LMFDB - Embedded newform 920.2.bv.a.217.23

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			217.23
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.848778 - 0.184640i) q^{3} +(-1.60020 - 1.56185i) q^{5} +(-0.374263 + 0.204363i) q^{7} +(-2.04256 + 0.932808i) q^{9} +O(q^{10})$	\(q+(0.848778 - 0.184640i) q^{3} +(-1.60020 - 1.56185i) q^{5} +(-0.374263 + 0.204363i) q^{7} +(-2.04256 + 0.932808i) q^{9} +(-2.23938 - 1.94043i) q^{11} +(-0.424711 + 0.777801i) q^{13} +(-1.64659 - 1.03020i) q^{15} +(1.07483 + 0.804606i) q^{17} +(-0.658927 + 4.58294i) q^{19} +(-0.279933 + 0.242563i) q^{21} +(-4.18454 - 2.34300i) q^{23} +(0.121279 + 4.99853i) q^{25} +(-3.64757 + 2.73054i) q^{27} +(-5.23183 + 0.752224i) q^{29} +(-3.96340 + 2.54712i) q^{31} +(-2.25902 - 1.23352i) q^{33} +(0.918079 + 0.257519i) q^{35} +(-4.91396 - 1.83281i) q^{37} +(-0.216872 + 0.738599i) q^{39} +(4.09008 - 8.95602i) q^{41} +(0.0259205 + 0.119154i) q^{43} +(4.72541 + 1.69749i) q^{45} +(6.05896 + 6.05896i) q^{47} +(-3.68618 + 5.73580i) q^{49} +(1.06085 + 0.484475i) q^{51} +(-3.21544 - 5.88865i) q^{53} +(0.552798 + 6.60265i) q^{55} +(0.286913 + 4.01156i) q^{57} +(0.934221 + 3.18166i) q^{59} +(-3.18389 - 4.95423i) q^{61} +(0.573825 - 0.766540i) q^{63} +(1.89443 - 0.581303i) q^{65} +(-8.31468 - 0.594678i) q^{67} +(-3.98436 - 1.21605i) q^{69} +(0.788913 + 0.910454i) q^{71} +(-4.30365 - 5.74900i) q^{73} +(1.02587 + 4.22025i) q^{75} +(1.23467 + 0.268586i) q^{77} +(15.6226 - 4.58721i) q^{79} +(1.81963 - 2.09996i) q^{81} +(-3.58818 + 9.62029i) q^{83} +(-0.463269 - 2.96624i) q^{85} +(-4.30177 + 1.60448i) q^{87} +(-5.80133 - 3.72829i) q^{89} -0.377898i q^{91} +(-2.89374 + 2.89374i) q^{93} +(8.21226 - 6.30448i) q^{95} +(4.07796 + 10.9334i) q^{97} +(6.38413 + 1.87455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.848778	−	0.184640i	0.490042	−	0.106602i	0.0392470	−	0.999230i	$-0.487504\pi$
$3$	0.848778	−	0.184640i	0.490042	−	0.106602i	0.450795	+	0.892627i	$0.351140\pi$
$4$		0			0
$5$	−1.60020	−	1.56185i	−0.715631	−	0.698478i
$5$	−1.60020	−	1.56185i	−0.715631	−	0.698478i
$6$		0			0
$7$	−0.374263	+	0.204363i	−0.141458	+	0.0772420i	−0.548419	−	0.836203i	$-0.684770\pi$
$7$	−0.374263	+	0.204363i	−0.141458	+	0.0772420i	0.406961	+	0.913445i	$0.366588\pi$
$8$		0			0
$9$	−2.04256	+	0.932808i	−0.680855	+	0.310936i
$10$		0			0
$11$	−2.23938	−	1.94043i	−0.675199	−	0.585063i	0.248291	−	0.968685i	$-0.420131\pi$
$11$	−2.23938	−	1.94043i	−0.675199	−	0.585063i	−0.923490	+	0.383623i	$0.874676\pi$
$12$		0			0
$13$	−0.424711	+	0.777801i	−0.117794	+	0.215723i	−0.929923	−	0.367755i	$-0.880127\pi$
$13$	−0.424711	+	0.777801i	−0.117794	+	0.215723i	0.812129	+	0.583478i	$0.198308\pi$
$14$		0			0
$15$	−1.64659	−	1.03020i	−0.425149	−	0.265996i
$16$		0			0
$17$	1.07483	+	0.804606i	0.260684	+	0.195146i	0.721623	−	0.692286i	$-0.243396\pi$
$17$	1.07483	+	0.804606i	0.260684	+	0.195146i	−0.460939	+	0.887432i	$0.652487\pi$
$18$		0			0
$19$	−0.658927	+	4.58294i	−0.151168	+	1.05140i	0.763097	+	0.646283i	$0.223678\pi$
$19$	−0.658927	+	4.58294i	−0.151168	+	1.05140i	−0.914266	+	0.405115i	$0.867231\pi$
$20$		0			0
$21$	−0.279933	+	0.242563i	−0.0610863	+	0.0529316i
$22$		0			0
$23$	−4.18454	−	2.34300i	−0.872536	−	0.488549i
$23$	−4.18454	−	2.34300i	−0.872536	−	0.488549i
$24$		0			0
$25$	0.121279	+	4.99853i	0.0242557	+	0.999706i
$26$		0			0
$27$	−3.64757	+	2.73054i	−0.701975	+	0.525492i
$28$		0			0
$29$	−5.23183	+	0.752224i	−0.971527	+	0.139684i	−0.609762	−	0.792585i	$-0.708735\pi$
$29$	−5.23183	+	0.752224i	−0.971527	+	0.139684i	−0.361765	+	0.932269i	$0.617826\pi$
$30$		0			0
$31$	−3.96340	+	2.54712i	−0.711847	+	0.457476i	−0.845792	−	0.533512i	$-0.820872\pi$
$31$	−3.96340	+	2.54712i	−0.711847	+	0.457476i	0.133945	+	0.990989i	$0.457235\pi$
$32$		0			0
$33$	−2.25902	−	1.23352i	−0.393245	−	0.214728i
$34$		0			0
$35$	0.918079	+	0.257519i	0.155184	+	0.0435287i
$36$		0			0
$37$	−4.91396	−	1.83281i	−0.807850	−	0.301312i	−0.0886028	−	0.996067i	$-0.528240\pi$
$37$	−4.91396	−	1.83281i	−0.807850	−	0.301312i	−0.719247	+	0.694755i	$0.755513\pi$
$38$		0			0
$39$	−0.216872	+	0.738599i	−0.0347274	+	0.118271i
$40$		0			0
$41$	4.09008	−	8.95602i	0.638763	−	1.39870i	−0.262291	−	0.964989i	$-0.584478\pi$
$41$	4.09008	−	8.95602i	0.638763	−	1.39870i	0.901054	−	0.433707i	$-0.142795\pi$
$42$		0			0
$43$	0.0259205	+	0.119154i	0.00395283	+	0.0181709i	0.979081	−	0.203471i	$-0.0652222\pi$
$43$	0.0259205	+	0.119154i	0.00395283	+	0.0181709i	−0.975128	+	0.221642i	$0.928859\pi$
$44$		0			0
$45$	4.72541	+	1.69749i	0.704423	+	0.253047i
$46$		0			0
$47$	6.05896	+	6.05896i	0.883790	+	0.883790i	0.993918	−	0.110127i	$-0.0351258\pi$
$47$	6.05896	+	6.05896i	0.883790	+	0.883790i	−0.110127	+	0.993918i	$0.535126\pi$
$48$		0			0
$49$	−3.68618	+	5.73580i	−0.526597	+	0.819401i
$50$		0			0
$51$	1.06085	+	0.484475i	0.148549	+	0.0678401i
$52$		0			0
$53$	−3.21544	−	5.88865i	−0.441675	−	0.808868i	0.558106	−	0.829769i	$-0.311528\pi$
$53$	−3.21544	−	5.88865i	−0.441675	−	0.808868i	−0.999782	+	0.0209018i	$0.993346\pi$
$54$		0			0
$55$	0.552798	+	6.60265i	0.0745393	+	0.890301i
$56$		0			0
$57$	0.286913	+	4.01156i	0.0380025	+	0.531345i
$58$		0			0
$59$	0.934221	+	3.18166i	0.121625	+	0.414217i	0.997687	−	0.0679823i	$-0.0216561\pi$
$59$	0.934221	+	3.18166i	0.121625	+	0.414217i	−0.876061	+	0.482200i	$0.839838\pi$
$60$		0			0
$61$	−3.18389	−	4.95423i	−0.407656	−	0.634324i	0.575348	−	0.817908i	$-0.304866\pi$
$61$	−3.18389	−	4.95423i	−0.407656	−	0.634324i	−0.983004	+	0.183584i	$0.941230\pi$
$62$		0			0
$63$	0.573825	−	0.766540i	0.0722951	−	0.0965750i
$64$		0			0
$65$	1.89443	−	0.581303i	0.234975	−	0.0721018i
$66$		0			0
$67$	−8.31468	−	0.594678i	−1.01580	−	0.0726515i	−0.446502	−	0.894783i	$-0.647330\pi$
$67$	−8.31468	−	0.594678i	−1.01580	−	0.0726515i	−0.569298	+	0.822131i	$0.692785\pi$
$68$		0			0
$69$	−3.98436	−	1.21605i	−0.479660	−	0.146396i
$70$		0			0
$71$	0.788913	+	0.910454i	0.0936268	+	0.108051i	0.800629	−	0.599160i	$-0.204499\pi$
$71$	0.788913	+	0.910454i	0.0936268	+	0.108051i	−0.707003	+	0.707211i	$0.749953\pi$
$72$		0			0
$73$	−4.30365	−	5.74900i	−0.503704	−	0.672869i	0.474563	−	0.880222i	$-0.342606\pi$
$73$	−4.30365	−	5.74900i	−0.503704	−	0.672869i	−0.978266	+	0.207352i	$0.933515\pi$
$74$		0			0
$75$	1.02587	+	4.22025i	0.118457	+	0.487312i
$76$		0			0
$77$	1.23467	+	0.268586i	0.140704	+	0.0306082i
$78$		0			0
$79$	15.6226	−	4.58721i	1.75768	−	0.516102i	0.765778	−	0.643105i	$-0.222354\pi$
$79$	15.6226	−	4.58721i	1.75768	−	0.516102i	0.991902	+	0.127003i	$0.0405358\pi$
$80$		0			0
$81$	1.81963	−	2.09996i	0.202181	−	0.233329i
$82$		0			0
$83$	−3.58818	+	9.62029i	−0.393854	+	1.05596i	0.577095	+	0.816677i	$0.304186\pi$
$83$	−3.58818	+	9.62029i	−0.393854	+	1.05596i	−0.970949	+	0.239287i	$0.923086\pi$
$84$		0			0
