LMFDB - Embedded newform 2970.2.t.a.791.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2970,2,Mod(791,2970)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2970, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2970.791"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2970.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$23.7155694003$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 990)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			791.1
Character	$\chi$	$=$	2970.791
Dual form			2970.2.t.a.2771.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-4.54797 - 2.62577i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(-0.660985 + 3.25009i) q^{11} +(-5.39031 + 3.11210i) q^{13} +(4.54797 - 2.62577i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.35881 q^{17} +0.748972i q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.48417 - 2.19748i) q^{22} +(-2.87695 + 1.66101i) q^{23} +(0.500000 - 0.866025i) q^{25} -6.22419i q^{26} +5.25154i q^{28} +(5.20486 - 9.01507i) q^{29} +(2.83113 + 4.90367i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.17940 - 3.77484i) q^{34} +5.25154 q^{35} -7.09847 q^{37} +(-0.648629 - 0.374486i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(2.75133 + 4.76544i) q^{41} +(-1.41561 - 0.817304i) q^{43} +(3.14515 - 1.05262i) q^{44} -3.32202i q^{46} +(-0.640537 - 0.369814i) q^{47} +(10.2894 + 17.8217i) q^{49} +(0.500000 + 0.866025i) q^{50} +(5.39031 + 3.11210i) q^{52} -2.46463i q^{53} +(-1.05262 - 3.14515i) q^{55} +(-4.54797 - 2.62577i) q^{56} +(5.20486 + 9.01507i) q^{58} +(0.877216 - 0.506461i) q^{59} +(-0.800939 - 0.462422i) q^{61} -5.66227 q^{62} +1.00000 q^{64} +(3.11210 - 5.39031i) q^{65} +(-0.821341 - 1.42261i) q^{67} +(2.17940 + 3.77484i) q^{68} +(-2.62577 + 4.54797i) q^{70} -6.56094i q^{71} +9.67062i q^{73} +(3.54924 - 6.14746i) q^{74} +(0.648629 - 0.374486i) q^{76} +(11.5401 - 13.0457i) q^{77} +(-10.6885 - 6.17100i) q^{79} -1.00000i q^{80} -5.50266 q^{82} +(2.86275 - 4.95842i) q^{83} +(3.77484 - 2.17940i) q^{85} +(1.41561 - 0.817304i) q^{86} +(-0.660985 + 3.25009i) q^{88} -8.41930i q^{89} +32.6866 q^{91} +(2.87695 + 1.66101i) q^{92} +(0.640537 - 0.369814i) q^{94} +(-0.374486 - 0.648629i) q^{95} +(8.16763 - 14.1467i) q^{97} -20.5787 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2970\mathbb{Z}\right)^\times$.

$n$	$541$	$1541$	$2377$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		0			0
$7$	−4.54797	−	2.62577i	−1.71897	−	0.992448i	−0.920817	−	0.389995i	$-0.872477\pi$
$7$	−4.54797	−	2.62577i	−1.71897	−	0.992448i	−0.798154	−	0.602453i	$-0.794190\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	−0.660985	+	3.25009i	−0.199295	+	0.979940i
$11$	−0.660985	+	3.25009i	−0.199295	+	0.979940i
$12$		0			0
$13$	−5.39031	+	3.11210i	−1.49500	+	0.863140i	−0.999984	−	0.00574230i	$-0.998172\pi$
$13$	−5.39031	+	3.11210i	−1.49500	+	0.863140i	−0.495019	+	0.868882i	$0.664839\pi$
$14$	4.54797	−	2.62577i	1.21550	−	0.701767i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.35881			−1.05717			−0.528583	−	0.848881i	$-0.677277\pi$
$17$	−4.35881			−1.05717			−0.528583	+	0.848881i	$0.677277\pi$
$18$		0			0
$19$			0.748972i			0.171826i	0.996303	+	0.0859130i	$0.0273807\pi$
$19$			0.748972i			0.171826i	−0.996303	+	0.0859130i	$0.972619\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		0			0
$22$	−2.48417	−	2.19748i	−0.529627	−	0.468503i
$23$	−2.87695	+	1.66101i	−0.599886	+	0.346344i	−0.768997	−	0.639253i	$-0.779244\pi$
$23$	−2.87695	+	1.66101i	−0.599886	+	0.346344i	0.169111	+	0.985597i	$0.445910\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	6.22419i		−	1.22066i
$27$		0			0
$28$			5.25154i			0.992448i
$29$	5.20486	−	9.01507i	0.966517	−	1.67406i	0.261036	−	0.965329i	$-0.415936\pi$
$29$	5.20486	−	9.01507i	0.966517	−	1.67406i	0.705482	−	0.708728i	$-0.250731\pi$
$30$		0			0
$31$	2.83113	+	4.90367i	0.508487	+	0.880725i	0.999952	+	0.00982755i	$0.00312826\pi$
$31$	2.83113	+	4.90367i	0.508487	+	0.880725i	−0.491465	+	0.870897i	$0.663538\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.17940	−	3.77484i	0.373765	−	0.647380i
$35$	5.25154			0.887673
$36$		0			0
$37$	−7.09847			−1.16698			−0.583491	−	0.812120i	$-0.698314\pi$
$37$	−7.09847			−1.16698			−0.583491	+	0.812120i	$0.698314\pi$
$38$	−0.648629	−	0.374486i	−0.105222	−	0.0607497i
$39$		0			0
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	2.75133	+	4.76544i	0.429686	+	0.744237i	0.996845	−	0.0793706i	$-0.0252910\pi$
$41$	2.75133	+	4.76544i	0.429686	+	0.744237i	−0.567160	+	0.823608i	$0.691958\pi$
$42$		0			0
$43$	−1.41561	−	0.817304i	−0.215879	−	0.124638i	0.388162	−	0.921591i	$-0.373110\pi$
$43$	−1.41561	−	0.817304i	−0.215879	−	0.124638i	−0.604041	+	0.796954i	$0.706444\pi$
$44$	3.14515	−	1.05262i	0.474150	−	0.158688i
$45$		0			0
$46$		−	3.32202i		−	0.489805i
$47$	−0.640537	−	0.369814i	−0.0934319	−	0.0539429i	0.452556	−	0.891736i	$-0.350512\pi$
$47$	−0.640537	−	0.369814i	−0.0934319	−	0.0539429i	−0.545988	+	0.837793i	$0.683846\pi$
$48$		0			0
$49$	10.2894	+	17.8217i	1.46991	+	2.54595i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	5.39031	+	3.11210i	0.747501	+	0.431570i
$53$		−	2.46463i		−	0.338542i	−0.985570	−	0.169271i	$-0.945859\pi$
$53$		−	2.46463i		−	0.338542i	0.985570	−	0.169271i	$-0.0541414\pi$
$54$		0			0
$55$	−1.05262	−	3.14515i	−0.141935	−	0.424093i
$56$	−4.54797	−	2.62577i	−0.607748	−	0.350884i
$57$		0			0
$58$	5.20486	+	9.01507i	0.683431	+	1.18374i
$59$	0.877216	−	0.506461i	0.114204	−	0.0659356i	−0.441810	−	0.897109i	$-0.645663\pi$
$59$	0.877216	−	0.506461i	0.114204	−	0.0659356i	0.556014	+	0.831173i	$0.312330\pi$
$60$		0			0
$61$	−0.800939	−	0.462422i	−0.102550	−	0.0592071i	0.447848	−	0.894110i	$-0.352191\pi$
$61$	−0.800939	−	0.462422i	−0.102550	−	0.0592071i	−0.550398	+	0.834903i	$0.685524\pi$
$62$	−5.66227			−0.719109
$63$		0			0
$64$	1.00000			0.125000
$65$	3.11210	−	5.39031i	0.386008	−	0.668585i
$66$		0			0
$67$	−0.821341	−	1.42261i	−0.100343	−	0.173799i	0.811483	−	0.584376i	$-0.198661\pi$
$67$	−0.821341	−	1.42261i	−0.100343	−	0.173799i	−0.911826	+	0.410577i	$0.865327\pi$
$68$	2.17940	+	3.77484i	0.264292	+	0.457766i
$69$		0			0
$70$	−2.62577	+	4.54797i	−0.313840	+	0.543586i
$71$		−	6.56094i		−	0.778640i	−0.921103	−	0.389320i	$-0.872710\pi$
$71$		−	6.56094i		−	0.778640i	0.921103	−	0.389320i	$-0.127290\pi$
$72$		0			0
$73$			9.67062i			1.13186i	0.824453	+	0.565930i	$0.191483\pi$
$73$			9.67062i			1.13186i	−0.824453	+	0.565930i	$0.808517\pi$
$74$	3.54924	−	6.14746i	0.412590	−	0.714627i
$75$		0			0
$76$	0.648629	−	0.374486i	0.0744028	−	0.0429565i
$77$	11.5401	−	13.0457i	1.31512	−	1.48670i
$78$		0			0
$79$	−10.6885	−	6.17100i	−1.20255	−	0.694292i	−0.241427	−	0.970419i	$-0.577616\pi$
$79$	−10.6885	−	6.17100i	−1.20255	−	0.694292i	−0.961121	+	0.276127i	$0.910949\pi$
$80$		−	1.00000i		−	0.111803i
$81$		0			0
$82$	−5.50266			−0.607667
$83$	2.86275	−	4.95842i	0.314227	−	0.544258i	−0.665046	−	0.746803i	$-0.731588\pi$
$83$	2.86275	−	4.95842i	0.314227	−	0.544258i	0.979273	+	0.202545i	$0.0649213\pi$
