LMFDB - Embedded newform 1386.2.r.d.1277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(89,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("1386.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.r (of order $6$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1277.1
Character	$\chi$	$=$	1386.1277
Dual form			1386.2.r.d.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.36138 + 2.35797i) q^{5} +(-2.13605 - 1.56119i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.36138 + 2.35797i) q^{5} +(-2.13605 - 1.56119i) q^{7} +1.00000i q^{8} +(-2.35797 - 1.36138i) q^{10} +(0.866025 + 0.500000i) q^{11} -0.193887i q^{13} +(2.63046 + 0.284003i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.07388 - 5.32411i) q^{17} +(0.269276 - 0.155466i) q^{19} +2.72275 q^{20} -1.00000 q^{22} +(4.50799 - 2.60269i) q^{23} +(-1.20669 + 2.09005i) q^{25} +(0.0969436 + 0.167911i) q^{26} +(-2.42005 + 1.06928i) q^{28} +4.17192i q^{29} +(1.38127 + 0.797476i) q^{31} +(0.866025 + 0.500000i) q^{32} +6.14775i q^{34} +(0.773269 - 7.16211i) q^{35} +(2.21011 + 3.82803i) q^{37} +(-0.155466 + 0.269276i) q^{38} +(-2.35797 + 1.36138i) q^{40} +4.29859 q^{41} +4.10271 q^{43} +(0.866025 - 0.500000i) q^{44} +(-2.60269 + 4.50799i) q^{46} +(3.63535 + 6.29661i) q^{47} +(2.12540 + 6.66953i) q^{49} -2.41339i q^{50} +(-0.167911 - 0.0969436i) q^{52} +(-1.04499 - 0.603325i) q^{53} +2.72275i q^{55} +(1.56119 - 2.13605i) q^{56} +(-2.08596 - 3.61299i) q^{58} +(5.43057 - 9.40603i) q^{59} +(-8.20619 + 4.73784i) q^{61} -1.59495 q^{62} -1.00000 q^{64} +(0.457181 - 0.263953i) q^{65} +(2.69458 - 4.66714i) q^{67} +(-3.07388 - 5.32411i) q^{68} +(2.91138 + 6.58920i) q^{70} +9.63462i q^{71} +(-2.50213 - 1.44461i) q^{73} +(-3.82803 - 2.21011i) q^{74} -0.310933i q^{76} +(-1.06928 - 2.42005i) q^{77} +(-7.60345 - 13.1696i) q^{79} +(1.36138 - 2.35797i) q^{80} +(-3.72268 + 2.14929i) q^{82} +10.0883 q^{83} +16.7388 q^{85} +(-3.55305 + 2.05135i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(5.67955 + 9.83727i) q^{89} +(-0.302694 + 0.414152i) q^{91} -5.20538i q^{92} +(-6.29661 - 3.63535i) q^{94} +(0.733171 + 0.423296i) q^{95} +6.77249i q^{97} +(-5.17542 - 4.71329i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 8 * q^7	$ 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.36138	+	2.35797i	0.608826	+	1.05452i	0.991434	+	0.130607i	$0.0416926\pi$
$5$	1.36138	+	2.35797i	0.608826	+	1.05452i	−0.382608	+	0.923911i	$0.624974\pi$
$6$		0			0
$7$	−2.13605	−	1.56119i	−0.807350	−	0.590073i
$7$	−2.13605	−	1.56119i	−0.807350	−	0.590073i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.35797	−	1.36138i	−0.745657	−	0.430505i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$12$		0			0
$13$		−	0.193887i		−	0.0537746i	−0.999638	−	0.0268873i	$-0.991440\pi$
$13$		−	0.193887i		−	0.0537746i	0.999638	−	0.0268873i	$-0.00855953\pi$
$14$	2.63046	+	0.284003i	0.703021	+	0.0759029i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.07388	−	5.32411i	0.745524	−	1.29129i	−0.204425	−	0.978882i	$-0.565532\pi$
$17$	3.07388	−	5.32411i	0.745524	−	1.29129i	0.949949	−	0.312404i	$-0.101134\pi$
$18$		0			0
$19$	0.269276	−	0.155466i	0.0617760	−	0.0356664i	−0.468794	−	0.883308i	$-0.655311\pi$
$19$	0.269276	−	0.155466i	0.0617760	−	0.0356664i	0.530570	+	0.847641i	$0.321978\pi$
$20$	2.72275			0.608826
$21$		0			0
$22$	−1.00000			−0.213201
$23$	4.50799	−	2.60269i	0.939981	−	0.542698i	0.0500264	−	0.998748i	$-0.484069\pi$
$23$	4.50799	−	2.60269i	0.939981	−	0.542698i	0.889954	+	0.456050i	$0.150736\pi$
$24$		0			0
$25$	−1.20669	+	2.09005i	−0.241339	+	0.418011i
$26$	0.0969436	+	0.167911i	0.0190122	+	0.0329301i
$27$		0			0
$28$	−2.42005	+	1.06928i	−0.457347	+	0.202075i
$29$			4.17192i			0.774705i	0.921932	+	0.387353i	$0.126610\pi$
$29$			4.17192i			0.774705i	−0.921932	+	0.387353i	$0.873390\pi$
$30$		0			0
$31$	1.38127	+	0.797476i	0.248083	+	0.143231i	0.618886	−	0.785481i	$-0.287584\pi$
$31$	1.38127	+	0.797476i	0.248083	+	0.143231i	−0.370803	+	0.928712i	$0.620918\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			6.14775i			1.05433i
$35$	0.773269	−	7.16211i	0.130706	−	1.21062i
$36$		0			0
$37$	2.21011	+	3.82803i	0.363340	+	0.629324i	0.988508	−	0.151167i	$-0.0483030\pi$
$37$	2.21011	+	3.82803i	0.363340	+	0.629324i	−0.625168	+	0.780490i	$0.714970\pi$
$38$	−0.155466	+	0.269276i	−0.0252200	+	0.0436823i
$39$		0			0
$40$	−2.35797	+	1.36138i	−0.372828	+	0.215253i
$41$	4.29859			0.671326			0.335663	−	0.941982i	$-0.391040\pi$
$41$	4.29859			0.671326			0.335663	+	0.941982i	$0.391040\pi$
$42$		0			0
$43$	4.10271			0.625657			0.312829	−	0.949810i	$-0.398723\pi$
$43$	4.10271			0.625657			0.312829	+	0.949810i	$0.398723\pi$
$44$	0.866025	−	0.500000i	0.130558	−	0.0753778i
$45$		0			0
$46$	−2.60269	+	4.50799i	−0.383746	+	0.664667i
$47$	3.63535	+	6.29661i	0.530270	+	0.918454i	0.999376	+	0.0353126i	$0.0112427\pi$
$47$	3.63535	+	6.29661i	0.530270	+	0.918454i	−0.469107	+	0.883142i	$0.655424\pi$
$48$		0			0
$49$	2.12540	+	6.66953i	0.303628	+	0.952791i
$50$		−	2.41339i		−	0.341304i
$51$		0			0
$52$	−0.167911	−	0.0969436i	−0.0232851	−	0.0134437i
$53$	−1.04499	−	0.603325i	−0.143540	−	0.0828730i	0.426510	−	0.904483i	$-0.359743\pi$
$53$	−1.04499	−	0.603325i	−0.143540	−	0.0828730i	−0.570050	+	0.821610i	$0.693076\pi$
$54$		0			0
$55$			2.72275i			0.367136i
$56$	1.56119	−	2.13605i	0.208622	−	0.285441i
$57$		0			0
$58$	−2.08596	−	3.61299i	−0.273900	−	0.474408i
$59$	5.43057	−	9.40603i	0.707001	−	1.22456i	−0.258964	−	0.965887i	$-0.583381\pi$
$59$	5.43057	−	9.40603i	0.707001	−	1.22456i	0.965965	−	0.258674i	$-0.0832855\pi$
$60$		0			0
$61$	−8.20619	+	4.73784i	−1.05069	+	0.606619i	−0.922844	−	0.385175i	$-0.874141\pi$
$61$	−8.20619	+	4.73784i	−1.05069	+	0.606619i	−0.127851	+	0.991793i	$0.540808\pi$
$62$	−1.59495			−0.202559
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.457181	−	0.263953i	0.0567063	−	0.0327394i
$66$		0			0
$67$	2.69458	−	4.66714i	0.329195	−	0.570182i	−0.653158	−	0.757222i	$-0.726556\pi$
$67$	2.69458	−	4.66714i	0.329195	−	0.570182i	0.982352	+	0.187040i	$0.0598894\pi$
$68$	−3.07388	−	5.32411i	−0.372762	−	0.645643i
$69$		0			0
$70$	2.91138	+	6.58920i	0.347977	+	0.787560i
$71$			9.63462i			1.14342i	0.820456	+	0.571710i	$0.193720\pi$
$71$			9.63462i			1.14342i	−0.820456	+	0.571710i	$0.806280\pi$
$72$		0			0
$73$	−2.50213	−	1.44461i	−0.292853	−	0.169079i	0.346375	−	0.938096i	$-0.387412\pi$
$73$	−2.50213	−	1.44461i	−0.292853	−	0.169079i	−0.639228	+	0.769018i	$0.720746\pi$
$74$	−3.82803	−	2.21011i	−0.444999	−	0.256920i
$75$		0			0
$76$		−	0.310933i		−	0.0356664i
$77$	−1.06928	−	2.42005i	−0.121856	−	0.275790i
$78$		0			0
$79$	−7.60345	−	13.1696i	−0.855455	−	1.48169i	−0.876223	−	0.481907i	$-0.839944\pi$
$79$	−7.60345	−	13.1696i	−0.855455	−	1.48169i	0.0207679	−	0.999784i	$-0.493389\pi$
$80$	1.36138	−	2.35797i	0.152207	−	0.263629i
$81$		0			0
$82$	−3.72268	+	2.14929i	−0.411102	+	0.237350i
$83$	10.0883			1.10734			0.553668	−	0.832737i	$-0.313228\pi$
$83$	10.0883			1.10734			0.553668	+	0.832737i	$0.313228\pi$
$84$		0			0
