LMFDB - Embedded newform 572.2.p.a.485.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(309,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("572.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			485.4
Character	$\chi$	$=$	572.485
Dual form			572.2.p.a.309.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909010 + 1.57445i) q^{3} -1.10453i q^{5} +(0.391551 - 0.226062i) q^{7} +(-0.152598 - 0.264307i) q^{9} +O(q^{10})$	\(q+(-0.909010 + 1.57445i) q^{3} -1.10453i q^{5} +(0.391551 - 0.226062i) q^{7} +(-0.152598 - 0.264307i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(3.00109 + 1.99836i) q^{13} +(1.73902 + 1.00403i) q^{15} +(2.90403 + 5.02993i) q^{17} +(-0.434699 + 0.250974i) q^{19} +0.821971i q^{21} +(-1.69579 + 2.93720i) q^{23} +3.78002 q^{25} -4.89921 q^{27} +(-3.57713 + 6.19577i) q^{29} -0.559743i q^{31} +(1.57445 - 0.909010i) q^{33} +(-0.249692 - 0.432479i) q^{35} +(-1.12610 - 0.650154i) q^{37} +(-5.87435 + 2.90854i) q^{39} +(1.68197 + 0.971085i) q^{41} +(-1.10970 - 1.92206i) q^{43} +(-0.291934 + 0.168548i) q^{45} +8.24486i q^{47} +(-3.39779 + 5.88515i) q^{49} -10.5592 q^{51} +10.4766 q^{53} +(-0.552263 + 0.956548i) q^{55} -0.912550i q^{57} +(6.68558 - 3.85992i) q^{59} +(-0.127115 - 0.220169i) q^{61} +(-0.119500 - 0.0689931i) q^{63} +(2.20724 - 3.31478i) q^{65} +(2.01992 + 1.16620i) q^{67} +(-3.08298 - 5.33988i) q^{69} +(-14.2566 + 8.23105i) q^{71} -9.33433i q^{73} +(-3.43608 + 5.95146i) q^{75} -0.452124 q^{77} +13.1660 q^{79} +(4.91122 - 8.50648i) q^{81} -10.2140i q^{83} +(5.55569 - 3.20758i) q^{85} +(-6.50329 - 11.2640i) q^{87} +(-2.62610 - 1.51618i) q^{89} +(1.62684 + 0.104028i) q^{91} +(0.881287 + 0.508812i) q^{93} +(0.277207 + 0.480136i) q^{95} +(10.8419 - 6.25957i) q^{97} +0.305195i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.909010	+	1.57445i	−0.524817	+	0.909010i	0.474765	+	0.880112i	$0.342533\pi$
$3$	−0.909010	+	1.57445i	−0.524817	+	0.909010i	−0.999582	+	0.0288974i	$0.990800\pi$
$4$		0			0
$5$		−	1.10453i		−	0.493959i	−0.969021	−	0.246980i	$-0.920562\pi$
$5$		−	1.10453i		−	0.493959i	0.969021	−	0.246980i	$-0.0794381\pi$
$6$		0			0
$7$	0.391551	−	0.226062i	0.147992	−	0.0854435i	−0.424175	−	0.905580i	$-0.639436\pi$
$7$	0.391551	−	0.226062i	0.147992	−	0.0854435i	0.572168	+	0.820137i	$0.306103\pi$
$8$		0			0
$9$	−0.152598	−	0.264307i	−0.0508659	−	0.0881023i
$10$		0			0
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$11$	−0.866025	−	0.500000i	−0.261116	−	0.150756i
$12$		0			0
$13$	3.00109	+	1.99836i	0.832353	+	0.554246i
$13$	3.00109	+	1.99836i	0.832353	+	0.554246i
$14$		0			0
$15$	1.73902	+	1.00403i	0.449014	+	0.259238i
$16$		0			0
$17$	2.90403	+	5.02993i	0.704331	+	1.21994i	0.966933	+	0.255032i	$0.0820860\pi$
$17$	2.90403	+	5.02993i	0.704331	+	1.21994i	−0.262602	+	0.964904i	$0.584581\pi$
$18$		0			0
$19$	−0.434699	+	0.250974i	−0.0997268	+	0.0575773i	−0.549034	−	0.835800i	$-0.685004\pi$
$19$	−0.434699	+	0.250974i	−0.0997268	+	0.0575773i	0.449307	+	0.893377i	$0.351671\pi$
$20$		0			0
$21$			0.821971i			0.179369i
$22$		0			0
$23$	−1.69579	+	2.93720i	−0.353597	+	0.612448i	−0.986877	−	0.161475i	$-0.948375\pi$
$23$	−1.69579	+	2.93720i	−0.353597	+	0.612448i	0.633280	+	0.773923i	$0.281708\pi$
$24$		0			0
$25$	3.78002			0.756004
$26$		0			0
$27$	−4.89921			−0.942853
$28$		0			0
$29$	−3.57713	+	6.19577i	−0.664257	+	1.15053i	0.315230	+	0.949015i	$0.397918\pi$
$29$	−3.57713	+	6.19577i	−0.664257	+	1.15053i	−0.979486	+	0.201511i	$0.935415\pi$
$30$		0			0
$31$		−	0.559743i		−	0.100533i	−0.998736	−	0.0502664i	$-0.983993\pi$
$31$		−	0.559743i		−	0.100533i	0.998736	−	0.0502664i	$-0.0160070\pi$
$32$		0			0
$33$	1.57445	−	0.909010i	0.274077	−	0.158238i
$34$		0			0
$35$	−0.249692	−	0.432479i	−0.0422056	−	0.0731022i
$36$		0			0
$37$	−1.12610	−	0.650154i	−0.185130	−	0.106885i	0.404571	−	0.914507i	$-0.367421\pi$
$37$	−1.12610	−	0.650154i	−0.185130	−	0.106885i	−0.589701	+	0.807622i	$0.700754\pi$
$38$		0			0
$39$	−5.87435	+	2.90854i	−0.940648	+	0.465739i
$40$		0			0
$41$	1.68197	+	0.971085i	0.262679	+	0.151658i	0.625556	−	0.780179i	$-0.284872\pi$
$41$	1.68197	+	0.971085i	0.262679	+	0.151658i	−0.362877	+	0.931837i	$0.618205\pi$
$42$		0			0
$43$	−1.10970	−	1.92206i	−0.169228	−	0.293111i	0.768921	−	0.639344i	$-0.220794\pi$
$43$	−1.10970	−	1.92206i	−0.169228	−	0.293111i	−0.938149	+	0.346233i	$0.887461\pi$
$44$		0			0
$45$	−0.291934	+	0.168548i	−0.0435189	+	0.0251257i
$46$		0			0
$47$			8.24486i			1.20264i	0.799010	+	0.601318i	$0.205358\pi$
$47$			8.24486i			1.20264i	−0.799010	+	0.601318i	$0.794642\pi$
$48$		0			0
$49$	−3.39779	+	5.88515i	−0.485399	+	0.840735i
$50$		0			0
$51$	−10.5592			−1.47858
$52$		0			0
$53$	10.4766			1.43907			0.719537	−	0.694455i	$-0.244354\pi$
$53$	10.4766			1.43907			0.719537	+	0.694455i	$0.244354\pi$
$54$		0			0
$55$	−0.552263	+	0.956548i	−0.0744672	+	0.128981i
$56$		0			0
$57$		−	0.912550i		−	0.120870i
$58$		0			0
$59$	6.68558	−	3.85992i	0.870389	−	0.502519i	0.00291131	−	0.999996i	$-0.499073\pi$
$59$	6.68558	−	3.85992i	0.870389	−	0.502519i	0.867477	+	0.497477i	$0.165740\pi$
$60$		0			0
$61$	−0.127115	−	0.220169i	−0.0162754	−	0.0281897i	0.857773	−	0.514029i	$-0.171848\pi$
$61$	−0.127115	−	0.220169i	−0.0162754	−	0.0281897i	−0.874048	+	0.485839i	$0.838514\pi$
$62$		0			0
$63$	−0.119500	−	0.0689931i	−0.0150555	−	0.00869232i
$64$		0			0
$65$	2.20724	−	3.31478i	0.273775	−	0.411148i
$66$		0			0
$67$	2.01992	+	1.16620i	0.246773	+	0.142474i	0.618286	−	0.785953i	$-0.287827\pi$
$67$	2.01992	+	1.16620i	0.246773	+	0.142474i	−0.371513	+	0.928428i	$0.621161\pi$
$68$		0			0
$69$	−3.08298	−	5.33988i	−0.371147	−	0.642846i
$70$		0			0
$71$	−14.2566	+	8.23105i	−1.69195	+	0.976846i	−0.739002	+	0.673703i	$0.764703\pi$
$71$	−14.2566	+	8.23105i	−1.69195	+	0.976846i	−0.952945	+	0.303143i	$0.901964\pi$
$72$		0			0
$73$		−	9.33433i		−	1.09250i	−0.837622	−	0.546250i	$-0.816055\pi$
$73$		−	9.33433i		−	1.09250i	0.837622	−	0.546250i	$-0.183945\pi$
$74$		0			0
$75$	−3.43608	+	5.95146i	−0.396764	+	0.687215i
$76$		0			0
$77$	−0.452124			−0.0515244
$78$		0			0
$79$	13.1660			1.48129			0.740644	−	0.671897i	$-0.234520\pi$
$79$	13.1660			1.48129			0.740644	+	0.671897i	$0.234520\pi$
$80$		0			0
$81$	4.91122	−	8.50648i	0.545691	−	0.945165i
$82$		0			0
$83$		−	10.2140i		−	1.12113i	−0.828109	−	0.560567i	$-0.810583\pi$
