LMFDB - Embedded newform 460.2.i.b.413.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(137,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("460.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.i (of order $4$, degree $2$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 18x^{14} + 146x^{12} - 798x^{10} + 3934x^{8} - 19950x^{6} + 91250x^{4} - 281250x^{2} + 390625 $ x^16 - 18x^14 + 146x^12 - 798x^10 + 3934x^8 - 19950x^6 + 91250x^4 - 281250*x^2 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			413.3
Root			$-2.23266 + 0.123447i$ of defining polynomial
Character	$\chi$	$=$	460.413
Dual form			460.2.i.b.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.237125 + 0.237125i) q^{3} +(-2.23266 - 0.123447i) q^{5} +(1.69421 + 1.69421i) q^{7} -2.88754i q^{9} +O(q^{10})$	\(q+(0.237125 + 0.237125i) q^{3} +(-2.23266 - 0.123447i) q^{5} +(1.69421 + 1.69421i) q^{7} -2.88754i q^{9} +5.55617i q^{11} +(2.65542 + 2.65542i) q^{13} +(-0.500147 - 0.558692i) q^{15} +(0.435244 + 0.435244i) q^{17} +1.92086 q^{19} +0.803478i q^{21} +(0.546205 + 4.76463i) q^{23} +(4.96952 + 0.551231i) q^{25} +(1.39608 - 1.39608i) q^{27} +7.41329i q^{29} -0.525750 q^{31} +(-1.31751 + 1.31751i) q^{33} +(-3.57344 - 3.99173i) q^{35} +(-1.94110 - 1.94110i) q^{37} +1.25933i q^{39} -6.78508 q^{41} +(1.88256 - 1.88256i) q^{43} +(-0.356459 + 6.44690i) q^{45} +(7.54296 - 7.54296i) q^{47} -1.25933i q^{49} +0.206415i q^{51} +(-0.467258 + 0.467258i) q^{53} +(0.685894 - 12.4050i) q^{55} +(0.455484 + 0.455484i) q^{57} +7.72412i q^{59} -0.714153i q^{61} +(4.89209 - 4.89209i) q^{63} +(-5.60083 - 6.25644i) q^{65} +(-4.97934 - 4.97934i) q^{67} +(-1.00029 + 1.25933i) q^{69} -4.93904 q^{71} +(0.547956 + 0.547956i) q^{73} +(1.04769 + 1.30911i) q^{75} +(-9.41329 + 9.41329i) q^{77} +9.07438 q^{79} -8.00054 q^{81} +(10.7036 - 10.7036i) q^{83} +(-0.918022 - 1.02548i) q^{85} +(-1.75788 + 1.75788i) q^{87} -13.0332 q^{89} +8.99764i q^{91} +(-0.124668 - 0.124668i) q^{93} +(-4.28862 - 0.237125i) q^{95} +(-3.99177 - 3.99177i) q^{97} +16.0437 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3}+O(q^{10}) $ 16 * q + 4 * q^3	$ 16 q + 4 q^{3} + 12 q^{13} + 12 q^{23} + 36 q^{25} + 52 q^{27} - 8 q^{31} + 16 q^{35} - 48 q^{41} + 4 q^{47} + 24 q^{55} + 8 q^{71} - 52 q^{73} - 56 q^{75} - 64 q^{77} - 152 q^{81} + 28 q^{85} + 28 q^{87} + 84 q^{93} - 68 q^{95}+O(q^{100}) $ 16 * q + 4 * q^3 + 12 * q^13 + 12 * q^23 + 36 * q^25 + 52 * q^27 - 8 * q^31 + 16 * q^35 - 48 * q^41 + 4 * q^47 + 24 * q^55 + 8 * q^71 - 52 * q^73 - 56 * q^75 - 64 * q^77 - 152 * q^81 + 28 * q^85 + 28 * q^87 + 84 * q^93 - 68 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	0.237125	+	0.237125i	0.136904	+	0.136904i	0.772238	−	0.635334i	$-0.219137\pi$
$3$	0.237125	+	0.237125i	0.136904	+	0.136904i	−0.635334	+	0.772238i	$0.719137\pi$
$4$		0			0
$5$	−2.23266	−	0.123447i	−0.998475	−	0.0552073i
$5$	−2.23266	−	0.123447i	−0.998475	−	0.0552073i
$6$		0			0
$7$	1.69421	+	1.69421i	0.640350	+	0.640350i	0.950641	−	0.310292i	$-0.100427\pi$
$7$	1.69421	+	1.69421i	0.640350	+	0.640350i	−0.310292	+	0.950641i	$0.600427\pi$
$8$		0			0
$9$		−	2.88754i		−	0.962514i
$10$		0			0
$11$			5.55617i			1.67525i	0.546248	+	0.837624i	$0.316056\pi$
$11$			5.55617i			1.67525i	−0.546248	+	0.837624i	$0.683944\pi$
$12$		0			0
$13$	2.65542	+	2.65542i	0.736480	+	0.736480i	0.971895	−	0.235415i	$-0.0756450\pi$
$13$	2.65542	+	2.65542i	0.736480	+	0.736480i	−0.235415	+	0.971895i	$0.575645\pi$
$14$		0			0
$15$	−0.500147	−	0.558692i	−0.129137	−	0.144254i
$16$		0			0
$17$	0.435244	+	0.435244i	0.105562	+	0.105562i	0.757915	−	0.652353i	$-0.226218\pi$
$17$	0.435244	+	0.435244i	0.105562	+	0.105562i	−0.652353	+	0.757915i	$0.726218\pi$
$18$		0			0
$19$	1.92086			0.440676			0.220338	−	0.975424i	$-0.429284\pi$
$19$	1.92086			0.440676			0.220338	+	0.975424i	$0.429284\pi$
$20$		0			0
$21$			0.803478i			0.175333i
$22$		0			0
$23$	0.546205	+	4.76463i	0.113892	+	0.993493i
$23$	0.546205	+	4.76463i	0.113892	+	0.993493i
$24$		0			0
$25$	4.96952	+	0.551231i	0.993904	+	0.110246i
$26$		0			0
$27$	1.39608	−	1.39608i	0.268677	−	0.268677i
$28$		0			0
$29$			7.41329i			1.37661i	0.725420	+	0.688307i	$0.241646\pi$
$29$			7.41329i			1.37661i	−0.725420	+	0.688307i	$0.758354\pi$
$30$		0			0
$31$	−0.525750			−0.0944275			−0.0472137	−	0.998885i	$-0.515034\pi$
$31$	−0.525750			−0.0944275			−0.0472137	+	0.998885i	$0.515034\pi$
$32$		0			0
$33$	−1.31751	+	1.31751i	−0.229348	+	0.229348i
$34$		0			0
$35$	−3.57344	−	3.99173i	−0.604021	−	0.674725i
$36$		0			0
$37$	−1.94110	−	1.94110i	−0.319115	−	0.319115i	0.529312	−	0.848427i	$-0.322450\pi$
$37$	−1.94110	−	1.94110i	−0.319115	−	0.319115i	−0.848427	+	0.529312i	$0.822450\pi$
$38$		0			0
$39$			1.25933i			0.201654i
$40$		0			0
$41$	−6.78508			−1.05965			−0.529826	−	0.848106i	$-0.677743\pi$
$41$	−6.78508			−1.05965			−0.529826	+	0.848106i	$0.677743\pi$
$42$		0			0
$43$	1.88256	−	1.88256i	0.287087	−	0.287087i	−0.548840	−	0.835927i	$-0.684930\pi$
$43$	1.88256	−	1.88256i	0.287087	−	0.287087i	0.835927	+	0.548840i	$0.184930\pi$
$44$		0			0
$45$	−0.356459	+	6.44690i	−0.0531378	+	0.961047i
$46$		0			0
$47$	7.54296	−	7.54296i	1.10025	−	1.10025i	0.105874	−	0.994380i	$-0.466236\pi$
$47$	7.54296	−	7.54296i	1.10025	−	1.10025i	0.994380	−	0.105874i	$-0.0337640\pi$
$48$		0			0
$49$		−	1.25933i		−	0.179904i
$50$		0			0
$51$			0.206415i			0.0289038i
$52$		0			0
$53$	−0.467258	+	0.467258i	−0.0641828	+	0.0641828i	−0.738470	−	0.674287i	$-0.764451\pi$
$53$	−0.467258	+	0.467258i	−0.0641828	+	0.0641828i	0.674287	+	0.738470i	$0.264451\pi$
$54$		0			0
$55$	0.685894	−	12.4050i	0.0924859	−	1.67269i
$56$		0			0
$57$	0.455484	+	0.455484i	0.0603304	+	0.0603304i
$58$		0			0
$59$			7.72412i			1.00560i	0.864404	+	0.502798i	$0.167696\pi$
$59$			7.72412i			1.00560i	−0.864404	+	0.502798i	$0.832304\pi$
$60$		0			0
$61$		−	0.714153i		−	0.0914379i	−0.998954	−	0.0457189i	$-0.985442\pi$
$61$		−	0.714153i		−	0.0914379i	0.998954	−	0.0457189i	$-0.0145579\pi$
$62$		0			0
$63$	4.89209	−	4.89209i	0.616346	−	0.616346i
$64$		0			0
$65$	−5.60083	−	6.25644i	−0.694697	−	0.776016i
$66$		0			0
$67$	−4.97934	−	4.97934i	−0.608324	−	0.608324i	0.334184	−	0.942508i	$-0.391539\pi$
$67$	−4.97934	−	4.97934i	−0.608324	−	0.608324i	−0.942508	+	0.334184i	$0.891539\pi$
$68$		0			0
$69$	−1.00029	+	1.25933i	−0.120421	+	0.151606i
$70$		0			0
