LMFDB - Embedded newform 920.2.bv.a.17.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07094 + 0.584775i) q^{3} +(1.80656 + 1.31770i) q^{5} +(-2.43642 - 3.25467i) q^{7} +(-0.816980 + 1.27125i) q^{9} +(1.21800 - 0.556244i) q^{11} +(1.32143 + 0.989210i) q^{13} +(-2.70527 - 0.354745i) q^{15} +(0.0608051 + 0.850167i) q^{17} +(2.89714 + 3.34347i) q^{19} +(4.51250 + 2.06079i) q^{21} +(1.11655 + 4.66405i) q^{23} +(1.52732 + 4.76102i) q^{25} +(0.392683 - 5.49042i) q^{27} +(5.55196 + 4.81080i) q^{29} +(-4.57200 + 1.34246i) q^{31} +(-0.979127 + 1.30796i) q^{33} +(-0.112840 - 9.09023i) q^{35} +(-7.64488 + 1.66304i) q^{37} +(-1.99363 - 0.286641i) q^{39} +(-0.0100982 + 0.00648973i) q^{41} +(2.57469 + 4.71519i) q^{43} +(-3.15105 + 1.22004i) q^{45} +(0.883714 + 0.883714i) q^{47} +(-2.68463 + 9.14301i) q^{49} +(-0.562275 - 0.874917i) q^{51} +(-0.834514 + 0.624709i) q^{53} +(2.93336 + 0.600081i) q^{55} +(-5.05783 - 1.88647i) q^{57} +(2.99919 - 0.431219i) q^{59} +(2.14000 + 7.28816i) q^{61} +(6.12799 - 0.438283i) q^{63} +(1.08376 + 3.52832i) q^{65} +(-0.148110 - 0.397099i) q^{67} +(-3.92317 - 4.34196i) q^{69} +(-4.03329 + 8.83168i) q^{71} +(-2.77739 - 0.198643i) q^{73} +(-4.41978 - 4.20561i) q^{75} +(-4.77795 - 2.60896i) q^{77} +(1.17612 + 8.18007i) q^{79} +(0.906883 + 1.98580i) q^{81} +(-1.65960 - 7.62905i) q^{83} +(-1.01042 + 1.61600i) q^{85} +(-8.75904 - 1.90541i) q^{87} +(11.0149 + 3.23428i) q^{89} -6.71094i q^{91} +(4.11128 - 4.11128i) q^{93} +(0.828143 + 9.85775i) q^{95} +(0.272889 - 1.25445i) q^{97} +(-0.287963 + 2.00282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.07094	+	0.584775i	−0.618305	+	0.337620i	−0.757687	−	0.652619i	$-0.773670\pi$
$3$	−1.07094	+	0.584775i	−0.618305	+	0.337620i	0.139381	+	0.990239i	$0.455489\pi$
$4$		0			0
$5$	1.80656	+	1.31770i	0.807918	+	0.589295i
$5$	1.80656	+	1.31770i	0.807918	+	0.589295i
$6$		0			0
$7$	−2.43642	−	3.25467i	−0.920879	−	1.23015i	−0.972835	−	0.231500i	$-0.925637\pi$
$7$	−2.43642	−	3.25467i	−0.920879	−	1.23015i	0.0519563	−	0.998649i	$-0.483454\pi$
$8$		0			0
$9$	−0.816980	+	1.27125i	−0.272327	+	0.423749i
$10$		0			0
$11$	1.21800	−	0.556244i	0.367242	−	0.167714i	−0.223242	−	0.974763i	$-0.571664\pi$
$11$	1.21800	−	0.556244i	0.367242	−	0.167714i	0.590484	+	0.807049i	$0.298937\pi$
$12$		0			0
$13$	1.32143	+	0.989210i	0.366499	+	0.274357i	0.766615	−	0.642107i	$-0.221939\pi$
$13$	1.32143	+	0.989210i	0.366499	+	0.274357i	−0.400117	+	0.916464i	$0.631030\pi$
$14$		0			0
$15$	−2.70527	−	0.354745i	−0.698498	−	0.0915947i
$16$		0			0
$17$	0.0608051	+	0.850167i	0.0147474	+	0.206196i	0.999483	+	0.0321408i	$0.0102325\pi$
$17$	0.0608051	+	0.850167i	0.0147474	+	0.206196i	−0.984736	+	0.174055i	$0.944313\pi$
$18$		0			0
$19$	2.89714	+	3.34347i	0.664648	+	0.767045i	0.983529	−	0.180750i	$-0.0578524\pi$
$19$	2.89714	+	3.34347i	0.664648	+	0.767045i	−0.318881	+	0.947795i	$0.603307\pi$
$20$		0			0
$21$	4.51250	+	2.06079i	0.984707	+	0.449701i
$22$		0			0
$23$	1.11655	+	4.66405i	0.232816	+	0.972521i
$23$	1.11655	+	4.66405i	0.232816	+	0.972521i
$24$		0			0
$25$	1.52732	+	4.76102i	0.305463	+	0.952204i
$26$		0			0
$27$	0.392683	−	5.49042i	0.0755718	−	1.05663i
$28$		0			0
$29$	5.55196	+	4.81080i	1.03097	+	0.893344i	0.994368	−	0.105986i	$-0.0337999\pi$
$29$	5.55196	+	4.81080i	1.03097	+	0.893344i	0.0366059	+	0.999330i	$0.488345\pi$
$30$		0			0
$31$	−4.57200	+	1.34246i	−0.821155	+	0.241113i	−0.665213	−	0.746653i	$-0.731659\pi$
$31$	−4.57200	+	1.34246i	−0.821155	+	0.241113i	−0.155942	+	0.987766i	$0.549841\pi$
$32$		0			0
$33$	−0.979127	+	1.30796i	−0.170444	+	0.227687i
$34$		0			0
$35$	−0.112840	−	9.09023i	−0.0190735	−	1.53653i
$36$		0			0
$37$	−7.64488	+	1.66304i	−1.25681	+	0.273402i	−0.791184	−	0.611579i	$-0.790535\pi$
$37$	−7.64488	+	1.66304i	−1.25681	+	0.273402i	−0.465627	+	0.884981i	$0.654171\pi$
$38$		0			0
$39$	−1.99363	−	0.286641i	−0.319237	−	0.0458993i
$40$		0			0
$41$	−0.0100982	+	0.00648973i	−0.00157708	+	0.00101353i	−0.541429	−	0.840746i	$-0.682117\pi$
$41$	−0.0100982	+	0.00648973i	−0.00157708	+	0.00101353i	0.539852	+	0.841760i	$0.318480\pi$
$42$		0			0
$43$	2.57469	+	4.71519i	0.392636	+	0.719060i	0.996980	−	0.0776643i	$-0.0247462\pi$
$43$	2.57469	+	4.71519i	0.392636	+	0.719060i	−0.604343	+	0.796724i	$0.706564\pi$
$44$		0			0
$45$	−3.15105	+	1.22004i	−0.469731	+	0.181873i
$46$		0			0
$47$	0.883714	+	0.883714i	0.128903	+	0.128903i	0.768615	−	0.639712i	$-0.220946\pi$
$47$	0.883714	+	0.883714i	0.128903	+	0.128903i	−0.639712	+	0.768615i	$0.720946\pi$
$48$		0			0
$49$	−2.68463	+	9.14301i	−0.383518	+	1.30614i
$50$		0			0
$51$	−0.562275	−	0.874917i	−0.0787342	−	0.122513i
$52$		0			0
$53$	−0.834514	+	0.624709i	−0.114629	+	0.0858104i	−0.655054	−	0.755582i	$-0.727354\pi$
$53$	−0.834514	+	0.624709i	−0.114629	+	0.0858104i	0.540425	+	0.841392i	$0.318263\pi$
$54$		0			0
$55$	2.93336	+	0.600081i	0.395534	+	0.0809148i
$56$		0			0
$57$	−5.05783	−	1.88647i	−0.669926	−	0.249869i
$58$		0			0
$59$	2.99919	−	0.431219i	0.390462	−	0.0561399i	0.0557117	−	0.998447i	$-0.482257\pi$
$59$	2.99919	−	0.431219i	0.390462	−	0.0561399i	0.334750	+	0.942307i	$0.391348\pi$
$60$		0			0
$61$	2.14000	+	7.28816i	0.273999	+	0.933153i	0.975410	+	0.220397i	$0.0707353\pi$
$61$	2.14000	+	7.28816i	0.273999	+	0.933153i	−0.701412	+	0.712756i	$0.747447\pi$
$62$		0			0
$63$	6.12799	−	0.438283i	0.772054	−	0.0552184i
$64$		0			0
$65$	1.08376	+	3.52832i	0.134423	+	0.437634i
$66$		0			0
$67$	−0.148110	−	0.397099i	−0.0180946	−	0.0485134i	0.927588	−	0.373604i	$-0.121878\pi$
$67$	−0.148110	−	0.397099i	−0.0180946	−	0.0485134i	−0.945683	+	0.325090i	$0.894605\pi$
$68$		0			0
$69$	−3.92317	−	4.34196i	−0.472294	−	0.522711i
$70$		0			0
$71$	−4.03329	+	8.83168i	−0.478664	+	1.04813i	0.504165	+	0.863607i	$0.331800\pi$
$71$	−4.03329	+	8.83168i	−0.478664	+	1.04813i	−0.982829	+	0.184520i	$0.940927\pi$
$72$		0			0
$73$	−2.77739	−	0.198643i	−0.325069	−	0.0232494i	−0.0921489	−	0.995745i	$-0.529374\pi$
$73$	−2.77739	−	0.198643i	−0.325069	−	0.0232494i	−0.232920	+	0.972496i	$0.574828\pi$
$74$		0			0
$75$	−4.41978	−	4.20561i	−0.510353	−	0.485622i
$76$		0			0
$77$	−4.77795	−	2.60896i	−0.544498	−	0.297319i
$78$		0			0
$79$	1.17612	+	8.18007i	0.132324	+	0.920330i	0.942515	+	0.334165i	$0.108454\pi$
$79$	1.17612	+	8.18007i	0.132324	+	0.920330i	−0.810191	+	0.586166i	$0.800637\pi$
$80$		0			0
$81$	0.906883	+	1.98580i	0.100765	+	0.220644i
$82$		0			0
$83$	−1.65960	−	7.62905i	−0.182165	−	0.837397i	−0.973980	−	0.226636i	$-0.927227\pi$
$83$	−1.65960	−	7.62905i	−0.182165	−	0.837397i	0.791815	−	0.610761i	$-0.209136\pi$
$84$		0			0
$85$	−1.01042	+	1.61600i	−0.109595	+	0.175280i
$86$		0			0
$87$	−8.75904	−	1.90541i	−0.939067	−	0.204282i
$88$		0			0
