LMFDB - Embedded newform 920.2.bv.a.217.22

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			217.22
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.758029 - 0.164899i) q^{3} +(2.15800 - 0.585709i) q^{5} +(-2.48810 + 1.35861i) q^{7} +(-2.18148 + 0.996249i) q^{9} +O(q^{10})$	\(q+(0.758029 - 0.164899i) q^{3} +(2.15800 - 0.585709i) q^{5} +(-2.48810 + 1.35861i) q^{7} +(-2.18148 + 0.996249i) q^{9} +(1.93136 + 1.67353i) q^{11} +(-0.00861689 + 0.0157806i) q^{13} +(1.53924 - 0.799836i) q^{15} +(5.08060 + 3.80329i) q^{17} +(-0.577600 + 4.01730i) q^{19} +(-1.66202 + 1.44015i) q^{21} +(4.16500 + 2.37755i) q^{23} +(4.31389 - 2.52791i) q^{25} +(-3.35242 + 2.50959i) q^{27} +(8.22458 - 1.18252i) q^{29} +(0.792972 - 0.509612i) q^{31} +(1.73999 + 0.950108i) q^{33} +(-4.57357 + 4.38917i) q^{35} +(-2.12105 - 0.791112i) q^{37} +(-0.00392963 + 0.0133831i) q^{39} +(2.12007 - 4.64231i) q^{41} +(-0.155838 - 0.716377i) q^{43} +(-4.12411 + 3.42761i) q^{45} +(-0.448430 - 0.448430i) q^{47} +(0.560357 - 0.871933i) q^{49} +(4.47840 + 2.04522i) q^{51} +(-0.911407 - 1.66912i) q^{53} +(5.14808 + 2.48026i) q^{55} +(0.224611 + 3.14047i) q^{57} +(-1.43060 - 4.87217i) q^{59} +(-6.37492 - 9.91957i) q^{61} +(4.07424 - 5.44254i) q^{63} +(-0.00935234 + 0.0391016i) q^{65} +(-12.0258 - 0.860099i) q^{67} +(3.54925 + 1.11545i) q^{69} +(3.07852 + 3.55280i) q^{71} +(-0.956827 - 1.27817i) q^{73} +(2.85320 - 2.62759i) q^{75} +(-7.07910 - 1.53996i) q^{77} +(5.06805 - 1.48811i) q^{79} +(2.58406 - 2.98216i) q^{81} +(-4.70203 + 12.6066i) q^{83} +(13.1915 + 5.23173i) q^{85} +(6.03947 - 2.25261i) q^{87} +(1.15897 + 0.744828i) q^{89} -0.0509708i q^{91} +(0.517061 - 0.517061i) q^{93} +(1.10651 + 9.00762i) q^{95} +(0.675459 + 1.81098i) q^{97} +(-5.88048 - 1.72667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.758029	−	0.164899i	0.437648	−	0.0952045i	0.0116574	−	0.999932i	$-0.496289\pi$
$3$	0.758029	−	0.164899i	0.437648	−	0.0952045i	0.425991	+	0.904728i	$0.359926\pi$
$4$		0			0
$5$	2.15800	−	0.585709i	0.965085	−	0.261937i
$5$	2.15800	−	0.585709i	0.965085	−	0.261937i
$6$		0			0
$7$	−2.48810	+	1.35861i	−0.940414	+	0.513505i	−0.874877	−	0.484345i	$-0.839058\pi$
$7$	−2.48810	+	1.35861i	−0.940414	+	0.513505i	−0.0655374	+	0.997850i	$0.520876\pi$
$8$		0			0
$9$	−2.18148	+	0.996249i	−0.727160	+	0.332083i
$10$		0			0
$11$	1.93136	+	1.67353i	0.582328	+	0.504590i	0.895473	−	0.445115i	$-0.146837\pi$
$11$	1.93136	+	1.67353i	0.582328	+	0.504590i	−0.313146	+	0.949705i	$0.601383\pi$
$12$		0			0
$13$	−0.00861689	+	0.0157806i	−0.00238989	+	0.00437676i	−0.878871	−	0.477059i	$-0.841703\pi$
$13$	−0.00861689	+	0.0157806i	−0.00238989	+	0.00437676i	0.876481	+	0.481436i	$0.159885\pi$
$14$		0			0
$15$	1.53924	−	0.799836i	0.397430	−	0.206517i
$16$		0			0
$17$	5.08060	+	3.80329i	1.23223	+	0.922433i	0.998753	−	0.0499297i	$-0.0158997\pi$
$17$	5.08060	+	3.80329i	1.23223	+	0.922433i	0.233474	+	0.972363i	$0.424991\pi$
$18$		0			0
$19$	−0.577600	+	4.01730i	−0.132511	+	0.921632i	0.809756	+	0.586767i	$0.199600\pi$
$19$	−0.577600	+	4.01730i	−0.132511	+	0.921632i	−0.942266	+	0.334864i	$0.891309\pi$
$20$		0			0
$21$	−1.66202	+	1.44015i	−0.362683	+	0.314266i
$22$		0			0
$23$	4.16500	+	2.37755i	0.868463	+	0.495754i
$23$	4.16500	+	2.37755i	0.868463	+	0.495754i
$24$		0			0
$25$	4.31389	−	2.52791i	0.862778	−	0.505583i
$26$		0			0
$27$	−3.35242	+	2.50959i	−0.645174	+	0.482971i
$28$		0			0
$29$	8.22458	−	1.18252i	1.52727	−	0.219588i	0.673085	−	0.739565i	$-0.264969\pi$
$29$	8.22458	−	1.18252i	1.52727	−	0.219588i	0.854180	+	0.519977i	$0.174060\pi$
$30$		0			0
$31$	0.792972	−	0.509612i	0.142422	−	0.0915290i	−0.467489	−	0.883999i	$-0.654841\pi$
$31$	0.792972	−	0.509612i	0.142422	−	0.0915290i	0.609911	+	0.792470i	$0.291205\pi$
$32$		0			0
$33$	1.73999	+	0.950108i	0.302894	+	0.165393i
$34$		0			0
$35$	−4.57357	+	4.38917i	−0.773074	+	0.741905i
$36$		0			0
$37$	−2.12105	−	0.791112i	−0.348699	−	0.130058i	0.169011	−	0.985614i	$-0.445943\pi$
$37$	−2.12105	−	0.791112i	−0.348699	−	0.130058i	−0.517710	+	0.855556i	$0.673215\pi$
$38$		0			0
$39$	−0.00392963	+	0.0133831i	−0.000629245	+	0.00214301i
$40$		0			0
$41$	2.12007	−	4.64231i	0.331100	−	0.725008i	−0.668729	−	0.743506i	$-0.733161\pi$
$41$	2.12007	−	4.64231i	0.331100	−	0.725008i	0.999829	+	0.0184986i	$0.00588862\pi$
$42$		0			0
$43$	−0.155838	−	0.716377i	−0.0237651	−	0.109246i	0.963736	−	0.266856i	$-0.0859849\pi$
$43$	−0.155838	−	0.716377i	−0.0237651	−	0.109246i	−0.987501	+	0.157610i	$0.949621\pi$
$44$		0			0
$45$	−4.12411	+	3.42761i	−0.614786	+	0.510958i
$46$		0			0
$47$	−0.448430	−	0.448430i	−0.0654103	−	0.0654103i	0.673645	−	0.739055i	$-0.264728\pi$
$47$	−0.448430	−	0.448430i	−0.0654103	−	0.0654103i	−0.739055	+	0.673645i	$0.764728\pi$
$48$		0			0
$49$	0.560357	−	0.871933i	0.0800510	−	0.124562i
$50$		0			0
$51$	4.47840	+	2.04522i	0.627102	+	0.286388i
$52$		0			0
$53$	−0.911407	−	1.66912i	−0.125191	−	0.229271i	0.807565	−	0.589779i	$-0.200785\pi$
$53$	−0.911407	−	1.66912i	−0.125191	−	0.229271i	−0.932756	+	0.360508i	$0.882603\pi$
$54$		0			0
$55$	5.14808	+	2.48026i	0.694166	+	0.334439i
$56$		0			0
$57$	0.224611	+	3.14047i	0.0297505	+	0.415966i
$58$		0			0
$59$	−1.43060	−	4.87217i	−0.186248	−	0.634302i	−0.998686	−	0.0512543i	$-0.983678\pi$
$59$	−1.43060	−	4.87217i	−0.186248	−	0.634302i	0.812438	−	0.583048i	$-0.198140\pi$
$60$		0			0
$61$	−6.37492	−	9.91957i	−0.816225	−	1.27007i	−0.959871	−	0.280442i	$-0.909519\pi$
$61$	−6.37492	−	9.91957i	−0.816225	−	1.27007i	0.143646	−	0.989629i	$-0.454117\pi$
$62$		0			0
$63$	4.07424	−	5.44254i	0.513306	−	0.685696i
$64$		0			0
$65$	−0.00935234	+	0.0391016i	−0.00116001	+	0.00484995i
$66$		0			0
$67$	−12.0258	−	0.860099i	−1.46918	−	0.105078i	−0.686331	−	0.727289i	$-0.740780\pi$
$67$	−12.0258	−	0.860099i	−1.46918	−	0.105078i	−0.782849	+	0.622212i	$0.786234\pi$
$68$		0			0
$69$	3.54925	+	1.11545i	0.427279	+	0.134284i
$70$		0			0
$71$	3.07852	+	3.55280i	0.365353	+	0.421640i	0.908426	−	0.418045i	$-0.137285\pi$
$71$	3.07852	+	3.55280i	0.365353	+	0.421640i	−0.543073	+	0.839686i	$0.682739\pi$
$72$		0			0
$73$	−0.956827	−	1.27817i	−0.111988	−	0.149599i	0.741045	−	0.671455i	$-0.234330\pi$
$73$	−0.956827	−	1.27817i	−0.111988	−	0.149599i	−0.853033	+	0.521857i	$0.825240\pi$
$74$		0			0
$75$	2.85320	−	2.62759i	0.329459	−	0.303408i
$76$		0			0
$77$	−7.07910	−	1.53996i	−0.806739	−	0.175495i
$78$		0			0
$79$	5.06805	−	1.48811i	0.570200	−	0.167426i	0.0160917	−	0.999871i	$-0.494878\pi$
$79$	5.06805	−	1.48811i	0.570200	−	0.167426i	0.554108	+	0.832445i	$0.313059\pi$
$80$		0			0
$81$	2.58406	−	2.98216i	0.287118	−	0.331352i
$82$		0			0
$83$	−4.70203	+	12.6066i	−0.516115	+	1.38376i	0.373748	+	0.927530i	$0.378073\pi$
$83$	−4.70203	+	12.6066i	−0.516115	+	1.38376i	−0.889863	+	0.456228i	$0.849200\pi$
$84$		0			0
