LMFDB - Embedded newform 644.2.bc.a.493.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.7
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.254278 - 0.493230i) q^{3} +(1.20176 - 0.114755i) q^{5} +(1.86059 - 1.88101i) q^{7} +(1.56155 - 2.19289i) q^{9} +O(q^{10})$	\(q+(-0.254278 - 0.493230i) q^{3} +(1.20176 - 0.114755i) q^{5} +(1.86059 - 1.88101i) q^{7} +(1.56155 - 2.19289i) q^{9} +(0.0516023 - 0.0178597i) q^{11} +(1.70296 + 5.79975i) q^{13} +(-0.362183 - 0.563567i) q^{15} +(-6.74436 - 2.70004i) q^{17} +(2.94775 - 1.18010i) q^{19} +(-1.40088 - 0.439401i) q^{21} +(3.30629 - 3.47397i) q^{23} +(-3.47857 + 0.670440i) q^{25} +(-3.12648 - 0.449519i) q^{27} +(-0.826050 - 5.74531i) q^{29} +(9.41195 - 0.448346i) q^{31} +(-0.0219303 - 0.0209105i) q^{33} +(2.02014 - 2.47404i) q^{35} +(-0.587148 - 0.418106i) q^{37} +(2.42758 - 2.31470i) q^{39} +(6.80578 + 3.10809i) q^{41} +(-2.60404 + 4.05197i) q^{43} +(1.62497 - 2.81454i) q^{45} +(4.17191 - 2.40865i) q^{47} +(-0.0763987 - 6.99958i) q^{49} +(0.383203 + 4.01308i) q^{51} +(6.25386 + 6.55886i) q^{53} +(0.0599643 - 0.0273848i) q^{55} +(-1.33161 - 1.15385i) q^{57} +(1.97493 + 0.479112i) q^{59} +(-9.06615 - 4.67393i) q^{61} +(-1.21944 - 7.01737i) q^{63} +(2.71210 + 6.77451i) q^{65} +(-0.0293251 - 0.152153i) q^{67} +(-2.55418 - 0.747407i) q^{69} +(-6.77963 - 7.82411i) q^{71} +(-3.21617 + 4.08970i) q^{73} +(1.21521 + 1.54526i) q^{75} +(0.0624165 - 0.130294i) q^{77} +(-5.33746 + 5.59777i) q^{79} +(-2.06819 - 5.97564i) q^{81} +(-1.34867 - 2.95317i) q^{83} +(-8.41498 - 2.47086i) q^{85} +(-2.62371 + 1.86834i) q^{87} +(0.140614 - 2.95185i) q^{89} +(14.0779 + 7.58767i) q^{91} +(-2.61439 - 4.52825i) q^{93} +(3.40708 - 1.75647i) q^{95} +(-2.28479 + 5.00300i) q^{97} +(0.0414152 - 0.141047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

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
$3$	−0.254278	−	0.493230i	−0.146807	−	0.284767i	0.803953	−	0.594692i	$-0.202726\pi$
$3$	−0.254278	−	0.493230i	−0.146807	−	0.284767i	−0.950761	+	0.309926i	$0.899696\pi$
$4$		0			0
$5$	1.20176	−	0.114755i	0.537446	−	0.0513198i	0.177196	−	0.984176i	$-0.443297\pi$
$5$	1.20176	−	0.114755i	0.537446	−	0.0513198i	0.360250	+	0.932856i	$0.382691\pi$
$6$		0			0
$7$	1.86059	−	1.88101i	0.703237	−	0.710955i
$7$	1.86059	−	1.88101i	0.703237	−	0.710955i
$8$		0			0
$9$	1.56155	−	2.19289i	0.520517	−	0.730964i
$10$		0			0
$11$	0.0516023	−	0.0178597i	0.0155587	−	0.00538491i	−0.319278	−	0.947661i	$-0.603440\pi$
$11$	0.0516023	−	0.0178597i	0.0155587	−	0.00538491i	0.334836	+	0.942276i	$0.391319\pi$
$12$		0			0
$13$	1.70296	+	5.79975i	0.472316	+	1.60856i	0.759379	+	0.650649i	$0.225503\pi$
$13$	1.70296	+	5.79975i	0.472316	+	1.60856i	−0.287063	+	0.957912i	$0.592679\pi$
$14$		0			0
$15$	−0.362183	−	0.563567i	−0.0935151	−	0.145512i
$16$		0			0
$17$	−6.74436	−	2.70004i	−1.63575	−	0.654855i	−0.642021	−	0.766687i	$-0.721904\pi$
$17$	−6.74436	−	2.70004i	−1.63575	−	0.654855i	−0.993727	+	0.111832i	$0.964328\pi$
$18$		0			0
$19$	2.94775	−	1.18010i	0.676261	−	0.270734i	−0.00800373	−	0.999968i	$-0.502548\pi$
$19$	2.94775	−	1.18010i	0.676261	−	0.270734i	0.684264	+	0.729234i	$0.260123\pi$
$20$		0			0
$21$	−1.40088	−	0.439401i	−0.305697	−	0.0958851i
$22$		0			0
$23$	3.30629	−	3.47397i	0.689409	−	0.724373i
$23$	3.30629	−	3.47397i	0.689409	−	0.724373i
$24$		0			0
$25$	−3.47857	+	0.670440i	−0.695715	+	0.134088i
$26$		0			0
$27$	−3.12648	−	0.449519i	−0.601691	−	0.0865100i
$28$		0			0
$29$	−0.826050	−	5.74531i	−0.153394	−	1.06688i	−0.910477	−	0.413559i	$-0.864286\pi$
$29$	−0.826050	−	5.74531i	−0.153394	−	1.06688i	0.757084	−	0.653318i	$-0.226623\pi$
$30$		0			0
$31$	9.41195	−	0.448346i	1.69044	−	0.0805254i	0.819861	−	0.572562i	$-0.194050\pi$
$31$	9.41195	−	0.448346i	1.69044	−	0.0805254i	0.870574	+	0.492037i	$0.163747\pi$
$32$		0			0
$33$	−0.0219303	−	0.0209105i	−0.00381757	−	0.00364005i
$34$		0			0
$35$	2.02014	−	2.47404i	0.341466	−	0.418190i
$36$		0			0
$37$	−0.587148	−	0.418106i	−0.0965265	−	0.0687362i	0.530775	−	0.847513i	$-0.321901\pi$
$37$	−0.587148	−	0.418106i	−0.0965265	−	0.0687362i	−0.627301	+	0.778777i	$0.715840\pi$
$38$		0			0
$39$	2.42758	−	2.31470i	0.388725	−	0.370648i
$40$		0			0
$41$	6.80578	+	3.10809i	1.06288	+	0.485403i	0.868585	−	0.495540i	$-0.165030\pi$
$41$	6.80578	+	3.10809i	1.06288	+	0.485403i	0.194298	+	0.980942i	$0.437757\pi$
$42$		0			0
$43$	−2.60404	+	4.05197i	−0.397113	+	0.617920i	−0.981021	−	0.193900i	$-0.937886\pi$
$43$	−2.60404	+	4.05197i	−0.397113	+	0.617920i	0.583908	+	0.811820i	$0.301523\pi$
$44$		0			0
$45$	1.62497	−	2.81454i	0.242237	−	0.419566i
$46$		0			0
$47$	4.17191	−	2.40865i	0.608536	−	0.351338i	−0.163856	−	0.986484i	$-0.552393\pi$
$47$	4.17191	−	2.40865i	0.608536	−	0.351338i	0.772392	+	0.635146i	$0.219060\pi$
$48$		0			0
$49$	−0.0763987	−	6.99958i	−0.0109141	−	0.999940i
$50$		0			0
$51$	0.383203	+	4.01308i	0.0536591	+	0.561944i
$52$		0			0
$53$	6.25386	+	6.55886i	0.859034	+	0.900928i	0.995973	−	0.0896510i	$-0.0285752\pi$
$53$	6.25386	+	6.55886i	0.859034	+	0.900928i	−0.136940	+	0.990579i	$0.543727\pi$
$54$		0			0
$55$	0.0599643	−	0.0273848i	0.00808559	−	0.00369256i
$56$		0			0
$57$	−1.33161	−	1.15385i	−0.176376	−	0.152831i
$58$		0			0
$59$	1.97493	+	0.479112i	0.257114	+	0.0623751i	0.362244	−	0.932083i	$-0.382011\pi$
$59$	1.97493	+	0.479112i	0.257114	+	0.0623751i	−0.105130	+	0.994458i	$0.533526\pi$
$60$		0			0
$61$	−9.06615	−	4.67393i	−1.16080	−	0.598435i	−0.233356	−	0.972391i	$-0.574971\pi$
$61$	−9.06615	−	4.67393i	−1.16080	−	0.598435i	−0.927446	+	0.373956i	$0.878001\pi$
$62$		0			0
$63$	−1.21944	−	7.01737i	−0.153635	−	0.884106i
$64$		0			0
$65$	2.71210	+	6.77451i	0.336395	+	0.840274i
$66$		0			0
$67$	−0.0293251	−	0.152153i	−0.00358264	−	0.0185885i	0.980093	−	0.198537i	$-0.0636190\pi$
$67$	−0.0293251	−	0.152153i	−0.00358264	−	0.0185885i	−0.983676	+	0.179949i	$0.942407\pi$
$68$		0			0
$69$	−2.55418	−	0.747407i	−0.307487	−	0.0899773i
$70$		0			0
$71$	−6.77963	−	7.82411i	−0.804594	−	0.928550i	0.194030	−	0.980996i	$-0.437844\pi$
$71$	−6.77963	−	7.82411i	−0.804594	−	0.928550i	−0.998624	+	0.0524451i	$0.983299\pi$
$72$		0			0
$73$	−3.21617	+	4.08970i	−0.376425	+	0.478663i	−0.936945	−	0.349478i	$-0.886359\pi$
$73$	−3.21617	+	4.08970i	−0.376425	+	0.478663i	0.560520	+	0.828141i	$0.310601\pi$
$74$		0			0
$75$	1.21521	+	1.54526i	0.140320	+	0.178431i
$76$		0			0
$77$	0.0624165	−	0.130294i	0.00711302	−	0.0148484i
$78$		0			0
$79$	−5.33746	+	5.59777i	−0.600512	+	0.629798i	−0.951892	−	0.306434i	$-0.900864\pi$
$79$	−5.33746	+	5.59777i	−0.600512	+	0.629798i	0.351380	+	0.936233i	$0.385712\pi$
$80$		0			0
$81$	−2.06819	−	5.97564i	−0.229799	−	0.663960i
$82$		0			0
$83$	−1.34867	−	2.95317i	−0.148036	−	0.324153i	0.821059	−	0.570844i	$-0.193384\pi$
$83$	−1.34867	−	2.95317i	−0.148036	−	0.324153i	−0.969094	+	0.246691i	$0.920657\pi$
