LMFDB - Embedded newform 961.2.k.a.5.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(5,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(186)) chi = DirichletCharacter(H, H._module([88])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.k (of order $93$, degree $60$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$4920$
Relative dimension:	$82$ over $\Q(\zeta_{93})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{93}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	961.5
Dual form			961.2.k.a.769.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.04201 - 1.75301i) q^{2} +(0.0800879 + 0.946076i) q^{3} +(0.793911 + 5.18237i) q^{4} +(0.610803 + 0.366540i) q^{5} +(1.49494 - 2.07229i) q^{6} +(0.839904 + 1.25128i) q^{7} +(4.61642 - 7.40635i) q^{8} +(2.06866 - 0.352764i) q^{9} +(-0.604719 - 1.81922i) q^{10} +(-0.750303 + 0.485453i) q^{11} +(-4.83934 + 1.16614i) q^{12} +(2.77183 - 3.34136i) q^{13} +(0.478408 - 4.02748i) q^{14} +(-0.297856 + 0.607221i) q^{15} +(-12.4054 + 3.89221i) q^{16} +(6.36706 - 0.865606i) q^{17} +(-4.84263 - 2.90604i) q^{18} +(-3.51191 - 3.45309i) q^{19} +(-1.41462 + 3.45641i) q^{20} +(-1.11654 + 0.894825i) q^{21} +(2.38313 + 0.323988i) q^{22} +(0.645017 + 0.358014i) q^{23} +(7.37669 + 3.77432i) q^{24} +(-2.11360 - 3.96432i) q^{25} +(-11.5175 + 1.96405i) q^{26} +(1.21337 + 4.68631i) q^{27} +(-5.81778 + 5.34610i) q^{28} +(2.13941 + 1.18747i) q^{29} +(1.67269 - 0.717807i) q^{30} +(-5.41611 - 1.29065i) q^{31} +(16.1149 + 6.91546i) q^{32} +(-0.519365 - 0.670964i) q^{33} +(-14.5190 - 9.39392i) q^{34} +(0.0543729 + 1.07214i) q^{35} +(3.47049 + 10.4405i) q^{36} +(0.491118 + 0.0837492i) q^{37} +(1.11806 + 13.2076i) q^{38} +(3.38317 + 2.35476i) q^{39} +(5.53444 - 2.83173i) q^{40} +(8.27663 + 0.279696i) q^{41} +(3.84861 + 0.130058i) q^{42} +(-0.290053 + 0.872587i) q^{43} +(-3.11147 - 3.50294i) q^{44} +(1.39285 + 0.542778i) q^{45} +(-0.689530 - 1.86179i) q^{46} +(-3.28851 - 1.82527i) q^{47} +(-4.67584 - 11.4247i) q^{48} +(1.79119 - 4.37650i) q^{49} +(-2.63350 + 11.8003i) q^{50} +(1.32885 + 5.95439i) q^{51} +(19.5168 + 11.7119i) q^{52} +(5.04367 + 2.36921i) q^{53} +(5.73742 - 11.6965i) q^{54} +(-0.636225 + 0.0215002i) q^{55} +(13.1448 - 0.444206i) q^{56} +(2.98562 - 3.59908i) q^{57} +(-2.28705 - 6.17521i) q^{58} +(5.19320 + 0.885583i) q^{59} +(-3.38332 - 1.06152i) q^{60} +(0.224271 - 0.235933i) q^{61} +(8.79722 + 12.1300i) q^{62} +(2.17889 + 2.29219i) q^{63} +(-9.33230 - 19.0252i) q^{64} +(2.91778 - 1.02493i) q^{65} +(-0.115657 + 2.28057i) q^{66} +(0.0123015 - 0.0300568i) q^{67} +(9.54076 + 32.3093i) q^{68} +(-0.287050 + 0.638908i) q^{69} +(1.76844 - 2.28464i) q^{70} +(10.6844 - 10.5055i) q^{71} +(6.93712 - 16.9498i) q^{72} +(2.84109 + 2.12341i) q^{73} +(-0.856054 - 1.03195i) q^{74} +(3.58128 - 2.31712i) q^{75} +(15.1071 - 20.9415i) q^{76} +(-1.23762 - 0.531104i) q^{77} +(-2.78056 - 10.7392i) q^{78} +(-7.41676 + 5.54324i) q^{79} +(-9.00389 - 2.16969i) q^{80} +(1.60335 - 0.563210i) q^{81} +(-16.4106 - 15.0801i) q^{82} +(-2.59539 + 13.8081i) q^{83} +(-5.52375 - 5.07590i) q^{84} +(4.20630 + 1.80506i) q^{85} +(2.12194 - 1.27337i) q^{86} +(-0.952093 + 2.11914i) q^{87} +(0.131724 + 7.79806i) q^{88} +(-2.78463 - 5.67686i) q^{89} +(-1.89272 - 3.55003i) q^{90} +(6.50904 + 0.661905i) q^{91} +(-1.34328 + 3.62695i) q^{92} +(0.787290 - 5.22741i) q^{93} +(3.51546 + 9.49202i) q^{94} +(-0.879392 - 3.39641i) q^{95} +(-5.25194 + 15.7998i) q^{96} +(-1.63574 + 10.6775i) q^{97} +(-11.3297 + 5.79688i) q^{98} +(-1.38087 + 1.26892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4920 q - 58 q^{2} - 64 q^{3} - 226 q^{4} - 60 q^{5} - 56 q^{6} - 60 q^{7} - 56 q^{8} + 18 q^{9} - 61 q^{10} - 64 q^{11} - 72 q^{12} - 64 q^{13} - 65 q^{14} + 66 q^{15} - 234 q^{16} - 68 q^{17} - 70 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) $ 4920 * q - 58 * q^2 - 64 * q^3 - 226 * q^4 - 60 * q^5 - 56 * q^6 - 60 * q^7 - 56 * q^8 + 18 * q^9 - 61 * q^10 - 64 * q^11 - 72 * q^12 - 64 * q^13 - 65 * q^14 + 66 * q^15 - 234 * q^16 - 68 * q^17 - 70 * q^18 - 56 * q^19 - 57 * q^20 - 68 * q^21 + 76 * q^22 - 46 * q^23 + 72 * q^24 + 10 * q^25 + 56 * q^26 - 58 * q^27 - 49 * q^28 - 46 * q^29 - 74 * q^30 - 42 * q^31 - 86 * q^32 - 90 * q^33 - 64 * q^34 - 202 * q^35 + 34 * q^36 - 60 * q^37 - 61 * q^38 - 58 * q^39 + 62 * q^40 - 56 * q^41 - 730 * q^42 + 60 * q^43 - 88 * q^44 - 58 * q^45 + 108 * q^46 + 34 * q^47 - 68 * q^48 + 10 * q^49 + 104 * q^50 - 60 * q^51 - 48 * q^52 - 56 * q^53 - 58 * q^54 - 64 * q^55 - 500 * q^56 - 64 * q^57 - 62 * q^58 - 64 * q^59 + 82 * q^60 + 124 * q^61 + 383 * q^62 + 30 * q^63 + 48 * q^64 - 64 * q^65 - 18 * q^66 - 58 * q^67 - 300 * q^68 - 50 * q^69 - 80 * q^70 - 68 * q^71 - 55 * q^72 - 370 * q^73 - 64 * q^74 - 54 * q^75 + 261 * q^76 - 34 * q^77 - 98 * q^78 - 84 * q^79 + 480 * q^80 + 20 * q^81 + 299 * q^82 - 68 * q^83 + 288 * q^84 + 198 * q^85 - 88 * q^86 + 101 * q^87 - 44 * q^88 - 46 * q^89 - 55 * q^90 + 453 * q^91 - 46 * q^92 - 40 * q^93 - 768 * q^94 + 61 * q^95 - 64 * q^96 - 102 * q^97 - 51 * q^98 - 86 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{44}{93}\right)$

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 $

$2$	−2.04201	−	1.75301i	−1.44392	−	1.23956i	−0.922351	−	0.386353i	$-0.873735\pi$
$2$	−2.04201	−	1.75301i	−1.44392	−	1.23956i	−0.521567	−	0.853210i	$-0.674652\pi$
$3$	0.0800879	+	0.946076i	0.0462388	+	0.546217i	0.981397	+	0.191988i	$0.0614933\pi$
$3$	0.0800879	+	0.946076i	0.0462388	+	0.546217i	−0.935159	+	0.354229i	$0.884743\pi$
$4$	0.793911	+	5.18237i	0.396955	+	2.59119i
$5$	0.610803	+	0.366540i	0.273160	+	0.163922i	0.644566	−	0.764549i	$-0.277038\pi$
$5$	0.610803	+	0.366540i	0.273160	+	0.163922i	−0.371406	+	0.928470i	$0.621124\pi$
$6$	1.49494	−	2.07229i	0.610305	−	0.846009i
$7$	0.839904	+	1.25128i	0.317454	+	0.472939i	0.954636	−	0.297774i	$-0.0962443\pi$
$7$	0.839904	+	1.25128i	0.317454	+	0.472939i	−0.637182	+	0.770713i	$0.719900\pi$
$8$	4.61642	−	7.40635i	1.63215	−	2.61854i
$9$	2.06866	−	0.352764i	0.689555	−	0.117588i
$10$	−0.604719	−	1.81922i	−0.191229	−	0.575288i
$11$	−0.750303	+	0.485453i	−0.226225	+	0.146369i	−0.651382	−	0.758750i	$-0.725810\pi$
$11$	−0.750303	+	0.485453i	−0.226225	+	0.146369i	0.425157	+	0.905120i	$0.360219\pi$
$12$	−4.83934	+	1.16614i	−1.39700	+	0.336637i
$13$	2.77183	−	3.34136i	0.768767	−	0.926727i	−0.230155	−	0.973154i	$-0.573923\pi$
$13$	2.77183	−	3.34136i	0.768767	−	0.926727i	0.998922	+	0.0464273i	$0.0147836\pi$
$14$	0.478408	−	4.02748i	0.127860	−	1.07639i
$15$	−0.297856	+	0.607221i	−0.0769062	+	0.156784i
$16$	−12.4054	+	3.89221i	−3.10134	+	0.973052i
$17$	6.36706	−	0.865606i	1.54424	−	0.209940i	0.687689	−	0.726006i	$-0.258625\pi$
$17$	6.36706	−	0.865606i	1.54424	−	0.209940i	0.856549	+	0.516065i	$0.172604\pi$
$18$	−4.84263	−	2.90604i	−1.14142	−	0.684959i
$19$	−3.51191	−	3.45309i	−0.805687	−	0.792193i	0.175657	−	0.984451i	$-0.443795\pi$
$19$	−3.51191	−	3.45309i	−0.805687	−	0.792193i	−0.981344	+	0.192259i	$0.938419\pi$
$20$	−1.41462	+	3.45641i	−0.316319	+	0.772877i
$21$	−1.11654	+	0.894825i	−0.243648	+	0.195267i
$22$	2.38313	+	0.323988i	0.508084	+	0.0690744i
$23$	0.645017	+	0.358014i	0.134495	+	0.0746510i	0.551112	−	0.834431i	$-0.314204\pi$
$23$	0.645017	+	0.358014i	0.134495	+	0.0746510i	−0.416617	+	0.909082i	$0.636784\pi$
$24$	7.37669	+	3.77432i	1.50576	+	0.770430i
$25$	−2.11360	−	3.96432i	−0.422720	−	0.792865i
$26$	−11.5175	+	1.96405i	−2.25877	+	0.385183i
$27$	1.21337	+	4.68631i	0.233513	+	0.901881i
$28$	−5.81778	+	5.34610i	−1.09946	+	1.01032i
$29$	2.13941	+	1.18747i	0.397278	+	0.220507i	0.671251	−	0.741230i	$-0.265757\pi$
$29$	2.13941	+	1.18747i	0.397278	+	0.220507i	−0.273973	+	0.961737i	$0.588338\pi$
$30$	1.67269	−	0.717807i	0.305390	−	0.131053i
$31$	−5.41611	−	1.29065i	−0.972762	−	0.231808i
$31$	−5.41611	−	1.29065i	−0.972762	−	0.231808i
$32$	16.1149	+	6.91546i	2.84874	+	1.22249i
$33$	−0.519365	−	0.670964i	−0.0904098	−	0.116800i
$34$	−14.5190	−	9.39392i	−2.48999	−	1.61104i
$35$	0.0543729	+	1.07214i	0.00919070	+	0.181225i
$36$	3.47049	+	10.4405i	0.578415	+	1.74009i
$37$	0.491118	+	0.0837492i	0.0807393	+	0.0137683i	0.208330	−	0.978059i	$-0.433197\pi$
$37$	0.491118	+	0.0837492i	0.0807393	+	0.0137683i	−0.127590	+	0.991827i	$0.540724\pi$
$38$	1.11806	+	13.2076i	0.181374	+	2.14256i
$39$	3.38317	+	2.35476i	0.541741	+	0.377063i
$40$	5.53444	−	2.83173i	0.875073	−	0.447735i
$41$	8.27663	+	0.279696i	1.29259	+	0.0436811i	0.672059	−	0.740498i	$-0.265410\pi$
$41$	8.27663	+	0.279696i	1.29259	+	0.0436811i	0.620534	+	0.784179i	$0.286916\pi$
$42$	3.84861	+	0.130058i	0.593854	+	0.0200684i
$43$	−0.290053	+	0.872587i	−0.0442326	+	0.133068i	−0.968728	−	0.248125i	$-0.920186\pi$
$43$	−0.290053	+	0.872587i	−0.0442326	+	0.133068i	0.924495	+	0.381193i	$0.124487\pi$
$44$	−3.11147	−	3.50294i	−0.469072	−	0.528089i
$45$	1.39285	+	0.542778i	0.207634	+	0.0809126i
$46$	−0.689530	−	1.86179i	−0.101666	−	0.274505i
$47$	−3.28851	−	1.82527i	−0.479679	−	0.266244i	0.226847	−	0.973930i	$-0.427158\pi$
$47$	−3.28851	−	1.82527i	−0.479679	−	0.266244i	−0.706526	+	0.707687i	$0.749739\pi$
$48$	−4.67584	−	11.4247i	−0.674900	−	1.64901i
$49$	1.79119	−	4.37650i	0.255885	−	0.625215i
$50$	−2.63350	+	11.8003i	−0.372434	+	1.66882i
$51$	1.32885	+	5.95439i	0.186077	+	0.833782i
$52$	19.5168	+	11.7119i	2.70649	+	1.62415i
$53$	5.04367	+	2.36921i	0.692801	+	0.325436i	0.739199	−	0.673487i	$-0.235204\pi$
$53$	5.04367	+	2.36921i	0.692801	+	0.325436i	−0.0463978	+	0.998923i	$0.514774\pi$
$54$	5.73742	−	11.6965i	0.780764	−	1.59170i
$55$	−0.636225	+	0.0215002i	−0.0857886	+	0.00289909i
$56$	13.1448	−	0.444206i	1.75654	−	0.0593596i
$57$	2.98562	−	3.59908i	0.395455	−	0.476710i
$58$	−2.28705	−	6.17521i	−0.300304	−	0.810845i
