LMFDB - Embedded newform 960.2.w.g.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(127,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("960.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.w (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Root			$-0.394157 + 1.35818i$ of defining polynomial
Character	$\chi$	$=$	960.127
Dual form			960.2.w.g.703.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(1.75233 + 1.38900i) q^{5} +(2.47817 - 2.47817i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(1.75233 + 1.38900i) q^{5} +(2.47817 - 2.47817i) q^{7} +1.00000i q^{9} -3.02831i q^{11} +(-0.363328 + 0.363328i) q^{13} +(-0.256912 - 2.22126i) q^{15} +(-2.36333 - 2.36333i) q^{17} +4.95634 q^{19} -3.50466 q^{21} +(-0.900390 - 0.900390i) q^{23} +(1.14134 + 4.86799i) q^{25} +(0.707107 - 0.707107i) q^{27} -3.50466i q^{29} +3.85607i q^{31} +(-2.14134 + 2.14134i) q^{33} +(7.78477 - 0.900390i) q^{35} +(0.363328 + 0.363328i) q^{37} +0.513824 q^{39} +2.72666 q^{41} +(-3.92870 - 3.92870i) q^{43} +(-1.38900 + 1.75233i) q^{45} +(5.85673 - 5.85673i) q^{47} -5.28267i q^{49} +3.34225i q^{51} +(-3.14134 + 3.14134i) q^{53} +(4.20633 - 5.30660i) q^{55} +(-3.50466 - 3.50466i) q^{57} -8.68516 q^{59} +15.2920 q^{61} +(2.47817 + 2.47817i) q^{63} +(-1.14134 + 0.132007i) q^{65} +(3.92870 - 3.92870i) q^{67} +1.27334i q^{69} -4.25583i q^{71} +(9.28267 - 9.28267i) q^{73} +(2.63514 - 4.24924i) q^{75} +(-7.50466 - 7.50466i) q^{77} +0.399759 q^{79} -1.00000 q^{81} +(0.199879 + 0.199879i) q^{83} +(-0.858664 - 7.42401i) q^{85} +(-2.47817 + 2.47817i) q^{87} +4.28267i q^{89} +1.80078i q^{91} +(2.72666 - 2.72666i) q^{93} +(8.68516 + 6.88438i) q^{95} +(6.73599 + 6.73599i) q^{97} +3.02831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 4 q^{13} - 20 q^{17} - 20 q^{25} + 8 q^{33} - 4 q^{37} + 16 q^{41} - 4 q^{45} - 4 q^{53} + 32 q^{61} + 20 q^{65} + 44 q^{73} - 48 q^{77} - 12 q^{81} - 44 q^{85} + 16 q^{93} - 20 q^{97}+O(q^{100}) $ 12 * q + 4 * q^13 - 20 * q^17 - 20 * q^25 + 8 * q^33 - 4 * q^37 + 16 * q^41 - 4 * q^45 - 4 * q^53 + 32 * q^61 + 20 * q^65 + 44 * q^73 - 48 * q^77 - 12 * q^81 - 44 * q^85 + 16 * q^93 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	1.75233	+	1.38900i	0.783667	+	0.621181i
$5$	1.75233	+	1.38900i	0.783667	+	0.621181i
$6$		0			0
$7$	2.47817	−	2.47817i	0.936661	−	0.936661i	−0.0614493	−	0.998110i	$-0.519572\pi$
$7$	2.47817	−	2.47817i	0.936661	−	0.936661i	0.998110	+	0.0614493i	$0.0195722\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	3.02831i		−	0.913069i	−0.889706	−	0.456534i	$-0.849091\pi$
$11$		−	3.02831i		−	0.913069i	0.889706	−	0.456534i	$-0.150909\pi$
$12$		0			0
$13$	−0.363328	+	0.363328i	−0.100769	+	0.100769i	−0.755694	−	0.654925i	$-0.772700\pi$
$13$	−0.363328	+	0.363328i	−0.100769	+	0.100769i	0.654925	+	0.755694i	$0.272700\pi$
$14$		0			0
$15$	−0.256912	−	2.22126i	−0.0663344	−	0.573527i
$16$		0			0
$17$	−2.36333	−	2.36333i	−0.573191	−	0.573191i	0.359828	−	0.933019i	$-0.382836\pi$
$17$	−2.36333	−	2.36333i	−0.573191	−	0.573191i	−0.933019	+	0.359828i	$0.882836\pi$
$18$		0			0
$19$	4.95634			1.13706			0.568532	−	0.822661i	$-0.307512\pi$
$19$	4.95634			1.13706			0.568532	+	0.822661i	$0.307512\pi$
$20$		0			0
$21$	−3.50466			−0.764780
$22$		0			0
$23$	−0.900390	−	0.900390i	−0.187744	−	0.187744i	0.606976	−	0.794720i	$-0.292382\pi$
$23$	−0.900390	−	0.900390i	−0.187744	−	0.187744i	−0.794720	+	0.606976i	$0.792382\pi$
$24$		0			0
$25$	1.14134	+	4.86799i	0.228267	+	0.973599i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	3.50466i		−	0.650800i	−0.945576	−	0.325400i	$-0.894501\pi$
$29$		−	3.50466i		−	0.650800i	0.945576	−	0.325400i	$-0.105499\pi$
$30$		0			0
$31$			3.85607i			0.692571i	0.938129	+	0.346286i	$0.112557\pi$
$31$			3.85607i			0.692571i	−0.938129	+	0.346286i	$0.887443\pi$
$32$		0			0
$33$	−2.14134	+	2.14134i	−0.372759	+	0.372759i
$34$		0			0
$35$	7.78477	−	0.900390i	1.31587	−	0.152194i
$36$		0			0
$37$	0.363328	+	0.363328i	0.0597308	+	0.0597308i	0.736341	−	0.676610i	$-0.236552\pi$
$37$	0.363328	+	0.363328i	0.0597308	+	0.0597308i	−0.676610	+	0.736341i	$0.736552\pi$
$38$		0			0
$39$	0.513824			0.0822776
$40$		0			0
$41$	2.72666			0.425832			0.212916	−	0.977070i	$-0.431704\pi$
$41$	2.72666			0.425832			0.212916	+	0.977070i	$0.431704\pi$
$42$		0			0
$43$	−3.92870	−	3.92870i	−0.599121	−	0.599121i	0.340958	−	0.940079i	$-0.389249\pi$
$43$	−3.92870	−	3.92870i	−0.599121	−	0.599121i	−0.940079	+	0.340958i	$0.889249\pi$
$44$		0			0
$45$	−1.38900	+	1.75233i	−0.207060	+	0.261222i
$46$		0			0
$47$	5.85673	−	5.85673i	0.854292	−	0.854292i	−0.136366	−	0.990659i	$-0.543542\pi$
$47$	5.85673	−	5.85673i	0.854292	−	0.854292i	0.990659	+	0.136366i	$0.0435423\pi$
$48$		0			0
$49$		−	5.28267i		−	0.754667i
$50$		0			0
$51$			3.34225i			0.468009i
$52$		0			0
$53$	−3.14134	+	3.14134i	−0.431496	+	0.431496i	−0.889137	−	0.457641i	$-0.848694\pi$
$53$	−3.14134	+	3.14134i	−0.431496	+	0.431496i	0.457641	+	0.889137i	$0.348694\pi$
$54$		0			0
$55$	4.20633	−	5.30660i	0.567181	−	0.715542i
$56$		0			0
$57$	−3.50466	−	3.50466i	−0.464204	−	0.464204i
$58$		0			0
$59$	−8.68516			−1.13071			−0.565356	−	0.824847i	$-0.691261\pi$
$59$	−8.68516			−1.13071			−0.565356	+	0.824847i	$0.691261\pi$
$60$		0			0
$61$	15.2920			1.95794			0.978970	−	0.204004i	$-0.0653956\pi$
$61$	15.2920			1.95794			0.978970	+	0.204004i	$0.0653956\pi$
$62$		0			0
$63$	2.47817	+	2.47817i	0.312220	+	0.312220i
$64$		0			0
$65$	−1.14134	+	0.132007i	−0.141565	+	0.0163735i
$66$		0			0
$67$	3.92870	−	3.92870i	0.479967	−	0.479967i	−0.425154	−	0.905121i	$-0.639780\pi$
$67$	3.92870	−	3.92870i	0.479967	−	0.479967i	0.905121	+	0.425154i	$0.139780\pi$
$68$		0			0
$69$			1.27334i			0.153293i
$70$		0			0
$71$		−	4.25583i		−	0.505075i	−0.967587	−	0.252537i	$-0.918735\pi$
$71$		−	4.25583i		−	0.505075i	0.967587	−	0.252537i	$-0.0812650\pi$
$72$		0			0
$73$	9.28267	−	9.28267i	1.08645	−	1.08645i	0.0905640	−	0.995891i	$-0.471133\pi$
$73$	9.28267	−	9.28267i	1.08645	−	1.08645i	0.995891	−	0.0905640i	$-0.0288670\pi$
$74$		0			0
$75$	2.63514	−	4.24924i	0.304280	−	0.490660i
$76$		0			0
$77$	−7.50466	−	7.50466i	−0.855236	−	0.855236i
$78$		0			0
$79$	0.399759			0.0449764			0.0224882	−	0.999747i	$-0.492841\pi$
$79$	0.399759			0.0449764			0.0224882	+	0.999747i	$0.492841\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	0.199879	+	0.199879i	0.0219396	+	0.0219396i	0.717991	−	0.696052i	$-0.245062\pi$
