LMFDB - Embedded newform 1148.2.n.e.365.1

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			365.1
Character	$\chi$	$=$	1148.365
Dual form			1148.2.n.e.953.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28641 q^{3} +(-0.815322 + 2.50930i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.22766 q^{9} +O(q^{10})$	\(q-2.28641 q^{3} +(-0.815322 + 2.50930i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.22766 q^{9} +(-1.72446 - 5.30734i) q^{11} +(1.00138 - 0.727546i) q^{13} +(1.86416 - 5.73729i) q^{15} +(-0.144210 - 0.443834i) q^{17} +(-2.66632 - 1.93720i) q^{19} +(-1.84974 - 1.34392i) q^{21} +(0.607844 - 0.441625i) q^{23} +(-1.58676 - 1.15285i) q^{25} +1.76588 q^{27} +(-0.433514 + 1.33422i) q^{29} +(1.42526 + 4.38651i) q^{31} +(3.94282 + 12.1347i) q^{33} +(-2.13454 + 1.55083i) q^{35} +(-0.000945850 + 0.00291103i) q^{37} +(-2.28957 + 1.66347i) q^{39} +(3.18765 + 5.55328i) q^{41} +(4.80937 - 3.49421i) q^{43} +(-1.81626 + 5.58987i) q^{45} +(2.92558 - 2.12556i) q^{47} +(0.309017 + 0.951057i) q^{49} +(0.329724 + 1.01479i) q^{51} +(1.30725 - 4.02329i) q^{53} +14.7237 q^{55} +(6.09630 + 4.42922i) q^{57} +(0.140019 - 0.101730i) q^{59} +(9.52668 + 6.92154i) q^{61} +(1.80222 + 1.30939i) q^{63} +(1.00919 + 3.10595i) q^{65} +(1.51906 - 4.67519i) q^{67} +(-1.38978 + 1.00973i) q^{69} +(0.221011 + 0.680201i) q^{71} -3.00251 q^{73} +(3.62799 + 2.63589i) q^{75} +(1.72446 - 5.30734i) q^{77} +10.9295 q^{79} -10.7205 q^{81} +5.64278 q^{83} +1.23129 q^{85} +(0.991190 - 3.05057i) q^{87} +(6.96074 + 5.05728i) q^{89} +1.23778 q^{91} +(-3.25873 - 10.0294i) q^{93} +(7.03492 - 5.11117i) q^{95} +(1.25934 - 3.87584i) q^{97} +(-3.84151 - 11.8229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−2.28641			−1.32006			−0.660029	−	0.751240i	$-0.729456\pi$
$3$	−2.28641			−1.32006			−0.660029	+	0.751240i	$0.729456\pi$
$4$		0			0
$5$	−0.815322	+	2.50930i	−0.364623	+	1.12219i	0.585594	+	0.810605i	$0.300861\pi$
$5$	−0.815322	+	2.50930i	−0.364623	+	1.12219i	−0.950217	+	0.311589i	$0.899139\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$		0			0
$9$	2.22766			0.742554
$10$		0			0
$11$	−1.72446	−	5.30734i	−0.519944	−	1.60022i	−0.774103	−	0.633060i	$-0.781799\pi$
$11$	−1.72446	−	5.30734i	−0.519944	−	1.60022i	0.254159	−	0.967162i	$-0.418201\pi$
$12$		0			0
$13$	1.00138	−	0.727546i	0.277733	−	0.201785i	−0.440195	−	0.897902i	$-0.645091\pi$
$13$	1.00138	−	0.727546i	0.277733	−	0.201785i	0.717928	+	0.696117i	$0.245091\pi$
$14$		0			0
$15$	1.86416	−	5.73729i	0.481323	−	1.48136i
$16$		0			0
$17$	−0.144210	−	0.443834i	−0.0349762	−	0.107646i	0.932044	−	0.362345i	$-0.118024\pi$
$17$	−0.144210	−	0.443834i	−0.0349762	−	0.107646i	−0.967020	+	0.254699i	$0.918024\pi$
$18$		0			0
$19$	−2.66632	−	1.93720i	−0.611697	−	0.444424i	0.238315	−	0.971188i	$-0.423405\pi$
$19$	−2.66632	−	1.93720i	−0.611697	−	0.444424i	−0.850011	+	0.526764i	$0.823405\pi$
$20$		0			0
$21$	−1.84974	−	1.34392i	−0.403647	−	0.293267i
$22$		0			0
$23$	0.607844	−	0.441625i	0.126744	−	0.0920851i	−0.522607	−	0.852574i	$-0.675040\pi$
$23$	0.607844	−	0.441625i	0.126744	−	0.0920851i	0.649351	+	0.760489i	$0.275040\pi$
$24$		0			0
$25$	−1.58676	−	1.15285i	−0.317352	−	0.230570i
$26$		0			0
$27$	1.76588			0.339844
$28$		0			0
$29$	−0.433514	+	1.33422i	−0.0805015	+	0.247758i	−0.983205	−	0.182505i	$-0.941579\pi$
$29$	−0.433514	+	1.33422i	−0.0805015	+	0.247758i	0.902703	+	0.430263i	$0.141579\pi$
$30$		0			0
$31$	1.42526	+	4.38651i	0.255985	+	0.787840i	0.993634	+	0.112656i	$0.0359359\pi$
$31$	1.42526	+	4.38651i	0.255985	+	0.787840i	−0.737649	+	0.675184i	$0.764064\pi$
$32$		0			0
$33$	3.94282	+	12.1347i	0.686356	+	2.11239i
$34$		0			0
$35$	−2.13454	+	1.55083i	−0.360803	+	0.262139i
$36$		0			0
$37$	−0.000945850		0.00291103i	−0.000155497		0.000478570i	−0.951134	−	0.308778i	$-0.900080\pi$
$37$	−0.000945850		0.00291103i	−0.000155497		0.000478570i	0.950979	+	0.309256i	$0.100080\pi$
$38$		0			0
$39$	−2.28957	+	1.66347i	−0.366624	+	0.266368i
$40$		0			0
$41$	3.18765	+	5.55328i	0.497827	+	0.867277i
$41$	3.18765	+	5.55328i	0.497827	+	0.867277i
$42$		0			0
$43$	4.80937	−	3.49421i	0.733422	−	0.532862i	−0.157222	−	0.987563i	$-0.550254\pi$
$43$	4.80937	−	3.49421i	0.733422	−	0.532862i	0.890644	+	0.454701i	$0.150254\pi$
$44$		0			0
$45$	−1.81626	+	5.58987i	−0.270752	+	0.833289i
$46$		0			0
$47$	2.92558	−	2.12556i	0.426740	−	0.310045i	−0.353604	−	0.935395i	$-0.615044\pi$
$47$	2.92558	−	2.12556i	0.426740	−	0.310045i	0.780344	+	0.625351i	$0.215044\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$		0			0
$51$	0.329724	+	1.01479i	0.0461706	+	0.142098i
$52$		0			0
$53$	1.30725	−	4.02329i	0.179564	−	0.552641i	−0.820248	−	0.572007i	$-0.806165\pi$
$53$	1.30725	−	4.02329i	0.179564	−	0.552641i	0.999812	+	0.0193663i	$0.00616487\pi$
$54$		0			0
$55$	14.7237			1.98534
$56$		0			0
$57$	6.09630	+	4.42922i	0.807475	+	0.586665i
$58$		0			0
$59$	0.140019	−	0.101730i	0.0182290	−	0.0132441i	−0.578633	−	0.815588i	$-0.696414\pi$
$59$	0.140019	−	0.101730i	0.0182290	−	0.0132441i	0.596862	+	0.802344i	$0.296414\pi$
$60$		0			0
$61$	9.52668	+	6.92154i	1.21977	+	0.886212i	0.996081	−	0.0884496i	$-0.0281912\pi$
$61$	9.52668	+	6.92154i	1.21977	+	0.886212i	0.223685	+	0.974661i	$0.428191\pi$
$62$		0			0
$63$	1.80222	+	1.30939i	0.227058	+	0.164967i
$64$		0			0
$65$	1.00919	+	3.10595i	0.125174	+	0.385246i
$66$		0			0
$67$	1.51906	−	4.67519i	0.185583	−	0.571165i	−0.814375	−	0.580339i	$-0.802920\pi$
$67$	1.51906	−	4.67519i	0.185583	−	0.571165i	0.999958	+	0.00917352i	$0.00292006\pi$
$68$		0			0
$69$	−1.38978	+	1.00973i	−0.167310	+	0.121558i
$70$		0			0
$71$	0.221011	+	0.680201i	0.0262291	+	0.0807250i	0.963314	−	0.268376i	$-0.0864870\pi$
$71$	0.221011	+	0.680201i	0.0262291	+	0.0807250i	−0.937085	+	0.349101i	$0.886487\pi$
$72$		0			0
$73$	−3.00251			−0.351418			−0.175709	−	0.984442i	$-0.556222\pi$
$73$	−3.00251			−0.351418			−0.175709	+	0.984442i	$0.556222\pi$
$74$		0			0
$75$	3.62799	+	2.63589i	0.418924	+	0.304366i
$76$		0			0
$77$	1.72446	−	5.30734i	0.196520	−	0.604827i
$78$		0			0
$79$	10.9295			1.22966			0.614832	−	0.788658i	$-0.289224\pi$
$79$	10.9295			1.22966			0.614832	+	0.788658i	$0.289224\pi$
$80$		0			0
$81$	−10.7205			−1.19117
$82$		0			0
$83$	5.64278			0.619376			0.309688	−	0.950838i	$-0.399775\pi$
$83$	5.64278			0.619376			0.309688	+	0.950838i	$0.399775\pi$
$84$		0			0
$85$	1.23129			0.133552
$86$		0			0
$87$	0.991190	−	3.05057i	0.106267	−	0.327055i
