LMFDB - Embedded newform 572.2.p.a.309.11

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			309.11
Character	$\chi$	$=$	572.309
Dual form			572.2.p.a.485.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44478 + 2.50242i) q^{3} +0.307799i q^{5} +(-1.50558 - 0.869246i) q^{7} +(-2.67475 + 4.63280i) q^{9} +O(q^{10})$	\(q+(1.44478 + 2.50242i) q^{3} +0.307799i q^{5} +(-1.50558 - 0.869246i) q^{7} +(-2.67475 + 4.63280i) q^{9} +(-0.866025 + 0.500000i) q^{11} +(-1.23765 + 3.38648i) q^{13} +(-0.770245 + 0.444701i) q^{15} +(-2.39552 + 4.14916i) q^{17} +(-0.414854 - 0.239516i) q^{19} -5.02346i q^{21} +(3.80793 + 6.59553i) q^{23} +4.90526 q^{25} -6.78900 q^{27} +(-2.94990 - 5.10938i) q^{29} +0.819313i q^{31} +(-2.50242 - 1.44478i) q^{33} +(0.267553 - 0.463416i) q^{35} +(7.49284 - 4.32599i) q^{37} +(-10.2625 + 1.79556i) q^{39} +(3.16868 - 1.82944i) q^{41} +(-3.20591 + 5.55279i) q^{43} +(-1.42597 - 0.823287i) q^{45} -9.33128i q^{47} +(-1.98882 - 3.44474i) q^{49} -13.8440 q^{51} +6.39172 q^{53} +(-0.153900 - 0.266562i) q^{55} -1.38419i q^{57} +(4.87505 + 2.81461i) q^{59} +(5.27568 - 9.13775i) q^{61} +(8.05410 - 4.65003i) q^{63} +(-1.04236 - 0.380949i) q^{65} +(-10.4001 + 6.00448i) q^{67} +(-11.0032 + 19.0581i) q^{69} +(2.52901 + 1.46013i) q^{71} -8.15921i q^{73} +(7.08700 + 12.2750i) q^{75} +1.73849 q^{77} +6.15399 q^{79} +(-1.78433 - 3.09055i) q^{81} +13.8113i q^{83} +(-1.27711 - 0.737340i) q^{85} +(8.52389 - 14.7638i) q^{87} +(5.99284 - 3.45997i) q^{89} +(4.80707 - 4.02278i) q^{91} +(-2.05027 + 1.18372i) q^{93} +(0.0737228 - 0.127692i) q^{95} +(7.14295 + 4.12399i) q^{97} -5.34950i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.44478	+	2.50242i	0.834141	+	1.44478i	0.894728	+	0.446612i	$0.147370\pi$
$3$	1.44478	+	2.50242i	0.834141	+	1.44478i	−0.0605863	+	0.998163i	$0.519297\pi$
$4$		0			0
$5$			0.307799i			0.137652i	0.997629	+	0.0688260i	$0.0219253\pi$
$5$			0.307799i			0.137652i	−0.997629	+	0.0688260i	$0.978075\pi$
$6$		0			0
$7$	−1.50558	−	0.869246i	−0.569055	−	0.328544i	0.187717	−	0.982223i	$-0.439891\pi$
$7$	−1.50558	−	0.869246i	−0.569055	−	0.328544i	−0.756772	+	0.653679i	$0.773225\pi$
$8$		0			0
$9$	−2.67475	+	4.63280i	−0.891584	+	1.54427i
$10$		0			0
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$		0			0
$13$	−1.23765	+	3.38648i	−0.343263	+	0.939239i
$13$	−1.23765	+	3.38648i	−0.343263	+	0.939239i
$14$		0			0
$15$	−0.770245	+	0.444701i	−0.198876	+	0.114821i
$16$		0			0
$17$	−2.39552	+	4.14916i	−0.580999	+	1.00632i	0.414362	+	0.910112i	$0.364005\pi$
$17$	−2.39552	+	4.14916i	−0.580999	+	1.00632i	−0.995361	+	0.0962080i	$0.969329\pi$
$18$		0			0
$19$	−0.414854	−	0.239516i	−0.0951740	−	0.0549487i	0.451658	−	0.892191i	$-0.350833\pi$
$19$	−0.414854	−	0.239516i	−0.0951740	−	0.0549487i	−0.546832	+	0.837243i	$0.684166\pi$
$20$		0			0
$21$		−	5.02346i		−	1.09621i
$22$		0			0
$23$	3.80793	+	6.59553i	0.794008	+	1.37526i	0.923467	+	0.383677i	$0.125343\pi$
$23$	3.80793	+	6.59553i	0.794008	+	1.37526i	−0.129459	+	0.991585i	$0.541324\pi$
$24$		0			0
$25$	4.90526			0.981052
$26$		0			0
$27$	−6.78900			−1.30654
$28$		0			0
$29$	−2.94990	−	5.10938i	−0.547783	−	0.948789i	−0.998426	−	0.0560841i	$-0.982138\pi$
$29$	−2.94990	−	5.10938i	−0.547783	−	0.948789i	0.450643	−	0.892704i	$-0.351195\pi$
$30$		0			0
$31$			0.819313i			0.147153i	0.997290	+	0.0735765i	$0.0234413\pi$
$31$			0.819313i			0.147153i	−0.997290	+	0.0735765i	$0.976559\pi$
$32$		0			0
$33$	−2.50242	−	1.44478i	−0.435616	−	0.251503i
$34$		0			0
$35$	0.267553	−	0.463416i	0.0452248	−	0.0783316i
$36$		0			0
$37$	7.49284	−	4.32599i	1.23182	−	0.711189i	0.264407	−	0.964411i	$-0.414824\pi$
$37$	7.49284	−	4.32599i	1.23182	−	0.711189i	0.967408	+	0.253222i	$0.0814903\pi$
$38$		0			0
$39$	−10.2625	+	1.79556i	−1.64332	+	0.287520i
$40$		0			0
$41$	3.16868	−	1.82944i	0.494865	−	0.285710i	−0.231726	−	0.972781i	$-0.574437\pi$
$41$	3.16868	−	1.82944i	0.494865	−	0.285710i	0.726590	+	0.687071i	$0.241104\pi$
$42$		0			0
$43$	−3.20591	+	5.55279i	−0.488896	+	0.846793i	−0.999918	−	0.0127747i	$-0.995934\pi$
$43$	−3.20591	+	5.55279i	−0.488896	+	0.846793i	0.511022	+	0.859567i	$0.329267\pi$
$44$		0			0
$45$	−1.42597	−	0.823287i	−0.212572	−	0.122728i
$46$		0			0
$47$		−	9.33128i		−	1.36111i	−0.732698	−	0.680554i	$-0.761739\pi$
$47$		−	9.33128i		−	1.36111i	0.732698	−	0.680554i	$-0.238261\pi$
$48$		0			0
$49$	−1.98882	−	3.44474i	−0.284117	−	0.492106i
$50$		0			0
$51$	−13.8440			−1.93854
$52$		0			0
$53$	6.39172			0.877970			0.438985	−	0.898494i	$-0.355338\pi$
$53$	6.39172			0.877970			0.438985	+	0.898494i	$0.355338\pi$
$54$		0			0
$55$	−0.153900	−	0.266562i	−0.0207518	−	0.0359432i
$56$		0			0
$57$		−	1.38419i		−	0.183340i
$58$		0			0
$59$	4.87505	+	2.81461i	0.634677	+	0.366431i	0.782561	−	0.622574i	$-0.213913\pi$
$59$	4.87505	+	2.81461i	0.634677	+	0.366431i	−0.147884	+	0.989005i	$0.547246\pi$
$60$		0			0
$61$	5.27568	−	9.13775i	0.675482	−	1.16997i	−0.300846	−	0.953673i	$-0.597269\pi$
$61$	5.27568	−	9.13775i	0.675482	−	1.16997i	0.976328	−	0.216296i	$-0.0693976\pi$
$62$		0			0
$63$	8.05410	−	4.65003i	1.01472	−	0.585849i
$64$		0			0
$65$	−1.04236	−	0.380949i	−0.129288	−	0.0472509i
$66$		0			0
$67$	−10.4001	+	6.00448i	−1.27057	+	0.733564i	−0.975095	−	0.221786i	$-0.928811\pi$
$67$	−10.4001	+	6.00448i	−1.27057	+	0.733564i	−0.295475	+	0.955350i	$0.595478\pi$
$68$		0			0
$69$	−11.0032	+	19.0581i	−1.32463	+	2.29433i
$70$		0			0
$71$	2.52901	+	1.46013i	0.300138	+	0.173285i	0.642505	−	0.766281i	$-0.277895\pi$
$71$	2.52901	+	1.46013i	0.300138	+	0.173285i	−0.342367	+	0.939566i	$0.611228\pi$
$72$		0			0
$73$		−	8.15921i		−	0.954963i	−0.878642	−	0.477481i	$-0.841550\pi$
$73$		−	8.15921i		−	0.954963i	0.878642	−	0.477481i	$-0.158450\pi$
$74$		0			0
$75$	7.08700	+	12.2750i	0.818336	+	1.41740i
$76$		0			0
$77$	1.73849			0.198120
$78$		0			0
$79$	6.15399			0.692378			0.346189	−	0.938165i	$-0.387476\pi$
$79$	6.15399			0.692378			0.346189	+	0.938165i	$0.387476\pi$
$80$		0			0
$81$	−1.78433	−	3.09055i	−0.198259	−	0.343395i
$82$		0			0
$83$			13.8113i			1.51599i	0.652262	+	0.757994i	$0.273820\pi$
$83$			13.8113i			1.51599i	−0.652262	+	0.757994i	$0.726180\pi$
$84$		0			0
$85$	−1.27711	−	0.737340i	−0.138522	−	0.0799757i
$86$		0			0
$87$	8.52389	−	14.7638i	0.913857	−	1.58285i
