LMFDB - Embedded newform 920.2.bv.a.217.12

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			217.12
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16193 + 0.252761i) q^{3} +(-2.21107 + 0.333401i) q^{5} +(-3.31103 + 1.80796i) q^{7} +(-1.44271 + 0.658865i) q^{9} +O(q^{10})$	\(q+(-1.16193 + 0.252761i) q^{3} +(-2.21107 + 0.333401i) q^{5} +(-3.31103 + 1.80796i) q^{7} +(-1.44271 + 0.658865i) q^{9} +(2.85252 + 2.47173i) q^{11} +(0.632824 - 1.15893i) q^{13} +(2.48483 - 0.946261i) q^{15} +(-3.12846 - 2.34194i) q^{17} +(-0.174948 + 1.21679i) q^{19} +(3.39019 - 2.93762i) q^{21} +(3.10282 - 3.65685i) q^{23} +(4.77769 - 1.47435i) q^{25} +(4.36556 - 3.26802i) q^{27} +(-1.68187 + 0.241816i) q^{29} +(2.63296 - 1.69210i) q^{31} +(-3.93918 - 2.15095i) q^{33} +(6.71816 - 5.10144i) q^{35} +(-6.09775 - 2.27434i) q^{37} +(-0.442361 + 1.50654i) q^{39} +(0.616498 - 1.34994i) q^{41} +(-2.02477 - 9.30770i) q^{43} +(2.97028 - 1.93780i) q^{45} +(5.17350 + 5.17350i) q^{47} +(3.90974 - 6.08367i) q^{49} +(4.22699 + 1.93040i) q^{51} +(-6.61374 - 12.1122i) q^{53} +(-7.13122 - 4.51413i) q^{55} +(-0.104281 - 1.45804i) q^{57} +(2.63780 + 8.98353i) q^{59} +(-0.888176 - 1.38203i) q^{61} +(3.58567 - 4.78990i) q^{63} +(-1.01283 + 2.77346i) q^{65} +(3.61640 + 0.258650i) q^{67} +(-2.68093 + 5.03325i) q^{69} +(-1.30292 - 1.50365i) q^{71} +(7.36347 + 9.83644i) q^{73} +(-5.17866 + 2.92070i) q^{75} +(-13.9136 - 3.02672i) q^{77} +(-3.37219 + 0.990164i) q^{79} +(-1.13052 + 1.30469i) q^{81} +(-1.51175 + 4.05317i) q^{83} +(7.69806 + 4.13516i) q^{85} +(1.89309 - 0.706085i) q^{87} +(12.2904 + 7.89859i) q^{89} +4.98138i q^{91} +(-2.63160 + 2.63160i) q^{93} +(-0.0188565 - 2.74874i) q^{95} +(-3.82433 - 10.2534i) q^{97} +(-5.74391 - 1.68656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.16193	+	0.252761i	−0.670838	+	0.145932i	−0.535069	−	0.844809i	$-0.679714\pi$
$3$	−1.16193	+	0.252761i	−0.670838	+	0.145932i	−0.135769	+	0.990740i	$0.543351\pi$
$4$		0			0
$5$	−2.21107	+	0.333401i	−0.988822	+	0.149102i
$5$	−2.21107	+	0.333401i	−0.988822	+	0.149102i
$6$		0			0
$7$	−3.31103	+	1.80796i	−1.25145	+	0.683345i	−0.961791	−	0.273784i	$-0.911725\pi$
$7$	−3.31103	+	1.80796i	−1.25145	+	0.683345i	−0.289662	+	0.957129i	$0.593543\pi$
$8$		0			0
$9$	−1.44271	+	0.658865i	−0.480905	+	0.219622i
$10$		0			0
$11$	2.85252	+	2.47173i	0.860068	+	0.745254i	0.968543	−	0.248846i	$-0.0800512\pi$
$11$	2.85252	+	2.47173i	0.860068	+	0.745254i	−0.108475	+	0.994099i	$0.534597\pi$
$12$		0			0
$13$	0.632824	−	1.15893i	0.175514	−	0.321429i	−0.775082	−	0.631860i	$-0.782292\pi$
$13$	0.632824	−	1.15893i	0.175514	−	0.321429i	0.950596	+	0.310431i	$0.100473\pi$
$14$		0			0
$15$	2.48483	−	0.946261i	0.641581	−	0.244324i
$16$		0			0
$17$	−3.12846	−	2.34194i	−0.758763	−	0.568003i	0.148327	−	0.988938i	$-0.452611\pi$
$17$	−3.12846	−	2.34194i	−0.758763	−	0.568003i	−0.907091	+	0.420935i	$0.861702\pi$
$18$		0			0
$19$	−0.174948	+	1.21679i	−0.0401358	+	0.279151i	−0.999999	−	0.00131754i	$-0.999581\pi$
$19$	−0.174948	+	1.21679i	−0.0401358	+	0.279151i	0.959863	+	0.280468i	$0.0904897\pi$
$20$		0			0
$21$	3.39019	−	2.93762i	0.739801	−	0.641041i
$22$		0			0
$23$	3.10282	−	3.65685i	0.646982	−	0.762505i
$23$	3.10282	−	3.65685i	0.646982	−	0.762505i
$24$		0			0
$25$	4.77769	−	1.47435i	0.955537	−	0.294870i
$26$		0			0
$27$	4.36556	−	3.26802i	0.840153	−	0.628930i
$28$		0			0
$29$	−1.68187	+	0.241816i	−0.312316	+	0.0449042i	−0.296690	−	0.954974i	$-0.595883\pi$
$29$	−1.68187	+	0.241816i	−0.312316	+	0.0449042i	−0.0156251	+	0.999878i	$0.504974\pi$
$30$		0			0
$31$	2.63296	−	1.69210i	0.472893	−	0.303910i	−0.282400	−	0.959297i	$-0.591131\pi$
$31$	2.63296	−	1.69210i	0.472893	−	0.303910i	0.755294	+	0.655387i	$0.227494\pi$
$32$		0			0
$33$	−3.93918	−	2.15095i	−0.685723	−	0.374433i
$34$		0			0
$35$	6.71816	−	5.10144i	1.13558	−	0.862300i
$36$		0			0
$37$	−6.09775	−	2.27434i	−1.00246	−	0.373899i	−0.205977	−	0.978557i	$-0.566037\pi$
$37$	−6.09775	−	2.27434i	−1.00246	−	0.373899i	−0.796486	+	0.604657i	$0.793310\pi$
$38$		0			0
$39$	−0.442361	+	1.50654i	−0.0708345	+	0.241240i
$40$		0			0
$41$	0.616498	−	1.34994i	0.0962808	−	0.210826i	−0.855363	−	0.518029i	$-0.826666\pi$
$41$	0.616498	−	1.34994i	0.0962808	−	0.210826i	0.951644	+	0.307203i	$0.0993932\pi$
$42$		0			0
$43$	−2.02477	−	9.30770i	−0.308774	−	1.41941i	−0.826052	−	0.563594i	$-0.809418\pi$
$43$	−2.02477	−	9.30770i	−0.308774	−	1.41941i	0.517278	−	0.855817i	$-0.326945\pi$
$44$		0			0
$45$	2.97028	−	1.93780i	0.442783	−	0.288870i
$46$		0			0
$47$	5.17350	+	5.17350i	0.754632	+	0.754632i	0.975340	−	0.220708i	$-0.0708367\pi$
$47$	5.17350	+	5.17350i	0.754632	+	0.754632i	−0.220708	+	0.975340i	$0.570837\pi$
$48$		0			0
$49$	3.90974	−	6.08367i	0.558534	−	0.869096i
$50$		0			0
$51$	4.22699	+	1.93040i	0.591897	+	0.270310i
$52$		0			0
$53$	−6.61374	−	12.1122i	−0.908467	−	1.66373i	−0.734087	−	0.679055i	$-0.762390\pi$
$53$	−6.61374	−	12.1122i	−0.908467	−	1.66373i	−0.174380	−	0.984678i	$-0.555792\pi$
$54$		0			0
$55$	−7.13122	−	4.51413i	−0.961573	−	0.608685i
$56$		0			0
$57$	−0.104281	−	1.45804i	−0.0138123	−	0.193122i
$58$		0			0
$59$	2.63780	+	8.98353i	0.343413	+	1.16956i	0.932404	+	0.361417i	$0.117707\pi$
$59$	2.63780	+	8.98353i	0.343413	+	1.16956i	−0.588992	+	0.808139i	$0.700475\pi$
$60$		0			0
$61$	−0.888176	−	1.38203i	−0.113719	−	0.176951i	0.779728	−	0.626118i	$-0.215357\pi$
$61$	−0.888176	−	1.38203i	−0.113719	−	0.176951i	−0.893448	+	0.449167i	$0.851721\pi$
$62$		0			0
$63$	3.58567	−	4.78990i	0.451752	−	0.603470i
$64$		0			0
$65$	−1.01283	+	2.77346i	−0.125626	+	0.344006i
$66$		0			0
$67$	3.61640	+	0.258650i	0.441814	+	0.0315991i	0.290475	−	0.956883i	$-0.406187\pi$
$67$	3.61640	+	0.258650i	0.441814	+	0.0315991i	0.151339	+	0.988482i	$0.451641\pi$
$68$		0			0
$69$	−2.68093	+	5.03325i	−0.322747	+	0.605933i
$70$		0			0
$71$	−1.30292	−	1.50365i	−0.154628	−	0.178450i	0.673150	−	0.739506i	$-0.264941\pi$
$71$	−1.30292	−	1.50365i	−0.154628	−	0.178450i	−0.827778	+	0.561056i	$0.810395\pi$
$72$		0			0
$73$	7.36347	+	9.83644i	0.861829	+	1.15127i	0.987252	+	0.159165i	$0.0508803\pi$
$73$	7.36347	+	9.83644i	0.861829	+	1.15127i	−0.125423	+	0.992103i	$0.540029\pi$
$74$		0			0
$75$	−5.17866	+	2.92070i	−0.597980	+	0.337253i
$76$		0			0
$77$	−13.9136	−	3.02672i	−1.58560	−	0.344926i
$78$		0			0
$79$	−3.37219	+	0.990164i	−0.379401	+	0.111402i	−0.465872	−	0.884852i	$-0.654259\pi$
$79$	−3.37219	+	0.990164i	−0.379401	+	0.111402i	0.0864708	+	0.996254i	$0.472441\pi$
$80$		0			0
$81$	−1.13052	+	1.30469i	−0.125613	+	0.144965i
$82$		0			0
$83$	−1.51175	+	4.05317i	−0.165936	+	0.444893i	−0.993129	−	0.117026i	$-0.962664\pi$
$83$	−1.51175	+	4.05317i	−0.165936	+	0.444893i	0.827192	+	0.561919i	$0.189937\pi$
$84$		0			0
$85$	7.69806	+	4.13516i	0.834972	+	0.448521i
