LMFDB - Embedded newform 702.2.bg.a.125.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(125,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("702.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bg (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.14
Character	$\chi$	$=$	702.125
Dual form			702.2.bg.a.629.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.926266 + 3.45687i) q^{5} +(4.42416 + 1.18545i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.57882i q^{10} +(0.277511 - 1.03569i) q^{11} +(-3.47629 - 0.956779i) q^{13} +(3.96659 + 2.29011i) q^{14} +(0.500000 + 0.866025i) q^{16} -4.13440 q^{17} +(-3.55072 - 3.55072i) q^{19} +(-0.926266 + 3.45687i) q^{20} +(0.536110 - 0.928570i) q^{22} +(1.26396 - 2.18925i) q^{23} +(-6.76187 + 3.90397i) q^{25} +(-3.11020 - 1.82391i) q^{26} +(3.23871 + 3.23871i) q^{28} +(0.654210 - 0.377708i) q^{29} +(8.68512 - 2.32717i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.99353 - 1.07006i) q^{34} +16.3918i q^{35} +(1.53470 - 1.53470i) q^{37} +(-2.51074 - 4.34872i) q^{38} +(-1.78941 + 3.09935i) q^{40} +(-0.112341 - 0.419264i) q^{41} +(-2.15504 + 1.24421i) q^{43} +(0.758175 - 0.758175i) q^{44} +(1.78751 - 1.78751i) q^{46} +(-0.366030 + 1.36604i) q^{47} +(12.1057 + 6.98923i) q^{49} +(-7.54188 + 2.02084i) q^{50} +(-2.53216 - 2.56674i) q^{52} -11.0932i q^{53} +3.83728 q^{55} +(2.29011 + 3.96659i) q^{56} +(0.729677 - 0.195516i) q^{58} +(-9.66293 + 2.58917i) q^{59} +(5.37935 + 9.31732i) q^{61} +8.99150 q^{62} +1.00000i q^{64} +(0.0874941 - 12.9033i) q^{65} +(8.82122 - 2.36364i) q^{67} +(-3.58050 - 2.06720i) q^{68} +(-4.24251 + 15.8333i) q^{70} +(-2.42867 + 2.42867i) q^{71} +(3.17686 - 3.17686i) q^{73} +(1.87961 - 1.08520i) q^{74} +(-1.29965 - 4.85037i) q^{76} +(2.45551 - 4.25306i) q^{77} +(-0.638454 - 1.10583i) q^{79} +(-2.53061 + 2.53061i) q^{80} -0.434054i q^{82} +(6.13302 + 1.64334i) q^{83} +(-3.82956 - 14.2921i) q^{85} +(-2.40363 + 0.644051i) q^{86} +(0.928570 - 0.536110i) q^{88} +(-6.96929 - 6.96929i) q^{89} +(-14.2454 - 8.35390i) q^{91} +(2.18925 - 1.26396i) q^{92} +(-0.707116 + 1.22476i) q^{94} +(8.98547 - 15.5633i) q^{95} +(0.666716 - 2.48822i) q^{97} +(9.88427 + 9.88427i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} + 8 q^{28} - 4 q^{31} + 8 q^{37} + 48 q^{41} + 24 q^{47} + 24 q^{50} - 4 q^{52} - 48 q^{65} + 28 q^{67} - 56 q^{73} + 48 q^{74} + 4 q^{76} + 48 q^{79} + 24 q^{83}+ \cdots + 20 q^{97}+O(q^{100}) $ 56 * q + 4 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 + 8 * q^28 - 4 * q^31 + 8 * q^37 + 48 * q^41 + 24 * q^47 + 24 * q^50 - 4 * q^52 - 48 * q^65 + 28 * q^67 - 56 * q^73 + 48 * q^74 + 4 * q^76 + 48 * q^79 + 24 * q^83 + 48 * q^86 - 8 * q^91 - 48 * q^92 + 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.926266	+	3.45687i	0.414239	+	1.54596i	0.786356	+	0.617774i	$0.211965\pi$
$5$	0.926266	+	3.45687i	0.414239	+	1.54596i	−0.372117	+	0.928186i	$0.621368\pi$
$6$		0			0
$7$	4.42416	+	1.18545i	1.67217	+	0.448058i	0.965696	−	0.259676i	$-0.0836159\pi$
$7$	4.42416	+	1.18545i	1.67217	+	0.448058i	0.706479	+	0.707734i	$0.250283\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$			3.57882i			1.13172i
$11$	0.277511	−	1.03569i	0.0836728	−	0.312271i	−0.911387	−	0.411551i	$-0.864987\pi$
$11$	0.277511	−	1.03569i	0.0836728	−	0.312271i	0.995060	+	0.0992799i	$0.0316539\pi$
$12$		0			0
$13$	−3.47629	−	0.956779i	−0.964149	−	0.265363i
$13$	−3.47629	−	0.956779i	−0.964149	−	0.265363i
$14$	3.96659	+	2.29011i	1.06012	+	0.612058i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−4.13440			−1.00274			−0.501370	−	0.865233i	$-0.667171\pi$
$17$	−4.13440			−1.00274			−0.501370	+	0.865233i	$0.667171\pi$
$18$		0			0
$19$	−3.55072	−	3.55072i	−0.814591	−	0.814591i	0.170728	−	0.985318i	$-0.445388\pi$
$19$	−3.55072	−	3.55072i	−0.814591	−	0.814591i	−0.985318	+	0.170728i	$0.945388\pi$
$20$	−0.926266	+	3.45687i	−0.207119	+	0.772980i
$21$		0			0
$22$	0.536110	−	0.928570i	0.114299	−	0.197972i
$23$	1.26396	−	2.18925i	0.263554	−	0.456489i	−0.703630	−	0.710567i	$-0.748439\pi$
$23$	1.26396	−	2.18925i	0.263554	−	0.456489i	0.967184	+	0.254078i	$0.0817718\pi$
$24$		0			0
$25$	−6.76187	+	3.90397i	−1.35237	+	0.780793i
$26$	−3.11020	−	1.82391i	−0.609961	−	0.357698i
$27$		0			0
$28$	3.23871	+	3.23871i	0.612058	+	0.612058i
$29$	0.654210	−	0.377708i	0.121484	−	0.0701387i	−0.438027	−	0.898962i	$-0.644322\pi$
$29$	0.654210	−	0.377708i	0.121484	−	0.0701387i	0.559511	+	0.828823i	$0.310989\pi$
$30$		0			0
$31$	8.68512	−	2.32717i	1.55989	−	0.417972i	0.627264	−	0.778807i	$-0.284175\pi$
$31$	8.68512	−	2.32717i	1.55989	−	0.417972i	0.932630	+	0.360835i	$0.117508\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	−3.99353	−	1.07006i	−0.684884	−	0.183514i
$35$			16.3918i			2.77072i
$36$		0			0
$37$	1.53470	−	1.53470i	0.252303	−	0.252303i	−0.569611	−	0.821914i	$-0.692906\pi$
$37$	1.53470	−	1.53470i	0.252303	−	0.252303i	0.821914	+	0.569611i	$0.192906\pi$
$38$	−2.51074	−	4.34872i	−0.407295	−	0.705456i
$39$		0			0
$40$	−1.78941	+	3.09935i	−0.282930	+	0.490050i
$41$	−0.112341	−	0.419264i	−0.0175448	−	0.0654780i	0.956598	−	0.291409i	$-0.0941242\pi$
$41$	−0.112341	−	0.419264i	−0.0175448	−	0.0654780i	−0.974143	+	0.225931i	$0.927457\pi$
$42$		0			0
$43$	−2.15504	+	1.24421i	−0.328640	+	0.189740i	−0.655237	−	0.755423i	$-0.727431\pi$
$43$	−2.15504	+	1.24421i	−0.328640	+	0.189740i	0.326597	+	0.945164i	$0.394098\pi$
$44$	0.758175	−	0.758175i	0.114299	−	0.114299i
$45$		0			0
$46$	1.78751	−	1.78751i	0.263554	−	0.263554i
$47$	−0.366030	+	1.36604i	−0.0533910	+	0.199258i	−0.987470	−	0.157810i	$-0.949557\pi$
$47$	−0.366030	+	1.36604i	−0.0533910	+	0.199258i	0.934079	+	0.357068i	$0.116223\pi$
$48$		0			0
$49$	12.1057	+	6.98923i	1.72939	+	0.998462i
$50$	−7.54188	+	2.02084i	−1.06658	+	0.285790i
$51$		0			0
$52$	−2.53216	−	2.56674i	−0.351148	−	0.355943i
$53$		−	11.0932i		−	1.52376i	−0.647716	−	0.761882i	$-0.724276\pi$
$53$		−	11.0932i		−	1.52376i	0.647716	−	0.761882i	$-0.275724\pi$
$54$		0			0
$55$	3.83728			0.517419
$56$	2.29011	+	3.96659i	0.306029	+	0.530058i
$57$		0			0
$58$	0.729677	−	0.195516i	0.0958112	−	0.0256725i
$59$	−9.66293	+	2.58917i	−1.25801	+	0.337082i	−0.825424	−	0.564513i	$-0.809064\pi$
$59$	−9.66293	+	2.58917i	−1.25801	+	0.337082i	−0.432582	+	0.901595i	$0.642397\pi$
$60$		0			0
$61$	5.37935	+	9.31732i	0.688756	+	1.19296i	0.972241	+	0.233983i	$0.0751761\pi$
$61$	5.37935	+	9.31732i	0.688756	+	1.19296i	−0.283485	+	0.958977i	$0.591491\pi$
$62$	8.99150			1.14192
$63$		0			0
$64$			1.00000i			0.125000i
$65$	0.0874941	−	12.9033i	0.0108523	−	1.60046i
$66$		0			0
$67$	8.82122	−	2.36364i	1.07768	−	0.288765i	0.324037	−	0.946044i	$-0.394960\pi$
$67$	8.82122	−	2.36364i	1.07768	−	0.288765i	0.753647	+	0.657280i	$0.228293\pi$
$68$	−3.58050	−	2.06720i	−0.434199	−	0.250685i
$69$		0			0
$70$	−4.24251	+	15.8333i	−0.507077	+	1.89244i
$71$	−2.42867	+	2.42867i	−0.288230	+	0.288230i	−0.836380	−	0.548150i	$-0.815332\pi$
$71$	−2.42867	+	2.42867i	−0.288230	+	0.288230i	0.548150	+	0.836380i	$0.315332\pi$
$72$		0			0
$73$	3.17686	−	3.17686i	0.371824	−	0.371824i	−0.496317	−	0.868141i	$-0.665315\pi$
$73$	3.17686	−	3.17686i	0.371824	−	0.371824i	0.868141	+	0.496317i	$0.165315\pi$
$74$	1.87961	−	1.08520i	0.218501	−	0.126151i
$75$		0			0
$76$	−1.29965	−	4.85037i	−0.149080	−	0.556376i
$77$	2.45551	−	4.25306i	0.279831	−	0.484681i
$78$		0			0
$79$	−0.638454	−	1.10583i	−0.0718316	−	0.124416i	0.827872	−	0.560916i	$-0.189551\pi$
