LMFDB - Embedded newform 572.2.x.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(25,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("572.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.x (of order $10$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	572.25
Dual form			572.2.x.a.389.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.741447 - 2.28194i) q^{3} +(-0.419790 + 0.577792i) q^{5} +(-2.31756 - 0.753022i) q^{7} +(-2.23045 + 1.62052i) q^{9} +O(q^{10})$	\(q+(-0.741447 - 2.28194i) q^{3} +(-0.419790 + 0.577792i) q^{5} +(-2.31756 - 0.753022i) q^{7} +(-2.23045 + 1.62052i) q^{9} +(-1.25855 + 3.06856i) q^{11} +(1.46762 - 3.29334i) q^{13} +(1.62974 + 0.529534i) q^{15} +(-2.59647 - 1.88645i) q^{17} +(-6.09026 + 1.97885i) q^{19} +5.84686i q^{21} -6.67231 q^{23} +(1.38747 + 4.27018i) q^{25} +(-0.471718 - 0.342723i) q^{27} +(-1.27443 + 3.92229i) q^{29} +(3.51344 + 4.83584i) q^{31} +(7.93541 + 0.596748i) q^{33} +(1.40798 - 1.02296i) q^{35} +(5.41010 + 1.75785i) q^{37} +(-8.60336 - 0.907194i) q^{39} +(6.85610 - 2.22768i) q^{41} +5.96764 q^{43} -1.96901i q^{45} +(-7.38681 + 2.40012i) q^{47} +(-0.859065 - 0.624147i) q^{49} +(-2.37961 + 7.32369i) q^{51} +(-0.313539 + 0.227800i) q^{53} +(-1.24466 - 2.01533i) q^{55} +(9.03121 + 12.4304i) q^{57} +(-10.8162 - 3.51441i) q^{59} +(-11.6430 - 8.45911i) q^{61} +(6.38949 - 2.07607i) q^{63} +(1.28677 + 2.23049i) q^{65} -9.32495i q^{67} +(4.94716 + 15.2258i) q^{69} +(-3.67717 + 5.06118i) q^{71} +(-14.4467 - 4.69403i) q^{73} +(8.71556 - 6.33222i) q^{75} +(5.22745 - 6.16387i) q^{77} +(7.26158 - 5.27585i) q^{79} +(-2.98819 + 9.19670i) q^{81} +(7.28538 - 10.0275i) q^{83} +(2.17995 - 0.708308i) q^{85} +9.89535 q^{87} +5.70354i q^{89} +(-5.88127 + 6.52736i) q^{91} +(8.43005 - 11.6030i) q^{93} +(1.41327 - 4.34961i) q^{95} +(-10.2505 - 14.1085i) q^{97} +(-2.16553 - 8.88377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^9	$ 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) $ 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.741447	−	2.28194i	−0.428075	−	1.31748i	−0.900019	−	0.435850i	$-0.856448\pi$
$3$	−0.741447	−	2.28194i	−0.428075	−	1.31748i	0.471945	−	0.881628i	$-0.343552\pi$
$4$		0			0
$5$	−0.419790	+	0.577792i	−0.187736	+	0.258396i	−0.892502	−	0.451043i	$-0.851052\pi$
$5$	−0.419790	+	0.577792i	−0.187736	+	0.258396i	0.704766	+	0.709440i	$0.251052\pi$
$6$		0			0
$7$	−2.31756	−	0.753022i	−0.875956	−	0.284615i	−0.163679	−	0.986514i	$-0.552336\pi$
$7$	−2.31756	−	0.753022i	−0.875956	−	0.284615i	−0.712277	+	0.701898i	$0.752336\pi$
$8$		0			0
$9$	−2.23045	+	1.62052i	−0.743484	+	0.540172i
$10$		0			0
$11$	−1.25855	+	3.06856i	−0.379466	+	0.925206i
$11$	−1.25855	+	3.06856i	−0.379466	+	0.925206i
$12$		0			0
$13$	1.46762	−	3.29334i	0.407046	−	0.913408i
$13$	1.46762	−	3.29334i	0.407046	−	0.913408i
$14$		0			0
$15$	1.62974	+	0.529534i	0.420797	+	0.136725i
$16$		0			0
$17$	−2.59647	−	1.88645i	−0.629737	−	0.457530i	0.226572	−	0.973994i	$-0.427248\pi$
$17$	−2.59647	−	1.88645i	−0.629737	−	0.457530i	−0.856309	+	0.516464i	$0.827248\pi$
$18$		0			0
$19$	−6.09026	+	1.97885i	−1.39720	+	0.453979i	−0.908285	−	0.418352i	$-0.862608\pi$
$19$	−6.09026	+	1.97885i	−1.39720	+	0.453979i	−0.488917	+	0.872330i	$0.662608\pi$
$20$		0			0
$21$			5.84686i			1.27589i
$22$		0			0
$23$	−6.67231			−1.39127			−0.695636	−	0.718394i	$-0.744878\pi$
$23$	−6.67231			−1.39127			−0.695636	+	0.718394i	$0.744878\pi$
$24$		0			0
$25$	1.38747	+	4.27018i	0.277493	+	0.854036i
$26$		0			0
$27$	−0.471718	−	0.342723i	−0.0907821	−	0.0659571i
$28$		0			0
$29$	−1.27443	+	3.92229i	−0.236656	+	0.728351i	0.760242	+	0.649640i	$0.225080\pi$
$29$	−1.27443	+	3.92229i	−0.236656	+	0.728351i	−0.996897	+	0.0787112i	$0.974920\pi$
$30$		0			0
$31$	3.51344	+	4.83584i	0.631032	+	0.868542i	0.998098	−	0.0616536i	$-0.0196374\pi$
$31$	3.51344	+	4.83584i	0.631032	+	0.868542i	−0.367065	+	0.930195i	$0.619637\pi$
$32$		0			0
$33$	7.93541	+	0.596748i	1.38138	+	0.103881i
$34$		0			0
$35$	1.40798	−	1.02296i	0.237992	−	0.172911i
$36$		0			0
$37$	5.41010	+	1.75785i	0.889415	+	0.288988i	0.717861	−	0.696186i	$-0.245121\pi$
$37$	5.41010	+	1.75785i	0.889415	+	0.288988i	0.171554	+	0.985175i	$0.445121\pi$
$38$		0			0
$39$	−8.60336	−	0.907194i	−1.37764	−	0.145267i
$40$		0			0
$41$	6.85610	−	2.22768i	1.07074	−	0.347905i	0.279966	−	0.960010i	$-0.409677\pi$
$41$	6.85610	−	2.22768i	1.07074	−	0.347905i	0.790777	+	0.612105i	$0.209677\pi$
$42$		0			0
$43$	5.96764			0.910056			0.455028	−	0.890477i	$-0.349629\pi$
$43$	5.96764			0.910056			0.455028	+	0.890477i	$0.349629\pi$
$44$		0			0
$45$		−	1.96901i		−	0.293523i
$46$		0			0
$47$	−7.38681	+	2.40012i	−1.07748	+	0.350093i	−0.793395	−	0.608707i	$-0.791689\pi$
$47$	−7.38681	+	2.40012i	−1.07748	+	0.350093i	−0.284082	+	0.958800i	$0.591689\pi$
$48$		0			0
$49$	−0.859065	−	0.624147i	−0.122724	−	0.0891639i
$50$		0			0
$51$	−2.37961	+	7.32369i	−0.333212	+	1.02552i
$52$		0			0
$53$	−0.313539	+	0.227800i	−0.0430680	+	0.0312907i	−0.609111	−	0.793085i	$-0.708474\pi$
$53$	−0.313539	+	0.227800i	−0.0430680	+	0.0312907i	0.566043	+	0.824376i	$0.308474\pi$
$54$		0			0
$55$	−1.24466	−	2.01533i	−0.167830	−	0.271747i
$56$		0			0
$57$	9.03121	+	12.4304i	1.19621	+	1.64645i
$58$		0			0
$59$	−10.8162	−	3.51441i	−1.40816	−	0.457537i	−0.496337	−	0.868130i	$-0.665322\pi$
$59$	−10.8162	−	3.51441i	−1.40816	−	0.457537i	−0.911819	+	0.410593i	$0.865322\pi$
$60$		0			0
$61$	−11.6430	−	8.45911i	−1.49073	−	1.08308i	−0.973897	−	0.226992i	$-0.927111\pi$
$61$	−11.6430	−	8.45911i	−1.49073	−	1.08308i	−0.516833	−	0.856086i	$-0.672889\pi$
$62$		0			0
$63$	6.38949	−	2.07607i	0.805000	−	0.261560i
$64$		0			0
$65$	1.28677	+	2.23049i	0.159604	+	0.276659i
$66$		0			0
$67$		−	9.32495i		−	1.13922i	−0.821914	−	0.569612i	$-0.807094\pi$
$67$		−	9.32495i		−	1.13922i	0.821914	−	0.569612i	$-0.192906\pi$
$68$		0			0
$69$	4.94716	+	15.2258i	0.595569	+	1.83297i
$70$		0			0
$71$	−3.67717	+	5.06118i	−0.436399	+	0.600652i	−0.969407	−	0.245458i	$-0.921062\pi$
$71$	−3.67717	+	5.06118i	−0.436399	+	0.600652i	0.533008	+	0.846110i	$0.321062\pi$
$72$		0			0
$73$	−14.4467	−	4.69403i	−1.69086	−	0.549395i	−0.703894	−	0.710305i	$-0.748557\pi$
$73$	−14.4467	−	4.69403i	−1.69086	−	0.549395i	−0.986969	+	0.160911i	$0.948557\pi$
$74$		0			0
$75$	8.71556	−	6.33222i	1.00639	−	0.731182i
$76$		0			0
$77$	5.22745	−	6.16387i	0.595723	−	0.702438i
$78$		0			0
$79$	7.26158	−	5.27585i	0.816991	−	0.593579i	−0.0988577	−	0.995102i	$-0.531519\pi$
$79$	7.26158	−	5.27585i	0.816991	−	0.593579i	0.915849	+	0.401523i	$0.131519\pi$
