LMFDB - Embedded newform 840.2.da.a.89.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(89,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 3, 5]))

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

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

chi := DirichletCharacter("840.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.da (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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.12
Character	$\chi$	$=$	840.89
Dual form			840.2.da.a.689.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.381836 + 1.68944i) q^{3} +(1.27267 - 1.83856i) q^{5} +(1.96308 + 1.77379i) q^{7} +(-2.70840 - 1.29018i) q^{9} +O(q^{10})$	\(q+(-0.381836 + 1.68944i) q^{3} +(1.27267 - 1.83856i) q^{5} +(1.96308 + 1.77379i) q^{7} +(-2.70840 - 1.29018i) q^{9} +(3.95951 - 2.28602i) q^{11} -1.57517 q^{13} +(2.62018 + 2.85213i) q^{15} +(4.06751 - 2.34838i) q^{17} +(0.0201141 + 0.0116129i) q^{19} +(-3.74628 + 2.63920i) q^{21} +(-0.0964144 + 0.166995i) q^{23} +(-1.76060 - 4.67977i) q^{25} +(3.21384 - 4.08305i) q^{27} +4.98429i q^{29} +(5.92678 - 3.42183i) q^{31} +(2.35022 + 7.56223i) q^{33} +(5.75957 - 1.35178i) q^{35} +(1.79834 + 1.03827i) q^{37} +(0.601455 - 2.66115i) q^{39} -5.85645 q^{41} +6.60899i q^{43} +(-5.81898 + 3.33759i) q^{45} +(4.93457 + 2.84898i) q^{47} +(0.707338 + 6.96417i) q^{49} +(2.41432 + 7.76850i) q^{51} +(-5.13922 - 8.90140i) q^{53} +(0.836172 - 10.1892i) q^{55} +(-0.0272995 + 0.0295473i) q^{57} +(-1.24724 - 2.16029i) q^{59} +(8.02451 + 4.63295i) q^{61} +(-3.02830 - 7.33685i) q^{63} +(-2.00468 + 2.89604i) q^{65} +(-5.87567 + 3.39232i) q^{67} +(-0.245313 - 0.226651i) q^{69} +13.0928i q^{71} +(7.23510 + 12.5316i) q^{73} +(8.57845 - 1.18753i) q^{75} +(11.8277 + 2.53570i) q^{77} +(6.60158 - 11.4343i) q^{79} +(5.67090 + 6.98863i) q^{81} +1.02664i q^{83} +(0.858979 - 10.4671i) q^{85} +(-8.42065 - 1.90318i) q^{87} +(-0.594890 + 1.03038i) q^{89} +(-3.09218 - 2.79402i) q^{91} +(3.51791 + 11.3195i) q^{93} +(0.0469496 - 0.0222016i) q^{95} +0.721802 q^{97} +(-13.6733 + 1.08301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{3} - 3 q^{5} - q^{9}+O(q^{10}) $ 48 * q - 3 * q^3 - 3 * q^5 - q^9	$ 48 q - 3 q^{3} - 3 q^{5} - q^{9} - 14 q^{15} + 5 q^{21} - 2 q^{23} + q^{25} + 6 q^{31} - 24 q^{33} + 4 q^{35} + 2 q^{39} - 3 q^{45} + 12 q^{51} + 6 q^{53} - 20 q^{57} + 18 q^{61} + 26 q^{63} - 10 q^{65} - 3 q^{75} - 2 q^{77} + 2 q^{79} - 9 q^{81} + 15 q^{87} + 24 q^{91} - 8 q^{93} - 6 q^{95} - 12 q^{99}+O(q^{100}) $ 48 * q - 3 * q^3 - 3 * q^5 - q^9 - 14 * q^15 + 5 * q^21 - 2 * q^23 + q^25 + 6 * q^31 - 24 * q^33 + 4 * q^35 + 2 * q^39 - 3 * q^45 + 12 * q^51 + 6 * q^53 - 20 * q^57 + 18 * q^61 + 26 * q^63 - 10 * q^65 - 3 * q^75 - 2 * q^77 + 2 * q^79 - 9 * q^81 + 15 * q^87 + 24 * q^91 - 8 * q^93 - 6 * q^95 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.381836	+	1.68944i	−0.220453	+	0.975398i
$3$	−0.381836	+	1.68944i	−0.220453	+	0.975398i
$4$		0			0
$5$	1.27267	−	1.83856i	0.569157	−	0.822229i
$5$	1.27267	−	1.83856i	0.569157	−	0.822229i
$6$		0			0
$7$	1.96308	+	1.77379i	0.741973	+	0.670430i
$7$	1.96308	+	1.77379i	0.741973	+	0.670430i
$8$		0			0
$9$	−2.70840	−	1.29018i	−0.902801	−	0.430058i
$10$		0			0
$11$	3.95951	−	2.28602i	1.19384	−	0.689262i	0.234663	−	0.972077i	$-0.424601\pi$
$11$	3.95951	−	2.28602i	1.19384	−	0.689262i	0.959175	+	0.282815i	$0.0912681\pi$
$12$		0			0
$13$	−1.57517			−0.436873			−0.218437	−	0.975851i	$-0.570096\pi$
$13$	−1.57517			−0.436873			−0.218437	+	0.975851i	$0.570096\pi$
$14$		0			0
$15$	2.62018	+	2.85213i	0.676528	+	0.736417i
$16$		0			0
$17$	4.06751	−	2.34838i	0.986516	−	0.569565i	0.0822846	−	0.996609i	$-0.473778\pi$
$17$	4.06751	−	2.34838i	0.986516	−	0.569565i	0.904231	+	0.427044i	$0.140445\pi$
$18$		0			0
$19$	0.0201141	+	0.0116129i	0.00461449	+	0.00266418i	0.502305	−	0.864690i	$-0.332485\pi$
$19$	0.0201141	+	0.0116129i	0.00461449	+	0.00266418i	−0.497691	+	0.867354i	$0.665819\pi$
$20$		0			0
$21$	−3.74628	+	2.63920i	−0.817506	+	0.575921i
$22$		0			0
$23$	−0.0964144	+	0.166995i	−0.0201038	+	0.0348208i	−0.875902	−	0.482489i	$-0.839733\pi$
$23$	−0.0964144	+	0.166995i	−0.0201038	+	0.0348208i	0.855798	+	0.517309i	$0.173066\pi$
$24$		0			0
$25$	−1.76060	−	4.67977i	−0.352121	−	0.935955i
$26$		0			0
$27$	3.21384	−	4.08305i	0.618503	−	0.785782i
$28$		0			0
$29$			4.98429i			0.925560i	0.886473	+	0.462780i	$0.153148\pi$
$29$			4.98429i			0.925560i	−0.886473	+	0.462780i	$0.846852\pi$
$30$		0			0
$31$	5.92678	−	3.42183i	1.06448	−	0.614579i	0.137813	−	0.990458i	$-0.455993\pi$
$31$	5.92678	−	3.42183i	1.06448	−	0.614579i	0.926668	+	0.375880i	$0.122659\pi$
$32$		0			0
$33$	2.35022	+	7.56223i	0.409120	+	1.31642i
$34$		0			0
$35$	5.75957	−	1.35178i	0.973546	−	0.228492i
$36$		0			0
$37$	1.79834	+	1.03827i	0.295645	+	0.170691i	0.640485	−	0.767971i	$-0.278733\pi$
$37$	1.79834	+	1.03827i	0.295645	+	0.170691i	−0.344840	+	0.938662i	$0.612067\pi$
$38$		0			0
$39$	0.601455	−	2.66115i	0.0963099	−	0.426125i
$40$		0			0
$41$	−5.85645			−0.914624			−0.457312	−	0.889306i	$-0.651188\pi$
$41$	−5.85645			−0.914624			−0.457312	+	0.889306i	$0.651188\pi$
$42$		0			0
$43$			6.60899i			1.00786i	0.863744	+	0.503931i	$0.168113\pi$
$43$			6.60899i			1.00786i	−0.863744	+	0.503931i	$0.831887\pi$
$44$		0			0
$45$	−5.81898	+	3.33759i	−0.867442	+	0.497538i
$46$		0			0
$47$	4.93457	+	2.84898i	0.719781	+	0.415566i	0.814672	−	0.579922i	$-0.196917\pi$
$47$	4.93457	+	2.84898i	0.719781	+	0.415566i	−0.0948910	+	0.995488i	$0.530250\pi$
$48$		0			0
$49$	0.707338	+	6.96417i	0.101048	+	0.994882i
$50$		0			0
$51$	2.41432	+	7.76850i	0.338072	+	1.08781i
$52$		0			0
$53$	−5.13922	−	8.90140i	−0.705927	−	1.22270i	−0.966356	−	0.257208i	$-0.917197\pi$
$53$	−5.13922	−	8.90140i	−0.705927	−	1.22270i	0.260429	−	0.965493i	$-0.416136\pi$
$54$		0			0
$55$	0.836172	−	10.1892i	0.112749	−	1.37391i
$56$		0			0
$57$	−0.0272995	+	0.0295473i	−0.00361591	+	0.00391364i
$58$		0			0
$59$	−1.24724	−	2.16029i	−0.162377	−	0.281246i	0.773343	−	0.633987i	$-0.218583\pi$
$59$	−1.24724	−	2.16029i	−0.162377	−	0.281246i	−0.935721	+	0.352741i	$0.885250\pi$
$60$		0			0
$61$	8.02451	+	4.63295i	1.02743	+	0.593189i	0.916248	−	0.400611i	$-0.131202\pi$
$61$	8.02451	+	4.63295i	1.02743	+	0.593189i	0.111185	+	0.993800i	$0.464535\pi$
$62$		0			0
$63$	−3.02830	−	7.33685i	−0.381530	−	0.924356i
$64$		0			0
$65$	−2.00468	+	2.89604i	−0.248649	+	0.359210i
$66$		0			0
$67$	−5.87567	+	3.39232i	−0.717827	+	0.414438i	−0.813952	−	0.580932i	$-0.802688\pi$
$67$	−5.87567	+	3.39232i	−0.717827	+	0.414438i	0.0961254	+	0.995369i	$0.469355\pi$
$68$		0			0
$69$	−0.245313	−	0.226651i	−0.0295322	−	0.0272855i
$70$		0			0
$71$			13.0928i			1.55383i	0.629603	+	0.776917i	$0.283218\pi$
