LMFDB - Embedded newform 784.2.bb.b.111.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.13
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.b.671.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.881327 + 1.10515i) q^{3} +(2.63324 - 2.09994i) q^{5} +(-0.910280 + 2.48423i) q^{7} +(0.222946 - 0.976789i) q^{9} +O(q^{10})$	\(q+(0.881327 + 1.10515i) q^{3} +(2.63324 - 2.09994i) q^{5} +(-0.910280 + 2.48423i) q^{7} +(0.222946 - 0.976789i) q^{9} +(-1.56674 + 0.357599i) q^{11} +(5.11774 - 1.16809i) q^{13} +(4.64150 + 1.05939i) q^{15} +(-2.40539 + 4.99485i) q^{17} +4.03223 q^{19} +(-3.54770 + 1.18342i) q^{21} +(-1.36491 - 2.83426i) q^{23} +(1.41161 - 6.18467i) q^{25} +(5.09665 - 2.45442i) q^{27} +(5.93852 + 2.85984i) q^{29} -0.690893 q^{31} +(-1.77601 - 1.41632i) q^{33} +(2.81975 + 8.45311i) q^{35} +(-4.31900 - 2.07992i) q^{37} +(5.80132 + 4.62639i) q^{39} +(2.04860 - 1.63370i) q^{41} +(-5.73291 - 4.57185i) q^{43} +(-1.46413 - 3.04029i) q^{45} +(1.83457 + 8.03779i) q^{47} +(-5.34278 - 4.52269i) q^{49} +(-7.63999 + 1.74378i) q^{51} +(-4.20637 + 2.02568i) q^{53} +(-3.37468 + 4.23171i) q^{55} +(3.55371 + 4.45621i) q^{57} +(5.62252 - 7.05041i) q^{59} +(-4.60786 + 9.56833i) q^{61} +(2.22362 + 1.44300i) q^{63} +(11.0233 - 13.8228i) q^{65} -9.32900i q^{67} +(1.92935 - 4.00633i) q^{69} +(1.34733 + 2.79776i) q^{71} +(-3.73578 - 0.852667i) q^{73} +(8.07907 - 3.89068i) q^{75} +(0.537817 - 4.21766i) q^{77} +7.64657i q^{79} +(4.49624 + 2.16528i) q^{81} +(-3.67543 + 16.1031i) q^{83} +(4.15490 + 18.2038i) q^{85} +(2.07323 + 9.08340i) q^{87} +(4.52603 + 1.03304i) q^{89} +(-1.75677 + 13.7769i) q^{91} +(-0.608903 - 0.763540i) q^{93} +(10.6178 - 8.46744i) q^{95} -18.7538i q^{97} +1.61010i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 24 q^{9}+O(q^{10}) $ 120 * q - 24 * q^9	$ 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) $ 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

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			0
$2$		0			0
$3$	0.881327	+	1.10515i	0.508834	+	0.638058i	0.968197	−	0.250191i	$-0.0804934\pi$
$3$	0.881327	+	1.10515i	0.508834	+	0.638058i	−0.459362	+	0.888249i	$0.651922\pi$
$4$		0			0
$5$	2.63324	−	2.09994i	1.17762	−	0.939122i	0.178626	−	0.983917i	$-0.442835\pi$
$5$	2.63324	−	2.09994i	1.17762	−	0.939122i	0.998996	+	0.0447950i	$0.0142634\pi$
$6$		0			0
$7$	−0.910280	+	2.48423i	−0.344053	+	0.938950i
$7$	−0.910280	+	2.48423i	−0.344053	+	0.938950i
$8$		0			0
$9$	0.222946	−	0.976789i	0.0743152	−	0.325596i
$10$		0			0
$11$	−1.56674	+	0.357599i	−0.472391	+	0.107820i	−0.452087	−	0.891974i	$-0.649320\pi$
$11$	−1.56674	+	0.357599i	−0.472391	+	0.107820i	−0.0203037	+	0.999794i	$0.506463\pi$
$12$		0			0
$13$	5.11774	−	1.16809i	1.41941	−	0.323970i	0.557137	−	0.830421i	$-0.311900\pi$
$13$	5.11774	−	1.16809i	1.41941	−	0.323970i	0.862269	+	0.506451i	$0.169043\pi$
$14$		0			0
$15$	4.64150	+	1.05939i	1.19843	+	0.273534i
$16$		0			0
$17$	−2.40539	+	4.99485i	−0.583393	+	1.21143i	0.375278	+	0.926912i	$0.377547\pi$
$17$	−2.40539	+	4.99485i	−0.583393	+	1.21143i	−0.958671	+	0.284516i	$0.908167\pi$
$18$		0			0
$19$	4.03223			0.925056			0.462528	−	0.886605i	$-0.346942\pi$
$19$	4.03223			0.925056			0.462528	+	0.886605i	$0.346942\pi$
$20$		0			0
$21$	−3.54770	+	1.18342i	−0.774171	+	0.258244i
$22$		0			0
$23$	−1.36491	−	2.83426i	−0.284603	−	0.590984i	0.708833	−	0.705376i	$-0.249222\pi$
$23$	−1.36491	−	2.83426i	−0.284603	−	0.590984i	−0.993436	+	0.114393i	$0.963508\pi$
$24$		0			0
$25$	1.41161	−	6.18467i	0.282322	−	1.23693i
$26$		0			0
$27$	5.09665	−	2.45442i	0.980850	−	0.472353i
$28$		0			0
$29$	5.93852	+	2.85984i	1.10276	+	0.531059i	0.894524	−	0.447021i	$-0.147515\pi$
$29$	5.93852	+	2.85984i	1.10276	+	0.531059i	0.208232	+	0.978080i	$0.433229\pi$
$30$		0			0
$31$	−0.690893			−0.124088			−0.0620440	−	0.998073i	$-0.519762\pi$
$31$	−0.690893			−0.124088			−0.0620440	+	0.998073i	$0.519762\pi$
$32$		0			0
$33$	−1.77601	−	1.41632i	−0.309164	−	0.246550i
$34$		0			0
$35$	2.81975	+	8.45311i	0.476624	+	1.42884i
$36$		0			0
$37$	−4.31900	−	2.07992i	−0.710039	−	0.341937i	0.0437601	−	0.999042i	$-0.486066\pi$
$37$	−4.31900	−	2.07992i	−0.710039	−	0.341937i	−0.753799	+	0.657106i	$0.771781\pi$
$38$		0			0
$39$	5.80132	+	4.62639i	0.928954	+	0.740816i
$40$		0			0
$41$	2.04860	−	1.63370i	0.319937	−	0.255141i	−0.450331	−	0.892862i	$-0.648694\pi$
$41$	2.04860	−	1.63370i	0.319937	−	0.255141i	0.770268	+	0.637721i	$0.220123\pi$
$42$		0			0
$43$	−5.73291	−	4.57185i	−0.874261	−	0.697200i	0.0798002	−	0.996811i	$-0.474572\pi$
$43$	−5.73291	−	4.57185i	−0.874261	−	0.697200i	−0.954062	+	0.299611i	$0.903143\pi$
$44$		0			0
$45$	−1.46413	−	3.04029i	−0.218259	−	0.453220i
$46$		0			0
$47$	1.83457	+	8.03779i	0.267600	+	1.17243i	0.912796	+	0.408415i	$0.133918\pi$
$47$	1.83457	+	8.03779i	0.267600	+	1.17243i	−0.645196	+	0.764017i	$0.723224\pi$
$48$		0			0
$49$	−5.34278	−	4.52269i	−0.763255	−	0.646098i
$50$		0			0
$51$	−7.63999	+	1.74378i	−1.06981	+	0.244178i
$52$		0			0
$53$	−4.20637	+	2.02568i	−0.577789	+	0.278248i	−0.699868	−	0.714272i	$-0.746758\pi$
$53$	−4.20637	+	2.02568i	−0.577789	+	0.278248i	0.122080	+	0.992520i	$0.461044\pi$
$54$		0			0
$55$	−3.37468	+	4.23171i	−0.455042	+	0.570604i
$56$		0			0
$57$	3.55371	+	4.45621i	0.470700	+	0.590240i
$58$		0			0
$59$	5.62252	−	7.05041i	0.731989	−	0.917885i	−0.266960	−	0.963707i	$-0.586019\pi$
$59$	5.62252	−	7.05041i	0.731989	−	0.917885i	0.998950	+	0.0458221i	$0.0145907\pi$
$60$		0			0
$61$	−4.60786	+	9.56833i	−0.589977	+	1.22510i	0.365714	+	0.930727i	$0.380825\pi$
$61$	−4.60786	+	9.56833i	−0.589977	+	1.22510i	−0.955691	+	0.294372i	$0.904890\pi$
$62$		0			0
$63$	2.22362	+	1.44300i	0.280150	+	0.181801i
$64$		0			0
$65$	11.0233	−	13.8228i	1.36728	−	1.71451i
$66$		0			0
$67$		−	9.32900i		−	1.13972i	−0.821742	−	0.569860i	$-0.806998\pi$
$67$		−	9.32900i		−	1.13972i	0.821742	−	0.569860i	$-0.193002\pi$
$68$		0			0
$69$	1.92935	−	4.00633i	0.232266	−	0.482306i
$70$		0			0
$71$	1.34733	+	2.79776i	0.159899	+	0.332033i	0.965491	−	0.260438i	$-0.0838669\pi$
$71$	1.34733	+	2.79776i	0.159899	+	0.332033i	−0.805592	+	0.592471i	$0.798153\pi$
$72$		0			0
$73$	−3.73578	−	0.852667i	−0.437240	−	0.0997972i	−0.00176585	−	0.999998i	$-0.500562\pi$
$73$	−3.73578	−	0.852667i	−0.437240	−	0.0997972i	−0.435474	+	0.900201i	$0.643419\pi$
$74$		0			0
$75$	8.07907	−	3.89068i	0.932891	−	0.449256i
$76$		0			0
$77$	0.537817	−	4.21766i	0.0612900	−	0.480648i
$78$		0			0
$79$			7.64657i			0.860306i	0.902756	+	0.430153i	$0.141540\pi$
$79$			7.64657i			0.860306i	−0.902756	+	0.430153i	$0.858460\pi$
$80$		0			0
$81$	4.49624	+	2.16528i	0.499583	+	0.240586i