$84$		0			0
$85$	3.77484	−	2.17940i	0.409439	−	0.236390i
$86$	1.41561	−	0.817304i	0.152649	−	0.0881321i
$87$		0			0
$88$	−0.660985	+	3.25009i	−0.0704613	+	0.346461i
$89$		−	8.41930i		−	0.892444i	−0.894922	−	0.446222i	$-0.852769\pi$
$89$		−	8.41930i		−	0.892444i	0.894922	−	0.446222i	$-0.147231\pi$
$90$		0			0
$91$	32.6866			3.42649
$92$	2.87695	+	1.66101i	0.299943	+	0.173172i
$93$		0			0
$94$	0.640537	−	0.369814i	0.0660663	−	0.0381434i
$95$	−0.374486	−	0.648629i	−0.0384215	−	0.0665479i
$96$		0			0
$97$	8.16763	−	14.1467i	0.829297	−	1.43638i	−0.0692933	−	0.997596i	$-0.522074\pi$
$97$	8.16763	−	14.1467i	0.829297	−	1.43638i	0.898590	−	0.438788i	$-0.144592\pi$
$98$	−20.5787			−2.07876
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−3.41322	+	5.91188i	−0.339628	+	0.588254i	−0.984363	−	0.176153i	$-0.943635\pi$
$101$	−3.41322	+	5.91188i	−0.339628	+	0.588254i	0.644734	+	0.764407i	$0.276968\pi$
$102$		0			0
$103$	0.536621	+	0.929456i	0.0528749	+	0.0915820i	0.891251	−	0.453510i	$-0.149828\pi$
$103$	0.536621	+	0.929456i	0.0528749	+	0.0915820i	−0.838377	+	0.545092i	$0.816495\pi$
$104$	−5.39031	+	3.11210i	−0.528563	+	0.305166i
$105$		0			0
$106$	2.13443	+	1.23231i	0.207314	+	0.119693i
$107$	13.1135			1.26773			0.633863	−	0.773445i	$-0.281468\pi$
$107$	13.1135			1.26773			0.633863	+	0.773445i	$0.281468\pi$
$108$		0			0
$109$		−	12.7274i		−	1.21906i	−0.792762	−	0.609531i	$-0.791358\pi$
$109$		−	12.7274i		−	1.21906i	0.792762	−	0.609531i	$-0.208642\pi$
$110$	3.25009	+	0.660985i	0.309884	+	0.0630225i
$111$		0			0
$112$	4.54797	−	2.62577i	0.429743	−	0.248112i
$113$	6.01231	−	3.47121i	0.565591	−	0.326544i	−0.189796	−	0.981824i	$-0.560783\pi$
$113$	6.01231	−	3.47121i	0.565591	−	0.326544i	0.755386	+	0.655280i	$0.227449\pi$
$114$		0			0
$115$	1.66101	−	2.87695i	0.154890	−	0.268277i
$116$	−10.4097			−0.966517
$117$		0			0
$118$			1.01292i			0.0932470i
$119$	19.8237	+	11.4452i	1.81724	+	1.04918i
$120$		0			0
$121$	−10.1262	−	4.29653i	−0.920563	−	0.390593i
$122$	0.800939	−	0.462422i	0.0725136	−	0.0418657i
$123$		0			0
$124$	2.83113	−	4.90367i	0.254243	−	0.440362i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			2.60810i			0.231432i	0.993282	+	0.115716i	$0.0369162\pi$
$127$			2.60810i			0.231432i	−0.993282	+	0.115716i	$0.963084\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	3.11210	+	5.39031i	0.272949	+	0.472761i
$131$	−0.604819	−	1.04758i	−0.0528433	−	0.0915273i	0.838394	−	0.545065i	$-0.183495\pi$
$131$	−0.604819	−	1.04758i	−0.0528433	−	0.0915273i	−0.891237	+	0.453538i	$0.850162\pi$
$132$		0			0
$133$	1.96663	−	3.40630i	0.170528	−	0.295364i
$134$	1.64268			0.141906
$135$		0			0
$136$	−4.35881			−0.373765
$137$	14.8740	+	8.58754i	1.27078	+	0.733683i	0.975134	−	0.221616i	$-0.0711332\pi$
$137$	14.8740	+	8.58754i	1.27078	+	0.733683i	0.295642	+	0.955299i	$0.404467\pi$
$138$		0			0
$139$	10.5934	−	6.11608i	0.898517	−	0.518759i	0.0217983	−	0.999762i	$-0.493061\pi$
$139$	10.5934	−	6.11608i	0.898517	−	0.518759i	0.876719	+	0.481003i	$0.159728\pi$
$140$	−2.62577	−	4.54797i	−0.221918	−	0.384374i
$141$		0			0
$142$	5.68194	+	3.28047i	0.476818	+	0.275291i
$143$	−6.55168	−	19.5760i	−0.547879	−	1.63703i
$144$		0			0
$145$			10.4097i			0.864479i
$146$	−8.37500	−	4.83531i	−0.693120	−	0.400173i
$147$		0			0
$148$	3.54924	+	6.14746i	0.291745	+	0.505318i
$149$	2.09557	+	3.62963i	0.171676	+	0.297351i	0.939006	−	0.343901i	$-0.111749\pi$
$149$	2.09557	+	3.62963i	0.171676	+	0.297351i	−0.767330	+	0.641252i	$0.778415\pi$
$150$		0			0
$151$	−9.01876	−	5.20698i	−0.733936	−	0.423738i	0.0859241	−	0.996302i	$-0.472616\pi$
$151$	−9.01876	−	5.20698i	−0.733936	−	0.423738i	−0.819860	+	0.572563i	$0.805949\pi$
$152$			0.748972i			0.0607497i
$153$		0			0
$154$	5.52786	+	16.5169i	0.445447	+	1.33097i
$155$	−4.90367	−	2.83113i	−0.393872	−	0.227402i
$156$		0			0
$157$	5.55695	+	9.62492i	0.443493	+	0.768152i	0.997946	−	0.0640627i	$-0.0204058\pi$
$157$	5.55695	+	9.62492i	0.443493	+	0.768152i	−0.554453	+	0.832215i	$0.687072\pi$
$158$	10.6885	−	6.17100i	0.850330	−	0.490938i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	17.4457			1.37491
$162$		0			0
$163$	−2.63238			−0.206184			−0.103092	−	0.994672i	$-0.532874\pi$
$163$	−2.63238			−0.206184			−0.103092	+	0.994672i	$0.532874\pi$
$164$	2.75133	−	4.76544i	0.214843	−	0.372119i
$165$		0			0
$166$	2.86275	+	4.95842i	0.222192	+	0.384848i
$167$	2.05504	+	3.55943i	0.159024	+	0.275437i	0.934517	−	0.355919i	$-0.115832\pi$
$167$	2.05504	+	3.55943i	0.159024	+	0.275437i	−0.775493	+	0.631356i	$0.782499\pi$
$168$		0			0
$169$	12.8703	−	22.2920i	0.990021	−	1.71477i
$170$			4.35881i			0.334305i
$171$		0			0
$172$			1.63461i			0.124638i
$173$	2.40803	−	4.17083i	0.183079	−	0.317102i	−0.759849	−	0.650100i	$-0.774727\pi$
$173$	2.40803	−	4.17083i	0.183079	−	0.317102i	0.942928	+	0.332998i	$0.108060\pi$
$174$		0			0
$175$	−4.54797	+	2.62577i	−0.343794	+	0.198490i
$176$	−2.48417	−	2.19748i	−0.187251	−	0.165641i
$177$		0			0
$178$	7.29133	+	4.20965i	0.546508	+	0.315527i
$179$			11.7239i			0.876288i	0.898905	+	0.438144i	$0.144364\pi$
$179$			11.7239i			0.876288i	−0.898905	+	0.438144i	$0.855636\pi$
$180$		0			0
$181$	−11.5905			−0.861515			−0.430757	−	0.902468i	$-0.641754\pi$
$181$	−11.5905			−0.861515			−0.430757	+	0.902468i	$0.641754\pi$
$182$	−16.3433	+	28.3074i	−1.21145	+	2.09829i
$183$		0			0
$184$	−2.87695	+	1.66101i	−0.212092	+	0.122451i
$185$	6.14746	−	3.54924i	0.451970	−	0.260945i
$186$		0			0
$187$	2.88111	−	14.1665i	0.210688	−	1.03596i
$188$			0.739628i			0.0539429i
$189$		0			0
$190$	0.748972			0.0543362
$191$	5.16248	+	2.98056i	0.373544	+	0.215666i	0.675005	−	0.737813i	$-0.264141\pi$
$191$	5.16248	+	2.98056i	0.373544	+	0.215666i	−0.301462	+	0.953478i	$0.597475\pi$
$192$		0			0
$193$	8.79421	−	5.07734i	0.633021	−	0.365475i	−0.148900	−	0.988852i	$-0.547573\pi$
$193$	8.79421	−	5.07734i	0.633021	−	0.365475i	0.781921	+	0.623377i	$0.214240\pi$
$194$	8.16763	+	14.1467i	0.586402	+	1.01568i
$195$		0			0
$196$	10.2894	−	17.8217i	0.734954	−	1.27298i
$197$	25.8739			1.84344			0.921721	−	0.387854i	$-0.126784\pi$
$197$	25.8739			1.84344			0.921721	+	0.387854i	$0.126784\pi$
$198$		0			0
$199$	−19.0396			−1.34968			−0.674842	−	0.737962i	$-0.735788\pi$
$199$	−19.0396			−1.34968			−0.674842	+	0.737962i	$0.735788\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−3.41322	−	5.91188i	−0.240154	−	0.415958i
$203$	−47.3431	+	27.3335i	−3.32283	+	1.91844i
$204$		0			0
$205$	−4.76544	−	2.75133i	−0.332833	−	0.192161i
$206$	−1.07324			−0.0747764
$207$		0			0
$208$		−	6.22419i		−	0.431570i
$209$	−2.43423	−	0.495060i	−0.168379	−	0.0342440i
$210$		0			0
$211$	−14.2014	+	8.19916i	−0.977662	+	0.564454i	−0.901564	−	0.432647i	$-0.857580\pi$
$211$	−14.2014	+	8.19916i	−0.977662	+	0.564454i	−0.0760987	+	0.997100i	$0.524246\pi$
$212$	−2.13443	+	1.23231i	−0.146593	+	0.0846356i
$213$		0			0
$214$	−6.55673	+	11.3566i	−0.448209	+	0.776320i
$215$	1.63461			0.111479
$216$		0			0
$217$		−	29.7357i		−	2.01859i
$218$	11.0222	+	6.36369i	0.746520	+	0.431004i
$219$		0			0
