LMFDB - Embedded newform 845.2.w.a.116.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(51,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("845.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.w (of order $26$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$744$
Relative dimension:	$62$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			116.25
Character	$\chi$	$=$	845.116
Dual form			845.2.w.a.51.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.430117 - 0.485501i) q^{2} +(-0.374141 - 0.986528i) q^{3} +(0.190362 - 1.56777i) q^{4} +(0.239316 + 0.970942i) q^{5} +(-0.318036 + 0.605968i) q^{6} +(-2.62885 + 1.81457i) q^{7} +(-1.91065 + 1.31882i) q^{8} +(1.41228 - 1.25117i) q^{9} +O(q^{10})$	\(q+(-0.430117 - 0.485501i) q^{2} +(-0.374141 - 0.986528i) q^{3} +(0.190362 - 1.56777i) q^{4} +(0.239316 + 0.970942i) q^{5} +(-0.318036 + 0.605968i) q^{6} +(-2.62885 + 1.81457i) q^{7} +(-1.91065 + 1.31882i) q^{8} +(1.41228 - 1.25117i) q^{9} +(0.368460 - 0.533806i) q^{10} +(-2.76587 + 3.12202i) q^{11} +(-1.61787 + 0.398770i) q^{12} +(3.11786 + 1.81078i) q^{13} +(2.01169 + 0.495837i) q^{14} +(0.868323 - 0.599360i) q^{15} +(-1.60470 - 0.395523i) q^{16} +(3.19901 + 4.63457i) q^{17} +(-1.21489 - 0.147514i) q^{18} +1.49981i q^{19} +(1.56777 - 0.190362i) q^{20} +(2.77368 + 1.91453i) q^{21} +2.70539 q^{22} +5.81150 q^{23} +(2.01591 + 1.39148i) q^{24} +(-0.885456 + 0.464723i) q^{25} +(-0.461909 - 2.29257i) q^{26} +(-4.56541 - 2.39611i) q^{27} +(2.34440 + 4.46687i) q^{28} +(1.50022 - 1.32908i) q^{29} +(-0.664471 - 0.163777i) q^{30} +(-0.452236 + 0.861663i) q^{31} +(2.65599 + 5.06057i) q^{32} +(4.11478 + 1.56053i) q^{33} +(0.874141 - 3.54653i) q^{34} +(-2.39097 - 2.11821i) q^{35} +(-1.69270 - 2.45230i) q^{36} +(-1.23796 + 2.35873i) q^{37} +(0.728161 - 0.645094i) q^{38} +(0.619866 - 3.75335i) q^{39} +(-1.73775 - 1.53951i) q^{40} +(5.97959 - 2.26776i) q^{41} +(-0.263498 - 2.17010i) q^{42} +(-5.18658 + 2.72212i) q^{43} +(4.36810 + 4.93057i) q^{44} +(1.55279 + 1.07181i) q^{45} +(-2.49962 - 2.82149i) q^{46} +(-5.52452 + 0.670799i) q^{47} +(0.210189 + 1.73106i) q^{48} +(1.13599 - 2.99536i) q^{49} +(0.606473 + 0.230005i) q^{50} +(3.37525 - 4.88989i) q^{51} +(3.43242 - 4.54340i) q^{52} +(3.99520 + 5.78805i) q^{53} +(0.800344 + 3.24712i) q^{54} +(-3.69321 - 1.93835i) q^{55} +(2.62972 - 6.93400i) q^{56} +(1.47961 - 0.561141i) q^{57} +(-1.29054 - 0.156700i) q^{58} +(-1.99247 - 8.08376i) q^{59} +(-0.774365 - 1.47543i) q^{60} +(0.123834 - 0.179404i) q^{61} +(0.612853 - 0.151055i) q^{62} +(-1.44234 + 5.85181i) q^{63} +(0.142398 - 0.375474i) q^{64} +(-1.01201 + 3.46061i) q^{65} +(-1.01220 - 2.66894i) q^{66} +(11.5020 - 1.39659i) q^{67} +(7.87492 - 4.13308i) q^{68} +(-2.17432 - 5.73320i) q^{69} +2.07190i q^{70} +(-4.90636 + 1.86074i) q^{71} +(-1.04829 + 4.25308i) q^{72} +(-4.55544 + 5.14203i) q^{73} +(1.67763 - 0.413500i) q^{74} +(0.789747 + 0.699655i) q^{75} +(2.35137 + 0.285507i) q^{76} +(1.60595 - 13.2262i) q^{77} +(-2.08887 + 1.31343i) q^{78} +(-0.601664 - 4.95515i) q^{79} -1.65273i q^{80} +(0.0265532 - 0.218686i) q^{81} +(-3.67292 - 1.92770i) q^{82} +(14.2560 + 5.40660i) q^{83} +(3.52956 - 3.98405i) q^{84} +(-3.73432 + 4.21518i) q^{85} +(3.55243 + 1.34726i) q^{86} +(-1.87246 - 0.982744i) q^{87} +(1.16720 - 9.61277i) q^{88} +14.5111i q^{89} +(-0.147514 - 1.21489i) q^{90} +(-11.4822 + 0.897295i) q^{91} +(1.10629 - 9.11111i) q^{92} +(1.01925 + 0.123760i) q^{93} +(2.70186 + 2.39364i) q^{94} +(-1.45623 + 0.358929i) q^{95} +(3.99868 - 4.51358i) q^{96} +(-0.460196 + 1.86709i) q^{97} +(-1.94286 + 0.736829i) q^{98} +7.86972i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9}+O(q^{10}) $ 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9	$ 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9} - 2 q^{10} - 122 q^{13} - 4 q^{14} - 66 q^{16} - 12 q^{17} - 78 q^{18} - 24 q^{22} + 140 q^{23} + 156 q^{24} + 62 q^{25} - 14 q^{26} + 28 q^{27} + 8 q^{29} - 20 q^{30} - 52 q^{31} - 26 q^{32} - 130 q^{34} + 4 q^{35} + 70 q^{36} + 126 q^{38} + 16 q^{39} + 6 q^{40} - 24 q^{42} - 24 q^{43} - 78 q^{47} - 94 q^{48} - 32 q^{49} - 12 q^{51} + 110 q^{52} - 156 q^{54} + 16 q^{55} + 16 q^{56} - 78 q^{57} - 104 q^{58} - 104 q^{59} + 28 q^{61} + 106 q^{62} + 14 q^{64} - 2 q^{65} - 308 q^{66} - 104 q^{67} - 18 q^{68} + 20 q^{69} - 78 q^{71} - 338 q^{72} - 4 q^{75} - 286 q^{76} - 52 q^{77} + 312 q^{78} - 12 q^{79} - 78 q^{81} + 268 q^{82} + 12 q^{87} - 72 q^{88} + 26 q^{90} - 136 q^{91} + 52 q^{92} - 130 q^{93} + 124 q^{94} - 16 q^{95} + 338 q^{96}+O(q^{100}) $ 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9 - 2 * q^10 - 122 * q^13 - 4 * q^14 - 66 * q^16 - 12 * q^17 - 78 * q^18 - 24 * q^22 + 140 * q^23 + 156 * q^24 + 62 * q^25 - 14 * q^26 + 28 * q^27 + 8 * q^29 - 20 * q^30 - 52 * q^31 - 26 * q^32 - 130 * q^34 + 4 * q^35 + 70 * q^36 + 126 * q^38 + 16 * q^39 + 6 * q^40 - 24 * q^42 - 24 * q^43 - 78 * q^47 - 94 * q^48 - 32 * q^49 - 12 * q^51 + 110 * q^52 - 156 * q^54 + 16 * q^55 + 16 * q^56 - 78 * q^57 - 104 * q^58 - 104 * q^59 + 28 * q^61 + 106 * q^62 + 14 * q^64 - 2 * q^65 - 308 * q^66 - 104 * q^67 - 18 * q^68 + 20 * q^69 - 78 * q^71 - 338 * q^72 - 4 * q^75 - 286 * q^76 - 52 * q^77 + 312 * q^78 - 12 * q^79 - 78 * q^81 + 268 * q^82 + 12 * q^87 - 72 * q^88 + 26 * q^90 - 136 * q^91 + 52 * q^92 - 130 * q^93 + 124 * q^94 - 16 * q^95 + 338 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{26}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.430117	−	0.485501i	−0.304138	−	0.343301i	0.576494	−	0.817101i	$-0.304420\pi$
$2$	−0.430117	−	0.485501i	−0.304138	−	0.343301i	−0.880632	+	0.473800i	$0.842882\pi$