$71$			13.0928i			1.55383i	−0.629603	+	0.776917i	$0.716782\pi$
$72$		0			0
$73$	7.23510	+	12.5316i	0.846804	+	1.46671i	0.884045	+	0.467402i	$0.154810\pi$
$73$	7.23510	+	12.5316i	0.846804	+	1.46671i	−0.0372407	+	0.999306i	$0.511857\pi$
$74$		0			0
$75$	8.57845	−	1.18753i	0.990554	−	0.137124i
$76$		0			0
$77$	11.8277	+	2.53570i	1.34790	+	0.288970i
$78$		0			0
$79$	6.60158	−	11.4343i	0.742736	−	1.28646i	−0.208509	−	0.978020i	$-0.566861\pi$
$79$	6.60158	−	11.4343i	0.742736	−	1.28646i	0.951245	−	0.308436i	$-0.0998055\pi$
$80$		0			0
$81$	5.67090	+	6.98863i	0.630100	+	0.776514i
$82$		0			0
$83$			1.02664i			0.112688i	0.998411	+	0.0563442i	$0.0179444\pi$
$83$			1.02664i			0.112688i	−0.998411	+	0.0563442i	$0.982056\pi$
$84$		0			0
$85$	0.858979	−	10.4671i	0.0931694	−	1.13531i
$86$		0			0
$87$	−8.42065	−	1.90318i	−0.902789	−	0.204042i
$88$		0			0
$89$	−0.594890	+	1.03038i	−0.0630583	+	0.109220i	−0.895831	−	0.444395i	$-0.853419\pi$
$89$	−0.594890	+	1.03038i	−0.0630583	+	0.109220i	0.832773	+	0.553615i	$0.186752\pi$
$90$		0			0
$91$	−3.09218	−	2.79402i	−0.324148	−	0.292893i
$92$		0			0
$93$	3.51791	+	11.3195i	0.364791	+	1.17378i
$94$		0			0
$95$	0.0469496	−	0.0222016i	0.00481693	−	0.00227783i
$96$		0			0
$97$	0.721802			0.0732879			0.0366440	−	0.999328i	$-0.488333\pi$
$97$	0.721802			0.0732879			0.0366440	+	0.999328i	$0.488333\pi$
$98$		0			0
$99$	−13.6733	+	1.08301i	−1.37422	+	0.108847i
$100$		0			0
$101$	−7.55211	−	13.0806i	−0.751463	−	1.30157i	−0.947114	−	0.320899i	$-0.896015\pi$
$101$	−7.55211	−	13.0806i	−0.751463	−	1.30157i	0.195650	−	0.980674i	$-0.437318\pi$
$102$		0			0
$103$	−2.17456	+	3.76645i	−0.214266	+	0.371120i	−0.953045	−	0.302828i	$-0.902069\pi$
$103$	−2.17456	+	3.76645i	−0.214266	+	0.371120i	0.738779	+	0.673947i	$0.235403\pi$
$104$		0			0
$105$	0.0845340	+	10.2466i	0.00824968	+	0.999966i
$106$		0			0
$107$	−6.53479	+	11.3186i	−0.631742	+	1.09421i	0.355453	+	0.934694i	$0.384327\pi$
$107$	−6.53479	+	11.3186i	−0.631742	+	1.09421i	−0.987195	+	0.159516i	$0.949007\pi$
$108$		0			0
$109$	−3.63655	−	6.29868i	−0.348318	−	0.603304i	0.637633	−	0.770340i	$-0.279914\pi$
$109$	−3.63655	−	6.29868i	−0.348318	−	0.603304i	−0.985951	+	0.167036i	$0.946580\pi$
$110$		0			0
$111$	−2.44076	+	2.64173i	−0.231667	+	0.250742i
$112$		0			0
$113$	−13.9519			−1.31249			−0.656243	−	0.754550i	$-0.727855\pi$
$113$	−13.9519			−1.31249			−0.656243	+	0.754550i	$0.727855\pi$
$114$		0			0
$115$	0.184326	+	0.389793i	0.0171884	+	0.0363484i
$116$		0			0
$117$	4.26619	+	2.03224i	0.394409	+	0.187881i
$118$		0			0
$119$	12.1504	+	2.60486i	1.11382	+	0.238787i
$120$		0			0
$121$	4.95181	−	8.57679i	0.450165	−	0.779708i
$122$		0			0
$123$	2.23620	−	9.89412i	0.201632	−	0.892123i
$124$		0			0
$125$	−10.8447	−	2.71885i	−0.969981	−	0.243181i
$126$		0			0
$127$		−	9.98070i		−	0.885644i	−0.896610	−	0.442822i	$-0.853977\pi$
$127$		−	9.98070i		−	0.885644i	0.896610	−	0.442822i	$-0.146023\pi$
$128$		0			0
$129$	−11.1655	−	2.52355i	−0.983066	−	0.222186i
$130$		0			0
$131$	6.23882	−	10.8060i	0.545088	−	0.944121i	−0.453513	−	0.891250i	$-0.649829\pi$
$131$	6.23882	−	10.8060i	0.545088	−	0.944121i	0.998601	−	0.0528709i	$-0.0168372\pi$
$132$		0			0
$133$	0.0188867	+	0.0584751i	0.00163768	+	0.00507044i
$134$		0			0
$135$	−3.41676	−	11.1052i	−0.294068	−	0.955785i
$136$		0			0
$137$	−3.56853	−	6.18087i	−0.304880	−	0.528067i	0.672355	−	0.740229i	$-0.265283\pi$
$137$	−3.56853	−	6.18087i	−0.304880	−	0.528067i	−0.977235	+	0.212162i	$0.931950\pi$
$138$		0			0
$139$		−	9.40154i		−	0.797428i	−0.917075	−	0.398714i	$-0.869457\pi$
$139$		−	9.40154i		−	0.797428i	0.917075	−	0.398714i	$-0.130543\pi$
$140$		0			0
$141$	−6.69736	+	7.24881i	−0.564020	+	0.610460i
$142$		0			0
$143$	−6.23689	+	3.60087i	−0.521555	+	0.301120i
$144$		0			0
$145$	9.16392	+	6.34338i	0.761022	+	0.526789i
$146$		0			0
$147$	−12.0356	−	1.46416i	−0.992681	−	0.120762i
$148$		0			0
$149$	1.18404	+	0.683607i	0.0970005	+	0.0560033i	0.547716	−	0.836665i	$-0.315498\pi$
$149$	1.18404	+	0.683607i	0.0970005	+	0.0560033i	−0.450715	+	0.892668i	$0.648831\pi$
$150$		0			0
$151$	11.4085	+	19.7601i	0.928411	+	1.60806i	0.785981	+	0.618251i	$0.212158\pi$
$151$	11.4085	+	19.7601i	0.928411	+	1.60806i	0.142431	+	0.989805i	$0.454508\pi$
$152$		0			0
$153$	−14.0463	+	1.11255i	−1.13557	+	0.0899446i
$154$		0			0
$155$	1.25162	−	15.2516i	0.100533	−	1.22504i
$156$		0			0
$157$	−11.6334	−	20.1496i	−0.928443	−	1.60811i	−0.785929	−	0.618317i	$-0.787815\pi$
$157$	−11.6334	−	20.1496i	−0.928443	−	1.60811i	−0.142514	−	0.989793i	$-0.545519\pi$
$158$		0			0
$159$	17.0007	−	5.28353i	1.34824	−	0.419011i
$160$		0			0
$161$	−0.485482	+	0.156804i	−0.0382614	+	0.0123579i
$162$		0			0
$163$	−19.5250	−	11.2727i	−1.52931	−	0.882950i	−0.999391	−	0.0349039i	$-0.988887\pi$
$163$	−19.5250	−	11.2727i	−1.52931	−	0.882950i	−0.529923	−	0.848046i	$-0.677779\pi$
$164$		0			0
$165$	16.8947	+	5.30324i	1.31525	+	0.412857i
$166$		0			0
$167$			2.56225i			0.198273i	0.995074	+	0.0991364i	$0.0316080\pi$
$167$			2.56225i			0.198273i	−0.995074	+	0.0991364i	$0.968392\pi$
$168$		0			0
$169$	−10.5188			−0.809142
$170$		0			0
$171$	−0.0394944	−	0.0574031i	−0.00302021	−	0.00438972i
$172$		0			0
$173$	−19.0147	−	10.9782i	−1.44566	−	0.834654i	−0.447444	−	0.894312i	$-0.647666\pi$
$173$	−19.0147	−	10.9782i	−1.44566	−	0.834654i	−0.998219	+	0.0596581i	$0.980999\pi$
$174$		0			0
$175$	4.84474	−	12.3097i	0.366228	−	0.930525i
$176$		0			0
$177$	4.12592	−	1.28227i	0.310123	−	0.0963811i
$178$		0			0
$179$	−5.32644	+	3.07522i	−0.398117	+	0.229853i	−0.685671	−	0.727911i	$-0.740491\pi$
$179$	−5.32644	+	3.07522i	−0.398117	+	0.229853i	0.287554	+	0.957764i	$0.407158\pi$
$180$		0			0
$181$		−	21.8923i		−	1.62725i	−0.581393	−	0.813623i	$-0.697492\pi$
$181$		−	21.8923i		−	1.62725i	0.581393	−	0.813623i	$-0.302508\pi$
$182$		0			0
$183$	−10.8911	+	11.7879i	−0.805096	+	0.871386i
$184$		0			0
$185$	4.19762	−	1.98497i	0.308615	−	0.145938i
$186$		0			0
$187$	10.7369	−	18.5968i	0.785159	−	1.35994i
$188$		0			0
$189$	13.5515	−	2.31466i	0.985724	−	0.168367i
$190$		0			0
$191$	6.72916	+	3.88508i	0.486905	+	0.281115i	0.723290	−	0.690545i	$-0.242629\pi$
$191$	6.72916	+	3.88508i	0.486905	+	0.281115i	−0.236385	+	0.971660i	$0.575963\pi$
$192$		0			0
$193$	−7.48274	+	4.32016i	−0.538620	+	0.310972i	−0.744519	−	0.667601i	$-0.767321\pi$
$193$	−7.48274	+	4.32016i	−0.538620	+	0.310972i	0.205900	+	0.978573i	$0.433988\pi$
$194$		0			0
$195$	−4.12723	−	4.49259i	−0.295557	−	0.321721i
$196$		0			0
$197$	10.0102			0.713196			0.356598	−	0.934258i	$-0.383937\pi$
$197$	10.0102			0.713196			0.356598	+	0.934258i	$0.383937\pi$
$198$		0			0
$199$	16.4751	−	9.51189i	1.16789	−	0.674280i	0.214705	−	0.976679i	$-0.431121\pi$
$199$	16.4751	−	9.51189i	1.16789	−	0.674280i	0.953181	+	0.302399i	$0.0977875\pi$