$83$		−	10.2140i		−	1.12113i	0.828109	−	0.560567i	$-0.189417\pi$
$84$		0			0
$85$	5.55569	−	3.20758i	0.602599	−	0.347911i
$86$		0			0
$87$	−6.50329	−	11.2640i	−0.697226	−	1.20763i
$88$		0			0
$89$	−2.62610	−	1.51618i	−0.278366	−	0.160715i	0.354317	−	0.935125i	$-0.384713\pi$
$89$	−2.62610	−	1.51618i	−0.278366	−	0.160715i	−0.632683	+	0.774411i	$0.718047\pi$
$90$		0			0
$91$	1.62684	+	0.104028i	0.170539	+	0.0109051i
$92$		0			0
$93$	0.881287	+	0.508812i	0.0913853	+	0.0527613i
$94$		0			0
$95$	0.277207	+	0.480136i	0.0284408	+	0.0492610i
$96$		0			0
$97$	10.8419	−	6.25957i	1.10083	−	0.635563i	0.164389	−	0.986396i	$-0.447435\pi$
$97$	10.8419	−	6.25957i	1.10083	−	0.635563i	0.936438	+	0.350833i	$0.114102\pi$
$98$		0			0
$99$			0.305195i			0.0306733i
$100$		0			0
$101$	−2.47905	+	4.29384i	−0.246675	+	0.427253i	−0.962601	−	0.270922i	$-0.912671\pi$
$101$	−2.47905	+	4.29384i	−0.246675	+	0.427253i	0.715926	+	0.698176i	$0.246005\pi$
$102$		0			0
$103$	9.71644			0.957389			0.478695	−	0.877981i	$-0.341110\pi$
$103$	9.71644			0.957389			0.478695	+	0.877981i	$0.341110\pi$
$104$		0			0
$105$	0.907889			0.0886009
$106$		0			0
$107$	2.24402	−	3.88676i	0.216938	−	0.375748i	−0.736932	−	0.675966i	$-0.763726\pi$
$107$	2.24402	−	3.88676i	0.216938	−	0.375748i	0.953870	+	0.300219i	$0.0970597\pi$
$108$		0			0
$109$		−	15.5442i		−	1.48887i	−0.667697	−	0.744433i	$-0.732720\pi$
$109$		−	15.5442i		−	1.48887i	0.667697	−	0.744433i	$-0.267280\pi$
$110$		0			0
$111$	2.04727	−	1.18199i	0.194318	−	0.112190i
$112$		0			0
$113$	−2.85258	−	4.94081i	−0.268348	−	0.464792i	0.700087	−	0.714057i	$-0.253144\pi$
$113$	−2.85258	−	4.94081i	−0.268348	−	0.464792i	−0.968435	+	0.249265i	$0.919811\pi$
$114$		0			0
$115$	3.24421	+	1.87305i	0.302524	+	0.174662i
$116$		0			0
$117$	0.0702216	−	1.09815i	0.00649199	−	0.101524i
$118$		0			0
$119$	2.27415	+	1.31298i	0.208471	+	0.120361i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		0			0
$123$	−3.05785	+	1.76545i	−0.275717	+	0.159185i
$124$		0			0
$125$		−	9.69777i		−	0.867394i
$126$		0			0
$127$	−7.78716	+	13.4878i	−0.690999	+	1.19684i	0.280513	+	0.959850i	$0.409496\pi$
$127$	−7.78716	+	13.4878i	−0.690999	+	1.19684i	−0.971511	+	0.236994i	$0.923838\pi$
$128$		0			0
$129$	4.03491			0.355254
$130$		0			0
$131$	5.37338			0.469474			0.234737	−	0.972059i	$-0.424577\pi$
$131$	5.37338			0.469474			0.234737	+	0.972059i	$0.424577\pi$
$132$		0			0
$133$	−0.113471	+	0.196538i	−0.00983921	+	0.0170420i
$134$		0			0
$135$			5.41130i			0.465731i
$136$		0			0
$137$	3.97996	−	2.29783i	0.340031	−	0.196317i	−0.320255	−	0.947331i	$-0.603769\pi$
$137$	3.97996	−	2.29783i	0.340031	−	0.196317i	0.660286	+	0.751014i	$0.270435\pi$
$138$		0			0
$139$	−7.03261	−	12.1808i	−0.596498	−	1.03316i	−0.993334	−	0.115275i	$-0.963225\pi$
$139$	−7.03261	−	12.1808i	−0.596498	−	1.03316i	0.396836	−	0.917890i	$-0.370108\pi$
$140$		0			0
$141$	−12.9811	−	7.49466i	−1.09321	−	0.631164i
$142$		0			0
$143$	−1.59984	−	3.23118i	−0.133785	−	0.270205i
$144$		0			0
$145$	6.84339	+	3.95104i	0.568313	+	0.328116i
$146$		0			0
$147$	−6.17725	−	10.6993i	−0.509491	−	0.882465i
$148$		0			0
$149$	−1.89534	+	1.09427i	−0.155272	+	0.0896464i	−0.575623	−	0.817715i	$-0.695240\pi$
$149$	−1.89534	+	1.09427i	−0.155272	+	0.0896464i	0.420351	+	0.907362i	$0.361907\pi$
$150$		0			0
$151$		−	12.3355i		−	1.00385i	−0.864912	−	0.501923i	$-0.832626\pi$
$151$		−	12.3355i		−	1.00385i	0.864912	−	0.501923i	$-0.167374\pi$
$152$		0			0
$153$	0.886296	−	1.53511i	0.0716528	−	0.124106i
$154$		0			0
$155$	−0.618251			−0.0496591
$156$		0			0
$157$	−5.13610			−0.409905			−0.204953	−	0.978772i	$-0.565704\pi$
$157$	−5.13610			−0.409905			−0.204953	+	0.978772i	$0.565704\pi$
$158$		0			0
$159$	−9.52334	+	16.4949i	−0.755250	+	1.30813i
$160$		0			0
$161$			1.53342i			0.120850i
$162$		0			0
$163$	12.0454	−	6.95442i	0.943470	−	0.544712i	0.0524234	−	0.998625i	$-0.483305\pi$
$163$	12.0454	−	6.95442i	0.943470	−	0.544712i	0.891046	+	0.453912i	$0.149972\pi$
$164$		0			0
$165$	−1.00403	−	1.73902i	−0.0781633	−	0.135383i
$166$		0			0
$167$	−7.06348	−	4.07810i	−0.546588	−	0.315573i	0.201157	−	0.979559i	$-0.435530\pi$
$167$	−7.06348	−	4.07810i	−0.546588	−	0.315573i	−0.747745	+	0.663986i	$0.768863\pi$
$168$		0			0
$169$	5.01309	+	11.9945i	0.385623	+	0.922657i
$170$		0			0
$171$	0.132668	+	0.0765959i	0.0101454	+	0.00585744i
$172$		0			0
$173$	−9.41620	−	16.3093i	−0.715901	−	1.23998i	−0.962611	−	0.270887i	$-0.912683\pi$
$173$	−9.41620	−	16.3093i	−0.715901	−	1.23998i	0.246710	−	0.969089i	$-0.420650\pi$
$174$		0			0
$175$	1.48007	−	0.854520i	0.111883	−	0.0645957i
$176$		0			0
$177$			14.0348i			1.05492i
$178$		0			0
$179$	−8.31787	+	14.4070i	−0.621707	+	1.07683i	0.367461	+	0.930039i	$0.380227\pi$
$179$	−8.31787	+	14.4070i	−0.621707	+	1.07683i	−0.989168	+	0.146789i	$0.953106\pi$
$180$		0			0
$181$	−18.9294			−1.40701			−0.703506	−	0.710690i	$-0.748383\pi$
$181$	−18.9294			−1.40701			−0.703506	+	0.710690i	$0.748383\pi$
$182$		0			0
$183$	0.462194			0.0341663
$184$		0			0
$185$	−0.718112	+	1.24381i	−0.0527967	+	0.0914465i
$186$		0			0
$187$		−	5.80806i		−	0.424727i
$188$		0			0
$189$	−1.91829	+	1.10753i	−0.139535	+	0.0805607i
$190$		0			0
$191$	4.63591	+	8.02963i	0.335442	+	0.581003i	0.983570	−	0.180529i	$-0.0577809\pi$
$191$	4.63591	+	8.02963i	0.335442	+	0.581003i	−0.648127	+	0.761532i	$0.724448\pi$
$192$		0			0
$193$	3.29716	+	1.90362i	0.237335	+	0.137025i	0.613951	−	0.789344i	$-0.289579\pi$
$193$	3.29716	+	1.90362i	0.237335	+	0.137025i	−0.376616	+	0.926369i	$0.622912\pi$
$194$		0			0
$195$	3.21256	+	6.48837i	0.230056	+	0.464642i
$196$		0			0
$197$	−4.12131	−	2.37944i	−0.293631	−	0.169528i	0.345947	−	0.938254i	$-0.387558\pi$
$197$	−4.12131	−	2.37944i	−0.293631	−	0.169528i	−0.639578	+	0.768726i	$0.720891\pi$
$198$		0			0
$199$	1.58554	+	2.74624i	0.112396	+	0.194676i	0.916736	−	0.399494i	$-0.130814\pi$
$199$	1.58554	+	2.74624i	0.112396	+	0.194676i	−0.804340	+	0.594170i	$0.797481\pi$
$200$		0			0
$201$	−3.67226	+	2.12018i	−0.259021	+	0.149546i
$202$		0			0
$203$			3.23462i			0.227026i
$204$		0			0
$205$	1.07259	−	1.85778i	0.0749129	−	0.129753i
$206$		0			0
$207$	1.03509			0.0719441
$208$		0			0
$209$	0.501947			0.0347204
$210$		0			0
$211$	7.56205	−	13.0979i	0.520593	−	0.901693i	−0.479120	−	0.877749i	$-0.659044\pi$
