LMFDB - Embedded newform 1456.2.cc.b.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, degree $2$, not 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1456.673
Dual form			1456.2.cc.b.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.633975i) q^{3} -1.00000i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(0.366025 + 0.633975i) q^{3} -1.00000i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.23205 - 2.13397i) q^{9} +(-0.633975 + 0.366025i) q^{11} +(2.59808 + 2.50000i) q^{13} +(0.633975 - 0.366025i) q^{15} +(-2.86603 + 4.96410i) q^{17} +(1.26795 + 0.732051i) q^{19} +0.732051i q^{21} +(-0.633975 - 1.09808i) q^{23} +4.00000 q^{25} +4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} -5.26795i q^{31} +(-0.464102 - 0.267949i) q^{33} +(0.500000 - 0.866025i) q^{35} +(4.50000 - 2.59808i) q^{37} +(-0.633975 + 2.56218i) q^{39} +(-2.13397 + 1.23205i) q^{41} +(6.09808 - 10.5622i) q^{43} +(-2.13397 - 1.23205i) q^{45} +2.92820i q^{47} +(0.500000 + 0.866025i) q^{49} -4.19615 q^{51} +1.53590 q^{53} +(0.366025 + 0.633975i) q^{55} +1.07180i q^{57} +(9.29423 + 5.36603i) q^{59} +(5.86603 - 10.1603i) q^{61} +(2.13397 - 1.23205i) q^{63} +(2.50000 - 2.59808i) q^{65} +(-10.0981 + 5.83013i) q^{67} +(0.464102 - 0.803848i) q^{69} +(12.0000 + 6.92820i) q^{71} +11.3923i q^{73} +(1.46410 + 2.53590i) q^{75} -0.732051 q^{77} +3.80385 q^{79} +(-2.23205 - 3.86603i) q^{81} +3.80385i q^{83} +(4.96410 + 2.86603i) q^{85} +(-1.09808 + 1.90192i) q^{87} +(2.19615 - 1.26795i) q^{89} +(1.00000 + 3.46410i) q^{91} +(3.33975 - 1.92820i) q^{93} +(0.732051 - 1.26795i) q^{95} +(-4.73205 - 2.73205i) q^{97} +1.80385i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{9} - 6 q^{11} + 6 q^{15} - 8 q^{17} + 12 q^{19} - 6 q^{23} + 16 q^{25} + 16 q^{27} + 6 q^{29} + 12 q^{33} + 2 q^{35} + 18 q^{37} - 6 q^{39} - 12 q^{41} + 14 q^{43} - 12 q^{45} + 2 q^{49} + 4 q^{51} + 20 q^{53} - 2 q^{55} + 6 q^{59} + 20 q^{61} + 12 q^{63} + 10 q^{65} - 30 q^{67} - 12 q^{69} + 48 q^{71} - 8 q^{75} + 4 q^{77} + 36 q^{79} - 2 q^{81} + 6 q^{85} + 6 q^{87} - 12 q^{89} + 4 q^{91} + 48 q^{93} - 4 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^9 - 6 * q^11 + 6 * q^15 - 8 * q^17 + 12 * q^19 - 6 * q^23 + 16 * q^25 + 16 * q^27 + 6 * q^29 + 12 * q^33 + 2 * q^35 + 18 * q^37 - 6 * q^39 - 12 * q^41 + 14 * q^43 - 12 * q^45 + 2 * q^49 + 4 * q^51 + 20 * q^53 - 2 * q^55 + 6 * q^59 + 20 * q^61 + 12 * q^63 + 10 * q^65 - 30 * q^67 - 12 * q^69 + 48 * q^71 - 8 * q^75 + 4 * q^77 + 36 * q^79 - 2 * q^81 + 6 * q^85 + 6 * q^87 - 12 * q^89 + 4 * q^91 + 48 * q^93 - 4 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	0.952129	−	0.305695i	$-0.0988889\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	−0.740805	+	0.671721i	$0.765556\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i	−0.974679	−	0.223607i	$-0.928217\pi$
$5$		−	1.00000i		−	0.447214i	0.974679	−	0.223607i	$-0.0717831\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$		0			0
$11$	−0.633975	+	0.366025i	−0.191151	+	0.110361i	−0.592521	−	0.805555i	$-0.701867\pi$
$11$	−0.633975	+	0.366025i	−0.191151	+	0.110361i	0.401371	+	0.915916i	$0.368534\pi$
$12$		0			0
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$		0			0
$15$	0.633975	−	0.366025i	0.163692	−	0.0945074i
$16$		0			0
$17$	−2.86603	+	4.96410i	−0.695113	+	1.20397i	0.275029	+	0.961436i	$0.411312\pi$
$17$	−2.86603	+	4.96410i	−0.695113	+	1.20397i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$	1.26795	+	0.732051i	0.290887	+	0.167944i	0.638342	−	0.769753i	$-0.279621\pi$
$19$	1.26795	+	0.732051i	0.290887	+	0.167944i	−0.347455	+	0.937697i	$0.612954\pi$
$20$		0			0
$21$			0.732051i			0.159747i
$22$		0			0
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$		−	5.26795i		−	0.946152i	−0.881022	−	0.473076i	$-0.843144\pi$
$31$		−	5.26795i		−	0.946152i	0.881022	−	0.473076i	$-0.156856\pi$
$32$		0			0
$33$	−0.464102	−	0.267949i	−0.0807897	−	0.0466440i
$34$		0			0
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$		0			0
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	−0.633975	+	2.56218i	−0.101517	+	0.410277i
$40$		0			0
$41$	−2.13397	+	1.23205i	−0.333271	+	0.192414i	−0.657292	−	0.753636i	$-0.728298\pi$
$41$	−2.13397	+	1.23205i	−0.333271	+	0.192414i	0.324021	+	0.946050i	$0.394965\pi$
$42$		0			0
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.146544	−	0.989204i	$-0.453185\pi$
$43$	6.09808	−	10.5622i	0.929948	−	1.61072i	0.783404	−	0.621513i	$-0.213482\pi$
$44$		0			0
$45$	−2.13397	−	1.23205i	−0.318114	−	0.183663i
$46$		0			0
$47$			2.92820i			0.427122i	0.976930	+	0.213561i	$0.0685063\pi$
$47$			2.92820i			0.427122i	−0.976930	+	0.213561i	$0.931494\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$	−4.19615			−0.587579
$52$		0			0
$53$	1.53590			0.210972			0.105486	−	0.994421i	$-0.466360\pi$
$53$	1.53590			0.210972			0.105486	+	0.994421i	$0.466360\pi$
$54$		0			0
$55$	0.366025	+	0.633975i	0.0493549	+	0.0854851i
$56$		0			0
$57$			1.07180i			0.141963i
$58$		0			0
$59$	9.29423	+	5.36603i	1.21001	+	0.698597i	0.962760	−	0.270356i	$-0.0871414\pi$
$59$	9.29423	+	5.36603i	1.21001	+	0.698597i	0.247245	+	0.968953i	$0.420475\pi$
$60$		0			0
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	−0.196238	−	0.980556i	$-0.562873\pi$
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	0.947306	−	0.320331i	$-0.103794\pi$
$62$		0			0
$63$	2.13397	−	1.23205i	0.268856	−	0.155224i
$64$		0			0
$65$	2.50000	−	2.59808i	0.310087	−	0.322252i
$66$		0			0
$67$	−10.0981	+	5.83013i	−1.23368	+	0.712263i	−0.967794	−	0.251742i	$-0.918996\pi$
$67$	−10.0981	+	5.83013i	−1.23368	+	0.712263i	−0.265882	+	0.964006i	$0.585663\pi$
$68$		0			0
$69$	0.464102	−	0.803848i	0.0558713	−	0.0967719i
$70$		0			0
$71$	12.0000	+	6.92820i	1.42414	+	0.822226i	0.996649	−	0.0817942i	$-0.0260650\pi$
$71$	12.0000	+	6.92820i	1.42414	+	0.822226i	0.427489	+	0.904021i	$0.359398\pi$
$72$		0			0
$73$			11.3923i			1.33337i	0.745340	+	0.666684i	$0.232287\pi$
$73$			11.3923i			1.33337i	−0.745340	+	0.666684i	$0.767713\pi$
$74$		0			0
$75$	1.46410	+	2.53590i	0.169060	+	0.292820i
$76$		0			0
$77$	−0.732051			−0.0834249
$78$		0			0
$79$	3.80385			0.427966			0.213983	−	0.976837i	$-0.431356\pi$
$79$	3.80385			0.427966			0.213983	+	0.976837i	$0.431356\pi$
$80$		0			0
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$		0			0
$83$			3.80385i			0.417527i	0.977966	+	0.208763i	$0.0669438\pi$
$83$			3.80385i			0.417527i	−0.977966	+	0.208763i	$0.933056\pi$
$84$		0			0
$85$	4.96410	+	2.86603i	0.538432	+	0.310864i
$86$		0			0
