LMFDB - Embedded newform 252.2.be.a.179.5

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			179.5
Character	$\chi$	$=$	252.179
Dual form			252.2.be.a.107.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.783636 - 1.17725i) q^{2} +(-0.771830 + 1.84507i) q^{4} +(2.15525 - 1.24433i) q^{5} +(-2.64453 - 0.0803545i) q^{7} +(2.77694 - 0.537226i) q^{8} +O(q^{10})$	\(q+(-0.783636 - 1.17725i) q^{2} +(-0.771830 + 1.84507i) q^{4} +(2.15525 - 1.24433i) q^{5} +(-2.64453 - 0.0803545i) q^{7} +(2.77694 - 0.537226i) q^{8} +(-3.15382 - 1.56216i) q^{10} +(2.30393 - 3.99053i) q^{11} +5.22221 q^{13} +(1.97775 + 3.17624i) q^{14} +(-2.80856 - 2.84816i) q^{16} +(-4.85928 - 2.80550i) q^{17} +(2.76570 - 1.59678i) q^{19} +(0.632394 + 4.93699i) q^{20} +(-6.50329 + 0.414819i) q^{22} +(0.359366 + 0.622440i) q^{23} +(0.596726 - 1.03356i) q^{25} +(-4.09231 - 6.14784i) q^{26} +(2.18939 - 4.81732i) q^{28} -4.53656i q^{29} +(-1.01944 - 0.588574i) q^{31} +(-1.15211 + 5.53829i) q^{32} +(0.505125 + 7.91907i) q^{34} +(-5.79960 + 3.11749i) q^{35} +(-1.35648 - 2.34949i) q^{37} +(-4.04710 - 2.00462i) q^{38} +(5.31650 - 4.61329i) q^{40} +3.83670i q^{41} +11.1773i q^{43} +(5.58456 + 7.33093i) q^{44} +(0.451155 - 0.910829i) q^{46} +(2.70905 + 4.69222i) q^{47} +(6.98709 + 0.425000i) q^{49} +(-1.68437 + 0.107439i) q^{50} +(-4.03066 + 9.63533i) q^{52} +(1.79114 + 1.03411i) q^{53} -11.4674i q^{55} +(-7.38687 + 1.19757i) q^{56} +(-5.34066 + 3.55501i) q^{58} +(-2.05821 + 3.56492i) q^{59} +(0.505125 + 0.874903i) q^{61} +(0.105972 + 1.66136i) q^{62} +(7.42278 - 2.98369i) q^{64} +(11.2552 - 6.49816i) q^{65} +(10.9505 + 6.32230i) q^{67} +(8.92688 - 6.80033i) q^{68} +(8.21484 + 4.38460i) q^{70} +7.31012 q^{71} +(-4.81894 + 8.34664i) q^{73} +(-1.70295 + 3.43806i) q^{74} +(0.811513 + 6.33534i) q^{76} +(-6.41348 + 10.3680i) q^{77} +(7.65524 - 4.41975i) q^{79} +(-9.59719 - 2.64371i) q^{80} +(4.51675 - 3.00658i) q^{82} -13.7657 q^{83} -13.9639 q^{85} +(13.1585 - 8.75895i) q^{86} +(4.25407 - 12.3192i) q^{88} +(-7.38369 + 4.26297i) q^{89} +(-13.8103 - 0.419628i) q^{91} +(-1.42581 + 0.182637i) q^{92} +(3.40100 - 6.86622i) q^{94} +(3.97384 - 6.88289i) q^{95} -10.7232 q^{97} +(-4.97500 - 8.55858i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.783636	−	1.17725i	−0.554114	−	0.832441i
$2$	−0.783636	−	1.17725i	−0.554114	−	0.832441i
$3$		0			0
$3$		0			0
$4$	−0.771830	+	1.84507i	−0.385915	+	0.922534i
$5$	2.15525	−	1.24433i	0.963856	−	0.556482i	0.0664982	−	0.997787i	$-0.478817\pi$
$5$	2.15525	−	1.24433i	0.963856	−	0.556482i	0.897358	+	0.441304i	$0.145484\pi$
$6$		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
$10$	−3.15382	−	1.56216i	−0.997325	−	0.493998i
$11$	2.30393	−	3.99053i	0.694662	−	1.20319i	−0.275632	−	0.961263i	$-0.588887\pi$
$11$	2.30393	−	3.99053i	0.694662	−	1.20319i	0.970294	−	0.241927i	$-0.0777796\pi$
$12$		0			0
$13$	5.22221			1.44838			0.724190	−	0.689600i	$-0.242214\pi$
$13$	5.22221			1.44838			0.724190	+	0.689600i	$0.242214\pi$
$14$	1.97775	+	3.17624i	0.528576	+	0.848886i
$15$		0			0
$16$	−2.80856	−	2.84816i	−0.702139	−	0.712040i
$17$	−4.85928	−	2.80550i	−1.17855	−	0.680435i	−0.222870	−	0.974848i	$-0.571542\pi$
$17$	−4.85928	−	2.80550i	−1.17855	−	0.680435i	−0.955678	+	0.294413i	$0.904876\pi$
$18$		0			0
$19$	2.76570	−	1.59678i	0.634495	−	0.366326i	−0.147996	−	0.988988i	$-0.547282\pi$
$19$	2.76570	−	1.59678i	0.634495	−	0.366326i	0.782491	+	0.622662i	$0.213949\pi$
$20$	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	$-0.142792\pi$
$23$	0.359366	+	0.622440i	0.0749329	+	0.129788i	−0.826124	+	0.563488i	$0.809459\pi$
$24$		0			0
$25$	0.596726	−	1.03356i	0.119345	−	0.206712i
$26$	−4.09231	−	6.14784i	−0.802568	−	1.20569i
$27$		0			0
$28$	2.18939	−	4.81732i	0.413755	−	0.910388i
$29$		−	4.53656i		−	0.842418i	−0.906964	−	0.421209i	$-0.861606\pi$
$29$		−	4.53656i		−	0.842418i	0.906964	−	0.421209i	$-0.138394\pi$
$30$		0			0
$31$	−1.01944	−	0.588574i	−0.183097	−	0.105711i	0.405650	−	0.914028i	$-0.367045\pi$
$31$	−1.01944	−	0.588574i	−0.183097	−	0.105711i	−0.588747	+	0.808317i	$0.700379\pi$
$32$	−1.15211	+	5.53829i	−0.203666	+	0.979041i
$33$		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	0.732715	−	0.680536i	$-0.238253\pi$
$37$	−1.35648	−	2.34949i	−0.223004	−	0.386254i	−0.955719	+	0.294282i	$0.904920\pi$
$38$	−4.04710	−	2.00462i	−0.656527	−	0.325193i
$39$		0			0
$40$	5.31650	−	4.61329i	0.840613	−	0.729425i
$41$			3.83670i			0.599192i	0.954066	+	0.299596i	$0.0968519\pi$
$41$			3.83670i			0.599192i	−0.954066	+	0.299596i	$0.903148\pi$
$42$		0			0
$43$			11.1773i			1.70453i	0.523113	+	0.852263i	$0.324771\pi$
$43$			11.1773i			1.70453i	−0.523113	+	0.852263i	$0.675229\pi$
$44$	5.58456	+	7.33093i	0.841904	+	1.10518i
$45$		0			0
$46$	0.451155	−	0.910829i	0.0665191	−	0.134294i
$47$	2.70905	+	4.69222i	0.395156	+	0.684430i	0.993121	−	0.117092i	$-0.0373572\pi$
$47$	2.70905	+	4.69222i	0.395156	+	0.684430i	−0.597965	+	0.801522i	$0.704024\pi$
$48$		0			0
$49$	6.98709	+	0.425000i	0.998155	+	0.0607142i
$50$	−1.68437	+	0.107439i	−0.238206	+	0.0151942i
$51$		0			0
$52$	−4.03066	+	9.63533i	−0.558952	+	1.33618i
$53$	1.79114	+	1.03411i	0.246032	+	0.142046i	0.617946	−	0.786221i	$-0.287965\pi$
$53$	1.79114	+	1.03411i	0.246032	+	0.142046i	−0.371914	+	0.928267i	$0.621298\pi$
$54$		0			0
$55$		−	11.4674i		−	1.54627i
$56$	−7.38687	+	1.19757i	−0.987112	+	0.160032i
$57$		0			0
$58$	−5.34066	+	3.55501i	−0.701263	+	0.466796i
$59$	−2.05821	+	3.56492i	−0.267956	+	0.464113i	−0.968334	−	0.249659i	$-0.919681\pi$
$59$	−2.05821	+	3.56492i	−0.267956	+	0.464113i	0.700378	+	0.713772i	$0.253015\pi$
$60$		0			0
$61$	0.505125	+	0.874903i	0.0646747	+	0.112020i	0.896550	−	0.442943i	$-0.146066\pi$
$61$	0.505125	+	0.874903i	0.0646747	+	0.112020i	−0.831875	+	0.554963i	$0.812732\pi$
$62$	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	$-0.0523938\pi$
$67$	10.9505	+	6.32230i	1.33782	+	0.772391i	0.351337	+	0.936249i	$0.385727\pi$
$68$	8.92688	−	6.80033i	1.08254	−	0.824661i
$69$		0			0
$70$	8.21484	+	4.38460i	0.981861	+	0.524060i
$71$	7.31012			0.867552			0.433776	−	0.901021i	$-0.357181\pi$
$71$	7.31012			0.867552			0.433776	+	0.901021i	$0.357181\pi$
