LMFDB - Embedded newform 720.2.bd.h.523.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(307,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-2,0,-2,-8,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			523.6
Root			$0.0912451 + 1.41127i$ of defining polynomial
Character	$\chi$	$=$	720.523
Dual form			720.2.bd.h.307.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0912451 - 1.41127i) q^{2} +(-1.98335 + 0.257542i) q^{4} +(0.453294 + 2.18964i) q^{5} +(1.25143 - 1.25143i) q^{7} +(0.544432 + 2.77553i) q^{8} +(3.04881 - 0.839513i) q^{10} +(-2.47980 + 2.47980i) q^{11} -1.81790 q^{13} +(-1.88029 - 1.65192i) q^{14} +(3.86734 - 1.02159i) q^{16} +(-4.52932 + 4.52932i) q^{17} +(-2.39150 + 2.39150i) q^{19} +(-1.46296 - 4.22608i) q^{20} +(3.72594 + 3.27340i) q^{22} +(-4.06513 - 4.06513i) q^{23} +(-4.58905 + 1.98510i) q^{25} +(0.165874 + 2.56554i) q^{26} +(-2.15973 + 2.80432i) q^{28} +(6.27721 + 6.27721i) q^{29} +4.33993i q^{31} +(-1.79462 - 5.36464i) q^{32} +(6.80535 + 5.97880i) q^{34} +(3.30745 + 2.17292i) q^{35} -2.92026 q^{37} +(3.59326 + 3.15684i) q^{38} +(-5.83064 + 2.45024i) q^{40} -4.26875i q^{41} +10.4167 q^{43} +(4.27966 - 5.55697i) q^{44} +(-5.36607 + 6.10791i) q^{46} +(-0.150104 - 0.150104i) q^{47} +3.86784i q^{49} +(3.22024 + 6.29524i) q^{50} +(3.60552 - 0.468185i) q^{52} +10.6378i q^{53} +(-6.55396 - 4.30580i) q^{55} +(4.15471 + 2.79207i) q^{56} +(8.28606 - 9.43159i) q^{58} +(-3.17716 - 3.17716i) q^{59} +(-4.76865 + 4.76865i) q^{61} +(6.12480 - 0.395997i) q^{62} +(-7.40719 + 3.02218i) q^{64} +(-0.824041 - 3.98054i) q^{65} +10.8215 q^{67} +(7.81672 - 10.1497i) q^{68} +(2.76478 - 4.86596i) q^{70} +5.04598 q^{71} +(2.92958 - 2.92958i) q^{73} +(0.266459 + 4.12126i) q^{74} +(4.12727 - 5.35910i) q^{76} +6.20661i q^{77} -4.75216 q^{79} +(3.98996 + 8.00501i) q^{80} +(-6.02435 + 0.389502i) q^{82} -15.3571i q^{83} +(-11.9707 - 7.86446i) q^{85} +(-0.950471 - 14.7007i) q^{86} +(-8.23287 - 5.53270i) q^{88} -3.95627 q^{89} +(-2.27497 + 2.27497i) q^{91} +(9.10952 + 7.01563i) q^{92} +(-0.198141 + 0.225533i) q^{94} +(-6.32059 - 4.15248i) q^{95} +(2.46797 - 2.46797i) q^{97} +(5.45856 - 0.352921i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{13} + 10 q^{14} + 26 q^{16} - 12 q^{17} - 16 q^{19} + 4 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 20 q^{26} + 22 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 2 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^13 + 10 * q^14 + 26 * q^16 - 12 * q^17 - 16 * q^19 + 4 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 20 * q^26 + 22 * q^28 - 12 * q^32 - 6 * q^34 + 12 * q^35 + 24 * q^37 + 22 * q^38 - 10 * q^40 - 8 * q^43 + 22 * q^44 - 18 * q^46 + 18 * q^50 + 24 * q^52 - 4 * q^55 + 26 * q^56 - 2 * q^58 - 16 * q^59 - 12 * q^61 - 12 * q^62 - 26 * q^64 - 4 * q^65 - 16 * q^67 + 2 * q^68 - 10 * q^70 + 20 * q^73 - 8 * q^74 + 26 * q^76 - 48 * q^79 + 16 * q^80 + 80 * q^82 + 4 * q^85 - 4 * q^86 + 94 * q^88 + 40 * q^89 - 24 * q^91 + 30 * q^92 - 58 * q^94 - 72 * q^95 - 28 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0912451	−	1.41127i	−0.0645200	−	0.997916i
$2$	−0.0912451	−	1.41127i	−0.0645200	−	0.997916i
$3$		0			0
$3$		0			0
$4$	−1.98335	+	0.257542i	−0.991674	+	0.128771i
$5$	0.453294	+	2.18964i	0.202719	+	0.979237i
$5$	0.453294	+	2.18964i	0.202719	+	0.979237i
$6$		0			0
$7$	1.25143	−	1.25143i	0.472996	−	0.472996i	−0.429887	−	0.902883i	$-0.641446\pi$
$7$	1.25143	−	1.25143i	0.472996	−	0.472996i	0.902883	+	0.429887i	$0.141446\pi$
$8$	0.544432	+	2.77553i	0.192486	+	0.981300i
$9$		0			0
$10$	3.04881	−	0.839513i	0.964117	−	0.265477i
$11$	−2.47980	+	2.47980i	−0.747689	+	0.747689i	−0.974045	−	0.226356i	$-0.927319\pi$
$11$	−2.47980	+	2.47980i	−0.747689	+	0.747689i	0.226356	+	0.974045i	$0.427319\pi$
$12$		0			0
$13$	−1.81790			−0.504194			−0.252097	−	0.967702i	$-0.581120\pi$
$13$	−1.81790			−0.504194			−0.252097	+	0.967702i	$0.581120\pi$
$14$	−1.88029	−	1.65192i	−0.502529	−	0.441493i
$15$		0			0
$16$	3.86734	−	1.02159i	0.966836	−	0.255398i
$17$	−4.52932	+	4.52932i	−1.09852	+	1.09852i	−0.103936	+	0.994584i	$0.533144\pi$
$17$	−4.52932	+	4.52932i	−1.09852	+	1.09852i	−0.994584	+	0.103936i	$0.966856\pi$
$18$		0			0
$19$	−2.39150	+	2.39150i	−0.548649	+	0.548649i	−0.926050	−	0.377401i	$-0.876818\pi$
$19$	−2.39150	+	2.39150i	−0.548649	+	0.548649i	0.377401	+	0.926050i	$0.376818\pi$
$20$	−1.46296	−	4.22608i	−0.327129	−	0.944980i
$21$		0			0
$22$	3.72594	+	3.27340i	0.794372	+	0.697890i
$23$	−4.06513	−	4.06513i	−0.847639	−	0.847639i	0.142199	−	0.989838i	$-0.454583\pi$
$23$	−4.06513	−	4.06513i	−0.847639	−	0.847639i	−0.989838	+	0.142199i	$0.954583\pi$
$24$		0			0
$25$	−4.58905	+	1.98510i	−0.917810	+	0.397020i
$26$	0.165874	+	2.56554i	0.0325306	+	0.503143i
$27$		0			0
$28$	−2.15973	+	2.80432i	−0.408150	+	0.529967i
$29$	6.27721	+	6.27721i	1.16565	+	1.16565i	0.983219	+	0.182430i	$0.0583963\pi$
$29$	6.27721	+	6.27721i	1.16565	+	1.16565i	0.182430	+	0.983219i	$0.441604\pi$
$30$		0			0
$31$			4.33993i			0.779474i	0.920926	+	0.389737i	$0.127434\pi$
$31$			4.33993i			0.779474i	−0.920926	+	0.389737i	$0.872566\pi$
$32$	−1.79462	−	5.36464i	−0.317246	−	0.948343i
$33$		0			0
$34$	6.80535	+	5.97880i	1.16711	+	1.02535i
$35$	3.30745	+	2.17292i	0.559061	+	0.367290i
$36$		0			0
$37$	−2.92026			−0.480087			−0.240044	−	0.970762i	$-0.577162\pi$
$37$	−2.92026			−0.480087			−0.240044	+	0.970762i	$0.577162\pi$
$38$	3.59326	+	3.15684i	0.582904	+	0.512107i
$39$		0			0
$40$	−5.83064	+	2.45024i	−0.921904	+	0.387417i
$41$		−	4.26875i		−	0.666667i	−0.942809	−	0.333334i	$-0.891826\pi$
$41$		−	4.26875i		−	0.666667i	0.942809	−	0.333334i	$-0.108174\pi$
$42$		0			0
$43$	10.4167			1.58853			0.794264	−	0.607572i	$-0.207856\pi$
$43$	10.4167			1.58853			0.794264	+	0.607572i	$0.207856\pi$
$44$	4.27966	−	5.55697i	0.645183	−	0.837745i
$45$		0			0
$46$	−5.36607	+	6.10791i	−0.791183	+	0.900562i
$47$	−0.150104	−	0.150104i	−0.0218950	−	0.0218950i	0.696075	−	0.717970i	$-0.254928\pi$
$47$	−0.150104	−	0.150104i	−0.0218950	−	0.0218950i	−0.717970	+	0.696075i	$0.754928\pi$
$48$		0			0
$49$			3.86784i			0.552549i
$50$	3.22024	+	6.29524i	0.455410	+	0.890282i
$51$		0			0
$52$	3.60552	−	0.468185i	0.499996	−	0.0649256i
$53$			10.6378i			1.46122i	0.682797	+	0.730608i	$0.260763\pi$
$53$			10.6378i			1.46122i	−0.682797	+	0.730608i	$0.739237\pi$
$54$		0			0
$55$	−6.55396	−	4.30580i	−0.883736	−	0.580594i
$56$	4.15471	+	2.79207i	0.555196	+	0.373106i
$57$		0			0
$58$	8.28606	−	9.43159i	1.08801	−	1.23843i
$59$	−3.17716	−	3.17716i	−0.413632	−	0.413632i	0.469370	−	0.883002i	$-0.344481\pi$
$59$	−3.17716	−	3.17716i	−0.413632	−	0.413632i	−0.883002	+	0.469370i	$0.844481\pi$
$60$		0			0
$61$	−4.76865	+	4.76865i	−0.610563	+	0.610563i	−0.943093	−	0.332530i	$-0.892098\pi$
$61$	−4.76865	+	4.76865i	−0.610563	+	0.610563i	0.332530	+	0.943093i	$0.392098\pi$
$62$	6.12480	−	0.395997i	0.777850	−	0.0502917i
$63$		0			0
$64$	−7.40719	+	3.02218i	−0.925899	+	0.377772i
$65$	−0.824041	−	3.98054i	−0.102210	−	0.493725i
$66$		0			0
$67$	10.8215			1.32206			0.661029	−	0.750361i	$-0.270120\pi$
$67$	10.8215			1.32206			0.661029	+	0.750361i	$0.270120\pi$
$68$	7.81672	−	10.1497i	0.947917	−	1.23083i
$69$		0			0
$70$	2.76478	−	4.86596i	0.330454	−	0.581594i
$71$	5.04598			0.598847			0.299424	−	0.954120i	$-0.403206\pi$
$71$	5.04598			0.598847			0.299424	+	0.954120i	$0.403206\pi$
$72$		0			0
$73$	2.92958	−	2.92958i	0.342881	−	0.342881i	−0.514568	−	0.857449i	$-0.672048\pi$