$83$	0.199879	+	0.199879i	0.0219396	+	0.0219396i	−0.696052	+	0.717991i	$0.745062\pi$
$84$		0			0
$85$	−0.858664	−	7.42401i	−0.0931352	−	0.805247i
$86$		0			0
$87$	−2.47817	+	2.47817i	−0.265688	+	0.265688i
$88$		0			0
$89$			4.28267i			0.453962i	0.973899	+	0.226981i	$0.0728856\pi$
$89$			4.28267i			0.453962i	−0.973899	+	0.226981i	$0.927114\pi$
$90$		0			0
$91$			1.80078i			0.188773i
$92$		0			0
$93$	2.72666	−	2.72666i	0.282741	−	0.282741i
$94$		0			0
$95$	8.68516	+	6.88438i	0.891079	+	0.706323i
$96$		0			0
$97$	6.73599	+	6.73599i	0.683936	+	0.683936i	0.960885	−	0.276949i	$-0.0893233\pi$
$97$	6.73599	+	6.73599i	0.683936	+	0.683936i	−0.276949	+	0.960885i	$0.589323\pi$
$98$		0			0
$99$	3.02831			0.304356
$100$		0			0
$101$	−5.78734			−0.575862			−0.287931	−	0.957651i	$-0.592967\pi$
$101$	−5.78734			−0.575862			−0.287931	+	0.957651i	$0.592967\pi$
$102$		0			0
$103$	−13.0914	−	13.0914i	−1.28993	−	1.28993i	−0.934827	−	0.355104i	$-0.884445\pi$
$103$	−13.0914	−	13.0914i	−1.28993	−	1.28993i	−0.355104	−	0.934827i	$-0.615555\pi$
$104$		0			0
$105$	−6.14134	−	4.86799i	−0.599333	−	0.475067i
$106$		0			0
$107$	9.71281	−	9.71281i	0.938973	−	0.938973i	−0.0592694	−	0.998242i	$-0.518877\pi$
$107$	9.71281	−	9.71281i	0.938973	−	0.938973i	0.998242	+	0.0592694i	$0.0188771\pi$
$108$		0			0
$109$			10.4626i			1.00214i	0.865407	+	0.501070i	$0.167060\pi$
$109$			10.4626i			1.00214i	−0.865407	+	0.501070i	$0.832940\pi$
$110$		0			0
$111$		−	0.513824i		−	0.0487700i
$112$		0			0
$113$	−10.6460	+	10.6460i	−1.00149	+	1.00149i	−0.00149259	+	0.999999i	$0.500475\pi$
$113$	−10.6460	+	10.6460i	−1.00149	+	1.00149i	−0.999999	+	0.00149259i	$0.999525\pi$
$114$		0			0
$115$	−0.327137	−	2.82843i	−0.0305057	−	0.263752i
$116$		0			0
$117$	−0.363328	−	0.363328i	−0.0335897	−	0.0335897i
$118$		0			0
$119$	−11.7135			−1.07377
$120$		0			0
$121$	1.82936			0.166305
$122$		0			0
$123$	−1.92804	−	1.92804i	−0.173845	−	0.173845i
$124$		0			0
$125$	−4.76166	+	10.1157i	−0.425896	+	0.904772i
$126$		0			0
$127$	−1.77766	+	1.77766i	−0.157742	+	0.157742i	−0.781565	−	0.623823i	$-0.785578\pi$
$127$	−1.77766	+	1.77766i	−0.157742	+	0.157742i	0.623823	+	0.781565i	$0.285578\pi$
$128$		0			0
$129$			5.55602i			0.489180i
$130$		0			0
$131$			18.1981i			1.58997i	0.606626	+	0.794987i	$0.292523\pi$
$131$			18.1981i			1.58997i	−0.606626	+	0.794987i	$0.707477\pi$
$132$		0			0
$133$	12.2827	−	12.2827i	1.06504	−	1.06504i
$134$		0			0
$135$	2.22126	−	0.256912i	0.191176	−	0.0221115i
$136$		0			0
$137$	−5.91934	−	5.91934i	−0.505724	−	0.505724i	0.407487	−	0.913211i	$-0.366405\pi$
$137$	−5.91934	−	5.91934i	−0.505724	−	0.505724i	−0.913211	+	0.407487i	$0.866405\pi$
$138$		0			0
$139$	−12.4140			−1.05294			−0.526470	−	0.850194i	$-0.676485\pi$
$139$	−12.4140			−1.05294			−0.526470	+	0.850194i	$0.676485\pi$
$140$		0			0
$141$	−8.28267			−0.697527
$142$		0			0
$143$	1.10027	+	1.10027i	0.0920091	+	0.0920091i
$144$		0			0
$145$	4.86799	−	6.14134i	0.404265	−	0.510010i
$146$		0			0
$147$	−3.73541	+	3.73541i	−0.308092	+	0.308092i
$148$		0			0
$149$			5.78734i			0.474117i	0.971495	+	0.237059i	$0.0761833\pi$
$149$			5.78734i			0.474117i	−0.971495	+	0.237059i	$0.923817\pi$
$150$		0			0
$151$			18.0708i			1.47058i	0.677751	+	0.735292i	$0.262955\pi$
$151$			18.0708i			1.47058i	−0.677751	+	0.735292i	$0.737045\pi$
$152$		0			0
$153$	2.36333	−	2.36333i	0.191064	−	0.191064i
$154$		0			0
$155$	−5.35610	+	6.75712i	−0.430213	+	0.542745i
$156$		0			0
$157$	3.91934	+	3.91934i	0.312798	+	0.312798i	0.845992	−	0.533195i	$-0.179009\pi$
$157$	3.91934	+	3.91934i	0.312798	+	0.312798i	−0.533195	+	0.845992i	$0.679009\pi$
$158$		0			0
$159$	4.44252			0.352315
$160$		0			0
$161$	−4.46264			−0.351705
$162$		0			0
$163$	3.22819	+	3.22819i	0.252851	+	0.252851i	0.822139	−	0.569287i	$-0.192781\pi$
$163$	3.22819	+	3.22819i	0.252851	+	0.252851i	−0.569287	+	0.822139i	$0.692781\pi$
$164$		0			0
$165$	−6.72666	+	0.778008i	−0.523669	+	0.0605678i
$166$		0			0
$167$	−6.95700	+	6.95700i	−0.538349	+	0.538349i	−0.923044	−	0.384695i	$-0.874307\pi$
$167$	−6.95700	+	6.95700i	−0.538349	+	0.538349i	0.384695	+	0.923044i	$0.374307\pi$
$168$		0			0
$169$			12.7360i			0.979691i
$170$		0			0
$171$			4.95634i			0.379021i
$172$		0			0
$173$	−0.627343	+	0.627343i	−0.0476960	+	0.0476960i	−0.730553	−	0.682857i	$-0.760737\pi$
$173$	−0.627343	+	0.627343i	−0.0476960	+	0.0476960i	0.682857	+	0.730553i	$0.260737\pi$
$174$		0			0
$175$	14.8921	+	9.23530i	1.12574	+	0.698123i
$176$		0			0
$177$	6.14134	+	6.14134i	0.461611	+	0.461611i
$178$		0			0
$179$	−8.93968			−0.668183			−0.334091	−	0.942541i	$-0.608429\pi$
$179$	−8.93968			−0.668183			−0.334091	+	0.942541i	$0.608429\pi$
$180$		0			0
$181$	1.00933			0.0750228			0.0375114	−	0.999296i	$-0.488057\pi$
$181$	1.00933			0.0750228			0.0375114	+	0.999296i	$0.488057\pi$
$182$		0			0
$183$	−10.8131	−	10.8131i	−0.799326	−	0.799326i
$184$		0			0
$185$	0.132007	+	1.14134i	0.00970538	+	0.0839127i
$186$		0			0
$187$	−7.15688	+	7.15688i	−0.523363	+	0.523363i
$188$		0			0
$189$		−	3.50466i		−	0.254927i
$190$		0			0
$191$			21.6262i			1.56481i	0.622768	+	0.782407i	$0.286008\pi$
$191$			21.6262i			1.56481i	−0.622768	+	0.782407i	$0.713992\pi$
$192$		0			0
$193$	11.5653	−	11.5653i	0.832492	−	0.832492i	−0.155365	−	0.987857i	$-0.549655\pi$
$193$	11.5653	−	11.5653i	0.832492	−	0.832492i	0.987857	+	0.155365i	$0.0496555\pi$
$194$		0			0
$195$	0.900390	+	0.713703i	0.0644783	+	0.0511093i
$196$		0			0
$197$	9.42401	+	9.42401i	0.671433	+	0.671433i	0.958046	−	0.286614i	$-0.0925296\pi$
$197$	9.42401	+	9.42401i	0.671433	+	0.671433i	−0.286614	+	0.958046i	$0.592530\pi$
$198$		0			0
$199$	−11.0130			−0.780688			−0.390344	−	0.920669i	$-0.627644\pi$
$199$	−11.0130			−0.780688			−0.390344	+	0.920669i	$0.627644\pi$
$200$		0			0
$201$	−5.55602			−0.391891
$202$		0			0
$203$	−8.68516	−	8.68516i	−0.609579	−	0.609579i
$204$		0			0
$205$	4.77801	+	3.78734i	0.333711	+	0.264519i
$206$		0			0
$207$	0.900390	−	0.900390i	0.0625814	−	0.0625814i
$208$		0			0
$209$		−	15.0093i		−	1.03822i
$210$		0			0
$211$			27.9835i			1.92646i	0.268669	+	0.963232i	$0.413416\pi$
$211$			27.9835i			1.92646i	−0.268669	+	0.963232i	$0.586584\pi$
$212$		0			0
$213$	−3.00933	+	3.00933i	−0.206196	+	0.206196i
