LMFDB - Embedded newform 1386.2.r.d.89.12

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			89.12
Character	$\chi$	$=$	1386.89
Dual form			1386.2.r.d.1277.12

$q$-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 $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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	0.382608	+	0.923911i	$0.375026\pi$
$5$	−1.36138	+	2.35797i	−0.608826	+	1.05452i	−0.991434	+	0.130607i	$0.958307\pi$
$6$		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	$0.00855953\pi$
$13$			0.193887i			0.0537746i	−0.999638	+	0.0268873i	$0.991440\pi$
$14$	−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	−0.949949	−	0.312404i	$-0.898866\pi$
$17$	−3.07388	−	5.32411i	−0.745524	−	1.29129i	0.204425	−	0.978882i	$-0.434468\pi$
$18$		0			0
$19$	0.269276	+	0.155466i	0.0617760	+	0.0356664i	0.530570	−	0.847641i	$-0.321978\pi$
$19$	0.269276	+	0.155466i	0.0617760	+	0.0356664i	−0.468794	+	0.883308i	$0.655311\pi$
$20$	−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	$-0.515931\pi$
$23$	−4.50799	−	2.60269i	−0.939981	−	0.542698i	−0.889954	+	0.456050i	$0.849264\pi$
$24$		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	−0.370803	−	0.928712i	$-0.620918\pi$
$31$	1.38127	−	0.797476i	0.248083	−	0.143231i	0.618886	+	0.785481i	$0.287584\pi$
$32$	−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	−0.625168	−	0.780490i	$-0.714970\pi$
$37$	2.21011	−	3.82803i	0.363340	−	0.629324i	0.988508	+	0.151167i	$0.0483030\pi$
$38$	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	$-0.608960\pi$
$41$	−4.29859			−0.671326			−0.335663	+	0.941982i	$0.608960\pi$
$42$		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	0.469107	+	0.883142i	$0.344576\pi$
$47$	−3.63535	+	6.29661i	−0.530270	+	0.918454i	−0.999376	+	0.0353126i	$0.988757\pi$
$48$		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	$-0.640257\pi$
$53$	1.04499	−	0.603325i	0.143540	−	0.0828730i	0.570050	+	0.821610i	$0.306924\pi$
$54$		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	−0.965965	−	0.258674i	$-0.916714\pi$
$59$	−5.43057	−	9.40603i	−0.707001	−	1.22456i	0.258964	−	0.965887i	$-0.416619\pi$
$60$		0			0
$61$	−8.20619	−	4.73784i	−1.05069	−	0.606619i	−0.127851	−	0.991793i	$-0.540808\pi$
$61$	−8.20619	−	4.73784i	−1.05069	−	0.606619i	−0.922844	+	0.385175i	$0.874141\pi$
$62$	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	0.982352	−	0.187040i	$-0.0598894\pi$
$67$	2.69458	+	4.66714i	0.329195	+	0.570182i	−0.653158	+	0.757222i	$0.726556\pi$
$68$	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	−0.639228	−	0.769018i	$-0.720746\pi$
$73$	−2.50213	+	1.44461i	−0.292853	+	0.169079i	0.346375	+	0.938096i	$0.387412\pi$
$74$	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	0.0207679	+	0.999784i	$0.493389\pi$
$79$	−7.60345	+	13.1696i	−0.855455	+	1.48169i	−0.876223	+	0.481907i	$0.839944\pi$
$80$	−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	$-0.686772\pi$
$83$	−10.0883			−1.10734			−0.553668	+	0.832737i	$0.686772\pi$
$84$		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	0.390482	+	0.920610i	$0.372308\pi$
$89$	−5.67955	+	9.83727i	−0.602031	+	1.04275i	−0.992513	+	0.122138i	$0.961025\pi$
$90$		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	$-0.888279\pi$
$97$		−	6.77249i		−	0.687642i	0.939035	−	0.343821i	$-0.111721\pi$
$98$	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	0.987018	+	0.160608i	$0.0513456\pi$
