LMFDB - Embedded newform 1452.2.i.n.565.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1452,2,Mod(493,1452)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1452, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1452.493"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1452 = 2^{2} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1452.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,1,0,1,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5942783735$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			565.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	1452.565
Dual form			1452.2.i.n.1213.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.42705 - 1.76336i) q^{13} +(0.309017 + 0.951057i) q^{15} +(-5.66312 + 4.11450i) q^{17} +(-1.23607 + 3.80423i) q^{19} +2.00000 q^{21} -2.00000 q^{23} +(-1.23607 + 3.80423i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-0.927051 - 2.85317i) q^{29} +(-1.61803 - 1.17557i) q^{35} +(2.78115 + 8.55951i) q^{37} +(2.42705 - 1.76336i) q^{39} +(-2.78115 + 8.55951i) q^{41} +2.00000 q^{43} -1.00000 q^{45} +(-3.70820 + 11.4127i) q^{47} +(2.42705 - 1.76336i) q^{49} +(-2.16312 - 6.65740i) q^{51} +(10.5172 + 7.64121i) q^{53} +(-3.23607 - 2.35114i) q^{57} +(-1.85410 - 5.70634i) q^{59} +(-1.61803 + 1.17557i) q^{61} +(-0.618034 + 1.90211i) q^{63} -3.00000 q^{65} -14.0000 q^{67} +(0.618034 - 1.90211i) q^{69} +(4.85410 - 3.52671i) q^{71} +(-1.85410 - 5.70634i) q^{73} +(-3.23607 - 2.35114i) q^{75} +(-12.9443 - 9.40456i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-6.47214 + 4.70228i) q^{83} +(-2.16312 + 6.65740i) q^{85} +3.00000 q^{87} +1.00000 q^{89} +(-1.85410 + 5.70634i) q^{91} +(1.23607 + 3.80423i) q^{95} +(-5.66312 - 4.11450i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} + q^{5} + 2 q^{7} - q^{9} - 3 q^{13} - q^{15} - 7 q^{17} + 4 q^{19} + 8 q^{21} - 8 q^{23} + 4 q^{25} + q^{27} + 3 q^{29} - 2 q^{35} - 9 q^{37} + 3 q^{39} + 9 q^{41} + 8 q^{43} - 4 q^{45}+ \cdots - 7 q^{97}+O(q^{100}) $ 4 * q + q^3 + q^5 + 2 * q^7 - q^9 - 3 * q^13 - q^15 - 7 * q^17 + 4 * q^19 + 8 * q^21 - 8 * q^23 + 4 * q^25 + q^27 + 3 * q^29 - 2 * q^35 - 9 * q^37 + 3 * q^39 + 9 * q^41 + 8 * q^43 - 4 * q^45 + 12 * q^47 + 3 * q^49 + 7 * q^51 + 13 * q^53 - 4 * q^57 + 6 * q^59 - 2 * q^61 + 2 * q^63 - 12 * q^65 - 56 * q^67 - 2 * q^69 + 6 * q^71 + 6 * q^73 - 4 * q^75 - 16 * q^79 - q^81 - 8 * q^83 + 7 * q^85 + 12 * q^87 + 4 * q^89 + 6 * q^91 - 4 * q^95 - 7 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i	−0.392000	−	0.919965i	$-0.628217\pi$
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i	0.753804	+	0.657099i	$0.228217\pi$
$6$		0			0
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	−0.997305	−	0.0733714i	$-0.976624\pi$
$7$	−0.618034	−	1.90211i	−0.233595	−	0.718931i	0.763710	−	0.645560i	$-0.223376\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−2.42705	−	1.76336i	−0.673143	−	0.489067i	0.197933	−	0.980216i	$-0.436577\pi$
$13$	−2.42705	−	1.76336i	−0.673143	−	0.489067i	−0.871076	+	0.491149i	$0.836577\pi$
$14$		0			0
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$		0			0
$17$	−5.66312	+	4.11450i	−1.37351	+	0.997912i	−0.376054	+	0.926598i	$0.622719\pi$
$17$	−5.66312	+	4.11450i	−1.37351	+	0.997912i	−0.997454	+	0.0713144i	$0.977281\pi$
$18$		0			0
$19$	−1.23607	+	3.80423i	−0.283573	+	0.872749i	0.703249	+	0.710943i	$0.251732\pi$
$19$	−1.23607	+	3.80423i	−0.283573	+	0.872749i	−0.986823	+	0.161806i	$0.948268\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$	−2.00000			−0.417029			−0.208514	−	0.978019i	$-0.566863\pi$
$23$	−2.00000			−0.417029			−0.208514	+	0.978019i	$0.566863\pi$
$24$		0			0
$25$	−1.23607	+	3.80423i	−0.247214	+	0.760845i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	−0.927051	−	2.85317i	−0.172149	−	0.529820i	0.827343	−	0.561697i	$-0.189851\pi$
$29$	−0.927051	−	2.85317i	−0.172149	−	0.529820i	−0.999492	+	0.0318771i	$0.989851\pi$
$30$		0			0
$31$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$31$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.61803	−	1.17557i	−0.273498	−	0.198708i
$36$		0			0
$37$	2.78115	+	8.55951i	0.457219	+	1.40717i	0.868510	+	0.495671i	$0.165078\pi$
$37$	2.78115	+	8.55951i	0.457219	+	1.40717i	−0.411292	+	0.911504i	$0.634922\pi$
$38$		0			0
$39$	2.42705	−	1.76336i	0.388639	−	0.282363i
$40$		0			0
$41$	−2.78115	+	8.55951i	−0.434343	+	1.33677i	0.459415	+	0.888222i	$0.348059\pi$
$41$	−2.78115	+	8.55951i	−0.434343	+	1.33677i	−0.893758	+	0.448549i	$0.851941\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	−3.70820	+	11.4127i	−0.540897	+	1.66471i	0.189653	+	0.981851i	$0.439264\pi$
$47$	−3.70820	+	11.4127i	−0.540897	+	1.66471i	−0.730550	+	0.682859i	$0.760736\pi$
$48$		0			0
$49$	2.42705	−	1.76336i	0.346722	−	0.251908i
$50$		0			0
$51$	−2.16312	−	6.65740i	−0.302897	−	0.932222i
$52$		0			0
$53$	10.5172	+	7.64121i	1.44465	+	1.04960i	0.987045	+	0.160446i	$0.0512932\pi$
$53$	10.5172	+	7.64121i	1.44465	+	1.04960i	0.457607	+	0.889155i	$0.348707\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.23607	−	2.35114i	−0.428628	−	0.311416i
$58$		0			0
$59$	−1.85410	−	5.70634i	−0.241384	−	0.742902i	−0.996210	−	0.0869778i	$-0.972279\pi$
$59$	−1.85410	−	5.70634i	−0.241384	−	0.742902i	0.754827	−	0.655924i	$-0.227721\pi$
$60$		0			0
$61$	−1.61803	+	1.17557i	−0.207168	+	0.150516i	−0.686531	−	0.727100i	$-0.740868\pi$
$61$	−1.61803	+	1.17557i	−0.207168	+	0.150516i	0.479363	+	0.877616i	$0.340868\pi$
$62$		0			0
$63$	−0.618034	+	1.90211i	−0.0778650	+	0.239644i
$64$		0			0
$65$	−3.00000			−0.372104
$66$		0			0
$67$	−14.0000			−1.71037			−0.855186	−	0.518321i	$-0.826557\pi$
$67$	−14.0000			−1.71037			−0.855186	+	0.518321i	$0.826557\pi$
$68$		0			0
$69$	0.618034	−	1.90211i	0.0744025	−	0.228988i
$70$		0			0
$71$	4.85410	−	3.52671i	0.576076	−	0.418544i	−0.261231	−	0.965276i	$-0.584129\pi$
$71$	4.85410	−	3.52671i	0.576076	−	0.418544i	0.837307	+	0.546733i	$0.184129\pi$
$72$		0			0
$73$	−1.85410	−	5.70634i	−0.217006	−	0.667876i	−0.999005	−	0.0445966i	$-0.985800\pi$
$73$	−1.85410	−	5.70634i	−0.217006	−	0.667876i	0.781999	−	0.623280i	$-0.214200\pi$
$74$		0			0
$75$	−3.23607	−	2.35114i	−0.373669	−	0.271486i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−12.9443	−	9.40456i	−1.45634	−	1.05810i	−0.984296	−	0.176523i	$-0.943515\pi$