$71$	−4.93904			−0.586157			−0.293078	−	0.956088i	$-0.594680\pi$
$71$	−4.93904			−0.586157			−0.293078	+	0.956088i	$0.594680\pi$
$72$		0			0
$73$	0.547956	+	0.547956i	0.0641334	+	0.0641334i	0.738446	−	0.674313i	$-0.235560\pi$
$73$	0.547956	+	0.547956i	0.0641334	+	0.0641334i	−0.674313	+	0.738446i	$0.735560\pi$
$74$		0			0
$75$	1.04769	+	1.30911i	0.120977	+	0.151163i
$76$		0			0
$77$	−9.41329	+	9.41329i	−1.07274	+	1.07274i
$78$		0			0
$79$	9.07438			1.02095			0.510474	−	0.859893i	$-0.329470\pi$
$79$	9.07438			1.02095			0.510474	+	0.859893i	$0.329470\pi$
$80$		0			0
$81$	−8.00054			−0.888949
$82$		0			0
$83$	10.7036	−	10.7036i	1.17488	−	1.17488i	0.193842	−	0.981033i	$-0.437905\pi$
$83$	10.7036	−	10.7036i	1.17488	−	1.17488i	0.981033	−	0.193842i	$-0.0620951\pi$
$84$		0			0
$85$	−0.918022	−	1.02548i	−0.0995735	−	0.111229i
$86$		0			0
$87$	−1.75788	+	1.75788i	−0.188464	+	0.188464i
$88$		0			0
$89$	−13.0332			−1.38152			−0.690758	−	0.723086i	$-0.742723\pi$
$89$	−13.0332			−1.38152			−0.690758	+	0.723086i	$0.742723\pi$
$90$		0			0
$91$			8.99764i			0.943209i
$92$		0			0
$93$	−0.124668	−	0.124668i	−0.0129275	−	0.0129275i
$94$		0			0
$95$	−4.28862	−	0.237125i	−0.440004	−	0.0243285i
$96$		0			0
$97$	−3.99177	−	3.99177i	−0.405302	−	0.405302i	0.474794	−	0.880097i	$-0.342522\pi$
$97$	−3.99177	−	3.99177i	−0.405302	−	0.405302i	−0.880097	+	0.474794i	$0.842522\pi$
$98$		0			0
$99$	16.0437			1.61245
$100$		0			0
$101$	2.20492			0.219398			0.109699	−	0.993965i	$-0.465011\pi$
$101$	2.20492			0.219398			0.109699	+	0.993965i	$0.465011\pi$
$102$		0			0
$103$	2.08268	−	2.08268i	0.205212	−	0.205212i	−0.597016	−	0.802229i	$-0.703647\pi$
$103$	2.08268	−	2.08268i	0.205212	−	0.205212i	0.802229	+	0.597016i	$0.203647\pi$
$104$		0			0
$105$	0.0991871	−	1.79389i	0.00967967	−	0.175066i
$106$		0			0
$107$	−2.68603	−	2.68603i	−0.259669	−	0.259669i	0.565251	−	0.824919i	$-0.308779\pi$
$107$	−2.68603	−	2.68603i	−0.259669	−	0.259669i	−0.824919	+	0.565251i	$0.808779\pi$
$108$		0			0
$109$	7.99735			0.766007			0.383004	−	0.923747i	$-0.374890\pi$
$109$	7.99735			0.766007			0.383004	+	0.923747i	$0.374890\pi$
$110$		0			0
$111$		−	0.920567i		−	0.0873764i
$112$		0			0
$113$	12.9629	−	12.9629i	1.21944	−	1.21944i	0.251618	−	0.967827i	$-0.419037\pi$
$113$	12.9629	−	12.9629i	1.21944	−	1.21944i	0.967827	−	0.251618i	$-0.0809628\pi$
$114$		0			0
$115$	−0.631309	−	10.7052i	−0.0588698	−	0.998266i
$116$		0			0
$117$	7.66763	−	7.66763i	0.708872	−	0.708872i
$118$		0			0
$119$			1.47479i			0.135194i
$120$		0			0
$121$	−19.8710			−1.80645
$122$		0			0
$123$	−1.60891	−	1.60891i	−0.145071	−	0.145071i
$124$		0			0
$125$	−11.0272	−	1.84418i	−0.986302	−	0.164949i
$126$		0			0
$127$	−3.75288	+	3.75288i	−0.333014	+	0.333014i	−0.853730	−	0.520716i	$-0.825665\pi$
$127$	−3.75288	+	3.75288i	−0.333014	+	0.333014i	0.520716	+	0.853730i	$0.325665\pi$
$128$		0			0
$129$	0.892802			0.0786069
$130$		0			0
$131$	5.77562			0.504619			0.252309	−	0.967647i	$-0.418810\pi$
$131$	5.77562			0.504619			0.252309	+	0.967647i	$0.418810\pi$
$132$		0			0
$133$	3.25433	+	3.25433i	0.282187	+	0.282187i
$134$		0			0
$135$	−3.28932	+	2.94464i	−0.283100	+	0.253434i
$136$		0			0
$137$	−10.7484	−	10.7484i	−0.918294	−	0.918294i	0.0786117	−	0.996905i	$-0.474951\pi$
$137$	−10.7484	−	10.7484i	−0.918294	−	0.918294i	−0.996905	+	0.0786117i	$0.974951\pi$
$138$		0			0
$139$		−	10.9390i		−	0.927838i	−0.885878	−	0.463919i	$-0.846443\pi$
$139$		−	10.9390i		−	0.927838i	0.885878	−	0.463919i	$-0.153557\pi$
$140$		0			0
$141$	3.57725			0.301259
$142$		0			0
$143$	−14.7539	+	14.7539i	−1.23379	+	1.23379i
$144$		0			0
$145$	0.915151	−	16.5513i	0.0759992	−	1.37451i
$146$		0			0
$147$	0.298619	−	0.298619i	0.0246297	−	0.0246297i
$148$		0			0
$149$	−13.5132			−1.10704			−0.553521	−	0.832835i	$-0.686716\pi$
$149$	−13.5132			−1.10704			−0.553521	+	0.832835i	$0.686716\pi$
$150$		0			0
$151$	−18.2333			−1.48381			−0.741904	−	0.670507i	$-0.766077\pi$
$151$	−18.2333			−1.48381			−0.741904	+	0.670507i	$0.766077\pi$
$152$		0			0
$153$	1.25679	−	1.25679i	0.101605	−	0.101605i
$154$		0			0
$155$	1.17382	+	0.0649024i	0.0942834	+	0.00521309i
$156$		0			0
$157$	13.6686	+	13.6686i	1.09087	+	1.09087i	0.995436	+	0.0954344i	$0.0304240\pi$
$157$	13.6686	+	13.6686i	1.09087	+	1.09087i	0.0954344	+	0.995436i	$0.469576\pi$
$158$		0			0
$159$	−0.221597			−0.0175738
$160$		0			0
$161$	−7.14687	+	8.99764i	−0.563253	+	0.709114i
$162$		0			0
$163$	−10.0122	−	10.0122i	−0.784217	−	0.784217i	0.196322	−	0.980539i	$-0.437100\pi$
$163$	−10.0122	−	10.0122i	−0.784217	−	0.784217i	−0.980539	+	0.196322i	$0.937100\pi$
$164$		0			0
$165$	3.10418	−	2.77890i	0.241660	−	0.216337i
$166$		0			0
$167$	7.66763	−	7.66763i	0.593339	−	0.593339i	−0.345193	−	0.938532i	$-0.612187\pi$
$167$	7.66763	−	7.66763i	0.593339	−	0.593339i	0.938532	+	0.345193i	$0.112187\pi$
$168$		0			0
$169$			1.10246i			0.0848048i
$170$		0			0
$171$		−	5.54657i		−	0.424157i
$172$		0			0
$173$	16.2449	+	16.2449i	1.23508	+	1.23508i	0.961990	+	0.273085i	$0.0880441\pi$
$173$	16.2449	+	16.2449i	1.23508	+	1.23508i	0.273085	+	0.961990i	$0.411956\pi$
$174$		0			0
$175$	7.48549	+	9.35329i	0.565850	+	0.707042i
$176$		0			0
$177$	−1.83158	+	1.83158i	−0.137670	+	0.137670i
$178$		0			0
$179$			14.7851i			1.10509i	0.833483	+	0.552544i	$0.186343\pi$
$179$			14.7851i			1.10509i	−0.833483	+	0.552544i	$0.813657\pi$
$180$		0			0
$181$			24.2349i			1.80136i	0.434480	+	0.900681i	$0.356932\pi$
$181$			24.2349i			1.80136i	−0.434480	+	0.900681i	$0.643068\pi$
$182$		0			0
$183$	0.169344	−	0.169344i	0.0125182	−	0.0125182i
$184$		0			0
$185$	4.09419	+	4.57344i	0.301011	+	0.336246i
$186$		0			0
$187$	−2.41829	+	2.41829i	−0.176843	+	0.176843i
$188$		0			0
$189$	4.73051			0.344094
$190$		0			0
$191$		−	18.3062i		−	1.32459i	−0.749243	−	0.662295i	$-0.769582\pi$
$191$		−	18.3062i		−	1.32459i	0.749243	−	0.662295i	$-0.230418\pi$
$192$		0			0
$193$	15.6339	+	15.6339i	1.12535	+	1.12535i	0.990923	+	0.134427i	$0.0429195\pi$
$193$	15.6339	+	15.6339i	1.12535	+	1.12535i	0.134427	+	0.990923i	$0.457080\pi$
$194$		0			0
$195$	0.155461	−	2.81166i	0.0111328	−	0.201347i
$196$		0			0
$197$	14.2621	−	14.2621i	1.01613	−	1.01613i	0.0162638	−	0.999868i	$-0.494823\pi$
$197$	14.2621	−	14.2621i	1.01613	−	1.01613i	0.999868	−	0.0162638i	$-0.00517716\pi$
$198$		0			0
$199$	20.5102			1.45393			0.726966	−	0.686674i	$-0.240930\pi$