$89$	11.0149	+	3.23428i	1.16758	+	0.342833i	0.807374	−	0.590040i	$-0.200888\pi$
$89$	11.0149	+	3.23428i	1.16758	+	0.342833i	0.360207	+	0.932872i	$0.382706\pi$
$90$		0			0
$91$		−	6.71094i		−	0.703498i
$92$		0			0
$93$	4.11128	−	4.11128i	0.426320	−	0.426320i
$94$		0			0
$95$	0.828143	+	9.85775i	0.0849657	+	1.01138i
$96$		0			0
$97$	0.272889	−	1.25445i	0.0277077	−	0.127370i	−0.961215	−	0.275798i	$-0.911058\pi$
$97$	0.272889	−	1.25445i	0.0277077	−	0.127370i	0.988923	+	0.148428i	$0.0474214\pi$
$98$		0			0
$99$	−0.287963	+	2.00282i	−0.0289413	+	0.201291i
$100$		0			0
$101$	0.767945	+	0.493528i	0.0764134	+	0.0491079i	0.578290	−	0.815832i	$-0.303720\pi$
$101$	0.767945	+	0.493528i	0.0764134	+	0.0491079i	−0.501876	+	0.864939i	$0.667357\pi$
$102$		0			0
$103$	0.0186687	−	0.0500528i	0.00183948	−	0.00493185i	−0.936027	−	0.351929i	$-0.885526\pi$
$103$	0.0186687	−	0.0500528i	0.00183948	−	0.00493185i	0.937866	+	0.346997i	$0.112799\pi$
$104$		0			0
$105$	5.43659	+	9.66907i	0.530557	+	0.943605i
$106$		0			0
$107$	−4.46975	+	8.18573i	−0.432107	+	0.791344i	−0.999484	−	0.0321136i	$-0.989776\pi$
$107$	−4.46975	+	8.18573i	−0.432107	+	0.791344i	0.567378	+	0.823458i	$0.307958\pi$
$108$		0			0
$109$	2.73263	−	3.15363i	0.261739	−	0.302063i	−0.609635	−	0.792682i	$-0.708684\pi$
$109$	2.73263	−	3.15363i	0.261739	−	0.302063i	0.871374	+	0.490619i	$0.163229\pi$
$110$		0			0
$111$	7.21467	−	6.25155i	0.684787	−	0.593371i
$112$		0			0
$113$	15.4989	−	5.78080i	1.45802	−	0.543812i	0.509481	−	0.860482i	$-0.329837\pi$
$113$	15.4989	−	5.78080i	1.45802	−	0.543812i	0.948536	+	0.316670i	$0.102565\pi$
$114$		0			0
$115$	−4.12872	+	9.89716i	−0.385005	+	0.922915i
$116$		0			0
$117$	−2.33711	+	0.871697i	−0.216066	+	0.0805884i
$118$		0			0
$119$	2.61887	−	2.26926i	0.240071	−	0.208023i
$120$		0			0
$121$	−6.02934	+	6.95823i	−0.548122	+	0.632566i
$122$		0			0
$123$	0.00701951	−	0.0128553i	0.000632928	−	0.00115912i
$124$		0			0
$125$	−3.51443	+	10.6136i	−0.314340	+	0.949311i
$126$		0			0
$127$	5.78703	−	15.5156i	0.513515	−	1.37679i	−0.378843	−	0.925461i	$-0.623678\pi$
$127$	5.78703	−	15.5156i	0.513515	−	1.37679i	0.892359	−	0.451327i	$-0.149049\pi$
$128$		0			0
$129$	−5.51465	−	3.54405i	−0.485538	−	0.312036i
$130$		0			0
$131$	0.643818	−	4.47785i	0.0562506	−	0.391231i	−0.942174	−	0.335124i	$-0.891222\pi$
$131$	0.643818	−	4.47785i	0.0562506	−	0.391231i	0.998425	−	0.0561078i	$-0.0178690\pi$
$132$		0			0
$133$	3.82327	−	17.5753i	0.331520	−	1.52397i
$134$		0			0
$135$	7.94415	−	9.40133i	0.683724	−	0.809138i
$136$		0			0
$137$	9.39149	−	9.39149i	0.802369	−	0.802369i	−0.181096	−	0.983465i	$-0.557965\pi$
$137$	9.39149	−	9.39149i	0.802369	−	0.802369i	0.983465	+	0.181096i	$0.0579646\pi$
$138$		0			0
$139$			20.8682i			1.77002i	0.465570	+	0.885011i	$0.345849\pi$
$139$			20.8682i			1.77002i	−0.465570	+	0.885011i	$0.654151\pi$
$140$		0			0
$141$	−1.46318	−	0.429627i	−0.123222	−	0.0361811i
$142$		0			0
$143$	2.15975	+	0.469824i	0.180607	+	0.0392887i
$144$		0			0
$145$	3.69074	+	16.0068i	0.306499	+	1.32930i
$146$		0			0
$147$	−2.47154	−	11.3615i	−0.203849	−	0.937079i
$148$		0			0
$149$	−5.27807	−	11.5574i	−0.432396	−	0.946816i	−0.992932	−	0.118685i	$-0.962132\pi$
$149$	−5.27807	−	11.5574i	−0.432396	−	0.946816i	0.560536	−	0.828130i	$-0.310595\pi$
$150$		0			0
$151$	−0.0969597	−	0.674369i	−0.00789047	−	0.0548794i	0.985496	−	0.169700i	$-0.0542798\pi$
$151$	−0.0969597	−	0.674369i	−0.00789047	−	0.0548794i	−0.993386	+	0.114820i	$0.963371\pi$
$152$		0			0
$153$	−1.13045	−	0.617271i	−0.0913913	−	0.0499034i
$154$		0			0
$155$	−10.0285	−	3.59930i	−0.805512	−	0.289103i
$156$		0			0
$157$	12.3191	+	0.881077i	0.983169	+	0.0703176i	0.553658	−	0.832744i	$-0.313231\pi$
$157$	12.3191	+	0.881077i	0.983169	+	0.0703176i	0.429511	+	0.903062i	$0.358686\pi$
$158$		0			0
$159$	0.528396	−	1.15703i	0.0419046	−	0.0917582i
$160$		0			0
$161$	12.4596	−	14.9976i	0.981950	−	1.18197i
$162$		0			0
$163$	−8.44582	−	22.6441i	−0.661527	−	1.77362i	−0.633154	−	0.774026i	$-0.718240\pi$
$163$	−8.44582	−	22.6441i	−0.661527	−	1.77362i	−0.0283736	−	0.999597i	$-0.509033\pi$
$164$		0			0
$165$	−3.49236	+	1.07271i	−0.271879	+	0.0835103i
$166$		0			0
$167$	−14.0945	+	1.00806i	−1.09066	+	0.0780059i	−0.605065	−	0.796176i	$-0.706853\pi$
$167$	−14.0945	+	1.00806i	−1.09066	+	0.0780059i	−0.485599	+	0.874182i	$0.661398\pi$
$168$		0			0
$169$	−2.89488	−	9.85907i	−0.222683	−	0.758390i
$170$		0			0
$171$	−6.61728	+	0.951421i	−0.506036	+	0.0727570i
$172$		0			0
$173$	−2.49459	−	0.930435i	−0.189660	−	0.0707397i	0.252839	−	0.967508i	$-0.418636\pi$
$173$	−2.49459	−	0.930435i	−0.189660	−	0.0707397i	−0.442500	+	0.896769i	$0.645908\pi$
$174$		0			0
$175$	11.7744	−	16.5707i	0.890059	−	1.25263i
$176$		0			0
$177$	−2.95978	+	2.21566i	−0.222471	+	0.166539i
$178$		0			0
$179$	−11.7907	−	18.3467i	−0.881278	−	1.37129i	−0.928076	−	0.372390i	$-0.878538\pi$
$179$	−11.7907	−	18.3467i	−0.881278	−	1.37129i	0.0467986	−	0.998904i	$-0.485098\pi$
$180$		0			0
$181$	5.61046	−	19.1075i	0.417022	−	1.42025i	−0.436741	−	0.899587i	$-0.643868\pi$
$181$	5.61046	−	19.1075i	0.417022	−	1.42025i	0.853764	−	0.520661i	$-0.174314\pi$
$182$		0			0
$183$	−6.55374	−	6.55374i	−0.484466	−	0.484466i
$184$		0			0
$185$	−16.0023	−	7.06930i	−1.17651	−	0.519745i
$186$		0			0
$187$	0.546961	+	1.00168i	0.0399977	+	0.0732504i
$188$		0			0
$189$	−18.8262	+	12.0989i	−1.36941	+	0.880065i
$190$		0			0
$191$	−1.04899	−	0.150821i	−0.0759019	−	0.0109130i	0.104259	−	0.994550i	$-0.466753\pi$
$191$	−1.04899	−	0.150821i	−0.0759019	−	0.0109130i	−0.180161	+	0.983637i	$0.557662\pi$
$192$		0			0
$193$	12.7306	−	2.76938i	0.916371	−	0.199344i	0.270437	−	0.962738i	$-0.412832\pi$
$193$	12.7306	−	2.76938i	0.916371	−	0.199344i	0.645934	+	0.763393i	$0.276468\pi$
$194$		0			0
$195$	−3.22391	−	3.14485i	−0.230869	−	0.225207i
$196$		0			0
$197$	5.35232	−	7.14986i	0.381337	−	0.509406i	−0.568273	−	0.822840i	$-0.692388\pi$
$197$	5.35232	−	7.14986i	0.381337	−	0.509406i	0.949610	+	0.313433i	$0.101479\pi$
$198$		0			0
$199$	−5.54204	+	1.62729i	−0.392865	+	0.115356i	−0.472198	−	0.881493i	$-0.656539\pi$
$199$	−5.54204	+	1.62729i	−0.392865	+	0.115356i	0.0793328	+	0.996848i	$0.474721\pi$
$200$		0			0
$201$	0.390831	+	0.338657i	0.0275671	+	0.0238870i
$202$		0			0
$203$	2.13069	−	29.7909i	0.149545	−	2.09091i
$204$		0			0
$205$	−0.0267946	−	0.00158237i	−0.00187141	−	0.000110518i
$206$		0			0
$207$	−6.84135	−	2.39103i	−0.475507	−	0.166188i
$208$		0			0
$209$	5.38851	+	2.46085i	0.372731	+	0.170221i
$210$		0			0
$211$	9.17733	+	10.5912i	0.631793	+	0.729128i	0.977901	−	0.209066i	$-0.0670425\pi$
$211$	9.17733	+	10.5912i	0.631793	+	0.729128i	−0.346108	+	0.938195i	$0.612497\pi$
$212$		0			0
$213$	−0.845149	−	11.8167i	−0.0579087	−	0.809669i
$214$		0			0