$200$		0			0
$201$	−3.48757	−	11.2219i	−0.245994	−	0.791531i
$202$		0			0
$203$	−8.84108	+	9.78454i	−0.620522	+	0.686740i
$204$		0			0
$205$	−7.45335	+	10.7674i	−0.520565	+	0.752031i
$206$		0			0
$207$	0.476581	−	0.327897i	0.0331247	−	0.0227904i
$208$		0			0
$209$	0.106189			0.00734527
$210$		0			0
$211$	−22.9031			−1.57671			−0.788356	−	0.615220i	$-0.789067\pi$
$211$	−22.9031			−1.57671			−0.788356	+	0.615220i	$0.789067\pi$
$212$		0			0
$213$	−22.1195	−	4.99931i	−1.51561	−	0.342547i
$214$		0			0
$215$	12.1510	+	8.41109i	0.828693	+	0.573632i
$216$		0			0
$217$	17.7043	+	3.79555i	1.20185	+	0.257659i
$218$		0			0
$219$	−23.9339	+	7.43826i	−1.61730	+	0.502631i
$220$		0			0
$221$	−6.40701	+	3.69909i	−0.430982	+	0.248828i
$222$		0			0
$223$	1.13076			0.0757211			0.0378605	−	0.999283i	$-0.487946\pi$
$223$	1.13076			0.0757211			0.0378605	+	0.999283i	$0.487946\pi$
$224$		0			0
$225$	−1.26930	+	14.9462i	−0.0846202	+	0.996413i
$226$		0			0
$227$	−0.0771562	+	0.0445462i	−0.00512104	+	0.00295663i	−0.502558	−	0.864543i	$-0.667608\pi$
$227$	−0.0771562	+	0.0445462i	−0.00512104	+	0.00295663i	0.497437	+	0.867500i	$0.334274\pi$
$228$		0			0
$229$	7.76866	+	4.48524i	0.513368	+	0.296393i	0.734217	−	0.678915i	$-0.237550\pi$
$229$	7.76866	+	4.48524i	0.513368	+	0.296393i	−0.220849	+	0.975308i	$0.570883\pi$
$230$		0			0
$231$	−8.80016	+	19.0140i	−0.579008	+	1.25103i
$232$		0			0
$233$	−11.0036	+	19.0589i	−0.720873	+	1.24859i	0.239778	+	0.970828i	$0.422925\pi$
$233$	−11.0036	+	19.0589i	−0.720873	+	1.24859i	−0.960650	+	0.277760i	$0.910408\pi$
$234$		0			0
$235$	11.5181	−	5.44669i	0.751359	−	0.355303i
$236$		0			0
$237$	16.7968	+	15.5190i	1.09107	+	1.00807i
$238$		0			0
$239$			26.9277i			1.74181i	0.491450	+	0.870906i	$0.336467\pi$
$239$			26.9277i			1.74181i	−0.491450	+	0.870906i	$0.663533\pi$
$240$		0			0
$241$	14.5893	−	8.42312i	0.939778	−	0.542581i	0.0498872	−	0.998755i	$-0.484114\pi$
$241$	14.5893	−	8.42312i	0.939778	−	0.542581i	0.889891	+	0.456174i	$0.150780\pi$
$242$		0			0
$243$	−13.9722	+	6.91212i	−0.896318	+	0.443413i
$244$		0			0
$245$	13.7043	+	7.56263i	0.875533	+	0.483159i
$246$		0			0
$247$	−0.0316831	−	0.0182922i	−0.00201595	−	0.00116391i
$248$		0			0
$249$	−1.73445	−	0.392008i	−0.109916	−	0.0248425i
$250$		0			0
$251$	−8.43606			−0.532479			−0.266240	−	0.963907i	$-0.585781\pi$
$251$	−8.43606			−0.532479			−0.266240	+	0.963907i	$0.585781\pi$
$252$		0			0
$253$			0.881623i			0.0554271i
$254$		0			0
$255$	17.3555	+	5.44789i	1.08684	+	0.341160i
$256$		0			0
$257$	−15.2289	−	8.79239i	−0.949951	−	0.548454i	−0.0568852	−	0.998381i	$-0.518117\pi$
$257$	−15.2289	−	8.79239i	−0.949951	−	0.548454i	−0.893066	+	0.449926i	$0.851450\pi$
$258$		0			0
$259$	1.68860	+	5.22808i	0.104925	+	0.324857i
$260$		0			0
$261$	6.43061	−	13.4995i	0.398045	−	0.835596i
$262$		0			0
$263$	4.53721	+	7.85868i	0.279776	+	0.484587i	0.971329	−	0.237739i	$-0.0764064\pi$
$263$	4.53721	+	7.85868i	0.279776	+	0.484587i	−0.691553	+	0.722326i	$0.743073\pi$
$264$		0			0
$265$	−22.9063	−	1.87980i	−1.40712	−	0.115475i
$266$		0			0
$267$	−1.51361	−	1.39847i	−0.0926317	−	0.0855848i
$268$		0			0
$269$	13.1072	+	22.7023i	0.799158	+	1.38418i	0.920165	+	0.391531i	$0.128055\pi$
$269$	13.1072	+	22.7023i	0.799158	+	1.38418i	−0.121006	+	0.992652i	$0.538612\pi$
$270$		0			0
$271$	−19.0011	−	10.9703i	−1.15424	−	0.666399i	−0.204321	−	0.978904i	$-0.565499\pi$
$271$	−19.0011	−	10.9703i	−1.15424	−	0.666399i	−0.949916	+	0.312505i	$0.898832\pi$
$272$		0			0
$273$	5.90102	−	4.15718i	0.357146	−	0.251604i
$274$		0			0
$275$	−17.6692	−	14.5048i	−1.06549	−	0.874674i
$276$		0			0
$277$	−20.6278	+	11.9094i	−1.23940	+	0.715569i	−0.968972	−	0.247171i	$-0.920499\pi$
$277$	−20.6278	+	11.9094i	−1.23940	+	0.715569i	−0.270430	+	0.962740i	$0.587166\pi$
$278$		0			0
$279$	−20.4669	+	1.62111i	−1.22532	+	0.0970531i
$280$		0			0
$281$		−	0.605728i		−	0.0361347i	−0.999837	−	0.0180674i	$-0.994249\pi$
$281$		−	0.605728i		−	0.0361347i	0.999837	−	0.0180674i	$-0.00575133\pi$
$282$		0			0
$283$	15.3583	+	26.6013i	0.912955	+	1.58128i	0.809869	+	0.586611i	$0.199538\pi$
$283$	15.3583	+	26.6013i	0.912955	+	1.58128i	0.103086	+	0.994672i	$0.467128\pi$
$284$		0			0
$285$	0.0195811	+	0.0877959i	0.00115989	+	0.00520058i
$286$		0			0
$287$	−11.4967	−	10.3881i	−0.678627	−	0.613191i
$288$		0			0
$289$	2.52975	−	4.38165i	0.148809	−	0.257744i
$290$		0			0
$291$	−0.275610	+	1.21944i	−0.0161565	+	0.0714849i
$292$		0			0
$293$		−	22.7443i		−	1.32874i	−0.747405	−	0.664369i	$-0.768700\pi$
$293$		−	22.7443i		−	1.32874i	0.747405	−	0.664369i	$-0.231300\pi$
$294$		0			0
$295$	−5.55916	−	0.456212i	−0.323667	−	0.0265617i
$296$		0			0
$297$	3.39128	−	23.5138i	0.196782	−	1.36441i
$298$		0			0
$299$	0.151869	−	0.263045i	0.00878281	−	0.0152123i
$300$		0			0
$301$	−11.7230	+	12.9740i	−0.675700	+	0.747806i
$302$		0			0
$303$	24.9826	−	7.76417i	1.43521	−	0.446040i
$304$		0			0
$305$	18.7306	−	8.85731i	1.07251	−	0.507168i
$306$		0			0
$307$	4.56762			0.260688			0.130344	−	0.991469i	$-0.458392\pi$
$307$	4.56762			0.260688			0.130344	+	0.991469i	$0.458392\pi$
$308$		0			0
$309$	−5.53286	−	5.11195i	−0.314754	−	0.290809i
$310$		0			0
$311$	6.15556	+	10.6617i	0.349050	+	0.604572i	0.986081	−	0.166266i	$-0.0531711\pi$
$311$	6.15556	+	10.6617i	0.349050	+	0.604572i	−0.637031	+	0.770838i	$0.719838\pi$
$312$		0			0
$313$	3.33440	−	5.77536i	0.188472	−	0.326442i	−0.756269	−	0.654261i	$-0.772980\pi$
$313$	3.33440	−	5.77536i	0.188472	−	0.326442i	0.944741	+	0.327818i	$0.106313\pi$
$314$		0			0
$315$	−17.3433	−	3.76970i	−0.977183	−	0.212399i
$316$		0			0
$317$	4.81329	−	8.33686i	0.270341	−	0.468245i	−0.698608	−	0.715505i	$-0.746197\pi$
$317$	4.81329	−	8.33686i	0.270341	−	0.468245i	0.968949	+	0.247260i	$0.0795301\pi$
$318$		0			0
$319$	11.3942	+	19.7353i	0.637953	+	1.10497i
$320$		0			0
$321$	−16.6268	−	15.3620i	−0.928020	−	0.857422i
$322$		0			0
$323$	0.109086			0.00606969
$324$		0			0
$325$	2.77325	+	7.37143i	0.153832	+	0.408893i
$326$		0			0
$327$	12.0298	−	3.73866i	0.665249	−	0.206748i
$328$		0			0
$329$	4.63345	+	14.3456i	0.255451	+	0.790901i
$330$		0			0
$331$	−5.97347	+	10.3464i	−0.328332	+	0.568687i	−0.982181	−	0.187938i	$-0.939820\pi$
$331$	−5.97347	+	10.3464i	−0.328332	+	0.568687i	0.653849	+	0.756625i	$0.273153\pi$
$332$		0			0
$333$	−3.53107	−	5.13223i	−0.193502	−	0.281244i
$334$		0			0
$335$	−1.24083	+	15.1201i	−0.0677937	+	0.826098i
$336$		0			0
$337$		−	8.59087i		−	0.467975i	−0.972240	−	0.233987i	$-0.924823\pi$
$337$		−	8.59087i		−	0.467975i	0.972240	−	0.233987i	$-0.0751774\pi$
$338$		0			0
$339$	5.32734	−	23.5709i	0.289341	−	1.28020i
$340$		0			0
$341$	15.6448	−	27.0975i	0.847212	−	1.46741i
$342$		0			0
$343$	−10.9644	+	14.9259i	−0.592023	+	0.805921i
$344$		0			0
