LMFDB - Embedded newform 252.2.be.a.107.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(107,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("252.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.10
Character	$\chi$	$=$	252.107
Dual form			252.2.be.a.179.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.627710 - 1.26727i) q^{2} +(-1.21196 - 1.59096i) q^{4} +(2.15525 + 1.24433i) q^{5} +(2.64453 - 0.0803545i) q^{7} +(-2.77694 + 0.537226i) q^{8} +O(q^{10})$	\(q+(0.627710 - 1.26727i) q^{2} +(-1.21196 - 1.59096i) q^{4} +(2.15525 + 1.24433i) q^{5} +(2.64453 - 0.0803545i) q^{7} +(-2.77694 + 0.537226i) q^{8} +(2.92978 - 1.95021i) q^{10} +(-2.30393 - 3.99053i) q^{11} +5.22221 q^{13} +(1.55817 - 3.40178i) q^{14} +(-1.06230 + 3.85636i) q^{16} +(-4.85928 + 2.80550i) q^{17} +(-2.76570 - 1.59678i) q^{19} +(-0.632394 - 4.93699i) q^{20} +(-6.50329 + 0.414819i) q^{22} +(-0.359366 + 0.622440i) q^{23} +(0.596726 + 1.03356i) q^{25} +(3.27803 - 6.61796i) q^{26} +(-3.33291 - 4.10995i) q^{28} +4.53656i q^{29} +(1.01944 - 0.588574i) q^{31} +(4.22025 + 3.76690i) q^{32} +(0.505125 + 7.91907i) q^{34} +(5.79960 + 3.11749i) q^{35} +(-1.35648 + 2.34949i) q^{37} +(-3.75961 + 2.50258i) q^{38} +(-6.65348 - 2.29758i) q^{40} -3.83670i q^{41} +11.1773i q^{43} +(-3.55649 + 8.50184i) q^{44} +(0.563224 + 0.846126i) q^{46} +(-2.70905 + 4.69222i) q^{47} +(6.98709 - 0.425000i) q^{49} +(1.68437 - 0.107439i) q^{50} +(-6.32912 - 8.30832i) q^{52} +(1.79114 - 1.03411i) q^{53} -11.4674i q^{55} +(-7.30053 + 1.64385i) q^{56} +(5.74906 + 2.84764i) q^{58} +(2.05821 + 3.56492i) q^{59} +(0.505125 - 0.874903i) q^{61} +(-0.105972 - 1.66136i) q^{62} +(7.42278 - 2.98369i) q^{64} +(11.2552 + 6.49816i) q^{65} +(-10.9505 + 6.32230i) q^{67} +(10.3527 + 4.33075i) q^{68} +(7.59118 - 5.39280i) q^{70} -7.31012 q^{71} +(-4.81894 - 8.34664i) q^{73} +(2.12597 + 3.19383i) q^{74} +(0.811513 + 6.33534i) q^{76} +(-6.41348 - 10.3680i) q^{77} +(-7.65524 - 4.41975i) q^{79} +(-7.08811 + 6.98956i) q^{80} +(-4.86215 - 2.40833i) q^{82} +13.7657 q^{83} -13.9639 q^{85} +(14.1647 + 7.01612i) q^{86} +(8.54170 + 9.84373i) q^{88} +(-7.38369 - 4.26297i) q^{89} +(13.8103 - 0.419628i) q^{91} +(1.42581 - 0.182637i) q^{92} +(4.24582 + 6.37846i) q^{94} +(-3.97384 - 6.88289i) q^{95} -10.7232 q^{97} +(3.84727 - 9.12132i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) $ 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.627710	−	1.26727i	0.443858	−	0.896097i
$2$	0.627710	−	1.26727i	0.443858	−	0.896097i
$3$		0			0
$3$		0			0
$4$	−1.21196	−	1.59096i	−0.605981	−	0.795479i
$5$	2.15525	+	1.24433i	0.963856	+	0.556482i	0.897358	−	0.441304i	$-0.145484\pi$
$5$	2.15525	+	1.24433i	0.963856	+	0.556482i	0.0664982	+	0.997787i	$0.478817\pi$
$6$		0			0
$7$	2.64453	−	0.0803545i	0.999539	−	0.0303711i
$7$	2.64453	−	0.0803545i	0.999539	−	0.0303711i
$8$	−2.77694	+	0.537226i	−0.981796	+	0.189938i
$9$		0			0
$10$	2.92978	−	1.95021i	0.926477	−	0.616710i
$11$	−2.30393	−	3.99053i	−0.694662	−	1.20319i	−0.970294	−	0.241927i	$-0.922220\pi$
$11$	−2.30393	−	3.99053i	−0.694662	−	1.20319i	0.275632	−	0.961263i	$-0.411113\pi$
$12$		0			0
$13$	5.22221			1.44838			0.724190	−	0.689600i	$-0.242214\pi$
$13$	5.22221			1.44838			0.724190	+	0.689600i	$0.242214\pi$
$14$	1.55817	−	3.40178i	0.416437	−	0.909164i
$15$		0			0
$16$	−1.06230	+	3.85636i	−0.265575	+	0.964090i
$17$	−4.85928	+	2.80550i	−1.17855	+	0.680435i	−0.955678	−	0.294413i	$-0.904876\pi$
$17$	−4.85928	+	2.80550i	−1.17855	+	0.680435i	−0.222870	+	0.974848i	$0.571542\pi$
$18$		0			0
$19$	−2.76570	−	1.59678i	−0.634495	−	0.366326i	0.147996	−	0.988988i	$-0.452718\pi$
$19$	−2.76570	−	1.59678i	−0.634495	−	0.366326i	−0.782491	+	0.622662i	$0.786051\pi$
$20$	−0.632394	−	4.93699i	−0.141408	−	1.10394i
$21$		0			0
$22$	−6.50329	+	0.414819i	−1.38651	+	0.0884397i
$23$	−0.359366	+	0.622440i	−0.0749329	+	0.129788i	−0.901057	−	0.433700i	$-0.857208\pi$
$23$	−0.359366	+	0.622440i	−0.0749329	+	0.129788i	0.826124	+	0.563488i	$0.190541\pi$
$24$		0			0
$25$	0.596726	+	1.03356i	0.119345	+	0.206712i
$26$	3.27803	−	6.61796i	0.642875	−	1.29789i
$27$		0			0
$28$	−3.33291	−	4.10995i	−0.629861	−	0.776708i
$29$			4.53656i			0.842418i	0.906964	+	0.421209i	$0.138394\pi$
$29$			4.53656i			0.842418i	−0.906964	+	0.421209i	$0.861606\pi$
$30$		0			0
$31$	1.01944	−	0.588574i	0.183097	−	0.105711i	−0.405650	−	0.914028i	$-0.632955\pi$
$31$	1.01944	−	0.588574i	0.183097	−	0.105711i	0.588747	+	0.808317i	$0.299621\pi$
$32$	4.22025	+	3.76690i	0.746041	+	0.665900i
$33$		0			0
$34$	0.505125	+	7.91907i	0.0866283	+	1.35811i
$35$	5.79960	+	3.11749i	0.980312	+	0.526952i
$36$		0			0
$37$	−1.35648	+	2.34949i	−0.223004	+	0.386254i	−0.955719	−	0.294282i	$-0.904920\pi$
$37$	−1.35648	+	2.34949i	−0.223004	+	0.386254i	0.732715	+	0.680536i	$0.238253\pi$
$38$	−3.75961	+	2.50258i	−0.609889	+	0.405972i
$39$		0			0
$40$	−6.65348	−	2.29758i	−1.05201	−	0.363279i
$41$		−	3.83670i		−	0.599192i	−0.954066	−	0.299596i	$-0.903148\pi$
$41$		−	3.83670i		−	0.599192i	0.954066	−	0.299596i	$-0.0968519\pi$
$42$		0			0
$43$			11.1773i			1.70453i	0.523113	+	0.852263i	$0.324771\pi$
$43$			11.1773i			1.70453i	−0.523113	+	0.852263i	$0.675229\pi$
$44$	−3.55649	+	8.50184i	−0.536161	+	1.28170i
$45$		0			0
$46$	0.563224	+	0.846126i	0.0830428	+	0.124754i
$47$	−2.70905	+	4.69222i	−0.395156	+	0.684430i	−0.993121	−	0.117092i	$-0.962643\pi$
$47$	−2.70905	+	4.69222i	−0.395156	+	0.684430i	0.597965	+	0.801522i	$0.295976\pi$
$48$		0			0
$49$	6.98709	−	0.425000i	0.998155	−	0.0607142i
$50$	1.68437	−	0.107439i	0.238206	−	0.0151942i
$51$		0			0
$52$	−6.32912	−	8.30832i	−0.877690	−	1.15216i
$53$	1.79114	−	1.03411i	0.246032	−	0.142046i	−0.371914	−	0.928267i	$-0.621298\pi$
$53$	1.79114	−	1.03411i	0.246032	−	0.142046i	0.617946	+	0.786221i	$0.287965\pi$
$54$		0			0
$55$		−	11.4674i		−	1.54627i
$56$	−7.30053	+	1.64385i	−0.975575	+	0.219669i
$57$		0			0
$58$	5.74906	+	2.84764i	0.754888	+	0.373914i
$59$	2.05821	+	3.56492i	0.267956	+	0.464113i	0.968334	−	0.249659i	$-0.0803186\pi$
$59$	2.05821	+	3.56492i	0.267956	+	0.464113i	−0.700378	+	0.713772i	$0.746985\pi$
$60$		0			0
$61$	0.505125	−	0.874903i	0.0646747	−	0.112020i	−0.831875	−	0.554963i	$-0.812732\pi$
$61$	0.505125	−	0.874903i	0.0646747	−	0.112020i	0.896550	+	0.442943i	$0.146066\pi$
$62$	−0.105972	−	1.66136i	−0.0134584	−	0.210993i
$63$		0			0
$64$	7.42278	−	2.98369i	0.927847	−	0.372961i
$65$	11.2552	+	6.49816i	1.39603	+	0.805998i
$66$		0			0
$67$	−10.9505	+	6.32230i	−1.33782	+	0.772391i	−0.986484	−	0.163858i	$-0.947606\pi$
$67$	−10.9505	+	6.32230i	−1.33782	+	0.772391i	−0.351337	+	0.936249i	$0.614273\pi$
$68$	10.3527	+	4.33075i	1.25545	+	0.525180i
$69$		0			0
$70$	7.59118	−	5.39280i	0.907320	−	0.644563i
$71$	−7.31012			−0.867552			−0.433776	−	0.901021i	$-0.642819\pi$
$71$	−7.31012			−0.867552			−0.433776	+	0.901021i	$0.642819\pi$
$72$		0			0
$73$	−4.81894	−	8.34664i	−0.564014	−	0.976900i	−0.997141	−	0.0755675i	$-0.975923\pi$
$73$	−4.81894	−	8.34664i	−0.564014	−	0.976900i	0.433127	−	0.901333i	$-0.357410\pi$
$74$	2.12597	+	3.19383i	0.247139	+	0.371275i
$75$		0			0
$76$	0.811513	+	6.33534i	0.0930870	+	0.726714i
$77$	−6.41348	−	10.3680i	−0.730884	−	1.18154i
$78$		0			0
$79$	−7.65524	−	4.41975i	−0.861281	−	0.497261i	0.00315980	−	0.999995i	$-0.498994\pi$
$79$	−7.65524	−	4.41975i	−0.861281	−	0.497261i	−0.864441	+	0.502734i	$0.832328\pi$
$80$	−7.08811	+	6.98956i	−0.792475	+	0.781456i
$81$		0			0
$82$	−4.86215	−	2.40833i	−0.536934	−	0.265956i
