LMFDB - Embedded newform 560.2.ci.e.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 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("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.e.33.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35944 - 0.364260i) q^{3} +(-2.13431 - 0.666887i) q^{5} +(-2.59782 + 0.501338i) q^{7} +(-0.882692 + 0.509622i) q^{9} +O(q^{10})$	\(q+(1.35944 - 0.364260i) q^{3} +(-2.13431 - 0.666887i) q^{5} +(-2.59782 + 0.501338i) q^{7} +(-0.882692 + 0.509622i) q^{9} +(-1.86869 + 3.23667i) q^{11} +(-4.55026 - 4.55026i) q^{13} +(-3.14438 - 0.129149i) q^{15} +(-1.58528 - 5.91633i) q^{17} +(0.616087 + 1.06709i) q^{19} +(-3.34895 + 1.62782i) q^{21} +(2.69174 + 0.721250i) q^{23} +(4.11052 + 2.84668i) q^{25} +(-3.99986 + 3.99986i) q^{27} -2.82808i q^{29} +(-5.94396 - 3.43175i) q^{31} +(-1.36138 + 5.08074i) q^{33} +(5.87887 + 0.662443i) q^{35} +(-2.01646 + 7.52551i) q^{37} +(-7.84327 - 4.52831i) q^{39} +5.56966i q^{41} +(1.95176 - 1.95176i) q^{43} +(2.22379 - 0.499034i) q^{45} +(11.1512 + 2.98797i) q^{47} +(6.49732 - 2.60477i) q^{49} +(-4.31017 - 7.46543i) q^{51} +(-2.53082 - 9.44513i) q^{53} +(6.14686 - 5.66184i) q^{55} +(1.22623 + 1.22623i) q^{57} +(0.916152 - 1.58682i) q^{59} +(-3.43491 + 1.98315i) q^{61} +(2.03758 - 1.76643i) q^{63} +(6.67713 + 12.7462i) q^{65} +(-7.93605 + 2.12646i) q^{67} +3.92198 q^{69} -0.570063 q^{71} +(-2.03783 + 0.546036i) q^{73} +(6.62493 + 2.37259i) q^{75} +(3.23186 - 9.34513i) q^{77} +(-9.47466 + 5.47020i) q^{79} +(-2.45170 + 4.24647i) q^{81} +(-8.80820 - 8.80820i) q^{83} +(-0.562062 + 13.6845i) q^{85} +(-1.03016 - 3.84459i) q^{87} +(-3.00362 - 5.20243i) q^{89} +(14.1020 + 9.53952i) q^{91} +(-9.33049 - 2.50010i) q^{93} +(-0.603286 - 2.68836i) q^{95} +(3.70694 - 3.70694i) q^{97} -3.80931i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7}+O(q^{10}) $ 48 * q + 4 * q^7	$ 48 q + 4 q^{7} - 4 q^{11} - 8 q^{15} - 4 q^{21} + 4 q^{23} - 8 q^{25} - 36 q^{33} - 24 q^{35} + 8 q^{37} + 16 q^{43} + 48 q^{45} - 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} + 68 q^{63} + 12 q^{65} + 16 q^{67} + 64 q^{71} - 48 q^{73} + 48 q^{75} + 4 q^{77} - 40 q^{85} + 12 q^{87} + 80 q^{91} - 24 q^{95}+O(q^{100}) $ 48 * q + 4 * q^7 - 4 * q^11 - 8 * q^15 - 4 * q^21 + 4 * q^23 - 8 * q^25 - 36 * q^33 - 24 * q^35 + 8 * q^37 + 16 * q^43 + 48 * q^45 - 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 + 68 * q^63 + 12 * q^65 + 16 * q^67 + 64 * q^71 - 48 * q^73 + 48 * q^75 + 4 * q^77 - 40 * q^85 + 12 * q^87 + 80 * q^91 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.35944	−	0.364260i	0.784872	−	0.210306i	0.155940	−	0.987767i	$-0.450159\pi$
$3$	1.35944	−	0.364260i	0.784872	−	0.210306i	0.628931	+	0.777461i	$0.283493\pi$
$4$		0			0
$5$	−2.13431	−	0.666887i	−0.954491	−	0.298241i
$5$	−2.13431	−	0.666887i	−0.954491	−	0.298241i
$6$		0			0
$7$	−2.59782	+	0.501338i	−0.981883	+	0.189488i
$7$	−2.59782	+	0.501338i	−0.981883	+	0.189488i
$8$		0			0
$9$	−0.882692	+	0.509622i	−0.294231	+	0.169874i
$10$		0			0
$11$	−1.86869	+	3.23667i	−0.563432	+	0.975893i	0.433762	+	0.901028i	$0.357186\pi$
$11$	−1.86869	+	3.23667i	−0.563432	+	0.975893i	−0.997194	+	0.0748654i	$0.976147\pi$
$12$		0			0
$13$	−4.55026	−	4.55026i	−1.26201	−	1.26201i	−0.950115	−	0.311899i	$-0.899035\pi$
$13$	−4.55026	−	4.55026i	−1.26201	−	1.26201i	−0.311899	−	0.950115i	$-0.600965\pi$
$14$		0			0
$15$	−3.14438	−	0.129149i	−0.811874	−	0.0333461i
$16$		0			0
$17$	−1.58528	−	5.91633i	−0.384486	−	1.43492i	−0.838975	−	0.544169i	$-0.816845\pi$
$17$	−1.58528	−	5.91633i	−0.384486	−	1.43492i	0.454489	−	0.890752i	$-0.349822\pi$
$18$		0			0
$19$	0.616087	+	1.06709i	0.141340	+	0.244808i	0.928001	−	0.372577i	$-0.121526\pi$
$19$	0.616087	+	1.06709i	0.141340	+	0.244808i	−0.786661	+	0.617385i	$0.788192\pi$
$20$		0			0
$21$	−3.34895	+	1.62782i	−0.730802	+	0.355219i
$22$		0			0
$23$	2.69174	+	0.721250i	0.561267	+	0.150391i	0.528288	−	0.849065i	$-0.322834\pi$
$23$	2.69174	+	0.721250i	0.561267	+	0.150391i	0.0329787	+	0.999456i	$0.489501\pi$
$24$		0			0
$25$	4.11052	+	2.84668i	0.822105	+	0.569337i
$26$		0			0
$27$	−3.99986	+	3.99986i	−0.769774	+	0.769774i
$28$		0			0
$29$		−	2.82808i		−	0.525161i	−0.964910	−	0.262580i	$-0.915427\pi$
$29$		−	2.82808i		−	0.525161i	0.964910	−	0.262580i	$-0.0845735\pi$
$30$		0			0
$31$	−5.94396	−	3.43175i	−1.06757	−	0.616360i	−0.140051	−	0.990144i	$-0.544727\pi$
$31$	−5.94396	−	3.43175i	−1.06757	−	0.616360i	−0.927516	+	0.373784i	$0.878060\pi$
$32$		0			0
$33$	−1.36138	+	5.08074i	−0.236986	+	0.884444i
$34$		0			0
$35$	5.87887	+	0.662443i	0.993711	+	0.111973i
$36$		0			0
$37$	−2.01646	+	7.52551i	−0.331503	+	1.23719i	0.576108	+	0.817374i	$0.304571\pi$
$37$	−2.01646	+	7.52551i	−0.331503	+	1.23719i	−0.907611	+	0.419813i	$0.862096\pi$
$38$		0			0
$39$	−7.84327	−	4.52831i	−1.25593	−	0.725110i
$40$		0			0
$41$			5.56966i			0.869835i	0.900470	+	0.434917i	$0.143222\pi$
$41$			5.56966i			0.869835i	−0.900470	+	0.434917i	$0.856778\pi$
$42$		0			0
$43$	1.95176	−	1.95176i	0.297641	−	0.297641i	−0.542448	−	0.840089i	$-0.682503\pi$
$43$	1.95176	−	1.95176i	0.297641	−	0.297641i	0.840089	+	0.542448i	$0.182503\pi$
$44$		0			0
$45$	2.22379	−	0.499034i	0.331504	−	0.0743916i
$46$		0			0
$47$	11.1512	+	2.98797i	1.62658	+	0.435840i	0.952924	−	0.303209i	$-0.0980579\pi$
$47$	11.1512	+	2.98797i	1.62658	+	0.435840i	0.673652	+	0.739048i	$0.264725\pi$
$48$		0			0
$49$	6.49732	−	2.60477i	0.928189	−	0.372110i
$50$		0			0
$51$	−4.31017	−	7.46543i	−0.603544	−	1.04537i
$52$		0			0
$53$	−2.53082	−	9.44513i	−0.347634	−	1.29739i	−0.889504	−	0.456927i	$-0.848950\pi$
$53$	−2.53082	−	9.44513i	−0.347634	−	1.29739i	0.541870	−	0.840462i	$-0.317716\pi$
$54$		0			0
$55$	6.14686	−	5.66184i	0.828842	−	0.763442i
$56$		0			0
$57$	1.22623	+	1.22623i	0.162418	+	0.162418i
$58$		0			0
$59$	0.916152	−	1.58682i	0.119273	−	0.206587i	−0.800207	−	0.599724i	$-0.795277\pi$
$59$	0.916152	−	1.58682i	0.119273	−	0.206587i	0.919480	+	0.393137i	$0.128610\pi$
$60$		0			0
$61$	−3.43491	+	1.98315i	−0.439795	+	0.253916i	−0.703511	−	0.710685i	$-0.748385\pi$
$61$	−3.43491	+	1.98315i	−0.439795	+	0.253916i	0.263716	+	0.964600i	$0.415052\pi$
$62$		0			0
$63$	2.03758	−	1.76643i	0.256711	−	0.222550i
$64$		0			0
$65$	6.67713	+	12.7462i	0.828196	+	1.58097i
$66$		0			0
$67$	−7.93605	+	2.12646i	−0.969542	+	0.259788i	−0.708635	−	0.705576i	$-0.750689\pi$
$67$	−7.93605	+	2.12646i	−0.969542	+	0.259788i	−0.260908	+	0.965364i	$0.584022\pi$
$68$		0			0
$69$	3.92198			0.472151
$70$		0			0
$71$	−0.570063			−0.0676540			−0.0338270	−	0.999428i	$-0.510770\pi$
$71$	−0.570063			−0.0676540			−0.0338270	+	0.999428i	$0.510770\pi$
$72$		0			0
$73$	−2.03783	+	0.546036i	−0.238510	+	0.0639087i	−0.376094	−	0.926581i	$-0.622733\pi$
$73$	−2.03783	+	0.546036i	−0.238510	+	0.0639087i	0.137584	+	0.990490i	$0.456066\pi$