$345$	−0.728914	+	0.162570i	−0.0392434	+	0.00875246i
$346$		0			0
$347$	11.0394	+	19.1207i	0.592624	+	1.02646i	0.993877	+	0.110488i	$0.0352414\pi$
$347$	11.0394	+	19.1207i	0.592624	+	1.02646i	−0.401253	+	0.915967i	$0.631425\pi$
$348$		0			0
$349$			1.44889i			0.0775573i	0.999248	+	0.0387787i	$0.0123467\pi$
$349$			1.44889i			0.0775573i	−0.999248	+	0.0387787i	$0.987653\pi$
$350$		0			0
$351$	−5.06233	+	6.43148i	−0.270207	+	0.343287i
$352$		0			0
$353$	17.4981	−	10.1026i	0.931332	−	0.537705i	0.0440991	−	0.999027i	$-0.485958\pi$
$353$	17.4981	−	10.1026i	0.931332	−	0.537705i	0.887232	+	0.461323i	$0.152625\pi$
$354$		0			0
$355$	24.0720	+	16.6629i	1.27761	+	0.884376i
$356$		0			0
$357$	−9.04019	+	19.5326i	−0.478458	+	1.03378i
$358$		0			0
$359$	−6.81277	−	3.93336i	−0.359564	−	0.207595i	0.309325	−	0.950956i	$-0.399897\pi$
$359$	−6.81277	−	3.93336i	−0.359564	−	0.207595i	−0.668890	+	0.743362i	$0.733230\pi$
$360$		0			0
$361$	−9.49973	−	16.4540i	−0.499986	−	0.866001i
$362$		0			0
$363$	12.5992	+	11.6407i	0.661286	+	0.610979i
$364$		0			0
$365$	32.2479	+	2.64642i	1.68793	+	0.138520i
$366$		0			0
$367$	8.75729	+	15.1681i	0.457127	+	0.791767i	0.998808	−	0.0488172i	$-0.0155452\pi$
$367$	8.75729	+	15.1681i	0.457127	+	0.791767i	−0.541681	+	0.840584i	$0.682212\pi$
$368$		0			0
$369$	15.8616	+	7.55585i	0.825724	+	0.393342i
$370$		0			0
$371$	5.70052	−	26.5900i	0.295956	−	1.38049i
$372$		0			0
$373$	17.6990	+	10.2185i	0.916418	+	0.529094i	0.882491	−	0.470330i	$-0.155865\pi$
$373$	17.6990	+	10.2185i	0.916418	+	0.529094i	0.0339275	+	0.999424i	$0.489198\pi$
$374$		0			0
$375$	8.73423	−	17.2833i	0.451033	−	0.892507i
$376$		0			0
$377$		−	7.85110i		−	0.404352i
$378$		0			0
$379$	−22.3214			−1.14657			−0.573286	−	0.819355i	$-0.694332\pi$
$379$	−22.3214			−1.14657			−0.573286	+	0.819355i	$0.694332\pi$
$380$		0			0
$381$	16.8618	+	3.81098i	0.863855	+	0.195243i
$382$		0			0
$383$	−0.403621	−	0.233031i	−0.0206241	−	0.0119073i	0.489653	−	0.871918i	$-0.337124\pi$
$383$	−0.403621	−	0.233031i	−0.0206241	−	0.0119073i	−0.510277	+	0.860010i	$0.670457\pi$
$384$		0			0
$385$	19.7149	−	18.5189i	1.00476	−	0.943811i
$386$		0			0
$387$	8.52676	−	17.8998i	0.433439	−	0.909899i
$388$		0			0
$389$	14.1455	−	8.16690i	0.717205	−	0.414078i	−0.0965184	−	0.995331i	$-0.530771\pi$
$389$	14.1455	−	8.16690i	0.717205	−	0.414078i	0.813723	+	0.581253i	$0.197437\pi$
$390$		0			0
$391$			0.905669i			0.0458017i
$392$		0			0
$393$	15.8738	+	14.6662i	0.800727	+	0.739812i
$394$		0			0
$395$	−12.6209	−	26.6895i	−0.635028	−	1.34289i
$396$		0			0
$397$	−9.37186	+	16.2325i	−0.470360	+	0.814688i	−0.999425	−	0.0338935i	$-0.989209\pi$
$397$	−9.37186	+	16.2325i	−0.470360	+	0.814688i	0.529065	+	0.848581i	$0.322543\pi$
$398$		0			0
$399$	−0.106002	+	0.00958002i	−0.00530673	+	0.000479601i
$400$		0			0
$401$	3.15425	+	1.82111i	0.157516	+	0.0909417i	0.576686	−	0.816966i	$-0.304346\pi$
$401$	3.15425	+	1.82111i	0.157516	+	0.0909417i	−0.419170	+	0.907908i	$0.637679\pi$
$402$		0			0
$403$	−9.33568	+	5.38996i	−0.465043	+	0.268493i
$404$		0			0
$405$	20.0662	−	1.53204i	0.997098	−	0.0761275i
$406$		0			0
$407$	9.49405			0.470603
$408$		0			0
$409$	−2.51215	+	1.45039i	−0.124218	+	0.0717171i	−0.560821	−	0.827937i	$-0.689515\pi$
$409$	−2.51215	+	1.45039i	−0.124218	+	0.0717171i	0.436604	+	0.899654i	$0.356181\pi$
$410$		0			0
$411$	11.8048	−	3.66873i	0.582287	−	0.180965i
$412$		0			0
$413$	1.38347	−	6.45317i	0.0680759	−	0.317540i
$414$		0			0
$415$	1.88754	+	1.30658i	0.0926557	+	0.0641374i
$416$		0			0
$417$	15.8833	+	3.58984i	0.777809	+	0.175795i
$418$		0			0
$419$	−15.8585			−0.774736			−0.387368	−	0.921925i	$-0.626616\pi$
$419$	−15.8585			−0.774736			−0.387368	+	0.921925i	$0.626616\pi$
$420$		0			0
$421$	9.26063			0.451335			0.225668	−	0.974204i	$-0.427544\pi$
$421$	9.26063			0.451335			0.225668	+	0.974204i	$0.427544\pi$
$422$		0			0
$423$	−9.68913	−	14.0826i	−0.471102	−	0.684721i
$424$		0			0
$425$	−18.1511	−	14.9005i	−0.880460	−	0.722778i
$426$		0			0
$427$	7.53484	+	23.3286i	0.364637	+	1.12895i
$428$		0			0
$429$	−3.70198	−	11.9118i	−0.178733	−	0.575107i
$430$		0			0
$431$	−13.1009	+	7.56382i	−0.631050	+	0.364337i	−0.781158	−	0.624333i	$-0.785371\pi$
$431$	−13.1009	+	7.56382i	−0.631050	+	0.364337i	0.150109	+	0.988669i	$0.452038\pi$
$432$		0			0
$433$	−2.69681			−0.129601			−0.0648003	−	0.997898i	$-0.520641\pi$
$433$	−2.69681			−0.129601			−0.0648003	+	0.997898i	$0.520641\pi$
$434$		0			0
$435$	−14.2158	+	13.0597i	−0.681598	+	0.626167i
$436$		0			0
$437$	−0.00387858	+	0.00223930i	−0.000185537	+	0.000107120i
$438$		0			0
$439$	7.77101	+	4.48659i	0.370890	+	0.214133i	0.673847	−	0.738871i	$-0.264641\pi$
$439$	7.77101	+	4.48659i	0.370890	+	0.214133i	−0.302957	+	0.953004i	$0.597974\pi$
$440$		0			0
$441$	7.06924	−	19.7744i	0.336631	−	0.941637i
$442$		0			0
$443$	19.1374	−	33.1469i	0.909244	−	1.57486i	0.0941261	−	0.995560i	$-0.469994\pi$
$443$	19.1374	−	33.1469i	0.909244	−	1.57486i	0.815117	−	0.579296i	$-0.196672\pi$
$444$		0			0
$445$	1.13731	+	2.40508i	0.0539139	+	0.114012i
$446$		0			0
$447$	−1.60702	+	1.73934i	−0.0760095	+	0.0822680i
$448$		0			0
$449$			0.746605i			0.0352345i	0.999845	+	0.0176172i	$0.00560803\pi$
$449$			0.746605i			0.0352345i	−0.999845	+	0.0176172i	$0.994392\pi$
$450$		0			0
$451$	−23.1887	+	13.3880i	−1.09191	+	0.630416i
$452$		0			0
$453$	−37.7397	+	11.7289i	−1.77316	+	0.551070i
$454$		0			0
$455$	−9.07230	+	2.12928i	−0.425316	+	0.0998220i
$456$		0			0
$457$	4.35184	+	2.51254i	0.203571	+	0.117531i	0.598320	−	0.801257i	$-0.295835\pi$
$457$	4.35184	+	2.51254i	0.203571	+	0.117531i	−0.394749	+	0.918789i	$0.629169\pi$
$458$		0			0
$459$	3.48377	−	24.1551i	0.162609	−	1.12746i
$460$		0			0
$461$	−26.5502			−1.23656			−0.618282	−	0.785956i	$-0.712171\pi$
$461$	−26.5502			−1.23656			−0.618282	+	0.785956i	$0.712171\pi$
$462$		0			0
$463$		−	9.30452i		−	0.432418i	−0.976347	−	0.216209i	$-0.930631\pi$
$463$		−	9.30452i		−	0.432418i	0.976347	−	0.216209i	$-0.0693692\pi$
$464$		0			0
$465$	25.2887	+	7.93815i	1.17274	+	0.368123i
$466$		0			0
$467$	9.45358	+	5.45803i	0.437460	+	0.252567i	0.702520	−	0.711664i	$-0.252058\pi$
$467$	9.45358	+	5.45803i	0.437460	+	0.252567i	−0.265060	+	0.964232i	$0.585392\pi$
$468$		0			0
$469$	−17.5516	−	3.76282i	−0.810460	−	0.173751i
$470$		0			0
$471$	38.4835	−	11.9600i	1.77322	−	0.551088i
$472$		0			0
$473$	15.1083	+	26.1684i	0.694681	+	1.20322i
$474$		0			0
$475$	0.0189327	−	0.114575i	0.000868691	−	0.00525706i
$476$		0			0
$477$	2.43473	+	30.7391i	0.111479	+	1.40745i
$478$		0			0
$479$	−9.01995	−	15.6230i	−0.412132	−	0.713834i	0.582991	−	0.812479i	$-0.301882\pi$
$479$	−9.01995	−	15.6230i	−0.412132	−	0.713834i	−0.995123	+	0.0986452i	$0.968549\pi$
$480$		0			0
$481$	−2.83269	−	1.63545i	−0.129159	−	0.0745702i
$482$		0			0