$211$	7.56205	−	13.0979i	0.520593	−	0.901693i	0.999713	−	0.0239442i	$-0.00762241\pi$
$212$		0			0
$213$		−	29.9284i		−	2.05066i
$214$		0			0
$215$	−2.12296	+	1.22569i	−0.144785	+	0.0835916i
$216$		0			0
$217$	−0.126537	−	0.219168i	−0.00858987	−	0.0148781i
$218$		0			0
$219$	14.6964	+	8.48500i	0.993094	+	0.573363i
$220$		0			0
$221$	−1.33636	+	20.8986i	−0.0898934	+	1.40579i
$222$		0			0
$223$	3.80069	+	2.19433i	0.254513	+	0.146943i	0.621829	−	0.783153i	$-0.286390\pi$
$223$	3.80069	+	2.19433i	0.254513	+	0.146943i	−0.367316	+	0.930096i	$0.619723\pi$
$224$		0			0
$225$	−0.576822	−	0.999086i	−0.0384548	−	0.0666057i
$226$		0			0
$227$	−23.5085	+	13.5726i	−1.56031	+	0.900846i	−0.563086	+	0.826398i	$0.690386\pi$
$227$	−23.5085	+	13.5726i	−1.56031	+	0.900846i	−0.997225	+	0.0744476i	$0.976281\pi$
$228$		0			0
$229$			18.0945i			1.19572i	0.801600	+	0.597861i	$0.203982\pi$
$229$			18.0945i			1.19572i	−0.801600	+	0.597861i	$0.796018\pi$
$230$		0			0
$231$	0.410986	−	0.711848i	0.0270409	−	0.0468362i
$232$		0			0
$233$	−6.52762			−0.427639			−0.213819	−	0.976873i	$-0.568590\pi$
$233$	−6.52762			−0.427639			−0.213819	+	0.976873i	$0.568590\pi$
$234$		0			0
$235$	9.10666			0.594053
$236$		0			0
$237$	−11.9680	+	20.7292i	−0.777406	+	1.34651i
$238$		0			0
$239$			7.48040i			0.483867i	0.970293	+	0.241933i	$0.0777815\pi$
$239$			7.48040i			0.483867i	−0.970293	+	0.241933i	$0.922218\pi$
$240$		0			0
$241$	23.1012	−	13.3375i	1.48808	−	0.859142i	0.488170	−	0.872748i	$-0.337665\pi$
$241$	23.1012	−	13.3375i	1.48808	−	0.859142i	0.999907	+	0.0136064i	$0.00433118\pi$
$242$		0			0
$243$	1.57988	+	2.73644i	0.101350	+	0.175543i
$244$		0			0
$245$	6.50030	+	3.75295i	0.415289	+	0.239767i
$246$		0			0
$247$	−1.80611	−	0.115492i	−0.114920	−	0.00734856i
$248$		0			0
$249$	16.0815	+	9.28464i	1.01912	+	0.588390i
$250$		0			0
$251$	−6.46176	−	11.1921i	−0.407863	−	0.706439i	0.586787	−	0.809741i	$-0.300392\pi$
$251$	−6.46176	−	11.1921i	−0.407863	−	0.706439i	−0.994650	+	0.103302i	$0.967059\pi$
$252$		0			0
$253$	2.93720	−	1.69579i	0.184660	−	0.106613i
$254$		0			0
$255$			11.6629i			0.730358i
$256$		0			0
$257$	6.34568	−	10.9910i	0.395833	−	0.685602i	−0.597374	−	0.801963i	$-0.703789\pi$
$257$	6.34568	−	10.9910i	0.395833	−	0.685602i	0.993207	+	0.116360i	$0.0371227\pi$
$258$		0			0
$259$	−0.587901			−0.0365304
$260$		0			0
$261$	2.18345			0.135152
$262$		0			0
$263$	8.75665	−	15.1670i	0.539958	−	0.935235i	−0.458947	−	0.888464i	$-0.651773\pi$
$263$	8.75665	−	15.1670i	0.539958	−	0.935235i	0.998906	−	0.0467719i	$-0.0148934\pi$
$264$		0			0
$265$		−	11.5717i		−	0.710843i
$266$		0			0
$267$	4.77430	−	2.75644i	0.292182	−	0.168692i
$268$		0			0
$269$	7.63104	+	13.2174i	0.465273	+	0.805876i	0.999214	−	0.0396455i	$-0.0126229\pi$
$269$	7.63104	+	13.2174i	0.465273	+	0.805876i	−0.533941	+	0.845522i	$0.679290\pi$
$270$		0			0
$271$	17.4718	+	10.0873i	1.06133	+	0.612761i	0.925801	−	0.378012i	$-0.123392\pi$
$271$	17.4718	+	10.0873i	1.06133	+	0.612761i	0.135533	+	0.990773i	$0.456725\pi$
$272$		0			0
$273$	−1.64260	+	2.46681i	−0.0994145	+	0.149298i
$274$		0			0
$275$	−3.27359	−	1.89001i	−0.197405	−	0.113972i
$276$		0			0
$277$	−10.5255	−	18.2308i	−0.632419	−	1.09538i	−0.987056	−	0.160377i	$-0.948729\pi$
$277$	−10.5255	−	18.2308i	−0.632419	−	1.09538i	0.354637	−	0.935004i	$-0.384604\pi$
$278$		0			0
$279$	−0.147944	+	0.0854154i	−0.00885716	+	0.00511369i
$280$		0			0
$281$			18.5941i			1.10923i	0.832106	+	0.554616i	$0.187135\pi$
$281$			18.5941i			1.10923i	−0.832106	+	0.554616i	$0.812865\pi$
$282$		0			0
$283$	3.80071	−	6.58301i	0.225928	−	0.391320i	−0.730669	−	0.682732i	$-0.760792\pi$
$283$	3.80071	−	6.58301i	0.225928	−	0.391320i	0.956598	+	0.291412i	$0.0941251\pi$
$284$		0			0
$285$	−1.00794			−0.0597049
$286$		0			0
$287$	0.878103			0.0518328
$288$		0			0
$289$	−8.36677	+	14.4917i	−0.492163	+	0.852452i
$290$		0			0
$291$			22.7600i			1.33422i
$292$		0			0
$293$	15.1720	−	8.75958i	0.886360	−	0.511740i	0.0136096	−	0.999907i	$-0.495668\pi$
$293$	15.1720	−	8.75958i	0.886360	−	0.511740i	0.872750	+	0.488167i	$0.162334\pi$
$294$		0			0
$295$	−4.26339	−	7.38440i	−0.248224	−	0.429936i
$296$		0			0
$297$	4.24284	+	2.44960i	0.246194	+	0.142140i
$298$		0			0
$299$	−10.9588	+	5.42599i	−0.633764	+	0.313793i
$300$		0			0
$301$	−0.869009	−	0.501723i	−0.0500889	−	0.0289188i
$302$		0			0
$303$	−4.50696	−	7.80629i	−0.258918	−	0.448460i
$304$		0			0
$305$	−0.243182	+	0.140401i	−0.0139246	+	0.00803936i
$306$		0			0
$307$		−	12.6549i		−	0.722255i	−0.932516	−	0.361128i	$-0.882392\pi$
$307$		−	12.6549i		−	0.722255i	0.932516	−	0.361128i	$-0.117608\pi$
$308$		0			0
$309$	−8.83234	+	15.2981i	−0.502454	+	0.870276i
$310$		0			0
$311$	−26.7775			−1.51841			−0.759206	−	0.650851i	$-0.774412\pi$
$311$	−26.7775			−1.51841			−0.759206	+	0.650851i	$0.774412\pi$
$312$		0			0
$313$	6.77215			0.382784			0.191392	−	0.981514i	$-0.438700\pi$
$313$	6.77215			0.382784			0.191392	+	0.981514i	$0.438700\pi$
$314$		0			0
$315$	−0.0762047	+	0.131990i	−0.00429365	+	0.00743682i
$316$		0			0
$317$			19.3041i			1.08423i	0.840306	+	0.542113i	$0.182375\pi$
$317$			19.3041i			1.08423i	−0.840306	+	0.542113i	$0.817625\pi$
$318$		0			0
$319$	6.19577	−	3.57713i	0.346897	−	0.200281i
$320$		0			0
$321$	4.07968	+	7.06621i	0.227705	+	0.394397i
$322$		0			0
$323$	−2.52476	−	1.45767i	−0.140481	−	0.0811069i
$324$		0			0
$325$	11.3442	+	7.55385i	0.629262	+	0.419012i
$326$		0			0
$327$	24.4736	+	14.1298i	1.35339	+	0.781382i
$328$		0			0
$329$	1.86385	+	3.22829i	0.102757	+	0.177981i
$330$		0			0
$331$	−12.4512	+	7.18870i	−0.684379	+	0.395127i	−0.801503	−	0.597991i	$-0.795966\pi$
$331$	−12.4512	+	7.18870i	−0.684379	+	0.395127i	0.117124	+	0.993117i	$0.462633\pi$
$332$		0			0
$333$			0.396848i			0.0217471i
$334$		0			0
$335$	1.28810	−	2.23106i	0.0703766	−	0.121896i
$336$		0			0
$337$	26.9872			1.47009			0.735043	−	0.678021i	$-0.237162\pi$
$337$	26.9872			1.47009			0.735043	+	0.678021i	$0.237162\pi$
$338$		0			0
$339$	10.3721			0.563334
$340$		0			0
$341$	−0.279871	+	0.484751i	−0.0151559	+	0.0262508i
$342$		0			0
$343$			6.23732i			0.336784i
$344$		0			0
$345$	−5.89804	+	3.40523i	−0.317540	+	0.183332i
$346$		0			0
$347$	−3.70245	−	6.41283i	−0.198758	−	0.344259i	0.749368	−	0.662154i	$-0.230357\pi$
$347$	−3.70245	−	6.41283i	−0.198758	−	0.344259i	−0.948126	+	0.317895i	$0.897024\pi$