$79$	−0.638454	−	1.10583i	−0.0718316	−	0.124416i	−0.899704	+	0.436500i	$0.856218\pi$
$80$	−2.53061	+	2.53061i	−0.282930	+	0.282930i
$81$		0			0
$82$		−	0.434054i		−	0.0479332i
$83$	6.13302	+	1.64334i	0.673186	+	0.180380i	0.579190	−	0.815193i	$-0.303369\pi$
$83$	6.13302	+	1.64334i	0.673186	+	0.180380i	0.0939965	+	0.995573i	$0.470036\pi$
$84$		0			0
$85$	−3.82956	−	14.2921i	−0.415374	−	1.55020i
$86$	−2.40363	+	0.644051i	−0.259190	+	0.0694498i
$87$		0			0
$88$	0.928570	−	0.536110i	0.0989859	−	0.0571496i
$89$	−6.96929	−	6.96929i	−0.738743	−	0.738743i	0.233591	−	0.972335i	$-0.424952\pi$
$89$	−6.96929	−	6.96929i	−0.738743	−	0.738743i	−0.972335	+	0.233591i	$0.924952\pi$
$90$		0			0
$91$	−14.2454	−	8.35390i	−1.49333	−	0.875727i
$92$	2.18925	−	1.26396i	0.228245	−	0.131777i
$93$		0			0
$94$	−0.707116	+	1.22476i	−0.0729335	+	0.126324i
$95$	8.98547	−	15.5633i	0.921890	−	1.59676i
$96$		0			0
$97$	0.666716	−	2.48822i	0.0676947	−	0.252640i	−0.923783	−	0.382916i	$-0.874920\pi$
$97$	0.666716	−	2.48822i	0.0676947	−	0.252640i	0.991478	+	0.130276i	$0.0415864\pi$
$98$	9.88427	+	9.88427i	0.998462	+	0.998462i
$99$		0			0
$100$	−7.80793			−0.780793
$101$	4.80845	+	8.32848i	0.478459	+	0.828715i	0.999695	−	0.0246975i	$-0.00786224\pi$
$101$	4.80845	+	8.32848i	0.478459	+	0.828715i	−0.521236	+	0.853413i	$0.674529\pi$
$102$		0			0
$103$	−9.13951	−	5.27670i	−0.900543	−	0.519929i	−0.0231667	−	0.999732i	$-0.507375\pi$
$103$	−9.13951	−	5.27670i	−0.900543	−	0.519929i	−0.877376	+	0.479803i	$0.840708\pi$
$104$	−1.78156	−	3.13465i	−0.174697	−	0.307378i
$105$		0			0
$106$	2.87112	−	10.7152i	0.278868	−	1.04075i
$107$			8.87442i			0.857923i	0.903323	+	0.428961i	$0.141120\pi$
$107$			8.87442i			0.857923i	−0.903323	+	0.428961i	$0.858880\pi$
$108$		0			0
$109$	−13.3375	−	13.3375i	−1.27750	−	1.27750i	−0.942064	−	0.335432i	$-0.891118\pi$
$109$	−13.3375	−	13.3375i	−1.27750	−	1.27750i	−0.335432	−	0.942064i	$-0.608882\pi$
$110$	3.70653	+	0.993162i	0.353404	+	0.0946942i
$111$		0			0
$112$	1.18545	+	4.42416i	0.112014	+	0.418044i
$113$	−1.66894	−	0.963564i	−0.157001	−	0.0906445i	0.419441	−	0.907782i	$-0.362226\pi$
$113$	−1.66894	−	0.963564i	−0.157001	−	0.0906445i	−0.576442	+	0.817138i	$0.695559\pi$
$114$		0			0
$115$	8.73871	+	2.34153i	0.814889	+	0.218349i
$116$	0.755417			0.0701387
$117$		0			0
$118$	−10.0038			−0.920924
$119$	−18.2913	−	4.90113i	−1.67676	−	0.449286i
$120$		0			0
$121$	8.53065	+	4.92517i	0.775513	+	0.447743i
$122$	2.78456	+	10.3921i	0.252102	+	0.940858i
$123$		0			0
$124$	8.68512	+	2.32717i	0.779947	+	0.208986i
$125$	−7.10576	−	7.10576i	−0.635559	−	0.635559i
$126$		0			0
$127$			5.55792i			0.493186i	0.969119	+	0.246593i	$0.0793111\pi$
$127$			5.55792i			0.493186i	−0.969119	+	0.246593i	$0.920689\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	3.42414	−	12.4410i	0.300317	−	1.09115i
$131$	−4.63129	−	2.67388i	−0.404638	−	0.233618i	0.283845	−	0.958870i	$-0.408390\pi$
$131$	−4.63129	−	2.67388i	−0.404638	−	0.233618i	−0.688483	+	0.725252i	$0.741723\pi$
$132$		0			0
$133$	−11.4997	−	19.9181i	−0.997154	−	1.72712i
$134$	9.13240			0.788919
$135$		0			0
$136$	−2.92347	−	2.92347i	−0.250685	−	0.250685i
$137$	0.131653	−	0.491334i	0.0112478	−	0.0419775i	−0.960074	−	0.279747i	$-0.909750\pi$
$137$	0.131653	−	0.491334i	0.0112478	−	0.0419775i	0.971322	+	0.237769i	$0.0764162\pi$
$138$		0			0
$139$	−3.49301	+	6.05008i	−0.296274	+	0.513161i	−0.975280	−	0.220971i	$-0.929077\pi$
$139$	−3.49301	+	6.05008i	−0.296274	+	0.513161i	0.679007	+	0.734132i	$0.262411\pi$
$140$	−8.19589	+	14.1957i	−0.692679	+	1.19976i
$141$		0			0
$142$	−2.97450	+	1.71733i	−0.249615	+	0.144115i
$143$	−1.95563	+	3.33482i	−0.163538	+	0.278872i
$144$		0			0
$145$	1.91166	+	1.91166i	0.158755	+	0.158755i
$146$	3.89085	−	2.24638i	0.322009	−	0.185912i
$147$		0			0
$148$	2.09644	−	0.561739i	0.172326	−	0.0461746i
$149$	−4.16059	−	15.5275i	−0.340848	−	1.27206i	−0.897388	−	0.441243i	$-0.854538\pi$
$149$	−4.16059	−	15.5275i	−0.340848	−	1.27206i	0.556539	−	0.830821i	$-0.312129\pi$
$150$		0			0
$151$	2.68543	+	0.719558i	0.218537	+	0.0585568i	0.366426	−	0.930447i	$-0.380581\pi$
$151$	2.68543	+	0.719558i	0.218537	+	0.0585568i	−0.147889	+	0.989004i	$0.547248\pi$
$152$		−	5.02147i		−	0.407295i
$153$		0			0
$154$	3.47261	−	3.47261i	0.279831	−	0.279831i
$155$	16.0895	+	27.8678i	1.29234	+	2.23839i
$156$		0			0
$157$	−6.91473	+	11.9767i	−0.551856	+	0.955842i	0.446285	+	0.894891i	$0.352747\pi$
$157$	−6.91473	+	11.9767i	−0.551856	+	0.955842i	−0.998141	+	0.0609515i	$0.980587\pi$
$158$	−0.330488	−	1.23340i	−0.0262922	−	0.0981238i
$159$		0			0
$160$	−3.09935	+	1.78941i	−0.245025	+	0.141465i
$161$	8.18721	−	8.18721i	0.645243	−	0.645243i
$162$		0			0
$163$	−15.3749	+	15.3749i	−1.20426	+	1.20426i	−0.231400	+	0.972859i	$0.574331\pi$
$163$	−15.3749	+	15.3749i	−1.20426	+	1.20426i	−0.972859	+	0.231400i	$0.925669\pi$
$164$	0.112341	−	0.419264i	0.00877238	−	0.0327390i
$165$		0			0
$166$	5.49871	+	3.17468i	0.426783	+	0.246403i
$167$	14.2638	−	3.82198i	1.10377	−	0.295754i	0.339471	−	0.940617i	$-0.389752\pi$
$167$	14.2638	−	3.82198i	1.10377	−	0.295754i	0.764298	+	0.644863i	$0.223085\pi$
$168$		0			0
$169$	11.1691	+	6.65208i	0.859165	+	0.511698i
$170$		−	14.7963i		−	1.13482i
$171$		0			0
$172$	−2.48842			−0.189740
$173$	−4.94488	−	8.56478i	−0.375952	−	0.651168i	0.614517	−	0.788904i	$-0.289351\pi$
$173$	−4.94488	−	8.56478i	−0.375952	−	0.651168i	−0.990469	+	0.137736i	$0.956018\pi$
$174$		0			0
$175$	−34.5435	+	9.25591i	−2.61124	+	0.699681i
$176$	1.03569	−	0.277511i	0.0780677	−	0.0209182i
$177$		0			0
$178$	−4.92803	−	8.53560i	−0.369372	−	0.639771i
$179$	−5.77755			−0.431835			−0.215917	−	0.976412i	$-0.569274\pi$
$179$	−5.77755			−0.431835			−0.215917	+	0.976412i	$0.569274\pi$
$180$		0			0
$181$			0.380715i			0.0282983i	0.999900	+	0.0141492i	$0.00450397\pi$
$181$			0.380715i			0.0282983i	−0.999900	+	0.0141492i	$0.995496\pi$
$182$	−11.5979	−	11.7562i	−0.859692	−	0.871431i
$183$		0			0
$184$	2.44179	−	0.654275i	0.180011	−	0.0482338i
$185$	6.72679	+	3.88372i	0.494564	+	0.285537i
$186$		0			0
$187$	−1.14734	+	4.28194i	−0.0839021	+	0.313127i
$188$	−1.00001	+	1.00001i	−0.0729335	+	0.0729335i
$189$		0			0
$190$	12.7074	−	12.7074i	0.921890	−	0.921890i
$191$	9.11205	−	5.26085i	0.659325	−	0.380662i	−0.132695	−	0.991157i	$-0.542363\pi$
$191$	9.11205	−	5.26085i	0.659325	−	0.380662i	0.792020	+	0.610495i	$0.209030\pi$
$192$		0			0
$193$	−2.06271	−	7.69813i	−0.148477	−	0.554124i	−0.999576	−	0.0291185i	$-0.990730\pi$
$193$	−2.06271	−	7.69813i	−0.148477	−	0.554124i	0.851099	−	0.525005i	$-0.175937\pi$
$194$	1.28800	−	2.23087i	0.0924727	−	0.160167i
$195$		0			0
$196$	6.98923	+	12.1057i	0.499231	+	0.864693i
$197$	15.8934	−	15.8934i	1.13235	−	1.13235i	0.142570	−	0.989785i	$-0.454463\pi$
$197$	15.8934	−	15.8934i	1.13235	−	1.13235i	0.989785	−	0.142570i	$-0.0455365\pi$
$198$		0			0
$199$		−	11.7833i		−	0.835293i	−0.908610	−	0.417646i	$-0.862855\pi$
$199$		−	11.7833i		−	0.835293i	0.908610	−	0.417646i	$-0.137145\pi$
$200$	−7.54188	−	2.02084i	−0.533292	−	0.142895i
$201$		0			0
$202$	2.48904	+	9.28922i	0.175128	+	0.653587i
$203$	3.34208	−	0.895509i	0.234568	−	0.0628524i
$204$		0			0
$205$	1.34528	−	0.776699i	0.0939586	−	0.0542470i
$206$	−7.46238	−	7.46238i	−0.519929	−	0.519929i
$207$		0			0
$208$	−0.909549	−	3.48894i	−0.0630659	−	0.241915i
$209$	−4.66279	+	2.69206i	−0.322532	+	0.186214i
$210$		0			0