$483$	−0.0795369	−	0.880066i	−0.00361905	−	0.0400444i
$484$		0			0
$485$	0.918619	−	1.32708i	0.0417123	−	0.0602595i
$486$		0			0
$487$	−31.4337	+	18.1482i	−1.42440	+	0.822375i	−0.996671	−	0.0815333i	$-0.974018\pi$
$487$	−31.4337	+	18.1482i	−1.42440	+	0.822375i	−0.427725	+	0.903909i	$0.640685\pi$
$488$		0			0
$489$	26.4999	−	28.6819i	1.19837	−	1.29704i
$490$		0			0
$491$			12.9137i			0.582786i	0.956603	+	0.291393i	$0.0941187\pi$
$491$			12.9137i			0.582786i	−0.956603	+	0.291393i	$0.905881\pi$
$492$		0			0
$493$	11.7050	+	20.2736i	0.527166	+	0.913079i
$494$		0			0
$495$	−15.4105	+	26.5175i	−0.692650	+	1.19187i
$496$		0			0
$497$	−23.2239	+	25.7022i	−1.04174	+	1.15290i
$498$		0			0
$499$	−11.7602	+	20.3692i	−0.526458	+	0.911852i	0.473067	+	0.881027i	$0.343147\pi$
$499$	−11.7602	+	20.3692i	−0.526458	+	0.911852i	−0.999525	+	0.0308254i	$0.990186\pi$
$500$		0			0
$501$	−4.32876	−	0.978358i	−0.193395	−	0.0437098i
$502$		0			0
$503$			5.11496i			0.228065i	0.993477	+	0.114032i	$0.0363768\pi$
$503$			5.11496i			0.228065i	−0.993477	+	0.114032i	$0.963623\pi$
$504$		0			0
$505$	−33.6609	−	2.76238i	−1.49789	−	0.122924i
$506$		0			0
$507$	4.01647	−	17.7709i	0.178378	−	0.789235i
$508$		0			0
$509$	−15.6297	+	27.0714i	−0.692774	+	1.19992i	0.278151	+	0.960537i	$0.410278\pi$
$509$	−15.6297	+	27.0714i	−0.692774	+	1.19992i	−0.970925	+	0.239382i	$0.923055\pi$
$510$		0			0
$511$	−8.02530	+	37.4340i	−0.355018	+	1.65598i
$512$		0			0
$513$	0.112059	−	0.0448049i	0.00494754	−	0.00197818i
$514$		0			0
$515$	4.15734	+	8.79153i	0.183194	+	0.387401i
$516$		0			0
$517$	26.0513			1.14574
$518$		0			0
$519$	25.8074	−	27.9324i	1.13282	−	1.22609i
$520$		0			0
$521$	−9.97790	−	17.2822i	−0.437140	−	0.757148i	0.560328	−	0.828271i	$-0.310675\pi$
$521$	−9.97790	−	17.2822i	−0.437140	−	0.757148i	−0.997468	+	0.0711229i	$0.977342\pi$
$522$		0			0
$523$	15.2872	−	26.4783i	0.668464	−	1.15781i	−0.309870	−	0.950779i	$-0.600286\pi$
$523$	15.2872	−	26.4783i	0.668464	−	1.15781i	0.978334	−	0.207034i	$-0.0663812\pi$
$524$		0			0
$525$	18.9466	+	12.8852i	0.826896	+	0.562354i
$526$		0			0
$527$	16.0715	−	27.8366i	0.700085	−	1.21258i
$528$		0			0
$529$	11.4814	+	19.8864i	0.499192	+	0.864625i
$530$		0			0
$531$	0.590887	+	7.46010i	0.0256423	+	0.323741i
$532$		0			0
$533$	9.22490			0.399575
$534$		0			0
$535$	12.4933	+	26.4195i	0.540130	+	1.14221i
$536$		0			0
$537$	−3.16157	−	10.1729i	−0.136432	−	0.438994i
$538$		0			0
$539$	18.7210	+	25.9577i	0.806369	+	1.11808i
$540$		0			0
$541$	20.1289	−	34.8642i	0.865407	−	1.49893i	−0.00123544	−	0.999999i	$-0.500393\pi$
$541$	20.1289	−	34.8642i	0.865407	−	1.49893i	0.866642	−	0.498930i	$-0.166273\pi$
$542$		0			0
$543$	36.9858	+	8.35928i	1.58721	+	0.358731i
$544$		0			0
$545$	−16.2086	−	1.33016i	−0.694302	−	0.0569778i
$546$		0			0
$547$		−	13.0498i		−	0.557967i	−0.960296	−	0.278984i	$-0.910002\pi$
$547$		−	13.0498i		−	0.557967i	0.960296	−	0.278984i	$-0.0899975\pi$
$548$		0			0
$549$	−15.7563	−	22.9009i	−0.672462	−	0.977388i
$550$		0			0
$551$	−0.0578820	+	0.100254i	−0.00246585	+	0.00427098i
$552$		0			0
$553$	33.2414	−	10.7365i	1.41357	−	0.456564i
$554$		0			0
$555$	1.75069	+	7.84956i	0.0743125	+	0.333195i
$556$		0			0
$557$	−14.7291	−	25.5116i	−0.624093	−	1.08096i	−0.988716	−	0.149805i	$-0.952135\pi$
$557$	−14.7291	−	25.5116i	−0.624093	−	1.08096i	0.364623	−	0.931155i	$-0.381198\pi$
$558$		0			0
$559$		−	10.4103i		−	0.440308i
$560$		0			0
$561$	27.3185	+	25.2403i	1.15339	+	1.06564i
$562$		0			0
$563$	−33.8141	+	19.5226i	−1.42509	+	0.822778i	−0.996728	−	0.0808279i	$-0.974244\pi$
$563$	−33.8141	+	19.5226i	−1.42509	+	0.822778i	−0.428365	+	0.903606i	$0.640910\pi$
$564$		0			0
$565$	−17.7562	+	25.6514i	−0.747011	+	1.07916i
$566$		0			0
$567$	−1.26396	+	23.7782i	−0.0530813	+	0.998590i
$568$		0			0
$569$	31.8770	+	18.4042i	1.33635	+	0.771543i	0.986265	−	0.165174i	$-0.0528184\pi$
$569$	31.8770	+	18.4042i	1.33635	+	0.771543i	0.350088	+	0.936717i	$0.386152\pi$
$570$		0			0
$571$	3.27778	+	5.67728i	0.137171	+	0.237587i	0.926425	−	0.376480i	$-0.122866\pi$
$571$	3.27778	+	5.67728i	0.137171	+	0.237587i	−0.789254	+	0.614067i	$0.789532\pi$
$572$		0			0
$573$	−9.13304	+	9.88504i	−0.381538	+	0.412953i
$574$		0			0
$575$	0.951245	+	0.157186i	0.0396696	+	0.00655512i
$576$		0			0
$577$	−5.50501	−	9.53496i	−0.229177	−	0.396945i	0.728388	−	0.685165i	$-0.240270\pi$
$577$	−5.50501	−	9.53496i	−0.229177	−	0.396945i	−0.957564	+	0.288220i	$0.906937\pi$
$578$		0			0
$579$	−4.44147	−	14.2912i	−0.184581	−	0.593923i
$580$		0			0
$581$	−1.82105	+	2.01537i	−0.0755497	+	0.0836118i
$582$		0			0
$583$	−40.6976	−	23.4968i	−1.68552	−	0.973137i
$584$		0			0
$585$	9.16587	−	5.25726i	0.378962	−	0.217361i
$586$		0			0
$587$			21.2051i			0.875227i	0.899163	+	0.437614i	$0.144176\pi$
$587$			21.2051i			0.875227i	−0.899163	+	0.437614i	$0.855824\pi$
$588$		0			0
$589$	0.158949			0.00654938
$590$		0			0
$591$	−3.82225	+	16.9116i	−0.157226	+	0.695650i
$592$		0			0
$593$	32.8813	+	18.9841i	1.35027	+	0.779582i	0.988288	−	0.152601i	$-0.0487651\pi$
$593$	32.8813	+	18.9841i	1.35027	+	0.779582i	0.361987	+	0.932183i	$0.382098\pi$
$594$		0			0
$595$	20.2526	−	19.0240i	0.830277	−	0.779909i
$596$		0			0
$597$	9.77898	+	31.4656i	0.400227	+	1.28780i
$598$		0			0
$599$	20.8018	−	12.0099i	0.849937	−	0.490711i	−0.0106928	−	0.999943i	$-0.503404\pi$
$599$	20.8018	−	12.0099i	0.849937	−	0.490711i	0.860629	+	0.509232i	$0.170070\pi$
$600$		0			0
$601$			38.3360i			1.56376i	0.623431	+	0.781878i	$0.285738\pi$
$601$			38.3360i			1.56376i	−0.623431	+	0.781878i	$0.714262\pi$
$602$		0			0
$603$	20.2904	−	1.60712i	0.826287	−	0.0654472i
$604$		0			0
$605$	−9.46690	−	20.0197i	−0.384884	−	0.813915i
$606$		0			0
$607$	14.2254	−	24.6391i	0.577390	−	1.00007i	−0.418388	−	0.908268i	$-0.637405\pi$
$607$	14.2254	−	24.6391i	0.577390	−	1.00007i	0.995777	−	0.0917998i	$-0.0292620\pi$
$608$		0			0
$609$	−13.1545	−	18.6726i	−0.533049	−	0.756650i
$610$		0			0
$611$	−7.77278	−	4.48762i	−0.314453	−	0.181550i
$612$		0			0
$613$	0.287485	−	0.165979i	0.0116114	−	0.00670384i	−0.494183	−	0.869358i	$-0.664533\pi$
$613$	0.287485	−	0.165979i	0.0116114	−	0.00670384i	0.505794	+	0.862654i	$0.331199\pi$
$614$		0			0
$615$	−15.3450	−	16.7034i	−0.618769	−	0.673545i
$616$		0			0
$617$	−3.89790			−0.156924			−0.0784618	−	0.996917i	$-0.525001\pi$
$617$	−3.89790			−0.156924			−0.0784618	+	0.996917i	$0.525001\pi$
$618$		0			0
$619$	−36.6297	+	21.1482i	−1.47227	+	0.850018i	−0.999514	−	0.0311740i	$-0.990075\pi$
$619$	−36.6297	+	21.1482i	−1.47227	+	0.850018i	−0.472760	+	0.881191i	$0.656742\pi$
$620$		0			0
$621$	0.371987	+	0.930358i	0.0149273	+	0.0373340i
$622$		0			0
$623$	−2.99549	+	0.967505i	−0.120012	+	0.0387623i
$624$		0			0
$625$	−18.8006	+	16.4784i	−0.752022	+	0.659138i
$626$		0			0