$85$	−0.463269	−	2.96624i	−0.0502486	−	0.321734i
$86$		0			0
$87$	−4.30177	+	1.60448i	−0.461198	+	0.172018i
$88$		0			0
$89$	−5.80133	−	3.72829i	−0.614940	−	0.395198i	0.195767	−	0.980651i	$-0.437281\pi$
$89$	−5.80133	−	3.72829i	−0.614940	−	0.395198i	−0.810707	+	0.585452i	$0.800917\pi$
$90$		0			0
$91$		−	0.377898i		−	0.0396144i
$92$		0			0
$93$	−2.89374	+	2.89374i	−0.300067	+	0.300067i
$94$		0			0
$95$	8.21226	−	6.30448i	0.842560	−	0.646826i
$96$		0			0
$97$	4.07796	+	10.9334i	0.414054	+	1.11012i	0.961866	+	0.273521i	$0.0881883\pi$
$97$	4.07796	+	10.9334i	0.414054	+	1.11012i	−0.547812	+	0.836602i	$0.684539\pi$
$98$		0			0
$99$	6.38413	+	1.87455i	0.641629	+	0.188399i
$100$		0			0
$101$	−5.75139	−	12.5938i	−0.572285	−	1.25313i	−0.945572	−	0.325413i	$-0.894497\pi$
$101$	−5.75139	−	12.5938i	−0.572285	−	1.25313i	0.373287	−	0.927716i	$-0.378231\pi$
$102$		0			0
$103$	2.79543	−	0.199933i	0.275442	−	0.0197000i	0.0670650	−	0.997749i	$-0.478637\pi$
$103$	2.79543	−	0.199933i	0.275442	−	0.0197000i	0.208377	+	0.978049i	$0.433182\pi$
$104$		0			0
$105$	0.826794	+	0.0490622i	0.0806869	+	0.00478798i
$106$		0			0
$107$	1.31798	−	6.05866i	0.127414	−	0.585713i	−0.868522	−	0.495651i	$-0.834930\pi$
$107$	1.31798	−	6.05866i	0.127414	−	0.585713i	0.995936	−	0.0900625i	$-0.0287067\pi$
$108$		0			0
$109$	−2.35878	−	16.4057i	−0.225930	−	1.57138i	−0.714994	−	0.699130i	$-0.753571\pi$
$109$	−2.35878	−	16.4057i	−0.225930	−	1.57138i	0.489064	−	0.872248i	$-0.337338\pi$
$110$		0			0
$111$	−4.50927	−	0.648335i	−0.428001	−	0.0615373i
$112$		0			0
$113$	−0.240075	+	3.35668i	−0.0225843	+	0.315770i	0.973585	+	0.228325i	$0.0733249\pi$
$113$	−0.240075	+	3.35668i	−0.0225843	+	0.315770i	−0.996169	+	0.0874454i	$0.972130\pi$
$114$		0			0
$115$	3.03669	+	10.2849i	0.283173	+	0.959069i
$116$		0			0
$117$	0.141962	−	1.98488i	0.0131243	−	0.183502i
$118$		0			0
$119$	−0.566700	−	0.0814792i	−0.0519493	−	0.00746919i
$120$		0			0
$121$	−0.315924	−	2.19730i	−0.0287203	−	0.199754i
$122$		0			0
$123$	1.81793	−	8.35687i	0.163917	−	0.753514i
$124$		0			0
$125$	7.61286	−	8.18806i	0.680915	−	0.732363i
$126$		0			0
$127$	−13.9286	+	0.996190i	−1.23596	+	0.0883976i	−0.673978	−	0.738752i	$-0.735416\pi$
$127$	−13.9286	+	0.996190i	−1.23596	+	0.0883976i	−0.561982	+	0.827149i	$0.689961\pi$
$128$		0			0
$129$	0.0440014	+	0.0963497i	0.00387411	+	0.00848312i
$130$		0			0
$131$	7.22847	+	2.12247i	0.631554	+	0.185441i	0.581815	−	0.813321i	$-0.302343\pi$
$131$	7.22847	+	2.12247i	0.631554	+	0.185441i	0.0497394	+	0.998762i	$0.484161\pi$
$132$		0			0
$133$	−0.689972	−	1.84989i	−0.0598281	−	0.160405i
$134$		0			0
$135$	10.1015	+	1.32754i	0.869400	+	0.114256i
$136$		0			0
$137$	0.309372	−	0.309372i	0.0264315	−	0.0264315i	−0.693768	−	0.720199i	$-0.744050\pi$
$137$	0.309372	−	0.309372i	0.0264315	−	0.0264315i	0.720199	+	0.693768i	$0.244050\pi$
$138$		0			0
$139$			8.70245i			0.738132i	0.929403	+	0.369066i	$0.120322\pi$
$139$			8.70245i			0.738132i	−0.929403	+	0.369066i	$0.879678\pi$
$140$		0			0
$141$	6.26144	+	4.02398i	0.527309	+	0.338881i
$142$		0			0
$143$	2.46036	−	0.917667i	0.205746	−	0.0767392i
$144$		0			0
$145$	9.54683	+	6.96760i	0.792821	+	0.578628i
$146$		0			0
$147$	−2.06969	+	5.54904i	−0.170705	+	0.457677i
$148$		0			0
$149$	5.79555	−	6.68842i	0.474790	−	0.547937i	−0.466948	−	0.884285i	$-0.654646\pi$
$149$	5.79555	−	6.68842i	0.474790	−	0.547937i	0.941738	+	0.336348i	$0.109192\pi$
$150$		0			0
$151$	−14.5175	+	4.26274i	−1.18142	+	0.346897i	−0.812722	−	0.582652i	$-0.802015\pi$
$151$	−14.5175	+	4.26274i	−1.18142	+	0.346897i	−0.368699	+	0.929549i	$0.620197\pi$
$152$		0			0
$153$	−2.94595	−	0.640851i	−0.238166	−	0.0518098i
$154$		0			0
$155$	10.3204	+	2.11431i	0.828957	+	0.169826i
$156$		0			0
$157$	0.694195	+	0.927336i	0.0554028	+	0.0740095i	0.827387	−	0.561632i	$-0.189826\pi$
$157$	0.694195	+	0.927336i	0.0554028	+	0.0740095i	−0.771984	+	0.635642i	$0.780736\pi$
$158$		0			0
$159$	−3.81648	−	4.40445i	−0.302667	−	0.349296i
$160$		0			0
$161$	2.04494	+	0.0217335i	0.161164	+	0.00171284i
$162$		0			0
$163$	−11.5148	−	0.823555i	−0.901909	−	0.0645058i	−0.387322	−	0.921944i	$-0.626600\pi$
$163$	−11.5148	−	0.823555i	−0.901909	−	0.0645058i	−0.514586	+	0.857439i	$0.672054\pi$
$164$		0			0
$165$	1.68832	+	5.50211i	0.131435	+	0.428339i
$166$		0			0
$167$	−7.60958	+	10.1652i	−0.588847	+	0.786608i	−0.991689	−	0.128662i	$-0.958932\pi$
$167$	−7.60958	+	10.1652i	−0.588847	+	0.786608i	0.402841	+	0.915270i	$0.368023\pi$
$168$		0			0
$169$	6.60374	+	10.2756i	0.507980	+	0.790432i
$170$		0			0
$171$	−2.92910	−	9.97560i	−0.223994	−	0.762853i
$172$		0			0
$173$	−0.210802	−	2.94740i	−0.0160270	−	0.224086i	−0.999153	−	0.0411555i	$-0.986896\pi$
$173$	−0.210802	−	2.94740i	−0.0160270	−	0.224086i	0.983126	−	0.182931i	$-0.0585585\pi$
$174$		0			0
$175$	−1.06691	−	1.84598i	−0.0806505	−	0.139543i
$176$		0			0
$177$	1.38041	+	2.52803i	0.103758	+	0.190019i
$178$		0			0
$179$	19.1275	+	8.73522i	1.42965	+	0.652901i	0.971731	−	0.236090i	$-0.0758661\pi$
$179$	19.1275	+	8.73522i	1.42965	+	0.652901i	0.457923	+	0.888992i	$0.348593\pi$
$180$		0			0
$181$	8.35847	−	13.0060i	0.621280	−	0.966731i	−0.377884	−	0.925853i	$-0.623348\pi$
$181$	8.35847	−	13.0060i	0.621280	−	0.966731i	0.999164	−	0.0408776i	$-0.0130154\pi$
$182$		0			0
$183$	−3.61717	−	3.61717i	−0.267389	−	0.267389i
$184$		0			0
$185$	5.00075	+	10.6077i	0.367662	+	0.779894i
$186$		0			0
$187$	−0.845663	−	3.88745i	−0.0618410	−	0.284279i
$188$		0			0
$189$	0.807130	−	1.76737i	0.0587101	−	0.128557i
$190$		0			0
$191$	3.41068	−	11.6157i	0.246788	−	0.840484i	−0.739174	−	0.673515i	$-0.764784\pi$
$191$	3.41068	−	11.6157i	0.246788	−	0.840484i	0.985962	−	0.166969i	$-0.0533981\pi$
$192$		0			0
$193$	15.9777	+	5.95939i	1.15010	+	0.428966i	0.850954	−	0.525240i	$-0.176024\pi$
$193$	15.9777	+	5.95939i	1.15010	+	0.428966i	0.299149	+	0.954206i	$0.403297\pi$
$194$		0			0
$195$	1.50062	−	0.843185i	0.107461	−	0.0603818i
$196$		0			0
$197$	−17.3887	−	9.49494i	−1.23889	−	0.676486i	−0.279930	−	0.960020i	$-0.590311\pi$
$197$	−17.3887	−	9.49494i	−1.23889	−	0.676486i	−0.958962	+	0.283534i	$0.908493\pi$
$198$		0			0
$199$	3.02488	−	1.94397i	0.214428	−	0.137805i	−0.429018	−	0.903296i	$-0.641140\pi$
$199$	3.02488	−	1.94397i	0.214428	−	0.137805i	0.643446	+	0.765491i	$0.277504\pi$
$200$		0			0
$201$	−7.16712	+	1.03048i	−0.505530	+	0.0726842i
$202$		0			0
$203$	1.80435	−	1.35072i	0.126641	−	0.0948022i
$204$		0			0
$205$	−20.5329	+	7.94336i	−1.43408	+	0.554788i
$206$		0			0
$207$	10.7328	+	0.882359i	0.745978	+	0.0613282i
$208$		0			0
$209$	10.3685	−	8.98434i	0.717203	−	0.621460i
$210$		0			0
$211$	−3.50880	+	24.4042i	−0.241556	+	1.68006i	0.402767	+	0.915303i	$0.368049\pi$
$211$	−3.50880	+	24.4042i	−0.241556	+	1.68006i	−0.644323	+	0.764754i	$0.722861\pi$
$212$		0			0
$213$	0.837719	+	0.627109i	0.0573996	+	0.0429688i