$211$	10.3429	−	17.9145i	0.712037	−	1.23328i	−0.252054	−	0.967713i	$-0.581106\pi$
$211$	10.3429	−	17.9145i	0.712037	−	1.23328i	0.964091	−	0.265572i	$-0.0855607\pi$
$212$	5.54658	−	9.60696i	0.380941	−	0.659809i
$213$		0			0
$214$	−2.29687	+	8.57203i	−0.157011	+	0.585972i
$215$	−6.29721	−	6.29721i	−0.429466	−	0.429466i
$216$		0			0
$217$	41.1831			2.79569
$218$	−9.43100	−	16.3350i	−0.638748	−	1.10634i
$219$		0			0
$220$	3.32318	+	1.91864i	0.224049	+	0.129355i
$221$	14.3724	+	3.95571i	0.966791	+	0.266090i
$222$		0			0
$223$	−4.06125	+	15.1568i	−0.271962	+	1.01497i	0.685889	+	0.727707i	$0.259414\pi$
$223$	−4.06125	+	15.1568i	−0.271962	+	1.01497i	−0.957850	+	0.287268i	$0.907253\pi$
$224$			4.58023i			0.306029i
$225$		0			0
$226$	−1.36269	−	1.36269i	−0.0906445	−	0.0906445i
$227$	−15.4357	−	4.13598i	−1.02450	−	0.274514i	−0.292825	−	0.956166i	$-0.594595\pi$
$227$	−15.4357	−	4.13598i	−1.02450	−	0.274514i	−0.731677	+	0.681652i	$0.761262\pi$
$228$		0			0
$229$	2.36858	+	8.83967i	0.156520	+	0.584142i	0.998970	+	0.0453674i	$0.0144458\pi$
$229$	2.36858	+	8.83967i	0.156520	+	0.584142i	−0.842450	+	0.538774i	$0.818887\pi$
$230$	7.83491	+	4.52349i	0.516619	+	0.298270i
$231$		0			0
$232$	0.729677	+	0.195516i	0.0479056	+	0.0128363i
$233$	24.6878			1.61735			0.808676	−	0.588255i	$-0.200185\pi$
$233$	24.6878			1.61735			0.808676	+	0.588255i	$0.200185\pi$
$234$		0			0
$235$	−5.06128			−0.330161
$236$	−9.66293	−	2.58917i	−0.629003	−	0.168541i
$237$		0			0
$238$	−16.3995	−	9.46825i	−1.06302	−	0.613736i
$239$	4.05596	+	15.1370i	0.262358	+	0.979134i	0.963848	+	0.266454i	$0.0858520\pi$
$239$	4.05596	+	15.1370i	0.262358	+	0.979134i	−0.701490	+	0.712680i	$0.747481\pi$
$240$		0			0
$241$	−3.50953	−	0.940376i	−0.226069	−	0.0605750i	0.144006	−	0.989577i	$-0.454001\pi$
$241$	−3.50953	−	0.940376i	−0.226069	−	0.0605750i	−0.370075	+	0.929002i	$0.620668\pi$
$242$	6.96524	+	6.96524i	0.447743	+	0.447743i
$243$		0			0
$244$			10.7587i			0.688756i
$245$	−12.9478	+	48.3218i	−0.827203	+	3.08716i
$246$		0			0
$247$	8.94607	+	15.7406i	0.569225	+	1.00155i
$248$	7.78686	+	4.49575i	0.494466	+	0.285480i
$249$		0			0
$250$	−5.02453	−	8.70275i	−0.317779	−	0.550410i
$251$	−24.3205			−1.53509			−0.767547	−	0.640992i	$-0.778523\pi$
$251$	−24.3205			−1.53509			−0.767547	+	0.640992i	$0.778523\pi$
$252$		0			0
$253$	−1.91661	−	1.91661i	−0.120496	−	0.120496i
$254$	−1.43850	+	5.36854i	−0.0902593	+	0.336852i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.79901	+	6.58009i	−0.236976	+	0.410454i	−0.959845	−	0.280531i	$-0.909490\pi$
$257$	−3.79901	+	6.58009i	−0.236976	+	0.410454i	0.722869	+	0.690985i	$0.242823\pi$
$258$		0			0
$259$	8.60906	−	4.97044i	0.534941	−	0.308848i
$260$	6.52743	−	11.1308i	0.404814	−	0.690306i
$261$		0			0
$262$	−3.78143	−	3.78143i	−0.233618	−	0.233618i
$263$	23.6385	−	13.6477i	1.45761	−	0.841552i	0.458718	−	0.888582i	$-0.348309\pi$
$263$	23.6385	−	13.6477i	1.45761	−	0.841552i	0.998894	+	0.0470295i	$0.0149755\pi$
$264$		0			0
$265$	38.3476	−	10.2752i	2.35568	−	0.631202i
$266$	−5.95271	−	22.2158i	−0.364984	−	1.36214i
$267$		0			0
$268$	8.82122	+	2.36364i	0.538842	+	0.144382i
$269$		−	14.8321i		−	0.904327i	−0.891935	−	0.452164i	$-0.850652\pi$
$269$		−	14.8321i		−	0.904327i	0.891935	−	0.452164i	$-0.149348\pi$
$270$		0			0
$271$	−16.0694	+	16.0694i	−0.976147	+	0.976147i	−0.999722	−	0.0235754i	$-0.992495\pi$
$271$	−16.0694	+	16.0694i	−0.976147	+	0.976147i	0.0235754	+	0.999722i	$0.492495\pi$
$272$	−2.06720	−	3.58050i	−0.125343	−	0.217100i
$273$		0			0
$274$	0.254333	−	0.440518i	0.0153648	−	0.0266127i
$275$	2.16679	+	8.08656i	0.130662	+	0.487638i
$276$		0			0
$277$	−20.1564	+	11.6373i	−1.21108	+	0.699218i	−0.962995	−	0.269520i	$-0.913135\pi$
$277$	−20.1564	+	11.6373i	−1.21108	+	0.699218i	−0.248087	+	0.968738i	$0.579802\pi$
$278$	−4.93987	+	4.93987i	−0.296274	+	0.296274i
$279$		0			0
$280$	−11.5907	+	11.5907i	−0.692679	+	0.692679i
$281$	−0.838571	+	3.12959i	−0.0500250	+	0.186696i	−0.986417	−	0.164260i	$-0.947476\pi$
$281$	−0.838571	+	3.12959i	−0.0500250	+	0.186696i	0.936392	+	0.350955i	$0.114143\pi$
$282$		0			0
$283$	−4.80758	−	2.77566i	−0.285781	−	0.164996i	0.350257	−	0.936654i	$-0.386094\pi$
$283$	−4.80758	−	2.77566i	−0.285781	−	0.164996i	−0.636038	+	0.771658i	$0.719428\pi$
$284$	−3.31763	+	0.888956i	−0.196865	+	0.0527498i
$285$		0			0
$286$	−2.75211	+	2.71504i	−0.162736	+	0.160544i
$287$		−	1.98806i		−	0.117352i
$288$		0			0
$289$	0.0933004			0.00548826
$290$	1.35175	+	2.34130i	0.0793775	+	0.137486i
$291$		0			0
$292$	4.33967	−	1.16281i	0.253960	−	0.0680484i
$293$	−16.6590	+	4.46378i	−0.973232	+	0.260777i	−0.710192	−	0.704008i	$-0.751392\pi$
$293$	−16.6590	+	4.46378i	−0.973232	+	0.260777i	−0.263040	+	0.964785i	$0.584725\pi$
$294$		0			0
$295$	−17.9009	−	31.0052i	−1.04223	−	1.80519i
$296$	2.17039			0.126151
$297$		0			0
$298$		−	16.0753i		−	0.931215i
$299$	−6.48852	+	6.40112i	−0.375241	+	0.370186i
$300$		0			0
$301$	−11.0092	+	2.94990i	−0.634558	+	0.170029i
$302$	2.40769	+	1.39008i	0.138547	+	0.0799901i
$303$		0			0
$304$	1.29965	−	4.85037i	0.0745402	−	0.278188i
$305$	−27.2261	+	27.2261i	−1.55896	+	1.55896i
$306$		0			0
$307$	−0.629117	+	0.629117i	−0.0359056	+	0.0359056i	−0.724832	−	0.688926i	$-0.758082\pi$
$307$	−0.629117	+	0.629117i	−0.0359056	+	0.0359056i	0.688926	+	0.724832i	$0.258082\pi$
$308$	4.25306	−	2.45551i	0.242341	−	0.139915i
$309$		0			0
$310$	8.32852	+	31.0824i	0.473028	+	1.76536i
$311$	−7.56960	+	13.1109i	−0.429233	+	0.743453i	−0.996805	−	0.0798707i	$-0.974549\pi$
$311$	−7.56960	+	13.1109i	−0.429233	+	0.743453i	0.567573	+	0.823323i	$0.307883\pi$
$312$		0			0
$313$	−6.51021	−	11.2760i	−0.367979	−	0.637358i	0.621271	−	0.783596i	$-0.286617\pi$
$313$	−6.51021	−	11.2760i	−0.367979	−	0.637358i	−0.989249	+	0.146238i	$0.953283\pi$
$314$	−9.77891	+	9.77891i	−0.551856	+	0.551856i
$315$		0			0
$316$		−	1.27691i		−	0.0718316i
$317$	11.8433	+	3.17341i	0.665188	+	0.178237i	0.575586	−	0.817741i	$-0.304774\pi$
$317$	11.8433	+	3.17341i	0.665188	+	0.178237i	0.0896019	+	0.995978i	$0.471441\pi$
$318$		0			0
$319$	−0.209637	−	0.782374i	−0.0117374	−	0.0438046i
$320$	−3.45687	+	0.926266i	−0.193245	+	0.0517798i
$321$		0			0
$322$	10.0272	−	5.78923i	0.558796	−	0.322621i
$323$	14.6801	+	14.6801i	0.816823	+	0.816823i
$324$		0			0
$325$	27.2414	−	7.10170i	1.51108	−	0.393931i
$326$	−18.8304	+	10.8717i	−1.04292	+	0.602129i
$327$		0			0
$328$	0.217027	−	0.375901i	0.0119833	−	0.0207557i
$329$	−3.23875	+	5.60968i	−0.178558	+	0.309272i
$330$		0			0
$331$	−2.19780	+	8.20228i	−0.120802	+	0.450838i	−0.999655	−	0.0262533i	$-0.991642\pi$
$331$	−2.19780	+	8.20228i	−0.120802	+	0.450838i	0.878854	+	0.477092i	$0.158309\pi$
$332$	4.48968	+	4.48968i	0.246403	+	0.246403i
$333$		0			0
$334$	14.7670			0.808015
$335$	16.3416	+	28.3045i	0.892837	+	1.54644i
$336$		0			0
$337$	−10.2132	−	5.89659i	−0.556348	−	0.321207i	0.195331	−	0.980737i	$-0.437422\pi$
$337$	−10.2132	−	5.89659i	−0.556348	−	0.321207i	−0.751678	+	0.659530i	$0.770755\pi$
$338$	9.06689	+	9.31620i	0.493174	+	0.506734i
$339$		0			0
$340$	3.82956	−	14.2921i	0.207687	−	0.775098i
$341$		−	9.64087i		−	0.522082i
$342$		0			0
$343$	22.6012	+	22.6012i	1.22035	+	1.22035i
$344$	−2.40363	−	0.644051i	−0.129595	−	0.0347249i
$345$		0			0
$346$	−2.55966	−	9.55277i	−0.137608	−	0.513560i
$347$	−24.1293	−	13.9310i	−1.29533	−	0.747857i	−0.315733	−	0.948848i	$-0.602251\pi$
$347$	−24.1293	−	13.9310i	−1.29533	−	0.747857i	−0.979593	+	0.200991i	$0.935584\pi$
$348$		0			0