$72$		0			0
$73$	−4.81894	+	8.34664i	−0.564014	+	0.976900i	0.433127	+	0.901333i	$0.357410\pi$
$73$	−4.81894	+	8.34664i	−0.564014	+	0.976900i	−0.997141	+	0.0755675i	$0.975923\pi$
$74$	−1.70295	+	3.43806i	−0.197964	+	0.399666i
$75$		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	$-0.501006\pi$
$79$	7.65524	−	4.41975i	0.861281	−	0.497261i	0.864441	+	0.502734i	$0.167672\pi$
$80$	−9.59719	−	2.64371i	−1.07300	−	0.295575i
$81$		0			0
$82$	4.51675	−	3.00658i	0.498792	−	0.332021i
$83$	−13.7657			−1.51099			−0.755493	−	0.655157i	$-0.772603\pi$
$83$	−13.7657			−1.51099			−0.755493	+	0.655157i	$0.772603\pi$
$84$		0			0
$85$	−13.9639			−1.51460
$86$	13.1585	−	8.75895i	1.41892	−	0.944502i
$87$		0			0
$88$	4.25407	−	12.3192i	0.453485	−	1.31323i
$89$	−7.38369	+	4.26297i	−0.782669	+	0.451874i	−0.837375	−	0.546628i	$-0.815911\pi$
$89$	−7.38369	+	4.26297i	−0.782669	+	0.451874i	0.0547061	+	0.998503i	$0.482578\pi$
$90$		0			0
$91$	−13.8103	−	0.419628i	−1.44771	−	0.0439889i
$92$	−1.42581	+	0.182637i	−0.148651	+	0.0190412i
$93$		0			0
$94$	3.40100	−	6.86622i	0.350786	−	0.708196i
$95$	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	$0.683238\pi$
$98$	−4.97500	−	8.55858i	−0.502551	−	0.864548i
$99$		0			0
$100$	1.44642	+	1.89873i	0.144642	+	0.189873i
$101$	−3.32268	−	1.91835i	−0.330619	−	0.190883i	0.325497	−	0.945543i	$-0.394468\pi$
$101$	−3.32268	−	1.91835i	−0.330619	−	0.190883i	−0.656116	+	0.754660i	$0.727802\pi$
$102$		0			0
$103$	−14.4431	+	8.33870i	−1.42312	+	0.821636i	−0.996564	−	0.0828265i	$-0.973605\pi$
$103$	−14.4431	+	8.33870i	−1.42312	+	0.821636i	−0.426552	+	0.904463i	$0.640272\pi$
$104$	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	$-0.256107\pi$
$107$	−2.86844	−	4.96829i	−0.277303	−	0.480303i	−0.970714	+	0.240240i	$0.922774\pi$
$108$		0			0
$109$	1.41352	−	2.44830i	0.135391	−	0.234504i	−0.790356	−	0.612648i	$-0.790104\pi$
$109$	1.41352	−	2.44830i	0.135391	−	0.234504i	0.925747	+	0.378144i	$0.123438\pi$
$110$	−13.5000	+	8.98630i	−1.28718	+	0.856810i
$111$		0			0
$112$	7.19845	+	7.75772i	0.680190	+	0.733036i
$113$			5.59651i			0.526476i	0.964731	+	0.263238i	$0.0847904\pi$
$113$			5.59651i			0.526476i	−0.964731	+	0.263238i	$0.915210\pi$
$114$		0			0
$115$	1.54904	+	0.894341i	0.144449	+	0.0833977i
$116$	8.37026	+	3.50145i	0.777159	+	0.325102i
$117$		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
$122$	0.634144	−	1.28026i	0.0574127	−	0.115910i
$123$		0			0
$124$	1.87279	−	1.42666i	0.168182	−	0.128118i
$125$			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	$-0.236103\pi$
$128$	−9.32929	−	6.40033i	−0.824601	−	0.565715i
$129$		0			0
$130$	−16.4699	−	8.15792i	−1.44451	−	0.715497i
$131$	−2.07666	−	3.59688i	−0.181438	−	0.314261i	0.760932	−	0.648831i	$-0.224742\pi$
$131$	−2.07666	−	3.59688i	−0.181438	−	0.314261i	−0.942371	+	0.334571i	$0.891409\pi$
$132$		0			0
$133$	−7.44228	+	4.00049i	−0.645328	+	0.346886i
$134$	−1.13832	−	17.8459i	−0.0983356	−	1.54165i
$135$		0			0
$136$	−15.0011	−	5.18019i	−1.28633	−	0.444197i
$137$	14.1437	+	8.16585i	1.20838	+	0.697656i	0.962404	−	0.271621i	$-0.0875598\pi$
$137$	14.1437	+	8.16585i	1.20838	+	0.697656i	0.245971	+	0.969277i	$0.420893\pi$
$138$		0			0
$139$		−	10.2903i		−	0.872811i	−0.899750	−	0.436406i	$-0.856251\pi$
$139$		−	10.2903i		−	0.872811i	0.899750	−	0.436406i	$-0.143749\pi$
$140$	−1.27568	−	13.1068i	−0.107814	−	1.10773i
$141$		0			0
$142$	−5.72847	−	8.60583i	−0.480723	−	0.722185i
$143$	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	−0.687062	−	0.726599i	$-0.741100\pi$
$149$	−4.89898	+	2.82843i	−0.401340	+	0.231714i	0.285722	+	0.958313i	$0.407767\pi$
$150$		0			0
$151$	10.5330	+	6.08123i	0.857164	+	0.494884i	0.863061	−	0.505099i	$-0.168544\pi$
$151$	10.5330	+	6.08123i	0.857164	+	0.494884i	−0.00589781	+	0.999983i	$0.501877\pi$
$152$	6.82234	−	5.91995i	0.553365	−	0.480172i
$153$		0			0
$154$	17.2315	−	0.574432i	1.38855	−	0.0462891i
$155$	−2.92953			−0.235305
$156$		0			0
$157$	−3.51950	+	6.09596i	−0.280887	+	0.486510i	−0.971603	−	0.236615i	$-0.923962\pi$
$157$	−3.51950	+	6.09596i	−0.280887	+	0.486510i	0.690716	+	0.723126i	$0.257295\pi$
$158$	−11.2021	−	5.54864i	−0.891189	−	0.441426i
$159$		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	$-0.644351\pi$
$163$	1.54904	−	0.894341i	0.121330	−	0.0700502i	0.559437	+	0.828873i	$0.311017\pi$
$164$	−7.07897	−	2.96128i	−0.552775	−	0.231237i
$165$		0			0
$166$	10.7873	+	16.2057i	0.837259	+	1.25781i
$167$	−8.26973			−0.639931			−0.319965	−	0.947429i	$-0.603671\pi$
$167$	−8.26973			−0.639931			−0.319965	+	0.947429i	$0.603671\pi$
$168$		0			0
$169$	14.2715			1.09781
$170$	10.9426	+	16.4390i	0.839261	+	1.26081i
$171$		0			0
$172$	−20.6229	−	8.62700i	−1.57248	−	0.657802i
$173$	16.7552	−	9.67360i	1.27387	−	0.735470i	0.298158	−	0.954517i	$-0.403628\pi$
$173$	16.7552	−	9.67360i	1.27387	−	0.735470i	0.975714	+	0.219046i	$0.0702946\pi$
$174$		0			0
$175$	−1.66111	+	2.68533i	−0.125568	+	0.202992i
$176$	−17.8364	+	4.64566i	−1.34447	+	0.350180i
$177$		0			0
$178$	10.8047	+	5.35182i	0.809847	+	0.401136i
$179$	−6.02688	+	10.4389i	−0.450470	+	0.780237i	−0.998415	−	0.0562770i	$-0.982077\pi$
$179$	−6.02688	+	10.4389i	−0.450470	+	0.780237i	0.547945	+	0.836514i	$0.315410\pi$
$180$		0			0
$181$	20.7992			1.54599			0.772997	−	0.634410i	$-0.218757\pi$
$181$	20.7992			1.54599			0.772997	+	0.634410i	$0.218757\pi$
$182$	10.3282	+	16.5870i	0.765580	+	1.22951i
$183$		0			0
$184$	1.33233	+	1.53542i	0.0982204	+	0.113192i
$185$	−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	$-0.292149\pi$
$191$	−5.30815	−	9.19399i	−0.384084	−	0.665253i	−0.991642	+	0.129022i	$0.958816\pi$
$192$		0			0
$193$	−6.49634	+	11.2520i	−0.467617	+	0.809936i	−0.999315	−	0.0369977i	$-0.988221\pi$
$193$	−6.49634	+	11.2520i	−0.467617	+	0.809936i	0.531699	+	0.846934i	$0.321554\pi$
$194$	8.40309	+	12.6239i	0.603307	+	0.906342i
$195$		0			0
$196$	−6.17700	+	12.5636i	−0.441214	+	0.897402i
$197$		−	3.18852i		−	0.227173i	−0.993528	−	0.113586i	$-0.963766\pi$
$197$		−	3.18852i		−	0.227173i	0.993528	−	0.113586i	$-0.0362339\pi$
$198$		0			0