$3$	−0.374141	−	0.986528i	−0.216010	−	0.569572i	0.782586	−	0.622543i	$-0.213900\pi$
$3$	−0.374141	−	0.986528i	−0.216010	−	0.569572i	−0.998596	+	0.0529706i	$0.983131\pi$
$4$	0.190362	−	1.56777i	0.0951811	−	0.783887i
$5$	0.239316	+	0.970942i	0.107025	+	0.434218i
$5$	0.239316	+	0.970942i	0.107025	+	0.434218i
$6$	−0.318036	+	0.605968i	−0.129838	+	0.247385i
$7$	−2.62885	+	1.81457i	−0.993614	+	0.685842i	−0.949690	−	0.313193i	$-0.898601\pi$
$7$	−2.62885	+	1.81457i	−0.993614	+	0.685842i	−0.0439242	+	0.999035i	$0.513986\pi$
$8$	−1.91065	+	1.31882i	−0.675516	+	0.466275i
$9$	1.41228	−	1.25117i	0.470759	−	0.417056i
$10$	0.368460	−	0.533806i	0.116517	−	0.168804i
$11$	−2.76587	+	3.12202i	−0.833940	+	0.941324i	−0.998989	−	0.0449616i	$-0.985683\pi$
$11$	−2.76587	+	3.12202i	−0.833940	+	0.941324i	0.165049	+	0.986285i	$0.447222\pi$
$12$	−1.61787	+	0.398770i	−0.467040	+	0.115115i
$13$	3.11786	+	1.81078i	0.864740	+	0.502220i
$13$	3.11786	+	1.81078i	0.864740	+	0.502220i
$14$	2.01169	+	0.495837i	0.537647	+	0.132518i
$15$	0.868323	−	0.599360i	0.224200	−	0.154754i
$16$	−1.60470	−	0.395523i	−0.401175	−	0.0988808i
$17$	3.19901	+	4.63457i	0.775874	+	1.12405i	0.989129	+	0.147051i	$0.0469783\pi$
$17$	3.19901	+	4.63457i	0.775874	+	1.12405i	−0.213254	+	0.976997i	$0.568406\pi$
$18$	−1.21489	−	0.147514i	−0.286352	−	0.0347694i
$19$			1.49981i			0.344080i	0.985090	+	0.172040i	$0.0550359\pi$
$19$			1.49981i			0.344080i	−0.985090	+	0.172040i	$0.944964\pi$
$20$	1.56777	−	0.190362i	0.350565	−	0.0425663i
$21$	2.77368	+	1.91453i	0.605267	+	0.417786i
$22$	2.70539			0.576791
$23$	5.81150			1.21178			0.605890	−	0.795548i	$-0.292817\pi$
$23$	5.81150			1.21178			0.605890	+	0.795548i	$0.292817\pi$
$24$	2.01591	+	1.39148i	0.411495	+	0.284035i
$25$	−0.885456	+	0.464723i	−0.177091	+	0.0929446i
$26$	−0.461909	−	2.29257i	−0.0905878	−	0.449611i
$27$	−4.56541	−	2.39611i	−0.878614	−	0.461132i
$28$	2.34440	+	4.46687i	0.443049	+	0.844160i
$29$	1.50022	−	1.32908i	0.278583	−	0.246803i	−0.512248	−	0.858838i	$-0.671187\pi$
$29$	1.50022	−	1.32908i	0.278583	−	0.246803i	0.790831	+	0.612034i	$0.209649\pi$
$30$	−0.664471	−	0.163777i	−0.121315	−	0.0299015i
$31$	−0.452236	+	0.861663i	−0.0812239	+	0.154759i	−0.922680	−	0.385566i	$-0.874006\pi$
$31$	−0.452236	+	0.861663i	−0.0812239	+	0.154759i	0.841457	+	0.540325i	$0.181699\pi$
$32$	2.65599	+	5.06057i	0.469518	+	0.894591i
$33$	4.11478	+	1.56053i	0.716291	+	0.271653i
$34$	0.874141	−	3.54653i	0.149914	−	0.608225i
$35$	−2.39097	−	2.11821i	−0.404147	−	0.358043i
$36$	−1.69270	−	2.45230i	−0.282117	−	0.408717i
$37$	−1.23796	+	2.35873i	−0.203519	+	0.387773i	−0.965727	−	0.259559i	$-0.916423\pi$
$37$	−1.23796	+	2.35873i	−0.203519	+	0.387773i	0.762208	+	0.647332i	$0.224115\pi$
$38$	0.728161	−	0.645094i	0.118123	−	0.104648i
$39$	0.619866	−	3.75335i	0.0992580	−	0.601016i
$40$	−1.73775	−	1.53951i	−0.274762	−	0.243418i