$86$		0			0
$87$	1.89309	−	0.706085i	0.202960	−	0.0757002i
$88$		0			0
$89$	12.2904	+	7.89859i	1.30278	+	0.837249i	0.993512	−	0.113724i	$-0.0362781\pi$
$89$	12.2904	+	7.89859i	1.30278	+	0.837249i	0.309273	+	0.950973i	$0.399914\pi$
$90$		0			0
$91$			4.98138i			0.522190i
$92$		0			0
$93$	−2.63160	+	2.63160i	−0.272884	+	0.272884i
$94$		0			0
$95$	−0.0188565	−	2.74874i	−0.00193464	−	0.282015i
$96$		0			0
$97$	−3.82433	−	10.2534i	−0.388302	−	1.04108i	−0.973198	−	0.229969i	$-0.926138\pi$
$97$	−3.82433	−	10.2534i	−0.388302	−	1.04108i	0.584896	−	0.811108i	$-0.301135\pi$
$98$		0			0
$99$	−5.74391	−	1.68656i	−0.577285	−	0.169506i
$100$		0			0
$101$	−5.41166	−	11.8499i	−0.538480	−	1.17911i	−0.961957	−	0.273200i	$-0.911918\pi$
$101$	−5.41166	−	11.8499i	−0.538480	−	1.17911i	0.423477	−	0.905907i	$-0.360809\pi$
$102$		0			0
$103$	19.5448	−	1.39787i	1.92581	−	0.137737i	0.944291	−	0.329111i	$-0.106749\pi$
$103$	19.5448	−	1.39787i	1.92581	−	0.137737i	0.981517	+	0.191375i	$0.0612946\pi$
$104$		0			0
$105$	−6.51656	+	7.62558i	−0.635951	+	0.744181i
$106$		0			0
$107$	0.630925	−	2.90031i	0.0609938	−	0.280384i	−0.936541	−	0.350558i	$-0.885992\pi$
$107$	0.630925	−	2.90031i	0.0609938	−	0.280384i	0.997535	+	0.0701742i	$0.0223555\pi$
$108$		0			0
$109$	−2.33465	−	16.2379i	−0.223619	−	1.55531i	−0.724184	−	0.689607i	$-0.757783\pi$
$109$	−2.33465	−	16.2379i	−0.223619	−	1.55531i	0.500564	−	0.865699i	$-0.333126\pi$
$110$		0			0
$111$	7.65999	+	1.10134i	0.727054	+	0.104535i
$112$		0			0
$113$	0.473676	−	6.62285i	0.0445597	−	0.623026i	−0.925280	−	0.379284i	$-0.876170\pi$
$113$	0.473676	−	6.62285i	0.0445597	−	0.623026i	0.969840	−	0.243742i	$-0.0783750\pi$
$114$		0			0
$115$	−5.64136	+	9.12003i	−0.526060	+	0.850448i
$116$		0			0
$117$	−0.149405	+	2.08895i	−0.0138125	+	0.193124i
$118$		0			0
$119$	14.5926	+	2.09810i	1.33770	+	0.192332i
$120$		0			0
$121$	0.462000	+	3.21328i	0.0420000	+	0.292117i
$122$		0			0
$123$	−0.375111	+	1.72436i	−0.0338226	+	0.155480i
$124$		0			0
$125$	−10.0723	+	4.85278i	−0.900891	+	0.434046i
$126$		0			0
$127$	−11.5969	+	0.829428i	−1.02906	+	0.0735998i	−0.575645	−	0.817700i	$-0.695249\pi$
$127$	−11.5969	+	0.829428i	−1.02906	+	0.0735998i	−0.453415	+	0.891299i	$0.649794\pi$
$128$		0			0
$129$	4.70525	+	10.3031i	0.414275	+	0.907135i
$130$		0			0
$131$	11.6286	+	3.41446i	1.01599	+	0.298323i	0.747004	−	0.664820i	$-0.231492\pi$
$131$	11.6286	+	3.41446i	1.01599	+	0.298323i	0.268991	+	0.963143i	$0.413310\pi$
$132$		0			0
$133$	−1.62065	−	4.34513i	−0.140528	−	0.376771i
$134$		0			0
$135$	−8.56301	+	8.68131i	−0.736987	+	0.747168i
$136$		0			0
$137$	−2.84104	+	2.84104i	−0.242726	+	0.242726i	−0.817977	−	0.575251i	$-0.804904\pi$
$137$	−2.84104	+	2.84104i	−0.242726	+	0.242726i	0.575251	+	0.817977i	$0.304904\pi$
$138$		0			0
$139$		−	20.7804i		−	1.76257i	−0.472587	−	0.881284i	$-0.656680\pi$
$139$		−	20.7804i		−	1.76257i	0.472587	−	0.881284i	$-0.343320\pi$
$140$		0			0
$141$	−7.31888	−	4.70356i	−0.616361	−	0.396111i
$142$		0			0
$143$	4.66970	−	1.74171i	0.390500	−	0.145649i
$144$		0			0
$145$	3.63812	−	1.09541i	0.302129	−	0.0909690i
$146$		0			0
$147$	−3.00511	+	8.05701i	−0.247857	+	0.664531i
$148$		0			0
$149$	−7.59137	+	8.76091i	−0.621909	+	0.717722i	−0.976068	−	0.217464i	$-0.930222\pi$
$149$	−7.59137	+	8.76091i	−0.621909	+	0.717722i	0.354159	+	0.935185i	$0.384767\pi$
$150$		0			0
$151$	−5.59174	+	1.64188i	−0.455049	+	0.133614i	−0.501221	−	0.865319i	$-0.667116\pi$
$151$	−5.59174	+	1.64188i	−0.455049	+	0.133614i	0.0461725	+	0.998933i	$0.485298\pi$
$152$		0			0
$153$	6.05649	+	1.31751i	0.489639	+	0.106514i
$154$		0			0
$155$	−5.25751	+	4.61919i	−0.422294	+	0.371022i
$156$		0			0
$157$	−8.07433	−	10.7860i	−0.644401	−	0.860820i	0.352791	−	0.935702i	$-0.385233\pi$
$157$	−8.07433	−	10.7860i	−0.644401	−	0.860820i	−0.997192	+	0.0748826i	$0.976142\pi$
$158$		0			0
$159$	10.7462	+	12.4017i	0.852226	+	0.983521i
$160$		0			0
$161$	−3.66210	+	17.7177i	−0.288614	+	1.39635i
$162$		0			0
$163$	−17.6243	−	1.26052i	−1.38044	−	0.0987312i	−0.638721	−	0.769439i	$-0.720536\pi$
$163$	−17.6243	−	1.26052i	−1.38044	−	0.0987312i	−0.741722	+	0.670707i	$0.765991\pi$
$164$		0			0
$165$	9.42694	+	3.44259i	0.733886	+	0.268005i
$166$		0			0
$167$	−10.2072	+	13.6353i	−0.789860	+	1.05513i	0.207185	+	0.978302i	$0.433570\pi$
$167$	−10.2072	+	13.6353i	−0.789860	+	1.05513i	−0.997044	+	0.0768271i	$0.975521\pi$
$168$		0			0
$169$	6.08568	+	9.46950i	0.468129	+	0.728423i
$170$		0			0
$171$	−0.549301	−	1.87075i	−0.0420061	−	0.143060i
$172$		0			0
$173$	1.37256	+	19.1909i	0.104354	+	1.45906i	0.732397	+	0.680878i	$0.238402\pi$
$173$	1.37256	+	19.1909i	0.104354	+	1.45906i	−0.628043	+	0.778179i	$0.716144\pi$
$174$		0			0
$175$	−13.1535	+	13.5195i	−0.994313	+	1.02198i
$176$		0			0
$177$	−5.33562	−	9.77146i	−0.401050	−	0.734468i
$178$		0			0
$179$	4.65367	+	2.12526i	0.347831	+	0.158849i	0.581667	−	0.813427i	$-0.302401\pi$
$179$	4.65367	+	2.12526i	0.347831	+	0.158849i	−0.233836	+	0.972276i	$0.575128\pi$
$180$		0			0
$181$	8.82877	−	13.7378i	0.656237	−	1.02113i	−0.340487	−	0.940249i	$-0.610592\pi$
$181$	8.82877	−	13.7378i	0.656237	−	1.02113i	0.996724	−	0.0808759i	$-0.0257718\pi$
$182$		0			0
$183$	1.38132	+	1.38132i	0.102110	+	0.102110i
$184$		0			0
$185$	14.2408	+	2.99574i	1.04701	+	0.220251i
$186$		0			0
$187$	−3.13538	−	14.4131i	−0.229282	−	1.05399i
$188$		0			0
$189$	−8.54607	+	18.7133i	−0.621635	+	1.36119i
$190$		0			0
$191$	1.58046	−	5.38254i	0.114358	−	0.389467i	−0.882345	−	0.470603i	$-0.844037\pi$
$191$	1.58046	−	5.38254i	0.114358	−	0.389467i	0.996703	+	0.0811356i	$0.0258547\pi$
$192$		0			0
$193$	0.233471	+	0.0870802i	0.0168056	+	0.00626817i	0.357853	−	0.933778i	$-0.383509\pi$
$193$	0.233471	+	0.0870802i	0.0168056	+	0.00626817i	−0.341047	+	0.940046i	$0.610782\pi$
$194$		0			0
$195$	0.475809	−	3.47856i	0.0340734	−	0.249105i
$196$		0			0
$197$	0.673476	+	0.367745i	0.0479831	+	0.0262008i	0.503061	−	0.864251i	$-0.332207\pi$
$197$	0.673476	+	0.367745i	0.0479831	+	0.0262008i	−0.455078	+	0.890451i	$0.650389\pi$
$198$		0			0
$199$	4.15998	−	2.67346i	0.294893	−	0.189517i	−0.384825	−	0.922989i	$-0.625738\pi$
$199$	4.15998	−	2.67346i	0.294893	−	0.189517i	0.679719	+	0.733473i	$0.262102\pi$
$200$		0			0
$201$	−4.26737	+	0.613555i	−0.300997	+	0.0432768i
$202$		0			0
$203$	5.13154	−	3.84142i	0.360163	−	0.269615i
$204$		0			0
$205$	−0.913049	+	3.19036i	−0.0637701	+	0.222825i
$206$		0			0
$207$	−2.06711	+	7.32012i	−0.143674	+	0.508784i
$208$		0			0
$209$	−3.50661	+	3.03850i	−0.242558	+	0.210177i
$210$		0			0
$211$	1.54764	−	10.7641i	0.106544	−	0.741031i	−0.864587	−	0.502484i	$-0.832420\pi$
$211$	1.54764	−	10.7641i	0.106544	−	0.741031i	0.971131	−	0.238547i	$-0.0766712\pi$
$212$		0			0
$213$	1.89395	+	1.41780i	0.129772	+	0.0971458i
