LMFDB - Embedded newform 1380.2.t.a.1057.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(1057,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1380.1057");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.2
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(0.811448 + 2.08364i) q^{5} +(-3.03238 + 3.03238i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(0.811448 + 2.08364i) q^{5} +(-3.03238 + 3.03238i) q^{7} -1.00000i q^{9} +0.215171i q^{11} +(-0.104194 + 0.104194i) q^{13} +(-2.04714 - 0.899575i) q^{15} +(-0.838023 + 0.838023i) q^{17} -3.62662 q^{19} -4.28843i q^{21} +(1.87448 + 4.41433i) q^{23} +(-3.68310 + 3.38153i) q^{25} +(0.707107 + 0.707107i) q^{27} -5.72737i q^{29} -0.698870 q^{31} +(-0.152149 - 0.152149i) q^{33} +(-8.77900 - 3.85776i) q^{35} +(3.51166 - 3.51166i) q^{37} -0.147353i q^{39} -1.54131 q^{41} +(1.20047 + 1.20047i) q^{43} +(2.08364 - 0.811448i) q^{45} +(-3.22380 - 3.22380i) q^{47} -11.3906i q^{49} -1.18514i q^{51} +(-0.708888 - 0.708888i) q^{53} +(-0.448340 + 0.174600i) q^{55} +(2.56441 - 2.56441i) q^{57} -2.79531i q^{59} -5.64983i q^{61} +(3.03238 + 3.03238i) q^{63} +(-0.301651 - 0.132555i) q^{65} +(-5.33023 + 5.33023i) q^{67} +(-4.44686 - 1.79594i) q^{69} -12.8841 q^{71} +(9.19956 - 9.19956i) q^{73} +(0.213245 - 4.99545i) q^{75} +(-0.652481 - 0.652481i) q^{77} -0.634427 q^{79} -1.00000 q^{81} +(3.22905 + 3.22905i) q^{83} +(-2.42615 - 1.06612i) q^{85} +(4.04986 + 4.04986i) q^{87} -9.91726 q^{89} -0.631912i q^{91} +(0.494175 - 0.494175i) q^{93} +(-2.94281 - 7.55657i) q^{95} +(-11.7379 + 11.7379i) q^{97} +0.215171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) $ 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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
$5$	0.811448	+	2.08364i	0.362891	+	0.931832i
$5$	0.811448	+	2.08364i	0.362891	+	0.931832i
$6$		0			0
$7$	−3.03238	+	3.03238i	−1.14613	+	1.14613i	−0.158825	+	0.987307i	$0.550770\pi$
$7$	−3.03238	+	3.03238i	−1.14613	+	1.14613i	−0.987307	+	0.158825i	$0.949230\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			0.215171i			0.0648766i	0.999474	+	0.0324383i	$0.0103272\pi$
$11$			0.215171i			0.0648766i	−0.999474	+	0.0324383i	$0.989673\pi$
$12$		0			0
$13$	−0.104194	+	0.104194i	−0.0288983	+	0.0288983i	−0.721408	−	0.692510i	$-0.756505\pi$
$13$	−0.104194	+	0.104194i	−0.0288983	+	0.0288983i	0.692510	+	0.721408i	$0.256505\pi$
$14$		0			0
$15$	−2.04714	−	0.899575i	−0.528568	−	0.232269i
$16$		0			0
$17$	−0.838023	+	0.838023i	−0.203250	+	0.203250i	−0.801391	−	0.598141i	$-0.795906\pi$
$17$	−0.838023	+	0.838023i	−0.203250	+	0.203250i	0.598141	+	0.801391i	$0.295906\pi$
$18$		0			0
$19$	−3.62662			−0.832004			−0.416002	−	0.909364i	$-0.636569\pi$
$19$	−3.62662			−0.832004			−0.416002	+	0.909364i	$0.636569\pi$
$20$		0			0
$21$		−	4.28843i		−	0.935812i
$22$		0			0
$23$	1.87448	+	4.41433i	0.390857	+	0.920451i
$23$	1.87448	+	4.41433i	0.390857	+	0.920451i
$24$		0			0
$25$	−3.68310	+	3.38153i	−0.736621	+	0.676306i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	5.72737i		−	1.06355i	−0.846887	−	0.531773i	$-0.821526\pi$
$29$		−	5.72737i		−	1.06355i	0.846887	−	0.531773i	$-0.178474\pi$
$30$		0			0
$31$	−0.698870			−0.125521			−0.0627603	−	0.998029i	$-0.519990\pi$
$31$	−0.698870			−0.125521			−0.0627603	+	0.998029i	$0.519990\pi$
$32$		0			0
$33$	−0.152149	−	0.152149i	−0.0264858	−	0.0264858i
$34$		0			0
$35$	−8.77900	−	3.85776i	−1.48392	−	0.652081i
$36$		0			0
$37$	3.51166	−	3.51166i	0.577313	−	0.577313i	−0.356849	−	0.934162i	$-0.616149\pi$
$37$	3.51166	−	3.51166i	0.577313	−	0.577313i	0.934162	+	0.356849i	$0.116149\pi$
$38$		0			0
$39$		−	0.147353i		−	0.0235953i
$40$		0			0
$41$	−1.54131			−0.240712			−0.120356	−	0.992731i	$-0.538404\pi$
$41$	−1.54131			−0.240712			−0.120356	+	0.992731i	$0.538404\pi$
$42$		0			0
$43$	1.20047	+	1.20047i	0.183070	+	0.183070i	0.792692	−	0.609622i	$-0.208679\pi$
$43$	1.20047	+	1.20047i	0.183070	+	0.183070i	−0.609622	+	0.792692i	$0.708679\pi$
$44$		0			0
$45$	2.08364	−	0.811448i	0.310611	−	0.120964i
$46$		0			0
$47$	−3.22380	−	3.22380i	−0.470239	−	0.470239i	0.431753	−	0.901992i	$-0.357895\pi$
$47$	−3.22380	−	3.22380i	−0.470239	−	0.470239i	−0.901992	+	0.431753i	$0.857895\pi$
$48$		0			0
$49$		−	11.3906i		−	1.62723i
$50$		0			0
$51$		−	1.18514i		−	0.165953i
$52$		0			0
$53$	−0.708888	−	0.708888i	−0.0973732	−	0.0973732i	0.656742	−	0.754115i	$-0.271934\pi$
$53$	−0.708888	−	0.708888i	−0.0973732	−	0.0973732i	−0.754115	+	0.656742i	$0.771934\pi$
$54$		0			0
$55$	−0.448340	+	0.174600i	−0.0604541	+	0.0235431i
$56$		0			0
$57$	2.56441	−	2.56441i	0.339664	−	0.339664i
$58$		0			0
$59$		−	2.79531i		−	0.363919i	−0.983306	−	0.181959i	$-0.941756\pi$
$59$		−	2.79531i		−	0.363919i	0.983306	−	0.181959i	$-0.0582439\pi$
$60$		0			0
$61$		−	5.64983i		−	0.723386i	−0.932297	−	0.361693i	$-0.882199\pi$
$61$		−	5.64983i		−	0.723386i	0.932297	−	0.361693i	$-0.117801\pi$
$62$		0			0
$63$	3.03238	+	3.03238i	0.382044	+	0.382044i
$64$		0			0
$65$	−0.301651	−	0.132555i	−0.0374152	−	0.0164414i
$66$		0			0
$67$	−5.33023	+	5.33023i	−0.651191	+	0.651191i	−0.953280	−	0.302089i	$-0.902316\pi$
$67$	−5.33023	+	5.33023i	−0.651191	+	0.651191i	0.302089	+	0.953280i	$0.402316\pi$
$68$		0			0
$69$	−4.44686	−	1.79594i	−0.535339	−	0.216206i
$70$		0			0
$71$	−12.8841			−1.52906			−0.764532	−	0.644586i	$-0.777030\pi$
$71$	−12.8841			−1.52906			−0.764532	+	0.644586i	$0.777030\pi$
$72$		0			0
$73$	9.19956	−	9.19956i	1.07673	−	1.07673i	0.0799269	−	0.996801i	$-0.474531\pi$
$73$	9.19956	−	9.19956i	1.07673	−	1.07673i	0.996801	−	0.0799269i	$-0.0254687\pi$
$74$		0			0
$75$	0.213245	−	4.99545i	0.0246234	−	0.576825i
$76$		0			0
$77$	−0.652481	−	0.652481i	−0.0743571	−	0.0743571i
$78$		0			0
$79$	−0.634427			−0.0713786			−0.0356893	−	0.999363i	$-0.511363\pi$
$79$	−0.634427			−0.0713786			−0.0356893	+	0.999363i	$0.511363\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	3.22905	+	3.22905i	0.354434	+	0.354434i	0.861756	−	0.507322i	$-0.169365\pi$
$83$	3.22905	+	3.22905i	0.354434	+	0.354434i	−0.507322	+	0.861756i	$0.669365\pi$
$84$		0			0
$85$	−2.42615	−	1.06612i	−0.263153	−	0.115637i