$73$	2.92958	−	2.92958i	0.342881	−	0.342881i	0.857449	+	0.514568i	$0.172048\pi$
$74$	0.266459	+	4.12126i	0.0309752	+	0.479087i
$75$		0			0
$76$	4.12727	−	5.35910i	0.473431	−	0.614731i
$77$			6.20661i			0.707309i
$78$		0			0
$79$	−4.75216			−0.534660			−0.267330	−	0.963605i	$-0.586141\pi$
$79$	−4.75216			−0.534660			−0.267330	+	0.963605i	$0.586141\pi$
$80$	3.98996	+	8.00501i	0.446091	+	0.894987i
$81$		0			0
$82$	−6.02435	+	0.389502i	−0.665278	+	0.0430134i
$83$		−	15.3571i		−	1.68567i	−0.538175	−	0.842833i	$-0.680886\pi$
$83$		−	15.3571i		−	1.68567i	0.538175	−	0.842833i	$-0.319114\pi$
$84$		0			0
$85$	−11.9707	−	7.86446i	−1.29840	−	0.853020i
$86$	−0.950471	−	14.7007i	−0.102492	−	1.58522i
$87$		0			0
$88$	−8.23287	−	5.53270i	−0.877627	−	0.589788i
$89$	−3.95627			−0.419364			−0.209682	−	0.977770i	$-0.567243\pi$
$89$	−3.95627			−0.419364			−0.209682	+	0.977770i	$0.567243\pi$
$90$		0			0
$91$	−2.27497	+	2.27497i	−0.238482	+	0.238482i
$92$	9.10952	+	7.01563i	0.949733	+	0.731430i
$93$		0			0
$94$	−0.198141	+	0.225533i	−0.0204367	+	0.0232620i
$95$	−6.32059	−	4.15248i	−0.648478	−	0.426035i
$96$		0			0
$97$	2.46797	−	2.46797i	0.250585	−	0.250585i	−0.570626	−	0.821210i	$-0.693299\pi$
$97$	2.46797	−	2.46797i	0.250585	−	0.250585i	0.821210	+	0.570626i	$0.193299\pi$
$98$	5.45856	−	0.352921i	0.551398	−	0.0356504i
$99$		0			0
$100$	8.59044	−	5.11902i	0.859044	−	0.511902i
$101$	−9.40099	−	9.40099i	−0.935433	−	0.935433i	0.0626050	−	0.998038i	$-0.480059\pi$
$101$	−9.40099	−	9.40099i	−0.935433	−	0.935433i	−0.998038	+	0.0626050i	$0.980059\pi$
$102$		0			0
$103$	3.79353	+	3.79353i	0.373788	+	0.373788i	0.868855	−	0.495067i	$-0.164857\pi$
$103$	3.79353	+	3.79353i	0.373788	+	0.373788i	−0.495067	+	0.868855i	$0.664857\pi$
$104$	−0.989720	−	5.04563i	−0.0970500	−	0.494765i
$105$		0			0
$106$	15.0128	−	0.970648i	1.45817	−	0.0942776i
$107$			12.1814i			1.17762i	0.808271	+	0.588810i	$0.200403\pi$
$107$			12.1814i			1.17762i	−0.808271	+	0.588810i	$0.799597\pi$
$108$		0			0
$109$	4.04384	+	4.04384i	0.387329	+	0.387329i	0.873734	−	0.486404i	$-0.161692\pi$
$109$	4.04384	+	4.04384i	0.387329	+	0.387329i	−0.486404	+	0.873734i	$0.661692\pi$
$110$	−5.47862	+	9.64227i	−0.522366	+	0.919354i
$111$		0			0
$112$	3.56126	−	6.11817i	0.336508	−	0.578112i
$113$	−12.4221	−	12.4221i	−1.16857	−	1.16857i	−0.982545	−	0.186023i	$-0.940440\pi$
$113$	−12.4221	−	12.4221i	−1.16857	−	1.16857i	−0.186023	−	0.982545i	$-0.559560\pi$
$114$		0			0
$115$	7.05848	−	10.7439i	0.658207	−	1.00187i
$116$	−14.0665	−	10.8333i	−1.30605	−	1.00584i
$117$		0			0
$118$	−4.19393	+	4.77373i	−0.386082	+	0.439457i
$119$			11.3362i			1.03919i
$120$		0			0
$121$		−	1.29886i		−	0.118078i
$122$	7.16495	+	6.29472i	0.648684	+	0.569897i
$123$		0			0
$124$	−1.11771	−	8.60759i	−0.100374	−	0.772984i
$125$	−6.42685	−	9.14853i	−0.574835	−	0.818270i
$126$		0			0
$127$	7.35799	+	7.35799i	0.652916	+	0.652916i	0.953694	−	0.300778i	$-0.0972463\pi$
$127$	7.35799	+	7.35799i	0.652916	+	0.652916i	−0.300778	+	0.953694i	$0.597246\pi$
$128$	4.94097	+	10.1778i	0.436724	+	0.899596i
$129$		0			0
$130$	−5.54241	+	1.52615i	−0.486102	+	0.133852i
$131$	4.51593	+	4.51593i	0.394559	+	0.394559i	0.876309	−	0.481750i	$-0.159999\pi$
$131$	4.51593	+	4.51593i	0.394559	+	0.394559i	−0.481750	+	0.876309i	$0.659999\pi$
$132$		0			0
$133$			5.98560i			0.519018i
$134$	−0.987409	−	15.2720i	−0.0852991	−	1.31930i
$135$		0			0
$136$	−15.0372	−	10.1054i	−1.28943	−	0.866528i
$137$	2.55390	+	2.55390i	0.218194	+	0.218194i	0.807737	−	0.589543i	$-0.200692\pi$
$137$	2.55390	+	2.55390i	0.218194	+	0.218194i	−0.589543	+	0.807737i	$0.700692\pi$
$138$		0			0
$139$	2.95289	+	2.95289i	0.250461	+	0.250461i	0.821159	−	0.570699i	$-0.193328\pi$
$139$	2.95289	+	2.95289i	0.250461	+	0.250461i	−0.570699	+	0.821159i	$0.693328\pi$
$140$	−7.11944	−	3.45784i	−0.601703	−	0.292241i
$141$		0			0
$142$	−0.460420	−	7.12122i	−0.0386376	−	0.597600i
$143$	4.50803	−	4.50803i	0.376980	−	0.376980i
$144$		0			0
$145$	−10.8994	+	16.5903i	−0.905147	+	1.37775i
$146$	−4.40172	−	3.86710i	−0.364289	−	0.320044i
$147$		0			0
$148$	5.79189	−	0.752089i	0.476090	−	0.0618214i
$149$	−15.1940	+	15.1940i	−1.24474	+	1.24474i	−0.286728	+	0.958012i	$0.592568\pi$
$149$	−15.1940	+	15.1940i	−1.24474	+	1.24474i	−0.958012	+	0.286728i	$0.907432\pi$
$150$		0			0
$151$	−2.66712			−0.217047			−0.108523	−	0.994094i	$-0.534612\pi$
$151$	−2.66712			−0.217047			−0.108523	+	0.994094i	$0.534612\pi$
$152$	−7.93971	−	5.33569i	−0.643996	−	0.432782i
$153$		0			0
$154$	8.75918	−	0.566322i	0.705835	−	0.0456355i
$155$	−9.50288	+	1.96726i	−0.763290	+	0.158014i
$156$		0			0
$157$			3.79875i			0.303173i	0.988444	+	0.151587i	$0.0484383\pi$
$157$			3.79875i			0.303173i	−0.988444	+	0.151587i	$0.951562\pi$
$158$	0.433611	+	6.70657i	0.0344963	+	0.533546i
$159$		0			0
$160$	10.9331	−	6.36132i	0.864341	−	0.502907i
$161$	−10.1745			−0.801860
$162$		0			0
$163$		−	20.0096i		−	1.56727i	−0.621219	−	0.783637i	$-0.713362\pi$
$163$		−	20.0096i		−	1.56727i	0.621219	−	0.783637i	$-0.286638\pi$
$164$	1.09938	+	8.46642i	0.0858475	+	0.661117i
$165$		0			0
$166$	−21.6730	+	1.40126i	−1.68215	+	0.108759i
$167$	7.50240	−	7.50240i	0.580553	−	0.580553i	−0.354502	−	0.935055i	$-0.615350\pi$
$167$	7.50240	−	7.50240i	0.580553	−	0.580553i	0.935055	+	0.354502i	$0.115350\pi$
$168$		0			0
$169$	−9.69526			−0.745789
$170$	−10.0066	+	17.6114i	−0.767470	+	1.35073i
$171$		0			0
$172$	−20.6599	+	2.68274i	−1.57530	+	0.204557i
$173$	15.3776			1.16914			0.584568	−	0.811345i	$-0.301264\pi$
$173$	15.3776			1.16914			0.584568	+	0.811345i	$0.301264\pi$
$174$		0			0
$175$	−3.25866	+	8.22709i	−0.246332	+	0.621910i
$176$	−7.05691	+	12.1236i	−0.531934	+	0.913851i
$177$		0			0
$178$	0.360990	+	5.58335i	0.0270573	+	0.418490i
$179$	5.67467	−	5.67467i	0.424145	−	0.424145i	−0.462483	−	0.886628i	$-0.653041\pi$
$179$	5.67467	−	5.67467i	0.424145	−	0.424145i	0.886628	+	0.462483i	$0.153041\pi$
$180$		0			0
$181$	−0.760920	−	0.760920i	−0.0565587	−	0.0565587i	0.678262	−	0.734820i	$-0.262734\pi$
$181$	−0.760920	−	0.760920i	−0.0565587	−	0.0565587i	−0.734820	+	0.678262i	$0.762734\pi$
$182$	3.41817	+	3.00301i	0.253372	+	0.222598i
$183$		0			0
$184$	9.06973	−	13.4961i	0.668630	−	0.994946i
$185$	−1.32373	−	6.39431i	−0.0973229	−	0.470119i
$186$		0			0
$187$		−	22.4636i		−	1.64270i
$188$	0.336367	+	0.259051i	0.0245321	+	0.0188932i
$189$		0			0
$190$	−5.28353	+	9.29893i	−0.383308	+	0.674615i
$191$			15.1246i			1.09437i	0.837010	+	0.547187i	$0.184301\pi$
$191$			15.1246i			1.09437i	−0.837010	+	0.547187i	$0.815699\pi$
$192$		0			0
$193$	−7.66759	−	7.66759i	−0.551925	−	0.551925i	0.375071	−	0.926996i	$-0.377618\pi$
$193$	−7.66759	−	7.66759i	−0.551925	−	0.551925i	−0.926996	+	0.375071i	$0.877618\pi$
$194$	−3.70816	−	3.25778i	−0.266230	−	0.233895i
$195$		0			0
$196$	−0.996133	−	7.67128i	−0.0711523	−	0.547949i
$197$	25.5893			1.82316			0.911581	−	0.411120i	$-0.134862\pi$
$197$	25.5893			1.82316			0.911581	+	0.411120i	$0.134862\pi$
$198$		0			0
$199$		−	13.0408i		−	0.924440i	−0.886765	−	0.462220i	$-0.847053\pi$
$199$		−	13.0408i		−	0.924440i	0.886765	−	0.462220i	$-0.152947\pi$
$200$	−8.00814	−	11.6563i	−0.566261	−	0.824226i
$201$		0			0
$202$	−12.4095	+	14.1251i	−0.873130	+	0.993838i
$203$	15.7110			1.10270
$204$		0			0
$205$	9.34703	−	1.93500i	0.652825	−	0.135146i
$206$	5.00754	−	5.69983i	0.348892	−	0.397126i
$207$		0			0
$208$	−7.03043	+	1.85715i	−0.487472	+	0.128770i
