LMFDB - Embedded newform 702.2.bg.a.629.14

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			629.14
Character	$\chi$	$=$	702.629
Dual form			702.2.bg.a.125.14

$q$-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 $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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	−0.372117	−	0.928186i	$-0.621368\pi$
$5$	0.926266	−	3.45687i	0.414239	−	1.54596i	0.786356	−	0.617774i	$-0.211965\pi$
$6$		0			0
$7$	4.42416	−	1.18545i	1.67217	−	0.448058i	0.706479	−	0.707734i	$-0.250283\pi$
$7$	4.42416	−	1.18545i	1.67217	−	0.448058i	0.965696	+	0.259676i	$0.0836159\pi$
$8$	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	0.995060	−	0.0992799i	$-0.0316539\pi$
$11$	0.277511	+	1.03569i	0.0836728	+	0.312271i	−0.911387	+	0.411551i	$0.864987\pi$
$12$		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	−0.985318	−	0.170728i	$-0.945388\pi$
$19$	−3.55072	+	3.55072i	−0.814591	+	0.814591i	0.170728	+	0.985318i	$0.445388\pi$
$20$	−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	0.967184	−	0.254078i	$-0.0817718\pi$
$23$	1.26396	+	2.18925i	0.263554	+	0.456489i	−0.703630	+	0.710567i	$0.748439\pi$
$24$		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	0.559511	−	0.828823i	$-0.310989\pi$
$29$	0.654210	+	0.377708i	0.121484	+	0.0701387i	−0.438027	+	0.898962i	$0.644322\pi$
$30$		0			0
$31$	8.68512	+	2.32717i	1.55989	+	0.417972i	0.932630	−	0.360835i	$-0.117508\pi$
$31$	8.68512	+	2.32717i	1.55989	+	0.417972i	0.627264	+	0.778807i	$0.284175\pi$
$32$	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	0.821914	−	0.569611i	$-0.192906\pi$
$37$	1.53470	+	1.53470i	0.252303	+	0.252303i	−0.569611	+	0.821914i	$0.692906\pi$
$38$	−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	−0.974143	−	0.225931i	$-0.927457\pi$
$41$	−0.112341	+	0.419264i	−0.0175448	+	0.0654780i	0.956598	+	0.291409i	$0.0941242\pi$
$42$		0			0
$43$	−2.15504	−	1.24421i	−0.328640	−	0.189740i	0.326597	−	0.945164i	$-0.394098\pi$
$43$	−2.15504	−	1.24421i	−0.328640	−	0.189740i	−0.655237	+	0.755423i	$0.727431\pi$
$44$	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	0.934079	−	0.357068i	$-0.116223\pi$
$47$	−0.366030	−	1.36604i	−0.0533910	−	0.199258i	−0.987470	+	0.157810i	$0.949557\pi$
$48$		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	$0.275724\pi$
$53$			11.0932i			1.52376i	−0.647716	+	0.761882i	$0.724276\pi$
$54$		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	−0.432582	−	0.901595i	$-0.642397\pi$
$59$	−9.66293	−	2.58917i	−1.25801	−	0.337082i	−0.825424	+	0.564513i	$0.809064\pi$
$60$		0			0
$61$	5.37935	−	9.31732i	0.688756	−	1.19296i	−0.283485	−	0.958977i	$-0.591491\pi$
$61$	5.37935	−	9.31732i	0.688756	−	1.19296i	0.972241	−	0.233983i	$-0.0751761\pi$
$62$	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	0.753647	−	0.657280i	$-0.228293\pi$
$67$	8.82122	+	2.36364i	1.07768	+	0.288765i	0.324037	+	0.946044i	$0.394960\pi$
$68$	−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	0.548150	−	0.836380i	$-0.315332\pi$
$71$	−2.42867	−	2.42867i	−0.288230	−	0.288230i	−0.836380	+	0.548150i	$0.815332\pi$
$72$		0			0
$73$	3.17686	+	3.17686i	0.371824	+	0.371824i	0.868141	−	0.496317i	$-0.165315\pi$
$73$	3.17686	+	3.17686i	0.371824	+	0.371824i	−0.496317	+	0.868141i	$0.665315\pi$
$74$	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	−0.899704	−	0.436500i	$-0.856218\pi$
$79$	−0.638454	+	1.10583i	−0.0718316	+	0.124416i	0.827872	+	0.560916i	$0.189551\pi$