$214$		0			0
$215$	−1.42741	−	12.3414i	−0.0973483	−	0.841673i
$216$		0			0
$217$	9.55602	+	9.55602i	0.648705	+	0.648705i
$218$		0			0
$219$	−13.1277			−0.887086
$220$		0			0
$221$	1.71733			0.115520
$222$		0			0
$223$	8.53479	+	8.53479i	0.571531	+	0.571531i	0.932556	−	0.361025i	$-0.117573\pi$
$223$	8.53479	+	8.53479i	0.571531	+	0.571531i	−0.361025	+	0.932556i	$0.617573\pi$
$224$		0			0
$225$	−4.86799	+	1.14134i	−0.324533	+	0.0760891i
$226$		0			0
$227$	−1.02765	+	1.02765i	−0.0682074	+	0.0682074i	−0.740388	−	0.672180i	$-0.765358\pi$
$227$	−1.02765	+	1.02765i	−0.0682074	+	0.0682074i	0.672180	+	0.740388i	$0.265358\pi$
$228$		0			0
$229$		−	8.84802i		−	0.584693i	−0.956312	−	0.292347i	$-0.905564\pi$
$229$		−	8.84802i		−	0.584693i	0.956312	−	0.292347i	$-0.0944361\pi$
$230$		0			0
$231$			10.6132i			0.698297i
$232$		0			0
$233$	−4.91002	+	4.91002i	−0.321666	+	0.321666i	−0.849406	−	0.527740i	$-0.823040\pi$
$233$	−4.91002	+	4.91002i	−0.321666	+	0.321666i	0.527740	+	0.849406i	$0.323040\pi$
$234$		0			0
$235$	18.3980	−	2.12792i	1.20015	−	0.138810i
$236$		0			0
$237$	−0.282672	−	0.282672i	−0.0183615	−	0.0183615i
$238$		0			0
$239$	−19.0259			−1.23068			−0.615340	−	0.788262i	$-0.710981\pi$
$239$	−19.0259			−1.23068			−0.615340	+	0.788262i	$0.710981\pi$
$240$		0			0
$241$	2.90663			0.187232			0.0936161	−	0.995608i	$-0.470157\pi$
$241$	2.90663			0.187232			0.0936161	+	0.995608i	$0.470157\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	7.33765	−	9.25700i	0.468785	−	0.591408i
$246$		0			0
$247$	−1.80078	+	1.80078i	−0.114581	+	0.114581i
$248$		0			0
$249$		−	0.282672i		−	0.0179136i
$250$		0			0
$251$			2.77379i			0.175080i	0.996161	+	0.0875401i	$0.0279006\pi$
$251$			2.77379i			0.175080i	−0.996161	+	0.0875401i	$0.972099\pi$
$252$		0			0
$253$	−2.72666	+	2.72666i	−0.171423	+	0.171423i
$254$		0			0
$255$	−4.64240	+	5.85673i	−0.290718	+	0.366763i
$256$		0			0
$257$	−2.08066	−	2.08066i	−0.129788	−	0.129788i	0.639229	−	0.769017i	$-0.279254\pi$
$257$	−2.08066	−	2.08066i	−0.129788	−	0.129788i	−0.769017	+	0.639229i	$0.779254\pi$
$258$		0			0
$259$	1.80078			0.111895
$260$		0			0
$261$	3.50466			0.216933
$262$		0			0
$263$	−4.75646	−	4.75646i	−0.293296	−	0.293296i	0.545085	−	0.838381i	$-0.316497\pi$
$263$	−4.75646	−	4.75646i	−0.293296	−	0.293296i	−0.838381	+	0.545085i	$0.816497\pi$
$264$		0			0
$265$	−9.86799	+	1.14134i	−0.606186	+	0.0701117i
$266$		0			0
$267$	3.02831	−	3.02831i	0.185329	−	0.185329i
$268$		0			0
$269$		−	21.6846i		−	1.32214i	−0.750326	−	0.661068i	$-0.770104\pi$
$269$		−	21.6846i		−	1.32214i	0.750326	−	0.661068i	$-0.229896\pi$
$270$		0			0
$271$		−	3.15556i		−	0.191687i	−0.995396	−	0.0958434i	$-0.969445\pi$
$271$		−	3.15556i		−	0.191687i	0.995396	−	0.0958434i	$-0.0305548\pi$
$272$		0			0
$273$	1.27334	−	1.27334i	0.0770663	−	0.0770663i
$274$		0			0
$275$	14.7418	−	3.45632i	0.888962	−	0.208424i
$276$		0			0
$277$	3.53397	+	3.53397i	0.212336	+	0.212336i	0.805259	−	0.592923i	$-0.202026\pi$
$277$	3.53397	+	3.53397i	0.212336	+	0.212336i	−0.592923	+	0.805259i	$0.702026\pi$
$278$		0			0
$279$	−3.85607			−0.230857
$280$		0			0
$281$	0.179969			0.0107361			0.00536804	−	0.999986i	$-0.498291\pi$
$281$	0.179969			0.0107361			0.00536804	+	0.999986i	$0.498291\pi$
$282$		0			0
$283$	−9.84007	−	9.84007i	−0.584931	−	0.584931i	0.351323	−	0.936254i	$-0.385732\pi$
$283$	−9.84007	−	9.84007i	−0.584931	−	0.584931i	−0.936254	+	0.351323i	$0.885732\pi$
$284$		0			0
$285$	−1.27334	−	11.0093i	−0.0754264	−	0.652136i
$286$		0			0
$287$	6.75712	−	6.75712i	0.398860	−	0.398860i
$288$		0			0
$289$		−	5.82936i		−	0.342903i
$290$		0			0
$291$		−	9.52612i		−	0.558431i
$292$		0			0
$293$	−15.8680	+	15.8680i	−0.927018	+	0.927018i	−0.997512	−	0.0704942i	$-0.977542\pi$
$293$	−15.8680	+	15.8680i	−0.927018	+	0.927018i	0.0704942	+	0.997512i	$0.477542\pi$
$294$		0			0
$295$	−15.2193	−	12.0637i	−0.886101	−	0.702377i
$296$		0			0
$297$	−2.14134	−	2.14134i	−0.124253	−	0.124253i
$298$		0			0
$299$	0.654274			0.0378376
$300$		0			0
$301$	−19.4720			−1.12235
$302$		0			0
$303$	4.09226	+	4.09226i	0.235094	+	0.235094i
$304$		0			0
$305$	26.7967	+	21.2406i	1.53437	+	1.21624i
$306$		0			0
$307$	−7.78477	+	7.78477i	−0.444300	+	0.444300i	−0.893454	−	0.449154i	$-0.851725\pi$
$307$	−7.78477	+	7.78477i	−0.444300	+	0.444300i	0.449154	+	0.893454i	$0.351725\pi$
$308$		0			0
$309$			18.5140i			1.05322i
$310$		0			0
$311$			7.05788i			0.400215i	0.979774	+	0.200108i	$0.0641292\pi$
$311$			7.05788i			0.400215i	−0.979774	+	0.200108i	$0.935871\pi$
$312$		0			0
$313$	−11.3013	+	11.3013i	−0.638789	+	0.638789i	−0.950257	−	0.311468i	$-0.899179\pi$
$313$	−11.3013	+	11.3013i	−0.638789	+	0.638789i	0.311468	+	0.950257i	$0.399179\pi$
$314$		0			0
$315$	0.900390	+	7.78477i	0.0507312	+	0.438622i
$316$		0			0
$317$	−19.4754	−	19.4754i	−1.09385	−	1.09385i	−0.995114	−	0.0987310i	$-0.968522\pi$
$317$	−19.4754	−	19.4754i	−1.09385	−	1.09385i	−0.0987310	−	0.995114i	$-0.531478\pi$
$318$		0			0
$319$	−10.6132			−0.594225
$320$		0			0
$321$	−13.7360			−0.766668
$322$		0			0
$323$	−11.7135	−	11.7135i	−0.651755	−	0.651755i
$324$		0			0
$325$	−2.18336	−	1.35400i	−0.121111	−	0.0751064i
$326$		0			0
$327$	7.39820	−	7.39820i	0.409122	−	0.409122i
$328$		0			0
$329$		−	29.0280i		−	1.60036i
$330$		0			0
$331$		−	15.0143i		−	0.825259i	−0.910899	−	0.412630i	$-0.864610\pi$
$331$		−	15.0143i		−	0.825259i	0.910899	−	0.412630i	$-0.135390\pi$
$332$		0			0
$333$	−0.363328	+	0.363328i	−0.0199103	+	0.0199103i
$334$		0			0
$335$	12.3414	−	1.42741i	0.674280	−	0.0779875i
$336$		0			0
$337$	−21.5840	−	21.5840i	−1.17576	−	1.17576i	−0.980815	−	0.194940i	$-0.937549\pi$
$337$	−21.5840	−	21.5840i	−1.17576	−	1.17576i	−0.194940	−	0.980815i	$-0.562451\pi$
$338$		0			0
$339$	15.0557			0.817714
$340$		0			0
$341$	11.6774			0.632365
$342$		0			0
$343$	4.25583	+	4.25583i	0.229793	+	0.229793i
$344$		0			0
$345$	−1.76868	+	2.23132i	−0.0952225	+	0.120130i
$346$		0			0
$347$	−16.9969	+	16.9969i	−0.912444	+	0.912444i	−0.996464	−	0.0840201i	$-0.973224\pi$
$347$	−16.9969	+	16.9969i	−0.912444	+	0.912444i	0.0840201	+	0.996464i	$0.473224\pi$
$348$		0			0
$349$			4.38538i			0.234744i	0.993088	+	0.117372i	$0.0374469\pi$
$349$			4.38538i			0.234744i	−0.993088	+	0.117372i	$0.962553\pi$
$350$		0			0
$351$			0.513824i			0.0274259i
$352$		0			0