$214$		0			0
$215$	7.58011	+	19.9049i	0.516959	+	1.35751i
$216$		0			0
$217$	−5.65856	+	10.3629i	−0.384128	+	0.703478i
$218$		0			0
$219$	−11.0421	−	9.56801i	−0.746154	−	0.646546i
$220$		0			0
$221$	−4.69390	+	2.14363i	−0.315746	+	0.144196i
$222$		0			0
$223$	−2.24231	+	1.22440i	−0.150156	+	0.0819916i	−0.552571	−	0.833466i	$-0.686353\pi$
$223$	−2.24231	+	1.22440i	−0.150156	+	0.0819916i	0.402414	+	0.915458i	$0.368171\pi$
$224$		0			0
$225$	−5.92144	+	5.27492i	−0.394763	+	0.351661i
$226$		0			0
$227$	−18.4466	+	4.01281i	−1.22434	+	0.266340i	−0.777852	−	0.628448i	$-0.783690\pi$
$227$	−18.4466	+	4.01281i	−1.22434	+	0.266340i	−0.446492	+	0.894788i	$0.647327\pi$
$228$		0			0
$229$	1.04003			0.0687269			0.0343634	−	0.999409i	$-0.489060\pi$
$229$	1.04003			0.0687269			0.0343634	+	0.999409i	$0.489060\pi$
$230$		0			0
$231$	16.9316			1.11402
$232$		0			0
$233$	11.0381	−	2.40119i	0.723130	−	0.157307i	0.164087	−	0.986446i	$-0.447532\pi$
$233$	11.0381	−	2.40119i	0.723130	−	0.157307i	0.559043	+	0.829138i	$0.311169\pi$
$234$		0			0
$235$	−13.1638	−	9.71413i	−0.858714	−	0.633680i
$236$		0			0
$237$	3.66796	−	2.00286i	0.238259	−	0.130100i
$238$		0			0
$239$	0.0301011	−	0.0137467i	0.00194708	−	0.000889202i	−0.414441	−	0.910076i	$-0.636023\pi$
$239$	0.0301011	−	0.0137467i	0.00194708	−	0.000889202i	0.416388	+	0.909187i	$0.363296\pi$
$240$		0			0
$241$	−8.96172	−	7.76538i	−0.577275	−	0.500212i	0.316581	−	0.948566i	$-0.397465\pi$
$241$	−8.96172	−	7.76538i	−0.577275	−	0.500212i	−0.893856	+	0.448354i	$0.852011\pi$
$242$		0			0
$243$	−6.85661	+	12.5569i	−0.439852	+	0.805528i
$244$		0			0
$245$	−6.61642	+	14.7550i	−0.422707	+	0.942660i
$246$		0			0
$247$	1.29946	+	0.972765i	0.0826828	+	0.0618956i
$248$		0			0
$249$	0.732060	−	5.09159i	0.0463924	−	0.322666i
$250$		0			0
$251$	−16.2645	+	14.0932i	−1.02660	+	0.889557i	−0.993942	−	0.109909i	$-0.964944\pi$
$251$	−16.2645	+	14.0932i	−1.02660	+	0.889557i	−0.0326622	+	0.999466i	$0.510399\pi$
$252$		0			0
$253$	17.8896	−	2.76192i	1.12471	−	0.173640i
$254$		0			0
$255$	−9.98978	−	2.85897i	−0.625584	−	0.179036i
$256$		0			0
$257$	7.34979	−	5.50198i	0.458467	−	0.343204i	−0.344950	−	0.938621i	$-0.612104\pi$
$257$	7.34979	−	5.50198i	0.458467	−	0.343204i	0.803417	+	0.595417i	$0.203013\pi$
$258$		0			0
$259$	24.3018	−	3.49407i	1.51004	−	0.217111i
$260$		0			0
$261$	2.26713	−	1.45700i	0.140332	−	0.0901859i
$262$		0			0
$263$	−17.2912	−	9.44173i	−1.06622	−	0.582202i	−0.152402	−	0.988319i	$-0.548701\pi$
$263$	−17.2912	−	9.44173i	−1.06622	−	0.582202i	−0.913821	+	0.406117i	$0.866883\pi$
$264$		0			0
$265$	18.6617	+	24.5758i	1.14638	+	1.50968i
$266$		0			0
$267$	−16.2770	−	6.07102i	−0.996139	−	0.371541i
$268$		0			0
$269$	0.297750	−	1.01404i	0.0181541	−	0.0618273i	−0.949918	−	0.312500i	$-0.898834\pi$
$269$	0.297750	−	1.01404i	0.0181541	−	0.0618273i	0.968072	+	0.250673i	$0.0806518\pi$
$270$		0			0
$271$	5.43112	−	11.8925i	0.329917	−	0.722418i	−0.669882	−	0.742468i	$-0.733655\pi$
$271$	5.43112	−	11.8925i	0.329917	−	0.722418i	0.999799	+	0.0200501i	$0.00638257\pi$
$272$		0			0
$273$	−1.25910	−	5.78799i	−0.0762042	−	0.350305i
$274$		0			0
$275$	17.2727	+	7.60352i	1.04158	+	0.458509i
$276$		0			0
$277$	−20.8264	−	20.8264i	−1.25133	−	1.25133i	−0.955122	−	0.296213i	$-0.904276\pi$
$277$	−20.8264	−	20.8264i	−1.25133	−	1.25133i	−0.296213	−	0.955122i	$-0.595724\pi$
$278$		0			0
$279$	−2.68374	+	4.17598i	−0.160671	+	0.250009i
$280$		0			0
$281$	−2.68048	−	1.22413i	−0.159904	−	0.0730257i	0.333855	−	0.942624i	$-0.391650\pi$
$281$	−2.68048	−	1.22413i	−0.159904	−	0.0730257i	−0.493759	+	0.869599i	$0.664378\pi$
$282$		0			0
$283$	−2.88077	−	5.27573i	−0.171244	−	0.313610i	0.777936	−	0.628343i	$-0.216267\pi$
$283$	−2.88077	−	5.27573i	−0.171244	−	0.313610i	−0.949180	+	0.314734i	$0.898085\pi$
$284$		0			0
$285$	0.716685	+	3.18906i	0.0424527	+	0.188904i
$286$		0			0
$287$	0.399398	+	5.58431i	0.0235757	+	0.329631i
$288$		0			0
$289$	−0.486853	−	1.65807i	−0.0286384	−	0.0975334i
$290$		0			0
$291$	7.03525	+	10.9471i	0.412414	+	0.641728i
$292$		0			0
$293$	14.2791	−	19.0746i	0.834192	−	1.11435i	−0.157728	−	0.987483i	$-0.550417\pi$
$293$	14.2791	−	19.0746i	0.834192	−	1.11435i	0.991920	−	0.126867i	$-0.0404923\pi$
$294$		0			0
$295$	−8.82750	−	18.9838i	−0.513957	−	1.10528i
$296$		0			0
$297$	20.5305	+	1.46837i	1.19130	+	0.0852035i
$298$		0			0
$299$	−2.27449	−	5.91009i	−0.131537	−	0.341789i
$300$		0			0
$301$	23.5320	+	27.1574i	1.35636	+	1.56533i
$302$		0			0
$303$	9.28314	+	12.4008i	0.533302	+	0.712408i
$304$		0			0
$305$	2.42459	+	2.75965i	0.138832	+	0.158017i
$306$		0			0
$307$	18.7021	+	4.06839i	1.06738	+	0.232195i	0.711752	−	0.702431i	$-0.247902\pi$
$307$	18.7021	+	4.06839i	1.06738	+	0.232195i	0.355632	+	0.934626i	$0.384266\pi$
$308$		0			0
$309$	−22.3563	+	6.56440i	−1.27180	+	0.373436i
$310$		0			0
$311$	8.70169	−	10.0423i	0.493428	−	0.569446i	−0.453351	−	0.891332i	$-0.649771\pi$
$311$	8.70169	−	10.0423i	0.493428	−	0.569446i	0.946778	+	0.321886i	$0.104317\pi$
$312$		0			0
$313$	−4.69516	+	12.5882i	−0.265386	+	0.711528i	0.734086	+	0.679056i	$0.237611\pi$
$313$	−4.69516	+	12.5882i	−0.265386	+	0.711528i	−0.999473	+	0.0324721i	$0.989662\pi$
$314$		0			0
$315$	−6.33123	+	11.7863i	−0.356724	+	0.664082i
$316$		0			0
$317$	1.40370	−	0.523552i	0.0788395	−	0.0294056i	−0.309735	−	0.950823i	$-0.600240\pi$
$317$	1.40370	−	0.523552i	0.0788395	−	0.0294056i	0.388574	+	0.921417i	$0.372968\pi$
$318$		0			0
$319$	−5.39528	−	3.46734i	−0.302078	−	0.194134i
$320$		0			0
$321$			3.52942i			0.196993i
$322$		0			0
$323$	3.39696	−	3.39696i	0.189012	−	0.189012i
$324$		0			0
$325$	1.31477	−	6.47001i	0.0729301	−	0.358891i
$326$		0			0
$327$	6.81700	+	18.2771i	0.376981	+	1.01073i
$328$		0			0
$329$	−26.4831	−	7.77615i	−1.46006	−	0.428713i
$330$		0			0
$331$	−9.47026	−	20.7370i	−0.520532	−	1.13981i	−0.969238	−	0.246127i	$-0.920842\pi$
$331$	−9.47026	−	20.7370i	−0.520532	−	1.13981i	0.448705	−	0.893680i	$-0.351885\pi$
$332$		0			0
$333$	10.2958	−	0.736369i	0.564206	−	0.0403528i
$334$		0			0
$335$	−8.08236	+	0.633818i	−0.441587	+	0.0346292i
$336$		0			0
$337$	7.26431	−	33.3935i	0.395712	−	1.81906i	−0.159315	−	0.987228i	$-0.550928\pi$
$337$	7.26431	−	33.3935i	0.395712	−	1.81906i	0.555027	−	0.831832i	$-0.312708\pi$
$338$		0			0
$339$	1.12363	+	7.81499i	0.0610270	+	0.424452i
$340$		0			0
$341$	11.6930	+	1.68120i	0.633210	+	0.0910419i
$342$		0			0
$343$	−0.0623504	+	0.871772i	−0.00336660	+	0.0470713i
$344$		0			0
$345$	4.24965	−	12.0227i	0.228793	−	0.647281i
$346$		0			0
$347$	2.21898	−	31.0254i	0.119121	−	1.66553i	−0.489450	−	0.872031i	$-0.662802\pi$
$347$	2.21898	−	31.0254i	0.119121	−	1.66553i	0.608571	−	0.793500i	$-0.291743\pi$
$348$		0			0
$349$	−17.9994	−	2.58792i	−0.963485	−	0.138528i	−0.357421	−	0.933944i	$-0.616344\pi$
