LMFDB - Embedded newform 1620.2.e.a.971.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (of order $2$, degree $1$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.4
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.a.971.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38301 + 0.295458i) q^{2} +(1.82541 - 0.817240i) q^{4} +1.00000i q^{5} -1.21861i q^{7} +(-2.28309 + 1.66958i) q^{8} +O(q^{10})$	\(q+(-1.38301 + 0.295458i) q^{2} +(1.82541 - 0.817240i) q^{4} +1.00000i q^{5} -1.21861i q^{7} +(-2.28309 + 1.66958i) q^{8} +(-0.295458 - 1.38301i) q^{10} -3.73360 q^{11} +1.24413 q^{13} +(0.360047 + 1.68534i) q^{14} +(2.66424 - 2.98359i) q^{16} -0.279741i q^{17} -0.369793i q^{19} +(0.817240 + 1.82541i) q^{20} +(5.16359 - 1.10312i) q^{22} +3.54672 q^{23} -1.00000 q^{25} +(-1.72064 + 0.367589i) q^{26} +(-0.995894 - 2.22446i) q^{28} +1.80050i q^{29} +6.56736i q^{31} +(-2.80313 + 4.91350i) q^{32} +(0.0826518 + 0.386884i) q^{34} +1.21861 q^{35} -7.25827 q^{37} +(0.109258 + 0.511426i) q^{38} +(-1.66958 - 2.28309i) q^{40} +11.1533i q^{41} +0.149290i q^{43} +(-6.81534 + 3.05124i) q^{44} +(-4.90514 + 1.04791i) q^{46} -7.93163 q^{47} +5.51500 q^{49} +(1.38301 - 0.295458i) q^{50} +(2.27105 - 1.01676i) q^{52} +3.61699i q^{53} -3.73360i q^{55} +(2.03456 + 2.78219i) q^{56} +(-0.531971 - 2.49010i) q^{58} +8.63030 q^{59} +11.7947 q^{61} +(-1.94038 - 9.08270i) q^{62} +(2.42501 - 7.62360i) q^{64} +1.24413i q^{65} -1.29874i q^{67} +(-0.228616 - 0.510642i) q^{68} +(-1.68534 + 0.360047i) q^{70} -0.390184 q^{71} -12.7883 q^{73} +(10.0382 - 2.14451i) q^{74} +(-0.302210 - 0.675024i) q^{76} +4.54979i q^{77} +14.8757i q^{79} +(2.98359 + 2.66424i) q^{80} +(-3.29533 - 15.4251i) q^{82} -15.6631 q^{83} +0.279741 q^{85} +(-0.0441088 - 0.206468i) q^{86} +(8.52414 - 6.23353i) q^{88} +12.9750i q^{89} -1.51611i q^{91} +(6.47422 - 2.89852i) q^{92} +(10.9695 - 2.34346i) q^{94} +0.369793 q^{95} -1.66413 q^{97} +(-7.62727 + 1.62945i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) $ 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.38301	+	0.295458i	−0.977933	+	0.208920i
$2$	−1.38301	+	0.295458i	−0.977933	+	0.208920i
$3$		0			0
$3$		0			0
$4$	1.82541	−	0.817240i	0.912705	−	0.408620i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$		−	1.21861i		−	0.460590i	−0.973121	−	0.230295i	$-0.926031\pi$
$7$		−	1.21861i		−	0.460590i	0.973121	−	0.230295i	$-0.0739691\pi$
$8$	−2.28309	+	1.66958i	−0.807195	+	0.590285i
$9$		0			0
$10$	−0.295458	−	1.38301i	−0.0934320	−	0.437345i
$11$	−3.73360			−1.12572			−0.562861	−	0.826552i	$-0.690299\pi$
$11$	−3.73360			−1.12572			−0.562861	+	0.826552i	$0.690299\pi$
$12$		0			0
$13$	1.24413			0.345061			0.172530	−	0.985004i	$-0.444806\pi$
$13$	1.24413			0.345061			0.172530	+	0.985004i	$0.444806\pi$
$14$	0.360047	+	1.68534i	0.0962266	+	0.450426i
$15$		0			0
$16$	2.66424	−	2.98359i	0.666060	−	0.745898i
$17$		−	0.279741i		−	0.0678472i	−0.999424	−	0.0339236i	$-0.989200\pi$
$17$		−	0.279741i		−	0.0678472i	0.999424	−	0.0339236i	$-0.0108003\pi$
$18$		0			0
$19$		−	0.369793i		−	0.0848364i	−0.999100	−	0.0424182i	$-0.986494\pi$
$19$		−	0.369793i		−	0.0848364i	0.999100	−	0.0424182i	$-0.0135062\pi$
$20$	0.817240	+	1.82541i	0.182740	+	0.408174i
$21$		0			0
$22$	5.16359	−	1.10312i	1.10088	−	0.235186i
$23$	3.54672			0.739543			0.369771	−	0.929123i	$-0.379436\pi$
$23$	3.54672			0.739543			0.369771	+	0.929123i	$0.379436\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.72064	+	0.367589i	−0.337446	+	0.0720902i
$27$		0			0
$28$	−0.995894	−	2.22446i	−0.188206	−	0.420383i
$29$			1.80050i			0.334344i	0.985928	+	0.167172i	$0.0534635\pi$
$29$			1.80050i			0.334344i	−0.985928	+	0.167172i	$0.946536\pi$
$30$		0			0
$31$			6.56736i			1.17953i	0.807574	+	0.589766i	$0.200780\pi$
$31$			6.56736i			1.17953i	−0.807574	+	0.589766i	$0.799220\pi$
$32$	−2.80313	+	4.91350i	−0.495528	+	0.868592i
$33$		0			0
$34$	0.0826518	+	0.386884i	0.0141747	+	0.0663500i
$35$	1.21861			0.205982
$36$		0			0
$37$	−7.25827			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$37$	−7.25827			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$38$	0.109258	+	0.511426i	0.0177240	+	0.0829643i
$39$		0			0
$40$	−1.66958	−	2.28309i	−0.263984	−	0.360988i
$41$			11.1533i			1.74186i	0.491411	+	0.870928i	$0.336481\pi$
$41$			11.1533i			1.74186i	−0.491411	+	0.870928i	$0.663519\pi$
$42$		0			0
$43$			0.149290i			0.0227664i	0.999935	+	0.0113832i	$0.00362347\pi$
$43$			0.149290i			0.0227664i	−0.999935	+	0.0113832i	$0.996377\pi$
$44$	−6.81534	+	3.05124i	−1.02745	+	0.459992i
$45$		0			0
$46$	−4.90514	+	1.04791i	−0.723223	+	0.154505i
$47$	−7.93163			−1.15695			−0.578474	−	0.815701i	$-0.696351\pi$
$47$	−7.93163			−1.15695			−0.578474	+	0.815701i	$0.696351\pi$
$48$		0			0
$49$	5.51500			0.787857
$50$	1.38301	−	0.295458i	0.195587	−	0.0417840i
$51$		0			0
$52$	2.27105	−	1.01676i	0.314938	−	0.140999i
$53$			3.61699i			0.496831i	0.968654	+	0.248416i	$0.0799099\pi$
$53$			3.61699i			0.496831i	−0.968654	+	0.248416i	$0.920090\pi$
$54$		0			0
$55$		−	3.73360i		−	0.503438i
$56$	2.03456	+	2.78219i	0.271879	+	0.371786i
$57$		0			0
$58$	−0.531971	−	2.49010i	−0.0698512	−	0.326966i
$59$	8.63030			1.12357			0.561784	−	0.827284i	$-0.310115\pi$
$59$	8.63030			1.12357			0.561784	+	0.827284i	$0.310115\pi$
$60$		0			0
$61$	11.7947			1.51015			0.755076	−	0.655637i	$-0.227600\pi$
$61$	11.7947			1.51015			0.755076	+	0.655637i	$0.227600\pi$
$62$	−1.94038	−	9.08270i	−0.246428	−	1.15350i
$63$		0			0
$64$	2.42501	−	7.62360i	0.303127	−	0.952950i
$65$			1.24413i			0.154316i
$66$		0			0
$67$		−	1.29874i		−	0.158666i	−0.996848	−	0.0793330i	$-0.974721\pi$
$67$		−	1.29874i		−	0.158666i	0.996848	−	0.0793330i	$-0.0252790\pi$
$68$	−0.228616	−	0.510642i	−0.0277237	−	0.0619245i
$69$		0			0
$70$	−1.68534	+	0.360047i	−0.201437	+	0.0430338i
$71$	−0.390184			−0.0463064			−0.0231532	−	0.999732i	$-0.507371\pi$
$71$	−0.390184			−0.0463064			−0.0231532	+	0.999732i	$0.507371\pi$
$72$		0			0
$73$	−12.7883			−1.49675			−0.748376	−	0.663274i	$-0.769166\pi$
$73$	−12.7883			−1.49675			−0.748376	+	0.663274i	$0.769166\pi$
$74$	10.0382	−	2.14451i	1.16692	−	0.249294i
$75$		0			0
$76$	−0.302210	−	0.675024i	−0.0346658	−	0.0774306i
$77$			4.54979i			0.518496i
$78$		0			0
$79$			14.8757i			1.67365i	0.547469	+	0.836826i	$0.315591\pi$
$79$			14.8757i			1.67365i	−0.547469	+	0.836826i	$0.684409\pi$
$80$	2.98359	+	2.66424i	0.333576	+	0.297871i