$85$	13.1915	+	5.23173i	1.43082	+	0.567461i
$86$		0			0
$87$	6.03947	−	2.25261i	0.647499	−	0.241505i
$88$		0			0
$89$	1.15897	+	0.744828i	0.122851	+	0.0789516i	0.600623	−	0.799532i	$-0.294919\pi$
$89$	1.15897	+	0.744828i	0.122851	+	0.0789516i	−0.477772	+	0.878484i	$0.658556\pi$
$90$		0			0
$91$		−	0.0509708i		−	0.00534320i
$92$		0			0
$93$	0.517061	−	0.517061i	0.0536167	−	0.0536167i
$94$		0			0
$95$	1.10651	+	9.00762i	0.113525	+	0.924162i
$96$		0			0
$97$	0.675459	+	1.81098i	0.0685825	+	0.183877i	0.966719	−	0.255839i	$-0.0823518\pi$
$97$	0.675459	+	1.81098i	0.0685825	+	0.183877i	−0.898137	+	0.439716i	$0.855079\pi$
$98$		0			0
$99$	−5.88048	−	1.72667i	−0.591011	−	0.173536i
$100$		0			0
$101$	2.01802	+	4.41885i	0.200801	+	0.439692i	0.983066	−	0.183254i	$-0.0586630\pi$
$101$	2.01802	+	4.41885i	0.200801	+	0.439692i	−0.782265	+	0.622946i	$0.785936\pi$
$102$		0			0
$103$	−4.07651	+	0.291558i	−0.401671	+	0.0287281i	−0.270714	−	0.962660i	$-0.587260\pi$
$103$	−4.07651	+	0.291558i	−0.401671	+	0.0287281i	−0.130957	+	0.991388i	$0.541805\pi$
$104$		0			0
$105$	−2.74312	+	4.08130i	−0.267702	+	0.398294i
$106$		0			0
$107$	−1.52609	+	7.01533i	−0.147533	+	0.678198i	0.842655	+	0.538454i	$0.180991\pi$
$107$	−1.52609	+	7.01533i	−0.147533	+	0.678198i	−0.990188	+	0.139744i	$0.955372\pi$
$108$		0			0
$109$	2.48820	+	17.3058i	0.238326	+	1.65759i	0.660312	+	0.750992i	$0.270424\pi$
$109$	2.48820	+	17.3058i	0.238326	+	1.65759i	−0.421986	+	0.906603i	$0.638667\pi$
$110$		0			0
$111$	−1.73827	−	0.249926i	−0.164989	−	0.0237219i
$112$		0			0
$113$	0.402050	−	5.62140i	0.0378217	−	0.528817i	−0.942858	−	0.333195i	$-0.891873\pi$
$113$	0.402050	−	5.62140i	0.0378217	−	0.528817i	0.980680	−	0.195621i	$-0.0626723\pi$
$114$		0			0
$115$	10.3806	+	2.69126i	0.967997	+	0.250962i
$116$		0			0
$117$	0.00307612	−	0.0430097i	0.000284387	−	0.00397625i
$118$		0			0
$119$	−17.8082	−	2.56044i	−1.63248	−	0.234715i
$120$		0			0
$121$	−0.636022	−	4.42363i	−0.0578202	−	0.402148i
$122$		0			0
$123$	0.841564	−	3.86861i	0.0758812	−	0.348820i
$124$		0			0
$125$	7.82873	−	7.98191i	0.700223	−	0.713924i
$126$		0			0
$127$	10.4641	−	0.748409i	0.928542	−	0.0664106i	0.401131	−	0.916021i	$-0.368617\pi$
$127$	10.4641	−	0.748409i	0.928542	−	0.0664106i	0.527411	+	0.849610i	$0.323163\pi$
$128$		0			0
$129$	−0.236260	−	0.517337i	−0.0208015	−	0.0455490i
$130$		0			0
$131$	−7.70796	−	2.26326i	−0.673448	−	0.197742i	−0.0729102	−	0.997339i	$-0.523229\pi$
$131$	−7.70796	−	2.26326i	−0.673448	−	0.197742i	−0.600538	+	0.799596i	$0.705047\pi$
$132$		0			0
$133$	−4.02080	−	10.7802i	−0.348648	−	0.934761i
$134$		0			0
$135$	−5.76462	+	7.37923i	−0.496140	+	0.635103i
$136$		0			0
$137$	−3.45238	+	3.45238i	−0.294957	+	0.294957i	−0.839035	−	0.544078i	$-0.816880\pi$
$137$	−3.45238	+	3.45238i	−0.294957	+	0.294957i	0.544078	+	0.839035i	$0.316880\pi$
$138$		0			0
$139$		−	7.46818i		−	0.633442i	−0.948519	−	0.316721i	$-0.897418\pi$
$139$		−	7.46818i		−	0.633442i	0.948519	−	0.316721i	$-0.102582\pi$
$140$		0			0
$141$	−0.413869	−	0.265977i	−0.0348540	−	0.0223993i
$142$		0			0
$143$	−0.0430518	+	0.0160575i	−0.00360017	+	0.00134279i
$144$		0			0
$145$	17.0560	−	7.36907i	1.41642	−	0.611968i
$146$		0			0
$147$	0.280986	−	0.753352i	0.0231753	−	0.0621355i
$148$		0			0
$149$	14.2003	−	16.3880i	1.16333	−	1.34256i	0.234471	−	0.972123i	$-0.424664\pi$
$149$	14.2003	−	16.3880i	1.16333	−	1.34256i	0.928860	−	0.370432i	$-0.120790\pi$
$150$		0			0
$151$	−18.0307	+	5.29430i	−1.46732	+	0.430844i	−0.915227	−	0.402940i	$-0.867988\pi$
$151$	−18.0307	+	5.29430i	−1.46732	+	0.430844i	−0.552092	+	0.833783i	$0.686170\pi$
$152$		0			0
$153$	−14.8723	−	3.23526i	−1.20235	−	0.261555i
$154$		0			0
$155$	1.41275	−	1.56419i	0.113474	−	0.125639i
$156$		0			0
$157$	−2.34865	−	3.13743i	−0.187443	−	0.250394i	0.696970	−	0.717101i	$-0.254531\pi$
$157$	−2.34865	−	3.13743i	−0.187443	−	0.250394i	−0.884412	+	0.466707i	$0.845440\pi$
$158$		0			0
$159$	−0.966109	−	1.11495i	−0.0766174	−	0.0884212i
$160$		0			0
$161$	−13.5931	−	0.256988i	−1.07129	−	0.0202535i
$162$		0			0
$163$	−0.830401	−	0.0593915i	−0.0650421	−	0.00465190i	0.0387802	−	0.999248i	$-0.487653\pi$
$163$	−0.830401	−	0.0593915i	−0.0650421	−	0.00465190i	−0.103822	+	0.994596i	$0.533107\pi$
$164$		0			0
$165$	4.31138	+	1.03120i	0.335641	+	0.0802788i
$166$		0			0
$167$	−9.36931	+	12.5159i	−0.725019	+	0.968512i	0.274956	+	0.961457i	$0.411337\pi$
$167$	−9.36931	+	12.5159i	−0.725019	+	0.968512i	−0.999975	+	0.00705509i	$0.997754\pi$
$168$		0			0
$169$	7.02816	+	10.9360i	0.540627	+	0.841233i
$170$		0			0
$171$	−2.74220	−	9.33909i	−0.209702	−	0.714178i
$172$		0			0
$173$	−1.30064	−	18.1854i	−0.0988861	−	1.38261i	−0.768477	−	0.639878i	$-0.778985\pi$
$173$	−1.30064	−	18.1854i	−0.0988861	−	1.38261i	0.669591	−	0.742730i	$-0.266470\pi$
$174$		0			0
$175$	−7.29896	+	12.1506i	−0.551750	+	0.918498i
$176$		0			0
$177$	−1.88785	−	3.45734i	−0.141900	−	0.259870i
$178$		0			0
$179$	−6.87750	−	3.14085i	−0.514049	−	0.234758i	0.141462	−	0.989944i	$-0.454820\pi$
$179$	−6.87750	−	3.14085i	−0.514049	−	0.234758i	−0.655511	+	0.755185i	$0.727547\pi$
$180$		0			0
$181$	6.40159	−	9.96107i	0.475827	−	0.740401i	−0.517507	−	0.855679i	$-0.673140\pi$
$181$	6.40159	−	9.96107i	0.475827	−	0.740401i	0.993333	+	0.115279i	$0.0367761\pi$
$182$		0			0
$183$	−6.46810	−	6.46810i	−0.478136	−	0.478136i
$184$		0			0
$185$	−5.04058	−	0.464896i	−0.370591	−	0.0341798i
$186$		0			0
$187$	3.44754	+	15.8481i	0.252109	+	1.15893i
$188$		0			0
$189$	4.93162	−	10.7987i	0.358723	−	0.785493i
$190$		0			0
$191$	7.34067	−	25.0000i	0.531152	−	1.80894i	−0.0546768	−	0.998504i	$-0.517413\pi$
$191$	7.34067	−	25.0000i	0.531152	−	1.80894i	0.585829	−	0.810435i	$-0.300769\pi$
$192$		0			0
$193$	−13.7462	−	5.12709i	−0.989477	−	0.369056i	−0.197964	−	0.980209i	$-0.563433\pi$
$193$	−13.7462	−	5.12709i	−0.989477	−	0.369056i	−0.791512	+	0.611154i	$0.790706\pi$
$194$		0			0
$195$	−0.000641530		0.0311823i	−4.59409e−5		0.00223301i
$196$		0			0
$197$	0.233324	+	0.127405i	0.0166237	+	0.00907720i	0.487539	−	0.873101i	$-0.337895\pi$
$197$	0.233324	+	0.127405i	0.0166237	+	0.00907720i	−0.470916	+	0.882178i	$0.656076\pi$
$198$		0			0
$199$	−9.03928	+	5.80919i	−0.640777	+	0.411803i	−0.820286	−	0.571954i	$-0.806186\pi$
$199$	−9.03928	+	5.80919i	−0.640777	+	0.411803i	0.179508	+	0.983756i	$0.442549\pi$
$200$		0			0
$201$	−9.25770	+	1.33106i	−0.652988	+	0.0938855i
$202$		0			0
$203$	−18.8570	+	14.1162i	−1.32350	+	0.990762i
$204$		0			0
$205$	1.85607	−	11.2598i	0.129633	−	0.786421i
$206$		0			0
$207$	−11.4545	−	1.03720i	−0.796143	−	0.0720904i
$208$		0			0
$209$	−7.83865	+	6.79223i	−0.542210	+	0.469828i
$210$		0			0
$211$	3.50941	−	24.4085i	0.241598	−	1.68035i	−0.402511	−	0.915415i	$-0.631862\pi$
$211$	3.50941	−	24.4085i	0.241598	−	1.68035i	0.644108	−	0.764934i	$-0.277229\pi$
$212$		0			0