$209$		−	11.8609i		−	0.820437i
$210$		0			0
$211$	−4.04713	−	4.04713i	−0.278616	−	0.278616i	0.553940	−	0.832556i	$-0.313124\pi$
$211$	−4.04713	−	4.04713i	−0.278616	−	0.278616i	−0.832556	+	0.553940i	$0.813124\pi$
$212$	−2.73969	−	21.0985i	−0.188162	−	1.44905i
$213$		0			0
$214$	17.1912	−	1.11149i	1.17517	−	0.0759801i
$215$	4.72182	+	22.8088i	0.322025	+	1.55555i
$216$		0			0
$217$	5.43112	+	5.43112i	0.368688	+	0.368688i
$218$	5.33795	−	6.07591i	0.361532	−	0.411513i
$219$		0			0
$220$	14.1077	+	6.85198i	0.951142	+	0.461960i
$221$	8.23382	−	8.23382i	0.553867	−	0.553867i
$222$		0			0
$223$	−6.94039	+	6.94039i	−0.464763	+	0.464763i	−0.900213	−	0.435450i	$-0.856589\pi$
$223$	−6.94039	+	6.94039i	−0.464763	+	0.464763i	0.435450	+	0.900213i	$0.356589\pi$
$224$	−8.95931	−	4.46764i	−0.598619	−	0.298507i
$225$		0			0
$226$	−16.3974	+	18.6643i	−1.09074	+	1.24153i
$227$	3.34643			0.222110			0.111055	−	0.993814i	$-0.464577\pi$
$227$	3.34643			0.222110			0.111055	+	0.993814i	$0.464577\pi$
$228$		0			0
$229$	−11.9644	+	11.9644i	−0.790629	+	0.790629i	−0.981596	−	0.190968i	$-0.938837\pi$
$229$	−11.9644	+	11.9644i	−0.790629	+	0.790629i	0.190968	+	0.981596i	$0.438837\pi$
$230$	−15.8065	−	8.98107i	−1.04225	−	0.592194i
$231$		0			0
$232$	−14.0051	+	20.8401i	−0.919480	+	1.36822i
$233$	−12.4324	+	12.4324i	−0.814474	+	0.814474i	−0.985301	−	0.170827i	$-0.945356\pi$
$233$	−12.4324	+	12.4324i	−0.814474	+	0.814474i	0.170827	+	0.985301i	$0.445356\pi$
$234$		0			0
$235$	0.260633	−	0.396716i	0.0170018	−	0.0258789i
$236$	7.11968	+	5.48317i	0.463452	+	0.356924i
$237$		0			0
$238$	15.9985	−	1.03438i	1.03703	−	0.0670487i
$239$	−24.7355			−1.60000			−0.800002	−	0.599997i	$-0.795168\pi$
$239$	−24.7355			−1.60000			−0.800002	+	0.599997i	$0.795168\pi$
$240$		0			0
$241$	17.1334			1.10366			0.551829	−	0.833957i	$-0.313930\pi$
$241$	17.1334			1.10366			0.551829	+	0.833957i	$0.313930\pi$
$242$	−1.83304	+	0.118515i	−0.117832	+	0.00761841i
$243$		0			0
$244$	8.22976	−	10.6860i	0.526857	−	0.684102i
$245$	−8.46918	+	1.75327i	−0.541076	+	0.112012i
$246$		0			0
$247$	4.34750	−	4.34750i	0.276625	−	0.276625i
$248$	−12.0456	+	2.36279i	−0.764898	+	0.150038i
$249$		0			0
$250$	−12.3246	+	9.90475i	−0.779476	+	0.626432i
$251$	21.3875	−	21.3875i	1.34997	−	1.34997i	0.464274	−	0.885692i	$-0.346315\pi$
$251$	21.3875	−	21.3875i	1.34997	−	1.34997i	0.885692	−	0.464274i	$-0.153685\pi$
$252$		0			0
$253$	20.1615			1.26754
$254$	9.71271	−	11.0555i	0.609430	−	0.693682i
$255$		0			0
$256$	13.9127	−	7.90170i	0.869544	−	0.493856i
$257$	17.3996	−	17.3996i	1.08536	−	1.08536i	0.0893560	−	0.996000i	$-0.471519\pi$
$257$	17.3996	−	17.3996i	1.08536	−	1.08536i	0.996000	−	0.0893560i	$-0.0284809\pi$
$258$		0			0
$259$	−3.65450	+	3.65450i	−0.227080	+	0.227080i
$260$	2.65952	+	7.68257i	0.164936	+	0.476453i
$261$		0			0
$262$	5.96113	−	6.78524i	0.368280	−	0.419193i
$263$	−8.76818	−	8.76818i	−0.540669	−	0.540669i	0.383056	−	0.923725i	$-0.374872\pi$
$263$	−8.76818	−	8.76818i	−0.540669	−	0.540669i	−0.923725	+	0.383056i	$0.874872\pi$
$264$		0			0
$265$	−23.2930	+	4.82206i	−1.43088	+	0.296217i
$266$	8.44728	−	0.546157i	0.517936	−	0.0334870i
$267$		0			0
$268$	−21.4628	+	2.78700i	−1.31105	+	0.170243i
$269$	14.1435	+	14.1435i	0.862347	+	0.862347i	0.991610	−	0.129263i	$-0.0412611\pi$
$269$	14.1435	+	14.1435i	0.862347	+	0.862347i	−0.129263	+	0.991610i	$0.541261\pi$
$270$		0			0
$271$		−	24.2463i		−	1.47286i	−0.676515	−	0.736429i	$-0.736510\pi$
$271$		−	24.2463i		−	1.47286i	0.676515	−	0.736429i	$-0.263490\pi$
$272$	−12.8893	+	22.1435i	−0.781529	+	1.34265i
$273$		0			0
$274$	3.37120	−	3.83727i	0.203662	−	0.231818i
$275$	6.45728	−	16.3026i	0.389389	−	0.983084i
$276$		0			0
$277$	0.247833			0.0148909			0.00744543	−	0.999972i	$-0.497630\pi$
$277$	0.247833			0.0148909			0.00744543	+	0.999972i	$0.497630\pi$
$278$	3.89788	−	4.43675i	0.233779	−	0.266099i
$279$		0			0
$280$	−4.23033	+	10.3629i	−0.252810	+	0.619304i
$281$			13.2279i			0.789109i	0.918872	+	0.394555i	$0.129101\pi$
$281$			13.2279i			0.789109i	−0.918872	+	0.394555i	$0.870899\pi$
$282$		0			0
$283$	−22.2111			−1.32031			−0.660157	−	0.751128i	$-0.729510\pi$
$283$	−22.2111			−1.32031			−0.660157	+	0.751128i	$0.729510\pi$
$284$	−10.0079	+	1.29955i	−0.593862	+	0.0771142i
$285$		0			0
$286$	−6.77336	−	5.95069i	−0.400517	−	0.351872i
$287$	−5.34205	−	5.34205i	−0.315331	−	0.315331i
$288$		0			0
$289$		−	24.0294i		−	1.41349i
$290$	24.4078	+	13.8682i	1.43328	+	0.814369i
$291$		0			0
$292$	−5.05588	+	6.56486i	−0.295873	+	0.384179i
$293$		−	2.93570i		−	0.171505i	−0.996316	−	0.0857526i	$-0.972671\pi$
$293$		−	2.93570i		−	0.171505i	0.996316	−	0.0857526i	$-0.0273295\pi$
$294$		0			0
$295$	5.51666	−	8.39704i	0.321192	−	0.488894i
$296$	−1.58988	−	8.10527i	−0.0924099	−	0.471110i
$297$		0			0
$298$	22.8291	+	20.0564i	1.32246	+	1.16184i
$299$	7.38999	+	7.38999i	0.427374	+	0.427374i
$300$		0			0
$301$	13.0358	−	13.0358i	0.751368	−	0.751368i
$302$	0.243361	+	3.76401i	0.0140039	+	0.216595i
$303$		0			0
$304$	−6.80563	+	11.6919i	−0.390329	+	0.670577i
$305$	−12.6032	−	8.28003i	−0.721659	−	0.474113i
$306$		0			0
$307$	20.2428			1.15532			0.577659	−	0.816278i	$-0.303966\pi$
$307$	20.2428			1.15532			0.577659	+	0.816278i	$0.303966\pi$
$308$	−1.59846	−	12.3099i	−0.0910809	−	0.701420i
$309$		0			0
$310$	3.64342	+	13.2316i	0.206933	+	0.751504i
$311$	14.0432			0.796315			0.398157	−	0.917317i	$-0.369650\pi$
$311$	14.0432			0.796315			0.398157	+	0.917317i	$0.369650\pi$
$312$		0			0
$313$	10.3861	−	10.3861i	0.587058	−	0.587058i	−0.349775	−	0.936834i	$-0.613742\pi$
$313$	10.3861	−	10.3861i	0.587058	−	0.587058i	0.936834	+	0.349775i	$0.113742\pi$
$314$	5.36105	−	0.346617i	0.302542	−	0.0195607i
$315$		0			0
$316$	9.42520	−	1.22388i	0.530209	−	0.0688488i
$317$			11.6769i			0.655839i	0.944706	+	0.327920i	$0.106347\pi$
$317$			11.6769i			0.655839i	−0.944706	+	0.327920i	$0.893653\pi$
$318$		0			0
$319$	−31.1325			−1.74309
$320$	−9.97512	−	14.8491i	−0.557626	−	0.830092i
$321$		0			0
$322$	0.928370	+	14.3589i	0.0517360	+	0.800190i
$323$		−	21.6637i		−	1.20540i
$324$		0			0
$325$	8.34241	−	3.60871i	0.462754	−	0.200175i
$326$	−28.2389	+	1.82578i	−1.56401	+	0.101121i
$327$		0			0
$328$	11.8481	−	2.32404i	0.654200	−	0.128324i
$329$	−0.375690			−0.0207125
$330$		0			0
$331$	−12.0411	+	12.0411i	−0.661841	+	0.661841i	−0.955814	−	0.293973i	$-0.905022\pi$
$331$	−12.0411	+	12.0411i	−0.661841	+	0.661841i	0.293973	+	0.955814i	$0.405022\pi$
$332$	3.95511	+	30.4586i	0.217065	+	1.67163i
$333$		0			0
$334$	−11.2725	−	9.90334i	−0.616801	−	0.541887i
$335$	4.90532	+	23.6952i	0.268006	+	1.29461i
$336$		0			0
$337$	−0.558895	+	0.558895i	−0.0304449	+	0.0304449i	−0.722165	−	0.691720i	$-0.756853\pi$
$337$	−0.558895	+	0.558895i	−0.0304449	+	0.0304449i	0.691720	+	0.722165i	$0.256853\pi$
$338$	0.884644	+	13.6826i	0.0481183	+	0.744235i
$339$		0			0
$340$	25.7675	+	12.5150i	1.39744	+	0.678722i
$341$	−10.7622	−	10.7622i	−0.582804	−	0.582804i
$342$		0			0
$343$	13.6004	+	13.6004i	0.734350	+	0.734350i
$344$	5.67117	+	28.9119i	0.305769	+	1.55882i
$345$		0			0
$346$	−1.40313	−	21.7019i	−0.0754326	−	1.16670i
$347$			0.0770157i			0.00413442i	0.999998	+	0.00206721i	$0.000658013\pi$
$347$			0.0770157i			0.00413442i	−0.999998	+	0.00206721i	$0.999342\pi$
$348$		0			0
$349$	15.0145	+	15.0145i	0.803708	+	0.803708i	0.983673	−	0.179965i	$-0.0575984\pi$
$349$	15.0145	+	15.0145i	0.803708	+	0.803708i	−0.179965	+	0.983673i	$0.557598\pi$