$81$		0			0
$82$	−3.29533	−	15.4251i	−0.363909	−	1.70342i
$83$	−15.6631			−1.71925			−0.859623	−	0.510928i	$-0.829302\pi$
$83$	−15.6631			−1.71925			−0.859623	+	0.510928i	$0.829302\pi$
$84$		0			0
$85$	0.279741			0.0303422
$86$	−0.0441088	−	0.206468i	−0.00475637	−	0.0222641i
$87$		0			0
$88$	8.52414	−	6.23353i	0.908677	−	0.664497i
$89$			12.9750i			1.37535i	0.726019	+	0.687674i	$0.241368\pi$
$89$			12.9750i			1.37535i	−0.726019	+	0.687674i	$0.758632\pi$
$90$		0			0
$91$		−	1.51611i		−	0.158932i
$92$	6.47422	−	2.89852i	0.674984	−	0.302192i
$93$		0			0
$94$	10.9695	−	2.34346i	1.13142	−	0.241710i
$95$	0.369793			0.0379400
$96$		0			0
$97$	−1.66413			−0.168967			−0.0844836	−	0.996425i	$-0.526924\pi$
$97$	−1.66413			−0.168967			−0.0844836	+	0.996425i	$0.526924\pi$
$98$	−7.62727	+	1.62945i	−0.770471	+	0.164599i
$99$		0			0
$100$	−1.82541	+	0.817240i	−0.182541	+	0.0817240i
$101$		−	9.90018i		−	0.985104i	−0.870283	−	0.492552i	$-0.836064\pi$
$101$		−	9.90018i		−	0.985104i	0.870283	−	0.492552i	$-0.163936\pi$
$102$		0			0
$103$			10.7921i			1.06338i	0.846939	+	0.531690i	$0.178443\pi$
$103$			10.7921i			1.06338i	−0.846939	+	0.531690i	$0.821557\pi$
$104$	−2.84047	+	2.07718i	−0.278531	+	0.203684i
$105$		0			0
$106$	−1.06867	−	5.00231i	−0.103798	−	0.485867i
$107$	15.7187			1.51958			0.759791	−	0.650167i	$-0.225301\pi$
$107$	15.7187			1.51958			0.759791	+	0.650167i	$0.225301\pi$
$108$		0			0
$109$	−1.06356			−0.101871			−0.0509353	−	0.998702i	$-0.516220\pi$
$109$	−1.06356			−0.101871			−0.0509353	+	0.998702i	$0.516220\pi$
$110$	1.10312	+	5.16359i	0.105178	+	0.492329i
$111$		0			0
$112$	−3.63583	−	3.24666i	−0.343553	−	0.306780i
$113$		−	18.0330i		−	1.69640i	−0.529676	−	0.848200i	$-0.677687\pi$
$113$		−	18.0330i		−	1.69640i	0.529676	−	0.848200i	$-0.322313\pi$
$114$		0			0
$115$			3.54672i			0.330734i
$116$	1.47144	+	3.28664i	0.136620	+	0.305157i
$117$		0			0
$118$	−11.9357	+	2.54989i	−1.09877	+	0.234736i
$119$	−0.340895			−0.0312498
$120$		0			0
$121$	2.93975			0.267250
$122$	−16.3121	+	3.48483i	−1.47683	+	0.315501i
$123$		0			0
$124$	5.36711	+	11.9881i	0.481981	+	1.07657i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			14.4843i			1.28527i	0.766172	+	0.642635i	$0.222159\pi$
$127$			14.4843i			1.28527i	−0.766172	+	0.642635i	$0.777841\pi$
$128$	−1.10136	+	11.2600i	−0.0973471	+	0.995250i
$129$		0			0
$130$	−0.367589	−	1.72064i	−0.0322397	−	0.150910i
$131$	−12.9159			−1.12847			−0.564236	−	0.825614i	$-0.690829\pi$
$131$	−12.9159			−1.12847			−0.564236	+	0.825614i	$0.690829\pi$
$132$		0			0
$133$	−0.450633			−0.0390748
$134$	0.383722	+	1.79616i	0.0331485	+	0.155165i
$135$		0			0
$136$	0.467050	+	0.638675i	0.0400492	+	0.0547659i
$137$			7.50275i			0.641004i	0.947248	+	0.320502i	$0.103852\pi$
$137$			7.50275i			0.641004i	−0.947248	+	0.320502i	$0.896148\pi$
$138$		0			0
$139$			0.859601i			0.0729104i	0.999335	+	0.0364552i	$0.0116066\pi$
$139$			0.859601i			0.0729104i	−0.999335	+	0.0364552i	$0.988393\pi$
$140$	2.22446	−	0.995894i	0.188001	−	0.0841684i
$141$		0			0
$142$	0.539627	−	0.115283i	0.0452845	−	0.00967434i
$143$	−4.64510			−0.388442
$144$		0			0
$145$	−1.80050			−0.149523
$146$	17.6862	−	3.77839i	1.46372	−	0.312702i
$147$		0			0
$148$	−13.2493	+	5.93174i	−1.08909	+	0.487586i
$149$			7.82775i			0.641274i	0.947202	+	0.320637i	$0.103897\pi$
$149$			7.82775i			0.641274i	−0.947202	+	0.320637i	$0.896103\pi$
$150$		0			0
$151$			20.2918i			1.65133i	0.564163	+	0.825664i	$0.309199\pi$
$151$			20.2918i			1.65133i	−0.564163	+	0.825664i	$0.690801\pi$
$152$	0.617399	+	0.844272i	0.0500777	+	0.0684795i
$153$		0			0
$154$	−1.34427	−	6.29238i	−0.108324	−	0.507055i
$155$	−6.56736			−0.527503
$156$		0			0
$157$	−2.75944			−0.220227			−0.110113	−	0.993919i	$-0.535121\pi$
$157$	−2.75944			−0.220227			−0.110113	+	0.993919i	$0.535121\pi$
$158$	−4.39515	−	20.5732i	−0.349660	−	1.63672i
$159$		0			0
$160$	−4.91350	−	2.80313i	−0.388446	−	0.221607i
$161$		−	4.32206i		−	0.340626i
$162$		0			0
$163$			17.3907i			1.36215i	0.732216	+	0.681073i	$0.238486\pi$
$163$			17.3907i			1.36215i	−0.732216	+	0.681073i	$0.761514\pi$
$164$	9.11493	+	20.3594i	0.711757	+	1.58980i
$165$		0			0
$166$	21.6621	−	4.62778i	1.68131	−	0.359185i
$167$	2.23791			0.173174			0.0865872	−	0.996244i	$-0.472404\pi$
$167$	2.23791			0.173174			0.0865872	+	0.996244i	$0.472404\pi$
$168$		0			0
$169$	−11.4521			−0.880933
$170$	−0.386884	+	0.0826518i	−0.0296726	+	0.00633910i
$171$		0			0
$172$	0.122005	+	0.272515i	0.00930282	+	0.0207790i
$173$			1.92296i			0.146200i	0.997325	+	0.0730999i	$0.0232892\pi$
$173$			1.92296i			0.146200i	−0.997325	+	0.0730999i	$0.976711\pi$
$174$		0			0
$175$			1.21861i			0.0921180i
$176$	−9.94719	+	11.1395i	−0.749798	+	0.839674i
$177$		0			0
$178$	−3.83357	−	17.9445i	−0.287338	−	1.34500i
$179$	17.3137			1.29409			0.647045	−	0.762452i	$-0.276005\pi$
$179$	17.3137			1.29409			0.647045	+	0.762452i	$0.276005\pi$
$180$		0			0
$181$	6.94363			0.516116			0.258058	−	0.966129i	$-0.416917\pi$
$181$	6.94363			0.516116			0.258058	+	0.966129i	$0.416917\pi$
$182$	0.447947	+	2.09679i	0.0332040	+	0.155424i
$183$		0			0
$184$	−8.09749	+	5.92153i	−0.596955	+	0.436541i
$185$		−	7.25827i		−	0.533638i
$186$		0			0
$187$			1.04444i			0.0763771i
$188$	−14.4785	+	6.48204i	−1.05595	+	0.472752i
$189$		0			0
$190$	−0.511426	+	0.109258i	−0.0371028	+	0.00792643i
$191$	−23.7905			−1.72142			−0.860712	−	0.509093i	$-0.829981\pi$
$191$	−23.7905			−1.72142			−0.860712	+	0.509093i	$0.829981\pi$
$192$		0			0
$193$	−13.6678			−0.983831			−0.491915	−	0.870643i	$-0.663703\pi$
$193$	−13.6678			−0.983831			−0.491915	+	0.870643i	$0.663703\pi$
$194$	2.30151	−	0.491681i	0.165238	−	0.0353007i
$195$		0			0
$196$	10.0671	−	4.50707i	0.719081	−	0.321934i
$197$		−	3.51586i		−	0.250495i	−0.992126	−	0.125247i	$-0.960028\pi$
$197$		−	3.51586i		−	0.250495i	0.992126	−	0.125247i	$-0.0399725\pi$
$198$		0			0
$199$			11.9455i			0.846796i	0.905944	+	0.423398i	$0.139163\pi$
$199$			11.9455i			0.846796i	−0.905944	+	0.423398i	$0.860837\pi$
$200$	2.28309	−	1.66958i	0.161439	−	0.118057i
$201$		0			0
$202$	2.92508	+	13.6920i	0.205808	+	0.963366i
$203$	2.19410			0.153995
$204$		0			0
$205$	−11.1533			−0.778981
$206$	−3.18862	−	14.9256i	−0.222162	−	1.03991i
$207$		0			0
$208$	3.31467	−	3.71199i	0.229831	−	0.257380i
$209$			1.38066i			0.0955022i
$210$		0			0
$211$			24.2847i			1.67183i	0.548859	+	0.835915i	$0.315063\pi$