$84$		0			0
$85$	−8.41498	−	2.47086i	−0.912733	−	0.268003i
$86$		0			0
$87$	−2.62371	+	1.86834i	−0.281291	+	0.200307i
$88$		0			0
$89$	0.140614	−	2.95185i	0.0149051	−	0.312896i	−0.979087	−	0.203443i	$-0.934787\pi$
$89$	0.140614	−	2.95185i	0.0149051	−	0.312896i	0.993992	−	0.109453i	$-0.0349100\pi$
$90$		0			0
$91$	14.0779	+	7.58767i	1.47576	+	0.795404i
$92$		0			0
$93$	−2.61439	−	4.52825i	−0.271099	−	0.469558i
$94$		0			0
$95$	3.40708	−	1.75647i	0.349559	−	0.180210i
$96$		0			0
$97$	−2.28479	+	5.00300i	−0.231985	+	0.507977i	−0.989446	−	0.144904i	$-0.953713\pi$
$97$	−2.28479	+	5.00300i	−0.231985	+	0.507977i	0.757460	+	0.652881i	$0.226440\pi$
$98$		0			0
$99$	0.0414152	−	0.141047i	0.00416238	−	0.0141758i
$100$		0			0
$101$	−1.73312	+	18.1500i	−0.172452	+	1.80599i	0.332773	+	0.943007i	$0.392016\pi$
$101$	−1.73312	+	18.1500i	−0.172452	+	1.80599i	−0.505225	+	0.862988i	$0.668590\pi$
$102$		0			0
$103$	13.7354	+	2.64728i	1.35339	+	0.260845i	0.813830	−	0.581103i	$-0.197379\pi$
$103$	13.7354	+	2.64728i	1.35339	+	0.260845i	0.539560	+	0.841947i	$0.318591\pi$
$104$		0			0
$105$	−1.73395	−	0.367299i	−0.169216	−	0.0358447i
$106$		0			0
$107$	−2.63850	+	5.11797i	−0.255073	+	0.494773i	−0.981251	−	0.192734i	$-0.938265\pi$
$107$	−2.63850	+	5.11797i	−0.255073	+	0.494773i	0.726178	+	0.687507i	$0.241295\pi$
$108$		0			0
$109$	−5.97371	+	14.9216i	−0.572178	+	1.42923i	0.306525	+	0.951863i	$0.400834\pi$
$109$	−5.97371	+	14.9216i	−0.572178	+	1.42923i	−0.878703	+	0.477369i	$0.841591\pi$
$110$		0			0
$111$	−0.0569239	+	0.395914i	−0.00540297	+	0.0375785i
$112$		0			0
$113$	−5.79204	+	5.01883i	−0.544869	+	0.472132i	−0.883266	−	0.468871i	$-0.844661\pi$
$113$	−5.79204	+	5.01883i	−0.544869	+	0.472132i	0.338397	+	0.941003i	$0.390115\pi$
$114$		0			0
$115$	3.57473	−	4.55431i	0.333345	−	0.424691i
$116$		0			0
$117$	15.3775	+	5.32220i	1.42165	+	0.492037i
$118$		0			0
$119$	−17.6273	+	7.66255i	−1.61589	+	0.702425i
$120$		0			0
$121$	−8.64424	+	6.79791i	−0.785840	+	0.617991i
$122$		0			0
$123$	−0.197552	−	4.14713i	−0.0178127	−	0.373934i
$124$		0			0
$125$	−9.89514	+	2.90548i	−0.885048	+	0.259874i
$126$		0			0
$127$	−6.48281	+	7.48156i	−0.575256	+	0.663881i	−0.966578	−	0.256373i	$-0.917473\pi$
$127$	−6.48281	+	7.48156i	−0.575256	+	0.663881i	0.391322	+	0.920254i	$0.372018\pi$
$128$		0			0
$129$	2.66070	+	0.254067i	0.234262	+	0.0223693i
$130$		0			0
$131$	15.8314	−	3.84066i	1.38320	−	0.335560i	0.525971	−	0.850502i	$-0.323702\pi$
$131$	15.8314	−	3.84066i	1.38320	−	0.335560i	0.857225	+	0.514943i	$0.172187\pi$
$132$		0			0
$133$	3.26478	−	7.74044i	0.283092	−	0.671181i
$134$		0			0
$135$	−3.80887	−	0.181439i	−0.327816	−	0.0156158i
$136$		0			0
$137$	−8.11123	−	4.68302i	−0.692989	−	0.400098i	0.111742	−	0.993737i	$-0.464357\pi$
$137$	−8.11123	−	4.68302i	−0.692989	−	0.400098i	−0.804731	+	0.593640i	$0.797690\pi$
$138$		0			0
$139$			19.2522i			1.63295i	0.577381	+	0.816475i	$0.304075\pi$
$139$			19.2522i			1.63295i	−0.577381	+	0.816475i	$0.695925\pi$
$140$		0			0
$141$	−2.24885	−	1.44525i	−0.189387	−	0.121712i
$142$		0			0
$143$	0.191458	+	0.268866i	0.0160106	+	0.0224837i
$144$		0			0
$145$	−1.65202	−	6.80971i	−0.137193	−	0.565516i
$146$		0			0
$147$	−3.43298	+	1.81752i	−0.283147	+	0.149907i
$148$		0			0
$149$	4.17987	−	21.6872i	0.342428	−	1.77669i	−0.247152	−	0.968977i	$-0.579495\pi$
$149$	4.17987	−	21.6872i	0.342428	−	1.77669i	0.589581	−	0.807710i	$-0.299293\pi$
$150$		0			0
$151$	0.795098	−	3.27744i	0.0647041	−	0.266714i	−0.930266	−	0.366886i	$-0.880424\pi$
$151$	0.795098	−	3.27744i	0.0647041	−	0.266714i	0.994970	+	0.100172i	$0.0319392\pi$
$152$		0			0
$153$	−16.4526	+	10.5734i	−1.33011	+	0.854811i
$154$		0			0
$155$	11.2595	−	1.61887i	0.904385	−	0.130031i
$156$		0			0
$157$	5.34611	+	4.20423i	0.426666	+	0.335534i	0.808291	−	0.588783i	$-0.200393\pi$
$157$	5.34611	+	4.20423i	0.426666	+	0.335534i	−0.381625	+	0.924317i	$0.624635\pi$
$158$		0			0
$159$	1.64481	−	4.75236i	0.130442	−	0.376887i
$160$		0			0
$161$	−0.382921	−	12.6828i	−0.0301784	−	0.999545i
$162$		0			0
$163$	2.79276	−	8.06916i	0.218746	−	0.632026i	−0.781224	−	0.624251i	$-0.785404\pi$
$163$	2.79276	−	8.06916i	0.218746	−	0.632026i	0.999970	−	0.00777426i	$-0.00247465\pi$
$164$		0			0
$165$	−0.0287546	−	0.0226129i	−0.00223854	−	0.00176041i
$166$		0			0
$167$	−12.8679	+	1.85013i	−0.995750	+	0.143167i	−0.620876	−	0.783909i	$-0.713223\pi$
$167$	−12.8679	+	1.85013i	−0.995750	+	0.143167i	−0.374874	+	0.927076i	$0.622314\pi$
$168$		0			0
$169$	−19.8007	+	12.7251i	−1.52313	+	0.978856i
$170$		0			0
$171$	2.01523	−	8.30689i	0.154109	−	0.635244i
$172$		0			0
$173$	−2.26971	+	11.7764i	−0.172563	+	0.895341i	0.787661	+	0.616109i	$0.211292\pi$
$173$	−2.26971	+	11.7764i	−0.172563	+	0.895341i	−0.960224	+	0.279232i	$0.909920\pi$
$174$		0			0
$175$	−5.21110	+	7.79065i	−0.393922	+	0.588918i
$176$		0			0
$177$	−0.265868	−	1.09592i	−0.0199838	−	0.0823745i
$178$		0			0
$179$	9.10193	+	12.7819i	0.680310	+	0.955362i	0.999969	+	0.00782941i	$0.00249220\pi$
$179$	9.10193	+	12.7819i	0.680310	+	0.955362i	−0.319659	+	0.947533i	$0.603568\pi$
$180$		0			0
$181$	5.32996	+	3.42536i	0.396173	+	0.254605i	0.723526	−	0.690297i	$-0.242520\pi$
$181$	5.32996	+	3.42536i	0.396173	+	0.254605i	−0.327353	+	0.944902i	$0.606157\pi$
$182$		0			0
$183$			5.66018i			0.418412i
$184$		0			0
$185$	−0.753593	−	0.435087i	−0.0554053	−	0.0319883i
$186$		0			0
$187$	−0.396247	−	0.0188756i	−0.0289764	−	0.00138032i
$188$		0			0
$189$	−6.66264	+	5.04456i	−0.484636	+	0.366938i
$190$		0			0
$191$	−16.0542	+	3.89471i	−1.16164	+	0.281811i	−0.769839	−	0.638239i	$-0.779663\pi$
$191$	−16.0542	+	3.89471i	−1.16164	+	0.281811i	−0.391802	+	0.920050i	$0.628148\pi$
$192$		0			0
$193$	23.8117	+	2.27374i	1.71400	+	0.163667i	0.905363	−	0.424638i	$-0.139599\pi$
$193$	23.8117	+	2.27374i	1.71400	+	0.163667i	0.808639	+	0.588305i	$0.200205\pi$
$194$		0			0
$195$	2.65176	−	3.06030i	0.189897	−	0.219153i
$196$		0			0
$197$	−6.59821	+	1.93741i	−0.470103	+	0.138035i	−0.508200	−	0.861239i	$-0.669689\pi$
$197$	−6.59821	+	1.93741i	−0.470103	+	0.138035i	0.0380964	+	0.999274i	$0.487871\pi$
$198$		0			0
$199$	1.11038	+	23.3096i	0.0787124	+	1.65238i	0.600737	+	0.799447i	$0.294874\pi$
$199$	1.11038	+	23.3096i	0.0787124	+	1.65238i	−0.522025	+	0.852930i	$0.674823\pi$
$200$		0			0
$201$	−0.0675898	+	0.0531532i	−0.00476742	+	0.00374914i
$202$		0			0
$203$	−12.3439	−	9.13586i	−0.866374	−	0.641212i
$204$		0			0
$205$	8.53561	+	2.95420i	0.596153	+	0.206331i
$206$		0			0
$207$	−2.45510	−	12.6751i	−0.170641	−	0.880982i
$208$		0			0
$209$	0.131034	−	0.113542i	0.00906384	−	0.00785386i
$210$		0			0
$211$	2.93985	−	20.4471i	0.202388	−	1.40764i	−0.594784	−	0.803886i	$-0.702762\pi$
$211$	2.93985	−	20.4471i	0.202388	−	1.40764i	0.797171	−	0.603753i	$-0.206329\pi$
$212$		0			0