$86$		0			0
$87$	4.04986	+	4.04986i	0.434191	+	0.434191i
$88$		0			0
$89$	−9.91726			−1.05123			−0.525614	−	0.850723i	$-0.676164\pi$
$89$	−9.91726			−1.05123			−0.525614	+	0.850723i	$0.676164\pi$
$90$		0			0
$91$		−	0.631912i		−	0.0662424i
$92$		0			0
$93$	0.494175	−	0.494175i	0.0512436	−	0.0512436i
$94$		0			0
$95$	−2.94281	−	7.55657i	−0.301926	−	0.775288i
$96$		0			0
$97$	−11.7379	+	11.7379i	−1.19180	+	1.19180i	−0.215239	+	0.976561i	$0.569053\pi$
$97$	−11.7379	+	11.7379i	−1.19180	+	1.19180i	−0.976561	+	0.215239i	$0.930947\pi$
$98$		0			0
$99$	0.215171			0.0216255
$100$		0			0
$101$	−5.54705			−0.551952			−0.275976	−	0.961165i	$-0.589001\pi$
$101$	−5.54705			−0.551952			−0.275976	+	0.961165i	$0.589001\pi$
$102$		0			0
$103$	4.58781	+	4.58781i	0.452050	+	0.452050i	0.896035	−	0.443984i	$-0.146435\pi$
$103$	4.58781	+	4.58781i	0.452050	+	0.452050i	−0.443984	+	0.896035i	$0.646435\pi$
$104$		0			0
$105$	8.93554	−	3.47984i	0.872020	−	0.339598i
$106$		0			0
$107$	−1.79337	+	1.79337i	−0.173372	+	0.173372i	−0.788459	−	0.615087i	$-0.789121\pi$
$107$	−1.79337	+	1.79337i	−0.173372	+	0.173372i	0.615087	+	0.788459i	$0.289121\pi$
$108$		0			0
$109$	7.68766			0.736344			0.368172	−	0.929758i	$-0.379984\pi$
$109$	7.68766			0.736344			0.368172	+	0.929758i	$0.379984\pi$
$110$		0			0
$111$			4.96623i			0.471374i
$112$		0			0
$113$	6.32548	+	6.32548i	0.595051	+	0.595051i	0.938991	−	0.343941i	$-0.111762\pi$
$113$	6.32548	+	6.32548i	0.595051	+	0.595051i	−0.343941	+	0.938991i	$0.611762\pi$
$114$		0			0
$115$	−7.67682	+	7.48775i	−0.715867	+	0.698236i
$116$		0			0
$117$	0.104194	+	0.104194i	0.00963276	+	0.00963276i
$118$		0			0
$119$		−	5.08240i		−	0.465903i
$120$		0			0
$121$	10.9537			0.995791
$122$		0			0
$123$	1.08987	−	1.08987i	0.0982701	−	0.0982701i
$124$		0			0
$125$	−10.0345	−	4.93032i	−0.897516	−	0.440981i
$126$		0			0
$127$	−11.2672	−	11.2672i	−0.999801	−	0.999801i	0.000198560	−	1.00000i	$-0.499937\pi$
$127$	−11.2672	−	11.2672i	−0.999801	−	0.999801i	−1.00000		0.000198560i	$0.999937\pi$
$128$		0			0
$129$	−1.69772			−0.149476
$130$		0			0
$131$	−5.77607			−0.504658			−0.252329	−	0.967642i	$-0.581196\pi$
$131$	−5.77607			−0.504658			−0.252329	+	0.967642i	$0.581196\pi$
$132$		0			0
$133$	10.9973	−	10.9973i	0.953586	−	0.953586i
$134$		0			0
$135$	−0.899575	+	2.04714i	−0.0774231	+	0.176189i
$136$		0			0
$137$	−9.96930	+	9.96930i	−0.851735	+	0.851735i	−0.990347	−	0.138612i	$-0.955736\pi$
$137$	−9.96930	+	9.96930i	−0.851735	+	0.851735i	0.138612	+	0.990347i	$0.455736\pi$
$138$		0			0
$139$			11.5738i			0.981680i	0.871250	+	0.490840i	$0.163310\pi$
$139$			11.5738i			0.981680i	−0.871250	+	0.490840i	$0.836690\pi$
$140$		0			0
$141$	4.55914			0.383949
$142$		0			0
$143$	−0.0224196	−	0.0224196i	−0.00187482	−	0.00187482i
$144$		0			0
$145$	11.9338	−	4.64746i	0.991045	−	0.385951i
$146$		0			0
$147$	8.05440	+	8.05440i	0.664316	+	0.664316i
$148$		0			0
$149$	−15.9034			−1.30285			−0.651427	−	0.758711i	$-0.725829\pi$
$149$	−15.9034			−1.30285			−0.651427	+	0.758711i	$0.725829\pi$
$150$		0			0
$151$	11.6604			0.948907			0.474454	−	0.880280i	$-0.342646\pi$
$151$	11.6604			0.948907			0.474454	+	0.880280i	$0.342646\pi$
$152$		0			0
$153$	0.838023	+	0.838023i	0.0677501	+	0.0677501i
$154$		0			0
$155$	−0.567096	−	1.45619i	−0.0455503	−	0.116964i
$156$		0			0
$157$	−0.200645	+	0.200645i	−0.0160132	+	0.0160132i	−0.715068	−	0.699055i	$-0.753604\pi$
$157$	−0.200645	+	0.200645i	−0.0160132	+	0.0160132i	0.699055	+	0.715068i	$0.253604\pi$
$158$		0			0
$159$	1.00252			0.0795049
$160$		0			0
$161$	−19.0701	−	7.70177i	−1.50293	−	0.606985i
$162$		0			0
$163$	−9.31466	+	9.31466i	−0.729580	+	0.729580i	−0.970536	−	0.240956i	$-0.922539\pi$
$163$	−9.31466	+	9.31466i	−0.729580	+	0.729580i	0.240956	+	0.970536i	$0.422539\pi$
$164$		0			0
$165$	0.193563	−	0.440485i	0.0150688	−	0.0342917i
$166$		0			0
$167$	−11.1138	−	11.1138i	−0.860015	−	0.860015i	0.131325	−	0.991339i	$-0.458077\pi$
$167$	−11.1138	−	11.1138i	−0.860015	−	0.860015i	−0.991339	+	0.131325i	$0.958077\pi$
$168$		0			0
$169$			12.9783i			0.998330i
$170$		0			0
$171$			3.62662i			0.277335i
$172$		0			0
$173$	−18.2799	+	18.2799i	−1.38980	+	1.38980i	−0.564072	+	0.825726i	$0.690766\pi$
$173$	−18.2799	+	18.2799i	−1.38980	+	1.38980i	−0.825726	+	0.564072i	$0.809234\pi$
$174$		0			0
$175$	0.914486	−	21.4226i	0.0691286	−	1.61940i
$176$		0			0
$177$	1.97658	+	1.97658i	0.148569	+	0.148569i
$178$		0			0
$179$			14.9592i			1.11810i	0.829133	+	0.559051i	$0.188834\pi$
$179$			14.9592i			1.11810i	−0.829133	+	0.559051i	$0.811166\pi$
$180$		0			0
$181$		−	19.9710i		−	1.48443i	−0.670160	−	0.742216i	$-0.733775\pi$
$181$		−	19.9710i		−	1.48443i	0.670160	−	0.742216i	$-0.266225\pi$
$182$		0			0
$183$	3.99503	+	3.99503i	0.295321	+	0.295321i
$184$		0			0
$185$	10.1665	+	4.46750i	0.747460	+	0.328457i
$186$		0			0
$187$	−0.180319	−	0.180319i	−0.0131862	−	0.0131862i
$188$		0			0
$189$	−4.28843			−0.311937
$190$		0			0
$191$		−	16.1750i		−	1.17038i	−0.810896	−	0.585190i	$-0.801020\pi$
$191$		−	16.1750i		−	1.17038i	0.810896	−	0.585190i	$-0.198980\pi$
$192$		0			0
$193$	19.3337	−	19.3337i	1.39167	−	1.39167i	0.570084	−	0.821587i	$-0.306911\pi$
$193$	19.3337	−	19.3337i	1.39167	−	1.39167i	0.821587	−	0.570084i	$-0.193089\pi$
$194$		0			0
$195$	0.307030	−	0.119569i	0.0219869	−	0.00856253i
$196$		0			0
$197$	7.06672	+	7.06672i	0.503483	+	0.503483i	0.912519	−	0.409035i	$-0.134135\pi$
$197$	7.06672	+	7.06672i	0.503483	+	0.503483i	−0.409035	+	0.912519i	$0.634135\pi$
$198$		0			0
$199$	13.4983			0.956872			0.478436	−	0.878123i	$-0.341204\pi$
$199$	13.4983			0.956872			0.478436	+	0.878123i	$0.341204\pi$
$200$		0			0
$201$		−	7.53808i		−	0.531695i
$202$		0			0
$203$	17.3675	+	17.3675i	1.21896	+	1.21896i
$204$		0			0
$205$	−1.25069	−	3.21153i	−0.0873520	−	0.224303i
$206$		0			0
$207$	4.41433	−	1.87448i	0.306817	−	0.130286i
$208$		0			0
$209$		−	0.780345i		−	0.0539776i
$210$		0			0
$211$	−0.224954			−0.0154865			−0.00774325	−	0.999970i	$-0.502465\pi$
$211$	−0.224954			−0.0154865			−0.00774325	+	0.999970i	$0.502465\pi$
$212$		0			0
$213$	9.11045	−	9.11045i	0.624238	−	0.624238i
$214$		0			0