$87$	−1.09808	+	1.90192i	−0.117726	+	0.203908i
$88$		0			0
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	−0.379068	−	0.925369i	$-0.623755\pi$
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	0.611859	+	0.790967i	$0.290422\pi$
$90$		0			0
$91$	1.00000	+	3.46410i	0.104828	+	0.363137i
$92$		0			0
$93$	3.33975	−	1.92820i	0.346316	−	0.199945i
$94$		0			0
$95$	0.732051	−	1.26795i	0.0751068	−	0.130089i
$96$		0			0
$97$	−4.73205	−	2.73205i	−0.480467	−	0.277398i	0.240144	−	0.970737i	$-0.422805\pi$
$97$	−4.73205	−	2.73205i	−0.480467	−	0.277398i	−0.720611	+	0.693340i	$0.756139\pi$
$98$		0			0
$99$			1.80385i			0.181294i
$100$		0			0
$101$	0.598076	+	1.03590i	0.0595108	+	0.103076i	0.894246	−	0.447576i	$-0.147713\pi$
$101$	0.598076	+	1.03590i	0.0595108	+	0.103076i	−0.834735	+	0.550652i	$0.814379\pi$
$102$		0			0
$103$	−8.39230			−0.826918			−0.413459	−	0.910523i	$-0.635680\pi$
$103$	−8.39230			−0.826918			−0.413459	+	0.910523i	$0.635680\pi$
$104$		0			0
$105$	0.732051			0.0714408
$106$		0			0
$107$	5.46410	+	9.46410i	0.528235	+	0.914929i	0.999458	+	0.0329154i	$0.0104792\pi$
$107$	5.46410	+	9.46410i	0.528235	+	0.914929i	−0.471224	+	0.882014i	$0.656187\pi$
$108$		0			0
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$		0			0
$111$	3.29423	+	1.90192i	0.312674	+	0.180523i
$112$		0			0
$113$	−5.69615	+	9.86603i	−0.535849	+	0.928118i	0.463273	+	0.886216i	$0.346675\pi$
$113$	−5.69615	+	9.86603i	−0.535849	+	0.928118i	−0.999122	+	0.0419019i	$0.986658\pi$
$114$		0			0
$115$	−1.09808	+	0.633975i	−0.102396	+	0.0591184i
$116$		0			0
$117$	8.53590	−	2.46410i	0.789144	−	0.227806i
$118$		0			0
$119$	−4.96410	+	2.86603i	−0.455058	+	0.262728i
$120$		0			0
$121$	−5.23205	+	9.06218i	−0.475641	+	0.823834i
$122$		0			0
$123$	−1.56218	−	0.901924i	−0.140857	−	0.0813237i
$124$		0			0
$125$		−	9.00000i		−	0.804984i
$126$		0			0
$127$	−4.92820	−	8.53590i	−0.437307	−	0.757438i	0.560173	−	0.828375i	$-0.310734\pi$
$127$	−4.92820	−	8.53590i	−0.437307	−	0.757438i	−0.997481	+	0.0709368i	$0.977401\pi$
$128$		0			0
$129$	8.92820			0.786084
$130$		0			0
$131$	5.07180			0.443125			0.221562	−	0.975146i	$-0.428884\pi$
$131$	5.07180			0.443125			0.221562	+	0.975146i	$0.428884\pi$
$132$		0			0
$133$	0.732051	+	1.26795i	0.0634769	+	0.109945i
$134$		0			0
$135$		−	4.00000i		−	0.344265i
$136$		0			0
$137$	−5.30385	−	3.06218i	−0.453138	−	0.261620i	0.256016	−	0.966672i	$-0.417590\pi$
$137$	−5.30385	−	3.06218i	−0.453138	−	0.261620i	−0.709155	+	0.705053i	$0.750923\pi$
$138$		0			0
$139$	−0.169873	+	0.294229i	−0.0144084	+	0.0249561i	−0.873140	−	0.487470i	$-0.837920\pi$
$139$	−0.169873	+	0.294229i	−0.0144084	+	0.0249561i	0.858731	+	0.512426i	$0.171253\pi$
$140$		0			0
$141$	−1.85641	+	1.07180i	−0.156338	+	0.0902616i
$142$		0			0
$143$	−2.56218	−	0.633975i	−0.214260	−	0.0530156i
$144$		0			0
$145$	2.59808	−	1.50000i	0.215758	−	0.124568i
$146$		0			0
$147$	−0.366025	+	0.633975i	−0.0301893	+	0.0522893i
$148$		0			0
$149$	−14.8923	−	8.59808i	−1.22003	−	0.704382i	−0.255102	−	0.966914i	$-0.582109\pi$
$149$	−14.8923	−	8.59808i	−1.22003	−	0.704382i	−0.964923	+	0.262532i	$0.915442\pi$
$150$		0			0
$151$		−	12.3923i		−	1.00847i	−0.863566	−	0.504236i	$-0.831774\pi$
$151$		−	12.3923i		−	1.00847i	0.863566	−	0.504236i	$-0.168226\pi$
$152$		0			0
$153$	7.06218	+	12.2321i	0.570943	+	0.988903i
$154$		0			0
$155$	−5.26795			−0.423132
$156$		0			0
$157$	13.7321			1.09594			0.547968	−	0.836499i	$-0.315401\pi$
$157$	13.7321			1.09594			0.547968	+	0.836499i	$0.315401\pi$
$158$		0			0
$159$	0.562178	+	0.973721i	0.0445836	+	0.0772211i
$160$		0			0
$161$		−	1.26795i		−	0.0999284i
$162$		0			0
$163$	0.633975	+	0.366025i	0.0496567	+	0.0286693i	0.524623	−	0.851335i	$-0.324206\pi$
$163$	0.633975	+	0.366025i	0.0496567	+	0.0286693i	−0.474966	+	0.880004i	$0.657540\pi$
$164$		0			0
$165$	−0.267949	+	0.464102i	−0.0208598	+	0.0361303i
$166$		0			0
$167$	4.56218	−	2.63397i	0.353032	−	0.203823i	−0.312988	−	0.949757i	$-0.601330\pi$
$167$	4.56218	−	2.63397i	0.353032	−	0.203823i	0.666020	+	0.745934i	$0.267997\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	3.12436	−	1.80385i	0.238925	−	0.137944i
$172$		0			0
$173$	−10.4641	+	18.1244i	−0.795571	+	1.37797i	0.126905	+	0.991915i	$0.459496\pi$
$173$	−10.4641	+	18.1244i	−0.795571	+	1.37797i	−0.922476	+	0.386054i	$0.873838\pi$
$174$		0			0
$175$	3.46410	+	2.00000i	0.261861	+	0.151186i
$176$		0			0
$177$			7.85641i			0.590524i
$178$		0			0
$179$	−8.19615	−	14.1962i	−0.612609	−	1.06107i	−0.990799	−	0.135342i	$-0.956787\pi$
$179$	−8.19615	−	14.1962i	−0.612609	−	1.06107i	0.378190	−	0.925728i	$-0.376547\pi$
$180$		0			0
$181$	3.19615			0.237568			0.118784	−	0.992920i	$-0.462100\pi$
$181$	3.19615			0.237568			0.118784	+	0.992920i	$0.462100\pi$
$182$		0			0
$183$	8.58846			0.634877
$184$		0			0
$185$	−2.59808	−	4.50000i	−0.191014	−	0.330847i
$186$		0			0
$187$		−	4.19615i		−	0.306853i
$188$		0			0
$189$	3.46410	+	2.00000i	0.251976	+	0.145479i
$190$		0			0
$191$	3.56218	−	6.16987i	0.257750	−	0.446436i	−0.707889	−	0.706324i	$-0.750352\pi$
$191$	3.56218	−	6.16987i	0.257750	−	0.446436i	0.965639	+	0.259888i	$0.0836855\pi$
$192$		0			0
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.998240	−	0.0593065i	$-0.981111\pi$
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.447759	+	0.894154i	$0.647778\pi$
$194$		0			0
$195$	2.56218	+	0.633975i	0.183481	+	0.0453999i
$196$		0			0
$197$	6.12436	−	3.53590i	0.436342	−	0.251922i	−0.265703	−	0.964055i	$-0.585604\pi$
$197$	6.12436	−	3.53590i	0.436342	−	0.251922i	0.702045	+	0.712133i	$0.252271\pi$
$198$		0			0
$199$	2.73205	−	4.73205i	0.193670	−	0.335446i	−0.752794	−	0.658256i	$-0.771294\pi$
$199$	2.73205	−	4.73205i	0.193670	−	0.335446i	0.946464	+	0.322810i	$0.104628\pi$
$200$		0			0
$201$	−7.39230	−	4.26795i	−0.521413	−	0.301038i
$202$		0			0
$203$			3.00000i			0.210559i
$204$		0			0
$205$	1.23205	+	2.13397i	0.0860502	+	0.149043i
$206$		0			0
$207$	−3.12436			−0.217158
$208$		0			0
$209$	−1.07180			−0.0741377
$210$		0			0
$211$	−10.6340	−	18.4186i	−0.732073	−	1.26799i	−0.955996	−	0.293381i	$-0.905220\pi$
$211$	−10.6340	−	18.4186i	−0.732073	−	1.26799i	0.223923	−	0.974607i	$-0.428114\pi$
$212$		0			0
$213$			10.1436i			0.695028i
$214$		0			0
$215$	−10.5622	−	6.09808i	−0.720335	−	0.415885i
$216$		0			0
$217$	2.63397	−	4.56218i	0.178806	−	0.309701i
$218$		0			0
$219$	−7.22243	+	4.16987i	−0.488047	+	0.281774i
$220$		0			0
$221$	−19.8564	+	5.73205i	−1.33569	+	0.385579i
$222$		0			0
$223$	−10.7321	+	6.19615i	−0.718671	+	0.414925i	−0.814263	−	0.580496i	$-0.802859\pi$