$80$	−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	0.0939965	−	0.995573i	$-0.470036\pi$
$83$	6.13302	−	1.64334i	0.673186	−	0.180380i	0.579190	+	0.815193i	$0.303369\pi$
$84$		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	−0.972335	−	0.233591i	$-0.924952\pi$
$89$	−6.96929	+	6.96929i	−0.738743	+	0.738743i	0.233591	+	0.972335i	$0.424952\pi$
$90$		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	0.991478	−	0.130276i	$-0.0415864\pi$
$97$	0.666716	+	2.48822i	0.0676947	+	0.252640i	−0.923783	+	0.382916i	$0.874920\pi$
$98$	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	−0.521236	−	0.853413i	$-0.674529\pi$
$101$	4.80845	−	8.32848i	0.478459	−	0.828715i	0.999695	+	0.0246975i	$0.00786224\pi$
$102$		0			0
$103$	−9.13951	+	5.27670i	−0.900543	+	0.519929i	−0.877376	−	0.479803i	$-0.840708\pi$
$103$	−9.13951	+	5.27670i	−0.900543	+	0.519929i	−0.0231667	+	0.999732i	$0.507375\pi$
$104$	−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	$-0.858880\pi$
$107$		−	8.87442i		−	0.857923i	0.903323	−	0.428961i	$-0.141120\pi$
$108$		0			0
$109$	−13.3375	+	13.3375i	−1.27750	+	1.27750i	−0.335432	+	0.942064i	$0.608882\pi$
$109$	−13.3375	+	13.3375i	−1.27750	+	1.27750i	−0.942064	+	0.335432i	$0.891118\pi$
$110$	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	−0.576442	−	0.817138i	$-0.695559\pi$
$113$	−1.66894	+	0.963564i	−0.157001	+	0.0906445i	0.419441	+	0.907782i	$0.362226\pi$
$114$		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	$-0.920689\pi$
$127$		−	5.55792i		−	0.493186i	0.969119	−	0.246593i	$-0.0793111\pi$
$128$	−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	−0.688483	−	0.725252i	$-0.741723\pi$
$131$	−4.63129	+	2.67388i	−0.404638	+	0.233618i	0.283845	+	0.958870i	$0.408390\pi$
$132$		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	0.971322	−	0.237769i	$-0.0764162\pi$
$137$	0.131653	+	0.491334i	0.0112478	+	0.0419775i	−0.960074	+	0.279747i	$0.909750\pi$
$138$		0			0
$139$	−3.49301	−	6.05008i	−0.296274	−	0.513161i	0.679007	−	0.734132i	$-0.262411\pi$
$139$	−3.49301	−	6.05008i	−0.296274	−	0.513161i	−0.975280	+	0.220971i	$0.929077\pi$
$140$	−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	0.556539	+	0.830821i	$0.312129\pi$
$149$	−4.16059	+	15.5275i	−0.340848	+	1.27206i	−0.897388	+	0.441243i	$0.854538\pi$
$150$		0			0
$151$	2.68543	−	0.719558i	0.218537	−	0.0585568i	−0.147889	−	0.989004i	$-0.547248\pi$
$151$	2.68543	−	0.719558i	0.218537	−	0.0585568i	0.366426	+	0.930447i	$0.380581\pi$
$152$			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	−0.998141	−	0.0609515i	$-0.980587\pi$
$157$	−6.91473	−	11.9767i	−0.551856	−	0.955842i	0.446285	−	0.894891i	$-0.352747\pi$
$158$	−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	−0.972859	−	0.231400i	$-0.925669\pi$
$163$	−15.3749	−	15.3749i	−1.20426	−	1.20426i	−0.231400	−	0.972859i	$-0.574331\pi$
$164$	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	0.764298	−	0.644863i	$-0.223085\pi$
$167$	14.2638	+	3.82198i	1.10377	+	0.295754i	0.339471	+	0.940617i	$0.389752\pi$
$168$		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	−0.990469	−	0.137736i	$-0.956018\pi$
$173$	−4.94488	+	8.56478i	−0.375952	+	0.651168i	0.614517	+	0.788904i	$0.289351\pi$
$174$		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	$-0.995496\pi$
$181$		−	0.380715i		−	0.0282983i	0.999900	−	0.0141492i	$-0.00450397\pi$
$182$	−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	0.792020	−	0.610495i	$-0.209030\pi$
$191$	9.11205	+	5.26085i	0.659325	+	0.380662i	−0.132695	+	0.991157i	$0.542363\pi$