$199$	20.5102			1.45393			0.726966	+	0.686674i	$0.240930\pi$
$200$		0			0
$201$		−	2.36146i		−	0.166564i
$202$		0			0
$203$	−12.5596	+	12.5596i	−0.881514	+	0.881514i
$204$		0			0
$205$	15.1488	+	0.837600i	1.05804	+	0.0585005i
$206$		0			0
$207$	13.7581	−	1.57719i	0.956252	−	0.109622i
$208$		0			0
$209$			10.6726i			0.738241i
$210$		0			0
$211$	15.1978			1.04626			0.523131	−	0.852252i	$-0.324764\pi$
$211$	15.1978			1.04626			0.523131	+	0.852252i	$0.324764\pi$
$212$		0			0
$213$	−1.17117	−	1.17117i	−0.0802473	−	0.0802473i
$214$		0			0
$215$	−4.43550	+	3.97071i	−0.302499	+	0.270800i
$216$		0			0
$217$	−0.890729	−	0.890729i	−0.0604666	−	0.0604666i
$218$		0			0
$219$			0.259868i			0.0175603i
$220$		0			0
$221$			2.31151i			0.155489i
$222$		0			0
$223$	11.3103	+	11.3103i	0.757393	+	0.757393i	0.975847	−	0.218454i	$-0.0701013\pi$
$223$	11.3103	+	11.3103i	0.757393	+	0.757393i	−0.218454	+	0.975847i	$0.570101\pi$
$224$		0			0
$225$	1.59170	−	14.3497i	0.106114	−	0.956647i
$226$		0			0
$227$	−1.68026	−	1.68026i	−0.111523	−	0.111523i	0.649143	−	0.760666i	$-0.275127\pi$
$227$	−1.68026	−	1.68026i	−0.111523	−	0.111523i	−0.760666	+	0.649143i	$0.775127\pi$
$228$		0			0
$229$	−18.8881			−1.24816			−0.624080	−	0.781360i	$-0.714526\pi$
$229$	−18.8881			−1.24816			−0.624080	+	0.781360i	$0.714526\pi$
$230$		0			0
$231$	−4.46426			−0.293726
$232$		0			0
$233$	−5.07371	−	5.07371i	−0.332390	−	0.332390i	0.521104	−	0.853493i	$-0.325520\pi$
$233$	−5.07371	−	5.07371i	−0.332390	−	0.332390i	−0.853493	+	0.521104i	$0.825520\pi$
$234$		0			0
$235$	−17.7720	+	15.9097i	−1.15932	+	1.03783i
$236$		0			0
$237$	2.15176	+	2.15176i	0.139772	+	0.139772i
$238$		0			0
$239$			18.9325i			1.22464i	0.790610	+	0.612321i	$0.209764\pi$
$239$			18.9325i			1.22464i	−0.790610	+	0.612321i	$0.790236\pi$
$240$		0			0
$241$			9.89044i			0.637100i	0.947906	+	0.318550i	$0.103196\pi$
$241$			9.89044i			0.637100i	−0.947906	+	0.318550i	$0.896804\pi$
$242$		0			0
$243$	−6.08538	−	6.08538i	−0.390377	−	0.390377i
$244$		0			0
$245$	−0.155461	+	2.81166i	−0.00993204	+	0.179630i
$246$		0			0
$247$	5.10068	+	5.10068i	0.324549	+	0.324549i
$248$		0			0
$249$	5.07619			0.321691
$250$		0			0
$251$			3.62272i			0.228664i	0.993443	+	0.114332i	$0.0364728\pi$
$251$			3.62272i			0.228664i	−0.993443	+	0.114332i	$0.963527\pi$
$252$		0			0
$253$	−26.4731	+	3.03481i	−1.66435	+	0.190797i
$254$		0			0
$255$	0.0254813	−	0.460853i	0.00159570	−	0.0288598i
$256$		0			0
$257$	−5.86034	+	5.86034i	−0.365558	+	0.365558i	−0.865854	−	0.500296i	$-0.833224\pi$
$257$	−5.86034	+	5.86034i	−0.365558	+	0.365558i	0.500296	+	0.865854i	$0.333224\pi$
$258$		0			0
$259$		−	6.57725i		−	0.408690i
$260$		0			0
$261$	21.4062			1.32501
$262$		0			0
$263$	−15.9661	+	15.9661i	−0.984513	+	0.984513i	−0.999882	−	0.0153685i	$-0.995108\pi$
$263$	−15.9661	+	15.9661i	−0.984513	+	0.984513i	0.0153685	+	0.999882i	$0.495108\pi$
$264$		0			0
$265$	1.10091	−	0.985546i	0.0676283	−	0.0605416i
$266$		0			0
$267$	−3.09050	−	3.09050i	−0.189135	−	0.189135i
$268$		0			0
$269$		−	27.5442i		−	1.67940i	−0.543053	−	0.839699i	$-0.682732\pi$
$269$		−	27.5442i		−	1.67940i	0.543053	−	0.839699i	$-0.317268\pi$
$270$		0			0
$271$	23.2233			1.41072			0.705359	−	0.708851i	$-0.250786\pi$
$271$	23.2233			1.41072			0.705359	+	0.708851i	$0.250786\pi$
$272$		0			0
$273$	−2.13357	+	2.13357i	−0.129129	+	0.129129i
$274$		0			0
$275$	−3.06273	+	27.6115i	−0.184690	+	1.66504i
$276$		0			0
$277$	−9.22558	+	9.22558i	−0.554311	+	0.554311i	−0.927682	−	0.373371i	$-0.878202\pi$
$277$	−9.22558	+	9.22558i	−0.554311	+	0.554311i	0.373371	+	0.927682i	$0.378202\pi$
$278$		0			0
$279$			1.51813i			0.0908878i
$280$		0			0
$281$			4.47913i			0.267203i	0.991035	+	0.133601i	$0.0426542\pi$
$281$			4.47913i			0.267203i	−0.991035	+	0.133601i	$0.957346\pi$
$282$		0			0
$283$	13.0277	−	13.0277i	0.774417	−	0.774417i	−0.204458	−	0.978875i	$-0.565543\pi$
$283$	13.0277	−	13.0277i	0.774417	−	0.774417i	0.978875	+	0.204458i	$0.0655432\pi$
$284$		0			0
$285$	−0.960712	−	1.07317i	−0.0569077	−	0.0635690i
$286$		0			0
$287$	−11.4953	−	11.4953i	−0.678548	−	0.678548i
$288$		0			0
$289$		−	16.6211i		−	0.977713i
$290$		0			0
$291$		−	1.89310i		−	0.110975i
$292$		0			0
$293$	17.5250	−	17.5250i	1.02382	−	1.02382i	0.0241147	−	0.999709i	$-0.492323\pi$
$293$	17.5250	−	17.5250i	1.02382	−	1.02382i	0.999709	−	0.0241147i	$-0.00767670\pi$
$294$		0			0
$295$	0.953522	−	17.2453i	0.0555162	−	1.00406i
$296$		0			0
$297$	7.75688	+	7.75688i	0.450100	+	0.450100i
$298$		0			0
$299$	−11.2017	+	14.1025i	−0.647809	+	0.815566i
$300$		0			0
$301$	6.37888			0.367672
$302$		0			0
$303$	0.522843	+	0.522843i	0.0300365	+	0.0300365i
$304$		0			0
$305$	−0.0881602	+	1.59446i	−0.00504804	+	0.0912984i
$306$		0			0
$307$	10.4598	−	10.4598i	0.596972	−	0.596972i	−0.342534	−	0.939506i	$-0.611285\pi$
$307$	10.4598	−	10.4598i	0.596972	−	0.596972i	0.939506	+	0.342534i	$0.111285\pi$
$308$		0			0
$309$	0.987711			0.0561889
$310$		0			0
$311$	10.5158			0.596294			0.298147	−	0.954520i	$-0.403631\pi$
$311$	10.5158			0.596294			0.298147	+	0.954520i	$0.403631\pi$
$312$		0			0
$313$	21.2497	−	21.2497i	1.20110	−	1.20110i	0.227271	−	0.973832i	$-0.427020\pi$
$313$	21.2497	−	21.2497i	1.20110	−	1.20110i	0.973832	−	0.227271i	$-0.0729803\pi$
$314$		0			0
$315$	−11.5263	+	10.3185i	−0.649433	+	0.581379i
$316$		0			0
$317$	−12.9785	+	12.9785i	−0.728943	+	0.728943i	−0.970409	−	0.241466i	$-0.922372\pi$
$317$	−12.9785	+	12.9785i	−0.728943	+	0.728943i	0.241466	+	0.970409i	$0.422372\pi$
$318$		0			0
$319$	−41.1895			−2.30617
$320$		0			0
$321$		−	1.27385i		−	0.0710995i
$322$		0			0
$323$	0.836044	+	0.836044i	0.0465187	+	0.0465187i
$324$		0			0
$325$	11.7324	+	14.6599i	0.650796	+	0.813184i
$326$		0			0
$327$	1.89637	+	1.89637i	0.104870	+	0.104870i
$328$		0			0
$329$	25.5587			1.40909
$330$		0			0
$331$	−4.06804			−0.223600			−0.111800	−	0.993731i	$-0.535662\pi$
$331$	−4.06804			−0.223600			−0.111800	+	0.993731i	$0.535662\pi$
$332$		0			0
$333$	−5.60501	+	5.60501i	−0.307153	+	0.307153i
$334$		0			0
$335$	10.5025	+	11.7319i	0.573812	+	0.640980i
$336$		0			0
$337$	9.26903	+	9.26903i	0.504916	+	0.504916i	0.912962	−	0.408046i	$-0.133790\pi$
$337$	9.26903	+	9.26903i	0.504916	+	0.504916i	−0.408046	+	0.912962i	$0.633790\pi$
$338$		0			0
$339$	6.14765			0.333894
$340$		0			0
$341$		−	2.92115i		−	0.158189i
