LMFDB - Embedded newform 840.2.da.a.689.3

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			689.3
Character	$\chi$	$=$	840.689
Dual form			840.2.da.a.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65401 + 0.514040i) q^{3} +(-0.955903 - 2.02145i) q^{5} +(-1.96308 + 1.77379i) q^{7} +(2.47153 - 1.70046i) q^{9} +O(q^{10})$	\(q+(-1.65401 + 0.514040i) q^{3} +(-0.955903 - 2.02145i) q^{5} +(-1.96308 + 1.77379i) q^{7} +(2.47153 - 1.70046i) q^{9} +(-3.95951 - 2.28602i) q^{11} +1.57517 q^{13} +(2.62018 + 2.85213i) q^{15} +(4.06751 + 2.34838i) q^{17} +(0.0201141 - 0.0116129i) q^{19} +(2.33516 - 3.94297i) q^{21} +(-0.0964144 - 0.166995i) q^{23} +(-3.17250 + 3.86461i) q^{25} +(-3.21384 + 4.08305i) q^{27} +4.98429i q^{29} +(5.92678 + 3.42183i) q^{31} +(7.72419 + 1.74577i) q^{33} +(5.46213 + 2.27269i) q^{35} +(-1.79834 + 1.03827i) q^{37} +(-2.60535 + 0.809699i) q^{39} +5.85645 q^{41} +6.60899i q^{43} +(-5.79993 - 3.37059i) q^{45} +(4.93457 - 2.84898i) q^{47} +(0.707338 - 6.96417i) q^{49} +(-7.93487 - 1.79339i) q^{51} +(-5.13922 + 8.90140i) q^{53} +(-0.836172 + 10.1892i) q^{55} +(-0.0272995 + 0.0295473i) q^{57} +(1.24724 - 2.16029i) q^{59} +(8.02451 - 4.63295i) q^{61} +(-1.83554 + 7.72210i) q^{63} +(-1.50571 - 3.18412i) q^{65} +(5.87567 + 3.39232i) q^{67} +(0.245313 + 0.226651i) q^{69} +13.0928i q^{71} +(-7.23510 + 12.5316i) q^{73} +(3.26080 - 8.02292i) q^{75} +(11.8277 - 2.53570i) q^{77} +(6.60158 + 11.4343i) q^{79} +(3.21688 - 8.40545i) q^{81} -1.02664i q^{83} +(0.858979 - 10.4671i) q^{85} +(-2.56212 - 8.24409i) q^{87} +(0.594890 + 1.03038i) q^{89} +(-3.09218 + 2.79402i) q^{91} +(-11.5619 - 2.61315i) q^{93} +(-0.0427019 - 0.0295588i) q^{95} -0.721802 q^{97} +(-13.6733 + 1.08301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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
$3$	−1.65401	+	0.514040i	−0.954946	+	0.296781i
$3$	−1.65401	+	0.514040i	−0.954946	+	0.296781i
$4$		0			0
$5$	−0.955903	−	2.02145i	−0.427493	−	0.904019i
$5$	−0.955903	−	2.02145i	−0.427493	−	0.904019i
$6$		0			0
$7$	−1.96308	+	1.77379i	−0.741973	+	0.670430i
$7$	−1.96308	+	1.77379i	−0.741973	+	0.670430i
$8$		0			0
$9$	2.47153	−	1.70046i	0.823842	−	0.566819i
$10$		0			0
$11$	−3.95951	−	2.28602i	−1.19384	−	0.689262i	−0.234663	−	0.972077i	$-0.575399\pi$
$11$	−3.95951	−	2.28602i	−1.19384	−	0.689262i	−0.959175	+	0.282815i	$0.908732\pi$
$12$		0			0
$13$	1.57517			0.436873			0.218437	−	0.975851i	$-0.429904\pi$
$13$	1.57517			0.436873			0.218437	+	0.975851i	$0.429904\pi$
$14$		0			0
$15$	2.62018	+	2.85213i	0.676528	+	0.736417i
$16$		0			0
$17$	4.06751	+	2.34838i	0.986516	+	0.569565i	0.904231	−	0.427044i	$-0.140445\pi$
$17$	4.06751	+	2.34838i	0.986516	+	0.569565i	0.0822846	+	0.996609i	$0.473778\pi$
$18$		0			0
$19$	0.0201141	−	0.0116129i	0.00461449	−	0.00266418i	−0.497691	−	0.867354i	$-0.665819\pi$
$19$	0.0201141	−	0.0116129i	0.00461449	−	0.00266418i	0.502305	+	0.864690i	$0.332485\pi$
$20$		0			0
$21$	2.33516	−	3.94297i	0.509573	−	0.860427i
$22$		0			0
$23$	−0.0964144	−	0.166995i	−0.0201038	−	0.0348208i	0.855798	−	0.517309i	$-0.173066\pi$
$23$	−0.0964144	−	0.166995i	−0.0201038	−	0.0348208i	−0.875902	+	0.482489i	$0.839733\pi$
$24$		0			0
$25$	−3.17250	+	3.86461i	−0.634500	+	0.772923i
$26$		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	0.926668	−	0.375880i	$-0.122659\pi$
$31$	5.92678	+	3.42183i	1.06448	+	0.614579i	0.137813	+	0.990458i	$0.455993\pi$
$32$		0			0
$33$	7.72419	+	1.74577i	1.34461	+	0.303900i
$34$		0			0
$35$	5.46213	+	2.27269i	0.923269	+	0.384154i
$36$		0			0
$37$	−1.79834	+	1.03827i	−0.295645	+	0.170691i	−0.640485	−	0.767971i	$-0.721267\pi$
$37$	−1.79834	+	1.03827i	−0.295645	+	0.170691i	0.344840	+	0.938662i	$0.387933\pi$
$38$		0			0
$39$	−2.60535	+	0.809699i	−0.417190	+	0.129656i
$40$		0			0
$41$	5.85645			0.914624			0.457312	−	0.889306i	$-0.348812\pi$
$41$	5.85645			0.914624			0.457312	+	0.889306i	$0.348812\pi$
$42$		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
$45$	−5.79993	−	3.37059i	−0.864602	−	0.502458i
$46$		0			0
$47$	4.93457	−	2.84898i	0.719781	−	0.415566i	−0.0948910	−	0.995488i	$-0.530250\pi$
$47$	4.93457	−	2.84898i	0.719781	−	0.415566i	0.814672	+	0.579922i	$0.196917\pi$
$48$		0			0
$49$	0.707338	−	6.96417i	0.101048	−	0.994882i
$50$		0			0
$51$	−7.93487	−	1.79339i	−1.11110	−	0.251124i
$52$		0			0
$53$	−5.13922	+	8.90140i	−0.705927	+	1.22270i	0.260429	+	0.965493i	$0.416136\pi$
$53$	−5.13922	+	8.90140i	−0.705927	+	1.22270i	−0.966356	+	0.257208i	$0.917197\pi$
$54$		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	$-0.781417\pi$
$59$	1.24724	−	2.16029i	0.162377	−	0.281246i	0.935721	+	0.352741i	$0.114750\pi$
$60$		0			0
$61$	8.02451	−	4.63295i	1.02743	−	0.593189i	0.111185	−	0.993800i	$-0.464535\pi$
$61$	8.02451	−	4.63295i	1.02743	−	0.593189i	0.916248	+	0.400611i	$0.131202\pi$
$62$		0			0
$63$	−1.83554	+	7.72210i	−0.231256	+	0.972893i
$64$		0			0
$65$	−1.50571	−	3.18412i	−0.186760	−	0.394941i
$66$		0			0
$67$	5.87567	+	3.39232i	0.717827	+	0.414438i	0.813952	−	0.580932i	$-0.197312\pi$
$67$	5.87567	+	3.39232i	0.717827	+	0.414438i	−0.0961254	+	0.995369i	$0.530645\pi$
$68$		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	0.0372407	+	0.999306i	$0.488143\pi$
$73$	−7.23510	+	12.5316i	−0.846804	+	1.46671i	−0.884045	+	0.467402i	$0.845190\pi$
$74$		0			0
$75$	3.26080	−	8.02292i	0.376524	−	0.926407i
$76$		0			0
$77$	11.8277	−	2.53570i	1.34790	−	0.288970i