$214$		0			0
$215$	0.144623	−	0.231155i	0.00986320	−	0.0157646i
$216$		0			0
$217$	0.962816	−	1.76327i	0.0653602	−	0.119698i
$218$		0			0
$219$	−4.71434	−	4.08500i	−0.318565	−	0.276039i
$220$		0			0
$221$	−1.08231	+	0.494277i	−0.0728044	+	0.0332486i
$222$		0			0
$223$	5.24291	−	2.86285i	0.351091	−	0.191710i	−0.294019	−	0.955799i	$-0.594993\pi$
$223$	5.24291	−	2.86285i	0.351091	−	0.191710i	0.645111	+	0.764089i	$0.276811\pi$
$224$		0			0
$225$	−4.91038	−	10.0967i	−0.327359	−	0.673112i
$226$		0			0
$227$	6.97487	−	1.51729i	0.462939	−	0.100706i	0.0249540	−	0.999689i	$-0.492056\pi$
$227$	6.97487	−	1.51729i	0.462939	−	0.100706i	0.437985	+	0.898982i	$0.355692\pi$
$228$		0			0
$229$	17.9480			1.18604			0.593019	−	0.805189i	$-0.297936\pi$
$229$	17.9480			1.18604			0.593019	+	0.805189i	$0.297936\pi$
$230$		0			0
$231$	1.09755			0.0722137
$232$		0			0
$233$	1.24796	−	0.271477i	0.0817566	−	0.0177851i	−0.171501	−	0.985184i	$-0.554862\pi$
$233$	1.24796	−	0.271477i	0.0817566	−	0.0177851i	0.253258	+	0.967399i	$0.418498\pi$
$234$		0			0
$235$	−0.232388	−	19.1587i	−0.0151593	−	1.24978i
$236$		0			0
$237$	12.4131	−	6.77809i	0.806320	−	0.440284i
$238$		0			0
$239$	2.88535	−	1.31769i	0.186638	−	0.0852346i	−0.319904	−	0.947450i	$-0.603651\pi$
$239$	2.88535	−	1.31769i	0.186638	−	0.0852346i	0.506542	+	0.862215i	$0.330924\pi$
$240$		0			0
$241$	0.426459	+	0.369529i	0.0274707	+	0.0238035i	0.668488	−	0.743723i	$-0.266942\pi$
$241$	0.426459	+	0.369529i	0.0274707	+	0.0238035i	−0.641017	+	0.767526i	$0.721487\pi$
$242$		0			0
$243$	7.70764	−	14.1155i	0.494446	−	0.905509i
$244$		0			0
$245$	14.8571	−	3.42119i	0.949183	−	0.218572i
$246$		0			0
$247$	−3.28476	−	2.45894i	−0.209004	−	0.156459i
$248$		0			0
$249$	−1.26928	+	8.82801i	−0.0804371	+	0.559453i
$250$		0			0
$251$	5.85602	−	5.07427i	0.369629	−	0.320285i	−0.450164	−	0.892946i	$-0.648634\pi$
$251$	5.85602	−	5.07427i	0.369629	−	0.320285i	0.819792	+	0.572661i	$0.194089\pi$
$252$		0			0
$253$	4.82433	+	13.3667i	0.303303	+	0.840356i
$254$		0			0
$255$	−0.940901	−	2.43215i	−0.0589215	−	0.152307i
$256$		0			0
$257$	−24.8960	+	18.6369i	−1.55297	+	1.16254i	−0.630683	+	0.776040i	$0.717225\pi$
$257$	−24.8960	+	18.6369i	−1.55297	+	1.16254i	−0.922289	+	0.386500i	$0.873684\pi$
$258$		0			0
$259$	2.21367	−	0.318278i	0.137551	−	0.0197768i
$260$		0			0
$261$	9.98467	−	6.41676i	0.618035	−	0.397187i
$262$		0			0
$263$	4.07378	+	2.22445i	0.251200	+	0.137166i	0.599916	−	0.800063i	$-0.295200\pi$
$263$	4.07378	+	2.22445i	0.251200	+	0.137166i	−0.348716	+	0.937228i	$0.613382\pi$
$264$		0			0
$265$	−4.05180	+	14.4450i	−0.248900	+	0.887351i
$266$		0			0
$267$	−5.61244	−	2.09333i	−0.343476	−	0.128110i
$268$		0			0
$269$	4.65400	−	15.8501i	0.283759	−	0.966396i	−0.687063	−	0.726598i	$-0.741100\pi$
$269$	4.65400	−	15.8501i	0.283759	−	0.966396i	0.970823	−	0.239798i	$-0.0770813\pi$
$270$		0			0
$271$	−1.35624	+	2.96975i	−0.0823857	+	0.180399i	−0.946342	−	0.323168i	$-0.895252\pi$
$271$	−1.35624	+	2.96975i	−0.0823857	+	0.180399i	0.863956	+	0.503567i	$0.167979\pi$
$272$		0			0
$273$	−0.0697752	−	0.320751i	−0.00422298	−	0.0194127i
$274$		0			0
$275$	9.42773	−	11.4289i	0.568513	−	0.689191i
$276$		0			0
$277$	15.2461	+	15.2461i	0.916047	+	0.916047i	0.996739	−	0.0806920i	$-0.0257130\pi$
$277$	15.2461	+	15.2461i	0.916047	+	0.916047i	−0.0806920	+	0.996739i	$0.525713\pi$
$278$		0			0
$279$	5.71952	−	8.89974i	0.342419	−	0.532814i
$280$		0			0
$281$	−2.51229	−	1.14733i	−0.149871	−	0.0684437i	0.339068	−	0.940762i	$-0.389888\pi$
$281$	−2.51229	−	1.14733i	−0.149871	−	0.0684437i	−0.488938	+	0.872318i	$0.662616\pi$
$282$		0			0
$283$	−8.87826	−	16.2593i	−0.527758	−	0.966516i	−0.996533	−	0.0831986i	$-0.973486\pi$
$283$	−8.87826	−	16.2593i	−0.527758	−	0.966516i	0.468775	−	0.883317i	$-0.344695\pi$
$284$		0			0
$285$	5.80632	−	6.86742i	0.343937	−	0.406791i
$286$		0			0
$287$	0.299515	+	4.18777i	0.0176798	+	0.247196i
$288$		0			0
$289$	−4.28159	−	14.5818i	−0.251858	−	0.857750i
$290$		0			0
$291$	5.48004	+	8.52711i	0.321246	+	0.499868i
$292$		0			0
$293$	−1.19685	+	1.59880i	−0.0699206	+	0.0934030i	−0.834138	−	0.551556i	$-0.814034\pi$
$293$	−1.19685	+	1.59880i	−0.0699206	+	0.0934030i	0.764218	+	0.644959i	$0.223125\pi$
$294$		0			0
$295$	3.47433	−	6.55041i	0.202283	−	0.381379i
$296$		0			0
$297$	13.4667	+	0.963159i	0.781418	+	0.0558881i
$298$		0			0
$299$	3.59961	−	2.25964i	0.208171	−	0.130678i
$300$		0			0
$301$	−0.0340519	−	0.0392979i	−0.00196272	−	0.00226510i
$302$		0			0
$303$	−7.20698	−	9.62740i	−0.414030	−	0.553080i
$304$		0			0
$305$	−2.64288	+	12.9005i	−0.151331	+	0.738681i
$306$		0			0
$307$	−17.0706	−	3.71348i	−0.974270	−	0.211939i	−0.302868	−	0.953033i	$-0.597944\pi$
$307$	−17.0706	−	3.71348i	−0.974270	−	0.211939i	−0.671402	+	0.741093i	$0.734308\pi$
$308$		0			0
$309$	2.33578	−	0.685848i	0.132878	−	0.0390165i
$310$		0			0
$311$	7.25865	−	8.37692i	0.411600	−	0.475012i	−0.511660	−	0.859188i	$-0.670969\pi$
$311$	7.25865	−	8.37692i	0.411600	−	0.475012i	0.923260	+	0.384176i	$0.125515\pi$
$312$		0			0
$313$	3.67415	−	9.85079i	0.207675	−	0.556799i	−0.790795	−	0.612081i	$-0.790333\pi$
$313$	3.67415	−	9.85079i	0.207675	−	0.556799i	0.998471	+	0.0552813i	$0.0176055\pi$
$314$		0			0
$315$	−2.11545	+	0.330392i	−0.119192	+	0.0186155i
$316$		0			0
$317$	−2.14621	+	0.800496i	−0.120543	+	0.0449603i	−0.409012	−	0.912529i	$-0.634127\pi$
$317$	−2.14621	+	0.800496i	−0.120543	+	0.0449603i	0.288469	+	0.957489i	$0.406854\pi$
$318$		0			0
$319$	13.1757	+	8.46751i	0.737697	+	0.474089i
$320$		0			0
$321$		−	5.38581i		−	0.300607i
$322$		0			0
$323$	−4.39569	+	4.39569i	−0.244583	+	0.244583i
$324$		0			0
$325$	−3.93937	−	2.02860i	−0.218517	−	0.112527i
$326$		0			0
$327$	−5.03123	−	13.4892i	−0.278228	−	0.745957i
$328$		0			0
$329$	−3.50587	−	1.02942i	−0.193285	−	0.0567536i
$330$		0			0
$331$	−8.95459	−	19.6078i	−0.492189	−	1.07774i	−0.978930	−	0.204197i	$-0.934542\pi$
$331$	−8.95459	−	19.6078i	−0.492189	−	1.07774i	0.486741	−	0.873546i	$-0.338186\pi$
$332$		0			0
$333$	11.7467	−	0.840143i	0.643717	−	0.0460395i
$334$		0			0
$335$	12.3764	+	13.9379i	0.676193	+	0.761506i
$336$		0			0
$337$	−6.70940	+	30.8426i	−0.365485	+	1.68011i	0.316384	+	0.948631i	$0.397531\pi$
$337$	−6.70940	+	30.8426i	−0.365485	+	1.68011i	−0.681869	+	0.731474i	$0.738833\pi$
$338$		0			0
$339$	0.416009	+	2.89341i	0.0225945	+	0.157148i
$340$		0			0
$341$	13.8181	+	1.98674i	0.748291	+	0.107588i
$342$		0			0
$343$	0.420359	−	5.87738i	0.0226972	−	0.317349i
$344$		0			0
$345$	4.47648	+	8.16888i	0.241006	+	0.439797i
$346$		0			0
$347$	−1.34083	+	18.7473i	−0.0719797	+	1.00641i	0.825228	+	0.564800i	$0.191047\pi$
$347$	−1.34083	+	18.7473i	−0.0719797	+	1.00641i	−0.897208	+	0.441608i	$0.854408\pi$
$348$		0			0
$349$	−21.8941	−	3.14790i	−1.17197	−	0.168503i	−0.471287	−	0.881980i	$-0.656210\pi$