$82$		0			0
$83$	−3.67543	+	16.1031i	−0.403431	+	1.76755i	0.209902	+	0.977722i	$0.432685\pi$
$83$	−3.67543	+	16.1031i	−0.403431	+	1.76755i	−0.613333	+	0.789824i	$0.710172\pi$
$84$		0			0
$85$	4.15490	+	18.2038i	0.450663	+	1.97448i
$86$		0			0
$87$	2.07323	+	9.08340i	0.222273	+	0.973843i
$88$		0			0
$89$	4.52603	+	1.03304i	0.479758	+	0.109502i	0.455559	−	0.890206i	$-0.349439\pi$
$89$	4.52603	+	1.03304i	0.479758	+	0.109502i	0.0241987	+	0.999707i	$0.492297\pi$
$90$		0			0
$91$	−1.75677	+	13.7769i	−0.184160	+	1.44421i
$92$		0			0
$93$	−0.608903	−	0.763540i	−0.0631403	−	0.0791754i
$94$		0			0
$95$	10.6178	−	8.46744i	1.08937	−	0.868741i
$96$		0			0
$97$		−	18.7538i		−	1.90416i	−0.305842	−	0.952082i	$-0.598938\pi$
$97$		−	18.7538i		−	1.90416i	0.305842	−	0.952082i	$-0.401062\pi$
$98$		0			0
$99$			1.61010i			0.161821i
$100$		0			0
$101$	−4.93108	+	3.93240i	−0.490661	+	0.391289i	−0.837329	−	0.546699i	$-0.815884\pi$
$101$	−4.93108	+	3.93240i	−0.490661	+	0.391289i	0.346669	+	0.937988i	$0.387313\pi$
$102$		0			0
$103$	−4.87607	−	6.11440i	−0.480454	−	0.602470i	0.481242	−	0.876588i	$-0.340186\pi$
$103$	−4.87607	−	6.11440i	−0.480454	−	0.602470i	−0.961696	+	0.274117i	$0.911614\pi$
$104$		0			0
$105$	−6.85683	+	10.5662i	−0.669158	+	1.03115i
$106$		0			0
$107$	−15.1156	−	3.45003i	−1.46128	−	0.333527i	−0.583312	−	0.812248i	$-0.698244\pi$
$107$	−15.1156	−	3.45003i	−1.46128	−	0.333527i	−0.877967	+	0.478721i	$0.841101\pi$
$108$		0			0
$109$	2.58988	+	11.3470i	0.248065	+	1.08684i	0.933462	+	0.358675i	$0.116772\pi$
$109$	2.58988	+	11.3470i	0.248065	+	1.08684i	−0.685397	+	0.728170i	$0.740371\pi$
$110$		0			0
$111$	−1.50783	−	6.60622i	−0.143117	−	0.627035i
$112$		0			0
$113$	0.592463	−	2.59575i	0.0557343	−	0.244188i	−0.939385	−	0.342863i	$-0.888603\pi$
$113$	0.592463	−	2.59575i	0.0557343	−	0.244188i	0.995120	+	0.0986752i	$0.0314605\pi$
$114$		0			0
$115$	−9.54591	−	4.59707i	−0.890160	−	0.428679i
$116$		0			0
$117$		−	5.25937i		−	0.486229i
$118$		0			0
$119$	−10.2188	−	10.5222i	−0.936752	−	0.964573i
$120$		0			0
$121$	−7.58385	+	3.65219i	−0.689441	+	0.332017i
$122$		0			0
$123$	3.61097	+	0.824179i	0.325590	+	0.0743137i
$124$		0			0
$125$	−1.96363	−	4.07752i	−0.175632	−	0.364704i
$126$		0			0
$127$	5.16020	−	10.7153i	0.457894	−	0.950827i	−0.536381	−	0.843976i	$-0.680209\pi$
$127$	5.16020	−	10.7153i	0.457894	−	0.950827i	0.994275	−	0.106851i	$-0.0340767\pi$
$128$		0			0
$129$		−	10.3650i		−	0.912589i
$130$		0			0
$131$	8.34911	−	10.4694i	0.729465	−	0.914720i	−0.269367	−	0.963038i	$-0.586815\pi$
$131$	8.34911	−	10.4694i	0.729465	−	0.914720i	0.998832	+	0.0483175i	$0.0153859\pi$
$132$		0			0
$133$	−3.67045	+	10.0170i	−0.318269	+	0.868582i
$134$		0			0
$135$	8.26658	−	17.1657i	0.711474	−	1.47739i
$136$		0			0
$137$	−7.15893	+	8.97702i	−0.611629	+	0.766958i	−0.987140	−	0.159860i	$-0.948896\pi$
$137$	−7.15893	+	8.97702i	−0.611629	+	0.766958i	0.375511	+	0.926818i	$0.377467\pi$
$138$		0			0
$139$	−7.03789	−	8.82523i	−0.596946	−	0.748546i	0.387953	−	0.921679i	$-0.373182\pi$
$139$	−7.03789	−	8.82523i	−0.596946	−	0.748546i	−0.984898	+	0.173133i	$0.944611\pi$
$140$		0			0
$141$	−7.26610	+	9.11140i	−0.611916	+	0.767318i
$142$		0			0
$143$	−7.60048	+	3.66020i	−0.635584	+	0.306081i
$144$		0			0
$145$	21.6431	−	4.93989i	1.79736	−	0.410235i
$146$		0			0
$147$	0.289503	−	9.89053i	0.0238778	−	0.815758i
$148$		0			0
$149$	2.19660	+	9.62394i	0.179953	+	0.788424i	0.981650	+	0.190694i	$0.0610737\pi$
$149$	2.19660	+	9.62394i	0.179953	+	0.788424i	−0.801697	+	0.597731i	$0.796069\pi$
$150$		0			0
$151$	−3.50280	−	7.27364i	−0.285054	−	0.591921i	0.708444	−	0.705767i	$-0.249397\pi$
$151$	−3.50280	−	7.27364i	−0.285054	−	0.591921i	−0.993498	+	0.113846i	$0.963683\pi$
$152$		0			0
$153$	4.34264	+	3.46314i	0.351081	+	0.279978i
$154$		0			0
$155$	−1.81929	+	1.45083i	−0.146129	+	0.116534i
$156$		0			0
$157$	−14.1742	−	11.3035i	−1.13122	−	0.902119i	−0.135163	−	0.990823i	$-0.543156\pi$
$157$	−14.1742	−	11.3035i	−1.13122	−	0.902119i	−0.996058	+	0.0887047i	$0.971727\pi$
$158$		0			0
$159$	−5.94586	−	2.86338i	−0.471537	−	0.227080i
$160$		0			0
$161$	8.28339	−	0.810773i	0.652823	−	0.0638978i
$162$		0			0
$163$	−11.9709	−	9.54646i	−0.937632	−	0.747737i	0.0301448	−	0.999546i	$-0.490403\pi$
$163$	−11.9709	−	9.54646i	−0.937632	−	0.747737i	−0.967777	+	0.251809i	$0.918975\pi$
$164$		0			0
$165$	−7.65087			−0.595620
$166$		0			0
$167$	−19.6015	−	9.43957i	−1.51681	−	0.730456i	−0.524173	−	0.851612i	$-0.675626\pi$
$167$	−19.6015	−	9.43957i	−1.51681	−	0.730456i	−0.992634	+	0.121156i	$0.961340\pi$
$168$		0			0
$169$	13.1142	−	6.31548i	1.00879	−	0.485806i
$170$		0			0
$171$	0.898967	−	3.93863i	0.0687457	−	0.301195i
$172$		0			0
$173$	0.677634	+	1.40712i	0.0515195	+	0.106981i	0.925139	−	0.379628i	$-0.123948\pi$
$173$	0.677634	+	1.40712i	0.0515195	+	0.106981i	−0.873620	+	0.486609i	$0.838234\pi$
$174$		0			0
$175$	14.0792	+	9.13654i	1.06429	+	0.690658i
$176$		0			0
$177$	12.7470			0.958125
$178$		0			0
$179$	−5.85243	+	12.1527i	−0.437431	+	0.908335i	0.559408	+	0.828892i	$0.311028\pi$
$179$	−5.85243	+	12.1527i	−0.437431	+	0.908335i	−0.996839	+	0.0794431i	$0.974686\pi$
$180$		0			0
$181$	−17.4612	−	3.98540i	−1.29788	−	0.296232i	−0.482876	−	0.875689i	$-0.660408\pi$
$181$	−17.4612	−	3.98540i	−1.29788	−	0.296232i	−0.815003	+	0.579457i	$0.803265\pi$
$182$		0			0
$183$	−14.6355	+	3.34045i	−1.08188	+	0.246933i
$184$		0			0
$185$	−15.7407	+	3.59271i	−1.15728	+	0.264141i
$186$		0			0
$187$	1.98248	−	8.68581i	0.144973	−	0.635169i
$188$		0			0
$189$	1.45796	+	14.8954i	0.106051	+	1.08348i
$190$		0			0
$191$	4.47567	−	3.56923i	0.323848	−	0.258260i	−0.448047	−	0.894010i	$-0.647880\pi$
$191$	4.47567	−	3.56923i	0.323848	−	0.258260i	0.771895	+	0.635750i	$0.219309\pi$
$192$		0			0
$193$	−10.3516	−	12.9805i	−0.745127	−	0.934360i	0.254336	−	0.967116i	$-0.418143\pi$
$193$	−10.3516	−	12.9805i	−0.745127	−	0.934360i	−0.999463	+	0.0327561i	$0.989572\pi$
$194$		0			0
$195$	24.9914			1.78967
$196$		0			0
$197$	−6.51352			−0.464069			−0.232035	−	0.972708i	$-0.574538\pi$
$197$	−6.51352			−0.464069			−0.232035	+	0.972708i	$0.574538\pi$
$198$		0			0
$199$	0.561975	+	0.704694i	0.0398373	+	0.0499544i	0.801351	−	0.598194i	$-0.204115\pi$
$199$	0.561975	+	0.704694i	0.0398373	+	0.0499544i	−0.761514	+	0.648149i	$0.775543\pi$
$200$		0			0
$201$	10.3099	−	8.22190i	0.727207	−	0.579928i
$202$		0			0
$203$	−12.5102	+	12.1494i	−0.878045	+	0.852720i
$204$		0			0
$205$	1.96378	−	8.60386i	0.137156	−	0.600920i
$206$		0			0
$207$	−3.07277	+	0.701340i	−0.213572	+	0.0487465i
$208$		0			0
$209$	−6.31747	+	1.44192i	−0.436988	+	0.0997397i
$210$		0			0