$85$	16.7388			1.81558
$86$	−3.55305	+	2.05135i	−0.383135	+	0.221203i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	5.67955	+	9.83727i	0.602031	+	1.04275i	0.992513	+	0.122138i	$0.0389750\pi$
$89$	5.67955	+	9.83727i	0.602031	+	1.04275i	−0.390482	+	0.920610i	$0.627692\pi$
$90$		0			0
$91$	−0.302694	+	0.414152i	−0.0317309	+	0.0434149i
$92$		−	5.20538i		−	0.542698i
$93$		0			0
$94$	−6.29661	−	3.63535i	−0.649445	−	0.374957i
$95$	0.733171	+	0.423296i	0.0752217	+	0.0434293i
$96$		0			0
$97$			6.77249i			0.687642i	0.939035	+	0.343821i	$0.111721\pi$
$97$			6.77249i			0.687642i	−0.939035	+	0.343821i	$0.888279\pi$
$98$	−5.17542	−	4.71329i	−0.522796	−	0.476114i
$99$		0			0
$100$	1.20669	+	2.09005i	0.120669	+	0.209005i
$101$	−6.35755	+	11.0116i	−0.632600	+	1.09570i	0.354418	+	0.935087i	$0.384679\pi$
$101$	−6.35755	+	11.0116i	−0.632600	+	1.09570i	−0.987018	+	0.160608i	$0.948654\pi$
$102$		0			0
$103$	1.88096	−	1.08597i	0.185336	−	0.107004i	−0.404461	−	0.914555i	$-0.632541\pi$
$103$	1.88096	−	1.08597i	0.185336	−	0.107004i	0.589797	+	0.807551i	$0.299208\pi$
$104$	0.193887			0.0190122
$105$		0			0
$106$	1.20665			0.117200
$107$	4.39707	−	2.53865i	0.425081	−	0.245421i	−0.272168	−	0.962250i	$-0.587741\pi$
$107$	4.39707	−	2.53865i	0.425081	−	0.245421i	0.697249	+	0.716829i	$0.254407\pi$
$108$		0			0
$109$	0.813357	−	1.40878i	0.0779054	−	0.134936i	−0.824441	−	0.565948i	$-0.808510\pi$
$109$	0.813357	−	1.40878i	0.0779054	−	0.134936i	0.902346	+	0.431012i	$0.141843\pi$
$110$	−1.36138	−	2.35797i	−0.129802	−	0.224824i
$111$		0			0
$112$	−0.284003	+	2.63046i	−0.0268357	+	0.248556i
$113$			9.08122i			0.854290i	0.904183	+	0.427145i	$0.140481\pi$
$113$			9.08122i			0.854290i	−0.904183	+	0.427145i	$0.859519\pi$
$114$		0			0
$115$	12.2741	+	7.08648i	1.14457	+	0.660818i
$116$	3.61299	+	2.08596i	0.335457	+	0.193676i
$117$		0			0
$118$			10.8611i			0.999850i
$119$	−14.8779	+	6.57366i	−1.36385	+	0.602606i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	4.73784	−	8.20619i	0.428944	−	0.742953i
$123$		0			0
$124$	1.38127	−	0.797476i	0.124042	−	0.0716155i
$125$	7.04271			0.629919
$126$		0			0
$127$	3.00619			0.266756			0.133378	−	0.991065i	$-0.457418\pi$
$127$	3.00619			0.266756			0.133378	+	0.991065i	$0.457418\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.263953	+	0.457181i	−0.0231502	+	0.0400974i
$131$	3.10422	+	5.37666i	0.271217	+	0.469761i	0.969174	−	0.246378i	$-0.0792406\pi$
$131$	3.10422	+	5.37666i	0.271217	+	0.469761i	−0.697957	+	0.716140i	$0.745907\pi$
$132$		0			0
$133$	−0.817897	−	0.0883057i	−0.0709207	−	0.00765708i
$134$			5.38915i			0.465552i
$135$		0			0
$136$	5.32411	+	3.07388i	0.456539	+	0.263583i
$137$	8.22265	+	4.74735i	0.702508	+	0.405593i	0.808281	−	0.588797i	$-0.200398\pi$
$137$	8.22265	+	4.74735i	0.702508	+	0.405593i	−0.105773	+	0.994390i	$0.533732\pi$
$138$		0			0
$139$		−	13.2020i		−	1.11978i	−0.828568	−	0.559888i	$-0.810844\pi$
$139$		−	13.2020i		−	1.11978i	0.828568	−	0.559888i	$-0.189156\pi$
$140$	−5.81593	−	4.25072i	−0.491536	−	0.359252i
$141$		0			0
$142$	−4.81731	−	8.34383i	−0.404260	−	0.700198i
$143$	0.0969436	−	0.167911i	0.00810683	−	0.0140414i
$144$		0			0
$145$	−9.83727	+	5.67955i	−0.816941	+	0.471661i
$146$	2.88921			0.239113
$147$		0			0
$148$	4.42022			0.363340
$149$	11.9136	−	6.87830i	0.975997	−	0.563492i	0.0749376	−	0.997188i	$-0.476124\pi$
$149$	11.9136	−	6.87830i	0.975997	−	0.563492i	0.901059	+	0.433696i	$0.142791\pi$
$150$		0			0
$151$	10.4182	−	18.0449i	0.847823	−	1.46847i	−0.0353230	−	0.999376i	$-0.511246\pi$
$151$	10.4182	−	18.0449i	0.847823	−	1.46847i	0.883146	−	0.469097i	$-0.155421\pi$
$152$	0.155466	+	0.269276i	0.0126100	+	0.0218411i
$153$		0			0
$154$	2.13605	+	1.56119i	0.172128	+	0.125804i
$155$			4.34266i			0.348811i
$156$		0			0
$157$	13.5367	+	7.81541i	1.08034	+	0.623737i	0.930989	−	0.365046i	$-0.118947\pi$
$157$	13.5367	+	7.81541i	1.08034	+	0.623737i	0.149355	+	0.988784i	$0.452280\pi$
$158$	13.1696	+	7.60345i	1.04771	+	0.604898i
$159$		0			0
$160$			2.72275i			0.215253i
$161$	−13.6926	−	1.47834i	−1.07912	−	0.116510i
$162$		0			0
$163$	−2.53891	−	4.39752i	−0.198863	−	0.344441i	0.749297	−	0.662234i	$-0.230392\pi$
$163$	−2.53891	−	4.39752i	−0.198863	−	0.344441i	−0.948160	+	0.317793i	$0.897058\pi$
$164$	2.14929	−	3.72268i	0.167832	−	0.290693i
$165$		0			0
$166$	−8.73673	+	5.04416i	−0.678102	+	0.391502i
$167$	3.13718			0.242762			0.121381	−	0.992606i	$-0.461268\pi$
$167$	3.13718			0.242762			0.121381	+	0.992606i	$0.461268\pi$
$168$		0			0
$169$	12.9624			0.997108
$170$	−14.4962	+	8.36940i	−1.11181	+	0.641904i
$171$		0			0
$172$	2.05135	−	3.55305i	0.156414	−	0.270918i
$173$	8.61420	+	14.9202i	0.654925	+	1.13436i	0.981913	+	0.189335i	$0.0606332\pi$
$173$	8.61420	+	14.9202i	0.654925	+	1.13436i	−0.326987	+	0.945029i	$0.606033\pi$
$174$		0			0
$175$	5.84051	−	2.58058i	0.441501	−	0.195074i
$176$		−	1.00000i		−	0.0753778i
$177$		0			0
$178$	−9.83727	−	5.67955i	−0.737334	−	0.425700i
$179$	−10.0700	−	5.81389i	−0.752664	−	0.434551i	0.0739917	−	0.997259i	$-0.476426\pi$
$179$	−10.0700	−	5.81389i	−0.752664	−	0.434551i	−0.826656	+	0.562708i	$0.809759\pi$
$180$		0			0
$181$			10.3940i			0.772577i	0.922378	+	0.386288i	$0.126243\pi$
$181$			10.3940i			0.772577i	−0.922378	+	0.386288i	$0.873757\pi$
$182$	0.0550645	−	0.510013i	0.00408165	−	0.0378047i
$183$		0			0
$184$	2.60269	+	4.50799i	0.191873	+	0.332333i
$185$	−6.01759	+	10.4228i	−0.442422	+	0.766297i
$186$		0			0
$187$	5.32411	−	3.07388i	0.389337	−	0.224784i
$188$	7.27069			0.530270
$189$		0			0
$190$	−0.846593			−0.0614183
$191$	−15.4420	+	8.91542i	−1.11734	+	0.645097i	−0.940721	−	0.339182i	$-0.889850\pi$
$191$	−15.4420	+	8.91542i	−1.11734	+	0.645097i	−0.176620	+	0.984279i	$0.556516\pi$
$192$		0			0
$193$	−7.66535	+	13.2768i	−0.551764	+	0.955683i	0.446383	+	0.894842i	$0.352712\pi$
$193$	−7.66535	+	13.2768i	−0.551764	+	0.955683i	−0.998147	+	0.0608416i	$0.980622\pi$
$194$	−3.38624	−	5.86514i	−0.243118	−	0.421093i
$195$		0			0
$196$	6.83868	+	1.49412i	0.488477	+	0.106723i
$197$		−	23.5506i		−	1.67791i	−0.544199	−	0.838956i	$-0.683166\pi$
$197$		−	23.5506i		−	1.67791i	0.544199	−	0.838956i	$-0.316834\pi$
$198$		0			0
$199$	−11.4609	−	6.61697i	−0.812443	−	0.469064i	0.0353603	−	0.999375i	$-0.488742\pi$
$199$	−11.4609	−	6.61697i	−0.812443	−	0.469064i	−0.847804	+	0.530310i	$0.822075\pi$
$200$	−2.09005	−	1.20669i	−0.147789	−	0.0853260i
$201$		0			0
$202$		−	12.7151i		−	0.894632i
$203$	6.51314	−	8.91141i	0.457133	−	0.625458i
$204$		0			0
$205$	5.85199	+	10.1360i	0.408721	+	0.707926i
$206$	−1.08597	+	1.88096i	−0.0756632	+	0.131052i
$207$		0			0
$208$	−0.167911	+	0.0969436i	−0.0116425	+	0.00672183i
$209$	0.310933			0.0215077
$210$		0			0
$211$	0.937344			0.0645294			0.0322647	−	0.999479i	$-0.489728\pi$
$211$	0.937344			0.0645294			0.0322647	+	0.999479i	$0.489728\pi$
$212$	−1.04499	+	0.603325i	−0.0717702	+	0.0414365i
$213$		0			0
$214$	−2.53865	+	4.39707i	−0.173539	+	0.300578i
$215$	5.58533	+	9.67408i	0.380916	+	0.659767i
$216$		0			0
$217$	−1.70545	−	3.85986i	−0.115773	−	0.262025i