$348$		0			0
$349$	−6.92673	−	3.99915i	−0.370779	−	0.214070i	0.303019	−	0.952984i	$-0.402005\pi$
$349$	−6.92673	−	3.99915i	−0.370779	−	0.214070i	−0.673799	+	0.738915i	$0.735339\pi$
$350$		0			0
$351$	−14.7030	−	9.79039i	−0.784786	−	0.522573i
$352$		0			0
$353$	−9.87497	−	5.70132i	−0.525592	−	0.303450i	0.213628	−	0.976915i	$-0.431472\pi$
$353$	−9.87497	−	5.70132i	−0.525592	−	0.303450i	−0.739219	+	0.673465i	$0.764805\pi$
$354$		0			0
$355$	9.09141	+	15.7468i	0.482522	+	0.835753i
$356$		0			0
$357$	−4.13445	+	2.38703i	−0.218819	+	0.126335i
$358$		0			0
$359$		−	9.31791i		−	0.491780i	−0.969298	−	0.245890i	$-0.920920\pi$
$359$		−	9.31791i		−	0.491780i	0.969298	−	0.245890i	$-0.0790803\pi$
$360$		0			0
$361$	−9.37402	+	16.2363i	−0.493370	+	0.854541i
$362$		0			0
$363$	−1.81802			−0.0954213
$364$		0			0
$365$	−10.3100			−0.539651
$366$		0			0
$367$	6.47481	−	11.2147i	0.337982	−	0.585402i	−0.646071	−	0.763277i	$-0.723589\pi$
$367$	6.47481	−	11.2147i	0.337982	−	0.585402i	0.984053	+	0.177875i	$0.0569223\pi$
$368$		0			0
$369$		−	0.592741i		−	0.0308569i
$370$		0			0
$371$	4.10213	−	2.36837i	0.212972	−	0.122959i
$372$		0			0
$373$	−2.78314	−	4.82054i	−0.144106	−	0.249598i	0.784933	−	0.619580i	$-0.212697\pi$
$373$	−2.78314	−	4.82054i	−0.144106	−	0.249598i	−0.929039	+	0.369982i	$0.879364\pi$
$374$		0			0
$375$	15.2687	+	8.81536i	0.788470	+	0.455223i
$376$		0			0
$377$	−23.1167	+	11.4457i	−1.19057	+	0.589482i
$378$		0			0
$379$	15.3437	+	8.85866i	0.788151	+	0.455039i	0.839311	−	0.543651i	$-0.182959\pi$
$379$	15.3437	+	8.85866i	0.788151	+	0.455039i	−0.0511605	+	0.998690i	$0.516292\pi$
$380$		0			0
$381$	−14.1572	−	24.5210i	−0.725296	−	1.25625i
$382$		0			0
$383$	1.30216	−	0.751803i	0.0665373	−	0.0384153i	−0.466362	−	0.884594i	$-0.654436\pi$
$383$	1.30216	−	0.751803i	0.0665373	−	0.0384153i	0.532900	+	0.846178i	$0.321102\pi$
$384$		0			0
$385$			0.499383i			0.0254509i
$386$		0			0
$387$	−0.338675	+	0.586603i	−0.0172158	+	0.0298187i
$388$		0			0
$389$	−10.4956			−0.532148			−0.266074	−	0.963953i	$-0.585727\pi$
$389$	−10.4956			−0.532148			−0.266074	+	0.963953i	$0.585727\pi$
$390$		0			0
$391$	−19.6985			−0.996197
$392$		0			0
$393$	−4.88445	+	8.46012i	−0.246388	+	0.426757i
$394$		0			0
$395$		−	14.5422i		−	0.731696i
$396$		0			0
$397$	−17.4730	+	10.0881i	−0.876946	+	0.506305i	−0.869650	−	0.493669i	$-0.835656\pi$
$397$	−17.4730	+	10.0881i	−0.876946	+	0.506305i	−0.00729545	+	0.999973i	$0.502322\pi$
$398$		0			0
$399$	−0.206293	−	0.357310i	−0.0103276	−	0.0178879i
$400$		0			0
$401$	18.2073	+	10.5120i	0.909228	+	0.524943i	0.880183	−	0.474635i	$-0.157420\pi$
$401$	18.2073	+	10.5120i	0.909228	+	0.524943i	0.0290456	+	0.999578i	$0.490753\pi$
$402$		0			0
$403$	1.11857	−	1.67984i	0.0557199	−	0.0836787i
$404$		0			0
$405$	−9.39564	−	5.42457i	−0.466873	−	0.269549i
$406$		0			0
$407$	0.650154	+	1.12610i	0.0322269	+	0.0558187i
$408$		0			0
$409$	−30.3686	+	17.5333i	−1.50163	+	0.866966i	−0.501630	+	0.865082i	$0.667266\pi$
$409$	−30.3686	+	17.5333i	−1.50163	+	0.866966i	−0.999998	+	0.00188367i	$0.999400\pi$
$410$		0			0
$411$			8.35500i			0.412122i
$412$		0			0
$413$	1.74517	−	3.02272i	0.0858740	−	0.148738i
$414$		0			0
$415$	−11.2816			−0.553794
$416$		0			0
$417$	25.5708			1.25221
$418$		0			0
$419$	0.460413	−	0.797458i	0.0224926	−	0.0389584i	−0.854560	−	0.519353i	$-0.826173\pi$
$419$	0.460413	−	0.797458i	0.0224926	−	0.0389584i	0.877053	+	0.480394i	$0.159506\pi$
$420$		0			0
$421$		−	19.9206i		−	0.970873i	−0.874272	−	0.485437i	$-0.838661\pi$
$421$		−	19.9206i		−	0.970873i	0.874272	−	0.485437i	$-0.161339\pi$
$422$		0			0
$423$	2.17917	−	1.25815i	0.105955	−	0.0611731i
$424$		0			0
$425$	10.9773	+	19.0132i	0.532477	+	0.922277i
$426$		0			0
$427$	−0.0995438	−	0.0574716i	−0.00481726	−	0.00278125i
$428$		0			0
$429$	6.54160	+	0.418304i	0.315832	+	0.0201959i
$430$		0			0
$431$	−14.9760	−	8.64640i	−0.721369	−	0.416483i	0.0938873	−	0.995583i	$-0.470071\pi$
$431$	−14.9760	−	8.64640i	−0.721369	−	0.416483i	−0.815256	+	0.579100i	$0.803404\pi$
$432$		0			0
$433$	−15.9617	−	27.6464i	−0.767070	−	1.32860i	−0.939145	−	0.343520i	$-0.888381\pi$
$433$	−15.9617	−	27.6464i	−0.767070	−	1.32860i	0.172076	−	0.985084i	$-0.444953\pi$
$434$		0			0
$435$	−12.4414	+	7.18306i	−0.596521	+	0.344401i
$436$		0			0
$437$		−	1.70239i		−	0.0814366i
$438$		0			0
$439$	−0.587970	+	1.01839i	−0.0280623	+	0.0486053i	−0.879715	−	0.475500i	$-0.842267\pi$
$439$	−0.587970	+	1.01839i	−0.0280623	+	0.0486053i	0.851653	+	0.524106i	$0.175600\pi$
$440$		0			0
$441$	2.07398			0.0987609
$442$		0			0
$443$	34.5281			1.64048			0.820240	−	0.572019i	$-0.193840\pi$
$443$	34.5281			1.64048			0.820240	+	0.572019i	$0.193840\pi$
$444$		0			0
$445$	−1.67466	+	2.90060i	−0.0793865	+	0.137501i
$446$		0			0
$447$		−	3.97882i		−	0.188192i
$448$		0			0
$449$	−7.49449	+	4.32695i	−0.353687	+	0.204201i	−0.666308	−	0.745677i	$-0.732126\pi$
$449$	−7.49449	+	4.32695i	−0.353687	+	0.204201i	0.312621	+	0.949878i	$0.398793\pi$
$450$		0			0
$451$	−0.971085	−	1.68197i	−0.0457266	−	0.0792008i
$452$		0			0
$453$	19.4216	+	11.2131i	0.912506	+	0.526835i
$454$		0			0
$455$	0.114902	−	1.79688i	0.00538668	−	0.0842391i
$456$		0			0
$457$	16.3051	+	9.41374i	0.762719	+	0.440356i	0.830271	−	0.557359i	$-0.188185\pi$
$457$	16.3051	+	9.41374i	0.762719	+	0.440356i	−0.0675518	+	0.997716i	$0.521519\pi$
$458$		0			0
$459$	−14.2274	−	24.6427i	−0.664080	−	1.15022i
$460$		0			0
$461$	32.5985	−	18.8208i	1.51827	−	0.876571i	0.518497	−	0.855080i	$-0.326492\pi$
$461$	32.5985	−	18.8208i	1.51827	−	0.876571i	0.999769	−	0.0214914i	$-0.00684145\pi$
$462$		0			0
$463$			1.28913i			0.0599108i	0.999551	+	0.0299554i	$0.00953653\pi$
$463$			1.28913i			0.0599108i	−0.999551	+	0.0299554i	$0.990463\pi$
$464$		0			0
$465$	0.561996	−	0.973405i	0.0260619	−	0.0451406i
$466$		0			0
$467$	−12.2089			−0.564963			−0.282481	−	0.959273i	$-0.591158\pi$
$467$	−12.2089			−0.564963			−0.282481	+	0.959273i	$0.591158\pi$
$468$		0			0
$469$	1.05454			0.0486941
$470$		0			0
$471$	4.66876	−	8.08654i	0.215125	−	0.372608i
$472$		0			0
$473$			2.21940i			0.102048i
$474$		0			0
$475$	−1.64317	+	0.948685i	−0.0753939	+	0.0435287i
$476$		0			0
$477$	−1.59871	−	2.76904i	−0.0731997	−	0.126786i
$478$		0			0