$83$	13.7657			1.51099			0.755493	−	0.655157i	$-0.227397\pi$
$83$	13.7657			1.51099			0.755493	+	0.655157i	$0.227397\pi$
$84$		0			0
$85$	−13.9639			−1.51460
$86$	14.1647	+	7.01612i	1.52742	+	0.756567i
$87$		0			0
$88$	8.54170	+	9.84373i	0.910548	+	1.04935i
$89$	−7.38369	−	4.26297i	−0.782669	−	0.451874i	0.0547061	−	0.998503i	$-0.482578\pi$
$89$	−7.38369	−	4.26297i	−0.782669	−	0.451874i	−0.837375	+	0.546628i	$0.815911\pi$
$90$		0			0
$91$	13.8103	−	0.419628i	1.44771	−	0.0439889i
$92$	1.42581	−	0.182637i	0.148651	−	0.0190412i
$93$		0			0
$94$	4.24582	+	6.37846i	0.437923	+	0.657888i
$95$	−3.97384	−	6.88289i	−0.407707	−	0.706170i
$96$		0			0
$97$	−10.7232			−1.08878			−0.544388	−	0.838833i	$-0.683238\pi$
$97$	−10.7232			−1.08878			−0.544388	+	0.838833i	$0.683238\pi$
$98$	3.84727	−	9.12132i	0.388633	−	0.921393i
$99$		0			0
$100$	0.921143	−	2.20200i	0.0921143	−	0.220200i
$101$	−3.32268	+	1.91835i	−0.330619	+	0.190883i	−0.656116	−	0.754660i	$-0.727802\pi$
$101$	−3.32268	+	1.91835i	−0.330619	+	0.190883i	0.325497	+	0.945543i	$0.394468\pi$
$102$		0			0
$103$	14.4431	+	8.33870i	1.42312	+	0.821636i	0.996564	−	0.0828265i	$-0.0263947\pi$
$103$	14.4431	+	8.33870i	1.42312	+	0.821636i	0.426552	+	0.904463i	$0.359728\pi$
$104$	−14.5018	+	2.80550i	−1.42201	+	0.275102i
$105$		0			0
$106$	−0.186190	−	2.91898i	−0.0180844	−	0.283517i
$107$	2.86844	−	4.96829i	0.277303	−	0.480303i	−0.693411	−	0.720543i	$-0.743893\pi$
$107$	2.86844	−	4.96829i	0.277303	−	0.480303i	0.970714	+	0.240240i	$0.0772261\pi$
$108$		0			0
$109$	1.41352	+	2.44830i	0.135391	+	0.234504i	0.925747	−	0.378144i	$-0.123438\pi$
$109$	1.41352	+	2.44830i	0.135391	+	0.234504i	−0.790356	+	0.612648i	$0.790104\pi$
$110$	−14.5324	−	7.19822i	−1.38561	−	0.686324i
$111$		0			0
$112$	−2.49941	+	10.2836i	−0.236172	+	0.971711i
$113$		−	5.59651i		−	0.526476i	−0.964731	−	0.263238i	$-0.915210\pi$
$113$		−	5.59651i		−	0.526476i	0.964731	−	0.263238i	$-0.0847904\pi$
$114$		0			0
$115$	−1.54904	+	0.894341i	−0.144449	+	0.0833977i
$116$	7.21748	−	5.49813i	0.670126	−	0.510489i
$117$		0			0
$118$	5.80968	−	0.370576i	0.534825	−	0.0341143i
$119$	−12.6251	+	7.80971i	−1.15734	+	0.715915i
$120$		0			0
$121$	−5.11623	+	8.86157i	−0.465112	+	0.805597i
$122$	−0.791669	−	1.18932i	−0.0716743	−	0.107676i
$123$		0			0
$124$	−2.17192	−	0.908559i	−0.195044	−	0.0815910i
$125$		−	9.47322i		−	0.847311i
$126$		0			0
$127$		−	15.2266i		−	1.35114i	−0.737294	−	0.675572i	$-0.763897\pi$
$127$		−	15.2266i		−	1.35114i	0.737294	−	0.675572i	$-0.236103\pi$
$128$	0.878205	−	11.2796i	0.0776231	−	0.996983i
$129$		0			0
$130$	15.2999	−	10.1844i	1.34189	−	0.893230i
$131$	2.07666	−	3.59688i	0.181438	−	0.314261i	−0.760932	−	0.648831i	$-0.775258\pi$
$131$	2.07666	−	3.59688i	0.181438	−	0.314261i	0.942371	+	0.334571i	$0.108591\pi$
$132$		0			0
$133$	−7.44228	−	4.00049i	−0.645328	−	0.346886i
$134$	1.13832	+	17.8459i	0.0983356	+	1.54165i
$135$		0			0
$136$	11.9867	−	10.4012i	1.02785	−	0.891899i
$137$	14.1437	−	8.16585i	1.20838	−	0.697656i	0.245971	−	0.969277i	$-0.420893\pi$
$137$	14.1437	−	8.16585i	1.20838	−	0.697656i	0.962404	+	0.271621i	$0.0875598\pi$
$138$		0			0
$139$		−	10.2903i		−	0.872811i	−0.899750	−	0.436406i	$-0.856251\pi$
$139$		−	10.2903i		−	0.872811i	0.899750	−	0.436406i	$-0.143749\pi$
$140$	−2.06910	−	13.0052i	−0.174871	−	1.09914i
$141$		0			0
$142$	−4.58863	+	9.26392i	−0.385070	+	0.777411i
$143$	−12.0316	−	20.8394i	−1.00614	−	1.74268i
$144$		0			0
$145$	−5.64499	+	9.77740i	−0.468791	+	0.811969i
$146$	−13.6024	+	0.867640i	−1.12574	+	0.0718064i
$147$		0			0
$148$	5.38194	−	0.689389i	0.442393	−	0.0566674i
$149$	−4.89898	−	2.82843i	−0.401340	−	0.231714i	0.285722	−	0.958313i	$-0.407767\pi$
$149$	−4.89898	−	2.82843i	−0.401340	−	0.231714i	−0.687062	+	0.726599i	$0.741100\pi$
$150$		0			0
$151$	−10.5330	+	6.08123i	−0.857164	+	0.494884i	−0.863061	−	0.505099i	$-0.831456\pi$
$151$	−10.5330	+	6.08123i	−0.857164	+	0.494884i	0.00589781	+	0.999983i	$0.498123\pi$
$152$	8.53800	+	2.94835i	0.692523	+	0.239142i
$153$		0			0
$154$	−17.1648	+	1.61957i	−1.38318	+	0.130509i
$155$	2.92953			0.235305
$156$		0			0
$157$	−3.51950	−	6.09596i	−0.280887	−	0.486510i	0.690716	−	0.723126i	$-0.257295\pi$
$157$	−3.51950	−	6.09596i	−0.280887	−	0.486510i	−0.971603	+	0.236615i	$0.923962\pi$
$158$	−10.4063	+	6.92695i	−0.827881	+	0.551079i
$159$		0			0
$160$	4.40840	+	13.3700i	0.348515	+	1.05699i
$161$	−0.900338	+	1.67494i	−0.0709566	+	0.132004i
$162$		0			0
$163$	−1.54904	−	0.894341i	−0.121330	−	0.0700502i	0.438107	−	0.898923i	$-0.355649\pi$
$163$	−1.54904	−	0.894341i	−0.121330	−	0.0700502i	−0.559437	+	0.828873i	$0.688983\pi$
$164$	−6.10403	+	4.64993i	−0.476645	+	0.363099i
$165$		0			0
$166$	8.64089	−	17.4449i	0.670663	−	1.35399i
$167$	8.26973			0.639931			0.319965	−	0.947429i	$-0.396329\pi$
$167$	8.26973			0.639931			0.319965	+	0.947429i	$0.396329\pi$
$168$		0			0
$169$	14.2715			1.09781
$170$	−8.76529	+	17.6961i	−0.672267	+	1.35723i
$171$		0			0
$172$	17.7827	−	13.5465i	1.35592	−	1.03291i
$173$	16.7552	+	9.67360i	1.27387	+	0.735470i	0.975714	−	0.219046i	$-0.0702946\pi$
$173$	16.7552	+	9.67360i	1.27387	+	0.735470i	0.298158	+	0.954517i	$0.403628\pi$
$174$		0			0
$175$	1.66111	+	2.68533i	0.125568	+	0.202992i
$176$	17.8364	−	4.64566i	1.34447	−	0.350180i
$177$		0			0
$178$	−10.0372	+	6.68124i	−0.752317	+	0.500780i
$179$	6.02688	+	10.4389i	0.450470	+	0.780237i	0.998415	−	0.0562770i	$-0.0179230\pi$
$179$	6.02688	+	10.4389i	0.450470	+	0.780237i	−0.547945	+	0.836514i	$0.684590\pi$
$180$		0			0
$181$	20.7992			1.54599			0.772997	−	0.634410i	$-0.218757\pi$
$181$	20.7992			1.54599			0.772997	+	0.634410i	$0.218757\pi$
$182$	8.13707	−	17.7648i	0.603160	−	1.31682i
$183$		0			0
$184$	0.663546	−	1.92154i	0.0489173	−	0.141658i
$185$	−5.84709	+	3.37582i	−0.429887	+	0.248195i
$186$		0			0
$187$	22.3909	+	12.9274i	1.63739	+	0.945345i
$188$	10.7484	−	1.37679i	0.783907	−	0.100413i
$189$		0			0
$190$	−11.2169	+	0.715482i	−0.813761	+	0.0519065i
$191$	5.30815	−	9.19399i	0.384084	−	0.665253i	−0.607557	−	0.794276i	$-0.707851\pi$
$191$	5.30815	−	9.19399i	0.384084	−	0.665253i	0.991642	+	0.129022i	$0.0411839\pi$
$192$		0			0
$193$	−6.49634	−	11.2520i	−0.467617	−	0.809936i	0.531699	−	0.846934i	$-0.321554\pi$
$193$	−6.49634	−	11.2520i	−0.467617	−	0.809936i	−0.999315	+	0.0369977i	$0.988221\pi$
$194$	−6.73106	+	13.5892i	−0.483262	+	0.975650i
$195$		0			0
$196$	−9.14424	−	10.6011i	−0.653160	−	0.757220i
$197$			3.18852i			0.227173i	0.993528	+	0.113586i	$0.0362339\pi$
$197$			3.18852i			0.227173i	−0.993528	+	0.113586i	$0.963766\pi$
$198$		0			0
$199$	−12.1672	+	7.02473i	−0.862509	+	0.497970i	−0.864852	−	0.502027i	$-0.832588\pi$
$199$	−12.1672	+	7.02473i	−0.862509	+	0.497970i	0.00234247	+	0.999997i	$0.499254\pi$
$200$	−2.21233	−	2.54956i	−0.156435	−	0.180281i
$201$		0			0
$202$	0.345395	+	5.41491i	0.0243019	+	0.380992i
$203$	0.364533	+	11.9971i	0.0255852	+	0.842029i
$204$		0			0
$205$	4.77413	−	8.26904i	0.333440	−	0.577534i
$206$	19.6335	−	13.0690i	1.36793	−	0.910561i
$207$		0			0
$208$	−5.54755	+	20.1387i	−0.384653	+	1.39637i
$209$			14.7155i			1.01789i
$210$		0			0
$211$			9.12962i			0.628509i	0.949339	+	0.314255i	$0.101755\pi$
$211$			9.12962i			0.628509i	−0.949339	+	0.314255i	$0.898245\pi$
$212$	−3.81602	−	1.59632i	−0.262085	−	0.109636i
$213$		0			0
$214$	−4.49563	−	6.75374i	−0.307315	−	0.461676i
$215$	−13.9083	+	24.0899i	−0.948539	+	1.64292i
$216$		0			0
$217$	2.64865	−	1.63842i	0.179802	−	0.111223i