$88$		0			0
$89$	5.99284	−	3.45997i	0.635240	−	0.366756i	−0.147539	−	0.989056i	$-0.547135\pi$
$89$	5.99284	−	3.45997i	0.635240	−	0.366756i	0.782779	+	0.622300i	$0.213802\pi$
$90$		0			0
$91$	4.80707	−	4.02278i	0.503917	−	0.421702i
$92$		0			0
$93$	−2.05027	+	1.18372i	−0.212603	+	0.122746i
$94$		0			0
$95$	0.0737228	−	0.127692i	0.00756380	−	0.0131009i
$96$		0			0
$97$	7.14295	+	4.12399i	0.725257	+	0.418727i	0.816684	−	0.577084i	$-0.195810\pi$
$97$	7.14295	+	4.12399i	0.725257	+	0.418727i	−0.0914275	+	0.995812i	$0.529143\pi$
$98$		0			0
$99$		−	5.34950i		−	0.537645i
$100$		0			0
$101$	5.90336	+	10.2249i	0.587407	+	1.01742i	0.994571	+	0.104063i	$0.0331844\pi$
$101$	5.90336	+	10.2249i	0.587407	+	1.01742i	−0.407164	+	0.913355i	$0.633482\pi$
$102$		0			0
$103$	5.33744			0.525914			0.262957	−	0.964808i	$-0.415302\pi$
$103$	5.33744			0.525914			0.262957	+	0.964808i	$0.415302\pi$
$104$		0			0
$105$	1.54622			0.150895
$106$		0			0
$107$	2.04043	+	3.53413i	0.197256	+	0.341657i	0.947638	−	0.319348i	$-0.103464\pi$
$107$	2.04043	+	3.53413i	0.197256	+	0.341657i	−0.750382	+	0.661004i	$0.770130\pi$
$108$		0			0
$109$		−	15.3023i		−	1.46569i	−0.680393	−	0.732847i	$-0.738191\pi$
$109$		−	15.3023i		−	1.46569i	0.680393	−	0.732847i	$-0.261809\pi$
$110$		0			0
$111$	21.6509	+	12.5002i	2.05502	+	1.18646i
$112$		0			0
$113$	−4.12723	+	7.14858i	−0.388257	+	0.672481i	−0.992215	−	0.124535i	$-0.960256\pi$
$113$	−4.12723	+	7.14858i	−0.388257	+	0.672481i	0.603958	+	0.797016i	$0.293589\pi$
$114$		0			0
$115$	−2.03010	+	1.17208i	−0.189308	+	0.109297i
$116$		0			0
$117$	−12.3785	−	14.7918i	−1.14439	−	1.36750i
$118$		0			0
$119$	7.21329	−	4.16460i	0.661241	−	0.381768i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	9.15606	+	5.28626i	0.825574	+	0.476646i
$124$		0			0
$125$			3.04883i			0.272696i
$126$		0			0
$127$	−2.72009	−	4.71133i	−0.241369	−	0.418063i	0.719736	−	0.694248i	$-0.244263\pi$
$127$	−2.72009	−	4.71133i	−0.241369	−	0.418063i	−0.961104	+	0.276185i	$0.910930\pi$
$128$		0			0
$129$	−18.5272			−1.63123
$130$		0			0
$131$	−11.5220			−1.00668			−0.503339	−	0.864089i	$-0.667895\pi$
$131$	−11.5220			−1.00668			−0.503339	+	0.864089i	$0.667895\pi$
$132$		0			0
$133$	0.416397	+	0.721220i	0.0361062	+	0.0625377i
$134$		0			0
$135$		−	2.08965i		−	0.179849i
$136$		0			0
$137$	−14.8503	−	8.57383i	−1.26875	−	0.732511i	−0.293996	−	0.955807i	$-0.594985\pi$
$137$	−14.8503	−	8.57383i	−1.26875	−	0.732511i	−0.974751	+	0.223295i	$0.928319\pi$
$138$		0			0
$139$	−0.534916	+	0.926501i	−0.0453709	+	0.0785848i	−0.887819	−	0.460193i	$-0.847780\pi$
$139$	−0.534916	+	0.926501i	−0.0453709	+	0.0785848i	0.842448	+	0.538777i	$0.181114\pi$
$140$		0			0
$141$	23.3508	−	13.4816i	1.96649	−	1.13536i
$142$		0			0
$143$	−0.621399	−	3.55160i	−0.0519640	−	0.297000i
$144$		0			0
$145$	1.57266	−	0.907978i	0.130603	−	0.0754035i
$146$		0			0
$147$	5.74680	−	9.95375i	0.473988	−	0.820972i
$148$		0			0
$149$	11.2980	+	6.52290i	0.925567	+	0.534377i	0.885407	−	0.464817i	$-0.153880\pi$
$149$	11.2980	+	6.52290i	0.925567	+	0.534377i	0.0401605	+	0.999193i	$0.487213\pi$
$150$		0			0
$151$		−	13.7974i		−	1.12282i	−0.827538	−	0.561409i	$-0.810259\pi$
$151$		−	13.7974i		−	1.12282i	0.827538	−	0.561409i	$-0.189741\pi$
$152$		0			0
$153$	−12.8148	−	22.1960i	−1.03602	−	1.79444i
$154$		0			0
$155$	−0.252184			−0.0202559
$156$		0			0
$157$	−6.69746			−0.534515			−0.267258	−	0.963625i	$-0.586117\pi$
$157$	−6.69746			−0.534515			−0.267258	+	0.963625i	$0.586117\pi$
$158$		0			0
$159$	9.23460	+	15.9948i	0.732351	+	1.26847i
$160$		0			0
$161$		−	13.2401i		−	1.04347i
$162$		0			0
$163$	1.07777	+	0.622253i	0.0844178	+	0.0487386i	0.541615	−	0.840627i	$-0.317813\pi$
$163$	1.07777	+	0.622253i	0.0844178	+	0.0487386i	−0.457197	+	0.889366i	$0.651147\pi$
$164$		0			0
$165$	0.444701	−	0.770245i	0.0346199	−	0.0599635i
$166$		0			0
$167$	−3.64507	+	2.10448i	−0.282064	+	0.162850i	−0.634357	−	0.773040i	$-0.718735\pi$
$167$	−3.64507	+	2.10448i	−0.282064	+	0.162850i	0.352293	+	0.935890i	$0.385402\pi$
$168$		0			0
$169$	−9.93643	−	8.38256i	−0.764341	−	0.644812i
$170$		0			0
$171$	2.21926	−	1.28129i	0.169711	−	0.0979827i
$172$		0			0
$173$	−2.27562	+	3.94148i	−0.173012	+	0.299665i	−0.939471	−	0.342627i	$-0.888683\pi$
$173$	−2.27562	+	3.94148i	−0.173012	+	0.299665i	0.766460	+	0.642293i	$0.222017\pi$
$174$		0			0
$175$	−7.38525	−	4.26388i	−0.558273	−	0.322319i
$176$		0			0
$177$			16.2659i			1.22262i
$178$		0			0
$179$	9.05568	+	15.6849i	0.676854	+	1.17234i	0.975923	+	0.218114i	$0.0699903\pi$
$179$	9.05568	+	15.6849i	0.676854	+	1.17234i	−0.299070	+	0.954231i	$0.596676\pi$
$180$		0			0
$181$	−18.6142			−1.38358			−0.691792	−	0.722097i	$-0.743178\pi$
$181$	−18.6142			−1.38358			−0.691792	+	0.722097i	$0.743178\pi$
$182$		0			0
$183$	30.4887			2.25379
$184$		0			0
$185$	1.33154	+	2.30629i	0.0978966	+	0.169562i
$186$		0			0
$187$		−	4.79104i		−	0.350356i
$188$		0			0
$189$	10.2214	+	5.90132i	0.743496	+	0.429258i
$190$		0			0
$191$	6.60935	−	11.4477i	0.478236	−	0.828328i	−0.521453	−	0.853280i	$-0.674610\pi$
$191$	6.60935	−	11.4477i	0.478236	−	0.828328i	0.999689	+	0.0249515i	$0.00794314\pi$
$192$		0			0
$193$	11.0926	−	6.40431i	0.798462	−	0.460992i	−0.0444709	−	0.999011i	$-0.514160\pi$
$193$	11.0926	−	6.40431i	0.798462	−	0.460992i	0.842933	+	0.538018i	$0.180827\pi$
$194$		0			0
$195$	−0.552673	−	3.15880i	−0.0395778	−	0.226206i
$196$		0			0
$197$	16.4049	−	9.47139i	1.16880	−	0.674809i	0.215405	−	0.976525i	$-0.430893\pi$
$197$	16.4049	−	9.47139i	1.16880	−	0.674809i	0.953398	+	0.301716i	$0.0975594\pi$
$198$		0			0
$199$	−1.90345	+	3.29686i	−0.134932	+	0.233709i	−0.925571	−	0.378573i	$-0.876415\pi$
$199$	−1.90345	+	3.29686i	−0.134932	+	0.233709i	0.790640	+	0.612282i	$0.209748\pi$
$200$		0			0
$201$	−30.0515	−	17.3503i	−2.11967	−	1.22379i
$202$		0			0
$203$			10.2568i			0.719884i
$204$		0			0
$205$	0.563100	+	0.975318i	0.0393286	+	0.0681192i
$206$		0			0
$207$	−40.7410			−2.83170
$208$		0			0
$209$	0.479032			0.0331353
$210$		0			0
$211$	−8.84102	−	15.3131i	−0.608641	−	1.05420i	−0.991465	−	0.130375i	$-0.958382\pi$
$211$	−8.84102	−	15.3131i	−0.608641	−	1.05420i	0.382824	−	0.923821i	$-0.374952\pi$
$212$		0			0
$213$			8.43821i			0.578177i
$214$		0			0
$215$	−1.70915	−	0.986776i	−0.116563	−	0.0672975i
