LMFDB - Embedded newform 640.2.x.a.81.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(81,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("640.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.x (of order $8$, degree $4$, not 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.9
Character	$\chi$	$=$	640.81
Dual form			640.2.x.a.561.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.293011 + 0.121369i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-1.60956 + 1.60956i) q^{7} +(-2.05020 - 2.05020i) q^{9} +O(q^{10})$	\(q+(0.293011 + 0.121369i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-1.60956 + 1.60956i) q^{7} +(-2.05020 - 2.05020i) q^{9} +(-1.67662 + 0.694479i) q^{11} +(0.978679 - 2.36274i) q^{13} -0.317153i q^{15} -7.38531i q^{17} +(2.51097 - 6.06201i) q^{19} +(-0.666968 + 0.276267i) q^{21} +(0.415483 + 0.415483i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-0.716006 - 1.72859i) q^{27} +(1.25776 + 0.520982i) q^{29} -10.3170 q^{31} -0.575556 q^{33} +(2.10299 + 0.871086i) q^{35} +(2.88274 + 6.95955i) q^{37} +(0.573527 - 0.573527i) q^{39} +(-3.16408 - 3.16408i) q^{41} +(1.66790 - 0.690868i) q^{43} +(-1.10956 + 2.67871i) q^{45} -9.77862i q^{47} +1.81865i q^{49} +(0.896349 - 2.16398i) q^{51} +(-1.69543 + 0.702269i) q^{53} +(1.28323 + 1.28323i) q^{55} +(1.47148 - 1.47148i) q^{57} +(-0.870931 - 2.10261i) q^{59} +(2.77121 + 1.14787i) q^{61} +6.59981 q^{63} -2.55741 q^{65} +(7.25385 + 3.00464i) q^{67} +(0.0713143 + 0.172168i) q^{69} +(-6.44757 + 6.44757i) q^{71} +(-8.80279 - 8.80279i) q^{73} +(-0.293011 + 0.121369i) q^{75} +(1.58081 - 3.81642i) q^{77} -0.377013i q^{79} +8.10484i q^{81} +(1.61547 - 3.90008i) q^{83} +(-6.82314 + 2.82624i) q^{85} +(0.305307 + 0.305307i) q^{87} +(0.367841 - 0.367841i) q^{89} +(2.22773 + 5.37821i) q^{91} +(-3.02299 - 1.25216i) q^{93} -6.56147 q^{95} +18.3365 q^{97} +(4.86122 + 2.01358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) $ 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	0.293011	+	0.121369i	0.169170	+	0.0700725i	0.465661	−	0.884963i	$-0.345817\pi$
$3$	0.293011	+	0.121369i	0.169170	+	0.0700725i	−0.296491	+	0.955036i	$0.595817\pi$
$4$		0			0
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$6$		0			0
$7$	−1.60956	+	1.60956i	−0.608356	+	0.608356i	−0.942516	−	0.334161i	$-0.891547\pi$
$7$	−1.60956	+	1.60956i	−0.608356	+	0.608356i	0.334161	+	0.942516i	$0.391547\pi$
$8$		0			0
$9$	−2.05020	−	2.05020i	−0.683398	−	0.683398i
$10$		0			0
$11$	−1.67662	+	0.694479i	−0.505520	+	0.209393i	−0.620843	−	0.783935i	$-0.713210\pi$
$11$	−1.67662	+	0.694479i	−0.505520	+	0.209393i	0.115323	+	0.993328i	$0.463210\pi$
$12$		0			0
$13$	0.978679	−	2.36274i	0.271437	−	0.655306i	−0.728108	−	0.685462i	$-0.759600\pi$
$13$	0.978679	−	2.36274i	0.271437	−	0.655306i	0.999545	+	0.0301557i	$0.00960031\pi$
$14$		0			0
$15$		−	0.317153i		−	0.0818885i
$16$		0			0
$17$		−	7.38531i		−	1.79120i	−0.444858	−	0.895601i	$-0.646746\pi$
$17$		−	7.38531i		−	1.79120i	0.444858	−	0.895601i	$-0.353254\pi$
$18$		0			0
$19$	2.51097	−	6.06201i	0.576055	−	1.39072i	−0.320272	−	0.947326i	$-0.603774\pi$
$19$	2.51097	−	6.06201i	0.576055	−	1.39072i	0.896327	−	0.443394i	$-0.146226\pi$
$20$		0			0
$21$	−0.666968	+	0.276267i	−0.145544	+	0.0602865i
$22$		0			0
$23$	0.415483	+	0.415483i	0.0866342	+	0.0866342i	0.749096	−	0.662462i	$-0.230488\pi$
$23$	0.415483	+	0.415483i	0.0866342	+	0.0866342i	−0.662462	+	0.749096i	$0.730488\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	−0.716006	−	1.72859i	−0.137796	−	0.332668i
$28$		0			0
$29$	1.25776	+	0.520982i	0.233561	+	0.0967440i	0.496394	−	0.868097i	$-0.334657\pi$
$29$	1.25776	+	0.520982i	0.233561	+	0.0967440i	−0.262834	+	0.964841i	$0.584657\pi$
$30$		0			0
$31$	−10.3170			−1.85298			−0.926492	−	0.376314i	$-0.877191\pi$
$31$	−10.3170			−1.85298			−0.926492	+	0.376314i	$0.877191\pi$
$32$		0			0
$33$	−0.575556			−0.100191
$34$		0			0
$35$	2.10299	+	0.871086i	0.355470	+	0.147240i
$36$		0			0
$37$	2.88274	+	6.95955i	0.473920	+	1.14414i	0.962417	+	0.271578i	$0.0875453\pi$
$37$	2.88274	+	6.95955i	0.473920	+	1.14414i	−0.488497	+	0.872566i	$0.662455\pi$
$38$		0			0
$39$	0.573527	−	0.573527i	0.0918379	−	0.0918379i
$40$		0			0
$41$	−3.16408	−	3.16408i	−0.494146	−	0.494146i	0.415463	−	0.909610i	$-0.363619\pi$
$41$	−3.16408	−	3.16408i	−0.494146	−	0.494146i	−0.909610	+	0.415463i	$0.863619\pi$
$42$		0			0
$43$	1.66790	−	0.690868i	0.254353	−	0.105356i	−0.251864	−	0.967763i	$-0.581044\pi$
$43$	1.66790	−	0.690868i	0.254353	−	0.105356i	0.506217	+	0.862406i	$0.331044\pi$
$44$		0			0
$45$	−1.10956	+	2.67871i	−0.165403	+	0.399318i
$46$		0			0
$47$		−	9.77862i		−	1.42636i	−0.700982	−	0.713179i	$-0.747255\pi$
$47$		−	9.77862i		−	1.42636i	0.700982	−	0.713179i	$-0.252745\pi$
$48$		0			0
$49$			1.81865i			0.259807i
$50$		0			0
$51$	0.896349	−	2.16398i	0.125514	−	0.303017i
$52$		0			0
$53$	−1.69543	+	0.702269i	−0.232885	+	0.0964641i	−0.496074	−	0.868280i	$-0.665226\pi$
$53$	−1.69543	+	0.702269i	−0.232885	+	0.0964641i	0.263189	+	0.964744i	$0.415226\pi$
$54$		0			0
$55$	1.28323	+	1.28323i	0.173031	+	0.173031i
$56$		0			0
$57$	1.47148	−	1.47148i	0.194902	−	0.194902i
$58$		0			0
$59$	−0.870931	−	2.10261i	−0.113386	−	0.273737i	0.856992	−	0.515329i	$-0.172330\pi$
$59$	−0.870931	−	2.10261i	−0.113386	−	0.273737i	−0.970378	+	0.241592i	$0.922330\pi$
$60$		0			0
$61$	2.77121	+	1.14787i	0.354818	+	0.146970i	0.552970	−	0.833201i	$-0.313494\pi$
$61$	2.77121	+	1.14787i	0.354818	+	0.146970i	−0.198153	+	0.980171i	$0.563494\pi$
$62$		0			0
$63$	6.59981			0.831498
$64$		0			0
$65$	−2.55741			−0.317208
$66$		0			0
$67$	7.25385	+	3.00464i	0.886199	+	0.367076i	0.778898	−	0.627151i	$-0.215779\pi$
$67$	7.25385	+	3.00464i	0.886199	+	0.367076i	0.107301	+	0.994227i	$0.465779\pi$
$68$		0			0
$69$	0.0713143	+	0.172168i	0.00858523	+	0.0207266i
$70$		0			0
$71$	−6.44757	+	6.44757i	−0.765186	+	0.765186i	−0.977255	−	0.212069i	$-0.931980\pi$
$71$	−6.44757	+	6.44757i	−0.765186	+	0.765186i	0.212069	+	0.977255i	$0.431980\pi$
$72$		0			0
$73$	−8.80279	−	8.80279i	−1.03029	−	1.03029i	−0.999527	−	0.0307614i	$-0.990207\pi$
$73$	−8.80279	−	8.80279i	−1.03029	−	1.03029i	−0.0307614	−	0.999527i	$-0.509793\pi$
$74$		0			0
$75$	−0.293011	+	0.121369i	−0.0338340	+	0.0140145i
$76$		0			0
$77$	1.58081	−	3.81642i	0.180150	−	0.434921i
$78$		0			0
$79$		−	0.377013i		−	0.0424173i	−0.999775	−	0.0212086i	$-0.993249\pi$
$79$		−	0.377013i		−	0.0424173i	0.999775	−	0.0212086i	$-0.00675143\pi$
$80$		0			0
$81$			8.10484i			0.900538i
$82$		0			0
