LMFDB - Embedded newform 920.2.bv.a.17.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.17
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0822135 + 0.0448920i) q^{3} +(-1.59045 - 1.57177i) q^{5} +(3.12275 + 4.17150i) q^{7} +(-1.61718 + 2.51638i) q^{9} +(-3.36211 + 1.53542i) q^{11} +(-1.74996 - 1.31000i) q^{13} +(0.201316 + 0.0578226i) q^{15} +(-0.442284 - 6.18393i) q^{17} +(-2.05565 - 2.37235i) q^{19} +(-0.443999 - 0.202768i) q^{21} +(-4.77306 + 0.466813i) q^{23} +(0.0590597 + 4.99965i) q^{25} +(0.0400361 - 0.559777i) q^{27} +(-1.75914 - 1.52430i) q^{29} +(-0.693792 + 0.203716i) q^{31} +(0.207482 - 0.277164i) q^{33} +(1.59008 - 11.5428i) q^{35} +(-8.16416 + 1.77600i) q^{37} +(0.202679 + 0.0291408i) q^{39} +(-4.34358 + 2.79145i) q^{41} +(0.396781 + 0.726651i) q^{43} +(6.52722 - 1.46034i) q^{45} +(6.39744 + 6.39744i) q^{47} +(-5.67774 + 19.3366i) q^{49} +(0.313971 + 0.488548i) q^{51} +(-8.20433 + 6.14168i) q^{53} +(7.76059 + 2.84245i) q^{55} +(0.275502 + 0.102757i) q^{57} +(-1.11563 + 0.160403i) q^{59} +(1.41688 + 4.82546i) q^{61} +(-15.5471 + 1.11195i) q^{63} +(0.724194 + 4.83403i) q^{65} +(1.29574 + 3.47401i) q^{67} +(0.371454 - 0.252650i) q^{69} +(5.27911 - 11.5596i) q^{71} +(1.25599 + 0.0898299i) q^{73} +(-0.229300 - 0.408388i) q^{75} +(-16.9040 - 9.23029i) q^{77} +(0.267327 + 1.85930i) q^{79} +(-3.70596 - 8.11493i) q^{81} +(-3.06361 - 14.0832i) q^{83} +(-9.01631 + 10.5304i) q^{85} +(0.213054 + 0.0463470i) q^{87} +(11.9814 + 3.51804i) q^{89} -11.3907i q^{91} +(0.0478939 - 0.0478939i) q^{93} +(-0.459383 + 7.00411i) q^{95} +(-2.27190 + 10.4438i) q^{97} +(1.57342 - 10.9434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0822135	+	0.0448920i	−0.0474660	+	0.0259184i	−0.502807	−	0.864399i	$-0.667699\pi$
$3$	−0.0822135	+	0.0448920i	−0.0474660	+	0.0259184i	0.455341	+	0.890317i	$0.349517\pi$
$4$		0			0
$5$	−1.59045	−	1.57177i	−0.711271	−	0.702918i
$5$	−1.59045	−	1.57177i	−0.711271	−	0.702918i
$6$		0			0
$7$	3.12275	+	4.17150i	1.18029	+	1.57668i	0.729381	+	0.684107i	$0.239808\pi$
$7$	3.12275	+	4.17150i	1.18029	+	1.57668i	0.450906	+	0.892572i	$0.351101\pi$
$8$		0			0
$9$	−1.61718	+	2.51638i	−0.539060	+	0.838793i
$10$		0			0
$11$	−3.36211	+	1.53542i	−1.01371	+	0.462947i	−0.851805	−	0.523859i	$-0.824492\pi$
$11$	−3.36211	+	1.53542i	−1.01371	+	0.462947i	−0.161908	+	0.986806i	$0.551765\pi$
$12$		0			0
$13$	−1.74996	−	1.31000i	−0.485351	−	0.363329i	0.328404	−	0.944537i	$-0.393489\pi$
$13$	−1.74996	−	1.31000i	−0.485351	−	0.363329i	−0.813755	+	0.581208i	$0.802580\pi$
$14$		0			0
$15$	0.201316	+	0.0578226i	0.0519797	+	0.0149297i
$16$		0			0
$17$	−0.442284	−	6.18393i	−0.107270	−	1.49982i	−0.711314	−	0.702874i	$-0.751900\pi$
$17$	−0.442284	−	6.18393i	−0.107270	−	1.49982i	0.604045	−	0.796950i	$-0.293555\pi$
$18$		0			0
$19$	−2.05565	−	2.37235i	−0.471599	−	0.544254i	0.469257	−	0.883062i	$-0.344522\pi$
$19$	−2.05565	−	2.37235i	−0.471599	−	0.544254i	−0.940856	+	0.338808i	$0.889976\pi$
$20$		0			0
$21$	−0.443999	−	0.202768i	−0.0968885	−	0.0442475i
$22$		0			0
$23$	−4.77306	+	0.466813i	−0.995251	+	0.0973372i
$23$	−4.77306	+	0.466813i	−0.995251	+	0.0973372i
$24$		0			0
$25$	0.0590597	+	4.99965i	0.0118119	+	0.999930i
$26$		0			0
$27$	0.0400361	−	0.559777i	0.00770494	−	0.107729i
$28$		0			0
$29$	−1.75914	−	1.52430i	−0.326664	−	0.283056i	0.476053	−	0.879417i	$-0.342067\pi$
$29$	−1.75914	−	1.52430i	−0.326664	−	0.283056i	−0.802716	+	0.596361i	$0.796613\pi$
$30$		0			0
$31$	−0.693792	+	0.203716i	−0.124609	+	0.0365884i	−0.343442	−	0.939174i	$-0.611593\pi$
$31$	−0.693792	+	0.203716i	−0.124609	+	0.0365884i	0.218834	+	0.975762i	$0.429775\pi$
$32$		0			0
$33$	0.207482	−	0.277164i	0.0361181	−	0.0482481i
$34$		0			0
$35$	1.59008	−	11.5428i	0.268773	−	1.95109i
$36$		0			0
$37$	−8.16416	+	1.77600i	−1.34218	+	0.291973i	−0.825595	−	0.564263i	$-0.809160\pi$
$37$	−8.16416	+	1.77600i	−1.34218	+	0.291973i	−0.516584	+	0.856236i	$0.672797\pi$
$38$		0			0
$39$	0.202679	+	0.0291408i	0.0324546	+	0.00466626i
$40$		0			0
$41$	−4.34358	+	2.79145i	−0.678354	+	0.435951i	−0.833928	−	0.551873i	$-0.813913\pi$
$41$	−4.34358	+	2.79145i	−0.678354	+	0.435951i	0.155575	+	0.987824i	$0.450277\pi$
$42$		0			0
$43$	0.396781	+	0.726651i	0.0605086	+	0.110813i	0.906183	−	0.422886i	$-0.138983\pi$
$43$	0.396781	+	0.726651i	0.0605086	+	0.110813i	−0.845674	+	0.533700i	$0.820801\pi$
$44$		0			0
$45$	6.52722	−	1.46034i	0.973020	−	0.217694i
$46$		0			0
$47$	6.39744	+	6.39744i	0.933163	+	0.933163i	0.997902	−	0.0647394i	$-0.0206216\pi$
$47$	6.39744	+	6.39744i	0.933163	+	0.933163i	−0.0647394	+	0.997902i	$0.520622\pi$
$48$		0			0
$49$	−5.67774	+	19.3366i	−0.811106	+	2.76237i
$50$		0			0
$51$	0.313971	+	0.488548i	0.0439647	+	0.0684104i
$52$		0			0
$53$	−8.20433	+	6.14168i	−1.12695	+	0.843625i	−0.989161	−	0.146836i	$-0.953091\pi$
$53$	−8.20433	+	6.14168i	−1.12695	+	0.843625i	−0.137790	+	0.990461i	$0.544000\pi$
$54$		0			0
$55$	7.76059	+	2.84245i	1.04644	+	0.383277i
$56$		0			0
$57$	0.275502	+	0.102757i	0.0364911	+	0.0136105i
$58$		0			0
$59$	−1.11563	+	0.160403i	−0.145242	+	0.0208827i	−0.214552	−	0.976712i	$-0.568829\pi$
$59$	−1.11563	+	0.160403i	−0.145242	+	0.0208827i	0.0693102	+	0.997595i	$0.477920\pi$
$60$		0			0
$61$	1.41688	+	4.82546i	0.181413	+	0.617837i	0.999110	+	0.0421875i	$0.0134327\pi$
$61$	1.41688	+	4.82546i	0.181413	+	0.617837i	−0.817696	+	0.575650i	$0.804749\pi$
$62$		0			0
$63$	−15.5471	+	1.11195i	−1.95875	+	0.140093i
$64$		0			0
$65$	0.724194	+	4.83403i	0.0898252	+	0.599587i
$66$		0			0
$67$	1.29574	+	3.47401i	0.158300	+	0.424418i	0.991752	−	0.128174i	$-0.0409115\pi$
$67$	1.29574	+	3.47401i	0.158300	+	0.424418i	−0.833452	+	0.552592i	$0.813639\pi$
$68$		0			0
$69$	0.371454	−	0.252650i	0.0447178	−	0.0304155i
$70$		0			0
$71$	5.27911	−	11.5596i	0.626515	−	1.37188i	−0.284169	−	0.958774i	$-0.591718\pi$
$71$	5.27911	−	11.5596i	0.626515	−	1.37188i	0.910684	−	0.413103i	$-0.135555\pi$
$72$		0			0
$73$	1.25599	+	0.0898299i	0.147002	+	0.0105138i	0.144646	−	0.989483i	$-0.453796\pi$
$73$	1.25599	+	0.0898299i	0.147002	+	0.0105138i	0.00235582	+	0.999997i	$0.499250\pi$
$74$		0			0
$75$	−0.229300	−	0.408388i	−0.0264773	−	0.0471565i
$76$		0			0
$77$	−16.9040	−	9.23029i	−1.92639	−	1.05189i
$78$		0			0
$79$	0.267327	+	1.85930i	0.0300766	+	0.209187i	0.999318	−	0.0369245i	$-0.0117561\pi$
$79$	0.267327	+	1.85930i	0.0300766	+	0.209187i	−0.969241	+	0.246112i	$0.920847\pi$
$80$		0			0
$81$	−3.70596	−	8.11493i	−0.411774	−	0.901658i
$82$		0			0
$83$	−3.06361	−	14.0832i	−0.336275	−	1.54583i	−0.765982	−	0.642862i	$-0.777747\pi$
$83$	−3.06361	−	14.0832i	−0.336275	−	1.54583i	0.429708	−	0.902968i	$-0.358617\pi$
$84$		0			0
$85$	−9.01631	+	10.5304i	−0.977956	+	1.14218i
$86$		0			0
$87$	0.213054	+	0.0463470i	0.0228418	+	0.00496892i