$216$		0			0
$217$	0.712185	−	1.23354i	0.0483463	−	0.0837382i
$218$		0			0
$219$	20.4178	−	11.7882i	1.37971	−	0.796574i
$220$		0			0
$221$	−11.0862	−	13.2476i	−0.745740	−	0.891130i
$222$		0			0
$223$	1.20474	−	0.695559i	0.0806755	−	0.0465780i	−0.459120	−	0.888374i	$-0.651835\pi$
$223$	1.20474	−	0.695559i	0.0806755	−	0.0465780i	0.539795	+	0.841796i	$0.318502\pi$
$224$		0			0
$225$	−13.1203	+	22.7251i	−0.874690	+	1.51501i
$226$		0			0
$227$	15.3848	+	8.88239i	1.02112	+	0.589545i	0.914429	−	0.404747i	$-0.132640\pi$
$227$	15.3848	+	8.88239i	1.02112	+	0.589545i	0.106693	+	0.994292i	$0.465974\pi$
$228$		0			0
$229$		−	5.29500i		−	0.349904i	−0.984577	−	0.174952i	$-0.944023\pi$
$229$		−	5.29500i		−	0.349904i	0.984577	−	0.174952i	$-0.0559770\pi$
$230$		0			0
$231$	2.51173	+	4.35045i	0.165260	+	0.286238i
$232$		0			0
$233$	3.79999			0.248946			0.124473	−	0.992223i	$-0.460276\pi$
$233$	3.79999			0.248946			0.124473	+	0.992223i	$0.460276\pi$
$234$		0			0
$235$	2.87216			0.187359
$236$		0			0
$237$	8.89113	+	15.3999i	0.577541	+	1.00033i
$238$		0			0
$239$			20.6007i			1.33255i	0.745708	+	0.666273i	$0.232111\pi$
$239$			20.6007i			1.33255i	−0.745708	+	0.666273i	$0.767889\pi$
$240$		0			0
$241$	−1.07738	−	0.622026i	−0.0694002	−	0.0400682i	0.464898	−	0.885364i	$-0.346091\pi$
$241$	−1.07738	−	0.622026i	−0.0694002	−	0.0400682i	−0.534299	+	0.845296i	$0.679424\pi$
$242$		0			0
$243$	−5.02759	+	8.70804i	−0.322520	+	0.558621i
$244$		0			0
$245$	1.06029	−	0.612158i	0.0677394	−	0.0391093i
$246$		0			0
$247$	1.32456	−	1.10845i	0.0842797	−	0.0705293i
$248$		0			0
$249$	−34.5617	+	19.9542i	−2.19026	+	1.26455i
$250$		0			0
$251$	−5.70407	+	9.87973i	−0.360037	+	0.623603i	−0.987967	−	0.154667i	$-0.950569\pi$
$251$	−5.70407	+	9.87973i	−0.360037	+	0.623603i	0.627929	+	0.778270i	$0.283903\pi$
$252$		0			0
$253$	−6.59553	−	3.80793i	−0.414657	−	0.239402i
$254$		0			0
$255$		−	4.26116i		−	0.266844i
$256$		0			0
$257$	−4.78446	−	8.28693i	−0.298447	−	0.516925i	0.677334	−	0.735675i	$-0.263135\pi$
$257$	−4.78446	−	8.28693i	−0.298447	−	0.516925i	−0.975781	+	0.218751i	$0.929802\pi$
$258$		0			0
$259$	−15.0414			−0.934628
$260$		0			0
$261$	31.5610			1.95358
$262$		0			0
$263$	−0.550322	−	0.953186i	−0.0339343	−	0.0587759i	0.848559	−	0.529100i	$-0.177470\pi$
$263$	−0.550322	−	0.953186i	−0.0339343	−	0.0587759i	−0.882494	+	0.470324i	$0.844137\pi$
$264$		0			0
$265$			1.96737i			0.120854i
$266$		0			0
$267$	17.3166	+	9.99775i	1.05976	+	0.611853i
$268$		0			0
$269$	−7.03235	+	12.1804i	−0.428770	+	0.742651i	−0.996764	−	0.0803815i	$-0.974386\pi$
$269$	−7.03235	+	12.1804i	−0.428770	+	0.742651i	0.567994	+	0.823032i	$0.307719\pi$
$270$		0			0
$271$	−24.6062	+	14.2064i	−1.49472	+	0.862976i	−0.999982	−	0.00606737i	$-0.998069\pi$
$271$	−24.6062	+	14.2064i	−1.49472	+	0.862976i	−0.494736	+	0.869043i	$0.664735\pi$
$272$		0			0
$273$	17.0118	+	6.21730i	1.02960	+	0.376288i
$274$		0			0
$275$	−4.24808	+	2.45263i	−0.256169	+	0.147899i
$276$		0			0
$277$	−6.37089	+	11.0347i	−0.382790	+	0.663011i	−0.991460	−	0.130412i	$-0.958370\pi$
$277$	−6.37089	+	11.0347i	−0.382790	+	0.663011i	0.608670	+	0.793423i	$0.291703\pi$
$278$		0			0
$279$	−3.79572	−	2.19146i	−0.227244	−	0.131199i
$280$		0			0
$281$		−	2.36207i		−	0.140909i	−0.997515	−	0.0704547i	$-0.977555\pi$
$281$		−	2.36207i		−	0.140909i	0.997515	−	0.0704547i	$-0.0224450\pi$
$282$		0			0
$283$	−11.5032	−	19.9242i	−0.683797	−	1.18437i	−0.973813	−	0.227349i	$-0.926994\pi$
$283$	−11.5032	−	19.9242i	−0.683797	−	1.18437i	0.290017	−	0.957022i	$-0.406339\pi$
$284$		0			0
$285$	0.426052			0.0252371
$286$		0			0
$287$	−6.36093			−0.375474
$288$		0			0
$289$	−2.97704	−	5.15639i	−0.175120	−	0.303317i
$290$		0			0
$291$			23.8329i			1.39711i
$292$		0			0
$293$	18.1264	+	10.4653i	1.05895	+	0.611388i	0.925143	−	0.379619i	$-0.123945\pi$
$293$	18.1264	+	10.4653i	1.05895	+	0.611388i	0.133812	+	0.991007i	$0.457278\pi$
$294$		0			0
$295$	−0.866336	+	1.50054i	−0.0504400	+	0.0873647i
$296$		0			0
$297$	5.87945	−	3.39450i	0.341160	−	0.196969i
$298$		0			0
$299$	−27.0485	+	4.73248i	−1.56425	+	0.273687i
$300$		0			0
$301$	9.65349	−	5.57344i	0.556418	−	0.321248i
$302$		0			0
$303$	−17.0581	+	29.5454i	−0.979960	+	1.69734i
$304$		0			0
$305$	2.81259	+	1.62385i	0.161049	+	0.0929815i
$306$		0			0
$307$			14.1400i			0.807011i	0.914977	+	0.403505i	$0.132208\pi$
$307$			14.1400i			0.807011i	−0.914977	+	0.403505i	$0.867792\pi$
$308$		0			0
$309$	7.71141	+	13.3565i	0.438687	+	0.759828i
$310$		0			0
$311$	16.0892			0.912332			0.456166	−	0.889895i	$-0.349222\pi$
$311$	16.0892			0.912332			0.456166	+	0.889895i	$0.349222\pi$
$312$		0			0
$313$	29.2700			1.65444			0.827220	−	0.561878i	$-0.189921\pi$
$313$	29.2700			1.65444			0.827220	+	0.561878i	$0.189921\pi$
$314$		0			0
$315$	1.43128	+	2.47905i	0.0806434	+	0.139678i
$316$		0			0
$317$		−	8.63500i		−	0.484990i	−0.970153	−	0.242495i	$-0.922034\pi$
$317$		−	8.63500i		−	0.484990i	0.970153	−	0.242495i	$-0.0779658\pi$
$318$		0			0
$319$	5.10938	+	2.94990i	0.286071	+	0.165163i
$320$		0			0
$321$	−5.89592	+	10.2120i	−0.329078	+	0.569980i
$322$		0			0
$323$	1.98758	−	1.14753i	0.110592	−	0.0638503i
$324$		0			0
$325$	−6.07101	+	16.6115i	−0.336759	+	0.921442i
$326$		0			0
$327$	38.2929	−	22.1084i	2.11760	−	1.22260i
$328$		0			0
$329$	−8.11118	+	14.0490i	−0.447184	+	0.774545i
$330$		0			0
$331$	−21.0479	−	12.1520i	−1.15690	−	0.667936i	−0.206340	−	0.978480i	$-0.566155\pi$
$331$	−21.0479	−	12.1520i	−1.15690	−	0.667936i	−0.950559	+	0.310545i	$0.899489\pi$
$332$		0			0
$333$			46.2838i			2.53634i
$334$		0			0
$335$	−1.84818	−	3.20113i	−0.100977	−	0.174897i
$336$		0			0
$337$	35.2074			1.91787			0.958934	−	0.283629i	$-0.0915384\pi$
$337$	35.2074			1.91787			0.958934	+	0.283629i	$0.0915384\pi$
$338$		0			0
$339$	−23.8517			−1.29545
$340$		0			0
$341$	−0.409657	−	0.709546i	−0.0221842	−	0.0384241i
$342$		0			0
$343$			19.0846i			1.03047i
$344$		0			0
$345$	−5.86607	−	3.38678i	−0.315819	−	0.182338i
$346$		0			0
$347$	−3.69972	+	6.40811i	−0.198612	+	0.344005i	−0.948078	−	0.318036i	$-0.896977\pi$
$347$	−3.69972	+	6.40811i	−0.198612	+	0.344005i	0.749467	+	0.662042i	$0.230310\pi$
$348$		0			0
$349$	−21.7930	+	12.5822i	−1.16655	+	0.673510i	−0.952866	−	0.303392i	$-0.901881\pi$
