LMFDB - Embedded newform 728.2.c.a.365.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(365,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.365"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			365.11
Character	$\chi$	$=$	728.365
Dual form			728.2.c.a.365.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.687700 - 1.23575i) q^{2} +3.16783i q^{3} +(-1.05414 + 1.69965i) q^{4} -1.11795i q^{5} +(3.91463 - 2.17851i) q^{6} -1.00000 q^{7} +(2.82526 + 0.133800i) q^{8} -7.03512 q^{9} +(-1.38150 + 0.768812i) q^{10} -4.51562i q^{11} +(-5.38418 - 3.33932i) q^{12} -1.00000i q^{13} +(0.687700 + 1.23575i) q^{14} +3.54146 q^{15} +(-1.77759 - 3.58332i) q^{16} -4.44816 q^{17} +(4.83805 + 8.69362i) q^{18} -6.89036i q^{19} +(1.90011 + 1.17847i) q^{20} -3.16783i q^{21} +(-5.58016 + 3.10539i) q^{22} -2.66314 q^{23} +(-0.423854 + 8.94993i) q^{24} +3.75020 q^{25} +(-1.23575 + 0.687700i) q^{26} -12.7825i q^{27} +(1.05414 - 1.69965i) q^{28} +6.01139i q^{29} +(-2.43546 - 4.37635i) q^{30} +10.4802 q^{31} +(-3.20562 + 4.66090i) q^{32} +14.3047 q^{33} +(3.05900 + 5.49680i) q^{34} +1.11795i q^{35} +(7.41598 - 11.9572i) q^{36} -2.80922i q^{37} +(-8.51474 + 4.73850i) q^{38} +3.16783 q^{39} +(0.149581 - 3.15849i) q^{40} -4.93559 q^{41} +(-3.91463 + 2.17851i) q^{42} -4.88533i q^{43} +(7.67496 + 4.76009i) q^{44} +7.86489i q^{45} +(1.83144 + 3.29097i) q^{46} -6.35415 q^{47} +(11.3513 - 5.63109i) q^{48} +1.00000 q^{49} +(-2.57901 - 4.63429i) q^{50} -14.0910i q^{51} +(1.69965 + 1.05414i) q^{52} +6.02877i q^{53} +(-15.7960 + 8.79056i) q^{54} -5.04822 q^{55} +(-2.82526 - 0.133800i) q^{56} +21.8275 q^{57} +(7.42855 - 4.13403i) q^{58} -15.1683i q^{59} +(-3.73318 + 6.01923i) q^{60} -6.44954i q^{61} +(-7.20725 - 12.9509i) q^{62} +7.03512 q^{63} +(7.96420 + 0.756038i) q^{64} -1.11795 q^{65} +(-9.83734 - 17.6770i) q^{66} -5.98352i q^{67} +(4.68897 - 7.56030i) q^{68} -8.43637i q^{69} +(1.38150 - 0.768812i) q^{70} +0.527201 q^{71} +(-19.8760 - 0.941297i) q^{72} -7.57660 q^{73} +(-3.47148 + 1.93190i) q^{74} +11.8800i q^{75} +(11.7112 + 7.26339i) q^{76} +4.51562i q^{77} +(-2.17851 - 3.91463i) q^{78} +4.85576 q^{79} +(-4.00596 + 1.98725i) q^{80} +19.3875 q^{81} +(3.39421 + 6.09914i) q^{82} -2.98647i q^{83} +(5.38418 + 3.33932i) q^{84} +4.97281i q^{85} +(-6.03703 + 3.35964i) q^{86} -19.0430 q^{87} +(0.604189 - 12.7578i) q^{88} +5.07956 q^{89} +(9.71900 - 5.40868i) q^{90} +1.00000i q^{91} +(2.80732 - 4.52640i) q^{92} +33.1995i q^{93} +(4.36975 + 7.85212i) q^{94} -7.70306 q^{95} +(-14.7649 - 10.1549i) q^{96} -17.4191 q^{97} +(-0.687700 - 1.23575i) q^{98} +31.7679i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) $ 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.687700	−	1.23575i	−0.486277	−	0.873804i
$2$	−0.687700	−	1.23575i	−0.486277	−	0.873804i
$3$			3.16783i			1.82894i	0.404648	+	0.914472i	$0.367394\pi$
$3$			3.16783i			1.82894i	−0.404648	+	0.914472i	$0.632606\pi$
$4$	−1.05414	+	1.69965i	−0.527069	+	0.849823i
$5$		−	1.11795i		−	0.499961i	−0.968251	−	0.249980i	$-0.919576\pi$
$5$		−	1.11795i		−	0.499961i	0.968251	−	0.249980i	$-0.0804242\pi$
$6$	3.91463	−	2.17851i	1.59814	−	0.889374i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.82526	+	0.133800i	0.998880	+	0.0473053i
$9$	−7.03512			−2.34504
$10$	−1.38150	+	0.768812i	−0.436868	+	0.243120i
$11$		−	4.51562i		−	1.36151i	−0.732511	−	0.680756i	$-0.761652\pi$
$11$		−	4.51562i		−	1.36151i	0.732511	−	0.680756i	$-0.238348\pi$
$12$	−5.38418	−	3.33932i	−1.55428	−	0.963979i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.687700	+	1.23575i	0.183796	+	0.330267i
$15$	3.54146			0.914401
$16$	−1.77759	−	3.58332i	−0.444397	−	0.895830i
$17$	−4.44816			−1.07884			−0.539419	−	0.842038i	$-0.681356\pi$
$17$	−4.44816			−1.07884			−0.539419	+	0.842038i	$0.681356\pi$
$18$	4.83805	+	8.69362i	1.14034	+	2.04911i
$19$		−	6.89036i		−	1.58076i	−0.612619	−	0.790379i	$-0.709884\pi$
$19$		−	6.89036i		−	1.58076i	0.612619	−	0.790379i	$-0.290116\pi$
$20$	1.90011	+	1.17847i	0.424878	+	0.263514i
$21$		−	3.16783i		−	0.691276i
$22$	−5.58016	+	3.10539i	−1.18969	+	0.662072i
$23$	−2.66314			−0.555303			−0.277652	−	0.960682i	$-0.589556\pi$
$23$	−2.66314			−0.555303			−0.277652	+	0.960682i	$0.589556\pi$
$24$	−0.423854	+	8.94993i	−0.0865189	+	1.82690i
$25$	3.75020			0.750039
$26$	−1.23575	+	0.687700i	−0.242350	+	0.134869i
$27$		−	12.7825i		−	2.46000i
$28$	1.05414	−	1.69965i	0.199213	−	0.321203i
$29$			6.01139i			1.11629i	0.829745	+	0.558143i	$0.188486\pi$
$29$			6.01139i			1.11629i	−0.829745	+	0.558143i	$0.811514\pi$
$30$	−2.43546	−	4.37635i	−0.444653	−	0.799008i
$31$	10.4802			1.88230			0.941152	−	0.337983i	$-0.109745\pi$
$31$	10.4802			1.88230			0.941152	+	0.337983i	$0.109745\pi$
$32$	−3.20562	+	4.66090i	−0.566680	+	0.823938i
$33$	14.3047			2.49013
$34$	3.05900	+	5.49680i	0.524615	+	0.942693i
$35$			1.11795i			0.188967i
$36$	7.41598	−	11.9572i	1.23600	−	1.99287i
$37$		−	2.80922i		−	0.461833i	−0.972974	−	0.230916i	$-0.925828\pi$
$37$		−	2.80922i		−	0.461833i	0.972974	−	0.230916i	$-0.0741724\pi$
$38$	−8.51474	+	4.73850i	−1.38127	+	0.768686i
$39$	3.16783			0.507258
$40$	0.149581	−	3.15849i	0.0236508	−	0.499401i
$41$	−4.93559			−0.770810			−0.385405	−	0.922748i	$-0.625938\pi$
$41$	−4.93559			−0.770810			−0.385405	+	0.922748i	$0.625938\pi$
$42$	−3.91463	+	2.17851i	−0.604040	+	0.336152i
$43$		−	4.88533i		−	0.745006i	−0.928031	−	0.372503i	$-0.878500\pi$
$43$		−	4.88533i		−	0.745006i	0.928031	−	0.372503i	$-0.121500\pi$
$44$	7.67496	+	4.76009i	1.15704	+	0.717610i
$45$			7.86489i			1.17243i
$46$	1.83144	+	3.29097i	0.270031	+	0.485227i
$47$	−6.35415			−0.926849			−0.463424	−	0.886136i	$-0.653379\pi$
$47$	−6.35415			−0.926849			−0.463424	+	0.886136i	$0.653379\pi$
$48$	11.3513	−	5.63109i	1.63842	−	0.812778i
$49$	1.00000			0.142857
$50$	−2.57901	−	4.63429i	−0.364727	−	0.655388i
$51$		−	14.0910i		−	1.97314i
$52$	1.69965	+	1.05414i	0.235698	+	0.146183i
$53$			6.02877i			0.828116i	0.910251	+	0.414058i	$0.135889\pi$
$53$			6.02877i			0.828116i	−0.910251	+	0.414058i	$0.864111\pi$
$54$	−15.7960	+	8.79056i	−2.14956	+	1.19624i
$55$	−5.04822			−0.680702
$56$	−2.82526	−	0.133800i	−0.377541	−	0.0178797i
$57$	21.8275			2.89112
$58$	7.42855	−	4.13403i	0.975416	−	0.542825i
$59$		−	15.1683i		−	1.97475i	−0.158400	−	0.987375i	$-0.550633\pi$
$59$		−	15.1683i		−	1.97475i	0.158400	−	0.987375i	$-0.449367\pi$
$60$	−3.73318	+	6.01923i	−0.481952	+	0.777079i
$61$		−	6.44954i		−	0.825779i	−0.910781	−	0.412890i	$-0.864520\pi$
$61$		−	6.44954i		−	0.825779i	0.910781	−	0.412890i	$-0.135480\pi$
$62$	−7.20725	−	12.9509i	−0.915322	−	1.64477i
$63$	7.03512			0.886341
$64$	7.96420	+	0.756038i	0.995524	+	0.0945048i
$65$	−1.11795			−0.138664
$66$	−9.83734	−	17.6770i	−1.21089	−	2.17589i
$67$		−	5.98352i		−	0.731004i	−0.930811	−	0.365502i	$-0.880897\pi$
$67$		−	5.98352i		−	0.731004i	0.930811	−	0.365502i	$-0.119103\pi$
$68$	4.68897	−	7.56030i	0.568622	−	0.916821i
$69$		−	8.43637i		−	1.01562i
$70$	1.38150	−	0.768812i	0.165121	−	0.0918906i
$71$	0.527201			0.0625672			0.0312836	−	0.999511i	$-0.490040\pi$
$71$	0.527201			0.0625672			0.0312836	+	0.999511i	$0.490040\pi$
$72$	−19.8760	−	0.941297i	−2.34241	−	0.110933i
$73$	−7.57660			−0.886774			−0.443387	−	0.896330i	$-0.646223\pi$
$73$	−7.57660			−0.886774			−0.443387	+	0.896330i	$0.646223\pi$
$74$	−3.47148	+	1.93190i	−0.403552	+	0.224579i
$75$			11.8800i			1.37178i
$76$	11.7112	+	7.26339i	1.34336	+	0.833167i
$77$			4.51562i			0.514603i
$78$	−2.17851	−	3.91463i	−0.246668	−	0.443244i
$79$	4.85576			0.546316			0.273158	−	0.961969i	$-0.411932\pi$
$79$	4.85576			0.546316			0.273158	+	0.961969i	$0.411932\pi$
$80$	−4.00596	+	1.98725i	−0.447880	+	0.222181i