$479$	7.59431	+	4.38457i	0.346993	+	0.200336i	0.663360	−	0.748300i	$-0.269130\pi$
$479$	7.59431	+	4.38457i	0.346993	+	0.200336i	−0.316367	+	0.948637i	$0.602463\pi$
$480$		0			0
$481$	−2.08028	−	4.20153i	−0.0948528	−	0.191573i
$482$		0			0
$483$	−2.41429	−	1.39389i	−0.109854	−	0.0634243i
$484$		0			0
$485$	−6.91385	−	11.9751i	−0.313942	−	0.543763i
$486$		0			0
$487$	35.2154	−	20.3316i	1.59576	−	0.921313i	0.603469	−	0.797386i	$-0.293785\pi$
$487$	35.2154	−	20.3316i	1.59576	−	0.921313i	0.992291	−	0.123927i	$-0.0395488\pi$
$488$		0			0
$489$			25.2866i			1.14350i
$490$		0			0
$491$	7.30364	−	12.6503i	0.329609	−	0.570899i	−0.652826	−	0.757508i	$-0.726417\pi$
$491$	7.30364	−	12.6503i	0.329609	−	0.570899i	0.982434	+	0.186609i	$0.0597499\pi$
$492$		0			0
$493$	−41.5524			−1.87142
$494$		0			0
$495$	0.337096			0.0151513
$496$		0			0
$497$	−3.72146	+	6.44576i	−0.166930	+	0.289132i
$498$		0			0
$499$			18.2453i			0.816770i	0.912810	+	0.408385i	$0.133908\pi$
$499$			18.2453i			0.816770i	−0.912810	+	0.408385i	$0.866092\pi$
$500$		0			0
$501$	12.8415	−	7.41407i	0.573718	−	0.331236i
$502$		0			0
$503$	−12.9069	−	22.3555i	−0.575492	−	0.996781i	−0.995988	−	0.0894867i	$-0.971477\pi$
$503$	−12.9069	−	22.3555i	−0.575492	−	0.996781i	0.420496	−	0.907294i	$-0.361856\pi$
$504$		0			0
$505$	4.74266	+	2.73818i	0.211046	+	0.121847i
$506$		0			0
$507$	−23.4418	−	3.01028i	−1.04109	−	0.133691i
$508$		0			0
$509$	−30.9668	−	17.8787i	−1.37258	−	0.792459i	−0.381327	−	0.924440i	$-0.624533\pi$
$509$	−30.9668	−	17.8787i	−1.37258	−	0.792459i	−0.991252	+	0.131981i	$0.957866\pi$
$510$		0			0
$511$	−2.11014	−	3.65487i	−0.0933471	−	0.161682i
$512$		0			0
$513$	2.12968	−	1.22957i	0.0940277	−	0.0542869i
$514$		0			0
$515$		−	10.7321i		−	0.472911i
$516$		0			0
$517$	4.12243	−	7.14026i	0.181304	−	0.314028i
$518$		0			0
$519$	34.2377			1.50287
$520$		0			0
$521$	−22.4327			−0.982794			−0.491397	−	0.870936i	$-0.663513\pi$
$521$	−22.4327			−0.982794			−0.491397	+	0.870936i	$0.663513\pi$
$522$		0			0
$523$	16.5960	−	28.7452i	0.725694	−	1.25694i	−0.232994	−	0.972478i	$-0.574852\pi$
$523$	16.5960	−	28.7452i	0.725694	−	1.25694i	0.958688	−	0.284461i	$-0.0918145\pi$
$524$		0			0
$525$			3.10707i			0.135604i
$526$		0			0
$527$	2.81546	−	1.62551i	0.122644	−	0.0708083i
$528$		0			0
$529$	5.74858	+	9.95684i	0.249938	+	0.432906i
$530$		0			0
$531$	−2.04041	−	1.17803i	−0.0885462	−	0.0511222i
$532$		0			0
$533$	3.10716	+	6.27550i	0.134586	+	0.271822i
$534$		0			0
$535$	−4.29303	−	2.47858i	−0.185604	−	0.107159i
$536$		0			0
$537$	−15.1221	−	26.1922i	−0.652565	−	1.13028i
$538$		0			0
$539$	5.88515	−	3.39779i	0.253491	−	0.146353i
$540$		0			0
$541$		−	26.0058i		−	1.11808i	−0.829142	−	0.559038i	$-0.811171\pi$
$541$		−	26.0058i		−	1.11808i	0.829142	−	0.559038i	$-0.188829\pi$
$542$		0			0
$543$	17.2070	−	29.8034i	0.738423	−	1.27899i
$544$		0			0
$545$	−17.1690			−0.735439
$546$		0			0
$547$	17.3308			0.741010			0.370505	−	0.928831i	$-0.379185\pi$
$547$	17.3308			0.741010			0.370505	+	0.928831i	$0.379185\pi$
$548$		0			0
$549$	−0.0387948	+	0.0671945i	−0.00165572	+	0.00286779i
$550$		0			0
$551$		−	3.59106i		−	0.152984i
$552$		0			0
$553$	5.15516	−	2.97633i	0.219220	−	0.126566i
$554$		0			0
$555$	−1.30554	−	2.26127i	−0.0554172	−	0.0959854i
$556$		0			0
$557$	24.2884	+	14.0229i	1.02913	+	0.594170i	0.916736	−	0.399493i	$-0.130814\pi$
$557$	24.2884	+	14.0229i	1.02913	+	0.594170i	0.112397	+	0.993663i	$0.464147\pi$
$558$		0			0
$559$	0.510656	−	7.98585i	0.0215985	−	0.337766i
$560$		0			0
$561$	9.14450	+	5.27958i	0.386081	+	0.222904i
$562$		0			0
$563$	−5.31820	−	9.21140i	−0.224136	−	0.388214i	0.731924	−	0.681386i	$-0.238623\pi$
$563$	−5.31820	−	9.21140i	−0.224136	−	0.388214i	−0.956060	+	0.293172i	$0.905289\pi$
$564$		0			0
$565$	−5.45725	+	3.15075i	−0.229588	+	0.132553i
$566$		0			0
$567$		−	4.44097i		−	0.186503i
$568$		0			0
$569$	9.80003	−	16.9741i	0.410838	−	0.711593i	−0.584143	−	0.811651i	$-0.698569\pi$
$569$	9.80003	−	16.9741i	0.410838	−	0.711593i	0.994982	+	0.100057i	$0.0319027\pi$
$570$		0			0
$571$	1.79410			0.0750809			0.0375404	−	0.999295i	$-0.488048\pi$
$571$	1.79410			0.0750809			0.0375404	+	0.999295i	$0.488048\pi$
$572$		0			0
$573$	−16.8563			−0.704184
$574$		0			0
$575$	−6.41013	+	11.1027i	−0.267321	+	0.463013i
$576$		0			0
$577$		−	30.2839i		−	1.26074i	−0.776296	−	0.630368i	$-0.782904\pi$
$577$		−	30.2839i		−	1.26074i	0.776296	−	0.630368i	$-0.217096\pi$
$578$		0			0
$579$	−5.99431	+	3.46082i	−0.249115	+	0.143827i
$580$		0			0
$581$	−2.30900	−	3.99931i	−0.0957936	−	0.165919i
$582$		0			0
$583$	−9.07301	−	5.23831i	−0.375766	−	0.216948i
$584$		0			0
$585$	−1.21294	−	0.0775616i	−0.0501489	−	0.00320678i
$586$		0			0
$587$	20.7316	+	11.9694i	0.855685	+	0.494030i	0.862565	−	0.505946i	$-0.168857\pi$
$587$	20.7316	+	11.9694i	0.855685	+	0.494030i	−0.00687970	+	0.999976i	$0.502190\pi$
$588$		0			0
$589$	0.140481	+	0.243320i	0.00578840	+	0.0100258i
$590$		0			0
$591$	7.49262	−	4.32586i	0.308205	−	0.177942i
$592$		0			0
$593$			4.46741i			0.183455i	0.995784	+	0.0917273i	$0.0292388\pi$
$593$			4.46741i			0.183455i	−0.995784	+	0.0917273i	$0.970761\pi$
$594$		0			0
$595$	1.45022	−	2.51186i	0.0594534	−	0.102976i
$596$		0			0
$597$	−5.76509			−0.235949
$598$		0			0
$599$	−0.583453			−0.0238392			−0.0119196	−	0.999929i	$-0.503794\pi$
$599$	−0.583453			−0.0238392			−0.0119196	+	0.999929i	$0.503794\pi$
$600$		0			0
$601$	12.0663	−	20.8995i	0.492196	−	0.852509i	−0.507764	−	0.861497i	$-0.669528\pi$
$601$	12.0663	−	20.8995i	0.492196	−	0.852509i	0.999960	+	0.00898784i	$0.00286096\pi$
$602$		0			0
$603$		−	0.711840i		−	0.0289883i
$604$		0			0
$605$	0.956548	−	0.552263i	0.0388892	−	0.0224527i
$606$		0			0
$607$	4.48015	+	7.75985i	0.181844	+	0.314963i	0.942508	−	0.334182i	$-0.108460\pi$
$607$	4.48015	+	7.75985i	0.181844	+	0.314963i	−0.760665	+	0.649145i	$0.775127\pi$
$608$		0			0
$609$	−5.09275	−	2.94030i	−0.206369	−	0.119147i
$610$		0			0
$611$	−16.4762	+	24.7436i	−0.666557	+	1.00102i
$612$		0			0
$613$	−11.8327	−	6.83161i	−0.477918	−	0.275926i	0.241630	−	0.970368i	$-0.422318\pi$
$613$	−11.8327	−	6.83161i	−0.477918	−	0.275926i	−0.719549	+	0.694442i	$0.755651\pi$
$614$		0			0
$615$	1.94999	+	3.37748i	0.0786311	+	0.136193i
$616$		0			0
$617$	11.0074	−	6.35513i	0.443141	−	0.255848i	−0.261788	−	0.965125i	$-0.584312\pi$
