LMFDB - Embedded newform 352.2.u.a.63.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(63,352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("352.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.u (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			63.7
Character	$\chi$	$=$	352.63
Dual form			352.2.u.a.95.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.203695 - 0.0661845i) q^{3} +(-2.13352 - 1.55009i) q^{5} +(0.527338 - 1.62298i) q^{7} +(-2.38994 + 1.73639i) q^{9} +(1.26343 - 3.06655i) q^{11} +(-2.73662 - 3.76664i) q^{13} +(-0.537180 - 0.174540i) q^{15} +(-1.77161 + 2.43842i) q^{17} +(-0.492146 - 1.51467i) q^{19} -0.365494i q^{21} -8.03509i q^{23} +(0.604034 + 1.85903i) q^{25} +(-0.749568 + 1.03169i) q^{27} +(-2.32022 - 0.753886i) q^{29} +(5.53948 + 7.62444i) q^{31} +(0.0543955 - 0.708261i) q^{33} +(-3.64085 + 2.64524i) q^{35} +(1.53910 - 4.73687i) q^{37} +(-0.806730 - 0.586124i) q^{39} +(1.57746 - 0.512547i) q^{41} +9.57239 q^{43} +7.79055 q^{45} +(-3.70413 + 1.20354i) q^{47} +(3.30714 + 2.40278i) q^{49} +(-0.199483 + 0.613946i) q^{51} +(-5.94812 + 4.32156i) q^{53} +(-7.44899 + 4.58412i) q^{55} +(-0.200496 - 0.275958i) q^{57} +(-9.81950 - 3.19055i) q^{59} +(1.64877 - 2.26934i) q^{61} +(1.55782 + 4.79449i) q^{63} +12.2782i q^{65} +3.30153i q^{67} +(-0.531799 - 1.63671i) q^{69} +(2.88284 - 3.96789i) q^{71} +(10.6384 + 3.45664i) q^{73} +(0.246078 + 0.338697i) q^{75} +(-4.31070 - 3.66763i) q^{77} +(-0.845348 + 0.614182i) q^{79} +(2.65423 - 8.16887i) q^{81} +(7.73406 + 5.61912i) q^{83} +(7.55954 - 2.45624i) q^{85} -0.522514 q^{87} +5.42112 q^{89} +(-7.55630 + 2.45519i) q^{91} +(1.63298 + 1.18643i) q^{93} +(-1.29788 + 3.99445i) q^{95} +(-2.20369 + 1.60107i) q^{97} +(2.30523 + 9.52268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{9} + 4 q^{25} + 36 q^{33} + 40 q^{41} - 96 q^{45} - 4 q^{49} - 8 q^{53} + 20 q^{57} - 8 q^{69} - 40 q^{73} - 72 q^{77} - 72 q^{81} - 80 q^{85} - 40 q^{89} + 8 q^{93} + 4 q^{97}+O(q^{100}) $ 48 * q + 4 * q^9 + 4 * q^25 + 36 * q^33 + 40 * q^41 - 96 * q^45 - 4 * q^49 - 8 * q^53 + 20 * q^57 - 8 * q^69 - 40 * q^73 - 72 * q^77 - 72 * q^81 - 80 * q^85 - 40 * q^89 + 8 * q^93 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.203695	−	0.0661845i	0.117603	−	0.0382117i	−0.249624	−	0.968343i	$-0.580307\pi$
$3$	0.203695	−	0.0661845i	0.117603	−	0.0382117i	0.367227	+	0.930131i	$0.380307\pi$
$4$		0			0
$5$	−2.13352	−	1.55009i	−0.954139	−	0.693223i	−0.00235695	−	0.999997i	$-0.500750\pi$
$5$	−2.13352	−	1.55009i	−0.954139	−	0.693223i	−0.951782	+	0.306775i	$0.900750\pi$
$6$		0			0
$7$	0.527338	−	1.62298i	0.199315	−	0.613429i	−0.800584	−	0.599220i	$-0.795477\pi$
$7$	0.527338	−	1.62298i	0.199315	−	0.613429i	0.999899	−	0.0142080i	$-0.00452271\pi$
$8$		0			0
$9$	−2.38994	+	1.73639i	−0.796647	+	0.578798i
$10$		0			0
$11$	1.26343	−	3.06655i	0.380938	−	0.924601i
$11$	1.26343	−	3.06655i	0.380938	−	0.924601i
$12$		0			0
$13$	−2.73662	−	3.76664i	−0.759003	−	1.04468i	−0.997296	−	0.0734848i	$-0.976588\pi$
$13$	−2.73662	−	3.76664i	−0.759003	−	1.04468i	0.238293	−	0.971193i	$-0.423412\pi$
$14$		0			0
$15$	−0.537180	−	0.174540i	−0.138699	−	0.0450661i
$16$		0			0
$17$	−1.77161	+	2.43842i	−0.429679	+	0.591403i	−0.967880	−	0.251414i	$-0.919104\pi$
$17$	−1.77161	+	2.43842i	−0.429679	+	0.591403i	0.538200	+	0.842817i	$0.319104\pi$
$18$		0			0
$19$	−0.492146	−	1.51467i	−0.112906	−	0.347489i	0.878598	−	0.477561i	$-0.158479\pi$
$19$	−0.492146	−	1.51467i	−0.112906	−	0.347489i	−0.991505	+	0.130072i	$0.958479\pi$
$20$		0			0
$21$		−	0.365494i		−	0.0797574i
$22$		0			0
$23$		−	8.03509i		−	1.67543i	−0.546106	−	0.837716i	$-0.683890\pi$
$23$		−	8.03509i		−	1.67543i	0.546106	−	0.837716i	$-0.316110\pi$
$24$		0			0
$25$	0.604034	+	1.85903i	0.120807	+	0.371805i
$26$		0			0
$27$	−0.749568	+	1.03169i	−0.144254	+	0.198549i
$28$		0			0
$29$	−2.32022	−	0.753886i	−0.430855	−	0.139993i	0.0855577	−	0.996333i	$-0.472733\pi$
$29$	−2.32022	−	0.753886i	−0.430855	−	0.139993i	−0.516412	+	0.856340i	$0.672733\pi$
$30$		0			0
$31$	5.53948	+	7.62444i	0.994920	+	1.36939i	0.928391	+	0.371605i	$0.121192\pi$
$31$	5.53948	+	7.62444i	0.994920	+	1.36939i	0.0665288	+	0.997785i	$0.478808\pi$
$32$		0			0
$33$	0.0543955	−	0.708261i	0.00946905	−	0.123292i
$34$		0			0
$35$	−3.64085	+	2.64524i	−0.615417	+	0.447126i
$36$		0			0
$37$	1.53910	−	4.73687i	0.253027	−	0.778736i	−0.741185	−	0.671300i	$-0.765736\pi$
$37$	1.53910	−	4.73687i	0.253027	−	0.778736i	0.994212	−	0.107436i	$-0.0342640\pi$
$38$		0			0
$39$	−0.806730	−	0.586124i	−0.129180	−	0.0938549i
$40$		0			0
$41$	1.57746	−	0.512547i	0.246357	−	0.0800464i	−0.183235	−	0.983069i	$-0.558657\pi$
$41$	1.57746	−	0.512547i	0.246357	−	0.0800464i	0.429593	+	0.903023i	$0.358657\pi$
$42$		0			0
$43$	9.57239			1.45978			0.729888	−	0.683567i	$-0.239572\pi$
$43$	9.57239			1.45978			0.729888	+	0.683567i	$0.239572\pi$
$44$		0			0
$45$	7.79055			1.16135
$46$		0			0
$47$	−3.70413	+	1.20354i	−0.540303	+	0.175555i	−0.566439	−	0.824103i	$-0.691679\pi$
$47$	−3.70413	+	1.20354i	−0.540303	+	0.175555i	0.0261367	+	0.999658i	$0.491679\pi$
$48$		0			0
$49$	3.30714	+	2.40278i	0.472449	+	0.343254i
$50$		0			0
$51$	−0.199483	+	0.613946i	−0.0279332	+	0.0859697i
$52$		0			0
$53$	−5.94812	+	4.32156i	−0.817037	+	0.593612i	−0.915862	−	0.401493i	$-0.868491\pi$
$53$	−5.94812	+	4.32156i	−0.817037	+	0.593612i	0.0988255	+	0.995105i	$0.468491\pi$
$54$		0			0
$55$	−7.44899	+	4.58412i	−1.00442	+	0.618123i
$56$		0			0
$57$	−0.200496	−	0.275958i	−0.0265563	−	0.0365516i
$58$		0			0
$59$	−9.81950	−	3.19055i	−1.27839	−	0.415374i	−0.410377	−	0.911916i	$-0.634603\pi$
$59$	−9.81950	−	3.19055i	−1.27839	−	0.415374i	−0.868013	+	0.496542i	$0.834603\pi$
$60$		0			0
$61$	1.64877	−	2.26934i	0.211103	−	0.290559i	−0.690314	−	0.723510i	$-0.742528\pi$
$61$	1.64877	−	2.26934i	0.211103	−	0.290559i	0.901417	+	0.432951i	$0.142528\pi$
$62$		0			0
$63$	1.55782	+	4.79449i	0.196267	+	0.604049i
$64$		0			0
$65$			12.2782i			1.52293i
$66$		0			0
$67$			3.30153i			0.403346i	0.979453	+	0.201673i	$0.0646379\pi$
$67$			3.30153i			0.403346i	−0.979453	+	0.201673i	$0.935362\pi$
$68$		0			0
$69$	−0.531799	−	1.63671i	−0.0640210	−	0.197036i
$70$		0			0
$71$	2.88284	−	3.96789i	0.342130	−	0.470901i	−0.602932	−	0.797792i	$-0.706001\pi$
$71$	2.88284	−	3.96789i	0.342130	−	0.470901i	0.945062	+	0.326891i	$0.106001\pi$
$72$		0			0
$73$	10.6384	+	3.45664i	1.24513	+	0.404569i	0.856175	−	0.516686i	$-0.172834\pi$
$73$	10.6384	+	3.45664i	1.24513	+	0.404569i	0.388960	+	0.921255i	$0.372834\pi$
$74$		0			0
$75$	0.246078	+	0.338697i	0.0284146	+	0.0391093i
$76$		0			0
$77$	−4.31070	−	3.66763i	−0.491250	−	0.417965i