$101$	6.35755	+	11.0116i	0.632600	+	1.09570i	−0.354418	+	0.935087i	$0.615321\pi$
$102$		0			0
$103$	1.88096	+	1.08597i	0.185336	+	0.107004i	0.589797	−	0.807551i	$-0.299208\pi$
$103$	1.88096	+	1.08597i	0.185336	+	0.107004i	−0.404461	+	0.914555i	$0.632541\pi$
$104$	−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	$-0.412259\pi$
$107$	−4.39707	−	2.53865i	−0.425081	−	0.245421i	−0.697249	+	0.716829i	$0.745593\pi$
$108$		0			0
$109$	0.813357	+	1.40878i	0.0779054	+	0.134936i	0.902346	−	0.431012i	$-0.141843\pi$
$109$	0.813357	+	1.40878i	0.0779054	+	0.134936i	−0.824441	+	0.565948i	$0.808510\pi$
$110$	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	$-0.920759\pi$
$131$	−3.10422	+	5.37666i	−0.271217	+	0.469761i	0.697957	+	0.716140i	$0.254093\pi$
$132$		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	$-0.799602\pi$
$137$	−8.22265	+	4.74735i	−0.702508	+	0.405593i	0.105773	+	0.994390i	$0.466268\pi$
$138$		0			0
$139$			13.2020i			1.11978i	0.828568	+	0.559888i	$0.189156\pi$
$139$			13.2020i			1.11978i	−0.828568	+	0.559888i	$0.810844\pi$
$140$	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	$-0.523876\pi$
$149$	−11.9136	−	6.87830i	−0.975997	−	0.563492i	−0.901059	+	0.433696i	$0.857209\pi$
$150$		0			0
$151$	10.4182	+	18.0449i	0.847823	+	1.46847i	0.883146	+	0.469097i	$0.155421\pi$
$151$	10.4182	+	18.0449i	0.847823	+	1.46847i	−0.0353230	+	0.999376i	$0.511246\pi$
$152$	−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	0.149355	−	0.988784i	$-0.452280\pi$
$157$	13.5367	−	7.81541i	1.08034	−	0.623737i	0.930989	+	0.365046i	$0.118947\pi$
$158$	−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	−0.948160	−	0.317793i	$-0.897058\pi$
$163$	−2.53891	+	4.39752i	−0.198863	+	0.344441i	0.749297	+	0.662234i	$0.230392\pi$
$164$	−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	$-0.538732\pi$
$167$	−3.13718			−0.242762			−0.121381	+	0.992606i	$0.538732\pi$
$168$		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	0.326987	+	0.945029i	$0.393967\pi$
$173$	−8.61420	+	14.9202i	−0.654925	+	1.13436i	−0.981913	+	0.189335i	$0.939367\pi$
$174$		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	$-0.523574\pi$
$179$	10.0700	−	5.81389i	0.752664	−	0.434551i	0.826656	+	0.562708i	$0.190241\pi$
$180$		0			0
$181$		−	10.3940i		−	0.772577i	−0.922378	−	0.386288i	$-0.873757\pi$
$181$		−	10.3940i		−	0.772577i	0.922378	−	0.386288i	$-0.126243\pi$
$182$	−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	$-0.110150\pi$
$191$	15.4420	+	8.91542i	1.11734	+	0.645097i	0.176620	+	0.984279i	$0.443484\pi$
$192$		0			0
$193$	−7.66535	−	13.2768i	−0.551764	−	0.955683i	−0.998147	−	0.0608416i	$-0.980622\pi$
$193$	−7.66535	−	13.2768i	−0.551764	−	0.955683i	0.446383	−	0.894842i	$-0.352712\pi$
$194$	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	−0.847804	−	0.530310i	$-0.822075\pi$
$199$	−11.4609	+	6.61697i	−0.812443	+	0.469064i	0.0353603	+	0.999375i	$0.488742\pi$
$200$	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	$0.118631\pi$
$223$			10.8750i			0.728242i	−0.931352	+	0.364121i	$0.881369\pi$
$224$	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	$-0.249368\pi$
$227$	−3.87060	−	6.70408i	−0.256901	−	0.444965i	−0.965410	+	0.260736i	$0.916035\pi$
$228$		0			0
$229$	4.44434	+	2.56594i	0.293691	+	0.169562i	0.639605	−	0.768704i	$-0.279098\pi$