$211$			24.2847i			1.67183i	−0.548859	+	0.835915i	$0.684937\pi$
$212$	2.95594	+	6.60248i	0.203015	+	0.453460i
$213$		0			0
$214$	−21.7390	+	4.64421i	−1.48605	+	0.317471i
$215$	−0.149290			−0.0101815
$216$		0			0
$217$	8.00303			0.543281
$218$	1.47091	−	0.314237i	0.0996226	−	0.0212828i
$219$		0			0
$220$	−3.05124	−	6.81534i	−0.205715	−	0.459490i
$221$		−	0.348036i		−	0.0234114i
$222$		0			0
$223$		−	24.2622i		−	1.62472i	−0.583158	−	0.812359i	$-0.698183\pi$
$223$		−	24.2622i		−	1.62472i	0.583158	−	0.812359i	$-0.301817\pi$
$224$	5.98762	+	3.41591i	0.400065	+	0.228235i
$225$		0			0
$226$	5.32798	+	24.9397i	0.354412	+	1.65896i
$227$	10.0524			0.667198			0.333599	−	0.942715i	$-0.391737\pi$
$227$	10.0524			0.667198			0.333599	+	0.942715i	$0.391737\pi$
$228$		0			0
$229$	−3.31060			−0.218770			−0.109385	−	0.993999i	$-0.534888\pi$
$229$	−3.31060			−0.218770			−0.109385	+	0.993999i	$0.534888\pi$
$230$	−1.04791	−	4.90514i	−0.0690970	−	0.323435i
$231$		0			0
$232$	−3.00607	−	4.11070i	−0.197358	−	0.269881i
$233$			5.27887i			0.345830i	0.984937	+	0.172915i	$0.0553186\pi$
$233$			5.27887i			0.345830i	−0.984937	+	0.172915i	$0.944681\pi$
$234$		0			0
$235$		−	7.93163i		−	0.517403i
$236$	15.7538	−	7.05302i	1.02549	−	0.459113i
$237$		0			0
$238$	0.471459	−	0.100720i	0.0305602	−	0.00652871i
$239$	9.22606			0.596784			0.298392	−	0.954443i	$-0.403550\pi$
$239$	9.22606			0.596784			0.298392	+	0.954443i	$0.403550\pi$
$240$		0			0
$241$	−13.3468			−0.859742			−0.429871	−	0.902890i	$-0.641441\pi$
$241$	−13.3468			−0.859742			−0.429871	+	0.902890i	$0.641441\pi$
$242$	−4.06569	+	0.868572i	−0.261352	+	0.0558339i
$243$		0			0
$244$	21.5301	−	9.63907i	1.37832	−	0.617078i
$245$			5.51500i			0.352340i
$246$		0			0
$247$		−	0.460073i		−	0.0292737i
$248$	−10.9647	−	14.9939i	−0.696261	−	0.952113i
$249$		0			0
$250$	0.295458	+	1.38301i	0.0186864	+	0.0874690i
$251$	−5.71415			−0.360674			−0.180337	−	0.983605i	$-0.557719\pi$
$251$	−5.71415			−0.360674			−0.180337	+	0.983605i	$0.557719\pi$
$252$		0			0
$253$	−13.2420			−0.832520
$254$	−4.27949	−	20.0318i	−0.268519	−	1.25691i
$255$		0			0
$256$	−1.80366	−	15.8980i	−0.112729	−	0.993626i
$257$			19.0831i			1.19037i	0.803589	+	0.595185i	$0.202921\pi$
$257$			19.0831i			1.19037i	−0.803589	+	0.595185i	$0.797079\pi$
$258$		0			0
$259$			8.84497i			0.549600i
$260$	1.01676	+	2.27105i	0.0630565	+	0.140845i
$261$		0			0
$262$	17.8628	−	3.81612i	1.10357	−	0.235760i
$263$	−4.00842			−0.247170			−0.123585	−	0.992334i	$-0.539439\pi$
$263$	−4.00842			−0.247170			−0.123585	+	0.992334i	$0.539439\pi$
$264$		0			0
$265$	−3.61699			−0.222190
$266$	0.623228	−	0.133143i	0.0382125	−	0.00816352i
$267$		0			0
$268$	−1.06138	−	2.37073i	−0.0648341	−	0.144815i
$269$		−	7.23921i		−	0.441382i	−0.975344	−	0.220691i	$-0.929169\pi$
$269$		−	7.23921i		−	0.441382i	0.975344	−	0.220691i	$-0.0708313\pi$
$270$		0			0
$271$		−	11.8293i		−	0.718577i	−0.933227	−	0.359289i	$-0.883019\pi$
$271$		−	11.8293i		−	0.718577i	0.933227	−	0.359289i	$-0.116981\pi$
$272$	−0.834635	−	0.745298i	−0.0506072	−	0.0451903i
$273$		0			0
$274$	−2.21675	−	10.3764i	−0.133919	−	0.626858i
$275$	3.73360			0.225144
$276$		0			0
$277$	22.2346			1.33595			0.667974	−	0.744185i	$-0.267162\pi$
$277$	22.2346			1.33595			0.667974	+	0.744185i	$0.267162\pi$
$278$	−0.253976	−	1.18883i	−0.0152325	−	0.0713015i
$279$		0			0
$280$	−2.78219	+	2.03456i	−0.166268	+	0.121588i
$281$		−	10.2263i		−	0.610051i	−0.952344	−	0.305025i	$-0.901335\pi$
$281$		−	10.2263i		−	0.610051i	0.952344	−	0.305025i	$-0.0986649\pi$
$282$		0			0
$283$		−	13.1938i		−	0.784288i	−0.919904	−	0.392144i	$-0.871733\pi$
$283$		−	13.1938i		−	0.784288i	0.919904	−	0.392144i	$-0.128267\pi$
$284$	−0.712246	+	0.318874i	−0.0422640	+	0.0189217i
$285$		0			0
$286$	6.42419	−	1.37243i	0.379871	−	0.0811535i
$287$	13.5915			0.802281
$288$		0			0
$289$	16.9217			0.995397
$290$	2.49010	−	0.531971i	0.146224	−	0.0312384i
$291$		0			0
$292$	−23.3438	+	10.4511i	−1.36609	+	0.611603i
$293$		−	26.6502i		−	1.55692i	−0.627695	−	0.778459i	$-0.716001\pi$
$293$		−	26.6502i		−	1.55692i	0.627695	−	0.778459i	$-0.283999\pi$
$294$		0			0
$295$			8.63030i			0.502475i
$296$	16.5713	−	12.1182i	0.963186	−	0.704359i
$297$		0			0
$298$	−2.31277	−	10.8258i	−0.133975	−	0.627123i
$299$	4.41260			0.255187
$300$		0			0
$301$	0.181925			0.0104860
$302$	−5.99538	−	28.0637i	−0.344996	−	1.61489i
$303$		0			0
$304$	−1.10331	−	0.985218i	−0.0632794	−	0.0565061i
$305$			11.7947i			0.675361i
$306$		0			0
$307$			30.0854i			1.71707i	0.512759	+	0.858533i	$0.328624\pi$
$307$			30.0854i			1.71707i	−0.512759	+	0.858533i	$0.671376\pi$
$308$	3.71827	+	8.30522i	0.211868	+	0.473234i
$309$		0			0
$310$	9.08270	−	1.94038i	0.515863	−	0.110206i
$311$	−20.1040			−1.13999			−0.569996	−	0.821648i	$-0.693055\pi$
$311$	−20.1040			−1.13999			−0.569996	+	0.821648i	$0.693055\pi$
$312$		0			0
$313$	−13.9513			−0.788577			−0.394288	−	0.918987i	$-0.629009\pi$
$313$	−13.9513			−0.788577			−0.394288	+	0.918987i	$0.629009\pi$
$314$	3.81632	−	0.815297i	0.215367	−	0.0460099i
$315$		0			0
$316$	12.1570	+	27.1543i	0.683887	+	1.52755i
$317$		−	34.7712i		−	1.95294i	−0.215648	−	0.976471i	$-0.569186\pi$
$317$		−	34.7712i		−	1.95294i	0.215648	−	0.976471i	$-0.430814\pi$
$318$		0			0
$319$		−	6.72233i		−	0.376378i
$320$	7.62360	+	2.42501i	0.426172	+	0.135562i
$321$		0			0
$322$	1.27699	+	5.97744i	0.0711637	+	0.333109i
$323$	−0.103447			−0.00575592
$324$		0			0
$325$	−1.24413			−0.0690121
$326$	−5.13822	−	24.0514i	−0.284580	−	1.33209i
$327$		0			0
$328$	−18.6213	−	25.4640i	−1.02819	−	1.40602i
$329$			9.66554i			0.532879i
$330$		0			0
$331$		−	10.1966i		−	0.560454i	−0.959934	−	0.280227i	$-0.909590\pi$
$331$		−	10.1966i		−	0.560454i	0.959934	−	0.280227i	$-0.0904098\pi$
$332$	−28.5915	+	12.8005i	−1.56916	+	0.702518i
$333$		0			0
$334$	−3.09504	+	0.661207i	−0.169353	+	0.0361796i
$335$	1.29874			0.0709576
$336$		0			0
$337$	12.2794			0.668902			0.334451	−	0.942413i	$-0.391449\pi$
$337$	12.2794			0.668902			0.334451	+	0.942413i	$0.391449\pi$
$338$	15.8384	−	3.38362i	0.861493	−	0.184045i
$339$		0			0
$340$	0.510642	−	0.228616i	0.0276935	−	0.0123984i
$341$		−	24.5199i		−	1.32783i
$342$		0			0
$343$		−	15.2509i		−	0.823469i
$344$	−0.249251	−	0.340842i	−0.0134387	−	0.0183770i
$345$		0			0
$346$	−0.568153	−	2.65946i	−0.0305441	−	0.142974i
$347$	25.0895			1.34687			0.673436	−	0.739245i	$-0.264818\pi$