$353$	−2.62734	+	2.62734i	−0.139839	+	0.139839i	−0.773561	−	0.633722i	$-0.781526\pi$
$353$	−2.62734	+	2.62734i	−0.139839	+	0.139839i	0.633722	+	0.773561i	$0.281526\pi$
$354$		0			0
$355$	5.91137	−	7.45763i	0.313743	−	0.395810i
$356$		0			0
$357$	8.28267	+	8.28267i	0.438366	+	0.438366i
$358$		0			0
$359$	34.9952			1.84697			0.923487	−	0.383630i	$-0.125326\pi$
$359$	34.9952			1.84697			0.923487	+	0.383630i	$0.125326\pi$
$360$		0			0
$361$	5.56534			0.292913
$362$		0			0
$363$	−1.29355	−	1.29355i	−0.0678939	−	0.0678939i
$364$		0			0
$365$	29.1600	−	3.37266i	1.52630	−	0.176533i
$366$		0			0
$367$	9.93581	−	9.93581i	0.518645	−	0.518645i	−0.398516	−	0.917161i	$-0.630475\pi$
$367$	9.93581	−	9.93581i	0.518645	−	0.518645i	0.917161	+	0.398516i	$0.130475\pi$
$368$		0			0
$369$			2.72666i			0.141944i
$370$		0			0
$371$			15.5695i			0.808330i
$372$		0			0
$373$	7.08998	−	7.08998i	0.367105	−	0.367105i	−0.499315	−	0.866421i	$-0.666415\pi$
$373$	7.08998	−	7.08998i	0.367105	−	0.367105i	0.866421	+	0.499315i	$0.166415\pi$
$374$		0			0
$375$	10.5199	−	3.78585i	0.543243	−	0.195500i
$376$		0			0
$377$	1.27334	+	1.27334i	0.0655805	+	0.0655805i
$378$		0			0
$379$	−30.0388			−1.54299			−0.771495	−	0.636235i	$-0.780491\pi$
$379$	−30.0388			−1.54299			−0.771495	+	0.636235i	$0.780491\pi$
$380$		0			0
$381$	2.51399			0.128796
$382$		0			0
$383$	−11.9133	−	11.9133i	−0.608744	−	0.608744i	0.333874	−	0.942618i	$-0.391644\pi$
$383$	−11.9133	−	11.9133i	−0.608744	−	0.608744i	−0.942618	+	0.333874i	$0.891644\pi$
$384$		0			0
$385$	−2.72666	−	23.5747i	−0.138963	−	1.20148i
$386$		0			0
$387$	3.92870	−	3.92870i	0.199707	−	0.199707i
$388$		0			0
$389$		−	16.3340i		−	0.828168i	−0.910239	−	0.414084i	$-0.864102\pi$
$389$		−	16.3340i		−	0.828168i	0.910239	−	0.414084i	$-0.135898\pi$
$390$		0			0
$391$			4.25583i			0.215227i
$392$		0			0
$393$	12.8680	−	12.8680i	0.649104	−	0.649104i
$394$		0			0
$395$	0.700510	+	0.555267i	0.0352465	+	0.0279385i
$396$		0			0
$397$	19.1927	+	19.1927i	0.963253	+	0.963253i	0.999348	−	0.0360950i	$-0.0114919\pi$
$397$	19.1927	+	19.1927i	0.963253	+	0.963253i	−0.0360950	+	0.999348i	$0.511492\pi$
$398$		0			0
$399$	−17.3703			−0.869604
$400$		0			0
$401$	26.5653			1.32661			0.663305	−	0.748349i	$-0.269153\pi$
$401$	26.5653			1.32661			0.663305	+	0.748349i	$0.269153\pi$
$402$		0			0
$403$	−1.40102	−	1.40102i	−0.0697898	−	0.0697898i
$404$		0			0
$405$	−1.75233	−	1.38900i	−0.0870741	−	0.0690202i
$406$		0			0
$407$	1.10027	−	1.10027i	0.0545383	−	0.0545383i
$408$		0			0
$409$			25.3947i			1.25569i	0.778339	+	0.627844i	$0.216062\pi$
$409$			25.3947i			1.25569i	−0.778339	+	0.627844i	$0.783938\pi$
$410$		0			0
$411$			8.37122i			0.412922i
$412$		0			0
$413$	−21.5233	+	21.5233i	−1.05909	+	1.05909i
$414$		0			0
$415$	0.0726218	+	0.627889i	0.00356487	+	0.0308218i
$416$		0			0
$417$	8.77801	+	8.77801i	0.429861	+	0.429861i
$418$		0			0
$419$	40.0788			1.95798			0.978988	−	0.203919i	$-0.0653679\pi$
$419$	40.0788			1.95798			0.978988	+	0.203919i	$0.0653679\pi$
$420$		0			0
$421$	−19.3947			−0.945240			−0.472620	−	0.881266i	$-0.656692\pi$
$421$	−19.3947			−0.945240			−0.472620	+	0.881266i	$0.656692\pi$
$422$		0			0
$423$	5.85673	+	5.85673i	0.284764	+	0.284764i
$424$		0			0
$425$	8.80731	−	14.2020i	0.427217	−	0.688899i
$426$		0			0
$427$	37.8962	−	37.8962i	1.83393	−	1.83393i
$428$		0			0
$429$		−	1.55602i		−	0.0751251i
$430$		0			0
$431$			15.8241i			0.762218i	0.924530	+	0.381109i	$0.124458\pi$
$431$			15.8241i			0.762218i	−0.924530	+	0.381109i	$0.875542\pi$
$432$		0			0
$433$	−21.1214	+	21.1214i	−1.01503	+	1.01503i	−0.0151424	+	0.999885i	$0.504820\pi$
$433$	−21.1214	+	21.1214i	−1.01503	+	1.01503i	−0.999885	+	0.0151424i	$0.995180\pi$
$434$		0			0
$435$	−7.78477	+	0.900390i	−0.373251	+	0.0431704i
$436$		0			0
$437$	−4.46264	−	4.46264i	−0.213477	−	0.213477i
$438$		0			0
$439$	6.61188			0.315568			0.157784	−	0.987474i	$-0.449565\pi$
$439$	6.61188			0.315568			0.157784	+	0.987474i	$0.449565\pi$
$440$		0			0
$441$	5.28267			0.251556
$442$		0			0
$443$	14.5419	+	14.5419i	0.690906	+	0.690906i	0.962431	−	0.271525i	$-0.0875280\pi$
$443$	14.5419	+	14.5419i	0.690906	+	0.690906i	−0.271525	+	0.962431i	$0.587528\pi$
$444$		0			0
$445$	−5.94865	+	7.50466i	−0.281993	+	0.355755i
$446$		0			0
$447$	4.09226	−	4.09226i	0.193557	−	0.193557i
$448$		0			0
$449$			33.6120i			1.58625i	0.609060	+	0.793124i	$0.291547\pi$
$449$			33.6120i			1.58625i	−0.609060	+	0.793124i	$0.708453\pi$
$450$		0			0
$451$		−	8.25715i		−	0.388814i
$452$		0			0
$453$	12.7780	−	12.7780i	0.600363	−	0.600363i
$454$		0			0
$455$	−2.50129	+	3.15556i	−0.117262	+	0.147935i
$456$		0			0
$457$	15.5653	+	15.5653i	0.728116	+	0.728116i	0.970244	−	0.242128i	$-0.0778454\pi$
$457$	15.5653	+	15.5653i	0.728116	+	0.728116i	−0.242128	+	0.970244i	$0.577845\pi$
$458$		0			0
$459$	−3.34225			−0.156003
$460$		0			0
$461$	26.1473			1.21780			0.608900	−	0.793247i	$-0.291611\pi$
$461$	26.1473			1.21780			0.608900	+	0.793247i	$0.291611\pi$
$462$		0			0
$463$	−5.77898	−	5.77898i	−0.268572	−	0.268572i	0.559953	−	0.828525i	$-0.310819\pi$
$463$	−5.77898	−	5.77898i	−0.268572	−	0.268572i	−0.828525	+	0.559953i	$0.810819\pi$
$464$		0			0
$465$	8.56534	−	0.990671i	0.397208	−	0.0459413i
$466$		0			0
$467$	2.25517	−	2.25517i	0.104357	−	0.104357i	−0.653000	−	0.757357i	$-0.726490\pi$
$467$	2.25517	−	2.25517i	0.104357	−	0.104357i	0.757357	+	0.653000i	$0.226490\pi$
$468$		0			0
$469$		−	19.4720i		−	0.899132i
$470$		0			0
$471$		−	5.54279i		−	0.255398i
$472$		0			0
$473$	−11.8973	+	11.8973i	−0.547038	+	0.547038i
$474$		0			0
$475$	5.65685	+	24.1274i	0.259554	+	1.10704i
$476$		0			0
$477$	−3.14134	−	3.14134i	−0.143832	−	0.143832i
$478$		0			0
$479$	−1.40102			−0.0640143			−0.0320071	−	0.999488i	$-0.510190\pi$
$479$	−1.40102			−0.0640143			−0.0320071	+	0.999488i	$0.510190\pi$
$480$		0			0
$481$	−0.264015			−0.0120380
$482$		0			0
$483$	3.15556	+	3.15556i	0.143583	+	0.143583i
$484$		0			0
$485$	2.44737	+	21.1600i	0.111130	+	0.960826i
$486$		0			0
$487$	−0.978144	+	0.978144i	−0.0443239	+	0.0443239i	−0.728921	−	0.684597i	$-0.759978\pi$
$487$	−0.978144	+	0.978144i	−0.0443239	+	0.0443239i	0.684597	+	0.728921i	$0.259978\pi$
$488$		0			0
$489$		−	4.56534i		−	0.206452i
$490$		0			0
$491$		−	36.1134i		−	1.62978i	−0.579619	−	0.814888i	$-0.696799\pi$