$88$		0			0
$89$	11.9814	+	3.51804i	1.27002	+	0.372912i	0.846215	−	0.532841i	$-0.178876\pi$
$89$	11.9814	+	3.51804i	1.27002	+	0.372912i	0.423806	+	0.905753i	$0.360694\pi$
$90$		0			0
$91$		−	11.3907i		−	1.19407i
$92$		0			0
$93$	0.0478939	−	0.0478939i	0.00496637	−	0.00496637i
$94$		0			0
$95$	−0.459383	+	7.00411i	−0.0471317	+	0.718607i
$96$		0			0
$97$	−2.27190	+	10.4438i	−0.230677	+	1.06040i	0.705455	+	0.708754i	$0.250743\pi$
$97$	−2.27190	+	10.4438i	−0.230677	+	1.06040i	−0.936132	+	0.351649i	$0.885621\pi$
$98$		0			0
$99$	1.57342	−	10.9434i	0.158135	−	1.09985i
$100$		0			0
$101$	−1.66564	−	1.07044i	−0.165738	−	0.106513i	0.455142	−	0.890419i	$-0.349588\pi$
$101$	−1.66564	−	1.07044i	−0.165738	−	0.106513i	−0.620880	+	0.783905i	$0.713225\pi$
$102$		0			0
$103$	2.67522	−	7.17254i	0.263597	−	0.706731i	−0.735962	−	0.677023i	$-0.763270\pi$
$103$	2.67522	−	7.17254i	0.263597	−	0.706731i	0.999559	−	0.0297077i	$-0.00945764\pi$
$104$		0			0
$105$	0.387453	+	1.02036i	0.0378116	+	0.0995766i
$106$		0			0
$107$	−8.22621	+	15.0652i	−0.795258	+	1.45641i	0.0923106	+	0.995730i	$0.470575\pi$
$107$	−8.22621	+	15.0652i	−0.795258	+	1.45641i	−0.887568	+	0.460676i	$0.847607\pi$
$108$		0			0
$109$	10.7923	−	12.4550i	1.03372	−	1.19297i	0.0527863	−	0.998606i	$-0.483190\pi$
$109$	10.7923	−	12.4550i	1.03372	−	1.19297i	0.980929	−	0.194365i	$-0.0622648\pi$
$110$		0			0
$111$	0.591476	−	0.512517i	0.0561404	−	0.0486459i
$112$		0			0
$113$	3.33266	−	1.24302i	0.313510	−	0.116933i	−0.187784	−	0.982210i	$-0.560130\pi$
$113$	3.33266	−	1.24302i	0.313510	−	0.116933i	0.501294	+	0.865277i	$0.332858\pi$
$114$		0			0
$115$	8.32503	+	6.75972i	0.776313	+	0.630347i
$116$		0			0
$117$	6.12645	−	2.28505i	0.566391	−	0.211253i
$118$		0			0
$119$	24.4151	−	21.1558i	2.23813	−	1.93935i
$120$		0			0
$121$	1.74276	−	2.01126i	0.158433	−	0.182841i
$122$		0			0
$123$	0.231788	−	0.424487i	0.0208996	−	0.0382747i
$124$		0			0
$125$	7.76438	−	8.04452i	0.694468	−	0.719524i
$126$		0			0
$127$	1.08271	−	2.90286i	0.0960751	−	0.257587i	−0.880018	−	0.474940i	$-0.842470\pi$
$127$	1.08271	−	2.90286i	0.0960751	−	0.257587i	0.976093	+	0.217353i	$0.0697423\pi$
$128$		0			0
$129$	−0.0652416	−	0.0419282i	−0.00574420	−	0.00369157i
$130$		0			0
$131$	0.187109	−	1.30137i	0.0163478	−	0.113701i	−0.980014	−	0.198931i	$-0.936253\pi$
$131$	0.187109	−	1.30137i	0.0163478	−	0.113701i	0.996361	+	0.0852292i	$0.0271623\pi$
$132$		0			0
$133$	3.47697	−	15.9834i	0.301492	−	1.38594i
$134$		0			0
$135$	−0.943518	+	0.827370i	−0.0812051	+	0.0712087i
$136$		0			0
$137$	−13.6508	+	13.6508i	−1.16627	+	1.16627i	−0.183188	+	0.983078i	$0.558642\pi$
$137$	−13.6508	+	13.6508i	−1.16627	+	1.16627i	−0.983078	+	0.183188i	$0.941358\pi$
$138$		0			0
$139$			14.1071i			1.19655i	0.801291	+	0.598275i	$0.204147\pi$
$139$			14.1071i			1.19655i	−0.801291	+	0.598275i	$0.795853\pi$
$140$		0			0
$141$	−0.813150	−	0.238762i	−0.0684796	−	0.0201074i
$142$		0			0
$143$	7.89495	+	1.71744i	0.660208	+	0.143620i
$144$		0			0
$145$	0.401964	+	5.18929i	0.0333813	+	0.430947i
$146$		0			0
$147$	−0.401272	−	1.84462i	−0.0330963	−	0.152141i
$148$		0			0
$149$	−4.09582	−	8.96860i	−0.335543	−	0.734736i	0.664377	−	0.747398i	$-0.268697\pi$
$149$	−4.09582	−	8.96860i	−0.335543	−	0.734736i	−0.999920	+	0.0126614i	$0.995970\pi$
$150$		0			0
$151$	−0.807321	−	5.61504i	−0.0656989	−	0.456946i	−0.995942	−	0.0900011i	$-0.971313\pi$
$151$	−0.807321	−	5.61504i	−0.0656989	−	0.456946i	0.930243	−	0.366945i	$-0.119596\pi$
$152$		0			0
$153$	16.2764	+	8.88757i	1.31587	+	0.718518i
$154$		0			0
$155$	1.42364	+	0.766484i	0.114349	+	0.0615655i
$156$		0			0
$157$	13.9863	+	1.00032i	1.11623	+	0.0798340i	0.617239	−	0.786776i	$-0.288251\pi$
$157$	13.9863	+	1.00032i	1.11623	+	0.0798340i	0.498987	+	0.866610i	$0.333706\pi$
$158$		0			0
$159$	0.398795	−	0.873238i	0.0316265	−	0.0692523i
$160$		0			0
$161$	−16.8524	−	18.4531i	−1.32815	−	1.45431i
$162$		0			0
$163$	7.18895	+	19.2743i	0.563082	+	1.50968i	0.836600	+	0.547815i	$0.184540\pi$
$163$	7.18895	+	19.2743i	0.563082	+	1.50968i	−0.273518	+	0.961867i	$0.588187\pi$
$164$		0			0
$165$	−0.765629	+	0.114700i	−0.0596042	+	0.00892940i
$166$		0			0
$167$	−20.3718	+	1.45702i	−1.57642	+	0.112748i	−0.831927	−	0.554886i	$-0.812762\pi$
$167$	−20.3718	+	1.45702i	−1.57642	+	0.112748i	−0.744490	+	0.667633i	$0.767307\pi$
$168$		0			0
$169$	−2.31628	−	7.88852i	−0.178175	−	0.606809i
$170$		0			0
$171$	9.29408	−	1.33629i	0.710736	−	0.102188i
$172$		0			0
$173$	4.03657	+	1.50556i	0.306895	+	0.114466i	0.498193	−	0.867066i	$-0.333997\pi$
$173$	4.03657	+	1.50556i	0.306895	+	0.114466i	−0.191298	+	0.981532i	$0.561270\pi$
$174$		0			0
$175$	−20.6716	+	15.8590i	−1.56263	+	1.19883i
$176$		0			0
$177$	0.0845188	−	0.0632700i	0.00635282	−	0.00475566i
$178$		0			0
$179$	8.73930	+	13.5986i	0.653206	+	1.01641i	0.997003	+	0.0773644i	$0.0246505\pi$
$179$	8.73930	+	13.5986i	0.653206	+	1.01641i	−0.343797	+	0.939044i	$0.611713\pi$
$180$		0			0
$181$	2.83153	−	9.64330i	0.210466	−	0.716781i	−0.784814	−	0.619732i	$-0.787241\pi$
$181$	2.83153	−	9.64330i	0.210466	−	0.716781i	0.995280	−	0.0970491i	$-0.0309404\pi$
$182$		0			0
$183$	−0.333112	−	0.333112i	−0.0246243	−	0.0246243i
$184$		0			0
$185$	15.7762	+	10.0076i	1.15989	+	0.735770i
$186$		0			0
$187$	10.9820	+	20.1119i	0.803080	+	1.47073i
$188$		0			0
$189$	2.46013	−	1.58103i	0.178948	−	0.115003i
$190$		0			0
$191$	13.5513	+	1.94839i	0.980541	+	0.140980i	0.613901	−	0.789383i	$-0.289599\pi$
$191$	13.5513	+	1.94839i	0.980541	+	0.140980i	0.366639	+	0.930363i	$0.380508\pi$
$192$		0			0
$193$	−23.9812	+	5.21680i	−1.72621	+	0.375513i	−0.962760	−	0.270358i	$-0.912858\pi$
$193$	−23.9812	+	5.21680i	−1.72621	+	0.375513i	−0.763446	+	0.645871i	$0.776494\pi$
$194$		0			0
$195$	−0.276548	−	0.364912i	−0.0198040	−	0.0261319i
$196$		0			0
$197$	−6.33826	+	8.46693i	−0.451582	+	0.603243i	−0.967337	−	0.253493i	$-0.918421\pi$
$197$	−6.33826	+	8.46693i	−0.451582	+	0.603243i	0.515755	+	0.856736i	$0.327512\pi$
$198$		0			0
$199$	−4.47558	+	1.31415i	−0.317265	+	0.0931575i	−0.436488	−	0.899710i	$-0.643778\pi$
$199$	−4.47558	+	1.31415i	−0.317265	+	0.0931575i	0.119223	+	0.992868i	$0.461960\pi$
$200$		0			0
$201$	−0.262483	−	0.227443i	−0.0185141	−	0.0160426i
$202$		0			0
$203$	0.865284	−	12.0982i	0.0607310	−	0.849130i
$204$		0			0
$205$	11.2958	+	2.38746i	0.788931	+	0.166748i
$206$		0			0
$207$	6.54421	−	12.7657i	0.454854	−	0.887281i
$208$		0			0
$209$	10.5539	+	4.81979i	0.730026	+	0.333392i
$210$		0			0
$211$	0.725033	+	0.836732i	0.0499133	+	0.0576030i	0.780157	−	0.625584i	$-0.215139\pi$
$211$	0.725033	+	0.836732i	0.0499133	+	0.0576030i	−0.730244	+	0.683187i	$0.760594\pi$
$212$		0			0
$213$	0.0849209	+	1.18735i	0.00581868	+	0.0813558i
$214$		0			0
$215$	0.511069	−	1.77935i	0.0348546	−	0.121351i