$74$		0			0
$75$	6.62493	+	2.37259i	0.764981	+	0.273963i
$76$		0			0
$77$	3.23186	−	9.34513i	0.368304	−	1.06498i
$78$		0			0
$79$	−9.47466	+	5.47020i	−1.06598	+	0.615445i	−0.927081	−	0.374861i	$-0.877690\pi$
$79$	−9.47466	+	5.47020i	−1.06598	+	0.615445i	−0.138901	+	0.990306i	$0.544357\pi$
$80$		0			0
$81$	−2.45170	+	4.24647i	−0.272411	+	0.471831i
$82$		0			0
$83$	−8.80820	−	8.80820i	−0.966826	−	0.966826i	0.0326414	−	0.999467i	$-0.489608\pi$
$83$	−8.80820	−	8.80820i	−0.966826	−	0.966826i	−0.999467	+	0.0326414i	$0.989608\pi$
$84$		0			0
$85$	−0.562062	+	13.6845i	−0.0609642	+	1.48429i
$86$		0			0
$87$	−1.03016	−	3.84459i	−0.110444	−	0.412184i
$88$		0			0
$89$	−3.00362	−	5.20243i	−0.318383	−	0.551456i	0.661767	−	0.749709i	$-0.269807\pi$
$89$	−3.00362	−	5.20243i	−0.318383	−	0.551456i	−0.980151	+	0.198253i	$0.936473\pi$
$90$		0			0
$91$	14.1020	+	9.53952i	1.47829	+	1.00001i
$92$		0			0
$93$	−9.33049	−	2.50010i	−0.967527	−	0.259248i
$94$		0			0
$95$	−0.603286	−	2.68836i	−0.0618959	−	0.275820i
$96$		0			0
$97$	3.70694	−	3.70694i	0.376383	−	0.376383i	−0.493413	−	0.869795i	$-0.664251\pi$
$97$	3.70694	−	3.70694i	0.376383	−	0.376383i	0.869795	+	0.493413i	$0.164251\pi$
$98$		0			0
$99$		−	3.80931i		−	0.382850i
$100$		0			0
$101$	3.46339	+	1.99959i	0.344620	+	0.198967i	0.662313	−	0.749227i	$-0.269575\pi$
$101$	3.46339	+	1.99959i	0.344620	+	0.198967i	−0.317693	+	0.948194i	$0.602908\pi$
$102$		0			0
$103$	−0.711944	+	2.65701i	−0.0701500	+	0.261803i	−0.992090	−	0.125530i	$-0.959937\pi$
$103$	−0.711944	+	2.65701i	−0.0701500	+	0.261803i	0.921940	+	0.387333i	$0.126604\pi$
$104$		0			0
$105$	8.23326	−	1.24089i	0.803484	−	0.121099i
$106$		0			0
$107$	2.19864	−	8.20544i	0.212551	−	0.793250i	−0.774464	−	0.632618i	$-0.781980\pi$
$107$	2.19864	−	8.20544i	0.212551	−	0.793250i	0.987014	−	0.160632i	$-0.0513531\pi$
$108$		0			0
$109$	−9.96993	−	5.75614i	−0.954946	−	0.551339i	−0.0603324	−	0.998178i	$-0.519216\pi$
$109$	−9.96993	−	5.75614i	−0.954946	−	0.551339i	−0.894614	+	0.446840i	$0.852549\pi$
$110$		0			0
$111$			10.9650i			1.04075i
$112$		0			0
$113$	7.36636	−	7.36636i	0.692969	−	0.692969i	−0.269915	−	0.962884i	$-0.586996\pi$
$113$	7.36636	−	7.36636i	0.692969	−	0.692969i	0.962884	+	0.269915i	$0.0869957\pi$
$114$		0			0
$115$	−5.26401	−	3.33446i	−0.490871	−	0.310940i
$116$		0			0
$117$	6.33539	+	1.69756i	0.585707	+	0.156940i
$118$		0			0
$119$	7.08435	+	14.5748i	0.649421	+	1.33607i
$120$		0			0
$121$	−1.48403	−	2.57041i	−0.134912	−	0.233674i
$122$		0			0
$123$	2.02880	+	7.57160i	0.182931	+	0.682708i
$124$		0			0
$125$	−6.87470	−	8.81695i	−0.614892	−	0.788612i
$126$		0			0
$127$	8.56353	+	8.56353i	0.759890	+	0.759890i	0.976302	−	0.216412i	$-0.0694355\pi$
$127$	8.56353	+	8.56353i	0.759890	+	0.759890i	−0.216412	+	0.976302i	$0.569435\pi$
$128$		0			0
$129$	1.94235	−	3.36425i	0.171014	−	0.296206i
$130$		0			0
$131$	−1.01451	+	0.585728i	−0.0886381	+	0.0511753i	−0.543664	−	0.839303i	$-0.682963\pi$
$131$	−1.01451	+	0.585728i	−0.0886381	+	0.0511753i	0.455026	+	0.890478i	$0.349630\pi$
$132$		0			0
$133$	−2.13546	−	2.46325i	−0.185168	−	0.213591i
$134$		0			0
$135$	11.2044	−	5.86947i	0.964320	−	0.505164i
$136$		0			0
$137$	9.91154	−	2.65579i	0.846800	−	0.226899i	0.190770	−	0.981635i	$-0.438901\pi$
$137$	9.91154	−	2.65579i	0.846800	−	0.226899i	0.656029	+	0.754735i	$0.272235\pi$
$138$		0			0
$139$	−8.10664			−0.687596			−0.343798	−	0.939044i	$-0.611714\pi$
$139$	−8.10664			−0.687596			−0.343798	+	0.939044i	$0.611714\pi$
$140$		0			0
$141$	16.2478			1.36831
$142$		0			0
$143$	23.2307	−	6.22465i	1.94265	−	0.520532i
$144$		0			0
$145$	−1.88601	+	6.03598i	−0.156624	+	0.501261i
$146$		0			0
$147$	7.88388	−	5.90774i	0.650252	−	0.487262i
$148$		0			0
$149$	−5.60127	+	3.23390i	−0.458874	+	0.264931i	−0.711571	−	0.702614i	$-0.752016\pi$
$149$	−5.60127	+	3.23390i	−0.458874	+	0.264931i	0.252697	+	0.967546i	$0.418683\pi$
$150$		0			0
$151$	−3.00407	+	5.20320i	−0.244468	+	0.423430i	−0.961982	−	0.273114i	$-0.911947\pi$
$151$	−3.00407	+	5.20320i	−0.244468	+	0.423430i	0.717514	+	0.696544i	$0.245280\pi$
$152$		0			0
$153$	4.41441	+	4.41441i	0.356884	+	0.356884i
$154$		0			0
$155$	10.3976	+	11.2884i	0.835159	+	0.906702i
$156$		0			0
$157$	1.77930	+	6.64043i	0.142003	+	0.529964i	0.999871	+	0.0160922i	$0.00512252\pi$
$157$	1.77930	+	6.64043i	0.142003	+	0.529964i	−0.857867	+	0.513871i	$0.828211\pi$
$158$		0			0
$159$	−6.88097	−	11.9182i	−0.545697	−	0.945174i
$160$		0			0
$161$	−7.35425	−	0.524203i	−0.579596	−	0.0413130i
$162$		0			0
$163$	−12.6434	−	3.38778i	−0.990305	−	0.265351i	−0.272926	−	0.962035i	$-0.587992\pi$
$163$	−12.6434	−	3.38778i	−0.990305	−	0.265351i	−0.717379	+	0.696683i	$0.754658\pi$
$164$		0			0
$165$	6.29389	−	9.93597i	0.489978	−	0.773514i
$166$		0			0
$167$	−6.33743	+	6.33743i	−0.490405	+	0.490405i	−0.908434	−	0.418029i	$-0.862721\pi$
$167$	−6.33743	+	6.33743i	−0.490405	+	0.490405i	0.418029	+	0.908434i	$0.362721\pi$
$168$		0			0
$169$			28.4097i			2.18536i
$170$		0			0
$171$	−1.08763	−	0.627943i	−0.0831731	−	0.0480200i
$172$		0			0
$173$	0.523701	−	1.95448i	0.0398162	−	0.148596i	−0.943156	−	0.332350i	$-0.892158\pi$
$173$	0.523701	−	1.95448i	0.0398162	−	0.148596i	0.982972	+	0.183754i	$0.0588250\pi$
$174$		0			0
$175$	−12.1055	−	5.33440i	−0.915093	−	0.403243i
$176$		0			0
$177$	0.667435	−	2.49090i	0.0501675	−	0.187228i
$178$		0			0
$179$	3.54703	+	2.04788i	0.265118	+	0.153066i	0.626667	−	0.779287i	$-0.284419\pi$
$179$	3.54703	+	2.04788i	0.265118	+	0.153066i	−0.361549	+	0.932353i	$0.617752\pi$
$180$		0			0
$181$		−	10.6327i		−	0.790323i	−0.918612	−	0.395162i	$-0.870689\pi$
$181$		−	10.6327i		−	0.790323i	0.918612	−	0.395162i	$-0.129311\pi$
$182$		0			0
$183$	−3.94716	+	3.94716i	−0.291783	+	0.291783i
$184$		0			0
$185$	9.32240	−	14.7170i	0.685397	−	1.08202i
$186$		0			0
$187$	22.1116	+	5.92479i	1.61696	+	0.433264i
$188$		0			0
$189$	8.38563	−	12.3962i	0.609965	−	0.901690i
$190$		0			0
$191$	6.36951	+	11.0323i	0.460882	+	0.798271i	0.999005	−	0.0445955i	$-0.0141999\pi$
$191$	6.36951	+	11.0323i	0.460882	+	0.798271i	−0.538123	+	0.842866i	$0.680867\pi$
$192$		0			0
$193$	−2.98349	−	11.1345i	−0.214756	−	0.801482i	−0.986252	−	0.165247i	$-0.947158\pi$
$193$	−2.98349	−	11.1345i	−0.214756	−	0.801482i	0.771496	−	0.636234i	$-0.219509\pi$
$194$		0			0
$195$	13.7201	+	14.8954i	0.982514	+	1.06668i
$196$		0			0
$197$	−4.36293	−	4.36293i	−0.310846	−	0.310846i	0.534391	−	0.845237i	$-0.320541\pi$
$197$	−4.36293	−	4.36293i	−0.310846	−	0.310846i	−0.845237	+	0.534391i	$0.820541\pi$
$198$		0			0
$199$	8.80171	−	15.2450i	0.623937	−	1.08069i	−0.364809	−	0.931082i	$-0.618866\pi$
$199$	8.80171	−	15.2450i	0.623937	−	1.08069i	0.988745	−	0.149608i	$-0.0478011\pi$
$200$		0			0
$201$	−10.0140	+	5.78157i	−0.706331	+	0.407801i
$202$		0			0
$203$	1.41782	+	7.34683i	0.0995117	+	0.515646i