$80$		0			0
$81$	−2.98819	+	9.19670i	−0.332021	+	1.02186i
$82$		0			0
$83$	7.28538	−	10.0275i	0.799675	−	1.10066i	−0.193161	−	0.981167i	$-0.561874\pi$
$83$	7.28538	−	10.0275i	0.799675	−	1.10066i	0.992835	−	0.119491i	$-0.0381262\pi$
$84$		0			0
$85$	2.17995	−	0.708308i	0.236448	−	0.0768267i
$86$		0			0
$87$	9.89535			1.06089
$88$		0			0
$89$			5.70354i			0.604574i	0.953217	+	0.302287i	$0.0977501\pi$
$89$			5.70354i			0.604574i	−0.953217	+	0.302287i	$0.902250\pi$
$90$		0			0
$91$	−5.88127	+	6.52736i	−0.616524	+	0.684254i
$92$		0			0
$93$	8.43005	−	11.6030i	0.874156	−	1.20317i
$94$		0			0
$95$	1.41327	−	4.34961i	0.144999	−	0.446260i
$96$		0			0
$97$	−10.2505	−	14.1085i	−1.04078	−	1.43251i	−0.896540	−	0.442962i	$-0.853928\pi$
$97$	−10.2505	−	14.1085i	−1.04078	−	1.43251i	−0.144236	−	0.989543i	$-0.546072\pi$
$98$		0			0
$99$	−2.16553	−	8.88377i	−0.217644	−	0.892852i
$100$		0			0
$101$	1.54165	−	1.12007i	0.153399	−	0.111451i	−0.508438	−	0.861099i	$-0.669777\pi$
$101$	1.54165	−	1.12007i	0.153399	−	0.111451i	0.661837	+	0.749647i	$0.269777\pi$
$102$		0			0
$103$	0.916460	−	2.82057i	0.0903015	−	0.277919i	−0.895699	−	0.444660i	$-0.853324\pi$
$103$	0.916460	−	2.82057i	0.0903015	−	0.277919i	0.986001	+	0.166741i	$0.0533244\pi$
$104$		0			0
$105$	−3.37827	−	2.45446i	−0.329685	−	0.239530i
$106$		0			0
$107$	−1.54784	−	4.76376i	−0.149635	−	0.460530i	0.847943	−	0.530088i	$-0.177841\pi$
$107$	−1.54784	−	4.76376i	−0.149635	−	0.460530i	−0.997578	+	0.0695578i	$0.977841\pi$
$108$		0			0
$109$		−	6.14108i		−	0.588209i	−0.955773	−	0.294104i	$-0.904979\pi$
$109$		−	6.14108i		−	0.588209i	0.955773	−	0.294104i	$-0.0950213\pi$
$110$		0			0
$111$		−	13.6489i		−	1.29549i
$112$		0			0
$113$	2.89731	+	8.91700i	0.272556	+	0.838841i	0.989856	+	0.142076i	$0.0453777\pi$
$113$	2.89731	+	8.91700i	0.272556	+	0.838841i	−0.717300	+	0.696765i	$0.754622\pi$
$114$		0			0
$115$	2.80097	−	3.85521i	0.261192	−	0.359500i
$116$		0			0
$117$	2.06345	+	9.72394i	0.190766	+	0.898978i
$118$		0			0
$119$	4.59695	+	6.32716i	0.421402	+	0.580009i
$120$		0			0
$121$	−7.83213	−	7.72384i	−0.712012	−	0.702168i
$122$		0			0
$123$	−10.1669	−	13.9935i	−0.916715	−	1.26175i
$124$		0			0
$125$	−6.44589	−	2.09440i	−0.576538	−	0.187329i
$126$		0			0
$127$	3.55547	+	2.58320i	0.315497	+	0.229222i	0.734252	−	0.678877i	$-0.237533\pi$
$127$	3.55547	+	2.58320i	0.315497	+	0.229222i	−0.418754	+	0.908100i	$0.637533\pi$
$128$		0			0
$129$	−4.42469	−	13.6178i	−0.389572	−	1.19898i
$130$		0			0
$131$	−1.72103			−0.150367			−0.0751837	−	0.997170i	$-0.523954\pi$
$131$	−1.72103			−0.150367			−0.0751837	+	0.997170i	$0.523954\pi$
$132$		0			0
$133$	15.6047			1.35310
$134$		0			0
$135$	0.396045	−	0.128683i	0.0340861	−	0.0110753i
$136$		0			0
$137$	−6.96727	+	9.58963i	−0.595254	+	0.819297i	−0.995263	−	0.0972140i	$-0.969007\pi$
$137$	−6.96727	+	9.58963i	−0.595254	+	0.819297i	0.400009	+	0.916511i	$0.369007\pi$
$138$		0			0
$139$	1.34107	−	4.12740i	0.113748	−	0.350082i	−0.877936	−	0.478779i	$-0.841080\pi$
$139$	1.34107	−	4.12740i	0.113748	−	0.350082i	0.991684	+	0.128697i	$0.0410796\pi$
$140$		0			0
$141$	10.9539	+	15.0767i	0.922481	+	1.26969i
$142$		0			0
$143$	8.25874	+	8.64831i	0.690630	+	0.723208i
$144$		0			0
$145$	−1.73128	−	2.38290i	−0.143775	−	0.197889i
$146$		0			0
$147$	−0.787315	+	2.42311i	−0.0649366	+	0.199854i
$148$		0			0
$149$	10.9146	−	15.0227i	0.894159	−	1.23070i	−0.0781344	−	0.996943i	$-0.524896\pi$
$149$	10.9146	−	15.0227i	0.894159	−	1.23070i	0.972294	−	0.233762i	$-0.0751037\pi$
$150$		0			0
$151$	5.01448	−	1.62930i	0.408072	−	0.132591i	−0.0977856	−	0.995208i	$-0.531176\pi$
$151$	5.01448	−	1.62930i	0.408072	−	0.132591i	0.505858	+	0.862617i	$0.331176\pi$
$152$		0			0
$153$	8.84832			0.715344
$154$		0			0
$155$	−4.26901			−0.342895
$156$		0			0
$157$	2.95603	+	9.09772i	0.235917	+	0.726077i	0.996998	+	0.0774212i	$0.0246686\pi$
$157$	2.95603	+	9.09772i	0.235917	+	0.726077i	−0.761082	+	0.648656i	$0.775331\pi$
$158$		0			0
$159$	0.752298	+	0.546576i	0.0596611	+	0.0433463i
$160$		0			0
$161$	15.4635	+	5.02439i	1.21869	+	0.395978i
$162$		0			0
$163$	−5.29831	−	7.29250i	−0.414996	−	0.571193i	0.549432	−	0.835538i	$-0.314844\pi$
$163$	−5.29831	−	7.29250i	−0.414996	−	0.571193i	−0.964428	+	0.264346i	$0.914844\pi$
$164$		0			0
$165$	−3.67601	+	4.33451i	−0.286177	+	0.337441i
$166$		0			0
$167$	5.33615	+	7.34458i	0.412924	+	0.568341i	0.963929	−	0.266161i	$-0.0857554\pi$
$167$	5.33615	+	7.34458i	0.412924	+	0.568341i	−0.551005	+	0.834502i	$0.685755\pi$
$168$		0			0
$169$	−8.69216	−	9.66677i	−0.668627	−	0.743598i
$170$		0			0
$171$	10.3773	−	14.2831i	0.793570	−	1.09226i
$172$		0			0
$173$	0.666580	+	2.05152i	0.0506791	+	0.155974i	0.973193	−	0.229989i	$-0.0738691\pi$
$173$	0.666580	+	2.05152i	0.0506791	+	0.155974i	−0.922514	+	0.385963i	$0.873869\pi$
$174$		0			0
$175$		−	10.9412i		−	0.827077i
$176$		0			0
$177$			27.2878i			2.05107i
$178$		0			0
$179$	0.328774	+	1.01186i	0.0245737	+	0.0756302i	0.962591	−	0.270958i	$-0.0873403\pi$
$179$	0.328774	+	1.01186i	0.0245737	+	0.0756302i	−0.938018	+	0.346588i	$0.887340\pi$
$180$		0			0
$181$	15.3975	+	11.1869i	1.14449	+	0.831519i	0.987738	−	0.156119i	$-0.0498984\pi$
$181$	15.3975	+	11.1869i	1.14449	+	0.831519i	0.156750	+	0.987638i	$0.449898\pi$
$182$		0			0
$183$	−10.6705	+	32.8405i	−0.788789	+	2.42764i
$184$		0			0
$185$	−3.28678	+	2.38798i	−0.241649	+	0.175568i
$186$		0			0
$187$	9.05645	−	5.59325i	0.662273	−	0.409019i
$188$		0			0
$189$	0.835157	+	1.14950i	0.0607488	+	0.0836135i
$190$		0			0
$191$	−6.40884	+	19.7244i	−0.463727	+	1.42721i	0.396848	+	0.917884i	$0.370104\pi$
$191$	−6.40884	+	19.7244i	−0.463727	+	1.42721i	−0.860576	+	0.509322i	$0.829896\pi$
$192$		0			0
$193$	3.55554	−	4.89378i	0.255933	−	0.352262i	−0.661645	−	0.749817i	$-0.730141\pi$
$193$	3.55554	−	4.89378i	0.255933	−	0.352262i	0.917578	+	0.397555i	$0.130141\pi$
$194$		0			0
$195$	4.13578	−	4.59012i	0.296169	−	0.328705i
$196$		0			0
$197$			4.18451i			0.298134i	0.988827	+	0.149067i	$0.0476270\pi$
$197$			4.18451i			0.298134i	−0.988827	+	0.149067i	$0.952373\pi$
$198$		0			0
$199$	−18.1807			−1.28879			−0.644396	−	0.764692i	$-0.722891\pi$
$199$	−18.1807			−1.28879			−0.644396	+	0.764692i	$0.722891\pi$
$200$		0			0
$201$	−21.2790	+	6.91395i	−1.50090	+	0.487673i
$202$		0			0
$203$	5.90714	−	8.13048i	0.414600	−	0.570648i
$204$		0			0
$205$	−1.59099	+	4.89656i	−0.111119	+	0.341990i
$206$		0			0
$207$	14.8823	−	10.8126i	1.03439	−	0.751527i
$208$		0			0
$209$	1.59266	−	21.1788i	0.110167	−	1.46497i
$210$		0			0