$218$			1.62671i			0.110175i
$219$		0			0
$220$	2.35797	+	1.36138i	0.158975	+	0.0917840i
$221$	−1.03228	−	0.595985i	−0.0694384	−	0.0400903i
$222$		0			0
$223$		−	10.8750i		−	0.728242i	−0.931352	−	0.364121i	$-0.881369\pi$
$223$		−	10.8750i		−	0.728242i	0.931352	−	0.364121i	$-0.118631\pi$
$224$	−1.06928	−	2.42005i	−0.0714442	−	0.161696i
$225$		0			0
$226$	−4.54061	−	7.86457i	−0.302037	−	0.523143i
$227$	3.87060	−	6.70408i	0.256901	−	0.444965i	−0.708509	−	0.705701i	$-0.750632\pi$
$227$	3.87060	−	6.70408i	0.256901	−	0.444965i	0.965410	+	0.260736i	$0.0839653\pi$
$228$		0			0
$229$	4.44434	−	2.56594i	0.293691	−	0.169562i	−0.345914	−	0.938266i	$-0.612431\pi$
$229$	4.44434	−	2.56594i	0.293691	−	0.169562i	0.639605	+	0.768704i	$0.279098\pi$
$230$	−14.1730			−0.934537
$231$		0			0
$232$	−4.17192			−0.273900
$233$	−16.5376	+	9.54801i	−1.08342	+	0.625511i	−0.931816	−	0.362931i	$-0.881776\pi$
$233$	−16.5376	+	9.54801i	−1.08342	+	0.625511i	−0.151600	+	0.988442i	$0.548443\pi$
$234$		0			0
$235$	−9.89815	+	17.1441i	−0.645684	+	1.11836i
$236$	−5.43057	−	9.40603i	−0.353500	−	0.612280i
$237$		0			0
$238$	9.59778	−	13.1319i	0.622132	−	0.851214i
$239$			12.4259i			0.803762i	0.915692	+	0.401881i	$0.131643\pi$
$239$			12.4259i			0.803762i	−0.915692	+	0.401881i	$0.868357\pi$
$240$		0			0
$241$	−19.5847	−	11.3072i	−1.26156	−	0.728363i	−0.288185	−	0.957575i	$-0.593052\pi$
$241$	−19.5847	−	11.3072i	−1.26156	−	0.728363i	−0.973377	+	0.229212i	$0.926385\pi$
$242$	−0.866025	−	0.500000i	−0.0556702	−	0.0321412i
$243$		0			0
$244$			9.47569i			0.606619i
$245$	−12.8331	+	14.0914i	−0.819878	+	0.900265i
$246$		0			0
$247$	−0.0301429	−	0.0522091i	−0.00191795	−	0.00332198i
$248$	−0.797476	+	1.38127i	−0.0506398	+	0.0877107i
$249$		0			0
$250$	−6.09917	+	3.52136i	−0.385745	+	0.222710i
$251$	−6.22476			−0.392903			−0.196452	−	0.980514i	$-0.562942\pi$
$251$	−6.22476			−0.392903			−0.196452	+	0.980514i	$0.562942\pi$
$252$		0			0
$253$	5.20538			0.327259
$254$	−2.60344	+	1.50310i	−0.163354	+	0.0943126i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.6647	−	21.9359i	−0.790003	−	1.36832i	−0.925964	−	0.377611i	$-0.876746\pi$
$257$	−12.6647	−	21.9359i	−0.790003	−	1.36832i	0.135962	−	0.990714i	$-0.456588\pi$
$258$		0			0
$259$	1.25536	−	11.6272i	0.0780040	−	0.722482i
$260$		−	0.527907i		−	0.0327394i
$261$		0			0
$262$	−5.37666	−	3.10422i	−0.332171	−	0.191779i
$263$	−20.6740	−	11.9361i	−1.27481	−	0.736014i	−0.298924	−	0.954277i	$-0.596628\pi$
$263$	−20.6740	−	11.9361i	−1.27481	−	0.736014i	−0.975890	+	0.218263i	$0.929961\pi$
$264$		0			0
$265$		−	3.28541i		−	0.201821i
$266$	0.752472	−	0.332474i	0.0461370	−	0.0203853i
$267$		0			0
$268$	−2.69458	−	4.66714i	−0.164597	−	0.285091i
$269$	−1.06611	+	1.84656i	−0.0650019	+	0.112587i	−0.896695	−	0.442649i	$-0.854039\pi$
$269$	−1.06611	+	1.84656i	−0.0650019	+	0.112587i	0.831693	+	0.555236i	$0.187372\pi$
$270$		0			0
$271$	−23.5382	+	13.5898i	−1.42984	+	0.825520i	−0.997108	−	0.0760010i	$-0.975785\pi$
$271$	−23.5382	+	13.5898i	−1.42984	+	0.825520i	−0.432735	+	0.901521i	$0.642451\pi$
$272$	−6.14775			−0.372762
$273$		0			0
$274$	−9.49469			−0.573595
$275$	−2.09005	+	1.20669i	−0.126035	+	0.0727663i
$276$		0			0
$277$	5.00742	−	8.67311i	0.300867	−	0.521117i	−0.675466	−	0.737391i	$-0.736057\pi$
$277$	5.00742	−	8.67311i	0.300867	−	0.521117i	0.976333	+	0.216275i	$0.0693907\pi$
$278$	6.60098	+	11.4332i	0.395901	+	0.685720i
$279$		0			0
$280$	7.16211	+	0.773269i	0.428018	+	0.0462117i
$281$		−	28.1787i		−	1.68100i	−0.541813	−	0.840499i	$-0.682262\pi$
$281$		−	28.1787i		−	1.68100i	0.541813	−	0.840499i	$-0.317738\pi$
$282$		0			0
$283$	23.7390	+	13.7057i	1.41114	+	0.814721i	0.995496	−	0.0948077i	$-0.0302236\pi$
$283$	23.7390	+	13.7057i	1.41114	+	0.814721i	0.415642	+	0.909528i	$0.363557\pi$
$284$	8.34383	+	4.81731i	0.495115	+	0.285855i
$285$		0			0
$286$			0.193887i			0.0114648i
$287$	−9.18198	−	6.71089i	−0.541995	−	0.396131i
$288$		0			0
$289$	−10.3974	−	18.0089i	−0.611613	−	1.05934i
$290$	5.67955	−	9.83727i	0.333515	−	0.577664i
$291$		0			0
$292$	−2.50213	+	1.44461i	−0.146426	+	0.0845393i
$293$	6.42673			0.375454			0.187727	−	0.982221i	$-0.439888\pi$
$293$	6.42673			0.375454			0.187727	+	0.982221i	$0.439888\pi$
$294$		0			0
$295$	29.5722			1.72176
$296$	−3.82803	+	2.21011i	−0.222499	+	0.128460i
$297$		0			0
$298$	−6.87830	+	11.9136i	−0.398449	+	0.690134i
$299$	−0.504628	−	0.874041i	−0.0291834	−	0.0505471i
$300$		0			0
$301$	−8.76358	−	6.40509i	−0.505124	−	0.369183i
$302$			20.8365i			1.19900i
$303$		0			0
$304$	−0.269276	−	0.155466i	−0.0154440	−	0.00891660i
$305$	−22.3434	−	12.9000i	−1.27938	−	0.738651i
$306$		0			0
$307$		−	21.7703i		−	1.24250i	−0.783614	−	0.621248i	$-0.786626\pi$
$307$		−	21.7703i		−	1.24250i	0.783614	−	0.621248i	$-0.213374\pi$
$308$	−2.63046	−	0.284003i	−0.149885	−	0.0161826i
$309$		0			0
$310$	−2.17133	−	3.76085i	−0.123323	−	0.213602i
$311$	6.47129	−	11.2086i	0.366953	−	0.635582i	−0.622134	−	0.782910i	$-0.713734\pi$
$311$	6.47129	−	11.2086i	0.366953	−	0.635582i	0.989088	+	0.147329i	$0.0470676\pi$
$312$		0			0
$313$	−1.55581	+	0.898250i	−0.0879398	+	0.0507721i	−0.543325	−	0.839522i	$-0.682835\pi$
$313$	−1.55581	+	0.898250i	−0.0879398	+	0.0507721i	0.455385	+	0.890294i	$0.349502\pi$
$314$	−15.6308			−0.882098
$315$		0			0
$316$	−15.2069			−0.855455
$317$	−25.0485	+	14.4617i	−1.40686	+	0.812252i	−0.995084	−	0.0990327i	$-0.968425\pi$
$317$	−25.0485	+	14.4617i	−1.40686	+	0.812252i	−0.411777	+	0.911285i	$0.635092\pi$
$318$		0			0
$319$	−2.08596	+	3.61299i	−0.116791	+	0.202288i
$320$	−1.36138	−	2.35797i	−0.0761033	−	0.131815i
$321$		0			0
$322$	12.5973	−	5.56600i	0.702019	−	0.310181i
$323$		−	1.91154i		−	0.106361i
$324$		0			0
$325$	0.405234	+	0.233962i	0.0224784	+	0.0129779i
$326$	4.39752	+	2.53891i	0.243556	+	0.140617i
$327$		0			0
$328$			4.29859i			0.237350i
$329$	2.06490	−	19.1253i	0.113841	−	1.05441i
$330$		0			0
$331$	−17.8278	−	30.8786i	−0.979904	−	1.69724i	−0.662700	−	0.748885i	$-0.730589\pi$
$331$	−17.8278	−	30.8786i	−0.979904	−	1.69724i	−0.317204	−	0.948357i	$-0.602744\pi$
$332$	5.04416	−	8.73673i	0.276834	−	0.479491i
$333$		0			0
$334$	−2.71688	+	1.56859i	−0.148661	+	0.0858294i
$335$	14.6733			0.801690
$336$		0			0
$337$	18.6472			1.01578			0.507890	−	0.861422i	$-0.330426\pi$
$337$	18.6472			1.01578			0.507890	+	0.861422i	$0.330426\pi$
$338$	−11.2258	+	6.48120i	−0.610602	+	0.352531i
$339$		0			0
$340$	8.36940	−	14.4962i	0.453895	−	0.786169i
$341$	0.797476	+	1.38127i	0.0431857	+	0.0747999i
$342$		0			0
$343$	5.87243	−	17.5646i	0.317081	−	0.948398i
$344$			4.10271i			0.221203i
$345$		0			0
$346$	−14.9202	−	8.61420i	−0.802116	−	0.463102i
$347$	26.9301	+	15.5481i	1.44569	+	0.834667i	0.998220	−	0.0596342i	$-0.0189934\pi$
$347$	26.9301	+	15.5481i	1.44569	+	0.834667i	0.447465	+	0.894301i	$0.352327\pi$
$348$		0			0
$349$		−	13.5679i		−	0.726272i	−0.931736	−	0.363136i	$-0.881706\pi$
$349$		−	13.5679i		−	0.726272i	0.931736	−	0.363136i	$-0.118294\pi$