$59$	5.19320	+	0.885583i	0.676097	+	0.115293i	0.495956	−	0.868348i	$-0.334818\pi$
$59$	5.19320	+	0.885583i	0.676097	+	0.115293i	0.180141	+	0.983641i	$0.442345\pi$
$60$	−3.38332	−	1.06152i	−0.436785	−	0.137042i
$61$	0.224271	−	0.235933i	0.0287150	−	0.0302082i	−0.710278	−	0.703921i	$-0.751431\pi$
$61$	0.224271	−	0.235933i	0.0287150	−	0.0302082i	0.738993	+	0.673713i	$0.235302\pi$
$62$	8.79722	+	12.1300i	1.11725	+	1.54051i
$63$	2.17889	+	2.29219i	0.274514	+	0.288788i
$64$	−9.33230	−	19.0252i	−1.16654	−	2.37815i
$65$	2.91778	−	1.02493i	0.361906	−	0.127127i
$66$	−0.115657	+	2.28057i	−0.0142364	+	0.280718i
$67$	0.0123015	−	0.0300568i	0.00150287	−	0.00367203i	−0.924734	−	0.380614i	$-0.875713\pi$
$67$	0.0123015	−	0.0300568i	0.00150287	−	0.00367203i	0.926237	+	0.376942i	$0.123024\pi$
$68$	9.54076	+	32.3093i	1.15699	+	3.91807i
$69$	−0.287050	+	0.638908i	−0.0345568	+	0.0769154i
$70$	1.76844	−	2.28464i	0.211370	−	0.273067i
$71$	10.6844	−	10.5055i	1.26801	−	1.24677i	0.313150	−	0.949704i	$-0.398616\pi$
$71$	10.6844	−	10.5055i	1.26801	−	1.24677i	0.954857	−	0.297065i	$-0.0960080\pi$
$72$	6.93712	−	16.9498i	0.817547	−	1.99755i
$73$	2.84109	+	2.12341i	0.332524	+	0.248526i	0.751886	−	0.659293i	$-0.229144\pi$
$73$	2.84109	+	2.12341i	0.332524	+	0.248526i	−0.419362	+	0.907819i	$0.637746\pi$
$74$	−0.856054	−	1.03195i	−0.0995143	−	0.119962i
$75$	3.58128	−	2.31712i	0.413530	−	0.267558i
$76$	15.1071	−	20.9415i	1.73290	−	2.40215i
$77$	−1.23762	−	0.531104i	−0.141040	−	0.0605249i
$78$	−2.78056	−	10.7392i	−0.314836	−	1.21597i
$79$	−7.41676	+	5.54324i	−0.834451	+	0.623663i	−0.928262	−	0.371927i	$-0.878697\pi$
$79$	−7.41676	+	5.54324i	−0.834451	+	0.623663i	0.0938109	+	0.995590i	$0.470095\pi$
$80$	−9.00389	−	2.16969i	−1.00667	−	0.242578i
$81$	1.60335	−	0.563210i	0.178150	−	0.0625788i
$82$	−16.4106	−	15.0801i	−1.81225	−	1.66532i
$83$	−2.59539	+	13.8081i	−0.284881	+	1.51564i	0.483327	+	0.875440i	$0.339428\pi$
$83$	−2.59539	+	13.8081i	−0.284881	+	1.51564i	−0.768208	+	0.640200i	$0.778851\pi$
$84$	−5.52375	−	5.07590i	−0.602690	−	0.553827i
$85$	4.20630	+	1.80506i	0.456237	+	0.195787i
$86$	2.12194	−	1.27337i	0.228815	−	0.137311i
$87$	−0.952093	+	2.11914i	−0.102075	+	0.227196i
$88$	0.131724	+	7.79806i	0.0140418	+	0.831276i
$89$	−2.78463	−	5.67686i	−0.295171	−	0.601746i	0.698304	−	0.715802i	$-0.253938\pi$
$89$	−2.78463	−	5.67686i	−0.295171	−	0.601746i	−0.993474	+	0.114055i	$0.963616\pi$
$90$	−1.89272	−	3.55003i	−0.199510	−	0.374206i
$91$	6.50904	+	0.661905i	0.682333	+	0.0693865i
$92$	−1.34328	+	3.62695i	−0.140046	+	0.378136i
$93$	0.787290	−	5.22741i	0.0816381	−	0.542057i
$94$	3.51546	+	9.49202i	0.362592	+	0.979027i
$95$	−0.879392	−	3.39641i	−0.0902237	−	0.348465i
$96$	−5.25194	+	15.7998i	−0.536024	+	1.61256i
$97$	−1.63574	+	10.6775i	−0.166084	+	1.08414i	0.743535	+	0.668697i	$0.233148\pi$
$97$	−1.63574	+	10.6775i	−0.166084	+	1.08414i	−0.909619	+	0.415443i	$0.863626\pi$
$98$	−11.3297	+	5.79688i	−1.14447	+	0.585574i
$99$	−1.38087	+	1.26892i	−0.138783	+	0.127531i
$100$	18.8666	−	14.1008i	1.88666	−	1.41008i
$101$	10.5865	+	9.08821i	1.05340	+	0.904311i	0.995571	−	0.0940159i	$-0.0299705\pi$
$101$	10.5865	+	9.08821i	1.05340	+	0.904311i	0.0578253	+	0.998327i	$0.481583\pi$
$102$	7.72456	−	14.4884i	0.764846	−	1.43457i
$103$	−14.4280	−	13.2582i	−1.42163	−	1.30637i	−0.887372	−	0.461055i	$-0.847471\pi$
$103$	−14.4280	−	13.2582i	−1.42163	−	1.30637i	−0.534263	−	0.845319i	$-0.679411\pi$
$104$	−11.9514	−	35.9542i	−1.17193	−	3.52560i
$105$	−1.00997	+	0.137307i	−0.0985633	+	0.0133998i
$106$	−6.14598	−	13.6795i	−0.596950	−	1.32867i
$107$	−6.02580	−	7.26393i	−0.582536	−	0.702230i	0.393627	−	0.919270i	$-0.371220\pi$
$107$	−6.02580	−	7.26393i	−0.582536	−	0.702230i	−0.976163	+	0.217040i	$0.930360\pi$
$108$	−23.3229	+	10.0086i	−2.24425	+	0.963083i
$109$	1.74494	−	2.79950i	0.167135	−	0.268144i	−0.754419	−	0.656393i	$-0.772081\pi$
$109$	1.74494	−	2.79950i	0.167135	−	0.268144i	0.921554	+	0.388249i	$0.126920\pi$
$110$	1.33687	+	1.07140i	0.127465	+	0.102154i
$111$	−0.0399004	+	0.471342i	−0.00378718	+	0.0447378i
$112$	−15.2896	−	12.2535i	−1.44473	−	1.15785i
$113$	−10.8540	−	1.47560i	−1.02106	−	0.138813i	−0.395073	−	0.918650i	$-0.629281\pi$
$113$	−10.8540	−	1.47560i	−1.02106	−	0.138813i	−0.625983	+	0.779837i	$0.715302\pi$
$114$	−12.4059	+	2.11554i	−1.16192	+	0.198139i
$115$	0.262752	+	0.455100i	0.0245018	+	0.0424383i
$116$	−4.45540	+	12.0299i	−0.413674	+	1.11695i
$117$	4.55527	−	7.88996i	0.421135	−	0.729427i
$118$	−9.05212	−	10.9121i	−0.833315	−	1.00454i
$119$	6.43083	+	7.23993i	0.589513	+	0.663684i
$120$	3.12227	+	5.00922i	0.285023	+	0.457277i
$121$	−4.18073	+	9.30536i	−0.380067	+	0.845941i
$122$	−0.871557	+	0.0886287i	−0.0789070	+	0.00802406i
$123$	0.398245	+	7.85272i	0.0359085	+	0.708056i
$124$	2.38874	−	29.0930i	0.214515	−	2.61262i
$125$	0.342488	−	6.75328i	0.0306330	−	0.604032i
$126$	−0.431085	−	8.50027i	−0.0384041	−	0.757264i
$127$	0.705565	+	1.05114i	0.0626088	+	0.0932737i	0.860288	−	0.509808i	$-0.170283\pi$
$127$	0.705565	+	1.05114i	0.0626088	+	0.0932737i	−0.797680	+	0.603081i	$0.793939\pi$
$128$	−5.50371	+	21.2566i	−0.486464	+	1.87883i
$129$	−0.848763	−	0.204528i	−0.0747294	−	0.0180077i
$130$	−7.75485	−	3.02198i	−0.680145	−	0.265045i
$131$	16.9501	−	2.30438i	1.48094	−	0.201335i	0.650952	−	0.759119i	$-0.274370\pi$
$131$	16.9501	−	2.30438i	1.48094	−	0.201335i	0.829986	+	0.557784i	$0.188348\pi$
$132$	3.06486	−	3.22423i	0.266762	−	0.280633i
$133$	1.37111	−	7.29464i	0.118890	−	0.632525i
$134$	−0.0778097	+	0.0398117i	−0.00672173	+	0.00343921i
$135$	−0.976589	+	3.30716i	−0.0840514	+	0.284635i
$136$	22.9820	−	51.1527i	1.97069	−	4.38631i
$137$	7.61280	−	2.10891i	0.650406	−	0.180176i	0.0738951	−	0.997266i	$-0.476457\pi$
$137$	7.61280	−	2.10891i	0.650406	−	0.180176i	0.576510	+	0.817090i	$0.304414\pi$
$138$	1.70617	−	0.801454i	0.145239	−	0.0682243i
$139$	1.97938	−	5.34449i	0.167889	−	0.453314i	−0.826004	−	0.563665i	$-0.809391\pi$
$139$	1.97938	−	5.34449i	0.167889	−	0.453314i	0.993893	+	0.110351i	$0.0351974\pi$
$140$	−5.51308	+	1.13297i	−0.465940	+	0.0957531i
$141$	1.46348	−	3.25737i	0.123247	−	0.274320i
$142$	−40.2338	+	2.72239i	−3.37635	+	0.228458i
$143$	−0.457638	+	3.85262i	−0.0382696	+	0.322172i
$144$	−24.2895	+	12.4278i	−2.02413	+	1.03565i
$145$	0.871502	+	1.50949i	0.0723743	+	0.125356i
$146$	−2.07917	−	9.31647i	−0.172074	−	0.771036i
$147$	4.28396	+	1.34410i	0.353335	+	0.110859i
$148$	−0.0441156	+	2.61165i	−0.00362628	+	0.214676i
$149$	4.97687	−	1.19929i	0.407721	−	0.0982494i	−0.0251975	−	0.999682i	$-0.508021\pi$
$149$	4.97687	−	1.19929i	0.407721	−	0.0982494i	0.432918	+	0.901433i	$0.357484\pi$
$150$	−11.3749	−	1.54643i	−0.928759	−	0.126265i
$151$	2.59059	+	3.34677i	0.210819	+	0.272356i	0.884372	−	0.466783i	$-0.154587\pi$
$151$	2.59059	+	3.34677i	0.210819	+	0.272356i	−0.673552	+	0.739140i	$0.735232\pi$
$152$	−41.7872	+	10.0696i	−3.38939	+	0.816749i
$153$	12.8659	−	4.03672i	1.04015	−	0.326349i
$154$	1.59620	+	3.25407i	0.128625	+	0.262221i
$155$	−2.83510	−	2.77355i	−0.227721	−	0.222777i
$156$	−9.51729	+	19.4023i	−0.761993	+	1.55343i
$157$	−3.70021	+	24.1537i	−0.295309	+	1.92767i	0.0716348	+	0.997431i	$0.477178\pi$
$157$	−3.70021	+	24.1537i	−0.295309	+	1.92767i	−0.366944	+	0.930243i	$0.619596\pi$
$158$	24.8624	+	1.68229i	1.97795	+	0.133836i
$159$	−1.83751	+	4.96144i	−0.145724	+	0.393468i
$160$	7.30826	+	10.1308i	0.577769	+	0.800906i
$161$	0.0937777	+	1.10779i	0.00739072	+	0.0873063i
$162$	−4.26137	−	1.66061i	−0.334805	−	0.130470i
$163$	10.5092	+	11.0557i	0.823144	+	0.865947i	0.992828	−	0.119551i	$-0.0381455\pi$
$163$	10.5092	+	11.0557i	0.823144	+	0.865947i	−0.169684	+	0.985499i	$0.554275\pi$
$164$	5.12142	+	43.1147i	0.399916	+	3.36669i
$165$	−0.0712948	−	0.600195i	−0.00555029	−	0.0467251i
$166$	29.5056	−	23.6466i	2.29008	−	1.83533i
$167$	−8.85396	−	13.1905i	−0.685140	−	1.02071i	−0.997494	−	0.0707467i	$-0.977462\pi$
$167$	−8.85396	−	13.1905i	−0.685140	−	1.02071i	0.312355	−	0.949966i	$-0.398882\pi$
$168$	1.47299	+	12.4004i	0.113644	+	0.956708i
$169$	−1.08023	−	5.74708i	−0.0830943	−	0.442083i
$170$	−5.42501	−	11.0596i	−0.416079	−	0.848235i
$171$	−8.48309	−	5.90440i	−0.648718	−	0.451521i
$172$	−4.75235	−	0.810406i	−0.362363	−	0.0617929i
$173$	2.66966	+	11.9624i	0.202971	+	0.909482i	0.965064	+	0.262014i	$0.0843868\pi$
$173$	2.66966	+	11.9624i	0.202971	+	0.909482i	−0.762093	+	0.647467i	$0.775828\pi$
$174$	5.65905	−	2.65828i	0.429012	−	0.201524i
$175$	3.18525	−	5.97435i	0.240783	−	0.451619i
$176$	7.41830	−	8.94255i	0.559175	−	0.674070i
$177$	−0.421916	+	4.98408i	−0.0317132	+	0.374627i
$178$	−4.26533	+	16.4737i	−0.319700	+	1.23475i
$179$	0.225863	+	0.423634i	0.0168818	+	0.0316639i	0.890717	−	0.454558i	$-0.150203\pi$
$179$	0.225863	+	0.423634i	0.0168818	+	0.0316639i	−0.873835	+	0.486222i	$0.838375\pi$
$180$	−1.70708	+	7.64918i	−0.127238	+	0.570136i
$181$	6.26725	−	4.05497i	0.465841	−	0.301403i	−0.288979	−	0.957336i	$-0.593316\pi$
$181$	6.26725	−	4.05497i	0.465841	−	0.301403i	0.754820	+	0.655932i	$0.227724\pi$
$182$	−12.1312	−	12.7620i	−0.899224	−	0.945983i
$183$	0.241172	+	0.193282i	0.0178280	+	0.0142878i
$184$	5.62924	−	3.12449i	0.414993	−	0.230340i
$185$	0.269279	+	0.231169i	0.0197978	+	0.0169958i
$186$	−10.7713	+	9.29430i	−0.789793	+	0.681491i
$187$	−4.35701	+	3.74037i	−0.318616	+	0.273523i
$188$	6.84847	−	18.4914i	0.499476	−	1.34863i
$189$	−4.84476	+	5.45431i	−0.352405	+	0.396743i
$190$	−4.15821	+	8.47708i	−0.301668	+	0.614992i
$191$	−0.0998569	+	1.17961i	−0.00722539	+	0.0853533i	−0.999134	−	0.0415970i	$-0.986755\pi$
$191$	−0.0998569	+	1.17961i	−0.00722539	+	0.0853533i	0.991909	+	0.126950i	$0.0405189\pi$
$192$	17.2519	−	10.3527i	1.24505	−	0.747145i
$193$	11.7778	+	14.1978i	0.847784	+	1.02198i	0.999437	+	0.0335460i	$0.0106800\pi$