$216$		0			0
$217$	−3.01634	−	2.25800i	−0.204762	−	0.153283i
$218$		0			0
$219$	−0.107292	+	0.0489985i	−0.00725010	+	0.00331101i
$220$		0			0
$221$	−7.32699	+	11.4010i	−0.492866	+	0.766915i
$222$		0			0
$223$	−1.88894	−	2.52333i	−0.126493	−	0.168975i	0.732824	−	0.680418i	$-0.238202\pi$
$223$	−1.88894	−	2.52333i	−0.126493	−	0.168975i	−0.859317	+	0.511443i	$0.829111\pi$
$224$		0			0
$225$	−12.6765	−	7.93671i	−0.845102	−	0.529114i
$226$		0			0
$227$	0.531065	−	0.289984i	0.0352480	−	0.0192469i	−0.461528	−	0.887125i	$-0.652699\pi$
$227$	0.531065	−	0.289984i	0.0352480	−	0.0192469i	0.496776	+	0.867879i	$0.334517\pi$
$228$		0			0
$229$	−4.05820			−0.268174			−0.134087	−	0.990970i	$-0.542810\pi$
$229$	−4.05820			−0.268174			−0.134087	+	0.990970i	$0.542810\pi$
$230$		0			0
$231$	1.80410			0.118701
$232$		0			0
$233$	4.35266	−	2.37673i	0.285152	−	0.155705i	−0.330307	−	0.943873i	$-0.607152\pi$
$233$	4.35266	−	2.37673i	0.285152	−	0.155705i	0.615459	+	0.788169i	$0.288971\pi$
$234$		0			0
$235$	−0.119483	−	20.2301i	−0.00779419	−	1.31967i
$236$		0			0
$237$	−0.105445	−	0.140859i	−0.00684941	−	0.00914974i
$238$		0			0
$239$	8.48775	−	13.2072i	0.549027	−	0.854302i	−0.450228	−	0.892914i	$-0.648657\pi$
$239$	8.48775	−	13.2072i	0.549027	−	0.854302i	0.999254	+	0.0386117i	$0.0122935\pi$
$240$		0			0
$241$	−1.35109	+	0.617023i	−0.0870315	+	0.0397460i	−0.458455	−	0.888718i	$-0.651597\pi$
$241$	−1.35109	+	0.617023i	−0.0870315	+	0.0397460i	0.371424	+	0.928464i	$0.378870\pi$
$242$		0			0
$243$	2.01678	+	1.50975i	0.129377	+	0.0968502i
$244$		0			0
$245$	39.4229	−	21.8298i	2.51864	−	1.39465i
$246$		0			0
$247$	0.489522	+	6.84441i	0.0311475	+	0.435499i
$248$		0			0
$249$	0.884092	+	1.02030i	0.0560270	+	0.0646587i
$250$		0			0
$251$	19.3359	+	8.83043i	1.22047	+	0.557372i	0.918302	−	0.395882i	$-0.129561\pi$
$251$	19.3359	+	8.83043i	1.22047	+	0.557372i	0.302172	+	0.953253i	$0.402288\pi$
$252$		0			0
$253$	15.3308	−	8.89813i	0.963837	−	0.559421i
$254$		0			0
$255$	0.268532	−	1.27050i	0.0168161	−	0.0795619i
$256$		0			0
$257$	−1.08572	+	15.1803i	−0.0677251	+	0.946921i	0.844059	+	0.536251i	$0.180160\pi$
$257$	−1.08572	+	15.1803i	−0.0677251	+	0.946921i	−0.911784	+	0.410670i	$0.865295\pi$
$258$		0			0
$259$	−32.9032	−	28.5108i	−2.04450	−	1.77157i
$260$		0			0
$261$	6.68056	−	1.96159i	0.413516	−	0.121419i
$262$		0			0
$263$	7.20082	−	9.61917i	0.444022	−	0.593144i	−0.521569	−	0.853209i	$-0.674653\pi$
$263$	7.20082	−	9.61917i	0.444022	−	0.593144i	0.965591	+	0.260065i	$0.0837441\pi$
$264$		0			0
$265$	22.7019	+	3.12730i	1.39457	+	0.192109i
$266$		0			0
$267$	−1.14296	+	0.248636i	−0.0699481	+	0.0152163i
$268$		0			0
$269$	7.23305	+	1.03996i	0.441007	+	0.0634073i	0.359242	−	0.933244i	$-0.383035\pi$
$269$	7.23305	+	1.03996i	0.441007	+	0.0634073i	0.0817650	+	0.996652i	$0.473944\pi$
$270$		0			0
$271$	−5.54876	+	3.56597i	−0.337063	+	0.216617i	−0.698212	−	0.715891i	$-0.746021\pi$
$271$	−5.54876	+	3.56597i	−0.337063	+	0.216617i	0.361149	+	0.932508i	$0.382385\pi$
$272$		0			0
$273$	0.511353	+	0.936474i	0.0309485	+	0.0566780i
$274$		0			0
$275$	−7.87514	−	16.7187i	−0.474889	−	1.00817i
$276$		0			0
$277$	−9.26408	−	9.26408i	−0.556625	−	0.556625i	0.371720	−	0.928345i	$-0.378768\pi$
$277$	−9.26408	−	9.26408i	−0.556625	−	0.556625i	−0.928345	+	0.371720i	$0.878768\pi$
$278$		0			0
$279$	0.609360	−	2.07529i	0.0364814	−	0.124244i
$280$		0			0
$281$	3.20148	+	4.98161i	0.190985	+	0.297178i	0.923519	−	0.383552i	$-0.125299\pi$
$281$	3.20148	+	4.98161i	0.190985	+	0.297178i	−0.732535	+	0.680730i	$0.761663\pi$
$282$		0			0
$283$	20.5383	−	15.3748i	1.22087	−	0.913934i	0.222732	−	0.974880i	$-0.428502\pi$
$283$	20.5383	−	15.3748i	1.22087	−	0.913934i	0.998141	+	0.0609454i	$0.0194116\pi$
$284$		0			0
$285$	−0.276661	−	0.596456i	−0.0163880	−	0.0353310i
$286$		0			0
$287$	−25.2084	−	9.40227i	−1.48801	−	0.554998i
$288$		0			0
$289$	−21.2185	+	3.05076i	−1.24815	+	0.179456i
$290$		0			0
$291$	−0.282060	−	0.960608i	−0.0165347	−	0.0563119i
$292$		0			0
$293$	−14.3219	+	1.02432i	−0.836696	+	0.0598417i	−0.483109	−	0.875560i	$-0.660493\pi$
$293$	−14.3219	+	1.02432i	−0.836696	+	0.0598417i	−0.353587	+	0.935402i	$0.615038\pi$
$294$		0			0
$295$	2.02647	+	1.49840i	0.117985	+	0.0872402i
$296$		0			0
$297$	0.724889	+	1.94350i	0.0420623	+	0.112773i
$298$		0			0
$299$	8.96417	+	5.43581i	0.518411	+	0.314361i
$300$		0			0
$301$	−1.79218	+	3.92432i	−0.103299	+	0.226194i
$302$		0			0
$303$	0.184993	+	0.0132310i	0.0106276	+	0.000760098i
$304$		0			0
$305$	5.33105	−	9.90168i	0.305255	−	0.566968i
$306$		0			0
$307$	9.03920	+	4.93578i	0.515895	+	0.281700i	0.716031	−	0.698068i	$-0.245957\pi$
$307$	9.03920	+	4.93578i	0.515895	+	0.281700i	−0.200137	+	0.979768i	$0.564139\pi$
$308$		0			0
$309$	0.102050	+	0.709775i	0.00580544	+	0.0403777i
$310$		0			0
$311$	−2.93295	−	6.42227i	−0.166313	−	0.364174i	0.808065	−	0.589094i	$-0.200515\pi$
$311$	−2.93295	−	6.42227i	−0.166313	−	0.364174i	−0.974377	+	0.224920i	$0.927788\pi$
$312$		0			0
$313$	−6.05696	−	27.8434i	−0.342360	−	1.57380i	−0.750492	−	0.660880i	$-0.770183\pi$
$313$	−6.05696	−	27.8434i	−0.342360	−	1.57380i	0.408132	−	0.912923i	$-0.366180\pi$
$314$		0			0
$315$	26.4746	+	22.6680i	1.49168	+	1.27720i
$316$		0			0
$317$	22.4721	+	4.88851i	1.26216	+	0.274566i	0.793368	−	0.608742i	$-0.208326\pi$
$317$	22.4721	+	4.88851i	1.26216	+	0.274566i	0.468793	+	0.883308i	$0.344689\pi$
$318$		0			0
$319$	8.25485	+	2.42384i	0.462183	+	0.135709i
$320$		0			0
$321$		−	1.60785i		−	0.0897416i
$322$		0			0
$323$	−13.7613	+	13.7613i	−0.765697	+	0.765697i
$324$		0			0
$325$	6.44620	−	8.82654i	0.357571	−	0.489609i
$326$		0			0
$327$	−0.328145	+	1.50846i	−0.0181464	+	0.0834178i
$328$		0			0
$329$	−6.70934	+	46.6645i	−0.369898	+	2.57270i
$330$		0			0
$331$	16.4282	+	10.5577i	0.902973	+	0.580306i	0.907671	−	0.419683i	$-0.137859\pi$
$331$	16.4282	+	10.5577i	0.902973	+	0.580306i	−0.00469731	+	0.999989i	$0.501495\pi$
$332$		0			0
$333$	8.73380	−	23.4162i	0.478609	−	1.28320i
$334$		0			0
$335$	3.39955	−	7.56185i	0.185737	−	0.413148i
$336$		0			0
$337$	9.73706	−	17.8321i	0.530412	−	0.971376i	−0.465840	−	0.884869i	$-0.654248\pi$
$337$	9.73706	−	17.8321i	0.530412	−	0.971376i	0.996251	−	0.0865071i	$-0.0275705\pi$
$338$		0			0
$339$	−0.218188	+	0.251802i	−0.0118503	+	0.0136760i
$340$		0			0
$341$	2.01981	−	1.75018i	0.109379	−	0.0947775i
$342$		0			0
$343$	−64.2167	+	23.9516i	−3.46738	+	1.29327i
$344$		0			0
$345$	−0.987888	−	0.182013i	−0.0531861	−	0.00979927i
$346$		0			0
$347$	−16.7555	+	6.24949i	−0.899484	+	0.335490i	−0.756315	−	0.654208i	$-0.773002\pi$
$347$	−16.7555	+	6.24949i	−0.899484	+	0.335490i	−0.143170	+	0.989698i	$0.545729\pi$
$348$		0			0
$349$	−3.02435	+	2.62061i	−0.161890	+	0.140278i	−0.732039	−	0.681263i	$-0.761431\pi$