$78$		0			0
$79$	6.60158	+	11.4343i	0.742736	+	1.28646i	0.951245	+	0.308436i	$0.0998055\pi$
$79$	6.60158	+	11.4343i	0.742736	+	1.28646i	−0.208509	+	0.978020i	$0.566861\pi$
$80$		0			0
$81$	3.21688	−	8.40545i	0.357431	−	0.933939i
$82$		0			0
$83$		−	1.02664i		−	0.112688i	−0.998411	−	0.0563442i	$-0.982056\pi$
$83$		−	1.02664i		−	0.112688i	0.998411	−	0.0563442i	$-0.0179444\pi$
$84$		0			0
$85$	0.858979	−	10.4671i	0.0931694	−	1.13531i
$86$		0			0
$87$	−2.56212	−	8.24409i	−0.274689	−	0.883859i
$88$		0			0
$89$	0.594890	+	1.03038i	0.0630583	+	0.109220i	0.895831	−	0.444395i	$-0.146581\pi$
$89$	0.594890	+	1.03038i	0.0630583	+	0.109220i	−0.832773	+	0.553615i	$0.813248\pi$
$90$		0			0
$91$	−3.09218	+	2.79402i	−0.324148	+	0.292893i
$92$		0			0
$93$	−11.5619	−	2.61315i	−1.19892	−	0.270971i
$94$		0			0
$95$	−0.0427019	−	0.0295588i	−0.00438113	−	0.00303267i
$96$		0			0
$97$	−0.721802			−0.0732879			−0.0366440	−	0.999328i	$-0.511667\pi$
$97$	−0.721802			−0.0732879			−0.0366440	+	0.999328i	$0.511667\pi$
$98$		0			0
$99$	−13.6733	+	1.08301i	−1.37422	+	0.108847i
$100$		0			0
$101$	7.55211	−	13.0806i	0.751463	−	1.30157i	−0.195650	−	0.980674i	$-0.562682\pi$
$101$	7.55211	−	13.0806i	0.751463	−	1.30157i	0.947114	−	0.320899i	$-0.103985\pi$
$102$		0			0
$103$	2.17456	+	3.76645i	0.214266	+	0.371120i	0.953045	−	0.302828i	$-0.0979307\pi$
$103$	2.17456	+	3.76645i	0.214266	+	0.371120i	−0.738779	+	0.673947i	$0.764597\pi$
$104$		0			0
$105$	−10.2027	−	0.951300i	−0.995681	−	0.0928374i
$106$		0			0
$107$	−6.53479	−	11.3186i	−0.631742	−	1.09421i	−0.987195	−	0.159516i	$-0.949007\pi$
$107$	−6.53479	−	11.3186i	−0.631742	−	1.09421i	0.355453	−	0.934694i	$-0.384327\pi$
$108$		0			0
$109$	−3.63655	+	6.29868i	−0.348318	+	0.603304i	−0.985951	−	0.167036i	$-0.946580\pi$
$109$	−3.63655	+	6.29868i	−0.348318	+	0.603304i	0.637633	+	0.770340i	$0.279914\pi$
$110$		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
$115$	−0.245408	+	0.354527i	−0.0228844	+	0.0330598i
$116$		0			0
$117$	3.89307	−	2.67851i	0.359914	−	0.247628i
$118$		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
$123$	−9.68666	+	3.01045i	−0.873417	+	0.271443i
$124$		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
$129$	−3.39728	−	10.9314i	−0.299114	−	0.962453i
$130$		0			0
$131$	−6.23882	−	10.8060i	−0.545088	−	0.944121i	−0.998601	−	0.0528709i	$-0.983163\pi$
$131$	−6.23882	−	10.8060i	−0.545088	−	0.944121i	0.453513	−	0.891250i	$-0.350171\pi$
$132$		0			0
$133$	−0.0188867	+	0.0584751i	−0.00163768	+	0.00507044i
$134$		0			0
$135$	11.3258	+	2.59361i	0.974768	+	0.223222i
$136$		0			0
$137$	−3.56853	+	6.18087i	−0.304880	+	0.528067i	−0.977235	−	0.212162i	$-0.931950\pi$
$137$	−3.56853	+	6.18087i	−0.304880	+	0.528067i	0.672355	+	0.740229i	$0.265283\pi$
$138$		0			0
$139$			9.40154i			0.797428i	0.917075	+	0.398714i	$0.130543\pi$
$139$			9.40154i			0.797428i	−0.917075	+	0.398714i	$0.869457\pi$
$140$		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
$145$	10.0755	−	4.76450i	0.836723	−	0.395670i
$146$		0			0
$147$	2.40991	+	11.8824i	0.198766	+	0.980047i
$148$		0			0
$149$	−1.18404	+	0.683607i	−0.0970005	+	0.0560033i	−0.547716	−	0.836665i	$-0.684502\pi$
$149$	−1.18404	+	0.683607i	−0.0970005	+	0.0560033i	0.450715	+	0.892668i	$0.351169\pi$
$150$		0			0
$151$	11.4085	−	19.7601i	0.928411	−	1.60806i	0.142431	−	0.989805i	$-0.454508\pi$
$151$	11.4085	−	19.7601i	0.928411	−	1.60806i	0.785981	−	0.618251i	$-0.212158\pi$
$152$		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	0.142514	−	0.989793i	$-0.454481\pi$
$157$	11.6334	−	20.1496i	0.928443	−	1.60811i	0.785929	−	0.618317i	$-0.212185\pi$
$158$		0			0
$159$	3.92468	−	17.3648i	0.311247	−	1.37712i
$160$		0			0
$161$	0.485482	+	0.156804i	0.0382614	+	0.0123579i
$162$		0			0
$163$	19.5250	−	11.2727i	1.52931	−	0.882950i	0.529923	−	0.848046i	$-0.322221\pi$
$163$	19.5250	−	11.2727i	1.52931	−	0.882950i	0.999391	−	0.0349039i	$-0.0111125\pi$
$164$		0			0
$165$	−3.85459	−	17.2828i	−0.300080	−	1.34547i
$166$		0			0
$167$		−	2.56225i		−	0.198273i	−0.995074	−	0.0991364i	$-0.968392\pi$
$167$		−	2.56225i		−	0.198273i	0.995074	−	0.0991364i	$-0.0316080\pi$
$168$		0			0
$169$	−10.5188			−0.809142
$170$		0			0
$171$	0.0299653	−	0.0629047i	0.00229150	−	0.00481044i
$172$		0			0
$173$	−19.0147	+	10.9782i	−1.44566	+	0.834654i	−0.998219	−	0.0596581i	$-0.980999\pi$
$173$	−19.0147	+	10.9782i	−1.44566	+	0.834654i	−0.447444	+	0.894312i	$0.647666\pi$
$174$		0			0
$175$	−0.627152	−	13.2139i	−0.0474083	−	0.998876i
$176$		0			0
$177$	−0.952485	+	4.21429i	−0.0715931	+	0.316765i
$178$		0			0
$179$	5.32644	+	3.07522i	0.398117	+	0.229853i	0.685671	−	0.727911i	$-0.259509\pi$
$179$	5.32644	+	3.07522i	0.398117	+	0.229853i	−0.287554	+	0.957764i	$0.592842\pi$
$180$		0			0
$181$			21.8923i			1.62725i	0.581393	+	0.813623i	$0.302508\pi$
$181$			21.8923i			1.62725i	−0.581393	+	0.813623i	$0.697492\pi$
$182$		0			0
$183$	−10.8911	+	11.7879i	−0.805096	+	0.871386i
$184$		0			0
$185$	3.81785	+	2.64276i	0.280694	+	0.194300i
$186$		0			0
$187$	−10.7369	−	18.5968i	−0.785159	−	1.35994i
$188$		0			0
$189$	−0.933459	−	13.7160i	−0.0678991	−	0.997692i
$190$		0			0
$191$	−6.72916	+	3.88508i	−0.486905	+	0.281115i	−0.723290	−	0.690545i	$-0.757371\pi$
$191$	−6.72916	+	3.88508i	−0.486905	+	0.281115i	0.236385	+	0.971660i	$0.424037\pi$
$192$		0			0
$193$	7.48274	+	4.32016i	0.538620	+	0.310972i	0.744519	−	0.667601i	$-0.232679\pi$