$204$		0			0
$205$	3.71433	−	11.8874i	0.259420	−	0.830249i
$206$		0			0
$207$	−2.74354	+	0.735130i	−0.190689	+	0.0510951i
$208$		0			0
$209$	−4.60511			−0.318542
$210$		0			0
$211$	−22.0556			−1.51837			−0.759185	−	0.650875i	$-0.774402\pi$
$211$	−22.0556			−1.51837			−0.759185	+	0.650875i	$0.774402\pi$
$212$		0			0
$213$	−0.774964	+	0.207651i	−0.0530997	+	0.0142280i
$214$		0			0
$215$	−5.46727	+	2.86405i	−0.372864	+	0.195327i
$216$		0			0
$217$	17.1618	+	5.93512i	1.16502	+	0.402902i
$218$		0			0
$219$	−2.57141	+	1.48460i	−0.173760	+	0.100320i
$220$		0			0
$221$	−19.7074	+	34.1343i	−1.32566	+	2.29612i
$222$		0			0
$223$	−8.37713	−	8.37713i	−0.560974	−	0.560974i	0.368610	−	0.929584i	$-0.379834\pi$
$223$	−8.37713	−	8.37713i	−0.560974	−	0.560974i	−0.929584	+	0.368610i	$0.879834\pi$
$224$		0			0
$225$	−5.07906	−	0.417929i	−0.338604	−	0.0278620i
$226$		0			0
$227$	−3.05323	−	11.3948i	−0.202650	−	0.756300i	−0.990153	−	0.139989i	$-0.955293\pi$
$227$	−3.05323	−	11.3948i	−0.202650	−	0.756300i	0.787503	−	0.616311i	$-0.211374\pi$
$228$		0			0
$229$	−3.21704	−	5.57208i	−0.212588	−	0.368214i	0.739936	−	0.672678i	$-0.234856\pi$
$229$	−3.21704	−	5.57208i	−0.212588	−	0.368214i	−0.952524	+	0.304464i	$0.901523\pi$
$230$		0			0
$231$	0.989449	−	13.8814i	0.0651010	−	0.913326i
$232$		0			0
$233$	14.6729	+	3.93160i	0.961256	+	0.257568i	0.705132	−	0.709076i	$-0.250888\pi$
$233$	14.6729	+	3.93160i	0.961256	+	0.257568i	0.256124	+	0.966644i	$0.417554\pi$
$234$		0			0
$235$	−21.8075	−	13.8139i	−1.42257	−	0.901117i
$236$		0			0
$237$	−10.8876	+	10.8876i	−0.707228	+	0.707228i
$238$		0			0
$239$			17.0337i			1.10182i	0.834566	+	0.550908i	$0.185718\pi$
$239$			17.0337i			1.10182i	−0.834566	+	0.550908i	$0.814282\pi$
$240$		0			0
$241$	−0.561340	−	0.324090i	−0.0361591	−	0.0208765i	0.481811	−	0.876275i	$-0.339979\pi$
$241$	−0.561340	−	0.324090i	−0.0361591	−	0.0208765i	−0.517971	+	0.855398i	$0.673312\pi$
$242$		0			0
$243$	2.60604	−	9.72586i	0.167177	−	0.623914i
$244$		0			0
$245$	−15.6044	+	1.22640i	−0.996926	+	0.0783518i
$246$		0			0
$247$	2.05220	−	7.65890i	0.130578	−	0.487324i
$248$		0			0
$249$	−15.1827	−	8.76572i	−0.962163	−	0.555505i
$250$		0			0
$251$			2.99161i			0.188828i	0.995533	+	0.0944142i	$0.0300978\pi$
$251$			2.99161i			0.188828i	−0.995533	+	0.0944142i	$0.969902\pi$
$252$		0			0
$253$	−7.36449	+	7.36449i	−0.463002	+	0.463002i
$254$		0			0
$255$	4.22062	+	18.8079i	0.264305	+	1.17780i
$256$		0			0
$257$	4.56640	+	1.22356i	0.284844	+	0.0763237i	0.398412	−	0.917206i	$-0.369561\pi$
$257$	4.56640	+	1.22356i	0.284844	+	0.0763237i	−0.113568	+	0.993530i	$0.536228\pi$
$258$		0			0
$259$	1.46556	−	20.5608i	0.0910652	−	1.27759i
$260$		0			0
$261$	1.44125	+	2.49632i	0.0892112	+	0.154518i
$262$		0			0
$263$	−6.44367	−	24.0481i	−0.397334	−	1.48287i	−0.817769	−	0.575547i	$-0.804789\pi$
$263$	−6.44367	−	24.0481i	−0.397334	−	1.48287i	0.420435	−	0.907323i	$-0.361877\pi$
$264$		0			0
$265$	−0.897304	+	21.8466i	−0.0551210	+	1.34202i
$266$		0			0
$267$	−5.97828	−	5.97828i	−0.365865	−	0.365865i
$268$		0			0
$269$	−0.153942	+	0.266636i	−0.00938603	+	0.0162571i	−0.870680	−	0.491849i	$-0.836321\pi$
$269$	−0.153942	+	0.266636i	−0.00938603	+	0.0162571i	0.861294	+	0.508107i	$0.169654\pi$
$270$		0			0
$271$	−24.2593	+	14.0061i	−1.47365	+	0.850812i	−0.999560	−	0.0296653i	$-0.990556\pi$
$271$	−24.2593	+	14.0061i	−1.47365	+	0.850812i	−0.474089	+	0.880477i	$0.657223\pi$
$272$		0			0
$273$	22.6456	+	7.83160i	1.37057	+	0.473990i
$274$		0			0
$275$	−16.8951	+	7.98483i	−1.01881	+	0.481504i
$276$		0			0
$277$	−27.3318	+	7.32354i	−1.64221	+	0.440029i	−0.957417	−	0.288708i	$-0.906774\pi$
$277$	−27.3318	+	7.32354i	−1.64221	+	0.440029i	−0.684793	+	0.728737i	$0.740108\pi$
$278$		0			0
$279$	6.99558			0.418814
$280$		0			0
$281$	−2.60283			−0.155272			−0.0776358	−	0.996982i	$-0.524737\pi$
$281$	−2.60283			−0.155272			−0.0776358	+	0.996982i	$0.524737\pi$
$282$		0			0
$283$	−17.4371	+	4.67227i	−1.03653	+	0.277738i	−0.736675	−	0.676247i	$-0.763605\pi$
$283$	−17.4371	+	4.67227i	−1.03653	+	0.277738i	−0.299856	+	0.953985i	$0.596939\pi$
$284$		0			0
$285$	−1.79939	−	3.43491i	−0.106587	−	0.203467i
$286$		0			0
$287$	−2.79228	−	14.4690i	−0.164823	−	0.854076i
$288$		0			0
$289$	−17.7675	+	10.2581i	−1.04515	+	0.603415i
$290$		0			0
$291$	3.68906	−	6.38965i	0.216257	−	0.374568i
$292$		0			0
$293$	17.2326	+	17.2326i	1.00674	+	1.00674i	0.999977	+	0.00676223i	$0.00215250\pi$
$293$	17.2326	+	17.2326i	1.00674	+	1.00674i	0.00676223	+	0.999977i	$0.497848\pi$
$294$		0			0
$295$	−3.01358	+	2.77579i	−0.175457	+	0.161613i
$296$		0			0
$297$	−5.47172	−	20.4207i	−0.317502	−	1.18493i
$298$		0			0
$299$	−8.96625	−	15.5300i	−0.518532	−	0.898123i
$300$		0			0
$301$	−4.09183	+	6.04882i	−0.235849	+	0.348648i
$302$		0			0
$303$	5.43663	+	1.45674i	0.312327	+	0.0836876i
$304$		0			0
$305$	8.65368	−	1.94194i	0.495508	−	0.111195i
$306$		0			0
$307$	11.3375	−	11.3375i	0.647063	−	0.647063i	−0.305219	−	0.952282i	$-0.598730\pi$
$307$	11.3375	−	11.3375i	0.647063	−	0.647063i	0.952282	+	0.305219i	$0.0987298\pi$
$308$		0			0
$309$			3.87137i			0.220235i
$310$		0			0
$311$	−17.9899	−	10.3865i	−1.02011	−	0.588962i	−0.105975	−	0.994369i	$-0.533796\pi$
$311$	−17.9899	−	10.3865i	−1.02011	−	0.588962i	−0.914136	+	0.405407i	$0.867130\pi$
$312$		0			0
$313$	−1.96776	+	7.34380i	−0.111225	+	0.415096i	−0.998977	−	0.0452258i	$-0.985599\pi$
$313$	−1.96776	+	7.34380i	−0.111225	+	0.415096i	0.887752	+	0.460322i	$0.152266\pi$
$314$		0			0
$315$	−5.52683	+	2.41127i	−0.311402	+	0.135860i
$316$		0			0
$317$	−0.442998	+	1.65329i	−0.0248812	+	0.0928581i	−0.977250	−	0.212091i	$-0.931973\pi$
$317$	−0.442998	+	1.65329i	−0.0248812	+	0.0928581i	0.952369	+	0.304949i	$0.0986394\pi$
$318$		0			0
$319$	9.15356	+	5.28481i	0.512501	+	0.295892i
$320$		0			0
$321$		−	11.9557i		−	0.667300i
$322$		0			0
$323$	5.33661	−	5.33661i	0.296937	−	0.296937i
$324$		0			0
$325$	−5.75080	−	31.6571i	−0.318997	−	1.75602i
$326$		0			0
$327$	−15.6502	−	4.19347i	−0.865460	−	0.231899i
$328$		0			0
$329$	−30.4669	−	2.17165i	−1.67969	−	0.119727i
$330$		0			0
$331$	13.0087	+	22.5317i	0.715023	+	1.23846i	0.962951	+	0.269678i	$0.0869171\pi$
$331$	13.0087	+	22.5317i	0.715023	+	1.23846i	−0.247928	+	0.968779i	$0.579750\pi$
$332$		0			0
$333$	−2.05526	−	7.67034i	−0.112628	−	0.420332i
$334$		0			0
$335$	18.3561	+	0.753938i	1.00290	+	0.0411921i
$336$		0			0
$337$	−22.0521	−	22.0521i	−1.20125	−	1.20125i	−0.973785	−	0.227468i	$-0.926955\pi$
$337$	−22.0521	−	22.0521i	−1.20125	−	1.20125i	−0.227468	−	0.973785i	$-0.573045\pi$
$338$		0			0
$339$	7.33083	−	12.6974i	0.398156	−	0.689627i
$340$		0			0
$341$	22.2149	−	12.8258i	1.20300	−	0.694554i
$342$		0			0
$343$	−15.5730	+	10.0241i	−0.840862	+	0.541249i
$344$		0			0
$345$	−8.37070	−	2.61552i	−0.450663	−	0.140815i
$346$		0			0