$83$	1.61547	−	3.90008i	0.177320	−	0.428089i	−0.810082	−	0.586316i	$-0.800578\pi$
$83$	1.61547	−	3.90008i	0.177320	−	0.428089i	0.987403	+	0.158227i	$0.0505777\pi$
$84$		0			0
$85$	−6.82314	+	2.82624i	−0.740073	+	0.306548i
$86$		0			0
$87$	0.305307	+	0.305307i	0.0327323	+	0.0327323i
$88$		0			0
$89$	0.367841	−	0.367841i	0.0389911	−	0.0389911i	−0.687342	−	0.726334i	$-0.741223\pi$
$89$	0.367841	−	0.367841i	0.0389911	−	0.0389911i	0.726334	+	0.687342i	$0.241223\pi$
$90$		0			0
$91$	2.22773	+	5.37821i	0.233529	+	0.563789i
$92$		0			0
$93$	−3.02299	−	1.25216i	−0.313469	−	0.129843i
$94$		0			0
$95$	−6.56147			−0.673193
$96$		0			0
$97$	18.3365			1.86179			0.930893	−	0.365292i	$-0.119031\pi$
$97$	18.3365			1.86179			0.930893	+	0.365292i	$0.119031\pi$
$98$		0			0
$99$	4.86122	+	2.01358i	0.488571	+	0.202373i
$100$		0			0
$101$	5.04091	+	12.1698i	0.501589	+	1.21094i	0.948618	+	0.316423i	$0.102482\pi$
$101$	5.04091	+	12.1698i	0.501589	+	1.21094i	−0.447029	+	0.894519i	$0.647518\pi$
$102$		0			0
$103$	−2.17025	+	2.17025i	−0.213842	+	0.213842i	−0.805897	−	0.592056i	$-0.798317\pi$
$103$	−2.17025	+	2.17025i	−0.213842	+	0.213842i	0.592056	+	0.805897i	$0.298317\pi$
$104$		0			0
$105$	0.510475	+	0.510475i	0.0498173	+	0.0498173i
$106$		0			0
$107$	9.91795	−	4.10815i	0.958805	−	0.397150i	0.152272	−	0.988339i	$-0.451341\pi$
$107$	9.91795	−	4.10815i	0.958805	−	0.397150i	0.806533	+	0.591189i	$0.201341\pi$
$108$		0			0
$109$	2.08557	−	5.03500i	0.199761	−	0.482266i	−0.791976	−	0.610552i	$-0.790948\pi$
$109$	2.08557	−	5.03500i	0.199761	−	0.482266i	0.991737	+	0.128286i	$0.0409476\pi$
$110$		0			0
$111$			2.38910i			0.226763i
$112$		0			0
$113$			0.313493i			0.0294909i	0.999891	+	0.0147455i	$0.00469379\pi$
$113$			0.313493i			0.0294909i	−0.999891	+	0.0147455i	$0.995306\pi$
$114$		0			0
$115$	0.224858	−	0.542855i	0.0209681	−	0.0506215i
$116$		0			0
$117$	−6.85056	+	2.83760i	−0.633335	+	0.262336i
$118$		0			0
$119$	11.8871	+	11.8871i	1.08969	+	1.08969i
$120$		0			0
$121$	−5.44942	+	5.44942i	−0.495402	+	0.495402i
$122$		0			0
$123$	−0.543089	−	1.31113i	−0.0489687	−	0.118221i
$124$		0			0
$125$	0.923880	+	0.382683i	0.0826343	+	0.0342282i
$126$		0			0
$127$	−12.4806			−1.10747			−0.553736	−	0.832692i	$-0.686798\pi$
$127$	−12.4806			−1.10747			−0.553736	+	0.832692i	$0.686798\pi$
$128$		0			0
$129$	0.572564			0.0504114
$130$		0			0
$131$	−7.82165	−	3.23983i	−0.683380	−	0.283065i	0.0138588	−	0.999904i	$-0.495588\pi$
$131$	−7.82165	−	3.23983i	−0.683380	−	0.283065i	−0.697239	+	0.716839i	$0.745588\pi$
$132$		0			0
$133$	5.71561	+	13.7987i	0.495606	+	1.19650i
$134$		0			0
$135$	−1.32301	+	1.32301i	−0.113866	+	0.113866i
$136$		0			0
$137$	−3.92858	−	3.92858i	−0.335641	−	0.335641i	0.519083	−	0.854724i	$-0.326274\pi$
$137$	−3.92858	−	3.92858i	−0.335641	−	0.335641i	−0.854724	+	0.519083i	$0.826274\pi$
$138$		0			0
$139$	−19.9838	+	8.27757i	−1.69501	+	0.702094i	−0.999859	−	0.0167735i	$-0.994661\pi$
$139$	−19.9838	+	8.27757i	−1.69501	+	0.702094i	−0.695147	+	0.718868i	$0.744661\pi$
$140$		0			0
$141$	1.18682	−	2.86524i	0.0999484	−	0.241297i
$142$		0			0
$143$			4.64109i			0.388107i
$144$		0			0
$145$		−	1.36139i		−	0.113057i
$146$		0			0
$147$	−0.220728	+	0.532884i	−0.0182053	+	0.0439515i
$148$		0			0
$149$	18.4798	−	7.65457i	1.51392	−	0.627087i	0.537559	−	0.843226i	$-0.319347\pi$
$149$	18.4798	−	7.65457i	1.51392	−	0.627087i	0.976363	+	0.216139i	$0.0693466\pi$
$150$		0			0
$151$	4.77030	+	4.77030i	0.388202	+	0.388202i	0.874046	−	0.485844i	$-0.161488\pi$
$151$	4.77030	+	4.77030i	0.388202	+	0.388202i	−0.485844	+	0.874046i	$0.661488\pi$
$152$		0			0
$153$	−15.1413	+	15.1413i	−1.22410	+	1.22410i
$154$		0			0
$155$	3.94814	+	9.53165i	0.317122	+	0.765600i
$156$		0			0
$157$	6.15321	+	2.54874i	0.491080	+	0.203412i	0.614461	−	0.788948i	$-0.289374\pi$
$157$	6.15321	+	2.54874i	0.491080	+	0.203412i	−0.123381	+	0.992359i	$0.539374\pi$
$158$		0			0
$159$	−0.582013			−0.0461566
$160$		0			0
$161$	−1.33749			−0.105409
$162$		0			0
$163$	11.4190	+	4.72992i	0.894408	+	0.370476i	0.782068	−	0.623194i	$-0.214165\pi$
$163$	11.4190	+	4.72992i	0.894408	+	0.370476i	0.112341	+	0.993670i	$0.464165\pi$
$164$		0			0
$165$	0.220256	+	0.531745i	0.0171469	+	0.0413963i
$166$		0			0
$167$	8.66291	−	8.66291i	0.670356	−	0.670356i	−0.287442	−	0.957798i	$-0.592805\pi$
$167$	8.66291	−	8.66291i	0.670356	−	0.670356i	0.957798	+	0.287442i	$0.0928049\pi$
$168$		0			0
$169$	4.56766	+	4.56766i	0.351358	+	0.351358i
$170$		0			0
$171$	−17.5763	+	7.28033i	−1.34409	+	0.556741i
$172$		0			0
$173$	5.54142	−	13.3782i	0.421306	−	1.01712i	−0.560656	−	0.828049i	$-0.689451\pi$
$173$	5.54142	−	13.3782i	0.421306	−	1.01712i	0.981963	−	0.189075i	$-0.0605489\pi$
$174$		0			0
$175$		−	2.27626i		−	0.172069i
$176$		0			0
$177$		−	0.721793i		−	0.0542533i
$178$		0			0
$179$	7.64754	−	18.4628i	0.571604	−	1.37997i	−0.328585	−	0.944474i	$-0.606572\pi$
$179$	7.64754	−	18.4628i	0.571604	−	1.37997i	0.900189	−	0.435500i	$-0.143428\pi$
$180$		0			0
$181$	−15.4032	+	6.38022i	−1.14491	+	0.474238i	−0.872825	−	0.488034i	$-0.837714\pi$
$181$	−15.4032	+	6.38022i	−1.14491	+	0.474238i	−0.272088	+	0.962272i	$0.587714\pi$
$182$		0			0
$183$	0.672679	+	0.672679i	0.0497259	+	0.0497259i
$184$		0			0
$185$	5.32661	−	5.32661i	0.391620	−	0.391620i
$186$		0			0
$187$	5.12894	+	12.3824i	0.375066	+	0.905488i
$188$		0			0
$189$	3.93472	+	1.62982i	0.286209	+	0.118552i
$190$		0			0
$191$	18.9632			1.37213			0.686065	−	0.727540i	$-0.259336\pi$
$191$	18.9632			1.37213			0.686065	+	0.727540i	$0.259336\pi$
$192$		0			0
$193$	16.1047			1.15924			0.579622	−	0.814886i	$-0.303200\pi$
$193$	16.1047			1.15924			0.579622	+	0.814886i	$0.303200\pi$
$194$		0			0
$195$	−0.749349	−	0.310391i	−0.0536620	−	0.0222275i
$196$		0			0
$197$	−2.70952	−	6.54136i	−0.193045	−	0.466052i	0.797486	−	0.603337i	$-0.206163\pi$
$197$	−2.70952	−	6.54136i	−0.193045	−	0.466052i	−0.990532	+	0.137284i	$0.956163\pi$
$198$		0			0
$199$	−4.98724	+	4.98724i	−0.353536	+	0.353536i	−0.861424	−	0.507887i	$-0.830427\pi$
$199$	−4.98724	+	4.98724i	−0.353536	+	0.353536i	0.507887	+	0.861424i	$0.330427\pi$
$200$		0			0
$201$	1.76079	+	1.76079i	0.124196	+	0.124196i
$202$		0			0
$203$	−2.86299	+	1.18589i	−0.200943	+	0.0832332i
$204$		0			0
$205$	−1.71239	+	4.13407i	−0.119598	+	0.288736i
$206$		0			0
$207$		−	1.70364i		−	0.118411i
$208$		0			0
$209$			11.9075i			0.823659i
$210$		0			0
$211$	−9.46477	+	22.8500i	−0.651581	+	1.57306i	0.158901	+	0.987294i	$0.449205\pi$
$211$	−9.46477	+	22.8500i	−0.651581	+	1.57306i	−0.810483	+	0.585762i	$0.800795\pi$
$212$		0			0
$213$	−2.67174	+	1.10667i	−0.183065	+	0.0758280i