$81$	19.3875			2.15417
$82$	3.39421	+	6.09914i	0.374827	+	0.673537i
$83$		−	2.98647i		−	0.327808i	−0.986476	−	0.163904i	$-0.947591\pi$
$83$		−	2.98647i		−	0.327808i	0.986476	−	0.163904i	$-0.0524087\pi$
$84$	5.38418	+	3.33932i	0.587462	+	0.364350i
$85$			4.97281i			0.539377i
$86$	−6.03703	+	3.35964i	−0.650990	+	0.362280i
$87$	−19.0430			−2.04163
$88$	0.604189	−	12.7578i	0.0644068	−	1.35999i
$89$	5.07956			0.538432			0.269216	−	0.963080i	$-0.413235\pi$
$89$	5.07956			0.538432			0.269216	+	0.963080i	$0.413235\pi$
$90$	9.71900	−	5.40868i	1.02447	−	0.570125i
$91$			1.00000i			0.104828i
$92$	2.80732	−	4.52640i	0.292683	−	0.471909i
$93$			33.1995i			3.44263i
$94$	4.36975	+	7.85212i	0.450706	+	0.809885i
$95$	−7.70306			−0.790317
$96$	−14.7649	−	10.1549i	−1.50694	−	1.03643i
$97$	−17.4191			−1.76864			−0.884320	−	0.466881i	$-0.845378\pi$
$97$	−17.4191			−1.76864			−0.884320	+	0.466881i	$0.845378\pi$
$98$	−0.687700	−	1.23575i	−0.0694682	−	0.124829i
$99$			31.7679i			3.19280i
$100$	−3.95322	+	6.37400i	−0.395322	+	0.637400i
$101$		−	12.0937i		−	1.20337i	−0.798733	−	0.601685i	$-0.794496\pi$
$101$		−	12.0937i		−	1.20337i	0.798733	−	0.601685i	$-0.205504\pi$
$102$	−17.4129	+	9.69038i	−1.72413	+	0.959491i
$103$	−10.2847			−1.01338			−0.506689	−	0.862129i	$-0.669131\pi$
$103$	−10.2847			−1.01338			−0.506689	+	0.862129i	$0.669131\pi$
$104$	0.133800	−	2.82526i	0.0131201	−	0.277040i
$105$	−3.54146			−0.345611
$106$	7.45003	−	4.14599i	0.723611	−	0.402694i
$107$			3.16408i			0.305883i	0.988235	+	0.152942i	$0.0488746\pi$
$107$			3.16408i			0.305883i	−0.988235	+	0.152942i	$0.951125\pi$
$108$	21.7258	+	13.4746i	2.09057	+	1.29659i
$109$			9.48432i			0.908433i	0.890891	+	0.454216i	$0.150081\pi$
$109$			9.48432i			0.908433i	−0.890891	+	0.454216i	$0.849919\pi$
$110$	3.47166	+	6.23832i	0.331010	+	0.594801i
$111$	8.89912			0.844667
$112$	1.77759	+	3.58332i	0.167966	+	0.338592i
$113$	−10.2704			−0.966163			−0.483081	−	0.875575i	$-0.660482\pi$
$113$	−10.2704			−0.966163			−0.483081	+	0.875575i	$0.660482\pi$
$114$	−15.0107	−	26.9732i	−1.40589	−	2.52627i
$115$			2.97725i			0.277630i
$116$	−10.2172	−	6.33683i	−0.948646	−	0.588360i
$117$			7.03512i			0.650397i
$118$	−18.7442	+	10.4313i	−1.72555	+	0.960276i
$119$	4.44816			0.407762
$120$	10.0055	+	0.473846i	0.913377	+	0.0432561i
$121$	−9.39084			−0.853713
$122$	−7.97000	+	4.43535i	−0.721570	+	0.401558i
$123$		−	15.6351i		−	1.40977i
$124$	−11.0476	+	17.8127i	−0.992103	+	1.59962i
$125$		−	9.78225i		−	0.874951i
$126$	−4.83805	−	8.69362i	−0.431008	−	0.774489i
$127$	21.8163			1.93588			0.967941	−	0.251179i	$-0.0808182\pi$
$127$	21.8163			1.93588			0.967941	+	0.251179i	$0.0808182\pi$
$128$	−4.54271	−	10.3617i	−0.401522	−	0.915849i
$129$	15.4759			1.36258
$130$	0.768812	+	1.38150i	0.0674293	+	0.121165i
$131$			15.7094i			1.37253i	0.727350	+	0.686266i	$0.240751\pi$
$131$			15.7094i			1.37253i	−0.727350	+	0.686266i	$0.759249\pi$
$132$	−15.0791	+	24.3129i	−1.31247	+	2.11617i
$133$			6.89036i			0.597470i
$134$	−7.39412	+	4.11487i	−0.638754	+	0.355471i
$135$	−14.2902			−1.22990
$136$	−12.5672	−	0.595163i	−1.07763	−	0.0510348i
$137$	0.178216			0.0152260			0.00761299	−	0.999971i	$-0.497577\pi$
$137$	0.178216			0.0152260			0.00761299	+	0.999971i	$0.497577\pi$
$138$	−10.4252	+	5.80169i	−0.887453	+	0.493873i
$139$			12.0375i			1.02100i	0.859877	+	0.510502i	$0.170540\pi$
$139$			12.0375i			1.02100i	−0.859877	+	0.510502i	$0.829460\pi$
$140$	−1.90011	−	1.17847i	−0.160589	−	0.0995988i
$141$		−	20.1289i		−	1.69516i
$142$	−0.362556	−	0.651486i	−0.0304250	−	0.0546715i
$143$	−4.51562			−0.377615
$144$	12.5055	+	25.2091i	1.04213	+	2.10076i
$145$	6.72041			0.558100
$146$	5.21043	+	9.36275i	0.431218	+	0.774867i
$147$			3.16783i			0.261278i
$148$	4.77468	+	2.96130i	0.392476	+	0.243418i
$149$		−	2.45649i		−	0.201243i	−0.994925	−	0.100622i	$-0.967917\pi$
$149$		−	2.45649i		−	0.201243i	0.994925	−	0.100622i	$-0.0320832\pi$
$150$	14.6806	−	8.16985i	1.19867	−	0.667066i
$151$	−7.03048			−0.572133			−0.286066	−	0.958210i	$-0.592348\pi$
$151$	−7.03048			−0.572133			−0.286066	+	0.958210i	$0.592348\pi$
$152$	0.921928	−	19.4671i	0.0747783	−	1.57899i
$153$	31.2933			2.52992
$154$	5.58016	−	3.10539i	0.449662	−	0.250240i
$155$		−	11.7163i		−	0.941079i
$156$	−3.33932	+	5.38418i	−0.267360	+	0.431079i
$157$		−	3.93708i		−	0.314213i	−0.987582	−	0.157107i	$-0.949783\pi$
$157$		−	3.93708i		−	0.314213i	0.987582	−	0.157107i	$-0.0502166\pi$
$158$	−3.33931	−	6.00049i	−0.265661	−	0.477373i
$159$	−19.0981			−1.51458
$160$	5.21064	+	3.58372i	0.411937	+	0.283318i
$161$	2.66314			0.209885
$162$	−13.3328	−	23.9581i	−1.04752	−	1.88232i
$163$		−	13.7052i		−	1.07347i	−0.843750	−	0.536736i	$-0.819657\pi$
$163$		−	13.7052i		−	1.07347i	0.843750	−	0.536736i	$-0.180343\pi$
$164$	5.20279	−	8.38876i	0.406270	−	0.655052i
$165$		−	15.9919i		−	1.24497i
$166$	−3.69052	+	2.05380i	−0.286440	+	0.159405i
$167$	−10.1840			−0.788061			−0.394031	−	0.919097i	$-0.628920\pi$
$167$	−10.1840			−0.788061			−0.394031	+	0.919097i	$0.628920\pi$
$168$	0.423854	−	8.94993i	0.0327011	−	0.690502i
$169$	−1.00000			−0.0769231
$170$	6.14513	−	3.41980i	0.471310	−	0.262287i
$171$			48.4745i			3.70694i
$172$	8.30334	+	5.14981i	0.633123	+	0.392670i
$173$			6.19802i			0.471227i	0.971847	+	0.235614i	$0.0757099\pi$
$173$			6.19802i			0.471227i	−0.971847	+	0.235614i	$0.924290\pi$
$174$	13.0959	+	23.5323i	0.992797	+	1.78398i
$175$	−3.75020			−0.283488
$176$	−16.1809	+	8.02692i	−1.21968	+	0.605052i
$177$	48.0507			3.61171
$178$	−3.49321	−	6.27705i	−0.261827	−	0.470485i
$179$		−	11.4822i		−	0.858220i	−0.903252	−	0.429110i	$-0.858827\pi$
$179$		−	11.4822i		−	0.858220i	0.903252	−	0.429110i	$-0.141173\pi$
$180$	−13.3675	−	8.29067i	−0.996356	−	0.617950i
$181$		−	26.3811i		−	1.96089i	−0.196787	−	0.980446i	$-0.563051\pi$
$181$		−	26.3811i		−	1.96089i	0.196787	−	0.980446i	$-0.436949\pi$
$182$	1.23575	−	0.687700i	0.0915996	−	0.0509757i
$183$	20.4310			1.51030
$184$	−7.52407	−	0.356328i	−0.554682	−	0.0262688i
$185$	−3.14056			−0.230898
$186$	41.0262	−	22.8313i	3.00819	−	1.67407i
$187$			20.0862i			1.46885i
$188$	6.69815	−	10.7998i	0.488513	−	0.787657i
$189$			12.7825i			0.929793i
$190$	5.29739	+	9.51902i	0.384313	+	0.690582i
$191$	8.81111			0.637549			0.318775	−	0.947831i	$-0.396729\pi$
$191$	8.81111			0.637549			0.318775	+	0.947831i	$0.396729\pi$
$192$	−2.39500	+	25.2292i	−0.172844	+	1.82076i
$193$	−0.353957			−0.0254784			−0.0127392	−	0.999919i	$-0.504055\pi$
$193$	−0.353957			−0.0254784			−0.0127392	+	0.999919i	$0.504055\pi$
$194$	11.9791	+	21.5256i	0.860050	+	1.54545i
$195$		−	3.54146i		−	0.253609i
$196$	−1.05414	+	1.69965i	−0.0752955	+	0.121403i
$197$			5.33967i			0.380436i	0.981742	+	0.190218i	$0.0609195\pi$
$197$			5.33967i			0.380436i	−0.981742	+	0.190218i	$0.939081\pi$
$198$	39.2571	−	21.8468i	2.78988	−	1.55259i
$199$	13.5233			0.958642			0.479321	−	0.877640i	$-0.340883\pi$
$199$	13.5233			0.958642			0.479321	+	0.877640i	$0.340883\pi$
$200$	10.5953	+	0.501775i	0.749199	+	0.0354809i
$201$	18.9548			1.33697
$202$	−14.9448	+	8.31686i	−1.05151	+	0.585172i
$203$		−	6.01139i		−	0.421917i
$204$	23.9497	+	14.8539i	1.67682	+	1.03998i
$205$			5.51773i			0.385375i
$206$	7.07277	+	12.7092i	0.492783	+	0.885495i
$207$	18.7355			1.30221
$208$	−3.58332	+	1.77759i	−0.248458	+	0.123254i
$209$	−31.1143			−2.15222
$210$	2.43546	+	4.37635i	0.168063	+	0.301997i
$211$			7.02940i			0.483924i	0.970286	+	0.241962i	$0.0777909\pi$
$211$			7.02940i			0.483924i	−0.970286	+	0.241962i	$0.922209\pi$
$212$	−10.2468	−	6.35516i	−0.703752	−	0.436474i
$213$			1.67008i			0.114432i
$214$	3.91000	−	2.17594i	0.267282	−	0.148744i
$215$	−5.46154			−0.372474