$215$	−1.56189	+	11.9109i	−0.106520	+	0.812320i
$216$		0			0
$217$	15.5085	+	11.6096i	1.05279	+	0.788108i
$218$		0			0
$219$	3.09057	−	1.41142i	0.208841	−	0.0953747i
$220$		0			0
$221$	−0.760643	+	1.18358i	−0.0511664	+	0.0796165i
$222$		0			0
$223$	10.5623	+	14.1095i	0.707301	+	0.944843i	0.999935	−	0.0113810i	$-0.00362277\pi$
$223$	10.5623	+	14.1095i	0.707301	+	0.944843i	−0.292634	+	0.956224i	$0.594532\pi$
$224$		0			0
$225$	−7.30022	−	1.94807i	−0.486681	−	0.129871i
$226$		0			0
$227$	−17.9808	+	9.81827i	−1.19343	+	0.651661i	−0.948160	−	0.317794i	$-0.897058\pi$
$227$	−17.9808	+	9.81827i	−1.19343	+	0.651661i	−0.245269	+	0.969455i	$0.578876\pi$
$228$		0			0
$229$	−17.3640			−1.14744			−0.573722	−	0.819050i	$-0.694501\pi$
$229$	−17.3640			−1.14744			−0.573722	+	0.819050i	$0.694501\pi$
$230$		0			0
$231$	6.64254			0.437047
$232$		0			0
$233$	−22.2091	+	12.1271i	−1.45496	+	0.794470i	−0.995593	−	0.0937748i	$-0.970107\pi$
$233$	−22.2091	+	12.1271i	−1.45496	+	0.794470i	−0.459370	+	0.888245i	$0.651925\pi$
$234$		0			0
$235$	0.432009	+	2.76096i	0.0281812	+	0.180105i
$236$		0			0
$237$	−6.04305	−	8.07257i	−0.392538	−	0.524370i
$238$		0			0
$239$	11.9041	−	18.5231i	0.770009	−	1.19816i	−0.205599	−	0.978636i	$-0.565914\pi$
$239$	11.9041	−	18.5231i	0.770009	−	1.19816i	0.975608	−	0.219521i	$-0.0704495\pi$
$240$		0			0
$241$	28.0058	−	12.7898i	1.80401	−	0.823865i	0.848331	−	0.529466i	$-0.177608\pi$
$241$	28.0058	−	12.7898i	1.80401	−	0.823865i	0.955682	−	0.294400i	$-0.0951197\pi$
$242$		0			0
$243$	11.0871	+	8.29974i	0.711241	+	0.532428i
$244$		0			0
$245$	−16.8977	+	12.9798i	−1.07956	+	0.829252i
$246$		0			0
$247$	0.520965	+	7.28404i	0.0331482	+	0.463472i
$248$		0			0
$249$	6.23860	+	7.19973i	0.395356	+	0.456265i
$250$		0			0
$251$	8.02684	+	3.66573i	0.506649	+	0.231379i	0.652305	−	0.757956i	$-0.273802\pi$
$251$	8.02684	+	3.66573i	0.506649	+	0.231379i	−0.145656	+	0.989335i	$0.546529\pi$
$252$		0			0
$253$	3.95431	+	5.05975i	0.248605	+	0.318104i
$254$		0			0
$255$	0.137098	−	2.32150i	0.00858539	−	0.145378i
$256$		0			0
$257$	1.98043	−	27.6900i	0.123536	−	1.72726i	−0.437289	−	0.899321i	$-0.644061\pi$
$257$	1.98043	−	27.6900i	0.123536	−	1.72726i	0.560825	−	0.827934i	$-0.310484\pi$
$258$		0			0
$259$	24.0388	+	20.8297i	1.49370	+	1.29429i
$260$		0			0
$261$	−10.6516	+	3.12758i	−0.659315	+	0.193592i
$262$		0			0
$263$	−14.1029	+	18.8392i	−0.869621	+	1.16168i	0.116091	+	0.993239i	$0.462964\pi$
$263$	−14.1029	+	18.8392i	−0.869621	+	1.16168i	−0.985712	+	0.168439i	$0.946127\pi$
$264$		0			0
$265$	−2.33078	+	0.0289328i	−0.143179	+	0.00177732i
$266$		0			0
$267$	−13.6876	+	2.97756i	−0.837669	+	0.182224i
$268$		0			0
$269$	−25.7186	−	3.69777i	−1.56809	−	0.225457i	−0.697178	−	0.716898i	$-0.745561\pi$
$269$	−25.7186	−	3.69777i	−1.56809	−	0.225457i	−0.870911	+	0.491441i	$0.836470\pi$
$270$		0			0
$271$	13.3162	−	8.55777i	0.808899	−	0.519848i	−0.0696098	−	0.997574i	$-0.522175\pi$
$271$	13.3162	−	8.55777i	0.808899	−	0.519848i	0.878509	+	0.477727i	$0.158539\pi$
$272$		0			0
$273$	3.92439	+	7.18699i	0.237515	+	0.434976i
$274$		0			0
$275$	4.50856	+	4.94938i	0.271877	+	0.298459i
$276$		0			0
$277$	−4.36695	−	4.36695i	−0.262384	−	0.262384i	0.563638	−	0.826022i	$-0.309401\pi$
$277$	−4.36695	−	4.36695i	−0.262384	−	0.262384i	−0.826022	+	0.563638i	$0.809401\pi$
$278$		0			0
$279$	2.02864	−	6.90890i	0.121451	−	0.413625i
$280$		0			0
$281$	13.0555	+	20.3148i	0.778827	+	1.21188i	0.972976	+	0.230906i	$0.0741690\pi$
$281$	13.0555	+	20.3148i	0.778827	+	1.21188i	−0.194149	+	0.980972i	$0.562195\pi$
$282$		0			0
$283$	18.6947	−	13.9947i	1.11128	−	0.831896i	0.124224	−	0.992254i	$-0.460356\pi$
$283$	18.6947	−	13.9947i	1.11128	−	0.831896i	0.987059	+	0.160358i	$0.0512648\pi$
$284$		0			0
$285$	−6.65146	−	10.0727i	−0.393998	−	0.596658i
$286$		0			0
$287$	0.0457254	+	0.0170547i	0.00269908	+	0.00100671i
$288$		0			0
$289$	16.1079	−	2.31596i	0.947522	−	0.136233i
$290$		0			0
$291$	0.441325	+	1.50302i	0.0258710	+	0.0881084i
$292$		0			0
$293$	5.58066	−	0.399137i	0.326026	−	0.0233178i	0.0926329	−	0.995700i	$-0.470472\pi$
$293$	5.58066	−	0.399137i	0.326026	−	0.0233178i	0.233393	+	0.972383i	$0.425017\pi$
$294$		0			0
$295$	5.98644	+	3.17302i	0.348544	+	0.184741i
$296$		0			0
$297$	−2.57572	−	6.90578i	−0.149459	−	0.400714i
$298$		0			0
$299$	−3.13828	+	7.26771i	−0.181491	+	0.420302i
$300$		0			0
$301$	9.07338	−	19.8679i	0.522981	−	1.14517i
$302$		0			0
$303$	−1.11102	−	0.0794620i	−0.0638266	−	0.00456497i
$304$		0			0
$305$	−5.73760	+	15.9864i	−0.328534	+	0.915377i
$306$		0			0
$307$	−3.25108	−	1.77523i	−0.185549	−	0.101317i	0.383789	−	0.923421i	$-0.374619\pi$
$307$	−3.25108	−	1.77523i	−0.185549	−	0.101317i	−0.569339	+	0.822103i	$0.692801\pi$
$308$		0			0
$309$	0.00927663	+	0.0645204i	0.000527729	+	0.00367044i
$310$		0			0
$311$	4.56427	+	9.99436i	0.258816	+	0.566728i	0.993778	−	0.111380i	$-0.0355272\pi$
$311$	4.56427	+	9.99436i	0.258816	+	0.566728i	−0.734962	+	0.678109i	$0.762800\pi$
$312$		0			0
$313$	6.63811	+	30.5149i	0.375208	+	1.72480i	0.647037	+	0.762459i	$0.276008\pi$
$313$	6.63811	+	30.5149i	0.375208	+	1.72480i	−0.271829	+	0.962346i	$0.587628\pi$
$314$		0			0
$315$	11.6481	+	7.28309i	0.656297	+	0.410356i
$316$		0			0
$317$	−12.2692	−	2.66901i	−0.689109	−	0.149907i	−0.145643	−	0.989337i	$-0.546525\pi$
$317$	−12.2692	−	2.66901i	−0.689109	−	0.149907i	−0.543467	+	0.839431i	$0.682889\pi$
$318$		0			0
$319$	9.43829	+	2.77133i	0.528443	+	0.155165i
$320$		0			0
$321$		−	11.3802i		−	0.635180i
$322$		0			0
$323$	−2.66635	+	2.66635i	−0.148360	+	0.148360i
$324$		0			0
$325$	−2.69141	+	7.80219i	−0.149292	+	0.432787i
$326$		0			0
$327$	−1.08231	+	4.97531i	−0.0598520	+	0.275135i
$328$		0			0
$329$	0.723103	−	5.02929i	0.0398660	−	0.277274i
$330$		0			0
$331$	12.1057	+	7.77989i	0.665392	+	0.427621i	0.829262	−	0.558861i	$-0.188761\pi$
$331$	12.1057	+	7.77989i	0.665392	+	0.427621i	−0.163870	+	0.986482i	$0.552398\pi$
$332$		0			0
$333$	4.13158	−	11.0772i	0.226409	−	0.607027i
$334$		0			0
$335$	0.255689	−	0.912549i	0.0139698	−	0.0498579i
$336$		0			0
$337$	9.39973	−	17.2143i	0.512036	−	0.937723i	−0.485932	−	0.873997i	$-0.661520\pi$
$337$	9.39973	−	17.2143i	0.512036	−	0.937723i	0.997967	−	0.0637266i	$-0.0202986\pi$
$338$		0			0
$339$	−13.2179	+	15.2543i	−0.717897	+	0.828498i
$340$		0			0
$341$	−4.82198	+	4.17827i	−0.261125	+	0.226266i
$342$		0			0
$343$	9.63359	−	3.59314i	0.520165	−	0.194011i
$344$		0			0
$345$	−1.36602	−	13.0136i	−0.0735441	−	0.700628i
$346$		0			0
$347$	−10.1574	+	3.78852i	−0.545279	+	0.203378i	−0.606981	−	0.794716i	$-0.707620\pi$
$347$	−10.1574	+	3.78852i	−0.545279	+	0.203378i	0.0617026	+	0.998095i	$0.480347\pi$
$348$		0			0
$349$	−14.6510	+	12.6952i	−0.784251	+	0.679557i	−0.951941	−	0.306283i	$-0.900915\pi$