$347$	−21.3424	+	5.71867i	−1.14572	+	0.306994i	−0.781248	−	0.624221i	$-0.785417\pi$
$347$	−21.3424	+	5.71867i	−1.14572	+	0.306994i	−0.364470	+	0.931215i	$0.618750\pi$
$348$		0			0
$349$	21.6246			1.15754			0.578770	−	0.815491i	$-0.303533\pi$
$349$	21.6246			1.15754			0.578770	+	0.815491i	$0.303533\pi$
$350$		0			0
$351$	36.4008			1.94293
$352$		0			0
$353$	−3.65400	+	0.979086i	−0.194483	+	0.0521115i	−0.354746	−	0.934963i	$-0.615433\pi$
$353$	−3.65400	+	0.979086i	−0.194483	+	0.0521115i	0.160263	+	0.987074i	$0.448766\pi$
$354$		0			0
$355$	1.21669	+	0.380167i	0.0645751	+	0.0201772i
$356$		0			0
$357$	14.9397	+	17.2330i	0.790695	+	0.912066i
$358$		0			0
$359$	−3.68781	+	2.12916i	−0.194635	+	0.112373i	−0.594151	−	0.804354i	$-0.702512\pi$
$359$	−3.68781	+	2.12916i	−0.194635	+	0.112373i	0.399516	+	0.916726i	$0.369178\pi$
$360$		0			0
$361$	8.74087	−	15.1396i	0.460046	−	0.796823i
$362$		0			0
$363$	−2.95374	−	2.95374i	−0.155031	−	0.155031i
$364$		0			0
$365$	4.71351	+	0.193598i	0.246716	+	0.0101334i
$366$		0			0
$367$	6.08811	+	22.7211i	0.317797	+	1.18603i	0.921357	+	0.388716i	$0.127081\pi$
$367$	6.08811	+	22.7211i	0.317797	+	1.18603i	−0.603561	+	0.797317i	$0.706252\pi$
$368$		0			0
$369$	−2.83842	−	4.91629i	−0.147762	−	0.255932i
$370$		0			0
$371$	11.3098	+	23.2679i	0.587176	+	1.20801i
$372$		0			0
$373$	7.55500	+	2.02436i	0.391183	+	0.104817i	0.449049	−	0.893507i	$-0.351763\pi$
$373$	7.55500	+	2.02436i	0.391183	+	0.104817i	−0.0578658	+	0.998324i	$0.518430\pi$
$374$		0			0
$375$	−12.5574	−	9.48191i	−0.648460	−	0.489644i
$376$		0			0
$377$	−12.8685	+	12.8685i	−0.662760	+	0.662760i
$378$		0			0
$379$			24.6449i			1.26592i	0.774184	+	0.632961i	$0.218161\pi$
$379$			24.6449i			1.26592i	−0.774184	+	0.632961i	$0.781839\pi$
$380$		0			0
$381$	14.7609	+	8.52223i	0.756225	+	0.436607i
$382$		0			0
$383$	−6.07201	+	22.6611i	−0.310265	+	1.15793i	0.618052	+	0.786137i	$0.287922\pi$
$383$	−6.07201	+	22.6611i	−0.310265	+	1.15793i	−0.928317	+	0.371789i	$0.878745\pi$
$384$		0			0
$385$	−13.1299	+	17.7901i	−0.669163	+	0.906667i
$386$		0			0
$387$	−0.728143	+	2.71747i	−0.0370136	+	0.138137i
$388$		0			0
$389$	20.5933	+	11.8895i	1.04412	+	0.602823i	0.920998	−	0.389568i	$-0.127376\pi$
$389$	20.5933	+	11.8895i	1.04412	+	0.602823i	0.123123	+	0.992391i	$0.460709\pi$
$390$		0			0
$391$		−	17.0686i		−	0.863198i
$392$		0			0
$393$	−1.16581	+	1.16581i	−0.0588071	+	0.0588071i
$394$		0			0
$395$	23.8698	−	5.35654i	1.20102	−	0.269517i
$396$		0			0
$397$	22.3418	+	5.98647i	1.12130	+	0.300452i	0.771410	−	0.636338i	$-0.219552\pi$
$397$	22.3418	+	5.98647i	1.12130	+	0.300452i	0.349892	+	0.936790i	$0.386218\pi$
$398$		0			0
$399$	−3.80028	−	2.57077i	−0.190252	−	0.128699i
$400$		0			0
$401$	−18.8264	−	32.6083i	−0.940147	−	1.62838i	−0.765187	−	0.643808i	$-0.777354\pi$
$401$	−18.8264	−	32.6083i	−0.940147	−	1.62838i	−0.174960	−	0.984576i	$-0.555980\pi$
$402$		0			0
$403$	11.4312	+	42.6619i	0.569430	+	2.12514i
$404$		0			0
$405$	8.06461	−	7.42827i	0.400733	−	0.369114i
$406$		0			0
$407$	−20.5895	−	20.5895i	−1.02058	−	1.02058i
$408$		0			0
$409$	−3.10540	+	5.37871i	−0.153552	+	0.265960i	−0.932531	−	0.361090i	$-0.882405\pi$
$409$	−3.10540	+	5.37871i	−0.153552	+	0.265960i	0.778979	+	0.627050i	$0.215738\pi$
$410$		0			0
$411$	12.5067	−	7.22076i	0.616911	−	0.356174i
$412$		0			0
$413$	−1.58446	+	4.58158i	−0.0779663	+	0.225445i
$414$		0			0
$415$	12.9253	+	24.6735i	0.634479	+	1.21117i
$416$		0			0
$417$	−11.0205	+	2.95292i	−0.539674	+	0.144605i
$418$		0			0
$419$	12.9069			0.630541			0.315270	−	0.949002i	$-0.397905\pi$
$419$	12.9069			0.630541			0.315270	+	0.949002i	$0.397905\pi$
$420$		0			0
$421$	−25.0983			−1.22322			−0.611608	−	0.791161i	$-0.709477\pi$
$421$	−25.0983			−1.22322			−0.611608	+	0.791161i	$0.709477\pi$
$422$		0			0
$423$	−11.3658	+	3.04547i	−0.552626	+	0.148076i
$424$		0			0
$425$	10.3256	−	28.8320i	0.500866	−	1.39856i
$426$		0			0
$427$	7.92904	−	6.87390i	0.383713	−	0.332651i
$428$		0			0
$429$	29.3133	−	16.9241i	1.41526	−	0.817101i
$430$		0			0
$431$	14.1918	−	24.5809i	0.683593	−	1.18402i	−0.290283	−	0.956941i	$-0.593750\pi$
$431$	14.1918	−	24.5809i	0.683593	−	1.18402i	0.973877	−	0.227078i	$-0.0729171\pi$
$432$		0			0
$433$	−20.7667	−	20.7667i	−0.997984	−	0.997984i	0.00201350	−	0.999998i	$-0.499359\pi$
$433$	−20.7667	−	20.7667i	−0.997984	−	0.997984i	−0.999998	+	0.00201350i	$0.999359\pi$
$434$		0			0
$435$	−0.365243	+	8.89254i	−0.0175121	+	0.426365i
$436$		0			0
$437$	0.888706	+	3.31669i	0.0425125	+	0.158659i
$438$		0			0
$439$	2.84512	+	4.92790i	0.135790	+	0.235196i	0.925899	−	0.377771i	$-0.123309\pi$
$439$	2.84512	+	4.92790i	0.135790	+	0.235196i	−0.790109	+	0.612967i	$0.789976\pi$
$440$		0			0
$441$	−4.40768	+	5.61039i	−0.209890	+	0.267161i
$442$		0			0
$443$	−12.6459	−	3.38845i	−0.600824	−	0.160990i	−0.0544285	−	0.998518i	$-0.517334\pi$
$443$	−12.6459	−	3.38845i	−0.600824	−	0.160990i	−0.546395	+	0.837527i	$0.684000\pi$
$444$		0			0
$445$	2.94122	+	13.1067i	0.139427	+	0.621315i
$446$		0			0
$447$	−6.43660	+	6.43660i	−0.304441	+	0.304441i
$448$		0			0
$449$			11.4035i			0.538163i	0.963117	+	0.269081i	$0.0867200\pi$
$449$			11.4035i			0.538163i	−0.963117	+	0.269081i	$0.913280\pi$
$450$		0			0
$451$	−18.0272	−	10.4080i	−0.848866	−	0.490093i
$452$		0			0
$453$	−2.18853	+	8.16769i	−0.102826	+	0.383751i
$454$		0			0
$455$	−23.7361	−	29.7647i	−1.11277	−	1.39539i
$456$		0			0
$457$	−0.658264	+	2.45668i	−0.0307923	+	0.114918i	−0.979611	−	0.200901i	$-0.935613\pi$
$457$	−0.658264	+	2.45668i	−0.0307923	+	0.114918i	0.948819	+	0.315820i	$0.102280\pi$
$458$		0			0
$459$	30.0054	+	17.3236i	1.40053	+	0.808597i
$460$		0			0
$461$		−	28.3975i		−	1.32260i	−0.750121	−	0.661301i	$-0.770005\pi$
$461$		−	28.3975i		−	1.32260i	0.750121	−	0.661301i	$-0.229995\pi$
$462$		0			0
$463$	8.29144	−	8.29144i	0.385336	−	0.385336i	−0.487684	−	0.873020i	$-0.662158\pi$
$463$	8.29144	−	8.29144i	0.385336	−	0.385336i	0.873020	+	0.487684i	$0.162158\pi$
$464$		0			0
$465$	18.2468	+	11.5584i	0.846177	+	0.536006i
$466$		0			0
$467$	−1.67367	−	0.448458i	−0.0774481	−	0.0207522i	0.219887	−	0.975525i	$-0.429431\pi$
$467$	−1.67367	−	0.448458i	−0.0774481	−	0.0207522i	−0.297335	+	0.954773i	$0.596098\pi$
$468$		0			0
$469$	19.5503	−	9.50279i	0.902751	−	0.438798i
$470$		0			0
$471$	4.83768	+	8.37912i	0.222909	+	0.386089i
$472$		0			0
$473$	2.66997	+	9.96446i	0.122765	+	0.458166i
$474$		0			0
$475$	−0.505238	+	6.14012i	−0.0231819	+	0.281728i
$476$		0			0
$477$	7.04738	+	7.04738i	0.322677	+	0.322677i
$478$		0			0
$479$	10.7131	−	18.5557i	0.489496	−	0.847831i	−0.510431	−	0.859919i	$-0.670514\pi$
$479$	10.7131	−	18.5557i	0.489496	−	0.847831i	0.999927	+	0.0120872i	$0.00384756\pi$
$480$		0			0
$481$	43.4184	−	25.0676i	1.97971	−	1.14299i
$482$		0			0
$483$	−10.1886	+	1.96624i	−0.463597	+	0.0894669i
