LMFDB - Embedded newform 325.2.n.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("325.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	325.101
Dual form			325.2.n.b.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395644 - 0.228425i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.895644 + 1.55130i) q^{4} +(0.395644 + 0.228425i) q^{6} +(1.50000 + 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.29129 + 1.32288i) q^{11} -1.79129 q^{12} +(1.00000 + 3.46410i) q^{13} +0.791288 q^{14} +(-1.39564 - 2.41733i) q^{16} +(-2.29129 + 3.96863i) q^{17} -0.913701i q^{18} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-0.604356 + 1.04678i) q^{22} +(2.29129 + 3.96863i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(1.18693 + 1.14213i) q^{26} +5.00000 q^{27} +(-2.68693 + 1.55130i) q^{28} +(-2.29129 - 3.96863i) q^{29} -6.20520i q^{31} +(-4.10436 - 2.36965i) q^{32} +(-2.29129 - 1.32288i) q^{33} +2.09355i q^{34} +(1.79129 + 3.10260i) q^{36} +(6.87386 - 3.96863i) q^{37} +0.791288 q^{38} +(-2.50000 + 2.59808i) q^{39} +(2.29129 - 1.32288i) q^{41} +(0.395644 + 0.685275i) q^{42} +(5.29129 - 9.16478i) q^{43} -4.73930i q^{44} +(1.81307 + 1.04678i) q^{46} -1.82740i q^{47} +(1.39564 - 2.41733i) q^{48} +(-2.00000 - 3.46410i) q^{49} -4.58258 q^{51} +(-6.26951 - 1.55130i) q^{52} -7.58258 q^{53} +(1.97822 - 1.14213i) q^{54} +(-1.50000 + 2.59808i) q^{56} +1.73205i q^{57} +(-1.81307 - 1.04678i) q^{58} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(-1.41742 - 2.45505i) q^{62} +(3.00000 - 1.73205i) q^{63} +3.41742 q^{64} -1.20871 q^{66} +(-0.873864 + 0.504525i) q^{67} +(-4.10436 - 7.10895i) q^{68} +(-2.29129 + 3.96863i) q^{69} +(6.08258 + 3.51178i) q^{71} +(3.00000 + 1.73205i) q^{72} +(1.81307 - 3.14033i) q^{74} +(-2.68693 + 1.55130i) q^{76} -4.58258 q^{77} +(-0.395644 + 1.59898i) q^{78} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.604356 - 1.04678i) q^{82} -6.01450i q^{83} +(-2.68693 - 1.55130i) q^{84} -4.83465i q^{86} +(2.29129 - 3.96863i) q^{87} +(-2.29129 - 3.96863i) q^{88} +(-8.29129 + 4.78698i) q^{89} +(-1.50000 + 6.06218i) q^{91} -8.20871 q^{92} +(5.37386 - 3.10260i) q^{93} +(-0.417424 - 0.723000i) q^{94} -4.73930i q^{96} +(9.87386 + 5.70068i) q^{97} +(-1.58258 - 0.913701i) q^{98} +5.29150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 2 q^{3} + q^{4} - 3 q^{6} + 6 q^{7} + 4 q^{9} + 2 q^{12} + 4 q^{13} - 6 q^{14} - q^{16} + 6 q^{19} - 7 q^{22} - 6 q^{24} - 9 q^{26} + 20 q^{27} + 3 q^{28} - 21 q^{32} - 2 q^{36} - 6 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 + 2 * q^3 + q^4 - 3 * q^6 + 6 * q^7 + 4 * q^9 + 2 * q^12 + 4 * q^13 - 6 * q^14 - q^16 + 6 * q^19 - 7 * q^22 - 6 * q^24 - 9 * q^26 + 20 * q^27 + 3 * q^28 - 21 * q^32 - 2 * q^36 - 6 * q^38 - 10 * q^39 - 3 * q^42 + 12 * q^43 + 21 * q^46 + q^48 - 8 * q^49 + 7 * q^52 - 12 * q^53 - 15 * q^54 - 6 * q^56 - 21 * q^58 + 30 * q^59 + 12 * q^61 - 24 * q^62 + 12 * q^63 + 32 * q^64 - 14 * q^66 + 24 * q^67 - 21 * q^68 + 6 * q^71 + 12 * q^72 + 21 * q^74 + 3 * q^76 + 3 * q^78 - 24 * q^79 - 2 * q^81 + 7 * q^82 + 3 * q^84 - 24 * q^89 - 6 * q^91 - 42 * q^92 - 6 * q^93 - 20 * q^94 + 12 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.395644	−	0.228425i	0.279763	−	0.161521i	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	0.395644	−	0.228425i	0.279763	−	0.161521i	0.633316	+	0.773893i	$0.281693\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−0.895644	+	1.55130i	−0.447822	+	0.775650i
$5$		0			0
$5$		0			0
$6$	0.395644	+	0.228425i	0.161521	+	0.0932542i
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	−0.188982	+	0.981981i	$0.560519\pi$
$8$			1.73205i			0.612372i
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	−2.29129	+	1.32288i	−0.690849	+	0.398862i	−0.803930	−	0.594724i	$-0.797261\pi$
$11$	−2.29129	+	1.32288i	−0.690849	+	0.398862i	0.113081	+	0.993586i	$0.463928\pi$
$12$	−1.79129			−0.517100
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	0.791288			0.211481
$15$		0			0
$16$	−1.39564	−	2.41733i	−0.348911	−	0.604332i
$17$	−2.29129	+	3.96863i	−0.555719	+	0.962533i	0.442128	+	0.896952i	$0.354224\pi$
$17$	−2.29129	+	3.96863i	−0.555719	+	0.962533i	−0.997847	+	0.0655816i	$0.979110\pi$
$18$		−	0.913701i		−	0.215361i
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$			1.73205i			0.377964i
$22$	−0.604356	+	1.04678i	−0.128849	+	0.223173i
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	0.999675	−	0.0254855i	$-0.00811315\pi$
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	−0.521909	+	0.853001i	$0.674780\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$		0			0
$26$	1.18693	+	1.14213i	0.232776	+	0.223989i
$27$	5.00000			0.962250
$28$	−2.68693	+	1.55130i	−0.507782	+	0.293168i
$29$	−2.29129	−	3.96863i	−0.425481	−	0.736956i	0.570984	−	0.820961i	$-0.306562\pi$
$29$	−2.29129	−	3.96863i	−0.425481	−	0.736956i	−0.996465	+	0.0840058i	$0.973229\pi$
$30$		0			0
$31$		−	6.20520i		−	1.11449i	−0.830349	−	0.557244i	$-0.811859\pi$
$31$		−	6.20520i		−	1.11449i	0.830349	−	0.557244i	$-0.188141\pi$
$32$	−4.10436	−	2.36965i	−0.725555	−	0.418899i
$33$	−2.29129	−	1.32288i	−0.398862	−	0.230283i
$34$			2.09355i			0.359041i
$35$		0			0
$36$	1.79129	+	3.10260i	0.298548	+	0.517100i
$37$	6.87386	−	3.96863i	1.13006	−	0.652438i	0.186107	−	0.982529i	$-0.440413\pi$
$37$	6.87386	−	3.96863i	1.13006	−	0.652438i	0.943949	+	0.330091i	$0.107080\pi$
$38$	0.791288			0.128364
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	−0.310293	−	0.950641i	$-0.600427\pi$
$41$	2.29129	−	1.32288i	0.357839	−	0.206598i	0.668132	+	0.744042i	$0.267094\pi$
$42$	0.395644	+	0.685275i	0.0610492	+	0.105740i
$43$	5.29129	−	9.16478i	0.806914	−	1.39762i	−0.108078	−	0.994142i	$-0.534469\pi$
$43$	5.29129	−	9.16478i	0.806914	−	1.39762i	0.914991	−	0.403473i	$-0.132197\pi$
$44$		−	4.73930i		−	0.714477i
$45$		0			0
$46$	1.81307	+	1.04678i	0.267322	+	0.154339i
$47$		−	1.82740i		−	0.266554i	−0.991079	−	0.133277i	$-0.957450\pi$
$47$		−	1.82740i		−	0.266554i	0.991079	−	0.133277i	$-0.0425500\pi$
$48$	1.39564	−	2.41733i	0.201444	−	0.348911i
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$		0			0
$51$	−4.58258			−0.641689
$52$	−6.26951	−	1.55130i	−0.869424	−	0.215127i
$53$	−7.58258			−1.04155			−0.520773	−	0.853695i	$-0.674356\pi$
$53$	−7.58258			−1.04155			−0.520773	+	0.853695i	$0.674356\pi$
$54$	1.97822	−	1.14213i	0.269202	−	0.155424i
$55$		0			0
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$			1.73205i			0.229416i
$58$	−1.81307	−	1.04678i	−0.238068	−	0.137448i
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.995796	+	0.0915940i	$0.0291962\pi$
$59$	12.0826	+	6.97588i	1.57302	+	0.908182i	0.577221	+	0.816588i	$0.304137\pi$
$60$		0			0
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	−0.817082	−	0.576522i	$-0.804410\pi$
$61$	0.708712	−	1.22753i	0.0907413	−	0.157169i	0.907823	+	0.419353i	$0.137743\pi$
$62$	−1.41742	−	2.45505i	−0.180013	−	0.311792i
$63$	3.00000	−	1.73205i	0.377964	−	0.218218i
$64$	3.41742			0.427178
$65$		0			0
$66$	−1.20871			−0.148782
$67$	−0.873864	+	0.504525i	−0.106759	+	0.0616376i	−0.552429	−	0.833560i	$-0.686299\pi$
$67$	−0.873864	+	0.504525i	−0.106759	+	0.0616376i	0.445670	+	0.895198i	$0.352966\pi$
$68$	−4.10436	−	7.10895i	−0.497726	−	0.862087i
$69$	−2.29129	+	3.96863i	−0.275839	+	0.477767i
$70$		0			0
$71$	6.08258	+	3.51178i	0.721869	+	0.416771i	0.815440	−	0.578841i	$-0.196495\pi$
$71$	6.08258	+	3.51178i	0.721869	+	0.416771i	−0.0935712	+	0.995613i	$0.529828\pi$
$72$	3.00000	+	1.73205i	0.353553	+	0.204124i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	1.81307	−	3.14033i	0.210765	−	0.365056i
$75$		0			0
$76$	−2.68693	+	1.55130i	−0.308212	+	0.177946i
$77$	−4.58258			−0.522233
$78$	−0.395644	+	1.59898i	−0.0447979	+	0.181048i
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.604356	−	1.04678i	0.0667400	−	0.115597i