$617$	11.0074	−	6.35513i	0.443141	−	0.255848i	0.704929	+	0.709278i	$0.250979\pi$
$618$		0			0
$619$			42.4524i			1.70631i	0.521660	+	0.853154i	$0.325313\pi$
$619$			42.4524i			1.70631i	−0.521660	+	0.853154i	$0.674687\pi$
$620$		0			0
$621$	8.30803	−	14.3899i	0.333390	−	0.577448i
$622$		0			0
$623$	−1.37100			−0.0549281
$624$		0			0
$625$	8.18867			0.327547
$626$		0			0
$627$	−0.456275	+	0.790291i	−0.0182219	+	0.0315612i
$628$		0			0
$629$		−	7.55227i		−	0.301129i
$630$		0			0
$631$	28.7944	−	16.6245i	1.14629	−	0.661809i	0.198307	−	0.980140i	$-0.436456\pi$
$631$	28.7944	−	16.6245i	1.14629	−	0.661809i	0.947980	+	0.318331i	$0.103122\pi$
$632$		0			0
$633$	13.7480	+	23.8122i	0.546432	+	0.946448i
$634$		0			0
$635$	14.8976	+	8.60112i	0.591192	+	0.341325i
$636$		0			0
$637$	−21.9577	+	10.8718i	−0.869997	+	0.430758i
$638$		0			0
$639$	4.35105	+	2.51208i	0.172125	+	0.0993763i
$640$		0			0
$641$	13.6373	+	23.6205i	0.538640	+	0.932953i	0.998978	+	0.0452085i	$0.0143952\pi$
$641$	13.6373	+	23.6205i	0.538640	+	0.932953i	−0.460337	+	0.887744i	$0.652271\pi$
$642$		0			0
$643$	9.44596	−	5.45363i	0.372512	−	0.215070i	−0.302043	−	0.953294i	$-0.597669\pi$
$643$	9.44596	−	5.45363i	0.372512	−	0.215070i	0.674555	+	0.738224i	$0.264335\pi$
$644$		0			0
$645$		−	4.45667i		−	0.175481i
$646$		0			0
$647$	7.92762	−	13.7310i	0.311667	−	0.539823i	−0.667057	−	0.745007i	$-0.732446\pi$
$647$	7.92762	−	13.7310i	0.311667	−	0.539823i	0.978723	+	0.205184i	$0.0657794\pi$
$648$		0			0
$649$	−7.71985			−0.303030
$650$		0			0
$651$	0.460092			0.0180324
$652$		0			0
$653$	−9.08573	+	15.7369i	−0.355552	+	0.615834i	−0.987212	−	0.159411i	$-0.949040\pi$
$653$	−9.08573	+	15.7369i	−0.355552	+	0.615834i	0.631660	+	0.775245i	$0.282374\pi$
$654$		0			0
$655$		−	5.93504i		−	0.231901i
$656$		0			0
$657$	−2.46713	+	1.42440i	−0.0962518	+	0.0555710i
$658$		0			0
$659$	9.98576	+	17.2958i	0.388990	+	0.673750i	0.992314	−	0.123746i	$-0.0394907\pi$
$659$	9.98576	+	17.2958i	0.388990	+	0.673750i	−0.603324	+	0.797496i	$0.706157\pi$
$660$		0			0
$661$	−28.3617	−	16.3746i	−1.10314	−	0.636898i	−0.166096	−	0.986110i	$-0.553116\pi$
$661$	−28.3617	−	16.3746i	−1.10314	−	0.636898i	−0.937044	+	0.349211i	$0.886450\pi$
$662$		0			0
$663$	−31.6890	−	21.1010i	−1.23070	−	0.819497i
$664$		0			0
$665$	0.217081	+	0.125332i	0.00841806	+	0.00486017i
$666$		0			0
$667$	−12.1321	−	21.0135i	−0.469758	−	0.813645i
$668$		0			0
$669$	−6.90973	+	3.98933i	−0.267146	+	0.154237i
$670$		0			0
$671$			0.254229i			0.00981441i
$672$		0			0
$673$	−9.84322	+	17.0490i	−0.379428	+	0.657189i	−0.990979	−	0.134016i	$-0.957213\pi$
$673$	−9.84322	+	17.0490i	−0.379428	+	0.657189i	0.611551	+	0.791205i	$0.290546\pi$
$674$		0			0
$675$	−18.5191			−0.712801
$676$		0			0
$677$	−5.20446			−0.200024			−0.100012	−	0.994986i	$-0.531888\pi$
$677$	−5.20446			−0.200024			−0.100012	+	0.994986i	$0.531888\pi$
$678$		0			0
$679$	2.83010	−	4.90188i	0.108609	−	0.188117i
$680$		0			0
$681$		−	49.3505i		−	1.89112i
$682$		0			0
$683$	35.0806	−	20.2538i	1.34232	−	0.774990i	0.355174	−	0.934800i	$-0.384422\pi$
$683$	35.0806	−	20.2538i	1.34232	−	0.774990i	0.987148	+	0.159810i	$0.0510882\pi$
$684$		0			0
$685$	−2.53802	−	4.39597i	−0.0969726	−	0.167961i
$686$		0			0
$687$	−28.4890	−	16.4481i	−1.08692	−	0.627535i
$688$		0			0
$689$	31.4413	+	20.9361i	1.19782	+	0.797601i
$690$		0			0
$691$	13.7630	+	7.94607i	0.523569	+	0.302283i	0.738394	−	0.674370i	$-0.235585\pi$
$691$	13.7630	+	7.94607i	0.523569	+	0.302283i	−0.214825	+	0.976653i	$0.568918\pi$
$692$		0			0
$693$	0.0689931	+	0.119500i	0.00262083	+	0.00453941i
$694$		0			0
$695$	−13.4540	+	7.76770i	−0.510341	+	0.294646i
$696$		0			0
$697$			11.2802i			0.427269i
$698$		0			0
$699$	5.93367	−	10.2774i	0.224432	−	0.388728i
$700$		0			0
$701$	−27.1241			−1.02446			−0.512232	−	0.858847i	$-0.671181\pi$
$701$	−27.1241			−1.02446			−0.512232	+	0.858847i	$0.671181\pi$
$702$		0			0
$703$	0.652686			0.0246165
$704$		0			0
$705$	−8.27805	+	14.3380i	−0.311769	+	0.540000i
$706$		0			0
$707$			2.24168i			0.0843071i
$708$		0			0
$709$	−8.27247	+	4.77612i	−0.310679	+	0.179371i	−0.647230	−	0.762294i	$-0.724073\pi$
$709$	−8.27247	+	4.77612i	−0.310679	+	0.179371i	0.336551	+	0.941665i	$0.390740\pi$
$710$		0			0
$711$	−2.00910	−	3.47986i	−0.0753470	−	0.130505i
$712$		0			0
$713$	1.64407	+	0.949207i	0.0615711	+	0.0355481i
$714$		0			0
$715$	−3.56892	+	1.76706i	−0.133470	+	0.0660845i
$716$		0			0
$717$	−11.7775	−	6.79975i	−0.439839	−	0.253941i
$718$		0			0
$719$	6.88909	+	11.9322i	0.256920	+	0.444998i	0.965415	−	0.260718i	$-0.0839591\pi$
$719$	6.88909	+	11.9322i	0.256920	+	0.444998i	−0.708496	+	0.705715i	$0.750626\pi$
$720$		0			0
$721$	3.80449	−	2.19652i	0.141686	−	0.0818027i
$722$		0			0
$723$			48.4956i			1.80357i
$724$		0			0
$725$	−13.5216	+	23.4202i	−0.502181	+	0.869803i
$726$		0			0
$727$	−14.2891			−0.529952			−0.264976	−	0.964255i	$-0.585364\pi$
$727$	−14.2891			−0.529952			−0.264976	+	0.964255i	$0.585364\pi$
$728$		0			0
$729$	23.7228			0.878622
$730$		0			0
$731$	6.44520	−	11.1634i	0.238384	−	0.412894i
$732$		0			0
$733$			44.4628i			1.64227i	0.570734	+	0.821135i	$0.306659\pi$
$733$			44.4628i			1.64227i	−0.570734	+	0.821135i	$0.693341\pi$
$734$		0			0
$735$	−11.8177	+	6.82294i	−0.435901	+	0.251668i
$736$		0			0
$737$	−1.16620	−	2.01992i	−0.0429577	−	0.0744049i
$738$		0			0
$739$	35.2080	+	20.3273i	1.29515	+	0.747753i	0.979562	−	0.201144i	$-0.0644660\pi$
$739$	35.2080	+	20.3273i	1.29515	+	0.747753i	0.315585	+	0.948897i	$0.397799\pi$
$740$		0			0
$741$	1.82361	−	2.73864i	0.0669918	−	0.100607i
$742$		0			0
$743$	−6.45422	−	3.72635i	−0.236782	−	0.136706i	0.376915	−	0.926248i	$-0.376985\pi$
$743$	−6.45422	−	3.72635i	−0.236782	−	0.136706i	−0.613697	+	0.789542i	$0.710318\pi$
$744$		0			0
$745$	1.20865	+	2.09345i	0.0442816	+	0.0766981i
$746$		0			0
$747$	−2.69963	+	1.55863i	−0.0987744	+	0.0570274i
$748$		0			0
$749$		−	2.02916i		−	0.0741437i
$750$		0			0
$751$	−8.20197	+	14.2062i	−0.299294	+	0.518392i	−0.975975	−	0.217884i	$-0.930084\pi$
$751$	−8.20197	+	14.2062i	−0.299294	+	0.518392i	0.676681	+	0.736277i	$0.263418\pi$
$752$		0			0
$753$	23.4952			0.856213
$754$		0			0
$755$	−13.6248			−0.495859
$756$		0			0
$757$	−24.1592	+	41.8450i	−0.878082	+	1.52088i	−0.0246382	+	0.999696i	$0.507843\pi$