$347$	25.0895			1.34687			0.673436	+	0.739245i	$0.264818\pi$
$348$		0			0
$349$	6.04355			0.323504			0.161752	−	0.986831i	$-0.448286\pi$
$349$	6.04355			0.323504			0.161752	+	0.986831i	$0.448286\pi$
$350$	−0.360047	−	1.68534i	−0.0192453	−	0.0900852i
$351$		0			0
$352$	10.4658	−	18.3450i	0.557827	−	0.977793i
$353$			15.8718i			0.844771i	0.906416	+	0.422386i	$0.138807\pi$
$353$			15.8718i			0.844771i	−0.906416	+	0.422386i	$0.861193\pi$
$354$		0			0
$355$		−	0.390184i		−	0.0207088i
$356$	10.6037	+	23.6847i	0.561995	+	1.25529i
$357$		0			0
$358$	−23.9450	+	5.11548i	−1.26553	+	0.270362i
$359$	20.9079			1.10348			0.551738	−	0.834018i	$-0.313965\pi$
$359$	20.9079			1.10348			0.551738	+	0.834018i	$0.313965\pi$
$360$		0			0
$361$	18.8633			0.992803
$362$	−9.60308	+	2.05155i	−0.504727	+	0.107827i
$363$		0			0
$364$	−1.23903	−	2.76752i	−0.0649426	−	0.145058i
$365$		−	12.7883i		−	0.669368i
$366$		0			0
$367$		−	7.16399i		−	0.373957i	−0.982364	−	0.186979i	$-0.940130\pi$
$367$		−	7.16399i		−	0.373957i	0.982364	−	0.186979i	$-0.0598695\pi$
$368$	9.44932	−	10.5820i	0.492580	−	0.551624i
$369$		0			0
$370$	2.14451	+	10.0382i	0.111488	+	0.521862i
$371$	4.40768			0.228836
$372$		0			0
$373$	−29.1874			−1.51127			−0.755634	−	0.654994i	$-0.772671\pi$
$373$	−29.1874			−1.51127			−0.755634	+	0.654994i	$0.772671\pi$
$374$	−0.308588	−	1.44447i	−0.0159567	−	0.0746917i
$375$		0			0
$376$	18.1086	−	13.2425i	0.933882	−	0.682929i
$377$			2.24006i			0.115369i
$378$		0			0
$379$			6.93884i			0.356424i	0.983992	+	0.178212i	$0.0570313\pi$
$379$			6.93884i			0.356424i	−0.983992	+	0.178212i	$0.942969\pi$
$380$	0.675024	−	0.302210i	0.0346280	−	0.0155030i
$381$		0			0
$382$	32.9025	−	7.02910i	1.68344	−	0.359640i
$383$	25.8944			1.32314			0.661571	−	0.749882i	$-0.269890\pi$
$383$	25.8944			1.32314			0.661571	+	0.749882i	$0.269890\pi$
$384$		0			0
$385$	−4.54979			−0.231879
$386$	18.9027	−	4.03826i	0.962120	−	0.205542i
$387$		0			0
$388$	−3.03772	+	1.36000i	−0.154217	+	0.0690433i
$389$		−	13.4174i		−	0.680289i	−0.940373	−	0.340145i	$-0.889524\pi$
$389$		−	13.4174i		−	0.680289i	0.940373	−	0.340145i	$-0.110476\pi$
$390$		0			0
$391$		−	0.992165i		−	0.0501760i
$392$	−12.5912	+	9.20772i	−0.635954	+	0.465060i
$393$		0			0
$394$	1.03879	+	4.86246i	0.0523334	+	0.244967i
$395$	−14.8757			−0.748480
$396$		0			0
$397$	18.2580			0.916345			0.458173	−	0.888863i	$-0.348504\pi$
$397$	18.2580			0.916345			0.458173	+	0.888863i	$0.348504\pi$
$398$	−3.52940	−	16.5207i	−0.176913	−	0.828109i
$399$		0			0
$400$	−2.66424	+	2.98359i	−0.133212	+	0.149180i
$401$		−	0.261906i		−	0.0130790i	−0.999979	−	0.00653949i	$-0.997918\pi$
$401$		−	0.261906i		−	0.0130790i	0.999979	−	0.00653949i	$-0.00208160\pi$
$402$		0			0
$403$			8.17068i			0.407010i
$404$	−8.09082	−	18.0719i	−0.402533	−	0.899109i
$405$		0			0
$406$	−3.03445	+	0.648263i	−0.150597	+	0.0321728i
$407$	27.0994			1.34327
$408$		0			0
$409$	4.37562			0.216360			0.108180	−	0.994131i	$-0.465498\pi$
$409$	4.37562			0.216360			0.108180	+	0.994131i	$0.465498\pi$
$410$	15.4251	−	3.29533i	0.761791	−	0.162745i
$411$		0			0
$412$	8.81976	+	19.7001i	0.434518	+	0.970552i
$413$		−	10.5169i		−	0.517505i
$414$		0			0
$415$		−	15.6631i		−	0.768871i
$416$	−3.48747	+	6.11305i	−0.170987	+	0.299717i
$417$		0			0
$418$	−0.407927	−	1.90946i	−0.0199523	−	0.0933948i
$419$	8.10274			0.395845			0.197922	−	0.980218i	$-0.436581\pi$
$419$	8.10274			0.395845			0.197922	+	0.980218i	$0.436581\pi$
$420$		0			0
$421$	21.9406			1.06932			0.534660	−	0.845067i	$-0.320440\pi$
$421$	21.9406			1.06932			0.534660	+	0.845067i	$0.320440\pi$
$422$	−7.17512	−	33.5859i	−0.349279	−	1.63494i
$423$		0			0
$424$	−6.03884	−	8.25791i	−0.293272	−	0.401040i
$425$			0.279741i			0.0135694i
$426$		0			0
$427$		−	14.3731i		−	0.695561i
$428$	28.6930	−	12.8459i	1.38693	−	0.620931i
$429$		0			0
$430$	0.206468	−	0.0441088i	0.00995679	−	0.00212711i
$431$	−22.4611			−1.08191			−0.540955	−	0.841051i	$-0.681937\pi$
$431$	−22.4611			−1.08191			−0.540955	+	0.841051i	$0.681937\pi$
$432$		0			0
$433$	25.0546			1.20405			0.602023	−	0.798479i	$-0.294362\pi$
$433$	25.0546			1.20405			0.602023	+	0.798479i	$0.294362\pi$
$434$	−11.0682	+	2.36456i	−0.531292	+	0.113502i
$435$		0			0
$436$	−1.94143	+	0.869184i	−0.0929778	+	0.0416263i
$437$		−	1.31155i		−	0.0627402i
$438$		0			0
$439$		−	32.6507i		−	1.55833i	−0.626816	−	0.779167i	$-0.715642\pi$
$439$		−	32.6507i		−	1.55833i	0.626816	−	0.779167i	$-0.284358\pi$
$440$	6.23353	+	8.52414i	0.297172	+	0.406373i
$441$		0			0
$442$	0.102830	+	0.481335i	0.00489112	+	0.0228948i
$443$	−0.969524			−0.0460635			−0.0230317	−	0.999735i	$-0.507332\pi$
$443$	−0.969524			−0.0460635			−0.0230317	+	0.999735i	$0.507332\pi$
$444$		0			0
$445$	−12.9750			−0.615074
$446$	7.16846	+	33.5548i	0.339436	+	1.58886i
$447$		0			0
$448$	−9.29017	−	2.95514i	−0.438919	−	0.139617i
$449$		−	24.0836i		−	1.13658i	−0.822829	−	0.568289i	$-0.807606\pi$
$449$		−	24.0836i		−	1.13658i	0.822829	−	0.568289i	$-0.192394\pi$
$450$		0			0
$451$		−	41.6420i		−	1.96085i
$452$	−14.7373	−	32.9176i	−0.693183	−	1.54831i
$453$		0			0
$454$	−13.9025	+	2.97005i	−0.652475	+	0.139391i
$455$	1.51611			0.0710763
$456$		0			0
$457$	−9.62123			−0.450062			−0.225031	−	0.974352i	$-0.572248\pi$
$457$	−9.62123			−0.450062			−0.225031	+	0.974352i	$0.572248\pi$
$458$	4.57858	−	0.978142i	0.213943	−	0.0457056i
$459$		0			0
$460$	2.89852	+	6.47422i	0.135144	+	0.301862i
$461$		−	20.4856i		−	0.954109i	−0.878874	−	0.477054i	$-0.841704\pi$
$461$		−	20.4856i		−	0.954109i	0.878874	−	0.477054i	$-0.158296\pi$
$462$		0			0
$463$		−	15.3624i		−	0.713952i	−0.934114	−	0.356976i	$-0.883808\pi$
$463$		−	15.3624i		−	0.713952i	0.934114	−	0.356976i	$-0.116192\pi$
$464$	5.37195	+	4.79695i	0.249387	+	0.222693i
$465$		0			0
$466$	−1.55968	−	7.30070i	−0.0722509	−	0.338199i
$467$	−16.8309			−0.778842			−0.389421	−	0.921060i	$-0.627325\pi$
$467$	−16.8309			−0.778842			−0.389421	+	0.921060i	$0.627325\pi$
$468$		0			0
$469$	−1.58265			−0.0730800
$470$	2.34346	+	10.9695i	0.108096	+	0.505985i
$471$		0			0
$472$	−19.7038	+	14.4090i	−0.906939	+	0.663226i
$473$		−	0.557387i		−	0.0256287i
$474$		0			0
$475$			0.369793i			0.0169673i
$476$	−0.622272	+	0.278593i	−0.0285218	+	0.0127693i
$477$		0			0
$478$	−12.7597	+	2.72591i	−0.583615	+	0.124680i
$479$	12.3376			0.563721			0.281861	−	0.959455i	$-0.409048\pi$
$479$	12.3376			0.563721			0.281861	+	0.959455i	$0.409048\pi$
$480$		0			0