$214$		0			0
$215$	−1.27656	−	1.27656i	−0.0870605	−	0.0870605i
$216$		0			0
$217$	16.6058	−	16.6058i	1.12727	−	1.12727i
$218$		0			0
$219$	−1.51093	−	3.64770i	−0.102099	−	0.246489i
$220$		0			0
$221$	−17.4496	−	7.22785i	−1.17379	−	0.486198i
$222$		0			0
$223$	5.98382			0.400706			0.200353	−	0.979724i	$-0.435791\pi$
$223$	5.98382			0.400706			0.200353	+	0.979724i	$0.435791\pi$
$224$		0			0
$225$	2.89941			0.193294
$226$		0			0
$227$	12.7078	+	5.26374i	0.843446	+	0.349367i	0.762212	−	0.647328i	$-0.224114\pi$
$227$	12.7078	+	5.26374i	0.843446	+	0.349367i	0.0812349	+	0.996695i	$0.474114\pi$
$228$		0			0
$229$	−8.98996	−	21.7037i	−0.594073	−	1.43422i	−0.879537	−	0.475830i	$-0.842148\pi$
$229$	−8.98996	−	21.7037i	−0.594073	−	1.43422i	0.285464	−	0.958389i	$-0.407852\pi$
$230$		0			0
$231$	0.926391	−	0.926391i	0.0609520	−	0.0609520i
$232$		0			0
$233$	6.27849	+	6.27849i	0.411317	+	0.411317i	0.882197	−	0.470880i	$-0.156063\pi$
$233$	6.27849	+	6.27849i	0.411317	+	0.411317i	−0.470880	+	0.882197i	$0.656063\pi$
$234$		0			0
$235$	−9.03427	+	3.74212i	−0.589331	+	0.244109i
$236$		0			0
$237$	0.0457577	−	0.110469i	0.00297228	−	0.00717573i
$238$		0			0
$239$		−	13.8062i		−	0.893049i	−0.894771	−	0.446524i	$-0.852662\pi$
$239$		−	13.8062i		−	0.893049i	0.894771	−	0.446524i	$-0.147338\pi$
$240$		0			0
$241$			3.69408i			0.237957i	0.992897	+	0.118978i	$0.0379619\pi$
$241$			3.69408i			0.237957i	−0.992897	+	0.118978i	$0.962038\pi$
$242$		0			0
$243$	−3.13170	+	7.56059i	−0.200898	+	0.485012i
$244$		0			0
$245$	1.68021	−	0.695967i	0.107345	−	0.0444637i
$246$		0			0
$247$	−11.8655	−	11.8655i	−0.754985	−	0.754985i
$248$		0			0
$249$	0.946698	−	0.946698i	0.0599946	−	0.0599946i
$250$		0			0
$251$	−7.03861	−	16.9927i	−0.444273	−	1.07257i	−0.974434	−	0.224673i	$-0.927869\pi$
$251$	−7.03861	−	16.9927i	−0.444273	−	1.07257i	0.530161	−	0.847897i	$-0.322131\pi$
$252$		0			0
$253$	−0.985152	−	0.408063i	−0.0619360	−	0.0256547i
$254$		0			0
$255$	−2.34227			−0.146679
$256$		0			0
$257$	1.30672			0.0815109			0.0407554	−	0.999169i	$-0.487024\pi$
$257$	1.30672			0.0815109			0.0407554	+	0.999169i	$0.487024\pi$
$258$		0			0
$259$	−15.8417	−	6.56186i	−0.984357	−	0.407734i
$260$		0			0
$261$	−1.51054	−	3.64677i	−0.0935003	−	0.225730i
$262$		0			0
$263$	11.8686	−	11.8686i	0.731847	−	0.731847i	−0.239138	−	0.970986i	$-0.576865\pi$
$263$	11.8686	−	11.8686i	0.731847	−	0.731847i	0.970986	+	0.239138i	$0.0768649\pi$
$264$		0			0
$265$	1.29762	+	1.29762i	0.0797124	+	0.0797124i
$266$		0			0
$267$	0.152426	−	0.0631370i	0.00932833	−	0.00386392i
$268$		0			0
$269$	0.344230	−	0.831045i	0.0209881	−	0.0506697i	−0.913038	−	0.407874i	$-0.866270\pi$
$269$	0.344230	−	0.831045i	0.0209881	−	0.0506697i	0.934026	+	0.357205i	$0.116270\pi$
$270$		0			0
$271$			0.822969i			0.0499918i	0.999688	+	0.0249959i	$0.00795727\pi$
$271$			0.822969i			0.0499918i	−0.999688	+	0.0249959i	$0.992043\pi$
$272$		0			0
$273$			1.84625i			0.111740i
$274$		0			0
$275$	0.694479	−	1.67662i	0.0418787	−	0.101104i
$276$		0			0
$277$	−8.15264	+	3.37693i	−0.489845	+	0.202900i	−0.613913	−	0.789373i	$-0.710406\pi$
$277$	−8.15264	+	3.37693i	−0.489845	+	0.202900i	0.124069	+	0.992274i	$0.460406\pi$
$278$		0			0
$279$	21.1518	+	21.1518i	1.26633	+	1.26633i
$280$		0			0
$281$	−14.1292	+	14.1292i	−0.842879	+	0.842879i	−0.989232	−	0.146353i	$-0.953246\pi$
$281$	−14.1292	+	14.1292i	−0.842879	+	0.842879i	0.146353	+	0.989232i	$0.453246\pi$
$282$		0			0
$283$	−7.85004	−	18.9517i	−0.466636	−	1.12656i	−0.965622	−	0.259949i	$-0.916294\pi$
$283$	−7.85004	−	18.9517i	−0.466636	−	1.12656i	0.498986	−	0.866610i	$-0.333706\pi$
$284$		0			0
$285$	−1.92258	−	0.796360i	−0.113884	−	0.0471723i
$286$		0			0
$287$	10.1855			0.601234
$288$		0			0
$289$	−37.5429			−2.20840
$290$		0			0
$291$	5.37278	+	2.22548i	0.314958	+	0.130460i
$292$		0			0
$293$	−3.54865	−	8.56721i	−0.207315	−	0.500502i	0.785684	−	0.618628i	$-0.212311\pi$
$293$	−3.54865	−	8.56721i	−0.207315	−	0.500502i	−0.992999	+	0.118126i	$0.962311\pi$
$294$		0			0
$295$	−1.60927	+	1.60927i	−0.0936954	+	0.0936954i
$296$		0			0
$297$	2.40094	+	2.40094i	0.139317	+	0.139317i
$298$		0			0
$299$	1.38830	−	0.575054i	0.0802877	−	0.0332562i
$300$		0			0
$301$	−1.57259	+	3.79658i	−0.0906428	+	0.218831i
$302$		0			0
$303$			4.17770i			0.240003i
$304$		0			0
$305$		−	2.99954i		−	0.171753i
$306$		0			0
$307$	4.21674	−	10.1801i	0.240662	−	0.581010i	−0.756687	−	0.653778i	$-0.773183\pi$
$307$	4.21674	−	10.1801i	0.240662	−	0.581010i	0.997349	+	0.0727678i	$0.0231832\pi$
$308$		0			0
$309$	−0.899310	+	0.372506i	−0.0511600	+	0.0211911i
$310$		0			0
$311$	−11.1659	−	11.1659i	−0.633158	−	0.633158i	0.315701	−	0.948859i	$-0.397760\pi$
$311$	−11.1659	−	11.1659i	−0.633158	−	0.633158i	−0.948859	+	0.315701i	$0.897760\pi$
$312$		0			0
$313$	−2.12975	+	2.12975i	−0.120380	+	0.120380i	−0.764731	−	0.644350i	$-0.777128\pi$
$313$	−2.12975	+	2.12975i	−0.120380	+	0.120380i	0.644350	+	0.764731i	$0.277128\pi$
$314$		0			0
$315$	−2.52564	−	6.09743i	−0.142304	−	0.343551i
$316$		0			0
$317$	−27.9850	−	11.5918i	−1.57179	−	0.651058i	−0.584706	−	0.811245i	$-0.698790\pi$
$317$	−27.9850	−	11.5918i	−1.57179	−	0.651058i	−0.987087	+	0.160187i	$0.948790\pi$
$318$		0			0
$319$	−2.47060			−0.138327
$320$		0			0
$321$	3.40467			0.190030
$322$		0			0
$323$	−44.7698	−	18.5443i	−2.49106	−	1.03183i
$324$		0			0
$325$	0.978679	+	2.36274i	0.0542873	+	0.131061i
$326$		0			0
$327$	1.22219	−	1.22219i	0.0675871	−	0.0675871i
$328$		0			0
$329$	15.7392	+	15.7392i	0.867733	+	0.867733i
$330$		0			0
$331$	31.0032	−	12.8419i	1.70409	−	0.705856i	0.704096	−	0.710104i	$-0.251352\pi$
$331$	31.0032	−	12.8419i	1.70409	−	0.705856i	0.999991	+	0.00424838i	$0.00135231\pi$
$332$		0			0
$333$	8.35826	−	20.1786i	0.458030	−	1.10578i
$334$		0			0
$335$		−	7.85151i		−	0.428974i
$336$		0			0
$337$		−	2.38161i		−	0.129734i	−0.997894	−	0.0648672i	$-0.979338\pi$
$337$		−	2.38161i		−	0.129734i	0.997894	−	0.0648672i	$-0.0206624\pi$
$338$		0			0
$339$	−0.0380483	+	0.0918568i	−0.00206650	+	0.00498898i
$340$		0			0
$341$	17.2977	−	7.16492i	0.936721	−	0.388002i
$342$		0			0
$343$	−14.1941	−	14.1941i	−0.766411	−	0.766411i
$344$		0			0
$345$	0.131772	−	0.131772i	0.00709435	−	0.00709435i
$346$		0			0
$347$	4.91390	+	11.8632i	0.263792	+	0.636850i	0.999167	−	0.0408104i	$-0.0129940\pi$
$347$	4.91390	+	11.8632i	0.263792	+	0.636850i	−0.735375	+	0.677660i	$0.762994\pi$
$348$		0			0
$349$	14.1263	+	5.85130i	0.756163	+	0.313213i	0.727253	−	0.686369i	$-0.240797\pi$
$349$	14.1263	+	5.85130i	0.756163	+	0.313213i	0.0289095	+	0.999582i	$0.490797\pi$
