.91994	−	2.84801i	1.18191	−	0.858706i	0.992386	+	0.123170i	$0.0393061\pi$
$12$		0			0
$13$	−0.142146	+	0.437481i	−0.0394242	+	0.121335i	−0.968832	−	0.247720i	$-0.920319\pi$
$13$	−0.142146	+	0.437481i	−0.0394242	+	0.121335i	0.929407	+	0.369055i	$0.120319\pi$
$14$		0			0
$15$	2.73925	+	1.99018i	0.707272	+	0.513863i
$16$		0			0
$17$	1.61984	−	1.17688i	0.392869	−	0.285436i	−0.373761	−	0.927525i	$-0.621932\pi$
$17$	1.61984	−	1.17688i	0.392869	−	0.285436i	0.766630	+	0.642089i	$0.221932\pi$
$18$		0			0
$19$	0.659977	+	2.03120i	0.151409	+	0.465989i	0.997779	−	0.0666058i	$-0.0212170\pi$
$19$	0.659977	+	2.03120i	0.151409	+	0.465989i	−0.846370	+	0.532595i	$0.821217\pi$
$20$		0			0
$21$	−0.700966	−	2.15735i	−0.152963	−	0.470773i
$22$		0			0
$23$	−1.05167	+	3.23671i	−0.219289	+	0.674901i	0.779533	+	0.626362i	$0.215457\pi$
$23$	−1.05167	+	3.23671i	−0.219289	+	0.674901i	−0.998821	+	0.0485395i	$0.984543\pi$
$24$		0			0
$25$	−0.856588	−	2.63631i	−0.171318	−	0.527261i
$26$		0			0
$27$	−1.93829			−0.373024
$28$		0			0
$29$	1.34241	+	0.975318i	0.249279	+	0.181112i	0.705407	−	0.708802i	$-0.250764\pi$
$29$	1.34241	+	0.975318i	0.249279	+	0.181112i	−0.456128	+	0.889914i	$0.650764\pi$
$30$		0			0
$31$	3.63564	−	2.64145i	0.652980	−	0.474418i	−0.211305	−	0.977420i	$-0.567771\pi$
$31$	3.63564	−	2.64145i	0.652980	−	0.474418i	0.864285	+	0.503002i	$0.167771\pi$
$32$		0			0
$33$	8.89190	−	6.46034i	1.54788	−	1.12460i
$34$		0			0
$35$	0.461256	−	1.41960i	0.0779665	−	0.239956i
$36$		0			0
$37$	−0.968975	−	0.704002i	−0.159299	−	0.115737i	0.505280	−	0.862955i	$-0.331389\pi$
$37$	−0.968975	−	0.704002i	−0.159299	−	0.115737i	−0.664579	+	0.747218i	$0.731389\pi$
$38$		0			0
$39$	−0.322440	+	0.992369i	−0.0516318	+	0.158906i
$40$		0			0
$41$	1.88733	−	6.11866i	0.294752	−	0.955574i
$41$	1.88733	−	6.11866i	0.294752	−	0.955574i
$42$		0			0
$43$	−2.34385	+	7.21362i	−0.357433	+	1.10007i	0.597152	+	0.802128i	$0.296299\pi$
$43$	−2.34385	+	7.21362i	−0.357433	+	1.10007i	−0.954585	+	0.297939i	$0.903701\pi$
$44$		0			0
$45$	2.59089	+	1.88239i	0.386227	+	0.280610i
$46$		0			0
$47$	−2.75545	+	8.48040i	−0.401924	+	1.23699i	0.521513	+	0.853243i	$0.325368\pi$
$47$	−2.75545	+	8.48040i	−0.401924	+	1.23699i	−0.923437	+	0.383750i	$0.874632\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	3.67440	−	2.66961i	0.514519	−	0.373820i
$52$		0			0
$53$	7.81908	+	5.68089i	1.07403	+	0.780330i	0.976633	−	0.214915i	$-0.0689474\pi$
$53$	7.81908	+	5.68089i	1.07403	+	0.780330i	0.0973999	+	0.995245i	$0.468947\pi$
$54$		0			0
$55$	7.23240			0.975216
$56$		0			0
$57$	1.49707	+	4.60752i	0.198292	+	0.610280i
$58$		0			0
$59$	1.89193	−	5.82277i	0.246309	−	0.758060i	−0.749110	−	0.662446i	$-0.769518\pi$
$59$	1.89193	−	5.82277i	0.246309	−	0.758060i	0.995418	−	0.0956144i	$-0.0304816\pi$
$60$		0			0
$61$	1.05462	+	3.24578i	0.135030	+	0.415579i	0.995595	−	0.0937618i	$-0.0298892\pi$
$61$	1.05462	+	3.24578i	0.135030	+	0.415579i	−0.860565	+	0.509341i	$0.829889\pi$
$62$		0			0
$63$	−0.663001	−	2.04051i	−0.0835302	−	0.257080i
$64$		0			0
$65$	−0.555482	+	0.403581i	−0.0688991	+	0.0500581i
$66$		0			0
$67$	−6.57143	−	4.77442i	−0.802828	−	0.583289i	0.108914	−	0.994051i	$-0.465263\pi$
$67$	−6.57143	−	4.77442i	−0.802828	−	0.583289i	−0.911742	+	0.410762i	$0.865263\pi$
$68$		0			0
$69$	−2.38558	+	7.34207i	−0.287190	+	0.883881i
$70$		0			0
$71$	−0.586448	+	0.426080i	−0.0695986	+	0.0505664i	−0.622041	−	0.782985i	$-0.713696\pi$
$71$	−0.586448	+	0.426080i	−0.0695986	+	0.0505664i	0.552442	+	0.833551i	$0.313696\pi$
$72$		0			0
$73$	−3.52188			−0.412205			−0.206102	−	0.978530i	$-0.566078\pi$
$73$	−3.52188			−0.412205			−0.206102	+	0.978530i	$0.566078\pi$
$74$		0			0
$75$	−1.94306	−	5.98012i	−0.224365	−	0.690525i
$76$		0			0
$77$	−3.91994	−	2.84801i	−0.446719	−	0.324560i
$78$		0			0
$79$	−7.17021			−0.806712			−0.403356	−	0.915043i	$-0.632156\pi$
$79$	−7.17021			−0.806712			−0.403356	+	0.915043i	$0.632156\pi$
$80$		0			0
$81$	−10.8333			−1.20370
$82$		0			0
$83$	−6.91274			−0.758772			−0.379386	−	0.925239i	$-0.623865\pi$
$83$	−6.91274			−0.758772			−0.379386	+	0.925239i	$0.623865\pi$
$84$		0			0
$85$	2.98865			0.324164
$86$		0			0
$87$	3.04509	+	2.21239i	0.326468	+	0.237193i
$88$		0			0
$89$	1.92909	+	5.93712i	0.204483	+	0.629333i	0.999734	+	0.0230533i	$0.00733876\pi$
$89$	1.92909	+	5.93712i	0.204483	+	0.629333i	−0.795252	+	0.606280i	$0.792661\pi$
$90$		0			0
$91$	0.459994			0.0482205
$92$		0			0
$93$	8.24699	−	5.99179i	0.855173	−	0.621319i
$94$		0			0
$95$	−0.985118	+	3.03188i	−0.101071	+	0.311065i
$96$		0			0
$97$	2.29899	+	1.67031i	0.233427	+	0.169595i	0.698350	−	0.715757i	$-0.253918\pi$
$97$	2.29899	+	1.67031i	0.233427	+	0.169595i	−0.464923	+	0.885351i	$0.653918\pi$
$98$		0			0
$99$	8.41030	−	6.11044i	0.845267	−	0.614122i
$100$		0			0
$101$	−0.845785	−	2.60306i	−0.0841588	−	0.259014i	0.900118	−	0.435646i	$-0.143480\pi$
$101$	−0.845785	−	2.60306i	−0.0841588	−	0.259014i	−0.984277	+	0.176632i	$0.943480\pi$
$102$		0			0
$103$	2.99412	+	9.21496i	0.295019	+	0.907977i	0.983215	+	0.182451i	$0.0584031\pi$
$103$	2.99412	+	9.21496i	0.295019	+	0.907977i	−0.688195	+	0.725525i	$0.741597\pi$
$104$		0			0
$105$	1.04630	−	3.22018i	0.102109	−	0.314258i
$106$		0			0
$107$	−1.25329	−	3.85722i	−0.121160	−	0.372892i	0.872022	−	0.489467i	$-0.162809\pi$
$107$	−1.25329	−	3.85722i	−0.121160	−	0.372892i	−0.993182	+	0.116575i	$0.962809\pi$
$108$		0			0
$109$	−5.57729			−0.534208			−0.267104	−	0.963668i	$-0.586067\pi$
$109$	−5.57729			−0.534208			−0.267104	+	0.963668i	$0.586067\pi$
$110$		0			0
$111$	−2.19800	−	1.59694i	−0.208625	−	0.151575i
$112$		0			0
$113$	−4.89792	+	3.55855i	−0.460757	+	0.334760i	−0.793828	−	0.608142i	$-0.791915\pi$
$113$	−4.89792	+	3.55855i	−0.460757	+	0.334760i	0.333071	+	0.942902i	$0.391915\pi$
$114$		0			0
$115$	−4.10975	+	2.98591i	−0.383236	+	0.278437i
$116$		0			0
$117$	−0.304977	+	0.938621i	−0.0281951	+	0.0867756i
$118$		0			0
$119$	−1.61984	−	1.17688i	−0.148491	−	0.107885i
$120$		0			0
$121$	3.85564	−	11.8664i	0.350513	−	1.07877i
$122$		0			0
$123$	4.28118	−	13.8794i	0.386021	−	1.25146i
$124$		0			0
$125$	3.58487	−	11.0331i	0.320641	−	0.986831i
