LMFDB - Embedded newform 384.2.n.a.241.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(49,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("384.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.n (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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			241.4
Character	$\chi$	$=$	384.241
Dual form			384.2.n.a.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 - 0.923880i) q^{3} +(3.68816 + 1.52768i) q^{5} +(1.63704 + 1.63704i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.382683 - 0.923880i) q^{3} +(3.68816 + 1.52768i) q^{5} +(1.63704 + 1.63704i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.20420 + 2.90719i) q^{11} +(-3.30127 + 1.36743i) q^{13} -3.99203i q^{15} -0.511560i q^{17} +(0.254077 - 0.105242i) q^{19} +(0.885960 - 2.13890i) q^{21} +(3.17185 - 3.17185i) q^{23} +(7.73315 + 7.73315i) q^{25} +(0.923880 + 0.382683i) q^{27} +(-2.75087 - 6.64118i) q^{29} +5.82083 q^{31} +3.14672 q^{33} +(3.53678 + 8.53855i) q^{35} +(-5.53467 - 2.29253i) q^{37} +(2.52668 + 2.52668i) q^{39} +(3.94823 - 3.94823i) q^{41} +(-1.30801 + 3.15781i) q^{43} +(-3.68816 + 1.52768i) q^{45} -9.41403i q^{47} -1.64019i q^{49} +(-0.472620 + 0.195765i) q^{51} +(2.50482 - 6.04717i) q^{53} +(-8.88255 + 8.88255i) q^{55} +(-0.194462 - 0.194462i) q^{57} +(-13.3423 - 5.52657i) q^{59} +(3.35835 + 8.10777i) q^{61} -2.31513 q^{63} -14.2646 q^{65} +(1.11643 + 2.69530i) q^{67} +(-4.14422 - 1.71659i) q^{69} +(-1.26611 - 1.26611i) q^{71} +(-7.51616 + 7.51616i) q^{73} +(4.18515 - 10.1038i) q^{75} +(-6.73052 + 2.78787i) q^{77} -0.709730i q^{79} -1.00000i q^{81} +(1.40823 - 0.583309i) q^{83} +(0.781502 - 1.88671i) q^{85} +(-5.08294 + 5.08294i) q^{87} +(-0.0856897 - 0.0856897i) q^{89} +(-7.64285 - 3.16577i) q^{91} +(-2.22754 - 5.37775i) q^{93} +1.09785 q^{95} -0.677647 q^{97} +(-1.20420 - 2.90719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$1$

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
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$		0			0
$5$	3.68816	+	1.52768i	1.64939	+	0.683201i	0.997195	−	0.0748462i	$-0.0238466\pi$
$5$	3.68816	+	1.52768i	1.64939	+	0.683201i	0.652199	+	0.758048i	$0.273847\pi$
$6$		0			0
$7$	1.63704	+	1.63704i	0.618743	+	0.618743i	0.945209	−	0.326466i	$-0.105858\pi$
$7$	1.63704	+	1.63704i	0.618743	+	0.618743i	−0.326466	+	0.945209i	$0.605858\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	−1.20420	+	2.90719i	−0.363080	+	0.876552i	0.631767	+	0.775158i	$0.282330\pi$
$11$	−1.20420	+	2.90719i	−0.363080	+	0.876552i	−0.994846	+	0.101393i	$0.967670\pi$
$12$		0			0
$13$	−3.30127	+	1.36743i	−0.915607	+	0.379257i	−0.790200	−	0.612849i	$-0.790024\pi$
$13$	−3.30127	+	1.36743i	−0.915607	+	0.379257i	−0.125407	+	0.992105i	$0.540024\pi$
$14$		0			0
$15$		−	3.99203i		−	1.03074i
$16$		0			0
$17$		−	0.511560i		−	0.124071i	−0.998074	−	0.0620357i	$-0.980241\pi$
$17$		−	0.511560i		−	0.124071i	0.998074	−	0.0620357i	$-0.0197593\pi$
$18$		0			0
$19$	0.254077	−	0.105242i	0.0582894	−	0.0241442i	−0.353348	−	0.935492i	$-0.614957\pi$
$19$	0.254077	−	0.105242i	0.0582894	−	0.0241442i	0.411638	+	0.911348i	$0.364957\pi$
$20$		0			0
$21$	0.885960	−	2.13890i	0.193332	−	0.466746i
$22$		0			0
$23$	3.17185	−	3.17185i	0.661376	−	0.661376i	−0.294329	−	0.955704i	$-0.595096\pi$
$23$	3.17185	−	3.17185i	0.661376	−	0.661376i	0.955704	+	0.294329i	$0.0950960\pi$
$24$		0			0
$25$	7.73315	+	7.73315i	1.54663	+	1.54663i
$26$		0			0
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$		0			0
$29$	−2.75087	−	6.64118i	−0.510823	−	1.23324i	−0.943405	−	0.331642i	$-0.892397\pi$
$29$	−2.75087	−	6.64118i	−0.510823	−	1.23324i	0.432582	−	0.901595i	$-0.357603\pi$
$30$		0			0
$31$	5.82083			1.04545			0.522726	−	0.852501i	$-0.324915\pi$
$31$	5.82083			1.04545			0.522726	+	0.852501i	$0.324915\pi$
$32$		0			0
$33$	3.14672			0.547774
$34$		0			0
$35$	3.53678	+	8.53855i	0.597825	+	1.44328i
$36$		0			0
$37$	−5.53467	−	2.29253i	−0.909894	−	0.376890i	−0.121878	−	0.992545i	$-0.538892\pi$
$37$	−5.53467	−	2.29253i	−0.909894	−	0.376890i	−0.788016	+	0.615655i	$0.788892\pi$
$38$		0			0
$39$	2.52668	+	2.52668i	0.404593	+	0.404593i
$40$		0			0
$41$	3.94823	−	3.94823i	0.616610	−	0.616610i	−0.328050	−	0.944660i	$-0.606392\pi$
$41$	3.94823	−	3.94823i	0.616610	−	0.616610i	0.944660	+	0.328050i	$0.106392\pi$
$42$		0			0
$43$	−1.30801	+	3.15781i	−0.199469	+	0.481561i	−0.991686	−	0.128678i	$-0.958927\pi$
$43$	−1.30801	+	3.15781i	−0.199469	+	0.481561i	0.792217	+	0.610239i	$0.208927\pi$
$44$		0			0
$45$	−3.68816	+	1.52768i	−0.549798	+	0.227734i
$46$		0			0
$47$		−	9.41403i		−	1.37318i	−0.727046	−	0.686589i	$-0.759107\pi$
$47$		−	9.41403i		−	1.37318i	0.727046	−	0.686589i	$-0.240893\pi$
$48$		0			0
$49$		−	1.64019i		−	0.234313i
$50$		0			0
$51$	−0.472620	+	0.195765i	−0.0661800	+	0.0274127i
$52$		0			0
$53$	2.50482	−	6.04717i	0.344063	−	0.830642i	−0.653233	−	0.757157i	$-0.726588\pi$
$53$	2.50482	−	6.04717i	0.344063	−	0.830642i	0.997296	−	0.0734852i	$-0.0234122\pi$
$54$		0			0
$55$	−8.88255	+	8.88255i	−1.19772	+	1.19772i
$56$		0			0
$57$	−0.194462	−	0.194462i	−0.0257572	−	0.0257572i
$58$		0			0
$59$	−13.3423	−	5.52657i	−1.73702	−	0.719498i	−0.998999	−	0.0447232i	$-0.985759\pi$
$59$	−13.3423	−	5.52657i	−1.73702	−	0.719498i	−0.738023	−	0.674775i	$-0.764241\pi$
$60$		0			0
$61$	3.35835	+	8.10777i	0.429992	+	1.03809i	0.979289	+	0.202466i	$0.0648955\pi$
$61$	3.35835	+	8.10777i	0.429992	+	1.03809i	−0.549297	+	0.835627i	$0.685104\pi$
$62$		0			0
$63$	−2.31513			−0.291678
$64$		0			0
$65$	−14.2646			−1.76931
$66$		0			0
$67$	1.11643	+	2.69530i	0.136394	+	0.329283i	0.977288	−	0.211916i	$-0.0679704\pi$
$67$	1.11643	+	2.69530i	0.136394	+	0.329283i	−0.840894	+	0.541199i	$0.817970\pi$
$68$		0			0
$69$	−4.14422	−	1.71659i	−0.498905	−	0.206653i
$70$		0			0
$71$	−1.26611	−	1.26611i	−0.150259	−	0.150259i	0.627975	−	0.778234i	$-0.283884\pi$
$71$	−1.26611	−	1.26611i	−0.150259	−	0.150259i	−0.778234	+	0.627975i	$0.783884\pi$
$72$		0			0
$73$	−7.51616	+	7.51616i	−0.879700	+	0.879700i	−0.993503	−	0.113804i	$-0.963697\pi$
$73$	−7.51616	+	7.51616i	−0.879700	+	0.879700i	0.113804	+	0.993503i	$0.463697\pi$
$74$		0			0
$75$	4.18515	−	10.1038i	0.483260	−	1.16669i
$76$		0			0
$77$	−6.73052	+	2.78787i	−0.767014	+	0.317707i
$78$		0			0
$79$		−	0.709730i		−	0.0798509i	−0.999203	−	0.0399254i	$-0.987288\pi$
$79$		−	0.709730i		−	0.0798509i	0.999203	−	0.0399254i	$-0.0127120\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	1.40823	−	0.583309i	0.154574	−	0.0640265i	−0.304055	−	0.952654i	$-0.598341\pi$
