LMFDB - Embedded newform 960.2.bl.a.49.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(49,960)]

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([0, 1, 0, 2]))

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

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

chi := DirichletCharacter("960.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bl (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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.20
Character	$\chi$	$=$	960.49
Dual form			960.2.bl.a.529.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(1.07735 + 1.95942i) q^{5} +1.22137 q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(1.07735 + 1.95942i) q^{5} +1.22137 q^{7} +1.00000i q^{9} +(-1.38208 - 1.38208i) q^{11} +(2.12237 + 2.12237i) q^{13} +(-0.623711 + 2.14732i) q^{15} +6.00218i q^{17} +(3.06223 - 3.06223i) q^{19} +(0.863636 + 0.863636i) q^{21} -2.90813 q^{23} +(-2.67861 + 4.22197i) q^{25} +(-0.707107 + 0.707107i) q^{27} +(3.18392 - 3.18392i) q^{29} +3.88079 q^{31} -1.95456i q^{33} +(1.31584 + 2.39316i) q^{35} +(2.44376 - 2.44376i) q^{37} +3.00149i q^{39} +2.38396i q^{41} +(-9.00811 + 9.00811i) q^{43} +(-1.95942 + 1.07735i) q^{45} -0.586179i q^{47} -5.50826 q^{49} +(-4.24418 + 4.24418i) q^{51} +(-2.36822 + 2.36822i) q^{53} +(1.21908 - 4.19706i) q^{55} +4.33065 q^{57} +(-8.43447 - 8.43447i) q^{59} +(9.98062 - 9.98062i) q^{61} +1.22137i q^{63} +(-1.87206 + 6.44516i) q^{65} +(3.82203 + 3.82203i) q^{67} +(-2.05636 - 2.05636i) q^{69} +11.5314i q^{71} +1.31108 q^{73} +(-4.87945 + 1.09132i) q^{75} +(-1.68803 - 1.68803i) q^{77} +12.5967 q^{79} -1.00000 q^{81} +(2.91633 + 2.91633i) q^{83} +(-11.7608 + 6.46647i) q^{85} +4.50274 q^{87} +9.58659i q^{89} +(2.59220 + 2.59220i) q^{91} +(2.74413 + 2.74413i) q^{93} +(9.29930 + 2.70108i) q^{95} -9.45309i q^{97} +(1.38208 - 1.38208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{19} + 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} + 16 q^{61} + 16 q^{65} - 16 q^{69} + 16 q^{75} + 96 q^{79} - 48 q^{81} + 32 q^{91} + 48 q^{95}+O(q^{100}) $ 48 * q - 8 * q^19 + 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 + 16 * q^61 + 16 * q^65 - 16 * q^69 + 16 * q^75 + 96 * q^79 - 48 * q^81 + 32 * q^91 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.07735	+	1.95942i	0.481808	+	0.876277i
$5$	1.07735	+	1.95942i	0.481808	+	0.876277i
$6$		0			0
$7$	1.22137			0.461633			0.230817	−	0.972997i	$-0.425860\pi$
$7$	1.22137			0.461633			0.230817	+	0.972997i	$0.425860\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.38208	−	1.38208i	−0.416713	−	0.416713i	0.467356	−	0.884069i	$-0.345207\pi$
$11$	−1.38208	−	1.38208i	−0.416713	−	0.416713i	−0.884069	+	0.467356i	$0.845207\pi$
$12$		0			0
$13$	2.12237	+	2.12237i	0.588641	+	0.588641i	0.937263	−	0.348622i	$-0.113350\pi$
$13$	2.12237	+	2.12237i	0.588641	+	0.588641i	−0.348622	+	0.937263i	$0.613350\pi$
$14$		0			0
$15$	−0.623711	+	2.14732i	−0.161042	+	0.554436i
$16$		0			0
$17$			6.00218i			1.45574i	0.685714	+	0.727871i	$0.259490\pi$
$17$			6.00218i			1.45574i	−0.685714	+	0.727871i	$0.740510\pi$
$18$		0			0
$19$	3.06223	−	3.06223i	0.702525	−	0.702525i	−0.262427	−	0.964952i	$-0.584523\pi$
$19$	3.06223	−	3.06223i	0.702525	−	0.702525i	0.964952	+	0.262427i	$0.0845230\pi$
$20$		0			0
$21$	0.863636	+	0.863636i	0.188461	+	0.188461i
$22$		0			0
$23$	−2.90813			−0.606387			−0.303193	−	0.952929i	$-0.598053\pi$
$23$	−2.90813			−0.606387			−0.303193	+	0.952929i	$0.598053\pi$
$24$		0			0
$25$	−2.67861	+	4.22197i	−0.535723	+	0.844394i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	3.18392	−	3.18392i	0.591239	−	0.591239i	−0.346727	−	0.937966i	$-0.612707\pi$
$29$	3.18392	−	3.18392i	0.591239	−	0.591239i	0.937966	+	0.346727i	$0.112707\pi$
$30$		0			0
$31$	3.88079			0.697011			0.348505	−	0.937307i	$-0.386689\pi$
$31$	3.88079			0.697011			0.348505	+	0.937307i	$0.386689\pi$
$32$		0			0
$33$		−	1.95456i		−	0.340245i
$34$		0			0
$35$	1.31584	+	2.39316i	0.222418	+	0.404518i
$36$		0			0
$37$	2.44376	−	2.44376i	0.401752	−	0.401752i	−0.477098	−	0.878850i	$-0.658311\pi$
$37$	2.44376	−	2.44376i	0.401752	−	0.401752i	0.878850	+	0.477098i	$0.158311\pi$
$38$		0			0
$39$			3.00149i			0.480623i
$40$		0			0
$41$			2.38396i			0.372312i	0.982520	+	0.186156i	$0.0596029\pi$
$41$			2.38396i			0.372312i	−0.982520	+	0.186156i	$0.940397\pi$
$42$		0			0
$43$	−9.00811	+	9.00811i	−1.37372	+	1.37372i	−0.518871	+	0.854852i	$0.673648\pi$
$43$	−9.00811	+	9.00811i	−1.37372	+	1.37372i	−0.854852	+	0.518871i	$0.826352\pi$
$44$		0			0
$45$	−1.95942	+	1.07735i	−0.292092	+	0.160603i
$46$		0			0
$47$		−	0.586179i		−	0.0855030i	−0.999086	−	0.0427515i	$-0.986388\pi$
$47$		−	0.586179i		−	0.0855030i	0.999086	−	0.0427515i	$-0.0136124\pi$
$48$		0			0
$49$	−5.50826			−0.786895
$50$		0			0
$51$	−4.24418	+	4.24418i	−0.594304	+	0.594304i
$52$		0			0
$53$	−2.36822	+	2.36822i	−0.325300	+	0.325300i	−0.850796	−	0.525496i	$-0.823880\pi$
$53$	−2.36822	+	2.36822i	−0.325300	+	0.325300i	0.525496	+	0.850796i	$0.323880\pi$
$54$		0			0
$55$	1.21908	−	4.19706i	0.164381	−	0.565931i
$56$		0			0
$57$	4.33065			0.573609
$58$		0			0
$59$	−8.43447	−	8.43447i	−1.09807	−	1.09807i	−0.994636	−	0.103438i	$-0.967016\pi$
$59$	−8.43447	−	8.43447i	−1.09807	−	1.09807i	−0.103438	−	0.994636i	$-0.532984\pi$
$60$		0			0
$61$	9.98062	−	9.98062i	1.27789	−	1.27789i	0.336040	−	0.941848i	$-0.390912\pi$
$61$	9.98062	−	9.98062i	1.27789	−	1.27789i	0.941848	−	0.336040i	$-0.109088\pi$
$62$		0			0
$63$			1.22137i			0.153878i
$64$		0			0
$65$	−1.87206	+	6.44516i	−0.232201	+	0.799424i
$66$		0			0
$67$	3.82203	+	3.82203i	0.466936	+	0.466936i	0.900920	−	0.433985i	$-0.142893\pi$
$67$	3.82203	+	3.82203i	0.466936	+	0.466936i	−0.433985	+	0.900920i	$0.642893\pi$
$68$		0			0
$69$	−2.05636	−	2.05636i	−0.247556	−	0.247556i
$70$		0			0
$71$			11.5314i			1.36852i	0.729238	+	0.684260i	$0.239875\pi$
$71$			11.5314i			1.36852i	−0.729238	+	0.684260i	$0.760125\pi$
$72$		0			0
$73$	1.31108			0.153450			0.0767250	−	0.997052i	$-0.475554\pi$
$73$	1.31108			0.153450			0.0767250	+	0.997052i	$0.475554\pi$
$74$		0			0
$75$	−4.87945	+	1.09132i	−0.563430	+	0.126014i
$76$		0			0
$77$	−1.68803	−	1.68803i	−0.192368	−	0.192368i
$78$		0			0
$79$	12.5967			1.41724			0.708619	−	0.705592i	$-0.249319\pi$