$79$	−12.9443	−	9.40456i	−1.45634	−	1.05810i	−0.472048	−	0.881573i	$-0.656485\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−6.47214	+	4.70228i	−0.710409	+	0.516143i	−0.883306	−	0.468798i	$-0.844687\pi$
$83$	−6.47214	+	4.70228i	−0.710409	+	0.516143i	0.172896	+	0.984940i	$0.444687\pi$
$84$		0			0
$85$	−2.16312	+	6.65740i	−0.234623	+	0.722096i
$86$		0			0
$87$	3.00000			0.321634
$88$		0			0
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	−1.85410	+	5.70634i	−0.194363	+	0.598187i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.23607	+	3.80423i	0.126818	+	0.390305i
$96$		0			0
$97$	−5.66312	−	4.11450i	−0.575003	−	0.417764i	0.261916	−	0.965091i	$-0.415646\pi$
$97$	−5.66312	−	4.11450i	−0.575003	−	0.417764i	−0.836919	+	0.547327i	$0.815646\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.61803	+	1.17557i	0.161000	+	0.116974i	0.665368	−	0.746515i	$-0.268274\pi$
$101$	1.61803	+	1.17557i	0.161000	+	0.116974i	−0.504368	+	0.863489i	$0.668274\pi$
$102$		0			0
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	0.817211	−	0.576339i	$-0.195519\pi$
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	−0.999901	+	0.0140765i	$0.995519\pi$
$104$		0			0
$105$	1.61803	−	1.17557i	0.157904	−	0.114724i
$106$		0			0
$107$	4.32624	−	13.3148i	0.418233	−	1.28719i	−0.491094	−	0.871107i	$-0.663403\pi$
$107$	4.32624	−	13.3148i	0.418233	−	1.28719i	0.909327	−	0.416083i	$-0.136597\pi$
$108$		0			0
$109$	3.00000			0.287348			0.143674	−	0.989625i	$-0.454108\pi$
$109$	3.00000			0.287348			0.143674	+	0.989625i	$0.454108\pi$
$110$		0			0
$111$	−9.00000			−0.854242
$112$		0			0
$113$	−5.87132	+	18.0701i	−0.552328	+	1.69989i	0.150571	+	0.988599i	$0.451889\pi$
$113$	−5.87132	+	18.0701i	−0.552328	+	1.69989i	−0.702898	+	0.711290i	$0.748111\pi$
$114$		0			0
$115$	−1.61803	+	1.17557i	−0.150882	+	0.109623i
$116$		0			0
$117$	0.927051	+	2.85317i	0.0857059	+	0.263776i
$118$		0			0
$119$	11.3262	+	8.22899i	1.03827	+	0.754351i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−7.28115	−	5.29007i	−0.656519	−	0.476989i
$124$		0			0
$125$	2.78115	+	8.55951i	0.248754	+	0.765586i
$126$		0			0
$127$	9.70820	−	7.05342i	0.861464	−	0.625890i	−0.0668190	−	0.997765i	$-0.521285\pi$
$127$	9.70820	−	7.05342i	0.861464	−	0.625890i	0.928283	+	0.371875i	$0.121285\pi$
$128$		0			0
$129$	−0.618034	+	1.90211i	−0.0544149	+	0.167472i
$130$		0			0
$131$	−22.0000			−1.92215			−0.961074	−	0.276289i	$-0.910895\pi$
$131$	−22.0000			−1.92215			−0.961074	+	0.276289i	$0.910895\pi$
$132$		0			0
$133$	8.00000			0.693688
$134$		0			0
$135$	0.309017	−	0.951057i	0.0265959	−	0.0818539i
$136$		0			0
$137$	8.09017	−	5.87785i	0.691190	−	0.502179i	−0.185861	−	0.982576i	$-0.559507\pi$
$137$	8.09017	−	5.87785i	0.691190	−	0.502179i	0.877051	+	0.480397i	$0.159507\pi$
$138$		0			0
$139$	−4.32624	−	13.3148i	−0.366947	−	1.12935i	−0.948753	−	0.316018i	$-0.897654\pi$
$139$	−4.32624	−	13.3148i	−0.366947	−	1.12935i	0.581806	−	0.813327i	$-0.302346\pi$
$140$		0			0
$141$	−9.70820	−	7.05342i	−0.817578	−	0.594005i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−2.42705	−	1.76336i	−0.201556	−	0.146439i
$146$		0			0
$147$	0.927051	+	2.85317i	0.0764619	+	0.235325i
$148$		0			0
$149$	−10.5172	+	7.64121i	−0.861604	+	0.625992i	−0.928321	−	0.371780i	$-0.878748\pi$
$149$	−10.5172	+	7.64121i	−0.861604	+	0.625992i	0.0667166	+	0.997772i	$0.478748\pi$
$150$		0			0
$151$	2.47214	−	7.60845i	0.201180	−	0.619167i	−0.798669	−	0.601770i	$-0.794462\pi$
$151$	2.47214	−	7.60845i	0.201180	−	0.619167i	0.999849	−	0.0173966i	$-0.00553779\pi$
$152$		0			0
$153$	7.00000			0.565916
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.32624	−	13.3148i	0.345271	−	1.06264i	−0.616167	−	0.787616i	$-0.711315\pi$
$157$	4.32624	−	13.3148i	0.345271	−	1.06264i	0.961438	−	0.275020i	$-0.0886846\pi$
$158$		0			0
$159$	−10.5172	+	7.64121i	−0.834070	+	0.605987i
$160$		0			0
$161$	1.23607	+	3.80423i	0.0974158	+	0.299815i
$162$		0			0
$163$	1.61803	+	1.17557i	0.126734	+	0.0920778i	0.649347	−	0.760493i	$-0.275042\pi$
$163$	1.61803	+	1.17557i	0.126734	+	0.0920778i	−0.522612	+	0.852570i	$0.675042\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	14.5623	+	10.5801i	1.12687	+	0.818715i	0.985236	−	0.171204i	$-0.0547658\pi$
$167$	14.5623	+	10.5801i	1.12687	+	0.818715i	0.141630	+	0.989920i	$0.454766\pi$
$168$		0			0
$169$	−1.23607	−	3.80423i	−0.0950822	−	0.292633i
$170$		0			0
$171$	3.23607	−	2.35114i	0.247468	−	0.179796i
$172$		0			0
$173$	−4.32624	+	13.3148i	−0.328918	+	1.01230i	0.640723	+	0.767772i	$0.278635\pi$
$173$	−4.32624	+	13.3148i	−0.328918	+	1.01230i	−0.969641	+	0.244533i	$0.921365\pi$
$174$		0			0
$175$	8.00000			0.604743
$176$		0			0
$177$	6.00000			0.450988
$178$		0			0
$179$	2.47214	−	7.60845i	0.184776	−	0.568682i	−0.815168	−	0.579224i	$-0.803356\pi$
$179$	2.47214	−	7.60845i	0.184776	−	0.568682i	0.999944	+	0.0105417i	$0.00335560\pi$
$180$		0			0
$181$	−10.5172	+	7.64121i	−0.781739	+	0.567967i	−0.905500	−	0.424345i	$-0.860504\pi$
$181$	−10.5172	+	7.64121i	−0.781739	+	0.567967i	0.123762	+	0.992312i	$0.460504\pi$
$182$		0			0
$183$	−0.618034	−	1.90211i	−0.0456864	−	0.140608i
$184$		0			0
$185$	7.28115	+	5.29007i	0.535321	+	0.388933i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.61803	−	1.17557i	−0.117695	−	0.0855102i
$190$		0			0
$191$	−3.70820	−	11.4127i	−0.268316	−	0.825792i	−0.990911	−	0.134520i	$-0.957051\pi$
$191$	−3.70820	−	11.4127i	−0.268316	−	0.825792i	0.722595	−	0.691272i	$-0.242949\pi$
$192$		0			0
$193$	−4.04508	+	2.93893i	−0.291172	+	0.211549i	−0.723775	−	0.690036i	$-0.757595\pi$
$193$	−4.04508	+	2.93893i	−0.291172	+	0.211549i	0.432604	+	0.901584i	$0.357595\pi$
$194$		0			0
$195$	0.927051	−	2.85317i	0.0663875	−	0.204320i
$196$		0			0
$197$	−7.00000			−0.498729			−0.249365	−	0.968410i	$-0.580222\pi$
$197$	−7.00000			−0.498729			−0.249365	+	0.968410i	$0.580222\pi$
$198$		0			0
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$		0			0
$201$	4.32624	−	13.3148i	0.305149	−	0.939153i
$202$		0			0
$203$	−4.85410	+	3.52671i	−0.340691	+	0.247527i
$204$		0			0
$205$	2.78115	+	8.55951i	0.194244	+	0.597822i
$206$		0			0
$207$	1.61803	+	1.17557i	0.112461	+	0.0817078i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	11.3262	+	8.22899i	0.779730	+	0.566507i	0.904898	−	0.425628i	$-0.139947\pi$