$83$	1.40823	−	0.583309i	0.154574	−	0.0640265i	0.458629	+	0.888628i	$0.348341\pi$
$84$		0			0
$85$	0.781502	−	1.88671i	0.0847658	−	0.204643i
$86$		0			0
$87$	−5.08294	+	5.08294i	−0.544949	+	0.544949i
$88$		0			0
$89$	−0.0856897	−	0.0856897i	−0.00908309	−	0.00908309i	0.702551	−	0.711634i	$-0.252044\pi$
$89$	−0.0856897	−	0.0856897i	−0.00908309	−	0.00908309i	−0.711634	+	0.702551i	$0.752044\pi$
$90$		0			0
$91$	−7.64285	−	3.16577i	−0.801188	−	0.331863i
$92$		0			0
$93$	−2.22754	−	5.37775i	−0.230985	−	0.557646i
$94$		0			0
$95$	1.09785			0.112638
$96$		0			0
$97$	−0.677647			−0.0688046			−0.0344023	−	0.999408i	$-0.510953\pi$
$97$	−0.677647			−0.0688046			−0.0344023	+	0.999408i	$0.510953\pi$
$98$		0			0
$99$	−1.20420	−	2.90719i	−0.121027	−	0.292184i
$100$		0			0
$101$	10.0095	+	4.14605i	0.995978	+	0.412548i	0.820321	−	0.571904i	$-0.193795\pi$
$101$	10.0095	+	4.14605i	0.995978	+	0.412548i	0.175657	+	0.984451i	$0.443795\pi$
$102$		0			0
$103$	−8.25191	−	8.25191i	−0.813085	−	0.813085i	0.172010	−	0.985095i	$-0.444974\pi$
$103$	−8.25191	−	8.25191i	−0.813085	−	0.813085i	−0.985095	+	0.172010i	$0.944974\pi$
$104$		0			0
$105$	6.53512	−	6.53512i	0.637763	−	0.637763i
$106$		0			0
$107$	0.162056	−	0.391238i	0.0156665	−	0.0378224i	−0.915853	−	0.401514i	$-0.868484\pi$
$107$	0.162056	−	0.391238i	0.0156665	−	0.0378224i	0.931519	+	0.363692i	$0.118484\pi$
$108$		0			0
$109$	5.41943	−	2.24480i	0.519087	−	0.215013i	−0.107729	−	0.994180i	$-0.534358\pi$
$109$	5.41943	−	2.24480i	0.519087	−	0.215013i	0.626816	+	0.779167i	$0.284358\pi$
$110$		0			0
$111$			5.99068i			0.568610i
$112$		0			0
$113$		−	3.60406i		−	0.339041i	−0.985527	−	0.169521i	$-0.945778\pi$
$113$		−	3.60406i		−	0.339041i	0.985527	−	0.169521i	$-0.0542219\pi$
$114$		0			0
$115$	16.5438	−	6.85269i	1.54272	−	0.639016i
$116$		0			0
$117$	1.36743	−	3.30127i	0.126419	−	0.305202i
$118$		0			0
$119$	0.837445	−	0.837445i	0.0767684	−	0.0767684i
$120$		0			0
$121$	0.776498	+	0.776498i	0.0705908	+	0.0705908i
$122$		0			0
$123$	−5.15861	−	2.13677i	−0.465136	−	0.192666i
$124$		0			0
$125$	9.06884	+	21.8941i	0.811142	+	1.95827i
$126$		0			0
$127$	0.146652			0.0130133			0.00650663	−	0.999979i	$-0.497929\pi$
$127$	0.146652			0.0130133			0.00650663	+	0.999979i	$0.497929\pi$
$128$		0			0
$129$	3.41799			0.300937
$130$		0			0
$131$	−1.16280	−	2.80726i	−0.101595	−	0.245271i	0.864907	−	0.501933i	$-0.167377\pi$
$131$	−1.16280	−	2.80726i	−0.101595	−	0.245271i	−0.966501	+	0.256661i	$0.917377\pi$
$132$		0			0
$133$	0.588221	+	0.243649i	0.0510053	+	0.0211271i
$134$		0			0
$135$	2.82279	+	2.82279i	0.242947	+	0.242947i
$136$		0			0
$137$	−11.6890	+	11.6890i	−0.998662	+	0.998662i	−0.999999	−	0.00133685i	$-0.999574\pi$
$137$	−11.6890	+	11.6890i	−0.998662	+	0.998662i	0.00133685	+	0.999999i	$0.499574\pi$
$138$		0			0
$139$	−7.96071	+	19.2188i	−0.675218	+	1.63012i	0.0973963	+	0.995246i	$0.468949\pi$
$139$	−7.96071	+	19.2188i	−0.675218	+	1.63012i	−0.772615	+	0.634875i	$0.781051\pi$
$140$		0			0
$141$	−8.69743	+	3.60259i	−0.732456	+	0.303393i
$142$		0			0
$143$		−	11.2441i		−	0.940277i
$144$		0			0
$145$		−	28.6962i		−	2.38309i
$146$		0			0
$147$	−1.51534	+	0.627674i	−0.124983	+	0.0517697i
$148$		0			0
$149$	−0.110593	+	0.266995i	−0.00906011	+	0.0218730i	−0.928345	−	0.371720i	$-0.878768\pi$
$149$	−0.110593	+	0.266995i	−0.00906011	+	0.0218730i	0.919285	+	0.393593i	$0.128768\pi$
$150$		0			0
$151$	4.70680	−	4.70680i	0.383034	−	0.383034i	−0.489160	−	0.872194i	$-0.662697\pi$
$151$	4.70680	−	4.70680i	0.383034	−	0.383034i	0.872194	+	0.489160i	$0.162697\pi$
$152$		0			0
$153$	0.361727	+	0.361727i	0.0292439	+	0.0292439i
$154$		0			0
$155$	21.4681	+	8.89240i	1.72436	+	0.714255i
$156$		0			0
$157$	−7.43264	−	17.9440i	−0.593189	−	1.43208i	−0.880407	−	0.474220i	$-0.842730\pi$
$157$	−7.43264	−	17.9440i	−0.593189	−	1.43208i	0.287218	−	0.957865i	$-0.407270\pi$
$158$		0			0
$159$	−6.54540			−0.519084
$160$		0			0
$161$	10.3849			0.818444
$162$		0			0
$163$	−5.94686	−	14.3570i	−0.465794	−	1.12453i	−0.965982	−	0.258609i	$-0.916736\pi$
$163$	−5.94686	−	14.3570i	−0.465794	−	1.12453i	0.500188	−	0.865917i	$-0.333264\pi$
$164$		0			0
$165$	11.6056	+	4.80720i	0.903496	+	0.374240i
$166$		0			0
$167$	10.7086	+	10.7086i	0.828655	+	0.828655i	0.987331	−	0.158676i	$-0.0507225\pi$
$167$	10.7086	+	10.7086i	0.828655	+	0.828655i	−0.158676	+	0.987331i	$0.550723\pi$
$168$		0			0
$169$	−0.163883	+	0.163883i	−0.0126064	+	0.0126064i
$170$		0			0
$171$	−0.105242	+	0.254077i	−0.00804808	+	0.0194298i
$172$		0			0
$173$	2.46513	−	1.02109i	0.187420	−	0.0776320i	−0.287000	−	0.957931i	$-0.592658\pi$
$173$	2.46513	−	1.02109i	0.187420	−	0.0776320i	0.474420	+	0.880299i	$0.342658\pi$
$174$		0			0
$175$			25.3190i			1.91393i
$176$		0			0
$177$			14.4416i			1.08550i
$178$		0			0
$179$	−9.77295	+	4.04809i	−0.730465	+	0.302568i	−0.716743	−	0.697337i	$-0.754368\pi$
$179$	−9.77295	+	4.04809i	−0.730465	+	0.302568i	−0.0137219	+	0.999906i	$0.504368\pi$
$180$		0			0
$181$	−7.36413	+	17.7786i	−0.547371	+	1.32147i	0.372056	+	0.928210i	$0.378653\pi$
$181$	−7.36413	+	17.7786i	−0.547371	+	1.32147i	−0.919427	+	0.393261i	$0.871347\pi$
$182$		0			0
$183$	6.20542	−	6.20542i	0.458718	−	0.458718i
$184$		0			0
$185$	−16.9105	−	16.9105i	−1.24328	−	1.24328i
$186$		0			0
$187$	1.48720	+	0.616020i	0.108755	+	0.0450478i
$188$		0			0
$189$	0.885960	+	2.13890i	0.0644441	+	0.155582i
$190$		0			0
$191$	−10.1764			−0.736335			−0.368168	−	0.929759i	$-0.620015\pi$
$191$	−10.1764			−0.736335			−0.368168	+	0.929759i	$0.620015\pi$
$192$		0			0
$193$	−7.17480			−0.516454			−0.258227	−	0.966084i	$-0.583138\pi$
$193$	−7.17480			−0.516454			−0.258227	+	0.966084i	$0.583138\pi$
$194$		0			0
$195$	5.45883	+	13.1788i	0.390915	+	0.943751i
$196$		0			0
$197$	9.81153	+	4.06407i	0.699042	+	0.289553i	0.703762	−	0.710436i	$-0.251502\pi$
$197$	9.81153	+	4.06407i	0.699042	+	0.289553i	−0.00471943	+	0.999989i	$0.501502\pi$
$198$		0			0
$199$	7.92887	+	7.92887i	0.562063	+	0.562063i	0.929893	−	0.367830i	$-0.119899\pi$
$199$	7.92887	+	7.92887i	0.562063	+	0.562063i	−0.367830	+	0.929893i	$0.619899\pi$
$200$		0			0
$201$	2.06289	−	2.06289i	0.145505	−	0.145505i
$202$		0			0
$203$	6.36861	−	15.3752i	0.446989	−	1.07913i
$204$		0			0
$205$	20.5933	−	8.53004i	1.43830	−	0.595764i
$206$		0			0
$207$			4.48567i			0.311775i
$208$		0			0
$209$			0.865385i			0.0598599i
$210$		0			0
$211$	23.9700	−	9.92869i	1.65016	−	0.683519i	0.652898	−	0.757446i	$-0.273553\pi$