$213$	−2.13518	+	5.33341i	−0.146300	+	0.365439i
$214$		0			0
$215$	−2.66447	+	5.16834i	−0.181715	+	0.352478i
$216$		0			0
$217$	16.6684	−	18.5382i	1.13153	−	1.25845i
$218$		0			0
$219$	2.83496	+	0.546394i	0.191569	+	0.0369219i
$220$		0			0
$221$	4.17415	−	43.7137i	0.280784	−	2.94050i
$222$		0			0
$223$	−3.86172	+	13.1518i	−0.258600	+	0.880710i	0.723176	+	0.690664i	$0.242682\pi$
$223$	−3.86172	+	13.1518i	−0.258600	+	0.880710i	−0.981775	+	0.190045i	$0.939136\pi$
$224$		0			0
$225$	−3.96177	+	8.67507i	−0.264118	+	0.578338i
$226$		0			0
$227$	15.9436	−	8.21951i	1.05822	−	0.545548i	0.160915	−	0.986968i	$-0.448555\pi$
$227$	15.9436	−	8.21951i	1.05822	−	0.545548i	0.897301	+	0.441420i	$0.145525\pi$
$228$		0			0
$229$	1.31697	+	2.28105i	0.0870277	+	0.150736i	0.906253	−	0.422735i	$-0.138930\pi$
$229$	1.31697	+	2.28105i	0.0870277	+	0.150736i	−0.819226	+	0.573471i	$0.805596\pi$
$230$		0			0
$231$	−0.0801361	+	0.00234522i	−0.00527257	+	0.000154304i
$232$		0			0
$233$	−0.853689	+	17.9211i	−0.0559270	+	1.17405i	0.780205	+	0.625524i	$0.215115\pi$
$233$	−0.853689	+	17.9211i	−0.0559270	+	1.17405i	−0.836132	+	0.548529i	$0.815188\pi$
$234$		0			0
$235$	4.73725	−	3.37338i	0.309024	−	0.220055i
$236$		0			0
$237$	4.11819	+	1.20921i	0.267505	+	0.0785466i
$238$		0			0
$239$	−11.0396	−	24.1734i	−0.714094	−	1.56365i	−0.822000	−	0.569488i	$-0.807142\pi$
$239$	−11.0396	−	24.1734i	−0.714094	−	1.56365i	0.107906	−	0.994161i	$-0.465586\pi$
$240$		0			0
$241$	−1.49674	−	4.32455i	−0.0964136	−	0.278569i	0.886473	−	0.462780i	$-0.153148\pi$
$241$	−1.49674	−	4.32455i	−0.0964136	−	0.278569i	−0.982887	+	0.184211i	$0.941027\pi$
$242$		0			0
$243$	−8.96058	+	9.39758i	−0.574821	+	0.602855i
$244$		0			0
$245$	−0.895048	−	8.40309i	−0.0571825	−	0.536853i
$246$		0			0
$247$	11.8642	+	15.0865i	0.754900	+	0.959934i
$248$		0			0
$249$	−1.11366	+	1.41613i	−0.0705751	+	0.0897435i
$250$		0			0
$251$	1.32314	+	1.52699i	0.0835161	+	0.0963827i	0.795970	−	0.605337i	$-0.206961\pi$
$251$	1.32314	+	1.52699i	0.0835161	+	0.0963827i	−0.712453	+	0.701719i	$0.752416\pi$
$252$		0			0
$253$	0.108568	−	0.238314i	0.00682560	−	0.0149827i
$254$		0			0
$255$	0.921040	+	4.77881i	0.0576777	+	0.299261i
$256$		0			0
$257$	−2.99909	−	7.49137i	−0.187078	−	0.467299i	0.804946	−	0.593349i	$-0.202194\pi$
$257$	−2.99909	−	7.49137i	−0.187078	−	0.467299i	−0.992024	+	0.126050i	$0.959770\pi$
$258$		0			0
$259$	−1.87890	+	0.326507i	−0.116749	+	0.0202881i
$260$		0			0
$261$	−13.8888	−	7.16015i	−0.859693	−	0.443202i
$262$		0			0
$263$	−2.99359	−	0.726236i	−0.184593	−	0.0447817i	0.142397	−	0.989810i	$-0.454519\pi$
$263$	−2.99359	−	0.726236i	−0.184593	−	0.0447817i	−0.326990	+	0.945028i	$0.606034\pi$
$264$		0			0
$265$	8.26833	+	7.16455i	0.507919	+	0.440115i
$266$		0			0
$267$	−1.49170	+	0.681236i	−0.0912904	+	0.0416909i
$268$		0			0
$269$	0.216372	+	0.226924i	0.0131924	+	0.0138358i	0.730297	−	0.683130i	$-0.239382\pi$
$269$	0.216372	+	0.226924i	0.0131924	+	0.0138358i	−0.717105	+	0.696965i	$0.754533\pi$
$270$		0			0
$271$	−2.25822	−	23.6492i	−0.137177	−	1.43658i	−0.757806	−	0.652480i	$-0.773729\pi$
$271$	−2.25822	−	23.6492i	−0.137177	−	1.43658i	0.620629	−	0.784105i	$-0.286877\pi$
$272$		0			0
$273$	0.162774	−	8.87302i	0.00985154	−	0.537019i
$274$		0			0
$275$	−0.167528	+	0.0967226i	−0.0101023	+	0.00583259i
$276$		0			0
$277$	−3.67361	+	6.36287i	−0.220726	+	0.382308i	−0.955028	−	0.296514i	$-0.904176\pi$
$277$	−3.67361	+	6.36287i	−0.220726	+	0.382308i	0.734303	+	0.678822i	$0.237509\pi$
$278$		0			0
$279$	13.7141	−	21.3395i	0.821040	−	1.27756i
$280$		0			0
$281$	−7.72499	−	3.52788i	−0.460834	−	0.210456i	0.171449	−	0.985193i	$-0.445155\pi$
$281$	−7.72499	−	3.52788i	−0.460834	−	0.210456i	−0.632284	+	0.774737i	$0.717882\pi$
$282$		0			0
$283$	−12.4964	+	11.9153i	−0.742836	+	0.708293i	−0.963693	−	0.267014i	$-0.913963\pi$
$283$	−12.4964	+	11.9153i	−0.742836	+	0.708293i	0.220857	+	0.975306i	$0.429115\pi$
$284$		0			0
$285$	−1.73269	−	1.23384i	−0.102636	−	0.0730866i
$286$		0			0
$287$	18.5091	−	7.01884i	1.09256	−	0.414309i
$288$		0			0
$289$	25.8928	+	24.6887i	1.52310	+	1.45228i
$290$		0			0
$291$	3.04860	−	0.145223i	0.178712	−	0.00851311i
$292$		0			0
$293$	2.42425	+	16.8610i	0.141626	+	0.985032i	0.929402	+	0.369070i	$0.120324\pi$
$293$	2.42425	+	16.8610i	0.141626	+	0.985032i	−0.787775	+	0.615963i	$0.788767\pi$
$294$		0			0
$295$	2.42838	+	0.349148i	0.141386	+	0.0203282i
$296$		0			0
$297$	−0.169362	+	0.0326418i	−0.00982736	+	0.00189407i
$298$		0			0
$299$	25.7786	+	13.2596i	1.49082	+	0.766823i
$300$		0			0
$301$	2.77674	+	12.4373i	0.160049	+	0.716874i
$302$		0			0
$303$	9.39283	−	3.76032i	0.539604	−	0.216025i
$304$		0			0
$305$	−11.4317	−	4.57658i	−0.654579	−	0.262054i
$306$		0			0
$307$	6.22766	+	9.69043i	0.355431	+	0.553062i	0.972221	−	0.234066i	$-0.0752033\pi$
$307$	6.22766	+	9.69043i	0.355431	+	0.553062i	−0.616789	+	0.787128i	$0.711567\pi$
$308$		0			0
$309$	−2.18689	−	7.44786i	−0.124408	−	0.423694i
$310$		0			0
$311$	8.80867	−	3.04871i	0.499494	−	0.172876i	−0.0656923	−	0.997840i	$-0.520926\pi$
$311$	8.80867	−	3.04871i	0.499494	−	0.172876i	0.565186	+	0.824963i	$0.308804\pi$
$312$		0			0
$313$	−7.05280	+	9.90427i	−0.398648	+	0.559822i	−0.964297	−	0.264824i	$-0.914686\pi$
$313$	−7.05280	+	9.90427i	−0.398648	+	0.559822i	0.565649	+	0.824646i	$0.308626\pi$
$314$		0			0
$315$	−2.27076	−	8.29329i	−0.127943	−	0.467274i
$316$		0			0
$317$	11.9464	−	1.14075i	0.670979	−	0.0640707i	0.245994	−	0.969271i	$-0.420886\pi$
$317$	11.9464	−	1.14075i	0.670979	−	0.0640707i	0.424984	+	0.905201i	$0.360280\pi$
$318$		0			0
$319$	−0.145236	−	0.281718i	−0.00813164	−	0.0157732i
$320$		0			0
$321$	3.19525			0.178341
$322$		0			0
$323$	−23.0670			−1.28348
$324$		0			0
$325$	−9.81225	−	19.0331i	−0.544286	−	1.05577i
$326$		0			0
$327$	8.87877	−	0.847820i	0.490997	−	0.0468845i
$328$		0			0
$329$	3.23152	−	12.3289i	0.178160	−	0.679716i
$330$		0			0
$331$	14.4195	−	20.2494i	0.792569	−	1.11301i	−0.198557	−	0.980089i	$-0.563626\pi$
$331$	14.4195	−	20.2494i	0.792569	−	1.11301i	0.991127	−	0.132919i	$-0.0424350\pi$
$332$		0			0
$333$	−1.83372	+	0.634658i	−0.100487	+	0.0347791i
$334$		0			0
$335$	−0.0527022	−	0.179487i	−0.00287943	−	0.00980643i
$336$		0			0
$337$	4.74839	+	7.38864i	0.258661	+	0.402485i	0.946159	−	0.323702i	$-0.104927\pi$
$337$	4.74839	+	7.38864i	0.258661	+	0.402485i	−0.687498	+	0.726186i	$0.741291\pi$
$338$		0			0
$339$	3.94823	+	1.58063i	0.214438	+	0.0858481i
$340$		0			0
$341$	0.477671	−	0.191231i	0.0258673	−	0.0103557i
$342$		0			0
$343$	−13.3084	−	12.8797i	−0.718588	−	0.695436i
$344$		0			0
$345$	−3.15529	−	0.605104i	−0.169875	−	0.0325777i
$346$		0			0
$347$	−7.37023	+	1.42050i	−0.395655	+	0.0762562i	−0.383198	−	0.923666i	$-0.625177\pi$
$347$	−7.37023	+	1.42050i	−0.395655	+	0.0762562i	−0.0124566	+	0.999922i	$0.503965\pi$