$211$	23.7933	+	5.43066i	1.63800	+	0.373862i	0.939714	−	0.341961i	$-0.111091\pi$
$211$	23.7933	+	5.43066i	1.63800	+	0.373862i	0.698282	+	0.715823i	$0.253948\pi$
$212$		0			0
$213$	−1.90450	+	3.95474i	−0.130494	+	0.270974i
$214$		0			0
$215$	−24.6968			−1.68431
$216$		0			0
$217$	0.628906	−	1.71634i	0.0426929	−	0.116512i
$218$		0			0
$219$	−2.35012	−	4.88007i	−0.158806	−	0.329765i
$220$		0			0
$221$	−6.47573	+	28.3720i	−0.435605	+	1.90851i
$222$		0			0
$223$	−5.15990	+	2.48488i	−0.345533	+	0.166400i	−0.598598	−	0.801049i	$-0.704275\pi$
$223$	−5.15990	+	2.48488i	−0.345533	+	0.166400i	0.253066	+	0.967449i	$0.418561\pi$
$224$		0			0
$225$	−5.72640	−	2.75769i	−0.381760	−	0.183846i
$226$		0			0
$227$	−20.3678			−1.35186			−0.675928	−	0.736967i	$-0.736257\pi$
$227$	−20.3678			−1.35186			−0.675928	+	0.736967i	$0.736257\pi$
$228$		0			0
$229$	12.3867	+	9.87804i	0.818534	+	0.652759i	0.940507	−	0.339774i	$-0.110351\pi$
$229$	12.3867	+	9.87804i	0.818534	+	0.652759i	−0.121973	+	0.992533i	$0.538922\pi$
$230$		0			0
$231$	5.13514	−	3.12277i	0.337867	−	0.205463i
$232$		0			0
$233$	20.5149	+	9.87946i	1.34398	+	0.647225i	0.961004	−	0.276535i	$-0.0891860\pi$
$233$	20.5149	+	9.87946i	1.34398	+	0.647225i	0.382973	+	0.923760i	$0.374900\pi$
$234$		0			0
$235$	21.7098	+	17.3130i	1.41619	+	1.12937i
$236$		0			0
$237$	−8.45060	+	6.73913i	−0.548925	+	0.437753i
$238$		0			0
$239$	−8.99095	−	7.17005i	−0.581577	−	0.463792i	0.287972	−	0.957639i	$-0.407019\pi$
$239$	−8.99095	−	7.17005i	−0.581577	−	0.463792i	−0.869549	+	0.493847i	$0.835590\pi$
$240$		0			0
$241$	−9.28316	−	19.2767i	−0.597981	−	1.24172i	−0.951890	−	0.306440i	$-0.900862\pi$
$241$	−9.28316	−	19.2767i	−0.597981	−	1.24172i	0.353909	−	0.935280i	$-0.384852\pi$
$242$		0			0
$243$	−2.20660	−	9.66773i	−0.141553	−	0.620185i
$244$		0			0
$245$	−23.5662	−	0.689801i	−1.50559	−	0.0440698i
$246$		0			0
$247$	20.6359	−	4.71001i	1.31303	−	0.299690i
$248$		0			0
$249$	−21.0356	+	10.1302i	−1.33308	+	0.641976i
$250$		0			0
$251$	−14.2657	+	17.8886i	−0.900442	+	1.12912i	0.0906420	+	0.995884i	$0.471108\pi$
$251$	−14.2657	+	17.8886i	−0.900442	+	1.12912i	−0.991084	+	0.133236i	$0.957463\pi$
$252$		0			0
$253$	3.15199	+	3.95247i	0.198164	+	0.248489i
$254$		0			0
$255$	−16.4561	+	20.6353i	−1.03052	+	1.29223i
$256$		0			0
$257$	9.74616	−	20.2381i	0.607949	−	1.26242i	−0.338925	−	0.940813i	$-0.610063\pi$
$257$	9.74616	−	20.2381i	0.607949	−	1.26242i	0.946874	−	0.321605i	$-0.104222\pi$
$258$		0			0
$259$	9.09849	−	8.83606i	0.565352	−	0.549046i
$260$		0			0
$261$	4.11743	−	5.16309i	0.254862	−	0.319587i
$262$		0			0
$263$			29.9141i			1.84458i	0.386498	+	0.922290i	$0.373685\pi$
$263$			29.9141i			1.84458i	−0.386498	+	0.922290i	$0.626315\pi$
$264$		0			0
$265$	−6.82257	+	14.1672i	−0.419107	+	0.870286i
$266$		0			0
$267$	2.84725	+	5.91237i	0.174249	+	0.361831i
$268$		0			0
$269$	9.47088	+	2.16167i	0.577450	+	0.131799i	0.501264	−	0.865295i	$-0.332869\pi$
$269$	9.47088	+	2.16167i	0.577450	+	0.131799i	0.0761859	+	0.997094i	$0.475726\pi$
$270$		0			0
$271$	17.6831	−	8.51575i	1.07417	−	0.517295i	0.188724	−	0.982030i	$-0.439565\pi$
$271$	17.6831	−	8.51575i	1.07417	−	0.517295i	0.885450	+	0.464735i	$0.153851\pi$
$272$		0			0
$273$	−16.7738	+	10.2005i	−1.01520	+	0.617361i
$274$		0			0
$275$			10.1946i			0.614756i
$276$		0			0
$277$	24.7455	+	11.9168i	1.48681	+	0.716012i	0.988533	−	0.151004i	$-0.0482506\pi$
$277$	24.7455	+	11.9168i	1.48681	+	0.716012i	0.498281	+	0.867016i	$0.333965\pi$
$278$		0			0
$279$	−0.154032	+	0.674856i	−0.00922163	+	0.0404026i
$280$		0			0
$281$	−0.819083	−	3.58864i	−0.0488624	−	0.214080i	0.944603	−	0.328216i	$-0.106447\pi$
$281$	−0.819083	−	3.58864i	−0.0488624	−	0.214080i	−0.993465	+	0.114136i	$0.963590\pi$
$282$		0			0
$283$	0.275848	+	1.20857i	0.0163975	+	0.0718419i	0.982465	−	0.186449i	$-0.0596979\pi$
$283$	0.275848	+	1.20857i	0.0163975	+	0.0718419i	−0.966067	+	0.258291i	$0.916841\pi$
$284$		0			0
$285$	18.7156	+	4.27170i	1.10861	+	0.253034i
$286$		0			0
$287$	2.19369	+	6.57631i	0.129489	+	0.388187i
$288$		0			0
$289$	−8.56326	−	10.7380i	−0.503721	−	0.631646i
$290$		0			0
$291$	20.7258	−	16.5283i	1.21497	−	0.968904i
$292$		0			0
$293$		−	29.0946i		−	1.69972i	−0.527006	−	0.849861i	$-0.676686\pi$
$293$		−	29.0946i		−	1.69972i	0.527006	−	0.849861i	$-0.323314\pi$
$294$		0			0
$295$		−	30.3724i		−	1.76835i
$296$		0			0
$297$	−7.10744	+	5.66800i	−0.412416	+	0.328891i
$298$		0			0
$299$	−10.2959	−	12.9107i	−0.595428	−	0.746643i
$300$		0			0
$301$	16.5761	−	10.0802i	0.955429	−	0.581014i
$302$		0			0
$303$	−8.69178	−	1.98384i	−0.499330	−	0.113969i
$304$		0			0
$305$	7.95930	+	34.8720i	0.455748	+	1.99676i
$306$		0			0
$307$	6.72757	+	29.4754i	0.383963	+	1.68225i	0.684925	+	0.728614i	$0.259835\pi$
$307$	6.72757	+	29.4754i	0.383963	+	1.68225i	−0.300962	+	0.953636i	$0.597308\pi$
$308$		0			0
$309$	2.45991	−	10.7776i	0.139939	−	0.613115i
$310$		0			0
$311$	17.0315	+	8.20191i	0.965765	+	0.465088i	0.849186	−	0.528094i	$-0.177093\pi$
$311$	17.0315	+	8.20191i	0.965765	+	0.465088i	0.116579	+	0.993181i	$0.462807\pi$
$312$		0			0
$313$			11.4590i			0.647699i	0.946109	+	0.323849i	$0.104977\pi$
$313$			11.4590i			0.647699i	−0.946109	+	0.323849i	$0.895023\pi$
$314$		0			0
$315$	8.88555	−	0.869712i	0.500644	−	0.0490027i
$316$		0			0
$317$	18.6668	−	8.98946i	1.04843	−	0.504898i	0.171336	−	0.985213i	$-0.445192\pi$
$317$	18.6668	−	8.98946i	1.04843	−	0.504898i	0.877096	+	0.480314i	$0.159477\pi$
$318$		0			0
$319$	−10.3268	−	2.35703i	−0.578191	−	0.131968i
$320$		0			0
$321$	−9.50897	−	19.7456i	−0.530739	−	1.10209i
$322$		0			0
$323$	−9.69908	+	20.1404i	−0.539671	+	1.12064i
$324$		0			0
$325$		−	33.3004i		−	1.84717i
$326$		0			0
$327$	−10.2576	+	12.8626i	−0.567246	+	0.711304i
$328$		0			0
$329$	−21.6377	−	2.75914i	−1.19292	−	0.152116i
$330$		0			0
$331$	1.38984	−	2.88604i	0.0763927	−	0.158631i	−0.859274	−	0.511515i	$-0.829085\pi$
$331$	1.38984	−	2.88604i	0.0763927	−	0.158631i	0.935667	+	0.352884i	$0.114799\pi$
$332$		0			0
$333$	−2.99454	+	3.75504i	−0.164100	+	0.205775i
$334$		0			0
$335$	−19.5904	−	24.5655i	−1.07034	−	1.34216i
$336$		0			0
$337$	−7.56029	+	9.48031i	−0.411835	+	0.516425i	−0.943879	−	0.330292i	$-0.892853\pi$
$337$	−7.56029	+	9.48031i	−0.411835	+	0.516425i	0.532044	+	0.846717i	$0.321424\pi$
$338$		0			0
$339$	3.39085	−	1.63295i	0.184165	−	0.0886894i
$340$		0			0
$341$	1.08245	−	0.247063i	0.0586181	−	0.0133792i
$342$		0			0
$343$	16.0988	−	9.15578i	0.869254	−	0.494366i
$344$		0			0
$345$	−3.33262	−	14.6012i	−0.179422	−	0.786100i
$346$		0			0
$347$	−8.35291	−	17.3450i	−0.448408	−	0.931128i	−0.995563	−	0.0940972i	$-0.970004\pi$