$211$	12.1430	−	8.82240i	0.835958	−	0.607359i	−0.0852803	−	0.996357i	$-0.527179\pi$
$211$	12.1430	−	8.82240i	0.835958	−	0.607359i	0.921239	+	0.388998i	$0.127179\pi$
$212$		0			0
$213$	14.2757	+	4.63847i	0.978157	+	0.317823i
$214$		0			0
$215$	−2.50516	+	3.44805i	−0.170850	+	0.235155i
$216$		0			0
$217$	−4.50113	−	13.8530i	−0.305556	−	0.940406i
$218$		0			0
$219$			36.4469i			2.46286i
$220$		0			0
$221$	−10.0233	+	5.78246i	−0.674243	+	0.388970i
$222$		0			0
$223$	17.0893	−	5.55266i	1.14439	−	0.371834i	0.325361	−	0.945590i	$-0.394514\pi$
$223$	17.0893	−	5.55266i	1.14439	−	0.371834i	0.819026	+	0.573756i	$0.194514\pi$
$224$		0			0
$225$	−10.0146	−	7.27601i	−0.667638	−	0.485068i
$226$		0			0
$227$	−16.4486	−	5.34449i	−1.09173	−	0.354726i	−0.292818	−	0.956168i	$-0.594593\pi$
$227$	−16.4486	−	5.34449i	−1.09173	−	0.354726i	−0.798916	+	0.601442i	$0.794593\pi$
$228$		0			0
$229$	−0.199561	−	0.274672i	−0.0131874	−	0.0181509i	0.802372	−	0.596824i	$-0.203571\pi$
$229$	−0.199561	−	0.274672i	−0.0131874	−	0.0181509i	−0.815560	+	0.578673i	$0.803571\pi$
$230$		0			0
$231$	−17.9414	−	7.35854i	−1.18046	−	0.484156i
$232$		0			0
$233$	−21.0386	+	15.2854i	−1.37828	+	1.00138i	−0.381244	+	0.924474i	$0.624504\pi$
$233$	−21.0386	+	15.2854i	−1.37828	+	1.00138i	−0.997038	+	0.0769068i	$0.975496\pi$
$234$		0			0
$235$	1.71414	−	5.27559i	0.111818	−	0.344141i
$236$		0			0
$237$	−17.4232	−	12.6587i	−1.13176	−	0.822272i
$238$		0			0
$239$	−8.30201	+	2.69749i	−0.537013	+	0.174486i	−0.564952	−	0.825124i	$-0.691105\pi$
$239$	−8.30201	+	2.69749i	−0.537013	+	0.174486i	0.0279395	+	0.999610i	$0.491105\pi$
$240$		0			0
$241$			9.57837i			0.616997i	0.951225	+	0.308499i	$0.0998265\pi$
$241$			9.57837i			0.616997i	−0.951225	+	0.308499i	$0.900173\pi$
$242$		0			0
$243$	21.4527			1.37619
$244$		0			0
$245$	0.721254	−	0.234350i	0.0460793	−	0.0149721i
$246$		0			0
$247$	−2.42121	+	22.9615i	−0.154058	+	1.46101i
$248$		0			0
$249$	−28.2838	−	9.18996i	−1.79241	−	0.582390i
$250$		0			0
$251$	15.4153	−	11.1999i	0.973004	−	0.706929i	0.0168696	−	0.999858i	$-0.494630\pi$
$251$	15.4153	−	11.1999i	0.973004	−	0.706929i	0.956134	+	0.292929i	$0.0946300\pi$
$252$		0			0
$253$	8.39740	−	20.4744i	0.527940	−	1.28721i
$254$		0			0
$255$	−3.23263	−	4.44933i	−0.202435	−	0.278628i
$256$		0			0
$257$	−2.84417	+	8.75346i	−0.177415	+	0.546026i	−0.999736	−	0.0229980i	$-0.992679\pi$
$257$	−2.84417	+	8.75346i	−0.177415	+	0.546026i	0.822321	+	0.569024i	$0.192679\pi$
$258$		0			0
$259$	−11.2145	−	8.14784i	−0.696838	−	0.506282i
$260$		0			0
$261$	−3.51359	−	10.8137i	−0.217486	−	0.669352i
$262$		0			0
$263$	6.19343			0.381903			0.190952	−	0.981599i	$-0.438843\pi$
$263$	6.19343			0.381903			0.190952	+	0.981599i	$0.438843\pi$
$264$		0			0
$265$		−	0.276789i		−	0.0170030i
$266$		0			0
$267$	13.0151	−	4.22887i	0.796513	−	0.258803i
$268$		0			0
$269$	19.7898	+	14.3781i	1.20660	+	0.876649i	0.994918	−	0.100688i	$-0.0321045\pi$
$269$	19.7898	+	14.3781i	1.20660	+	0.876649i	0.211686	+	0.977338i	$0.432104\pi$
$270$		0			0
$271$	−4.96136	−	1.61204i	−0.301381	−	0.0979246i	0.154423	−	0.988005i	$-0.450648\pi$
$271$	−4.96136	−	1.61204i	−0.301381	−	0.0979246i	−0.455804	+	0.890080i	$0.650648\pi$
$272$		0			0
$273$	19.2557	+	8.58100i	1.16541	+	0.519346i
$274$		0			0
$275$	−14.8495	−	1.11669i	−0.895458	−	0.0673391i
$276$		0			0
$277$	2.68838	−	1.95323i	0.161529	−	0.117358i	−0.504084	−	0.863654i	$-0.668170\pi$
$277$	2.68838	−	1.95323i	0.161529	−	0.117358i	0.665614	+	0.746297i	$0.268170\pi$
$278$		0			0
$279$	−15.6731	−	5.09250i	−0.938324	−	0.304880i
$280$		0			0
$281$	−9.88766	+	13.6092i	−0.589848	+	0.811856i	−0.994732	−	0.102512i	$-0.967312\pi$
$281$	−9.88766	+	13.6092i	−0.589848	+	0.811856i	0.404884	+	0.914368i	$0.367312\pi$
$282$		0			0
$283$	2.83384	+	8.72166i	0.168454	+	0.518449i	0.999274	−	0.0380925i	$-0.0121281\pi$
$283$	2.83384	+	8.72166i	0.168454	+	0.518449i	−0.830820	+	0.556541i	$0.812128\pi$
$284$		0			0
$285$	−10.9734			−0.650008
$286$		0			0
$287$	−17.5669			−1.03694
$288$		0			0
$289$	−2.07031	−	6.37176i	−0.121783	−	0.374809i
$290$		0			0
$291$	−24.5947	+	33.8516i	−1.44176	+	1.98442i
$292$		0			0
$293$	3.19466	+	1.03801i	0.186634	+	0.0606412i	0.400843	−	0.916147i	$-0.368717\pi$
$293$	3.19466	+	1.03801i	0.186634	+	0.0606412i	−0.214209	+	0.976788i	$0.568717\pi$
$294$		0			0
$295$	6.57115	−	4.77422i	0.382587	−	0.277966i
$296$		0			0
$297$	1.64534	−	1.01616i	0.0954726	−	0.0589637i
$298$		0			0
$299$	−9.79245	+	21.9742i	−0.566312	+	1.27080i
$300$		0			0
$301$	−13.8304	−	4.49376i	−0.797169	−	0.259016i
$302$		0			0
$303$	−3.69898	−	2.68747i	−0.212501	−	0.154391i
$304$		0			0
$305$	9.77521	−	3.17616i	0.559727	−	0.181866i
$306$		0			0
$307$		−	14.3959i		−	0.821619i	−0.911721	−	0.410809i	$-0.865246\pi$
$307$		−	14.3959i		−	0.821619i	0.911721	−	0.410809i	$-0.134754\pi$
$308$		0			0
$309$	−7.11588			−0.404808
$310$		0			0
$311$	−7.21733	−	22.2127i	−0.409257	−	1.25956i	−0.917288	−	0.398225i	$-0.869626\pi$
$311$	−7.21733	−	22.2127i	−0.409257	−	1.25956i	0.508030	−	0.861339i	$-0.330374\pi$
$312$		0			0
$313$	−2.57293	−	1.86934i	−0.145430	−	0.105661i	0.512691	−	0.858573i	$-0.328649\pi$
$313$	−2.57293	−	1.86934i	−0.145430	−	0.105661i	−0.658121	+	0.752912i	$0.728649\pi$
$314$		0			0
$315$	−1.48271	+	4.56331i	−0.0835412	+	0.257113i
$316$		0			0
$317$	6.32927	+	8.71149i	0.355487	+	0.489286i	0.948884	−	0.315624i	$-0.102214\pi$
$317$	6.32927	+	8.71149i	0.355487	+	0.489286i	−0.593397	+	0.804910i	$0.702214\pi$
$318$		0			0
$319$	−10.4319	−	8.84705i	−0.584072	−	0.495340i
$320$		0			0
$321$	−9.72298	+	7.06416i	−0.542684	+	0.394283i
$322$		0			0
$323$	19.5462	+	6.35094i	1.08758	+	0.353376i
$324$		0			0
$325$	16.0994	+	1.69763i	0.893035	+	0.0941674i
$326$		0			0
$327$	−14.0136	+	4.55328i	−0.774952	+	0.251797i
$328$		0			0
$329$	18.9267			1.04346
$330$		0			0
$331$			4.21659i			0.231765i	0.993263	+	0.115882i	$0.0369695\pi$
$331$			4.21659i			0.231765i	−0.993263	+	0.115882i	$0.963030\pi$
$332$		0			0
$333$	−14.9156	+	4.84637i	−0.817369	+	0.265579i
$334$		0			0
$335$	5.38788	+	3.91452i	0.294371	+	0.213873i
$336$		0			0
$337$	−1.20974	+	3.72319i	−0.0658986	+	0.202815i	−0.978584	−	0.205848i	$-0.934005\pi$
$337$	−1.20974	+	3.72319i	−0.0658986	+	0.202815i	0.912685	+	0.408663i	$0.134005\pi$
$338$		0			0
$339$	18.1998	−	13.2230i	0.988480	−	0.718173i
$340$		0			0
$341$	−19.2609	+	4.69509i	−1.04303	+	0.254253i
$342$		0			0
$343$	11.5473	+	15.8934i	0.623494	+	0.858166i
$344$		0			0
$345$	−10.8741	−	3.53322i	−0.585443	−	0.190222i
$346$		0			0
$347$	−27.5559	−	20.0205i	−1.47928	−	1.07476i	−0.977789	−	0.209591i	$-0.932787\pi$