$349$	−21.8941	−	3.14790i	−1.17197	−	0.168503i	−0.700679	+	0.713477i	$0.747119\pi$
$350$		0			0
$351$	−0.574649	−	3.99677i	−0.0306725	−	0.213332i
$352$		0			0
$353$	−5.60689	+	25.7744i	−0.298424	+	1.37184i	0.546728	+	0.837310i	$0.315873\pi$
$353$	−5.60689	+	25.7744i	−0.298424	+	1.37184i	−0.845153	+	0.534525i	$0.820491\pi$
$354$		0			0
$355$	0.159570	−	2.68907i	0.00846910	−	0.142721i
$356$		0			0
$357$	−0.496047	+	0.0354780i	−0.0262536	+	0.00187769i
$358$		0			0
$359$	8.61076	+	18.8549i	0.454459	+	0.995126i	0.988716	+	0.149804i	$0.0478641\pi$
$359$	8.61076	+	18.8549i	0.454459	+	0.995126i	−0.534257	+	0.845322i	$0.679409\pi$
$360$		0			0
$361$	−2.33878	−	0.686728i	−0.123094	−	0.0361436i
$362$		0			0
$363$	−0.673859	−	1.80669i	−0.0353684	−	0.0948264i
$364$		0			0
$365$	−2.09235	+	15.9212i	−0.109519	+	0.833352i
$366$		0			0
$367$	−16.7111	+	16.7111i	−0.872315	+	0.872315i	−0.992724	−	0.120409i	$-0.961579\pi$
$367$	−16.7111	+	16.7111i	−0.872315	+	0.872315i	0.120409	+	0.992724i	$0.461579\pi$
$368$		0			0
$369$			22.1085i			1.15092i
$370$		0			0
$371$	2.40684	+	1.54678i	0.124957	+	0.0803051i
$372$		0			0
$373$	−30.6065	+	11.4156i	−1.58474	+	0.591079i	−0.978870	−	0.204482i	$-0.934449\pi$
$373$	−30.6065	+	11.4156i	−1.58474	+	0.591079i	−0.605874	+	0.795561i	$0.707176\pi$
$374$		0			0
$375$	4.94978	−	8.35549i	0.255606	−	0.431476i
$376$		0			0
$377$	1.63694	−	4.38880i	0.0843066	−	0.226035i
$378$		0			0
$379$	−1.29170	+	1.49070i	−0.0663502	+	0.0765722i	−0.787954	−	0.615734i	$-0.788860\pi$
$379$	−1.29170	+	1.49070i	−0.0663502	+	0.0765722i	0.721604	+	0.692306i	$0.243405\pi$
$380$		0			0
$381$	−11.6383	+	3.41732i	−0.596249	+	0.175075i
$382$		0			0
$383$	−16.4670	−	3.58218i	−0.841425	−	0.183041i	−0.228858	−	0.973460i	$-0.573499\pi$
$383$	−16.4670	−	3.58218i	−0.841425	−	0.183041i	−0.612567	+	0.790419i	$0.709863\pi$
$384$		0			0
$385$	−1.55623	−	2.35816i	−0.0793128	−	0.120183i
$386$		0			0
$387$	−0.164092	−	0.219202i	−0.00834128	−	0.0111427i
$388$		0			0
$389$	−15.7098	−	18.1301i	−0.796519	−	0.919232i	0.201666	−	0.979454i	$-0.435364\pi$
$389$	−15.7098	−	18.1301i	−0.796519	−	0.919232i	−0.998185	+	0.0602227i	$0.980819\pi$
$390$		0			0
$391$	−2.61246	−	5.88522i	−0.132118	−	0.297629i
$392$		0			0
$393$	6.52726	+	0.466839i	0.329257	+	0.0235489i
$394$		0			0
$395$	−32.1638	−	17.0596i	−1.61834	−	0.858364i
$396$		0			0
$397$	−6.80402	+	9.08911i	−0.341484	+	0.456169i	−0.938104	−	0.346355i	$-0.887419\pi$
$397$	−6.80402	+	9.08911i	−0.341484	+	0.456169i	0.596619	+	0.802524i	$0.296510\pi$
$398$		0			0
$399$	−0.927197	−	1.44275i	−0.0464179	−	0.0722276i
$400$		0			0
$401$	−5.69914	−	19.4095i	−0.284601	−	0.969263i	−0.970406	−	0.241478i	$-0.922368\pi$
$401$	−5.69914	−	19.4095i	−0.284601	−	0.969263i	0.685805	−	0.727785i	$-0.259450\pi$
$402$		0			0
$403$	−0.297853	−	4.16452i	−0.0148371	−	0.207450i
$404$		0			0
$405$	−6.19158	+	0.518382i	−0.307662	+	0.0257586i
$406$		0			0
$407$	7.44777	+	13.6396i	0.369172	+	0.676088i
$408$		0			0
$409$	−2.11924	−	0.967826i	−0.104790	−	0.0478559i	0.362330	−	0.932050i	$-0.381981\pi$
$409$	−2.11924	−	0.967826i	−0.104790	−	0.0478559i	−0.467120	+	0.884194i	$0.654708\pi$
$410$		0			0
$411$	0.205466	−	0.319711i	0.0101349	−	0.0157702i
$412$		0			0
$413$	−0.999860	−	0.999860i	−0.0491999	−	0.0491999i
$414$		0			0
$415$	20.7672	−	9.79020i	1.01942	−	0.480582i
$416$		0			0
$417$	1.60682	+	7.38645i	0.0786865	+	0.361716i
$418$		0			0
$419$	3.47117	−	7.60079i	0.169578	−	0.371323i	−0.805694	−	0.592331i	$-0.798208\pi$
$419$	3.47117	−	7.60079i	0.169578	−	0.371323i	0.975272	+	0.221009i	$0.0709349\pi$
$420$		0			0
$421$	−8.65380	+	29.4721i	−0.421761	+	1.43638i	0.425380	+	0.905015i	$0.360141\pi$
$421$	−8.65380	+	29.4721i	−0.421761	+	1.43638i	−0.847140	+	0.531369i	$0.821678\pi$
$422$		0			0
$423$	−18.0277	−	6.72397i	−0.876535	−	0.326931i
$424$		0			0
$425$	−3.89149	+	5.47014i	−0.188765	+	0.265341i
$426$		0			0
$427$	2.20408	+	1.20352i	0.106663	+	0.0582422i
$428$		0			0
$429$	1.91886	−	1.23318i	0.0926436	−	0.0595384i
$430$		0			0
$431$	−8.23872	+	1.18455i	−0.396845	+	0.0570577i	−0.337849	−	0.941200i	$-0.609699\pi$
$431$	−8.23872	+	1.18455i	−0.396845	+	0.0570577i	−0.0589966	+	0.998258i	$0.518790\pi$
$432$		0			0
$433$	−7.48979	+	5.60678i	−0.359936	+	0.269445i	−0.763906	−	0.645327i	$-0.776721\pi$
$433$	−7.48979	+	5.60678i	−0.359936	+	0.269445i	0.403970	+	0.914772i	$0.367630\pi$
$434$		0			0
$435$	9.38964	+	4.15122i	0.450199	+	0.199036i
$436$		0			0
$437$	13.4951	−	17.6336i	0.645560	−	0.843530i
$438$		0			0
$439$	−16.6881	+	14.4603i	−0.796480	+	0.690154i	−0.954805	−	0.297233i	$-0.903936\pi$
$439$	−16.6881	+	14.4603i	−0.796480	+	0.690154i	0.158325	+	0.987387i	$0.449391\pi$
$440$		0			0
$441$	2.17885	−	15.1542i	0.103755	−	0.721630i
$442$		0			0
$443$	−14.3103	−	10.7126i	−0.679904	−	0.508970i	0.202608	−	0.979260i	$-0.435058\pi$
$443$	−14.3103	−	10.7126i	−0.679904	−	0.508970i	−0.882512	+	0.470290i	$0.844149\pi$
$444$		0			0
$445$	3.46028	+	15.0268i	0.164033	+	0.712339i
$446$		0			0
$447$	3.68418	−	6.74708i	0.174256	−	0.319126i
$448$		0			0
$449$	−11.0790	−	9.60003i	−0.522851	−	0.453053i	0.353008	−	0.935620i	$-0.385159\pi$
$449$	−11.0790	−	9.60003i	−0.522851	−	0.453053i	−0.875859	+	0.482567i	$0.839704\pi$
$450$		0			0
$451$	−26.5378	+	12.1194i	−1.24962	+	0.570681i
$452$		0			0
$453$	−11.5351	+	6.29864i	−0.541966	+	0.295936i
$454$		0			0
$455$	−0.590218	+	0.604712i	−0.0276698	+	0.0283493i
$456$		0			0
$457$	4.44992	−	0.968022i	0.208159	−	0.0452821i	−0.107277	−	0.994229i	$-0.534213\pi$
$457$	4.44992	−	0.968022i	0.208159	−	0.0452821i	0.315435	+	0.948947i	$0.397849\pi$
$458$		0			0
$459$	−6.11751			−0.285541
$460$		0			0
$461$	11.5566			0.538245			0.269122	−	0.963106i	$-0.413266\pi$
$461$	11.5566			0.538245			0.269122	+	0.963106i	$0.413266\pi$
$462$		0			0
$463$	−16.1466	+	3.51249i	−0.750398	+	0.163239i	−0.571470	−	0.820623i	$-0.693627\pi$
$463$	−16.1466	+	3.51249i	−0.750398	+	0.163239i	−0.178928	+	0.983862i	$0.557263\pi$
$464$		0			0
$465$	9.15015	−	0.110988i	0.424328	−	0.00514695i
$466$		0			0
$467$	−0.115918	+	0.0632960i	−0.00536404	+	0.00292899i	−0.481929	−	0.876210i	$-0.660064\pi$
$467$	−0.115918	+	0.0632960i	−0.00536404	+	0.00292899i	0.476565	+	0.879139i	$0.341882\pi$
$468$		0			0
$469$	3.23341	−	1.47665i	0.149305	−	0.0681853i
$470$		0			0
$471$	0.760441	+	0.658926i	0.0350393	+	0.0303617i
$472$		0			0
$473$	0.173166	−	0.317129i	0.00796216	−	0.0145816i
$474$		0			0
$475$	−22.9879	−	2.73785i	−1.05476	−	0.125621i
$476$		0			0
$477$	12.0607	+	9.02854i	0.552222	+	0.413389i
$478$		0			0
$479$	−2.50837	+	17.4461i	−0.114610	+	0.797131i	0.848726	+	0.528833i	$0.177370\pi$
$479$	−2.50837	+	17.4461i	−0.114610	+	0.797131i	−0.963336	+	0.268298i	$0.913539\pi$
$480$		0			0
$481$	3.51258	−	3.04366i	0.160160	−	0.138779i