$213$	2.91946	+	2.18548i	0.200038	+	0.149747i
$214$		0			0
$215$	−0.755886	−	1.45466i	−0.0515510	−	0.0992071i
$216$		0			0
$217$	−1.28063	+	2.34530i	−0.0869350	+	0.159210i
$218$		0			0
$219$	−0.936071	−	0.811111i	−0.0632538	−	0.0548098i
$220$		0			0
$221$	−0.103797	+	0.0474027i	−0.00698216	+	0.00318865i
$222$		0			0
$223$	10.4034	−	5.68071i	0.696666	−	0.380409i	−0.0915553	−	0.995800i	$-0.529184\pi$
$223$	10.4034	−	5.68071i	0.696666	−	0.380409i	0.788222	+	0.615391i	$0.211002\pi$
$224$		0			0
$225$	−6.89223	+	9.81230i	−0.459482	+	0.654153i
$226$		0			0
$227$	5.51722	−	1.20020i	0.366191	−	0.0796600i	−0.0257048	−	0.999670i	$-0.508183\pi$
$227$	5.51722	−	1.20020i	0.366191	−	0.0796600i	0.391896	+	0.920010i	$0.371819\pi$
$228$		0			0
$229$	15.6301			1.03287			0.516433	−	0.856328i	$-0.327259\pi$
$229$	15.6301			1.03287			0.516433	+	0.856328i	$0.327259\pi$
$230$		0			0
$231$	−5.62010			−0.369776
$232$		0			0
$233$	−26.1067	+	5.67916i	−1.71030	+	0.372054i	−0.958002	−	0.286763i	$-0.907421\pi$
$233$	−26.1067	+	5.67916i	−1.71030	+	0.372054i	−0.752303	+	0.658817i	$0.771057\pi$
$234$		0			0
$235$	−1.23036	−	0.705061i	−0.0802599	−	0.0459931i
$236$		0			0
$237$	3.59634	−	1.96375i	0.233607	−	0.127559i
$238$		0			0
$239$	23.1282	−	10.5623i	1.49604	−	0.683218i	0.511645	−	0.859197i	$-0.329036\pi$
$239$	23.1282	−	10.5623i	1.49604	−	0.683218i	0.984394	+	0.175979i	$0.0563092\pi$
$240$		0			0
$241$	9.90427	+	8.58210i	0.637990	+	0.552822i	0.912661	−	0.408717i	$-0.134024\pi$
$241$	9.90427	+	8.58210i	0.637990	+	0.552822i	−0.274671	+	0.961538i	$0.588569\pi$
$242$		0			0
$243$	7.48788	−	13.7130i	0.480348	−	0.879691i
$244$		0			0
$245$	0.698550	−	2.20983i	0.0446287	−	0.141181i
$246$		0			0
$247$	−0.0584185	−	0.0437315i	−0.00371708	−	0.00278257i
$248$		0			0
$249$	−1.48545	+	10.3316i	−0.0941368	+	0.654736i
$250$		0			0
$251$	9.05273	−	7.84424i	0.571403	−	0.495124i	−0.320562	−	0.947228i	$-0.603872\pi$
$251$	9.05273	−	7.84424i	0.571403	−	0.495124i	0.891965	+	0.452104i	$0.149326\pi$
$252$		0			0
$253$	4.06522	+	11.5622i	0.255578	+	0.726909i
$254$		0			0
$255$	10.8623	+	1.79053i	0.680222	+	0.112127i
$256$		0			0
$257$	−21.1180	+	15.8087i	−1.31730	+	0.986121i	−0.318028	+	0.948081i	$0.603020\pi$
$257$	−21.1180	+	15.8087i	−1.31730	+	0.986121i	−0.999276	+	0.0380398i	$0.987889\pi$
$258$		0			0
$259$	6.35221	−	0.913309i	0.394707	−	0.0567503i
$260$		0			0
$261$	−16.7637	+	10.7734i	−1.03765	+	0.666854i
$262$		0			0
$263$	−21.6933	−	11.8454i	−1.33766	−	0.730420i	−0.358508	−	0.933527i	$-0.616714\pi$
$263$	−21.6933	−	11.8454i	−1.33766	−	0.730420i	−0.979157	+	0.203106i	$0.934896\pi$
$264$		0			0
$265$	−2.94443	−	3.06813i	−0.180875	−	0.188474i
$266$		0			0
$267$	1.00136	+	0.373487i	0.0612821	+	0.0228570i
$268$		0			0
$269$	2.66857	−	9.08832i	0.162706	−	0.554124i	−0.837267	−	0.546794i	$-0.815848\pi$
$269$	2.66857	−	9.08832i	0.162706	−	0.554124i	0.999973	−	0.00733099i	$-0.00233355\pi$
$270$		0			0
$271$	9.46356	−	20.7223i	0.574870	−	1.25879i	−0.369293	−	0.929313i	$-0.620400\pi$
$271$	9.46356	−	20.7223i	0.574870	−	1.25879i	0.944164	−	0.329477i	$-0.106873\pi$
$272$		0			0
$273$	−0.00840504	−	0.0386374i	−0.000508696	−	0.00233844i
$274$		0			0
$275$	12.5622	+	2.33713i	0.757531	+	0.140934i
$276$		0			0
$277$	5.07909	+	5.07909i	0.305173	+	0.305173i	0.843034	−	0.537861i	$-0.180767\pi$
$277$	5.07909	+	5.07909i	0.305173	+	0.305173i	−0.537861	+	0.843034i	$0.680767\pi$
$278$		0			0
$279$	−1.22215	+	1.90171i	−0.0731683	+	0.113852i
$280$		0			0
$281$	−7.48404	−	3.41785i	−0.446460	−	0.203892i	0.179481	−	0.983761i	$-0.442558\pi$
$281$	−7.48404	−	3.41785i	−0.446460	−	0.203892i	−0.625942	+	0.779870i	$0.715285\pi$
$282$		0			0
$283$	14.4661	+	26.4926i	0.859918	+	1.57482i	0.817650	+	0.575716i	$0.195277\pi$
$283$	14.4661	+	26.4926i	0.859918	+	1.57482i	0.0422686	+	0.999106i	$0.486541\pi$
$284$		0			0
$285$	2.32411	+	6.64557i	0.137669	+	0.393650i
$286$		0			0
$287$	1.03212	+	14.4309i	0.0609240	+	0.851829i
$288$		0			0
$289$	6.55803	+	22.3346i	0.385767	+	1.31380i
$290$		0			0
$291$	0.810645	+	1.26139i	0.0475209	+	0.0739439i
$292$		0			0
$293$	17.9958	−	24.0395i	1.05132	−	1.40440i	0.141242	−	0.989975i	$-0.454890\pi$
$293$	17.9958	−	24.0395i	1.05132	−	1.40440i	0.910082	−	0.414429i	$-0.136019\pi$
$294$		0			0
$295$	−5.94090	−	9.67620i	−0.345892	−	0.563370i
$296$		0			0
$297$	−10.6746	−	0.763464i	−0.619405	−	0.0443007i
$298$		0			0
$299$	−0.0734086	+	0.0452394i	−0.00424533	+	0.00261626i
$300$		0			0
$301$	1.36102	+	1.57070i	0.0784477	+	0.0905334i
$302$		0			0
$303$	2.25838	+	3.01685i	0.129741	+	0.173313i
$304$		0			0
$305$	−19.5670	−	17.6725i	−1.12041	−	1.01193i
$306$		0			0
$307$	9.24803	+	2.01179i	0.527813	+	0.114819i	0.468573	−	0.883425i	$-0.344768\pi$
$307$	9.24803	+	2.01179i	0.527813	+	0.114819i	0.0592405	+	0.998244i	$0.481132\pi$
$308$		0			0
$309$	−3.04204	+	0.893223i	−0.173055	+	0.0508137i
$310$		0			0
$311$	6.06989	−	7.00503i	0.344192	−	0.397219i	−0.557090	−	0.830452i	$-0.688082\pi$
$311$	6.06989	−	7.00503i	0.344192	−	0.397219i	0.901282	+	0.433233i	$0.142627\pi$
$312$		0			0
$313$	−8.30102	+	22.2559i	−0.469201	+	1.25798i	0.459840	+	0.888002i	$0.347907\pi$
$313$	−8.30102	+	22.2559i	−0.469201	+	1.25798i	−0.929041	+	0.369976i	$0.879366\pi$
$314$		0			0
$315$	5.60444	−	14.1313i	0.315774	−	0.796209i
$316$		0			0
$317$	−24.8700	+	9.27604i	−1.39684	+	0.520994i	−0.931372	−	0.364070i	$-0.881387\pi$
$317$	−24.8700	+	9.27604i	−1.39684	+	0.520994i	−0.465468	+	0.885065i	$0.654114\pi$
$318$		0			0
$319$	17.8636	+	11.4802i	1.00017	+	0.642771i
$320$		0			0
$321$			5.56948i			0.310858i
$322$		0			0
$323$	−18.2135	+	18.2135i	−1.01343	+	1.01343i
$324$		0			0
$325$	0.00271983	+	0.0898587i	0.000150869	+	0.00498447i
$326$		0			0
$327$	4.73983	+	12.7080i	0.262113	+	0.702753i
$328$		0			0
$329$	1.72498	+	0.506500i	0.0951013	+	0.0279243i
$330$		0			0
$331$	−6.20286	−	13.5824i	−0.340940	−	0.746554i	0.659045	−	0.752104i	$-0.270961\pi$
$331$	−6.20286	−	13.5824i	−0.340940	−	0.746554i	−0.999985	+	0.00554953i	$0.998234\pi$
$332$		0			0
$333$	5.41518	−	0.387301i	0.296750	−	0.0212240i
$334$		0			0
$335$	−26.4553	+	5.18750i	−1.44541	+	0.283424i
$336$		0			0
$337$	1.76098	−	8.09511i	0.0959269	−	0.440969i	−0.903983	−	0.427568i	$-0.859371\pi$
$337$	1.76098	−	8.09511i	0.0959269	−	0.440969i	0.999910	−	0.0134012i	$-0.00426585\pi$
$338$		0			0
$339$	−0.622198	−	4.32748i	−0.0337931	−	0.235036i
$340$		0			0
$341$	2.38437	+	0.342820i	0.129121	+	0.0185648i
$342$		0			0
$343$	1.20605	−	16.8627i	0.0651204	−	0.910502i
$344$		0			0
$345$	8.31259	+	0.328302i	0.447535	+	0.0176752i
$346$		0			0
$347$	1.47435	−	20.6141i	0.0791472	−	1.10662i	−0.790340	−	0.612668i	$-0.790096\pi$
$347$	1.47435	−	20.6141i	0.0791472	−	1.10662i	0.869488	−	0.493955i	$-0.164449\pi$
$348$		0			0