$481$	−9.03026			−0.411744
$482$	18.4587	−	3.94341i	0.840770	−	0.179618i
$483$		0			0
$484$	5.36625	−	2.40248i	0.243920	−	0.109204i
$485$		−	1.66413i		−	0.0755644i
$486$		0			0
$487$			35.8894i			1.62631i	0.582050	+	0.813153i	$0.302251\pi$
$487$			35.8894i			1.62631i	−0.582050	+	0.813153i	$0.697749\pi$
$488$	−26.9283	+	19.6921i	−1.21899	+	0.891421i
$489$		0			0
$490$	−1.62945	−	7.62727i	−0.0736110	−	0.344565i
$491$	−11.2160			−0.506172			−0.253086	−	0.967444i	$-0.581446\pi$
$491$	−11.2160			−0.506172			−0.253086	+	0.967444i	$0.581446\pi$
$492$		0			0
$493$	0.503673			0.0226843
$494$	0.135932	+	0.636283i	0.00611587	+	0.0286277i
$495$		0			0
$496$	19.5943	+	17.4970i	0.879812	+	0.785639i
$497$			0.475481i			0.0213283i
$498$		0			0
$499$		−	35.9508i		−	1.60938i	−0.593697	−	0.804689i	$-0.702332\pi$
$499$		−	35.9508i		−	1.60938i	0.593697	−	0.804689i	$-0.297668\pi$
$500$	−0.817240	−	1.82541i	−0.0365481	−	0.0816348i
$501$		0			0
$502$	7.90270	−	1.68829i	0.352715	−	0.0753521i
$503$	9.05867			0.403906			0.201953	−	0.979395i	$-0.435271\pi$
$503$	9.05867			0.403906			0.201953	+	0.979395i	$0.435271\pi$
$504$		0			0
$505$	9.90018			0.440552
$506$	18.3138	−	3.91246i	0.814148	−	0.173930i
$507$		0			0
$508$	11.8371	+	26.4397i	0.525187	+	1.17307i
$509$		−	2.88961i		−	0.128080i	−0.997947	−	0.0640399i	$-0.979602\pi$
$509$		−	2.88961i		−	0.128080i	0.997947	−	0.0640399i	$-0.0203985\pi$
$510$		0			0
$511$			15.5839i			0.689389i
$512$	7.19167	+	21.4541i	0.317830	+	0.948148i
$513$		0			0
$514$	−5.63825	−	26.3920i	−0.248692	−	1.16410i
$515$	−10.7921			−0.475558
$516$		0			0
$517$	29.6135			1.30240
$518$	−2.61332	−	12.2326i	−0.114823	−	0.537472i
$519$		0			0
$520$	−2.07718	−	2.84047i	−0.0910903	−	0.124563i
$521$		−	2.89836i		−	0.126980i	−0.997982	−	0.0634898i	$-0.979777\pi$
$521$		−	2.89836i		−	0.126980i	0.997982	−	0.0634898i	$-0.0202230\pi$
$522$		0			0
$523$		−	4.76884i		−	0.208527i	−0.994550	−	0.104263i	$-0.966752\pi$
$523$		−	4.76884i		−	0.208527i	0.994550	−	0.104263i	$-0.0332485\pi$
$524$	−23.5769	+	10.5554i	−1.02996	+	0.461116i
$525$		0			0
$526$	5.54367	−	1.18432i	0.241716	−	0.0516388i
$527$	1.83716			0.0800281
$528$		0			0
$529$	−10.4208			−0.453076
$530$	5.00231	−	1.06867i	0.217287	−	0.0464199i
$531$		0			0
$532$	−0.822589	+	0.368275i	−0.0356638	+	0.0159667i
$533$			13.8762i			0.601046i
$534$		0			0
$535$			15.7187i			0.679578i
$536$	2.16834	+	2.96514i	0.0936582	+	0.128074i
$537$		0			0
$538$	2.13888	+	10.0119i	0.0922137	+	0.431642i
$539$	−20.5908			−0.886908
$540$		0			0
$541$	16.3669			0.703670			0.351835	−	0.936062i	$-0.385558\pi$
$541$	16.3669			0.703670			0.351835	+	0.936062i	$0.385558\pi$
$542$	3.49505	+	16.3599i	0.150125	+	0.702720i
$543$		0			0
$544$	1.37451	+	0.784152i	0.0589316	+	0.0336202i
$545$		−	1.06356i		−	0.0455579i
$546$		0			0
$547$		−	24.7215i		−	1.05702i	−0.848928	−	0.528508i	$-0.822752\pi$
$547$		−	24.7215i		−	1.05702i	0.848928	−	0.528508i	$-0.177248\pi$
$548$	6.13155	+	13.6956i	0.261927	+	0.585047i
$549$		0			0
$550$	−5.16359	+	1.10312i	−0.220176	+	0.0470372i
$551$	0.665812			0.0283645
$552$		0			0
$553$	18.1277			0.770867
$554$	−30.7506	+	6.56939i	−1.30647	+	0.279107i
$555$		0			0
$556$	0.702500	+	1.56912i	0.0297927	+	0.0665457i
$557$		−	0.391023i		−	0.0165682i	−0.999966	−	0.00828410i	$-0.997363\pi$
$557$		−	0.391023i		−	0.0165682i	0.999966	−	0.00828410i	$-0.00263694\pi$
$558$		0			0
$559$			0.185736i			0.00785581i
$560$	3.24666	−	3.63583i	0.137196	−	0.153642i
$561$		0			0
$562$	3.02144	+	14.1430i	0.127452	+	0.596588i
$563$	−12.3085			−0.518740			−0.259370	−	0.965778i	$-0.583515\pi$
$563$	−12.3085			−0.518740			−0.259370	+	0.965778i	$0.583515\pi$
$564$		0			0
$565$	18.0330			0.758653
$566$	3.89820	+	18.2471i	0.163854	+	0.766981i
$567$		0			0
$568$	0.890827	−	0.651444i	0.0373783	−	0.0273340i
$569$			27.0411i			1.13362i	0.823848	+	0.566811i	$0.191823\pi$
$569$			27.0411i			1.13362i	−0.823848	+	0.566811i	$0.808177\pi$
$570$		0			0
$571$			47.1381i			1.97267i	0.164757	+	0.986334i	$0.447316\pi$
$571$			47.1381i			1.97267i	−0.164757	+	0.986334i	$0.552684\pi$
$572$	−8.47920	+	3.79616i	−0.354533	+	0.158725i
$573$		0			0
$574$	−18.7971	+	4.01572i	−0.784577	+	0.167613i
$575$	−3.54672			−0.147909
$576$		0			0
$577$	−6.88412			−0.286590			−0.143295	−	0.989680i	$-0.545770\pi$
$577$	−6.88412			−0.286590			−0.143295	+	0.989680i	$0.545770\pi$
$578$	−23.4029	+	4.99966i	−0.973431	+	0.207959i
$579$		0			0
$580$	−3.28664	+	1.47144i	−0.136470	+	0.0610981i
$581$			19.0871i			0.791868i
$582$		0			0
$583$		−	13.5044i		−	0.559294i
$584$	29.1968	−	21.3510i	1.20817	−	0.883511i
$585$		0			0
$586$	7.87400	+	36.8573i	0.325272	+	1.52256i
$587$	35.4349			1.46256			0.731278	−	0.682080i	$-0.238924\pi$
$587$	35.4349			1.46256			0.731278	+	0.682080i	$0.238924\pi$
$588$		0			0
$589$	2.42857			0.100067
$590$	−2.54989	−	11.9357i	−0.104977	−	0.491387i
$591$		0			0
$592$	−19.3378	+	21.6557i	−0.794777	+	0.890045i
$593$			46.1833i			1.89652i	0.317492	+	0.948261i	$0.397159\pi$
$593$			46.1833i			1.89652i	−0.317492	+	0.948261i	$0.602841\pi$
$594$		0			0
$595$		−	0.340895i		−	0.0139753i
$596$	6.39715	+	14.2888i	0.262037	+	0.585294i
$597$		0			0
$598$	−6.10265	+	1.30374i	−0.249556	+	0.0533138i
$599$	−37.3715			−1.52696			−0.763478	−	0.645834i	$-0.776510\pi$
$599$	−37.3715			−1.52696			−0.763478	+	0.645834i	$0.776510\pi$
$600$		0			0
$601$	−10.5031			−0.428429			−0.214214	−	0.976787i	$-0.568719\pi$
$601$	−10.5031			−0.428429			−0.214214	+	0.976787i	$0.568719\pi$
$602$	−0.251604	+	0.0537512i	−0.0102546	+	0.00219074i
$603$		0			0
$604$	16.5833	+	37.0409i	0.674765	+	1.50717i
$605$			2.93975i			0.119518i
$606$		0			0
$607$		−	46.6876i		−	1.89499i	−0.319771	−	0.947495i	$-0.603606\pi$
$607$		−	46.6876i		−	1.89499i	0.319771	−	0.947495i	$-0.396394\pi$
$608$	1.81698	+	1.03658i	0.0736882	+	0.0420388i
$609$		0			0
$610$	−3.48483	−	16.3121i	−0.141097	−	0.660458i
$611$	−9.86801			−0.399217
$612$		0			0
$613$	−44.3439			−1.79103			−0.895516	−	0.445030i	$-0.853193\pi$
$613$	−44.3439			−1.79103			−0.895516	+	0.445030i	$0.853193\pi$
$614$	−8.88897	−	41.6083i	−0.358730	−	1.67917i
$615$		0			0
$616$	−7.59623	−	10.3876i	−0.306061	−	0.418528i
$617$		−	8.01553i		−	0.322693i	−0.986898	−	0.161347i	$-0.948416\pi$
$617$		−	8.01553i		−	0.322693i	0.986898	−	0.161347i	$-0.0515837\pi$
$618$		0			0
$619$		−	26.7549i		−	1.07537i	−0.843145	−	0.537686i	$-0.819299\pi$