$211$	11.3262	+	8.22899i	0.779730	+	0.566507i	−0.125168	+	0.992136i	$0.539947\pi$
$212$		0			0
$213$	1.85410	+	5.70634i	0.127041	+	0.390992i
$214$		0			0
$215$	1.61803	−	1.17557i	0.110349	−	0.0801732i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.00000			0.405442
$220$		0			0
$221$	21.0000			1.41261
$222$		0			0
$223$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$223$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$224$		0			0
$225$	3.23607	−	2.35114i	0.215738	−	0.156743i
$226$		0			0
$227$	5.56231	+	17.1190i	0.369183	+	1.13623i	0.947320	+	0.320289i	$0.103780\pi$
$227$	5.56231	+	17.1190i	0.369183	+	1.13623i	−0.578137	+	0.815940i	$0.696220\pi$
$228$		0			0
$229$	−23.4615	−	17.0458i	−1.55038	−	1.12642i	−0.943380	−	0.331714i	$-0.892373\pi$
$229$	−23.4615	−	17.0458i	−1.55038	−	1.12642i	−0.606999	−	0.794703i	$-0.707627\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.2254	+	14.6946i	1.32501	+	0.962677i	0.999855	+	0.0170171i	$0.00541696\pi$
$233$	20.2254	+	14.6946i	1.32501	+	0.962677i	0.325156	+	0.945660i	$0.394583\pi$
$234$		0			0
$235$	3.70820	+	11.4127i	0.241897	+	0.744481i
$236$		0			0
$237$	12.9443	−	9.40456i	0.840821	−	0.610892i
$238$		0			0
$239$	4.94427	−	15.2169i	0.319818	−	0.984300i	−0.653907	−	0.756575i	$-0.726871\pi$
$239$	4.94427	−	15.2169i	0.319818	−	0.984300i	0.973726	−	0.227725i	$-0.0731287\pi$
$240$		0			0
$241$	26.0000			1.67481			0.837404	−	0.546585i	$-0.184072\pi$
$241$	26.0000			1.67481			0.837404	+	0.546585i	$0.184072\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	0.927051	−	2.85317i	0.0592271	−	0.182282i
$246$		0			0
$247$	9.70820	−	7.05342i	0.617718	−	0.448799i
$248$		0			0
$249$	−2.47214	−	7.60845i	−0.156665	−	0.482166i
$250$		0			0
$251$	8.09017	+	5.87785i	0.510647	+	0.371007i	0.813069	−	0.582167i	$-0.197795\pi$
$251$	8.09017	+	5.87785i	0.510647	+	0.371007i	−0.302422	+	0.953174i	$0.597795\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−5.66312	−	4.11450i	−0.354638	−	0.257660i
$256$		0			0
$257$	−2.16312	−	6.65740i	−0.134932	−	0.415277i	0.860648	−	0.509201i	$-0.170059\pi$
$257$	−2.16312	−	6.65740i	−0.134932	−	0.415277i	−0.995579	+	0.0939239i	$0.970059\pi$
$258$		0			0
$259$	14.5623	−	10.5801i	0.904858	−	0.657418i
$260$		0			0
$261$	−0.927051	+	2.85317i	−0.0573830	+	0.176607i
$262$		0			0
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$	13.0000			0.798584
$266$		0			0
$267$	−0.309017	+	0.951057i	−0.0189115	+	0.0582037i
$268$		0			0
$269$	0.809017	−	0.587785i	0.0493266	−	0.0358379i	−0.562849	−	0.826560i	$-0.690295\pi$
$269$	0.809017	−	0.587785i	0.0493266	−	0.0358379i	0.612175	+	0.790722i	$0.290295\pi$
$270$		0			0
$271$	6.79837	+	20.9232i	0.412972	+	1.27100i	0.914052	+	0.405596i	$0.132936\pi$
$271$	6.79837	+	20.9232i	0.412972	+	1.27100i	−0.501081	+	0.865401i	$0.667064\pi$
$272$		0			0
$273$	−4.85410	−	3.52671i	−0.293784	−	0.213446i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.7533	+	9.99235i	0.826355	+	0.600382i	0.918526	−	0.395361i	$-0.129381\pi$
$277$	13.7533	+	9.99235i	0.826355	+	0.600382i	−0.0921707	+	0.995743i	$0.529381\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−17.7984	+	12.9313i	−1.06176	+	0.771415i	−0.974414	−	0.224763i	$-0.927839\pi$
$281$	−17.7984	+	12.9313i	−1.06176	+	0.771415i	−0.0873484	+	0.996178i	$0.527839\pi$
$282$		0			0
$283$	4.32624	−	13.3148i	0.257168	−	0.791482i	−0.736227	−	0.676735i	$-0.763394\pi$
$283$	4.32624	−	13.3148i	0.257168	−	0.791482i	0.993395	−	0.114747i	$-0.0366058\pi$
$284$		0			0
$285$	−4.00000			−0.236940
$286$		0			0
$287$	18.0000			1.06251
$288$		0			0
$289$	9.88854	−	30.4338i	0.581679	−	1.79022i
$290$		0			0
$291$	5.66312	−	4.11450i	0.331978	−	0.241196i
$292$		0			0
$293$	5.25329	+	16.1680i	0.306900	+	0.944542i	0.978961	+	0.204046i	$0.0654093\pi$
$293$	5.25329	+	16.1680i	0.306900	+	0.944542i	−0.672061	+	0.740496i	$0.734591\pi$
$294$		0			0
$295$	−4.85410	−	3.52671i	−0.282617	−	0.205333i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.85410	+	3.52671i	0.280720	+	0.203955i
$300$		0			0
$301$	−1.23607	−	3.80423i	−0.0712458	−	0.219272i
$302$		0			0
$303$	−1.61803	+	1.17557i	−0.0929536	+	0.0675348i
$304$		0			0
$305$	−0.618034	+	1.90211i	−0.0353885	+	0.108915i
$306$		0			0
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$		0			0
$311$	8.65248	−	26.6296i	0.490637	−	1.51003i	−0.333011	−	0.942923i	$-0.608065\pi$
$311$	8.65248	−	26.6296i	0.490637	−	1.51003i	0.823648	−	0.567102i	$-0.191935\pi$
$312$		0			0
$313$	0.809017	−	0.587785i	0.0457283	−	0.0332236i	−0.564686	−	0.825306i	$-0.691003\pi$
$313$	0.809017	−	0.587785i	0.0457283	−	0.0332236i	0.610415	+	0.792082i	$0.291003\pi$
$314$		0			0
$315$	0.618034	+	1.90211i	0.0348223	+	0.107172i
$316$		0			0
$317$	4.85410	+	3.52671i	0.272634	+	0.198080i	0.715698	−	0.698410i	$-0.246109\pi$
$317$	4.85410	+	3.52671i	0.272634	+	0.198080i	−0.443064	+	0.896490i	$0.646109\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	11.3262	+	8.22899i	0.632169	+	0.459298i
$322$		0			0
$323$	−8.65248	−	26.6296i	−0.481437	−	1.48171i
$324$		0			0
$325$	9.70820	−	7.05342i	0.538514	−	0.391254i
$326$		0			0
$327$	−0.927051	+	2.85317i	−0.0512660	+	0.157781i
$328$		0			0
$329$	24.0000			1.32316
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		0			0
$333$	2.78115	−	8.55951i	0.152406	−	0.469058i
$334$		0			0
$335$	−11.3262	+	8.22899i	−0.618818	+	0.449598i
$336$		0			0
$337$	−4.63525	−	14.2658i	−0.252498	−	0.777110i	−0.994312	−	0.106504i	$-0.966034\pi$
$337$	−4.63525	−	14.2658i	−0.252498	−	0.777110i	0.741814	−	0.670606i	$-0.233966\pi$
$338$		0			0
$339$	−15.3713	−	11.1679i	−0.834856	−	0.606558i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−16.1803	−	11.7557i	−0.873656	−	0.634748i
$344$		0			0
$345$	−0.618034	−	1.90211i	−0.0332738	−	0.102406i
$346$		0			0
$347$	6.47214	−	4.70228i	0.347442	−	0.252432i	−0.400353	−	0.916361i	$-0.631112\pi$
$347$	6.47214	−	4.70228i	0.347442	−	0.252432i	0.747795	+	0.663929i	$0.231112\pi$
$348$		0			0
$349$	0.927051	−	2.85317i	0.0496239	−	0.152727i	−0.923174	−	0.384383i	$-0.874414\pi$
$349$	0.927051	−	2.85317i	0.0496239	−	0.152727i	0.972798	+	0.231656i	$0.0744144\pi$
$350$		0			0
$351$	−3.00000			−0.160128
$352$		0			0