$83$		−	6.01450i		−	0.660177i	−0.943950	−	0.330089i	$-0.892921\pi$
$83$		−	6.01450i		−	0.660177i	0.943950	−	0.330089i	$-0.107079\pi$
$84$	−2.68693	−	1.55130i	−0.293168	−	0.169261i
$85$		0			0
$86$		−	4.83465i		−	0.521334i
$87$	2.29129	−	3.96863i	0.245652	−	0.425481i
$88$	−2.29129	−	3.96863i	−0.244252	−	0.423057i
$89$	−8.29129	+	4.78698i	−0.878875	+	0.507419i	−0.870287	−	0.492545i	$-0.836067\pi$
$89$	−8.29129	+	4.78698i	−0.878875	+	0.507419i	−0.00858752	+	0.999963i	$0.502734\pi$
$90$		0			0
$91$	−1.50000	+	6.06218i	−0.157243	+	0.635489i
$92$	−8.20871			−0.855817
$93$	5.37386	−	3.10260i	0.557244	−	0.321725i
$94$	−0.417424	−	0.723000i	−0.0430540	−	0.0745718i
$95$		0			0
$96$		−	4.73930i		−	0.483703i
$97$	9.87386	+	5.70068i	1.00254	+	0.578816i	0.908999	−	0.416799i	$-0.136848\pi$
$97$	9.87386	+	5.70068i	1.00254	+	0.578816i	0.0935404	+	0.995615i	$0.470182\pi$
$98$	−1.58258	−	0.913701i	−0.159864	−	0.0922977i
$99$			5.29150i			0.531816i
$100$		0			0
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−1.81307	+	1.04678i	−0.179521	+	0.103646i
$103$	−3.16515			−0.311872			−0.155936	−	0.987767i	$-0.549839\pi$
$103$	−3.16515			−0.311872			−0.155936	+	0.987767i	$0.549839\pi$
$104$	−6.00000	+	1.73205i	−0.588348	+	0.169842i
$105$		0			0
$106$	−3.00000	+	1.73205i	−0.291386	+	0.168232i
$107$	−5.29129	−	9.16478i	−0.511528	−	0.885993i	−0.999911	−	0.0133631i	$-0.995746\pi$
$107$	−5.29129	−	9.16478i	−0.511528	−	0.885993i	0.488383	−	0.872630i	$-0.337587\pi$
$108$	−4.47822	+	7.75650i	−0.430917	+	0.746370i
$109$		−	13.1334i		−	1.25795i	−0.777425	−	0.628976i	$-0.783474\pi$
$109$		−	13.1334i		−	1.25795i	0.777425	−	0.628976i	$-0.216526\pi$
$110$		0			0
$111$	6.87386	+	3.96863i	0.652438	+	0.376685i
$112$		−	4.83465i		−	0.456832i
$113$	−3.70871	+	6.42368i	−0.348886	+	0.604289i	−0.986052	−	0.166438i	$-0.946773\pi$
$113$	−3.70871	+	6.42368i	−0.348886	+	0.604289i	0.637166	+	0.770727i	$0.280107\pi$
$114$	0.395644	+	0.685275i	0.0370554	+	0.0641819i
$115$		0			0
$116$	8.20871			0.762160
$117$	7.00000	+	1.73205i	0.647150	+	0.160128i
$118$	6.37386			0.586762
$119$	−6.87386	+	3.96863i	−0.630126	+	0.363803i
$120$		0			0
$121$	−2.00000	+	3.46410i	−0.181818	+	0.314918i
$122$		−	0.647551i		−	0.0586265i
$123$	2.29129	+	1.32288i	0.206598	+	0.119280i
$124$	9.62614	+	5.55765i	0.864453	+	0.499092i
$125$		0			0
$126$	0.791288	−	1.37055i	0.0704935	−	0.122098i
$127$	8.87386	+	15.3700i	0.787428	+	1.36387i	0.927538	+	0.373729i	$0.121921\pi$
$127$	8.87386	+	15.3700i	0.787428	+	1.36387i	−0.140110	+	0.990136i	$0.544746\pi$
$128$	9.56080	−	5.51993i	0.845063	−	0.487897i
$129$	10.5826			0.931744
$130$		0			0
$131$	−7.58258			−0.662493			−0.331246	−	0.943544i	$-0.607469\pi$
$131$	−7.58258			−0.662493			−0.331246	+	0.943544i	$0.607469\pi$
$132$	4.10436	−	2.36965i	0.357238	−	0.206252i
$133$	1.50000	+	2.59808i	0.130066	+	0.225282i
$134$	−0.230493	+	0.399225i	−0.0199115	+	0.0344878i
$135$		0			0
$136$	−6.87386	−	3.96863i	−0.589429	−	0.340307i
$137$	−9.08258	−	5.24383i	−0.775977	−	0.448010i	0.0590258	−	0.998256i	$-0.481201\pi$
$137$	−9.08258	−	5.24383i	−0.775977	−	0.448010i	−0.835003	+	0.550246i	$0.814534\pi$
$138$			2.09355i			0.178215i
$139$	10.8739	−	18.8341i	0.922309	−	1.59749i	0.126476	−	0.991970i	$-0.459633\pi$
$139$	10.8739	−	18.8341i	0.922309	−	1.59749i	0.795833	−	0.605517i	$-0.207033\pi$
$140$		0			0
$141$	1.58258	−	0.913701i	0.133277	−	0.0769475i
$142$	3.20871			0.269269
$143$	−6.87386	−	6.61438i	−0.574821	−	0.553122i
$144$	−5.58258			−0.465215
$145$		0			0
$146$		0			0
$147$	2.00000	−	3.46410i	0.164957	−	0.285714i
$148$			14.2179i			1.16870i
$149$	14.4564	+	8.34643i	1.18432	+	0.683766i	0.957009	−	0.290057i	$-0.0936742\pi$
$149$	14.4564	+	8.34643i	1.18432	+	0.683766i	0.227308	+	0.973823i	$0.427008\pi$
$150$		0			0
$151$			9.66930i			0.786877i	0.919351	+	0.393438i	$0.128715\pi$
$151$			9.66930i			0.786877i	−0.919351	+	0.393438i	$0.871285\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$	4.58258	+	7.93725i	0.370479	+	0.641689i
$154$	−1.81307	+	1.04678i	−0.146101	+	0.0843516i
$155$		0			0
$156$	−1.79129	−	6.20520i	−0.143418	−	0.496814i
$157$	−9.16515			−0.731459			−0.365729	−	0.930721i	$-0.619180\pi$
$157$	−9.16515			−0.731459			−0.365729	+	0.930721i	$0.619180\pi$
$158$	−2.37386	+	1.37055i	−0.188854	+	0.109035i
$159$	−3.79129	−	6.56670i	−0.300669	−	0.520773i
$160$		0			0
$161$			7.93725i			0.625543i
$162$	−0.395644	−	0.228425i	−0.0310847	−	0.0179468i
$163$	18.2477	+	10.5353i	1.42927	+	0.825191i	0.997063	−	0.0765827i	$-0.0244009\pi$
$163$	18.2477	+	10.5353i	1.42927	+	0.825191i	0.432209	+	0.901773i	$0.357734\pi$
$164$			4.73930i			0.370077i
$165$		0			0
$166$	−1.37386	−	2.37960i	−0.106632	−	0.184693i
$167$	−8.29129	+	4.78698i	−0.641599	+	0.370427i	−0.785230	−	0.619204i	$-0.787455\pi$
$167$	−8.29129	+	4.78698i	−0.641599	+	0.370427i	0.143631	+	0.989631i	$0.454122\pi$
$168$	−3.00000			−0.231455
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$	9.47822	+	16.4168i	0.722707	+	1.25177i
$173$	−8.29129	+	14.3609i	−0.630375	+	1.09184i	0.357100	+	0.934066i	$0.383766\pi$
$173$	−8.29129	+	14.3609i	−0.630375	+	1.09184i	−0.987475	+	0.157775i	$0.949568\pi$
$174$		−	2.09355i		−	0.158712i
$175$		0			0
$176$	6.39564	+	3.69253i	0.482090	+	0.278335i
$177$			13.9518i			1.04868i
$178$	−2.18693	+	3.78788i	−0.163917	+	0.283913i
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	−0.975323	−	0.220781i	$-0.929139\pi$
$179$	−9.08258	−	15.7315i	−0.678864	−	1.17583i	0.296460	−	0.955045i	$-0.404194\pi$
$180$		0			0
$181$	8.74773			0.650213			0.325107	−	0.945677i	$-0.394600\pi$
$181$	8.74773			0.650213			0.325107	+	0.945677i	$0.394600\pi$
$182$	0.791288	+	2.74110i	0.0586542	+	0.203184i
$183$	1.41742			0.104779
$184$	−6.87386	+	3.96863i	−0.506748	+	0.292571i
$185$		0			0
$186$	1.41742	−	2.45505i	0.103931	−	0.180013i
$187$		−	12.1244i		−	0.886621i
$188$	2.83485	+	1.63670i	0.206753	+	0.119369i
$189$	7.50000	+	4.33013i	0.545545	+	0.314970i
$190$		0			0
$191$	8.29129	−	14.3609i	0.599937	−	1.03912i	−0.392893	−	0.919584i	$-0.628526\pi$
$191$	8.29129	−	14.3609i	0.599937	−	1.03912i	0.992830	−	0.119536i	$-0.0381408\pi$
$192$	1.70871	+	2.95958i	0.123316	+	0.213589i
$193$	−12.8739	+	7.43273i	−0.926681	+	0.535020i	−0.885760	−	0.464143i	$-0.846362\pi$
$193$	−12.8739	+	7.43273i	−0.926681	+	0.535020i	−0.0409206	+	0.999162i	$0.513029\pi$
$194$	5.20871			0.373964
$195$		0			0
$196$	7.16515			0.511797
$197$	−12.7087	+	7.33738i	−0.905458	+	0.522767i	−0.878967	−	0.476882i	$-0.841767\pi$
$197$	−12.7087	+	7.33738i	−0.905458	+	0.522767i	−0.0264912	+	0.999649i	$0.508433\pi$
$198$	1.20871	+	2.09355i	0.0858994	+	0.148782i
$199$	−5.29129	+	9.16478i	−0.375089	+	0.649674i	−0.990340	−	0.138657i	$-0.955721\pi$
$199$	−5.29129	+	9.16478i	−0.375089	+	0.649674i	0.615251	+	0.788331i	$0.289055\pi$
$200$		0			0
$201$	−0.873864	−	0.504525i	−0.0616376	−	0.0355865i
$202$	−3.56080	−	2.05583i	−0.250537	−	0.144647i
$203$		−	7.93725i		−	0.557086i
$204$	4.10436	−	7.10895i	0.287362	−	0.497726i
$205$		0			0
$206$	−1.25227	+	0.723000i	−0.0872500	+	0.0503738i
$207$	9.16515			0.637022
$208$	6.97822	−	7.25198i	0.483852	−	0.502834i
$209$	−4.58258			−0.316983
$210$		0			0
$211$	0.0825757	+	0.143025i	0.00568475	+	0.00984627i	0.868854	−	0.495069i	$-0.164857\pi$
$211$	0.0825757	+	0.143025i	0.00568475	+	0.00984627i	−0.863169	+	0.504915i	$0.831524\pi$
$212$	6.79129	−	11.7629i	0.466428	−	0.807876i
$213$			7.02355i			0.481246i
$214$	−4.18693	−	2.41733i	−0.286213	−	0.165245i
$215$		0			0
$216$			8.66025i			0.589256i
$217$	5.37386	−	9.30780i	0.364802	−	0.631855i
$218$	−3.00000	−	5.19615i	−0.203186	−	0.351928i
$219$		0			0
$220$		0			0
$221$	−16.0390	−	3.96863i	−1.07890	−	0.266959i
$222$	3.62614			0.243370
$223$	7.50000	−	4.33013i	0.502237	−	0.289967i	−0.227400	−	0.973801i	$-0.573022\pi$