$349$	−14.6510	+	12.6952i	−0.784251	+	0.679557i	0.167690	+	0.985840i	$0.446369\pi$
$350$		0			0
$351$	5.95008	−	6.86676i	0.317592	−	0.366520i
$352$		0			0
$353$	−6.70933	+	12.2872i	−0.357101	+	0.653983i	−0.993043	−	0.117755i	$-0.962430\pi$
$353$	−6.70933	+	12.2872i	−0.357101	+	0.653983i	0.635941	+	0.771738i	$0.280612\pi$
$354$		0			0
$355$	−18.9239	+	10.6403i	−1.00438	+	0.564727i
$356$		0			0
$357$	−1.47763	+	3.96168i	−0.0782045	+	0.209674i
$358$		0			0
$359$	−15.1568	−	9.74069i	−0.799945	−	0.514094i	0.0756526	−	0.997134i	$-0.475896\pi$
$359$	−15.1568	−	9.74069i	−0.799945	−	0.514094i	−0.875598	+	0.483041i	$0.839532\pi$
$360$		0			0
$361$	−0.0814332	+	0.566381i	−0.00428596	+	0.0298095i
$362$		0			0
$363$	2.38804	−	10.9776i	0.125339	−	0.576176i
$364$		0			0
$365$	−4.75577	−	4.01864i	−0.248928	−	0.210345i
$366$		0			0
$367$	−9.28332	+	9.28332i	−0.484585	+	0.484585i	−0.906592	−	0.422007i	$-0.861326\pi$
$367$	−9.28332	+	9.28332i	−0.484585	+	0.484585i	0.422007	+	0.906592i	$0.361326\pi$
$368$		0			0
$369$		−	0.0181393i		−	0.000944294i
$370$		0			0
$371$	4.06644	+	1.19402i	0.211119	+	0.0619902i
$372$		0			0
$373$	−27.3307	−	5.94543i	−1.41513	−	0.307843i	−0.560963	−	0.827841i	$-0.689569\pi$
$373$	−27.3307	−	5.94543i	−1.41513	−	0.307843i	−0.854168	+	0.519998i	$0.825933\pi$
$374$		0			0
$375$	−2.44286	−	13.4217i	−0.126149	−	0.693091i
$376$		0			0
$377$	2.57763	+	11.8492i	0.132755	+	0.610264i
$378$		0			0
$379$	8.39675	+	18.3863i	0.431312	+	0.944442i	0.993112	+	0.117169i	$0.0373818\pi$
$379$	8.39675	+	18.3863i	0.431312	+	0.944442i	−0.561800	+	0.827273i	$0.689891\pi$
$380$		0			0
$381$	2.87562	+	20.0003i	0.147322	+	1.02465i
$382$		0			0
$383$	−24.9911	−	13.6462i	−1.27699	−	0.697288i	−0.309667	−	0.950845i	$-0.600218\pi$
$383$	−24.9911	−	13.6462i	−1.27699	−	0.697288i	−0.967320	+	0.253557i	$0.918399\pi$
$384$		0			0
$385$	−5.19382	−	11.0092i	−0.264702	−	0.561079i
$386$		0			0
$387$	−8.09764	−	0.579155i	−0.411626	−	0.0294401i
$388$		0			0
$389$	11.0293	−	24.1509i	0.559209	−	1.22450i	−0.393137	−	0.919480i	$-0.628610\pi$
$389$	11.0293	−	24.1509i	0.559209	−	1.22450i	0.952347	−	0.305018i	$-0.0986625\pi$
$390$		0			0
$391$	−3.89732	+	1.23285i	−0.197096	+	0.0623479i
$392$		0			0
$393$	1.92905	+	5.17198i	0.0973076	+	0.260892i
$394$		0			0
$395$	−8.65419	+	16.3276i	−0.435439	+	0.821529i
$396$		0			0
$397$	31.7661	−	2.27195i	1.59429	−	0.114026i	0.754265	−	0.656570i	$-0.227993\pi$
$397$	31.7661	−	2.27195i	1.59429	−	0.114026i	0.840028	+	0.542543i	$0.182539\pi$
$398$		0			0
$399$	6.18313	+	21.0578i	0.309543	+	1.05421i
$400$		0			0
$401$	28.4526	−	4.09087i	1.42086	−	0.204288i	0.611332	−	0.791374i	$-0.290634\pi$
$401$	28.4526	−	4.09087i	1.42086	−	0.204288i	0.809524	+	0.587086i	$0.199725\pi$
$402$		0			0
$403$	−7.36955	−	2.74870i	−0.367103	−	0.136922i
$404$		0			0
$405$	−0.978352	+	4.78246i	−0.0486147	+	0.237642i
$406$		0			0
$407$	−8.38644	+	6.27801i	−0.415700	+	0.311189i
$408$		0			0
$409$	−10.2918	−	16.0143i	−0.508894	−	0.791855i	0.487812	−	0.872949i	$-0.337795\pi$
$409$	−10.2918	−	16.0143i	−0.508894	−	0.791855i	−0.996707	+	0.0810934i	$0.974159\pi$
$410$		0			0
$411$	−4.56577	+	15.5496i	−0.225213	+	0.767005i
$412$		0			0
$413$	−8.71076	−	8.71076i	−0.428628	−	0.428628i
$414$		0			0
$415$	7.05466	−	15.9692i	0.346300	−	0.783897i
$416$		0			0
$417$	−12.2032	−	22.3486i	−0.597595	−	1.09441i
$418$		0			0
$419$	25.6777	−	16.5021i	1.25444	−	0.806178i	0.266925	−	0.963717i	$-0.413993\pi$
$419$	25.6777	−	16.5021i	1.25444	−	0.806178i	0.987513	+	0.157540i	$0.0503562\pi$
$420$		0			0
$421$	−20.3583	−	2.92708i	−0.992203	−	0.142657i	−0.372952	−	0.927850i	$-0.621655\pi$
$421$	−20.3583	−	2.92708i	−0.992203	−	0.142657i	−0.619251	+	0.785193i	$0.712564\pi$
$422$		0			0
$423$	−1.84540	+	0.401441i	−0.0897262	+	0.0195187i
$424$		0			0
$425$	−3.95479	+	1.58797i	−0.191836	+	0.0770277i
$426$		0			0
$427$	18.5066	−	24.7220i	0.895599	−	1.19638i
$428$		0			0
$429$	−2.58769	+	0.759816i	−0.124935	+	0.0366842i
$430$		0			0
$431$	2.53265	+	2.19456i	0.121994	+	0.105708i	0.713721	−	0.700430i	$-0.247008\pi$
$431$	2.53265	+	2.19456i	0.121994	+	0.105708i	−0.591727	+	0.806138i	$0.701554\pi$
$432$		0			0
$433$	−2.36058	+	33.0052i	−0.113442	+	1.58613i	0.548224	+	0.836331i	$0.315304\pi$
$433$	−2.36058	+	33.0052i	−0.113442	+	1.58613i	−0.661666	+	0.749798i	$0.730150\pi$
$434$		0			0
$435$	−13.3130	−	14.9841i	−0.638307	−	0.718430i
$436$		0			0
$437$	−12.3593	+	17.2455i	−0.591226	+	0.824965i
$438$		0			0
$439$	2.45365	+	1.12054i	0.117106	+	0.0534806i	0.473107	−	0.881005i	$-0.343133\pi$
$439$	2.45365	+	1.12054i	0.117106	+	0.0534806i	−0.356000	+	0.934486i	$0.615860\pi$
$440$		0			0
$441$	−9.42972	−	10.8825i	−0.449034	−	0.518213i
$442$		0			0
$443$	1.18644	+	16.5886i	0.0563694	+	0.788148i	0.944491	+	0.328538i	$0.106556\pi$
$443$	1.18644	+	16.5886i	0.0563694	+	0.788148i	−0.888121	+	0.459609i	$0.847989\pi$
$444$		0			0
$445$	15.6373	+	20.3573i	0.741280	+	0.965030i
$446$		0			0
$447$	12.4109	+	9.29071i	0.587017	+	0.439435i
$448$		0			0
$449$	0.996767	−	0.455208i	0.0470404	−	0.0214826i	−0.391756	−	0.920069i	$-0.628132\pi$
$449$	0.996767	−	0.455208i	0.0470404	−	0.0214826i	0.438796	+	0.898587i	$0.355405\pi$
$450$		0			0
$451$	−0.00868979	+	0.0135216i	−0.000409186	+	0.000636706i
$452$		0			0
$453$	0.498192	+	0.665507i	0.0234071	+	0.0312682i
$454$		0			0
$455$	8.84303	−	12.1237i	0.414568	−	0.568369i
$456$		0			0
$457$	1.02044	−	0.557202i	0.0477341	−	0.0260648i	−0.455205	−	0.890387i	$-0.650434\pi$
$457$	1.02044	−	0.557202i	0.0477341	−	0.0260648i	0.502939	+	0.864322i	$0.332252\pi$
$458$		0			0
$459$	4.69165			0.218987
$460$		0			0
$461$	−30.7280			−1.43114			−0.715572	−	0.698539i	$-0.753834\pi$
$461$	−30.7280			−1.43114			−0.715572	+	0.698539i	$0.753834\pi$
$462$		0			0
$463$	−0.429190	+	0.234355i	−0.0199461	+	0.0108914i	−0.489191	−	0.872177i	$-0.662708\pi$
$463$	−0.429190	+	0.234355i	−0.0199461	+	0.0108914i	0.469245	+	0.883068i	$0.344526\pi$
$464$		0			0
$465$	12.8447	−	2.00982i	0.595660	−	0.0932034i
$466$		0			0
$467$	−0.600604	−	0.802313i	−0.0277926	−	0.0371266i	0.786430	−	0.617680i	$-0.211927\pi$
$467$	−0.600604	−	0.802313i	−0.0277926	−	0.0371266i	−0.814222	+	0.580553i	$0.802836\pi$
$468$		0			0
$469$	−0.931568	+	1.44955i	−0.0430158	+	0.0669339i
$470$		0			0
$471$	−13.7082	+	6.26031i	−0.631639	+	0.288460i
$472$		0			0
$473$	5.75878	+	4.31097i	0.264789	+	0.198218i
$474$		0			0
$475$	−11.4935	+	18.8999i	−0.527358	+	0.867185i
$476$		0			0
$477$	−0.112378	−	1.57125i	−0.00514543	−	0.0719425i
$478$		0			0
$479$	−3.03499	−	3.50257i	−0.138672	−	0.160037i	0.682165	−	0.731198i	$-0.261038\pi$
$479$	−3.03499	−	3.50257i	−0.138672	−	0.160037i	−0.820838	+	0.571162i	$0.806493\pi$
$480$		0			0