$220$	−2.19748	+	2.48417i	−0.148154	+	0.167483i
$221$	23.4953	−	13.5650i	1.58047	−	0.912483i
$222$		0			0
$223$	−10.9519	+	18.9692i	−0.733393	+	1.27027i	0.222032	+	0.975039i	$0.428731\pi$
$223$	−10.9519	+	18.9692i	−0.733393	+	1.27027i	−0.955425	+	0.295235i	$0.904602\pi$
$224$			5.25154i			0.350884i
$225$		0			0
$226$			6.94242i			0.461803i
$227$	−8.93371	+	15.4736i	−0.592951	+	1.02702i	0.400881	+	0.916130i	$0.368704\pi$
$227$	−8.93371	+	15.4736i	−0.592951	+	1.02702i	−0.993832	+	0.110892i	$0.964629\pi$
$228$		0			0
$229$	−4.31866	−	7.48013i	−0.285385	−	0.494301i	0.687318	−	0.726357i	$-0.258788\pi$
$229$	−4.31866	−	7.48013i	−0.285385	−	0.494301i	−0.972702	+	0.232056i	$0.925455\pi$
$230$	1.66101	+	2.87695i	0.109524	+	0.189700i
$231$		0			0
$232$	5.20486	−	9.01507i	0.341715	−	0.591869i
$233$	−16.6152			−1.08850			−0.544250	−	0.838923i	$-0.683186\pi$
$233$	−16.6152			−1.08850			−0.544250	+	0.838923i	$0.683186\pi$
$234$		0			0
$235$	0.739628			0.0482480
$236$	−0.877216	−	0.506461i	−0.0571019	−	0.0329678i
$237$		0			0
$238$	−19.8237	+	11.4452i	−1.28498	+	0.741885i
$239$	6.12388	+	10.6069i	0.396121	+	0.686102i	0.993244	−	0.116048i	$-0.0370228\pi$
$239$	6.12388	+	10.6069i	0.396121	+	0.686102i	−0.597123	+	0.802150i	$0.703689\pi$
$240$		0			0
$241$	13.4650	+	7.77403i	0.867358	+	0.500770i	0.866469	−	0.499230i	$-0.166384\pi$
$241$	13.4650	+	7.77403i	0.867358	+	0.500770i	0.000888829		1.00000i	$0.499717\pi$
$242$	8.78400	−	6.62128i	0.564657	−	0.425632i
$243$		0			0
$244$			0.924844i			0.0592071i
$245$	−17.8217	−	10.2894i	−1.13859	−	0.657363i
$246$		0			0
$247$	−2.33087	−	4.03719i	−0.148310	−	0.256880i
$248$	2.83113	+	4.90367i	0.179777	+	0.311383i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$		−	6.72650i		−	0.424573i	−0.977207	−	0.212286i	$-0.931909\pi$
$251$		−	6.72650i		−	0.424573i	0.977207	−	0.212286i	$-0.0680910\pi$
$252$		0			0
$253$	−3.49681	−	10.4483i	−0.219842	−	0.656876i
$254$	−2.25868	−	1.30405i	−0.141722	−	0.0818234i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.78608	−	5.64999i	0.610439	−	0.352437i	−0.162698	−	0.986676i	$-0.552020\pi$
$257$	9.78608	−	5.64999i	0.610439	−	0.352437i	0.773137	+	0.634239i	$0.218686\pi$
$258$		0			0
$259$	32.2836	+	18.6390i	2.00601	+	1.15817i
$260$	−6.22419			−0.386008
$261$		0			0
$262$	1.20964			0.0747317
$263$	2.98399	−	5.16843i	0.184001	−	0.318699i	−0.759239	−	0.650812i	$-0.774428\pi$
$263$	2.98399	−	5.16843i	0.184001	−	0.318699i	0.943239	+	0.332114i	$0.107762\pi$
$264$		0			0
$265$	1.23231	+	2.13443i	0.0757004	+	0.131117i
$266$	1.96663	+	3.40630i	0.120582	+	0.208854i
$267$		0			0
$268$	−0.821341	+	1.42261i	−0.0501714	+	0.0868994i
$269$			26.2484i			1.60039i	0.599738	+	0.800197i	$0.295272\pi$
$269$			26.2484i			1.60039i	−0.599738	+	0.800197i	$0.704728\pi$
$270$		0			0
$271$			7.60818i			0.462164i	0.972934	+	0.231082i	$0.0742266\pi$
$271$			7.60818i			0.462164i	−0.972934	+	0.231082i	$0.925773\pi$
$272$	2.17940	−	3.77484i	0.132146	−	0.228883i
$273$		0			0
$274$	−14.8740	+	8.58754i	−0.898574	+	0.518792i
$275$	2.48417	+	2.19748i	0.149801	+	0.132513i
$276$		0			0
$277$	8.68513	+	5.01436i	0.521839	+	0.301284i	0.737687	−	0.675143i	$-0.235918\pi$
$277$	8.68513	+	5.01436i	0.521839	+	0.301284i	−0.215848	+	0.976427i	$0.569252\pi$
$278$			12.2322i			0.733636i
$279$		0			0
$280$	5.25154			0.313840
$281$	−0.989858	+	1.71448i	−0.0590500	+	0.102278i	−0.894039	−	0.447989i	$-0.852140\pi$
$281$	−0.989858	+	1.71448i	−0.0590500	+	0.102278i	0.834989	+	0.550266i	$0.185474\pi$
$282$		0			0
$283$	−19.9164	+	11.4987i	−1.18391	+	0.683530i	−0.956915	−	0.290367i	$-0.906223\pi$
$283$	−19.9164	+	11.4987i	−1.18391	+	0.683530i	−0.226993	+	0.973896i	$0.572889\pi$
$284$	−5.68194	+	3.28047i	−0.337161	+	0.194660i
$285$		0			0
$286$	20.2292	+	4.11410i	1.19618	+	0.243272i
$287$		−	28.8975i		−	1.70576i
$288$		0			0
$289$	1.99921			0.117601
$290$	−9.01507	−	5.20486i	−0.529383	−	0.305640i
$291$		0			0
$292$	8.37500	−	4.83531i	0.490110	−	0.282965i
$293$	−4.62455	−	8.00995i	−0.270169	−	0.467946i	0.698736	−	0.715380i	$-0.253746\pi$
$293$	−4.62455	−	8.00995i	−0.270169	−	0.467946i	−0.968905	+	0.247433i	$0.920413\pi$
$294$		0			0
$295$	−0.506461	+	0.877216i	−0.0294873	+	0.0510735i
$296$	−7.09847			−0.412590
$297$		0			0
$298$	−4.19114			−0.242786
$299$	10.3384	−	17.9067i	0.597887	−	1.03557i
$300$		0			0
$301$	4.29211	+	7.43415i	0.247393	+	0.428497i
$302$	9.01876	−	5.20698i	0.518971	−	0.299628i
$303$		0			0
$304$	−0.648629	−	0.374486i	−0.0372014	−	0.0214783i
$305$	0.924844			0.0529564
$306$		0			0
$307$			4.44897i			0.253916i	0.991908	+	0.126958i	$0.0405214\pi$
$307$			4.44897i			0.253916i	−0.991908	+	0.126958i	$0.959479\pi$
$308$	−17.0680	−	3.47119i	−0.972540	−	0.197790i
$309$		0			0
$310$	4.90367	−	2.83113i	0.278510	−	0.160798i
$311$	16.4416	−	9.49258i	0.932319	−	0.538275i	0.0447747	−	0.998997i	$-0.485743\pi$
$311$	16.4416	−	9.49258i	0.932319	−	0.538275i	0.887544	+	0.460723i	$0.152410\pi$
$312$		0			0
$313$	11.2352	−	19.4599i	0.635049	−	1.09994i	−0.351456	−	0.936205i	$-0.614313\pi$
$313$	11.2352	−	19.4599i	0.635049	−	1.09994i	0.986505	−	0.163733i	$-0.0523535\pi$
$314$	−11.1139			−0.627194
$315$		0			0
$316$			12.3420i			0.694292i
$317$	7.53086	+	4.34795i	0.422975	+	0.244205i	0.696350	−	0.717703i	$-0.254806\pi$
$317$	7.53086	+	4.34795i	0.422975	+	0.244205i	−0.273374	+	0.961908i	$0.588140\pi$
$318$		0			0
$319$	25.8595	+	22.8751i	1.44785	+	1.28076i
$320$	−0.866025	+	0.500000i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	−8.72286	+	15.1084i	−0.486106	+	0.841960i
$323$		−	3.26463i		−	0.181649i
$324$		0			0
$325$			6.22419i			0.345256i
$326$	1.31619	−	2.27971i	0.0728971	−	0.126261i
$327$		0			0
$328$	2.75133	+	4.76544i	0.151917	+	0.263128i
$329$	1.94209	+	3.36381i	0.107071	+	0.185453i
$330$		0			0
$331$	−11.0808	+	19.1925i	−0.609054	+	1.05491i	0.382343	+	0.924021i	$0.375117\pi$
$331$	−11.0808	+	19.1925i	−0.609054	+	1.05491i	−0.991397	+	0.130892i	$0.958216\pi$
$332$	−5.72549			−0.314227
$333$		0			0
$334$	−4.11008			−0.224893
$335$	1.42261	+	0.821341i	0.0777252	+	0.0448747i
$336$		0			0
$337$	−8.20371	+	4.73641i	−0.446884	+	0.258009i	−0.706513	−	0.707700i	$-0.749733\pi$
$337$	−8.20371	+	4.73641i	−0.446884	+	0.258009i	0.259629	+	0.965708i	$0.416400\pi$
$338$	12.8703	+	22.2920i	0.700051	+	1.21252i
$339$		0			0
$340$	−3.77484	−	2.17940i	−0.204719	−	0.118195i
$341$	−17.8087	+	5.96019i	−0.964396	+	0.322763i
$342$		0			0
$343$		−	71.3092i		−	3.85033i
$344$	−1.41561	−	0.817304i	−0.0763247	−	0.0440661i
$345$		0			0
$346$	2.40803	+	4.17083i	0.129456	+	0.224225i
$347$	−14.1436	−	24.4975i	−0.759269	−	1.31509i	−0.943224	−	0.332158i	$-0.892223\pi$
$347$	−14.1436	−	24.4975i	−0.759269	−	1.31509i	0.183955	−	0.982935i	$-0.441110\pi$
$348$		0			0
$349$	21.0255	+	12.1391i	1.12547	+	0.649790i	0.942792	−	0.333382i	$-0.108190\pi$
$349$	21.0255	+	12.1391i	1.12547	+	0.649790i	0.182678	+	0.983173i	$0.441523\pi$
$350$		−	5.25154i		−	0.280707i
$351$		0			0
$352$	3.14515	−	1.05262i	0.167637	−	0.0561046i
$353$	10.3031	+	5.94847i	0.548377	+	0.316605i	0.748467	−	0.663172i	$-0.230790\pi$