$223$	−10.7321	+	6.19615i	−0.718671	+	0.414925i	0.0955922	+	0.995421i	$0.469526\pi$
$224$		0			0
$225$	4.92820	−	8.53590i	0.328547	−	0.569060i
$226$		0			0
$227$	−1.09808	−	0.633975i	−0.0728819	−	0.0420784i	0.463116	−	0.886298i	$-0.346731\pi$
$227$	−1.09808	−	0.633975i	−0.0728819	−	0.0420784i	−0.535998	+	0.844219i	$0.680065\pi$
$228$		0			0
$229$		−	24.3923i		−	1.61189i	−0.591991	−	0.805944i	$-0.701658\pi$
$229$		−	24.3923i		−	1.61189i	0.591991	−	0.805944i	$-0.298342\pi$
$230$		0			0
$231$	−0.267949	−	0.464102i	−0.0176298	−	0.0305356i
$232$		0			0
$233$	4.39230			0.287749			0.143875	−	0.989596i	$-0.454044\pi$
$233$	4.39230			0.287749			0.143875	+	0.989596i	$0.454044\pi$
$234$		0			0
$235$	2.92820			0.191015
$236$		0			0
$237$	1.39230	+	2.41154i	0.0904399	+	0.156647i
$238$		0			0
$239$			29.5167i			1.90927i	0.297772	+	0.954637i	$0.403756\pi$
$239$			29.5167i			1.90927i	−0.297772	+	0.954637i	$0.596244\pi$
$240$		0			0
$241$	−13.3301	−	7.69615i	−0.858669	−	0.495753i	0.00489737	−	0.999988i	$-0.498441\pi$
$241$	−13.3301	−	7.69615i	−0.858669	−	0.495753i	−0.863566	+	0.504235i	$0.831774\pi$
$242$		0			0
$243$	7.63397	−	13.2224i	0.489720	−	0.848219i
$244$		0			0
$245$	0.866025	−	0.500000i	0.0553283	−	0.0319438i
$246$		0			0
$247$	1.46410	+	5.07180i	0.0931586	+	0.322711i
$248$		0			0
$249$	−2.41154	+	1.39230i	−0.152825	+	0.0882337i
$250$		0			0
$251$	−11.4641	+	19.8564i	−0.723608	+	1.25333i	0.235937	+	0.971768i	$0.424184\pi$
$251$	−11.4641	+	19.8564i	−0.723608	+	1.25333i	−0.959545	+	0.281557i	$0.909149\pi$
$252$		0			0
$253$	0.803848	+	0.464102i	0.0505375	+	0.0291778i
$254$		0			0
$255$			4.19615i			0.262773i
$256$		0			0
$257$	0.669873	+	1.16025i	0.0417855	+	0.0723747i	0.886162	−	0.463376i	$-0.153362\pi$
$257$	0.669873	+	1.16025i	0.0417855	+	0.0723747i	−0.844376	+	0.535751i	$0.820029\pi$
$258$		0			0
$259$	5.19615			0.322873
$260$		0			0
$261$	7.39230			0.457572
$262$		0			0
$263$	−10.2942	−	17.8301i	−0.634769	−	1.09945i	−0.986564	−	0.163376i	$-0.947762\pi$
$263$	−10.2942	−	17.8301i	−0.634769	−	1.09945i	0.351795	−	0.936077i	$-0.385572\pi$
$264$		0			0
$265$		−	1.53590i		−	0.0943495i
$266$		0			0
$267$	1.60770	+	0.928203i	0.0983893	+	0.0568051i
$268$		0			0
$269$	14.3923	−	24.9282i	0.877514	−	1.51990i	0.0234543	−	0.999725i	$-0.492534\pi$
$269$	14.3923	−	24.9282i	0.877514	−	1.51990i	0.854060	−	0.520174i	$-0.174133\pi$
$270$		0			0
$271$	−6.16987	+	3.56218i	−0.374793	+	0.216387i	−0.675550	−	0.737314i	$-0.736094\pi$
$271$	−6.16987	+	3.56218i	−0.374793	+	0.216387i	0.300757	+	0.953701i	$0.402761\pi$
$272$		0			0
$273$	−1.83013	+	1.90192i	−0.110764	+	0.115110i
$274$		0			0
$275$	−2.53590	+	1.46410i	−0.152920	+	0.0882886i
$276$		0			0
$277$	4.69615	−	8.13397i	0.282164	−	0.488723i	−0.689753	−	0.724045i	$-0.742281\pi$
$277$	4.69615	−	8.13397i	0.282164	−	0.488723i	0.971918	+	0.235321i	$0.0756143\pi$
$278$		0			0
$279$	−11.2417	−	6.49038i	−0.673021	−	0.388569i
$280$		0			0
$281$		−	16.6603i		−	0.993867i	−0.867789	−	0.496934i	$-0.834459\pi$
$281$		−	16.6603i		−	0.993867i	0.867789	−	0.496934i	$-0.165541\pi$
$282$		0			0
$283$	5.29423	+	9.16987i	0.314709	+	0.545092i	0.979376	−	0.202048i	$-0.0647597\pi$
$283$	5.29423	+	9.16987i	0.314709	+	0.545092i	−0.664666	+	0.747140i	$0.731426\pi$
$284$		0			0
$285$	1.07180			0.0634878
$286$		0			0
$287$	−2.46410			−0.145451
$288$		0			0
$289$	−7.92820	−	13.7321i	−0.466365	−	0.807768i
$290$		0			0
$291$		−	4.00000i		−	0.234484i
$292$		0			0
$293$	15.0622	+	8.69615i	0.879942	+	0.508035i	0.870639	−	0.491922i	$-0.163706\pi$
$293$	15.0622	+	8.69615i	0.879942	+	0.508035i	0.00930260	+	0.999957i	$0.497039\pi$
$294$		0			0
$295$	5.36603	−	9.29423i	0.312422	−	0.541131i
$296$		0			0
$297$	−2.53590	+	1.46410i	−0.147148	+	0.0849558i
$298$		0			0
$299$	1.09808	−	4.43782i	0.0635034	−	0.256646i
$300$		0			0
$301$	10.5622	−	6.09808i	0.608794	−	0.351487i
$302$		0			0
$303$	−0.437822	+	0.758330i	−0.0251522	+	0.0435649i
$304$		0			0
$305$	−10.1603	−	5.86603i	−0.581774	−	0.335888i
$306$		0			0
$307$			23.5167i			1.34217i	0.741382	+	0.671083i	$0.234171\pi$
$307$			23.5167i			1.34217i	−0.741382	+	0.671083i	$0.765829\pi$
$308$		0			0
$309$	−3.07180	−	5.32051i	−0.174748	−	0.302673i
$310$		0			0
$311$	−10.1962			−0.578171			−0.289085	−	0.957303i	$-0.593351\pi$
$311$	−10.1962			−0.578171			−0.289085	+	0.957303i	$0.593351\pi$
$312$		0			0
$313$	−32.0000			−1.80875			−0.904373	−	0.426742i	$-0.859661\pi$
$313$	−32.0000			−1.80875			−0.904373	+	0.426742i	$0.859661\pi$
$314$		0			0
$315$	−1.23205	−	2.13397i	−0.0694182	−	0.120236i
$316$		0			0
$317$			7.05256i			0.396111i	0.980191	+	0.198056i	$0.0634627\pi$
$317$			7.05256i			0.396111i	−0.980191	+	0.198056i	$0.936537\pi$
$318$		0			0
$319$	−1.90192	−	1.09808i	−0.106487	−	0.0614805i
$320$		0			0
$321$	−4.00000	+	6.92820i	−0.223258	+	0.386695i
$322$		0			0
$323$	−7.26795	+	4.19615i	−0.404400	+	0.233480i
$324$		0			0
$325$	10.3923	+	10.0000i	0.576461	+	0.554700i
$326$		0			0
$327$	6.33975	−	3.66025i	0.350589	−	0.202413i
$328$		0			0
$329$	−1.46410	+	2.53590i	−0.0807185	+	0.139809i
$330$		0			0
$331$	−3.75833	−	2.16987i	−0.206577	−	0.119267i	0.393143	−	0.919477i	$-0.371388\pi$
$331$	−3.75833	−	2.16987i	−0.206577	−	0.119267i	−0.599719	+	0.800210i	$0.704721\pi$
$332$		0			0
$333$		−	12.8038i		−	0.701647i
$334$		0			0
$335$	5.83013	+	10.0981i	0.318534	+	0.551717i
$336$		0			0
$337$	−6.32051			−0.344300			−0.172150	−	0.985071i	$-0.555071\pi$
$337$	−6.32051			−0.344300			−0.172150	+	0.985071i	$0.555071\pi$
$338$		0			0
$339$	−8.33975			−0.452953
$340$		0			0
$341$	1.92820	+	3.33975i	0.104418	+	0.180857i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	−0.803848	−	0.464102i	−0.0432777	−	0.0249864i
$346$		0			0
$347$	14.4904	−	25.0981i	0.777884	−	1.34734i	−0.155275	−	0.987871i	$-0.549626\pi$
$347$	14.4904	−	25.0981i	0.777884	−	1.34734i	0.933159	−	0.359464i	$-0.117040\pi$
$348$		0			0
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$		0			0
$351$	10.3923	+	10.0000i	0.554700	+	0.533761i
$352$		0			0
$353$	−31.3301	+	18.0885i	−1.66753	+	0.962751i	−0.698573	+	0.715539i	$0.746181\pi$
$353$	−31.3301	+	18.0885i	−1.66753	+	0.962751i	−0.968961	+	0.247213i	$0.920485\pi$
$354$		0			0
$355$	6.92820	−	12.0000i	0.367711	−	0.636894i
$356$		0			0
$357$	−3.63397	−	2.09808i	−0.192330	−	0.111042i
$358$		0			0
$359$		−	16.3923i		−	0.865153i	−0.901597	−	0.432576i	$-0.857605\pi$
$359$		−	16.3923i		−	0.865153i	0.901597	−	0.432576i	$-0.142395\pi$
$360$		0			0
$361$	−8.42820	−	14.5981i	−0.443590	−	0.768320i