$229$	4.44434	+	2.56594i	0.293691	+	0.169562i	−0.345914	+	0.938266i	$0.612431\pi$
$230$	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	$-0.118224\pi$
$233$	16.5376	+	9.54801i	1.08342	+	0.625511i	0.151600	+	0.988442i	$0.451557\pi$
$234$		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	−0.973377	−	0.229212i	$-0.926385\pi$
$241$	−19.5847	+	11.3072i	−1.26156	+	0.728363i	−0.288185	+	0.957575i	$0.593052\pi$
$242$	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	$-0.437058\pi$
$251$	6.22476			0.392903			0.196452	+	0.980514i	$0.437058\pi$
$252$		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	−0.135962	−	0.990714i	$-0.543412\pi$
$257$	12.6647	−	21.9359i	0.790003	−	1.36832i	0.925964	−	0.377611i	$-0.123254\pi$
$258$		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	$-0.403372\pi$
$263$	20.6740	−	11.9361i	1.27481	−	0.736014i	0.975890	+	0.218263i	$0.0700390\pi$
$264$		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	$-0.145961\pi$
$269$	1.06611	+	1.84656i	0.0650019	+	0.112587i	−0.831693	+	0.555236i	$0.812628\pi$
$270$		0			0
$271$	−23.5382	−	13.5898i	−1.42984	−	0.825520i	−0.432735	−	0.901521i	$-0.642451\pi$
$271$	−23.5382	−	13.5898i	−1.42984	−	0.825520i	−0.997108	+	0.0760010i	$0.975785\pi$
$272$	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	0.976333	−	0.216275i	$-0.0693907\pi$
$277$	5.00742	+	8.67311i	0.300867	+	0.521117i	−0.675466	+	0.737391i	$0.736057\pi$
$278$	−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	0.415642	−	0.909528i	$-0.363557\pi$
$283$	23.7390	−	13.7057i	1.41114	−	0.814721i	0.995496	+	0.0948077i	$0.0302236\pi$
$284$	−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	$-0.560112\pi$
$293$	−6.42673			−0.375454			−0.187727	+	0.982221i	$0.560112\pi$
$294$		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	$0.213374\pi$
$307$			21.7703i			1.24250i	−0.783614	+	0.621248i	$0.786626\pi$
$308$	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	$-0.286266\pi$
$311$	−6.47129	−	11.2086i	−0.366953	−	0.635582i	−0.989088	+	0.147329i	$0.952932\pi$
$312$		0			0
$313$	−1.55581	−	0.898250i	−0.0879398	−	0.0507721i	0.455385	−	0.890294i	$-0.349502\pi$
$313$	−1.55581	−	0.898250i	−0.0879398	−	0.0507721i	−0.543325	+	0.839522i	$0.682835\pi$
$314$	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	$-0.0315748\pi$
$317$	25.0485	+	14.4617i	1.40686	+	0.812252i	0.411777	+	0.911285i	$0.364908\pi$
$318$		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	−0.317204	+	0.948357i	$0.602744\pi$
$331$	−17.8278	+	30.8786i	−0.979904	+	1.69724i	−0.662700	+	0.748885i	$0.730589\pi$
$332$	−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	$-0.981007\pi$
$347$	−26.9301	+	15.5481i	−1.44569	+	0.834667i	−0.447465	+	0.894301i	$0.647673\pi$
$348$		0			0
$349$			13.5679i			0.726272i	0.931736	+	0.363136i	$0.118294\pi$
$349$			13.5679i			0.726272i	−0.931736	+	0.363136i	$0.881706\pi$
$350$	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	$-0.183209\pi$
$353$	−0.975985	−	1.69046i	−0.0519465	−	0.0899739i	−0.890829	+	0.454338i	$0.849876\pi$
$354$		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	$-0.323052\pi$
$359$	1.05983	+	0.611893i	0.0559357	+	0.0322945i	−0.471771	+	0.881721i	$0.656385\pi$
$360$		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	0.147004	−	0.989136i	$-0.453037\pi$
$367$	20.6347	−	11.9134i	1.07712	−	0.621877i	0.930119	+	0.367259i	$0.119704\pi$