$349$	−21.7930	+	12.5822i	−1.16655	+	0.673510i	−0.213688	+	0.976902i	$0.568548\pi$
$350$		0			0
$351$	8.40243	−	22.9908i	0.448489	−	1.22716i
$352$		0			0
$353$	−27.6068	+	15.9388i	−1.46936	+	0.848337i	−0.999410	−	0.0343536i	$-0.989063\pi$
$353$	−27.6068	+	15.9388i	−1.46936	+	0.848337i	−0.469954	+	0.882691i	$0.655729\pi$
$354$		0			0
$355$	−0.449426	+	0.778428i	−0.0238530	+	0.0413147i
$356$		0			0
$357$	20.8432	+	12.0338i	1.10314	+	0.636897i
$358$		0			0
$359$		−	32.6156i		−	1.72139i	−0.509125	−	0.860693i	$-0.670031\pi$
$359$		−	32.6156i		−	1.72139i	0.509125	−	0.860693i	$-0.329969\pi$
$360$		0			0
$361$	−9.38526	−	16.2558i	−0.493961	−	0.855566i
$362$		0			0
$363$	2.88955			0.151662
$364$		0			0
$365$	2.51140			0.131453
$366$		0			0
$367$	−16.6506	−	28.8397i	−0.869154	−	1.50542i	−0.862863	−	0.505438i	$-0.831331\pi$
$367$	−16.6506	−	28.8397i	−0.869154	−	1.50542i	−0.00629090	−	0.999980i	$-0.502002\pi$
$368$		0			0
$369$			19.5732i			1.01894i
$370$		0			0
$371$	−9.62324	−	5.55598i	−0.499613	−	0.288452i
$372$		0			0
$373$	12.5287	−	21.7004i	0.648712	−	1.12360i	−0.334719	−	0.942318i	$-0.608641\pi$
$373$	12.5287	−	21.7004i	0.648712	−	1.12360i	0.983431	−	0.181284i	$-0.0580254\pi$
$374$		0			0
$375$	−7.62947	+	4.40488i	−0.393984	+	0.227467i
$376$		0			0
$377$	20.9538	−	3.66613i	1.07917	−	0.188815i
$378$		0			0
$379$	30.0625	−	17.3566i	1.54421	−	0.891548i	0.545641	−	0.838019i	$-0.316286\pi$
$379$	30.0625	−	17.3566i	1.54421	−	0.891548i	0.998566	−	0.0535293i	$-0.0170471\pi$
$380$		0			0
$381$	7.85983	−	13.6136i	0.402671	−	0.697447i
$382$		0			0
$383$	−31.2722	−	18.0550i	−1.59793	−	0.922568i	−0.991885	−	0.127141i	$-0.959420\pi$
$383$	−31.2722	−	18.0550i	−1.59793	−	0.922568i	−0.606050	−	0.795427i	$-0.707247\pi$
$384$		0			0
$385$			0.535107i			0.0272716i
$386$		0			0
$387$	−17.1500	−	29.7047i	−0.871783	−	1.50997i
$388$		0			0
$389$	−11.8572			−0.601184			−0.300592	−	0.953753i	$-0.597184\pi$
$389$	−11.8572			−0.601184			−0.300592	+	0.953753i	$0.597184\pi$
$390$		0			0
$391$	−36.4879			−1.84527
$392$		0			0
$393$	−16.6466	−	28.8328i	−0.839712	−	1.45442i
$394$		0			0
$395$			1.89419i			0.0953072i
$396$		0			0
$397$	14.8197	+	8.55614i	0.743778	+	0.429421i	0.823441	−	0.567401i	$-0.192051\pi$
$397$	14.8197	+	8.55614i	0.743778	+	0.429421i	−0.0796632	+	0.996822i	$0.525384\pi$
$398$		0			0
$399$	−1.20320	+	2.08400i	−0.0602353	+	0.104331i
$400$		0			0
$401$	−24.2539	+	14.0030i	−1.21118	+	0.699278i	−0.963017	−	0.269440i	$-0.913162\pi$
$401$	−24.2539	+	14.0030i	−1.21118	+	0.699278i	−0.248167	+	0.968717i	$0.579828\pi$
$402$		0			0
$403$	−2.77458	−	1.01403i	−0.138212	−	0.0505122i
$404$		0			0
$405$	0.951270	−	0.549216i	0.0472690	−	0.0272908i
$406$		0			0
$407$	−4.32599	+	7.49284i	−0.214432	+	0.371406i
$408$		0			0
$409$	−16.6546	−	9.61557i	−0.823519	−	0.475459i	0.0281092	−	0.999605i	$-0.491051\pi$
$409$	−16.6546	−	9.61557i	−0.823519	−	0.475459i	−0.851629	+	0.524146i	$0.824385\pi$
$410$		0			0
$411$		−	49.5490i		−	2.44407i
$412$		0			0
$413$	−4.89318	−	8.47524i	−0.240778	−	0.417039i
$414$		0			0
$415$	−4.25111			−0.208679
$416$		0			0
$417$	−3.09133			−0.151383
$418$		0			0
$419$	−5.59260	−	9.68667i	−0.273217	−	0.473225i	0.696467	−	0.717589i	$-0.254754\pi$
$419$	−5.59260	−	9.68667i	−0.273217	−	0.473225i	−0.969684	+	0.244364i	$0.921421\pi$
$420$		0			0
$421$		−	1.10535i		−	0.0538716i	−0.999637	−	0.0269358i	$-0.991425\pi$
$421$		−	1.10535i		−	0.0538716i	0.999637	−	0.0269358i	$-0.00857498\pi$
$422$		0			0
$423$	43.2300	+	24.9588i	2.10191	+	1.21354i
$424$		0			0
$425$	−11.7507	+	20.3527i	−0.569990	+	0.987252i
$426$		0			0
$427$	−15.8859	+	9.17173i	−0.768773	+	0.443851i
$428$		0			0
$429$	7.98983	−	6.68627i	0.385753	−	0.322816i
$430$		0			0
$431$	3.20839	−	1.85237i	0.154543	−	0.0892254i	−0.420734	−	0.907184i	$-0.638228\pi$
$431$	3.20839	−	1.85237i	0.154543	−	0.0892254i	0.575277	+	0.817959i	$0.304894\pi$
$432$		0			0
$433$	12.7989	−	22.1684i	0.615078	−	1.06535i	−0.375293	−	0.926906i	$-0.622458\pi$
$433$	12.7989	−	22.1684i	0.615078	−	1.06535i	0.990371	−	0.138439i	$-0.0442086\pi$
$434$		0			0
$435$	4.54429	+	2.62365i	0.217882	+	0.125794i
$436$		0			0
$437$		−	3.64824i		−	0.174519i
$438$		0			0
$439$	−0.588349	−	1.01905i	−0.0280804	−	0.0486366i	0.851644	−	0.524121i	$-0.175606\pi$
$439$	−0.588349	−	1.01905i	−0.0280804	−	0.0486366i	−0.879724	+	0.475485i	$0.842273\pi$
$440$		0			0
$441$	21.2784			1.01326
$442$		0			0
$443$	16.3210			0.775433			0.387716	−	0.921779i	$-0.373264\pi$
$443$	16.3210			0.775433			0.387716	+	0.921779i	$0.373264\pi$
$444$		0			0
$445$	1.06498	+	1.84459i	0.0504847	+	0.0874421i
$446$		0			0
$447$			37.6965i			1.78298i
$448$		0			0
$449$	−2.93419	−	1.69405i	−0.138473	−	0.0799473i	0.429163	−	0.903227i	$-0.358809\pi$
$449$	−2.93419	−	1.69405i	−0.138473	−	0.0799473i	−0.567636	+	0.823280i	$0.692142\pi$
$450$		0			0
$451$	−1.82944	+	3.16868i	−0.0861449	+	0.149207i
$452$		0			0
$453$	34.5270	−	19.9342i	1.62222	−	0.936589i
$454$		0			0
$455$	1.23821	+	1.47961i	0.0580481	+	0.0693653i
$456$		0			0
$457$	26.1952	−	15.1238i	1.22536	−	0.707462i	0.259305	−	0.965795i	$-0.416507\pi$
$457$	26.1952	−	15.1238i	1.22536	−	0.707462i	0.966056	+	0.258333i	$0.0831732\pi$
$458$		0			0
$459$	16.2632	−	28.1687i	0.759101	−	1.31480i
$460$		0			0
$461$	−20.8097	−	12.0145i	−0.969204	−	0.559570i	−0.0702104	−	0.997532i	$-0.522367\pi$
$461$	−20.8097	−	12.0145i	−0.969204	−	0.559570i	−0.898993	+	0.437962i	$0.855700\pi$
$462$		0			0
$463$		−	16.4129i		−	0.762773i	−0.924416	−	0.381387i	$-0.875447\pi$
$463$		−	16.4129i		−	0.762773i	0.924416	−	0.381387i	$-0.124553\pi$
$464$		0			0
$465$	−0.364349	−	0.631072i	−0.0168963	−	0.0292653i
$466$		0			0
$467$	15.4757			0.716129			0.358065	−	0.933697i	$-0.383437\pi$
$467$	15.4757			0.716129			0.358065	+	0.933697i	$0.383437\pi$
$468$		0			0
$469$	20.8775			0.964033
$470$		0			0
$471$	−9.67632	−	16.7599i	−0.445861	−	0.772254i
$472$		0			0
$473$		−	6.41181i		−	0.294815i
$474$		0			0
$475$	−2.03497	−	1.17489i	−0.0933706	−	0.0539075i
$476$		0			0
$477$	−17.0963	+	29.6116i	−0.782784	+	1.35582i
$478$		0			0
$479$	5.06446	−	2.92397i	0.231401	−	0.133600i	−0.379817	−	0.925062i	$-0.624013\pi$
$479$	5.06446	−	2.92397i	0.231401	−	0.133600i	0.611218	+	0.791462i	$0.290680\pi$
$480$		0			0