$349$	−17.9994	−	2.58792i	−0.963485	−	0.138528i	−0.606065	+	0.795415i	$0.707253\pi$
$350$		0			0
$351$	−1.02477	−	7.12746i	−0.0546984	−	0.380436i
$352$		0			0
$353$	−3.06291	+	14.0800i	−0.163022	+	0.749401i	0.820939	+	0.571016i	$0.193451\pi$
$353$	−3.06291	+	14.0800i	−0.163022	+	0.749401i	−0.983961	+	0.178384i	$0.942913\pi$
$354$		0			0
$355$	3.38216	+	2.89028i	0.179506	+	0.153400i
$356$		0			0
$357$	−17.4858	+	1.25061i	−0.925447	+	0.0661892i
$358$		0			0
$359$	−0.569950	−	1.24802i	−0.0300808	−	0.0658678i	0.893995	−	0.448077i	$-0.147891\pi$
$359$	−0.569950	−	1.24802i	−0.0300808	−	0.0658678i	−0.924076	+	0.382209i	$0.875164\pi$
$360$		0			0
$361$	16.7804	+	4.92717i	0.883179	+	0.259325i
$362$		0			0
$363$	−1.34900	−	3.61682i	−0.0708043	−	0.189834i
$364$		0			0
$365$	−19.5606	−	19.2941i	−1.02385	−	1.00990i
$366$		0			0
$367$	−0.453329	+	0.453329i	−0.0236636	+	0.0236636i	−0.718840	−	0.695176i	$-0.755326\pi$
$367$	−0.453329	+	0.453329i	−0.0236636	+	0.0236636i	0.695176	+	0.718840i	$0.255326\pi$
$368$		0			0
$369$			2.35377i			0.122532i
$370$		0			0
$371$	43.7967	+	28.1464i	2.27381	+	1.46129i
$372$		0			0
$373$	−20.2697	+	7.56022i	−1.04953	+	0.391454i	−0.814274	−	0.580480i	$-0.802865\pi$
$373$	−20.2697	+	7.56022i	−1.04953	+	0.391454i	−0.235253	+	0.971934i	$0.575592\pi$
$374$		0			0
$375$	10.4766	−	8.18445i	0.541011	−	0.422643i
$376$		0			0
$377$	−0.784079	+	2.10220i	−0.0403821	+	0.108269i
$378$		0			0
$379$	−4.18679	+	4.83182i	−0.215061	+	0.248194i	−0.853022	−	0.521875i	$-0.825233\pi$
$379$	−4.18679	+	4.83182i	−0.215061	+	0.248194i	0.637961	+	0.770069i	$0.279778\pi$
$380$		0			0
$381$	13.2651	−	3.89499i	0.679592	−	0.199546i
$382$		0			0
$383$	−38.1019	−	8.28855i	−1.94691	−	0.423525i	−0.991913	−	0.126923i	$-0.959490\pi$
$383$	−38.1019	−	8.28855i	−1.94691	−	0.423525i	−0.955001	−	0.296602i	$-0.904147\pi$
$384$		0			0
$385$	31.7731	+	2.05348i	1.61931	+	0.104655i
$386$		0			0
$387$	9.05368	+	12.0943i	0.460224	+	0.614788i
$388$		0			0
$389$	21.7293	+	25.0770i	1.10172	+	1.27145i	0.959528	+	0.281613i	$0.0908694\pi$
$389$	21.7293	+	25.0770i	1.10172	+	1.27145i	0.142191	+	0.989839i	$0.454585\pi$
$390$		0			0
$391$	−18.2711	+	4.17369i	−0.924012	+	0.211073i
$392$		0			0
$393$	−14.3746	−	1.02809i	−0.725103	−	0.0518604i
$394$		0			0
$395$	7.12604	−	3.31362i	0.358550	−	0.166726i
$396$		0			0
$397$	11.6315	−	15.5379i	0.583768	−	0.779823i	−0.407284	−	0.913302i	$-0.633524\pi$
$397$	11.6315	−	15.5379i	0.583768	−	0.779823i	0.991052	+	0.133479i	$0.0426149\pi$
$398$		0			0
$399$	2.98136	+	4.63908i	0.149254	+	0.232244i
$400$		0			0
$401$	−5.56926	−	18.9672i	−0.278115	−	0.947174i	−0.973529	−	0.228564i	$-0.926597\pi$
$401$	−5.56926	−	18.9672i	−0.278115	−	0.947174i	0.695413	−	0.718610i	$-0.255221\pi$
$402$		0			0
$403$	−0.294827	−	4.12221i	−0.0146864	−	0.205342i
$404$		0			0
$405$	2.06467	−	3.26168i	0.102594	−	0.162074i
$406$		0			0
$407$	−11.7724	−	21.5596i	−0.583537	−	1.06867i
$408$		0			0
$409$	−9.81565	−	4.48266i	−0.485353	−	0.221653i	0.157682	−	0.987490i	$-0.449598\pi$
$409$	−9.81565	−	4.48266i	−0.485353	−	0.221653i	−0.643035	+	0.765837i	$0.722325\pi$
$410$		0			0
$411$	2.58297	−	4.01918i	0.127408	−	0.198251i
$412$		0			0
$413$	−24.9757	−	24.9757i	−1.22898	−	1.22898i
$414$		0			0
$415$	1.99126	−	9.46586i	0.0977473	−	0.464661i
$416$		0			0
$417$	5.25248	+	24.1452i	0.257215	+	1.18240i
$418$		0			0
$419$	4.64754	−	10.1767i	0.227047	−	0.497164i	−0.761484	−	0.648184i	$-0.775529\pi$
$419$	4.64754	−	10.1767i	0.227047	−	0.497164i	0.988531	+	0.151020i	$0.0482559\pi$
$420$		0			0
$421$	7.70294	−	26.2338i	0.375419	−	1.27856i	−0.527797	−	0.849371i	$-0.676982\pi$
$421$	7.70294	−	26.2338i	0.375419	−	1.27856i	0.903215	−	0.429188i	$-0.141200\pi$
$422$		0			0
$423$	−10.8725	−	4.05524i	−0.528640	−	0.197172i
$424$		0			0
$425$	−18.3996	−	6.57660i	−0.892514	−	0.319012i
$426$		0			0
$427$	5.43944	+	2.97016i	0.263233	+	0.143736i
$428$		0			0
$429$	−4.98561	+	3.20406i	−0.240707	+	0.154693i
$430$		0			0
$431$	−6.20819	+	0.892603i	−0.299038	+	0.0429952i	−0.290201	−	0.956966i	$-0.593722\pi$
$431$	−6.20819	+	0.892603i	−0.299038	+	0.0429952i	−0.00883714	+	0.999961i	$0.502813\pi$
$432$		0			0
$433$	20.3637	−	15.2440i	0.978615	−	0.732582i	0.0150030	−	0.999887i	$-0.495224\pi$
$433$	20.3637	−	15.2440i	0.978615	−	0.732582i	0.963612	+	0.267306i	$0.0861333\pi$
$434$		0			0
$435$	−3.95034	+	2.19236i	−0.189404	+	0.105116i
$436$		0			0
$437$	3.90678	+	4.41523i	0.186887	+	0.211209i
$438$		0			0
$439$	−8.59930	+	7.45134i	−0.410422	+	0.355633i	−0.835468	−	0.549539i	$-0.814803\pi$
$439$	−8.59930	+	7.45134i	−0.410422	+	0.355633i	0.425046	+	0.905172i	$0.360258\pi$
$440$		0			0
$441$	−1.63231	+	11.3530i	−0.0777292	+	0.540619i
$442$		0			0
$443$	26.7475	+	20.0229i	1.27081	+	0.951319i	0.999936	−	0.0112953i	$-0.00359548\pi$
$443$	26.7475	+	20.0229i	1.27081	+	0.951319i	0.270877	+	0.962614i	$0.412686\pi$
$444$		0			0
$445$	−29.8085	−	13.3667i	−1.41306	−	0.633643i
$446$		0			0
$447$	6.60619	−	12.0983i	0.312462	−	0.572231i
$448$		0			0
$449$	8.21019	+	7.11417i	0.387463	+	0.335739i	0.826711	−	0.562628i	$-0.190209\pi$
$449$	8.21019	+	7.11417i	0.387463	+	0.335739i	−0.439248	+	0.898366i	$0.644755\pi$
$450$		0			0
$451$	5.09526	−	2.32693i	0.239927	−	0.109571i
$452$		0			0
$453$	6.08217	−	3.32112i	0.285766	−	0.156040i
$454$		0			0
$455$	−1.66080	−	11.0142i	−0.0778594	−	0.516353i
$456$		0			0
$457$	18.2585	−	3.97189i	0.854096	−	0.185797i	0.235857	−	0.971788i	$-0.424210\pi$
$457$	18.2585	−	3.97189i	0.854096	−	0.185797i	0.618239	+	0.785990i	$0.287847\pi$
$458$		0			0
$459$	−21.3110			−0.994711
$460$		0			0
$461$	−1.13990			−0.0530906			−0.0265453	−	0.999648i	$-0.508451\pi$
$461$	−1.13990			−0.0530906			−0.0265453	+	0.999648i	$0.508451\pi$
$462$		0			0
$463$	30.4689	−	6.62810i	1.41601	−	0.308034i	0.561503	−	0.827475i	$-0.310223\pi$
$463$	30.4689	−	6.62810i	1.41601	−	0.308034i	0.854506	+	0.519441i	$0.173860\pi$
$464$		0			0
$465$	4.94129	−	6.69604i	0.229147	−	0.310522i
$466$		0			0
$467$	−18.2867	+	9.98531i	−0.846209	+	0.462065i	−0.842990	−	0.537930i	$-0.819207\pi$
$467$	−18.2867	+	9.98531i	−0.846209	+	0.462065i	−0.00321954	+	0.999995i	$0.501025\pi$
$468$		0			0
$469$	−12.4417	+	5.68192i	−0.574503	+	0.262367i
$470$		0			0
$471$	12.1081	+	10.4917i	0.557910	+	0.483432i
$472$		0			0
$473$	17.2304	−	31.5551i	0.792254	−	1.45091i
$474$		0			0
$475$	0.958126	+	6.07137i	0.0439618	+	0.278574i
$476$		0			0
$477$	17.5220	+	13.1168i	0.802278	+	0.600578i
$478$		0			0
$479$	4.87406	−	33.8998i	0.222702	−	1.54892i	−0.505055	−	0.863087i	$-0.668528\pi$
$479$	4.87406	−	33.8998i	0.222702	−	1.54892i	0.727756	−	0.685836i	$-0.240563\pi$
$480$		0			0
$481$	−6.49460	+	5.62760i	−0.296128	+	0.256597i
$482$		0			0
