LMFDB - Embedded newform 1014.2.g.d.437.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.6
Root			$0.500000 + 0.331082i$ of defining polynomial
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.d.239.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.796225 - 1.53819i) q^{3} -1.00000i q^{4} +(-0.313444 + 0.313444i) q^{5} +(-1.65068 - 0.524648i) q^{6} +(0.203775 - 0.203775i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.73205 + 2.44949i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.796225 - 1.53819i) q^{3} -1.00000i q^{4} +(-0.313444 + 0.313444i) q^{5} +(-1.65068 - 0.524648i) q^{6} +(0.203775 - 0.203775i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.73205 + 2.44949i) q^{9} +0.443277i q^{10} +(-0.412157 - 0.412157i) q^{11} +(-1.53819 + 0.796225i) q^{12} -0.288181i q^{14} +(0.731708 + 0.232564i) q^{15} -1.00000 q^{16} -5.59813 q^{17} +(0.507306 + 2.95680i) q^{18} +(-4.97155 - 4.97155i) q^{19} +(0.313444 + 0.313444i) q^{20} +(-0.475695 - 0.151194i) q^{21} -0.582877 q^{22} -6.65190 q^{23} +(-0.524648 + 1.65068i) q^{24} +4.80351i q^{25} +(5.14688 + 0.713876i) q^{27} +(-0.203775 - 0.203775i) q^{28} -4.13015i q^{29} +(0.681844 - 0.352948i) q^{30} +(1.03573 + 1.03573i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.305805 + 0.962144i) q^{33} +(-3.95848 + 3.95848i) q^{34} +0.127744i q^{35} +(2.44949 + 1.73205i) q^{36} +(4.92046 - 4.92046i) q^{37} -7.03084 q^{38} +0.443277 q^{40} +(-5.39512 + 5.39512i) q^{41} +(-0.443277 + 0.229457i) q^{42} +3.76778i q^{43} +(-0.412157 + 0.412157i) q^{44} +(-0.224877 - 1.31068i) q^{45} +(-4.70360 + 4.70360i) q^{46} +(-3.71799 - 3.71799i) q^{47} +(0.796225 + 1.53819i) q^{48} +6.91695i q^{49} +(3.39659 + 3.39659i) q^{50} +(4.45737 + 8.61098i) q^{51} +3.64778i q^{53} +(4.14418 - 3.13461i) q^{54} +0.258376 q^{55} -0.288181 q^{56} +(-3.68871 + 11.6057i) q^{57} +(-2.92046 - 2.92046i) q^{58} +(-2.40926 - 2.40926i) q^{59} +(0.232564 - 0.731708i) q^{60} +10.5111 q^{61} +1.46474 q^{62} +(0.146196 + 0.852093i) q^{63} +1.00000i q^{64} +(0.464102 + 0.896575i) q^{66} +(-6.26033 - 6.26033i) q^{67} +5.59813i q^{68} +(5.29641 + 10.2319i) q^{69} +(0.0903287 + 0.0903287i) q^{70} +(10.8798 - 10.8798i) q^{71} +(2.95680 - 0.507306i) q^{72} +(-3.52053 + 3.52053i) q^{73} -6.95858i q^{74} +(7.38870 - 3.82467i) q^{75} +(-4.97155 + 4.97155i) q^{76} -0.167974 q^{77} +1.10886 q^{79} +(0.313444 - 0.313444i) q^{80} +(-3.00000 - 8.48528i) q^{81} +7.62986i q^{82} +(8.23032 - 8.23032i) q^{83} +(-0.151194 + 0.475695i) q^{84} +(1.75470 - 1.75470i) q^{85} +(2.66422 + 2.66422i) q^{86} +(-6.35295 + 3.28853i) q^{87} +0.582877i q^{88} +(-9.95774 - 9.95774i) q^{89} +(-1.08580 - 0.767778i) q^{90} +6.65190i q^{92} +(0.768472 - 2.41782i) q^{93} -5.25803 q^{94} +3.11661 q^{95} +(1.65068 + 0.524648i) q^{96} +(1.89781 + 1.89781i) q^{97} +(4.89102 + 4.89102i) q^{98} +(1.72345 - 0.295697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{7}+O(q^{10}) $ 16 * q + 16 * q^7	$ 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66} - 32 q^{67} - 56 q^{73} - 32 q^{76} - 96 q^{79} - 48 q^{81} - 24 q^{84} - 24 q^{85} - 96 q^{87} - 48 q^{93} + 48 q^{94} - 16 q^{97}+O(q^{100}) $ 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.796225	−	1.53819i	−0.459701	−	0.888074i
$3$	−0.796225	−	1.53819i	−0.459701	−	0.888074i
$4$		−	1.00000i		−	0.500000i
$5$	−0.313444	+	0.313444i	−0.140176	+	0.140176i	−0.773713	−	0.633536i	$-0.781603\pi$
$5$	−0.313444	+	0.313444i	−0.140176	+	0.140176i	0.633536	+	0.773713i	$0.281603\pi$
$6$	−1.65068	−	0.524648i	−0.673887	−	0.214186i
$7$	0.203775	−	0.203775i	0.0770196	−	0.0770196i	−0.667548	−	0.744567i	$-0.732656\pi$
$7$	0.203775	−	0.203775i	0.0770196	−	0.0770196i	0.744567	+	0.667548i	$0.232656\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.73205	+	2.44949i	−0.577350	+	0.816497i
$10$			0.443277i			0.140176i
$11$	−0.412157	−	0.412157i	−0.124270	−	0.124270i	0.642237	−	0.766506i	$-0.278007\pi$
$11$	−0.412157	−	0.412157i	−0.124270	−	0.124270i	−0.766506	+	0.642237i	$0.778007\pi$
$12$	−1.53819	+	0.796225i	−0.444037	+	0.229850i
$13$		0			0
$13$		0			0
$14$		−	0.288181i		−	0.0770196i
$15$	0.731708	+	0.232564i	0.188926	+	0.0600478i
$16$	−1.00000			−0.250000
$17$	−5.59813			−1.35775			−0.678873	−	0.734256i	$-0.737531\pi$
$17$	−5.59813			−1.35775			−0.678873	+	0.734256i	$0.737531\pi$
$18$	0.507306	+	2.95680i	0.119573	+	0.696923i
$19$	−4.97155	−	4.97155i	−1.14055	−	1.14055i	−0.988349	−	0.152203i	$-0.951363\pi$
$19$	−4.97155	−	4.97155i	−1.14055	−	1.14055i	−0.152203	−	0.988349i	$-0.548637\pi$
$20$	0.313444	+	0.313444i	0.0700882	+	0.0700882i
$21$	−0.475695	−	0.151194i	−0.103805	−	0.0329931i
$22$	−0.582877			−0.124270
$23$	−6.65190			−1.38702			−0.693509	−	0.720448i	$-0.743936\pi$
$23$	−6.65190			−1.38702			−0.693509	+	0.720448i	$0.743936\pi$
$24$	−0.524648	+	1.65068i	−0.107093	+	0.336944i
$25$			4.80351i			0.960701i
$26$		0			0
$27$	5.14688	+	0.713876i	0.990518	+	0.137386i
$28$	−0.203775	−	0.203775i	−0.0385098	−	0.0385098i
$29$		−	4.13015i		−	0.766949i	−0.923551	−	0.383475i	$-0.874727\pi$
$29$		−	4.13015i		−	0.766949i	0.923551	−	0.383475i	$-0.125273\pi$
$30$	0.681844	−	0.352948i	0.124487	−	0.0644392i
$31$	1.03573	+	1.03573i	0.186022	+	0.186022i	0.793974	−	0.607952i	$-0.208009\pi$
$31$	1.03573	+	1.03573i	0.186022	+	0.186022i	−0.607952	+	0.793974i	$0.708009\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.305805	+	0.962144i	−0.0532339	+	0.167488i
$34$	−3.95848	+	3.95848i	−0.678873	+	0.678873i
$35$			0.127744i			0.0215927i
$36$	2.44949	+	1.73205i	0.408248	+	0.288675i
$37$	4.92046	−	4.92046i	0.808918	−	0.808918i	−0.175552	−	0.984470i	$-0.556171\pi$
$37$	4.92046	−	4.92046i	0.808918	−	0.808918i	0.984470	+	0.175552i	$0.0561711\pi$
$38$	−7.03084			−1.14055
$39$		0			0
$40$	0.443277			0.0700882
$41$	−5.39512	+	5.39512i	−0.842577	+	0.842577i	−0.989193	−	0.146617i	$-0.953162\pi$
$41$	−5.39512	+	5.39512i	−0.842577	+	0.842577i	0.146617	+	0.989193i	$0.453162\pi$
$42$	−0.443277	+	0.229457i	−0.0683991	+	0.0354060i
$43$			3.76778i			0.574581i	0.957844	+	0.287290i	$0.0927545\pi$
$43$			3.76778i			0.574581i	−0.957844	+	0.287290i	$0.907246\pi$
$44$	−0.412157	+	0.412157i	−0.0621349	+	0.0621349i
$45$	−0.224877	−	1.31068i	−0.0335227	−	0.195385i
$46$	−4.70360	+	4.70360i	−0.693509	+	0.693509i
$47$	−3.71799	−	3.71799i	−0.542325	−	0.542325i	0.381885	−	0.924210i	$-0.375275\pi$
$47$	−3.71799	−	3.71799i	−0.542325	−	0.542325i	−0.924210	+	0.381885i	$0.875275\pi$
$48$	0.796225	+	1.53819i	0.114925	+	0.222018i
$49$			6.91695i			0.988136i
$50$	3.39659	+	3.39659i	0.480351	+	0.480351i
$51$	4.45737	+	8.61098i	0.624157	+	1.20578i
$52$		0			0
$53$			3.64778i			0.501062i	0.968109	+	0.250531i	$0.0806052\pi$
$53$			3.64778i			0.501062i	−0.968109	+	0.250531i	$0.919395\pi$
$54$	4.14418	−	3.13461i	0.563952	−	0.426566i
$55$	0.258376			0.0348394
$56$	−0.288181			−0.0385098
$57$	−3.68871	+	11.6057i	−0.488582	+	1.53721i
$58$	−2.92046	−	2.92046i	−0.383475	−	0.383475i
$59$	−2.40926	−	2.40926i	−0.313659	−	0.313659i	0.532666	−	0.846325i	$-0.321190\pi$
$59$	−2.40926	−	2.40926i	−0.313659	−	0.313659i	−0.846325	+	0.532666i	$0.821190\pi$
$60$	0.232564	−	0.731708i	0.0300239	−	0.0944632i
$61$	10.5111			1.34581			0.672903	−	0.739731i	$-0.265047\pi$
$61$	10.5111			1.34581			0.672903	+	0.739731i	$0.265047\pi$
$62$	1.46474			0.186022
$63$	0.146196	+	0.852093i	0.0184190	+	0.107354i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.464102	+	0.896575i	0.0571270	+	0.110361i
$67$	−6.26033	−	6.26033i	−0.764821	−	0.764821i	0.212369	−	0.977190i	$-0.431882\pi$
$67$	−6.26033	−	6.26033i	−0.764821	−	0.764821i	−0.977190	+	0.212369i	$0.931882\pi$
$68$			5.59813i			0.678873i
$69$	5.29641	+	10.2319i	0.637613	+	1.23177i
$70$	0.0903287	+	0.0903287i	0.0107963	+	0.0107963i
$71$	10.8798	−	10.8798i	1.29120	−	1.29120i	0.357149	−	0.934047i	$-0.383749\pi$
$71$	10.8798	−	10.8798i	1.29120	−	1.29120i	0.934047	−	0.357149i	$-0.116251\pi$
$72$	2.95680	−	0.507306i	0.348462	−	0.0597866i
$73$	−3.52053	+	3.52053i	−0.412047	+	0.412047i	−0.882451	−	0.470404i	$-0.844108\pi$
$73$	−3.52053	+	3.52053i	−0.412047	+	0.412047i	0.470404	+	0.882451i	$0.344108\pi$
$74$		−	6.95858i		−	0.808918i
$75$	7.38870	−	3.82467i	0.853174	−	0.441635i