$353$	10.3031	+	5.94847i	0.548377	+	0.316605i	−0.200090	+	0.979777i	$0.564124\pi$
$354$		0			0
$355$	3.28047	+	5.68194i	0.174109	+	0.301566i
$356$	−7.29133	+	4.20965i	−0.386439	+	0.223111i
$357$		0			0
$358$	−10.1532	−	5.86196i	−0.536614	−	0.309814i
$359$	−14.4825			−0.764359			−0.382180	−	0.924088i	$-0.624826\pi$
$359$	−14.4825			−0.764359			−0.382180	+	0.924088i	$0.624826\pi$
$360$		0			0
$361$	18.4390			0.970476
$362$	5.79525	−	10.0377i	0.304591	−	0.527568i
$363$		0			0
$364$	−16.3433	−	28.3074i	−0.856622	−	1.48371i
$365$	−4.83531	−	8.37500i	−0.253092	−	0.438368i
$366$		0			0
$367$	4.14790	−	7.18437i	0.216519	−	0.375021i	−0.737223	−	0.675650i	$-0.763863\pi$
$367$	4.14790	−	7.18437i	0.216519	−	0.375021i	0.953741	+	0.300629i	$0.0971965\pi$
$368$		−	3.32202i		−	0.173172i
$369$		0			0
$370$			7.09847i			0.369032i
$371$	−6.47155	+	11.2090i	−0.335986	+	0.581945i
$372$		0			0
$373$	10.5518	−	6.09206i	0.546349	−	0.315435i	−0.201299	−	0.979530i	$-0.564516\pi$
$373$	10.5518	−	6.09206i	0.546349	−	0.315435i	0.747648	+	0.664095i	$0.231183\pi$
$374$	10.8280	+	9.57838i	0.559904	+	0.495286i
$375$		0			0
$376$	−0.640537	−	0.369814i	−0.0330332	−	0.0190717i
$377$			64.7920i			3.33696i
$378$		0			0
$379$	−22.9047			−1.17653			−0.588267	−	0.808666i	$-0.700190\pi$
$379$	−22.9047			−1.17653			−0.588267	+	0.808666i	$0.700190\pi$
$380$	−0.374486	+	0.648629i	−0.0192107	+	0.0332740i
$381$		0			0
$382$	−5.16248	+	2.98056i	−0.264135	+	0.152499i
$383$	−16.5551	+	9.55806i	−0.845924	+	0.488394i	−0.859273	−	0.511517i	$-0.829084\pi$
$383$	−16.5551	+	9.55806i	−0.845924	+	0.488394i	0.0133497	+	0.999911i	$0.495751\pi$
$384$		0			0
$385$	−3.47119	+	17.0680i	−0.176908	+	0.869866i
$386$			10.1547i			0.516859i
$387$		0			0
$388$	−16.3353			−0.829297
$389$	−26.6198	−	15.3689i	−1.34968	−	0.779235i	−0.361472	−	0.932383i	$-0.617726\pi$
$389$	−26.6198	−	15.3689i	−1.34968	−	0.779235i	−0.988203	+	0.153148i	$0.951059\pi$
$390$		0			0
$391$	12.5401	−	7.24002i	0.634179	−	0.366143i
$392$	10.2894	+	17.8217i	0.519691	+	0.900131i
$393$		0			0
$394$	−12.9370	+	22.4075i	−0.651755	+	1.12887i
$395$	12.3420			0.620993
$396$		0			0
$397$	−19.1437			−0.960796			−0.480398	−	0.877051i	$-0.659508\pi$
$397$	−19.1437			−0.960796			−0.480398	+	0.877051i	$0.659508\pi$
$398$	9.51981	−	16.4888i	0.477185	−	0.826509i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	1.63962	−	0.946638i	0.0818789	−	0.0472728i	−0.458502	−	0.888694i	$-0.651614\pi$
$401$	1.63962	−	0.946638i	0.0818789	−	0.0472728i	0.540380	+	0.841421i	$0.318280\pi$
$402$		0			0
$403$	−30.5214	−	17.6215i	−1.52038	−	0.877790i
$404$	6.82645			0.339628
$405$		0			0
$406$		−	54.6670i		−	2.71308i
$407$	4.69199	−	23.0707i	0.232573	−	1.14357i
$408$		0			0
$409$	−3.27154	+	1.88883i	−0.161767	+	0.0933965i	−0.578698	−	0.815542i	$-0.696439\pi$
$409$	−3.27154	+	1.88883i	−0.161767	+	0.0933965i	0.416931	+	0.908938i	$0.363106\pi$
$410$	4.76544	−	2.75133i	0.235349	−	0.135879i
$411$		0			0
$412$	0.536621	−	0.929456i	0.0264374	−	0.0457910i
$413$	−5.31940			−0.261751
$414$		0			0
$415$			5.72549i			0.281053i
$416$	5.39031	+	3.11210i	0.264282	+	0.152583i
$417$		0			0
$418$	1.64585	−	1.86057i	0.0805011	−	0.0910036i
$419$	16.4092	−	9.47385i	0.801641	−	0.462828i	−0.0424036	−	0.999101i	$-0.513502\pi$
$419$	16.4092	−	9.47385i	0.801641	−	0.462828i	0.844045	+	0.536273i	$0.180168\pi$
$420$		0			0
$421$	4.89817	−	8.48389i	0.238722	−	0.413479i	−0.721626	−	0.692284i	$-0.756605\pi$
$421$	4.89817	−	8.48389i	0.238722	−	0.413479i	0.960348	+	0.278804i	$0.0899381\pi$
$422$		−	16.3983i		−	0.798258i
$423$		0			0
$424$		−	2.46463i		−	0.119693i
$425$	−2.17940	+	3.77484i	−0.105717	+	0.183107i
$426$		0			0
$427$	2.42843	+	4.20616i	0.117520	+	0.203551i
$428$	−6.55673	−	11.3566i	−0.316931	−	0.548941i
$429$		0			0
$430$	−0.817304	+	1.41561i	−0.0394139	+	0.0682669i
$431$	20.6446			0.994417			0.497209	−	0.867631i	$-0.334358\pi$
$431$	20.6446			0.994417			0.497209	+	0.867631i	$0.334358\pi$
$432$		0			0
$433$	19.8184			0.952411			0.476206	−	0.879334i	$-0.342012\pi$
$433$	19.8184			0.952411			0.476206	+	0.879334i	$0.342012\pi$
$434$	25.7518	+	14.8678i	1.23613	+	0.713678i
$435$		0			0
$436$	−11.0222	+	6.36369i	−0.527870	+	0.304766i
$437$	−1.24405	−	2.15476i	−0.0595109	−	0.103076i
$438$		0			0
$439$	16.5483	+	9.55418i	0.789809	+	0.455996i	0.839895	−	0.542749i	$-0.182616\pi$
$439$	16.5483	+	9.55418i	0.789809	+	0.455996i	−0.0500866	+	0.998745i	$0.515950\pi$
$440$	−1.05262	−	3.14515i	−0.0501815	−	0.149939i
$441$		0			0
$442$			27.1301i			1.29045i
$443$	0.733684	+	0.423593i	0.0348584	+	0.0201255i	0.517328	−	0.855787i	$-0.326927\pi$
$443$	0.733684	+	0.423593i	0.0348584	+	0.0201255i	−0.482470	+	0.875913i	$0.660260\pi$
$444$		0			0
$445$	4.20965	+	7.29133i	0.199556	+	0.345642i
$446$	−10.9519	−	18.9692i	−0.518587	−	0.898219i
$447$		0			0
$448$	−4.54797	−	2.62577i	−0.214871	−	0.124056i
$449$		−	30.6594i		−	1.44690i	−0.690374	−	0.723452i	$-0.742554\pi$
$449$		−	30.6594i		−	1.44690i	0.690374	−	0.723452i	$-0.257446\pi$
$450$		0			0
$451$	−17.3067	+	5.79219i	−0.814942	+	0.272744i
$452$	−6.01231	−	3.47121i	−0.282795	−	0.163272i
$453$		0			0
$454$	−8.93371	−	15.4736i	−0.419280	−	0.726214i
$455$	−28.3074	+	16.3433i	−1.32707	+	0.766186i
$456$		0			0
$457$	34.5586	+	19.9524i	1.61658	+	0.933333i	0.987796	+	0.155754i	$0.0497808\pi$
$457$	34.5586	+	19.9524i	1.61658	+	0.933333i	0.628785	+	0.777579i	$0.283553\pi$
$458$	8.63731			0.403595
$459$		0			0
$460$	−3.32202			−0.154890
$461$	20.0031	−	34.6465i	0.931639	−	1.61365i	0.151120	−	0.988515i	$-0.451712\pi$
$461$	20.0031	−	34.6465i	0.931639	−	1.61365i	0.780520	−	0.625131i	$-0.214955\pi$
$462$		0			0
$463$	0.670343	+	1.16107i	0.0311535	+	0.0539594i	0.881182	−	0.472778i	$-0.156749\pi$
$463$	0.670343	+	1.16107i	0.0311535	+	0.0539594i	−0.850028	+	0.526737i	$0.823415\pi$
$464$	5.20486	+	9.01507i	0.241629	+	0.418514i
$465$		0			0
$466$	8.30762	−	14.3892i	0.384843	−	0.666567i
$467$			4.43805i			0.205369i	0.994714	+	0.102684i	$0.0327431\pi$
$467$			4.43805i			0.205369i	−0.994714	+	0.102684i	$0.967257\pi$
$468$		0			0
$469$			8.62662i			0.398340i
$470$	−0.369814	+	0.640537i	−0.0170583	+	0.0295458i
$471$		0			0
$472$	0.877216	−	0.506461i	0.0403771	−	0.0233117i
$473$	3.59201	−	4.06064i	0.165161	−	0.186709i
$474$		0			0
$475$	0.648629	+	0.374486i	0.0297611	+	0.0171826i
$476$		−	22.8905i		−	1.04918i
$477$		0			0
$478$	−12.2478			−0.560200
$479$	−10.8806	+	18.8457i	−0.497145	+	0.861080i	−0.999995	−	0.00329348i	$-0.998952\pi$
$479$	−10.8806	+	18.8457i	−0.497145	+	0.861080i	0.502850	+	0.864374i	$0.332285\pi$
$480$		0			0
$481$	38.2629	−	22.0911i	1.74464	−	1.00727i
$482$	−13.4650	+	7.77403i	−0.613315	+	0.354098i
$483$		0			0
$484$	1.34220	+	10.9178i	0.0610090	+	0.496264i
$485$			16.3353i			0.741746i
$486$		0			0
$487$	−2.19251			−0.0993520			−0.0496760	−	0.998765i	$-0.515819\pi$
$487$	−2.19251			−0.0993520			−0.0496760	+	0.998765i	$0.515819\pi$
$488$	−0.800939	−	0.462422i	−0.0362568	−	0.0209329i
$489$		0			0
$490$	17.8217	−	10.2894i	0.805102	−	0.464826i