$211$	23.9700	−	9.92869i	1.65016	−	0.683519i	0.997264	+	0.0739270i	$0.0235532\pi$
$212$		0			0
$213$	−0.685213	+	1.65425i	−0.0469500	+	0.113347i
$214$		0			0
$215$	−9.64827	+	9.64827i	−0.658007	+	0.658007i
$216$		0			0
$217$	9.52894	+	9.52894i	0.646867	+	0.646867i
$218$		0			0
$219$	9.82033	+	4.06771i	0.663597	+	0.274871i
$220$		0			0
$221$	0.699522	+	1.68880i	0.0470550	+	0.113601i
$222$		0			0
$223$	0.573216			0.0383854			0.0191927	−	0.999816i	$-0.493890\pi$
$223$	0.573216			0.0383854			0.0191927	+	0.999816i	$0.493890\pi$
$224$		0			0
$225$	−10.9363			−0.729089
$226$		0			0
$227$	1.44349	+	3.48488i	0.0958075	+	0.231300i	0.964516	−	0.264023i	$-0.0850496\pi$
$227$	1.44349	+	3.48488i	0.0958075	+	0.231300i	−0.868709	+	0.495323i	$0.835050\pi$
$228$		0			0
$229$	−7.10429	−	2.94269i	−0.469465	−	0.194459i	0.135393	−	0.990792i	$-0.456770\pi$
$229$	−7.10429	−	2.94269i	−0.469465	−	0.194459i	−0.604858	+	0.796333i	$0.706770\pi$
$230$		0			0
$231$	5.15132	+	5.15132i	0.338932	+	0.338932i
$232$		0			0
$233$	1.38129	−	1.38129i	0.0904912	−	0.0904912i	−0.660412	−	0.750903i	$-0.729618\pi$
$233$	1.38129	−	1.38129i	0.0904912	−	0.0904912i	0.750903	+	0.660412i	$0.229618\pi$
$234$		0			0
$235$	14.3817	−	34.7204i	0.938157	−	2.26491i
$236$		0			0
$237$	−0.655705	+	0.271602i	−0.0425926	+	0.0176424i
$238$		0			0
$239$			4.58455i			0.296550i	0.988946	+	0.148275i	$0.0473721\pi$
$239$			4.58455i			0.296550i	−0.988946	+	0.148275i	$0.952628\pi$
$240$		0			0
$241$			15.9551i			1.02776i	0.857862	+	0.513880i	$0.171792\pi$
$241$			15.9551i			1.02776i	−0.857862	+	0.513880i	$0.828208\pi$
$242$		0			0
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$		0			0
$245$	2.50570	−	6.04929i	0.160083	−	0.386475i
$246$		0			0
$247$	−0.694866	+	0.694866i	−0.0442133	+	0.0442133i
$248$		0			0
$249$	−1.07781	−	1.07781i	−0.0683037	−	0.0683037i
$250$		0			0
$251$	20.0790	+	8.31700i	1.26738	+	0.524964i	0.912166	−	0.409822i	$-0.134409\pi$
$251$	20.0790	+	8.31700i	1.26738	+	0.524964i	0.355211	+	0.934786i	$0.384409\pi$
$252$		0			0
$253$	5.40164	+	13.0407i	0.339598	+	0.819862i
$254$		0			0
$255$	−2.04216			−0.127885
$256$		0			0
$257$	0.677979			0.0422912			0.0211456	−	0.999776i	$-0.493269\pi$
$257$	0.677979			0.0422912			0.0211456	+	0.999776i	$0.493269\pi$
$258$		0			0
$259$	−5.30750	−	12.8134i	−0.329792	−	0.796189i
$260$		0			0
$261$	6.64118	+	2.75087i	0.411079	+	0.170274i
$262$		0			0
$263$	−7.67357	−	7.67357i	−0.473173	−	0.473173i	0.429767	−	0.902940i	$-0.358596\pi$
$263$	−7.67357	−	7.67357i	−0.473173	−	0.473173i	−0.902940	+	0.429767i	$0.858596\pi$
$264$		0			0
$265$	18.4763	−	18.4763i	1.13499	−	1.13499i
$266$		0			0
$267$	−0.0463749	+	0.111959i	−0.00283810	+	0.00685178i
$268$		0			0
$269$	22.0482	−	9.13266i	1.34430	−	0.556828i	0.409602	−	0.912264i	$-0.365668\pi$
$269$	22.0482	−	9.13266i	1.34430	−	0.556828i	0.934701	+	0.355436i	$0.115668\pi$
$270$		0			0
$271$		−	0.778886i		−	0.0473140i	−0.999720	−	0.0236570i	$-0.992469\pi$
$271$		−	0.778886i		−	0.0473140i	0.999720	−	0.0236570i	$-0.00753096\pi$
$272$		0			0
$273$			8.27256i			0.500678i
$274$		0			0
$275$	−31.7940	+	13.1695i	−1.91725	+	0.794151i
$276$		0			0
$277$	1.47054	−	3.55020i	0.0883564	−	0.213311i	−0.873524	−	0.486780i	$-0.838171\pi$
$277$	1.47054	−	3.55020i	0.0883564	−	0.213311i	0.961881	+	0.273469i	$0.0881712\pi$
$278$		0			0
$279$	−4.11595	+	4.11595i	−0.246415	+	0.246415i
$280$		0			0
$281$	−3.60771	−	3.60771i	−0.215218	−	0.215218i	0.591262	−	0.806480i	$-0.298630\pi$
$281$	−3.60771	−	3.60771i	−0.215218	−	0.215218i	−0.806480	+	0.591262i	$0.798630\pi$
$282$		0			0
$283$	−12.3134	−	5.10036i	−0.731953	−	0.303185i	−0.0145986	−	0.999893i	$-0.504647\pi$
$283$	−12.3134	−	5.10036i	−0.731953	−	0.303185i	−0.717354	+	0.696709i	$0.754647\pi$
$284$		0			0
$285$	−0.420131	−	1.01429i	−0.0248864	−	0.0600811i
$286$		0			0
$287$	12.9268			0.763047
$288$		0			0
$289$	16.7383			0.984606
$290$		0			0
$291$	0.259324	+	0.626064i	0.0152019	+	0.0367005i
$292$		0			0
$293$	−21.1509	−	8.76099i	−1.23565	−	0.511822i	−0.333297	−	0.942822i	$-0.608161\pi$
$293$	−21.1509	−	8.76099i	−1.23565	−	0.511822i	−0.902352	+	0.431000i	$0.858161\pi$
$294$		0			0
$295$	−40.7657	−	40.7657i	−2.37347	−	2.37347i
$296$		0			0
$297$	−2.22507	+	2.22507i	−0.129112	+	0.129112i
$298$		0			0
$299$	−6.13384	+	14.8084i	−0.354729	+	0.856391i
$300$		0			0
$301$	−7.31072	+	3.02820i	−0.421383	+	0.174543i
$302$		0			0
$303$		−	10.8342i		−	0.622406i
$304$		0			0
$305$			35.0332i			2.00600i
$306$		0			0
$307$	−29.7333	+	12.3159i	−1.69697	+	0.702908i	−0.999901	−	0.0140946i	$-0.995513\pi$
$307$	−29.7333	+	12.3159i	−1.69697	+	0.702908i	−0.697070	+	0.717003i	$0.745513\pi$
$308$		0			0
$309$	−4.46590	+	10.7816i	−0.254056	+	0.613346i
$310$		0			0
$311$	5.08789	−	5.08789i	0.288508	−	0.288508i	−0.547982	−	0.836490i	$-0.684604\pi$
$311$	5.08789	−	5.08789i	0.288508	−	0.288508i	0.836490	+	0.547982i	$0.184604\pi$
$312$		0			0
$313$	−10.3695	−	10.3695i	−0.586117	−	0.586117i	0.350460	−	0.936578i	$-0.386025\pi$
$313$	−10.3695	−	10.3695i	−0.586117	−	0.586117i	−0.936578	+	0.350460i	$0.886025\pi$
$314$		0			0
$315$	−8.53855	−	3.53678i	−0.481093	−	0.199275i
$316$		0			0
$317$	−6.18851	−	14.9404i	−0.347582	−	0.839136i	−0.996904	−	0.0786232i	$-0.974948\pi$
$317$	−6.18851	−	14.9404i	−0.347582	−	0.839136i	0.649323	−	0.760513i	$-0.275052\pi$
$318$		0			0
$319$	22.6198			1.26647
$320$		0			0
$321$	−0.423473			−0.0236359
$322$		0			0
$323$	−0.0538378	−	0.129976i	−0.00299561	−	0.00723205i
$324$		0			0
$325$	−36.1037	−	14.9547i	−2.00268	−	0.829535i
$326$		0			0
$327$	−4.14785	−	4.14785i	−0.229377	−	0.229377i
$328$		0			0
$329$	15.4112	−	15.4112i	0.849645	−	0.849645i
$330$		0			0
$331$	−12.0185	+	29.0153i	−0.660599	+	1.59483i	0.136268	+	0.990672i	$0.456489\pi$
$331$	−12.0185	+	29.0153i	−0.660599	+	1.59483i	−0.796867	+	0.604155i	$0.793511\pi$
$332$		0			0
$333$	5.53467	−	2.29253i	0.303298	−	0.125630i
$334$		0			0
$335$			11.6462i			0.636302i
$336$		0			0
$337$		−	2.12023i		−	0.115496i	−0.998331	−	0.0577480i	$-0.981608\pi$
$337$		−	2.12023i		−	0.115496i	0.998331	−	0.0577480i	$-0.0183920\pi$
$338$		0			0
$339$	−3.32971	+	1.37921i	−0.180845	+	0.0749085i
$340$		0			0
$341$	−7.00944	+	16.9223i	−0.379582	+	0.916393i
$342$		0			0
$343$	14.1444	−	14.1444i	0.763723	−	0.763723i
$344$		0			0
$345$	−12.6621	−	12.6621i	−0.681705	−	0.681705i
$346$		0			0
$347$	−15.6587	−	6.48607i	−0.840606	−	0.348190i	−0.0795133	−	0.996834i	$-0.525337\pi$