$350$	11.9080	+	3.84816i	0.636507	+	0.205693i
$351$		0			0
$352$	17.7536	+	8.85296i	0.946268	+	0.471864i
$353$	23.6193	+	23.6193i	1.25713	+	1.25713i	0.952459	+	0.304668i	$0.0985456\pi$
$353$	23.6193	+	23.6193i	1.25713	+	1.25713i	0.304668	+	0.952459i	$0.401454\pi$
$354$		0			0
$355$	2.28731	+	11.0489i	0.121398	+	0.586413i
$356$	7.84666	−	1.01891i	0.415872	−	0.0540019i
$357$		0			0
$358$	−8.52627	−	7.49069i	−0.450627	−	0.395896i
$359$		−	9.21900i		−	0.486560i	−0.969956	−	0.243280i	$-0.921777\pi$
$359$		−	9.21900i		−	0.486560i	0.969956	−	0.243280i	$-0.0782234\pi$
$360$		0			0
$361$			7.56142i			0.397970i
$362$	−1.00443	+	1.14329i	−0.0527917	+	0.0600900i
$363$		0			0
$364$	3.92616	−	5.09796i	0.205787	−	0.267206i
$365$	7.74268	+	5.08676i	0.405270	+	0.266253i
$366$		0			0
$367$	3.46414	+	3.46414i	0.180827	+	0.180827i	0.791716	−	0.610889i	$-0.209188\pi$
$367$	3.46414	+	3.46414i	0.180827	+	0.180827i	−0.610889	+	0.791716i	$0.709188\pi$
$368$	−19.8742	−	11.5684i	−1.03601	−	0.603042i
$369$		0			0
$370$	−8.90330	+	2.45159i	−0.462860	+	0.127452i
$371$	13.3125	+	13.3125i	0.691150	+	0.691150i
$372$		0			0
$373$			19.1403i			0.991049i	0.868594	+	0.495524i	$0.165024\pi$
$373$			19.1403i			0.991049i	−0.868594	+	0.495524i	$0.834976\pi$
$374$	−31.7022	+	2.04970i	−1.63928	+	0.105987i
$375$		0			0
$376$	0.334898	−	0.498341i	0.0172711	−	0.0257000i
$377$	−11.4113	−	11.4113i	−0.587713	−	0.587713i
$378$		0			0
$379$	19.8802	+	19.8802i	1.02118	+	1.02118i	0.999771	+	0.0214054i	$0.00681406\pi$
$379$	19.8802	+	19.8802i	1.02118	+	1.02118i	0.0214054	+	0.999771i	$0.493186\pi$
$380$	13.6054	+	6.60799i	0.697941	+	0.338983i
$381$		0			0
$382$	21.3448	−	1.38004i	1.09209	−	0.0706090i
$383$	−8.84171	+	8.84171i	−0.451790	+	0.451790i	−0.895948	−	0.444158i	$-0.853503\pi$
$383$	−8.84171	+	8.84171i	−0.451790	+	0.451790i	0.444158	+	0.895948i	$0.353503\pi$
$384$		0			0
$385$	−13.5902	+	2.81342i	−0.692623	+	0.143385i
$386$	−10.1214	+	11.5206i	−0.515165	+	0.586385i
$387$		0			0
$388$	−4.25924	+	5.53046i	−0.216230	+	0.280766i
$389$	−1.06003	+	1.06003i	−0.0537454	+	0.0537454i	−0.733469	−	0.679723i	$-0.762100\pi$
$389$	−1.06003	+	1.06003i	−0.0537454	+	0.0537454i	0.679723	+	0.733469i	$0.262100\pi$
$390$		0			0
$391$	36.8245			1.86230
$392$	−10.7353	+	2.10578i	−0.542216	+	0.106358i
$393$		0			0
$394$	−2.33490	−	36.1133i	−0.117630	−	1.81936i
$395$	−2.15413	−	10.4055i	−0.108386	−	0.523559i
$396$		0			0
$397$		−	4.35137i		−	0.218389i	−0.994020	−	0.109194i	$-0.965173\pi$
$397$		−	4.35137i		−	0.218389i	0.994020	−	0.109194i	$-0.0348271\pi$
$398$	−18.4041	+	1.18991i	−0.922514	+	0.0596449i
$399$		0			0
$400$	−15.7195	+	12.3652i	−0.785973	+	0.618260i
$401$	21.1334			1.05535			0.527676	−	0.849445i	$-0.323063\pi$
$401$	21.1334			1.05535			0.527676	+	0.849445i	$0.323063\pi$
$402$		0			0
$403$		−	7.88954i		−	0.393006i
$404$	21.0666	+	16.2243i	1.04810	+	0.807188i
$405$		0			0
$406$	−1.43355	−	22.1724i	−0.0711459	−	1.10040i
$407$	7.24167	−	7.24167i	0.358956	−	0.358956i
$408$		0			0
$409$	−0.142915			−0.00706670			−0.00353335	−	0.999994i	$-0.501125\pi$
$409$	−0.142915			−0.00706670			−0.00353335	+	0.999994i	$0.501125\pi$
$410$	−3.58367	−	13.0146i	−0.176985	−	0.642745i
$411$		0			0
$412$	−8.50089	−	6.54690i	−0.418809	−	0.322543i
$413$	−7.95200			−0.391292
$414$		0			0
$415$	33.6266	−	6.96130i	1.65067	−	0.341717i
$416$	3.26242	+	9.75235i	0.159953	+	0.478149i
$417$		0			0
$418$	−16.7389	+	1.08225i	−0.818728	+	0.0529346i
$419$	3.14176	−	3.14176i	0.153485	−	0.153485i	−0.626187	−	0.779673i	$-0.715386\pi$
$419$	3.14176	−	3.14176i	0.153485	−	0.153485i	0.779673	+	0.626187i	$0.215386\pi$
$420$		0			0
$421$	25.8144	+	25.8144i	1.25812	+	1.25812i	0.951992	+	0.306124i	$0.0990322\pi$
$421$	25.8144	+	25.8144i	1.25812	+	1.25812i	0.306124	+	0.951992i	$0.400968\pi$
$422$	−5.34231	+	6.08087i	−0.260059	+	0.296012i
$423$		0			0
$424$	−29.5256	+	5.79156i	−1.43389	+	0.281263i
$425$	11.7941	−	29.7764i	0.572098	−	1.44437i
$426$		0			0
$427$			11.9353i			0.577588i
$428$	−3.13723	−	24.1600i	−0.151644	−	1.16782i
$429$		0			0
$430$	31.7584	−	8.74494i	1.53153	−	0.421718i
$431$			6.52096i			0.314104i	0.987590	+	0.157052i	$0.0501990\pi$
$431$			6.52096i			0.314104i	−0.987590	+	0.157052i	$0.949801\pi$
$432$		0			0
$433$	−25.1367	−	25.1367i	−1.20799	−	1.20799i	−0.971677	−	0.236314i	$-0.924061\pi$
$433$	−25.1367	−	25.1367i	−1.20799	−	1.20799i	−0.236314	−	0.971677i	$-0.575939\pi$
$434$	7.16920	−	8.16032i	0.344132	−	0.391708i
$435$		0			0
$436$	−9.06180	−	6.97888i	−0.433981	−	0.334228i
$437$	19.4436			0.930112
$438$		0			0
$439$			39.1063i			1.86644i	0.359305	+	0.933220i	$0.383014\pi$
$439$			39.1063i			1.86644i	−0.359305	+	0.933220i	$0.616986\pi$
$440$	8.38271	−	20.5350i	0.399630	−	0.978966i
$441$		0			0
$442$	−12.3714	−	10.8688i	−0.588448	−	0.516977i
$443$	20.4880			0.973414			0.486707	−	0.873565i	$-0.338198\pi$
$443$	20.4880			0.973414			0.486707	+	0.873565i	$0.338198\pi$
$444$		0			0
$445$	−1.79335	−	8.66281i	−0.0850131	−	0.410656i
$446$	10.4280	+	9.16147i	0.493781	+	0.433808i
$447$		0			0
$448$	−5.48754	+	13.0516i	−0.259262	+	0.616632i
$449$		−	4.34217i		−	0.204920i	−0.994737	−	0.102460i	$-0.967329\pi$
$449$		−	4.34217i		−	0.204920i	0.994737	−	0.102460i	$-0.0326713\pi$
$450$		0			0
$451$	10.5857	+	10.5857i	0.498460	+	0.498460i
$452$	27.8365	+	21.4381i	1.30932	+	1.00836i
$453$		0			0
$454$	−0.305345	−	4.72271i	−0.0143306	−	0.221648i
$455$	−6.01260	−	3.95014i	−0.281875	−	0.185185i
$456$		0			0
$457$	14.7916	+	14.7916i	0.691921	+	0.691921i	0.962654	−	0.270733i	$-0.0872661\pi$
$457$	14.7916	+	14.7916i	0.691921	+	0.691921i	−0.270733	+	0.962654i	$0.587266\pi$
$458$	17.9766	+	15.7932i	0.839993	+	0.737970i
$459$		0			0
$460$	−11.2324	+	23.1267i	−0.523714	+	1.07829i
$461$	15.0255	−	15.0255i	0.699809	−	0.699809i	−0.264561	−	0.964369i	$-0.585227\pi$
$461$	15.0255	−	15.0255i	0.699809	−	0.699809i	0.964369	+	0.264561i	$0.0852269\pi$
$462$		0			0
$463$	6.10691	−	6.10691i	0.283812	−	0.283812i	−0.550815	−	0.834627i	$-0.685683\pi$
$463$	6.10691	−	6.10691i	0.283812	−	0.283812i	0.834627	+	0.550815i	$0.185683\pi$
$464$	30.6889	+	17.8634i	1.42470	+	0.829287i
$465$		0			0
$466$	18.6798	+	16.4110i	0.865327	+	0.760227i
$467$	−23.9704			−1.10922			−0.554610	−	0.832111i	$-0.687132\pi$
$467$	−23.9704			−1.10922			−0.554610	+	0.832111i	$0.687132\pi$
$468$		0			0
$469$	13.5424	−	13.5424i	0.625328	−	0.625328i
$470$	−0.583653	−	0.331624i	−0.0269219	−	0.0152967i
$471$		0			0
$472$	7.08858	−	10.5481i	0.326278	−	0.485515i
$473$	−25.8313	+	25.8313i	−1.18773	+	1.18773i
$474$		0			0
$475$	6.22735	−	15.7221i	0.285730	−	0.721380i
$476$	−2.91956	−	22.4837i	−0.133818	−	1.03054i
$477$		0			0
$478$	2.25699	+	34.9083i	0.103232	+	1.59667i
$479$	−36.1197			−1.65035			−0.825176	−	0.564876i	$-0.808924\pi$
$479$	−36.1197			−1.65035			−0.825176	+	0.564876i	$0.808924\pi$
$480$		0			0
$481$	5.30872			0.242057
$482$	−1.56334	−	24.1798i	−0.0712080	−	1.10136i
$483$		0			0
$484$	0.334512	+	2.57609i	0.0152051	+	0.117095i
$485$	6.52269	+	4.28526i	0.296180	+	0.194583i
$486$		0			0
$487$	−25.3967	+	25.3967i	−1.15083	+	1.15083i	−0.164447	+	0.986386i	$0.552584\pi$
$487$	−25.3967	+	25.3967i	−1.15083	+	1.15083i	−0.986386	+	0.164447i	$0.947416\pi$
$488$	−15.8318	−	10.6393i	−0.716670	−	0.481621i
$489$		0			0
$490$	3.24710	+	11.7923i	0.146689	+	0.532722i
$491$	−6.18543	+	6.18543i	−0.279145	+	0.279145i	−0.832768	−	0.553623i	$-0.813245\pi$