$482$		0			0
$483$	1.73971	−	0.359132i	0.0791597	−	0.0163411i
$484$		0			0
$485$	10.5508	−	23.8648i	0.479087	−	1.08365i
$486$		0			0
$487$	−24.0327	+	17.9906i	−1.08903	+	0.815234i	−0.983810	−	0.179215i	$-0.942644\pi$
$487$	−24.0327	+	17.9906i	−1.08903	+	0.815234i	−0.105215	+	0.994449i	$0.533553\pi$
$488$		0			0
$489$	−9.92557	+	1.42708i	−0.448850	+	0.0645349i
$490$		0			0
$491$	16.9810	−	10.9130i	0.766341	−	0.492497i	−0.0981341	−	0.995173i	$-0.531287\pi$
$491$	16.9810	−	10.9130i	0.766341	−	0.492497i	0.864475	+	0.502676i	$0.167651\pi$
$492$		0			0
$493$	−6.22856	−	3.40105i	−0.280520	−	0.153176i
$494$		0			0
$495$	−7.28812	−	12.9707i	−0.327577	−	0.582988i
$496$		0			0
$497$	−0.481325	−	0.179525i	−0.0215904	−	0.00805279i
$498$		0			0
$499$	1.13434	−	3.86322i	0.0507802	−	0.172942i	−0.930198	−	0.367057i	$-0.880365\pi$
$499$	1.13434	−	3.86322i	0.0507802	−	0.172942i	0.980979	+	0.194115i	$0.0621836\pi$
$500$		0			0
$501$	−4.58194	+	10.0330i	−0.204706	+	0.448244i
$502$		0			0
$503$	2.30475	+	10.5948i	0.102764	+	0.472397i	0.999552	+	0.0299367i	$0.00953056\pi$
$503$	2.30475	+	10.5948i	0.102764	+	0.472397i	−0.896788	+	0.442460i	$0.854106\pi$
$504$		0			0
$505$	−10.4662	+	29.1354i	−0.465739	+	1.29651i
$506$		0			0
$507$	7.50240	+	7.50240i	0.333193	+	0.333193i
$508$		0			0
$509$	−19.6948	+	30.6456i	−0.872954	+	1.35834i	0.0599431	+	0.998202i	$0.480908\pi$
$509$	−19.6948	+	30.6456i	−0.872954	+	1.35834i	−0.932898	+	0.360142i	$0.882728\pi$
$510$		0			0
$511$	2.78558	+	1.27213i	0.123227	+	0.0562758i
$512$		0			0
$513$	−10.1104	−	18.5158i	−0.446385	−	0.817493i
$514$		0			0
$515$	−4.78551	−	4.04609i	−0.210875	−	0.178292i
$516$		0			0
$517$	−1.81130	−	25.3253i	−0.0796610	−	1.11381i
$518$		0			0
$519$	−0.723133	−	2.46276i	−0.0317420	−	0.108103i
$520$		0			0
$521$	16.2142	+	25.2298i	0.710358	+	1.10534i	0.989422	+	0.145066i	$0.0463393\pi$
$521$	16.2142	+	25.2298i	0.710358	+	1.10534i	−0.279064	+	0.960272i	$0.590024\pi$
$522$		0			0
$523$	6.38733	−	8.53247i	0.279298	−	0.373099i	−0.638853	−	0.769329i	$-0.720591\pi$
$523$	6.38733	−	8.53247i	0.279298	−	0.373099i	0.918151	+	0.396230i	$0.129682\pi$
$524$		0			0
$525$	−1.24641	−	1.36983i	−0.0543977	−	0.0597845i
$526$		0			0
$527$	−6.30940	−	0.451257i	−0.274842	−	0.0196571i
$528$		0			0
$529$	12.0207	+	19.6087i	0.522639	+	0.852554i
$530$		0			0
$531$	−4.87609	−	5.62730i	−0.211604	−	0.244204i
$532$		0			0
$533$	5.22890	+	6.98499i	0.226489	+	0.302554i
$534$		0			0
$535$	−11.5717	+	7.63659i	−0.500289	+	0.330159i
$536$		0			0
$537$	17.8479	+	3.88256i	0.770192	+	0.167545i
$538$		0			0
$539$	19.3847	−	5.69186i	0.834958	−	0.245166i
$540$		0			0
$541$	−10.0822	+	11.6355i	−0.433469	+	0.500249i	−0.929893	−	0.367831i	$-0.880101\pi$
$541$	−10.0822	+	11.6355i	−0.433469	+	0.500249i	0.496424	+	0.868080i	$0.334646\pi$
$542$		0			0
$543$	4.69305	−	12.5825i	0.201398	−	0.539969i
$544$		0			0
$545$	−21.8486	+	29.9364i	−0.935891	+	1.28233i
$546$		0			0
$547$	−9.81852	+	3.66212i	−0.419810	+	0.156581i	−0.550486	−	0.834844i	$-0.685558\pi$
$547$	−9.81852	+	3.66212i	−0.419810	+	0.156581i	0.130677	+	0.991425i	$0.458285\pi$
$548$		0			0
$549$	11.1246	+	7.14938i	0.474788	+	0.305128i
$550$		0			0
$551$		−	24.4728i		−	1.04258i
$552$		0			0
$553$	−4.90951	+	4.90951i	−0.208774	+	0.208774i
$554$		0			0
$555$	6.20313	+	8.08025i	0.263308	+	0.342987i
$556$		0			0
$557$	−15.1007	−	40.4865i	−0.639836	−	1.71547i	−0.696970	−	0.717100i	$-0.745469\pi$
$557$	−15.1007	−	40.4865i	−0.639836	−	1.71547i	0.0571338	−	0.998367i	$-0.481804\pi$
$558$		0			0
$559$	−0.103687	−	0.0304453i	−0.00438550	−	0.00128770i
$560$		0			0
$561$	−1.43556	−	3.14344i	−0.0606094	−	0.132716i
$562$		0			0
$563$	−3.90953	+	0.279615i	−0.164767	+	0.0117844i	−0.153479	−	0.988152i	$-0.549048\pi$
$563$	−3.90953	+	0.279615i	−0.164767	+	0.0117844i	−0.0112881	+	0.999936i	$0.503593\pi$
$564$		0			0
$565$	5.62679	−	4.99641i	0.236721	−	0.210200i
$566$		0			0
$567$	−0.251865	+	1.15780i	−0.0105773	+	0.0486231i
$568$		0			0
$569$	−4.75285	−	33.0568i	−0.199250	−	1.38581i	−0.806468	−	0.591277i	$-0.798624\pi$
$569$	−4.75285	−	33.0568i	−0.199250	−	1.38581i	0.607219	−	0.794535i	$-0.292285\pi$
$570$		0			0
$571$	30.3232	+	4.35981i	1.26898	+	0.182452i	0.743723	−	0.668488i	$-0.233058\pi$
$571$	30.3232	+	4.35981i	1.26898	+	0.182452i	0.525262	+	0.850941i	$0.323967\pi$
$572$		0			0
$573$	0.750183	−	10.4889i	0.0313393	−	0.438181i
$574$		0			0
$575$	11.2041	−	21.2007i	0.467242	−	0.884130i
$576$		0			0
$577$	1.80082	−	25.1788i	0.0749692	−	1.04821i	−0.811177	−	0.584800i	$-0.801173\pi$
$577$	1.80082	−	25.1788i	0.0749692	−	1.04821i	0.886146	−	0.463405i	$-0.153373\pi$
$578$		0			0
$579$	14.6619	+	2.10806i	0.609328	+	0.0876082i
$580$		0			0
$581$	−0.623108	−	4.33381i	−0.0258509	−	0.179797i
$582$		0			0
$583$	−4.22593	+	19.4263i	−0.175020	+	0.804554i
$584$		0			0
$585$	−3.32725	+	2.95449i	−0.137565	+	0.122153i
$586$		0			0
$587$	−47.3228	+	3.38459i	−1.95322	+	0.139697i	−0.991117	−	0.132990i	$-0.957542\pi$
$587$	−47.3228	+	3.38459i	−1.95322	+	0.139697i	−0.962103	+	0.272687i	$0.912088\pi$
$588$		0			0
$589$	−9.06171	−	19.8424i	−0.373381	−	0.817591i
$590$		0			0
$591$	−16.5123	−	4.84844i	−0.679225	−	0.199438i
$592$		0			0
$593$	−2.32208	−	6.22575i	−0.0953566	−	0.255661i	0.880510	−	0.474027i	$-0.157200\pi$
$593$	−2.32208	−	6.22575i	−0.0953566	−	0.255661i	−0.975867	+	0.218366i	$0.929927\pi$
$594$		0			0
$595$	0.779576	+	1.01548i	0.0319595	+	0.0416307i
$596$		0			0
$597$	2.20852	−	2.20852i	0.0903886	−	0.0903886i
$598$		0			0
$599$			2.55272i			0.104301i	0.998639	+	0.0521507i	$0.0166076\pi$
$599$			2.55272i			0.104301i	−0.998639	+	0.0521507i	$0.983392\pi$
$600$		0			0
$601$	4.54821	+	2.92296i	0.185525	+	0.119230i	0.630107	−	0.776509i	$-0.283011\pi$
$601$	4.54821	+	2.92296i	0.185525	+	0.119230i	−0.444581	+	0.895738i	$0.646648\pi$
$602$		0			0
$603$	17.5380	−	6.54133i	0.714202	−	0.266384i
$604$		0			0
$605$	−2.92630	+	4.00954i	−0.118971	+	0.163011i
$606$		0			0
$607$	10.2340	−	27.4383i	0.415384	−	1.11369i	−0.545833	−	0.837894i	$-0.683787\pi$
$607$	10.2340	−	27.4383i	0.415384	−	1.11369i	0.961217	−	0.275794i	$-0.0889407\pi$
$608$		0			0
$609$	1.28210	−	1.47962i	0.0519533	−	0.0599573i
$610$		0			0
$611$	−7.28597	+	2.13936i	−0.294759	+	0.0865491i
$612$		0			0
$613$	3.46566	+	0.753908i	0.139977	+	0.0304500i	0.282008	−	0.959412i	$-0.409000\pi$
$613$	3.46566	+	0.753908i	0.139977	+	0.0304500i	−0.142031	+	0.989862i	$0.545363\pi$
$614$		0			0
$615$	−15.9612	+	10.5333i	−0.643617	+	0.424745i
$616$		0			0
$617$	22.6767	+	30.2925i	0.912930	+	1.21953i	0.975167	+	0.221470i	$0.0710854\pi$
$617$	22.6767	+	30.2925i	0.912930	+	1.21953i	−0.0622377	+	0.998061i	$0.519824\pi$
$618$		0			0
$619$	−17.8321	−	20.5793i	−0.716731	−	0.827152i	0.274179	−	0.961679i	$-0.411594\pi$