$349$	7.85155	+	2.10382i	0.420284	+	0.112615i	0.462762	−	0.886483i	$-0.346859\pi$
$349$	7.85155	+	2.10382i	0.420284	+	0.112615i	−0.0424778	+	0.999097i	$0.513525\pi$
$350$	−35.7621			−1.91156
$351$		0			0
$352$	1.07222			0.0571496
$353$	−0.765102	−	0.205008i	−0.0407222	−	0.0109115i	0.238400	−	0.971167i	$-0.423377\pi$
$353$	−0.765102	−	0.205008i	−0.0407222	−	0.0109115i	−0.279123	+	0.960255i	$0.590044\pi$
$354$		0			0
$355$	−10.6452	−	6.14601i	−0.564989	−	0.326197i
$356$	−2.55094	−	9.52023i	−0.135199	−	0.504571i
$357$		0			0
$358$	−5.58069	−	1.49534i	−0.294948	−	0.0790312i
$359$	21.9230	+	21.9230i	1.15705	+	1.15705i	0.985107	+	0.171942i	$0.0550042\pi$
$359$	21.9230	+	21.9230i	1.15705	+	1.15705i	0.171942	+	0.985107i	$0.444996\pi$
$360$		0			0
$361$			6.21521i			0.327116i
$362$	−0.0985363	+	0.367743i	−0.00517895	+	0.0193281i
$363$		0			0
$364$	−8.15995	−	14.3574i	−0.427698	−	0.752533i
$365$	13.9246	+	8.03939i	0.728848	+	0.420801i
$366$		0			0
$367$	1.42913	+	2.47533i	0.0746002	+	0.129211i	0.900912	−	0.434001i	$-0.142899\pi$
$367$	1.42913	+	2.47533i	0.0746002	+	0.129211i	−0.826312	+	0.563212i	$0.809565\pi$
$368$	2.52792			0.131777
$369$		0			0
$370$	5.49240	+	5.49240i	0.285537	+	0.285537i
$371$	13.1504	−	49.0779i	0.682734	−	2.54800i
$372$		0			0
$373$	9.89249	−	17.1343i	0.512214	−	0.887180i	−0.487686	−	0.873019i	$-0.662159\pi$
$373$	9.89249	−	17.1343i	0.512214	−	0.887180i	0.999900	−	0.0141612i	$-0.00450780\pi$
$374$	−2.21650	+	3.83909i	−0.114612	+	0.198514i
$375$		0			0
$376$	−1.22476	+	0.707116i	−0.0631622	+	0.0364667i
$377$	−2.63561	+	0.687089i	−0.135741	+	0.0353869i
$378$		0			0
$379$	−3.26410	−	3.26410i	−0.167665	−	0.167665i	0.618287	−	0.785952i	$-0.287827\pi$
$379$	−3.26410	−	3.26410i	−0.167665	−	0.167665i	−0.785952	+	0.618287i	$0.787827\pi$
$380$	15.5633	−	8.98547i	0.798380	−	0.460945i
$381$		0			0
$382$	10.1632	−	2.72321i	0.519993	−	0.139332i
$383$	−1.38882	−	5.18315i	−0.0709654	−	0.264846i	0.921323	−	0.388798i	$-0.127110\pi$
$383$	−1.38882	−	5.18315i	−0.0709654	−	0.264846i	−0.992288	+	0.123952i	$0.960443\pi$
$384$		0			0
$385$	16.9767	+	4.54890i	0.865215	+	0.231834i
$386$		−	7.96969i		−	0.405647i
$387$		0			0
$388$	1.82150	−	1.82150i	0.0924727	−	0.0924727i
$389$	−12.8925	−	22.3304i	−0.653675	−	1.13220i	−0.982224	−	0.187711i	$-0.939893\pi$
$389$	−12.8925	−	22.3304i	−0.653675	−	1.13220i	0.328549	−	0.944487i	$-0.393440\pi$
$390$		0			0
$391$	−5.22573	+	9.05123i	−0.264277	+	0.457740i
$392$	3.61789	+	13.5022i	0.182731	+	0.681962i
$393$		0			0
$394$	19.4653	−	11.2383i	0.980648	−	0.566177i
$395$	3.23135	−	3.23135i	0.162587	−	0.162587i
$396$		0			0
$397$	−10.8989	+	10.8989i	−0.547000	+	0.547000i	−0.925572	−	0.378572i	$-0.876415\pi$
$397$	−10.8989	+	10.8989i	−0.547000	+	0.547000i	0.378572	+	0.925572i	$0.376415\pi$
$398$	3.04973	−	11.3817i	0.152869	−	0.570515i
$399$		0			0
$400$	−6.76187	−	3.90397i	−0.338093	−	0.195198i
$401$	−3.84186	+	1.02942i	−0.191853	+	0.0514070i	−0.353466	−	0.935447i	$-0.614997\pi$
$401$	−3.84186	+	1.02942i	−0.191853	+	0.0514070i	0.161613	+	0.986854i	$0.448330\pi$
$402$		0			0
$403$	−32.4186	−	0.219822i	−1.61488	−	0.0109501i
$404$			9.61690i			0.478459i
$405$		0			0
$406$	3.45998			0.171716
$407$	−1.16357	−	2.01536i	−0.0576760	−	0.0998977i
$408$		0			0
$409$	−26.9511	+	7.22152i	−1.33264	+	0.357081i	−0.853700	−	0.520765i	$-0.825647\pi$
$409$	−26.9511	+	7.22152i	−1.33264	+	0.357081i	−0.478944	+	0.877845i	$0.658980\pi$
$410$	1.50047	−	0.402049i	0.0741028	−	0.0198558i
$411$		0			0
$412$	−5.27670	−	9.13951i	−0.259964	−	0.450272i
$413$	−45.8196			−2.25464
$414$		0			0
$415$			22.7232i			1.11544i
$416$	0.0244478	−	3.60547i	0.00119865	−	0.176773i
$417$		0			0
$418$	−5.20067	+	1.39352i	−0.254373	+	0.0681591i
$419$	15.9003	+	9.18003i	0.776779	+	0.448474i	0.835288	−	0.549813i	$-0.185301\pi$
$419$	15.9003	+	9.18003i	0.776779	+	0.448474i	−0.0585084	+	0.998287i	$0.518634\pi$
$420$		0			0
$421$	−6.33652	+	23.6482i	−0.308823	+	1.15254i	0.620781	+	0.783984i	$0.286816\pi$
$421$	−6.33652	+	23.6482i	−0.308823	+	1.15254i	−0.929604	+	0.368560i	$0.879851\pi$
$422$	14.6271	−	14.6271i	0.712037	−	0.712037i
$423$		0			0
$424$	7.84405	−	7.84405i	0.380941	−	0.380941i
$425$	27.9563	−	16.1406i	1.35608	−	0.782933i
$426$		0			0
$427$	12.7539	+	47.5982i	0.617205	+	2.30344i
$428$	−4.43721	+	7.68547i	−0.214481	+	0.371491i
$429$		0			0
$430$	−4.45280	−	7.71248i	−0.214733	−	0.371929i
$431$	−14.5640	+	14.5640i	−0.701523	+	0.701523i	−0.964737	−	0.263214i	$-0.915217\pi$
$431$	−14.5640	+	14.5640i	−0.701523	+	0.701523i	0.263214	+	0.964737i	$0.415217\pi$
$432$		0			0
$433$			18.5433i			0.891136i	0.895248	+	0.445568i	$0.146998\pi$
$433$			18.5433i			0.891136i	−0.895248	+	0.445568i	$0.853002\pi$
$434$	39.7798	+	10.6590i	1.90949	+	0.511647i
$435$		0			0
$436$	−4.88185	−	18.2193i	−0.233798	−	0.872546i
$437$	−12.2614	+	3.28543i	−0.586541	+	0.157163i
$438$		0			0
$439$	3.74229	−	2.16061i	0.178610	−	0.103120i	−0.408030	−	0.912969i	$-0.633784\pi$
$439$	3.74229	−	2.16061i	0.178610	−	0.103120i	0.586639	+	0.809848i	$0.300451\pi$
$440$	2.71337	+	2.71337i	0.129355	+	0.129355i
$441$		0			0
$442$	12.8588	+	7.54077i	0.611633	+	0.358678i
$443$	−27.7852	+	16.0418i	−1.32011	+	0.762168i	−0.983747	−	0.179562i	$-0.942532\pi$
$443$	−27.7852	+	16.0418i	−1.32011	+	0.762168i	−0.336368	+	0.941731i	$0.609199\pi$
$444$		0			0
$445$	17.6365	−	30.5474i	0.836052	−	1.44808i
$446$	−7.84574	+	13.5892i	−0.371507	+	0.643468i
$447$		0			0
$448$	−1.18545	+	4.42416i	−0.0560072	+	0.209022i
$449$	25.3608	+	25.3608i	1.19685	+	1.19685i	0.975105	+	0.221743i	$0.0711746\pi$
$449$	25.3608	+	25.3608i	1.19685	+	1.19685i	0.221743	+	0.975105i	$0.428825\pi$
$450$		0			0
$451$	−0.465401			−0.0219149
$452$	−0.963564	−	1.66894i	−0.0453222	−	0.0785004i
$453$		0			0
$454$	−13.8392	−	7.99009i	−0.649508	−	0.374994i
$455$	15.6833	−	56.9826i	0.735245	−	2.67138i
$456$		0			0
$457$	6.84032	−	25.5284i	0.319977	−	1.19417i	−0.599289	−	0.800533i	$-0.704550\pi$
$457$	6.84032	−	25.5284i	0.319977	−	1.19417i	0.919266	−	0.393637i	$-0.128783\pi$
$458$			9.15150i			0.427622i
$459$		0			0
$460$	6.39718	+	6.39718i	0.298270	+	0.298270i
$461$	13.1223	+	3.51611i	0.611166	+	0.163762i	0.551109	−	0.834433i	$-0.314205\pi$
$461$	13.1223	+	3.51611i	0.611166	+	0.163762i	0.0600575	+	0.998195i	$0.480872\pi$
$462$		0			0
$463$	−0.373475	−	1.39383i	−0.0173568	−	0.0647766i	0.956704	−	0.291062i	$-0.0940085\pi$
$463$	−0.373475	−	1.39383i	−0.0173568	−	0.0647766i	−0.974061	+	0.226285i	$0.927342\pi$
$464$	0.654210	+	0.377708i	0.0303709	+	0.0175347i
$465$		0			0
$466$	23.8466	+	6.38967i	1.10467	+	0.295996i
$467$	13.3760			0.618969			0.309485	−	0.950904i	$-0.399843\pi$
$467$	13.3760			0.618969			0.309485	+	0.950904i	$0.399843\pi$
$468$		0			0
$469$	41.8285			1.93146
$470$	−4.88882	−	1.30996i	−0.225504	−	0.0604237i
$471$		0			0
$472$	−8.66354	−	5.00190i	−0.398772	−	0.230231i
$473$	0.690565	+	2.57722i	0.0317522	+	0.118501i
$474$		0			0
$475$	37.8714	+	10.1476i	1.73766	+	0.465604i
$476$	−13.3901	−	13.3901i	−0.613736	−	0.613736i
$477$		0			0
$478$			15.6710i			0.716776i
$479$	−8.96153	+	33.4449i	−0.409463	+	1.52814i	0.386210	+	0.922411i	$0.373784\pi$
$479$	−8.96153	+	33.4449i	−0.409463	+	1.52814i	−0.795673	+	0.605726i	$0.792883\pi$
$480$		0			0
$481$	−6.80342	+	3.86669i	−0.310209	+	0.176306i
$482$	−3.14656	−	1.81667i	−0.143322	−	0.0827469i
$483$		0			0
$484$	4.92517	+	8.53065i	0.223871	+	0.387757i
$485$	9.21900			0.418613