$350$	−3.76774	+	5.15511i	−0.201394	+	0.275552i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	0.975985	−	1.69046i	0.0519465	−	0.0899739i	−0.838883	−	0.544312i	$-0.816791\pi$
$353$	0.975985	−	1.69046i	0.0519465	−	0.0899739i	0.890829	+	0.454338i	$0.150124\pi$
$354$		0			0
$355$	−22.7182	+	13.1163i	−1.20576	+	0.696144i
$356$	11.3591			0.602031
$357$		0			0
$358$	11.6278			0.614548
$359$	−1.05983	+	0.611893i	−0.0559357	+	0.0322945i	−0.527707	−	0.849426i	$-0.676948\pi$
$359$	−1.05983	+	0.611893i	−0.0559357	+	0.0322945i	0.471771	+	0.881721i	$0.343615\pi$
$360$		0			0
$361$	−9.45166	+	16.3708i	−0.497456	+	0.861619i
$362$	−5.19698	−	9.00143i	−0.273147	−	0.473105i
$363$		0			0
$364$	0.207319	+	0.469217i	0.0108665	+	0.0245936i
$365$		−	7.86662i		−	0.411758i
$366$		0			0
$367$	20.6347	+	11.9134i	1.07712	+	0.621877i	0.930119	−	0.367259i	$-0.119704\pi$
$367$	20.6347	+	11.9134i	1.07712	+	0.621877i	0.147004	+	0.989136i	$0.453037\pi$
$368$	−4.50799	−	2.60269i	−0.234995	−	0.135675i
$369$		0			0
$370$		−	12.0352i		−	0.625679i
$371$	1.29024	+	2.92015i	0.0669862	+	0.151607i
$372$		0			0
$373$	−10.5452	−	18.2648i	−0.546008	−	0.945714i	−0.998543	−	0.0539668i	$-0.982813\pi$
$373$	−10.5452	−	18.2648i	−0.546008	−	0.945714i	0.452535	−	0.891747i	$-0.350520\pi$
$374$	−3.07388	+	5.32411i	−0.158946	+	0.275303i
$375$		0			0
$376$	−6.29661	+	3.63535i	−0.324723	+	0.187479i
$377$	0.808881			0.0416595
$378$		0			0
$379$	−29.6286			−1.52192			−0.760961	−	0.648798i	$-0.775272\pi$
$379$	−29.6286			−1.52192			−0.760961	+	0.648798i	$0.775272\pi$
$380$	0.733171	−	0.423296i	0.0376109	−	0.0217146i
$381$		0			0
$382$	8.91542	−	15.4420i	0.456152	−	0.790079i
$383$	2.05855	+	3.56551i	0.105187	+	0.182189i	0.913815	−	0.406132i	$-0.133123\pi$
$383$	2.05855	+	3.56551i	0.105187	+	0.182189i	−0.808628	+	0.588321i	$0.799789\pi$
$384$		0			0
$385$	4.25072	−	5.81593i	0.216637	−	0.296407i
$386$		−	15.3307i		−	0.780312i
$387$		0			0
$388$	5.86514	+	3.38624i	0.297758	+	0.171910i
$389$	−29.0363	−	16.7641i	−1.47220	−	0.849975i	−0.472689	−	0.881229i	$-0.656717\pi$
$389$	−29.0363	−	16.7641i	−1.47220	−	0.849975i	−0.999511	+	0.0312539i	$0.990050\pi$
$390$		0			0
$391$		−	32.0014i		−	1.61838i
$392$	−6.66953	+	2.12540i	−0.336862	+	0.107349i
$393$		0			0
$394$	11.7753	+	20.3954i	0.593232	+	1.02751i
$395$	20.7023	−	35.8575i	1.04165	−	1.80418i
$396$		0			0
$397$	1.46549	−	0.846104i	0.0735511	−	0.0424647i	−0.462773	−	0.886477i	$-0.653146\pi$
$397$	1.46549	−	0.846104i	0.0735511	−	0.0424647i	0.536325	+	0.844012i	$0.319812\pi$
$398$	13.2339			0.663357
$399$		0			0
$400$	2.41339			0.120669
$401$	−32.1813	+	18.5799i	−1.60706	+	0.927835i	−0.617033	+	0.786937i	$0.711665\pi$
$401$	−32.1813	+	18.5799i	−1.60706	+	0.927835i	−0.990024	+	0.140897i	$0.955001\pi$
$402$		0			0
$403$	0.154620	−	0.267810i	0.00770219	−	0.0133406i
$404$	6.35755	+	11.0116i	0.316300	+	0.547848i
$405$		0			0
$406$	−1.18484	+	10.9741i	−0.0588024	+	0.544634i
$407$			4.42022i			0.219102i
$408$		0			0
$409$	−2.23682	−	1.29143i	−0.110604	−	0.0638570i	0.443678	−	0.896186i	$-0.353673\pi$
$409$	−2.23682	−	1.29143i	−0.110604	−	0.0638570i	−0.554281	+	0.832329i	$0.687007\pi$
$410$	−10.1360	−	5.85199i	−0.500579	−	0.289009i
$411$		0			0
$412$		−	2.17194i		−	0.107004i
$413$	−26.2845	+	11.6136i	−1.29338	+	0.571468i
$414$		0			0
$415$	13.7340	+	23.7880i	0.674175	+	1.16771i
$416$	0.0969436	−	0.167911i	0.00475305	−	0.00823252i
$417$		0			0
$418$	−0.269276	+	0.155466i	−0.0131707	+	0.00760410i
$419$	22.0871			1.07903			0.539513	−	0.841978i	$-0.318609\pi$
$419$	22.0871			1.07903			0.539513	+	0.841978i	$0.318609\pi$
$420$		0			0
$421$	−3.60120			−0.175512			−0.0877559	−	0.996142i	$-0.527970\pi$
$421$	−3.60120			−0.175512			−0.0877559	+	0.996142i	$0.527970\pi$
$422$	−0.811764	+	0.468672i	−0.0395161	+	0.0228146i
$423$		0			0
$424$	0.603325	−	1.04499i	0.0293000	−	0.0507492i
$425$	7.41845	+	12.8491i	0.359847	+	0.623274i
$426$		0			0
$427$	24.9255	+	2.69112i	1.20623	+	0.130232i
$428$		−	5.07730i		−	0.245421i
$429$		0			0
$430$	−9.67408	−	5.58533i	−0.466526	−	0.269349i
$431$	−2.29763	−	1.32654i	−0.110673	−	0.0638970i	0.443642	−	0.896204i	$-0.353686\pi$
$431$	−2.29763	−	1.32654i	−0.110673	−	0.0638970i	−0.554315	+	0.832307i	$0.687020\pi$
$432$		0			0
$433$		−	21.3112i		−	1.02415i	−0.858940	−	0.512076i	$-0.828877\pi$
$433$		−	21.3112i		−	1.02415i	0.858940	−	0.512076i	$-0.171123\pi$
$434$	3.40689	+	2.49002i	0.163536	+	0.119525i
$435$		0			0
$436$	−0.813357	−	1.40878i	−0.0389527	−	0.0674681i
$437$	0.809261	−	1.40168i	0.0387122	−	0.0670515i
$438$		0			0
$439$	11.1839	−	6.45704i	0.533780	−	0.308178i	−0.208775	−	0.977964i	$-0.566948\pi$
$439$	11.1839	−	6.45704i	0.533780	−	0.308178i	0.742554	+	0.669786i	$0.233614\pi$
$440$	−2.72275			−0.129802
$441$		0			0
$442$	1.19197			0.0566962
$443$	20.9687	−	12.1063i	0.996251	−	0.575186i	0.0891141	−	0.996021i	$-0.471596\pi$
$443$	20.9687	−	12.1063i	0.996251	−	0.575186i	0.907137	+	0.420836i	$0.138263\pi$
$444$		0			0
$445$	−15.4640	+	26.7845i	−0.733064	+	1.26970i
$446$	5.43749	+	9.41801i	0.257473	+	0.445956i
$447$		0			0
$448$	2.13605	+	1.56119i	0.100919	+	0.0737591i
$449$		−	6.97436i		−	0.329140i	−0.986365	−	0.164570i	$-0.947376\pi$
$449$		−	6.97436i		−	0.329140i	0.986365	−	0.164570i	$-0.0526237\pi$
$450$		0			0
$451$	3.72268	+	2.14929i	0.175294	+	0.101206i
$452$	7.86457	+	4.54061i	0.369918	+	0.213572i
$453$		0			0
$454$			7.74120i			0.363312i
$455$	−1.38864	−	0.149927i	−0.0651004	−	0.00702868i
$456$		0			0
$457$	0.0495834	+	0.0858810i	0.00231941	+	0.00401734i	0.867183	−	0.497990i	$-0.165928\pi$
$457$	0.0495834	+	0.0858810i	0.00231941	+	0.00401734i	−0.864863	+	0.502007i	$0.832595\pi$
$458$	−2.56594	+	4.44434i	−0.119899	+	0.207671i
$459$		0			0
$460$	12.2741	−	7.08648i	0.572285	−	0.330409i
$461$	30.2189			1.40744			0.703718	−	0.710480i	$-0.251522\pi$
$461$	30.2189			1.40744			0.703718	+	0.710480i	$0.251522\pi$
$462$		0			0
$463$	−31.6191			−1.46946			−0.734731	−	0.678358i	$-0.762692\pi$
$463$	−31.6191			−1.46946			−0.734731	+	0.678358i	$0.762692\pi$
$464$	3.61299	−	2.08596i	0.167729	−	0.0968382i
$465$		0			0
$466$	9.54801	−	16.5376i	0.442303	−	0.766091i
$467$	12.6717	+	21.9481i	0.586378	+	1.01564i	0.994702	+	0.102800i	$0.0327801\pi$
$467$	12.6717	+	21.9481i	0.586378	+	1.01564i	−0.408324	+	0.912837i	$0.633887\pi$
$468$		0			0
$469$	−13.0420	+	5.76250i	−0.602224	+	0.266088i
$470$		−	19.7963i		−	0.913135i
$471$		0			0
$472$	9.40603	+	5.43057i	0.432948	+	0.249962i
$473$	3.55305	+	2.05135i	0.163369	+	0.0943214i
$474$		0			0
$475$			0.750400i			0.0344307i
$476$	−1.74598	+	16.1714i	−0.0800268	+	0.741217i
$477$		0			0
$478$	−6.21293	−	10.7611i	−0.284173	−	0.492202i
$479$	−16.3051	+	28.2413i	−0.745000	+	1.29038i	0.205194	+	0.978721i	$0.434217\pi$
$479$	−16.3051	+	28.2413i	−0.745000	+	1.29038i	−0.950195	+	0.311657i	$0.899116\pi$
$480$		0			0
$481$	0.742205	−	0.428512i	0.0338416	−	0.0195385i
$482$	22.6145			1.03006
$483$		0			0
$484$	1.00000			0.0454545
$485$	−15.9693	+	9.21990i	−0.725130	+	0.418654i
$486$		0			0
$487$	−2.05532	+	3.55991i	−0.0931353	+	0.161315i	−0.908829	−	0.417169i	$-0.863022\pi$