$218$	3.98994	−	0.254502i	0.270233	−	0.0172371i
$219$		0			0
$220$	−18.2442	+	13.8981i	−1.23003	+	0.937009i
$221$	−25.3762	+	14.6509i	−1.70699	+	0.985528i
$222$		0			0
$223$		−	23.8384i		−	1.59634i	−0.602434	−	0.798168i	$-0.705802\pi$
$223$		−	23.8384i		−	1.59634i	0.602434	−	0.798168i	$-0.294198\pi$
$224$	11.4633	+	9.62256i	0.765921	+	0.642935i
$225$		0			0
$226$	−7.09231	−	3.51298i	−0.471773	−	0.233680i
$227$	5.00619	+	8.67097i	0.332272	+	0.575512i	0.982957	−	0.183836i	$-0.0588514\pi$
$227$	5.00619	+	8.67097i	0.332272	+	0.575512i	−0.650685	+	0.759348i	$0.725518\pi$
$228$		0			0
$229$	2.66815	−	4.62137i	0.176316	−	0.305389i	−0.764300	−	0.644861i	$-0.776915\pi$
$229$	2.66815	−	4.62137i	0.176316	−	0.305389i	0.940616	+	0.339472i	$0.110248\pi$
$230$	0.161024	+	2.52445i	0.0106176	+	0.166457i
$231$		0			0
$232$	−2.43716	−	12.5977i	−0.160007	−	0.827082i
$233$	−7.59347	−	4.38409i	−0.497465	−	0.287211i	0.230201	−	0.973143i	$-0.426062\pi$
$233$	−7.59347	−	4.38409i	−0.497465	−	0.287211i	−0.727666	+	0.685932i	$0.759395\pi$
$234$		0			0
$235$	−11.6774	+	6.74192i	−0.761747	+	0.439795i
$236$	3.17717	−	7.59507i	0.206816	−	0.494397i
$237$		0			0
$238$	1.97215	+	20.9016i	0.127836	+	1.35485i
$239$	−13.1385			−0.849860			−0.424930	−	0.905226i	$-0.639701\pi$
$239$	−13.1385			−0.849860			−0.424930	+	0.905226i	$0.639701\pi$
$240$		0			0
$241$	11.0319	+	19.1078i	0.710627	+	1.23084i	0.964622	+	0.263636i	$0.0849218\pi$
$241$	11.0319	+	19.1078i	0.710627	+	1.23084i	−0.253996	+	0.967205i	$0.581745\pi$
$242$	8.01852	+	12.0462i	0.515450	+	0.774356i
$243$		0			0
$244$	−2.00413	+	0.256715i	−0.128301	+	0.0164345i
$245$	15.5877	+	7.77828i	0.995864	+	0.496936i
$246$		0			0
$247$	−14.4431	−	8.33870i	−0.918989	−	0.530579i
$248$	−2.51473	+	2.18210i	−0.159685	+	0.138564i
$249$		0			0
$250$	−12.0052	−	5.94643i	−0.759273	−	0.376085i
$251$	26.5149			1.67361			0.836804	−	0.547503i	$-0.184421\pi$
$251$	26.5149			1.67361			0.836804	+	0.547503i	$0.184421\pi$
$252$		0			0
$253$	3.31182			0.208212
$254$	−19.2963	−	9.55789i	−1.21076	−	0.599715i
$255$		0			0
$256$	−13.7430	−	8.19322i	−0.858940	−	0.512076i
$257$	−14.6698	−	8.46961i	−0.915076	−	0.528320i	−0.0330154	−	0.999455i	$-0.510511\pi$
$257$	−14.6698	−	8.46961i	−0.915076	−	0.528320i	−0.882061	+	0.471135i	$0.843844\pi$
$258$		0			0
$259$	−3.39846	+	6.32230i	−0.211170	+	0.392848i
$260$	−3.30250	−	25.7820i	−0.204812	−	1.59893i
$261$		0			0
$262$	−3.25469	−	4.88949i	−0.201075	−	0.302073i
$263$	−6.97969	−	12.0892i	−0.430386	−	0.745451i	0.566520	−	0.824048i	$-0.308289\pi$
$263$	−6.97969	−	12.0892i	−0.430386	−	0.745451i	−0.996906	+	0.0785971i	$0.974956\pi$
$264$		0			0
$265$	5.14712			0.316185
$266$	−9.74130	+	6.92026i	−0.597277	+	0.424308i
$267$		0			0
$268$	23.3301	+	9.75948i	1.42512	+	0.596155i
$269$	13.4582	−	7.77008i	0.820559	−	0.473750i	−0.0300501	−	0.999548i	$-0.509567\pi$
$269$	13.4582	−	7.77008i	0.820559	−	0.473750i	0.850609	+	0.525798i	$0.176233\pi$
$270$		0			0
$271$	−0.197214	−	0.113861i	−0.0119799	−	0.00691658i	0.493998	−	0.869463i	$-0.335535\pi$
$271$	−0.197214	−	0.113861i	−0.0119799	−	0.00691658i	−0.505978	+	0.862546i	$0.668868\pi$
$272$	−5.65703	−	21.7194i	−0.343008	−	1.31693i
$273$		0			0
$274$	−1.47025	−	23.0497i	−0.0888208	−	1.39248i
$275$	2.74964	−	4.76251i	0.165809	−	0.287190i
$276$		0			0
$277$	9.05140	+	15.6775i	0.543846	+	0.941968i	0.998679	+	0.0513915i	$0.0163656\pi$
$277$	9.05140	+	15.6775i	0.543846	+	0.941968i	−0.454833	+	0.890577i	$0.650301\pi$
$278$	−13.0406	−	6.45932i	−0.782124	−	0.387404i
$279$		0			0
$280$	−17.7799	−	5.54139i	−1.06255	−	0.331161i
$281$			16.5594i			0.987854i	0.869503	+	0.493927i	$0.164439\pi$
$281$			16.5594i			0.987854i	−0.869503	+	0.493927i	$0.835561\pi$
$282$		0			0
$283$	−2.76570	+	1.59678i	−0.164404	+	0.0949185i	−0.579944	−	0.814656i	$-0.696926\pi$
$283$	−2.76570	+	1.59678i	−0.164404	+	0.0949185i	0.415541	+	0.909575i	$0.363592\pi$
$284$	8.85958	+	11.6301i	0.525720	+	0.690120i
$285$		0			0
$286$	−33.9616	+	2.16627i	−2.00819	+	0.128094i
$287$	−0.308296	−	10.1463i	−0.0181981	−	0.598915i
$288$		0			0
$289$	7.24171	−	12.5430i	0.425983	−	0.737824i
$290$	8.84723	+	13.2911i	0.519527	+	0.780481i
$291$		0			0
$292$	−7.43880	+	17.7825i	−0.435323	+	1.04064i
$293$			3.17751i			0.185632i	0.995683	+	0.0928160i	$0.0295868\pi$
$293$			3.17751i			0.185632i	−0.995683	+	0.0928160i	$0.970413\pi$
$294$		0			0
$295$			10.2444i			0.596451i
$296$	2.50465	−	7.25312i	0.145580	−	0.421579i
$297$		0			0
$298$	−6.65953	+	4.43291i	−0.385776	+	0.256792i
$299$	−1.87668	+	3.25051i	−0.108531	+	0.187982i
$300$		0			0
$301$	0.898148	+	29.5588i	0.0517684	+	1.70374i
$302$	1.09491	+	17.1654i	0.0630052	+	0.987760i
$303$		0			0
$304$	9.09575	−	8.96927i	0.521677	−	0.514423i
$305$	2.17734	−	1.25709i	0.124674	−	0.0719807i
$306$		0			0
$307$			10.8559i			0.619579i	0.950805	+	0.309790i	$0.100259\pi$
$307$			10.8559i			0.619579i	−0.950805	+	0.309790i	$0.899741\pi$
$308$	−8.72209	+	22.7691i	−0.496987	+	1.29739i
$309$		0			0
$310$	1.83889	−	3.71251i	0.104442	−	0.210856i
$311$	9.34103	+	16.1791i	0.529681	+	0.917434i	0.999401	+	0.0346188i	$0.0110217\pi$
$311$	9.34103	+	16.1791i	0.529681	+	0.917434i	−0.469720	+	0.882816i	$0.655645\pi$
$312$		0			0
$313$	7.91566	−	13.7103i	0.447420	−	0.774954i	−0.550798	−	0.834639i	$-0.685676\pi$
$313$	7.91566	−	13.7103i	0.447420	−	0.774954i	0.998217	+	0.0596853i	$0.0190097\pi$
$314$	−9.93447	+	0.633680i	−0.560635	+	0.0357606i
$315$		0			0
$316$	2.24621	+	17.5357i	0.126359	+	0.986462i
$317$	5.31592	+	3.06915i	0.298572	+	0.172380i	0.641801	−	0.766871i	$-0.278187\pi$
$317$	5.31592	+	3.06915i	0.298572	+	0.172380i	−0.343229	+	0.939252i	$0.611521\pi$
$318$		0			0
$319$	18.1033	−	10.4519i	1.01359	−	0.585196i
$320$	19.7106	+	2.80582i	1.10186	+	0.156850i
$321$		0			0
$322$	1.55745	+	2.19235i	0.0867934	+	0.122175i
$323$	17.9191			0.997043
$324$		0			0
$325$	3.11623	+	5.39747i	0.172857	+	0.299398i
$326$	−2.10572	+	1.40167i	−0.116625	+	0.0776316i
$327$		0			0
$328$	2.06117	+	10.6543i	0.113809	+	0.588284i
$329$	−6.78713	+	12.6264i	−0.374187	+	0.696116i
$330$		0			0
$331$	−0.336392	−	0.194216i	−0.0184898	−	0.0106751i	0.490727	−	0.871314i	$-0.336731\pi$
$331$	−0.336392	−	0.194216i	−0.0184898	−	0.0106751i	−0.509216	+	0.860639i	$0.670065\pi$
$332$	−16.6835	−	21.9007i	−0.915628	−	1.20196i
$333$		0			0
$334$	5.19099	−	10.4800i	0.284038	−	0.573440i
$335$	−31.4681			−1.71929
$336$		0			0
$337$	6.10384			0.332497			0.166249	−	0.986084i	$-0.446835\pi$
$337$	6.10384			0.332497			0.166249	+	0.986084i	$0.446835\pi$
$338$	8.95834	−	18.0858i	0.487269	−	0.983740i
$339$		0			0
$340$	16.9237	+	22.2160i	0.917818	+	1.20483i
$341$	−4.69745	−	2.71207i	−0.254381	−	0.146867i
$342$		0			0
$343$	18.4434	−	1.68537i	0.995851	−	0.0910013i
$344$	−6.00475	−	31.0388i	−0.323754	−	1.67350i
$345$		0			0
$346$	22.7765	−	15.1612i	1.22447	−	0.815069i
$347$	−14.5134	−	25.1380i	−0.779120	−	1.34948i	−0.932449	−	0.361301i	$-0.882333\pi$
$347$	−14.5134	−	25.1380i	−0.779120	−	1.34948i	0.153329	−	0.988175i	$-0.451001\pi$
$348$		0			0
$349$	−27.2889			−1.46074			−0.730371	−	0.683050i	$-0.760653\pi$
$349$	−27.2889			−1.46074			−0.730371	+	0.683050i	$0.760653\pi$
$350$	4.44575	−	0.419474i	0.237635	−	0.0224218i
$351$		0			0
$352$	5.30876	−	25.5197i	0.282958	−	1.36021i
$353$	26.2242	−	15.1406i	1.39578	−	0.805851i	0.401829	−	0.915715i	$-0.368375\pi$
$353$	26.2242	−	15.1406i	1.39578	−	0.805851i	0.993947	+	0.109864i	$0.0350414\pi$
$354$		0			0