$491$	−6.18543	+	6.18543i	−0.279145	+	0.279145i	0.553623	+	0.832768i	$0.313245\pi$
$492$		0			0
$493$	−56.8629			−2.56098
$494$	−6.53218	−	5.73880i	−0.293897	−	0.258201i
$495$		0			0
$496$	4.43364	+	16.7840i	0.199076	+	0.753624i
$497$	6.31469	−	6.31469i	0.283253	−	0.283253i
$498$		0			0
$499$	−25.3089	+	25.3089i	−1.13298	+	1.13298i	−0.143306	+	0.989678i	$0.545773\pi$
$499$	−25.3089	+	25.3089i	−1.13298	+	1.13298i	−0.989678	+	0.143306i	$0.954227\pi$
$500$	15.1028	+	16.4895i	0.675418	+	0.737435i
$501$		0			0
$502$	−32.1349	−	28.2319i	−1.43425	−	1.26005i
$503$	−1.94744	−	1.94744i	−0.0868322	−	0.0868322i	0.662357	−	0.749189i	$-0.269556\pi$
$503$	−1.94744	−	1.94744i	−0.0868322	−	0.0868322i	−0.749189	+	0.662357i	$0.769556\pi$
$504$		0			0
$505$	16.3234	−	24.8462i	0.726381	−	1.10564i
$506$	−1.83963	−	28.4532i	−0.0817817	−	1.26490i
$507$		0			0
$508$	−16.4885	−	12.6985i	−0.731557	−	0.563403i
$509$	−17.9336	−	17.9336i	−0.794891	−	0.794891i	0.187394	−	0.982285i	$-0.439996\pi$
$509$	−17.9336	−	17.9336i	−0.794891	−	0.794891i	−0.982285	+	0.187394i	$0.939996\pi$
$510$		0			0
$511$		−	7.33232i		−	0.324363i
$512$	−12.4209	−	18.9135i	−0.548930	−	0.835868i
$513$		0			0
$514$	−26.1431	−	22.9678i	−1.15312	−	1.01307i
$515$	−6.58688	+	10.0261i	−0.290253	+	0.441801i
$516$		0			0
$517$	0.744459			0.0327413
$518$	5.49093	+	4.82402i	0.241258	+	0.211955i
$519$		0			0
$520$	10.5995	−	4.45429i	0.464818	−	0.195333i
$521$			11.3666i			0.497981i	0.968506	+	0.248990i	$0.0800988\pi$
$521$			11.3666i			0.497981i	−0.968506	+	0.248990i	$0.919901\pi$
$522$		0			0
$523$	19.1692			0.838209			0.419104	−	0.907938i	$-0.362344\pi$
$523$	19.1692			0.838209			0.419104	+	0.907938i	$0.362344\pi$
$524$	−10.1197	−	7.79362i	−0.442081	−	0.340466i
$525$		0			0
$526$	−11.5742	+	13.1743i	−0.504659	+	0.574427i
$527$	−19.6569	−	19.6569i	−0.856268	−	0.856268i
$528$		0			0
$529$			10.0506i			0.436983i
$530$	8.93058	+	32.4326i	0.387919	+	1.40878i
$531$		0			0
$532$	−1.54155	−	11.8715i	−0.0668345	−	0.514696i
$533$			7.76015i			0.336129i
$534$		0			0
$535$	−26.6729	+	5.52176i	−1.15317	+	0.238726i
$536$	5.89157	+	30.0355i	0.254477	+	1.29733i
$537$		0			0
$538$	18.6698	−	21.2509i	0.804912	−	0.916189i
$539$	−9.59149	−	9.59149i	−0.413135	−	0.413135i
$540$		0			0
$541$	−4.06490	+	4.06490i	−0.174764	+	0.174764i	−0.789069	−	0.614305i	$-0.789436\pi$
$541$	−4.06490	+	4.06490i	−0.174764	+	0.174764i	0.614305	+	0.789069i	$0.289436\pi$
$542$	−34.2180	+	2.21236i	−1.46979	+	0.0950288i
$543$		0			0
$544$	32.4265	+	16.1698i	1.39028	+	0.693273i
$545$	−7.02150	+	10.6876i	−0.300768	+	0.457806i
$546$		0			0
$547$	−28.7783			−1.23047			−0.615235	−	0.788344i	$-0.710939\pi$
$547$	−28.7783			−1.23047			−0.615235	+	0.788344i	$0.710939\pi$
$548$	−5.72301	−	4.40754i	−0.244475	−	0.188281i
$549$		0			0
$550$	−23.5965	−	7.62542i	−1.00616	−	0.325149i
$551$	−30.0239			−1.27906
$552$		0			0
$553$	−5.94700	+	5.94700i	−0.252892	+	0.252892i
$554$	−0.0226136	−	0.349759i	−0.000960759	−	0.0148598i
$555$		0			0
$556$	−6.61710	−	5.09611i	−0.280628	−	0.216123i
$557$			8.96058i			0.379672i	0.981816	+	0.189836i	$0.0607956\pi$
$557$			8.96058i			0.379672i	−0.981816	+	0.189836i	$0.939204\pi$
$558$		0			0
$559$	−18.9364			−0.800926
$560$	15.0109	+	5.02455i	0.634325	+	0.212326i
$561$		0			0
$562$	18.6681	−	1.20698i	0.787465	−	0.0509133i
$563$		−	9.62086i		−	0.405471i	−0.979234	−	0.202736i	$-0.935017\pi$
$563$		−	9.62086i		−	0.405471i	0.979234	−	0.202736i	$-0.0649832\pi$
$564$		0			0
$565$	21.5690	−	32.8307i	0.907414	−	1.38120i
$566$	2.02665	+	31.3458i	0.0851866	+	1.31756i
$567$		0			0
$568$	2.74719	+	14.0053i	0.115270	+	0.587649i
$569$	26.7360			1.12083			0.560415	−	0.828212i	$-0.310642\pi$
$569$	26.7360			1.12083			0.560415	+	0.828212i	$0.310642\pi$
$570$		0			0
$571$	−28.0517	+	28.0517i	−1.17393	+	1.17393i	−0.192661	+	0.981265i	$0.561712\pi$
$571$	−28.0517	+	28.0517i	−1.17393	+	1.17393i	−0.981265	+	0.192661i	$0.938288\pi$
$572$	−7.77998	+	10.1020i	−0.325297	+	0.422386i
$573$		0			0
$574$	−7.05162	+	8.02649i	−0.294329	+	0.335019i
$575$	26.7248	+	10.5854i	1.11450	+	0.441441i
$576$		0			0
$577$	17.8580	−	17.8580i	0.743437	−	0.743437i	−0.229801	−	0.973238i	$-0.573808\pi$
$577$	17.8580	−	17.8580i	0.743437	−	0.743437i	0.973238	+	0.229801i	$0.0738075\pi$
$578$	−33.9119	+	2.19256i	−1.41055	+	0.0911986i
$579$		0			0
$580$	17.3446	−	35.7113i	0.720197	−	1.48283i
$581$	−19.2184	−	19.2184i	−0.797314	−	0.797314i
$582$		0			0
$583$	−26.3797	−	26.3797i	−1.09254	−	1.09254i
$584$	9.72609	+	6.53619i	0.402469	+	0.270469i
$585$		0			0
$586$	−4.14305	+	0.267868i	−0.171148	+	0.0110655i
$587$		−	1.40264i		−	0.0578931i	−0.999581	−	0.0289465i	$-0.990785\pi$
$587$		−	1.40264i		−	0.0578931i	0.999581	−	0.0289465i	$-0.00921525\pi$
$588$		0			0
$589$	−10.3790	−	10.3790i	−0.427657	−	0.427657i
$590$	−12.3538	−	7.01929i	−0.508599	−	0.288980i
$591$		0			0
$592$	−11.2936	+	2.98331i	−0.464166	+	0.122613i
$593$	−5.81813	−	5.81813i	−0.238922	−	0.238922i	0.577482	−	0.816404i	$-0.304035\pi$
$593$	−5.81813	−	5.81813i	−0.238922	−	0.238922i	−0.816404	+	0.577482i	$0.804035\pi$
$594$		0			0
$595$	−24.8223	+	5.13865i	−1.01762	+	0.210664i
$596$	26.2219	−	34.0481i	1.07409	−	1.39466i
$597$		0			0
$598$	9.75495	−	11.1035i	0.398909	−	0.454058i
$599$			13.1194i			0.536045i	0.963413	+	0.268023i	$0.0863702\pi$
$599$			13.1194i			0.536045i	−0.963413	+	0.268023i	$0.913630\pi$
$600$		0			0
$601$		−	29.0758i		−	1.18603i	−0.805193	−	0.593013i	$-0.797938\pi$
$601$		−	29.0758i		−	1.18603i	0.805193	−	0.593013i	$-0.202062\pi$
$602$	−19.5864	−	17.2075i	−0.798281	−	0.701325i
$603$		0			0
$604$	5.28982	−	0.686895i	0.215240	−	0.0279494i
$605$	2.84404	−	0.588766i	0.115627	−	0.0239367i
$606$		0			0
$607$	−8.32107	−	8.32107i	−0.337742	−	0.337742i	0.517775	−	0.855517i	$-0.326760\pi$
$607$	−8.32107	−	8.32107i	−0.337742	−	0.337742i	−0.855517	+	0.517775i	$0.826760\pi$
$608$	17.1214	+	8.53773i	0.694364	+	0.346250i
$609$		0			0
$610$	−10.5353	+	18.5420i	−0.426564	+	0.750745i
$611$	0.272874	+	0.272874i	0.0110393	+	0.0110393i
$612$		0			0
$613$			17.2991i			0.698705i	0.936991	+	0.349353i	$0.113599\pi$
$613$			17.2991i			0.698705i	−0.936991	+	0.349353i	$0.886401\pi$
$614$	−1.84706	−	28.5680i	−0.0745411	−	1.15291i
$615$		0			0
$616$	−17.2267	+	3.37907i	−0.694082	+	0.136147i
$617$	15.9755	+	15.9755i	0.643149	+	0.643149i	0.951328	−	0.308179i	$-0.0997197\pi$
$617$	15.9755	+	15.9755i	0.643149	+	0.643149i	−0.308179	+	0.951328i	$0.599720\pi$
$618$		0			0
$619$	7.13212	+	7.13212i	0.286664	+	0.286664i	0.835760	−	0.549096i	$-0.185028\pi$
$619$	7.13212	+	7.13212i	0.286664	+	0.286664i	−0.549096	+	0.835760i	$0.685028\pi$
$620$	18.3409	−	6.34916i	0.736587	−	0.254988i
$621$		0			0
$622$	−1.28137	−	19.8187i	−0.0513782	−	0.794656i
$623$	−4.95100	+	4.95100i	−0.198358	+	0.198358i
$624$		0			0
$625$	17.1187	−	18.2195i	0.684750	−	0.728778i
$626$	−15.6053	−	13.7099i	−0.623712	−	0.547958i
$627$		0			0
$628$	−0.978339	−	7.53425i	−0.0390400	−	0.300649i
$629$	13.2268	−	13.2268i	0.527386	−	0.527386i
$630$		0			0
$631$	20.4868			0.815565			0.407782	−	0.913079i	$-0.366302\pi$
$631$	20.4868			0.815565			0.407782	+	0.913079i	$0.366302\pi$
$632$	−2.58723	−	13.1898i	−0.102914	−	0.524662i
$633$		0			0
$634$	16.4792	−	1.06546i	0.654473	−	0.0423147i
$635$	−12.7760	+	19.4467i	−0.507001	+	0.771718i
$636$		0			0
$637$		−	7.03133i		−	0.278592i
$638$	2.84069	+	43.9363i	0.112464	+	1.73945i
$639$		0			0
$640$	−20.0459	+	15.4325i	−0.792385	+	0.610022i