$78$		0			0
$79$	−0.845348	+	0.614182i	−0.0951091	+	0.0691008i	−0.634323	−	0.773068i	$-0.718721\pi$
$79$	−0.845348	+	0.614182i	−0.0951091	+	0.0691008i	0.539214	+	0.842169i	$0.318721\pi$
$80$		0			0
$81$	2.65423	−	8.16887i	0.294914	−	0.907652i
$82$		0			0
$83$	7.73406	+	5.61912i	0.848923	+	0.616779i	0.924849	−	0.380335i	$-0.124191\pi$
$83$	7.73406	+	5.61912i	0.848923	+	0.616779i	−0.0759260	+	0.997113i	$0.524191\pi$
$84$		0			0
$85$	7.55954	−	2.45624i	0.819947	−	0.266417i
$86$		0			0
$87$	−0.522514			−0.0560193
$88$		0			0
$89$	5.42112			0.574638			0.287319	−	0.957835i	$-0.407236\pi$
$89$	5.42112			0.574638			0.287319	+	0.957835i	$0.407236\pi$
$90$		0			0
$91$	−7.55630	+	2.45519i	−0.792116	+	0.257374i
$92$		0			0
$93$	1.63298	+	1.18643i	0.169333	+	0.123027i
$94$		0			0
$95$	−1.29788	+	3.99445i	−0.133159	+	0.409822i
$96$		0			0
$97$	−2.20369	+	1.60107i	−0.223751	+	0.162564i	−0.694013	−	0.719962i	$-0.744159\pi$
$97$	−2.20369	+	1.60107i	−0.223751	+	0.162564i	0.470263	+	0.882526i	$0.344159\pi$
$98$		0			0
$99$	2.30523	+	9.52268i	0.231684	+	0.957066i
$100$		0			0
$101$	4.88070	+	6.71770i	0.485647	+	0.668436i	0.979578	−	0.201065i	$-0.0644403\pi$
$101$	4.88070	+	6.71770i	0.485647	+	0.668436i	−0.493931	+	0.869501i	$0.664440\pi$
$102$		0			0
$103$	6.38505	+	2.07463i	0.629137	+	0.204419i	0.606193	−	0.795318i	$-0.292696\pi$
$103$	6.38505	+	2.07463i	0.629137	+	0.204419i	0.0229444	+	0.999737i	$0.492696\pi$
$104$		0			0
$105$	−0.566550	+	0.779790i	−0.0552897	+	0.0760997i
$106$		0			0
$107$	−3.85289	−	11.8580i	−0.372473	−	1.14635i	−0.945168	−	0.326585i	$-0.894102\pi$
$107$	−3.85289	−	11.8580i	−0.372473	−	1.14635i	0.572695	−	0.819769i	$-0.305898\pi$
$108$		0			0
$109$			15.1941i			1.45533i	0.685931	+	0.727667i	$0.259395\pi$
$109$			15.1941i			1.45533i	−0.685931	+	0.727667i	$0.740605\pi$
$110$		0			0
$111$		−	1.06674i		−	0.101251i
$112$		0			0
$113$	−5.77147	−	17.7628i	−0.542934	−	1.67098i	−0.725852	−	0.687851i	$-0.758554\pi$
$113$	−5.77147	−	17.7628i	−0.542934	−	1.67098i	0.182918	−	0.983128i	$-0.441446\pi$
$114$		0			0
$115$	−12.4551	+	17.1430i	−1.16145	+	1.59860i
$116$		0			0
$117$	13.0807	+	4.25019i	1.20931	+	0.392930i
$118$		0			0
$119$	3.02326	+	4.16116i	0.277142	+	0.381453i
$120$		0			0
$121$	−7.80750	−	7.74874i	−0.709773	−	0.704431i
$122$		0			0
$123$	0.287397	−	0.208806i	0.0259138	−	0.0188274i
$124$		0			0
$125$	−2.48172	+	7.63794i	−0.221971	+	0.683158i
$126$		0			0
$127$	−1.87275	−	1.36063i	−0.166180	−	0.120737i	0.501587	−	0.865107i	$-0.332750\pi$
$127$	−1.87275	−	1.36063i	−0.166180	−	0.120737i	−0.667767	+	0.744371i	$0.732750\pi$
$128$		0			0
$129$	1.94985	−	0.633544i	0.171675	−	0.0557804i
$130$		0			0
$131$	19.9100			1.73954			0.869771	−	0.493455i	$-0.164266\pi$
$131$	19.9100			1.73954			0.869771	+	0.493455i	$0.164266\pi$
$132$		0			0
$133$	−2.71781			−0.235664
$134$		0			0
$135$	3.19844	−	1.03923i	0.275278	−	0.0894431i
$136$		0			0
$137$	−16.5687	−	12.0379i	−1.41556	−	1.02846i	−0.992485	−	0.122369i	$-0.960951\pi$
$137$	−16.5687	−	12.0379i	−1.41556	−	1.02846i	−0.423074	−	0.906095i	$-0.639049\pi$
$138$		0			0
$139$	5.91406	−	18.2016i	0.501624	−	1.54384i	−0.304748	−	0.952433i	$-0.598572\pi$
$139$	5.91406	−	18.2016i	0.501624	−	1.54384i	0.806372	−	0.591408i	$-0.201428\pi$
$140$		0			0
$141$	−0.674857	+	0.490312i	−0.0568332	+	0.0412917i
$142$		0			0
$143$	−15.0081	+	3.63313i	−1.25504	+	0.303817i
$144$		0			0
$145$	3.78165	+	5.20499i	0.314049	+	0.432251i
$146$		0			0
$147$	0.832675	+	0.270553i	0.0686779	+	0.0223148i
$148$		0			0
$149$	−5.23114	+	7.20004i	−0.428552	+	0.589851i	−0.967620	−	0.252411i	$-0.918776\pi$
$149$	−5.23114	+	7.20004i	−0.428552	+	0.589851i	0.539068	+	0.842262i	$0.318776\pi$
$150$		0			0
$151$	−6.98388	−	21.4942i	−0.568340	−	1.74917i	−0.657812	−	0.753182i	$-0.728518\pi$
$151$	−6.98388	−	21.4942i	−0.568340	−	1.74917i	0.0894723	−	0.995989i	$-0.471482\pi$
$152$		0			0
$153$		−	8.90388i		−	0.719836i
$154$		0			0
$155$		−	24.8536i		−	1.99629i
$156$		0			0
$157$	−1.12642	−	3.46677i	−0.0898983	−	0.276678i	0.895992	−	0.444070i	$-0.146466\pi$
$157$	−1.12642	−	3.46677i	−0.0898983	−	0.276678i	−0.985891	+	0.167391i	$0.946466\pi$
$158$		0			0
$159$	−0.925581	+	1.27395i	−0.0734034	+	0.101031i
$160$		0			0
$161$	−13.0408	−	4.23721i	−1.02776	−	0.333939i
$162$		0			0
$163$	−3.66631	−	5.04624i	−0.287167	−	0.395252i	0.640924	−	0.767604i	$-0.278551\pi$
$163$	−3.66631	−	5.04624i	−0.287167	−	0.395252i	−0.928091	+	0.372352i	$0.878551\pi$
$164$		0			0
$165$	−1.21392	+	1.42677i	−0.0945039	+	0.111074i
$166$		0			0
$167$	16.8068	−	12.2109i	1.30055	−	0.944905i	0.300590	−	0.953753i	$-0.402816\pi$
$167$	16.8068	−	12.2109i	1.30055	−	0.944905i	0.999961	+	0.00884802i	$0.00281645\pi$
$168$		0			0
$169$	−2.68124	+	8.25202i	−0.206250	+	0.634771i
$170$		0			0
$171$	3.80626	+	2.76541i	0.291072	+	0.211476i
$172$		0			0
$173$	1.20413	−	0.391244i	0.0915480	−	0.0297458i	−0.262885	−	0.964827i	$-0.584674\pi$
$173$	1.20413	−	0.391244i	0.0915480	−	0.0297458i	0.354433	+	0.935081i	$0.384674\pi$
$174$		0			0
$175$	3.33569			0.252155
$176$		0			0
$177$	−2.21135			−0.166215
$178$		0			0
$179$	−16.3890	+	5.32511i	−1.22497	+	0.398018i	−0.848890	−	0.528569i	$-0.822729\pi$
$179$	−16.3890	+	5.32511i	−1.22497	+	0.398018i	−0.376082	+	0.926587i	$0.622729\pi$
$180$		0			0
$181$	−17.0365	−	12.3778i	−1.26632	−	0.920033i	−0.267267	−	0.963622i	$-0.586121\pi$
$181$	−17.0365	−	12.3778i	−1.26632	−	0.920033i	−0.999050	+	0.0435895i	$0.986121\pi$
$182$		0			0
$183$	0.185651	−	0.571375i	0.0137237	−	0.0422373i
$184$		0			0
$185$	−10.6263	+	7.72045i	−0.781260	+	0.567619i
$186$		0			0
$187$	5.23923	+	8.51351i	0.383130	+	0.622569i
$188$		0			0
$189$	1.27914	+	1.76058i	0.0930436	+	0.128064i
$190$		0			0
$191$	3.43605	+	1.11644i	0.248624	+	0.0807827i	0.430678	−	0.902506i	$-0.358275\pi$
$191$	3.43605	+	1.11644i	0.248624	+	0.0807827i	−0.182054	+	0.983289i	$0.558275\pi$
$192$		0			0
$193$	14.4497	−	19.8883i	1.04011	−	1.43159i	0.143036	−	0.989717i	$-0.454314\pi$
$193$	14.4497	−	19.8883i	1.04011	−	1.43159i	0.897077	−	0.441875i	$-0.145686\pi$
$194$		0			0
$195$	0.812629	+	2.50101i	0.0581935	+	0.179101i
$196$		0			0
$197$			11.1692i			0.795773i	0.917435	+	0.397887i	$0.130256\pi$
$197$			11.1692i			0.795773i	−0.917435	+	0.397887i	$0.869744\pi$
$198$		0			0
$199$			2.70968i			0.192084i	0.995377	+	0.0960421i	$0.0306183\pi$
$199$			2.70968i			0.192084i	−0.995377	+	0.0960421i	$0.969382\pi$
$200$		0			0
$201$	0.218510	+	0.672505i	0.0154125	+	0.0474349i
$202$		0			0
$203$	−2.44708	+	3.36812i	−0.171752	+	0.236396i
$204$		0			0
$205$	−4.16003	−	1.35168i	−0.290549	−	0.0944051i
$206$		0			0