$349$	−3.02435	+	2.62061i	−0.161890	+	0.140278i	0.570149	+	0.821541i	$0.306886\pi$
$350$		0			0
$351$	−0.803371	+	0.927139i	−0.0428807	+	0.0494870i
$352$		0			0
$353$	−3.87521	+	7.09691i	−0.206257	+	0.377731i	−0.960246	−	0.279156i	$-0.909945\pi$
$353$	−3.87521	+	7.09691i	−0.206257	+	0.377731i	0.753989	+	0.656887i	$0.228127\pi$
$354$		0			0
$355$	−26.5653	+	10.0875i	−1.40994	+	0.535387i
$356$		0			0
$357$	−1.05753	+	2.83534i	−0.0559703	+	0.150062i
$358$		0			0
$359$	5.37915	+	3.45697i	0.283901	+	0.182452i	0.674839	−	0.737965i	$-0.264213\pi$
$359$	5.37915	+	3.45697i	0.283901	+	0.182452i	−0.390938	+	0.920417i	$0.627849\pi$
$360$		0			0
$361$	1.30165	−	9.05318i	0.0685079	−	0.476483i
$362$		0			0
$363$	−0.0529894	+	0.243589i	−0.00278122	+	0.0127851i
$364$		0			0
$365$	−1.85639	−	2.11700i	−0.0971679	−	0.110809i
$366$		0			0
$367$	−9.22004	+	9.22004i	−0.481282	+	0.481282i	−0.905541	−	0.424259i	$-0.860535\pi$
$367$	−9.22004	+	9.22004i	−0.481282	+	0.481282i	0.424259	+	0.905541i	$0.360535\pi$
$368$		0			0
$369$		−	15.4444i		−	0.804002i
$370$		0			0
$371$	−51.2401	−	15.0454i	−2.66025	−	0.781120i
$372$		0			0
$373$	−15.7177	−	3.41918i	−0.813832	−	0.177038i	−0.213659	−	0.976908i	$-0.568538\pi$
$373$	−15.7177	−	3.41918i	−0.813832	−	0.177038i	−0.600173	+	0.799870i	$0.704902\pi$
$374$		0			0
$375$	−0.277203	+	1.00993i	−0.0143147	+	0.0521524i
$376$		0			0
$377$	1.08158	+	4.97193i	0.0557041	+	0.256068i
$378$		0			0
$379$	2.89732	+	6.34424i	0.148825	+	0.325882i	0.969332	−	0.245755i	$-0.0790359\pi$
$379$	2.89732	+	6.34424i	0.148825	+	0.325882i	−0.820507	+	0.571637i	$0.806309\pi$
$380$		0			0
$381$	0.0413017	+	0.287260i	0.00211595	+	0.0147168i
$382$		0			0
$383$	6.49950	+	3.54900i	0.332109	+	0.181345i	0.636648	−	0.771155i	$-0.280321\pi$
$383$	6.49950	+	3.54900i	0.332109	+	0.181345i	−0.304539	+	0.952500i	$0.598502\pi$
$384$		0			0
$385$	12.3771	+	41.2496i	0.630794	+	2.10227i
$386$		0			0
$387$	−2.47020	−	0.176672i	−0.125567	−	0.00898074i
$388$		0			0
$389$	5.34994	−	11.7147i	0.271253	−	0.593960i	−0.724160	−	0.689632i	$-0.757773\pi$
$389$	5.34994	−	11.7147i	0.271253	−	0.593960i	0.995413	+	0.0956713i	$0.0304998\pi$
$390$		0			0
$391$	4.99779	+	29.3098i	0.252749	+	1.48226i
$392$		0			0
$393$	0.0430383	+	0.115390i	0.00217099	+	0.00582066i
$394$		0			0
$395$	2.49722	−	3.37729i	0.125649	−	0.169930i
$396$		0			0
$397$	−24.3832	+	1.74392i	−1.22376	+	0.0875249i	−0.668218	−	0.743965i	$-0.732943\pi$
$397$	−24.3832	+	1.74392i	−1.22376	+	0.0875249i	−0.555540	+	0.831490i	$0.687488\pi$
$398$		0			0
$399$	0.431672	+	1.47014i	0.0216106	+	0.0735990i
$400$		0			0
$401$	11.6429	−	1.67400i	0.581420	−	0.0835956i	0.154672	−	0.987966i	$-0.450568\pi$
$401$	11.6429	−	1.67400i	0.581420	−	0.0835956i	0.426749	+	0.904370i	$0.359659\pi$
$402$		0			0
$403$	1.48097	+	0.552375i	0.0737726	+	0.0275158i
$404$		0			0
$405$	−6.86067	+	18.7313i	−0.340910	+	0.930766i
$406$		0			0
$407$	24.7218	−	18.5065i	1.22542	−	0.917335i
$408$		0			0
$409$	12.2604	+	19.0776i	0.606238	+	0.943325i	0.999712	+	0.0239890i	$0.00763665\pi$
$409$	12.2604	+	19.0776i	0.606238	+	0.943325i	−0.393474	+	0.919336i	$0.628727\pi$
$410$		0			0
$411$	0.509469	−	1.73509i	0.0251302	−	0.0855857i
$412$		0			0
$413$	−4.15294	−	4.15294i	−0.204353	−	0.204353i
$414$		0			0
$415$	−17.2630	+	27.2139i	−0.847410	+	1.33588i
$416$		0			0
$417$	−0.633296	−	1.15980i	−0.0310126	−	0.0567954i
$418$		0			0
$419$	−6.67893	+	4.29228i	−0.326287	+	0.209692i	−0.693520	−	0.720437i	$-0.743941\pi$
$419$	−6.67893	+	4.29228i	−0.326287	+	0.209692i	0.367234	+	0.930129i	$0.380305\pi$
$420$		0			0
$421$	−30.5073	−	4.38629i	−1.48684	−	0.213775i	−0.649457	−	0.760398i	$-0.725004\pi$
$421$	−30.5073	−	4.38629i	−1.48684	−	0.213775i	−0.837378	+	0.546624i	$0.815913\pi$
$422$		0			0
$423$	−26.4442	+	5.75258i	−1.28576	+	0.279700i
$424$		0			0
$425$	30.8914	−	2.57649i	1.49845	−	0.124978i
$426$		0			0
$427$	−15.7049	+	20.9792i	−0.760011	+	1.01526i
$428$		0			0
$429$	−0.726171	+	0.213223i	−0.0350598	+	0.0102945i
$430$		0			0
$431$	19.7726	+	17.1330i	0.952411	+	0.825269i	0.984709	−	0.174209i	$-0.0557369\pi$
$431$	19.7726	+	17.1330i	0.952411	+	0.825269i	−0.0322974	+	0.999478i	$0.510282\pi$
$432$		0			0
$433$	0.531798	−	7.43551i	0.0255566	−	0.357328i	−0.968542	−	0.248849i	$-0.919948\pi$
$433$	0.531798	−	7.43551i	0.0255566	−	0.357328i	0.994099	−	0.108478i	$-0.0345979\pi$
$434$		0			0
$435$	−0.266004	−	0.408585i	−0.0127539	−	0.0195901i
$436$		0			0
$437$	10.9192	+	10.3637i	0.522335	+	0.495765i
$438$		0			0
$439$	18.9660	+	8.66148i	0.905198	+	0.413390i	0.812942	−	0.582345i	$-0.197865\pi$
$439$	18.9660	+	8.66148i	0.905198	+	0.413390i	0.0922564	+	0.995735i	$0.470592\pi$
$440$		0			0
$441$	−39.4763	−	45.5581i	−1.87983	−	2.16943i
$442$		0			0
$443$	2.14618	+	30.0075i	0.101968	+	1.42570i	0.748664	+	0.662949i	$0.230696\pi$
$443$	2.14618	+	30.0075i	0.101968	+	1.42570i	−0.646696	+	0.762748i	$0.723850\pi$
$444$		0			0
$445$	−13.5262	−	24.4272i	−0.641202	−	1.15796i
$446$		0			0
$447$	0.739350	+	0.553470i	0.0349701	+	0.0261783i
$448$		0			0
$449$	−23.6470	+	10.7992i	−1.11597	+	0.509647i	−0.886063	−	0.463566i	$-0.846570\pi$
$449$	−23.6470	+	10.7992i	−1.11597	+	0.509647i	−0.229908	+	0.973212i	$0.573843\pi$
$450$		0			0
$451$	10.3175	−	16.0544i	0.485833	−	0.755972i
$452$		0			0
$453$	0.318443	+	0.425390i	0.0149618	+	0.0199866i
$454$		0			0
$455$	−17.9037	+	18.1164i	−0.839337	+	0.849310i
$456$		0			0
$457$	−15.5427	+	8.48697i	−0.727058	+	0.397004i	−0.799736	−	0.600352i	$-0.795027\pi$
$457$	−15.5427	+	8.48697i	−0.727058	+	0.397004i	0.0726783	+	0.997355i	$0.476845\pi$
$458$		0			0
$459$	−3.47933			−0.162401
$460$		0			0
$461$	−4.59398			−0.213963			−0.106981	−	0.994261i	$-0.534119\pi$
$461$	−4.59398			−0.213963			−0.106981	+	0.994261i	$0.534119\pi$
$462$		0			0
$463$	21.7956	−	11.9013i	1.01293	−	0.553101i	0.115057	−	0.993359i	$-0.463295\pi$
$463$	21.7956	−	11.9013i	1.01293	−	0.553101i	0.897871	+	0.440258i	$0.145113\pi$
$464$		0			0
$465$	−0.151451		0.000894497i	−0.00702338		4.14813e-5i
$466$		0			0
$467$	−18.3930	−	24.5702i	−0.851127	−	1.13697i	−0.989203	−	0.146550i	$-0.953183\pi$
$467$	−18.3930	−	24.5702i	−0.851127	−	1.13697i	0.138077	−	0.990422i	$-0.455908\pi$
$468$		0			0
$469$	−10.4456	+	16.2536i	−0.482332	+	0.750523i
$470$		0			0
$471$	−1.19477	+	0.545632i	−0.0550519	+	0.0251414i
$472$		0			0
$473$	−2.44974	−	1.83385i	−0.112639	−	0.0843205i
$474$		0			0
$475$	11.7395	−	10.4176i	0.538645	−	0.477994i
$476$		0			0
$477$	−2.18694	−	30.5774i	−0.100133	−	1.40004i
$478$		0			0
$479$	−22.7676	−	26.2752i	−1.04028	−	1.20054i	−0.979302	−	0.202404i	$-0.935125\pi$
$479$	−22.7676	−	26.2752i	−1.04028	−	1.20054i	−0.0609748	−	0.998139i	$-0.519421\pi$
$480$		0			0
$481$	16.6135	+	7.58713i	0.757510	+	0.345943i