$199$	12.1672	+	7.02473i	0.862509	+	0.497970i	0.864852	−	0.502027i	$-0.167412\pi$
$199$	12.1672	+	7.02473i	0.862509	+	0.497970i	−0.00234247	+	0.999997i	$0.500746\pi$
$200$	1.10182	−	3.19071i	0.0779103	−	0.225617i
$201$		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
$206$	21.1348	+	10.4686i	1.47253	+	0.729379i
$207$		0			0
$208$	−14.6669	−	14.8737i	−1.01696	−	1.03130i
$209$		−	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	$0.898245\pi$
$212$	−3.29046	+	2.50661i	−0.225990	+	0.172155i
$213$		0			0
$214$	−3.60110	+	7.27020i	−0.246166	+	0.496981i
$215$	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
$220$	21.1582	+	8.85092i	1.42649	+	0.596729i
$221$	−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	$-0.294198\pi$
$224$	3.49181	−	14.5536i	0.233306	−	0.972403i
$225$		0			0
$226$	6.58849	−	4.38563i	0.438260	−	0.291728i
$227$	−5.00619	+	8.67097i	−0.332272	+	0.575512i	−0.982957	−	0.183836i	$-0.941149\pi$
$227$	−5.00619	+	8.67097i	−0.332272	+	0.575512i	0.650685	+	0.759348i	$0.274482\pi$
$228$		0			0
$229$	2.66815	+	4.62137i	0.176316	+	0.305389i	0.940616	−	0.339472i	$-0.110248\pi$
$229$	2.66815	+	4.62137i	0.176316	+	0.305389i	−0.764300	+	0.644861i	$0.776915\pi$
$230$	−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	−0.727666	−	0.685932i	$-0.759395\pi$
$233$	−7.59347	+	4.38409i	−0.497465	+	0.287211i	0.230201	+	0.973143i	$0.426062\pi$
$234$		0			0
$235$	11.6774	+	6.74192i	0.761747	+	0.439795i
$236$	−4.98894	−	6.54905i	−0.324752	−	0.426307i
$237$		0			0
$238$	−0.699487	−	20.9828i	−0.0453410	−	1.36011i
$239$	13.1385			0.849860			0.424930	−	0.905226i	$-0.360299\pi$
$239$	13.1385			0.849860			0.424930	+	0.905226i	$0.360299\pi$
$240$		0			0
$241$	11.0319	−	19.1078i	0.710627	−	1.23084i	−0.253996	−	0.967205i	$-0.581745\pi$
$241$	11.0319	−	19.1078i	0.710627	−	1.23084i	0.964622	−	0.263636i	$-0.0849218\pi$
$242$	−6.42301	+	12.9673i	−0.412887	+	0.833571i
$243$		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
$248$	−3.14712	−	1.08677i	−0.199842	−	0.0690096i
$249$		0			0
$250$	11.1523	−	7.42355i	0.705336	−	0.469507i
$251$	−26.5149			−1.67361			−0.836804	−	0.547503i	$-0.815579\pi$
$251$	−26.5149			−1.67361			−0.836804	+	0.547503i	$0.815579\pi$
$252$		0			0
$253$	3.31182			0.208212
$254$	−17.9255	+	11.9321i	−1.12475	+	0.748688i
$255$		0			0
$256$	−0.224018	+	15.9984i	−0.0140011	+	0.999902i
$257$	−14.6698	+	8.46961i	−0.915076	+	0.528320i	−0.882061	−	0.471135i	$-0.843844\pi$
$257$	−14.6698	+	8.46961i	−0.915076	+	0.528320i	−0.0330154	+	0.999455i	$0.510511\pi$
$258$		0			0
$259$	3.39846	+	6.32230i	0.211170	+	0.392848i
$260$	3.30250	+	25.7820i	0.204812	+	1.59893i
$261$		0			0
$262$	−2.60708	+	5.26338i	−0.161066	+	0.325173i
$263$	6.97969	−	12.0892i	0.430386	−	0.745451i	−0.566520	−	0.824048i	$-0.691711\pi$
$263$	6.97969	−	12.0892i	0.430386	−	0.745451i	0.996906	+	0.0785971i	$0.0250441\pi$
$264$		0			0
$265$	5.14712			0.316185
$266$	10.5416	+	5.62649i	0.646347	+	0.344982i
$267$		0			0
$268$	−20.1170	+	15.3248i	−1.22884	+	0.936108i
$269$	13.4582	+	7.77008i	0.820559	+	0.473750i	0.850609	−	0.525798i	$-0.176233\pi$
$269$	13.4582	+	7.77008i	0.820559	+	0.473750i	−0.0300501	+	0.999548i	$0.509567\pi$
$270$		0			0
$271$	0.197214	−	0.113861i	0.0119799	−	0.00691658i	−0.493998	−	0.869463i	$-0.664465\pi$
$271$	0.197214	−	0.113861i	0.0119799	−	0.00691658i	0.505978	+	0.862546i	$0.331132\pi$
$272$	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	−0.454833	−	0.890577i	$-0.650301\pi$
$277$	9.05140	−	15.6775i	0.543846	−	0.941968i	0.998679	−	0.0513915i	$-0.0163656\pi$
$278$	−12.1142	+	8.06384i	−0.726564	+	0.483637i
$279$		0			0
$280$	−14.4304	+	11.7728i	−0.862378	+	0.703558i
$281$		−	16.5594i		−	0.987854i	−0.869503	−	0.493927i	$-0.835561\pi$
$281$		−	16.5594i		−	0.987854i	0.869503	−	0.493927i	$-0.164439\pi$
$282$		0			0
$283$	2.76570	+	1.59678i	0.164404	+	0.0949185i	0.579944	−	0.814656i	$-0.303074\pi$
$283$	2.76570	+	1.59678i	0.164404	+	0.0949185i	−0.415541	+	0.909575i	$0.636408\pi$
$284$	−5.64217	+	13.4877i	−0.334801	+	0.800346i
$285$		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
$290$	−7.08682	+	14.3075i	−0.416153	+	0.840164i
$291$		0			0
$292$	−11.6807	−	15.3335i	−0.683563	−	0.897323i
$293$		−	3.17751i		−	0.185632i	−0.995683	−	0.0928160i	$-0.970413\pi$
$293$		−	3.17751i		−	0.185632i	0.995683	−	0.0928160i	$-0.0295868\pi$
$294$		0			0
$295$			10.2444i			0.596451i
$296$	−5.02906	−	5.79565i	−0.292308	−	0.336865i
$297$		0			0
$298$	7.16878	+	3.55086i	0.415276	+	0.205696i
$299$	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
$304$	−12.3155	−	3.39251i	−0.706342	−	0.194574i
$305$	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	$0.899741\pi$
$308$	−14.1795	−	19.8356i	−0.807950	−	1.13024i
$309$		0			0
$310$	2.29568	+	3.44878i	0.130386	+	0.195878i
$311$	−9.34103	+	16.1791i	−0.529681	+	0.917434i	0.469720	+	0.882816i	$0.344355\pi$
$311$	−9.34103	+	16.1791i	−0.529681	+	0.917434i	−0.999401	+	0.0346188i	$0.988978\pi$
$312$		0			0
$313$	7.91566	+	13.7103i	0.447420	+	0.774954i	0.998217	−	0.0596853i	$-0.0190097\pi$
$313$	7.91566	+	13.7103i	0.447420	+	0.774954i	−0.550798	+	0.834639i	$0.685676\pi$
$314$	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	−0.343229	−	0.939252i	$-0.611521\pi$
$317$	5.31592	−	3.06915i	0.298572	−	0.172380i	0.641801	+	0.766871i	$0.278187\pi$
$318$		0			0
$319$	−18.1033	−	10.4519i	−1.01359	−	0.585196i
$320$	12.2852	−	15.6670i	0.686765	−	0.875811i
$321$		0			0
$322$	−1.26628	+	2.37246i	−0.0705671	+	0.132212i
$323$	−17.9191			−0.997043
$324$		0			0
$325$	3.11623	−	5.39747i	0.172857	−	0.299398i
$326$	−2.26675	−	1.12277i	−0.125544	−	0.0621846i
$327$		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	$-0.663269\pi$
$331$	0.336392	−	0.194216i	0.0184898	−	0.0106751i	0.509216	+	0.860639i	$0.329935\pi$
$332$	10.6248	−	25.3987i	0.583112	−	1.39394i
$333$		0			0
$334$	6.48046	+	9.73553i	0.354595	+	0.532705i
$335$	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	$0.446835\pi$
$338$	−11.1836	−	16.8011i	−0.608309	−	0.913858i
$339$		0			0
$340$	10.7778	−	25.7644i	0.584507	−	1.39727i
$341$	−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
$346$	−24.5182	−	12.1444i	−1.31811	−	0.652888i