$76$	−4.97155	+	4.97155i	−0.570276	+	0.570276i
$77$	−0.167974			−0.0191424
$78$		0			0
$79$	1.10886			0.124757			0.0623783	−	0.998053i	$-0.480131\pi$
$79$	1.10886			0.124757			0.0623783	+	0.998053i	$0.480131\pi$
$80$	0.313444	−	0.313444i	0.0350441	−	0.0350441i
$81$	−3.00000	−	8.48528i	−0.333333	−	0.942809i
$82$			7.62986i			0.842577i
$83$	8.23032	−	8.23032i	0.903395	−	0.903395i	−0.0923332	−	0.995728i	$-0.529433\pi$
$83$	8.23032	−	8.23032i	0.903395	−	0.903395i	0.995728	+	0.0923332i	$0.0294325\pi$
$84$	−0.151194	+	0.475695i	−0.0164966	+	0.0519026i
$85$	1.75470	−	1.75470i	0.190324	−	0.190324i
$86$	2.66422	+	2.66422i	0.287290	+	0.287290i
$87$	−6.35295	+	3.28853i	−0.681108	+	0.352567i
$88$			0.582877i			0.0621349i
$89$	−9.95774	−	9.95774i	−1.05552	−	1.05552i	−0.998365	−	0.0571524i	$-0.981798\pi$
$89$	−9.95774	−	9.95774i	−1.05552	−	1.05552i	−0.0571524	−	0.998365i	$-0.518202\pi$
$90$	−1.08580	−	0.767778i	−0.114454	−	0.0809309i
$91$		0			0
$92$			6.65190i			0.693509i
$93$	0.768472	−	2.41782i	0.0796869	−	0.250716i
$94$	−5.25803			−0.542325
$95$	3.11661			0.319757
$96$	1.65068	+	0.524648i	0.168472	+	0.0535466i
$97$	1.89781	+	1.89781i	0.192693	+	0.192693i	0.796859	−	0.604166i	$-0.206494\pi$
$97$	1.89781	+	1.89781i	0.192693	+	0.192693i	−0.604166	+	0.796859i	$0.706494\pi$
$98$	4.89102	+	4.89102i	0.494068	+	0.494068i
$99$	1.72345	−	0.295697i	0.173213	−	0.0297187i
$100$	4.80351			0.480351
$101$	−14.2406			−1.41699			−0.708497	−	0.705714i	$-0.750626\pi$
$101$	−14.2406			−1.41699			−0.708497	+	0.705714i	$0.750626\pi$
$102$	9.24072	+	2.93705i	0.914968	+	0.290811i
$103$			4.60903i			0.454141i	0.973878	+	0.227071i	$0.0729148\pi$
$103$			4.60903i			0.454141i	−0.973878	+	0.227071i	$0.927085\pi$
$104$		0			0
$105$	0.196494	−	0.101713i	0.0191759	−	0.00992617i
$106$	2.57937	+	2.57937i	0.250531	+	0.250531i
$107$			13.5120i			1.30625i	0.757248	+	0.653127i	$0.226543\pi$
$107$			13.5120i			1.30625i	−0.757248	+	0.653127i	$0.773457\pi$
$108$	0.713876	−	5.14688i	0.0686928	−	0.495259i
$109$	−2.06188	−	2.06188i	−0.197492	−	0.197492i	0.601432	−	0.798924i	$-0.294597\pi$
$109$	−2.06188	−	2.06188i	−0.197492	−	0.197492i	−0.798924	+	0.601432i	$0.794597\pi$
$110$	0.182699	−	0.182699i	0.0174197	−	0.0174197i
$111$	−11.4864	−	3.65080i	−1.09024	−	0.346519i
$112$	−0.203775	+	0.203775i	−0.0192549	+	0.0192549i
$113$		−	10.4166i		−	0.979916i	−0.871746	−	0.489958i	$-0.837012\pi$
$113$		−	10.4166i		−	0.979916i	0.871746	−	0.489958i	$-0.162988\pi$
$114$	5.59813	+	10.8148i	0.524313	+	1.01289i
$115$	2.08500	−	2.08500i	0.194427	−	0.194427i
$116$	−4.13015			−0.383475
$117$		0			0
$118$	−3.40721			−0.313659
$119$	−1.14076	+	1.14076i	−0.104573	+	0.104573i
$120$	−0.352948	−	0.681844i	−0.0322196	−	0.0622435i
$121$		−	10.6603i		−	0.969114i
$122$	7.43246	−	7.43246i	0.672903	−	0.672903i
$123$	12.5945	+	4.00299i	1.13560	+	0.360937i
$124$	1.03573	−	1.03573i	0.0930111	−	0.0930111i
$125$	−3.07285	−	3.07285i	−0.274844	−	0.274844i
$126$	0.705897	+	0.499144i	0.0628863	+	0.0444673i
$127$		−	0.241453i		−	0.0214255i	−0.999943	−	0.0107127i	$-0.996590\pi$
$127$		−	0.241453i		−	0.0214255i	0.999943	−	0.0107127i	$-0.00341004\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	5.79555	−	3.00000i	0.510270	−	0.264135i
$130$		0			0
$131$		−	8.09043i		−	0.706864i	−0.935460	−	0.353432i	$-0.885015\pi$
$131$		−	8.09043i		−	0.706864i	0.935460	−	0.353432i	$-0.114985\pi$
$132$	0.962144	+	0.305805i	0.0837439	+	0.0266169i
$133$	−2.02615			−0.175690
$134$	−8.85344			−0.764821
$135$	−1.83702	+	1.38950i	−0.158105	+	0.119589i
$136$	3.95848	+	3.95848i	0.339437	+	0.339437i
$137$	−0.0584822	−	0.0584822i	−0.00499647	−	0.00499647i	0.704604	−	0.709601i	$-0.251125\pi$
$137$	−0.0584822	−	0.0584822i	−0.00499647	−	0.00499647i	−0.709601	+	0.704604i	$0.751125\pi$
$138$	10.9802	+	3.48990i	0.934693	+	0.297080i
$139$	−6.24145			−0.529393			−0.264697	−	0.964332i	$-0.585272\pi$
$139$	−6.24145			−0.529393			−0.264697	+	0.964332i	$0.585272\pi$
$140$	0.127744			0.0107963
$141$	−2.75862	+	8.67933i	−0.232317	+	0.730932i
$142$		−	15.3864i		−	1.29120i
$143$		0			0
$144$	1.73205	−	2.44949i	0.144338	−	0.204124i
$145$	1.29457	+	1.29457i	0.107508	+	0.107508i
$146$			4.97878i			0.412047i
$147$	10.6396	−	5.50745i	0.877538	−	0.454247i
$148$	−4.92046	−	4.92046i	−0.404459	−	0.404459i
$149$	−10.2794	+	10.2794i	−0.842119	+	0.842119i	−0.989134	−	0.147015i	$-0.953033\pi$
$149$	−10.2794	+	10.2794i	−0.842119	+	0.842119i	0.147015	+	0.989134i	$0.453033\pi$
$150$	2.52015	−	7.92905i	0.205769	−	0.647404i
$151$	6.40358	−	6.40358i	0.521116	−	0.521116i	−0.396793	−	0.917908i	$-0.629877\pi$
$151$	6.40358	−	6.40358i	0.521116	−	0.521116i	0.917908	+	0.396793i	$0.129877\pi$
$152$			7.03084i			0.570276i
$153$	9.69625	−	13.7126i	0.783895	−	1.10859i
$154$	−0.118776	+	0.118776i	−0.00957122	+	0.00957122i
$155$	−0.649285			−0.0521519
$156$		0			0
$157$	−10.2127			−0.815065			−0.407532	−	0.913191i	$-0.633611\pi$
$157$	−10.2127			−0.815065			−0.407532	+	0.913191i	$0.633611\pi$
$158$	0.784083	−	0.784083i	0.0623783	−	0.0623783i
$159$	5.61098	−	2.90446i	0.444980	−	0.230339i
$160$		−	0.443277i		−	0.0350441i
$161$	−1.35549	+	1.35549i	−0.106828	+	0.106828i
$162$	−8.12132	−	3.87868i	−0.638071	−	0.304738i
$163$	9.81476	−	9.81476i	0.768751	−	0.768751i	−0.209136	−	0.977887i	$-0.567065\pi$
$163$	9.81476	−	9.81476i	0.768751	−	0.768751i	0.977887	+	0.209136i	$0.0670650\pi$
$164$	5.39512	+	5.39512i	0.421288	+	0.421288i
$165$	−0.205726	−	0.397431i	−0.0160157	−	0.0309400i
$166$		−	11.6394i		−	0.903395i
$167$	−9.48357	−	9.48357i	−0.733861	−	0.733861i	0.237522	−	0.971382i	$-0.423665\pi$
$167$	−9.48357	−	9.48357i	−0.733861	−	0.733861i	−0.971382	+	0.237522i	$0.923665\pi$
$168$	0.229457	+	0.443277i	0.0177030	+	0.0341996i
$169$		0			0
$170$		−	2.48152i		−	0.190324i
$171$	20.7888	−	3.56679i	1.58976	−	0.272759i
$172$	3.76778			0.287290
$173$	−1.10220			−0.0837986			−0.0418993	−	0.999122i	$-0.513341\pi$
$173$	−1.10220			−0.0837986			−0.0418993	+	0.999122i	$0.513341\pi$
$174$	−2.16687	+	6.81755i	−0.164270	+	0.516837i
$175$	0.978833	+	0.978833i	0.0739928	+	0.0739928i
$176$	0.412157	+	0.412157i	0.0310675	+	0.0310675i
$177$	−1.78758	+	5.62421i	−0.134363	+	0.422741i
$178$	−14.0824			−1.05552
$179$	−5.59555			−0.418231			−0.209115	−	0.977891i	$-0.567058\pi$
$179$	−5.59555			−0.418231			−0.209115	+	0.977891i	$0.567058\pi$
$180$	−1.31068	+	0.224877i	−0.0976923	+	0.0167613i
$181$		−	14.4687i		−	1.07545i	−0.843119	−	0.537727i	$-0.819283\pi$
$181$		−	14.4687i		−	1.07545i	0.843119	−	0.537727i	$-0.180717\pi$
$182$		0			0
$183$	−8.36919	−	16.1680i	−0.618668	−	1.19518i
$184$	4.70360	+	4.70360i	0.346754	+	0.346754i
$185$			3.08458i			0.226783i
$186$	−1.16626	−	2.25305i	−0.0855145	−	0.165201i
$187$	2.30731	+	2.30731i	0.168727	+	0.168727i
$188$	−3.71799	+	3.71799i	−0.271162	+	0.271162i
$189$	1.19427	−	0.903335i	0.0868707	−	0.0657079i
$190$	2.20377	−	2.20377i	0.159879	−	0.159879i
$191$			6.67573i			0.483039i	0.970396	+	0.241520i	$0.0776458\pi$
$191$			6.67573i			0.483039i	−0.970396	+	0.241520i	$0.922354\pi$
$192$	1.53819	−	0.796225i	0.111009	−	0.0574626i
$193$	4.30947	−	4.30947i	0.310203	−	0.310203i	−0.534785	−	0.844988i	$-0.679608\pi$
$193$	4.30947	−	4.30947i	0.310203	−	0.310203i	0.844988	+	0.534785i	$0.179608\pi$
$194$	2.68390			0.192693
$195$		0			0
$196$	6.91695			0.494068
$197$	−10.4569	+	10.4569i	−0.745022	+	0.745022i	−0.973540	−	0.228518i	$-0.926612\pi$
$197$	−10.4569	+	10.4569i	−0.745022	+	0.745022i	0.228518	+	0.973540i	$0.426612\pi$
$198$	1.00957	−	1.42775i	0.0717472	−	0.101466i
$199$		−	15.4803i		−	1.09737i	−0.836028	−	0.548686i	$-0.815128\pi$
$199$		−	15.4803i		−	1.09737i	0.836028	−	0.548686i	$-0.184872\pi$
$200$	3.39659	−	3.39659i	0.240175	−	0.240175i
$201$	−4.64494	+	14.6142i	−0.327629	+	1.03081i
$202$	−10.0696	+	10.0696i	−0.708497	+	0.708497i
$203$	−0.841620	−	0.841620i	−0.0590701	−	0.0590701i
$204$	8.61098	−	4.45737i	0.602889	−	0.312078i
$205$		−	3.38214i		−	0.236219i
$206$	3.25908	+	3.25908i	0.227071	+	0.227071i
$207$	11.5214	−	16.2938i	0.800795	−	1.13249i
$208$		0			0
$209$			4.09812i			0.283473i
$210$	0.0670206	−	0.210865i	0.00462486	−	0.0145510i
$211$	18.8144			1.29524			0.647619	−	0.761964i	$-0.275765\pi$