$215$	−1.52723	+	3.47547i	−0.104156	+	0.237025i
$216$		0			0
$217$	2.11924	−	2.11924i	0.143863	−	0.143863i
$218$		0			0
$219$			13.0101i			0.879144i
$220$		0			0
$221$		−	0.174634i		−	0.0117472i
$222$		0			0
$223$	−8.81447	+	8.81447i	−0.590260	+	0.590260i	−0.937702	−	0.347441i	$-0.887051\pi$
$223$	−8.81447	+	8.81447i	−0.590260	+	0.590260i	0.347441	+	0.937702i	$0.387051\pi$
$224$		0			0
$225$	3.38153	+	3.68310i	0.225435	+	0.245540i
$226$		0			0
$227$	−5.70286	+	5.70286i	−0.378512	+	0.378512i	−0.870565	−	0.492053i	$-0.836247\pi$
$227$	−5.70286	+	5.70286i	−0.378512	+	0.378512i	0.492053	+	0.870565i	$0.336247\pi$
$228$		0			0
$229$	3.83060			0.253133			0.126567	−	0.991958i	$-0.459604\pi$
$229$	3.83060			0.253133			0.126567	+	0.991958i	$0.459604\pi$
$230$		0			0
$231$	0.922748			0.0607123
$232$		0			0
$233$	16.0029	−	16.0029i	1.04838	−	1.04838i	0.0496146	−	0.998768i	$-0.484201\pi$
$233$	16.0029	−	16.0029i	1.04838	−	1.04838i	0.998768	−	0.0496146i	$-0.0157993\pi$
$234$		0			0
$235$	4.10128	−	9.33317i	0.267538	−	0.608829i
$236$		0			0
$237$	0.448607	−	0.448607i	0.0291402	−	0.0291402i
$238$		0			0
$239$			6.89887i			0.446251i	0.974790	+	0.223125i	$0.0716259\pi$
$239$			6.89887i			0.446251i	−0.974790	+	0.223125i	$0.928374\pi$
$240$		0			0
$241$			13.7556i			0.886078i	0.896502	+	0.443039i	$0.146100\pi$
$241$			13.7556i			0.886078i	−0.896502	+	0.443039i	$0.853900\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	23.7340	−	9.24291i	1.51631	−	0.590508i
$246$		0			0
$247$	0.377873	−	0.377873i	0.0240435	−	0.0240435i
$248$		0			0
$249$	−4.56656			−0.289394
$250$		0			0
$251$			11.1370i			0.702958i	0.936196	+	0.351479i	$0.114321\pi$
$251$			11.1370i			0.702958i	−0.936196	+	0.351479i	$0.885679\pi$
$252$		0			0
$253$	−0.949838	+	0.403335i	−0.0597158	+	0.0253575i
$254$		0			0
$255$	2.46941	−	0.961682i	0.154640	−	0.0602229i
$256$		0			0
$257$	−1.46949	−	1.46949i	−0.0916642	−	0.0916642i	0.659788	−	0.751452i	$-0.270646\pi$
$257$	−1.46949	−	1.46949i	−0.0916642	−	0.0916642i	−0.751452	+	0.659788i	$0.770646\pi$
$258$		0			0
$259$			21.2973i			1.32335i
$260$		0			0
$261$	−5.72737			−0.354515
$262$		0			0
$263$	13.9022	+	13.9022i	0.857245	+	0.857245i	0.991013	−	0.133768i	$-0.0427077\pi$
$263$	13.9022	+	13.9022i	0.857245	+	0.857245i	−0.133768	+	0.991013i	$0.542708\pi$
$264$		0			0
$265$	0.901841	−	2.05229i	0.0553996	−	0.126071i
$266$		0			0
$267$	7.01256	−	7.01256i	0.429162	−	0.429162i
$268$		0			0
$269$			16.4196i			1.00112i	0.865702	+	0.500559i	$0.166872\pi$
$269$			16.4196i			1.00112i	−0.865702	+	0.500559i	$0.833128\pi$
$270$		0			0
$271$	10.0045			0.607729			0.303865	−	0.952715i	$-0.401723\pi$
$271$	10.0045			0.607729			0.303865	+	0.952715i	$0.401723\pi$
$272$		0			0
$273$	0.446830	+	0.446830i	0.0270434	+	0.0270434i
$274$		0			0
$275$	−0.727609	−	0.792499i	−0.0438764	−	0.0477895i
$276$		0			0
$277$	20.3063	+	20.3063i	1.22009	+	1.22009i	0.967601	+	0.252484i	$0.0812475\pi$
$277$	20.3063	+	20.3063i	1.22009	+	1.22009i	0.252484	+	0.967601i	$0.418753\pi$
$278$		0			0
$279$			0.698870i			0.0418402i
$280$		0			0
$281$			23.3996i			1.39590i	0.716146	+	0.697951i	$0.245905\pi$
$281$			23.3996i			1.39590i	−0.716146	+	0.697951i	$0.754095\pi$
$282$		0			0
$283$	−4.37571	−	4.37571i	−0.260109	−	0.260109i	0.564989	−	0.825098i	$-0.308880\pi$
$283$	−4.37571	−	4.37571i	−0.260109	−	0.260109i	−0.825098	+	0.564989i	$0.808880\pi$
$284$		0			0
$285$	7.42419	+	3.26242i	0.439771	+	0.193249i
$286$		0			0
$287$	4.67382	−	4.67382i	0.275887	−	0.275887i
$288$		0			0
$289$			15.5954i			0.917379i
$290$		0			0
$291$		−	16.5999i		−	0.973101i
$292$		0			0
$293$	10.0346	+	10.0346i	0.586227	+	0.586227i	0.936608	−	0.350380i	$-0.113948\pi$
$293$	10.0346	+	10.0346i	0.586227	+	0.586227i	−0.350380	+	0.936608i	$0.613948\pi$
$294$		0			0
$295$	5.82442	−	2.26825i	0.339111	−	0.132063i
$296$		0			0
$297$	−0.152149	+	0.152149i	−0.00882859	+	0.00882859i
$298$		0			0
$299$	−0.655258	−	0.264637i	−0.0378945	−	0.0153044i
$300$		0			0
$301$	−7.28056			−0.419644
$302$		0			0
$303$	3.92235	−	3.92235i	0.225333	−	0.225333i
$304$		0			0
$305$	11.7722	−	4.58454i	0.674074	−	0.262510i
$306$		0			0
$307$	11.0814	+	11.0814i	0.632449	+	0.632449i	0.948682	−	0.316233i	$-0.102418\pi$
$307$	11.0814	+	11.0814i	0.632449	+	0.632449i	−0.316233	+	0.948682i	$0.602418\pi$
$308$		0			0
$309$	−6.48814			−0.369098
$310$		0			0
$311$	−15.1990			−0.861854			−0.430927	−	0.902387i	$-0.641813\pi$
$311$	−15.1990			−0.861854			−0.430927	+	0.902387i	$0.641813\pi$
$312$		0			0
$313$	−4.23380	−	4.23380i	−0.239309	−	0.239309i	0.577255	−	0.816564i	$-0.304124\pi$
$313$	−4.23380	−	4.23380i	−0.239309	−	0.239309i	−0.816564	+	0.577255i	$0.804124\pi$
$314$		0			0
$315$	−3.85776	+	8.77900i	−0.217360	+	0.494641i
$316$		0			0
$317$	8.80440	+	8.80440i	0.494504	+	0.494504i	0.909722	−	0.415218i	$-0.136295\pi$
$317$	8.80440	+	8.80440i	0.494504	+	0.494504i	−0.415218	+	0.909722i	$0.636295\pi$
$318$		0			0
$319$	1.23237			0.0689992
$320$		0			0
$321$		−	2.53621i		−	0.141558i
$322$		0			0
$323$	3.03919	−	3.03919i	0.169105	−	0.169105i
$324$		0			0
$325$	0.0314222	−	0.736094i	0.00174299	−	0.0408311i
$326$		0			0
$327$	−5.43600	+	5.43600i	−0.300611	+	0.300611i
$328$		0			0
$329$	19.5515			1.07791
$330$		0			0
$331$	21.1129			1.16047			0.580234	−	0.814450i	$-0.302961\pi$
$331$	21.1129			1.16047			0.580234	+	0.814450i	$0.302961\pi$
$332$		0			0
$333$	−3.51166	−	3.51166i	−0.192438	−	0.192438i
$334$		0			0
$335$	−15.4315	−	6.78107i	−0.843111	−	0.370489i
$336$		0			0
$337$	−8.51531	+	8.51531i	−0.463859	+	0.463859i	−0.899918	−	0.436059i	$-0.856374\pi$
$337$	−8.51531	+	8.51531i	−0.463859	+	0.463859i	0.436059	+	0.899918i	$0.356374\pi$
$338$		0			0
$339$	−8.94557			−0.485857
$340$		0			0
$341$		−	0.150377i		−	0.00814336i
$342$		0			0
$343$	13.3141	+	13.3141i	0.718893	+	0.718893i
$344$		0			0
$345$	0.133696	−	10.7230i	0.00719796	−	0.577305i
$346$		0			0
$347$	6.55655	+	6.55655i	0.351974	+	0.351974i	0.860844	−	0.508870i	$-0.169937\pi$
$347$	6.55655	+	6.55655i	0.351974	+	0.351974i	−0.508870	+	0.860844i	$0.669937\pi$
$348$		0			0
$349$		−	14.8855i		−	0.796803i	−0.917211	−	0.398402i	$-0.869565\pi$