$192$		0			0
$193$	−2.06271	+	7.69813i	−0.148477	+	0.554124i	0.851099	+	0.525005i	$0.175937\pi$
$193$	−2.06271	+	7.69813i	−0.148477	+	0.554124i	−0.999576	+	0.0291185i	$0.990730\pi$
$194$	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	0.989785	+	0.142570i	$0.0455365\pi$
$197$	15.8934	+	15.8934i	1.13235	+	1.13235i	0.142570	+	0.989785i	$0.454463\pi$
$198$		0			0
$199$			11.7833i			0.835293i	0.908610	+	0.417646i	$0.137145\pi$
$199$			11.7833i			0.835293i	−0.908610	+	0.417646i	$0.862855\pi$
$200$	−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	0.964091	+	0.265572i	$0.0855607\pi$
$211$	10.3429	+	17.9145i	0.712037	+	1.23328i	−0.252054	+	0.967713i	$0.581106\pi$
$212$	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	−0.957850	−	0.287268i	$-0.907253\pi$
$223$	−4.06125	−	15.1568i	−0.271962	−	1.01497i	0.685889	−	0.727707i	$-0.259414\pi$
$224$		−	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	−0.731677	−	0.681652i	$-0.761262\pi$
$227$	−15.4357	+	4.13598i	−1.02450	+	0.274514i	−0.292825	+	0.956166i	$0.594595\pi$
$228$		0			0
$229$	2.36858	−	8.83967i	0.156520	−	0.584142i	−0.842450	−	0.538774i	$-0.818887\pi$
$229$	2.36858	−	8.83967i	0.156520	−	0.584142i	0.998970	−	0.0453674i	$-0.0144458\pi$
$230$	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	−0.701490	−	0.712680i	$-0.747481\pi$
$239$	4.05596	−	15.1370i	0.262358	−	0.979134i	0.963848	−	0.266454i	$-0.0858520\pi$
$240$		0			0
$241$	−3.50953	+	0.940376i	−0.226069	+	0.0605750i	−0.370075	−	0.929002i	$-0.620668\pi$
$241$	−3.50953	+	0.940376i	−0.226069	+	0.0605750i	0.144006	+	0.989577i	$0.454001\pi$
$242$	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	0.722869	−	0.690985i	$-0.242823\pi$
$257$	−3.79901	−	6.58009i	−0.236976	−	0.410454i	−0.959845	+	0.280531i	$0.909490\pi$
$258$		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	0.998894	−	0.0470295i	$-0.0149755\pi$
$263$	23.6385	+	13.6477i	1.45761	+	0.841552i	0.458718	+	0.888582i	$0.348309\pi$
$264$		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	$0.149348\pi$
$269$			14.8321i			0.904327i	−0.891935	+	0.452164i	$0.850652\pi$
$270$		0			0
$271$	−16.0694	−	16.0694i	−0.976147	−	0.976147i	0.0235754	−	0.999722i	$-0.492495\pi$
$271$	−16.0694	−	16.0694i	−0.976147	−	0.976147i	−0.999722	+	0.0235754i	$0.992495\pi$
$272$	−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	−0.248087	−	0.968738i	$-0.579802\pi$
$277$	−20.1564	−	11.6373i	−1.21108	−	0.699218i	−0.962995	+	0.269520i	$0.913135\pi$
$278$	−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	0.936392	−	0.350955i	$-0.114143\pi$
$281$	−0.838571	−	3.12959i	−0.0500250	−	0.186696i	−0.986417	+	0.164260i	$0.947476\pi$
$282$		0			0
$283$	−4.80758	+	2.77566i	−0.285781	+	0.164996i	−0.636038	−	0.771658i	$-0.719428\pi$
$283$	−4.80758	+	2.77566i	−0.285781	+	0.164996i	0.350257	+	0.936654i	$0.386094\pi$
$284$	−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	−0.263040	−	0.964785i	$-0.584725\pi$
$293$	−16.6590	−	4.46378i	−0.973232	−	0.260777i	−0.710192	+	0.704008i	$0.751392\pi$
$294$		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	0.688926	−	0.724832i	$-0.258082\pi$
$307$	−0.629117	−	0.629117i	−0.0359056	−	0.0359056i	−0.724832	+	0.688926i	$0.758082\pi$
$308$	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	0.567573	−	0.823323i	$-0.307883\pi$
$311$	−7.56960	−	13.1109i	−0.429233	−	0.743453i	−0.996805	+	0.0798707i	$0.974549\pi$
$312$		0			0
$313$	−6.51021	+	11.2760i	−0.367979	+	0.637358i	−0.989249	−	0.146238i	$-0.953283\pi$