$348$		0			0
$349$	−9.93741	−	1.42878i	−0.531937	−	0.0764811i	−0.128888	−	0.991659i	$-0.541141\pi$
$349$	−9.93741	−	1.42878i	−0.531937	−	0.0764811i	−0.403050	+	0.915178i	$0.632050\pi$
$350$		0			0
$351$	−2.71716	−	18.8983i	−0.145031	−	1.00872i
$352$		0			0
$353$	13.6544	−	0.650441i	0.726752	−	0.0346195i	0.319054	−	0.947736i	$-0.396635\pi$
$353$	13.6544	−	0.650441i	0.726752	−	0.0346195i	0.407698	+	0.913117i	$0.366332\pi$
$354$		0			0
$355$	−9.04537	−	8.62474i	−0.480078	−	0.457754i
$356$		0			0
$357$	8.26163	+	6.74590i	0.437252	+	0.357031i
$358$		0			0
$359$	0.0313289	+	0.0223092i	0.00165348	+	0.00117744i	0.580883	−	0.813987i	$-0.302707\pi$
$359$	0.0313289	+	0.0223092i	0.00165348	+	0.00117744i	−0.579230	+	0.815164i	$0.696647\pi$
$360$		0			0
$361$	−6.45435	+	6.15421i	−0.339702	+	0.323906i
$362$		0			0
$363$	5.55097	+	2.53504i	0.291350	+	0.133055i
$364$		0			0
$365$	−3.39577	+	5.28392i	−0.177743	+	0.276573i
$366$		0			0
$367$	10.5118	−	18.2070i	0.548712	−	0.950398i	−0.449651	−	0.893204i	$-0.648452\pi$
$367$	10.5118	−	18.2070i	0.548712	−	0.950398i	0.998363	−	0.0571932i	$-0.0182151\pi$
$368$		0			0
$369$	17.4433	−	10.0709i	0.908061	−	0.524270i
$370$		0			0
$371$	23.9732	+	0.439784i	1.24462	+	0.0228324i
$372$		0			0
$373$	−3.29393	−	34.4956i	−0.170553	−	1.78611i	−0.525065	−	0.851062i	$-0.675959\pi$
$373$	−3.29393	−	34.4956i	−0.170553	−	1.78611i	0.354512	−	0.935051i	$-0.384647\pi$
$374$		0			0
$375$	3.94918	+	4.14178i	0.203935	+	0.213881i
$376$		0			0
$377$	31.9146	−	14.5749i	1.64368	−	0.750646i
$378$		0			0
$379$	0.244764	+	0.212089i	0.0125727	+	0.0108943i	0.661124	−	0.750276i	$-0.270080\pi$
$379$	0.244764	+	0.212089i	0.0125727	+	0.0108943i	−0.648552	+	0.761171i	$0.724625\pi$
$380$		0			0
$381$	5.33857	+	1.29512i	0.273503	+	0.0663511i
$382$		0			0
$383$	−20.6580	−	10.6499i	−1.05558	−	0.544187i	−0.159092	−	0.987264i	$-0.550857\pi$
$383$	−20.6580	−	10.6499i	−1.05558	−	0.544187i	−0.896484	+	0.443077i	$0.853887\pi$
$384$		0			0
$385$	0.0600580	−	0.163745i	0.00306084	−	0.00834524i
$386$		0			0
$387$	4.81919	+	12.0378i	0.244973	+	0.611913i
$388$		0			0
$389$	−5.75392	−	29.8542i	−0.291735	−	1.51367i	−0.771478	−	0.636256i	$-0.780482\pi$
$389$	−5.75392	−	29.8542i	−0.291735	−	1.51367i	0.479743	−	0.877409i	$-0.340730\pi$
$390$		0			0
$391$	−31.6787	+	14.5026i	−1.60206	+	0.733429i
$392$		0			0
$393$	−5.91990	−	6.83193i	−0.298619	−	0.344625i
$394$		0			0
$395$	−5.77201	+	7.33970i	−0.290421	+	0.369301i
$396$		0			0
$397$	13.6626	+	17.3734i	0.685708	+	0.871948i	0.996923	−	0.0783912i	$-0.0249783\pi$
$397$	13.6626	+	17.3734i	0.685708	+	0.871948i	−0.311215	+	0.950340i	$0.600736\pi$
$398$		0			0
$399$	−4.64798	+	0.357935i	−0.232690	+	0.0179191i
$400$		0			0
$401$	−23.2394	+	24.3727i	−1.16052	+	1.21712i	−0.188535	+	0.982067i	$0.560374\pi$
$401$	−23.2394	+	24.3727i	−1.16052	+	1.21712i	−0.971983	+	0.235050i	$0.924475\pi$
$402$		0			0
$403$	18.6285	+	53.8234i	0.927950	+	2.68113i
$404$		0			0
$405$	−3.17121	−	6.94398i	−0.157579	−	0.345049i
$406$		0			0
$407$	−0.0377654	−	0.0110889i	−0.00187196	−	0.000549658i
$408$		0			0
$409$	1.10952	−	0.790083i	0.0548621	−	0.0390671i	−0.552297	−	0.833647i	$-0.686249\pi$
$409$	1.10952	−	0.790083i	0.0548621	−	0.0390671i	0.607159	+	0.794580i	$0.292309\pi$
$410$		0			0
$411$	−0.247301	+	5.19149i	−0.0121985	+	0.256077i
$412$		0			0
$413$	4.57575	−	2.82343i	0.225158	−	0.138932i
$414$		0			0
$415$	−1.95967	−	3.39425i	−0.0961965	−	0.166617i
$416$		0			0
$417$	9.49576	−	4.89541i	0.465009	−	0.239729i
$418$		0			0
$419$	5.42193	−	11.8724i	0.264879	−	0.580003i	−0.729726	−	0.683739i	$-0.760353\pi$
$419$	5.42193	−	11.8724i	0.264879	−	0.580003i	0.994605	+	0.103736i	$0.0330798\pi$
$420$		0			0
$421$	6.86796	−	23.3901i	0.334724	−	1.13996i	−0.604485	−	0.796617i	$-0.706621\pi$
$421$	6.86796	−	23.3901i	0.334724	−	1.13996i	0.939208	−	0.343348i	$-0.111561\pi$
$422$		0			0
$423$	1.23274	−	12.9098i	0.0599377	−	0.627696i
$424$		0			0
$425$	25.2710	+	4.87058i	1.22582	+	0.236258i
$426$		0			0
$427$	−25.6601	+	8.35726i	−1.24178	+	0.404436i
$428$		0			0
$429$	0.0839291	−	0.162800i	0.00405213	−	0.00786004i
$430$		0			0
$431$	−12.3370	+	30.8163i	−0.594251	+	1.48437i	0.260576	+	0.965453i	$0.416088\pi$
$431$	−12.3370	+	30.8163i	−0.594251	+	1.48437i	−0.854827	+	0.518914i	$0.826337\pi$
$432$		0			0
$433$	−0.933326	+	6.49143i	−0.0448528	+	0.311958i	0.955028	+	0.296516i	$0.0958247\pi$
$433$	−0.933326	+	6.49143i	−0.0448528	+	0.311958i	−0.999881	+	0.0154423i	$0.995084\pi$
$434$		0			0
$435$	−2.93868	+	2.54638i	−0.140899	+	0.122090i
$436$		0			0
$437$	5.64648	−	14.1422i	0.270108	−	0.676511i
$438$		0			0
$439$	−18.4879	−	6.39873i	−0.882381	−	0.305395i	−0.151955	−	0.988387i	$-0.548557\pi$
$439$	−18.4879	−	6.39873i	−0.882381	−	0.305395i	−0.730425	+	0.682992i	$0.760678\pi$
$440$		0			0
$441$	−15.4686	−	10.7627i	−0.736602	−	0.512509i
$442$		0			0
$443$	4.52754	−	3.56049i	0.215110	−	0.169164i	−0.504790	−	0.863242i	$-0.668430\pi$
$443$	4.52754	−	3.56049i	0.215110	−	0.169164i	0.719900	+	0.694078i	$0.244188\pi$
$444$		0			0
$445$	−0.169754	−	3.56357i	−0.00804710	−	0.168929i
$446$		0			0
$447$	−11.7596	+	3.45294i	−0.556212	+	0.163319i
$448$		0			0
$449$	13.8293	−	15.9598i	0.652643	−	0.753190i	−0.328914	−	0.944360i	$-0.606683\pi$
$449$	13.8293	−	15.9598i	0.652643	−	0.753190i	0.981557	+	0.191170i	$0.0612280\pi$
$450$		0			0
$451$	0.406703	+	0.0388355i	0.0191509	+	0.00182869i
$452$		0			0
$453$	−1.81871	+	0.441214i	−0.0854503	+	0.0207300i
$454$		0			0
$455$	17.7890	+	7.50310i	0.833963	+	0.351751i
$456$		0			0
$457$	11.0508	+	0.526415i	0.516935	+	0.0246247i	0.304429	−	0.952535i	$-0.401534\pi$
$457$	11.0508	+	0.526415i	0.516935	+	0.0246247i	0.212506	+	0.977160i	$0.431837\pi$
$458$		0			0
$459$	19.8724	+	11.4733i	0.927563	+	0.535529i
$460$		0			0
$461$		−	0.542886i		−	0.0252847i	−0.999920	−	0.0126424i	$-0.995976\pi$
$461$		−	0.542886i		−	0.0252847i	0.999920	−	0.0126424i	$-0.00402429\pi$
$462$		0			0
$463$	15.5079	+	9.96632i	0.720713	+	0.463174i	0.848885	−	0.528578i	$-0.177275\pi$
$463$	15.5079	+	9.96632i	0.720713	+	0.463174i	−0.128172	+	0.991752i	$0.540911\pi$
$464$		0			0
$465$	−3.66152	−	5.14188i	−0.169799	−	0.238449i
$466$		0			0
$467$	−4.44578	−	18.3258i	−0.205726	−	0.848015i	−0.977297	−	0.211872i	$-0.932044\pi$
$467$	−4.44578	−	18.3258i	−0.205726	−	0.848015i	0.771571	−	0.636143i	$-0.219471\pi$
$468$		0			0
$469$	−0.340764	−	0.227934i	−0.0157350	−	0.0105250i
$470$		0			0
$471$	0.714255	−	3.70590i	0.0329111	−	0.170759i
$472$		0			0
$473$	−0.0620075	+	0.255599i	−0.00285111	+	0.0117524i
$474$		0			0
$475$	−9.46278	+	6.08136i	−0.434182	+	0.279032i
$476$		0			0
$477$	24.1486	−	3.47204i	1.10569	−	0.158974i
$478$		0			0
$479$	−10.0941	−	7.93805i	−0.461209	−	0.362699i	0.360355	−	0.932815i	$-0.382656\pi$
$479$	−10.0941	−	7.93805i	−0.461209	−	0.362699i	−0.821564	+	0.570116i	$0.806898\pi$