$79$	12.5967			1.41724			0.708619	+	0.705592i	$0.249319\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	2.91633	+	2.91633i	0.320108	+	0.320108i	0.848809	−	0.528700i	$-0.177320\pi$
$83$	2.91633	+	2.91633i	0.320108	+	0.320108i	−0.528700	+	0.848809i	$0.677320\pi$
$84$		0			0
$85$	−11.7608	+	6.46647i	−1.27563	+	0.701387i
$86$		0			0
$87$	4.50274			0.482744
$88$		0			0
$89$			9.58659i			1.01618i	0.861305	+	0.508088i	$0.169648\pi$
$89$			9.58659i			1.01618i	−0.861305	+	0.508088i	$0.830352\pi$
$90$		0			0
$91$	2.59220	+	2.59220i	0.271736	+	0.271736i
$92$		0			0
$93$	2.74413	+	2.74413i	0.284553	+	0.284553i
$94$		0			0
$95$	9.29930	+	2.70108i	0.954088	+	0.277125i
$96$		0			0
$97$		−	9.45309i		−	0.959816i	−0.877319	−	0.479908i	$-0.840670\pi$
$97$		−	9.45309i		−	0.959816i	0.877319	−	0.479908i	$-0.159330\pi$
$98$		0			0
$99$	1.38208	−	1.38208i	0.138904	−	0.138904i
$100$		0			0
$101$	−11.6519	−	11.6519i	−1.15940	−	1.15940i	−0.984604	−	0.174798i	$-0.944073\pi$
$101$	−11.6519	−	11.6519i	−1.15940	−	1.15940i	−0.174798	−	0.984604i	$-0.555927\pi$
$102$		0			0
$103$	2.15006			0.211852			0.105926	−	0.994374i	$-0.466219\pi$
$103$	2.15006			0.211852			0.105926	+	0.994374i	$0.466219\pi$
$104$		0			0
$105$	−0.761780	+	2.62266i	−0.0743421	+	0.255946i
$106$		0			0
$107$	13.4992	−	13.4992i	1.30501	−	1.30501i	0.380048	−	0.924967i	$-0.375908\pi$
$107$	13.4992	−	13.4992i	1.30501	−	1.30501i	0.924967	−	0.380048i	$-0.124092\pi$
$108$		0			0
$109$	10.7618	−	10.7618i	1.03079	−	1.03079i	0.0312781	−	0.999511i	$-0.490042\pi$
$109$	10.7618	−	10.7618i	1.03079	−	1.03079i	0.999511	−	0.0312781i	$-0.00995775\pi$
$110$		0			0
$111$	3.45601			0.328029
$112$		0			0
$113$			12.6206i			1.18725i	0.804742	+	0.593624i	$0.202304\pi$
$113$			12.6206i			1.18725i	−0.804742	+	0.593624i	$0.797696\pi$
$114$		0			0
$115$	−3.13308	−	5.69823i	−0.292162	−	0.531363i
$116$		0			0
$117$	−2.12237	+	2.12237i	−0.196214	+	0.196214i
$118$		0			0
$119$			7.33086i			0.672018i
$120$		0			0
$121$		−	7.17971i		−	0.652701i
$122$		0			0
$123$	−1.68571	+	1.68571i	−0.151996	+	0.151996i
$124$		0			0
$125$	−11.1584	−	0.699962i	−0.998038	−	0.0626065i
$126$		0			0
$127$		−	9.66786i		−	0.857883i	−0.903332	−	0.428942i	$-0.858887\pi$
$127$		−	9.66786i		−	0.857883i	0.903332	−	0.428942i	$-0.141113\pi$
$128$		0			0
$129$	−12.7394			−1.12164
$130$		0			0
$131$	−10.5362	+	10.5362i	−0.920553	+	0.920553i	−0.997068	−	0.0765154i	$-0.975621\pi$
$131$	−10.5362	+	10.5362i	−0.920553	+	0.920553i	0.0765154	+	0.997068i	$0.475621\pi$
$132$		0			0
$133$	3.74011	−	3.74011i	0.324309	−	0.324309i
$134$		0			0
$135$	−2.14732	−	0.623711i	−0.184812	−	0.0536805i
$136$		0			0
$137$	12.9189			1.10374			0.551869	−	0.833931i	$-0.313915\pi$
$137$	12.9189			1.10374			0.551869	+	0.833931i	$0.313915\pi$
$138$		0			0
$139$	−11.5153	−	11.5153i	−0.976718	−	0.976718i	0.0230167	−	0.999735i	$-0.492673\pi$
$139$	−11.5153	−	11.5153i	−0.976718	−	0.976718i	−0.999735	+	0.0230167i	$0.992673\pi$
$140$		0			0
$141$	0.414491	−	0.414491i	0.0349064	−	0.0349064i
$142$		0			0
$143$		−	5.86659i		−	0.490589i
$144$		0			0
$145$	9.66882	+	2.80841i	0.802952	+	0.233226i
$146$		0			0
$147$	−3.89493	−	3.89493i	−0.321249	−	0.321249i
$148$		0			0
$149$	11.8344	+	11.8344i	0.969513	+	0.969513i	0.999549	−	0.0300356i	$-0.00956208\pi$
$149$	11.8344	+	11.8344i	0.969513	+	0.969513i	−0.0300356	+	0.999549i	$0.509562\pi$
$150$		0			0
$151$			0.240930i			0.0196066i	0.999952	+	0.00980330i	$0.00312054\pi$
$151$			0.240930i			0.0196066i	−0.999952	+	0.00980330i	$0.996879\pi$
$152$		0			0
$153$	−6.00218			−0.485247
$154$		0			0
$155$	4.18099	+	7.60408i	0.335825	+	0.610775i
$156$		0			0
$157$	−7.19573	−	7.19573i	−0.574282	−	0.574282i	0.359040	−	0.933322i	$-0.383104\pi$
$157$	−7.19573	−	7.19573i	−0.574282	−	0.574282i	−0.933322	+	0.359040i	$0.883104\pi$
$158$		0			0
$159$	−3.34917			−0.265606
$160$		0			0
$161$	−3.55189			−0.279928
$162$		0			0
$163$	−11.7446	−	11.7446i	−0.919910	−	0.919910i	0.0771120	−	0.997022i	$-0.475430\pi$
$163$	−11.7446	−	11.7446i	−0.919910	−	0.919910i	−0.997022	+	0.0771120i	$0.975430\pi$
$164$		0			0
$165$	3.82979	−	2.10575i	0.298149	−	0.163932i
$166$		0			0
$167$	0.213418			0.0165148			0.00825739	−	0.999966i	$-0.497372\pi$
$167$	0.213418			0.0165148			0.00825739	+	0.999966i	$0.497372\pi$
$168$		0			0
$169$		−	3.99105i		−	0.307004i
$170$		0			0
$171$	3.06223	+	3.06223i	0.234175	+	0.234175i
$172$		0			0
$173$	−6.36918	−	6.36918i	−0.484240	−	0.484240i	0.422243	−	0.906483i	$-0.361243\pi$
$173$	−6.36918	−	6.36918i	−0.484240	−	0.484240i	−0.906483	+	0.422243i	$0.861243\pi$
$174$		0			0
$175$	−3.27157	+	5.15657i	−0.247307	+	0.389800i
$176$		0			0
$177$		−	11.9281i		−	0.896574i
$178$		0			0
$179$	6.53473	−	6.53473i	0.488428	−	0.488428i	−0.419382	−	0.907810i	$-0.637753\pi$
$179$	6.53473	−	6.53473i	0.488428	−	0.488428i	0.907810	+	0.419382i	$0.137753\pi$
$180$		0			0
$181$	5.23014	+	5.23014i	0.388753	+	0.388753i	0.874242	−	0.485490i	$-0.161359\pi$
$181$	5.23014	+	5.23014i	0.388753	+	0.388753i	−0.485490	+	0.874242i	$0.661359\pi$
$182$		0			0
$183$	14.1147			1.04339
$184$		0			0
$185$	7.42115	+	2.15555i	0.545614	+	0.158479i
$186$		0			0
$187$	8.29549	−	8.29549i	0.606626	−	0.606626i
$188$		0			0
$189$	−0.863636	+	0.863636i	−0.0628203	+	0.0628203i
$190$		0			0
$191$	−13.1318			−0.950181			−0.475090	−	0.879937i	$-0.657585\pi$
$191$	−13.1318			−0.950181			−0.475090	+	0.879937i	$0.657585\pi$
$192$		0			0
$193$		−	20.0131i		−	1.44057i	−0.693676	−	0.720287i	$-0.744010\pi$
$193$		−	20.0131i		−	1.44057i	0.693676	−	0.720287i	$-0.255990\pi$
$194$		0			0
$195$	−5.88117	+	3.23367i	−0.421159	+	0.231568i
$196$		0			0
$197$	19.2424	−	19.2424i	1.37096	−	1.37096i	0.511941	−	0.859021i	$-0.328927\pi$
$197$	19.2424	−	19.2424i	1.37096	−	1.37096i	0.859021	−	0.511941i	$-0.171073\pi$
$198$		0			0
$199$			5.18227i			0.367361i	0.982986	+	0.183681i	$0.0588012\pi$
$199$			5.18227i			0.367361i	−0.982986	+	0.183681i	$0.941199\pi$
$200$		0			0
$201$			5.40517i			0.381251i
$202$		0			0
$203$	3.88873	−	3.88873i	0.272935	−	0.272935i
$204$		0			0
$205$	−4.67116	+	2.56837i	−0.326248	+	0.179383i
$206$		0			0
$207$		−	2.90813i		−	0.202129i
$208$		0			0
$209$	−8.46451			−0.585502
$210$		0			0
$211$	5.53295	−	5.53295i	0.380904	−	0.380904i	−0.490524	−	0.871428i	$-0.663195\pi$
$211$	5.53295	−	5.53295i	0.380904	−	0.380904i	0.871428	+	0.490524i	$0.163195\pi$