$211$	18.8144			1.29524			0.647619	+	0.761964i	$0.275765\pi$
$212$	3.64778			0.250531
$213$	−25.3980	−	8.07243i	−1.74024	−	0.553114i
$214$	9.55443	+	9.55443i	0.653127	+	0.653127i
$215$	−1.18099	−	1.18099i	−0.0805427	−	0.0805427i
$216$	−3.13461	−	4.14418i	−0.213283	−	0.281976i
$217$	0.422110			0.0286547
$218$	−2.91594			−0.197492
$219$	8.21837	+	2.61210i	0.555346	+	0.176510i
$220$		−	0.258376i		−	0.0174197i
$221$		0			0
$222$	−10.7036	+	5.54059i	−0.718379	+	0.371860i
$223$	5.08804	+	5.08804i	0.340720	+	0.340720i	0.856638	−	0.515918i	$-0.172549\pi$
$223$	5.08804	+	5.08804i	0.340720	+	0.340720i	−0.515918	+	0.856638i	$0.672549\pi$
$224$			0.288181i			0.0192549i
$225$	−11.7661	−	8.31992i	−0.784409	−	0.554661i
$226$	−7.36568	−	7.36568i	−0.489958	−	0.489958i
$227$	−3.79025	+	3.79025i	−0.251568	+	0.251568i	−0.821613	−	0.570045i	$-0.806926\pi$
$227$	−3.79025	+	3.79025i	−0.251568	+	0.251568i	0.570045	+	0.821613i	$0.306926\pi$
$228$	11.6057	+	3.68871i	0.768604	+	0.244291i
$229$	8.24846	−	8.24846i	0.545074	−	0.545074i	−0.379938	−	0.925012i	$-0.624055\pi$
$229$	8.24846	−	8.24846i	0.545074	−	0.545074i	0.925012	+	0.379938i	$0.124055\pi$
$230$		−	2.94863i		−	0.194427i
$231$	0.133745	+	0.258376i	0.00879979	+	0.0169999i
$232$	−2.92046	+	2.92046i	−0.191737	+	0.191737i
$233$	−9.54763			−0.625486			−0.312743	−	0.949838i	$-0.601248\pi$
$233$	−9.54763			−0.625486			−0.312743	+	0.949838i	$0.601248\pi$
$234$		0			0
$235$	2.33077			0.152042
$236$	−2.40926	+	2.40926i	−0.156829	+	0.156829i
$237$	−0.882903	−	1.70564i	−0.0573507	−	0.110793i
$238$			1.61328i			0.104573i
$239$	20.6375	−	20.6375i	1.33493	−	1.33493i	0.434036	−	0.900895i	$-0.357089\pi$
$239$	20.6375	−	20.6375i	1.33493	−	1.33493i	0.900895	−	0.434036i	$-0.142911\pi$
$240$	−0.731708	−	0.232564i	−0.0472316	−	0.0150120i
$241$	7.88702	−	7.88702i	0.508048	−	0.508048i	−0.405879	−	0.913927i	$-0.633035\pi$
$241$	7.88702	−	7.88702i	0.508048	−	0.508048i	0.913927	+	0.405879i	$0.133035\pi$
$242$	−7.53794	−	7.53794i	−0.484557	−	0.484557i
$243$	−10.6633	+	11.3708i	−0.684050	+	0.729435i
$244$		−	10.5111i		−	0.672903i
$245$	−2.16808	−	2.16808i	−0.138513	−	0.138513i
$246$	11.7362	−	6.07508i	0.748270	−	0.387333i
$247$		0			0
$248$		−	1.46474i		−	0.0930111i
$249$	−19.2130	−	6.10660i	−1.21757	−	0.386990i
$250$	−4.34567			−0.274844
$251$	−4.46952			−0.282113			−0.141057	−	0.990002i	$-0.545050\pi$
$251$	−4.46952			−0.282113			−0.141057	+	0.990002i	$0.545050\pi$
$252$	0.852093	−	0.146196i	0.0536768	−	0.00920948i
$253$	2.74162	+	2.74162i	0.172364	+	0.172364i
$254$	−0.170733	−	0.170733i	−0.0107127	−	0.0107127i
$255$	−4.09620	−	1.30192i	−0.256514	−	0.0815297i
$256$	1.00000			0.0625000
$257$	11.9483			0.745315			0.372658	−	0.927969i	$-0.378447\pi$
$257$	11.9483			0.745315			0.372658	+	0.927969i	$0.378447\pi$
$258$	1.97676	−	6.21940i	0.123067	−	0.387203i
$259$		−	2.00533i		−	0.124605i
$260$		0			0
$261$	10.1168	+	7.15363i	0.626211	+	0.442798i
$262$	−5.72080	−	5.72080i	−0.353432	−	0.353432i
$263$		−	2.75121i		−	0.169647i	−0.996396	−	0.0848234i	$-0.972967\pi$
$263$		−	2.75121i		−	0.169647i	0.996396	−	0.0848234i	$-0.0270326\pi$
$264$	0.896575	−	0.464102i	0.0551804	−	0.0285635i
$265$	−1.14338	−	1.14338i	−0.0702371	−	0.0702371i
$266$	−1.43271	+	1.43271i	−0.0878449	+	0.0878449i
$267$	−7.38828	+	23.2455i	−0.452155	+	1.42260i
$268$	−6.26033	+	6.26033i	−0.382410	+	0.382410i
$269$		−	6.24027i		−	0.380476i	−0.981738	−	0.190238i	$-0.939074\pi$
$269$		−	6.24027i		−	0.380476i	0.981738	−	0.190238i	$-0.0609260\pi$
$270$	−0.316445	+	2.28149i	−0.0192582	+	0.138847i
$271$	−15.8164	+	15.8164i	−0.960780	+	0.960780i	−0.999259	−	0.0384794i	$-0.987749\pi$
$271$	−15.8164	+	15.8164i	−0.960780	+	0.960780i	0.0384794	+	0.999259i	$0.487749\pi$
$272$	5.59813			0.339437
$273$		0			0
$274$	−0.0827063			−0.00499647
$275$	1.97980	−	1.97980i	0.119386	−	0.119386i
$276$	10.2319	−	5.29641i	0.615887	−	0.318806i
$277$			5.59837i			0.336374i	0.985755	+	0.168187i	$0.0537912\pi$
$277$			5.59837i			0.336374i	−0.985755	+	0.168187i	$0.946209\pi$
$278$	−4.41337	+	4.41337i	−0.264697	+	0.264697i
$279$	−4.33094	+	0.743071i	−0.259286	+	0.0444865i
$280$	0.0903287	−	0.0903287i	0.00539817	−	0.00539817i
$281$	8.82870	+	8.82870i	0.526676	+	0.526676i	0.919580	−	0.392903i	$-0.128529\pi$
$281$	8.82870	+	8.82870i	0.526676	+	0.526676i	−0.392903	+	0.919580i	$0.628529\pi$
$282$	4.18658	+	8.08785i	0.249307	+	0.481624i
$283$		−	6.85872i		−	0.407709i	−0.979001	−	0.203854i	$-0.934653\pi$
$283$		−	6.85872i		−	0.407709i	0.979001	−	0.203854i	$-0.0653469\pi$
$284$	−10.8798	−	10.8798i	−0.645598	−	0.645598i
$285$	−2.48152	−	4.79393i	−0.146993	−	0.283968i
$286$		0			0
$287$			2.19878i			0.129790i
$288$	−0.507306	−	2.95680i	−0.0298933	−	0.174231i
$289$	14.3391			0.843474
$290$	1.83080			0.107508
$291$	1.40810	−	4.43026i	0.0825445	−	0.259707i
$292$	3.52053	+	3.52053i	0.206023	+	0.206023i
$293$	19.3431	+	19.3431i	1.13004	+	1.13004i	0.990170	+	0.139867i	$0.0446674\pi$
$293$	19.3431	+	19.3431i	1.13004	+	1.13004i	0.139867	+	0.990170i	$0.455333\pi$
$294$	3.62896	−	11.4177i	0.211645	−	0.665892i
$295$	1.51034			0.0879352
$296$	−6.95858			−0.404459
$297$	−1.82709	−	2.41555i	−0.106019	−	0.140164i
$298$			14.5372i			0.842119i
$299$		0			0
$300$	−3.82467	−	7.38870i	−0.220818	−	0.426587i
$301$	0.767778	+	0.767778i	0.0442540	+	0.0442540i
$302$		−	9.05603i		−	0.521116i
$303$	11.3387	+	21.9047i	0.651393	+	1.25839i
$304$	4.97155	+	4.97155i	0.285138	+	0.285138i
$305$	−3.29464	+	3.29464i	−0.188650	+	0.188650i
$306$	−2.83996	−	16.5525i	−0.162350	−	0.946245i
$307$	15.4869	−	15.4869i	0.883883	−	0.883883i	−0.110044	−	0.993927i	$-0.535099\pi$
$307$	15.4869	−	15.4869i	0.883883	−	0.883883i	0.993927	+	0.110044i	$0.0350992\pi$
$308$			0.167974i			0.00957122i
$309$	7.08956	−	3.66983i	0.403311	−	0.208769i
$310$	−0.459114	+	0.459114i	−0.0260759	+	0.0260759i
$311$	31.8012			1.80328			0.901642	−	0.432484i	$-0.142363\pi$
$311$	31.8012			1.80328			0.901642	+	0.432484i	$0.142363\pi$
$312$		0			0
$313$	−23.7424			−1.34200			−0.670999	−	0.741458i	$-0.734135\pi$
$313$	−23.7424			−1.34200			−0.670999	+	0.741458i	$0.734135\pi$
$314$	−7.22149	+	7.22149i	−0.407532	+	0.407532i
$315$	−0.312908	−	0.221259i	−0.0176303	−	0.0124665i
$316$		−	1.10886i		−	0.0623783i
$317$	−16.8936	+	16.8936i	−0.948841	+	0.948841i	−0.998754	−	0.0499128i	$-0.984106\pi$
$317$	−16.8936	+	16.8936i	−0.948841	+	0.948841i	0.0499128	+	0.998754i	$0.484106\pi$
$318$	1.91380	−	6.02133i	0.107321	−	0.337659i
$319$	−1.70227	+	1.70227i	−0.0953087	+	0.0953087i
$320$	−0.313444	−	0.313444i	−0.0175221	−	0.0175221i
$321$	20.7840	−	10.7586i	1.16005	−	0.600486i
$322$			1.91695i			0.106828i
$323$	27.8314	+	27.8314i	1.54858	+	1.54858i
$324$	−8.48528	+	3.00000i	−0.471405	+	0.166667i
$325$		0			0
$326$		−	13.8802i		−	0.768751i
$327$	−1.52984	+	4.81329i	−0.0846004	+	0.266175i
$328$	7.62986			0.421288
$329$	−1.51527			−0.0835393
$330$	−0.426496	−	0.135556i	−0.0234778	−	0.00746213i
$331$	11.6586	+	11.6586i	0.640813	+	0.640813i	0.950755	−	0.309942i	$-0.100310\pi$
$331$	11.6586	+	11.6586i	0.640813	+	0.640813i	−0.309942	+	0.950755i	$0.600310\pi$
$332$	−8.23032	−	8.23032i	−0.451697	−	0.451697i
$333$	3.53013	+	20.5751i	0.193450	+	1.12751i
$334$	−13.4118			−0.733861
$335$	3.92453			0.214420
$336$	0.475695	+	0.151194i	0.0259513	+	0.00824828i
$337$		−	3.24846i		−	0.176955i	−0.996078	−	0.0884775i	$-0.971800\pi$
$337$		−	3.24846i		−	0.176955i	0.996078	−	0.0884775i	$-0.0282001\pi$
$338$		0			0
$339$	−16.0228	+	8.29400i	−0.870238	+	0.450468i
$340$	−1.75470	−	1.75470i	−0.0951620	−	0.0951620i
$341$		−	0.853764i		−	0.0462339i
$342$	12.1778	−	17.2220i	0.658498	−	0.931257i
$343$	2.83592	+	2.83592i	0.153125	+	0.153125i
$344$	2.66422	−	2.66422i	0.143645	−	0.143645i
$345$	−4.86725	−	1.54699i	−0.262044	−	0.0832873i
$346$	−0.779372	+	0.779372i	−0.0418993	+	0.0418993i
$347$			8.21818i			0.441175i	0.975367	+	0.220587i	$0.0707974\pi$
$347$			8.21818i			0.441175i	−0.975367	+	0.220587i	$0.929203\pi$
$348$	3.28853	+	6.35295i	0.176284	+	0.340554i
$349$	5.66593	−	5.66593i	0.303290	−	0.303290i	−0.539010	−	0.842300i	$-0.681201\pi$
$349$	5.66593	−	5.66593i	0.303290	−	0.303290i	0.842300	+	0.539010i	$0.181201\pi$
$350$	1.38428			0.0739928
$351$		0			0