$207$	13.9521	+	19.2034i	0.969736	+	1.33473i
$208$		0			0
$209$	−5.26661	−	0.404484i	−0.364299	−	0.0279787i
$210$		0			0
$211$	2.85530	−	2.07450i	0.196567	−	0.142814i	−0.485148	−	0.874432i	$-0.661234\pi$
$211$	2.85530	−	2.07450i	0.196567	−	0.142814i	0.681715	+	0.731618i	$0.261234\pi$
$212$		0			0
$213$	0.324607	−	0.999038i	0.0222417	−	0.0684529i
$214$		0			0
$215$	−20.4229	−	14.8381i	−1.39283	−	1.01195i
$216$		0			0
$217$	15.2955	−	4.96980i	1.03833	−	0.337372i
$218$		0			0
$219$	2.39577			0.161891
$220$		0			0
$221$	14.0329			0.943953
$222$		0			0
$223$	11.4136	−	3.70852i	0.764315	−	0.248341i	0.0991852	−	0.995069i	$-0.468376\pi$
$223$	11.4136	−	3.70852i	0.764315	−	0.248341i	0.665129	+	0.746728i	$0.268376\pi$
$224$		0			0
$225$	−4.67161	−	3.39412i	−0.311440	−	0.226275i
$226$		0			0
$227$	2.49511	−	7.67915i	0.165606	−	0.509683i	−0.833474	−	0.552558i	$-0.813652\pi$
$227$	2.49511	−	7.67915i	0.165606	−	0.509683i	0.999080	+	0.0428750i	$0.0136517\pi$
$228$		0			0
$229$	−7.56635	+	5.49728i	−0.499999	+	0.363270i	−0.809016	−	0.587786i	$-0.800000\pi$
$229$	−7.56635	+	5.49728i	−0.499999	+	0.363270i	0.309018	+	0.951056i	$0.400000\pi$
$230$		0			0
$231$	−1.12081	−	0.461776i	−0.0737438	−	0.0303826i
$232$		0			0
$233$	−6.74813	−	9.28800i	−0.442084	−	0.608477i	0.528589	−	0.848878i	$-0.322721\pi$
$233$	−6.74813	−	9.28800i	−0.442084	−	0.608477i	−0.970674	+	0.240401i	$0.922721\pi$
$234$		0			0
$235$	9.76844	+	3.17396i	0.637223	+	0.207046i
$236$		0			0
$237$	−0.131544	+	0.181055i	−0.00854470	+	0.0117608i
$238$		0			0
$239$	−3.93294	−	12.1044i	−0.254401	−	0.782966i	−0.993947	−	0.109860i	$-0.964960\pi$
$239$	−3.93294	−	12.1044i	−0.254401	−	0.782966i	0.739546	−	0.673106i	$-0.235040\pi$
$240$		0			0
$241$			24.8637i			1.60161i	0.598925	+	0.800805i	$0.295595\pi$
$241$			24.8637i			1.60161i	−0.598925	+	0.800805i	$0.704405\pi$
$242$		0			0
$243$		−	5.66535i		−	0.363432i
$244$		0			0
$245$	−3.33132	−	10.2528i	−0.212830	−	0.655025i
$246$		0			0
$247$	−4.35840	+	5.99882i	−0.277318	+	0.381696i
$248$		0			0
$249$	1.94729	+	0.632712i	0.123404	+	0.0400965i
$250$		0			0
$251$	−8.52918	−	11.7394i	−0.538357	−	0.740985i	0.450018	−	0.893019i	$-0.351417\pi$
$251$	−8.52918	−	11.7394i	−0.538357	−	0.740985i	−0.988375	+	0.152035i	$0.951417\pi$
$252$		0			0
$253$	−24.6400	−	10.1518i	−1.54911	−	0.638235i
$254$		0			0
$255$	1.37728	−	1.00065i	0.0862483	−	0.0626631i
$256$		0			0
$257$	1.12403	−	3.45940i	0.0701149	−	0.215791i	−0.909859	−	0.414918i	$-0.863810\pi$
$257$	1.12403	−	3.45940i	0.0701149	−	0.215791i	0.979974	+	0.199126i	$0.0638104\pi$
$258$		0			0
$259$	−6.87621	−	4.99586i	−0.427267	−	0.310428i
$260$		0			0
$261$	6.85424	−	2.22708i	0.424267	−	0.137853i
$262$		0			0
$263$	16.1086			0.993301			0.496651	−	0.867951i	$-0.334563\pi$
$263$	16.1086			0.993301			0.496651	+	0.867951i	$0.334563\pi$
$264$		0			0
$265$	19.3892			1.19107
$266$		0			0
$267$	1.10426	−	0.358795i	0.0675794	−	0.0219579i
$268$		0			0
$269$	16.4972	+	11.9859i	1.00585	+	0.730795i	0.963335	−	0.268301i	$-0.0864620\pi$
$269$	16.4972	+	11.9859i	1.00585	+	0.730795i	0.0425179	+	0.999096i	$0.486462\pi$
$270$		0			0
$271$	−5.92048	+	18.2214i	−0.359643	+	1.10687i	0.593624	+	0.804742i	$0.297696\pi$
$271$	−5.92048	+	18.2214i	−0.359643	+	1.10687i	−0.953268	+	0.302126i	$0.902304\pi$
$272$		0			0
$273$	−1.37669	+	1.00022i	−0.0833208	+	0.0605361i
$274$		0			0
$275$	6.46396	+	0.496442i	0.389791	+	0.0299366i
$276$		0			0
$277$	3.52281	+	4.84874i	0.211665	+	0.291332i	0.901628	−	0.432513i	$-0.142373\pi$
$277$	3.52281	+	4.84874i	0.211665	+	0.291332i	−0.689962	+	0.723845i	$0.742373\pi$
$278$		0			0
$279$	−26.4780	−	8.60324i	−1.58520	−	0.515062i
$280$		0			0
$281$	−12.3012	+	16.9312i	−0.733831	+	1.01003i	0.265119	+	0.964216i	$0.414589\pi$
$281$	−12.3012	+	16.9312i	−0.733831	+	1.01003i	−0.998950	+	0.0458156i	$0.985411\pi$
$282$		0			0
$283$	7.83212	+	24.1048i	0.465571	+	1.43288i	0.858263	+	0.513211i	$0.171544\pi$
$283$	7.83212	+	24.1048i	0.465571	+	1.43288i	−0.392692	+	0.919670i	$0.628456\pi$
$284$		0			0
$285$			0.899550i			0.0532847i
$286$		0			0
$287$		−	2.83046i		−	0.167077i
$288$		0			0
$289$	2.44603	+	7.52811i	0.143884	+	0.442830i
$290$		0			0
$291$	−0.342914	+	0.471981i	−0.0201020	+	0.0276680i
$292$		0			0
$293$	−0.999919	−	0.324893i	−0.0584159	−	0.0189805i	0.279663	−	0.960098i	$-0.409777\pi$
$293$	−0.999919	−	0.324893i	−0.0584159	−	0.0189805i	−0.338079	+	0.941118i	$0.609777\pi$
$294$		0			0
$295$	16.0045	+	22.0282i	0.931815	+	1.28253i
$296$		0			0
$297$	2.21671	+	3.60206i	0.128627	+	0.209013i
$298$		0			0
$299$	−30.2653	+	21.9890i	−1.75029	+	1.27166i
$300$		0			0
$301$	5.04788	−	15.5358i	0.290955	−	0.895468i
$302$		0			0
$303$	1.43878	+	1.04534i	0.0826558	+	0.0600530i
$304$		0			0
$305$	−7.03536	+	2.28593i	−0.402844	+	0.130892i
$306$		0			0
$307$	3.34827			0.191096			0.0955478	−	0.995425i	$-0.469540\pi$
$307$	3.34827			0.191096			0.0955478	+	0.995425i	$0.469540\pi$
$308$		0			0
$309$	1.43791			0.0817999
$310$		0			0
$311$	−17.4265	+	5.66222i	−0.988167	+	0.321075i	−0.758127	−	0.652106i	$-0.773886\pi$
$311$	−17.4265	+	5.66222i	−0.988167	+	0.321075i	−0.230039	+	0.973181i	$0.573886\pi$
$312$		0			0
$313$	5.02926	+	3.65397i	0.284271	+	0.206535i	0.720778	−	0.693166i	$-0.243785\pi$
$313$	5.02926	+	3.65397i	0.284271	+	0.206535i	−0.436507	+	0.899701i	$0.643785\pi$
$314$		0			0
$315$	4.10825	−	12.6439i	0.231474	−	0.712404i
$316$		0			0
$317$	9.21860	−	6.69770i	0.517768	−	0.376181i	−0.297994	−	0.954568i	$-0.596318\pi$
$317$	9.21860	−	6.69770i	0.517768	−	0.376181i	0.815762	+	0.578387i	$0.196318\pi$
$318$		0			0
$319$	−5.24327	+	6.16261i	−0.293567	+	0.345040i
$320$		0			0
$321$	−1.56963	−	2.16041i	−0.0876082	−	0.120582i
$322$		0			0
$323$	4.56529	+	1.48335i	0.254019	+	0.0825359i
$324$		0			0
$325$	5.34927	−	7.36264i	0.296724	−	0.408406i
$326$		0			0
$327$	1.00562	+	3.09497i	0.0556107	+	0.171152i
$328$		0			0
$329$			6.64640i			0.366428i
$330$		0			0
$331$			7.30164i			0.401334i	0.979659	+	0.200667i	$0.0643110\pi$
$331$			7.30164i			0.401334i	−0.979659	+	0.200667i	$0.935689\pi$
$332$		0			0
$333$	4.54670	+	13.9933i	0.249158	+	0.766829i
$334$		0			0
$335$	5.11768	−	7.04388i	0.279609	−	0.384848i
$336$		0			0
$337$	18.7126	+	6.08008i	1.01934	+	0.331203i	0.770567	−	0.637359i	$-0.219973\pi$
$337$	18.7126	+	6.08008i	1.01934	+	0.331203i	0.248772	+	0.968562i	$0.419973\pi$
$338$		0			0
$339$	−2.35124	−	3.23620i	−0.127702	−	0.175766i
$340$		0			0
$341$	30.3795	−	7.35418i	1.64514	−	0.398251i
$342$		0			0
$343$	15.3078	−	11.1217i	0.826542	−	0.600518i
$344$		0			0
$345$	−1.40245	+	4.31629i	−0.0755052	+	0.232381i
$346$		0			0