$349$	−32.0944	−	4.61447i	−1.71797	−	0.247007i	−0.788272	−	0.615327i	$-0.789024\pi$
$349$	−32.0944	−	4.61447i	−1.71797	−	0.247007i	−0.929699	+	0.368319i	$0.879933\pi$
$350$		0			0
$351$	−0.0107155	−	0.0745282i	−0.000571953	−	0.00397802i
$352$		0			0
$353$	3.79284	−	17.4354i	0.201873	−	0.927993i	−0.759019	−	0.651068i	$-0.774321\pi$
$353$	3.79284	−	17.4354i	0.201873	−	0.927993i	0.960892	−	0.276925i	$-0.0893153\pi$
$354$		0			0
$355$	8.72434	+	5.86382i	0.463040	+	0.311219i
$356$		0			0
$357$	−13.9214	+	0.995676i	−0.736797	+	0.0526968i
$358$		0			0
$359$	−5.67923	−	12.4358i	−0.299738	−	0.656335i	0.698504	−	0.715606i	$-0.253850\pi$
$359$	−5.67923	−	12.4358i	−0.299738	−	0.656335i	−0.998242	+	0.0592714i	$0.981122\pi$
$360$		0			0
$361$	2.42529	+	0.712131i	0.127647	+	0.0374806i
$362$		0			0
$363$	−1.21158	−	3.24836i	−0.0635912	−	0.170495i
$364$		0			0
$365$	−2.81346	−	2.19787i	−0.147263	−	0.115042i
$366$		0			0
$367$	16.6894	−	16.6894i	0.871181	−	0.871181i	−0.121420	−	0.992601i	$-0.538745\pi$
$367$	16.6894	−	16.6894i	0.871181	−	0.871181i	0.992601	+	0.121420i	$0.0387449\pi$
$368$		0			0
$369$			12.2392i			0.637149i
$370$		0			0
$371$	4.53535	+	2.91469i	0.235464	+	0.151323i
$372$		0			0
$373$	31.5787	−	11.7783i	1.63508	−	0.609855i	0.646825	−	0.762638i	$-0.276096\pi$
$373$	31.5787	−	11.7783i	1.63508	−	0.609855i	0.988260	+	0.152783i	$0.0488237\pi$
$374$		0			0
$375$	4.61820	−	7.34147i	0.238483	−	0.379112i
$376$		0			0
$377$	−0.0522094	+	0.139979i	−0.00268892	+	0.00720927i
$378$		0			0
$379$	5.75730	−	6.64428i	0.295733	−	0.341294i	−0.588365	−	0.808595i	$-0.700228\pi$
$379$	5.75730	−	6.64428i	0.295733	−	0.341294i	0.884098	+	0.467302i	$0.154774\pi$
$380$		0			0
$381$	7.80870	−	2.29284i	0.400052	−	0.117466i
$382$		0			0
$383$	8.18325	+	1.78016i	0.418145	+	0.0909618i	0.416715	−	0.909037i	$-0.363181\pi$
$383$	8.18325	+	1.78016i	0.418145	+	0.0909618i	0.00142961	+	0.999999i	$0.499545\pi$
$384$		0			0
$385$	−16.1786	+	0.823057i	−0.824540	+	0.0419468i
$386$		0			0
$387$	1.05365	+	1.40751i	0.0535599	+	0.0715477i
$388$		0			0
$389$	6.27060	+	7.23666i	0.317932	+	0.366913i	0.892111	−	0.451817i	$-0.149224\pi$
$389$	6.27060	+	7.23666i	0.317932	+	0.366913i	−0.574179	+	0.818730i	$0.694678\pi$
$390$		0			0
$391$	12.1182	+	27.9201i	0.612844	+	1.41198i
$392$		0			0
$393$	−6.21607	−	0.444582i	−0.313559	−	0.0224262i
$394$		0			0
$395$	10.0652	−	6.17974i	0.506436	−	0.310936i
$396$		0			0
$397$	−14.5858	+	19.4844i	−0.732042	+	0.977893i	0.267854	+	0.963459i	$0.413685\pi$
$397$	−14.5858	+	19.4844i	−0.732042	+	0.977893i	−0.999896	+	0.0144337i	$0.995405\pi$
$398$		0			0
$399$	−4.82553	−	7.50866i	−0.241578	−	0.375903i
$400$		0			0
$401$	8.85643	+	30.1622i	0.442269	+	1.50623i	0.815647	+	0.578550i	$0.196381\pi$
$401$	8.85643	+	30.1622i	0.442269	+	1.50623i	−0.373378	+	0.927679i	$0.621801\pi$
$402$		0			0
$403$	0.00120906	+	0.0169049i	6.02276e−5	+	0.000842092i
$404$		0			0
$405$	3.82971	−	7.94900i	0.190300	−	0.394989i
$406$		0			0
$407$	−2.77257	−	5.07758i	−0.137431	−	0.251686i
$408$		0			0
$409$	18.0381	+	8.23771i	0.891925	+	0.407328i	0.808027	−	0.589146i	$-0.200536\pi$
$409$	18.0381	+	8.23771i	0.891925	+	0.407328i	0.0838983	+	0.996474i	$0.473263\pi$
$410$		0			0
$411$	−2.04771	+	3.18630i	−0.101006	+	0.157169i
$412$		0			0
$413$	10.1788	+	10.1788i	0.500868	+	0.500868i
$414$		0			0
$415$	−2.76315	+	29.9591i	−0.135638	+	1.47063i
$416$		0			0
$417$	−1.23150	−	5.66109i	−0.0603066	−	0.277225i
$418$		0			0
$419$	4.17589	−	9.14392i	0.204005	−	0.446710i	−0.779781	−	0.626052i	$-0.784670\pi$
$419$	4.17589	−	9.14392i	0.204005	−	0.446710i	0.983787	+	0.179342i	$0.0573970\pi$
$420$		0			0
$421$	−3.17439	+	10.8110i	−0.154710	+	0.526896i	−0.999972	−	0.00745699i	$-0.997626\pi$
$421$	−3.17439	+	10.8110i	−0.154710	+	0.526896i	0.845262	+	0.534353i	$0.179445\pi$
$422$		0			0
$423$	1.42499	+	0.531494i	0.0692854	+	0.0258421i
$424$		0			0
$425$	31.5315	+	3.56365i	1.52950	+	0.172863i
$426$		0			0
$427$	29.3383	+	16.0199i	1.41978	+	0.775257i
$428$		0			0
$429$	−0.0299866	+	0.0192712i	−0.00144777	+	0.000930424i
$430$		0			0
$431$	20.8201	−	2.99348i	1.00287	−	0.144191i	0.378732	−	0.925506i	$-0.376360\pi$
$431$	20.8201	−	2.99348i	1.00287	−	0.144191i	0.624136	+	0.781316i	$0.285451\pi$
$432$		0			0
$433$	−15.5761	+	11.6601i	−0.748539	+	0.560349i	−0.904020	−	0.427490i	$-0.859398\pi$
$433$	−15.5761	+	11.6601i	−0.748539	+	0.560349i	0.155481	+	0.987839i	$0.450307\pi$
$434$		0			0
$435$	11.7138	−	8.39848i	0.561633	−	0.402676i
$436$		0			0
$437$	−11.9570	+	15.3588i	−0.571983	+	0.734711i
$438$		0			0
$439$	20.1541	−	17.4636i	0.961902	−	0.833493i	−0.0241876	−	0.999707i	$-0.507700\pi$
$439$	20.1541	−	17.4636i	0.961902	−	0.833493i	0.986090	+	0.166215i	$0.0531544\pi$
$440$		0			0
$441$	−0.353746	+	2.46036i	−0.0168451	+	0.117160i
$442$		0			0
$443$	−15.1604	−	11.3490i	−0.720294	−	0.539205i	0.175062	−	0.984557i	$-0.443988\pi$
$443$	−15.1604	−	11.3490i	−0.720294	−	0.539205i	−0.895355	+	0.445352i	$0.853078\pi$
$444$		0			0
$445$	2.93731	+	0.928513i	0.139242	+	0.0440158i
$446$		0			0
$447$	8.06184	−	14.7642i	0.381312	−	0.698321i
$448$		0			0
$449$	−21.9758	−	19.0422i	−1.03710	−	0.898655i	−0.0421620	−	0.999111i	$-0.513425\pi$
$449$	−21.9758	−	19.0422i	−1.03710	−	0.898655i	−0.994942	+	0.100455i	$0.967970\pi$
$450$		0			0
$451$	11.8637	−	5.41797i	0.558640	−	0.255122i
$452$		0			0
$453$	−12.7948	+	6.98648i	−0.601151	+	0.328253i
$454$		0			0
$455$	−0.0298541	−	0.109995i	−0.00139958	−	0.00515664i
$456$		0			0
$457$	−3.62598	+	0.788785i	−0.169616	+	0.0368978i	−0.296571	−	0.955011i	$-0.595843\pi$
$457$	−3.62598	+	0.788785i	−0.169616	+	0.0368978i	0.126955	+	0.991908i	$0.459480\pi$
$458$		0			0
$459$	−26.5770			−1.24051
$460$		0			0
$461$	24.7437			1.15243			0.576215	−	0.817298i	$-0.304529\pi$
$461$	24.7437			1.15243			0.576215	+	0.817298i	$0.304529\pi$
$462$		0			0
$463$	−16.0148	+	3.48381i	−0.744271	+	0.161906i	−0.568682	−	0.822557i	$-0.692547\pi$
$463$	−16.0148	+	3.48381i	−0.744271	+	0.161906i	−0.175589	+	0.984464i	$0.556183\pi$
$464$		0			0
$465$	0.812968	−	1.41866i	0.0377005	−	0.0657889i
$466$		0			0
$467$	−34.9873	+	19.1045i	−1.61902	+	0.884052i	−0.624327	+	0.781163i	$0.714627\pi$
$467$	−34.9873	+	19.1045i	−1.61902	+	0.884052i	−0.994693	+	0.102888i	$0.967192\pi$
$468$		0			0
$469$	31.0899	−	14.1983i	1.43560	−	0.655615i
$470$		0			0
$471$	−2.29770	−	1.99097i	−0.105873	−	0.0917391i
$472$		0			0
$473$	0.897901	−	1.64438i	0.0412856	−	0.0756088i
$474$		0			0
$475$	7.66368	+	18.7903i	0.351634	+	0.862159i
$476$		0			0
$477$	3.65107	+	2.73316i	0.167171	+	0.125143i
$478$		0			0
$479$	−2.57993	+	17.9438i	−0.117880	+	0.819874i	0.842003	+	0.539473i	$0.181376\pi$
$479$	−2.57993	+	17.9438i	−0.117880	+	0.819874i	−0.959883	+	0.280401i	$0.909533\pi$
$480$		0			0
$481$	0.0307611	−	0.0266547i	0.00140259	−	0.00121535i
$482$		0			0