$352$	0.582877			0.0310675
$353$	1.97680	−	1.97680i	0.105214	−	0.105214i	−0.652540	−	0.757754i	$-0.726297\pi$
$353$	1.97680	−	1.97680i	0.105214	−	0.105214i	0.757754	+	0.652540i	$0.226297\pi$
$354$	2.71290	+	5.24093i	0.144189	+	0.278552i
$355$			6.82043i			0.361991i
$356$	−9.95774	+	9.95774i	−0.527759	+	0.527759i
$357$	2.66300	+	0.846401i	0.140941	+	0.0447963i
$358$	−3.95665	+	3.95665i	−0.209115	+	0.209115i
$359$	−11.6531	−	11.6531i	−0.615028	−	0.615028i	0.329224	−	0.944252i	$-0.393213\pi$
$359$	−11.6531	−	11.6531i	−0.615028	−	0.615028i	−0.944252	+	0.329224i	$0.893213\pi$
$360$	−0.767778	+	1.08580i	−0.0404655	+	0.0572268i
$361$			30.4327i			1.60172i
$362$	−10.2309	−	10.2309i	−0.537727	−	0.537727i
$363$	−16.3975	+	8.48796i	−0.860645	+	0.445503i
$364$		0			0
$365$		−	2.20698i		−	0.115519i
$366$	−17.3504	−	5.51461i	−0.906922	−	0.288253i
$367$	−37.1859			−1.94109			−0.970544	−	0.240924i	$-0.922550\pi$
$367$	−37.1859			−1.94109			−0.970544	+	0.240924i	$0.922550\pi$
$368$	6.65190			0.346754
$369$	−3.87067	−	22.5599i	−0.201499	−	1.17442i
$370$	2.18112	+	2.18112i	0.113391	+	0.113391i
$371$	0.743327	+	0.743327i	0.0385916	+	0.0385916i
$372$	−2.41782	−	0.768472i	−0.125358	−	0.0398434i
$373$	−7.88823			−0.408437			−0.204219	−	0.978925i	$-0.565465\pi$
$373$	−7.88823			−0.408437			−0.204219	+	0.978925i	$0.565465\pi$
$374$	3.26302			0.168727
$375$	−2.27994	+	7.17331i	−0.117736	+	0.370428i
$376$			5.25803i			0.271162i
$377$		0			0
$378$	0.205726	−	1.48323i	0.0105814	−	0.0762893i
$379$	−1.31661	−	1.31661i	−0.0676295	−	0.0676295i	0.672483	−	0.740113i	$-0.265228\pi$
$379$	−1.31661	−	1.31661i	−0.0676295	−	0.0676295i	−0.740113	+	0.672483i	$0.765228\pi$
$380$		−	3.11661i		−	0.159879i
$381$	−0.371400	+	0.192251i	−0.0190274	+	0.00984931i
$382$	4.72046	+	4.72046i	0.241520	+	0.241520i
$383$	−2.03681	+	2.03681i	−0.104076	+	0.104076i	−0.757227	−	0.653151i	$-0.773447\pi$
$383$	−2.03681	+	2.03681i	−0.104076	+	0.104076i	0.653151	+	0.757227i	$0.273447\pi$
$384$	0.524648	−	1.65068i	0.0267733	−	0.0842359i
$385$	0.0526505	−	0.0526505i	0.00268332	−	0.00268332i
$386$		−	6.09452i		−	0.310203i
$387$	−9.22913	−	6.52598i	−0.469143	−	0.331734i
$388$	1.89781	−	1.89781i	0.0963465	−	0.0963465i
$389$	−23.4187			−1.18738			−0.593688	−	0.804695i	$-0.702329\pi$
$389$	−23.4187			−1.18738			−0.593688	+	0.804695i	$0.702329\pi$
$390$		0			0
$391$	37.2382			1.88322
$392$	4.89102	−	4.89102i	0.247034	−	0.247034i
$393$	−12.4446	+	6.44181i	−0.627748	+	0.324946i
$394$			14.7883i			0.745022i
$395$	−0.347566	+	0.347566i	−0.0174879	+	0.0174879i
$396$	−0.295697	−	1.72345i	−0.0148593	−	0.0866066i
$397$	−13.0162	+	13.0162i	−0.653266	+	0.653266i	−0.953778	−	0.300512i	$-0.902843\pi$
$397$	−13.0162	+	13.0162i	−0.653266	+	0.653266i	0.300512	+	0.953778i	$0.402843\pi$
$398$	−10.9463	−	10.9463i	−0.548686	−	0.548686i
$399$	1.61328	+	3.11661i	0.0807648	+	0.156026i
$400$		−	4.80351i		−	0.240175i
$401$	4.79769	+	4.79769i	0.239585	+	0.239585i	0.816678	−	0.577093i	$-0.195813\pi$
$401$	4.79769	+	4.79769i	0.239585	+	0.239585i	−0.577093	+	0.816678i	$0.695813\pi$
$402$	7.04933	+	13.6183i	0.351589	+	0.679217i
$403$		0			0
$404$			14.2406i			0.708497i
$405$	3.59999	+	1.71933i	0.178885	+	0.0854342i
$406$	−1.19023			−0.0590701
$407$	−4.05600			−0.201048
$408$	2.93705	−	9.24072i	0.145405	−	0.457484i
$409$	−20.7093	−	20.7093i	−1.02401	−	1.02401i	−0.999705	−	0.0243059i	$-0.992262\pi$
$409$	−20.7093	−	20.7093i	−1.02401	−	1.02401i	−0.0243059	−	0.999705i	$-0.507738\pi$
$410$	−2.39153	−	2.39153i	−0.118109	−	0.118109i
$411$	−0.0433917	+	0.136522i	−0.00214035	+	0.00673412i
$412$	4.60903			0.227071
$413$	−0.981893			−0.0483158
$414$	−3.37455	−	19.6683i	−0.165850	−	0.966645i
$415$			5.15949i			0.253269i
$416$		0			0
$417$	4.96960	+	9.60053i	0.243362	+	0.470140i
$418$	2.89781	+	2.89781i	0.141736	+	0.141736i
$419$			9.24219i			0.451510i	0.974184	+	0.225755i	$0.0724850\pi$
$419$			9.24219i			0.451510i	−0.974184	+	0.225755i	$0.927515\pi$
$420$	−0.101713	−	0.196494i	−0.00496309	−	0.00958795i
$421$	18.4490	+	18.4490i	0.899149	+	0.899149i	0.995361	−	0.0962115i	$-0.0306725\pi$
$421$	18.4490	+	18.4490i	0.899149	+	0.899149i	−0.0962115	+	0.995361i	$0.530673\pi$
$422$	13.3038	−	13.3038i	0.647619	−	0.647619i
$423$	15.5469	−	2.66743i	0.755918	−	0.129695i
$424$	2.57937	−	2.57937i	0.125265	−	0.125265i
$425$		−	26.8906i		−	1.30439i
$426$	−23.6672	+	12.2510i	−1.14668	+	0.593564i
$427$	2.14189	−	2.14189i	0.103653	−	0.103653i
$428$	13.5120			0.653127
$429$		0			0
$430$	−1.67017			−0.0805427
$431$	15.8134	−	15.8134i	0.761705	−	0.761705i	−0.214925	−	0.976630i	$-0.568951\pi$
$431$	15.8134	−	15.8134i	0.761705	−	0.761705i	0.976630	+	0.214925i	$0.0689508\pi$
$432$	−5.14688	−	0.713876i	−0.247629	−	0.0343464i
$433$		−	3.94803i		−	0.189730i	−0.995490	−	0.0948652i	$-0.969758\pi$
$433$		−	3.94803i		−	0.189730i	0.995490	−	0.0948652i	$-0.0302420\pi$
$434$	0.298477	−	0.298477i	0.0143274	−	0.0143274i
$435$	0.960525	−	3.02206i	0.0460536	−	0.144897i
$436$	−2.06188	+	2.06188i	−0.0987462	+	0.0987462i
$437$	33.0703	+	33.0703i	1.58197	+	1.58197i
$438$	7.65830	−	3.96423i	0.365928	−	0.189418i
$439$			18.3100i			0.873889i	0.899489	+	0.436944i	$0.143939\pi$
$439$			18.3100i			0.873889i	−0.899489	+	0.436944i	$0.856061\pi$
$440$	−0.182699	−	0.182699i	−0.00870986	−	0.00870986i
$441$	−16.9430	−	11.9805i	−0.806810	−	0.570501i
$442$		0			0
$443$		−	5.86371i		−	0.278593i	−0.990251	−	0.139297i	$-0.955516\pi$
$443$		−	5.86371i		−	0.278593i	0.990251	−	0.139297i	$-0.0444841\pi$
$444$	−3.65080	+	11.4864i	−0.173259	+	0.545120i
$445$	6.24239			0.295918
$446$	7.19557			0.340720
$447$	23.9963	+	7.62693i	1.13499	+	0.360741i
$448$	0.203775	+	0.203775i	0.00962745	+	0.00962745i
$449$	−20.1557	−	20.1557i	−0.951207	−	0.951207i	0.0476571	−	0.998864i	$-0.484825\pi$
$449$	−20.1557	−	20.1557i	−0.951207	−	0.951207i	−0.998864	+	0.0476571i	$0.984825\pi$
$450$	−14.2030	+	2.43685i	−0.669535	+	0.114874i
$451$	4.44727			0.209414
$452$	−10.4166			−0.489958
$453$	−14.9486	−	4.75122i	−0.702347	−	0.223232i
$454$			5.36023i			0.251568i
$455$		0			0
$456$	10.8148	−	5.59813i	0.506447	−	0.262156i
$457$	13.5552	+	13.5552i	0.634084	+	0.634084i	0.949090	−	0.315006i	$-0.102006\pi$
$457$	13.5552	+	13.5552i	0.634084	+	0.634084i	−0.315006	+	0.949090i	$0.602006\pi$
$458$		−	11.6651i		−	0.545074i
$459$	−28.8129	−	3.99637i	−1.34487	−	0.186535i
$460$	−2.08500	−	2.08500i	−0.0972136	−	0.0972136i
$461$	20.9657	−	20.9657i	0.976471	−	0.976471i	−0.0232588	−	0.999729i	$-0.507404\pi$
$461$	20.9657	−	20.9657i	0.976471	−	0.976471i	0.999729	+	0.0232588i	$0.00740418\pi$
$462$	0.277272	+	0.0881273i	0.0128998	+	0.00410005i
$463$	−18.2554	+	18.2554i	−0.848400	+	0.848400i	−0.989934	−	0.141533i	$-0.954797\pi$
$463$	−18.2554	+	18.2554i	−0.848400	+	0.848400i	0.141533	+	0.989934i	$0.454797\pi$
$464$			4.13015i			0.191737i
$465$	0.516977	+	0.998724i	0.0239743	+	0.0463147i
$466$	−6.75120	+	6.75120i	−0.312743	+	0.312743i
$467$	−32.4456			−1.50140			−0.750701	−	0.660642i	$-0.770284\pi$
$467$	−32.4456			−1.50140			−0.750701	+	0.660642i	$0.770284\pi$
$468$		0			0
$469$	−2.55139			−0.117812
$470$	1.64810	−	1.64810i	0.0760212	−	0.0760212i
$471$	8.13164	+	15.7091i	0.374686	+	0.723838i
$472$			3.40721i			0.156829i
$473$	1.55291	−	1.55291i	0.0714031	−	0.0714031i
$474$	−1.83037	−	0.581761i	−0.0840719	−	0.0267212i
$475$	23.8809	−	23.8809i	1.09573	−	1.09573i
$476$	1.14076	+	1.14076i	0.0522865	+	0.0522865i
$477$	−8.93521	−	6.31815i	−0.409115	−	0.289288i
$478$		−	29.1859i		−	1.33493i
$479$	5.86220	+	5.86220i	0.267851	+	0.267851i	0.828234	−	0.560383i	$-0.189346\pi$
$479$	5.86220	+	5.86220i	0.267851	+	0.267851i	−0.560383	+	0.828234i	$0.689346\pi$
$480$	−0.681844	+	0.352948i	−0.0311218	+	0.0161098i
$481$		0			0
$482$		−	11.1539i		−	0.508048i
$483$	3.16427	+	1.00572i	0.143979	+	0.0457620i
$484$	−10.6603			−0.484557
$485$	−1.18971			−0.0540220
$486$	0.500258	+	15.5804i	0.0226921	+	0.706743i
$487$	−22.7198	−	22.7198i	−1.02953	−	1.02953i	−0.999550	−	0.0299840i	$-0.990454\pi$
$487$	−22.7198	−	22.7198i	−1.02953	−	1.02953i	−0.0299840	−	0.999550i	$-0.509546\pi$
$488$	−7.43246	−	7.43246i	−0.336451	−	0.336451i
$489$	−22.9117	−	7.28219i	−1.03610	−	0.329312i
$490$	−3.06613			−0.138513