$481$	−11.7473	−	5.36480i	−0.535629	−	0.244614i
$482$		0			0
$483$	−4.57319	+	23.3475i	−0.208087	+	1.06235i
$484$		0			0
$485$	2.14599	−	1.90665i	0.0974442	−	0.0865767i
$486$		0			0
$487$	−2.22417	+	31.0980i	−0.100787	+	1.40919i	0.655623	+	0.755088i	$0.272406\pi$
$487$	−2.22417	+	31.0980i	−0.100787	+	1.40919i	−0.756410	+	0.654097i	$0.773049\pi$
$488$		0			0
$489$	22.2866	+	19.3115i	1.00784	+	0.873296i
$490$		0			0
$491$	−0.135245	+	0.0397115i	−0.00610352	+	0.00179216i	−0.284783	−	0.958592i	$-0.591922\pi$
$491$	−0.135245	+	0.0397115i	−0.00610352	+	0.00179216i	0.278679	+	0.960384i	$0.410103\pi$
$492$		0			0
$493$	−3.75240	+	5.01261i	−0.168999	+	0.225757i
$494$		0			0
$495$	−3.15935	+	3.23877i	−0.142002	+	0.145572i
$496$		0			0
$497$	38.5710	−	8.39060i	1.73014	−	0.376370i
$498$		0			0
$499$	36.1577	+	5.19870i	1.61864	+	0.232726i	0.891256	−	0.453501i	$-0.149825\pi$
$499$	36.1577	+	5.19870i	1.61864	+	0.232726i	0.727387	+	0.686227i	$0.240734\pi$
$500$		0			0
$501$	14.5048	−	9.32168i	0.648027	−	0.416462i
$502$		0			0
$503$	10.4232	+	19.0887i	0.464748	+	0.851123i	0.999979	+	0.00641733i	$0.00204271\pi$
$503$	10.4232	+	19.0887i	0.464748	+	0.851123i	−0.535231	+	0.844706i	$0.679775\pi$
$504$		0			0
$505$	0.737015	+	1.90351i	0.0327967	+	0.0847052i
$506$		0			0
$507$	8.86558	+	8.86558i	0.393734	+	0.393734i
$508$		0			0
$509$	8.23773	−	28.0551i	0.365131	−	1.24352i	−0.548215	−	0.836337i	$-0.684693\pi$
$509$	8.23773	−	28.0551i	0.365131	−	1.24352i	0.913346	−	0.407184i	$-0.133489\pi$
$510$		0			0
$511$	6.12036	+	9.52347i	0.270749	+	0.421294i
$512$		0			0
$513$	19.4947	−	14.5936i	0.860713	−	0.644322i
$514$		0			0
$515$	0.0996809	−	0.0658235i	0.00439247	−	0.00290053i
$516$		0			0
$517$	1.56793	+	0.584807i	0.0689574	+	0.0257198i
$518$		0			0
$519$	3.21565	−	0.462340i	0.141151	−	0.0202945i
$520$		0			0
$521$	−4.97811	−	16.9539i	−0.218095	−	0.742764i	−0.993752	−	0.111609i	$-0.964400\pi$
$521$	−4.97811	−	16.9539i	−0.218095	−	0.742764i	0.775657	−	0.631155i	$-0.217419\pi$
$522$		0			0
$523$	44.1354	−	3.15663i	1.92991	−	0.138030i	0.946892	−	0.321553i	$-0.104205\pi$
$523$	44.1354	−	3.15663i	1.92991	−	0.138030i	0.983015	+	0.183523i	$0.0587502\pi$
$524$		0			0
$525$	−2.91945	+	24.6316i	−0.127415	+	1.07501i
$526$		0			0
$527$	−1.41932	−	3.80533i	−0.0618263	−	0.165763i
$528$		0			0
$529$	−20.5066	+	10.4153i	−0.891593	+	0.452838i
$530$		0			0
$531$	−1.90210	+	4.16501i	−0.0825440	+	0.180746i
$532$		0			0
$533$	−0.0197638	−	0.00141353i	−0.000856064	−	6.12269e-5i
$534$		0			0
$535$	−18.8612	+	8.89821i	−0.815442	+	0.384703i
$536$		0			0
$537$	23.3558	+	12.7532i	1.00788	+	0.550342i
$538$		0			0
$539$	1.81585	+	12.6295i	0.0782143	+	0.543992i
$540$		0			0
$541$	−3.97134	−	8.69602i	−0.170741	−	0.373871i	0.804846	−	0.593484i	$-0.202248\pi$
$541$	−3.97134	−	8.69602i	−0.170741	−	0.373871i	−0.975587	+	0.219613i	$0.929521\pi$
$542$		0			0
$543$	5.16514	+	23.7437i	0.221657	+	1.01894i
$544$		0			0
$545$	9.09221	−	2.09641i	0.389467	−	0.0898005i
$546$		0			0
$547$	−1.63871	−	0.356479i	−0.0700661	−	0.0152419i	0.177396	−	0.984140i	$-0.443233\pi$
$547$	−1.63871	−	0.356479i	−0.0700661	−	0.0152419i	−0.247462	+	0.968898i	$0.579596\pi$
$548$		0			0
$549$	−11.0134	−	3.23382i	−0.470040	−	0.138016i
$550$		0			0
$551$			32.5004i			1.38456i
$552$		0			0
$553$	23.7579	−	23.7579i	1.01029	−	1.01029i
$554$		0			0
$555$	21.2714	−	1.78700i	0.902922	−	0.0758539i
$556$		0			0
$557$	2.47069	−	11.3576i	0.104686	−	0.481236i	−0.894715	−	0.446638i	$-0.852621\pi$
$557$	2.47069	−	11.3576i	0.104686	−	0.481236i	0.999401	−	0.0345980i	$-0.0110151\pi$
$558$		0			0
$559$	−1.26204	+	8.77770i	−0.0533787	+	0.371257i
$560$		0			0
$561$	−1.17152	−	0.752890i	−0.0494616	−	0.0317871i
$562$		0			0
$563$	3.83561	−	10.2837i	0.161652	−	0.433405i	−0.830719	−	0.556691i	$-0.812071\pi$
$563$	3.83561	−	10.2837i	0.161652	−	0.433405i	0.992371	+	0.123286i	$0.0393434\pi$
$564$		0			0
$565$	35.6171	+	9.97963i	1.49842	+	0.419846i
$566$		0			0
$567$	4.25357	−	7.78983i	0.178633	−	0.327142i
$568$		0			0
$569$	−12.9010	+	14.8885i	−0.540837	+	0.624159i	−0.958723	−	0.284340i	$-0.908225\pi$
$569$	−12.9010	+	14.8885i	−0.540837	+	0.624159i	0.417887	+	0.908499i	$0.362771\pi$
$570$		0			0
$571$	−7.01070	+	6.07481i	−0.293389	+	0.254223i	−0.789100	−	0.614264i	$-0.789453\pi$
$571$	−7.01070	+	6.07481i	−0.293389	+	0.254223i	0.495711	+	0.868487i	$0.334907\pi$
$572$		0			0
$573$	1.21159	−	0.451901i	0.0506150	−	0.0188784i
$574$		0			0
$575$	−20.5003	+	12.4394i	−0.854921	+	0.518758i
$576$		0			0
$577$	−33.0120	+	12.3129i	−1.37431	+	0.512591i	−0.924721	−	0.380645i	$-0.875702\pi$
$577$	−33.0120	+	12.3129i	−1.37431	+	0.512591i	−0.449588	+	0.893236i	$0.648429\pi$
$578$		0			0
$579$	−12.0142	+	10.4104i	−0.499294	+	0.432641i
$580$		0			0
$581$	−20.7866	+	23.9890i	−0.862372	+	0.995231i
$582$		0			0
$583$	−0.668950	+	1.22509i	−0.0277051	+	0.0507381i
$584$		0			0
$585$	−5.37077	−	1.50485i	−0.222054	−	0.0622177i
$586$		0			0
$587$	4.91766	−	13.1847i	0.202973	−	0.544193i	−0.795084	−	0.606500i	$-0.792573\pi$
$587$	4.91766	−	13.1847i	0.202973	−	0.544193i	0.998057	+	0.0623071i	$0.0198458\pi$
$588$		0			0
$589$	−17.7342	−	11.3971i	−0.730724	−	0.469608i
$590$		0			0
$591$	−1.55093	+	10.7869i	−0.0637967	+	0.443716i
$592$		0			0
$593$	−6.33647	+	29.1283i	−0.260208	+	1.19615i	0.642631	+	0.766176i	$0.277843\pi$
$593$	−6.33647	+	29.1283i	−0.260208	+	1.19615i	−0.902839	+	0.429979i	$0.858521\pi$
$594$		0			0
$595$	7.72135	−	0.648665i	0.316544	−	0.0265927i
$596$		0			0
$597$	4.98358	−	4.98358i	0.203964	−	0.203964i
$598$		0			0
$599$		−	31.9108i		−	1.30384i	−0.758288	−	0.651919i	$-0.773964\pi$
$599$		−	31.9108i		−	1.30384i	0.758288	−	0.651919i	$-0.226036\pi$
$600$		0			0
$601$	−9.13983	−	2.68370i	−0.372822	−	0.109470i	0.0899537	−	0.995946i	$-0.471328\pi$
$601$	−9.13983	−	2.68370i	−0.372822	−	0.109470i	−0.462775	+	0.886476i	$0.653146\pi$
$602$		0			0
$603$	0.625814	+	0.136138i	0.0254851	+	0.00554395i
$604$		0			0
$605$	−20.0612	+	4.62558i	−0.815606	+	0.188056i
$606$		0			0
$607$	5.84192	+	26.8549i	0.237116	+	1.09001i	0.929599	+	0.368572i	$0.120153\pi$
$607$	5.84192	+	26.8549i	0.237116	+	1.09001i	−0.692483	+	0.721434i	$0.743483\pi$
$608$		0			0
$609$	15.1392	+	33.1501i	0.613470	+	1.34331i
$610$		0			0
$611$	0.293587	+	2.04194i	0.0118773	+	0.0826082i
$612$		0			0
$613$	−13.3999	−	7.31688i	−0.541216	−	0.295526i	0.185293	−	0.982683i	$-0.440677\pi$
$613$	−13.3999	−	7.31688i	−0.541216	−	0.295526i	−0.726509	+	0.687157i	$0.758858\pi$
$614$		0			0
$615$	0.0296206	−	0.0139742i	0.00119442	−	0.000563493i
$616$		0			0
$617$	−35.4427	−	2.53491i	−1.42687	−	0.102052i	−0.663579	−	0.748107i	$-0.730963\pi$
$617$	−35.4427	−	2.53491i	−1.42687	−	0.102052i	−0.763291	+	0.646055i	$0.776418\pi$