$347$	−8.35291	−	17.3450i	−0.448408	−	0.931128i	0.547155	−	0.837031i	$-0.315711\pi$
$348$		0			0
$349$	−17.6167	−	14.0489i	−0.943001	−	0.752018i	0.0258495	−	0.999666i	$-0.491771\pi$
$349$	−17.6167	−	14.0489i	−0.943001	−	0.752018i	−0.968850	+	0.247648i	$0.920342\pi$
$350$		0			0
$351$	23.2163	−	18.5144i	1.23920	−	0.988226i
$352$		0			0
$353$	14.5328	+	11.5895i	0.773502	+	0.616847i	0.928613	−	0.371050i	$-0.121002\pi$
$353$	14.5328	+	11.5895i	0.773502	+	0.616847i	−0.155111	+	0.987897i	$0.549573\pi$
$354$		0			0
$355$	9.42298	+	4.53787i	0.500120	+	0.240845i
$356$		0			0
$357$	2.62258	−	20.5668i	0.138802	−	1.08851i
$358$		0			0
$359$	2.13652	+	1.70381i	0.112761	+	0.0899239i	0.678247	−	0.734834i	$-0.262740\pi$
$359$	2.13652	+	1.70381i	0.112761	+	0.0899239i	−0.565486	+	0.824758i	$0.691311\pi$
$360$		0			0
$361$	−2.74115			−0.144271
$362$		0			0
$363$	−10.7201	−	5.16251i	−0.562657	−	0.270962i
$364$		0			0
$365$	−11.6278	+	5.59964i	−0.608625	+	0.293098i
$366$		0			0
$367$	0.0805665	−	0.352985i	0.00420554	−	0.0184257i	−0.972782	−	0.231724i	$-0.925563\pi$
$367$	0.0805665	−	0.352985i	0.00420554	−	0.0184257i	0.976987	+	0.213298i	$0.0684206\pi$
$368$		0			0
$369$	−1.13905	−	2.36527i	−0.0592968	−	0.123131i
$370$		0			0
$371$	−1.20328	−	12.2935i	−0.0624712	−	0.638247i
$372$		0			0
$373$	14.3767			0.744396			0.372198	−	0.928153i	$-0.378604\pi$
$373$	14.3767			0.744396			0.372198	+	0.928153i	$0.378604\pi$
$374$		0			0
$375$	2.77567	−	5.76373i	0.143335	−	0.297638i
$376$		0			0
$377$	33.7323	+	7.69919i	1.73730	+	0.396528i
$378$		0			0
$379$	12.8602	−	2.93526i	0.660585	−	0.150774i	0.120931	−	0.992661i	$-0.461412\pi$
$379$	12.8602	−	2.93526i	0.660585	−	0.150774i	0.539654	+	0.841887i	$0.318555\pi$
$380$		0			0
$381$	16.3898	−	3.74086i	0.839675	−	0.191650i
$382$		0			0
$383$	0.952009	−	4.17103i	0.0486454	−	0.213129i	−0.944764	−	0.327752i	$-0.893709\pi$
$383$	0.952009	−	4.17103i	0.0486454	−	0.213129i	0.993409	+	0.114623i	$0.0365660\pi$
$384$		0			0
$385$	−7.44064	−	12.2355i	−0.379210	−	0.623580i
$386$		0			0
$387$	−5.74386	+	4.58057i	−0.291977	+	0.232844i
$388$		0			0
$389$	−0.0513701	−	0.0644160i	−0.00260457	−	0.00326602i	0.780527	−	0.625121i	$-0.214951\pi$
$389$	−0.0513701	−	0.0644160i	−0.00260457	−	0.00326602i	−0.783132	+	0.621855i	$0.786379\pi$
$390$		0			0
$391$	17.4398			0.881970
$392$		0			0
$393$	18.9286			0.954821
$394$		0			0
$395$	16.0573	+	20.1353i	0.807933	+	1.01312i
$396$		0			0
$397$	−18.5965	+	14.8302i	−0.933329	+	0.744305i	−0.966907	−	0.255131i	$-0.917881\pi$
$397$	−18.5965	+	14.8302i	−0.933329	+	0.744305i	0.0335771	+	0.999436i	$0.489310\pi$
$398$		0			0
$399$	−14.3051	+	4.77183i	−0.716152	+	0.238890i
$400$		0			0
$401$	−5.78239	+	25.3343i	−0.288759	+	1.26514i	0.597471	+	0.801890i	$0.296172\pi$
$401$	−5.78239	+	25.3343i	−0.288759	+	1.26514i	−0.886230	+	0.463245i	$0.846685\pi$
$402$		0			0
$403$	−3.53581	+	0.807026i	−0.176131	+	0.0402008i
$404$		0			0
$405$	16.3867	−	3.74015i	0.814259	−	0.185849i
$406$		0			0
$407$	7.51054	+	1.71423i	0.372283	+	0.0849713i
$408$		0			0
$409$	10.6328	−	22.0792i	0.525756	−	1.09174i	−0.453898	−	0.891053i	$-0.649967\pi$
$409$	10.6328	−	22.0792i	0.525756	−	1.09174i	0.979655	−	0.200691i	$-0.0643186\pi$
$410$		0			0
$411$	−16.2303			−0.800582
$412$		0			0
$413$	12.3968	+	20.3855i	0.610005	+	1.00310i
$414$		0			0
$415$	24.1373	+	50.1216i	1.18485	+	2.46037i
$416$		0			0
$417$	3.55052	−	15.5558i	0.173869	−	0.761772i
$418$		0			0
$419$	−1.59188	+	0.766611i	−0.0777687	+	0.0374514i	−0.472364	−	0.881404i	$-0.656599\pi$
$419$	−1.59188	+	0.766611i	−0.0777687	+	0.0374514i	0.394595	+	0.918855i	$0.370885\pi$
$420$		0			0
$421$	32.7837	+	15.7878i	1.59778	+	0.769451i	0.999493	−	0.0318305i	$-0.0101337\pi$
$421$	32.7837	+	15.7878i	1.59778	+	0.769451i	0.598288	+	0.801281i	$0.295848\pi$
$422$		0			0
$423$	8.26023			0.401626
$424$		0			0
$425$	27.4960	+	21.9273i	1.33375	+	1.06363i
$426$		0			0
$427$	−19.5755	−	20.1568i	−0.947323	−	0.975458i
$428$		0			0
$429$	−10.7436	−	5.17383i	−0.518704	−	0.249795i
$430$		0			0
$431$	23.7080	+	18.9065i	1.14197	+	0.910693i	0.996896	−	0.0787271i	$-0.0250856\pi$
$431$	23.7080	+	18.9065i	1.14197	+	0.910693i	0.145077	+	0.989420i	$0.453657\pi$
$432$		0			0
$433$	−14.8804	+	11.8668i	−0.715108	+	0.570280i	−0.912022	−	0.410141i	$-0.865480\pi$
$433$	−14.8804	+	11.8668i	−0.715108	+	0.570280i	0.196914	+	0.980421i	$0.436908\pi$
$434$		0			0
$435$	24.5339	+	19.5651i	1.17631	+	0.938077i
$436$		0			0
$437$	−5.50361	−	11.4284i	−0.263274	−	0.546693i
$438$		0			0
$439$	3.77768	+	16.5511i	0.180299	+	0.789942i	0.981487	+	0.191529i	$0.0613445\pi$
$439$	3.77768	+	16.5511i	0.180299	+	0.789942i	−0.801188	+	0.598413i	$0.795798\pi$
$440$		0			0
$441$	−5.60886	+	4.21046i	−0.267088	+	0.200498i
$442$		0			0
$443$	−11.7267	+	2.67655i	−0.557155	+	0.127167i	−0.491821	−	0.870697i	$-0.663668\pi$
$443$	−11.7267	+	2.67655i	−0.557155	+	0.127167i	−0.0653340	+	0.997863i	$0.520811\pi$
$444$		0			0
$445$	14.0874	−	6.78415i	0.667809	−	0.321600i
$446$		0			0
$447$	−8.69997	+	10.9094i	−0.411494	+	0.515998i
$448$		0			0
$449$	3.35019	+	4.20100i	0.158105	+	0.198258i	0.854574	−	0.519329i	$-0.173818\pi$
$449$	3.35019	+	4.20100i	0.158105	+	0.198258i	−0.696469	+	0.717587i	$0.745247\pi$
$450$		0			0
$451$	−2.62542	+	3.29217i	−0.123626	+	0.155022i
$452$		0			0
$453$	4.95135	−	10.2816i	0.232634	−	0.483071i
$454$		0			0
$455$	24.3047	+	39.9671i	1.13942	+	1.87369i
$456$		0			0
$457$	16.2281	−	20.3494i	0.759117	−	0.951903i	−0.240708	−	0.970598i	$-0.577380\pi$
$457$	16.2281	−	20.3494i	0.759117	−	0.951903i	0.999825	+	0.0186950i	$0.00595114\pi$
$458$		0			0
$459$			31.3608i			1.46380i
$460$		0			0
$461$	−1.39262	+	2.89181i	−0.0648608	+	0.134685i	−0.930879	−	0.365328i	$-0.880957\pi$
$461$	−1.39262	+	2.89181i	−0.0648608	+	0.134685i	0.866018	+	0.500012i	$0.166671\pi$
$462$		0			0
$463$	10.9888	+	22.8185i	0.510693	+	1.06046i	0.983768	+	0.179443i	$0.0574295\pi$
$463$	10.9888	+	22.8185i	0.510693	+	1.06046i	−0.473076	+	0.881022i	$0.656856\pi$
$464$		0			0
$465$	−3.20678	−	0.731926i	−0.148711	−	0.0339422i
$466$		0			0
$467$	−6.30669	+	3.03714i	−0.291839	+	0.140542i	−0.574075	−	0.818803i	$-0.694638\pi$
$467$	−6.30669	+	3.03714i	−0.291839	+	0.140542i	0.282236	+	0.959345i	$0.408924\pi$
$468$		0			0
$469$	23.1754	+	8.49200i	1.07014	+	0.392124i
$470$		0			0
$471$		−	25.6266i		−	1.18081i
$472$		0			0
$473$	10.6169	+	5.11283i	0.488165	+	0.235088i
$474$		0			0
$475$	5.69193	−	24.9380i	0.261164	−	1.14423i
$476$		0			0
$477$	1.04087	+	4.56035i	0.0476581	+	0.208804i
$478$		0			0
$479$	3.99211	+	17.4906i	0.182404	+	0.799165i	0.980482	+	0.196610i	$0.0629933\pi$