$487$	−2.05532	+	3.55991i	−0.0931353	+	0.161315i	0.815694	+	0.578484i	$0.196356\pi$
$488$	−4.73784	−	8.20619i	−0.214472	−	0.371477i
$489$		0			0
$490$	4.06811	−	18.6201i	0.183779	−	0.841168i
$491$			4.57385i			0.206415i	0.994660	+	0.103207i	$0.0329106\pi$
$491$			4.57385i			0.206415i	−0.994660	+	0.103207i	$0.967089\pi$
$492$		0			0
$493$	22.2117	+	12.8240i	1.00037	+	0.577562i
$494$	0.0522091	+	0.0301429i	0.00234900	+	0.00135619i
$495$		0			0
$496$		−	1.59495i		−	0.0716155i
$497$	15.0414	−	20.5800i	0.674701	−	0.923140i
$498$		0			0
$499$	−18.3034	−	31.7024i	−0.819372	−	1.41919i	−0.906145	−	0.422967i	$-0.860989\pi$
$499$	−18.3034	−	31.7024i	−0.819372	−	1.41919i	0.0867728	−	0.996228i	$-0.472345\pi$
$500$	3.52136	−	6.09917i	0.157480	−	0.272763i
$501$		0			0
$502$	5.39080	−	3.11238i	0.240603	−	0.138912i
$503$	−17.0391			−0.759738			−0.379869	−	0.925040i	$-0.624031\pi$
$503$	−17.0391			−0.759738			−0.379869	+	0.925040i	$0.624031\pi$
$504$		0			0
$505$	−34.6201			−1.54057
$506$	−4.50799	+	2.60269i	−0.200405	+	0.115704i
$507$		0			0
$508$	1.50310	−	2.60344i	0.0666891	−	0.115509i
$509$	5.96804	+	10.3370i	0.264529	+	0.458177i	0.967440	−	0.253100i	$-0.0814502\pi$
$509$	5.96804	+	10.3370i	0.264529	+	0.458177i	−0.702911	+	0.711278i	$0.748117\pi$
$510$		0			0
$511$	3.08938	+	6.99205i	0.136666	+	0.309310i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	21.9359	+	12.6647i	0.967552	+	0.558616i
$515$	5.12138	+	2.95683i	0.225675	+	0.130294i
$516$		0			0
$517$			7.27069i			0.319765i
$518$	4.72645	+	10.6972i	0.207668	+	0.470006i
$519$		0			0
$520$	0.263953	+	0.457181i	0.0115751	+	0.0200487i
$521$	21.4867	−	37.2161i	0.941350	−	1.63047i	0.178452	−	0.983949i	$-0.442891\pi$
$521$	21.4867	−	37.2161i	0.941350	−	1.63047i	0.762899	−	0.646518i	$-0.223775\pi$
$522$		0			0
$523$	−31.1432	+	17.9806i	−1.36180	+	0.786235i	−0.989863	−	0.142024i	$-0.954639\pi$
$523$	−31.1432	+	17.9806i	−1.36180	+	0.786235i	−0.371935	+	0.928259i	$0.621306\pi$
$524$	6.20844			0.271217
$525$		0			0
$526$	23.8723			1.04088
$527$	8.49170	−	4.90268i	0.369904	−	0.213564i
$528$		0			0
$529$	2.04798	−	3.54720i	0.0890425	−	0.154226i
$530$	1.64270	+	2.84525i	0.0713545	+	0.123590i
$531$		0			0
$532$	−0.485424	+	0.664167i	−0.0210458	+	0.0287953i
$533$		−	0.833440i		−	0.0361003i
$534$		0			0
$535$	11.9721	+	6.91212i	0.517601	+	0.298837i
$536$	4.66714	+	2.69458i	0.201590	+	0.116388i
$537$		0			0
$538$		−	2.13222i		−	0.0919266i
$539$	−1.49412	+	6.83868i	−0.0643562	+	0.294563i
$540$		0			0
$541$	−1.56847	−	2.71667i	−0.0674337	−	0.116799i	0.830337	−	0.557261i	$-0.188148\pi$
$541$	−1.56847	−	2.71667i	−0.0674337	−	0.116799i	−0.897771	+	0.440463i	$0.854814\pi$
$542$	13.5898	−	23.5382i	0.583731	−	1.01105i
$543$		0			0
$544$	5.32411	−	3.07388i	0.228269	−	0.131791i
$545$	4.42914			0.189723
$546$		0			0
$547$	1.97672			0.0845184			0.0422592	−	0.999107i	$-0.486544\pi$
$547$	1.97672			0.0845184			0.0422592	+	0.999107i	$0.486544\pi$
$548$	8.22265	−	4.74735i	0.351254	−	0.202797i
$549$		0			0
$550$	1.20669	−	2.09005i	0.0514535	−	0.0891202i
$551$	0.648592	+	1.12339i	0.0276310	+	0.0478582i
$552$		0			0
$553$	−4.31880	+	40.0012i	−0.183654	+	1.70102i
$554$			10.0148i			0.425490i
$555$		0			0
$556$	−11.4332	−	6.60098i	−0.484877	−	0.279944i
$557$	12.2471	+	7.07088i	0.518927	+	0.299603i	0.736496	−	0.676442i	$-0.236479\pi$
$557$	12.2471	+	7.07088i	0.518927	+	0.299603i	−0.217568	+	0.976045i	$0.569813\pi$
$558$		0			0
$559$		−	0.795462i		−	0.0336445i
$560$	−6.58920	+	2.91138i	−0.278445	+	0.123028i
$561$		0			0
$562$	14.0893	+	24.4034i	0.594323	+	1.02940i
$563$	3.39720	−	5.88412i	0.143175	−	0.247986i	−0.785516	−	0.618842i	$-0.787602\pi$
$563$	3.39720	−	5.88412i	0.143175	−	0.247986i	0.928691	+	0.370856i	$0.120936\pi$
$564$		0			0
$565$	−21.4133	+	12.3630i	−0.900864	+	0.520114i
$566$	−27.4114			−1.15219
$567$		0			0
$568$	−9.63462			−0.404260
$569$	−37.4383	+	21.6150i	−1.56949	+	0.906147i	−0.573265	+	0.819370i	$0.694324\pi$
$569$	−37.4383	+	21.6150i	−1.56949	+	0.906147i	−0.996228	+	0.0867776i	$0.972343\pi$
$570$		0			0
$571$	−23.3065	+	40.3680i	−0.975346	+	1.68935i	−0.296556	+	0.955015i	$0.595838\pi$
$571$	−23.3065	+	40.3680i	−0.975346	+	1.68935i	−0.678790	+	0.734333i	$0.737495\pi$
$572$	−0.0969436	−	0.167911i	−0.00405341	−	0.00702072i
$573$		0			0
$574$	11.3073	+	1.22081i	0.471957	+	0.0509556i
$575$			12.5626i			0.523896i
$576$		0			0
$577$	32.6159	+	18.8308i	1.35782	+	0.783936i	0.989329	−	0.145697i	$-0.0465423\pi$
$577$	32.6159	+	18.8308i	1.35782	+	0.783936i	0.368488	+	0.929633i	$0.379876\pi$
$578$	18.0089	+	10.3974i	0.749070	+	0.432476i
$579$		0			0
$580$			11.3591i			0.471661i
$581$	−21.5491	−	15.7497i	−0.894008	−	0.653409i
$582$		0			0
$583$	−0.603325	−	1.04499i	−0.0249872	−	0.0432790i
$584$	1.44461	−	2.50213i	0.0597783	−	0.103539i
$585$		0			0
$586$	−5.56571	+	3.21337i	−0.229918	+	0.132743i
$587$	−43.9834			−1.81539			−0.907694	−	0.419632i	$-0.862159\pi$
$587$	−43.9834			−1.81539			−0.907694	+	0.419632i	$0.862159\pi$
$588$		0			0
$589$	0.495923			0.0204341
$590$	−25.6103	+	14.7861i	−1.05436	+	0.608735i
$591$		0			0
$592$	2.21011	−	3.82803i	0.0908350	−	0.157331i
$593$	9.09719	+	15.7568i	0.373577	+	0.647054i	0.990113	−	0.140272i	$-0.0447978\pi$
$593$	9.09719	+	15.7568i	0.373577	+	0.647054i	−0.616536	+	0.787327i	$0.711465\pi$
$594$		0			0
$595$	−35.7549	−	26.1324i	−1.46581	−	1.07132i
$596$		−	13.7566i		−	0.563492i
$597$		0			0
$598$	0.874041	+	0.504628i	0.0357422	+	0.0206358i
$599$	28.8965	+	16.6834i	1.18068	+	0.681665i	0.956171	−	0.292807i	$-0.0945894\pi$
$599$	28.8965	+	16.6834i	1.18068	+	0.681665i	0.224507	+	0.974472i	$0.427923\pi$
$600$		0			0
$601$			45.3210i			1.84868i	0.381566	+	0.924341i	$0.375385\pi$
$601$			45.3210i			1.84868i	−0.381566	+	0.924341i	$0.624615\pi$
$602$	10.7920	+	1.16518i	0.439850	+	0.0474892i
$603$		0			0
$604$	−10.4182	−	18.0449i	−0.423912	−	0.734237i
$605$	−1.36138	+	2.35797i	−0.0553478	+	0.0958653i
$606$		0			0
$607$	−5.26548	+	3.04003i	−0.213719	+	0.123391i	−0.603039	−	0.797712i	$-0.706044\pi$
$607$	−5.26548	+	3.04003i	−0.213719	+	0.123391i	0.389319	+	0.921103i	$0.372710\pi$
$608$	0.310933			0.0126100
$609$		0			0
$610$	25.8000			1.04461
$611$	1.22083	−	0.704847i	0.0493895	−	0.0285151i
$612$		0			0
$613$	−11.8152	+	20.4645i	−0.477211	+	0.826554i	−0.999659	−	0.0261170i	$-0.991686\pi$
$613$	−11.8152	+	20.4645i	−0.477211	+	0.826554i	0.522447	+	0.852671i	$0.325019\pi$
$614$	10.8851	+	18.8536i	0.439288	+	0.760870i
$615$		0			0
$616$	2.42005	−	1.06928i	0.0975066	−	0.0430825i
$617$		−	22.4859i		−	0.905248i	−0.891702	−	0.452624i	$-0.850488\pi$
$617$		−	22.4859i		−	0.905248i	0.891702	−	0.452624i	$-0.149512\pi$
$618$		0			0
$619$	5.68075	+	3.27978i	0.228329	+	0.131826i	0.609801	−	0.792555i	$-0.291249\pi$
$619$	5.68075	+	3.27978i	0.228329	+	0.131826i	−0.381472	+	0.924380i	$0.624583\pi$
$620$	3.76085	+	2.17133i	0.151040	+	0.0872027i
$621$		0			0
$622$			12.9426i			0.518950i
$623$	3.22601	−	29.8797i	0.129248	−	1.19710i
$624$		0			0
$625$	15.6212	+	27.0568i	0.624850	+	1.08227i
$626$	0.898250	−	1.55581i	0.0359013	−	0.0621828i