$313$	−6.51021	+	11.2760i	−0.367979	+	0.637358i	0.621271	+	0.783596i	$0.286617\pi$
$314$	−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	0.0896019	−	0.995978i	$-0.471441\pi$
$317$	11.8433	−	3.17341i	0.665188	−	0.178237i	0.575586	+	0.817741i	$0.304774\pi$
$318$		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	0.878854	−	0.477092i	$-0.158309\pi$
$331$	−2.19780	−	8.20228i	−0.120802	−	0.450838i	−0.999655	+	0.0262533i	$0.991642\pi$
$332$	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	−0.751678	−	0.659530i	$-0.770755\pi$
$337$	−10.2132	+	5.89659i	−0.556348	+	0.321207i	0.195331	+	0.980737i	$0.437422\pi$
$338$	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	−0.979593	−	0.200991i	$-0.935584\pi$
$347$	−24.1293	+	13.9310i	−1.29533	+	0.747857i	−0.315733	+	0.948848i	$0.602251\pi$
$348$		0			0
$349$	7.85155	−	2.10382i	0.420284	−	0.112615i	−0.0424778	−	0.999097i	$-0.513525\pi$
$349$	7.85155	−	2.10382i	0.420284	−	0.112615i	0.462762	+	0.886483i	$0.346859\pi$
$350$	−35.7621			−1.91156
$351$		0			0
$352$	1.07222			0.0571496
$353$	−0.765102	+	0.205008i	−0.0407222	+	0.0109115i	−0.279123	−	0.960255i	$-0.590044\pi$
$353$	−0.765102	+	0.205008i	−0.0407222	+	0.0109115i	0.238400	+	0.971167i	$0.423377\pi$
$354$		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	0.171942	−	0.985107i	$-0.444996\pi$
$359$	21.9230	−	21.9230i	1.15705	−	1.15705i	0.985107	−	0.171942i	$-0.0550042\pi$
$360$		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	−0.826312	−	0.563212i	$-0.809565\pi$
$367$	1.42913	−	2.47533i	0.0746002	−	0.129211i	0.900912	+	0.434001i	$0.142899\pi$
$368$	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	0.999900	+	0.0141612i	$0.00450780\pi$
$373$	9.89249	+	17.1343i	0.512214	+	0.887180i	−0.487686	+	0.873019i	$0.662159\pi$
$374$	−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	−0.785952	−	0.618287i	$-0.787827\pi$
$379$	−3.26410	+	3.26410i	−0.167665	+	0.167665i	0.618287	+	0.785952i	$0.287827\pi$
$380$	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	−0.992288	−	0.123952i	$-0.960443\pi$
$383$	−1.38882	+	5.18315i	−0.0709654	+	0.264846i	0.921323	+	0.388798i	$0.127110\pi$
$384$		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	0.328549	+	0.944487i	$0.393440\pi$
$389$	−12.8925	+	22.3304i	−0.653675	+	1.13220i	−0.982224	+	0.187711i	$0.939893\pi$
$390$		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	0.378572	−	0.925572i	$-0.376415\pi$
$397$	−10.8989	−	10.8989i	−0.547000	−	0.547000i	−0.925572	+	0.378572i	$0.876415\pi$
$398$	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	0.161613	−	0.986854i	$-0.448330\pi$
$401$	−3.84186	−	1.02942i	−0.191853	−	0.0514070i	−0.353466	+	0.935447i	$0.614997\pi$
$402$		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	−0.478944	−	0.877845i	$-0.658980\pi$
$409$	−26.9511	−	7.22152i	−1.33264	−	0.357081i	−0.853700	+	0.520765i	$0.825647\pi$
$410$	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	−0.0585084	−	0.998287i	$-0.518634\pi$
$419$	15.9003	−	9.18003i	0.776779	−	0.448474i	0.835288	+	0.549813i	$0.185301\pi$
$420$		0			0
$421$	−6.33652	−	23.6482i	−0.308823	−	1.15254i	−0.929604	−	0.368560i	$-0.879851\pi$
$421$	−6.33652	−	23.6482i	−0.308823	−	1.15254i	0.620781	−	0.783984i	$-0.286816\pi$
$422$	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	0.263214	−	0.964737i	$-0.415217\pi$
$431$	−14.5640	−	14.5640i	−0.701523	−	0.701523i	−0.964737	+	0.263214i	$0.915217\pi$
$432$		0			0
$433$		−	18.5433i		−	0.891136i	−0.895248	−	0.445568i	$-0.853002\pi$