$491$	26.4199			1.19231			0.596157	−	0.802868i	$-0.296694\pi$
$491$	26.4199			1.19231			0.596157	+	0.802868i	$0.296694\pi$
$492$	4.00299	−	12.5945i	0.180469	−	0.567802i
$493$			23.1211i			1.04132i
$494$		0			0
$495$	−0.447520	+	0.632890i	−0.0201145	+	0.0284463i
$496$	−1.03573	−	1.03573i	−0.0465055	−	0.0465055i
$497$		−	4.43406i		−	0.198895i
$498$	−17.9036	+	9.26761i	−0.802281	+	0.415291i
$499$	9.27427	+	9.27427i	0.415173	+	0.415173i	0.883536	−	0.468363i	$-0.155156\pi$
$499$	9.27427	+	9.27427i	0.415173	+	0.415173i	−0.468363	+	0.883536i	$0.655156\pi$
$500$	−3.07285	+	3.07285i	−0.137422	+	0.137422i
$501$	−7.03647	+	22.1386i	−0.314366	+	0.989079i
$502$	−3.16043	+	3.16043i	−0.141057	+	0.141057i
$503$			30.5434i			1.36186i	0.732348	+	0.680931i	$0.238424\pi$
$503$			30.5434i			1.36186i	−0.732348	+	0.680931i	$0.761576\pi$
$504$	0.499144	−	0.705897i	0.0222337	−	0.0314431i
$505$	4.46363	−	4.46363i	0.198629	−	0.198629i
$506$	3.87724			0.172364
$507$		0			0
$508$	−0.241453			−0.0107127
$509$	16.8650	−	16.8650i	0.747529	−	0.747529i	−0.226486	−	0.974014i	$-0.572724\pi$
$509$	16.8650	−	16.8650i	0.747529	−	0.747529i	0.974014	+	0.226486i	$0.0727237\pi$
$510$	−3.81705	+	1.97585i	−0.169022	+	0.0874921i
$511$			1.43479i			0.0634714i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−22.0389	−	29.1371i	−0.973042	−	1.28643i
$514$	8.44873	−	8.44873i	0.372658	−	0.372658i
$515$	−1.44467	−	1.44467i	−0.0636599	−	0.0636599i
$516$	−3.00000	−	5.79555i	−0.132068	−	0.255135i
$517$			3.06479i			0.134789i
$518$	−1.41798	−	1.41798i	−0.0623026	−	0.0623026i
$519$	0.877598	+	1.69539i	0.0385223	+	0.0744193i
$520$		0			0
$521$			42.5422i			1.86381i	0.362704	+	0.931904i	$0.381854\pi$
$521$			42.5422i			1.86381i	−0.362704	+	0.931904i	$0.618146\pi$
$522$	12.2120	−	2.09525i	0.534505	−	0.0917065i
$523$	−34.0800			−1.49021			−0.745107	−	0.666945i	$-0.767602\pi$
$523$	−34.0800			−1.49021			−0.745107	+	0.666945i	$0.767602\pi$
$524$	−8.09043			−0.353432
$525$	0.726259	−	2.28500i	0.0316965	−	0.0997257i
$526$	−1.94540	−	1.94540i	−0.0848234	−	0.0848234i
$527$	−5.79814	−	5.79814i	−0.252571	−	0.252571i
$528$	0.305805	−	0.962144i	0.0133085	−	0.0418719i
$529$	21.2478			0.923816
$530$	−1.61698			−0.0702371
$531$	10.0744	−	1.72850i	0.437192	−	0.0750104i
$532$			2.02615i			0.0878449i
$533$		0			0
$534$	11.2127	+	21.6613i	0.485222	+	0.937378i
$535$	−4.23526	−	4.23526i	−0.183106	−	0.183106i
$536$			8.85344i			0.382410i
$537$	4.45532	+	8.60701i	0.192261	+	0.371420i
$538$	−4.41254	−	4.41254i	−0.190238	−	0.190238i
$539$	2.85087	−	2.85087i	0.122796	−	0.122796i
$540$	1.38950	+	1.83702i	0.0597945	+	0.0790527i
$541$	−18.5013	+	18.5013i	−0.795434	+	0.795434i	−0.982372	−	0.186938i	$-0.940144\pi$
$541$	−18.5013	+	18.5013i	−0.795434	+	0.795434i	0.186938	+	0.982372i	$0.440144\pi$
$542$			22.3678i			0.960780i
$543$	−22.2557	+	11.5204i	−0.955082	+	0.494387i
$544$	3.95848	−	3.95848i	0.169718	−	0.169718i
$545$	1.29257			0.0553676
$546$		0			0
$547$	39.5058			1.68915			0.844573	−	0.535440i	$-0.179854\pi$
$547$	39.5058			1.68915			0.844573	+	0.535440i	$0.179854\pi$
$548$	−0.0584822	+	0.0584822i	−0.00249824	+	0.00249824i
$549$	−18.2057	+	25.7468i	−0.777001	+	1.09885i
$550$		−	2.79985i		−	0.119386i
$551$	−20.5332	+	20.5332i	−0.874746	+	0.874746i
$552$	3.48990	−	10.9802i	0.148540	−	0.467347i
$553$	0.225958	−	0.225958i	0.00960870	−	0.00960870i
$554$	3.95865	+	3.95865i	0.168187	+	0.168187i
$555$	4.74466	−	2.45602i	0.201400	−	0.104252i
$556$			6.24145i			0.264697i
$557$	11.1678	+	11.1678i	0.473193	+	0.473193i	0.902946	−	0.429753i	$-0.141399\pi$
$557$	11.1678	+	11.1678i	0.473193	+	0.473193i	−0.429753	+	0.902946i	$0.641399\pi$
$558$	−2.53700	+	3.58786i	−0.107400	+	0.151886i
$559$		0			0
$560$		−	0.127744i		−	0.00539817i
$561$	1.71194	−	5.38621i	0.0722781	−	0.227406i
$562$	12.4857			0.526676
$563$	21.3812			0.901109			0.450555	−	0.892749i	$-0.351226\pi$
$563$	21.3812			0.901109			0.450555	+	0.892749i	$0.351226\pi$
$564$	8.67933	+	2.75862i	0.365466	+	0.116159i
$565$	3.26504	+	3.26504i	0.137361	+	0.137361i
$566$	−4.84985	−	4.84985i	−0.203854	−	0.203854i
$567$	−2.34041	−	1.11776i	−0.0982880	−	0.0469416i
$568$	−15.3864			−0.645598
$569$	29.0407			1.21745			0.608725	−	0.793382i	$-0.291681\pi$
$569$	29.0407			1.21745			0.608725	+	0.793382i	$0.291681\pi$
$570$	−5.14452	−	1.63512i	−0.215480	−	0.0684877i
$571$			9.91137i			0.414778i	0.978259	+	0.207389i	$0.0664966\pi$
$571$			9.91137i			0.414778i	−0.978259	+	0.207389i	$0.933503\pi$
$572$		0			0
$573$	10.2685	−	5.31539i	0.428974	−	0.222054i
$574$	1.55477	+	1.55477i	0.0648949	+	0.0648949i
$575$		−	31.9524i		−	1.33251i
$576$	−2.44949	−	1.73205i	−0.102062	−	0.0721688i
$577$	4.91283	+	4.91283i	0.204524	+	0.204524i	0.801935	−	0.597411i	$-0.203804\pi$
$577$	4.91283	+	4.91283i	0.204524	+	0.204524i	−0.597411	+	0.801935i	$0.703804\pi$
$578$	10.1392	−	10.1392i	0.421737	−	0.421737i
$579$	−10.0601	−	3.19747i	−0.418083	−	0.132882i
$580$	1.29457	−	1.29457i	0.0537541	−	0.0537541i
$581$		−	3.35426i		−	0.139158i
$582$	−2.13699	−	4.12835i	−0.0885811	−	0.171126i
$583$	1.50346	−	1.50346i	0.0622669	−	0.0622669i
$584$	4.97878			0.206023
$585$		0			0
$586$	27.3553			1.13004
$587$	16.9836	−	16.9836i	0.700989	−	0.700989i	−0.263634	−	0.964623i	$-0.584921\pi$
$587$	16.9836	−	16.9836i	0.700989	−	0.700989i	0.964623	+	0.263634i	$0.0849211\pi$
$588$	−5.50745	−	10.6396i	−0.227123	−	0.438769i
$589$		−	10.2983i		−	0.424336i
$590$	1.06797	−	1.06797i	0.0439676	−	0.0439676i
$591$	24.4107	+	7.75863i	1.00412	+	0.319147i
$592$	−4.92046	+	4.92046i	−0.202229	+	0.202229i
$593$	−22.0744	−	22.0744i	−0.906489	−	0.906489i	0.0894984	−	0.995987i	$-0.471474\pi$
$593$	−22.0744	−	22.0744i	−0.906489	−	0.906489i	−0.995987	+	0.0894984i	$0.971474\pi$
$594$	−3.00000	−	0.416102i	−0.123091	−	0.0170729i
$595$		−	0.715128i		−	0.0293174i
$596$	10.2794	+	10.2794i	0.421060	+	0.421060i
$597$	−23.8117	+	12.3258i	−0.974548	+	0.504463i
$598$		0			0
$599$		−	35.2538i		−	1.44043i	−0.693750	−	0.720216i	$-0.744043\pi$
$599$		−	35.2538i		−	1.44043i	0.693750	−	0.720216i	$-0.255957\pi$
$600$	−7.92905	−	2.52015i	−0.323702	−	0.102885i
$601$	20.1767			0.823023			0.411512	−	0.911405i	$-0.365001\pi$
$601$	20.1767			0.823023			0.411512	+	0.911405i	$0.365001\pi$
$602$	1.08580			0.0442540
$603$	26.1778	−	4.49140i	1.06604	−	0.182904i
$604$	−6.40358	−	6.40358i	−0.260558	−	0.260558i
$605$	3.34139	+	3.34139i	0.135847	+	0.135847i
$606$	23.5067	+	7.47130i	0.954894	+	0.303501i
$607$	−4.85675			−0.197129			−0.0985647	−	0.995131i	$-0.531425\pi$
$607$	−4.85675			−0.197129			−0.0985647	+	0.995131i	$0.531425\pi$
$608$	7.03084			0.285138
$609$	−0.624452	+	1.96469i	−0.0253041	+	0.0796132i
$610$			4.65932i			0.188650i
$611$		0			0
$612$	−13.7126	−	9.69625i	−0.554297	−	0.391948i
$613$	0.643275	+	0.643275i	0.0259816	+	0.0259816i	0.719978	−	0.693997i	$-0.244152\pi$
$613$	0.643275	+	0.643275i	0.0259816	+	0.0259816i	−0.693997	+	0.719978i	$0.744152\pi$
$614$		−	21.9018i		−	0.883883i
$615$	−5.20237	+	2.69294i	−0.209780	+	0.108590i
$616$	0.118776	+	0.118776i	0.00478561	+	0.00478561i
$617$	−31.8135	+	31.8135i	−1.28076	+	1.28076i	−0.340529	+	0.940234i	$0.610606\pi$
$617$	−31.8135	+	31.8135i	−1.28076	+	1.28076i	−0.940234	+	0.340529i	$0.889394\pi$
$618$	2.41812	−	7.60804i	0.0972709	−	0.306040i
$619$	−11.7433	+	11.7433i	−0.472003	+	0.472003i	−0.902562	−	0.430559i	$-0.858316\pi$
$619$	−11.7433	+	11.7433i	−0.472003	+	0.472003i	0.430559	+	0.902562i	$0.358316\pi$
$620$			0.649285i			0.0260759i
$621$	−34.2365	−	4.74863i	−1.37386	−	0.190556i
$622$	22.4869	−	22.4869i	0.901642	−	0.901642i
$623$	−4.05827			−0.162591
$624$		0			0
$625$	−22.0912			−0.883648
$626$	−16.7884	+	16.7884i	−0.670999	+	0.670999i
$627$	6.30368	−	3.26302i	0.251745	−	0.130313i
$628$			10.2127i			0.407532i
$629$	−27.5454	+	27.5454i	−1.09831	+	1.09831i
$630$	−0.377713	+	0.0648053i	−0.0150484	+	0.00258190i
$631$	−25.8085	+	25.8085i	−1.02742	+	1.02742i	−0.0278066	+	0.999613i	$0.508852\pi$
$631$	−25.8085	+	25.8085i	−1.02742	+	1.02742i	−0.999613	+	0.0278066i	$0.991148\pi$
$632$	−0.784083	−	0.784083i	−0.0311891	−	0.0311891i
$633$	−14.9805	−	28.9401i	−0.595422	−	1.15027i
$634$			23.8912i			0.948841i
$635$	0.0756820	+	0.0756820i	0.00300335	+	0.00300335i