$619$		−	26.7549i		−	1.07537i	0.843145	−	0.537686i	$-0.180701\pi$
$620$	−11.9881	+	5.36711i	−0.481455	+	0.215548i
$621$		0			0
$622$	27.8039	−	5.93987i	1.11483	−	0.238167i
$623$	15.8114			0.633472
$624$		0			0
$625$	1.00000			0.0400000
$626$	19.2948	−	4.12203i	0.771175	−	0.164750i
$627$		0			0
$628$	−5.03710	+	2.25512i	−0.201002	+	0.0899891i
$629$			2.03044i			0.0809588i
$630$		0			0
$631$		−	46.9469i		−	1.86893i	−0.356058	−	0.934464i	$-0.615880\pi$
$631$		−	46.9469i		−	1.86893i	0.356058	−	0.934464i	$-0.384120\pi$
$632$	−24.8362	−	33.9627i	−0.987932	−	1.35096i
$633$		0			0
$634$	10.2734	+	48.0887i	0.408009	+	1.90985i
$635$	−14.4843			−0.574791
$636$		0			0
$637$	6.86140			0.271858
$638$	1.98617	+	9.29702i	0.0786330	+	0.368073i
$639$		0			0
$640$	−11.2600	−	1.10136i	−0.445090	−	0.0435349i
$641$			4.26642i			0.168513i	0.996444	+	0.0842567i	$0.0268516\pi$
$641$			4.26642i			0.168513i	−0.996444	+	0.0842567i	$0.973148\pi$
$642$		0			0
$643$		−	24.4305i		−	0.963444i	−0.876324	−	0.481722i	$-0.840012\pi$
$643$		−	24.4305i		−	0.963444i	0.876324	−	0.481722i	$-0.159988\pi$
$644$	−3.53216	−	7.88953i	−0.139187	−	0.310891i
$645$		0			0
$646$	0.143067	−	0.0305641i	0.00562890	−	0.00120253i
$647$	−0.915104			−0.0359765			−0.0179882	−	0.999838i	$-0.505726\pi$
$647$	−0.915104			−0.0359765			−0.0179882	+	0.999838i	$0.505726\pi$
$648$		0			0
$649$	−32.2221			−1.26483
$650$	1.72064	−	0.367589i	0.0674892	−	0.0144180i
$651$		0			0
$652$	14.2124	+	31.7452i	0.556599	+	1.24324i
$653$		−	5.92570i		−	0.231891i	−0.993256	−	0.115945i	$-0.963010\pi$
$653$		−	5.92570i		−	0.231891i	0.993256	−	0.115945i	$-0.0369897\pi$
$654$		0			0
$655$		−	12.9159i		−	0.504668i
$656$	33.2770	+	29.7151i	1.29925	+	1.16018i
$657$		0			0
$658$	−2.85576	−	13.3675i	−0.111329	−	0.521119i
$659$	22.2700			0.867515			0.433758	−	0.901030i	$-0.357187\pi$
$659$	22.2700			0.867515			0.433758	+	0.901030i	$0.357187\pi$
$660$		0			0
$661$	29.3623			1.14206			0.571031	−	0.820928i	$-0.306543\pi$
$661$	29.3623			1.14206			0.571031	+	0.820928i	$0.306543\pi$
$662$	3.01266	+	14.1019i	0.117090	+	0.548086i
$663$		0			0
$664$	35.7603	−	26.1508i	1.38777	−	1.01485i
$665$		−	0.450633i		−	0.0174748i
$666$		0			0
$667$			6.38586i			0.247262i
$668$	4.08509	−	1.82890i	0.158057	−	0.0707625i
$669$		0			0
$670$	−1.79616	+	0.383722i	−0.0693918	+	0.0148245i
$671$	−44.0366			−1.70001
$672$		0			0
$673$	−27.0200			−1.04155			−0.520773	−	0.853695i	$-0.674356\pi$
$673$	−27.0200			−1.04155			−0.520773	+	0.853695i	$0.674356\pi$
$674$	−16.9825	+	3.62805i	−0.654142	+	0.139747i
$675$		0			0
$676$	−20.9048	+	9.35914i	−0.804032	+	0.359967i
$677$			36.9889i			1.42160i	0.703394	+	0.710800i	$0.251667\pi$
$677$			36.9889i			1.42160i	−0.703394	+	0.710800i	$0.748333\pi$
$678$		0			0
$679$			2.02792i			0.0778246i
$680$	−0.638675	+	0.467050i	−0.0244921	+	0.0179106i
$681$		0			0
$682$	7.24459	+	33.9111i	0.277410	+	1.29852i
$683$	−28.1575			−1.07742			−0.538708	−	0.842493i	$-0.681087\pi$
$683$	−28.1575			−1.07742			−0.538708	+	0.842493i	$0.681087\pi$
$684$		0			0
$685$	−7.50275			−0.286665
$686$	4.50599	+	21.0920i	0.172039	+	0.805297i
$687$		0			0
$688$	0.445419	+	0.397743i	0.0169815	+	0.0151638i
$689$			4.50001i			0.171437i
$690$		0			0
$691$			46.5469i			1.77073i	0.464900	+	0.885363i	$0.346090\pi$
$691$			46.5469i			1.77073i	−0.464900	+	0.885363i	$0.653910\pi$
$692$	1.57152	+	3.51019i	0.0597401	+	0.133437i
$693$		0			0
$694$	−34.6989	+	7.41287i	−1.31715	+	0.281389i
$695$	−0.859601			−0.0326065
$696$		0			0
$697$	3.12004			0.118180
$698$	−8.35827	+	1.78561i	−0.316365	+	0.0675865i
$699$		0			0
$700$	0.995894	+	2.22446i	0.0376412	+	0.0840765i
$701$			5.97449i			0.225654i	0.993615	+	0.112827i	$0.0359905\pi$
$701$			5.97449i			0.225654i	−0.993615	+	0.112827i	$0.964009\pi$
$702$		0			0
$703$			2.68406i			0.101231i
$704$	−9.05403	+	28.4635i	−0.341237	+	1.07276i
$705$		0			0
$706$	−4.68945	−	21.9508i	−0.176490	−	0.826130i
$707$	−12.0644			−0.453729
$708$		0			0
$709$	31.5175			1.18367			0.591833	−	0.806061i	$-0.298404\pi$
$709$	31.5175			1.18367			0.591833	+	0.806061i	$0.298404\pi$
$710$	0.115283	+	0.539627i	0.00432650	+	0.0202519i
$711$		0			0
$712$	−21.6628	−	29.6231i	−0.811848	−	1.11017i
$713$			23.2926i			0.872315i
$714$		0			0
$715$		−	4.64510i		−	0.173717i
$716$	31.6047	−	14.1495i	1.18112	−	0.528791i
$717$		0			0
$718$	−28.9157	+	6.17740i	−1.07913	+	0.230538i
$719$	−10.9383			−0.407928			−0.203964	−	0.978978i	$-0.565383\pi$
$719$	−10.9383			−0.407928			−0.203964	+	0.978978i	$0.565383\pi$
$720$		0			0
$721$	13.1514			0.489782
$722$	−26.0880	+	5.57330i	−0.970894	+	0.207417i
$723$		0			0
$724$	12.6750	−	5.67461i	0.471061	−	0.210895i
$725$		−	1.80050i		−	0.0668688i
$726$		0			0
$727$		−	3.70645i		−	0.137465i	−0.997635	−	0.0687323i	$-0.978105\pi$
$727$		−	3.70645i		−	0.137465i	0.997635	−	0.0687323i	$-0.0218954\pi$
$728$	2.53126	+	3.46142i	0.0938149	+	0.128289i
$729$		0			0
$730$	3.77839	+	17.6862i	0.139845	+	0.654597i
$731$	0.0417625			0.00154464
$732$		0			0
$733$	−35.0524			−1.29469			−0.647345	−	0.762197i	$-0.724121\pi$
$733$	−35.0524			−1.29469			−0.647345	+	0.762197i	$0.724121\pi$
$734$	2.11666	+	9.90784i	0.0781272	+	0.365705i
$735$		0			0
$736$	−9.94193	+	17.4268i	−0.366464	+	0.642361i
$737$			4.84896i			0.178614i
$738$		0			0
$739$			7.19782i			0.264776i	0.991198	+	0.132388i	$0.0422645\pi$
$739$			7.19782i			0.264776i	−0.991198	+	0.132388i	$0.957735\pi$
$740$	−5.93174	−	13.2493i	−0.218055	−	0.487054i
$741$		0			0
$742$	−6.09585	+	1.30228i	−0.223786	+	0.0478084i
$743$	−2.76598			−0.101474			−0.0507371	−	0.998712i	$-0.516157\pi$
$743$	−2.76598			−0.101474			−0.0507371	+	0.998712i	$0.516157\pi$
$744$		0			0
$745$	−7.82775			−0.286787
$746$	40.3664	−	8.62366i	1.47792	−	0.315734i
$747$		0			0
$748$	0.853559	+	1.90653i	0.0312092	+	0.0697098i
$749$		−	19.1549i		−	0.699904i
$750$		0			0
$751$		−	13.8947i		−	0.507026i	−0.967332	−	0.253513i	$-0.918414\pi$
$751$		−	13.8947i		−	0.507026i	0.967332	−	0.253513i	$-0.0815860\pi$
$752$	−21.1318	+	23.6648i	−0.770596	+	0.862965i
$753$		0			0
$754$	−0.661843	−	3.09801i	−0.0241029	−	0.112823i
$755$	−20.2918			−0.738496
$756$		0			0
$757$	−47.4178			−1.72343			−0.861715	−	0.507392i	$-0.830610\pi$
$757$	−47.4178			−1.72343			−0.861715	+	0.507392i	$0.830610\pi$
$758$	−2.05013	−	9.59645i	−0.0744642	−	0.348559i
$759$		0			0
$760$	−0.844272	+	0.617399i	−0.0306250	+	0.0223954i
$761$			47.8081i			1.73304i	0.499140	+	0.866521i	$0.333649\pi$