$491$		−	36.1134i		−	1.62978i	0.579619	−	0.814888i	$-0.303201\pi$
$492$		0			0
$493$	−8.28267	+	8.28267i	−0.373033	+	0.373033i
$494$		0			0
$495$	5.30660	+	4.20633i	0.238514	+	0.189060i
$496$		0			0
$497$	−10.5467	−	10.5467i	−0.473084	−	0.473084i
$498$		0			0
$499$	6.35736			0.284595			0.142297	−	0.989824i	$-0.454551\pi$
$499$	6.35736			0.284595			0.142297	+	0.989824i	$0.454551\pi$
$500$		0			0
$501$	9.83869			0.439560
$502$		0			0
$503$	−17.1704	−	17.1704i	−0.765592	−	0.765592i	0.211735	−	0.977327i	$-0.432089\pi$
$503$	−17.1704	−	17.1704i	−0.765592	−	0.765592i	−0.977327	+	0.211735i	$0.932089\pi$
$504$		0			0
$505$	−10.1413	−	8.03863i	−0.451284	−	0.357714i
$506$		0			0
$507$	9.00570	−	9.00570i	0.399957	−	0.399957i
$508$		0			0
$509$			18.8739i			0.836572i	0.908315	+	0.418286i	$0.137369\pi$
$509$			18.8739i			0.836572i	−0.908315	+	0.418286i	$0.862631\pi$
$510$		0			0
$511$		−	46.0081i		−	2.03528i
$512$		0			0
$513$	3.50466	−	3.50466i	0.154735	−	0.154735i
$514$		0			0
$515$	−4.75646	−	41.1244i	−0.209595	−	1.81216i
$516$		0			0
$517$	−17.7360	−	17.7360i	−0.780028	−	0.780028i
$518$		0			0
$519$	0.887197			0.0389436
$520$		0			0
$521$	−33.9346			−1.48670			−0.743351	−	0.668901i	$-0.766765\pi$
$521$	−33.9346			−1.48670			−0.743351	+	0.668901i	$0.766765\pi$
$522$		0			0
$523$	3.78345	+	3.78345i	0.165439	+	0.165439i	0.784971	−	0.619532i	$-0.212678\pi$
$523$	3.78345	+	3.78345i	0.165439	+	0.165439i	−0.619532	+	0.784971i	$0.712678\pi$
$524$		0			0
$525$	−4.00000	−	17.0607i	−0.174574	−	0.744589i
$526$		0			0
$527$	9.11317	−	9.11317i	0.396976	−	0.396976i
$528$		0			0
$529$		−	21.3786i		−	0.929504i
$530$		0			0
$531$		−	8.68516i		−	0.376904i
$532$		0			0
$533$	−0.990671	+	0.990671i	−0.0429107	+	0.0429107i
$534$		0			0
$535$	30.5112	−	3.52894i	1.31911	−	0.152569i
$536$		0			0
$537$	6.32131	+	6.32131i	0.272784	+	0.272784i
$538$		0			0
$539$	−15.9976			−0.689063
$540$		0			0
$541$	−28.4813			−1.22451			−0.612253	−	0.790662i	$-0.709737\pi$
$541$	−28.4813			−1.22451			−0.612253	+	0.790662i	$0.709737\pi$
$542$		0			0
$543$	−0.713703	−	0.713703i	−0.0306279	−	0.0306279i
$544$		0			0
$545$	−14.5327	+	18.3340i	−0.622510	+	0.785343i
$546$		0			0
$547$	0.726896	−	0.726896i	0.0310798	−	0.0310798i	−0.691396	−	0.722476i	$-0.743004\pi$
$547$	0.726896	−	0.726896i	0.0310798	−	0.0310798i	0.722476	+	0.691396i	$0.243004\pi$
$548$		0			0
$549$			15.2920i			0.652647i
$550$		0			0
$551$		−	17.3703i		−	0.740001i
$552$		0			0
$553$	0.990671	−	0.990671i	0.0421276	−	0.0421276i
$554$		0			0
$555$	0.713703	−	0.900390i	0.0302950	−	0.0382194i
$556$		0			0
$557$	11.4427	+	11.4427i	0.484841	+	0.484841i	0.906674	−	0.421832i	$-0.138613\pi$
$557$	11.4427	+	11.4427i	0.484841	+	0.484841i	−0.421832	+	0.906674i	$0.638613\pi$
$558$		0			0
$559$	2.85481			0.120746
$560$		0			0
$561$	10.1214			0.427324
$562$		0			0
$563$	−7.08426	−	7.08426i	−0.298566	−	0.298566i	0.541886	−	0.840452i	$-0.317710\pi$
$563$	−7.08426	−	7.08426i	−0.298566	−	0.298566i	−0.840452	+	0.541886i	$0.817710\pi$
$564$		0			0
$565$	−33.4427	+	3.86799i	−1.40694	+	0.162728i
$566$		0			0
$567$	−2.47817	+	2.47817i	−0.104073	+	0.104073i
$568$		0			0
$569$		−	46.2427i		−	1.93860i	−0.245890	−	0.969298i	$-0.579080\pi$
$569$		−	46.2427i		−	1.93860i	0.245890	−	0.969298i	$-0.420920\pi$
$570$		0			0
$571$			31.2381i			1.30727i	0.756808	+	0.653637i	$0.226758\pi$
$571$			31.2381i			1.30727i	−0.756808	+	0.653637i	$0.773242\pi$
$572$		0			0
$573$	15.2920	−	15.2920i	0.638833	−	0.638833i
$574$		0			0
$575$	3.35544	−	5.41074i	0.139932	−	0.225643i
$576$		0			0
$577$	1.16131	+	1.16131i	0.0483461	+	0.0483461i	0.730866	−	0.682520i	$-0.239116\pi$
$577$	1.16131	+	1.16131i	0.0483461	+	0.0483461i	−0.682520	+	0.730866i	$0.739116\pi$
$578$		0			0
$579$	−16.3559			−0.679727
$580$		0			0
$581$	0.990671			0.0411000
$582$		0			0
$583$	9.51293	+	9.51293i	0.393985	+	0.393985i
$584$		0			0
$585$	−0.132007	−	1.14134i	−0.00545783	−	0.0471884i
$586$		0			0
$587$	23.6268	−	23.6268i	0.975183	−	0.975183i	−0.0245164	−	0.999699i	$-0.507805\pi$
$587$	23.6268	−	23.6268i	0.975183	−	0.975183i	0.999699	+	0.0245164i	$0.00780461\pi$
$588$		0			0
$589$			19.1120i			0.787498i
$590$		0			0
$591$		−	13.3276i		−	0.548223i
$592$		0			0
$593$	−0.260625	+	0.260625i	−0.0107026	+	0.0107026i	−0.712438	−	0.701735i	$-0.752409\pi$
$593$	−0.260625	+	0.260625i	−0.0107026	+	0.0107026i	0.701735	+	0.712438i	$0.252409\pi$
$594$		0			0
$595$	−20.5259	−	16.2701i	−0.841479	−	0.667007i
$596$		0			0
$597$	7.78734	+	7.78734i	0.318714	+	0.318714i
$598$		0			0
$599$	33.0851			1.35182			0.675910	−	0.736984i	$-0.263751\pi$
$599$	33.0851			1.35182			0.675910	+	0.736984i	$0.263751\pi$
$600$		0			0
$601$	−24.3200			−0.992033			−0.496016	−	0.868313i	$-0.665204\pi$
$601$	−24.3200			−0.992033			−0.496016	+	0.868313i	$0.665204\pi$
$602$		0			0
$603$	3.92870	+	3.92870i	0.159989	+	0.159989i
$604$		0			0
$605$	3.20565	+	2.54099i	0.130328	+	0.103306i
$606$		0			0
$607$	4.53347	−	4.53347i	0.184008	−	0.184008i	−0.609092	−	0.793100i	$-0.708466\pi$
$607$	4.53347	−	4.53347i	0.184008	−	0.184008i	0.793100	+	0.609092i	$0.208466\pi$
$608$		0			0
$609$			12.2827i			0.497719i
$610$		0			0
$611$			4.25583i			0.172173i
$612$		0			0
$613$	20.2793	−	20.2793i	0.819073	−	0.819073i	−0.166901	−	0.985974i	$-0.553376\pi$
$613$	20.2793	−	20.2793i	0.819073	−	0.819073i	0.985974	+	0.166901i	$0.0533761\pi$
$614$		0			0
$615$	−0.700510	−	6.05661i	−0.0282473	−	0.244226i
$616$		0			0
$617$	17.1086	+	17.1086i	0.688768	+	0.688768i	0.961960	−	0.273192i	$-0.0880793\pi$
$617$	17.1086	+	17.1086i	0.688768	+	0.688768i	−0.273192	+	0.961960i	$0.588079\pi$
$618$		0			0
$619$	29.4373			1.18319			0.591593	−	0.806237i	$-0.298499\pi$
$619$	29.4373			1.18319			0.591593	+	0.806237i	$0.298499\pi$
$620$		0			0
$621$	−1.27334			−0.0510975
$622$		0			0
$623$	10.6132	+	10.6132i	0.425209	+	0.425209i
$624$		0			0
$625$	−22.3947	+	11.1120i	−0.895788	+	0.444481i
$626$		0			0
$627$	−10.6132	+	10.6132i	−0.423850	+	0.423850i
$628$		0			0
$629$		−	1.71733i		−	0.0684743i
$630$		0			0
$631$			5.25710i			0.209282i	0.994510	+	0.104641i	$0.0333693\pi$
$631$			5.25710i			0.209282i	−0.994510	+	0.104641i	$0.966631\pi$
$632$		0			0
$633$	19.7873	−	19.7873i	0.786476	−	0.786476i
$634$		0			0
$635$	−5.58423	+	0.645875i	−0.221604	+	0.0256308i
$636$		0			0
$637$	1.91934	+	1.91934i	0.0760472	+	0.0760472i