$484$		0			0
$485$	−10.3839	+	5.43963i	−0.471507	+	0.247001i
$486$		0			0
$487$	37.5562	−	10.0631i	1.70183	−	0.456005i	0.728433	−	0.685117i	$-0.240249\pi$
$487$	37.5562	−	10.0631i	1.70183	−	0.456005i	0.973400	+	0.229112i	$0.0735822\pi$
$488$		0			0
$489$	−18.4219			−0.833067
$490$		0			0
$491$	5.54467			0.250228			0.125114	−	0.992142i	$-0.460070\pi$
$491$	5.54467			0.250228			0.125114	+	0.992142i	$0.460070\pi$
$492$		0			0
$493$	−16.7318	+	4.48329i	−0.753565	+	0.201917i
$494$		0			0
$495$	−2.54038	+	8.13023i	−0.114182	+	0.365427i
$496$		0			0
$497$	1.48092	−	0.285794i	0.0664283	−	0.0128196i
$498$		0			0
$499$	−4.28573	+	2.47437i	−0.191856	+	0.110768i	−0.592851	−	0.805312i	$-0.701998\pi$
$499$	−4.28573	+	2.47437i	−0.191856	+	0.110768i	0.400995	+	0.916080i	$0.368664\pi$
$500$		0			0
$501$	−6.30686	+	10.9238i	−0.281770	+	0.488040i
$502$		0			0
$503$	−14.3450	−	14.3450i	−0.639614	−	0.639614i	0.310846	−	0.950460i	$-0.399388\pi$
$503$	−14.3450	−	14.3450i	−0.639614	−	0.639614i	−0.950460	+	0.310846i	$0.899388\pi$
$504$		0			0
$505$	−6.05844	−	6.57743i	−0.269597	−	0.292692i
$506$		0			0
$507$	10.3485	+	38.6212i	0.459594	+	1.71523i
$508$		0			0
$509$	17.6679	+	30.6017i	0.783116	+	1.35640i	0.930118	+	0.367260i	$0.119704\pi$
$509$	17.6679	+	30.6017i	0.783116	+	1.35640i	−0.147002	+	0.989136i	$0.546962\pi$
$510$		0			0
$511$	5.02017	−	2.44015i	0.222079	−	0.107946i
$512$		0			0
$513$	−6.73249	−	1.80396i	−0.297247	−	0.0796470i
$514$		0			0
$515$	3.29143	−	5.19609i	0.145038	−	0.228967i
$516$		0			0
$517$	−30.5093	+	30.5093i	−1.34180	+	1.34180i
$518$		0			0
$519$		−	2.84775i		−	0.125002i
$520$		0			0
$521$	−19.0681	−	11.0090i	−0.835388	−	0.482312i	0.0203058	−	0.999794i	$-0.493536\pi$
$521$	−19.0681	−	11.0090i	−0.835388	−	0.482312i	−0.855694	+	0.517482i	$0.826869\pi$
$522$		0			0
$523$	6.80926	−	25.4125i	0.297748	−	1.11121i	−0.641262	−	0.767322i	$-0.721589\pi$
$523$	6.80926	−	25.4125i	0.297748	−	1.11121i	0.939010	−	0.343889i	$-0.111744\pi$
$524$		0			0
$525$	−18.3998	−	2.84222i	−0.803035	−	0.124045i
$526$		0			0
$527$	−10.8805	+	40.6067i	−0.473964	+	1.76886i
$528$		0			0
$529$	−13.1933	−	7.61716i	−0.573622	−	0.331181i
$530$		0			0
$531$			1.86757i			0.0810454i
$532$		0			0
$533$	25.3434	−	25.3434i	1.09774	−	1.09774i
$534$		0			0
$535$	−10.1647	+	16.0467i	−0.439457	+	0.693758i
$536$		0			0
$537$	5.56793	+	1.49192i	0.240274	+	0.0643812i
$538$		0			0
$539$	−3.71071	+	25.8972i	−0.159831	+	1.11547i
$540$		0			0
$541$	3.33567	+	5.77755i	0.143412	+	0.248396i	0.928779	−	0.370633i	$-0.120859\pi$
$541$	3.33567	+	5.77755i	0.143412	+	0.248396i	−0.785368	+	0.619030i	$0.787526\pi$
$542$		0			0
$543$	−3.87307	−	14.4545i	−0.166209	−	0.620302i
$544$		0			0
$545$	17.4402	+	18.9342i	0.747056	+	0.811052i
$546$		0			0
$547$	−8.18996	−	8.18996i	−0.350177	−	0.350177i	0.509998	−	0.860175i	$-0.329646\pi$
$547$	−8.18996	−	8.18996i	−0.350177	−	0.350177i	−0.860175	+	0.509998i	$0.829646\pi$
$548$		0			0
$549$	2.02131	−	3.50101i	0.0862674	−	0.149420i
$550$		0			0
$551$	3.01782	−	1.74234i	0.128564	−	0.0742262i
$552$		0			0
$553$	21.8710	−	18.9606i	0.930050	−	0.806286i
$554$		0			0
$555$	7.31240	−	23.4026i	0.310394	−	0.993386i
$556$		0			0
$557$	36.4271	−	9.76062i	1.54347	−	0.413571i	0.616083	−	0.787681i	$-0.288719\pi$
$557$	36.4271	−	9.76062i	1.54347	−	0.413571i	0.927384	+	0.374111i	$0.122052\pi$
$558$		0			0
$559$	−17.7621			−0.751255
$560$		0			0
$561$	32.2175			1.36023
$562$		0			0
$563$	37.2256	−	9.97457i	1.56887	−	0.420378i	0.633413	−	0.773814i	$-0.281653\pi$
$563$	37.2256	−	9.97457i	1.56887	−	0.420378i	0.935459	+	0.353436i	$0.114987\pi$
$564$		0			0
$565$	−20.6346	+	10.8095i	−0.868104	+	0.454760i
$566$		0			0
$567$	4.24016	−	12.2607i	0.178070	−	0.514901i
$568$		0			0
$569$	10.4114	−	6.01105i	0.436470	−	0.251996i	−0.265629	−	0.964075i	$-0.585580\pi$
$569$	10.4114	−	6.01105i	0.436470	−	0.251996i	0.702099	+	0.712079i	$0.252246\pi$
$570$		0			0
$571$	15.7498	−	27.2794i	0.659107	−	1.14161i	−0.321740	−	0.946828i	$-0.604268\pi$
$571$	15.7498	−	27.2794i	0.659107	−	1.14161i	0.980847	−	0.194779i	$-0.0623990\pi$
$572$		0			0
$573$	12.6776	+	12.6776i	0.529614	+	0.529614i
$574$		0			0
$575$	9.01130	+	10.6273i	0.375797	+	0.443187i
$576$		0			0
$577$	3.14609	+	11.7414i	0.130973	+	0.488800i	0.999982	−	0.00599739i	$-0.00190904\pi$
$577$	3.14609	+	11.7414i	0.130973	+	0.488800i	−0.869009	+	0.494797i	$0.835242\pi$
$578$		0			0
$579$	−8.11174	−	14.0499i	−0.337112	−	0.583896i
$580$		0			0
$581$	27.2980	+	18.4662i	1.13251	+	0.766108i
$582$		0			0
$583$	35.3001	+	9.45864i	1.46198	+	0.391737i
$584$		0			0
$585$	−12.3896	−	7.84811i	−0.512246	−	0.324479i
$586$		0			0
$587$	−19.1797	+	19.1797i	−0.791631	+	0.791631i	−0.981759	−	0.190128i	$-0.939110\pi$
$587$	−19.1797	+	19.1797i	−0.791631	+	0.791631i	0.190128	+	0.981759i	$0.439110\pi$
$588$		0			0
$589$		−	8.45702i		−	0.348465i
$590$		0			0
$591$	−7.52038	−	4.34189i	−0.309347	−	0.178602i
$592$		0			0
$593$	−7.89583	+	29.4676i	−0.324243	+	1.21009i	0.590828	+	0.806797i	$0.298801\pi$
$593$	−7.89583	+	29.4676i	−0.324243	+	1.21009i	−0.915071	+	0.403293i	$0.867866\pi$
$594$		0			0
$595$	−5.40041	−	35.8315i	−0.221395	−	1.46895i
$596$		0			0
$597$	6.41223	−	23.9307i	0.262435	−	0.979420i
$598$		0			0
$599$	13.8406	+	7.99090i	0.565513	+	0.326499i	0.755355	−	0.655315i	$-0.227464\pi$
$599$	13.8406	+	7.99090i	0.565513	+	0.326499i	−0.189842	+	0.981815i	$0.560798\pi$
$600$		0			0
$601$		−	35.9834i		−	1.46779i	−0.679260	−	0.733897i	$-0.737699\pi$
$601$		−	35.9834i		−	1.46779i	0.679260	−	0.733897i	$-0.262301\pi$
$602$		0			0
$603$	5.92139	−	5.92139i	0.241138	−	0.241138i
$604$		0			0
$605$	1.45319	+	6.47572i	0.0590807	+	0.263275i
$606$		0			0
$607$	1.70600	+	0.457120i	0.0692442	+	0.0185539i	0.293275	−	0.956028i	$-0.405255\pi$
$607$	1.70600	+	0.457120i	0.0692442	+	0.0185539i	−0.224031	+	0.974582i	$0.571922\pi$
$608$		0			0
$609$	4.60360	+	9.47110i	0.186547	+	0.383788i
$610$		0			0
$611$	−37.1450	−	64.3371i	−1.50273	−	2.60280i
$612$		0			0
$613$	−0.979533	−	3.65567i	−0.0395629	−	0.147651i	0.943319	−	0.331887i	$-0.107685\pi$
$613$	−0.979533	−	3.65567i	−0.0395629	−	0.147651i	−0.982882	+	0.184237i	$0.941019\pi$
$614$		0			0
$615$	0.719316	−	17.5131i	0.0290056	−	0.706196i
$616$		0			0
$617$	−2.94869	−	2.94869i	−0.118710	−	0.118710i	0.645256	−	0.763966i	$-0.276751\pi$
$617$	−2.94869	−	2.94869i	−0.118710	−	0.118710i	−0.763966	+	0.645256i	$0.776751\pi$
$618$		0			0
$619$	−15.6267	+	27.0662i	−0.628088	+	1.08788i	0.359847	+	0.933011i	$0.382829\pi$
$619$	−15.6267	+	27.0662i	−0.628088	+	1.08788i	−0.987935	+	0.154869i	$0.950504\pi$
$620$		0			0
$621$	−13.6515	+	7.88169i	−0.547816	+	0.316282i
$622$		0			0
$623$	10.4110	+	12.0091i	0.417110	+	0.481136i
$624$		0			0
$625$	8.79279	+	23.4027i	0.351712	+	0.936108i
$626$		0			0
$627$	−6.26036	+	1.67746i	−0.250015	+	0.0669912i