$347$	−27.5559	−	20.0205i	−1.47928	−	1.07476i	−0.501487	−	0.865165i	$-0.667213\pi$
$348$		0			0
$349$	−15.4504	+	5.02013i	−0.827040	+	0.268722i	−0.691798	−	0.722091i	$-0.743181\pi$
$349$	−15.4504	+	5.02013i	−0.827040	+	0.268722i	−0.135242	+	0.990813i	$0.543181\pi$
$350$		0			0
$351$	−1.82101	+	1.05054i	−0.0971982	+	0.0560735i
$352$		0			0
$353$		−	30.7526i		−	1.63680i	−0.574651	−	0.818399i	$-0.694862\pi$
$353$		−	30.7526i		−	1.63680i	0.574651	−	0.818399i	$-0.305138\pi$
$354$		0			0
$355$	−1.38067	−	4.24927i	−0.0732785	−	0.225528i
$356$		0			0
$357$	11.0298	−	15.1812i	0.583758	−	0.803474i
$358$		0			0
$359$	30.7472	+	9.99036i	1.62277	+	0.527271i	0.972594	−	0.232509i	$-0.0746935\pi$
$359$	30.7472	+	9.99036i	1.62277	+	0.527271i	0.650180	+	0.759780i	$0.274694\pi$
$360$		0			0
$361$	17.8042	−	12.9355i	0.937061	−	0.680814i
$362$		0			0
$363$	−11.8182	+	23.5993i	−0.620296	+	1.23864i
$364$		0			0
$365$	8.77677	−	6.37670i	0.459397	−	0.333772i
$366$		0			0
$367$	−10.0725	+	31.0000i	−0.525780	+	1.61818i	0.236988	+	0.971512i	$0.423840\pi$
$367$	−10.0725	+	31.0000i	−0.525780	+	1.61818i	−0.762768	+	0.646672i	$0.776160\pi$
$368$		0			0
$369$	−11.6822	+	16.0792i	−0.608151	+	0.837047i
$370$		0			0
$371$	0.898185	−	0.291838i	0.0466315	−	0.0151515i
$372$		0			0
$373$	6.66037			0.344861			0.172430	−	0.985022i	$-0.444838\pi$
$373$	6.66037			0.344861			0.172430	+	0.985022i	$0.444838\pi$
$374$		0			0
$375$			16.2620i			0.839767i
$376$		0			0
$377$	11.0471	+	9.95358i	0.568952	+	0.512636i
$378$		0			0
$379$	−10.7996	+	14.8643i	−0.554736	+	0.763529i	−0.990645	−	0.136462i	$-0.956427\pi$
$379$	−10.7996	+	14.8643i	−0.554736	+	0.763529i	0.435909	+	0.899991i	$0.356427\pi$
$380$		0			0
$381$	3.25852	−	10.0287i	0.166939	−	0.513785i
$382$		0			0
$383$	18.3376	+	25.2395i	0.937006	+	1.28968i	0.957063	+	0.289879i	$0.0936151\pi$
$383$	18.3376	+	25.2395i	0.937006	+	1.28968i	−0.0200574	+	0.999799i	$0.506385\pi$
$384$		0			0
$385$	1.36700	+	5.60791i	0.0696688	+	0.285806i
$386$		0			0
$387$	−13.3105	+	9.67066i	−0.676612	+	0.491587i
$388$		0			0
$389$	3.57717	−	11.0094i	0.181370	−	0.558198i	−0.818497	−	0.574510i	$-0.805193\pi$
$389$	3.57717	−	11.0094i	0.181370	−	0.558198i	0.999867	+	0.0163121i	$0.00519255\pi$
$390$		0			0
$391$	17.3245	+	12.5870i	0.876136	+	0.636550i
$392$		0			0
$393$	1.27606	+	3.92730i	0.0643685	+	0.198106i
$394$		0			0
$395$			6.41043i			0.322544i
$396$		0			0
$397$		−	3.58097i		−	0.179724i	−0.995954	−	0.0898620i	$-0.971357\pi$
$397$		−	3.58097i		−	0.179724i	0.995954	−	0.0898620i	$-0.0286426\pi$
$398$		0			0
$399$	−11.5700	−	35.6089i	−0.579227	−	1.78268i
$400$		0			0
$401$	−8.83756	+	12.1639i	−0.441327	+	0.607434i	−0.970506	−	0.241076i	$-0.922500\pi$
$401$	−8.83756	+	12.1639i	−0.441327	+	0.607434i	0.529180	+	0.848510i	$0.322500\pi$
$402$		0			0
$403$	21.0825	−	4.47376i	1.05019	−	0.222854i
$404$		0			0
$405$	−4.05936	−	5.58724i	−0.201711	−	0.277632i
$406$		0			0
$407$	−12.2029	+	14.3889i	−0.604876	+	0.713231i
$408$		0			0
$409$	−12.9588	−	17.8363i	−0.640771	−	0.881946i	0.357885	−	0.933766i	$-0.383498\pi$
$409$	−12.9588	−	17.8363i	−0.640771	−	0.881946i	−0.998656	+	0.0518196i	$0.983498\pi$
$410$		0			0
$411$	27.0488	+	8.78869i	1.33422	+	0.433514i
$412$		0			0
$413$	22.4209	+	16.2897i	1.10326	+	0.801566i
$414$		0			0
$415$	2.73546	+	8.41887i	0.134278	+	0.413266i
$416$		0			0
$417$	−10.4128			−0.509918
$418$		0			0
$419$	7.58198			0.370404			0.185202	−	0.982700i	$-0.440706\pi$
$419$	7.58198			0.370404			0.185202	+	0.982700i	$0.440706\pi$
$420$		0			0
$421$	12.0112	−	3.90269i	0.585392	−	0.190205i	−0.00132271	−	0.999999i	$-0.500421\pi$
$421$	12.0112	−	3.90269i	0.585392	−	0.190205i	0.586715	+	0.809794i	$0.300421\pi$
$422$		0			0
$423$	12.5865	−	17.3238i	0.611975	−	0.842312i
$424$		0			0
$425$	4.45295	−	13.7048i	0.216000	−	0.664779i
$426$		0			0
$427$	20.6134	+	28.3719i	0.997553	+	1.37301i
$428$		0			0
$429$	13.6115	−	25.2582i	0.657169	−	1.21948i
$430$		0			0
$431$	−4.46056	−	6.13944i	−0.214858	−	0.295726i	0.687961	−	0.725748i	$-0.258506\pi$
$431$	−4.46056	−	6.13944i	−0.214858	−	0.295726i	−0.902819	+	0.430021i	$0.858506\pi$
$432$		0			0
$433$	−5.92943	+	18.2489i	−0.284950	+	0.876987i	0.701463	+	0.712706i	$0.252531\pi$
$433$	−5.92943	+	18.2489i	−0.284950	+	0.876987i	−0.986414	+	0.164281i	$0.947469\pi$
$434$		0			0
$435$	−4.15397	+	5.71746i	−0.199168	+	0.274131i
$436$		0			0
$437$	40.6361	−	13.2035i	1.94389	−	0.631608i
$438$		0			0
$439$	−41.1826			−1.96554			−0.982770	−	0.184834i	$-0.940825\pi$
$439$	−41.1826			−1.96554			−0.982770	+	0.184834i	$0.940825\pi$
$440$		0			0
$441$	2.92754			0.139407
$442$		0			0
$443$	−7.45379	−	22.9404i	−0.354140	−	1.08993i	−0.956506	−	0.291712i	$-0.905775\pi$
$443$	−7.45379	−	22.9404i	−0.354140	−	1.08993i	0.602366	−	0.798220i	$-0.294225\pi$
$444$		0			0
$445$	−3.29546	−	2.39429i	−0.156220	−	0.113500i
$446$		0			0
$447$	−42.3734	−	13.7680i	−2.00419	−	0.651202i
$448$		0			0
$449$	−0.839348	−	1.15526i	−0.0396113	−	0.0545202i	0.788752	−	0.614712i	$-0.210728\pi$
$449$	−0.839348	−	1.15526i	−0.0396113	−	0.0545202i	−0.828363	+	0.560191i	$0.810728\pi$
$450$		0			0
$451$	−1.79293	+	23.8420i	−0.0844259	+	1.12268i
$452$		0			0
$453$	−7.43594	−	10.2347i	−0.349371	−	0.480868i
$454$		0			0
$455$	−1.30256	−	6.13827i	−0.0610649	−	0.287767i
$456$		0			0
$457$	0.732936	−	1.00880i	0.0342853	−	0.0471897i	−0.791530	−	0.611130i	$-0.790715\pi$
$457$	0.732936	−	1.00880i	0.0342853	−	0.0471897i	0.825815	+	0.563940i	$0.190715\pi$
$458$		0			0
$459$	0.578273	+	1.77974i	0.0269915	+	0.0830712i
$460$		0			0
$461$		−	35.7067i		−	1.66303i	−0.555504	−	0.831514i	$-0.687475\pi$
$461$		−	35.7067i		−	1.66303i	0.555504	−	0.831514i	$-0.312525\pi$
$462$		0			0
$463$		−	20.4807i		−	0.951820i	−0.879494	−	0.475910i	$-0.842119\pi$
$463$		−	20.4807i		−	0.951820i	0.879494	−	0.475910i	$-0.157881\pi$
$464$		0			0
$465$	3.16525	+	9.74163i	0.146785	+	0.451757i
$466$		0			0
$467$	25.6650	+	18.6467i	1.18764	+	0.862868i	0.993012	−	0.118010i	$-0.0376515\pi$
$467$	25.6650	+	18.6467i	1.18764	+	0.862868i	0.194624	+	0.980878i	$0.437651\pi$
$468$		0			0
$469$	−7.02189	+	21.6111i	−0.324241	+	0.997910i
$470$		0			0
$471$	18.5687	−	13.4910i	0.855601	−	0.621630i
$472$		0			0
$473$	−7.51054	+	18.3121i	−0.345335	+	0.841989i
$474$		0			0
$475$	−16.9001	−	23.2609i	−0.775428	−	1.06729i
$476$		0			0
$477$	0.330181	−	1.01619i	0.0151179	−	0.0465282i
$478$		0			0
$479$	−8.69016	+	11.9610i	−0.397063	+	0.546511i	−0.960004	−	0.279986i	$-0.909670\pi$