$480$		0			0
$481$	1.42502	−	4.11733i	0.0649754	−	0.187734i
$482$		0			0
$483$	−6.15817	+	3.41382i	−0.280206	+	0.155334i
$484$		0			0
$485$	−2.17167	+	6.27461i	−0.0986102	+	0.284916i
$486$		0			0
$487$	−29.5380	−	23.2290i	−1.33850	−	1.05261i	−0.993480	−	0.114009i	$-0.963631\pi$
$487$	−29.5380	−	23.2290i	−1.33850	−	1.05261i	−0.345017	−	0.938597i	$-0.612127\pi$
$488$		0			0
$489$	−4.69009	+	0.674333i	−0.212093	+	0.0304944i
$490$		0			0
$491$	15.4476	−	9.92756i	0.697139	−	0.448024i	−0.143478	−	0.989653i	$-0.545829\pi$
$491$	15.4476	−	9.92756i	0.697139	−	0.448024i	0.840618	+	0.541629i	$0.182192\pi$
$492$		0			0
$493$	−9.94135	+	40.9788i	−0.447736	+	1.84559i
$494$		0			0
$495$	0.0335855	−	0.174258i	0.00150956	−	0.00783232i
$496$		0			0
$497$	−27.3313	−	1.80492i	−1.22598	−	0.0809616i
$498$		0			0
$499$	1.04842	+	4.32163i	0.0469335	+	0.193463i	0.990452	−	0.137857i	$-0.0440214\pi$
$499$	1.04842	+	4.32163i	0.0469335	+	0.193463i	−0.943519	+	0.331319i	$0.892506\pi$
$500$		0			0
$501$	4.18457	+	5.87640i	0.186953	+	0.262538i
$502$		0			0
$503$	−17.8948	−	11.5003i	−0.797888	−	0.512771i	0.0770381	−	0.997028i	$-0.475454\pi$
$503$	−17.8948	−	11.5003i	−0.797888	−	0.512771i	−0.874926	+	0.484257i	$0.839090\pi$
$504$		0			0
$505$			22.0109i			0.979474i
$506$		0			0
$507$	11.3113	+	6.53058i	0.502352	+	0.290033i
$508$		0			0
$509$	18.4671	+	0.879696i	0.818540	+	0.0389918i	0.452674	−	0.891676i	$-0.350470\pi$
$509$	18.4671	+	0.879696i	0.818540	+	0.0389918i	0.365865	+	0.930668i	$0.380773\pi$
$510$		0			0
$511$	1.70878	+	13.6589i	0.0755919	+	0.604235i
$512$		0			0
$513$	−9.74655	+	2.36449i	−0.430321	+	0.104395i
$514$		0			0
$515$	16.8105	+	1.60521i	0.740760	+	0.0707340i
$516$		0			0
$517$	0.172262	−	0.198801i	0.00757609	−	0.00874327i
$518$		0			0
$519$	6.38560	−	1.87498i	0.280297	−	0.0823025i
$520$		0			0
$521$	−0.443536	−	9.31097i	−0.0194317	−	0.407921i	−0.987538	−	0.157381i	$-0.949695\pi$
$521$	−0.443536	−	9.31097i	−0.0194317	−	0.407921i	0.968106	−	0.250540i	$-0.0806081\pi$
$522$		0			0
$523$	−26.8377	+	21.1054i	−1.17353	+	0.922874i	−0.998100	−	0.0616175i	$-0.980374\pi$
$523$	−26.8377	+	21.1054i	−1.17353	+	0.922874i	−0.175430	+	0.984492i	$0.556132\pi$
$524$		0			0
$525$	5.16765	+	0.589283i	0.225535	+	0.0257184i
$526$		0			0
$527$	−64.6882	−	22.3888i	−2.81786	−	0.975271i
$528$		0			0
$529$	−1.13693	−	22.9719i	−0.0494315	−	0.998778i
$530$		0			0
$531$	4.13460	−	3.58265i	0.179426	−	0.155474i
$532$		0			0
$533$	−6.43620	+	44.7647i	−0.278783	+	1.93898i
$534$		0			0
$535$	−2.58354	+	6.45338i	−0.111696	+	0.279004i
$536$		0			0
$537$	3.98999	−	7.73949i	0.172181	−	0.333984i
$538$		0			0
$539$	−0.128953	−	0.359830i	−0.00555440	−	0.0154990i
$540$		0			0
$541$	43.7982	+	8.44142i	1.88303	+	0.362925i	0.995251	−	0.0973385i	$-0.0310330\pi$
$541$	43.7982	+	8.44142i	1.88303	+	0.362925i	0.887782	+	0.460264i	$0.152245\pi$
$542$		0			0
$543$	0.334199	−	3.49989i	0.0143418	−	0.150195i
$544$		0			0
$545$	−5.46667	+	18.6178i	−0.234167	+	0.797498i
$546$		0			0
$547$	−16.6125	+	36.3763i	−0.710300	+	1.55534i	0.116719	+	0.993165i	$0.462762\pi$
$547$	−16.6125	+	36.3763i	−0.710300	+	1.55534i	−0.827019	+	0.562175i	$0.809965\pi$
$548$		0			0
$549$	−24.4067	+	12.5825i	−1.04165	+	0.537009i
$550$		0			0
$551$	−9.21504	−	15.9609i	−0.392574	−	0.679958i
$552$		0			0
$553$	0.598625	+	20.4550i	0.0254561	+	0.869835i
$554$		0			0
$555$	−0.0229761	+	0.482328i	−0.000975282	+	0.0204737i
$556$		0			0
$557$	−8.08717	+	5.75885i	−0.342665	+	0.244010i	−0.738413	−	0.674349i	$-0.764425\pi$
$557$	−8.08717	+	5.75885i	−0.342665	+	0.244010i	0.395749	+	0.918359i	$0.370485\pi$
$558$		0			0
$559$	−27.9350	−	8.20245i	−1.18152	−	0.346927i
$560$		0			0
$561$	0.0914467	+	0.200240i	0.00386088	+	0.00845416i
$562$		0			0
$563$	−8.69838	−	25.1323i	−0.366593	−	1.05920i	−0.965952	−	0.258721i	$-0.916699\pi$
$563$	−8.69838	−	25.1323i	−0.366593	−	1.05920i	0.599359	−	0.800480i	$-0.295422\pi$
$564$		0			0
$565$	−6.38474	+	6.69612i	−0.268608	+	0.281708i
$566$		0			0
$567$	−15.0883	−	7.22794i	−0.633649	−	0.303545i
$568$		0			0
$569$	−5.91961	−	7.52740i	−0.248163	−	0.315565i	0.645973	−	0.763360i	$-0.276452\pi$
$569$	−5.91961	−	7.52740i	−0.248163	−	0.315565i	−0.894136	+	0.447795i	$0.852209\pi$
$570$		0			0
$571$	6.79203	−	8.63677i	0.284238	−	0.361437i	−0.622878	−	0.782319i	$-0.714037\pi$
$571$	6.79203	−	8.63677i	0.284238	−	0.361437i	0.907116	+	0.420881i	$0.138279\pi$
$572$		0			0
$573$	6.00321	+	6.92808i	0.250788	+	0.289424i
$574$		0			0
$575$	−9.17208	+	14.3011i	−0.382502	+	0.596398i
$576$		0			0
$577$	3.17708	+	16.4843i	0.132264	+	0.686249i	0.986159	+	0.165804i	$0.0530219\pi$
$577$	3.17708	+	16.4843i	0.132264	+	0.686249i	−0.853895	+	0.520445i	$0.825766\pi$
$578$		0			0
$579$	−4.93330	−	12.3228i	−0.205021	−	0.512118i
$580$		0			0
$581$	−8.06426	−	2.95779i	−0.334562	−	0.122710i
$582$		0			0
$583$	0.439853	+	0.226760i	0.0182168	+	0.00939144i
$584$		0			0
$585$	19.0909	+	4.63139i	0.789310	+	0.191485i
$586$		0			0
$587$	8.86278	+	7.67964i	0.365806	+	0.316973i	0.818296	−	0.574797i	$-0.194919\pi$
$587$	8.86278	+	7.67964i	0.365806	+	0.316973i	−0.452490	+	0.891769i	$0.649464\pi$
$588$		0			0
$589$	27.2150	−	12.4287i	1.12137	−	0.512114i
$590$		0			0
$591$	2.63337	+	2.76180i	0.108322	+	0.113605i
$592$		0			0
$593$	3.03814	+	31.8169i	0.124762	+	1.30656i	0.813505	+	0.581558i	$0.197557\pi$
$593$	3.03814	+	31.8169i	0.124762	+	1.30656i	−0.688743	+	0.725005i	$0.741837\pi$
$594$		0			0
$595$	−20.3046	+	11.2314i	−0.832406	+	0.460443i
$596$		0			0
$597$	11.2147	−	6.47480i	0.458986	−	0.264996i
$598$		0			0
$599$	0.591245	−	1.02407i	0.0241576	−	0.0418422i	−0.853694	−	0.520775i	$-0.825643\pi$
$599$	0.591245	−	1.02407i	0.0241576	−	0.0418422i	0.877851	+	0.478933i	$0.158976\pi$
$600$		0			0
$601$	20.1821	−	31.4040i	0.823246	−	1.28100i	−0.133785	−	0.991010i	$-0.542713\pi$
$601$	20.1821	−	31.4040i	0.823246	−	1.28100i	0.957031	−	0.289985i	$-0.0936504\pi$
$602$		0			0
$603$	−0.379449	−	0.173288i	−0.0154523	−	0.00705685i
$604$		0			0
$605$	−9.60825	+	9.16145i	−0.390631	+	0.372466i
$606$		0			0
$607$	15.8597	+	11.2936i	0.643725	+	0.458394i	0.854718	−	0.519093i	$-0.173730\pi$
$607$	15.8597	+	11.2936i	0.643725	+	0.458394i	−0.210993	+	0.977488i	$0.567670\pi$
$608$		0			0
$609$	−1.36730	+	8.41144i	−0.0554056	+	0.340849i
$610$		0			0
$611$	21.0742	+	20.0942i	0.852570	+	0.812924i
$612$		0			0
$613$	−29.7588	+	1.41759i	−1.20195	+	0.0572558i	−0.638980	−	0.769223i	$-0.720643\pi$
$613$	−29.7588	+	1.41759i	−1.20195	+	0.0572558i	−0.562967	+	0.826479i	$0.690340\pi$
$614$		0			0
$615$	−0.713314	−	4.96121i	−0.0287636	−	0.200055i
$616$		0			0
$617$	8.50801	+	1.22327i	0.342520	+	0.0492469i	0.311428	−	0.950270i	$-0.399193\pi$
$617$	8.50801	+	1.22327i	0.342520	+	0.0492469i	0.0310914	+	0.999517i	$0.490102\pi$