$628$		0			0
$629$	47.7201			1.90272
$630$		0			0
$631$	19.8658			0.790844			0.395422	−	0.918500i	$-0.370598\pi$
$631$	19.8658			0.790844			0.395422	+	0.918500i	$0.370598\pi$
$632$		0			0
$633$	−29.9832	+	8.03397i	−1.19173	+	0.319322i
$634$		0			0
$635$	−12.5663	−	23.9881i	−0.498677	−	0.951938i
$636$		0			0
$637$	−41.4169	−	17.7121i	−1.64100	−	0.701779i
$638$		0			0
$639$	0.503189	−	0.290517i	0.0199059	−	0.0114927i
$640$		0			0
$641$	−20.8732	+	36.1535i	−0.824443	+	1.42798i	0.0779013	+	0.996961i	$0.475178\pi$
$641$	−20.8732	+	36.1535i	−0.824443	+	1.42798i	−0.902344	+	0.431016i	$0.858155\pi$
$642$		0			0
$643$	4.58193	+	4.58193i	0.180694	+	0.180694i	0.791658	−	0.610964i	$-0.209218\pi$
$643$	4.58193	+	4.58193i	0.180694	+	0.180694i	−0.610964	+	0.791658i	$0.709218\pi$
$644$		0			0
$645$	−6.38915	+	5.88501i	−0.251572	+	0.231722i
$646$		0			0
$647$	−2.26436	−	8.45072i	−0.0890213	−	0.332232i	0.907024	−	0.421079i	$-0.138348\pi$
$647$	−2.26436	−	8.45072i	−0.0890213	−	0.332232i	−0.996045	+	0.0888468i	$0.971682\pi$
$648$		0			0
$649$	3.42401	+	5.93056i	0.134404	+	0.232795i
$650$		0			0
$651$	25.4923	+	1.81707i	0.999123	+	0.0712165i
$652$		0			0
$653$	3.34030	+	0.895030i	0.130716	+	0.0350252i	0.323584	−	0.946199i	$-0.395112\pi$
$653$	3.34030	+	0.895030i	0.130716	+	0.0350252i	−0.192868	+	0.981225i	$0.561779\pi$
$654$		0			0
$655$	2.55589	−	0.573558i	0.0998668	−	0.0224108i
$656$		0			0
$657$	1.52051	−	1.52051i	0.0593206	−	0.0593206i
$658$		0			0
$659$		−	1.86861i		−	0.0727907i	−0.999337	−	0.0363953i	$-0.988412\pi$
$659$		−	1.86861i		−	0.0727907i	0.999337	−	0.0363953i	$-0.0115876\pi$
$660$		0			0
$661$	40.7798	+	23.5442i	1.58615	+	0.915764i	0.993933	+	0.109984i	$0.0350801\pi$
$661$	40.7798	+	23.5442i	1.58615	+	0.915764i	0.592216	+	0.805779i	$0.298253\pi$
$662$		0			0
$663$	−14.3573	+	53.5820i	−0.557590	+	2.08095i
$664$		0			0
$665$	2.91501	+	6.68143i	0.113039	+	0.259095i
$666$		0			0
$667$	2.03975	−	7.61246i	0.0789795	−	0.294755i
$668$		0			0
$669$	−14.4396	−	8.33672i	−0.558268	−	0.322316i
$670$		0			0
$671$		−	14.8236i		−	0.572257i
$672$		0			0
$673$	−3.20914	+	3.20914i	−0.123703	+	0.123703i	−0.766248	−	0.642545i	$-0.777879\pi$
$673$	−3.20914	+	3.20914i	−0.123703	+	0.123703i	0.642545	+	0.766248i	$0.277879\pi$
$674$		0			0
$675$	−27.8279	+	5.05518i	−1.07109	+	0.194574i
$676$		0			0
$677$	−15.0789	−	4.04037i	−0.579528	−	0.155284i	−0.0428651	−	0.999081i	$-0.513649\pi$
$677$	−15.0789	−	4.04037i	−0.579528	−	0.155284i	−0.536663	+	0.843797i	$0.680315\pi$
$678$		0			0
$679$	−7.77153	+	11.4884i	−0.298244	+	0.440884i
$680$		0			0
$681$	−8.30135	−	14.3784i	−0.318109	−	0.550980i
$682$		0			0
$683$	6.07444	+	22.6701i	0.232432	+	0.867448i	0.979290	+	0.202464i	$0.0648949\pi$
$683$	6.07444	+	22.6701i	0.232432	+	0.867448i	−0.746858	+	0.664984i	$0.768438\pi$
$684$		0			0
$685$	−22.9254	−	0.941613i	−0.875933	−	0.0359772i
$686$		0			0
$687$	−6.40306	−	6.40306i	−0.244292	−	0.244292i
$688$		0			0
$689$	−31.4619	+	54.4937i	−1.19860	+	2.07604i
$690$		0			0
$691$	−12.8955	+	7.44520i	−0.490566	+	0.283229i	−0.724809	−	0.688949i	$-0.758072\pi$
$691$	−12.8955	+	7.44520i	−0.490566	+	0.283229i	0.234243	+	0.972178i	$0.424739\pi$
$692$		0			0
$693$	1.90975	+	9.89590i	0.0725455	+	0.375914i
$694$		0			0
$695$	17.3020	+	5.40621i	0.656304	+	0.205069i
$696$		0			0
$697$	32.9520	−	8.82945i	1.24814	−	0.334439i
$698$		0			0
$699$	21.3791			0.808630
$700$		0			0
$701$	23.9673			0.905232			0.452616	−	0.891705i	$-0.350491\pi$
$701$	23.9673			0.905232			0.452616	+	0.891705i	$0.350491\pi$
$702$		0			0
$703$	−9.27274	+	2.48462i	−0.349728	+	0.0937093i
$704$		0			0
$705$	−34.6778	−	10.8355i	−1.30604	−	0.408087i
$706$		0			0
$707$	−9.99973	−	3.45824i	−0.376079	−	0.130061i
$708$		0			0
$709$	0.893033	−	0.515593i	0.0335386	−	0.0193635i	−0.483137	−	0.875545i	$-0.660503\pi$
$709$	0.893033	−	0.515593i	0.0335386	−	0.0193635i	0.516676	+	0.856181i	$0.327169\pi$
$710$		0			0
$711$	5.57547	−	9.65699i	0.209096	−	0.362166i
$712$		0			0
$713$	−13.5245	−	13.5245i	−0.506495	−	0.506495i
$714$		0			0
$715$	−53.7326	−	2.20696i	−2.00949	−	0.0825356i
$716$		0			0
$717$	6.20468	+	23.1562i	0.231718	+	0.864784i
$718$		0			0
$719$	12.0529	+	20.8762i	0.449497	+	0.778552i	0.998353	−	0.0573650i	$-0.0182699\pi$
$719$	12.0529	+	20.8762i	0.449497	+	0.778552i	−0.548856	+	0.835917i	$0.684937\pi$
$720$		0			0
$721$	0.517440	−	7.25936i	0.0192705	−	0.270353i
$722$		0			0
$723$	−0.881160	−	0.236106i	−0.0327707	−	0.00878088i
$724$		0			0
$725$	8.05064	−	11.6249i	0.298993	−	0.431737i
$726$		0			0
$727$	0.650788	−	0.650788i	0.0241364	−	0.0241364i	−0.694936	−	0.719072i	$-0.744567\pi$
$727$	0.650788	−	0.650788i	0.0241364	−	0.0241364i	0.719072	+	0.694936i	$0.244567\pi$
$728$		0			0
$729$		−	28.8812i		−	1.06967i
$730$		0			0
$731$	−14.6414	−	8.45320i	−0.541531	−	0.312653i
$732$		0			0
$733$	−3.56180	+	13.2928i	−0.131558	+	0.490981i	−0.999988	−	0.00483005i	$-0.998463\pi$
$733$	−3.56180	+	13.2928i	−0.131558	+	0.490981i	0.868430	+	0.495811i	$0.165129\pi$
$734$		0			0
$735$	−20.7664	+	7.35126i	−0.765981	+	0.271155i
$736$		0			0
$737$	7.94739	−	29.6601i	0.292746	−	1.09254i
$738$		0			0
$739$	−12.8236	−	7.40373i	−0.471725	−	0.272351i	0.245236	−	0.969463i	$-0.421134\pi$
$739$	−12.8236	−	7.40373i	−0.471725	−	0.272351i	−0.716962	+	0.697113i	$0.754468\pi$
$740$		0			0
$741$		−	11.1593i		−	0.409948i
$742$		0			0
$743$	32.2779	−	32.2779i	1.18416	−	1.18416i	0.205505	−	0.978656i	$-0.434116\pi$
$743$	32.2779	−	32.2779i	1.18416	−	1.18416i	0.978656	−	0.205505i	$-0.0658836\pi$
$744$		0			0
$745$	14.1115	−	3.16671i	0.517005	−	0.116019i
$746$		0			0
$747$	12.2638	+	3.28607i	0.448708	+	0.120231i
$748$		0			0
$749$	−1.59797	+	22.4185i	−0.0583885	+	0.819154i
$750$		0			0
$751$	0.115708	+	0.200412i	0.00422223	+	0.00731312i	0.868129	−	0.496339i	$-0.165323\pi$
$751$	0.115708	+	0.200412i	0.00422223	+	0.00731312i	−0.863907	+	0.503652i	$0.831989\pi$
$752$		0			0
$753$	1.08972	+	4.06690i	0.0397117	+	0.148206i
$754$		0			0
$755$	9.88155	−	9.10184i	0.359626	−	0.331250i
$756$		0			0
$757$	−33.8884	−	33.8884i	−1.23169	−	1.23169i	−0.963313	−	0.268382i	$-0.913511\pi$
$757$	−33.8884	−	33.8884i	−1.23169	−	1.23169i	−0.268382	−	0.963313i	$-0.586489\pi$
$758$		0			0
$759$	−7.32897	+	12.6942i	−0.266025	+	0.460769i
$760$		0			0
$761$	−17.9623	+	10.3705i	−0.651132	+	0.375931i	−0.788890	−	0.614535i	$-0.789344\pi$
$761$	−17.9623	+	10.3705i	−0.651132	+	0.375931i	0.137758	+	0.990466i	$0.456010\pi$
$762$		0			0
$763$	28.7858	+	9.95511i	1.04212	+	0.360399i
$764$		0			0
$765$	−6.47778	−	12.3656i	−0.234205	−	0.447079i
$766$		0			0
$767$	−11.3892	+	3.05172i	−0.411239	+	0.110191i
$768$		0			0
$769$	52.0182			1.87583			0.937913	−	0.346872i	$-0.112756\pi$
$769$	52.0182			1.87583			0.937913	+	0.346872i	$0.112756\pi$
$770$		0			0