$619$	−17.8321	−	20.5793i	−0.716731	−	0.827152i	−0.990910	+	0.134527i	$0.957048\pi$
$620$		0			0
$621$	21.6610	−	2.87977i	0.869228	−	0.115561i
$622$		0			0
$623$	2.93315	+	0.209783i	0.117514	+	0.00840478i
$624$		0			0
$625$	−24.9706	+	1.21243i	−0.998823	+	0.0484972i
$626$		0			0
$627$	7.14167	−	9.54015i	0.285211	−	0.380997i
$628$		0			0
$629$	−3.80697	−	5.92376i	−0.151794	−	0.236196i
$630$		0			0
$631$	4.00284	+	13.6324i	0.159351	+	0.542698i	0.999999	+	0.00111752i	$0.000355717\pi$
$631$	4.00284	+	13.6324i	0.159351	+	0.542698i	−0.840649	+	0.541581i	$0.817826\pi$
$632$		0			0
$633$	1.52781	+	21.3616i	0.0607252	+	0.849049i
$634$		0			0
$635$	23.8444	+	20.1602i	0.946235	+	0.800031i
$636$		0			0
$637$	−2.89575	−	5.30317i	−0.114734	−	0.210119i
$638$		0			0
$639$	−2.46068	−	1.12376i	−0.0973432	−	0.0444551i
$640$		0			0
$641$	−1.65540	+	2.57585i	−0.0653843	+	0.101740i	−0.872406	−	0.488781i	$-0.837442\pi$
$641$	−1.65540	+	2.57585i	−0.0653843	+	0.101740i	0.807022	+	0.590521i	$0.201078\pi$
$642$		0			0
$643$	24.0255	+	24.0255i	0.947471	+	0.947471i	0.998688	−	0.0512162i	$-0.0163098\pi$
$643$	24.0255	+	24.0255i	0.947471	+	0.947471i	−0.0512162	+	0.998688i	$0.516310\pi$
$644$		0			0
$645$	0.0800723	−	0.222902i	0.00315284	−	0.00877677i
$646$		0			0
$647$	−1.99314	−	9.16230i	−0.0783582	−	0.360207i	0.921226	−	0.389027i	$-0.127189\pi$
$647$	−1.99314	−	9.16230i	−0.0783582	−	0.360207i	−0.999585	+	0.0288199i	$0.990825\pi$
$648$		0			0
$649$	4.08173	−	8.93775i	0.160222	−	0.350837i
$650$		0			0
$651$	0.491647	−	1.67440i	0.0192692	−	0.0656248i
$652$		0			0
$653$	−4.21435	−	1.57187i	−0.164920	−	0.0615121i	0.265648	−	0.964070i	$-0.414414\pi$
$653$	−4.21435	−	1.57187i	−0.164920	−	0.0615121i	−0.430568	+	0.902558i	$0.641687\pi$
$654$		0			0
$655$	−8.25203	−	14.6861i	−0.322433	−	0.573835i
$656$		0			0
$657$	14.1532	+	7.72822i	0.552168	+	0.301507i
$658$		0			0
$659$	−34.6554	+	22.2717i	−1.34998	+	0.867581i	−0.997665	−	0.0682992i	$-0.978243\pi$
$659$	−34.6554	+	22.2717i	−1.34998	+	0.867581i	−0.352318	+	0.935880i	$0.614606\pi$
$660$		0			0
$661$	−5.65503	+	0.813071i	−0.219955	+	0.0316248i	−0.251411	−	0.967880i	$-0.580895\pi$
$661$	−5.65503	+	0.813071i	−0.219955	+	0.0316248i	0.0314561	+	0.999505i	$0.489986\pi$
$662$		0			0
$663$	−0.827382	+	0.619370i	−0.0321328	+	0.0240543i
$664$		0			0
$665$	−1.78514	+	4.03782i	−0.0692249	+	0.156580i
$666$		0			0
$667$	23.6553	+	9.11047i	0.915935	+	0.352759i
$668$		0			0
$669$	3.92147	−	3.39797i	0.151613	−	0.131373i
$670$		0			0
$671$	−2.48342	+	17.2725i	−0.0958712	+	0.666799i
$672$		0			0
$673$	34.3396	+	25.7063i	1.32369	+	0.990904i	0.998983	+	0.0450907i	$0.0143577\pi$
$673$	34.3396	+	25.7063i	1.32369	+	0.990904i	0.324710	+	0.945814i	$0.394733\pi$
$674$		0			0
$675$	−14.0910	−	17.9013i	−0.542364	−	0.689022i
$676$		0			0
$677$	1.85410	−	3.39554i	0.0712590	−	0.130501i	−0.839621	−	0.543173i	$-0.817223\pi$
$677$	1.85410	−	3.39554i	0.0712590	−	0.130501i	0.910880	+	0.412672i	$0.135404\pi$
$678$		0			0
$679$	−3.76062	−	3.25860i	−0.144319	−	0.125054i
$680$		0			0
$681$	5.63997	−	2.57569i	0.216124	−	0.0987005i
$682$		0			0
$683$	21.1419	−	11.5443i	0.808971	−	0.441732i	−0.0208355	−	0.999783i	$-0.506633\pi$
$683$	21.1419	−	11.5443i	0.808971	−	0.441732i	0.829806	+	0.558051i	$0.188451\pi$
$684$		0			0
$685$	−0.978249	+	0.0118658i	−0.0373770	+	0.000453370i
$686$		0			0
$687$	15.2339	−	3.31393i	0.581208	−	0.126434i
$688$		0			0
$689$	5.94583			0.226518
$690$		0			0
$691$	−8.63568			−0.328517			−0.164258	−	0.986417i	$-0.552523\pi$
$691$	−8.63568			−0.328517			−0.164258	+	0.986417i	$0.552523\pi$
$692$		0			0
$693$	−2.77243	+	0.603106i	−0.105316	+	0.0229101i
$694$		0			0
$695$	13.5919	−	13.9257i	0.515570	−	0.528231i
$696$		0			0
$697$	11.6022	−	6.33528i	0.439465	−	0.239966i
$698$		0			0
$699$	1.00912	−	0.460848i	0.0381683	−	0.0174309i
$700$		0			0
$701$	7.40474	+	6.41624i	0.279673	+	0.242338i	0.783390	−	0.621531i	$-0.213489\pi$
$701$	7.40474	+	6.41624i	0.279673	+	0.242338i	−0.503717	+	0.863869i	$0.668034\pi$
$702$		0			0
$703$	11.6376	−	21.3127i	0.438921	−	0.803823i
$704$		0			0
$705$	−3.73472	−	16.2186i	−0.140658	−	0.610827i
$706$		0			0
$707$	4.72624	+	3.53802i	0.177749	+	0.133061i
$708$		0			0
$709$	−5.27200	+	36.6676i	−0.197994	+	1.37708i	0.612100	+	0.790780i	$0.290325\pi$
$709$	−5.27200	+	36.6676i	−0.197994	+	1.37708i	−0.810094	+	0.586299i	$0.800584\pi$
$710$		0			0
$711$	−27.6312	+	23.9426i	−1.03625	+	0.897916i
$712$		0			0
$713$	22.5529	−	1.37228i	0.844612	−	0.0513923i
$714$		0			0
$715$	−5.37032	−	2.37425i	−0.200839	−	0.0887920i
$716$		0			0
$717$	2.20572	−	1.65118i	0.0823741	−	0.0616645i
$718$		0			0
$719$	−43.7050	+	6.28383i	−1.62992	+	0.234347i	−0.895731	−	0.444597i	$-0.853347\pi$
$719$	−43.7050	+	6.28383i	−1.62992	+	0.234347i	−0.734190	+	0.678944i	$0.762438\pi$
$720$		0			0
$721$	−1.00537	+	0.646110i	−0.0374418	+	0.0240624i
$722$		0			0
$723$	0.430199	+	0.234907i	0.0159993	+	0.00873627i
$724$		0			0
$725$	−4.39452	−	26.0602i	−0.163208	−	0.967853i
$726$		0			0
$727$	44.1434	+	16.4646i	1.63719	+	0.610639i	0.988609	−	0.150508i	$-0.0480911\pi$
$727$	44.1434	+	16.4646i	1.63719	+	0.610639i	0.648579	+	0.761148i	$0.275364\pi$
$728$		0			0
$729$	1.58728	−	5.40579i	0.0587882	−	0.200214i
$730$		0			0
$731$	−0.0680123	+	0.148926i	−0.00251553	+	0.00550824i
$732$		0			0
$733$	−6.80670	−	31.2899i	−0.251411	−	1.15572i	−0.913674	−	0.406447i	$-0.866768\pi$
$733$	−6.80670	−	31.2899i	−0.251411	−	1.15572i	0.662263	−	0.749271i	$-0.269596\pi$
$734$		0			0
$735$	11.9787	−	5.64705i	0.441839	−	0.208294i
$736$		0			0
$737$	17.4658	+	17.4658i	0.643361	+	0.643361i
$738$		0			0
$739$	−12.0741	+	18.7877i	−0.444154	+	0.691118i	−0.989082	−	0.147365i	$-0.952921\pi$
$739$	−12.0741	+	18.7877i	−0.444154	+	0.691118i	0.544928	+	0.838483i	$0.316557\pi$
$740$		0			0
$741$	−3.24205	−	1.48060i	−0.119100	−	0.0543910i
$742$		0			0
$743$	25.2150	+	46.1778i	0.925049	+	1.69410i	0.692364	+	0.721548i	$0.256569\pi$
$743$	25.2150	+	46.1778i	0.925049	+	1.69410i	0.232685	+	0.972552i	$0.425249\pi$
$744$		0			0
$745$	−19.7203	+	1.65106i	−0.722497	+	0.0604901i
$746$		0			0
$747$	−1.64479	−	22.9971i	−0.0601796	−	0.841421i
$748$		0			0
$749$	0.744896	+	2.53688i	0.0272179	+	0.0926956i
$750$		0			0
$751$	21.2167	+	33.0138i	0.774209	+	1.20469i	0.974375	+	0.224930i	$0.0722154\pi$
$751$	21.2167	+	33.0138i	0.774209	+	1.20469i	−0.200166	+	0.979762i	$0.564148\pi$
$752$		0			0
$753$	4.03355	−	5.38819i	0.146991	−	0.196357i
$754$		0			0
$755$	29.8887	+	15.8529i	1.08776	+	0.576947i
$756$		0			0
$757$	−29.8616	−	2.13574i	−1.08534	−	0.0776248i	−0.482811	−	0.875724i	$-0.660384\pi$
$757$	−29.8616	−	2.13574i	−1.08534	−	0.0776248i	−0.602526	+	0.798099i	$0.705839\pi$
$758$		0			0
$759$	6.56282	+	10.4546i	0.238215	+	0.379477i
$760$		0			0
$761$	−27.3045	−	31.5111i	−0.989787	−	1.14227i	−0.989827	−	0.142275i	$-0.954558\pi$