$349$		−	14.8855i		−	0.796803i	0.917211	−	0.398402i	$-0.130435\pi$
$350$		0			0
$351$	−0.147353			−0.00786511
$352$		0			0
$353$	−0.525199	+	0.525199i	−0.0279535	+	0.0279535i	−0.720945	−	0.692992i	$-0.756292\pi$
$353$	−0.525199	+	0.525199i	−0.0279535	+	0.0279535i	0.692992	+	0.720945i	$0.256292\pi$
$354$		0			0
$355$	−10.4548	−	26.8459i	−0.554883	−	1.42483i
$356$		0			0
$357$	3.59380	+	3.59380i	0.190204	+	0.190204i
$358$		0			0
$359$	−12.7385			−0.672310			−0.336155	−	0.941807i	$-0.609127\pi$
$359$	−12.7385			−0.672310			−0.336155	+	0.941807i	$0.609127\pi$
$360$		0			0
$361$	−5.84762			−0.307770
$362$		0			0
$363$	−7.74544	+	7.74544i	−0.406530	+	0.406530i
$364$		0			0
$365$	26.6335	+	11.7036i	1.39406	+	0.612595i
$366$		0			0
$367$	−17.5337	+	17.5337i	−0.915251	+	0.915251i	−0.996679	−	0.0814283i	$-0.974052\pi$
$367$	−17.5337	+	17.5337i	−0.915251	+	0.915251i	0.0814283	+	0.996679i	$0.474052\pi$
$368$		0			0
$369$			1.54131i			0.0802372i
$370$		0			0
$371$	4.29923			0.223205
$372$		0			0
$373$	7.90853	+	7.90853i	0.409488	+	0.409488i	0.881560	−	0.472072i	$-0.156494\pi$
$373$	7.90853	+	7.90853i	0.409488	+	0.409488i	−0.472072	+	0.881560i	$0.656494\pi$
$374$		0			0
$375$	10.5818	−	3.60922i	0.546439	−	0.186380i
$376$		0			0
$377$	0.596758	+	0.596758i	0.0307346	+	0.0307346i
$378$		0			0
$379$	−6.04317			−0.310417			−0.155208	−	0.987882i	$-0.549605\pi$
$379$	−6.04317			−0.310417			−0.155208	+	0.987882i	$0.549605\pi$
$380$		0			0
$381$	15.9342			0.816334
$382$		0			0
$383$	−17.3884	−	17.3884i	−0.888507	−	0.888507i	0.105873	−	0.994380i	$-0.466236\pi$
$383$	−17.3884	−	17.3884i	−0.888507	−	0.888507i	−0.994380	+	0.105873i	$0.966236\pi$
$384$		0			0
$385$	0.830081	−	1.88899i	0.0423048	−	0.0962718i
$386$		0			0
$387$	1.20047	−	1.20047i	0.0610233	−	0.0610233i
$388$		0			0
$389$	−24.3413			−1.23415			−0.617076	−	0.786903i	$-0.711683\pi$
$389$	−24.3413			−1.23415			−0.617076	+	0.786903i	$0.711683\pi$
$390$		0			0
$391$	−5.27017	−	2.12845i	−0.266524	−	0.107640i
$392$		0			0
$393$	4.08430	−	4.08430i	0.206026	−	0.206026i
$394$		0			0
$395$	−0.514804	−	1.32192i	−0.0259026	−	0.0665128i
$396$		0			0
$397$	15.2651	+	15.2651i	0.766132	+	0.766132i	0.977423	−	0.211291i	$-0.0677668\pi$
$397$	15.2651	+	15.2651i	0.766132	+	0.766132i	−0.211291	+	0.977423i	$0.567767\pi$
$398$		0			0
$399$			15.5525i			0.778600i
$400$		0			0
$401$		−	24.4276i		−	1.21985i	−0.792458	−	0.609927i	$-0.791199\pi$
$401$		−	24.4276i		−	1.21985i	0.792458	−	0.609927i	$-0.208801\pi$
$402$		0			0
$403$	0.0728181	−	0.0728181i	0.00362733	−	0.00362733i
$404$		0			0
$405$	−0.811448	−	2.08364i	−0.0403212	−	0.103537i
$406$		0			0
$407$	0.755608	+	0.755608i	0.0374541	+	0.0374541i
$408$		0			0
$409$		−	20.4123i		−	1.00932i	−0.863317	−	0.504662i	$-0.831617\pi$
$409$		−	20.4123i		−	1.00932i	0.863317	−	0.504662i	$-0.168383\pi$
$410$		0			0
$411$		−	14.0987i		−	0.695439i
$412$		0			0
$413$	8.47644	+	8.47644i	0.417098	+	0.417098i
$414$		0			0
$415$	−4.10797	+	9.34838i	−0.201652	+	0.458894i
$416$		0			0
$417$	−8.18394	−	8.18394i	−0.400769	−	0.400769i
$418$		0			0
$419$	−18.4225			−0.899996			−0.449998	−	0.893030i	$-0.648575\pi$
$419$	−18.4225			−0.899996			−0.449998	+	0.893030i	$0.648575\pi$
$420$		0			0
$421$		−	14.1196i		−	0.688149i	−0.938942	−	0.344075i	$-0.888193\pi$
$421$		−	14.1196i		−	0.688149i	0.938942	−	0.344075i	$-0.111807\pi$
$422$		0			0
$423$	−3.22380	+	3.22380i	−0.156746	+	0.156746i
$424$		0			0
$425$	0.252726	−	5.92032i	0.0122590	−	0.287178i
$426$		0			0
$427$	17.1324	+	17.1324i	0.829096	+	0.829096i
$428$		0			0
$429$	0.0317061			0.00153079
$430$		0			0
$431$		−	0.731733i		−	0.0352464i	−0.999845	−	0.0176232i	$-0.994390\pi$
$431$		−	0.731733i		−	0.0352464i	0.999845	−	0.0176232i	$-0.00560992\pi$
$432$		0			0
$433$	−10.1943	−	10.1943i	−0.489907	−	0.489907i	0.418370	−	0.908277i	$-0.362602\pi$
$433$	−10.1943	−	10.1943i	−0.489907	−	0.489907i	−0.908277	+	0.418370i	$0.862602\pi$
$434$		0			0
$435$	−5.15220	+	11.7247i	−0.247029	+	0.562156i
$436$		0			0
$437$	−6.79804	−	16.0091i	−0.325195	−	0.765819i
$438$		0			0
$439$			11.5619i			0.551820i	0.961184	+	0.275910i	$0.0889791\pi$
$439$			11.5619i			0.551820i	−0.961184	+	0.275910i	$0.911021\pi$
$440$		0			0
$441$	−11.3906			−0.542411
$442$		0			0
$443$	1.60293	−	1.60293i	0.0761573	−	0.0761573i	−0.668002	−	0.744159i	$-0.732850\pi$
$443$	1.60293	−	1.60293i	0.0761573	−	0.0761573i	0.744159	+	0.668002i	$0.232850\pi$
$444$		0			0
$445$	−8.04734	−	20.6640i	−0.381481	−	0.979567i
$446$		0			0
$447$	11.2454	−	11.2454i	0.531888	−	0.531888i
$448$		0			0
$449$			18.3951i			0.868118i	0.900884	+	0.434059i	$0.142919\pi$
$449$			18.3951i			0.868118i	−0.900884	+	0.434059i	$0.857081\pi$
$450$		0			0
$451$		−	0.331645i		−	0.0156166i
$452$		0			0
$453$	−8.24513	+	8.24513i	−0.387390	+	0.387390i
$454$		0			0
$455$	1.31668	−	0.512764i	0.0617268	−	0.0240388i
$456$		0			0
$457$	−23.5949	+	23.5949i	−1.10372	+	1.10372i	−0.109764	+	0.993958i	$0.535009\pi$
$457$	−23.5949	+	23.5949i	−1.10372	+	1.10372i	−0.993958	+	0.109764i	$0.964991\pi$
$458$		0			0
$459$	−1.18514			−0.0553177
$460$		0			0
$461$	16.6820			0.776957			0.388479	−	0.921458i	$-0.373001\pi$
$461$	16.6820			0.776957			0.388479	+	0.921458i	$0.373001\pi$
$462$		0			0
$463$	−18.6150	+	18.6150i	−0.865115	+	0.865115i	−0.991927	−	0.126812i	$-0.959525\pi$
$463$	−18.6150	+	18.6150i	−0.865115	+	0.865115i	0.126812	+	0.991927i	$0.459525\pi$
$464$		0			0
$465$	1.43068	+	0.628685i	0.0663462	+	0.0291546i
$466$		0			0
$467$	−4.81980	+	4.81980i	−0.223034	+	0.223034i	−0.809775	−	0.586741i	$-0.800411\pi$
$467$	−4.81980	+	4.81980i	−0.223034	+	0.223034i	0.586741	+	0.809775i	$0.300411\pi$
$468$		0			0
$469$		−	32.3265i		−	1.49270i
$470$		0			0
$471$		−	0.283755i		−	0.0130747i
$472$		0			0
$473$	−0.258307	+	0.258307i	−0.0118770	+	0.0118770i
$474$		0			0
$475$	13.3572	−	12.2635i	0.612871	−	0.562689i
$476$		0			0
$477$	−0.708888	+	0.708888i	−0.0324577	+	0.0324577i
$478$		0			0
$479$	−23.7267			−1.08410			−0.542049	−	0.840347i	$-0.682351\pi$
$479$	−23.7267			−1.08410			−0.542049	+	0.840347i	$0.682351\pi$
$480$		0			0
$481$			0.731788i			0.0333667i