$355$	−15.7551	−	9.09622i	−0.836195	−	0.482777i
$356$	2.16653	+	16.9137i	0.114826	+	0.896424i
$357$		0			0
$358$	17.0120	−	1.08513i	0.899113	−	0.0573508i
$359$	−10.3890	+	17.9943i	−0.548312	+	0.949704i	0.450079	+	0.892989i	$0.351396\pi$
$359$	−10.3890	+	17.9943i	−0.548312	+	0.949704i	−0.998390	+	0.0567148i	$0.981937\pi$
$360$		0			0
$361$	−4.40061	−	7.62208i	−0.231611	−	0.401162i
$362$	13.0559	−	26.3583i	0.686201	−	1.38536i
$363$		0			0
$364$	−17.4052	−	21.4630i	−0.912278	−	1.12497i
$365$		−	23.9854i		−	1.25545i
$366$		0			0
$367$	17.7384	−	10.2412i	0.925934	−	0.534589i	0.0404110	−	0.999183i	$-0.487133\pi$
$367$	17.7384	−	10.2412i	0.925934	−	0.534589i	0.885523	+	0.464595i	$0.153800\pi$
$368$	−2.01860	−	2.04706i	−0.105227	−	0.106710i
$369$		0			0
$370$	0.607810	+	9.52889i	0.0315985	+	0.495384i
$371$	4.65362	−	2.87867i	0.241604	−	0.149453i
$372$		0			0
$373$	11.9800	−	20.7499i	0.620299	−	1.07439i	−0.369130	−	0.929378i	$-0.620344\pi$
$373$	11.9800	−	20.7499i	0.620299	−	1.07439i	0.989430	−	0.145012i	$-0.0463222\pi$
$374$	30.4375	−	20.2607i	1.57389	−	1.04766i
$375$		0			0
$376$	5.00209	−	14.4854i	0.257963	−	0.747026i
$377$			23.6909i			1.22014i
$378$		0			0
$379$		−	3.00154i		−	0.154179i	−0.997024	−	0.0770894i	$-0.975437\pi$
$379$		−	3.00154i		−	0.154179i	0.997024	−	0.0770894i	$-0.0245627\pi$
$380$	−6.13426	+	14.6640i	−0.314681	+	0.752248i
$381$		0			0
$382$	−8.31931	−	12.4980i	−0.425653	−	0.639455i
$383$	14.3407	−	24.8389i	0.732777	−	1.26921i	−0.222915	−	0.974838i	$-0.571557\pi$
$383$	14.3407	−	24.8389i	0.732777	−	1.26921i	0.955692	−	0.294369i	$-0.0951095\pi$
$384$		0			0
$385$	−0.921460	−	30.3260i	−0.0469620	−	1.54556i
$386$	−18.3372	+	1.16965i	−0.933337	+	0.0595338i
$387$		0			0
$388$	12.9961	+	17.0602i	0.659778	+	0.866099i
$389$	−10.4739	+	6.04712i	−0.531049	+	0.306601i	−0.741443	−	0.671015i	$-0.765858\pi$
$389$	−10.4739	+	6.04712i	−0.531049	+	0.306601i	0.210395	+	0.977617i	$0.432525\pi$
$390$		0			0
$391$		−	4.03281i		−	0.203948i
$392$	−19.1744	+	4.93384i	−0.968453	+	0.249197i
$393$		0			0
$394$	4.04073	+	2.00147i	0.203569	+	0.100832i
$395$	−10.9993	−	19.0513i	−0.553434	−	0.958576i
$396$		0			0
$397$	−2.62914	+	4.55381i	−0.131953	+	0.228549i	−0.924429	−	0.381353i	$-0.875458\pi$
$397$	−2.62914	+	4.55381i	−0.131953	+	0.228549i	0.792476	+	0.609903i	$0.208791\pi$
$398$	1.26479	+	19.8286i	0.0633981	+	0.993920i
$399$		0			0
$400$	−4.61968	+	1.20324i	−0.230984	+	0.0601621i
$401$	−16.0622	−	9.27350i	−0.802106	−	0.463096i	0.0421007	−	0.999113i	$-0.486595\pi$
$401$	−16.0622	−	9.27350i	−0.802106	−	0.463096i	−0.844207	+	0.536017i	$0.819928\pi$
$402$		0			0
$403$	5.32373	−	3.07366i	0.265194	−	0.153110i
$404$	7.07897	+	2.96128i	0.352192	+	0.147329i
$405$		0			0
$406$	15.4324	+	7.06871i	0.765896	+	0.350814i
$407$	12.5009			0.619649
$408$		0			0
$409$	8.76122	+	15.1749i	0.433214	+	0.750349i	0.997148	−	0.0754709i	$-0.0240460\pi$
$409$	8.76122	+	15.1749i	0.433214	+	0.750349i	−0.563934	+	0.825820i	$0.690713\pi$
$410$	−7.48236	−	11.2407i	−0.369527	−	0.555138i
$411$		0			0
$412$	−4.23789	−	33.0845i	−0.208786	−	1.62996i
$413$	5.72945	+	9.26215i	0.281928	+	0.455761i
$414$		0			0
$415$	29.6686	+	17.1292i	1.45637	+	0.840837i
$416$	22.0390	+	19.6715i	1.08055	+	0.964476i
$417$		0			0
$418$	18.6485	+	9.23704i	0.912129	+	0.451799i
$419$	−26.9149			−1.31488			−0.657439	−	0.753508i	$-0.728360\pi$
$419$	−26.9149			−1.31488			−0.657439	+	0.753508i	$0.728360\pi$
$420$		0			0
$421$	−4.71296			−0.229695			−0.114848	−	0.993383i	$-0.536638\pi$
$421$	−4.71296			−0.229695			−0.114848	+	0.993383i	$0.536638\pi$
$422$	11.5697	+	5.73075i	0.563205	+	0.278969i
$423$		0			0
$424$	−4.41833	+	3.83391i	−0.214573	+	0.186191i
$425$	−5.79932	−	3.34824i	−0.281308	−	0.162413i
$426$		0			0
$427$	1.26552	−	2.35430i	0.0612427	−	0.113932i
$428$	−11.3808	+	1.45780i	−0.550111	+	0.0704654i
$429$		0			0
$430$	21.7981	+	32.7471i	1.05120	+	1.57920i
$431$	−1.91047	−	3.30903i	−0.0920239	−	0.159390i	0.816339	−	0.577573i	$-0.196000\pi$
$431$	−1.91047	−	3.30903i	−0.0920239	−	0.159390i	−0.908363	+	0.418183i	$0.862667\pi$
$432$		0			0
$433$	−34.7992			−1.67234			−0.836172	−	0.548467i	$-0.815212\pi$
$433$	−34.7992			−1.67234			−0.836172	+	0.548467i	$0.815212\pi$
$434$	−0.413743	−	4.38501i	−0.0198603	−	0.210487i
$435$		0			0
$436$	2.18200	−	5.21610i	0.104499	−	0.249806i
$437$	1.98779	−	1.14765i	0.0950891	−	0.0548997i
$438$		0			0
$439$	−30.7278	−	17.7407i	−1.46656	−	0.846717i	−0.467256	−	0.884122i	$-0.654757\pi$
$439$	−30.7278	−	17.7407i	−1.46656	−	0.846717i	−0.999300	+	0.0374052i	$0.988091\pi$
$440$	6.16060	+	31.8444i	0.293695	+	1.51812i
$441$		0			0
$442$	2.63787	+	41.3550i	0.125471	+	1.96706i
$443$	5.47919	−	9.49024i	0.260324	−	0.450895i	−0.706004	−	0.708208i	$-0.749504\pi$
$443$	5.47919	−	9.49024i	0.260324	−	0.450895i	0.966328	+	0.257313i	$0.0828372\pi$
$444$		0			0
$445$	−10.6091	−	18.3755i	−0.502920	−	0.871083i
$446$	−30.2098	−	14.9636i	−1.43047	−	0.708546i
$447$		0			0
$448$	19.3900	−	8.48690i	0.916092	−	0.400968i
$449$		−	27.1675i		−	1.28211i	−0.767494	−	0.641056i	$-0.778497\pi$
$449$		−	27.1675i		−	1.28211i	0.767494	−	0.641056i	$-0.221503\pi$
$450$		0			0
$451$	−15.3105	+	8.83951i	−0.720942	+	0.416236i
$452$	−8.90382	+	6.78276i	−0.418800	+	0.319034i
$453$		0			0
$454$	14.1309	−	0.901354i	0.663197	−	0.0423026i
$455$	30.2867	+	16.2802i	1.41986	+	0.763227i
$456$		0			0
$457$	−19.2807	+	33.3952i	−0.901914	+	1.56216i	−0.0769071	+	0.997038i	$0.524505\pi$
$457$	−19.2807	+	33.3952i	−0.901914	+	1.56216i	−0.825007	+	0.565123i	$0.808829\pi$
$458$	−4.18172	−	6.28216i	−0.195399	−	0.293546i
$459$		0			0
$460$	3.30024	+	1.38056i	0.153874	+	0.0643689i
$461$		−	13.5543i		−	0.631287i	−0.948878	−	0.315643i	$-0.897780\pi$
$461$		−	13.5543i		−	0.631287i	0.948878	−	0.315643i	$-0.102220\pi$
$462$		0			0
$463$			17.7564i			0.825212i	0.910910	+	0.412606i	$0.135381\pi$
$463$			17.7564i			0.825212i	−0.910910	+	0.412606i	$0.864619\pi$
$464$	−17.4946	−	4.81918i	−0.812167	−	0.223725i
$465$		0			0
$466$	−10.3223	+	6.87106i	−0.478173	+	0.318296i
$467$	−5.39965	+	9.35248i	−0.249866	+	0.432781i	−0.963488	−	0.267750i	$-0.913720\pi$
$467$	−5.39965	+	9.35248i	−0.249866	+	0.432781i	0.713622	+	0.700531i	$0.247053\pi$
$468$		0			0
$469$	−28.4510	+	17.5994i	−1.31375	+	0.812666i
$470$	1.21387	+	19.0304i	0.0559916	+	0.877805i
$471$		0			0
$472$	−7.63068	−	8.79384i	−0.351231	−	0.404769i
$473$	44.6035	−	25.7518i	2.05087	−	1.18407i
$474$		0			0
$475$		−	3.81135i		−	0.174877i
$476$	27.7260	+	10.6209i	1.27082	+	0.486808i
$477$		0			0
$478$	−8.24717	+	16.6501i	−0.377217	+	0.761557i
$479$	9.48360	+	16.4261i	0.433317	+	0.750527i	0.997157	−	0.0753575i	$-0.0240098\pi$
$479$	9.48360	+	16.4261i	0.433317	+	0.750527i	−0.563840	+	0.825884i	$0.690676\pi$
$480$		0			0
$481$	−7.08381	+	12.2695i	−0.322994	+	0.559442i
$482$	31.1396	−	1.98627i	1.41837	−	0.0904721i
$483$		0			0
$484$	20.2991	−	2.60017i	0.922685	−	0.118190i
$485$	−23.1112	−	13.3432i	−1.04942	−	0.605885i
$486$		0			0
$487$	−12.5847	+	7.26579i	−0.570268	+	0.329245i	−0.757257	−	0.653118i	$-0.773461\pi$
$487$	−12.5847	+	7.26579i	−0.570268	+	0.329245i	0.186988	+	0.982362i	$0.440127\pi$
$488$	−0.932682	+	2.70092i	−0.0422205	+	0.122265i
$489$		0			0
$490$	19.6418	−	14.8714i	0.887325	−	0.671822i
$491$	−26.0025			−1.17348			−0.586738	−	0.809777i	$-0.699588\pi$
$491$	−26.0025			−1.17348			−0.586738	+	0.809777i	$0.699588\pi$
$492$		0			0
$493$	−12.7273	−	22.0444i	−0.573210	−	0.992829i