$486$		0			0
$487$	−7.44349	−	7.44349i	−0.337297	−	0.337297i	0.518052	−	0.855349i	$-0.326657\pi$
$487$	−7.44349	−	7.44349i	−0.337297	−	0.337297i	−0.855349	+	0.518052i	$0.826657\pi$
$488$	−2.78456	+	10.3921i	−0.126051	+	0.470429i
$489$		0			0
$490$	−25.0132	+	43.3241i	−1.12998	+	1.95718i
$491$	−10.6286	+	18.4092i	−0.479660	+	0.830795i	−0.999728	−	0.0233295i	$-0.992573\pi$
$491$	−10.6286	+	18.4092i	−0.479660	+	0.830795i	0.520068	+	0.854125i	$0.325907\pi$
$492$		0			0
$493$	−2.70477	+	1.56160i	−0.121817	+	0.0703309i
$494$	4.56728	+	17.5196i	0.205492	+	0.788246i
$495$		0			0
$496$	6.35795	+	6.35795i	0.285480	+	0.285480i
$497$	−13.6239	+	7.86576i	−0.611116	+	0.352828i
$498$		0			0
$499$	2.61532	−	0.700773i	0.117078	−	0.0313709i	−0.199804	−	0.979836i	$-0.564031\pi$
$499$	2.61532	−	0.700773i	0.117078	−	0.0313709i	0.316882	+	0.948465i	$0.397364\pi$
$500$	−2.60089	−	9.70665i	−0.116315	−	0.434095i
$501$		0			0
$502$	−23.4918	−	6.29460i	−1.04849	−	0.280942i
$503$		−	12.3938i		−	0.552614i	−0.961069	−	0.276307i	$-0.910889\pi$
$503$		−	12.3938i		−	0.552614i	0.961069	−	0.276307i	$-0.0891107\pi$
$504$		0			0
$505$	−24.3366	+	24.3366i	−1.08296	+	1.08296i
$506$	−1.35525	−	2.34736i	−0.0602480	−	0.104353i
$507$		0			0
$508$	−2.77896	+	4.81330i	−0.123297	+	0.213556i
$509$	5.30979	+	19.8164i	0.235352	+	0.878347i	0.977990	+	0.208653i	$0.0669079\pi$
$509$	5.30979	+	19.8164i	0.235352	+	0.878347i	−0.742637	+	0.669694i	$0.766425\pi$
$510$		0			0
$511$	17.8210	−	10.2889i	0.788352	−	0.455155i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−5.37262	+	5.37262i	−0.236976	+	0.236976i
$515$	9.77526	−	36.4818i	0.430749	−	1.60758i
$516$		0			0
$517$	1.31321	+	0.758185i	0.0577551	+	0.0333449i
$518$	9.60215	−	2.57289i	0.421894	−	0.113046i
$519$		0			0
$520$	9.18589	−	9.06215i	0.402828	−	0.397402i
$521$			14.6532i			0.641968i	0.947085	+	0.320984i	$0.104014\pi$
$521$			14.6532i			0.641968i	−0.947085	+	0.320984i	$0.895986\pi$
$522$		0			0
$523$	14.9734			0.654740			0.327370	−	0.944896i	$-0.393838\pi$
$523$	14.9734			0.654740			0.327370	+	0.944896i	$0.393838\pi$
$524$	−2.67388	−	4.63129i	−0.116809	−	0.202319i
$525$		0			0
$526$	26.3653	−	7.06456i	1.14958	−	0.308030i
$527$	−35.9078	+	9.62146i	−1.56417	+	0.419118i
$528$		0			0
$529$	8.30480	+	14.3843i	0.361078	+	0.625406i
$530$	39.7004			1.72448
$531$		0			0
$532$		−	22.9995i		−	0.997154i
$533$	−0.0106116	+	1.56497i	−0.000459641	+	0.0677862i
$534$		0			0
$535$	−30.6777	+	8.22007i	−1.32631	+	0.355385i
$536$	7.90889	+	4.56620i	0.341612	+	0.197230i
$537$		0			0
$538$	3.83882	−	14.3267i	0.165503	−	0.617667i
$539$	10.5981	−	10.5981i	0.456493	−	0.456493i
$540$		0			0
$541$	−24.2888	+	24.2888i	−1.04426	+	1.04426i	−0.0452820	+	0.998974i	$0.514419\pi$
$541$	−24.2888	+	24.2888i	−1.04426	+	1.04426i	−0.998974	+	0.0452820i	$0.985581\pi$
$542$	−19.6809	+	11.3628i	−0.845368	+	0.488073i
$543$		0			0
$544$	−1.07006	−	3.99353i	−0.0458786	−	0.171221i
$545$	33.7518	−	58.4599i	1.44577	−	2.50415i
$546$		0			0
$547$	0.832021	+	1.44110i	0.0355746	+	0.0616171i	0.883265	−	0.468875i	$-0.155341\pi$
$547$	0.832021	+	1.44110i	0.0355746	+	0.0616171i	−0.847690	+	0.530492i	$0.822007\pi$
$548$	0.359681	−	0.359681i	0.0153648	−	0.0153648i
$549$		0			0
$550$			8.37182i			0.356976i
$551$	−3.66405	−	0.981780i	−0.156094	−	0.0418252i
$552$		0			0
$553$	−1.51371	−	5.64924i	−0.0643695	−	0.240230i
$554$	−22.4816	+	6.02392i	−0.955150	+	0.255932i
$555$		0			0
$556$	−6.05008	+	3.49301i	−0.256580	+	0.148137i
$557$	−22.6692	−	22.6692i	−0.960523	−	0.960523i	0.0387266	−	0.999250i	$-0.487670\pi$
$557$	−22.6692	−	22.6692i	−0.960523	−	0.960523i	−0.999250	+	0.0387266i	$0.987670\pi$
$558$		0			0
$559$	8.68196	−	2.26334i	0.367208	−	0.0957292i
$560$	−14.1957	+	8.19589i	−0.599878	+	0.346340i
$561$		0			0
$562$	−1.61999	+	2.80591i	−0.0683354	+	0.118360i
$563$	−5.22488	+	9.04976i	−0.220203	+	0.381402i	−0.954869	−	0.297026i	$-0.904005\pi$
$563$	−5.22488	+	9.04976i	−0.220203	+	0.381402i	0.734667	+	0.678428i	$0.237338\pi$
$564$		0			0
$565$	1.78503	−	6.66183i	0.0750969	−	0.280265i
$566$	−3.92537	−	3.92537i	−0.164996	−	0.164996i
$567$		0			0
$568$	−3.43466			−0.144115
$569$	−5.22038	−	9.04197i	−0.218850	−	0.379059i	0.735607	−	0.677409i	$-0.236897\pi$
$569$	−5.22038	−	9.04197i	−0.218850	−	0.379059i	−0.954457	+	0.298350i	$0.903564\pi$
$570$		0			0
$571$	14.9685	+	8.64209i	0.626414	+	0.361660i	0.779362	−	0.626574i	$-0.215543\pi$
$571$	14.9685	+	8.64209i	0.626414	+	0.361660i	−0.152948	+	0.988234i	$0.548877\pi$
$572$	−3.36104	+	1.91023i	−0.140532	+	0.0798706i
$573$		0			0
$574$	0.514549	−	1.92032i	0.0214768	−	0.0801527i
$575$			19.7379i			0.823126i
$576$		0			0
$577$	−13.1381	−	13.1381i	−0.546947	−	0.546947i	0.378609	−	0.925557i	$-0.376402\pi$
$577$	−13.1381	−	13.1381i	−0.546947	−	0.546947i	−0.925557	+	0.378609i	$0.876402\pi$
$578$	0.0901213	+	0.0241479i	0.00374855	+	0.00100442i
$579$		0			0
$580$	0.699717	+	2.61138i	0.0290542	+	0.108432i
$581$	25.1853	+	14.5408i	1.04486	+	0.603253i
$582$		0			0
$583$	−11.4890	−	3.07848i	−0.475827	−	0.127497i
$584$	4.49276			0.185912
$585$		0			0
$586$	−17.2467			−0.712455
$587$	22.9881	+	6.15965i	0.948822	+	0.254236i	0.699862	−	0.714278i	$-0.253245\pi$
$587$	22.9881	+	6.15965i	0.948822	+	0.254236i	0.248960	+	0.968514i	$0.419911\pi$
$588$		0			0
$589$	−39.1015	−	22.5753i	−1.61115	−	0.930198i
$590$	−9.26618	−	34.5818i	−0.381482	−	1.42371i
$591$		0			0
$592$	2.09644	+	0.561739i	0.0861630	+	0.0230873i
$593$	−23.2354	−	23.2354i	−0.954164	−	0.954164i	0.0448310	−	0.998995i	$-0.485725\pi$
$593$	−23.2354	−	23.2354i	−0.954164	−	0.954164i	−0.998995	+	0.0448310i	$0.985725\pi$
$594$		0			0
$595$		−	67.7703i		−	2.77831i
$596$	4.16059	−	15.5275i	0.170424	−	0.636032i
$597$		0			0
$598$	−7.92416	+	4.50365i	−0.324043	+	0.184168i
$599$	3.73418	+	2.15593i	0.152575	+	0.0880889i	0.574344	−	0.818614i	$-0.305257\pi$
$599$	3.73418	+	2.15593i	0.152575	+	0.0880889i	−0.421769	+	0.906703i	$0.638591\pi$
$600$		0			0
$601$	−15.6036	−	27.0262i	−0.636484	−	1.10242i	−0.986199	−	0.165567i	$-0.947055\pi$
$601$	−15.6036	−	27.0262i	−0.636484	−	1.10242i	0.349714	−	0.936856i	$-0.386279\pi$
$602$	−11.3975			−0.464529
$603$		0			0
$604$	1.96587	+	1.96587i	0.0799901	+	0.0799901i
$605$	−9.12404	+	34.0514i	−0.370945	+	1.38439i
$606$		0			0
$607$	−4.69953	+	8.13983i	−0.190748	+	0.330385i	−0.945498	−	0.325627i	$-0.894425\pi$
$607$	−4.69953	+	8.13983i	−0.190748	+	0.330385i	0.754750	+	0.656012i	$0.227758\pi$
$608$	2.51074	−	4.34872i	0.101824	−	0.176364i
$609$		0			0
$610$	−33.3450	+	19.2517i	−1.35010	+	0.779480i
$611$	2.57943	−	4.39855i	0.104352	−	0.177946i
$612$		0			0
$613$	−17.1072	−	17.1072i	−0.690954	−	0.690954i	0.271488	−	0.962442i	$-0.412484\pi$
$613$	−17.1072	−	17.1072i	−0.690954	−	0.690954i	−0.962442	+	0.271488i	$0.912484\pi$
$614$	−0.770508	+	0.444853i	−0.0310952	+	0.0179528i
$615$		0			0
$616$	4.74367	−	1.27106i	0.191128	−	0.0512126i
$617$	−11.7214	−	43.7450i	−0.471888	−	1.76111i	−0.632979	−	0.774169i	$-0.718168\pi$
$617$	−11.7214	−	43.7450i	−0.471888	−	1.76111i	0.161091	−	0.986940i	$-0.448499\pi$
$618$		0			0
$619$	37.1618	+	9.95749i	1.49366	+	0.400225i	0.910971	−	0.412470i	$-0.135334\pi$
$619$	37.1618	+	9.95749i	1.49366	+	0.400225i	0.582689	+	0.812695i	$0.302000\pi$
$620$			32.1789i			1.29234i
$621$		0			0
$622$	−10.7050	+	10.7050i	−0.429233	+	0.429233i
$623$	−22.5715	−	39.0950i	−0.904308	−	1.56631i
$624$		0			0
$625$	−1.53794	+	2.66379i	−0.0615175	+	0.106551i