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$		0			0
$355$	1.85410	−	5.70634i	0.0984055	−	0.302861i
$356$		0			0
$357$	−11.3262	+	8.22899i	−0.599448	+	0.435525i
$358$		0			0
$359$	9.27051	+	28.5317i	0.489279	+	1.50585i	0.825687	+	0.564129i	$0.190788\pi$
$359$	9.27051	+	28.5317i	0.489279	+	1.50585i	−0.336408	+	0.941716i	$0.609212\pi$
$360$		0			0
$361$	2.42705	+	1.76336i	0.127740	+	0.0928082i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.85410	−	3.52671i	−0.254075	−	0.184597i
$366$		0			0
$367$	−3.09017	−	9.51057i	−0.161306	−	0.496447i	0.837440	−	0.546530i	$-0.184052\pi$
$367$	−3.09017	−	9.51057i	−0.161306	−	0.496447i	−0.998745	+	0.0500825i	$0.984052\pi$
$368$		0			0
$369$	7.28115	−	5.29007i	0.379042	−	0.275390i
$370$		0			0
$371$	8.03444	−	24.7275i	0.417127	−	1.28379i
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$		0			0
$375$	−9.00000			−0.464758
$376$		0			0
$377$	−2.78115	+	8.55951i	−0.143237	+	0.440837i
$378$		0			0
$379$	−21.0344	+	15.2824i	−1.08047	+	0.785005i	−0.977764	−	0.209707i	$-0.932749\pi$
$379$	−21.0344	+	15.2824i	−1.08047	+	0.785005i	−0.102702	+	0.994712i	$0.532749\pi$
$380$		0			0
$381$	3.70820	+	11.4127i	0.189977	+	0.584689i
$382$		0			0
$383$	8.09017	+	5.87785i	0.413388	+	0.300344i	0.774972	−	0.631995i	$-0.217764\pi$
$383$	8.09017	+	5.87785i	0.413388	+	0.300344i	−0.361584	+	0.932340i	$0.617764\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.61803	−	1.17557i	−0.0822493	−	0.0597576i
$388$		0			0
$389$	4.63525	+	14.2658i	0.235017	+	0.723307i	0.997119	+	0.0758507i	$0.0241672\pi$
$389$	4.63525	+	14.2658i	0.235017	+	0.723307i	−0.762102	+	0.647456i	$0.775833\pi$
$390$		0			0
$391$	11.3262	−	8.22899i	0.572792	−	0.416158i
$392$		0			0
$393$	6.79837	−	20.9232i	0.342933	−	1.05544i
$394$		0			0
$395$	−16.0000			−0.805047
$396$		0			0
$397$	25.0000			1.25471			0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000			1.25471			0.627357	+	0.778732i	$0.284137\pi$
$398$		0			0
$399$	−2.47214	+	7.60845i	−0.123762	+	0.380899i
$400$		0			0
$401$	8.89919	−	6.46564i	0.444404	−	0.322879i	−0.342978	−	0.939343i	$-0.611436\pi$
$401$	8.89919	−	6.46564i	0.444404	−	0.322879i	0.787382	+	0.616465i	$0.211436\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	25.0795	+	18.2213i	1.24010	+	0.900987i	0.997605	−	0.0691646i	$-0.0220334\pi$
$409$	25.0795	+	18.2213i	1.24010	+	0.900987i	0.242498	+	0.970152i	$0.422033\pi$
$410$		0			0
$411$	3.09017	+	9.51057i	0.152427	+	0.469122i
$412$		0			0
$413$	−9.70820	+	7.05342i	−0.477709	+	0.347076i
$414$		0			0
$415$	−2.47214	+	7.60845i	−0.121352	+	0.373484i
$416$		0			0
$417$	14.0000			0.685583
$418$		0			0
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$		0			0
$421$	1.54508	−	4.75528i	0.0753028	−	0.231758i	−0.906319	−	0.422594i	$-0.861120\pi$
$421$	1.54508	−	4.75528i	0.0753028	−	0.231758i	0.981622	+	0.190835i	$0.0611197\pi$
$422$		0			0
$423$	9.70820	−	7.05342i	0.472029	−	0.342949i
$424$		0			0
$425$	−8.65248	−	26.6296i	−0.419707	−	1.29172i
$426$		0			0
$427$	3.23607	+	2.35114i	0.156604	+	0.113780i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	24.2705	+	17.6336i	1.16907	+	0.849379i	0.990897	−	0.134621i	$-0.0429816\pi$
$431$	24.2705	+	17.6336i	1.16907	+	0.849379i	0.178172	+	0.983999i	$0.442982\pi$
$432$		0			0
$433$	3.39919	+	10.4616i	0.163354	+	0.502753i	0.998911	−	0.0466507i	$-0.0148548\pi$
$433$	3.39919	+	10.4616i	0.163354	+	0.502753i	−0.835557	+	0.549404i	$0.814855\pi$
$434$		0			0
$435$	2.42705	−	1.76336i	0.116368	−	0.0845464i
$436$		0			0
$437$	2.47214	−	7.60845i	0.118258	−	0.363962i
$438$		0			0
$439$	−4.00000			−0.190910			−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000			−0.190910			−0.0954548	+	0.995434i	$0.530431\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−0.618034	+	1.90211i	−0.0293637	+	0.0903721i	−0.964664	−	0.263482i	$-0.915129\pi$
$443$	−0.618034	+	1.90211i	−0.0293637	+	0.0903721i	0.935301	+	0.353854i	$0.115129\pi$
$444$		0			0
$445$	0.809017	−	0.587785i	0.0383511	−	0.0278637i
$446$		0			0
$447$	−4.01722	−	12.3637i	−0.190008	−	0.584785i
$448$		0			0
$449$	−23.4615	−	17.0458i	−1.10722	−	0.804440i	−0.124993	−	0.992158i	$-0.539891\pi$
$449$	−23.4615	−	17.0458i	−1.10722	−	0.804440i	−0.982223	+	0.187718i	$0.939891\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	6.47214	+	4.70228i	0.304087	+	0.220932i
$454$		0			0
$455$	1.85410	+	5.70634i	0.0869216	+	0.267517i
$456$		0			0
$457$	5.66312	−	4.11450i	0.264910	−	0.192468i	−0.447399	−	0.894334i	$-0.647650\pi$
$457$	5.66312	−	4.11450i	0.264910	−	0.192468i	0.712309	+	0.701866i	$0.247650\pi$
$458$		0			0
$459$	−2.16312	+	6.65740i	−0.100966	+	0.310741i
$460$		0			0
$461$	−11.0000			−0.512321			−0.256161	−	0.966634i	$-0.582458\pi$
$461$	−11.0000			−0.512321			−0.256161	+	0.966634i	$0.582458\pi$
$462$		0			0
$463$	−30.0000			−1.39422			−0.697109	−	0.716965i	$-0.745531\pi$
$463$	−30.0000			−1.39422			−0.697109	+	0.716965i	$0.745531\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−24.2705	+	17.6336i	−1.12311	+	0.815984i	−0.984677	−	0.174389i	$-0.944205\pi$
$467$	−24.2705	+	17.6336i	−1.12311	+	0.815984i	−0.138428	+	0.990372i	$0.544205\pi$
$468$		0			0
$469$	8.65248	+	26.6296i	0.399534	+	1.22964i
$470$		0			0
$471$	11.3262	+	8.22899i	0.521885	+	0.379172i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−12.9443	−	9.40456i	−0.593924	−	0.431511i
$476$		0			0
$477$	−4.01722	−	12.3637i	−0.183936	−	0.566097i
$478$		0			0
$479$	24.2705	−	17.6336i	1.10895	−	0.805698i	0.126450	−	0.991973i	$-0.459642\pi$
$479$	24.2705	−	17.6336i	1.10895	−	0.805698i	0.982498	+	0.186275i	$0.0596416\pi$
$480$		0			0
$481$	8.34346	−	25.6785i	0.380429	−	1.17084i
$482$		0			0
$483$	−4.00000			−0.182006
$484$		0			0
$485$	−7.00000			−0.317854
$486$		0			0
$487$	0.618034	−	1.90211i	0.0280058	−	0.0861930i	−0.936077	−	0.351796i	$-0.885571\pi$
$487$	0.618034	−	1.90211i	0.0280058	−	0.0861930i	0.964082	+	0.265603i	$0.0855711\pi$
$488$		0			0
$489$	−1.61803	+	1.17557i	−0.0731700	+	0.0531611i
$490$		0			0
$491$	−2.47214	−	7.60845i	−0.111566	−	0.343365i	0.879649	−	0.475623i	$-0.157777\pi$
$491$	−2.47214	−	7.60845i	−0.111566	−	0.343365i	−0.991215	+	0.132258i	$0.957777\pi$
$492$		0			0
$493$	16.9894	+	12.3435i	0.765162	+	0.555923i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.70820	−	7.05342i	−0.435472	−	0.316389i