$641$	−0.884584			−0.0349390			−0.0174695	−	0.999847i	$-0.505561\pi$
$641$	−0.884584			−0.0349390			−0.0174695	+	0.999847i	$0.505561\pi$
$642$		0			0
$643$		−	5.29313i		−	0.208741i	−0.994539	−	0.104370i	$-0.966717\pi$
$643$		−	5.29313i		−	0.208741i	0.994539	−	0.104370i	$-0.0332827\pi$
$644$	20.1795	−	2.62035i	0.795184	−	0.103256i
$645$		0			0
$646$	−30.5733	+	1.97671i	−1.20289	+	0.0777726i
$647$	−9.15703	+	9.15703i	−0.360000	+	0.360000i	−0.863813	−	0.503813i	$-0.831930\pi$
$647$	−9.15703	+	9.15703i	−0.360000	+	0.360000i	0.503813	+	0.863813i	$0.331930\pi$
$648$		0			0
$649$	15.7575			0.618536
$650$	−5.85405	−	11.4441i	−0.229615	−	0.448874i
$651$		0			0
$652$	5.15332	+	39.6861i	0.201820	+	1.55423i
$653$	−7.81012			−0.305634			−0.152817	−	0.988255i	$-0.548834\pi$
$653$	−7.81012			−0.305634			−0.152817	+	0.988255i	$0.548834\pi$
$654$		0			0
$655$	−7.84122	+	11.9353i	−0.306382	+	0.466351i
$656$	−4.36092	−	16.5087i	−0.170265	−	0.644558i
$657$		0			0
$658$	0.0342799	+	0.530199i	0.00133637	+	0.0206693i
$659$	−4.73630	+	4.73630i	−0.184500	+	0.184500i	−0.793313	−	0.608813i	$-0.791646\pi$
$659$	−4.73630	+	4.73630i	−0.184500	+	0.184500i	0.608813	+	0.793313i	$0.291646\pi$
$660$		0			0
$661$	−19.8678	−	19.8678i	−0.772766	−	0.772766i	0.205823	−	0.978589i	$-0.434013\pi$
$661$	−19.8678	−	19.8678i	−0.772766	−	0.772766i	−0.978589	+	0.205823i	$0.934013\pi$
$662$	18.0920	+	15.8946i	0.703164	+	0.617760i
$663$		0			0
$664$	42.6243	−	8.36091i	1.65414	−	0.324466i
$665$	−13.1063	+	2.71324i	−0.508241	+	0.105215i
$666$		0			0
$667$		−	51.0354i		−	1.97610i
$668$	−12.9477	+	16.8121i	−0.500961	+	0.650478i
$669$		0			0
$670$	32.9927	−	9.08479i	1.27462	−	0.350976i
$671$		−	23.6506i		−	0.913023i
$672$		0			0
$673$	−15.4993	−	15.4993i	−0.597455	−	0.597455i	0.342180	−	0.939635i	$-0.388835\pi$
$673$	−15.4993	−	15.4993i	−0.597455	−	0.597455i	−0.939635	+	0.342180i	$0.888835\pi$
$674$	0.839746	+	0.737753i	0.0323458	+	0.0284172i
$675$		0			0
$676$	19.2291	−	2.49694i	0.739580	−	0.0960361i
$677$	4.91631			0.188949			0.0944745	−	0.995527i	$-0.469883\pi$
$677$	4.91631			0.188949			0.0944745	+	0.995527i	$0.469883\pi$
$678$		0			0
$679$		−	6.17699i		−	0.237051i
$680$	15.3109	−	37.5067i	0.587145	−	1.43832i
$681$		0			0
$682$	−14.2063	+	16.1703i	−0.543988	+	0.619193i
$683$	38.8999			1.48846			0.744231	−	0.667922i	$-0.232816\pi$
$683$	38.8999			1.48846			0.744231	+	0.667922i	$0.232816\pi$
$684$		0			0
$685$	−4.43446	+	6.74979i	−0.169432	+	0.257896i
$686$	17.9528	−	20.4347i	0.685440	−	0.780200i
$687$		0			0
$688$	40.2849	−	10.6416i	1.53585	−	0.405707i
$689$		−	19.3384i		−	0.736735i
$690$		0			0
$691$	10.5822	+	10.5822i	0.402567	+	0.402567i	0.879137	−	0.476570i	$-0.158120\pi$
$691$	10.5822	+	10.5822i	0.402567	+	0.402567i	−0.476570	+	0.879137i	$0.658120\pi$
$692$	−30.4991	+	3.96037i	−1.15940	+	0.150551i
$693$		0			0
$694$	0.108690	−	0.00702730i	0.00412580	−	0.000266753i
$695$	−5.12724	+	7.80429i	−0.194487	+	0.296034i
$696$		0			0
$697$	19.3345	+	19.3345i	0.732347	+	0.732347i
$698$	19.8195	−	22.5595i	0.750178	−	0.853889i
$699$		0			0
$700$	4.34424	−	17.1564i	0.164197	−	0.648452i
$701$	−30.4758	+	30.4758i	−1.15106	+	1.15106i	−0.164715	+	0.986341i	$0.552671\pi$
$701$	−30.4758	+	30.4758i	−1.15106	+	1.15106i	−0.986341	+	0.164715i	$0.947329\pi$
$702$		0			0
$703$	6.98380	−	6.98380i	0.263399	−	0.263399i
$704$	10.8740	−	25.8628i	0.409828	−	0.974741i
$705$		0			0
$706$	31.1780	−	35.4882i	1.17340	−	1.33562i
$707$	−23.5294			−0.884913
$708$		0			0
$709$	−14.5515	+	14.5515i	−0.546493	+	0.546493i	−0.925425	−	0.378932i	$-0.876291\pi$
$709$	−14.5515	+	14.5515i	−0.546493	+	0.546493i	0.378932	+	0.925425i	$0.376291\pi$
$710$	15.3842	−	4.23616i	0.577359	−	0.158980i
$711$		0			0
$712$	−2.15392	−	10.9808i	−0.0807215	−	0.411522i
$713$	17.6424	−	17.6424i	0.660713	−	0.660713i
$714$		0			0
$715$	11.9144	+	7.82749i	0.445574	+	0.292732i
$716$	−9.79339	+	12.7163i	−0.365996	+	0.475231i
$717$		0			0
$718$	−13.0105	+	0.841188i	−0.485546	+	0.0313929i
$719$	31.9412			1.19120			0.595602	−	0.803279i	$-0.296913\pi$
$719$	31.9412			1.19120			0.595602	+	0.803279i	$0.296913\pi$
$720$		0			0
$721$	9.49468			0.353600
$722$	10.6712	−	0.689942i	0.397140	−	0.0256770i
$723$		0			0
$724$	1.70514	+	1.31320i	0.0633710	+	0.0488047i
$725$	−41.2673	−	16.3455i	−1.53263	−	0.607058i
$726$		0			0
$727$	−32.0532	+	32.0532i	−1.18879	+	1.18879i	−0.211384	+	0.977403i	$0.567797\pi$
$727$	−32.0532	+	32.0532i	−1.18879	+	1.18879i	−0.977403	+	0.211384i	$0.932203\pi$
$728$	−7.55283	−	5.07569i	−0.279926	−	0.188118i
$729$		0			0
$730$	6.47229	−	11.3911i	0.239550	−	0.421604i
$731$	−47.1804	+	47.1804i	−1.74503	+	1.74503i
$732$		0			0
$733$	24.7535			0.914293			0.457146	−	0.889391i	$-0.348872\pi$
$733$	24.7535			0.914293			0.457146	+	0.889391i	$0.348872\pi$
$734$	4.57274	−	5.20491i	0.168783	−	0.192117i
$735$		0			0
$736$	−14.5126	+	29.1033i	−0.534942	+	1.07276i
$737$	−26.8352	+	26.8352i	−0.988488	+	0.988488i
$738$		0			0
$739$	17.6246	−	17.6246i	0.648333	−	0.648333i	−0.304257	−	0.952590i	$-0.598408\pi$
$739$	17.6246	−	17.6246i	0.648333	−	0.648333i	0.952590	+	0.304257i	$0.0984081\pi$
$740$	4.27223	+	12.3412i	0.157050	+	0.453673i
$741$		0			0
$742$	17.5728	−	20.0022i	0.645117	−	0.734303i
$743$	4.45488	+	4.45488i	0.163434	+	0.163434i	0.784086	−	0.620652i	$-0.213132\pi$
$743$	4.45488	+	4.45488i	0.163434	+	0.163434i	−0.620652	+	0.784086i	$0.713132\pi$
$744$		0			0
$745$	−40.1567	−	26.3820i	−1.47123	−	0.966563i
$746$	27.0121	−	1.74646i	0.988984	−	0.0639424i
$747$		0			0
$748$	5.78533	+	44.5532i	0.211533	+	1.62903i
$749$	15.2442	+	15.2442i	0.557010	+	0.557010i
$750$		0			0
$751$		−	14.9291i		−	0.544770i	−0.962188	−	0.272385i	$-0.912188\pi$
$751$		−	14.9291i		−	0.544770i	0.962188	−	0.272385i	$-0.0878124\pi$
$752$	−0.733850	−	0.427160i	−0.0267608	−	0.0155769i
$753$		0			0
$754$	−15.0632	+	17.1456i	−0.548569	+	0.624407i
$755$	−1.20899	−	5.84002i	−0.0439995	−	0.212540i
$756$		0			0
$757$	43.9059			1.59579			0.797894	−	0.602798i	$-0.205947\pi$
$757$	43.9059			1.59579			0.797894	+	0.602798i	$0.205947\pi$
$758$	26.2423	−	29.8702i	0.953162	−	1.08493i
$759$		0			0
$760$	8.08422	−	19.8037i	0.293246	−	0.718357i
$761$			2.39481i			0.0868119i	0.999058	+	0.0434059i	$0.0138209\pi$
$761$			2.39481i			0.0868119i	−0.999058	+	0.0434059i	$0.986179\pi$
$762$		0			0
$763$	10.1212			0.366411
$764$	−3.89521	−	29.9973i	−0.140924	−	1.08526i
$765$		0			0
$766$	13.2848	+	11.6712i	0.479998	+	0.421699i
$767$	5.77575	+	5.77575i	0.208550	+	0.208550i
$768$		0			0
$769$		−	12.9527i		−	0.467085i	−0.972347	−	0.233542i	$-0.924968\pi$
$769$		−	12.9527i		−	0.467085i	0.972347	−	0.233542i	$-0.0750318\pi$
$770$	5.21053	+	18.9227i	0.187774	+	0.681928i
$771$		0			0
$772$	17.1822	+	13.2328i	0.618402	+	0.476258i
$773$			16.1575i			0.581143i	0.956853	+	0.290572i	$0.0938455\pi$
$773$			16.1575i			0.581143i	−0.956853	+	0.290572i	$0.906155\pi$
$774$		0			0
$775$	−8.61520	−	19.9161i	−0.309467	−	0.715409i
$776$	8.19359	+	5.50630i	0.294133	+	0.197665i
$777$		0			0
$778$	1.59270	+	1.39926i	0.0571011	+	0.0501658i
$779$	10.2087	+	10.2087i	0.365766	+	0.365766i
$780$		0			0
$781$	−12.5130	+	12.5130i	−0.447752	+	0.447752i
$782$	−3.36006	−	51.9693i	−0.120155	−	1.85842i
$783$		0			0
$784$	3.95136	+	14.9583i	0.141120	+	0.534224i
$785$	−8.31790	+	1.72195i	−0.296878	+	0.0614590i
$786$		0			0
$787$	−36.6090			−1.30497			−0.652485	−	0.757802i	$-0.726273\pi$
$787$	−36.6090			−1.30497			−0.652485	+	0.757802i	$0.726273\pi$