$626$	−3.36993	−	12.5768i	−0.134690	−	0.502668i
$627$		0			0
$628$	−11.9767	+	6.91473i	−0.477921	+	0.275928i
$629$	−6.34506	+	6.34506i	−0.252994	+	0.252994i
$630$		0			0
$631$	27.9315	−	27.9315i	1.11193	−	1.11193i	0.119045	−	0.992889i	$-0.462017\pi$
$631$	27.9315	−	27.9315i	1.11193	−	1.11193i	0.992889	−	0.119045i	$-0.0379833\pi$
$632$	0.330488	−	1.23340i	0.0131461	−	0.0490619i
$633$		0			0
$634$	10.6184	+	6.13056i	0.421712	+	0.243476i
$635$	−19.2130	+	5.14812i	−0.762446	+	0.204297i
$636$		0			0
$637$	−35.3958	−	35.8791i	−1.40243	−	1.42158i
$638$		−	0.809974i		−	0.0320672i
$639$		0			0
$640$	−3.57882			−0.141465
$641$	−1.42504	−	2.46825i	−0.0562859	−	0.0974900i	0.836510	−	0.547952i	$-0.184592\pi$
$641$	−1.42504	−	2.46825i	−0.0562859	−	0.0974900i	−0.892795	+	0.450462i	$0.851259\pi$
$642$		0			0
$643$	17.8708	−	4.78846i	0.704755	−	0.188838i	0.111395	−	0.993776i	$-0.464468\pi$
$643$	17.8708	−	4.78846i	0.704755	−	0.188838i	0.593359	+	0.804938i	$0.297801\pi$
$644$	11.1839	−	2.99673i	0.440709	−	0.118088i
$645$		0			0
$646$	10.3804	+	17.9794i	0.408412	+	0.707390i
$647$	35.2511			1.38587			0.692933	−	0.721002i	$-0.256318\pi$
$647$	35.2511			1.38587			0.692933	+	0.721002i	$0.256318\pi$
$648$		0			0
$649$			10.7263i			0.421043i
$650$	28.1512	+	0.190886i	1.10418	+	0.00748718i
$651$		0			0
$652$	−21.0026	+	5.62762i	−0.822524	+	0.220395i
$653$	2.91654	+	1.68387i	0.114133	+	0.0658948i	0.555980	−	0.831196i	$-0.312343\pi$
$653$	2.91654	+	1.68387i	0.114133	+	0.0658948i	−0.441847	+	0.897091i	$0.645677\pi$
$654$		0			0
$655$	4.95344	−	18.4865i	0.193547	−	0.722327i
$656$	0.306922	−	0.306922i	0.0119833	−	0.0119833i
$657$		0			0
$658$	−4.58029	+	4.58029i	−0.178558	+	0.178558i
$659$	−4.83089	+	2.78912i	−0.188185	+	0.108649i	−0.591133	−	0.806574i	$-0.701319\pi$
$659$	−4.83089	+	2.78912i	−0.188185	+	0.108649i	0.402948	+	0.915223i	$0.367986\pi$
$660$		0			0
$661$	0.662272	+	2.47163i	0.0257594	+	0.0961353i	0.977609	−	0.210431i	$-0.0674866\pi$
$661$	0.662272	+	2.47163i	0.0257594	+	0.0961353i	−0.951849	+	0.306566i	$0.900820\pi$
$662$	−4.24581	+	7.35397i	−0.165018	+	0.285820i
$663$		0			0
$664$	3.17468	+	5.49871i	0.123202	+	0.213391i
$665$	58.2026	−	58.2026i	2.25700	−	2.25700i
$666$		0			0
$667$		−	1.90964i		−	0.0739414i
$668$	14.2638	+	3.82198i	0.551885	+	0.147877i
$669$		0			0
$670$	8.45903	+	31.5695i	0.326801	+	1.21964i
$671$	11.1426	−	2.98566i	0.430157	−	0.115260i
$672$		0			0
$673$	8.56847	−	4.94701i	0.330290	−	0.190693i	−0.325680	−	0.945480i	$-0.605593\pi$
$673$	8.56847	−	4.94701i	0.330290	−	0.190693i	0.655970	+	0.754787i	$0.272260\pi$
$674$	−8.33903	−	8.33903i	−0.321207	−	0.321207i
$675$		0			0
$676$	6.34673	+	11.3454i	0.244105	+	0.436363i
$677$	21.3304	−	12.3151i	0.819796	−	0.473309i	−0.0305503	−	0.999533i	$-0.509726\pi$
$677$	21.3304	−	12.3151i	0.819796	−	0.473309i	0.850346	+	0.526224i	$0.176393\pi$
$678$		0			0
$679$	5.89931	−	10.2179i	0.226395	−	0.392127i
$680$	7.39814	−	12.8140i	0.283706	−	0.491393i
$681$		0			0
$682$	2.49524	−	9.31236i	0.0955477	−	0.356589i
$683$	−23.4615	−	23.4615i	−0.897728	−	0.897728i	0.0975073	−	0.995235i	$-0.468913\pi$
$683$	−23.4615	−	23.4615i	−0.897728	−	0.897728i	−0.995235	+	0.0975073i	$0.968913\pi$
$684$		0			0
$685$	1.82042			0.0695548
$686$	15.9815	+	27.6807i	0.610176	+	1.05685i
$687$		0			0
$688$	−2.15504	−	1.24421i	−0.0821600	−	0.0474351i
$689$	−10.6137	+	38.5630i	−0.404350	+	1.46913i
$690$		0			0
$691$	−3.98917	+	14.8878i	−0.151755	+	0.566359i	0.847606	+	0.530626i	$0.178043\pi$
$691$	−3.98917	+	14.8878i	−0.151755	+	0.566359i	−0.999361	+	0.0357326i	$0.988624\pi$
$692$		−	9.88975i		−	0.375952i
$693$		0			0
$694$	−19.7015	−	19.7015i	−0.747857	−	0.747857i
$695$	−24.1498	−	6.47092i	−0.916054	−	0.245456i
$696$		0			0
$697$	0.464464	+	1.73341i	0.0175928	+	0.0656574i
$698$	7.03951	+	4.06426i	0.266449	+	0.153835i
$699$		0			0
$700$	−34.5435	−	9.25591i	−1.30562	−	0.349840i
$701$	−19.3754			−0.731800			−0.365900	−	0.930654i	$-0.619239\pi$
$701$	−19.3754			−0.731800			−0.365900	+	0.930654i	$0.619239\pi$
$702$		0			0
$703$	−10.8986			−0.411047
$704$	1.03569	+	0.277511i	0.0390339	+	0.0104591i
$705$		0			0
$706$	−0.685971	−	0.396046i	−0.0258169	−	0.0149054i
$707$	11.4004	+	42.5467i	0.428754	+	1.60013i
$708$		0			0
$709$	21.3837	+	5.72975i	0.803082	+	0.215185i	0.636937	−	0.770916i	$-0.280201\pi$
$709$	21.3837	+	5.72975i	0.803082	+	0.215185i	0.166145	+	0.986101i	$0.446868\pi$
$710$	−8.69178	−	8.69178i	−0.326197	−	0.326197i
$711$		0			0
$712$		−	9.85607i		−	0.369372i
$713$	5.88291	−	21.9553i	0.220317	−	0.822233i
$714$		0			0
$715$	−13.3395	−	3.67143i	−0.498869	−	0.137304i
$716$	−5.00351	−	2.88878i	−0.186990	−	0.107959i
$717$		0			0
$718$	15.5019	+	26.8500i	0.578525	+	1.00203i
$719$	28.0174			1.04487			0.522436	−	0.852679i	$-0.325023\pi$
$719$	28.0174			1.04487			0.522436	+	0.852679i	$0.325023\pi$
$720$		0			0
$721$	−34.1794	−	34.1794i	−1.27291	−	1.27291i
$722$	−1.60861	+	6.00343i	−0.0598664	+	0.223425i
$723$		0			0
$724$	−0.190358	+	0.329709i	−0.00707458	+	0.0122535i
$725$	−2.94912	+	5.10803i	−0.109528	+	0.189707i
$726$		0			0
$727$	−26.1468	+	15.0959i	−0.969733	+	0.559876i	−0.899155	−	0.437631i	$-0.855818\pi$
$727$	−26.1468	+	15.0959i	−0.969733	+	0.559876i	−0.0705781	+	0.997506i	$0.522484\pi$
$728$	−4.16594	−	15.9801i	−0.154400	−	0.592264i
$729$		0			0
$730$	11.3694	+	11.3694i	0.420801	+	0.420801i
$731$	8.90979	−	5.14407i	0.329541	−	0.190260i
$732$		0			0
$733$	−30.2965	+	8.11792i	−1.11903	+	0.299842i	−0.770489	−	0.637453i	$-0.779988\pi$
$733$	−30.2965	+	8.11792i	−1.11903	+	0.299842i	−0.348537	+	0.937295i	$0.613321\pi$
$734$	0.739774	+	2.76087i	0.0273056	+	0.101906i
$735$		0			0
$736$	2.44179	+	0.654275i	0.0900055	+	0.0241169i
$737$		−	9.79195i		−	0.360691i
$738$		0			0
$739$	36.3493	−	36.3493i	1.33713	−	1.33713i	0.438307	−	0.898825i	$-0.355578\pi$
$739$	36.3493	−	36.3493i	1.33713	−	1.33713i	0.898825	−	0.438307i	$-0.144422\pi$
$740$	3.88372	+	6.72679i	0.142768	+	0.247282i
$741$		0			0
$742$	25.4046	−	44.0021i	0.932632	−	1.61537i
$743$	0.788263	+	2.94184i	0.0289186	+	0.107926i	0.978877	−	0.204452i	$-0.0655412\pi$
$743$	0.788263	+	2.94184i	0.0289186	+	0.107926i	−0.949958	+	0.312378i	$0.898875\pi$
$744$		0			0
$745$	49.8228	−	28.7652i	1.82537	−	1.05388i
$746$	13.9901	−	13.9901i	0.512214	−	0.512214i
$747$		0			0
$748$	−3.13460	+	3.13460i	−0.114612	+	0.114612i
$749$	−10.5202	+	39.2618i	−0.384399	+	1.43460i
$750$		0			0
$751$	3.94059	+	2.27510i	0.143794	+	0.0830196i	0.570171	−	0.821526i	$-0.306877\pi$
$751$	3.94059	+	2.27510i	0.143794	+	0.0830196i	−0.426377	+	0.904546i	$0.640210\pi$
$752$	−1.36604	+	0.366030i	−0.0498145	+	0.0133478i
$753$		0			0
$754$	−2.72363	−	0.0184683i	−0.0991888	−	0.000672574i
$755$			9.94968i			0.362106i
$756$		0			0
$757$	12.8805			0.468150			0.234075	−	0.972218i	$-0.424794\pi$
$757$	12.8805			0.468150			0.234075	+	0.972218i	$0.424794\pi$
$758$	−2.30806	−	3.99768i	−0.0838327	−	0.145202i
$759$		0			0
$760$	17.3586	−	4.65122i	0.629662	−	0.168718i
$761$	33.8916	−	9.08124i	1.22857	−	0.329195i	0.414548	−	0.910027i	$-0.363940\pi$
$761$	33.8916	−	9.08124i	1.22857	−	0.329195i	0.814023	+	0.580833i	$0.197273\pi$
$762$		0			0
$763$	−43.1961	−	74.8179i	−1.56380	−	2.70859i
$764$	10.5217			0.380662
$765$		0			0
$766$		−	5.36599i		−	0.193881i
$767$	36.0684	+	0.244570i	1.30235	+	0.00883093i
$768$		0			0
$769$	24.4941	−	6.56317i	0.883279	−	0.236674i	0.211458	−	0.977387i	$-0.432179\pi$