$347$	19.8309	+	14.4080i	1.06458	+	0.773462i	0.974930	−	0.222511i	$-0.0714255\pi$
$347$	19.8309	+	14.4080i	1.06458	+	0.773462i	0.0896491	+	0.995973i	$0.471425\pi$
$348$		0			0
$349$	3.94461	−	1.28168i	0.211150	−	0.0686068i	−0.201532	−	0.979482i	$-0.564592\pi$
$349$	3.94461	−	1.28168i	0.211150	−	0.0686068i	0.412682	+	0.910875i	$0.364592\pi$
$350$		0			0
$351$	5.93730			0.316909
$352$		0			0
$353$	16.3382			0.869595			0.434797	−	0.900528i	$-0.356820\pi$
$353$	16.3382			0.869595			0.434797	+	0.900528i	$0.356820\pi$
$354$		0			0
$355$	−12.3012	+	3.99690i	−0.652879	+	0.212133i
$356$		0			0
$357$	0.891227	+	0.647514i	0.0471687	+	0.0342701i
$358$		0			0
$359$	−6.64734	+	20.4584i	−0.350833	+	1.07975i	0.607553	+	0.794279i	$0.292151\pi$
$359$	−6.64734	+	20.4584i	−0.350833	+	1.07975i	−0.958386	+	0.285475i	$0.907849\pi$
$360$		0			0
$361$	13.3193	−	9.67704i	0.701016	−	0.509318i
$362$		0			0
$363$	−2.10320	−	1.06164i	−0.110389	−	0.0557218i
$364$		0			0
$365$	−17.3392	−	23.8654i	−0.907576	−	1.24917i
$366$		0			0
$367$	−24.7316	−	8.03579i	−1.29098	−	0.419465i	−0.418546	−	0.908196i	$-0.637460\pi$
$367$	−24.7316	−	8.03579i	−1.29098	−	0.419465i	−0.872435	+	0.488731i	$0.837460\pi$
$368$		0			0
$369$	−2.88004	+	3.96404i	−0.149929	+	0.206360i
$370$		0			0
$371$	3.87713	+	11.9326i	0.201291	+	0.619509i
$372$		0			0
$373$		−	14.6325i		−	0.757644i	−0.925469	−	0.378822i	$-0.876329\pi$
$373$		−	14.6325i		−	0.757644i	0.925469	−	0.378822i	$-0.123671\pi$
$374$		0			0
$375$			1.72006i			0.0888236i
$376$		0			0
$377$	3.50996	+	10.8026i	0.180772	+	0.556360i
$378$		0			0
$379$	−5.96084	+	8.20439i	−0.306188	+	0.421431i	−0.934188	−	0.356782i	$-0.883874\pi$
$379$	−5.96084	+	8.20439i	−0.306188	+	0.421431i	0.628000	+	0.778214i	$0.283874\pi$
$380$		0			0
$381$	−0.471523	−	0.153207i	−0.0241568	−	0.00784903i
$382$		0			0
$383$	12.9977	+	17.8898i	0.664151	+	0.914125i	0.999610	−	0.0279298i	$-0.00889149\pi$
$383$	12.9977	+	17.8898i	0.664151	+	0.914125i	−0.335459	+	0.942055i	$0.608891\pi$
$384$		0			0
$385$	3.51180	+	14.5069i	0.178978	+	0.739342i
$386$		0			0
$387$	−22.8774	+	16.6214i	−1.16292	+	0.844914i
$388$		0			0
$389$	0.280656	−	0.863770i	0.0142298	−	0.0437949i	−0.943689	−	0.330833i	$-0.892670\pi$
$389$	0.280656	−	0.863770i	0.0142298	−	0.0437949i	0.957919	+	0.287038i	$0.0926705\pi$
$390$		0			0
$391$	19.5929	+	14.2351i	0.990855	+	0.719898i
$392$		0			0
$393$	4.05556	−	1.31773i	0.204576	−	0.0664708i
$394$		0			0
$395$	2.75561			0.138650
$396$		0			0
$397$	−13.7241			−0.688795			−0.344397	−	0.938824i	$-0.611917\pi$
$397$	−13.7241			−0.688795			−0.344397	+	0.938824i	$0.611917\pi$
$398$		0			0
$399$	−0.553604	+	0.179877i	−0.0277149	+	0.00900510i
$400$		0			0
$401$	17.6269	+	12.8067i	0.880247	+	0.639537i	0.933317	−	0.359054i	$-0.116901\pi$
$401$	17.6269	+	12.8067i	0.880247	+	0.639537i	−0.0530696	+	0.998591i	$0.516901\pi$
$402$		0			0
$403$	13.5590	−	41.7304i	0.675424	−	2.07874i
$404$		0			0
$405$	−18.3253	+	13.3141i	−0.910594	+	0.661585i
$406$		0			0
$407$	−12.5813	−	10.7044i	−0.623633	−	0.530599i
$408$		0			0
$409$	13.1114	+	18.0462i	0.648315	+	0.892329i	0.999025	−	0.0441552i	$-0.0140596\pi$
$409$	13.1114	+	18.0462i	0.648315	+	0.892329i	−0.350710	+	0.936484i	$0.614060\pi$
$410$		0			0
$411$	−4.17168	−	1.35546i	−0.205774	−	0.0668600i
$412$		0			0
$413$	−10.3564	+	14.2543i	−0.509605	+	0.701411i
$414$		0			0
$415$	−7.79060	−	23.9770i	−0.382426	−	1.17699i
$416$		0			0
$417$		−	4.09900i		−	0.200729i
$418$		0			0
$419$			0.650359i			0.0317721i	0.999874	+	0.0158861i	$0.00505690\pi$
$419$			0.650359i			0.0317721i	−0.999874	+	0.0158861i	$0.994943\pi$
$420$		0			0
$421$	−9.68888	−	29.8193i	−0.472207	−	1.45330i	−0.849687	−	0.527287i	$-0.823209\pi$
$421$	−9.68888	−	29.8193i	−0.472207	−	1.45330i	0.377480	−	0.926018i	$-0.376791\pi$
$422$		0			0
$423$	6.76282	−	9.30822i	0.328820	−	0.452581i
$424$		0			0
$425$	−5.60319	−	1.82059i	−0.271795	−	0.0883115i
$426$		0			0
$427$	−2.81363	−	3.87262i	−0.136161	−	0.187409i
$428$		0			0
$429$	−2.81662	+	1.73336i	−0.135988	+	0.0836872i
$430$		0			0
$431$	7.90914	−	5.74632i	0.380970	−	0.276791i	−0.380775	−	0.924668i	$-0.624343\pi$
$431$	7.90914	−	5.74632i	0.380970	−	0.276791i	0.761745	+	0.647877i	$0.224343\pi$
$432$		0			0
$433$	3.60223	−	11.0865i	0.173112	−	0.532784i	−0.826430	−	0.563039i	$-0.809632\pi$
$433$	3.60223	−	11.0865i	0.173112	−	0.532784i	0.999542	+	0.0302550i	$0.00963193\pi$
$434$		0			0
$435$	1.11479	+	0.809945i	0.0534503	+	0.0388339i
$436$		0			0
$437$	−12.1705	+	3.95444i	−0.582195	+	0.189167i
$438$		0			0
$439$	−38.1079			−1.81879			−0.909395	−	0.415934i	$-0.863455\pi$
$439$	−38.1079			−1.81879			−0.909395	+	0.415934i	$0.863455\pi$
$440$		0			0
$441$	−12.0760			−0.575050
$442$		0			0
$443$	11.2524	−	3.65613i	0.534618	−	0.173708i	−0.0292512	−	0.999572i	$-0.509312\pi$
$443$	11.2524	−	3.65613i	0.534618	−	0.173708i	0.563869	+	0.825864i	$0.309312\pi$
$444$		0			0
$445$	−11.5661	−	8.40325i	−0.548285	−	0.398352i
$446$		0			0
$447$	−0.589025	+	1.81283i	−0.0278599	+	0.0857441i
$448$		0			0
$449$	−23.5892	+	17.1386i	−1.11324	+	0.808818i	−0.983171	−	0.182686i	$-0.941521\pi$
$449$	−23.5892	+	17.1386i	−1.11324	+	0.808818i	−0.130072	+	0.991505i	$0.541521\pi$
$450$		0			0
$451$	0.421250	−	5.48492i	0.0198359	−	0.258275i
$452$		0			0
$453$	−2.84516	−	3.91603i	−0.133677	−	0.183991i
$454$		0			0
$455$	19.9273	+	6.47477i	0.934206	+	0.303542i
$456$		0			0
$457$	−17.9011	+	24.6388i	−0.837379	+	1.15255i	0.149126	+	0.988818i	$0.452354\pi$
$457$	−17.9011	+	24.6388i	−0.837379	+	1.15255i	−0.986504	+	0.163735i	$0.947646\pi$
$458$		0			0
$459$	−1.18775	−	3.65552i	−0.0554394	−	0.170625i
$460$		0			0
$461$		−	4.84521i		−	0.225664i	−0.993614	−	0.112832i	$-0.964008\pi$
$461$		−	4.84521i		−	0.225664i	0.993614	−	0.112832i	$-0.0359922\pi$
$462$		0			0
$463$		−	7.94598i		−	0.369281i	−0.982806	−	0.184640i	$-0.940888\pi$
$463$		−	7.94598i		−	0.369281i	0.982806	−	0.184640i	$-0.0591121\pi$
$464$		0			0
$465$	−1.64492	−	5.06256i	−0.0762815	−	0.234770i
$466$		0			0
$467$	5.53410	−	7.61703i	0.256087	−	0.352474i	−0.661544	−	0.749906i	$-0.730099\pi$
$467$	5.53410	−	7.61703i	0.256087	−	0.352474i	0.917632	+	0.397432i	$0.130099\pi$
$468$		0			0
$469$	5.35832	+	1.74102i	0.247424	+	0.0803929i
$470$		0			0
$471$	−0.458893	−	0.631612i	−0.0211447	−	0.0291032i
$472$		0			0
$473$	12.0940	−	29.3542i	0.556084	−	1.34971i
$474$		0			0
$475$	2.51854	−	1.82983i	0.115559	−	0.0839582i
$476$		0			0
$477$	6.71171	−	20.6565i	0.307308	−	0.945798i
$478$		0			0
$479$	2.06571	+	1.50083i	0.0943848	+	0.0685746i	0.633977	−	0.773352i	$-0.281421\pi$
$479$	2.06571	+	1.50083i	0.0943848	+	0.0685746i	−0.539592	+	0.841927i	$0.681421\pi$