$41$	5.97959	−	2.26776i	0.933855	−	0.354165i	0.159704	−	0.987165i	$-0.448946\pi$
$41$	5.97959	−	2.26776i	0.933855	−	0.354165i	0.774151	+	0.633000i	$0.218177\pi$
$42$	−0.263498	−	2.17010i	−0.0406586	−	0.334854i
$43$	−5.18658	+	2.72212i	−0.790945	+	0.415120i	−0.811269	−	0.584673i	$-0.801223\pi$
$43$	−5.18658	+	2.72212i	−0.790945	+	0.415120i	0.0203235	+	0.999793i	$0.493530\pi$
$44$	4.36810	+	4.93057i	0.658516	+	0.743311i
$45$	1.55279	+	1.07181i	0.231476	+	0.159777i
$46$	−2.49962	−	2.82149i	−0.368549	−	0.416006i
$47$	−5.52452	+	0.670799i	−0.805835	+	0.0978461i	−0.513079	−	0.858341i	$-0.671495\pi$
$47$	−5.52452	+	0.670799i	−0.805835	+	0.0978461i	−0.292756	+	0.956187i	$0.594572\pi$
$48$	0.210189	+	1.73106i	0.0303382	+	0.249857i
$49$	1.13599	−	2.99536i	0.162284	−	0.427908i
$50$	0.606473	+	0.230005i	0.0857683	+	0.0325276i
$51$	3.37525	−	4.88989i	0.472630	−	0.684722i
$52$	3.43242	−	4.54340i	0.475990	−	0.630056i
$53$	3.99520	+	5.78805i	0.548783	+	0.795049i	0.995000	−	0.0998754i	$-0.0318444\pi$
$53$	3.99520	+	5.78805i	0.548783	+	0.795049i	−0.446217	+	0.894925i	$0.647229\pi$
$54$	0.800344	+	3.24712i	0.108913	+	0.441878i
$55$	−3.69321	−	1.93835i	−0.497993	−	0.261367i
$56$	2.62972	−	6.93400i	0.351411	−	0.926594i
$57$	1.47961	−	0.561141i	0.195979	−	0.0743249i
$58$	−1.29054	−	0.156700i	−0.169456	−	0.0205757i
$59$	−1.99247	−	8.08376i	−0.259397	−	1.05242i	−0.945685	−	0.325085i	$-0.894607\pi$
$59$	−1.99247	−	8.08376i	−0.259397	−	1.05242i	0.686287	−	0.727330i	$-0.259239\pi$
$60$	−0.774365	−	1.47543i	−0.0999701	−	0.190477i
$61$	0.123834	−	0.179404i	0.0158553	−	0.0229703i	−0.814976	−	0.579495i	$-0.803250\pi$
$61$	0.123834	−	0.179404i	0.0158553	−	0.0229703i	0.830831	+	0.556524i	$0.187865\pi$
$62$	0.612853	−	0.151055i	0.0778324	−	0.0191840i
$63$	−1.44234	+	5.85181i	−0.181718	+	0.737259i
$64$	0.142398	−	0.375474i	0.0177998	−	0.0469342i
$65$	−1.01201	+	3.46061i	−0.125524	+	0.429236i
$66$	−1.01220	−	2.66894i	−0.124593	−	0.328524i
$67$	11.5020	−	1.39659i	1.40519	−	0.170621i	0.617442	−	0.786616i	$-0.288169\pi$
$67$	11.5020	−	1.39659i	1.40519	−	0.170621i	0.787750	+	0.615995i	$0.211246\pi$
$68$	7.87492	−	4.13308i	0.954975	−	0.501209i
$69$	−2.17432	−	5.73320i	−0.261757	−	0.690196i
$70$			2.07190i			0.247639i
$71$	−4.90636	+	1.86074i	−0.582278	+	0.220829i	−0.628116	−	0.778120i	$-0.716173\pi$
$71$	−4.90636	+	1.86074i	−0.582278	+	0.220829i	0.0458378	+	0.998949i	$0.485404\pi$
$72$	−1.04829	+	4.25308i	−0.123542	+	0.501231i
$73$	−4.55544	+	5.14203i	−0.533174	+	0.601830i	−0.951947	−	0.306261i	$-0.900922\pi$
$73$	−4.55544	+	5.14203i	−0.533174	+	0.601830i	0.418773	+	0.908091i	$0.362460\pi$
$74$	1.67763	−	0.413500i	0.195021	−	0.0480684i
$75$	0.789747	+	0.699655i	0.0911922	+	0.0807892i
$76$	2.35137	+	0.285507i	0.269720	+	0.0327499i
$77$	1.60595	−	13.2262i	0.183015	−	1.50726i