$368$	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	0.452535	+	0.891747i	$0.350520\pi$
$373$	−10.5452	+	18.2648i	−0.546008	+	0.945714i	−0.998543	+	0.0539668i	$0.982813\pi$
$374$	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	$-0.866877\pi$
$383$	−2.05855	+	3.56551i	−0.105187	+	0.182189i	0.808628	+	0.588321i	$0.200211\pi$
$384$		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	$-0.343283\pi$
$389$	29.0363	−	16.7641i	1.47220	−	0.849975i	0.999511	+	0.0312539i	$0.00995003\pi$
$390$		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	0.536325	−	0.844012i	$-0.319812\pi$
$397$	1.46549	+	0.846104i	0.0735511	+	0.0424647i	−0.462773	+	0.886477i	$0.653146\pi$
$398$	−13.2339			−0.663357
$399$		0			0
$400$	2.41339			0.120669
$401$	32.1813	+	18.5799i	1.60706	+	0.927835i	0.990024	+	0.140897i	$0.0449988\pi$
$401$	32.1813	+	18.5799i	1.60706	+	0.927835i	0.617033	+	0.786937i	$0.288335\pi$
$402$		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	−0.554281	−	0.832329i	$-0.687007\pi$
$409$	−2.23682	+	1.29143i	−0.110604	+	0.0638570i	0.443678	+	0.896186i	$0.353673\pi$
$410$	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	$-0.681391\pi$
$419$	−22.0871			−1.07903			−0.539513	+	0.841978i	$0.681391\pi$
$420$		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	$-0.646314\pi$
$431$	2.29763	−	1.32654i	0.110673	−	0.0638970i	0.554315	+	0.832307i	$0.312980\pi$
$432$		0			0
$433$			21.3112i			1.02415i	0.858940	+	0.512076i	$0.171123\pi$
$433$			21.3112i			1.02415i	−0.858940	+	0.512076i	$0.828877\pi$
$434$	−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	0.742554	−	0.669786i	$-0.233614\pi$
$439$	11.1839	+	6.45704i	0.533780	+	0.308178i	−0.208775	+	0.977964i	$0.566948\pi$
$440$	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	$-0.528404\pi$
$443$	−20.9687	−	12.1063i	−0.996251	−	0.575186i	−0.907137	+	0.420836i	$0.861737\pi$
$444$		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	−0.864863	−	0.502007i	$-0.832595\pi$
$457$	0.0495834	−	0.0858810i	0.00231941	−	0.00401734i	0.867183	+	0.497990i	$0.165928\pi$
$458$	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	$-0.748478\pi$
$461$	−30.2189			−1.40744			−0.703718	+	0.710480i	$0.748478\pi$
$462$		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	0.408324	+	0.912837i	$0.366113\pi$
$467$	−12.6717	+	21.9481i	−0.586378	+	1.01564i	−0.994702	+	0.102800i	$0.967220\pi$
$468$		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	0.950195	+	0.311657i	$0.100884\pi$
$479$	16.3051	+	28.2413i	0.745000	+	1.29038i	−0.205194	+	0.978721i	$0.565783\pi$
$480$		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	0.815694	−	0.578484i	$-0.196356\pi$
$487$	−2.05532	−	3.55991i	−0.0931353	−	0.161315i	−0.908829	+	0.417169i	$0.863022\pi$
$488$	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	0.0867728	+	0.996228i	$0.472345\pi$
$499$	−18.3034	+	31.7024i	−0.819372	+	1.41919i	−0.906145	+	0.422967i	$0.860989\pi$
$500$	−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	$-0.375969\pi$
$503$	17.0391			0.759738			0.379869	+	0.925040i	$0.375969\pi$
$504$		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	$-0.918550\pi$
$509$	−5.96804	+	10.3370i	−0.264529	+	0.458177i	0.702911	+	0.711278i	$0.251883\pi$
$510$		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	−0.762899	−	0.646518i	$-0.776225\pi$