$347$	14.5134	−	25.1380i	0.779120	−	1.34948i	−0.153329	−	0.988175i	$-0.548999\pi$
$347$	14.5134	−	25.1380i	0.779120	−	1.34948i	0.932449	−	0.361301i	$-0.117667\pi$
$348$		0			0
$349$	−27.2889			−1.46074			−0.730371	−	0.683050i	$-0.760653\pi$
$349$	−27.2889			−1.46074			−0.730371	+	0.683050i	$0.760653\pi$
$350$	4.46301	−	0.148780i	0.238558	−	0.00795262i
$351$		0			0
$352$	19.4463	+	17.3574i	1.03649	+	0.925151i
$353$	26.2242	+	15.1406i	1.39578	+	0.805851i	0.993947	−	0.109864i	$-0.0350414\pi$
$353$	26.2242	+	15.1406i	1.39578	+	0.805851i	0.401829	+	0.915715i	$0.368375\pi$
$354$		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	0.998390	+	0.0567148i	$0.0180626\pi$
$359$	10.3890	+	17.9943i	0.548312	+	0.949704i	−0.450079	+	0.892989i	$0.648604\pi$
$360$		0			0
$361$	−4.40061	+	7.62208i	−0.231611	+	0.401162i
$362$	−16.2990	−	24.4859i	−0.856657	−	1.28695i
$363$		0			0
$364$	11.4334	−	25.1571i	0.599275	−	1.31859i
$365$			23.9854i			1.25545i
$366$		0			0
$367$	−17.7384	−	10.2412i	−0.925934	−	0.534589i	−0.0404110	−	0.999183i	$-0.512867\pi$
$367$	−17.7384	−	10.2412i	−0.925934	−	0.534589i	−0.885523	+	0.464595i	$0.846200\pi$
$368$	0.763508	−	2.77169i	0.0398006	−	0.144484i
$369$		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	0.989430	+	0.145012i	$0.0463222\pi$
$373$	11.9800	+	20.7499i	0.620299	+	1.07439i	−0.369130	+	0.929378i	$0.620344\pi$
$374$	32.7651	+	16.2293i	1.69424	+	0.839197i
$375$		0			0
$376$	10.0437	+	11.5746i	0.517962	+	0.596916i
$377$		−	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	$-0.0245627\pi$
$380$	9.63228	+	12.6444i	0.494126	+	0.648646i
$381$		0			0
$382$	−6.66395	+	13.4537i	−0.340958	+	0.688354i
$383$	−14.3407	−	24.8389i	−0.732777	−	1.26921i	−0.955692	−	0.294369i	$-0.904890\pi$
$383$	−14.3407	−	24.8389i	−0.732777	−	1.26921i	0.222915	−	0.974838i	$-0.428443\pi$
$384$		0			0
$385$	−0.921460	+	30.3260i	−0.0469620	+	1.54556i
$386$	18.3372	−	1.16965i	0.933337	−	0.0595338i
$387$		0			0
$388$	8.27649	−	19.7851i	0.420175	−	1.00443i
$389$	−10.4739	−	6.04712i	−0.531049	−	0.306601i	0.210395	−	0.977617i	$-0.432525\pi$
$389$	−10.4739	−	6.04712i	−0.531049	−	0.306601i	−0.741443	+	0.671015i	$0.765858\pi$
$390$		0			0
$391$		−	4.03281i		−	0.203948i
$392$	19.6310	−	2.57344i	0.991517	−	0.129979i
$393$		0			0
$394$	−3.75369	+	2.49864i	−0.189108	+	0.125880i
$395$	10.9993	−	19.0513i	0.553434	−	0.958576i
$396$		0			0
$397$	−2.62914	−	4.55381i	−0.131953	−	0.228549i	0.792476	−	0.609903i	$-0.208791\pi$
$397$	−2.62914	−	4.55381i	−0.131953	−	0.228549i	−0.924429	+	0.381353i	$0.875458\pi$
$398$	−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	−0.844207	−	0.536017i	$-0.819928\pi$
$401$	−16.0622	+	9.27350i	−0.802106	+	0.463096i	0.0421007	+	0.999113i	$0.486595\pi$
$402$		0			0
$403$	−5.32373	−	3.07366i	−0.265194	−	0.153110i
$404$	6.10403	−	4.64993i	0.303687	−	0.231343i
$405$		0			0
$406$	14.4092	−	8.97219i	0.715116	−	0.445282i
$407$	−12.5009			−0.619649
$408$		0			0
$409$	8.76122	−	15.1749i	0.433214	−	0.750349i	−0.563934	−	0.825820i	$-0.690713\pi$
$409$	8.76122	−	15.1749i	0.433214	−	0.750349i	0.997148	+	0.0754709i	$0.0240460\pi$
$410$	5.99353	−	12.1003i	0.296000	−	0.597589i
$411$		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
$416$	−6.01654	+	28.9221i	−0.294985	+	1.41802i
$417$		0			0
$418$	−17.3238	+	11.5316i	−0.847334	+	0.564028i
$419$	26.9149			1.31488			0.657439	−	0.753508i	$-0.271640\pi$
$419$	26.9149			1.31488			0.657439	+	0.753508i	$0.271640\pi$
$420$		0			0
$421$	−4.71296			−0.229695			−0.114848	−	0.993383i	$-0.536638\pi$
$421$	−4.71296			−0.229695			−0.114848	+	0.993383i	$0.536638\pi$
$422$	10.7478	−	7.15430i	0.523196	−	0.348266i
$423$		0			0
$424$	5.52943	+	1.90942i	0.268533	+	0.0927299i
$425$	−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
$430$	17.4608	−	35.2513i	0.842033	−	1.69997i
$431$	1.91047	−	3.30903i	0.0920239	−	0.159390i	−0.816339	−	0.577573i	$-0.804000\pi$
$431$	1.91047	−	3.30903i	0.0920239	−	0.159390i	0.908363	+	0.418183i	$0.137333\pi$
$432$		0			0
$433$	−34.7992			−1.67234			−0.836172	−	0.548467i	$-0.815212\pi$
$433$	−34.7992			−1.67234			−0.836172	+	0.548467i	$0.815212\pi$
$434$	−0.146747	−	4.40204i	−0.00704409	−	0.211305i
$435$		0			0
$436$	3.42627	+	4.49772i	0.164089	+	0.215402i
$437$	1.98779	+	1.14765i	0.0950891	+	0.0548997i
$438$		0			0
$439$	30.7278	−	17.7407i	1.46656	−	0.846717i	0.467256	−	0.884122i	$-0.345243\pi$
$439$	30.7278	−	17.7407i	1.46656	−	0.846717i	0.999300	+	0.0374052i	$0.0119092\pi$
$440$	−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	$-0.250496\pi$
$443$	−5.47919	−	9.49024i	−0.260324	−	0.450895i	−0.966328	+	0.257313i	$0.917163\pi$
$444$		0			0
$445$	−10.6091	+	18.3755i	−0.502920	+	0.871083i
$446$	−28.0637	+	18.6806i	−1.32886	+	0.884553i
$447$		0			0
$448$	−19.8695	+	7.29399i	−0.938746	+	0.344609i
$449$			27.1675i			1.28211i	0.767494	+	0.641056i	$0.221503\pi$
$449$			27.1675i			1.28211i	−0.767494	+	0.641056i	$0.778497\pi$
$450$		0			0
$451$	15.3105	+	8.83951i	0.720942	+	0.416236i
$452$	−10.3259	−	4.31956i	−0.485692	−	0.203175i
$453$		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	−0.825007	−	0.565123i	$-0.808829\pi$
$457$	−19.2807	−	33.3952i	−0.901914	−	1.56216i	−0.0769071	−	0.997038i	$-0.524505\pi$
$458$	3.34965	−	6.76255i	0.156519	−	0.315993i
$459$		0			0
$460$	−2.84572	+	2.16781i	−0.132682	+	0.101075i
$461$			13.5543i			0.631287i	0.948878	+	0.315643i	$0.102220\pi$
$461$			13.5543i			0.631287i	−0.948878	+	0.315643i	$0.897780\pi$
$462$		0			0
$463$			17.7564i			0.825212i	0.910910	+	0.412606i	$0.135381\pi$
$463$			17.7564i			0.825212i	−0.910910	+	0.412606i	$0.864619\pi$
$464$	−12.9208	+	12.7412i	−0.599835	+	0.591494i
$465$		0			0
$466$	11.1117	+	5.50387i	0.514739	+	0.254962i
$467$	5.39965	+	9.35248i	0.249866	+	0.432781i	0.963488	−	0.267750i	$-0.0862800\pi$
$467$	5.39965	+	9.35248i	0.249866	+	0.432781i	−0.713622	+	0.700531i	$0.752947\pi$
$468$		0			0
$469$	−28.4510	−	17.5994i	−1.31375	−	0.812666i
$470$	−1.21387	−	19.0304i	−0.0559916	−	0.877805i
$471$		0			0
$472$	−3.80035	+	11.0053i	−0.174925	+	0.506559i
$473$	44.6035	+	25.7518i	2.05087	+	1.18407i
$474$		0			0