$483$	−10.3463	+	2.04669i	−0.470775	+	0.0931275i
$484$		0			0
$485$	2.51834	+	3.51245i	0.114352	+	0.159492i
$486$		0			0
$487$	16.1396	−	12.0819i	0.731354	−	0.547485i	−0.167426	−	0.985885i	$-0.553546\pi$
$487$	16.1396	−	12.0819i	0.731354	−	0.547485i	0.898780	+	0.438400i	$0.144455\pi$
$488$		0			0
$489$	−0.639262	+	0.0919120i	−0.0289084	+	0.00415640i
$490$		0			0
$491$	−13.5419	+	8.70284i	−0.611136	+	0.392754i	−0.809283	−	0.587419i	$-0.800144\pi$
$491$	−13.5419	+	8.70284i	−0.611136	+	0.392754i	0.198147	+	0.980172i	$0.436508\pi$
$492$		0			0
$493$	46.2832	+	25.2726i	2.08449	+	1.13822i
$494$		0			0
$495$	−13.7014	−	0.281886i	−0.615831	−	0.0126698i
$496$		0			0
$497$	−12.4865	−	4.65724i	−0.560098	−	0.208906i
$498$		0			0
$499$	0.153235	−	0.521871i	0.00685975	−	0.0233621i	−0.955992	−	0.293393i	$-0.905216\pi$
$499$	0.153235	−	0.521871i	0.00685975	−	0.0233621i	0.962852	+	0.270031i	$0.0870338\pi$
$500$		0			0
$501$	−5.03834	+	11.0324i	−0.225096	+	0.492892i
$502$		0			0
$503$	7.48799	+	34.4217i	0.333873	+	1.53479i	0.771851	+	0.635804i	$0.219331\pi$
$503$	7.48799	+	34.4217i	0.333873	+	1.53479i	−0.437978	+	0.898986i	$0.644305\pi$
$504$		0			0
$505$	6.94304	+	8.35389i	0.308961	+	0.371743i
$506$		0			0
$507$	7.13088	+	7.13088i	0.316694	+	0.316694i
$508$		0			0
$509$	8.31484	−	12.9381i	0.368549	−	0.573473i	−0.606605	−	0.795004i	$-0.707469\pi$
$509$	8.31484	−	12.9381i	0.368549	−	0.573473i	0.975153	+	0.221530i	$0.0711052\pi$
$510$		0			0
$511$	4.11722	+	1.88027i	0.182135	+	0.0831782i
$512$		0			0
$513$	−8.14542	−	14.9172i	−0.359629	−	0.658611i
$514$		0			0
$515$	−8.62633	+	3.01683i	−0.380121	+	0.132937i
$516$		0			0
$517$	−0.115618	−	1.61655i	−0.00508486	−	0.0710956i
$518$		0			0
$519$	−3.98468	−	13.5706i	−0.174908	−	0.595681i
$520$		0			0
$521$	1.25038	+	1.94563i	0.0547802	+	0.0852397i	0.867563	−	0.497327i	$-0.165685\pi$
$521$	1.25038	+	1.94563i	0.0547802	+	0.0852397i	−0.812783	+	0.582566i	$0.802049\pi$
$522$		0			0
$523$	11.0011	−	14.6957i	0.481044	−	0.642600i	−0.492712	−	0.870192i	$-0.663994\pi$
$523$	11.0011	−	14.6957i	0.481044	−	0.642600i	0.973757	+	0.227592i	$0.0730853\pi$
$524$		0			0
$525$	−3.52920	+	10.4141i	−0.154027	+	0.454508i
$526$		0			0
$527$	5.96697	+	0.426766i	0.259925	+	0.0185902i
$528$		0			0
$529$	11.6945	+	19.8050i	0.508457	+	0.861087i
$530$		0			0
$531$	7.97471	+	9.20331i	0.346073	+	0.399390i
$532$		0			0
$533$	0.0549903	+	0.0734584i	0.00238189	+	0.00318184i
$534$		0			0
$535$	0.815642	+	16.0329i	0.0352633	+	0.693163i
$536$		0			0
$537$	−5.73127	−	1.24676i	−0.247323	−	0.0538017i
$538$		0			0
$539$	2.54146	−	0.746241i	0.109469	−	0.0321429i
$540$		0			0
$541$	−2.30711	+	2.66255i	−0.0991904	+	0.114472i	−0.803174	−	0.595744i	$-0.796857\pi$
$541$	−2.30711	+	2.66255i	−0.0991904	+	0.114472i	0.703984	+	0.710216i	$0.251403\pi$
$542$		0			0
$543$	3.21002	−	8.60640i	0.137755	−	0.369336i
$544$		0			0
$545$	15.5057	+	35.8885i	0.664190	+	1.53729i
$546$		0			0
$547$	19.9787	−	7.45166i	0.854226	−	0.318610i	0.116071	−	0.993241i	$-0.462970\pi$
$547$	19.9787	−	7.45166i	0.854226	−	0.318610i	0.738155	+	0.674631i	$0.235697\pi$
$548$		0			0
$549$	23.7891	+	15.2883i	1.01530	+	0.652491i
$550$		0			0
$551$			33.7236i			1.43667i
$552$		0			0
$553$	−10.5881	+	10.5881i	−0.450250	+	0.450250i
$554$		0			0
$555$	−3.89757	+	0.478783i	−0.165443	+	0.0203232i
$556$		0			0
$557$	−5.53160	−	14.8308i	−0.234382	−	0.628401i	0.765505	−	0.643429i	$-0.222489\pi$
$557$	−5.53160	−	14.8308i	−0.234382	−	0.628401i	−0.999887	+	0.0150280i	$0.995216\pi$
$558$		0			0
$559$	0.0126477	+	0.00371371i	0.000534942	+	0.000157073i
$560$		0			0
$561$	5.22667	+	11.4448i	0.220670	+	0.483200i
$562$		0			0
$563$	46.1805	−	3.30289i	1.94627	−	0.139200i	0.957482	−	0.288493i	$-0.0931543\pi$
$563$	46.1805	−	3.30289i	1.94627	−	0.139200i	0.988793	+	0.149293i	$0.0476997\pi$
$564$		0			0
$565$	−2.42488	−	12.3664i	−0.102015	−	0.520260i
$566$		0			0
$567$	−2.37782	+	10.9307i	−0.0998590	+	0.459044i
$568$		0			0
$569$	−1.80398	−	12.5470i	−0.0756269	−	0.525997i	−0.992056	−	0.125799i	$-0.959851\pi$
$569$	−1.80398	−	12.5470i	−0.0756269	−	0.525997i	0.916429	−	0.400198i	$-0.131059\pi$
$570$		0			0
$571$	13.2699	+	1.90793i	0.555329	+	0.0798442i	0.414265	−	0.910156i	$-0.364039\pi$
$571$	13.2699	+	1.90793i	0.555329	+	0.0798442i	0.141064	+	0.990001i	$0.454948\pi$
$572$		0			0
$573$	1.44196	−	20.1612i	0.0602387	−	0.842247i
$574$		0			0
$575$	23.9776	−	0.272280i	0.999936	−	0.0113549i
$576$		0			0
$577$	0.238572	−	3.33567i	0.00993187	−	0.138866i	−0.990067	−	0.140599i	$-0.955097\pi$
$577$	0.238572	−	3.33567i	0.00993187	−	0.138866i	0.999998	+	0.00173331i	$0.000551730\pi$
$578$		0			0
$579$	−11.2655	−	1.61973i	−0.468178	−	0.0673139i
$580$		0			0
$581$	−5.42833	−	37.7548i	−0.225205	−	1.56633i
$582$		0			0
$583$	1.03307	−	4.74894i	0.0427854	−	0.196681i
$584$		0			0
$585$	−0.0185529	−	0.0946165i	−0.000767069	−	0.00391191i
$586$		0			0
$587$	1.47821	−	0.105723i	0.0610122	−	0.00436368i	−0.0407997	−	0.999167i	$-0.512991\pi$
$587$	1.47821	−	0.105723i	0.0610122	−	0.00436368i	0.101812	+	0.994804i	$0.467536\pi$
$588$		0			0
$589$	1.58924	+	3.47996i	0.0654836	+	0.143389i
$590$		0			0
$591$	0.197875	+	0.0581014i	0.00813950	+	0.00238997i
$592$		0			0
$593$	7.43808	+	19.9423i	0.305445	+	0.818931i	0.995464	+	0.0951392i	$0.0303296\pi$
$593$	7.43808	+	19.9423i	0.305445	+	0.818931i	−0.690019	+	0.723792i	$0.742398\pi$
$594$		0			0
$595$	−39.9298	+	4.90503i	−1.63696	+	0.201087i
$596$		0			0
$597$	−5.89410	+	5.89410i	−0.241230	+	0.241230i
$598$		0			0
$599$			33.1106i			1.35286i	0.736505	+	0.676432i	$0.236475\pi$
$599$			33.1106i			1.35286i	−0.736505	+	0.676432i	$0.763525\pi$
$600$		0			0
$601$	−19.1692	−	12.3193i	−0.781929	−	0.502515i	0.0877444	−	0.996143i	$-0.472034\pi$
$601$	−19.1692	−	12.3193i	−0.781929	−	0.502515i	−0.869673	+	0.493628i	$0.835670\pi$
$602$		0			0
$603$	27.0908	−	10.1044i	1.10322	−	0.411481i
$604$		0			0
$605$	−3.96349	−	9.17365i	−0.161139	−	0.372962i
$606$		0			0
$607$	2.82060	−	7.56232i	0.114485	−	0.306945i	−0.867053	−	0.498217i	$-0.833988\pi$
$607$	2.82060	−	7.56232i	0.114485	−	0.306945i	0.981537	+	0.191272i	$0.0612612\pi$
$608$		0			0
$609$	−11.9664	+	13.8100i	−0.484904	+	0.559609i
$610$		0			0
$611$	0.0109406	−	0.00321245i	0.000442609	−	0.000129962i
$612$		0			0
$613$	−10.6570	−	2.31828i	−0.430431	−	0.0936345i	−0.00786983	−	0.999969i	$-0.502505\pi$
$613$	−10.6570	−	2.31828i	−0.430431	−	0.0936345i	−0.422561	+	0.906335i	$0.638869\pi$
$614$		0			0
$615$	−0.449786	−	8.84135i	−0.0181371	−	0.356517i
$616$		0			0
$617$	25.2327	+	33.7070i	1.01583	+	1.35699i	0.932780	+	0.360447i	$0.117376\pi$
$617$	25.2327	+	33.7070i	1.01583	+	1.35699i	0.0830518	+	0.996545i	$0.473533\pi$
$618$		0			0
$619$	−17.6346	−	20.3515i	−0.708796	−	0.817994i	0.281117	−	0.959674i	$-0.409295\pi$