$347$	−15.6587	−	6.48607i	−0.840606	−	0.348190i	−0.761092	+	0.648644i	$0.775337\pi$
$348$		0			0
$349$	−2.54342	−	6.14035i	−0.136146	−	0.328685i	0.841072	−	0.540923i	$-0.181925\pi$
$349$	−2.54342	−	6.14035i	−0.136146	−	0.328685i	−0.977218	+	0.212238i	$0.931925\pi$
$350$		0			0
$351$	−3.57327			−0.190727
$352$		0			0
$353$	26.7822			1.42547			0.712737	−	0.701431i	$-0.247455\pi$
$353$	26.7822			1.42547			0.712737	+	0.701431i	$0.247455\pi$
$354$		0			0
$355$	−2.73539	−	6.60382i	−0.145179	−	0.350494i
$356$		0			0
$357$	−1.09417	−	0.453222i	−0.0579098	−	0.0239870i
$358$		0			0
$359$	21.9626	+	21.9626i	1.15914	+	1.15914i	0.984661	+	0.174480i	$0.0558243\pi$
$359$	21.9626	+	21.9626i	1.15914	+	1.15914i	0.174480	+	0.984661i	$0.444176\pi$
$360$		0			0
$361$	−13.3815	+	13.3815i	−0.704292	+	0.704292i
$362$		0			0
$363$	0.420238	−	1.01454i	0.0220568	−	0.0532498i
$364$		0			0
$365$	−39.2031	+	16.2385i	−2.05198	+	0.849959i
$366$		0			0
$367$		−	20.1290i		−	1.05073i	−0.850878	−	0.525363i	$-0.823929\pi$
$367$		−	20.1290i		−	1.05073i	0.850878	−	0.525363i	$-0.176071\pi$
$368$		0			0
$369$			5.58364i			0.290673i
$370$		0			0
$371$	13.9999	−	5.79897i	0.726841	−	0.301067i
$372$		0			0
$373$	0.278651	−	0.672724i	0.0144280	−	0.0348323i	−0.916501	−	0.400032i	$-0.868999\pi$
$373$	0.278651	−	0.672724i	0.0144280	−	0.0348323i	0.930929	+	0.365199i	$0.118999\pi$
$374$		0			0
$375$	16.7570	−	16.7570i	0.865329	−	0.865329i
$376$		0			0
$377$	18.1627	+	18.1627i	0.935427	+	0.935427i
$378$		0			0
$379$	33.2934	+	13.7906i	1.71017	+	0.708375i	0.999991	+	0.00435195i	$0.00138527\pi$
$379$	33.2934	+	13.7906i	1.71017	+	0.708375i	0.710177	+	0.704023i	$0.248615\pi$
$380$		0			0
$381$	−0.0561213	−	0.135489i	−0.00287518	−	0.00694130i
$382$		0			0
$383$	−30.6643			−1.56687			−0.783435	−	0.621473i	$-0.786534\pi$
$383$	−30.6643			−1.56687			−0.783435	+	0.621473i	$0.786534\pi$
$384$		0			0
$385$	−29.0822			−1.48217
$386$		0			0
$387$	−1.30801	−	3.15781i	−0.0664897	−	0.160520i
$388$		0			0
$389$	−9.95840	−	4.12490i	−0.504911	−	0.209141i	0.115664	−	0.993288i	$-0.463101\pi$
$389$	−9.95840	−	4.12490i	−0.504911	−	0.209141i	−0.620575	+	0.784147i	$0.713101\pi$
$390$		0			0
$391$	−1.62259	−	1.62259i	−0.0820579	−	0.0820579i
$392$		0			0
$393$	−2.14858	+	2.14858i	−0.108382	+	0.108382i
$394$		0			0
$395$	1.08424	−	2.61760i	0.0545542	−	0.131706i
$396$		0			0
$397$	33.1225	−	13.7198i	1.66237	−	0.688577i	0.664118	−	0.747628i	$-0.268807\pi$
$397$	33.1225	−	13.7198i	1.66237	−	0.688577i	0.998255	+	0.0590504i	$0.0188073\pi$
$398$		0			0
$399$		−	0.636686i		−	0.0318742i
$400$		0			0
$401$			1.21160i			0.0605046i	0.999542	+	0.0302523i	$0.00963107\pi$
$401$			1.21160i			0.0605046i	−0.999542	+	0.0302523i	$0.990369\pi$
$402$		0			0
$403$	−19.2161	+	7.95958i	−0.957224	+	0.396495i
$404$		0			0
$405$	1.52768	−	3.68816i	0.0759113	−	0.183266i
$406$		0			0
$407$	13.3297	−	13.3297i	0.660728	−	0.660728i
$408$		0			0
$409$	−20.0380	−	20.0380i	−0.990817	−	0.990817i	0.00914144	−	0.999958i	$-0.497090\pi$
$409$	−20.0380	−	20.0380i	−0.990817	−	0.990817i	−0.999958	+	0.00914144i	$0.997090\pi$
$410$		0			0
$411$	15.2725	+	6.32606i	0.753335	+	0.312042i
$412$		0			0
$413$	−12.7947	−	30.8892i	−0.629587	−	1.51996i
$414$		0			0
$415$	6.08490			0.298696
$416$		0			0
$417$	20.8023			1.01869
$418$		0			0
$419$	−1.34843	−	3.25539i	−0.0658749	−	0.159036i	0.887514	−	0.460781i	$-0.152431\pi$
$419$	−1.34843	−	3.25539i	−0.0658749	−	0.159036i	−0.953389	+	0.301745i	$0.902431\pi$
$420$		0			0
$421$	10.4207	+	4.31639i	0.507873	+	0.210368i	0.621881	−	0.783112i	$-0.286369\pi$
$421$	10.4207	+	4.31639i	0.507873	+	0.210368i	−0.114008	+	0.993480i	$0.536369\pi$
$422$		0			0
$423$	6.65673	+	6.65673i	0.323661	+	0.323661i
$424$		0			0
$425$	3.95597	−	3.95597i	0.191893	−	0.191893i
$426$		0			0
$427$	−7.77500	+	18.7705i	−0.376258	+	0.908368i
$428$		0			0
$429$	−10.3882	+	4.30292i	−0.501546	+	0.207747i
$430$		0			0
$431$			35.6433i			1.71688i	0.512914	+	0.858440i	$0.328566\pi$
$431$			35.6433i			1.71688i	−0.512914	+	0.858440i	$0.671434\pi$
$432$		0			0
$433$		−	9.75449i		−	0.468771i	−0.972144	−	0.234385i	$-0.924692\pi$
$433$		−	9.75449i		−	0.468771i	0.972144	−	0.234385i	$-0.0753078\pi$
$434$		0			0
$435$	−26.5118	+	10.9816i	−1.27114	+	0.526525i
$436$		0			0
$437$	0.472082	−	1.13971i	0.0225828	−	0.0545196i
$438$		0			0
$439$	11.2645	−	11.2645i	0.537625	−	0.537625i	−0.385206	−	0.922831i	$-0.625870\pi$
$439$	11.2645	−	11.2645i	0.537625	−	0.537625i	0.922831	+	0.385206i	$0.125870\pi$
$440$		0			0
$441$	1.15979	+	1.15979i	0.0552281	+	0.0552281i
$442$		0			0
$443$	−22.1985	−	9.19492i	−1.05468	−	0.436864i	−0.213122	−	0.977026i	$-0.568363\pi$
$443$	−22.1985	−	9.19492i	−1.05468	−	0.436864i	−0.841561	+	0.540162i	$0.818363\pi$
$444$		0			0
$445$	−0.185130	−	0.446944i	−0.00877601	−	0.0211872i
$446$		0			0
$447$	0.288993			0.0136689
$448$		0			0
$449$	−12.5831			−0.593834			−0.296917	−	0.954903i	$-0.595958\pi$
$449$	−12.5831			−0.593834			−0.296917	+	0.954903i	$0.595958\pi$
$450$		0			0
$451$	6.72381	+	16.2327i	0.316612	+	0.764369i
$452$		0			0
$453$	−6.14974	−	2.54730i	−0.288940	−	0.119683i
$454$		0			0
$455$	−23.3517	−	23.3517i	−1.09475	−	1.09475i
$456$		0			0
$457$	−28.8488	+	28.8488i	−1.34949	+	1.34949i	−0.463273	+	0.886216i	$0.653325\pi$
$457$	−28.8488	+	28.8488i	−1.34949	+	1.34949i	−0.886216	+	0.463273i	$0.846675\pi$
$458$		0			0
$459$	0.195765	−	0.472620i	0.00913755	−	0.0220600i
$460$		0			0
$461$	11.8188	−	4.89549i	0.550454	−	0.228006i	−0.0900809	−	0.995934i	$-0.528713\pi$
$461$	11.8188	−	4.89549i	0.550454	−	0.228006i	0.640535	+	0.767929i	$0.278713\pi$
$462$		0			0
$463$			18.0311i			0.837976i	0.907992	+	0.418988i	$0.137615\pi$
$463$			18.0311i			0.837976i	−0.907992	+	0.418988i	$0.862385\pi$
$464$		0			0
$465$		−	23.2370i		−	1.07759i
$466$		0			0
$467$	22.2527	−	9.21739i	1.02973	−	0.426530i	0.197118	−	0.980380i	$-0.436842\pi$
$467$	22.2527	−	9.21739i	1.02973	−	0.426530i	0.832616	+	0.553850i	$0.186842\pi$
$468$		0			0
$469$	−2.58467	+	6.23995i	−0.119349	+	0.288134i
$470$		0			0
$471$	−13.7337	+	13.7337i	−0.632817	+	0.632817i
$472$		0			0
$473$	−7.60526	−	7.60526i	−0.349690	−	0.349690i
$474$		0			0
$475$	2.77867	+	1.15096i	0.127494	+	0.0528099i
$476$		0			0
$477$	2.50482	+	6.04717i	0.114688	+	0.276881i
$478$		0			0
$479$	−11.2525			−0.514141			−0.257070	−	0.966393i	$-0.582757\pi$
$479$	−11.2525			−0.514141			−0.257070	+	0.966393i	$0.582757\pi$
$480$		0			0
$481$	21.4063			0.976043
$482$		0			0
$483$	−3.97412	−	9.59438i	−0.180829	−	0.436560i