$788$	−50.7525	+	6.59033i	−1.80798	+	0.234771i
$789$		0			0
$790$	−14.4884	+	3.98950i	−0.515475	+	0.141940i
$791$	−31.0907			−1.10546
$792$		0			0
$793$	8.66891	−	8.66891i	0.307842	−	0.307842i
$794$	−6.14094	+	0.397041i	−0.217934	+	0.0140904i
$795$		0			0
$796$	3.35857	+	25.8645i	0.119041	+	0.916744i
$797$			3.96964i			0.140612i	0.997525	+	0.0703060i	$0.0223976\pi$
$797$			3.96964i			0.140612i	−0.997525	+	0.0703060i	$0.977602\pi$
$798$		0			0
$799$	1.35974			0.0481041
$800$	18.8849	+	21.0561i	0.667683	+	0.744446i
$801$		0			0
$802$	−1.92832	−	29.8249i	−0.0680914	−	1.05315i
$803$			14.5295i			0.512737i
$804$		0			0
$805$	−4.61202	−	22.2784i	−0.162552	−	0.785211i
$806$	−11.1342	+	0.719881i	−0.392187	+	0.0253567i
$807$		0			0
$808$	20.9746	−	31.2110i	0.737883	−	1.09800i
$809$	54.3213			1.90984			0.954918	−	0.296868i	$-0.0959423\pi$
$809$	54.3213			1.90984			0.954918	+	0.296868i	$0.0959423\pi$
$810$		0			0
$811$	−15.8944	+	15.8944i	−0.558127	+	0.558127i	−0.928774	−	0.370647i	$-0.879136\pi$
$811$	−15.8944	+	15.8944i	−0.558127	+	0.558127i	0.370647	+	0.928774i	$0.379136\pi$
$812$	−31.1604	+	4.04624i	−1.09351	+	0.141995i
$813$		0			0
$814$	−10.8807	−	9.55916i	−0.381368	−	0.335048i
$815$	43.8139	−	9.07024i	1.53473	−	0.317717i
$816$		0			0
$817$	−24.9115	+	24.9115i	−0.871544	+	0.871544i
$818$	0.0130403	+	0.201691i	0.000455943	+	0.00705197i
$819$		0			0
$820$	−18.0401	+	6.24503i	−0.629987	+	0.218086i
$821$	25.7579	+	25.7579i	0.898956	+	0.898956i	0.995344	−	0.0963881i	$-0.0307290\pi$
$821$	25.7579	+	25.7579i	0.898956	+	0.898956i	−0.0963881	+	0.995344i	$0.530729\pi$
$822$		0			0
$823$	−9.20810	−	9.20810i	−0.320974	−	0.320974i	0.528167	−	0.849141i	$-0.322880\pi$
$823$	−9.20810	−	9.20810i	−0.320974	−	0.320974i	−0.849141	+	0.528167i	$0.822880\pi$
$824$	−8.46376	+	12.5944i	−0.294849	+	0.438747i
$825$		0			0
$826$	0.725581	+	11.2224i	0.0252462	+	0.390477i
$827$		−	40.4359i		−	1.40609i	−0.711143	−	0.703047i	$-0.751822\pi$
$827$		−	40.4359i		−	1.40609i	0.711143	−	0.703047i	$-0.248178\pi$
$828$		0			0
$829$	18.6969	+	18.6969i	0.649370	+	0.649370i	0.952841	−	0.303471i	$-0.0981454\pi$
$829$	18.6969	+	18.6969i	0.649370	+	0.649370i	−0.303471	+	0.952841i	$0.598145\pi$
$830$	−12.8925	−	46.8210i	−0.447506	−	1.62518i
$831$		0			0
$832$	13.4655	−	5.49400i	0.466832	−	0.190470i
$833$	−17.5187	−	17.5187i	−0.606986	−	0.606986i
$834$		0			0
$835$	19.8284	+	13.0268i	0.686189	+	0.450810i
$836$	3.05469	+	23.5243i	0.105649	+	0.813606i
$837$		0			0
$838$	−4.72054	−	4.14720i	−0.163068	−	0.143262i
$839$			7.89003i			0.272394i	0.990682	+	0.136197i	$0.0434880\pi$
$839$			7.89003i			0.272394i	−0.990682	+	0.136197i	$0.956512\pi$
$840$		0			0
$841$			49.8068i			1.71748i
$842$	34.0755	−	38.7864i	1.17432	−	1.33667i
$843$		0			0
$844$	9.06919	+	6.98457i	0.312174	+	0.240419i
$845$	−4.39480	−	21.2291i	−0.151186	−	0.730304i
$846$		0			0
$847$	−1.62543	−	1.62543i	−0.0558506	−	0.0558506i
$848$	10.8675	+	41.1401i	0.373192	+	1.41276i
$849$		0			0
$850$	−43.0986	−	13.9277i	−1.47827	−	0.477715i
$851$	11.8712	+	11.8712i	0.406941	+	0.406941i
$852$		0			0
$853$			6.59967i			0.225968i	0.993597	+	0.112984i	$0.0360409\pi$
$853$			6.59967i			0.225968i	−0.993597	+	0.112984i	$0.963959\pi$
$854$	16.8438	−	1.08903i	0.576385	−	0.0372660i
$855$		0			0
$856$	−33.8099	+	6.63194i	−1.15560	+	0.226675i
$857$	−31.8196	−	31.8196i	−1.08694	−	1.08694i	−0.995842	−	0.0910940i	$-0.970964\pi$
$857$	−31.8196	−	31.8196i	−1.08694	−	1.08694i	−0.0910940	−	0.995842i	$-0.529036\pi$
$858$		0			0
$859$	−12.6182	−	12.6182i	−0.430527	−	0.430527i	0.458280	−	0.888808i	$-0.348466\pi$
$859$	−12.6182	−	12.6182i	−0.430527	−	0.430527i	−0.888808	+	0.458280i	$0.848466\pi$
$860$	−15.2392	−	44.0217i	−0.519654	−	1.50113i
$861$		0			0
$862$	9.20282	−	0.595006i	0.313449	−	0.0202660i
$863$	6.97660	−	6.97660i	0.237486	−	0.237486i	−0.578322	−	0.815808i	$-0.696292\pi$
$863$	6.97660	−	6.97660i	0.237486	−	0.237486i	0.815808	+	0.578322i	$0.196292\pi$
$864$		0			0
$865$	6.97056	+	33.6714i	0.237006	+	1.14486i
$866$	−33.1809	+	37.7681i	−1.12753	+	1.28341i
$867$		0			0
$868$	−12.1705	−	9.37306i	−0.413095	−	0.318142i
$869$	11.7844	−	11.7844i	0.399760	−	0.399760i
$870$		0			0
$871$	−19.6724			−0.666573
$872$	−9.02222	+	13.4254i	−0.305531	+	0.454642i
$873$		0			0
$874$	−1.77413	−	27.4401i	−0.0600108	−	0.928174i
$875$	−19.4915	−	3.40600i	−0.658933	−	0.115144i
$876$		0			0
$877$		−	22.3460i		−	0.754572i	−0.926097	−	0.377286i	$-0.876857\pi$
$877$		−	22.3460i		−	0.754572i	0.926097	−	0.377286i	$-0.123143\pi$
$878$	55.1894	−	3.56825i	1.86255	−	0.120423i
$879$		0			0
$880$	−29.7452	−	9.95653i	−1.00271	−	0.335635i
$881$	18.6246			0.627478			0.313739	−	0.949509i	$-0.398418\pi$
$881$	18.6246			0.627478			0.313739	+	0.949509i	$0.398418\pi$
$882$		0			0
$883$		−	8.08610i		−	0.272119i	−0.990701	−	0.136060i	$-0.956556\pi$
$883$		−	8.08610i		−	0.272119i	0.990701	−	0.136060i	$-0.0434438\pi$
$884$	−14.2100	+	18.4511i	−0.477933	+	0.620578i
$885$		0			0
$886$	−1.86943	−	28.9140i	−0.0628046	−	0.971386i
$887$	−10.9628	+	10.9628i	−0.368095	+	0.368095i	−0.866782	−	0.498687i	$-0.833816\pi$
$887$	−10.9628	+	10.9628i	−0.368095	+	0.368095i	0.498687	+	0.866782i	$0.333816\pi$
$888$		0			0
$889$	18.4160			0.617654
$890$	−12.0619	+	3.32134i	−0.404316	+	0.111332i
$891$		0			0
$892$	11.9778	−	15.5527i	0.401046	−	0.520742i
$893$	0.717950			0.0240253
$894$		0			0
$895$	14.9978	+	9.85320i	0.501321	+	0.329356i
$896$	18.9200	+	6.55348i	0.632074	+	0.218937i
$897$		0			0
$898$	−6.12797	+	0.396202i	−0.204493	+	0.0132214i
$899$	−27.2426	+	27.2426i	−0.908593	+	0.908593i
$900$		0			0
$901$	−48.1820	−	48.1820i	−1.60518	−	1.60518i
$902$	13.9733	−	15.9051i	0.465261	−	0.529582i
$903$		0			0
$904$	27.7149	−	41.2408i	0.921783	−	1.37165i
$905$	1.32122	−	2.01106i	0.0439189	−	0.0668499i
$906$		0			0
$907$			8.71157i			0.289263i	0.989486	+	0.144631i	$0.0461997\pi$
$907$			8.71157i			0.289263i	−0.989486	+	0.144631i	$0.953800\pi$
$908$	−6.63714	+	0.861848i	−0.220261	+	0.0286014i
$909$		0			0
$910$	−5.02608	+	8.84581i	−0.166613	+	0.293236i
$911$			2.71760i			0.0900381i	0.998986	+	0.0450190i	$0.0143348\pi$
$911$			2.71760i			0.0900381i	−0.998986	+	0.0450190i	$0.985665\pi$
$912$		0			0
$913$	38.0827	+	38.0827i	1.26035	+	1.26035i
$914$	19.5252	−	22.2245i	0.645837	−	0.735122i
$915$		0			0
$916$	20.6482	−	26.8109i	0.682236	−	0.885856i
$917$	11.3027			0.373250
$918$		0			0
$919$		−	26.3244i		−	0.868361i	−0.900826	−	0.434181i	$-0.857038\pi$
$919$		−	26.3244i		−	0.868361i	0.900826	−	0.434181i	$-0.142962\pi$
$920$	33.6629	+	13.7417i	1.10983	+	0.453052i
$921$		0			0
$922$	−22.5760	−	19.8340i	−0.743502	−	0.653199i
$923$	−9.17306			−0.301935
$924$		0			0
$925$	13.4012	−	5.79701i	0.440629	−	0.190604i
$926$	−9.17571	−	8.06126i	−0.301532	−	0.264909i
$927$		0			0
$928$	22.4098	−	44.9402i	0.735638	−	1.47523i
$929$			17.2416i			0.565677i	0.959168	+	0.282839i	$0.0912761\pi$
$929$			17.2416i			0.565677i	−0.959168	+	0.282839i	$0.908724\pi$
$930$		0			0
$931$	−9.24996	−	9.24996i	−0.303155	−	0.303155i
$932$	21.4559	−	27.8597i	0.702812	−	0.912574i
$933$		0			0
$934$	2.18718	+	33.8287i	0.0715668	+	1.10691i
$935$	49.1873	−	10.1826i	1.60860	−	0.333008i
$936$		0			0
$937$	−6.71407	−	6.71407i	−0.219339	−	0.219339i	0.588881	−	0.808220i	$-0.299569\pi$
$937$	−6.71407	−	6.71407i	−0.219339	−	0.219339i	−0.808220	+	0.588881i	$0.799569\pi$
$938$	−20.3476	−	17.8762i	−0.664372	−	0.583679i