$494$	−19.6335	+	13.0690i	−0.883351	+	0.588002i
$495$		0			0
$496$	1.18680	+	4.55657i	0.0532891	+	0.204596i
$497$	−19.3318	+	0.587401i	−0.867152	+	0.0263485i
$498$		0			0
$499$	2.37527	+	1.37136i	0.106332	+	0.0613907i	0.552223	−	0.833697i	$-0.313780\pi$
$499$	2.37527	+	1.37136i	0.106332	+	0.0613907i	−0.445891	+	0.895087i	$0.647113\pi$
$500$	−15.0715	+	11.4812i	−0.674018	+	0.513454i
$501$		0			0
$502$	16.6437	−	33.6017i	0.742844	−	1.49972i
$503$	21.5337			0.960139			0.480070	−	0.877230i	$-0.340611\pi$
$503$	21.5337			0.960139			0.480070	+	0.877230i	$0.340611\pi$
$504$		0			0
$505$	−9.54826			−0.424892
$506$	2.07886	−	4.19698i	0.0924167	−	0.186579i
$507$		0			0
$508$	−24.2249	+	18.4541i	−1.07481	+	0.818767i
$509$	11.3748	+	6.56726i	0.504180	+	0.291089i	0.730438	−	0.682979i	$-0.239316\pi$
$509$	11.3748	+	6.56726i	0.504180	+	0.291089i	−0.226258	+	0.974067i	$0.572649\pi$
$510$		0			0
$511$	−13.4145	−	21.6857i	−0.593423	−	0.959320i
$512$	−19.0097	+	12.2732i	−0.840117	+	0.542405i
$513$		0			0
$514$	−19.9417	+	13.2742i	−0.879589	+	0.585499i
$515$	20.7522	+	35.9439i	0.914452	+	1.58388i
$516$		0			0
$517$	24.9659			1.09800
$518$	5.87883	+	8.27534i	0.258301	+	0.363597i
$519$		0			0
$520$	−34.7458	−	11.9984i	−1.52371	−	0.526167i
$521$	6.30391	−	3.63957i	0.276179	−	0.159452i	−0.355513	−	0.934671i	$-0.615694\pi$
$521$	6.30391	−	3.63957i	0.276179	−	0.159452i	0.631693	+	0.775219i	$0.282361\pi$
$522$		0			0
$523$	−2.41646	−	1.39515i	−0.105665	−	0.0610055i	0.446236	−	0.894915i	$-0.352764\pi$
$523$	−2.41646	−	1.39515i	−0.105665	−	0.0610055i	−0.551901	+	0.833910i	$0.686097\pi$
$524$	−8.23931	+	1.05540i	−0.359936	+	0.0461053i
$525$		0			0
$526$	−19.7015	+	1.25668i	−0.859027	+	0.0547938i
$527$	−3.30250	+	5.72009i	−0.143859	+	0.249171i
$528$		0			0
$529$	11.2417	+	19.4712i	0.488770	+	0.846575i
$530$	3.23090	−	6.52281i	0.140341	−	0.283333i
$531$		0			0
$532$	2.65514	+	16.6888i	0.115115	+	0.723551i
$533$		−	20.0360i		−	0.867858i
$534$		0			0
$535$	12.3644	−	7.13859i	0.534560	−	0.308628i
$536$	27.0125	−	23.4395i	1.16676	−	1.01243i
$537$		0			0
$538$	−1.39899	−	21.9325i	−0.0603146	−	0.945578i
$539$	−17.7938	−	26.9030i	−0.766432	−	1.15880i
$540$		0			0
$541$	−0.303559	+	0.525780i	−0.0130510	+	0.0226050i	−0.872477	−	0.488655i	$-0.837488\pi$
$541$	−0.303559	+	0.525780i	−0.0130510	+	0.0226050i	0.859426	+	0.511260i	$0.170821\pi$
$542$	−0.268086	+	0.178452i	−0.0115153	+	0.00766515i
$543$		0			0
$544$	−31.0754	−	6.46448i	−1.33235	−	0.277162i
$545$			7.03558i			0.301371i
$546$		0			0
$547$		−	11.1295i		−	0.475865i	−0.971282	−	0.237933i	$-0.923530\pi$
$547$		−	11.1295i		−	0.475865i	0.971282	−	0.237933i	$-0.0764697\pi$
$548$	−30.1331	−	12.6053i	−1.28722	−	0.538472i
$549$		0			0
$550$	−4.30943	−	6.47402i	−0.183755	−	0.276053i
$551$	7.24387	−	12.5467i	0.308599	−	0.534509i
$552$		0			0
$553$	−20.5997	−	11.0730i	−0.875986	−	0.470874i
$554$	25.5493	−	1.62969i	1.08549	−	0.0692387i
$555$		0			0
$556$	−16.3714	+	12.4714i	−0.694303	+	0.528907i
$557$	−25.6805	+	14.8266i	−1.08812	+	0.628225i	−0.933075	−	0.359682i	$-0.882885\pi$
$557$	−25.6805	+	14.8266i	−1.08812	+	0.628225i	−0.155043	+	0.987908i	$0.549552\pi$
$558$		0			0
$559$			58.3703i			2.46880i
$560$	−18.1831	+	19.0537i	−0.768376	+	0.805164i
$561$		0			0
$562$	20.9853	+	10.3945i	0.885213	+	0.438466i
$563$	16.4174	+	28.4358i	0.691910	+	1.19842i	0.971211	+	0.238220i	$0.0765640\pi$
$563$	16.4174	+	28.4358i	0.691910	+	1.19842i	−0.279301	+	0.960204i	$0.590103\pi$
$564$		0			0
$565$	6.96392	−	12.0619i	0.292974	−	0.507447i
$566$	0.287496	+	4.50721i	0.0120844	+	0.189452i
$567$		0			0
$568$	20.2998	−	3.92718i	0.851759	−	0.164781i
$569$	−7.94054	−	4.58447i	−0.332885	−	0.192191i	0.324236	−	0.945976i	$-0.394893\pi$
$569$	−7.94054	−	4.58447i	−0.332885	−	0.192191i	−0.657121	+	0.753785i	$0.728226\pi$
$570$		0			0
$571$	21.1743	−	12.2250i	0.886115	−	0.511599i	0.0134453	−	0.999910i	$-0.495720\pi$
$571$	21.1743	−	12.2250i	0.886115	−	0.511599i	0.872670	+	0.488311i	$0.162387\pi$
$572$	−18.5727	+	44.3984i	−0.776565	+	1.85639i
$573$		0			0
$574$	−13.0516	−	5.97822i	−0.544764	−	0.249526i
$575$	−0.857772			−0.0357716
$576$		0			0
$577$	6.00925	+	10.4083i	0.250168	+	0.433304i	0.963572	−	0.267449i	$-0.0861807\pi$
$577$	6.00925	+	10.4083i	0.250168	+	0.433304i	−0.713404	+	0.700753i	$0.752847\pi$
$578$	−11.3497	−	17.0506i	−0.472087	−	0.709211i
$579$		0			0
$580$	22.3969	−	2.86889i	0.929983	−	0.119124i
$581$	36.4039	−	1.10614i	1.51029	−	0.0458904i
$582$		0			0
$583$	−8.25333	−	4.76506i	−0.341818	−	0.197349i
$584$	17.8659	+	20.5893i	0.739297	+	0.851989i
$585$		0			0
$586$	4.02677	+	1.99455i	0.166344	+	0.0823942i
$587$	−18.8618			−0.778510			−0.389255	−	0.921130i	$-0.627267\pi$
$587$	−18.8618			−0.778510			−0.389255	+	0.921130i	$0.627267\pi$
$588$		0			0
$589$	−3.75929			−0.154899
$590$	12.9824	+	6.43049i	0.534478	+	0.264739i
$591$		0			0
$592$	−7.61949	−	7.72693i	−0.313159	−	0.317575i
$593$	7.65096	+	4.41729i	0.314187	+	0.181396i	0.648799	−	0.760960i	$-0.275272\pi$
$593$	7.65096	+	4.41729i	0.314187	+	0.181396i	−0.334611	+	0.942356i	$0.608605\pi$
$594$		0			0
$595$	−36.9280	+	1.12206i	−1.51390	+	0.0460001i
$596$	1.43746	+	11.2220i	0.0588808	+	0.459672i
$597$		0			0
$598$	2.94127	+	4.41865i	0.120278	+	0.180692i
$599$	13.9015	+	24.0781i	0.568000	+	0.983805i	0.996764	+	0.0803885i	$0.0256161\pi$
$599$	13.9015	+	24.0781i	0.568000	+	0.983805i	−0.428763	+	0.903417i	$0.641051\pi$
$600$		0			0
$601$	−12.1977			−0.497556			−0.248778	−	0.968561i	$-0.580029\pi$
$601$	−12.1977			−0.497556			−0.248778	+	0.968561i	$0.580029\pi$
$602$	38.0228	+	17.4161i	1.54969	+	0.709829i
$603$		0			0
$604$	22.4406	+	9.38736i	0.913094	+	0.381966i
$605$	−22.0535	+	12.7326i	−0.896601	+	0.517653i
$606$		0			0
$607$	−9.10887	−	5.25901i	−0.369718	−	0.213457i	0.303617	−	0.952794i	$-0.401806\pi$
$607$	−9.10887	−	5.25901i	−0.369718	−	0.213457i	−0.673335	+	0.739337i	$0.735139\pi$
$608$	−5.65703	−	17.1569i	−0.229423	−	0.695804i
$609$		0			0
$610$	−0.226336	−	3.54837i	−0.00916408	−	0.143669i
$611$	−14.1472	+	24.5037i	−0.572336	+	0.991315i
$612$		0			0
$613$	−19.7052	−	34.1304i	−0.795884	−	1.37851i	−0.922276	−	0.386532i	$-0.873673\pi$
$613$	−19.7052	−	34.1304i	−0.795884	−	1.37851i	0.126392	−	0.991980i	$-0.459660\pi$
$614$	13.7574	+	6.81436i	0.555203	+	0.275005i
$615$		0			0
$616$	23.3798	+	25.3457i	0.941998	+	1.02121i
$617$			35.9618i			1.44777i	0.689922	+	0.723884i	$0.257645\pi$
$617$			35.9618i			1.44777i	−0.689922	+	0.723884i	$0.742355\pi$
$618$		0			0
$619$	21.1743	−	12.2250i	0.851065	−	0.491363i	−0.00994487	−	0.999951i	$-0.503166\pi$
$619$	21.1743	−	12.2250i	0.851065	−	0.491363i	0.861010	+	0.508588i	$0.169832\pi$
$620$	−3.55047	−	4.66076i	−0.142590	−	0.187181i
$621$		0			0
$622$	26.3668	−	1.68183i	1.05721	−	0.0674354i
$623$	−19.8689	−	10.6803i	−0.796032	−	0.427895i
$624$		0			0
$625$	14.7715	−	25.5849i	0.590859	−	1.02340i
$626$	−12.4060	−	18.6374i	−0.495843	−	0.744901i
$627$		0			0
$628$	−5.43292	+	12.9875i	−0.216797	+	0.518256i
$629$		−	15.2224i		−	0.606958i
$630$		0			0
$631$			5.08034i			0.202245i	0.994874	+	0.101123i	$0.0322434\pi$
$631$			5.08034i			0.202245i	−0.994874	+	0.101123i	$0.967757\pi$
$632$	23.6325	+	8.16079i	0.940051	+	0.324619i
$633$		0			0
$634$	7.22630	−	4.81019i	0.286993	−	0.191037i
$635$	18.9470	−	32.8171i	0.751887	−	1.30231i
$636$		0			0
$637$	36.4880	−	2.21944i	1.44571	−	0.0879373i
$638$	−1.88185	−	29.5026i	−0.0745031	−	1.16802i
$639$		0			0
$640$	15.9283	−	23.2175i	0.629621	−	0.917752i