$482$		0			0
$483$	2.21389	+	0.760557i	0.100735	+	0.0346065i
$484$		0			0
$485$	20.0286	−	13.0394i	0.909450	−	0.592087i
$486$		0			0
$487$	−2.63312	+	36.8159i	−0.119318	+	1.66829i	0.487256	+	0.873259i	$0.337998\pi$
$487$	−2.63312	+	36.8159i	−0.119318	+	1.66829i	−0.606574	+	0.795027i	$0.707457\pi$
$488$		0			0
$489$	−1.45629	−	1.26188i	−0.0658558	−	0.0570644i
$490$		0			0
$491$	−11.2432	+	3.30129i	−0.507397	+	0.148985i	−0.525404	−	0.850853i	$-0.676086\pi$
$491$	−11.2432	+	3.30129i	−0.507397	+	0.148985i	0.0180074	+	0.999838i	$0.494268\pi$
$492$		0			0
$493$	−8.64814	+	11.5526i	−0.389493	+	0.520301i
$494$		0			0
$495$	−19.7030	+	14.9318i	−0.885582	+	0.671136i
$496$		0			0
$497$	64.7064	−	14.0760i	2.90248	−	0.631395i
$498$		0			0
$499$	29.6737	+	4.26643i	1.32838	+	0.190992i	0.769706	−	0.638399i	$-0.220403\pi$
$499$	29.6737	+	4.26643i	1.32838	+	0.190992i	0.558670	+	0.829390i	$0.311312\pi$
$500$		0			0
$501$	1.60943	−	1.03432i	0.0719040	−	0.0462099i
$502$		0			0
$503$	−16.1298	−	29.5396i	−0.719194	−	1.31711i	−0.939794	−	0.341741i	$-0.888983\pi$
$503$	−16.1298	−	29.5396i	−0.719194	−	1.31711i	0.220600	−	0.975364i	$-0.429198\pi$
$504$		0			0
$505$	0.966628	+	4.32050i	0.0430144	+	0.192260i
$506$		0			0
$507$	0.544560	+	0.544560i	0.0241848	+	0.0241848i
$508$		0			0
$509$	−5.85578	+	19.9430i	−0.259553	+	0.883956i	0.721858	+	0.692041i	$0.243288\pi$
$509$	−5.85578	+	19.9430i	−0.259553	+	0.883956i	−0.981411	+	0.191916i	$0.938530\pi$
$510$		0			0
$511$	3.54740	+	5.51986i	0.156928	+	0.244184i
$512$		0			0
$513$	−1.41029	+	1.05573i	−0.0622657	+	0.0466115i
$514$		0			0
$515$	−15.5284	+	7.20272i	−0.684263	+	0.317390i
$516$		0			0
$517$	−31.3316	−	11.6861i	−1.37796	−	0.513954i
$518$		0			0
$519$	−0.399448	+	0.0574320i	−0.0175338	+	0.00252098i
$520$		0			0
$521$	−6.36709	−	21.6843i	−0.278947	−	0.950007i	−0.973139	−	0.230217i	$-0.926056\pi$
$521$	−6.36709	−	21.6843i	−0.278947	−	0.950007i	0.694192	−	0.719790i	$-0.255762\pi$
$522$		0			0
$523$	−25.5022	+	1.82395i	−1.11513	+	0.0797558i	−0.616718	−	0.787184i	$-0.711538\pi$
$523$	−25.5022	+	1.82395i	−1.11513	+	0.0797558i	−0.498413	+	0.866940i	$0.666084\pi$
$524$		0			0
$525$	0.987544	−	2.23182i	0.0431000	−	0.0974044i
$526$		0			0
$527$	1.56662	+	4.20027i	0.0682430	+	0.182966i
$528$		0			0
$529$	22.5642	−	4.45625i	0.981051	−	0.193750i
$530$		0			0
$531$	1.40053	−	3.06674i	0.0607780	−	0.133085i
$532$		0			0
$533$	11.2579	+	0.805180i	0.487633	+	0.0348762i
$534$		0			0
$535$	36.7624	−	11.0307i	1.58938	−	0.476898i
$536$		0			0
$537$	−1.32896	−	0.725666i	−0.0573488	−	0.0313148i
$538$		0			0
$539$	−10.6007	−	73.7295i	−0.456604	−	3.17575i
$540$		0			0
$541$	15.5497	+	34.0491i	0.668534	+	1.46389i	0.874350	+	0.485295i	$0.161288\pi$
$541$	15.5497	+	34.0491i	0.668534	+	1.46389i	−0.205816	+	0.978591i	$0.565985\pi$
$542$		0			0
$543$	0.200117	+	0.919922i	0.00858784	+	0.0394777i
$544$		0			0
$545$	−36.7410	+	2.84597i	−1.57381	+	0.121908i
$546$		0			0
$547$	24.9800	+	5.43406i	1.06807	+	0.232344i	0.712045	−	0.702134i	$-0.247769\pi$
$547$	24.9800	+	5.43406i	1.06807	+	0.232344i	0.356022	+	0.934478i	$0.384133\pi$
$548$		0			0
$549$	−14.4341	−	4.23822i	−0.616030	−	0.180883i
$550$		0			0
$551$			7.30671i			0.311276i
$552$		0			0
$553$	−6.92126	+	6.92126i	−0.294322	+	0.294322i
$554$		0			0
$555$	−1.74627	−	0.114534i	−0.0741251	−	0.00486169i
$556$		0			0
$557$	2.91394	−	13.3952i	0.123468	−	0.567572i	−0.873296	−	0.487189i	$-0.838022\pi$
$557$	2.91394	−	13.3952i	0.123468	−	0.567572i	0.996764	−	0.0803824i	$-0.0256141\pi$
$558$		0			0
$559$	0.257563	−	1.79139i	0.0108938	−	0.0757678i
$560$		0			0
$561$	−1.80573	−	1.16047i	−0.0762380	−	0.0489952i
$562$		0			0
$563$	−7.20354	+	19.3134i	−0.303593	+	0.813964i	0.692147	+	0.721757i	$0.256665\pi$
$563$	−7.20354	+	19.3134i	−0.303593	+	0.813964i	−0.995740	+	0.0922075i	$0.970608\pi$
$564$		0			0
$565$	−7.25416	−	3.26122i	−0.305185	−	0.137201i
$566$		0			0
$567$	22.2786	−	40.8003i	0.935615	−	1.71345i
$568$		0			0
$569$	5.30428	−	6.12147i	0.222367	−	0.256625i	−0.633594	−	0.773666i	$-0.718421\pi$
$569$	5.30428	−	6.12147i	0.222367	−	0.256625i	0.855961	+	0.517041i	$0.172966\pi$
$570$		0			0
$571$	−16.5118	+	14.3075i	−0.690996	+	0.598752i	−0.927921	−	0.372776i	$-0.878406\pi$
$571$	−16.5118	+	14.3075i	−0.690996	+	0.598752i	0.236925	+	0.971528i	$0.423860\pi$
$572$		0			0
$573$	−1.20157	+	0.448163i	−0.0501963	+	0.0187223i
$574$		0			0
$575$	−2.61580	−	23.8361i	−0.109086	−	0.994032i
$576$		0			0
$577$	−6.94505	+	2.59037i	−0.289126	+	0.107838i	−0.489843	−	0.871811i	$-0.662946\pi$
$577$	−6.94505	+	2.59037i	−0.289126	+	0.107838i	0.200716	+	0.979649i	$0.435673\pi$
$578$		0			0
$579$	1.73739	−	1.50546i	0.0722034	−	0.0625646i
$580$		0			0
$581$	49.1811	−	56.7580i	2.04038	−	2.35472i
$582$		0			0
$583$	18.1537	−	33.2461i	0.751851	−	1.37691i
$584$		0			0
$585$	−13.3354	−	5.99514i	−0.551351	−	0.247868i
$586$		0			0
$587$	−8.34600	+	22.3765i	−0.344476	+	0.923577i	0.643008	+	0.765859i	$0.277686\pi$
$587$	−8.34600	+	22.3765i	−0.344476	+	0.923577i	−0.987484	+	0.157717i	$0.949587\pi$
$588$		0			0
$589$	1.90948	+	1.22715i	0.0786787	+	0.0505637i
$590$		0			0
$591$	0.140994	−	0.980633i	0.00579971	−	0.0403378i
$592$		0			0
$593$	−9.86386	+	45.3434i	−0.405060	+	1.86203i	0.0941617	+	0.995557i	$0.469983\pi$
$593$	−9.86386	+	45.3434i	−0.405060	+	1.86203i	−0.499222	+	0.866474i	$0.666381\pi$
$594$		0			0
$595$	−72.0832	−	4.72776i	−2.95512	−	0.193819i
$596$		0			0
$597$	0.308958	−	0.308958i	0.0126448	−	0.0126448i
$598$		0			0
$599$		−	21.0837i		−	0.861457i	−0.902482	−	0.430729i	$-0.858257\pi$
$599$		−	21.0837i		−	0.861457i	0.902482	−	0.430729i	$-0.141743\pi$
$600$		0			0
$601$	3.89733	+	1.14436i	0.158976	+	0.0466794i	0.360252	−	0.932855i	$-0.382691\pi$
$601$	3.89733	+	1.14436i	0.158976	+	0.0466794i	−0.201276	+	0.979534i	$0.564509\pi$
$602$		0			0
$603$	−10.8374	−	2.35753i	−0.441332	−	0.0960059i
$604$		0			0
$605$	−5.93302	+	0.459573i	−0.241211	+	0.0186843i
$606$		0			0
$607$	8.53964	+	39.2561i	0.346613	+	1.59336i	0.739098	+	0.673598i	$0.235252\pi$
$607$	8.53964	+	39.2561i	0.346613	+	1.59336i	−0.392485	+	0.919759i	$0.628384\pi$
$608$		0			0
$609$	0.471976	+	1.03348i	0.0191254	+	0.0418789i
$610$		0			0
$611$	−2.81459	−	19.5759i	−0.113866	−	0.791956i
$612$		0			0
$613$	31.9886	+	17.4671i	1.29201	+	0.705489i	0.970427	−	0.241393i	$-0.0776043\pi$
$613$	31.9886	+	17.4671i	1.29201	+	0.705489i	0.321580	+	0.946882i	$0.395786\pi$
$614$		0			0
$615$	−1.03584	+	0.310808i	−0.0417693	+	0.0125330i
$616$		0			0
$617$	−36.9027	−	2.63934i	−1.48565	−	0.106256i	−0.695214	−	0.718803i	$-0.744690\pi$
$617$	−36.9027	−	2.63934i	−1.48565	−	0.106256i	−0.790434	+	0.612547i	$0.790145\pi$
$618$		0			0
$619$	−9.25412	+	20.2637i	−0.371954	+	0.814466i	0.627406	+	0.778693i	$0.284117\pi$