$212$		0			0
$213$	−8.15390	+	8.15390i	−0.558696	+	0.558696i
$214$		0			0
$215$	−27.3555	−	7.94570i	−1.86563	−	0.541892i
$216$		0			0
$217$	4.73987			0.321763
$218$		0			0
$219$	0.927072	+	0.927072i	0.0626457	+	0.0626457i
$220$		0			0
$221$	−12.7389	+	12.7389i	−0.856909	+	0.856909i
$222$		0			0
$223$			0.639576i			0.0428292i	0.999771	+	0.0214146i	$0.00681700\pi$
$223$			0.639576i			0.0428292i	−0.999771	+	0.0214146i	$0.993183\pi$
$224$		0			0
$225$	−4.22197	−	2.67861i	−0.281465	−	0.178574i
$226$		0			0
$227$	0.272194	+	0.272194i	0.0180662	+	0.0180662i	0.716082	−	0.698016i	$-0.245934\pi$
$227$	0.272194	+	0.272194i	0.0180662	+	0.0180662i	−0.698016	+	0.716082i	$0.745934\pi$
$228$		0			0
$229$	4.80055	+	4.80055i	0.317229	+	0.317229i	0.847702	−	0.530473i	$-0.177986\pi$
$229$	4.80055	+	4.80055i	0.317229	+	0.317229i	−0.530473	+	0.847702i	$0.677986\pi$
$230$		0			0
$231$		−	2.38723i		−	0.157068i
$232$		0			0
$233$	−21.8025			−1.42833			−0.714166	−	0.699977i	$-0.753194\pi$
$233$	−21.8025			−1.42833			−0.714166	+	0.699977i	$0.753194\pi$
$234$		0			0
$235$	1.14857	−	0.631522i	0.0749243	−	0.0411960i
$236$		0			0
$237$	8.90720	+	8.90720i	0.578585	+	0.578585i
$238$		0			0
$239$	−2.01781			−0.130521			−0.0652606	−	0.997868i	$-0.520788\pi$
$239$	−2.01781			−0.130521			−0.0652606	+	0.997868i	$0.520788\pi$
$240$		0			0
$241$	15.4653			0.996209			0.498105	−	0.867117i	$-0.334030\pi$
$241$	15.4653			0.996209			0.498105	+	0.867117i	$0.334030\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−5.93435	−	10.7930i	−0.379132	−	0.689538i
$246$		0			0
$247$	12.9984			0.827069
$248$		0			0
$249$			4.12431i			0.261367i
$250$		0			0
$251$	−3.43023	−	3.43023i	−0.216514	−	0.216514i	0.590514	−	0.807028i	$-0.298925\pi$
$251$	−3.43023	−	3.43023i	−0.216514	−	0.216514i	−0.807028	+	0.590514i	$0.798925\pi$
$252$		0			0
$253$	4.01927	+	4.01927i	0.252689	+	0.252689i
$254$		0			0
$255$	−12.8886	−	3.74362i	−0.807115	−	0.234435i
$256$		0			0
$257$		−	19.3076i		−	1.20437i	−0.798355	−	0.602187i	$-0.794296\pi$
$257$		−	19.3076i		−	1.20437i	0.798355	−	0.602187i	$-0.205704\pi$
$258$		0			0
$259$	2.98473	−	2.98473i	0.185462	−	0.185462i
$260$		0			0
$261$	3.18392	+	3.18392i	0.197080	+	0.197080i
$262$		0			0
$263$	−9.26068			−0.571038			−0.285519	−	0.958373i	$-0.592166\pi$
$263$	−9.26068			−0.571038			−0.285519	+	0.958373i	$0.592166\pi$
$264$		0			0
$265$	−7.19173	−	2.08891i	−0.441785	−	0.128321i
$266$		0			0
$267$	−6.77874	+	6.77874i	−0.414852	+	0.414852i
$268$		0			0
$269$	5.68909	−	5.68909i	0.346870	−	0.346870i	−0.512073	−	0.858942i	$-0.671122\pi$
$269$	5.68909	−	5.68909i	0.346870	−	0.346870i	0.858942	+	0.512073i	$0.171122\pi$
$270$		0			0
$271$	−1.56587			−0.0951199			−0.0475599	−	0.998868i	$-0.515145\pi$
$271$	−1.56587			−0.0951199			−0.0475599	+	0.998868i	$0.515145\pi$
$272$		0			0
$273$			3.66592i			0.221872i
$274$		0			0
$275$	9.53716	−	2.13304i	0.575113	−	0.128627i
$276$		0			0
$277$	11.2915	−	11.2915i	0.678441	−	0.678441i	−0.281206	−	0.959647i	$-0.590734\pi$
$277$	11.2915	−	11.2915i	0.678441	−	0.678441i	0.959647	+	0.281206i	$0.0907345\pi$
$278$		0			0
$279$			3.88079i			0.232337i
$280$		0			0
$281$		−	15.8017i		−	0.942653i	−0.881959	−	0.471326i	$-0.843775\pi$
$281$		−	15.8017i		−	0.942653i	0.881959	−	0.471326i	$-0.156225\pi$
$282$		0			0
$283$	−2.32452	+	2.32452i	−0.138178	+	0.138178i	−0.772813	−	0.634634i	$-0.781151\pi$
$283$	−2.32452	+	2.32452i	−0.138178	+	0.138178i	0.634634	+	0.772813i	$0.281151\pi$
$284$		0			0
$285$	4.66565	+	8.48555i	0.276369	+	0.502640i
$286$		0			0
$287$			2.91169i			0.171871i
$288$		0			0
$289$	−19.0261			−1.11918
$290$		0			0
$291$	6.68434	−	6.68434i	0.391843	−	0.391843i
$292$		0			0
$293$	7.44154	−	7.44154i	0.434739	−	0.434739i	−0.455498	−	0.890237i	$-0.650539\pi$
$293$	7.44154	−	7.44154i	0.434739	−	0.434739i	0.890237	+	0.455498i	$0.150539\pi$
$294$		0			0
$295$	7.43971	−	25.6135i	0.433157	−	1.49128i
$296$		0			0
$297$	1.95456			0.113415
$298$		0			0
$299$	−6.17214	−	6.17214i	−0.356944	−	0.356944i
$300$		0			0
$301$	−11.0022	+	11.0022i	−0.634156	+	0.634156i
$302$		0			0
$303$		−	16.4782i		−	0.946648i
$304$		0			0
$305$	30.3088	+	8.80351i	1.73548	+	0.504088i
$306$		0			0
$307$	−3.28621	−	3.28621i	−0.187554	−	0.187554i	0.607084	−	0.794638i	$-0.292339\pi$
$307$	−3.28621	−	3.28621i	−0.187554	−	0.187554i	−0.794638	+	0.607084i	$0.792339\pi$
$308$		0			0
$309$	1.52032	+	1.52032i	0.0864881	+	0.0864881i
$310$		0			0
$311$		−	29.0235i		−	1.64577i	−0.568206	−	0.822886i	$-0.692362\pi$
$311$		−	29.0235i		−	1.64577i	0.568206	−	0.822886i	$-0.307638\pi$
$312$		0			0
$313$	5.50831			0.311348			0.155674	−	0.987808i	$-0.450245\pi$
$313$	5.50831			0.311348			0.155674	+	0.987808i	$0.450245\pi$
$314$		0			0
$315$	−2.39316	+	1.31584i	−0.134839	+	0.0741394i
$316$		0			0
$317$	−10.6401	−	10.6401i	−0.597609	−	0.597609i	0.342067	−	0.939676i	$-0.388873\pi$
$317$	−10.6401	−	10.6401i	−0.597609	−	0.597609i	−0.939676	+	0.342067i	$0.888873\pi$
$318$		0			0
$319$	−8.80086			−0.492754
$320$		0			0
$321$	19.0907			1.06554
$322$		0			0
$323$	18.3801	+	18.3801i	1.02269	+	1.02269i
$324$		0			0
$325$	−14.6456	+	3.27558i	−0.812393	+	0.181696i
$326$		0			0
$327$	15.2194			0.841636
$328$		0			0
$329$		−	0.715939i		−	0.0394710i
$330$		0			0
$331$	8.08181	+	8.08181i	0.444217	+	0.444217i	0.893426	−	0.449210i	$-0.148294\pi$
$331$	8.08181	+	8.08181i	0.444217	+	0.444217i	−0.449210	+	0.893426i	$0.648294\pi$
$332$		0			0
$333$	2.44376	+	2.44376i	0.133917	+	0.133917i
$334$		0			0
$335$	−3.37126	+	11.6066i	−0.184192	+	0.634138i
$336$		0			0
$337$			24.4098i			1.32969i	0.746983	+	0.664843i	$0.231502\pi$
$337$			24.4098i			1.32969i	−0.746983	+	0.664843i	$0.768498\pi$
$338$		0			0
$339$	−8.92413	+	8.92413i	−0.484692	+	0.484692i
$340$		0			0
$341$	−5.36357	−	5.36357i	−0.290453	−	0.290453i
$342$		0			0
$343$	−15.2772			−0.824890
$344$		0			0
$345$	1.81383	−	6.24468i	0.0976534	−	0.336202i
$346$		0			0
$347$	−1.40907	+	1.40907i	−0.0756427	+	0.0756427i	−0.743916	−	0.668273i	$-0.767034\pi$
$347$	−1.40907	+	1.40907i	−0.0756427	+	0.0756427i	0.668273	+	0.743916i	$0.267034\pi$
$348$		0			0
$349$	−6.11269	+	6.11269i	−0.327205	+	0.327205i	−0.851523	−	0.524318i	$-0.824320\pi$
$349$	−6.11269	+	6.11269i	−0.327205	+	0.327205i	0.524318	+	0.851523i	$0.324320\pi$
$350$		0			0
$351$	−3.00149			−0.160208