$618$		0			0
$619$	6.15513	−	1.18630i	0.247396	−	0.0476816i	−0.0640458	−	0.997947i	$-0.520400\pi$
$619$	6.15513	−	1.18630i	0.247396	−	0.0476816i	0.311441	+	0.950265i	$0.399188\pi$
$620$		0			0
$621$	−11.8986	+	9.37504i	−0.477476	+	0.376207i
$622$		0			0
$623$	−5.29084	−	5.75669i	−0.211973	−	0.230637i
$624$		0			0
$625$	4.88593	−	1.95603i	0.195437	−	0.0782413i
$626$		0			0
$627$	−0.0893215	−	0.0357589i	−0.00356716	−	0.00142807i
$628$		0			0
$629$	2.83104	+	4.40518i	0.112881	+	0.175646i
$630$		0			0
$631$	3.51512	+	11.9714i	0.139935	+	0.476574i	0.999401	−	0.0346190i	$-0.0110218\pi$
$631$	3.51512	+	11.9714i	0.139935	+	0.476574i	−0.859466	+	0.511193i	$0.829204\pi$
$632$		0			0
$633$	−10.8327	+	3.74923i	−0.430560	+	0.149018i
$634$		0			0
$635$	−6.93227	+	9.73501i	−0.275099	+	0.386322i
$636$		0			0
$637$	40.4657	−	12.3631i	1.60331	−	0.489844i
$638$		0			0
$639$	−27.7442	+	2.64925i	−1.09754	+	0.104803i
$640$		0			0
$641$	1.71554	+	3.32769i	0.0677599	+	0.131436i	0.920283	−	0.391254i	$-0.127959\pi$
$641$	1.71554	+	3.32769i	0.0677599	+	0.131436i	−0.852523	+	0.522690i	$0.824928\pi$
$642$		0			0
$643$	4.00794			0.158058			0.0790288	−	0.996872i	$-0.474818\pi$
$643$	4.00794			0.158058			0.0790288	+	0.996872i	$0.474818\pi$
$644$		0			0
$645$	3.22670			0.127051
$646$		0			0
$647$	−8.58531	−	16.6532i	−0.337523	−	0.654704i	0.657597	−	0.753370i	$-0.271573\pi$
$647$	−8.58531	−	16.6532i	−0.337523	−	0.654704i	−0.995121	+	0.0986657i	$0.968543\pi$
$648$		0			0
$649$	0.110468	−	0.0105484i	0.00433623	−	0.000414060i
$650$		0			0
$651$	−13.3820	−	3.50754i	−0.524482	−	0.137471i
$652$		0			0
$653$	−22.1709	+	31.1347i	−0.867615	+	1.21840i	0.106944	+	0.994265i	$0.465893\pi$
$653$	−22.1709	+	31.1347i	−0.867615	+	1.21840i	−0.974559	+	0.224130i	$0.928046\pi$
$654$		0			0
$655$	18.5849	−	6.43229i	0.726171	−	0.251330i
$656$		0			0
$657$	3.94605	+	13.4390i	0.153950	+	0.524305i
$658$		0			0
$659$	−0.311477	−	0.484668i	−0.0121334	−	0.0188800i	0.835134	−	0.550047i	$-0.185390\pi$
$659$	−0.311477	−	0.484668i	−0.0121334	−	0.0188800i	−0.847267	+	0.531167i	$0.821754\pi$
$660$		0			0
$661$	−6.21757	−	2.48914i	−0.241836	−	0.0968163i	0.247579	−	0.968868i	$-0.420365\pi$
$661$	−6.21757	−	2.48914i	−0.241836	−	0.0968163i	−0.489414	+	0.872051i	$0.662789\pi$
$662$		0			0
$663$	−22.6223	+	9.05660i	−0.878577	+	0.351729i
$664$		0			0
$665$	3.03524	−	9.67683i	0.117702	−	0.375252i
$666$		0			0
$667$	−22.6902	−	16.1260i	−0.878567	−	0.624400i
$668$		0			0
$669$	7.46881	−	1.43950i	0.288761	−	0.0556541i
$670$		0			0
$671$	−0.551309	−	0.0792663i	−0.0212831	−	0.00306004i
$672$		0			0
$673$	−3.07055	−	21.3561i	−0.118361	−	0.823218i	−0.959361	−	0.282183i	$-0.908942\pi$
$673$	−3.07055	−	21.3561i	−0.118361	−	0.823218i	0.841000	−	0.541035i	$-0.181967\pi$
$674$		0			0
$675$	11.1771	−	0.532429i	0.430205	−	0.0204932i
$676$		0			0
$677$	−11.4060	−	10.8756i	−0.438368	−	0.417983i	0.438487	−	0.898737i	$-0.355514\pi$
$677$	−11.4060	−	10.8756i	−0.438368	−	0.417983i	−0.876855	+	0.480754i	$0.840363\pi$
$678$		0			0
$679$	5.15962	+	13.6062i	0.198008	+	0.522160i
$680$		0			0
$681$	−8.10822	−	5.77384i	−0.310708	−	0.221254i
$682$		0			0
$683$	−25.3925	+	24.2117i	−0.971619	+	0.926437i	−0.997315	−	0.0732332i	$-0.976668\pi$
$683$	−25.3925	+	24.2117i	−0.971619	+	0.926437i	0.0256961	+	0.999670i	$0.491820\pi$
$684$		0			0
$685$	−10.2852	−	4.69709i	−0.392977	−	0.179467i
$686$		0			0
$687$	0.790209	−	1.22959i	0.0301484	−	0.0469118i
$688$		0			0
$689$	−27.3896	+	47.4403i	−1.04346	+	1.80733i
$690$		0			0
$691$	29.5764	−	17.0760i	1.12514	−	0.649600i	0.182433	−	0.983218i	$-0.441603\pi$
$691$	29.5764	−	17.0760i	1.12514	−	0.649600i	0.942708	+	0.333618i	$0.108270\pi$
$692$		0			0
$693$	−0.188254	−	0.340334i	−0.00715120	−	0.0129282i
$694$		0			0
$695$	2.20928	+	23.1366i	0.0838027	+	0.877622i
$696$		0			0
$697$	−37.5087	−	39.3380i	−1.42074	−	1.49003i
$698$		0			0
$699$	9.05632	−	4.13588i	0.342542	−	0.156433i
$700$		0			0
$701$	25.4010	+	22.0101i	0.959382	+	0.831310i	0.985728	−	0.168343i	$-0.0538417\pi$
$701$	25.4010	+	22.0101i	0.959382	+	0.831310i	−0.0263459	+	0.999653i	$0.508387\pi$
$702$		0			0
$703$	−2.22417	−	0.539579i	−0.0838863	−	0.0203506i
$704$		0			0
$705$	−2.86843	−	1.47878i	−0.108031	−	0.0556941i
$706$		0			0
$707$	30.9158	+	37.0298i	1.16271	+	1.39265i
$708$		0			0
$709$	0.754705	+	1.88516i	0.0283435	+	0.0707987i	0.941865	−	0.335993i	$-0.109072\pi$
$709$	0.754705	+	1.88516i	0.0283435	+	0.0707987i	−0.913521	+	0.406792i	$0.866648\pi$
$710$		0			0
$711$	3.94059	+	20.4457i	0.147783	+	0.766774i
$712$		0			0
$713$	29.5611	−	34.1792i	1.10707	−	1.28002i
$714$		0			0
$715$	0.260942	+	0.301143i	0.00975866	+	0.0112621i
$716$		0			0
$717$	−9.11593	+	11.5918i	−0.340441	+	0.432905i
$718$		0			0
$719$	1.25927	+	1.60130i	0.0469630	+	0.0597183i	0.808967	−	0.587854i	$-0.200027\pi$
$719$	1.25927	+	1.60130i	0.0469630	+	0.0597183i	−0.762004	+	0.647572i	$0.775785\pi$
$720$		0			0
$721$	30.5356	−	20.9109i	1.13720	−	0.778764i
$722$		0			0
$723$	−1.75241	+	1.83788i	−0.0651729	+	0.0683513i
$724$		0			0
$725$	6.72536	+	19.4317i	0.249774	+	0.721674i
$726$		0			0
$727$	−19.6475	−	43.0220i	−0.728684	−	1.59560i	−0.801319	−	0.598237i	$-0.795868\pi$
$727$	−19.6475	−	43.0220i	−0.728684	−	1.59560i	0.0726348	−	0.997359i	$-0.476859\pi$
$728$		0			0
$729$	−11.2882	−	3.31451i	−0.418081	−	0.122760i
$730$		0			0
$731$	28.5031	−	20.2970i	1.05422	−	0.750710i
$732$		0			0
$733$	0.967265	−	20.3054i	0.0357268	−	0.749997i	−0.907940	−	0.419100i	$-0.862346\pi$
$733$	0.967265	−	20.3054i	0.0357268	−	0.749997i	0.943667	−	0.330897i	$-0.107351\pi$
$734$		0			0
$735$	−3.91706	+	2.57818i	−0.144483	+	0.0950977i
$736$		0			0
$737$	−0.00423066	−	0.00732772i	−0.000155838	−	0.000269920i
$738$		0			0
$739$	−10.3688	+	5.34548i	−0.381422	+	0.196637i	−0.638265	−	0.769816i	$-0.720348\pi$
$739$	−10.3688	+	5.34548i	−0.381422	+	0.196637i	0.256844	+	0.966453i	$0.417317\pi$
$740$		0			0
$741$	4.42434	−	9.68795i	0.162532	−	0.355896i
$742$		0			0
$743$	−7.09290	+	24.1562i	−0.260213	+	0.886205i	0.720944	+	0.692993i	$0.243708\pi$
$743$	−7.09290	+	24.1562i	−0.260213	+	0.886205i	−0.981157	+	0.193211i	$0.938110\pi$
$744$		0			0
$745$	2.53451	−	26.5426i	0.0928573	−	0.972445i
$746$		0			0
$747$	−8.58200	−	1.65405i	−0.313999	−	0.0605184i
$748$		0			0
$749$	4.71779	+	14.4855i	0.172384	+	0.529288i
$750$		0			0
$751$	1.20358	−	2.33461i	0.0439191	−	0.0851911i	−0.865855	−	0.500296i	$-0.833225\pi$
$751$	1.20358	−	2.33461i	0.0439191	−	0.0851911i	0.909774	+	0.415104i	$0.136255\pi$
$752$		0			0
$753$	0.416711	−	1.04089i	0.0151858	−	0.0379323i
$754$		0			0
$755$	0.579419	−	4.02995i	0.0210872	−	0.146665i
$756$		0			0
$757$	23.9447	−	20.7482i	0.870287	−	0.754108i	−0.100275	−	0.994960i	$-0.531972\pi$
$757$	23.9447	−	20.7482i	0.870287	−	0.754108i	0.970562	+	0.240852i	$0.0774269\pi$