$479$	−8.69016	+	11.9610i	−0.397063	+	0.546511i	0.562940	+	0.826497i	$0.309670\pi$
$480$		0			0
$481$	13.7292	−	15.2374i	0.625997	−	0.694767i
$482$		0			0
$483$		−	39.0121i		−	1.77511i
$484$		0			0
$485$	12.4548			0.565545
$486$		0			0
$487$	16.6446	−	5.40815i	0.754238	−	0.245067i	0.0934341	−	0.995625i	$-0.470216\pi$
$487$	16.6446	−	5.40815i	0.754238	−	0.245067i	0.660804	+	0.750559i	$0.270216\pi$
$488$		0			0
$489$	−12.7126	+	17.4974i	−0.574885	+	0.791261i
$490$		0			0
$491$	−9.32685	+	28.7051i	−0.420915	+	1.29544i	0.485937	+	0.873994i	$0.338478\pi$
$491$	−9.32685	+	28.7051i	−0.420915	+	1.29544i	−0.906852	+	0.421449i	$0.861522\pi$
$492$		0			0
$493$	10.7082	−	7.77997i	0.482274	−	0.350392i
$494$		0			0
$495$	6.04204	+	2.47809i	0.271569	+	0.111382i
$496$		0			0
$497$	12.3332	−	8.96063i	0.553222	−	0.401939i
$498$		0			0
$499$	−7.72762	−	2.51086i	−0.345936	−	0.112401i	0.130896	−	0.991396i	$-0.458215\pi$
$499$	−7.72762	−	2.51086i	−0.345936	−	0.112401i	−0.476831	+	0.878995i	$0.658215\pi$
$500$		0			0
$501$	12.8034	−	17.6224i	0.572015	−	0.787310i
$502$		0			0
$503$	1.71170	+	5.26807i	0.0763210	+	0.234892i	0.981937	−	0.189206i	$-0.0605913\pi$
$503$	1.71170	+	5.26807i	0.0763210	+	0.234892i	−0.905616	+	0.424098i	$0.860591\pi$
$504$		0			0
$505$			1.36094i			0.0605613i
$506$		0			0
$507$	−15.6142	+	27.0024i	−0.693451	+	1.19922i
$508$		0			0
$509$	−26.0643	+	8.46880i	−1.15528	+	0.375373i	−0.823129	−	0.567854i	$-0.807774\pi$
$509$	−26.0643	+	8.46880i	−1.15528	+	0.375373i	−0.332150	+	0.943227i	$0.607774\pi$
$510$		0			0
$511$	29.9465	+	21.7574i	1.32476	+	0.962491i
$512$		0			0
$513$	3.55108	+	1.15382i	0.156784	+	0.0509422i
$514$		0			0
$515$	1.24498	+	1.71357i	0.0548605	+	0.0755090i
$516$		0			0
$517$	1.93172	−	25.6875i	0.0849569	−	1.12974i
$518$		0			0
$519$	4.18721	−	3.04219i	0.183798	−	0.133537i
$520$		0			0
$521$	−10.6391	+	32.7438i	−0.466108	+	1.43453i	0.391476	+	0.920189i	$0.371965\pi$
$521$	−10.6391	+	32.7438i	−0.466108	+	1.43453i	−0.857584	+	0.514345i	$0.828035\pi$
$522$		0			0
$523$	7.16024	+	5.20222i	0.313095	+	0.227477i	0.733223	−	0.679988i	$-0.238015\pi$
$523$	7.16024	+	5.20222i	0.313095	+	0.227477i	−0.420128	+	0.907465i	$0.638015\pi$
$524$		0			0
$525$	−24.9671	+	8.11232i	−1.08966	+	0.354051i
$526$		0			0
$527$		−	19.1840i		−	0.835669i
$528$		0			0
$529$	21.5197			0.935640
$530$		0			0
$531$	29.8203	−	9.68919i	1.29409	−	0.420475i
$532$		0			0
$533$	2.72567	−	25.8488i	0.118062	−	1.11964i
$534$		0			0
$535$	3.40223	+	1.10545i	0.147091	+	0.0477929i
$536$		0			0
$537$	2.06524	−	1.50049i	0.0891217	−	0.0647507i
$538$		0			0
$539$	2.99641	−	1.85058i	0.129064	−	0.0797099i
$540$		0			0
$541$	−4.53347	−	6.23979i	−0.194909	−	0.268269i	0.700365	−	0.713785i	$-0.253020\pi$
$541$	−4.53347	−	6.23979i	−0.194909	−	0.268269i	−0.895274	+	0.445515i	$0.853020\pi$
$542$		0			0
$543$	14.1115	−	43.4307i	0.605582	−	1.86379i
$544$		0			0
$545$	3.54826	+	2.57797i	0.151991	+	0.110428i
$546$		0			0
$547$	−4.42735	−	13.6260i	−0.189300	−	0.582605i	0.810696	−	0.585467i	$-0.199089\pi$
$547$	−4.42735	−	13.6260i	−0.189300	−	0.582605i	−0.999996	+	0.00286232i	$0.999089\pi$
$548$		0			0
$549$	39.6772			1.69338
$550$		0			0
$551$		−	26.4097i		−	1.12509i
$552$		0			0
$553$	−20.8020	+	6.75898i	−0.884590	+	0.287421i
$554$		0			0
$555$	7.88620	+	5.72966i	0.334751	+	0.243211i
$556$		0			0
$557$	−13.6117	−	4.42270i	−0.576745	−	0.187396i	0.00609705	−	0.999981i	$-0.498059\pi$
$557$	−13.6117	−	4.42270i	−0.576745	−	0.187396i	−0.582842	+	0.812586i	$0.698059\pi$
$558$		0			0
$559$	8.75825	−	19.6534i	0.370434	−	0.831252i
$560$		0			0
$561$	−19.4783	−	16.5192i	−0.822376	−	0.697440i
$562$		0			0
$563$	−12.9727	+	9.42524i	−0.546735	+	0.397227i	−0.826580	−	0.562819i	$-0.809717\pi$
$563$	−12.9727	+	9.42524i	−0.546735	+	0.397227i	0.279845	+	0.960045i	$0.409717\pi$
$564$		0			0
$565$	−6.36843	−	2.06923i	−0.267922	−	0.0870531i
$566$		0			0
$567$	13.8506	−	19.0637i	0.581672	−	0.800602i
$568$		0			0
$569$	−11.6717	−	35.9219i	−0.489304	−	1.50592i	−0.825649	−	0.564184i	$-0.809191\pi$
$569$	−11.6717	−	35.9219i	−0.489304	−	1.50592i	0.336345	−	0.941739i	$-0.390809\pi$
$570$		0			0
$571$	−0.538638			−0.0225413			−0.0112707	−	0.999936i	$-0.503588\pi$
$571$	−0.538638			−0.0225413			−0.0112707	+	0.999936i	$0.503588\pi$
$572$		0			0
$573$	49.7617			2.07882
$574$		0			0
$575$	−9.25760	−	28.4920i	−0.386069	−	1.18820i
$576$		0			0
$577$	14.3033	−	19.6867i	0.595452	−	0.819570i	−0.399830	−	0.916589i	$-0.630931\pi$
$577$	14.3033	−	19.6867i	0.595452	−	0.819570i	0.995283	+	0.0970193i	$0.0309309\pi$
$578$		0			0
$579$	−13.8036	−	4.48505i	−0.573656	−	0.186392i
$580$		0			0
$581$	−24.4352	+	17.7532i	−1.01374	+	0.736528i
$582$		0			0
$583$	−0.304414	−	1.24881i	−0.0126075	−	0.0517205i
$584$		0			0
$585$	−6.48463	−	2.88977i	−0.268106	−	0.119477i
$586$		0			0
$587$	−35.1778	−	11.4299i	−1.45194	−	0.471764i	−0.526343	−	0.850272i	$-0.676437\pi$
$587$	−35.1778	−	11.4299i	−1.45194	−	0.471764i	−0.925598	+	0.378508i	$0.876437\pi$
$588$		0			0
$589$	−30.9672	−	22.4990i	−1.27598	−	0.927053i
$590$		0			0
$591$	9.54879	−	3.10259i	0.392785	−	0.127623i
$592$		0			0
$593$			27.3845i			1.12455i	0.826951	+	0.562274i	$0.190073\pi$
$593$			27.3845i			1.12455i	−0.826951	+	0.562274i	$0.809927\pi$
$594$		0			0
$595$	−5.58553			−0.228985
$596$		0			0
$597$	13.4800	+	41.4871i	0.551699	+	1.69796i
$598$		0			0
$599$	17.8712	+	12.9842i	0.730196	+	0.530518i	0.889625	−	0.456691i	$-0.150965\pi$
$599$	17.8712	+	12.9842i	0.730196	+	0.530518i	−0.159429	+	0.987209i	$0.550965\pi$
$600$		0			0
$601$	12.8776	−	39.6333i	0.525290	−	1.61668i	−0.238452	−	0.971154i	$-0.576640\pi$
$601$	12.8776	−	39.6333i	0.525290	−	1.61668i	0.763742	−	0.645522i	$-0.223360\pi$
$602$		0			0
$603$	15.1112	+	20.7988i	0.615377	+	0.846994i
$604$		0			0
$605$	7.75063	−	1.28294i	0.315108	−	0.0521591i
$606$		0			0
$607$	1.85234	−	1.34580i	0.0751842	−	0.0546245i	−0.549558	−	0.835455i	$-0.685204\pi$
$607$	1.85234	−	1.34580i	0.0751842	−	0.0546245i	0.624742	+	0.780831i	$0.285204\pi$
$608$		0			0
$609$	−22.9331	−	7.45142i	−0.929296	−	0.301947i
$610$		0			0
$611$	−2.93665	+	27.8497i	−0.118804	+	1.12668i
$612$		0			0
$613$	−28.4890	+	9.25662i	−1.15066	+	0.373872i	−0.821391	−	0.570365i	$-0.806802\pi$
$613$	−28.4890	+	9.25662i	−1.15066	+	0.373872i	−0.329267	+	0.944237i	$0.606802\pi$
$614$		0			0
$615$	12.3533			0.498132
$616$		0			0
$617$		−	14.4709i		−	0.582578i	−0.956635	−	0.291289i	$-0.905916\pi$
$617$		−	14.4709i		−	0.582578i	0.956635	−	0.291289i	$-0.0940841\pi$
$618$		0			0
$619$	21.9330	−	7.12645i	0.881560	−	0.286436i	0.166955	−	0.985965i	$-0.446607\pi$