$769$	24.4941	−	6.56317i	0.883279	−	0.236674i	0.671821	+	0.740713i	$0.265512\pi$
$770$	15.2209	+	8.78781i	0.548524	+	0.316691i
$771$		0			0
$772$	2.06271	−	7.69813i	0.0742385	−	0.277062i
$773$	−12.4785	+	12.4785i	−0.448821	+	0.448821i	−0.894962	−	0.446142i	$-0.852798\pi$
$773$	−12.4785	+	12.4785i	−0.448821	+	0.448821i	0.446142	+	0.894962i	$0.352798\pi$
$774$		0			0
$775$	−49.6424	+	49.6424i	−1.78321	+	1.78321i
$776$	2.23087	−	1.28800i	0.0800837	−	0.0462364i
$777$		0			0
$778$	−6.67364	−	24.9064i	−0.239262	−	0.892936i
$779$	−1.08979	+	1.88758i	−0.0390459	+	0.0676295i
$780$		0			0
$781$	1.84136	+	3.18933i	0.0658890	+	0.114123i
$782$	−7.39030	+	7.39030i	−0.264277	+	0.264277i
$783$		0			0
$784$			13.9785i			0.499231i
$785$	−47.8067	−	12.8098i	−1.70629	−	0.457200i
$786$		0			0
$787$	8.78278	+	32.7778i	0.313072	+	1.16840i	0.925771	+	0.378085i	$0.123417\pi$
$787$	8.78278	+	32.7778i	0.313072	+	1.16840i	−0.612698	+	0.790317i	$0.709916\pi$
$788$	21.7107	−	5.81737i	0.773412	−	0.207235i
$789$		0			0
$790$	3.95758	−	2.28491i	0.140804	−	0.0812934i
$791$	−6.24141	−	6.24141i	−0.221919	−	0.221919i
$792$		0			0
$793$	−9.78558	−	37.5365i	−0.347496	−	1.33296i
$794$	−13.3484	+	7.70668i	−0.473716	+	0.273500i
$795$		0			0
$796$	5.89163	−	10.2046i	0.208823	−	0.361692i
$797$	4.36366	−	7.55809i	0.154569	−	0.267721i	−0.778333	−	0.627852i	$-0.783934\pi$
$797$	4.36366	−	7.55809i	0.154569	−	0.267721i	0.932902	+	0.360130i	$0.117268\pi$
$798$		0			0
$799$	1.51332	−	5.64778i	0.0535373	−	0.199804i
$800$	−5.52104	−	5.52104i	−0.195198	−	0.195198i
$801$		0			0
$802$	−3.97739			−0.140446
$803$	−2.40862	−	4.17185i	−0.0849982	−	0.147221i
$804$		0			0
$805$	35.8857	+	20.7186i	1.26480	+	0.730235i
$806$	−31.2570	−	8.60287i	−1.10098	−	0.303023i
$807$		0			0
$808$	−2.48904	+	9.28922i	−0.0875640	+	0.326793i
$809$		−	16.8882i		−	0.593758i	−0.954915	−	0.296879i	$-0.904054\pi$
$809$		−	16.8882i		−	0.593758i	0.954915	−	0.296879i	$-0.0959458\pi$
$810$		0			0
$811$	−22.1364	−	22.1364i	−0.777313	−	0.777313i	0.202060	−	0.979373i	$-0.435236\pi$
$811$	−22.1364	−	22.1364i	−0.777313	−	0.777313i	−0.979373	+	0.202060i	$0.935236\pi$
$812$	3.34208	+	0.895509i	0.117284	+	0.0314262i
$813$		0			0
$814$	−0.602308	−	2.24784i	−0.0211109	−	0.0787869i
$815$	−67.3905	−	38.9079i	−2.36059	−	1.36289i
$816$		0			0
$817$	12.0698	+	3.23409i	0.422268	+	0.113146i
$818$	−27.9018			−0.975563
$819$		0			0
$820$	1.55340			0.0542470
$821$	−34.4115	−	9.22053i	−1.20097	−	0.321799i	−0.397756	−	0.917491i	$-0.630211\pi$
$821$	−34.4115	−	9.22053i	−1.20097	−	0.321799i	−0.803213	+	0.595692i	$0.796878\pi$
$822$		0			0
$823$	−26.7859	−	15.4649i	−0.933699	−	0.539071i	−0.0457195	−	0.998954i	$-0.514558\pi$
$823$	−26.7859	−	15.4649i	−0.933699	−	0.539071i	−0.887980	+	0.459883i	$0.847891\pi$
$824$	−2.73142	−	10.1938i	−0.0951536	−	0.355118i
$825$		0			0
$826$	−44.2584	−	11.8590i	−1.53995	−	0.412627i
$827$	35.1434	+	35.1434i	1.22206	+	1.22206i	0.966899	+	0.255158i	$0.0821273\pi$
$827$	35.1434	+	35.1434i	1.22206	+	1.22206i	0.255158	+	0.966899i	$0.417873\pi$
$828$		0			0
$829$			19.6669i			0.683058i	0.939871	+	0.341529i	$0.110945\pi$
$829$			19.6669i			0.683058i	−0.939871	+	0.341529i	$0.889055\pi$
$830$	−5.88120	+	21.9489i	−0.204140	+	0.761859i
$831$		0			0
$832$	0.956779	−	3.47629i	0.0331703	−	0.120519i
$833$	−50.0499	−	28.8963i	−1.73413	−	1.00120i
$834$		0			0
$835$	26.4242	+	45.7681i	0.914448	+	1.58387i
$836$	−5.38413			−0.186214
$837$		0			0
$838$	12.9825	+	12.9825i	0.448474	+	0.448474i
$839$	−10.2614	+	38.2961i	−0.354263	+	1.32213i	0.527147	+	0.849774i	$0.323262\pi$
$839$	−10.2614	+	38.2961i	−0.354263	+	1.32213i	−0.881410	+	0.472353i	$0.843405\pi$
$840$		0			0
$841$	−14.2147	+	24.6205i	−0.490161	+	0.848984i
$842$	−12.2412	+	21.2024i	−0.421860	+	0.730684i
$843$		0			0
$844$	17.9145	−	10.3429i	0.616642	−	0.356019i
$845$	−12.6498	+	44.7719i	−0.435165	+	1.54020i
$846$		0			0
$847$	31.9024	+	31.9024i	1.09618	+	1.09618i
$848$	9.60696	−	5.54658i	0.329904	−	0.190470i
$849$		0			0
$850$	31.1812	−	8.35497i	1.06951	−	0.286573i
$851$	−1.42003	−	5.29963i	−0.0486781	−	0.181669i
$852$		0			0
$853$	−0.0667930	−	0.0178971i	−0.00228695	−	0.000612786i	0.257675	−	0.966232i	$-0.417043\pi$
$853$	−0.0667930	−	0.0178971i	−0.00228695	−	0.000612786i	−0.259962	+	0.965619i	$0.583710\pi$
$854$			49.2773i			1.68624i
$855$		0			0
$856$	−6.27516	+	6.27516i	−0.214481	+	0.214481i
$857$	−9.61874	−	16.6601i	−0.328570	−	0.569099i	0.653659	−	0.756790i	$-0.273233\pi$
$857$	−9.61874	−	16.6601i	−0.328570	−	0.569099i	−0.982228	+	0.187690i	$0.939900\pi$
$858$		0			0
$859$	2.13530	−	3.69845i	0.0728556	−	0.126190i	−0.827296	−	0.561766i	$-0.810122\pi$
$859$	2.13530	−	3.69845i	0.0728556	−	0.126190i	0.900152	+	0.435576i	$0.143455\pi$
$860$	−2.30494	−	8.60215i	−0.0785978	−	0.293331i
$861$		0			0
$862$	−17.8372	+	10.2983i	−0.607537	+	0.350762i
$863$	−20.8127	+	20.8127i	−0.708471	+	0.708471i	−0.966214	−	0.257743i	$-0.917021\pi$
$863$	−20.8127	+	20.8127i	−0.708471	+	0.708471i	0.257743	+	0.966214i	$0.417021\pi$
$864$		0			0
$865$	25.0271	−	25.0271i	0.850946	−	0.850946i
$866$	−4.79937	+	17.9115i	−0.163089	+	0.608657i
$867$		0			0
$868$	35.6656	+	20.5915i	1.21057	+	0.698922i
$869$	−1.32247	+	0.354356i	−0.0448619	+	0.0120207i
$870$		0			0
$871$	−32.9266	−	0.223267i	−1.11567	−	0.00756511i
$872$		−	18.8620i		−	0.638748i
$873$		0			0
$874$	−12.6939			−0.429378
$875$	−23.0135	−	39.8605i	−0.777998	−	1.34753i
$876$		0			0
$877$	−43.8456	+	11.7484i	−1.48056	+	0.396715i	−0.906537	−	0.422125i	$-0.861284\pi$
$877$	−43.8456	+	11.7484i	−1.48056	+	0.396715i	−0.574022	+	0.818840i	$0.694618\pi$
$878$	4.17398	−	1.11842i	0.140865	−	0.0377447i
$879$		0			0
$880$	1.91864	+	3.32318i	0.0646774	+	0.112024i
$881$	32.8947			1.10825			0.554125	−	0.832434i	$-0.313053\pi$
$881$	32.8947			1.10825			0.554125	+	0.832434i	$0.313053\pi$
$882$		0			0
$883$		−	14.1665i		−	0.476742i	−0.971174	−	0.238371i	$-0.923387\pi$
$883$		−	14.1665i		−	0.476742i	0.971174	−	0.238371i	$-0.0766134\pi$
$884$	10.4690	+	10.6119i	0.352110	+	0.356918i
$885$		0			0
$886$	−30.9904	+	8.30384i	−1.04114	+	0.278973i
$887$	3.64939	+	2.10697i	0.122534	+	0.0707453i	0.560014	−	0.828483i	$-0.310796\pi$
$887$	3.64939	+	2.10697i	0.122534	+	0.0707453i	−0.437480	+	0.899228i	$0.644129\pi$
$888$		0			0
$889$	−6.58864	+	24.5891i	−0.220976	+	0.824693i
$890$	24.9418	−	24.9418i	0.836052	−	0.836052i
$891$		0			0
$892$	−11.0956	+	11.0956i	−0.371507	+	0.371507i
$893$	6.15011	−	3.55077i	0.205805	−	0.118822i
$894$		0			0
$895$	−5.35155	−	19.9723i	−0.178883	−	0.667599i
$896$	−2.29011	+	3.96659i	−0.0765073	+	0.132515i
$897$		0			0
$898$	17.9328	+	31.0605i	0.598424	+	1.03650i
$899$	4.80290	−	4.80290i	0.160186	−	0.160186i
$900$		0			0
$901$			45.8636i			1.52794i
$902$	−0.449543	−	0.120455i	−0.0149681	−	0.00401070i
$903$		0			0
$904$	−0.498777	−	1.86146i	−0.0165891	−	0.0619113i
$905$	−1.31608	+	0.352644i	−0.0437481	+	0.0117223i
$906$		0			0
$907$	−21.0079	+	12.1289i	−0.697556	+	0.402734i	−0.806436	−	0.591321i	$-0.798607\pi$
$907$	−21.0079	+	12.1289i	−0.697556	+	0.402734i	0.108881	+	0.994055i	$0.465273\pi$
$908$	−11.2997	−	11.2997i	−0.374994	−	0.374994i
$909$		0			0
$910$	29.8971	−	50.9818i	0.991079	−	1.69003i
$911$	19.1529	−	11.0580i	0.634565	−	0.366366i	−0.147953	−	0.988994i	$-0.547268\pi$
$911$	19.1529	−	11.0580i	0.634565	−	0.366366i	0.782518	+	0.622628i	$0.213935\pi$
$912$		0			0
$913$	3.40396	−	5.89583i	0.112655	−	0.195124i