$758$		0			0
$759$	−0.145150	+	0.00704906i	−0.00526862	+	0.000255865i
$760$		0			0
$761$	5.29580	+	1.83289i	0.191973	+	0.0664424i	0.421363	−	0.906892i	$-0.361552\pi$
$761$	5.29580	+	1.83289i	0.191973	+	0.0664424i	−0.229390	+	0.973335i	$0.573673\pi$
$762$		0			0
$763$	16.9531	+	38.9996i	0.613742	+	1.41188i
$764$		0			0
$765$	−18.5588	+	14.5948i	−0.670994	+	0.527675i
$766$		0			0
$767$	0.584492	+	12.2700i	0.0211048	+	0.443044i
$768$		0			0
$769$	41.3412	−	12.1389i	1.49080	−	0.437739i	0.568006	−	0.823025i	$-0.307715\pi$
$769$	41.3412	−	12.1389i	1.49080	−	0.437739i	0.922797	+	0.385285i	$0.125897\pi$
$770$		0			0
$771$	−2.93237	+	3.38413i	−0.105607	+	0.121877i
$772$		0			0
$773$	−10.5626	−	1.00861i	−0.379911	−	0.0362771i	−0.0966461	−	0.995319i	$-0.530812\pi$
$773$	−10.5626	−	1.00861i	−0.379911	−	0.0362771i	−0.283265	+	0.959042i	$0.591418\pi$
$774$		0			0
$775$	−32.4396	+	7.86975i	−1.16526	+	0.282690i
$776$		0			0
$777$	0.638807	+	0.843709i	0.0229171	+	0.0302679i
$778$		0			0
$779$	23.7296	+	1.13038i	0.850201	+	0.0405001i
$780$		0			0
$781$	−0.489581	−	0.282660i	−0.0175186	−	0.0101144i
$782$		0			0
$783$			18.3339i			0.655200i
$784$		0			0
$785$	6.90722	+	4.43900i	0.246529	+	0.158435i
$786$		0			0
$787$	10.5620	+	14.8323i	0.376495	+	0.528714i	0.958734	−	0.284304i	$-0.0917625\pi$
$787$	10.5620	+	14.8323i	0.376495	+	0.528714i	−0.582239	+	0.813018i	$0.697823\pi$
$788$		0			0
$789$	0.403001	+	1.66119i	0.0143472	+	0.0591400i
$790$		0			0
$791$	−1.33615	+	20.2329i	−0.0475079	+	0.719399i
$792$		0			0
$793$	11.6683	−	60.5409i	0.414353	−	2.14987i
$794$		0			0
$795$	1.43132	−	5.89997i	0.0507636	−	0.209250i
$796$		0			0
$797$	−15.9899	+	10.2761i	−0.566392	+	0.363998i	−0.792282	−	0.610155i	$-0.791107\pi$
$797$	−15.9899	+	10.2761i	−0.566392	+	0.363998i	0.225890	+	0.974153i	$0.427471\pi$
$798$		0			0
$799$	−34.6404	+	4.98053i	−1.22549	+	0.176199i
$800$		0			0
$801$	−6.25352	−	4.91782i	−0.220957	−	0.173763i
$802$		0			0
$803$	−0.0929211	+	0.268478i	−0.00327911	+	0.00947437i
$804$		0			0
$805$	−1.91559	−	15.1978i	−0.0675157	−	0.535652i
$806$		0			0
$807$	0.0569073	−	0.164423i	0.00200323	−	0.00578796i
$808$		0			0
$809$	−6.52160	−	5.12864i	−0.229287	−	0.180314i	0.496905	−	0.867805i	$-0.334470\pi$
$809$	−6.52160	−	5.12864i	−0.229287	−	0.180314i	−0.726193	+	0.687491i	$0.758712\pi$
$810$		0			0
$811$	−16.8866	+	2.42792i	−0.592968	+	0.0852559i	−0.432265	−	0.901747i	$-0.642285\pi$
$811$	−16.8866	+	2.42792i	−0.592968	+	0.0852559i	−0.160703	+	0.987003i	$0.551376\pi$
$812$		0			0
$813$	−11.0903	+	7.12728i	−0.388953	+	0.249965i
$814$		0			0
$815$	2.43027	−	10.0177i	0.0851287	−	0.350905i
$816$		0			0
$817$	−2.89434	+	15.0172i	−0.101260	+	0.525387i
$818$		0			0
$819$	38.6223	−	19.0228i	1.34957	−	0.664709i
$820$		0			0
$821$	−6.71538	−	27.6812i	−0.234369	−	0.966080i	−0.960446	−	0.278467i	$-0.910174\pi$
$821$	−6.71538	−	27.6812i	−0.234369	−	0.966080i	0.726077	−	0.687613i	$-0.241341\pi$
$822$		0			0
$823$	1.74011	+	2.44365i	0.0606566	+	0.0851802i	0.843790	−	0.536673i	$-0.180319\pi$
$823$	1.74011	+	2.44365i	0.0606566	+	0.0851802i	−0.783133	+	0.621854i	$0.786380\pi$
$824$		0			0
$825$	0.0903053	+	0.0580357i	0.00314403	+	0.00202054i
$826$		0			0
$827$		−	55.4354i		−	1.92768i	−0.266483	−	0.963840i	$-0.585862\pi$
$827$		−	55.4354i		−	1.92768i	0.266483	−	0.963840i	$-0.414138\pi$
$828$		0			0
$829$	−19.7311	−	11.3917i	−0.685288	−	0.395651i	0.116556	−	0.993184i	$-0.462814\pi$
$829$	−19.7311	−	11.3917i	−0.685288	−	0.395651i	−0.801845	+	0.597533i	$0.796148\pi$
$830$		0			0
$831$	4.07248	+	0.193996i	0.141273	+	0.00672964i
$832$		0			0
$833$	−18.3839	+	47.4140i	−0.636963	+	1.64280i
$834$		0			0
$835$	−15.2519	+	3.70007i	−0.527814	+	0.128046i
$836$		0			0
$837$	−29.6278	−	2.82911i	−1.02409	−	0.0977883i
$838$		0			0
$839$	25.0539	−	28.9138i	0.864958	−	0.998215i	−0.135015	−	0.990844i	$-0.543108\pi$
$839$	25.0539	−	28.9138i	0.864958	−	0.998215i	0.999973	−	0.00737106i	$-0.00234630\pi$
$840$		0			0
$841$	−4.50089	+	1.32158i	−0.155203	+	0.0455718i
$842$		0			0
$843$	0.224234	+	4.70726i	0.00772304	+	0.162127i
$844$		0			0
$845$	−22.3355	+	17.5648i	−0.768365	+	0.604249i
$846$		0			0
$847$	−3.29647	+	28.9080i	−0.113268	+	0.993292i
$848$		0			0
$849$	9.05456	+	3.13381i	0.310752	+	0.107552i
$850$		0			0
$851$	−3.39377	+	0.657355i	−0.116337	+	0.0225338i
$852$		0			0
$853$	−2.26269	+	1.96063i	−0.0774730	+	0.0671308i	−0.692736	−	0.721191i	$-0.743595\pi$
$853$	−2.26269	+	1.96063i	−0.0774730	+	0.0671308i	0.615263	+	0.788322i	$0.289050\pi$
$854$		0			0
$855$	1.46858	−	10.2142i	0.0502243	−	0.349318i
$856$		0			0
$857$	0.834516	−	2.08452i	0.0285065	−	0.0712058i	−0.913432	−	0.406992i	$-0.866578\pi$
$857$	0.834516	−	2.08452i	0.0285065	−	0.0712058i	0.941938	+	0.335786i	$0.109002\pi$
$858$		0			0
$859$	−5.50660	+	10.6813i	−0.187883	+	0.364442i	−0.963898	−	0.266273i	$-0.914208\pi$
$859$	−5.50660	+	10.6813i	−0.187883	+	0.364442i	0.776015	+	0.630715i	$0.217238\pi$
$860$		0			0
$861$	−8.16836	−	7.34452i	−0.278377	−	0.250301i
$862$		0			0
$863$	−1.77364	−	0.341841i	−0.0603755	−	0.0116364i	0.158974	−	0.987283i	$-0.449181\pi$
$863$	−1.77364	−	0.341841i	−0.0603755	−	0.0116364i	−0.219350	+	0.975646i	$0.570394\pi$
$864$		0			0
$865$	−1.37626	+	14.4129i	−0.0467944	+	0.490053i
$866$		0			0
$867$	5.59326	−	19.0489i	0.189957	−	0.646934i
$868$		0			0
$869$	−0.175451	+	0.384183i	−0.00595176	+	0.0130325i
$870$		0			0
$871$	0.832511	−	0.429189i	0.0282086	−	0.0145425i
$872$		0			0
$873$	7.40321	+	12.8227i	0.250561	+	0.433984i
$874$		0			0
$875$	−12.9456	+	24.0188i	−0.437641	+	0.811982i
$876$		0			0
$877$	2.26758	−	47.6024i	0.0765707	−	1.60742i	−0.554832	−	0.831962i	$-0.687217\pi$
$877$	2.26758	−	47.6024i	0.0765707	−	1.60742i	0.631403	−	0.775455i	$-0.282479\pi$
$878$		0			0
$879$	7.69994	−	5.48310i	0.259712	−	0.184940i
$880$		0			0
$881$	−37.0805	−	10.8878i	−1.24928	−	0.366820i	−0.410783	−	0.911733i	$-0.634744\pi$
$881$	−37.0805	−	10.8878i	−1.24928	−	0.366820i	−0.838493	+	0.544913i	$0.816563\pi$
$882$		0			0
$883$	12.0865	+	26.4658i	0.406743	+	0.890644i	0.996542	+	0.0830934i	$0.0264800\pi$
$883$	12.0865	+	26.4658i	0.406743	+	0.890644i	−0.589798	+	0.807551i	$0.700793\pi$
$884$		0			0
$885$	−0.445273	−	1.28653i	−0.0149677	−	0.0432462i
$886$		0			0
$887$	3.58559	−	3.76046i	0.120392	−	0.126264i	−0.660779	−	0.750580i	$-0.729774\pi$
$887$	3.58559	−	3.76046i	0.120392	−	0.126264i	0.781171	+	0.624317i	$0.214622\pi$
$888$		0			0
$889$	2.01103	+	26.1144i	0.0674479	+	0.875848i
$890$		0			0
$891$	−0.213447	−	0.271419i	−0.00715073	−	0.00909290i
$892$		0			0
$893$	9.45530	−	12.0234i	0.316410	−	0.402348i
$894$		0			0
$895$	12.4052	+	14.3163i	0.414659	+	0.478542i
$896$		0			0
$897$	−0.0148944	−	16.0864i	−0.000497309	−	0.537110i
$898$		0			0
$899$	−10.3506	−	53.7042i	−0.345213	−	1.79113i
$900$		0			0