$619$	21.9330	−	7.12645i	0.881560	−	0.286436i	0.714605	+	0.699528i	$0.246607\pi$
$620$		0			0
$621$	3.14745	+	2.28675i	0.126303	+	0.0917643i
$622$		0			0
$623$	4.29489	−	13.2183i	0.172071	−	0.529580i
$624$		0			0
$625$	−14.2461	+	10.3504i	−0.569844	+	0.414016i
$626$		0			0
$627$	−49.5096	+	12.0686i	−1.97722	+	0.481974i
$628$		0			0
$629$	−10.7311	−	14.7701i	−0.427876	−	0.588921i
$630$		0			0
$631$	38.7459	+	12.5893i	1.54245	+	0.501172i	0.952051	−	0.305941i	$-0.0989709\pi$
$631$	38.7459	+	12.5893i	1.54245	+	0.501172i	0.590398	+	0.807113i	$0.298971\pi$
$632$		0			0
$633$	−29.1356	−	21.1682i	−1.15804	−	0.841362i
$634$		0			0
$635$	−2.98511	+	0.969920i	−0.118460	+	0.0384901i
$636$		0			0
$637$	−3.31631	+	1.91318i	−0.131397	+	0.0758029i
$638$		0			0
$639$		−	17.2476i		−	0.682306i
$640$		0			0
$641$	−3.52314	−	10.8431i	−0.139156	−	0.428278i	0.857057	−	0.515221i	$-0.172290\pi$
$641$	−3.52314	−	10.8431i	−0.139156	−	0.428278i	−0.996213	+	0.0869433i	$0.972290\pi$
$642$		0			0
$643$	14.9093	−	20.5208i	0.587964	−	0.809263i	−0.406576	−	0.913617i	$-0.633277\pi$
$643$	14.9093	−	20.5208i	0.587964	−	0.809263i	0.994540	+	0.104354i	$0.0332775\pi$
$644$		0			0
$645$	9.72568	+	3.16007i	0.382948	+	0.124427i
$646$		0			0
$647$	29.3111	−	21.2958i	1.15234	−	0.837224i	0.163550	−	0.986535i	$-0.447706\pi$
$647$	29.3111	−	21.2958i	1.15234	−	0.837224i	0.988790	+	0.149311i	$0.0477056\pi$
$648$		0			0
$649$	24.3969	−	28.7673i	0.957663	−	1.12921i
$650$		0			0
$651$	−28.2745	+	20.5426i	−1.10816	+	0.805128i
$652$		0			0
$653$	−8.17830	+	25.1702i	−0.320042	+	0.984986i	0.653588	+	0.756851i	$0.273263\pi$
$653$	−8.17830	+	25.1702i	−0.320042	+	0.984986i	−0.973629	+	0.228136i	$0.926737\pi$
$654$		0			0
$655$	0.722474	−	0.994400i	0.0282294	−	0.0388544i
$656$		0			0
$657$	39.8295	−	12.9414i	1.55390	−	0.504892i
$658$		0			0
$659$	−4.04122			−0.157424			−0.0787119	−	0.996897i	$-0.525081\pi$
$659$	−4.04122			−0.157424			−0.0787119	+	0.996897i	$0.525081\pi$
$660$		0			0
$661$			1.45326i			0.0565252i	0.999601	+	0.0282626i	$0.00899747\pi$
$661$			1.45326i			0.0565252i	−0.999601	+	0.0282626i	$0.991003\pi$
$662$		0			0
$663$	20.6270	+	18.5853i	0.801087	+	0.721793i
$664$		0			0
$665$	−6.55069	+	9.01626i	−0.254025	+	0.349635i
$666$		0			0
$667$	8.50339	−	26.1708i	0.329253	−	1.01334i
$668$		0			0
$669$	−25.3417	−	34.8798i	−0.979766	−	1.34853i
$670$		0			0
$671$	40.6105	−	25.0810i	1.56775	−	0.968241i
$672$		0			0
$673$	−11.9694	+	8.69627i	−0.461386	+	0.335217i	−0.794075	−	0.607820i	$-0.792044\pi$
$673$	−11.9694	+	8.69627i	−0.461386	+	0.335217i	0.332689	+	0.943037i	$0.392044\pi$
$674$		0			0
$675$	0.808997	−	2.48984i	0.0311383	−	0.0958338i
$676$		0			0
$677$	16.4838	+	11.9762i	0.633524	+	0.460282i	0.857619	−	0.514285i	$-0.171943\pi$
$677$	16.4838	+	11.9762i	0.633524	+	0.460282i	−0.224096	+	0.974567i	$0.571943\pi$
$678$		0			0
$679$	13.1320	+	40.4162i	0.503961	+	1.55103i
$680$		0			0
$681$			41.4974i			1.59019i
$682$		0			0
$683$			43.3616i			1.65918i	0.558370	+	0.829592i	$0.311427\pi$
$683$			43.3616i			1.65918i	−0.558370	+	0.829592i	$0.688573\pi$
$684$		0			0
$685$	−2.61601	−	8.05126i	−0.0999528	−	0.307623i
$686$		0			0
$687$	−0.478821	+	0.659041i	−0.0182682	+	0.0251440i
$688$		0			0
$689$	0.290064	+	1.36692i	0.0110505	+	0.0520754i
$690$		0			0
$691$	7.52713	+	10.3602i	0.286345	+	0.394121i	0.927823	−	0.373021i	$-0.121678\pi$
$691$	7.52713	+	10.3602i	0.286345	+	0.394121i	−0.641477	+	0.767142i	$0.721678\pi$
$692$		0			0
$693$	−1.67091	+	22.2194i	−0.0634727	+	0.844044i
$694$		0			0
$695$	1.82181	+	2.50750i	0.0691052	+	0.0951151i
$696$		0			0
$697$	−22.0041	−	7.14955i	−0.833463	−	0.270809i
$698$		0			0
$699$	50.4794	+	36.6754i	1.90931	+	1.38719i
$700$		0			0
$701$	−0.826424	−	2.54347i	−0.0312136	−	0.0960656i	0.934236	−	0.356655i	$-0.116083\pi$
$701$	−0.826424	−	2.54347i	−0.0312136	−	0.0960656i	−0.965450	+	0.260590i	$0.916083\pi$
$702$		0			0
$703$	−36.4274			−1.37389
$704$		0			0
$705$	−13.3095			−0.501265
$706$		0			0
$707$	−4.41630	+	1.43494i	−0.166092	+	0.0539665i
$708$		0			0
$709$	−26.2854	+	36.1788i	−0.987169	+	1.35872i	−0.0542926	+	0.998525i	$0.517290\pi$
$709$	−26.2854	+	36.1788i	−0.987169	+	1.35872i	−0.932876	+	0.360197i	$0.882710\pi$
$710$		0			0
$711$	−7.64699	+	23.5350i	−0.286785	+	0.882632i
$712$		0			0
$713$	−23.4428	−	32.2662i	−0.877938	−	1.20838i
$714$		0			0
$715$	−8.46386	+	1.14135i	−0.316530	+	0.0426842i
$716$		0			0
$717$	12.3110	+	16.9446i	0.459763	+	0.632809i
$718$		0			0
$719$	−5.83459	+	17.9570i	−0.217594	+	0.669684i	0.781366	+	0.624073i	$0.214523\pi$
$719$	−5.83459	+	17.9570i	−0.217594	+	0.669684i	−0.998959	+	0.0456108i	$0.985477\pi$
$720$		0			0
$721$	−4.24791	+	5.84674i	−0.158200	+	0.217744i
$722$		0			0
$723$	21.8573	−	7.10186i	0.812880	−	0.264121i
$724$		0			0
$725$	−18.5171			−0.687709
$726$		0			0
$727$	7.66977			0.284456			0.142228	−	0.989834i	$-0.454573\pi$
$727$	7.66977			0.284456			0.142228	+	0.989834i	$0.454573\pi$
$728$		0			0
$729$	−6.94144	−	21.3636i	−0.257090	−	0.791243i
$730$		0			0
$731$	−15.4948	−	11.2576i	−0.573096	−	0.416378i
$732$		0			0
$733$	22.7198	+	7.38210i	0.839174	+	0.272664i	0.696905	−	0.717164i	$-0.254560\pi$
$733$	22.7198	+	7.38210i	0.839174	+	0.272664i	0.142269	+	0.989828i	$0.454560\pi$
$734$		0			0
$735$	−1.06954	−	1.47210i	−0.0394507	−	0.0542993i
$736$		0			0
$737$	28.6142	+	11.7359i	1.05402	+	0.432296i
$738$		0			0
$739$	26.2849	+	36.1781i	0.966907	+	1.33083i	0.943594	+	0.331106i	$0.107422\pi$
$739$	26.2849	+	36.1781i	0.966907	+	1.33083i	0.0233138	+	0.999728i	$0.492578\pi$
$740$		0			0
$741$	54.1919	−	11.4997i	1.99079	−	0.422452i
$742$		0			0
$743$	−11.3766	+	15.6585i	−0.417367	+	0.574456i	−0.964996	−	0.262265i	$-0.915531\pi$
$743$	−11.3766	+	15.6585i	−0.417367	+	0.574456i	0.547629	+	0.836721i	$0.315531\pi$
$744$		0			0
$745$	4.09813	+	12.6127i	0.150144	+	0.462095i
$746$		0			0
$747$			34.1719i			1.25028i
$748$		0			0
$749$			12.2059i			0.445993i
$750$		0			0
$751$	1.06281	+	3.27098i	0.0387823	+	0.119360i	0.968573	−	0.248728i	$-0.0800126\pi$
$751$	1.06281	+	3.27098i	0.0387823	+	0.119360i	−0.929791	+	0.368088i	$0.880013\pi$
$752$		0			0
$753$	−36.9870	−	26.8726i	−1.34788	−	0.979293i
$754$		0			0
$755$	−1.16363	+	3.58129i	−0.0423489	+	0.130336i
$756$		0			0
$757$	−11.6788	+	8.48513i	−0.424473	+	0.308397i	−0.779435	−	0.626483i	$-0.784494\pi$
$757$	−11.6788	+	8.48513i	−0.424473	+	0.308397i	0.354962	+	0.934881i	$0.384494\pi$
$758$		0			0
$759$	−52.9475	−	3.98169i	−1.92187	−	0.144526i
$760$		0			0