$914$	13.2145	−	22.8882i	0.437097	−	0.757073i
$915$		0			0
$916$	−2.36858	+	8.83967i	−0.0782602	+	0.292071i
$917$	−17.3198	−	17.3198i	−0.571951	−	0.571951i
$918$		0			0
$919$	10.7824			0.355679			0.177839	−	0.984060i	$-0.443089\pi$
$919$	10.7824			0.355679			0.177839	+	0.984060i	$0.443089\pi$
$920$	4.52349	+	7.83491i	0.149135	+	0.258309i
$921$		0			0
$922$	11.7651	+	6.79260i	0.387464	+	0.223702i
$923$	10.7665	−	6.11906i	0.354383	−	0.201411i
$924$		0			0
$925$	−4.38602	+	16.3688i	−0.144211	+	0.538204i
$926$		−	1.44300i		−	0.0474198i
$927$		0			0
$928$	0.534160	+	0.534160i	0.0175347	+	0.0175347i
$929$	−14.0136	−	3.75492i	−0.459770	−	0.123195i	0.0214972	−	0.999769i	$-0.493157\pi$
$929$	−14.0136	−	3.75492i	−0.459770	−	0.123195i	−0.481267	+	0.876574i	$0.659823\pi$
$930$		0			0
$931$	−18.1672	−	67.8008i	−0.595405	−	2.22208i
$932$	21.3803	+	12.3439i	0.700334	+	0.404338i
$933$		0			0
$934$	12.9203	+	3.46197i	0.422764	+	0.113279i
$935$	−15.8649			−0.518837
$936$		0			0
$937$	6.22872			0.203483			0.101742	−	0.994811i	$-0.467558\pi$
$937$	6.22872			0.203483			0.101742	+	0.994811i	$0.467558\pi$
$938$	40.4032	+	10.8260i	1.31921	+	0.353481i
$939$		0			0
$940$	−4.38320	−	2.53064i	−0.142964	−	0.0825404i
$941$	−5.52621	−	20.6241i	−0.180149	−	0.672326i	−0.995617	−	0.0935237i	$-0.970187\pi$
$941$	−5.52621	−	20.6241i	−0.180149	−	0.672326i	0.815468	−	0.578802i	$-0.196480\pi$
$942$		0			0
$943$	−1.05987	−	0.283990i	−0.0345140	−	0.00924800i
$944$	−7.07375	−	7.07375i	−0.230231	−	0.230231i
$945$		0			0
$946$			2.66814i			0.0867486i
$947$	12.5429	−	46.8109i	0.407590	−	1.52115i	−0.391637	−	0.920120i	$-0.628091\pi$
$947$	12.5429	−	46.8109i	0.407590	−	1.52115i	0.799228	−	0.601029i	$-0.205242\pi$
$948$		0			0
$949$	−14.0832	+	8.00413i	−0.457161	+	0.259825i
$950$	33.9545	+	19.6037i	1.10163	+	0.636027i
$951$		0			0
$952$	−9.46825	−	16.3995i	−0.306868	−	0.531511i
$953$	41.9198			1.35791			0.678957	−	0.734178i	$-0.262432\pi$
$953$	41.9198			1.35791			0.678957	+	0.734178i	$0.262432\pi$
$954$		0			0
$955$	26.6263	+	26.6263i	0.861606	+	0.861606i
$956$	−4.05596	+	15.1370i	−0.131179	+	0.489567i
$957$		0			0
$958$	−17.3124	+	29.9859i	−0.559337	+	0.968800i
$959$	1.16490	−	2.01767i	0.0376167	−	0.0651540i
$960$		0			0
$961$	43.1688	−	24.9235i	1.39254	−	0.803984i
$962$	−7.57237	+	1.97408i	−0.244143	+	0.0636468i
$963$		0			0
$964$	−2.56916	−	2.56916i	−0.0827469	−	0.0827469i
$965$	24.7008	−	14.2610i	0.795148	−	0.459079i
$966$		0			0
$967$	24.8884	−	6.66882i	0.800356	−	0.214455i	0.164616	−	0.986358i	$-0.447362\pi$
$967$	24.8884	−	6.66882i	0.800356	−	0.214455i	0.635740	+	0.771903i	$0.280695\pi$
$968$	2.54946	+	9.51470i	0.0819426	+	0.305814i
$969$		0			0
$970$	8.90487	+	2.38605i	0.285918	+	0.0766116i
$971$			34.0629i			1.09313i	0.837417	+	0.546565i	$0.184065\pi$
$971$			34.0629i			1.09313i	−0.837417	+	0.546565i	$0.815935\pi$
$972$		0			0
$973$	−22.6257	+	22.6257i	−0.725347	+	0.725347i
$974$	−5.26334	−	9.11638i	−0.168648	−	0.292108i
$975$		0			0
$976$	−5.37935	+	9.31732i	−0.172189	+	0.298240i
$977$	4.44761	+	16.5987i	0.142292	+	0.531040i	0.999861	+	0.0166715i	$0.00530693\pi$
$977$	4.44761	+	16.5987i	0.142292	+	0.531040i	−0.857569	+	0.514368i	$0.828026\pi$
$978$		0			0
$979$	−9.15205	+	5.28394i	−0.292501	+	0.168875i
$980$	−35.3740	+	35.3740i	−1.12998	+	1.12998i
$981$		0			0
$982$	−15.0310	+	15.0310i	−0.479660	+	0.479660i
$983$	0.120461	−	0.449565i	0.00384210	−	0.0143389i	−0.963978	−	0.265981i	$-0.914304\pi$
$983$	0.120461	−	0.449565i	0.00384210	−	0.0143389i	0.967820	+	0.251642i	$0.0809707\pi$
$984$		0			0
$985$	69.6628	+	40.2198i	2.21964	+	1.28151i
$986$	−3.01678	+	0.808343i	−0.0960738	+	0.0257429i
$987$		0			0
$988$	−0.122764	+	18.1048i	−0.00390564	+	0.575989i
$989$			6.29054i			0.200028i
$990$		0			0
$991$	37.1861			1.18126			0.590628	−	0.806944i	$-0.298880\pi$
$991$	37.1861			1.18126			0.590628	+	0.806944i	$0.298880\pi$
$992$	4.49575	+	7.78686i	0.142740	+	0.247233i
$993$		0			0
$994$	−15.1955	+	4.07162i	−0.481972	+	0.129144i
$995$	40.7332	−	10.9144i	1.29133	−	0.346011i
$996$		0			0
$997$	23.5272	+	40.7502i	0.745113	+	1.29057i	0.950142	+	0.311817i	$0.100938\pi$
$997$	23.5272	+	40.7502i	0.745113	+	1.29057i	−0.205029	+	0.978756i	$0.565729\pi$
$998$	2.70758			0.0857070
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bg.a.125.14		56
3.2	odd	2		234.2.bd.a.203.4	yes	56
9.2	odd	6	inner	702.2.bg.a.359.14		56
9.7	even	3		234.2.bd.a.47.4	yes	56
13.5	odd	4	inner	702.2.bg.a.395.14		56
39.5	even	4		234.2.bd.a.5.4	✓	56
117.70	odd	12		234.2.bd.a.83.4	yes	56
117.83	even	12	inner	702.2.bg.a.629.14		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.bd.a.5.4	✓	56	39.5	even	4
234.2.bd.a.47.4	yes	56	9.7	even	3
234.2.bd.a.83.4	yes	56	117.70	odd	12
234.2.bd.a.203.4	yes	56	3.2	odd	2
702.2.bg.a.125.14		56	1.1	even	1	trivial
702.2.bg.a.359.14		56	9.2	odd	6	inner
702.2.bg.a.395.14		56	13.5	odd	4	inner
702.2.bg.a.629.14		56	117.83	even	12	inner

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bg (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.926266 + 3.45687i) q^{5} +(4.42416 + 1.18545i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.57882i q^{10} +(0.277511 - 1.03569i) q^{11} +(-3.47629 - 0.956779i) q^{13} +(3.96659 + 2.29011i) q^{14} +(0.500000 + 0.866025i) q^{16} -4.13440 q^{17} +(-3.55072 - 3.55072i) q^{19} +(-0.926266 + 3.45687i) q^{20} +(0.536110 - 0.928570i) q^{22} +(1.26396 - 2.18925i) q^{23} +(-6.76187 + 3.90397i) q^{25} +(-3.11020 - 1.82391i) q^{26} +(3.23871 + 3.23871i) q^{28} +(0.654210 - 0.377708i) q^{29} +(8.68512 - 2.32717i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.99353 - 1.07006i) q^{34} +16.3918i q^{35} +(1.53470 - 1.53470i) q^{37} +(-2.51074 - 4.34872i) q^{38} +(-1.78941 + 3.09935i) q^{40} +(-0.112341 - 0.419264i) q^{41} +(-2.15504 + 1.24421i) q^{43} +(0.758175 - 0.758175i) q^{44} +(1.78751 - 1.78751i) q^{46} +(-0.366030 + 1.36604i) q^{47} +(12.1057 + 6.98923i) q^{49} +(-7.54188 + 2.02084i) q^{50} +(-2.53216 - 2.56674i) q^{52} -11.0932i q^{53} +3.83728 q^{55} +(2.29011 + 3.96659i) q^{56} +(0.729677 - 0.195516i) q^{58} +(-9.66293 + 2.58917i) q^{59} +(5.37935 + 9.31732i) q^{61} +8.99150 q^{62} +1.00000i q^{64} +(0.0874941 - 12.9033i) q^{65} +(8.82122 - 2.36364i) q^{67} +(-3.58050 - 2.06720i) q^{68} +(-4.24251 + 15.8333i) q^{70} +(-2.42867 + 2.42867i) q^{71} +(3.17686 - 3.17686i) q^{73} +(1.87961 - 1.08520i) q^{74} +(-1.29965 - 4.85037i) q^{76} +(2.45551 - 4.25306i) q^{77} +(-0.638454 - 1.10583i) q^{79} +(-2.53061 + 2.53061i) q^{80} -0.434054i q^{82} +(6.13302 + 1.64334i) q^{83} +(-3.82956 - 14.2921i) q^{85} +(-2.40363 + 0.644051i) q^{86} +(0.928570 - 0.536110i) q^{88} +(-6.96929 - 6.96929i) q^{89} +(-14.2454 - 8.35390i) q^{91} +(2.18925 - 1.26396i) q^{92} +(-0.707116 + 1.22476i) q^{94} +(8.98547 - 15.5633i) q^{95} +(0.666716 - 2.48822i) q^{97} +(9.88427 + 9.88427i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} + 8 q^{28} - 4 q^{31} + 8 q^{37} + 48 q^{41} + 24 q^{47} + 24 q^{50} - 4 q^{52} - 48 q^{65} + 28 q^{67} - 56 q^{73} + 48 q^{74} + 4 q^{76} + 48 q^{79} + 24 q^{83}+ \cdots + 20 q^{97}+O(q^{100}) \) 56 * q + 4 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 + 8 * q^28 - 4 * q^31 + 8 * q^37 + 48 * q^41 + 24 * q^47 + 24 * q^50 - 4 * q^52 - 48 * q^65 + 28 * q^67 - 56 * q^73 + 48 * q^74 + 4 * q^76 + 48 * q^79 + 24 * q^83 + 48 * q^86 - 8 * q^91 - 48 * q^92 + 20 * q^97

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