$193$	11.7778	+	14.1978i	0.847784	+	1.02198i	−0.151653	+	0.988434i	$0.548460\pi$
$194$	22.0580	−	18.9362i	1.58367	−	1.35954i
$195$	1.20334	+	2.67836i	0.0861729	+	0.191801i
$196$	24.1027	+	5.80808i	1.72162	+	0.414863i
$197$	−4.67791	+	0.316527i	−0.333288	+	0.0225516i	−0.233205	−	0.972428i	$-0.574921\pi$
$197$	−4.67791	+	0.316527i	−0.333288	+	0.0225516i	−0.100082	+	0.994979i	$0.531911\pi$
$198$	5.04418	−	0.170460i	0.358474	−	0.0121141i
$199$	11.6059	+	0.392202i	0.822718	+	0.0278025i	0.442140	−	0.896946i	$-0.354220\pi$
$199$	11.6059	+	0.392202i	0.822718	+	0.0278025i	0.380578	+	0.924749i	$0.375725\pi$
$200$	−39.1184	−	2.64691i	−2.76609	−	0.187165i
$201$	0.0294212	+	0.00923098i	0.00207521	+	0.000651103i
$202$	−5.68603	−	37.1164i	−0.400067	−	2.61150i
$203$	0.311044	+	3.67435i	0.0218310	+	0.257889i
$204$	−29.8029	+	11.6139i	−2.08662	+	0.813133i
$205$	4.95288	+	3.20455i	0.345924	+	0.223816i
$206$	6.22033	+	52.3659i	0.433391	+	3.64850i
$207$	1.46062	+	0.513071i	0.101520	+	0.0356609i
$208$	−21.3803	+	52.2393i	−1.48245	+	3.62215i
$209$	4.31131	+	0.885996i	0.298219	+	0.0612856i
$210$	2.30307	+	1.49011i	0.158927	+	0.102827i
$211$	−10.7513	−	8.61639i	−0.740149	−	0.593177i	0.180497	−	0.983576i	$-0.442230\pi$
$211$	−10.7513	−	8.61639i	−0.740149	−	0.593177i	−0.920646	+	0.390399i	$0.872337\pi$
$212$	−8.27391	+	28.0191i	−0.568254	+	1.92436i
$213$	10.7947	+	9.26691i	0.739638	+	0.634958i
$214$	−0.428991	+	25.3963i	−0.0293252	+	1.73605i
$215$	−0.497003	+	0.426663i	−0.0338953	+	0.0290982i
$216$	40.3099	+	12.6473i	2.74274	+	0.860541i
$217$	−2.93405	−	7.86108i	−0.199176	−	0.533645i
$218$	−8.47074	+	2.65771i	−0.573711	+	0.180003i
$219$	−1.78137	+	2.85794i	−0.120374	+	0.193122i
$220$	−0.616528	−	3.28009i	−0.0415663	−	0.221143i
$221$	14.7561	−	23.6739i	0.992601	−	1.59248i
$222$	0.907743	−	0.892539i	0.0609237	−	0.0599033i
$223$	16.3158	+	10.5565i	1.09259	+	0.706915i	0.958796	−	0.284095i	$-0.0916931\pi$
$223$	16.3158	+	10.5565i	1.09259	+	0.706915i	0.133792	+	0.991009i	$0.457284\pi$
$224$	4.88183	+	25.9726i	0.326181	+	1.73537i
$225$	−5.77080	−	7.45526i	−0.384720	−	0.497017i
$226$	19.5772	+	22.0403i	1.30225	+	1.46610i
$227$	5.05172	−	7.52598i	0.335294	−	0.499517i	−0.624193	−	0.781270i	$-0.714572\pi$
$227$	5.05172	−	7.52598i	0.335294	−	0.499517i	0.959487	+	0.281754i	$0.0909161\pi$
$228$	21.0221	+	12.6153i	1.39222	+	0.835466i
$229$	7.49745	−	12.9860i	0.495445	−	0.858137i	−0.504541	−	0.863388i	$-0.668338\pi$
$229$	7.49745	−	12.9860i	0.495445	−	0.858137i	0.999986	+	0.00525119i	$0.00167151\pi$
$230$	0.261252	−	1.38993i	0.0172264	−	0.0916490i
$231$	0.403346	−	1.21342i	0.0265382	−	0.0798369i
$232$	18.6712	−	10.3634i	1.22582	−	0.680388i
$233$	−8.66119	+	11.1893i	−0.567414	+	0.733038i	−0.984414	−	0.175869i	$-0.943727\pi$
$233$	−8.66119	+	11.1893i	−0.567414	+	0.733038i	0.417000	+	0.908906i	$0.363081\pi$
$234$	−23.1330	+	8.12594i	−1.51225	+	0.531209i
$235$	−1.33960	−	2.32026i	−0.0873859	−	0.151357i
$236$	−0.466489	+	27.6162i	−0.0303659	+	1.79766i
$237$	−5.83832	−	6.57287i	−0.379239	−	0.426954i
$238$	−0.440157	−	26.0573i	−0.0285311	−	1.68904i
$239$	−10.2435	+	12.3483i	−0.662599	+	0.798745i	−0.989224	−	0.146409i	$-0.953228\pi$
$239$	−10.2435	+	12.3483i	−0.662599	+	0.798745i	0.326625	+	0.945154i	$0.394089\pi$
$240$	1.33158	−	8.69212i	0.0859534	−	0.561074i
$241$	−10.5489	−	0.713782i	−0.679514	−	0.0459787i	−0.276282	−	0.961077i	$-0.589102\pi$
$241$	−10.5489	−	0.713782i	−0.679514	−	0.0459787i	−0.403232	+	0.915098i	$0.632113\pi$
$242$	24.8494	−	11.6728i	1.59738	−	0.750354i
$243$	6.61288	+	14.7188i	0.424216	+	0.944208i
$244$	1.40075	+	0.974948i	0.0896736	+	0.0624147i
$245$	2.69823	−	2.01664i	0.172384	−	0.128838i
$246$	12.9527	−	16.7335i	0.825831	−	1.06689i
$247$	−21.2724	+	2.16319i	−1.35353	+	0.137641i
$248$	−34.5620	+	34.1554i	−2.19469	+	2.16887i
$249$	−13.2714	−	1.34957i	−0.841041	−	0.0855255i
$250$	−12.5379	+	13.1899i	−0.792967	+	0.834201i
$251$	21.5920	+	11.0477i	1.36288	+	0.697323i	0.974544	−	0.224196i	$-0.0719757\pi$
$251$	21.5920	+	11.0477i	1.36288	+	0.697323i	0.388333	+	0.921519i	$0.373051\pi$
$252$	−10.1491	+	13.1116i	−0.639335	+	0.825953i
$253$	−0.657757	+	0.0445065i	−0.0413528	+	0.00279810i
$254$	0.401889	−	3.38330i	0.0252167	−	0.212287i
$255$	−1.37085	+	4.12404i	−0.0858462	+	0.258257i
$256$	13.7163	−	9.54683i	0.857269	−	0.596677i
$257$	−9.78437	−	5.87155i	−0.610332	−	0.366257i	0.175699	−	0.984444i	$-0.443781\pi$
$257$	−9.78437	−	5.87155i	−0.610332	−	0.366257i	−0.786031	+	0.618187i	$0.787868\pi$
$258$	1.37464	+	1.90554i	0.0855815	+	0.118633i
$259$	0.307699	+	0.684867i	0.0191195	+	0.0425555i
$260$	7.62802	+	14.3073i	0.473070	+	0.887303i
$261$	4.84461	+	1.70177i	0.299874	+	0.105337i
$262$	−38.6519	−	25.0081i	−2.38792	−	1.54501i
$263$	3.61895	−	13.9772i	0.223154	−	0.861871i	−0.755296	−	0.655384i	$-0.772507\pi$
$263$	3.61895	−	13.9772i	0.223154	−	0.861871i	0.978449	−	0.206487i	$-0.0662030\pi$
$264$	−7.36700	+	0.749151i	−0.453408	+	0.0461071i
$265$	2.21228	+	3.29583i	0.135899	+	0.202461i
$266$	−15.5874	+	12.4922i	−0.955723	+	0.765943i
$267$	5.14773	−	3.08912i	0.315036	−	0.189051i
$268$	0.165532	+	0.0398886i	0.0101115	+	0.00243659i
$269$	−21.9597	+	8.55746i	−1.33891	+	0.521758i	−0.922000	−	0.387191i	$-0.873445\pi$
$269$	−21.9597	+	8.55746i	−1.33891	+	0.521758i	−0.416908	+	0.908949i	$0.636886\pi$
$270$	7.79168	−	5.04129i	0.474187	−	0.306803i
$271$	−16.0800	−	1.63518i	−0.976790	−	0.0993298i	−0.400256	−	0.916403i	$-0.631079\pi$
$271$	−16.0800	−	1.63518i	−0.976790	−	0.0993298i	−0.576534	+	0.817073i	$0.695595\pi$
$272$	−75.6165	+	35.5201i	−4.58493	+	2.15372i
$273$	−0.104916	+	6.21105i	−0.00634983	+	0.375910i
$274$	−19.2423	−	9.03888i	−1.16247	−	0.546059i
$275$	3.51033	+	1.94839i	0.211681	+	0.117492i
$276$	−3.53895	−	0.980365i	−0.213020	−	0.0590110i
$277$	−2.59459	+	5.28943i	−0.155894	+	0.317811i	−0.961577	−	0.274536i	$-0.911476\pi$
$277$	−2.59459	+	5.28943i	−0.155894	+	0.317811i	0.805683	+	0.592347i	$0.201798\pi$
$278$	−13.4109	+	7.44363i	−0.804329	+	0.446439i
$279$	−11.6594	−	0.759317i	−0.698030	−	0.0454591i
$280$	8.19168	+	4.54675i	0.489546	+	0.271720i
$281$	−24.6815	+	17.1789i	−1.47238	+	1.02480i	−0.483619	+	0.875279i	$0.660678\pi$
$281$	−24.6815	+	17.1789i	−1.47238	+	1.02480i	−0.988758	+	0.149526i	$0.952225\pi$
$282$	−8.69862	+	4.08608i	−0.517995	+	0.243323i
$283$	1.79013	−	1.88321i	0.106412	−	0.111945i	−0.669422	−	0.742882i	$-0.733458\pi$
$283$	1.79013	−	1.88321i	0.106412	−	0.111945i	0.775834	+	0.630937i	$0.217329\pi$
$284$	62.9257	+	47.0303i	3.73395	+	2.79073i
$285$	3.14283	−	1.10398i	0.186165	−	0.0653943i
$286$	7.68817	−	7.06485i	0.454611	−	0.417753i
$287$	6.60160	+	10.5913i	0.389680	+	0.625184i
$288$	35.7759	+	8.62100i	2.10812	+	0.507997i
$289$	23.4071	−	6.48428i	1.37689	−	0.381428i
$290$	0.866525	−	4.61013i	0.0508841	−	0.270716i
$291$	−10.2328	−	0.692391i	−0.599856	−	0.0405887i
$292$	−8.74874	+	16.4094i	−0.511981	+	0.960286i
$293$	−7.97808	+	7.33125i	−0.466084	+	0.428296i	−0.874887	−	0.484327i	$-0.839065\pi$
$293$	−7.97808	+	7.33125i	−0.466084	+	0.428296i	0.408803	+	0.912623i	$0.365946\pi$
$294$	−6.39166	−	10.2545i	−0.372769	−	0.598053i
$295$	2.84742	+	2.44443i	0.165783	+	0.142320i
$296$	2.88748	−	3.25077i	0.167831	−	0.188947i
$297$	−3.18538	−	2.92712i	−0.184834	−	0.169849i
$298$	−12.2652	−	6.27553i	−0.710502	−	0.363532i
$299$	2.98413	−	1.16288i	0.172577	−	0.0672512i
$300$	14.8514	+	16.7199i	0.857445	+	0.965326i
$301$	−1.33547	+	0.369953i	−0.0769749	+	0.0213237i
$302$	0.576898	−	11.3755i	0.0331967	−	0.654584i
$303$	−7.75028	+	10.7435i	−0.445242	+	0.617197i
$304$	57.0067	+	29.1677i	3.26956	+	1.67288i
$305$	0.223465	−	0.0619045i	0.0127955	−	0.00354464i
$306$	−33.3488	−	14.3111i	−1.90642	−	0.818110i
$307$	−5.90639	−	14.4313i	−0.337096	−	0.823640i	−0.997361	−	0.0726078i	$-0.976868\pi$
$307$	−5.90639	−	14.4313i	−0.337096	−	0.823640i	0.660265	−	0.751033i	$-0.270444\pi$
$308$	1.76982	−	6.83545i	0.100845	−	0.389486i
$309$	11.3878	−	14.7118i	0.647829	−	0.836926i
$310$	0.927242	+	10.6336i	0.0526638	+	0.603946i
$311$	−1.51645	−	1.95909i	−0.0859899	−	0.111090i	0.745828	−	0.666139i	$-0.232054\pi$
$311$	−1.51645	−	1.95909i	−0.0859899	−	0.111090i	−0.831817	+	0.555049i	$0.812699\pi$
$312$	33.0583	−	14.1864i	1.87156	−	0.803148i
$313$	−6.82750	+	30.5930i	−0.385913	+	1.72922i	0.259820	+	0.965657i	$0.416337\pi$
$313$	−6.82750	+	30.5930i	−0.385913	+	1.72922i	−0.645733	+	0.763563i	$0.723448\pi$
$314$	49.8974	−	42.8355i	2.81588	−	2.41735i
$315$	0.490693	+	2.19872i	0.0276474	+	0.123884i
$316$	−34.6154	−	34.0356i	−1.94727	−	1.91465i
$317$	9.94720	−	2.39700i	0.558690	−	0.134629i	0.0549582	−	0.998489i	$-0.482497\pi$
$317$	9.94720	−	2.39700i	0.558690	−	0.134629i	0.503732	+	0.863860i	$0.331960\pi$
$318$	12.4497	−	6.91012i	0.698142	−	0.387500i
$319$	−2.18166	+	0.147620i	−0.122150	+	0.00826514i
$320$	1.27329	−	15.0413i	0.0711789	−	0.840834i
$321$	6.38963	−	6.28261i	0.356634	−	0.350661i
$322$	1.75047	−	2.42652i	0.0975501	−	0.135224i
$323$	−25.3495	−	18.9461i	−1.41049	−	1.05419i
$324$	4.19168	+	7.86204i	0.232871	+	0.436780i
$325$	−19.1048	−	3.92613i	−1.05974	−	0.217782i
$326$	−2.07921	−	40.9985i	−0.115157	−	2.27070i
$327$	2.78829	+	1.42664i	0.154193	+	0.0788935i
$328$	40.2799	−	60.0085i	2.22409	−	3.31341i
$329$	−0.478111	−	5.64790i	−0.0263591	−	0.311379i
$330$	−0.906562	+	1.35058i	−0.0499046	+	0.0743472i
$331$	9.68257	−	18.1609i	0.532202	−	0.998213i	−0.461604	−	0.887086i	$-0.652726\pi$
$331$	9.68257	−	18.1609i	0.532202	−	0.998213i	0.993806	−	0.111127i	$-0.0354461\pi$
$332$	−73.6195	−	2.48785i	−4.04039	−	0.136539i
$333$	1.04550			0.0572932
$334$	−5.04320	+	42.4562i	−0.275952	+	2.32310i
$335$	0.0185308	−	0.0138498i	0.00101245	−	0.000756697i
$336$	10.3682	−	15.4464i	0.565632	−	0.842672i
$337$	29.0554	+	9.11620i	1.58275	+	0.496591i	0.958610	−	0.284722i	$-0.0919013\pi$