$483$	−0.223264	−	21.5123i	−0.0101588	−	0.978844i
$484$		0			0
$485$	11.8744	+	21.3960i	0.539187	+	0.971543i
$486$		0			0
$487$	−10.1366	+	7.58814i	−0.459332	+	0.343851i	−0.803752	−	0.594964i	$-0.797166\pi$
$487$	−10.1366	+	7.58814i	−0.459332	+	0.343851i	0.344421	+	0.938815i	$0.388075\pi$
$488$		0			0
$489$	20.7967	−	2.99012i	0.940461	−	0.135218i
$490$		0			0
$491$	−15.7370	+	10.1135i	−0.710200	+	0.456418i	−0.845216	−	0.534426i	$-0.820528\pi$
$491$	−15.7370	+	10.1135i	−0.710200	+	0.456418i	0.135015	+	0.990844i	$0.456892\pi$
$492$		0			0
$493$	5.82798	+	3.18232i	0.262479	+	0.143325i
$494$		0			0
$495$	13.2625	+	1.81409i	0.596105	+	0.0815373i
$496$		0			0
$497$	7.03253	+	2.62300i	0.315452	+	0.117658i
$498$		0			0
$499$	3.76998	−	12.8394i	0.168768	−	0.574770i	−0.831060	−	0.556183i	$-0.812265\pi$
$499$	3.76998	−	12.8394i	0.168768	−	0.574770i	0.999827	−	0.0185865i	$-0.00591660\pi$
$500$		0			0
$501$	8.41358	−	18.4232i	0.375891	−	0.823086i
$502$		0			0
$503$	0.293552	+	1.34944i	0.0130888	+	0.0601684i	0.983228	−	0.182380i	$-0.0583802\pi$
$503$	0.293552	+	1.34944i	0.0130888	+	0.0601684i	−0.970139	+	0.242549i	$0.922017\pi$
$504$		0			0
$505$	15.9163	+	24.3967i	0.708268	+	1.08564i
$506$		0			0
$507$	−9.46463	−	9.46463i	−0.420339	−	0.420339i
$508$		0			0
$509$	10.5456	−	16.4093i	0.467425	−	0.727328i	−0.524876	−	0.851179i	$-0.675888\pi$
$509$	10.5456	−	16.4093i	0.467425	−	0.727328i	0.992301	+	0.123851i	$0.0395246\pi$
$510$		0			0
$511$	−42.1646	−	19.2559i	−1.86525	−	0.851832i
$512$		0			0
$513$	3.21274	+	5.88370i	0.141846	+	0.259772i
$514$		0			0
$515$	−42.7490	+	9.60707i	−1.88374	+	0.423338i
$516$		0			0
$517$	1.97006	+	27.5450i	0.0866430	+	1.21143i
$518$		0			0
$519$	−6.44553	−	21.9515i	−0.282927	−	0.963562i
$520$		0			0
$521$	7.68099	+	11.9519i	0.336510	+	0.523620i	0.967732	−	0.251982i	$-0.0810825\pi$
$521$	7.68099	+	11.9519i	0.336510	+	0.523620i	−0.631222	+	0.775603i	$0.717446\pi$
$522$		0			0
$523$	−18.2513	+	24.3809i	−0.798074	+	1.06610i	0.198226	+	0.980156i	$0.436482\pi$
$523$	−18.2513	+	24.3809i	−0.798074	+	1.06610i	−0.996300	+	0.0859455i	$0.972609\pi$
$524$		0			0
$525$	11.8662	−	19.0333i	0.517884	−	0.830683i
$526$		0			0
$527$	−12.1999	−	0.872553i	−0.531436	−	0.0380090i
$528$		0			0
$529$	−3.74503	−	22.6931i	−0.162828	−	0.986655i
$530$		0			0
$531$	−9.72453	−	11.2227i	−0.422009	−	0.487024i
$532$		0			0
$533$	−1.17435	−	1.56875i	−0.0508669	−	0.0679502i
$534$		0			0
$535$	−0.428052	+	6.62316i	−0.0185063	+	0.286344i
$536$		0			0
$537$	−5.94440	−	1.29312i	−0.256520	−	0.0558024i
$538$		0			0
$539$	26.1898	−	7.69002i	1.12807	−	0.331233i
$540$		0			0
$541$	3.00657	−	3.46977i	0.129263	−	0.149177i	−0.687428	−	0.726252i	$-0.741261\pi$
$541$	3.00657	−	3.46977i	0.129263	−	0.149177i	0.816691	+	0.577075i	$0.195806\pi$
$542$		0			0
$543$	−6.78598	+	18.1939i	−0.291214	+	0.780775i
$544$		0			0
$545$	10.5758	+	35.1248i	0.453018	+	1.50458i
$546$		0			0
$547$	1.89070	−	0.705193i	0.0808403	−	0.0301519i	−0.308719	−	0.951153i	$-0.599900\pi$
$547$	1.89070	−	0.705193i	0.0808403	−	0.0301519i	0.389559	+	0.921002i	$0.372627\pi$
$548$		0			0
$549$	2.19195	+	1.40868i	0.0935503	+	0.0601212i
$550$		0			0
$551$		−	2.08879i		−	0.0889853i
$552$		0			0
$553$	9.37526	−	9.37526i	0.398677	−	0.398677i
$554$		0			0
$555$	−17.3040	+	0.118706i	−0.734513	+	0.00503880i
$556$		0			0
$557$	15.2041	+	40.7637i	0.644218	+	1.72722i	0.685505	+	0.728068i	$0.259581\pi$
$557$	15.2041	+	40.7637i	0.644218	+	1.72722i	−0.0412870	+	0.999147i	$0.513146\pi$
$558$		0			0
$559$	−12.0683	−	3.54357i	−0.510435	−	0.149877i
$560$		0			0
$561$	7.28616	+	15.9545i	0.307622	+	0.673598i
$562$		0			0
$563$	4.77553	−	0.341553i	0.201265	−	0.0143947i	0.0296571	−	0.999560i	$-0.490558\pi$
$563$	4.77553	−	0.341553i	0.201265	−	0.0143947i	0.171608	+	0.985165i	$0.445104\pi$
$564$		0			0
$565$	1.16074	+	14.8015i	0.0488325	+	0.622705i
$566$		0			0
$567$	1.38436	−	6.36380i	0.0581376	−	0.267254i
$568$		0			0
$569$	5.15335	+	35.8423i	0.216040	+	1.50259i	0.752460	+	0.658637i	$0.228867\pi$
$569$	5.15335	+	35.8423i	0.216040	+	1.50259i	−0.536421	+	0.843951i	$0.680224\pi$
$570$		0			0
$571$	25.3984	+	3.65174i	1.06289	+	0.152821i	0.651508	−	0.758642i	$-0.274137\pi$
$571$	25.3984	+	3.65174i	1.06289	+	0.152821i	0.411383	+	0.911463i	$0.365046\pi$
$572$		0			0
$573$	−0.475874	+	6.65359i	−0.0198799	+	0.277958i
$574$		0			0
$575$	9.43283	−	22.0459i	0.393376	−	0.919378i
$576$		0			0
$577$	0.222058	−	3.10478i	0.00924441	−	0.129254i	−0.990734	−	0.135816i	$-0.956634\pi$
$577$	0.222058	−	3.10478i	0.00924441	−	0.129254i	0.999978	+	0.00656242i	$0.00208890\pi$
$578$		0			0
$579$	−0.293287	−	0.0421682i	−0.0121886	−	0.00175245i
$580$		0			0
$581$	−2.32250	−	16.1534i	−0.0963536	−	0.670154i
$582$		0			0
$583$	11.0721	−	50.8976i	0.458559	−	2.10796i
$584$		0			0
$585$	−0.366114	−	4.66863i	−0.0151369	−	0.193024i
$586$		0			0
$587$	31.1035	−	2.22457i	1.28378	−	0.0918177i	0.587285	−	0.809380i	$-0.300197\pi$
$587$	31.1035	−	2.22457i	1.28378	−	0.0918177i	0.696494	+	0.717562i	$0.254742\pi$
$588$		0			0
$589$	1.59830	+	3.49978i	0.0658567	+	0.144206i
$590$		0			0
$591$	−0.875480	−	0.257064i	−0.0360124	−	0.0105742i
$592$		0			0
$593$	6.94893	+	18.6308i	0.285358	+	0.765075i	0.997980	+	0.0635268i	$0.0202348\pi$
$593$	6.94893	+	18.6308i	0.285358	+	0.765075i	−0.712622	+	0.701548i	$0.752492\pi$
$594$		0			0
$595$	−32.9648	+	0.226140i	−1.35142	+	0.00927084i
$596$		0			0
$597$	−4.15784	+	4.15784i	−0.170169	+	0.170169i
$598$		0			0
$599$		−	42.2696i		−	1.72709i	−0.504272	−	0.863545i	$-0.668239\pi$
$599$		−	42.2696i		−	1.72709i	0.504272	−	0.863545i	$-0.331761\pi$
$600$		0			0
$601$	−35.2127	−	22.6298i	−1.43636	−	0.923090i	−0.999725	−	0.0234488i	$-0.992535\pi$
$601$	−35.2127	−	22.6298i	−1.43636	−	0.923090i	−0.436631	−	0.899641i	$-0.643828\pi$
$602$		0			0
$603$	−5.38785	+	2.00956i	−0.219410	+	0.0818358i
$604$		0			0
$605$	−2.09283	−	6.95077i	−0.0850856	−	0.282589i
$606$		0			0
$607$	−3.92826	+	10.5321i	−0.159443	+	0.427483i	−0.991966	−	0.126508i	$-0.959623\pi$
$607$	−3.92826	+	10.5321i	−0.159443	+	0.427483i	0.832523	+	0.553991i	$0.186896\pi$
$608$		0			0
$609$	−4.99150	+	5.76050i	−0.202266	+	0.233427i
$610$		0			0
$611$	9.26963	−	2.72181i	0.375009	−	0.110113i
$612$		0			0
$613$	31.0736	+	6.75964i	1.25505	+	0.273019i	0.790464	−	0.612509i	$-0.209840\pi$
$613$	31.0736	+	6.75964i	1.25505	+	0.273019i	0.464586	+	0.885528i	$0.346203\pi$
$614$		0			0
$615$	0.254495	−	3.93775i	0.0102622	−	0.158785i
$616$		0			0
$617$	−13.3847	−	17.8799i	−0.538848	−	0.719817i	0.445651	−	0.895207i	$-0.352972\pi$
$617$	−13.3847	−	17.8799i	−0.538848	−	0.719817i	−0.984499	+	0.175390i	$0.943881\pi$
$618$		0			0
$619$	−5.08627	−	5.86987i	−0.204435	−	0.235930i	0.644269	−	0.764799i	$-0.277162\pi$