$619$	−17.6346	−	20.3515i	−0.708796	−	0.817994i	−0.989913	+	0.141680i	$0.954750\pi$
$620$		0			0
$621$	−19.9295	+	2.48190i	−0.799744	+	0.0995954i
$622$		0			0
$623$	−3.89558	−	0.278617i	−0.156073	−	0.0111626i
$624$		0			0
$625$	12.2193	−	21.8103i	0.488772	−	0.872412i
$626$		0			0
$627$	−4.82189	+	6.44129i	−0.192568	+	0.257240i
$628$		0			0
$629$	−7.76739	−	12.0863i	−0.309706	−	0.481912i
$630$		0			0
$631$	−1.83219	−	6.23986i	−0.0729383	−	0.248405i	0.914951	−	0.403565i	$-0.132229\pi$
$631$	−1.83219	−	6.23986i	−0.0729383	−	0.248405i	−0.987889	+	0.155160i	$0.950411\pi$
$632$		0			0
$633$	−1.36470	−	19.0810i	−0.0542421	−	0.758403i
$634$		0			0
$635$	22.1432	−	7.74400i	0.878726	−	0.307311i
$636$		0			0
$637$	0.00893113	+	0.0163561i	0.000353864	+	0.000648054i
$638$		0			0
$639$	−10.2552	−	4.68340i	−0.405690	−	0.185272i
$640$		0			0
$641$	−15.1286	+	23.5405i	−0.597543	+	0.929795i	0.402355	+	0.915484i	$0.368192\pi$
$641$	−15.1286	+	23.5405i	−0.597543	+	0.929795i	−0.999898	+	0.0143112i	$0.995444\pi$
$642$		0			0
$643$	−7.51568	−	7.51568i	−0.296390	−	0.296390i	0.543208	−	0.839598i	$-0.317209\pi$
$643$	−7.51568	−	7.51568i	−0.296390	−	0.296390i	−0.839598	+	0.543208i	$0.817209\pi$
$644$		0			0
$645$	−0.812856	−	0.978031i	−0.0320062	−	0.0385099i
$646$		0			0
$647$	−6.46528	−	29.7204i	−0.254176	−	1.16843i	−0.910356	−	0.413825i	$-0.864192\pi$
$647$	−6.46528	−	29.7204i	−0.254176	−	1.16843i	0.656180	−	0.754604i	$-0.272171\pi$
$648$		0			0
$649$	5.39074	−	11.8041i	0.211605	−	0.463351i
$650$		0			0
$651$	−0.584018	+	1.98898i	−0.0228895	+	0.0779544i
$652$		0			0
$653$	12.4923	+	4.65938i	0.488860	+	0.182335i	0.581793	−	0.813337i	$-0.302351\pi$
$653$	12.4923	+	4.65938i	0.488860	+	0.182335i	−0.0929326	+	0.995672i	$0.529624\pi$
$654$		0			0
$655$	−17.9594	−	0.369488i	−0.701731	−	0.0144371i
$656$		0			0
$657$	3.36067	+	1.83507i	0.131112	+	0.0715928i
$658$		0			0
$659$	−0.949566	+	0.610249i	−0.0369899	+	0.0237719i	−0.559005	−	0.829164i	$-0.688817\pi$
$659$	−0.949566	+	0.610249i	−0.0369899	+	0.0237719i	0.522015	+	0.852936i	$0.325180\pi$
$660$		0			0
$661$	−43.8173	+	6.29998i	−1.70430	+	0.245041i	−0.924552	−	0.381057i	$-0.875560\pi$
$661$	−43.8173	+	6.29998i	−1.70430	+	0.245041i	−0.779745	+	0.626098i	$0.784651\pi$
$662$		0			0
$663$	−0.0708647	+	0.0530487i	−0.00275216	+	0.00206024i
$664$		0			0
$665$	−14.9909	−	20.9086i	−0.581323	−	0.810800i
$666$		0			0
$667$	37.0669	+	14.6292i	1.43524	+	0.566443i
$668$		0			0
$669$	6.94937	−	6.02166i	0.268678	−	0.232811i
$670$		0			0
$671$	4.28847	−	29.8269i	0.165554	−	1.15146i
$672$		0			0
$673$	−9.21201	−	6.89603i	−0.355097	−	0.265822i	0.406804	−	0.913515i	$-0.366643\pi$
$673$	−9.21201	−	6.89603i	−0.355097	−	0.265822i	−0.761901	+	0.647693i	$0.775734\pi$
$674$		0			0
$675$	−8.11795	+	19.3007i	−0.312460	+	0.742886i
$676$		0			0
$677$	−0.166120	+	0.304226i	−0.00638451	+	0.0116924i	−0.880852	−	0.473392i	$-0.843029\pi$
$677$	−0.166120	+	0.304226i	−0.00638451	+	0.0116924i	0.874467	+	0.485085i	$0.161211\pi$
$678$		0			0
$679$	−4.14101	−	3.58821i	−0.158918	−	0.137703i
$680$		0			0
$681$	3.98430	−	1.81957i	0.152679	−	0.0697261i
$682$		0			0
$683$	−25.1496	+	13.7327i	−0.962321	+	0.525467i	−0.881973	−	0.471300i	$-0.843785\pi$
$683$	−25.1496	+	13.7327i	−0.962321	+	0.525467i	−0.0803481	+	0.996767i	$0.525603\pi$
$684$		0			0
$685$	−5.42814	+	9.47232i	−0.207398	+	0.361919i
$686$		0			0
$687$	11.8481	−	2.57739i	0.452032	−	0.0983335i
$688$		0			0
$689$	0.0341933			0.00130266
$690$		0			0
$691$	−24.1962			−0.920468			−0.460234	−	0.887798i	$-0.652235\pi$
$691$	−24.1962			−0.920468			−0.460234	+	0.887798i	$0.652235\pi$
$692$		0			0
$693$	16.9771	−	3.69314i	0.644907	−	0.140291i
$694$		0			0
$695$	−4.37418	−	16.1163i	−0.165922	−	0.611326i
$696$		0			0
$697$	28.4273	−	15.5225i	1.07676	−	0.587956i
$698$		0			0
$699$	−18.8531	+	8.60993i	−0.713090	+	0.325658i
$700$		0			0
$701$	−37.7525	−	32.7127i	−1.42589	−	1.23554i	−0.930205	−	0.367041i	$-0.880371\pi$
$701$	−37.7525	−	32.7127i	−1.42589	−	1.23554i	−0.495687	−	0.868501i	$-0.665084\pi$
$702$		0			0
$703$	4.40325	−	8.06395i	0.166072	−	0.304138i
$704$		0			0
$705$	−1.04891	−	0.331571i	−0.0395043	−	0.0124877i
$706$		0			0
$707$	−11.0245	−	8.25286i	−0.414620	−	0.310381i
$708$		0			0
$709$	−2.02900	+	14.1120i	−0.0762006	+	0.529987i	0.915590	+	0.402114i	$0.131724\pi$
$709$	−2.02900	+	14.1120i	−0.0762006	+	0.529987i	−0.991790	+	0.127874i	$0.959185\pi$
$710$		0			0
$711$	−9.57331	+	8.29532i	−0.359027	+	0.311099i
$712$		0			0
$713$	4.51436	−	0.237205i	0.169064	−	0.00888341i
$714$		0			0
$715$	−0.0835006	+	0.0598678i	−0.00312274	+	0.00223893i
$716$		0			0
$717$	15.7901	−	11.8203i	0.589693	−	0.441439i
$718$		0			0
$719$	−44.7328	+	6.43160i	−1.66825	+	0.239858i	−0.910745	−	0.412969i	$-0.864492\pi$
$719$	−44.7328	+	6.43160i	−1.66825	+	0.239858i	−0.757506	+	0.652828i	$0.773583\pi$
$720$		0			0
$721$	9.74667	−	6.26381i	0.362985	−	0.233276i
$722$		0			0
$723$	8.92290	+	4.87227i	0.331846	+	0.181202i
$724$		0			0
$725$	32.4906	−	25.8923i	1.20667	−	0.961615i
$726$		0			0
$727$	−35.7506	−	13.3343i	−1.32592	−	0.494541i	−0.416012	−	0.909359i	$-0.636573\pi$
$727$	−35.7506	−	13.3343i	−1.32592	−	0.494541i	−0.909905	+	0.414818i	$0.863845\pi$
$728$		0			0
$729$	0.0796391	−	0.271226i	0.00294960	−	0.0100454i
$730$		0			0
$731$	1.93284	−	4.23232i	0.0714886	−	0.156538i
$732$		0			0
$733$	2.82113	+	12.9685i	0.104201	+	0.479003i	0.999441	+	0.0334201i	$0.0106399\pi$
$733$	2.82113	+	12.9685i	0.104201	+	0.479003i	−0.895241	+	0.445583i	$0.852996\pi$
$734$		0			0
$735$	0.165121	−	1.79031i	0.00609059	−	0.0660365i
$736$		0			0
$737$	−21.7867	−	21.7867i	−0.802523	−	0.802523i
$738$		0			0
$739$	13.6290	−	21.2071i	0.501351	−	0.780118i	−0.494684	−	0.869073i	$-0.664716\pi$
$739$	13.6290	−	21.2071i	0.501351	−	0.780118i	0.996036	+	0.0889550i	$0.0283527\pi$
$740$		0			0
$741$	−0.0514942	−	0.0235166i	−0.00189169	−	0.000863904i
$742$		0			0
$743$	24.0063	+	43.9642i	0.880705	+	1.61289i	0.786714	+	0.617317i	$0.211780\pi$
$743$	24.0063	+	43.9642i	0.880705	+	1.61289i	0.0939902	+	0.995573i	$0.470038\pi$
$744$		0			0
$745$	21.0455	−	43.6824i	0.771048	−	1.60040i
$746$		0			0
$747$	−2.30195	−	32.1855i	−0.0842241	−	1.17761i
$748$		0			0
$749$	−5.73401	−	19.5282i	−0.209516	−	0.713546i
$750$		0			0
$751$	−6.50729	−	10.1255i	−0.237454	−	0.369486i	0.701991	−	0.712186i	$-0.252295\pi$
$751$	−6.50729	−	10.1255i	−0.237454	−	0.369486i	−0.939445	+	0.342700i	$0.888658\pi$
$752$		0			0
$753$	5.56872	−	7.43894i	0.202936	−	0.271090i
$754$		0			0
$755$	−35.8093	+	21.9858i	−1.30323	+	0.800146i
$756$		0			0
$757$	19.0787	+	1.36453i	0.693426	+	0.0495948i	0.413604	−	0.910457i	$-0.364270\pi$
$757$	19.0787	+	1.36453i	0.693426	+	0.0495948i	0.279822	+	0.960052i	$0.409724\pi$
$758$		0			0
$759$	4.98815	+	8.09412i	0.181058	+	0.293798i
$760$		0			0