$475$		−	3.81135i		−	0.174877i
$476$	−24.1539	+	17.2664i	−1.10709	+	0.791402i
$477$		0			0
$478$	−10.2958	−	15.4673i	−0.470919	−	0.707458i
$479$	−9.48360	+	16.4261i	−0.433317	+	0.750527i	−0.997157	−	0.0753575i	$-0.975990\pi$
$479$	−9.48360	+	16.4261i	−0.433317	+	0.750527i	0.563840	+	0.825884i	$0.309324\pi$
$480$		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	$-0.226539\pi$
$487$	12.5847	+	7.26579i	0.570268	+	0.329245i	−0.186988	+	0.982362i	$0.559873\pi$
$488$	1.87272	+	2.15819i	0.0847742	+	0.0976965i
$489$		0			0
$490$	−21.3721	−	12.2553i	−0.965492	−	0.553638i
$491$	26.0025			1.17348			0.586738	−	0.809777i	$-0.300412\pi$
$491$	26.0025			1.17348			0.586738	+	0.809777i	$0.300412\pi$
$492$		0			0
$493$	−12.7273	+	22.0444i	−0.573210	+	0.992829i
$494$	−21.1348	−	10.4686i	−0.950900	−	0.471003i
$495$		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	$-0.686220\pi$
$499$	−2.37527	+	1.37136i	−0.106332	+	0.0613907i	0.445891	+	0.895087i	$0.352887\pi$
$500$	−17.4787	−	7.31172i	−0.781673	−	0.326990i
$501$		0			0
$502$	20.7780	+	31.2147i	0.927370	+	1.39318i
$503$	−21.5337			−0.960139			−0.480070	−	0.877230i	$-0.659389\pi$
$503$	−21.5337			−0.960139			−0.480070	+	0.877230i	$0.659389\pi$
$504$		0			0
$505$	−9.54826			−0.424892
$506$	−2.59526	−	3.89884i	−0.115373	−	0.173324i
$507$		0			0
$508$	28.0941	+	11.7524i	1.24648	+	0.521426i
$509$	11.3748	−	6.56726i	0.504180	−	0.291089i	−0.226258	−	0.974067i	$-0.572649\pi$
$509$	11.3748	−	6.56726i	0.504180	−	0.291089i	0.730438	+	0.682979i	$0.239316\pi$
$510$		0			0
$511$	13.4145	−	21.6857i	0.593423	−	0.959320i
$512$	19.0097	−	12.2732i	0.840117	−	0.542405i
$513$		0			0
$514$	21.4666	+	10.6329i	0.946852	+	0.468997i
$515$	−20.7522	+	35.9439i	−0.914452	+	1.58388i
$516$		0			0
$517$	24.9659			1.09800
$518$	4.77976	−	8.95521i	0.210011	−	0.393469i
$519$		0			0
$520$	27.7639	−	24.0916i	1.21753	−	1.05648i
$521$	6.30391	+	3.63957i	0.276179	+	0.159452i	0.631693	−	0.775219i	$-0.282361\pi$
$521$	6.30391	+	3.63957i	0.276179	+	0.159452i	−0.355513	+	0.934671i	$0.615694\pi$
$522$		0			0
$523$	2.41646	−	1.39515i	0.105665	−	0.0610055i	−0.446236	−	0.894915i	$-0.647236\pi$
$523$	2.41646	−	1.39515i	0.105665	−	0.0610055i	0.551901	+	0.833910i	$0.313903\pi$
$524$	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
$530$	−4.03347	−	6.05945i	−0.175203	−	0.263205i
$531$		0			0
$532$	−1.63700	−	16.8192i	−0.0709729	−	0.729205i
$533$			20.0360i			0.867858i
$534$		0			0
$535$	−12.3644	−	7.13859i	−0.534560	−	0.308628i
$536$	33.8055	+	11.6737i	1.46017	+	0.504228i
$537$		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	0.859426	−	0.511260i	$-0.170821\pi$
$541$	−0.303559	−	0.525780i	−0.0130510	−	0.0226050i	−0.872477	+	0.488655i	$0.837488\pi$
$542$	−0.288587	−	0.142944i	−0.0123959	−	0.00613996i
$543$		0			0
$544$	21.1361	−	23.6798i	0.906203	−	1.01526i
$545$		−	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	$-0.0764697\pi$
$548$	−25.9831	+	19.7934i	−1.10994	+	0.845532i
$549$		0			0
$550$	−3.45195	+	6.96908i	−0.147192	+	0.297163i
$551$	−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
$556$	18.9863	+	7.94236i	0.805198	+	0.336831i
$557$	−25.6805	−	14.8266i	−1.08812	−	0.628225i	−0.155043	−	0.987908i	$-0.549552\pi$
$557$	−25.6805	−	14.8266i	−1.08812	−	0.628225i	−0.933075	+	0.359682i	$0.882885\pi$
$558$		0			0
$559$			58.3703i			2.46880i
$560$	25.1676	+	7.76254i	1.06353	+	0.328027i
$561$		0			0
$562$	−19.4946	+	12.9766i	−0.822330	+	0.547384i
$563$	−16.4174	+	28.4358i	−0.691910	+	1.19842i	0.279301	+	0.960204i	$0.409897\pi$
$563$	−16.4174	+	28.4358i	−0.691910	+	1.19842i	−0.971211	+	0.238220i	$0.923436\pi$
$564$		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	−0.657121	−	0.753785i	$-0.728226\pi$
$569$	−7.94054	+	4.58447i	−0.332885	+	0.192191i	0.324236	+	0.945976i	$0.394893\pi$
$570$		0			0
$571$	−21.1743	−	12.2250i	−0.886115	−	0.511599i	−0.0134453	−	0.999910i	$-0.504280\pi$
$571$	−21.1743	−	12.2250i	−0.886115	−	0.511599i	−0.872670	+	0.488311i	$0.837613\pi$
$572$	29.1637	+	38.2836i	1.21940	+	1.60072i
$573$		0			0
$574$	−12.1863	+	7.58804i	−0.508645	+	0.316719i
$575$	0.857772			0.0357716
$576$		0			0
$577$	6.00925	−	10.4083i	0.250168	−	0.433304i	−0.713404	−	0.700753i	$-0.752847\pi$
$577$	6.00925	−	10.4083i	0.250168	−	0.433304i	0.963572	+	0.267449i	$0.0861807\pi$
$578$	9.09139	−	18.3545i	0.378152	−	0.763445i
$579$		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
$584$	−8.89786	+	25.7670i	−0.368196	+	1.06624i
$585$		0			0
$586$	−3.74072	+	2.49001i	−0.154528	+	0.102861i
$587$	18.8618			0.778510			0.389255	−	0.921130i	$-0.372733\pi$
$587$	18.8618			0.778510			0.389255	+	0.921130i	$0.372733\pi$
$588$		0			0
$589$	−3.75929			−0.154899
$590$	12.0602	−	8.02786i	0.496510	−	0.330502i
$591$		0			0
$592$	−2.88197	+	10.4621i	−0.118448	+	0.429991i
$593$	7.65096	−	4.41729i	0.314187	−	0.181396i	−0.334611	−	0.942356i	$-0.608605\pi$
$593$	7.65096	−	4.41729i	0.314187	−	0.181396i	0.648799	+	0.760960i	$0.275272\pi$
$594$		0			0
$595$	36.9280	+	1.12206i	1.51390	+	0.0460001i
$596$	−1.43746	−	11.2220i	−0.0588808	−	0.459672i
$597$		0			0
$598$	2.35602	−	4.75654i	0.0963450	−	0.194509i
$599$	−13.9015	+	24.0781i	−0.568000	+	0.983805i	0.428763	+	0.903417i	$0.358949\pi$
$599$	−13.9015	+	24.0781i	−0.568000	+	0.983805i	−0.996764	+	0.0803885i	$0.974384\pi$
$600$		0			0
$601$	−12.1977			−0.497556			−0.248778	−	0.968561i	$-0.580029\pi$
$601$	−12.1977			−0.497556			−0.248778	+	0.968561i	$0.580029\pi$
$602$	−35.5019	+	22.1060i	−1.44695	+	0.900972i
$603$		0			0
$604$	−19.3500	+	14.7404i	−0.787339	+	0.599780i
$605$	−22.0535	−	12.7326i	−0.896601	−	0.517653i
$606$		0			0
$607$	9.10887	−	5.25901i	0.369718	−	0.213457i	−0.303617	−	0.952794i	$-0.598194\pi$
$607$	9.10887	−	5.25901i	0.369718	−	0.213457i	0.673335	+	0.739337i	$0.264861\pi$
$608$	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	0.126392	+	0.991980i	$0.459660\pi$
$613$	−19.7052	+	34.1304i	−0.795884	+	1.37851i	−0.922276	+	0.386532i	$0.873673\pi$
$614$	12.7801	−	8.50708i	0.515763	−	0.343318i
$615$		0			0
$616$	−12.2399	+	32.2367i	−0.493160	+	1.29885i
$617$		−	35.9618i		−	1.44777i	−0.689922	−	0.723884i	$-0.742355\pi$