$342$		0			0
$343$	13.9930	−	13.9930i	0.755551	−	0.755551i
$344$		0			0
$345$	2.38877	−	2.68817i	0.128607	−	0.144726i
$346$		0			0
$347$	−16.6211	+	16.6211i	−0.892269	+	0.892269i	−0.994736	−	0.102468i	$-0.967326\pi$
$347$	−16.6211	+	16.6211i	−0.892269	+	0.892269i	0.102468	+	0.994736i	$0.467326\pi$
$348$		0			0
$349$		−	19.1918i		−	1.02731i	−0.857995	−	0.513657i	$-0.828290\pi$
$349$		−	19.1918i		−	1.02731i	0.857995	−	0.513657i	$-0.171710\pi$
$350$		0			0
$351$	7.41437			0.395750
$352$		0			0
$353$	−23.1662	−	23.1662i	−1.23301	−	1.23301i	−0.962802	−	0.270209i	$-0.912907\pi$
$353$	−23.1662	−	23.1662i	−1.23301	−	1.23301i	−0.270209	−	0.962802i	$-0.587093\pi$
$354$		0			0
$355$	11.0272	+	0.609712i	0.585263	+	0.0323601i
$356$		0			0
$357$	−0.349709	+	0.349709i	−0.0185086	+	0.0185086i
$358$		0			0
$359$	22.3170			1.17785			0.588923	−	0.808189i	$-0.299552\pi$
$359$	22.3170			1.17785			0.588923	+	0.808189i	$0.299552\pi$
$360$		0			0
$361$	−15.3103			−0.805805
$362$		0			0
$363$	−4.71191	−	4.71191i	−0.247311	−	0.247311i
$364$		0			0
$365$	−1.15575	−	1.29104i	−0.0604950	−	0.0675762i
$366$		0			0
$367$	−11.2742	−	11.2742i	−0.588506	−	0.588506i	0.348721	−	0.937227i	$-0.386616\pi$
$367$	−11.2742	−	11.2742i	−0.588506	−	0.588506i	−0.937227	+	0.348721i	$0.886616\pi$
$368$		0			0
$369$			19.5922i			1.01993i
$370$		0			0
$371$	−1.58326			−0.0821989
$372$		0			0
$373$	−24.0730	+	24.0730i	−1.24645	+	1.24645i	−0.289180	+	0.957275i	$0.593383\pi$
$373$	−24.0730	+	24.0730i	−1.24645	+	1.24645i	−0.957275	+	0.289180i	$0.906617\pi$
$374$		0			0
$375$	−2.17752	−	3.05213i	−0.112447	−	0.157611i
$376$		0			0
$377$	−19.6854	+	19.6854i	−1.01385	+	1.01385i
$378$		0			0
$379$	−26.7558			−1.37435			−0.687176	−	0.726491i	$-0.741150\pi$
$379$	−26.7558			−1.37435			−0.687176	+	0.726491i	$0.741150\pi$
$380$		0			0
$381$	−1.77980			−0.0911821
$382$		0			0
$383$	−3.73641	+	3.73641i	−0.190921	+	0.190921i	−0.796094	−	0.605173i	$-0.793104\pi$
$383$	−3.73641	+	3.73641i	−0.190921	+	0.190921i	0.605173	+	0.796094i	$0.293104\pi$
$384$		0			0
$385$	22.1787	−	19.8546i	1.13033	−	1.01188i
$386$		0			0
$387$	−5.43596	−	5.43596i	−0.276325	−	0.276325i
$388$		0			0
$389$	−3.31180			−0.167915			−0.0839575	−	0.996469i	$-0.526756\pi$
$389$	−3.31180			−0.167915			−0.0839575	+	0.996469i	$0.526756\pi$
$390$		0			0
$391$	−1.83604	+	2.31151i	−0.0928527	+	0.116898i
$392$		0			0
$393$	1.36955	+	1.36955i	0.0690844	+	0.0690844i
$394$		0			0
$395$	−20.2600	−	1.12021i	−1.01939	−	0.0563638i
$396$		0			0
$397$	8.65488	−	8.65488i	0.434376	−	0.434376i	−0.455738	−	0.890114i	$-0.650625\pi$
$397$	8.65488	−	8.65488i	0.434376	−	0.434376i	0.890114	+	0.455738i	$0.150625\pi$
$398$		0			0
$399$			1.54337i			0.0772651i
$400$		0			0
$401$		−	22.7142i		−	1.13430i	−0.823616	−	0.567148i	$-0.808047\pi$
$401$		−	22.7142i		−	1.13430i	0.823616	−	0.567148i	$-0.191953\pi$
$402$		0			0
$403$	−1.39608	−	1.39608i	−0.0695439	−	0.0695439i
$404$		0			0
$405$	17.8625	+	0.987645i	0.887593	+	0.0490765i
$406$		0			0
$407$	10.7851	−	10.7851i	0.534597	−	0.534597i
$408$		0			0
$409$		−	30.1114i		−	1.48891i	−0.667671	−	0.744457i	$-0.732709\pi$
$409$		−	30.1114i		−	1.48891i	0.667671	−	0.744457i	$-0.267291\pi$
$410$		0			0
$411$		−	5.09741i		−	0.251437i
$412$		0			0
$413$	−13.0863	+	13.0863i	−0.643933	+	0.643933i
$414$		0			0
$415$	−25.2189	+	22.5762i	−1.23795	+	1.10822i
$416$		0			0
$417$	2.59392	−	2.59392i	0.127025	−	0.127025i
$418$		0			0
$419$	−8.68672			−0.424374			−0.212187	−	0.977229i	$-0.568059\pi$
$419$	−8.68672			−0.424374			−0.212187	+	0.977229i	$0.568059\pi$
$420$		0			0
$421$		−	17.8878i		−	0.871798i	−0.899996	−	0.435899i	$-0.856431\pi$
$421$		−	17.8878i		−	0.871798i	0.899996	−	0.435899i	$-0.143569\pi$
$422$		0			0
$423$	−21.7806	−	21.7806i	−1.05901	−	1.05901i
$424$		0			0
$425$	1.92304	+	2.40288i	0.0932809	+	0.116557i
$426$		0			0
$427$	1.20992	−	1.20992i	0.0585522	−	0.0585522i
$428$		0			0
$429$	−6.99706			−0.337821
$430$		0			0
$431$		−	32.4013i		−	1.56071i	−0.625335	−	0.780357i	$-0.715037\pi$
$431$		−	32.4013i		−	1.56071i	0.625335	−	0.780357i	$-0.284963\pi$
$432$		0			0
$433$	11.5838	−	11.5838i	0.556684	−	0.556684i	−0.371678	−	0.928362i	$-0.621217\pi$
$433$	11.5838	−	11.5838i	0.556684	−	0.556684i	0.928362	+	0.371678i	$0.121217\pi$
$434$		0			0
$435$	4.14174	−	3.70773i	0.198581	−	0.177772i
$436$		0			0
$437$	1.04918	+	9.15218i	0.0501893	+	0.437808i
$438$		0			0
$439$			9.72122i			0.463968i	0.972720	+	0.231984i	$0.0745218\pi$
$439$			9.72122i			0.463968i	−0.972720	+	0.231984i	$0.925478\pi$
$440$		0			0
$441$	−3.63637			−0.173161
$442$		0			0
$443$	13.9657	+	13.9657i	0.663531	+	0.663531i	0.956211	−	0.292680i	$-0.0945470\pi$
$443$	13.9657	+	13.9657i	0.663531	+	0.663531i	−0.292680	+	0.956211i	$0.594547\pi$
$444$		0			0
$445$	29.0987	+	1.60891i	1.37941	+	0.0762698i
$446$		0			0
$447$	−3.20431	−	3.20431i	−0.151559	−	0.151559i
$448$		0			0
$449$		−	35.4406i		−	1.67255i	−0.548313	−	0.836273i	$-0.684730\pi$
$449$		−	35.4406i		−	1.67255i	0.548313	−	0.836273i	$-0.315270\pi$
$450$		0			0
$451$		−	37.6990i		−	1.77518i
$452$		0			0
$453$	−4.32358	−	4.32358i	−0.203139	−	0.203139i
$454$		0			0
$455$	1.11073	−	20.0887i	0.0520720	−	0.941771i
$456$		0			0
$457$	3.87672	+	3.87672i	0.181345	+	0.181345i	0.791942	−	0.610597i	$-0.209070\pi$
$457$	3.87672	+	3.87672i	0.181345	+	0.181345i	−0.610597	+	0.791942i	$0.709070\pi$
$458$		0			0
$459$	1.21528			0.0567242
$460$		0			0
$461$	−2.32738			−0.108397			−0.0541983	−	0.998530i	$-0.517260\pi$
$461$	−2.32738			−0.108397			−0.0541983	+	0.998530i	$0.517260\pi$
$462$		0			0
$463$	−4.77509	−	4.77509i	−0.221917	−	0.221917i	0.587388	−	0.809305i	$-0.300156\pi$
$463$	−4.77509	−	4.77509i	−0.221917	−	0.221917i	−0.809305	+	0.587388i	$0.800156\pi$
$464$		0			0
$465$	0.262952	+	0.293732i	0.0121941	+	0.0136215i
$466$		0			0
$467$	13.6067	+	13.6067i	0.629644	+	0.629644i	0.947978	−	0.318335i	$-0.103124\pi$
$467$	13.6067	+	13.6067i	0.629644	+	0.629644i	−0.318335	+	0.947978i	$0.603124\pi$
$468$		0			0
$469$		−	16.8721i		−	0.779080i
$470$		0			0
$471$			6.48232i			0.298689i
$472$		0			0
$473$	10.4598	+	10.4598i	0.480942	+	0.480942i
$474$		0			0
$475$	9.54576	+	1.05884i	0.437989	+	0.0485828i
$476$		0			0
$477$	1.34923	+	1.34923i	0.0617769	+	0.0617769i
$478$		0			0
$479$	−2.31151			−0.105616			−0.0528078	−	0.998605i	$-0.516817\pi$