$479$	3.99211	+	17.4906i	0.182404	+	0.799165i	−0.798078	+	0.602555i	$0.794150\pi$
$480$		0			0
$481$	−24.5330	−	5.59950i	−1.11861	−	0.255315i
$482$		0			0
$483$	8.19640	+	8.43983i	0.372949	+	0.384025i
$484$		0			0
$485$	−39.3820	−	49.3834i	−1.78824	−	2.24239i
$486$		0			0
$487$	−2.77067	+	2.20954i	−0.125551	+	0.100124i	−0.684252	−	0.729245i	$-0.739871\pi$
$487$	−2.77067	+	2.20954i	−0.125551	+	0.100124i	0.558701	+	0.829369i	$0.311300\pi$
$488$		0			0
$489$		−	21.6432i		−	0.978738i
$490$		0			0
$491$		−	18.1908i		−	0.820941i	−0.911874	−	0.410471i	$-0.865364\pi$
$491$		−	18.1908i		−	0.820941i	0.911874	−	0.410471i	$-0.134636\pi$
$492$		0			0
$493$	−28.5689	+	22.7830i	−1.28668	+	1.02609i
$494$		0			0
$495$	3.38112	+	4.23979i	0.151970	+	0.190564i
$496$		0			0
$497$	−8.17672	+	0.800332i	−0.366776	+	0.0358998i
$498$		0			0
$499$	0.229016	+	0.0522714i	0.0102522	+	0.00233999i	0.227644	−	0.973744i	$-0.426898\pi$
$499$	0.229016	+	0.0522714i	0.0102522	+	0.00233999i	−0.217392	+	0.976084i	$0.569755\pi$
$500$		0			0
$501$	−6.84317	−	29.9819i	−0.305730	−	1.33949i
$502$		0			0
$503$	−5.98534	−	26.2235i	−0.266873	−	1.16925i	−0.913629	−	0.406550i	$-0.866732\pi$
$503$	−5.98534	−	26.2235i	−0.266873	−	1.16925i	0.646755	−	0.762697i	$-0.276125\pi$
$504$		0			0
$505$	−4.72691	+	20.7099i	−0.210345	+	0.921580i
$506$		0			0
$507$	18.5375	+	8.92717i	0.823278	+	0.396470i
$508$		0			0
$509$			8.44298i			0.374229i	0.982338	+	0.187114i	$0.0599135\pi$
$509$			8.44298i			0.374229i	−0.982338	+	0.187114i	$0.940087\pi$
$510$		0			0
$511$	5.51882	−	8.50436i	0.244138	−	0.376211i
$512$		0			0
$513$	20.5508	−	9.89676i	0.907342	−	0.436953i
$514$		0			0
$515$	−25.6798	−	5.86124i	−1.13159	−	0.258277i
$516$		0			0
$517$	−5.74861	−	11.9371i	−0.252824	−	0.524994i
$518$		0			0
$519$	−0.957861	+	1.98902i	−0.0420455	+	0.0873083i
$520$		0			0
$521$			21.0888i			0.923915i	0.886902	+	0.461958i	$0.152853\pi$
$521$			21.0888i			0.923915i	−0.886902	+	0.461958i	$0.847147\pi$
$522$		0			0
$523$	−6.28041	+	7.87539i	−0.274623	+	0.344367i	−0.899947	−	0.435998i	$-0.856395\pi$
$523$	−6.28041	+	7.87539i	−0.274623	+	0.344367i	0.625324	+	0.780365i	$0.284967\pi$
$524$		0			0
$525$	2.31111	+	23.6119i	0.100865	+	1.03051i
$526$		0			0
$527$	1.66187	−	3.45090i	0.0723921	−	0.150324i
$528$		0			0
$529$	8.17022	−	10.2451i	0.355227	−	0.445440i
$530$		0			0
$531$	−5.63325	−	7.06387i	−0.244462	−	0.306546i
$532$		0			0
$533$	8.57587	−	10.7538i	0.371462	−	0.465799i
$534$		0			0
$535$	−47.0479	+	22.6571i	−2.03406	+	0.979550i
$536$		0			0
$537$	−18.5885	+	4.24269i	−0.802151	+	0.183086i
$538$		0			0
$539$	9.98808	+	5.17532i	0.430217	+	0.222917i
$540$		0			0
$541$	2.36154	+	10.3466i	0.101530	+	0.444834i	0.999983	+	0.00576419i	$0.00183481\pi$
$541$	2.36154	+	10.3466i	0.101530	+	0.444834i	−0.898453	+	0.439070i	$0.855308\pi$
$542$		0			0
$543$	−10.9845	−	22.8096i	−0.471392	−	0.978855i
$544$		0			0
$545$	30.6478	+	24.4408i	1.31281	+	1.04693i
$546$		0			0
$547$	31.5155	−	25.1328i	1.34750	−	1.07460i	0.357448	−	0.933933i	$-0.383647\pi$
$547$	31.5155	−	25.1328i	1.34750	−	1.07460i	0.990057	−	0.140666i	$-0.0449243\pi$
$548$		0			0
$549$	8.31893	+	6.63413i	0.355043	+	0.283138i
$550$		0			0
$551$	23.9455	+	11.5315i	1.02011	+	0.491259i
$552$		0			0
$553$	−18.9958	−	6.96052i	−0.807785	−	0.295991i
$554$		0			0
$555$	−17.8432	−	14.2294i	−0.757400	−	0.604006i
$556$		0			0
$557$	6.15790			0.260919			0.130459	−	0.991454i	$-0.458355\pi$
$557$	6.15790			0.260919			0.130459	+	0.991454i	$0.458355\pi$
$558$		0			0
$559$	−34.6799	−	16.7010i	−1.46680	−	0.706375i
$560$		0			0
$561$	11.3463	−	5.46410i	0.479042	−	0.230695i
$562$		0			0
$563$	2.68301	−	11.7550i	0.113075	−	0.495415i	−0.886397	−	0.462926i	$-0.846800\pi$
$563$	2.68301	−	11.7550i	0.113075	−	0.495415i	0.999472	−	0.0324888i	$-0.0103433\pi$
$564$		0			0
$565$	−3.89083	−	8.07938i	−0.163688	−	0.339902i
$566$		0			0
$567$	−9.47188	+	9.19869i	−0.397782	+	0.386309i
$568$		0			0
$569$	0.214996			0.00901311			0.00450655	−	0.999990i	$-0.498566\pi$
$569$	0.214996			0.00901311			0.00450655	+	0.999990i	$0.498566\pi$
$570$		0			0
$571$	−11.1594	+	23.1728i	−0.467008	+	0.969752i	0.525864	+	0.850569i	$0.323742\pi$
$571$	−11.1594	+	23.1728i	−0.467008	+	0.969752i	−0.992872	+	0.119184i	$0.961972\pi$
$572$		0			0
$573$	7.88905	+	1.80062i	0.329570	+	0.0752222i
$574$		0			0
$575$	−19.4557	+	4.44063i	−0.811357	+	0.185187i
$576$		0			0
$577$	−29.6214	+	6.76090i	−1.23316	+	0.281460i	−0.788946	−	0.614463i	$-0.789373\pi$
$577$	−29.6214	+	6.76090i	−1.23316	+	0.281460i	−0.444210	+	0.895923i	$0.646516\pi$
$578$		0			0
$579$	5.22226	−	22.8802i	0.217030	−	0.950869i
$580$		0			0
$581$	−36.6581	−	23.7889i	−1.52084	−	0.986932i
$582$		0			0
$583$	5.86592	−	4.67791i	0.242941	−	0.193739i
$584$		0			0
$585$	−11.0444	−	13.8492i	−0.456628	−	0.572594i
$586$		0			0
$587$	33.3317			1.37575			0.687873	−	0.725832i	$-0.258545\pi$
$587$	33.3317			1.37575			0.687873	+	0.725832i	$0.258545\pi$
$588$		0			0
$589$	−2.78584			−0.114788
$590$		0			0
$591$	−5.74054	−	7.19841i	−0.236134	−	0.296103i
$592$		0			0
$593$	7.76751	−	6.19438i	0.318973	−	0.254373i	−0.450893	−	0.892578i	$-0.648894\pi$
$593$	7.76751	−	6.19438i	0.318973	−	0.254373i	0.769866	+	0.638205i	$0.220323\pi$
$594$		0			0
$595$	−49.0046	−	6.24884i	−2.00899	−	0.256177i
$596$		0			0
$597$	−0.283508	+	1.24213i	−0.0116032	+	0.0508370i
$598$		0			0
$599$	8.81715	−	2.01246i	0.360259	−	0.0822267i	−0.0385604	−	0.999256i	$-0.512277\pi$
$599$	8.81715	−	2.01246i	0.360259	−	0.0822267i	0.398819	+	0.917030i	$0.369420\pi$
$600$		0			0
$601$	−17.4967	+	3.99352i	−0.713707	+	0.162899i	−0.563932	−	0.825821i	$-0.690712\pi$
$601$	−17.4967	+	3.99352i	−0.713707	+	0.162899i	−0.149775	+	0.988720i	$0.547855\pi$
$602$		0			0
$603$	−9.11246	−	2.07986i	−0.371088	−	0.0846985i
$604$		0			0
$605$	−12.3007	+	25.5427i	−0.500096	+	1.03846i
$606$		0			0
$607$	38.5583			1.56503			0.782516	−	0.622631i	$-0.213936\pi$
$607$	38.5583			1.56503			0.782516	+	0.622631i	$0.213936\pi$
$608$		0			0
$609$	−24.4525	−	3.11807i	−0.990864	−	0.126350i
$610$		0			0
$611$	18.7777	+	38.9924i	0.759666	+	1.57746i
$612$		0			0
$613$	−3.17540	+	13.9123i	−0.128253	+	0.561914i	0.869440	+	0.494038i	$0.164480\pi$
$613$	−3.17540	+	13.9123i	−0.128253	+	0.561914i	−0.997694	+	0.0678766i	$0.978378\pi$
$614$		0			0
$615$	11.2393	−	5.41255i	0.453211	−	0.218255i
$616$		0			0
$617$	−10.0389	−	4.83446i	−0.404150	−	0.194628i	0.220755	−	0.975329i	$-0.429148\pi$
$617$	−10.0389	−	4.83446i	−0.404150	−	0.194628i	−0.624905	+	0.780701i	$0.714862\pi$
$618$		0			0
$619$	33.6588			1.35286			0.676430	−	0.736507i	$-0.263526\pi$