$491$	16.6168	+	28.7811i	0.749904	+	1.29887i	0.947868	+	0.318663i	$0.103234\pi$
$491$	16.6168	+	28.7811i	0.749904	+	1.29887i	−0.197964	+	0.980209i	$0.563433\pi$
$492$		0			0
$493$	−22.6870	+	39.2950i	−1.02177	+	1.76976i
$494$	4.66175			0.209742
$495$		0			0
$496$	−5.66227			−0.254243
$497$	−17.2275	+	29.8389i	−0.772760	+	1.33846i
$498$		0			0
$499$	−11.7512	−	20.3537i	−0.526057	−	0.911157i	−0.999539	−	0.0303538i	$-0.990337\pi$
$499$	−11.7512	−	20.3537i	−0.526057	−	0.911157i	0.473482	−	0.880803i	$-0.342997\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$		0			0
$502$	5.82532	+	3.36325i	0.259997	+	0.150109i
$503$	−1.96441			−0.0875886			−0.0437943	−	0.999041i	$-0.513945\pi$
$503$	−1.96441			−0.0875886			−0.0437943	+	0.999041i	$0.513945\pi$
$504$		0			0
$505$		−	6.82645i		−	0.303773i
$506$	10.7969	+	2.19580i	0.479979	+	0.0976154i
$507$		0			0
$508$	2.25868	−	1.30405i	0.100213	−	0.0578579i
$509$	−0.489274	+	0.282483i	−0.0216867	+	0.0125208i	−0.510804	−	0.859697i	$-0.670652\pi$
$509$	−0.489274	+	0.282483i	−0.0216867	+	0.0125208i	0.489117	+	0.872218i	$0.337319\pi$
$510$		0			0
$511$	25.3928	−	43.9817i	1.12331	−	1.94564i
$512$	1.00000			0.0441942
$513$		0			0
$514$			11.3000i			0.498421i
$515$	−0.929456	−	0.536621i	−0.0409567	−	0.0236464i
$516$		0			0
$517$	1.62532	−	1.83736i	0.0714813	−	0.0808071i
$518$	−32.2836	+	18.6390i	−1.41846	+	0.818949i
$519$		0			0
$520$	3.11210	−	5.39031i	0.136474	−	0.236381i
$521$			7.99680i			0.350346i	0.984538	+	0.175173i	$0.0560485\pi$
$521$			7.99680i			0.350346i	−0.984538	+	0.175173i	$0.943951\pi$
$522$		0			0
$523$			23.4207i			1.02411i	0.858951	+	0.512057i	$0.171116\pi$
$523$			23.4207i			1.02411i	−0.858951	+	0.512057i	$0.828884\pi$
$524$	−0.604819	+	1.04758i	−0.0264217	+	0.0457636i
$525$		0			0
$526$	2.98399	+	5.16843i	0.130108	+	0.225354i
$527$	−12.3404	−	21.3742i	−0.537555	−	0.931073i
$528$		0			0
$529$	−5.98210	+	10.3613i	−0.260092	+	0.450492i
$530$	−2.46463			−0.107057
$531$		0			0
$532$	−3.93326			−0.170528
$533$	−29.6610	−	17.1248i	−1.28476	−	0.741758i
$534$		0			0
$535$	−11.3566	+	6.55673i	−0.490988	+	0.283472i
$536$	−0.821341	−	1.42261i	−0.0354765	−	0.0614472i
$537$		0			0
$538$	−22.7318	−	13.1242i	−0.980037	−	0.565825i
$539$	−64.7232	+	21.6615i	−2.78783	+	0.933026i
$540$		0			0
$541$			3.02049i			0.129861i	0.997890	+	0.0649304i	$0.0206825\pi$
$541$			3.02049i			0.129861i	−0.997890	+	0.0649304i	$0.979317\pi$
$542$	−6.58888	−	3.80409i	−0.283017	−	0.163400i
$543$		0			0
$544$	2.17940	+	3.77484i	0.0934412	+	0.161845i
$545$	6.36369	+	11.0222i	0.272591	+	0.472141i
$546$		0			0
$547$	−21.5408	−	12.4366i	−0.921017	−	0.531750i	−0.0370579	−	0.999313i	$-0.511799\pi$
$547$	−21.5408	−	12.4366i	−0.921017	−	0.531750i	−0.883959	+	0.467563i	$0.845132\pi$
$548$		−	17.1751i		−	0.733683i
$549$		0			0
$550$	−3.14515	+	1.05262i	−0.134110	+	0.0448837i
$551$	6.75204	+	3.89829i	0.287647	+	0.166073i
$552$		0			0
$553$	32.4073	+	56.1310i	1.37810	+	2.38693i
$554$	−8.68513	+	5.01436i	−0.368996	+	0.213040i
$555$		0			0
$556$	−10.5934	−	6.11608i	−0.449259	−	0.259380i
$557$	3.70445			0.156963			0.0784814	−	0.996916i	$-0.474993\pi$
$557$	3.70445			0.156963			0.0784814	+	0.996916i	$0.474993\pi$
$558$		0			0
$559$	10.1741			0.430319
$560$	−2.62577	+	4.54797i	−0.110959	+	0.192187i
$561$		0			0
$562$	−0.989858	−	1.71448i	−0.0417546	−	0.0723211i
$563$	−13.9825	−	24.2185i	−0.589294	−	1.02069i	−0.994325	−	0.106384i	$-0.966073\pi$
$563$	−13.9825	−	24.2185i	−0.589294	−	1.02069i	0.405031	−	0.914303i	$-0.367261\pi$
$564$		0			0
$565$	−3.47121	+	6.01231i	−0.146035	+	0.252940i
$566$		−	22.9975i		−	0.966657i
$567$		0			0
$568$		−	6.56094i		−	0.275291i
$569$	5.20091	−	9.00824i	0.218034	−	0.377645i	−0.736173	−	0.676793i	$-0.763369\pi$
$569$	5.20091	−	9.00824i	0.218034	−	0.377645i	0.954207	+	0.299148i	$0.0967024\pi$
$570$		0			0
$571$	−25.5328	+	14.7414i	−1.06852	+	0.616908i	−0.927775	−	0.373139i	$-0.878281\pi$
$571$	−25.5328	+	14.7414i	−1.06852	+	0.616908i	−0.140740	+	0.990047i	$0.544948\pi$
$572$	−13.6775	+	15.4619i	−0.571885	+	0.646496i
$573$		0			0
$574$	25.0259	+	14.4487i	1.04456	+	0.603078i
$575$			3.32202i			0.138538i
$576$		0			0
$577$	−11.3733			−0.473475			−0.236738	−	0.971574i	$-0.576078\pi$
$577$	−11.3733			−0.473475			−0.236738	+	0.971574i	$0.576078\pi$
$578$	−0.999607	+	1.73137i	−0.0415782	+	0.0720155i
$579$		0			0
$580$	9.01507	−	5.20486i	0.374331	−	0.216120i
$581$	−26.0394	+	15.0338i	−1.08030	+	0.623709i
$582$		0			0
$583$	8.01026	+	1.62908i	0.331751	+	0.0674697i
$584$			9.67062i			0.400173i
$585$		0			0
$586$	9.24909			0.382076
$587$	18.1289	+	10.4667i	0.748259	+	0.432007i	0.825064	−	0.565039i	$-0.191139\pi$
$587$	18.1289	+	10.4667i	0.748259	+	0.432007i	−0.0768057	+	0.997046i	$0.524472\pi$
$588$		0			0
$589$	−3.67271	+	2.12044i	−0.151331	+	0.0873712i
$590$	−0.506461	−	0.877216i	−0.0208507	−	0.0361144i
$591$		0			0
$592$	3.54924	−	6.14746i	0.145873	−	0.252659i
$593$	39.7650			1.63295			0.816476	−	0.577380i	$-0.195925\pi$
$593$	39.7650			1.63295			0.816476	+	0.577380i	$0.195925\pi$
$594$		0			0
$595$	−22.8905			−0.938418
$596$	2.09557	−	3.62963i	0.0858378	−	0.148675i
$597$		0			0
$598$	10.3384	+	17.9067i	0.422770	+	0.732259i
$599$	30.0865	−	17.3704i	1.22930	−	0.709737i	0.262416	−	0.964955i	$-0.415481\pi$
$599$	30.0865	−	17.3704i	1.22930	−	0.709737i	0.966883	+	0.255218i	$0.0821473\pi$
$600$		0			0
$601$	−22.3427	−	12.8995i	−0.911376	−	0.526183i	−0.0305024	−	0.999535i	$-0.509711\pi$
$601$	−22.3427	−	12.8995i	−0.911376	−	0.526183i	−0.880874	+	0.473352i	$0.843044\pi$
$602$	−8.58421			−0.349866
$603$		0			0
$604$			10.4140i			0.423738i
$605$	10.9178	−	1.34220i	0.443872	−	0.0545681i
$606$		0			0
$607$	29.9048	−	17.2656i	1.21380	−	0.700788i	0.250215	−	0.968190i	$-0.419499\pi$
$607$	29.9048	−	17.2656i	1.21380	−	0.700788i	0.963585	+	0.267403i	$0.0861654\pi$
$608$	0.648629	−	0.374486i	0.0263054	−	0.0151874i
$609$		0			0
$610$	−0.462422	+	0.800939i	−0.0187229	+	0.0324291i
$611$	4.60359			0.186241
$612$		0			0
$613$		−	6.59175i		−	0.266238i	−0.991100	−	0.133119i	$-0.957501\pi$
$613$		−	6.59175i		−	0.266238i	0.991100	−	0.133119i	$-0.0424993\pi$
$614$	−3.85292	−	2.22448i	−0.155491	−	0.0897729i
$615$		0			0
$616$	11.5401	−	13.0457i	0.464966	−	0.525627i
$617$	−22.5798	+	13.0364i	−0.909027	+	0.524827i	−0.880118	−	0.474755i	$-0.842537\pi$
$617$	−22.5798	+	13.0364i	−0.909027	+	0.524827i	−0.0289089	+	0.999582i	$0.509203\pi$
$618$		0			0
$619$	8.53992	−	14.7916i	0.343248	−	0.594524i	−0.641786	−	0.766884i	$-0.721806\pi$
$619$	8.53992	−	14.7916i	0.343248	−	0.594524i	0.985034	+	0.172361i	$0.0551394\pi$
$620$			5.66227i			0.227402i
$621$		0			0
$622$			18.9852i			0.761235i
$623$	−22.1072	+	38.2907i	−0.885704	+	1.53408i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	11.2352	+	19.4599i	0.449048	+	0.777773i
$627$		0			0
$628$	5.55695	−	9.62492i	0.221746	−	0.384076i
$629$	30.9409			1.23369
$630$		0			0
$631$	−40.0533			−1.59450			−0.797248	−	0.603651i	$-0.793712\pi$
$631$	−40.0533			−1.59450			−0.797248	+	0.603651i	$0.793712\pi$