$216$	1.71030	−	36.1140i	0.116371	−	2.45725i
$217$	−10.4802			−0.711444
$218$	11.7202	−	6.52236i	0.793793	−	0.441750i
$219$		−	24.0013i		−	1.62186i
$220$	5.32152	−	8.58019i	0.358777	−	0.578476i
$221$			4.44816i			0.299216i
$222$	−6.11992	−	10.9971i	−0.410742	−	0.738074i
$223$	−15.1940			−1.01747			−0.508734	−	0.860924i	$-0.669886\pi$
$223$	−15.1940			−1.01747			−0.508734	+	0.860924i	$0.669886\pi$
$224$	3.20562	−	4.66090i	0.214185	−	0.311419i
$225$	−26.3831			−1.75887
$226$	7.06299	+	12.6917i	0.469823	+	0.844237i
$227$		−	3.08660i		−	0.204865i	−0.994740	−	0.102432i	$-0.967337\pi$
$227$		−	3.08660i		−	0.204865i	0.994740	−	0.102432i	$-0.0326625\pi$
$228$	−23.0091	+	37.0989i	−1.52382	+	2.45694i
$229$			8.10820i			0.535805i	0.963446	+	0.267902i	$0.0863305\pi$
$229$			8.10820i			0.535805i	−0.963446	+	0.267902i	$0.913669\pi$
$230$	3.67912	−	2.04745i	0.242594	−	0.135005i
$231$	−14.3047			−0.941180
$232$	−0.804322	+	16.9837i	−0.0528063	+	1.11504i
$233$	11.7007			0.766541			0.383270	−	0.923636i	$-0.374798\pi$
$233$	11.7007			0.766541			0.383270	+	0.923636i	$0.374798\pi$
$234$	8.69362	−	4.83805i	0.568320	−	0.316273i
$235$			7.10361i			0.463388i
$236$	25.7808	+	15.9895i	1.67819	+	1.04083i
$237$			15.3822i			0.999181i
$238$	−3.05900	−	5.49680i	−0.198286	−	0.356305i
$239$	−26.1557			−1.69187			−0.845935	−	0.533286i	$-0.820957\pi$
$239$	−26.1557			−1.69187			−0.845935	+	0.533286i	$0.820957\pi$
$240$	−6.29526	−	12.6902i	−0.406357	−	0.819148i
$241$	−13.3340			−0.858916			−0.429458	−	0.903087i	$-0.641295\pi$
$241$	−13.3340			−0.858916			−0.429458	+	0.903087i	$0.641295\pi$
$242$	6.45808	+	11.6047i	0.415141	+	0.745978i
$243$			23.0686i			1.47985i
$244$	10.9619	+	6.79870i	0.701766	+	0.435242i
$245$		−	1.11795i		−	0.0714230i
$246$	−19.3210	+	10.7523i	−1.23186	+	0.685539i
$247$	−6.89036			−0.438423
$248$	29.6094	+	1.40225i	1.88020	+	0.0890430i
$249$	9.46061			0.599542
$250$	−12.0884	+	6.72726i	−0.764536	+	0.425469i
$251$		−	15.0492i		−	0.949896i	−0.880014	−	0.474948i	$-0.842467\pi$
$251$		−	15.0492i		−	0.949896i	0.880014	−	0.474948i	$-0.157533\pi$
$252$	−7.41598	+	11.9572i	−0.467163	+	0.753233i
$253$			12.0257i			0.756052i
$254$	−15.0031	−	26.9594i	−0.941375	−	1.69158i
$255$	−15.7530			−0.986490
$256$	−9.68035	+	12.7393i	−0.605022	+	0.796209i
$257$	1.36042			0.0848609			0.0424305	−	0.999099i	$-0.486490\pi$
$257$	1.36042			0.0848609			0.0424305	+	0.999099i	$0.486490\pi$
$258$	−10.6428	−	19.1243i	−0.662590	−	1.19062i
$259$			2.80922i			0.174556i
$260$	1.17847	−	1.90011i	0.0730856	−	0.117840i
$261$		−	42.2908i		−	2.61774i
$262$	19.4128	−	10.8033i	1.19932	−	0.667431i
$263$	−11.1149			−0.685373			−0.342687	−	0.939450i	$-0.611337\pi$
$263$	−11.1149			−0.685373			−0.342687	+	0.939450i	$0.611337\pi$
$264$	40.4145	+	1.91397i	2.48734	+	0.117796i
$265$	6.73985			0.414026
$266$	8.51474	−	4.73850i	0.522072	−	0.290536i
$267$			16.0912i			0.984763i
$268$	10.1699	+	6.30745i	0.621224	+	0.385289i
$269$			7.18479i			0.438064i	0.975718	+	0.219032i	$0.0702900\pi$
$269$			7.18479i			0.438064i	−0.975718	+	0.219032i	$0.929710\pi$
$270$	9.82737	+	17.6591i	0.598075	+	1.07470i
$271$	26.3646			1.60154			0.800769	−	0.598974i	$-0.204425\pi$
$271$	26.3646			1.60154			0.800769	+	0.598974i	$0.204425\pi$
$272$	7.90701	+	15.9392i	0.479433	+	0.966455i
$273$	−3.16783			−0.191726
$274$	−0.122559	−	0.220229i	−0.00740405	−	0.0133045i
$275$		−	16.9345i		−	1.02119i
$276$	14.3388	+	8.89309i	0.863096	+	0.535301i
$277$			9.62372i			0.578233i	0.957294	+	0.289116i	$0.0933615\pi$
$277$			9.62372i			0.578233i	−0.957294	+	0.289116i	$0.906639\pi$
$278$	14.8752	−	8.27816i	0.892157	−	0.496491i
$279$	−73.7296			−4.41408
$280$	−0.149581	+	3.15849i	−0.00893917	+	0.188756i
$281$	−13.8037			−0.823460			−0.411730	−	0.911306i	$-0.635075\pi$
$281$	−13.8037			−0.823460			−0.411730	+	0.911306i	$0.635075\pi$
$282$	−24.8742	+	13.8426i	−1.48123	+	0.824316i
$283$			7.76345i			0.461489i	0.973014	+	0.230744i	$0.0741161\pi$
$283$			7.76345i			0.461489i	−0.973014	+	0.230744i	$0.925884\pi$
$284$	−0.555742	+	0.896054i	−0.0329772	+	0.0531710i
$285$		−	24.4019i		−	1.44545i
$286$	3.10539	+	5.58016i	0.183626	+	0.329962i
$287$	4.93559			0.291339
$288$	22.5519	−	32.7900i	1.32889	−	1.93217i
$289$	2.78615			0.163891
$290$	−4.62163	−	8.30472i	−0.271391	−	0.487670i
$291$		−	55.1806i		−	3.23475i
$292$	7.98677	−	12.8775i	0.467391	−	0.753600i
$293$			23.4220i			1.36833i	0.729329	+	0.684163i	$0.239832\pi$
$293$			23.4220i			1.36833i	−0.729329	+	0.684163i	$0.760168\pi$
$294$	3.91463	−	2.17851i	0.228306	−	0.127053i
$295$	−16.9574			−0.987298
$296$	0.375873	−	7.93678i	0.0218472	−	0.461316i
$297$	−57.7211			−3.34932
$298$	−3.03560	+	1.68933i	−0.175847	+	0.0978602i
$299$			2.66314i			0.154013i
$300$	−20.1917	−	12.5231i	−1.16577	−	0.723022i
$301$			4.88533i			0.281586i
$302$	4.83486	+	8.68789i	0.278215	+	0.499932i
$303$	38.3108			2.20090
$304$	−24.6904	+	12.2482i	−1.41609	+	0.702484i
$305$	−7.21024			−0.412857
$306$	−21.5204	−	38.6706i	−1.23024	−	2.21065i
$307$			7.12411i			0.406594i	0.979117	+	0.203297i	$0.0651657\pi$
$307$			7.12411i			0.406594i	−0.979117	+	0.203297i	$0.934834\pi$
$308$	−7.67496	−	4.76009i	−0.437321	−	0.271231i
$309$		−	32.5800i		−	1.85341i
$310$	−14.4784	+	8.05732i	−0.822319	+	0.457625i
$311$	−16.3917			−0.929486			−0.464743	−	0.885446i	$-0.653853\pi$
$311$	−16.3917			−0.929486			−0.464743	+	0.885446i	$0.653853\pi$
$312$	8.94993	+	0.423854i	0.506690	+	0.0239960i
$313$	14.5603			0.822998			0.411499	−	0.911410i	$-0.365005\pi$
$313$	14.5603			0.822998			0.411499	+	0.911410i	$0.365005\pi$
$314$	−4.86523	+	2.70753i	−0.274561	+	0.152795i
$315$		−	7.86489i		−	0.443136i
$316$	−5.11864	+	8.25307i	−0.287946	+	0.464272i
$317$		−	24.5206i		−	1.37721i	−0.725135	−	0.688607i	$-0.758223\pi$
$317$		−	24.5206i		−	1.37721i	0.725135	−	0.688607i	$-0.241777\pi$
$318$	13.1338	+	23.6004i	0.736505	+	1.32345i
$319$	27.1452			1.51984
$320$	0.845210	−	8.90355i	0.0472487	−	0.497723i
$321$	−10.0233			−0.559443
$322$	−1.83144	−	3.29097i	−0.102062	−	0.183398i
$323$			30.6494i			1.70538i
$324$	−20.4371	+	32.9519i	−1.13539	+	1.83066i
$325$		−	3.75020i		−	0.208023i
$326$	−16.9361	+	9.42505i	−0.938005	+	0.522005i
$327$	−30.0447			−1.66147
$328$	−13.9443	−	0.660381i	−0.769947	−	0.0364634i
$329$	6.35415			0.350316
$330$	−19.7619	+	10.9976i	−1.08786	+	0.605399i
$331$		−	1.15297i		−	0.0633727i	−0.999498	−	0.0316864i	$-0.989912\pi$
$331$		−	1.15297i		−	0.0633727i	0.999498	−	0.0316864i	$-0.0100878\pi$
$332$	5.07594	+	3.14815i	0.278578	+	0.172777i
$333$			19.7632i			1.08302i
$334$	7.00353	+	12.5848i	0.383216	+	0.688611i
$335$	−6.68926			−0.365473
$336$	−11.3513	+	5.63109i	−0.619266	+	0.307201i
$337$	34.0718			1.85601			0.928004	−	0.372569i	$-0.121523\pi$
$337$	34.0718			1.85601			0.928004	+	0.372569i	$0.121523\pi$
$338$	0.687700	+	1.23575i	0.0374060	+	0.0672157i
$339$		−	32.5350i		−	1.76706i
$340$	−8.45201	−	5.24202i	−0.458375	−	0.284289i
$341$		−	47.3247i		−	2.56278i
$342$	59.9022	−	33.3359i	3.23914	−	1.80260i
$343$	−1.00000			−0.0539949
$344$	0.653656	−	13.8023i	0.0352428	−	0.744172i
$345$	−9.43141			−0.507770
$346$	7.65918	−	4.26238i	0.411760	−	0.229147i
$347$			10.9924i			0.590103i	0.955481	+	0.295051i	$0.0953367\pi$
$347$			10.9924i			0.590103i	−0.955481	+	0.295051i	$0.904663\pi$
$348$	20.0740	−	32.3664i	1.07608	−	1.73502i
$349$		−	6.05336i		−	0.324029i	−0.986788	−	0.162014i	$-0.948201\pi$
$349$		−	6.05336i		−	0.324029i	0.986788	−	0.162014i	$-0.0517991\pi$
$350$	2.57901	+	4.63429i	0.137854	+	0.247713i
$351$	−12.7825			−0.682282
$352$	21.0469	+	14.4754i	1.12180	+	0.771541i
$353$	6.11657			0.325552			0.162776	−	0.986663i	$-0.447955\pi$