$619$	−5.08627	−	5.86987i	−0.204435	−	0.235930i	−0.848703	+	0.528869i	$0.822616\pi$
$620$		0			0
$621$	1.59491	−	26.1042i	0.0640015	−	1.04753i
$622$		0			0
$623$	−54.9744	−	3.93185i	−2.20250	−	0.157526i
$624$		0			0
$625$	20.6526	−	14.0880i	0.826104	−	0.563518i
$626$		0			0
$627$	3.30641	−	4.41684i	0.132045	−	0.176392i
$628$		0			0
$629$	13.7502	+	21.3957i	0.548256	+	0.853103i
$630$		0			0
$631$	9.07907	+	30.9205i	0.361432	+	1.23092i	0.916809	+	0.399326i	$0.130756\pi$
$631$	9.07907	+	30.9205i	0.361432	+	1.23092i	−0.555377	+	0.831599i	$0.687426\pi$
$632$		0			0
$633$	0.922502	+	12.8983i	0.0366661	+	0.512660i
$634$		0			0
$635$	25.3651	−	5.70035i	1.00658	−	0.226212i
$636$		0			0
$637$	−4.57638	−	8.38101i	−0.181323	−	0.332068i
$638$		0			0
$639$	2.87043	+	1.31088i	0.113553	+	0.0518578i
$640$		0			0
$641$	16.5398	−	25.7364i	0.653283	−	1.01653i	−0.343713	−	0.939075i	$-0.611685\pi$
$641$	16.5398	−	25.7364i	0.653283	−	1.01653i	0.996996	−	0.0774538i	$-0.0246790\pi$
$642$		0			0
$643$	0.289569	+	0.289569i	0.0114195	+	0.0114195i	0.712793	−	0.701374i	$-0.247430\pi$
$643$	0.289569	+	0.289569i	0.0114195	+	0.0114195i	−0.701374	+	0.712793i	$0.747430\pi$
$644$		0			0
$645$	−13.8387	−	21.2121i	−0.544899	−	0.835226i
$646$		0			0
$647$	−0.531593	−	2.44369i	−0.0208991	−	0.0960715i	0.965516	−	0.260344i	$-0.0838360\pi$
$647$	−0.531593	−	2.44369i	−0.0208991	−	0.0960715i	−0.986415	+	0.164273i	$0.947472\pi$
$648$		0			0
$649$	−14.6804	+	32.1457i	−0.576258	+	1.26183i
$650$		0			0
$651$	3.95549	−	13.4712i	0.155028	−	0.527976i
$652$		0			0
$653$	−33.4339	−	12.4702i	−1.30837	−	0.487997i	−0.404006	−	0.914757i	$-0.632382\pi$
$653$	−33.4339	−	12.4702i	−1.30837	−	0.487997i	−0.904365	+	0.426759i	$0.859655\pi$
$654$		0			0
$655$	−26.8500	−	3.67264i	−1.04912	−	0.143502i
$656$		0			0
$657$	−17.1043	−	9.33964i	−0.667301	−	0.364374i
$658$		0			0
$659$	15.0131	−	9.64834i	0.584828	−	0.375846i	−0.214516	−	0.976721i	$-0.568817\pi$
$659$	15.0131	−	9.64834i	0.584828	−	0.375846i	0.799343	+	0.600875i	$0.205181\pi$
$660$		0			0
$661$	−38.5455	+	5.54201i	−1.49925	+	0.215559i	−0.842559	−	0.538604i	$-0.818952\pi$
$661$	−38.5455	+	5.54201i	−1.49925	+	0.215559i	−0.656688	+	0.754163i	$0.728043\pi$
$662$		0			0
$663$	4.91214	−	3.67718i	0.190772	−	0.142810i
$664$		0			0
$665$	5.03205	+	9.06707i	0.195134	+	0.351606i
$666$		0			0
$667$	−4.33425	+	6.90065i	−0.167823	+	0.267194i
$668$		0			0
$669$	2.29592	−	1.98943i	0.0887654	−	0.0769156i
$670$		0			0
$671$	0.882453	−	6.13760i	0.0340667	−	0.236939i
$672$		0			0
$673$	12.1732	+	9.11271i	0.469241	+	0.351269i	0.807583	−	0.589754i	$-0.200775\pi$
$673$	12.1732	+	9.11271i	0.469241	+	0.351269i	−0.338342	+	0.941023i	$0.609866\pi$
$674$		0			0
$675$	16.0391	−	22.0499i	0.617345	−	0.848702i
$676$		0			0
$677$	3.07176	−	5.62551i	0.118057	−	0.216206i	−0.811967	−	0.583703i	$-0.801603\pi$
$677$	3.07176	−	5.62551i	0.118057	−	0.216206i	0.930025	+	0.367497i	$0.119785\pi$
$678$		0			0
$679$	31.2003	+	27.0352i	1.19736	+	1.03752i
$680$		0			0
$681$	20.4193	−	9.32517i	0.782469	−	0.357341i
$682$		0			0
$683$	−28.6447	+	15.6412i	−1.09606	+	0.598493i	−0.922370	−	0.386308i	$-0.873750\pi$
$683$	−28.6447	+	15.6412i	−1.09606	+	0.598493i	−0.173688	+	0.984801i	$0.555568\pi$
$684$		0			0
$685$	5.33453	−	7.22894i	0.203822	−	0.276204i
$686$		0			0
$687$	−1.20843	+	0.262878i	−0.0461046	+	0.0100294i
$688$		0			0
$689$	−18.2225			−0.694221
$690$		0			0
$691$	−14.2831			−0.543356			−0.271678	−	0.962388i	$-0.587579\pi$
$691$	−14.2831			−0.543356			−0.271678	+	0.962388i	$0.587579\pi$
$692$		0			0
$693$	22.0675	−	4.80050i	0.838276	−	0.182356i
$694$		0			0
$695$	6.92820	+	45.9469i	0.262802	+	1.74287i
$696$		0			0
$697$	−5.09017	+	2.77944i	−0.192804	+	0.105279i
$698$		0			0
$699$	−12.2185	+	5.58001i	−0.462147	+	0.211055i
$700$		0			0
$701$	−24.7101	−	21.4114i	−0.933288	−	0.808699i	0.0484715	−	0.998825i	$-0.484565\pi$
$701$	−24.7101	−	21.4114i	−0.933288	−	0.808699i	−0.981760	+	0.190126i	$0.939110\pi$
$702$		0			0
$703$	3.83418	−	7.02178i	0.144609	−	0.264831i
$704$		0			0
$705$	17.7507	+	7.95979i	0.668532	+	0.299783i
$706$		0			0
$707$	39.3423	+	29.4513i	1.47962	+	1.10763i
$708$		0			0
$709$	−2.04637	+	14.2328i	−0.0768529	+	0.534524i	0.914631	+	0.404291i	$0.132482\pi$
$709$	−2.04637	+	14.2328i	−0.0768529	+	0.534524i	−0.991483	+	0.130233i	$0.958427\pi$
$710$		0			0
$711$	4.21272	−	3.65034i	0.157989	−	0.136899i
$712$		0			0
$713$	1.98185	−	14.8786i	0.0742207	−	0.557208i
$714$		0			0
$715$	−9.74437	+	5.40793i	−0.364419	+	0.202245i
$716$		0			0
$717$	−0.0315006	+	0.0235811i	−0.00117641	+	0.000880652i
$718$		0			0
$719$	47.8812	−	6.88427i	1.78567	−	0.256740i	0.831395	−	0.555682i	$-0.187543\pi$
$719$	47.8812	−	6.88427i	1.78567	−	0.256740i	0.954271	+	0.298942i	$0.0966337\pi$
$720$		0			0
$721$	−62.1863	+	39.9647i	−2.31594	+	1.48836i
$722$		0			0
$723$	12.3756	+	6.75761i	0.460255	+	0.251318i
$724$		0			0
$725$	−7.67893	+	3.63499i	−0.285188	+	0.135000i
$726$		0			0
$727$	20.6710	+	7.70990i	0.766646	+	0.285944i	0.702203	−	0.711977i	$-0.252200\pi$
$727$	20.6710	+	7.70990i	0.766646	+	0.285944i	0.0644436	+	0.997921i	$0.479473\pi$
$728$		0			0
$729$	6.25206	−	21.2926i	0.231558	−	0.788614i
$730$		0			0
$731$	−15.4636	+	33.8607i	−0.571943	+	1.25238i
$732$		0			0
$733$	−8.09974	−	37.2339i	−0.299171	−	1.37527i	−0.843831	−	0.536609i	$-0.819705\pi$
$733$	−8.09974	−	37.2339i	−0.299171	−	1.37527i	0.544660	−	0.838657i	$-0.316659\pi$
$734$		0			0
$735$	3.95830	−	18.8165i	0.146004	−	0.694058i
$736$		0			0
$737$	9.67656	+	9.67656i	0.356441	+	0.356441i
$738$		0			0
$739$	1.69841	−	2.64277i	0.0624769	−	0.0972160i	−0.808610	−	0.588346i	$-0.799779\pi$
$739$	1.69841	−	2.64277i	0.0624769	−	0.0972160i	0.871087	+	0.491130i	$0.163416\pi$
$740$		0			0
$741$	−1.75576	−	0.801827i	−0.0644993	−	0.0294558i
$742$		0			0
$743$	5.83648	+	10.6887i	0.214120	+	0.392131i	0.962559	−	0.271073i	$-0.0873783\pi$
$743$	5.83648	+	10.6887i	0.214120	+	0.392131i	−0.748439	+	0.663203i	$0.769196\pi$
$744$		0			0
$745$	13.8642	−	21.9020i	0.507944	−	0.802426i
$746$		0			0
$747$	−0.489464	−	6.84360i	−0.0179085	−	0.250394i
$748$		0			0
$749$	3.15464	+	10.7437i	0.115268	+	0.392567i
$750$		0			0
$751$	5.50683	+	8.56880i	0.200947	+	0.312680i	0.927072	−	0.374883i	$-0.122317\pi$
$751$	5.50683	+	8.56880i	0.200947	+	0.312680i	−0.726125	+	0.687563i	$0.758681\pi$
$752$		0			0
$753$	15.3359	−	20.4863i	0.558870	−	0.746563i
$754$		0			0
$755$	11.8163	−	5.49461i	0.430040	−	0.199969i
$756$		0			0
$757$	−46.3136	−	3.31242i	−1.68330	−	0.120392i	−0.803364	−	0.595488i	$-0.796959\pi$
$757$	−46.3136	−	3.31242i	−1.68330	−	0.120392i	−0.879934	+	0.475096i	$0.842413\pi$
$758$		0			0
$759$	−20.0883	+	7.73094i	−0.729157	+	0.280615i
$760$		0			0
$761$	10.8085	+	12.4737i	0.391810	+	0.452172i	0.917044	−	0.398785i	$-0.130568\pi$