$193$	7.48274	+	4.32016i	0.538620	+	0.310972i	−0.205900	+	0.978573i	$0.566012\pi$
$194$		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	0.953181	−	0.302399i	$-0.0977875\pi$
$199$	16.4751	+	9.51189i	1.16789	+	0.674280i	0.214705	+	0.976679i	$0.431121\pi$
$200$		0			0
$201$	−11.4622	−	2.59062i	−0.808483	−	0.182728i
$202$		0			0
$203$	−8.84108	−	9.78454i	−0.620522	−	0.686740i
$204$		0			0
$205$	−5.59820	−	11.8385i	−0.390995	−	0.826838i
$206$		0			0
$207$	−0.522258	−	0.248783i	−0.0362994	−	0.0172916i
$208$		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
$213$	−6.73024	−	21.6557i	−0.461148	−	1.48383i
$214$		0			0
$215$	13.3597	−	6.31755i	0.911126	−	0.430853i
$216$		0			0
$217$	−17.7043	+	3.79555i	−1.20185	+	0.257659i
$218$		0			0
$219$	5.52524	−	24.4465i	0.373361	−	1.65194i
$220$		0			0
$221$	6.40701	+	3.69909i	0.430982	+	0.248828i
$222$		0			0
$223$	−1.13076			−0.0757211			−0.0378605	−	0.999283i	$-0.512054\pi$
$223$	−1.13076			−0.0757211			−0.0378605	+	0.999283i	$0.512054\pi$
$224$		0			0
$225$	−1.26930	+	14.9462i	−0.0846202	+	0.996413i
$226$		0			0
$227$	−0.0771562	−	0.0445462i	−0.00512104	−	0.00295663i	0.497437	−	0.867500i	$-0.334274\pi$
$227$	−0.0771562	−	0.0445462i	−0.00512104	−	0.00295663i	−0.502558	+	0.864543i	$0.667608\pi$
$228$		0			0
$229$	7.76866	−	4.48524i	0.513368	−	0.296393i	−0.220849	−	0.975308i	$-0.570883\pi$
$229$	7.76866	−	4.48524i	0.513368	−	0.296393i	0.734217	+	0.678915i	$0.237550\pi$
$230$		0			0
$231$	−18.2598	+	10.2740i	−1.20141	+	0.675981i
$232$		0			0
$233$	−11.0036	−	19.0589i	−0.720873	−	1.24859i	−0.960650	−	0.277760i	$-0.910408\pi$
$233$	−11.0036	−	19.0589i	−0.720873	−	1.24859i	0.239778	−	0.970828i	$-0.422925\pi$
$234$		0			0
$235$	−10.4760	−	7.25163i	−0.683380	−	0.473044i
$236$		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	0.889891	−	0.456174i	$-0.150780\pi$
$241$	14.5893	+	8.42312i	0.939778	+	0.542581i	0.0498872	+	0.998755i	$0.484114\pi$
$242$		0			0
$243$	−1.00003	+	15.5563i	−0.0641520	+	0.997940i
$244$		0			0
$245$	−14.7539	+	5.22722i	−0.942589	+	0.333955i
$246$		0			0
$247$	0.0316831	−	0.0182922i	0.00201595	−	0.00116391i
$248$		0			0
$249$	0.527734	+	1.69808i	0.0334438	+	0.107611i
$250$		0			0
$251$	8.43606			0.532479			0.266240	−	0.963907i	$-0.414219\pi$
$251$	8.43606			0.532479			0.266240	+	0.963907i	$0.414219\pi$
$252$		0			0
$253$			0.881623i			0.0554271i
$254$		0			0
$255$	3.95973	+	17.7542i	0.247968	+	1.11181i
$256$		0			0
$257$	−15.2289	+	8.79239i	−0.949951	+	0.548454i	−0.893066	−	0.449926i	$-0.851450\pi$
$257$	−15.2289	+	8.79239i	−0.949951	+	0.548454i	−0.0568852	+	0.998381i	$0.518117\pi$
$258$		0			0
$259$	1.68860	−	5.22808i	0.104925	−	0.324857i
$260$		0			0
$261$	8.47558	+	12.3188i	0.524625	+	0.762515i
$262$		0			0
$263$	4.53721	−	7.85868i	0.279776	−	0.484587i	−0.691553	−	0.722326i	$-0.743073\pi$
$263$	4.53721	−	7.85868i	0.279776	−	0.484587i	0.971329	+	0.237739i	$0.0764064\pi$
$264$		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	0.121006	+	0.992652i	$0.461388\pi$
$269$	−13.1072	+	22.7023i	−0.799158	+	1.38418i	−0.920165	+	0.391531i	$0.871945\pi$
$270$		0			0
$271$	−19.0011	+	10.9703i	−1.15424	+	0.666399i	−0.949916	−	0.312505i	$-0.898832\pi$
$271$	−19.0011	+	10.9703i	−1.15424	+	0.666399i	−0.204321	+	0.978904i	$0.565499\pi$
$272$		0			0
$273$	3.67827	−	6.21085i	0.222619	−	0.375898i
$274$		0			0
$275$	21.3961	−	8.04956i	1.29024	−	0.485407i
$276$		0			0
$277$	20.6278	+	11.9094i	1.23940	+	0.715569i	0.968972	−	0.247171i	$-0.0795009\pi$
$277$	20.6278	+	11.9094i	1.23940	+	0.715569i	0.270430	+	0.962740i	$0.412834\pi$
$278$		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	−0.103086	+	0.994672i	$0.532872\pi$
$283$	−15.3583	+	26.6013i	−0.912955	+	1.58128i	−0.809869	+	0.586611i	$0.800462\pi$
$284$		0			0
$285$	0.0858240	+	0.0269402i	0.00508378	+	0.00159580i
$286$		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
$291$	1.19387	−	0.371035i	0.0699860	−	0.0217505i
$292$		0			0
$293$			22.7443i			1.32874i	0.747405	+	0.664369i	$0.231300\pi$
$293$			22.7443i			1.32874i	−0.747405	+	0.664369i	$0.768700\pi$
$294$		0			0
$295$	−5.55916	−	0.456212i	−0.323667	−	0.0265617i
$296$		0			0
$297$	22.0592	−	8.81995i	1.28000	−	0.511786i
$298$		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
$303$	−5.76733	+	25.5177i	−0.331324	+	1.46595i
$304$		0			0
$305$	−17.0359	−	11.7925i	−0.975474	−	0.675235i
$306$		0			0
$307$	−4.56762			−0.260688			−0.130344	−	0.991469i	$-0.541608\pi$
$307$	−4.56762			−0.260688			−0.130344	+	0.991469i	$0.541608\pi$
$308$		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	$-0.946829\pi$
$311$	−6.15556	+	10.6617i	−0.349050	+	0.604572i	0.637031	+	0.770838i	$0.280162\pi$
$312$		0			0
$313$	−3.33440	−	5.77536i	−0.188472	−	0.326442i	0.756269	−	0.654261i	$-0.227020\pi$
$313$	−3.33440	−	5.77536i	−0.188472	−	0.326442i	−0.944741	+	0.327818i	$0.893687\pi$
$314$		0			0
$315$	17.3644	−	3.67113i	0.978374	−	0.206845i
$316$		0			0
$317$	4.81329	+	8.33686i	0.270341	+	0.468245i	0.968949	−	0.247260i	$-0.0795301\pi$
$317$	4.81329	+	8.33686i	0.270341	+	0.468245i	−0.698608	+	0.715505i	$0.746197\pi$
$318$		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
$325$	−4.99722	+	6.08742i	−0.277196	+	0.337669i
$326$		0			0
$327$	2.77713	−	12.2874i	0.153575	−	0.679497i
$328$		0			0
$329$	−4.63345	+	14.3456i	−0.255451	+	0.790901i
$330$		0			0