$480$		0			0
$481$	−22.0540	+	7.16578i	−1.00558	+	0.326732i
$482$		0			0
$483$	−2.93678			−0.133628
$484$		0			0
$485$	7.18342			0.326182
$486$		0			0
$487$	27.3061	−	8.87230i	1.23736	−	0.402042i	0.383984	−	0.923340i	$-0.374552\pi$
$487$	27.3061	−	8.87230i	1.23736	−	0.402042i	0.853375	+	0.521298i	$0.174552\pi$
$488$		0			0
$489$	−1.08079	−	0.785241i	−0.0488751	−	0.0355098i
$490$		0			0
$491$	−3.33105	+	10.2519i	−0.150328	+	0.462663i	−0.997658	−	0.0684048i	$-0.978209\pi$
$491$	−3.33105	+	10.2519i	−0.150328	+	0.462663i	0.847329	+	0.531068i	$0.178209\pi$
$492$		0			0
$493$	5.94882	−	4.32207i	0.267922	−	0.194656i
$494$		0			0
$495$	9.84280	−	23.8902i	0.442401	−	1.07378i
$496$		0			0
$497$	−4.91957	−	6.77120i	−0.220673	−	0.303730i
$498$		0			0
$499$	7.92074	+	2.57361i	0.354581	+	0.115210i	0.480891	−	0.876780i	$-0.340313\pi$
$499$	7.92074	+	2.57361i	0.354581	+	0.115210i	−0.126310	+	0.991991i	$0.540313\pi$
$500$		0			0
$501$	2.61530	−	3.59965i	0.116843	−	0.160820i
$502$		0			0
$503$	7.80947	+	24.0351i	0.348207	+	1.07167i	0.959844	+	0.280533i	$0.0905112\pi$
$503$	7.80947	+	24.0351i	0.348207	+	1.07167i	−0.611637	+	0.791138i	$0.709489\pi$
$504$		0			0
$505$		−	21.8979i		−	0.974443i
$506$		0			0
$507$			1.85835i			0.0825324i
$508$		0			0
$509$	5.17119	+	15.9153i	0.229209	+	0.705433i	0.997837	+	0.0657370i	$0.0209398\pi$
$509$	5.17119	+	15.9153i	0.229209	+	0.705433i	−0.768628	+	0.639696i	$0.779060\pi$
$510$		0			0
$511$	11.2201	−	15.4431i	0.496348	−	0.683165i
$512$		0			0
$513$	1.93157	+	0.627605i	0.0852809	+	0.0277095i
$514$		0			0
$515$	−10.4068	−	14.3237i	−0.458577	−	0.631177i
$516$		0			0
$517$	−0.989166	+	12.8795i	−0.0435035	+	0.566440i
$518$		0			0
$519$	0.219380	−	0.159389i	0.00962972	−	0.00699640i
$520$		0			0
$521$	−0.407845	+	1.25522i	−0.0178680	+	0.0549921i	−0.959593	−	0.281392i	$-0.909204\pi$
$521$	−0.407845	+	1.25522i	−0.0178680	+	0.0549921i	0.941725	+	0.336384i	$0.109204\pi$
$522$		0			0
$523$	−7.13883	−	5.18667i	−0.312159	−	0.226797i	0.420663	−	0.907217i	$-0.361797\pi$
$523$	−7.13883	−	5.18667i	−0.312159	−	0.226797i	−0.732823	+	0.680420i	$0.761797\pi$
$524$		0			0
$525$	0.679464	−	0.220771i	0.0296542	−	0.00963524i
$526$		0			0
$527$	−28.4054			−1.23736
$528$		0			0
$529$	−41.5627			−1.80707
$530$		0			0
$531$	29.0081	−	9.42529i	1.25884	−	0.409023i
$532$		0			0
$533$	−6.24749	−	4.53906i	−0.270609	−	0.196609i
$534$		0			0
$535$	−10.1607	+	31.2716i	−0.439287	+	1.35199i
$536$		0			0
$537$	−2.98592	+	2.16940i	−0.128852	+	0.0936164i
$538$		0			0
$539$	11.5466	−	7.10579i	0.497347	−	0.306068i
$540$		0			0
$541$	9.39770	+	12.9348i	0.404039	+	0.556111i	0.961752	−	0.273922i	$-0.0883211\pi$
$541$	9.39770	+	12.9348i	0.404039	+	0.556111i	−0.557713	+	0.830034i	$0.688321\pi$
$542$		0			0
$543$	−4.28948	−	1.39374i	−0.184079	−	0.0598109i
$544$		0			0
$545$	23.5523	−	32.4170i	1.00887	−	1.38859i
$546$		0			0
$547$	−5.70569	−	17.5603i	−0.243958	−	0.750825i	−0.995806	−	0.0914889i	$-0.970837\pi$
$547$	−5.70569	−	17.5603i	−0.243958	−	0.750825i	0.751848	−	0.659336i	$-0.229163\pi$
$548$		0			0
$549$			8.28649i			0.353659i
$550$		0			0
$551$			3.88540i			0.165523i
$552$		0			0
$553$	0.551020	+	1.69586i	0.0234317	+	0.0721155i
$554$		0			0
$555$	−1.65355	+	2.27591i	−0.0701892	+	0.0966071i
$556$		0			0
$557$	−8.92952	−	2.90138i	−0.378356	−	0.122935i	0.113664	−	0.993519i	$-0.463741\pi$
$557$	−8.92952	−	2.90138i	−0.378356	−	0.122935i	−0.492020	+	0.870584i	$0.663741\pi$
$558$		0			0
$559$	−26.1960	−	36.0557i	−1.10797	−	1.52500i
$560$		0			0
$561$	1.63067	+	1.38740i	0.0688468	+	0.0585762i
$562$		0			0
$563$	−6.53518	+	4.74809i	−0.275425	+	0.200108i	−0.716919	−	0.697156i	$-0.754448\pi$
$563$	−6.53518	+	4.74809i	−0.275425	+	0.200108i	0.441494	+	0.897264i	$0.354448\pi$
$564$		0			0
$565$	−15.2204	+	46.8435i	−0.640326	+	1.97072i
$566$		0			0
$567$	−11.8582	−	8.61551i	−0.497999	−	0.361817i
$568$		0			0
$569$	18.8892	−	6.13747i	0.791876	−	0.257296i	0.114973	−	0.993369i	$-0.463322\pi$
$569$	18.8892	−	6.13747i	0.791876	−	0.257296i	0.676903	+	0.736072i	$0.263322\pi$
$570$		0			0
$571$	16.7680			0.701720			0.350860	−	0.936428i	$-0.385889\pi$
$571$	16.7680			0.701720			0.350860	+	0.936428i	$0.385889\pi$
$572$		0			0
$573$	0.773796			0.0323258
$574$		0			0
$575$	14.9374	−	4.85347i	0.622934	−	0.202404i
$576$		0			0
$577$	−4.01160	−	2.91460i	−0.167005	−	0.121336i	0.501143	−	0.865364i	$-0.332913\pi$
$577$	−4.01160	−	2.91460i	−0.167005	−	0.121336i	−0.668148	+	0.744028i	$0.732913\pi$
$578$		0			0
$579$	1.62703	−	5.00750i	0.0676173	−	0.208105i
$580$		0			0
$581$	13.1982	−	9.58904i	0.547553	−	0.397820i
$582$		0			0
$583$	5.73728	+	23.7002i	0.237614	+	0.981562i
$584$		0			0
$585$	−21.3198	−	29.3442i	−0.881466	−	1.21323i
$586$		0			0
$587$	−5.43860	−	1.76711i	−0.224475	−	0.0729364i	0.194620	−	0.980879i	$-0.437653\pi$
$587$	−5.43860	−	1.76711i	−0.224475	−	0.0729364i	−0.419095	+	0.907942i	$0.637653\pi$
$588$		0			0
$589$	8.82228	−	12.1428i	0.363516	−	0.500336i
$590$		0			0
$591$	0.739229	+	2.27511i	0.0304078	+	0.0935856i
$592$		0			0
$593$		−	14.0454i		−	0.576773i	−0.957514	−	0.288387i	$-0.906881\pi$
$593$		−	14.0454i		−	0.576773i	0.957514	−	0.288387i	$-0.0931189\pi$
$594$		0			0
$595$		−	13.5642i		−	0.556080i
$596$		0			0
$597$	0.179339	+	0.551949i	0.00733986	+	0.0225898i
$598$		0			0
$599$	11.0126	−	15.1575i	0.449961	−	0.619318i	−0.522428	−	0.852683i	$-0.674974\pi$
$599$	11.0126	−	15.1575i	0.449961	−	0.619318i	0.972389	+	0.233365i	$0.0749737\pi$
$600$		0			0
$601$	−43.8706	−	14.2544i	−1.78952	−	0.581449i	−0.790018	−	0.613084i	$-0.789929\pi$
$601$	−43.8706	−	14.2544i	−1.78952	−	0.581449i	−0.999499	+	0.0316347i	$0.989929\pi$
$602$		0			0
$603$	−5.73275	−	7.89046i	−0.233456	−	0.321324i
$604$		0			0
$605$	4.64620	+	28.6344i	0.188895	+	1.16416i
$606$		0			0
$607$	28.8580	−	20.9666i	1.17131	−	0.851007i	0.180145	−	0.983640i	$-0.442343\pi$
$607$	28.8580	−	20.9666i	1.17131	−	0.851007i	0.991165	+	0.132634i	$0.0423433\pi$
$608$		0			0
$609$	−0.275541	+	0.848029i	−0.0111655	+	0.0343639i
$610$		0			0
$611$	14.6701	+	10.6585i	0.593490	+	0.431196i
$612$		0			0
$613$	−43.4181	+	14.1074i	−1.75364	+	0.569792i	−0.996510	−	0.0834738i	$-0.973399\pi$
$613$	−43.4181	+	14.1074i	−1.75364	+	0.569792i	−0.757129	+	0.653266i	$0.773399\pi$
$614$		0			0
$615$	−0.936838			−0.0377769
$616$		0			0
$617$	−2.07721			−0.0836252			−0.0418126	−	0.999125i	$-0.513313\pi$
$617$	−2.07721			−0.0836252			−0.0418126	+	0.999125i	$0.513313\pi$
$618$		0			0
$619$	−44.2752	+	14.3859i	−1.77957	+	0.578218i	−0.998907	−	0.0467325i	$-0.985119\pi$
$619$	−44.2752	+	14.3859i	−1.77957	+	0.578218i	−0.780664	+	0.624950i	$0.785119\pi$