$627$	−0.0405468	+	0.179400i	−0.00161928	+	0.00716455i
$628$		0			0
$629$	9.75301			0.388878
$630$		0			0
$631$	24.1993			0.963360			0.481680	−	0.876347i	$-0.340027\pi$
$631$	24.1993			0.963360			0.481680	+	0.876347i	$0.340027\pi$
$632$		0			0
$633$	8.74520	−	38.6933i	0.347590	−	1.53792i
$634$		0			0
$635$	−18.3501	−	12.7022i	−0.728202	−	0.504070i
$636$		0			0
$637$	−1.11418	−	10.9697i	−0.0441453	−	0.434637i
$638$		0			0
$639$	16.8921	−	35.4607i	0.668239	−	1.40280i
$640$		0			0
$641$	−24.8431	+	14.3432i	−0.981243	+	0.566521i	−0.902645	−	0.430385i	$-0.858378\pi$
$641$	−24.8431	+	14.3432i	−0.981243	+	0.566521i	−0.0785980	+	0.996906i	$0.525044\pi$
$642$		0			0
$643$	−33.7651			−1.33157			−0.665783	−	0.746145i	$-0.731902\pi$
$643$	−33.7651			−1.33157			−0.665783	+	0.746145i	$0.731902\pi$
$644$		0			0
$645$	−18.8497	+	17.3168i	−0.742207	+	0.681846i
$646$		0			0
$647$	3.78572	−	2.18568i	0.148832	−	0.0859281i	−0.423735	−	0.905786i	$-0.639281\pi$
$647$	3.78572	−	2.18568i	0.148832	−	0.0859281i	0.572567	+	0.819858i	$0.305948\pi$
$648$		0			0
$649$	−9.87696	−	5.70246i	−0.387704	−	0.223841i
$650$		0			0
$651$	−13.1725	+	28.4611i	−0.516271	+	1.11548i
$652$		0			0
$653$	2.10337	−	3.64315i	0.0823113	−	0.142567i	−0.821931	−	0.569587i	$-0.807103\pi$
$653$	2.10337	−	3.64315i	0.0823113	−	0.142567i	0.904242	+	0.427020i	$0.140436\pi$
$654$		0			0
$655$	−11.9274	−	25.2229i	−0.466042	−	0.985540i
$656$		0			0
$657$	−3.42766	−	43.2751i	−0.133726	−	1.68832i
$658$		0			0
$659$			41.3660i			1.61139i	0.592329	+	0.805696i	$0.298209\pi$
$659$			41.3660i			1.61139i	−0.592329	+	0.805696i	$0.701791\pi$
$660$		0			0
$661$	−6.42328	+	3.70848i	−0.249837	+	0.144243i	−0.619689	−	0.784847i	$-0.712741\pi$
$661$	−6.42328	+	3.70848i	−0.249837	+	0.144243i	0.369853	+	0.929090i	$0.379408\pi$
$662$		0			0
$663$	−3.80296	−	12.2367i	−0.147695	−	0.475234i
$664$		0			0
$665$	0.131547	+	0.0396955i	0.00510116	+	0.00153932i
$666$		0			0
$667$	−0.832350	−	0.480557i	−0.0322287	−	0.0186073i
$668$		0			0
$669$	−0.431763	+	1.91034i	−0.0166929	+	0.0738582i
$670$		0			0
$671$	42.3642			1.63545
$672$		0			0
$673$		−	15.5806i		−	0.600587i	−0.953847	−	0.300293i	$-0.902915\pi$
$673$		−	15.5806i		−	0.600587i	0.953847	−	0.300293i	$-0.0970846\pi$
$674$		0			0
$675$	−24.7660	−	7.85140i	−0.953244	−	0.302201i
$676$		0			0
$677$	−11.1207	−	6.42051i	−0.427401	−	0.246760i	0.270838	−	0.962625i	$-0.412699\pi$
$677$	−11.1207	−	6.42051i	−0.427401	−	0.246760i	−0.698239	+	0.715865i	$0.746033\pi$
$678$		0			0
$679$	1.41695	+	1.28033i	0.0543777	+	0.0491344i
$680$		0			0
$681$	−0.0457970	−	0.147360i	−0.00175495	−	0.00564685i
$682$		0			0
$683$	−15.1628	−	26.2628i	−0.580190	−	1.00492i	−0.995456	−	0.0952184i	$-0.969645\pi$
$683$	−15.1628	−	26.2628i	−0.580190	−	1.00492i	0.415267	−	0.909700i	$-0.363688\pi$
$684$		0			0
$685$	−15.9055	−	1.30528i	−0.607716	−	0.0498722i
$686$		0			0
$687$	−10.5439	+	11.4121i	−0.402274	+	0.435397i
$688$		0			0
$689$	8.09514	+	14.0212i	0.308400	+	0.534165i
$690$		0			0
$691$	8.57027	+	4.94805i	0.326028	+	0.188233i	0.654076	−	0.756429i	$-0.273057\pi$
$691$	8.57027	+	4.94805i	0.326028	+	0.188233i	−0.328048	+	0.944661i	$0.606391\pi$
$692$		0			0
$693$	−28.7628	−	22.1276i	−1.09261	−	0.840557i
$694$		0			0
$695$	−17.2853	−	11.9651i	−0.655668	−	0.453862i
$696$		0			0
$697$	−23.8212	+	13.7532i	−0.902291	+	0.520938i
$698$		0			0
$699$	−27.9972	−	25.8673i	−1.05895	−	0.978392i
$700$		0			0
$701$		−	9.88682i		−	0.373420i	−0.982415	−	0.186710i	$-0.940217\pi$
$701$		−	9.88682i		−	0.373420i	0.982415	−	0.186710i	$-0.0597825\pi$
$702$		0			0
$703$	0.0241146	+	0.0417678i	0.000909501	+	0.00157530i
$704$		0			0
$705$	4.80382	+	21.5389i	0.180922	+	0.811201i
$706$		0			0
$707$	8.37694	−	39.0742i	0.315047	−	1.46953i
$708$		0			0
$709$	−26.5650	+	46.0119i	−0.997670	+	1.72801i	−0.439745	+	0.898123i	$0.644931\pi$
$709$	−26.5650	+	46.0119i	−0.997670	+	1.72801i	−0.557925	+	0.829891i	$0.688402\pi$
$710$		0			0
$711$	−32.6320	+	22.4514i	−1.22379	+	0.841994i
$712$		0			0
$713$			1.31965i			0.0494214i
$714$		0			0
$715$	−1.31711	+	16.0496i	−0.0492572	+	0.600222i
$716$		0			0
$717$	−45.4928	−	10.2820i	−1.69896	−	0.383987i
$718$		0			0
$719$	3.10194	−	5.37272i	0.115683	−	0.200369i	−0.802370	−	0.596827i	$-0.796428\pi$
$719$	3.10194	−	5.37272i	0.115683	−	0.200369i	0.918053	+	0.396459i	$0.129761\pi$
$720$		0			0
$721$	−10.9497	+	3.53662i	−0.407789	+	0.131711i
$722$		0			0
$723$	8.65964	+	27.8639i	0.322056	+	1.03627i
$724$		0			0
$725$	23.3253	−	8.77536i	0.866282	−	0.325909i
$726$		0			0
$727$	22.6957			0.841735			0.420868	−	0.907122i	$-0.361726\pi$
$727$	22.6957			0.841735			0.420868	+	0.907122i	$0.361726\pi$
$728$		0			0
$729$	−6.34252	−	26.2445i	−0.234908	−	0.972018i
$730$		0			0
$731$	15.5204	+	26.8821i	0.574043	+	0.994271i
$732$		0			0
$733$	6.48996	−	11.2409i	0.239712	−	0.415193i	−0.720920	−	0.693019i	$-0.756280\pi$
$733$	6.48996	−	11.2409i	0.239712	−	0.415193i	0.960632	+	0.277825i	$0.0896137\pi$
$734$		0			0
$735$	−18.0094	+	20.2648i	−0.664286	+	0.747479i
$736$		0			0
$737$	−15.5098	+	26.8638i	−0.571312	+	0.989542i
$738$		0			0
$739$	−26.2551	−	45.4752i	−0.965811	−	1.67283i	−0.707420	−	0.706794i	$-0.750141\pi$
$739$	−26.2551	−	45.4752i	−0.965811	−	1.67283i	−0.258391	−	0.966040i	$-0.583192\pi$
$740$		0			0
$741$	0.0430013	−	0.0465420i	0.00157969	−	0.00170976i
$742$		0			0
$743$	−21.0232			−0.771265			−0.385632	−	0.922652i	$-0.626017\pi$
$743$	−21.0232			−0.771265			−0.385632	+	0.922652i	$0.626017\pi$
$744$		0			0
$745$	2.76375	−	1.30692i	0.101256	−	0.0478820i
$746$		0			0
$747$	1.32455	−	2.78056i	0.0484626	−	0.101735i
$748$		0			0
$749$	−32.9051	+	10.6279i	−1.20233	+	0.388336i
$750$		0			0
$751$	7.73267	−	13.3934i	0.282169	−	0.488731i	−0.689750	−	0.724048i	$-0.742279\pi$
$751$	7.73267	−	13.3934i	0.282169	−	0.488731i	0.971919	+	0.235317i	$0.0756128\pi$
$752$		0			0
$753$	3.22119	−	14.2522i	0.117387	−	0.519379i
$754$		0			0
$755$	50.8495	+	4.17296i	1.85060	+	0.151869i
$756$		0			0
$757$		−	28.5557i		−	1.03788i	−0.854812	−	0.518938i	$-0.826328\pi$
$757$		−	28.5557i		−	1.03788i	0.854812	−	0.518938i	$-0.173672\pi$
$758$		0			0
$759$	−1.48945	−	0.336635i	−0.0540635	−	0.0122191i
$760$		0			0
$761$	24.6618	−	42.7156i	0.893991	−	1.54844i	0.0589430	−	0.998261i	$-0.481227\pi$
$761$	24.6618	−	42.7156i	0.893991	−	1.54844i	0.835048	−	0.550177i	$-0.185440\pi$
$762$		0			0
$763$	4.03372	−	18.8153i	0.146031	−	0.681158i
$764$		0			0
$765$	−15.8308	+	27.2408i	−0.572364	+	0.984894i
$766$		0			0
$767$	1.96462	+	3.40282i	0.0709383	+	0.122869i
$768$		0			0
$769$			3.85691i			0.139084i	0.997579	+	0.0695419i	$0.0221538\pi$
$769$			3.85691i			0.139084i	−0.997579	+	0.0695419i	$0.977846\pi$
$770$		0			0
$771$	20.6691	−	22.3710i	0.744381	−	0.805671i
$772$		0			0