$482$		0			0
$483$	18.9305	−	8.03860i	0.861370	−	0.365769i
$484$		0			0
$485$	−33.9822	−	14.9328i	−1.54305	−	0.678064i
$486$		0			0
$487$	−14.6954	−	14.6954i	−0.665911	−	0.665911i	0.290856	−	0.956767i	$-0.406060\pi$
$487$	−14.6954	−	14.6954i	−0.665911	−	0.665911i	−0.956767	+	0.290856i	$0.906060\pi$
$488$		0			0
$489$		−	13.1729i		−	0.595700i
$490$		0			0
$491$	40.8845			1.84509			0.922546	−	0.385887i	$-0.126105\pi$
$491$	40.8845			1.84509			0.922546	+	0.385887i	$0.126105\pi$
$492$		0			0
$493$	4.79966	+	4.79966i	0.216166	+	0.216166i
$494$		0			0
$495$	0.174600	+	0.448340i	0.00784771	+	0.0201514i
$496$		0			0
$497$	39.0695	−	39.0695i	1.75251	−	1.75251i
$498$		0			0
$499$		−	37.3570i		−	1.67233i	−0.548477	−	0.836165i	$-0.684792\pi$
$499$		−	37.3570i		−	1.67233i	0.548477	−	0.836165i	$-0.315208\pi$
$500$		0			0
$501$	15.7173			0.702199
$502$		0			0
$503$	−25.2242	−	25.2242i	−1.12469	−	1.12469i	−0.991026	−	0.133667i	$-0.957325\pi$
$503$	−25.2242	−	25.2242i	−1.12469	−	1.12469i	−0.133667	−	0.991026i	$-0.542675\pi$
$504$		0			0
$505$	−4.50114	−	11.5580i	−0.200298	−	0.514326i
$506$		0			0
$507$	−9.17703	−	9.17703i	−0.407566	−	0.407566i
$508$		0			0
$509$		−	4.22065i		−	0.187077i	−0.995616	−	0.0935385i	$-0.970182\pi$
$509$		−	4.22065i		−	0.187077i	0.995616	−	0.0935385i	$-0.0298178\pi$
$510$		0			0
$511$			55.7931i			2.46814i
$512$		0			0
$513$	−2.56441	−	2.56441i	−0.113221	−	0.113221i
$514$		0			0
$515$	−5.83657	+	13.2821i	−0.257190	+	0.585280i
$516$		0			0
$517$	0.693669	−	0.693669i	0.0305075	−	0.0305075i
$518$		0			0
$519$		−	25.8517i		−	1.13476i
$520$		0			0
$521$		−	42.8659i		−	1.87799i	−0.343930	−	0.938995i	$-0.611758\pi$
$521$		−	42.8659i		−	1.87799i	0.343930	−	0.938995i	$-0.388242\pi$
$522$		0			0
$523$	26.9318	+	26.9318i	1.17764	+	1.17764i	0.980343	+	0.197301i	$0.0632175\pi$
$523$	26.9318	+	26.9318i	1.17764	+	1.17764i	0.197301	+	0.980343i	$0.436783\pi$
$524$		0			0
$525$	14.5015	+	15.7947i	0.632896	+	0.689339i
$526$		0			0
$527$	0.585669	−	0.585669i	0.0255121	−	0.0255121i
$528$		0			0
$529$	−15.9726	+	16.5492i	−0.694462	+	0.719530i
$530$		0			0
$531$	−2.79531			−0.121306
$532$		0			0
$533$	0.160595	−	0.160595i	0.00695615	−	0.00695615i
$534$		0			0
$535$	−5.19197	−	2.28151i	−0.224468	−	0.0986384i
$536$		0			0
$537$	−10.5777	−	10.5777i	−0.456463	−	0.456463i
$538$		0			0
$539$	2.45094			0.105569
$540$		0			0
$541$	14.2957			0.614621			0.307311	−	0.951609i	$-0.400571\pi$
$541$	14.2957			0.614621			0.307311	+	0.951609i	$0.400571\pi$
$542$		0			0
$543$	14.1216	+	14.1216i	0.606017	+	0.606017i
$544$		0			0
$545$	6.23814	+	16.0183i	0.267212	+	0.686149i
$546$		0			0
$547$	14.5082	+	14.5082i	0.620324	+	0.620324i	0.945614	−	0.325290i	$-0.105462\pi$
$547$	14.5082	+	14.5082i	0.620324	+	0.620324i	−0.325290	+	0.945614i	$0.605462\pi$
$548$		0			0
$549$	−5.64983			−0.241129
$550$		0			0
$551$			20.7710i			0.884874i
$552$		0			0
$553$	1.92382	−	1.92382i	0.0818092	−	0.0818092i
$554$		0			0
$555$	−10.3478	+	4.02984i	−0.439241	+	0.171057i
$556$		0			0
$557$	−15.8544	+	15.8544i	−0.671770	+	0.671770i	−0.958124	−	0.286354i	$-0.907557\pi$
$557$	−15.8544	+	15.8544i	−0.671770	+	0.671770i	0.286354	+	0.958124i	$0.407557\pi$
$558$		0			0
$559$	−0.250164			−0.0105808
$560$		0			0
$561$	0.255009			0.0107665
$562$		0			0
$563$	23.1463	+	23.1463i	0.975501	+	0.975501i	0.999707	−	0.0242059i	$-0.00770572\pi$
$563$	23.1463	+	23.1463i	0.975501	+	0.975501i	−0.0242059	+	0.999707i	$0.507706\pi$
$564$		0			0
$565$	−8.04721	+	18.3128i	−0.338549	+	0.770426i
$566$		0			0
$567$	3.03238	−	3.03238i	0.127348	−	0.127348i
$568$		0			0
$569$	−5.83671			−0.244687			−0.122344	−	0.992488i	$-0.539041\pi$
$569$	−5.83671			−0.244687			−0.122344	+	0.992488i	$0.539041\pi$
$570$		0			0
$571$			21.2359i			0.888693i	0.895855	+	0.444346i	$0.146564\pi$
$571$			21.2359i			0.888693i	−0.895855	+	0.444346i	$0.853436\pi$
$572$		0			0
$573$	11.4374	+	11.4374i	0.477805	+	0.477805i
$574$		0			0
$575$	−21.8311	−	9.91981i	−0.910420	−	0.413685i
$576$		0			0
$577$	1.49537	+	1.49537i	0.0622532	+	0.0622532i	0.737548	−	0.675295i	$-0.235984\pi$
$577$	1.49537	+	1.49537i	0.0622532	+	0.0622532i	−0.675295	+	0.737548i	$0.735984\pi$
$578$		0			0
$579$			27.3420i			1.13629i
$580$		0			0
$581$	−19.5834			−0.812456
$582$		0			0
$583$	0.152532	−	0.152532i	0.00631725	−	0.00631725i
$584$		0			0
$585$	−0.132555	+	0.301651i	−0.00548047	+	0.0124717i
$586$		0			0
$587$	−14.7668	−	14.7668i	−0.609489	−	0.609489i	0.333323	−	0.942813i	$-0.391830\pi$
$587$	−14.7668	−	14.7668i	−0.609489	−	0.609489i	−0.942813	+	0.333323i	$0.891830\pi$
$588$		0			0
$589$	2.53453			0.104434
$590$		0			0
$591$	−9.99385			−0.411092
$592$		0			0
$593$	−7.60422	+	7.60422i	−0.312268	+	0.312268i	−0.845788	−	0.533520i	$-0.820869\pi$
$593$	−7.60422	+	7.60422i	−0.312268	+	0.312268i	0.533520	+	0.845788i	$0.320869\pi$
$594$		0			0
$595$	10.5899	−	4.12411i	0.434143	−	0.169072i
$596$		0			0
$597$	−9.54476	+	9.54476i	−0.390641	+	0.390641i
$598$		0			0
$599$		−	27.2751i		−	1.11443i	−0.830369	−	0.557214i	$-0.811870\pi$
$599$		−	27.2751i		−	1.11443i	0.830369	−	0.557214i	$-0.188130\pi$
$600$		0			0
$601$	−20.9458			−0.854396			−0.427198	−	0.904158i	$-0.640499\pi$
$601$	−20.9458			−0.854396			−0.427198	+	0.904158i	$0.640499\pi$
$602$		0			0
$603$	5.33023	+	5.33023i	0.217064	+	0.217064i
$604$		0			0
$605$	8.88836	+	22.8236i	0.361363	+	0.927910i
$606$		0			0
$607$	−8.25929	−	8.25929i	−0.335234	−	0.335234i	0.519336	−	0.854570i	$-0.326179\pi$
$607$	−8.25929	−	8.25929i	−0.335234	−	0.335234i	−0.854570	+	0.519336i	$0.826179\pi$
$608$		0			0
$609$	−24.5614			−0.995279
$610$		0			0
$611$	0.671802			0.0271782
$612$		0			0
$613$	−15.6194	−	15.6194i	−0.630863	−	0.630863i	0.317422	−	0.948285i	$-0.397183\pi$
$613$	−15.6194	−	15.6194i	−0.630863	−	0.630863i	−0.948285	+	0.317422i	$0.897183\pi$
$614$		0			0
$615$	3.15526	+	1.38652i	0.127232	+	0.0559099i
$616$		0			0
$617$	−26.5077	+	26.5077i	−1.06716	+	1.06716i	−0.0695832	+	0.997576i	$0.522167\pi$
$617$	−26.5077	+	26.5077i	−1.06716	+	1.06716i	−0.997576	+	0.0695832i	$0.977833\pi$
$618$		0			0
$619$	29.5180			1.18643			0.593214	−	0.805045i	$-0.297859\pi$