$484$		0			0
$485$	−2.49927	−	1.03523i	−0.113486	−	0.0470074i
$486$		0			0
$487$	23.1247	+	23.1247i	1.04788	+	1.04788i	0.998795	+	0.0490867i	$0.0156311\pi$
$487$	23.1247	+	23.1247i	1.04788	+	1.04788i	0.0490867	+	0.998795i	$0.484369\pi$
$488$		0			0
$489$	−10.9884	+	10.9884i	−0.496911	+	0.496911i
$490$		0			0
$491$	9.92916	−	23.9711i	0.448097	−	1.08180i	−0.524937	−	0.851141i	$-0.675911\pi$
$491$	9.92916	−	23.9711i	0.448097	−	1.08180i	0.973034	−	0.230661i	$-0.0740888\pi$
$492$		0			0
$493$	−3.39736	+	1.40723i	−0.153010	+	0.0633786i
$494$		0			0
$495$		−	12.5618i		−	0.564612i
$496$		0			0
$497$		−	4.14534i		−	0.185944i
$498$		0			0
$499$	0.662766	−	0.274527i	0.0296695	−	0.0122895i	−0.367799	−	0.929905i	$-0.619889\pi$
$499$	0.662766	−	0.274527i	0.0296695	−	0.0122895i	0.397469	+	0.917616i	$0.369889\pi$
$500$		0			0
$501$	5.79544	−	13.9914i	0.258921	−	0.625091i
$502$		0			0
$503$	5.46400	−	5.46400i	0.243628	−	0.243628i	−0.574721	−	0.818349i	$-0.694890\pi$
$503$	5.46400	−	5.46400i	0.243628	−	0.243628i	0.818349	+	0.574721i	$0.194890\pi$
$504$		0			0
$505$	30.5826	+	30.5826i	1.36091	+	1.36091i
$506$		0			0
$507$	0.214123	+	0.0886927i	0.00950954	+	0.00393898i
$508$		0			0
$509$	−3.15891	−	7.62628i	−0.140016	−	0.338029i	0.838280	−	0.545240i	$-0.183561\pi$
$509$	−3.15891	−	7.62628i	−0.140016	−	0.338029i	−0.978296	+	0.207211i	$0.933561\pi$
$510$		0			0
$511$	−24.6085			−1.08862
$512$		0			0
$513$	0.275011			0.0121421
$514$		0			0
$515$	−17.8280	−	43.0407i	−0.785597	−	1.89660i
$516$		0			0
$517$	27.3684	+	11.3364i	1.20366	+	0.498573i
$518$		0			0
$519$	−1.88673	−	1.88673i	−0.0828182	−	0.0828182i
$520$		0			0
$521$	17.3737	−	17.3737i	0.761157	−	0.761157i	−0.215375	−	0.976531i	$-0.569097\pi$
$521$	17.3737	−	17.3737i	0.761157	−	0.761157i	0.976531	+	0.215375i	$0.0690973\pi$
$522$		0			0
$523$	−6.26194	+	15.1177i	−0.273816	+	0.661049i	−0.999640	−	0.0268308i	$-0.991458\pi$
$523$	−6.26194	+	15.1177i	−0.273816	+	0.661049i	0.725824	+	0.687880i	$0.241458\pi$
$524$		0			0
$525$	23.3917	−	9.68915i	1.02090	−	0.422869i
$526$		0			0
$527$		−	2.97770i		−	0.129711i
$528$		0			0
$529$			2.87879i			0.125165i
$530$		0			0
$531$	13.3423	−	5.52657i	0.579008	−	0.239833i
$532$		0			0
$533$	−7.63524	+	18.4331i	−0.330719	+	0.798426i
$534$		0			0
$535$	1.19538	−	1.19538i	0.0516806	−	0.0516806i
$536$		0			0
$537$	7.47990	+	7.47990i	0.322781	+	0.322781i
$538$		0			0
$539$	4.76835	+	1.97512i	0.205388	+	0.0850743i
$540$		0			0
$541$	10.7750	+	26.0132i	0.463255	+	1.11840i	0.967053	+	0.254574i	$0.0819354\pi$
$541$	10.7750	+	26.0132i	0.463255	+	1.11840i	−0.503799	+	0.863821i	$0.668065\pi$
$542$		0			0
$543$	19.2434			0.825813
$544$		0			0
$545$	23.4171			1.00308
$546$		0			0
$547$	13.7101	+	33.0991i	0.586201	+	1.41521i	0.887109	+	0.461561i	$0.152710\pi$
$547$	13.7101	+	33.0991i	0.586201	+	1.41521i	−0.300908	+	0.953653i	$0.597290\pi$
$548$		0			0
$549$	−8.10777	−	3.35835i	−0.346031	−	0.143331i
$550$		0			0
$551$	−1.39787	−	1.39787i	−0.0595512	−	0.0595512i
$552$		0			0
$553$	1.16186	−	1.16186i	0.0494072	−	0.0494072i
$554$		0			0
$555$	−9.15187	+	22.0946i	−0.388475	+	0.937862i
$556$		0			0
$557$	−21.4363	+	8.87921i	−0.908286	+	0.376224i	−0.787400	−	0.616442i	$-0.788573\pi$
$557$	−21.4363	+	8.87921i	−0.908286	+	0.376224i	−0.120886	+	0.992666i	$0.538573\pi$
$558$		0			0
$559$		−	12.2134i		−	0.516571i
$560$		0			0
$561$		−	1.60974i		−	0.0679632i
$562$		0			0
$563$	41.3211	−	17.1158i	1.74148	−	0.721343i	0.742822	−	0.669489i	$-0.233487\pi$
$563$	41.3211	−	17.1158i	1.74148	−	0.721343i	0.998655	−	0.0518544i	$-0.0165132\pi$
$564$		0			0
$565$	5.50586	−	13.2923i	0.231633	−	0.559212i
$566$		0			0
$567$	1.63704	−	1.63704i	0.0687493	−	0.0687493i
$568$		0			0
$569$	29.0924	+	29.0924i	1.21962	+	1.21962i	0.967767	+	0.251848i	$0.0810384\pi$
$569$	29.0924	+	29.0924i	1.21962	+	1.21962i	0.251848	+	0.967767i	$0.418962\pi$
$570$		0			0
$571$	−0.414172	−	0.171556i	−0.0173326	−	0.00717938i	0.374000	−	0.927429i	$-0.377986\pi$
$571$	−0.414172	−	0.171556i	−0.0173326	−	0.00717938i	−0.391333	+	0.920249i	$0.627986\pi$
$572$		0			0
$573$	3.89432	+	9.40172i	0.162688	+	0.392763i
$574$		0			0
$575$	49.0567			2.04581
$576$		0			0
$577$	23.7041			0.986813			0.493406	−	0.869799i	$-0.335752\pi$
$577$	23.7041			0.986813			0.493406	+	0.869799i	$0.335752\pi$
$578$		0			0
$579$	2.74568	+	6.62865i	0.114107	+	0.275477i
$580$		0			0
$581$	3.26024	+	1.35043i	0.135257	+	0.0560255i
$582$		0			0
$583$	14.5640	+	14.5640i	0.603178	+	0.603178i
$584$		0			0
$585$	10.0866	−	10.0866i	0.417029	−	0.417029i
$586$		0			0
$587$	6.09999	−	14.7267i	0.251773	−	0.607835i	−0.746574	−	0.665302i	$-0.768303\pi$
$587$	6.09999	−	14.7267i	0.251773	−	0.607835i	0.998347	+	0.0574676i	$0.0183026\pi$
$588$		0			0
$589$	1.47894	−	0.612598i	0.0609388	−	0.0252417i
$590$		0			0
$591$		−	10.6199i		−	0.436845i
$592$		0			0
$593$		−	6.36035i		−	0.261188i	−0.991436	−	0.130594i	$-0.958312\pi$
$593$		−	6.36035i		−	0.261188i	0.991436	−	0.130594i	$-0.0416885\pi$
$594$		0			0
$595$	4.36798	−	1.80928i	0.179070	−	0.0741731i
$596$		0			0
$597$	4.29107	−	10.3596i	0.175622	−	0.423989i
$598$		0			0
$599$	4.61895	−	4.61895i	0.188725	−	0.188725i	−0.606420	−	0.795145i	$-0.707395\pi$
$599$	4.61895	−	4.61895i	0.188725	−	0.188725i	0.795145	+	0.606420i	$0.207395\pi$
$600$		0			0
$601$	−10.9077	−	10.9077i	−0.444936	−	0.444936i	0.448731	−	0.893667i	$-0.351876\pi$
$601$	−10.9077	−	10.9077i	−0.444936	−	0.444936i	−0.893667	+	0.448731i	$0.851876\pi$
$602$		0			0
$603$	−2.69530	−	1.11643i	−0.109761	−	0.0454645i
$604$		0			0
$605$	1.67760	+	4.05009i	0.0682043	+	0.164660i
$606$		0			0
$607$	0.957019			0.0388442			0.0194221	−	0.999811i	$-0.493817\pi$
$607$	0.957019			0.0388442			0.0194221	+	0.999811i	$0.493817\pi$
$608$		0			0
$609$	−16.6420			−0.674367
$610$		0			0
$611$	12.8730	+	31.0782i	0.520787	+	1.25729i
$612$		0			0
$613$	−2.24424	−	0.929594i	−0.0906440	−	0.0375460i	0.336901	−	0.941540i	$-0.390621\pi$
$613$	−2.24424	−	0.929594i	−0.0906440	−	0.0375460i	−0.427545	+	0.903994i	$0.640621\pi$
$614$		0			0
$615$	−15.7615	−	15.7615i	−0.635564	−	0.635564i
$616$		0			0
$617$	−22.5163	+	22.5163i	−0.906472	+	0.906472i	−0.995986	−	0.0895138i	$-0.971469\pi$
$617$	−22.5163	+	22.5163i	−0.906472	+	0.906472i	0.0895138	+	0.995986i	$0.471469\pi$
$618$		0			0
$619$	3.44381	−	8.31410i	0.138419	−	0.334172i	−0.839436	−	0.543459i	$-0.817114\pi$
$619$	3.44381	−	8.31410i	0.138419	−	0.334172i	0.977854	+	0.209287i	$0.0671143\pi$
$620$		0			0