$627$		0			0
$628$	13.5367	−	7.81541i	0.540172	−	0.311869i
$629$	27.1744			1.08352
$630$		0			0
$631$	−9.60407			−0.382332			−0.191166	−	0.981558i	$-0.561227\pi$
$631$	−9.60407			−0.382332			−0.191166	+	0.981558i	$0.561227\pi$
$632$	13.1696	−	7.60345i	0.523857	−	0.302449i
$633$		0			0
$634$	14.4617	−	25.0485i	0.574349	−	0.994801i
$635$	4.09256	+	7.08852i	0.162408	+	0.281299i
$636$		0			0
$637$	1.29314	−	0.412087i	0.0512359	−	0.0163275i
$638$		−	4.17192i		−	0.165168i
$639$		0			0
$640$	2.35797	+	1.36138i	0.0932071	+	0.0538131i
$641$	−25.3563	−	14.6395i	−1.00151	−	0.578224i	−0.0928182	−	0.995683i	$-0.529588\pi$
$641$	−25.3563	−	14.6395i	−1.00151	−	0.578224i	−0.908696	+	0.417459i	$0.862921\pi$
$642$		0			0
$643$		−	16.6438i		−	0.656368i	−0.944614	−	0.328184i	$-0.893563\pi$
$643$		−	16.6438i		−	0.656368i	0.944614	−	0.328184i	$-0.106437\pi$
$644$	−8.12656	+	11.1189i	−0.320231	+	0.438147i
$645$		0			0
$646$	0.955768	+	1.65544i	0.0376042	+	0.0651324i
$647$	−20.7616	+	35.9602i	−0.816223	+	1.41374i	0.0922233	+	0.995738i	$0.470603\pi$
$647$	−20.7616	+	35.9602i	−0.816223	+	1.41374i	−0.908446	+	0.418001i	$0.862731\pi$
$648$		0			0
$649$	9.40603	−	5.43057i	0.369219	−	0.213169i
$650$	−0.467924			−0.0183535
$651$		0			0
$652$	−5.07782			−0.198863
$653$	−30.7284	+	17.7410i	−1.20249	+	0.694260i	−0.961109	−	0.276169i	$-0.910935\pi$
$653$	−30.7284	+	17.7410i	−1.20249	+	0.694260i	−0.241385	+	0.970429i	$0.577602\pi$
$654$		0			0
$655$	−8.45202	+	14.6393i	−0.330248	+	0.572006i
$656$	−2.14929	−	3.72268i	−0.0839158	−	0.145346i
$657$		0			0
$658$	7.77440	+	17.5954i	0.303078	+	0.685942i
$659$		−	1.37768i		−	0.0536668i	−0.999640	−	0.0268334i	$-0.991458\pi$
$659$		−	1.37768i		−	0.0536668i	0.999640	−	0.0268334i	$-0.00854237\pi$
$660$		0			0
$661$	20.1453	+	11.6309i	0.783561	+	0.452389i	0.837691	−	0.546145i	$-0.183905\pi$
$661$	20.1453	+	11.6309i	0.783561	+	0.452389i	−0.0541298	+	0.998534i	$0.517238\pi$
$662$	30.8786	+	17.8278i	1.20013	+	0.692896i
$663$		0			0
$664$			10.0883i			0.391502i
$665$	−0.905243	−	2.04880i	−0.0351038	−	0.0794489i
$666$		0			0
$667$	10.8582	+	18.8070i	0.420431	+	0.728208i
$668$	1.56859	−	2.71688i	0.0606905	−	0.105119i
$669$		0			0
$670$	−12.7075	+	7.33666i	−0.490933	+	0.283440i
$671$	−9.47569			−0.365805
$672$		0			0
$673$	−44.3559			−1.70979			−0.854896	−	0.518799i	$-0.826379\pi$
$673$	−44.3559			−1.70979			−0.854896	+	0.518799i	$0.826379\pi$
$674$	−16.1490	+	9.32362i	−0.622036	+	0.359133i
$675$		0			0
$676$	6.48120	−	11.2258i	0.249277	−	0.431761i
$677$	−16.3344	−	28.2920i	−0.627781	−	1.08735i	−0.987996	−	0.154480i	$-0.950630\pi$
$677$	−16.3344	−	28.2920i	−0.627781	−	1.08735i	0.360214	−	0.932870i	$-0.382704\pi$
$678$		0			0
$679$	10.5731	−	14.4664i	0.405759	−	0.555168i
$680$			16.7388i			0.641904i
$681$		0			0
$682$	−1.38127	−	0.797476i	−0.0528915	−	0.0305369i
$683$	13.7043	+	7.91217i	0.524380	+	0.302751i	0.738725	−	0.674007i	$-0.235428\pi$
$683$	13.7043	+	7.91217i	0.524380	+	0.302751i	−0.214345	+	0.976758i	$0.568762\pi$
$684$		0			0
$685$			25.8517i			0.987743i
$686$	3.69662	+	18.1476i	0.141138	+	0.692878i
$687$		0			0
$688$	−2.05135	−	3.55305i	−0.0782072	−	0.135459i
$689$	−0.116977	+	0.202610i	−0.00445647	+	0.00771882i
$690$		0			0
$691$	26.4940	−	15.2963i	1.00788	−	0.581899i	0.0973085	−	0.995254i	$-0.468977\pi$
$691$	26.4940	−	15.2963i	1.00788	−	0.581899i	0.910570	+	0.413355i	$0.135643\pi$
$692$	17.2284			0.654925
$693$		0			0
$694$	−31.0962			−1.18040
$695$	31.1299	−	17.9729i	1.18082	−	0.681749i
$696$		0			0
$697$	13.2133	−	22.8861i	0.500490	−	0.866874i
$698$	6.78394	+	11.7501i	0.256776	+	0.444749i
$699$		0			0
$700$	0.685408	−	6.34832i	0.0259060	−	0.239944i
$701$		−	6.04929i		−	0.228479i	−0.993453	−	0.114239i	$-0.963557\pi$
$701$		−	6.04929i		−	0.228479i	0.993453	−	0.114239i	$-0.0364431\pi$
$702$		0			0
$703$	1.19026	+	0.687196i	0.0448914	+	0.0259181i
$704$	−0.866025	−	0.500000i	−0.0326396	−	0.0188445i
$705$		0			0
$706$			1.95197i			0.0734634i
$707$	30.7712	−	13.5960i	1.15727	−	0.511330i
$708$		0			0
$709$	6.64611	+	11.5114i	0.249600	+	0.432320i	0.963415	−	0.268015i	$-0.0863675\pi$
$709$	6.64611	+	11.5114i	0.249600	+	0.432320i	−0.713815	+	0.700334i	$0.753034\pi$
$710$	13.1163	−	22.7182i	0.492248	−	0.852598i
$711$		0			0
$712$	−9.83727	+	5.67955i	−0.368667	+	0.212850i
$713$	8.30233			0.310925
$714$		0			0
$715$	0.527907			0.0197426
$716$	−10.0700	+	5.81389i	−0.376332	+	0.217275i
$717$		0			0
$718$	0.611893	−	1.05983i	0.0228356	−	0.0395525i
$719$	5.80479	+	10.0542i	0.216482	+	0.374958i	0.953730	−	0.300664i	$-0.0972084\pi$
$719$	5.80479	+	10.0542i	0.216482	+	0.374958i	−0.737248	+	0.675622i	$0.763875\pi$
$720$		0			0
$721$	−5.71321	−	0.616837i	−0.212771	−	0.0229722i
$722$		−	18.9033i		−	0.703509i
$723$		0			0
$724$	9.00143	+	5.19698i	0.334536	+	0.193144i
$725$	−8.71952	−	5.03422i	−0.323835	−	0.186966i
$726$		0			0
$727$			16.0147i			0.593953i	0.954885	+	0.296977i	$0.0959783\pi$
$727$			16.0147i			0.593953i	−0.954885	+	0.296977i	$0.904022\pi$
$728$	−0.414152	−	0.302694i	−0.0153495	−	0.0112186i
$729$		0			0
$730$	3.93331	+	6.81269i	0.145578	+	0.252149i
$731$	12.6112	−	21.8433i	0.466443	−	0.807902i
$732$		0			0
$733$	17.5271	−	10.1193i	0.647377	−	0.373763i	−0.140074	−	0.990141i	$-0.544734\pi$
$733$	17.5271	−	10.1193i	0.647377	−	0.373763i	0.787450	+	0.616378i	$0.211401\pi$
$734$	−23.8269			−0.879467
$735$		0			0
$736$	5.20538			0.191873
$737$	4.66714	−	2.69458i	0.171916	−	0.0992560i
$738$		0			0
$739$	−5.78566	+	10.0211i	−0.212829	+	0.368630i	−0.952599	−	0.304229i	$-0.901601\pi$
$739$	−5.78566	+	10.0211i	−0.212829	+	0.368630i	0.739770	+	0.672860i	$0.234934\pi$
$740$	6.01759	+	10.4228i	0.221211	+	0.383149i
$741$		0			0
$742$	−2.57746	−	1.88380i	−0.0946216	−	0.0691566i
$743$		−	9.50531i		−	0.348716i	−0.984682	−	0.174358i	$-0.944215\pi$
$743$		−	9.50531i		−	0.348716i	0.984682	−	0.174358i	$-0.0557850\pi$
$744$		0			0
$745$	32.4377	+	18.7279i	1.18842	+	0.686137i
$746$	18.2648	+	10.5452i	0.668720	+	0.386086i
$747$		0			0
$748$		−	6.14775i		−	0.224784i
$749$	−13.3557	−	1.44197i	−0.488005	−	0.0526884i
$750$		0			0
$751$	−13.5445	−	23.4597i	−0.494245	−	0.856057i	0.505733	−	0.862690i	$-0.331222\pi$
$751$	−13.5445	−	23.4597i	−0.494245	−	0.856057i	−0.999978	+	0.00663281i	$0.997889\pi$
$752$	3.63535	−	6.29661i	0.132567	−	0.229614i
$753$		0			0
$754$	−0.700511	+	0.404440i	−0.0255111	+	0.0147289i
$755$	56.7325			2.06471
$756$		0			0
$757$	47.9214			1.74173			0.870867	−	0.491518i	$-0.163558\pi$
$757$	47.9214			1.74173			0.870867	+	0.491518i	$0.163558\pi$
$758$	25.6592	−	14.8143i	0.931983	−	0.538081i
$759$		0			0
$760$	−0.423296	+	0.733171i	−0.0153546	+	0.0265949i
$761$	−8.27095	−	14.3257i	−0.299822	−	0.519306i	0.676273	−	0.736651i	$-0.263594\pi$
$761$	−8.27095	−	14.3257i	−0.299822	−	0.519306i	−0.976095	+	0.217345i	$0.930260\pi$
$762$		0			0
$763$	−3.93673	+	1.73941i	−0.142519	+	0.0629709i
$764$			17.8308i			0.645097i
$765$		0			0
$766$	−3.56551	−	2.05855i	−0.128827	−	0.0743783i
$767$	−1.82371	−	1.05292i	−0.0658503	−	0.0380187i