$619$	29.5180			1.18643			0.593214	+	0.805045i	$0.297859\pi$
$620$		0			0
$621$	−1.79594	+	4.44686i	−0.0720687	+	0.178446i
$622$		0			0
$623$	30.0729	−	30.0729i	1.20484	−	1.20484i
$624$		0			0
$625$	2.13051	−	24.9091i	0.0852203	−	0.996362i
$626$		0			0
$627$	0.551787	+	0.551787i	0.0220363	+	0.0220363i
$628$		0			0
$629$			5.88569i			0.234678i
$630$		0			0
$631$			35.6030i			1.41733i	0.705543	+	0.708667i	$0.250703\pi$
$631$			35.6030i			1.41733i	−0.705543	+	0.708667i	$0.749297\pi$
$632$		0			0
$633$	0.159067	−	0.159067i	0.00632234	−	0.00632234i
$634$		0			0
$635$	14.3340	−	32.6195i	0.568828	−	1.29447i
$636$		0			0
$637$	1.18684	+	1.18684i	0.0470243	+	0.0470243i
$638$		0			0
$639$			12.8841i			0.509688i
$640$		0			0
$641$		−	41.7123i		−	1.64753i	−0.566928	−	0.823767i	$-0.691868\pi$
$641$		−	41.7123i		−	1.64753i	0.566928	−	0.823767i	$-0.308132\pi$
$642$		0			0
$643$	−22.5757	−	22.5757i	−0.890298	−	0.890298i	0.104253	−	0.994551i	$-0.466755\pi$
$643$	−22.5757	−	22.5757i	−0.890298	−	0.890298i	−0.994551	+	0.104253i	$0.966755\pi$
$644$		0			0
$645$	−1.37761	−	3.53744i	−0.0542434	−	0.139286i
$646$		0			0
$647$	7.63039	+	7.63039i	0.299982	+	0.299982i	0.841007	−	0.541025i	$-0.181964\pi$
$647$	7.63039	+	7.63039i	0.299982	+	0.299982i	−0.541025	+	0.841007i	$0.681964\pi$
$648$		0			0
$649$	0.601471			0.0236098
$650$		0			0
$651$			2.99705i			0.117464i
$652$		0			0
$653$	−20.1678	+	20.1678i	−0.789225	+	0.789225i	−0.981367	−	0.192142i	$-0.938457\pi$
$653$	−20.1678	+	20.1678i	−0.789225	+	0.789225i	0.192142	+	0.981367i	$0.438457\pi$
$654$		0			0
$655$	−4.68698	−	12.0352i	−0.183135	−	0.470256i
$656$		0			0
$657$	−9.19956	−	9.19956i	−0.358909	−	0.358909i
$658$		0			0
$659$	−10.8395			−0.422246			−0.211123	−	0.977460i	$-0.567712\pi$
$659$	−10.8395			−0.422246			−0.211123	+	0.977460i	$0.567712\pi$
$660$		0			0
$661$			24.9016i			0.968561i	0.874913	+	0.484281i	$0.160919\pi$
$661$			24.9016i			0.968561i	−0.874913	+	0.484281i	$0.839081\pi$
$662$		0			0
$663$	0.123485	+	0.123485i	0.00479576	+	0.00479576i
$664$		0			0
$665$	31.8381	+	13.9906i	1.23463	+	0.542534i
$666$		0			0
$667$	25.2825	−	10.7359i	0.978942	−	0.415694i
$668$		0			0
$669$		−	12.4655i		−	0.481945i
$670$		0			0
$671$	1.21568			0.0469309
$672$		0			0
$673$	−13.3603	+	13.3603i	−0.515003	+	0.515003i	−0.916055	−	0.401052i	$-0.868645\pi$
$673$	−13.3603	+	13.3603i	−0.515003	+	0.515003i	0.401052	+	0.916055i	$0.368645\pi$
$674$		0			0
$675$	−4.99545	−	0.213245i	−0.192275	−	0.00820780i
$676$		0			0
$677$	2.26529	−	2.26529i	0.0870623	−	0.0870623i	−0.662234	−	0.749297i	$-0.730392\pi$
$677$	2.26529	−	2.26529i	0.0870623	−	0.0870623i	0.749297	+	0.662234i	$0.230392\pi$
$678$		0			0
$679$		−	71.1874i		−	2.73192i
$680$		0			0
$681$		−	8.06506i		−	0.309054i
$682$		0			0
$683$	34.0081	−	34.0081i	1.30128	−	1.30128i	0.373756	−	0.927527i	$-0.378070\pi$
$683$	34.0081	−	34.0081i	1.30128	−	1.30128i	0.927527	−	0.373756i	$-0.121930\pi$
$684$		0			0
$685$	−28.8620	−	12.6829i	−1.10276	−	0.484587i
$686$		0			0
$687$	−2.70864	+	2.70864i	−0.103341	+	0.103341i
$688$		0			0
$689$	0.147724			0.00562784
$690$		0			0
$691$	−40.3873			−1.53641			−0.768203	−	0.640206i	$-0.778849\pi$
$691$	−40.3873			−1.53641			−0.768203	+	0.640206i	$0.778849\pi$
$692$		0			0
$693$	−0.652481	+	0.652481i	−0.0247857	+	0.0247857i
$694$		0			0
$695$	−24.1157	+	9.39157i	−0.914761	+	0.356242i
$696$		0			0
$697$	1.29165	−	1.29165i	0.0489247	−	0.0489247i
$698$		0			0
$699$			22.6315i			0.856001i
$700$		0			0
$701$			5.40854i			0.204278i	0.994770	+	0.102139i	$0.0325686\pi$
$701$			5.40854i			0.204278i	−0.994770	+	0.102139i	$0.967431\pi$
$702$		0			0
$703$	−12.7354	+	12.7354i	−0.480326	+	0.480326i
$704$		0			0
$705$	3.69950	+	9.49959i	0.139331	+	0.357775i
$706$		0			0
$707$	16.8207	−	16.8207i	0.632609	−	0.632609i
$708$		0			0
$709$	6.66092			0.250156			0.125078	−	0.992147i	$-0.460082\pi$
$709$	6.66092			0.250156			0.125078	+	0.992147i	$0.460082\pi$
$710$		0			0
$711$			0.634427i			0.0237929i
$712$		0			0
$713$	−1.31002	−	3.08504i	−0.0490606	−	0.115536i
$714$		0			0
$715$	0.0285220	−	0.0649067i	0.00106666	−	0.00242737i
$716$		0			0
$717$	−4.87823	−	4.87823i	−0.182181	−	0.182181i
$718$		0			0
$719$			11.2952i			0.421239i	0.977568	+	0.210620i	$0.0675482\pi$
$719$			11.2952i			0.421239i	−0.977568	+	0.210620i	$0.932452\pi$
$720$		0			0
$721$	−27.8240			−1.03622
$722$		0			0
$723$	−9.72669	−	9.72669i	−0.361740	−	0.361740i
$724$		0			0
$725$	19.3673	+	21.0945i	0.719282	+	0.783430i
$726$		0			0
$727$	37.0807	−	37.0807i	1.37525	−	1.37525i	0.522777	−	0.852469i	$-0.324896\pi$
$727$	37.0807	−	37.0807i	1.37525	−	1.37525i	0.852469	−	0.522777i	$-0.175104\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−2.01204			−0.0744181
$732$		0			0
$733$	−7.98845	−	7.98845i	−0.295060	−	0.295060i	0.544015	−	0.839075i	$-0.316903\pi$
$733$	−7.98845	−	7.98845i	−0.295060	−	0.295060i	−0.839075	+	0.544015i	$0.816903\pi$
$734$		0			0
$735$	−10.2467	+	23.3182i	−0.377956	+	0.860104i
$736$		0			0
$737$	−1.14691	−	1.14691i	−0.0422471	−	0.0422471i
$738$		0			0
$739$		−	3.73466i		−	0.137382i	−0.997638	−	0.0686908i	$-0.978118\pi$
$739$		−	3.73466i		−	0.137382i	0.997638	−	0.0686908i	$-0.0218822\pi$
$740$		0			0
$741$			0.534393i			0.0196314i
$742$		0			0
$743$	4.03236	+	4.03236i	0.147933	+	0.147933i	0.777194	−	0.629261i	$-0.216642\pi$
$743$	4.03236	+	4.03236i	0.147933	+	0.147933i	−0.629261	+	0.777194i	$0.716642\pi$
$744$		0			0
$745$	−12.9048	−	33.1369i	−0.472794	−	1.21404i
$746$		0			0
$747$	3.22905	−	3.22905i	0.118145	−	0.118145i
$748$		0			0
$749$		−	10.8764i		−	0.397414i
$750$		0			0
$751$		−	24.1213i		−	0.880199i	−0.897949	−	0.440100i	$-0.854943\pi$
$751$		−	24.1213i		−	0.880199i	0.897949	−	0.440100i	$-0.145057\pi$
$752$		0			0
$753$	−7.87502	−	7.87502i	−0.286982	−	0.286982i
$754$		0			0
$755$	9.46179	+	24.2960i	0.344350	+	0.884222i
$756$		0			0
$757$	−29.8976	+	29.8976i	−1.08665	+	1.08665i	−0.0907742	+	0.995872i	$0.528934\pi$
$757$	−29.8976	+	29.8976i	−1.08665	+	1.08665i	−0.995872	+	0.0907742i	$0.971066\pi$
$758$		0			0
$759$	0.386435	−	0.956838i	0.0140267	−	0.0347310i
$760$		0			0