$353$	6.11657			0.325552			0.162776	+	0.986663i	$0.447955\pi$
$354$	−33.0444	−	59.3784i	−1.75629	−	3.15593i
$355$		−	0.589382i		−	0.0312812i
$356$	−5.35455	+	8.63345i	−0.283791	+	0.457572i
$357$			14.0910i			0.745775i
$358$	−14.1891	+	7.89631i	−0.749916	+	0.417333i
$359$	1.19941			0.0633027			0.0316513	−	0.999499i	$-0.489923\pi$
$359$	1.19941			0.0633027			0.0316513	+	0.999499i	$0.489923\pi$
$360$	−1.05232	+	22.2204i	−0.0554621	+	1.17112i
$361$	−28.4771			−1.49879
$362$	−32.6004	+	18.1423i	−1.71344	+	0.953538i
$363$		−	29.7485i		−	1.56139i
$364$	−1.69965	−	1.05414i	−0.0890856	−	0.0552518i
$365$			8.47023i			0.443352i
$366$	−14.0504	−	25.2476i	−0.734427	−	1.31971i
$367$	6.89769			0.360056			0.180028	−	0.983661i	$-0.442381\pi$
$367$	6.89769			0.360056			0.180028	+	0.983661i	$0.442381\pi$
$368$	4.73397	+	9.54288i	0.246775	+	0.497457i
$369$	34.7225			1.80758
$370$	2.15976	+	3.88093i	0.112281	+	0.201760i
$371$		−	6.02877i		−	0.312998i
$372$	−56.4274	−	34.9969i	−2.92563	−	1.81450i
$373$			11.8425i			0.613180i	0.951842	+	0.306590i	$0.0991881\pi$
$373$			11.8425i			0.613180i	−0.951842	+	0.306590i	$0.900812\pi$
$374$	24.8215	−	13.8133i	1.28349	−	0.714269i
$375$	30.9885			1.60024
$376$	−17.9521	−	0.850184i	−0.925811	−	0.0438449i
$377$	6.01139			0.309602
$378$	15.7960	−	8.79056i	0.812458	−	0.452138i
$379$		−	25.1816i		−	1.29349i	−0.762705	−	0.646746i	$-0.776129\pi$
$379$		−	25.1816i		−	1.29349i	0.762705	−	0.646746i	$-0.223871\pi$
$380$	8.12008	−	13.0925i	0.416551	−	0.671629i
$381$			69.1101i			3.54062i
$382$	−6.05940	−	10.8883i	−0.310026	−	0.557093i
$383$	−5.10219			−0.260710			−0.130355	−	0.991467i	$-0.541612\pi$
$383$	−5.10219			−0.260710			−0.130355	+	0.991467i	$0.541612\pi$
$384$	32.8239	−	14.3905i	1.67504	−	0.734362i
$385$	5.04822			0.257281
$386$	0.243416	+	0.437401i	0.0123896	+	0.0222631i
$387$			34.3689i			1.74707i
$388$	18.3621	−	29.6063i	0.932195	−	1.50303i
$389$			10.1680i			0.515536i	0.966207	+	0.257768i	$0.0829871\pi$
$389$			10.1680i			0.515536i	−0.966207	+	0.257768i	$0.917013\pi$
$390$	−4.37635	+	2.43546i	−0.221605	+	0.123324i
$391$	11.8461			0.599082
$392$	2.82526	+	0.133800i	0.142697	+	0.00675791i
$393$	−49.7645			−2.51029
$394$	6.59848	−	3.67209i	0.332427	−	0.184997i
$395$		−	5.42848i		−	0.273137i
$396$	−53.9942	−	33.4878i	−2.71331	−	1.68282i
$397$			18.3066i			0.918779i	0.888235	+	0.459390i	$0.151932\pi$
$397$			18.3066i			0.918779i	−0.888235	+	0.459390i	$0.848068\pi$
$398$	−9.29998	−	16.7114i	−0.466166	−	0.837666i
$399$	−21.8275			−1.09274
$400$	−6.66631	−	13.4381i	−0.333315	−	0.671907i
$401$	17.2034			0.859099			0.429549	−	0.903043i	$-0.358672\pi$
$401$	17.2034			0.859099			0.429549	+	0.903043i	$0.358672\pi$
$402$	−13.0352	−	23.4233i	−0.650136	−	1.16825i
$403$		−	10.4802i		−	0.522057i
$404$	20.5550	+	12.7484i	1.02265	+	0.634259i
$405$		−	21.6742i		−	1.07700i
$406$	−7.42855	+	4.13403i	−0.368673	+	0.205169i
$407$	−12.6854			−0.628791
$408$	1.88537	−	39.8108i	0.0933398	−	1.97093i
$409$	8.95836			0.442962			0.221481	−	0.975165i	$-0.428911\pi$
$409$	8.95836			0.442962			0.221481	+	0.975165i	$0.428911\pi$
$410$	6.81851	−	3.79454i	0.336742	−	0.187399i
$411$			0.564556i			0.0278475i
$412$	10.8415	−	17.4803i	0.534120	−	0.861192i
$413$			15.1683i			0.746385i
$414$	−12.8844	−	23.1523i	−0.633234	−	1.13788i
$415$	−3.33871			−0.163891
$416$	4.66090	+	3.20562i	0.228519	+	0.157169i
$417$	−38.1325			−1.86736
$418$	21.3973	+	38.4493i	1.04658	+	1.88062i
$419$		−	0.476426i		−	0.0232749i	−0.999932	−	0.0116375i	$-0.996296\pi$
$419$		−	0.476426i		−	0.0232749i	0.999932	−	0.0116375i	$-0.00370440\pi$
$420$	3.73318	−	6.01923i	0.182161	−	0.293708i
$421$			4.92425i			0.239993i	0.992774	+	0.119997i	$0.0382884\pi$
$421$			4.92425i			0.239993i	−0.992774	+	0.119997i	$0.961712\pi$
$422$	8.68655	−	4.83412i	0.422855	−	0.235321i
$423$	44.7022			2.17350
$424$	−0.806648	+	17.0329i	−0.0391743	+	0.827189i
$425$	−16.6815			−0.809171
$426$	2.06379	−	1.14851i	0.0999912	−	0.0556457i
$427$			6.44954i			0.312115i
$428$	−5.37781	−	3.33537i	−0.259946	−	0.161221i
$429$		−	14.3047i		−	0.690638i
$430$	3.75590	+	6.74908i	0.181126	+	0.325470i
$431$	17.7040			0.852770			0.426385	−	0.904542i	$-0.359787\pi$
$431$	17.7040			0.852770			0.426385	+	0.904542i	$0.359787\pi$
$432$	−45.8039	+	22.7221i	−2.20374	+	1.09322i
$433$	−13.1961			−0.634165			−0.317083	−	0.948398i	$-0.602703\pi$
$433$	−13.1961			−0.634165			−0.317083	+	0.948398i	$0.602703\pi$
$434$	7.20725	+	12.9509i	0.345959	+	0.621663i
$435$			21.2891i			1.02073i
$436$	−16.1200	−	9.99777i	−0.772007	−	0.478806i
$437$			18.3500i			0.877800i
$438$	−29.6596	+	16.5057i	−1.41719	+	0.788674i
$439$	−18.7265			−0.893767			−0.446884	−	0.894592i	$-0.647466\pi$
$439$	−18.7265			−0.893767			−0.446884	+	0.894592i	$0.647466\pi$
$440$	−14.2626	−	0.675451i	−0.679940	−	0.0322009i
$441$	−7.03512			−0.335006
$442$	5.49680	−	3.05900i	0.261456	−	0.145502i
$443$			20.1309i			0.956450i	0.878237	+	0.478225i	$0.158720\pi$
$443$			20.1309i			0.956450i	−0.878237	+	0.478225i	$0.841280\pi$
$444$	−9.38089	+	15.1253i	−0.445197	+	0.717817i
$445$		−	5.67868i		−	0.269195i
$446$	10.4489	+	18.7760i	0.494772	+	0.889068i
$447$	7.78173			0.368063
$448$	−7.96420	−	0.756038i	−0.376273	−	0.0357194i
$449$	−10.7517			−0.507403			−0.253702	−	0.967283i	$-0.581648\pi$
$449$	−10.7517			−0.507403			−0.253702	+	0.967283i	$0.581648\pi$
$450$	18.1436	+	32.6028i	0.855299	+	1.53691i
$451$			22.2873i			1.04947i
$452$	10.8265	−	17.4561i	0.509234	−	0.821067i
$453$		−	22.2713i		−	1.04640i
$454$	−3.81425	+	2.12265i	−0.179012	+	0.0996210i
$455$	1.11795			0.0524101
$456$	61.6683	+	2.92051i	2.88788	+	0.136765i
$457$	3.24345			0.151722			0.0758610	−	0.997118i	$-0.475829\pi$
$457$	3.24345			0.151722			0.0758610	+	0.997118i	$0.475829\pi$
$458$	10.0197	−	5.57601i	0.468189	−	0.260550i
$459$			56.8588i			2.65394i
$460$	−5.06027	−	3.13843i	−0.235936	−	0.146330i
$461$			27.3854i			1.27546i	0.770258	+	0.637732i	$0.220127\pi$
$461$			27.3854i			1.27546i	−0.770258	+	0.637732i	$0.779873\pi$
$462$	9.83734	+	17.6770i	0.457675	+	0.822408i
$463$	41.5405			1.93055			0.965276	−	0.261233i	$-0.0841291\pi$
$463$	41.5405			1.93055			0.965276	+	0.261233i	$0.0841291\pi$
$464$	21.5407	−	10.6858i	1.00000	−	0.496075i
$465$	37.1153			1.72118
$466$	−8.04660	−	14.4591i	−0.372751	−	0.669807i
$467$		−	22.2758i		−	1.03080i	−0.856949	−	0.515400i	$-0.827643\pi$
$467$		−	22.2758i		−	1.03080i	0.856949	−	0.515400i	$-0.172357\pi$
$468$	−11.9572	−	7.41598i	−0.552722	−	0.342804i
$469$			5.98352i			0.276293i
$470$	8.77825	−	4.88515i	0.404911	−	0.225335i
$471$	12.4720			0.574678
$472$	2.02952	−	42.8545i	0.0934162	−	1.97254i
$473$	−22.0603			−1.01433
$474$	19.0085	−	10.5783i	0.873089	−	0.485879i
$475$		−	25.8402i		−	1.18563i
$476$	−4.68897	+	7.56030i	−0.214919	+	0.346526i
$477$		−	42.4131i		−	1.94196i
$478$	17.9873	+	32.3218i	0.822718	+	1.47836i
$479$	33.6848			1.53910			0.769549	−	0.638588i	$-0.220481\pi$
$479$	33.6848			1.53910			0.769549	+	0.638588i	$0.220481\pi$
$480$	−11.3526	+	16.5064i	−0.518172	+	0.753410i
$481$	−2.80922			−0.128089
$482$	9.16977	+	16.4774i	0.417671	+	0.750525i
$483$			8.43637i			0.383868i
$484$	9.89924	−	15.9611i	0.449965	−	0.725505i
$485$			19.4736i			0.884251i
$486$	28.5070	−	15.8643i	1.29310	−	0.719620i
$487$	8.82614			0.399951			0.199975	−	0.979801i	$-0.435914\pi$
$487$	8.82614			0.399951			0.199975	+	0.979801i	$0.435914\pi$
$488$	0.862947	−	18.2216i	0.0390638	−	0.824855i
$489$	43.4156			1.96332
$490$	−1.38150	+	0.768812i	−0.0624097	+	0.0347314i
$491$			8.33126i			0.375984i	0.982171	+	0.187992i	$0.0601980\pi$
$491$			8.33126i			0.375984i	−0.982171	+	0.187992i	$0.939802\pi$
$492$	26.5741	+	16.4815i	1.19805	+	0.743045i