$479$	−2.31151			−0.105616			−0.0528078	+	0.998605i	$0.516817\pi$
$480$		0			0
$481$		−	10.3089i		−	0.470043i
$482$		0			0
$483$	−3.82827	+	0.438863i	−0.174192	+	0.0199690i
$484$		0			0
$485$	8.41948	+	9.40502i	0.382309	+	0.427060i
$486$		0			0
$487$	−22.0687	+	22.0687i	−1.00003	+	1.00003i	−2.86468e−5		1.00000i	$0.500009\pi$
$487$	−22.0687	+	22.0687i	−1.00003	+	1.00003i	−1.00000		2.86468e-5i	$0.999991\pi$
$488$		0			0
$489$		−	4.74829i		−	0.214725i
$490$		0			0
$491$	2.01945			0.0911366			0.0455683	−	0.998961i	$-0.485490\pi$
$491$	2.01945			0.0911366			0.0455683	+	0.998961i	$0.485490\pi$
$492$		0			0
$493$	−3.22659	+	3.22659i	−0.145318	+	0.145318i
$494$		0			0
$495$	−35.8200	−	1.98055i	−1.60999	−	0.0890190i
$496$		0			0
$497$	−8.36776	−	8.36776i	−0.375345	−	0.375345i
$498$		0			0
$499$			11.8266i			0.529431i	0.964327	+	0.264715i	$0.0852780\pi$
$499$			11.8266i			0.529431i	−0.964327	+	0.264715i	$0.914722\pi$
$500$		0			0
$501$	3.63637			0.162461
$502$		0			0
$503$	−17.6409	+	17.6409i	−0.786569	+	0.786569i	−0.980930	−	0.194361i	$-0.937737\pi$
$503$	−17.6409	+	17.6409i	−0.786569	+	0.786569i	0.194361	+	0.980930i	$0.437737\pi$
$504$		0			0
$505$	−4.92284	−	0.272192i	−0.219064	−	0.0121124i
$506$		0			0
$507$	−0.261421	+	0.261421i	−0.0116101	+	0.0116101i
$508$		0			0
$509$		−	3.36888i		−	0.149323i	−0.997209	−	0.0746615i	$-0.976212\pi$
$509$		−	3.36888i		−	0.149323i	0.997209	−	0.0746615i	$-0.0237876\pi$
$510$		0			0
$511$			1.85670i			0.0821356i
$512$		0			0
$513$	2.68168	−	2.68168i	0.118399	−	0.118399i
$514$		0			0
$515$	−4.90701	+	4.39281i	−0.216229	+	0.193570i
$516$		0			0
$517$	41.9099	+	41.9099i	1.84320	+	1.84320i
$518$		0			0
$519$			7.70414i			0.338174i
$520$		0			0
$521$		−	38.1023i		−	1.66929i	−0.550787	−	0.834646i	$-0.685673\pi$
$521$		−	38.1023i		−	1.66929i	0.550787	−	0.834646i	$-0.314327\pi$
$522$		0			0
$523$	10.2246	−	10.2246i	0.447090	−	0.447090i	−0.447296	−	0.894386i	$-0.647613\pi$
$523$	10.2246	−	10.2246i	0.447090	−	0.447090i	0.894386	+	0.447296i	$0.147613\pi$
$524$		0			0
$525$	−0.442902	+	3.99290i	−0.0193298	+	0.174264i
$526$		0			0
$527$	−0.228830	−	0.228830i	−0.00996797	−	0.00996797i
$528$		0			0
$529$	−22.4033	+	5.20492i	−0.974057	+	0.226301i
$530$		0			0
$531$	22.3037			0.967900
$532$		0			0
$533$	−18.0172	−	18.0172i	−0.780412	−	0.780412i
$534$		0			0
$535$	5.66541	+	6.32858i	0.244937	+	0.273608i
$536$		0			0
$537$	−3.50591	+	3.50591i	−0.151291	+	0.151291i
$538$		0			0
$539$	6.99706			0.301385
$540$		0			0
$541$	14.6046			0.627900			0.313950	−	0.949440i	$-0.398348\pi$
$541$	14.6046			0.627900			0.313950	+	0.949440i	$0.398348\pi$
$542$		0			0
$543$	−5.74669	+	5.74669i	−0.246614	+	0.246614i
$544$		0			0
$545$	−17.8553	−	0.987251i	−0.764839	−	0.0422892i
$546$		0			0
$547$	−0.136753	+	0.136753i	−0.00584714	+	0.00584714i	−0.710024	−	0.704177i	$-0.751316\pi$
$547$	−0.136753	+	0.136753i	−0.00584714	+	0.00584714i	0.704177	+	0.710024i	$0.251316\pi$
$548$		0			0
$549$	−2.06215			−0.0880103
$550$		0			0
$551$			14.2399i			0.606640i
$552$		0			0
$553$	15.3739	+	15.3739i	0.653764	+	0.653764i
$554$		0			0
$555$	−0.113642	+	2.05531i	−0.00482382	+	0.0872431i
$556$		0			0
$557$	−27.2348	−	27.2348i	−1.15398	−	1.15398i	−0.985748	−	0.168227i	$-0.946196\pi$
$557$	−27.2348	−	27.2348i	−1.15398	−	1.15398i	−0.168227	−	0.985748i	$-0.553804\pi$
$558$		0			0
$559$	9.99794			0.422868
$560$		0			0
$561$	−1.14687			−0.0484211
$562$		0			0
$563$	−11.7093	+	11.7093i	−0.493487	+	0.493487i	−0.909403	−	0.415916i	$-0.863461\pi$
$563$	−11.7093	+	11.7093i	−0.493487	+	0.493487i	0.415916	+	0.909403i	$0.363461\pi$
$564$		0			0
$565$	−30.5419	+	27.3414i	−1.28491	+	1.15026i
$566$		0			0
$567$	−13.5546	−	13.5546i	−0.569238	−	0.569238i
$568$		0			0
$569$	28.0392			1.17546			0.587732	−	0.809055i	$-0.300021\pi$
$569$	28.0392			1.17546			0.587732	+	0.809055i	$0.300021\pi$
$570$		0			0
$571$		−	5.76557i		−	0.241281i	−0.992696	−	0.120641i	$-0.961505\pi$
$571$		−	5.76557i		−	0.241281i	0.992696	−	0.120641i	$-0.0384949\pi$
$572$		0			0
$573$	4.34086	−	4.34086i	0.181342	−	0.181342i
$574$		0			0
$575$	0.0879670	+	23.9790i	0.00366848	+	0.999993i
$576$		0			0
$577$	−12.9662	+	12.9662i	−0.539792	+	0.539792i	−0.923468	−	0.383676i	$-0.874658\pi$
$577$	−12.9662	+	12.9662i	−0.539792	+	0.539792i	0.383676	+	0.923468i	$0.374658\pi$
$578$		0			0
$579$			7.41437i			0.308131i
$580$		0			0
$581$	36.2683			1.50466
$582$		0			0
$583$	−2.59616	−	2.59616i	−0.107522	−	0.107522i
$584$		0			0
$585$	−18.0657	+	16.1726i	−0.746926	+	0.668656i
$586$		0			0
$587$	22.6919	−	22.6919i	0.936596	−	0.936596i	−0.0615105	−	0.998106i	$-0.519592\pi$
$587$	22.6919	−	22.6919i	0.936596	−	0.936596i	0.998106	+	0.0615105i	$0.0195918\pi$
$588$		0			0
$589$	−1.00989			−0.0416119
$590$		0			0
$591$	6.76380			0.278225
$592$		0			0
$593$	−12.5163	−	12.5163i	−0.513983	−	0.513983i	0.401762	−	0.915744i	$-0.368398\pi$
$593$	−12.5163	−	12.5163i	−0.513983	−	0.513983i	−0.915744	+	0.401762i	$0.868398\pi$
$594$		0			0
$595$	0.182058	−	3.29270i	0.00746367	−	0.134987i
$596$		0			0
$597$	4.86349	+	4.86349i	0.199049	+	0.199049i
$598$		0			0
$599$		−	20.5607i		−	0.840088i	−0.907504	−	0.420044i	$-0.862015\pi$
$599$		−	20.5607i		−	0.840088i	0.907504	−	0.420044i	$-0.137985\pi$
$600$		0			0
$601$	−4.89045			−0.199486			−0.0997428	−	0.995013i	$-0.531802\pi$
$601$	−4.89045			−0.199486			−0.0997428	+	0.995013i	$0.531802\pi$
$602$		0			0
$603$	−14.3781	+	14.3781i	−0.585520	+	0.585520i
$604$		0			0
$605$	44.3651	+	2.45302i	1.80370	+	0.0997295i
$606$		0			0
$607$	−1.79663	+	1.79663i	−0.0729229	+	0.0729229i	−0.742628	−	0.669705i	$-0.766421\pi$
$607$	−1.79663	+	1.79663i	−0.0729229	+	0.0729229i	0.669705	+	0.742628i	$0.266421\pi$
$608$		0			0
$609$	−5.95641			−0.241366
$610$		0			0
$611$	40.0594			1.62063
$612$		0			0
$613$	14.4325	−	14.4325i	0.582922	−	0.582922i	−0.352783	−	0.935705i	$-0.614765\pi$
$613$	14.4325	−	14.4325i	0.582922	−	0.582922i	0.935705	+	0.352783i	$0.114765\pi$
$614$		0			0
$615$	3.39354	+	3.79077i	0.136841	+	0.152859i
$616$		0			0
$617$	11.3571	+	11.3571i	0.457218	+	0.457218i	0.897741	−	0.440523i	$-0.145207\pi$
$617$	11.3571	+	11.3571i	0.457218	+	0.457218i	−0.440523	+	0.897741i	$0.645207\pi$
$618$		0			0
$619$	10.4230			0.418934			0.209467	−	0.977816i	$-0.432827\pi$
$619$	10.4230			0.418934			0.209467	+	0.977816i	$0.432827\pi$
$620$		0			0