$331$	−5.97347	−	10.3464i	−0.328332	−	0.568687i	0.653849	−	0.756625i	$-0.273153\pi$
$331$	−5.97347	−	10.3464i	−0.328332	−	0.568687i	−0.982181	+	0.187938i	$0.939820\pi$
$332$		0			0
$333$	−2.67910	+	5.62411i	−0.146814	+	0.308200i
$334$		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
$339$	23.0767	−	7.17184i	1.25335	−	0.389521i
$340$		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
$345$	0.223667	−	0.712543i	0.0120418	−	0.0383620i
$346$		0			0
$347$	11.0394	−	19.1207i	0.592624	−	1.02646i	−0.401253	−	0.915967i	$-0.631425\pi$
$347$	11.0394	−	19.1207i	0.592624	−	1.02646i	0.993877	−	0.110488i	$-0.0352414\pi$
$348$		0			0
$349$		−	1.44889i		−	0.0775573i	−0.999248	−	0.0387787i	$-0.987653\pi$
$349$		−	1.44889i		−	0.0775573i	0.999248	−	0.0387787i	$-0.0123467\pi$
$350$		0			0
$351$	−5.06233	+	6.43148i	−0.270207	+	0.343287i
$352$		0			0
$353$	17.4981	+	10.1026i	0.931332	+	0.537705i	0.887232	−	0.461323i	$-0.152625\pi$
$353$	17.4981	+	10.1026i	0.931332	+	0.537705i	0.0440991	+	0.999027i	$0.485958\pi$
$354$		0			0
$355$	26.4665	−	12.5155i	1.40470	−	0.664253i
$356$		0			0
$357$	18.7579	−	10.5542i	0.992771	−	0.558590i
$358$		0			0
$359$	6.81277	−	3.93336i	0.359564	−	0.207595i	−0.309325	−	0.950956i	$-0.600103\pi$
$359$	6.81277	−	3.93336i	0.359564	−	0.207595i	0.668890	+	0.743362i	$0.266770\pi$
$360$		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	$-0.984455\pi$
$367$	−8.75729	+	15.1681i	−0.457127	+	0.791767i	0.541681	+	0.840584i	$0.317788\pi$
$368$		0			0
$369$	14.4744	−	9.95866i	0.753506	−	0.518427i
$370$		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	$-0.844135\pi$
$373$	−17.6990	+	10.2185i	−0.916418	+	0.529094i	−0.0339275	+	0.999424i	$0.510802\pi$
$374$		0			0
$375$	−19.3349	+	1.07760i	−0.998451	+	0.0556471i
$376$		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
$381$	5.13048	+	16.5082i	0.262842	+	0.845741i
$382$		0			0
$383$	−0.403621	+	0.233031i	−0.0206241	+	0.0119073i	−0.510277	−	0.860010i	$-0.670457\pi$
$383$	−0.403621	+	0.233031i	−0.0206241	+	0.0119073i	0.489653	+	0.871918i	$0.337124\pi$
$384$		0			0
$385$	−16.4320	−	21.4853i	−0.837450	−	1.09499i
$386$		0			0
$387$	11.2383	+	16.3343i	0.571276	+	0.830319i
$388$		0			0
$389$	−14.1455	−	8.16690i	−0.717205	−	0.414078i	0.0965184	−	0.995331i	$-0.469229\pi$
$389$	−14.1455	−	8.16690i	−0.717205	−	0.414078i	−0.813723	+	0.581253i	$0.802563\pi$
$390$		0			0
$391$		−	0.905669i		−	0.0458017i
$392$		0			0
$393$	15.8738	+	14.6662i	0.800727	+	0.739812i
$394$		0			0
$395$	16.8033	−	24.2748i	0.845467	−	1.22140i
$396$		0			0
$397$	9.37186	+	16.2325i	0.470360	+	0.814688i	0.999425	−	0.0338935i	$-0.0107907\pi$
$397$	9.37186	+	16.2325i	0.470360	+	0.814688i	−0.529065	+	0.848581i	$0.677457\pi$
$398$		0			0
$399$	0.00118031	−	0.106427i	5.90896e−5	−	0.00532803i
$400$		0			0
$401$	−3.15425	+	1.82111i	−0.157516	+	0.0909417i	−0.576686	−	0.816966i	$-0.695654\pi$
$401$	−3.15425	+	1.82111i	−0.157516	+	0.0909417i	0.419170	+	0.907908i	$0.362321\pi$
$402$		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	0.436604	−	0.899654i	$-0.356181\pi$
$409$	−2.51215	−	1.45039i	−0.124218	−	0.0717171i	−0.560821	+	0.827937i	$0.689515\pi$
$410$		0			0
$411$	2.72518	−	12.0576i	0.134423	−	0.594758i
$412$		0			0
$413$	1.38347	+	6.45317i	0.0680759	+	0.317540i
$414$		0			0
$415$	−2.07530	+	0.981369i	−0.101872	+	0.0481735i
$416$		0			0
$417$	−4.83276	−	15.5503i	−0.236662	−	0.761500i
$418$		0			0
$419$	15.8585			0.774736			0.387368	−	0.921925i	$-0.373384\pi$
$419$	15.8585			0.774736			0.387368	+	0.921925i	$0.373384\pi$
$420$		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
$423$	7.35136	−	15.4323i	0.357435	−	0.750346i
$424$		0			0
$425$	−21.9797	+	8.26912i	−1.06617	+	0.401111i
$426$		0			0
$427$	−7.53484	+	23.3286i	−0.364637	+	1.12895i
$428$		0			0
$429$	12.1669	+	2.74988i	0.587424	+	0.132766i
$430$		0			0
$431$	13.1009	+	7.56382i	0.631050	+	0.364337i	0.781158	−	0.624333i	$-0.214629\pi$
$431$	13.1009	+	7.56382i	0.631050	+	0.364337i	−0.150109	+	0.988669i	$0.547962\pi$
$432$		0			0
$433$	2.69681			0.129601			0.0648003	−	0.997898i	$-0.479359\pi$
$433$	2.69681			0.129601			0.0648003	+	0.997898i	$0.479359\pi$
$434$		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	−0.302957	−	0.953004i	$-0.597974\pi$
$439$	7.77101	−	4.48659i	0.370890	−	0.214133i	0.673847	+	0.738871i	$0.264641\pi$
$440$		0			0
$441$	−10.0941	−	18.4149i	−0.480670	−	0.876901i
$442$		0			0
$443$	19.1374	+	33.1469i	0.909244	+	1.57486i	0.815117	+	0.579296i	$0.196672\pi$
$443$	19.1374	+	33.1469i	0.909244	+	1.57486i	0.0941261	+	0.995560i	$0.469994\pi$
$444$		0			0
$445$	1.51420	−	2.18748i	0.0717801	−	0.103697i
$446$		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
$453$	−8.71235	+	38.5479i	−0.409342	+	1.81114i
$454$		0			0
$455$	8.60378	+	3.57986i	0.403351	+	0.167827i
$456$		0			0
$457$	−4.35184	+	2.51254i	−0.203571	+	0.117531i	−0.598320	−	0.801257i	$-0.704165\pi$
$457$	−4.35184	+	2.51254i	−0.203571	+	0.117531i	0.394749	+	0.918789i	$0.370831\pi$
$458$		0			0
$459$	−22.6608	+	9.06052i	−1.05772	+	0.422909i
$460$		0			0
$461$	26.5502			1.23656			0.618282	−	0.785956i	$-0.287829\pi$
$461$	26.5502			1.23656			0.618282	+	0.785956i	$0.287829\pi$
$462$		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
$465$	5.76974	+	25.8698i	0.267565	+	1.19968i
$466$		0			0
$467$	9.45358	−	5.45803i	0.437460	−	0.252567i	−0.265060	−	0.964232i	$-0.585392\pi$
$467$	9.45358	−	5.45803i	0.437460	−	0.252567i	0.702520	+	0.711664i	$0.252058\pi$