$641$	−23.1295	+	13.3538i	−0.913561	+	0.527445i	−0.881575	−	0.472044i	$-0.843517\pi$
$641$	−23.1295	+	13.3538i	−0.913561	+	0.527445i	−0.0319859	+	0.999488i	$0.510183\pi$
$642$		0			0
$643$			24.3919i			0.961924i	0.876741	+	0.480962i	$0.159713\pi$
$643$			24.3919i			0.961924i	−0.876741	+	0.480962i	$0.840287\pi$
$644$	3.75593	−	0.597559i	0.148004	−	0.0235471i
$645$		0			0
$646$	11.2480	−	22.7083i	0.442545	−	0.893447i
$647$	−2.41921	−	4.19019i	−0.0951088	−	0.164733i	0.814545	−	0.580100i	$-0.196987\pi$
$647$	−2.41921	−	4.19019i	−0.0951088	−	0.164733i	−0.909654	+	0.415367i	$0.863653\pi$
$648$		0			0
$649$	9.48395	−	16.4267i	0.372278	−	0.644804i
$650$	8.79615	−	0.561071i	0.345014	−	0.0220070i
$651$		0			0
$652$	0.454522	+	3.54837i	0.0178004	+	0.138965i
$653$	19.5592	+	11.2925i	0.765412	+	0.441911i	0.831235	−	0.555921i	$-0.187634\pi$
$653$	19.5592	+	11.2925i	0.765412	+	0.441911i	−0.0658236	+	0.997831i	$0.520967\pi$
$654$		0			0
$655$	8.95142	−	5.16811i	0.349761	−	0.201935i
$656$	14.7957	+	4.07572i	0.577675	+	0.159130i
$657$		0			0
$658$	11.7407	+	16.5269i	0.457702	+	0.644284i
$659$	13.4237			0.522911			0.261456	−	0.965215i	$-0.415797\pi$
$659$	13.4237			0.522911			0.261456	+	0.965215i	$0.415797\pi$
$660$		0			0
$661$	7.10185	+	12.3008i	0.276230	+	0.478444i	0.970445	−	0.241324i	$-0.0775815\pi$
$661$	7.10185	+	12.3008i	0.276230	+	0.478444i	−0.694215	+	0.719768i	$0.744248\pi$
$662$	−0.457281	+	0.304389i	−0.0177727	+	0.0118304i
$663$		0			0
$664$	−38.2266	+	7.39531i	−1.48348	+	0.286994i
$665$	−11.0620	−	17.8827i	−0.428967	−	0.693462i
$666$		0			0
$667$	−2.82373	−	1.63028i	−0.109335	−	0.0631248i
$668$	−10.0226	−	13.1568i	−0.387786	−	0.509052i
$669$		0			0
$670$	−19.7529	+	39.8787i	−0.763120	+	1.54065i
$671$	−4.65510			−0.179708
$672$		0			0
$673$	11.3016			0.435643			0.217822	−	0.975989i	$-0.430105\pi$
$673$	11.3016			0.435643			0.217822	+	0.975989i	$0.430105\pi$
$674$	3.83144	−	7.73523i	0.147582	−	0.297950i
$675$		0			0
$676$	−17.2965	−	22.7053i	−0.665249	−	0.873281i
$677$	−2.75180	−	1.58875i	−0.105760	−	0.0610608i	0.446187	−	0.894940i	$-0.352782\pi$
$677$	−2.75180	−	1.58875i	−0.105760	−	0.0610608i	−0.551947	+	0.833879i	$0.686115\pi$
$678$		0			0
$679$	−28.3579	+	0.861658i	−1.08827	+	0.0330674i
$680$	38.7770	−	7.50178i	1.48703	−	0.287680i
$681$		0			0
$682$	−6.38557	+	4.25056i	−0.244516	+	0.162762i
$683$	3.13262	+	5.42586i	0.119866	+	0.207615i	0.919715	−	0.392588i	$-0.128420\pi$
$683$	3.13262	+	5.42586i	0.119866	+	0.207615i	−0.799848	+	0.600202i	$0.795087\pi$
$684$		0			0
$685$	40.6441			1.55293
$686$	9.44129	−	24.4308i	0.360470	−	0.932771i
$687$		0			0
$688$	−43.1038	−	11.8737i	−1.64332	−	0.452679i
$689$	9.35369	−	5.40036i	0.356347	−	0.205737i
$690$		0			0
$691$	13.9691	+	8.06506i	0.531409	+	0.306809i	0.741590	−	0.670853i	$-0.234072\pi$
$691$	13.9691	+	8.06506i	0.531409	+	0.306809i	−0.210181	+	0.977663i	$0.567405\pi$
$692$	−4.91632	−	38.3808i	−0.186890	−	1.45902i
$693$		0			0
$694$	−40.9669	+	2.61311i	−1.55508	+	0.0991923i
$695$	12.8045	−	22.1781i	0.485704	−	0.841264i
$696$		0			0
$697$	10.7639	+	18.6436i	0.407711	+	0.706176i
$698$	−17.1295	+	34.5825i	−0.648362	+	1.30897i
$699$		0			0
$700$	2.25905	−	5.89728i	0.0853841	−	0.222896i
$701$			50.8903i			1.92210i	0.276373	+	0.961050i	$0.410867\pi$
$701$			50.8903i			1.92210i	−0.276373	+	0.961050i	$0.589133\pi$
$702$		0			0
$703$	7.50322	−	4.33198i	0.282989	−	0.163384i
$704$	−29.0081	−	22.7466i	−1.09328	−	0.857295i
$705$		0			0
$706$	−2.72603	−	42.7371i	−0.102595	−	1.60843i
$707$	−8.63278	+	5.34013i	−0.324669	+	0.200836i
$708$		0			0
$709$	−10.6871	+	18.5107i	−0.401364	+	0.695182i	−0.993891	−	0.110368i	$-0.964797\pi$
$709$	−10.6871	+	18.5107i	−0.401364	+	0.695182i	0.592527	+	0.805550i	$0.298130\pi$
$710$	−21.4170	+	14.2562i	−0.803767	+	0.535027i
$711$		0			0
$712$	22.7942	+	7.87131i	0.854250	+	0.294990i
$713$			0.846054i			0.0316850i
$714$		0			0
$715$		−	59.8854i		−	2.23959i
$716$	9.30346	−	22.2400i	0.347686	−	0.831149i
$717$		0			0
$718$	16.2824	+	24.4609i	0.607655	+	0.912874i
$719$	12.1927	−	21.1183i	0.454709	−	0.787579i	−0.543962	−	0.839110i	$-0.683077\pi$
$719$	12.1927	−	21.1183i	0.454709	−	0.787579i	0.998671	+	0.0515302i	$0.0164099\pi$
$720$		0			0
$721$	38.8651	+	20.8914i	1.44741	+	0.778036i
$722$	−12.4216	+	0.792321i	−0.462283	+	0.0294871i
$723$		0			0
$724$	−25.2079	−	33.0907i	−0.936843	−	1.22981i
$725$	−4.68881	+	2.70708i	−0.174138	+	0.100539i
$726$		0			0
$727$			37.0825i			1.37531i	0.726037	+	0.687656i	$0.241360\pi$
$727$			37.0825i			1.37531i	−0.726037	+	0.687656i	$0.758640\pi$
$728$	−38.1249	+	8.58452i	−1.41300	+	0.318164i
$729$		0			0
$730$	−30.3961	−	15.0559i	−1.12501	−	0.557243i
$731$	−31.3580	−	54.3137i	−1.15982	−	2.00887i
$732$		0			0
$733$	−22.5631	+	39.0805i	−0.833388	+	1.44347i	0.0619491	+	0.998079i	$0.480268\pi$
$733$	−22.5631	+	39.0805i	−0.833388	+	1.44347i	−0.895337	+	0.445390i	$0.853065\pi$
$734$	−1.84392	−	28.9079i	−0.0680602	−	1.06701i
$735$		0			0
$736$	−3.86128	+	1.27315i	−0.142329	+	0.0469291i
$737$	50.4586	+	29.1323i	1.85867	+	1.07310i
$738$		0			0
$739$	37.2786	−	21.5228i	1.37132	−	0.791729i	0.380222	−	0.924895i	$-0.375848\pi$
$739$	37.2786	−	21.5228i	1.37132	−	0.791729i	0.991094	+	0.133166i	$0.0425143\pi$
$740$	12.4572	+	5.21112i	0.457937	+	0.191565i
$741$		0			0
$742$	−0.726939	−	7.70438i	−0.0266868	−	0.282837i
$743$	−7.52770			−0.276165			−0.138082	−	0.990421i	$-0.544094\pi$
$743$	−7.52770			−0.276165			−0.138082	+	0.990421i	$0.544094\pi$
$744$		0			0
$745$	−7.03901	−	12.1919i	−0.257889	−	0.446677i
$746$	−18.7759	−	28.2068i	−0.687433	−	1.03272i
$747$		0			0
$748$	−6.56996	−	51.2905i	−0.240222	−	1.87537i
$749$	7.18646	−	13.3693i	0.262588	−	0.488503i
$750$		0			0
$751$	38.1316	+	22.0153i	1.39144	+	0.803349i	0.993475	−	0.114051i	$-0.0363828\pi$
$751$	38.1316	+	22.0153i	1.39144	+	0.803349i	0.397966	+	0.917400i	$0.369716\pi$
$752$	−15.2171	−	15.4316i	−0.554909	−	0.562733i
$753$		0			0
$754$	30.0228	+	14.8710i	1.09337	+	0.541569i
$755$	−30.2683			−1.10158
$756$		0			0
$757$	7.64185			0.277748			0.138874	−	0.990310i	$-0.455652\pi$
$757$	7.64185			0.277748			0.138874	+	0.990310i	$0.455652\pi$
$758$	−3.80377	−	1.88410i	−0.138159	−	0.0684335i
$759$		0			0
$760$	14.7328	+	16.9785i	0.534414	+	0.615876i
$761$	−15.1210	−	8.73011i	−0.548135	−	0.316466i	0.200234	−	0.979748i	$-0.435830\pi$
$761$	−15.1210	−	8.73011i	−0.548135	−	0.316466i	−0.748370	+	0.663282i	$0.769163\pi$
$762$		0			0
$763$	3.93484	+	6.36101i	0.142451	+	0.230284i
$764$	−21.0605	+	2.69771i	−0.761943	+	0.0975996i
$765$		0			0
$766$	−22.4758	−	33.7652i	−0.812084	−	1.21999i
$767$	10.7484	+	18.6168i	0.388102	+	0.672212i
$768$		0			0
$769$	3.13489			0.113047			0.0565235	−	0.998401i	$-0.481998\pi$
$769$	3.13489			0.113047			0.0565235	+	0.998401i	$0.481998\pi$
$770$	−39.0097	−	17.8682i	−1.40581	−	0.643925i
$771$		0			0
$772$	−10.0281	+	23.9724i	−0.360921	+	0.862785i
$773$	−16.4737	+	9.51107i	−0.592516	+	0.342090i	−0.766092	−	0.642731i	$-0.777801\pi$
$773$	−16.4737	+	9.51107i	−0.592516	+	0.342090i	0.173575	+	0.984821i	$0.444468\pi$
$774$		0			0
$775$	1.21665	+	0.702436i	0.0437035	+	0.0252322i
$776$	29.7777	−	5.76078i	1.06896	−	0.206800i
$777$		0			0
$778$	1.08877	+	17.0692i	0.0390344	+	0.611959i
$779$	−6.12635	+	10.6112i	−0.219499	+	0.380184i
$780$		0			0
$781$	16.8420	+	29.1713i	0.602656	+	1.04383i
$782$	−5.11067	−	2.53143i	−0.182757	−	0.0905238i
$783$		0			0
$784$	−5.78343	+	27.3962i	−0.206551	+	0.978436i