$636$	−2.90446	−	5.61098i	−0.115169	−	0.222490i
$637$		0			0
$638$			2.40737i			0.0953087i
$639$	7.80560	+	45.4944i	0.308785	+	1.79973i
$640$	−0.443277			−0.0175221
$641$	0.848907			0.0335298			0.0167649	−	0.999859i	$-0.494663\pi$
$641$	0.848907			0.0335298			0.0167649	+	0.999859i	$0.494663\pi$
$642$	7.08904	−	22.3040i	0.279782	−	0.880269i
$643$	−12.2124	−	12.2124i	−0.481610	−	0.481610i	0.424036	−	0.905645i	$-0.360613\pi$
$643$	−12.2124	−	12.2124i	−0.481610	−	0.481610i	−0.905645	+	0.424036i	$0.860613\pi$
$644$	1.35549	+	1.35549i	0.0534138	+	0.0534138i
$645$	−0.876250	+	2.75692i	−0.0345023	+	0.108553i
$646$	39.3595			1.54858
$647$	−15.7525			−0.619293			−0.309646	−	0.950852i	$-0.600211\pi$
$647$	−15.7525			−0.619293			−0.309646	+	0.950852i	$0.600211\pi$
$648$	−3.87868	+	8.12132i	−0.152369	+	0.319036i
$649$			1.98598i			0.0779567i
$650$		0			0
$651$	−0.336095	−	0.649285i	−0.0131726	−	0.0254475i
$652$	−9.81476	−	9.81476i	−0.384376	−	0.384376i
$653$			24.6413i			0.964289i	0.876092	+	0.482145i	$0.160142\pi$
$653$			24.6413i			0.964289i	−0.876092	+	0.482145i	$0.839858\pi$
$654$	2.32175	+	4.48527i	0.0907874	+	0.175388i
$655$	2.53590	+	2.53590i	0.0990857	+	0.0990857i
$656$	5.39512	−	5.39512i	0.210644	−	0.210644i
$657$	−2.52576	−	14.7212i	−0.0985394	−	0.574330i
$658$	−1.07145	+	1.07145i	−0.0417697	+	0.0417697i
$659$			17.7144i			0.690056i	0.938592	+	0.345028i	$0.112131\pi$
$659$			17.7144i			0.690056i	−0.938592	+	0.345028i	$0.887869\pi$
$660$	−0.397431	+	0.205726i	−0.0154700	+	0.00800786i
$661$	−6.70314	+	6.70314i	−0.260722	+	0.260722i	−0.825347	−	0.564625i	$-0.809021\pi$
$661$	−6.70314	+	6.70314i	−0.260722	+	0.260722i	0.564625	+	0.825347i	$0.309021\pi$
$662$	16.4877			0.640813
$663$		0			0
$664$	−11.6394			−0.451697
$665$	0.635086	−	0.635086i	0.0246276	−	0.0246276i
$666$	17.0450	+	12.0526i	0.660479	+	0.467029i
$667$			27.4733i			1.06377i
$668$	−9.48357	+	9.48357i	−0.366930	+	0.366930i
$669$	3.77514	−	11.8776i	0.145955	−	0.459214i
$670$	2.77506	−	2.77506i	0.107210	−	0.107210i
$671$	−4.33221	−	4.33221i	−0.167243	−	0.167243i
$672$	0.443277	−	0.229457i	0.0170998	−	0.00885150i
$673$		−	0.173307i		−	0.00668051i	−0.999994	−	0.00334025i	$-0.998937\pi$
$673$		−	0.173307i		−	0.00668051i	0.999994	−	0.00334025i	$-0.00106324\pi$
$674$	−2.29701	−	2.29701i	−0.0884775	−	0.0884775i
$675$	−3.42911	+	24.7231i	−0.131986	+	0.951591i
$676$		0			0
$677$			2.12205i			0.0815568i	0.999168	+	0.0407784i	$0.0129838\pi$
$677$			2.12205i			0.0815568i	−0.999168	+	0.0407784i	$0.987016\pi$
$678$	−5.46507	+	17.1946i	−0.209885	+	0.660353i
$679$	0.773450			0.0296823
$680$	−2.48152			−0.0951620
$681$	8.84802	+	2.81223i	0.339057	+	0.107765i
$682$	−0.603702	−	0.603702i	−0.0231169	−	0.0231169i
$683$	22.6901	+	22.6901i	0.868214	+	0.868214i	0.992275	−	0.124061i	$-0.0395918\pi$
$683$	22.6901	+	22.6901i	0.868214	+	0.868214i	−0.124061	+	0.992275i	$0.539592\pi$
$684$	−3.56679	−	20.7888i	−0.136379	−	0.794878i
$685$	0.0366618			0.00140078
$686$	4.01060			0.153125
$687$	−19.2553	−	6.12006i	−0.734636	−	0.233495i
$688$		−	3.76778i		−	0.143645i
$689$		0			0
$690$	−4.53556	+	2.34778i	−0.172666	+	0.0893783i
$691$	−21.5583	−	21.5583i	−0.820118	−	0.820118i	0.166007	−	0.986125i	$-0.446913\pi$
$691$	−21.5583	−	21.5583i	−0.820118	−	0.820118i	−0.986125	+	0.166007i	$0.946913\pi$
$692$			1.10220i			0.0418993i
$693$	0.290940	−	0.411451i	0.0110519	−	0.0156297i
$694$	5.81113	+	5.81113i	0.220587	+	0.220587i
$695$	1.95635	−	1.95635i	0.0742085	−	0.0742085i
$696$	6.81755	+	2.16687i	0.258419	+	0.0821351i
$697$	30.2026	−	30.2026i	1.14401	−	1.14401i
$698$		−	8.01283i		−	0.303290i
$699$	7.60207	+	14.6861i	0.287537	+	0.555478i
$700$	0.978833	−	0.978833i	0.0369964	−	0.0369964i
$701$	1.23549			0.0466638			0.0233319	−	0.999728i	$-0.492573\pi$
$701$	1.23549			0.0466638			0.0233319	+	0.999728i	$0.492573\pi$
$702$		0			0
$703$	−48.9246			−1.84523
$704$	0.412157	−	0.412157i	0.0155337	−	0.0155337i
$705$	−1.85581	−	3.58516i	−0.0698940	−	0.135025i
$706$		−	2.79561i		−	0.105214i
$707$	−2.90188	+	2.90188i	−0.109136	+	0.109136i
$708$	5.62421	+	1.78758i	0.211371	+	0.0671815i
$709$	−11.1940	+	11.1940i	−0.420399	+	0.420399i	−0.885341	−	0.464942i	$-0.846075\pi$
$709$	−11.1940	+	11.1940i	−0.420399	+	0.420399i	0.464942	+	0.885341i	$0.346075\pi$
$710$	4.82277	+	4.82277i	0.180995	+	0.180995i
$711$	−1.92060	+	2.71614i	−0.0720282	+	0.101863i
$712$			14.0824i			0.527759i
$713$	−6.88956	−	6.88956i	−0.258016	−	0.258016i
$714$	2.48152	−	1.28453i	0.0928686	−	0.0480723i
$715$		0			0
$716$			5.59555i			0.209115i
$717$	−48.1766	−	15.3123i	−1.79919	−	0.571849i
$718$	−16.4800			−0.615028
$719$	3.10067			0.115635			0.0578176	−	0.998327i	$-0.481586\pi$
$719$	3.10067			0.115635			0.0578176	+	0.998327i	$0.481586\pi$
$720$	0.224877	+	1.31068i	0.00838067	+	0.0488461i
$721$	0.939204	+	0.939204i	0.0349778	+	0.0349778i
$722$	21.5192	+	21.5192i	0.800860	+	0.800860i
$723$	−18.4116	−	5.85188i	−0.684734	−	0.217634i
$724$	−14.4687			−0.537727
$725$	19.8392			0.736809
$726$	−5.59288	+	17.5967i	−0.207571	+	0.653074i
$727$		−	20.0877i		−	0.745011i	−0.928030	−	0.372506i	$-0.878499\pi$
$727$		−	20.0877i		−	0.745011i	0.928030	−	0.372506i	$-0.121501\pi$
$728$		0			0
$729$	25.9808	+	7.34847i	0.962250	+	0.272166i
$730$	−1.56057	−	1.56057i	−0.0577593	−	0.0577593i
$731$		−	21.0925i		−	0.780135i
$732$	−16.1680	+	8.36919i	−0.597588	+	0.309334i
$733$	−35.4832	−	35.4832i	−1.31060	−	1.31060i	−0.920972	−	0.389628i	$-0.872604\pi$
$733$	−35.4832	−	35.4832i	−1.31060	−	1.31060i	−0.389628	−	0.920972i	$-0.627396\pi$
$734$	−26.2944	+	26.2944i	−0.970544	+	0.970544i
$735$	−1.60864	+	5.06119i	−0.0593354	+	0.186685i
$736$	4.70360	−	4.70360i	0.173377	−	0.173377i
$737$			5.16047i			0.190088i
$738$	−18.6893	−	13.2153i	−0.687961	−	0.486462i
$739$	−16.4638	+	16.4638i	−0.605629	+	0.605629i	−0.941801	−	0.336172i	$-0.890868\pi$
$739$	−16.4638	+	16.4638i	−0.605629	+	0.605629i	0.336172	+	0.941801i	$0.390868\pi$
$740$	3.08458			0.113391
$741$		0			0
$742$	1.05122			0.0385916
$743$	−18.9507	+	18.9507i	−0.695235	+	0.695235i	−0.963379	−	0.268144i	$-0.913590\pi$
$743$	−18.9507	+	18.9507i	−0.695235	+	0.695235i	0.268144	+	0.963379i	$0.413590\pi$
$744$	−2.25305	+	1.16626i	−0.0826007	+	0.0427573i
$745$		−	6.44402i		−	0.236091i
$746$	−5.57782	+	5.57782i	−0.204219	+	0.204219i
$747$	5.90475	+	34.4154i	0.216044	+	1.25919i
$748$	2.30731	−	2.30731i	0.0843635	−	0.0843635i
$749$	2.75341	+	2.75341i	0.100607	+	0.100607i
$750$	3.46013	+	6.68446i	0.126346	+	0.244082i
$751$		−	17.8164i		−	0.650131i	−0.945692	−	0.325065i	$-0.894614\pi$
$751$		−	17.8164i		−	0.650131i	0.945692	−	0.325065i	$-0.105386\pi$
$752$	3.71799	+	3.71799i	0.135581	+	0.135581i
$753$	3.55874	+	6.87496i	0.129688	+	0.250537i
$754$		0			0
$755$			4.01433i			0.146096i
$756$	−0.903335	−	1.19427i	−0.0328540	−	0.0434353i
$757$	24.7813			0.900690			0.450345	−	0.892855i	$-0.351301\pi$
$757$	24.7813			0.900690			0.450345	+	0.892855i	$0.351301\pi$
$758$	−1.86196			−0.0676295
$759$	2.03419	−	6.40009i	0.0738363	−	0.232308i
$760$	−2.20377	−	2.20377i	−0.0799393	−	0.0799393i
$761$	−10.7526	−	10.7526i	−0.389781	−	0.389781i	0.484828	−	0.874609i	$-0.338882\pi$
$761$	−10.7526	−	10.7526i	−0.389781	−	0.389781i	−0.874609	+	0.484828i	$0.838882\pi$
$762$	−0.126678	+	0.398562i	−0.00458905	+	0.0144384i
$763$	−0.840319			−0.0304216
$764$	6.67573			0.241520
$765$	1.25889	+	7.33735i	0.0455153	+	0.265283i
$766$			2.88048i			0.104076i
$767$		0			0
$768$	−0.796225	−	1.53819i	−0.0287313	−	0.0555046i
$769$	−12.9589	−	12.9589i	−0.467311	−	0.467311i	0.433731	−	0.901042i	$-0.357197\pi$
$769$	−12.9589	−	12.9589i	−0.467311	−	0.467311i	−0.901042	+	0.433731i	$0.857197\pi$
$770$		−	0.0744591i		−	0.00268332i
$771$	−9.51355	−	18.3788i	−0.342622	−	0.661895i
$772$	−4.30947	−	4.30947i	−0.155101	−	0.155101i
$773$	23.8031	−	23.8031i	0.856138	−	0.856138i	−0.134742	−	0.990881i	$-0.543021\pi$
$773$	23.8031	−	23.8031i	0.856138	−	0.856138i	0.990881	+	0.134742i	$0.0430207\pi$
$774$	−11.1406	+	1.91142i	−0.400439	+	0.0687044i
$775$	−4.97512	+	4.97512i	−0.178712	+	0.178712i
$776$		−	2.68390i		−	0.0963465i
$777$	−3.08458	+	1.59669i	−0.110659	+	0.0572811i
$778$	−16.5595	+	16.5595i	−0.593688	+	0.593688i
$779$	53.6443			1.92201
$780$		0			0