$337$	29.0554	+	9.11620i	1.58275	+	0.496591i	0.624139	+	0.781313i	$0.285450\pi$
$338$	−7.86884	+	13.6292i	−0.428008	+	0.741332i
$339$	0.526762	−	10.3869i	0.0286098	−	0.564137i
$340$	−6.01510	+	23.2317i	−0.326214	+	1.25991i
$341$	4.69027	−	1.66088i	0.253992	−	0.0899419i
$342$	6.97208	+	26.9278i	0.377007	+	1.45609i
$343$	17.3139	−	3.55810i	0.934863	−	0.192119i
$344$	5.12368	+	6.17646i	0.276250	+	0.333012i
$345$	−0.409516	+	0.285032i	−0.0220476	+	0.0153456i
$346$	15.5186	−	29.1072i	0.834287	−	1.56481i
$347$	3.36379	−	10.1195i	0.180578	−	0.543245i	−0.818954	−	0.573860i	$-0.805445\pi$
$347$	3.36379	−	10.1195i	0.180578	−	0.543245i	0.999531	+	0.0306148i	$0.00974651\pi$
$348$	−11.7381	−	3.25169i	−0.629226	−	0.174309i
$349$	−6.64338	−	13.5435i	−0.355612	−	0.724965i	0.643571	−	0.765387i	$-0.277452\pi$
$349$	−6.64338	−	13.5435i	−0.355612	−	0.724965i	−0.999183	+	0.0404222i	$0.987130\pi$
$350$	−16.9774	+	6.61591i	−0.907480	+	0.353635i
$351$	19.0219	+	8.93534i	1.01531	+	0.476933i
$352$	−15.4482	+	2.63434i	−0.823392	+	0.140411i
$353$	−12.9778	−	31.7091i	−0.690736	−	1.68771i	−0.725419	−	0.688308i	$-0.758354\pi$
$353$	−12.9778	−	31.7091i	−0.690736	−	1.68771i	0.0346824	−	0.999398i	$-0.488958\pi$
$354$	9.59869	−	9.43792i	0.510164	−	0.501620i
$355$	10.3767	−	2.50051i	0.550741	−	0.132713i
$356$	27.2089	−	18.9379i	1.44207	−	1.00371i
$357$	−6.33449	+	6.66388i	−0.335257	+	0.352690i
$358$	0.281420	−	1.26100i	0.0148735	−	0.0666461i
$359$	−23.8540	−	11.2052i	−1.25897	−	0.591387i	−0.323979	−	0.946064i	$-0.605021\pi$
$359$	−23.8540	−	11.2052i	−1.25897	−	0.591387i	−0.934989	+	0.354677i	$0.884591\pi$
$360$	10.4500	−	7.81024i	0.550762	−	0.411636i
$361$	0.0887935	+	5.25658i	0.00467334	+	0.276662i
$362$	−19.9062	−	2.70626i	−1.04624	−	0.142238i
$363$	−9.13840	−	3.21004i	−0.479641	−	0.168484i
$364$	1.73736	+	34.2578i	0.0910623	+	1.79560i
$365$	0.957031	+	2.33836i	0.0500933	+	0.122395i
$366$	−0.153651	−	0.817460i	−0.00803144	−	0.0427293i
$367$	3.87352	+	32.6092i	0.202196	+	1.70219i	0.612690	+	0.790324i	$0.290088\pi$
$367$	3.87352	+	32.6092i	0.202196	+	1.70219i	−0.410494	+	0.911863i	$0.634644\pi$
$368$	−9.39514	−	1.93075i	−0.489755	−	0.100647i
$369$	17.2202	−	2.34110i	0.896450	−	0.121873i
$370$	−0.144630	−	0.944096i	−0.00751897	−	0.0490812i
$371$	1.27166	+	8.30094i	0.0660212	+	0.430963i
$372$	27.7154	−	0.0700680i	1.43698	−	0.00363286i
$373$	−3.09105	+	20.1773i	−0.160048	+	1.04474i	0.759141	+	0.650926i	$0.225619\pi$
$373$	−3.09105	+	20.1773i	−0.160048	+	1.04474i	−0.919190	+	0.393815i	$0.871155\pi$
$374$	15.4539			0.799105
$375$	6.41654	−	0.216837i	0.331349	−	0.0111974i
$376$	−28.6998	+	15.9297i	−1.48008	+	0.821510i
$377$	9.89782	−	3.85707i	0.509764	−	0.198649i
$378$	19.4545	−	2.64485i	1.00063	−	0.136037i
$379$	−17.2094	−	16.9212i	−0.883990	−	0.869184i	0.108173	−	0.994132i	$-0.465500\pi$
$379$	−17.2094	−	16.9212i	−0.883990	−	0.869184i	−0.992163	+	0.124948i	$0.960124\pi$
$380$	16.9033	−	7.25379i	0.867122	−	0.372111i
$381$	−0.937952	+	0.751701i	−0.0480527	+	0.0385108i
$382$	2.27177	−	2.23372i	0.116234	−	0.114287i
$383$	−6.97278	−	3.27539i	−0.356293	−	0.167365i	0.238705	−	0.971092i	$-0.423277\pi$
$383$	−6.97278	−	3.27539i	−0.356293	−	0.167365i	−0.594998	+	0.803727i	$0.702847\pi$
$384$	−20.5511	−	3.50453i	−1.04874	−	0.178840i
$385$	−0.561271	−	0.778036i	−0.0286050	−	0.0396524i
$386$	0.838489	−	49.6386i	0.0426780	−	2.52654i
$387$	−0.292204	+	1.90741i	−0.0148536	+	0.0969591i
$388$	−56.6337			−2.87514
$389$	−7.75376	+	0.262026i	−0.393131	+	0.0132852i	−0.229680	−	0.973266i	$-0.573768\pi$
$389$	−7.75376	+	0.262026i	−0.393131	+	0.0132852i	−0.163451	+	0.986551i	$0.552263\pi$
$390$	2.23795	−	7.57869i	0.113323	−	0.383762i
$391$	4.41676	+	1.72116i	0.223365	+	0.0870430i
$392$	−24.1450	−	33.4700i	−1.21951	−	1.69049i
$393$	3.53762	+	15.8515i	0.178449	+	0.799604i
$394$	10.1072	+	7.55407i	0.509194	+	0.380568i
$395$	−6.56200	+	0.667290i	−0.330170	+	0.0335750i
$396$	−7.67230	−	6.14880i	−0.385548	−	0.308989i
$397$	−25.4488	−	7.04987i	−1.27724	−	0.353823i	−0.438686	−	0.898641i	$-0.644556\pi$
$397$	−25.4488	−	7.04987i	−1.27724	−	0.353823i	−0.838554	+	0.544818i	$0.816599\pi$
$398$	−23.0117	−	21.1460i	−1.15347	−	1.05996i
$399$	7.01109	+	0.712958i	0.350993	+	0.0356925i
$400$	41.6499	+	40.9523i	2.08250	+	2.04762i
$401$	−7.81351	−	21.0971i	−0.390188	−	1.05354i	−0.970912	−	0.239438i	$-0.923037\pi$
$401$	−7.81351	−	21.0971i	−0.390188	−	1.05354i	0.580723	−	0.814101i	$-0.302770\pi$
$402$	−0.0438965	−	0.0704254i	−0.00218936	−	0.00351250i
$403$	−19.3250	+	14.5197i	−0.962649	+	0.723278i
$404$	−38.6938	+	62.0784i	−1.92509	+	3.08852i
$405$	1.18577	+	0.243682i	0.0589215	+	0.0121087i
$406$	5.80601	−	8.04832i	0.288147	−	0.399431i
$407$	−0.409143	+	0.175577i	−0.0202805	+	0.00870304i
$408$	50.2349	+	17.6460i	2.48700	+	0.873607i
$409$	−15.2577	−	22.7308i	−0.754447	−	1.12397i	−0.988423	−	0.151723i	$-0.951518\pi$
$409$	−15.2577	−	22.7308i	−0.754447	−	1.12397i	0.233976	−	0.972242i	$-0.424826\pi$
$410$	−4.49621	−	15.2262i	−0.222052	−	0.751966i
$411$	2.60488	+	7.03339i	0.128489	+	0.346931i
$412$	57.2546	−	85.2972i	2.82073	−	4.20229i
$413$	3.25368	+	7.24194i	0.160103	+	0.356353i
$414$	−2.08318	−	3.60817i	−0.102383	−	0.177332i
$415$	−6.64651	+	7.48274i	−0.326264	+	0.367313i
$416$	67.7749	−	34.6773i	3.32294	−	1.70020i
$417$	5.21482	+	1.44462i	0.255371	+	0.0707432i
$418$	−7.25057	−	9.36696i	−0.354637	−	0.458153i
$419$	11.2893	+	11.8763i	0.551516	+	0.580195i	0.939963	−	0.341276i	$-0.110859\pi$
$419$	11.2893	+	11.8763i	0.551516	+	0.580195i	−0.388447	+	0.921471i	$0.626988\pi$
$420$	−1.51340	−	5.12505i	−0.0738465	−	0.250077i
$421$	16.3212	+	2.21887i	0.795445	+	0.108141i	0.521106	−	0.853492i	$-0.325519\pi$
$421$	16.3212	+	2.21887i	0.795445	+	0.108141i	0.274339	+	0.961633i	$0.411541\pi$
$422$	6.84964	+	36.4418i	0.333435	+	1.77396i
$423$	−7.44673	−	2.61581i	−0.362072	−	0.127185i
$424$	40.8309	−	26.4179i	1.98292	−	1.28297i
$425$	−16.8889	−	23.4115i	−0.819234	−	1.13563i
$426$	−5.79783	−	37.8462i	−0.280906	−	1.83365i
$427$	0.483585	+	0.0824645i	0.0234023	+	0.00399074i
$428$	32.8605	−	36.9948i	1.58837	−	1.78821i
$429$	−3.68152	−	0.124411i	−0.177746	−	0.00600663i
$430$	1.76283			0.0850111
$431$	−1.23431	+	10.3910i	−0.0594544	+	0.500517i	0.931239	+	0.364408i	$0.118729\pi$
$431$	−1.23431	+	10.3910i	−0.0594544	+	0.500517i	−0.990694	+	0.136109i	$0.956540\pi$
$432$	−33.2924	−	53.4127i	−1.60178	−	2.56982i
$433$	−18.3224	−	12.7527i	−0.880517	−	0.612858i	0.0418711	−	0.999123i	$-0.486668\pi$
$433$	−18.3224	−	12.7527i	−0.880517	−	0.612858i	−0.922388	+	0.386265i	$0.873765\pi$
$434$	−7.78918	+	21.1958i	−0.373893	+	1.01743i
$435$	−1.35829	+	0.945399i	−0.0651251	+	0.0453284i
$436$	15.8934	+	6.82040i	0.761156	+	0.326638i
$437$	−1.02899	−	3.48461i	−0.0492232	−	0.166692i
$438$	8.64757	−	2.71319i	0.413197	−	0.129641i
$439$	−5.06784	−	8.77776i	−0.241875	−	0.418940i	0.719373	−	0.694624i	$-0.244429\pi$
$439$	−5.06784	−	8.77776i	−0.241875	−	0.418940i	−0.961248	+	0.275684i	$0.911096\pi$
$440$	−2.77784	+	4.81136i	−0.132428	+	0.229373i
$441$	2.16151	−	9.68539i	0.102929	−	0.461209i
$442$	−71.6326	+	22.4749i	−3.40722	+	1.06902i
$443$	−7.85901	+	26.6141i	−0.373393	+	1.26447i	0.534463	+	0.845192i	$0.320514\pi$
$443$	−7.85901	+	26.6141i	−0.373393	+	1.26447i	−0.907856	+	0.419282i	$0.862282\pi$
$444$	−2.47435	+	0.167425i	−0.117427	+	0.00794562i
$445$	0.379932	−	4.48813i	0.0180105	−	0.212758i
$446$	−14.8115	−	50.1582i	−0.701343	−	2.37506i
$447$	1.53320	+	4.61245i	0.0725180	+	0.218161i
$448$	15.9676	−	27.6566i	0.754396	−	1.30665i
$449$	−29.8326	−	3.03368i	−1.40789	−	0.143168i	−0.632454	−	0.774598i	$-0.717952\pi$
$449$	−29.8326	−	3.03368i	−1.40789	−	0.143168i	−0.775433	+	0.631430i	$0.782468\pi$
$450$	−1.28510	+	25.3399i	−0.0605800	+	1.19454i
$451$	−6.34576	+	3.80806i	−0.298810	+	0.179314i
$452$	−0.969947	−	57.4208i	−0.0456225	−	2.70085i
$453$	−2.95882	+	2.71893i	−0.139018	+	0.127747i
$454$	−23.5087	+	6.51243i	−1.10332	+	0.305643i
$455$	3.73313	+	2.79012i	0.175012	+	0.130803i
$456$	−12.8732	−	38.7274i	−0.602843	−	1.81358i
$457$	−13.1698	+	2.70647i	−0.616058	+	0.126603i	−0.499115	−	0.866536i	$-0.666342\pi$
$457$	−13.1698	+	2.70647i	−0.616058	+	0.126603i	−0.116943	+	0.993139i	$0.537309\pi$
$458$	−38.0743	+	13.3744i	−1.77910	+	0.624943i
$459$	11.7821	+	28.7877i	0.549941	+	1.34369i
$460$	−2.14990	+	1.72299i	−0.100240	+	0.0803348i
$461$	12.7465	−	1.29619i	0.593662	−	0.0603695i	0.200271	−	0.979741i	$-0.435818\pi$
$461$	12.7465	−	1.29619i	0.593662	−	0.0603695i	0.393391	+	0.919371i	$0.371302\pi$
$462$	−2.95076	+	1.77074i	−0.137282	+	0.0823821i
$463$	−17.6645	−	18.5830i	−0.820938	−	0.863626i	0.171650	−	0.985158i	$-0.445090\pi$
$463$	−17.6645	−	18.5830i	−0.820938	−	0.863626i	−0.992588	+	0.121532i	$0.961219\pi$
$464$	−31.1620	−	6.40395i	−1.44666	−	0.297296i
$465$	2.39693	−	2.90435i	0.111155	−	0.134686i
$466$	37.3012	−	7.66560i	1.72795	−	0.355102i
$467$	4.23794	+	2.94969i	0.196108	+	0.136495i	0.665231	−	0.746638i	$-0.268333\pi$
$467$	4.23794	+	2.94969i	0.196108	+	0.136495i	−0.469123	+	0.883133i	$0.655430\pi$
$468$	44.5052	+	17.3432i	2.05725	+	0.801689i
$469$	0.0479416	−	0.00985224i	0.00221374	−	0.000454934i
$470$	−1.33195	+	7.08631i	−0.0614382	+	0.326867i
$471$	−23.1476	−	1.56626i	−1.06658	−	0.0721694i
$472$	30.5329	−	34.3744i	1.40539	−	1.58221i
$473$	−0.205972	−	0.795511i	−0.00947061	−	0.0365776i
$474$	0.399603	+	23.6565i	0.0183544	+	1.08658i
$475$	−6.26640	+	21.2208i	−0.287522	+	0.973677i
$476$	−32.4145	+	39.0748i	−1.48572	+	1.79099i
$477$	11.2694	+	3.12187i	0.515992	+	0.142941i
$478$	42.5640	−	7.25834i	1.94683	−	0.331989i
$479$	8.75136	+	8.60478i	0.399860	+	0.393163i	0.872917	−	0.487869i	$-0.162226\pi$
$479$	8.75136	+	8.60478i	0.399860	+	0.393163i	−0.473057	+	0.881032i	$0.656849\pi$