$352$		0			0
$353$			10.7150i			0.570304i	0.958482	+	0.285152i	$0.0920441\pi$
$353$			10.7150i			0.570304i	−0.958482	+	0.285152i	$0.907956\pi$
$354$		0			0
$355$	−22.5947	+	12.4234i	−1.19920	+	0.659363i
$356$		0			0
$357$	−5.18370	+	5.18370i	−0.274350	+	0.274350i
$358$		0			0
$359$			31.7234i			1.67430i	0.546975	+	0.837149i	$0.315779\pi$
$359$			31.7234i			1.67430i	−0.546975	+	0.837149i	$0.684221\pi$
$360$		0			0
$361$			0.245451i			0.0129185i
$362$		0			0
$363$	5.07682	−	5.07682i	0.266464	−	0.266464i
$364$		0			0
$365$	1.41250	+	2.56895i	0.0739334	+	0.134465i
$366$		0			0
$367$		−	31.8025i		−	1.66008i	−0.557707	−	0.830038i	$-0.688319\pi$
$367$		−	31.8025i		−	1.66008i	0.557707	−	0.830038i	$-0.311681\pi$
$368$		0			0
$369$	−2.38396			−0.124104
$370$		0			0
$371$	−2.89246	+	2.89246i	−0.150169	+	0.150169i
$372$		0			0
$373$	−17.3861	+	17.3861i	−0.900220	+	0.900220i	−0.995455	−	0.0952347i	$-0.969640\pi$
$373$	−17.3861	+	17.3861i	−0.900220	+	0.900220i	0.0952347	+	0.995455i	$0.469640\pi$
$374$		0			0
$375$	−7.39524	−	8.38513i	−0.381888	−	0.433006i
$376$		0			0
$377$	13.5149			0.696054
$378$		0			0
$379$	16.4215	+	16.4215i	0.843513	+	0.843513i	0.989314	−	0.145801i	$-0.0465758\pi$
$379$	16.4215	+	16.4215i	0.843513	+	0.843513i	−0.145801	+	0.989314i	$0.546576\pi$
$380$		0			0
$381$	6.83621	−	6.83621i	0.350229	−	0.350229i
$382$		0			0
$383$			9.00561i			0.460165i	0.973171	+	0.230083i	$0.0738997\pi$
$383$			9.00561i			0.460165i	−0.973171	+	0.230083i	$0.926100\pi$
$384$		0			0
$385$	1.48894	−	5.12615i	0.0758835	−	0.261253i
$386$		0			0
$387$	−9.00811	−	9.00811i	−0.457908	−	0.457908i
$388$		0			0
$389$	1.84497	+	1.84497i	0.0935438	+	0.0935438i	0.752330	−	0.658786i	$-0.228930\pi$
$389$	1.84497	+	1.84497i	0.0935438	+	0.0935438i	−0.658786	+	0.752330i	$0.728930\pi$
$390$		0			0
$391$		−	17.4551i		−	0.882742i
$392$		0			0
$393$	−14.9005			−0.751628
$394$		0			0
$395$	13.5711	+	24.6821i	0.682836	+	1.24189i
$396$		0			0
$397$	24.0894	+	24.0894i	1.20901	+	1.20901i	0.971348	+	0.237663i	$0.0763814\pi$
$397$	24.0894	+	24.0894i	1.20901	+	1.20901i	0.237663	+	0.971348i	$0.423619\pi$
$398$		0			0
$399$	5.28931			0.264797
$400$		0			0
$401$	−10.4494			−0.521817			−0.260909	−	0.965364i	$-0.584022\pi$
$401$	−10.4494			−0.521817			−0.260909	+	0.965364i	$0.584022\pi$
$402$		0			0
$403$	8.23650	+	8.23650i	0.410289	+	0.410289i
$404$		0			0
$405$	−1.07735	−	1.95942i	−0.0535342	−	0.0973641i
$406$		0			0
$407$	−6.75496			−0.334831
$408$		0			0
$409$			6.67465i			0.330040i	0.986290	+	0.165020i	$0.0527689\pi$
$409$			6.67465i			0.330040i	−0.986290	+	0.165020i	$0.947231\pi$
$410$		0			0
$411$	9.13506	+	9.13506i	0.450599	+	0.450599i
$412$		0			0
$413$	−10.3016	−	10.3016i	−0.506907	−	0.506907i
$414$		0			0
$415$	−2.57238	+	8.85621i	−0.126273	+	0.434734i
$416$		0			0
$417$		−	16.2851i		−	0.797487i
$418$		0			0
$419$	15.8121	−	15.8121i	0.772472	−	0.772472i	−0.206066	−	0.978538i	$-0.566066\pi$
$419$	15.8121	−	15.8121i	0.772472	−	0.772472i	0.978538	+	0.206066i	$0.0660663\pi$
$420$		0			0
$421$	−1.69730	−	1.69730i	−0.0827211	−	0.0827211i	0.664536	−	0.747257i	$-0.268629\pi$
$421$	−1.69730	−	1.69730i	−0.0827211	−	0.0827211i	−0.747257	+	0.664536i	$0.768629\pi$
$422$		0			0
$423$	0.586179			0.0285010
$424$		0			0
$425$	−25.3410	−	16.0775i	−1.22922	−	0.779874i
$426$		0			0
$427$	12.1900	−	12.1900i	0.589915	−	0.589915i
$428$		0			0
$429$	4.14830	−	4.14830i	0.200282	−	0.200282i
$430$		0			0
$431$	−7.28686			−0.350996			−0.175498	−	0.984480i	$-0.556153\pi$
$431$	−7.28686			−0.350996			−0.175498	+	0.984480i	$0.556153\pi$
$432$		0			0
$433$		−	2.13785i		−	0.102738i	−0.998680	−	0.0513692i	$-0.983641\pi$
$433$		−	2.13785i		−	0.102738i	0.998680	−	0.0513692i	$-0.0163585\pi$
$434$		0			0
$435$	4.85105	+	8.82274i	0.232590	+	0.423018i
$436$		0			0
$437$	−8.90537	+	8.90537i	−0.426002	+	0.426002i
$438$		0			0
$439$			33.2103i			1.58504i	0.609846	+	0.792520i	$0.291231\pi$
$439$			33.2103i			1.58504i	−0.609846	+	0.792520i	$0.708769\pi$
$440$		0			0
$441$		−	5.50826i		−	0.262298i
$442$		0			0
$443$	12.4343	−	12.4343i	0.590771	−	0.590771i	−0.347068	−	0.937840i	$-0.612823\pi$
$443$	12.4343	−	12.4343i	0.590771	−	0.590771i	0.937840	+	0.347068i	$0.112823\pi$
$444$		0			0
$445$	−18.7841	+	10.3282i	−0.890452	+	0.489602i
$446$		0			0
$447$			16.7364i			0.791604i
$448$		0			0
$449$	10.8408			0.511607			0.255803	−	0.966729i	$-0.417660\pi$
$449$	10.8408			0.511607			0.255803	+	0.966729i	$0.417660\pi$
$450$		0			0
$451$	3.29482	−	3.29482i	0.155147	−	0.155147i
$452$		0			0
$453$	−0.170363	+	0.170363i	−0.00800436	+	0.00800436i
$454$		0			0
$455$	−2.28648	+	7.87190i	−0.107192	+	0.369041i
$456$		0			0
$457$	−32.6178			−1.52580			−0.762899	−	0.646518i	$-0.776224\pi$
$457$	−32.6178			−1.52580			−0.762899	+	0.646518i	$0.776224\pi$
$458$		0			0
$459$	−4.24418	−	4.24418i	−0.198101	−	0.198101i
$460$		0			0
$461$	−18.9449	+	18.9449i	−0.882353	+	0.882353i	−0.993773	−	0.111421i	$-0.964460\pi$
$461$	−18.9449	+	18.9449i	−0.882353	+	0.882353i	0.111421	+	0.993773i	$0.464460\pi$
$462$		0			0
$463$			37.7663i			1.75515i	0.479441	+	0.877574i	$0.340840\pi$
$463$			37.7663i			1.75515i	−0.479441	+	0.877574i	$0.659160\pi$
$464$		0			0
$465$	−2.42049	+	8.33330i	−0.112248	+	0.386448i
$466$		0			0
$467$	3.10601	+	3.10601i	0.143729	+	0.143729i	0.775310	−	0.631581i	$-0.217594\pi$
$467$	3.10601	+	3.10601i	0.143729	+	0.143729i	−0.631581	+	0.775310i	$0.717594\pi$
$468$		0			0
$469$	4.66810	+	4.66810i	0.215553	+	0.215553i
$470$		0			0
$471$		−	10.1763i		−	0.468899i
$472$		0			0
$473$	24.8999			1.14490
$474$		0			0
$475$	4.72611	+	21.1312i	0.216849	+	0.969566i
$476$		0			0
$477$	−2.36822	−	2.36822i	−0.108433	−	0.108433i
$478$		0			0
$479$	8.23987			0.376489			0.188245	−	0.982122i	$-0.439720\pi$
$479$	8.23987			0.376489			0.188245	+	0.982122i	$0.439720\pi$
$480$		0			0
$481$	10.3732			0.472976
$482$		0			0
$483$	−2.51157	−	2.51157i	−0.114280	−	0.114280i
$484$		0			0
$485$	18.5225	−	10.1843i	0.841064	−	0.462446i
$486$		0			0
$487$	−15.7527			−0.713822			−0.356911	−	0.934138i	$-0.616170\pi$
$487$	−15.7527			−0.713822			−0.356911	+	0.934138i	$0.616170\pi$
$488$		0			0
$489$		−	16.6094i		−	0.751104i
$490$		0			0
$491$	9.14298	+	9.14298i	0.412617	+	0.412617i	0.882649	−	0.470032i	$-0.155758\pi$