$619$	−9.25412	+	20.2637i	−0.371954	+	0.814466i	−0.999360	+	0.0357737i	$0.988610\pi$
$620$		0			0
$621$	0.0702169	+	2.69054i	0.00281771	+	0.107968i
$622$		0			0
$623$	22.7392	+	60.9662i	0.911027	+	2.44256i
$624$		0			0
$625$	−24.9930	+	0.590556i	−0.999721	+	0.0236222i
$626$		0			0
$627$	−1.08404	+	0.0775321i	−0.0432924	+	0.00309633i
$628$		0			0
$629$	14.5936	+	49.7011i	0.581884	+	1.98171i
$630$		0			0
$631$	−16.2403	+	2.33500i	−0.646515	+	0.0929548i	−0.457769	−	0.889071i	$-0.651351\pi$
$631$	−16.2403	+	2.33500i	−0.646515	+	0.0929548i	−0.188746	+	0.982026i	$0.560442\pi$
$632$		0			0
$633$	−0.0971701	−	0.0362426i	−0.00386216	−	0.00144051i
$634$		0			0
$635$	−6.28464	+	2.91508i	−0.249398	+	0.115681i
$636$		0			0
$637$	35.2668	−	26.4004i	1.39732	−	1.04602i
$638$		0			0
$639$	20.5512	+	31.9783i	0.812992	+	1.26504i
$640$		0			0
$641$	−13.0786	+	44.5416i	−0.516573	+	1.75929i	0.124930	+	0.992166i	$0.460129\pi$
$641$	−13.0786	+	44.5416i	−0.516573	+	1.75929i	−0.641503	+	0.767121i	$0.721689\pi$
$642$		0			0
$643$	2.82024	+	2.82024i	0.111220	+	0.111220i	0.760526	−	0.649307i	$-0.224941\pi$
$643$	2.82024	+	2.82024i	0.111220	+	0.111220i	−0.649307	+	0.760526i	$0.724941\pi$
$644$		0			0
$645$	0.0378618	+	0.169230i	0.00149081	+	0.00666341i
$646$		0			0
$647$	4.11924	+	7.54383i	0.161944	+	0.296578i	0.946033	−	0.324070i	$-0.105051\pi$
$647$	4.11924	+	7.54383i	0.161944	+	0.296578i	−0.784089	+	0.620648i	$0.786869\pi$
$648$		0			0
$649$	3.50457	−	2.25225i	0.137566	−	0.0884085i
$650$		0			0
$651$	0.349350	+	0.0502289i	0.0136921	+	0.00196863i
$652$		0			0
$653$	4.86422	−	1.05815i	0.190352	−	0.0414085i	−0.116379	−	0.993205i	$-0.537129\pi$
$653$	4.86422	−	1.05815i	0.190352	−	0.0414085i	0.306730	+	0.951796i	$0.400765\pi$
$654$		0			0
$655$	−2.34305	+	1.77567i	−0.0915505	+	0.0693813i
$656$		0			0
$657$	−2.25720	+	3.01527i	−0.0880618	+	0.117637i
$658$		0			0
$659$	16.1318	−	4.73672i	0.628405	−	0.184516i	0.0480038	−	0.998847i	$-0.484714\pi$
$659$	16.1318	−	4.73672i	0.628405	−	0.184516i	0.580401	+	0.814331i	$0.302896\pi$
$660$		0			0
$661$	8.96638	+	7.76941i	0.348752	+	0.302195i	0.811567	−	0.584260i	$-0.198615\pi$
$661$	8.96638	+	7.76941i	0.348752	+	0.302195i	−0.462815	+	0.886455i	$0.653161\pi$
$662$		0			0
$663$	0.0905633	−	1.26624i	0.00351719	−	0.0491767i
$664$		0			0
$665$	−30.6522	+	19.9558i	−1.18864	+	0.773851i
$666$		0			0
$667$	9.10803	+	6.45439i	0.352664	+	0.249915i
$668$		0			0
$669$	0.268574	+	0.122654i	0.0103837	+	0.00474207i
$670$		0			0
$671$	−12.1728	−	14.0482i	−0.469927	−	0.542325i
$672$		0			0
$673$	0.813003	+	11.3673i	0.0313390	+	0.438176i	0.988763	+	0.149491i	$0.0477635\pi$
$673$	0.813003	+	11.3673i	0.0313390	+	0.438176i	−0.957424	+	0.288685i	$0.906782\pi$
$674$		0			0
$675$	2.80106	+	0.167106i	0.107813	+	0.00643192i
$676$		0			0
$677$	−36.4239	−	27.2666i	−1.39988	−	1.04794i	−0.990784	−	0.135452i	$-0.956752\pi$
$677$	−36.4239	−	27.2666i	−1.39988	−	1.04794i	−0.409101	−	0.912489i	$-0.634158\pi$
$678$		0			0
$679$	−50.6607	+	23.1360i	−1.94418	+	0.887877i
$680$		0			0
$681$	−0.0306428	+	0.0476811i	−0.00117424	+	0.00182715i
$682$		0			0
$683$	−18.5080	−	24.7237i	−0.708188	−	0.946028i	0.291758	−	0.956492i	$-0.405760\pi$
$683$	−18.5080	−	24.7237i	−0.708188	−	0.946028i	−0.999945	+	0.0104644i	$0.996669\pi$
$684$		0			0
$685$	43.1668	−	0.254951i	1.64932	−	0.00974117i
$686$		0			0
$687$	0.333639	−	0.182181i	0.0127291	−	0.00695063i
$688$		0			0
$689$	22.4028			0.853480
$690$		0			0
$691$	−2.37208			−0.0902382			−0.0451191	−	0.998982i	$-0.514367\pi$
$691$	−2.37208			−0.0902382			−0.0451191	+	0.998982i	$0.514367\pi$
$692$		0			0
$693$	50.5637	−	27.6099i	1.92076	−	1.04881i
$694$		0			0
$695$	22.1732	−	22.4366i	0.841076	−	0.851070i
$696$		0			0
$697$	19.1833	+	25.6258i	0.726617	+	0.970647i
$698$		0			0
$699$	−0.251151	+	0.390799i	−0.00949941	+	0.0147814i
$700$		0			0
$701$	−46.3864	+	21.1839i	−1.75199	+	0.800106i	−0.764070	+	0.645133i	$0.776802\pi$
$701$	−46.3864	+	21.1839i	−1.75199	+	0.800106i	−0.987919	+	0.154973i	$0.950471\pi$
$702$		0			0
$703$	20.9960	+	15.7174i	0.791877	+	0.592792i
$704$		0			0
$705$	0.917994	+	1.65783i	0.0345737	+	0.0624374i
$706$		0			0
$707$	−0.736024	−	10.2910i	−0.0276810	−	0.387032i
$708$		0			0
$709$	−18.0763	−	20.8612i	−0.678871	−	0.783459i	0.306866	−	0.951753i	$-0.400720\pi$
$709$	−18.0763	−	20.8612i	−0.678871	−	0.783459i	−0.985737	+	0.168294i	$0.946174\pi$
$710$		0			0
$711$	−5.11101	−	2.33412i	−0.191678	−	0.0875363i
$712$		0			0
$713$	3.21641	−	1.29622i	0.120456	−	0.0485438i
$714$		0			0
$715$	−9.85709	−	15.1406i	−0.368634	−	0.566225i
$716$		0			0
$717$	−0.104911	+	1.46684i	−0.00391796	+	0.0547802i
$718$		0			0
$719$	−4.52564	−	3.92149i	−0.168778	−	0.146247i	0.566376	−	0.824147i	$-0.308345\pi$
$719$	−4.52564	−	3.92149i	−0.168778	−	0.146247i	−0.735154	+	0.677900i	$0.762890\pi$
$720$		0			0
$721$	38.2743	−	11.2383i	1.42541	−	0.418538i
$722$		0			0
$723$	0.0833787	−	0.111381i	0.00310089	−	0.00414230i
$724$		0			0
$725$	7.51708	−	8.88510i	0.279177	−	0.329984i
$726$		0			0
$727$	13.7349	−	2.98785i	0.509401	−	0.110813i	0.0494831	−	0.998775i	$-0.484243\pi$
$727$	13.7349	−	2.98785i	0.509401	−	0.110813i	0.459917	+	0.887962i	$0.347879\pi$
$728$		0			0
$729$	26.2573	+	3.77523i	0.972494	+	0.139823i
$730$		0			0
$731$	4.31807	−	2.77506i	0.159710	−	0.102639i
$732$		0			0
$733$	3.72159	+	6.81559i	0.137460	+	0.251740i	0.937337	−	0.348425i	$-0.113283\pi$
$733$	3.72159	+	6.81559i	0.137460	+	0.251740i	−0.799876	+	0.600165i	$0.795102\pi$
$734$		0			0
$735$	−2.26112	+	3.56448i	−0.0834025	+	0.131478i
$736$		0			0
$737$	−9.69049	−	9.69049i	−0.356954	−	0.356954i
$738$		0			0
$739$	0.354436	−	1.20710i	0.0130381	−	0.0444038i	−0.952717	−	0.303859i	$-0.901725\pi$
$739$	0.354436	−	1.20710i	0.0130381	−	0.0444038i	0.965755	+	0.259455i	$0.0835430\pi$
$740$		0			0
$741$	−0.347504	−	0.540728i	−0.0127659	−	0.0198641i
$742$		0			0
$743$	−3.81643	+	2.85694i	−0.140011	+	0.104811i	−0.666987	−	0.745069i	$-0.732417\pi$
$743$	−3.81643	+	2.85694i	−0.140011	+	0.104811i	0.526976	+	0.849880i	$0.323326\pi$
$744$		0			0
$745$	−7.58240	+	20.7018i	−0.277798	+	0.758455i
$746$		0			0
$747$	40.3930	+	15.0658i	1.47790	+	0.551229i
$748$		0			0
$749$	−88.5328	+	12.7291i	−3.23492	+	0.465111i
$750$		0			0
$751$	−5.37467	−	18.3044i	−0.196124	−	0.667938i	−0.997557	−	0.0698536i	$-0.977747\pi$
$751$	−5.37467	−	18.3044i	−0.196124	−	0.667938i	0.801433	−	0.598085i	$-0.204071\pi$
$752$		0			0
$753$	−1.98609	+	0.142048i	−0.0723772	+	0.00517652i
$754$		0			0
$755$	−7.54157	+	10.1994i	−0.274466	+	0.371193i
$756$		0			0
$757$	−2.94391	−	7.89292i	−0.106998	−	0.286873i	0.872406	−	0.488781i	$-0.162558\pi$
$757$	−2.94391	−	7.89292i	−0.106998	−	0.286873i	−0.979404	+	0.201908i	$0.935286\pi$