$88$		0			0
$89$	6.96074	+	5.05728i	0.737837	+	0.536070i	0.892033	−	0.451970i	$-0.149279\pi$
$89$	6.96074	+	5.05728i	0.737837	+	0.536070i	−0.154196	+	0.988040i	$0.549279\pi$
$90$		0			0
$91$	1.23778			0.129754
$92$		0			0
$93$	−3.25873	−	10.0294i	−0.337915	−	1.04000i
$94$		0			0
$95$	7.03492	−	5.11117i	0.721768	−	0.524395i
$96$		0			0
$97$	1.25934	−	3.87584i	0.127866	−	0.393532i	−0.866546	−	0.499097i	$-0.833665\pi$
$97$	1.25934	−	3.87584i	0.127866	−	0.393532i	0.994412	+	0.105565i	$0.0336651\pi$
$98$		0			0
$99$	−3.84151	−	11.8229i	−0.386086	−	1.18825i
$100$		0			0
$101$	−8.46711	−	6.15172i	−0.842509	−	0.612119i	0.0805614	−	0.996750i	$-0.474329\pi$
$101$	−8.46711	−	6.15172i	−0.842509	−	0.612119i	−0.923070	+	0.384631i	$0.874329\pi$
$102$		0			0
$103$	14.9526	+	10.8637i	1.47332	+	1.07043i	0.979634	+	0.200791i	$0.0643513\pi$
$103$	14.9526	+	10.8637i	1.47332	+	1.07043i	0.493687	+	0.869639i	$0.335649\pi$
$104$		0			0
$105$	4.88043	−	3.54584i	0.476281	−	0.346038i
$106$		0			0
$107$	−6.29753	−	4.57542i	−0.608805	−	0.442323i	0.240188	−	0.970726i	$-0.422791\pi$
$107$	−6.29753	−	4.57542i	−0.608805	−	0.442323i	−0.848993	+	0.528403i	$0.822791\pi$
$108$		0			0
$109$	18.1629			1.73969			0.869846	−	0.493323i	$-0.164218\pi$
$109$	18.1629			1.73969			0.869846	+	0.493323i	$0.164218\pi$
$110$		0			0
$111$	0.00216260	−	0.00665580i	0.000205265	−	0.000631740i
$112$		0			0
$113$	1.19207	+	3.66881i	0.112140	+	0.345132i	0.991340	−	0.131321i	$-0.0419220\pi$
$113$	1.19207	+	3.66881i	0.112140	+	0.345132i	−0.879200	+	0.476454i	$0.841922\pi$
$114$		0			0
$115$	0.612581	+	1.88533i	0.0571235	+	0.175808i
$116$		0			0
$117$	2.23074	−	1.62073i	0.206232	−	0.149836i
$118$		0			0
$119$	0.144210	−	0.443834i	0.0132197	−	0.0406862i
$120$		0			0
$121$	−16.2949	+	11.8389i	−1.48135	+	1.07627i
$122$		0			0
$123$	−7.28826	−	12.6971i	−0.657160	−	1.14486i
$124$		0			0
$125$	−6.48613	+	4.71245i	−0.580137	+	0.421494i
$126$		0			0
$127$	1.33300	−	4.10255i	0.118284	−	0.364042i	−0.874333	−	0.485326i	$-0.838701\pi$
$127$	1.33300	−	4.10255i	0.118284	−	0.364042i	0.992618	+	0.121284i	$0.0387010\pi$
$128$		0			0
$129$	−10.9962	+	7.98919i	−0.968160	+	0.703409i
$130$		0			0
$131$	−2.12252	−	6.53244i	−0.185445	−	0.570742i	0.814510	−	0.580149i	$-0.197006\pi$
$131$	−2.12252	−	6.53244i	−0.185445	−	0.570742i	−0.999956	+	0.00940693i	$0.997006\pi$
$132$		0			0
$133$	−1.01844	−	3.13445i	−0.0883104	−	0.271791i
$134$		0			0
$135$	−1.43976	+	4.43113i	−0.123915	+	0.381371i
$136$		0			0
$137$	4.12510			0.352431			0.176215	−	0.984352i	$-0.443614\pi$
$137$	4.12510			0.352431			0.176215	+	0.984352i	$0.443614\pi$
$138$		0			0
$139$	13.4255	+	9.75417i	1.13873	+	0.827338i	0.986942	−	0.161075i	$-0.0514961\pi$
$139$	13.4255	+	9.75417i	1.13873	+	0.827338i	0.151790	+	0.988413i	$0.451496\pi$
$140$		0			0
$141$	−6.68907	+	4.85990i	−0.563321	+	0.409277i
$142$		0			0
$143$	−5.58818	−	4.06005i	−0.467307	−	0.339518i
$144$		0			0
$145$	−2.99450	−	2.17563i	−0.248680	−	0.180677i
$146$		0			0
$147$	−0.706539	−	2.17450i	−0.0582743	−	0.179350i
$148$		0			0
$149$	0.317187	−	0.976200i	0.0259849	−	0.0799734i	−0.937223	−	0.348730i	$-0.886613\pi$
$149$	0.317187	−	0.976200i	0.0259849	−	0.0799734i	0.963208	+	0.268757i	$0.0866129\pi$
$150$		0			0
$151$	3.18087	−	2.31104i	0.258856	−	0.188070i	−0.450787	−	0.892632i	$-0.648857\pi$
$151$	3.18087	−	2.31104i	0.258856	−	0.188070i	0.709642	+	0.704562i	$0.248857\pi$
$152$		0			0
$153$	−0.321252	−	0.988712i	−0.0259717	−	0.0799326i
$154$		0			0
$155$	−12.1691			−0.977448
$156$		0			0
$157$	−4.59131	−	3.33578i	−0.366427	−	0.266225i	0.389301	−	0.921111i	$-0.372717\pi$
$157$	−4.59131	−	3.33578i	−0.366427	−	0.266225i	−0.755728	+	0.654886i	$0.772717\pi$
$158$		0			0
$159$	−2.98890	+	9.19888i	−0.237035	+	0.729518i
$160$		0			0
$161$	0.751337			0.0592137
$162$		0			0
$163$	−13.5161			−1.05866			−0.529332	−	0.848415i	$-0.677557\pi$
$163$	−13.5161			−1.05866			−0.529332	+	0.848415i	$0.677557\pi$
$164$		0			0
$165$	−33.6644			−2.62077
$166$		0			0
$167$	−12.2733			−0.949740			−0.474870	−	0.880056i	$-0.657505\pi$
$167$	−12.2733			−0.949740			−0.474870	+	0.880056i	$0.657505\pi$
$168$		0			0
$169$	−3.54378	+	10.9066i	−0.272598	+	0.838972i
$170$		0			0
$171$	−5.93966	−	4.31542i	−0.454218	−	0.330008i
$172$		0			0
$173$	24.4998			1.86268			0.931341	−	0.364149i	$-0.118640\pi$
$173$	24.4998			1.86268			0.931341	+	0.364149i	$0.118640\pi$
$174$		0			0
$175$	−0.606089	−	1.86535i	−0.0458160	−	0.141007i
$176$		0			0
$177$	−0.320141	+	0.232596i	−0.0240633	+	0.0174830i
$178$		0			0
$179$	4.29543	−	13.2200i	0.321055	−	0.988107i	−0.652135	−	0.758103i	$-0.726126\pi$
$179$	4.29543	−	13.2200i	0.321055	−	0.988107i	0.973190	−	0.230003i	$-0.0738737\pi$
$180$		0			0
$181$	−0.541715	−	1.66723i	−0.0402654	−	0.123924i	0.928903	−	0.370323i	$-0.120753\pi$
$181$	−0.541715	−	1.66723i	−0.0402654	−	0.123924i	−0.969169	+	0.246398i	$0.920753\pi$
$182$		0			0
$183$	−21.7819	−	15.8255i	−1.61016	−	1.16985i
$184$		0			0
$185$	−0.00653348	−	0.00474685i	−0.000480351	−	0.000348995i
$186$		0			0
$187$	−2.10689	+	1.53075i	−0.154071	+	0.111939i
$188$		0			0
$189$	1.42863	+	1.03796i	0.103917	+	0.0755004i
$190$		0			0
$191$	6.32091			0.457365			0.228683	−	0.973501i	$-0.426558\pi$
$191$	6.32091			0.457365			0.228683	+	0.973501i	$0.426558\pi$
$192$		0			0
$193$	−8.02996	+	24.7137i	−0.578009	+	1.77893i	0.0476869	+	0.998862i	$0.484815\pi$
$193$	−8.02996	+	24.7137i	−0.578009	+	1.77893i	−0.625696	+	0.780067i	$0.715185\pi$
$194$		0			0
$195$	−2.30741	−	7.10148i	−0.165237	−	0.508547i
$196$		0			0
$197$	−3.89014	−	11.9726i	−0.277161	−	0.853014i	−0.988639	−	0.150306i	$-0.951974\pi$
$197$	−3.89014	−	11.9726i	−0.277161	−	0.853014i	0.711478	−	0.702708i	$-0.248026\pi$
$198$		0			0
$199$	19.6741	−	14.2941i	1.39466	−	1.01328i	0.399328	−	0.916808i	$-0.369244\pi$
$199$	19.6741	−	14.2941i	1.39466	−	1.01328i	0.995336	−	0.0964739i	$-0.0307564\pi$
$200$		0			0
$201$	−3.47319	+	10.6894i	−0.244980	+	0.753972i
$202$		0			0
$203$	−1.13495	+	0.824593i	−0.0796582	+	0.0578750i
$204$		0			0
$205$	−16.5338	+	3.47106i	−1.15477	+	0.242429i
$206$		0			0
$207$	1.35407	−	0.983791i	0.0941145	−	0.0683782i
$208$		0			0
$209$	−5.68340	+	17.4917i	−0.393129	+	1.20993i
$210$		0			0
$211$	−6.97480	+	5.06749i	−0.480165	+	0.348860i	−0.801390	−	0.598143i	$-0.795906\pi$
$211$	−6.97480	+	5.06749i	−0.480165	+	0.348860i	0.321225	+	0.947003i	$0.395906\pi$
$212$		0			0