$761$	25.5334	+	29.4671i	0.925585	+	1.06818i	0.997493	+	0.0707709i	$0.0225459\pi$
$761$	25.5334	+	29.4671i	0.925585	+	1.06818i	−0.0719074	+	0.997411i	$0.522909\pi$
$762$		0			0
$763$	−29.7027	−	39.6781i	−1.07531	−	1.43644i
$764$		0			0
$765$	−33.9892	+	1.72913i	−1.22888	+	0.0625169i
$766$		0			0
$767$	0.0892133	+	0.0194072i	0.00322130	+	0.000700752i
$768$		0			0
$769$	−18.9473	+	5.56342i	−0.683255	+	0.200622i	−0.604897	−	0.796303i	$-0.706786\pi$
$769$	−18.9473	+	5.56342i	−0.683255	+	0.200622i	−0.0783580	+	0.996925i	$0.524968\pi$
$770$		0			0
$771$	−13.4012	+	15.4658i	−0.482632	+	0.556987i
$772$		0			0
$773$	−4.99372	+	13.3887i	−0.179612	+	0.481558i	−0.995289	−	0.0969491i	$-0.969092\pi$
$773$	−4.99372	+	13.3887i	−0.179612	+	0.481558i	0.815678	+	0.578507i	$0.196364\pi$
$774$		0			0
$775$	2.13254	−	4.20297i	0.0766030	−	0.150975i
$776$		0			0
$777$	4.66455	−	1.73979i	0.167340	−	0.0624145i
$778$		0			0
$779$	17.4250	+	11.1984i	0.624316	+	0.401223i
$780$		0			0
$781$			12.0138i			0.429886i
$782$		0			0
$783$	−24.6046	+	24.6046i	−0.879297	+	0.879297i
$784$		0			0
$785$	−6.90599	−	5.39493i	−0.246485	−	0.192553i
$786$		0			0
$787$	−11.9215	−	31.9629i	−0.424957	−	1.13935i	−0.956349	−	0.292228i	$-0.905603\pi$
$787$	−11.9215	−	31.9629i	−0.424957	−	1.13935i	0.531392	−	0.847126i	$-0.321669\pi$
$788$		0			0
$789$	−18.3974	−	5.40197i	−0.654966	−	0.192315i
$790$		0			0
$791$	6.63693	+	14.5328i	0.235982	+	0.516729i
$792$		0			0
$793$	0.211469	−	0.0151246i	0.00750949	−	0.000537090i
$794$		0			0
$795$	−2.73789	−	1.84020i	−0.0971031	−	0.0652651i
$796$		0			0
$797$	4.46603	−	20.5300i	0.158195	−	0.727209i	−0.827880	−	0.560906i	$-0.810453\pi$
$797$	4.46603	−	20.5300i	0.158195	−	0.727209i	0.986075	−	0.166304i	$-0.0531833\pi$
$798$		0			0
$799$	−0.572785	−	3.98381i	−0.0202637	−	0.140937i
$800$		0			0
$801$	−3.27031	−	0.470200i	−0.115551	−	0.0166137i
$802$		0			0
$803$	0.291085	−	4.06989i	0.0102722	−	0.143623i
$804$		0			0
$805$	−29.4844	+	7.40703i	−1.03919	+	0.261063i
$806$		0			0
$807$	0.524198	−	7.32925i	0.0184527	−	0.258002i
$808$		0			0
$809$	−41.2001	−	5.92368i	−1.44852	−	0.208265i	−0.627254	−	0.778815i	$-0.715821\pi$
$809$	−41.2001	−	5.92368i	−1.44852	−	0.208265i	−0.821263	+	0.570549i	$0.806730\pi$
$810$		0			0
$811$	0.694968	+	4.83361i	0.0244036	+	0.169731i	0.998378	−	0.0569254i	$-0.0181297\pi$
$811$	0.694968	+	4.83361i	0.0244036	+	0.169731i	−0.973975	+	0.226656i	$0.927221\pi$
$812$		0			0
$813$	3.75656	−	17.2686i	0.131748	−	0.605637i
$814$		0			0
$815$	−1.82679	+	0.358207i	−0.0639896	+	0.0125474i
$816$		0			0
$817$	2.96791	−	0.212269i	0.103834	−	0.00742636i
$818$		0			0
$819$	0.0507796	+	0.111192i	0.00177438	+	0.00388536i
$820$		0			0
$821$	14.5481	+	4.27172i	0.507734	+	0.149084i	0.525559	−	0.850757i	$-0.323856\pi$
$821$	14.5481	+	4.27172i	0.507734	+	0.149084i	−0.0178254	+	0.999841i	$0.505674\pi$
$822$		0			0
$823$	−0.579902	−	1.55478i	−0.0202141	−	0.0541961i	0.926451	−	0.376416i	$-0.122844\pi$
$823$	−0.579902	−	1.55478i	−0.0202141	−	0.0541961i	−0.946665	+	0.322220i	$0.895571\pi$
$824$		0			0
$825$	9.90793	−	0.299891i	0.344950	−	0.0104409i
$826$		0			0
$827$	27.1096	−	27.1096i	0.942694	−	0.942694i	−0.0557509	−	0.998445i	$-0.517755\pi$
$827$	27.1096	−	27.1096i	0.942694	−	0.942694i	0.998445	+	0.0557509i	$0.0177553\pi$
$828$		0			0
$829$			39.2468i			1.36310i	0.731772	+	0.681550i	$0.238694\pi$
$829$			39.2468i			1.36310i	−0.731772	+	0.681550i	$0.761306\pi$
$830$		0			0
$831$	4.68763	+	3.01256i	0.162612	+	0.104504i
$832$		0			0
$833$	6.16316	−	2.29874i	0.213541	−	0.0796467i
$834$		0			0
$835$	−12.8882	+	32.4970i	−0.446016	+	1.12461i
$836$		0			0
$837$	−1.37946	+	3.69847i	−0.0476810	+	0.127838i
$838$		0			0
$839$	−21.7643	+	25.1173i	−0.751387	+	0.867146i	−0.994702	−	0.102801i	$-0.967220\pi$
$839$	−21.7643	+	25.1173i	−0.751387	+	0.867146i	0.243315	+	0.969947i	$0.421765\pi$
$840$		0			0
$841$	38.4200	−	11.2811i	1.32483	−	0.389005i
$842$		0			0
$843$	−6.23672	−	1.35672i	−0.214804	−	0.0467277i
$844$		0			0
$845$	21.5721	+	19.4834i	0.742101	+	0.670251i
$846$		0			0
$847$	7.59247	+	10.1423i	0.260880	+	0.348495i
$848$		0			0
$849$	15.3343	+	17.6967i	0.526272	+	0.607350i
$850$		0			0
$851$	−6.95328	−	8.33789i	−0.238355	−	0.285819i
$852$		0			0
$853$	−41.8843	−	2.99562i	−1.43409	−	0.102568i	−0.667455	−	0.744650i	$-0.732616\pi$
$853$	−41.8843	−	2.99562i	−1.43409	−	0.102568i	−0.766636	+	0.642082i	$0.778071\pi$
$854$		0			0
$855$	−11.3877	−	18.5476i	−0.389450	−	0.634314i
$856$		0			0
$857$	21.4405	−	28.6412i	0.732394	−	0.978363i	−0.267497	−	0.963559i	$-0.586196\pi$
$857$	21.4405	−	28.6412i	0.732394	−	0.978363i	0.999890	−	0.0148046i	$-0.00471261\pi$
$858$		0			0
$859$	21.8153	+	33.9452i	0.744327	+	1.15820i	0.982371	+	0.186941i	$0.0598573\pi$
$859$	21.8153	+	33.9452i	0.744327	+	1.15820i	−0.238044	+	0.971254i	$0.576506\pi$
$860$		0			0
$861$	3.16202	+	10.7688i	0.107761	+	0.367001i
$862$		0			0
$863$	0.672448	+	9.40205i	0.0228904	+	0.320050i	0.995977	+	0.0896097i	$0.0285620\pi$
$863$	0.672448	+	9.40205i	0.0228904	+	0.320050i	−0.973087	+	0.230440i	$0.925983\pi$
$864$		0			0
$865$	−13.4581	−	38.4821i	−0.457590	−	1.30843i
$866$		0			0
$867$	8.65414	+	15.8489i	0.293910	+	0.538256i
$868$		0			0
$869$	12.2786	+	5.60747i	0.416524	+	0.190220i
$870$		0			0
$871$	0.117197	−	0.182363i	0.00397109	−	0.00617913i
$872$		0			0
$873$	−3.27768	−	3.27768i	−0.110933	−	0.110933i
$874$		0			0
$875$	−8.63442	+	30.4960i	−0.291897	+	1.03095i
$876$		0			0
$877$	8.77979	+	40.3601i	0.296473	+	1.36286i	0.848570	+	0.529083i	$0.177464\pi$
$877$	8.77979	+	40.3601i	0.296473	+	1.36286i	−0.552098	+	0.833779i	$0.686172\pi$
$878$		0			0
$879$	9.67721	−	21.1901i	0.326404	−	0.714726i
$880$		0			0
$881$	−2.32410	+	7.91517i	−0.0783010	+	0.266669i	−0.989334	−	0.145665i	$-0.953468\pi$
$881$	−2.32410	+	7.91517i	−0.0783010	+	0.266669i	0.911033	+	0.412333i	$0.135286\pi$
$882$		0			0
$883$	39.6365	+	14.7837i	1.33388	+	0.497510i	0.912389	−	0.409324i	$-0.134236\pi$
$883$	39.6365	+	14.7837i	1.33388	+	0.497510i	0.421487	+	0.906834i	$0.361508\pi$
$884$		0			0
$885$	−6.09897	−	6.35519i	−0.205015	−	0.213627i
$886$		0			0
$887$	2.75893	+	1.50649i	0.0926360	+	0.0505831i	0.524899	−	0.851164i	$-0.324103\pi$
$887$	2.75893	+	1.50649i	0.0926360	+	0.0505831i	−0.432263	+	0.901747i	$0.642285\pi$
$888$		0			0
$889$	−25.0190	+	16.0788i	−0.839112	+	0.539264i
$890$		0			0
$891$	9.98151	−	1.43512i	0.334393	−	0.0480785i
$892$		0			0
$893$	2.06049	−	1.54247i	0.0689518	−	0.0516166i
$894$		0			0
$895$	−16.6812	−	2.74973i	−0.557593	−	0.0919132i
$896$		0			0
$897$	−0.0481859	+	0.0463978i	−0.00160888	+	0.00154918i
$898$		0			0
$899$	5.91923	−	5.12904i	0.197417	−	0.171063i
$900$		0			0
$901$	1.71764	−	11.9465i	0.0572230	−	0.397995i
$902$		0			0
$903$	1.29070	+	0.966203i	0.0429517	+	0.0321532i
$904$		0			0