$785$		−	17.5177i		−	0.625235i
$786$		0			0
$787$	−3.98235	+	2.29921i	−0.141956	+	0.0819581i	−0.569296	−	0.822133i	$-0.692784\pi$
$787$	−3.98235	+	2.29921i	−0.141956	+	0.0819581i	0.427340	+	0.904091i	$0.359451\pi$
$788$	5.07281	−	3.86437i	0.180711	−	0.137662i
$789$		0			0
$790$	−31.0476	+	1.98040i	−1.10462	+	0.0704594i
$791$	−0.449705	−	14.8001i	−0.0159897	−	0.526233i
$792$		0			0
$793$	2.63787	−	4.56893i	0.0936735	−	0.162247i
$794$	4.12058	+	6.19031i	0.146234	+	0.219686i
$795$		0			0
$796$	25.9222	+	10.8438i	0.918789	+	0.384348i
$797$		−	40.4802i		−	1.43388i	−0.697134	−	0.716941i	$-0.745542\pi$
$797$		−	40.4802i		−	1.43388i	0.697134	−	0.716941i	$-0.254458\pi$
$798$		0			0
$799$		−	30.4010i		−	1.07551i
$800$	−1.37498	+	6.60969i	−0.0486131	+	0.233688i
$801$		0			0
$802$	−21.8344	+	14.5341i	−0.771001	+	0.513217i
$803$	−22.2050	+	38.4602i	−0.783598	+	1.35723i
$804$		0			0
$805$	−4.02463	+	2.48958i	−0.141850	+	0.0877463i
$806$	−0.553406	−	8.67599i	−0.0194929	−	0.305599i
$807$		0			0
$808$	8.19629	−	7.11217i	0.288344	−	0.250205i
$809$	8.54248	−	4.93200i	0.300338	−	0.173400i	−0.342257	−	0.939606i	$-0.611191\pi$
$809$	8.54248	−	4.93200i	0.300338	−	0.173400i	0.642595	+	0.766206i	$0.277858\pi$
$810$		0			0
$811$		−	28.0467i		−	0.984854i	−0.870354	−	0.492427i	$-0.836110\pi$
$811$		−	28.0467i		−	0.984854i	0.870354	−	0.492427i	$-0.163890\pi$
$812$	18.6450	−	15.1199i	0.654313	−	0.530606i
$813$		0			0
$814$	7.84697	−	15.8421i	0.275036	−	0.555266i
$815$	−2.22571	−	3.85505i	−0.0779634	−	0.135037i
$816$		0			0
$817$	17.8477	−	30.9131i	0.624412	−	1.08151i
$818$	24.7302	−	1.57744i	0.864671	−	0.0551539i
$819$		0			0
$820$	−18.9418	+	2.42631i	−0.661475	+	0.0847303i
$821$	−22.9634	−	13.2579i	−0.801427	−	0.462704i	0.0425431	−	0.999095i	$-0.486454\pi$
$821$	−22.9634	−	13.2579i	−0.801427	−	0.462704i	−0.843970	+	0.536391i	$0.819787\pi$
$822$		0			0
$823$	−17.6534	+	10.1922i	−0.615359	+	0.355277i	−0.775060	−	0.631888i	$-0.782280\pi$
$823$	−17.6534	+	10.1922i	−0.615359	+	0.355277i	0.159701	+	0.987165i	$0.448947\pi$
$824$	−44.5872	−	15.3969i	−1.55327	−	0.536376i
$825$		0			0
$826$	15.3341	−	1.44683i	0.533542	−	0.0503418i
$827$	17.5032			0.608645			0.304322	−	0.952569i	$-0.401570\pi$
$827$	17.5032			0.608645			0.304322	+	0.952569i	$0.401570\pi$
$828$		0			0
$829$	−5.39915	−	9.35160i	−0.187520	−	0.324794i	0.756903	−	0.653528i	$-0.226712\pi$
$829$	−5.39915	−	9.35160i	−0.187520	−	0.324794i	−0.944423	+	0.328733i	$0.893378\pi$
$830$	40.3306	−	26.8460i	1.39989	−	0.931839i
$831$		0			0
$832$	38.7633	−	15.5814i	1.34388	−	0.540189i
$833$	−32.7598	+	21.6675i	−1.13506	+	0.750734i
$834$		0			0
$835$	17.8233	+	10.2903i	0.616801	+	0.356110i
$836$	23.4117	−	17.8346i	0.809711	−	0.616822i
$837$		0			0
$838$	−16.8947	+	34.1085i	−0.583619	+	1.17826i
$839$	8.78448			0.303274			0.151637	−	0.988436i	$-0.451546\pi$
$839$	8.78448			0.303274			0.151637	+	0.988436i	$0.451546\pi$
$840$		0			0
$841$	8.41964			0.290332
$842$	−2.95837	+	5.97260i	−0.101952	+	0.205829i
$843$		0			0
$844$	14.5248	−	11.0647i	0.499966	−	0.380864i
$845$	30.7585	+	17.7584i	1.05813	+	0.610909i
$846$		0			0
$847$	−12.8180	+	23.8458i	−0.440430	+	0.819352i
$848$	2.08519	+	8.00581i	0.0716057	+	0.274921i
$849$		0			0
$850$	−7.88342	+	5.24760i	−0.270399	+	0.179991i
$851$	−0.974943	−	1.68865i	−0.0334206	−	0.0578862i
$852$		0			0
$853$	3.87338			0.132622			0.0663110	−	0.997799i	$-0.478877\pi$
$853$	3.87338			0.132622			0.0663110	+	0.997799i	$0.478877\pi$
$854$	−2.18916	−	3.08157i	−0.0749115	−	0.105449i
$855$		0			0
$856$	−5.29640	+	15.3376i	−0.181027	+	0.524230i
$857$	−37.4794	+	21.6387i	−1.28027	+	0.739165i	−0.976898	−	0.213707i	$-0.931446\pi$
$857$	−37.4794	+	21.6387i	−1.28027	+	0.739165i	−0.303374	+	0.952872i	$0.598113\pi$
$858$		0			0
$859$	−13.7614	−	7.94516i	−0.469534	−	0.271086i	0.246511	−	0.969140i	$-0.420716\pi$
$859$	−13.7614	−	7.94516i	−0.469534	−	0.271086i	−0.716045	+	0.698055i	$0.754049\pi$
$860$	55.1824	−	7.06848i	1.88170	−	0.241033i
$861$		0			0
$862$	−5.39266	+	0.343976i	−0.183675	+	0.0117159i
$863$	5.27921	−	9.14387i	0.179707	−	0.311261i	−0.762073	−	0.647491i	$-0.775819\pi$
$863$	5.27921	−	9.14387i	0.179707	−	0.311261i	0.941780	+	0.336230i	$0.109152\pi$
$864$		0			0
$865$	24.0744	+	41.6980i	0.818553	+	1.41777i
$866$	−21.8438	+	44.1001i	−0.742283	+	1.49858i
$867$		0			0
$868$	−5.81672	−	2.22819i	−0.197432	−	0.0756296i
$869$			40.7313i			1.38171i
$870$		0			0
$871$	−57.1860	+	33.0163i	−1.93767	+	1.11872i
$872$	−5.24056	−	6.03939i	−0.177468	−	0.204519i
$873$		0			0
$874$	−0.206633	−	3.23947i	−0.00698945	−	0.109577i
$875$	−0.761215	−	25.0522i	−0.0257338	−	0.846920i
$876$		0			0
$877$	0.877972	−	1.52069i	0.0296470	−	0.0513501i	−0.850821	−	0.525455i	$-0.823895\pi$
$877$	0.877972	−	1.52069i	0.0296470	−	0.0513501i	0.880468	+	0.474105i	$0.157228\pi$
$878$	−41.7704	+	27.8045i	−1.40968	+	0.938355i
$879$		0			0
$880$	44.2226	+	12.1819i	1.49074	+	0.410650i
$881$			39.9987i			1.34759i	0.738917	+	0.673796i	$0.235337\pi$
$881$			39.9987i			1.34759i	−0.738917	+	0.673796i	$0.764663\pi$
$882$		0			0
$883$		−	15.9005i		−	0.535096i	−0.963545	−	0.267548i	$-0.913787\pi$
$883$		−	15.9005i		−	0.535096i	0.963545	−	0.267548i	$-0.0862133\pi$
$884$	54.0639	+	22.6161i	1.81837	+	0.760660i
$885$		0			0
$886$	−8.58738	−	12.9007i	−0.288499	−	0.433409i
$887$	16.6867	−	28.9023i	0.560286	−	0.970443i	−0.437186	−	0.899371i	$-0.644025\pi$
$887$	16.6867	−	28.9023i	0.560286	−	0.970443i	0.997471	−	0.0710719i	$-0.0226420\pi$
$888$		0			0
$889$	−1.22353	−	40.2672i	−0.0410357	−	1.35052i
$890$	−29.9462	+	1.91015i	−1.00380	+	0.0640284i
$891$		0			0
$892$	−37.9259	+	28.8912i	−1.26985	+	0.967349i
$893$	14.9848	−	8.65150i	0.501449	−	0.289511i
$894$		0			0
$895$			29.9978i			1.00272i
$896$	1.41608	−	29.8997i	0.0473078	−	0.998880i
$897$		0			0
$898$	−34.4286	−	17.0533i	−1.14890	−	0.569075i
$899$	2.67010	+	4.62475i	0.0890529	+	0.154244i
$900$		0			0
$901$	−5.80242	+	10.0501i	−0.193307	+	0.334817i
$902$	1.59154	+	24.9512i	0.0529923	+	0.830784i
$903$		0			0
$904$	3.00659	+	15.5412i	0.0999977	+	0.516892i
$905$	44.8275	+	25.8812i	1.49012	+	0.860319i
$906$		0			0
$907$	31.8593	−	18.3940i	1.05787	−	0.610762i	0.133028	−	0.991112i	$-0.457530\pi$
$907$	31.8593	−	18.3940i	1.05787	−	0.610762i	0.924842	+	0.380351i	$0.124197\pi$
$908$	7.72785	−	18.4735i	0.256458	−	0.613065i
$909$		0			0
$910$	39.6427	−	28.1623i	1.31414	−	0.933573i
$911$	46.9066			1.55409			0.777043	−	0.629448i	$-0.216719\pi$
$911$	46.9066			1.55409			0.777043	+	0.629448i	$0.216719\pi$
$912$		0			0
$913$	−31.7154	−	54.9326i	−1.04963	−	1.81800i
$914$	30.2181	+	45.3964i	0.999527	+	1.50158i
$915$		0			0
$916$	−10.5861	+	1.35601i	−0.349775	+	0.0448037i
$917$	5.20276	−	9.67892i	0.171810	−	0.319626i
$918$		0			0
$919$	−15.6017	−	9.00763i	−0.514652	−	0.297134i	0.220092	−	0.975479i	$-0.429364\pi$
$919$	−15.6017	−	9.00763i	−0.514652	−	0.297134i	−0.734744	+	0.678345i	$0.762698\pi$
$920$	3.82114	−	3.31572i	0.125979	−	0.109316i
$921$		0			0
$922$	−17.1770	−	8.50816i	−0.565694	−	0.280201i
$923$	−38.1750			−1.25654
$924$		0			0
$925$	−3.23779			−0.106458
$926$	22.5023	+	11.1459i	0.739470	+	0.366277i
$927$		0			0
$928$	−17.0888	+	19.1454i	−0.560966	+	0.628478i
$929$	−28.2618	−	16.3170i	−0.927241	−	0.535343i	−0.0413031	−	0.999147i	$-0.513151\pi$
$929$	−28.2618	−	16.3170i	−0.927241	−	0.535343i	−0.885938	+	0.463804i	$0.846484\pi$
$930$		0			0
$931$	−20.0028	−	9.98139i	−0.655565	−	0.327127i