$761$	36.5670			1.32555			0.662777	−	0.748817i	$-0.269378\pi$
$761$	36.5670			1.32555			0.662777	+	0.748817i	$0.269378\pi$
$762$		0			0
$763$	−23.3119	+	23.3119i	−0.843947	+	0.843947i
$764$		0			0
$765$	−1.06612	+	2.42615i	−0.0385458	+	0.0877176i
$766$		0			0
$767$	0.291255	+	0.291255i	0.0105166	+	0.0105166i
$768$		0			0
$769$	0.328757			0.0118553			0.00592763	−	0.999982i	$-0.498113\pi$
$769$	0.328757			0.0118553			0.00592763	+	0.999982i	$0.498113\pi$
$770$		0			0
$771$	2.07817			0.0748435
$772$		0			0
$773$	−17.6256	−	17.6256i	−0.633950	−	0.633950i	0.315106	−	0.949056i	$-0.397960\pi$
$773$	−17.6256	−	17.6256i	−0.633950	−	0.633950i	−0.949056	+	0.315106i	$0.897960\pi$
$774$		0			0
$775$	2.57401	−	2.36325i	0.0924611	−	0.0848904i
$776$		0			0
$777$	−15.0595	−	15.0595i	−0.540256	−	0.540256i
$778$		0			0
$779$	5.58973			0.200273
$780$		0			0
$781$		−	2.77229i		−	0.0992005i
$782$		0			0
$783$	4.04986	−	4.04986i	0.144730	−	0.144730i
$784$		0			0
$785$	−0.580884	−	0.255258i	−0.0207326	−	0.00911056i
$786$		0			0
$787$	−18.0525	+	18.0525i	−0.643503	+	0.643503i	−0.951415	−	0.307912i	$-0.900370\pi$
$787$	−18.0525	+	18.0525i	−0.643503	+	0.643503i	0.307912	+	0.951415i	$0.400370\pi$
$788$		0			0
$789$	−19.6606			−0.699937
$790$		0			0
$791$	−38.3625			−1.36401
$792$		0			0
$793$	0.588679	+	0.588679i	0.0209046	+	0.0209046i
$794$		0			0
$795$	0.813492	+	2.08889i	0.0288516	+	0.0740852i
$796$		0			0
$797$	−8.96650	+	8.96650i	−0.317610	+	0.317610i	−0.847848	−	0.530239i	$-0.822102\pi$
$797$	−8.96650	+	8.96650i	−0.317610	+	0.317610i	0.530239	+	0.847848i	$0.322102\pi$
$798$		0			0
$799$	5.40323			0.191153
$800$		0			0
$801$			9.91726i			0.350409i
$802$		0			0
$803$	1.97948	+	1.97948i	0.0698544	+	0.0698544i
$804$		0			0
$805$	0.573347	−	45.9847i	0.0202078	−	1.62075i
$806$		0			0
$807$	−11.6104	−	11.6104i	−0.408705	−	0.408705i
$808$		0			0
$809$			35.3410i			1.24252i	0.783603	+	0.621262i	$0.213380\pi$
$809$			35.3410i			1.24252i	−0.783603	+	0.621262i	$0.786620\pi$
$810$		0			0
$811$	−42.5878			−1.49546			−0.747730	−	0.664003i	$-0.768856\pi$
$811$	−42.5878			−1.49546			−0.747730	+	0.664003i	$0.768856\pi$
$812$		0			0
$813$	−7.07424	+	7.07424i	−0.248104	+	0.248104i
$814$		0			0
$815$	−26.9667	−	11.8500i	−0.944604	−	0.415088i
$816$		0			0
$817$	−4.35365	−	4.35365i	−0.152315	−	0.152315i
$818$		0			0
$819$	−0.631912			−0.0220808
$820$		0			0
$821$	41.9013			1.46237			0.731183	−	0.682182i	$-0.238969\pi$
$821$	41.9013			1.46237			0.731183	+	0.682182i	$0.238969\pi$
$822$		0			0
$823$	25.1719	−	25.1719i	0.877437	−	0.877437i	−0.115832	−	0.993269i	$-0.536953\pi$
$823$	25.1719	−	25.1719i	0.877437	−	0.877437i	0.993269	+	0.115832i	$0.0369533\pi$
$824$		0			0
$825$	1.07488	+	0.0458842i	0.0374225	+	0.00159748i
$826$		0			0
$827$	−0.851694	+	0.851694i	−0.0296163	+	0.0296163i	−0.721760	−	0.692144i	$-0.756666\pi$
$827$	−0.851694	+	0.851694i	−0.0296163	+	0.0296163i	0.692144	+	0.721760i	$0.256666\pi$
$828$		0			0
$829$			17.5175i			0.608408i	0.952607	+	0.304204i	$0.0983905\pi$
$829$			17.5175i			0.608408i	−0.952607	+	0.304204i	$0.901610\pi$
$830$		0			0
$831$	−28.7174			−0.996195
$832$		0			0
$833$	9.54562	+	9.54562i	0.330736	+	0.330736i
$834$		0			0
$835$	14.1389	−	32.1755i	0.489298	−	1.11348i
$836$		0			0
$837$	−0.494175	−	0.494175i	−0.0170812	−	0.0170812i
$838$		0			0
$839$	−17.1704			−0.592788			−0.296394	−	0.955066i	$-0.595784\pi$
$839$	−17.1704			−0.592788			−0.296394	+	0.955066i	$0.595784\pi$
$840$		0			0
$841$	−3.80273			−0.131129
$842$		0			0
$843$	−16.5460	−	16.5460i	−0.569875	−	0.569875i
$844$		0			0
$845$	−27.0421	+	10.5312i	−0.930275	+	0.362285i
$846$		0			0
$847$	−33.2158	+	33.2158i	−1.14131	+	1.14131i
$848$		0			0
$849$	6.18819			0.212378
$850$		0			0
$851$	22.0841	+	8.91906i	0.757035	+	0.305742i
$852$		0			0
$853$	−24.2539	+	24.2539i	−0.830438	+	0.830438i	−0.987577	−	0.157139i	$-0.949773\pi$
$853$	−24.2539	+	24.2539i	−0.830438	+	0.830438i	0.157139	+	0.987577i	$0.449773\pi$
$854$		0			0
$855$	−7.55657	+	2.94281i	−0.258429	+	0.100642i
$856$		0			0
$857$	−17.1452	−	17.1452i	−0.585669	−	0.585669i	0.350786	−	0.936455i	$-0.385914\pi$
$857$	−17.1452	−	17.1452i	−0.585669	−	0.585669i	−0.936455	+	0.350786i	$0.885914\pi$
$858$		0			0
$859$			5.82647i			0.198797i	0.995048	+	0.0993983i	$0.0316918\pi$
$859$			5.82647i			0.198797i	−0.995048	+	0.0993983i	$0.968308\pi$
$860$		0			0
$861$			6.60978i			0.225261i
$862$		0			0
$863$	22.8904	−	22.8904i	0.779197	−	0.779197i	−0.200498	−	0.979694i	$-0.564256\pi$
$863$	22.8904	−	22.8904i	0.779197	−	0.779197i	0.979694	+	0.200498i	$0.0642559\pi$
$864$		0			0
$865$	−52.9220	−	23.2556i	−1.79940	−	0.790713i
$866$		0			0
$867$	−11.0276	−	11.0276i	−0.374518	−	0.374518i
$868$		0			0
$869$		−	0.136510i		−	0.00463080i
$870$		0			0
$871$		−	1.11076i		−	0.0376366i
$872$		0			0
$873$	11.7379	+	11.7379i	0.397267	+	0.397267i
$874$		0			0
$875$	45.3791	−	15.4779i	1.53409	−	0.523249i
$876$		0			0
$877$	1.61273	+	1.61273i	0.0544582	+	0.0544582i	0.733811	−	0.679353i	$-0.237740\pi$
$877$	1.61273	+	1.61273i	0.0544582	+	0.0544582i	−0.679353	+	0.733811i	$0.737740\pi$
$878$		0			0
$879$	−14.1911			−0.478653
$880$		0			0
$881$		−	34.5149i		−	1.16284i	−0.813604	−	0.581419i	$-0.802498\pi$
$881$		−	34.5149i		−	1.16284i	0.813604	−	0.581419i	$-0.197502\pi$
$882$		0			0
$883$	−0.737702	+	0.737702i	−0.0248257	+	0.0248257i	−0.719411	−	0.694585i	$-0.755588\pi$
$883$	−0.737702	+	0.737702i	−0.0248257	+	0.0248257i	0.694585	+	0.719411i	$0.255588\pi$
$884$		0			0
$885$	−2.51459	+	5.72238i	−0.0845271	+	0.192356i
$886$		0			0
$887$	−28.3308	−	28.3308i	−0.951256	−	0.951256i	0.0476096	−	0.998866i	$-0.484840\pi$
$887$	−28.3308	−	28.3308i	−0.951256	−	0.951256i	−0.998866	+	0.0476096i	$0.984840\pi$
$888$		0			0
$889$	68.3328			2.29181
$890$		0			0
$891$		−	0.215171i		−	0.00720851i
$892$		0			0
$893$	11.6915	+	11.6915i	0.391241	+	0.391241i
$894$		0			0
$895$	−31.1696	+	12.1386i	−1.04188	+	0.405749i
$896$		0			0
$897$	0.650464	−	0.276211i	0.0217184	−	0.00922240i
$898$		0			0
$899$			4.00268i			0.133497i
$900$		0			0
$901$	1.18813			0.0395823
$902$		0			0
$903$	5.14813	−	5.14813i	0.171319	−	0.171319i