$901$	−24.4691	−	61.1210i	−0.815185	−	2.03623i
$902$		0			0
$903$	5.42839	−	4.53210i	0.180645	−	0.150819i
$904$		0			0
$905$	6.79843	+	3.50483i	0.225987	+	0.116505i
$906$		0			0
$907$	−8.64691	−	2.09772i	−0.287116	−	0.0696536i	0.0896144	−	0.995977i	$-0.471437\pi$
$907$	−8.64691	−	2.09772i	−0.287116	−	0.0696536i	−0.376730	+	0.926323i	$0.622952\pi$
$908$		0			0
$909$	37.0947	+	32.1427i	1.23035	+	1.06611i
$910$		0			0
$911$	37.8524	−	17.2866i	1.25410	−	0.572730i	0.326113	−	0.945331i	$-0.394261\pi$
$911$	37.8524	−	17.2866i	1.25410	−	0.572730i	0.927992	+	0.372601i	$0.121534\pi$
$912$		0			0
$913$	−0.122337	−	0.128304i	−0.00404877	−	0.00424623i
$914$		0			0
$915$	0.649531	+	6.80220i	0.0214728	+	0.224874i
$916$		0			0
$917$	22.2315	−	36.9249i	0.734147	−	1.21937i
$918$		0			0
$919$	32.0954	−	18.5303i	1.05873	−	0.611258i	0.133649	−	0.991029i	$-0.457330\pi$
$919$	32.0954	−	18.5303i	1.05873	−	0.611258i	0.925081	+	0.379771i	$0.123997\pi$
$920$		0			0
$921$	3.19606	−	5.53573i	0.105314	−	0.182409i
$922$		0			0
$923$	33.8324	−	52.6442i	1.11361	−	1.73281i
$924$		0			0
$925$	2.32275	+	1.06077i	0.0763716	+	0.0348778i
$926$		0			0
$927$	27.2538	−	25.9864i	0.895131	−	0.853506i
$928$		0			0
$929$	7.50324	+	5.34303i	0.246173	+	0.175299i	0.696483	−	0.717573i	$-0.254747\pi$
$929$	7.50324	+	5.34303i	0.246173	+	0.175299i	−0.450310	+	0.892872i	$0.648686\pi$
$930$		0			0
$931$	−8.48542	−	20.5429i	−0.278099	−	0.673266i
$932$		0			0
$933$	−3.74356	−	3.56948i	−0.122559	−	0.116860i
$934$		0			0
$935$	−0.478361	+	0.0227872i	−0.0156441	+	0.000745220i
$936$		0			0
$937$	−1.94607	−	13.5352i	−0.0635755	−	0.442177i	−0.996602	−	0.0823693i	$-0.973751\pi$
$937$	−1.94607	−	13.5352i	−0.0635755	−	0.442177i	0.933026	−	0.359808i	$-0.117158\pi$
$938$		0			0
$939$	6.67845	+	0.960216i	0.217943	+	0.0313355i
$940$		0			0
$941$	44.5777	−	8.59164i	1.45319	−	0.280080i	0.599297	−	0.800527i	$-0.295447\pi$
$941$	44.5777	−	8.59164i	1.45319	−	0.280080i	0.853894	+	0.520447i	$0.174235\pi$
$942$		0			0
$943$	33.2993	−	13.3668i	1.08437	−	0.435283i
$944$		0			0
$945$	−7.42804	+	6.82694i	−0.241634	+	0.222081i
$946$		0			0
$947$	2.60034	−	1.04102i	0.0844997	−	0.0338286i	−0.329028	−	0.944320i	$-0.606721\pi$
$947$	2.60034	−	1.04102i	0.0844997	−	0.0338286i	0.413527	+	0.910492i	$0.364297\pi$
$948$		0			0
$949$	−29.1962	−	11.6884i	−0.947749	−	0.379422i
$950$		0			0
$951$	−3.60036	−	5.60227i	−0.116750	−	0.181666i
$952$		0			0
$953$	−15.0853	−	51.3758i	−0.488661	−	1.66423i	−0.722049	−	0.691842i	$-0.756799\pi$
$953$	−15.0853	−	51.3758i	−0.488661	−	1.66423i	0.233388	−	0.972384i	$-0.425019\pi$
$954$		0			0
$955$	−18.8464	+	6.52281i	−0.609856	+	0.211073i
$956$		0			0
$957$	−0.102022	+	0.143269i	−0.00329789	+	0.00463124i
$958$		0			0
$959$	−23.9005	+	6.54412i	−0.771788	+	0.211321i
$960$		0			0
$961$	57.5241	−	5.49289i	1.85562	−	0.177190i
$962$		0			0
$963$	7.10301	+	13.7779i	0.228891	+	0.443987i
$964$		0			0
$965$	28.8770			0.929582
$966$		0			0
$967$	44.4679			1.42999			0.714996	−	0.699129i	$-0.246428\pi$
$967$	44.4679			1.42999			0.714996	+	0.699129i	$0.246428\pi$
$968$		0			0
$969$	5.86543	+	11.3774i	0.188425	+	0.365493i
$970$		0			0
$971$	−23.1922	+	2.21459i	−0.744273	+	0.0710695i	−0.460301	−	0.887763i	$-0.652258\pi$
$971$	−23.1922	+	2.21459i	−0.744273	+	0.0710695i	−0.283972	+	0.958832i	$0.591652\pi$
$972$		0			0
$973$	36.2136	+	35.8205i	1.16095	+	1.14835i
$974$		0			0
$975$	−6.89267	+	9.67940i	−0.220742	+	0.309989i
$976$		0			0
$977$	21.6038	−	7.47715i	0.691167	−	0.239215i	0.0411701	−	0.999152i	$-0.486891\pi$
$977$	21.6038	−	7.47715i	0.691167	−	0.239215i	0.649997	+	0.759937i	$0.274770\pi$
$978$		0			0
$979$	−0.0454633	−	0.154834i	−0.00145301	−	0.00494851i
$980$		0			0
$981$	23.3932	+	36.4006i	0.746889	+	1.16218i
$982$		0			0
$983$	42.2590	+	16.9180i	1.34785	+	0.539599i	0.929546	−	0.368706i	$-0.120199\pi$
$983$	42.2590	+	16.9180i	1.34785	+	0.539599i	0.418308	+	0.908305i	$0.362623\pi$
$984$		0			0
$985$	−7.70717	+	3.08549i	−0.245571	+	0.0983118i
$986$		0			0
$987$	−6.90271	+	1.54109i	−0.219716	+	0.0490535i
$988$		0			0
$989$	5.46671	+	22.4434i	0.173831	+	0.713657i
$990$		0			0
$991$	41.6416	−	8.02575i	1.32279	−	0.254946i	0.521513	−	0.853243i	$-0.325368\pi$
$991$	41.6416	−	8.02575i	1.32279	−	0.254946i	0.801275	+	0.598297i	$0.204156\pi$
$992$		0			0
$993$	−13.6542	−	1.96318i	−0.433302	−	0.0622995i
$994$		0			0
$995$	4.00930	+	27.8853i	0.127103	+	0.884023i
$996$		0			0
$997$	−29.3753	+	1.39932i	−0.930326	+	0.0443169i	−0.507270	−	0.861787i	$-0.669345\pi$
$997$	−29.3753	+	1.39932i	−0.930326	+	0.0443169i	−0.423055	+	0.906104i	$0.639042\pi$
$998$		0			0
$999$	1.64776	+	1.57113i	0.0521327	+	0.0497085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.7	yes	320
7.5	odd	6	inner	644.2.bc.a.33.7	✓	320
23.7	odd	22	inner	644.2.bc.a.605.7	yes	320
161.145	even	66	inner	644.2.bc.a.145.7	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.7	✓	320	7.5	odd	6	inner
644.2.bc.a.145.7	yes	320	161.145	even	66	inner
644.2.bc.a.493.7	yes	320	1.1	even	1	trivial
644.2.bc.a.605.7	yes	320	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.254278 - 0.493230i) q^{3} +(1.20176 - 0.114755i) q^{5} +(1.86059 - 1.88101i) q^{7} +(1.56155 - 2.19289i) q^{9} +O(q^{10})\)	\(q+(-0.254278 - 0.493230i) q^{3} +(1.20176 - 0.114755i) q^{5} +(1.86059 - 1.88101i) q^{7} +(1.56155 - 2.19289i) q^{9} +(0.0516023 - 0.0178597i) q^{11} +(1.70296 + 5.79975i) q^{13} +(-0.362183 - 0.563567i) q^{15} +(-6.74436 - 2.70004i) q^{17} +(2.94775 - 1.18010i) q^{19} +(-1.40088 - 0.439401i) q^{21} +(3.30629 - 3.47397i) q^{23} +(-3.47857 + 0.670440i) q^{25} +(-3.12648 - 0.449519i) q^{27} +(-0.826050 - 5.74531i) q^{29} +(9.41195 - 0.448346i) q^{31} +(-0.0219303 - 0.0209105i) q^{33} +(2.02014 - 2.47404i) q^{35} +(-0.587148 - 0.418106i) q^{37} +(2.42758 - 2.31470i) q^{39} +(6.80578 + 3.10809i) q^{41} +(-2.60404 + 4.05197i) q^{43} +(1.62497 - 2.81454i) q^{45} +(4.17191 - 2.40865i) q^{47} +(-0.0763987 - 6.99958i) q^{49} +(0.383203 + 4.01308i) q^{51} +(6.25386 + 6.55886i) q^{53} +(0.0599643 - 0.0273848i) q^{55} +(-1.33161 - 1.15385i) q^{57} +(1.97493 + 0.479112i) q^{59} +(-9.06615 - 4.67393i) q^{61} +(-1.21944 - 7.01737i) q^{63} +(2.71210 + 6.77451i) q^{65} +(-0.0293251 - 0.152153i) q^{67} +(-2.55418 - 0.747407i) q^{69} +(-6.77963 - 7.82411i) q^{71} +(-3.21617 + 4.08970i) q^{73} +(1.21521 + 1.54526i) q^{75} +(0.0624165 - 0.130294i) q^{77} +(-5.33746 + 5.59777i) q^{79} +(-2.06819 - 5.97564i) q^{81} +(-1.34867 - 2.95317i) q^{83} +(-8.41498 - 2.47086i) q^{85} +(-2.62371 + 1.86834i) q^{87} +(0.140614 - 2.95185i) q^{89} +(14.0779 + 7.58767i) q^{91} +(-2.61439 - 4.52825i) q^{93} +(3.40708 - 1.75647i) q^{95} +(-2.28479 + 5.00300i) q^{97} +(0.0414152 - 0.141047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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