$757$	−24.1592	+	41.8450i	−0.878082	+	1.52088i	−0.853443	+	0.521186i	$0.825490\pi$
$758$		0			0
$759$			6.16596i			0.223810i
$760$		0			0
$761$	−9.29567	+	5.36686i	−0.336968	+	0.194548i	−0.658930	−	0.752204i	$-0.728991\pi$
$761$	−9.29567	+	5.36686i	−0.336968	+	0.194548i	0.321963	+	0.946752i	$0.395657\pi$
$762$		0			0
$763$	−3.51396	−	6.08636i	−0.127214	−	0.220341i
$764$		0			0
$765$	−1.69557	−	0.978937i	−0.0613034	−	0.0353935i
$766$		0			0
$767$	27.7776	+	1.77624i	1.00299	+	0.0641363i
$768$		0			0
$769$	−41.1258	−	23.7440i	−1.48304	−	0.856231i	−0.483222	−	0.875498i	$-0.660533\pi$
$769$	−41.1258	−	23.7440i	−1.48304	−	0.856231i	−0.999814	+	0.0192668i	$0.993867\pi$
$770$		0			0
$771$	11.5366	+	19.9819i	0.415480	+	0.719632i
$772$		0			0
$773$	32.3230	−	18.6617i	1.16258	−	0.671214i	0.210656	−	0.977560i	$-0.432440\pi$
$773$	32.3230	−	18.6617i	1.16258	−	0.671214i	0.951920	+	0.306346i	$0.0991065\pi$
$774$		0			0
$775$		−	2.11584i		−	0.0760032i
$776$		0			0
$777$	0.534408	−	0.925622i	0.0191718	−	0.0332065i
$778$		0			0
$779$	−0.974866			−0.0349282
$780$		0			0
$781$	16.4621			0.589060
$782$		0			0
$783$	17.5251	−	30.3544i	0.626296	−	1.08478i
$784$		0			0
$785$			5.67296i			0.202476i
$786$		0			0
$787$	−4.81134	+	2.77783i	−0.171506	+	0.0990188i	−0.583296	−	0.812260i	$-0.698237\pi$
$787$	−4.81134	+	2.77783i	−0.171506	+	0.0990188i	0.411790	+	0.911279i	$0.364904\pi$
$788$		0			0
$789$	15.9198	+	27.5739i	0.566759	+	0.981655i
$790$		0			0
$791$	−2.23386	−	1.28972i	−0.0794269	−	0.0458572i
$792$		0			0
$793$	0.0584950	−	0.914768i	0.00207722	−	0.0324844i
$794$		0			0
$795$	18.2191	+	10.5188i	0.646164	+	0.373063i
$796$		0			0
$797$	−3.93936	−	6.82317i	−0.139539	−	0.241689i	0.787783	−	0.615953i	$-0.211229\pi$
$797$	−3.93936	−	6.82317i	−0.139539	−	0.241689i	−0.927322	+	0.374264i	$0.877895\pi$
$798$		0			0
$799$	−41.4710	+	23.9433i	−1.46714	+	0.847054i
$800$		0			0
$801$			0.925462i			0.0326996i
$802$		0			0
$803$	−4.66717	+	8.08377i	−0.164701	+	0.285270i
$804$		0			0
$805$	1.69370			0.0596951
$806$		0			0
$807$	−27.7468			−0.976733
$808$		0			0
$809$	−13.5810	+	23.5230i	−0.477482	+	0.827023i	−0.999667	−	0.0258090i	$-0.991784\pi$
$809$	−13.5810	+	23.5230i	−0.477482	+	0.827023i	0.522185	+	0.852832i	$0.325117\pi$
$810$		0			0
$811$			32.3156i			1.13475i	0.823458	+	0.567377i	$0.192042\pi$
$811$			32.3156i			1.13475i	−0.823458	+	0.567377i	$0.807958\pi$
$812$		0			0
$813$	−31.7640	+	18.3390i	−1.11401	+	0.643175i
$814$		0			0
$815$	−7.68134	−	13.3045i	−0.269066	−	0.466036i
$816$		0			0
$817$	0.964771	+	0.557011i	0.0337531	+	0.0194873i
$818$		0			0
$819$	−0.220756	−	0.445858i	−0.00771383	−	0.0155795i
$820$		0			0
$821$	6.02793	+	3.48023i	0.210376	+	0.121461i	0.601486	−	0.798883i	$-0.294575\pi$
$821$	6.02793	+	3.48023i	0.210376	+	0.121461i	−0.391110	+	0.920344i	$0.627909\pi$
$822$		0			0
$823$	27.8576	+	48.2507i	0.971054	+	1.68191i	0.692386	+	0.721527i	$0.256560\pi$
$823$	27.8576	+	48.2507i	0.971054	+	1.68191i	0.278668	+	0.960387i	$0.410107\pi$
$824$		0			0
$825$	5.95146	−	3.43608i	0.207203	−	0.119629i
$826$		0			0
$827$		−	29.2473i		−	1.01703i	−0.861054	−	0.508514i	$-0.830195\pi$
$827$		−	29.2473i		−	1.01703i	0.861054	−	0.508514i	$-0.169805\pi$
$828$		0			0
$829$	−16.2400	+	28.1285i	−0.564038	+	0.976943i	0.433100	+	0.901346i	$0.357420\pi$
$829$	−16.2400	+	28.1285i	−0.564038	+	0.976943i	−0.997138	+	0.0755972i	$0.975914\pi$
$830$		0			0
$831$	38.2713			1.32762
$832$		0			0
$833$	−39.4691			−1.36752
$834$		0			0
$835$	−4.50437	+	7.80180i	−0.155880	+	0.269992i
$836$		0			0
$837$			2.74230i			0.0947876i
$838$		0			0
$839$	−0.420429	+	0.242735i	−0.0145148	+	0.00838014i	−0.507240	−	0.861805i	$-0.669334\pi$
$839$	−0.420429	+	0.242735i	−0.0145148	+	0.00838014i	0.492725	+	0.870185i	$0.336001\pi$
$840$		0			0
$841$	−11.0917	−	19.2114i	−0.382474	−	0.662464i
$842$		0			0
$843$	−29.2755	−	16.9022i	−1.00830	−	0.582144i
$844$		0			0
$845$	13.2483	−	5.53709i	0.455755	−	0.190482i
$846$		0			0
$847$	0.391551	+	0.226062i	0.0134539	+	0.00776759i
$848$		0			0
$849$	6.90976	+	11.9680i	0.237142	+	0.410742i
$850$		0			0
$851$	3.81926	−	2.20505i	0.130923	−	0.0755882i
$852$		0			0
$853$		−	39.2018i		−	1.34224i	−0.741347	−	0.671122i	$-0.765813\pi$
$853$		−	39.2018i		−	1.34224i	0.741347	−	0.671122i	$-0.234187\pi$
$854$		0			0
$855$	0.0846022	−	0.146535i	0.00289333	−	0.00501140i
$856$		0			0
$857$	45.4444			1.55235			0.776176	−	0.630516i	$-0.217157\pi$
$857$	45.4444			1.55235			0.776176	+	0.630516i	$0.217157\pi$
$858$		0			0
$859$	2.10809			0.0719272			0.0359636	−	0.999353i	$-0.488550\pi$
$859$	2.10809			0.0719272			0.0359636	+	0.999353i	$0.488550\pi$
$860$		0			0
$861$	−0.798204	+	1.38253i	−0.0272027	+	0.0471165i
$862$		0			0
$863$			43.3026i			1.47404i	0.675872	+	0.737019i	$0.263767\pi$
$863$			43.3026i			1.47404i	−0.675872	+	0.737019i	$0.736233\pi$
$864$		0			0
$865$	−18.0141	+	10.4004i	−0.612498	+	0.353626i
$866$		0			0
$867$	−15.2110	−	26.3462i	−0.516591	−	0.894762i
$868$		0			0
$869$	−11.4021	−	6.58299i	−0.386789	−	0.223313i
$870$		0			0
$871$	3.73148	+	7.53642i	0.126436	+	0.255362i
$872$		0			0
$873$	−3.30889	−	1.91039i	−0.111989	−	0.0646569i
$874$		0			0
$875$	−2.19230	−	3.79717i	−0.0741132	−	0.128368i
$876$		0			0
$877$	−6.09071	+	3.51647i	−0.205669	+	0.118743i	−0.599297	−	0.800527i	$-0.704553\pi$
$877$	−6.09071	+	3.51647i	−0.205669	+	0.118743i	0.393628	+	0.919270i	$0.371220\pi$
$878$		0			0
$879$			31.8502i			1.07428i
$880$		0			0
$881$	12.8980	−	22.3401i	0.434546	−	0.752656i	−0.562712	−	0.826653i	$-0.690242\pi$
$881$	12.8980	−	22.3401i	0.434546	−	0.752656i	0.997258	+	0.0739968i	$0.0235755\pi$
$882$		0			0
$883$	−17.9038			−0.602510			−0.301255	−	0.953544i	$-0.597406\pi$
$883$	−17.9038			−0.602510			−0.301255	+	0.953544i	$0.597406\pi$
$884$		0			0
$885$	15.5018			0.521089
$886$		0			0
$887$	18.9136	−	32.7593i	0.635056	−	1.09995i	−0.351448	−	0.936207i	$-0.614311\pi$
$887$	18.9136	−	32.7593i	0.635056	−	1.09995i	0.986503	−	0.163741i	$-0.0523561\pi$
$888$		0			0
$889$			7.04153i			0.236165i
$890$		0			0
$891$	−8.50648	+	4.91122i	−0.284978	+	0.164532i
$892$		0			0
$893$	−2.06924	−	3.58403i	−0.0692445	−	0.119935i
$894$		0			0
$895$	15.9129	+	9.18731i	0.531909	+	0.307098i
$896$		0			0
$897$	1.41871	−	22.1864i	0.0473694	−	0.740782i
$898$		0			0
$899$	3.46804	+	2.00227i	0.115666	+	0.0667795i