$771$	6.65342			0.239617
$772$		0			0
$773$	−47.9189	+	12.8398i	−1.72352	+	0.461817i	−0.978675	−	0.205415i	$-0.934146\pi$
$773$	−47.9189	+	12.8398i	−1.72352	+	0.461817i	−0.744850	+	0.667232i	$0.767479\pi$
$774$		0			0
$775$	−14.6637	−	31.0269i	−0.526735	−	1.11452i
$776$		0			0
$777$	−5.49716	−	28.4850i	−0.197210	−	1.02189i
$778$		0			0
$779$	−5.94335	+	3.43139i	−0.212943	+	0.122942i
$780$		0			0
$781$	1.06527	−	1.84511i	0.0381184	−	0.0660230i
$782$		0			0
$783$	11.3119	+	11.3119i	0.404255	+	0.404255i
$784$		0			0
$785$	0.630852	−	15.3593i	0.0225161	−	0.548197i
$786$		0			0
$787$	5.89457	+	21.9988i	0.210119	+	0.784174i	0.987828	+	0.155550i	$0.0497149\pi$
$787$	5.89457	+	21.9988i	0.210119	+	0.784174i	−0.777709	+	0.628624i	$0.783618\pi$
$788$		0			0
$789$	−17.5195	−	30.3447i	−0.623712	−	1.08030i
$790$		0			0
$791$	−15.4434	+	22.8295i	−0.549105	+	0.811724i
$792$		0			0
$793$	24.6535	+	6.60590i	0.875473	+	0.234582i
$794$		0			0
$795$	6.73801	+	30.0259i	0.238972	+	1.06491i
$796$		0			0
$797$	−19.2056	+	19.2056i	−0.680298	+	0.680298i	−0.960067	−	0.279770i	$-0.909742\pi$
$797$	−19.2056	+	19.2056i	−0.680298	+	0.680298i	0.279770	+	0.960067i	$0.409742\pi$
$798$		0			0
$799$		−	70.7112i		−	2.50158i
$800$		0			0
$801$	5.30255	+	3.06143i	0.187356	+	0.108170i
$802$		0			0
$803$	2.04075	−	7.61617i	0.0720164	−	0.268769i
$804$		0			0
$805$	15.3466	+	6.02327i	0.540898	+	0.212292i
$806$		0			0
$807$	−0.112150	+	0.418550i	−0.00394787	+	0.0147337i
$808$		0			0
$809$	31.8924	+	18.4131i	1.12128	+	0.647370i	0.941727	−	0.336379i	$-0.109202\pi$
$809$	31.8924	+	18.4131i	1.12128	+	0.647370i	0.179550	+	0.983749i	$0.442536\pi$
$810$		0			0
$811$			15.8918i			0.558036i	0.960286	+	0.279018i	$0.0900089\pi$
$811$			15.8918i			0.558036i	−0.960286	+	0.279018i	$0.909991\pi$
$812$		0			0
$813$	−27.8772	+	27.8772i	−0.977695	+	0.977695i
$814$		0			0
$815$	24.7256	+	15.6623i	0.866098	+	0.548625i
$816$		0			0
$817$	3.28517	+	0.880259i	0.114934	+	0.0307963i
$818$		0			0
$819$	−17.3092	−	1.23378i	−0.604834	−	0.0431119i
$820$		0			0
$821$	2.11251	+	3.65898i	0.0737272	+	0.127699i	0.900532	−	0.434790i	$-0.143177\pi$
$821$	2.11251	+	3.65898i	0.0737272	+	0.127699i	−0.826805	+	0.562489i	$0.809844\pi$
$822$		0			0
$823$	13.4418	+	50.1654i	0.468551	+	1.74866i	0.644839	+	0.764319i	$0.276925\pi$
$823$	13.4418	+	50.1654i	0.468551	+	1.74866i	−0.176287	+	0.984339i	$0.556409\pi$
$824$		0			0
$825$	−20.0592	+	17.0091i	−0.698373	+	0.592180i
$826$		0			0
$827$	−8.41389	−	8.41389i	−0.292580	−	0.292580i	0.545519	−	0.838099i	$-0.316333\pi$
$827$	−8.41389	−	8.41389i	−0.292580	−	0.292580i	−0.838099	+	0.545519i	$0.816333\pi$
$828$		0			0
$829$	15.4011	−	26.6755i	0.534903	−	0.926479i	−0.464265	−	0.885696i	$-0.653682\pi$
$829$	15.4011	−	26.6755i	0.534903	−	0.926479i	0.999168	−	0.0407825i	$-0.0129851\pi$
$830$		0			0
$831$	−34.4882	+	19.9118i	−1.19638	+	0.690732i
$832$		0			0
$833$	−25.7107	−	34.3110i	−0.890825	−	1.18881i
$834$		0			0
$835$	17.7524	−	9.29966i	0.614345	−	0.321828i
$836$		0			0
$837$	37.5015	−	10.0485i	1.29624	−	0.347327i
$838$		0			0
$839$	−34.0803			−1.17658			−0.588292	−	0.808649i	$-0.700199\pi$
$839$	−34.0803			−1.17658			−0.588292	+	0.808649i	$0.700199\pi$
$840$		0			0
$841$	21.0020			0.724206
$842$		0			0
$843$	−3.53838	+	0.948106i	−0.121868	+	0.0326545i
$844$		0			0
$845$	18.9461	−	60.6350i	0.651764	−	2.08591i
$846$		0			0
$847$	5.14388	+	5.93346i	0.176746	+	0.203876i
$848$		0			0
$849$	−22.0028	+	12.7033i	−0.755134	+	0.435977i
$850$		0			0
$851$	−10.8556	+	18.8024i	−0.372124	+	0.644537i
$852$		0			0
$853$	−31.8639	−	31.8639i	−1.09100	−	1.09100i	−0.995422	−	0.0955790i	$-0.969530\pi$
$853$	−31.8639	−	31.8639i	−1.09100	−	1.09100i	−0.0955790	−	0.995422i	$-0.530470\pi$
$854$		0			0
$855$	1.90257	+	2.06555i	0.0650664	+	0.0706403i
$856$		0			0
$857$	−1.20650	−	4.50274i	−0.0412134	−	0.153811i	0.942253	−	0.334903i	$-0.108703\pi$
$857$	−1.20650	−	4.50274i	−0.0412134	−	0.153811i	−0.983466	+	0.181092i	$0.942037\pi$
$858$		0			0
$859$	−5.08567	−	8.80865i	−0.173521	−	0.300547i	0.766127	−	0.642689i	$-0.222181\pi$
$859$	−5.08567	−	8.80865i	−0.173521	−	0.300547i	−0.939648	+	0.342142i	$0.888848\pi$
$860$		0			0
$861$	−9.06640	−	18.6525i	−0.308982	−	0.635677i
$862$		0			0
$863$	−24.7750	−	6.63845i	−0.843352	−	0.225976i	−0.188822	−	0.982011i	$-0.560467\pi$
$863$	−24.7750	−	6.63845i	−0.843352	−	0.225976i	−0.654530	+	0.756036i	$0.727134\pi$
$864$		0			0
$865$	−2.42115	+	3.82220i	−0.0823217	+	0.129959i
$866$		0			0
$867$	−20.4172	+	20.4172i	−0.693403	+	0.693403i
$868$		0			0
$869$		−	40.8885i		−	1.38705i
$870$		0			0
$871$	45.7870	+	26.4351i	1.55143	+	0.895720i
$872$		0			0
$873$	−1.38295	+	5.16123i	−0.0468056	+	0.174681i
$874$		0			0
$875$	22.2795	+	19.4583i	0.753184	+	0.657810i
$876$		0			0
$877$	−9.20193	+	34.3421i	−0.310727	+	1.15965i	0.617175	+	0.786826i	$0.288277\pi$
$877$	−9.20193	+	34.3421i	−0.310727	+	1.15965i	−0.927902	+	0.372824i	$0.878390\pi$
$878$		0			0
$879$	29.7038	+	17.1495i	1.00188	+	0.578438i
$880$		0			0
$881$			6.87670i			0.231682i	0.993268	+	0.115841i	$0.0369563\pi$
$881$			6.87670i			0.231682i	−0.993268	+	0.115841i	$0.963044\pi$
$882$		0			0
$883$	−3.32125	+	3.32125i	−0.111769	+	0.111769i	−0.760779	−	0.649011i	$-0.775183\pi$
$883$	−3.32125	+	3.32125i	−0.111769	+	0.111769i	0.649011	+	0.760779i	$0.275183\pi$
$884$		0			0
$885$	−3.08566	+	4.87124i	−0.103723	+	0.163745i
$886$		0			0
$887$	0.887559	+	0.237821i	0.0298013	+	0.00798524i	0.273689	−	0.961818i	$-0.411756\pi$
$887$	0.887559	+	0.237821i	0.0298013	+	0.00798524i	−0.243888	+	0.969804i	$0.578423\pi$
$888$		0			0
$889$	−26.5397	−	17.9533i	−0.890113	−	0.602133i
$890$		0			0
$891$	−9.16296	−	15.8707i	−0.306971	−	0.531689i
$892$		0			0
$893$	3.68169	+	13.7403i	0.123203	+	0.459801i
$894$		0			0
$895$	−6.20475	−	6.73628i	−0.207402	−	0.225169i
$896$		0			0
$897$	−17.8460	−	17.8460i	−0.595861	−	0.595861i
$898$		0			0
$899$	−9.70525	+	16.8100i	−0.323688	+	0.560644i
$900$		0			0
$901$	−51.8685	+	29.9463i	−1.72799	+	0.997656i
$902$		0			0
$903$	−3.35925	+	9.71348i	−0.111789	+	0.323245i
$904$		0			0
$905$	−7.09082	+	22.6935i	−0.235707	+	0.754356i
$906$		0			0
$907$	−24.1687	+	6.47600i	−0.802510	+	0.215032i	−0.636686	−	0.771123i	$-0.719695\pi$
$907$	−24.1687	+	6.47600i	−0.802510	+	0.215032i	−0.165824	+	0.986155i	$0.553028\pi$
$908$		0			0
$909$	−4.07614			−0.135197
$910$		0			0
$911$	−32.2439			−1.06829			−0.534144	−	0.845394i	$-0.679366\pi$
$911$	−32.2439			−1.06829			−0.534144	+	0.845394i	$0.679366\pi$
$912$		0			0
$913$	44.9691	−	12.0494i	1.48826	−	0.398778i
$914$		0			0
$915$	11.0568	−	5.79214i	0.365525	−	0.191482i
$916$		0			0
$917$	2.34186	−	2.03023i	0.0773352	−	0.0670440i
$918$		0			0
$919$	41.7517	−	24.1054i	1.37726	−	0.795163i	0.385433	−	0.922736i	$-0.374052\pi$
$919$	41.7517	−	24.1054i	1.37726	−	0.795163i	0.991829	+	0.127573i	$0.0407187\pi$