$905$	7.98032	−	25.2454i	0.265275	−	0.839186i
$906$		0			0
$907$	12.9945	−	23.7977i	0.431477	−	0.790191i	−0.567984	−	0.823040i	$-0.692276\pi$
$907$	12.9945	−	23.7977i	0.431477	−	0.790191i	0.999460	+	0.0328492i	$0.0104581\pi$
$908$		0			0
$909$	−8.80455	−	7.62918i	−0.292028	−	0.253044i
$910$		0			0
$911$	32.0694	−	14.6456i	1.06251	−	0.485231i	0.194048	−	0.980992i	$-0.437838\pi$
$911$	32.0694	−	14.6456i	1.06251	−	0.485231i	0.868459	+	0.495761i	$0.165111\pi$
$912$		0			0
$913$	−30.1790	+	16.4790i	−0.998779	+	0.545374i
$914$		0			0
$915$	−17.7466	−	10.1697i	−0.586683	−	0.336200i
$916$		0			0
$917$	22.2531	−	4.84086i	0.734862	−	0.159859i
$918$		0			0
$919$	−47.9912			−1.58308			−0.791542	−	0.611115i	$-0.790721\pi$
$919$	−47.9912			−1.58308			−0.791542	+	0.611115i	$0.790721\pi$
$920$		0			0
$921$	7.34202			0.241928
$922$		0			0
$923$	−0.0825928	+	0.0179670i	−0.00271858	+	0.000591390i
$924$		0			0
$925$	−11.1498	+	1.94907i	−0.366605	+	0.0640850i
$926$		0			0
$927$	8.60237	−	4.69725i	0.282539	−	0.154278i
$928$		0			0
$929$	−6.19544	+	2.82936i	−0.203266	+	0.0928283i	−0.514447	−	0.857522i	$-0.672003\pi$
$929$	−6.19544	+	2.82936i	−0.203266	+	0.0928283i	0.311181	+	0.950351i	$0.399275\pi$
$930$		0			0
$931$	3.17915	+	2.75475i	0.104193	+	0.0902833i
$932$		0			0
$933$	3.44603	−	6.31094i	0.112818	−	0.206611i
$934$		0			0
$935$	16.7221	+	32.1809i	0.546873	+	1.05243i
$936$		0			0
$937$	−33.7503	−	25.2652i	−1.10257	−	0.825377i	−0.116751	−	0.993161i	$-0.537248\pi$
$937$	−33.7503	−	25.2652i	−1.10257	−	0.825377i	−0.985824	+	0.167784i	$0.946339\pi$
$938$		0			0
$939$	−2.62244	+	18.2394i	−0.0855799	+	0.595222i
$940$		0			0
$941$	22.7967	−	19.7534i	0.743150	−	0.643944i	−0.198667	−	0.980067i	$-0.563661\pi$
$941$	22.7967	−	19.7534i	0.743150	−	0.643944i	0.941818	+	0.336123i	$0.109116\pi$
$942$		0			0
$943$	19.8675	−	14.2947i	0.646973	−	0.465499i
$944$		0			0
$945$	4.31750	−	26.1921i	0.140448	−	0.852030i
$946$		0			0
$947$	−27.6943	+	20.7317i	−0.899943	+	0.673689i	−0.945622	−	0.325267i	$-0.894546\pi$
$947$	−27.6943	+	20.7317i	−0.899943	+	0.673689i	0.0456788	+	0.998956i	$0.485455\pi$
$948$		0			0
$949$	0.0284152	−	0.00408549i	0.000922397	−	0.000132621i
$950$		0			0
$951$	−17.3226	+	11.1325i	−0.561723	+	0.360998i
$952$		0			0
$953$	36.0380	+	19.6782i	1.16739	+	0.637441i	0.941599	−	0.336736i	$-0.109323\pi$
$953$	36.0380	+	19.6782i	1.16739	+	0.637441i	0.225787	+	0.974177i	$0.427505\pi$
$954$		0			0
$955$	1.19840	−	58.2495i	0.0387792	−	1.88491i
$956$		0			0
$957$	15.4342	+	5.75667i	0.498917	+	0.186087i
$958$		0			0
$959$	3.89945	−	13.2803i	0.125920	−	0.428844i
$960$		0			0
$961$	−12.5088	+	27.3904i	−0.403509	+	0.883561i
$962$		0			0
$963$	−3.65988	−	16.8242i	−0.117938	−	0.542151i
$964$		0			0
$965$	−32.6673	−	3.01293i	−1.05160	−	0.0969896i
$966$		0			0
$967$	−26.5509	−	26.5509i	−0.853821	−	0.853821i	0.136781	−	0.990601i	$-0.456324\pi$
$967$	−26.5509	−	26.5509i	−0.853821	−	0.853821i	−0.990601	+	0.136781i	$0.956324\pi$
$968$		0			0
$969$	−10.8030	+	16.8098i	−0.347042	+	0.540007i
$970$		0			0
$971$	−17.1097	−	7.81374i	−0.549077	−	0.250755i	0.121505	−	0.992591i	$-0.461228\pi$
$971$	−17.1097	−	7.81374i	−0.549077	−	0.250755i	−0.670581	+	0.741836i	$0.733955\pi$
$972$		0			0
$973$	10.1463	+	18.5816i	0.325276	+	0.595698i
$974$		0			0
$975$	0.0168793	+	0.0676670i	0.000540571	+	0.00216708i
$976$		0			0
$977$	−1.73867	−	24.3098i	−0.0556250	−	0.777739i	−0.946339	−	0.323175i	$-0.895250\pi$
$977$	−1.73867	−	24.3098i	−0.0556250	−	0.777739i	0.890714	−	0.454564i	$-0.150205\pi$
$978$		0			0
$979$	0.991905	+	3.37812i	0.0317014	+	0.107965i
$980$		0			0
$981$	−22.6688	−	35.2734i	−0.723760	−	1.12619i
$982$		0			0
$983$	−8.08652	+	10.8023i	−0.257920	+	0.344541i	−0.910746	−	0.412967i	$-0.864492\pi$
$983$	−8.08652	+	10.8023i	−0.257920	+	0.344541i	0.652826	+	0.757508i	$0.273583\pi$
$984$		0			0
$985$	0.578134	+	0.138279i	0.0184209	+	0.00440592i
$986$		0			0
$987$	1.39111	+	0.0994939i	0.0442794	+	0.00316693i
$988$		0			0
$989$	1.05416	−	3.35422i	0.0335202	−	0.106658i
$990$		0			0
$991$	26.4391	+	30.5124i	0.839866	+	0.969257i	0.999840	−	0.0178640i	$-0.00568659\pi$
$991$	26.4391	+	30.5124i	0.839866	+	0.969257i	−0.159974	+	0.987121i	$0.551141\pi$
$992$		0			0
$993$	−6.94166	−	9.27298i	−0.220287	−	0.294269i
$994$		0			0
$995$	−16.1042	+	17.8306i	−0.510538	+	0.565268i
$996$		0			0
$997$	27.6265	+	6.00977i	0.874939	+	0.190331i	0.627542	−	0.778583i	$-0.284061\pi$
$997$	27.6265	+	6.00977i	0.874939	+	0.190331i	0.247397	+	0.968914i	$0.420425\pi$
$998$		0			0
$999$	9.09603	−	2.67083i	0.287786	−	0.0845015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.22	yes	720
5.3	odd	4	inner	920.2.bv.a.33.22	✓	720
23.7	odd	22	inner	920.2.bv.a.697.22	yes	720
115.53	even	44	inner	920.2.bv.a.513.22	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.22	✓	720	5.3	odd	4	inner
920.2.bv.a.217.22	yes	720	1.1	even	1	trivial
920.2.bv.a.513.22	yes	720	115.53	even	44	inner
920.2.bv.a.697.22	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)

\(f(q)\)	\(=\)	\(q+(0.758029 - 0.164899i) q^{3} +(2.15800 - 0.585709i) q^{5} +(-2.48810 + 1.35861i) q^{7} +(-2.18148 + 0.996249i) q^{9} +O(q^{10})\)	\(q+(0.758029 - 0.164899i) q^{3} +(2.15800 - 0.585709i) q^{5} +(-2.48810 + 1.35861i) q^{7} +(-2.18148 + 0.996249i) q^{9} +(1.93136 + 1.67353i) q^{11} +(-0.00861689 + 0.0157806i) q^{13} +(1.53924 - 0.799836i) q^{15} +(5.08060 + 3.80329i) q^{17} +(-0.577600 + 4.01730i) q^{19} +(-1.66202 + 1.44015i) q^{21} +(4.16500 + 2.37755i) q^{23} +(4.31389 - 2.52791i) q^{25} +(-3.35242 + 2.50959i) q^{27} +(8.22458 - 1.18252i) q^{29} +(0.792972 - 0.509612i) q^{31} +(1.73999 + 0.950108i) q^{33} +(-4.57357 + 4.38917i) q^{35} +(-2.12105 - 0.791112i) q^{37} +(-0.00392963 + 0.0133831i) q^{39} +(2.12007 - 4.64231i) q^{41} +(-0.155838 - 0.716377i) q^{43} +(-4.12411 + 3.42761i) q^{45} +(-0.448430 - 0.448430i) q^{47} +(0.560357 - 0.871933i) q^{49} +(4.47840 + 2.04522i) q^{51} +(-0.911407 - 1.66912i) q^{53} +(5.14808 + 2.48026i) q^{55} +(0.224611 + 3.14047i) q^{57} +(-1.43060 - 4.87217i) q^{59} +(-6.37492 - 9.91957i) q^{61} +(4.07424 - 5.44254i) q^{63} +(-0.00935234 + 0.0391016i) q^{65} +(-12.0258 - 0.860099i) q^{67} +(3.54925 + 1.11545i) q^{69} +(3.07852 + 3.55280i) q^{71} +(-0.956827 - 1.27817i) q^{73} +(2.85320 - 2.62759i) q^{75} +(-7.07910 - 1.53996i) q^{77} +(5.06805 - 1.48811i) q^{79} +(2.58406 - 2.98216i) q^{81} +(-4.70203 + 12.6066i) q^{83} +(13.1915 + 5.23173i) q^{85} +(6.03947 - 2.25261i) q^{87} +(1.15897 + 0.744828i) q^{89} -0.0509708i q^{91} +(0.517061 - 0.517061i) q^{93} +(1.10651 + 9.00762i) q^{95} +(0.675459 + 1.81098i) q^{97} +(-5.88048 - 1.72667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 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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