$480$	−8.99915	+	7.72552i	−0.410753	+	0.352620i
$481$	1.64113	−	1.40886i	0.0748291	−	0.0642387i
$482$	20.2897	+	19.9498i	0.924169	+	0.908690i
$483$	−1.04055	+	0.177442i	−0.0473465	+	0.00807388i
$484$	−51.5430	−	14.2785i	−2.34286	−	0.649023i
$485$	−4.91286	+	5.92232i	−0.223082	+	0.268919i
$486$	12.2985	−	41.6482i	0.557872	−	1.88920i
$487$	−0.216951	−	12.8435i	−0.00983097	−	0.581993i	−0.961490	−	0.274838i	$-0.911376\pi$
$487$	−0.216951	−	12.8435i	−0.00983097	−	0.581993i	0.951659	−	0.307155i	$-0.0993770\pi$
$488$	−0.712076	−	2.75020i	−0.0322342	−	0.124496i
$489$	−9.61785	+	10.8279i	−0.434934	+	0.489656i
$490$	−9.04499	−	0.612021i	−0.408611	−	0.0276483i
$491$	−1.35172	+	7.19147i	−0.0610021	+	0.324547i	−0.999802	−	0.0199173i	$-0.993660\pi$
$491$	−1.35172	+	7.19147i	−0.0610021	+	0.324547i	0.938800	+	0.344464i	$0.111939\pi$
$492$	−40.3796	+	8.29821i	−1.82045	+	0.374112i
$493$	14.6496	+	5.70879i	0.659785	+	0.257111i
$494$	47.2306	+	32.8734i	2.12500	+	1.47905i
$495$	−1.30855	+	0.268914i	−0.0588150	+	0.0120868i
$496$	72.2123	−	5.06961i	3.24243	−	0.227632i
$497$	22.1191	+	4.54560i	0.992179	+	0.203898i
$498$	24.7345	+	26.0207i	1.10838	+	1.16602i
$499$	−11.5558	+	6.93456i	−0.517308	+	0.310434i	−0.749240	−	0.662298i	$-0.769581\pi$
$499$	−11.5558	+	6.93456i	−0.517308	+	0.310434i	0.231932	+	0.972732i	$0.425495\pi$
$500$	35.2699	−	3.58660i	1.57732	−	0.160398i
$501$	11.7701	−	9.43291i	0.525850	−	0.421431i
$502$	−24.7245	−	60.4104i	−1.10351	−	2.69625i
$503$	−41.0169	+	14.4080i	−1.82885	+	0.642421i	−0.832808	+	0.553563i	$0.813268\pi$
$503$	−41.0169	+	14.4080i	−1.82885	+	0.642421i	−0.996044	+	0.0888580i	$0.971678\pi$
$504$	27.0354	−	5.55591i	1.20425	−	0.247480i
$505$	3.13508	+	9.43148i	0.139509	+	0.419695i
$506$	1.42117	+	1.06217i	0.0631785	+	0.0472192i
$507$	5.35066	−	1.48225i	0.237631	−	0.0658289i
$508$	−4.88725	+	4.49101i	−0.216837	+	0.199257i
$509$	−0.443267	−	26.2414i	−0.0196474	−	1.16313i	−0.823149	−	0.567826i	$-0.807785\pi$
$509$	−0.443267	−	26.2414i	−0.0196474	−	1.16313i	0.803501	−	0.595303i	$-0.202968\pi$
$510$	10.0288	−	6.01821i	0.444081	−	0.266491i
$511$	−0.270736	+	5.33845i	−0.0119766	+	0.236159i
$512$	−1.05474	−	0.107257i	−0.0466135	−	0.00474013i
$513$	11.9210	−	20.6478i	0.526325	−	0.911621i
$514$	9.68691	+	29.1418i	0.427271	+	1.28539i
$515$	−3.95300	−	13.3866i	−0.174190	−	0.589885i
$516$	0.386100	−	4.56098i	0.0169971	−	0.200786i
$517$	3.35347	−	0.226909i	0.147485	−	0.00997946i
$518$	0.572253	−	1.93790i	0.0251433	−	0.0851465i
$519$	−11.1035	+	3.48374i	−0.487389	+	0.152919i
$520$	5.87871	−	26.3416i	0.257798	−	1.15516i
$521$	3.02820	−	5.24500i	0.132668	−	0.229788i	−0.792036	−	0.610474i	$-0.790979\pi$
$521$	3.02820	−	5.24500i	0.132668	−	0.229788i	0.924704	+	0.380686i	$0.124312\pi$
$522$	−6.90953	−	11.9677i	−0.302422	−	0.523810i
$523$	4.03120	−	1.26480i	0.176272	−	0.0553057i	−0.209947	−	0.977713i	$-0.567329\pi$
$523$	4.03120	−	1.26480i	0.176272	−	0.0553057i	0.386219	+	0.922407i	$0.373781\pi$
$524$	25.3990	+	86.0124i	1.10956	+	3.75747i
$525$	5.90729	+	2.53502i	0.257815	+	0.110637i
$526$	−31.8920	+	22.1975i	−1.39056	+	0.967858i
$527$	−35.6019	−	3.52944i	−1.55084	−	0.153745i
$528$	9.05445	+	6.30208i	0.394044	+	0.274263i
$529$	−11.8783	−	19.0570i	−0.516448	−	0.828564i
$530$	1.26011	−	10.6082i	0.0547357	−	0.460793i
$531$	11.0554			0.479763
$532$	38.8921	+	1.31430i	1.68619	+	0.0569820i
$533$	23.8760	−	26.8799i	1.03418	−	1.16430i
$534$	−15.9270	−	2.71598i	−0.689227	−	0.117532i
$535$	−1.01806	−	6.64552i	−0.0440144	−	0.287311i
$536$	−0.165823	−	0.229864i	−0.00716245	−	0.00992862i
$537$	−0.382701	+	0.247611i	−0.0165148	+	0.0106852i
$538$	59.8432	+	21.0211i	2.58002	+	0.906285i
$539$	0.780647	+	4.15324i	0.0336248	+	0.178893i
$540$	−17.9143	−	2.43546i	−0.770908	−	0.104805i
$541$	−8.38289	−	28.3882i	−0.360409	−	1.22050i	−0.920061	−	0.391775i	$-0.871861\pi$
$541$	−8.38289	−	28.3882i	−0.360409	−	1.22050i	0.559652	−	0.828727i	$-0.310935\pi$
$542$	29.9690	+	31.5274i	1.28728	+	1.35422i
$543$	4.33824	+	5.60454i	0.186172	+	0.240514i
$544$	108.591	+	30.0820i	4.65579	+	1.28975i
$545$	2.09195	−	1.07035i	0.0896092	−	0.0458490i
$546$	11.1023	−	12.4991i	0.475133	−	0.534912i
$547$	5.47720	+	9.48679i	0.234188	+	0.405626i	0.959036	−	0.283283i	$-0.0914235\pi$
$547$	5.47720	+	9.48679i	0.234188	+	0.405626i	−0.724848	+	0.688909i	$0.758090\pi$
$548$	16.9730	+	37.7781i	0.725052	+	1.61380i
$549$	0.380713	−	0.567182i	0.0162484	−	0.0242067i
$550$	−3.75258	−	10.1323i	−0.160011	−	0.432041i
$551$	−3.41297	−	11.5578i	−0.145398	−	0.492380i
$552$	3.40683	+	5.07546i	0.145004	+	0.216026i
$553$	−13.1655	−	4.62465i	−0.559854	−	0.196660i
$554$	14.5706	−	6.25273i	0.619045	−	0.265653i
$555$	−0.197137	+	0.273272i	−0.00836800	+	0.0115998i
$556$	29.2686	+	6.01485i	1.24127	+	0.255087i
$557$	−10.8476	+	17.4034i	−0.459629	+	0.737407i	−0.994180	−	0.107729i	$-0.965642\pi$
$557$	−10.8476	+	17.4034i	−0.459629	+	0.737407i	0.534551	+	0.845136i	$0.320481\pi$
$558$	22.4775	+	21.9895i	0.951549	+	0.930892i
$559$	2.11165	+	3.38783i	0.0893133	+	0.143290i
$560$	−4.84752	−	13.0887i	−0.204845	−	0.553098i
$561$	−3.88762	−	3.82250i	−0.164135	−	0.161386i
$562$	80.5146	+	8.18753i	3.39630	+	0.345370i
$563$	18.5784	+	17.0721i	0.782987	+	0.719505i	0.964557	−	0.263873i	$-0.0849999\pi$
$563$	18.5784	+	17.0721i	0.782987	+	0.719505i	−0.181571	+	0.983378i	$0.558118\pi$
$564$	18.0428	+	4.99823i	0.759737	+	0.210463i
$565$	−6.08877	−	4.87972i	−0.256157	−	0.205291i
$566$	−6.95675	+	0.707432i	−0.292414	+	0.0297356i
$567$	2.05139	+	1.53320i	0.0861505	+	0.0643883i
$568$	−28.4835	−	127.630i	−1.19514	−	5.35524i
$569$	21.9536	+	30.4322i	0.920344	+	1.27579i	0.960982	+	0.276612i	$0.0892116\pi$
$569$	21.9536	+	30.4322i	0.920344	+	1.27579i	−0.0406376	+	0.999174i	$0.512939\pi$
$570$	−8.35298	−	3.25507i	−0.349868	−	0.136340i
$571$	−7.97723	+	27.0144i	−0.333837	+	1.13052i	0.607856	+	0.794047i	$0.292030\pi$
$571$	−7.97723	+	27.0144i	−0.333837	+	1.13052i	−0.941693	+	0.336473i	$0.890766\pi$
$572$	−20.3291	+	0.686988i	−0.850001	+	0.0287244i
$573$	−1.12399			−0.0469555
$574$	5.08608	−	33.2002i	0.212289	−	1.38575i
$575$	0.0559756	−	3.31375i	0.00233434	−	0.138193i
$576$	−26.0168	−	36.0646i	−1.08403	−	1.50269i
$577$	18.9069	+	3.22414i	0.787103	+	0.134223i	0.547675	−	0.836691i	$-0.315513\pi$
$577$	18.9069	+	3.22414i	0.787103	+	0.134223i	0.239428	+	0.970914i	$0.423040\pi$
$578$	−59.1646	−	27.7919i	−2.46092	−	1.15599i
$579$	−12.4889	+	12.2797i	−0.519022	+	0.510329i
$580$	−7.13083	+	5.71485i	−0.296092	+	0.237296i
$581$	−19.4577	+	8.34996i	−0.807242	+	0.346415i
$582$	19.6816	+	19.3520i	0.815830	+	0.802166i
$583$	−4.93442	+	0.670837i	−0.204363	+	0.0277832i
$584$	28.8424	−	11.2396i	1.19351	−	0.465096i
$585$	5.67435	−	3.14952i	0.234606	−	0.130217i
$586$	29.1430	−	0.984843i	1.20389	−	0.0406835i
$587$	26.2401			1.08304			0.541522	−	0.840687i	$-0.317848\pi$
$587$	26.2401			1.08304			0.541522	+	0.840687i	$0.317848\pi$
$588$	−3.56455	+	23.2682i	−0.147000	+	0.959563i
$589$	14.5641	+	23.2349i	0.600105	+	0.957379i
$590$	−1.52935	−	9.98310i	−0.0629625	−	0.410998i
$591$	−0.674103	−	4.40031i	−0.0277289	−	0.181005i
$592$	−6.41847	+	0.872595i	−0.263797	+	0.0358634i
$593$	−1.85188	−	0.380571i	−0.0760476	−	0.0156282i	0.163123	−	0.986606i	$-0.447843\pi$
$593$	−1.85188	−	0.380571i	−0.0760476	−	0.0156282i	−0.239171	+	0.970978i	$0.576876\pi$
$594$	1.37331	+	11.5612i	0.0563475	+	0.474361i
$595$	1.27425	+	6.77933i	0.0522391	+	0.277925i
$596$	10.1663	+	24.8399i	0.416430	+	1.01748i
$597$	0.558437	+	11.0114i	0.0228553	+	0.450668i
$598$	−8.13216	−	2.85658i	−0.332549	−	0.116814i
$599$	−43.6590	−	5.93548i	−1.78386	−	0.242517i	−0.833248	−	0.552899i	$-0.813521\pi$
$599$	−43.6590	−	5.93548i	−1.78386	−	0.242517i	−0.950612	+	0.310382i	$0.899543\pi$
$600$	−0.628733	−	37.2210i	−0.0256679	−	1.51954i
$601$	−5.65447	+	4.22611i	−0.230650	+	0.172387i	−0.707751	−	0.706462i	$-0.750290\pi$
$601$	−5.65447	+	4.22611i	−0.230650	+	0.172387i	0.477100	+	0.878849i	$0.341688\pi$
$602$	3.37556	+	1.58563i	0.137578	+	0.0646256i
$603$	0.0148447	−	0.0665171i	0.000604524	−	0.00270878i
$604$	−15.2875	+	16.0824i	−0.622040	+	0.654386i
$605$	−5.96439	+	4.15134i	−0.242487	+	0.168776i
$606$	34.6595	−	8.35199i	1.40795	−	0.339276i
$607$	−6.95925	+	6.84269i	−0.282467	+	0.277736i	−0.828453	−	0.560058i	$-0.810779\pi$
$607$	−6.95925	+	6.84269i	−0.282467	+	0.277736i	0.545986	+	0.837794i	$0.316155\pi$
$608$	−32.7145	−	79.9328i	−1.32675	−	3.24170i
$609$	−3.45130	+	0.588542i	−0.139854	+	0.0238489i
$610$	−0.564836	−	0.265326i	−0.0228695	−	0.0107427i
$611$	−15.2141	+	5.92877i	−0.615496	+	0.239852i
$612$	31.1342	+	63.4714i	1.25853	+	2.56568i
$613$	−20.2925	−	5.62147i	−0.819608	−	0.227049i	−0.168177	−	0.985757i	$-0.553788\pi$
$613$	−20.2925	−	5.62147i	−0.819608	−	0.227049i	−0.651431	+	0.758708i	$0.725831\pi$
$614$	−13.2373	+	39.8229i	−0.534216	+	1.60712i
$615$	−2.63509	+	4.94244i	−0.106257	+	0.199298i
$616$	−9.64691	+	6.71444i	−0.388685	+	0.270533i
$617$	3.16242	+	3.81221i	0.127314	+	0.153474i	0.829473	−	0.558546i	$-0.188641\pi$
$617$	3.16242	+	3.81221i	0.127314	+	0.153474i	−0.702159	+	0.712020i	$0.747780\pi$
$618$	−49.0439	+	10.0788i	−1.97283	+	0.405428i
$619$	−9.29045	−	35.8818i	−0.373415	−	1.44221i	−0.832601	−	0.553873i	$-0.813149\pi$
$619$	−9.29045	−	35.8818i	−0.373415	−	1.44221i	0.459187	−	0.888340i	$-0.348141\pi$
$620$	12.1228	−	16.8945i	0.486862	−	0.678500i
$621$	−0.895119	+	3.45715i	−0.0359199	+	0.138731i
$622$	−0.337697	+	6.65882i	−0.0135404	+	0.266994i
$623$	4.76451	−	8.25237i	0.190886	−	0.330624i
$624$	−51.1347	−	16.0436i	−2.04702	−	0.642258i
$625$	−9.83455	+	14.6514i	−0.393382	+	0.586056i
$626$	67.5716	−	50.5026i	2.70070	−	2.01849i
$627$	−0.492936	+	4.14978i	−0.0196860	+	0.165726i
$628$	−128.111			−5.11219