$932$	2.22808	+	17.3942i	0.0729833	+	0.569768i
$933$		0			0
$934$	8.46272	+	12.7135i	0.276909	+	0.415998i
$935$	32.1720	+	55.7235i	1.05214	+	1.82235i
$936$		0			0
$937$	4.08001			0.133288			0.0666441	−	0.997777i	$-0.478771\pi$
$937$	4.08001			0.133288			0.0666441	+	0.997777i	$0.478771\pi$
$938$	4.44431	+	47.1025i	0.145112	+	1.53795i
$939$		0			0
$940$	24.8786	+	10.4072i	0.811451	+	0.339447i
$941$	−21.3871	+	12.3478i	−0.697198	+	0.402527i	−0.806303	−	0.591503i	$-0.798535\pi$
$941$	−21.3871	+	12.3478i	−0.697198	+	0.402527i	0.109105	+	0.994030i	$0.465202\pi$
$942$		0			0
$943$	2.38811	+	1.37878i	0.0777677	+	0.0448992i
$944$	−15.9341	+	4.15018i	−0.518609	+	0.135077i
$945$		0			0
$946$	−4.63657	−	72.6895i	−0.150748	−	2.36334i
$947$	−18.4653	+	31.9828i	−0.600040	+	1.03930i	0.392774	+	0.919635i	$0.371515\pi$
$947$	−18.4653	+	31.9828i	−0.600040	+	1.03930i	−0.992814	+	0.119665i	$0.961818\pi$
$948$		0			0
$949$	−25.1655	−	43.5879i	−0.816906	−	1.41492i
$950$	−4.83003	−	2.39242i	−0.156707	−	0.0776205i
$951$		0			0
$952$	30.8635	−	28.4696i	1.00029	−	0.922705i
$953$		−	61.5883i		−	1.99504i	−0.0703720	−	0.997521i	$-0.522419\pi$
$953$		−	61.5883i		−	1.99504i	0.0703720	−	0.997521i	$-0.477581\pi$
$954$		0			0
$955$	22.8807	−	13.2102i	0.740404	−	0.427472i
$956$	15.9234	+	20.9028i	0.514998	+	0.676046i
$957$		0			0
$958$	26.7693	−	1.70750i	0.864876	−	0.0551669i
$959$	36.7472	−	22.7314i	1.18663	−	0.734034i
$960$		0			0
$961$	−14.8072	+	25.6468i	−0.477650	+	0.827315i
$962$	11.1023	+	16.6788i	0.357951	+	0.537747i
$963$		0			0
$964$	17.0295	−	40.7092i	0.548483	−	1.31115i
$965$		−	32.3344i		−	1.04088i
$966$		0			0
$967$			22.8368i			0.734381i	0.930146	+	0.367191i	$0.119680\pi$
$967$			22.8368i			0.734381i	−0.930146	+	0.367191i	$0.880320\pi$
$968$	9.44679	−	27.3566i	0.303631	−	0.879275i
$969$		0			0
$970$	−31.4166	+	20.9125i	−1.00873	+	0.671459i
$971$	−24.0937	+	41.7315i	−0.773203	+	1.33923i	0.162596	+	0.986693i	$0.448013\pi$
$971$	−24.0937	+	41.7315i	−0.773203	+	1.33923i	−0.935799	+	0.352534i	$0.885320\pi$
$972$		0			0
$973$	−0.826871	−	27.2130i	−0.0265083	−	0.872409i
$974$	1.30819	+	20.5091i	0.0419172	+	0.657154i
$975$		0			0
$976$	2.83735	+	2.87736i	0.0908213	+	0.0921019i
$977$	27.2570	−	15.7368i	0.872028	−	0.503466i	0.00400663	−	0.999992i	$-0.498725\pi$
$977$	27.2570	−	15.7368i	0.872028	−	0.503466i	0.868022	+	0.496526i	$0.165391\pi$
$978$		0			0
$979$			39.2865i			1.25560i
$980$	−6.51681	−	34.2264i	−0.208172	−	1.09332i
$981$		0			0
$982$	−16.3220	+	32.9523i	−0.520857	+	1.05155i
$983$	20.0440	+	34.7172i	0.639304	+	1.10731i	0.985586	+	0.169176i	$0.0541107\pi$
$983$	20.0440	+	34.7172i	0.639304	+	1.10731i	−0.346282	+	0.938130i	$0.612556\pi$
$984$		0			0
$985$	−3.96758	+	6.87205i	−0.126418	+	0.218962i
$986$	−35.9253	+	2.29153i	−1.14410	+	0.0729772i
$987$		0			0
$988$	4.23789	+	33.0845i	0.134825	+	1.05256i
$989$	−6.95721	−	4.01675i	−0.221226	−	0.127725i
$990$		0			0
$991$	44.6593	−	25.7841i	1.41865	−	0.819058i	0.422469	−	0.906377i	$-0.361163\pi$
$991$	44.6593	−	25.7841i	1.41865	−	0.819058i	0.996180	+	0.0873196i	$0.0278301\pi$
$992$	6.51939	+	1.35620i	0.206991	+	0.0430594i
$993$		0			0
$994$	−11.3904	+	24.8674i	−0.361281	+	0.788747i
$995$	−34.9644			−1.10845
$996$		0			0
$997$	10.7581	+	18.6335i	0.340712	+	0.590130i	0.984565	−	0.175019i	$-0.0559986\pi$
$997$	10.7581	+	18.6335i	0.340712	+	0.590130i	−0.643853	+	0.765149i	$0.722665\pi$
$998$	3.22887	−	2.14930i	0.102208	−	0.0680349i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.be.a.107.10	yes	32
3.2	odd	2	inner	252.2.be.a.107.7	yes	32
4.3	odd	2	inner	252.2.be.a.107.5	✓	32
7.2	even	3		1764.2.e.i.1079.2		16
7.4	even	3	inner	252.2.be.a.179.12	yes	32
7.5	odd	6		1764.2.e.h.1079.2		16
12.11	even	2	inner	252.2.be.a.107.12	yes	32
21.2	odd	6		1764.2.e.i.1079.15		16
21.5	even	6		1764.2.e.h.1079.15		16
21.11	odd	6	inner	252.2.be.a.179.5	yes	32
28.11	odd	6	inner	252.2.be.a.179.7	yes	32
28.19	even	6		1764.2.e.h.1079.16		16
28.23	odd	6		1764.2.e.i.1079.16		16
84.11	even	6	inner	252.2.be.a.179.10	yes	32
84.23	even	6		1764.2.e.i.1079.1		16
84.47	odd	6		1764.2.e.h.1079.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.5	✓	32	4.3	odd	2	inner
252.2.be.a.107.7	yes	32	3.2	odd	2	inner
252.2.be.a.107.10	yes	32	1.1	even	1	trivial
252.2.be.a.107.12	yes	32	12.11	even	2	inner
252.2.be.a.179.5	yes	32	21.11	odd	6	inner
252.2.be.a.179.7	yes	32	28.11	odd	6	inner
252.2.be.a.179.10	yes	32	84.11	even	6	inner
252.2.be.a.179.12	yes	32	7.4	even	3	inner
1764.2.e.h.1079.1		16	84.47	odd	6
1764.2.e.h.1079.2		16	7.5	odd	6
1764.2.e.h.1079.15		16	21.5	even	6
1764.2.e.h.1079.16		16	28.19	even	6
1764.2.e.i.1079.1		16	84.23	even	6
1764.2.e.i.1079.2		16	7.2	even	3
1764.2.e.i.1079.15		16	21.2	odd	6
1764.2.e.i.1079.16		16	28.23	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.627710 - 1.26727i) q^{2} +(-1.21196 - 1.59096i) q^{4} +(2.15525 + 1.24433i) q^{5} +(2.64453 - 0.0803545i) q^{7} +(-2.77694 + 0.537226i) q^{8} +O(q^{10})\)	\(q+(0.627710 - 1.26727i) q^{2} +(-1.21196 - 1.59096i) q^{4} +(2.15525 + 1.24433i) q^{5} +(2.64453 - 0.0803545i) q^{7} +(-2.77694 + 0.537226i) q^{8} +(2.92978 - 1.95021i) q^{10} +(-2.30393 - 3.99053i) q^{11} +5.22221 q^{13} +(1.55817 - 3.40178i) q^{14} +(-1.06230 + 3.85636i) q^{16} +(-4.85928 + 2.80550i) q^{17} +(-2.76570 - 1.59678i) q^{19} +(-0.632394 - 4.93699i) q^{20} +(-6.50329 + 0.414819i) q^{22} +(-0.359366 + 0.622440i) q^{23} +(0.596726 + 1.03356i) q^{25} +(3.27803 - 6.61796i) q^{26} +(-3.33291 - 4.10995i) q^{28} +4.53656i q^{29} +(1.01944 - 0.588574i) q^{31} +(4.22025 + 3.76690i) q^{32} +(0.505125 + 7.91907i) q^{34} +(5.79960 + 3.11749i) q^{35} +(-1.35648 + 2.34949i) q^{37} +(-3.75961 + 2.50258i) q^{38} +(-6.65348 - 2.29758i) q^{40} -3.83670i q^{41} +11.1773i q^{43} +(-3.55649 + 8.50184i) q^{44} +(0.563224 + 0.846126i) q^{46} +(-2.70905 + 4.69222i) q^{47} +(6.98709 - 0.425000i) q^{49} +(1.68437 - 0.107439i) q^{50} +(-6.32912 - 8.30832i) q^{52} +(1.79114 - 1.03411i) q^{53} -11.4674i q^{55} +(-7.30053 + 1.64385i) q^{56} +(5.74906 + 2.84764i) q^{58} +(2.05821 + 3.56492i) q^{59} +(0.505125 - 0.874903i) q^{61} +(-0.105972 - 1.66136i) q^{62} +(7.42278 - 2.98369i) q^{64} +(11.2552 + 6.49816i) q^{65} +(-10.9505 + 6.32230i) q^{67} +(10.3527 + 4.33075i) q^{68} +(7.59118 - 5.39280i) q^{70} -7.31012 q^{71} +(-4.81894 - 8.34664i) q^{73} +(2.12597 + 3.19383i) q^{74} +(0.811513 + 6.33534i) q^{76} +(-6.41348 - 10.3680i) q^{77} +(-7.65524 - 4.41975i) q^{79} +(-7.08811 + 6.98956i) q^{80} +(-4.86215 - 2.40833i) q^{82} +13.7657 q^{83} -13.9639 q^{85} +(14.1647 + 7.01612i) q^{86} +(8.54170 + 9.84373i) q^{88} +(-7.38369 - 4.26297i) q^{89} +(13.8103 - 0.419628i) q^{91} +(1.42581 - 0.182637i) q^{92} +(4.24582 + 6.37846i) q^{94} +(-3.97384 - 6.88289i) q^{95} -10.7232 q^{97} +(3.84727 - 9.12132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{13} + 4 q^{16} - 32 q^{22} + 24 q^{25} - 44 q^{28} - 16 q^{34} + 8 q^{37} - 52 q^{40} - 24 q^{46} - 16 q^{49} - 52 q^{52} - 12 q^{58} - 16 q^{61} + 120 q^{64} + 60 q^{70} - 8 q^{73} + 72 q^{76} + 68 q^{82} - 32 q^{85} + 44 q^{88} + 60 q^{94} - 176 q^{97}+O(q^{100}) \) 32 * q + 16 * q^13 + 4 * q^16 - 32 * q^22 + 24 * q^25 - 44 * q^28 - 16 * q^34 + 8 * q^37 - 52 * q^40 - 24 * q^46 - 16 * q^49 - 52 * q^52 - 12 * q^58 - 16 * q^61 + 120 * q^64 + 60 * q^70 - 8 * q^73 + 72 * q^76 + 68 * q^82 - 32 * q^85 + 44 * q^88 + 60 * q^94 - 176 * q^97

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