$491$	9.14298	+	9.14298i	0.412617	+	0.412617i	−0.470032	+	0.882649i	$0.655758\pi$
$492$		0			0
$493$	19.1104	+	19.1104i	0.860691	+	0.860691i
$494$		0			0
$495$	4.19706	+	1.21908i	0.188644	+	0.0547935i
$496$		0			0
$497$			14.0840i			0.631754i
$498$		0			0
$499$	5.93929	−	5.93929i	0.265879	−	0.265879i	−0.561558	−	0.827437i	$-0.689798\pi$
$499$	5.93929	−	5.93929i	0.265879	−	0.265879i	0.827437	+	0.561558i	$0.189798\pi$
$500$		0			0
$501$	0.150909	+	0.150909i	0.00674213	+	0.00674213i
$502$		0			0
$503$	−3.53406			−0.157576			−0.0787879	−	0.996891i	$-0.525105\pi$
$503$	−3.53406			−0.157576			−0.0787879	+	0.996891i	$0.525105\pi$
$504$		0			0
$505$	10.2776	−	35.3840i	0.457349	−	1.57457i
$506$		0			0
$507$	2.82210	−	2.82210i	0.125334	−	0.125334i
$508$		0			0
$509$	8.43955	−	8.43955i	0.374076	−	0.374076i	−0.494883	−	0.868960i	$-0.664789\pi$
$509$	8.43955	−	8.43955i	0.374076	−	0.374076i	0.868960	+	0.494883i	$0.164789\pi$
$510$		0			0
$511$	1.60131			0.0708376
$512$		0			0
$513$			4.33065i			0.191203i
$514$		0			0
$515$	2.31638	+	4.21286i	0.102072	+	0.185641i
$516$		0			0
$517$	−0.810146	+	0.810146i	−0.0356302	+	0.0356302i
$518$		0			0
$519$		−	9.00739i		−	0.395380i
$520$		0			0
$521$			9.64810i			0.422691i	0.977411	+	0.211345i	$0.0677845\pi$
$521$			9.64810i			0.422691i	−0.977411	+	0.211345i	$0.932216\pi$
$522$		0			0
$523$	−25.7409	+	25.7409i	−1.12557	+	1.12557i	−0.134683	+	0.990889i	$0.543002\pi$
$523$	−25.7409	+	25.7409i	−1.12557	+	1.12557i	−0.990889	+	0.134683i	$0.956998\pi$
$524$		0			0
$525$	−5.95959	+	1.33290i	−0.260098	+	0.0581724i
$526$		0			0
$527$			23.2932i			1.01467i
$528$		0			0
$529$	−14.5428			−0.632295
$530$		0			0
$531$	8.43447	−	8.43447i	0.366025	−	0.366025i
$532$		0			0
$533$	−5.05965	+	5.05965i	−0.219158	+	0.219158i
$534$		0			0
$535$	40.9939	+	11.9071i	1.77232	+	0.514788i
$536$		0			0
$537$	9.24150			0.398800
$538$		0			0
$539$	7.61287	+	7.61287i	0.327909	+	0.327909i
$540$		0			0
$541$	−19.2087	+	19.2087i	−0.825846	+	0.825846i	−0.986939	−	0.161093i	$-0.948498\pi$
$541$	−19.2087	+	19.2087i	−0.825846	+	0.825846i	0.161093	+	0.986939i	$0.448498\pi$
$542$		0			0
$543$			7.39653i			0.317415i
$544$		0			0
$545$	32.6810	+	9.49252i	1.39990	+	0.406615i
$546$		0			0
$547$	27.9722	+	27.9722i	1.19600	+	1.19600i	0.975353	+	0.220652i	$0.0708185\pi$
$547$	27.9722	+	27.9722i	1.19600	+	1.19600i	0.220652	+	0.975353i	$0.429181\pi$
$548$		0			0
$549$	9.98062	+	9.98062i	0.425963	+	0.425963i
$550$		0			0
$551$		−	19.4998i		−	0.830719i
$552$		0			0
$553$	15.3852			0.654244
$554$		0			0
$555$	3.72334	+	6.77175i	0.158047	+	0.287445i
$556$		0			0
$557$	15.4266	+	15.4266i	0.653647	+	0.653647i	0.953869	−	0.300222i	$-0.0970608\pi$
$557$	15.4266	+	15.4266i	0.653647	+	0.653647i	−0.300222	+	0.953869i	$0.597061\pi$
$558$		0			0
$559$	−38.2372			−1.61726
$560$		0			0
$561$	11.7316			0.495308
$562$		0			0
$563$	−18.2389	−	18.2389i	−0.768676	−	0.768676i	0.209197	−	0.977874i	$-0.432915\pi$
$563$	−18.2389	−	18.2389i	−0.768676	−	0.768676i	−0.977874	+	0.209197i	$0.932915\pi$
$564$		0			0
$565$	−24.7290	+	13.5969i	−1.04036	+	0.572025i
$566$		0			0
$567$	−1.22137			−0.0512926
$568$		0			0
$569$		−	34.0254i		−	1.42642i	−0.700950	−	0.713210i	$-0.747240\pi$
$569$		−	34.0254i		−	1.42642i	0.700950	−	0.713210i	$-0.252760\pi$
$570$		0			0
$571$	17.9297	+	17.9297i	0.750335	+	0.750335i	0.974542	−	0.224207i	$-0.0719790\pi$
$571$	17.9297	+	17.9297i	0.750335	+	0.750335i	−0.224207	+	0.974542i	$0.571979\pi$
$572$		0			0
$573$	−9.28556	−	9.28556i	−0.387910	−	0.387910i
$574$		0			0
$575$	7.78976	−	12.2780i	0.324855	−	0.512029i
$576$		0			0
$577$			0.122769i			0.00511093i	0.999997	+	0.00255547i	$0.000813431\pi$
$577$			0.122769i			0.00511093i	−0.999997	+	0.00255547i	$0.999187\pi$
$578$		0			0
$579$	14.1514	−	14.1514i	0.588112	−	0.588112i
$580$		0			0
$581$	3.56190	+	3.56190i	0.147773	+	0.147773i
$582$		0			0
$583$	6.54614			0.271113
$584$		0			0
$585$	−6.44516	−	1.87206i	−0.266475	−	0.0774003i
$586$		0			0
$587$	−6.93139	+	6.93139i	−0.286089	+	0.286089i	−0.835531	−	0.549443i	$-0.814840\pi$
$587$	−6.93139	+	6.93139i	−0.286089	+	0.286089i	0.549443	+	0.835531i	$0.314840\pi$
$588$		0			0
$589$	11.8839	−	11.8839i	0.489667	−	0.489667i
$590$		0			0
$591$	27.2128			1.11939
$592$		0			0
$593$			21.4611i			0.881303i	0.897678	+	0.440652i	$0.145253\pi$
$593$			21.4611i			0.881303i	−0.897678	+	0.440652i	$0.854747\pi$
$594$		0			0
$595$	−14.3642	+	7.89793i	−0.588874	+	0.323784i
$596$		0			0
$597$	−3.66442	+	3.66442i	−0.149975	+	0.149975i
$598$		0			0
$599$			4.94482i			0.202040i	0.994884	+	0.101020i	$0.0322106\pi$
$599$			4.94482i			0.202040i	−0.994884	+	0.101020i	$0.967789\pi$
$600$		0			0
$601$			20.1862i			0.823414i	0.911316	+	0.411707i	$0.135067\pi$
$601$			20.1862i			0.823414i	−0.911316	+	0.411707i	$0.864933\pi$
$602$		0			0
$603$	−3.82203	+	3.82203i	−0.155645	+	0.155645i
$604$		0			0
$605$	14.0680	−	7.73509i	0.571947	−	0.314476i
$606$		0			0
$607$			23.8529i			0.968161i	0.875024	+	0.484080i	$0.160846\pi$
$607$			23.8529i			0.968161i	−0.875024	+	0.484080i	$0.839154\pi$
$608$		0			0
$609$	5.49949			0.222851
$610$		0			0
$611$	1.24409	−	1.24409i	0.0503305	−	0.0503305i
$612$		0			0
$613$	24.1159	−	24.1159i	0.974031	−	0.974031i	−0.0256404	−	0.999671i	$-0.508162\pi$
$613$	24.1159	−	24.1159i	0.974031	−	0.974031i	0.999671	+	0.0256404i	$0.00816249\pi$
$614$		0			0
$615$	−5.11912	−	1.48690i	−0.206423	−	0.0599576i
$616$		0			0
$617$	−8.63876			−0.347783			−0.173892	−	0.984765i	$-0.555634\pi$
$617$	−8.63876			−0.347783			−0.173892	+	0.984765i	$0.555634\pi$
$618$		0			0
$619$	−32.3601	−	32.3601i	−1.30066	−	1.30066i	−0.927945	−	0.372716i	$-0.878427\pi$
$619$	−32.3601	−	32.3601i	−1.30066	−	1.30066i	−0.372716	−	0.927945i	$-0.621573\pi$
$620$		0			0
$621$	2.05636	−	2.05636i	0.0825188	−	0.0825188i
$622$		0			0
$623$			11.7087i			0.469101i
$624$		0			0
$625$	−10.6500	−	22.6181i	−0.426002	−	0.904722i
$626$		0			0
$627$	−5.98531	−	5.98531i	−0.239030	−	0.239030i
$628$		0			0
$629$	14.6679	+	14.6679i	0.584848	+	0.584848i
$630$		0			0
$631$		−	11.3652i		−	0.452443i	−0.974076	−	0.226222i	$-0.927363\pi$
$631$		−	11.3652i		−	0.452443i	0.974076	−	0.226222i	$-0.0726373\pi$
$632$		0			0
$633$	7.82477			0.311007
$634$		0			0
$635$	18.9433	−	10.4157i	0.751744	−	0.413335i
$636$		0			0
$637$	−11.6906	−	11.6906i	−0.463199	−	0.463199i
$638$		0			0