$78$	−2.08887	+	1.31343i	−0.236518	+	0.148717i
$79$	−0.601664	−	4.95515i	−0.0676925	−	0.557498i	−0.986616	−	0.163062i	$-0.947863\pi$
$79$	−0.601664	−	4.95515i	−0.0676925	−	0.557498i	0.918923	−	0.394436i	$-0.129060\pi$
$80$		−	1.65273i		−	0.184780i
$81$	0.0265532	−	0.218686i	0.00295036	−	0.0242984i
$82$	−3.67292	−	1.92770i	−0.405606	−	0.212879i
$83$	14.2560	+	5.40660i	1.56480	+	0.593451i	0.976562	−	0.215235i	$-0.0690516\pi$
$83$	14.2560	+	5.40660i	1.56480	+	0.593451i	0.588241	+	0.808686i	$0.299821\pi$
$84$	3.52956	−	3.98405i	0.385107	−	0.434695i
$85$	−3.73432	+	4.21518i	−0.405044	+	0.457200i
$86$	3.55243	+	1.34726i	0.383068	+	0.145279i
$87$	−1.87246	−	0.982744i	−0.200749	−	0.105361i
$88$	1.16720	−	9.61277i	0.124424	−	1.02472i
$89$			14.5111i			1.53817i	0.639145	+	0.769086i	$0.279288\pi$
$89$			14.5111i			1.53817i	−0.639145	+	0.769086i	$0.720712\pi$
$90$	−0.147514	−	1.21489i	−0.0155493	−	0.128060i
$91$	−11.4822	+	0.897295i	−1.20366	+	0.0940621i
$92$	1.10629	−	9.11111i	0.115339	−	0.949899i
$93$	1.01925	+	0.123760i	0.105692	+	0.0128333i
$94$	2.70186	+	2.39364i	0.278676	+	0.246885i
$95$	−1.45623	+	0.358929i	−0.149406	+	0.0368253i
$96$	3.99868	−	4.51358i	0.408113	−	0.460665i
$97$	−0.460196	+	1.86709i	−0.0467258	+	0.189574i	−0.989667	−	0.143386i	$-0.954201\pi$
$97$	−0.460196	+	1.86709i	−0.0467258	+	0.189574i	0.942941	+	0.332960i	$0.108047\pi$
$98$	−1.94286	+	0.736829i	−0.196258	+	0.0744309i
$99$			7.86972i			0.790936i
$100$	0.560023	+	1.47666i	0.0560023	+	0.147666i
$101$	6.39259	−	3.35509i	0.636087	−	0.333844i	−0.115667	−	0.993288i	$-0.536901\pi$
$101$	6.39259	−	3.35509i	0.636087	−	0.333844i	0.751754	+	0.659444i	$0.229208\pi$
$102$	−3.82580	+	0.464537i	−0.378811	+	0.0459960i
$103$	−0.222427	−	0.586492i	−0.0219164	−	0.0577888i	0.923611	−	0.383330i	$-0.125223\pi$
$103$	−0.222427	−	0.586492i	−0.0219164	−	0.0577888i	−0.945528	+	0.325541i	$0.894454\pi$
$104$	−8.34524	+	0.652152i	−0.818318	+	0.0639488i
$105$	−1.19512	+	3.15126i	−0.116631	+	0.307532i
$106$	1.09170	−	4.42921i	0.106036	−	0.430203i
$107$	12.5477	−	3.09272i	1.21303	−	0.298985i	0.419635	−	0.907693i	$-0.362158\pi$
$107$	12.5477	−	3.09272i	1.21303	−	0.298985i	0.793394	+	0.608708i	$0.208312\pi$
$108$	−4.62564	+	6.70140i	−0.445103	+	0.644843i
$109$	6.22177	+	11.8546i	0.595938	+	1.13546i	0.977463	+	0.211106i	$0.0677065\pi$
$109$	6.22177	+	11.8546i	0.595938	+	1.13546i	−0.381526	+	0.924358i	$0.624601\pi$
$110$	0.647442	+	2.62678i	0.0617312	+	0.250453i
$111$	2.79013	+	0.338783i	0.264827	+	0.0321558i
$112$	4.93623	−	1.87206i	0.466430	−	0.176893i
$113$	−6.79666	+	17.9213i	−0.639376	+	1.68589i	0.0849046	+	0.996389i	$0.472941\pi$
$113$	−6.79666	+	17.9213i	−0.639376	+	1.68589i	−0.724280	+	0.689506i	$0.757828\pi$
$114$	−0.908838	−	0.476995i	−0.0851205	−	0.0446747i
$115$	1.39078	+	5.64262i	0.129691	+	0.526177i