$433$		−	18.5433i		−	0.891136i	0.895248	−	0.445568i	$-0.146998\pi$
$434$	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	0.586639	−	0.809848i	$-0.300451\pi$
$439$	3.74229	+	2.16061i	0.178610	+	0.103120i	−0.408030	+	0.912969i	$0.633784\pi$
$440$	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	−0.336368	−	0.941731i	$-0.609199\pi$
$443$	−27.7852	−	16.0418i	−1.32011	−	0.762168i	−0.983747	+	0.179562i	$0.942532\pi$
$444$		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	0.221743	−	0.975105i	$-0.428825\pi$
$449$	25.3608	−	25.3608i	1.19685	−	1.19685i	0.975105	−	0.221743i	$-0.0711746\pi$
$450$		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	0.919266	+	0.393637i	$0.128783\pi$
$457$	6.84032	+	25.5284i	0.319977	+	1.19417i	−0.599289	+	0.800533i	$0.704550\pi$
$458$		−	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	0.0600575	−	0.998195i	$-0.480872\pi$
$461$	13.1223	−	3.51611i	0.611166	−	0.163762i	0.551109	+	0.834433i	$0.314205\pi$
$462$		0			0
$463$	−0.373475	+	1.39383i	−0.0173568	+	0.0647766i	−0.974061	−	0.226285i	$-0.927342\pi$
$463$	−0.373475	+	1.39383i	−0.0173568	+	0.0647766i	0.956704	+	0.291062i	$0.0940085\pi$
$464$	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	−0.795673	−	0.605726i	$-0.792883\pi$
$479$	−8.96153	−	33.4449i	−0.409463	−	1.52814i	0.386210	−	0.922411i	$-0.373784\pi$
$480$		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	−0.855349	−	0.518052i	$-0.826657\pi$
$487$	−7.44349	+	7.44349i	−0.337297	+	0.337297i	0.518052	+	0.855349i	$0.326657\pi$
$488$	−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	0.520068	−	0.854125i	$-0.325907\pi$
$491$	−10.6286	−	18.4092i	−0.479660	−	0.830795i	−0.999728	+	0.0233295i	$0.992573\pi$
$492$		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	0.316882	−	0.948465i	$-0.397364\pi$
$499$	2.61532	+	0.700773i	0.117078	+	0.0313709i	−0.199804	+	0.979836i	$0.564031\pi$
$500$	−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	$0.0891107\pi$
$503$			12.3938i			0.552614i	−0.961069	+	0.276307i	$0.910889\pi$
$504$		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	−0.742637	−	0.669694i	$-0.766425\pi$
$509$	5.30979	−	19.8164i	0.235352	−	0.878347i	0.977990	−	0.208653i	$-0.0669079\pi$
$510$		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	$-0.895986\pi$
$521$		−	14.6532i		−	0.641968i	0.947085	−	0.320984i	$-0.104014\pi$
$522$		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	−0.998974	−	0.0452820i	$-0.985581\pi$
$541$	−24.2888	−	24.2888i	−1.04426	−	1.04426i	−0.0452820	−	0.998974i	$-0.514419\pi$
$542$	−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	−0.847690	−	0.530492i	$-0.822007\pi$
$547$	0.832021	−	1.44110i	0.0355746	−	0.0616171i	0.883265	+	0.468875i	$0.155341\pi$
$548$	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	−0.999250	−	0.0387266i	$-0.987670\pi$
$557$	−22.6692	+	22.6692i	−0.960523	+	0.960523i	0.0387266	+	0.999250i	$0.487670\pi$
$558$		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	0.734667	−	0.678428i	$-0.237338\pi$
$563$	−5.22488	−	9.04976i	−0.220203	−	0.381402i	−0.954869	+	0.297026i	$0.904005\pi$
$564$		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	−0.954457	−	0.298350i	$-0.903564\pi$
$569$	−5.22038	+	9.04197i	−0.218850	+	0.379059i	0.735607	+	0.677409i	$0.236897\pi$
$570$		0			0
$571$	14.9685	−	8.64209i	0.626414	−	0.361660i	−0.152948	−	0.988234i	$-0.548877\pi$
$571$	14.9685	−	8.64209i	0.626414	−	0.361660i	0.779362	+	0.626574i	$0.215543\pi$