$223$	7.50000	−	4.33013i	0.502237	−	0.289967i	0.729637	+	0.683835i	$0.239689\pi$
$224$	−4.10436	−	7.10895i	−0.274234	−	0.474987i
$225$		0			0
$226$			3.38865i			0.225410i
$227$	−0.708712	−	0.409175i	−0.0470389	−	0.0271579i	0.476296	−	0.879285i	$-0.341979\pi$
$227$	−0.708712	−	0.409175i	−0.0470389	−	0.0271579i	−0.523335	+	0.852127i	$0.675312\pi$
$228$	−2.68693	−	1.55130i	−0.177946	−	0.102737i
$229$			26.2668i			1.73576i	0.496774	+	0.867880i	$0.334518\pi$
$229$			26.2668i			1.73576i	−0.496774	+	0.867880i	$0.665482\pi$
$230$		0			0
$231$	−2.29129	−	3.96863i	−0.150756	−	0.261116i
$232$	6.87386	−	3.96863i	0.451291	−	0.260553i
$233$	−2.83485			−0.185717			−0.0928586	−	0.995679i	$-0.529600\pi$
$233$	−2.83485			−0.185717			−0.0928586	+	0.995679i	$0.529600\pi$
$234$	3.16515	−	0.913701i	0.206912	−	0.0597305i
$235$		0			0
$236$	−21.6434	+	12.4958i	−1.40886	+	0.813408i
$237$	−3.00000	−	5.19615i	−0.194871	−	0.337526i
$238$	−1.81307	+	3.14033i	−0.117524	+	0.203557i
$239$			0.190700i			0.0123354i	0.999981	+	0.00616769i	$0.00196325\pi$
$239$			0.190700i			0.0123354i	−0.999981	+	0.00616769i	$0.998037\pi$
$240$		0			0
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$			1.82740i			0.117470i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	1.26951	+	2.19885i	0.0812719	+	0.140767i
$245$		0			0
$246$	1.20871			0.0770647
$247$	−1.50000	+	6.06218i	−0.0954427	+	0.385727i
$248$	10.7477			0.682481
$249$	5.20871	−	3.00725i	0.330089	−	0.190577i
$250$		0			0
$251$	0.0825757	−	0.143025i	0.00521213	−	0.00902768i	−0.863408	−	0.504507i	$-0.831674\pi$
$251$	0.0825757	−	0.143025i	0.00521213	−	0.00902768i	0.868620	+	0.495479i	$0.165008\pi$
$252$			6.20520i			0.390891i
$253$	−10.5000	−	6.06218i	−0.660129	−	0.381126i
$254$	7.02178	+	4.05403i	0.440586	+	0.254372i
$255$		0			0
$256$	−0.895644	+	1.55130i	−0.0559777	+	0.0969563i
$257$	−9.08258	−	15.7315i	−0.566556	−	0.981303i	−0.996903	−	0.0786397i	$-0.974942\pi$
$257$	−9.08258	−	15.7315i	−0.566556	−	0.981303i	0.430348	−	0.902663i	$-0.358391\pi$
$258$	4.18693	−	2.41733i	0.260667	−	0.150496i
$259$	13.7477			0.854242
$260$		0			0
$261$	−9.16515			−0.567309
$262$	−3.00000	+	1.73205i	−0.185341	+	0.107006i
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$	2.29129	−	3.96863i	0.141019	−	0.244252i
$265$		0			0
$266$	1.18693	+	0.685275i	0.0727755	+	0.0420169i
$267$	−8.29129	−	4.78698i	−0.507419	−	0.292958i
$268$		−	1.80750i		−	0.110411i
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	−0.254597	−	0.967047i	$-0.581943\pi$
$271$	7.50000	−	4.33013i	0.455593	−	0.263036i	0.710189	+	0.704011i	$0.248609\pi$
$272$	12.7913			0.775586
$273$	−6.00000	+	1.73205i	−0.363137	+	0.104828i
$274$	−4.79129			−0.289452
$275$		0			0
$276$	−4.10436	−	7.10895i	−0.247053	−	0.427909i
$277$	−3.70871	+	6.42368i	−0.222835	+	0.385961i	−0.955668	−	0.294447i	$-0.904864\pi$
$277$	−3.70871	+	6.42368i	−0.222835	+	0.385961i	0.732833	+	0.680409i	$0.238198\pi$
$278$		−	9.93545i		−	0.595889i
$279$	−10.7477	−	6.20520i	−0.643450	−	0.371496i
$280$		0			0
$281$		−	3.65480i		−	0.218027i	−0.994040	−	0.109014i	$-0.965231\pi$
$281$		−	3.65480i		−	0.218027i	0.994040	−	0.109014i	$-0.0347692\pi$
$282$	0.417424	−	0.723000i	0.0248573	−	0.0430540i
$283$	−13.8739	−	24.0302i	−0.824716	−	1.42845i	−0.902136	−	0.431451i	$-0.858002\pi$
$283$	−13.8739	−	24.0302i	−0.824716	−	1.42845i	0.0774209	−	0.996998i	$-0.475331\pi$
$284$	−10.8956	+	6.29060i	−0.646538	+	0.373279i
$285$		0			0
$286$	−4.23049	−	1.04678i	−0.250154	−	0.0618971i
$287$	4.58258			0.270501
$288$	−8.20871	+	4.73930i	−0.483703	+	0.279266i
$289$	−2.00000	−	3.46410i	−0.117647	−	0.203771i
$290$		0			0
$291$			11.4014i			0.668359i
$292$		0			0
$293$	−15.7087	−	9.06943i	−0.917713	−	0.529842i	−0.0348081	−	0.999394i	$-0.511082\pi$
$293$	−15.7087	−	9.06943i	−0.917713	−	0.529842i	−0.882905	+	0.469552i	$0.844415\pi$
$294$		−	1.82740i		−	0.106576i
$295$		0			0
$296$	6.87386	+	11.9059i	0.399535	+	0.692015i
$297$	−11.4564	+	6.61438i	−0.664770	+	0.383805i
$298$	7.62614			0.441770
$299$	−11.4564	+	11.9059i	−0.662543	+	0.688535i
$300$		0			0
$301$	15.8739	−	9.16478i	0.914954	−	0.528249i
$302$	2.20871	+	3.82560i	0.127097	+	0.220139i
$303$	4.50000	−	7.79423i	0.258518	−	0.447767i
$304$		−	4.83465i		−	0.277286i
$305$		0			0
$306$	3.62614	+	2.09355i	0.207292	+	0.119680i
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$	4.10436	−	7.10895i	0.233867	−	0.405070i
$309$	−1.58258	−	2.74110i	−0.0900296	−	0.155936i
$310$		0			0
$311$	7.58258			0.429968			0.214984	−	0.976618i	$-0.431030\pi$
$311$	7.58258			0.429968			0.214984	+	0.976618i	$0.431030\pi$
$312$	−4.50000	−	4.33013i	−0.254762	−	0.245145i
$313$	3.25227			0.183829			0.0919147	−	0.995767i	$-0.470701\pi$
$313$	3.25227			0.183829			0.0919147	+	0.995767i	$0.470701\pi$
$314$	−3.62614	+	2.09355i	−0.204635	+	0.118146i
$315$		0			0
$316$	5.37386	−	9.30780i	0.302303	−	0.523605i
$317$			0.190700i			0.0107108i	0.999986	+	0.00535540i	$0.00170469\pi$
$317$			0.190700i			0.0107108i	−0.999986	+	0.00535540i	$0.998295\pi$
$318$	−3.00000	−	1.73205i	−0.168232	−	0.0971286i
$319$	10.5000	+	6.06218i	0.587887	+	0.339417i
$320$		0			0
$321$	5.29129	−	9.16478i	0.295331	−	0.511528i
$322$	1.81307	+	3.14033i	0.101038	+	0.175004i
$323$	−6.87386	+	3.96863i	−0.382472	+	0.220820i
$324$	1.79129			0.0995160
$325$		0			0
$326$	9.62614			0.533142
$327$	11.3739	−	6.56670i	0.628976	−	0.363140i
$328$	2.29129	+	3.96863i	0.126515	+	0.219131i
$329$	1.58258	−	2.74110i	0.0872502	−	0.151122i
$330$		0			0
$331$	−3.87386	−	2.23658i	−0.212927	−	0.122933i	0.389744	−	0.920923i	$-0.372563\pi$
$331$	−3.87386	−	2.23658i	−0.212927	−	0.122933i	−0.602671	+	0.797990i	$0.705897\pi$
$332$	9.33030	+	5.38685i	0.512067	+	0.295642i
$333$		−	15.8745i		−	0.869918i
$334$	−2.18693	+	3.78788i	−0.119664	+	0.207263i
$335$		0			0
$336$	4.18693	−	2.41733i	0.228416	−	0.131876i
$337$	−30.7477			−1.67494			−0.837468	−	0.546487i	$-0.815965\pi$
$337$	−30.7477			−1.67494			−0.837468	+	0.546487i	$0.815965\pi$
$338$	−2.76951	+	5.25378i	−0.150641	+	0.285768i
$339$	−7.41742			−0.402859
$340$		0			0
$341$	8.20871	+	14.2179i	0.444527	+	0.769943i
$342$	0.791288	−	1.37055i	0.0427879	−	0.0741109i
$343$		−	19.0526i		−	1.02874i
$344$	15.8739	+	9.16478i	0.855861	+	0.494132i
$345$		0			0
$346$			7.57575i			0.407275i
$347$	−10.6652	+	18.4726i	−0.572535	+	0.991660i	0.423769	+	0.905770i	$0.360707\pi$
$347$	−10.6652	+	18.4726i	−0.572535	+	0.991660i	−0.996305	+	0.0858901i	$0.972627\pi$
$348$	4.10436	+	7.10895i	0.220017	+	0.381080i
$349$	−2.12614	+	1.22753i	−0.113809	+	0.0657079i	−0.555824	−	0.831300i	$-0.687597\pi$
$349$	−2.12614	+	1.22753i	−0.113809	+	0.0657079i	0.442015	+	0.897008i	$0.354264\pi$
$350$		0			0
$351$	5.00000	+	17.3205i	0.266880	+	0.924500i
$352$	12.5390			0.668332
$353$	−5.91742	+	3.41643i	−0.314953	+	0.181838i	−0.649141	−	0.760668i	$-0.724871\pi$
$353$	−5.91742	+	3.41643i	−0.314953	+	0.181838i	0.334188	+	0.942506i	$0.391538\pi$
$354$	3.18693	+	5.51993i	0.169384	+	0.293381i
$355$		0			0
$356$		−	17.1497i		−	0.908933i
$357$	−6.87386	−	3.96863i	−0.363803	−	0.210042i
$358$	−7.18693	−	4.14938i	−0.379841	−	0.219301i
$359$		−	19.5293i		−	1.03072i	−0.856975	−	0.515359i	$-0.827659\pi$
$359$		−	19.5293i		−	1.03072i	0.856975	−	0.515359i	$-0.172341\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	3.46099	−	1.99820i	0.181905	−	0.105023i
$363$	−4.00000			−0.209946
$364$	−8.06080	−	7.75650i	−0.422500	−	0.406551i
$365$		0			0
$366$	0.560795	−	0.323775i	0.0293132	−	0.0169240i
$367$	−0.873864	−	1.51358i	−0.0456153	−	0.0790080i	0.842316	−	0.538984i	$-0.181192\pi$
$367$	−0.873864	−	1.51358i	−0.0456153	−	0.0790080i	−0.887932	+	0.459976i	$0.847858\pi$
$368$	6.39564	−	11.0776i	0.333396	−	0.577459i
$369$		−	5.29150i		−	0.275465i
$370$		0			0
$371$	−11.3739	−	6.56670i	−0.590502	−	0.340926i
$372$			11.1153i			0.576302i