$768$		0			0
$769$			5.14692i			0.185603i	0.995685	+	0.0928013i	$0.0295821\pi$
$769$			5.14692i			0.185603i	−0.995685	+	0.0928013i	$0.970418\pi$
$770$	−0.773269	+	7.16211i	−0.0278667	+	0.258104i
$771$		0			0
$772$	7.66535	+	13.2768i	0.275882	+	0.477842i
$773$	2.10953	−	3.65382i	0.0758746	−	0.131419i	−0.825592	−	0.564268i	$-0.809158\pi$
$773$	2.10953	−	3.65382i	0.0758746	−	0.131419i	0.901466	+	0.432849i	$0.142492\pi$
$774$		0			0
$775$	−3.33353	+	1.92462i	−0.119744	+	0.0691343i
$776$	−6.77249			−0.243118
$777$		0			0
$778$	33.5283			1.20205
$779$	1.15750	−	0.668285i	0.0414719	−	0.0239438i
$780$		0			0
$781$	−4.81731	+	8.34383i	−0.172377	+	0.298566i
$782$	16.0007	+	27.7140i	0.572183	+	0.991050i
$783$		0			0
$784$	4.71329	−	5.17542i	0.168332	−	0.184836i
$785$			42.5588i			1.51899i
$786$		0			0
$787$	−30.2097	−	17.4416i	−1.07686	−	0.621724i	−0.146811	−	0.989165i	$-0.546901\pi$
$787$	−30.2097	−	17.4416i	−1.07686	−	0.621724i	−0.930047	+	0.367440i	$0.880234\pi$
$788$	−20.3954	−	11.7753i	−0.726557	−	0.419478i
$789$		0			0
$790$			41.4046i			1.47311i
$791$	14.1775	−	19.3979i	0.504093	−	0.689711i
$792$		0			0
$793$	0.918607	+	1.59107i	0.0326207	+	0.0565007i
$794$	−0.846104	+	1.46549i	−0.0300271	+	0.0520085i
$795$		0			0
$796$	−11.4609	+	6.61697i	−0.406222	+	0.234532i
$797$	17.4825			0.619262			0.309631	−	0.950857i	$-0.399795\pi$
$797$	17.4825			0.619262			0.309631	+	0.950857i	$0.399795\pi$
$798$		0			0
$799$	44.6984			1.58132
$800$	−2.09005	+	1.20669i	−0.0738945	+	0.0426630i
$801$		0			0
$802$	18.5799	−	32.1813i	0.656078	−	1.13636i
$803$	−1.44461	−	2.50213i	−0.0509791	−	0.0882984i
$804$		0			0
$805$	−15.1548	−	34.2993i	−0.534138	−	1.20889i
$806$			0.309241i			0.0108925i
$807$		0			0
$808$	−11.0116	−	6.35755i	−0.387387	−	0.223658i
$809$	22.8674	+	13.2025i	0.803975	+	0.464175i	0.844859	−	0.534989i	$-0.179684\pi$
$809$	22.8674	+	13.2025i	0.803975	+	0.464175i	−0.0408842	+	0.999164i	$0.513017\pi$
$810$		0			0
$811$			31.4016i			1.10266i	0.834287	+	0.551330i	$0.185879\pi$
$811$			31.4016i			1.10266i	−0.834287	+	0.551330i	$0.814121\pi$
$812$	−4.46094	−	10.0962i	−0.156548	−	0.354309i
$813$		0			0
$814$	−2.21011	−	3.82803i	−0.0774644	−	0.134172i
$815$	6.91283	−	11.9734i	0.242146	−	0.419409i
$816$		0			0
$817$	1.10476	−	0.637833i	0.0386506	−	0.0223149i
$818$	2.58286			0.0903075
$819$		0			0
$820$	11.7040			0.408721
$821$	46.8857	−	27.0695i	1.63632	−	0.944731i	0.654239	−	0.756288i	$-0.272989\pi$
$821$	46.8857	−	27.0695i	1.63632	−	0.944731i	0.982084	−	0.188444i	$-0.0603443\pi$
$822$		0			0
$823$	−13.6961	+	23.7223i	−0.477416	+	0.826909i	−0.999665	−	0.0258842i	$-0.991760\pi$
$823$	−13.6961	+	23.7223i	−0.477416	+	0.826909i	0.522249	+	0.852793i	$0.325093\pi$
$824$	1.08597	+	1.88096i	0.0378316	+	0.0655262i
$825$		0			0
$826$	16.9563	−	23.1999i	0.589984	−	0.807229i
$827$		−	25.1390i		−	0.874168i	−0.899421	−	0.437084i	$-0.856011\pi$
$827$		−	25.1390i		−	0.874168i	0.899421	−	0.437084i	$-0.143989\pi$
$828$		0			0
$829$	−20.4945	−	11.8325i	−0.711804	−	0.410960i	0.0999244	−	0.994995i	$-0.468140\pi$
$829$	−20.4945	−	11.8325i	−0.711804	−	0.410960i	−0.811729	+	0.584035i	$0.801473\pi$
$830$	−23.7880	−	13.7340i	−0.825693	−	0.476714i
$831$		0			0
$832$			0.193887i			0.00672183i
$833$	42.0425	+	9.18547i	1.45669	+	0.318258i
$834$		0			0
$835$	4.27088	+	7.39738i	0.147800	+	0.255997i
$836$	0.155466	−	0.269276i	0.00537691	−	0.00931309i
$837$		0			0
$838$	−19.1280	+	11.0435i	−0.660765	+	0.381493i
$839$	5.46018			0.188506			0.0942532	−	0.995548i	$-0.469954\pi$
$839$	5.46018			0.188506			0.0942532	+	0.995548i	$0.469954\pi$
$840$		0			0
$841$	11.5951			0.399832
$842$	3.11873	−	1.80060i	0.107479	−	0.0620528i
$843$		0			0
$844$	0.468672	−	0.811764i	0.0161324	−	0.0279421i
$845$	17.6467	+	30.5650i	0.607066	+	1.05147i
$846$		0			0
$847$	0.284003	−	2.63046i	0.00975845	−	0.0903838i
$848$			1.20665i			0.0414365i
$849$		0			0
$850$	−12.8491	−	7.41845i	−0.440721	−	0.254451i
$851$	19.9263	+	11.5045i	0.683065	+	0.394368i
$852$		0			0
$853$			9.29168i			0.318141i	0.987267	+	0.159071i	$0.0508497\pi$
$853$			9.29168i			0.318141i	−0.987267	+	0.159071i	$0.949150\pi$
$854$	−22.9316	+	10.1322i	−0.784705	+	0.346715i
$855$		0			0
$856$	2.53865	+	4.39707i	0.0867693	+	0.150289i
$857$	7.51046	−	13.0085i	0.256552	−	0.444362i	−0.708764	−	0.705446i	$-0.750747\pi$
$857$	7.51046	−	13.0085i	0.256552	−	0.444362i	0.965316	+	0.261084i	$0.0840801\pi$
$858$		0			0
$859$	28.6855	−	16.5616i	0.978737	−	0.565074i	0.0768486	−	0.997043i	$-0.475514\pi$
$859$	28.6855	−	16.5616i	0.978737	−	0.565074i	0.901889	+	0.431969i	$0.142181\pi$
$860$	11.1707			0.380916
$861$		0			0
$862$	2.65307			0.0903640
$863$	−8.04372	+	4.64405i	−0.273812	+	0.158085i	−0.630619	−	0.776093i	$-0.717199\pi$
$863$	−8.04372	+	4.64405i	−0.273812	+	0.158085i	0.356807	+	0.934178i	$0.383865\pi$
$864$		0			0
$865$	−23.4543	+	40.6241i	−0.797471	+	1.38126i
$866$	10.6556	+	18.4561i	0.362092	+	0.627162i
$867$		0			0
$868$	−4.19546	−	0.452971i	−0.142403	−	0.0153748i
$869$		−	15.2069i		−	0.515859i
$870$		0			0
$871$	−0.904899	−	0.522443i	−0.0306613	−	0.0177023i
$872$	1.40878	+	0.813357i	0.0477071	+	0.0275437i
$873$		0			0
$874$			1.61852i			0.0547473i
$875$	−15.0436	−	10.9950i	−0.508566	−	0.371698i
$876$		0			0
$877$	7.74463	+	13.4141i	0.261518	+	0.452962i	0.966645	−	0.256118i	$-0.0824437\pi$
$877$	7.74463	+	13.4141i	0.261518	+	0.452962i	−0.705128	+	0.709080i	$0.749110\pi$
$878$	−6.45704	+	11.1839i	−0.217915	+	0.377439i
$879$		0			0
$880$	2.35797	−	1.36138i	0.0794873	−	0.0458920i
$881$	−33.5368			−1.12988			−0.564942	−	0.825130i	$-0.691102\pi$
$881$	−33.5368			−1.12988			−0.564942	+	0.825130i	$0.691102\pi$
$882$		0			0
$883$	18.5616			0.624648			0.312324	−	0.949976i	$-0.398893\pi$
$883$	18.5616			0.624648			0.312324	+	0.949976i	$0.398893\pi$
$884$	−1.03228	+	0.595985i	−0.0347192	+	0.0200451i
$885$		0			0
$886$	−12.1063	+	20.9687i	−0.406718	+	0.704456i
$887$	−11.7850	−	20.4122i	−0.395701	−	0.685375i	0.597489	−	0.801877i	$-0.296165\pi$
$887$	−11.7850	−	20.4122i	−0.395701	−	0.685375i	−0.993190	+	0.116502i	$0.962832\pi$
$888$		0			0
$889$	−6.42137	−	4.69322i	−0.215366	−	0.157406i
$890$		−	30.9280i		−	1.03671i
$891$		0			0
$892$	−9.41801	−	5.43749i	−0.315338	−	0.182061i
$893$	1.95782	+	1.13035i	0.0655159	+	0.0378256i
$894$		0			0
$895$		−	31.6596i		−	1.05826i
$896$	−2.63046	−	0.284003i	−0.0878776	−	0.00948787i
$897$		0			0
$898$	3.48718	+	6.03997i	0.116369	+	0.201557i
$899$	−3.32700	+	5.76254i	−0.110962	+	0.192191i
$900$		0			0
$901$	−6.42433	+	3.70909i	−0.214026	+	0.123568i
$902$	−4.29859			−0.143127
$903$		0			0
$904$	−9.08122			−0.302037
$905$	−24.5087	+	14.1501i	−0.814696	+	0.470365i
$906$		0			0
$907$	25.6867	−	44.4907i	0.852913	−	1.47729i	−0.0256543	−	0.999671i	$-0.508167\pi$
$907$	25.6867	−	44.4907i	0.852913	−	1.47729i	0.878568	−	0.477618i	$-0.158500\pi$
$908$	−3.87060	−	6.70408i	−0.128450	−	0.222483i
$909$		0			0
$910$	1.27756	−	0.564479i	0.0423507	−	0.0187123i
$911$			14.4547i			0.478906i	0.970908	+	0.239453i	$0.0769681\pi$