$619$	33.6588			1.35286			0.676430	+	0.736507i	$0.263526\pi$
$620$		0			0
$621$	−13.9129	−	11.0952i	−0.558305	−	0.445234i
$622$		0			0
$623$	−6.68625	+	10.3033i	−0.267879	+	0.412794i
$624$		0			0
$625$	14.8442	+	7.14859i	0.593768	+	0.285944i
$626$		0			0
$627$	−7.16129	−	5.71094i	−0.285994	−	0.228073i
$628$		0			0
$629$	20.7777	−	16.5697i	0.828463	−	0.660677i
$630$		0			0
$631$	−30.2613	−	24.1326i	−1.20468	−	0.960703i	−0.204847	−	0.978794i	$-0.565670\pi$
$631$	−30.2613	−	24.1326i	−1.20468	−	0.960703i	−0.999836	+	0.0180914i	$0.994241\pi$
$632$		0			0
$633$	14.9680	+	31.0813i	0.594923	+	1.23537i
$634$		0			0
$635$	−8.91337	−	39.0520i	−0.353716	−	1.54973i
$636$		0			0
$637$	−32.6259	−	16.9051i	−1.29268	−	0.669803i
$638$		0			0
$639$	3.03320	−	0.692308i	0.119992	−	0.0273873i
$640$		0			0
$641$	9.51340	−	4.58141i	0.375757	−	0.180955i	−0.236467	−	0.971640i	$-0.575989\pi$
$641$	9.51340	−	4.58141i	0.375757	−	0.180955i	0.612224	+	0.790685i	$0.290275\pi$
$642$		0			0
$643$	−21.6521	+	27.1509i	−0.853875	+	1.07073i	0.142841	+	0.989746i	$0.454376\pi$
$643$	−21.6521	+	27.1509i	−0.853875	+	1.07073i	−0.996716	+	0.0809794i	$0.974195\pi$
$644$		0			0
$645$	−21.7659	−	27.2936i	−0.857032	−	1.07468i
$646$		0			0
$647$	19.2456	−	24.1332i	0.756623	−	0.948775i	−0.243152	−	0.969988i	$-0.578182\pi$
$647$	19.2456	−	24.1332i	0.756623	−	0.948775i	0.999775	+	0.0212135i	$0.00675296\pi$
$648$		0			0
$649$	−6.28782	+	13.0568i	−0.246819	+	0.512524i
$650$		0			0
$651$	2.45108	−	0.817618i	0.0960653	−	0.0320450i
$652$		0			0
$653$	−15.3200	+	19.2106i	−0.599517	+	0.751770i	−0.985303	−	0.170818i	$-0.945359\pi$
$653$	−15.3200	+	19.2106i	−0.599517	+	0.751770i	0.385786	+	0.922588i	$0.373930\pi$
$654$		0			0
$655$		−	45.1012i		−	1.76225i
$656$		0			0
$657$	−1.66575	+	3.45897i	−0.0649871	+	0.134947i
$658$		0			0
$659$	−11.7099	−	24.3158i	−0.456152	−	0.947210i	−0.994525	−	0.104503i	$-0.966675\pi$
$659$	−11.7099	−	24.3158i	−0.456152	−	0.947210i	0.538372	−	0.842707i	$-0.319039\pi$
$660$		0			0
$661$	27.6011	+	6.29977i	1.07356	+	0.245032i	0.722535	−	0.691335i	$-0.242977\pi$
$661$	27.6011	+	6.29977i	1.07356	+	0.245032i	0.351023	+	0.936367i	$0.385834\pi$
$662$		0			0
$663$	−37.0626	+	17.8484i	−1.43939	+	0.693174i
$664$		0			0
$665$	11.3699	+	34.0849i	0.440904	+	1.32175i
$666$		0			0
$667$		−	20.7347i		−	0.802851i
$668$		0			0
$669$	−7.29372	−	3.51247i	−0.281991	−	0.135800i
$670$		0			0
$671$	3.79772	−	16.6389i	0.146609	−	0.642337i
$672$		0			0
$673$	0.804569	+	3.52505i	0.0310138	+	0.135881i	0.988065	−	0.154040i	$-0.0492284\pi$
$673$	0.804569	+	3.52505i	0.0310138	+	0.135881i	−0.957051	+	0.289920i	$0.906371\pi$
$674$		0			0
$675$	−7.98527	−	34.9858i	−0.307353	−	1.34660i
$676$		0			0
$677$	−18.9640	−	4.32840i	−0.728844	−	0.166354i	−0.158031	−	0.987434i	$-0.550515\pi$
$677$	−18.9640	−	4.32840i	−0.728844	−	0.166354i	−0.570813	+	0.821080i	$0.693372\pi$
$678$		0			0
$679$	46.5888	+	17.0712i	1.78792	+	0.655134i
$680$		0			0
$681$	−17.9507	−	22.5094i	−0.687871	−	0.862563i
$682$		0			0
$683$	−31.0867	+	24.7908i	−1.18950	+	0.948595i	−0.999449	−	0.0331791i	$-0.989437\pi$
$683$	−31.0867	+	24.7908i	−1.18950	+	0.948595i	−0.190051	+	0.981774i	$0.560865\pi$
$684$		0			0
$685$			38.6720i			1.47758i
$686$		0			0
$687$			22.3949i			0.854419i
$688$		0			0
$689$	−19.1609	+	15.2803i	−0.729972	+	0.582134i
$690$		0			0
$691$	−5.22768	−	6.55531i	−0.198870	−	0.249376i	0.672390	−	0.740197i	$-0.265268\pi$
$691$	−5.22768	−	6.55531i	−0.198870	−	0.249376i	−0.871260	+	0.490822i	$0.836697\pi$
$692$		0			0
$693$	−3.99986	−	1.46564i	−0.151942	−	0.0556752i
$694$		0			0
$695$	−37.0649	−	8.45983i	−1.40595	−	0.320900i
$696$		0			0
$697$	3.23241	+	14.1621i	0.122436	+	0.536428i
$698$		0			0
$699$	7.16207	+	31.3791i	0.270894	+	1.18687i
$700$		0			0
$701$	−4.88523	+	21.4036i	−0.184513	+	0.808403i	0.794933	+	0.606697i	$0.207506\pi$
$701$	−4.88523	+	21.4036i	−0.184513	+	0.808403i	−0.979446	+	0.201706i	$0.935351\pi$
$702$		0			0
$703$	−17.4152	−	8.38670i	−0.656826	−	0.316311i
$704$		0			0
$705$			39.2509i			1.47827i
$706$		0			0
$707$	−5.28033	−	15.8295i	−0.198587	−	0.595330i
$708$		0			0
$709$	−4.09142	+	1.97032i	−0.153656	+	0.0739971i	−0.509132	−	0.860689i	$-0.670033\pi$
$709$	−4.09142	+	1.97032i	−0.153656	+	0.0739971i	0.355475	+	0.934686i	$0.384319\pi$
$710$		0			0
$711$	7.46908	+	1.70477i	0.280112	+	0.0639338i
$712$		0			0
$713$	0.943004	+	1.95817i	0.0353158	+	0.0733340i
$714$		0			0
$715$	−12.3277	+	25.5987i	−0.461030	+	0.957339i
$716$		0			0
$717$		−	16.2555i		−	0.607073i
$718$		0			0
$719$	−15.1120	+	18.9499i	−0.563584	+	0.706712i	−0.979216	−	0.202821i	$-0.934989\pi$
$719$	−15.1120	+	18.9499i	−0.563584	+	0.706712i	0.415632	+	0.909533i	$0.363560\pi$
$720$		0			0
$721$	19.6282	−	6.54747i	0.730991	−	0.243840i
$722$		0			0
$723$	13.1221	−	27.2483i	0.488016	−	1.01338i
$724$		0			0
$725$	26.0700	−	32.6908i	0.968217	−	1.21411i
$726$		0			0
$727$	11.9100	+	14.9347i	0.441717	+	0.553896i	0.951995	−	0.306114i	$-0.0990288\pi$
$727$	11.9100	+	14.9347i	0.441717	+	0.553896i	−0.510278	+	0.860010i	$0.670457\pi$
$728$		0			0
$729$	18.0740	−	22.6641i	0.669409	−	0.839412i
$730$		0			0
$731$	36.6256	−	17.6379i	1.35465	−	0.652363i
$732$		0			0
$733$	20.9464	−	4.78088i	0.773673	−	0.176586i	0.182582	−	0.983191i	$-0.441555\pi$
$733$	20.9464	−	4.78088i	0.773673	−	0.176586i	0.591091	+	0.806605i	$0.298697\pi$
$734$		0			0
$735$	−20.0072	−	26.6521i	−0.737977	−	0.983078i
$736$		0			0
$737$	3.33604	+	14.6162i	0.122885	+	0.538393i
$738$		0			0
$739$	−0.300392	−	0.623771i	−0.0110501	−	0.0229458i	0.895371	−	0.445321i	$-0.146911\pi$
$739$	−0.300392	−	0.623771i	−0.0110501	−	0.0229458i	−0.906421	+	0.422376i	$0.861196\pi$
$740$		0			0
$741$	23.3922	+	18.6547i	0.859335	+	0.685296i
$742$		0			0
$743$	−25.2159	+	20.1090i	−0.925081	+	0.737728i	−0.965212	−	0.261467i	$-0.915794\pi$
$743$	−25.2159	+	20.1090i	−0.925081	+	0.737728i	0.0401312	+	0.999194i	$0.487222\pi$
$744$		0			0
$745$	25.9939	+	20.7294i	0.952343	+	0.759468i
$746$		0			0
$747$	14.9099	+	7.18024i	0.545525	+	0.262711i
$748$		0			0
$749$	22.3301	−	34.4101i	0.815924	−	1.25732i
$750$		0			0
$751$	−20.5766	−	16.4093i	−0.750851	−	0.598784i	0.171478	−	0.985188i	$-0.445146\pi$
$751$	−20.5766	−	16.4093i	−0.750851	−	0.598784i	−0.922330	+	0.386404i	$0.873717\pi$
$752$		0			0
$753$	−32.3423			−1.17862
$754$		0			0
$755$	−24.4979	−	11.7976i	−0.891572	−	0.429358i
$756$		0			0
$757$	12.8059	−	6.16699i	0.465438	−	0.224143i	−0.186441	−	0.982466i	$-0.559695\pi$
$757$	12.8059	−	6.16699i	0.465438	−	0.224143i	0.651879	+	0.758323i	$0.273981\pi$
$758$		0			0
$759$	−1.59013	+	6.96683i	−0.0577182	+	0.252880i