$498$		0			0
$499$	−3.09017	−	9.51057i	−0.138335	−	0.425751i	0.857759	−	0.514052i	$-0.171856\pi$
$499$	−3.09017	−	9.51057i	−0.138335	−	0.425751i	−0.996094	+	0.0883009i	$0.971856\pi$
$500$		0			0
$501$	−14.5623	+	10.5801i	−0.650596	+	0.472686i
$502$		0			0
$503$	−4.32624	+	13.3148i	−0.192897	+	0.593677i	0.807097	+	0.590418i	$0.201037\pi$
$503$	−4.32624	+	13.3148i	−0.192897	+	0.593677i	−0.999995	+	0.00325871i	$0.998963\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$		0			0
$507$	4.00000			0.177646
$508$		0			0
$509$	0.618034	−	1.90211i	0.0273939	−	0.0843097i	−0.936425	−	0.350868i	$-0.885887\pi$
$509$	0.618034	−	1.90211i	0.0273939	−	0.0843097i	0.963819	+	0.266558i	$0.0858865\pi$
$510$		0			0
$511$	−9.70820	+	7.05342i	−0.429466	+	0.312025i
$512$		0			0
$513$	1.23607	+	3.80423i	0.0545737	+	0.167961i
$514$		0			0
$515$	−4.85410	−	3.52671i	−0.213897	−	0.155405i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−11.3262	−	8.22899i	−0.497167	−	0.361213i
$520$		0			0
$521$	−9.27051	−	28.5317i	−0.406148	−	1.25000i	−0.919933	−	0.392077i	$-0.871757\pi$
$521$	−9.27051	−	28.5317i	−0.406148	−	1.25000i	0.513784	−	0.857920i	$-0.328243\pi$
$522$		0			0
$523$	−32.3607	+	23.5114i	−1.41503	+	1.02808i	−0.422467	+	0.906378i	$0.638836\pi$
$523$	−32.3607	+	23.5114i	−1.41503	+	1.02808i	−0.992566	+	0.121704i	$0.961164\pi$
$524$		0			0
$525$	−2.47214	+	7.60845i	−0.107893	+	0.332060i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−19.0000			−0.826087
$530$		0			0
$531$	−1.85410	+	5.70634i	−0.0804612	+	0.247634i
$532$		0			0
$533$	21.8435	−	15.8702i	0.946145	−	0.687415i
$534$		0			0
$535$	−4.32624	−	13.3148i	−0.187040	−	0.575649i
$536$		0			0
$537$	6.47214	+	4.70228i	0.279293	+	0.202918i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−21.0344	−	15.2824i	−0.904341	−	0.657042i	0.0352361	−	0.999379i	$-0.488782\pi$
$541$	−21.0344	−	15.2824i	−0.904341	−	0.657042i	−0.939577	+	0.342337i	$0.888782\pi$
$542$		0			0
$543$	−4.01722	−	12.3637i	−0.172395	−	0.530579i
$544$		0			0
$545$	2.42705	−	1.76336i	0.103963	−	0.0755339i
$546$		0			0
$547$	−2.47214	+	7.60845i	−0.105701	+	0.325314i	−0.989894	−	0.141807i	$-0.954709\pi$
$547$	−2.47214	+	7.60845i	−0.105701	+	0.325314i	0.884193	+	0.467121i	$0.154709\pi$
$548$		0			0
$549$	2.00000			0.0853579
$550$		0			0
$551$	12.0000			0.511217
$552$		0			0
$553$	−9.88854	+	30.4338i	−0.420504	+	1.29418i
$554$		0			0
$555$	−7.28115	+	5.29007i	−0.309068	+	0.224551i
$556$		0			0
$557$	−5.56231	−	17.1190i	−0.235682	−	0.725356i	−0.997030	−	0.0770122i	$-0.975462\pi$
$557$	−5.56231	−	17.1190i	−0.235682	−	0.725356i	0.761348	−	0.648344i	$-0.224538\pi$
$558$		0			0
$559$	−4.85410	−	3.52671i	−0.205307	−	0.149164i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.61803	−	1.17557i	−0.0681920	−	0.0495444i	0.553167	−	0.833070i	$-0.313419\pi$
$563$	−1.61803	−	1.17557i	−0.0681920	−	0.0495444i	−0.621359	+	0.783526i	$0.713419\pi$
$564$		0			0
$565$	5.87132	+	18.0701i	0.247008	+	0.760214i
$566$		0			0
$567$	1.61803	−	1.17557i	0.0679510	−	0.0493693i
$568$		0			0
$569$	−6.79837	+	20.9232i	−0.285003	+	0.877148i	0.701395	+	0.712773i	$0.252561\pi$
$569$	−6.79837	+	20.9232i	−0.285003	+	0.877148i	−0.986398	+	0.164375i	$0.947439\pi$
$570$		0			0
$571$	14.0000			0.585882			0.292941	−	0.956131i	$-0.405366\pi$
$571$	14.0000			0.585882			0.292941	+	0.956131i	$0.405366\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$		0			0
$575$	2.47214	−	7.60845i	0.103095	−	0.317294i
$576$		0			0
$577$	10.5172	−	7.64121i	0.437838	−	0.318108i	−0.346938	−	0.937888i	$-0.612778\pi$
$577$	10.5172	−	7.64121i	0.437838	−	0.318108i	0.784775	+	0.619781i	$0.212778\pi$
$578$		0			0
$579$	−1.54508	−	4.75528i	−0.0642115	−	0.197623i
$580$		0			0
$581$	12.9443	+	9.40456i	0.537019	+	0.390167i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	2.42705	+	1.76336i	0.100346	+	0.0729058i
$586$		0			0
$587$	7.41641	+	22.8254i	0.306108	+	0.942103i	0.979261	+	0.202601i	$0.0649393\pi$
$587$	7.41641	+	22.8254i	0.306108	+	0.942103i	−0.673154	+	0.739503i	$0.735061\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	2.16312	−	6.65740i	0.0889788	−	0.273849i
$592$		0			0
$593$	3.00000			0.123195			0.0615976	−	0.998101i	$-0.480380\pi$
$593$	3.00000			0.123195			0.0615976	+	0.998101i	$0.480380\pi$
$594$		0			0
$595$	14.0000			0.573944
$596$		0			0
$597$	3.09017	−	9.51057i	0.126472	−	0.389242i
$598$		0			0
$599$	19.4164	−	14.1068i	0.793333	−	0.576390i	−0.115618	−	0.993294i	$-0.536885\pi$
$599$	19.4164	−	14.1068i	0.793333	−	0.576390i	0.908951	+	0.416904i	$0.136885\pi$
$600$		0			0
$601$	1.54508	+	4.75528i	0.0630253	+	0.193972i	0.977611	−	0.210420i	$-0.0674831\pi$
$601$	1.54508	+	4.75528i	0.0630253	+	0.193972i	−0.914586	+	0.404392i	$0.867483\pi$
$602$		0			0
$603$	11.3262	+	8.22899i	0.461240	+	0.335111i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.47214	−	4.70228i	−0.262696	−	0.190860i	0.448639	−	0.893713i	$-0.351909\pi$
$607$	−6.47214	−	4.70228i	−0.262696	−	0.190860i	−0.711335	+	0.702853i	$0.751909\pi$
$608$		0			0
$609$	−1.85410	−	5.70634i	−0.0751320	−	0.231233i
$610$		0			0
$611$	29.1246	−	21.1603i	1.17826	−	0.856053i
$612$		0			0
$613$	−10.1976	+	31.3849i	−0.411876	+	1.26762i	0.503140	+	0.864205i	$0.332178\pi$
$613$	−10.1976	+	31.3849i	−0.411876	+	1.26762i	−0.915016	+	0.403418i	$0.867822\pi$
$614$		0			0
$615$	−9.00000			−0.362915
$616$		0			0
$617$	−7.00000			−0.281809			−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000			−0.281809			−0.140905	+	0.990023i	$0.545001\pi$
$618$		0			0
$619$	−6.79837	+	20.9232i	−0.273250	+	0.840976i	0.716427	+	0.697662i	$0.245776\pi$
$619$	−6.79837	+	20.9232i	−0.273250	+	0.840976i	−0.989677	+	0.143315i	$0.954224\pi$
$620$		0			0
$621$	−1.61803	+	1.17557i	−0.0649295	+	0.0471740i
$622$		0			0
$623$	−0.618034	−	1.90211i	−0.0247610	−	0.0762065i
$624$		0			0
$625$	−8.89919	−	6.46564i	−0.355967	−	0.258626i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−50.9681	−	37.0305i	−2.03223	−	1.47650i
$630$		0			0
$631$	6.79837	+	20.9232i	0.270639	+	0.832941i	0.990340	+	0.138657i	$0.0442787\pi$
$631$	6.79837	+	20.9232i	0.270639	+	0.832941i	−0.719701	+	0.694284i	$0.755721\pi$
$632$		0			0
$633$	−11.3262	+	8.22899i	−0.450178	+	0.327073i