$781$	−8.96837			−0.320914
$782$	26.3314	−	26.3314i	0.941608	−	0.941608i
$783$	2.94841	−	21.2574i	0.105368	−	0.759677i
$784$		−	6.91695i		−	0.247034i
$785$	3.20112	−	3.20112i	0.114253	−	0.114253i
$786$	−4.24463	+	13.3547i	−0.151401	+	0.476347i
$787$	6.66227	−	6.66227i	0.237484	−	0.237484i	−0.578323	−	0.815808i	$-0.696293\pi$
$787$	6.66227	−	6.66227i	0.237484	−	0.237484i	0.815808	+	0.578323i	$0.196293\pi$
$788$	10.4569	+	10.4569i	0.372511	+	0.372511i
$789$	−4.23188	+	2.19058i	−0.150659	+	0.0779868i
$790$			0.491532i			0.0174879i
$791$	−2.12265	−	2.12265i	−0.0754728	−	0.0754728i
$792$	−1.42775	−	1.00957i	−0.0507330	−	0.0358736i
$793$		0			0
$794$			18.4077i			0.653266i
$795$	−0.848344	+	2.66911i	−0.0300877	+	0.0946637i
$796$	−15.4803			−0.548686
$797$	46.8501			1.65951			0.829757	−	0.558124i	$-0.188479\pi$
$797$	46.8501			1.65951			0.829757	+	0.558124i	$0.188479\pi$
$798$	3.34453	+	1.06302i	0.118395	+	0.0376304i
$799$	20.8138	+	20.8138i	0.736339	+	0.736339i
$800$	−3.39659	−	3.39659i	−0.120088	−	0.120088i
$801$	41.6387	−	7.14407i	1.47123	−	0.252423i
$802$	6.78495			0.239585
$803$	2.90202			0.102410
$804$	14.6142	+	4.64494i	0.515403	+	0.163814i
$805$		−	0.849740i		−	0.0299494i
$806$		0			0
$807$	−9.59871	+	4.96866i	−0.337891	+	0.174905i
$808$	10.0696	+	10.0696i	0.354248	+	0.354248i
$809$		−	40.6329i		−	1.42858i	−0.699851	−	0.714289i	$-0.746750\pi$
$809$		−	40.6329i		−	1.42858i	0.699851	−	0.714289i	$-0.253250\pi$
$810$	3.76133	−	1.32983i	0.132160	−	0.0467255i
$811$	−16.5531	−	16.5531i	−0.581257	−	0.581257i	0.353992	−	0.935249i	$-0.384824\pi$
$811$	−16.5531	−	16.5531i	−0.581257	−	0.581257i	−0.935249	+	0.353992i	$0.884824\pi$
$812$	−0.841620	+	0.841620i	−0.0295351	+	0.0295351i
$813$	36.9221	+	11.7352i	1.29492	+	0.411572i
$814$	−2.86802	+	2.86802i	−0.100524	+	0.100524i
$815$			6.15276i			0.215522i
$816$	−4.45737	−	8.61098i	−0.156039	−	0.301445i
$817$	18.7317	−	18.7317i	0.655340	−	0.655340i
$818$	−29.2874			−1.02401
$819$		0			0
$820$	−3.38214			−0.118109
$821$	2.49011	−	2.49011i	0.0869053	−	0.0869053i	−0.662318	−	0.749223i	$-0.730427\pi$
$821$	2.49011	−	2.49011i	0.0869053	−	0.0869053i	0.749223	+	0.662318i	$0.230427\pi$
$822$	0.0658528	+	0.127218i	0.00229688	+	0.00443723i
$823$		−	10.3686i		−	0.361426i	−0.983536	−	0.180713i	$-0.942160\pi$
$823$		−	10.3686i		−	0.361426i	0.983536	−	0.180713i	$-0.0578405\pi$
$824$	3.25908	−	3.25908i	0.113535	−	0.113535i
$825$	−4.62166	−	1.46894i	−0.160906	−	0.0511418i
$826$	−0.694303	+	0.694303i	−0.0241579	+	0.0241579i
$827$	5.61338	+	5.61338i	0.195196	+	0.195196i	0.797937	−	0.602741i	$-0.205925\pi$
$827$	5.61338	+	5.61338i	0.195196	+	0.195196i	−0.602741	+	0.797937i	$0.705925\pi$
$828$	−16.2938	−	11.5214i	−0.566247	−	0.400397i
$829$		−	2.03548i		−	0.0706950i	−0.999375	−	0.0353475i	$-0.988746\pi$
$829$		−	2.03548i		−	0.0706950i	0.999375	−	0.0353475i	$-0.0112538\pi$
$830$	3.64831	+	3.64831i	0.126635	+	0.126635i
$831$	8.61135	−	4.45757i	0.298725	−	0.154631i
$832$		0			0
$833$		−	38.7220i		−	1.34164i
$834$	10.3026	+	3.27456i	0.356751	+	0.113389i
$835$	5.94514			0.205740
$836$	4.09812			0.141736
$837$	4.59138	+	6.07015i	0.158701	+	0.209815i
$838$	6.53521	+	6.53521i	0.225755	+	0.225755i
$839$	−11.0461	−	11.0461i	−0.381354	−	0.381354i	0.490236	−	0.871590i	$-0.336911\pi$
$839$	−11.0461	−	11.0461i	−0.381354	−	0.381354i	−0.871590	+	0.490236i	$0.836911\pi$
$840$	−0.210865	−	0.0670206i	−0.00727552	−	0.00231243i
$841$	11.9419			0.411789
$842$	26.0908			0.899149
$843$	6.55058	−	20.6098i	0.225614	−	0.709841i
$844$		−	18.8144i		−	0.647619i
$845$		0			0
$846$	9.10718	−	12.8795i	0.313111	−	0.442806i
$847$	−2.17229	−	2.17229i	−0.0746408	−	0.0746408i
$848$		−	3.64778i		−	0.125265i
$849$	−10.5500	+	5.46109i	−0.362075	+	0.187424i
$850$	−19.0146	−	19.0146i	−0.652194	−	0.652194i
$851$	−32.7304	+	32.7304i	−1.12198	+	1.12198i
$852$	−8.07243	+	25.3980i	−0.276557	+	0.870121i
$853$	−21.4461	+	21.4461i	−0.734300	+	0.734300i	−0.971469	−	0.237168i	$-0.923781\pi$
$853$	−21.4461	+	21.4461i	−0.734300	+	0.734300i	0.237168	+	0.971469i	$0.423781\pi$
$854$		−	3.02909i		−	0.103653i
$855$	−5.39812	+	7.63410i	−0.184612	+	0.261081i
$856$	9.55443	−	9.55443i	0.326564	−	0.326564i
$857$	17.8872			0.611017			0.305508	−	0.952189i	$-0.401174\pi$
$857$	17.8872			0.611017			0.305508	+	0.952189i	$0.401174\pi$
$858$		0			0
$859$	−1.29875			−0.0443127			−0.0221564	−	0.999755i	$-0.507053\pi$
$859$	−1.29875			−0.0443127			−0.0221564	+	0.999755i	$0.507053\pi$
$860$	−1.18099	+	1.18099i	−0.0402714	+	0.0402714i
$861$	3.38214	−	1.75072i	0.115263	−	0.0596645i
$862$		−	22.3635i		−	0.761705i
$863$	−15.1285	+	15.1285i	−0.514979	+	0.514979i	−0.916048	−	0.401069i	$-0.868639\pi$
$863$	−15.1285	+	15.1285i	−0.514979	+	0.514979i	0.401069	+	0.916048i	$0.368639\pi$
$864$	−4.14418	+	3.13461i	−0.140988	+	0.106642i
$865$	0.345478	−	0.345478i	0.0117466	−	0.0117466i
$866$	−2.79168	−	2.79168i	−0.0948652	−	0.0948652i
$867$	−11.4171	−	22.0562i	−0.387746	−	0.749067i
$868$		−	0.422110i		−	0.0143274i
$869$	−0.457024	−	0.457024i	−0.0155035	−	0.0155035i
$870$	−1.45773	−	2.81612i	−0.0494216	−	0.0954753i
$871$		0			0
$872$			2.91594i			0.0987462i
$873$	−7.93575	+	1.36156i	−0.268584	+	0.0460818i
$874$	46.7684			1.58197
$875$	−1.25234			−0.0423368
$876$	2.61210	−	8.21837i	0.0882548	−	0.277673i
$877$	15.7315	+	15.7315i	0.531215	+	0.531215i	0.920934	−	0.389719i	$-0.127428\pi$
$877$	15.7315	+	15.7315i	0.531215	+	0.531215i	−0.389719	+	0.920934i	$0.627428\pi$
$878$	12.9471	+	12.9471i	0.436944	+	0.436944i
$879$	14.3519	−	45.1549i	0.484077	−	1.52304i
$880$	−0.258376			−0.00870986
$881$	20.5028			0.690758			0.345379	−	0.938463i	$-0.387750\pi$
$881$	20.5028			0.690758			0.345379	+	0.938463i	$0.387750\pi$
$882$	−20.4520	+	3.50901i	−0.688655	+	0.118155i
$883$		−	27.7709i		−	0.934566i	−0.884108	−	0.467283i	$-0.845233\pi$
$883$		−	27.7709i		−	0.934566i	0.884108	−	0.467283i	$-0.154767\pi$
$884$		0			0
$885$	−1.20257	−	2.32318i	−0.0404239	−	0.0780929i
$886$	−4.14627	−	4.14627i	−0.139297	−	0.139297i
$887$			13.2051i			0.443385i	0.975117	+	0.221692i	$0.0711581\pi$
$887$			13.2051i			0.443385i	−0.975117	+	0.221692i	$0.928842\pi$
$888$	5.54059	+	10.7036i	0.185930	+	0.359189i
$889$	−0.0492020	−	0.0492020i	−0.00165018	−	0.00165018i
$890$	4.41403	−	4.41403i	0.147959	−	0.147959i
$891$	−2.26079	+	4.73373i	−0.0757395	+	0.158586i
$892$	5.08804	−	5.08804i	0.170360	−	0.170360i
$893$			36.9684i			1.23710i
$894$	22.3610	−	11.5749i	0.747864	−	0.387123i
$895$	1.75389	−	1.75389i	0.0586261	−	0.0586261i
$896$	0.288181			0.00962745
$897$		0			0
$898$	−28.5045			−0.951207
$899$	4.27771	−	4.27771i	0.142670	−	0.142670i
$900$	−8.31992	+	11.7661i	−0.277331	+	0.392205i
$901$		−	20.4208i		−	0.680315i
$902$	3.14469	−	3.14469i	0.104707	−	0.104707i
$903$	0.569664	−	1.79231i	0.0189572	−	0.0596444i
$904$	−7.36568	+	7.36568i	−0.244979	+	0.244979i
$905$	4.53514	+	4.53514i	0.150753	+	0.150753i
$906$	−13.9299	+	7.21064i	−0.462789	+	0.239557i
$907$		−	27.9622i		−	0.928470i	−0.885712	−	0.464235i	$-0.846329\pi$
$907$		−	27.9622i		−	0.928470i	0.885712	−	0.464235i	$-0.153671\pi$
$908$	3.79025	+	3.79025i	0.125784	+	0.125784i
$909$	24.6655	−	34.8822i	0.818101	−	1.15697i
$910$		0			0
$911$			33.2713i			1.10233i	0.834397	+	0.551164i	$0.185816\pi$
$911$			33.2713i			1.10233i	−0.834397	+	0.551164i	$0.814184\pi$
$912$	3.68871	−	11.6057i	0.122145	−	0.384302i
$913$	−6.78436			−0.224530
$914$	19.1699			0.634084
$915$	7.69105	+	2.44450i	0.254258	+	0.0808127i
$916$	−8.24846	−	8.24846i	−0.272537	−	0.272537i
$917$	−1.64863	−	1.64863i	−0.0544424	−	0.0544424i
$918$	−23.1997	+	17.5479i	−0.765703	+	0.579168i
$919$	14.4374			0.476244			0.238122	−	0.971235i	$-0.423468\pi$
$919$	14.4374			0.476244			0.238122	+	0.971235i	$0.423468\pi$
$920$	−2.94863			−0.0972136
$921$	−36.1528	−	11.4907i	−1.19127	−	0.378632i
$922$		−	29.6500i		−	0.976471i
$923$		0			0
$924$	0.258376	−	0.133745i	0.00849995	−	0.00439990i
$925$	23.6354	+	23.6354i	0.777128	+	0.777128i
$926$			25.8170i			0.848400i
$927$	−11.2898	−	7.98308i	−0.370805	−	0.262199i
$928$	2.92046	+	2.92046i	0.0958687	+	0.0958687i
$929$	−9.95732	+	9.95732i	−0.326689	+	0.326689i	−0.851326	−	0.524637i	$-0.824201\pi$