$350$		0			0
$351$	−4.78496			−0.255402
$352$		0			0
$353$	19.2569			1.02494			0.512471	−	0.858704i	$-0.328730\pi$
$353$	19.2569			1.02494			0.512471	+	0.858704i	$0.328730\pi$
$354$		0			0
$355$	8.42416	+	3.48940i	0.447108	+	0.185198i
$356$		0			0
$357$	2.04032	+	4.92577i	0.107985	+	0.260699i
$358$		0			0
$359$	20.9465	−	20.9465i	1.10551	−	1.10551i	0.111778	−	0.993733i	$-0.464345\pi$
$359$	20.9465	−	20.9465i	1.10551	−	1.10551i	0.993733	−	0.111778i	$-0.0356547\pi$
$360$		0			0
$361$	−17.0080	−	17.0080i	−0.895156	−	0.895156i
$362$		0			0
$363$	−2.25813	+	0.935348i	−0.118521	+	0.0490931i
$364$		0			0
$365$	−4.76403	+	11.5014i	−0.249361	+	0.602010i
$366$		0			0
$367$		−	34.6590i		−	1.80919i	−0.426276	−	0.904593i	$-0.640175\pi$
$367$		−	34.6590i		−	1.80919i	0.426276	−	0.904593i	$-0.359825\pi$
$368$		0			0
$369$			12.9740i			0.675398i
$370$		0			0
$371$	1.59855	−	3.85923i	0.0829924	−	0.200361i
$372$		0			0
$373$	15.5081	−	6.42366i	0.802978	−	0.332604i	0.0568295	−	0.998384i	$-0.481901\pi$
$373$	15.5081	−	6.42366i	0.802978	−	0.332604i	0.746149	+	0.665780i	$0.231901\pi$
$374$		0			0
$375$	0.224261	+	0.224261i	0.0115808	+	0.0115808i
$376$		0			0
$377$	2.46189	−	2.46189i	0.126794	−	0.126794i
$378$		0			0
$379$	4.30952	+	10.4041i	0.221365	+	0.534423i	0.995076	−	0.0991163i	$-0.0316016\pi$
$379$	4.30952	+	10.4041i	0.221365	+	0.534423i	−0.773711	+	0.633539i	$0.781602\pi$
$380$		0			0
$381$	−3.65695	−	1.51476i	−0.187351	−	0.0776034i
$382$		0			0
$383$	14.2820			0.729777			0.364889	−	0.931051i	$-0.381107\pi$
$383$	14.2820			0.729777			0.364889	+	0.931051i	$0.381107\pi$
$384$		0			0
$385$	−4.13086			−0.210528
$386$		0			0
$387$	−4.83594	−	2.00311i	−0.245825	−	0.101824i
$388$		0			0
$389$	−10.5580	−	25.4892i	−0.535311	−	1.29236i	−0.927964	−	0.372669i	$-0.878443\pi$
$389$	−10.5580	−	25.4892i	−0.535311	−	1.29236i	0.392653	−	0.919687i	$-0.371557\pi$
$390$		0			0
$391$	3.06847	−	3.06847i	0.155179	−	0.155179i
$392$		0			0
$393$	−1.89861	−	1.89861i	−0.0957723	−	0.0957723i
$394$		0			0
$395$	−0.348315	+	0.144277i	−0.0175256	+	0.00725935i
$396$		0			0
$397$	−11.8143	+	28.5223i	−0.592943	+	1.43149i	0.287704	+	0.957719i	$0.407108\pi$
$397$	−11.8143	+	28.5223i	−0.592943	+	1.43149i	−0.880647	+	0.473773i	$0.842892\pi$
$398$		0			0
$399$			4.73687i			0.237140i
$400$		0			0
$401$		−	18.2687i		−	0.912296i	−0.889904	−	0.456148i	$-0.849229\pi$
$401$		−	18.2687i		−	0.912296i	0.889904	−	0.456148i	$-0.150771\pi$
$402$		0			0
$403$	−10.0970	+	24.3763i	−0.502968	+	1.21427i
$404$		0			0
$405$	7.48790	−	3.10159i	0.372077	−	0.154119i
$406$		0			0
$407$	−9.66652	−	9.66652i	−0.479152	−	0.479152i
$408$		0			0
$409$	9.53547	−	9.53547i	0.471499	−	0.471499i	−0.430901	−	0.902399i	$-0.641804\pi$
$409$	9.53547	−	9.53547i	0.471499	−	0.471499i	0.902399	+	0.430901i	$0.141804\pi$
$410$		0			0
$411$	−0.674308	−	1.62792i	−0.0332612	−	0.0802996i
$412$		0			0
$413$	4.78609	+	1.98246i	0.235508	+	0.0975507i
$414$		0			0
$415$	−4.22142			−0.207221
$416$		0			0
$417$	−6.86012			−0.335942
$418$		0			0
$419$	−9.90746	−	4.10380i	−0.484011	−	0.200484i	0.127316	−	0.991862i	$-0.459364\pi$
$419$	−9.90746	−	4.10380i	−0.484011	−	0.200484i	−0.611327	+	0.791378i	$0.709364\pi$
$420$		0			0
$421$	−2.03777	−	4.91961i	−0.0993148	−	0.239767i	0.866411	−	0.499331i	$-0.166421\pi$
$421$	−2.03777	−	4.91961i	−0.0993148	−	0.239767i	−0.965726	+	0.259564i	$0.916421\pi$
$422$		0			0
$423$	−20.0481	+	20.0481i	−0.974771	+	0.974771i
$424$		0			0
$425$	5.22221	+	5.22221i	0.253314	+	0.253314i
$426$		0			0
$427$	−6.30800	+	2.61286i	−0.305265	+	0.126445i
$428$		0			0
$429$	−0.563285	+	1.35989i	−0.0271956	+	0.0656561i
$430$		0			0
$431$			17.7688i			0.855893i	0.903804	+	0.427947i	$0.140763\pi$
$431$			17.7688i			0.855893i	−0.903804	+	0.427947i	$0.859237\pi$
$432$		0			0
$433$			6.42229i			0.308636i	0.988021	+	0.154318i	$0.0493180\pi$
$433$			6.42229i			0.308636i	−0.988021	+	0.154318i	$0.950682\pi$
$434$		0			0
$435$	0.165231	−	0.398903i	0.00792222	−	0.0191259i
$436$		0			0
$437$	3.56193	−	1.47540i	0.170390	−	0.0705779i
$438$		0			0
$439$	14.1767	+	14.1767i	0.676619	+	0.676619i	0.959234	−	0.282614i	$-0.0912017\pi$
$439$	14.1767	+	14.1767i	0.676619	+	0.676619i	−0.282614	+	0.959234i	$0.591202\pi$
$440$		0			0
$441$	3.72859	−	3.72859i	0.177552	−	0.177552i
$442$		0			0
$443$	−0.449523	−	1.08524i	−0.0213575	−	0.0515615i	0.912841	−	0.408315i	$-0.133884\pi$
$443$	−0.449523	−	1.08524i	−0.0213575	−	0.0515615i	−0.934198	+	0.356754i	$0.883884\pi$
$444$		0			0
$445$	−0.480608	−	0.199074i	−0.0227830	−	0.00943703i
$446$		0			0
$447$	6.34380			0.300051
$448$		0			0
$449$	−31.1260			−1.46893			−0.734463	−	0.678649i	$-0.762566\pi$
$449$	−31.1260			−1.46893			−0.734463	+	0.678649i	$0.762566\pi$
$450$		0			0
$451$	7.50235	+	3.10758i	0.353272	+	0.146330i
$452$		0			0
$453$	0.818783	+	1.97672i	0.0384698	+	0.0928743i
$454$		0			0
$455$	4.11630	−	4.11630i	0.192975	−	0.192975i
$456$		0			0
$457$	−1.39582	−	1.39582i	−0.0652935	−	0.0652935i	0.673706	−	0.738999i	$-0.264701\pi$
$457$	−1.39582	−	1.39582i	−0.0652935	−	0.0652935i	−0.738999	+	0.673706i	$0.764701\pi$
$458$		0			0
$459$	−12.7662	+	5.28793i	−0.595875	+	0.246820i
$460$		0			0
$461$	8.03657	−	19.4020i	0.374300	−	0.903641i	−0.618711	−	0.785619i	$-0.712345\pi$
$461$	8.03657	−	19.4020i	0.374300	−	0.903641i	0.993011	−	0.118022i	$-0.0376553\pi$
$462$		0			0
$463$			36.0394i			1.67489i	0.546519	+	0.837447i	$0.315953\pi$
$463$			36.0394i			1.67489i	−0.546519	+	0.837447i	$0.684047\pi$
$464$		0			0
$465$			3.27206i			0.151738i
$466$		0			0
$467$	−11.2009	+	27.0414i	−0.518317	+	1.25133i	0.420620	+	0.907237i	$0.361813\pi$
$467$	−11.2009	+	27.0414i	−0.518317	+	1.25133i	−0.938936	+	0.344091i	$0.888187\pi$
$468$		0			0
$469$	−16.5116	+	6.83935i	−0.762437	+	0.315812i
$470$		0			0
$471$	1.49362	+	1.49362i	0.0688223	+	0.0688223i
$472$		0			0
$473$	−2.31665	+	2.31665i	−0.106520	+	0.106520i
$474$		0			0
$475$	2.51097	+	6.06201i	0.115211	+	0.278144i
$476$		0			0
$477$	4.91575	+	2.03617i	0.225077	+	0.0932298i
$478$		0			0
$479$	−26.0608			−1.19075			−0.595375	−	0.803448i	$-0.702996\pi$
$479$	−26.0608			−1.19075			−0.595375	+	0.803448i	$0.702996\pi$
$480$		0			0
$481$	19.2649			0.878403
$482$		0			0
$483$	−0.391899	−	0.162330i	−0.0178320	−	0.00738626i
$484$		0			0
$485$	−7.01706	−	16.9407i	−0.318628	−	0.769237i
$486$		0			0
$487$	−14.7637	+	14.7637i	−0.669008	+	0.669008i	−0.957486	−	0.288478i	$-0.906851\pi$
$487$	−14.7637	+	14.7637i	−0.669008	+	0.669008i	0.288478	+	0.957486i	$0.406851\pi$
$488$		0			0