$911$			14.4547i			0.478906i	−0.970908	+	0.239453i	$0.923032\pi$
$912$		0			0
$913$	8.73673	+	5.04416i	0.289144	+	0.166937i
$914$	−0.0858810	−	0.0495834i	−0.00284069	−	0.00164007i
$915$		0			0
$916$		−	5.13189i		−	0.169562i
$917$	1.76321	−	16.3311i	0.0582264	−	0.539300i
$918$		0			0
$919$	−22.6474	−	39.2265i	−0.747070	−	1.29396i	−0.949221	−	0.314609i	$-0.898127\pi$
$919$	−22.6474	−	39.2265i	−0.747070	−	1.29396i	0.202151	−	0.979354i	$-0.435207\pi$
$920$	−7.08648	+	12.2741i	−0.233634	+	0.404666i
$921$		0			0
$922$	−26.1703	+	15.1095i	−0.861874	+	0.497603i
$923$	1.86803			0.0614869
$924$		0			0
$925$	−10.6677			−0.350752
$926$	27.3829	−	15.8095i	0.899858	−	0.519533i
$927$		0			0
$928$	−2.08596	+	3.61299i	−0.0684749	+	0.118602i
$929$	29.6524	+	51.3595i	0.972865	+	1.68505i	0.686808	+	0.726839i	$0.259011\pi$
$929$	29.6524	+	51.3595i	0.972865	+	1.68505i	0.286057	+	0.958212i	$0.407655\pi$
$930$		0			0
$931$	1.60921	+	1.46551i	0.0527396	+	0.0480303i
$932$			19.0960i			0.625511i
$933$		0			0
$934$	−21.9481	−	12.6717i	−0.718164	−	0.414632i
$935$	14.4962	+	8.36940i	0.474078	+	0.273709i
$936$		0			0
$937$			38.2633i			1.25001i	0.780621	+	0.625005i	$0.214903\pi$
$937$			38.2633i			1.25001i	−0.780621	+	0.625005i	$0.785097\pi$
$938$	8.41346	−	11.5115i	0.274709	−	0.375863i
$939$		0			0
$940$	9.89815	+	17.1441i	0.322842	+	0.559179i
$941$	−2.04961	+	3.55002i	−0.0668152	+	0.115727i	−0.897498	−	0.441019i	$-0.854617\pi$
$941$	−2.04961	+	3.55002i	−0.0668152	+	0.115727i	0.830683	+	0.556746i	$0.187950\pi$
$942$		0			0
$943$	19.3780	−	11.1879i	0.631034	−	0.364328i
$944$	−10.8611			−0.353500
$945$		0			0
$946$	−4.10271			−0.133391
$947$	19.3014	−	11.1437i	0.627211	−	0.362120i	−0.152460	−	0.988310i	$-0.548720\pi$
$947$	19.3014	−	11.1437i	0.627211	−	0.362120i	0.779671	+	0.626189i	$0.215386\pi$
$948$		0			0
$949$	−0.280091	+	0.485131i	−0.00909213	+	0.0157480i
$950$	−0.375200	−	0.649866i	−0.0121731	−	0.0210844i
$951$		0			0
$952$	−6.57366	−	14.8779i	−0.213053	−	0.482194i
$953$			6.17864i			0.200146i	0.994980	+	0.100073i	$0.0319076\pi$
$953$			6.17864i			0.200146i	−0.994980	+	0.100073i	$0.968092\pi$
$954$		0			0
$955$	−42.0446	−	24.2745i	−1.36053	−	0.785504i
$956$	10.7611	+	6.21293i	0.348039	+	0.200941i
$957$		0			0
$958$		−	32.6103i		−	1.05359i
$959$	−10.1525	−	22.9776i	−0.327840	−	0.741987i
$960$		0			0
$961$	−14.2281	−	24.6437i	−0.458970	−	0.794959i
$962$	−0.428512	+	0.742205i	−0.0138158	+	0.0239296i
$963$		0			0
$964$	−19.5847	+	11.3072i	−0.630781	+	0.364181i
$965$	−41.7417			−1.34371
$966$		0			0
$967$	2.02187			0.0650191			0.0325095	−	0.999471i	$-0.489650\pi$
$967$	2.02187			0.0650191			0.0325095	+	0.999471i	$0.489650\pi$
$968$	−0.866025	+	0.500000i	−0.0278351	+	0.0160706i
$969$		0			0
$970$	9.21990	−	15.9693i	0.296033	−	0.512745i
$971$	−8.39201	−	14.5354i	−0.269313	−	0.466463i	0.699372	−	0.714758i	$-0.253463\pi$
$971$	−8.39201	−	14.5354i	−0.269313	−	0.466463i	−0.968684	+	0.248295i	$0.920130\pi$
$972$		0			0
$973$	−20.6107	+	28.2000i	−0.660750	+	0.904052i
$974$		−	4.11063i		−	0.131713i
$975$		0			0
$976$	8.20619	+	4.73784i	0.262674	+	0.151655i
$977$	−17.2826	−	9.97813i	−0.552920	−	0.319229i	0.197379	−	0.980327i	$-0.436757\pi$
$977$	−17.2826	−	9.97813i	−0.552920	−	0.319229i	−0.750299	+	0.661099i	$0.770090\pi$
$978$		0			0
$979$			11.3591i			0.363038i
$980$	5.78693	+	18.1595i	0.184857	+	0.580084i
$981$		0			0
$982$	−2.28693	−	3.96107i	−0.0729787	−	0.126403i
$983$	−9.37668	+	16.2409i	−0.299070	+	0.518004i	−0.975923	−	0.218114i	$-0.930010\pi$
$983$	−9.37668	+	16.2409i	−0.299070	+	0.518004i	0.676854	+	0.736117i	$0.263343\pi$
$984$		0			0
$985$	55.5318	−	32.0613i	1.76939	−	1.02156i
$986$	−25.6479			−0.816796
$987$		0			0
$988$	−0.0602858			−0.00191795
$989$	18.4950	−	10.6781i	0.588106	−	0.339543i
$990$		0			0
$991$	−0.643923	+	1.11531i	−0.0204549	+	0.0354289i	−0.876072	−	0.482181i	$-0.839845\pi$
$991$	−0.643923	+	1.11531i	−0.0204549	+	0.0354289i	0.855617	+	0.517610i	$0.173178\pi$
$992$	0.797476	+	1.38127i	0.0253199	+	0.0438553i
$993$		0			0
$994$	−2.73626	+	25.3435i	−0.0867889	+	0.803848i
$995$		−	36.0327i		−	1.14231i
$996$		0			0
$997$	−44.0369	−	25.4247i	−1.39466	−	0.805208i	−0.400835	−	0.916150i	$-0.631280\pi$
$997$	−44.0369	−	25.4247i	−1.39466	−	0.805208i	−0.993827	+	0.110942i	$0.964613\pi$
$998$	31.7024	+	18.3034i	1.00352	+	0.579384i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.r.d.1277.1	yes	24
3.2	odd	2	inner	1386.2.r.d.1277.12	yes	24
7.5	odd	6	inner	1386.2.r.d.89.12	yes	24
21.5	even	6	inner	1386.2.r.d.89.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.d.89.1	✓	24	21.5	even	6	inner
1386.2.r.d.89.12	yes	24	7.5	odd	6	inner
1386.2.r.d.1277.1	yes	24	1.1	even	1	trivial
1386.2.r.d.1277.12	yes	24	3.2	odd	2	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.36138 + 2.35797i) q^{5} +(-2.13605 - 1.56119i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.36138 + 2.35797i) q^{5} +(-2.13605 - 1.56119i) q^{7} +1.00000i q^{8} +(-2.35797 - 1.36138i) q^{10} +(0.866025 + 0.500000i) q^{11} -0.193887i q^{13} +(2.63046 + 0.284003i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.07388 - 5.32411i) q^{17} +(0.269276 - 0.155466i) q^{19} +2.72275 q^{20} -1.00000 q^{22} +(4.50799 - 2.60269i) q^{23} +(-1.20669 + 2.09005i) q^{25} +(0.0969436 + 0.167911i) q^{26} +(-2.42005 + 1.06928i) q^{28} +4.17192i q^{29} +(1.38127 + 0.797476i) q^{31} +(0.866025 + 0.500000i) q^{32} +6.14775i q^{34} +(0.773269 - 7.16211i) q^{35} +(2.21011 + 3.82803i) q^{37} +(-0.155466 + 0.269276i) q^{38} +(-2.35797 + 1.36138i) q^{40} +4.29859 q^{41} +4.10271 q^{43} +(0.866025 - 0.500000i) q^{44} +(-2.60269 + 4.50799i) q^{46} +(3.63535 + 6.29661i) q^{47} +(2.12540 + 6.66953i) q^{49} -2.41339i q^{50} +(-0.167911 - 0.0969436i) q^{52} +(-1.04499 - 0.603325i) q^{53} +2.72275i q^{55} +(1.56119 - 2.13605i) q^{56} +(-2.08596 - 3.61299i) q^{58} +(5.43057 - 9.40603i) q^{59} +(-8.20619 + 4.73784i) q^{61} -1.59495 q^{62} -1.00000 q^{64} +(0.457181 - 0.263953i) q^{65} +(2.69458 - 4.66714i) q^{67} +(-3.07388 - 5.32411i) q^{68} +(2.91138 + 6.58920i) q^{70} +9.63462i q^{71} +(-2.50213 - 1.44461i) q^{73} +(-3.82803 - 2.21011i) q^{74} -0.310933i q^{76} +(-1.06928 - 2.42005i) q^{77} +(-7.60345 - 13.1696i) q^{79} +(1.36138 - 2.35797i) q^{80} +(-3.72268 + 2.14929i) q^{82} +10.0883 q^{83} +16.7388 q^{85} +(-3.55305 + 2.05135i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(5.67955 + 9.83727i) q^{89} +(-0.302694 + 0.414152i) q^{91} -5.20538i q^{92} +(-6.29661 - 3.63535i) q^{94} +(0.733171 + 0.423296i) q^{95} +6.77249i q^{97} +(-5.17542 - 4.71329i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 8 * q^7	\( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 + 8 * q^7 - 12 * q^16 + 12 * q^19 - 24 * q^22 + 4 * q^25 + 4 * q^28 + 20 * q^37 + 24 * q^43 + 12 * q^46 + 40 * q^49 - 28 * q^58 - 120 * q^61 - 24 * q^64 - 32 * q^67 + 48 * q^70 - 48 * q^73 - 64 * q^79 - 48 * q^82 + 32 * q^85 - 12 * q^88 + 56 * q^91 + 60 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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