$761$	−27.3045	−	31.5111i	−0.989787	−	1.14227i	4.03770e−5	−	1.00000i	$-0.499987\pi$
$762$		0			0
$763$	4.23552	+	5.65799i	0.153336	+	0.204833i
$764$		0			0
$765$	3.71319	+	5.62660i	0.134251	+	0.203430i
$766$		0			0
$767$	−2.87148	−	0.624651i	−0.103683	−	0.0225549i
$768$		0			0
$769$	−16.1585	+	4.74457i	−0.582692	+	0.171094i	−0.559776	−	0.828644i	$-0.689113\pi$
$769$	−16.1585	+	4.74457i	−0.582692	+	0.171094i	−0.0229152	+	0.999737i	$0.507295\pi$
$770$		0			0
$771$	−17.6901	+	20.4154i	−0.637093	+	0.735244i
$772$		0			0
$773$	8.52254	−	22.8498i	0.306535	−	0.821851i	−0.688763	−	0.724987i	$-0.741846\pi$
$773$	8.52254	−	22.8498i	0.306535	−	0.821851i	0.995298	−	0.0968644i	$-0.0308813\pi$
$774$		0			0
$775$	−13.2125	−	19.5022i	−0.474608	−	0.700541i
$776$		0			0
$777$	1.82015	−	0.678881i	0.0652975	−	0.0243547i
$778$		0			0
$779$	38.3498	+	24.6460i	1.37403	+	0.883033i
$780$		0			0
$781$		−	3.56969i		−	0.127733i
$782$		0			0
$783$	17.0295	−	17.0295i	0.608584	−	0.608584i
$784$		0			0
$785$	0.337505	−	2.56815i	0.0120461	−	0.0916612i
$786$		0			0
$787$	−18.7971	−	50.3969i	−0.670043	−	1.79646i	−0.601596	−	0.798800i	$-0.705468\pi$
$787$	−18.7971	−	50.3969i	−0.670043	−	1.79646i	−0.0684471	−	0.997655i	$-0.521804\pi$
$788$		0			0
$789$	3.86846	+	1.13588i	0.137721	+	0.0404385i
$790$		0			0
$791$	−0.596132	−	1.30535i	−0.0211960	−	0.0464128i
$792$		0			0
$793$	5.20564	−	0.372315i	0.184858	−	0.0132213i
$794$		0			0
$795$	−0.771943	+	13.0088i	−0.0273780	+	0.461373i
$796$		0			0
$797$	8.36004	−	38.4305i	0.296128	−	1.36128i	−0.553040	−	0.833155i	$-0.686532\pi$
$797$	8.36004	−	38.4305i	0.296128	−	1.36128i	0.849168	−	0.528123i	$-0.177104\pi$
$798$		0			0
$799$	1.63726	+	11.3874i	0.0579222	+	0.402858i
$800$		0			0
$801$	15.3274	+	2.20374i	0.541566	+	0.0778655i
$802$		0			0
$803$	−1.51805	+	21.2251i	−0.0535709	+	0.749019i
$804$		0			0
$805$	−3.23837	−	3.22866i	−0.114138	−	0.113795i
$806$		0			0
$807$	1.02365	−	14.3125i	0.0360342	−	0.503824i
$808$		0			0
$809$	−4.00432	−	0.575735i	−0.140785	−	0.0202418i	0.0715622	−	0.997436i	$-0.477202\pi$
$809$	−4.00432	−	0.575735i	−0.140785	−	0.0202418i	−0.212347	+	0.977194i	$0.568111\pi$
$810$		0			0
$811$	−0.480966	−	3.34519i	−0.0168890	−	0.117466i	0.979633	−	0.200797i	$-0.0643531\pi$
$811$	−0.480966	−	3.34519i	−0.0168890	−	0.117466i	−0.996522	+	0.0833313i	$0.973444\pi$
$812$		0			0
$813$	−0.602811	+	2.77108i	−0.0211415	+	0.0971859i
$814$		0			0
$815$	17.1397	+	19.3022i	0.600378	+	0.676126i
$816$		0			0
$817$	−0.563157	+	0.0402778i	−0.0197024	+	0.00140914i
$818$		0			0
$819$	0.352506	+	0.771880i	0.0123175	+	0.0269717i
$820$		0			0
$821$	0.207186	+	0.0608353i	0.00723084	+	0.00212317i	0.285346	−	0.958425i	$-0.407891\pi$
$821$	0.207186	+	0.0608353i	0.00723084	+	0.00212317i	−0.278115	+	0.960548i	$0.589710\pi$
$822$		0			0
$823$	17.0309	+	45.6615i	0.593658	+	1.59166i	0.791329	+	0.611391i	$0.209390\pi$
$823$	17.0309	+	45.6615i	0.593658	+	1.59166i	−0.197671	+	0.980268i	$0.563338\pi$
$824$		0			0
$825$	5.89180	−	11.4414i	0.205126	−	0.398337i
$826$		0			0
$827$	−0.189776	+	0.189776i	−0.00659916	+	0.00659916i	−0.710399	−	0.703800i	$-0.751485\pi$
$827$	−0.189776	+	0.189776i	−0.00659916	+	0.00659916i	0.703800	+	0.710399i	$0.251485\pi$
$828$		0			0
$829$			10.7735i			0.374178i	0.982343	+	0.187089i	$0.0599053\pi$
$829$			10.7735i			0.374178i	−0.982343	+	0.187089i	$0.940095\pi$
$830$		0			0
$831$	15.7556	+	10.1255i	0.546554	+	0.351249i
$832$		0			0
$833$	−8.57707	+	3.19908i	−0.297178	+	0.110842i
$834$		0			0
$835$	28.0533	−	4.38138i	0.970826	−	0.151624i
$836$		0			0
$837$	7.50176	−	20.1130i	0.259299	−	0.695207i
$838$		0			0
$839$	32.9435	−	38.0189i	1.13734	−	1.31256i	0.193893	−	0.981023i	$-0.437888\pi$
$839$	32.9435	−	38.0189i	1.13734	−	1.31256i	0.943443	−	0.331534i	$-0.107566\pi$
$840$		0			0
$841$	−1.01908	+	0.299230i	−0.0351408	+	0.0103183i
$842$		0			0
$843$	−2.34422	−	0.509954i	−0.0807393	−	0.0175638i
$844$		0			0
$845$	5.48162	−	26.7570i	0.188574	−	0.920470i
$846$		0			0
$847$	0.567285	+	0.757804i	0.0194922	+	0.0260385i
$848$		0			0
$849$	−10.5378	−	12.1613i	−0.361656	−	0.417374i
$850$		0			0
$851$	16.2684	+	19.1829i	0.557672	+	0.657580i
$852$		0			0
$853$	42.5716	+	3.04478i	1.45762	+	0.104251i	0.777517	−	0.628862i	$-0.216479\pi$
$853$	42.5716	+	3.04478i	1.45762	+	0.104251i	0.680107	+	0.733113i	$0.261933\pi$
$854$		0			0
$855$	−10.8932	+	20.5378i	−0.372539	+	0.702376i
$856$		0			0
$857$	2.48607	−	3.32100i	0.0849224	−	0.113443i	−0.756068	−	0.654493i	$-0.772882\pi$
$857$	2.48607	−	3.32100i	0.0849224	−	0.113443i	0.840990	+	0.541050i	$0.181973\pi$
$858$		0			0
$859$	−15.3469	−	23.8802i	−0.523628	−	0.814781i	0.474216	−	0.880408i	$-0.342732\pi$
$859$	−15.3469	−	23.8802i	−0.523628	−	0.814781i	−0.997844	+	0.0656273i	$0.979095\pi$
$860$		0			0
$861$	1.02745	+	3.49919i	0.0350155	+	0.119252i
$862$		0			0
$863$	−2.56507	−	35.8643i	−0.0873159	−	1.22084i	−0.832518	−	0.553998i	$-0.813102\pi$
$863$	−2.56507	−	35.8643i	−0.0873159	−	1.22084i	0.745202	−	0.666838i	$-0.232353\pi$
$864$		0			0
$865$	−4.26605	+	5.04566i	−0.145050	+	0.171558i
$866$		0			0
$867$	−6.32650	−	11.5861i	−0.214859	−	0.393485i
$868$		0			0
$869$	−43.8861	−	20.0421i	−1.48874	−	0.679883i
$870$		0			0
$871$	3.99388	−	6.21460i	0.135328	−	0.210574i
$872$		0			0
$873$	−18.5283	−	18.5283i	−0.627088	−	0.627088i
$874$		0			0
$875$	−1.17587	+	4.62028i	−0.0397518	+	0.156194i
$876$		0			0
$877$	−1.62039	−	7.44882i	−0.0547167	−	0.251529i	0.941661	−	0.336562i	$-0.109264\pi$
$877$	−1.62039	−	7.44882i	−0.0547167	−	0.251529i	−0.996378	+	0.0850330i	$0.972900\pi$
$878$		0			0
$879$	−0.720655	+	1.57801i	−0.0243071	+	0.0532251i
$880$		0			0
$881$	6.99339	−	23.8173i	0.235613	−	0.802425i	−0.753775	−	0.657132i	$-0.771769\pi$
$881$	6.99339	−	23.8173i	0.235613	−	0.802425i	0.989389	−	0.145293i	$-0.0464125\pi$
$882$		0			0
$883$	44.4198	+	16.5677i	1.49485	+	0.557549i	0.958160	−	0.286233i	$-0.0924030\pi$
$883$	44.4198	+	16.5677i	1.49485	+	0.557549i	0.536687	+	0.843782i	$0.319676\pi$
$884$		0			0
$885$	1.73946	−	6.20134i	0.0584714	−	0.208456i
$886$		0			0
$887$	−0.852468	−	0.465483i	−0.0286231	−	0.0156294i	0.464874	−	0.885377i	$-0.346100\pi$
$887$	−0.852468	−	0.465483i	−0.0286231	−	0.0156294i	−0.493497	+	0.869748i	$0.664282\pi$
$888$		0			0
$889$	5.00936	−	3.21932i	0.168009	−	0.107973i
$890$		0			0
$891$	−8.14967	+	1.17175i	−0.273024	+	0.0392550i
$892$		0			0
$893$	−31.7603	+	23.7754i	−1.06282	+	0.795615i
$894$		0			0
$895$	−16.9647	−	43.8523i	−0.567068	−	1.46582i
$896$		0			0
$897$	2.63805	−	2.58256i	0.0880819	−	0.0862293i
$898$		0			0
$899$	18.8198	−	16.3075i	0.627676	−	0.543884i
$900$		0			0
$901$	1.28199	−	8.91644i	0.0427093	−	0.297050i
$902$		0			0
$903$	−0.0361585	−	0.0270679i	−0.00120328	−	0.000900763i
$904$		0			0