$758$		0			0
$759$	−0.860942	+	1.41978i	−0.0312502	+	0.0515346i
$760$		0			0
$761$	2.69497	−	5.90117i	0.0976927	−	0.213917i	−0.854475	−	0.519492i	$-0.826121\pi$
$761$	2.69497	−	5.90117i	0.0976927	−	0.213917i	0.952168	+	0.305575i	$0.0988486\pi$
$762$		0			0
$763$	85.6576	+	6.12635i	3.10101	+	0.221789i
$764$		0			0
$765$	−11.9175	−	39.7180i	−0.430878	−	1.43601i
$766$		0			0
$767$	2.16243	+	1.18077i	0.0780807	+	0.0426353i
$768$		0			0
$769$	−5.20768	−	36.2202i	−0.187794	−	1.30613i	−0.837704	−	0.546124i	$-0.816103\pi$
$769$	−5.20768	−	36.2202i	−0.187794	−	1.30613i	0.649910	−	0.760011i	$-0.274806\pi$
$770$		0			0
$771$	−0.592213	−	1.29677i	−0.0213280	−	0.0467019i
$772$		0			0
$773$	−8.21535	−	37.7653i	−0.295486	−	1.35833i	−0.850277	−	0.526336i	$-0.823566\pi$
$773$	−8.21535	−	37.7653i	−0.295486	−	1.35833i	0.554791	−	0.831989i	$-0.312798\pi$
$774$		0			0
$775$	−1.05948	−	3.45669i	−0.0380578	−	0.124168i
$776$		0			0
$777$	3.98499	+	0.866882i	0.142961	+	0.0310992i
$778$		0			0
$779$	15.5512	+	4.56624i	0.557179	+	0.163602i
$780$		0			0
$781$			46.9704i			1.68073i
$782$		0			0
$783$	−0.923698	+	0.923698i	−0.0330103	+	0.0330103i
$784$		0			0
$785$	−20.6722	−	23.5742i	−0.737822	−	0.841399i
$786$		0			0
$787$	8.65982	−	39.8085i	0.308689	−	1.41902i	−0.517527	−	0.855667i	$-0.673147\pi$
$787$	8.65982	−	39.8085i	0.308689	−	1.41902i	0.826216	−	0.563354i	$-0.190489\pi$
$788$		0			0
$789$	−0.160181	+	1.11409i	−0.00570261	+	0.0396625i
$790$		0			0
$791$	15.5923	+	10.0205i	0.554398	+	0.356290i
$792$		0			0
$793$	3.84188	−	10.3005i	0.136429	−	0.365781i
$794$		0			0
$795$	−2.00679	+	0.762027i	−0.0711737	+	0.0270263i
$796$		0			0
$797$	0.907934	−	1.66276i	0.0321607	−	0.0588979i	−0.861104	−	0.508428i	$-0.830227\pi$
$797$	0.907934	−	1.66276i	0.0321607	−	0.0588979i	0.893265	+	0.449530i	$0.148409\pi$
$798$		0			0
$799$	36.7319	−	42.3908i	1.29948	−	1.49968i
$800$		0			0
$801$	−28.2287	+	24.4603i	−0.997413	+	0.864263i
$802$		0			0
$803$	−4.36069	+	1.62645i	−0.153885	+	0.0573962i
$804$		0			0
$805$	−2.20122	+	55.8368i	−0.0775827	+	1.96799i
$806$		0			0
$807$	−0.641341	+	0.239208i	−0.0225763	+	0.00842051i
$808$		0			0
$809$	14.3327	−	12.4194i	0.503912	−	0.436643i	−0.365440	−	0.930835i	$-0.619082\pi$
$809$	14.3327	−	12.4194i	0.503912	−	0.436643i	0.869353	+	0.494192i	$0.164536\pi$
$810$		0			0
$811$	−25.9379	+	29.9339i	−0.910802	+	1.05112i	0.0876859	+	0.996148i	$0.472053\pi$
$811$	−25.9379	+	29.9339i	−0.910802	+	1.05112i	−0.998488	+	0.0549733i	$0.982493\pi$
$812$		0			0
$813$	0.296100	−	0.542266i	0.0103847	−	0.0190181i
$814$		0			0
$815$	18.8612	−	41.9542i	0.660679	−	1.46959i
$816$		0			0
$817$	0.908224	−	2.43504i	0.0317747	−	0.0851914i
$818$		0			0
$819$	28.6634	+	18.4209i	1.00158	+	0.643677i
$820$		0			0
$821$	1.55883	−	10.8419i	0.0544035	−	0.378385i	−0.944371	−	0.328883i	$-0.893328\pi$
$821$	1.55883	−	10.8419i	0.0544035	−	0.378385i	0.998774	−	0.0495014i	$-0.0157632\pi$
$822$		0			0
$823$	1.01471	−	4.66453i	0.0353704	−	0.162595i	−0.956074	−	0.293126i	$-0.905304\pi$
$823$	1.01471	−	4.66453i	0.0353704	−	0.162595i	0.991444	+	0.130531i	$0.0416681\pi$
$824$		0			0
$825$	1.39798	+	1.02097i	0.0486713	+	0.0355456i
$826$		0			0
$827$	30.5587	−	30.5587i	1.06263	−	1.06263i	0.0647275	−	0.997903i	$-0.479382\pi$
$827$	30.5587	−	30.5587i	1.06263	−	1.06263i	0.997903	−	0.0647275i	$-0.0206178\pi$
$828$		0			0
$829$			9.00927i			0.312905i	0.987686	+	0.156452i	$0.0500058\pi$
$829$			9.00927i			0.312905i	−0.987686	+	0.156452i	$0.949994\pi$
$830$		0			0
$831$	1.17752	+	0.345750i	0.0408476	+	0.0119939i
$832$		0			0
$833$	122.088	+	26.5585i	4.23008	+	0.920198i
$834$		0			0
$835$	34.6904	+	29.7025i	1.20051	+	1.02790i
$836$		0			0
$837$	0.0862588	+	0.396525i	0.00298154	+	0.0137059i
$838$		0			0
$839$	−5.77968	−	12.6557i	−0.199537	−	0.436924i	0.783240	−	0.621719i	$-0.213565\pi$
$839$	−5.77968	−	12.6557i	−0.199537	−	0.436924i	−0.982777	+	0.184794i	$0.940838\pi$
$840$		0			0
$841$	−3.35606	−	23.3419i	−0.115726	−	0.804894i
$842$		0			0
$843$	−0.486840	−	0.265835i	−0.0167676	−	0.00915583i
$844$		0			0
$845$	−8.71503	+	16.1869i	−0.299806	+	0.556848i
$846$		0			0
$847$	13.8322	+	0.989296i	0.475279	+	0.0339926i
$848$		0			0
$849$	−0.998320	+	2.18602i	−0.0342623	+	0.0750239i
$850$		0			0
$851$	38.1389	−	12.2881i	1.30739	−	0.421231i
$852$		0			0
$853$	−14.5223	−	38.9357i	−0.497232	−	1.33313i	−0.907073	−	0.420974i	$-0.861688\pi$
$853$	−14.5223	−	38.9357i	−0.497232	−	1.33313i	0.409840	−	0.912157i	$-0.365584\pi$
$854$		0			0
$855$	−16.8821	−	12.4829i	−0.577356	−	0.426906i
$856$		0			0
$857$	−50.0636	+	3.58062i	−1.71014	+	0.122312i	−0.891801	−	0.452427i	$-0.850558\pi$
$857$	−50.0636	+	3.58062i	−1.71014	+	0.122312i	−0.818337	+	0.574738i	$0.805104\pi$
$858$		0			0
$859$	−6.21934	−	21.1811i	−0.212201	−	0.722690i	−0.994952	−	0.100355i	$-0.968002\pi$
$859$	−6.21934	−	21.1811i	−0.212201	−	0.722690i	0.782751	−	0.622335i	$-0.213816\pi$
$860$		0			0
$861$	2.49456	−	0.358664i	0.0850144	−	0.0122232i
$862$		0			0
$863$	4.80760	+	1.79314i	0.163653	+	0.0610393i	0.429955	−	0.902850i	$-0.358529\pi$
$863$	4.80760	+	1.79314i	0.163653	+	0.0610393i	−0.266303	+	0.963889i	$0.585802\pi$
$864$		0			0
$865$	−4.05356	−	8.73909i	−0.137825	−	0.297138i
$866$		0			0
$867$	1.60749	−	1.20335i	0.0545933	−	0.0408680i
$868$		0			0
$869$	−3.75359	−	5.84069i	−0.127332	−	0.198132i
$870$		0			0
$871$	2.28347	−	7.77679i	0.0773725	−	0.263507i
$872$		0			0
$873$	−22.6064	−	22.6064i	−0.765110	−	0.765110i
$874$		0			0
$875$	57.8039	+	7.26814i	1.95413	+	0.245708i
$876$		0			0
$877$	−18.0652	−	33.0839i	−0.610017	−	1.11716i	−0.981992	−	0.188920i	$-0.939501\pi$
$877$	−18.0652	−	33.0839i	−0.610017	−	1.11716i	0.371976	−	0.928243i	$-0.378680\pi$
$878$		0			0
$879$	1.13147	−	0.727153i	0.0381636	−	0.0245263i
$880$		0			0
$881$	−3.51891	−	0.505942i	−0.118555	−	0.0170456i	0.0827819	−	0.996568i	$-0.473620\pi$
$881$	−3.51891	−	0.505942i	−0.118555	−	0.0170456i	−0.201337	+	0.979522i	$0.564529\pi$
$882$		0			0
$883$	−19.1818	+	4.17274i	−0.645519	+	0.140424i	−0.523394	−	0.852091i	$-0.675334\pi$
$883$	−19.1818	+	4.17274i	−0.645519	+	0.140424i	−0.122125	+	0.992515i	$0.538971\pi$
$884$		0			0
$885$	−0.233869	−	0.0322167i	−0.00786142	−	0.00108295i
$886$		0			0
$887$	−9.99376	+	13.3501i	−0.335558	+	0.448252i	−0.936306	−	0.351186i	$-0.885779\pi$
$887$	−9.99376	+	13.3501i	−0.335558	+	0.448252i	0.600748	+	0.799438i	$0.294869\pi$
$888$		0			0
$889$	15.4903	−	4.54837i	0.519529	−	0.152547i
$890$		0			0
$891$	24.9197	+	21.5930i	0.834840	+	0.723393i
$892$		0			0
$893$	2.02605	−	28.3279i	0.0677991	−	0.947956i
$894$		0			0
$895$	7.47452	−	35.3641i	0.249846	−	1.18209i
$896$		0			0
$897$	−0.981001	−	0.0444777i	−0.0327547	−	0.00148507i
$898$		0			0
$899$	1.53100	+	0.699184i	0.0510617	+	0.0233191i