$629$	3.19947	+	0.108121i	0.127571	+	0.00431107i
$630$	2.85238	−	5.35000i	0.113641	−	0.213149i
$631$	−8.21905	+	12.2446i	−0.327195	+	0.487451i	−0.957315	−	0.289047i	$-0.906662\pi$
$631$	−8.21905	+	12.2446i	−0.327195	+	0.487451i	0.630120	+	0.776498i	$0.283006\pi$
$632$	6.81633	+	80.5211i	0.271139	+	3.20296i
$633$	7.29071	−	10.8616i	0.289780	−	0.431710i
$634$	−24.5142	−	12.5428i	−0.973584	−	0.498139i
$635$	0.0456762	+	0.900658i	0.00181261	+	0.0357415i
$636$	−27.1708	−	5.58375i	−1.07739	−	0.221410i
$637$	−9.65860	−	18.1159i	−0.382687	−	0.717779i
$638$	4.71375	+	3.52303i	0.186619	+	0.139478i
$639$	18.3965	−	25.5014i	0.727755	−	1.00882i
$640$	−11.1531	+	10.9663i	−0.440864	+	0.433479i
$641$	3.32504	−	39.2786i	0.131331	−	1.55141i	−0.559766	−	0.828650i	$-0.689109\pi$
$641$	3.32504	−	39.2786i	0.131331	−	1.55141i	0.691098	−	0.722761i	$-0.257127\pi$
$642$	−24.0611	+	1.62808i	−0.949618	+	0.0642550i
$643$	6.09912	−	3.38529i	0.240526	−	0.133503i	−0.360426	−	0.932788i	$-0.617369\pi$
$643$	6.09912	−	3.38529i	0.240526	−	0.133503i	0.600952	+	0.799285i	$0.294788\pi$
$644$	−5.66655	+	1.36548i	−0.223293	+	0.0538074i
$645$	−0.443459	−	0.436032i	−0.0174612	−	0.0171687i
$646$	18.5514	+	83.1260i	0.729894	+	3.27055i
$647$	−3.20478	+	2.75122i	−0.125993	+	0.108161i	−0.712120	−	0.702058i	$-0.752265\pi$
$647$	−3.20478	+	2.75122i	−0.125993	+	0.108161i	0.586127	+	0.810219i	$0.300652\pi$
$648$	3.23041	−	14.4750i	0.126903	−	0.568632i
$649$	−4.32638	+	1.85660i	−0.169825	+	0.0728778i
$650$	32.1296	+	41.5080i	1.26023	+	1.62808i
$651$	7.20220	−	3.40541i	0.282276	−	0.133468i
$652$	−48.9513	+	63.2398i	−1.91708	+	2.47666i
$653$	0.129732	−	0.501053i	0.00507679	−	0.0196077i	−0.965489	−	0.260444i	$-0.916131\pi$
$653$	0.129732	−	0.501053i	0.00507679	−	0.0196077i	0.970566	+	0.240836i	$0.0774215\pi$
$654$	−3.19280	−	7.80111i	−0.124848	−	0.305048i
$655$	11.1978	+	4.80537i	0.437536	+	0.187761i
$656$	−103.763	+	28.7447i	−4.05128	+	1.12229i
$657$	6.62632	+	3.39039i	0.258517	+	0.132272i
$658$	−8.92451	+	12.3712i	−0.347913	+	0.482279i
$659$	0.976642	−	19.2577i	0.0380446	−	0.750175i	−0.906582	−	0.422029i	$-0.861318\pi$
$659$	0.976642	−	19.2577i	0.0380446	−	0.750175i	0.944627	−	0.328146i	$-0.106424\pi$
$660$	3.05383	−	0.845977i	0.118870	−	0.0329296i
$661$	−4.56389	−	5.13810i	−0.177515	−	0.199849i	0.652184	−	0.758061i	$-0.273853\pi$
$661$	−4.56389	−	5.13810i	−0.177515	−	0.199849i	−0.829698	+	0.558212i	$0.811488\pi$
$662$	−51.6081	+	20.1111i	−2.00580	+	0.781640i
$663$	23.5791	+	12.0644i	0.915737	+	0.468541i
$664$	90.2866	+	82.9665i	3.50380	+	3.21972i
$665$	3.51125	−	3.95302i	0.136160	−	0.153292i
$666$	−2.13492	−	1.83277i	−0.0827266	−	0.0710185i
$667$	0.954824	+	1.53187i	0.0369709	+	0.0593144i
$668$	61.3289	−	56.3566i	2.37289	−	2.18050i
$669$	−8.68053	+	16.2815i	−0.335609	+	0.629477i
$670$	−0.0621190	−	0.00420322i	−0.00239986	−	0.000162385i
$671$	−0.0537370	+	0.285895i	−0.00207449	+	0.0110368i
$672$	−24.1811	+	6.69867i	−0.932805	+	0.258407i
$673$	−18.6409	−	4.49193i	−0.718553	−	0.173151i	−0.141594	−	0.989925i	$-0.545223\pi$
$673$	−18.6409	−	4.49193i	−0.718553	−	0.173151i	−0.576958	+	0.816774i	$0.695760\pi$
$674$	−43.3507	−	69.5497i	−1.66981	−	2.67895i
$675$	16.0135	−	14.7152i	0.616359	−	0.566387i
$676$	28.9259	−	10.1608i	1.11253	−	0.390800i
$677$	8.86574	+	6.62619i	0.340738	+	0.254665i	0.755334	−	0.655340i	$-0.227475\pi$
$677$	8.86574	+	6.62619i	0.340738	+	0.254665i	−0.414596	+	0.910006i	$0.636077\pi$
$678$	−19.2839	+	20.2866i	−0.740593	+	0.779104i
$679$	−14.7344	+	6.92135i	−0.565456	+	0.265617i
$680$	32.7870	−	22.8204i	1.25732	−	0.875122i
$681$	7.52473	+	4.17657i	0.288348	+	0.160046i
$682$	−12.4891	−	4.83054i	−0.478233	−	0.184971i
$683$	7.94137	−	4.40782i	0.303868	−	0.168660i	−0.325985	−	0.945375i	$-0.605696\pi$
$683$	7.94137	−	4.40782i	0.303868	−	0.168660i	0.629853	+	0.776715i	$0.283115\pi$
$684$	23.8640	−	48.6501i	0.912464	−	1.86018i
$685$	5.42292	+	1.50227i	0.207199	+	0.0573986i
$686$	−41.5925	−	23.0857i	−1.58801	−	0.881418i
$687$	12.8862	+	6.05314i	0.491638	+	0.230942i
$688$	0.201921	−	11.9537i	0.00769815	−	0.455731i
$689$	21.8966	−	10.2857i	0.834193	−	0.391853i
$690$	1.33590	+	0.135848i	0.0508568	+	0.00517163i
$691$	−21.3819	+	13.8342i	−0.813404	+	0.526280i	−0.881936	−	0.471369i	$-0.843760\pi$
$691$	−21.3819	+	13.8342i	−0.813404	+	0.526280i	0.0685320	+	0.997649i	$0.478168\pi$
$692$	−59.8740	+	23.3322i	−2.27607	+	0.886958i
$693$	−2.74757	−	0.662088i	−0.104372	−	0.0251507i
$694$	−24.6085	+	14.7674i	−0.934126	+	0.560564i
$695$	3.16798	−	2.53891i	0.120168	−	0.0963064i
$696$	11.2999	+	16.8344i	0.428320	+	0.638105i
$697$	52.9399	−	5.38346i	2.00524	−	0.203913i
$698$	−10.1759	+	39.3017i	−0.385165	+	1.48759i
$699$	−11.2796	−	7.29801i	−0.426634	−	0.276036i
$700$	33.4901	+	11.7641i	1.26581	+	0.444640i
$701$	−9.68555	−	18.1665i	−0.365818	−	0.686139i	0.630089	−	0.776523i	$-0.283018\pi$
$701$	−9.68555	−	18.1665i	−0.365818	−	0.686139i	−0.995907	+	0.0903842i	$0.971190\pi$
$702$	−23.1792	−	51.5916i	−0.874842	−	1.94720i
$703$	−1.43557	−	1.98999i	−0.0541435	−	0.0750540i
$704$	16.2379	+	9.74426i	0.611988	+	0.367251i
$705$	2.08785	−	1.45319i	0.0786330	−	0.0547302i
$706$	−29.0856	+	87.5004i	−1.09465	+	3.29312i
$707$	−2.48024	+	20.8799i	−0.0932789	+	0.785269i
$708$	−26.1643	+	1.77039i	−0.983316	+	0.0665352i
$709$	22.5369	−	29.1153i	0.846393	−	1.09345i	−0.148134	−	0.988967i	$-0.547327\pi$
$709$	22.5369	−	29.1153i	0.846393	−	1.09345i	0.994527	−	0.104482i	$-0.0333184\pi$
$710$	−25.5728	−	13.0845i	−0.959731	−	0.491051i
$711$	−13.3873	+	14.0835i	−0.502064	+	0.528172i
$712$	−54.8999	−	5.58277i	−2.05746	−	0.209223i
$713$	−3.03141	−	2.77153i	−0.113527	−	0.103795i
$714$	24.6169	−	2.50330i	0.921265	−	0.0936835i
$715$	−1.69167	+	2.18545i	−0.0632647	+	0.0817313i
$716$	−2.01612	+	1.50683i	−0.0753458	+	0.0563130i
$717$	−12.5028	−	8.70221i	−0.466926	−	0.324990i
$718$	29.0674	+	64.6974i	1.08479	+	2.41448i
$719$	22.4707	−	10.5554i	0.838015	−	0.393649i	0.0421417	−	0.999112i	$-0.486582\pi$
$719$	22.4707	−	10.5554i	0.838015	−	0.393649i	0.795873	+	0.605463i	$0.207012\pi$
$720$	−19.3914	−	1.31210i	−0.722675	−	0.0488992i
$721$	4.47161	−	29.1891i	0.166531	−	1.08706i
$722$	9.03350	−	10.8896i	0.336192	−	0.405270i
$723$	−0.169548	−	10.0372i	−0.00630554	−	0.373288i
$724$	25.9900	+	29.2600i	0.965911	+	1.08744i
$725$	0.185661	−	10.9911i	0.00689527	−	0.408200i
$726$	13.0335	+	22.5746i	0.483717	+	0.837822i
$727$	−5.45185	+	1.91507i	−0.202198	+	0.0710260i	−0.430608	−	0.902539i	$-0.641701\pi$
$727$	−5.45185	+	1.91507i	−0.202198	+	0.0710260i	0.228410	+	0.973565i	$0.426647\pi$
$728$	34.9507	−	45.1526i	1.29536	−	1.67347i
$729$	−8.93786	+	4.96092i	−0.331032	+	0.183738i
$730$	2.14489	−	6.45263i	0.0793859	−	0.238822i
$731$	−1.09147	+	5.80688i	−0.0403693	+	0.214775i
$732$	−0.810192	+	1.40329i	−0.0299455	+	0.0518672i
$733$	−10.3183	−	6.19195i	−0.381115	−	0.228705i	0.311131	−	0.950367i	$-0.399292\pi$
$733$	−10.3183	−	6.19195i	−0.381115	−	0.228705i	−0.692245	+	0.721662i	$0.743378\pi$
$734$	49.2544	−	73.3786i	1.81801	−	2.70845i
$735$	2.12399	+	2.39122i	0.0783445	+	0.0882015i
$736$	7.91858	+	10.2300i	0.291883	+	0.377081i
$737$	0.00536131	+	0.0285235i	0.000197486	+	0.00105068i
$738$	−39.2679	−	25.4067i	−1.44547	−	0.935232i
$739$	−32.4385	+	31.8952i	−1.19327	+	1.17328i	−0.212700	+	0.977117i	$0.568226\pi$
$739$	−32.4385	+	31.8952i	−1.19327	+	1.17328i	−0.980571	+	0.196167i	$0.937151\pi$
$740$	−0.984218	+	1.57903i	−0.0361806	+	0.0580464i
$741$	−3.75021	−	19.9521i	−0.137767	−	0.732958i
$742$	11.9549	−	19.1798i	0.438877	−	0.704113i
$743$	35.1832	−	11.0388i	1.29075	−	0.404975i	0.424881	−	0.905249i	$-0.360316\pi$
$743$	35.1832	−	11.0388i	1.29075	−	0.404975i	0.865867	+	0.500274i	$0.166768\pi$
$744$	−35.0816	−	29.9629i	−1.28615	−	1.09849i
$745$	3.47947	+	1.09169i	0.127478	+	0.0399965i
$746$	41.6829	−	35.7836i	1.52612	−	1.31013i
$747$	−0.497972	+	29.4800i	−0.0182199	+	1.07862i
$748$	−22.8431	−	19.6101i	−0.835225	−	0.717018i
$749$	4.02811	−	13.6409i	0.147184	−	0.498429i
$750$	−13.4828	−	10.8055i	−0.492321	−	0.394560i
$751$	18.7082	+	12.1043i	0.682670	+	0.441694i	0.837638	−	0.546226i	$-0.183936\pi$
$751$	18.7082	+	12.1043i	0.682670	+	0.441694i	−0.154968	+	0.987920i	$0.549527\pi$
$752$	47.8996	+	9.84361i	1.74672	+	0.358960i
$753$	−8.72267	+	21.3125i	−0.317872	+	0.776670i
$754$	−26.9729	−	9.47477i	−0.982296	−	0.345051i
$755$	0.355618	+	2.99377i	0.0129423	+	0.108954i
$756$	−32.1126	−	20.7771i	−1.16792	−	0.755657i
$757$	−44.4408	+	17.3181i	−1.61523	+	0.629437i	−0.988693	−	0.149957i	$-0.952087\pi$
$757$	−44.4408	+	17.3181i	−1.61523	+	0.629437i	−0.626535	+	0.779393i	$0.715527\pi$
$758$	5.47886	+	64.7215i	0.199001	+	2.35079i
$759$	−0.0947849	−	0.618723i	−0.00344047	−	0.0224582i
$760$	−29.2147	−	9.16616i	−1.05973	−	0.332492i
$761$	23.1460	+	1.56615i	0.839041	+	0.0567730i	0.480772	−	0.876845i	$-0.340356\pi$
$761$	23.1460	+	1.56615i	0.839041	+	0.0567730i	0.358269	+	0.933618i	$0.383367\pi$
$762$	3.23304	+	0.109256i	0.117121	+	0.00395791i
$763$	4.96854	−	0.167904i	0.179873	−	0.00607854i
$764$	−6.19244	+	0.419006i	−0.224034	+	0.0151591i
$765$	9.33818	+	2.25024i	0.337623	+	0.0813576i
$766$	8.49670	+	18.9117i	0.306998	+	0.683308i
$767$	17.3537	−	14.8977i	0.626606	−	0.537923i
$768$	10.1305	+	12.2121i	0.365554	+	0.440665i
$769$	−10.6311	+	6.37965i	−0.383366	+	0.230056i	−0.693217	−	0.720729i	$-0.743807\pi$
$769$	−10.6311	+	6.37965i	−0.383366	+	0.230056i	0.309850	+	0.950785i	$0.399721\pi$
$770$	−0.217783	+	2.57267i	−0.00784837	+	0.0927125i
$771$	4.77132	−	9.72700i	0.171835	−	0.350309i
$772$	−64.2278	+	72.3087i	−2.31161	+	2.60245i
$773$	−18.3483	+	49.5418i	−0.659942	+	1.78190i	−0.0374115	+	0.999300i	$0.511911\pi$
$773$	−18.3483	+	49.5418i	−0.659942	+	1.78190i	−0.622530	+	0.782596i	$0.713895\pi$