$489$	2.77184	+	2.77184i	0.125347	+	0.125347i
$490$		0			0
$491$	20.1986	−	8.36652i	0.911548	−	0.377576i	0.122899	−	0.992419i	$-0.460781\pi$
$491$	20.1986	−	8.36652i	0.911548	−	0.377576i	0.788649	+	0.614844i	$0.210781\pi$
$492$		0			0
$493$	3.84762	−	9.28897i	0.173288	−	0.418354i
$494$		0			0
$495$		−	5.26174i		−	0.236498i
$496$		0			0
$497$		−	20.7555i		−	0.931010i
$498$		0			0
$499$	7.45400	−	17.9956i	0.333687	−	0.805592i	−0.664606	−	0.747194i	$-0.731401\pi$
$499$	7.45400	−	17.9956i	0.333687	−	0.805592i	0.998293	−	0.0583981i	$-0.0185993\pi$
$500$		0			0
$501$	3.58974	−	1.48692i	0.160378	−	0.0664306i
$502$		0			0
$503$	−16.4931	−	16.4931i	−0.735392	−	0.735392i	0.236291	−	0.971682i	$-0.424068\pi$
$503$	−16.4931	−	16.4931i	−0.735392	−	0.735392i	−0.971682	+	0.236291i	$0.924068\pi$
$504$		0			0
$505$	9.31438	−	9.31438i	0.414485	−	0.414485i
$506$		0			0
$507$	0.784001	+	1.89275i	0.0348187	+	0.0840598i
$508$		0			0
$509$	24.7711	+	10.2605i	1.09796	+	0.454789i	0.856775	−	0.515690i	$-0.172464\pi$
$509$	24.7711	+	10.2605i	1.09796	+	0.454789i	0.241184	+	0.970479i	$0.422464\pi$
$510$		0			0
$511$	28.3372			1.25356
$512$		0			0
$513$	−12.2766			−0.542026
$514$		0			0
$515$	2.83557	+	1.17453i	0.124950	+	0.0517561i
$516$		0			0
$517$	6.79104	+	16.3950i	0.298670	+	0.721053i
$518$		0			0
$519$	3.24739	−	3.24739i	0.142545	−	0.142545i
$520$		0			0
$521$	24.0045	+	24.0045i	1.05166	+	1.05166i	0.998591	+	0.0530647i	$0.0168990\pi$
$521$	24.0045	+	24.0045i	1.05166	+	1.05166i	0.0530647	+	0.998591i	$0.483101\pi$
$522$		0			0
$523$	37.8171	−	15.6643i	1.65363	−	0.684954i	0.656061	−	0.754708i	$-0.272221\pi$
$523$	37.8171	−	15.6643i	1.65363	−	0.684954i	0.997564	+	0.0697536i	$0.0222213\pi$
$524$		0			0
$525$	0.276267	−	0.666968i	0.0120573	−	0.0291089i
$526$		0			0
$527$			76.1941i			3.31907i
$528$		0			0
$529$		−	22.6547i		−	0.984989i
$530$		0			0
$531$	−2.52519	+	6.09635i	−0.109584	+	0.264559i
$532$		0			0
$533$	−10.5725	+	4.37928i	−0.457947	+	0.189688i
$534$		0			0
$535$	−7.59087	−	7.59087i	−0.328182	−	0.328182i
$536$		0			0
$537$	4.48162	−	4.48162i	0.193396	−	0.193396i
$538$		0			0
$539$	−1.26301	−	3.04918i	−0.0544018	−	0.131338i
$540$		0			0
$541$	2.84870	+	1.17997i	0.122475	+	0.0507309i	0.443079	−	0.896482i	$-0.353886\pi$
$541$	2.84870	+	1.17997i	0.122475	+	0.0507309i	−0.320604	+	0.947213i	$0.603886\pi$
$542$		0			0
$543$	−5.28767			−0.226916
$544$		0			0
$545$	−5.44985			−0.233446
$546$		0			0
$547$	13.7687	+	5.70317i	0.588706	+	0.243850i	0.657094	−	0.753809i	$-0.271786\pi$
$547$	13.7687	+	5.70317i	0.588706	+	0.243850i	−0.0683878	+	0.997659i	$0.521786\pi$
$548$		0			0
$549$	−3.32816	−	8.03490i	−0.142043	−	0.342921i
$550$		0			0
$551$	6.31640	−	6.31640i	0.269088	−	0.269088i
$552$		0			0
$553$	0.606824	+	0.606824i	0.0258048	+	0.0258048i
$554$		0			0
$555$	2.20724	−	0.914269i	0.0936921	−	0.0388086i
$556$		0			0
$557$	−9.72475	+	23.4776i	−0.412051	+	0.994778i	0.572536	+	0.819880i	$0.305960\pi$
$557$	−9.72475	+	23.4776i	−0.412051	+	0.994778i	−0.984586	+	0.174899i	$0.944040\pi$
$558$		0			0
$559$		−	4.61696i		−	0.195277i
$560$		0			0
$561$			4.25066i			0.179463i
$562$		0			0
$563$	−10.3818	+	25.0639i	−0.437540	+	1.05632i	0.539256	+	0.842142i	$0.318706\pi$
$563$	−10.3818	+	25.0639i	−0.437540	+	1.05632i	−0.976796	+	0.214173i	$0.931294\pi$
$564$		0			0
$565$	0.289629	−	0.119968i	0.0121848	−	0.00504711i
$566$		0			0
$567$	−13.0452	−	13.0452i	−0.547847	−	0.547847i
$568$		0			0
$569$	−9.62870	+	9.62870i	−0.403656	+	0.403656i	−0.879519	−	0.475863i	$-0.842136\pi$
$569$	−9.62870	+	9.62870i	−0.403656	+	0.403656i	0.475863	+	0.879519i	$0.342136\pi$
$570$		0			0
$571$	5.73826	+	13.8534i	0.240139	+	0.579746i	0.997296	−	0.0734860i	$-0.0234124\pi$
$571$	5.73826	+	13.8534i	0.240139	+	0.579746i	−0.757157	+	0.653232i	$0.773412\pi$
$572$		0			0
$573$	5.55643	+	2.30155i	0.232123	+	0.0961486i
$574$		0			0
$575$	−0.587582			−0.0245039
$576$		0			0
$577$	1.82574			0.0760065			0.0380032	−	0.999278i	$-0.487900\pi$
$577$	1.82574			0.0760065			0.0380032	+	0.999278i	$0.487900\pi$
$578$		0			0
$579$	4.71886	+	1.95462i	0.196109	+	0.0812310i
$580$		0			0
$581$	3.67722	+	8.87759i	0.152557	+	0.368304i
$582$		0			0
$583$	2.35488	−	2.35488i	0.0975291	−	0.0975291i
$584$		0			0
$585$	5.24319	+	5.24319i	0.216779	+	0.216779i
$586$		0			0
$587$	20.7193	−	8.58222i	0.855178	−	0.354226i	0.0883581	−	0.996089i	$-0.471838\pi$
$587$	20.7193	−	8.58222i	0.855178	−	0.354226i	0.766820	+	0.641863i	$0.221838\pi$
$588$		0			0
$589$	−25.9056	+	62.5416i	−1.06742	+	2.57698i
$590$		0			0
$591$		−	2.24554i		−	0.0923692i
$592$		0			0
$593$		−	16.7018i		−	0.685861i	−0.939361	−	0.342930i	$-0.888581\pi$
$593$		−	16.7018i		−	0.685861i	0.939361	−	0.342930i	$-0.111419\pi$
$594$		0			0
$595$	6.43325	−	15.5312i	0.263737	−	0.636718i
$596$		0			0
$597$	−2.06661	+	0.856020i	−0.0845809	+	0.0350345i
$598$		0			0
$599$	−3.28515	−	3.28515i	−0.134227	−	0.134227i	0.636801	−	0.771028i	$-0.280257\pi$
$599$	−3.28515	−	3.28515i	−0.134227	−	0.134227i	−0.771028	+	0.636801i	$0.780257\pi$
$600$		0			0
$601$	9.22429	−	9.22429i	0.376267	−	0.376267i	−0.493487	−	0.869753i	$-0.664278\pi$
$601$	9.22429	−	9.22429i	0.376267	−	0.376267i	0.869753	+	0.493487i	$0.164278\pi$
$602$		0			0
$603$	−8.71171	−	21.0319i	−0.354768	−	0.856486i
$604$		0			0
$605$	7.12001	+	2.94920i	0.289470	+	0.119902i
$606$		0			0
$607$	−25.0480			−1.01667			−0.508333	−	0.861161i	$-0.669738\pi$
$607$	−25.0480			−1.01667			−0.508333	+	0.861161i	$0.669738\pi$
$608$		0			0
$609$	−0.982818			−0.0398258
$610$		0			0
$611$	−23.1043	−	9.57013i	−0.934701	−	0.387166i
$612$		0			0
$613$	15.4705	+	37.3490i	0.624847	+	1.50851i	0.845950	+	0.533263i	$0.179034\pi$
$613$	15.4705	+	37.3490i	0.624847	+	1.50851i	−0.221103	+	0.975250i	$0.570966\pi$
$614$		0			0
$615$	−1.00350	+	1.00350i	−0.0404649	+	0.0404649i
$616$		0			0
$617$	−2.33250	−	2.33250i	−0.0939027	−	0.0939027i	0.658595	−	0.752498i	$-0.271151\pi$
$617$	−2.33250	−	2.33250i	−0.0939027	−	0.0939027i	−0.752498	+	0.658595i	$0.771151\pi$
$618$		0			0
$619$	−6.01712	+	2.49237i	−0.241848	+	0.100177i	−0.500315	−	0.865843i	$-0.666783\pi$
$619$	−6.01712	+	2.49237i	−0.241848	+	0.100177i	0.258467	+	0.966020i	$0.416783\pi$
$620$		0			0
$621$	0.420713	−	1.01569i	0.0168826	−	0.0407582i
$622$		0			0
$623$			1.18412i			0.0474409i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	−1.44520	+	3.48903i	−0.0577158	+	0.139338i
$628$		0			0
$629$	51.3985	−	21.2899i	2.04939	−	0.848886i
$630$		0			0
$631$	−16.9308	−	16.9308i	−0.674006	−	0.674006i	0.284631	−	0.958637i	$-0.408129\pi$