$116$	−1.79811	−	2.60501i	−0.166950	−	0.241869i
$117$	6.66888	−	1.34365i	0.616538	−	0.124220i
$118$	−3.06768	+	4.44431i	−0.282403	+	0.409132i
$119$	−16.8195	−	6.37879i	−1.54184	−	0.584742i
$120$	−0.868608	+	2.29033i	−0.0792927	+	0.209078i
$121$	−0.771075	−	6.35037i	−0.0700977	−	0.577307i
$122$	−0.140364	+	0.0170432i	−0.0127079	+	0.00154302i
$123$	−4.47441	−	5.05057i	−0.403444	−	0.455395i
$124$	1.26480	+	0.873031i	0.113583	+	0.0784005i
$125$	−0.663123	−	0.748511i	−0.0593115	−	0.0669488i
$126$	3.46144	−	1.81670i	0.308369	−	0.161845i
$127$	2.13624	+	17.5935i	0.189560	+	1.56117i	0.708098	+	0.706114i	$0.249554\pi$
$127$	2.13624	+	17.5935i	0.189560	+	1.56117i	−0.518538	+	0.855055i	$0.673523\pi$
$128$	10.4441	−	3.96092i	0.923136	−	0.350099i
$129$	4.62596	+	4.09824i	0.407293	+	0.360830i
$130$	2.11541	−	0.997136i	0.185534	−	0.0874546i
$131$	−3.36797	+	2.98376i	−0.294261	+	0.260693i	−0.797316	−	0.603562i	$-0.793748\pi$
$131$	−3.36797	+	2.98376i	−0.294261	+	0.260693i	0.503055	+	0.864254i	$0.332209\pi$
$132$	3.22986	−	6.15398i	0.281123	−	0.535635i
$133$	−2.72151	−	3.94279i	−0.235985	−	0.341883i
$134$	−5.62525	−	4.98354i	−0.485947	−	0.430512i
$135$	1.23391	−	5.00618i	0.106198	−	0.430863i
$136$	−12.2244	−	4.63609i	−1.04823	−	0.397541i
$137$	−3.51023	−	6.68818i	−0.299899	−	0.571409i	0.688147	−	0.725572i	$-0.258425\pi$
$137$	−3.51023	−	6.68818i	−0.299899	−	0.571409i	−0.988046	+	0.154162i	$0.950732\pi$
$138$	−1.84827	+	3.52158i	−0.157335	+	0.299777i
$139$	−13.8566	−	3.41535i	−1.17530	−	0.289686i	−0.397145	−	0.917756i	$-0.629999\pi$
$139$	−13.8566	−	3.41535i	−1.17530	−	0.289686i	−0.778157	+	0.628070i	$0.783845\pi$
$140$	−3.77602	+	3.34526i	−0.319132	+	0.282726i
$141$	2.72871	+	5.19912i	0.229799	+	0.437845i
$142$	3.01370	+	1.58171i	0.252904	+	0.132734i
$143$	−14.2769	+	4.72565i	−1.19389	+	0.395179i
$144$	−2.76115	+	1.44916i	−0.230096	+	0.120763i
$145$	1.64948	+	1.13855i	0.136982	+	0.0945518i
$146$	4.45584			0.368768
$147$	−3.38002			−0.278779
$148$	3.46230	+	2.38985i	0.284599	+	0.196445i
$149$	−2.91613	+	0.354082i	−0.238899	+	0.0290075i	−0.239110	−	0.970992i	$-0.576856\pi$
$149$	−2.91613	+	0.354082i	−0.238899	+	0.0290075i	0.000211620		1.00000i	$0.499933\pi$
$150$		−	0.684357i		−	0.0558775i
$151$	−10.1922	−	1.23756i	−0.829433	−	0.100711i	−0.305202	−	0.952288i	$-0.598724\pi$
$151$	−10.1922	−	1.23756i	−0.829433	−	0.100711i	−0.524231	+	0.851576i	$0.675647\pi$
$152$	−1.97799	−	2.86561i	−0.160436	−	0.232432i
$153$	10.3165	+	2.54279i	0.834041	+	0.205573i
$154$	−7.11208	+	4.90911i	−0.573108	+	0.395588i
$155$	−0.944852	−	0.232885i	−0.0758923	−	0.0187058i
$156$	−5.76639	−	1.68630i	−0.461681	−	0.135012i
$157$	−7.02257	+	1.73091i	−0.560462	+	0.138141i	−0.509362	−	0.860552i	$-0.670119\pi$
$157$	−7.02257	+	1.73091i	−0.560462	+	0.138141i	−0.0510995	+	0.998694i	$0.516273\pi$
$158$	−2.14695	+	2.42340i	−0.170802	+	0.192796i