$774$	3.94039	−	3.38271i	0.141634	−	0.121589i
$775$	6.33091	+	24.1991i	0.227413	+	0.869258i
$776$	71.5304	+	61.4069i	2.56779	+	2.20438i
$777$	−0.623293	+	0.345956i	−0.0223605	+	0.0124111i
$778$	16.2926	+	13.0573i	0.584117	+	0.468128i
$779$	−28.1010	−	29.5622i	−1.00682	−	1.05918i
$780$	−12.9249	+	8.36253i	−0.462786	+	0.299427i
$781$	−2.91665	+	13.0691i	−0.104366	+	0.467648i
$782$	−6.00185	−	11.2572i	−0.214626	−	0.402558i
$783$	−2.96895	+	11.4668i	−0.106102	+	0.409789i
$784$	−5.18615	+	61.2638i	−0.185220	+	2.18799i
$785$	−11.1134	+	13.3969i	−0.396654	+	0.478155i
$786$	20.5640	−	38.5704i	0.733494	−	1.37576i
$787$	24.2006	−	11.3680i	0.862657	−	0.405224i	0.0575424	−	0.998343i	$-0.481674\pi$
$787$	24.2006	−	11.3680i	0.862657	−	0.405224i	0.805115	+	0.593119i	$0.202104\pi$
$788$	−5.35421	−	23.9914i	−0.190736	−	0.854659i
$789$	13.5133	+	2.30439i	0.481087	+	0.0820386i
$790$	14.5694	+	10.1406i	0.518357	+	0.360787i
$791$	−7.26990	−	14.8207i	−0.258488	−	0.526964i
$792$	3.02337	+	16.0851i	0.107431	+	0.571559i
$793$	−0.166697	−	1.40334i	−0.00591958	−	0.0498340i
$794$	39.6083	+	59.0079i	1.40564	+	2.09411i
$795$	−2.94092	+	2.35694i	−0.104304	+	0.0835920i
$796$	7.18148	+	60.4573i	0.254541	+	2.14285i
$797$	1.75152	+	14.7451i	0.0620419	+	0.522299i	0.989085	+	0.147345i	$0.0470728\pi$
$797$	1.75152	+	14.7451i	0.0620419	+	0.522299i	−0.927043	+	0.374954i	$0.877658\pi$
$798$	−13.0669	−	13.7464i	−0.462563	−	0.486616i
$799$	−22.5181	−	8.77507i	−0.796634	−	0.310440i
$800$	−6.64535	−	78.5013i	−0.234949	−	2.77544i
$801$	−7.76307	−	10.7612i	−0.274295	−	0.380228i
$802$	−21.0281	+	56.7776i	−0.742529	+	2.00489i
$803$	−3.16249	−	0.213987i	−0.111602	−	0.00755144i
$804$	−0.0244805	+	0.159800i	−0.000863362	+	0.00563573i
$805$	−0.348770	+	0.711017i	−0.0122925	+	0.0250601i
$806$	64.9151	+	4.22758i	2.28654	+	0.148910i
$807$	−9.85471	−	20.0902i	−0.346902	−	0.707209i
$808$	116.182	−	36.4524i	4.08728	−	1.28239i
$809$	31.3346	−	7.55078i	1.10167	−	0.265471i	0.357800	−	0.933798i	$-0.383527\pi$
$809$	31.3346	−	7.55078i	1.10167	−	0.265471i	0.743868	+	0.668327i	$0.232989\pi$
$810$	−1.99418	−	2.57627i	−0.0700683	−	0.0905208i
$811$	−27.3727	−	3.72134i	−0.961186	−	0.130674i	−0.362787	−	0.931872i	$-0.618175\pi$
$811$	−27.3727	−	3.72134i	−0.961186	−	0.130674i	−0.598399	+	0.801198i	$0.704196\pi$
$812$	−18.7949	+	4.52905i	−0.659572	+	0.158939i
$813$	0.259187	−	15.3438i	0.00909007	−	0.538132i
$814$	1.14326	+	0.358701i	0.0400713	+	0.0125725i
$815$	2.36671	+	10.6049i	0.0829023	+	0.371473i
$816$	−39.6606	−	68.6942i	−1.38840	−	2.40478i
$817$	4.03176	−	2.06287i	0.141053	−	0.0721706i
$818$	−8.69079	+	73.1634i	−0.303866	+	2.55810i
$819$	13.6985	−	0.926898i	0.478665	−	0.0323884i
$820$	−12.6751	+	28.2118i	−0.442632	+	0.985198i
$821$	30.0359	−	6.17254i	1.04826	−	0.215423i	0.354074	−	0.935218i	$-0.384796\pi$
$821$	30.0359	−	6.17254i	1.04826	−	0.215423i	0.694187	+	0.719794i	$0.255764\pi$
$822$	7.01039	−	18.9286i	0.244515	−	0.660211i
$823$	−43.4972	+	20.4323i	−1.51622	+	0.712226i	−0.990382	−	0.138361i	$-0.955817\pi$
$823$	−43.4972	+	20.4323i	−1.51622	+	0.712226i	−0.525834	+	0.850587i	$0.676247\pi$
$824$	−164.801	+	45.6534i	−5.74111	+	1.59041i
$825$	−1.56219	+	3.47708i	−0.0543885	+	0.121056i
$826$	6.05114	−	20.4918i	0.210546	−	0.713002i
$827$	31.2722	−	16.0006i	1.08744	−	0.556395i	0.183052	−	0.983103i	$-0.441402\pi$
$827$	31.2722	−	16.0006i	1.08744	−	0.556395i	0.904389	+	0.426709i	$0.140327\pi$
$828$	−1.49933	+	7.97680i	−0.0521052	+	0.277213i
$829$	7.26076	−	7.63831i	0.252177	−	0.265290i	−0.586463	−	0.809976i	$-0.699480\pi$
$829$	7.26076	−	7.63831i	0.252177	−	0.265290i	0.838640	+	0.544686i	$0.183351\pi$
$830$	26.6895	−	3.62846i	0.926407	−	0.125946i
$831$	−5.21200	−	2.03106i	−0.180802	−	0.0704566i
$832$	−89.4375	−	21.5519i	−3.10069	−	0.747179i
$833$	7.61631	−	29.4159i	0.263889	−	1.01920i
$834$	−8.11628	−	12.0915i	−0.281044	−	0.418696i
$835$	−0.573179	−	11.3021i	−0.0198357	−	0.391126i
$836$	−1.16877	+	23.0462i	−0.0404228	+	0.797070i
$837$	−0.523345	−	26.9476i	−0.0180894	−	0.931445i
$838$	−2.23354	−	44.0416i	−0.0771563	−	1.52139i
$839$	−21.3874	+	2.17488i	−0.738374	+	0.0750853i	−0.463131	−	0.886290i	$-0.653274\pi$
$839$	−21.3874	+	2.17488i	−0.738374	+	0.0750853i	−0.275242	+	0.961375i	$0.588758\pi$
$840$	−3.64552	+	8.11409i	−0.125782	+	0.279963i
$841$	−12.1730	−	19.5297i	−0.419758	−	0.673439i
$842$	−29.4383	−	33.1421i	−1.01451	−	1.14215i
$843$	−18.2292	−	21.9748i	−0.627847	−	0.756852i
$844$	36.1178	−	62.5578i	1.24323	−	2.15333i
$845$	1.44673	−	3.90628i	0.0497689	−	0.134380i
$846$	10.6207	+	18.3957i	0.365149	+	0.632456i
$847$	−15.1550	+	2.58435i	−0.520732	+	0.0887992i
$848$	−71.7900	−	9.75990i	−2.46528	−	0.335156i
$849$	1.92503	+	1.54277i	0.0660669	+	0.0529479i
$850$	−6.55322	+	77.4130i	−0.224774	+	2.65524i
$851$	0.286796	+	0.229847i	0.00983125	+	0.00787904i
$852$	−39.4546	+	63.2990i	−1.35169	+	2.16859i
$853$	17.9163	−	7.68847i	0.613441	−	0.263248i	−0.0650208	−	0.997884i	$-0.520711\pi$
$853$	17.9163	−	7.68847i	0.613441	−	0.263248i	0.678462	+	0.734636i	$0.262647\pi$
$854$	−0.842923	−	1.01612i	−0.0288442	−	0.0347709i
$855$	−3.01730	−	6.71582i	−0.103189	−	0.229676i
$856$	−81.6168	+	11.0959i	−2.78960	+	0.379249i
$857$	−3.22127	−	9.69077i	−0.110036	−	0.331030i	0.879383	−	0.476115i	$-0.157956\pi$
$857$	−3.22127	−	9.69077i	−0.110036	−	0.331030i	−0.989419	+	0.145085i	$0.953654\pi$
$858$	7.29961	+	6.70779i	0.249205	+	0.229000i
$859$	8.68699	−	16.2936i	0.296396	−	0.555929i	−0.689297	−	0.724479i	$-0.742080\pi$
$859$	8.68699	−	16.2936i	0.296396	−	0.555929i	0.985693	+	0.168550i	$0.0539084\pi$
$860$	−2.60570	−	2.23692i	−0.0888538	−	0.0762784i
$861$	−9.49145	+	7.09385i	−0.323468	+	0.241758i
$862$	20.7360	−	19.0548i	0.706269	−	0.649008i
$863$	44.7102	−	22.8762i	1.52195	−	0.778714i	0.524593	−	0.851353i	$-0.324218\pi$
$863$	44.7102	−	22.8762i	1.52195	−	0.778714i	0.997358	+	0.0726395i	$0.0231422\pi$
$864$	−12.8546	+	83.9106i	−0.437323	+	2.85470i
$865$	−2.75404	+	8.28519i	−0.0936403	+	0.281705i
$866$	15.0588	+	58.1604i	0.511718	+	1.97637i
$867$	8.00925	+	21.6256i	0.272008	+	0.734444i
$868$	38.4097	−	21.4463i	1.30371	−	0.727935i
$869$	2.87384	−	7.75960i	0.0974883	−	0.263226i
$870$	4.43093	+	0.450582i	0.150223	+	0.0152762i
$871$	−0.0663331	−	0.124416i	−0.00224761	−	0.00421568i
$872$	−12.6787	−	25.8473i	−0.429356	−	0.875302i
$873$	0.382860	+	22.6653i	0.0129578	+	0.767104i
$874$	−4.00735	+	8.91944i	−0.135550	+	0.301704i
$875$	8.73789	−	5.24356i	0.295395	−	0.177265i
$876$	−16.2252	−	6.96277i	−0.548198	−	0.235250i
$877$	−15.9826	−	14.6868i	−0.539696	−	0.495939i	0.359704	−	0.933066i	$-0.382878\pi$
$877$	−15.9826	−	14.6868i	−0.539696	−	0.495939i	−0.899400	+	0.437127i	$0.855996\pi$
$878$	−5.03890	+	26.8082i	−0.170055	+	0.904734i
$879$	−7.57486	−	6.96072i	−0.255494	−	0.234779i
$880$	7.80892	−	2.74304i	0.263239	−	0.0924678i
$881$	29.2862	+	7.05716i	0.986677	+	0.237762i	0.695200	−	0.718816i	$-0.255316\pi$
$881$	29.2862	+	7.05716i	0.986677	+	0.237762i	0.291477	+	0.956578i	$0.405853\pi$
$882$	−21.3924	+	15.9885i	−0.720318	+	0.538361i
$883$	−3.12614	−	12.0739i	−0.105203	−	0.406318i	0.893918	−	0.448230i	$-0.147945\pi$
$883$	−3.12614	−	12.0739i	−0.105203	−	0.406318i	−0.999121	+	0.0419122i	$0.986655\pi$
$884$	134.402	+	57.6765i	4.52044	+	1.93987i
$885$	−2.08457	+	2.88964i	−0.0700721	+	0.0971343i
$886$	62.7029	−	40.5693i	2.10654	−	1.36295i
$887$	21.1595	+	25.5072i	0.710468	+	0.856449i	0.994755	−	0.102290i	$-0.0326169\pi$
$887$	21.1595	+	25.5072i	0.710468	+	0.856449i	−0.284287	+	0.958739i	$0.591757\pi$
$888$	3.30673	+	2.47143i	0.110967	+	0.0829357i
$889$	−0.722664	+	1.76572i	−0.0242374	+	0.0592202i
$890$	−8.64354	+	8.49877i	−0.289732	+	0.284879i
$891$	−0.929589	+	1.20093i	−0.0311424	+	0.0402327i
$892$	−41.7543	+	92.9356i	−1.39804	+	3.11171i
$893$	5.24613	+	17.7657i	0.175555	+	0.594508i
$894$	4.95484	−	12.1064i	0.165714	−	0.404898i
$895$	−0.0173212	+	0.341545i	−0.000578984	+	0.0114166i
$896$	−31.2205	+	10.9668i	−1.04300	+	0.366375i
$897$	1.33917	+	2.73008i	0.0447135	+	0.0911547i
$898$	55.6004	+	58.4915i	1.85541	+	1.95189i
$899$	−10.0546	−	9.19268i	−0.335341	−	0.306593i
$900$	34.0544	−	35.8252i	1.13515	−	1.19417i
$901$	34.1641	+	10.7191i	1.13817	+	0.357104i
$902$	19.6336	+	3.34808i	0.653729	+	0.111479i
$903$	−0.456958	−	1.23382i	−0.0152066	−	0.0410590i
$904$	−61.0353	+	73.5764i	−2.03000	+	2.44711i
$905$	5.31436	−	0.179591i	0.176655	−	0.00596979i
$906$	10.8082	−	0.365247i	0.359080	−	0.0121345i
$907$	−1.59264	+	3.24682i	−0.0528827	+	0.107809i	−0.922626	−	0.385695i	$-0.873962\pi$
$907$	−1.59264	+	3.24682i	−0.0528827	+	0.107809i	0.869743	+	0.493504i	$0.164284\pi$
$908$	43.0131	+	20.2049i	1.42744	+	0.670524i
$909$	25.1059	+	15.0659i	0.832710	+	0.499705i
$910$	−2.73199	−	12.2416i	−0.0905646	−	0.405806i
$911$	4.49207	−	20.1283i	0.148829	−	0.666881i	−0.842850	−	0.538148i	$-0.819124\pi$
$911$	4.49207	−	20.1283i	0.148829	−	0.666881i	0.991679	−	0.128733i	$-0.0410909\pi$
$912$	−23.0293	+	56.2686i	−0.762578	+	1.86324i
$913$	−4.75587	−	11.6202i	−0.157396	−	0.384573i
$914$	31.6373	+	17.5601i	1.04647	+	0.580838i
$915$	0.0764631	+	0.206457i	0.00252779	+	0.00682524i
$916$	73.2504	+	28.5449i	2.42026	+	0.943150i
$917$	17.1199	+	19.2739i	0.565349	+	0.636479i
$918$	26.4059	−	79.4388i	0.871525	−	2.62187i
$919$	30.4115	+	1.02771i	1.00318	+	0.0339010i	0.530804	−	0.847495i	$-0.321890\pi$
$919$	30.4115	+	1.02771i	1.00318	+	0.0339010i	0.472379	+	0.881396i	$0.343395\pi$
$920$	4.58361	+	0.154896i	0.151117	+	0.00510676i
$921$	13.1801	−	6.74367i	0.434300	−	0.222211i
$922$	−28.3006	−	19.6978i	−0.932031	−	0.648713i
$923$	−5.48718	−	64.8198i	−0.180613	−	2.13357i
$924$	6.60859	+	1.12695i	0.217407	+	0.0370738i
$925$	−0.706017	−	2.12396i	−0.0232137	−	0.0698355i
$926$	3.49485	+	68.9126i	0.114848	+	2.26461i