$126$		0			0
$127$	2.51590	+	1.82791i	0.223250	+	0.162201i	0.693788	−	0.720179i	$-0.255940\pi$
$127$	2.51590	+	1.82791i	0.223250	+	0.162201i	−0.470538	+	0.882380i	$0.655940\pi$
$128$		0			0
$129$	−5.31672	+	16.3632i	−0.468111	+	1.44070i
$130$		0			0
$131$	−1.28273	+	0.931960i	−0.112073	+	0.0814257i	−0.642410	−	0.766361i	$-0.722065\pi$
$131$	−1.28273	+	0.931960i	−0.112073	+	0.0814257i	0.530337	+	0.847787i	$0.322065\pi$
$132$		0			0
$133$	1.72784	−	1.25535i	0.149823	−	0.108853i
$134$		0			0
$135$	−2.34065	−	1.70058i	−0.201451	−	0.146363i
$136$		0			0
$137$	−7.19770			−0.614941			−0.307471	−	0.951558i	$-0.599483\pi$
$137$	−7.19770			−0.614941			−0.307471	+	0.951558i	$0.599483\pi$
$138$		0			0
$139$	−3.22120	−	9.91385i	−0.273219	−	0.840881i	−0.989685	−	0.143260i	$-0.954242\pi$
$139$	−3.22120	−	9.91385i	−0.273219	−	0.840881i	0.716466	−	0.697622i	$-0.245758\pi$
$140$		0			0
$141$	−6.25038	+	19.2367i	−0.526377	+	1.62002i
$142$		0			0
$143$	0.688743	+	2.11973i	0.0575956	+	0.177261i
$144$		0			0
$145$	0.765367	+	2.35556i	0.0635603	+	0.195618i
$146$		0			0
$147$	−1.83515	+	1.33332i	−0.151361	+	0.109970i
$148$		0			0
$149$	−15.3409	−	11.1458i	−1.25678	−	0.913102i	−0.258182	−	0.966096i	$-0.583123\pi$
$149$	−15.3409	−	11.1458i	−1.25678	−	0.913102i	−0.998595	+	0.0529948i	$0.983123\pi$
$150$		0			0
$151$	4.01769	−	12.3652i	0.326955	−	1.00626i	−0.643596	−	0.765365i	$-0.722558\pi$
$151$	4.01769	−	12.3652i	0.326955	−	1.00626i	0.970551	−	0.240897i	$-0.0774418\pi$
$152$		0			0
$153$	3.47539	−	2.52502i	0.280969	−	0.204136i
$154$		0			0
$155$	6.70785			0.538787
$156$		0			0
$157$	5.59742	+	17.2271i	0.446723	+	1.37487i	0.880583	+	0.473892i	$0.157151\pi$
$157$	5.59742	+	17.2271i	0.446723	+	1.37487i	−0.433860	+	0.900980i	$0.642849\pi$
$158$		0			0
$159$	17.7366	+	12.8864i	1.40660	+	1.02196i
$160$		0			0
$161$	3.40328			0.268216
$162$		0			0
$163$	1.11836			0.0875971			0.0437985	−	0.999040i	$-0.486054\pi$
$163$	1.11836			0.0875971			0.0437985	+	0.999040i	$0.486054\pi$
$164$		0			0
$165$	16.4058			1.27719
$166$		0			0
$167$	−1.32968			−0.102894			−0.0514468	−	0.998676i	$-0.516383\pi$
$167$	−1.32968			−0.102894			−0.0514468	+	0.998676i	$0.516383\pi$
$168$		0			0
$169$	10.3460	+	7.51684i	0.795849	+	0.578218i
$170$		0			0
$171$	1.41599	+	4.35797i	0.108283	+	0.333262i
$172$		0			0
$173$	−8.83737			−0.671893			−0.335947	−	0.941881i	$-0.609056\pi$
$173$	−8.83737			−0.671893			−0.335947	+	0.941881i	$0.609056\pi$
$174$		0			0
$175$	−2.24258	+	1.62933i	−0.169523	+	0.123166i
$176$		0			0
$177$	4.29161	−	13.2082i	0.322577	−	0.992790i
$178$		0			0
$179$	−14.2275	−	10.3369i	−1.06342	−	0.772616i	−0.0886980	−	0.996059i	$-0.528271\pi$
$179$	−14.2275	−	10.3369i	−1.06342	−	0.772616i	−0.974717	+	0.223442i	$0.928271\pi$
$180$		0			0
$181$	−2.47037	+	1.79483i	−0.183621	+	0.133408i	−0.675798	−	0.737086i	$-0.736201\pi$
$181$	−2.47037	+	1.79483i	−0.183621	+	0.133408i	0.492178	+	0.870495i	$0.336201\pi$
$182$		0			0
$183$	2.39226	+	7.36263i	0.176841	+	0.544261i
$184$		0			0
$185$	−0.552456	−	1.70028i	−0.0406173	−	0.125007i
$186$		0			0
$187$	2.99791	−	9.22663i	0.219229	−	0.674718i
$188$		0			0
$189$	0.598965	+	1.84342i	0.0435683	+	0.134089i
$190$		0			0
$191$	−9.34899			−0.676469			−0.338234	−	0.941062i	$-0.609830\pi$
$191$	−9.34899			−0.676469			−0.338234	+	0.941062i	$0.609830\pi$
$192$		0			0
$193$	14.4450	+	10.4949i	1.03977	+	0.755439i	0.970241	−	0.242141i	$-0.0778496\pi$
$193$	14.4450	+	10.4949i	1.03977	+	0.755439i	0.0695314	+	0.997580i	$0.477850\pi$
$194$		0			0
$195$	−1.26004	+	0.915473i	−0.0902334	+	0.0655584i
$196$		0			0
$197$	−4.97735	+	3.61626i	−0.354622	+	0.257648i	−0.750805	−	0.660524i	$-0.770334\pi$
$197$	−4.97735	+	3.61626i	−0.354622	+	0.257648i	0.396184	+	0.918171i	$0.370334\pi$
$198$		0			0
$199$	2.93574	−	9.03529i	0.208109	−	0.640495i	−0.791462	−	0.611218i	$-0.790680\pi$
$199$	2.93574	−	9.03529i	0.208109	−	0.640495i	0.999571	−	0.0292763i	$-0.00932027\pi$
$200$		0			0
$201$	−14.9065	−	10.8302i	−1.05142	−	0.763901i
$202$		0			0
$203$	0.512755	−	1.57810i	0.0359884	−	0.110761i
$204$		0			0
$205$	7.64739	−	5.73292i	0.534117	−	0.400405i
$206$		0			0
$207$	−2.25638	+	6.94442i	−0.156829	+	0.482670i
$208$		0			0
$209$	8.37194	+	6.08257i	0.579099	+	0.420740i
$210$		0			0
$211$	−6.61682	+	20.3645i	−0.455520	+	1.40195i	0.415003	+	0.909820i	$0.363781\pi$
$211$	−6.61682	+	20.3645i	−0.455520	+	1.40195i	−0.870523	+	0.492128i	$0.836219\pi$
$212$		0			0
$213$	−1.33028	+	0.966508i	−0.0911495	+	0.0662240i
$214$		0			0
$215$	−9.15935	+	6.65466i	−0.624662	+	0.453844i
$216$		0			0
$217$	−3.63564	−	2.64145i	−0.246803	−	0.179313i
$218$		0			0
$219$	−7.98894			−0.539842
$220$		0			0
$221$	0.284610	+	0.875938i	0.0191449	+	0.0589220i
$222$		0			0
$223$	0.105893	−	0.325907i	0.00709115	−	0.0218243i	−0.947448	−	0.319909i	$-0.896348\pi$
$223$	0.105893	−	0.325907i	0.00709115	−	0.0218243i	0.954539	+	0.298084i	$0.0963477\pi$
$224$		0			0
$225$	−1.83782	−	5.65623i	−0.122521	−	0.377082i
$226$		0			0
$227$	−4.91131	−	15.1155i	−0.325975	−	1.00325i	−0.970998	−	0.239086i	$-0.923152\pi$
$227$	−4.91131	−	15.1155i	−0.325975	−	1.00325i	0.645023	−	0.764163i	$-0.276848\pi$
$228$		0			0
$229$	10.1437	−	7.36984i	0.670315	−	0.487013i	−0.199815	−	0.979834i	$-0.564034\pi$
$229$	10.1437	−	7.36984i	0.670315	−	0.487013i	0.870131	+	0.492821i	$0.164034\pi$
$230$		0			0
$231$	−8.89190	−	6.46034i	−0.585044	−	0.425059i
$232$		0			0
$233$	5.60987	−	17.2654i	0.367515	−	1.13109i	−0.580877	−	0.813992i	$-0.697290\pi$
$233$	5.60987	−	17.2654i	0.367515	−	1.13109i	0.948391	−	0.317102i	$-0.102710\pi$
$234$		0			0
$235$	−10.7678	+	7.82327i	−0.702415	+	0.510334i
$236$		0			0
$237$	−16.2647			−1.05651
$238$		0			0
$239$	6.39548	+	19.6833i	0.413689	+	1.27320i	0.913418	+	0.407023i	$0.133433\pi$
$239$	6.39548	+	19.6833i	0.413689	+	1.27320i	−0.499729	+	0.866182i	$0.666567\pi$
$240$		0			0
$241$	7.12422	+	5.17605i	0.458911	+	0.333418i	0.793104	−	0.609086i	$-0.208464\pi$
$241$	7.12422	+	5.17605i	0.458911	+	0.333418i	−0.334193	+	0.942505i	$0.608464\pi$
$242$		0			0
$243$	−18.7591			−1.20340
$244$		0			0
$245$	−1.49266			−0.0953623