$900$		0			0
$901$	30.4244	+	52.6966i	1.01358	+	1.75558i
$902$		0			0
$903$	1.57988	−	0.912142i	0.0525750	−	0.0303542i
$904$		0			0
$905$			20.9080i			0.695006i
$906$		0			0
$907$	−19.5191	+	33.8081i	−0.648121	+	1.12258i	0.335450	+	0.942058i	$0.391112\pi$
$907$	−19.5191	+	33.8081i	−0.648121	+	1.12258i	−0.983571	+	0.180520i	$0.942222\pi$
$908$		0			0
$909$	1.51319			0.0501893
$910$		0			0
$911$	43.1679			1.43022			0.715108	−	0.699014i	$-0.246377\pi$
$911$	43.1679			1.43022			0.715108	+	0.699014i	$0.246377\pi$
$912$		0			0
$913$	−5.10701	+	8.84559i	−0.169017	+	0.292746i
$914$		0			0
$915$		−	0.510505i		−	0.0168768i
$916$		0			0
$917$	2.10395	−	1.21472i	0.0694786	−	0.0401135i
$918$		0			0
$919$	17.0623	+	29.5527i	0.562832	+	0.974853i	0.997248	+	0.0741410i	$0.0236215\pi$
$919$	17.0623	+	29.5527i	0.562832	+	0.974853i	−0.434416	+	0.900712i	$0.643045\pi$
$920$		0			0
$921$	19.9246	+	11.5035i	0.656537	+	0.379052i
$922$		0			0
$923$	−59.2340	−	3.78772i	−1.94971	−	0.124674i
$924$		0			0
$925$	−4.25668	−	2.45760i	−0.139959	−	0.0808053i
$926$		0			0
$927$	−1.48271	−	2.56812i	−0.0486985	−	0.0843482i
$928$		0			0
$929$	40.1150	−	23.1604i	1.31613	−	0.759867i	0.333026	−	0.942918i	$-0.391930\pi$
$929$	40.1150	−	23.1604i	1.31613	−	0.759867i	0.983104	+	0.183050i	$0.0585971\pi$
$930$		0			0
$931$		−	3.41102i		−	0.111792i
$932$		0			0
$933$	24.3410	−	42.1598i	0.796888	−	1.38025i
$934$		0			0
$935$	−6.41515			−0.209798
$936$		0			0
$937$	−6.45390			−0.210840			−0.105420	−	0.994428i	$-0.533619\pi$
$937$	−6.45390			−0.210840			−0.105420	+	0.994428i	$0.533619\pi$
$938$		0			0
$939$	−6.15595	+	10.6624i	−0.200892	+	0.347955i
$940$		0			0
$941$		−	19.0275i		−	0.620278i	−0.950691	−	0.310139i	$-0.899624\pi$
$941$		−	19.0275i		−	0.620278i	0.950691	−	0.310139i	$-0.100376\pi$
$942$		0			0
$943$	−5.70453	+	3.29351i	−0.185765	+	0.107252i
$944$		0			0
$945$	1.22329	+	2.11880i	0.0397937	+	0.0689247i
$946$		0			0
$947$	46.3190	+	26.7423i	1.50517	+	0.869007i	0.999982	+	0.00599521i	$0.00190835\pi$
$947$	46.3190	+	26.7423i	1.50517	+	0.869007i	0.505183	+	0.863012i	$0.331425\pi$
$948$		0			0
$949$	18.6534	−	28.0132i	0.605514	−	0.909346i
$950$		0			0
$951$	−30.3933	−	17.5476i	−0.985572	−	0.569020i
$952$		0			0
$953$	−14.8366	−	25.6977i	−0.480604	−	0.832431i	0.519148	−	0.854684i	$-0.326249\pi$
$953$	−14.8366	−	25.6977i	−0.480604	−	0.832431i	−0.999752	+	0.0222534i	$0.992916\pi$
$954$		0			0
$955$	8.86893	−	5.12048i	0.286992	−	0.165695i
$956$		0			0
$957$			13.0066i			0.420443i
$958$		0			0
$959$	1.03891	−	1.79944i	0.0335480	−	0.0581069i
$960$		0			0
$961$	30.6867			0.989893
$962$		0			0
$963$	−1.36973			−0.0441390
$964$		0			0
$965$	2.10260	−	3.64180i	0.0676850	−	0.117234i
$966$		0			0
$967$		−	1.81392i		−	0.0583319i	−0.999575	−	0.0291659i	$-0.990715\pi$
$967$		−	1.81392i		−	0.0583319i	0.999575	−	0.0291659i	$-0.00928512\pi$
$968$		0			0
$969$	4.59006	−	2.65007i	0.147454	−	0.0851325i
$970$		0			0
$971$	−18.8902	−	32.7188i	−0.606216	−	1.05000i	−0.991858	−	0.127348i	$-0.959353\pi$
$971$	−18.8902	−	32.7188i	−0.606216	−	1.05000i	0.385642	−	0.922648i	$-0.373980\pi$
$972$		0			0
$973$	−5.50725	−	3.17961i	−0.176554	−	0.101934i
$974$		0			0
$975$	−22.2052	+	10.9943i	−0.711134	+	0.352101i
$976$		0			0
$977$	30.0245	+	17.3346i	0.960569	+	0.554584i	0.896348	−	0.443351i	$-0.146211\pi$
$977$	30.0245	+	17.3346i	0.960569	+	0.554584i	0.0642205	+	0.997936i	$0.479544\pi$
$978$		0			0
$979$	1.51618	+	2.62610i	0.0484573	+	0.0839305i
$980$		0			0
$981$	−4.10844	+	2.37201i	−0.131172	+	0.0757325i
$982$		0			0
$983$		−	21.0815i		−	0.672396i	−0.941791	−	0.336198i	$-0.890859\pi$
$983$		−	21.0815i		−	0.672396i	0.941791	−	0.336198i	$-0.109141\pi$
$984$		0			0
$985$	−2.62815	+	4.55209i	−0.0837399	+	0.145042i
$986$		0			0
$987$	−6.77704			−0.215715
$988$		0			0
$989$	7.52728			0.239354
$990$		0			0
$991$	−5.77212	+	9.99760i	−0.183357	+	0.317584i	−0.943022	−	0.332731i	$-0.892030\pi$
$991$	−5.77212	+	9.99760i	−0.183357	+	0.317584i	0.759664	+	0.650315i	$0.225363\pi$
$992$		0			0
$993$		−	26.1384i		−	0.829477i
$994$		0			0
$995$	3.03329	−	1.75127i	0.0961618	−	0.0555191i
$996$		0			0
$997$	7.20698	+	12.4829i	0.228247	+	0.395336i	0.957289	−	0.289133i	$-0.0933672\pi$
$997$	7.20698	+	12.4829i	0.228247	+	0.395336i	−0.729041	+	0.684470i	$0.760034\pi$
$998$		0			0
$999$	5.51700	+	3.18524i	0.174550	+	0.100777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.p.a.485.4	yes	24
13.6	odd	12		7436.2.a.u.1.9		12
13.7	odd	12		7436.2.a.v.1.9		12
13.10	even	6	inner	572.2.p.a.309.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.p.a.309.4	✓	24	13.10	even	6	inner
572.2.p.a.485.4	yes	24	1.1	even	1	trivial
7436.2.a.u.1.9		12	13.6	odd	12
7436.2.a.v.1.9		12	13.7	odd	12

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909010 + 1.57445i) q^{3} -1.10453i q^{5} +(0.391551 - 0.226062i) q^{7} +(-0.152598 - 0.264307i) q^{9} +O(q^{10})\)	\(q+(-0.909010 + 1.57445i) q^{3} -1.10453i q^{5} +(0.391551 - 0.226062i) q^{7} +(-0.152598 - 0.264307i) q^{9} +(-0.866025 - 0.500000i) q^{11} +(3.00109 + 1.99836i) q^{13} +(1.73902 + 1.00403i) q^{15} +(2.90403 + 5.02993i) q^{17} +(-0.434699 + 0.250974i) q^{19} +0.821971i q^{21} +(-1.69579 + 2.93720i) q^{23} +3.78002 q^{25} -4.89921 q^{27} +(-3.57713 + 6.19577i) q^{29} -0.559743i q^{31} +(1.57445 - 0.909010i) q^{33} +(-0.249692 - 0.432479i) q^{35} +(-1.12610 - 0.650154i) q^{37} +(-5.87435 + 2.90854i) q^{39} +(1.68197 + 0.971085i) q^{41} +(-1.10970 - 1.92206i) q^{43} +(-0.291934 + 0.168548i) q^{45} +8.24486i q^{47} +(-3.39779 + 5.88515i) q^{49} -10.5592 q^{51} +10.4766 q^{53} +(-0.552263 + 0.956548i) q^{55} -0.912550i q^{57} +(6.68558 - 3.85992i) q^{59} +(-0.127115 - 0.220169i) q^{61} +(-0.119500 - 0.0689931i) q^{63} +(2.20724 - 3.31478i) q^{65} +(2.01992 + 1.16620i) q^{67} +(-3.08298 - 5.33988i) q^{69} +(-14.2566 + 8.23105i) q^{71} -9.33433i q^{73} +(-3.43608 + 5.95146i) q^{75} -0.452124 q^{77} +13.1660 q^{79} +(4.91122 - 8.50648i) q^{81} -10.2140i q^{83} +(5.55569 - 3.20758i) q^{85} +(-6.50329 - 11.2640i) q^{87} +(-2.62610 - 1.51618i) q^{89} +(1.62684 + 0.104028i) q^{91} +(0.881287 + 0.508812i) q^{93} +(0.277207 + 0.480136i) q^{95} +(10.8419 - 6.25957i) q^{97} +0.305195i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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