$761$	6.69826	+	9.21936i	0.242812	+	0.334202i	0.912978	−	0.408010i	$-0.133777\pi$
$761$	6.69826	+	9.21936i	0.242812	+	0.334202i	−0.670166	+	0.742211i	$0.733777\pi$
$762$		0			0
$763$	−4.62436	+	14.2323i	−0.167413	+	0.515245i
$764$		0			0
$765$	−3.71444	+	5.11249i	−0.134296	+	0.184842i
$766$		0			0
$767$	−27.4483	+	30.4637i	−0.991102	+	1.09998i
$768$		0			0
$769$			9.67392i			0.348851i	0.984670	+	0.174425i	$0.0558067\pi$
$769$			9.67392i			0.348851i	−0.984670	+	0.174425i	$0.944193\pi$
$770$		0			0
$771$	22.0837			0.795324
$772$		0			0
$773$	40.2111	−	13.0654i	1.44629	−	0.469928i	0.522439	−	0.852677i	$-0.325022\pi$
$773$	40.2111	−	13.0654i	1.44629	−	0.469928i	0.923853	+	0.382748i	$0.125022\pi$
$774$		0			0
$775$	−15.7751	+	21.7126i	−0.566659	+	0.779939i
$776$		0			0
$777$	−10.2779	+	31.6321i	−0.368717	+	1.13480i
$778$		0			0
$779$	−37.3472	+	27.1343i	−1.33810	+	0.972188i
$780$		0			0
$781$	−10.9027	−	17.6533i	−0.390128	−	0.631686i
$782$		0			0
$783$	1.94543	−	1.41344i	0.0695240	−	0.0505122i
$784$		0			0
$785$	−6.49750	−	2.11117i	−0.231906	−	0.0753508i
$786$		0			0
$787$	−3.84535	+	5.29267i	−0.137072	+	0.188663i	−0.872035	−	0.489444i	$-0.837200\pi$
$787$	−3.84535	+	5.29267i	−0.137072	+	0.188663i	0.734963	+	0.678108i	$0.237200\pi$
$788$		0			0
$789$	−4.59210	−	14.1330i	−0.163483	−	0.503149i
$790$		0			0
$791$		−	22.8474i		−	0.812361i
$792$		0			0
$793$	−44.9462	+	25.9294i	−1.59609	+	0.920781i
$794$		0			0
$795$	−0.631615	+	0.205224i	−0.0224011	+	0.00727855i
$796$		0			0
$797$	−18.7340	−	13.6111i	−0.663593	−	0.482129i	0.204281	−	0.978912i	$-0.434514\pi$
$797$	−18.7340	−	13.6111i	−0.663593	−	0.482129i	−0.867874	+	0.496784i	$0.834514\pi$
$798$		0			0
$799$	23.7073	+	7.70298i	0.838705	+	0.272512i
$800$		0			0
$801$	−9.24268	−	12.7215i	−0.326574	−	0.449491i
$802$		0			0
$803$	32.5858	−	38.4230i	1.14993	−	1.35592i
$804$		0			0
$805$	−9.39448	+	6.82549i	−0.331112	+	0.240567i
$806$		0			0
$807$	18.1369	−	55.8197i	0.638450	−	1.96495i
$808$		0			0
$809$	−23.2404	−	16.8852i	−0.817091	−	0.593651i	0.0987870	−	0.995109i	$-0.468504\pi$
$809$	−23.2404	−	16.8852i	−0.817091	−	0.593651i	−0.915878	+	0.401457i	$0.868504\pi$
$810$		0			0
$811$	34.8576	−	11.3259i	1.22402	−	0.397707i	0.375474	−	0.926833i	$-0.377480\pi$
$811$	34.8576	−	11.3259i	1.22402	−	0.397707i	0.848543	+	0.529126i	$0.177480\pi$
$812$		0			0
$813$			12.5168i			0.438982i
$814$		0			0
$815$	6.43773			0.225504
$816$		0			0
$817$	−36.3445	+	11.8090i	−1.27153	+	0.413146i
$818$		0			0
$819$	2.54017	−	24.0897i	0.0887606	−	0.841761i
$820$		0			0
$821$	−9.14338	−	2.97086i	−0.319106	−	0.103684i	0.145084	−	0.989419i	$-0.453655\pi$
$821$	−9.14338	−	2.97086i	−0.319106	−	0.103684i	−0.464190	+	0.885735i	$0.653655\pi$
$822$		0			0
$823$	−34.4445	+	25.0254i	−1.20066	+	0.872329i	−0.994349	−	0.106157i	$-0.966145\pi$
$823$	−34.4445	+	25.0254i	−1.20066	+	0.872329i	−0.206309	+	0.978487i	$0.566145\pi$
$824$		0			0
$825$	8.46189	+	34.7136i	0.294605	+	1.20857i
$826$		0			0
$827$	−1.53083	−	2.10701i	−0.0532323	−	0.0732679i	0.781571	−	0.623816i	$-0.214419\pi$
$827$	−1.53083	−	2.10701i	−0.0532323	−	0.0732679i	−0.834803	+	0.550548i	$0.814419\pi$
$828$		0			0
$829$	9.64131	−	29.6729i	0.334857	−	1.03058i	−0.631936	−	0.775021i	$-0.717739\pi$
$829$	9.64131	−	29.6729i	0.334857	−	1.03058i	0.966793	−	0.255562i	$-0.0822606\pi$
$830$		0			0
$831$	−6.45044	−	4.68652i	−0.223763	−	0.162573i
$832$		0			0
$833$	1.05312	+	3.24116i	0.0364883	+	0.112300i
$834$		0			0
$835$	−6.48371			−0.224378
$836$		0			0
$837$		−	3.48529i		−	0.120469i
$838$		0			0
$839$	−19.3402	+	6.28400i	−0.667697	+	0.216948i	−0.623201	−	0.782062i	$-0.714168\pi$
$839$	−19.3402	+	6.28400i	−0.667697	+	0.216948i	−0.0444958	+	0.999010i	$0.514168\pi$
$840$		0			0
$841$	9.70128	+	7.04840i	0.334527	+	0.243048i
$842$		0			0
$843$	38.3865	+	12.4725i	1.32210	+	0.429577i
$844$		0			0
$845$	9.23426	−	0.964242i	0.317668	−	0.0331709i
$846$		0			0
$847$	12.3352	+	23.7983i	0.423843	+	0.817718i
$848$		0			0
$849$	17.8011	−	12.9333i	0.610934	−	0.443869i
$850$		0			0
$851$	−36.0979	−	11.7289i	−1.23742	−	0.402062i
$852$		0			0
$853$	−4.16361	+	5.73071i	−0.142559	+	0.196216i	−0.874326	−	0.485339i	$-0.838696\pi$
$853$	−4.16361	+	5.73071i	−0.142559	+	0.196216i	0.731767	+	0.681555i	$0.238696\pi$
$854$		0			0
$855$	3.89638	+	11.9918i	0.133253	+	0.410111i
$856$		0			0
$857$	31.2494			1.06746			0.533729	−	0.845656i	$-0.320790\pi$
$857$	31.2494			1.06746			0.533729	+	0.845656i	$0.320790\pi$
$858$		0			0
$859$	−16.6176			−0.566984			−0.283492	−	0.958975i	$-0.591493\pi$
$859$	−16.6176			−0.566984			−0.283492	+	0.958975i	$0.591493\pi$
$860$		0			0
$861$	13.0249	+	40.0867i	0.443889	+	1.36615i
$862$		0			0
$863$	5.08266	−	6.99568i	0.173016	−	0.238136i	−0.713699	−	0.700452i	$-0.752982\pi$
$863$	5.08266	−	6.99568i	0.173016	−	0.238136i	0.886715	+	0.462317i	$0.152982\pi$
$864$		0			0
$865$	−1.46518	−	0.476065i	−0.0498175	−	0.0161867i
$866$		0			0
$867$	−13.0049	+	9.44864i	−0.441671	+	0.320893i
$868$		0			0
$869$	7.05023	+	28.9225i	0.239163	+	0.981128i
$870$		0			0
$871$	−30.7102	−	13.6855i	−1.04058	−	0.463716i
$872$		0			0
$873$	45.7263	+	14.8574i	1.54760	+	0.502846i
$874$		0			0
$875$	13.3616	+	9.70780i	0.451706	+	0.328183i
$876$		0			0
$877$	−10.4779	+	3.40447i	−0.353813	+	0.114961i	−0.480530	−	0.876978i	$-0.659556\pi$
$877$	−10.4779	+	3.40447i	−0.353813	+	0.114961i	0.126718	+	0.991939i	$0.459556\pi$
$878$		0			0
$879$		−	8.05966i		−	0.271846i
$880$		0			0
$881$	−47.1649			−1.58903			−0.794513	−	0.607247i	$-0.792274\pi$
$881$	−47.1649			−1.58903			−0.794513	+	0.607247i	$0.792274\pi$
$882$		0			0
$883$	0.0314220	+	0.0967071i	0.00105744	+	0.00325445i	0.951584	−	0.307389i	$-0.0994554\pi$
$883$	0.0314220	+	0.0967071i	0.00105744	+	0.00325445i	−0.950526	+	0.310644i	$0.899455\pi$
$884$		0			0
$885$	−15.7666	−	11.4551i	−0.529990	−	0.385060i
$886$		0			0
$887$	15.8583	−	48.8069i	0.532470	−	1.63878i	−0.216582	−	0.976264i	$-0.569491\pi$
$887$	15.8583	−	48.8069i	0.532470	−	1.63878i	0.749052	−	0.662511i	$-0.230509\pi$
$888$		0			0
$889$	−6.29483	−	8.66409i	−0.211122	−	0.290584i
$890$		0			0
$891$	−24.4599	−	20.7439i	−0.819436	−	0.694947i
$892$		0			0
$893$	40.2381	−	29.2347i	1.34652	−	0.978303i
$894$		0			0
$895$	−0.722662	−	0.234807i	−0.0241559	−	0.00784874i
$896$		0			0
$897$	57.4043	+	6.05308i	1.91667	+	0.202106i
$898$		0			0
$899$	−23.4452	+	7.61781i	−0.781941	+	0.254068i
$900$		0			0
$901$	1.24383			0.0414379
$902$		0			0
$903$			34.8919i			1.16113i
$904$		0			0
$905$	−12.9275	+	4.20038i	−0.429723	+	0.139625i
$906$		0			0