$621$	7.41437	+	5.88927i	0.297528	+	0.236328i
$622$		0			0
$623$	−22.0809	−	22.0809i	−0.884653	−	0.884653i
$624$		0			0
$625$	24.3923	+	5.47871i	0.975692	+	0.219148i
$626$		0			0
$627$	−2.53075	+	2.53075i	−0.101068	+	0.101068i
$628$		0			0
$629$		−	1.68971i		−	0.0673730i
$630$		0			0
$631$			40.8170i			1.62490i	0.583031	+	0.812450i	$0.301867\pi$
$631$			40.8170i			1.62490i	−0.583031	+	0.812450i	$0.698133\pi$
$632$		0			0
$633$	3.60379	+	3.60379i	0.143238	+	0.143238i
$634$		0			0
$635$	8.84218	−	7.91562i	0.350891	−	0.314122i
$636$		0			0
$637$	3.34405	−	3.34405i	0.132496	−	0.132496i
$638$		0			0
$639$			14.2617i			0.564184i
$640$		0			0
$641$			42.1898i			1.66640i	0.552974	+	0.833198i	$0.313493\pi$
$641$			42.1898i			1.66640i	−0.552974	+	0.833198i	$0.686507\pi$
$642$		0			0
$643$	−21.0360	+	21.0360i	−0.829580	+	0.829580i	−0.987459	−	0.157879i	$-0.949535\pi$
$643$	−21.0360	+	21.0360i	−0.829580	+	0.829580i	0.157879	+	0.987459i	$0.449535\pi$
$644$		0			0
$645$	−1.99332	−	0.110214i	−0.0784870	−	0.00433967i
$646$		0			0
$647$	22.2306	−	22.2306i	0.873974	−	0.873974i	−0.118929	−	0.992903i	$-0.537946\pi$
$647$	22.2306	−	22.2306i	0.873974	−	0.873974i	0.992903	+	0.118929i	$0.0379460\pi$
$648$		0			0
$649$	−42.9165			−1.68462
$650$		0			0
$651$		−	0.422428i		−	0.0165563i
$652$		0			0
$653$	−11.7442	−	11.7442i	−0.459588	−	0.459588i	0.438932	−	0.898520i	$-0.355357\pi$
$653$	−11.7442	−	11.7442i	−0.459588	−	0.459588i	−0.898520	+	0.438932i	$0.855357\pi$
$654$		0			0
$655$	−12.8950	−	0.712985i	−0.503849	−	0.0278586i
$656$		0			0
$657$	1.58225	−	1.58225i	0.0617293	−	0.0617293i
$658$		0			0
$659$	23.4036			0.911675			0.455838	−	0.890063i	$-0.349340\pi$
$659$	23.4036			0.911675			0.455838	+	0.890063i	$0.349340\pi$
$660$		0			0
$661$			22.3907i			0.870899i	0.900213	+	0.435449i	$0.143411\pi$
$661$			22.3907i			0.870899i	−0.900213	+	0.435449i	$0.856589\pi$
$662$		0			0
$663$	−0.548117	+	0.548117i	−0.0212871	+	0.0212871i
$664$		0			0
$665$	−6.86408	−	7.66755i	−0.266177	−	0.297335i
$666$		0			0
$667$	−35.3216	+	4.04918i	−1.36766	+	0.156785i
$668$		0			0
$669$			5.36391i			0.207381i
$670$		0			0
$671$	3.96795			0.153181
$672$		0			0
$673$	−11.5824	−	11.5824i	−0.446468	−	0.446468i	0.447711	−	0.894178i	$-0.352239\pi$
$673$	−11.5824	−	11.5824i	−0.446468	−	0.446468i	−0.894178	+	0.447711i	$0.852239\pi$
$674$		0			0
$675$	7.70744	−	6.16831i	0.296659	−	0.237418i
$676$		0			0
$677$	6.64702	+	6.64702i	0.255466	+	0.255466i	0.823207	−	0.567741i	$-0.192183\pi$
$677$	6.64702	+	6.64702i	0.255466	+	0.255466i	−0.567741	+	0.823207i	$0.692183\pi$
$678$		0			0
$679$		−	13.5257i		−	0.519071i
$680$		0			0
$681$		−	0.796862i		−	0.0305358i
$682$		0			0
$683$	12.1341	+	12.1341i	0.464299	+	0.464299i	0.900062	−	0.435762i	$-0.143521\pi$
$683$	12.1341	+	12.1341i	0.464299	+	0.464299i	−0.435762	+	0.900062i	$0.643521\pi$
$684$		0			0
$685$	22.6705	+	25.3242i	0.866197	+	0.967590i
$686$		0			0
$687$	−4.47884	−	4.47884i	−0.170878	−	0.170878i
$688$		0			0
$689$	−2.48153			−0.0945387
$690$		0			0
$691$	−22.2848			−0.847755			−0.423877	−	0.905720i	$-0.639331\pi$
$691$	−22.2848			−0.847755			−0.423877	+	0.905720i	$0.639331\pi$
$692$		0			0
$693$	27.1813	+	27.1813i	1.03253	+	1.03253i
$694$		0			0
$695$	−1.35040	+	24.4231i	−0.0512234	+	0.926422i
$696$		0			0
$697$	−2.95317	−	2.95317i	−0.111859	−	0.111859i
$698$		0			0
$699$		−	2.40621i		−	0.0910111i
$700$		0			0
$701$		−	1.20372i		−	0.0454640i	−0.999742	−	0.0227320i	$-0.992764\pi$
$701$		−	1.20372i		−	0.0454640i	0.999742	−	0.0227320i	$-0.00723645\pi$
$702$		0			0
$703$	−3.72858	−	3.72858i	−0.140626	−	0.140626i
$704$		0			0
$705$	−7.98677	−	0.441602i	−0.300799	−	0.0166317i
$706$		0			0
$707$	3.73560	+	3.73560i	0.140492	+	0.140492i
$708$		0			0
$709$	−36.5049			−1.37097			−0.685486	−	0.728086i	$-0.740410\pi$
$709$	−36.5049			−1.37097			−0.685486	+	0.728086i	$0.740410\pi$
$710$		0			0
$711$		−	26.2027i		−	0.982677i
$712$		0			0
$713$	−0.287167	−	2.50500i	−0.0107545	−	0.0938130i
$714$		0			0
$715$	34.7618	−	31.1192i	1.30002	−	1.16379i
$716$		0			0
$717$	−4.48937	+	4.48937i	−0.167659	+	0.167659i
$718$		0			0
$719$		−	11.5502i		−	0.430749i	−0.976532	−	0.215374i	$-0.930903\pi$
$719$		−	11.5502i		−	0.430749i	0.976532	−	0.215374i	$-0.0690972\pi$
$720$		0			0
$721$	7.05698			0.262816
$722$		0			0
$723$	−2.34527	+	2.34527i	−0.0872216	+	0.0872216i
$724$		0			0
$725$	−4.08644	+	36.8405i	−0.151767	+	1.36822i
$726$		0			0
$727$	27.9819	+	27.9819i	1.03779	+	1.03779i	0.999257	+	0.0385340i	$0.0122688\pi$
$727$	27.9819	+	27.9819i	1.03779	+	1.03779i	0.0385340	+	0.999257i	$0.487731\pi$
$728$		0			0
$729$			21.1156i			0.782060i
$730$		0			0
$731$	1.63874			0.0606111
$732$		0			0
$733$	−32.8100	+	32.8100i	−1.21186	+	1.21186i	−0.241451	+	0.970413i	$0.577623\pi$
$733$	−32.8100	+	32.8100i	−1.21186	+	1.21186i	−0.970413	+	0.241451i	$0.922377\pi$
$734$		0			0
$735$	−0.703578	+	0.629850i	−0.0259519	+	0.0232324i
$736$		0			0
$737$	27.6661	−	27.6661i	1.01909	−	1.01909i
$738$		0			0
$739$		−	4.30428i		−	0.158336i	−0.996861	−	0.0791678i	$-0.974774\pi$
$739$		−	4.30428i		−	0.158336i	0.996861	−	0.0791678i	$-0.0252263\pi$
$740$		0			0
$741$			2.41900i			0.0888642i
$742$		0			0
$743$	33.8349	−	33.8349i	1.24128	−	1.24128i	0.281813	−	0.959469i	$-0.409064\pi$
$743$	33.8349	−	33.8349i	1.24128	−	1.24128i	0.959469	−	0.281813i	$-0.0909359\pi$
$744$		0			0
$745$	30.1703	+	1.66816i	1.10535	+	0.0611168i
$746$		0			0
$747$	−30.9072	−	30.9072i	−1.13083	−	1.13083i
$748$		0			0
$749$		−	9.10139i		−	0.332557i
$750$		0			0
$751$			23.2961i			0.850088i	0.905173	+	0.425044i	$0.139741\pi$
$751$			23.2961i			0.850088i	−0.905173	+	0.425044i	$0.860259\pi$
$752$		0			0
$753$	−0.859039	+	0.859039i	−0.0313051	+	0.0313051i
$754$		0			0
$755$	40.7088	+	2.25086i	1.48154	+	0.0819170i
$756$		0			0
$757$	11.0154	+	11.0154i	0.400360	+	0.400360i	0.878360	−	0.478000i	$-0.158638\pi$
$757$	11.0154	+	11.0154i	0.400360	+	0.400360i	−0.478000	+	0.878360i	$0.658638\pi$
$758$		0			0
$759$	−6.99706	−	5.55780i	−0.253977	−	0.201735i
$760$		0			0
$761$	2.31975			0.0840909			0.0420455	−	0.999116i	$-0.486613\pi$
$761$	2.31975			0.0840909			0.0420455	+	0.999116i	$0.486613\pi$
$762$		0			0
$763$	13.5492	+	13.5492i	0.490512	+	0.490512i
$764$		0			0
$765$	−2.96112	+	2.65083i	−0.107060	+	0.0958409i
$766$		0			0
$767$	−20.5108	+	20.5108i	−0.740601	+	0.740601i
$768$		0			0