$213$	−0.505320	−	1.55522i	−0.0346240	−	0.106562i
$214$		0			0
$215$	4.84685	+	14.9171i	0.330552	+	1.01734i
$216$		0			0
$217$	−1.42526	+	4.38651i	−0.0967532	+	0.297776i
$218$		0			0
$219$	6.86497			0.463892
$220$		0			0
$221$	−0.467320	−	0.339527i	−0.0314353	−	0.0228391i
$222$		0			0
$223$	8.26908	−	6.00784i	0.553739	−	0.402315i	−0.275423	−	0.961323i	$-0.588818\pi$
$223$	8.26908	−	6.00784i	0.553739	−	0.402315i	0.829162	+	0.559008i	$0.188818\pi$
$224$		0			0
$225$	−3.53477	−	2.56816i	−0.235651	−	0.171211i
$226$		0			0
$227$	−21.5788	−	15.6779i	−1.43224	−	1.04058i	−0.989595	−	0.143881i	$-0.954042\pi$
$227$	−21.5788	−	15.6779i	−1.43224	−	1.04058i	−0.442641	−	0.896699i	$-0.645958\pi$
$228$		0			0
$229$	2.94238	+	9.05570i	0.194438	+	0.598418i	0.999983	+	0.00588307i	$0.00187265\pi$
$229$	2.94238	+	9.05570i	0.194438	+	0.598418i	−0.805545	+	0.592535i	$0.798127\pi$
$230$		0			0
$231$	−3.94282	+	12.1347i	−0.259418	+	0.798407i
$232$		0			0
$233$	5.65893	−	4.11145i	0.370729	−	0.269350i	−0.386784	−	0.922170i	$-0.626414\pi$
$233$	5.65893	−	4.11145i	0.370729	−	0.269350i	0.757513	+	0.652820i	$0.226414\pi$
$234$		0			0
$235$	2.94838	+	9.07418i	0.192331	+	0.591934i
$236$		0			0
$237$	−24.9893			−1.62323
$238$		0			0
$239$	−7.25004	−	5.26746i	−0.468966	−	0.340724i	0.328072	−	0.944653i	$-0.393601\pi$
$239$	−7.25004	−	5.26746i	−0.468966	−	0.340724i	−0.797038	+	0.603929i	$0.793601\pi$
$240$		0			0
$241$	5.16855	−	15.9072i	0.332935	−	1.02467i	−0.634795	−	0.772681i	$-0.718915\pi$
$241$	5.16855	−	15.9072i	0.332935	−	1.02467i	0.967730	−	0.251989i	$-0.0810846\pi$
$242$		0			0
$243$	19.2138			1.23257
$244$		0			0
$245$	−2.63844			−0.168564
$246$		0			0
$247$	−4.07941			−0.259567
$248$		0			0
$249$	−12.9017			−0.817612
$250$		0			0
$251$	−3.58483	+	11.0330i	−0.226272	+	0.696394i	0.771888	+	0.635759i	$0.219313\pi$
$251$	−3.58483	+	11.0330i	−0.226272	+	0.696394i	−0.998160	+	0.0606356i	$0.980687\pi$
$252$		0			0
$253$	−3.39205	−	2.46447i	−0.213257	−	0.154940i
$254$		0			0
$255$	−2.81523			−0.176297
$256$		0			0
$257$	−3.20278	−	9.85714i	−0.199784	−	0.614872i	−0.999887	−	0.0150096i	$-0.995222\pi$
$257$	−3.20278	−	9.85714i	−0.199784	−	0.614872i	0.800103	−	0.599862i	$-0.204778\pi$
$258$		0			0
$259$	−0.00247627	+	0.00179911i	−0.000153868	+	0.000111792i
$260$		0			0
$261$	−0.965722	+	2.97219i	−0.0597767	+	0.183974i
$262$		0			0
$263$	−4.03630	−	12.4225i	−0.248889	−	0.766002i	−0.994972	−	0.100149i	$-0.968068\pi$
$263$	−4.03630	−	12.4225i	−0.248889	−	0.766002i	0.746083	−	0.665853i	$-0.231932\pi$
$264$		0			0
$265$	9.02982	+	6.56055i	0.554697	+	0.403011i
$266$		0			0
$267$	−15.9151	−	11.5630i	−0.973988	−	0.707644i
$268$		0			0
$269$	14.9699	−	10.8762i	0.912728	−	0.663136i	−0.0289751	−	0.999580i	$-0.509224\pi$
$269$	14.9699	−	10.8762i	0.912728	−	0.663136i	0.941703	+	0.336444i	$0.109224\pi$
$270$		0			0
$271$	4.08633	+	2.96889i	0.248227	+	0.180347i	0.704940	−	0.709266i	$-0.250974\pi$
$271$	4.08633	+	2.96889i	0.248227	+	0.180347i	−0.456714	+	0.889614i	$0.650974\pi$
$272$		0			0
$273$	−2.83006			−0.171283
$274$		0			0
$275$	−3.38226	+	10.4095i	−0.203958	+	0.627718i
$276$		0			0
$277$	−8.46421	−	26.0502i	−0.508565	−	1.56520i	−0.794693	−	0.607011i	$-0.792368\pi$
$277$	−8.46421	−	26.0502i	−0.508565	−	1.56520i	0.286128	−	0.958191i	$-0.407632\pi$
$278$		0			0
$279$	3.17500	+	9.77166i	0.190083	+	0.585014i
$280$		0			0
$281$	16.4452	−	11.9482i	0.981041	−	0.712768i	0.0230997	−	0.999733i	$-0.492646\pi$
$281$	16.4452	−	11.9482i	0.981041	−	0.712768i	0.957941	+	0.286965i	$0.0926465\pi$
$282$		0			0
$283$	0.881266	−	2.71226i	0.0523858	−	0.161227i	−0.921441	−	0.388518i	$-0.872987\pi$
$283$	0.881266	−	2.71226i	0.0523858	−	0.161227i	0.973827	+	0.227291i	$0.0729870\pi$
$284$		0			0
$285$	−16.0847	+	11.6862i	−0.952776	+	0.692232i
$286$		0			0
$287$	−0.685276	+	6.36635i	−0.0404506	+	0.375794i
$288$		0			0
$289$	13.5771	−	9.86434i	0.798653	−	0.580255i
$290$		0			0
$291$	−2.87936	+	8.86176i	−0.168791	+	0.519485i
$292$		0			0
$293$	−16.9126	+	12.2878i	−0.988048	+	0.717859i	−0.959493	−	0.281734i	$-0.909091\pi$
$293$	−16.9126	+	12.2878i	−0.988048	+	0.717859i	−0.0285549	+	0.999592i	$0.509091\pi$
$294$		0			0
$295$	0.141111	+	0.434294i	0.00821577	+	0.0252855i
$296$		0			0
$297$	−3.04519	−	9.37213i	−0.176700	−	0.543826i
$298$		0			0
$299$	0.287382	−	0.884470i	0.0166197	−	0.0511502i
$300$		0			0
$301$	5.94471			0.342647
$302$		0			0
$303$	19.3593	+	14.0653i	1.11216	+	0.808032i
$304$		0			0
$305$	−25.1355	+	18.2620i	−1.43926	+	1.04568i
$306$		0			0
$307$	−8.90843	−	6.47236i	−0.508431	−	0.369397i	0.303797	−	0.952737i	$-0.401746\pi$
$307$	−8.90843	−	6.47236i	−0.508431	−	0.369397i	−0.812228	+	0.583340i	$0.801746\pi$
$308$		0			0
$309$	−34.1877	−	24.8388i	−1.94487	−	1.41303i
$310$		0			0
$311$	−1.83605	−	5.65077i	−0.104113	−	0.320426i	0.885408	−	0.464814i	$-0.153879\pi$
$311$	−1.83605	−	5.65077i	−0.104113	−	0.320426i	−0.989521	+	0.144388i	$0.953879\pi$
$312$		0			0
$313$	−2.56973	+	7.90880i	−0.145249	+	0.447032i	−0.997043	−	0.0768457i	$-0.975515\pi$
$313$	−2.56973	+	7.90880i	−0.145249	+	0.447032i	0.851794	+	0.523878i	$0.175515\pi$
$314$		0			0
$315$	−4.75503	+	3.45473i	−0.267916	+	0.194652i
$316$		0			0
$317$	−2.09067	−	6.43441i	−0.117424	−	0.361393i	0.875021	−	0.484085i	$-0.160847\pi$
$317$	−2.09067	−	6.43441i	−0.117424	−	0.361393i	−0.992445	+	0.122692i	$0.960847\pi$
$318$		0			0
$319$	7.82873			0.438324
$320$		0			0
$321$	14.3987	+	10.4613i	0.803659	+	0.583892i
$322$		0			0
$323$	−0.475282	+	1.46277i	−0.0264454	+	0.0813906i
$324$		0			0
$325$	−2.42771			−0.134665
$326$		0			0
$327$	−41.5279			−2.29650
$328$		0			0
$329$	3.61622			0.199369
$330$		0			0
$331$	10.6233			0.583912			0.291956	−	0.956432i	$-0.405694\pi$
$331$	10.6233			0.583912			0.291956	+	0.956432i	$0.405694\pi$
$332$		0			0
$333$	−0.00210703	+	0.00648478i	−0.000115465	+	0.000355364i
$334$		0			0
$335$	10.4929	+	7.62357i	0.573291	+	0.416520i
$336$		0			0
$337$	16.5785			0.903091			0.451546	−	0.892248i	$-0.350873\pi$
$337$	16.5785			0.903091			0.451546	+	0.892248i	$0.350873\pi$
$338$		0			0
$339$	−2.72555	−	8.38839i	−0.148032	−	0.455595i
$340$		0			0
$341$	20.8229	−	15.1287i	1.12762	−	0.819265i
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$		0			0
$345$	−1.40061	−	4.31064i	−0.0754064	−	0.232077i
$346$		0			0
$347$	20.7842	+	15.1006i	1.11576	+	0.810645i	0.983561	−	0.180579i	$-0.0577971\pi$
$347$	20.7842	+	15.1006i	1.11576	+	0.810645i	0.132196	+	0.991224i	$0.457797\pi$