$521$	−21.4867	−	37.2161i	−0.941350	−	1.63047i	−0.178452	−	0.983949i	$-0.557109\pi$
$522$		0			0
$523$	−31.1432	−	17.9806i	−1.36180	−	0.786235i	−0.371935	−	0.928259i	$-0.621306\pi$
$523$	−31.1432	−	17.9806i	−1.36180	−	0.786235i	−0.989863	+	0.142024i	$0.954639\pi$
$524$	−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	−0.897771	−	0.440463i	$-0.854814\pi$
$541$	−1.56847	+	2.71667i	−0.0674337	+	0.116799i	0.830337	+	0.557261i	$0.188148\pi$
$542$	−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	$-0.763521\pi$
$557$	−12.2471	+	7.07088i	−0.518927	+	0.299603i	0.217568	+	0.976045i	$0.430187\pi$
$558$		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	$-0.212398\pi$
$563$	−3.39720	−	5.88412i	−0.143175	−	0.247986i	−0.928691	+	0.370856i	$0.879064\pi$
$564$		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	0.996228	+	0.0867776i	$0.0276570\pi$
$569$	37.4383	+	21.6150i	1.56949	+	0.906147i	0.573265	+	0.819370i	$0.305676\pi$
$570$		0			0
$571$	−23.3065	−	40.3680i	−0.975346	−	1.68935i	−0.678790	−	0.734333i	$-0.737495\pi$
$571$	−23.3065	−	40.3680i	−0.975346	−	1.68935i	−0.296556	−	0.955015i	$-0.595838\pi$
$572$	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	0.368488	−	0.929633i	$-0.379876\pi$
$577$	32.6159	−	18.8308i	1.35782	−	0.783936i	0.989329	+	0.145697i	$0.0465423\pi$
$578$	−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	$-0.137841\pi$
$587$	43.9834			1.81539			0.907694	+	0.419632i	$0.137841\pi$
$588$		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	$-0.955202\pi$
$593$	−9.09719	+	15.7568i	−0.373577	+	0.647054i	0.616536	+	0.787327i	$0.288535\pi$
$594$		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	$-0.905411\pi$
$599$	−28.8965	+	16.6834i	−1.18068	+	0.681665i	−0.224507	+	0.974472i	$0.572077\pi$
$600$		0			0
$601$		−	45.3210i		−	1.84868i	−0.381566	−	0.924341i	$-0.624615\pi$
$601$		−	45.3210i		−	1.84868i	0.381566	−	0.924341i	$-0.375385\pi$
$602$	−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	0.389319	−	0.921103i	$-0.372710\pi$
$607$	−5.26548	−	3.04003i	−0.213719	−	0.123391i	−0.603039	+	0.797712i	$0.706044\pi$
$608$	−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	0.522447	−	0.852671i	$-0.325019\pi$
$613$	−11.8152	−	20.4645i	−0.477211	−	0.826554i	−0.999659	+	0.0261170i	$0.991686\pi$
$614$	−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	−0.381472	−	0.924380i	$-0.624583\pi$
$619$	5.68075	−	3.27978i	0.228329	−	0.131826i	0.609801	+	0.792555i	$0.291249\pi$
$620$	−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	$-0.470412\pi$
$641$	25.3563	−	14.6395i	1.00151	−	0.578224i	0.908696	+	0.417459i	$0.137079\pi$
$642$		0			0
$643$			16.6438i			0.656368i	0.944614	+	0.328184i	$0.106437\pi$
$643$			16.6438i			0.656368i	−0.944614	+	0.328184i	$0.893563\pi$
$644$	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	0.908446	+	0.418001i	$0.137269\pi$
$647$	20.7616	+	35.9602i	0.816223	+	1.41374i	−0.0922233	+	0.995738i	$0.529397\pi$
$648$		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	$-0.0890650\pi$
$653$	30.7284	+	17.7410i	1.20249	+	0.694260i	0.241385	+	0.970429i	$0.422398\pi$
$654$		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	−0.0541298	−	0.998534i	$-0.517238\pi$
$661$	20.1453	−	11.6309i	0.783561	−	0.452389i	0.837691	+	0.546145i	$0.183905\pi$
$662$	−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	−0.360214	−	0.932870i	$-0.617296\pi$