$639$	−11.5314			−0.456173
$640$		0			0
$641$	−13.9081			−0.549336			−0.274668	−	0.961539i	$-0.588568\pi$
$641$	−13.9081			−0.549336			−0.274668	+	0.961539i	$0.588568\pi$
$642$		0			0
$643$	−18.4850	−	18.4850i	−0.728977	−	0.728977i	0.241439	−	0.970416i	$-0.422381\pi$
$643$	−18.4850	−	18.4850i	−0.728977	−	0.728977i	−0.970416	+	0.241439i	$0.922381\pi$
$644$		0			0
$645$	−13.7248	−	24.9618i	−0.540415	−	0.982868i
$646$		0			0
$647$	−1.15900			−0.0455649			−0.0227825	−	0.999740i	$-0.507253\pi$
$647$	−1.15900			−0.0455649			−0.0227825	+	0.999740i	$0.507253\pi$
$648$		0			0
$649$			23.3142i			0.915163i
$650$		0			0
$651$	3.35159	+	3.35159i	0.131359	+	0.131359i
$652$		0			0
$653$	11.8412	+	11.8412i	0.463383	+	0.463383i	0.899763	−	0.436380i	$-0.143740\pi$
$653$	11.8412	+	11.8412i	0.463383	+	0.463383i	−0.436380	+	0.899763i	$0.643740\pi$
$654$		0			0
$655$	−31.9960	−	9.29358i	−1.25019	−	0.363130i
$656$		0			0
$657$			1.31108i			0.0511500i
$658$		0			0
$659$	1.22941	−	1.22941i	0.0478909	−	0.0478909i	−0.682756	−	0.730647i	$-0.739219\pi$
$659$	1.22941	−	1.22941i	0.0478909	−	0.0478909i	0.730647	+	0.682756i	$0.239219\pi$
$660$		0			0
$661$	13.2100	+	13.2100i	0.513810	+	0.513810i	0.915692	−	0.401882i	$-0.131644\pi$
$661$	13.2100	+	13.2100i	0.513810	+	0.513810i	−0.401882	+	0.915692i	$0.631644\pi$
$662$		0			0
$663$	−18.0155			−0.699663
$664$		0			0
$665$	11.3578	+	3.29900i	0.440438	+	0.127930i
$666$		0			0
$667$	−9.25924	+	9.25924i	−0.358519	+	0.358519i
$668$		0			0
$669$	−0.452248	+	0.452248i	−0.0174849	+	0.0174849i
$670$		0			0
$671$	−27.5880			−1.06502
$672$		0			0
$673$		−	4.69175i		−	0.180854i	−0.995903	−	0.0904268i	$-0.971177\pi$
$673$		−	4.69175i		−	0.180854i	0.995903	−	0.0904268i	$-0.0288231\pi$
$674$		0			0
$675$	−1.09132	−	4.87945i	−0.0420048	−	0.187810i
$676$		0			0
$677$	−36.1893	+	36.1893i	−1.39087	+	1.39087i	−0.567483	+	0.823385i	$0.692083\pi$
$677$	−36.1893	+	36.1893i	−1.39087	+	1.39087i	−0.823385	+	0.567483i	$0.807917\pi$
$678$		0			0
$679$		−	11.5457i		−	0.443083i
$680$		0			0
$681$			0.384941i			0.0147510i
$682$		0			0
$683$	18.7839	−	18.7839i	0.718744	−	0.718744i	−0.249604	−	0.968348i	$-0.580300\pi$
$683$	18.7839	−	18.7839i	0.718744	−	0.718744i	0.968348	+	0.249604i	$0.0803004\pi$
$684$		0			0
$685$	13.9183	+	25.3135i	0.531790	+	0.967181i
$686$		0			0
$687$			6.78901i			0.259017i
$688$		0			0
$689$	−10.0525			−0.382969
$690$		0			0
$691$	−12.0077	+	12.0077i	−0.456795	+	0.456795i	−0.897602	−	0.440807i	$-0.854692\pi$
$691$	−12.0077	+	12.0077i	−0.456795	+	0.456795i	0.440807	+	0.897602i	$0.354692\pi$
$692$		0			0
$693$	1.68803	−	1.68803i	0.0641228	−	0.0641228i
$694$		0			0
$695$	10.1572	−	34.9694i	0.385286	−	1.32647i
$696$		0			0
$697$	−14.3089			−0.541990
$698$		0			0
$699$	−15.4167	−	15.4167i	−0.583114	−	0.583114i
$700$		0			0
$701$	−18.6671	+	18.6671i	−0.705046	+	0.705046i	−0.965489	−	0.260443i	$-0.916131\pi$
$701$	−18.6671	+	18.6671i	−0.705046	+	0.705046i	0.260443	+	0.965489i	$0.416131\pi$
$702$		0			0
$703$		−	14.9668i		−	0.564482i
$704$		0			0
$705$	1.25871	+	0.365606i	0.0474059	+	0.0137695i
$706$		0			0
$707$	−14.2312	−	14.2312i	−0.535219	−	0.535219i
$708$		0			0
$709$	−0.320563	−	0.320563i	−0.0120390	−	0.0120390i	0.701062	−	0.713101i	$-0.252710\pi$
$709$	−0.320563	−	0.320563i	−0.0120390	−	0.0120390i	−0.713101	+	0.701062i	$0.752710\pi$
$710$		0			0
$711$			12.5967i			0.472413i
$712$		0			0
$713$	−11.2858			−0.422658
$714$		0			0
$715$	11.4951	−	6.32039i	0.429892	−	0.236369i
$716$		0			0
$717$	−1.42681	−	1.42681i	−0.0532850	−	0.0532850i
$718$		0			0
$719$	48.8907			1.82332			0.911658	−	0.410951i	$-0.134803\pi$
$719$	48.8907			1.82332			0.911658	+	0.410951i	$0.134803\pi$
$720$		0			0
$721$	2.62601			0.0977977
$722$		0			0
$723$	10.9356	+	10.9356i	0.406701	+	0.406701i
$724$		0			0
$725$	4.91391	+	21.9709i	0.182498	+	0.815978i
$726$		0			0
$727$	−24.5201			−0.909401			−0.454700	−	0.890644i	$-0.650254\pi$
$727$	−24.5201			−0.909401			−0.454700	+	0.890644i	$0.650254\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−54.0683	−	54.0683i	−1.99979	−	1.99979i
$732$		0			0
$733$	−27.3958	−	27.3958i	−1.01189	−	1.01189i	−0.999928	−	0.0119594i	$-0.996193\pi$
$733$	−27.3958	−	27.3958i	−1.01189	−	1.01189i	−0.0119594	−	0.999928i	$-0.503807\pi$
$734$		0			0
$735$	3.43557	−	11.8280i	0.126723	−	0.436283i
$736$		0			0
$737$		−	10.5647i		−	0.389156i
$738$		0			0
$739$	−19.1011	+	19.1011i	−0.702644	+	0.702644i	−0.964977	−	0.262333i	$-0.915508\pi$
$739$	−19.1011	+	19.1011i	−0.702644	+	0.702644i	0.262333	+	0.964977i	$0.415508\pi$
$740$		0			0
$741$	9.19127	+	9.19127i	0.337650	+	0.337650i
$742$		0			0
$743$	−0.305994			−0.0112258			−0.00561291	−	0.999984i	$-0.501787\pi$
$743$	−0.305994			−0.0112258			−0.00561291	+	0.999984i	$0.501787\pi$
$744$		0			0
$745$	−10.4387	+	35.9384i	−0.382443	+	1.31668i
$746$		0			0
$747$	−2.91633	+	2.91633i	−0.106703	+	0.106703i
$748$		0			0
$749$	16.4874	−	16.4874i	0.602438	−	0.602438i
$750$		0			0
$751$	7.13631			0.260408			0.130204	−	0.991487i	$-0.458437\pi$
$751$	7.13631			0.260408			0.130204	+	0.991487i	$0.458437\pi$
$752$		0			0
$753$		−	4.85108i		−	0.176783i
$754$		0			0
$755$	−0.472082	+	0.259567i	−0.0171808	+	0.00944660i
$756$		0			0
$757$	25.8469	−	25.8469i	0.939422	−	0.939422i	−0.0588455	−	0.998267i	$-0.518742\pi$
$757$	25.8469	−	25.8469i	0.939422	−	0.939422i	0.998267	+	0.0588455i	$0.0187419\pi$
$758$		0			0
$759$			5.68410i			0.206320i
$760$		0			0
$761$			11.9718i			0.433979i	0.976174	+	0.216989i	$0.0696237\pi$
$761$			11.9718i			0.433979i	−0.976174	+	0.216989i	$0.930376\pi$
$762$		0			0
$763$	13.1440	−	13.1440i	0.475846	−	0.475846i
$764$		0			0
$765$	−6.46647	−	11.7608i	−0.233796	−	0.425211i
$766$		0			0
$767$		−	35.8022i		−	1.29274i
$768$		0			0
$769$	−27.2266			−0.981816			−0.490908	−	0.871211i	$-0.663335\pi$
$769$	−27.2266			−0.981816			−0.490908	+	0.871211i	$0.663335\pi$
$770$		0			0
$771$	13.6525	−	13.6525i	0.491684	−	0.491684i
$772$		0			0
$773$	8.83729	−	8.83729i	0.317855	−	0.317855i	−0.530088	−	0.847943i	$-0.677841\pi$
$773$	8.83729	−	8.83729i	0.317855	−	0.317855i	0.847943	+	0.530088i	$0.177841\pi$
$774$		0			0
$775$	−10.3951	+	16.3846i	−0.373405	+	0.588552i
$776$		0			0
$777$	4.22105			0.151429
$778$		0			0
$779$	7.30024	+	7.30024i	0.261558	+	0.261558i
$780$		0			0