$348$		0			0
$349$	19.2627	+	13.9952i	1.03111	+	0.749146i	0.968531	−	0.248894i	$-0.0800670\pi$
$349$	19.2627	+	13.9952i	1.03111	+	0.749146i	0.0625803	+	0.998040i	$0.480067\pi$
$350$		0			0
$351$	1.76832	−	1.28476i	0.0943860	−	0.0685755i
$352$		0			0
$353$	−15.9575	−	11.5938i	−0.849335	−	0.617078i	0.0756279	−	0.997136i	$-0.475904\pi$
$353$	−15.9575	−	11.5938i	−0.849335	−	0.617078i	−0.924962	+	0.380058i	$0.875904\pi$
$354$		0			0
$355$	−1.88702			−0.100153
$356$		0			0
$357$	−0.329724	+	1.01479i	−0.0174508	+	0.0537081i
$358$		0			0
$359$	−4.17638	−	12.8536i	−0.220421	−	0.678385i	−0.998724	−	0.0504970i	$-0.983919\pi$
$359$	−4.17638	−	12.8536i	−0.220421	−	0.678385i	0.778303	−	0.627888i	$-0.216081\pi$
$360$		0			0
$361$	−2.51478	−	7.73969i	−0.132357	−	0.407352i
$362$		0			0
$363$	37.2567	−	27.0686i	1.95547	−	1.42073i
$364$		0			0
$365$	2.44801	−	7.53422i	0.128135	−	0.394359i
$366$		0			0
$367$	−7.45693	+	5.41778i	−0.389249	+	0.282806i	−0.765148	−	0.643855i	$-0.777334\pi$
$367$	−7.45693	+	5.41778i	−0.389249	+	0.282806i	0.375899	+	0.926661i	$0.377334\pi$
$368$		0			0
$369$	7.10099	+	12.3708i	0.369663	+	0.643999i
$370$		0			0
$371$	3.42241	−	2.48653i	0.177683	−	0.129094i
$372$		0			0
$373$	−0.410404	+	1.26309i	−0.0212499	+	0.0654005i	−0.961119	−	0.276134i	$-0.910947\pi$
$373$	−0.410404	+	1.26309i	−0.0212499	+	0.0654005i	0.939869	+	0.341535i	$0.110947\pi$
$374$		0			0
$375$	14.8299	−	10.7746i	0.765815	−	0.556397i
$376$		0			0
$377$	0.536593	+	1.65146i	0.0276360	+	0.0850547i
$378$		0			0
$379$	−2.76235	−	8.50165i	−0.141893	−	0.436700i	0.854706	−	0.519113i	$-0.173738\pi$
$379$	−2.76235	−	8.50165i	−0.141893	−	0.436700i	−0.996598	+	0.0824125i	$0.973738\pi$
$380$		0			0
$381$	−3.04778	+	9.38009i	−0.156142	+	0.480557i
$382$		0			0
$383$	−13.1670			−0.672804			−0.336402	−	0.941718i	$-0.609210\pi$
$383$	−13.1670			−0.672804			−0.336402	+	0.941718i	$0.609210\pi$
$384$		0			0
$385$	11.9117	+	8.65437i	0.607078	+	0.441068i
$386$		0			0
$387$	10.7136	−	7.78392i	0.544605	−	0.395679i
$388$		0			0
$389$	22.5805	+	16.4057i	1.14488	+	0.831803i	0.987791	−	0.155782i	$-0.0497898\pi$
$389$	22.5805	+	16.4057i	1.14488	+	0.831803i	0.157087	+	0.987585i	$0.449790\pi$
$390$		0			0
$391$	−0.283666	−	0.206095i	−0.0143456	−	0.0104227i
$392$		0			0
$393$	4.85294	+	14.9358i	0.244799	+	0.753413i
$394$		0			0
$395$	−8.91106	+	27.4254i	−0.448364	+	1.37992i
$396$		0			0
$397$	24.0855	−	17.4991i	1.20882	−	0.878256i	0.213693	−	0.976901i	$-0.431451\pi$
$397$	24.0855	−	17.4991i	1.20882	−	0.878256i	0.995123	+	0.0986446i	$0.0314507\pi$
$398$		0			0
$399$	2.32858	+	7.16663i	0.116575	+	0.358780i
$400$		0			0
$401$	31.3933			1.56771			0.783854	−	0.620945i	$-0.213251\pi$
$401$	31.3933			1.56771			0.783854	+	0.620945i	$0.213251\pi$
$402$		0			0
$403$	4.61862	+	3.35563i	0.230070	+	0.167156i
$404$		0			0
$405$	8.74066	−	26.9010i	0.434327	−	1.33672i
$406$		0			0
$407$	0.0170809			0.000846668
$408$		0			0
$409$	−10.6785			−0.528017			−0.264008	−	0.964520i	$-0.585045\pi$
$409$	−10.6785			−0.528017			−0.264008	+	0.964520i	$0.585045\pi$
$410$		0			0
$411$	−9.43166			−0.465229
$412$		0			0
$413$	0.173073			0.00851639
$414$		0			0
$415$	−4.60068	+	14.1594i	−0.225839	+	0.695060i
$416$		0			0
$417$	−30.6961	−	22.3020i	−1.50319	−	1.09213i
$418$		0			0
$419$	−28.8955			−1.41164			−0.705819	−	0.708392i	$-0.749421\pi$
$419$	−28.8955			−1.41164			−0.705819	+	0.708392i	$0.749421\pi$
$420$		0			0
$421$	−6.59607	−	20.3006i	−0.321473	−	0.989391i	−0.973008	−	0.230773i	$-0.925875\pi$
$421$	−6.59607	−	20.3006i	−0.321473	−	0.989391i	0.651535	−	0.758619i	$-0.274125\pi$
$422$		0			0
$423$	6.51720	−	4.73503i	0.316877	−	0.230225i
$424$		0			0
$425$	−0.282846	+	0.870512i	−0.0137201	+	0.0422260i
$426$		0			0
$427$	3.63887	+	11.1993i	0.176097	+	0.541971i
$428$		0			0
$429$	12.7768	+	9.28292i	0.616872	+	0.448184i
$430$		0			0
$431$	24.8580	+	18.0604i	1.19737	+	0.869940i	0.994023	−	0.109167i	$-0.0348183\pi$
$431$	24.8580	+	18.0604i	1.19737	+	0.869940i	0.203346	+	0.979107i	$0.434818\pi$
$432$		0			0
$433$	16.3218	−	11.8585i	0.784377	−	0.569883i	−0.121912	−	0.992541i	$-0.538903\pi$
$433$	16.3218	−	11.8585i	0.784377	−	0.569883i	0.906290	+	0.422657i	$0.138903\pi$
$434$		0			0
$435$	6.84666	+	4.97439i	0.328272	+	0.238504i
$436$		0			0
$437$	−2.47622			−0.118454
$438$		0			0
$439$	1.52453	−	4.69202i	0.0727618	−	0.223938i	−0.908062	−	0.418837i	$-0.862438\pi$
$439$	1.52453	−	4.69202i	0.0727618	−	0.223938i	0.980823	+	0.194899i	$0.0624379\pi$
$440$		0			0
$441$	0.688385	+	2.11863i	0.0327802	+	0.100887i
$442$		0			0
$443$	−1.13252	−	3.48553i	−0.0538075	−	0.165602i	0.920541	−	0.390645i	$-0.127748\pi$
$443$	−1.13252	−	3.48553i	−0.0538075	−	0.165602i	−0.974349	+	0.225042i	$0.927748\pi$
$444$		0			0
$445$	−18.3655	+	13.3433i	−0.870607	+	0.632533i
$446$		0			0
$447$	−0.725218	+	2.23199i	−0.0343016	+	0.105570i
$448$		0			0
$449$	−22.8314	+	16.5880i	−1.07748	+	0.782835i	−0.977242	−	0.212128i	$-0.931961\pi$
$449$	−22.8314	+	16.5880i	−1.07748	+	0.782835i	−0.100239	+	0.994963i	$0.531961\pi$
$450$		0			0
$451$	23.9762	−	26.4943i	1.12899	−	1.24757i
$452$		0			0
$453$	−7.27277	+	5.28397i	−0.341704	+	0.248263i
$454$		0			0
$455$	−1.00919	+	3.10595i	−0.0473113	+	0.145609i
$456$		0			0
$457$	30.8737	−	22.4310i	1.44421	−	1.04928i	0.457067	−	0.889432i	$-0.348900\pi$
$457$	30.8737	−	22.4310i	1.44421	−	1.04928i	0.987142	−	0.159847i	$-0.0511001\pi$
$458$		0			0
$459$	−0.254658	−	0.783758i	−0.0118864	−	0.0365827i
$460$		0			0
$461$	8.26868	+	25.4484i	0.385111	+	1.18525i	0.936400	+	0.350935i	$0.114136\pi$
$461$	8.26868	+	25.4484i	0.385111	+	1.18525i	−0.551289	+	0.834315i	$0.685864\pi$
$462$		0			0
$463$	−11.7429	+	36.1408i	−0.545737	+	1.67961i	0.173494	+	0.984835i	$0.444494\pi$
$463$	−11.7429	+	36.1408i	−0.545737	+	1.67961i	−0.719231	+	0.694771i	$0.755506\pi$
$464$		0			0
$465$	27.8236			1.29029
$466$		0			0
$467$	−31.9597	−	23.2201i	−1.47892	−	1.07450i	−0.977903	−	0.209059i	$-0.932960\pi$
$467$	−31.9597	−	23.2201i	−1.47892	−	1.07450i	−0.501016	−	0.865438i	$-0.667040\pi$
$468$		0			0
$469$	3.97695	−	2.88943i	0.183639	−	0.133421i
$470$		0			0
$471$	10.4976	+	7.62696i	0.483705	+	0.351432i
$472$		0			0
$473$	−26.8385	−	19.4993i	−1.23404	−	0.896580i
$474$		0			0
$475$	1.99752	+	6.14774i	0.0916526	+	0.282078i
$476$		0			0
$477$	2.91210	−	8.96252i	0.133336	−	0.410366i
$478$		0			0
$479$	−31.5835	+	22.9468i	−1.44309	+	1.04846i	−0.455701	+	0.890133i	$0.650611\pi$