$468$		0			0
$469$	−17.5516	+	3.76282i	−0.810460	+	0.173751i
$470$		0			0
$471$	−8.88406	+	39.3077i	−0.409356	+	1.81120i
$472$		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	$-0.698118\pi$
$479$	9.01995	−	15.6230i	0.412132	−	0.713834i	0.995123	+	0.0986452i	$0.0314509\pi$
$480$		0			0
$481$	−2.83269	+	1.63545i	−0.129159	+	0.0745702i
$482$		0			0
$483$	−0.883598	−	0.00979939i	−0.0402051	−	0.000445888i
$484$		0			0
$485$	0.689973	+	1.45909i	0.0313301	+	0.0662537i
$486$		0			0
$487$	31.4337	+	18.1482i	1.42440	+	0.822375i	0.996671	−	0.0815333i	$-0.0259817\pi$
$487$	31.4337	+	18.1482i	1.42440	+	0.822375i	0.427725	+	0.903909i	$0.359315\pi$
$488$		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
$495$	15.2596	+	26.6046i	0.685869	+	1.19579i
$496$		0			0
$497$	−23.2239	−	25.7022i	−1.04174	−	1.15290i
$498$		0			0
$499$	−11.7602	−	20.3692i	−0.526458	−	0.911852i	−0.999525	−	0.0308254i	$-0.990186\pi$
$499$	−11.7602	−	20.3692i	−0.526458	−	0.911852i	0.473067	−	0.881027i	$-0.343147\pi$
$500$		0			0
$501$	1.31710	+	4.23800i	0.0588436	+	0.189340i
$502$		0			0
$503$		−	5.11496i		−	0.228065i	−0.993477	−	0.114032i	$-0.963623\pi$
$503$		−	5.11496i		−	0.228065i	0.993477	−	0.114032i	$-0.0363768\pi$
$504$		0			0
$505$	−33.6609	−	2.76238i	−1.49789	−	0.122924i
$506$		0			0
$507$	17.3983	−	5.40711i	0.772686	−	0.240138i
$508$		0			0
$509$	15.6297	+	27.0714i	0.692774	+	1.19992i	0.970925	+	0.239382i	$0.0769450\pi$
$509$	15.6297	+	27.0714i	0.692774	+	1.19992i	−0.278151	+	0.960537i	$0.589722\pi$
$510$		0			0
$511$	−8.02530	−	37.4340i	−0.355018	−	1.65598i
$512$		0			0
$513$	−0.0172275	+	0.119449i	−0.000760612	+	0.00527379i
$514$		0			0
$515$	5.53502	−	7.99613i	0.243902	−	0.352351i
$516$		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	$-0.689325\pi$
$521$	9.97790	−	17.2822i	0.437140	−	0.757148i	0.997468	+	0.0711229i	$0.0226582\pi$
$522$		0			0
$523$	−15.2872	−	26.4783i	−0.668464	−	1.15781i	−0.978334	−	0.207034i	$-0.933619\pi$
$523$	−15.2872	−	26.4783i	−0.668464	−	1.15781i	0.309870	−	0.950779i	$-0.399714\pi$
$524$		0			0
$525$	7.82978	+	21.5336i	0.341720	+	0.939802i
$526$		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
$535$	−16.6333	+	24.0292i	−0.719121	+	1.03887i
$536$		0			0
$537$	−10.3908	−	2.34846i	−0.448396	−	0.101343i
$538$		0			0
$539$	−18.7210	+	25.9577i	−0.806369	+	1.11808i
$540$		0			0
$541$	20.1289	+	34.8642i	0.865407	+	1.49893i	0.866642	+	0.498930i	$0.166273\pi$
$541$	20.1289	+	34.8642i	0.865407	+	1.49893i	−0.00123544	+	0.999999i	$0.500393\pi$
$542$		0			0
$543$	−11.2535	−	36.2103i	−0.482936	−	1.55393i
$544$		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
$549$	11.9546	−	25.0958i	0.510212	−	1.07106i
$550$		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
$555$	−7.67326	−	2.40864i	−0.325712	−	0.102241i
$556$		0			0
$557$	−14.7291	+	25.5116i	−0.624093	+	1.08096i	0.364623	+	0.931155i	$0.381198\pi$
$557$	−14.7291	+	25.5116i	−0.624093	+	1.08096i	−0.988716	+	0.149805i	$0.952135\pi$
$558$		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	−0.428365	−	0.903606i	$-0.640910\pi$
$563$	−33.8141	−	19.5226i	−1.42509	−	0.822778i	−0.996728	+	0.0808279i	$0.974244\pi$
$564$		0			0
$565$	13.3367	+	28.2031i	0.561078	+	1.18651i
$566$		0			0
$567$	8.59452	+	22.2066i	0.360936	+	0.932591i
$568$		0			0
$569$	−31.8770	+	18.4042i	−1.33635	+	0.771543i	−0.986265	−	0.165174i	$-0.947182\pi$
$569$	−31.8770	+	18.4042i	−1.33635	+	0.771543i	−0.350088	+	0.936717i	$0.613848\pi$
$570$		0			0
$571$	3.27778	−	5.67728i	0.137171	−	0.237587i	−0.789254	−	0.614067i	$-0.789532\pi$
$571$	3.27778	−	5.67728i	0.137171	−	0.237587i	0.926425	+	0.376480i	$0.122866\pi$
$572$		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	$-0.759730\pi$
$577$	5.50501	−	9.53496i	0.229177	−	0.396945i	0.957564	+	0.288220i	$0.0930633\pi$
$578$		0			0
$579$	−14.5973	−	3.29918i	−0.606643	−	0.137109i
$580$		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
$585$	−9.13586	−	5.30924i	−0.377721	−	0.219510i
$586$		0			0
$587$		−	21.2051i		−	0.875227i	−0.899163	−	0.437614i	$-0.855824\pi$
$587$		−	21.2051i		−	0.875227i	0.899163	−	0.437614i	$-0.144176\pi$
$588$		0			0
$589$	0.158949			0.00654938
$590$		0			0
$591$	−16.5570	+	5.14563i	−0.681064	+	0.211663i
$592$		0			0
$593$	32.8813	−	18.9841i	1.35027	−	0.779582i	0.361987	−	0.932183i	$-0.382098\pi$
$593$	32.8813	−	18.9841i	1.35027	−	0.779582i	0.988288	+	0.152601i	$0.0487651\pi$
$594$		0			0
$595$	16.8801	+	22.0713i	0.692019	+	0.904836i
$596$		0			0
$597$	−32.1395	−	7.26395i	−1.31538	−	0.297294i
$598$		0			0
$599$	−20.8018	−	12.0099i	−0.849937	−	0.490711i	0.0106928	−	0.999943i	$-0.496596\pi$
$599$	−20.8018	−	12.0099i	−0.849937	−	0.490711i	−0.860629	+	0.509232i	$0.829930\pi$
$600$		0			0
$601$		−	38.3360i		−	1.56376i	−0.623431	−	0.781878i	$-0.714262\pi$
$601$		−	38.3360i		−	1.56376i	0.623431	−	0.781878i	$-0.285738\pi$
$602$		0			0
$603$	20.2904	−	1.60712i	0.826287	−	0.0654472i
$604$		0			0
$605$	12.6041	−	18.2084i	0.512429	−	0.740277i
$606$		0			0
$607$	−14.2254	−	24.6391i	−0.577390	−	1.00007i	−0.995777	−	0.0917998i	$-0.970738\pi$
$607$	−14.2254	−	24.6391i	−0.577390	−	1.00007i	0.418388	−	0.908268i	$-0.362595\pi$
$608$		0			0
$609$	19.6529	+	11.6391i	0.796377	+	0.471640i
$610$		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	$-0.335467\pi$
$613$	−0.287485	−	0.165979i	−0.0116114	−	0.00670384i	−0.505794	+	0.862654i	$0.668801\pi$