$362$		0			0
$363$	−7.66025			−0.402059
$364$		0			0
$365$	11.3923			0.596300
$366$		0			0
$367$	16.9545	+	29.3660i	0.885017	+	1.53289i	0.845694	+	0.533667i	$0.179187\pi$
$367$	16.9545	+	29.3660i	0.885017	+	1.53289i	0.0393224	+	0.999227i	$0.487480\pi$
$368$		0			0
$369$			6.07180i			0.316085i
$370$		0			0
$371$	1.33013	+	0.767949i	0.0690568	+	0.0398699i
$372$		0			0
$373$	16.2321	−	28.1147i	0.840464	−	1.45573i	−0.0490394	−	0.998797i	$-0.515616\pi$
$373$	16.2321	−	28.1147i	0.840464	−	1.45573i	0.889503	−	0.456929i	$-0.151051\pi$
$374$		0			0
$375$	5.70577	−	3.29423i	0.294645	−	0.170113i
$376$		0			0
$377$	−2.59808	+	10.5000i	−0.133808	+	0.540778i
$378$		0			0
$379$	−19.2224	+	11.0981i	−0.987390	+	0.570070i	−0.904493	−	0.426488i	$-0.859751\pi$
$379$	−19.2224	+	11.0981i	−0.987390	+	0.570070i	−0.0828969	+	0.996558i	$0.526417\pi$
$380$		0			0
$381$	3.60770	−	6.24871i	0.184828	−	0.320131i
$382$		0			0
$383$	−28.2224	−	16.2942i	−1.44210	−	0.832596i	−0.444109	−	0.895973i	$-0.646480\pi$
$383$	−28.2224	−	16.2942i	−1.44210	−	0.832596i	−0.997990	+	0.0633765i	$0.979813\pi$
$384$		0			0
$385$			0.732051i			0.0373088i
$386$		0			0
$387$	−15.0263	−	26.0263i	−0.763829	−	1.32299i
$388$		0			0
$389$	−24.3205			−1.23310			−0.616549	−	0.787316i	$-0.711470\pi$
$389$	−24.3205			−1.23310			−0.616549	+	0.787316i	$0.711470\pi$
$390$		0			0
$391$	7.26795			0.367556
$392$		0			0
$393$	1.85641	+	3.21539i	0.0936433	+	0.162195i
$394$		0			0
$395$		−	3.80385i		−	0.191392i
$396$		0			0
$397$	−25.5167	−	14.7321i	−1.28064	−	0.739380i	−0.303678	−	0.952775i	$-0.598215\pi$
$397$	−25.5167	−	14.7321i	−1.28064	−	0.739380i	−0.976966	+	0.213394i	$0.931548\pi$
$398$		0			0
$399$	−0.535898	+	0.928203i	−0.0268285	+	0.0464683i
$400$		0			0
$401$	−28.6244	+	16.5263i	−1.42943	+	0.825283i	−0.997076	−	0.0764198i	$-0.975651\pi$
$401$	−28.6244	+	16.5263i	−1.42943	+	0.825283i	−0.432356	+	0.901703i	$0.642318\pi$
$402$		0			0
$403$	13.1699	−	13.6865i	0.656038	−	0.681775i
$404$		0			0
$405$	−3.86603	+	2.23205i	−0.192104	+	0.110911i
$406$		0			0
$407$	−1.90192	+	3.29423i	−0.0942749	+	0.163289i
$408$		0			0
$409$	22.7942	+	13.1603i	1.12710	+	0.650733i	0.943204	−	0.332213i	$-0.107795\pi$
$409$	22.7942	+	13.1603i	1.12710	+	0.650733i	0.183898	+	0.982945i	$0.441129\pi$
$410$		0			0
$411$		−	4.48334i		−	0.221147i
$412$		0			0
$413$	5.36603	+	9.29423i	0.264045	+	0.457339i
$414$		0			0
$415$	3.80385			0.186724
$416$		0			0
$417$	−0.248711			−0.0121794
$418$		0			0
$419$	2.56218	+	4.43782i	0.125171	+	0.216802i	0.921800	−	0.387667i	$-0.126719\pi$
$419$	2.56218	+	4.43782i	0.125171	+	0.216802i	−0.796629	+	0.604469i	$0.793386\pi$
$420$		0			0
$421$			14.1244i			0.688379i	0.938900	+	0.344189i	$0.111846\pi$
$421$			14.1244i			0.688379i	−0.938900	+	0.344189i	$0.888154\pi$
$422$		0			0
$423$	6.24871	+	3.60770i	0.303823	+	0.175412i
$424$		0			0
$425$	−11.4641	+	19.8564i	−0.556091	+	0.963177i
$426$		0			0
$427$	10.1603	−	5.86603i	0.491689	−	0.283877i
$428$		0			0
$429$	−0.535898	−	1.85641i	−0.0258734	−	0.0896281i
$430$		0			0
$431$	−22.9808	+	13.2679i	−1.10694	+	0.639095i	−0.938036	−	0.346537i	$-0.887357\pi$
$431$	−22.9808	+	13.2679i	−1.10694	+	0.639095i	−0.168908	+	0.985632i	$0.554024\pi$
$432$		0			0
$433$	10.8660	−	18.8205i	0.522188	−	0.904456i	−0.477479	−	0.878643i	$-0.658449\pi$
$433$	10.8660	−	18.8205i	0.522188	−	0.904456i	0.999667	−	0.0258127i	$-0.00821735\pi$
$434$		0			0
$435$	1.90192	+	1.09808i	0.0911903	+	0.0526487i
$436$		0			0
$437$		−	1.85641i		−	0.0888040i
$438$		0			0
$439$	9.63397	+	16.6865i	0.459805	+	0.796405i	0.998950	−	0.0458077i	$-0.0145861\pi$
$439$	9.63397	+	16.6865i	0.459805	+	0.796405i	−0.539146	+	0.842212i	$0.681253\pi$
$440$		0			0
$441$	2.46410			0.117338
$442$		0			0
$443$	−35.3205			−1.67813			−0.839064	−	0.544033i	$-0.816897\pi$
$443$	−35.3205			−1.67813			−0.839064	+	0.544033i	$0.816897\pi$
$444$		0			0
$445$	−1.26795	−	2.19615i	−0.0601066	−	0.104108i
$446$		0			0
$447$		−	12.5885i		−	0.595414i
$448$		0			0
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	0.820491	−	0.571660i	$-0.193700\pi$
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	−0.0848262	+	0.996396i	$0.527033\pi$
$450$		0			0
$451$	0.901924	−	1.56218i	0.0424699	−	0.0735601i
$452$		0			0
$453$	7.85641	−	4.53590i	0.369126	−	0.213115i
$454$		0			0
$455$	3.46410	−	1.00000i	0.162400	−	0.0468807i
$456$		0			0
$457$	−12.3564	+	7.13397i	−0.578008	+	0.333713i	−0.760341	−	0.649524i	$-0.774968\pi$
$457$	−12.3564	+	7.13397i	−0.578008	+	0.333713i	0.182333	+	0.983237i	$0.441635\pi$
$458$		0			0
$459$	−11.4641	+	19.8564i	−0.535098	+	0.926818i
$460$		0			0
$461$	7.20577	+	4.16025i	0.335606	+	0.193762i	0.658327	−	0.752732i	$-0.271264\pi$
$461$	7.20577	+	4.16025i	0.335606	+	0.193762i	−0.322721	+	0.946494i	$0.604598\pi$
$462$		0			0
$463$			3.94744i			0.183453i	0.995784	+	0.0917266i	$0.0292386\pi$
$463$			3.94744i			0.183453i	−0.995784	+	0.0917266i	$0.970761\pi$
$464$		0			0
$465$	−1.92820	−	3.33975i	−0.0894183	−	0.154877i
$466$		0			0
$467$	−24.7321			−1.14446			−0.572231	−	0.820092i	$-0.693922\pi$
$467$	−24.7321			−1.14446			−0.572231	+	0.820092i	$0.693922\pi$
$468$		0			0
$469$	−11.6603			−0.538421
$470$		0			0
$471$	5.02628	+	8.70577i	0.231599	+	0.401141i
$472$		0			0
$473$			8.92820i			0.410519i
$474$		0			0
$475$	5.07180	+	2.92820i	0.232710	+	0.134355i
$476$		0			0
$477$	1.89230	−	3.27757i	0.0866427	−	0.150070i
$478$		0			0
$479$	−27.8827	+	16.0981i	−1.27399	+	0.735540i	−0.975737	−	0.218946i	$-0.929738\pi$
$479$	−27.8827	+	16.0981i	−1.27399	+	0.735540i	−0.298256	+	0.954486i	$0.596405\pi$
$480$		0			0
$481$	18.1865	+	4.50000i	0.829235	+	0.205182i
$482$		0			0
$483$	0.803848	−	0.464102i	0.0365763	−	0.0211174i
$484$		0			0
$485$	−2.73205	+	4.73205i	−0.124056	+	0.214871i
$486$		0			0
$487$	−27.1244	−	15.6603i	−1.22912	−	0.709634i	−0.262276	−	0.964993i	$-0.584473\pi$
$487$	−27.1244	−	15.6603i	−1.22912	−	0.709634i	−0.966846	+	0.255359i	$0.917806\pi$
$488$		0			0
$489$			0.535898i			0.0242342i
$490$		0			0
$491$	13.8564	+	24.0000i	0.625331	+	1.08310i	0.988477	+	0.151373i	$0.0483693\pi$
$491$	13.8564	+	24.0000i	0.625331	+	1.08310i	−0.363146	+	0.931732i	$0.618297\pi$
$492$		0			0
$493$	−17.1962			−0.774476
$494$		0			0
$495$	1.80385			0.0810769
$496$		0			0
$497$	6.92820	+	12.0000i	0.310772	+	0.538274i
$498$		0			0
$499$		−	11.2679i		−	0.504423i	−0.967672	−	0.252211i	$-0.918842\pi$
$499$		−	11.2679i		−	0.504423i	0.967672	−	0.252211i	$-0.0811578\pi$
$500$		0			0
$501$	3.33975	+	1.92820i	0.149209	+	0.0861458i
$502$		0			0