$761$			47.8081i			1.73304i	−0.499140	+	0.866521i	$0.666351\pi$
$762$		0			0
$763$			1.29606i			0.0469206i
$764$	−43.4275	+	19.4426i	−1.57115	+	0.703408i
$765$		0			0
$766$	−35.8121	+	7.65071i	−1.29394	+	0.276431i
$767$	10.7372			0.387699
$768$		0			0
$769$	−1.59757			−0.0576099			−0.0288049	−	0.999585i	$-0.509170\pi$
$769$	−1.59757			−0.0576099			−0.0288049	+	0.999585i	$0.509170\pi$
$770$	6.29238	−	1.34427i	0.226762	−	0.0484441i
$771$		0			0
$772$	−24.9494	+	11.1699i	−0.897947	+	0.402013i
$773$		−	31.8893i		−	1.14698i	−0.819214	−	0.573489i	$-0.805590\pi$
$773$		−	31.8893i		−	1.14698i	0.819214	−	0.573489i	$-0.194410\pi$
$774$		0			0
$775$		−	6.56736i		−	0.235907i
$776$	3.79937	−	2.77840i	0.136389	−	0.0997388i
$777$		0			0
$778$	3.96428	+	18.5563i	0.142126	+	0.665277i
$779$	4.12442			0.147773
$780$		0			0
$781$	1.45679			0.0521281
$782$	0.293143	+	1.37217i	0.0104828	+	0.0490687i
$783$		0			0
$784$	14.6933	−	16.4545i	0.524760	−	0.587661i
$785$		−	2.75944i		−	0.0984885i
$786$		0			0
$787$			21.9838i			0.783638i	0.920042	+	0.391819i	$0.128154\pi$
$787$			21.9838i			0.783638i	−0.920042	+	0.391819i	$0.871846\pi$
$788$	−2.87330	−	6.41789i	−0.102357	−	0.228628i
$789$		0			0
$790$	20.5732	−	4.39515i	0.731963	−	0.156373i
$791$	−21.9751			−0.781345
$792$		0			0
$793$	14.6742			0.521094
$794$	−25.2510	+	5.39448i	−0.896124	+	0.191443i
$795$		0			0
$796$	9.76236	+	21.8055i	0.346018	+	0.772874i
$797$		−	13.9307i		−	0.493451i	−0.969085	−	0.246725i	$-0.920645\pi$
$797$		−	13.9307i		−	0.493451i	0.969085	−	0.246725i	$-0.0793546\pi$
$798$		0			0
$799$			2.21881i			0.0784957i
$800$	2.80313	−	4.91350i	0.0991056	−	0.173718i
$801$		0			0
$802$	0.0773823	+	0.362218i	0.00273246	+	0.0127904i
$803$	47.7462			1.68493
$804$		0			0
$805$	4.32206			0.152333
$806$	−2.41409	−	11.3001i	−0.0850327	−	0.398029i
$807$		0			0
$808$	16.5291	+	22.6030i	0.581492	+	0.795171i
$809$			25.5519i			0.898358i	0.893442	+	0.449179i	$0.148283\pi$
$809$			25.5519i			0.898358i	−0.893442	+	0.449179i	$0.851717\pi$
$810$		0			0
$811$		−	40.7325i		−	1.43031i	−0.698965	−	0.715156i	$-0.746356\pi$
$811$		−	40.7325i		−	1.43031i	0.698965	−	0.715156i	$-0.253644\pi$
$812$	4.00513	−	1.79310i	0.140552	−	0.0629256i
$813$		0			0
$814$	−37.4787	+	8.00674i	−1.31363	+	0.280636i
$815$	−17.3907			−0.609170
$816$		0			0
$817$	0.0552063			0.00193142
$818$	−6.05150	+	1.29281i	−0.211586	+	0.0452020i
$819$		0			0
$820$	−20.3594	+	9.11493i	−0.710980	+	0.318307i
$821$			5.79991i			0.202418i	0.994865	+	0.101209i	$0.0322711\pi$
$821$			5.79991i			0.202418i	−0.994865	+	0.101209i	$0.967729\pi$
$822$		0			0
$823$			5.92767i			0.206625i	0.994649	+	0.103313i	$0.0329443\pi$
$823$			5.92767i			0.206625i	−0.994649	+	0.103313i	$0.967056\pi$
$824$	−18.0183	−	24.6394i	−0.627698	−	0.858355i
$825$		0			0
$826$	3.10731	+	14.5450i	0.108117	+	0.506085i
$827$	46.3860			1.61300			0.806500	−	0.591234i	$-0.201359\pi$
$827$	46.3860			1.61300			0.806500	+	0.591234i	$0.201359\pi$
$828$		0			0
$829$	−31.2972			−1.08700			−0.543498	−	0.839411i	$-0.682900\pi$
$829$	−31.2972			−1.08700			−0.543498	+	0.839411i	$0.682900\pi$
$830$	4.62778	+	21.6621i	0.160633	+	0.751904i
$831$		0			0
$832$	3.01704	−	9.48478i	0.104597	−	0.328826i
$833$		−	1.54277i		−	0.0534539i
$834$		0			0
$835$			2.23791i			0.0774459i
$836$	1.12833	+	2.52027i	0.0390241	+	0.0871653i
$837$		0			0
$838$	−11.2061	+	2.39402i	−0.387109	+	0.0827000i
$839$	31.4963			1.08737			0.543687	−	0.839288i	$-0.317028\pi$
$839$	31.4963			1.08737			0.543687	+	0.839288i	$0.317028\pi$
$840$		0			0
$841$	25.7582			0.888214
$842$	−30.3440	+	6.48253i	−1.04572	+	0.223403i
$843$		0			0
$844$	19.8465	+	44.3296i	0.683143	+	1.52589i
$845$		−	11.4521i		−	0.393965i
$846$		0			0
$847$		−	3.58240i		−	0.123093i
$848$	10.7916	+	9.63651i	0.370586	+	0.330919i
$849$		0			0
$850$	−0.0826518	−	0.386884i	−0.00283493	−	0.0132700i
$851$	−25.7431			−0.882461
$852$		0			0
$853$	17.7214			0.606768			0.303384	−	0.952868i	$-0.401884\pi$
$853$	17.7214			0.606768			0.303384	+	0.952868i	$0.401884\pi$
$854$	4.24664	+	19.8780i	0.145317	+	0.680212i
$855$		0			0
$856$	−35.8872	+	26.2436i	−1.22660	+	0.896987i
$857$			24.0939i			0.823033i	0.911402	+	0.411517i	$0.135001\pi$
$857$			24.0939i			0.823033i	−0.911402	+	0.411517i	$0.864999\pi$
$858$		0			0
$859$			20.9968i			0.716401i	0.933645	+	0.358201i	$0.116610\pi$
$859$			20.9968i			0.716401i	−0.933645	+	0.358201i	$0.883390\pi$
$860$	−0.272515	+	0.122005i	−0.00929267	+	0.00416035i
$861$		0			0
$862$	31.0638	−	6.63629i	1.05804	−	0.226033i
$863$	16.2651			0.553670			0.276835	−	0.960917i	$-0.410714\pi$
$863$	16.2651			0.553670			0.276835	+	0.960917i	$0.410714\pi$
$864$		0			0
$865$	−1.92296			−0.0653825
$866$	−34.6506	+	7.40257i	−1.17748	+	0.251549i
$867$		0			0
$868$	14.6088	−	6.54039i	0.495855	−	0.221995i
$869$		−	55.5400i		−	1.88407i
$870$		0			0
$871$		−	1.61580i		−	0.0547494i
$872$	2.42821	−	1.77570i	0.0822294	−	0.0601327i
$873$		0			0
$874$	0.387509	+	1.81389i	0.0131077	+	0.0613557i
$875$	−1.21861			−0.0411964
$876$		0			0
$877$	−41.8052			−1.41166			−0.705830	−	0.708381i	$-0.749426\pi$
$877$	−41.8052			−1.41166			−0.705830	+	0.708381i	$0.749426\pi$
$878$	9.64692	+	45.1562i	0.325568	+	1.52395i
$879$		0			0
$880$	−11.1395	−	9.94719i	−0.375514	−	0.335320i
$881$		−	29.4914i		−	0.993589i	−0.867868	−	0.496795i	$-0.834510\pi$
$881$		−	29.4914i		−	0.993589i	0.867868	−	0.496795i	$-0.165490\pi$
$882$		0			0
$883$		−	40.4400i		−	1.36091i	−0.732788	−	0.680457i	$-0.761781\pi$
$883$		−	40.4400i		−	1.36091i	0.732788	−	0.680457i	$-0.238219\pi$
$884$	−0.284429	−	0.635308i	−0.00956637	−	0.0213677i
$885$		0			0
$886$	1.34086	−	0.286454i	0.0450470	−	0.00962359i
$887$	22.2411			0.746784			0.373392	−	0.927674i	$-0.378195\pi$
$887$	22.2411			0.746784			0.373392	+	0.927674i	$0.378195\pi$
$888$		0			0
$889$	17.6506			0.591983
$890$	17.9445	−	3.83357i	0.601501	−	0.128501i
$891$		0			0
$892$	−19.8280	−	44.2884i	−0.663892	−	1.48289i
$893$			2.93307i			0.0981513i
$894$		0			0
$895$			17.3137i			0.578735i
$896$	13.7215	+	1.34212i	0.458403	+	0.0448371i
$897$		0			0
$898$	7.11570	+	33.3078i	0.237454	+	1.11150i
$899$	−11.8245			−0.394370
$900$		0			0
$901$	1.01182			0.0337086
$902$	12.3035	+	57.5911i	0.409660	+	1.91757i
$903$		0			0
$904$	30.1075	+	41.1709i	1.00136	+	1.36933i
$905$			6.94363i			0.230814i
$906$		0			0
$907$		−	10.6115i		−	0.352350i	−0.984359	−	0.176175i	$-0.943628\pi$