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	0.647225	+	0.762299i	$0.275929\pi$
$374$	−2.76951	−	4.79693i	−0.143208	−	0.248043i
$375$		0			0
$376$	3.16515			0.163230
$377$	11.4564	−	11.9059i	0.590037	−	0.613184i
$378$	3.95644			0.203497
$379$	9.24773	−	5.33918i	0.475024	−	0.274255i	−0.243317	−	0.969947i	$-0.578235\pi$
$379$	9.24773	−	5.33918i	0.475024	−	0.274255i	0.718340	+	0.695692i	$0.244902\pi$
$380$		0			0
$381$	−8.87386	+	15.3700i	−0.454622	+	0.787428i
$382$		−	7.57575i		−	0.387609i
$383$	20.4564	+	11.8105i	1.04528	+	0.603490i	0.921323	−	0.388798i	$-0.127110\pi$
$383$	20.4564	+	11.8105i	1.04528	+	0.603490i	0.123952	+	0.992288i	$0.460443\pi$
$384$	9.56080	+	5.51993i	0.487897	+	0.281688i
$385$		0			0
$386$	−3.39564	+	5.88143i	−0.172834	+	0.299357i
$387$	−10.5826	−	18.3296i	−0.537943	−	0.931744i
$388$	−17.6869	+	10.2116i	−0.897918	+	0.518413i
$389$	−3.16515			−0.160480			−0.0802398	−	0.996776i	$-0.525569\pi$
$389$	−3.16515			−0.160480			−0.0802398	+	0.996776i	$0.525569\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	6.00000	−	3.46410i	0.303046	−	0.174964i
$393$	−3.79129	−	6.56670i	−0.191245	−	0.331246i
$394$	−3.35208	+	5.80598i	−0.168876	+	0.292501i
$395$		0			0
$396$	−8.20871	−	4.73930i	−0.412503	−	0.238159i
$397$	17.6216	+	10.1738i	0.884402	+	0.510610i	0.872107	−	0.489315i	$-0.162753\pi$
$397$	17.6216	+	10.1738i	0.884402	+	0.510610i	0.0122949	+	0.999924i	$0.496086\pi$
$398$			4.83465i			0.242339i
$399$	−1.50000	+	2.59808i	−0.0750939	+	0.130066i
$400$		0			0
$401$	−25.8303	+	14.9131i	−1.28990	+	0.744726i	−0.978637	−	0.205596i	$-0.934087\pi$
$401$	−25.8303	+	14.9131i	−1.28990	+	0.744726i	−0.311267	+	0.950323i	$0.600753\pi$
$402$	−0.460985			−0.0229918
$403$	21.4955	−	6.20520i	1.07076	−	0.309103i
$404$	16.1216			0.802079
$405$		0			0
$406$	−1.81307	−	3.14033i	−0.0899811	−	0.155852i
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$		−	7.93725i		−	0.392953i
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$		0			0
$411$		−	10.4877i		−	0.517318i
$412$	2.83485	−	4.91010i	0.139663	−	0.241903i
$413$	12.0826	+	20.9276i	0.594545	+	1.02978i
$414$	3.62614	−	2.09355i	0.178215	−	0.102892i
$415$		0			0
$416$	4.10436	−	16.5876i	0.201233	−	0.813272i
$417$	21.7477			1.06499
$418$	−1.81307	+	1.04678i	−0.0886801	+	0.0511995i
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	0.928447	−	0.371465i	$-0.121144\pi$
$419$	2.91742	+	5.05313i	0.142526	+	0.246861i	−0.785922	+	0.618326i	$0.787811\pi$
$420$		0			0
$421$		−	5.48220i		−	0.267186i	−0.991036	−	0.133593i	$-0.957348\pi$
$421$		−	5.48220i		−	0.267186i	0.991036	−	0.133593i	$-0.0426515\pi$
$422$	0.0653411	+	0.0377247i	0.00318076	+	0.00183641i
$423$	−3.16515	−	1.82740i	−0.153895	−	0.0888513i
$424$		−	13.1334i		−	0.637815i
$425$		0			0
$426$	1.60436	+	2.77883i	0.0777313	+	0.134635i
$427$	2.12614	−	1.22753i	0.102891	−	0.0594041i
$428$	18.9564			0.916294
$429$	2.29129	−	9.26013i	0.110624	−	0.447083i
$430$		0			0
$431$	7.33485	−	4.23478i	0.353307	−	0.203982i	−0.312834	−	0.949808i	$-0.601278\pi$
$431$	7.33485	−	4.23478i	0.353307	−	0.203982i	0.666141	+	0.745826i	$0.267945\pi$
$432$	−6.97822	−	12.0866i	−0.335740	−	0.581518i
$433$	4.87386	−	8.44178i	0.234223	−	0.405686i	−0.724824	−	0.688934i	$-0.758079\pi$
$433$	4.87386	−	8.44178i	0.234223	−	0.405686i	0.959047	+	0.283248i	$0.0914121\pi$
$434$		−	4.91010i		−	0.235692i
$435$		0			0
$436$	20.3739	+	11.7629i	0.975731	+	0.563339i
$437$			7.93725i			0.379690i
$438$		0			0
$439$	7.24773	+	12.5534i	0.345915	+	0.599143i	0.985520	−	0.169562i	$-0.0542352\pi$
$439$	7.24773	+	12.5534i	0.345915	+	0.599143i	−0.639604	+	0.768704i	$0.720902\pi$
$440$		0			0
$441$	−8.00000			−0.380952
$442$	−7.25227	+	2.09355i	−0.344955	+	0.0995801i
$443$	−19.9129			−0.946089			−0.473045	−	0.881038i	$-0.656845\pi$
$443$	−19.9129			−0.946089			−0.473045	+	0.881038i	$0.656845\pi$
$444$	−12.3131	+	7.10895i	−0.584352	+	0.337376i
$445$		0			0
$446$	1.97822	−	3.42638i	0.0936714	−	0.162244i
$447$			16.6929i			0.789545i
$448$	5.12614	+	2.95958i	0.242187	+	0.139827i
$449$	−9.54356	−	5.50998i	−0.450388	−	0.260032i	0.257606	−	0.966250i	$-0.417066\pi$
$449$	−9.54356	−	5.50998i	−0.450388	−	0.260032i	−0.707994	+	0.706218i	$0.750400\pi$
$450$		0			0
$451$	−3.50000	+	6.06218i	−0.164809	+	0.285457i
$452$	−6.64337	−	11.5067i	−0.312478	−	0.541228i
$453$	−8.37386	+	4.83465i	−0.393438	+	0.227152i
$454$	−0.373864			−0.0175463
$455$		0			0
$456$	−3.00000			−0.140488
$457$	1.50000	−	0.866025i	0.0701670	−	0.0405110i	−0.464506	−	0.885570i	$-0.653768\pi$
$457$	1.50000	−	0.866025i	0.0701670	−	0.0405110i	0.534673	+	0.845059i	$0.320435\pi$
$458$	6.00000	+	10.3923i	0.280362	+	0.485601i
$459$	−11.4564	+	19.8431i	−0.534741	+	0.926198i
$460$		0			0
$461$	31.0390	+	17.9204i	1.44563	+	0.834635i	0.998217	−	0.0596914i	$-0.0190117\pi$
$461$	31.0390	+	17.9204i	1.44563	+	0.834635i	0.447414	+	0.894327i	$0.352345\pi$
$462$	−1.81307	−	1.04678i	−0.0843516	−	0.0487004i
$463$			39.4002i			1.83108i	0.402223	+	0.915542i	$0.368238\pi$
$463$			39.4002i			1.83108i	−0.402223	+	0.915542i	$0.631762\pi$
$464$	−6.39564	+	11.0776i	−0.296910	+	0.514264i
$465$		0			0
$466$	−1.12159	+	0.647551i	−0.0519567	+	0.0299972i
$467$	24.3303			1.12587			0.562936	−	0.826500i	$-0.309672\pi$
$467$	24.3303			1.12587			0.562936	+	0.826500i	$0.309672\pi$
$468$	−8.95644	+	9.30780i	−0.414012	+	0.430253i
$469$	−1.74773			−0.0807025
$470$		0			0
$471$	−4.58258	−	7.93725i	−0.211154	−	0.365729i
$472$	−12.0826	+	20.9276i	−0.556146	+	0.963272i
$473$			27.9989i			1.28739i
$474$	−2.37386	−	1.37055i	−0.109035	−	0.0629515i
$475$		0			0
$476$		−	14.2179i		−	0.651677i
$477$	−7.58258	+	13.1334i	−0.347182	+	0.601337i
$478$	0.0435608	+	0.0754495i	0.00199242	+	0.00345098i
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	−0.589427	−	0.807821i	$-0.700647\pi$
$479$	−4.03901	+	2.33193i	−0.184547	+	0.106548i	0.404880	+	0.914370i	$0.367313\pi$
$480$		0			0
$481$	20.6216	+	19.8431i	0.940264	+	0.904769i
$482$	−0.791288			−0.0360422
$483$	−6.87386	+	3.96863i	−0.312772	+	0.180579i
$484$	−3.58258	−	6.20520i	−0.162844	−	0.282055i
$485$		0			0
$486$		−	7.30960i		−	0.331570i
$487$	−9.24773	−	5.33918i	−0.419055	−	0.241941i	0.275618	−	0.961267i	$-0.411117\pi$
$487$	−9.24773	−	5.33918i	−0.419055	−	0.241941i	−0.694673	+	0.719326i	$0.744451\pi$
$488$	2.12614	+	1.22753i	0.0962457	+	0.0555675i
$489$			21.0707i			0.952848i
$490$		0			0
$491$	−9.70871	−	16.8160i	−0.438148	−	0.758895i	0.559399	−	0.828899i	$-0.311032\pi$
$491$	−9.70871	−	16.8160i	−0.438148	−	0.758895i	−0.997547	+	0.0700041i	$0.977699\pi$
$492$	−4.10436	+	2.36965i	−0.185039	+	0.106832i
$493$	21.0000			0.945792
$494$	0.791288	+	2.74110i	0.0356017	+	0.123328i
$495$		0			0
$496$	−15.0000	+	8.66025i	−0.673520	+	0.388857i
$497$	6.08258	+	10.5353i	0.272841	+	0.472574i
$498$	1.37386	−	2.37960i	0.0615643	−	0.106632i
$499$			0.723000i			0.0323659i	0.999869	+	0.0161830i	$0.00515142\pi$
$499$			0.723000i			0.0323659i	−0.999869	+	0.0161830i	$0.994849\pi$
$500$		0			0
$501$	−8.29129	−	4.78698i	−0.370427	−	0.213866i
$502$		−	0.0754495i		−	0.00336747i
$503$	0.0825757	−	0.143025i	0.00368187	−	0.00637718i	−0.864179	−	0.503185i	$-0.832161\pi$
$503$	0.0825757	−	0.143025i	0.00368187	−	0.00637718i	0.867860	+	0.496808i	$0.165495\pi$
$504$	3.00000	+	5.19615i	0.133631	+	0.231455i
$505$		0			0
$506$	−5.53901			−0.246239
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	−31.7913			−1.41051
$509$	7.33485	−	4.23478i	0.325111	−	0.187703i	−0.328557	−	0.944484i	$-0.606562\pi$
$509$	7.33485	−	4.23478i	0.325111	−	0.187703i	0.653669	+	0.756781i	$0.273229\pi$
$510$		0			0
$511$		0			0
$512$			22.8981i			1.01196i
$513$	7.50000	+	4.33013i	0.331133	+	0.191180i
$514$	−7.18693	−	4.14938i	−0.317002	−	0.183021i
$515$		0			0
$516$	−9.47822	+	16.4168i	−0.417255	+	0.722707i