$677$	16.3344	−	28.2920i	0.627781	−	1.08735i	0.987996	−	0.154480i	$-0.0493702\pi$
$678$		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	$-0.764572\pi$
$683$	−13.7043	+	7.91217i	−0.524380	+	0.302751i	0.214345	+	0.976758i	$0.431238\pi$
$684$		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	0.910570	−	0.413355i	$-0.135643\pi$
$691$	26.4940	+	15.2963i	1.00788	+	0.581899i	0.0973085	+	0.995254i	$0.468977\pi$
$692$	−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	−0.713815	−	0.700334i	$-0.753034\pi$
$709$	6.64611	−	11.5114i	0.249600	−	0.432320i	0.963415	+	0.268015i	$0.0863675\pi$
$710$	−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	$-0.902792\pi$
$719$	−5.80479	+	10.0542i	−0.216482	+	0.374958i	0.737248	+	0.675622i	$0.236125\pi$
$720$		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	$-0.904022\pi$
$727$		−	16.0147i		−	0.593953i	0.954885	−	0.296977i	$-0.0959783\pi$
$728$	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	0.787450	−	0.616378i	$-0.211401\pi$
$733$	17.5271	+	10.1193i	0.647377	+	0.373763i	−0.140074	+	0.990141i	$0.544734\pi$
$734$	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	0.739770	−	0.672860i	$-0.234934\pi$
$739$	−5.78566	−	10.0211i	−0.212829	−	0.368630i	−0.952599	+	0.304229i	$0.901601\pi$
$740$	−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	−0.999978	−	0.00663281i	$-0.997889\pi$
$751$	−13.5445	+	23.4597i	−0.494245	+	0.856057i	0.505733	+	0.862690i	$0.331222\pi$
$752$	−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	$-0.736406\pi$
$761$	8.27095	−	14.3257i	0.299822	−	0.519306i	0.976095	+	0.217345i	$0.0697395\pi$
$762$		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	$-0.970418\pi$
$769$		−	5.14692i		−	0.185603i	0.995685	−	0.0928013i	$-0.0295821\pi$
$770$	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	$-0.190842\pi$
$773$	−2.10953	−	3.65382i	−0.0758746	−	0.131419i	−0.901466	+	0.432849i	$0.857508\pi$
$774$		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	−0.930047	−	0.367440i	$-0.880234\pi$
$787$	−30.2097	+	17.4416i	−1.07686	+	0.621724i	−0.146811	+	0.989165i	$0.546901\pi$
$788$	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	$-0.600205\pi$
$797$	−17.4825			−0.619262			−0.309631	+	0.950857i	$0.600205\pi$
$798$		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	$-0.820316\pi$
$809$	−22.8674	+	13.2025i	−0.803975	+	0.464175i	0.0408842	+	0.999164i	$0.486983\pi$
$810$		0			0
$811$		−	31.4016i		−	1.10266i	−0.834287	−	0.551330i	$-0.814121\pi$
$811$		−	31.4016i		−	1.10266i	0.834287	−	0.551330i	$-0.185879\pi$
$812$	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	−0.982084	−	0.188444i	$-0.939656\pi$
$821$	−46.8857	−	27.0695i	−1.63632	−	0.944731i	−0.654239	−	0.756288i	$-0.727011\pi$
$822$		0			0
$823$	−13.6961	−	23.7223i	−0.477416	−	0.826909i	0.522249	−	0.852793i	$-0.325093\pi$
$823$	−13.6961	−	23.7223i	−0.477416	−	0.826909i	−0.999665	+	0.0258842i	$0.991760\pi$
$824$	−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	−0.811729	−	0.584035i	$-0.801473\pi$
$829$	−20.4945	+	11.8325i	−0.711804	+	0.410960i	0.0999244	+	0.994995i	$0.468140\pi$
$830$	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	$-0.530046\pi$
$839$	−5.46018			−0.188506			−0.0942532	+	0.995548i	$0.530046\pi$
$840$		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	$-0.949150\pi$
$853$		−	9.29168i		−	0.318141i	0.987267	−	0.159071i	$-0.0508497\pi$