$503$	10.3660	−	17.9545i	0.462198	−	0.800551i	−0.536872	−	0.843664i	$-0.680394\pi$
$503$	10.3660	−	17.9545i	0.462198	−	0.800551i	0.999070	+	0.0431129i	$0.0137275\pi$
$504$		0			0
$505$	1.03590	−	0.598076i	0.0460969	−	0.0266140i
$506$		0			0
$507$	−8.05256	+	5.07180i	−0.357627	+	0.225246i
$508$		0			0
$509$	−23.7224	+	13.6962i	−1.05148	+	0.607071i	−0.923063	−	0.384649i	$-0.874322\pi$
$509$	−23.7224	+	13.6962i	−1.05148	+	0.607071i	−0.128415	+	0.991720i	$0.540989\pi$
$510$		0			0
$511$	−5.69615	+	9.86603i	−0.251983	+	0.436447i
$512$		0			0
$513$	5.07180	+	2.92820i	0.223925	+	0.129283i
$514$		0			0
$515$			8.39230i			0.369809i
$516$		0			0
$517$	−1.07180	−	1.85641i	−0.0471376	−	0.0816447i
$518$		0			0
$519$	−15.3205			−0.672496
$520$		0			0
$521$	44.3731			1.94402			0.972010	−	0.234941i	$-0.0754896\pi$
$521$	44.3731			1.94402			0.972010	+	0.234941i	$0.0754896\pi$
$522$		0			0
$523$	10.7321	+	18.5885i	0.469280	+	0.812816i	0.999383	−	0.0351165i	$-0.0111802\pi$
$523$	10.7321	+	18.5885i	0.469280	+	0.812816i	−0.530103	+	0.847933i	$0.677847\pi$
$524$		0			0
$525$			2.92820i			0.127797i
$526$		0			0
$527$	26.1506	+	15.0981i	1.13914	+	0.657683i
$528$		0			0
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$		0			0
$531$	22.9019	−	13.2224i	0.993859	−	0.573805i
$532$		0			0
$533$	−8.62436	−	2.13397i	−0.373562	−	0.0924327i
$534$		0			0
$535$	9.46410	−	5.46410i	0.409169	−	0.236234i
$536$		0			0
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$		0			0
$539$	−0.633975	−	0.366025i	−0.0273072	−	0.0157658i
$540$		0			0
$541$			8.26795i			0.355467i	0.984079	+	0.177733i	$0.0568765\pi$
$541$			8.26795i			0.355467i	−0.984079	+	0.177733i	$0.943124\pi$
$542$		0			0
$543$	1.16987	+	2.02628i	0.0502041	+	0.0869560i
$544$		0			0
$545$	−10.0000			−0.428353
$546$		0			0
$547$	30.4449			1.30173			0.650864	−	0.759194i	$-0.274407\pi$
$547$	30.4449			1.30173			0.650864	+	0.759194i	$0.274407\pi$
$548$		0			0
$549$	−14.4545	−	25.0359i	−0.616902	−	1.06851i
$550$		0			0
$551$			4.39230i			0.187118i
$552$		0			0
$553$	3.29423	+	1.90192i	0.140085	+	0.0808780i
$554$		0			0
$555$	1.90192	−	3.29423i	0.0807322	−	0.139832i
$556$		0			0
$557$	22.6244	−	13.0622i	0.958625	−	0.553462i	0.0628752	−	0.998021i	$-0.479973\pi$
$557$	22.6244	−	13.0622i	0.958625	−	0.553462i	0.895749	+	0.444559i	$0.146640\pi$
$558$		0			0
$559$	42.2487	−	12.1962i	1.78693	−	0.515842i
$560$		0			0
$561$	2.66025	−	1.53590i	0.112316	−	0.0648457i
$562$		0			0
$563$	14.2224	−	24.6340i	0.599404	−	1.03820i	−0.393505	−	0.919322i	$-0.628738\pi$
$563$	14.2224	−	24.6340i	0.599404	−	1.03820i	0.992909	−	0.118876i	$-0.0379290\pi$
$564$		0			0
$565$	9.86603	+	5.69615i	0.415067	+	0.239639i
$566$		0			0
$567$		−	4.46410i		−	0.187475i
$568$		0			0
$569$	−5.66025	−	9.80385i	−0.237290	−	0.410999i	0.722646	−	0.691219i	$-0.242926\pi$
$569$	−5.66025	−	9.80385i	−0.237290	−	0.410999i	−0.959936	+	0.280220i	$0.909593\pi$
$570$		0			0
$571$	−5.46410			−0.228666			−0.114333	−	0.993443i	$-0.536473\pi$
$571$	−5.46410			−0.228666			−0.114333	+	0.993443i	$0.536473\pi$
$572$		0			0
$573$	5.21539			0.217876
$574$		0			0
$575$	−2.53590	−	4.39230i	−0.105754	−	0.183172i
$576$		0			0
$577$			34.1769i			1.42280i	0.702786	+	0.711402i	$0.251939\pi$
$577$			34.1769i			1.42280i	−0.702786	+	0.711402i	$0.748061\pi$
$578$		0			0
$579$	−14.7058	−	8.49038i	−0.611151	−	0.352848i
$580$		0			0
$581$	−1.90192	+	3.29423i	−0.0789051	+	0.136668i
$582$		0			0
$583$	−0.973721	+	0.562178i	−0.0403274	+	0.0232830i
$584$		0			0
$585$	−2.46410	−	8.53590i	−0.101878	−	0.352916i
$586$		0			0
$587$	24.9282	−	14.3923i	1.02890	−	0.594034i	0.112229	−	0.993682i	$-0.464201\pi$
$587$	24.9282	−	14.3923i	1.02890	−	0.594034i	0.916668	+	0.399648i	$0.130868\pi$
$588$		0			0
$589$	3.85641	−	6.67949i	0.158900	−	0.275224i
$590$		0			0
$591$	4.48334	+	2.58846i	0.184420	+	0.106475i
$592$		0			0
$593$		−	3.14359i		−	0.129092i	−0.997915	−	0.0645460i	$-0.979440\pi$
$593$		−	3.14359i		−	0.129092i	0.997915	−	0.0645460i	$-0.0205599\pi$
$594$		0			0
$595$	2.86603	+	4.96410i	0.117496	+	0.203508i
$596$		0			0
$597$	4.00000			0.163709
$598$		0			0
$599$	−30.9282			−1.26369			−0.631846	−	0.775094i	$-0.717703\pi$
$599$	−30.9282			−1.26369			−0.631846	+	0.775094i	$0.717703\pi$
$600$		0			0
$601$	11.5263	+	19.9641i	0.470167	+	0.814353i	0.999418	−	0.0341125i	$-0.0108604\pi$
$601$	11.5263	+	19.9641i	0.470167	+	0.814353i	−0.529251	+	0.848465i	$0.677527\pi$
$602$		0			0
$603$			28.7321i			1.17006i
$604$		0			0
$605$	9.06218	+	5.23205i	0.368430	+	0.212713i
$606$		0			0
$607$	−4.92820	+	8.53590i	−0.200030	+	0.346461i	−0.948538	−	0.316664i	$-0.897437\pi$
$607$	−4.92820	+	8.53590i	−0.200030	+	0.346461i	0.748508	+	0.663126i	$0.230770\pi$
$608$		0			0
$609$	−1.90192	+	1.09808i	−0.0770698	+	0.0444963i
$610$		0			0
$611$	−7.32051	+	7.60770i	−0.296156	+	0.307774i
$612$		0			0
$613$	13.8397	−	7.99038i	0.558982	−	0.322728i	−0.193755	−	0.981050i	$-0.562067\pi$
$613$	13.8397	−	7.99038i	0.558982	−	0.322728i	0.752737	+	0.658322i	$0.228733\pi$
$614$		0			0
$615$	−0.901924	+	1.56218i	−0.0363691	+	0.0629931i
$616$		0			0
$617$	−28.7487	−	16.5981i	−1.15738	−	0.668213i	−0.206705	−	0.978403i	$-0.566274\pi$
$617$	−28.7487	−	16.5981i	−1.15738	−	0.668213i	−0.950675	+	0.310190i	$0.899607\pi$
$618$		0			0
$619$		−	34.0526i		−	1.36869i	−0.729159	−	0.684344i	$-0.760089\pi$
$619$		−	34.0526i		−	1.36869i	0.729159	−	0.684344i	$-0.239911\pi$
$620$		0			0
$621$	−2.53590	−	4.39230i	−0.101762	−	0.176257i
$622$		0			0
$623$	2.53590			0.101599
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−0.392305	−	0.679492i	−0.0156671	−	0.0271363i
$628$		0			0
$629$			29.7846i			1.18759i
$630$		0			0
$631$	−9.12436	−	5.26795i	−0.363235	−	0.209714i	0.307264	−	0.951624i	$-0.400587\pi$
$631$	−9.12436	−	5.26795i	−0.363235	−	0.209714i	−0.670499	+	0.741911i	$0.733920\pi$
$632$		0			0
$633$	7.78461	−	13.4833i	0.309410	−	0.535915i
$634$		0			0
$635$	−8.53590	+	4.92820i	−0.338737	+	0.195570i
$636$		0			0
$637$	−0.866025	+	3.50000i	−0.0343132	+	0.138675i
$638$		0			0
$639$	29.5692	−	17.0718i	1.16974	−	0.675350i
$640$		0			0
$641$	22.2321	−	38.5070i	0.878113	−	1.52094i	0.0247042	−	0.999695i	$-0.492136\pi$
$641$	22.2321	−	38.5070i	0.878113	−	1.52094i	0.853409	−	0.521242i	$-0.174531\pi$
$642$		0			0
$643$	−30.9282	−	17.8564i	−1.21969	−	0.704188i	−0.254838	−	0.966984i	$-0.582022\pi$
$643$	−30.9282	−	17.8564i	−1.21969	−	0.704188i	−0.964851	+	0.262796i	$0.915355\pi$
$644$		0			0
$645$		−	8.92820i		−	0.351548i
$646$		0			0