$246$		0			0
$247$	−0.982423			−0.0625101
$248$		0			0
$249$	−15.6807			−0.993722
$250$		0			0
$251$	−17.4391	−	12.6703i	−1.10075	−	0.799740i	−0.119566	−	0.992826i	$-0.538150\pi$
$251$	−17.4391	−	12.6703i	−1.10075	−	0.799740i	−0.981182	+	0.193086i	$0.938150\pi$
$252$		0			0
$253$	5.09568	+	15.6829i	0.320363	+	0.985976i
$254$		0			0
$255$	6.77936			0.424540
$256$		0			0
$257$	1.80807	−	1.31364i	0.112784	−	0.0819426i	−0.529963	−	0.848020i	$-0.677794\pi$
$257$	1.80807	−	1.31364i	0.112784	−	0.0819426i	0.642748	+	0.766078i	$0.277794\pi$
$258$		0			0
$259$	−0.370116	+	1.13910i	−0.0229979	+	0.0707802i
$260$		0			0
$261$	2.88016	+	2.09256i	0.178278	+	0.129526i
$262$		0			0
$263$	−21.5807	+	15.6793i	−1.33073	+	0.966829i	−0.330994	+	0.943633i	$0.607384\pi$
$263$	−21.5807	+	15.6793i	−1.33073	+	0.966829i	−0.999731	+	0.0231958i	$0.992616\pi$
$264$		0			0
$265$	4.45800	+	13.7203i	0.273853	+	0.842832i
$266$		0			0
$267$	4.37589	+	13.4676i	0.267800	+	0.824203i
$268$		0			0
$269$	−0.940293	+	2.89392i	−0.0573307	+	0.176446i	−0.975621	−	0.219462i	$-0.929570\pi$
$269$	−0.940293	+	2.89392i	−0.0573307	+	0.176446i	0.918290	+	0.395907i	$0.129570\pi$
$270$		0			0
$271$	−7.99218	−	24.5974i	−0.485490	−	1.49419i	−0.831269	−	0.555870i	$-0.812385\pi$
$271$	−7.99218	−	24.5974i	−0.485490	−	1.49419i	0.345779	−	0.938316i	$-0.387615\pi$
$272$		0			0
$273$	1.04344			0.0631518
$274$		0			0
$275$	−10.8660	−	7.89461i	−0.655244	−	0.476063i
$276$		0			0
$277$	15.3444	−	11.1484i	0.921957	−	0.669841i	−0.0220535	−	0.999757i	$-0.507020\pi$
$277$	15.3444	−	11.1484i	0.921957	−	0.669841i	0.944010	+	0.329916i	$0.107020\pi$
$278$		0			0
$279$	7.80032	−	5.66726i	0.466993	−	0.339290i
$280$		0			0
$281$	4.85931	−	14.9554i	0.289882	−	0.892166i	−0.695010	−	0.719000i	$-0.744600\pi$
$281$	4.85931	−	14.9554i	0.289882	−	0.892166i	0.984893	−	0.173166i	$-0.0553999\pi$
$282$		0			0
$283$	−11.6159	−	8.43943i	−0.690492	−	0.501672i	0.186330	−	0.982487i	$-0.440341\pi$
$283$	−11.6159	−	8.43943i	−0.690492	−	0.501672i	−0.876822	+	0.480815i	$0.840341\pi$
$284$		0			0
$285$	−2.23462	+	6.87744i	−0.132367	+	0.407384i
$286$		0			0
$287$	−6.40241	+	0.0958079i	−0.377922	+	0.00565536i
$288$		0			0
$289$	−4.01446	+	12.3552i	−0.236145	+	0.726779i
$290$		0			0
$291$	5.21496	+	3.78889i	0.305707	+	0.222109i
$292$		0			0
$293$	−8.80497	+	27.0989i	−0.514392	+	1.58314i	0.269993	+	0.962862i	$0.412978\pi$
$293$	−8.80497	+	27.0989i	−0.514392	+	1.58314i	−0.784385	+	0.620274i	$0.787022\pi$
$294$		0			0
$295$	7.39335	−	5.37158i	0.430457	−	0.312745i
$296$		0			0
$297$	−7.59799	+	5.52026i	−0.440880	+	0.320318i
$298$		0			0
$299$	−1.26651	−	0.920172i	−0.0732441	−	0.0532149i
$300$		0			0
$301$	7.58485			0.437184
$302$		0			0
$303$	−1.91856	−	5.90471i	−0.110218	−	0.339217i
$304$		0			0
$305$	−1.57418	+	4.84483i	−0.0901373	+	0.277414i
$306$		0			0
$307$	−8.39884	−	25.8490i	−0.479347	−	1.47528i	−0.840004	−	0.542580i	$-0.817447\pi$
$307$	−8.39884	−	25.8490i	−0.479347	−	1.47528i	0.360657	−	0.932699i	$-0.382553\pi$
$308$		0			0
$309$	6.79178	+	20.9030i	0.386371	+	1.18913i
$310$		0			0
$311$	−13.0434	+	9.47661i	−0.739625	+	0.537369i	−0.892594	−	0.450862i	$-0.851117\pi$
$311$	−13.0434	+	9.47661i	−0.739625	+	0.537369i	0.152968	+	0.988231i	$0.451117\pi$
$312$		0			0
$313$	−9.40442	−	6.83271i	−0.531569	−	0.386208i	0.289375	−	0.957216i	$-0.406552\pi$
$313$	−9.40442	−	6.83271i	−0.531569	−	0.386208i	−0.820944	+	0.571008i	$0.806552\pi$
$314$		0			0
$315$	0.989632	−	3.04577i	0.0557595	−	0.171610i
$316$		0			0
$317$	−17.1031	+	12.4261i	−0.960605	+	0.697921i	−0.953291	−	0.302053i	$-0.902328\pi$
$317$	−17.1031	+	12.4261i	−0.960605	+	0.697921i	−0.00731404	+	0.999973i	$0.502328\pi$
$318$		0			0
$319$	8.03989			0.450147
$320$		0			0
$321$	−2.84292	−	8.74962i	−0.158677	−	0.488356i
$322$		0			0
$323$	3.45954	+	2.51350i	0.192494	+	0.139855i
$324$		0			0
$325$	1.27509			0.0707295
$326$		0			0
$327$	−12.6514			−0.699623
$328$		0			0
$329$	8.91682			0.491600
$330$		0			0
$331$	−22.5887			−1.24159			−0.620795	−	0.783973i	$-0.713190\pi$
$331$	−22.5887			−1.24159			−0.620795	+	0.783973i	$0.713190\pi$
$332$		0			0
$333$	−2.07895	−	1.51045i	−0.113926	−	0.0827719i
$334$		0			0
$335$	−3.74666	−	11.5310i	−0.204702	−	0.630008i
$336$		0			0
$337$	16.4814			0.897797			0.448898	−	0.893583i	$-0.351816\pi$
$337$	16.4814			0.897797			0.448898	+	0.893583i	$0.351816\pi$
$338$		0			0
$339$	−11.1103	+	8.07211i	−0.603429	+	0.438417i
$340$		0			0
$341$	6.72865	−	20.7087i	0.364377	−	1.12144i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$		0			0
$345$	−9.32244	+	6.77315i	−0.501904	+	0.364654i
$346$		0			0
$347$	3.19119	+	9.82147i	0.171312	+	0.527244i	0.999446	−	0.0332864i	$-0.0105973\pi$
$347$	3.19119	+	9.82147i	0.171312	+	0.527244i	−0.828134	+	0.560530i	$0.810597\pi$
$348$		0			0
$349$	1.55418	+	4.78327i	0.0831932	+	0.256042i	0.983997	−	0.178183i	$-0.0570220\pi$
$349$	1.55418	+	4.78327i	0.0831932	+	0.256042i	−0.900804	+	0.434226i	$0.857022\pi$
$350$		0			0
$351$	0.275520	−	0.847965i	0.0147062	−	0.0452610i
$352$		0			0
$353$	8.62546	+	26.5464i	0.459087	+	1.41292i	0.866269	+	0.499577i	$0.166511\pi$
$353$	8.62546	+	26.5464i	0.459087	+	1.41292i	−0.407183	+	0.913347i	$0.633489\pi$
$354$		0			0
$355$	−1.08201			−0.0574272
$356$		0			0
$357$	−3.67440	−	2.66961i	−0.194470	−	0.141291i
$358$		0			0
$359$	2.26797	−	1.64778i	0.119699	−	0.0869664i	−0.526325	−	0.850283i	$-0.676431\pi$
$359$	2.26797	−	1.64778i	0.119699	−	0.0869664i	0.646024	+	0.763317i	$0.276431\pi$
$360$		0			0
$361$	11.6811	−	8.48683i	0.614796	−	0.446675i
$362$		0			0
$363$	8.74602	−	26.9175i	0.459047	−	1.41280i
$364$		0			0
$365$	−4.25297	−	3.08996i	−0.222610	−	0.161736i
$366$		0			0
$367$	7.94960	−	24.4664i	0.414966	−	1.27713i	−0.497315	−	0.867570i	$-0.665681\pi$
$367$	7.94960	−	24.4664i	0.414966	−	1.27713i	0.912281	−	0.409564i	$-0.134319\pi$
$368$		0			0
$369$	4.04930	−	13.1277i	0.210798	−	0.683399i
$370$		0			0
$371$	2.98662	−	9.19187i	0.155058	−	0.477218i
$372$		0			0
$373$	22.7090	+	16.4991i	1.17583	+	0.854289i	0.991695	−	0.128612i	$-0.0410523\pi$
$373$	22.7090	+	16.4991i	1.17583	+	0.854289i	0.184133	+	0.982901i	$0.441052\pi$