$929$	−9.95732	+	9.95732i	−0.326689	+	0.326689i	0.524637	+	0.851326i	$0.324201\pi$
$930$	1.07176	+	0.340646i	0.0351445	+	0.0111702i
$931$	34.3880	−	34.3880i	1.12702	−	1.12702i
$932$			9.54763i			0.312743i
$933$	−25.3210	−	48.9163i	−0.828971	−	1.60145i
$934$	−22.9425	+	22.9425i	−0.750701	+	0.750701i
$935$	−1.44642			−0.0473031
$936$		0			0
$937$	25.6098			0.836635			0.418317	−	0.908301i	$-0.362620\pi$
$937$	25.6098			0.836635			0.418317	+	0.908301i	$0.362620\pi$
$938$	−1.80411	+	1.80411i	−0.0589062	+	0.0589062i
$939$	18.9043	+	36.5202i	0.616918	+	1.19179i
$940$		−	2.33077i		−	0.0760212i
$941$	24.7798	−	24.7798i	0.807800	−	0.807800i	−0.176501	−	0.984300i	$-0.556478\pi$
$941$	24.7798	−	24.7798i	0.807800	−	0.807800i	0.984300	+	0.176501i	$0.0564779\pi$
$942$	16.8580	+	5.35809i	0.549262	+	0.174576i
$943$	35.8878	−	35.8878i	1.16867	−	1.16867i
$944$	2.40926	+	2.40926i	0.0784147	+	0.0784147i
$945$	−0.0911934	+	0.657483i	−0.00296652	+	0.0213879i
$946$		−	2.19615i		−	0.0714031i
$947$	8.13217	+	8.13217i	0.264260	+	0.264260i	0.826782	−	0.562522i	$-0.190169\pi$
$947$	8.13217	+	8.13217i	0.264260	+	0.264260i	−0.562522	+	0.826782i	$0.690169\pi$
$948$	−1.70564	+	0.882903i	−0.0553965	+	0.0286753i
$949$		0			0
$950$		−	33.7727i		−	1.09573i
$951$	39.4367	+	12.5345i	1.27882	+	0.406458i
$952$	1.61328			0.0522865
$953$	−48.5516			−1.57274			−0.786370	−	0.617755i	$-0.788042\pi$
$953$	−48.5516			−1.57274			−0.786370	+	0.617755i	$0.788042\pi$
$954$	−10.7858	+	1.85054i	−0.349202	+	0.0599135i
$955$	−2.09247	−	2.09247i	−0.0677107	−	0.0677107i
$956$	−20.6375	−	20.6375i	−0.667466	−	0.667466i
$957$	3.97380	+	1.26302i	0.128455	+	0.0408277i
$958$	8.29040			0.267851
$959$	−0.0238344			−0.000769653
$960$	−0.232564	+	0.731708i	−0.00750598	+	0.0236158i
$961$		−	28.8545i		−	0.930792i
$962$		0			0
$963$	−33.0975	−	23.4035i	−1.06655	−	0.754167i
$964$	−7.88702	−	7.88702i	−0.254024	−	0.254024i
$965$			2.70156i			0.0869662i
$966$	2.94863	−	1.52633i	0.0948707	−	0.0491087i
$967$	−15.4257	−	15.4257i	−0.496058	−	0.496058i	0.414150	−	0.910209i	$-0.364079\pi$
$967$	−15.4257	−	15.4257i	−0.496058	−	0.496058i	−0.910209	+	0.414150i	$0.864079\pi$
$968$	−7.53794	+	7.53794i	−0.242279	+	0.242279i
$969$	20.6499	−	64.9700i	0.663370	−	2.08714i
$970$	−0.841253	+	0.841253i	−0.0270110	+	0.0270110i
$971$		−	7.66202i		−	0.245886i	−0.992414	−	0.122943i	$-0.960767\pi$
$971$		−	7.66202i		−	0.245886i	0.992414	−	0.122943i	$-0.0392332\pi$
$972$	11.3708	+	10.6633i	0.364717	+	0.342025i
$973$	−1.27185	+	1.27185i	−0.0407737	+	0.0407737i
$974$	−32.1307			−1.02953
$975$		0			0
$976$	−10.5111			−0.336451
$977$	−14.2640	+	14.2640i	−0.456346	+	0.456346i	−0.897454	−	0.441108i	$-0.854586\pi$
$977$	−14.2640	+	14.2640i	−0.456346	+	0.456346i	0.441108	+	0.897454i	$0.354586\pi$
$978$	−21.3503	+	11.0517i	−0.682708	+	0.353396i
$979$			8.20829i			0.262338i
$980$	−2.16808	+	2.16808i	−0.0692567	+	0.0692567i
$981$	8.62184	−	1.47927i	0.275274	−	0.0472296i
$982$	18.6817	−	18.6817i	0.596157	−	0.596157i
$983$	0.922992	+	0.922992i	0.0294389	+	0.0294389i	0.721673	−	0.692234i	$-0.243373\pi$
$983$	0.922992	+	0.922992i	0.0294389	+	0.0294389i	−0.692234	+	0.721673i	$0.743373\pi$
$984$	−6.07508	−	11.7362i	−0.193667	−	0.374135i
$985$		−	6.55530i		−	0.208869i
$986$	16.3491	+	16.3491i	0.520661	+	0.520661i
$987$	1.20649	+	2.33077i	0.0384031	+	0.0741891i
$988$		0			0
$989$		−	25.0629i		−	0.796953i
$990$	0.131076	+	0.763965i	0.00416586	+	0.0242804i
$991$	20.5965			0.654269			0.327135	−	0.944978i	$-0.393917\pi$
$991$	20.5965			0.654269			0.327135	+	0.944978i	$0.393917\pi$
$992$	−1.46474			−0.0465055
$993$	8.65024	−	27.2159i	0.274507	−	0.863672i
$994$	−3.13536	−	3.13536i	−0.0994475	−	0.0994475i
$995$	4.85222	+	4.85222i	0.153826	+	0.153826i
$996$	−6.10660	+	19.2130i	−0.193495	+	0.608786i
$997$	−32.1789			−1.01912			−0.509558	−	0.860436i	$-0.670191\pi$
$997$	−32.1789			−1.01912			−0.509558	+	0.860436i	$0.670191\pi$
$998$	13.1158			0.415173
$999$	28.8376	−	21.8124i	0.912381	−	0.690114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.d.437.6		16
3.2	odd	2	inner	1014.2.g.d.437.2		16
13.4	even	6		78.2.k.a.11.3	yes	16
13.5	odd	4	inner	1014.2.g.d.239.2		16
13.8	odd	4		1014.2.g.c.239.6		16
13.11	odd	12		78.2.k.a.71.2	yes	16
13.12	even	2		1014.2.g.c.437.2		16
39.5	even	4	inner	1014.2.g.d.239.6		16
39.8	even	4		1014.2.g.c.239.2		16
39.11	even	12		78.2.k.a.71.3	yes	16
39.17	odd	6		78.2.k.a.11.2	✓	16
39.38	odd	2		1014.2.g.c.437.6		16
52.11	even	12		624.2.cn.d.305.1		16
52.43	odd	6		624.2.cn.d.401.3		16
156.11	odd	12		624.2.cn.d.305.3		16
156.95	even	6		624.2.cn.d.401.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.11.2	✓	16	39.17	odd	6
78.2.k.a.11.3	yes	16	13.4	even	6
78.2.k.a.71.2	yes	16	13.11	odd	12
78.2.k.a.71.3	yes	16	39.11	even	12
624.2.cn.d.305.1		16	52.11	even	12
624.2.cn.d.305.3		16	156.11	odd	12
624.2.cn.d.401.1		16	156.95	even	6
624.2.cn.d.401.3		16	52.43	odd	6
1014.2.g.c.239.2		16	39.8	even	4
1014.2.g.c.239.6		16	13.8	odd	4
1014.2.g.c.437.2		16	13.12	even	2
1014.2.g.c.437.6		16	39.38	odd	2
1014.2.g.d.239.2		16	13.5	odd	4	inner
1014.2.g.d.239.6		16	39.5	even	4	inner
1014.2.g.d.437.2		16	3.2	odd	2	inner
1014.2.g.d.437.6		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.796225 - 1.53819i) q^{3} -1.00000i q^{4} +(-0.313444 + 0.313444i) q^{5} +(-1.65068 - 0.524648i) q^{6} +(0.203775 - 0.203775i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.73205 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.796225 - 1.53819i) q^{3} -1.00000i q^{4} +(-0.313444 + 0.313444i) q^{5} +(-1.65068 - 0.524648i) q^{6} +(0.203775 - 0.203775i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.73205 + 2.44949i) q^{9} +0.443277i q^{10} +(-0.412157 - 0.412157i) q^{11} +(-1.53819 + 0.796225i) q^{12} -0.288181i q^{14} +(0.731708 + 0.232564i) q^{15} -1.00000 q^{16} -5.59813 q^{17} +(0.507306 + 2.95680i) q^{18} +(-4.97155 - 4.97155i) q^{19} +(0.313444 + 0.313444i) q^{20} +(-0.475695 - 0.151194i) q^{21} -0.582877 q^{22} -6.65190 q^{23} +(-0.524648 + 1.65068i) q^{24} +4.80351i q^{25} +(5.14688 + 0.713876i) q^{27} +(-0.203775 - 0.203775i) q^{28} -4.13015i q^{29} +(0.681844 - 0.352948i) q^{30} +(1.03573 + 1.03573i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.305805 + 0.962144i) q^{33} +(-3.95848 + 3.95848i) q^{34} +0.127744i q^{35} +(2.44949 + 1.73205i) q^{36} +(4.92046 - 4.92046i) q^{37} -7.03084 q^{38} +0.443277 q^{40} +(-5.39512 + 5.39512i) q^{41} +(-0.443277 + 0.229457i) q^{42} +3.76778i q^{43} +(-0.412157 + 0.412157i) q^{44} +(-0.224877 - 1.31068i) q^{45} +(-4.70360 + 4.70360i) q^{46} +(-3.71799 - 3.71799i) q^{47} +(0.796225 + 1.53819i) q^{48} +6.91695i q^{49} +(3.39659 + 3.39659i) q^{50} +(4.45737 + 8.61098i) q^{51} +3.64778i q^{53} +(4.14418 - 3.13461i) q^{54} +0.258376 q^{55} -0.288181 q^{56} +(-3.68871 + 11.6057i) q^{57} +(-2.92046 - 2.92046i) q^{58} +(-2.40926 - 2.40926i) q^{59} +(0.232564 - 0.731708i) q^{60} +10.5111 q^{61} +1.46474 q^{62} +(0.146196 + 0.852093i) q^{63} +1.00000i q^{64} +(0.464102 + 0.896575i) q^{66} +(-6.26033 - 6.26033i) q^{67} +5.59813i q^{68} +(5.29641 + 10.2319i) q^{69} +(0.0903287 + 0.0903287i) q^{70} +(10.8798 - 10.8798i) q^{71} +(2.95680 - 0.507306i) q^{72} +(-3.52053 + 3.52053i) q^{73} -6.95858i q^{74} +(7.38870 - 3.82467i) q^{75} +(-4.97155 + 4.97155i) q^{76} -0.167974 q^{77} +1.10886 q^{79} +(0.313444 - 0.313444i) q^{80} +(-3.00000 - 8.48528i) q^{81} +7.62986i q^{82} +(8.23032 - 8.23032i) q^{83} +(-0.151194 + 0.475695i) q^{84} +(1.75470 - 1.75470i) q^{85} +(2.66422 + 2.66422i) q^{86} +(-6.35295 + 3.28853i) q^{87} +0.582877i q^{88} +(-9.95774 - 9.95774i) q^{89} +(-1.08580 - 0.767778i) q^{90} +6.65190i q^{92} +(0.768472 - 2.41782i) q^{93} -5.25803 q^{94} +3.11661 q^{95} +(1.65068 + 0.524648i) q^{96} +(1.89781 + 1.89781i) q^{97} +(4.89102 + 4.89102i) q^{98} +(1.72345 - 0.295697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{7}+O(q^{10}) \) 16 * q + 16 * q^7	\( 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66} - 32 q^{67} - 56 q^{73} - 32 q^{76} - 96 q^{79} - 48 q^{81} - 24 q^{84} - 24 q^{85} - 96 q^{87} - 48 q^{93} + 48 q^{94} - 16 q^{97}+O(q^{100}) \) 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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