$481$	5.37634	+	30.7284i	0.245140	+	1.40109i
$482$		0			0
$483$	33.1324	−	19.1290i	1.50758	−	0.870399i
$484$		0			0
$485$	−1.26936	+	2.19860i	−0.0576387	+	0.0998331i
$486$		0			0
$487$	−32.5434	−	18.7890i	−1.47468	−	0.851409i	−0.475091	−	0.879937i	$-0.657585\pi$
$487$	−32.5434	−	18.7890i	−1.47468	−	0.851409i	−0.999593	+	0.0285275i	$0.990918\pi$
$488$		0			0
$489$			3.59606i			0.162620i
$490$		0			0
$491$	12.2892	+	21.2855i	0.554604	+	0.960602i	0.997934	+	0.0642435i	$0.0204634\pi$
$491$	12.2892	+	21.2855i	0.554604	+	0.960602i	−0.443331	+	0.896358i	$0.646203\pi$
$492$		0			0
$493$	28.2662			1.27305
$494$		0			0
$495$	1.64657			0.0740080
$496$		0			0
$497$	−2.53842	−	4.39667i	−0.113864	−	0.197217i
$498$		0			0
$499$			7.32852i			0.328070i	0.986455	+	0.164035i	$0.0524510\pi$
$499$			7.32852i			0.328070i	−0.986455	+	0.164035i	$0.947549\pi$
$500$		0			0
$501$	−10.5326	−	6.08101i	−0.470563	−	0.271679i
$502$		0			0
$503$	−10.6413	+	18.4312i	−0.474470	+	0.821807i	−0.999573	−	0.0292322i	$-0.990694\pi$
$503$	−10.6413	+	18.4312i	−0.474470	+	0.821807i	0.525102	+	0.851039i	$0.324027\pi$
$504$		0			0
$505$	−3.14723	+	1.81705i	−0.140050	+	0.0808577i
$506$		0			0
$507$	6.62082	−	36.9761i	0.294041	−	1.64217i
$508$		0			0
$509$	15.4287	−	8.90778i	0.683867	−	0.394831i	−0.117444	−	0.993080i	$-0.537470\pi$
$509$	15.4287	−	8.90778i	0.683867	−	0.394831i	0.801310	+	0.598249i	$0.204137\pi$
$510$		0			0
$511$	−7.09236	+	12.2843i	−0.313747	+	0.543427i
$512$		0			0
$513$	2.81644	+	1.62607i	0.124349	+	0.0717929i
$514$		0			0
$515$			1.64286i			0.0723932i
$516$		0			0
$517$	4.66564	+	8.08113i	0.205195	+	0.355407i
$518$		0			0
$519$	−13.1510			−0.577266
$520$		0			0
$521$	44.1705			1.93514			0.967572	−	0.252595i	$-0.0812840\pi$
$521$	44.1705			1.93514			0.967572	+	0.252595i	$0.0812840\pi$
$522$		0			0
$523$	7.10525	+	12.3067i	0.310691	+	0.538133i	0.978512	−	0.206189i	$-0.0661062\pi$
$523$	7.10525	+	12.3067i	0.310691	+	0.538133i	−0.667821	+	0.744322i	$0.732773\pi$
$524$		0			0
$525$		−	24.6414i		−	1.07544i
$526$		0			0
$527$	−3.39947	−	1.96268i	−0.148083	−	0.0854958i
$528$		0			0
$529$	−17.5006	+	30.3120i	−0.760897	+	1.31791i
$530$		0			0
$531$	−26.0791	+	15.0568i	−1.13174	+	0.653408i
$532$		0			0
$533$	2.27362	+	12.9949i	0.0984815	+	0.562870i
$534$		0			0
$535$	−1.08780	+	0.628043i	−0.0470298	+	0.0271526i
$536$		0			0
$537$	−26.1669	+	45.3223i	−1.12918	+	1.95580i
$538$		0			0
$539$	3.44474	+	1.98882i	0.148375	+	0.0856646i
$540$		0			0
$541$		−	25.6917i		−	1.10457i	−0.833654	−	0.552287i	$-0.813755\pi$
$541$		−	25.6917i		−	1.10457i	0.833654	−	0.552287i	$-0.186245\pi$
$542$		0			0
$543$	−26.8934	−	46.5807i	−1.15410	−	1.99897i
$544$		0			0
$545$	4.71004			0.201756
$546$		0			0
$547$	−32.3397			−1.38275			−0.691373	−	0.722498i	$-0.742994\pi$
$547$	−32.3397			−1.38275			−0.691373	+	0.722498i	$0.742994\pi$
$548$		0			0
$549$	28.2223	+	48.8824i	1.20450	+	2.08625i
$550$		0			0
$551$			2.82619i			0.120400i
$552$		0			0
$553$	−9.26531	−	5.34933i	−0.394001	−	0.227477i
$554$		0			0
$555$	−3.84755	+	6.66415i	−0.163319	+	0.282877i
$556$		0			0
$557$	34.0283	−	19.6463i	1.44183	−	0.832439i	0.443855	−	0.896099i	$-0.353611\pi$
$557$	34.0283	−	19.6463i	1.44183	−	0.832439i	0.997972	+	0.0636597i	$0.0202772\pi$
$558$		0			0
$559$	−14.8366	−	17.7291i	−0.627521	−	0.749863i
$560$		0			0
$561$	11.9892	−	6.92198i	0.506185	−	0.292246i
$562$		0			0
$563$	15.4971	−	26.8418i	0.653125	−	1.13125i	−0.329235	−	0.944248i	$-0.606791\pi$
$563$	15.4971	−	26.8418i	0.653125	−	1.13125i	0.982360	−	0.186998i	$-0.0598759\pi$
$564$		0			0
$565$	−2.20033	−	1.27036i	−0.0925685	−	0.0534444i
$566$		0			0
$567$			6.20409i			0.260547i
$568$		0			0
$569$	−21.7600	−	37.6895i	−0.912229	−	1.58003i	−0.810909	−	0.585173i	$-0.801027\pi$
$569$	−21.7600	−	37.6895i	−0.912229	−	1.58003i	−0.101320	−	0.994854i	$-0.532307\pi$
$570$		0			0
$571$	37.9072			1.58637			0.793183	−	0.608983i	$-0.208422\pi$
$571$	37.9072			1.58637			0.793183	+	0.608983i	$0.208422\pi$
$572$		0			0
$573$	38.1961			1.59566
$574$		0			0
$575$	18.6789	+	32.3528i	0.778963	+	1.34920i
$576$		0			0
$577$			31.6665i			1.31829i	0.752014	+	0.659147i	$0.229082\pi$
$577$			31.6665i			1.31829i	−0.752014	+	0.659147i	$0.770918\pi$
$578$		0			0
$579$	32.0526	+	18.5056i	1.33206	+	0.769066i
$580$		0			0
$581$	12.0054	−	20.7940i	0.498069	−	0.862681i
$582$		0			0
$583$	−5.53539	+	3.19586i	−0.229252	+	0.132359i
$584$		0			0
$585$	4.55290	−	3.81008i	0.188239	−	0.157528i
$586$		0			0
$587$	−7.81817	+	4.51382i	−0.322690	+	0.186305i	−0.652591	−	0.757710i	$-0.726318\pi$
$587$	−7.81817	+	4.51382i	−0.322690	+	0.186305i	0.329901	+	0.944016i	$0.392985\pi$
$588$		0			0
$589$	0.196239	−	0.339895i	0.00808587	−	0.0140051i
$590$		0			0
$591$	47.4029	+	27.3681i	1.94989	+	1.12577i
$592$		0			0
$593$			5.01191i			0.205815i	0.994691	+	0.102907i	$0.0328145\pi$
$593$			5.01191i			0.205815i	−0.994691	+	0.102907i	$0.967185\pi$
$594$		0			0
$595$	1.28186	+	2.22025i	0.0525511	+	0.0910212i
$596$		0			0
$597$	−11.0002			−0.450208
$598$		0			0
$599$	−12.5444			−0.512549			−0.256275	−	0.966604i	$-0.582495\pi$
$599$	−12.5444			−0.512549			−0.256275	+	0.966604i	$0.582495\pi$
$600$		0			0
$601$	−14.8089	−	25.6499i	−0.604070	−	1.04628i	−0.992198	−	0.124674i	$-0.960212\pi$
$601$	−14.8089	−	25.6499i	−0.604070	−	1.04628i	0.388128	−	0.921605i	$-0.373122\pi$
$602$		0			0
$603$		−	64.2420i		−	2.61614i
$604$		0			0
$605$	0.266562	+	0.153900i	0.0108373	+	0.00625691i
$606$		0			0
$607$	−7.12586	+	12.3423i	−0.289230	+	0.500960i	−0.973626	−	0.228150i	$-0.926732\pi$
$607$	−7.12586	+	12.3423i	−0.289230	+	0.500960i	0.684396	+	0.729110i	$0.260066\pi$
$608$		0			0
$609$	−25.6668	+	14.8187i	−1.04007	+	0.600485i
$610$		0			0
$611$	31.6001	+	11.5489i	1.27841	+	0.467218i
$612$		0			0
$613$	−37.2063	+	21.4811i	−1.50275	+	0.867612i	−0.502754	+	0.864430i	$0.667680\pi$
$613$	−37.2063	+	21.4811i	−1.50275	+	0.867612i	−0.999995	+	0.00318243i	$0.998987\pi$
$614$		0			0
$615$	−1.62711	+	2.81823i	−0.0656113	+	0.113642i
$616$		0			0
$617$	−35.8561	−	20.7015i	−1.44351	−	0.833413i	−0.445431	−	0.895316i	$-0.646950\pi$
$617$	−35.8561	−	20.7015i	−1.44351	−	0.833413i	−0.998082	+	0.0619035i	$0.980283\pi$
$618$		0			0
$619$			25.4256i			1.02194i	0.859598	+	0.510970i	$0.170714\pi$