$907$		−	10.6115i		−	0.352350i	0.984359	−	0.176175i	$-0.0563724\pi$
$908$	18.3497	−	8.21518i	0.608955	−	0.272630i
$909$		0			0
$910$	−2.09679	+	0.447947i	−0.0695079	+	0.0148493i
$911$	20.1523			0.667674			0.333837	−	0.942631i	$-0.391656\pi$
$911$	20.1523			0.667674			0.333837	+	0.942631i	$0.391656\pi$
$912$		0			0
$913$	58.4797			1.93539
$914$	13.3062	−	2.84267i	0.440131	−	0.0940271i
$915$		0			0
$916$	−6.04320	+	2.70555i	−0.199673	+	0.0893940i
$917$			15.7395i			0.519763i
$918$		0			0
$919$			45.8866i			1.51366i	0.653612	+	0.756829i	$0.273253\pi$
$919$			45.8866i			1.51366i	−0.653612	+	0.756829i	$0.726747\pi$
$920$	−5.92153	−	8.09749i	−0.195227	−	0.266966i
$921$		0			0
$922$	6.05263	+	28.3317i	0.199333	+	0.933054i
$923$	−0.485442			−0.0159785
$924$		0			0
$925$	7.25827			0.238650
$926$	4.53894	+	21.2463i	0.149159	+	0.698197i
$927$		0			0
$928$	−8.84674	−	5.04703i	−0.290408	−	0.165677i
$929$			13.6490i			0.447808i	0.974611	+	0.223904i	$0.0718803\pi$
$929$			13.6490i			0.447808i	−0.974611	+	0.223904i	$0.928120\pi$
$930$		0			0
$931$		−	2.03941i		−	0.0668390i
$932$	4.31410	+	9.63609i	0.141313	+	0.315641i
$933$		0			0
$934$	23.2773	−	4.97283i	0.761655	−	0.162716i
$935$	−1.04444			−0.0341569
$936$		0			0
$937$	−2.61312			−0.0853669			−0.0426834	−	0.999089i	$-0.513591\pi$
$937$	−2.61312			−0.0853669			−0.0426834	+	0.999089i	$0.513591\pi$
$938$	2.18881	−	0.467606i	0.0714673	−	0.0152679i
$939$		0			0
$940$	−6.48204	−	14.4785i	−0.211421	−	0.472236i
$941$		−	53.5401i		−	1.74536i	−0.488294	−	0.872679i	$-0.662381\pi$
$941$		−	53.5401i		−	1.74536i	0.488294	−	0.872679i	$-0.337619\pi$
$942$		0			0
$943$			39.5577i			1.28818i
$944$	22.9932	−	25.7493i	0.748364	−	0.838068i
$945$		0			0
$946$	0.164684	+	0.770870i	0.00535435	+	0.0250631i
$947$	16.3058			0.529868			0.264934	−	0.964267i	$-0.414650\pi$
$947$	16.3058			0.529868			0.264934	+	0.964267i	$0.414650\pi$
$948$		0			0
$949$	−15.9103			−0.516470
$950$	−0.109258	−	0.511426i	−0.00354481	−	0.0165929i
$951$		0			0
$952$	0.778294	−	0.569151i	0.0252246	−	0.0184463i
$953$			52.1980i			1.69086i	0.534086	+	0.845430i	$0.320656\pi$
$953$			52.1980i			1.69086i	−0.534086	+	0.845430i	$0.679344\pi$
$954$		0			0
$955$		−	23.7905i		−	0.769844i
$956$	16.8413	−	7.53991i	0.544688	−	0.243858i
$957$		0			0
$958$	−17.0630	+	3.64525i	−0.551281	+	0.117773i
$959$	9.14291			0.295240
$960$		0			0
$961$	−12.1302			−0.391298
$962$	12.4889	−	2.66806i	0.402658	−	0.0860217i
$963$		0			0
$964$	−24.3634	+	10.9075i	−0.784691	+	0.351308i
$965$		−	13.6678i		−	0.439982i
$966$		0			0
$967$		−	37.5988i		−	1.20910i	−0.796569	−	0.604548i	$-0.793354\pi$
$967$		−	37.5988i		−	1.20910i	0.796569	−	0.604548i	$-0.206646\pi$
$968$	−6.71172	+	4.90814i	−0.215723	+	0.157754i
$969$		0			0
$970$	0.491681	+	2.30151i	0.0157869	+	0.0738969i
$971$	−16.7233			−0.536677			−0.268339	−	0.963325i	$-0.586475\pi$
$971$	−16.7233			−0.536677			−0.268339	+	0.963325i	$0.586475\pi$
$972$		0			0
$973$	1.04752			0.0335818
$974$	−10.6038	−	49.6353i	−0.339768	−	1.59042i
$975$		0			0
$976$	31.4238	−	35.1905i	1.00585	−	1.12642i
$977$			34.8812i			1.11595i	0.829858	+	0.557974i	$0.188421\pi$
$977$			34.8812i			1.11595i	−0.829858	+	0.557974i	$0.811579\pi$
$978$		0			0
$979$		−	48.4435i		−	1.54826i
$980$	4.50707	+	10.0671i	0.143973	+	0.321583i
$981$		0			0
$982$	15.5118	−	3.31386i	0.495002	−	0.105749i
$983$	0.182596			0.00582391			0.00291195	−	0.999996i	$-0.499073\pi$
$983$	0.182596			0.00582391			0.00291195	+	0.999996i	$0.499073\pi$
$984$		0			0
$985$	3.51586			0.112025
$986$	−0.696583	+	0.148814i	−0.0221837	+	0.00473921i
$987$		0			0
$988$	−0.375990	−	0.839821i	−0.0119618	−	0.0267183i
$989$			0.529489i			0.0168368i
$990$		0			0
$991$		−	32.2371i		−	1.02404i	−0.858972	−	0.512022i	$-0.828897\pi$
$991$		−	32.2371i		−	1.02404i	0.858972	−	0.512022i	$-0.171103\pi$
$992$	−32.2687	−	18.4092i	−1.02453	−	0.584492i
$993$		0			0
$994$	−0.140485	−	0.657593i	−0.00445590	−	0.0208576i
$995$	−11.9455			−0.378699
$996$		0			0
$997$	21.6662			0.686176			0.343088	−	0.939303i	$-0.388527\pi$
$997$	21.6662			0.686176			0.343088	+	0.939303i	$0.388527\pi$
$998$	10.6219	+	49.7201i	0.336232	+	1.57386i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.a.971.4	yes	48
3.2	odd	2	inner	1620.2.e.a.971.45	yes	48
4.3	odd	2	inner	1620.2.e.a.971.46	yes	48
12.11	even	2	inner	1620.2.e.a.971.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.e.a.971.3	✓	48	12.11	even	2	inner
1620.2.e.a.971.4	yes	48	1.1	even	1	trivial
1620.2.e.a.971.45	yes	48	3.2	odd	2	inner
1620.2.e.a.971.46	yes	48	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38301 + 0.295458i) q^{2} +(1.82541 - 0.817240i) q^{4} +1.00000i q^{5} -1.21861i q^{7} +(-2.28309 + 1.66958i) q^{8} +O(q^{10})\)	\(q+(-1.38301 + 0.295458i) q^{2} +(1.82541 - 0.817240i) q^{4} +1.00000i q^{5} -1.21861i q^{7} +(-2.28309 + 1.66958i) q^{8} +(-0.295458 - 1.38301i) q^{10} -3.73360 q^{11} +1.24413 q^{13} +(0.360047 + 1.68534i) q^{14} +(2.66424 - 2.98359i) q^{16} -0.279741i q^{17} -0.369793i q^{19} +(0.817240 + 1.82541i) q^{20} +(5.16359 - 1.10312i) q^{22} +3.54672 q^{23} -1.00000 q^{25} +(-1.72064 + 0.367589i) q^{26} +(-0.995894 - 2.22446i) q^{28} +1.80050i q^{29} +6.56736i q^{31} +(-2.80313 + 4.91350i) q^{32} +(0.0826518 + 0.386884i) q^{34} +1.21861 q^{35} -7.25827 q^{37} +(0.109258 + 0.511426i) q^{38} +(-1.66958 - 2.28309i) q^{40} +11.1533i q^{41} +0.149290i q^{43} +(-6.81534 + 3.05124i) q^{44} +(-4.90514 + 1.04791i) q^{46} -7.93163 q^{47} +5.51500 q^{49} +(1.38301 - 0.295458i) q^{50} +(2.27105 - 1.01676i) q^{52} +3.61699i q^{53} -3.73360i q^{55} +(2.03456 + 2.78219i) q^{56} +(-0.531971 - 2.49010i) q^{58} +8.63030 q^{59} +11.7947 q^{61} +(-1.94038 - 9.08270i) q^{62} +(2.42501 - 7.62360i) q^{64} +1.24413i q^{65} -1.29874i q^{67} +(-0.228616 - 0.510642i) q^{68} +(-1.68534 + 0.360047i) q^{70} -0.390184 q^{71} -12.7883 q^{73} +(10.0382 - 2.14451i) q^{74} +(-0.302210 - 0.675024i) q^{76} +4.54979i q^{77} +14.8757i q^{79} +(2.98359 + 2.66424i) q^{80} +(-3.29533 - 15.4251i) q^{82} -15.6631 q^{83} +0.279741 q^{85} +(-0.0441088 - 0.206468i) q^{86} +(8.52414 - 6.23353i) q^{88} +12.9750i q^{89} -1.51611i q^{91} +(6.47422 - 2.89852i) q^{92} +(10.9695 - 2.34346i) q^{94} +0.369793 q^{95} -1.66413 q^{97} +(-7.62727 + 1.62945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) \) 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more