$920$		0			0
$921$	11.2828	−	19.5423i	0.371780	−	0.643942i
$922$		0			0
$923$	2.59393	+	2.59393i	0.0853803	+	0.0853803i
$924$		0			0
$925$	−29.7114	+	25.1936i	−0.976906	+	0.828360i
$926$		0			0
$927$	−0.725645	−	2.70815i	−0.0238333	−	0.0889472i
$928$		0			0
$929$	−18.1318	−	31.4051i	−0.594884	−	1.03037i	−0.993563	−	0.113279i	$-0.963865\pi$
$929$	−18.1318	−	31.4051i	−0.594884	−	1.03037i	0.398679	−	0.917090i	$-0.369469\pi$
$930$		0			0
$931$	6.78245	+	5.32848i	0.222286	+	0.174634i
$932$		0			0
$933$	−28.2395	−	7.56674i	−0.924518	−	0.247724i
$934$		0			0
$935$	−43.2418	−	27.3913i	−1.41416	−	0.895790i
$936$		0			0
$937$	−0.255843	+	0.255843i	−0.00835802	+	0.00835802i	−0.711273	−	0.702915i	$-0.751881\pi$
$937$	−0.255843	+	0.255843i	−0.00835802	+	0.00835802i	0.702915	+	0.711273i	$0.251881\pi$
$938$		0			0
$939$			10.7002i			0.349188i
$940$		0			0
$941$	−20.3365	−	11.7413i	−0.662949	−	0.382754i	0.130450	−	0.991455i	$-0.458358\pi$
$941$	−20.3365	−	11.7413i	−0.662949	−	0.382754i	−0.793400	+	0.608701i	$0.791691\pi$
$942$		0			0
$943$	−4.01712	+	14.9921i	−0.130815	+	0.488210i
$944$		0			0
$945$	−26.1644	+	20.8650i	−0.851127	+	0.678739i
$946$		0			0
$947$	10.7955	−	40.2893i	0.350806	−	1.30923i	−0.534874	−	0.844932i	$-0.679641\pi$
$947$	10.7955	−	40.2893i	0.350806	−	1.30923i	0.885680	−	0.464296i	$-0.153692\pi$
$948$		0			0
$949$	11.7573	+	6.78806i	0.381657	+	0.220350i
$950$		0			0
$951$			2.40891i			0.0781143i
$952$		0			0
$953$	5.97702	−	5.97702i	0.193615	−	0.193615i	−0.603641	−	0.797256i	$-0.706284\pi$
$953$	5.97702	−	5.97702i	0.193615	−	0.193615i	0.797256	+	0.603641i	$0.206284\pi$
$954$		0			0
$955$	−6.23717	−	27.7941i	−0.201830	−	0.899396i
$956$		0			0
$957$	14.3687	+	3.85009i	0.464475	+	0.124456i
$958$		0			0
$959$	−24.4169	+	11.8683i	−0.788464	+	0.383247i
$960$		0			0
$961$	8.05379	+	13.9496i	0.259800	+	0.449986i
$962$		0			0
$963$	2.24095	+	8.36335i	0.0722137	+	0.269505i
$964$		0			0
$965$	−1.05780	+	25.7542i	−0.0340518	+	0.829056i
$966$		0			0
$967$	−34.9020	−	34.9020i	−1.12237	−	1.12237i	−0.991384	−	0.130988i	$-0.958185\pi$
$967$	−34.9020	−	34.9020i	−1.12237	−	1.12237i	−0.130988	−	0.991384i	$-0.541815\pi$
$968$		0			0
$969$	5.31088	−	9.19871i	0.170610	−	0.295505i
$970$		0			0
$971$	40.5558	−	23.4149i	1.30150	−	0.751419i	0.320836	−	0.947135i	$-0.396036\pi$
$971$	40.5558	−	23.4149i	1.30150	−	0.751419i	0.980661	+	0.195716i	$0.0627030\pi$
$972$		0			0
$973$	21.0596	−	4.06417i	0.675139	−	0.130291i
$974$		0			0
$975$	−19.3493	−	40.9410i	−0.619672	−	1.31116i
$976$		0			0
$977$	−4.82951	+	1.29406i	−0.154510	+	0.0414008i	−0.335245	−	0.942131i	$-0.608819\pi$
$977$	−4.82951	+	1.29406i	−0.154510	+	0.0414008i	0.180735	+	0.983532i	$0.442152\pi$
$978$		0			0
$979$	22.4514			0.717550
$980$		0			0
$981$	11.7338			0.374633
$982$		0			0
$983$	−52.1438	+	13.9719i	−1.66313	+	0.445634i	−0.963245	−	0.268624i	$-0.913431\pi$
$983$	−52.1438	+	13.9719i	−1.66313	+	0.445634i	−0.699883	+	0.714258i	$0.746764\pi$
$984$		0			0
$985$	6.40225	+	12.2214i	0.203993	+	0.389407i
$986$		0			0
$987$	−42.2089	+	8.14565i	−1.34352	+	0.259279i
$988$		0			0
$989$	6.66135	−	3.84593i	0.211819	−	0.122294i
$990$		0			0
$991$	−0.608356	+	1.05370i	−0.0193251	+	0.0334720i	−0.875526	−	0.483171i	$-0.839485\pi$
$991$	−0.608356	+	1.05370i	−0.0193251	+	0.0334720i	0.856201	+	0.516643i	$0.172818\pi$
$992$		0			0
$993$	25.8919	+	25.8919i	0.821656	+	0.821656i
$994$		0			0
$995$	−28.9522	+	26.6678i	−0.917848	+	0.845425i
$996$		0			0
$997$	−5.31777	−	19.8462i	−0.168416	−	0.628536i	−0.997580	−	0.0695305i	$-0.977850\pi$
$997$	−5.31777	−	19.8462i	−0.168416	−	0.628536i	0.829164	−	0.559005i	$-0.188817\pi$
$998$		0			0
$999$	−22.0355	−	38.1665i	−0.697171	−	1.20754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.e.17.9		48
4.3	odd	2		280.2.bo.a.17.4	✓	48
5.3	odd	4	inner	560.2.ci.e.353.9		48
7.5	odd	6	inner	560.2.ci.e.257.9		48
20.3	even	4		280.2.bo.a.73.4	yes	48
28.19	even	6		280.2.bo.a.257.4	yes	48
35.33	even	12	inner	560.2.ci.e.33.9		48
140.103	odd	12		280.2.bo.a.33.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.4	✓	48	4.3	odd	2
280.2.bo.a.33.4	yes	48	140.103	odd	12
280.2.bo.a.73.4	yes	48	20.3	even	4
280.2.bo.a.257.4	yes	48	28.19	even	6
560.2.ci.e.17.9		48	1.1	even	1	trivial
560.2.ci.e.33.9		48	35.33	even	12	inner
560.2.ci.e.257.9		48	7.5	odd	6	inner
560.2.ci.e.353.9		48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35944 - 0.364260i) q^{3} +(-2.13431 - 0.666887i) q^{5} +(-2.59782 + 0.501338i) q^{7} +(-0.882692 + 0.509622i) q^{9} +O(q^{10})\)	\(q+(1.35944 - 0.364260i) q^{3} +(-2.13431 - 0.666887i) q^{5} +(-2.59782 + 0.501338i) q^{7} +(-0.882692 + 0.509622i) q^{9} +(-1.86869 + 3.23667i) q^{11} +(-4.55026 - 4.55026i) q^{13} +(-3.14438 - 0.129149i) q^{15} +(-1.58528 - 5.91633i) q^{17} +(0.616087 + 1.06709i) q^{19} +(-3.34895 + 1.62782i) q^{21} +(2.69174 + 0.721250i) q^{23} +(4.11052 + 2.84668i) q^{25} +(-3.99986 + 3.99986i) q^{27} -2.82808i q^{29} +(-5.94396 - 3.43175i) q^{31} +(-1.36138 + 5.08074i) q^{33} +(5.87887 + 0.662443i) q^{35} +(-2.01646 + 7.52551i) q^{37} +(-7.84327 - 4.52831i) q^{39} +5.56966i q^{41} +(1.95176 - 1.95176i) q^{43} +(2.22379 - 0.499034i) q^{45} +(11.1512 + 2.98797i) q^{47} +(6.49732 - 2.60477i) q^{49} +(-4.31017 - 7.46543i) q^{51} +(-2.53082 - 9.44513i) q^{53} +(6.14686 - 5.66184i) q^{55} +(1.22623 + 1.22623i) q^{57} +(0.916152 - 1.58682i) q^{59} +(-3.43491 + 1.98315i) q^{61} +(2.03758 - 1.76643i) q^{63} +(6.67713 + 12.7462i) q^{65} +(-7.93605 + 2.12646i) q^{67} +3.92198 q^{69} -0.570063 q^{71} +(-2.03783 + 0.546036i) q^{73} +(6.62493 + 2.37259i) q^{75} +(3.23186 - 9.34513i) q^{77} +(-9.47466 + 5.47020i) q^{79} +(-2.45170 + 4.24647i) q^{81} +(-8.80820 - 8.80820i) q^{83} +(-0.562062 + 13.6845i) q^{85} +(-1.03016 - 3.84459i) q^{87} +(-3.00362 - 5.20243i) q^{89} +(14.1020 + 9.53952i) q^{91} +(-9.33049 - 2.50010i) q^{93} +(-0.603286 - 2.68836i) q^{95} +(3.70694 - 3.70694i) q^{97} -3.80931i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7}+O(q^{10}) \) 48 * q + 4 * q^7	\( 48 q + 4 q^{7} - 4 q^{11} - 8 q^{15} - 4 q^{21} + 4 q^{23} - 8 q^{25} - 36 q^{33} - 24 q^{35} + 8 q^{37} + 16 q^{43} + 48 q^{45} - 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} + 68 q^{63} + 12 q^{65} + 16 q^{67} + 64 q^{71} - 48 q^{73} + 48 q^{75} + 4 q^{77} - 40 q^{85} + 12 q^{87} + 80 q^{91} - 24 q^{95}+O(q^{100}) \) 48 * q + 4 * q^7 - 4 * q^11 - 8 * q^15 - 4 * q^21 + 4 * q^23 - 8 * q^25 - 36 * q^33 - 24 * q^35 + 8 * q^37 + 16 * q^43 + 48 * q^45 - 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 + 68 * q^63 + 12 * q^65 + 16 * q^67 + 64 * q^71 - 48 * q^73 + 48 * q^75 + 4 * q^77 - 40 * q^85 + 12 * q^87 + 80 * q^91 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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