$647$	6.92820	+	12.0000i	0.272376	+	0.471769i	0.969470	−	0.245211i	$-0.0788573\pi$
$647$	6.92820	+	12.0000i	0.272376	+	0.471769i	−0.697094	+	0.716980i	$0.745524\pi$
$648$		0			0
$649$	−7.85641			−0.308391
$650$		0			0
$651$	3.85641			0.151144
$652$		0			0
$653$	−6.19615	−	10.7321i	−0.242474	−	0.419978i	0.718944	−	0.695068i	$-0.244626\pi$
$653$	−6.19615	−	10.7321i	−0.242474	−	0.419978i	−0.961418	+	0.275090i	$0.911292\pi$
$654$		0			0
$655$		−	5.07180i		−	0.198171i
$656$		0			0
$657$	24.3109	+	14.0359i	0.948458	+	0.547593i
$658$		0			0
$659$	4.39230	−	7.60770i	0.171100	−	0.296354i	−0.767705	−	0.640804i	$-0.778601\pi$
$659$	4.39230	−	7.60770i	0.171100	−	0.296354i	0.938805	+	0.344450i	$0.111935\pi$
$660$		0			0
$661$	1.66987	−	0.964102i	0.0649505	−	0.0374992i	−0.467173	−	0.884166i	$-0.654727\pi$
$661$	1.66987	−	0.964102i	0.0649505	−	0.0374992i	0.532124	+	0.846667i	$0.321394\pi$
$662$		0			0
$663$	−10.9019	−	10.4904i	−0.423396	−	0.407413i
$664$		0			0
$665$	1.26795	−	0.732051i	0.0491690	−	0.0283877i
$666$		0			0
$667$	1.90192	−	3.29423i	0.0736428	−	0.127553i
$668$		0			0
$669$	−7.85641	−	4.53590i	−0.303746	−	0.175368i
$670$		0			0
$671$			8.58846i			0.331554i
$672$		0			0
$673$	10.8923	+	18.8660i	0.419867	+	0.727232i	0.995926	−	0.0901768i	$-0.0287432\pi$
$673$	10.8923	+	18.8660i	0.419867	+	0.727232i	−0.576058	+	0.817409i	$0.695410\pi$
$674$		0			0
$675$	16.0000			0.615840
$676$		0			0
$677$	27.8564			1.07061			0.535304	−	0.844659i	$-0.320197\pi$
$677$	27.8564			1.07061			0.535304	+	0.844659i	$0.320197\pi$
$678$		0			0
$679$	−2.73205	−	4.73205i	−0.104846	−	0.181599i
$680$		0			0
$681$		−	0.928203i		−	0.0355688i
$682$		0			0
$683$	−5.66025	−	3.26795i	−0.216584	−	0.125045i	0.387784	−	0.921750i	$-0.373241\pi$
$683$	−5.66025	−	3.26795i	−0.216584	−	0.125045i	−0.604367	+	0.796706i	$0.706574\pi$
$684$		0			0
$685$	−3.06218	+	5.30385i	−0.117000	+	0.202650i
$686$		0			0
$687$	15.4641	−	8.92820i	0.589992	−	0.340632i
$688$		0			0
$689$	3.99038	+	3.83975i	0.152021	+	0.146283i
$690$		0			0
$691$	−5.07180	+	2.92820i	−0.192940	+	0.111394i	−0.593358	−	0.804938i	$-0.702198\pi$
$691$	−5.07180	+	2.92820i	−0.192940	+	0.111394i	0.400418	+	0.916333i	$0.368865\pi$
$692$		0			0
$693$	−0.901924	+	1.56218i	−0.0342613	+	0.0593422i
$694$		0			0
$695$	0.294229	+	0.169873i	0.0111607	+	0.00644365i
$696$		0			0
$697$		−	14.1244i		−	0.534998i
$698$		0			0
$699$	1.60770	+	2.78461i	0.0608086	+	0.105324i
$700$		0			0
$701$	−14.5359			−0.549013			−0.274507	−	0.961585i	$-0.588515\pi$
$701$	−14.5359			−0.549013			−0.274507	+	0.961585i	$0.588515\pi$
$702$		0			0
$703$	7.60770			0.286930
$704$		0			0
$705$	1.07180	+	1.85641i	0.0403662	+	0.0699163i
$706$		0			0
$707$			1.19615i			0.0449859i
$708$		0			0
$709$	−5.64359	−	3.25833i	−0.211950	−	0.122369i	0.390268	−	0.920702i	$-0.372383\pi$
$709$	−5.64359	−	3.25833i	−0.211950	−	0.122369i	−0.602217	+	0.798332i	$0.705716\pi$
$710$		0			0
$711$	4.68653	−	8.11731i	0.175759	−	0.304423i
$712$		0			0
$713$	−5.78461	+	3.33975i	−0.216635	+	0.125074i
$714$		0			0
$715$	−0.633975	+	2.56218i	−0.0237093	+	0.0958200i
$716$		0			0
$717$	−18.7128	+	10.8038i	−0.698843	+	0.403477i
$718$		0			0
$719$	3.09808	−	5.36603i	0.115539	−	0.200119i	−0.802456	−	0.596711i	$-0.796474\pi$
$719$	3.09808	−	5.36603i	0.115539	−	0.200119i	0.917995	+	0.396592i	$0.129807\pi$
$720$		0			0
$721$	−7.26795	−	4.19615i	−0.270673	−	0.156273i
$722$		0			0
$723$		−	11.2679i		−	0.419060i
$724$		0			0
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$		0			0
$727$	53.8564			1.99742			0.998712	−	0.0507424i	$-0.0161587\pi$
$727$	53.8564			1.99742			0.998712	+	0.0507424i	$0.0161587\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$		0			0
$731$	34.9545	+	60.5429i	1.29284	+	2.23926i
$732$		0			0
$733$		−	2.46410i		−	0.0910137i	−0.998964	−	0.0455068i	$-0.985510\pi$
$733$		−	2.46410i		−	0.0910137i	0.998964	−	0.0455068i	$-0.0144903\pi$
$734$		0			0
$735$	0.633975	+	0.366025i	0.0233845	+	0.0135011i
$736$		0			0
$737$	4.26795	−	7.39230i	0.157212	−	0.272299i
$738$		0			0
$739$	−5.66025	+	3.26795i	−0.208216	+	0.120213i	−0.600482	−	0.799638i	$-0.705025\pi$
$739$	−5.66025	+	3.26795i	−0.208216	+	0.120213i	0.392266	+	0.919852i	$0.371691\pi$
$740$		0			0
$741$	−2.67949	+	2.78461i	−0.0984336	+	0.102295i
$742$		0			0
$743$	4.39230	−	2.53590i	0.161138	−	0.0930331i	−0.417262	−	0.908786i	$-0.637010\pi$
$743$	4.39230	−	2.53590i	0.161138	−	0.0930331i	0.578401	+	0.815753i	$0.303677\pi$
$744$		0			0
$745$	−8.59808	+	14.8923i	−0.315009	+	0.545612i
$746$		0			0
$747$	8.11731	+	4.68653i	0.296997	+	0.171471i
$748$		0			0
$749$			10.9282i			0.399308i
$750$		0			0
$751$	−3.22243	−	5.58142i	−0.117588	−	0.203669i	0.801223	−	0.598366i	$-0.204183\pi$
$751$	−3.22243	−	5.58142i	−0.117588	−	0.203669i	−0.918811	+	0.394697i	$0.870850\pi$
$752$		0			0
$753$	−16.7846			−0.611665
$754$		0			0
$755$	−12.3923			−0.451002
$756$		0			0
$757$	22.1962	+	38.4449i	0.806733	+	1.39730i	0.915115	+	0.403193i	$0.132100\pi$
$757$	22.1962	+	38.4449i	0.806733	+	1.39730i	−0.108382	+	0.994109i	$0.534567\pi$
$758$		0			0
$759$			0.679492i			0.0246640i
$760$		0			0
$761$	15.8038	+	9.12436i	0.572889	+	0.330758i	0.758302	−	0.651903i	$-0.226029\pi$
$761$	15.8038	+	9.12436i	0.572889	+	0.330758i	−0.185413	+	0.982661i	$0.559362\pi$
$762$		0			0
$763$	5.00000	−	8.66025i	0.181012	−	0.313522i
$764$		0			0
$765$	12.2321	−	7.06218i	0.442251	−	0.255334i
$766$		0			0
$767$	10.7321	+	37.1769i	0.387512	+	1.34238i
$768$		0			0
$769$	0.339746	−	0.196152i	0.0122516	−	0.00707344i	−0.493862	−	0.869540i	$-0.664415\pi$
$769$	0.339746	−	0.196152i	0.0122516	−	0.00707344i	0.506113	+	0.862467i	$0.331082\pi$
$770$		0			0
$771$	−0.490381	+	0.849365i	−0.0176606	+	0.0305891i
$772$		0			0
$773$	40.0526	+	23.1244i	1.44059	+	0.831725i	0.997889	−	0.0649438i	$-0.0206868\pi$
$773$	40.0526	+	23.1244i	1.44059	+	0.831725i	0.442701	+	0.896669i	$0.354020\pi$
$774$		0			0
$775$		−	21.0718i		−	0.756921i
$776$		0			0
$777$	1.90192	+	3.29423i	0.0682311	+	0.118180i
$778$		0			0
$779$	−3.60770			−0.129259
$780$		0			0
$781$	−10.1436			−0.362966
$782$		0			0
$783$	6.00000	+	10.3923i	0.214423	+	0.371391i
$784$		0			0
$785$		−	13.7321i		−	0.490118i
$786$		0			0
$787$	38.9545	+	22.4904i	1.38858	+	0.801696i	0.993155	−	0.116804i	$-0.0372649\pi$
$787$	38.9545	+	22.4904i	1.38858	+	0.801696i	0.395422	+	0.918499i	$0.370598\pi$
$788$		0			0
$789$	7.53590	−	13.0526i	0.268285	−	0.464683i
$790$		0			0
$791$	−9.86603	+	5.69615i	−0.350795	+	0.202532i
$792$		0			0
$793$	40.6410	−	11.7321i	1.44320	−	0.416617i
$794$		0			0