$638$		0			0
$639$	4.25583			0.168358
$640$		0			0
$641$	20.0773			0.793004			0.396502	−	0.918034i	$-0.370224\pi$
$641$	20.0773			0.793004			0.396502	+	0.918034i	$0.370224\pi$
$642$		0			0
$643$	−9.28480	−	9.28480i	−0.366157	−	0.366157i	0.499917	−	0.866073i	$-0.333364\pi$
$643$	−9.28480	−	9.28480i	−0.366157	−	0.366157i	−0.866073	+	0.499917i	$0.833364\pi$
$644$		0			0
$645$	−7.71733	+	9.73599i	−0.303869	+	0.383354i
$646$		0			0
$647$	−28.7387	+	28.7387i	−1.12983	+	1.12983i	−0.139630	+	0.990204i	$0.544591\pi$
$647$	−28.7387	+	28.7387i	−1.12983	+	1.12983i	−0.990204	+	0.139630i	$0.955409\pi$
$648$		0			0
$649$			26.3013i			1.03242i
$650$		0			0
$651$		−	13.5142i		−	0.529665i
$652$		0			0
$653$	11.9380	−	11.9380i	0.467170	−	0.467170i	−0.433826	−	0.900996i	$-0.642837\pi$
$653$	11.9380	−	11.9380i	0.467170	−	0.467170i	0.900996	+	0.433826i	$0.142837\pi$
$654$		0			0
$655$	−25.2772	+	31.8891i	−0.987663	+	1.24601i
$656$		0			0
$657$	9.28267	+	9.28267i	0.362152	+	0.362152i
$658$		0			0
$659$	−17.9963			−0.701038			−0.350519	−	0.936556i	$-0.613995\pi$
$659$	−17.9963			−0.701038			−0.350519	+	0.936556i	$0.613995\pi$
$660$		0			0
$661$	9.06794			0.352702			0.176351	−	0.984327i	$-0.443571\pi$
$661$	9.06794			0.352702			0.176351	+	0.984327i	$0.443571\pi$
$662$		0			0
$663$	−1.21433	−	1.21433i	−0.0471608	−	0.0471608i
$664$		0			0
$665$	38.5840	−	4.46264i	1.49622	−	0.173054i
$666$		0			0
$667$	−3.15556	+	3.15556i	−0.122184	+	0.122184i
$668$		0			0
$669$		−	12.0700i		−	0.466654i
$670$		0			0
$671$		−	46.3089i		−	1.78773i
$672$		0			0
$673$	35.7640	−	35.7640i	1.37860	−	1.37860i	0.531611	−	0.846988i	$-0.321587\pi$
$673$	35.7640	−	35.7640i	1.37860	−	1.37860i	0.846988	−	0.531611i	$-0.178413\pi$
$674$		0			0
$675$	4.24924	+	2.63514i	0.163553	+	0.101427i
$676$		0			0
$677$	−16.2020	−	16.2020i	−0.622694	−	0.622694i	0.323525	−	0.946219i	$-0.395132\pi$
$677$	−16.2020	−	16.2020i	−0.622694	−	0.622694i	−0.946219	+	0.323525i	$0.895132\pi$
$678$		0			0
$679$	33.3859			1.28123
$680$		0			0
$681$	1.45331			0.0556911
$682$		0			0
$683$	33.3943	+	33.3943i	1.27780	+	1.27780i	0.941899	+	0.335897i	$0.109039\pi$
$683$	33.3943	+	33.3943i	1.27780	+	1.27780i	0.335897	+	0.941899i	$0.390961\pi$
$684$		0			0
$685$	−2.15066	−	18.5946i	−0.0821727	−	0.710465i
$686$		0			0
$687$	−6.25649	+	6.25649i	−0.238700	+	0.238700i
$688$		0			0
$689$		−	2.28267i		−	0.0869629i
$690$		0			0
$691$		−	24.6365i		−	0.937216i	−0.883406	−	0.468608i	$-0.844756\pi$
$691$		−	24.6365i		−	0.937216i	0.883406	−	0.468608i	$-0.155244\pi$
$692$		0			0
$693$	7.50466	−	7.50466i	0.285079	−	0.285079i
$694$		0			0
$695$	−21.7534	−	17.2431i	−0.825154	−	0.654067i
$696$		0			0
$697$	−6.44398	−	6.44398i	−0.244083	−	0.244083i
$698$		0			0
$699$	6.94381			0.262639
$700$		0			0
$701$	23.0420			0.870285			0.435143	−	0.900362i	$-0.356698\pi$
$701$	23.0420			0.870285			0.435143	+	0.900362i	$0.356698\pi$
$702$		0			0
$703$	1.80078	+	1.80078i	0.0679177	+	0.0679177i
$704$		0			0
$705$	−14.5140	−	11.5047i	−0.546629	−	0.433291i
$706$		0			0
$707$	−14.3420	+	14.3420i	−0.539387	+	0.539387i
$708$		0			0
$709$			37.7360i			1.41720i	0.705608	+	0.708602i	$0.250674\pi$
$709$			37.7360i			1.41720i	−0.705608	+	0.708602i	$0.749326\pi$
$710$		0			0
$711$			0.399759i			0.0149921i
$712$		0			0
$713$	3.47197	−	3.47197i	0.130026	−	0.130026i
$714$		0			0
$715$	0.399759	+	3.45632i	0.0149501	+	0.129259i
$716$		0			0
$717$	13.4533	+	13.4533i	0.502423	+	0.502423i
$718$		0			0
$719$	−41.3423			−1.54181			−0.770903	−	0.636953i	$-0.780195\pi$
$719$	−41.3423			−1.54181			−0.770903	+	0.636953i	$0.780195\pi$
$720$		0			0
$721$	−64.8853			−2.41646
$722$		0			0
$723$	−2.05529	−	2.05529i	−0.0764372	−	0.0764372i
$724$		0			0
$725$	17.0607	−	4.00000i	0.633618	−	0.148556i
$726$		0			0
$727$	−9.48981	+	9.48981i	−0.351958	+	0.351958i	−0.860838	−	0.508880i	$-0.830060\pi$
$727$	−9.48981	+	9.48981i	−0.351958	+	0.351958i	0.508880	+	0.860838i	$0.330060\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			18.5696i			0.686821i
$732$		0			0
$733$	−3.21134	+	3.21134i	−0.118614	+	0.118614i	−0.763922	−	0.645308i	$-0.776729\pi$
$733$	−3.21134	+	3.21134i	−0.118614	+	0.118614i	0.645308	+	0.763922i	$0.276729\pi$
$734$		0			0
$735$	−11.7342	+	1.35718i	−0.432822	+	0.0500604i
$736$		0			0
$737$	−11.8973	−	11.8973i	−0.438243	−	0.438243i
$738$		0			0
$739$	25.3832			0.933737			0.466868	−	0.884327i	$-0.345382\pi$
$739$	25.3832			0.933737			0.466868	+	0.884327i	$0.345382\pi$
$740$		0			0
$741$	2.54669			0.0935549
$742$		0			0
$743$	32.7400	+	32.7400i	1.20111	+	1.20111i	0.973828	+	0.227285i	$0.0729850\pi$
$743$	32.7400	+	32.7400i	1.20111	+	1.20111i	0.227285	+	0.973828i	$0.427015\pi$
$744$		0			0
$745$	−8.03863	+	10.1413i	−0.294513	+	0.371550i
$746$		0			0
$747$	−0.199879	+	0.199879i	−0.00731321	+	0.00731321i
$748$		0			0
$749$		−	48.1400i		−	1.75900i
$750$		0			0
$751$			24.4810i			0.893323i	0.894703	+	0.446662i	$0.147387\pi$
$751$			24.4810i			0.893323i	−0.894703	+	0.446662i	$0.852613\pi$
$752$		0			0
$753$	1.96137	−	1.96137i	0.0714762	−	0.0714762i
$754$		0			0
$755$	−25.1005	+	31.6661i	−0.913499	+	1.15245i
$756$		0			0
$757$	−22.9473	−	22.9473i	−0.834035	−	0.834035i	0.154031	−	0.988066i	$-0.450774\pi$
$757$	−22.9473	−	22.9473i	−0.834035	−	0.834035i	−0.988066	+	0.154031i	$0.950774\pi$
$758$		0			0
$759$	3.85607			0.139967
$760$		0			0
$761$	37.0466			1.34294			0.671470	−	0.741032i	$-0.265663\pi$
$761$	37.0466			1.34294			0.671470	+	0.741032i	$0.265663\pi$
$762$		0			0
$763$	25.9282	+	25.9282i	0.938665	+	0.938665i
$764$		0			0
$765$	7.42401	−	0.858664i	0.268416	−	0.0310451i
$766$		0			0
$767$	3.15556	−	3.15556i	0.113941	−	0.113941i
$768$		0			0
$769$			6.62395i			0.238866i	0.992842	+	0.119433i	$0.0381077\pi$
$769$			6.62395i			0.238866i	−0.992842	+	0.119433i	$0.961892\pi$
$770$		0			0
$771$			2.94249i			0.105971i
$772$		0			0
$773$	−16.2606	+	16.2606i	−0.584854	+	0.584854i	−0.936233	−	0.351379i	$-0.885713\pi$
$773$	−16.2606	+	16.2606i	−0.584854	+	0.584854i	0.351379	+	0.936233i	$0.385713\pi$
$774$		0			0
$775$	−18.7713	+	4.40108i	−0.674287	+	0.158091i
$776$		0			0
$777$	−1.27334	−	1.27334i	−0.0456809	−	0.0456809i
$778$		0			0
$779$	13.5142			0.484198
$780$		0			0
$781$	−12.8880			−0.461168
$782$		0			0
$783$	−2.47817	−	2.47817i	−0.0885626	−	0.0885626i
$784$		0			0