$517$	2.41742	+	4.18710i	0.106318	+	0.184149i
$518$	5.43920	−	3.14033i	0.238985	−	0.137978i
$519$	−16.5826			−0.727894
$520$		0			0
$521$	27.4955			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$521$	27.4955			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$522$	−3.62614	+	2.09355i	−0.158712	+	0.0916322i
$523$	0.0825757	+	0.143025i	0.00361078	+	0.00625406i	0.867825	−	0.496870i	$-0.165517\pi$
$523$	0.0825757	+	0.143025i	0.00361078	+	0.00625406i	−0.864214	+	0.503124i	$0.832184\pi$
$524$	6.79129	−	11.7629i	0.296679	−	0.513863i
$525$		0			0
$526$	3.56080	+	2.05583i	0.155258	+	0.0896383i
$527$	24.6261	+	14.2179i	1.07273	+	0.619342i
$528$			7.38505i			0.321393i
$529$	1.00000	−	1.73205i	0.0434783	−	0.0753066i
$530$		0			0
$531$	24.1652	−	13.9518i	1.04868	−	0.605455i
$532$	−5.37386			−0.232987
$533$	6.87386	+	6.61438i	0.297740	+	0.286501i
$534$	−4.37386			−0.189276
$535$		0			0
$536$	−0.873864	−	1.51358i	−0.0377452	−	0.0653765i
$537$	9.08258	−	15.7315i	0.391942	−	0.678864i
$538$		−	6.85275i		−	0.295443i
$539$	9.16515	+	5.29150i	0.394771	+	0.227921i
$540$		0			0
$541$			10.3923i			0.446800i	0.974727	+	0.223400i	$0.0717156\pi$
$541$			10.3923i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$542$	1.97822	−	3.42638i	0.0849718	−	0.147175i
$543$	4.37386	+	7.57575i	0.187700	+	0.325107i
$544$	18.8085	−	10.8591i	0.806409	−	0.465580i
$545$		0			0
$546$	−1.97822	+	2.05583i	−0.0846600	+	0.0879812i
$547$	−28.7477			−1.22916			−0.614582	−	0.788853i	$-0.710675\pi$
$547$	−28.7477			−1.22916			−0.614582	+	0.788853i	$0.710675\pi$
$548$	16.2695	−	9.39320i	0.694999	−	0.401258i
$549$	−1.41742	−	2.45505i	−0.0604942	−	0.104779i
$550$		0			0
$551$		−	7.93725i		−	0.338138i
$552$	−6.87386	−	3.96863i	−0.292571	−	0.168916i
$553$	−9.00000	−	5.19615i	−0.382719	−	0.220963i
$554$			3.38865i			0.143970i
$555$		0			0
$556$	19.4782	+	33.7373i	0.826061	+	1.43078i
$557$	6.70871	−	3.87328i	0.284257	−	0.164116i	−0.351092	−	0.936341i	$-0.614190\pi$
$557$	6.70871	−	3.87328i	0.284257	−	0.164116i	0.635349	+	0.772225i	$0.280856\pi$
$558$	−5.66970			−0.240017
$559$	37.0390	+	9.16478i	1.56658	+	0.387629i
$560$		0			0
$561$	10.5000	−	6.06218i	0.443310	−	0.255945i
$562$	−0.834849	−	1.44600i	−0.0352160	−	0.0609958i
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	−0.945134	−	0.326682i	$-0.894069\pi$
$563$	−4.50000	+	7.79423i	−0.189652	+	0.328488i	0.755482	+	0.655169i	$0.227403\pi$
$564$			3.27340i			0.137835i
$565$		0			0
$566$	−10.9782	−	6.33828i	−0.461449	−	0.266418i
$567$		−	1.73205i		−	0.0727393i
$568$	−6.08258	+	10.5353i	−0.255219	+	0.442053i
$569$	−3.87386	−	6.70973i	−0.162401	−	0.281286i	0.773328	−	0.634006i	$-0.218590\pi$
$569$	−3.87386	−	6.70973i	−0.162401	−	0.281286i	−0.935729	+	0.352719i	$0.885257\pi$
$570$		0			0
$571$	−35.0780			−1.46797			−0.733985	−	0.679166i	$-0.762342\pi$
$571$	−35.0780			−1.46797			−0.733985	+	0.679166i	$0.762342\pi$
$572$	16.4174	−	4.73930i	0.686447	−	0.198160i
$573$	16.5826			0.692747
$574$	1.81307	−	1.04678i	0.0756760	−	0.0436916i
$575$		0			0
$576$	3.41742	−	5.91915i	0.142393	−	0.246631i
$577$			6.92820i			0.288425i	0.989547	+	0.144212i	$0.0460649\pi$
$577$			6.92820i			0.288425i	−0.989547	+	0.144212i	$0.953935\pi$
$578$	−1.58258	−	0.913701i	−0.0658265	−	0.0380049i
$579$	−12.8739	−	7.43273i	−0.535020	−	0.308894i
$580$		0			0
$581$	5.20871	−	9.02175i	0.216094	−	0.374285i
$582$	2.60436	+	4.51088i	0.107954	+	0.186982i
$583$	17.3739	−	10.0308i	0.719552	−	0.415433i
$584$		0			0
$585$		0			0
$586$	−8.28674			−0.342322
$587$	34.2042	−	19.7478i	1.41176	−	0.815078i	0.416203	−	0.909272i	$-0.363361\pi$
$587$	34.2042	−	19.7478i	1.41176	−	0.815078i	0.995554	+	0.0941934i	$0.0300272\pi$
$588$	3.58258	+	6.20520i	0.147743	+	0.255898i
$589$	5.37386	−	9.30780i	0.221426	−	0.383521i
$590$		0			0
$591$	−12.7087	−	7.33738i	−0.522767	−	0.301819i
$592$	−19.1869	−	11.0776i	−0.788578	−	0.455286i
$593$		−	21.1660i		−	0.869184i	−0.900627	−	0.434592i	$-0.856893\pi$
$593$		−	21.1660i		−	0.869184i	0.900627	−	0.434592i	$-0.143107\pi$
$594$	−3.02178	+	5.23388i	−0.123985	+	0.214749i
$595$		0			0
$596$	−25.8956	+	14.9509i	−1.06073	+	0.612411i
$597$	−10.5826			−0.433116
$598$	−1.81307	+	7.32743i	−0.0741419	+	0.299641i
$599$	15.4955			0.633127			0.316564	−	0.948571i	$-0.397471\pi$
$599$	15.4955			0.633127			0.316564	+	0.948571i	$0.397471\pi$
$600$		0			0
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	0.640398	−	0.768043i	$-0.278769\pi$
$601$	−8.45644	−	14.6470i	−0.344945	−	0.597463i	−0.985344	+	0.170580i	$0.945436\pi$
$602$	4.18693	−	7.25198i	0.170647	−	0.295569i
$603$			2.01810i			0.0821834i
$604$	−15.0000	−	8.66025i	−0.610341	−	0.352381i
$605$		0			0
$606$		−	4.11165i		−	0.167024i
$607$	3.87386	−	6.70973i	0.157235	−	0.272339i	−0.776635	−	0.629950i	$-0.783075\pi$
$607$	3.87386	−	6.70973i	0.157235	−	0.272339i	0.933871	+	0.357611i	$0.116409\pi$
$608$	−4.10436	−	7.10895i	−0.166454	−	0.288306i
$609$	6.87386	−	3.96863i	0.278543	−	0.160817i
$610$		0			0
$611$	6.33030	−	1.82740i	0.256097	−	0.0739287i
$612$	−16.4174			−0.663635
$613$	5.12614	−	2.95958i	0.207043	−	0.119536i	−0.392894	−	0.919584i	$-0.628526\pi$
$613$	5.12614	−	2.95958i	0.207043	−	0.119536i	0.599936	+	0.800048i	$0.295193\pi$
$614$	−5.53901	−	9.59386i	−0.223536	−	0.387176i
$615$		0			0
$616$		−	7.93725i		−	0.319801i
$617$	12.0826	+	6.97588i	0.486426	+	0.280838i	0.723091	−	0.690753i	$-0.242721\pi$
$617$	12.0826	+	6.97588i	0.486426	+	0.280838i	−0.236664	+	0.971591i	$0.576054\pi$
$618$	−1.25227	−	0.723000i	−0.0503738	−	0.0290833i
$619$		−	29.7309i		−	1.19499i	−0.801874	−	0.597493i	$-0.796164\pi$
$619$		−	29.7309i		−	1.19499i	0.801874	−	0.597493i	$-0.203836\pi$
$620$		0			0
$621$	11.4564	+	19.8431i	0.459731	+	0.796278i
$622$	3.00000	−	1.73205i	0.120289	−	0.0694489i
$623$	−16.5826			−0.664367
$624$	9.76951	+	2.41733i	0.391093	+	0.0967705i
$625$		0			0
$626$	1.28674	−	0.742901i	0.0514286	−	0.0296923i
$627$	−2.29129	−	3.96863i	−0.0915052	−	0.158492i
$628$	8.20871	−	14.2179i	0.327563	−	0.567356i
$629$			36.3731i			1.45029i
$630$		0			0
$631$	−5.12614	−	2.95958i	−0.204068	−	0.117819i	0.394483	−	0.918903i	$-0.370924\pi$
$631$	−5.12614	−	2.95958i	−0.204068	−	0.117819i	−0.598552	+	0.801084i	$0.704257\pi$
$632$		−	10.3923i		−	0.413384i
$633$	−0.0825757	+	0.143025i	−0.00328209	+	0.00568475i
$634$	0.0435608	+	0.0754495i	0.00173002	+	0.00299648i
$635$		0			0
$636$	13.5826			0.538584
$637$	10.0000	−	10.3923i	0.396214	−	0.411758i
$638$	5.53901			0.219292
$639$	12.1652	−	7.02355i	0.481246	−	0.277847i
$640$		0			0
$641$	−9.08258	+	15.7315i	−0.358740	+	0.621356i	−0.987751	−	0.156041i	$-0.950127\pi$
$641$	−9.08258	+	15.7315i	−0.358740	+	0.621356i	0.629010	+	0.777397i	$0.283460\pi$
$642$		−	4.83465i		−	0.190809i
$643$	−18.8739	−	10.8968i	−0.744313	−	0.429729i	0.0793227	−	0.996849i	$-0.474724\pi$
$643$	−18.8739	−	10.8968i	−0.744313	−	0.429729i	−0.823635	+	0.567120i	$0.808058\pi$
$644$	−12.3131	−	7.10895i	−0.485203	−	0.280132i
$645$		0			0
$646$	−1.81307	+	3.14033i	−0.0713342	+	0.123554i
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	0.999357	+	0.0358667i	$0.0114192\pi$
$647$	13.5000	+	23.3827i	0.530740	+	0.919268i	−0.468617	+	0.883402i	$0.655247\pi$
$648$	1.50000	−	0.866025i	0.0589256	−	0.0340207i
$649$	−36.9129			−1.44896
$650$		0			0
$651$	10.7477			0.421237
$652$	−32.6869	+	18.8718i	−1.28012	+	0.739077i
$653$	−21.4129	−	37.0882i	−0.837951	−	1.45137i	−0.891605	−	0.452814i	$-0.850420\pi$
$653$	−21.4129	−	37.0882i	−0.837951	−	1.45137i	0.0536545	−	0.998560i	$-0.482913\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$		0			0
$656$	−6.39564	−	3.69253i	−0.249708	−	0.144169i
$657$		0			0
$658$		−	1.44600i		−	0.0563710i
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	0.399725	+	0.916635i	$0.369106\pi$
$659$	−15.2477	+	26.4098i	−0.593967	+	1.02878i	−0.993692	+	0.112146i	$0.964228\pi$