$632$	−10.6885	−	6.17100i	−0.425165	−	0.245469i
$633$		0			0
$634$	−7.53086	+	4.34795i	−0.299089	+	0.172679i
$635$	−1.30405	−	2.25868i	−0.0517497	−	0.0896331i
$636$		0			0
$637$	−110.926	−	64.0429i	−4.39503	−	2.53747i
$638$	−32.7402	+	10.9574i	−1.29620	+	0.433809i
$639$		0			0
$640$		−	1.00000i		−	0.0395285i
$641$	−22.5994	−	13.0478i	−0.892623	−	0.515356i	−0.0178236	−	0.999841i	$-0.505674\pi$
$641$	−22.5994	−	13.0478i	−0.892623	−	0.515356i	−0.874800	+	0.484485i	$0.839007\pi$
$642$		0			0
$643$	−13.5959	−	23.5487i	−0.536168	−	0.928671i	−0.999106	−	0.0422797i	$-0.986538\pi$
$643$	−13.5959	−	23.5487i	−0.536168	−	0.928671i	0.462938	−	0.886391i	$-0.346795\pi$
$644$	−8.72286	−	15.1084i	−0.343729	−	0.595356i
$645$		0			0
$646$	2.82725	+	1.63231i	0.111237	+	0.0642225i
$647$		−	49.6172i		−	1.95065i	−0.220766	−	0.975327i	$-0.570856\pi$
$647$		−	49.6172i		−	1.95065i	0.220766	−	0.975327i	$-0.429144\pi$
$648$		0			0
$649$	1.06622	+	3.18579i	0.0418527	+	0.125053i
$650$	−5.39031	−	3.11210i	−0.211425	−	0.122066i
$651$		0			0
$652$	1.31619	+	2.27971i	0.0515460	+	0.0892803i
$653$	−11.5265	+	6.65480i	−0.451065	+	0.260422i	−0.708280	−	0.705932i	$-0.750528\pi$
$653$	−11.5265	+	6.65480i	−0.451065	+	0.260422i	0.257215	+	0.966354i	$0.417195\pi$
$654$		0			0
$655$	1.04758	+	0.604819i	0.0409322	+	0.0236322i
$656$	−5.50266			−0.214843
$657$		0			0
$658$	−3.88419			−0.151421
$659$	0.890304	−	1.54205i	0.0346813	−	0.0600698i	−0.848164	−	0.529734i	$-0.822292\pi$
$659$	0.890304	−	1.54205i	0.0346813	−	0.0600698i	0.882845	+	0.469664i	$0.155625\pi$
$660$		0			0
$661$	−1.07164	−	1.85613i	−0.0416818	−	0.0721950i	0.844432	−	0.535663i	$-0.179938\pi$
$661$	−1.07164	−	1.85613i	−0.0416818	−	0.0721950i	−0.886114	+	0.463468i	$0.846605\pi$
$662$	−11.0808	−	19.1925i	−0.430666	−	0.745936i
$663$		0			0
$664$	2.86275	−	4.95842i	0.111096	−	0.192424i
$665$			3.93326i			0.152525i
$666$		0			0
$667$			34.5812i			1.33899i
$668$	2.05504	−	3.55943i	0.0795119	−	0.137719i
$669$		0			0
$670$	−1.42261	+	0.821341i	−0.0549600	+	0.0317312i
$671$	2.03232	−	2.29747i	0.0784570	−	0.0886929i
$672$		0			0
$673$	−0.768862	−	0.443903i	−0.0296375	−	0.0171112i	0.485108	−	0.874454i	$-0.338780\pi$
$673$	−0.768862	−	0.443903i	−0.0296375	−	0.0171112i	−0.514746	+	0.857343i	$0.672114\pi$
$674$		−	9.47283i		−	0.364880i
$675$		0			0
$676$	−25.7406			−0.990021
$677$	0.0859441	−	0.148859i	0.00330310	−	0.00572114i	−0.864369	−	0.502858i	$-0.832282\pi$
$677$	0.0859441	−	0.148859i	0.00330310	−	0.00572114i	0.867672	+	0.497137i	$0.165615\pi$
$678$		0			0
$679$	−74.2923	+	42.8927i	−2.85108	+	1.64607i
$680$	3.77484	−	2.17940i	0.144758	−	0.0835763i
$681$		0			0
$682$	3.74268	−	18.4029i	0.143315	−	0.704683i
$683$			37.6674i			1.44130i	0.693297	+	0.720652i	$0.256157\pi$
$683$			37.6674i			1.44130i	−0.693297	+	0.720652i	$0.743843\pi$
$684$		0			0
$685$	−17.1751			−0.656226
$686$	61.7556	+	35.6546i	2.35784	+	1.36130i
$687$		0			0
$688$	1.41561	−	0.817304i	0.0539697	−	0.0311594i
$689$	7.67015	+	13.2851i	0.292210	+	0.506122i
$690$		0			0
$691$	22.4912	−	38.9559i	0.855606	−	1.48195i	−0.0204751	−	0.999790i	$-0.506518\pi$
$691$	22.4912	−	38.9559i	0.855606	−	1.48195i	0.876081	−	0.482163i	$-0.160149\pi$
$692$	−4.81606			−0.183079
$693$		0			0
$694$	28.2872			1.07377
$695$	−6.11608	+	10.5934i	−0.231996	+	0.401829i
$696$		0			0
$697$	−11.9925	−	20.7717i	−0.454249	−	0.786783i
$698$	−21.0255	+	12.1391i	−0.795827	+	0.459471i
$699$		0			0
$700$	4.54797	+	2.62577i	0.171897	+	0.0992448i
$701$	18.7504			0.708191			0.354095	−	0.935209i	$-0.384789\pi$
$701$	18.7504			0.708191			0.354095	+	0.935209i	$0.384789\pi$
$702$		0			0
$703$		−	5.31656i		−	0.200518i
$704$	−0.660985	+	3.25009i	−0.0249118	+	0.122492i
$705$		0			0
$706$	−10.3031	+	5.94847i	−0.387761	+	0.223874i
$707$	31.0465	−	17.9247i	1.16762	−	0.674127i
$708$		0			0
$709$	−0.424093	+	0.734550i	−0.0159271	+	0.0275866i	−0.873879	−	0.486143i	$-0.838403\pi$
$709$	−0.424093	+	0.734550i	−0.0159271	+	0.0275866i	0.857952	+	0.513730i	$0.171737\pi$
$710$	−6.56094			−0.246228
$711$		0			0
$712$		−	8.41930i		−	0.315527i
$713$	−16.2901	−	9.40507i	−0.610068	−	0.352223i
$714$		0			0
$715$	15.4619	+	13.6775i	0.578244	+	0.511510i
$716$	10.1532	−	5.86196i	0.379444	−	0.219072i
$717$		0			0
$718$	7.24127	−	12.5422i	0.270242	−	0.468072i
$719$			11.8199i			0.440809i	0.975409	+	0.220405i	$0.0707378\pi$
$719$			11.8199i			0.440809i	−0.975409	+	0.220405i	$0.929262\pi$
$720$		0			0
$721$		−	5.63618i		−	0.209902i
$722$	−9.21952	+	15.9687i	−0.343115	+	0.594293i
$723$		0			0
$724$	5.79525	+	10.0377i	0.215379	+	0.373047i
$725$	−5.20486	−	9.01507i	−0.193303	−	0.334811i
$726$		0			0
$727$	18.9116	−	32.7559i	0.701394	−	1.21485i	−0.266583	−	0.963812i	$-0.585895\pi$
$727$	18.9116	−	32.7559i	0.701394	−	1.21485i	0.967977	−	0.251038i	$-0.0807720\pi$
$728$	32.6866			1.21145
$729$		0			0
$730$	9.67062			0.357926
$731$	6.17038	+	3.56247i	0.228220	+	0.131763i
$732$		0			0
$733$	6.67442	−	3.85348i	0.246525	−	0.142332i	−0.371647	−	0.928374i	$-0.621207\pi$
$733$	6.67442	−	3.85348i	0.246525	−	0.142332i	0.618172	+	0.786043i	$0.287873\pi$
$734$	4.14790	+	7.18437i	0.153102	+	0.265180i
$735$		0			0
$736$	2.87695	+	1.66101i	0.106046	+	0.0612256i
$737$	5.16649	−	1.72911i	0.190310	−	0.0636927i
$738$		0			0
$739$		−	38.3377i		−	1.41027i	−0.709071	−	0.705137i	$-0.750885\pi$
$739$		−	38.3377i		−	1.41027i	0.709071	−	0.705137i	$-0.249115\pi$
$740$	−6.14746	−	3.54924i	−0.225985	−	0.130472i
$741$		0			0
$742$	−6.47155	−	11.2090i	−0.237578	−	0.411497i
$743$	−8.40585	−	14.5594i	−0.308381	−	0.534131i	0.669628	−	0.742697i	$-0.266454\pi$
$743$	−8.40585	−	14.5594i	−0.308381	−	0.534131i	−0.978008	+	0.208566i	$0.933120\pi$
$744$		0			0
$745$	−3.62963	−	2.09557i	−0.132979	−	0.0767757i
$746$			12.1841i			0.446092i
$747$		0			0
$748$	−13.7091	+	4.58815i	−0.501255	+	0.167759i
$749$	−59.6396	−	34.4330i	−2.17918	−	1.25815i
$750$		0			0
$751$	−18.0406	−	31.2472i	−0.658310	−	1.14023i	−0.981053	−	0.193740i	$-0.937938\pi$
$751$	−18.0406	−	31.2472i	−0.658310	−	1.14023i	0.322743	−	0.946487i	$-0.395395\pi$
$752$	0.640537	−	0.369814i	0.0233580	−	0.0134857i
$753$		0			0
$754$	−56.1115	−	32.3960i	−2.04346	−	1.17979i
$755$	10.4140			0.379003
$756$		0			0
$757$	−26.6674			−0.969242			−0.484621	−	0.874724i	$-0.661042\pi$
$757$	−26.6674			−0.969242			−0.484621	+	0.874724i	$0.661042\pi$
$758$	11.4523	−	19.8360i	0.415968	−	0.720478i
$759$		0			0
$760$	−0.374486	−	0.648629i	−0.0135840	−	0.0235282i
$761$	−5.58743	−	9.67771i	−0.202544	−	0.350817i	0.746803	−	0.665045i	$-0.231588\pi$
$761$	−5.58743	−	9.67771i	−0.202544	−	0.350817i	−0.949348	+	0.314228i	$0.898254\pi$
$762$		0			0
$763$	−33.4192	+	57.8838i	−1.20986	+	2.09553i
$764$		−	5.96111i		−	0.215666i
$765$		0			0
$766$		−	19.1161i		−	0.690694i
$767$	−3.15231	+	5.45996i	−0.113823	+	0.197148i
$768$		0			0
$769$	40.0727	−	23.1360i	1.44506	−	0.834304i	0.446877	−	0.894596i	$-0.352536\pi$
$769$	40.0727	−	23.1360i	1.44506	−	0.834304i	0.998181	+	0.0602912i	$0.0192029\pi$
$770$	−13.0457	−	11.5401i	−0.470135	−	0.415878i
$771$		0			0