$621$	4.14422	−	1.71659i	0.166302	−	0.0688844i
$622$		0			0
$623$		−	0.280555i		−	0.0112402i
$624$		0			0
$625$			39.9216i			1.59687i
$626$		0			0
$627$	0.799511	−	0.331168i	0.0319294	−	0.0132256i
$628$		0			0
$629$	−1.17277	+	2.83131i	−0.0467613	+	0.112892i
$630$		0			0
$631$	−28.2240	+	28.2240i	−1.12358	+	1.12358i	−0.132379	+	0.991199i	$0.542262\pi$
$631$	−28.2240	+	28.2240i	−1.12358	+	1.12358i	−0.991199	+	0.132379i	$0.957738\pi$
$632$		0			0
$633$	−18.3458	−	18.3458i	−0.729181	−	0.729181i
$634$		0			0
$635$	0.540876	+	0.224038i	0.0214640	+	0.00889068i
$636$		0			0
$637$	2.24285	+	5.41471i	0.0888649	+	0.214539i
$638$		0			0
$639$	1.79055			0.0708329
$640$		0			0
$641$	−30.2846			−1.19617			−0.598084	−	0.801433i	$-0.704071\pi$
$641$	−30.2846			−1.19617			−0.598084	+	0.801433i	$0.704071\pi$
$642$		0			0
$643$	−0.944867	−	2.28111i	−0.0372619	−	0.0899582i	0.904153	−	0.427209i	$-0.140503\pi$
$643$	−0.944867	−	2.28111i	−0.0372619	−	0.0899582i	−0.941415	+	0.337251i	$0.890503\pi$
$644$		0			0
$645$	12.6061	+	5.22161i	0.496364	+	0.205601i
$646$		0			0
$647$	−8.32184	−	8.32184i	−0.327165	−	0.327165i	0.524342	−	0.851508i	$-0.324311\pi$
$647$	−8.32184	−	8.32184i	−0.327165	−	0.327165i	−0.851508	+	0.524342i	$0.824311\pi$
$648$		0			0
$649$	32.1336	−	32.1336i	1.26136	−	1.26136i
$650$		0			0
$651$	5.15703	−	12.4502i	0.202120	−	0.487960i
$652$		0			0
$653$	19.1159	−	7.91806i	0.748062	−	0.309858i	0.0241116	−	0.999709i	$-0.492324\pi$
$653$	19.1159	−	7.91806i	0.748062	−	0.309858i	0.723951	+	0.689852i	$0.242324\pi$
$654$		0			0
$655$		−	12.1300i		−	0.473959i
$656$		0			0
$657$		−	10.6295i		−	0.414694i
$658$		0			0
$659$	−29.0382	+	12.0280i	−1.13117	+	0.468546i	−0.868178	−	0.496253i	$-0.834709\pi$
$659$	−29.0382	+	12.0280i	−1.13117	+	0.468546i	−0.262991	+	0.964798i	$0.584709\pi$
$660$		0			0
$661$	−6.92538	+	16.7193i	−0.269366	+	0.650307i	−0.999454	−	0.0330463i	$-0.989479\pi$
$661$	−6.92538	+	16.7193i	−0.269366	+	0.650307i	0.730088	+	0.683353i	$0.239479\pi$
$662$		0			0
$663$	1.29255	−	1.29255i	0.0501984	−	0.0501984i
$664$		0			0
$665$	1.79723	+	1.79723i	0.0696937	+	0.0696937i
$666$		0			0
$667$	−29.7901	−	12.3395i	−1.15348	−	0.477787i
$668$		0			0
$669$	−0.219360	−	0.529583i	−0.00848096	−	0.0204749i
$670$		0			0
$671$	−27.6150			−1.06606
$672$		0			0
$673$	−19.3968			−0.747691			−0.373846	−	0.927491i	$-0.621961\pi$
$673$	−19.3968			−0.747691			−0.373846	+	0.927491i	$0.621961\pi$
$674$		0			0
$675$	4.18515	+	10.1038i	0.161087	+	0.388897i
$676$		0			0
$677$	−1.10973	−	0.459664i	−0.0426503	−	0.0176663i	0.361256	−	0.932467i	$-0.382348\pi$
$677$	−1.10973	−	0.459664i	−0.0426503	−	0.0176663i	−0.403907	+	0.914800i	$0.632348\pi$
$678$		0			0
$679$	−1.10934	−	1.10934i	−0.0425724	−	0.0425724i
$680$		0			0
$681$	2.66721	−	2.66721i	0.102208	−	0.102208i
$682$		0			0
$683$	2.49553	−	6.02475i	0.0954889	−	0.230531i	−0.868916	−	0.494959i	$-0.835183\pi$
$683$	2.49553	−	6.02475i	0.0954889	−	0.230531i	0.964405	+	0.264428i	$0.0851832\pi$
$684$		0			0
$685$	−60.9682	+	25.2539i	−2.32948	+	0.964900i
$686$		0			0
$687$			7.68963i			0.293378i
$688$		0			0
$689$			23.3885i			0.891030i
$690$		0			0
$691$	12.2382	−	5.06922i	0.465563	−	0.192842i	−0.137556	−	0.990494i	$-0.543925\pi$
$691$	12.2382	−	5.06922i	0.465563	−	0.192842i	0.603118	+	0.797652i	$0.293925\pi$
$692$		0			0
$693$	2.78787	−	6.73052i	0.105902	−	0.255671i
$694$		0			0
$695$	−58.7207	+	58.7207i	−2.22740	+	2.22740i
$696$		0			0
$697$	−2.01976	−	2.01976i	−0.0765037	−	0.0765037i
$698$		0			0
$699$	−1.80474	−	0.747548i	−0.0682615	−	0.0282748i
$700$		0			0
$701$	14.9505	+	36.0936i	0.564671	+	1.36324i	0.905994	+	0.423291i	$0.139125\pi$
$701$	14.9505	+	36.0936i	0.564671	+	1.36324i	−0.341322	+	0.939946i	$0.610875\pi$
$702$		0			0
$703$	−1.64751			−0.0621369
$704$		0			0
$705$	−37.5811			−1.41539
$706$		0			0
$707$	9.59863	+	23.1731i	0.360994	+	0.871516i
$708$		0			0
$709$	31.0545	+	12.8632i	1.16627	+	0.483087i	0.879959	−	0.475049i	$-0.157570\pi$
$709$	31.0545	+	12.8632i	1.16627	+	0.483087i	0.286315	+	0.958136i	$0.407570\pi$
$710$		0			0
$711$	0.501855	+	0.501855i	0.0188210	+	0.0188210i
$712$		0			0
$713$	18.4628	−	18.4628i	0.691437	−	0.691437i
$714$		0			0
$715$	17.1774	−	41.4699i	0.642399	−	1.55089i
$716$		0			0
$717$	4.23557	−	1.75443i	0.158180	−	0.0655205i
$718$		0			0
$719$			12.6636i			0.472274i	0.971720	+	0.236137i	$0.0758815\pi$
$719$			12.6636i			0.472274i	−0.971720	+	0.236137i	$0.924119\pi$
$720$		0			0
$721$		−	27.0174i		−	1.00618i
$722$		0			0
$723$	14.7406	−	6.10576i	0.548209	−	0.227076i
$724$		0			0
$725$	30.0844	−	72.6302i	1.11731	−	2.69742i
$726$		0			0
$727$	−33.0425	+	33.0425i	−1.22548	+	1.22548i	−0.259821	+	0.965657i	$0.583664\pi$
$727$	−33.0425	+	33.0425i	−1.22548	+	1.22548i	−0.965657	+	0.259821i	$0.916336\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$	1.61541	+	0.669124i	0.0597480	+	0.0247484i
$732$		0			0
$733$	1.87261	+	4.52088i	0.0691664	+	0.166982i	0.954682	−	0.297626i	$-0.0961950\pi$
$733$	1.87261	+	4.52088i	0.0691664	+	0.166982i	−0.885516	+	0.464609i	$0.846195\pi$
$734$		0			0
$735$	−6.54770			−0.241516
$736$		0			0
$737$	−9.18015			−0.338155
$738$		0			0
$739$	−15.0628	−	36.3648i	−0.554093	−	1.33770i	−0.914380	−	0.404857i	$-0.867321\pi$
$739$	−15.0628	−	36.3648i	−0.554093	−	1.33770i	0.360287	−	0.932842i	$-0.382679\pi$
$740$		0			0
$741$	0.907887	+	0.376059i	0.0333520	+	0.0138149i
$742$		0			0
$743$	20.9250	+	20.9250i	0.767664	+	0.767664i	0.977695	−	0.210031i	$-0.0673563\pi$
$743$	20.9250	+	20.9250i	0.767664	+	0.767664i	−0.210031	+	0.977695i	$0.567356\pi$
$744$		0			0
$745$	−0.815767	+	0.815767i	−0.0298874	+	0.0298874i
$746$		0			0
$747$	−0.583309	+	1.40823i	−0.0213422	+	0.0515246i
$748$		0			0
$749$	0.905765	−	0.375180i	0.0330959	−	0.0137088i
$750$		0			0
$751$		−	2.47050i		−	0.0901497i	−0.998984	−	0.0450749i	$-0.985647\pi$
$751$		−	2.47050i		−	0.0901497i	0.998984	−	0.0450749i	$-0.0143526\pi$
$752$		0			0
$753$		−	21.7334i		−	0.792008i
$754$		0			0
$755$	24.5499	−	10.1689i	0.893464	−	0.370085i
$756$		0			0
$757$	2.84324	−	6.86420i	0.103339	−	0.249483i	−0.863750	−	0.503921i	$-0.831890\pi$
$757$	2.84324	−	6.86420i	0.103339	−	0.249483i	0.967089	+	0.254437i	$0.0818903\pi$
$758$		0			0
$759$	9.98092	−	9.98092i	0.362284	−	0.362284i
$760$		0			0
$761$	−29.8039	−	29.8039i	−1.08039	−	1.08039i	−0.996473	−	0.0839198i	$-0.973256\pi$
$761$	−29.8039	−	29.8039i	−1.08039	−	1.08039i	−0.0839198	−	0.996473i	$-0.526744\pi$
$762$		0			0
$763$	12.5467	+	5.19700i	0.454220	+	0.188144i