$617$		−	35.9618i		−	1.44777i	0.689922	−	0.723884i	$-0.257645\pi$
$618$		0			0
$619$	−21.1743	−	12.2250i	−0.851065	−	0.491363i	0.00994487	−	0.999951i	$-0.496834\pi$
$619$	−21.1743	−	12.2250i	−0.851065	−	0.491363i	−0.861010	+	0.508588i	$0.830168\pi$
$620$	2.26110	−	5.40518i	0.0908079	−	0.217077i
$621$		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
$626$	9.93747	−	20.0626i	0.397181	−	0.801863i
$627$		0			0
$628$	−8.53100	−	11.1988i	−0.340424	−	0.446880i
$629$			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	$0.967757\pi$
$632$	18.8837	−	16.3860i	0.751154	−	0.651799i
$633$		0			0
$634$	−7.77889	−	3.85307i	−0.308939	−	0.153025i
$635$	−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
$640$	−28.0711	−	2.18556i	−1.10961	−	0.0863917i
$641$	−23.1295	−	13.3538i	−0.913561	−	0.527445i	−0.0319859	−	0.999488i	$-0.510183\pi$
$641$	−23.1295	−	13.3538i	−0.913561	−	0.527445i	−0.881575	+	0.472044i	$0.843517\pi$
$642$		0			0
$643$			24.3919i			0.961924i	0.876741	+	0.480962i	$0.159713\pi$
$643$			24.3919i			0.961924i	−0.876741	+	0.480962i	$0.840287\pi$
$644$	3.78528	−	0.368418i	0.149161	−	0.0145177i
$645$		0			0
$646$	14.0420	+	21.0952i	0.552476	+	0.829979i
$647$	2.41921	−	4.19019i	0.0951088	−	0.164733i	−0.814545	−	0.580100i	$-0.803013\pi$
$647$	2.41921	−	4.19019i	0.0951088	−	0.164733i	0.909654	+	0.415367i	$0.136347\pi$
$648$		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	−0.0658236	−	0.997831i	$-0.520967\pi$
$653$	19.5592	−	11.2925i	0.765412	−	0.441911i	0.831235	+	0.555921i	$0.187634\pi$
$654$		0			0
$655$	−8.95142	−	5.16811i	−0.349761	−	0.201935i
$656$	10.9275	−	10.7756i	0.426648	−	0.420716i
$657$		0			0
$658$	−9.54577	+	17.8846i	−0.372133	+	0.697216i
$659$	−13.4237			−0.522911			−0.261456	−	0.965215i	$-0.584203\pi$
$659$	−13.4237			−0.522911			−0.261456	+	0.965215i	$0.584203\pi$
$660$		0			0
$661$	7.10185	−	12.3008i	0.276230	−	0.478444i	−0.694215	−	0.719768i	$-0.744248\pi$
$661$	7.10185	−	12.3008i	0.276230	−	0.478444i	0.970445	+	0.241324i	$0.0775815\pi$
$662$	−0.492249	−	0.243822i	−0.0191318	−	0.00947642i
$663$		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
$668$	6.38283	−	15.2582i	0.246959	−	0.590358i
$669$		0			0
$670$	−24.6596	−	37.0458i	−0.952682	−	1.43121i
$671$	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	$0.430105\pi$
$674$	−4.78319	−	7.18574i	−0.184242	−	0.276784i
$675$		0			0
$676$	−11.0151	+	26.3318i	−0.423660	+	1.01276i
$677$	−2.75180	+	1.58875i	−0.105760	+	0.0610608i	−0.551947	−	0.833879i	$-0.686115\pi$
$677$	−2.75180	+	1.58875i	−0.105760	+	0.0610608i	0.446187	+	0.894940i	$0.352782\pi$
$678$		0			0
$679$	28.3579	+	0.861658i	1.08827	+	0.0330674i
$680$	−38.7770	+	7.50178i	−1.48703	+	0.287680i
$681$		0			0
$682$	6.87387	+	3.40479i	0.263214	+	0.130376i
$683$	−3.13262	+	5.42586i	−0.119866	+	0.207615i	−0.919715	−	0.392588i	$-0.871580\pi$
$683$	−3.13262	+	5.42586i	−0.119866	+	0.207615i	0.799848	+	0.600202i	$0.204913\pi$
$684$		0			0
$685$	40.6441			1.55293
$686$	12.4688	+	23.0332i	0.476062	+	0.879412i
$687$		0			0
$688$	31.8348	−	31.3922i	1.21369	−	1.19681i
$689$	9.35369	+	5.40036i	0.356347	+	0.205737i
$690$		0			0
$691$	−13.9691	+	8.06506i	−0.531409	+	0.306809i	−0.741590	−	0.670853i	$-0.765928\pi$
$691$	−13.9691	+	8.06506i	−0.531409	+	0.306809i	0.210181	+	0.977663i	$0.432595\pi$
$692$	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
$698$	21.3846	+	32.1259i	0.809418	+	1.21598i
$699$		0			0
$700$	−3.67253	−	5.13749i	−0.138808	−	0.194179i
$701$		−	50.8903i		−	1.92210i	−0.276373	−	0.961050i	$-0.589133\pi$
$701$		−	50.8903i		−	1.92210i	0.276373	−	0.961050i	$-0.410867\pi$
$702$		0			0
$703$	−7.50322	−	4.33198i	−0.282989	−	0.163384i
$704$	5.19510	−	36.4950i	0.195798	−	1.37546i
$705$		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	0.592527	−	0.805550i	$-0.298130\pi$
$709$	−10.6871	−	18.5107i	−0.401364	−	0.695182i	−0.993891	+	0.110368i	$0.964797\pi$
$710$	−23.0548	−	11.4196i	−0.865231	−	0.428569i
$711$		0			0
$712$	−18.2139	+	15.8047i	−0.682594	+	0.592307i
$713$		−	0.846054i		−	0.0316850i
$714$		0			0
$715$		−	59.8854i		−	2.23959i
$716$	−14.6087	−	19.1770i	−0.545953	−	0.716680i
$717$		0			0
$718$	13.0426	−	26.3315i	0.486745	−	0.982681i
$719$	−12.1927	−	21.1183i	−0.454709	−	0.787579i	0.543962	−	0.839110i	$-0.316923\pi$
$719$	−12.1927	−	21.1183i	−0.454709	−	0.787579i	−0.998671	+	0.0515302i	$0.983590\pi$
$720$		0			0
$721$	38.8651	−	20.8914i	1.44741	−	0.778036i
$722$	12.4216	−	0.792321i	0.462283	−	0.0294871i
$723$		0			0
$724$	−16.0535	+	38.3760i	−0.596622	+	1.42623i
$725$	−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	$0.758640\pi$
$728$	−38.5758	+	6.25396i	−1.42971	+	0.231787i
$729$		0			0
$730$	28.2368	−	18.7958i	1.04509	−	0.695665i
$731$	31.3580	−	54.3137i	1.15982	−	2.00887i
$732$		0			0
$733$	−22.5631	−	39.0805i	−0.833388	−	1.44347i	−0.895337	−	0.445390i	$-0.853065\pi$
$733$	−22.5631	−	39.0805i	−0.833388	−	1.44347i	0.0619491	−	0.998079i	$-0.480268\pi$
$734$	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	$-0.624152\pi$
$739$	−37.2786	−	21.5228i	−1.37132	−	0.791729i	−0.991094	+	0.133166i	$0.957486\pi$
$740$	10.7416	−	8.18273i	0.394868	−	0.300803i
$741$		0			0
$742$	0.257832	+	7.73430i	0.00946531	+	0.283935i
$743$	7.52770			0.276165			0.138082	−	0.990421i	$-0.455906\pi$
$743$	7.52770			0.276165			0.138082	+	0.990421i	$0.455906\pi$
$744$		0			0
$745$	−7.03901	+	12.1919i	−0.257889	+	0.446677i
$746$	15.0399	−	30.3638i	0.550649	−	1.11170i
$747$		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	$-0.963617\pi$
$751$	−38.1316	+	22.0153i	−1.39144	+	0.803349i	−0.397966	+	0.917400i	$0.630284\pi$
$752$	5.75565	−	20.8942i	0.209887	−	0.761932i
$753$		0			0
$754$	−27.8900	+	18.5650i	−1.01570	+	0.676097i
$755$	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	$0.455652\pi$
$758$	−3.53356	+	2.35211i	−0.128345	+	0.0854327i
$759$		0			0
$760$	7.33745	−	21.2482i	0.266157	−	0.770754i
$761$	−15.1210	+	8.73011i	−0.548135	+	0.316466i	−0.748370	−	0.663282i	$-0.769163\pi$
$761$	−15.1210	+	8.73011i	−0.548135	+	0.316466i	0.200234	+	0.979748i	$0.435830\pi$
$762$		0			0
$763$	−3.93484	+	6.36101i	−0.142451	+	0.230284i