$634$		0			0
$635$	3.70820	−	11.4127i	0.147156	−	0.452898i
$636$		0			0
$637$	−9.00000			−0.356593
$638$		0			0
$639$	−6.00000			−0.237356
$640$		0			0
$641$	−12.0517	+	37.0912i	−0.476012	+	1.46501i	0.368576	+	0.929598i	$0.379845\pi$
$641$	−12.0517	+	37.0912i	−0.476012	+	1.46501i	−0.844588	+	0.535417i	$0.820155\pi$
$642$		0			0
$643$	32.3607	−	23.5114i	1.27618	−	0.927200i	0.276750	−	0.960942i	$-0.410743\pi$
$643$	32.3607	−	23.5114i	1.27618	−	0.927200i	0.999431	+	0.0337424i	$0.0107426\pi$
$644$		0			0
$645$	0.618034	+	1.90211i	0.0243351	+	0.0748956i
$646$		0			0
$647$	−25.8885	−	18.8091i	−1.01778	−	0.739463i	−0.0519563	−	0.998649i	$-0.516546\pi$
$647$	−25.8885	−	18.8091i	−1.01778	−	0.739463i	−0.965827	+	0.259186i	$0.916546\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12.9787	+	39.9444i	0.507896	+	1.56314i	0.795846	+	0.605499i	$0.207026\pi$
$653$	12.9787	+	39.9444i	0.507896	+	1.56314i	−0.287950	+	0.957645i	$0.592974\pi$
$654$		0			0
$655$	−17.7984	+	12.9313i	−0.695440	+	0.505267i
$656$		0			0
$657$	−1.85410	+	5.70634i	−0.0723354	+	0.222625i
$658$		0			0
$659$	48.0000			1.86981			0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000			1.86981			0.934907	+	0.354892i	$0.115482\pi$
$660$		0			0
$661$	−3.00000			−0.116686			−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000			−0.116686			−0.0583432	+	0.998297i	$0.518582\pi$
$662$		0			0
$663$	−6.48936	+	19.9722i	−0.252026	+	0.775655i
$664$		0			0
$665$	6.47214	−	4.70228i	0.250979	−	0.182347i
$666$		0			0
$667$	1.85410	+	5.70634i	0.0717911	+	0.220950i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	30.7426	+	22.3358i	1.18504	+	0.860983i	0.992731	−	0.120351i	$-0.0384019\pi$
$673$	30.7426	+	22.3358i	1.18504	+	0.860983i	0.192310	+	0.981334i	$0.438402\pi$
$674$		0			0
$675$	1.23607	+	3.80423i	0.0475763	+	0.146425i
$676$		0			0
$677$	−13.7533	+	9.99235i	−0.528582	+	0.384037i	−0.819827	−	0.572611i	$-0.805930\pi$
$677$	−13.7533	+	9.99235i	−0.528582	+	0.384037i	0.291245	+	0.956648i	$0.405930\pi$
$678$		0			0
$679$	−4.32624	+	13.3148i	−0.166026	+	0.510975i
$680$		0			0
$681$	−18.0000			−0.689761
$682$		0			0
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$		0			0
$685$	3.09017	−	9.51057i	0.118069	−	0.363380i
$686$		0			0
$687$	23.4615	−	17.0458i	0.895112	−	0.650337i
$688$		0			0
$689$	−12.0517	−	37.0912i	−0.459132	−	1.41306i
$690$		0			0
$691$	14.5623	+	10.5801i	0.553976	+	0.402487i	0.829249	−	0.558879i	$-0.188768\pi$
$691$	14.5623	+	10.5801i	0.553976	+	0.402487i	−0.275273	+	0.961366i	$0.588768\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.3262	−	8.22899i	−0.429629	−	0.312144i
$696$		0			0
$697$	−19.4681	−	59.9166i	−0.737406	−	2.26950i
$698$		0			0
$699$	−20.2254	+	14.6946i	−0.764996	+	0.555802i
$700$		0			0
$701$	−8.34346	+	25.6785i	−0.315128	+	0.969865i	0.660574	+	0.750761i	$0.270313\pi$
$701$	−8.34346	+	25.6785i	−0.315128	+	0.969865i	−0.975702	+	0.219103i	$0.929687\pi$
$702$		0			0
$703$	−36.0000			−1.35777
$704$		0			0
$705$	−12.0000			−0.451946
$706$		0			0
$707$	1.23607	−	3.80423i	0.0464871	−	0.143073i
$708$		0			0
$709$	−4.85410	+	3.52671i	−0.182300	+	0.132448i	−0.675192	−	0.737642i	$-0.735939\pi$
$709$	−4.85410	+	3.52671i	−0.182300	+	0.132448i	0.492893	+	0.870090i	$0.335939\pi$
$710$		0			0
$711$	4.94427	+	15.2169i	0.185425	+	0.570678i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.9443	+	9.40456i	0.483413	+	0.351220i
$718$		0			0
$719$	12.9787	+	39.9444i	0.484024	+	1.48967i	0.833389	+	0.552687i	$0.186397\pi$
$719$	12.9787	+	39.9444i	0.484024	+	1.48967i	−0.349365	+	0.936987i	$0.613603\pi$
$720$		0			0
$721$	−9.70820	+	7.05342i	−0.361552	+	0.262683i
$722$		0			0
$723$	−8.03444	+	24.7275i	−0.298804	+	0.919624i
$724$		0			0
$725$	12.0000			0.445669
$726$		0			0
$727$	−6.00000			−0.222528			−0.111264	−	0.993791i	$-0.535490\pi$
$727$	−6.00000			−0.222528			−0.111264	+	0.993791i	$0.535490\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−11.3262	+	8.22899i	−0.418916	+	0.304360i
$732$		0			0
$733$	−5.25329	−	16.1680i	−0.194035	−	0.597177i	−0.999986	−	0.00519616i	$-0.998346\pi$
$733$	−5.25329	−	16.1680i	−0.194035	−	0.597177i	0.805952	−	0.591981i	$-0.201654\pi$
$734$		0			0
$735$	2.42705	+	1.76336i	0.0895231	+	0.0650424i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−32.3607	−	23.5114i	−1.19041	−	0.864881i	−0.197100	−	0.980383i	$-0.563152\pi$
$739$	−32.3607	−	23.5114i	−1.19041	−	0.864881i	−0.993307	+	0.115502i	$0.963152\pi$
$740$		0			0
$741$	3.70820	+	11.4127i	0.136224	+	0.419255i
$742$		0			0
$743$	−21.0344	+	15.2824i	−0.771679	+	0.560657i	−0.902470	−	0.430752i	$-0.858248\pi$
$743$	−21.0344	+	15.2824i	−0.771679	+	0.560657i	0.130791	+	0.991410i	$0.458248\pi$
$744$		0			0
$745$	−4.01722	+	12.3637i	−0.147180	+	0.452972i
$746$		0			0
$747$	8.00000			0.292705
$748$		0			0
$749$	−28.0000			−1.02310
$750$		0			0
$751$	−10.5066	+	32.3359i	−0.383390	+	1.17995i	0.554251	+	0.832350i	$0.313005\pi$
$751$	−10.5066	+	32.3359i	−0.383390	+	1.17995i	−0.937641	+	0.347605i	$0.886995\pi$
$752$		0			0
$753$	−8.09017	+	5.87785i	−0.294822	+	0.214201i
$754$		0			0
$755$	−2.47214	−	7.60845i	−0.0899702	−	0.276900i
$756$		0			0
$757$	34.7877	+	25.2748i	1.26438	+	0.918627i	0.998964	−	0.0455066i	$-0.0144902\pi$
$757$	34.7877	+	25.2748i	1.26438	+	0.918627i	0.265418	+	0.964134i	$0.414490\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.8435	−	15.8702i	−0.791825	−	0.575294i	0.116680	−	0.993170i	$-0.462775\pi$
$761$	−21.8435	−	15.8702i	−0.791825	−	0.575294i	−0.908504	+	0.417875i	$0.862775\pi$
$762$		0			0
$763$	−1.85410	−	5.70634i	−0.0671230	−	0.206583i
$764$		0			0
$765$	5.66312	−	4.11450i	0.204750	−	0.148760i
$766$		0			0
$767$	−5.56231	+	17.1190i	−0.200843	+	0.618132i
$768$		0			0
$769$	41.0000			1.47850			0.739249	−	0.673432i	$-0.235181\pi$
$769$	41.0000			1.47850			0.739249	+	0.673432i	$0.235181\pi$
$770$		0			0
$771$	7.00000			0.252099
$772$		0			0
$773$	−9.27051	+	28.5317i	−0.333437	+	1.02621i	0.634050	+	0.773292i	$0.281391\pi$
$773$	−9.27051	+	28.5317i	−0.333437	+	1.02621i	−0.967487	+	0.252921i	$0.918609\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.56231	+	17.1190i	0.199547	+	0.614141i
$778$		0			0
$779$	−29.1246	−	21.1603i	−1.04350	−	0.758145i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−2.42705	−	1.76336i	−0.0867357	−	0.0630172i