$772$	−8.79421	−	5.07734i	−0.316510	−	0.182737i
$773$			3.86173i			0.138897i	0.997586	+	0.0694483i	$0.0221239\pi$
$773$			3.86173i			0.138897i	−0.997586	+	0.0694483i	$0.977876\pi$
$774$		0			0
$775$	5.66227			0.203395
$776$	8.16763	−	14.1467i	0.293201	−	0.507839i
$777$		0			0
$778$	26.6198	−	15.3689i	0.954364	−	0.551003i
$779$	−3.56919	+	2.06067i	−0.127879	+	0.0738312i
$780$		0			0
$781$	21.3237	+	4.33668i	0.763020	+	0.155179i
$782$			14.4800i			0.517805i
$783$		0			0
$784$	−20.5787			−0.734954
$785$	−9.62492	−	5.55695i	−0.343528	−	0.198336i
$786$		0			0
$787$	16.4345	−	9.48845i	0.585826	−	0.338227i	−0.177619	−	0.984099i	$-0.556840\pi$
$787$	16.4345	−	9.48845i	0.585826	−	0.338227i	0.763445	+	0.645872i	$0.223506\pi$
$788$	−12.9370	−	22.4075i	−0.460860	−	0.798234i
$789$		0			0
$790$	−6.17100	+	10.6885i	−0.219554	+	0.380279i
$791$	−36.4584			−1.29631
$792$		0			0
$793$	5.75641			0.204416
$794$	9.57186	−	16.5789i	0.339693	−	0.588365i
$795$		0			0
$796$	9.51981	+	16.4888i	0.337421	+	0.584430i
$797$	−22.5593	+	13.0246i	−0.799091	+	0.461355i	−0.843153	−	0.537673i	$-0.819303\pi$
$797$	−22.5593	+	13.0246i	−0.799091	+	0.461355i	0.0440623	+	0.999029i	$0.485970\pi$
$798$		0			0
$799$	2.79198	+	1.61195i	0.0987731	+	0.0570266i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$			1.89328i			0.0668539i
$803$	−31.4304	−	6.39214i	−1.10916	−	0.225574i
$804$		0			0
$805$	−15.1084	+	8.72286i	−0.532502	+	0.307440i
$806$	30.5214	−	17.6215i	1.07507	−	0.620692i
$807$		0			0
$808$	−3.41322	+	5.91188i	−0.120077	+	0.207979i
$809$	19.6768			0.691800			0.345900	−	0.938271i	$-0.387574\pi$
$809$	19.6768			0.691800			0.345900	+	0.938271i	$0.387574\pi$
$810$		0			0
$811$			21.6225i			0.759270i	0.925136	+	0.379635i	$0.123950\pi$
$811$			21.6225i			0.759270i	−0.925136	+	0.379635i	$0.876050\pi$
$812$	47.3431	+	27.3335i	1.66142	+	0.959219i
$813$		0			0
$814$	17.6338	+	15.5987i	0.618065	+	0.546735i
$815$	2.27971	−	1.31619i	0.0798547	−	0.0461042i
$816$		0			0
$817$	0.612138	−	1.06025i	0.0214160	−	0.0370936i
$818$		−	3.77765i		−	0.132083i
$819$		0			0
$820$			5.50266i			0.192161i
$821$	0.412392	−	0.714283i	0.0143926	−	0.0249287i	−0.858739	−	0.512413i	$-0.828752\pi$
$821$	0.412392	−	0.714283i	0.0143926	−	0.0249287i	0.873132	+	0.487484i	$0.162085\pi$
$822$		0			0
$823$	−18.7187	−	32.4217i	−0.652492	−	1.13015i	−0.982516	−	0.186176i	$-0.940390\pi$
$823$	−18.7187	−	32.4217i	−0.652492	−	1.13015i	0.330025	−	0.943972i	$-0.392943\pi$
$824$	0.536621	+	0.929456i	0.0186941	+	0.0323791i
$825$		0			0
$826$	2.65970	−	4.60674i	0.0925428	−	0.160289i
$827$	−37.1032			−1.29020			−0.645102	−	0.764096i	$-0.723185\pi$
$827$	−37.1032			−1.29020			−0.645102	+	0.764096i	$0.723185\pi$
$828$		0			0
$829$	−36.7868			−1.27766			−0.638829	−	0.769349i	$-0.720581\pi$
$829$	−36.7868			−1.27766			−0.638829	+	0.769349i	$0.720581\pi$
$830$	−4.95842	−	2.86275i	−0.172109	−	0.0993674i
$831$		0			0
$832$	−5.39031	+	3.11210i	−0.186875	+	0.107892i
$833$	−44.8493	−	77.6813i	−1.55394	−	2.69150i
$834$		0			0
$835$	−3.55943	−	2.05504i	−0.123179	−	0.0711176i
$836$	0.788380	+	2.35563i	0.0272667	+	0.0814713i
$837$		0			0
$838$			18.9477i			0.654537i
$839$	−13.0381	−	7.52757i	−0.450126	−	0.259880i	0.257757	−	0.966210i	$-0.417016\pi$
$839$	−13.0381	−	7.52757i	−0.450126	−	0.259880i	−0.707883	+	0.706329i	$0.750350\pi$
$840$		0			0
$841$	−39.6810	−	68.7296i	−1.36831	−	2.36999i
$842$	4.89817	+	8.48389i	0.168802	+	0.292374i
$843$		0			0
$844$	14.2014	+	8.19916i	0.488831	+	0.282227i
$845$			25.7406i			0.885502i
$846$		0			0
$847$	34.7719	+	46.1296i	1.19478	+	1.58503i
$848$	2.13443	+	1.23231i	0.0732966	+	0.0423178i
$849$		0			0
$850$	−2.17940	−	3.77484i	−0.0747530	−	0.129476i
$851$	20.4219	−	11.7906i	0.700055	−	0.404177i
$852$		0			0
$853$	22.8609	+	13.1987i	0.782742	+	0.451916i	0.837401	−	0.546589i	$-0.184074\pi$
$853$	22.8609	+	13.1987i	0.782742	+	0.451916i	−0.0546593	+	0.998505i	$0.517407\pi$
$854$	−4.85686			−0.166198
$855$		0			0
$856$	13.1135			0.448209
$857$	27.1443	−	47.0154i	0.927233	−	1.60601i	0.139302	−	0.990250i	$-0.455514\pi$
$857$	27.1443	−	47.0154i	0.927233	−	1.60601i	0.787930	−	0.615764i	$-0.211153\pi$
$858$		0			0
$859$	7.15517	+	12.3931i	0.244131	+	0.422847i	0.961887	−	0.273447i	$-0.0881639\pi$
$859$	7.15517	+	12.3931i	0.244131	+	0.422847i	−0.717756	+	0.696295i	$0.754831\pi$
$860$	−0.817304	−	1.41561i	−0.0278698	−	0.0482720i
$861$		0			0
$862$	−10.3223	+	17.8788i	−0.351580	+	0.608954i
$863$		−	9.34374i		−	0.318064i	−0.987273	−	0.159032i	$-0.949163\pi$
$863$		−	9.34374i		−	0.318064i	0.987273	−	0.159032i	$-0.0508374\pi$
$864$		0			0
$865$			4.81606i			0.163751i
$866$	−9.90919	+	17.1632i	−0.336728	+	0.583230i
$867$		0			0
$868$	−25.7518	+	14.8678i	−0.874074	+	0.504647i
$869$	27.1212	−	30.6596i	0.920025	−	1.04006i
$870$		0			0
$871$	8.85457	+	5.11219i	0.300026	+	0.173220i
$872$		−	12.7274i		−	0.431004i
$873$		0			0
$874$	2.48810			0.0841612
$875$	2.62577	−	4.54797i	0.0887673	−	0.153749i
$876$		0			0
$877$	26.9922	−	15.5840i	0.911462	−	0.526233i	0.0305610	−	0.999533i	$-0.490271\pi$
$877$	26.9922	−	15.5840i	0.911462	−	0.526233i	0.880901	+	0.473300i	$0.156937\pi$
$878$	−16.5483	+	9.55418i	−0.558479	+	0.322438i
$879$		0			0
$880$	3.25009	+	0.660985i	0.109561	+	0.0222818i
$881$			55.9686i			1.88563i	0.333318	+	0.942814i	$0.391832\pi$
$881$			55.9686i			1.88563i	−0.333318	+	0.942814i	$0.608168\pi$
$882$		0			0
$883$	−16.4039			−0.552034			−0.276017	−	0.961153i	$-0.589015\pi$
$883$	−16.4039			−0.552034			−0.276017	+	0.961153i	$0.589015\pi$
$884$	−23.4953	−	13.5650i	−0.790233	−	0.456241i
$885$		0			0
$886$	−0.733684	+	0.423593i	−0.0246486	+	0.0142309i
$887$	−23.6084	−	40.8910i	−0.792693	−	1.37298i	−0.924294	−	0.381682i	$-0.875345\pi$
$887$	−23.6084	−	40.8910i	−0.792693	−	1.37298i	0.131601	−	0.991303i	$-0.457988\pi$
$888$		0			0
$889$	6.84828	−	11.8616i	0.229684	−	0.397824i
$890$	−8.41930			−0.282215
$891$		0			0
$892$	21.9038			0.733393
$893$	0.276980	−	0.479744i	0.00926880	−	0.0160540i
$894$		0			0
$895$	−5.86196	−	10.1532i	−0.195944	−	0.339385i
$896$	4.54797	−	2.62577i	0.151937	−	0.0877209i
$897$		0			0
$898$	26.5518	+	15.3297i	0.886044	+	0.511558i
$899$	58.9426			1.96585
$900$		0			0
$901$			10.7428i			0.357896i
$902$	3.63718	−	17.8842i	0.121105	−	0.595477i
$903$		0			0
$904$	6.01231	−	3.47121i	0.199967	−	0.115451i
$905$	10.0377	−	5.79525i	0.333663	−	0.192641i
$906$		0			0
$907$	−12.7126	+	22.0189i	−0.422115	+	0.731125i	−0.996146	−	0.0877088i	$-0.972045\pi$
$907$	−12.7126	+	22.0189i	−0.422115	+	0.731125i	0.574031	+	0.818833i	$0.305379\pi$
$908$	17.8674			0.592951
$909$		0			0
$910$		−	32.6866i		−	1.08355i
$911$	−2.74924	−	1.58727i	−0.0910864	−	0.0525887i	0.453765	−	0.891121i	$-0.350081\pi$
$911$	−2.74924	−	1.58727i	−0.0910864	−	0.0525887i	−0.544851	+	0.838533i	$0.683414\pi$
$912$		0			0
$913$	14.2231	+	12.5816i	0.470716	+	0.416391i
$914$	−34.5586	+	19.9524i	−1.14310	+	0.659966i
$915$		0			0
$916$	−4.31866	+	7.48013i	−0.142692	+	0.247151i
$917$			6.35247i			0.209777i
$918$		0			0
$919$		−	13.8687i		−	0.457485i	−0.973487	−	0.228743i	$-0.926539\pi$