$927$	−34.5237	−	22.3372i	−1.13391	−	0.733649i
$928$	26.2645	+	33.9309i	0.862175	+	1.11384i
$929$	−34.1145	−	14.6397i	−1.11926	−	0.480312i	−0.246833	−	0.969058i	$-0.579390\pi$
$929$	−34.1145	−	14.6397i	−1.11926	−	0.480312i	−0.872426	+	0.488746i	$0.837454\pi$
$930$	−9.98590	+	1.72886i	−0.327451	+	0.0566916i
$931$	−21.4030	+	9.18473i	−0.701454	+	0.301018i
$932$	−64.8636	−	36.0022i	−2.12468	−	1.17929i
$933$	1.73200	−	1.59157i	0.0567030	−	0.0521058i
$934$	−3.48307	−	13.4524i	−0.113970	−	0.440177i
$935$	−4.03227	+	0.687613i	−0.131869	+	0.0224874i
$936$	−37.4068	−	70.1612i	−1.22268	−	2.29329i
$937$	−10.7919	−	5.52173i	−0.352556	−	0.180387i	0.270198	−	0.962805i	$-0.412911\pi$
$937$	−10.7919	−	5.52173i	−0.352556	−	0.180387i	−0.622754	+	0.782418i	$0.713986\pi$
$938$	−0.115168	−	0.0639235i	−0.00376037	−	0.00208718i
$939$	−29.4901	−	4.00920i	−0.962374	−	0.130835i
$940$	10.9609	−	8.78438i	0.357505	−	0.286515i
$941$	−7.66126	+	18.7191i	−0.249750	+	0.610225i	−0.998621	−	0.0524902i	$-0.983284\pi$
$941$	−7.66126	+	18.7191i	−0.249750	+	0.610225i	0.748872	+	0.662715i	$0.230596\pi$
$942$	44.5218	+	43.7761i	1.45060	+	1.42630i
$943$	5.23844	+	3.14356i	0.170587	+	0.102368i
$944$	−67.8704	+	9.22703i	−2.20899	+	0.300314i
$945$	−4.95842	+	1.55571i	−0.161297	+	0.0506074i
$946$	−0.973940	+	1.98551i	−0.0316655	+	0.0645545i
$947$	4.46630	−	37.5996i	0.145135	−	1.22182i	−0.710295	−	0.703904i	$-0.751438\pi$
$947$	4.46630	−	37.5996i	0.145135	−	1.22182i	0.855430	−	0.517918i	$-0.173293\pi$
$948$	29.4280	−	35.4746i	0.955777	−	1.15216i
$949$	14.9701	−	3.60737i	0.485949	−	0.117100i
$950$	49.9962	−	32.3480i	1.62209	−	1.04951i
$951$	3.06439	+	9.21883i	0.0993697	+	0.298941i
$952$	83.3089	−	14.2065i	2.70006	−	0.460434i
$953$	−8.26281	+	13.2565i	−0.267659	+	0.429419i	−0.954863	−	0.297045i	$-0.903999\pi$
$953$	−8.26281	+	13.2565i	−0.267659	+	0.429419i	0.687205	+	0.726464i	$0.258838\pi$
$954$	−17.5396	−	26.1303i	−0.567866	−	0.845999i
$955$	−0.493365	+	0.683906i	−0.0159649	+	0.0221307i
$956$	−72.1260	−	43.2824i	−2.33272	−	1.39985i
$957$	−0.314385	−	2.05219i	−0.0101626	−	0.0663380i
$958$	−2.78611	−	32.9122i	−0.0900152	−	1.06335i
$959$	9.03285	+	7.75445i	0.291686	+	0.250404i
$960$	14.3322			0.462569
$961$	27.6684	+	13.9806i	0.892530	+	0.450988i
$962$	−5.82095			−0.187675
$963$	−15.0278	−	12.9009i	−0.484264	−	0.415727i
$964$	−4.67579	−	55.2350i	−0.150597	−	1.77900i
$965$	1.98986	+	12.9891i	0.0640557	+	0.418134i
$966$	2.43586	+	1.46175i	0.0783725	+	0.0470309i
$967$	−10.5510	+	14.6259i	−0.339297	+	0.470336i	−0.945802	−	0.324744i	$-0.894722\pi$
$967$	−10.5510	+	14.6259i	−0.339297	+	0.470336i	0.606505	+	0.795080i	$0.292571\pi$
$968$	49.6188	+	73.9214i	1.59481	+	2.37592i
$969$	15.8942	−	25.4999i	0.510596	−	0.819176i
$970$	20.4140	−	3.48114i	0.655453	−	0.111773i
$971$	18.8792	+	56.7956i	0.605862	+	1.82266i	0.567467	+	0.823396i	$0.307923\pi$
$971$	18.8792	+	56.7956i	0.605862	+	1.82266i	0.0383947	+	0.999263i	$0.487776\pi$
$972$	−71.0280	+	45.9558i	−2.27823	+	1.47403i
$973$	8.34994	−	2.01210i	0.267687	−	0.0645051i
$974$	−22.0717	+	26.6068i	−0.707222	+	0.852537i
$975$	2.18435	−	18.3890i	0.0699553	−	0.588919i
$976$	−1.86387	+	3.79975i	−0.0596609	+	0.121627i
$977$	35.0397	−	10.9938i	1.12102	−	0.351722i	0.318246	−	0.948008i	$-0.396906\pi$
$977$	35.0397	−	10.9938i	1.12102	−	0.351722i	0.802772	+	0.596286i	$0.203358\pi$
$978$	38.6212	−	5.25057i	1.23497	−	0.167895i
$979$	4.84517	+	2.90756i	0.154852	+	0.0929260i
$980$	12.5931	+	12.3822i	0.402273	+	0.395535i
$981$	2.62214	−	6.40679i	0.0837184	−	0.204553i
$982$	15.3669	−	12.3155i	0.490378	−	0.393003i
$983$	−3.91548	−	0.532312i	−0.124884	−	0.0169781i	0.0720015	−	0.997405i	$-0.477061\pi$
$983$	−3.91548	−	0.532312i	−0.124884	−	0.0169781i	−0.196886	+	0.980426i	$0.563083\pi$
$984$	59.9985	+	33.3019i	1.91268	+	1.06163i
$985$	−2.97331	−	1.52131i	−0.0947374	−	0.0484728i
$986$	−19.9071	−	37.3382i	−0.633970	−	1.18909i
$987$	5.30505	−	0.904657i	0.168862	−	0.0287956i
$988$	−28.0989	−	108.524i	−0.893944	−	3.45262i
$989$	−0.499487	+	0.458991i	−0.0158828	+	0.0145951i
$990$	3.14348	+	1.74477i	0.0999064	+	0.0554526i
$991$	25.0503	−	10.7499i	0.795749	−	0.341483i	0.0423974	−	0.999101i	$-0.486500\pi$
$991$	25.0503	−	10.7499i	0.795749	−	0.341483i	0.753351	+	0.657618i	$0.228436\pi$
$992$	−78.3548	−	58.2537i	−2.48777	−	1.84956i
$993$	17.9570	+	7.70597i	0.569849	+	0.244542i
$994$	−37.1990	−	48.0572i	−1.17988	−	1.52428i
$995$	6.94514	+	4.49357i	0.220176	+	0.142456i
$996$	−3.54233	−	69.8488i	−0.112243	−	2.21324i
$997$	−7.90299	−	23.7751i	−0.250290	−	0.752966i	−0.996214	−	0.0869347i	$-0.972293\pi$
$997$	−7.90299	−	23.7751i	−0.250290	−	0.752966i	0.745924	−	0.666031i	$-0.232008\pi$
$998$	35.7534	+	6.09693i	1.13175	+	0.192995i
$999$	0.203433	+	2.40315i	0.00643635	+	0.0760323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.k.a.5.3	✓	4920
961.769	even	93	inner	961.2.k.a.769.3	yes	4920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.k.a.5.3	✓	4920	1.1	even	1	trivial
961.2.k.a.769.3	yes	4920	961.769	even	93	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.k (of order \(93\), degree \(60\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.04201 - 1.75301i) q^{2} +(0.0800879 + 0.946076i) q^{3} +(0.793911 + 5.18237i) q^{4} +(0.610803 + 0.366540i) q^{5} +(1.49494 - 2.07229i) q^{6} +(0.839904 + 1.25128i) q^{7} +(4.61642 - 7.40635i) q^{8} +(2.06866 - 0.352764i) q^{9} +(-0.604719 - 1.81922i) q^{10} +(-0.750303 + 0.485453i) q^{11} +(-4.83934 + 1.16614i) q^{12} +(2.77183 - 3.34136i) q^{13} +(0.478408 - 4.02748i) q^{14} +(-0.297856 + 0.607221i) q^{15} +(-12.4054 + 3.89221i) q^{16} +(6.36706 - 0.865606i) q^{17} +(-4.84263 - 2.90604i) q^{18} +(-3.51191 - 3.45309i) q^{19} +(-1.41462 + 3.45641i) q^{20} +(-1.11654 + 0.894825i) q^{21} +(2.38313 + 0.323988i) q^{22} +(0.645017 + 0.358014i) q^{23} +(7.37669 + 3.77432i) q^{24} +(-2.11360 - 3.96432i) q^{25} +(-11.5175 + 1.96405i) q^{26} +(1.21337 + 4.68631i) q^{27} +(-5.81778 + 5.34610i) q^{28} +(2.13941 + 1.18747i) q^{29} +(1.67269 - 0.717807i) q^{30} +(-5.41611 - 1.29065i) q^{31} +(16.1149 + 6.91546i) q^{32} +(-0.519365 - 0.670964i) q^{33} +(-14.5190 - 9.39392i) q^{34} +(0.0543729 + 1.07214i) q^{35} +(3.47049 + 10.4405i) q^{36} +(0.491118 + 0.0837492i) q^{37} +(1.11806 + 13.2076i) q^{38} +(3.38317 + 2.35476i) q^{39} +(5.53444 - 2.83173i) q^{40} +(8.27663 + 0.279696i) q^{41} +(3.84861 + 0.130058i) q^{42} +(-0.290053 + 0.872587i) q^{43} +(-3.11147 - 3.50294i) q^{44} +(1.39285 + 0.542778i) q^{45} +(-0.689530 - 1.86179i) q^{46} +(-3.28851 - 1.82527i) q^{47} +(-4.67584 - 11.4247i) q^{48} +(1.79119 - 4.37650i) q^{49} +(-2.63350 + 11.8003i) q^{50} +(1.32885 + 5.95439i) q^{51} +(19.5168 + 11.7119i) q^{52} +(5.04367 + 2.36921i) q^{53} +(5.73742 - 11.6965i) q^{54} +(-0.636225 + 0.0215002i) q^{55} +(13.1448 - 0.444206i) q^{56} +(2.98562 - 3.59908i) q^{57} +(-2.28705 - 6.17521i) q^{58} +(5.19320 + 0.885583i) q^{59} +(-3.38332 - 1.06152i) q^{60} +(0.224271 - 0.235933i) q^{61} +(8.79722 + 12.1300i) q^{62} +(2.17889 + 2.29219i) q^{63} +(-9.33230 - 19.0252i) q^{64} +(2.91778 - 1.02493i) q^{65} +(-0.115657 + 2.28057i) q^{66} +(0.0123015 - 0.0300568i) q^{67} +(9.54076 + 32.3093i) q^{68} +(-0.287050 + 0.638908i) q^{69} +(1.76844 - 2.28464i) q^{70} +(10.6844 - 10.5055i) q^{71} +(6.93712 - 16.9498i) q^{72} +(2.84109 + 2.12341i) q^{73} +(-0.856054 - 1.03195i) q^{74} +(3.58128 - 2.31712i) q^{75} +(15.1071 - 20.9415i) q^{76} +(-1.23762 - 0.531104i) q^{77} +(-2.78056 - 10.7392i) q^{78} +(-7.41676 + 5.54324i) q^{79} +(-9.00389 - 2.16969i) q^{80} +(1.60335 - 0.563210i) q^{81} +(-16.4106 - 15.0801i) q^{82} +(-2.59539 + 13.8081i) q^{83} +(-5.52375 - 5.07590i) q^{84} +(4.20630 + 1.80506i) q^{85} +(2.12194 - 1.27337i) q^{86} +(-0.952093 + 2.11914i) q^{87} +(0.131724 + 7.79806i) q^{88} +(-2.78463 - 5.67686i) q^{89} +(-1.89272 - 3.55003i) q^{90} +(6.50904 + 0.661905i) q^{91} +(-1.34328 + 3.62695i) q^{92} +(0.787290 - 5.22741i) q^{93} +(3.51546 + 9.49202i) q^{94} +(-0.879392 - 3.39641i) q^{95} +(-5.25194 + 15.7998i) q^{96} +(-1.63574 + 10.6775i) q^{97} +(-11.3297 + 5.79688i) q^{98} +(-1.38087 + 1.26892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4920 q - 58 q^{2} - 64 q^{3} - 226 q^{4} - 60 q^{5} - 56 q^{6} - 60 q^{7} - 56 q^{8} + 18 q^{9} - 61 q^{10} - 64 q^{11} - 72 q^{12} - 64 q^{13} - 65 q^{14} + 66 q^{15} - 234 q^{16} - 68 q^{17} - 70 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) \) 4920 * q - 58 * q^2 - 64 * q^3 - 226 * q^4 - 60 * q^5 - 56 * q^6 - 60 * q^7 - 56 * q^8 + 18 * q^9 - 61 * q^10 - 64 * q^11 - 72 * q^12 - 64 * q^13 - 65 * q^14 + 66 * q^15 - 234 * q^16 - 68 * q^17 - 70 * q^18 - 56 * q^19 - 57 * q^20 - 68 * q^21 + 76 * q^22 - 46 * q^23 + 72 * q^24 + 10 * q^25 + 56 * q^26 - 58 * q^27 - 49 * q^28 - 46 * q^29 - 74 * q^30 - 42 * q^31 - 86 * q^32 - 90 * q^33 - 64 * q^34 - 202 * q^35 + 34 * q^36 - 60 * q^37 - 61 * q^38 - 58 * q^39 + 62 * q^40 - 56 * q^41 - 730 * q^42 + 60 * q^43 - 88 * q^44 - 58 * q^45 + 108 * q^46 + 34 * q^47 - 68 * q^48 + 10 * q^49 + 104 * q^50 - 60 * q^51 - 48 * q^52 - 56 * q^53 - 58 * q^54 - 64 * q^55 - 500 * q^56 - 64 * q^57 - 62 * q^58 - 64 * q^59 + 82 * q^60 + 124 * q^61 + 383 * q^62 + 30 * q^63 + 48 * q^64 - 64 * q^65 - 18 * q^66 - 58 * q^67 - 300 * q^68 - 50 * q^69 - 80 * q^70 - 68 * q^71 - 55 * q^72 - 370 * q^73 - 64 * q^74 - 54 * q^75 + 261 * q^76 - 34 * q^77 - 98 * q^78 - 84 * q^79 + 480 * q^80 + 20 * q^81 + 299 * q^82 - 68 * q^83 + 288 * q^84 + 198 * q^85 - 88 * q^86 + 101 * q^87 - 44 * q^88 - 46 * q^89 - 55 * q^90 + 453 * q^91 - 46 * q^92 - 40 * q^93 - 768 * q^94 + 61 * q^95 - 64 * q^96 - 102 * q^97 - 51 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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