$781$	15.9373	−	15.9373i	0.570280	−	0.570280i
$782$		0			0
$783$			4.50274i			0.160915i
$784$		0			0
$785$	6.34707	−	21.8518i	0.226537	−	0.779923i
$786$		0			0
$787$	21.7150	+	21.7150i	0.774058	+	0.774058i	0.978813	−	0.204755i	$-0.0656399\pi$
$787$	21.7150	+	21.7150i	0.774058	+	0.774058i	−0.204755	+	0.978813i	$0.565640\pi$
$788$		0			0
$789$	−6.54829	−	6.54829i	−0.233125	−	0.233125i
$790$		0			0
$791$			15.4144i			0.548073i
$792$		0			0
$793$	42.3652			1.50443
$794$		0			0
$795$	−3.60824	−	6.56241i	−0.127971	−	0.232745i
$796$		0			0
$797$	−28.4134	−	28.4134i	−1.00645	−	1.00645i	−0.999979	−	0.00647582i	$-0.997939\pi$
$797$	−28.4134	−	28.4134i	−1.00645	−	1.00645i	−0.00647582	−	0.999979i	$-0.502061\pi$
$798$		0			0
$799$	3.51835			0.124470
$800$		0			0
$801$	−9.58659			−0.338726
$802$		0			0
$803$	−1.81201	−	1.81201i	−0.0639446	−	0.0639446i
$804$		0			0
$805$	−3.82664	−	6.95963i	−0.134871	−	0.245295i
$806$		0			0
$807$	8.04558			0.283218
$808$		0			0
$809$			26.4356i			0.929426i	0.885461	+	0.464713i	$0.153842\pi$
$809$			26.4356i			0.929426i	−0.885461	+	0.464713i	$0.846158\pi$
$810$		0			0
$811$	−15.0962	−	15.0962i	−0.530100	−	0.530100i	0.390502	−	0.920602i	$-0.372301\pi$
$811$	−15.0962	−	15.0962i	−0.530100	−	0.530100i	−0.920602	+	0.390502i	$0.872301\pi$
$812$		0			0
$813$	−1.10724	−	1.10724i	−0.0388325	−	0.0388325i
$814$		0			0
$815$	10.3595	−	35.6657i	0.362877	−	1.24932i
$816$		0			0
$817$			55.1699i			1.93015i
$818$		0			0
$819$	−2.59220	+	2.59220i	−0.0905787	+	0.0905787i
$820$		0			0
$821$	−29.4997	−	29.4997i	−1.02955	−	1.02955i	−0.999550	−	0.0299962i	$-0.990450\pi$
$821$	−29.4997	−	29.4997i	−1.02955	−	1.02955i	−0.0299962	−	0.999550i	$-0.509550\pi$
$822$		0			0
$823$	21.2908			0.742152			0.371076	−	0.928602i	$-0.378989\pi$
$823$	21.2908			0.742152			0.371076	+	0.928602i	$0.378989\pi$
$824$		0			0
$825$	8.25208	+	5.23551i	0.287301	+	0.182277i
$826$		0			0
$827$	−14.4619	+	14.4619i	−0.502888	+	0.502888i	−0.912334	−	0.409446i	$-0.865722\pi$
$827$	−14.4619	+	14.4619i	−0.502888	+	0.502888i	0.409446	+	0.912334i	$0.365722\pi$
$828$		0			0
$829$	5.64651	−	5.64651i	0.196111	−	0.196111i	−0.602219	−	0.798331i	$-0.705717\pi$
$829$	5.64651	−	5.64651i	0.196111	−	0.196111i	0.798331	+	0.602219i	$0.205717\pi$
$830$		0			0
$831$	15.9686			0.553945
$832$		0			0
$833$		−	33.0616i		−	1.14552i
$834$		0			0
$835$	0.229927	+	0.418175i	0.00795695	+	0.0144715i
$836$		0			0
$837$	−2.74413	+	2.74413i	−0.0948512	+	0.0948512i
$838$		0			0
$839$		−	21.4686i		−	0.741178i	−0.928797	−	0.370589i	$-0.879156\pi$
$839$		−	21.4686i		−	0.741178i	0.928797	−	0.370589i	$-0.120844\pi$
$840$		0			0
$841$			8.72534i			0.300874i
$842$		0			0
$843$	11.1735	−	11.1735i	0.384836	−	0.384836i
$844$		0			0
$845$	7.82012	−	4.29977i	0.269020	−	0.147917i
$846$		0			0
$847$		−	8.76905i		−	0.301308i
$848$		0			0
$849$	−3.28736			−0.112822
$850$		0			0
$851$	−7.10678	+	7.10678i	−0.243617	+	0.243617i
$852$		0			0
$853$	−5.10917	+	5.10917i	−0.174935	+	0.174935i	−0.789143	−	0.614209i	$-0.789475\pi$
$853$	−5.10917	+	5.10917i	−0.174935	+	0.174935i	0.614209	+	0.789143i	$0.289475\pi$
$854$		0			0
$855$	−2.70108	+	9.29930i	−0.0923748	+	0.318029i
$856$		0			0
$857$	−7.14205			−0.243968			−0.121984	−	0.992532i	$-0.538926\pi$
$857$	−7.14205			−0.243968			−0.121984	+	0.992532i	$0.538926\pi$
$858$		0			0
$859$	−12.9070	−	12.9070i	−0.440381	−	0.440381i	0.451759	−	0.892140i	$-0.350797\pi$
$859$	−12.9070	−	12.9070i	−0.440381	−	0.440381i	−0.892140	+	0.451759i	$0.850797\pi$
$860$		0			0
$861$	−2.05887	+	2.05887i	−0.0701662	+	0.0701662i
$862$		0			0
$863$		−	34.4382i		−	1.17229i	−0.810206	−	0.586145i	$-0.800645\pi$
$863$		−	34.4382i		−	1.17229i	0.810206	−	0.586145i	$-0.199355\pi$
$864$		0			0
$865$	5.61801	−	19.3417i	0.191018	−	0.657639i
$866$		0			0
$867$	−13.4535	−	13.4535i	−0.456905	−	0.456905i
$868$		0			0
$869$	−17.4096	−	17.4096i	−0.590581	−	0.590581i
$870$		0			0
$871$			16.2236i			0.549715i
$872$		0			0
$873$	9.45309			0.319939
$874$		0			0
$875$	−13.6285	−	0.854909i	−0.460727	−	0.0289012i
$876$		0			0
$877$	−20.5999	−	20.5999i	−0.695609	−	0.695609i	0.267851	−	0.963460i	$-0.413686\pi$
$877$	−20.5999	−	20.5999i	−0.695609	−	0.695609i	−0.963460	+	0.267851i	$0.913686\pi$
$878$		0			0
$879$	10.5239			0.354963
$880$		0			0
$881$	22.0289			0.742171			0.371086	−	0.928599i	$-0.378986\pi$
$881$	22.0289			0.742171			0.371086	+	0.928599i	$0.378986\pi$
$882$		0			0
$883$	−15.2149	−	15.2149i	−0.512022	−	0.512022i	0.403123	−	0.915146i	$-0.367925\pi$
$883$	−15.2149	−	15.2149i	−0.512022	−	0.512022i	−0.915146	+	0.403123i	$0.867925\pi$
$884$		0			0
$885$	23.3722	−	12.8508i	0.785647	−	0.431976i
$886$		0			0
$887$	41.6823			1.39956			0.699778	−	0.714361i	$-0.253282\pi$
$887$	41.6823			1.39956			0.699778	+	0.714361i	$0.253282\pi$
$888$		0			0
$889$		−	11.8080i		−	0.396027i
$890$		0			0
$891$	1.38208	+	1.38208i	0.0463014	+	0.0463014i
$892$		0			0
$893$	−1.79502	−	1.79502i	−0.0600679	−	0.0600679i
$894$		0			0
$895$	19.8445	+	5.76403i	0.663327	+	0.192670i
$896$		0			0
$897$		−	8.72872i		−	0.291444i
$898$		0			0
$899$	12.3561	−	12.3561i	0.412100	−	0.412100i
$900$		0			0
$901$	−14.2145	−	14.2145i	−0.473552	−	0.473552i
$902$		0			0
$903$	−15.5595			−0.517786
$904$		0			0
$905$	−4.61330	+	15.8827i	−0.153351	+	0.527959i
$906$		0			0
$907$	−27.7322	+	27.7322i	−0.920834	+	0.920834i	−0.997088	−	0.0762544i	$-0.975704\pi$
$907$	−27.7322	+	27.7322i	−0.920834	+	0.920834i	0.0762544	+	0.997088i	$0.475704\pi$
$908$		0			0
$909$	11.6519	−	11.6519i	0.386468	−	0.386468i
$910$		0			0
$911$	−32.3043			−1.07029			−0.535145	−	0.844760i	$-0.679743\pi$
$911$	−32.3043			−1.07029			−0.535145	+	0.844760i	$0.679743\pi$
$912$		0			0
$913$		−	8.06119i		−	0.266787i
$914$		0			0
$915$	15.2066	+	27.6566i	0.502714	+	0.914299i
$916$		0			0
$917$	−12.8686	+	12.8686i	−0.424958	+	0.424958i
$918$		0			0
$919$			54.5387i			1.79907i	0.436853	+	0.899533i	$0.356093\pi$
$919$			54.5387i			1.79907i	−0.436853	+	0.899533i	$0.643907\pi$
$920$		0			0
$921$		−	4.64740i		−	0.153137i
$922$		0			0
$923$	−24.4739	+	24.4739i	−0.805567	+	0.805567i
$924$		0			0
$925$	3.77159	+	16.8634i	0.124009	+	0.554465i
$926$		0			0
$927$			2.15006i			0.0706172i
$928$		0			0
$929$	−41.8714			−1.37375			−0.686877	−	0.726773i	$-0.741019\pi$
$929$	−41.8714			−1.37375			−0.686877	+	0.726773i	$0.741019\pi$