$919$		−	13.8687i		−	0.457485i	0.973487	−	0.228743i	$-0.0734615\pi$
$920$	1.66101	−	2.87695i	0.0547618	−	0.0948502i
$921$		0			0
$922$	20.0031	+	34.6465i	0.658769	+	1.14102i
$923$	20.4183	+	35.3655i	0.672075	+	1.16407i
$924$		0			0
$925$	−3.54924	+	6.14746i	−0.116698	+	0.202127i
$926$	−1.34069			−0.0440577
$927$		0			0
$928$	−10.4097			−0.341715
$929$	27.8096	+	16.0559i	0.912405	+	0.526777i	0.881204	−	0.472736i	$-0.156734\pi$
$929$	27.8096	+	16.0559i	0.912405	+	0.526777i	0.0312007	+	0.999513i	$0.490067\pi$
$930$		0			0
$931$	−13.3479	+	7.70644i	−0.437461	+	0.252568i
$932$	8.30762	+	14.3892i	0.272125	+	0.471334i
$933$		0			0
$934$	−3.84347	−	2.21903i	−0.125762	−	0.0726088i
$935$	4.58815	+	13.7091i	0.150049	+	0.448336i
$936$		0			0
$937$		−	22.7790i		−	0.744158i	−0.928201	−	0.372079i	$-0.878645\pi$
$937$		−	22.7790i		−	0.744158i	0.928201	−	0.372079i	$-0.121355\pi$
$938$	−7.47087	−	4.31331i	−0.243933	−	0.140835i
$939$		0			0
$940$	−0.369814	−	0.640537i	−0.0120620	−	0.0208920i
$941$	12.1465	+	21.0384i	0.395965	+	0.685832i	0.993224	−	0.116217i	$-0.0370767\pi$
$941$	12.1465	+	21.0384i	0.395965	+	0.685832i	−0.597259	+	0.802049i	$0.703743\pi$
$942$		0			0
$943$	−15.8309	−	9.13996i	−0.515524	−	0.297638i
$944$			1.01292i			0.0329678i
$945$		0			0
$946$	1.72061	+	5.14109i	0.0559420	+	0.167151i
$947$	32.6946	+	18.8763i	1.06243	+	0.613396i	0.926104	−	0.377268i	$-0.123136\pi$
$947$	32.6946	+	18.8763i	1.06243	+	0.613396i	0.136329	+	0.990664i	$0.456470\pi$
$948$		0			0
$949$	−30.0959	−	52.1276i	−0.976954	−	1.69213i
$950$	−0.648629	+	0.374486i	−0.0210443	+	0.0121499i
$951$		0			0
$952$	19.8237	+	11.4452i	0.642491	+	0.370942i
$953$	32.1754			1.04226			0.521132	−	0.853476i	$-0.325510\pi$
$953$	32.1754			1.04226			0.521132	+	0.853476i	$0.325510\pi$
$954$		0			0
$955$	−5.96111			−0.192897
$956$	6.12388	−	10.6069i	0.198060	−	0.343051i
$957$		0			0
$958$	−10.8806	−	18.8457i	−0.351535	−	0.608876i
$959$	−45.0978	−	78.1117i	−1.45628	−	2.52236i
$960$		0			0
$961$	−0.530645	+	0.919104i	−0.0171176	+	0.0296485i
$962$			44.1822i			1.42449i
$963$		0			0
$964$		−	15.5481i		−	0.500770i
$965$	−5.07734	+	8.79421i	−0.163445	+	0.283096i
$966$		0			0
$967$	24.6705	−	14.2435i	0.793351	−	0.458042i	−0.0477898	−	0.998857i	$-0.515218\pi$
$967$	24.6705	−	14.2435i	0.793351	−	0.458042i	0.841141	+	0.540816i	$0.181884\pi$
$968$	−10.1262	−	4.29653i	−0.325468	−	0.138096i
$969$		0			0
$970$	−14.1467	−	8.16763i	−0.454225	−	0.262247i
$971$		−	7.25145i		−	0.232710i	−0.993208	−	0.116355i	$-0.962879\pi$
$971$		−	7.25145i		−	0.232710i	0.993208	−	0.116355i	$-0.0371211\pi$
$972$		0			0
$973$	−64.2377			−2.05937
$974$	1.09625	−	1.89877i	0.0351263	−	0.0608405i
$975$		0			0
$976$	0.800939	−	0.462422i	0.0256374	−	0.0148018i
$977$	−9.85390	+	5.68915i	−0.315254	+	0.182012i	−0.649275	−	0.760554i	$-0.724928\pi$
$977$	−9.85390	+	5.68915i	−0.315254	+	0.182012i	0.334021	+	0.942566i	$0.391594\pi$
$978$		0			0
$979$	27.3635	+	5.56503i	0.874541	+	0.177859i
$980$			20.5787i			0.657363i
$981$		0			0
$982$	−33.2335			−1.06052
$983$	37.4974	+	21.6492i	1.19598	+	0.690501i	0.959657	−	0.281173i	$-0.0907235\pi$
$983$	37.4974	+	21.6492i	1.19598	+	0.690501i	0.236325	+	0.971674i	$0.424057\pi$
$984$		0			0
$985$	−22.4075	+	12.9370i	−0.713962	+	0.412206i
$986$	−22.6870	−	39.2950i	−0.722500	−	1.25141i
$987$		0			0
$988$	−2.33087	+	4.03719i	−0.0741549	+	0.128440i
$989$	5.43019			0.172670
$990$		0			0
$991$	−20.6875			−0.657161			−0.328581	−	0.944476i	$-0.606570\pi$
$991$	−20.6875			−0.657161			−0.328581	+	0.944476i	$0.606570\pi$
$992$	2.83113	−	4.90367i	0.0898886	−	0.155692i
$993$		0			0
$994$	−17.2275	−	29.8389i	−0.546424	−	0.946434i
$995$	16.4888	−	9.51981i	0.522730	−	0.301798i
$996$		0			0
$997$	35.9742	+	20.7697i	1.13932	+	0.657784i	0.946261	−	0.323404i	$-0.104827\pi$
$997$	35.9742	+	20.7697i	1.13932	+	0.657784i	0.193055	+	0.981188i	$0.438161\pi$
$998$	23.5024			0.743957
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2970.2.t.a.791.1		48
3.2	odd	2		990.2.t.b.461.1	yes	48
9.4	even	3		990.2.t.a.131.1	✓	48
9.5	odd	6		2970.2.t.b.2771.1		48
11.10	odd	2		2970.2.t.b.791.1		48
33.32	even	2		990.2.t.a.461.1	yes	48
99.32	even	6	inner	2970.2.t.a.2771.1		48
99.76	odd	6		990.2.t.b.131.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.1	✓	48	9.4	even	3
990.2.t.a.461.1	yes	48	33.32	even	2
990.2.t.b.131.1	yes	48	99.76	odd	6
990.2.t.b.461.1	yes	48	3.2	odd	2
2970.2.t.a.791.1		48	1.1	even	1	trivial
2970.2.t.a.2771.1		48	99.32	even	6	inner
2970.2.t.b.791.1		48	11.10	odd	2
2970.2.t.b.2771.1		48	9.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2970.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-4.54797 - 2.62577i) q^{7} +1.00000 q^{8} -1.00000i q^{10} +(-0.660985 + 3.25009i) q^{11} +(-5.39031 + 3.11210i) q^{13} +(4.54797 - 2.62577i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.35881 q^{17} +0.748972i q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.48417 - 2.19748i) q^{22} +(-2.87695 + 1.66101i) q^{23} +(0.500000 - 0.866025i) q^{25} -6.22419i q^{26} +5.25154i q^{28} +(5.20486 - 9.01507i) q^{29} +(2.83113 + 4.90367i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.17940 - 3.77484i) q^{34} +5.25154 q^{35} -7.09847 q^{37} +(-0.648629 - 0.374486i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(2.75133 + 4.76544i) q^{41} +(-1.41561 - 0.817304i) q^{43} +(3.14515 - 1.05262i) q^{44} -3.32202i q^{46} +(-0.640537 - 0.369814i) q^{47} +(10.2894 + 17.8217i) q^{49} +(0.500000 + 0.866025i) q^{50} +(5.39031 + 3.11210i) q^{52} -2.46463i q^{53} +(-1.05262 - 3.14515i) q^{55} +(-4.54797 - 2.62577i) q^{56} +(5.20486 + 9.01507i) q^{58} +(0.877216 - 0.506461i) q^{59} +(-0.800939 - 0.462422i) q^{61} -5.66227 q^{62} +1.00000 q^{64} +(3.11210 - 5.39031i) q^{65} +(-0.821341 - 1.42261i) q^{67} +(2.17940 + 3.77484i) q^{68} +(-2.62577 + 4.54797i) q^{70} -6.56094i q^{71} +9.67062i q^{73} +(3.54924 - 6.14746i) q^{74} +(0.648629 - 0.374486i) q^{76} +(11.5401 - 13.0457i) q^{77} +(-10.6885 - 6.17100i) q^{79} -1.00000i q^{80} -5.50266 q^{82} +(2.86275 - 4.95842i) q^{83} +(3.77484 - 2.17940i) q^{85} +(1.41561 - 0.817304i) q^{86} +(-0.660985 + 3.25009i) q^{88} -8.41930i q^{89} +32.6866 q^{91} +(2.87695 + 1.66101i) q^{92} +(0.640537 - 0.369814i) q^{94} +(-0.374486 - 0.648629i) q^{95} +(8.16763 - 14.1467i) q^{97} -20.5787 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} + 12 q^{11} - 24 q^{13} - 24 q^{16} - 12 q^{17} - 6 q^{22} - 36 q^{23} + 24 q^{25} - 24 q^{32} + 6 q^{34} + 6 q^{38} - 6 q^{41} - 30 q^{43} - 6 q^{44} + 24 q^{49} + 24 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 + 12 * q^11 - 24 * q^13 - 24 * q^16 - 12 * q^17 - 6 * q^22 - 36 * q^23 + 24 * q^25 - 24 * q^32 + 6 * q^34 + 6 * q^38 - 6 * q^41 - 30 * q^43 - 6 * q^44 + 24 * q^49 + 24 * q^50 + 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 + 6 * q^68 - 6 * q^76 + 18 * q^77 + 12 * q^82 + 36 * q^83 + 30 * q^86 + 12 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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