$572$	−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	−0.925557	−	0.378609i	$-0.876402\pi$
$577$	−13.1381	+	13.1381i	−0.546947	+	0.546947i	0.378609	+	0.925557i	$0.376402\pi$
$578$	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	0.248960	−	0.968514i	$-0.419911\pi$
$587$	22.9881	−	6.15965i	0.948822	−	0.254236i	0.699862	+	0.714278i	$0.253245\pi$
$588$		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	−0.998995	−	0.0448310i	$-0.985725\pi$
$593$	−23.2354	+	23.2354i	−0.954164	+	0.954164i	0.0448310	+	0.998995i	$0.485725\pi$
$594$		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	−0.421769	−	0.906703i	$-0.638591\pi$
$599$	3.73418	−	2.15593i	0.152575	−	0.0880889i	0.574344	+	0.818614i	$0.305257\pi$
$600$		0			0
$601$	−15.6036	+	27.0262i	−0.636484	+	1.10242i	0.349714	+	0.936856i	$0.386279\pi$
$601$	−15.6036	+	27.0262i	−0.636484	+	1.10242i	−0.986199	+	0.165567i	$0.947055\pi$
$602$	−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	0.754750	−	0.656012i	$-0.227758\pi$
$607$	−4.69953	−	8.13983i	−0.190748	−	0.330385i	−0.945498	+	0.325627i	$0.894425\pi$
$608$	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	−0.962442	−	0.271488i	$-0.912484\pi$
$613$	−17.1072	+	17.1072i	−0.690954	+	0.690954i	0.271488	+	0.962442i	$0.412484\pi$
$614$	−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	0.161091	+	0.986940i	$0.448499\pi$
$617$	−11.7214	+	43.7450i	−0.471888	+	1.76111i	−0.632979	+	0.774169i	$0.718168\pi$
$618$		0			0
$619$	37.1618	−	9.95749i	1.49366	−	0.400225i	0.582689	−	0.812695i	$-0.302000\pi$
$619$	37.1618	−	9.95749i	1.49366	−	0.400225i	0.910971	+	0.412470i	$0.135334\pi$
$620$		−	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	0.992889	+	0.119045i	$0.0379833\pi$
$631$	27.9315	+	27.9315i	1.11193	+	1.11193i	0.119045	+	0.992889i	$0.462017\pi$
$632$	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	−0.892795	−	0.450462i	$-0.851259\pi$
$641$	−1.42504	+	2.46825i	−0.0562859	+	0.0974900i	0.836510	+	0.547952i	$0.184592\pi$
$642$		0			0
$643$	17.8708	+	4.78846i	0.704755	+	0.188838i	0.593359	−	0.804938i	$-0.297801\pi$
$643$	17.8708	+	4.78846i	0.704755	+	0.188838i	0.111395	+	0.993776i	$0.464468\pi$
$644$	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	−0.441847	−	0.897091i	$-0.645677\pi$
$653$	2.91654	−	1.68387i	0.114133	−	0.0658948i	0.555980	+	0.831196i	$0.312343\pi$
$654$		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	0.402948	−	0.915223i	$-0.367986\pi$
$659$	−4.83089	−	2.78912i	−0.188185	−	0.108649i	−0.591133	+	0.806574i	$0.701319\pi$
$660$		0			0
$661$	0.662272	−	2.47163i	0.0257594	−	0.0961353i	−0.951849	−	0.306566i	$-0.900820\pi$
$661$	0.662272	−	2.47163i	0.0257594	−	0.0961353i	0.977609	+	0.210431i	$0.0674866\pi$
$662$	−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	0.655970	−	0.754787i	$-0.272260\pi$
$673$	8.56847	+	4.94701i	0.330290	+	0.190693i	−0.325680	+	0.945480i	$0.605593\pi$
$674$	−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	0.850346	−	0.526224i	$-0.176393\pi$
$677$	21.3304	+	12.3151i	0.819796	+	0.473309i	−0.0305503	+	0.999533i	$0.509726\pi$
$678$		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	−0.995235	−	0.0975073i	$-0.968913\pi$
$683$	−23.4615	+	23.4615i	−0.897728	+	0.897728i	0.0975073	+	0.995235i	$0.468913\pi$
$684$		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	−0.999361	−	0.0357326i	$-0.988624\pi$
$691$	−3.98917	−	14.8878i	−0.151755	−	0.566359i	0.847606	−	0.530626i	$-0.178043\pi$
$692$			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	0.166145	−	0.986101i	$-0.446868\pi$