$374$		0			0
$375$	8.13183	−	25.0272i	0.419926	−	1.29240i
$376$		0			0
$377$	−0.617501	+	0.448641i	−0.0318029	+	0.0231062i
$378$		0			0
$379$	−23.7100	+	17.2263i	−1.21790	+	0.884856i	−0.995924	−	0.0901966i	$-0.971250\pi$
$379$	−23.7100	+	17.2263i	−1.21790	+	0.884856i	−0.221975	+	0.975052i	$0.571250\pi$
$380$		0			0
$381$	5.70700	+	4.14638i	0.292379	+	0.212425i
$382$		0			0
$383$	−33.0361			−1.68807			−0.844033	−	0.536291i	$-0.819825\pi$
$383$	−33.0361			−1.68807			−0.844033	+	0.536291i	$0.819825\pi$
$384$		0			0
$385$	−2.23493	−	6.87842i	−0.113903	−	0.350557i
$386$		0			0
$387$	−5.02876	+	15.4769i	−0.255626	+	0.786737i
$388$		0			0
$389$	11.1730	+	34.3868i	0.566491	+	1.74348i	0.663478	+	0.748196i	$0.269080\pi$
$389$	11.1730	+	34.3868i	0.566491	+	1.74348i	−0.0969867	+	0.995286i	$0.530920\pi$
$390$		0			0
$391$	2.10569	+	6.48065i	0.106489	+	0.327741i
$392$		0			0
$393$	−2.90972	+	2.11403i	−0.146776	+	0.106639i
$394$		0			0
$395$	−8.65864	−	6.29087i	−0.435663	−	0.316528i
$396$		0			0
$397$	8.40441	−	25.8661i	0.421805	−	1.29818i	−0.484215	−	0.874949i	$-0.660895\pi$
$397$	8.40441	−	25.8661i	0.421805	−	1.29818i	0.906020	−	0.423234i	$-0.139105\pi$
$398$		0			0
$399$	3.91939	−	2.84760i	0.196215	−	0.142558i
$400$		0			0
$401$	−6.11928			−0.305582			−0.152791	−	0.988259i	$-0.548826\pi$
$401$	−6.11928			−0.305582			−0.152791	+	0.988259i	$0.548826\pi$
$402$		0			0
$403$	0.638790	+	1.96599i	0.0318204	+	0.0979331i
$404$		0			0
$405$	−13.0821	−	9.50473i	−0.650057	−	0.472294i
$406$		0			0
$407$	−5.80333			−0.287660
$408$		0			0
$409$	−6.36177			−0.314570			−0.157285	−	0.987553i	$-0.550274\pi$
$409$	−6.36177			−0.314570			−0.157285	+	0.987553i	$0.550274\pi$
$410$		0			0
$411$	−16.3271			−0.805355
$412$		0			0
$413$	−6.12242			−0.301265
$414$		0			0
$415$	−8.34772	−	6.06497i	−0.409773	−	0.297718i
$416$		0			0
$417$	−7.30689	−	22.4883i	−0.357820	−	1.10126i
$418$		0			0
$419$	28.7255			1.40333			0.701666	−	0.712506i	$-0.252440\pi$
$419$	28.7255			1.40333			0.701666	+	0.712506i	$0.252440\pi$
$420$		0			0
$421$	11.1469	−	8.09870i	0.543267	−	0.394707i	−0.282030	−	0.959406i	$-0.591008\pi$
$421$	11.1469	−	8.09870i	0.543267	−	0.394707i	0.825297	+	0.564699i	$0.191008\pi$
$422$		0			0
$423$	−5.91186	+	18.1948i	−0.287444	+	0.884663i
$424$		0			0
$425$	−4.49016	−	3.26229i	−0.217805	−	0.158244i
$426$		0			0
$427$	2.76102	−	2.00600i	0.133615	−	0.0970772i
$428$		0			0
$429$	1.56233	+	4.80834i	0.0754298	+	0.232149i
$430$		0			0
$431$	8.78666	+	27.0426i	0.423239	+	1.30259i	0.904671	+	0.426111i	$0.140117\pi$
$431$	8.78666	+	27.0426i	0.423239	+	1.30259i	−0.481432	+	0.876483i	$0.659883\pi$
$432$		0			0
$433$	−2.76380	+	8.50611i	−0.132820	+	0.408777i	−0.995245	−	0.0974079i	$-0.968945\pi$
$433$	−2.76380	+	8.50611i	−0.132820	+	0.408777i	0.862425	+	0.506185i	$0.168945\pi$
$434$		0			0
$435$	1.73614	+	5.34328i	0.0832415	+	0.256191i
$436$		0			0
$437$	−7.26849			−0.347699
$438$		0			0
$439$	−3.42122	−	2.48566i	−0.163286	−	0.118634i	0.503142	−	0.864204i	$-0.332177\pi$
$439$	−3.42122	−	2.48566i	−0.163286	−	0.118634i	−0.666428	+	0.745570i	$0.732177\pi$
$440$		0			0
$441$	−1.73576	+	1.26110i	−0.0826551	+	0.0600525i
$442$		0			0
$443$	1.54716	−	1.12407i	0.0735076	−	0.0534064i	−0.550425	−	0.834885i	$-0.685534\pi$
$443$	1.54716	−	1.12407i	0.0735076	−	0.0534064i	0.623932	+	0.781479i	$0.285534\pi$
$444$		0			0
$445$	−2.87946	+	8.86207i	−0.136500	+	0.420103i
$446$		0			0
$447$	−34.7989	−	25.2829i	−1.64593	−	1.19584i
$448$		0			0
$449$	−2.42695	+	7.46940i	−0.114535	+	0.352503i	−0.991850	−	0.127413i	$-0.959333\pi$
$449$	−2.42695	+	7.46940i	−0.114535	+	0.352503i	0.877315	+	0.479915i	$0.159333\pi$
$450$		0			0
$451$	−10.0277	−	29.3599i	−0.472187	−	1.38251i
$452$		0			0
$453$	9.11361	−	28.0488i	0.428195	−	1.31785i
$454$		0			0
$455$	0.555482	+	0.403581i	0.0260414	+	0.0189202i
$456$		0			0
$457$	5.50388	−	16.9392i	0.257461	−	0.792383i	−0.735874	−	0.677118i	$-0.763228\pi$
$457$	5.50388	−	16.9392i	0.257461	−	0.792383i	0.993335	−	0.115264i	$-0.0367716\pi$
$458$		0			0
$459$	−3.13972	+	2.28114i	−0.146550	+	0.106475i
$460$		0			0
$461$	−7.98292	+	5.79993i	−0.371802	+	0.270130i	−0.757958	−	0.652304i	$-0.773803\pi$
$461$	−7.98292	+	5.79993i	−0.371802	+	0.270130i	0.386156	+	0.922433i	$0.373803\pi$
$462$		0			0
$463$	10.2527	+	7.44901i	0.476483	+	0.346185i	0.799962	−	0.600050i	$-0.204853\pi$
$463$	10.2527	+	7.44901i	0.476483	+	0.346185i	−0.323480	+	0.946235i	$0.604853\pi$
$464$		0			0
$465$	15.2159			0.705620
$466$		0			0
$467$	0.445878	+	1.37227i	0.0206328	+	0.0635012i	0.960843	−	0.277094i	$-0.0893714\pi$
$467$	0.445878	+	1.37227i	0.0206328	+	0.0635012i	−0.940210	+	0.340595i	$0.889371\pi$
$468$		0			0
$469$	−2.51006	+	7.72518i	−0.115904	+	0.356716i
$470$		0			0
$471$	12.6970	+	39.0775i	0.585049	+	1.80060i
$472$		0			0
$473$	11.3567	+	34.9523i	0.522181	+	1.60711i
$474$		0			0
$475$	4.78953	−	3.47980i	0.219759	−	0.159664i
$476$		0			0
$477$	16.7759	+	12.1884i	0.768118	+	0.558070i
$478$		0			0
$479$	1.18177	−	3.63711i	0.0539963	−	0.166184i	−0.920422	−	0.390927i	$-0.872154\pi$
$479$	1.18177	−	3.63711i	0.0539963	−	0.166184i	0.974418	+	0.224744i	$0.0721544\pi$
$480$		0			0
$481$	0.445723	−	0.323837i	0.0203232	−	0.0147657i
$482$		0			0
$483$	7.71991			0.351268
$484$		0			0
$485$	1.31075	+	4.03409i	0.0595183	+	0.183179i
$486$		0			0
$487$	21.7369	+	15.7928i	0.984994	+	0.715640i	0.958819	−	0.284017i	$-0.0916673\pi$
$487$	21.7369	+	15.7928i	0.984994	+	0.715640i	0.0261749	+	0.999657i	$0.491667\pi$
$488$		0			0
$489$	2.53687			0.114721
$490$		0			0
$491$	−8.39831			−0.379011			−0.189505	−	0.981880i	$-0.560688\pi$
$491$	−8.39831			−0.379011			−0.189505	+	0.981880i	$0.560688\pi$
$492$		0			0
$493$	3.32233			0.149630
$494$		0			0
$495$	15.5172			0.697447
$496$		0			0
$497$	0.586448	+	0.426080i	0.0263058	+	0.0191123i
$498$		0			0
$499$	7.08499	+	21.8054i	0.317168	+	0.976142i	0.974853	+	0.222849i	$0.0715357\pi$
$499$	7.08499	+	21.8054i	0.317168	+	0.976142i	−0.657685	+	0.753293i	$0.728464\pi$
$500$		0			0
$501$	−3.01620			−0.134754
$502$		0			0
$503$	18.3713	−	13.3475i	0.819134	−	0.595135i	−0.0973305	−	0.995252i	$-0.531030\pi$