$769$	−15.2220			−0.548920			−0.274460	−	0.961598i	$-0.588499\pi$
$769$	−15.2220			−0.548920			−0.274460	+	0.961598i	$0.588499\pi$
$770$		0			0
$771$	−2.77927			−0.100093
$772$		0			0
$773$	0.882262	−	0.882262i	0.0317328	−	0.0317328i	−0.691062	−	0.722795i	$-0.742857\pi$
$773$	0.882262	−	0.882262i	0.0317328	−	0.0317328i	0.722795	+	0.691062i	$0.242857\pi$
$774$		0			0
$775$	−2.61273	−	0.289810i	−0.0938519	−	0.0104103i
$776$		0			0
$777$	1.55963	−	1.55963i	0.0559514	−	0.0559514i
$778$		0			0
$779$	−13.0332			−0.466963
$780$		0			0
$781$		−	27.4422i		−	0.981957i
$782$		0			0
$783$	10.3496	+	10.3496i	0.369864	+	0.369864i
$784$		0			0
$785$	−28.8299	−	32.2046i	−1.02898	−	1.14943i
$786$		0			0
$787$	35.5674	+	35.5674i	1.26784	+	1.26784i	0.947201	+	0.320641i	$0.103898\pi$
$787$	35.5674	+	35.5674i	1.26784	+	1.26784i	0.320641	+	0.947201i	$0.396102\pi$
$788$		0			0
$789$	−7.57194			−0.269568
$790$		0			0
$791$	43.9236			1.56174
$792$		0			0
$793$	1.89637	−	1.89637i	0.0673421	−	0.0673421i
$794$		0			0
$795$	0.494751	+	0.0273556i	0.0175470	+	0.000970202i
$796$		0			0
$797$	−7.37158	−	7.37158i	−0.261115	−	0.261115i	0.564392	−	0.825507i	$-0.309111\pi$
$797$	−7.37158	−	7.37158i	−0.261115	−	0.261115i	−0.825507	+	0.564392i	$0.809111\pi$
$798$		0			0
$799$	6.56606			0.232290
$800$		0			0
$801$			37.6339i			1.32973i
$802$		0			0
$803$	−3.04454	+	3.04454i	−0.107439	+	0.107439i
$804$		0			0
$805$	17.0673	−	19.2064i	0.601542	−	0.676936i
$806$		0			0
$807$	6.53141	−	6.53141i	0.229917	−	0.229917i
$808$		0			0
$809$			27.8450i			0.978978i	0.872009	+	0.489489i	$0.162817\pi$
$809$			27.8450i			0.978978i	−0.872009	+	0.489489i	$0.837183\pi$
$810$		0			0
$811$	−49.9498			−1.75398			−0.876988	−	0.480513i	$-0.840451\pi$
$811$	−49.9498			−1.75398			−0.876988	+	0.480513i	$0.840451\pi$
$812$		0			0
$813$	5.50684	+	5.50684i	0.193133	+	0.193133i
$814$		0			0
$815$	21.1179	+	23.5898i	0.739726	+	0.826315i
$816$		0			0
$817$	3.61613	−	3.61613i	0.126512	−	0.126512i
$818$		0			0
$819$	25.9811			0.907852
$820$		0			0
$821$	−37.0759			−1.29396			−0.646979	−	0.762508i	$-0.723968\pi$
$821$	−37.0759			−1.29396			−0.646979	+	0.762508i	$0.723968\pi$
$822$		0			0
$823$	0.660413	+	0.660413i	0.0230205	+	0.0230205i	0.718523	−	0.695503i	$-0.244818\pi$
$823$	0.660413	+	0.660413i	0.0230205	+	0.0230205i	−0.695503	+	0.718523i	$0.744818\pi$
$824$		0			0
$825$	−7.27363	+	5.82113i	−0.253235	+	0.202666i
$826$		0			0
$827$	27.0527	+	27.0527i	0.940716	+	0.940716i	0.998338	−	0.0576226i	$-0.0183520\pi$
$827$	27.0527	+	27.0527i	0.940716	+	0.940716i	−0.0576226	+	0.998338i	$0.518352\pi$
$828$		0			0
$829$		−	37.3353i		−	1.29671i	−0.761339	−	0.648353i	$-0.775458\pi$
$829$		−	37.3353i		−	1.29671i	0.761339	−	0.648353i	$-0.224542\pi$
$830$		0			0
$831$	−4.37523			−0.151775
$832$		0			0
$833$	0.548117	−	0.548117i	0.0189911	−	0.0189911i
$834$		0			0
$835$	−18.0657	+	16.1726i	−0.625191	+	0.559677i
$836$		0			0
$837$	−0.733991	+	0.733991i	−0.0253704	+	0.0253704i
$838$		0			0
$839$	18.0287			0.622420			0.311210	−	0.950341i	$-0.399266\pi$
$839$	18.0287			0.622420			0.311210	+	0.950341i	$0.399266\pi$
$840$		0			0
$841$	−25.9569			−0.895066
$842$		0			0
$843$	−1.06211	+	1.06211i	−0.0365812	+	0.0365812i
$844$		0			0
$845$	0.136096	−	2.46142i	0.00468184	−	0.0846755i
$846$		0			0
$847$	−33.6656	−	33.6656i	−1.15676	−	1.15676i
$848$		0			0
$849$	6.17840			0.212042
$850$		0			0
$851$	8.18838	−	10.3089i	0.280694	−	0.353383i
$852$		0			0
$853$	−33.9885	−	33.9885i	−1.16374	−	1.16374i	−0.983650	−	0.180093i	$-0.942360\pi$
$853$	−33.9885	−	33.9885i	−1.16374	−	1.16374i	−0.180093	−	0.983650i	$-0.557640\pi$
$854$		0			0
$855$	−0.684709	+	12.3836i	−0.0234166	+	0.423510i
$856$		0			0
$857$	5.41108	−	5.41108i	0.184839	−	0.184839i	−0.608622	−	0.793461i	$-0.708277\pi$
$857$	5.41108	−	5.41108i	0.184839	−	0.184839i	0.793461	+	0.608622i	$0.208277\pi$
$858$		0			0
$859$			34.2433i			1.16837i	0.811622	+	0.584184i	$0.198585\pi$
$859$			34.2433i			1.16837i	−0.811622	+	0.584184i	$0.801415\pi$
$860$		0			0
$861$		−	5.45166i		−	0.185792i
$862$		0			0
$863$	25.9583	+	25.9583i	0.883632	+	0.883632i	0.993902	−	0.110269i	$-0.0351714\pi$
$863$	25.9583	+	25.9583i	0.883632	+	0.883632i	−0.110269	+	0.993902i	$0.535171\pi$
$864$		0			0
$865$	−34.2639	−	38.2746i	−1.16501	−	1.30138i
$866$		0			0
$867$	3.94129	−	3.94129i	0.133853	−	0.133853i
$868$		0			0
$869$			50.4188i			1.71034i
$870$		0			0
$871$		−	26.4445i		−	0.896036i
$872$		0			0
$873$	−11.5264	+	11.5264i	−0.390109	+	0.390109i
$874$		0			0
$875$	−15.5579	−	21.8068i	−0.525953	−	0.737203i
$876$		0			0
$877$	−24.3502	+	24.3502i	−0.822249	+	0.822249i	−0.986430	−	0.164181i	$-0.947502\pi$
$877$	−24.3502	+	24.3502i	−0.822249	+	0.822249i	0.164181	+	0.986430i	$0.447502\pi$
$878$		0			0
$879$	8.31125			0.280332
$880$		0			0
$881$			0.218997i			0.00737820i	0.999993	+	0.00368910i	$0.00117428\pi$
$881$			0.218997i			0.00737820i	−0.999993	+	0.00368910i	$0.998826\pi$
$882$		0			0
$883$	−14.5113	−	14.5113i	−0.488344	−	0.488344i	0.419439	−	0.907783i	$-0.362227\pi$
$883$	−14.5113	−	14.5113i	−0.488344	−	0.488344i	−0.907783	+	0.419439i	$0.862227\pi$
$884$		0			0
$885$	4.31540	−	3.86320i	0.145061	−	0.129860i
$886$		0			0
$887$	−12.6798	+	12.6798i	−0.425747	+	0.425747i	−0.887177	−	0.461430i	$-0.847337\pi$
$887$	−12.6798	+	12.6798i	−0.425747	+	0.425747i	0.461430	+	0.887177i	$0.347337\pi$
$888$		0			0
$889$	−12.7163			−0.426491
$890$		0			0
$891$		−	44.4523i		−	1.48921i
$892$		0			0
$893$	14.4890	−	14.4890i	0.484855	−	0.484855i
$894$		0			0
$895$	1.82518	−	33.0100i	0.0610090	−	1.10340i
$896$		0			0
$897$	−6.00024	+	0.687853i	−0.200342	+	0.0229667i
$898$		0			0
$899$		−	3.89754i		−	0.129990i
$900$		0			0
$901$	−0.406743			−0.0135506
$902$		0			0
$903$	1.51259	+	1.51259i	0.0503359	+	0.0503359i
$904$		0			0
$905$	2.99173	−	54.1081i	0.0994484	−	1.79862i
$906$		0			0
$907$	−26.1326	−	26.1326i	−0.867719	−	0.867719i	0.124501	−	0.992219i	$-0.460267\pi$
$907$	−26.1326	−	26.1326i	−0.867719	−	0.867719i	−0.992219	+	0.124501i	$0.960267\pi$
$908$		0			0
$909$		−	6.36682i		−	0.211174i
$910$		0			0
$911$			24.8223i			0.822400i	0.911545	+	0.411200i	$0.134890\pi$
$911$			24.8223i			0.822400i	−0.911545	+	0.411200i	$0.865110\pi$
$912$		0			0
$913$	59.4711	+	59.4711i	1.96821	+	1.96821i
$914$		0			0
$915$	−0.398991	+	0.357181i	−0.0131902	+	0.0118080i
$916$		0			0