$785$	1.42401	+	12.3120i	0.0508250	+	0.439433i
$786$		0			0
$787$	−31.2117	+	31.2117i	−1.11258	+	1.11258i	−0.119776	+	0.992801i	$0.538218\pi$
$787$	−31.2117	+	31.2117i	−1.11258	+	1.11258i	−0.992801	+	0.119776i	$0.961782\pi$
$788$		0			0
$789$			6.72666i			0.239475i
$790$		0			0
$791$			52.7652i			1.87612i
$792$		0			0
$793$	−5.55602	+	5.55602i	−0.197300	+	0.197300i
$794$		0			0
$795$	7.78477	+	6.17068i	0.276097	+	0.218851i
$796$		0			0
$797$	−17.3540	−	17.3540i	−0.614710	−	0.614710i	0.329460	−	0.944170i	$-0.393133\pi$
$797$	−17.3540	−	17.3540i	−0.614710	−	0.614710i	−0.944170	+	0.329460i	$0.893133\pi$
$798$		0			0
$799$	−27.6828			−0.979346
$800$		0			0
$801$	−4.28267			−0.151321
$802$		0			0
$803$	−28.1108	−	28.1108i	−0.992008	−	0.992008i
$804$		0			0
$805$	−7.82003	−	6.19863i	−0.275620	−	0.218473i
$806$		0			0
$807$	−15.3334	+	15.3334i	−0.539760	+	0.539760i
$808$		0			0
$809$			27.4320i			0.964458i	0.876045	+	0.482229i	$0.160173\pi$
$809$			27.4320i			0.964458i	−0.876045	+	0.482229i	$0.839827\pi$
$810$		0			0
$811$		−	27.1840i		−	0.954559i	−0.878751	−	0.477280i	$-0.841623\pi$
$811$		−	27.1840i		−	0.954559i	0.878751	−	0.477280i	$-0.158377\pi$
$812$		0			0
$813$	−2.23132	+	2.23132i	−0.0782558	+	0.0782558i
$814$		0			0
$815$	1.17289	+	10.1408i	0.0410846	+	0.355217i
$816$		0			0
$817$	−19.4720	−	19.4720i	−0.681238	−	0.681238i
$818$		0			0
$819$	−1.80078			−0.0629243
$820$		0			0
$821$	−23.6074			−0.823903			−0.411951	−	0.911206i	$-0.635153\pi$
$821$	−23.6074			−0.823903			−0.411951	+	0.911206i	$0.635153\pi$
$822$		0			0
$823$	−24.6596	−	24.6596i	−0.859579	−	0.859579i	0.131709	−	0.991288i	$-0.457954\pi$
$823$	−24.6596	−	24.6596i	−0.859579	−	0.859579i	−0.991288	+	0.131709i	$0.957954\pi$
$824$		0			0
$825$	−12.8680	−	7.98002i	−0.448006	−	0.277829i
$826$		0			0
$827$	−13.5406	+	13.5406i	−0.470854	+	0.470854i	−0.902191	−	0.431337i	$-0.858042\pi$
$827$	−13.5406	+	13.5406i	−0.470854	+	0.470854i	0.431337	+	0.902191i	$0.358042\pi$
$828$		0			0
$829$			9.00933i			0.312907i	0.987685	+	0.156453i	$0.0500061\pi$
$829$			9.00933i			0.312907i	−0.987685	+	0.156453i	$0.949994\pi$
$830$		0			0
$831$		−	4.99779i		−	0.173371i
$832$		0			0
$833$	−12.4847	+	12.4847i	−0.432569	+	0.432569i
$834$		0			0
$835$	−21.8543	+	2.52768i	−0.756299	+	0.0874738i
$836$		0			0
$837$	2.72666	+	2.72666i	0.0942470	+	0.0942470i
$838$		0			0
$839$	10.2597			0.354203			0.177102	−	0.984193i	$-0.443328\pi$
$839$	10.2597			0.354203			0.177102	+	0.984193i	$0.443328\pi$
$840$		0			0
$841$	16.7173			0.576460
$842$		0			0
$843$	−0.127258	−	0.127258i	−0.00438298	−	0.00438298i
$844$		0			0
$845$	−17.6903	+	22.3177i	−0.608566	+	0.767751i
$846$		0			0
$847$	4.53347	−	4.53347i	0.155772	−	0.155772i
$848$		0			0
$849$			13.9160i			0.477594i
$850$		0			0
$851$		−	0.654274i		−	0.0224282i
$852$		0			0
$853$	−17.1086	+	17.1086i	−0.585789	+	0.585789i	−0.936488	−	0.350699i	$-0.885944\pi$
$853$	−17.1086	+	17.1086i	−0.585789	+	0.585789i	0.350699	+	0.936488i	$0.385944\pi$
$854$		0			0
$855$	−6.88438	+	8.68516i	−0.235441	+	0.297026i
$856$		0			0
$857$	−26.7674	−	26.7674i	−0.914356	−	0.914356i	0.0822556	−	0.996611i	$-0.473788\pi$
$857$	−26.7674	−	26.7674i	−0.914356	−	0.914356i	−0.996611	+	0.0822556i	$0.973788\pi$
$858$		0			0
$859$	−28.6378			−0.977109			−0.488554	−	0.872533i	$-0.662476\pi$
$859$	−28.6378			−0.977109			−0.488554	+	0.872533i	$0.662476\pi$
$860$		0			0
$861$	−9.55602			−0.325668
$862$		0			0
$863$	15.8157	+	15.8157i	0.538371	+	0.538371i	0.923050	−	0.384679i	$-0.125688\pi$
$863$	15.8157	+	15.8157i	0.538371	+	0.538371i	−0.384679	+	0.923050i	$0.625688\pi$
$864$		0			0
$865$	−1.97070	+	0.227931i	−0.0670057	+	0.00774990i
$866$		0			0
$867$	−4.12198	+	4.12198i	−0.139990	+	0.139990i
$868$		0			0
$869$		−	1.21059i		−	0.0410665i
$870$		0			0
$871$			2.85481i			0.0967316i
$872$		0			0
$873$	−6.73599	+	6.73599i	−0.227979	+	0.227979i
$874$		0			0
$875$	13.2681	+	36.8686i	0.448545	+	1.24638i
$876$		0			0
$877$	17.3727	+	17.3727i	0.586633	+	0.586633i	0.936718	−	0.350085i	$-0.113847\pi$
$877$	17.3727	+	17.3727i	0.586633	+	0.586633i	−0.350085	+	0.936718i	$0.613847\pi$
$878$		0			0
$879$	22.4407			0.756907
$880$		0			0
$881$	56.5254			1.90439			0.952194	−	0.305493i	$-0.0988211\pi$
$881$	56.5254			1.90439			0.952194	+	0.305493i	$0.0988211\pi$
$882$		0			0
$883$	−15.1962	−	15.1962i	−0.511392	−	0.511392i	0.403561	−	0.914953i	$-0.367772\pi$
$883$	−15.1962	−	15.1962i	−0.511392	−	0.511392i	−0.914953	+	0.403561i	$0.867772\pi$
$884$		0			0
$885$	2.23132	+	19.2920i	0.0750050	+	0.648494i
$886$		0			0
$887$	11.0676	−	11.0676i	0.371613	−	0.371613i	−0.496451	−	0.868065i	$-0.665364\pi$
$887$	11.0676	−	11.0676i	0.371613	−	0.371613i	0.868065	+	0.496451i	$0.165364\pi$
$888$		0			0
$889$			8.81070i			0.295501i
$890$		0			0
$891$			3.02831i			0.101452i
$892$		0			0
$893$	29.0280	−	29.0280i	0.971385	−	0.971385i
$894$		0			0
$895$	−15.6653	−	12.4172i	−0.523633	−	0.415063i
$896$		0			0
$897$	−0.462642	−	0.462642i	−0.0154472	−	0.0154472i
$898$		0			0
$899$	13.5142			0.450725
$900$		0			0
$901$	14.8480			0.494659
$902$		0			0
$903$	13.7688	+	13.7688i	0.458196	+	0.458196i
$904$		0			0
$905$	1.76868	+	1.40196i	0.0587929	+	0.0466028i
$906$		0			0
$907$	−28.1654	+	28.1654i	−0.935217	+	0.935217i	−0.998026	−	0.0628084i	$-0.979994\pi$
$907$	−28.1654	+	28.1654i	−0.935217	+	0.935217i	0.0628084	+	0.998026i	$0.479994\pi$
$908$		0			0
$909$		−	5.78734i		−	0.191954i
$910$		0			0
$911$		−	34.8499i		−	1.15463i	−0.816522	−	0.577315i	$-0.804101\pi$
$911$		−	34.8499i		−	1.15463i	0.816522	−	0.577315i	$-0.195899\pi$
$912$		0			0
$913$	0.605296	−	0.605296i	0.0200324	−	0.0200324i
$914$		0			0
$915$	−3.92870	−	33.9675i	−0.129879	−	1.12293i
$916$		0			0
$917$	45.0980	+	45.0980i	1.48927	+	1.48927i
$918$		0			0
$919$	21.1171			0.696590			0.348295	−	0.937385i	$-0.386761\pi$
$919$	21.1171			0.696590			0.348295	+	0.937385i	$0.386761\pi$
$920$		0			0
$921$	11.0093			0.362770
$922$		0			0
$923$	1.54626	+	1.54626i	0.0508959	+	0.0508959i
$924$		0			0
$925$	−1.35400	+	2.18336i	−0.0445192	+	0.0717884i
$926$		0			0
$927$	13.0914	−	13.0914i	0.429977	−	0.429977i
$928$		0			0
$929$		−	39.0653i		−	1.28169i	−0.767670	−	0.640845i	$-0.778584\pi$
$929$		−	39.0653i		−	1.28169i	0.767670	−	0.640845i	$-0.221416\pi$
$930$		0			0
$931$		−	26.1827i		−	0.858105i
$932$		0			0