$479$	−31.5835	+	22.9468i	−1.44309	+	1.04846i	−0.987386	+	0.158331i	$0.949389\pi$
$480$		0			0
$481$	0.00117075	+	0.00360320i	5.33816e−5	+	0.000164292i
$482$		0			0
$483$	−1.71786			−0.0781655
$484$		0			0
$485$	8.69889	+	6.32012i	0.394996	+	0.286982i
$486$		0			0
$487$	−0.681748	+	2.09820i	−0.0308929	+	0.0950787i	−0.965314	−	0.261091i	$-0.915918\pi$
$487$	−0.681748	+	2.09820i	−0.0308929	+	0.0950787i	0.934421	+	0.356170i	$0.115918\pi$
$488$		0			0
$489$	30.9034			1.39750
$490$		0			0
$491$	−29.5676			−1.33437			−0.667184	−	0.744893i	$-0.732500\pi$
$491$	−29.5676			−1.33437			−0.667184	+	0.744893i	$0.732500\pi$
$492$		0			0
$493$	0.654689			0.0294857
$494$		0			0
$495$	32.7994			1.47422
$496$		0			0
$497$	−0.221011	+	0.680201i	−0.00991368	+	0.0305112i
$498$		0			0
$499$	22.7606	+	16.5365i	1.01890	+	0.740276i	0.966058	−	0.258327i	$-0.0831712\pi$
$499$	22.7606	+	16.5365i	1.01890	+	0.740276i	0.0528446	+	0.998603i	$0.483171\pi$
$500$		0			0
$501$	28.0619			1.25371
$502$		0			0
$503$	4.03506	+	12.4186i	0.179914	+	0.553720i	0.999824	−	0.0187737i	$-0.00597621\pi$
$503$	4.03506	+	12.4186i	0.179914	+	0.553720i	−0.819909	+	0.572493i	$0.805976\pi$
$504$		0			0
$505$	22.3399	−	16.2309i	0.994114	−	0.722266i
$506$		0			0
$507$	8.10253	−	24.9370i	0.359846	−	1.10749i
$508$		0			0
$509$	−5.15735	−	15.8727i	−0.228596	−	0.703545i	−0.997907	−	0.0646707i	$-0.979400\pi$
$509$	−5.15735	−	15.8727i	−0.228596	−	0.703545i	0.769311	−	0.638875i	$-0.220600\pi$
$510$		0			0
$511$	−2.42909	−	1.76483i	−0.107456	−	0.0780716i
$512$		0			0
$513$	−4.70841	−	3.42086i	−0.207881	−	0.151035i
$514$		0			0
$515$	−39.4514	+	28.6631i	−1.73844	+	1.26305i
$516$		0			0
$517$	−16.3261	−	11.8616i	−0.718021	−	0.521673i
$518$		0			0
$519$	−56.0164			−2.45885
$520$		0			0
$521$	−4.66470	+	14.3565i	−0.204364	+	0.628968i	0.795375	+	0.606118i	$0.207274\pi$
$521$	−4.66470	+	14.3565i	−0.204364	+	0.628968i	−0.999739	+	0.0228500i	$0.992726\pi$
$522$		0			0
$523$	−4.44354	−	13.6758i	−0.194303	−	0.598002i	−0.999984	−	0.00565266i	$-0.998201\pi$
$523$	−4.44354	−	13.6758i	−0.194303	−	0.598002i	0.805682	−	0.592349i	$-0.201799\pi$
$524$		0			0
$525$	1.38577	+	4.26495i	0.0604798	+	0.186138i
$526$		0			0
$527$	1.74134	−	1.26516i	0.0758542	−	0.0551113i
$528$		0			0
$529$	−6.93295	+	21.3374i	−0.301433	+	0.927714i
$530$		0			0
$531$	0.311916	−	0.226620i	0.0135360	−	0.00983447i
$532$		0			0
$533$	7.23232	+	3.24179i	0.313267	+	0.140418i
$534$		0			0
$535$	16.6156	−	12.0720i	0.718357	−	0.521917i
$536$		0			0
$537$	−9.82110	+	30.2262i	−0.423812	+	1.30436i
$538$		0			0
$539$	4.51469	−	3.28011i	0.194461	−	0.141285i
$540$		0			0
$541$	3.65991	+	11.2640i	0.157352	+	0.484279i	0.998392	−	0.0566941i	$-0.0180560\pi$
$541$	3.65991	+	11.2640i	0.157352	+	0.484279i	−0.841040	+	0.540973i	$0.818056\pi$
$542$		0			0
$543$	1.23858	+	3.81196i	0.0531526	+	0.163587i
$544$		0			0
$545$	−14.8086	+	45.5763i	−0.634332	+	1.95227i
$546$		0			0
$547$	−23.9572			−1.02434			−0.512169	−	0.858885i	$-0.671158\pi$
$547$	−23.9572			−1.02434			−0.512169	+	0.858885i	$0.671158\pi$
$548$		0			0
$549$	21.2222	+	15.4188i	0.905742	+	0.658060i
$550$		0			0
$551$	3.74053	−	2.71766i	0.159352	−	0.115776i
$552$		0			0
$553$	8.84215	+	6.42420i	0.376006	+	0.273185i
$554$		0			0
$555$	0.0149382	+	0.0108532i	0.000634091	+	0.000460694i
$556$		0			0
$557$	−5.04695	−	15.5329i	−0.213846	−	0.658151i	−0.999233	−	0.0391461i	$-0.987536\pi$
$557$	−5.04695	−	15.5329i	−0.213846	−	0.658151i	0.785387	−	0.619005i	$-0.212464\pi$
$558$		0			0
$559$	2.27381	−	6.99808i	0.0961721	−	0.295987i
$560$		0			0
$561$	4.81721	−	3.49991i	0.203383	−	0.147766i
$562$		0			0
$563$	12.6705	+	38.9959i	0.534000	+	1.64348i	0.745801	+	0.666169i	$0.232067\pi$
$563$	12.6705	+	38.9959i	0.534000	+	1.64348i	−0.211801	+	0.977313i	$0.567933\pi$
$564$		0			0
$565$	−10.1781			−0.428194
$566$		0			0
$567$	−8.67307	−	6.30136i	−0.364235	−	0.264632i
$568$		0			0
$569$	−0.806540	+	2.48228i	−0.0338119	+	0.104062i	−0.966538	−	0.256523i	$-0.917423\pi$
$569$	−0.806540	+	2.48228i	−0.0338119	+	0.104062i	0.932726	+	0.360585i	$0.117423\pi$
$570$		0			0
$571$	36.0516			1.50871			0.754355	−	0.656466i	$-0.227950\pi$
$571$	36.0516			1.50871			0.754355	+	0.656466i	$0.227950\pi$
$572$		0			0
$573$	−14.4522			−0.603749
$574$		0			0
$575$	−1.47363			−0.0614547
$576$		0			0
$577$	26.2244			1.09174			0.545869	−	0.837871i	$-0.316200\pi$
$577$	26.2244			1.09174			0.545869	+	0.837871i	$0.316200\pi$
$578$		0			0
$579$	18.3598	−	56.5055i	0.763006	−	2.34829i
$580$		0			0
$581$	4.56511	+	3.31674i	0.189393	+	0.137602i
$582$		0			0
$583$	−23.6072			−0.977712
$584$		0			0
$585$	2.24812	+	6.91901i	0.0929485	+	0.286066i
$586$		0			0
$587$	−20.3714	+	14.8007i	−0.840817	+	0.610889i	−0.922599	−	0.385761i	$-0.873939\pi$
$587$	−20.3714	+	14.8007i	−0.840817	+	0.610889i	0.0817819	+	0.996650i	$0.473939\pi$
$588$		0			0
$589$	4.69732	−	14.4569i	0.193550	−	0.595685i
$590$		0			0
$591$	8.89445	+	27.3743i	0.365869	+	1.12603i
$592$		0			0
$593$	15.6856	+	11.3963i	0.644131	+	0.467988i	0.861267	−	0.508153i	$-0.169672\pi$
$593$	15.6856	+	11.3963i	0.644131	+	0.467988i	−0.217136	+	0.976141i	$0.569672\pi$
$594$		0			0
$595$	0.996136	+	0.723735i	0.0408376	+	0.0296702i
$596$		0			0
$597$	−44.9831	+	32.6822i	−1.84104	+	1.33759i
$598$		0			0
$599$	13.8777	+	10.0828i	0.567029	+	0.411971i	0.834025	−	0.551727i	$-0.186031\pi$
$599$	13.8777	+	10.0828i	0.567029	+	0.411971i	−0.266995	+	0.963698i	$0.586031\pi$
$600$		0			0
$601$	−1.65422			−0.0674769			−0.0337384	−	0.999431i	$-0.510741\pi$
$601$	−1.65422			−0.0674769			−0.0337384	+	0.999431i	$0.510741\pi$
$602$		0			0
$603$	3.38395	−	10.4147i	0.137805	−	0.424121i
$604$		0			0
$605$	−16.4219	−	50.5413i	−0.667644	−	2.05480i
$606$		0			0
$607$	−0.869906	−	2.67730i	−0.0353084	−	0.108668i	0.931849	−	0.362846i	$-0.118195\pi$
$607$	−0.869906	−	2.67730i	−0.0353084	−	0.108668i	−0.967157	+	0.254178i	$0.918195\pi$
$608$		0			0
$609$	2.59497	−	1.88535i	0.105153	−	0.0763984i
$610$		0			0
$611$	1.38318	−	4.25699i	0.0559575	−	0.172219i
$612$		0			0
$613$	−3.43454	+	2.49534i	−0.138720	+	0.100786i	−0.654981	−	0.755645i	$-0.727323\pi$
$613$	−3.43454	+	2.49534i	−0.138720	+	0.100786i	0.516261	+	0.856431i	$0.327323\pi$
$614$		0			0
$615$	37.8030	−	7.93625i	1.52437	−	0.320021i
$616$		0			0
$617$	22.1814	−	16.1158i	0.892991	−	0.648796i	−0.0436652	−	0.999046i	$-0.513903\pi$