$761$	10.8085	+	12.4737i	0.391810	+	0.452172i	−0.525235	+	0.850957i	$0.676023\pi$
$762$		0			0
$763$	37.0876	+	49.5432i	1.34266	+	1.79358i
$764$		0			0
$765$	−13.8306	−	0.893868i	−0.500047	−	0.0323178i
$766$		0			0
$767$	12.0806	+	2.62796i	0.436203	+	0.0948902i
$768$		0			0
$769$	4.63318	−	1.36043i	0.167077	−	0.0490582i	−0.197124	−	0.980379i	$-0.563160\pi$
$769$	4.63318	−	1.36043i	0.167077	−	0.0490582i	0.364201	+	0.931320i	$0.381342\pi$
$770$		0			0
$771$	−7.14922	+	8.25064i	−0.257473	+	0.297139i
$772$		0			0
$773$	−12.4199	+	33.2992i	−0.446715	+	1.19769i	0.497240	+	0.867613i	$0.334347\pi$
$773$	−12.4199	+	33.2992i	−0.446715	+	1.19769i	−0.943955	+	0.330075i	$0.892926\pi$
$774$		0			0
$775$	10.0847	−	11.9662i	0.362253	−	0.429839i
$776$		0			0
$777$	−27.3537	+	10.2024i	−0.981308	+	0.366009i
$778$		0			0
$779$	1.53474	+	0.986318i	0.0549878	+	0.0353385i
$780$		0			0
$781$		−	7.50964i		−	0.268716i
$782$		0			0
$783$	−6.55205	+	6.55205i	−0.234151	+	0.234151i
$784$		0			0
$785$	21.4490	+	21.1567i	0.765548	+	0.755116i
$786$		0			0
$787$	9.14130	+	24.5088i	0.325852	+	0.873643i	0.991818	+	0.127661i	$0.0407469\pi$
$787$	9.14130	+	24.5088i	0.325852	+	0.873643i	−0.665966	+	0.745982i	$0.731980\pi$
$788$		0			0
$789$	22.4776	+	6.60002i	0.800224	+	0.234967i
$790$		0			0
$791$	10.4055	+	22.7849i	0.369977	+	0.810137i
$792$		0			0
$793$	−2.16373	+	0.154753i	−0.0768364	+	0.00549545i
$794$		0			0
$795$	−27.8953	−	23.8383i	−0.989344	−	0.845459i
$796$		0			0
$797$	5.59447	−	25.7174i	0.198166	−	0.910956i	−0.765414	−	0.643538i	$-0.777466\pi$
$797$	5.59447	−	25.7174i	0.198166	−	0.910956i	0.963581	−	0.267418i	$-0.0861704\pi$
$798$		0			0
$799$	−4.06908	−	28.3011i	−0.143954	−	1.00122i
$800$		0			0
$801$	−22.9357	−	3.29766i	−0.810393	−	0.116517i
$802$		0			0
$803$	−3.30852	+	46.2592i	−0.116755	+	1.63245i
$804$		0			0
$805$	2.19007	−	40.3961i	0.0771898	−	1.42378i
$806$		0			0
$807$	−0.0896522	+	1.25350i	−0.00315591	+	0.0441253i
$808$		0			0
$809$	−3.17032	−	0.455823i	−0.111463	−	0.0160259i	0.0863578	−	0.996264i	$-0.472477\pi$
$809$	−3.17032	−	0.455823i	−0.111463	−	0.0160259i	−0.197820	+	0.980238i	$0.563386\pi$
$810$		0			0
$811$	−3.07589	−	21.3933i	−0.108009	−	0.751219i	−0.969790	−	0.243940i	$-0.921560\pi$
$811$	−3.07589	−	21.3933i	−0.108009	−	0.751219i	0.861781	−	0.507280i	$-0.169349\pi$
$812$		0			0
$813$	−3.30459	+	15.1910i	−0.115897	+	0.532770i
$814$		0			0
$815$	39.3889	−	3.08888i	1.37973	−	0.108199i
$816$		0			0
$817$	11.6797	−	0.835352i	0.408622	−	0.0292252i
$818$		0			0
$819$	−3.28206	−	7.18670i	−0.114684	−	0.251124i
$820$		0			0
$821$	−10.4366	−	3.06447i	−0.364241	−	0.106951i	0.0944904	−	0.995526i	$-0.469878\pi$
$821$	−10.4366	−	3.06447i	−0.364241	−	0.106951i	−0.458731	+	0.888575i	$0.651696\pi$
$822$		0			0
$823$	16.7076	+	44.7949i	0.582392	+	1.56145i	0.809212	+	0.587517i	$0.199894\pi$
$823$	16.7076	+	44.7949i	0.582392	+	1.56145i	−0.226820	+	0.973937i	$0.572833\pi$
$824$		0			0
$825$	−21.9914	−	4.46886i	−0.765643	−	0.155586i
$826$		0			0
$827$	−8.48374	+	8.48374i	−0.295009	+	0.295009i	−0.839055	−	0.544046i	$-0.816892\pi$
$827$	−8.48374	+	8.48374i	−0.295009	+	0.295009i	0.544046	+	0.839055i	$0.316892\pi$
$828$		0			0
$829$		−	24.9559i		−	0.866753i	−0.901213	−	0.433376i	$-0.857322\pi$
$829$		−	24.9559i		−	0.866753i	0.901213	−	0.433376i	$-0.142678\pi$
$830$		0			0
$831$	29.4628	+	18.9346i	1.02205	+	0.656833i
$832$		0			0
$833$	−26.4790	+	9.87617i	−0.917445	+	0.342189i
$834$		0			0
$835$	18.0229	−	33.5517i	0.623709	−	1.16110i
$836$		0			0
$837$	5.96453	−	15.9915i	0.206164	−	0.552747i
$838$		0			0
$839$	−37.1610	+	42.8861i	−1.28294	+	1.48059i	−0.489425	+	0.872046i	$0.662793\pi$
$839$	−37.1610	+	42.8861i	−1.28294	+	1.48059i	−0.793517	+	0.608548i	$0.791752\pi$
$840$		0			0
$841$	−25.0551	+	7.35684i	−0.863968	+	0.253684i
$842$		0			0
$843$	3.42393	+	0.744831i	0.117926	+	0.0256533i
$844$		0			0
$845$	−16.6130	−	18.9088i	−0.571505	−	0.650482i
$846$		0			0
$847$	−7.33919	−	9.80401i	−0.252178	−	0.336870i
$848$		0			0
$849$	4.68074	+	5.40186i	0.160643	+	0.185391i
$850$		0			0
$851$	−27.2371	+	15.2416i	−0.933676	+	0.522477i
$852$		0			0
$853$	−19.8361	−	1.41871i	−0.679176	−	0.0485756i	−0.272511	−	0.962153i	$-0.587854\pi$
$853$	−19.8361	−	1.41871i	−0.679176	−	0.0485756i	−0.406666	+	0.913577i	$0.633309\pi$
$854$		0			0
$855$	1.83825	+	3.95322i	0.0628669	+	0.135197i
$856$		0			0
$857$	8.83441	−	11.8014i	0.301778	−	0.403128i	−0.623862	−	0.781535i	$-0.714437\pi$
$857$	8.83441	−	11.8014i	0.301778	−	0.403128i	0.925639	+	0.378407i	$0.123528\pi$
$858$		0			0
$859$	−5.35696	−	8.33559i	−0.182777	−	0.284407i	0.737759	−	0.675064i	$-0.235884\pi$
$859$	−5.35696	−	8.33559i	−0.182777	−	0.284407i	−0.920536	+	0.390657i	$0.872248\pi$
$860$		0			0
$861$	−1.87557	−	6.38760i	−0.0639192	−	0.217689i
$862$		0			0
$863$	2.67587	+	37.4135i	0.0910876	+	1.27357i	0.813278	+	0.581876i	$0.197681\pi$
$863$	2.67587	+	37.4135i	0.0910876	+	1.27357i	−0.722190	+	0.691695i	$0.756864\pi$
$864$		0			0
$865$	−9.43310	−	41.9748i	−0.320735	−	1.42719i
$866$		0			0
$867$	0.984782	+	1.80349i	0.0334450	+	0.0612499i
$868$		0			0
$869$	−12.0667	−	5.51066i	−0.409334	−	0.186936i
$870$		0			0
$871$	2.58830	−	4.02748i	0.0877013	−	0.136466i
$872$		0			0
$873$	12.2730	+	12.2730i	0.415379	+	0.415379i
$874$		0			0
$875$	24.5760	−	34.2780i	0.830820	−	1.15881i
$876$		0			0
$877$	−2.70737	−	12.4456i	−0.0914214	−	0.420258i	−0.999997	−	0.00253657i	$-0.999193\pi$
$877$	−2.70737	−	12.4456i	−0.0914214	−	0.420258i	0.908575	−	0.417721i	$-0.137171\pi$
$878$		0			0
$879$	−11.7699	+	25.7725i	−0.396988	+	0.869283i
$880$		0			0
$881$	−14.6664	+	49.9492i	−0.494124	+	1.68283i	0.214074	+	0.976817i	$0.431327\pi$
$881$	−14.6664	+	49.9492i	−0.494124	+	1.68283i	−0.708198	+	0.706014i	$0.750492\pi$
$882$		0			0
$883$	−1.44950	−	0.540634i	−0.0487794	−	0.0181938i	0.324956	−	0.945729i	$-0.394650\pi$
$883$	−1.44950	−	0.540634i	−0.0487794	−	0.0181938i	−0.373735	+	0.927535i	$0.621923\pi$
$884$		0			0
$885$	15.0553	+	19.8265i	0.506077	+	0.666461i
$886$		0			0
$887$	26.1584	+	14.2836i	0.878313	+	0.479595i	0.854098	−	0.520111i	$-0.174110\pi$
$887$	26.1584	+	14.2836i	0.878313	+	0.479595i	0.0242150	+	0.999707i	$0.492291\pi$
$888$		0			0
$889$	36.8982	−	23.7131i	1.23753	−	0.795310i
$890$		0			0
$891$	−6.44966	+	0.927321i	−0.216072	+	0.0310664i
$892$		0			0
$893$	−7.20015	+	5.38996i	−0.240944	+	0.180368i
$894$		0			0
$895$	−10.9982	−	3.14756i	−0.367628	−	0.105211i
$896$		0			0
$897$	4.13663	+	6.29218i	0.138118	+	0.210090i
$898$		0			0
$899$	−4.01912	+	3.48258i	−0.134045	+	0.116151i
$900$		0			0
$901$	−7.67509	+	53.3814i	−0.255694	+	1.77839i
$902$		0			0
$903$	−34.2068	−	25.6069i	−1.13833	−	0.852144i
$904$		0			0
$905$	−14.9408	+	33.3189i	−0.496650	+	1.10756i