$619$			25.4256i			1.02194i	−0.859598	+	0.510970i	$0.829286\pi$
$620$		0			0
$621$	−25.8520	−	44.7770i	−1.03741	−	1.79684i
$622$		0			0
$623$	−12.0303			−0.481982
$624$		0			0
$625$	23.5879			0.943515
$626$		0			0
$627$	0.692093	+	1.19874i	0.0276395	+	0.0478731i
$628$		0			0
$629$			41.4520i			1.65280i
$630$		0			0
$631$	41.4761	+	23.9462i	1.65114	+	0.953284i	0.976606	+	0.215036i	$0.0689869\pi$
$631$	41.4761	+	23.9462i	1.65114	+	0.953284i	0.674530	+	0.738248i	$0.264346\pi$
$632$		0			0
$633$	25.5466	−	44.2480i	1.01538	−	1.75870i
$634$		0			0
$635$	1.45014	−	0.837241i	0.0575472	−	0.0332249i
$636$		0			0
$637$	14.1270	−	2.47170i	0.559732	−	0.0979324i
$638$		0			0
$639$	−13.5290	+	7.81094i	−0.535197	+	0.308996i
$640$		0			0
$641$	−14.8741	+	25.7628i	−0.587494	+	1.01757i	0.407066	+	0.913399i	$0.366552\pi$
$641$	−14.8741	+	25.7628i	−0.587494	+	1.01757i	−0.994560	+	0.104170i	$0.966781\pi$
$642$		0			0
$643$	15.6273	+	9.02245i	0.616282	+	0.355811i	0.775420	−	0.631446i	$-0.217538\pi$
$643$	15.6273	+	9.02245i	0.616282	+	0.355811i	−0.159138	+	0.987256i	$0.550872\pi$
$644$		0			0
$645$		−	5.70268i		−	0.224543i
$646$		0			0
$647$	9.64436	+	16.7045i	0.379159	+	0.656722i	0.990940	−	0.134305i	$-0.0428801\pi$
$647$	9.64436	+	16.7045i	0.379159	+	0.656722i	−0.611781	+	0.791027i	$0.709547\pi$
$648$		0			0
$649$	−5.62922			−0.220966
$650$		0			0
$651$	4.11579			0.161311
$652$		0			0
$653$	−17.3291	−	30.0148i	−0.678138	−	1.17457i	−0.975541	−	0.219818i	$-0.929454\pi$
$653$	−17.3291	−	30.0148i	−0.678138	−	1.17457i	0.297403	−	0.954752i	$-0.403880\pi$
$654$		0			0
$655$		−	3.54645i		−	0.138571i
$656$		0			0
$657$	37.8000	+	21.8238i	1.47472	+	0.851429i
$658$		0			0
$659$	5.73810	−	9.93869i	0.223525	−	0.387156i	−0.732351	−	0.680927i	$-0.761577\pi$
$659$	5.73810	−	9.93869i	0.223525	−	0.387156i	0.955876	+	0.293771i	$0.0949103\pi$
$660$		0			0
$661$	−6.47640	+	3.73915i	−0.251903	+	0.145436i	−0.620635	−	0.784099i	$-0.713125\pi$
$661$	−6.47640	+	3.73915i	−0.251903	+	0.145436i	0.368732	+	0.929536i	$0.379792\pi$
$662$		0			0
$663$	17.1340	−	46.8822i	0.665430	−	1.82075i
$664$		0			0
$665$	−0.221991	+	0.128167i	−0.00860845	+	0.00497009i
$666$		0			0
$667$	22.4660	−	38.9123i	0.869889	−	1.50669i
$668$		0			0
$669$	3.48116	+	2.00985i	0.134590	+	0.0777053i
$670$		0			0
$671$			10.5514i			0.407331i
$672$		0			0
$673$	−18.7008	−	32.3908i	−0.720863	−	1.24857i	−0.960654	−	0.277747i	$-0.910412\pi$
$673$	−18.7008	−	32.3908i	−0.720863	−	1.24857i	0.239791	−	0.970825i	$-0.422921\pi$
$674$		0			0
$675$	−33.3018			−1.28179
$676$		0			0
$677$	24.2911			0.933584			0.466792	−	0.884367i	$-0.345410\pi$
$677$	24.2911			0.933584			0.466792	+	0.884367i	$0.345410\pi$
$678$		0			0
$679$	−7.16952	−	12.4180i	−0.275141	−	0.476558i
$680$		0			0
$681$			51.3322i			1.96706i
$682$		0			0
$683$	−31.6258	−	18.2592i	−1.21013	−	0.698667i	−0.247340	−	0.968929i	$-0.579556\pi$
$683$	−31.6258	−	18.2592i	−1.21013	−	0.698667i	−0.962787	+	0.270262i	$0.912890\pi$
$684$		0			0
$685$	2.63902	−	4.57091i	0.100832	−	0.174646i
$686$		0			0
$687$	13.2503	−	7.65009i	0.505532	−	0.291869i
$688$		0			0
$689$	−7.91073	+	21.6454i	−0.301375	+	0.824624i
$690$		0			0
$691$	33.2386	−	19.1903i	1.26446	−	0.730035i	0.290524	−	0.956868i	$-0.406170\pi$
$691$	33.2386	−	19.1903i	1.26446	−	0.730035i	0.973934	+	0.226833i	$0.0728371\pi$
$692$		0			0
$693$	−4.65003	+	8.05410i	−0.176640	+	0.305950i
$694$		0			0
$695$	−0.285176	−	0.164647i	−0.0108174	−	0.00624540i
$696$		0			0
$697$			17.5298i			0.663990i
$698$		0			0
$699$	5.49014	+	9.50919i	0.207656	+	0.359671i
$700$		0			0
$701$	−8.36971			−0.316119			−0.158060	−	0.987430i	$-0.550524\pi$
$701$	−8.36971			−0.316119			−0.158060	+	0.987430i	$0.550524\pi$
$702$		0			0
$703$	−4.14458			−0.156316
$704$		0			0
$705$	4.14963	+	7.18737i	0.156284	+	0.270692i
$706$		0			0
$707$		−	20.5259i		−	0.771956i
$708$		0			0
$709$	−10.8124	−	6.24253i	−0.406067	−	0.234443i	0.283031	−	0.959111i	$-0.408660\pi$
$709$	−10.8124	−	6.24253i	−0.406067	−	0.234443i	−0.689099	+	0.724668i	$0.741993\pi$
$710$		0			0
$711$	−16.4604	+	28.5102i	−0.617312	+	1.06922i
$712$		0			0
$713$	−5.40380	+	3.11989i	−0.202374	+	0.116841i
$714$		0			0
$715$	1.09318	−	0.191266i	0.0408826	−	0.00715295i
$716$		0			0
$717$	−51.5516	+	29.7633i	−1.92523	+	1.11153i
$718$		0			0
$719$	1.33406	−	2.31066i	0.0497521	−	0.0861731i	−0.840077	−	0.542467i	$-0.817490\pi$
$719$	1.33406	−	2.31066i	0.0497521	−	0.0861731i	0.889829	+	0.456294i	$0.150824\pi$
$720$		0			0
$721$	−8.03594	−	4.63955i	−0.299274	−	0.172786i
$722$		0			0
$723$		−	3.59475i		−	0.133690i
$724$		0			0
$725$	−14.4700	−	25.0628i	−0.537404	−	0.930811i
$726$		0			0
$727$	21.6435			0.802715			0.401357	−	0.915922i	$-0.368539\pi$
$727$	21.6435			0.802715			0.401357	+	0.915922i	$0.368539\pi$
$728$		0			0
$729$	−39.7609			−1.47263
$730$		0			0
$731$	−15.3596	−	26.6037i	−0.568096	−	0.983972i
$732$		0			0
$733$		−	4.35574i		−	0.160883i	−0.996759	−	0.0804415i	$-0.974367\pi$
$733$		−	4.35574i		−	0.160883i	0.996759	−	0.0804415i	$-0.0256330\pi$
$734$		0			0
$735$	3.06376	+	1.76886i	0.113008	+	0.0652454i
$736$		0			0
$737$	6.00448	−	10.4001i	0.221178	−	0.383091i
$738$		0			0
$739$	−24.2362	+	13.9928i	−0.891544	+	0.514733i	−0.874447	−	0.485121i	$-0.838776\pi$
$739$	−24.2362	+	13.9928i	−0.891544	+	0.514733i	−0.0170965	+	0.999854i	$0.505442\pi$
$740$		0			0
$741$	4.68751	+	1.71314i	0.172200	+	0.0629339i
$742$		0			0
$743$	18.4864	−	10.6731i	0.678201	−	0.391559i	−0.120976	−	0.992655i	$-0.538602\pi$
$743$	18.4864	−	10.6731i	0.678201	−	0.391559i	0.799177	+	0.601096i	$0.205269\pi$
$744$		0			0
$745$	−2.00774	+	3.47751i	−0.0735580	+	0.127406i
$746$		0			0
$747$	−63.9851	−	36.9418i	−2.34109	−	1.35163i
$748$		0			0
$749$		−	7.09454i		−	0.259229i
$750$		0			0
$751$	−5.09422	−	8.82345i	−0.185891	−	0.321972i	0.757985	−	0.652271i	$-0.226184\pi$
$751$	−5.09422	−	8.82345i	−0.185891	−	0.321972i	−0.943876	+	0.330299i	$0.892850\pi$
$752$		0			0
$753$	−32.9644			−1.20129
$754$		0			0
$755$	4.24684			0.154558
$756$		0			0
$757$	8.43232	+	14.6052i	0.306478	+	0.530835i	0.977589	−	0.210521i	$-0.0675162\pi$
$757$	8.43232	+	14.6052i	0.306478	+	0.530835i	−0.671112	+	0.741356i	$0.734183\pi$
$758$		0			0
$759$		−	22.0064i		−	0.798782i
$760$		0			0