$617$	22.1814	−	16.1158i	0.892991	−	0.648796i	0.936656	+	0.350250i	$0.113903\pi$
$618$		0			0
$619$	1.36021	−	4.18629i	0.0546714	−	0.168261i	−0.919992	−	0.391936i	$-0.871805\pi$
$619$	1.36021	−	4.18629i	0.0546714	−	0.168261i	0.974664	+	0.223675i	$0.0718054\pi$
$620$		0			0
$621$	1.07338	−	0.779857i	0.0430733	−	0.0312946i
$622$		0			0
$623$	2.65877	+	8.18284i	0.106521	+	0.327839i
$624$		0			0
$625$	−9.56712	−	29.4446i	−0.382685	−	1.17778i
$626$		0			0
$627$	12.9946	−	39.9931i	0.518953	−	1.59717i
$628$		0			0
$629$	0.00142841			5.69546e−5
$630$		0			0
$631$	−8.79107	−	6.38709i	−0.349967	−	0.254266i	0.398888	−	0.917000i	$-0.369396\pi$
$631$	−8.79107	−	6.38709i	−0.349967	−	0.254266i	−0.748855	+	0.662734i	$0.769396\pi$
$632$		0			0
$633$	15.9472	−	11.5863i	0.633846	−	0.460516i
$634$		0			0
$635$	9.20771	+	6.68979i	0.365397	+	0.265476i
$636$		0			0
$637$	1.00138	+	0.727546i	0.0396762	+	0.0288264i
$638$		0			0
$639$	0.492337	+	1.51526i	0.0194765	+	0.0599426i
$640$		0			0
$641$	0.682266	−	2.09980i	0.0269479	−	0.0829370i	−0.936678	−	0.350192i	$-0.886116\pi$
$641$	0.682266	−	2.09980i	0.0269479	−	0.0829370i	0.963626	+	0.267255i	$0.0861165\pi$
$642$		0			0
$643$	−9.28643	+	6.74699i	−0.366221	+	0.266075i	−0.755642	−	0.654985i	$-0.772675\pi$
$643$	−9.28643	+	6.74699i	−0.366221	+	0.266075i	0.389421	+	0.921060i	$0.372675\pi$
$644$		0			0
$645$	−11.0819	−	34.1065i	−0.436348	−	1.34294i
$646$		0			0
$647$	−35.4167			−1.39237			−0.696187	−	0.717861i	$-0.745122\pi$
$647$	−35.4167			−1.39237			−0.696187	+	0.717861i	$0.745122\pi$
$648$		0			0
$649$	−0.781373	−	0.567701i	−0.0306716	−	0.0222842i
$650$		0			0
$651$	3.25873	−	10.0294i	0.127720	−	0.393081i
$652$		0			0
$653$	38.1244			1.49192			0.745962	−	0.665988i	$-0.231990\pi$
$653$	38.1244			1.49192			0.745962	+	0.665988i	$0.231990\pi$
$654$		0			0
$655$	18.1224			0.708101
$656$		0			0
$657$	−6.68858			−0.260947
$658$		0			0
$659$	6.35522			0.247564			0.123782	−	0.992309i	$-0.460498\pi$
$659$	6.35522			0.247564			0.123782	+	0.992309i	$0.460498\pi$
$660$		0			0
$661$	−9.90427	+	30.4822i	−0.385232	+	1.18562i	0.551080	+	0.834452i	$0.314216\pi$
$661$	−9.90427	+	30.4822i	−0.385232	+	1.18562i	−0.936312	+	0.351169i	$0.885784\pi$
$662$		0			0
$663$	1.06848	+	0.776298i	0.0414964	+	0.0301489i
$664$		0			0
$665$	8.69564			0.337203
$666$		0			0
$667$	0.325715	+	1.00245i	0.0126117	+	0.0388149i
$668$		0			0
$669$	−18.9065	+	13.7364i	−0.730967	+	0.531079i
$670$		0			0
$671$	20.3066	−	62.4972i	0.783926	−	2.41268i
$672$		0			0
$673$	−6.09495	−	18.7583i	−0.234943	−	0.723080i	−0.997129	−	0.0757222i	$-0.975874\pi$
$673$	−6.09495	−	18.7583i	−0.234943	−	0.723080i	0.762186	−	0.647358i	$-0.224126\pi$
$674$		0			0
$675$	−2.80203	−	2.03580i	−0.107850	−	0.0783579i
$676$		0			0
$677$	−20.9798	−	15.2427i	−0.806319	−	0.585825i	0.106442	−	0.994319i	$-0.466054\pi$
$677$	−20.9798	−	15.2427i	−0.806319	−	0.585825i	−0.912761	+	0.408494i	$0.866054\pi$
$678$		0			0
$679$	3.29699	−	2.39540i	0.126527	−	0.0919271i
$680$		0			0
$681$	49.3380	+	35.8461i	1.89063	+	1.37363i
$682$		0			0
$683$	40.6465			1.55529			0.777647	−	0.628701i	$-0.216413\pi$
$683$	40.6465			1.55529			0.777647	+	0.628701i	$0.216413\pi$
$684$		0			0
$685$	−3.36328	+	10.3511i	−0.128504	+	0.395496i
$686$		0			0
$687$	−6.72747	−	20.7050i	−0.256669	−	0.789946i
$688$		0			0
$689$	−1.61808	−	4.97993i	−0.0616438	−	0.189720i
$690$		0			0
$691$	20.2139	−	14.6863i	0.768975	−	0.558693i	−0.132675	−	0.991160i	$-0.542357\pi$
$691$	20.2139	−	14.6863i	0.768975	−	0.558693i	0.901650	+	0.432467i	$0.142357\pi$
$692$		0			0
$693$	3.84151	−	11.8229i	0.145927	−	0.449117i
$694$		0			0
$695$	−35.4222	+	25.7357i	−1.34364	+	0.976213i
$696$		0			0
$697$	2.00504	−	2.21563i	0.0759464	−	0.0839228i
$698$		0			0
$699$	−12.9386	+	9.40046i	−0.489384	+	0.355558i
$700$		0			0
$701$	−3.97639	+	12.2381i	−0.150186	+	0.462225i	−0.997641	−	0.0686415i	$-0.978134\pi$
$701$	−3.97639	+	12.2381i	−0.150186	+	0.462225i	0.847455	+	0.530867i	$0.178134\pi$
$702$		0			0
$703$	0.00816118	−	0.00592944i	0.000307805	−	0.000223633i
$704$		0			0
$705$	−6.74120	−	20.7473i	−0.253888	−	0.781388i
$706$		0			0
$707$	−3.23415	−	9.95369i	−0.121633	−	0.374347i
$708$		0			0
$709$	−7.37040	+	22.6838i	−0.276801	+	0.851906i	0.711936	+	0.702244i	$0.247819\pi$
$709$	−7.37040	+	22.6838i	−0.276801	+	0.851906i	−0.988737	+	0.149662i	$0.952181\pi$
$710$		0			0
$711$	24.3472			0.913092
$712$		0			0
$713$	2.80353	+	2.03688i	0.104993	+	0.0762819i
$714$		0			0
$715$	14.7440	−	10.7122i	0.551396	−	0.400613i
$716$		0			0
$717$	16.5765	+	12.0436i	0.619062	+	0.449775i
$718$		0			0
$719$	−13.5486	−	9.84362i	−0.505277	−	0.367105i	0.305752	−	0.952111i	$-0.401092\pi$
$719$	−13.5486	−	9.84362i	−0.505277	−	0.367105i	−0.811029	+	0.585006i	$0.801092\pi$
$720$		0			0
$721$	5.71138	+	17.5778i	0.212703	+	0.654632i
$722$		0			0
$723$	−11.8174	+	36.3702i	−0.439494	+	1.35262i
$724$		0			0
$725$	2.22604	−	1.61731i	0.0826730	−	0.0600654i
$726$		0			0
$727$	−10.5939	−	32.6046i	−0.392905	−	1.20924i	−0.930581	−	0.366086i	$-0.880698\pi$
$727$	−10.5939	−	32.6046i	−0.392905	−	1.20924i	0.537676	−	0.843152i	$-0.319302\pi$
$728$		0			0
$729$	−11.7691			−0.435892
$730$		0			0
$731$	−2.24441	−	1.63066i	−0.0830126	−	0.0603122i
$732$		0			0
$733$	−12.9989	+	40.0065i	−0.480125	+	1.47767i	0.358795	+	0.933416i	$0.383188\pi$
$733$	−12.9989	+	40.0065i	−0.480125	+	1.47767i	−0.838919	+	0.544256i	$0.816812\pi$
$734$		0			0
$735$	6.03254			0.222514
$736$		0			0
$737$	−27.4324			−1.01048
$738$		0			0
$739$	15.7018			0.577600			0.288800	−	0.957389i	$-0.406744\pi$
$739$	15.7018			0.577600			0.288800	+	0.957389i	$0.406744\pi$
$740$		0			0
$741$	9.32719			0.342643
$742$		0			0
$743$	8.97576	−	27.6246i	0.329289	−	1.01345i	−0.640179	−	0.768226i	$-0.721140\pi$
$743$	8.97576	−	27.6246i	0.329289	−	1.01345i	0.969467	−	0.245221i	$-0.0788604\pi$
$744$		0			0
$745$	2.19097	+	1.59183i	0.0802710	+	0.0583203i
$746$		0			0
$747$	12.5702			0.459920
$748$		0			0
$749$	−2.40544	−	7.40319i	−0.0878930	−	0.270507i
$750$		0			0
$751$	−12.6421	+	9.18504i	−0.461317	+	0.335167i	−0.794048	−	0.607855i	$-0.792030\pi$
$751$	−12.6421	+	9.18504i	−0.461317	+	0.335167i	0.332730	+	0.943022i	$0.392030\pi$
$752$		0			0
$753$	8.19638	−	25.2259i	0.298693	−	0.919281i
$754$		0			0
$755$	3.20566	+	9.86600i	0.116666	+	0.359061i
$756$		0			0
$757$	5.25239	+	3.81609i	0.190901	+	0.138698i	0.679131	−	0.734017i	$-0.262357\pi$