$795$	0.973721	−	0.562178i	0.0345343	−	0.0199384i
$796$		0			0
$797$	−4.46410	+	7.73205i	−0.158127	+	0.273883i	−0.934193	−	0.356768i	$-0.883879\pi$
$797$	−4.46410	+	7.73205i	−0.158127	+	0.273883i	0.776067	+	0.630651i	$0.217212\pi$
$798$		0			0
$799$	−14.5359	−	8.39230i	−0.514243	−	0.296898i
$800$		0			0
$801$		−	6.24871i		−	0.220787i
$802$		0			0
$803$	−4.16987	−	7.22243i	−0.147152	−	0.254874i
$804$		0			0
$805$	−1.26795			−0.0446893
$806$		0			0
$807$	21.0718			0.741762
$808$		0			0
$809$	3.62436	+	6.27757i	0.127426	+	0.220708i	0.922678	−	0.385570i	$-0.125995\pi$
$809$	3.62436	+	6.27757i	0.127426	+	0.220708i	−0.795253	+	0.606278i	$0.792662\pi$
$810$		0			0
$811$			20.8756i			0.733043i	0.930410	+	0.366522i	$0.119451\pi$
$811$			20.8756i			0.733043i	−0.930410	+	0.366522i	$0.880549\pi$
$812$		0			0
$813$	−4.51666	−	2.60770i	−0.158406	−	0.0914559i
$814$		0			0
$815$	0.366025	−	0.633975i	0.0128213	−	0.0222072i
$816$		0			0
$817$	15.4641	−	8.92820i	0.541020	−	0.312358i
$818$		0			0
$819$	8.62436	+	2.13397i	0.301359	+	0.0745671i
$820$		0			0
$821$	−26.7846	+	15.4641i	−0.934789	+	0.539701i	−0.888323	−	0.459219i	$-0.848129\pi$
$821$	−26.7846	+	15.4641i	−0.934789	+	0.539701i	−0.0464662	+	0.998920i	$0.514796\pi$
$822$		0			0
$823$	−1.12436	+	1.94744i	−0.0391926	+	0.0678835i	−0.884956	−	0.465674i	$-0.845812\pi$
$823$	−1.12436	+	1.94744i	−0.0391926	+	0.0678835i	0.845764	+	0.533558i	$0.179145\pi$
$824$		0			0
$825$	−1.85641	−	1.07180i	−0.0646318	−	0.0373152i
$826$		0			0
$827$			20.4449i			0.710938i	0.934688	+	0.355469i	$0.115679\pi$
$827$			20.4449i			0.710938i	−0.934688	+	0.355469i	$0.884321\pi$
$828$		0			0
$829$	−3.20577	−	5.55256i	−0.111341	−	0.192848i	0.804970	−	0.593315i	$-0.202181\pi$
$829$	−3.20577	−	5.55256i	−0.111341	−	0.192848i	−0.916311	+	0.400467i	$0.868848\pi$
$830$		0			0
$831$	6.87564			0.238513
$832$		0			0
$833$	−5.73205			−0.198604
$834$		0			0
$835$	−2.63397	−	4.56218i	−0.0911524	−	0.157881i
$836$		0			0
$837$		−	21.0718i		−	0.728348i
$838$		0			0
$839$	−27.4641	−	15.8564i	−0.948166	−	0.547424i	−0.0556553	−	0.998450i	$-0.517725\pi$
$839$	−27.4641	−	15.8564i	−0.948166	−	0.547424i	−0.892511	+	0.451026i	$0.851058\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	10.5622	−	6.09808i	0.363781	−	0.210029i
$844$		0			0
$845$	12.9904	−	0.500000i	0.446883	−	0.0172005i
$846$		0			0
$847$	−9.06218	+	5.23205i	−0.311380	+	0.179775i
$848$		0			0
$849$	−3.87564	+	6.71281i	−0.133012	+	0.230383i
$850$		0			0
$851$	−5.70577	−	3.29423i	−0.195591	−	0.112925i
$852$		0			0
$853$		−	19.0000i		−	0.650548i	−0.945620	−	0.325274i	$-0.894544\pi$
$853$		−	19.0000i		−	0.650548i	0.945620	−	0.325274i	$-0.105456\pi$
$854$		0			0
$855$	−1.80385	−	3.12436i	−0.0616903	−	0.106851i
$856$		0			0
$857$	0.947441			0.0323640			0.0161820	−	0.999869i	$-0.494849\pi$
$857$	0.947441			0.0323640			0.0161820	+	0.999869i	$0.494849\pi$
$858$		0			0
$859$	32.8372			1.12039			0.560195	−	0.828361i	$-0.310726\pi$
$859$	32.8372			1.12039			0.560195	+	0.828361i	$0.310726\pi$
$860$		0			0
$861$	−0.901924	−	1.56218i	−0.0307375	−	0.0532389i
$862$		0			0
$863$			44.4449i			1.51292i	0.654040	+	0.756460i	$0.273073\pi$
$863$			44.4449i			1.51292i	−0.654040	+	0.756460i	$0.726927\pi$
$864$		0			0
$865$	18.1244	+	10.4641i	0.616247	+	0.355790i
$866$		0			0
$867$	5.80385	−	10.0526i	0.197109	−	0.341403i
$868$		0			0
$869$	−2.41154	+	1.39230i	−0.0818060	+	0.0472307i
$870$		0			0
$871$	−40.8109	−	10.0981i	−1.38282	−	0.342160i
$872$		0			0
$873$	−11.6603	+	6.73205i	−0.394640	+	0.227845i
$874$		0			0
$875$	4.50000	−	7.79423i	0.152128	−	0.263493i
$876$		0			0
$877$	1.62436	+	0.937822i	0.0548506	+	0.0316680i	0.527175	−	0.849757i	$-0.323251\pi$
$877$	1.62436	+	0.937822i	0.0548506	+	0.0316680i	−0.472324	+	0.881425i	$0.656585\pi$
$878$		0			0
$879$			12.7321i			0.429441i
$880$		0			0
$881$	−17.1865	−	29.7679i	−0.579029	−	1.00291i	−0.995591	−	0.0938004i	$-0.970098\pi$
$881$	−17.1865	−	29.7679i	−0.579029	−	1.00291i	0.416562	−	0.909107i	$-0.363235\pi$
$882$		0			0
$883$	−23.5167			−0.791399			−0.395699	−	0.918380i	$-0.629498\pi$
$883$	−23.5167			−0.791399			−0.395699	+	0.918380i	$0.629498\pi$
$884$		0			0
$885$	7.85641			0.264090
$886$		0			0
$887$	1.46410	+	2.53590i	0.0491597	+	0.0851471i	0.889558	−	0.456822i	$-0.151012\pi$
$887$	1.46410	+	2.53590i	0.0491597	+	0.0851471i	−0.840398	+	0.541969i	$0.817679\pi$
$888$		0			0
$889$		−	9.85641i		−	0.330573i
$890$		0			0
$891$	2.83013	+	1.63397i	0.0948128	+	0.0547402i
$892$		0			0
$893$	−2.14359	+	3.71281i	−0.0717326	+	0.124245i
$894$		0			0
$895$	−14.1962	+	8.19615i	−0.474525	+	0.273967i
$896$		0			0
$897$	3.21539	−	0.928203i	0.107359	−	0.0309918i
$898$		0			0
$899$	13.6865	−	7.90192i	0.456471	−	0.263544i
$900$		0			0
$901$	−4.40192	+	7.62436i	−0.146649	+	0.254004i
$902$		0			0
$903$	7.73205	+	4.46410i	0.257307	+	0.148556i
$904$		0			0
$905$		−	3.19615i		−	0.106244i
$906$		0			0
$907$	11.0263	+	19.0981i	0.366122	+	0.634141i	0.988955	−	0.148213i	$-0.0473521\pi$
$907$	11.0263	+	19.0981i	0.366122	+	0.634141i	−0.622834	+	0.782354i	$0.714019\pi$
$908$		0			0
$909$	2.94744			0.0977605
$910$		0			0
$911$	40.1051			1.32874			0.664371	−	0.747403i	$-0.268700\pi$
$911$	40.1051			1.32874			0.664371	+	0.747403i	$0.268700\pi$
$912$		0			0
$913$	−1.39230	−	2.41154i	−0.0460786	−	0.0798104i
$914$		0			0
$915$		−	8.58846i		−	0.283926i
$916$		0			0
$917$	4.39230	+	2.53590i	0.145047	+	0.0837427i
$918$		0			0
$919$	0.392305	−	0.679492i	0.0129409	−	0.0224144i	−0.859482	−	0.511165i	$-0.829214\pi$
$919$	0.392305	−	0.679492i	0.0129409	−	0.0224144i	0.872423	+	0.488751i	$0.162547\pi$
$920$		0			0
$921$	−14.9090	+	8.60770i	−0.491267	+	0.283633i
$922$		0			0
$923$	13.8564	+	48.0000i	0.456089	+	1.57994i
$924$		0			0
$925$	18.0000	−	10.3923i	0.591836	−	0.341697i
$926$		0			0
$927$	−10.3397	+	17.9090i	−0.339602	+	0.588208i
$928$		0			0
$929$	−47.7224	−	27.5526i	−1.56572	−	0.903970i	−0.996659	−	0.0816764i	$-0.973973\pi$
$929$	−47.7224	−	27.5526i	−1.56572	−	0.903970i	−0.569063	−	0.822294i	$-0.692694\pi$
$930$		0			0
$931$			1.46410i			0.0479840i
$932$		0			0
$933$	−3.73205	−	6.46410i	−0.122182	−	0.211625i
$934$		0			0
$935$	−4.19615			−0.137229
$936$		0			0
$937$	55.5885			1.81600			0.907998	−	0.418975i	$-0.137610\pi$
$937$	55.5885			1.81600			0.907998	+	0.418975i	$0.137610\pi$
$938$		0			0
$939$	−11.7128	−	20.2872i	−0.382233	−	0.662047i
$940$		0			0
$941$		−	11.3205i		−	0.369038i	−0.982829	−	0.184519i	$-0.940927\pi$
$941$		−	11.3205i		−	0.369038i	0.982829	−	0.184519i	$-0.0590727\pi$
$942$		0			0