$618$		0			0
$619$	1.93373	−	4.23427i	0.0777230	−	0.170190i	−0.866782	−	0.498688i	$-0.833815\pi$
$619$	1.93373	−	4.23427i	0.0777230	−	0.170190i	0.944504	+	0.328499i	$0.106543\pi$
$620$		0			0
$621$	26.0460	−	4.29883i	1.04519	−	0.172506i
$622$		0			0
$623$	−16.3105	−	43.7300i	−0.653465	−	1.75201i
$624$		0			0
$625$	−20.3346	+	14.5432i	−0.813385	+	0.581726i
$626$		0			0
$627$	−7.20979	+	0.515655i	−0.287931	+	0.0205933i
$628$		0			0
$629$	−1.87871	−	6.39830i	−0.0749091	−	0.255117i
$630$		0			0
$631$	−48.4682	+	6.96868i	−1.92949	+	0.277419i	−0.996576	−	0.0826816i	$-0.973652\pi$
$631$	−48.4682	+	6.96868i	−1.92949	+	0.277419i	−0.932914	+	0.360100i	$0.882742\pi$
$632$		0			0
$633$	−16.0218	−	5.97582i	−0.636810	−	0.237518i
$634$		0			0
$635$	30.8996	−	20.4043i	1.22621	−	0.809720i
$636$		0			0
$637$	−12.5919	+	9.42618i	−0.498909	+	0.373479i
$638$		0			0
$639$	−7.93212	−	12.3426i	−0.313790	−	0.488266i
$640$		0			0
$641$	−5.08931	+	17.3326i	−0.201016	+	0.684596i	0.795851	+	0.605493i	$0.207024\pi$
$641$	−5.08931	+	17.3326i	−0.201016	+	0.684596i	−0.996866	+	0.0791036i	$0.974794\pi$
$642$		0			0
$643$	11.3099	+	11.3099i	0.446019	+	0.446019i	0.894029	−	0.448010i	$-0.147867\pi$
$643$	11.3099	+	11.3099i	0.446019	+	0.446019i	−0.448010	+	0.894029i	$0.647867\pi$
$644$		0			0
$645$	−5.29254	−	13.6692i	−0.208394	−	0.538225i
$646$		0			0
$647$	−19.1935	−	35.1504i	−0.754576	−	1.38190i	−0.918496	−	0.395430i	$-0.870596\pi$
$647$	−19.1935	−	35.1504i	−0.754576	−	1.38190i	0.163920	−	0.986474i	$-0.447586\pi$
$648$		0			0
$649$	3.41317	−	2.19351i	0.133979	−	0.0861028i
$650$		0			0
$651$	−23.3976	−	3.36407i	−0.917026	−	0.131848i
$652$		0			0
$653$	48.4789	−	10.5459i	1.89713	−	0.412695i	0.897527	−	0.440960i	$-0.145362\pi$
$653$	48.4789	−	10.5459i	1.89713	−	0.412695i	0.999600	+	0.0282651i	$0.00899826\pi$
$654$		0			0
$655$	7.06357	−	7.24114i	0.275997	−	0.282935i
$656$		0			0
$657$	2.52160	−	3.36846i	0.0983769	−	0.131416i
$658$		0			0
$659$	−24.7815	+	7.27649i	−0.965349	+	0.283452i	−0.726163	−	0.687522i	$-0.758698\pi$
$659$	−24.7815	+	7.27649i	−0.965349	+	0.283452i	−0.239185	+	0.970974i	$0.576880\pi$
$660$		0			0
$661$	−24.8546	−	21.5366i	−0.966730	−	0.837676i	0.0200405	−	0.999799i	$-0.493620\pi$
$661$	−24.8546	−	21.5366i	−0.966730	−	0.837676i	−0.986771	+	0.162123i	$0.948166\pi$
$662$		0			0
$663$	0.122470	−	1.71235i	0.00475633	−	0.0665021i
$664$		0			0
$665$	30.0660	−	26.7129i	1.16591	−	1.03588i
$666$		0			0
$667$	−16.2388	+	31.2661i	−0.628767	+	1.21063i
$668$		0			0
$669$	−19.5624	−	8.93385i	−0.756326	−	0.345403i
$670$		0			0
$671$	6.66052	+	7.68665i	0.257127	+	0.296740i
$672$		0			0
$673$	2.00066	+	27.9729i	0.0771199	+	1.07828i	0.877750	+	0.479119i	$0.159044\pi$
$673$	2.00066	+	27.9729i	0.0771199	+	1.07828i	−0.800630	+	0.599159i	$0.795502\pi$
$674$		0			0
$675$	26.7398	−	6.51603i	1.02921	−	0.250802i
$676$		0			0
$677$	29.0797	+	21.7688i	1.11762	+	0.836643i	0.987928	−	0.154911i	$-0.0495092\pi$
$677$	29.0797	+	21.7688i	1.11762	+	0.836643i	0.129695	+	0.991554i	$0.458600\pi$
$678$		0			0
$679$	−4.74770	+	2.16820i	−0.182200	+	0.0832079i
$680$		0			0
$681$	13.5148	−	21.0295i	0.517889	−	0.805851i
$682$		0			0
$683$	−24.5638	−	32.8134i	−0.939909	−	1.25557i	−0.966695	−	0.255930i	$-0.917618\pi$
$683$	−24.5638	−	32.8134i	−0.939909	−	1.25557i	0.0267867	−	0.999641i	$-0.491473\pi$
$684$		0			0
$685$	29.3415	−	4.59109i	1.12108	−	0.175416i
$686$		0			0
$687$	18.5957	−	10.1540i	0.709471	−	0.387400i
$688$		0			0
$689$	−1.72072			−0.0655542
$690$		0			0
$691$	−12.5963			−0.479185			−0.239592	−	0.970874i	$-0.577014\pi$
$691$	−12.5963			−0.479185			−0.239592	+	0.970874i	$0.577014\pi$
$692$		0			0
$693$	7.22013	−	3.94249i	0.274270	−	0.149763i
$694$		0			0
$695$	−27.4982	+	37.6997i	−1.04306	+	1.43003i
$696$		0			0
$697$	−0.00613137	−	0.00819056i	−0.000232242	−	0.000310239i
$698$		0			0
$699$	16.6929	−	25.9746i	0.631382	−	0.982450i
$700$		0			0
$701$	2.38649	−	1.08987i	0.0901363	−	0.0411639i	−0.369837	−	0.929097i	$-0.620586\pi$
$701$	2.38649	−	1.08987i	0.0901363	−	0.0411639i	0.459973	+	0.887933i	$0.347859\pi$
$702$		0			0
$703$	−27.7086	−	20.7424i	−1.04505	−	0.782314i
$704$		0			0
$705$	−2.07719	−	2.70418i	−0.0782316	−	0.101845i
$706$		0			0
$707$	−0.264761	−	3.70185i	−0.00995738	−	0.139222i
$708$		0			0
$709$	−15.7252	−	18.1478i	−0.590572	−	0.681556i	0.379271	−	0.925285i	$-0.376175\pi$
$709$	−15.7252	−	18.1478i	−0.590572	−	0.681556i	−0.969843	+	0.243729i	$0.921629\pi$
$710$		0			0
$711$	−11.3598	−	5.18783i	−0.426024	−	0.194559i
$712$		0			0
$713$	−11.3661	−	19.8251i	−0.425666	−	0.742455i
$714$		0			0
$715$	3.28262	+	3.69467i	0.122763	+	0.138173i
$716$		0			0
$717$	−1.91665	+	26.7982i	−0.0715785	+	1.00080i
$718$		0			0
$719$	33.3339	+	28.8840i	1.24315	+	1.07719i	0.994074	+	0.108706i	$0.0346707\pi$
$719$	33.3339	+	28.8840i	1.24315	+	1.07719i	0.249071	+	0.968485i	$0.419875\pi$
$720$		0			0
$721$	−0.208390	+	0.0611889i	−0.00776086	+	0.00227879i
$722$		0			0
$723$	−22.5133	+	30.0742i	−0.837278	+	1.11847i
$724$		0			0
$725$	−14.4247	+	33.7806i	−0.535721	+	1.25458i
$726$		0			0
$727$	28.8215	−	6.26974i	1.06893	−	0.232532i	0.356516	−	0.934289i	$-0.383965\pi$
$727$	28.8215	−	6.26974i	1.06893	−	0.232532i	0.712416	+	0.701757i	$0.247601\pi$
$728$		0			0
$729$	−23.2097	−	3.33705i	−0.859618	−	0.123594i
$730$		0			0
$731$	−3.85214	+	2.47562i	−0.142477	+	0.0915642i
$732$		0			0
$733$	−15.0124	−	27.4932i	−0.554497	−	1.01549i	−0.993152	−	0.116830i	$-0.962727\pi$
$733$	−15.0124	−	27.4932i	−0.554497	−	1.01549i	0.438655	−	0.898656i	$-0.355455\pi$
$734$		0			0
$735$	10.5061	−	23.7820i	0.387523	−	0.877210i
$736$		0			0
$737$	−0.401283	−	0.401283i	−0.0147814	−	0.0147814i
$738$		0			0
$739$	12.0878	−	41.1672i	0.444656	−	1.51436i	−0.366998	−	0.930222i	$-0.619614\pi$
$739$	12.0878	−	41.1672i	0.444656	−	1.51436i	0.811654	−	0.584138i	$-0.198567\pi$
$740$		0			0
$741$	−4.81745	−	7.49609i	−0.176973	−	0.275376i
$742$		0			0
$743$	−14.6599	+	10.9742i	−0.537819	+	0.402606i	−0.833365	−	0.552722i	$-0.813589\pi$
$743$	−14.6599	+	10.9742i	−0.537819	+	0.402606i	0.295547	+	0.955328i	$0.404498\pi$
$744$		0			0
$745$	5.69402	−	27.8340i	0.208613	−	1.01976i
$746$		0			0
$747$	11.0543	+	4.12303i	0.404454	+	0.150854i
$748$		0			0
$749$	37.5320	−	5.39629i	1.37139	−	0.197176i
$750$		0			0
$751$	5.21331	+	17.7549i	0.190236	+	0.647886i	0.998273	+	0.0587528i	$0.0187124\pi$
$751$	5.21331	+	17.7549i	0.190236	+	0.647886i	−0.808036	+	0.589133i	$0.799469\pi$
$752$		0			0
$753$	−10.7399	+	0.768130i	−0.391382	+	0.0279922i
$754$		0			0
$755$	0.713455	−	1.34605i	0.0259653	−	0.0489879i
$756$		0			0
$757$	−1.21798	−	3.26554i	−0.0442683	−	0.118688i	0.912934	−	0.408106i	$-0.133811\pi$
$757$	−1.21798	−	3.26554i	−0.0442683	−	0.118688i	−0.957203	+	0.289419i	$0.906538\pi$