$709$	21.3837	−	5.72975i	0.803082	−	0.215185i	0.636937	+	0.770916i	$0.280201\pi$
$710$	−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	−0.0705781	−	0.997506i	$-0.522484\pi$
$727$	−26.1468	−	15.0959i	−0.969733	−	0.559876i	−0.899155	+	0.437631i	$0.855818\pi$
$728$	−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	−0.348537	−	0.937295i	$-0.613321\pi$
$733$	−30.2965	−	8.11792i	−1.11903	−	0.299842i	−0.770489	+	0.637453i	$0.779988\pi$
$734$	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	0.898825	+	0.438307i	$0.144422\pi$
$739$	36.3493	+	36.3493i	1.33713	+	1.33713i	0.438307	+	0.898825i	$0.355578\pi$
$740$	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	−0.949958	−	0.312378i	$-0.898875\pi$
$743$	0.788263	−	2.94184i	0.0289186	−	0.107926i	0.978877	+	0.204452i	$0.0655412\pi$
$744$		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	−0.426377	−	0.904546i	$-0.640210\pi$
$751$	3.94059	−	2.27510i	0.143794	−	0.0830196i	0.570171	+	0.821526i	$0.306877\pi$
$752$	−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	0.814023	−	0.580833i	$-0.197273\pi$
$761$	33.8916	+	9.08124i	1.22857	+	0.329195i	0.414548	+	0.910027i	$0.363940\pi$
$762$		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	0.671821	−	0.740713i	$-0.265512\pi$
$769$	24.4941	+	6.56317i	0.883279	+	0.236674i	0.211458	+	0.977387i	$0.432179\pi$
$770$	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	0.446142	−	0.894962i	$-0.352798\pi$
$773$	−12.4785	−	12.4785i	−0.448821	−	0.448821i	−0.894962	+	0.446142i	$0.852798\pi$
$774$		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	−0.612698	−	0.790317i	$-0.709916\pi$
$787$	8.78278	−	32.7778i	0.313072	−	1.16840i	0.925771	−	0.378085i	$-0.123417\pi$
$788$	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	0.932902	−	0.360130i	$-0.117268\pi$
$797$	4.36366	+	7.55809i	0.154569	+	0.267721i	−0.778333	+	0.627852i	$0.783934\pi$
$798$		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	$0.0959458\pi$
$809$			16.8882i			0.593758i	−0.954915	+	0.296879i	$0.904054\pi$
$810$		0			0
$811$	−22.1364	+	22.1364i	−0.777313	+	0.777313i	−0.979373	−	0.202060i	$-0.935236\pi$
$811$	−22.1364	+	22.1364i	−0.777313	+	0.777313i	0.202060	+	0.979373i	$0.435236\pi$
$812$	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	−0.803213	−	0.595692i	$-0.796878\pi$
$821$	−34.4115	+	9.22053i	−1.20097	+	0.321799i	−0.397756	+	0.917491i	$0.630211\pi$
$822$		0			0
$823$	−26.7859	+	15.4649i	−0.933699	+	0.539071i	−0.887980	−	0.459883i	$-0.847891\pi$
$823$	−26.7859	+	15.4649i	−0.933699	+	0.539071i	−0.0457195	+	0.998954i	$0.514558\pi$
$824$	−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	0.255158	−	0.966899i	$-0.417873\pi$
$827$	35.1434	−	35.1434i	1.22206	−	1.22206i	0.966899	−	0.255158i	$-0.0821273\pi$
$828$		0			0
$829$		−	19.6669i		−	0.683058i	−0.939871	−	0.341529i	$-0.889055\pi$
$829$		−	19.6669i		−	0.683058i	0.939871	−	0.341529i	$-0.110945\pi$
$830$	−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	−0.881410	−	0.472353i	$-0.843405\pi$
$839$	−10.2614	−	38.2961i	−0.354263	−	1.32213i	0.527147	−	0.849774i	$-0.323262\pi$
$840$		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	−0.259962	−	0.965619i	$-0.583710\pi$
$853$	−0.0667930	+	0.0178971i	−0.00228695	+	0.000612786i	0.257675	+	0.966232i	$0.417043\pi$
$854$		−	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	−0.982228	−	0.187690i	$-0.939900\pi$
$857$	−9.61874	+	16.6601i	−0.328570	+	0.569099i	0.653659	+	0.756790i	$0.273233\pi$