$907$	−26.6069	−	19.3311i	−0.883468	−	0.641877i	0.0506987	−	0.998714i	$-0.483855\pi$
$907$	−26.6069	−	19.3311i	−0.883468	−	0.641877i	−0.934167	+	0.356837i	$0.883855\pi$
$908$		0			0
$909$	−1.62347	+	4.99652i	−0.0538471	+	0.165724i
$910$		0			0
$911$	21.5993	−	15.6928i	0.715618	−	0.519927i	−0.169363	−	0.985554i	$-0.554171\pi$
$911$	21.5993	−	15.6928i	0.715618	−	0.519927i	0.884981	+	0.465627i	$0.154171\pi$
$912$		0			0
$913$	21.6009	+	34.9757i	0.714886	+	1.15753i
$914$		0			0
$915$	−14.4956	−	19.9515i	−0.479210	−	0.659576i
$916$		0			0
$917$	3.98860	+	1.29598i	0.131715	+	0.0427969i
$918$		0			0
$919$	−39.2454	−	28.5135i	−1.29459	−	0.940572i	−0.294699	−	0.955590i	$-0.595219\pi$
$919$	−39.2454	−	28.5135i	−1.29459	−	0.940572i	−0.999887	+	0.0150180i	$0.995219\pi$
$920$		0			0
$921$	−32.8506	+	10.6738i	−1.08246	+	0.351714i
$922$		0			0
$923$	11.2715	+	19.5381i	0.371006	+	0.643103i
$924$		0			0
$925$			25.5410i			0.839785i
$926$		0			0
$927$	2.52667	+	7.77629i	0.0829867	+	0.255407i
$928$		0			0
$929$	1.10474	−	1.52055i	0.0362455	−	0.0498876i	−0.790510	−	0.612450i	$-0.790184\pi$
$929$	1.10474	−	1.52055i	0.0362455	−	0.0498876i	0.826755	+	0.562562i	$0.190184\pi$
$930$		0			0
$931$	6.46702	+	2.10126i	0.211948	+	0.0688661i
$932$		0			0
$933$	−45.3367	+	32.9390i	−1.48426	+	1.07837i
$934$		0			0
$935$	−0.570076	+	7.58074i	−0.0186435	+	0.247917i
$936$		0			0
$937$	32.1803	−	23.3803i	1.05128	−	0.763802i	0.0788274	−	0.996888i	$-0.474882\pi$
$937$	32.1803	−	23.3803i	1.05128	−	0.763802i	0.972456	+	0.233086i	$0.0748824\pi$
$938$		0			0
$939$	−2.35803	+	7.25728i	−0.0769515	+	0.236832i
$940$		0			0
$941$	18.0076	−	24.7853i	0.587031	−	0.807979i	−0.407413	−	0.913244i	$-0.633569\pi$
$941$	18.0076	−	24.7853i	0.587031	−	0.807979i	0.994444	+	0.105265i	$0.0335691\pi$
$942$		0			0
$943$	−45.7460	+	14.8638i	−1.48970	+	0.484031i
$944$		0			0
$945$	−1.01476			−0.0330102
$946$		0			0
$947$		−	40.6184i		−	1.31992i	−0.751300	−	0.659961i	$-0.770573\pi$
$947$		−	40.6184i		−	1.31992i	0.751300	−	0.659961i	$-0.229427\pi$
$948$		0			0
$949$	−36.6614	+	40.6889i	−1.19008	+	1.32082i
$950$		0			0
$951$	15.1863	−	20.9021i	0.492449	−	0.677798i
$952$		0			0
$953$	5.34607	−	16.4535i	0.173176	−	0.532982i	−0.826369	−	0.563129i	$-0.809598\pi$
$953$	5.34607	−	16.4535i	0.173176	−	0.532982i	0.999545	+	0.0301470i	$0.00959753\pi$
$954$		0			0
$955$	−8.70622	−	11.9831i	−0.281727	−	0.387763i
$956$		0			0
$957$	−12.4538	+	30.3645i	−0.402573	+	0.981545i
$958$		0			0
$959$	23.3683	−	16.9780i	0.754601	−	0.548250i
$960$		0			0
$961$	−1.46152	+	4.49808i	−0.0471456	+	0.145099i
$962$		0			0
$963$	11.1721	+	8.11704i	0.360017	+	0.261568i
$964$		0			0
$965$	1.33501	+	4.10872i	0.0429754	+	0.132265i
$966$		0			0
$967$			8.44764i			0.271658i	0.990732	+	0.135829i	$0.0433697\pi$
$967$			8.44764i			0.271658i	−0.990732	+	0.135829i	$0.956630\pi$
$968$		0			0
$969$		−	49.3121i		−	1.58413i
$970$		0			0
$971$	−11.3924	−	35.0622i	−0.365600	−	1.12520i	−0.949605	−	0.313450i	$-0.898515\pi$
$971$	−11.3924	−	35.0622i	−0.365600	−	1.12520i	0.584005	−	0.811750i	$-0.301485\pi$
$972$		0			0
$973$	−6.21605	+	8.55565i	−0.199277	+	0.274282i
$974$		0			0
$975$	−8.06299	−	37.9966i	−0.258222	−	1.21687i
$976$		0			0
$977$	−0.524036	−	0.721274i	−0.0167654	−	0.0230756i	0.800552	−	0.599263i	$-0.204540\pi$
$977$	−0.524036	−	0.721274i	−0.0167654	−	0.0230756i	−0.817317	+	0.576188i	$0.804540\pi$
$978$		0			0
$979$	−17.5017	−	7.17816i	−0.559355	−	0.229415i
$980$		0			0
$981$	9.95172	+	13.6974i	0.317734	+	0.437323i
$982$		0			0
$983$	−30.7386	−	9.98758i	−0.980409	−	0.318554i	−0.225399	−	0.974267i	$-0.572368\pi$
$983$	−30.7386	−	9.98758i	−0.980409	−	0.318554i	−0.755011	+	0.655712i	$0.772368\pi$
$984$		0			0
$985$	−2.41777	−	1.75661i	−0.0770367	−	0.0559704i
$986$		0			0
$987$	−14.0332	−	43.1896i	−0.446681	−	1.37474i
$988$		0			0
$989$	−39.8179			−1.26614
$990$		0			0
$991$	9.15453			0.290803			0.145402	−	0.989373i	$-0.453553\pi$
$991$	9.15453			0.290803			0.145402	+	0.989373i	$0.453553\pi$
$992$		0			0
$993$	9.62199	−	3.12638i	0.305345	−	0.0992125i
$994$		0			0
$995$	7.63206	−	10.5046i	0.241953	−	0.333019i
$996$		0			0
$997$	−4.97214	+	15.3027i	−0.157469	+	0.484641i	−0.998403	−	0.0564980i	$-0.982007\pi$
$997$	−4.97214	+	15.3027i	−0.157469	+	0.484641i	0.840933	+	0.541139i	$0.182007\pi$
$998$		0			0
$999$	−1.94958	−	2.68337i	−0.0616821	−	0.0848982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.x.a.25.3	✓	56
11.4	even	5	inner	572.2.x.a.389.4	yes	56
13.12	even	2	inner	572.2.x.a.25.4	yes	56
143.103	even	10	inner	572.2.x.a.389.3	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.x.a.25.3	✓	56	1.1	even	1	trivial
572.2.x.a.25.4	yes	56	13.12	even	2	inner
572.2.x.a.389.3	yes	56	143.103	even	10	inner
572.2.x.a.389.4	yes	56	11.4	even	5	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.741447 - 2.28194i) q^{3} +(-0.419790 + 0.577792i) q^{5} +(-2.31756 - 0.753022i) q^{7} +(-2.23045 + 1.62052i) q^{9} +O(q^{10})\)	\(q+(-0.741447 - 2.28194i) q^{3} +(-0.419790 + 0.577792i) q^{5} +(-2.31756 - 0.753022i) q^{7} +(-2.23045 + 1.62052i) q^{9} +(-1.25855 + 3.06856i) q^{11} +(1.46762 - 3.29334i) q^{13} +(1.62974 + 0.529534i) q^{15} +(-2.59647 - 1.88645i) q^{17} +(-6.09026 + 1.97885i) q^{19} +5.84686i q^{21} -6.67231 q^{23} +(1.38747 + 4.27018i) q^{25} +(-0.471718 - 0.342723i) q^{27} +(-1.27443 + 3.92229i) q^{29} +(3.51344 + 4.83584i) q^{31} +(7.93541 + 0.596748i) q^{33} +(1.40798 - 1.02296i) q^{35} +(5.41010 + 1.75785i) q^{37} +(-8.60336 - 0.907194i) q^{39} +(6.85610 - 2.22768i) q^{41} +5.96764 q^{43} -1.96901i q^{45} +(-7.38681 + 2.40012i) q^{47} +(-0.859065 - 0.624147i) q^{49} +(-2.37961 + 7.32369i) q^{51} +(-0.313539 + 0.227800i) q^{53} +(-1.24466 - 2.01533i) q^{55} +(9.03121 + 12.4304i) q^{57} +(-10.8162 - 3.51441i) q^{59} +(-11.6430 - 8.45911i) q^{61} +(6.38949 - 2.07607i) q^{63} +(1.28677 + 2.23049i) q^{65} -9.32495i q^{67} +(4.94716 + 15.2258i) q^{69} +(-3.67717 + 5.06118i) q^{71} +(-14.4467 - 4.69403i) q^{73} +(8.71556 - 6.33222i) q^{75} +(5.22745 - 6.16387i) q^{77} +(7.26158 - 5.27585i) q^{79} +(-2.98819 + 9.19670i) q^{81} +(7.28538 - 10.0275i) q^{83} +(2.17995 - 0.708308i) q^{85} +9.89535 q^{87} +5.70354i q^{89} +(-5.88127 + 6.52736i) q^{91} +(8.43005 - 11.6030i) q^{93} +(1.41327 - 4.34961i) q^{95} +(-10.2505 - 14.1085i) q^{97} +(-2.16553 - 8.88377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^9	\( 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) \) 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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