$761$	24.5801	+	14.1913i	0.891029	+	0.514436i	0.874279	−	0.485424i	$-0.161335\pi$
$761$	24.5801	+	14.1913i	0.891029	+	0.514436i	0.0167499	+	0.999860i	$0.494668\pi$
$762$		0			0
$763$	−13.3015	+	23.0388i	−0.481546	+	0.834061i
$764$		0			0
$765$	6.83190	−	3.94440i	0.247008	−	0.142610i
$766$		0			0
$767$	−15.5652	+	13.0257i	−0.562028	+	0.470332i
$768$		0			0
$769$	0.944544	−	0.545333i	0.0340611	−	0.0196652i	−0.482873	−	0.875691i	$-0.660407\pi$
$769$	0.944544	−	0.545333i	0.0340611	−	0.0196652i	0.516934	+	0.856025i	$0.327073\pi$
$770$		0			0
$771$	13.8249	−	23.9455i	0.497893	−	0.862376i
$772$		0			0
$773$	−10.2427	−	5.91362i	−0.368404	−	0.212698i	0.304357	−	0.952558i	$-0.401558\pi$
$773$	−10.2427	−	5.91362i	−0.368404	−	0.212698i	−0.672761	+	0.739860i	$0.734892\pi$
$774$		0			0
$775$			4.01895i			0.144365i
$776$		0			0
$777$	−21.7315	−	37.6400i	−0.779612	−	1.35033i
$778$		0			0
$779$	−1.75272			−0.0627977
$780$		0			0
$781$	−2.92025			−0.104495
$782$		0			0
$783$	20.0269	+	34.6876i	0.715703	+	1.23963i
$784$		0			0
$785$		−	2.06147i		−	0.0735771i
$786$		0			0
$787$	−11.0172	−	6.36081i	−0.392722	−	0.226738i	0.290617	−	0.956840i	$-0.406140\pi$
$787$	−11.0172	−	6.36081i	−0.392722	−	0.226738i	−0.683339	+	0.730101i	$0.739473\pi$
$788$		0			0
$789$	1.59018	−	2.75428i	0.0566120	−	0.0980549i
$790$		0			0
$791$	12.4277	−	7.17516i	0.441880	−	0.255119i
$792$		0			0
$793$	24.4153	+	29.1753i	0.867013	+	1.03605i
$794$		0			0
$795$	−4.92319	+	2.84240i	−0.174607	+	0.100810i
$796$		0			0
$797$	9.44538	−	16.3599i	0.334573	−	0.579497i	−0.648830	−	0.760933i	$-0.724741\pi$
$797$	9.44538	−	16.3599i	0.334573	−	0.579497i	0.983403	+	0.181437i	$0.0580747\pi$
$798$		0			0
$799$	38.7170	+	22.3533i	1.36971	+	0.790802i
$800$		0			0
$801$			37.0182i			1.30797i
$802$		0			0
$803$	4.07960	+	7.06608i	0.143966	+	0.249357i
$804$		0			0
$805$	4.07530			0.143635
$806$		0			0
$807$	−40.6406			−1.43062
$808$		0			0
$809$	−0.00458033	−	0.00793336i	−0.000161036	−	0.000278922i	0.865945	−	0.500139i	$-0.166718\pi$
$809$	−0.00458033	−	0.00793336i	−0.000161036	−	0.000278922i	−0.866106	+	0.499861i	$0.833385\pi$
$810$		0			0
$811$		−	2.69134i		−	0.0945059i	−0.998883	−	0.0472529i	$-0.984953\pi$
$811$		−	2.69134i		−	0.0945059i	0.998883	−	0.0472529i	$-0.0150467\pi$
$812$		0			0
$813$	−71.1007	−	41.0500i	−2.49361	−	1.43969i
$814$		0			0
$815$	−0.191529	+	0.331738i	−0.00670897	+	0.0116203i
$816$		0			0
$817$	2.65996	−	1.53573i	0.0930603	−	0.0537284i
$818$		0			0
$819$	5.77905	+	33.0301i	0.201936	+	1.15417i
$820$		0			0
$821$	−34.1734	+	19.7300i	−1.19266	+	0.688583i	−0.958909	−	0.283713i	$-0.908434\pi$
$821$	−34.1734	+	19.7300i	−1.19266	+	0.688583i	−0.233752	+	0.972296i	$0.575100\pi$
$822$		0			0
$823$	−12.9084	+	22.3581i	−0.449960	+	0.779354i	−0.998383	−	0.0568473i	$-0.981895\pi$
$823$	−12.9084	+	22.3581i	−0.449960	+	0.779354i	0.548423	+	0.836201i	$0.315229\pi$
$824$		0			0
$825$	−12.2750	−	7.08700i	−0.427362	−	0.246738i
$826$		0			0
$827$			32.0742i			1.11533i	0.830066	+	0.557665i	$0.188303\pi$
$827$			32.0742i			1.11533i	−0.830066	+	0.557665i	$0.811697\pi$
$828$		0			0
$829$	12.8307	+	22.2235i	0.445629	+	0.771853i	0.998096	−	0.0616825i	$-0.0196466\pi$
$829$	12.8307	+	22.2235i	0.445629	+	0.771853i	−0.552467	+	0.833535i	$0.686313\pi$
$830$		0			0
$831$	−36.8180			−1.27720
$832$		0			0
$833$	19.0571			0.660288
$834$		0			0
$835$	−0.647759	−	1.12195i	−0.0224166	−	0.0388267i
$836$		0			0
$837$		−	5.56232i		−	0.192262i
$838$		0			0
$839$	8.55872	+	4.94138i	0.295480	+	0.170595i	0.640411	−	0.768033i	$-0.278764\pi$
$839$	8.55872	+	4.94138i	0.295480	+	0.170595i	−0.344931	+	0.938628i	$0.612098\pi$
$840$		0			0
$841$	−2.90386	+	5.02963i	−0.100133	+	0.173436i
$842$		0			0
$843$	5.91090	−	3.41266i	0.203582	−	0.117538i
$844$		0			0
$845$	2.58015	−	3.05843i	0.0887598	−	0.105213i
$846$		0			0
$847$	−1.50558	+	0.869246i	−0.0517323	+	0.0298677i
$848$		0			0
$849$	33.2392	−	57.5720i	1.14077	−	1.97586i
$850$		0			0
$851$	57.0644	+	32.9462i	1.95614	+	1.12938i
$852$		0			0
$853$			35.6979i			1.22227i	0.791525	+	0.611136i	$0.209287\pi$
$853$			35.6979i			1.22227i	−0.791525	+	0.611136i	$0.790713\pi$
$854$		0			0
$855$	0.394380	+	0.683087i	0.0134875	+	0.0233611i
$856$		0			0
$857$	14.1382			0.482950			0.241475	−	0.970407i	$-0.422369\pi$
$857$	14.1382			0.482950			0.241475	+	0.970407i	$0.422369\pi$
$858$		0			0
$859$	−27.0352			−0.922429			−0.461215	−	0.887289i	$-0.652586\pi$
$859$	−27.0352			−0.922429			−0.461215	+	0.887289i	$0.652586\pi$
$860$		0			0
$861$	−9.19012	−	15.9177i	−0.313198	−	0.542475i
$862$		0			0
$863$		−	31.0709i		−	1.05767i	−0.848726	−	0.528833i	$-0.822630\pi$
$863$		−	31.0709i		−	1.05767i	0.848726	−	0.528833i	$-0.177370\pi$
$864$		0			0
$865$	−1.21319	−	0.700433i	−0.0412496	−	0.0238154i
$866$		0			0
$867$	8.60231	−	14.8996i	0.292150	−	0.506019i
$868$		0			0
$869$	−5.32951	+	3.07699i	−0.180791	+	0.104380i
$870$		0			0
$871$	−7.46236	−	42.6510i	−0.252852	−	1.44518i
$872$		0			0
$873$	−38.2112	+	22.0613i	−1.29325	+	0.746661i
$874$		0			0
$875$	2.65019	−	4.59026i	0.0895927	−	0.155179i
$876$		0			0
$877$	45.9546	+	26.5319i	1.55178	+	0.895919i	0.997997	+	0.0632553i	$0.0201482\pi$
$877$	45.9546	+	26.5319i	1.55178	+	0.895919i	0.553779	+	0.832663i	$0.313185\pi$
$878$		0			0
$879$			60.4799i			2.03993i
$880$		0			0
$881$	22.1848	+	38.4251i	0.747424	+	1.29458i	0.949054	+	0.315114i	$0.102043\pi$
$881$	22.1848	+	38.4251i	0.747424	+	1.29458i	−0.201630	+	0.979462i	$0.564624\pi$
$882$		0			0
$883$	43.2750			1.45632			0.728160	−	0.685407i	$-0.240376\pi$
$883$	43.2750			1.45632			0.728160	+	0.685407i	$0.240376\pi$
$884$		0			0
$885$	−5.00664			−0.168296
$886$		0			0
$887$	4.74022	+	8.21029i	0.159161	+	0.275675i	0.934566	−	0.355789i	$-0.115788\pi$
$887$	4.74022	+	8.21029i	0.159161	+	0.275675i	−0.775405	+	0.631464i	$0.782454\pi$
$888$		0			0
$889$			9.45770i			0.317201i
$890$		0			0
$891$	3.09055	+	1.78433i	0.103537	+	0.0597773i
$892$		0			0
$893$	−2.23499	+	3.87112i	−0.0747911	+	0.129542i
$894$		0			0
$895$	−4.82780	+	2.78733i	−0.161376	+	0.0931703i
$896$		0			0
$897$	−50.9217	−	60.8494i	−1.70022	−	2.03170i
$898$		0			0
$899$	4.18619	−	2.41690i	0.139617	−	0.0806080i
$900$		0			0
$901$	−15.3115	+	26.5203i	−0.510100	+	0.883519i
$902$		0			0