$917$	9.78510	+	9.78510i	0.323132	+	0.323132i
$918$		0			0
$919$	10.3089			0.340058			0.170029	−	0.985439i	$-0.445614\pi$
$919$	10.3089			0.340058			0.170029	+	0.985439i	$0.445614\pi$
$920$		0			0
$921$	4.96056			0.163456
$922$		0			0
$923$	−13.1152	−	13.1152i	−0.431692	−	0.431692i
$924$		0			0
$925$	−8.57635	−	10.7163i	−0.281989	−	0.352351i
$926$		0			0
$927$	−6.01383	−	6.01383i	−0.197520	−	0.197520i
$928$		0			0
$929$			27.6117i			0.905909i	0.891534	+	0.452955i	$0.149630\pi$
$929$			27.6117i			0.905909i	−0.891534	+	0.452955i	$0.850370\pi$
$930$		0			0
$931$		−	2.41900i		−	0.0792795i
$932$		0			0
$933$	2.49355	+	2.49355i	0.0816351	+	0.0816351i
$934$		0			0
$935$	5.69775	−	5.10068i	0.186336	−	0.166810i
$936$		0			0
$937$	−5.72139	−	5.72139i	−0.186910	−	0.186910i	0.607449	−	0.794359i	$-0.292193\pi$
$937$	−5.72139	−	5.72139i	−0.186910	−	0.186910i	−0.794359	+	0.607449i	$0.792193\pi$
$938$		0			0
$939$	10.0777			0.328872
$940$		0			0
$941$		−	4.31871i		−	0.140786i	−0.997519	−	0.0703930i	$-0.977575\pi$
$941$		−	4.31871i		−	0.140786i	0.997519	−	0.0703930i	$-0.0224253\pi$
$942$		0			0
$943$	−3.70604	−	32.3284i	−0.120685	−	1.05276i
$944$		0			0
$945$	−10.5616	−	0.583969i	−0.343569	−	0.0189965i
$946$		0			0
$947$	41.4515	−	41.4515i	1.34699	−	1.34699i	0.458086	−	0.888908i	$-0.348535\pi$
$947$	41.4515	−	41.4515i	1.34699	−	1.34699i	0.888908	−	0.458086i	$-0.151465\pi$
$948$		0			0
$949$			2.91010i			0.0944659i
$950$		0			0
$951$	−6.15504			−0.199591
$952$		0			0
$953$	27.8044	−	27.8044i	0.900672	−	0.900672i	−0.0948219	−	0.995494i	$-0.530228\pi$
$953$	27.8044	−	27.8044i	0.900672	−	0.900672i	0.995494	+	0.0948219i	$0.0302281\pi$
$954$		0			0
$955$	−2.25985	+	40.8715i	−0.0731271	+	1.32257i
$956$		0			0
$957$	−9.76706	−	9.76706i	−0.315724	−	0.315724i
$958$		0			0
$959$		−	36.4198i		−	1.17606i
$960$		0			0
$961$	−30.7236			−0.991083
$962$		0			0
$963$	−7.75604	+	7.75604i	−0.249935	+	0.249935i
$964$		0			0
$965$	−32.9751	−	36.8350i	−1.06151	−	1.18576i
$966$		0			0
$967$	17.4321	−	17.4321i	0.560577	−	0.560577i	−0.368894	−	0.929471i	$-0.620264\pi$
$967$	17.4321	−	17.4321i	0.560577	−	0.560577i	0.929471	+	0.368894i	$0.120264\pi$
$968$		0			0
$969$			0.396494i			0.0127372i
$970$		0			0
$971$			30.0252i			0.963555i	0.876294	+	0.481777i	$0.160009\pi$
$971$			30.0252i			0.963555i	−0.876294	+	0.481777i	$0.839991\pi$
$972$		0			0
$973$	18.5330	−	18.5330i	0.594141	−	0.594141i
$974$		0			0
$975$	−0.694183	+	6.25827i	−0.0222316	+	0.200425i
$976$		0			0
$977$	1.18647	+	1.18647i	0.0379585	+	0.0379585i	0.725831	−	0.687873i	$-0.241455\pi$
$977$	1.18647	+	1.18647i	0.0379585	+	0.0379585i	−0.687873	+	0.725831i	$0.741455\pi$
$978$		0			0
$979$		−	72.4146i		−	2.31438i
$980$		0			0
$981$		−	23.0927i		−	0.737293i
$982$		0			0
$983$	12.7320	−	12.7320i	0.406088	−	0.406088i	−0.474284	−	0.880372i	$-0.657293\pi$
$983$	12.7320	−	12.7320i	0.406088	−	0.406088i	0.880372	+	0.474284i	$0.157293\pi$
$984$		0			0
$985$	−33.6030	+	30.0817i	−1.07068	+	0.958484i
$986$		0			0
$987$	6.06060	+	6.06060i	0.192911	+	0.192911i
$988$		0			0
$989$	9.99794	+	7.94141i	0.317916	+	0.252522i
$990$		0			0
$991$	−3.95248			−0.125555			−0.0627774	−	0.998028i	$-0.519996\pi$
$991$	−3.95248			−0.125555			−0.0627774	+	0.998028i	$0.519996\pi$
$992$		0			0
$993$	−0.964635	−	0.964635i	−0.0306118	−	0.0306118i
$994$		0			0
$995$	−45.7923	−	2.53193i	−1.45171	−	0.0802676i
$996$		0			0
$997$	−27.3544	+	27.3544i	−0.866323	+	0.866323i	−0.992063	−	0.125740i	$-0.959870\pi$
$997$	−27.3544	+	27.3544i	−0.866323	+	0.866323i	0.125740	+	0.992063i	$0.459870\pi$
$998$		0			0
$999$	−5.41988			−0.171477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.i.b.413.3	yes	16
5.2	odd	4	inner	460.2.i.b.137.4	yes	16
5.3	odd	4		2300.2.i.d.1057.6		16
5.4	even	2		2300.2.i.d.1793.5		16
23.22	odd	2	inner	460.2.i.b.413.4	yes	16
115.22	even	4	inner	460.2.i.b.137.3	✓	16
115.68	even	4		2300.2.i.d.1057.5		16
115.114	odd	2		2300.2.i.d.1793.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.i.b.137.3	✓	16	115.22	even	4	inner
460.2.i.b.137.4	yes	16	5.2	odd	4	inner
460.2.i.b.413.3	yes	16	1.1	even	1	trivial
460.2.i.b.413.4	yes	16	23.22	odd	2	inner
2300.2.i.d.1057.5		16	115.68	even	4
2300.2.i.d.1057.6		16	5.3	odd	4
2300.2.i.d.1793.5		16	5.4	even	2
2300.2.i.d.1793.6		16	115.114	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.237125 + 0.237125i) q^{3} +(-2.23266 - 0.123447i) q^{5} +(1.69421 + 1.69421i) q^{7} -2.88754i q^{9} +O(q^{10})\)	\(q+(0.237125 + 0.237125i) q^{3} +(-2.23266 - 0.123447i) q^{5} +(1.69421 + 1.69421i) q^{7} -2.88754i q^{9} +5.55617i q^{11} +(2.65542 + 2.65542i) q^{13} +(-0.500147 - 0.558692i) q^{15} +(0.435244 + 0.435244i) q^{17} +1.92086 q^{19} +0.803478i q^{21} +(0.546205 + 4.76463i) q^{23} +(4.96952 + 0.551231i) q^{25} +(1.39608 - 1.39608i) q^{27} +7.41329i q^{29} -0.525750 q^{31} +(-1.31751 + 1.31751i) q^{33} +(-3.57344 - 3.99173i) q^{35} +(-1.94110 - 1.94110i) q^{37} +1.25933i q^{39} -6.78508 q^{41} +(1.88256 - 1.88256i) q^{43} +(-0.356459 + 6.44690i) q^{45} +(7.54296 - 7.54296i) q^{47} -1.25933i q^{49} +0.206415i q^{51} +(-0.467258 + 0.467258i) q^{53} +(0.685894 - 12.4050i) q^{55} +(0.455484 + 0.455484i) q^{57} +7.72412i q^{59} -0.714153i q^{61} +(4.89209 - 4.89209i) q^{63} +(-5.60083 - 6.25644i) q^{65} +(-4.97934 - 4.97934i) q^{67} +(-1.00029 + 1.25933i) q^{69} -4.93904 q^{71} +(0.547956 + 0.547956i) q^{73} +(1.04769 + 1.30911i) q^{75} +(-9.41329 + 9.41329i) q^{77} +9.07438 q^{79} -8.00054 q^{81} +(10.7036 - 10.7036i) q^{83} +(-0.918022 - 1.02548i) q^{85} +(-1.75788 + 1.75788i) q^{87} -13.0332 q^{89} +8.99764i q^{91} +(-0.124668 - 0.124668i) q^{93} +(-4.28862 - 0.237125i) q^{95} +(-3.99177 - 3.99177i) q^{97} +16.0437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3}+O(q^{10}) \) 16 * q + 4 * q^3	\( 16 q + 4 q^{3} + 12 q^{13} + 12 q^{23} + 36 q^{25} + 52 q^{27} - 8 q^{31} + 16 q^{35} - 48 q^{41} + 4 q^{47} + 24 q^{55} + 8 q^{71} - 52 q^{73} - 56 q^{75} - 64 q^{77} - 152 q^{81} + 28 q^{85} + 28 q^{87} + 84 q^{93} - 68 q^{95}+O(q^{100}) \) 16 * q + 4 * q^3 + 12 * q^13 + 12 * q^23 + 36 * q^25 + 52 * q^27 - 8 * q^31 + 16 * q^35 - 48 * q^41 + 4 * q^47 + 24 * q^55 + 8 * q^71 - 52 * q^73 - 56 * q^75 - 64 * q^77 - 152 * q^81 + 28 * q^85 + 28 * q^87 + 84 * q^93 - 68 * q^95

Introduction

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