$943$	2.70577	+	1.56218i	0.0881120	+	0.0508715i
$944$		0			0
$945$	2.00000	−	3.46410i	0.0650600	−	0.112687i
$946$		0			0
$947$	−46.0070	+	26.5622i	−1.49503	+	0.863155i	−0.999984	−	0.00571294i	$-0.998182\pi$
$947$	−46.0070	+	26.5622i	−1.49503	+	0.863155i	−0.495044	+	0.868868i	$0.664848\pi$
$948$		0			0
$949$	−28.4808	+	29.5981i	−0.924525	+	0.960794i
$950$		0			0
$951$	−4.47114	+	2.58142i	−0.144987	+	0.0837081i
$952$		0			0
$953$	18.5885	−	32.1962i	0.602139	−	1.04294i	−0.390357	−	0.920663i	$-0.627649\pi$
$953$	18.5885	−	32.1962i	0.602139	−	1.04294i	0.992497	−	0.122272i	$-0.0390181\pi$
$954$		0			0
$955$	−6.16987	−	3.56218i	−0.199652	−	0.115269i
$956$		0			0
$957$		−	1.60770i		−	0.0519694i
$958$		0			0
$959$	−3.06218	−	5.30385i	−0.0988829	−	0.171270i
$960$		0			0
$961$	3.24871			0.104797
$962$		0			0
$963$	26.9282			0.867749
$964$		0			0
$965$	11.5981	+	20.0885i	0.373355	+	0.646670i
$966$		0			0
$967$		−	13.5167i		−	0.434666i	−0.976097	−	0.217333i	$-0.930264\pi$
$967$		−	13.5167i		−	0.434666i	0.976097	−	0.217333i	$-0.0697358\pi$
$968$		0			0
$969$	−5.32051	−	3.07180i	−0.170919	−	0.0986803i
$970$		0			0
$971$	−10.1962	+	17.6603i	−0.327210	+	0.566745i	−0.981957	−	0.189104i	$-0.939442\pi$
$971$	−10.1962	+	17.6603i	−0.327210	+	0.566745i	0.654747	+	0.755848i	$0.272775\pi$
$972$		0			0
$973$	−0.294229	+	0.169873i	−0.00943254	+	0.00544588i
$974$		0			0
$975$	−2.53590	+	10.2487i	−0.0812137	+	0.328221i
$976$		0			0
$977$	20.8923	−	12.0622i	0.668404	−	0.385903i	−0.127068	−	0.991894i	$-0.540557\pi$
$977$	20.8923	−	12.0622i	0.668404	−	0.385903i	0.795472	+	0.605991i	$0.207223\pi$
$978$		0			0
$979$	−0.928203	+	1.60770i	−0.0296655	+	0.0513822i
$980$		0			0
$981$	−21.3397	−	12.3205i	−0.681326	−	0.393364i
$982$		0			0
$983$		−	44.1051i		−	1.40673i	−0.710826	−	0.703367i	$-0.751679\pi$
$983$		−	44.1051i		−	1.40673i	0.710826	−	0.703367i	$-0.248321\pi$
$984$		0			0
$985$	−3.53590	−	6.12436i	−0.112663	−	0.195138i
$986$		0			0
$987$	−2.14359			−0.0682313
$988$		0			0
$989$	−15.4641			−0.491730
$990$		0			0
$991$	−22.6865	−	39.2942i	−0.720661	−	1.24822i	−0.960735	−	0.277468i	$-0.910505\pi$
$991$	−22.6865	−	39.2942i	−0.720661	−	1.24822i	0.240074	−	0.970755i	$-0.422828\pi$
$992$		0			0
$993$		−	3.17691i		−	0.100816i
$994$		0			0
$995$	−4.73205	−	2.73205i	−0.150016	−	0.0866118i
$996$		0			0
$997$	10.9904	−	19.0359i	0.348069	−	0.602873i	−0.637838	−	0.770171i	$-0.720171\pi$
$997$	10.9904	−	19.0359i	0.348069	−	0.602873i	0.985906	+	0.167298i	$0.0535042\pi$
$998$		0			0
$999$	18.0000	−	10.3923i	0.569495	−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.b.673.2		4
4.3	odd	2		182.2.m.a.127.2	yes	4
12.11	even	2		1638.2.bj.c.127.1		4
13.4	even	6	inner	1456.2.cc.b.225.2		4
28.3	even	6		1274.2.o.a.569.2		4
28.11	odd	6		1274.2.o.b.569.2		4
28.19	even	6		1274.2.v.b.361.1		4
28.23	odd	6		1274.2.v.a.361.1		4
28.27	even	2		1274.2.m.a.491.2		4
52.3	odd	6		2366.2.d.k.337.4		4
52.11	even	12		2366.2.a.q.1.2		2
52.15	even	12		2366.2.a.s.1.2		2
52.23	odd	6		2366.2.d.k.337.2		4
52.43	odd	6		182.2.m.a.43.2	✓	4
156.95	even	6		1638.2.bj.c.1135.1		4
364.95	odd	6		1274.2.v.a.667.1		4
364.199	even	6		1274.2.v.b.667.1		4
364.251	even	6		1274.2.m.a.589.2		4
364.303	odd	6		1274.2.o.b.459.1		4
364.355	even	6		1274.2.o.a.459.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.a.43.2	✓	4	52.43	odd	6
182.2.m.a.127.2	yes	4	4.3	odd	2
1274.2.m.a.491.2		4	28.27	even	2
1274.2.m.a.589.2		4	364.251	even	6
1274.2.o.a.459.1		4	364.355	even	6
1274.2.o.a.569.2		4	28.3	even	6
1274.2.o.b.459.1		4	364.303	odd	6
1274.2.o.b.569.2		4	28.11	odd	6
1274.2.v.a.361.1		4	28.23	odd	6
1274.2.v.a.667.1		4	364.95	odd	6
1274.2.v.b.361.1		4	28.19	even	6
1274.2.v.b.667.1		4	364.199	even	6
1456.2.cc.b.225.2		4	13.4	even	6	inner
1456.2.cc.b.673.2		4	1.1	even	1	trivial
1638.2.bj.c.127.1		4	12.11	even	2
1638.2.bj.c.1135.1		4	156.95	even	6
2366.2.a.q.1.2		2	52.11	even	12
2366.2.a.s.1.2		2	52.15	even	12
2366.2.d.k.337.2		4	52.23	odd	6
2366.2.d.k.337.4		4	52.3	odd	6

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.633975i) q^{3} -1.00000i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 0.633975i) q^{3} -1.00000i q^{5} +(0.866025 + 0.500000i) q^{7} +(1.23205 - 2.13397i) q^{9} +(-0.633975 + 0.366025i) q^{11} +(2.59808 + 2.50000i) q^{13} +(0.633975 - 0.366025i) q^{15} +(-2.86603 + 4.96410i) q^{17} +(1.26795 + 0.732051i) q^{19} +0.732051i q^{21} +(-0.633975 - 1.09808i) q^{23} +4.00000 q^{25} +4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} -5.26795i q^{31} +(-0.464102 - 0.267949i) q^{33} +(0.500000 - 0.866025i) q^{35} +(4.50000 - 2.59808i) q^{37} +(-0.633975 + 2.56218i) q^{39} +(-2.13397 + 1.23205i) q^{41} +(6.09808 - 10.5622i) q^{43} +(-2.13397 - 1.23205i) q^{45} +2.92820i q^{47} +(0.500000 + 0.866025i) q^{49} -4.19615 q^{51} +1.53590 q^{53} +(0.366025 + 0.633975i) q^{55} +1.07180i q^{57} +(9.29423 + 5.36603i) q^{59} +(5.86603 - 10.1603i) q^{61} +(2.13397 - 1.23205i) q^{63} +(2.50000 - 2.59808i) q^{65} +(-10.0981 + 5.83013i) q^{67} +(0.464102 - 0.803848i) q^{69} +(12.0000 + 6.92820i) q^{71} +11.3923i q^{73} +(1.46410 + 2.53590i) q^{75} -0.732051 q^{77} +3.80385 q^{79} +(-2.23205 - 3.86603i) q^{81} +3.80385i q^{83} +(4.96410 + 2.86603i) q^{85} +(-1.09808 + 1.90192i) q^{87} +(2.19615 - 1.26795i) q^{89} +(1.00000 + 3.46410i) q^{91} +(3.33975 - 1.92820i) q^{93} +(0.732051 - 1.26795i) q^{95} +(-4.73205 - 2.73205i) q^{97} +1.80385i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{9} - 6 q^{11} + 6 q^{15} - 8 q^{17} + 12 q^{19} - 6 q^{23} + 16 q^{25} + 16 q^{27} + 6 q^{29} + 12 q^{33} + 2 q^{35} + 18 q^{37} - 6 q^{39} - 12 q^{41} + 14 q^{43} - 12 q^{45} + 2 q^{49} + 4 q^{51} + 20 q^{53} - 2 q^{55} + 6 q^{59} + 20 q^{61} + 12 q^{63} + 10 q^{65} - 30 q^{67} - 12 q^{69} + 48 q^{71} - 8 q^{75} + 4 q^{77} + 36 q^{79} - 2 q^{81} + 6 q^{85} + 6 q^{87} - 12 q^{89} + 4 q^{91} + 48 q^{93} - 4 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^9 - 6 * q^11 + 6 * q^15 - 8 * q^17 + 12 * q^19 - 6 * q^23 + 16 * q^25 + 16 * q^27 + 6 * q^29 + 12 * q^33 + 2 * q^35 + 18 * q^37 - 6 * q^39 - 12 * q^41 + 14 * q^43 - 12 * q^45 + 2 * q^49 + 4 * q^51 + 20 * q^53 - 2 * q^55 + 6 * q^59 + 20 * q^61 + 12 * q^63 + 10 * q^65 - 30 * q^67 - 12 * q^69 + 48 * q^71 - 8 * q^75 + 4 * q^77 + 36 * q^79 - 2 * q^81 + 6 * q^85 + 6 * q^87 - 12 * q^89 + 4 * q^91 + 48 * q^93 - 4 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

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Database

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