$903$	27.8942	+	16.1047i	0.928262	+	0.535932i
$904$		0			0
$905$		−	5.72944i		−	0.190453i
$906$		0			0
$907$	2.47445	+	4.28587i	0.0821626	+	0.142310i	0.904179	−	0.427155i	$-0.140484\pi$
$907$	2.47445	+	4.28587i	0.0821626	+	0.142310i	−0.822016	+	0.569464i	$0.807151\pi$
$908$		0			0
$909$	−63.1601			−2.09489
$910$		0			0
$911$	−3.67871			−0.121881			−0.0609406	−	0.998141i	$-0.519410\pi$
$911$	−3.67871			−0.121881			−0.0609406	+	0.998141i	$0.519410\pi$
$912$		0			0
$913$	−6.90565	−	11.9609i	−0.228544	−	0.395849i
$914$		0			0
$915$			9.38440i			0.310239i
$916$		0			0
$917$	17.3472	+	10.0154i	0.572855	+	0.330738i
$918$		0			0
$919$	−9.56128	+	16.5606i	−0.315398	+	0.546285i	−0.979522	−	0.201337i	$-0.935471\pi$
$919$	−9.56128	+	16.5606i	−0.315398	+	0.546285i	0.664124	+	0.747622i	$0.268805\pi$
$920$		0			0
$921$	−35.3842	+	20.4291i	−1.16595	+	0.673161i
$922$		0			0
$923$	−8.07472	+	6.75731i	−0.265783	+	0.222419i
$924$		0			0
$925$	36.7543	−	21.2201i	1.20847	−	0.697713i
$926$		0			0
$927$	−14.2763	+	24.7273i	−0.468896	+	0.812152i
$928$		0			0
$929$	−36.0206	−	20.7965i	−1.18180	−	0.682312i	−0.225369	−	0.974273i	$-0.572359\pi$
$929$	−36.0206	−	20.7965i	−1.18180	−	0.682312i	−0.956430	+	0.291962i	$0.905692\pi$
$930$		0			0
$931$			1.90542i			0.0624475i
$932$		0			0
$933$	23.2452	+	40.2619i	0.761014	+	1.31812i
$934$		0			0
$935$	1.47468			0.0482272
$936$		0			0
$937$	14.1268			0.461503			0.230752	−	0.973013i	$-0.425881\pi$
$937$	14.1268			0.461503			0.230752	+	0.973013i	$0.425881\pi$
$938$		0			0
$939$	42.2886	+	73.2460i	1.38004	+	2.39029i
$940$		0			0
$941$			27.2065i			0.886906i	0.896298	+	0.443453i	$0.146247\pi$
$941$			27.2065i			0.886906i	−0.896298	+	0.443453i	$0.853753\pi$
$942$		0			0
$943$	24.1322	+	13.9327i	0.785853	+	0.453713i
$944$		0			0
$945$	−1.81642	+	3.14613i	−0.0590882	+	0.102344i
$946$		0			0
$947$	−11.2126	+	6.47359i	−0.364360	+	0.210363i	−0.670992	−	0.741465i	$-0.734131\pi$
$947$	−11.2126	+	6.47359i	−0.364360	+	0.210363i	0.306632	+	0.951828i	$0.400798\pi$
$948$		0			0
$949$	27.6309	+	10.0983i	0.896939	+	0.327804i
$950$		0			0
$951$	21.6084	−	12.4756i	0.700701	−	0.404550i
$952$		0			0
$953$	11.8492	−	20.5234i	0.383833	−	0.664818i	−0.607774	−	0.794110i	$-0.707937\pi$
$953$	11.8492	−	20.5234i	0.383833	−	0.664818i	0.991607	+	0.129292i	$0.0412705\pi$
$954$		0			0
$955$	3.52360	+	2.03435i	0.114021	+	0.0658301i
$956$		0			0
$957$			17.0478i			0.551077i
$958$		0			0
$959$	14.9055	+	25.8171i	0.481325	+	0.833679i
$960$		0			0
$961$	30.3287			0.978346
$962$		0			0
$963$	−21.8305			−0.703480
$964$		0			0
$965$	1.97124	+	3.41429i	0.0634566	+	0.109910i
$966$		0			0
$967$			27.8864i			0.896766i	0.893842	+	0.448383i	$0.148000\pi$
$967$			27.8864i			0.896766i	−0.893842	+	0.448383i	$0.852000\pi$
$968$		0			0
$969$	5.74322	+	3.31585i	0.184499	+	0.106520i
$970$		0			0
$971$	11.3442	−	19.6487i	0.364052	−	0.630556i	−0.624572	−	0.780968i	$-0.714726\pi$
$971$	11.3442	−	19.6487i	0.364052	−	0.630556i	0.988624	+	0.150411i	$0.0480597\pi$
$972$		0			0
$973$	1.61072	−	0.929947i	0.0516372	−	0.0298127i
$974$		0			0
$975$	−50.3404	+	8.80770i	−1.61218	+	0.282072i
$976$		0			0
$977$	23.1871	−	13.3871i	0.741821	−	0.428290i	−0.0809101	−	0.996721i	$-0.525783\pi$
$977$	23.1871	−	13.3871i	0.741821	−	0.428290i	0.822731	+	0.568431i	$0.192449\pi$
$978$		0			0
$979$	−3.45997	+	5.99284i	−0.110581	+	0.191532i
$980$		0			0
$981$	70.8926	+	40.9298i	2.26343	+	1.30679i
$982$		0			0
$983$		−	48.1994i		−	1.53732i	−0.639656	−	0.768662i	$-0.720923\pi$
$983$		−	48.1994i		−	1.53732i	0.639656	−	0.768662i	$-0.279077\pi$
$984$		0			0
$985$	2.91529	+	5.04943i	0.0928888	+	0.160888i
$986$		0			0
$987$	−46.8753			−1.49206
$988$		0			0
$989$	−48.8314			−1.55275
$990$		0			0
$991$	1.44490	+	2.50265i	0.0458989	+	0.0794992i	0.888062	−	0.459723i	$-0.152051\pi$
$991$	1.44490	+	2.50265i	0.0458989	+	0.0794992i	−0.842163	+	0.539223i	$0.818718\pi$
$992$		0			0
$993$		−	70.2278i		−	2.22861i
$994$		0			0
$995$	−1.01477	−	0.585879i	−0.0321705	−	0.0185736i
$996$		0			0
$997$	−2.89368	+	5.01199i	−0.0916437	+	0.158731i	−0.908203	−	0.418530i	$-0.862545\pi$
$997$	−2.89368	+	5.01199i	−0.0916437	+	0.158731i	0.816559	+	0.577262i	$0.195879\pi$
$998$		0			0
$999$	−50.8689	+	29.3692i	−1.60942	+	0.929200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.p.a.309.11	✓	24
13.2	odd	12		7436.2.a.v.1.2		12
13.4	even	6	inner	572.2.p.a.485.11	yes	24
13.11	odd	12		7436.2.a.u.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.p.a.309.11	✓	24	1.1	even	1	trivial
572.2.p.a.485.11	yes	24	13.4	even	6	inner
7436.2.a.u.1.2		12	13.11	odd	12
7436.2.a.v.1.2		12	13.2	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)

\(f(q)\)	\(=\)	\(q+(1.44478 + 2.50242i) q^{3} +0.307799i q^{5} +(-1.50558 - 0.869246i) q^{7} +(-2.67475 + 4.63280i) q^{9} +O(q^{10})\)	\(q+(1.44478 + 2.50242i) q^{3} +0.307799i q^{5} +(-1.50558 - 0.869246i) q^{7} +(-2.67475 + 4.63280i) q^{9} +(-0.866025 + 0.500000i) q^{11} +(-1.23765 + 3.38648i) q^{13} +(-0.770245 + 0.444701i) q^{15} +(-2.39552 + 4.14916i) q^{17} +(-0.414854 - 0.239516i) q^{19} -5.02346i q^{21} +(3.80793 + 6.59553i) q^{23} +4.90526 q^{25} -6.78900 q^{27} +(-2.94990 - 5.10938i) q^{29} +0.819313i q^{31} +(-2.50242 - 1.44478i) q^{33} +(0.267553 - 0.463416i) q^{35} +(7.49284 - 4.32599i) q^{37} +(-10.2625 + 1.79556i) q^{39} +(3.16868 - 1.82944i) q^{41} +(-3.20591 + 5.55279i) q^{43} +(-1.42597 - 0.823287i) q^{45} -9.33128i q^{47} +(-1.98882 - 3.44474i) q^{49} -13.8440 q^{51} +6.39172 q^{53} +(-0.153900 - 0.266562i) q^{55} -1.38419i q^{57} +(4.87505 + 2.81461i) q^{59} +(5.27568 - 9.13775i) q^{61} +(8.05410 - 4.65003i) q^{63} +(-1.04236 - 0.380949i) q^{65} +(-10.4001 + 6.00448i) q^{67} +(-11.0032 + 19.0581i) q^{69} +(2.52901 + 1.46013i) q^{71} -8.15921i q^{73} +(7.08700 + 12.2750i) q^{75} +1.73849 q^{77} +6.15399 q^{79} +(-1.78433 - 3.09055i) q^{81} +13.8113i q^{83} +(-1.27711 - 0.737340i) q^{85} +(8.52389 - 14.7638i) q^{87} +(5.99284 - 3.45997i) q^{89} +(4.80707 - 4.02278i) q^{91} +(-2.05027 + 1.18372i) q^{93} +(0.0737228 - 0.127692i) q^{95} +(7.14295 + 4.12399i) q^{97} -5.34950i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \) 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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