$503$	18.3713	−	13.3475i	0.819134	−	0.595135i	0.916464	+	0.400117i	$0.131030\pi$
$504$		0			0
$505$	1.26247	−	3.88547i	0.0561790	−	0.172901i
$506$		0			0
$507$	23.4687	+	17.0510i	1.04228	+	0.757261i
$508$		0			0
$509$	25.4733	−	18.5074i	1.12908	−	0.820327i	0.143522	−	0.989647i	$-0.454157\pi$
$509$	25.4733	−	18.5074i	1.12908	−	0.820327i	0.985561	+	0.169320i	$0.0541572\pi$
$510$		0			0
$511$	1.08832	+	3.34951i	0.0481445	+	0.148173i
$512$		0			0
$513$	−1.27923	−	3.93705i	−0.0564792	−	0.173825i
$514$		0			0
$515$	−4.46919	+	13.7548i	−0.196936	+	0.606107i
$516$		0			0
$517$	13.3510	+	41.0902i	0.587177	+	1.80715i
$518$		0			0
$519$	−20.0465			−0.879942
$520$		0			0
$521$	5.54040	+	4.02534i	0.242730	+	0.176353i	0.702498	−	0.711685i	$-0.252068\pi$
$521$	5.54040	+	4.02534i	0.242730	+	0.176353i	−0.459769	+	0.888039i	$0.652068\pi$
$522$		0			0
$523$	32.3595	−	23.5106i	1.41498	−	1.02805i	0.422410	−	0.906405i	$-0.361184\pi$
$523$	32.3595	−	23.5106i	1.41498	−	1.02805i	0.992574	−	0.121641i	$-0.0388156\pi$
$524$		0			0
$525$	−5.08700	+	3.69592i	−0.222015	+	0.161303i
$526$		0			0
$527$	2.78048	−	8.55745i	0.121120	−	0.372768i
$528$		0			0
$529$	9.23710	+	6.71114i	0.401613	+	0.291789i
$530$		0			0
$531$	4.05917	−	12.4928i	0.176153	−	0.542143i
$532$		0			0
$533$	2.40852	+	1.69542i	0.104324	+	0.0734366i
$534$		0			0
$535$	1.87073	−	5.75751i	0.0808786	−	0.248919i
$536$		0			0
$537$	−32.2733	−	23.4479i	−1.39270	−	1.01185i
$538$		0			0
$539$	−1.49729	+	4.60817i	−0.0644927	+	0.198488i
$540$		0			0
$541$	18.2204	−	13.2379i	0.783355	−	0.569140i	−0.122629	−	0.992453i	$-0.539133\pi$
$541$	18.2204	−	13.2379i	0.783355	−	0.569140i	0.905984	+	0.423312i	$0.139133\pi$
$542$		0			0
$543$	−5.60371	+	4.07133i	−0.240478	+	0.174718i
$544$		0			0
$545$	−6.73505	−	4.89330i	−0.288498	−	0.209606i
$546$		0			0
$547$	19.4929			0.833457			0.416729	−	0.909031i	$-0.363177\pi$
$547$	19.4929			0.833457			0.416729	+	0.909031i	$0.363177\pi$
$548$		0			0
$549$	2.26270	+	6.96386i	0.0965695	+	0.297210i
$550$		0			0
$551$	−1.09511	+	3.37039i	−0.0466531	+	0.143583i
$552$		0			0
$553$	2.21572	+	6.81928i	0.0942219	+	0.289985i
$554$		0			0
$555$	−1.25318	−	3.85688i	−0.0531943	−	0.163715i
$556$		0			0
$557$	25.1806	−	18.2947i	1.06693	−	0.775173i	0.0915756	−	0.995798i	$-0.470810\pi$
$557$	25.1806	−	18.2947i	1.06693	−	0.775173i	0.975359	+	0.220625i	$0.0708097\pi$
$558$		0			0
$559$	−2.82265	−	2.05078i	−0.119385	−	0.0867386i
$560$		0			0
$561$	6.80039	−	20.9294i	0.287113	−	0.883642i
$562$		0			0
$563$	3.47179	−	2.52241i	0.146319	−	0.106307i	−0.512218	−	0.858856i	$-0.671176\pi$
$563$	3.47179	−	2.52241i	0.146319	−	0.106307i	0.658536	+	0.752549i	$0.271176\pi$
$564$		0			0
$565$	−9.03678			−0.380180
$566$		0			0
$567$	3.34768	+	10.3031i	0.140589	+	0.432689i
$568$		0			0
$569$	−12.6049	−	9.15803i	−0.528427	−	0.383924i	0.291342	−	0.956619i	$-0.405898\pi$
$569$	−12.6049	−	9.15803i	−0.528427	−	0.383924i	−0.819769	+	0.572694i	$0.805898\pi$
$570$		0			0
$571$	13.5318			0.566289			0.283144	−	0.959077i	$-0.408622\pi$
$571$	13.5318			0.566289			0.283144	+	0.959077i	$0.408622\pi$
$572$		0			0
$573$	−21.2070			−0.885935
$574$		0			0
$575$	9.43381			0.393417
$576$		0			0
$577$	25.5513			1.06372			0.531858	−	0.846834i	$-0.321494\pi$
$577$	25.5513			1.06372			0.531858	+	0.846834i	$0.321494\pi$
$578$		0			0
$579$	32.7666	+	23.8063i	1.36173	+	0.989357i
$580$		0			0
$581$	2.13615	+	6.57441i	0.0886226	+	0.272752i
$582$		0			0
$583$	46.8296			1.93948
$584$		0			0
$585$	−1.19180	+	0.865890i	−0.0492747	+	0.0358001i
$586$		0			0
$587$	8.50681	−	26.1813i	0.351114	−	1.08062i	−0.607115	−	0.794614i	$-0.707673\pi$
$587$	8.50681	−	26.1813i	0.351114	−	1.08062i	0.958229	−	0.286003i	$-0.0923266\pi$
$588$		0			0
$589$	7.76474	+	5.64141i	0.319941	+	0.232450i
$590$		0			0
$591$	−11.2905	+	8.20302i	−0.464429	+	0.337427i
$592$		0			0
$593$	−7.13621	−	21.9630i	−0.293049	−	0.901912i	−0.983870	−	0.178886i	$-0.942751\pi$
$593$	−7.13621	−	21.9630i	−0.293049	−	0.901912i	0.690821	−	0.723026i	$-0.257249\pi$
$594$		0			0
$595$	−0.923543	−	2.84237i	−0.0378616	−	0.116526i
$596$		0			0
$597$	6.65936	−	20.4954i	0.272549	−	0.838821i
$598$		0			0
$599$	6.80407	+	20.9408i	0.278007	+	0.855617i	0.988408	+	0.151820i	$0.0485135\pi$
$599$	6.80407	+	20.9408i	0.278007	+	0.855617i	−0.710401	+	0.703797i	$0.751487\pi$
$600$		0			0
$601$	4.75669			0.194030			0.0970148	−	0.995283i	$-0.469071\pi$
$601$	4.75669			0.194030			0.0970148	+	0.995283i	$0.469071\pi$
$602$		0			0
$603$	−14.0991	−	10.2436i	−0.574160	−	0.417152i
$604$		0			0
$605$	15.0672	−	10.9469i	0.612567	−	0.445056i
$606$		0			0
$607$	1.69775	−	1.23349i	0.0689097	−	0.0500658i	−0.552797	−	0.833316i	$-0.686440\pi$
$607$	1.69775	−	1.23349i	0.0689097	−	0.0500658i	0.621707	+	0.783250i	$0.286440\pi$
$608$		0			0
$609$	1.16312	−	3.57971i	0.0471320	−	0.145057i
$610$		0			0
$611$	−3.31833	−	2.41091i	−0.134245	−	0.0975350i
$612$		0			0
$613$	−2.31136	+	7.11362i	−0.0933548	+	0.287316i	−0.986821	−	0.161813i	$-0.948266\pi$
$613$	−2.31136	+	7.11362i	−0.0933548	+	0.287316i	0.893467	+	0.449130i	$0.148266\pi$
$614$		0			0
$615$	17.3471	−	13.0044i	0.699504	−	0.524388i
$616$		0			0
$617$	9.49875	−	29.2342i	0.382405	−	1.17692i	−0.555940	−	0.831223i	$-0.687641\pi$
$617$	9.49875	−	29.2342i	0.382405	−	1.17692i	0.938345	−	0.345700i	$-0.112359\pi$
$618$		0			0
$619$	38.1357	+	27.7072i	1.53280	+	1.11365i	0.954656	+	0.297712i	$0.0962235\pi$
$619$	38.1357	+	27.7072i	1.53280	+	1.11365i	0.578146	+	0.815933i	$0.303776\pi$
$620$		0			0
$621$	2.03845	−	6.27369i	0.0818000	−	0.251754i
$622$		0			0
$623$	5.05041	−	3.66934i	0.202340	−	0.147009i
$624$		0			0
$625$	2.79618	−	2.03154i	0.111847	−	0.0812617i
$626$		0			0
$627$	18.9907	+	13.7975i	0.758415	+	0.551021i
$628$		0			0
$629$	−2.39811			−0.0956190
$630$		0			0
$631$	3.66438	+	11.2778i	0.145877	+	0.448963i	0.997123	−	0.0758043i	$-0.0241524\pi$
$631$	3.66438	+	11.2778i	0.145877	+	0.448963i	−0.851246	+	0.524767i	$0.824152\pi$
$632$		0			0
$633$	−15.0094	+	46.1942i	−0.596570	+	1.83605i
$634$		0			0
$635$	1.43443	+	4.41471i	0.0569235	+	0.175192i
$636$		0			0