$758$		0			0
$759$	−7.19363	−	3.10629i	−0.261112	−	0.112751i
$760$		0			0
$761$	9.68209	−	21.2008i	0.350976	−	0.768529i	−0.648994	−	0.760793i	$-0.724810\pi$
$761$	9.68209	−	21.2008i	0.350976	−	0.768529i	0.999970	−	0.00773628i	$-0.00246256\pi$
$762$		0			0
$763$	−16.9218	−	1.21027i	−0.612612	−	0.0438149i
$764$		0			0
$765$	−1.22884	−	2.60473i	−0.0444288	−	0.0941743i
$766$		0			0
$767$	4.38979	+	2.39701i	0.158506	+	0.0865509i
$768$		0			0
$769$	2.04474	+	14.2215i	0.0737352	+	0.512840i	0.992899	+	0.118963i	$0.0379571\pi$
$769$	2.04474	+	14.2215i	0.0737352	+	0.512840i	−0.919163	+	0.393876i	$0.871134\pi$
$770$		0			0
$771$	14.0715	+	30.8123i	0.506774	+	1.10968i
$772$		0			0
$773$	10.6411	+	48.9165i	0.382735	+	1.75940i	0.616738	+	0.787168i	$0.288454\pi$
$773$	10.6411	+	48.9165i	0.382735	+	1.75940i	−0.234003	+	0.972236i	$0.575183\pi$
$774$		0			0
$775$	−13.3744	−	19.7170i	−0.480421	−	0.708256i
$776$		0			0
$777$	−37.9247	−	8.25001i	−1.36054	−	0.295967i
$778$		0			0
$779$	−0.0509541	−	0.0149615i	−0.00182562	−	0.000536051i
$780$		0			0
$781$			13.0005i			0.465195i
$782$		0			0
$783$	28.5935	−	28.5935i	1.02185	−	1.02185i
$784$		0			0
$785$	21.0941	+	17.8246i	0.752882	+	0.636187i
$786$		0			0
$787$	1.28641	−	5.91354i	0.0458557	−	0.210795i	−0.948518	−	0.316723i	$-0.897418\pi$
$787$	1.28641	−	5.91354i	0.0458557	−	0.210795i	0.994374	+	0.105928i	$0.0337812\pi$
$788$		0			0
$789$	4.08656	−	28.4226i	0.145485	−	1.01187i
$790$		0			0
$791$	−56.5764	−	36.3595i	−2.01163	−	1.29279i
$792$		0			0
$793$	−4.38166	+	11.7477i	−0.155597	+	0.417173i
$794$		0			0
$795$	2.47920	−	1.39397i	0.0879281	−	0.0494389i
$796$		0			0
$797$	9.16429	−	16.7831i	0.324616	−	0.594490i	−0.663504	−	0.748172i	$-0.730932\pi$
$797$	9.16429	−	16.7831i	0.324616	−	0.594490i	0.988120	+	0.153683i	$0.0491134\pi$
$798$		0			0
$799$	−0.697570	+	0.805039i	−0.0246782	+	0.0284802i
$800$		0			0
$801$	−13.1105	+	11.3604i	−0.463238	+	0.401398i
$802$		0			0
$803$	−3.49337	+	1.30296i	−0.123278	+	0.0459804i
$804$		0			0
$805$	42.2712	−	10.6760i	1.48987	−	0.376279i
$806$		0			0
$807$	29.7053	−	11.0795i	1.04568	−	0.390017i
$808$		0			0
$809$	30.5662	−	26.4857i	1.07465	−	0.931189i	0.0768205	−	0.997045i	$-0.475523\pi$
$809$	30.5662	−	26.4857i	1.07465	−	0.931189i	0.997829	+	0.0658557i	$0.0209777\pi$
$810$		0			0
$811$	36.6283	−	42.2713i	1.28619	−	1.48434i	0.500486	−	0.865744i	$-0.333155\pi$
$811$	36.6283	−	42.2713i	1.28619	−	1.48434i	0.785706	−	0.618600i	$-0.212300\pi$
$812$		0			0
$813$	−9.25638	+	16.9518i	−0.324635	+	0.594525i
$814$		0			0
$815$	14.5803	−	52.0370i	0.510727	−	1.82278i
$816$		0			0
$817$	−8.30589	+	22.2689i	−0.290586	+	0.779092i
$818$		0			0
$819$	8.53126	+	5.48271i	0.298106	+	0.191581i
$820$		0			0
$821$	3.70611	−	25.7765i	0.129344	−	0.899607i	−0.817044	−	0.576575i	$-0.804389\pi$
$821$	3.70611	−	25.7765i	0.129344	−	0.899607i	0.946388	−	0.323032i	$-0.104702\pi$
$822$		0			0
$823$	4.31700	−	19.8449i	0.150481	−	0.691750i	−0.838645	−	0.544679i	$-0.816652\pi$
$823$	4.31700	−	19.8449i	0.150481	−	0.691750i	0.989126	−	0.147072i	$-0.0469848\pi$
$824$		0			0
$825$	−7.72266	−	2.66397i	−0.268869	−	0.0927477i
$826$		0			0
$827$	−9.70906	+	9.70906i	−0.337617	+	0.337617i	−0.855470	−	0.517853i	$-0.826732\pi$
$827$	−9.70906	+	9.70906i	−0.337617	+	0.337617i	0.517853	+	0.855470i	$0.326732\pi$
$828$		0			0
$829$		−	6.66980i		−	0.231652i	−0.993270	−	0.115826i	$-0.963049\pi$
$829$		−	6.66980i		−	0.231652i	0.993270	−	0.115826i	$-0.0369515\pi$
$830$		0			0
$831$	7.23040	+	2.12304i	0.250820	+	0.0736474i
$832$		0			0
$833$	−7.93632	−	1.72644i	−0.274977	−	0.0598176i
$834$		0			0
$835$	−26.7909	−	16.7512i	−0.927136	−	0.579701i
$836$		0			0
$837$	5.57532	+	25.6293i	0.192711	+	0.885880i
$838$		0			0
$839$	17.6718	+	38.6958i	0.610098	+	1.33593i	0.922507	+	0.385981i	$0.126137\pi$
$839$	17.6718	+	38.6958i	0.610098	+	1.33593i	−0.312408	+	0.949948i	$0.601136\pi$
$840$		0			0
$841$	3.55333	+	24.7140i	0.122529	+	0.852206i
$842$		0			0
$843$	−25.8612	−	14.1213i	−0.890707	−	0.486363i
$844$		0			0
$845$	7.76155	−	21.6256i	0.267005	−	0.743943i
$846$		0			0
$847$	37.3367	+	2.67038i	1.28291	+	0.0917552i
$848$		0			0
$849$	−11.8371	+	25.9196i	−0.406247	+	0.889558i
$850$		0			0
$851$	−16.2924	−	33.7992i	−0.558496	−	1.15862i
$852$		0			0
$853$	1.65430	+	4.43535i	0.0566421	+	0.151863i	0.962189	−	0.272383i	$-0.0878118\pi$
$853$	1.65430	+	4.43535i	0.0566421	+	0.151863i	−0.905547	+	0.424246i	$0.860539\pi$
$854$		0			0
$855$	−13.2082	−	7.00081i	−0.451711	−	0.239423i
$856$		0			0
$857$	31.6946	−	2.26684i	1.08267	−	0.0774339i	0.481415	−	0.876493i	$-0.340123\pi$
$857$	31.6946	−	2.26684i	1.08267	−	0.0774339i	0.601253	+	0.799059i	$0.294668\pi$
$858$		0			0
$859$	7.22686	+	24.6124i	0.246577	+	0.839765i	0.986032	+	0.166558i	$0.0532654\pi$
$859$	7.22686	+	24.6124i	0.246577	+	0.839765i	−0.739454	+	0.673207i	$0.764916\pi$
$860$		0			0
$861$	−0.0589421	+	0.00847459i	−0.00200874	+	0.000288813i
$862$		0			0
$863$	−13.1217	−	4.89414i	−0.446668	−	0.166598i	0.116057	−	0.993243i	$-0.462974\pi$
$863$	−13.1217	−	4.89414i	−0.446668	−	0.166598i	−0.562725	+	0.826644i	$0.690247\pi$
$864$		0			0
$865$	−3.28059	−	4.96802i	−0.111544	−	0.168918i
$866$		0			0
$867$	−15.8962	+	11.8997i	−0.539863	+	0.404136i
$868$		0			0
$869$	5.98263	+	9.30916i	0.202947	+	0.315792i
$870$		0			0
$871$	0.197097	−	0.671251i	0.00667838	−	0.0227445i
$872$		0			0
$873$	1.37177	+	1.37177i	0.0464274	+	0.0464274i
$874$		0			0
$875$	43.1064	−	14.4209i	1.45726	−	0.487515i
$876$		0			0
$877$	11.8176	+	21.6423i	0.399051	+	0.730808i	0.997523	−	0.0703358i	$-0.0224071\pi$
$877$	11.8176	+	21.6423i	0.399051	+	0.730808i	−0.598472	+	0.801144i	$0.704225\pi$
$878$		0			0
$879$	−5.74313	+	3.69088i	−0.193711	+	0.124490i
$880$		0			0
$881$	32.8948	+	4.72956i	1.10825	+	0.159343i	0.672050	−	0.740505i	$-0.265414\pi$
$881$	32.8948	+	4.72956i	1.10825	+	0.159343i	0.436203	+	0.899848i	$0.356323\pi$
$882$		0			0
$883$	6.40150	−	1.39256i	0.215428	−	0.0468634i	−0.103556	−	0.994624i	$-0.533022\pi$
$883$	6.40150	−	1.39256i	0.215428	−	0.0468634i	0.318984	+	0.947760i	$0.396658\pi$
$884$		0			0
$885$	−8.26660	+	0.102616i	−0.277879	+	0.00344940i
$886$		0			0
$887$	11.4502	−	15.2957i	0.384461	−	0.513579i	−0.566008	−	0.824400i	$-0.691513\pi$
$887$	11.4502	−	15.2957i	0.384461	−	0.513579i	0.950469	+	0.310820i	$0.100604\pi$
$888$		0			0
$889$	−64.5978	+	18.9676i	−2.16654	+	0.636154i
$890$		0			0
$891$	2.20917	+	1.91426i	0.0740101	+	0.0641301i
$892$		0			0
$893$	−0.394434	+	5.51491i	−0.0131992	+	0.184550i
$894$		0			0
$895$	2.87489	−	48.6810i	0.0960969	−	1.62723i
$896$		0			0
$897$	−0.889081	−	9.61844i	−0.0296855	−	0.321150i
$898$		0			0
$899$	−31.8419	−	14.5417i	−1.06199	−	0.484993i