$660$		0			0
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	−0.158443	−	0.987368i	$-0.550647\pi$
$661$	15.8739	−	9.16478i	0.617422	−	0.356469i	0.775865	+	0.630900i	$0.217314\pi$
$662$	−2.04356			−0.0794252
$663$	−4.58258	−	15.8745i	−0.177972	−	0.616515i
$664$	10.4174			0.404274
$665$		0			0
$666$	−3.62614	−	6.28065i	−0.140510	−	0.243370i
$667$	10.5000	−	18.1865i	0.406562	−	0.704185i
$668$		−	17.1497i		−	0.663542i
$669$	7.50000	+	4.33013i	0.289967	+	0.167412i
$670$		0			0
$671$			3.75015i			0.144773i
$672$	4.10436	−	7.10895i	0.158329	−	0.274234i
$673$	−12.0826	−	20.9276i	−0.465749	−	0.806701i	0.533486	−	0.845809i	$-0.320882\pi$
$673$	−12.0826	−	20.9276i	−0.465749	−	0.806701i	−0.999235	+	0.0391079i	$0.987548\pi$
$674$	−12.1652	+	7.02355i	−0.468584	+	0.270537i
$675$		0			0
$676$	−0.895644	−	23.2695i	−0.0344478	−	0.894981i
$677$	2.83485			0.108952			0.0544760	−	0.998515i	$-0.482651\pi$
$677$	2.83485			0.108952			0.0544760	+	0.998515i	$0.482651\pi$
$678$	−2.93466	+	1.69433i	−0.112705	+	0.0650702i
$679$	9.87386	+	17.1020i	0.378924	+	0.656316i
$680$		0			0
$681$		−	0.818350i		−	0.0313593i
$682$	6.49545	+	3.75015i	0.248724	+	0.143601i
$683$	28.6652	+	16.5498i	1.09684	+	0.633262i	0.935390	−	0.353619i	$-0.115049\pi$
$683$	28.6652	+	16.5498i	1.09684	+	0.633262i	0.161452	+	0.986881i	$0.448382\pi$
$684$			6.20520i			0.237262i
$685$		0			0
$686$	−4.35208	−	7.53803i	−0.166163	−	0.287803i
$687$	−22.7477	+	13.1334i	−0.867880	+	0.501071i
$688$	−29.5390			−1.12616
$689$	−7.58258	−	26.2668i	−0.288873	−	1.00069i
$690$		0			0
$691$	17.1261	−	9.88778i	0.651509	−	0.376149i	−0.137525	−	0.990498i	$-0.543915\pi$
$691$	17.1261	−	9.88778i	0.651509	−	0.376149i	0.789034	+	0.614349i	$0.210581\pi$
$692$	−14.8521	−	25.7246i	−0.564591	−	0.977901i
$693$	−4.58258	+	7.93725i	−0.174078	+	0.301511i
$694$			9.74475i			0.369906i
$695$		0			0
$696$	6.87386	+	3.96863i	0.260553	+	0.150430i
$697$			12.1244i			0.459243i
$698$	−0.560795	+	0.971326i	−0.0212264	+	0.0367652i
$699$	−1.41742	−	2.45505i	−0.0536119	−	0.0928586i
$700$		0			0
$701$	−21.1652			−0.799397			−0.399698	−	0.916647i	$-0.630885\pi$
$701$	−21.1652			−0.799397			−0.399698	+	0.916647i	$0.630885\pi$
$702$	5.93466	+	5.71063i	0.223989	+	0.215534i
$703$	13.7477			0.518505
$704$	−7.83030	+	4.52083i	−0.295116	+	0.170385i
$705$		0			0
$706$	−1.56080	+	2.70338i	−0.0587413	+	0.101743i
$707$		−	15.5885i		−	0.586264i
$708$	−21.6434	−	12.4958i	−0.813408	−	0.469621i
$709$	−31.5000	−	18.1865i	−1.18301	−	0.683010i	−0.226299	−	0.974058i	$-0.572663\pi$
$709$	−31.5000	−	18.1865i	−1.18301	−	0.683010i	−0.956708	+	0.291048i	$0.905996\pi$
$710$		0			0
$711$	−6.00000	+	10.3923i	−0.225018	+	0.389742i
$712$	−8.29129	−	14.3609i	−0.310729	−	0.538199i
$713$	24.6261	−	14.2179i	0.922256	−	0.532465i
$714$	−3.62614			−0.135705
$715$		0			0
$716$	32.5390			1.21604
$717$	−0.165151	+	0.0953502i	−0.00616769	+	0.00356092i
$718$	−4.46099	−	7.72665i	−0.166482	−	0.288356i
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	−0.542025	−	0.840363i	$-0.682342\pi$
$719$	12.2477	−	21.2137i	0.456763	−	0.791137i	0.998788	+	0.0492257i	$0.0156754\pi$
$720$		0			0
$721$	−4.74773	−	2.74110i	−0.176815	−	0.102084i
$722$	−6.33030	−	3.65480i	−0.235589	−	0.136018i
$723$		−	1.73205i		−	0.0644157i
$724$	−7.83485	+	13.5704i	−0.291180	+	0.504338i
$725$		0			0
$726$	−1.58258	+	0.913701i	−0.0587349	+	0.0339106i
$727$	15.2523			0.565675			0.282838	−	0.959168i	$-0.408724\pi$
$727$	15.2523			0.565675			0.282838	+	0.959168i	$0.408724\pi$
$728$	−10.5000	−	2.59808i	−0.389156	−	0.0962911i
$729$	13.0000			0.481481
$730$		0			0
$731$	24.2477	+	41.9983i	0.896835	+	1.55336i
$732$	−1.26951	+	2.19885i	−0.0469223	+	0.0812719i
$733$			22.8027i			0.842237i	0.907006	+	0.421119i	$0.138362\pi$
$733$			22.8027i			0.842237i	−0.907006	+	0.421119i	$0.861638\pi$
$734$	−0.691478	−	0.399225i	−0.0255229	−	0.0147357i
$735$		0			0
$736$		−	21.7182i		−	0.800544i
$737$	1.33485	−	2.31203i	0.0491698	−	0.0851646i
$738$	−1.20871	−	2.09355i	−0.0444933	−	0.0770647i
$739$	14.7523	−	8.51723i	0.542671	−	0.313311i	−0.203490	−	0.979077i	$-0.565228\pi$
$739$	14.7523	−	8.51723i	0.542671	−	0.313311i	0.746161	+	0.665766i	$0.231895\pi$
$740$		0			0
$741$	−6.00000	+	1.73205i	−0.220416	+	0.0636285i
$742$	−6.00000			−0.220267
$743$	−4.96099	+	2.86423i	−0.182001	+	0.105078i	−0.588232	−	0.808692i	$-0.700176\pi$
$743$	−4.96099	+	2.86423i	−0.182001	+	0.105078i	0.406232	+	0.913770i	$0.366843\pi$
$744$	5.37386	+	9.30780i	0.197015	+	0.341241i
$745$		0			0
$746$			5.93905i			0.217444i
$747$	−10.4174	−	6.01450i	−0.381154	−	0.220059i
$748$	18.8085	+	10.8591i	0.687708	+	0.397048i
$749$		−	18.3296i		−	0.669748i
$750$		0			0
$751$	−5.87386	−	10.1738i	−0.214340	−	0.371248i	0.738728	−	0.674004i	$-0.235427\pi$
$751$	−5.87386	−	10.1738i	−0.214340	−	0.371248i	−0.953068	+	0.302755i	$0.902093\pi$
$752$	−4.41742	+	2.55040i	−0.161087	+	0.0930036i
$753$	0.165151			0.00601845
$754$	1.81307	−	7.32743i	0.0660281	−	0.266849i
$755$		0			0
$756$	−13.4347	+	7.75650i	−0.488614	+	0.282101i
$757$	4.87386	+	8.44178i	0.177144	+	0.306822i	0.940901	−	0.338682i	$-0.109981\pi$
$757$	4.87386	+	8.44178i	0.177144	+	0.306822i	−0.763757	+	0.645503i	$0.776648\pi$
$758$	2.43920	−	4.22483i	0.0885959	−	0.153453i
$759$		−	12.1244i		−	0.440086i
$760$		0			0
$761$	−30.7087	−	17.7297i	−1.11319	−	0.642701i	−0.173536	−	0.984827i	$-0.555519\pi$
$761$	−30.7087	−	17.7297i	−1.11319	−	0.642701i	−0.939654	+	0.342127i	$0.888853\pi$
$762$			8.10805i			0.293724i
$763$	11.3739	−	19.7001i	0.411762	−	0.713192i
$764$	14.8521	+	25.7246i	0.537330	+	0.930682i
$765$		0			0
$766$	10.7913			0.389905
$767$	−12.0826	+	48.8311i	−0.436277	+	1.76319i
$768$	−1.79129			−0.0646375
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	−0.236433	−	0.971648i	$-0.575978\pi$
$769$	13.5000	−	7.79423i	0.486822	−	0.281067i	0.723255	+	0.690581i	$0.242645\pi$
$770$		0			0
$771$	9.08258	−	15.7315i	0.327101	−	0.566556i
$772$		−	26.6283i		−	0.958374i
$773$	−20.9174	−	12.0767i	−0.752347	−	0.434368i	0.0741940	−	0.997244i	$-0.476362\pi$
$773$	−20.9174	−	12.0767i	−0.752347	−	0.434368i	−0.826541	+	0.562876i	$0.809695\pi$
$774$	−8.37386	−	4.83465i	−0.300992	−	0.173778i
$775$		0			0
$776$	−9.87386	+	17.1020i	−0.354451	+	0.613927i
$777$	6.87386	+	11.9059i	0.246598	+	0.427121i
$778$	−1.25227	+	0.723000i	−0.0448962	+	0.0259208i
$779$	4.58258			0.164188
$780$		0			0
$781$	−18.5826			−0.664937
$782$	−8.30852	+	4.79693i	−0.297112	+	0.171538i
$783$	−11.4564	−	19.8431i	−0.409420	−	0.709136i
$784$	−5.58258	+	9.66930i	−0.199378	+	0.345332i
$785$		0			0
$786$	−3.00000	−	1.73205i	−0.107006	−	0.0617802i
$787$	−14.1261	−	8.15573i	−0.503542	−	0.290720i	0.226633	−	0.973980i	$-0.427228\pi$
$787$	−14.1261	−	8.15573i	−0.503542	−	0.290720i	−0.730175	+	0.683260i	$0.760562\pi$
$788$		−	26.2867i		−	0.936425i
$789$	−4.50000	+	7.79423i	−0.160204	+	0.277482i
$790$		0			0
$791$	−11.1261	+	6.42368i	−0.395600	+	0.228400i
$792$	−9.16515			−0.325669
$793$	4.96099	+	1.22753i	0.176170	+	0.0435907i
$794$	9.29583			0.329897
$795$		0			0
$796$	−9.47822	−	16.4168i	−0.335947	−	0.581877i
$797$	22.0390	−	38.1727i	0.780662	−	1.35215i	−0.150895	−	0.988550i	$-0.548215\pi$
$797$	22.0390	−	38.1727i	0.780662	−	1.35215i	0.931557	−	0.363596i	$-0.118451\pi$
$798$			1.37055i			0.0485170i
$799$	7.25227	+	4.18710i	0.256567	+	0.148129i
$800$		0			0
$801$			19.1479i			0.676558i
$802$	−6.81307	+	11.8006i	−0.240578	+	0.416693i
$803$		0			0
$804$	1.56534	−	0.903750i	0.0552053	−	0.0318728i
$805$		0			0
$806$	7.08712	−	7.36515i	0.249633	−	0.259426i
$807$	15.0000			0.528025
$808$	13.5000	−	7.79423i	0.474928	−	0.274200i
$809$	27.4129	+	47.4805i	0.963785	+	1.66933i	0.712843	+	0.701323i	$0.247407\pi$
$809$	27.4129	+	47.4805i	0.963785	+	1.66933i	0.250942	+	0.968002i	$0.419260\pi$
$810$		0			0