$906$		0			0
$907$	−20.2960	+	37.1693i	−0.673917	+	1.23419i	0.287153	+	0.957885i	$0.407291\pi$
$907$	−20.2960	+	37.1693i	−0.673917	+	1.23419i	−0.961071	+	0.276303i	$0.910891\pi$
$908$		0			0
$909$	15.6150	+	13.5304i	0.517915	+	0.448776i
$910$		0			0
$911$	−13.9089	+	6.35200i	−0.460824	+	0.210451i	−0.632279	−	0.774741i	$-0.717880\pi$
$911$	−13.9089	+	6.35200i	−0.460824	+	0.210451i	0.171455	+	0.985192i	$0.445153\pi$
$912$		0			0
$913$	−14.3306	+	7.82511i	−0.474274	+	0.258973i
$914$		0			0
$915$	−3.51473	−	2.59366i	−0.116193	−	0.0857438i
$916$		0			0
$917$	−44.6759	+	9.71864i	−1.47533	+	0.320938i
$918$		0			0
$919$	20.9135			0.689872			0.344936	−	0.938626i	$-0.387901\pi$
$919$	20.9135			0.689872			0.344936	+	0.938626i	$0.387901\pi$
$920$		0			0
$921$	−22.7588			−0.749927
$922$		0			0
$923$	−2.56714	+	0.558446i	−0.0844983	+	0.0183815i
$924$		0			0
$925$	−32.4863	−	1.87589i	−1.06814	−	0.0616788i
$926$		0			0
$927$	−27.2766	+	14.8941i	−0.895880	+	0.489188i
$928$		0			0
$929$	−33.6702	+	15.3767i	−1.10468	+	0.504492i	−0.882405	−	0.470491i	$-0.844077\pi$
$929$	−33.6702	+	15.3767i	−1.10468	+	0.504492i	−0.222279	+	0.974983i	$0.571350\pi$
$930$		0			0
$931$	6.71855	+	5.82166i	0.220192	+	0.190797i
$932$		0			0
$933$	−7.57241	+	13.8678i	−0.247910	+	0.454013i
$934$		0			0
$935$	11.7379	+	30.8231i	0.383871	+	1.00802i
$936$		0			0
$937$	44.4785	+	33.2962i	1.45305	+	1.08774i	0.978198	+	0.207672i	$0.0665888\pi$
$937$	44.4785	+	33.2962i	1.45305	+	1.08774i	0.474850	+	0.880066i	$0.342502\pi$
$938$		0			0
$939$	2.27361	−	15.8133i	0.0741966	−	0.516048i
$940$		0			0
$941$	−31.2335	+	27.0640i	−1.01818	+	0.882261i	−0.993082	−	0.117424i	$-0.962536\pi$
$941$	−31.2335	+	27.0640i	−1.01818	+	0.882261i	−0.0251013	+	0.999685i	$0.507991\pi$
$942$		0			0
$943$	−3.02365	−	6.44306i	−0.0984635	−	0.209815i
$944$		0			0
$945$	12.6570	−	44.2257i	0.411731	−	1.43866i
$946$		0			0
$947$	34.1768	−	25.5845i	1.11060	−	0.831383i	0.123634	−	0.992328i	$-0.460545\pi$
$947$	34.1768	−	25.5845i	1.11060	−	0.831383i	0.986963	+	0.160945i	$0.0514541\pi$
$948$		0			0
$949$	16.0595	−	2.30901i	0.521314	−	0.0749537i
$950$		0			0
$951$	−1.49866	+	0.963129i	−0.0485973	+	0.0312316i
$952$		0			0
$953$	−42.1344	−	23.0071i	−1.36487	−	0.745275i	−0.381069	−	0.924547i	$-0.624444\pi$
$953$	−42.1344	−	23.0071i	−1.36487	−	0.745275i	−0.983800	+	0.179272i	$0.942626\pi$
$954$		0			0
$955$	−1.69996	+	12.4281i	−0.0550094	+	0.402165i
$956$		0			0
$957$	7.14532	+	2.66507i	0.230975	+	0.0861494i
$958$		0			0
$959$	4.27028	−	14.5433i	0.137895	−	0.469626i
$960$		0			0
$961$	−8.80860	+	19.2881i	−0.284148	+	0.622198i
$962$		0			0
$963$	1.00067	+	4.60002i	0.0322462	+	0.148233i
$964$		0			0
$965$	−0.545254	−	0.114701i	−0.0175524	−	0.00369236i
$966$		0			0
$967$	29.3650	+	29.3650i	0.944314	+	0.944314i	0.998529	−	0.0542150i	$-0.0172656\pi$
$967$	29.3650	+	29.3650i	0.944314	+	0.944314i	−0.0542150	+	0.998529i	$0.517266\pi$
$968$		0			0
$969$	−3.08839	+	4.80563i	−0.0992135	+	0.154379i
$970$		0			0
$971$	1.93645	+	0.884345i	0.0621435	+	0.0283800i	0.446244	−	0.894911i	$-0.352761\pi$
$971$	1.93645	+	0.884345i	0.0621435	+	0.0283800i	−0.384101	+	0.923291i	$0.625489\pi$
$972$		0			0
$973$	37.5701	+	68.8045i	1.20444	+	2.20577i
$974$		0			0
$975$	0.107708	+	7.84999i	0.00344941	+	0.251401i
$976$		0			0
$977$	−2.73095	−	38.1837i	−0.0873708	−	1.22160i	−0.832248	−	0.554403i	$-0.812947\pi$
$977$	−2.73095	−	38.1837i	−0.0873708	−	1.22160i	0.744878	−	0.667201i	$-0.232508\pi$
$978$		0			0
$979$	15.5356	+	52.9095i	0.496521	+	1.69100i
$980$		0			0
$981$	14.0668	+	21.8884i	0.449119	+	0.698843i
$982$		0			0
$983$	−14.4634	+	19.3208i	−0.461309	+	0.616237i	−0.969525	−	0.244993i	$-0.921214\pi$
$983$	−14.4634	+	19.3208i	−0.461309	+	0.616237i	0.508216	+	0.861230i	$0.330305\pi$
$984$		0			0
$985$	−1.61171	−	0.588575i	−0.0513534	−	0.0187535i
$986$		0			0
$987$	32.7369	+	2.34139i	1.04203	+	0.0745273i
$988$		0			0
$989$	−40.3193	−	21.4759i	−1.28208	−	0.682892i
$990$		0			0
$991$	−9.76340	−	11.2676i	−0.310145	−	0.357926i	0.579182	−	0.815198i	$-0.303372\pi$
$991$	−9.76340	−	11.2676i	−0.310145	−	0.357926i	−0.889327	+	0.457272i	$0.848827\pi$
$992$		0			0
$993$	16.2452	+	21.7011i	0.515527	+	0.688663i
$994$		0			0
$995$	−8.30669	+	7.29816i	−0.263340	+	0.231367i
$996$		0			0
$997$	−2.87204	−	0.624774i	−0.0909584	−	0.0197868i	0.166856	−	0.985981i	$-0.446639\pi$
$997$	−2.87204	−	0.624774i	−0.0909584	−	0.0197868i	−0.257814	+	0.966195i	$0.583002\pi$
$998$		0			0
$999$	−34.0527	+	9.99876i	−1.07738	+	0.316347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.12	yes	720
5.3	odd	4	inner	920.2.bv.a.33.12	✓	720
23.7	odd	22	inner	920.2.bv.a.697.12	yes	720
115.53	even	44	inner	920.2.bv.a.513.12	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.12	✓	720	5.3	odd	4	inner
920.2.bv.a.217.12	yes	720	1.1	even	1	trivial
920.2.bv.a.513.12	yes	720	115.53	even	44	inner
920.2.bv.a.697.12	yes	720	23.7	odd	22	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)

\(f(q)\)	\(=\)	\(q+(-1.16193 + 0.252761i) q^{3} +(-2.21107 + 0.333401i) q^{5} +(-3.31103 + 1.80796i) q^{7} +(-1.44271 + 0.658865i) q^{9} +O(q^{10})\)	\(q+(-1.16193 + 0.252761i) q^{3} +(-2.21107 + 0.333401i) q^{5} +(-3.31103 + 1.80796i) q^{7} +(-1.44271 + 0.658865i) q^{9} +(2.85252 + 2.47173i) q^{11} +(0.632824 - 1.15893i) q^{13} +(2.48483 - 0.946261i) q^{15} +(-3.12846 - 2.34194i) q^{17} +(-0.174948 + 1.21679i) q^{19} +(3.39019 - 2.93762i) q^{21} +(3.10282 - 3.65685i) q^{23} +(4.77769 - 1.47435i) q^{25} +(4.36556 - 3.26802i) q^{27} +(-1.68187 + 0.241816i) q^{29} +(2.63296 - 1.69210i) q^{31} +(-3.93918 - 2.15095i) q^{33} +(6.71816 - 5.10144i) q^{35} +(-6.09775 - 2.27434i) q^{37} +(-0.442361 + 1.50654i) q^{39} +(0.616498 - 1.34994i) q^{41} +(-2.02477 - 9.30770i) q^{43} +(2.97028 - 1.93780i) q^{45} +(5.17350 + 5.17350i) q^{47} +(3.90974 - 6.08367i) q^{49} +(4.22699 + 1.93040i) q^{51} +(-6.61374 - 12.1122i) q^{53} +(-7.13122 - 4.51413i) q^{55} +(-0.104281 - 1.45804i) q^{57} +(2.63780 + 8.98353i) q^{59} +(-0.888176 - 1.38203i) q^{61} +(3.58567 - 4.78990i) q^{63} +(-1.01283 + 2.77346i) q^{65} +(3.61640 + 0.258650i) q^{67} +(-2.68093 + 5.03325i) q^{69} +(-1.30292 - 1.50365i) q^{71} +(7.36347 + 9.83644i) q^{73} +(-5.17866 + 2.92070i) q^{75} +(-13.9136 - 3.02672i) q^{77} +(-3.37219 + 0.990164i) q^{79} +(-1.13052 + 1.30469i) q^{81} +(-1.51175 + 4.05317i) q^{83} +(7.69806 + 4.13516i) q^{85} +(1.89309 - 0.706085i) q^{87} +(12.2904 + 7.89859i) q^{89} +4.98138i q^{91} +(-2.63160 + 2.63160i) q^{93} +(-0.0188565 - 2.74874i) q^{95} +(-3.82433 - 10.2534i) q^{97} +(-5.74391 - 1.68656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * 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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