$905$	−33.6886	+	7.75761i	−1.11985	+	0.257872i
$906$		0			0
$907$	8.86858	−	16.2416i	0.294476	−	0.539293i	−0.687993	−	0.725717i	$-0.741508\pi$
$907$	8.86858	−	16.2416i	0.294476	−	0.539293i	0.982469	+	0.186424i	$0.0596898\pi$
$908$		0			0
$909$	23.4952	+	20.3587i	0.779286	+	0.675255i
$910$		0			0
$911$	−6.57703	+	3.00363i	−0.217907	+	0.0995147i	−0.521378	−	0.853326i	$-0.674582\pi$
$911$	−6.57703	+	3.00363i	−0.217907	+	0.0995147i	0.303471	+	0.952841i	$0.401854\pi$
$912$		0			0
$913$	26.7028	−	14.5808i	0.883735	−	0.482556i
$914$		0			0
$915$	0.138735	+	11.4377i	0.00458643	+	0.378117i
$916$		0			0
$917$	−3.13911	+	0.682871i	−0.103662	+	0.0225504i
$918$		0			0
$919$	45.9848			1.51690			0.758448	−	0.651733i	$-0.225958\pi$
$919$	45.9848			1.51690			0.758448	+	0.651733i	$0.225958\pi$
$920$		0			0
$921$	−15.1748			−0.500027
$922$		0			0
$923$	−1.04321	+	0.226937i	−0.0343378	+	0.00746972i
$924$		0			0
$925$	8.56540	−	24.7848i	0.281629	−	0.814920i
$926$		0			0
$927$	−5.52334	+	3.01597i	−0.181410	+	0.0990575i
$928$		0			0
$929$	42.8325	−	19.5610i	1.40529	−	0.641774i	0.438825	−	0.898573i	$-0.355395\pi$
$929$	42.8325	−	19.5610i	1.40529	−	0.641774i	0.966465	+	0.256798i	$0.0826675\pi$
$930$		0			0
$931$	−23.8579	−	20.6730i	−0.781912	−	0.677530i
$932$		0			0
$933$	4.61426	−	8.45039i	0.151064	−	0.276653i
$934$		0			0
$935$	−4.71837	+	7.54149i	−0.154307	+	0.246633i
$936$		0			0
$937$	13.4393	+	10.0605i	0.439043	+	0.328663i	0.795828	−	0.605523i	$-0.207036\pi$
$937$	13.4393	+	10.0605i	0.439043	+	0.328663i	−0.356785	+	0.934187i	$0.616127\pi$
$938$		0			0
$939$	1.29969	−	9.03953i	0.0424137	−	0.294994i
$940$		0			0
$941$	−9.61413	+	8.33069i	−0.313412	+	0.271573i	−0.797334	−	0.603538i	$-0.793757\pi$
$941$	−9.61413	+	8.33069i	−0.313412	+	0.271573i	0.483923	+	0.875111i	$0.339212\pi$
$942$		0			0
$943$	−38.0990	+	27.8938i	−1.24068	+	0.908346i
$944$		0			0
$945$	−4.05192	+	1.56753i	−0.131809	+	0.0509918i
$946$		0			0
$947$	27.0400	−	20.2419i	0.878681	−	0.657772i	−0.0616262	−	0.998099i	$-0.519629\pi$
$947$	27.0400	−	20.2419i	0.878681	−	0.657772i	0.940307	+	0.340327i	$0.110538\pi$
$948$		0			0
$949$	6.29938	−	0.905715i	0.204487	−	0.0294007i
$950$		0			0
$951$	−1.67385	+	1.07572i	−0.0542784	+	0.0348826i
$952$		0			0
$953$	35.5328	+	19.4024i	1.15102	+	0.628505i	0.937346	−	0.348400i	$-0.113275\pi$
$953$	35.5328	+	19.4024i	1.15102	+	0.628505i	0.213674	+	0.976905i	$0.431457\pi$
$954$		0			0
$955$	−23.5997	+	13.2605i	−0.763670	+	0.429100i
$956$		0			0
$957$	12.7467	+	4.75427i	0.412042	+	0.153684i
$958$		0			0
$959$	−0.0525624	+	0.179011i	−0.00169733	+	0.00578057i
$960$		0			0
$961$	−3.65717	+	8.00809i	−0.117973	+	0.258326i
$962$		0			0
$963$	2.95951	+	13.6046i	0.0953687	+	0.438403i
$964$		0			0
$965$	−16.2599	−	34.4910i	−0.523426	−	1.11030i
$966$		0			0
$967$	0.202315	+	0.202315i	0.00650603	+	0.00650603i	0.710352	−	0.703846i	$-0.248536\pi$
$967$	0.202315	+	0.202315i	0.00650603	+	0.00650603i	−0.703846	+	0.710352i	$0.748536\pi$
$968$		0			0
$969$	−2.91935	+	4.54259i	−0.0937829	+	0.145929i
$970$		0			0
$971$	−7.91372	−	3.61408i	−0.253964	−	0.115981i	0.284366	−	0.958716i	$-0.408217\pi$
$971$	−7.91372	−	3.61408i	−0.253964	−	0.115981i	−0.538329	+	0.842735i	$0.680944\pi$
$972$		0			0
$973$	−1.77846	−	3.25701i	−0.0570148	−	0.104415i
$974$		0			0
$975$	−3.71821	−	0.994466i	−0.119078	−	0.0318484i
$976$		0			0
$977$	−2.62942	−	36.7641i	−0.0841226	−	1.17619i	−0.847702	−	0.530473i	$-0.822014\pi$
$977$	−2.62942	−	36.7641i	−0.0841226	−	1.17619i	0.763579	−	0.645714i	$-0.223440\pi$
$978$		0			0
$979$	5.75689	+	19.6062i	0.183991	+	0.626616i
$980$		0			0
$981$	20.1213	+	31.3093i	0.642423	+	0.999630i
$982$		0			0
$983$	−22.1598	+	29.6021i	−0.706789	+	0.944160i	−0.999929	−	0.0119097i	$-0.996209\pi$
$983$	−22.1598	+	29.6021i	−0.706789	+	0.944160i	0.293140	+	0.956070i	$0.405300\pi$
$984$		0			0
$985$	12.9957	+	42.3522i	0.414079	+	1.34945i
$986$		0			0
$987$	−3.16578	−	0.226421i	−0.100768	−	0.00720707i
$988$		0			0
$989$	0.170714	−	0.559338i	0.00542838	−	0.0177859i
$990$		0			0
$991$	−10.8076	−	12.4726i	−0.343314	−	0.396205i	0.557667	−	0.830065i	$-0.311697\pi$
$991$	−10.8076	−	12.4726i	−0.343314	−	0.396205i	−0.900980	+	0.433860i	$0.857151\pi$
$992$		0			0
$993$	−11.2209	−	14.9893i	−0.356083	−	0.475671i
$994$		0			0
$995$	−7.87660	−	1.61365i	−0.249705	−	0.0511562i
$996$		0			0
$997$	11.4344	+	2.48741i	0.362132	+	0.0787770i	0.389950	−	0.920836i	$-0.372492\pi$
$997$	11.4344	+	2.48741i	0.362132	+	0.0787770i	−0.0278181	+	0.999613i	$0.508856\pi$
$998$		0			0
$999$	22.9286	−	6.73243i	0.725428	−	0.213005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.23	yes	720
5.3	odd	4	inner	920.2.bv.a.33.23	✓	720
23.7	odd	22	inner	920.2.bv.a.697.23	yes	720
115.53	even	44	inner	920.2.bv.a.513.23	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.23	✓	720	5.3	odd	4	inner
920.2.bv.a.217.23	yes	720	1.1	even	1	trivial
920.2.bv.a.513.23	yes	720	115.53	even	44	inner
920.2.bv.a.697.23	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)

\(f(q)\)	\(=\)	\(q+(0.848778 - 0.184640i) q^{3} +(-1.60020 - 1.56185i) q^{5} +(-0.374263 + 0.204363i) q^{7} +(-2.04256 + 0.932808i) q^{9} +O(q^{10})\)	\(q+(0.848778 - 0.184640i) q^{3} +(-1.60020 - 1.56185i) q^{5} +(-0.374263 + 0.204363i) q^{7} +(-2.04256 + 0.932808i) q^{9} +(-2.23938 - 1.94043i) q^{11} +(-0.424711 + 0.777801i) q^{13} +(-1.64659 - 1.03020i) q^{15} +(1.07483 + 0.804606i) q^{17} +(-0.658927 + 4.58294i) q^{19} +(-0.279933 + 0.242563i) q^{21} +(-4.18454 - 2.34300i) q^{23} +(0.121279 + 4.99853i) q^{25} +(-3.64757 + 2.73054i) q^{27} +(-5.23183 + 0.752224i) q^{29} +(-3.96340 + 2.54712i) q^{31} +(-2.25902 - 1.23352i) q^{33} +(0.918079 + 0.257519i) q^{35} +(-4.91396 - 1.83281i) q^{37} +(-0.216872 + 0.738599i) q^{39} +(4.09008 - 8.95602i) q^{41} +(0.0259205 + 0.119154i) q^{43} +(4.72541 + 1.69749i) q^{45} +(6.05896 + 6.05896i) q^{47} +(-3.68618 + 5.73580i) q^{49} +(1.06085 + 0.484475i) q^{51} +(-3.21544 - 5.88865i) q^{53} +(0.552798 + 6.60265i) q^{55} +(0.286913 + 4.01156i) q^{57} +(0.934221 + 3.18166i) q^{59} +(-3.18389 - 4.95423i) q^{61} +(0.573825 - 0.766540i) q^{63} +(1.89443 - 0.581303i) q^{65} +(-8.31468 - 0.594678i) q^{67} +(-3.98436 - 1.21605i) q^{69} +(0.788913 + 0.910454i) q^{71} +(-4.30365 - 5.74900i) q^{73} +(1.02587 + 4.22025i) q^{75} +(1.23467 + 0.268586i) q^{77} +(15.6226 - 4.58721i) q^{79} +(1.81963 - 2.09996i) q^{81} +(-3.58818 + 9.62029i) q^{83} +(-0.463269 - 2.96624i) q^{85} +(-4.30177 + 1.60448i) q^{87} +(-5.80133 - 3.72829i) q^{89} -0.377898i q^{91} +(-2.89374 + 2.89374i) q^{93} +(8.21226 - 6.30448i) q^{95} +(4.07796 + 10.9334i) q^{97} +(6.38413 + 1.87455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 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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