$760$		0			0
$761$	4.63249	+	9.61946i	0.167928	+	0.348705i	0.967902	−	0.251329i	$-0.0808677\pi$
$761$	4.63249	+	9.61946i	0.167928	+	0.348705i	−0.799974	+	0.600035i	$0.795153\pi$
$762$		0			0
$763$	−30.5460	−	3.89509i	−1.10584	−	0.141012i
$764$		0			0
$765$	18.7076			0.676375
$766$		0			0
$767$	20.5390	−	42.6498i	0.741622	−	1.53999i
$768$		0			0
$769$	−21.3548	−	4.87410i	−0.770075	−	0.175765i	−0.180606	−	0.983556i	$-0.557806\pi$
$769$	−21.3548	−	4.87410i	−0.770075	−	0.175765i	−0.589469	+	0.807791i	$0.700663\pi$
$770$		0			0
$771$	30.9557	−	7.06543i	1.11484	−	0.254455i
$772$		0			0
$773$	20.7343	−	4.73247i	0.745762	−	0.170215i	0.167279	−	0.985910i	$-0.446502\pi$
$773$	20.7343	−	4.73247i	0.745762	−	0.170215i	0.578483	+	0.815694i	$0.303645\pi$
$774$		0			0
$775$	−0.975272	+	4.27294i	−0.0350328	+	0.153489i
$776$		0			0
$777$	17.7839	+	2.26772i	0.637994	+	0.0813541i
$778$		0			0
$779$	8.26040	−	6.58745i	0.295960	−	0.236020i
$780$		0			0
$781$	−3.11140	−	3.90157i	−0.111335	−	0.139609i
$782$		0			0
$783$	37.2858			1.33249
$784$		0			0
$785$	−61.0607			−2.17935
$786$		0			0
$787$	9.31120	+	11.6759i	0.331909	+	0.416200i	0.919582	−	0.392898i	$-0.128527\pi$
$787$	9.31120	+	11.6759i	0.331909	+	0.416200i	−0.587673	+	0.809098i	$0.699956\pi$
$788$		0			0
$789$	−33.0595	+	26.3641i	−1.17695	+	0.938586i
$790$		0			0
$791$	5.90913	+	3.83467i	0.210105	+	0.136345i
$792$		0			0
$793$	−12.4052	+	54.3506i	−0.440521	+	1.93005i
$794$		0			0
$795$	−21.6698	+	4.94599i	−0.768549	+	0.175416i
$796$		0			0
$797$	17.8962	−	4.08468i	0.633914	−	0.144687i	0.106524	−	0.994310i	$-0.466028\pi$
$797$	17.8962	−	4.08468i	0.633914	−	0.144687i	0.527390	+	0.849623i	$0.323171\pi$
$798$		0			0
$799$	−44.5604	−	10.1706i	−1.57643	−	0.359811i
$800$		0			0
$801$	2.01812	−	4.19066i	0.0713066	−	0.148070i
$802$		0			0
$803$	6.15792			0.217308
$804$		0			0
$805$	20.1096	−	19.5296i	0.708770	−	0.688328i
$806$		0			0
$807$	5.95798	+	12.3719i	0.209731	+	0.435510i
$808$		0			0
$809$	6.13802	−	26.8924i	0.215801	−	0.945486i	−0.744741	−	0.667353i	$-0.767427\pi$
$809$	6.13802	−	26.8924i	0.215801	−	0.945486i	0.960542	−	0.278133i	$-0.0897157\pi$
$810$		0			0
$811$	8.20855	−	3.95303i	0.288241	−	0.138810i	−0.284176	−	0.958772i	$-0.591720\pi$
$811$	8.20855	−	3.95303i	0.288241	−	0.138810i	0.572417	+	0.819963i	$0.306006\pi$
$812$		0			0
$813$	24.9958	+	12.0373i	0.876641	+	0.422168i
$814$		0			0
$815$	−51.5693			−1.80639
$816$		0			0
$817$	−23.1164	−	18.4347i	−0.808741	−	0.644949i
$818$		0			0
$819$	13.0655	+	4.78750i	0.456545	+	0.167289i
$820$		0			0
$821$	−23.9210	−	11.5198i	−0.834850	−	0.402042i	−0.0329179	−	0.999458i	$-0.510480\pi$
$821$	−23.9210	−	11.5198i	−0.834850	−	0.402042i	−0.801932	+	0.597416i	$0.796194\pi$
$822$		0			0
$823$	−15.6332	−	12.4671i	−0.544940	−	0.434575i	0.311932	−	0.950104i	$-0.399024\pi$
$823$	−15.6332	−	12.4671i	−0.544940	−	0.434575i	−0.856872	+	0.515529i	$0.827595\pi$
$824$		0			0
$825$	−11.2665	+	8.98476i	−0.392250	+	0.312809i
$826$		0			0
$827$	9.01700	+	7.19082i	0.313552	+	0.250049i	0.767602	−	0.640927i	$-0.221450\pi$
$827$	9.01700	+	7.19082i	0.313552	+	0.250049i	−0.454050	+	0.890976i	$0.650021\pi$
$828$		0			0
$829$	−19.2879	−	40.0516i	−0.669895	−	1.39105i	−0.907651	−	0.419726i	$-0.862126\pi$
$829$	−19.2879	−	40.0516i	−0.669895	−	1.39105i	0.237756	−	0.971325i	$-0.423588\pi$
$830$		0			0
$831$	8.63904	+	37.8501i	0.299685	+	1.31301i
$832$		0			0
$833$	35.4416	−	15.8075i	1.22798	−	0.547699i
$834$		0			0
$835$	−71.4380	+	16.3052i	−2.47221	+	0.564266i
$836$		0			0
$837$	−3.52124	+	1.69574i	−0.121712	+	0.0586133i
$838$		0			0
$839$	11.2954	−	14.1640i	0.389961	−	0.488996i	−0.547637	−	0.836716i	$-0.684473\pi$
$839$	11.2954	−	14.1640i	0.389961	−	0.488996i	0.937598	+	0.347720i	$0.113044\pi$
$840$		0			0
$841$	9.00612	+	11.2933i	0.310556	+	0.389425i
$842$		0			0
$843$	3.24410	−	4.06797i	0.111733	−	0.140108i
$844$		0			0
$845$	21.2708	−	44.1693i	0.731738	−	1.51947i
$846$		0			0
$847$	−2.16945	−	22.1645i	−0.0745431	−	0.761582i
$848$		0			0
$849$	−1.09254	+	1.37000i	−0.0374957	+	0.0470182i
$850$		0			0
$851$			15.0800i			0.516937i
$852$		0			0
$853$	−3.44393	+	7.15140i	−0.117918	+	0.244859i	−0.951571	−	0.307430i	$-0.900531\pi$
$853$	−3.44393	+	7.15140i	−0.117918	+	0.244859i	0.833653	+	0.552289i	$0.186245\pi$
$854$		0			0
$855$	−5.90370	−	12.2592i	−0.201902	−	0.419254i
$856$		0			0
$857$	18.8343	+	4.29880i	0.643367	+	0.146844i	0.531743	−	0.846906i	$-0.321537\pi$
$857$	18.8343	+	4.29880i	0.643367	+	0.146844i	0.111625	+	0.993750i	$0.464395\pi$
$858$		0			0
$859$	11.5515	−	5.56290i	0.394132	−	0.189804i	−0.226312	−	0.974055i	$-0.572667\pi$
$859$	11.5515	−	5.56290i	0.394132	−	0.189804i	0.620444	+	0.784251i	$0.286953\pi$
$860$		0			0
$861$	−5.33444	+	8.22023i	−0.181797	+	0.280145i
$862$		0			0
$863$			47.5966i			1.62021i	0.586288	+	0.810103i	$0.300589\pi$
$863$			47.5966i			1.62021i	−0.586288	+	0.810103i	$0.699411\pi$
$864$		0			0
$865$	4.73924	+	2.28230i	0.161139	+	0.0776005i
$866$		0			0
$867$	4.32004	−	18.9273i	0.146716	−	0.642806i
$868$		0			0
$869$	−2.73441	−	11.9802i	−0.0927584	−	0.406401i
$870$		0			0
$871$	−10.8971	−	47.7434i	−0.369235	−	1.61772i
$872$		0			0
$873$	−18.3185	−	4.18109i	−0.619989	−	0.141508i
$874$		0			0
$875$	11.9169	−	1.16642i	0.402866	−	0.0394323i
$876$		0			0
$877$	16.7147	+	20.9595i	0.564414	+	0.707753i	0.979367	−	0.202090i	$-0.0647733\pi$
$877$	16.7147	+	20.9595i	0.564414	+	0.707753i	−0.414953	+	0.909843i	$0.636202\pi$
$878$		0			0
$879$	32.1538	−	25.6418i	1.08452	−	0.864877i
$880$		0			0
$881$		−	2.27598i		−	0.0766796i	−0.999265	−	0.0383398i	$-0.987793\pi$
$881$		−	2.27598i		−	0.0766796i	0.999265	−	0.0383398i	$-0.0122069\pi$
$882$		0			0
$883$		−	33.8549i		−	1.13931i	−0.821884	−	0.569655i	$-0.807077\pi$
$883$		−	33.8549i		−	1.13931i	0.821884	−	0.569655i	$-0.192923\pi$
$884$		0			0
$885$	33.5660	−	26.7680i	1.12831	−	0.899797i
$886$		0			0
$887$	−1.49765	−	1.87799i	−0.0502861	−	0.0630567i	0.756052	−	0.654511i	$-0.227125\pi$
$887$	−1.49765	−	1.87799i	−0.0502861	−	0.0630567i	−0.806339	+	0.591454i	$0.798554\pi$
$888$		0			0
$889$	21.9220	+	22.5730i	0.735239	+	0.757075i
$890$		0			0
$891$	−7.81876	−	1.78458i	−0.261938	−	0.0597857i
$892$		0			0
$893$	7.39741	+	32.4102i	0.247545	+	1.08457i
$894$		0			0
$895$	10.1091	+	44.2908i	0.337909	+	1.48048i
$896$		0			0
$897$	5.19414	−	22.7570i	0.173427	−	0.759835i
$898$		0			0
$899$	−4.10288	−	1.97584i	−0.136839	−	0.0658981i
$900$		0			0
$901$		−	25.8827i		−	0.862278i
$902$		0			0
$903$	25.7491	+	9.43506i	0.856875	+	0.313979i
$904$		0			0
$905$	−54.3486	+	26.1729i	−1.80661	+	0.870017i
$906$		0			0