$904$		0			0
$905$	41.6124	−	16.2054i	1.38324	−	0.538687i
$906$		0			0
$907$	35.8112	−	35.8112i	1.18909	−	1.18909i	0.211772	−	0.977319i	$-0.432077\pi$
$907$	35.8112	−	35.8112i	1.18909	−	1.18909i	0.977319	−	0.211772i	$-0.0679235\pi$
$908$		0			0
$909$			5.54705i			0.183984i
$910$		0			0
$911$			26.7794i			0.887240i	0.896215	+	0.443620i	$0.146306\pi$
$911$			26.7794i			0.887240i	−0.896215	+	0.443620i	$0.853694\pi$
$912$		0			0
$913$	−0.694799	+	0.694799i	−0.0229945	+	0.0229945i
$914$		0			0
$915$	−5.08244	+	11.5660i	−0.168020	+	0.382359i
$916$		0			0
$917$	17.5152	−	17.5152i	0.578404	−	0.578404i
$918$		0			0
$919$	−3.04224			−0.100354			−0.0501771	−	0.998740i	$-0.515979\pi$
$919$	−3.04224			−0.100354			−0.0501771	+	0.998740i	$0.515979\pi$
$920$		0			0
$921$	−15.6715			−0.516392
$922$		0			0
$923$	1.34245	−	1.34245i	0.0441873	−	0.0441873i
$924$		0			0
$925$	−1.05902	+	24.8086i	−0.0348205	+	0.815700i
$926$		0			0
$927$	4.58781	−	4.58781i	0.150683	−	0.150683i
$928$		0			0
$929$			43.8915i			1.44003i	0.693957	+	0.720016i	$0.255866\pi$
$929$			43.8915i			1.44003i	−0.693957	+	0.720016i	$0.744134\pi$
$930$		0			0
$931$			41.3095i			1.35387i
$932$		0			0
$933$	10.7473	−	10.7473i	0.351851	−	0.351851i
$934$		0			0
$935$	0.229400	−	0.522038i	0.00750217	−	0.0170725i
$936$		0			0
$937$	−28.5977	+	28.5977i	−0.934247	+	0.934247i	−0.997968	−	0.0637210i	$-0.979703\pi$
$937$	−28.5977	+	28.5977i	−0.934247	+	0.934247i	0.0637210	+	0.997968i	$0.479703\pi$
$938$		0			0
$939$	5.98750			0.195395
$940$		0			0
$941$			50.1600i			1.63517i	0.575808	+	0.817585i	$0.304687\pi$
$941$			50.1600i			1.63517i	−0.575808	+	0.817585i	$0.695313\pi$
$942$		0			0
$943$	−2.88915	−	6.80383i	−0.0940838	−	0.221563i
$944$		0			0
$945$	−3.47984	−	8.93554i	−0.113199	−	0.290673i
$946$		0			0
$947$	18.8171	+	18.8171i	0.611475	+	0.611475i	0.943330	−	0.331855i	$-0.107675\pi$
$947$	18.8171	+	18.8171i	0.611475	+	0.611475i	−0.331855	+	0.943330i	$0.607675\pi$
$948$		0			0
$949$			1.91708i			0.0622311i
$950$		0			0
$951$	−12.4513			−0.403761
$952$		0			0
$953$	26.5665	+	26.5665i	0.860572	+	0.860572i	0.991405	−	0.130832i	$-0.0417649\pi$
$953$	26.5665	+	26.5665i	0.860572	+	0.860572i	−0.130832	+	0.991405i	$0.541765\pi$
$954$		0			0
$955$	33.7028	−	13.1251i	1.09060	−	0.424720i
$956$		0			0
$957$	−0.871414	+	0.871414i	−0.0281688	+	0.0281688i
$958$		0			0
$959$		−	60.4614i		−	1.95240i
$960$		0			0
$961$	−30.5116			−0.984245
$962$		0			0
$963$	1.79337	+	1.79337i	0.0577906	+	0.0577906i
$964$		0			0
$965$	55.9728	+	24.5962i	1.80183	+	0.791778i
$966$		0			0
$967$	−42.5399	−	42.5399i	−1.36799	−	1.36799i	−0.863301	−	0.504690i	$-0.831607\pi$
$967$	−42.5399	−	42.5399i	−1.36799	−	1.36799i	−0.504690	−	0.863301i	$-0.668393\pi$
$968$		0			0
$969$			4.29806i			0.138074i
$970$		0			0
$971$		−	2.54245i		−	0.0815912i	−0.999168	−	0.0407956i	$-0.987011\pi$
$971$		−	2.54245i		−	0.0815912i	0.999168	−	0.0407956i	$-0.0129892\pi$
$972$		0			0
$973$	−35.0963	−	35.0963i	−1.12513	−	1.12513i
$974$		0			0
$975$	0.498278	+	0.542716i	0.0159577	+	0.0173808i
$976$		0			0
$977$	6.62149	−	6.62149i	0.211840	−	0.211840i	−0.593209	−	0.805049i	$-0.702139\pi$
$977$	6.62149	−	6.62149i	0.211840	−	0.211840i	0.805049	+	0.593209i	$0.202139\pi$
$978$		0			0
$979$		−	2.13391i		−	0.0682001i
$980$		0			0
$981$		−	7.68766i		−	0.245448i
$982$		0			0
$983$	−12.7066	−	12.7066i	−0.405279	−	0.405279i	0.474810	−	0.880088i	$-0.342517\pi$
$983$	−12.7066	−	12.7066i	−0.405279	−	0.405279i	−0.880088	+	0.474810i	$0.842517\pi$
$984$		0			0
$985$	−8.99022	+	20.4588i	−0.286452	+	0.651871i
$986$		0			0
$987$	−13.8250	+	13.8250i	−0.440055	+	0.440055i
$988$		0			0
$989$	−3.04901	+	7.54953i	−0.0969528	+	0.240061i
$990$		0			0
$991$	58.5638			1.86034			0.930170	−	0.367129i	$-0.119659\pi$
$991$	58.5638			1.86034			0.930170	+	0.367129i	$0.119659\pi$
$992$		0			0
$993$	−14.9290	+	14.9290i	−0.473759	+	0.473759i
$994$		0			0
$995$	10.9532	+	28.1257i	0.347240	+	0.891643i
$996$		0			0
$997$	−11.4575	−	11.4575i	−0.362862	−	0.362862i	0.502004	−	0.864865i	$-0.332596\pi$
$997$	−11.4575	−	11.4575i	−0.362862	−	0.362862i	−0.864865	+	0.502004i	$0.832596\pi$
$998$		0			0
$999$	4.96623			0.157125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.2	yes	48
5.3	odd	4	inner	1380.2.t.a.1333.1	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.1	✓	48
115.68	even	4	inner	1380.2.t.a.1333.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.1	✓	48	23.22	odd	2	inner
1380.2.t.a.1057.2	yes	48	1.1	even	1	trivial
1380.2.t.a.1333.1	yes	48	5.3	odd	4	inner
1380.2.t.a.1333.2	yes	48	115.68	even	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(0.811448 + 2.08364i) q^{5} +(-3.03238 + 3.03238i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(0.811448 + 2.08364i) q^{5} +(-3.03238 + 3.03238i) q^{7} -1.00000i q^{9} +0.215171i q^{11} +(-0.104194 + 0.104194i) q^{13} +(-2.04714 - 0.899575i) q^{15} +(-0.838023 + 0.838023i) q^{17} -3.62662 q^{19} -4.28843i q^{21} +(1.87448 + 4.41433i) q^{23} +(-3.68310 + 3.38153i) q^{25} +(0.707107 + 0.707107i) q^{27} -5.72737i q^{29} -0.698870 q^{31} +(-0.152149 - 0.152149i) q^{33} +(-8.77900 - 3.85776i) q^{35} +(3.51166 - 3.51166i) q^{37} -0.147353i q^{39} -1.54131 q^{41} +(1.20047 + 1.20047i) q^{43} +(2.08364 - 0.811448i) q^{45} +(-3.22380 - 3.22380i) q^{47} -11.3906i q^{49} -1.18514i q^{51} +(-0.708888 - 0.708888i) q^{53} +(-0.448340 + 0.174600i) q^{55} +(2.56441 - 2.56441i) q^{57} -2.79531i q^{59} -5.64983i q^{61} +(3.03238 + 3.03238i) q^{63} +(-0.301651 - 0.132555i) q^{65} +(-5.33023 + 5.33023i) q^{67} +(-4.44686 - 1.79594i) q^{69} -12.8841 q^{71} +(9.19956 - 9.19956i) q^{73} +(0.213245 - 4.99545i) q^{75} +(-0.652481 - 0.652481i) q^{77} -0.634427 q^{79} -1.00000 q^{81} +(3.22905 + 3.22905i) q^{83} +(-2.42615 - 1.06612i) q^{85} +(4.04986 + 4.04986i) q^{87} -9.91726 q^{89} -0.631912i q^{91} +(0.494175 - 0.494175i) q^{93} +(-2.94281 - 7.55657i) q^{95} +(-11.7379 + 11.7379i) q^{97} +0.215171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) \) 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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