$493$		−	26.7396i		−	1.20429i
$494$	4.73850	+	8.51474i	0.213195	+	0.383096i
$495$	35.5149			1.59627
$496$	−18.6295	−	37.5540i	−0.836491	−	1.68622i
$497$	−0.527201			−0.0236482
$498$	−6.50606	−	11.6909i	−0.291544	−	0.523882i
$499$		−	24.1391i		−	1.08061i	−0.841468	−	0.540306i	$-0.818308\pi$
$499$		−	24.1391i		−	1.08061i	0.841468	−	0.540306i	$-0.181692\pi$
$500$	16.6264	+	10.3118i	0.743553	+	0.461159i
$501$		−	32.2611i		−	1.44132i
$502$	−18.5970	+	10.3493i	−0.830024	+	0.461913i
$503$	23.5917			1.05190			0.525952	−	0.850514i	$-0.323709\pi$
$503$	23.5917			1.05190			0.525952	+	0.850514i	$0.323709\pi$
$504$	19.8760	+	0.941297i	0.885349	+	0.0419287i
$505$	−13.5201			−0.601638
$506$	14.8608	−	8.27010i	0.660641	−	0.367651i
$507$		−	3.16783i		−	0.140688i
$508$	−22.9973	+	37.0799i	−1.02034	+	1.64516i
$509$		−	28.5768i		−	1.26664i	−0.773889	−	0.633322i	$-0.781691\pi$
$509$		−	28.5768i		−	1.26664i	0.773889	−	0.633322i	$-0.218309\pi$
$510$	10.8333	+	19.4667i	0.479708	+	0.862000i
$511$	7.57660			0.335169
$512$	22.3998	+	3.20161i	0.989939	+	0.141493i
$513$	−88.0764			−3.88867
$514$	−0.935564	−	1.68114i	−0.0412660	−	0.0741519i
$515$			11.4977i			0.506650i
$516$	−16.3137	+	26.3035i	−0.718171	+	1.15795i
$517$			28.6930i			1.26192i
$518$	3.47148	−	1.93190i	0.152528	−	0.0848829i
$519$	−19.6343			−0.861848
$520$	−3.15849	−	0.149581i	−0.138509	−	0.00655956i
$521$	−13.2632			−0.581070			−0.290535	−	0.956864i	$-0.593833\pi$
$521$	−13.2632			−0.581070			−0.290535	+	0.956864i	$0.593833\pi$
$522$	−52.2607	+	29.0834i	−2.28739	+	1.27295i
$523$		−	21.7999i		−	0.953243i	−0.879109	−	0.476621i	$-0.841861\pi$
$523$		−	21.7999i		−	0.953243i	0.879109	−	0.476621i	$-0.158139\pi$
$524$	−26.7003	−	16.5598i	−1.16641	−	0.723419i
$525$		−	11.8800i		−	0.518484i
$526$	7.64371	+	13.7352i	0.333282	+	0.598882i
$527$	−46.6178			−2.03070
$528$	−25.4279	−	51.2583i	−1.10661	−	2.23073i
$529$	−15.9077			−0.691638
$530$	−4.63499	−	8.32874i	−0.201331	−	0.361777i
$531$			106.711i			4.63087i
$532$	−11.7112	−	7.26339i	−0.507744	−	0.314908i
$533$			4.93559i			0.213784i
$534$	19.8846	−	11.0659i	0.860490	−	0.478868i
$535$	3.53727			0.152930
$536$	0.800594	−	16.9050i	0.0345804	−	0.730185i
$537$	36.3736			1.56964
$538$	8.87858	−	4.94098i	0.382783	−	0.213021i
$539$		−	4.51562i		−	0.194502i
$540$	15.0638	−	24.2883i	0.648244	−	1.04520i
$541$			35.2967i			1.51753i	0.651367	+	0.758763i	$0.274196\pi$
$541$			35.2967i			1.51753i	−0.651367	+	0.758763i	$0.725804\pi$
$542$	−18.1310	−	32.5800i	−0.778791	−	1.39943i
$543$	83.5707			3.58636
$544$	14.2591	−	20.7324i	0.611356	−	0.888896i
$545$	10.6030			0.454181
$546$	2.17851	+	3.91463i	0.0932318	+	0.167531i
$547$		−	25.6660i		−	1.09740i	−0.836020	−	0.548699i	$-0.815123\pi$
$547$		−	25.6660i		−	1.09740i	0.836020	−	0.548699i	$-0.184877\pi$
$548$	−0.187864	+	0.302903i	−0.00802514	+	0.0129394i
$549$			45.3733i			1.93648i
$550$	−20.9267	+	11.6458i	−0.892317	+	0.496580i
$551$	41.4206			1.76458
$552$	1.12878	−	23.8349i	0.0480442	−	1.01448i
$553$	−4.85576			−0.206488
$554$	11.8925	−	6.61823i	0.505263	−	0.281182i
$555$		−	9.94874i		−	0.422301i
$556$	−20.4594	−	12.6891i	−0.867672	−	0.538139i
$557$		−	23.9095i		−	1.01308i	−0.862218	−	0.506538i	$-0.830925\pi$
$557$		−	23.9095i		−	1.01308i	0.862218	−	0.506538i	$-0.169075\pi$
$558$	50.7039	+	91.1111i	2.14647	+	3.85704i
$559$	−4.88533			−0.206628
$560$	4.00596	−	1.98725i	0.169283	−	0.0839766i
$561$	−63.6296			−2.68645
$562$	9.49281	+	17.0579i	0.400430	+	0.719543i
$563$		−	4.23760i		−	0.178594i	−0.996005	−	0.0892969i	$-0.971538\pi$
$563$		−	4.23760i		−	0.178594i	0.996005	−	0.0892969i	$-0.0284620\pi$
$564$	34.2119	+	21.2186i	1.44058	+	0.893463i
$565$			11.4818i			0.483044i
$566$	9.59365	−	5.33892i	0.403251	−	0.224412i
$567$	−19.3875			−0.814199
$568$	1.48948	+	0.0705393i	0.0624972	+	0.00295976i
$569$	14.1681			0.593958			0.296979	−	0.954884i	$-0.404021\pi$
$569$	14.1681			0.593958			0.296979	+	0.954884i	$0.404021\pi$
$570$	−30.1546	+	16.7812i	−1.26304	+	0.702888i
$571$			27.7699i			1.16213i	0.813856	+	0.581066i	$0.197364\pi$
$571$			27.7699i			1.16213i	−0.813856	+	0.581066i	$0.802636\pi$
$572$	4.76009	−	7.67496i	0.199029	−	0.320906i
$573$			27.9120i			1.16604i
$574$	−3.39421	−	6.09914i	−0.141671	−	0.254573i
$575$	−9.98730			−0.416499
$576$	−56.0290	−	5.31882i	−2.33454	−	0.221617i
$577$	10.7261			0.446534			0.223267	−	0.974757i	$-0.428328\pi$
$577$	10.7261			0.446534			0.223267	+	0.974757i	$0.428328\pi$
$578$	−1.91604	−	3.44298i	−0.0796966	−	0.143209i
$579$		−	1.12128i		−	0.0465986i
$580$	−7.08424	+	11.4223i	−0.294157	+	0.474286i
$581$			2.98647i			0.123900i
$582$	−68.1892	+	37.9477i	−2.82654	+	1.57298i
$583$	27.2237			1.12749
$584$	−21.4059	−	1.01375i	−0.885781	−	0.0419491i
$585$	7.86489			0.325173
$586$	28.9436	−	16.1073i	1.19565	−	0.665386i
$587$		−	38.0092i		−	1.56881i	−0.620251	−	0.784403i	$-0.712969\pi$
$587$		−	38.0092i		−	1.56881i	0.620251	−	0.784403i	$-0.287031\pi$
$588$	−5.38418	−	3.33932i	−0.222040	−	0.137711i
$589$		−	72.2125i		−	2.97547i
$590$	11.6616	+	20.9550i	0.480101	+	0.862705i
$591$	−16.9151			−0.695796
$592$	−10.0663	+	4.99364i	−0.413724	+	0.205237i
$593$	16.4663			0.676190			0.338095	−	0.941112i	$-0.390217\pi$
$593$	16.4663			0.676190			0.338095	+	0.941112i	$0.390217\pi$
$594$	39.6948	+	71.3287i	1.62870	+	2.92665i
$595$		−	4.97281i		−	0.203865i
$596$	4.17516	+	2.58948i	0.171021	+	0.106069i
$597$			42.8395i			1.75330i
$598$	3.29097	−	1.83144i	0.134578	−	0.0748932i
$599$	28.8517			1.17885			0.589425	−	0.807823i	$-0.299354\pi$
$599$	28.8517			1.17885			0.589425	+	0.807823i	$0.299354\pi$
$600$	−1.58954	+	33.5640i	−0.0648925	+	1.37024i
$601$	6.29534			0.256792			0.128396	−	0.991723i	$-0.459017\pi$
$601$	6.29534			0.256792			0.128396	+	0.991723i	$0.459017\pi$
$602$	6.03703	−	3.35964i	0.246051	−	0.136929i
$603$			42.0948i			1.71423i
$604$	7.41110	−	11.9493i	0.301553	−	0.486211i
$605$			10.4985i			0.426823i
$606$	−26.3463	−	47.3424i	−1.07025	−	1.92315i
$607$	15.7914			0.640954			0.320477	−	0.947256i	$-0.396157\pi$
$607$	15.7914			0.640954			0.320477	+	0.947256i	$0.396157\pi$
$608$	32.1153	+	22.0879i	1.30245	+	0.895783i
$609$	19.0430			0.771662
$610$	4.95849	+	8.91003i	0.200763	+	0.360757i
$611$			6.35415i			0.257062i
$612$	−32.9875	+	53.1876i	−1.33344	+	2.14998i
$613$			44.8229i			1.81038i	0.425008	+	0.905189i	$0.360271\pi$
$613$			44.8229i			1.81038i	−0.425008	+	0.905189i	$0.639729\pi$
$614$	8.80359	−	4.89925i	0.355284	−	0.197718i
$615$	−17.4792			−0.704829
$616$	−0.604189	+	12.7578i	−0.0243435	+	0.514027i
$617$	41.5256			1.67176			0.835879	−	0.548913i	$-0.184958\pi$
$617$	41.5256			1.67176			0.835879	+	0.548913i	$0.184958\pi$
$618$	−40.2607	+	22.4053i	−1.61952	+	0.901273i
$619$		−	40.6374i		−	1.63335i	−0.577095	−	0.816677i	$-0.695814\pi$
$619$		−	40.6374i		−	1.63335i	0.577095	−	0.816677i	$-0.304186\pi$
$620$	19.9136	+	12.3506i	0.799750	+	0.496013i
$621$			34.0417i			1.36605i
$622$	11.2725	+	20.2559i	0.451988	+	0.812189i
$623$	−5.07956			−0.203508
$624$	−5.63109	−	11.3513i	−0.225424	−	0.454417i
$625$	7.81494			0.312598
$626$	−10.0131	−	17.9929i	−0.400205	−	0.719139i
$627$		−	98.5646i		−	3.93629i
$628$	6.69164	+	4.15022i	0.267025	+	0.165612i
$629$			12.4959i			0.498243i
$630$	−9.71900	+	5.40868i	−0.387214	+	0.215487i
$631$	19.3579			0.770624			0.385312	−	0.922786i	$-0.374094\pi$
$631$	19.3579			0.770624			0.385312	+	0.922786i	$0.374094\pi$
$632$	13.7188	+	0.649699i	0.545704	+	0.0258437i
$633$	−22.2679			−0.885069
$634$	−30.3012	+	16.8628i	−1.20342	+	0.669708i
$635$		−	24.3894i		−	0.967865i
$636$	20.1320	−	32.4600i	0.798287	−	1.28712i
$637$		−	1.00000i		−	0.0396214i
$638$	−18.6677	−	33.5445i	−0.739062	−	1.32804i