$637$	−0.142146	−	0.437481i	−0.00563203	−	0.0173336i
$638$		0			0
$639$	−1.25823	+	0.914160i	−0.0497750	+	0.0361636i
$640$		0			0
$641$	−9.97036	−	7.24389i	−0.393806	−	0.286117i	0.373208	−	0.927748i	$-0.378258\pi$
$641$	−9.97036	−	7.24389i	−0.393806	−	0.286117i	−0.767013	+	0.641631i	$0.778258\pi$
$642$		0			0
$643$	5.53979	−	17.0497i	0.218468	−	0.672375i	−0.780421	−	0.625254i	$-0.784995\pi$
$643$	5.53979	−	17.0497i	0.218468	−	0.672375i	0.998889	−	0.0471210i	$-0.0150046\pi$
$644$		0			0
$645$	−20.7768	+	15.0952i	−0.818086	+	0.594375i
$646$		0			0
$647$	21.5888			0.848744			0.424372	−	0.905488i	$-0.360495\pi$
$647$	21.5888			0.848744			0.424372	+	0.905488i	$0.360495\pi$
$648$		0			0
$649$	−9.16702	−	28.2132i	−0.359837	−	1.10746i
$650$		0			0
$651$	−8.24699	−	5.99179i	−0.323225	−	0.234837i
$652$		0			0
$653$	33.3269			1.30418			0.652091	−	0.758140i	$-0.273892\pi$
$653$	33.3269			1.30418			0.652091	+	0.758140i	$0.273892\pi$
$654$		0			0
$655$	−2.36667			−0.0924736
$656$		0			0
$657$	−7.55624			−0.294797
$658$		0			0
$659$	−18.8162			−0.732974			−0.366487	−	0.930423i	$-0.619440\pi$
$659$	−18.8162			−0.732974			−0.366487	+	0.930423i	$0.619440\pi$
$660$		0			0
$661$	−16.9095	−	12.2854i	−0.657702	−	0.477849i	0.208184	−	0.978090i	$-0.433245\pi$
$661$	−16.9095	−	12.2854i	−0.657702	−	0.477849i	−0.865886	+	0.500241i	$0.833245\pi$
$662$		0			0
$663$	0.645601	+	1.98695i	0.0250730	+	0.0771669i
$664$		0			0
$665$	3.18791			0.123622
$666$		0			0
$667$	−4.56860	+	3.31928i	−0.176897	+	0.128523i
$668$		0			0
$669$	0.240206	−	0.739278i	0.00928690	−	0.0285821i
$670$		0			0
$671$	13.3780	+	9.71971i	0.516453	+	0.375225i
$672$		0			0
$673$	35.6575	−	25.9067i	1.37449	−	0.998628i	0.377123	−	0.926163i	$-0.376913\pi$
$673$	35.6575	−	25.9067i	1.37449	−	0.998628i	0.997371	−	0.0724650i	$-0.0230866\pi$
$674$		0			0
$675$	1.66032	+	5.10993i	0.0639056	+	0.196681i
$676$		0			0
$677$	−7.75732	−	23.8746i	−0.298138	−	0.917574i	−0.982149	−	0.188103i	$-0.939766\pi$
$677$	−7.75732	−	23.8746i	−0.298138	−	0.917574i	0.684011	−	0.729471i	$-0.260234\pi$
$678$		0			0
$679$	0.878136	−	2.70262i	0.0336998	−	0.103717i
$680$		0			0
$681$	−11.1407	−	34.2875i	−0.426912	−	1.31390i
$682$		0			0
$683$	4.18403			0.160098			0.0800488	−	0.996791i	$-0.474492\pi$
$683$	4.18403			0.160098			0.0800488	+	0.996791i	$0.474492\pi$
$684$		0			0
$685$	−8.69184	−	6.31499i	−0.332098	−	0.241283i
$686$		0			0
$687$	23.0097	−	16.7175i	0.877875	−	0.637814i
$688$		0			0
$689$	−3.59673	+	2.61318i	−0.137025	+	0.0995541i
$690$		0			0
$691$	−5.74672	+	17.6866i	−0.218615	+	0.672829i	0.780262	+	0.625453i	$0.215086\pi$
$691$	−5.74672	+	17.6866i	−0.218615	+	0.672829i	−0.998877	+	0.0473760i	$0.984914\pi$
$692$		0			0
$693$	−8.41030	−	6.11044i	−0.319481	−	0.232116i
$694$		0			0
$695$	4.80815	−	14.7980i	0.182384	−	0.561319i
$696$		0			0
$697$	−4.14376	−	12.1324i	−0.156956	−	0.459548i
$698$		0			0
$699$	12.7253	−	39.1644i	0.481314	−	1.48133i
$700$		0			0
$701$	−0.908870	−	0.660333i	−0.0343276	−	0.0249404i	0.570489	−	0.821305i	$-0.306754\pi$
$701$	−0.908870	−	0.660333i	−0.0343276	−	0.0249404i	−0.604817	+	0.796365i	$0.706754\pi$
$702$		0			0
$703$	0.790467	−	2.43281i	0.0298130	−	0.0917550i
$704$		0			0
$705$	−24.4254	+	17.7461i	−0.919914	+	0.668357i
$706$		0			0
$707$	−2.21429	+	1.60878i	−0.0832771	+	0.0605044i
$708$		0			0
$709$	35.9557	+	26.1234i	1.35035	+	0.981084i	0.998994	+	0.0448403i	$0.0142779\pi$
$709$	35.9557	+	26.1234i	1.35035	+	0.981084i	0.351352	+	0.936243i	$0.385722\pi$
$710$		0			0
$711$	−15.3838			−0.576937
$712$		0			0
$713$	4.72611	+	14.5455i	0.176994	+	0.544732i
$714$		0			0
$715$	−1.02806	+	3.16403i	−0.0384471	+	0.118328i
$716$		0			0
$717$	14.5073	+	44.6490i	0.541786	+	1.66745i
$718$		0			0
$719$	2.21109	+	6.80502i	0.0824596	+	0.253784i	0.983783	−	0.179362i	$-0.0574033\pi$
$719$	2.21109	+	6.80502i	0.0824596	+	0.253784i	−0.901324	+	0.433146i	$0.857403\pi$
$720$		0			0
$721$	7.83871	−	5.69516i	0.291929	−	0.212099i
$722$		0			0
$723$	16.1604	+	11.7412i	0.601011	+	0.436660i
$724$		0			0
$725$	1.42134	−	4.37445i	0.0527874	−	0.162463i
$726$		0			0
$727$	−20.8678	+	15.1614i	−0.773945	+	0.562304i	−0.903156	−	0.429313i	$-0.858756\pi$
$727$	−20.8678	+	15.1614i	−0.773945	+	0.562304i	0.129211	+	0.991617i	$0.458756\pi$
$728$		0			0
$729$	−10.0527			−0.372324
$730$		0			0
$731$	4.69293	+	14.4434i	0.173574	+	0.534207i
$732$		0			0
$733$	2.43015	+	1.76560i	0.0897595	+	0.0652141i	0.631760	−	0.775164i	$-0.282333\pi$
$733$	2.43015	+	1.76560i	0.0897595	+	0.0652141i	−0.542000	+	0.840378i	$0.682333\pi$
$734$		0			0
$735$	−3.38590			−0.124891
$736$		0			0
$737$	−39.3572			−1.44974
$738$		0			0
$739$	9.30003			0.342107			0.171054	−	0.985262i	$-0.445283\pi$
$739$	9.30003			0.342107			0.171054	+	0.985262i	$0.445283\pi$
$740$		0			0
$741$	−2.22850			−0.0818661
$742$		0			0
$743$	−8.71058	−	6.32861i	−0.319560	−	0.232174i	0.416428	−	0.909169i	$-0.363282\pi$
$743$	−8.71058	−	6.32861i	−0.319560	−	0.232174i	−0.735988	+	0.676995i	$0.763282\pi$
$744$		0			0
$745$	−8.74653	−	26.9191i	−0.320448	−	0.986238i
$746$		0			0
$747$	−14.8314			−0.542652
$748$		0			0
$749$	−3.28115	+	2.38389i	−0.119891	+	0.0871056i
$750$		0			0
$751$	1.28949	−	3.96863i	0.0470540	−	0.144817i	−0.924769	−	0.380529i	$-0.875742\pi$
$751$	1.28949	−	3.96863i	0.0470540	−	0.144817i	0.971823	+	0.235711i	$0.0757420\pi$
$752$		0			0
$753$	−39.5584	−	28.7409i	−1.44159	−	1.04738i
$754$		0			0
$755$	15.7004	−	11.4070i	0.571397	−	0.415144i
$756$		0			0
$757$	9.84823	+	30.3097i	0.357940	+	1.10163i	0.954285	+	0.298898i	$0.0966191\pi$
$757$	9.84823	+	30.3097i	0.357940	+	1.10163i	−0.596345	+	0.802728i	$0.703381\pi$
$758$		0			0
$759$	11.5589	+	35.5747i	0.419562	+	1.29128i
$760$		0			0
$761$	4.12190	−	12.6859i	0.149419	−	0.459864i	−0.848134	−	0.529782i	$-0.822274\pi$
$761$	4.12190	−	12.6859i	0.149419	−	0.459864i	0.997553	+	0.0699181i	$0.0222738\pi$
$762$		0			0
$763$	1.72348	+	5.30432i	0.0623941	+	0.192029i
$764$		0			0
$765$	6.41219			0.231833
$766$		0			0
$767$	2.27842	+	1.65537i	0.0822689	+	0.0597719i
$768$		0			0
$769$	26.2723	−	19.0879i	0.947404	−	0.688329i	−0.00278773	−	0.999996i	$-0.500887\pi$