$159$	4.21530	−	6.10692i	0.334295	−	0.484310i
$160$	−4.27790	+	3.78989i	−0.338198	+	0.299617i
$161$	−15.2776	+	10.5454i	−1.20404	+	0.831090i
$162$	−0.117593	+	0.0811687i	−0.00923900	+	0.00637722i
$163$	−6.54739	+	12.4750i	−0.512831	+	0.977118i	0.482057	+	0.876140i	$0.339890\pi$
$163$	−6.54739	+	12.4750i	−0.512831	+	0.977118i	−0.994889	+	0.100978i	$0.967803\pi$
$164$	−2.41704	−	9.80634i	−0.188739	−	0.765746i
$165$	−0.530453	+	4.36867i	−0.0412957	+	0.340101i
$166$	−3.50685	−	9.24679i	−0.272184	−	0.717690i
$167$	−8.53502	−	9.63405i	−0.660460	−	0.745505i	0.318865	−	0.947800i	$-0.396698\pi$
$167$	−8.53502	−	9.63405i	−0.660460	−	0.745505i	−0.979325	+	0.202295i	$0.935160\pi$
$168$	−7.82446			−0.603670
$169$	6.44215	+	11.2915i	0.495550	+	0.868580i
$170$	3.65267			0.280147
$171$	1.87652	+	2.11815i	0.143501	+	0.161979i
$172$	3.28035	+	8.64956i	0.250124	+	0.659523i
$173$	1.98264	−	16.3285i	0.150737	−	1.24143i	−0.699345	−	0.714784i	$-0.746525\pi$
$173$	1.98264	−	16.3285i	0.150737	−	1.24143i	0.850082	−	0.526650i	$-0.176552\pi$
$174$	0.328254	+	1.33178i	0.0248849	+	0.100962i
$175$	1.48446	−	2.82841i	0.112215	−	0.213808i
$176$	5.67322	−	3.91594i	0.427635	−	0.295175i
$177$	−7.22939	+	4.99009i	−0.543394	+	0.375078i
$178$	7.04516	−	6.24146i	0.528057	−	0.467817i
$179$	5.63841	−	8.16864i	0.421434	−	0.610553i	−0.553553	−	0.832814i	$-0.686728\pi$
$179$	5.63841	−	8.16864i	0.421434	−	0.610553i	0.974987	+	0.222261i	$0.0713437\pi$
$180$	1.97595	−	2.23039i	0.147279	−	0.166244i
$181$	13.2585	−	3.26792i	0.985495	−	0.242903i	0.286540	−	0.958068i	$-0.407495\pi$
$181$	13.2585	−	3.26792i	0.985495	−	0.242903i	0.698955	+	0.715166i	$0.253649\pi$
$182$	5.37432	+	5.18868i	0.398371	+	0.384611i
$183$	−0.223318	−	0.0550429i	−0.0165081	−	0.00406889i
$184$	−11.1037	+	7.66434i	−0.818577	+	0.565023i
$185$	−2.58645	−	0.637504i	−0.190160	−	0.0468702i
$186$	−0.378313	−	0.548081i	−0.0277392	−	0.0401872i
$187$	−23.3172	−	2.83123i	−1.70513	−	0.207040i
$188$			8.78890i			0.640996i
$189$	16.3497	−	1.98522i	1.18927	−	0.144403i
$190$	0.800609	+	0.552621i	0.0580823	+	0.0400913i
$191$	2.11636			0.153134			0.0765670	−	0.997064i	$-0.475604\pi$
$191$	2.11636			0.153134			0.0765670	+	0.997064i	$0.475604\pi$
$192$	−0.423692			−0.0305774
$193$	−11.6433	−	8.03680i	−0.838104	−	0.578501i	0.0698565	−	0.997557i	$-0.477746\pi$
$193$	−11.6433	−	8.03680i	−0.838104	−	0.578501i	−0.907961	+	0.419056i	$0.862361\pi$
$194$	1.10441	−	0.579640i	0.0792921	−	0.0416157i
$195$	3.79262	−	0.296381i	0.271595	−	0.0212243i
$196$	−4.47979	−	2.35117i	−0.319985	−	0.167941i
$197$	−10.1512	−	19.3415i	−0.723245	−	1.37803i	−0.917763	−	0.397129i	$-0.870007\pi$
$197$	−10.1512	−	19.3415i	−0.723245	−	1.37803i	0.194518	−	0.980899i	$-0.437686\pi$
$198$	3.82076	−	3.38490i	0.271530	−	0.240554i
$199$	−11.3821	−	2.80543i	−0.806855	−	0.198872i	−0.185748	−	0.982597i	$-0.559471\pi$