$639$	−3.70892			−0.146723
$640$	−11.5838	+	5.07850i	−0.457889	+	0.200745i
$641$	23.1842			0.915719			0.457860	−	0.889024i	$-0.348616\pi$
$641$	23.1842			0.915719			0.457860	+	0.889024i	$0.348616\pi$
$642$	6.89299	+	12.3862i	0.272045	+	0.488844i
$643$			36.1071i			1.42393i	0.702217	+	0.711963i	$0.252194\pi$
$643$			36.1071i			1.42393i	−0.702217	+	0.711963i	$0.747806\pi$
$644$	−2.80732	+	4.52640i	−0.110624	+	0.178365i
$645$		−	17.3012i		−	0.681235i
$646$	37.8749	−	21.0776i	1.49017	−	0.829288i
$647$	23.0515			0.906248			0.453124	−	0.891447i	$-0.350309\pi$
$647$	23.0515			0.906248			0.453124	+	0.891447i	$0.350309\pi$
$648$	54.7748	+	2.59404i	2.15176	+	0.101904i
$649$	−68.4945			−2.68864
$650$	−4.63429	+	2.57901i	−0.181772	+	0.101157i
$651$		−	33.1995i		−	1.30119i
$652$	23.2939	+	14.4471i	0.912261	+	0.565794i
$653$			10.6277i			0.415893i	0.978140	+	0.207946i	$0.0666780\pi$
$653$			10.6277i			0.415893i	−0.978140	+	0.207946i	$0.933322\pi$
$654$	20.6617	+	37.1276i	0.807937	+	1.45180i
$655$	17.5622			0.686213
$656$	8.77346	+	17.6858i	0.342546	+	0.690515i
$657$	53.3023			2.07952
$658$	−4.36975	−	7.85212i	−0.170351	−	0.306108i
$659$		−	31.8733i		−	1.24161i	−0.783965	−	0.620804i	$-0.786806\pi$
$659$		−	31.8733i		−	1.24161i	0.783965	−	0.620804i	$-0.213194\pi$
$660$	27.1805	+	16.8577i	1.05800	+	0.656183i
$661$		−	32.4525i		−	1.26225i	−0.775679	−	0.631127i	$-0.782593\pi$
$661$		−	32.4525i		−	1.26225i	0.775679	−	0.631127i	$-0.217407\pi$
$662$	−1.42477	+	0.792895i	−0.0553754	+	0.0308167i
$663$	−14.0910			−0.547249
$664$	0.399589	−	8.43755i	0.0155070	−	0.327441i
$665$	7.70306			0.298712
$666$	24.4223	−	13.5911i	0.946345	−	0.526646i
$667$		−	16.0092i		−	0.619878i
$668$	10.7353	−	17.3092i	0.415362	−	0.669712i
$669$		−	48.1321i		−	1.86089i
$670$	4.60020	+	8.26623i	0.177721	+	0.319352i
$671$	−29.1237			−1.12431
$672$	14.7649	+	10.1549i	0.569569	+	0.391732i
$673$	−26.9401			−1.03846			−0.519232	−	0.854633i	$-0.673782\pi$
$673$	−26.9401			−1.03846			−0.519232	+	0.854633i	$0.673782\pi$
$674$	−23.4312	−	42.1041i	−0.902535	−	1.62179i
$675$		−	47.9370i		−	1.84510i
$676$	1.05414	−	1.69965i	0.0405437	−	0.0653710i
$677$			27.8214i			1.06926i	0.845085	+	0.534632i	$0.179550\pi$
$677$			27.8214i			1.06926i	−0.845085	+	0.534632i	$0.820450\pi$
$678$	−40.2050	+	22.3743i	−1.54406	+	0.859280i
$679$	17.4191			0.668483
$680$	−0.665360	+	14.0495i	−0.0255154	+	0.538773i
$681$	9.77780			0.374686
$682$	−58.4814	+	32.5452i	−2.23937	+	1.24622i
$683$			36.9656i			1.41445i	0.706990	+	0.707224i	$0.250053\pi$
$683$			36.9656i			1.41445i	−0.706990	+	0.707224i	$0.749947\pi$
$684$	−82.3895	−	51.0988i	−3.15024	−	1.95381i
$685$		−	0.199235i		−	0.00761240i
$686$	0.687700	+	1.23575i	0.0262565	+	0.0471810i
$687$	−25.6854			−0.979958
$688$	−17.5057	+	8.68412i	−0.667399	+	0.331079i
$689$	6.02877			0.229678
$690$	6.48598	+	11.6548i	0.246917	+	0.443692i
$691$		−	23.6432i		−	0.899428i	−0.893173	−	0.449714i	$-0.851526\pi$
$691$		−	23.6432i		−	0.899428i	0.893173	−	0.449714i	$-0.148474\pi$
$692$	−10.5344	−	6.53357i	−0.400459	−	0.248369i
$693$		−	31.7679i		−	1.20676i
$694$	13.5838	−	7.55947i	0.515634	−	0.286954i
$695$	13.4572			0.510462
$696$	−53.8015	−	2.54795i	−2.03934	−	0.0965799i
$697$	21.9543			0.831579
$698$	−7.48041	+	4.16289i	−0.283138	+	0.157568i
$699$			37.0659i			1.40196i
$700$	3.95322	−	6.37400i	0.149418	−	0.240915i
$701$		−	7.24572i		−	0.273667i	−0.990594	−	0.136833i	$-0.956307\pi$
$701$		−	7.24572i		−	0.273667i	0.990594	−	0.136833i	$-0.0436925\pi$
$702$	8.79056	+	15.7960i	0.331778	+	0.596181i
$703$	−19.3565			−0.730046
$704$	3.41398	−	35.9633i	0.128669	−	1.35542i
$705$	−22.5030			−0.847511
$706$	−4.20636	−	7.55853i	−0.158309	−	0.284469i
$707$			12.0937i			0.454831i
$708$	−50.6520	+	81.6691i	−1.90362	+	3.06931i
$709$		−	6.77224i		−	0.254337i	−0.991881	−	0.127168i	$-0.959411\pi$
$709$		−	6.77224i		−	0.254337i	0.991881	−	0.127168i	$-0.0405889\pi$
$710$	−0.728327	+	0.405318i	−0.0273336	+	0.0152113i
$711$	−34.1608			−1.28113
$712$	14.3511	+	0.679644i	0.537829	+	0.0254707i
$713$	−27.9103			−1.04525
$714$	17.4129	−	9.69038i	0.651662	−	0.362653i
$715$			5.04822i			0.188793i
$716$	19.5157	+	12.1038i	0.729334	+	0.452341i
$717$		−	82.8566i		−	3.09434i
$718$	−0.824837	−	1.48217i	−0.0307827	−	0.0553142i
$719$	−49.7201			−1.85425			−0.927124	−	0.374756i	$-0.877727\pi$
$719$	−49.7201			−1.85425			−0.927124	+	0.374756i	$0.877727\pi$
$720$	28.1824	−	13.9805i	1.05030	−	0.521024i
$721$	10.2847			0.383021
$722$	19.5837	+	35.1904i	0.728829	+	1.30965i
$723$		−	42.2397i		−	1.57091i
$724$	44.8385	+	27.8093i	1.66641	+	1.03352i
$725$			22.5439i			0.837259i
$726$	−36.7617	+	20.4581i	−1.36435	+	0.759271i
$727$	−12.0287			−0.446121			−0.223060	−	0.974805i	$-0.571605\pi$
$727$	−12.0287			−0.446121			−0.223060	+	0.974805i	$0.571605\pi$
$728$	−0.133800	+	2.82526i	−0.00495895	+	0.104711i
$729$	−14.9149			−0.552402
$730$	10.4671	−	5.82498i	0.387403	−	0.215592i
$731$			21.7308i			0.803741i
$732$	−21.5371	+	34.7255i	−0.796034	+	1.28349i
$733$		−	31.1191i		−	1.14941i	−0.818360	−	0.574706i	$-0.805117\pi$
$733$		−	31.1191i		−	1.14941i	0.818360	−	0.574706i	$-0.194883\pi$
$734$	−4.74354	−	8.52379i	−0.175087	−	0.314619i
$735$	3.54146			0.130629
$736$	8.53703	−	12.4126i	0.314679	−	0.457536i
$737$	−27.0193			−0.995270
$738$	−23.8786	−	42.9082i	−0.878985	−	1.57947i
$739$			44.6644i			1.64301i	0.570204	+	0.821503i	$0.306864\pi$
$739$			44.6644i			1.64301i	−0.570204	+	0.821503i	$0.693136\pi$
$740$	3.31058	−	5.33784i	0.121699	−	0.196223i
$741$		−	21.8275i		−	0.801852i
$742$	−7.45003	+	4.14599i	−0.273499	+	0.152204i
$743$	−17.5023			−0.642099			−0.321049	−	0.947062i	$-0.604036\pi$
$743$	−17.5023			−0.642099			−0.321049	+	0.947062i	$0.604036\pi$
$744$	−4.44209	+	93.7973i	−0.162855	+	3.43878i
$745$	−2.74622			−0.100614
$746$	14.6343	−	8.14407i	0.535800	−	0.298176i
$747$			21.0102i			0.768722i
$748$	−34.1395	−	21.1736i	−1.24826	−	0.774185i
$749$		−	3.16408i		−	0.115613i
$750$	−21.3108	−	38.2939i	−0.778159	−	1.39829i
$751$	−26.6034			−0.970774			−0.485387	−	0.874300i	$-0.661321\pi$
$751$	−26.6034			−0.970774			−0.485387	+	0.874300i	$0.661321\pi$
$752$	11.2951	+	22.7690i	0.411889	+	0.830299i
$753$	47.6732			1.73731
$754$	−4.13403	−	7.42855i	−0.150553	−	0.270532i
$755$			7.85971i			0.286044i
$756$	−21.7258	−	13.4746i	−0.790160	−	0.490065i
$757$			28.6275i			1.04048i	0.854019	+	0.520242i	$0.174158\pi$
$757$			28.6275i			1.04048i	−0.854019	+	0.520242i	$0.825842\pi$
$758$	−31.1181	+	17.3174i	−1.13026	+	0.628996i
$759$	−38.0954			−1.38278
$760$	−21.7631	−	1.03067i	−0.789432	−	0.0373862i
$761$	23.5126			0.852332			0.426166	−	0.904645i	$-0.359864\pi$
$761$	23.5126			0.852332			0.426166	+	0.904645i	$0.359864\pi$
$762$	85.4026	−	47.5271i	3.09381	−	1.72172i
$763$		−	9.48432i		−	0.343355i
$764$	−9.28812	+	14.9758i	−0.336032	+	0.541804i
$765$		−	34.9843i		−	1.26486i
$766$	3.50878	+	6.30502i	0.126777	+	0.227809i
$767$	−15.1683			−0.547697
$768$	−40.3560	−	30.6657i	−1.45622	−	1.10655i
$769$	1.86478			0.0672456			0.0336228	−	0.999435i	$-0.489296\pi$
$769$	1.86478			0.0672456			0.0336228	+	0.999435i	$0.489296\pi$
$770$	−3.47166	−	6.23832i	−0.125110	−	0.224814i
$771$			4.30959i			0.155206i
$772$	0.373120	−	0.601602i	0.0134289	−	0.0216521i
$773$			30.6421i			1.10212i	0.834466	+	0.551060i	$0.185776\pi$
$773$			30.6421i			1.10212i	−0.834466	+	0.551060i	$0.814224\pi$
$774$	42.4712	−	23.6355i	1.52660	−	0.849560i
$775$	39.3029			1.41180
$776$	−49.2135	−	2.33067i	−1.76666	−	0.0836661i
$777$	−8.89912			−0.319254
$778$	12.5650	−	6.99251i	0.450478	−	0.250694i
$779$			34.0080i			1.21846i
$780$	6.01923	+	3.73318i	0.215523	+	0.133669i