$907$	15.1224	+	3.45159i	0.502131	+	0.114608i	0.466081	−	0.884742i	$-0.345665\pi$
$907$	15.1224	+	3.45159i	0.502131	+	0.114608i	0.0360496	+	0.999350i	$0.488523\pi$
$908$		0			0
$909$	2.74176	+	5.69333i	0.0909386	+	0.188836i
$910$		0			0
$911$	−7.85870	+	16.3188i	−0.260370	+	0.540665i	−0.989642	−	0.143560i	$-0.954145\pi$
$911$	−7.85870	+	16.3188i	−0.260370	+	0.540665i	0.729271	+	0.684225i	$0.239859\pi$
$912$		0			0
$913$		−	26.5438i		−	0.878471i
$914$		0			0
$915$	−31.5240	+	39.5298i	−1.04215	+	1.30682i
$916$		0			0
$917$	18.4085	+	30.2712i	0.607902	+	0.999644i
$918$		0			0
$919$	20.7379	−	43.0626i	0.684079	−	1.42050i	−0.212295	−	0.977206i	$-0.568094\pi$
$919$	20.7379	−	43.0626i	0.684079	−	1.42050i	0.896374	−	0.443299i	$-0.146192\pi$
$920$		0			0
$921$	−26.6455	+	33.4124i	−0.878000	+	1.10098i
$922$		0			0
$923$	10.1633	+	12.7444i	0.334530	+	0.419487i
$924$		0			0
$925$	−18.9603	+	23.7755i	−0.623412	+	0.781734i
$926$		0			0
$927$	−7.05958	+	3.39971i	−0.231867	+	0.111661i
$928$		0			0
$929$	9.01504	−	2.05762i	0.295774	−	0.0675085i	−0.0720590	−	0.997400i	$-0.522957\pi$
$929$	9.01504	−	2.05762i	0.295774	−	0.0675085i	0.367833	+	0.929892i	$0.380100\pi$
$930$		0			0
$931$	−21.5433	−	18.2365i	−0.706053	−	0.597677i
$932$		0			0
$933$	5.94594	+	26.0509i	0.194661	+	0.852867i
$934$		0			0
$935$	−13.0193	−	27.0349i	−0.425778	−	0.884137i
$936$		0			0
$937$	−4.44309	−	3.54325i	−0.145150	−	0.115753i	0.548223	−	0.836332i	$-0.315305\pi$
$937$	−4.44309	−	3.54325i	−0.145150	−	0.115753i	−0.693373	+	0.720579i	$0.743876\pi$
$938$		0			0
$939$	−12.6639	+	10.0991i	−0.413270	+	0.329571i
$940$		0			0
$941$	−12.8341	−	10.2349i	−0.418380	−	0.333647i	0.391567	−	0.920149i	$-0.371933\pi$
$941$	−12.8341	−	10.2349i	−0.418380	−	0.333647i	−0.809947	+	0.586503i	$0.800504\pi$
$942$		0			0
$943$	−7.42647	−	3.57640i	−0.241839	−	0.116464i
$944$		0			0
$945$	35.1187	+	36.1617i	1.14241	+	1.17634i
$946$		0			0
$947$	29.5673	+	23.5792i	0.960809	+	0.766220i	0.972305	−	0.233714i	$-0.0750879\pi$
$947$	29.5673	+	23.5792i	0.960809	+	0.766220i	−0.0114959	+	0.999934i	$0.503659\pi$
$948$		0			0
$949$	−20.1147			−0.652952
$950$		0			0
$951$	26.3863	+	12.7069i	0.855633	+	0.412051i
$952$		0			0
$953$	−40.1533	+	19.3368i	−1.30069	+	0.626381i	−0.950625	−	0.310343i	$-0.899556\pi$
$953$	−40.1533	+	19.3368i	−1.30069	+	0.626381i	−0.350068	+	0.936724i	$0.613842\pi$
$954$		0			0
$955$	4.29035	−	18.7973i	0.138833	−	0.608265i
$956$		0			0
$957$	−6.49643	−	13.4900i	−0.210000	−	0.436069i
$958$		0			0
$959$	−15.7843	−	25.9560i	−0.509703	−	0.838164i
$960$		0			0
$961$	−30.5227			−0.984602
$962$		0			0
$963$	−6.73991	+	13.9956i	−0.217191	+	0.451001i
$964$		0			0
$965$	−54.5167	−	12.4431i	−1.75496	−	0.400557i
$966$		0			0
$967$	−19.9355	+	4.55014i	−0.641081	+	0.146323i	−0.530690	−	0.847566i	$-0.678067\pi$
$967$	−19.9355	+	4.55014i	−0.641081	+	0.146323i	−0.110391	+	0.993888i	$0.535210\pi$
$968$		0			0
$969$	−30.8062	+	7.03130i	−0.989636	+	0.225878i
$970$		0			0
$971$	13.7570	−	60.2733i	0.441483	−	1.93426i	0.0976932	−	0.995217i	$-0.468854\pi$
$971$	13.7570	−	60.2733i	0.441483	−	1.93426i	0.343790	−	0.939047i	$-0.388289\pi$
$972$		0			0
$973$	28.3303	−	9.45029i	0.908229	−	0.302962i
$974$		0			0
$975$	36.8019	−	29.3485i	1.17860	−	0.939906i
$976$		0			0
$977$	−16.8828	−	21.1703i	−0.540127	−	0.677298i	0.434619	−	0.900615i	$-0.356883\pi$
$977$	−16.8828	−	21.1703i	−0.540127	−	0.677298i	−0.974746	+	0.223316i	$0.928312\pi$
$978$		0			0
$979$	−7.46054			−0.238440
$980$		0			0
$981$	11.6610			0.372308
$982$		0			0
$983$	−1.45884	−	1.82933i	−0.0465299	−	0.0583466i	0.758022	−	0.652229i	$-0.226166\pi$
$983$	−1.45884	−	1.82933i	−0.0465299	−	0.0583466i	−0.804552	+	0.593882i	$0.797594\pi$
$984$		0			0
$985$	−17.1517	+	13.6780i	−0.546498	+	0.435818i
$986$		0			0
$987$	−16.0206	−	26.3446i	−0.509942	−	0.838557i
$988$		0			0
$989$	−5.13290	+	22.4887i	−0.163217	+	0.715099i
$990$		0			0
$991$	34.1454	−	7.79346i	1.08466	−	0.247567i	0.357418	−	0.933945i	$-0.383657\pi$
$991$	34.1454	−	7.79346i	1.08466	−	0.247567i	0.727246	+	0.686377i	$0.240800\pi$
$992$		0			0
$993$	4.41441	−	1.00756i	0.140087	−	0.0319740i
$994$		0			0
$995$	2.95963	+	0.675516i	0.0938266	+	0.0214153i
$996$		0			0
$997$	−12.2466	+	25.4304i	−0.387854	+	0.805388i	0.612040	+	0.790827i	$0.290349\pi$
$997$	−12.2466	+	25.4304i	−0.387854	+	0.805388i	−0.999894	+	0.0145606i	$0.995365\pi$
$998$		0			0
$999$	−27.1174			−0.857956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.b.111.13	yes	120
4.3	odd	2	inner	784.2.bb.b.111.8	✓	120
49.34	odd	14	inner	784.2.bb.b.671.8	yes	120
196.83	even	14	inner	784.2.bb.b.671.13	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.b.111.8	✓	120	4.3	odd	2	inner
784.2.bb.b.111.13	yes	120	1.1	even	1	trivial
784.2.bb.b.671.8	yes	120	49.34	odd	14	inner
784.2.bb.b.671.13	yes	120	196.83	even	14	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.881327 + 1.10515i) q^{3} +(2.63324 - 2.09994i) q^{5} +(-0.910280 + 2.48423i) q^{7} +(0.222946 - 0.976789i) q^{9} +O(q^{10})\)	\(q+(0.881327 + 1.10515i) q^{3} +(2.63324 - 2.09994i) q^{5} +(-0.910280 + 2.48423i) q^{7} +(0.222946 - 0.976789i) q^{9} +(-1.56674 + 0.357599i) q^{11} +(5.11774 - 1.16809i) q^{13} +(4.64150 + 1.05939i) q^{15} +(-2.40539 + 4.99485i) q^{17} +4.03223 q^{19} +(-3.54770 + 1.18342i) q^{21} +(-1.36491 - 2.83426i) q^{23} +(1.41161 - 6.18467i) q^{25} +(5.09665 - 2.45442i) q^{27} +(5.93852 + 2.85984i) q^{29} -0.690893 q^{31} +(-1.77601 - 1.41632i) q^{33} +(2.81975 + 8.45311i) q^{35} +(-4.31900 - 2.07992i) q^{37} +(5.80132 + 4.62639i) q^{39} +(2.04860 - 1.63370i) q^{41} +(-5.73291 - 4.57185i) q^{43} +(-1.46413 - 3.04029i) q^{45} +(1.83457 + 8.03779i) q^{47} +(-5.34278 - 4.52269i) q^{49} +(-7.63999 + 1.74378i) q^{51} +(-4.20637 + 2.02568i) q^{53} +(-3.37468 + 4.23171i) q^{55} +(3.55371 + 4.45621i) q^{57} +(5.62252 - 7.05041i) q^{59} +(-4.60786 + 9.56833i) q^{61} +(2.22362 + 1.44300i) q^{63} +(11.0233 - 13.8228i) q^{65} -9.32900i q^{67} +(1.92935 - 4.00633i) q^{69} +(1.34733 + 2.79776i) q^{71} +(-3.73578 - 0.852667i) q^{73} +(8.07907 - 3.89068i) q^{75} +(0.537817 - 4.21766i) q^{77} +7.64657i q^{79} +(4.49624 + 2.16528i) q^{81} +(-3.67543 + 16.1031i) q^{83} +(4.15490 + 18.2038i) q^{85} +(2.07323 + 9.08340i) q^{87} +(4.52603 + 1.03304i) q^{89} +(-1.75677 + 13.7769i) q^{91} +(-0.608903 - 0.763540i) q^{93} +(10.6178 - 8.46744i) q^{95} -18.7538i q^{97} +1.61010i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 24 q^{9}+O(q^{10}) \) 120 * q - 24 * q^9	\( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) \) 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more