$769$	26.2723	−	19.0879i	0.947404	−	0.688329i	0.950191	+	0.311667i	$0.100887\pi$
$770$		0			0
$771$	4.10137	−	2.97982i	0.147707	−	0.107316i
$772$		0			0
$773$	−8.24290	+	25.3690i	−0.296477	+	0.912461i	0.686245	+	0.727371i	$0.259258\pi$
$773$	−8.24290	+	25.3690i	−0.296477	+	0.912461i	−0.982721	+	0.185091i	$0.940742\pi$
$774$		0			0
$775$	−10.0779	−	7.32203i	−0.362009	−	0.263015i
$776$		0			0
$777$	−0.839560	+	2.58390i	−0.0301191	+	0.0926969i
$778$		0			0
$779$	13.6738	−	0.204620i	0.489915	−	0.00733126i
$780$		0			0
$781$	−1.08537	+	3.34042i	−0.0388375	+	0.119530i
$782$		0			0
$783$	−2.60198	−	1.89045i	−0.0929872	−	0.0675592i
$784$		0			0
$785$	−8.35503	+	25.7141i	−0.298204	+	0.917777i
$786$		0			0
$787$	−7.61813	+	5.53489i	−0.271557	+	0.197298i	−0.715226	−	0.698893i	$-0.753676\pi$
$787$	−7.61813	+	5.53489i	−0.271557	+	0.197298i	0.443669	+	0.896190i	$0.353676\pi$
$788$		0			0
$789$	−48.9532	+	35.5666i	−1.74278	+	1.26620i
$790$		0			0
$791$	4.89792	+	3.55855i	0.174150	+	0.126527i
$792$		0			0
$793$	−1.56987			−0.0557479
$794$		0			0
$795$	10.1124	+	31.1228i	0.358650	+	1.10381i
$796$		0			0
$797$	−10.5337	+	32.4193i	−0.373122	+	1.14835i	0.571615	+	0.820522i	$0.306317\pi$
$797$	−10.5337	+	32.4193i	−0.373122	+	1.14835i	−0.944737	+	0.327830i	$0.893683\pi$
$798$		0			0
$799$	5.51705	+	16.9797i	0.195179	+	0.600700i
$800$		0			0
$801$	4.13888	+	12.7382i	0.146240	+	0.450081i
$802$		0			0
$803$	−13.8056	+	10.0303i	−0.487188	+	0.353963i
$804$		0			0
$805$	4.10975	+	2.98591i	0.144850	+	0.105239i
$806$		0			0
$807$	−2.13293	+	6.56450i	−0.0750829	+	0.231081i
$808$		0			0
$809$	33.4002	−	24.2666i	1.17429	−	0.853170i	0.182771	−	0.983155i	$-0.441493\pi$
$809$	33.4002	−	24.2666i	1.17429	−	0.853170i	0.991516	+	0.129986i	$0.0414932\pi$
$810$		0			0
$811$	18.5219			0.650393			0.325196	−	0.945647i	$-0.394570\pi$
$811$	18.5219			0.650393			0.325196	+	0.945647i	$0.394570\pi$
$812$		0			0
$813$	−18.1292	−	55.7961i	−0.635820	−	1.95685i
$814$		0			0
$815$	1.35052	+	0.981210i	0.0473066	+	0.0343703i
$816$		0			0
$817$	−16.1992			−0.566738
$818$		0			0
$819$	0.986925			0.0344859
$820$		0			0
$821$	−29.4262			−1.02698			−0.513490	−	0.858095i	$-0.671648\pi$
$821$	−29.4262			−1.02698			−0.513490	+	0.858095i	$0.671648\pi$
$822$		0			0
$823$	−36.7689			−1.28168			−0.640842	−	0.767672i	$-0.721415\pi$
$823$	−36.7689			−1.28168			−0.640842	+	0.767672i	$0.721415\pi$
$824$		0			0
$825$	−24.6481	−	17.9079i	−0.858137	−	0.623473i
$826$		0			0
$827$	8.91774	+	27.4460i	0.310100	+	0.954390i	0.977725	+	0.209892i	$0.0673112\pi$
$827$	8.91774	+	27.4460i	0.310100	+	0.954390i	−0.667625	+	0.744498i	$0.732689\pi$
$828$		0			0
$829$	17.5263			0.608714			0.304357	−	0.952558i	$-0.401558\pi$
$829$	17.5263			0.608714			0.304357	+	0.952558i	$0.401558\pi$
$830$		0			0
$831$	34.8069	−	25.2887i	1.20744	−	0.877254i
$832$		0			0
$833$	−0.618724	+	1.90424i	−0.0214375	+	0.0659779i
$834$		0			0
$835$	−1.60570	−	1.16661i	−0.0555675	−	0.0403721i
$836$		0			0
$837$	−7.04693	+	5.11989i	−0.243577	+	0.176969i
$838$		0			0
$839$	−12.7419	−	39.2154i	−0.439898	−	1.35387i	−0.887983	−	0.459876i	$-0.847894\pi$
$839$	−12.7419	−	39.2154i	−0.439898	−	1.35387i	0.448085	−	0.893991i	$-0.352106\pi$
$840$		0			0
$841$	−8.11067	−	24.9621i	−0.279678	−	0.860762i
$842$		0			0
$843$	11.0227	−	33.9245i	0.379643	−	1.16842i
$844$		0			0
$845$	5.89873	+	18.1544i	0.202923	+	0.624531i
$846$		0			0
$847$	−12.4771			−0.428718
$848$		0			0
$849$	−26.3491	−	19.1438i	−0.904300	−	0.657012i
$850$		0			0
$851$	3.29769	−	2.39592i	0.113044	−	0.0821309i
$852$		0			0
$853$	−36.2627	+	26.3464i	−1.24161	+	0.902084i	−0.997705	−	0.0677142i	$-0.978429\pi$
$853$	−36.2627	+	26.3464i	−1.24161	+	0.902084i	−0.243908	+	0.969798i	$0.578429\pi$
$854$		0			0
$855$	−2.11359	+	6.50495i	−0.0722831	+	0.222465i
$856$		0			0
$857$	−44.7068	−	32.4814i	−1.52716	−	1.10954i	−0.957793	−	0.287458i	$-0.907190\pi$
$857$	−44.7068	−	32.4814i	−1.52716	−	1.10954i	−0.569363	−	0.822086i	$-0.692810\pi$
$858$		0			0
$859$	10.5836	−	32.5729i	0.361107	−	1.11137i	−0.591277	−	0.806469i	$-0.701376\pi$
$859$	10.5836	−	32.5729i	0.361107	−	1.11137i	0.952383	−	0.304903i	$-0.0986241\pi$
$860$		0			0
$861$	−14.5230	+	0.217328i	−0.494944	+	0.00740652i
$862$		0			0
$863$	4.10620	−	12.6376i	0.139777	−	0.430188i	−0.856526	−	0.516104i	$-0.827382\pi$
$863$	4.10620	−	12.6376i	0.139777	−	0.430188i	0.996302	+	0.0859161i	$0.0273817\pi$
$864$		0			0
$865$	−10.6719	−	7.75357i	−0.362855	−	0.263629i
$866$		0			0
$867$	−9.10629	+	28.0263i	−0.309266	+	0.951822i
$868$		0			0
$869$	−28.1068	+	20.4208i	−0.953459	+	0.692728i
$870$		0			0
$871$	3.02282	−	2.19621i	0.102424	−	0.0744157i
$872$		0			0
$873$	4.93252	+	3.58368i	0.166940	+	0.121289i
$874$		0			0
$875$	−11.6009			−0.392182
$876$		0			0
$877$	6.02372	+	18.5391i	0.203407	+	0.626021i	0.999775	+	0.0212093i	$0.00675163\pi$
$877$	6.02372	+	18.5391i	0.203407	+	0.626021i	−0.796369	+	0.604812i	$0.793248\pi$
$878$		0			0
$879$	−19.9730	+	61.4705i	−0.673671	+	2.07335i
$880$		0			0
$881$	0.300834	+	0.925872i	0.0101354	+	0.0311934i	0.955996	−	0.293379i	$-0.0947797\pi$
$881$	0.300834	+	0.925872i	0.0101354	+	0.0311934i	−0.945861	+	0.324572i	$0.894780\pi$
$882$		0			0
$883$	7.53099	+	23.1780i	0.253438	+	0.780001i	0.994133	+	0.108161i	$0.0344961\pi$
$883$	7.53099	+	23.1780i	0.253438	+	0.780001i	−0.740696	+	0.671841i	$0.765504\pi$
$884$		0			0
$885$	16.7709	−	12.1847i	0.563746	−	0.409586i
$886$		0			0
$887$	−18.6061	−	13.5182i	−0.624733	−	0.453895i	0.229839	−	0.973229i	$-0.426180\pi$
$887$	−18.6061	−	13.5182i	−0.624733	−	0.453895i	−0.854572	+	0.519334i	$0.826180\pi$
$888$		0			0
$889$	0.960989	−	2.95762i	0.0322305	−	0.0991954i
$890$		0			0
$891$	−42.4660	+	30.8533i	−1.42266	+	1.03363i
$892$		0			0
$893$	−19.0439			−0.637280
$894$		0			0
$895$	−8.11174	−	24.9654i	−0.271146	−	0.834500i
$896$		0			0
$897$	−2.87291	−	2.08729i	−0.0959238	−	0.0696927i
$898$		0			0
$899$	7.45677			0.248697
$900$		0			0
$901$	19.3514			0.644689
$902$		0			0
$903$	17.2053			0.572556
$904$		0			0
$905$	−4.55789			−0.151509
$906$		0			0