$811$			50.5155i			1.77384i	0.461923	+	0.886920i	$0.347160\pi$
$811$			50.5155i			1.77384i	−0.461923	+	0.886920i	$0.652840\pi$
$812$	12.3131	+	7.10895i	0.432104	+	0.249475i
$813$	7.50000	+	4.33013i	0.263036	+	0.151864i
$814$			9.59386i			0.336264i
$815$		0			0
$816$	6.39564	+	11.0776i	0.223892	+	0.387793i
$817$	15.8739	−	9.16478i	0.555356	−	0.320635i
$818$	−3.95644			−0.138334
$819$	9.00000	+	8.66025i	0.314485	+	0.302614i
$820$		0			0
$821$	15.7087	−	9.06943i	0.548238	−	0.316525i	−0.200173	−	0.979761i	$-0.564150\pi$
$821$	15.7087	−	9.06943i	0.548238	−	0.316525i	0.748411	+	0.663235i	$0.230817\pi$
$822$	−2.39564	−	4.14938i	−0.0835577	−	0.144726i
$823$	−15.7087	+	27.2083i	−0.547571	+	0.948421i	0.450869	+	0.892590i	$0.351114\pi$
$823$	−15.7087	+	27.2083i	−0.547571	+	0.948421i	−0.998440	+	0.0558311i	$0.982219\pi$
$824$		−	5.48220i		−	0.190982i
$825$		0			0
$826$	9.56080	+	5.51993i	0.332663	+	0.192063i
$827$		−	10.7737i		−	0.374638i	−0.982299	−	0.187319i	$-0.940020\pi$
$827$		−	10.7737i		−	0.374638i	0.982299	−	0.187319i	$-0.0599799\pi$
$828$	−8.20871	+	14.2179i	−0.285272	+	0.494106i
$829$	16.6652	+	28.8649i	0.578805	+	1.00252i	0.995617	+	0.0935264i	$0.0298139\pi$
$829$	16.6652	+	28.8649i	0.578805	+	1.00252i	−0.416812	+	0.908993i	$0.636853\pi$
$830$		0			0
$831$	−7.41742			−0.257308
$832$	3.41742	+	11.8383i	0.118478	+	0.410419i
$833$	18.3303			0.635107
$834$	8.60436	−	4.96773i	0.297944	−	0.172018i
$835$		0			0
$836$	4.10436	−	7.10895i	0.141952	−	0.245868i
$837$		−	31.0260i		−	1.07242i
$838$	2.30852	+	1.33283i	0.0797466	+	0.0460417i
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.324613	−	0.945847i	$-0.605234\pi$
$839$	−37.8303	−	21.8413i	−1.30605	−	0.754047i	−0.981434	+	0.191800i	$0.938567\pi$
$840$		0			0
$841$	4.00000	−	6.92820i	0.137931	−	0.238904i
$842$	−1.25227	−	2.16900i	−0.0431562	−	0.0747487i
$843$	3.16515	−	1.82740i	0.109014	−	0.0629390i
$844$	−0.295834			−0.0101830
$845$		0			0
$846$	−1.66970			−0.0574054
$847$	−6.00000	+	3.46410i	−0.206162	+	0.119028i
$848$	10.5826	+	18.3296i	0.363407	+	0.629440i
$849$	13.8739	−	24.0302i	0.476150	−	0.824716i
$850$		0			0
$851$	31.5000	+	18.1865i	1.07981	+	0.623426i
$852$	−10.8956	−	6.29060i	−0.373279	−	0.215513i
$853$		−	5.63310i		−	0.192874i	−0.995339	−	0.0964369i	$-0.969255\pi$
$853$		−	5.63310i		−	0.192874i	0.995339	−	0.0964369i	$-0.0307446\pi$
$854$	0.560795	−	0.971326i	0.0191900	−	0.0332381i
$855$		0			0
$856$	15.8739	−	9.16478i	0.542557	−	0.313246i
$857$	4.74773			0.162179			0.0810896	−	0.996707i	$-0.474160\pi$
$857$	4.74773			0.162179			0.0810896	+	0.996707i	$0.474160\pi$
$858$	−1.20871	−	4.18710i	−0.0412648	−	0.142945i
$859$	−44.2432			−1.50956			−0.754779	−	0.655979i	$-0.772256\pi$
$859$	−44.2432			−1.50956			−0.754779	+	0.655979i	$0.772256\pi$
$860$		0			0
$861$	2.29129	+	3.96863i	0.0780869	+	0.135250i
$862$	1.93466	−	3.35093i	0.0658947	−	0.114133i
$863$			13.6657i			0.465186i	0.972574	+	0.232593i	$0.0747210\pi$
$863$			13.6657i			0.465186i	−0.972574	+	0.232593i	$0.925279\pi$
$864$	−20.5218	−	11.8483i	−0.698165	−	0.403086i
$865$		0			0
$866$		−	4.45325i		−	0.151328i
$867$	2.00000	−	3.46410i	0.0679236	−	0.117647i
$868$	9.62614	+	16.6730i	0.326732	+	0.565917i
$869$	13.7477	−	7.93725i	0.466360	−	0.269253i
$870$		0			0
$871$	−2.62159	−	2.52263i	−0.0888292	−	0.0854759i
$872$	22.7477			0.770335
$873$	19.7477	−	11.4014i	0.668359	−	0.385877i
$874$	1.81307	+	3.14033i	0.0613279	+	0.106223i
$875$		0			0
$876$		0			0
$877$	6.87386	+	3.96863i	0.232114	+	0.134011i	0.611547	−	0.791208i	$-0.290548\pi$
$877$	6.87386	+	3.96863i	0.232114	+	0.134011i	−0.379433	+	0.925219i	$0.623881\pi$
$878$	5.73504	+	3.31113i	0.193548	+	0.111745i
$879$		−	18.1389i		−	0.611809i
$880$		0			0
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	−0.990423	−	0.138068i	$-0.955911\pi$
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	0.375641	−	0.926765i	$-0.377422\pi$
$882$	−3.16515	+	1.82740i	−0.106576	+	0.0615318i
$883$	−36.2432			−1.21968			−0.609840	−	0.792524i	$-0.708766\pi$
$883$	−36.2432			−1.21968			−0.609840	+	0.792524i	$0.708766\pi$
$884$	20.5218	−	21.3269i	0.690222	−	0.717300i
$885$		0			0
$886$	−7.87841	+	4.54860i	−0.264680	+	0.152813i
$887$	27.2477	+	47.1944i	0.914889	+	1.58463i	0.807064	+	0.590465i	$0.201055\pi$
$887$	27.2477	+	47.1944i	0.914889	+	1.58463i	0.107826	+	0.994170i	$0.465611\pi$
$888$	−6.87386	+	11.9059i	−0.230672	+	0.399535i
$889$			30.7400i			1.03099i
$890$		0			0
$891$	2.29129	+	1.32288i	0.0767610	+	0.0443180i
$892$			15.5130i			0.519414i
$893$	1.58258	−	2.74110i	0.0529589	−	0.0917275i
$894$	3.81307	+	6.60443i	0.127528	+	0.220885i
$895$		0			0
$896$	19.1216			0.638808
$897$	−16.0390	−	3.96863i	−0.535527	−	0.132509i
$898$	−5.03447			−0.168002
$899$	−24.6261	+	14.2179i	−0.821328	+	0.474194i
$900$		0			0
$901$	17.3739	−	30.0924i	0.578807	−	1.00252i
$902$			3.19795i			0.106480i
$903$	15.8739	+	9.16478i	0.528249	+	0.304985i
$904$	−11.1261	−	6.42368i	−0.370050	−	0.213648i
$905$		0			0
$906$	−2.20871	+	3.82560i	−0.0733795	+	0.127097i
$907$	−3.12614	−	5.41463i	−0.103802	−	0.179790i	0.809446	−	0.587194i	$-0.199767\pi$
$907$	−3.12614	−	5.41463i	−0.103802	−	0.179790i	−0.913248	+	0.407404i	$0.866434\pi$
$908$	1.26951	−	0.732950i	0.0421301	−	0.0243238i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−7.91288			−0.262165			−0.131083	−	0.991371i	$-0.541845\pi$
$911$	−7.91288			−0.262165			−0.131083	+	0.991371i	$0.541845\pi$
$912$	4.18693	−	2.41733i	0.138643	−	0.0800457i
$913$	7.95644	+	13.7810i	0.263320	+	0.456083i
$914$	0.395644	−	0.685275i	0.0130867	−	0.0226669i
$915$		0			0
$916$	−40.7477	−	23.5257i	−1.34634	−	0.777311i
$917$	−11.3739	−	6.56670i	−0.375598	−	0.216852i
$918$			10.4678i			0.345487i
$919$	−27.0826	+	46.9084i	−0.893372	+	1.54737i	−0.0575648	+	0.998342i	$0.518334\pi$
$919$	−27.0826	+	46.9084i	−0.893372	+	1.54737i	−0.835807	+	0.549023i	$0.815000\pi$
$920$		0			0
$921$	21.0000	−	12.1244i	0.691974	−	0.399511i
$922$	16.3739			0.539244
$923$	−6.08258	+	24.5824i	−0.200210	+	0.809141i
$924$	8.20871			0.270047
$925$		0			0
$926$	9.00000	+	15.5885i	0.295758	+	0.512268i
$927$	−3.16515	+	5.48220i	−0.103957	+	0.180059i
$928$			21.7182i			0.712935i
$929$	−22.8303	−	13.1811i	−0.749038	−	0.432457i	0.0763082	−	0.997084i	$-0.475687\pi$
$929$	−22.8303	−	13.1811i	−0.749038	−	0.432457i	−0.825346	+	0.564627i	$0.809020\pi$
$930$		0			0
$931$		−	6.92820i		−	0.227063i
$932$	2.53901	−	4.39770i	0.0831682	−	0.144052i
$933$	3.79129	+	6.56670i	0.124121	+	0.214984i
$934$	9.62614	−	5.55765i	0.314977	−	0.181852i
$935$		0			0
$936$	−3.00000	+	12.1244i	−0.0980581	+	0.396297i
$937$	−31.4955			−1.02891			−0.514456	−	0.857517i	$-0.672006\pi$
$937$	−31.4955			−1.02891			−0.514456	+	0.857517i	$0.672006\pi$
$938$	−0.691478	+	0.399225i	−0.0225775	+	0.0130352i
$939$	1.62614	+	2.81655i	0.0530670	+	0.0919147i
$940$		0			0
$941$			26.4575i			0.862490i	0.902235	+	0.431245i	$0.141926\pi$
$941$			26.4575i			0.862490i	−0.902235	+	0.431245i	$0.858074\pi$
$942$	−3.62614	−	2.09355i	−0.118146	−	0.0682116i
$943$	10.5000	+	6.06218i	0.341927	+	0.197412i
$944$		−	38.9434i		−	1.26750i
$945$		0			0
$946$	6.39564	+	11.0776i	0.207940	+	0.360163i
$947$	12.4129	−	7.16658i	0.403364	−	0.232883i	−0.284570	−	0.958655i	$-0.591851\pi$
$947$	12.4129	−	7.16658i	0.403364	−	0.232883i	0.687935	+	0.725773i	$0.258518\pi$
$948$	10.7477			0.349070
$949$		0			0
$950$		0			0
$951$	−0.165151	+	0.0953502i	−0.00535540	+	0.00309194i
$952$	−6.87386	−	11.9059i	−0.222783	−	0.385872i
$953$	−4.03901	+	6.99578i	−0.130837	+	0.226616i	−0.923999	−	0.382394i	$-0.875100\pi$
$953$	−4.03901	+	6.99578i	−0.130837	+	0.226616i	0.793163	+	0.609010i	$0.208433\pi$
$954$			6.92820i			0.224309i
$955$		0			0
$956$	−0.295834	−	0.170800i	−0.00956794	−	0.00552406i
$957$			12.1244i			0.391925i
$958$	−1.06534	+	1.84522i	−0.0344196	+	0.0596165i