$620$		0			0
$621$	8.28973	+	6.02284i	0.332656	+	0.241688i
$622$		0			0
$623$	2.85876	−	8.79837i	0.114534	−	0.352499i
$624$		0			0
$625$	25.0412	−	18.1935i	1.00165	−	0.727740i
$626$		0			0
$627$	−1.09955	+	0.266177i	−0.0439119	+	0.0106301i
$628$		0			0
$629$	8.82376	+	12.1449i	0.351826	+	0.484247i
$630$		0			0
$631$	20.3051	+	6.59754i	0.808334	+	0.262644i	0.683892	−	0.729583i	$-0.260286\pi$
$631$	20.3051	+	6.59754i	0.808334	+	0.262644i	0.124442	+	0.992227i	$0.460286\pi$
$632$		0			0
$633$	0.444311	−	0.611541i	0.0176598	−	0.0243066i
$634$		0			0
$635$	1.88644	+	5.80587i	0.0748612	+	0.230399i
$636$		0			0
$637$		−	19.0323i		−	0.754088i
$638$		0			0
$639$			14.4887i			0.573166i
$640$		0			0
$641$	−6.29500	−	19.3740i	−0.248638	−	0.765228i	−0.995017	−	0.0997070i	$-0.968209\pi$
$641$	−6.29500	−	19.3740i	−0.248638	−	0.765228i	0.746379	−	0.665521i	$-0.231791\pi$
$642$		0			0
$643$	−3.39388	+	4.67128i	−0.133842	+	0.184217i	−0.870677	−	0.491855i	$-0.836319\pi$
$643$	−3.39388	+	4.67128i	−0.133842	+	0.184217i	0.736836	+	0.676072i	$0.236319\pi$
$644$		0			0
$645$	−5.14209	−	1.67077i	−0.202470	−	0.0657864i
$646$		0			0
$647$	11.5332	+	15.8740i	0.453416	+	0.624073i	0.973127	−	0.230269i	$-0.0739605\pi$
$647$	11.5332	+	15.8740i	0.453416	+	0.624073i	−0.519711	+	0.854342i	$0.673961\pi$
$648$		0			0
$649$	−22.1902	+	26.0810i	−0.871042	+	1.02377i
$650$		0			0
$651$	2.78669	−	2.02465i	0.109219	−	0.0793522i
$652$		0			0
$653$	−2.06475	+	6.35465i	−0.0807999	+	0.248677i	−0.983294	−	0.182026i	$-0.941734\pi$
$653$	−2.06475	+	6.35465i	−0.0807999	+	0.248677i	0.902494	+	0.430703i	$0.141734\pi$
$654$		0			0
$655$	−42.4783	−	30.8623i	−1.65977	−	1.20589i
$656$		0			0
$657$	−31.4273	+	10.2114i	−1.22610	+	0.398383i
$658$		0			0
$659$	11.0735			0.431362			0.215681	−	0.976464i	$-0.430803\pi$
$659$	11.0735			0.431362			0.215681	+	0.976464i	$0.430803\pi$
$660$		0			0
$661$	−11.6374			−0.452643			−0.226322	−	0.974053i	$-0.572670\pi$
$661$	−11.6374			−0.452643			−0.226322	+	0.974053i	$0.572670\pi$
$662$		0			0
$663$	2.85843	−	0.928759i	0.111012	−	0.0360700i
$664$		0			0
$665$	5.79850	+	4.21285i	0.224856	+	0.163367i
$666$		0			0
$667$	−6.05754	+	18.6432i	−0.234549	+	0.721868i
$668$		0			0
$669$	2.07946	−	1.51081i	0.0803965	−	0.0584114i
$670$		0			0
$671$	−4.87594	−	7.92318i	−0.188234	−	0.305871i
$672$		0			0
$673$	17.9197	+	24.6643i	0.690753	+	0.950741i	1.00000		0.000241320i	$-7.68145e-5\pi$
$673$	17.9197	+	24.6643i	0.690753	+	0.950741i	−0.309246	+	0.950982i	$0.600077\pi$
$674$		0			0
$675$	−2.37071	−	0.770289i	−0.0912486	−	0.0296485i
$676$		0			0
$677$	22.9500	−	31.5879i	0.882039	−	1.21402i	−0.0938136	−	0.995590i	$-0.529906\pi$
$677$	22.9500	−	31.5879i	0.882039	−	1.21402i	0.975852	−	0.218432i	$-0.0700942\pi$
$678$		0			0
$679$	1.43642	+	4.42085i	0.0551247	+	0.169656i
$680$		0			0
$681$		−	1.72934i		−	0.0662685i
$682$		0			0
$683$			35.4274i			1.35559i	0.735250	+	0.677796i	$0.237065\pi$
$683$			35.4274i			1.35559i	−0.735250	+	0.677796i	$0.762935\pi$
$684$		0			0
$685$	16.6898	+	51.3660i	0.637686	+	1.96260i
$686$		0			0
$687$	−1.17739	+	1.62054i	−0.0449204	+	0.0618276i
$688$		0			0
$689$	32.5555	+	10.5779i	1.24027	+	0.402987i
$690$		0			0
$691$	−26.5889	−	36.5965i	−1.01149	−	1.39220i	−0.918002	−	0.396576i	$-0.870198\pi$
$691$	−26.5889	−	36.5965i	−1.01149	−	1.39220i	−0.0934878	−	0.995620i	$-0.529802\pi$
$692$		0			0
$693$	16.6708	+	1.28034i	0.633270	+	0.0486361i
$694$		0			0
$695$	−40.8320	+	29.6662i	−1.54885	+	1.12530i
$696$		0			0
$697$	−1.54484	+	4.75453i	−0.0585150	+	0.180091i
$698$		0			0
$699$	−1.98928	−	1.44530i	−0.0752415	−	0.0546662i
$700$		0			0
$701$	26.0715	−	8.47114i	0.984707	−	0.319951i	0.227969	−	0.973668i	$-0.426792\pi$
$701$	26.0715	−	8.47114i	0.984707	−	0.319951i	0.756738	+	0.653718i	$0.226792\pi$
$702$		0			0
$703$	−7.93226			−0.299171
$704$		0			0
$705$	2.19985			0.0828511
$706$		0			0
$707$	13.4765	−	4.37877i	0.506835	−	0.164681i
$708$		0			0
$709$	27.3542	+	19.8740i	1.02731	+	0.746383i	0.967768	−	0.251843i	$-0.0810366\pi$
$709$	27.3542	+	19.8740i	1.02731	+	0.746383i	0.0595402	+	0.998226i	$0.481037\pi$
$710$		0			0
$711$	0.953871	−	2.93571i	0.0357730	−	0.110098i
$712$		0			0
$713$	61.2630	−	44.5102i	2.29432	−	1.66692i
$714$		0			0
$715$	37.6518	+	15.5126i	1.40810	+	0.580140i
$716$		0			0
$717$	−1.60224	−	2.20530i	−0.0598368	−	0.0823583i
$718$		0			0
$719$	37.8962	+	12.3132i	1.41329	+	0.459206i	0.913464	−	0.406920i	$-0.133397\pi$
$719$	37.8962	+	12.3132i	1.41329	+	0.459206i	0.499826	+	0.866126i	$0.333397\pi$
$720$		0			0
$721$	6.73415	−	9.26877i	0.250793	−	0.345187i
$722$		0			0
$723$	1.64559	+	5.06461i	0.0612002	+	0.188355i
$724$		0			0
$725$		−	4.76873i		−	0.177106i
$726$		0			0
$727$			29.9599i			1.11115i	0.831466	+	0.555576i	$0.187502\pi$
$727$			29.9599i			1.11115i	−0.831466	+	0.555576i	$0.812498\pi$
$728$		0			0
$729$	7.58772	+	23.3526i	0.281027	+	0.864911i
$730$		0			0
$731$	−16.9586	+	23.3415i	−0.627235	+	0.863315i
$732$		0			0
$733$	−12.5695	−	4.08409i	−0.464266	−	0.150849i	0.0675376	−	0.997717i	$-0.478486\pi$
$733$	−12.5695	−	4.08409i	−0.464266	−	0.150849i	−0.531804	+	0.846867i	$0.678486\pi$
$734$		0			0
$735$	−1.35715	−	1.86795i	−0.0500592	−	0.0689005i
$736$		0			0
$737$	10.1243	+	4.17125i	0.372934	+	0.153650i
$738$		0			0
$739$	25.8317	−	18.7679i	0.950236	−	0.690387i	−0.000626954	−	1.00000i	$-0.500200\pi$
$739$	25.8317	−	18.7679i	0.950236	−	0.690387i	0.950863	+	0.309613i	$0.100200\pi$
$740$		0			0
$741$	−0.490755	+	1.51039i	−0.0180283	+	0.0554855i
$742$		0			0
$743$	5.33357	+	3.87507i	0.195670	+	0.142162i	0.681306	−	0.731998i	$-0.261412\pi$
$743$	5.33357	+	3.87507i	0.195670	+	0.142162i	−0.485637	+	0.874161i	$0.661412\pi$
$744$		0			0
$745$	22.3215	−	7.25269i	0.817796	−	0.265718i
$746$		0			0
$747$	−28.2409			−1.03328
$748$		0			0
$749$	−21.2770			−0.777446
$750$		0			0
$751$	−1.78126	+	0.578765i	−0.0649990	+	0.0211195i	−0.341336	−	0.939941i	$-0.610879\pi$
$751$	−1.78126	+	0.578765i	−0.0649990	+	0.0211195i	0.276337	+	0.961061i	$0.410879\pi$
$752$		0			0
$753$	−2.51432	−	1.82676i	−0.0916268	−	0.0665708i
$754$		0			0
$755$	−18.4177	+	56.6839i	−0.670289	+	2.06294i
$756$		0			0
$757$	15.1985	−	11.0423i	0.552398	−	0.401341i	−0.276271	−	0.961080i	$-0.589099\pi$
$757$	15.1985	−	11.0423i	0.552398	−	0.401341i	0.828669	+	0.559739i	$0.189099\pi$
$758$		0			0
$759$	−5.69094	−	0.437073i	−0.206568	−	0.0158647i
$760$		0			0
$761$	4.41234	+	6.07307i	0.159947	+	0.220149i	0.881467	−	0.472245i	$-0.156556\pi$
$761$	4.41234	+	6.07307i	0.159947	+	0.220149i	−0.721520	+	0.692394i	$0.756556\pi$
$762$		0			0
$763$	24.6598	+	8.01244i	0.892743	+	0.290070i
$764$		0			0