$757$	5.25239	+	3.81609i	0.190901	+	0.138698i	−0.488229	+	0.872715i	$0.662357\pi$
$758$		0			0
$759$	7.75562	+	5.63479i	0.281511	+	0.204530i
$760$		0			0
$761$	5.40426	−	3.92642i	0.195904	−	0.142333i	−0.485509	−	0.874232i	$-0.661366\pi$
$761$	5.40426	−	3.92642i	0.195904	−	0.142333i	0.681413	+	0.731899i	$0.261366\pi$
$762$		0			0
$763$	14.6941	+	10.6759i	0.531963	+	0.386493i
$764$		0			0
$765$	2.74290			0.0991698
$766$		0			0
$767$	0.0661995	−	0.203741i	0.00239033	−	0.00735667i
$768$		0			0
$769$	−0.565091	−	1.73917i	−0.0203777	−	0.0627162i	0.940351	−	0.340207i	$-0.110497\pi$
$769$	−0.565091	−	1.73917i	−0.0203777	−	0.0627162i	−0.960728	+	0.277491i	$0.910497\pi$
$770$		0			0
$771$	7.32286	+	22.5374i	0.263726	+	0.811666i
$772$		0			0
$773$	−11.9107	+	8.65367i	−0.428400	+	0.311251i	−0.781009	−	0.624520i	$-0.785295\pi$
$773$	−11.9107	+	8.65367i	−0.428400	+	0.311251i	0.352609	+	0.935771i	$0.385295\pi$
$774$		0			0
$775$	2.79543	−	8.60346i	0.100415	−	0.309046i
$776$		0			0
$777$	0.00566176	−	0.00411351i	0.000203114	−	0.000147571i
$778$		0			0
$779$	2.25850	−	20.9819i	0.0809193	−	0.751756i
$780$		0			0
$781$	3.22893	−	2.34596i	0.115540	−	0.0839449i
$782$		0			0
$783$	−0.765534	+	2.35607i	−0.0273580	+	0.0841991i
$784$		0			0
$785$	12.1139	−	8.80125i	0.432363	−	0.314130i
$786$		0			0
$787$	15.3528	+	47.2511i	0.547268	+	1.68432i	0.715535	+	0.698577i	$0.246183\pi$
$787$	15.3528	+	47.2511i	0.547268	+	1.68432i	−0.168266	+	0.985742i	$0.553817\pi$
$788$		0			0
$789$	9.22864	+	28.4028i	0.328548	+	1.01117i
$790$		0			0
$791$	−1.19207	+	3.66881i	−0.0423850	+	0.130448i
$792$		0			0
$793$	14.5756			0.517594
$794$		0			0
$795$	−20.6458	−	15.0001i	−0.732233	−	0.531998i
$796$		0			0
$797$	−3.47696	+	2.52616i	−0.123160	+	0.0894812i	−0.647660	−	0.761929i	$-0.724252\pi$
$797$	−3.47696	+	2.52616i	−0.123160	+	0.0894812i	0.524500	+	0.851411i	$0.324252\pi$
$798$		0			0
$799$	−1.36529	−	0.991945i	−0.0483007	−	0.0350925i
$800$		0			0
$801$	15.5062	+	11.2659i	0.547884	+	0.398061i
$802$		0			0
$803$	5.17771	+	15.9354i	0.182717	+	0.562346i
$804$		0			0
$805$	−0.612581	+	1.88533i	−0.0215907	+	0.0664492i
$806$		0			0
$807$	−34.2272	+	24.8675i	−1.20485	+	0.875378i
$808$		0			0
$809$	4.36904	+	13.4465i	0.153607	+	0.472755i	0.998017	−	0.0629431i	$-0.0200487\pi$
$809$	4.36904	+	13.4465i	0.153607	+	0.472755i	−0.844410	+	0.535698i	$0.820049\pi$
$810$		0			0
$811$	−42.7031			−1.49951			−0.749755	−	0.661716i	$-0.769828\pi$
$811$	−42.7031			−1.49951			−0.749755	+	0.661716i	$0.769828\pi$
$812$		0			0
$813$	−9.34301	−	6.78809i	−0.327674	−	0.238069i
$814$		0			0
$815$	11.0200	−	33.9160i	0.386013	−	1.18803i
$816$		0			0
$817$	−19.5923			−0.685448
$818$		0			0
$819$	2.75735			0.0963494
$820$		0			0
$821$	−9.35907			−0.326634			−0.163317	−	0.986574i	$-0.552219\pi$
$821$	−9.35907			−0.326634			−0.163317	+	0.986574i	$0.552219\pi$
$822$		0			0
$823$	52.2836			1.82249			0.911246	−	0.411862i	$-0.135121\pi$
$823$	52.2836			1.82249			0.911246	+	0.411862i	$0.135121\pi$
$824$		0			0
$825$	7.73322	−	23.8004i	0.269236	−	0.828624i
$826$		0			0
$827$	27.8139	+	20.2080i	0.967184	+	0.702700i	0.954808	−	0.297223i	$-0.0960606\pi$
$827$	27.8139	+	20.2080i	0.967184	+	0.702700i	0.0123757	+	0.999923i	$0.496061\pi$
$828$		0			0
$829$	−17.5609			−0.609915			−0.304957	−	0.952366i	$-0.598642\pi$
$829$	−17.5609			−0.609915			−0.304957	+	0.952366i	$0.598642\pi$
$830$		0			0
$831$	19.3526	+	59.5613i	0.671336	+	2.06616i
$832$		0			0
$833$	0.377548	−	0.274304i	0.0130813	−	0.00950409i
$834$		0			0
$835$	10.0067	−	30.7975i	0.346297	−	1.06579i
$836$		0			0
$837$	2.51685	+	7.74606i	0.0869949	+	0.267743i
$838$		0			0
$839$	35.7779	+	25.9942i	1.23519	+	0.897419i	0.997268	−	0.0738651i	$-0.0235334\pi$
$839$	35.7779	+	25.9942i	1.23519	+	0.897419i	0.237923	+	0.971284i	$0.423533\pi$
$840$		0			0
$841$	21.8693	+	15.8890i	0.754113	+	0.547895i
$842$		0			0
$843$	−37.6005	+	27.3184i	−1.29503	+	0.940895i
$844$		0			0
$845$	−24.4787	−	17.7848i	−0.842093	−	0.611817i
$846$		0			0
$847$	−20.1416			−0.692073
$848$		0			0
$849$	−2.01493	+	6.20133i	−0.0691523	+	0.212829i
$850$		0			0
$851$	0.000710652		0.00218716i	2.43608e−5		7.49750e-5i
$852$		0			0
$853$	−6.84738	−	21.0741i	−0.234450	−	0.721563i	−0.997194	−	0.0748620i	$-0.976148\pi$
$853$	−6.84738	−	21.0741i	−0.234450	−	0.721563i	0.762744	−	0.646701i	$-0.223852\pi$
$854$		0			0
$855$	15.6714	−	11.3860i	0.535952	−	0.389392i
$856$		0			0
$857$	10.6528	−	32.7860i	0.363893	−	1.11995i	−0.586778	−	0.809748i	$-0.699604\pi$
$857$	10.6528	−	32.7860i	0.363893	−	1.11995i	0.950671	−	0.310201i	$-0.100396\pi$
$858$		0			0
$859$	−39.4654	+	28.6733i	−1.34654	+	0.978319i	−0.347364	+	0.937730i	$0.612923\pi$
$859$	−39.4654	+	28.6733i	−1.34654	+	0.978319i	−0.999176	+	0.0405886i	$0.987077\pi$
$860$		0			0
$861$	1.56682	−	14.5561i	0.0533971	−	0.496070i
$862$		0			0
$863$	23.9508	−	17.4012i	0.815293	−	0.592345i	−0.100067	−	0.994981i	$-0.531906\pi$
$863$	23.9508	−	17.4012i	0.815293	−	0.592345i	0.915360	+	0.402636i	$0.131906\pi$
$864$		0			0
$865$	−19.9752	+	61.4773i	−0.679176	+	2.09029i
$866$		0			0
$867$	−31.0428	+	22.5539i	−1.05427	+	0.765971i
$868$		0			0
$869$	−18.8475	−	58.0065i	−0.639356	−	1.96774i
$870$		0			0
$871$	−1.88026	−	5.78684i	−0.0637101	−	0.196080i
$872$		0			0
$873$	2.80538	−	8.63406i	0.0949476	−	0.292219i
$874$		0			0
$875$	−8.01730			−0.271034
$876$		0			0
$877$	3.71389	+	2.69830i	0.125409	+	0.0911152i	0.648722	−	0.761026i	$-0.275304\pi$
$877$	3.71389	+	2.69830i	0.125409	+	0.0911152i	−0.523312	+	0.852141i	$0.675304\pi$
$878$		0			0
$879$	38.6692	−	28.0948i	1.30428	−	0.947615i
$880$		0			0
$881$	28.7784	+	20.9088i	0.969570	+	0.704434i	0.955354	−	0.295465i	$-0.0954745\pi$
$881$	28.7784	+	20.9088i	0.969570	+	0.704434i	0.0142168	+	0.999899i	$0.495475\pi$
$882$		0			0
$883$	14.1667	+	10.2927i	0.476749	+	0.346378i	0.800066	−	0.599912i	$-0.204798\pi$
$883$	14.1667	+	10.2927i	0.476749	+	0.346378i	−0.323317	+	0.946291i	$0.604798\pi$
$884$		0			0
$885$	−0.322636	−	0.992972i	−0.0108453	−	0.0333784i
$886$		0			0
$887$	−2.27284	+	6.99508i	−0.0763145	+	0.234872i	−0.981935	−	0.189216i	$-0.939405\pi$
$887$	−2.27284	+	6.99508i	−0.0763145	+	0.234872i	0.905621	+	0.424088i	$0.139405\pi$
$888$		0			0
$889$	3.48983	−	2.53551i	0.117045	−	0.0850384i
$890$		0			0
$891$	18.4871	+	56.8974i	0.619340	+	1.90613i
$892$		0			0
$893$	−11.9182			−0.398826
$894$		0			0
$895$	29.6707	+	21.5570i	0.991783	+	0.720573i
$896$		0			0