$631$	−16.9308	−	16.9308i	−0.674006	−	0.674006i	−0.958637	+	0.284631i	$0.908129\pi$
$632$		0			0
$633$	−5.54656	+	5.54656i	−0.220456	+	0.220456i
$634$		0			0
$635$	4.77611	+	11.5306i	0.189534	+	0.457576i
$636$		0			0
$637$	4.29700	+	1.77987i	0.170253	+	0.0705212i
$638$		0			0
$639$	26.4376			1.04585
$640$		0			0
$641$	−22.2252			−0.877841			−0.438920	−	0.898526i	$-0.644639\pi$
$641$	−22.2252			−0.877841			−0.438920	+	0.898526i	$0.644639\pi$
$642$		0			0
$643$	16.0285	+	6.63921i	0.632101	+	0.261825i	0.675645	−	0.737227i	$-0.263865\pi$
$643$	16.0285	+	6.63921i	0.632101	+	0.261825i	−0.0435445	+	0.999051i	$0.513865\pi$
$644$		0			0
$645$	−0.219111	−	0.528980i	−0.00862748	−	0.0208286i
$646$		0			0
$647$	−1.45126	+	1.45126i	−0.0570547	+	0.0570547i	−0.735058	−	0.678004i	$-0.762845\pi$
$647$	−1.45126	+	1.45126i	−0.0570547	+	0.0570547i	0.678004	+	0.735058i	$0.262845\pi$
$648$		0			0
$649$	2.92044	+	2.92044i	0.114637	+	0.114637i
$650$		0			0
$651$	6.88110	−	2.85024i	0.269692	−	0.111710i
$652$		0			0
$653$	−14.1130	+	34.0717i	−0.552282	+	1.33333i	0.363478	+	0.931603i	$0.381589\pi$
$653$	−14.1130	+	34.0717i	−0.552282	+	1.33333i	−0.915760	+	0.401725i	$0.868411\pi$
$654$		0			0
$655$			8.46609i			0.330797i
$656$		0			0
$657$			36.0949i			1.40819i
$658$		0			0
$659$	−3.74597	+	9.04357i	−0.145922	+	0.352287i	−0.979894	−	0.199520i	$-0.936062\pi$
$659$	−3.74597	+	9.04357i	−0.145922	+	0.352287i	0.833972	+	0.551807i	$0.186062\pi$
$660$		0			0
$661$	−8.63050	+	3.57487i	−0.335688	+	0.139046i	−0.544159	−	0.838982i	$-0.683151\pi$
$661$	−8.63050	+	3.57487i	−0.335688	+	0.139046i	0.208471	+	0.978028i	$0.433151\pi$
$662$		0			0
$663$	−4.23568	−	4.23568i	−0.164500	−	0.164500i
$664$		0			0
$665$	10.5611	−	10.5611i	0.409541	−	0.409541i
$666$		0			0
$667$	0.306120	+	0.739038i	0.0118530	+	0.0286157i
$668$		0			0
$669$	1.75332	+	0.726250i	0.0677874	+	0.0280785i
$670$		0			0
$671$	−5.44345			−0.210142
$672$		0			0
$673$	−8.89348			−0.342818			−0.171409	−	0.985200i	$-0.554832\pi$
$673$	−8.89348			−0.342818			−0.171409	+	0.985200i	$0.554832\pi$
$674$		0			0
$675$	1.72859	+	0.716006i	0.0665336	+	0.0275591i
$676$		0			0
$677$	−4.70865	−	11.3677i	−0.180968	−	0.436895i	0.807199	−	0.590280i	$-0.200983\pi$
$677$	−4.70865	−	11.3677i	−0.180968	−	0.436895i	−0.988167	+	0.153385i	$0.950983\pi$
$678$		0			0
$679$	−29.5136	+	29.5136i	−1.13263	+	1.13263i
$680$		0			0
$681$	3.08467	+	3.08467i	0.118205	+	0.118205i
$682$		0			0
$683$	43.6495	−	18.0802i	1.67020	−	0.691820i	0.671416	−	0.741081i	$-0.265686\pi$
$683$	43.6495	−	18.0802i	1.67020	−	0.691820i	0.998786	+	0.0492603i	$0.0156864\pi$
$684$		0			0
$685$	−2.12613	+	5.13293i	−0.0812353	+	0.196119i
$686$		0			0
$687$		−	7.45051i		−	0.284255i
$688$		0			0
$689$			4.69315i			0.178795i
$690$		0			0
$691$	11.5043	−	27.7738i	0.437643	−	1.05656i	−0.539117	−	0.842231i	$-0.681242\pi$
$691$	11.5043	−	27.7738i	0.437643	−	1.05656i	0.976760	−	0.214334i	$-0.0687581\pi$
$692$		0			0
$693$	−11.0654	+	4.58343i	−0.420339	+	0.174110i
$694$		0			0
$695$	15.2950	+	15.2950i	0.580171	+	0.580171i
$696$		0			0
$697$	−23.3677	+	23.3677i	−0.885116	+	0.885116i
$698$		0			0
$699$	1.07765	+	2.60168i	0.0407605	+	0.0984046i
$700$		0			0
$701$	28.9707	+	12.0001i	1.09421	+	0.453236i	0.855472	−	0.517849i	$-0.173267\pi$
$701$	28.9707	+	12.0001i	1.09421	+	0.453236i	0.238736	+	0.971084i	$0.423267\pi$
$702$		0			0
$703$	49.4273			1.86419
$704$		0			0
$705$	−3.10132			−0.116802
$706$		0			0
$707$	−27.7017	−	11.4744i	−1.04183	−	0.431539i
$708$		0			0
$709$	−3.20821	−	7.74529i	−0.120487	−	0.290881i	0.852116	−	0.523352i	$-0.175319\pi$
$709$	−3.20821	−	7.74529i	−0.120487	−	0.290881i	−0.972603	+	0.232471i	$0.925319\pi$
$710$		0			0
$711$	−0.772951	+	0.772951i	−0.0289879	+	0.0289879i
$712$		0			0
$713$	−4.28653	−	4.28653i	−0.160532	−	0.160532i
$714$		0			0
$715$	4.28781	−	1.77607i	0.160355	−	0.0664212i
$716$		0			0
$717$	1.67565	−	4.04537i	0.0625781	−	0.151077i
$718$		0			0
$719$			14.7683i			0.550763i	0.961335	+	0.275382i	$0.0888042\pi$
$719$			14.7683i			0.550763i	−0.961335	+	0.275382i	$0.911196\pi$
$720$		0			0
$721$		−	6.98630i		−	0.260183i
$722$		0			0
$723$	−0.448348	+	1.08241i	−0.0166742	+	0.0402552i
$724$		0			0
$725$	−1.25776	+	0.520982i	−0.0467121	+	0.0193488i
$726$		0			0
$727$	1.55089	+	1.55089i	0.0575194	+	0.0575194i	0.735281	−	0.677762i	$-0.237050\pi$
$727$	1.55089	+	1.55089i	0.0575194	+	0.0575194i	−0.677762	+	0.735281i	$0.737050\pi$
$728$		0			0
$729$	15.3577	−	15.3577i	0.568805	−	0.568805i
$730$		0			0
$731$	−5.10228	−	12.3180i	−0.188715	−	0.455597i
$732$		0			0
$733$	−26.2102	−	10.8566i	−0.968095	−	0.400998i	−0.158092	−	0.987424i	$-0.550534\pi$
$733$	−26.2102	−	10.8566i	−0.968095	−	0.400998i	−0.810003	+	0.586426i	$0.800534\pi$
$734$		0			0
$735$	0.576790			0.0212752
$736$		0			0
$737$	−14.2486			−0.524855
$738$		0			0
$739$	37.8898	+	15.6945i	1.39380	+	0.577330i	0.948134	−	0.317871i	$-0.102968\pi$
$739$	37.8898	+	15.6945i	1.39380	+	0.577330i	0.445664	+	0.895201i	$0.352968\pi$
$740$		0			0
$741$	−2.03662	−	4.91683i	−0.0748171	−	0.180624i
$742$		0			0
$743$	1.20586	−	1.20586i	0.0442387	−	0.0442387i	−0.684641	−	0.728880i	$-0.740041\pi$
$743$	1.20586	−	1.20586i	0.0442387	−	0.0442387i	0.728880	+	0.684641i	$0.240041\pi$
$744$		0			0
$745$	−14.1438	−	14.1438i	−0.518189	−	0.518189i
$746$		0			0
$747$	−11.3079	+	4.68390i	−0.413736	+	0.171375i
$748$		0			0
$749$	−9.35121	+	22.5758i	−0.341686	+	0.824903i
$750$		0			0
$751$		−	20.3019i		−	0.740826i	−0.928867	−	0.370413i	$-0.879216\pi$
$751$		−	20.3019i		−	0.740826i	0.928867	−	0.370413i	$-0.120784\pi$
$752$		0			0
$753$		−	5.83332i		−	0.212578i
$754$		0			0
$755$	2.58167	−	6.23270i	0.0939565	−	0.226831i
$756$		0			0
$757$	−24.5385	+	10.1642i	−0.891867	+	0.369423i	−0.781088	−	0.624422i	$-0.785335\pi$
$757$	−24.5385	+	10.1642i	−0.891867	+	0.369423i	−0.110780	+	0.993845i	$0.535335\pi$
$758$		0			0
$759$	−0.239134	−	0.239134i	−0.00868001	−	0.00868001i
$760$		0			0
$761$	24.5868	−	24.5868i	0.891269	−	0.891269i	−0.103374	−	0.994643i	$-0.532964\pi$
$761$	24.5868	−	24.5868i	0.891269	−	0.891269i	0.994643	+	0.103374i	$0.0329637\pi$
$762$		0			0
$763$	4.74729	+	11.4610i	0.171863	+	0.414915i
$764$		0			0
$765$	19.7831	+	8.19443i	0.715260	+	0.296270i
$766$		0			0
$767$	−5.82029			−0.210159
$768$		0			0
$769$	−29.2433			−1.05454			−0.527270	−	0.849698i	$-0.676784\pi$
$769$	−29.2433			−1.05454			−0.527270	+	0.849698i	$0.676784\pi$
$770$		0			0
$771$	0.382883	+	0.158595i	0.0137892	+	0.00571167i
$772$		0			0
$773$	2.93776	+	7.09237i	0.105664	+	0.255095i	0.967865	−	0.251472i	$-0.0809145\pi$