$765$	−13.8018	+	18.9966i	−0.499007	+	0.686824i
$766$		0			0
$767$	14.8546	+	45.7179i	0.536370	+	1.65078i
$768$		0			0
$769$		−	38.7592i		−	1.39769i	−0.715272	−	0.698847i	$-0.753697\pi$
$769$		−	38.7592i		−	1.39769i	0.715272	−	0.698847i	$-0.246303\pi$
$770$		0			0
$771$		−	0.779056i		−	0.0280570i
$772$		0			0
$773$	2.56083	+	7.88143i	0.0921067	+	0.283475i	0.986489	−	0.163828i	$-0.0523843\pi$
$773$	2.56083	+	7.88143i	0.0921067	+	0.283475i	−0.894382	+	0.447304i	$0.852384\pi$
$774$		0			0
$775$	−10.8280	+	14.9035i	−0.388953	+	0.535348i
$776$		0			0
$777$	−1.73130	−	0.562533i	−0.0621100	−	0.0201808i
$778$		0			0
$779$	−1.55268	−	2.13708i	−0.0556305	−	0.0765688i
$780$		0			0
$781$	−8.52548	−	13.8535i	−0.305066	−	0.495718i
$782$		0			0
$783$	2.51694	−	1.82867i	0.0899482	−	0.0653512i
$784$		0			0
$785$	−2.97057	+	9.14248i	−0.106024	+	0.326309i
$786$		0			0
$787$	−19.1719	−	13.9292i	−0.683403	−	0.496521i	0.191082	−	0.981574i	$-0.438800\pi$
$787$	−19.1719	−	13.9292i	−0.683403	−	0.496521i	−0.874485	+	0.485053i	$0.838800\pi$
$788$		0			0
$789$	3.28125	−	1.06614i	0.116816	−	0.0379557i
$790$		0			0
$791$	−31.8721			−1.13324
$792$		0			0
$793$	−13.0598			−0.463768
$794$		0			0
$795$	3.94949	−	1.28327i	0.140074	−	0.0455128i
$796$		0			0
$797$	2.09283	+	1.52053i	0.0741318	+	0.0538599i	0.624234	−	0.781237i	$-0.285411\pi$
$797$	2.09283	+	1.52053i	0.0741318	+	0.0538599i	−0.550102	+	0.835097i	$0.685411\pi$
$798$		0			0
$799$	3.62754	−	11.1644i	0.128333	−	0.394969i
$800$		0			0
$801$	−12.9562	+	9.41320i	−0.457783	+	0.332599i
$802$		0			0
$803$	24.0409	−	28.2561i	0.848384	−	0.997137i
$804$		0			0
$805$	21.2547	+	29.2546i	0.749130	+	1.03109i
$806$		0			0
$807$	4.15368	+	1.34961i	0.146217	+	0.0475087i
$808$		0			0
$809$	−13.3866	+	18.4251i	−0.470649	+	0.647793i	−0.976674	−	0.214726i	$-0.931114\pi$
$809$	−13.3866	+	18.4251i	−0.470649	+	0.647793i	0.506025	+	0.862519i	$0.331114\pi$
$810$		0			0
$811$	10.5774	+	32.5539i	0.371423	+	1.14312i	0.945860	+	0.324574i	$0.105221\pi$
$811$	10.5774	+	32.5539i	0.371423	+	1.14312i	−0.574437	+	0.818549i	$0.694779\pi$
$812$		0			0
$813$			4.10344i			0.143914i
$814$		0			0
$815$			16.4494i			0.576196i
$816$		0			0
$817$	−4.71102	−	14.4990i	−0.164818	−	0.507256i
$818$		0			0
$819$	13.7959	−	18.9885i	0.482069	−	0.663511i
$820$		0			0
$821$	22.7174	+	7.38132i	0.792842	+	0.257610i	0.677314	−	0.735694i	$-0.263144\pi$
$821$	22.7174	+	7.38132i	0.792842	+	0.257610i	0.115528	+	0.993304i	$0.463144\pi$
$822$		0			0
$823$	−23.0372	−	31.7080i	−0.803026	−	1.10527i	−0.992362	−	0.123358i	$-0.960634\pi$
$823$	−23.0372	−	31.7080i	−0.803026	−	1.10527i	0.189336	−	0.981912i	$-0.439366\pi$
$824$		0			0
$825$	1.34953	−	0.326691i	0.0469847	−	0.0113739i
$826$		0			0
$827$	24.4107	−	17.7354i	0.848842	−	0.616720i	−0.0759846	−	0.997109i	$-0.524210\pi$
$827$	24.4107	−	17.7354i	0.848842	−	0.616720i	0.924826	+	0.380389i	$0.124210\pi$
$828$		0			0
$829$	−9.37044	+	28.8392i	−0.325449	+	1.00163i	0.645789	+	0.763516i	$0.276529\pi$
$829$	−9.37044	+	28.8392i	−0.325449	+	1.00163i	−0.971238	+	0.238112i	$0.923471\pi$
$830$		0			0
$831$	1.03849	+	0.754508i	0.0360249	+	0.0261736i
$832$		0			0
$833$	−11.7179	+	3.80739i	−0.406003	+	0.131918i
$834$		0			0
$835$	−54.7857			−1.89594
$836$		0			0
$837$	−12.0183			−0.415413
$838$		0			0
$839$	0.589942	−	0.191684i	0.0203670	−	0.00661765i	−0.298816	−	0.954311i	$-0.596592\pi$
$839$	0.589942	−	0.191684i	0.0203670	−	0.00661765i	0.319183	+	0.947693i	$0.396592\pi$
$840$		0			0
$841$	−18.6464	−	13.5474i	−0.642979	−	0.467152i
$842$		0			0
$843$	−1.38512	+	4.26296i	−0.0477060	+	0.146824i
$844$		0			0
$845$	18.5119	−	13.4497i	0.636828	−	0.462683i
$846$		0			0
$847$	−16.6932	+	8.58521i	−0.573586	+	0.294991i
$848$		0			0
$849$	3.19073	+	4.39166i	0.109505	+	0.150721i
$850$		0			0
$851$	−38.0611	−	12.3668i	−1.30472	−	0.423929i
$852$		0			0
$853$	−0.647166	+	0.890748i	−0.0221585	+	0.0304986i	−0.819953	−	0.572432i	$-0.806000\pi$
$853$	−0.647166	+	0.890748i	−0.0221585	+	0.0304986i	0.797794	+	0.602930i	$0.206000\pi$
$854$		0			0
$855$	−3.83409	−	11.8001i	−0.131123	−	0.403556i
$856$		0			0
$857$		−	11.9943i		−	0.409718i	−0.978792	−	0.204859i	$-0.934326\pi$
$857$		−	11.9943i		−	0.409718i	0.978792	−	0.204859i	$-0.0656735\pi$
$858$		0			0
$859$			54.2352i			1.85048i	0.379383	+	0.925240i	$0.376136\pi$
$859$			54.2352i			1.85048i	−0.379383	+	0.925240i	$0.623864\pi$
$860$		0			0
$861$	−0.187333	−	0.576552i	−0.00638429	−	0.0196488i
$862$		0			0
$863$	10.6446	−	14.6510i	0.362346	−	0.498726i	−0.588455	−	0.808530i	$-0.700263\pi$
$863$	10.6446	−	14.6510i	0.362346	−	0.498726i	0.950800	+	0.309804i	$0.100263\pi$
$864$		0			0
$865$	−3.17549	−	1.03178i	−0.107970	−	0.0350816i
$866$		0			0
$867$	0.996489	+	1.37155i	0.0338425	+	0.0465802i
$868$		0			0
$869$	0.815384	+	3.36828i	0.0276600	+	0.114261i
$870$		0			0
$871$	12.4357	−	9.03505i	0.421367	−	0.306141i
$872$		0			0
$873$	2.48659	−	7.65293i	0.0841583	−	0.259013i
$874$		0			0
$875$	11.0875	+	8.05555i	0.374826	+	0.272327i
$876$		0			0
$877$	39.1428	−	12.7183i	1.32176	−	0.429465i	0.438660	−	0.898653i	$-0.355453\pi$
$877$	39.1428	−	12.7183i	1.32176	−	0.429465i	0.883098	+	0.469188i	$0.155453\pi$
$878$		0			0
$879$	−0.225182			−0.00759518
$880$		0			0
$881$	−10.4577			−0.352329			−0.176165	−	0.984361i	$-0.556369\pi$
$881$	−10.4577			−0.352329			−0.176165	+	0.984361i	$0.556369\pi$
$882$		0			0
$883$	−4.98546	+	1.61987i	−0.167774	+	0.0545131i	−0.391700	−	0.920093i	$-0.628113\pi$
$883$	−4.98546	+	1.61987i	−0.167774	+	0.0545131i	0.223926	+	0.974606i	$0.428113\pi$
$884$		0			0
$885$	4.71796	+	3.42780i	0.158592	+	0.115224i
$886$		0			0
$887$	9.75900	−	30.0351i	0.327675	−	1.00848i	−0.642543	−	0.766249i	$-0.722121\pi$
$887$	9.75900	−	30.0351i	0.327675	−	1.00848i	0.970219	−	0.242231i	$-0.0778793\pi$
$888$		0			0
$889$	−3.19585	+	2.32192i	−0.107185	+	0.0778747i
$890$		0			0
$891$	−21.6968	−	18.4601i	−0.726872	−	0.618437i
$892$		0			0
$893$	3.64595	+	5.01822i	0.122007	+	0.167928i
$894$		0			0
$895$	43.2207	+	14.0433i	1.44471	+	0.469414i
$896$		0			0
$897$	−4.70956	+	6.48215i	−0.157248	+	0.216433i
$898$		0			0
$899$	−7.10487	−	21.8665i	−0.236961	−	0.729290i
$900$		0			0
$901$		−	22.1601i		−	0.738260i
$902$		0			0
$903$		−	3.49865i		−	0.116428i
$904$		0			0
$905$	17.1611	+	52.8165i	0.570455	+	1.75568i
$906$		0			0
$907$	21.7742	−	29.9696i	0.723000	−	0.995124i	−0.276419	−	0.961037i	$-0.589148\pi$
$907$	21.7742	−	29.9696i	0.723000	−	0.995124i	0.999419	−	0.0340867i	$-0.0108522\pi$
$908$		0			0
$909$	−23.3291	−	7.58010i	−0.773779	−	0.251416i
$910$		0			0
$911$	5.02486	+	6.91612i	0.166481	+	0.229141i	0.884104	−	0.467291i	$-0.154770\pi$