$900$		0			0
$901$	41.6084	+	48.0187i	1.38618	+	1.59973i
$902$		0			0
$903$	−0.0288293	−	0.403087i	−0.000959380	−	0.0134139i
$904$		0			0
$905$	−19.6605	+	10.8867i	−0.653536	+	0.361885i
$906$		0			0
$907$	−20.2185	−	15.1354i	−0.671343	−	0.502561i	0.208380	−	0.978048i	$-0.433181\pi$
$907$	−20.2185	−	15.1354i	−0.671343	−	0.502561i	−0.879723	+	0.475487i	$0.842272\pi$
$908$		0			0
$909$	5.38729	−	2.46029i	0.178685	−	0.0816028i
$910$		0			0
$911$	−3.60786	+	5.61394i	−0.119534	+	0.185998i	−0.895864	−	0.444328i	$-0.853442\pi$
$911$	−3.60786	+	5.61394i	−0.119534	+	0.185998i	0.776330	+	0.630326i	$0.217079\pi$
$912$		0			0
$913$	31.9238	+	42.6452i	1.05652	+	1.41135i
$914$		0			0
$915$	0.00622141	+	1.05337i	0.000205673	+	0.0348235i
$916$		0			0
$917$	6.01297	−	3.28333i	0.198566	−	0.108425i
$918$		0			0
$919$	−9.30621			−0.306984			−0.153492	−	0.988150i	$-0.549052\pi$
$919$	−9.30621			−0.306984			−0.153492	+	0.988150i	$0.549052\pi$
$920$		0			0
$921$	−0.964722			−0.0317887
$922$		0			0
$923$	−24.3814	+	13.3132i	−0.802523	+	0.438210i
$924$		0			0
$925$	−9.36157	−	40.7130i	−0.307807	−	1.33864i
$926$		0			0
$927$	13.7225	+	18.3311i	0.450707	+	0.602073i
$928$		0			0
$929$	−13.9736	+	21.7433i	−0.458458	+	0.713374i	−0.991122	−	0.132952i	$-0.957554\pi$
$929$	−13.9736	+	21.7433i	−0.458458	+	0.713374i	0.532665	+	0.846326i	$0.321191\pi$
$930$		0			0
$931$	57.5446	−	26.2798i	1.88595	−	0.861284i
$932$		0			0
$933$	0.529437	+	0.396332i	0.0173330	+	0.0129753i
$934$		0			0
$935$	14.1452	−	49.2482i	0.462597	−	1.61059i
$936$		0			0
$937$	−0.280166	−	3.91723i	−0.00915262	−	0.127970i	0.990821	−	0.135177i	$-0.0431604\pi$
$937$	−0.280166	−	3.91723i	−0.00915262	−	0.127970i	−0.999974	+	0.00720707i	$0.997706\pi$
$938$		0			0
$939$	1.74791	+	2.01720i	0.0570409	+	0.0658287i
$940$		0			0
$941$	10.6775	+	4.87624i	0.348076	+	0.158961i	0.581778	−	0.813347i	$-0.302357\pi$
$941$	10.6775	+	4.87624i	0.348076	+	0.158961i	−0.233703	+	0.972308i	$0.575084\pi$
$942$		0			0
$943$	19.4291	−	15.3514i	0.632698	−	0.499910i
$944$		0			0
$945$	−6.39774	−	1.35222i	−0.208119	−	0.0439877i
$946$		0			0
$947$	−0.499312	+	6.98129i	−0.0162255	+	0.226861i	0.982869	+	0.184307i	$0.0590041\pi$
$947$	−0.499312	+	6.98129i	−0.0162255	+	0.226861i	−0.999094	+	0.0425543i	$0.986450\pi$
$948$		0			0
$949$	−2.08025	−	1.80254i	−0.0675276	−	0.0585130i
$950$		0			0
$951$	−2.06697	+	0.606917i	−0.0670261	+	0.0196806i
$952$		0			0
$953$	6.37164	−	8.51151i	0.206398	−	0.275715i	−0.685383	−	0.728183i	$-0.740365\pi$
$953$	6.37164	−	8.51151i	0.206398	−	0.275715i	0.891781	+	0.452468i	$0.149456\pi$
$954$		0			0
$955$	−18.4903	−	24.3985i	−0.598332	−	0.789515i
$956$		0			0
$957$	−0.787472	+	0.171304i	−0.0254553	+	0.00553747i
$958$		0			0
$959$	−99.5722	−	14.3163i	−3.21536	−	0.462298i
$960$		0			0
$961$	−25.6390	+	16.4772i	−0.827065	+	0.531522i
$962$		0			0
$963$	−24.6065	−	45.0634i	−0.792932	−	1.45215i
$964$		0			0
$965$	46.3405	+	29.3960i	1.49175	+	0.946290i
$966$		0			0
$967$	−28.4658	−	28.4658i	−0.915397	−	0.915397i	0.0812932	−	0.996690i	$-0.474095\pi$
$967$	−28.4658	−	28.4658i	−0.915397	−	0.915397i	−0.996690	+	0.0812932i	$0.974095\pi$
$968$		0			0
$969$	0.513591	−	1.74913i	0.0164989	−	0.0561902i
$970$		0			0
$971$	31.8548	+	49.5670i	1.02227	+	1.59068i	0.785253	+	0.619175i	$0.212533\pi$
$971$	31.8548	+	49.5670i	1.02227	+	1.59068i	0.237015	+	0.971506i	$0.423831\pi$
$972$		0			0
$973$	−58.8478	+	44.0529i	−1.88657	+	1.41227i
$974$		0			0
$975$	−0.133724	+	1.01504i	−0.00428259	+	0.0325074i
$976$		0			0
$977$	46.8619	+	17.4786i	1.49925	+	0.559190i	0.959270	−	0.282491i	$-0.0911608\pi$
$977$	46.8619	+	17.4786i	1.49925	+	0.559190i	0.539976	+	0.841681i	$0.318433\pi$
$978$		0			0
$979$	−45.6843	+	6.56840i	−1.46008	+	0.209927i
$980$		0			0
$981$	13.8884	+	47.2995i	0.443422	+	1.51016i
$982$		0			0
$983$	24.8242	−	1.77546i	0.791769	−	0.0566284i	0.330405	−	0.943839i	$-0.392815\pi$
$983$	24.8242	−	1.77546i	0.791769	−	0.0566284i	0.461364	+	0.887211i	$0.347360\pi$
$984$		0			0
$985$	23.3888	−	3.50391i	0.745228	−	0.111644i
$986$		0			0
$987$	−1.54326	−	4.13765i	−0.0491226	−	0.131703i
$988$		0			0
$989$	−2.23307	−	3.28312i	−0.0710075	−	0.104397i
$990$		0			0
$991$	19.2444	−	42.1394i	0.611320	−	1.33860i	−0.310348	−	0.950623i	$-0.600446\pi$
$991$	19.2444	−	42.1394i	0.611320	−	1.33860i	0.921668	−	0.387980i	$-0.126827\pi$
$992$		0			0
$993$	−1.82457	−	0.130496i	−0.0579011	−	0.00414117i
$994$		0			0
$995$	9.18372	+	4.94451i	0.291144	+	0.156751i
$996$		0			0
$997$	22.0128	+	12.0199i	0.697151	+	0.380673i	0.788407	−	0.615154i	$-0.210906\pi$
$997$	22.0128	+	12.0199i	0.697151	+	0.380673i	−0.0912559	+	0.995827i	$0.529088\pi$
$998$		0			0
$999$	0.667306	+	4.64121i	0.0211126	+	0.146842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.17.17	✓	720
5.3	odd	4	inner	920.2.bv.a.753.17	yes	720
23.19	odd	22	inner	920.2.bv.a.617.17	yes	720
115.88	even	44	inner	920.2.bv.a.433.17	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.17	✓	720	1.1	even	1	trivial
920.2.bv.a.433.17	yes	720	115.88	even	44	inner
920.2.bv.a.617.17	yes	720	23.19	odd	22	inner
920.2.bv.a.753.17	yes	720	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0822135 + 0.0448920i) q^{3} +(-1.59045 - 1.57177i) q^{5} +(3.12275 + 4.17150i) q^{7} +(-1.61718 + 2.51638i) q^{9} +(-3.36211 + 1.53542i) q^{11} +(-1.74996 - 1.31000i) q^{13} +(0.201316 + 0.0578226i) q^{15} +(-0.442284 - 6.18393i) q^{17} +(-2.05565 - 2.37235i) q^{19} +(-0.443999 - 0.202768i) q^{21} +(-4.77306 + 0.466813i) q^{23} +(0.0590597 + 4.99965i) q^{25} +(0.0400361 - 0.559777i) q^{27} +(-1.75914 - 1.52430i) q^{29} +(-0.693792 + 0.203716i) q^{31} +(0.207482 - 0.277164i) q^{33} +(1.59008 - 11.5428i) q^{35} +(-8.16416 + 1.77600i) q^{37} +(0.202679 + 0.0291408i) q^{39} +(-4.34358 + 2.79145i) q^{41} +(0.396781 + 0.726651i) q^{43} +(6.52722 - 1.46034i) q^{45} +(6.39744 + 6.39744i) q^{47} +(-5.67774 + 19.3366i) q^{49} +(0.313971 + 0.488548i) q^{51} +(-8.20433 + 6.14168i) q^{53} +(7.76059 + 2.84245i) q^{55} +(0.275502 + 0.102757i) q^{57} +(-1.11563 + 0.160403i) q^{59} +(1.41688 + 4.82546i) q^{61} +(-15.5471 + 1.11195i) q^{63} +(0.724194 + 4.83403i) q^{65} +(1.29574 + 3.47401i) q^{67} +(0.371454 - 0.252650i) q^{69} +(5.27911 - 11.5596i) q^{71} +(1.25599 + 0.0898299i) q^{73} +(-0.229300 - 0.408388i) q^{75} +(-16.9040 - 9.23029i) q^{77} +(0.267327 + 1.85930i) q^{79} +(-3.70596 - 8.11493i) q^{81} +(-3.06361 - 14.0832i) q^{83} +(-9.01631 + 10.5304i) q^{85} +(0.213054 + 0.0463470i) q^{87} +(11.9814 + 3.51804i) q^{89} -11.3907i q^{91} +(0.0478939 - 0.0478939i) q^{93} +(-0.459383 + 7.00411i) q^{95} +(-2.27190 + 10.4438i) q^{97} +(1.57342 - 10.9434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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