$773$	2.93776	+	7.09237i	0.105664	+	0.255095i	−0.862201	+	0.506566i	$0.830914\pi$
$774$		0			0
$775$	7.29521	−	7.29521i	0.262052	−	0.262052i
$776$		0			0
$777$	−3.84539	−	3.84539i	−0.137953	−	0.137953i
$778$		0			0
$779$	−27.1256	+	11.2358i	−0.971875	+	0.402564i
$780$		0			0
$781$	6.33243	−	15.2878i	0.226592	−	0.547042i
$782$		0			0
$783$		−	2.54719i		−	0.0910290i
$784$		0			0
$785$		−	6.66019i		−	0.237712i
$786$		0			0
$787$	−12.4476	+	30.0512i	−0.443710	+	1.07121i	0.530927	+	0.847417i	$0.321844\pi$
$787$	−12.4476	+	30.0512i	−0.443710	+	1.07121i	−0.974637	+	0.223792i	$0.928156\pi$
$788$		0			0
$789$	4.91810	−	2.03714i	0.175089	−	0.0725242i
$790$		0			0
$791$	−0.504585	−	0.504585i	−0.0179410	−	0.0179410i
$792$		0			0
$793$	5.42426	−	5.42426i	0.192621	−	0.192621i
$794$		0			0
$795$	0.222727	+	0.537710i	0.00789930	+	0.0190706i
$796$		0			0
$797$	7.32434	+	3.03384i	0.259442	+	0.107464i	0.508613	−	0.860995i	$-0.330158\pi$
$797$	7.32434	+	3.03384i	0.259442	+	0.107464i	−0.249172	+	0.968459i	$0.580158\pi$
$798$		0			0
$799$	−72.2182			−2.55490
$800$		0			0
$801$	−1.50829			−0.0532929
$802$		0			0
$803$	20.8723	+	8.64558i	0.736567	+	0.305096i
$804$		0			0
$805$	0.511835	+	1.23568i	0.0180398	+	0.0435519i
$806$		0			0
$807$	0.201726	−	0.201726i	0.00710111	−	0.00710111i
$808$		0			0
$809$	24.7855	+	24.7855i	0.871411	+	0.871411i	0.992626	−	0.121215i	$-0.0386790\pi$
$809$	24.7855	+	24.7855i	0.871411	+	0.871411i	−0.121215	+	0.992626i	$0.538679\pi$
$810$		0			0
$811$	20.5016	−	8.49204i	0.719909	−	0.298196i	0.00751076	−	0.999972i	$-0.497609\pi$
$811$	20.5016	−	8.49204i	0.719909	−	0.298196i	0.712398	+	0.701776i	$0.247609\pi$
$812$		0			0
$813$	−0.0998830	+	0.241139i	−0.00350305	+	0.00845711i
$814$		0			0
$815$		−	12.3599i		−	0.432948i
$816$		0			0
$817$		−	11.8456i		−	0.414425i
$818$		0			0
$819$	6.45910	−	15.5936i	0.225699	−	0.544886i
$820$		0			0
$821$	43.4874	−	18.0131i	1.51772	−	0.628661i	0.540588	−	0.841287i	$-0.318202\pi$
$821$	43.4874	−	18.0131i	1.51772	−	0.628661i	0.977134	+	0.212627i	$0.0682018\pi$
$822$		0			0
$823$	5.83868	+	5.83868i	0.203524	+	0.203524i	0.801508	−	0.597984i	$-0.204031\pi$
$823$	5.83868	+	5.83868i	0.203524	+	0.203524i	−0.597984	+	0.801508i	$0.704031\pi$
$824$		0			0
$825$	0.406980	−	0.406980i	0.0141692	−	0.0141692i
$826$		0			0
$827$	−10.6275	−	25.6570i	−0.369553	−	0.892181i	−0.993823	−	0.110972i	$-0.964603\pi$
$827$	−10.6275	−	25.6570i	−0.369553	−	0.892181i	0.624270	−	0.781209i	$-0.285397\pi$
$828$		0			0
$829$	−26.2395	−	10.8688i	−0.911336	−	0.377488i	−0.122768	−	0.992435i	$-0.539177\pi$
$829$	−26.2395	−	10.8688i	−0.911336	−	0.377488i	−0.788568	+	0.614948i	$0.789177\pi$
$830$		0			0
$831$	−2.79867			−0.0970847
$832$		0			0
$833$	13.4313			0.465367
$834$		0			0
$835$	−11.3186	−	4.68833i	−0.391697	−	0.162246i
$836$		0			0
$837$	7.38702	+	17.8339i	0.255333	+	0.616428i
$838$		0			0
$839$	−6.95556	+	6.95556i	−0.240133	+	0.240133i	−0.816905	−	0.576772i	$-0.804312\pi$
$839$	−6.95556	+	6.95556i	−0.240133	+	0.240133i	0.576772	+	0.816905i	$0.304312\pi$
$840$		0			0
$841$	−19.1956	−	19.1956i	−0.661916	−	0.661916i
$842$		0			0
$843$	−5.85487	+	2.42517i	−0.201652	+	0.0835272i
$844$		0			0
$845$	2.47200	−	5.96794i	0.0850394	−	0.205303i
$846$		0			0
$847$		−	17.5423i		−	0.602761i
$848$		0			0
$849$		−	6.50580i		−	0.223278i
$850$		0			0
$851$	−1.69385	+	4.08931i	−0.0580643	+	0.140180i
$852$		0			0
$853$	16.3936	−	6.79046i	0.561307	−	0.232501i	−0.0839457	−	0.996470i	$-0.526752\pi$
$853$	16.3936	−	6.79046i	0.561307	−	0.232501i	0.645252	+	0.763969i	$0.276752\pi$
$854$		0			0
$855$	13.4523	+	13.4523i	0.460059	+	0.460059i
$856$		0			0
$857$	−17.8121	+	17.8121i	−0.608450	+	0.608450i	−0.942541	−	0.334091i	$-0.891571\pi$
$857$	−17.8121	+	17.8121i	−0.608450	+	0.608450i	0.334091	+	0.942541i	$0.391571\pi$
$858$		0			0
$859$	0.147925	+	0.357123i	0.00504714	+	0.0121849i	0.926383	−	0.376583i	$-0.122901\pi$
$859$	0.147925	+	0.357123i	0.00504714	+	0.0121849i	−0.921336	+	0.388768i	$0.872901\pi$
$860$		0			0
$861$	2.98447	+	1.23621i	0.101711	+	0.0421299i
$862$		0			0
$863$	−19.5548			−0.665654			−0.332827	−	0.942988i	$-0.608003\pi$
$863$	−19.5548			−0.665654			−0.332827	+	0.942988i	$0.608003\pi$
$864$		0			0
$865$	−14.4804			−0.492349
$866$		0			0
$867$	−11.0005	−	4.55654i	−0.373595	−	0.154748i
$868$		0			0
$869$	0.261828	+	0.632108i	0.00888190	+	0.0214428i
$870$		0			0
$871$	14.1984	−	14.1984i	0.481094	−	0.481094i
$872$		0			0
$873$	−37.5933	−	37.5933i	−1.27234	−	1.27234i
$874$		0			0
$875$	−2.10299	+	0.871086i	−0.0710940	+	0.0294481i
$876$		0			0
$877$	12.6444	−	30.5263i	0.426972	−	1.03080i	−0.553271	−	0.833002i	$-0.686620\pi$
$877$	12.6444	−	30.5263i	0.426972	−	1.03080i	0.980242	−	0.197800i	$-0.0633796\pi$
$878$		0			0
$879$		−	2.94098i		−	0.0991969i
$880$		0			0
$881$		−	22.2195i		−	0.748594i	−0.927309	−	0.374297i	$-0.877884\pi$
$881$		−	22.2195i		−	0.748594i	0.927309	−	0.374297i	$-0.122116\pi$
$882$		0			0
$883$	12.5873	−	30.3884i	0.423596	−	1.02265i	−0.557683	−	0.830054i	$-0.688309\pi$
$883$	12.5873	−	30.3884i	0.423596	−	1.02265i	0.981278	−	0.192596i	$-0.0616906\pi$
$884$		0			0
$885$	−0.666850	+	0.276218i	−0.0224159	+	0.00928497i
$886$		0			0
$887$	7.20816	+	7.20816i	0.242026	+	0.242026i	0.817688	−	0.575662i	$-0.195255\pi$
$887$	7.20816	+	7.20816i	0.242026	+	0.242026i	−0.575662	+	0.817688i	$0.695255\pi$
$888$		0			0
$889$	20.0882	−	20.0882i	0.673737	−	0.673737i
$890$		0			0
$891$	−5.62864	−	13.5887i	−0.188567	−	0.455240i
$892$		0			0
$893$	−59.2781	−	24.5538i	−1.98367	−	0.821661i
$894$		0			0
$895$	−19.9840			−0.667991
$896$		0			0
$897$	0.476582			0.0159126
$898$		0			0
$899$	−12.9763	−	5.37496i	−0.432784	−	0.179265i
$900$		0			0
$901$	5.18648	+	12.5213i	0.172787	+	0.417144i
$902$		0			0
$903$	−0.921575	+	0.921575i	−0.0306681	+	0.0306681i
$904$		0			0
$905$	11.7891	+	11.7891i	0.391883	+	0.391883i
$906$		0			0
$907$	11.3771	−	4.71257i	0.377772	−	0.156478i	−0.185714	−	0.982604i	$-0.559460\pi$
$907$	11.3771	−	4.71257i	0.377772	−	0.156478i	0.563486	+	0.826126i	$0.309460\pi$
$908$		0			0
$909$	14.6157	−	35.2854i	0.484771	−	1.17034i
$910$		0			0
$911$			44.0510i			1.45947i	0.683728	+	0.729737i	$0.260357\pi$
$911$			44.0510i			1.45947i	−0.683728	+	0.729737i	$0.739643\pi$
$912$		0			0
$913$			7.66086i			0.253537i
$914$		0			0
$915$	0.364051	−	0.878898i	0.0120352	−	0.0290555i
$916$		0			0
$917$	17.8041	−	7.37469i	0.587943	−	0.243534i
$918$		0			0
$919$	−3.78858	−	3.78858i	−0.124974	−	0.124974i	0.641854	−	0.766827i	$-0.278166\pi$
$919$	−3.78858	−	3.78858i	−0.124974	−	0.124974i	−0.766827	+	0.641854i	$0.778166\pi$