$907$	−8.97937	−	6.52390i	−0.298155	−	0.216622i	0.428642	−	0.903474i	$-0.358992\pi$
$907$	−8.97937	−	6.52390i	−0.298155	−	0.216622i	−0.726797	+	0.686852i	$0.758992\pi$
$908$		0			0
$909$	−1.81464	−	5.58490i	−0.0601880	−	0.185240i
$910$		0			0
$911$	−19.1761			−0.635332			−0.317666	−	0.948203i	$-0.602899\pi$
$911$	−19.1761			−0.635332			−0.317666	+	0.948203i	$0.602899\pi$
$912$		0			0
$913$	−27.0976	+	19.6875i	−0.896798	+	0.651562i
$914$		0			0
$915$	−3.57083	+	10.9899i	−0.118048	+	0.363314i
$916$		0			0
$917$	1.28273	+	0.931960i	0.0423596	+	0.0307760i
$918$		0			0
$919$	8.36123	−	6.07479i	0.275811	−	0.200389i	−0.441277	−	0.897371i	$-0.645474\pi$
$919$	8.36123	−	6.07479i	0.275811	−	0.200389i	0.717088	+	0.696982i	$0.245474\pi$
$920$		0			0
$921$	−19.0517	−	58.6351i	−0.627775	−	1.93209i
$922$		0			0
$923$	−0.103040	−	0.317125i	−0.00339161	−	0.0104383i
$924$		0			0
$925$	−1.02595	+	3.15755i	−0.0337331	+	0.103820i
$926$		0			0
$927$	6.42393	+	19.7708i	0.210990	+	0.649359i
$928$		0			0
$929$	−20.4875			−0.672175			−0.336087	−	0.941831i	$-0.609104\pi$
$929$	−20.4875			−0.672175			−0.336087	+	0.941831i	$0.609104\pi$
$930$		0			0
$931$	−1.72784	−	1.25535i	−0.0566277	−	0.0411424i
$932$		0			0
$933$	−29.5874	+	21.4965i	−0.968647	+	0.703763i
$934$		0			0
$935$	11.7153	−	8.51168i	0.383132	−	0.278362i
$936$		0			0
$937$	−4.86072	+	14.9598i	−0.158793	+	0.488714i	−0.998525	−	0.0542862i	$-0.982712\pi$
$937$	−4.86072	+	14.9598i	−0.158793	+	0.488714i	0.839733	+	0.543000i	$0.182712\pi$
$938$		0			0
$939$	−21.3327	−	15.4991i	−0.696167	−	0.505795i
$940$		0			0
$941$	17.4657	−	53.7540i	0.569367	−	1.75233i	−0.0852384	−	0.996361i	$-0.527165\pi$
$941$	17.4657	−	53.7540i	0.569367	−	1.75233i	0.654605	−	0.755971i	$-0.272835\pi$
$942$		0			0
$943$	17.8195	+	12.5436i	0.580282	+	0.408475i
$944$		0			0
$945$	−0.894049	+	2.75160i	−0.0290834	+	0.0895095i
$946$		0			0
$947$	13.9756	+	10.1539i	0.454147	+	0.329957i	0.791231	−	0.611517i	$-0.209441\pi$
$947$	13.9756	+	10.1539i	0.454147	+	0.329957i	−0.337084	+	0.941475i	$0.609441\pi$
$948$		0			0
$949$	0.500621	−	1.54075i	0.0162509	−	0.0500150i
$950$		0			0
$951$	−38.7962	+	28.1871i	−1.25805	+	0.914029i
$952$		0			0
$953$	−9.66252	+	7.02023i	−0.313000	+	0.227408i	−0.733183	−	0.680032i	$-0.761966\pi$
$953$	−9.66252	+	7.02023i	−0.313000	+	0.227408i	0.420183	+	0.907439i	$0.361966\pi$
$954$		0			0
$955$	−11.2897	−	8.20244i	−0.365326	−	0.265425i
$956$		0			0
$957$	18.2375			0.589533
$958$		0			0
$959$	2.22421	+	6.84542i	0.0718236	+	0.221050i
$960$		0			0
$961$	−3.33889	+	10.2761i	−0.107706	+	0.331486i
$962$		0			0
$963$	−2.68895	−	8.27573i	−0.0866501	−	0.266682i
$964$		0			0
$965$	8.23572	+	25.3469i	0.265117	+	0.815947i
$966$		0			0
$967$	19.5534	−	14.2064i	0.628795	−	0.456846i	−0.227188	−	0.973851i	$-0.572953\pi$
$967$	19.5534	−	14.2064i	0.628795	−	0.456846i	0.855983	+	0.517005i	$0.172953\pi$
$968$		0			0
$969$	7.84753	+	5.70156i	0.252099	+	0.183161i
$970$		0			0
$971$	1.57419	−	4.84487i	0.0505183	−	0.155479i	−0.922615	−	0.385723i	$-0.873952\pi$
$971$	1.57419	−	4.84487i	0.0505183	−	0.155479i	0.973133	+	0.230243i	$0.0739522\pi$
$972$		0			0
$973$	−8.43322	+	6.12709i	−0.270357	+	0.196426i
$974$		0			0
$975$	2.89239			0.0926305
$976$		0			0
$977$	−0.183961	−	0.566175i	−0.00588545	−	0.0181135i	0.948071	−	0.318060i	$-0.103031\pi$
$977$	−0.183961	−	0.566175i	−0.00588545	−	0.0181135i	−0.953956	+	0.299946i	$0.903031\pi$
$978$		0			0
$979$	24.4709	+	17.7791i	0.782092	+	0.568223i
$980$		0			0
$981$	−11.9662			−0.382050
$982$		0			0
$983$	8.43814			0.269135			0.134567	−	0.990904i	$-0.457036\pi$
$983$	8.43814			0.269135			0.134567	+	0.990904i	$0.457036\pi$
$984$		0			0
$985$	−9.18334			−0.292605
$986$		0			0
$987$	20.2267			0.643822
$988$		0			0
$989$	−20.8835	−	15.1727i	−0.664055	−	0.482465i
$990$		0			0
$991$	5.80297	+	17.8597i	0.184337	+	0.567332i	0.999936	−	0.0112854i	$-0.00359234\pi$
$991$	5.80297	+	17.8597i	0.184337	+	0.567332i	−0.815599	+	0.578618i	$0.803592\pi$
$992$		0			0
$993$	−51.2397			−1.62604
$994$		0			0
$995$	11.4724	−	8.33517i	0.363699	−	0.264243i
$996$		0			0
$997$	−1.02838	+	3.16501i	−0.0325690	+	0.100237i	−0.966020	−	0.258469i	$-0.916782\pi$
$997$	−1.02838	+	3.16501i	−0.0325690	+	0.100237i	0.933451	+	0.358706i	$0.116782\pi$
$998$		0			0
$999$	1.87816	+	1.36456i	0.0594222	+	0.0431728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.57.5	✓	24
41.18	even	5	inner	1148.2.n.e.141.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.57.5	✓	24	1.1	even	1	trivial
1148.2.n.e.141.5	yes	24	41.18	even	5	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.26837 q^{3} +(1.20758 + 0.877362i) q^{5} +(-0.309017 - 0.951057i) q^{7} +2.14552 q^{9} +O(q^{10})\)	\(q+2.26837 q^{3} +(1.20758 + 0.877362i) q^{5} +(-0.309017 - 0.951057i) q^{7} +2.14552 q^{9} +(3.91994 - 2.84801i) q^{11} +(-0.142146 + 0.437481i) q^{13} +(2.73925 + 1.99018i) q^{15} +(1.61984 - 1.17688i) q^{17} +(0.659977 + 2.03120i) q^{19} +(-0.700966 - 2.15735i) q^{21} +(-1.05167 + 3.23671i) q^{23} +(-0.856588 - 2.63631i) q^{25} -1.93829 q^{27} +(1.34241 + 0.975318i) q^{29} +(3.63564 - 2.64145i) q^{31} +(8.89190 - 6.46034i) q^{33} +(0.461256 - 1.41960i) q^{35} +(-0.968975 - 0.704002i) q^{37} +(-0.322440 + 0.992369i) q^{39} +(1.88733 - 6.11866i) q^{41} +(-2.34385 + 7.21362i) q^{43} +(2.59089 + 1.88239i) q^{45} +(-2.75545 + 8.48040i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(3.67440 - 2.66961i) q^{51} +(7.81908 + 5.68089i) q^{53} +7.23240 q^{55} +(1.49707 + 4.60752i) q^{57} +(1.89193 - 5.82277i) q^{59} +(1.05462 + 3.24578i) q^{61} +(-0.663001 - 2.04051i) q^{63} +(-0.555482 + 0.403581i) q^{65} +(-6.57143 - 4.77442i) q^{67} +(-2.38558 + 7.34207i) q^{69} +(-0.586448 + 0.426080i) q^{71} -3.52188 q^{73} +(-1.94306 - 5.98012i) q^{75} +(-3.91994 - 2.84801i) q^{77} -7.17021 q^{79} -10.8333 q^{81} -6.91274 q^{83} +2.98865 q^{85} +(3.04509 + 2.21239i) q^{87} +(1.92909 + 5.93712i) q^{89} +0.459994 q^{91} +(8.24699 - 5.99179i) q^{93} +(-0.985118 + 3.03188i) q^{95} +(2.29899 + 1.67031i) q^{97} +(8.41030 - 6.11044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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