$764$	21.0605	−	2.69771i	0.761943	−	0.0975996i
$765$		0			0
$766$	−18.0036	+	36.3472i	−0.650498	+	1.31328i
$767$	−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	$0.481998\pi$
$770$	36.4233	−	22.6798i	1.31261	−	0.817322i
$771$		0			0
$772$	−15.7466	−	20.6708i	−0.566733	−	0.743959i
$773$	−16.4737	−	9.51107i	−0.592516	−	0.342090i	0.173575	−	0.984821i	$-0.444468\pi$
$773$	−16.4737	−	9.51107i	−0.592516	−	0.342090i	−0.766092	+	0.642731i	$0.777801\pi$
$774$		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
$782$	−4.74762	+	3.16025i	−0.169775	+	0.113010i
$783$		0			0
$784$	−18.4132	−	21.0940i	−0.657613	−	0.753356i
$785$			17.5177i			0.625235i
$786$		0			0
$787$	3.98235	+	2.29921i	0.141956	+	0.0819581i	0.569296	−	0.822133i	$-0.307216\pi$
$787$	3.98235	+	2.29921i	0.141956	+	0.0819581i	−0.427340	+	0.904091i	$0.640549\pi$
$788$	5.88304	+	2.46100i	0.209575	+	0.0876694i
$789$		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
$794$	−3.30068	+	6.66369i	−0.117137	+	0.236485i
$795$		0			0
$796$	−22.3521	+	17.0274i	−0.792250	+	0.603520i
$797$			40.4802i			1.43388i	0.697134	+	0.716941i	$0.254458\pi$
$797$			40.4802i			1.43388i	−0.697134	+	0.716941i	$0.745542\pi$
$798$		0			0
$799$		−	30.4010i		−	1.07551i
$800$	5.03666	+	4.49562i	0.178073	+	0.158944i
$801$		0			0
$802$	23.5041	+	11.6421i	0.829959	+	0.411098i
$803$	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
$808$	−10.2575	−	3.54211i	−0.360856	−	0.124611i
$809$	8.54248	+	4.93200i	0.300338	+	0.173400i	0.642595	−	0.766206i	$-0.277858\pi$
$809$	8.54248	+	4.93200i	0.300338	+	0.173400i	−0.342257	+	0.939606i	$0.611191\pi$
$810$		0			0
$811$		−	28.0467i		−	0.984854i	−0.870354	−	0.492427i	$-0.836110\pi$
$811$		−	28.0467i		−	0.984854i	0.870354	−	0.492427i	$-0.163890\pi$
$812$	−21.8541	−	9.93228i	−0.766927	−	0.348555i
$813$		0			0
$814$	9.79619	+	14.7167i	0.343356	+	0.515821i
$815$	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	−0.843970	−	0.536391i	$-0.819787\pi$
$821$	−22.9634	+	13.2579i	−0.801427	+	0.462704i	0.0425431	+	0.999095i	$0.486454\pi$
$822$		0			0
$823$	17.6534	+	10.1922i	0.615359	+	0.355277i	0.775060	−	0.631888i	$-0.217720\pi$
$823$	17.6534	+	10.1922i	0.615359	+	0.355277i	−0.159701	+	0.987165i	$0.551053\pi$
$824$	−35.6277	+	30.9152i	−1.24115	+	1.07698i
$825$		0			0
$826$	−15.3937	+	0.513166i	−0.535614	+	0.0178553i
$827$	−17.5032			−0.608645			−0.304322	−	0.952569i	$-0.598430\pi$
$827$	−17.5032			−0.608645			−0.304322	+	0.952569i	$0.598430\pi$
$828$		0			0
$829$	−5.39915	+	9.35160i	−0.187520	+	0.324794i	−0.944423	−	0.328733i	$-0.893378\pi$
$829$	−5.39915	+	9.35160i	−0.187520	+	0.324794i	0.756903	+	0.653528i	$0.226712\pi$
$830$	43.4146	+	21.5043i	1.50694	+	0.746424i
$831$		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
$836$	27.1511	+	11.3578i	0.939039	+	0.392819i
$837$		0			0
$838$	−21.0915	−	31.6855i	−0.728593	−	1.09456i
$839$	−8.78448			−0.303274			−0.151637	−	0.988436i	$-0.548454\pi$
$839$	−8.78448			−0.303274			−0.151637	+	0.988436i	$0.548454\pi$
$840$		0			0
$841$	8.41964			0.290332
$842$	3.69324	+	5.54832i	0.127277	+	0.191208i
$843$		0			0
$844$	−16.8448	−	7.04652i	−0.579821	−	0.242551i
$845$	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
$850$	8.48626	+	4.20344i	0.291076	+	0.144177i
$851$	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	$0.478877\pi$
$854$	−1.77989	+	3.33474i	−0.0609065	+	0.114112i
$855$		0			0
$856$	−10.6346	−	12.2556i	−0.363483	−	0.418889i
$857$	−37.4794	−	21.6387i	−1.28027	−	0.739165i	−0.303374	−	0.952872i	$-0.598113\pi$
$857$	−37.4794	−	21.6387i	−1.28027	−	0.739165i	−0.976898	+	0.213707i	$0.931446\pi$
$858$		0			0
$859$	13.7614	−	7.94516i	0.469534	−	0.271086i	−0.246511	−	0.969140i	$-0.579284\pi$
$859$	13.7614	−	7.94516i	0.469534	−	0.271086i	0.716045	+	0.698055i	$0.245951\pi$
$860$	−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	$-0.224181\pi$
$863$	−5.27921	−	9.14387i	−0.179707	−	0.311261i	−0.941780	+	0.336230i	$0.890848\pi$
$864$		0			0
$865$	24.0744	−	41.6980i	0.818553	−	1.41777i
$866$	27.2699	+	40.9674i	0.926669	+	1.39213i
$867$		0			0
$868$	−5.06730	+	3.62235i	−0.171995	+	0.122951i
$869$		−	40.7313i		−	1.38171i
$870$		0			0
$871$	57.1860	+	33.0163i	1.93767	+	1.11872i
$872$	2.60998	−	7.55815i	0.0883852	−	0.255951i
$873$		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	0.880468	−	0.474105i	$-0.157228\pi$
$877$	0.877972	+	1.52069i	0.0296470	+	0.0513501i	−0.850821	+	0.525455i	$0.823895\pi$
$878$	−44.9646	−	22.2720i	−1.51748	−	0.751644i
$879$		0			0
$880$	−32.6611	+	32.2070i	−1.10101	+	1.08570i
$881$		−	39.9987i		−	1.34759i	−0.738917	−	0.673796i	$-0.764663\pi$
$881$		−	39.9987i		−	1.34759i	0.738917	−	0.673796i	$-0.235337\pi$
$882$		0			0
$883$		−	15.9005i		−	0.535096i	−0.963545	−	0.267548i	$-0.913787\pi$
$883$		−	15.9005i		−	0.535096i	0.963545	−	0.267548i	$-0.0862133\pi$
$884$	46.6181	−	35.5127i	1.56793	−	1.19442i
$885$		0			0
$886$	−6.87868	+	13.8873i	−0.231094	+	0.466552i
$887$	−16.6867	−	28.9023i	−0.560286	−	0.970443i	−0.997471	−	0.0710719i	$-0.977358\pi$
$887$	−16.6867	−	28.9023i	−0.560286	−	0.970443i	0.437186	−	0.899371i	$-0.355975\pi$
$888$		0			0
$889$	−1.22353	+	40.2672i	−0.0410357	+	1.35052i
$890$	29.9462	−	1.91015i	1.00380	−	0.0640284i
$891$		0			0
$892$	43.9835	+	18.3992i	1.47268	+	0.616050i
$893$	14.9848	+	8.65150i	0.501449	+	0.289511i
$894$		0			0
$895$			29.9978i			1.00272i
$896$	24.1573	+	17.6755i	0.807039	+	0.590498i
$897$		0			0
$898$	31.9829	−	21.2894i	1.06728	−	0.710436i
$899$	−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	$-0.542470\pi$
$907$	−31.8593	−	18.3940i	−1.05787	−	0.610762i	−0.924842	+	0.380351i	$0.875803\pi$
$908$	−12.1346	−	15.9293i	−0.402701	−	0.528631i
$909$		0			0
$910$	42.8996	+	22.8973i	1.42211	+	0.759038i
$911$	−46.9066			−1.55409			−0.777043	−	0.629448i	$-0.783281\pi$
$911$	−46.9066			−1.55409			−0.777043	+	0.629448i	$0.783281\pi$
$912$		0			0
$913$	−31.7154	+	54.9326i	−1.04963	+	1.81800i
$914$	−24.2054	+	48.8679i	−0.800643	+	1.61641i
$915$		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	$-0.570636\pi$
$919$	15.6017	−	9.00763i	0.514652	−	0.297134i	0.734744	+	0.678345i	$0.237302\pi$