$897$	−0.657072	+	2.02226i	−0.0219390	+	0.0675213i
$898$		0			0
$899$	−6.47044			−0.215801
$900$		0			0
$901$	−1.97419			−0.0657698
$902$		0			0
$903$	−13.5920			−0.452314
$904$		0			0
$905$	4.62525			0.153749
$906$		0			0
$907$	3.96084	−	12.1902i	0.131517	−	0.404769i	−0.863515	−	0.504324i	$-0.831742\pi$
$907$	3.96084	−	12.1902i	0.131517	−	0.404769i	0.995032	+	0.0995548i	$0.0317418\pi$
$908$		0			0
$909$	−18.8619	−	13.7039i	−0.625608	−	0.454531i
$910$		0			0
$911$	−25.8819			−0.857505			−0.428753	−	0.903422i	$-0.641047\pi$
$911$	−25.8819			−0.857505			−0.428753	+	0.903422i	$0.641047\pi$
$912$		0			0
$913$	−9.73074	−	29.9481i	−0.322041	−	0.991139i
$914$		0			0
$915$	57.4701	−	41.7544i	1.89990	−	1.38036i
$916$		0			0
$917$	2.12252	−	6.53244i	0.0700917	−	0.215720i
$918$		0			0
$919$	−12.7771	−	39.3239i	−0.421478	−	1.29718i	−0.906327	−	0.422577i	$-0.861125\pi$
$919$	−12.7771	−	39.3239i	−0.421478	−	1.29718i	0.484849	−	0.874598i	$-0.338875\pi$
$920$		0			0
$921$	20.3683	+	14.7984i	0.671159	+	0.487625i
$922$		0			0
$923$	0.716194	+	0.520345i	0.0235738	+	0.0171274i
$924$		0			0
$925$	0.00485682	−	0.00352868i	0.000159691	−	0.000116022i
$926$		0			0
$927$	33.3093	+	24.2006i	1.09402	+	0.794852i
$928$		0			0
$929$	−20.1094			−0.659768			−0.329884	−	0.944022i	$-0.607010\pi$
$929$	−20.1094			−0.659768			−0.329884	+	0.944022i	$0.607010\pi$
$930$		0			0
$931$	1.01844	−	3.13445i	0.0333782	−	0.102727i
$932$		0			0
$933$	4.19795	+	12.9200i	0.137435	+	0.422981i
$934$		0			0
$935$	−2.12331	−	6.53488i	−0.0694397	−	0.213713i
$936$		0			0
$937$	22.2019	−	16.1307i	0.725306	−	0.526966i	−0.162769	−	0.986664i	$-0.552043\pi$
$937$	22.2019	−	16.1307i	0.725306	−	0.526966i	0.888075	+	0.459699i	$0.152043\pi$
$938$		0			0
$939$	5.87544	−	18.0827i	0.191738	−	0.590108i
$940$		0			0
$941$	8.37987	−	6.08833i	0.273176	−	0.198474i	−0.442759	−	0.896640i	$-0.646000\pi$
$941$	8.37987	−	6.08833i	0.273176	−	0.198474i	0.715936	+	0.698166i	$0.246000\pi$
$942$		0			0
$943$	4.39006	+	1.96779i	0.142960	+	0.0640800i
$944$		0			0
$945$	−3.76934	+	2.73859i	−0.122617	+	0.0890863i
$946$		0			0
$947$	6.98252	−	21.4900i	0.226901	−	0.698330i	−0.771192	−	0.636603i	$-0.780339\pi$
$947$	6.98252	−	21.4900i	0.226901	−	0.698330i	0.998093	−	0.0617275i	$-0.0196610\pi$
$948$		0			0
$949$	−3.00666	+	2.18447i	−0.0976004	+	0.0709109i
$950$		0			0
$951$	4.78012	+	14.7117i	0.155006	+	0.477059i
$952$		0			0
$953$	−14.1718	−	43.6162i	−0.459069	−	1.41287i	−0.866291	−	0.499539i	$-0.833503\pi$
$953$	−14.1718	−	43.6162i	−0.459069	−	1.41287i	0.407223	−	0.913329i	$-0.366497\pi$
$954$		0			0
$955$	−5.15358	+	15.8611i	−0.166766	+	0.513253i
$956$		0			0
$957$	−17.8997			−0.578614
$958$		0			0
$959$	3.33727	+	2.42467i	0.107766	+	0.0782967i
$960$		0			0
$961$	7.86943	−	5.71748i	0.253853	−	0.184435i
$962$		0			0
$963$	−14.0288	−	10.1925i	−0.452071	−	0.328449i
$964$		0			0
$965$	−55.4671	−	40.2992i	−1.78555	−	1.29728i
$966$		0			0
$967$	6.38564	+	19.6530i	0.205348	+	0.631997i	0.999699	+	0.0245373i	$0.00781126\pi$
$967$	6.38564	+	19.6530i	0.205348	+	0.631997i	−0.794351	+	0.607459i	$0.792189\pi$
$968$		0			0
$969$	1.08669	−	3.34449i	0.0349095	−	0.107440i
$970$		0			0
$971$	−34.8298	+	25.3054i	−1.11774	+	0.812088i	−0.983865	−	0.178910i	$-0.942743\pi$
$971$	−34.8298	+	25.3054i	−1.11774	+	0.812088i	−0.133877	+	0.990998i	$0.542743\pi$
$972$		0			0
$973$	5.12807	+	15.7826i	0.164398	+	0.505966i
$974$		0			0
$975$	5.55073			0.177766
$976$		0			0
$977$	−5.69896	−	4.14054i	−0.182326	−	0.132467i	0.492879	−	0.870098i	$-0.335945\pi$
$977$	−5.69896	−	4.14054i	−0.182326	−	0.132467i	−0.675205	+	0.737631i	$0.735945\pi$
$978$		0			0
$979$	14.8372	−	45.6641i	0.474198	−	1.45943i
$980$		0			0
$981$	40.4608			1.29182
$982$		0			0
$983$	−15.1451			−0.483054			−0.241527	−	0.970394i	$-0.577648\pi$
$983$	−15.1451			−0.483054			−0.241527	+	0.970394i	$0.577648\pi$
$984$		0			0
$985$	33.2146			1.05831
$986$		0			0
$987$	−8.26815			−0.263178
$988$		0			0
$989$	1.38022	−	4.24788i	0.0438884	−	0.135075i
$990$		0			0
$991$	−34.8468	−	25.3177i	−1.10695	−	0.804243i	−0.124766	−	0.992186i	$-0.539818\pi$
$991$	−34.8468	−	25.3177i	−1.10695	−	0.804243i	−0.982180	+	0.187943i	$0.939818\pi$
$992$		0			0
$993$	−24.2893			−0.770797
$994$		0			0
$995$	19.8275	+	61.0227i	0.628573	+	1.93455i
$996$		0			0
$997$	−41.5608	+	30.1957i	−1.31624	+	0.956307i	−0.316272	+	0.948668i	$0.602431\pi$
$997$	−41.5608	+	30.1957i	−1.31624	+	0.956307i	−0.999971	+	0.00763802i	$0.997569\pi$
$998$		0			0
$999$	−0.00167026	+	0.00514053i	−5.28447e−5	+	0.000162639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.365.1	✓	24
41.10	even	5	inner	1148.2.n.e.953.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.365.1	✓	24	1.1	even	1	trivial
1148.2.n.e.953.1	yes	24	41.10	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)

\(f(q)\)	\(=\)	\(q-2.28641 q^{3} +(-0.815322 + 2.50930i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.22766 q^{9} +O(q^{10})\)	\(q-2.28641 q^{3} +(-0.815322 + 2.50930i) q^{5} +(0.809017 + 0.587785i) q^{7} +2.22766 q^{9} +(-1.72446 - 5.30734i) q^{11} +(1.00138 - 0.727546i) q^{13} +(1.86416 - 5.73729i) q^{15} +(-0.144210 - 0.443834i) q^{17} +(-2.66632 - 1.93720i) q^{19} +(-1.84974 - 1.34392i) q^{21} +(0.607844 - 0.441625i) q^{23} +(-1.58676 - 1.15285i) q^{25} +1.76588 q^{27} +(-0.433514 + 1.33422i) q^{29} +(1.42526 + 4.38651i) q^{31} +(3.94282 + 12.1347i) q^{33} +(-2.13454 + 1.55083i) q^{35} +(-0.000945850 + 0.00291103i) q^{37} +(-2.28957 + 1.66347i) q^{39} +(3.18765 + 5.55328i) q^{41} +(4.80937 - 3.49421i) q^{43} +(-1.81626 + 5.58987i) q^{45} +(2.92558 - 2.12556i) q^{47} +(0.309017 + 0.951057i) q^{49} +(0.329724 + 1.01479i) q^{51} +(1.30725 - 4.02329i) q^{53} +14.7237 q^{55} +(6.09630 + 4.42922i) q^{57} +(0.140019 - 0.101730i) q^{59} +(9.52668 + 6.92154i) q^{61} +(1.80222 + 1.30939i) q^{63} +(1.00919 + 3.10595i) q^{65} +(1.51906 - 4.67519i) q^{67} +(-1.38978 + 1.00973i) q^{69} +(0.221011 + 0.680201i) q^{71} -3.00251 q^{73} +(3.62799 + 2.63589i) q^{75} +(1.72446 - 5.30734i) q^{77} +10.9295 q^{79} -10.7205 q^{81} +5.64278 q^{83} +1.23129 q^{85} +(0.991190 - 3.05057i) q^{87} +(6.96074 + 5.05728i) q^{89} +1.23778 q^{91} +(-3.25873 - 10.0294i) q^{93} +(7.03492 - 5.11117i) q^{95} +(1.25934 - 3.87584i) q^{97} +(-3.84151 - 11.8229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 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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