$764$		0			0
$765$	0.781502	+	1.88671i	0.0282553	+	0.0682143i
$766$		0			0
$767$	51.6038			1.86330
$768$		0			0
$769$	−50.3024			−1.81395			−0.906976	−	0.421182i	$-0.861615\pi$
$769$	−50.3024			−1.81395			−0.906976	+	0.421182i	$0.861615\pi$
$770$		0			0
$771$	−0.259451	−	0.626371i	−0.00934391	−	0.0225582i
$772$		0			0
$773$	−0.373623	−	0.154760i	−0.0134383	−	0.00556632i	0.375954	−	0.926638i	$-0.377315\pi$
$773$	−0.373623	−	0.154760i	−0.0134383	−	0.00556632i	−0.389392	+	0.921072i	$0.627315\pi$
$774$		0			0
$775$	45.0134	+	45.0134i	1.61693	+	1.61693i
$776$		0			0
$777$	−9.80699	+	9.80699i	−0.351824	+	0.351824i
$778$		0			0
$779$	0.587635	−	1.41868i	0.0210542	−	0.0508294i
$780$		0			0
$781$	5.20546	−	2.15617i	0.186266	−	0.0771540i
$782$		0			0
$783$		−	7.18837i		−	0.256891i
$784$		0			0
$785$		−	77.5349i		−	2.76734i
$786$		0			0
$787$	13.9620	−	5.78325i	0.497692	−	0.206151i	−0.119695	−	0.992811i	$-0.538192\pi$
$787$	13.9620	−	5.78325i	0.497692	−	0.206151i	0.617386	+	0.786660i	$0.288192\pi$
$788$		0			0
$789$	−4.15291	+	10.0260i	−0.147847	+	0.356935i
$790$		0			0
$791$	5.89999	−	5.89999i	0.209779	−	0.209779i
$792$		0			0
$793$	−22.1736	−	22.1736i	−0.787408	−	0.787408i
$794$		0			0
$795$	−24.1405	−	9.99932i	−0.856175	−	0.354639i
$796$		0			0
$797$	−1.14025	−	2.75280i	−0.0403896	−	0.0975092i	0.902397	−	0.430905i	$-0.141806\pi$
$797$	−1.14025	−	2.75280i	−0.0403896	−	0.0975092i	−0.942787	+	0.333396i	$0.891806\pi$
$798$		0			0
$799$	−4.81584			−0.170372
$800$		0			0
$801$	0.121183			0.00428181
$802$		0			0
$803$	−12.8000	−	30.9019i	−0.451701	−	1.09050i
$804$		0			0
$805$	38.3011	+	15.8648i	1.34994	+	0.559162i
$806$		0			0
$807$	−16.8750	−	16.8750i	−0.594027	−	0.594027i
$808$		0			0
$809$	−15.2034	+	15.2034i	−0.534524	+	0.534524i	−0.921915	−	0.387392i	$-0.873376\pi$
$809$	−15.2034	+	15.2034i	−0.534524	+	0.534524i	0.387392	+	0.921915i	$0.373376\pi$
$810$		0			0
$811$	1.72375	−	4.16149i	0.0605289	−	0.146130i	−0.890721	−	0.454550i	$-0.849800\pi$
$811$	1.72375	−	4.16149i	0.0605289	−	0.146130i	0.951250	+	0.308420i	$0.0998002\pi$
$812$		0			0
$813$	−0.719597	+	0.298067i	−0.0252374	+	0.0104537i
$814$		0			0
$815$		−	62.0357i		−	2.17302i
$816$		0			0
$817$			0.939986i			0.0328859i
$818$		0			0
$819$	7.64285	−	3.16577i	0.267063	−	0.110621i
$820$		0			0
$821$	−18.5191	+	44.7092i	−0.646323	+	1.56036i	0.171684	+	0.985152i	$0.445079\pi$
$821$	−18.5191	+	44.7092i	−0.646323	+	1.56036i	−0.818007	+	0.575209i	$0.804921\pi$
$822$		0			0
$823$	9.78250	−	9.78250i	0.340996	−	0.340996i	−0.515745	−	0.856742i	$-0.672485\pi$
$823$	9.78250	−	9.78250i	0.340996	−	0.340996i	0.856742	+	0.515745i	$0.172485\pi$
$824$		0			0
$825$	24.3341	+	24.3341i	0.847204	+	0.847204i
$826$		0			0
$827$	−21.3770	−	8.85466i	−0.743352	−	0.307907i	−0.0213264	−	0.999773i	$-0.506789\pi$
$827$	−21.3770	−	8.85466i	−0.743352	−	0.307907i	−0.722026	+	0.691866i	$0.756789\pi$
$828$		0			0
$829$	−4.53604	−	10.9510i	−0.157543	−	0.380343i	0.825324	−	0.564660i	$-0.190993\pi$
$829$	−4.53604	−	10.9510i	−0.157543	−	0.380343i	−0.982867	+	0.184317i	$0.940993\pi$
$830$		0			0
$831$	−3.84271			−0.133302
$832$		0			0
$833$	−0.839056			−0.0290716
$834$		0			0
$835$	23.1356	+	55.8543i	0.800640	+	1.93292i
$836$		0			0
$837$	5.37775	+	2.22754i	0.185882	+	0.0769949i
$838$		0			0
$839$	−2.23832	−	2.23832i	−0.0772752	−	0.0772752i	0.667413	−	0.744688i	$-0.267402\pi$
$839$	−2.23832	−	2.23832i	−0.0772752	−	0.0772752i	−0.744688	+	0.667413i	$0.767402\pi$
$840$		0			0
$841$	−16.0319	+	16.0319i	−0.552826	+	0.552826i
$842$		0			0
$843$	−1.95248	+	4.71370i	−0.0672469	+	0.162348i
$844$		0			0
$845$	−0.854786	+	0.354064i	−0.0294055	+	0.0121802i
$846$		0			0
$847$			2.54232i			0.0873551i
$848$		0			0
$849$			13.3279i			0.457412i
$850$		0			0
$851$	−24.8267	+	10.2835i	−0.851047	+	0.352515i
$852$		0			0
$853$	8.29470	−	20.0252i	0.284005	−	0.685649i	−0.715916	−	0.698186i	$-0.753991\pi$
$853$	8.29470	−	20.0252i	0.284005	−	0.685649i	0.999921	+	0.0125373i	$0.00399085\pi$
$854$		0			0
$855$	−0.776301	+	0.776301i	−0.0265489	+	0.0265489i
$856$		0			0
$857$	20.9308	+	20.9308i	0.714984	+	0.714984i	0.967574	−	0.252590i	$-0.0812823\pi$
$857$	20.9308	+	20.9308i	0.714984	+	0.714984i	−0.252590	+	0.967574i	$0.581282\pi$
$858$		0			0
$859$	−4.72981	−	1.95915i	−0.161379	−	0.0668453i	0.300532	−	0.953772i	$-0.402836\pi$
$859$	−4.72981	−	1.95915i	−0.161379	−	0.0668453i	−0.461911	+	0.886927i	$0.652836\pi$
$860$		0			0
$861$	−4.94688	−	11.9428i	−0.168589	−	0.407011i
$862$		0			0
$863$	−52.6045			−1.79068			−0.895340	−	0.445384i	$-0.853067\pi$
$863$	−52.6045			−1.79068			−0.895340	+	0.445384i	$0.853067\pi$
$864$		0			0
$865$	10.6517			0.362168
$866$		0			0
$867$	−6.40547	−	15.4642i	−0.217541	−	0.525191i
$868$		0			0
$869$	2.06332	+	0.854656i	0.0699934	+	0.0289922i
$870$		0			0
$871$	−7.37126	−	7.37126i	−0.249766	−	0.249766i
$872$		0			0
$873$	0.479169	−	0.479169i	0.0162174	−	0.0162174i
$874$		0			0
$875$	−20.9955	+	50.6876i	−0.709778	+	1.71355i
$876$		0			0
$877$	−41.7255	+	17.2833i	−1.40897	+	0.583614i	−0.952063	−	0.305901i	$-0.901042\pi$
$877$	−41.7255	+	17.2833i	−1.40897	+	0.583614i	−0.456906	+	0.889515i	$0.651042\pi$
$878$		0			0
$879$			22.8936i			0.772181i
$880$		0			0
$881$		−	51.6942i		−	1.74162i	−0.491619	−	0.870811i	$-0.663595\pi$
$881$		−	51.6942i		−	1.74162i	0.491619	−	0.870811i	$-0.336405\pi$
$882$		0			0
$883$	−28.5743	+	11.8358i	−0.961601	+	0.398308i	−0.807579	−	0.589760i	$-0.799223\pi$
$883$	−28.5743	+	11.8358i	−0.961601	+	0.398308i	−0.154022	+	0.988067i	$0.549223\pi$
$884$		0			0
$885$	−22.0623	+	53.2630i	−0.741615	+	1.79042i
$886$		0			0
$887$	−10.8240	+	10.8240i	−0.363433	+	0.363433i	−0.865075	−	0.501642i	$-0.832729\pi$
$887$	−10.8240	+	10.8240i	−0.363433	+	0.363433i	0.501642	+	0.865075i	$0.332729\pi$
$888$		0			0
$889$	0.240075	+	0.240075i	0.00805187	+	0.00805187i
$890$		0			0
$891$	2.90719	+	1.20420i	0.0973946	+	0.0403422i
$892$		0			0
$893$	−0.990755	−	2.39189i	−0.0331543	−	0.0800417i
$894$		0			0
$895$	−42.2284			−1.41154
$896$		0			0
$897$	16.0285			0.535176
$898$		0			0
$899$	−16.0123	−	38.6572i	−0.534042	−	1.28929i
$900$		0			0
$901$	−3.09349	−	1.28136i	−0.103059	−	0.0426884i
$902$		0			0
$903$	5.59539	+	5.59539i	0.186203	+	0.186203i
$904$		0			0
$905$	−54.3201	+	54.3201i	−1.80566	+	1.80566i
$906$		0			0
$907$	12.4155	−	29.9736i	0.412249	−	0.995257i	−0.572284	−	0.820056i	$-0.693942\pi$
$907$	12.4155	−	29.9736i	0.412249	−	0.995257i	0.984533	−	0.175201i	$-0.0560577\pi$
$908$		0			0