$781$		−	2.38064i		−	0.0851860i
$782$	−8.14655	−	14.6388i	−0.291320	−	0.523481i
$783$	76.8408			2.74607
$784$	−1.77759	−	3.58332i	−0.0634853	−	0.127976i
$785$	−4.40144			−0.157094
$786$	34.2230	+	61.4963i	1.22070	+	2.19350i
$787$			52.8326i			1.88328i	0.336622	+	0.941640i	$0.390715\pi$
$787$			52.8326i			1.88328i	−0.336622	+	0.941640i	$0.609285\pi$
$788$	−9.07555	−	5.62875i	−0.323303	−	0.200516i
$789$		−	35.2100i		−	1.25351i
$790$	−6.70822	+	3.73317i	−0.238668	+	0.132820i
$791$	10.2704			0.365175
$792$	−4.25054	+	89.7527i	−0.151036	+	3.18922i
$793$	−6.44954			−0.229030
$794$	22.6223	−	12.5894i	0.802834	−	0.446782i
$795$			21.3507i			0.757230i
$796$	−14.2554	+	22.9848i	−0.505270	+	0.814676i
$797$			1.45717i			0.0516158i	0.999667	+	0.0258079i	$0.00821582\pi$
$797$			1.45717i			0.0516158i	−0.999667	+	0.0258079i	$0.991784\pi$
$798$	15.0107	+	26.9732i	0.531375	+	0.954841i
$799$	28.2643			0.999920
$800$	−12.0217	+	17.4793i	−0.425032	+	0.617986i
$801$	−35.7353			−1.26264
$802$	−11.8308	−	21.2591i	−0.417760	−	0.750685i
$803$			34.2131i			1.20735i
$804$	−19.9809	+	32.2164i	−0.704672	+	1.13618i
$805$		−	2.97725i		−	0.104934i
$806$	−12.9509	+	7.20725i	−0.456176	+	0.253865i
$807$	−22.7602			−0.801196
$808$	1.61814	−	34.1679i	0.0569259	−	1.20202i
$809$	12.8081			0.450308			0.225154	−	0.974323i	$-0.427712\pi$
$809$	12.8081			0.450308			0.225154	+	0.974323i	$0.427712\pi$
$810$	−26.7838	+	14.9054i	−0.941088	+	0.523721i
$811$			25.1200i			0.882083i	0.897487	+	0.441042i	$0.145391\pi$
$811$			25.1200i			0.882083i	−0.897487	+	0.441042i	$0.854609\pi$
$812$	10.2172	+	6.33683i	0.358554	+	0.222379i
$813$			83.5185i			2.92912i
$814$	8.72373	+	15.6759i	0.305767	+	0.549440i
$815$	−15.3217			−0.536694
$816$	−50.4926	+	25.0480i	−1.76759	+	0.876856i
$817$	−33.6617			−1.17767
$818$	−6.16066	−	11.0703i	−0.215403	−	0.387062i
$819$		−	7.03512i		−	0.245827i
$820$	−9.37818	−	5.81644i	−0.327500	−	0.203119i
$821$		−	38.6333i		−	1.34831i	−0.738590	−	0.674155i	$-0.764508\pi$
$821$		−	38.6333i		−	1.34831i	0.738590	−	0.674155i	$-0.235492\pi$
$822$	0.697648	−	0.388245i	0.0243333	−	0.0135416i
$823$	23.7386			0.827476			0.413738	−	0.910396i	$-0.364223\pi$
$823$	23.7386			0.827476			0.413738	+	0.910396i	$0.364223\pi$
$824$	−29.0569	−	1.37609i	−1.01224	−	0.0479382i
$825$	53.6454			1.86769
$826$	18.7442	−	10.4313i	0.652195	−	0.362950i
$827$			7.45758i			0.259325i	0.991558	+	0.129663i	$0.0413895\pi$
$827$			7.45758i			0.259325i	−0.991558	+	0.129663i	$0.958611\pi$
$828$	−19.7498	+	31.8437i	−0.686353	+	1.10665i
$829$		−	13.2732i		−	0.460998i	−0.973073	−	0.230499i	$-0.925964\pi$
$829$		−	13.2732i		−	0.460998i	0.973073	−	0.230499i	$-0.0740358\pi$
$830$	2.29603	+	4.12580i	0.0796965	+	0.143209i
$831$	−30.4862			−1.05756
$832$	0.756038	−	7.96420i	0.0262109	−	0.276109i
$833$	−4.44816			−0.154120
$834$	26.2238	+	47.1221i	0.908054	+	1.63171i
$835$			11.3852i			0.394000i
$836$	32.7987	−	52.8832i	1.13437	−	1.82900i
$837$		−	133.964i		−	4.63047i
$838$	−0.588742	+	0.327638i	−0.0203377	+	0.0113181i
$839$	−33.6190			−1.16066			−0.580328	−	0.814383i	$-0.697076\pi$
$839$	−33.6190			−1.16066			−0.580328	+	0.814383i	$0.697076\pi$
$840$	−10.0055	−	0.473846i	−0.345224	−	0.0163493i
$841$	−7.13678			−0.246096
$842$	6.08512	−	3.38641i	0.209707	−	0.116703i
$843$		−	43.7277i		−	1.50606i
$844$	−11.9475	−	7.40995i	−0.411249	−	0.255061i
$845$			1.11795i			0.0384585i
$846$	−30.7417	−	55.2406i	−1.05692	−	1.89921i
$847$	9.39084			0.322673
$848$	21.6030	−	10.7167i	0.741851	−	0.368013i
$849$	−24.5932			−0.844038
$850$	11.4719	+	20.6141i	0.393481	+	0.707057i
$851$			7.48135i			0.256457i
$852$	−2.83854	−	1.76049i	−0.0972469	−	0.0603135i
$853$			5.30251i			0.181554i	0.995871	+	0.0907772i	$0.0289351\pi$
$853$			5.30251i			0.181554i	−0.995871	+	0.0907772i	$0.971065\pi$
$854$	7.97000	−	4.43535i	0.272728	−	0.151775i
$855$	54.1919			1.85332
$856$	−0.423353	+	8.93935i	−0.0144699	+	0.305541i
$857$	−44.8103			−1.53069			−0.765346	−	0.643619i	$-0.777432\pi$
$857$	−44.8103			−1.53069			−0.765346	+	0.643619i	$0.777432\pi$
$858$	−17.6770	+	9.83734i	−0.603482	+	0.335841i
$859$			25.3400i			0.864590i	0.901732	+	0.432295i	$0.142296\pi$
$859$			25.3400i			0.864590i	−0.901732	+	0.432295i	$0.857704\pi$
$860$	5.75722	−	9.28269i	0.196319	−	0.316537i
$861$			15.6351i			0.532843i
$862$	−12.1750	−	21.8776i	−0.414683	−	0.745154i
$863$	−22.2518			−0.757462			−0.378731	−	0.925507i	$-0.623639\pi$
$863$	−22.2518			−0.757462			−0.378731	+	0.925507i	$0.623639\pi$
$864$	59.5781	+	40.9760i	2.02689	+	1.39403i
$865$	6.92906			0.235595
$866$	9.07498	+	16.3071i	0.308380	+	0.554137i
$867$			8.82604i			0.299748i
$868$	11.0476	−	17.8127i	0.374980	−	0.604601i
$869$		−	21.9268i		−	0.743815i
$870$	26.3079	−	14.6405i	0.891922	−	0.496360i
$871$	−5.98352			−0.202744
$872$	−1.26900	+	26.7957i	−0.0429737	+	0.907416i
$873$	122.545			4.14753
$874$	22.6759	−	12.6193i	0.767025	−	0.426854i
$875$			9.78225i			0.330700i
$876$	40.7938	+	25.3007i	1.37829	+	0.854832i
$877$			16.4120i			0.554194i	0.960842	+	0.277097i	$0.0893723\pi$
$877$			16.4120i			0.554194i	−0.960842	+	0.277097i	$0.910628\pi$
$878$	12.8782	+	23.1412i	0.434619	+	0.780978i
$879$	−74.1967			−2.50259
$880$	8.97367	+	18.0894i	0.302502	+	0.609794i
$881$	−13.3626			−0.450197			−0.225098	−	0.974336i	$-0.572270\pi$
$881$	−13.3626			−0.450197			−0.225098	+	0.974336i	$0.572270\pi$
$882$	4.83805	+	8.69362i	0.162906	+	0.292729i
$883$		−	49.7871i		−	1.67547i	−0.546077	−	0.837735i	$-0.683880\pi$
$883$		−	49.7871i		−	1.67547i	0.546077	−	0.837735i	$-0.316120\pi$
$884$	−7.56030	−	4.68897i	−0.254280	−	0.157707i
$885$		−	53.7181i		−	1.80571i
$886$	24.8767	−	13.8440i	0.835750	−	0.465100i
$887$	−4.91098			−0.164895			−0.0824473	−	0.996595i	$-0.526274\pi$
$887$	−4.91098			−0.164895			−0.0824473	+	0.996595i	$0.526274\pi$
$888$	25.1423	+	1.19070i	0.843721	+	0.0399573i
$889$	−21.8163			−0.731694
$890$	−7.01740	+	3.90523i	−0.235224	+	0.130903i
$891$		−	87.5467i		−	2.93293i
$892$	16.0166	−	25.8245i	0.536276	−	0.864668i
$893$			43.7824i			1.46512i
$894$	−5.35150	−	9.61624i	−0.178981	−	0.321615i
$895$	−12.8365			−0.429076
$896$	4.54271	+	10.3617i	0.151761	+	0.346158i
$897$	−8.43637			−0.281682
$898$	7.39393	+	13.2864i	0.246739	+	0.443371i
$899$			63.0007i			2.10119i
$900$	27.8114	−	44.8419i	0.927046	−	1.49473i
$901$		−	26.8170i		−	0.893403i
$902$	27.5414	−	15.3270i	0.917029	−	0.510332i
$903$	−15.4759			−0.515005
$904$	−29.0167	−	1.37418i	−0.965081	−	0.0457047i
$905$	−29.4927			−0.980370
$906$	−27.5217	+	15.3160i	−0.914348	+	0.508840i
$907$			14.1867i			0.471062i	0.971867	+	0.235531i	$0.0756829\pi$
$907$			14.1867i			0.471062i	−0.971867	+	0.235531i	$0.924317\pi$
$908$	5.24612	+	3.25370i	0.174099	+	0.107978i
$909$			85.0808i			2.82195i
$910$	−0.768812	−	1.38150i	−0.0254859	−	0.0457962i
$911$	−5.49425			−0.182033			−0.0910163	−	0.995849i	$-0.529012\pi$
$911$	−5.49425			−0.182033			−0.0910163	+	0.995849i	$0.529012\pi$
$912$	−38.8003	−	78.2148i	−1.28481	−	2.58995i
$913$	−13.4858			−0.446314
$914$	−2.23052	−	4.00808i	−0.0737790	−	0.132575i
$915$		−	22.8408i		−	0.755093i
$916$	−13.7811	−	8.54716i	−0.455339	−	0.282406i
$917$		−	15.7094i		−	0.518768i
$918$	70.2631	−	39.1018i	2.31903	−	1.29055i
$919$	53.9477			1.77957			0.889785	−	0.456379i	$-0.150854\pi$
$919$	53.9477			1.77957			0.889785	+	0.456379i	$0.150854\pi$
$920$	−0.398355	+	8.41151i	−0.0131334	+	0.277319i
$921$	−22.5679			−0.743638
$922$	33.8414	−	18.8329i	1.11451	−	0.620229i
$923$		−	0.527201i		−	0.0173530i
$924$	15.0791	−	24.3129i	0.496067	−	0.799836i
$925$		−	10.5351i		−	0.346393i
$926$	−28.5674	−	51.3335i	−0.938784	−	1.68692i
$927$	72.3539			2.37641
$928$	−28.0185	−	19.2703i	−0.919751	−	0.632577i