$933$	4.99067	−	4.99067i	0.163387	−	0.163387i
$934$		0			0
$935$	−22.4822	+	2.60030i	−0.735246	+	0.0850388i
$936$		0			0
$937$	1.82936	+	1.82936i	0.0597626	+	0.0597626i	0.736356	−	0.676594i	$-0.236545\pi$
$937$	1.82936	+	1.82936i	0.0597626	+	0.0597626i	−0.676594	+	0.736356i	$0.736545\pi$
$938$		0			0
$939$	15.9825			0.521569
$940$		0			0
$941$	−1.58193			−0.0515695			−0.0257847	−	0.999668i	$-0.508208\pi$
$941$	−1.58193			−0.0515695			−0.0257847	+	0.999668i	$0.508208\pi$
$942$		0			0
$943$	−2.45505	−	2.45505i	−0.0799476	−	0.0799476i
$944$		0			0
$945$	4.86799	−	6.14134i	0.158356	−	0.199778i
$946$		0			0
$947$	−15.9429	+	15.9429i	−0.518075	+	0.518075i	−0.916989	−	0.398913i	$-0.869387\pi$
$947$	−15.9429	+	15.9429i	−0.518075	+	0.518075i	0.398913	+	0.916989i	$0.369387\pi$
$948$		0			0
$949$			6.74531i			0.218962i
$950$		0			0
$951$			27.5423i			0.893121i
$952$		0			0
$953$	−27.2113	+	27.2113i	−0.881462	+	0.881462i	−0.993683	−	0.112221i	$-0.964203\pi$
$953$	−27.2113	+	27.2113i	−0.881462	+	0.881462i	0.112221	+	0.993683i	$0.464203\pi$
$954$		0			0
$955$	−30.0388	+	37.8962i	−0.972033	+	1.22629i
$956$		0			0
$957$	7.50466	+	7.50466i	0.242591	+	0.242591i
$958$		0			0
$959$	−29.3383			−0.947383
$960$		0			0
$961$	16.1307			0.520345
$962$		0			0
$963$	9.71281	+	9.71281i	0.312991	+	0.312991i
$964$		0			0
$965$	36.3306	−	4.20202i	1.16952	−	0.135268i
$966$		0			0
$967$	−14.8921	+	14.8921i	−0.478899	+	0.478899i	−0.904780	−	0.425880i	$-0.859964\pi$
$967$	−14.8921	+	14.8921i	−0.478899	+	0.478899i	0.425880	+	0.904780i	$0.359964\pi$
$968$		0			0
$969$			16.5653i			0.532156i
$970$		0			0
$971$		−	41.6250i		−	1.33581i	−0.744246	−	0.667905i	$-0.767191\pi$
$971$		−	41.6250i		−	1.33581i	0.744246	−	0.667905i	$-0.232809\pi$
$972$		0			0
$973$	−30.7640	+	30.7640i	−0.986248	+	0.986248i
$974$		0			0
$975$	0.586446	+	2.50129i	0.0187813	+	0.0801054i
$976$		0			0
$977$	−12.0807	−	12.0807i	−0.386494	−	0.386494i	0.486941	−	0.873435i	$-0.338113\pi$
$977$	−12.0807	−	12.0807i	−0.386494	−	0.386494i	−0.873435	+	0.486941i	$0.838113\pi$
$978$		0			0
$979$	12.9692			0.414499
$980$		0			0
$981$	−10.4626			−0.334046
$982$		0			0
$983$	22.2258	+	22.2258i	0.708893	+	0.708893i	0.966302	−	0.257410i	$-0.0828690\pi$
$983$	22.2258	+	22.2258i	0.708893	+	0.708893i	−0.257410	+	0.966302i	$0.582869\pi$
$984$		0			0
$985$	3.42401	+	29.6040i	0.109098	+	0.943261i
$986$		0			0
$987$	−20.5259	+	20.5259i	−0.653346	+	0.653346i
$988$		0			0
$989$			7.07472i			0.224963i
$990$		0			0
$991$			0.353523i			0.0112300i	0.999984	+	0.00561501i	$0.00178732\pi$
$991$			0.353523i			0.0112300i	−0.999984	+	0.00561501i	$0.998213\pi$
$992$		0			0
$993$	−10.6167	+	10.6167i	−0.336911	+	0.336911i
$994$		0			0
$995$	−19.2984	−	15.2970i	−0.611799	−	0.484949i
$996$		0			0
$997$	−27.9380	−	27.9380i	−0.884805	−	0.884805i	0.109213	−	0.994018i	$-0.465167\pi$
$997$	−27.9380	−	27.9380i	−0.884805	−	0.884805i	−0.994018	+	0.109213i	$0.965167\pi$
$998$		0			0
$999$	0.513824			0.0162567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.w.g.127.3		12
4.3	odd	2	inner	960.2.w.g.127.6		12
5.3	odd	4	inner	960.2.w.g.703.6		12
8.3	odd	2		60.2.j.a.7.6	yes	12
8.5	even	2		60.2.j.a.7.4	✓	12
20.3	even	4	inner	960.2.w.g.703.3		12
24.5	odd	2		180.2.k.e.127.3		12
24.11	even	2		180.2.k.e.127.1		12
40.3	even	4		60.2.j.a.43.4	yes	12
40.13	odd	4		60.2.j.a.43.6	yes	12
40.19	odd	2		300.2.j.d.7.1		12
40.27	even	4		300.2.j.d.43.3		12
40.29	even	2		300.2.j.d.7.3		12
40.37	odd	4		300.2.j.d.43.1		12
120.29	odd	2		900.2.k.n.307.4		12
120.53	even	4		180.2.k.e.163.1		12
120.59	even	2		900.2.k.n.307.6		12
120.77	even	4		900.2.k.n.343.6		12
120.83	odd	4		180.2.k.e.163.3		12
120.107	odd	4		900.2.k.n.343.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.4	✓	12	8.5	even	2
60.2.j.a.7.6	yes	12	8.3	odd	2
60.2.j.a.43.4	yes	12	40.3	even	4
60.2.j.a.43.6	yes	12	40.13	odd	4
180.2.k.e.127.1		12	24.11	even	2
180.2.k.e.127.3		12	24.5	odd	2
180.2.k.e.163.1		12	120.53	even	4
180.2.k.e.163.3		12	120.83	odd	4
300.2.j.d.7.1		12	40.19	odd	2
300.2.j.d.7.3		12	40.29	even	2
300.2.j.d.43.1		12	40.37	odd	4
300.2.j.d.43.3		12	40.27	even	4
900.2.k.n.307.4		12	120.29	odd	2
900.2.k.n.307.6		12	120.59	even	2
900.2.k.n.343.4		12	120.107	odd	4
900.2.k.n.343.6		12	120.77	even	4
960.2.w.g.127.3		12	1.1	even	1	trivial
960.2.w.g.127.6		12	4.3	odd	2	inner
960.2.w.g.703.3		12	20.3	even	4	inner
960.2.w.g.703.6		12	5.3	odd	4	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.w (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.75233 + 1.38900i) q^{5} +(2.47817 - 2.47817i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.75233 + 1.38900i) q^{5} +(2.47817 - 2.47817i) q^{7} +1.00000i q^{9} -3.02831i q^{11} +(-0.363328 + 0.363328i) q^{13} +(-0.256912 - 2.22126i) q^{15} +(-2.36333 - 2.36333i) q^{17} +4.95634 q^{19} -3.50466 q^{21} +(-0.900390 - 0.900390i) q^{23} +(1.14134 + 4.86799i) q^{25} +(0.707107 - 0.707107i) q^{27} -3.50466i q^{29} +3.85607i q^{31} +(-2.14134 + 2.14134i) q^{33} +(7.78477 - 0.900390i) q^{35} +(0.363328 + 0.363328i) q^{37} +0.513824 q^{39} +2.72666 q^{41} +(-3.92870 - 3.92870i) q^{43} +(-1.38900 + 1.75233i) q^{45} +(5.85673 - 5.85673i) q^{47} -5.28267i q^{49} +3.34225i q^{51} +(-3.14134 + 3.14134i) q^{53} +(4.20633 - 5.30660i) q^{55} +(-3.50466 - 3.50466i) q^{57} -8.68516 q^{59} +15.2920 q^{61} +(2.47817 + 2.47817i) q^{63} +(-1.14134 + 0.132007i) q^{65} +(3.92870 - 3.92870i) q^{67} +1.27334i q^{69} -4.25583i q^{71} +(9.28267 - 9.28267i) q^{73} +(2.63514 - 4.24924i) q^{75} +(-7.50466 - 7.50466i) q^{77} +0.399759 q^{79} -1.00000 q^{81} +(0.199879 + 0.199879i) q^{83} +(-0.858664 - 7.42401i) q^{85} +(-2.47817 + 2.47817i) q^{87} +4.28267i q^{89} +1.80078i q^{91} +(2.72666 - 2.72666i) q^{93} +(8.68516 + 6.88438i) q^{95} +(6.73599 + 6.73599i) q^{97} +3.02831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 4 q^{13} - 20 q^{17} - 20 q^{25} + 8 q^{33} - 4 q^{37} + 16 q^{41} - 4 q^{45} - 4 q^{53} + 32 q^{61} + 20 q^{65} + 44 q^{73} - 48 q^{77} - 12 q^{81} - 44 q^{85} + 16 q^{93} - 20 q^{97}+O(q^{100}) \) 12 * q + 4 * q^13 - 20 * q^17 - 20 * q^25 + 8 * q^33 - 4 * q^37 + 16 * q^41 - 4 * q^45 - 4 * q^53 + 32 * q^61 + 20 * q^65 + 44 * q^73 - 48 * q^77 - 12 * q^81 - 44 * q^85 + 16 * q^93 - 20 * q^97

Introduction

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