$939$		0			0
$940$	−0.414755	+	0.853950i	−0.0135278	+	0.0278528i
$941$	−10.9220	+	10.9220i	−0.356048	+	0.356048i	−0.862354	−	0.506306i	$-0.831011\pi$
$941$	−10.9220	+	10.9220i	−0.356048	+	0.356048i	0.506306	+	0.862354i	$0.331011\pi$
$942$		0			0
$943$	−17.3530	+	17.3530i	−0.565093	+	0.565093i
$944$	−15.5330	−	9.04142i	−0.505555	−	0.294273i
$945$		0			0
$946$	38.8119	+	34.0979i	1.26188	+	1.10862i
$947$	−8.31220			−0.270110			−0.135055	−	0.990838i	$-0.543121\pi$
$947$	−8.31220			−0.270110			−0.135055	+	0.990838i	$0.543121\pi$
$948$		0			0
$949$	−5.32566	+	5.32566i	−0.172878	+	0.172878i
$950$	−22.7563	−	7.35389i	−0.738312	−	0.238592i
$951$		0			0
$952$	−31.4642	+	6.17181i	−1.01976	+	0.200030i
$953$	−25.5971	+	25.5971i	−0.829170	+	0.829170i	−0.987402	−	0.158232i	$-0.949421\pi$
$953$	−25.5971	+	25.5971i	−0.829170	+	0.829170i	0.158232	+	0.987402i	$0.449421\pi$
$954$		0			0
$955$	−33.1173	+	6.85587i	−1.07165	+	0.221851i
$956$	49.0591	−	6.37043i	1.58668	−	0.206034i
$957$		0			0
$958$	3.29574	+	50.9745i	0.106481	+	1.64691i
$959$	6.39206			0.206410
$960$		0			0
$961$	12.1650			0.392420
$962$	−0.484395	−	7.49202i	−0.0156175	−	0.241553i
$963$		0			0
$964$	−33.9815	+	4.41257i	−1.09447	+	0.142119i
$965$	13.3136	−	20.2649i	0.428580	−	0.652351i
$966$		0			0
$967$	31.3819	−	31.3819i	1.00918	−	1.00918i	0.00921754	−	0.999958i	$-0.497066\pi$
$967$	31.3819	−	31.3819i	1.00918	−	1.00918i	0.999958	−	0.00921754i	$-0.00293408\pi$
$968$	3.60503	−	0.707141i	0.115870	−	0.0227284i
$969$		0			0
$970$	5.45248	−	9.59627i	0.175068	−	0.308118i
$971$	−5.68257	+	5.68257i	−0.182362	+	0.182362i	−0.792384	−	0.610022i	$-0.791161\pi$
$971$	−5.68257	+	5.68257i	−0.182362	+	0.182362i	0.610022	+	0.792384i	$0.291161\pi$
$972$		0			0
$973$	7.39067			0.236934
$974$	38.1588	+	33.5242i	1.22269	+	1.07418i
$975$		0			0
$976$	−13.5704	+	23.3136i	−0.434378	+	0.746251i
$977$	−15.4116	+	15.4116i	−0.493062	+	0.493062i	−0.909270	−	0.416208i	$-0.863359\pi$
$977$	−15.4116	+	15.4116i	−0.493062	+	0.493062i	0.416208	+	0.909270i	$0.363359\pi$
$978$		0			0
$979$	9.81078	−	9.81078i	0.313554	−	0.313554i
$980$	16.3458	−	5.65852i	0.522147	−	0.180755i
$981$		0			0
$982$	9.29369	+	8.16491i	0.296574	+	0.260553i
$983$	−10.5760	−	10.5760i	−0.337323	−	0.337323i	0.518036	−	0.855359i	$-0.326663\pi$
$983$	−10.5760	−	10.5760i	−0.337323	−	0.337323i	−0.855359	+	0.518036i	$0.826663\pi$
$984$		0			0
$985$	11.5995	+	56.0314i	0.369590	+	1.78531i
$986$	5.18846	+	80.2488i	0.165234	+	2.55564i
$987$		0			0
$988$	−7.50295	+	9.74228i	−0.238701	+	0.309943i
$989$	−42.3452	−	42.3452i	−1.34650	−	1.34650i
$990$		0			0
$991$			29.6786i			0.942771i	0.881927	+	0.471385i	$0.156246\pi$
$991$			29.6786i			0.942771i	−0.881927	+	0.471385i	$0.843754\pi$
$992$	23.2821	−	7.78850i	0.739209	−	0.247285i
$993$		0			0
$994$	−9.48790	−	8.33553i	−0.300938	−	0.264387i
$995$	28.5547	−	5.91133i	0.905246	−	0.187402i
$996$		0			0
$997$	−9.96003			−0.315437			−0.157719	−	0.987484i	$-0.550414\pi$
$997$	−9.96003			−0.315437			−0.157719	+	0.987484i	$0.550414\pi$
$998$	38.0270	+	33.4084i	1.20372	+	1.05752i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bd.h.523.6		20
3.2	odd	2		240.2.bc.f.43.5	yes	20
5.2	odd	4		720.2.z.h.667.10		20
12.11	even	2		960.2.bc.f.463.4		20
15.2	even	4		240.2.y.f.187.1	yes	20
16.3	odd	4		720.2.z.h.163.10		20
24.5	odd	2		1920.2.bc.k.1183.7		20
24.11	even	2		1920.2.bc.l.1183.7		20
48.5	odd	4		1920.2.y.k.223.10		20
48.11	even	4		1920.2.y.l.223.10		20
48.29	odd	4		960.2.y.f.943.1		20
48.35	even	4		240.2.y.f.163.1	✓	20
60.47	odd	4		960.2.y.f.847.1		20
80.67	even	4	inner	720.2.bd.h.307.6		20
120.77	even	4		1920.2.y.l.1567.10		20
120.107	odd	4		1920.2.y.k.1567.10		20
240.77	even	4		960.2.bc.f.367.4		20
240.107	odd	4		1920.2.bc.k.607.7		20
240.197	even	4		1920.2.bc.l.607.7		20
240.227	odd	4		240.2.bc.f.67.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.1	✓	20	48.35	even	4
240.2.y.f.187.1	yes	20	15.2	even	4
240.2.bc.f.43.5	yes	20	3.2	odd	2
240.2.bc.f.67.5	yes	20	240.227	odd	4
720.2.z.h.163.10		20	16.3	odd	4
720.2.z.h.667.10		20	5.2	odd	4
720.2.bd.h.307.6		20	80.67	even	4	inner
720.2.bd.h.523.6		20	1.1	even	1	trivial
960.2.y.f.847.1		20	60.47	odd	4
960.2.y.f.943.1		20	48.29	odd	4
960.2.bc.f.367.4		20	240.77	even	4
960.2.bc.f.463.4		20	12.11	even	2
1920.2.y.k.223.10		20	48.5	odd	4
1920.2.y.k.1567.10		20	120.107	odd	4
1920.2.y.l.223.10		20	48.11	even	4
1920.2.y.l.1567.10		20	120.77	even	4
1920.2.bc.k.607.7		20	240.107	odd	4
1920.2.bc.k.1183.7		20	24.5	odd	2
1920.2.bc.l.607.7		20	240.197	even	4
1920.2.bc.l.1183.7		20	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0912451 - 1.41127i) q^{2} +(-1.98335 + 0.257542i) q^{4} +(0.453294 + 2.18964i) q^{5} +(1.25143 - 1.25143i) q^{7} +(0.544432 + 2.77553i) q^{8} +(3.04881 - 0.839513i) q^{10} +(-2.47980 + 2.47980i) q^{11} -1.81790 q^{13} +(-1.88029 - 1.65192i) q^{14} +(3.86734 - 1.02159i) q^{16} +(-4.52932 + 4.52932i) q^{17} +(-2.39150 + 2.39150i) q^{19} +(-1.46296 - 4.22608i) q^{20} +(3.72594 + 3.27340i) q^{22} +(-4.06513 - 4.06513i) q^{23} +(-4.58905 + 1.98510i) q^{25} +(0.165874 + 2.56554i) q^{26} +(-2.15973 + 2.80432i) q^{28} +(6.27721 + 6.27721i) q^{29} +4.33993i q^{31} +(-1.79462 - 5.36464i) q^{32} +(6.80535 + 5.97880i) q^{34} +(3.30745 + 2.17292i) q^{35} -2.92026 q^{37} +(3.59326 + 3.15684i) q^{38} +(-5.83064 + 2.45024i) q^{40} -4.26875i q^{41} +10.4167 q^{43} +(4.27966 - 5.55697i) q^{44} +(-5.36607 + 6.10791i) q^{46} +(-0.150104 - 0.150104i) q^{47} +3.86784i q^{49} +(3.22024 + 6.29524i) q^{50} +(3.60552 - 0.468185i) q^{52} +10.6378i q^{53} +(-6.55396 - 4.30580i) q^{55} +(4.15471 + 2.79207i) q^{56} +(8.28606 - 9.43159i) q^{58} +(-3.17716 - 3.17716i) q^{59} +(-4.76865 + 4.76865i) q^{61} +(6.12480 - 0.395997i) q^{62} +(-7.40719 + 3.02218i) q^{64} +(-0.824041 - 3.98054i) q^{65} +10.8215 q^{67} +(7.81672 - 10.1497i) q^{68} +(2.76478 - 4.86596i) q^{70} +5.04598 q^{71} +(2.92958 - 2.92958i) q^{73} +(0.266459 + 4.12126i) q^{74} +(4.12727 - 5.35910i) q^{76} +6.20661i q^{77} -4.75216 q^{79} +(3.98996 + 8.00501i) q^{80} +(-6.02435 + 0.389502i) q^{82} -15.3571i q^{83} +(-11.9707 - 7.86446i) q^{85} +(-0.950471 - 14.7007i) q^{86} +(-8.23287 - 5.53270i) q^{88} -3.95627 q^{89} +(-2.27497 + 2.27497i) q^{91} +(9.10952 + 7.01563i) q^{92} +(-0.198141 + 0.225533i) q^{94} +(-6.32059 - 4.15248i) q^{95} +(2.46797 - 2.46797i) q^{97} +(5.45856 - 0.352921i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 2 q^{4} - 8 q^{5} - 4 q^{7} - 8 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{13} + 10 q^{14} + 26 q^{16} - 12 q^{17} - 16 q^{19} + 4 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 20 q^{26} + 22 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 2 * q^4 - 8 * q^5 - 4 * q^7 - 8 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^13 + 10 * q^14 + 26 * q^16 - 12 * q^17 - 16 * q^19 + 4 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 20 * q^26 + 22 * q^28 - 12 * q^32 - 6 * q^34 + 12 * q^35 + 24 * q^37 + 22 * q^38 - 10 * q^40 - 8 * q^43 + 22 * q^44 - 18 * q^46 + 18 * q^50 + 24 * q^52 - 4 * q^55 + 26 * q^56 - 2 * q^58 - 16 * q^59 - 12 * q^61 - 12 * q^62 - 26 * q^64 - 4 * q^65 - 16 * q^67 + 2 * q^68 - 10 * q^70 + 20 * q^73 - 8 * q^74 + 26 * q^76 - 48 * q^79 + 16 * q^80 + 80 * q^82 + 4 * q^85 - 4 * q^86 + 94 * q^88 + 40 * q^89 - 24 * q^91 + 30 * q^92 - 58 * q^94 - 72 * q^95 - 28 * q^97 - 4 * q^98

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