$858$		0			0
$859$	2.13530	+	3.69845i	0.0728556	+	0.126190i	0.900152	−	0.435576i	$-0.143455\pi$
$859$	2.13530	+	3.69845i	0.0728556	+	0.126190i	−0.827296	+	0.561766i	$0.810122\pi$
$860$	−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	0.257743	−	0.966214i	$-0.417021\pi$
$863$	−20.8127	−	20.8127i	−0.708471	−	0.708471i	−0.966214	+	0.257743i	$0.917021\pi$
$864$		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	−0.574022	−	0.818840i	$-0.694618\pi$
$877$	−43.8456	−	11.7484i	−1.48056	−	0.396715i	−0.906537	+	0.422125i	$0.861284\pi$
$878$	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	$0.0766134\pi$
$883$			14.1665i			0.476742i	−0.971174	+	0.238371i	$0.923387\pi$
$884$	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	−0.437480	−	0.899228i	$-0.644129\pi$
$887$	3.64939	−	2.10697i	0.122534	−	0.0707453i	0.560014	+	0.828483i	$0.310796\pi$
$888$		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	0.108881	−	0.994055i	$-0.465273\pi$
$907$	−21.0079	−	12.1289i	−0.697556	−	0.402734i	−0.806436	+	0.591321i	$0.798607\pi$
$908$	−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	0.782518	−	0.622628i	$-0.213935\pi$
$911$	19.1529	+	11.0580i	0.634565	+	0.366366i	−0.147953	+	0.988994i	$0.547268\pi$
$912$		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	−0.481267	−	0.876574i	$-0.659823\pi$
$929$	−14.0136	+	3.75492i	−0.459770	+	0.123195i	0.0214972	+	0.999769i	$0.493157\pi$
$930$		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	0.815468	+	0.578802i	$0.196480\pi$
$941$	−5.52621	+	20.6241i	−0.180149	+	0.672326i	−0.995617	+	0.0935237i	$0.970187\pi$
$942$		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	0.799228	+	0.601029i	$0.205242\pi$
$947$	12.5429	+	46.8109i	0.407590	+	1.52115i	−0.391637	+	0.920120i	$0.628091\pi$
$948$		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	0.635740	−	0.771903i	$-0.280695\pi$
$967$	24.8884	+	6.66882i	0.800356	+	0.214455i	0.164616	+	0.986358i	$0.447362\pi$
$968$	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	$-0.815935\pi$
$971$		−	34.0629i		−	1.09313i	0.837417	−	0.546565i	$-0.184065\pi$
$972$		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	−0.857569	−	0.514368i	$-0.828026\pi$
$977$	4.44761	−	16.5987i	0.142292	−	0.531040i	0.999861	−	0.0166715i	$-0.00530693\pi$
$978$		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	0.967820	−	0.251642i	$-0.0809707\pi$
$983$	0.120461	+	0.449565i	0.00384210	+	0.0143389i	−0.963978	+	0.265981i	$0.914304\pi$
$984$		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	−0.205029	−	0.978756i	$-0.565729\pi$
$997$	23.5272	−	40.7502i	0.745113	−	1.29057i	0.950142	−	0.311817i	$-0.100938\pi$
$998$	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.629.14		56
3.2	odd	2		234.2.bd.a.83.4	yes	56
9.4	even	3		234.2.bd.a.5.4	✓	56
9.5	odd	6	inner	702.2.bg.a.395.14		56
13.8	odd	4	inner	702.2.bg.a.359.14		56
39.8	even	4		234.2.bd.a.47.4	yes	56
117.86	even	12	inner	702.2.bg.a.125.14		56
117.112	odd	12		234.2.bd.a.203.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.bd.a.5.4	✓	56	9.4	even	3
234.2.bd.a.47.4	yes	56	39.8	even	4
234.2.bd.a.83.4	yes	56	3.2	odd	2
234.2.bd.a.203.4	yes	56	117.112	odd	12
702.2.bg.a.125.14		56	117.86	even	12	inner
702.2.bg.a.359.14		56	13.8	odd	4	inner
702.2.bg.a.395.14		56	9.5	odd	6	inner
702.2.bg.a.629.14		56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
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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