$959$	−9.08258	−	15.7315i	−0.293292	−	0.507996i
$960$		0			0
$961$	−7.50455			−0.242082
$962$	12.6915	+	3.14033i	0.409190	+	0.101248i
$963$	−21.1652			−0.682037
$964$	2.68693	−	1.55130i	0.0865402	−	0.0499640i
$965$		0			0
$966$	−1.81307	+	3.14033i	−0.0583345	+	0.101038i
$967$			37.3821i			1.20213i	0.799201	+	0.601064i	$0.205256\pi$
$967$			37.3821i			1.20213i	−0.799201	+	0.601064i	$0.794744\pi$
$968$	−6.00000	−	3.46410i	−0.192847	−	0.111340i
$969$	−6.87386	−	3.96863i	−0.220820	−	0.127491i
$970$		0			0
$971$	9.24773	−	16.0175i	0.296774	−	0.514027i	−0.678622	−	0.734487i	$-0.737423\pi$
$971$	9.24773	−	16.0175i	0.296774	−	0.514027i	0.975396	+	0.220460i	$0.0707560\pi$
$972$	14.3303	+	24.8208i	0.459645	+	0.796128i
$973$	32.6216	−	18.8341i	1.04580	−	0.603793i
$974$	−4.87841			−0.156314
$975$		0			0
$976$	−3.95644			−0.126643
$977$	−30.5780	+	17.6542i	−0.978278	+	0.564809i	−0.901750	−	0.432258i	$-0.857717\pi$
$977$	−30.5780	+	17.6542i	−0.978278	+	0.564809i	−0.0765281	+	0.997067i	$0.524383\pi$
$978$	4.81307	+	8.33648i	0.153905	+	0.266571i
$979$	12.6652	−	21.9367i	0.404780	−	0.701100i
$980$		0			0
$981$	−22.7477	−	13.1334i	−0.726279	−	0.419317i
$982$	−7.68239	−	4.43543i	−0.245155	−	0.141540i
$983$			55.0840i			1.75691i	0.477827	+	0.878454i	$0.341424\pi$
$983$			55.0840i			1.75691i	−0.477827	+	0.878454i	$0.658576\pi$
$984$	−2.29129	+	3.96863i	−0.0730436	+	0.126515i
$985$		0			0
$986$	8.30852	−	4.79693i	0.264597	−	0.152765i
$987$	3.16515			0.100748
$988$	−8.06080	−	7.75650i	−0.256448	−	0.246767i
$989$	48.4955			1.54207
$990$		0			0
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$	−14.7042	+	25.4684i	−0.466858	+	0.808621i
$993$		−	4.47315i		−	0.141951i
$994$	4.81307	+	2.77883i	0.152661	+	0.0881390i
$995$		0			0
$996$			10.7737i			0.341378i
$997$	0.0825757	−	0.143025i	0.00261520	−	0.00452966i	−0.864715	−	0.502263i	$-0.832501\pi$
$997$	0.0825757	−	0.143025i	0.00261520	−	0.00452966i	0.867330	+	0.497733i	$0.165834\pi$
$998$	0.165151	+	0.286051i	0.00522778	+	0.00905477i
$999$	34.3693	−	19.8431i	1.08740	−	0.627809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.b.101.2		4
5.2	odd	4		65.2.l.a.49.3	yes	8
5.3	odd	4		65.2.l.a.49.2	yes	8
5.4	even	2		325.2.n.c.101.1		4
13.2	odd	12		4225.2.a.bj.1.3		4
13.4	even	6	inner	325.2.n.b.251.2		4
13.11	odd	12		4225.2.a.bj.1.2		4
15.2	even	4		585.2.bf.a.244.2		8
15.8	even	4		585.2.bf.a.244.3		8
20.3	even	4		1040.2.df.b.49.4		8
20.7	even	4		1040.2.df.b.49.1		8
65.2	even	12		845.2.b.f.339.6		8
65.3	odd	12		845.2.d.c.844.5		8
65.4	even	6		325.2.n.c.251.1		4
65.7	even	12		845.2.n.c.529.3		8
65.8	even	4		845.2.n.c.484.3		8
65.12	odd	4		845.2.l.c.699.2		8
65.17	odd	12		65.2.l.a.4.2	✓	8
65.18	even	4		845.2.n.d.484.1		8
65.22	odd	12		845.2.l.c.654.3		8
65.23	odd	12		845.2.d.c.844.3		8
65.24	odd	12		4225.2.a.bk.1.3		4
65.28	even	12		845.2.b.f.339.3		8
65.32	even	12		845.2.n.d.529.1		8
65.33	even	12		845.2.n.d.529.2		8
65.37	even	12		845.2.b.f.339.4		8
65.38	odd	4		845.2.l.c.699.3		8
65.42	odd	12		845.2.d.c.844.4		8
65.43	odd	12		65.2.l.a.4.3	yes	8
65.47	even	4		845.2.n.d.484.2		8
65.48	odd	12		845.2.l.c.654.2		8
65.54	odd	12		4225.2.a.bk.1.2		4
65.57	even	4		845.2.n.c.484.4		8
65.58	even	12		845.2.n.c.529.4		8
65.62	odd	12		845.2.d.c.844.6		8
65.63	even	12		845.2.b.f.339.5		8
195.17	even	12		585.2.bf.a.199.3		8
195.173	even	12		585.2.bf.a.199.2		8
260.43	even	12		1040.2.df.b.849.1		8
260.147	even	12		1040.2.df.b.849.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	65.17	odd	12
65.2.l.a.4.3	yes	8	65.43	odd	12
65.2.l.a.49.2	yes	8	5.3	odd	4
65.2.l.a.49.3	yes	8	5.2	odd	4
325.2.n.b.101.2		4	1.1	even	1	trivial
325.2.n.b.251.2		4	13.4	even	6	inner
325.2.n.c.101.1		4	5.4	even	2
325.2.n.c.251.1		4	65.4	even	6
585.2.bf.a.199.2		8	195.173	even	12
585.2.bf.a.199.3		8	195.17	even	12
585.2.bf.a.244.2		8	15.2	even	4
585.2.bf.a.244.3		8	15.8	even	4
845.2.b.f.339.3		8	65.28	even	12
845.2.b.f.339.4		8	65.37	even	12
845.2.b.f.339.5		8	65.63	even	12
845.2.b.f.339.6		8	65.2	even	12
845.2.d.c.844.3		8	65.23	odd	12
845.2.d.c.844.4		8	65.42	odd	12
845.2.d.c.844.5		8	65.3	odd	12
845.2.d.c.844.6		8	65.62	odd	12
845.2.l.c.654.2		8	65.48	odd	12
845.2.l.c.654.3		8	65.22	odd	12
845.2.l.c.699.2		8	65.12	odd	4
845.2.l.c.699.3		8	65.38	odd	4
845.2.n.c.484.3		8	65.8	even	4
845.2.n.c.484.4		8	65.57	even	4
845.2.n.c.529.3		8	65.7	even	12
845.2.n.c.529.4		8	65.58	even	12
845.2.n.d.484.1		8	65.18	even	4
845.2.n.d.484.2		8	65.47	even	4
845.2.n.d.529.1		8	65.32	even	12
845.2.n.d.529.2		8	65.33	even	12
1040.2.df.b.49.1		8	20.7	even	4
1040.2.df.b.49.4		8	20.3	even	4
1040.2.df.b.849.1		8	260.43	even	12
1040.2.df.b.849.4		8	260.147	even	12
4225.2.a.bj.1.2		4	13.11	odd	12
4225.2.a.bj.1.3		4	13.2	odd	12
4225.2.a.bk.1.2		4	65.54	odd	12
4225.2.a.bk.1.3		4	65.24	odd	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395644 - 0.228425i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.895644 + 1.55130i) q^{4} +(0.395644 + 0.228425i) q^{6} +(1.50000 + 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.29129 + 1.32288i) q^{11} -1.79129 q^{12} +(1.00000 + 3.46410i) q^{13} +0.791288 q^{14} +(-1.39564 - 2.41733i) q^{16} +(-2.29129 + 3.96863i) q^{17} -0.913701i q^{18} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-0.604356 + 1.04678i) q^{22} +(2.29129 + 3.96863i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(1.18693 + 1.14213i) q^{26} +5.00000 q^{27} +(-2.68693 + 1.55130i) q^{28} +(-2.29129 - 3.96863i) q^{29} -6.20520i q^{31} +(-4.10436 - 2.36965i) q^{32} +(-2.29129 - 1.32288i) q^{33} +2.09355i q^{34} +(1.79129 + 3.10260i) q^{36} +(6.87386 - 3.96863i) q^{37} +0.791288 q^{38} +(-2.50000 + 2.59808i) q^{39} +(2.29129 - 1.32288i) q^{41} +(0.395644 + 0.685275i) q^{42} +(5.29129 - 9.16478i) q^{43} -4.73930i q^{44} +(1.81307 + 1.04678i) q^{46} -1.82740i q^{47} +(1.39564 - 2.41733i) q^{48} +(-2.00000 - 3.46410i) q^{49} -4.58258 q^{51} +(-6.26951 - 1.55130i) q^{52} -7.58258 q^{53} +(1.97822 - 1.14213i) q^{54} +(-1.50000 + 2.59808i) q^{56} +1.73205i q^{57} +(-1.81307 - 1.04678i) q^{58} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(-1.41742 - 2.45505i) q^{62} +(3.00000 - 1.73205i) q^{63} +3.41742 q^{64} -1.20871 q^{66} +(-0.873864 + 0.504525i) q^{67} +(-4.10436 - 7.10895i) q^{68} +(-2.29129 + 3.96863i) q^{69} +(6.08258 + 3.51178i) q^{71} +(3.00000 + 1.73205i) q^{72} +(1.81307 - 3.14033i) q^{74} +(-2.68693 + 1.55130i) q^{76} -4.58258 q^{77} +(-0.395644 + 1.59898i) q^{78} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.604356 - 1.04678i) q^{82} -6.01450i q^{83} +(-2.68693 - 1.55130i) q^{84} -4.83465i q^{86} +(2.29129 - 3.96863i) q^{87} +(-2.29129 - 3.96863i) q^{88} +(-8.29129 + 4.78698i) q^{89} +(-1.50000 + 6.06218i) q^{91} -8.20871 q^{92} +(5.37386 - 3.10260i) q^{93} +(-0.417424 - 0.723000i) q^{94} -4.73930i q^{96} +(9.87386 + 5.70068i) q^{97} +(-1.58258 - 0.913701i) q^{98} +5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 2 q^{3} + q^{4} - 3 q^{6} + 6 q^{7} + 4 q^{9} + 2 q^{12} + 4 q^{13} - 6 q^{14} - q^{16} + 6 q^{19} - 7 q^{22} - 6 q^{24} - 9 q^{26} + 20 q^{27} + 3 q^{28} - 21 q^{32} - 2 q^{36} - 6 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 + 2 * q^3 + q^4 - 3 * q^6 + 6 * q^7 + 4 * q^9 + 2 * q^12 + 4 * q^13 - 6 * q^14 - q^16 + 6 * q^19 - 7 * q^22 - 6 * q^24 - 9 * q^26 + 20 * q^27 + 3 * q^28 - 21 * q^32 - 2 * q^36 - 6 * q^38 - 10 * q^39 - 3 * q^42 + 12 * q^43 + 21 * q^46 + q^48 - 8 * q^49 + 7 * q^52 - 12 * q^53 - 15 * q^54 - 6 * q^56 - 21 * q^58 + 30 * q^59 + 12 * q^61 - 24 * q^62 + 12 * q^63 + 32 * q^64 - 14 * q^66 + 24 * q^67 - 21 * q^68 + 6 * q^71 + 12 * q^72 + 21 * q^74 + 3 * q^76 + 3 * q^78 - 24 * q^79 - 2 * q^81 + 7 * q^82 + 3 * q^84 - 24 * q^89 - 6 * q^91 - 42 * q^92 - 6 * q^93 - 20 * q^94 + 12 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more