$784$		0			0
$785$	−4.32624	−	13.3148i	−0.154410	−	0.475225i
$786$		0			0
$787$	−25.8885	+	18.8091i	−0.922827	+	0.670473i	−0.944226	−	0.329298i	$-0.893188\pi$
$787$	−25.8885	+	18.8091i	−0.922827	+	0.670473i	0.0213991	+	0.999771i	$0.493188\pi$
$788$		0			0
$789$	3.70820	−	11.4127i	0.132016	−	0.406302i
$790$		0			0
$791$	38.0000			1.35112
$792$		0			0
$793$	6.00000			0.213066
$794$		0			0
$795$	−4.01722	+	12.3637i	−0.142476	+	0.438496i
$796$		0			0
$797$	−33.9787	+	24.6870i	−1.20359	+	0.874458i	−0.994633	−	0.103468i	$-0.967006\pi$
$797$	−33.9787	+	24.6870i	−1.20359	+	0.874458i	−0.208955	+	0.977925i	$0.567006\pi$
$798$		0			0
$799$	−25.9574	−	79.8887i	−0.918308	−	2.82626i
$800$		0			0
$801$	−0.809017	−	0.587785i	−0.0285852	−	0.0207684i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	3.23607	+	2.35114i	0.114056	+	0.0828668i
$806$		0			0
$807$	0.309017	+	0.951057i	0.0108779	+	0.0334788i
$808$		0			0
$809$	27.5066	−	19.9847i	0.967080	−	0.702625i	0.0122956	−	0.999924i	$-0.496086\pi$
$809$	27.5066	−	19.9847i	0.967080	−	0.702625i	0.954784	+	0.297300i	$0.0960861\pi$
$810$		0			0
$811$	−6.18034	+	19.0211i	−0.217021	+	0.667922i	0.781983	+	0.623300i	$0.214208\pi$
$811$	−6.18034	+	19.0211i	−0.217021	+	0.667922i	−0.999004	+	0.0446223i	$0.985792\pi$
$812$		0			0
$813$	−22.0000			−0.771574
$814$		0			0
$815$	2.00000			0.0700569
$816$		0			0
$817$	−2.47214	+	7.60845i	−0.0864891	+	0.266186i
$818$		0			0
$819$	4.85410	−	3.52671i	0.169616	−	0.123233i
$820$		0			0
$821$	−3.09017	−	9.51057i	−0.107848	−	0.331921i	0.882541	−	0.470236i	$-0.155831\pi$
$821$	−3.09017	−	9.51057i	−0.107848	−	0.331921i	−0.990388	+	0.138315i	$0.955831\pi$
$822$		0			0
$823$	27.5066	+	19.9847i	0.958819	+	0.696623i	0.952876	−	0.303360i	$-0.0981083\pi$
$823$	27.5066	+	19.9847i	0.958819	+	0.696623i	0.00594286	+	0.999982i	$0.498108\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.61803	+	1.17557i	0.0562646	+	0.0408786i	0.615562	−	0.788088i	$-0.288929\pi$
$827$	1.61803	+	1.17557i	0.0562646	+	0.0408786i	−0.559297	+	0.828967i	$0.688929\pi$
$828$		0			0
$829$	15.1418	+	46.6018i	0.525898	+	1.61855i	0.762534	+	0.646948i	$0.223955\pi$
$829$	15.1418	+	46.6018i	0.525898	+	1.61855i	−0.236636	+	0.971598i	$0.576045\pi$
$830$		0			0
$831$	−13.7533	+	9.99235i	−0.477096	+	0.346631i
$832$		0			0
$833$	−6.48936	+	19.9722i	−0.224843	+	0.691995i
$834$		0			0
$835$	18.0000			0.622916
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.8328	−	45.6507i	0.512086	−	1.57604i	−0.276437	−	0.961032i	$-0.589154\pi$
$839$	14.8328	−	45.6507i	0.512086	−	1.57604i	0.788523	−	0.615006i	$-0.210846\pi$
$840$		0			0
$841$	16.1803	−	11.7557i	0.557943	−	0.405369i
$842$		0			0
$843$	−6.79837	−	20.9232i	−0.234148	−	0.720635i
$844$		0			0
$845$	−3.23607	−	2.35114i	−0.111324	−	0.0808817i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	11.3262	+	8.22899i	0.388715	+	0.282418i
$850$		0			0
$851$	−5.56231	−	17.1190i	−0.190673	−	0.586832i
$852$		0			0
$853$	−12.1353	+	8.81678i	−0.415503	+	0.301881i	−0.775826	−	0.630947i	$-0.782667\pi$
$853$	−12.1353	+	8.81678i	−0.415503	+	0.301881i	0.360323	+	0.932828i	$0.382667\pi$
$854$		0			0
$855$	1.23607	−	3.80423i	0.0422726	−	0.130102i
$856$		0			0
$857$	10.0000			0.341593			0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000			0.341593			0.170797	+	0.985306i	$0.445366\pi$
$858$		0			0
$859$	22.0000			0.750630			0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000			0.750630			0.375315	+	0.926897i	$0.377534\pi$
$860$		0			0
$861$	−5.56231	+	17.1190i	−0.189563	+	0.583415i
$862$		0			0
$863$	8.09017	−	5.87785i	0.275393	−	0.200084i	−0.441513	−	0.897255i	$-0.645558\pi$
$863$	8.09017	−	5.87785i	0.275393	−	0.200084i	0.716905	+	0.697171i	$0.245558\pi$
$864$		0			0
$865$	4.32624	+	13.3148i	0.147097	+	0.452716i
$866$		0			0
$867$	25.8885	+	18.8091i	0.879221	+	0.638791i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	33.9787	+	24.6870i	1.15132	+	0.836486i
$872$		0			0
$873$	2.16312	+	6.65740i	0.0732105	+	0.225319i
$874$		0			0
$875$	14.5623	−	10.5801i	0.492296	−	0.357674i
$876$		0			0
$877$	4.63525	−	14.2658i	0.156521	−	0.481723i	−0.841790	−	0.539804i	$-0.818498\pi$
$877$	4.63525	−	14.2658i	0.156521	−	0.481723i	0.998312	+	0.0580810i	$0.0184982\pi$
$878$		0			0
$879$	−17.0000			−0.573396
$880$		0			0
$881$	−23.0000			−0.774890			−0.387445	−	0.921893i	$-0.626642\pi$
$881$	−23.0000			−0.774890			−0.387445	+	0.921893i	$0.626642\pi$
$882$		0			0
$883$	−13.5967	+	41.8465i	−0.457567	+	1.40825i	0.410528	+	0.911848i	$0.365344\pi$
$883$	−13.5967	+	41.8465i	−0.457567	+	1.40825i	−0.868095	+	0.496398i	$0.834656\pi$
$884$		0			0
$885$	4.85410	−	3.52671i	0.163169	−	0.118549i
$886$		0			0
$887$	−1.85410	−	5.70634i	−0.0622547	−	0.191600i	0.915092	−	0.403245i	$-0.132118\pi$
$887$	−1.85410	−	5.70634i	−0.0622547	−	0.191600i	−0.977347	+	0.211645i	$0.932118\pi$
$888$		0			0
$889$	−19.4164	−	14.1068i	−0.651205	−	0.473128i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−38.8328	−	28.2137i	−1.29949	−	0.944135i
$894$		0			0
$895$	−2.47214	−	7.60845i	−0.0826344	−	0.254323i
$896$		0			0
$897$	−4.85410	+	3.52671i	−0.162074	+	0.117753i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−91.0000			−3.03165
$902$		0			0
$903$	4.00000			0.133112
$904$		0			0
$905$	−4.01722	+	12.3637i	−0.133537	+	0.410984i
$906$		0			0
$907$	21.0344	−	15.2824i	0.698437	−	0.507444i	−0.180986	−	0.983486i	$-0.557929\pi$
$907$	21.0344	−	15.2824i	0.698437	−	0.507444i	0.879423	+	0.476041i	$0.157929\pi$
$908$		0			0
$909$	−0.618034	−	1.90211i	−0.0204989	−	0.0630891i
$910$		0			0
$911$	−24.2705	−	17.6336i	−0.804118	−	0.584226i	0.108001	−	0.994151i	$-0.465555\pi$
$911$	−24.2705	−	17.6336i	−0.804118	−	0.584226i	−0.912119	+	0.409925i	$0.865555\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−1.61803	−	1.17557i	−0.0534906	−	0.0388632i
$916$		0			0
$917$	13.5967	+	41.8465i	0.449004	+	1.38189i
$918$		0			0
$919$	21.0344	−	15.2824i	0.693862	−	0.504120i	−0.184065	−	0.982914i	$-0.558926\pi$
$919$	21.0344	−	15.2824i	0.693862	−	0.504120i	0.877927	+	0.478794i	$0.158926\pi$
$920$		0			0
$921$	6.79837	−	20.9232i	0.224014	−	0.689444i
$922$		0			0
$923$	−18.0000			−0.592477
$924$		0			0
$925$	−36.0000			−1.18367