$909$	−10.0095	+	4.14605i	−0.331993	+	0.137516i
$910$		0			0
$911$		−	27.7454i		−	0.919247i	−0.888114	−	0.459623i	$-0.847984\pi$
$911$		−	27.7454i		−	0.919247i	0.888114	−	0.459623i	$-0.152016\pi$
$912$		0			0
$913$			4.79643i			0.158739i
$914$		0			0
$915$	32.3665	−	13.4066i	1.07000	−	0.443210i
$916$		0			0
$917$	2.69204	−	6.49915i	0.0888989	−	0.214621i
$918$		0			0
$919$	22.9579	−	22.9579i	0.757311	−	0.757311i	−0.218521	−	0.975832i	$-0.570123\pi$
$919$	22.9579	−	22.9579i	0.757311	−	0.757311i	0.975832	+	0.218521i	$0.0701233\pi$
$920$		0			0
$921$	22.7569	+	22.7569i	0.749866	+	0.749866i
$922$		0			0
$923$	5.91107	+	2.44845i	0.194565	+	0.0805916i
$924$		0			0
$925$	−25.0719	−	60.5289i	−0.824359	−	1.99018i
$926$		0			0
$927$	11.6700			0.383292
$928$		0			0
$929$	−14.7767			−0.484807			−0.242404	−	0.970175i	$-0.577936\pi$
$929$	−14.7767			−0.484807			−0.242404	+	0.970175i	$0.577936\pi$
$930$		0			0
$931$	−0.172618	−	0.416736i	−0.00565731	−	0.0136580i
$932$		0			0
$933$	−6.64765	−	2.75355i	−0.217634	−	0.0901471i
$934$		0			0
$935$	4.54396	+	4.54396i	0.148603	+	0.148603i
$936$		0			0
$937$	25.7038	−	25.7038i	0.839707	−	0.839707i	−0.149113	−	0.988820i	$-0.547642\pi$
$937$	25.7038	−	25.7038i	0.839707	−	0.839707i	0.988820	+	0.149113i	$0.0476418\pi$
$938$		0			0
$939$	−5.61192	+	13.5484i	−0.183138	+	0.442134i
$940$		0			0
$941$	−4.00523	+	1.65902i	−0.130567	+	0.0540826i	−0.447010	−	0.894529i	$-0.647511\pi$
$941$	−4.00523	+	1.65902i	−0.130567	+	0.0540826i	0.316443	+	0.948611i	$0.397511\pi$
$942$		0			0
$943$		−	25.0464i		−	0.815622i
$944$		0			0
$945$			9.24206i			0.300644i
$946$		0			0
$947$	15.2678	−	6.32413i	0.496136	−	0.205506i	−0.120562	−	0.992706i	$-0.538470\pi$
$947$	15.2678	−	6.32413i	0.496136	−	0.205506i	0.616699	+	0.787199i	$0.288470\pi$
$948$		0			0
$949$	14.5350	−	35.0907i	0.471827	−	1.13909i
$950$		0			0
$951$	−11.4349	+	11.4349i	−0.370801	+	0.370801i
$952$		0			0
$953$	19.6560	+	19.6560i	0.636719	+	0.636719i	0.949745	−	0.313026i	$-0.101343\pi$
$953$	19.6560	+	19.6560i	0.636719	+	0.636719i	−0.313026	+	0.949745i	$0.601343\pi$
$954$		0			0
$955$	−37.5320	−	15.5463i	−1.21451	−	0.503065i
$956$		0			0
$957$	−8.65622	−	20.8980i	−0.279816	−	0.675535i
$958$		0			0
$959$	−38.2709			−1.23583
$960$		0			0
$961$	2.88209			0.0929707
$962$		0			0
$963$	0.162056	+	0.391238i	0.00522218	+	0.0126075i
$964$		0			0
$965$	−26.4618	−	10.9608i	−0.851836	−	0.352842i
$966$		0			0
$967$	−13.4891	−	13.4891i	−0.433781	−	0.433781i	0.456131	−	0.889912i	$-0.349235\pi$
$967$	−13.4891	−	13.4891i	−0.433781	−	0.433781i	−0.889912	+	0.456131i	$0.849235\pi$
$968$		0			0
$969$	−0.0994792	+	0.0994792i	−0.00319573	+	0.00319573i
$970$		0			0
$971$	−16.3983	+	39.5889i	−0.526246	+	1.27047i	0.407720	+	0.913107i	$0.366324\pi$
$971$	−16.3983	+	39.5889i	−0.526246	+	1.27047i	−0.933966	+	0.357362i	$0.883676\pi$
$972$		0			0
$973$	−44.4940	+	18.4300i	−1.42641	+	0.590840i
$974$		0			0
$975$			39.0784i			1.25151i
$976$		0			0
$977$		−	15.7216i		−	0.502979i	−0.967860	−	0.251489i	$-0.919080\pi$
$977$		−	15.7216i		−	0.502979i	0.967860	−	0.251489i	$-0.0809203\pi$
$978$		0			0
$979$	0.352304	−	0.145929i	0.0112597	−	0.00466391i
$980$		0			0
$981$	−2.24480	+	5.41943i	−0.0716710	+	0.173029i
$982$		0			0
$983$	−10.9749	+	10.9749i	−0.350046	+	0.350046i	−0.860127	−	0.510080i	$-0.829616\pi$
$983$	−10.9749	+	10.9749i	−0.350046	+	0.350046i	0.510080	+	0.860127i	$0.329616\pi$
$984$		0			0
$985$	29.9778	+	29.9778i	0.955173	+	0.955173i
$986$		0			0
$987$	−20.1357	−	8.34046i	−0.640925	−	0.265480i
$988$		0			0
$989$	5.86728	+	14.1649i	0.186569	+	0.450417i
$990$		0			0
$991$	−32.2476			−1.02438			−0.512190	−	0.858872i	$-0.671166\pi$
$991$	−32.2476			−1.02438			−0.512190	+	0.858872i	$0.671166\pi$
$992$		0			0
$993$	31.4060			0.996638
$994$		0			0
$995$	17.1301	+	41.3557i	0.543061	+	1.31107i
$996$		0			0
$997$	22.2570	+	9.21915i	0.704886	+	0.291973i	0.706187	−	0.708026i	$-0.250414\pi$
$997$	22.2570	+	9.21915i	0.704886	+	0.291973i	−0.00130036	+	0.999999i	$0.500414\pi$
$998$		0			0
$999$	−4.23605	−	4.23605i	−0.134023	−	0.134023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.n.a.241.4		32
3.2	odd	2		1152.2.v.c.1009.1		32
4.3	odd	2		96.2.n.a.37.3	yes	32
8.3	odd	2		768.2.n.a.481.1		32
8.5	even	2		768.2.n.b.481.5		32
12.11	even	2		288.2.v.d.37.6		32
32.3	odd	8		768.2.n.a.289.1		32
32.13	even	8	inner	384.2.n.a.145.4		32
32.19	odd	8		96.2.n.a.13.3	✓	32
32.29	even	8		768.2.n.b.289.5		32
96.77	odd	8		1152.2.v.c.145.1		32
96.83	even	8		288.2.v.d.109.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.3	✓	32	32.19	odd	8
96.2.n.a.37.3	yes	32	4.3	odd	2
288.2.v.d.37.6		32	12.11	even	2
288.2.v.d.109.6		32	96.83	even	8
384.2.n.a.145.4		32	32.13	even	8	inner
384.2.n.a.241.4		32	1.1	even	1	trivial
768.2.n.a.289.1		32	32.3	odd	8
768.2.n.a.481.1		32	8.3	odd	2
768.2.n.b.289.5		32	32.29	even	8
768.2.n.b.481.5		32	8.5	even	2
1152.2.v.c.145.1		32	96.77	odd	8
1152.2.v.c.1009.1		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 - 0.923880i) q^{3} +(3.68816 + 1.52768i) q^{5} +(1.63704 + 1.63704i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.382683 - 0.923880i) q^{3} +(3.68816 + 1.52768i) q^{5} +(1.63704 + 1.63704i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.20420 + 2.90719i) q^{11} +(-3.30127 + 1.36743i) q^{13} -3.99203i q^{15} -0.511560i q^{17} +(0.254077 - 0.105242i) q^{19} +(0.885960 - 2.13890i) q^{21} +(3.17185 - 3.17185i) q^{23} +(7.73315 + 7.73315i) q^{25} +(0.923880 + 0.382683i) q^{27} +(-2.75087 - 6.64118i) q^{29} +5.82083 q^{31} +3.14672 q^{33} +(3.53678 + 8.53855i) q^{35} +(-5.53467 - 2.29253i) q^{37} +(2.52668 + 2.52668i) q^{39} +(3.94823 - 3.94823i) q^{41} +(-1.30801 + 3.15781i) q^{43} +(-3.68816 + 1.52768i) q^{45} -9.41403i q^{47} -1.64019i q^{49} +(-0.472620 + 0.195765i) q^{51} +(2.50482 - 6.04717i) q^{53} +(-8.88255 + 8.88255i) q^{55} +(-0.194462 - 0.194462i) q^{57} +(-13.3423 - 5.52657i) q^{59} +(3.35835 + 8.10777i) q^{61} -2.31513 q^{63} -14.2646 q^{65} +(1.11643 + 2.69530i) q^{67} +(-4.14422 - 1.71659i) q^{69} +(-1.26611 - 1.26611i) q^{71} +(-7.51616 + 7.51616i) q^{73} +(4.18515 - 10.1038i) q^{75} +(-6.73052 + 2.78787i) q^{77} -0.709730i q^{79} -1.00000i q^{81} +(1.40823 - 0.583309i) q^{83} +(0.781502 - 1.88671i) q^{85} +(-5.08294 + 5.08294i) q^{87} +(-0.0856897 - 0.0856897i) q^{89} +(-7.64285 - 3.16577i) q^{91} +(-2.22754 - 5.37775i) q^{93} +1.09785 q^{95} -0.677647 q^{97} +(-1.20420 - 2.90719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more