$773$	25.1407	−	14.5150i	0.904247	−	0.522067i	0.0256713	−	0.999670i	$-0.491828\pi$
$773$	25.1407	−	14.5150i	0.904247	−	0.522067i	0.878576	+	0.477603i	$0.158494\pi$
$774$		0			0
$775$	−26.4481	−	21.7115i	−0.950044	−	0.779900i
$776$		0			0
$777$	−9.47729	+	0.856520i	−0.339996	+	0.0307275i
$778$		0			0
$779$	−0.117797	−	0.0680103i	−0.00422052	−	0.00243672i
$780$		0			0
$781$	29.9305	+	51.8412i	1.07100	+	1.85503i
$782$		0			0
$783$	20.3511	+	16.0187i	0.727288	+	0.572461i
$784$		0			0
$785$	−51.8516	−	4.25520i	−1.85066	−	0.151875i
$786$		0			0
$787$	11.5679	+	20.0362i	0.412352	+	0.714215i	0.995146	−	0.0984048i	$-0.0313740\pi$
$787$	11.5679	+	20.0362i	0.412352	+	0.714215i	−0.582794	+	0.812620i	$0.698041\pi$
$788$		0			0
$789$	−15.0092	+	4.66461i	−0.534342	+	0.166065i
$790$		0			0
$791$	−27.3887	−	24.7478i	−0.973829	−	0.879930i
$792$		0			0
$793$	−12.6400	−	7.29768i	−0.448858	−	0.259148i
$794$		0			0
$795$	11.9223	−	37.9810i	0.422839	−	1.34705i
$796$		0			0
$797$			28.9627i			1.02591i	0.858415	+	0.512956i	$0.171450\pi$
$797$			28.9627i			1.02591i	−0.858415	+	0.512956i	$0.828550\pi$
$798$		0			0
$799$	26.7619			0.946767
$800$		0			0
$801$	2.94057	−	2.02317i	0.103900	−	0.0714853i
$802$		0			0
$803$	57.2949	+	33.0792i	2.02189	+	1.16734i
$804$		0			0
$805$	−0.329566	+	1.09215i	−0.0116157	+	0.0384932i
$806$		0			0
$807$	−43.3589	+	13.4752i	−1.52631	+	0.474350i
$808$		0			0
$809$	−1.47318	+	0.850541i	−0.0517943	+	0.0299034i	−0.525674	−	0.850686i	$-0.676187\pi$
$809$	−1.47318	+	0.850541i	−0.0517943	+	0.0299034i	0.473879	+	0.880590i	$0.342853\pi$
$810$		0			0
$811$			1.26175i			0.0443059i	0.999755	+	0.0221529i	$0.00705208\pi$
$811$			1.26175i			0.0443059i	−0.999755	+	0.0221529i	$0.992948\pi$
$812$		0			0
$813$	25.7890	−	27.9124i	0.904459	−	0.978930i
$814$		0			0
$815$	−45.5745	+	21.5513i	−1.59641	+	0.754909i
$816$		0			0
$817$	−0.0767494	+	0.132934i	−0.00268512	+	0.00465077i
$818$		0			0
$819$	4.77009	+	11.5568i	0.166680	+	0.403826i
$820$		0			0
$821$	19.4002	+	11.2007i	0.677072	+	0.390908i	0.798751	−	0.601662i	$-0.205495\pi$
$821$	19.4002	+	11.2007i	0.677072	+	0.390908i	−0.121679	+	0.992569i	$0.538828\pi$
$822$		0			0
$823$	18.3644	−	10.6027i	0.640144	−	0.369587i	−0.144526	−	0.989501i	$-0.546166\pi$
$823$	18.3644	−	10.6027i	0.640144	−	0.369587i	0.784670	+	0.619914i	$0.212832\pi$
$824$		0			0
$825$	31.2517	−	24.3126i	1.08805	−	0.846455i
$826$		0			0
$827$	−39.3474			−1.36824			−0.684122	−	0.729368i	$-0.739814\pi$
$827$	−39.3474			−1.36824			−0.684122	+	0.729368i	$0.739814\pi$
$828$		0			0
$829$	20.5440	−	11.8611i	0.713521	−	0.411952i	−0.0988421	−	0.995103i	$-0.531514\pi$
$829$	20.5440	−	11.8611i	0.713521	−	0.411952i	0.812364	+	0.583151i	$0.198181\pi$
$830$		0			0
$831$	−12.2439	−	39.3968i	−0.424734	−	1.36666i
$832$		0			0
$833$	19.2316	+	26.6657i	0.666335	+	0.923912i
$834$		0			0
$835$	4.71085	+	3.26091i	0.163026	+	0.112848i
$836$		0			0
$837$	5.07622	−	35.1965i	0.175460	−	1.21657i
$838$		0			0
$839$	13.8614			0.478550			0.239275	−	0.970952i	$-0.423090\pi$
$839$	13.8614			0.478550			0.239275	+	0.970952i	$0.423090\pi$
$840$		0			0
$841$	4.15685			0.143340
$842$		0			0
$843$	1.02334	+	0.231289i	0.0352457	+	0.00796600i
$844$		0			0
$845$	−13.3871	+	19.3395i	−0.460529	+	0.665300i
$846$		0			0
$847$	24.9342	−	8.05342i	0.856750	−	0.276719i
$848$		0			0
$849$	−50.8056	+	15.7895i	−1.74364	+	0.541895i
$850$		0			0
$851$	−0.346771	+	0.200209i	−0.0118872	+	0.00686306i
$852$		0			0
$853$	23.4548			0.803078			0.401539	−	0.915842i	$-0.368476\pi$
$853$	23.4548			0.803078			0.401539	+	0.915842i	$0.368476\pi$
$854$		0			0
$855$	−0.155802		0.000442496i	−0.00532833		1.51331e-5i
$856$		0			0
$857$	−40.7019	+	23.4993i	−1.39035	+	0.802720i	−0.993354	−	0.115100i	$-0.963281\pi$
$857$	−40.7019	+	23.4993i	−1.39035	+	0.802720i	−0.396997	+	0.917820i	$0.629948\pi$
$858$		0			0
$859$	20.8802	+	12.0552i	0.712424	+	0.411318i	0.811958	−	0.583716i	$-0.198402\pi$
$859$	20.8802	+	12.0552i	0.712424	+	0.411318i	−0.0995342	+	0.995034i	$0.531735\pi$
$860$		0			0
$861$	21.9399	−	15.4564i	0.747711	−	0.526751i
$862$		0			0
$863$	−2.82464	+	4.89242i	−0.0961519	+	0.166540i	−0.910089	−	0.414413i	$-0.863987\pi$
$863$	−2.82464	+	4.89242i	−0.0961519	+	0.166540i	0.813937	+	0.580953i	$0.197320\pi$
$864$		0			0
$865$	−44.3835	+	20.9881i	−1.50909	+	0.713617i
$866$		0			0
$867$	6.43658	+	5.94692i	0.218598	+	0.201968i
$868$		0			0
$869$		−	60.3655i		−	2.04776i
$870$		0			0
$871$	9.25516	−	5.34347i	0.313599	−	0.181057i
$872$		0			0
$873$	−1.95493	−	0.931252i	−0.0661644	−	0.0315181i
$874$		0			0
$875$	−16.4663	−	24.5736i	−0.556664	−	0.830738i
$876$		0			0
$877$	−0.425057	−	0.245407i	−0.0143531	−	0.00828679i	0.492806	−	0.870139i	$-0.335971\pi$
$877$	−0.425057	−	0.245407i	−0.0143531	−	0.00828679i	−0.507159	+	0.861852i	$0.669304\pi$
$878$		0			0
$879$	38.4252	+	8.68460i	1.29605	+	0.292924i
$880$		0			0
$881$	−27.5907			−0.929555			−0.464778	−	0.885427i	$-0.653866\pi$
$881$	−27.5907			−0.929555			−0.464778	+	0.885427i	$0.653866\pi$
$882$		0			0
$883$		−	31.5174i		−	1.06064i	−0.847796	−	0.530322i	$-0.822071\pi$
$883$		−	31.5174i		−	1.06064i	0.847796	−	0.530322i	$-0.177929\pi$
$884$		0			0
$885$	2.89343	−	9.21766i	0.0972615	−	0.309848i
$886$		0			0
$887$	−9.19558	−	5.30907i	−0.308757	−	0.178261i	0.337613	−	0.941285i	$-0.390381\pi$
$887$	−9.19558	−	5.30907i	−0.308757	−	0.178261i	−0.646370	+	0.763024i	$0.723714\pi$
$888$		0			0
$889$	17.7037	−	19.5929i	0.593762	−	0.657124i
$890$		0			0
$891$	38.4301	+	14.7077i	1.28746	+	0.492728i
$892$		0			0
$893$	0.0661696	+	0.114609i	0.00221428	+	0.00383525i
$894$		0			0
$895$	−1.12484	+	13.7067i	−0.0375993	+	0.458166i
$896$		0			0
$897$	0.386409	+	0.357013i	0.0129018	+	0.0119203i
$898$		0			0
$899$	17.0554	+	29.5408i	0.568829	+	0.985241i
$900$		0			0
$901$	−41.8077	−	24.1377i	−1.39282	−	0.804142i
$902$		0			0
$903$	−17.4425	−	24.7591i	−0.580448	−	0.823933i
$904$		0			0
$905$	−40.2504	−	27.8618i	−1.33797	−	0.926158i
$906$		0			0
$907$	−38.0167	+	21.9489i	−1.26232	+	0.728803i	−0.973523	−	0.228587i	$-0.926589\pi$
$907$	−38.0167	+	21.9489i	−1.26232	+	0.728803i	−0.288800	+	0.957390i	$0.593256\pi$
$908$		0			0
$909$	3.57784	+	45.1712i	0.118670	+	1.49823i
$910$		0			0
$911$		−	8.18050i		−	0.271032i	−0.990775	−	0.135516i	$-0.956731\pi$
$911$		−	8.18050i		−	0.271032i	0.990775	−	0.135516i	$-0.0432692\pi$
$912$		0			0
$913$	2.34693	+	4.06499i	0.0776719	+	0.134532i
$914$		0			0
$915$	7.81188	+	35.0261i	0.258253	+	1.15793i
$916$		0			0
$917$	31.4148	−	10.1466i	1.03741	−	0.335069i
$918$		0			0
$919$	−5.15414	+	8.92723i	−0.170019	+	0.294482i	−0.938426	−	0.345479i	$-0.887716\pi$
$919$	−5.15414	+	8.92723i	−0.170019	+	0.294482i	0.768407	+	0.639961i	$0.221050\pi$
$920$		0			0
$921$	−1.74408	+	7.71670i	−0.0574693	+	0.254274i