$911$	5.02486	+	6.91612i	0.166481	+	0.229141i	−0.717623	+	0.696432i	$0.754770\pi$
$912$		0			0
$913$	27.0028	−	16.6175i	0.893661	−	0.549960i
$914$		0			0
$915$	−1.28178	+	0.931264i	−0.0423742	+	0.0307867i
$916$		0			0
$917$	10.4993	−	32.3135i	0.346717	−	1.06708i
$918$		0			0
$919$	16.1076	+	11.7028i	0.531339	+	0.386041i	0.820858	−	0.571132i	$-0.193495\pi$
$919$	16.1076	+	11.7028i	0.531339	+	0.386041i	−0.289519	+	0.957172i	$0.593495\pi$
$920$		0			0
$921$	0.682025	−	0.221603i	0.0224735	−	0.00730208i
$922$		0			0
$923$	−22.8348			−0.751618
$924$		0			0
$925$	9.73563			0.320106
$926$		0			0
$927$	−18.8622	+	6.12871i	−0.619517	+	0.201293i
$928$		0			0
$929$	27.4137	+	19.9172i	0.899415	+	0.653464i	0.938316	−	0.345779i	$-0.112385\pi$
$929$	27.4137	+	19.9172i	0.899415	+	0.653464i	−0.0389003	+	0.999243i	$0.512385\pi$
$930$		0			0
$931$	2.01182	−	6.19175i	0.0659348	−	0.202926i
$932$		0			0
$933$	−3.17494	+	2.30673i	−0.103943	+	0.0755190i
$934$		0			0
$935$	2.01873	−	26.2850i	0.0660195	−	0.859612i
$936$		0			0
$937$	−5.73265	−	7.89032i	−0.187278	−	0.257766i	0.705046	−	0.709161i	$-0.250926\pi$
$937$	−5.73265	−	7.89032i	−0.187278	−	0.257766i	−0.892324	+	0.451396i	$0.850926\pi$
$938$		0			0
$939$	1.26627	+	0.411437i	0.0413232	+	0.0134267i
$940$		0			0
$941$	−19.9529	+	27.4628i	−0.650447	+	0.895263i	−0.999118	−	0.0419817i	$-0.986633\pi$
$941$	−19.9529	+	27.4628i	−0.650447	+	0.895263i	0.348672	+	0.937245i	$0.386633\pi$
$942$		0			0
$943$	−4.11836	−	12.6750i	−0.134112	−	0.412755i
$944$		0			0
$945$		−	5.73902i		−	0.186690i
$946$		0			0
$947$			41.3725i			1.34443i	0.740357	+	0.672213i	$0.234656\pi$
$947$			41.3725i			1.34443i	−0.740357	+	0.672213i	$0.765344\pi$
$948$		0			0
$949$	−16.0935	−	49.5307i	−0.522417	−	1.60783i
$950$		0			0
$951$	1.43450	−	1.97442i	0.0465168	−	0.0640249i
$952$		0			0
$953$	−32.8687	−	10.6797i	−1.06472	−	0.345949i	−0.276292	−	0.961074i	$-0.589106\pi$
$953$	−32.8687	−	10.6797i	−1.06472	−	0.345949i	−0.788430	+	0.615124i	$0.789106\pi$
$954$		0			0
$955$	−5.60029	−	7.70814i	−0.181221	−	0.249429i
$956$		0			0
$957$	−0.660158	+	1.60232i	−0.0213399	+	0.0517955i
$958$		0			0
$959$	−28.2745	+	20.5426i	−0.913031	+	0.663356i
$960$		0			0
$961$	−17.8667	+	54.9881i	−0.576345	+	1.77381i
$962$		0			0
$963$	29.7983	+	21.6497i	0.960236	+	0.697652i
$964$		0			0
$965$	−61.6575	+	20.0337i	−1.98482	+	0.644909i
$966$		0			0
$967$	25.7731			0.828808			0.414404	−	0.910093i	$-0.363990\pi$
$967$	25.7731			0.828808			0.414404	+	0.910093i	$0.363990\pi$
$968$		0			0
$969$	1.02810			0.0330274
$970$		0			0
$971$	28.0911	−	9.12735i	0.901486	−	0.292910i	0.178636	−	0.983915i	$-0.442832\pi$
$971$	28.0911	−	9.12735i	0.901486	−	0.292910i	0.722850	+	0.691005i	$0.242832\pi$
$972$		0			0
$973$	−26.4221	−	19.1968i	−0.847055	−	0.615421i
$974$		0			0
$975$	0.602327	−	1.85377i	0.0192899	−	0.0593682i
$976$		0			0
$977$	−11.7744	+	8.55462i	−0.376697	+	0.273687i	−0.759983	−	0.649943i	$-0.774793\pi$
$977$	−11.7744	+	8.55462i	−0.376697	+	0.273687i	0.383285	+	0.923630i	$0.374793\pi$
$978$		0			0
$979$	6.84920	−	16.6242i	0.218901	−	0.531311i
$980$		0			0
$981$	−26.3830	−	36.3131i	−0.842344	−	1.15939i
$982$		0			0
$983$	−34.0656	−	11.0686i	−1.08653	−	0.353033i	−0.289622	−	0.957141i	$-0.593530\pi$
$983$	−34.0656	−	11.0686i	−1.08653	−	0.353033i	−0.796903	+	0.604108i	$0.793530\pi$
$984$		0			0
$985$	17.3133	−	23.8297i	0.551648	−	0.759278i
$986$		0			0
$987$	0.439889	+	1.35384i	0.0140018	+	0.0430932i
$988$		0			0
$989$		−	76.9150i		−	2.44575i
$990$		0			0
$991$			0.375830i			0.0119386i	0.999982	+	0.00596931i	$0.00190010\pi$
$991$			0.375830i			0.0119386i	−0.999982	+	0.00596931i	$0.998100\pi$
$992$		0			0
$993$	0.483256	+	1.48731i	0.0153356	+	0.0471983i
$994$		0			0
$995$	4.20026	−	5.78116i	0.133157	−	0.183275i
$996$		0			0
$997$	20.0665	+	6.52001i	0.635513	+	0.206491i	0.609016	−	0.793158i	$-0.291565\pi$
$997$	20.0665	+	6.52001i	0.635513	+	0.206491i	0.0264975	+	0.999649i	$0.491565\pi$
$998$		0			0
$999$	3.73333	+	5.13848i	0.118117	+	0.162574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.u.a.63.7	yes	48
4.3	odd	2	inner	352.2.u.a.63.6	✓	48
8.3	odd	2		704.2.u.d.63.7		48
8.5	even	2		704.2.u.d.63.6		48
11.7	odd	10	inner	352.2.u.a.95.6	yes	48
44.7	even	10	inner	352.2.u.a.95.7	yes	48
88.29	odd	10		704.2.u.d.447.7		48
88.51	even	10		704.2.u.d.447.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.u.a.63.6	✓	48	4.3	odd	2	inner
352.2.u.a.63.7	yes	48	1.1	even	1	trivial
352.2.u.a.95.6	yes	48	11.7	odd	10	inner
352.2.u.a.95.7	yes	48	44.7	even	10	inner
704.2.u.d.63.6		48	8.5	even	2
704.2.u.d.63.7		48	8.3	odd	2
704.2.u.d.447.6		48	88.51	even	10
704.2.u.d.447.7		48	88.29	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203695 - 0.0661845i) q^{3} +(-2.13352 - 1.55009i) q^{5} +(0.527338 - 1.62298i) q^{7} +(-2.38994 + 1.73639i) q^{9} +(1.26343 - 3.06655i) q^{11} +(-2.73662 - 3.76664i) q^{13} +(-0.537180 - 0.174540i) q^{15} +(-1.77161 + 2.43842i) q^{17} +(-0.492146 - 1.51467i) q^{19} -0.365494i q^{21} -8.03509i q^{23} +(0.604034 + 1.85903i) q^{25} +(-0.749568 + 1.03169i) q^{27} +(-2.32022 - 0.753886i) q^{29} +(5.53948 + 7.62444i) q^{31} +(0.0543955 - 0.708261i) q^{33} +(-3.64085 + 2.64524i) q^{35} +(1.53910 - 4.73687i) q^{37} +(-0.806730 - 0.586124i) q^{39} +(1.57746 - 0.512547i) q^{41} +9.57239 q^{43} +7.79055 q^{45} +(-3.70413 + 1.20354i) q^{47} +(3.30714 + 2.40278i) q^{49} +(-0.199483 + 0.613946i) q^{51} +(-5.94812 + 4.32156i) q^{53} +(-7.44899 + 4.58412i) q^{55} +(-0.200496 - 0.275958i) q^{57} +(-9.81950 - 3.19055i) q^{59} +(1.64877 - 2.26934i) q^{61} +(1.55782 + 4.79449i) q^{63} +12.2782i q^{65} +3.30153i q^{67} +(-0.531799 - 1.63671i) q^{69} +(2.88284 - 3.96789i) q^{71} +(10.6384 + 3.45664i) q^{73} +(0.246078 + 0.338697i) q^{75} +(-4.31070 - 3.66763i) q^{77} +(-0.845348 + 0.614182i) q^{79} +(2.65423 - 8.16887i) q^{81} +(7.73406 + 5.61912i) q^{83} +(7.55954 - 2.45624i) q^{85} -0.522514 q^{87} +5.42112 q^{89} +(-7.55630 + 2.45519i) q^{91} +(1.63298 + 1.18643i) q^{93} +(-1.29788 + 3.99445i) q^{95} +(-2.20369 + 1.60107i) q^{97} +(2.30523 + 9.52268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{9} + 4 q^{25} + 36 q^{33} + 40 q^{41} - 96 q^{45} - 4 q^{49} - 8 q^{53} + 20 q^{57} - 8 q^{69} - 40 q^{73} - 72 q^{77} - 72 q^{81} - 80 q^{85} - 40 q^{89} + 8 q^{93} + 4 q^{97}+O(q^{100}) \) 48 * q + 4 * q^9 + 4 * q^25 + 36 * q^33 + 40 * q^41 - 96 * q^45 - 4 * q^49 - 8 * q^53 + 20 * q^57 - 8 * q^69 - 40 * q^73 - 72 * q^77 - 72 * q^81 - 80 * q^85 - 40 * q^89 + 8 * q^93 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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