$900$		0			0
$901$	−0.581849	−	0.671490i	−0.0193842	−	0.0223706i
$902$		0			0
$903$	1.90127	+	26.5832i	0.0632702	+	0.884632i
$904$		0			0
$905$	35.3136	−	27.1259i	1.17386	−	0.901695i
$906$		0			0
$907$	−6.03539	−	4.51804i	−0.200402	−	0.150019i	0.494364	−	0.869255i	$-0.335401\pi$
$907$	−6.03539	−	4.51804i	−0.200402	−	0.150019i	−0.694766	+	0.719236i	$0.744492\pi$
$908$		0			0
$909$	−1.25479	+	0.573045i	−0.0416188	+	0.0190067i
$910$		0			0
$911$	8.22683	−	12.8012i	0.272567	−	0.424122i	−0.677804	−	0.735243i	$-0.737068\pi$
$911$	8.22683	−	12.8012i	0.272567	−	0.424122i	0.950370	+	0.311121i	$0.100704\pi$
$912$		0			0
$913$	−6.26501	−	8.36907i	−0.207342	−	0.276976i
$914$		0			0
$915$	−3.20384	−	20.4756i	−0.105916	−	0.676903i
$916$		0			0
$917$	−16.1425	+	8.81449i	−0.533073	+	0.291080i
$918$		0			0
$919$	18.6058			0.613747			0.306874	−	0.951750i	$-0.400717\pi$
$919$	18.6058			0.613747			0.306874	+	0.951750i	$0.400717\pi$
$920$		0			0
$921$	4.51981			0.148933
$922$		0			0
$923$	−14.0661	+	7.68067i	−0.462991	+	0.252812i
$924$		0			0
$925$	−19.5939	−	33.8574i	−0.644244	−	1.11323i
$926$		0			0
$927$	0.0483775	+	0.0646247i	0.00158892	+	0.00212255i
$928$		0			0
$929$	21.5481	−	33.5294i	0.706969	−	1.10007i	−0.283046	−	0.959106i	$-0.591345\pi$
$929$	21.5481	−	33.5294i	0.706969	−	1.10007i	0.990015	−	0.140959i	$-0.0450187\pi$
$930$		0			0
$931$	−38.3471	+	17.5125i	−1.25678	+	0.573951i
$932$		0			0
$933$	−10.7325	−	8.03425i	−0.351366	−	0.263029i
$934$		0			0
$935$	−0.331805	+	2.53033i	−0.0108512	+	0.0827508i
$936$		0			0
$937$	3.52800	+	49.3279i	0.115255	+	1.61147i	0.645590	+	0.763685i	$0.276612\pi$
$937$	3.52800	+	49.3279i	0.115255	+	1.61147i	−0.530335	+	0.847788i	$0.677934\pi$
$938$		0			0
$939$	−24.9534	−	28.7977i	−0.814322	−	0.939778i
$940$		0			0
$941$	28.9967	+	13.2424i	0.945267	+	0.431689i	0.827571	−	0.561361i	$-0.189722\pi$
$941$	28.9967	+	13.2424i	0.945267	+	0.431689i	0.117696	+	0.993050i	$0.462449\pi$
$942$		0			0
$943$	−0.0415435	−	0.0398524i	−0.00135284	−	0.00129777i
$944$		0			0
$945$	−49.9535	−	2.95004i	−1.62499	−	0.0959647i
$946$		0			0
$947$	1.29907	−	18.1633i	0.0422140	−	0.590229i	−0.931688	−	0.363260i	$-0.881664\pi$
$947$	1.29907	−	18.1633i	0.0422140	−	0.590229i	0.973902	−	0.226969i	$-0.0728817\pi$
$948$		0			0
$949$	−3.47363	−	3.00992i	−0.112759	−	0.0977060i
$950$		0			0
$951$	14.7003	−	4.31641i	0.476691	−	0.139969i
$952$		0			0
$953$	−1.47447	+	1.96966i	−0.0477627	+	0.0638035i	−0.823787	−	0.566900i	$-0.808143\pi$
$953$	−1.47447	+	1.96966i	−0.0477627	+	0.0638035i	0.776024	+	0.630703i	$0.217234\pi$
$954$		0			0
$955$	−1.69632	−	1.65472i	−0.0548915	−	0.0535455i
$956$		0			0
$957$	−11.7284	+	2.55136i	−0.379126	+	0.0824738i
$958$		0			0
$959$	−53.4478	−	7.68463i	−1.72592	−	0.248150i
$960$		0			0
$961$	−6.97790	+	4.48442i	−0.225093	+	0.144659i
$962$		0			0
$963$	−6.75438	−	12.3697i	−0.217657	−	0.398609i
$964$		0			0
$965$	26.6479	+	11.7721i	0.857825	+	0.378959i
$966$		0			0
$967$	−12.0004	−	12.0004i	−0.385907	−	0.385907i	0.487318	−	0.873225i	$-0.337975\pi$
$967$	−12.0004	−	12.0004i	−0.385907	−	0.385907i	−0.873225	+	0.487318i	$0.837975\pi$
$968$		0			0
$969$	1.29627	−	4.41470i	0.0416423	−	0.141821i
$970$		0			0
$971$	−11.2382	−	17.4870i	−0.360652	−	0.561186i	0.612753	−	0.790274i	$-0.290062\pi$
$971$	−11.2382	−	17.4870i	−0.360652	−	0.561186i	−0.973406	+	0.229088i	$0.926426\pi$
$972$		0			0
$973$	67.9193	−	50.8437i	2.17739	−	1.62997i
$974$		0			0
$975$	−1.68020	−	9.92951i	−0.0538095	−	0.317999i
$976$		0			0
$977$	18.8379	+	7.02618i	0.602679	+	0.224788i	0.632236	−	0.774776i	$-0.282137\pi$
$977$	18.8379	+	7.02618i	0.602679	+	0.224788i	−0.0295576	+	0.999563i	$0.509410\pi$
$978$		0			0
$979$	15.2153	−	2.18763i	0.486283	−	0.0699169i
$980$		0			0
$981$	1.77653	+	6.05030i	0.0567202	+	0.193171i
$982$		0			0
$983$	40.3466	−	2.88564i	1.28686	−	0.0920377i	0.588916	−	0.808194i	$-0.299555\pi$
$983$	40.3466	−	2.88564i	1.28686	−	0.0920377i	0.697940	+	0.716157i	$0.254100\pi$
$984$		0			0
$985$	19.0907	−	5.86388i	0.608279	−	0.186839i
$986$		0			0
$987$	2.16661	+	5.80890i	0.0689639	+	0.184899i
$988$		0			0
$989$	−19.1171	+	17.2732i	−0.607888	+	0.549256i
$990$		0			0
$991$	17.6327	−	38.6102i	0.560121	−	1.22649i	−0.391772	−	0.920062i	$-0.628138\pi$
$991$	17.6327	−	38.6102i	0.560121	−	1.22649i	0.951893	−	0.306431i	$-0.0991349\pi$
$992$		0			0
$993$	−17.5140	−	1.25262i	−0.555789	−	0.0397508i
$994$		0			0
$995$	−12.1563	−	4.36297i	−0.385381	−	0.138316i
$996$		0			0
$997$	8.04494	+	4.39287i	0.254786	+	0.139124i	0.601567	−	0.798823i	$-0.294543\pi$
$997$	8.04494	+	4.39287i	0.254786	+	0.139124i	−0.346781	+	0.937946i	$0.612725\pi$
$998$		0			0
$999$	6.12879	+	42.6267i	0.193906	+	1.34865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.13	✓	720
5.3	odd	4	inner	920.2.bv.a.753.13	yes	720
23.19	odd	22	inner	920.2.bv.a.617.13	yes	720
115.88	even	44	inner	920.2.bv.a.433.13	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.13	✓	720	1.1	even	1	trivial
920.2.bv.a.433.13	yes	720	115.88	even	44	inner
920.2.bv.a.617.13	yes	720	23.19	odd	22	inner
920.2.bv.a.753.13	yes	720	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07094 + 0.584775i) q^{3} +(1.80656 + 1.31770i) q^{5} +(-2.43642 - 3.25467i) q^{7} +(-0.816980 + 1.27125i) q^{9} +(1.21800 - 0.556244i) q^{11} +(1.32143 + 0.989210i) q^{13} +(-2.70527 - 0.354745i) q^{15} +(0.0608051 + 0.850167i) q^{17} +(2.89714 + 3.34347i) q^{19} +(4.51250 + 2.06079i) q^{21} +(1.11655 + 4.66405i) q^{23} +(1.52732 + 4.76102i) q^{25} +(0.392683 - 5.49042i) q^{27} +(5.55196 + 4.81080i) q^{29} +(-4.57200 + 1.34246i) q^{31} +(-0.979127 + 1.30796i) q^{33} +(-0.112840 - 9.09023i) q^{35} +(-7.64488 + 1.66304i) q^{37} +(-1.99363 - 0.286641i) q^{39} +(-0.0100982 + 0.00648973i) q^{41} +(2.57469 + 4.71519i) q^{43} +(-3.15105 + 1.22004i) q^{45} +(0.883714 + 0.883714i) q^{47} +(-2.68463 + 9.14301i) q^{49} +(-0.562275 - 0.874917i) q^{51} +(-0.834514 + 0.624709i) q^{53} +(2.93336 + 0.600081i) q^{55} +(-5.05783 - 1.88647i) q^{57} +(2.99919 - 0.431219i) q^{59} +(2.14000 + 7.28816i) q^{61} +(6.12799 - 0.438283i) q^{63} +(1.08376 + 3.52832i) q^{65} +(-0.148110 - 0.397099i) q^{67} +(-3.92317 - 4.34196i) q^{69} +(-4.03329 + 8.83168i) q^{71} +(-2.77739 - 0.198643i) q^{73} +(-4.41978 - 4.20561i) q^{75} +(-4.77795 - 2.60896i) q^{77} +(1.17612 + 8.18007i) q^{79} +(0.906883 + 1.98580i) q^{81} +(-1.65960 - 7.62905i) q^{83} +(-1.01042 + 1.61600i) q^{85} +(-8.75904 - 1.90541i) q^{87} +(11.0149 + 3.23428i) q^{89} -6.71094i q^{91} +(4.11128 - 4.11128i) q^{93} +(0.828143 + 9.85775i) q^{95} +(0.272889 - 1.25445i) q^{97} +(-0.287963 + 2.00282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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