$926$		0			0
$927$	−1.85410	+	5.70634i	−0.0608967	+	0.187421i
$928$		0			0
$929$	−7.28115	+	5.29007i	−0.238887	+	0.173561i	−0.700787	−	0.713370i	$-0.747168\pi$
$929$	−7.28115	+	5.29007i	−0.238887	+	0.173561i	0.461900	+	0.886932i	$0.347168\pi$
$930$		0			0
$931$	3.70820	+	11.4127i	0.121531	+	0.374035i
$932$		0			0
$933$	22.6525	+	16.4580i	0.741609	+	0.538810i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−23.4615	−	17.0458i	−0.766454	−	0.556861i	0.134429	−	0.990923i	$-0.457080\pi$
$937$	−23.4615	−	17.0458i	−0.766454	−	0.556861i	−0.900883	+	0.434062i	$0.857080\pi$
$938$		0			0
$939$	0.309017	+	0.951057i	0.0100844	+	0.0310366i
$940$		0			0
$941$	21.8435	−	15.8702i	0.712076	−	0.517354i	−0.171766	−	0.985138i	$-0.554947\pi$
$941$	21.8435	−	15.8702i	0.712076	−	0.517354i	0.883843	+	0.467784i	$0.154947\pi$
$942$		0			0
$943$	5.56231	−	17.1190i	0.181134	−	0.557472i
$944$		0			0
$945$	−2.00000			−0.0650600
$946$		0			0
$947$	−18.0000			−0.584921			−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000			−0.584921			−0.292461	+	0.956278i	$0.594474\pi$
$948$		0			0
$949$	−5.56231	+	17.1190i	−0.180560	+	0.555707i
$950$		0			0
$951$	−4.85410	+	3.52671i	−0.157405	+	0.114361i
$952$		0			0
$953$	−10.1976	−	31.3849i	−0.330331	−	1.01666i	−0.968976	−	0.247154i	$-0.920505\pi$
$953$	−10.1976	−	31.3849i	−0.330331	−	1.01666i	0.638645	−	0.769502i	$-0.279495\pi$
$954$		0			0
$955$	−9.70820	−	7.05342i	−0.314150	−	0.228243i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.1803	−	11.7557i	−0.522490	−	0.379612i
$960$		0			0
$961$	−9.57953	−	29.4828i	−0.309017	−	0.951057i
$962$		0			0
$963$	−11.3262	+	8.22899i	−0.364983	+	0.265176i
$964$		0			0
$965$	−1.54508	+	4.75528i	−0.0497380	+	0.153078i
$966$		0			0
$967$	62.0000			1.99379			0.996893	−	0.0787703i	$-0.0250994\pi$
$967$	62.0000			1.99379			0.996893	+	0.0787703i	$0.0250994\pi$
$968$		0			0
$969$	28.0000			0.899490
$970$		0			0
$971$	12.9787	−	39.9444i	0.416507	−	1.28188i	−0.494389	−	0.869240i	$-0.664608\pi$
$971$	12.9787	−	39.9444i	0.416507	−	1.28188i	0.910896	−	0.412635i	$-0.135392\pi$
$972$		0			0
$973$	−22.6525	+	16.4580i	−0.726205	+	0.527619i
$974$		0			0
$975$	3.70820	+	11.4127i	0.118758	+	0.365498i
$976$		0			0
$977$	−33.1697	−	24.0992i	−1.06119	−	0.771002i	−0.0868840	−	0.996218i	$-0.527691\pi$
$977$	−33.1697	−	24.0992i	−1.06119	−	0.771002i	−0.974309	+	0.225217i	$0.927691\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−2.42705	−	1.76336i	−0.0774898	−	0.0562996i
$982$		0			0
$983$	−11.1246	−	34.2380i	−0.354820	−	1.09202i	−0.956114	−	0.292996i	$-0.905348\pi$
$983$	−11.1246	−	34.2380i	−0.354820	−	1.09202i	0.601294	−	0.799028i	$-0.294652\pi$
$984$		0			0
$985$	−5.66312	+	4.11450i	−0.180442	+	0.131099i
$986$		0			0
$987$	−7.41641	+	22.8254i	−0.236067	+	0.726539i
$988$		0			0
$989$	−4.00000			−0.127193
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$	−2.47214	+	7.60845i	−0.0784509	+	0.241447i
$994$		0			0
$995$	−8.09017	+	5.87785i	−0.256476	+	0.186340i
$996$		0			0
$997$	18.2320	+	56.1123i	0.577413	+	1.77710i	0.627811	+	0.778366i	$0.283951\pi$
$997$	18.2320	+	56.1123i	0.577413	+	1.77710i	−0.0503972	+	0.998729i	$0.516049\pi$
$998$		0			0
$999$	7.28115	+	5.29007i	0.230365	+	0.167370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.n.565.1		4
11.2	odd	10		1452.2.i.m.1237.1		4
11.3	even	5	inner	1452.2.i.n.1213.1		4
11.4	even	5	inner	1452.2.i.n.493.1		4
11.5	even	5		1452.2.a.a.1.1	✓	1
11.6	odd	10		1452.2.a.b.1.1	yes	1
11.7	odd	10		1452.2.i.m.493.1		4
11.8	odd	10		1452.2.i.m.1213.1		4
11.9	even	5	inner	1452.2.i.n.1237.1		4
11.10	odd	2		1452.2.i.m.565.1		4
33.5	odd	10		4356.2.a.h.1.1		1
33.17	even	10		4356.2.a.i.1.1		1
44.27	odd	10		5808.2.a.y.1.1		1
44.39	even	10		5808.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1452.2.a.a.1.1	✓	1	11.5	even	5
1452.2.a.b.1.1	yes	1	11.6	odd	10
1452.2.i.m.493.1		4	11.7	odd	10
1452.2.i.m.565.1		4	11.10	odd	2
1452.2.i.m.1213.1		4	11.8	odd	10
1452.2.i.m.1237.1		4	11.2	odd	10
1452.2.i.n.493.1		4	11.4	even	5	inner
1452.2.i.n.565.1		4	1.1	even	1	trivial
1452.2.i.n.1213.1		4	11.3	even	5	inner
1452.2.i.n.1237.1		4	11.9	even	5	inner
4356.2.a.h.1.1		1	33.5	odd	10
4356.2.a.i.1.1		1	33.17	even	10
5808.2.a.v.1.1		1	44.39	even	10
5808.2.a.y.1.1		1	44.27	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.618034 - 1.90211i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.42705 - 1.76336i) q^{13} +(0.309017 + 0.951057i) q^{15} +(-5.66312 + 4.11450i) q^{17} +(-1.23607 + 3.80423i) q^{19} +2.00000 q^{21} -2.00000 q^{23} +(-1.23607 + 3.80423i) q^{25} +(0.809017 - 0.587785i) q^{27} +(-0.927051 - 2.85317i) q^{29} +(-1.61803 - 1.17557i) q^{35} +(2.78115 + 8.55951i) q^{37} +(2.42705 - 1.76336i) q^{39} +(-2.78115 + 8.55951i) q^{41} +2.00000 q^{43} -1.00000 q^{45} +(-3.70820 + 11.4127i) q^{47} +(2.42705 - 1.76336i) q^{49} +(-2.16312 - 6.65740i) q^{51} +(10.5172 + 7.64121i) q^{53} +(-3.23607 - 2.35114i) q^{57} +(-1.85410 - 5.70634i) q^{59} +(-1.61803 + 1.17557i) q^{61} +(-0.618034 + 1.90211i) q^{63} -3.00000 q^{65} -14.0000 q^{67} +(0.618034 - 1.90211i) q^{69} +(4.85410 - 3.52671i) q^{71} +(-1.85410 - 5.70634i) q^{73} +(-3.23607 - 2.35114i) q^{75} +(-12.9443 - 9.40456i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-6.47214 + 4.70228i) q^{83} +(-2.16312 + 6.65740i) q^{85} +3.00000 q^{87} +1.00000 q^{89} +(-1.85410 + 5.70634i) q^{91} +(1.23607 + 3.80423i) q^{95} +(-5.66312 - 4.11450i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} + q^{5} + 2 q^{7} - q^{9} - 3 q^{13} - q^{15} - 7 q^{17} + 4 q^{19} + 8 q^{21} - 8 q^{23} + 4 q^{25} + q^{27} + 3 q^{29} - 2 q^{35} - 9 q^{37} + 3 q^{39} + 9 q^{41} + 8 q^{43} - 4 q^{45}+ \cdots - 7 q^{97}+O(q^{100}) \) 4 * q + q^3 + q^5 + 2 * q^7 - q^9 - 3 * q^13 - q^15 - 7 * q^17 + 4 * q^19 + 8 * q^21 - 8 * q^23 + 4 * q^25 + q^27 + 3 * q^29 - 2 * q^35 - 9 * q^37 + 3 * q^39 + 9 * q^41 + 8 * q^43 - 4 * q^45 + 12 * q^47 + 3 * q^49 + 7 * q^51 + 13 * q^53 - 4 * q^57 + 6 * q^59 - 2 * q^61 + 2 * q^63 - 12 * q^65 - 56 * q^67 - 2 * q^69 + 6 * q^71 + 6 * q^73 - 4 * q^75 - 16 * q^79 - q^81 - 8 * q^83 + 7 * q^85 + 12 * q^87 + 4 * q^89 + 6 * q^91 - 4 * q^95 - 7 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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