$920$	4.78206	+	1.65134i	0.157660	+	0.0544432i
$921$		0			0
$922$	15.9568	−	10.6216i	0.525509	−	0.349805i
$923$	38.1750			1.25654
$924$		0			0
$925$	−3.23779			−0.106458
$926$	20.9038	−	13.9146i	0.686940	−	0.457262i
$927$		0			0
$928$	25.1248	+	5.22660i	0.824761	+	0.171571i
$929$	−28.2618	+	16.3170i	−0.927241	+	0.535343i	−0.885938	−	0.463804i	$-0.846484\pi$
$929$	−28.2618	+	16.3170i	−0.927241	+	0.535343i	−0.0413031	+	0.999147i	$0.513151\pi$
$930$		0			0
$931$	20.0028	−	9.98139i	0.655565	−	0.327127i
$932$	−2.22808	−	17.3942i	−0.0729833	−	0.569768i
$933$		0			0
$934$	6.77883	−	13.6857i	0.221810	−	0.447809i
$935$	−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	$0.478771\pi$
$938$	1.57632	+	47.2855i	0.0514686	+	1.54393i
$939$		0			0
$940$	−21.4522	+	16.3419i	−0.699695	+	0.533014i
$941$	−21.3871	−	12.3478i	−0.697198	−	0.402527i	0.109105	−	0.994030i	$-0.465202\pi$
$941$	−21.3871	−	12.3478i	−0.697198	−	0.402527i	−0.806303	+	0.591503i	$0.798535\pi$
$942$		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	0.992814	+	0.119665i	$0.0381822\pi$
$947$	18.4653	+	31.9828i	0.600040	+	1.03930i	−0.392774	+	0.919635i	$0.628485\pi$
$948$		0			0
$949$	−25.1655	+	43.5879i	−0.816906	+	1.41492i
$950$	−4.48691	+	2.98671i	−0.145575	+	0.0969018i
$951$		0			0
$952$	39.2546	+	14.9046i	1.27225	+	0.483060i
$953$			61.5883i			1.99504i	0.0703720	+	0.997521i	$0.477581\pi$
$953$			61.5883i			1.99504i	−0.0703720	+	0.997521i	$0.522419\pi$
$954$		0			0
$955$	−22.8807	−	13.2102i	−0.740404	−	0.427472i
$956$	−10.1407	+	24.2415i	−0.327974	+	0.784025i
$957$		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
$962$	−8.89315	+	17.9542i	−0.286727	+	0.578868i
$963$		0			0
$964$	26.7405	+	35.1026i	0.861252	+	1.13058i
$965$			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	$0.880320\pi$
$968$	−18.9681	−	21.8595i	−0.609658	−	0.702590i
$969$		0			0
$970$	33.8190	+	16.7514i	1.08586	+	0.537854i
$971$	24.0937	+	41.7315i	0.773203	+	1.33923i	0.935799	+	0.352534i	$0.114680\pi$
$971$	24.0937	+	41.7315i	0.773203	+	1.33923i	−0.162596	+	0.986693i	$0.551987\pi$
$972$		0			0
$973$	−0.826871	+	27.2130i	−0.0265083	+	0.872409i
$974$	−1.30819	−	20.5091i	−0.0419172	−	0.657154i
$975$		0			0
$976$	1.07319	−	3.89589i	0.0343519	−	0.124704i
$977$	27.2570	+	15.7368i	0.872028	+	0.503466i	0.868022	−	0.496526i	$-0.165391\pi$
$977$	27.2570	+	15.7368i	0.872028	+	0.503466i	0.00400663	+	0.999992i	$0.498725\pi$
$978$		0			0
$979$			39.2865i			1.25560i
$980$	2.32037	+	34.7640i	0.0741216	+	1.11049i
$981$		0			0
$982$	−20.3765	−	30.6114i	−0.650240	−	0.976850i
$983$	−20.0440	+	34.7172i	−0.639304	+	1.10731i	0.346282	+	0.938130i	$0.387444\pi$
$983$	−20.0440	+	34.7172i	−0.639304	+	1.10731i	−0.985586	+	0.169176i	$0.945889\pi$
$984$		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	$-0.638837\pi$
$991$	−44.6593	−	25.7841i	−1.41865	−	0.819058i	−0.996180	+	0.0873196i	$0.972170\pi$
$992$	4.43420	−	4.96786i	0.140786	−	0.157730i
$993$		0			0
$994$	14.4576	+	23.2187i	0.458567	+	0.736452i
$995$	34.9644			1.10845
$996$		0			0
$997$	10.7581	−	18.6335i	0.340712	−	0.590130i	−0.643853	−	0.765149i	$-0.722665\pi$
$997$	10.7581	−	18.6335i	0.340712	−	0.590130i	0.984565	+	0.175019i	$0.0559986\pi$
$998$	3.47579	+	1.72164i	0.110024	+	0.0544975i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.be.a.107.5	✓	32	84.23	even	6	inner
252.2.be.a.107.7	yes	32	7.2	even	3	inner
252.2.be.a.107.10	yes	32	21.2	odd	6	inner
252.2.be.a.107.12	yes	32	28.23	odd	6	inner
252.2.be.a.179.5	yes	32	1.1	even	1	trivial
252.2.be.a.179.7	yes	32	12.11	even	2	inner
252.2.be.a.179.10	yes	32	4.3	odd	2	inner
252.2.be.a.179.12	yes	32	3.2	odd	2	inner
1764.2.e.h.1079.1		16	28.3	even	6
1764.2.e.h.1079.2		16	21.17	even	6
1764.2.e.h.1079.15		16	7.3	odd	6
1764.2.e.h.1079.16		16	84.59	odd	6
1764.2.e.i.1079.1		16	28.11	odd	6
1764.2.e.i.1079.2		16	21.11	odd	6
1764.2.e.i.1079.15		16	7.4	even	3
1764.2.e.i.1079.16		16	84.11	even	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)

\(f(q)\)	\(=\)	\(q+(-0.783636 - 1.17725i) q^{2} +(-0.771830 + 1.84507i) q^{4} +(2.15525 - 1.24433i) q^{5} +(-2.64453 - 0.0803545i) q^{7} +(2.77694 - 0.537226i) q^{8} +O(q^{10})\)	\(q+(-0.783636 - 1.17725i) q^{2} +(-0.771830 + 1.84507i) q^{4} +(2.15525 - 1.24433i) q^{5} +(-2.64453 - 0.0803545i) q^{7} +(2.77694 - 0.537226i) q^{8} +(-3.15382 - 1.56216i) q^{10} +(2.30393 - 3.99053i) q^{11} +5.22221 q^{13} +(1.97775 + 3.17624i) q^{14} +(-2.80856 - 2.84816i) q^{16} +(-4.85928 - 2.80550i) q^{17} +(2.76570 - 1.59678i) q^{19} +(0.632394 + 4.93699i) q^{20} +(-6.50329 + 0.414819i) q^{22} +(0.359366 + 0.622440i) q^{23} +(0.596726 - 1.03356i) q^{25} +(-4.09231 - 6.14784i) q^{26} +(2.18939 - 4.81732i) q^{28} -4.53656i q^{29} +(-1.01944 - 0.588574i) q^{31} +(-1.15211 + 5.53829i) q^{32} +(0.505125 + 7.91907i) q^{34} +(-5.79960 + 3.11749i) q^{35} +(-1.35648 - 2.34949i) q^{37} +(-4.04710 - 2.00462i) q^{38} +(5.31650 - 4.61329i) q^{40} +3.83670i q^{41} +11.1773i q^{43} +(5.58456 + 7.33093i) q^{44} +(0.451155 - 0.910829i) q^{46} +(2.70905 + 4.69222i) q^{47} +(6.98709 + 0.425000i) q^{49} +(-1.68437 + 0.107439i) q^{50} +(-4.03066 + 9.63533i) q^{52} +(1.79114 + 1.03411i) q^{53} -11.4674i q^{55} +(-7.38687 + 1.19757i) q^{56} +(-5.34066 + 3.55501i) q^{58} +(-2.05821 + 3.56492i) q^{59} +(0.505125 + 0.874903i) q^{61} +(0.105972 + 1.66136i) q^{62} +(7.42278 - 2.98369i) q^{64} +(11.2552 - 6.49816i) q^{65} +(10.9505 + 6.32230i) q^{67} +(8.92688 - 6.80033i) q^{68} +(8.21484 + 4.38460i) q^{70} +7.31012 q^{71} +(-4.81894 + 8.34664i) q^{73} +(-1.70295 + 3.43806i) q^{74} +(0.811513 + 6.33534i) q^{76} +(-6.41348 + 10.3680i) q^{77} +(7.65524 - 4.41975i) q^{79} +(-9.59719 - 2.64371i) q^{80} +(4.51675 - 3.00658i) q^{82} -13.7657 q^{83} -13.9639 q^{85} +(13.1585 - 8.75895i) q^{86} +(4.25407 - 12.3192i) q^{88} +(-7.38369 + 4.26297i) q^{89} +(-13.8103 - 0.419628i) q^{91} +(-1.42581 + 0.182637i) q^{92} +(3.40100 - 6.86622i) q^{94} +(3.97384 - 6.88289i) q^{95} -10.7232 q^{97} +(-4.97500 - 8.55858i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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