$614$		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	−0.472760	−	0.881191i	$-0.656742\pi$
$619$	−36.6297	−	21.1482i	−1.47227	−	0.850018i	−0.999514	+	0.0311740i	$0.990075\pi$
$620$		0			0
$621$	0.991707	+	0.143029i	0.0397958	+	0.00573956i
$622$		0			0
$623$	−2.99549	−	0.967505i	−0.120012	−	0.0387623i
$624$		0			0
$625$	−4.87048	−	24.5210i	−0.194819	−	0.980839i
$626$		0			0
$627$	0.175639	−	0.0545855i	0.00701433	−	0.00217994i
$628$		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
$633$	37.8820	−	11.7731i	1.50567	−	0.467938i
$634$		0			0
$635$	−20.1755	+	9.54057i	−0.800638	+	0.378606i
$636$		0			0
$637$	1.11418	−	10.9697i	0.0441453	−	0.434637i
$638$		0			0
$639$	22.2638	+	32.3593i	0.880743	+	1.28011i
$640$		0			0
$641$	24.8431	+	14.3432i	0.981243	+	0.566521i	0.902645	−	0.430385i	$-0.141622\pi$
$641$	24.8431	+	14.3432i	0.981243	+	0.566521i	0.0785980	+	0.996906i	$0.474956\pi$
$642$		0			0
$643$	33.7651			1.33157			0.665783	−	0.746145i	$-0.268098\pi$
$643$	33.7651			1.33157			0.665783	+	0.746145i	$0.268098\pi$
$644$		0			0
$645$	−18.8497	+	17.3168i	−0.742207	+	0.681846i
$646$		0			0
$647$	3.78572	+	2.18568i	0.148832	+	0.0859281i	0.572567	−	0.819858i	$-0.305948\pi$
$647$	3.78572	+	2.18568i	0.148832	+	0.0859281i	−0.423735	+	0.905786i	$0.639281\pi$
$648$		0			0
$649$	−9.87696	+	5.70246i	−0.387704	+	0.223841i
$650$		0			0
$651$	27.3321	−	15.3786i	1.07123	−	0.602736i
$652$		0			0
$653$	2.10337	+	3.64315i	0.0823113	+	0.142567i	0.904242	−	0.427020i	$-0.140436\pi$
$653$	2.10337	+	3.64315i	0.0823113	+	0.142567i	−0.821931	+	0.569587i	$0.807103\pi$
$654$		0			0
$655$	−15.8800	+	22.9409i	−0.620482	+	0.896375i
$656$		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	0.369853	−	0.929090i	$-0.379408\pi$
$661$	−6.42328	−	3.70848i	−0.249837	−	0.144243i	−0.619689	+	0.784847i	$0.712741\pi$
$662$		0			0
$663$	−12.4988	−	2.82489i	−0.485412	−	0.109710i
$664$		0			0
$665$	0.136258	−	0.0177181i	0.00528387	−	0.000687077i
$666$		0			0
$667$	0.832350	−	0.480557i	0.0322287	−	0.0186073i
$668$		0			0
$669$	1.87029	−	0.581254i	0.0723095	−	0.0224726i
$670$		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
$675$	−5.58350	−	25.3737i	−0.214909	−	0.976634i
$676$		0			0
$677$	−11.1207	+	6.42051i	−0.427401	+	0.246760i	−0.698239	−	0.715865i	$-0.746033\pi$
$677$	−11.1207	+	6.42051i	−0.427401	+	0.246760i	0.270838	+	0.962625i	$0.412699\pi$
$678$		0			0
$679$	1.41695	−	1.28033i	0.0543777	−	0.0491344i
$680$		0			0
$681$	0.150516	+	0.0340186i	0.00576779	+	0.00130360i
$682$		0			0
$683$	−15.1628	+	26.2628i	−0.580190	+	1.00492i	0.415267	+	0.909700i	$0.363688\pi$
$683$	−15.1628	+	26.2628i	−0.580190	+	1.00492i	−0.995456	+	0.0952184i	$0.969645\pi$
$684$		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	−0.328048	−	0.944661i	$-0.606391\pi$
$691$	8.57027	−	4.94805i	0.326028	−	0.188233i	0.654076	+	0.756429i	$0.273057\pi$
$692$		0			0
$693$	24.9207	−	26.3796i	0.946661	−	1.00208i
$694$		0			0
$695$	19.0047	−	8.98695i	0.720890	−	0.340895i
$696$		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
$705$	21.0551	+	6.60921i	0.792982	+	0.248917i
$706$		0			0
$707$	8.37694	+	39.0742i	0.315047	+	1.46953i
$708$		0			0
$709$	−26.5650	−	46.0119i	−0.997670	−	1.72801i	−0.557925	−	0.829891i	$-0.688402\pi$
$709$	−26.5650	−	46.0119i	−0.997670	−	1.72801i	−0.439745	−	0.898123i	$-0.644931\pi$
$710$		0			0
$711$	35.7595	+	17.0344i	1.34109	+	0.638840i
$712$		0			0
$713$		−	1.31965i		−	0.0494214i
$714$		0			0
$715$	−1.31711	+	16.0496i	−0.0492572	+	0.600222i
$716$		0			0
$717$	−13.8419	−	44.5389i	−0.516937	−	1.66333i
$718$		0			0
$719$	−3.10194	−	5.37272i	−0.115683	−	0.200369i	0.802370	−	0.596827i	$-0.203572\pi$
$719$	−3.10194	−	5.37272i	−0.115683	−	0.200369i	−0.918053	+	0.396459i	$0.870239\pi$
$720$		0			0
$721$	−10.9497	−	3.53662i	−0.407789	−	0.131711i
$722$		0			0
$723$	−28.4607	−	6.43250i	−1.05846	−	0.239227i
$724$		0			0
$725$	−19.2624	−	15.8127i	−0.715386	−	0.587268i
$726$		0			0
$727$	−22.6957			−0.841735			−0.420868	−	0.907122i	$-0.638274\pi$
$727$	−22.6957			−0.841735			−0.420868	+	0.907122i	$0.638274\pi$
$728$		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	$-0.243720\pi$
$733$	−6.48996	−	11.2409i	−0.239712	−	0.415193i	−0.960632	+	0.277825i	$0.910386\pi$
$734$		0			0
$735$	21.7161	−	16.2300i	0.801010	−	0.598651i
$736$		0			0
$737$	−15.5098	−	26.8638i	−0.571312	−	0.989542i
$738$		0			0
$739$	−26.2551	+	45.4752i	−0.965811	+	1.67283i	−0.258391	+	0.966040i	$0.583192\pi$
$739$	−26.2551	+	45.4752i	−0.965811	+	1.67283i	−0.707420	+	0.706794i	$0.750141\pi$
$740$		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
$745$	2.51370	+	1.74002i	0.0920950	+	0.0637493i
$746$		0			0
$747$	−1.74576	−	2.53737i	−0.0638740	−	0.0928375i
$748$		0			0
$749$	32.9051	+	10.6279i	1.20233	+	0.388336i
$750$		0			0
$751$	7.73267	+	13.3934i	0.282169	+	0.488731i	0.971919	−	0.235317i	$-0.0756128\pi$
$751$	7.73267	+	13.3934i	0.282169	+	0.488731i	−0.689750	+	0.724048i	$0.742279\pi$
$752$		0			0
$753$	−13.9534	+	4.33647i	−0.508489	+	0.158030i
$754$		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
$759$	−0.453189	−	1.45822i	−0.0164497	−	0.0529299i
$760$		0			0
$761$	−24.6618	−	42.7156i	−0.893991	−	1.54844i	−0.835048	−	0.550177i	$-0.814560\pi$
$761$	−24.6618	−	42.7156i	−0.893991	−	1.54844i	−0.0589430	−	0.998261i	$-0.518773\pi$
$762$		0			0
$763$	−4.03372	−	18.8153i	−0.146031	−	0.681158i