$920$		0			0
$921$	2.47110	−	2.47110i	0.0814256	−	0.0814256i
$922$		0			0
$923$	8.92383	+	21.5440i	0.293732	+	0.709131i
$924$		0			0
$925$	−6.95955	−	2.88274i	−0.228829	−	0.0947839i
$926$		0			0
$927$	8.89889			0.292278
$928$		0			0
$929$	5.02777			0.164956			0.0824779	−	0.996593i	$-0.473717\pi$
$929$	5.02777			0.164956			0.0824779	+	0.996593i	$0.473717\pi$
$930$		0			0
$931$	11.0247	+	4.56657i	0.361319	+	0.149663i
$932$		0			0
$933$	−1.91653	−	4.62691i	−0.0627443	−	0.151478i
$934$		0			0
$935$	9.47705	−	9.47705i	0.309933	−	0.309933i
$936$		0			0
$937$	28.9541	+	28.9541i	0.945889	+	0.945889i	0.998609	−	0.0527204i	$-0.0167892\pi$
$937$	28.9541	+	28.9541i	0.945889	+	0.945889i	−0.0527204	+	0.998609i	$0.516789\pi$
$938$		0			0
$939$	−0.882524	+	0.365553i	−0.0288001	+	0.0119294i
$940$		0			0
$941$	−10.5139	+	25.3828i	−0.342744	+	0.827457i	0.654692	+	0.755895i	$0.272798\pi$
$941$	−10.5139	+	25.3828i	−0.342744	+	0.827457i	−0.997436	+	0.0715615i	$0.977202\pi$
$942$		0			0
$943$		−	2.62925i		−	0.0856200i
$944$		0			0
$945$		−	4.25891i		−	0.138542i
$946$		0			0
$947$	8.78668	−	21.2129i	0.285529	−	0.689327i	−0.714417	−	0.699720i	$-0.753308\pi$
$947$	8.78668	−	21.2129i	0.285529	−	0.689327i	0.999946	+	0.0103928i	$0.00330819\pi$
$948$		0			0
$949$	−29.4138	+	12.1836i	−0.954812	+	0.395496i
$950$		0			0
$951$	−6.79302	−	6.79302i	−0.220279	−	0.220279i
$952$		0			0
$953$	−36.0669	+	36.0669i	−1.16832	+	1.16832i	−0.185717	+	0.982603i	$0.559461\pi$
$953$	−36.0669	+	36.0669i	−1.16832	+	1.16832i	−0.982603	+	0.185717i	$0.940539\pi$
$954$		0			0
$955$	−7.25691	−	17.5197i	−0.234828	−	0.566925i
$956$		0			0
$957$	−0.723913	−	0.299855i	−0.0234008	−	0.00969292i
$958$		0			0
$959$	12.6465			0.408378
$960$		0			0
$961$	75.4401			2.43355
$962$		0			0
$963$	−28.7563	−	11.9112i	−0.926657	−	0.383834i
$964$		0			0
$965$	−6.16301	−	14.8788i	−0.198394	−	0.478966i
$966$		0			0
$967$	−16.9345	+	16.9345i	−0.544577	+	0.544577i	−0.924867	−	0.380290i	$-0.875824\pi$
$967$	−16.9345	+	16.9345i	−0.544577	+	0.544577i	0.380290	+	0.924867i	$0.375824\pi$
$968$		0			0
$969$	−10.8673	−	10.8673i	−0.349110	−	0.349110i
$970$		0			0
$971$	−39.7120	+	16.4493i	−1.27442	+	0.527882i	−0.914305	−	0.405026i	$-0.867263\pi$
$971$	−39.7120	+	16.4493i	−1.27442	+	0.527882i	−0.360115	+	0.932908i	$0.617263\pi$
$972$		0			0
$973$	18.8419	−	45.4883i	0.604043	−	1.45829i
$974$		0			0
$975$			0.811090i			0.0259757i
$976$		0			0
$977$		−	7.35391i		−	0.235272i	−0.993057	−	0.117636i	$-0.962468\pi$
$977$		−	7.35391i		−	0.235272i	0.993057	−	0.117636i	$-0.0375317\pi$
$978$		0			0
$979$	−0.361272	+	0.872189i	−0.0115463	+	0.0278753i
$980$		0			0
$981$	−14.5986	+	6.04692i	−0.466096	+	0.193063i
$982$		0			0
$983$	−30.8499	−	30.8499i	−0.983960	−	0.983960i	0.0159138	−	0.999873i	$-0.494934\pi$
$983$	−30.8499	−	30.8499i	−0.983960	−	0.983960i	−0.999873	+	0.0159138i	$0.994934\pi$
$984$		0			0
$985$	−5.00654	+	5.00654i	−0.159522	+	0.159522i
$986$		0			0
$987$	2.70151	+	6.52203i	0.0859901	+	0.207599i
$988$		0			0
$989$	0.980030	+	0.405942i	0.0311631	+	0.0129082i
$990$		0			0
$991$	16.3725			0.520090			0.260045	−	0.965597i	$-0.416263\pi$
$991$	16.3725			0.520090			0.260045	+	0.965597i	$0.416263\pi$
$992$		0			0
$993$	10.6429			0.337741
$994$		0			0
$995$	6.51615	+	2.69908i	0.206576	+	0.0855665i
$996$		0			0
$997$	−10.6385	−	25.6837i	−0.336926	−	0.813412i	−0.998007	−	0.0630975i	$-0.979902\pi$
$997$	−10.6385	−	25.6837i	−0.336926	−	0.813412i	0.661081	−	0.750314i	$-0.270098\pi$
$998$		0			0
$999$	9.96617	−	9.96617i	0.315316	−	0.315316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.x.a.81.9		64
4.3	odd	2		160.2.x.a.61.3	yes	64
20.3	even	4		800.2.ba.e.349.5		64
20.7	even	4		800.2.ba.g.349.12		64
20.19	odd	2		800.2.y.c.701.14		64
32.11	odd	8		160.2.x.a.21.3	✓	64
32.21	even	8	inner	640.2.x.a.561.9		64
160.43	even	8		800.2.ba.g.149.12		64
160.107	even	8		800.2.ba.e.149.5		64
160.139	odd	8		800.2.y.c.501.14		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.x.a.21.3	✓	64	32.11	odd	8
160.2.x.a.61.3	yes	64	4.3	odd	2
640.2.x.a.81.9		64	1.1	even	1	trivial
640.2.x.a.561.9		64	32.21	even	8	inner
800.2.y.c.501.14		64	160.139	odd	8
800.2.y.c.701.14		64	20.19	odd	2
800.2.ba.e.149.5		64	160.107	even	8
800.2.ba.e.349.5		64	20.3	even	4
800.2.ba.g.149.12		64	160.43	even	8
800.2.ba.g.349.12		64	20.7	even	4

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.x (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.293011 + 0.121369i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-1.60956 + 1.60956i) q^{7} +(-2.05020 - 2.05020i) q^{9} +O(q^{10})\)	\(q+(0.293011 + 0.121369i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-1.60956 + 1.60956i) q^{7} +(-2.05020 - 2.05020i) q^{9} +(-1.67662 + 0.694479i) q^{11} +(0.978679 - 2.36274i) q^{13} -0.317153i q^{15} -7.38531i q^{17} +(2.51097 - 6.06201i) q^{19} +(-0.666968 + 0.276267i) q^{21} +(0.415483 + 0.415483i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-0.716006 - 1.72859i) q^{27} +(1.25776 + 0.520982i) q^{29} -10.3170 q^{31} -0.575556 q^{33} +(2.10299 + 0.871086i) q^{35} +(2.88274 + 6.95955i) q^{37} +(0.573527 - 0.573527i) q^{39} +(-3.16408 - 3.16408i) q^{41} +(1.66790 - 0.690868i) q^{43} +(-1.10956 + 2.67871i) q^{45} -9.77862i q^{47} +1.81865i q^{49} +(0.896349 - 2.16398i) q^{51} +(-1.69543 + 0.702269i) q^{53} +(1.28323 + 1.28323i) q^{55} +(1.47148 - 1.47148i) q^{57} +(-0.870931 - 2.10261i) q^{59} +(2.77121 + 1.14787i) q^{61} +6.59981 q^{63} -2.55741 q^{65} +(7.25385 + 3.00464i) q^{67} +(0.0713143 + 0.172168i) q^{69} +(-6.44757 + 6.44757i) q^{71} +(-8.80279 - 8.80279i) q^{73} +(-0.293011 + 0.121369i) q^{75} +(1.58081 - 3.81642i) q^{77} -0.377013i q^{79} +8.10484i q^{81} +(1.61547 - 3.90008i) q^{83} +(-6.82314 + 2.82624i) q^{85} +(0.305307 + 0.305307i) q^{87} +(0.367841 - 0.367841i) q^{89} +(2.22773 + 5.37821i) q^{91} +(-3.02299 - 1.25216i) q^{93} -6.56147 q^{95} +18.3365 q^{97} +(4.86122 + 2.01358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 16 q^{23} + 48 q^{27} + 48 q^{39} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{59} - 32 q^{61} - 80 q^{63} - 80 q^{67} - 32 q^{69} - 32 q^{71} - 32 q^{77} + 80 q^{83} + 96 q^{91} + 64 q^{95} + 64 q^{99}+O(q^{100}) \) 64 * q + 16 * q^23 + 48 * q^27 + 48 * q^39 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^59 - 32 * q^61 - 80 * q^63 - 80 * q^67 - 32 * q^69 - 32 * q^71 - 32 * q^77 + 80 * q^83 + 96 * q^91 + 64 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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