$922$		0			0
$923$		−	20.6234i		−	0.678828i
$924$		0			0
$925$	1.69271	−	10.2438i	0.0556560	−	0.336814i
$926$		0			0
$927$	10.7490	−	7.39551i	0.353043	−	0.242900i
$928$		0			0
$929$	−22.9667	+	39.7794i	−0.753512	+	1.30512i	0.192599	+	0.981278i	$0.438308\pi$
$929$	−22.9667	+	39.7794i	−0.753512	+	1.30512i	−0.946111	+	0.323843i	$0.895025\pi$
$930$		0			0
$931$	−0.0666466	+	0.148292i	−0.00218425	+	0.00486008i
$932$		0			0
$933$	−20.3628	+	6.32841i	−0.666647	+	0.207183i
$934$		0			0
$935$	−20.5268	−	43.4081i	−0.671300	−	1.41960i
$936$		0			0
$937$	−50.3541			−1.64500			−0.822499	−	0.568767i	$-0.807421\pi$
$937$	−50.3541			−1.64500			−0.822499	+	0.568767i	$0.807421\pi$
$938$		0			0
$939$	8.48391	+	7.83850i	0.276862	+	0.255800i
$940$		0			0
$941$	4.96200	+	8.59443i	0.161757	+	0.280171i	0.935499	−	0.353330i	$-0.114951\pi$
$941$	4.96200	+	8.59443i	0.161757	+	0.280171i	−0.773742	+	0.633501i	$0.781617\pi$
$942$		0			0
$943$	0.564646	−	0.977996i	0.0183874	−	0.0318479i
$944$		0			0
$945$	12.9910	−	27.8610i	0.422596	−	0.906318i
$946$		0			0
$947$	3.97339	−	6.88211i	0.129118	−	0.223638i	−0.794217	−	0.607634i	$-0.792119\pi$
$947$	3.97339	−	6.88211i	0.129118	−	0.223638i	0.923335	+	0.383995i	$0.125452\pi$
$948$		0			0
$949$	−11.3965	−	19.7393i	−0.369946	−	0.640765i
$950$		0			0
$951$	12.2467	+	11.3151i	0.397127	+	0.366916i
$952$		0			0
$953$	−42.8058			−1.38662			−0.693308	−	0.720641i	$-0.743848\pi$
$953$	−42.8058			−1.38662			−0.693308	+	0.720641i	$0.743848\pi$
$954$		0			0
$955$	15.7070	−	7.42752i	0.508266	−	0.240349i
$956$		0			0
$957$	−37.6924	+	11.7142i	−1.21842	+	0.378665i
$958$		0			0
$959$	3.95827	−	18.4633i	0.127819	−	0.596212i
$960$		0			0
$961$	7.91782	−	13.7141i	0.255414	−	0.442389i
$962$		0			0
$963$	32.3018	−	22.2243i	1.04091	−	0.716168i
$964$		0			0
$965$	−1.58021	+	19.2556i	−0.0508688	+	0.619861i
$966$		0			0
$967$		−	23.9826i		−	0.771227i	−0.922660	−	0.385613i	$-0.873990\pi$
$967$		−	23.9826i		−	0.771227i	0.922660	−	0.385613i	$-0.126010\pi$
$968$		0			0
$969$	−0.0416528	+	0.184293i	−0.00133808	+	0.00592036i
$970$		0			0
$971$	−0.893834	+	1.54817i	−0.0286845	+	0.0496830i	−0.880011	−	0.474953i	$-0.842465\pi$
$971$	−0.893834	+	1.54817i	−0.0286845	+	0.0496830i	0.851327	+	0.524636i	$0.175798\pi$
$972$		0			0
$973$	16.6764	−	18.4559i	0.534619	−	0.591670i
$974$		0			0
$975$	−13.5125	+	1.87056i	−0.432746	+	0.0599057i
$976$		0			0
$977$	8.56427	+	14.8337i	0.273995	+	0.474574i	0.969881	−	0.243579i	$-0.0783214\pi$
$977$	8.56427	+	14.8337i	0.273995	+	0.474574i	−0.695886	+	0.718152i	$0.744988\pi$
$978$		0			0
$979$			5.43974i			0.173855i
$980$		0			0
$981$	1.72283	+	21.7512i	0.0550057	+	0.694461i
$982$		0			0
$983$	47.1805	−	27.2397i	1.50483	−	0.868811i	0.504841	−	0.863212i	$-0.331551\pi$
$983$	47.1805	−	27.2397i	1.50483	−	0.868811i	0.999984	−	0.00559883i	$-0.00178217\pi$
$984$		0			0
$985$	12.7397	−	18.4043i	0.405921	−	0.586411i
$986$		0			0
$987$	−26.0053	+	2.35026i	−0.827758	+	0.0748095i
$988$		0			0
$989$	−1.10367	−	0.637202i	−0.0350945	−	0.0202618i
$990$		0			0
$991$	−11.6055	−	20.1013i	−0.368661	−	0.638540i	0.620695	−	0.784052i	$-0.286850\pi$
$991$	−11.6055	−	20.1013i	−0.368661	−	0.638540i	−0.989357	+	0.145512i	$0.953517\pi$
$992$		0			0
$993$	−15.1986	−	14.0424i	−0.482314	−	0.445623i
$994$		0			0
$995$	3.47922	−	42.3959i	0.110299	−	1.34404i
$996$		0			0
$997$	−3.30773	−	5.72916i	−0.104757	−	0.181444i	0.808882	−	0.587971i	$-0.200073\pi$
$997$	−3.30773	−	5.72916i	−0.104757	−	0.181444i	−0.913639	+	0.406527i	$0.866740\pi$
$998$		0			0
$999$	10.0189	−	4.00586i	0.316983	−	0.126740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.da.a.89.12	yes	48
3.2	odd	2		840.2.da.b.89.22	yes	48
5.4	even	2		840.2.da.b.89.13	yes	48
7.3	odd	6	inner	840.2.da.a.689.3	yes	48
15.14	odd	2	inner	840.2.da.a.89.3	✓	48
21.17	even	6		840.2.da.b.689.13	yes	48
35.24	odd	6		840.2.da.b.689.22	yes	48
105.59	even	6	inner	840.2.da.a.689.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.da.a.89.3	✓	48	15.14	odd	2	inner
840.2.da.a.89.12	yes	48	1.1	even	1	trivial
840.2.da.a.689.3	yes	48	7.3	odd	6	inner
840.2.da.a.689.12	yes	48	105.59	even	6	inner
840.2.da.b.89.13	yes	48	5.4	even	2
840.2.da.b.89.22	yes	48	3.2	odd	2
840.2.da.b.689.13	yes	48	21.17	even	6
840.2.da.b.689.22	yes	48	35.24	odd	6

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.da (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.381836 + 1.68944i) q^{3} +(1.27267 - 1.83856i) q^{5} +(1.96308 + 1.77379i) q^{7} +(-2.70840 - 1.29018i) q^{9} +O(q^{10})\)	\(q+(-0.381836 + 1.68944i) q^{3} +(1.27267 - 1.83856i) q^{5} +(1.96308 + 1.77379i) q^{7} +(-2.70840 - 1.29018i) q^{9} +(3.95951 - 2.28602i) q^{11} -1.57517 q^{13} +(2.62018 + 2.85213i) q^{15} +(4.06751 - 2.34838i) q^{17} +(0.0201141 + 0.0116129i) q^{19} +(-3.74628 + 2.63920i) q^{21} +(-0.0964144 + 0.166995i) q^{23} +(-1.76060 - 4.67977i) q^{25} +(3.21384 - 4.08305i) q^{27} +4.98429i q^{29} +(5.92678 - 3.42183i) q^{31} +(2.35022 + 7.56223i) q^{33} +(5.75957 - 1.35178i) q^{35} +(1.79834 + 1.03827i) q^{37} +(0.601455 - 2.66115i) q^{39} -5.85645 q^{41} +6.60899i q^{43} +(-5.81898 + 3.33759i) q^{45} +(4.93457 + 2.84898i) q^{47} +(0.707338 + 6.96417i) q^{49} +(2.41432 + 7.76850i) q^{51} +(-5.13922 - 8.90140i) q^{53} +(0.836172 - 10.1892i) q^{55} +(-0.0272995 + 0.0295473i) q^{57} +(-1.24724 - 2.16029i) q^{59} +(8.02451 + 4.63295i) q^{61} +(-3.02830 - 7.33685i) q^{63} +(-2.00468 + 2.89604i) q^{65} +(-5.87567 + 3.39232i) q^{67} +(-0.245313 - 0.226651i) q^{69} +13.0928i q^{71} +(7.23510 + 12.5316i) q^{73} +(8.57845 - 1.18753i) q^{75} +(11.8277 + 2.53570i) q^{77} +(6.60158 - 11.4343i) q^{79} +(5.67090 + 6.98863i) q^{81} +1.02664i q^{83} +(0.858979 - 10.4671i) q^{85} +(-8.42065 - 1.90318i) q^{87} +(-0.594890 + 1.03038i) q^{89} +(-3.09218 - 2.79402i) q^{91} +(3.51791 + 11.3195i) q^{93} +(0.0469496 - 0.0222016i) q^{95} +0.721802 q^{97} +(-13.6733 + 1.08301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 3 q^{5} - q^{9}+O(q^{10}) \) 48 * q - 3 * q^3 - 3 * q^5 - q^9	\( 48 q - 3 q^{3} - 3 q^{5} - q^{9} - 14 q^{15} + 5 q^{21} - 2 q^{23} + q^{25} + 6 q^{31} - 24 q^{33} + 4 q^{35} + 2 q^{39} - 3 q^{45} + 12 q^{51} + 6 q^{53} - 20 q^{57} + 18 q^{61} + 26 q^{63} - 10 q^{65} - 3 q^{75} - 2 q^{77} + 2 q^{79} - 9 q^{81} + 15 q^{87} + 24 q^{91} - 8 q^{93} - 6 q^{95} - 12 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 3 * q^5 - q^9 - 14 * q^15 + 5 * q^21 - 2 * q^23 + q^25 + 6 * q^31 - 24 * q^33 + 4 * q^35 + 2 * q^39 - 3 * q^45 + 12 * q^51 + 6 * q^53 - 20 * q^57 + 18 * q^61 + 26 * q^63 - 10 * q^65 - 3 * q^75 - 2 * q^77 + 2 * q^79 - 9 * q^81 + 15 * q^87 + 24 * q^91 - 8 * q^93 - 6 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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