$764$		0			0
$765$	−15.6758	−	27.3303i	−0.566761	−	0.988129i
$766$		0			0
$767$	1.96462	−	3.40282i	0.0709383	−	0.122869i
$768$		0			0
$769$		−	3.85691i		−	0.139084i	−0.997579	−	0.0695419i	$-0.977846\pi$
$769$		−	3.85691i		−	0.139084i	0.997579	−	0.0695419i	$-0.0221538\pi$
$770$		0			0
$771$	20.6691	−	22.3710i	0.744381	−	0.805671i
$772$		0			0
$773$	25.1407	+	14.5150i	0.904247	+	0.522067i	0.878576	−	0.477603i	$-0.158494\pi$
$773$	25.1407	+	14.5150i	0.904247	+	0.522067i	0.0256713	+	0.999670i	$0.491828\pi$
$774$		0			0
$775$	−32.0268	+	12.0490i	−1.15044	+	0.432812i
$776$		0			0
$777$	−0.105528	+	9.51533i	−0.00378580	+	0.341360i
$778$		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	$-0.968626\pi$
$787$	−11.5679	+	20.0362i	−0.412352	+	0.714215i	0.582794	+	0.812620i	$0.301959\pi$
$788$		0			0
$789$	−3.46494	+	15.3307i	−0.123355	+	0.545786i
$790$		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
$795$	−38.8536	+	8.66553i	−1.37800	+	0.307335i
$796$		0			0
$797$		−	28.9627i		−	1.02591i	−0.858415	−	0.512956i	$-0.828550\pi$
$797$		−	28.9627i		−	1.02591i	0.858415	−	0.512956i	$-0.171450\pi$
$798$		0			0
$799$	26.7619			0.946767
$800$		0			0
$801$	3.22241	+	1.53503i	0.113858	+	0.0542375i
$802$		0			0
$803$	57.2949	−	33.0792i	2.02189	−	1.16734i
$804$		0			0
$805$	−0.147102	−	1.13127i	−0.00518466	−	0.0398719i
$806$		0			0
$807$	10.0096	−	44.2875i	0.352354	−	1.55899i
$808$		0			0
$809$	1.47318	+	0.850541i	0.0517943	+	0.0299034i	0.525674	−	0.850686i	$-0.323813\pi$
$809$	1.47318	+	0.850541i	0.0517943	+	0.0299034i	−0.473879	+	0.880590i	$0.657147\pi$
$810$		0			0
$811$		−	1.26175i		−	0.0443059i	−0.999755	−	0.0221529i	$-0.992948\pi$
$811$		−	1.26175i		−	0.0443059i	0.999755	−	0.0221529i	$-0.00705208\pi$
$812$		0			0
$813$	25.7890	−	27.9124i	0.904459	−	0.978930i
$814$		0			0
$815$	−41.4512	−	28.6931i	−1.45197	−	1.00507i
$816$		0			0
$817$	0.0767494	+	0.132934i	0.00268512	+	0.00465077i
$818$		0			0
$819$	−2.89128	+	12.1636i	−0.101030	+	0.425031i
$820$		0			0
$821$	−19.4002	+	11.2007i	−0.677072	+	0.390908i	−0.798751	−	0.601662i	$-0.794505\pi$
$821$	−19.4002	+	11.2007i	−0.677072	+	0.390908i	0.121679	+	0.992569i	$0.461172\pi$
$822$		0			0
$823$	−18.3644	−	10.6027i	−0.640144	−	0.369587i	0.144526	−	0.989501i	$-0.453834\pi$
$823$	−18.3644	−	10.6027i	−0.640144	−	0.369587i	−0.784670	+	0.619914i	$0.787168\pi$
$824$		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	0.812364	−	0.583151i	$-0.198181\pi$
$829$	20.5440	+	11.8611i	0.713521	+	0.411952i	−0.0988421	+	0.995103i	$0.531514\pi$
$830$		0			0
$831$	−40.2405	−	9.09489i	−1.39593	−	0.315498i
$832$		0			0
$833$	19.2316	−	26.6657i	0.666335	−	0.923912i
$834$		0			0
$835$	−5.17946	+	2.44926i	−0.179242	+	0.0847602i
$836$		0			0
$837$	−33.0192	+	13.2021i	−1.14131	+	0.456332i
$838$		0			0
$839$	−13.8614			−0.478550			−0.239275	−	0.970952i	$-0.576910\pi$
$839$	−13.8614			−0.478550			−0.239275	+	0.970952i	$0.576910\pi$
$840$		0			0
$841$	4.15685			0.143340
$842$		0			0
$843$	0.311368	+	1.00188i	0.0107241	+	0.0345067i
$844$		0			0
$845$	10.0550	+	21.2633i	0.345902	+	0.731480i
$846$		0			0
$847$	−24.9342	−	8.05342i	−0.856750	−	0.276719i
$848$		0			0
$849$	11.7287	−	51.8937i	0.402527	−	1.78099i
$850$		0			0
$851$	0.346771	+	0.200209i	0.0118872	+	0.00686306i
$852$		0			0
$853$	−23.4548			−0.803078			−0.401539	−	0.915842i	$-0.631524\pi$
$853$	−23.4548			−0.803078			−0.401539	+	0.915842i	$0.631524\pi$
$854$		0			0
$855$	−0.155802		0.000442496i	−0.00532833		1.51331e-5i
$856$		0			0
$857$	−40.7019	−	23.4993i	−1.39035	−	0.802720i	−0.396997	−	0.917820i	$-0.629948\pi$
$857$	−40.7019	−	23.4993i	−1.39035	−	0.802720i	−0.993354	+	0.115100i	$0.963281\pi$
$858$		0			0
$859$	20.8802	−	12.0552i	0.712424	−	0.411318i	−0.0995342	−	0.995034i	$-0.531735\pi$
$859$	20.8802	−	12.0552i	0.712424	−	0.411318i	0.811958	+	0.583716i	$0.198402\pi$
$860$		0			0
$861$	13.6757	−	23.0918i	0.466068	−	0.786968i
$862$		0			0
$863$	−2.82464	−	4.89242i	−0.0961519	−	0.166540i	0.813937	−	0.580953i	$-0.197320\pi$
$863$	−2.82464	−	4.89242i	−0.0961519	−	0.166540i	−0.910089	+	0.414413i	$0.863987\pi$
$864$		0			0
$865$	40.3680	+	27.9432i	1.37255	+	0.950098i
$866$		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
$873$	−1.78395	+	1.22740i	−0.0603777	+	0.0415410i
$874$		0			0
$875$	−26.1117	+	13.8989i	−0.882736	+	0.469870i
$876$		0			0
$877$	0.425057	−	0.245407i	0.0143531	−	0.00828679i	−0.492806	−	0.870139i	$-0.664029\pi$
$877$	0.425057	−	0.245407i	0.0143531	−	0.00828679i	0.507159	+	0.861852i	$0.330696\pi$
$878$		0			0
$879$	−11.6915	−	37.6195i	−0.394344	−	1.26887i
$880$		0			0
$881$	27.5907			0.929555			0.464778	−	0.885427i	$-0.346134\pi$
$881$	27.5907			0.929555			0.464778	+	0.885427i	$0.346134\pi$
$882$		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
$885$	9.42944	−	2.10305i	0.316967	−	0.0706932i
$886$		0			0
$887$	−9.19558	+	5.30907i	−0.308757	+	0.178261i	−0.646370	−	0.763024i	$-0.723714\pi$
$887$	−9.19558	+	5.30907i	−0.308757	+	0.178261i	0.337613	+	0.941285i	$0.390381\pi$
$888$		0			0
$889$	17.7037	+	19.5929i	0.593762	+	0.657124i
$890$		0			0
$891$	−31.9524	+	25.9276i	−1.07044	+	0.868608i
$892$		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
$903$	26.0591	+	15.4330i	0.867192	+	0.513579i
$904$		0			0
$905$	44.2542	−	20.9269i	1.47106	−	0.695635i
$906$		0			0
$907$	38.0167	+	21.9489i	1.26232	+	0.728803i	0.973523	−	0.228587i	$-0.0734106\pi$