$930$		0			0
$931$	−16.8676	+	16.8676i	−0.552813	+	0.552813i
$932$		0			0
$933$	20.5227	−	20.5227i	0.671884	−	0.671884i
$934$		0			0
$935$	25.1915	+	7.31713i	0.823850	+	0.239296i
$936$		0			0
$937$	−12.5314			−0.409384			−0.204692	−	0.978826i	$-0.565619\pi$
$937$	−12.5314			−0.409384			−0.204692	+	0.978826i	$0.565619\pi$
$938$		0			0
$939$	3.89496	+	3.89496i	0.127107	+	0.127107i
$940$		0			0
$941$	40.1881	−	40.1881i	1.31009	−	1.31009i	0.388751	−	0.921343i	$-0.372907\pi$
$941$	40.1881	−	40.1881i	1.31009	−	1.31009i	0.921343	−	0.388751i	$-0.127093\pi$
$942$		0			0
$943$		−	6.93285i		−	0.225765i
$944$		0			0
$945$	−2.62266	−	0.761780i	−0.0853153	−	0.0247807i
$946$		0			0
$947$	−26.2243	−	26.2243i	−0.852174	−	0.852174i	0.138227	−	0.990401i	$-0.455860\pi$
$947$	−26.2243	−	26.2243i	−0.852174	−	0.852174i	−0.990401	+	0.138227i	$0.955860\pi$
$948$		0			0
$949$	2.78260	+	2.78260i	0.0903270	+	0.0903270i
$950$		0			0
$951$		−	15.0474i		−	0.487945i
$952$		0			0
$953$	−2.51475			−0.0814607			−0.0407304	−	0.999170i	$-0.512968\pi$
$953$	−2.51475			−0.0814607			−0.0407304	+	0.999170i	$0.512968\pi$
$954$		0			0
$955$	−14.1476	−	25.7306i	−0.457804	−	0.832622i
$956$		0			0
$957$	−6.22315	−	6.22315i	−0.201166	−	0.201166i
$958$		0			0
$959$	15.7787			0.509522
$960$		0			0
$961$	−15.9395			−0.514176
$962$		0			0
$963$	13.4992	+	13.4992i	0.435005	+	0.435005i
$964$		0			0
$965$	39.2139	−	21.5612i	1.26234	−	0.694079i
$966$		0			0
$967$	−51.5088			−1.65641			−0.828205	−	0.560425i	$-0.810638\pi$
$967$	−51.5088			−1.65641			−0.828205	+	0.560425i	$0.810638\pi$
$968$		0			0
$969$			25.9933i			0.835026i
$970$		0			0
$971$	26.0586	+	26.0586i	0.836259	+	0.836259i	0.988364	−	0.152105i	$-0.0486053\pi$
$971$	26.0586	+	26.0586i	0.836259	+	0.836259i	−0.152105	+	0.988364i	$0.548605\pi$
$972$		0			0
$973$	−14.0644	−	14.0644i	−0.450885	−	0.450885i
$974$		0			0
$975$	−12.6722	−	8.03984i	−0.405835	−	0.257481i
$976$		0			0
$977$		−	17.6258i		−	0.563899i	−0.959429	−	0.281950i	$-0.909019\pi$
$977$		−	17.6258i		−	0.563899i	0.959429	−	0.281950i	$-0.0909811\pi$
$978$		0			0
$979$	13.2494	−	13.2494i	0.423454	−	0.423454i
$980$		0			0
$981$	10.7618	+	10.7618i	0.343596	+	0.343596i
$982$		0			0
$983$	−1.64257			−0.0523899			−0.0261949	−	0.999657i	$-0.508339\pi$
$983$	−1.64257			−0.0523899			−0.0261949	+	0.999657i	$0.508339\pi$
$984$		0			0
$985$	58.4346	+	16.9729i	1.86188	+	0.540803i
$986$		0			0
$987$	0.506245	−	0.506245i	0.0161140	−	0.0161140i
$988$		0			0
$989$	26.1967	−	26.1967i	0.833008	−	0.833008i
$990$		0			0
$991$	62.3434			1.98040			0.990202	−	0.139642i	$-0.0445951\pi$
$991$	62.3434			1.98040			0.990202	+	0.139642i	$0.0445951\pi$
$992$		0			0
$993$			11.4294i			0.362701i
$994$		0			0
$995$	−10.1542	+	5.58314i	−0.321910	+	0.176997i
$996$		0			0
$997$	30.0563	−	30.0563i	0.951891	−	0.951891i	−0.0470037	−	0.998895i	$-0.514967\pi$
$997$	30.0563	−	30.0563i	0.951891	−	0.951891i	0.998895	+	0.0470037i	$0.0149672\pi$
$998$		0			0
$999$			3.45601i			0.109343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bl.a.49.20		48
4.3	odd	2		240.2.bl.a.229.8	yes	48
5.4	even	2	inner	960.2.bl.a.49.11		48
8.3	odd	2		1920.2.bl.a.1249.17		48
8.5	even	2		1920.2.bl.b.1249.8		48
12.11	even	2		720.2.bm.h.469.17		48
16.3	odd	4		240.2.bl.a.109.17	yes	48
16.5	even	4		1920.2.bl.b.289.17		48
16.11	odd	4		1920.2.bl.a.289.8		48
16.13	even	4	inner	960.2.bl.a.529.11		48
20.19	odd	2		240.2.bl.a.229.17	yes	48
40.19	odd	2		1920.2.bl.a.1249.8		48
40.29	even	2		1920.2.bl.b.1249.17		48
48.35	even	4		720.2.bm.h.109.8		48
60.59	even	2		720.2.bm.h.469.8		48
80.19	odd	4		240.2.bl.a.109.8	✓	48
80.29	even	4	inner	960.2.bl.a.529.20		48
80.59	odd	4		1920.2.bl.a.289.17		48
80.69	even	4		1920.2.bl.b.289.8		48
240.179	even	4		720.2.bm.h.109.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.8	✓	48	80.19	odd	4
240.2.bl.a.109.17	yes	48	16.3	odd	4
240.2.bl.a.229.8	yes	48	4.3	odd	2
240.2.bl.a.229.17	yes	48	20.19	odd	2
720.2.bm.h.109.8		48	48.35	even	4
720.2.bm.h.109.17		48	240.179	even	4
720.2.bm.h.469.8		48	60.59	even	2
720.2.bm.h.469.17		48	12.11	even	2
960.2.bl.a.49.11		48	5.4	even	2	inner
960.2.bl.a.49.20		48	1.1	even	1	trivial
960.2.bl.a.529.11		48	16.13	even	4	inner
960.2.bl.a.529.20		48	80.29	even	4	inner
1920.2.bl.a.289.8		48	16.11	odd	4
1920.2.bl.a.289.17		48	80.59	odd	4
1920.2.bl.a.1249.8		48	40.19	odd	2
1920.2.bl.a.1249.17		48	8.3	odd	2
1920.2.bl.b.289.8		48	80.69	even	4
1920.2.bl.b.289.17		48	16.5	even	4
1920.2.bl.b.1249.8		48	8.5	even	2
1920.2.bl.b.1249.17		48	40.29	even	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.07735 + 1.95942i) q^{5} +1.22137 q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.07735 + 1.95942i) q^{5} +1.22137 q^{7} +1.00000i q^{9} +(-1.38208 - 1.38208i) q^{11} +(2.12237 + 2.12237i) q^{13} +(-0.623711 + 2.14732i) q^{15} +6.00218i q^{17} +(3.06223 - 3.06223i) q^{19} +(0.863636 + 0.863636i) q^{21} -2.90813 q^{23} +(-2.67861 + 4.22197i) q^{25} +(-0.707107 + 0.707107i) q^{27} +(3.18392 - 3.18392i) q^{29} +3.88079 q^{31} -1.95456i q^{33} +(1.31584 + 2.39316i) q^{35} +(2.44376 - 2.44376i) q^{37} +3.00149i q^{39} +2.38396i q^{41} +(-9.00811 + 9.00811i) q^{43} +(-1.95942 + 1.07735i) q^{45} -0.586179i q^{47} -5.50826 q^{49} +(-4.24418 + 4.24418i) q^{51} +(-2.36822 + 2.36822i) q^{53} +(1.21908 - 4.19706i) q^{55} +4.33065 q^{57} +(-8.43447 - 8.43447i) q^{59} +(9.98062 - 9.98062i) q^{61} +1.22137i q^{63} +(-1.87206 + 6.44516i) q^{65} +(3.82203 + 3.82203i) q^{67} +(-2.05636 - 2.05636i) q^{69} +11.5314i q^{71} +1.31108 q^{73} +(-4.87945 + 1.09132i) q^{75} +(-1.68803 - 1.68803i) q^{77} +12.5967 q^{79} -1.00000 q^{81} +(2.91633 + 2.91633i) q^{83} +(-11.7608 + 6.46647i) q^{85} +4.50274 q^{87} +9.58659i q^{89} +(2.59220 + 2.59220i) q^{91} +(2.74413 + 2.74413i) q^{93} +(9.29930 + 2.70108i) q^{95} -9.45309i q^{97} +(1.38208 - 1.38208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{19} + 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} + 16 q^{61} + 16 q^{65} - 16 q^{69} + 16 q^{75} + 96 q^{79} - 48 q^{81} + 32 q^{91} + 48 q^{95}+O(q^{100}) \) 48 * q - 8 * q^19 + 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 + 16 * q^61 + 16 * q^65 - 16 * q^69 + 16 * q^75 + 96 * q^79 - 48 * q^81 + 32 * q^91 + 48 * q^95

Introduction

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