$854$	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	$-0.249253\pi$
$857$	−7.51046	−	13.0085i	−0.256552	−	0.444362i	−0.965316	+	0.261084i	$0.915920\pi$
$858$		0			0
$859$	28.6855	+	16.5616i	0.978737	+	0.565074i	0.901889	−	0.431969i	$-0.142181\pi$
$859$	28.6855	+	16.5616i	0.978737	+	0.565074i	0.0768486	+	0.997043i	$0.475514\pi$
$860$	−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	$-0.282801\pi$
$863$	8.04372	+	4.64405i	0.273812	+	0.158085i	−0.356807	+	0.934178i	$0.616135\pi$
$864$		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	−0.705128	−	0.709080i	$-0.749110\pi$
$877$	7.74463	−	13.4141i	0.261518	−	0.452962i	0.966645	+	0.256118i	$0.0824437\pi$
$878$	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	$-0.308898\pi$
$881$	33.5368			1.12988			0.564942	+	0.825130i	$0.308898\pi$
$882$		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	$-0.703835\pi$
$887$	11.7850	−	20.4122i	0.395701	−	0.685375i	0.993190	+	0.116502i	$0.0371682\pi$
$888$		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	0.878568	+	0.477618i	$0.158500\pi$
$907$	25.6867	+	44.4907i	0.852913	+	1.47729i	−0.0256543	+	0.999671i	$0.508167\pi$
$908$	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	0.202151	+	0.979354i	$0.435207\pi$
$919$	−22.6474	+	39.2265i	−0.747070	+	1.29396i	−0.949221	+	0.314609i	$0.898127\pi$
$920$	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	−0.286057	+	0.958212i	$0.592345\pi$
$929$	−29.6524	+	51.3595i	−0.972865	+	1.68505i	−0.686808	+	0.726839i	$0.740989\pi$
$930$		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	$-0.785097\pi$
$937$		−	38.2633i		−	1.25001i	0.780621	−	0.625005i	$-0.214903\pi$
$938$	−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	$-0.145383\pi$
$941$	2.04961	+	3.55002i	0.0668152	+	0.115727i	−0.830683	+	0.556746i	$0.812050\pi$
$942$		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	$-0.451280\pi$
$947$	−19.3014	−	11.1437i	−0.627211	−	0.362120i	−0.779671	+	0.626189i	$0.784614\pi$
$948$		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	$-0.746537\pi$
$971$	8.39201	−	14.5354i	0.269313	−	0.466463i	0.968684	+	0.248295i	$0.0798702\pi$
$972$		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	$-0.563243\pi$
$977$	17.2826	−	9.97813i	0.552920	−	0.319229i	0.750299	+	0.661099i	$0.229910\pi$
$978$		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	$-0.0699904\pi$
$983$	9.37668	+	16.2409i	0.299070	+	0.518004i	−0.676854	+	0.736117i	$0.736657\pi$
$984$		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	0.855617	−	0.517610i	$-0.173178\pi$
$991$	−0.643923	−	1.11531i	−0.0204549	−	0.0354289i	−0.876072	+	0.482181i	$0.839845\pi$
$992$	−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	−0.993827	−	0.110942i	$-0.964613\pi$
$997$	−44.0369	+	25.4247i	−1.39466	+	0.805208i	−0.400835	+	0.916150i	$0.631280\pi$
$998$	−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.89.12	yes	24
3.2	odd	2	inner	1386.2.r.d.89.1	✓	24
7.3	odd	6	inner	1386.2.r.d.1277.1	yes	24
21.17	even	6	inner	1386.2.r.d.1277.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.d.89.1	✓	24	3.2	odd	2	inner
1386.2.r.d.89.12	yes	24	1.1	even	1	trivial
1386.2.r.d.1277.1	yes	24	7.3	odd	6	inner
1386.2.r.d.1277.12	yes	24	21.17	even	6	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

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