$907$	38.0167	+	21.9489i	1.26232	+	0.728803i	0.288800	+	0.957390i	$0.406744\pi$
$908$		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
$915$	34.2395	+	10.7478i	1.13192	+	0.355311i
$916$		0			0
$917$	31.4148	+	10.1466i	1.03741	+	0.335069i
$918$		0			0
$919$	−5.15414	−	8.92723i	−0.170019	−	0.294482i	0.768407	−	0.639961i	$-0.221050\pi$
$919$	−5.15414	−	8.92723i	−0.170019	−	0.294482i	−0.938426	+	0.345479i	$0.887716\pi$
$920$		0			0
$921$	7.55490	−	2.34794i	0.248942	−	0.0773671i
$922$		0			0
$923$			20.6234i			0.678828i
$924$		0			0
$925$	1.69271	−	10.2438i	0.0556560	−	0.336814i
$926$		0			0
$927$	11.7792	+	5.61113i	0.386879	+	0.184294i
$928$		0			0
$929$	22.9667	+	39.7794i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$929$	22.9667	+	39.7794i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$930$		0			0
$931$	−0.0666466	−	0.148292i	−0.00218425	−	0.00486008i
$932$		0			0
$933$	4.70082	−	20.7989i	0.153898	−	0.680925i
$934$		0			0
$935$	−27.3291	+	39.4808i	−0.893758	+	1.29116i
$936$		0			0
$937$	50.3541			1.64500			0.822499	−	0.568767i	$-0.192579\pi$
$937$	50.3541			1.64500			0.822499	+	0.568767i	$0.192579\pi$
$938$		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	$-0.885049\pi$
$941$	−4.96200	+	8.59443i	−0.161757	+	0.280171i	0.773742	+	0.633501i	$0.218383\pi$
$942$		0			0
$943$	−0.564646	−	0.977996i	−0.0183874	−	0.0318479i
$944$		0			0
$945$	−26.8339	+	14.9981i	−0.872906	+	0.487888i
$946$		0			0
$947$	3.97339	+	6.88211i	0.129118	+	0.223638i	0.923335	−	0.383995i	$-0.125452\pi$
$947$	3.97339	+	6.88211i	0.129118	+	0.223638i	−0.794217	+	0.607634i	$0.792119\pi$
$948$		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
$955$	14.2859	+	9.88888i	0.462281	+	0.319997i
$956$		0			0
$957$	−8.70143	+	38.4996i	−0.281277	+	1.24452i
$958$		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
$963$	−35.3977	−	16.8621i	−1.14068	−	0.543372i
$964$		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
$969$	−0.180429	+	0.0560744i	−0.00579622	+	0.00180137i
$970$		0			0
$971$	0.893834	+	1.54817i	0.0286845	+	0.0496830i	0.880011	−	0.474953i	$-0.157535\pi$
$971$	0.893834	+	1.54817i	0.0286845	+	0.0496830i	−0.851327	+	0.524636i	$0.824202\pi$
$972$		0			0
$973$	−16.6764	−	18.4559i	−0.534619	−	0.591670i
$974$		0			0
$975$	5.13630	−	12.6374i	0.164493	−	0.404722i
$976$		0			0
$977$	8.56427	−	14.8337i	0.273995	−	0.474574i	−0.695886	−	0.718152i	$-0.744988\pi$
$977$	8.56427	−	14.8337i	0.273995	−	0.474574i	0.969881	+	0.243579i	$0.0783214\pi$
$978$		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	0.999984	+	0.00559883i	$0.00178217\pi$
$983$	47.1805	+	27.2397i	1.50483	+	0.868811i	0.504841	+	0.863212i	$0.331551\pi$
$984$		0			0
$985$	−9.56876	−	20.2351i	−0.304886	−	0.644743i
$986$		0			0
$987$	0.289565	−	26.1097i	0.00921696	−	0.831080i
$988$		0			0
$989$	1.10367	−	0.637202i	0.0350945	−	0.0202618i
$990$		0			0
$991$	−11.6055	+	20.1013i	−0.368661	+	0.638540i	−0.989357	−	0.145512i	$-0.953517\pi$
$991$	−11.6055	+	20.1013i	−0.368661	+	0.638540i	0.620695	+	0.784052i	$0.286850\pi$
$992$		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	$-0.799927\pi$
$997$	3.30773	−	5.72916i	0.104757	−	0.181444i	0.913639	+	0.406527i	$0.133260\pi$
$998$		0			0
$999$	1.54026	−	10.6795i	0.0487316	−	0.337885i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.da.a.89.3	✓	48	105.89	even	6	inner
840.2.da.a.89.12	yes	48	7.5	odd	6	inner
840.2.da.a.689.3	yes	48	1.1	even	1	trivial
840.2.da.a.689.12	yes	48	15.14	odd	2	inner
840.2.da.b.89.13	yes	48	35.19	odd	6
840.2.da.b.89.22	yes	48	21.5	even	6
840.2.da.b.689.13	yes	48	3.2	odd	2
840.2.da.b.689.22	yes	48	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-1.65401 + 0.514040i) q^{3} +(-0.955903 - 2.02145i) q^{5} +(-1.96308 + 1.77379i) q^{7} +(2.47153 - 1.70046i) q^{9} +O(q^{10})\)	\(q+(-1.65401 + 0.514040i) q^{3} +(-0.955903 - 2.02145i) q^{5} +(-1.96308 + 1.77379i) q^{7} +(2.47153 - 1.70046i) q^{9} +(-3.95951 - 2.28602i) q^{11} +1.57517 q^{13} +(2.62018 + 2.85213i) q^{15} +(4.06751 + 2.34838i) q^{17} +(0.0201141 - 0.0116129i) q^{19} +(2.33516 - 3.94297i) q^{21} +(-0.0964144 - 0.166995i) q^{23} +(-3.17250 + 3.86461i) q^{25} +(-3.21384 + 4.08305i) q^{27} +4.98429i q^{29} +(5.92678 + 3.42183i) q^{31} +(7.72419 + 1.74577i) q^{33} +(5.46213 + 2.27269i) q^{35} +(-1.79834 + 1.03827i) q^{37} +(-2.60535 + 0.809699i) q^{39} +5.85645 q^{41} +6.60899i q^{43} +(-5.79993 - 3.37059i) q^{45} +(4.93457 - 2.84898i) q^{47} +(0.707338 - 6.96417i) q^{49} +(-7.93487 - 1.79339i) q^{51} +(-5.13922 + 8.90140i) q^{53} +(-0.836172 + 10.1892i) q^{55} +(-0.0272995 + 0.0295473i) q^{57} +(1.24724 - 2.16029i) q^{59} +(8.02451 - 4.63295i) q^{61} +(-1.83554 + 7.72210i) q^{63} +(-1.50571 - 3.18412i) q^{65} +(5.87567 + 3.39232i) q^{67} +(0.245313 + 0.226651i) q^{69} +13.0928i q^{71} +(-7.23510 + 12.5316i) q^{73} +(3.26080 - 8.02292i) q^{75} +(11.8277 - 2.53570i) q^{77} +(6.60158 + 11.4343i) q^{79} +(3.21688 - 8.40545i) q^{81} -1.02664i q^{83} +(0.858979 - 10.4671i) q^{85} +(-2.56212 - 8.24409i) q^{87} +(0.594890 + 1.03038i) q^{89} +(-3.09218 + 2.79402i) q^{91} +(-11.5619 - 2.61315i) q^{93} +(-0.0427019 - 0.0295588i) q^{95} -0.721802 q^{97} +(-13.6733 + 1.08301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 3 q^{5} - q^{9}+O(q^{10}) \) 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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