$929$	−4.12817			−0.135441			−0.0677204	−	0.997704i	$-0.521573\pi$
$929$	−4.12817			−0.135441			−0.0677204	+	0.997704i	$0.521573\pi$
$930$	−25.5242	−	45.8651i	−0.836971	−	1.50398i
$931$		−	6.89036i		−	0.225822i
$932$	−12.3342	+	19.8871i	−0.404020	+	0.651424i
$933$		−	51.9259i		−	1.69998i
$934$	−27.5272	+	15.3191i	−0.900718	+	0.501255i
$935$	22.4553			0.734368
$936$	−0.941297	+	19.8760i	−0.0307672	+	0.649669i
$937$	6.95266			0.227134			0.113567	−	0.993530i	$-0.463772\pi$
$937$	6.95266			0.227134			0.113567	+	0.993530i	$0.463772\pi$
$938$	7.39412	−	4.11487i	0.241426	−	0.134355i
$939$			46.1245i			1.50522i
$940$	−12.0736	−	7.48818i	−0.393798	−	0.244237i
$941$			20.5079i			0.668539i	0.942478	+	0.334270i	$0.108490\pi$
$941$			20.5079i			0.668539i	−0.942478	+	0.334270i	$0.891510\pi$
$942$	−8.57698	−	15.4122i	−0.279453	−	0.502157i
$943$	13.1442			0.428033
$944$	−54.3530	+	26.9631i	−1.76904	+	0.877574i
$945$	14.2902			0.464860
$946$	15.1709	+	27.2610i	0.493248	+	0.886330i
$947$		−	20.6521i		−	0.671102i	−0.942022	−	0.335551i	$-0.891077\pi$
$947$		−	20.6521i		−	0.671102i	0.942022	−	0.335551i	$-0.108923\pi$
$948$	−26.1443	−	16.2149i	−0.849127	−	0.526637i
$949$			7.57660i			0.245947i
$950$	−31.9319	+	17.7703i	−1.03601	+	0.576545i
$951$	77.6769			2.51885
$952$	12.5672	+	0.595163i	0.407306	+	0.0192893i
$953$	61.2746			1.98488			0.992440	−	0.122730i	$-0.0391649\pi$
$953$	61.2746			1.98488			0.992440	+	0.122730i	$0.0391649\pi$
$954$	−52.4119	+	29.1675i	−1.69690	+	0.944333i
$955$		−	9.85035i		−	0.318750i
$956$	27.5717	−	44.4554i	0.891731	−	1.43779i
$957$			85.9911i			2.77970i
$958$	−23.1650	−	41.6259i	−0.748429	−	1.34487i
$959$	−0.178216			−0.00575488
$960$	28.2049	+	2.67748i	0.910308	+	0.0864153i
$961$	78.8351			2.54307
$962$	1.93190	+	3.47148i	0.0622870	+	0.111925i
$963$		−	22.2597i		−	0.717308i
$964$	14.0558	−	22.6630i	0.452708	−	0.729926i
$965$			0.395705i			0.0127382i
$966$	10.4252	−	5.80169i	0.335426	−	0.186666i
$967$	19.5810			0.629683			0.314842	−	0.949144i	$-0.398049\pi$
$967$	19.5810			0.629683			0.314842	+	0.949144i	$0.398049\pi$
$968$	−26.5316	−	1.25649i	−0.852757	−	0.0403852i
$969$	−97.0921			−3.11905
$970$	24.0644	−	13.3920i	0.772663	−	0.429991i
$971$		−	38.5437i		−	1.23693i	−0.785814	−	0.618463i	$-0.787756\pi$
$971$		−	38.5437i		−	1.23693i	0.785814	−	0.618463i	$-0.212244\pi$
$972$	−39.2085	−	24.3175i	−1.25761	−	0.779985i
$973$		−	12.0375i		−	0.385903i
$974$	−6.06974	−	10.9069i	−0.194487	−	0.349479i
$975$	11.8800			0.380463
$976$	−23.1108	+	11.4646i	−0.739758	+	0.366974i
$977$	27.8078			0.889651			0.444825	−	0.895617i	$-0.353266\pi$
$977$	27.8078			0.889651			0.444825	+	0.895617i	$0.353266\pi$
$978$	−29.8569	−	53.6507i	−0.954719	−	1.71556i
$979$		−	22.9374i		−	0.733082i
$980$	1.90011	+	1.17847i	0.0606969	+	0.0376448i
$981$		−	66.7233i		−	2.13031i
$982$	10.2953	−	5.72941i	0.328537	−	0.182833i
$983$	3.36489			0.107323			0.0536616	−	0.998559i	$-0.482911\pi$
$983$	3.36489			0.107323			0.0536616	+	0.998559i	$0.482911\pi$
$984$	2.09197	−	44.1732i	0.0666896	−	1.40819i
$985$	5.96947			0.190203
$986$	−33.0434	+	18.3888i	−1.05232	+	0.585620i
$987$			20.1289i			0.640708i
$988$	7.26339	−	11.7112i	0.231079	−	0.372582i
$989$			13.0103i			0.413705i
$990$	−24.4236	−	43.8873i	−0.776232	−	1.39483i
$991$	22.7862			0.723826			0.361913	−	0.932212i	$-0.382124\pi$
$991$	22.7862			0.723826			0.361913	+	0.932212i	$0.382124\pi$
$992$	−33.5957	+	48.8473i	−1.06666	+	1.55090i
$993$	3.65239			0.115905
$994$	0.362556	+	0.651486i	0.0114996	+	0.0206639i
$995$		−	15.1183i		−	0.479284i
$996$	−9.97278	+	16.0797i	−0.316000	+	0.509504i
$997$		−	41.0678i		−	1.30063i	−0.759664	−	0.650315i	$-0.774637\pi$
$997$		−	41.0678i		−	1.30063i	0.759664	−	0.650315i	$-0.225363\pi$
$998$	−29.8297	+	16.6004i	−0.944244	+	0.525477i
$999$	−35.9090			−1.13611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.c.a.365.11	✓	34
4.3	odd	2		2912.2.c.a.1457.1		34
8.3	odd	2		2912.2.c.a.1457.34		34
8.5	even	2	inner	728.2.c.a.365.12	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.c.a.365.11	✓	34	1.1	even	1	trivial
728.2.c.a.365.12	yes	34	8.5	even	2	inner
2912.2.c.a.1457.1		34	4.3	odd	2
2912.2.c.a.1457.34		34	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687700 - 1.23575i) q^{2} +3.16783i q^{3} +(-1.05414 + 1.69965i) q^{4} -1.11795i q^{5} +(3.91463 - 2.17851i) q^{6} -1.00000 q^{7} +(2.82526 + 0.133800i) q^{8} -7.03512 q^{9} +(-1.38150 + 0.768812i) q^{10} -4.51562i q^{11} +(-5.38418 - 3.33932i) q^{12} -1.00000i q^{13} +(0.687700 + 1.23575i) q^{14} +3.54146 q^{15} +(-1.77759 - 3.58332i) q^{16} -4.44816 q^{17} +(4.83805 + 8.69362i) q^{18} -6.89036i q^{19} +(1.90011 + 1.17847i) q^{20} -3.16783i q^{21} +(-5.58016 + 3.10539i) q^{22} -2.66314 q^{23} +(-0.423854 + 8.94993i) q^{24} +3.75020 q^{25} +(-1.23575 + 0.687700i) q^{26} -12.7825i q^{27} +(1.05414 - 1.69965i) q^{28} +6.01139i q^{29} +(-2.43546 - 4.37635i) q^{30} +10.4802 q^{31} +(-3.20562 + 4.66090i) q^{32} +14.3047 q^{33} +(3.05900 + 5.49680i) q^{34} +1.11795i q^{35} +(7.41598 - 11.9572i) q^{36} -2.80922i q^{37} +(-8.51474 + 4.73850i) q^{38} +3.16783 q^{39} +(0.149581 - 3.15849i) q^{40} -4.93559 q^{41} +(-3.91463 + 2.17851i) q^{42} -4.88533i q^{43} +(7.67496 + 4.76009i) q^{44} +7.86489i q^{45} +(1.83144 + 3.29097i) q^{46} -6.35415 q^{47} +(11.3513 - 5.63109i) q^{48} +1.00000 q^{49} +(-2.57901 - 4.63429i) q^{50} -14.0910i q^{51} +(1.69965 + 1.05414i) q^{52} +6.02877i q^{53} +(-15.7960 + 8.79056i) q^{54} -5.04822 q^{55} +(-2.82526 - 0.133800i) q^{56} +21.8275 q^{57} +(7.42855 - 4.13403i) q^{58} -15.1683i q^{59} +(-3.73318 + 6.01923i) q^{60} -6.44954i q^{61} +(-7.20725 - 12.9509i) q^{62} +7.03512 q^{63} +(7.96420 + 0.756038i) q^{64} -1.11795 q^{65} +(-9.83734 - 17.6770i) q^{66} -5.98352i q^{67} +(4.68897 - 7.56030i) q^{68} -8.43637i q^{69} +(1.38150 - 0.768812i) q^{70} +0.527201 q^{71} +(-19.8760 - 0.941297i) q^{72} -7.57660 q^{73} +(-3.47148 + 1.93190i) q^{74} +11.8800i q^{75} +(11.7112 + 7.26339i) q^{76} +4.51562i q^{77} +(-2.17851 - 3.91463i) q^{78} +4.85576 q^{79} +(-4.00596 + 1.98725i) q^{80} +19.3875 q^{81} +(3.39421 + 6.09914i) q^{82} -2.98647i q^{83} +(5.38418 + 3.33932i) q^{84} +4.97281i q^{85} +(-6.03703 + 3.35964i) q^{86} -19.0430 q^{87} +(0.604189 - 12.7578i) q^{88} +5.07956 q^{89} +(9.71900 - 5.40868i) q^{90} +1.00000i q^{91} +(2.80732 - 4.52640i) q^{92} +33.1995i q^{93} +(4.36975 + 7.85212i) q^{94} -7.70306 q^{95} +(-14.7649 - 10.1549i) q^{96} -17.4191 q^{97} +(-0.687700 - 1.23575i) q^{98} +31.7679i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 2 q^{2} - 2 q^{4} - 6 q^{6} - 34 q^{7} + 8 q^{8} - 26 q^{9} - 4 q^{12} - 2 q^{14} - 8 q^{15} - 6 q^{16} - 20 q^{17} + 14 q^{18} - 4 q^{20} - 10 q^{22} - 20 q^{23} + 10 q^{24} - 22 q^{25} + 2 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) \) 34 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 - 34 * q^7 + 8 * q^8 - 26 * q^9 - 4 * q^12 - 2 * q^14 - 8 * q^15 - 6 * q^16 - 20 * q^17 + 14 * q^18 - 4 * q^20 - 10 * q^22 - 20 * q^23 + 10 * q^24 - 22 * q^25 + 2 * q^28 - 60 * q^30 + 16 * q^31 + 12 * q^32 - 8 * q^33 + 28 * q^34 - 4 * q^36 - 28 * q^38 + 8 * q^39 + 64 * q^40 + 8 * q^41 + 6 * q^42 + 24 * q^44 + 16 * q^46 + 24 * q^48 + 34 * q^49 + 10 * q^50 - 4 * q^52 - 18 * q^54 - 32 * q^55 - 8 * q^56 + 8 * q^57 + 44 * q^58 - 24 * q^60 + 60 * q^62 + 26 * q^63 - 2 * q^64 - 20 * q^65 + 24 * q^66 + 12 * q^68 + 64 * q^71 - 92 * q^72 - 22 * q^74 + 4 * q^76 + 20 * q^79 - 56 * q^80 - 6 * q^81 - 20 * q^82 + 4 * q^84 - 12 * q^86 - 56 * q^87 - 34 * q^88 - 4 * q^90 - 54 * q^92 + 12 * q^94 + 42 * q^96 + 2 * q^98

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