$199$	−11.3821	−	2.80543i	−0.806855	−	0.198872i	−0.621107	+	0.783725i	$0.713317\pi$
$200$	1.07891	−	2.05568i	0.0762902	−	0.145359i
$201$	−5.68114	−	10.8245i	−0.400717	−	0.763502i
$202$	−4.37846	−	1.66053i	−0.308068	−	0.116835i
$203$	−1.53215	+	6.21619i	−0.107536	+	0.436291i
$204$	−7.02372	−	6.22248i	−0.491759	−	0.435661i
$205$	3.63287	+	5.26312i	0.253731	+	0.367592i
$206$	−0.189073	+	0.360249i	−0.0131733	+	0.0250997i
$207$	8.20744	−	7.27116i	0.570456	−	0.505380i
$208$	−4.28703	−	4.13895i	−0.297252	−	0.286984i
$209$	−4.68244	−	4.14828i	−0.323891	−	0.286943i
$210$	2.04398	−	0.775180i	0.141048	−	0.0534925i
$211$	−0.107357	−	0.884164i	−0.00739075	−	0.0608683i	0.988547	−	0.150914i	$-0.0482217\pi$
$211$	−0.107357	−	0.884164i	−0.00739075	−	0.0608683i	−0.995938	+	0.0900459i	$0.971299\pi$
$212$	9.83488	−	5.16174i	0.675462	−	0.354510i
$213$	3.67134	+	4.14408i	0.251556	+	0.283948i
$214$	−6.89849	−	4.76168i	−0.471571	−	0.325502i
$215$	−3.88425	−	4.38442i	−0.264904	−	0.299015i
$216$	11.8829	−	1.44285i	0.808532	−	0.0981736i
$217$	−0.374684	−	3.08580i	−0.0254352	−	0.209478i
$218$	3.07933	−	8.11954i	0.208559	−	0.549925i
$219$	6.77714	+	2.57023i	0.457956	+	0.173680i
$220$	−3.74194	+	5.42113i	−0.252281	+	0.365493i
$221$	1.58190	+	20.2427i	0.106410	+	1.36167i
$222$	−1.03560	−	1.50033i	−0.0695049	−	0.100695i
$223$	3.01165	+	12.2187i	0.201675	+	0.818227i	0.981379	+	0.192079i	$0.0615231\pi$
$223$	3.01165	+	12.2187i	0.201675	+	0.818227i	−0.779705	+	0.626148i	$0.784631\pi$
$224$	−16.1650	−	8.48403i	−1.08007	−	0.566863i
$225$	−0.669062	+	1.76417i	−0.0446041	+	0.117611i
$226$	11.6242	−	4.40847i	0.773229	−	0.293247i
$227$	−7.47077	−	0.907116i	−0.495853	−	0.0602074i	−0.131209	−	0.991355i	$-0.541886\pi$
$227$	−7.47077	−	0.907116i	−0.495853	−	0.0602074i	−0.364643	+	0.931147i	$0.618809\pi$
$228$	−0.598080	−	2.42651i	−0.0396088	−	0.160699i
$229$	−11.6274	−	22.1542i	−0.768361	−	1.46399i	−0.882393	−	0.470513i	$-0.844069\pi$
$229$	−11.6274	−	22.1542i	−0.768361	−	1.46399i	0.114032	−	0.993477i	$-0.463623\pi$
$230$	2.14130	−	3.10221i	0.141193	−	0.204554i
$231$	−13.6488	+	3.36414i	−0.898028	+	0.221344i
$232$	−1.11357	+	4.51792i	−0.0731092	+	0.296616i
$233$	−1.69878	+	4.47931i	−0.111291	+	0.293449i	−0.979078	−	0.203487i	$-0.934773\pi$
$233$	−1.69878	+	4.47931i	−0.111291	+	0.293449i	0.867787	+	0.496936i	$0.165542\pi$
$234$	−3.52074	−	2.65982i	−0.230158	−	0.173878i
$235$	−1.97341	−	5.20346i	−0.128731	−	0.339436i
$236$	−13.0528	+	1.58490i	−0.849664	+	0.103168i
$237$	−4.66329	+	2.44748i	−0.302913	+	0.158981i
$238$	4.13743	+	10.9095i	0.268190	+	0.707158i
$239$			12.5084i			0.809099i	0.914516	+	0.404549i	$0.132572\pi$
$239$			12.5084i			0.809099i	−0.914516	+	0.404549i	$0.867428\pi$
$240$	−1.63046	+	0.618352i	−0.105246	+	0.0399144i
$241$	4.18424	−	16.9761i	0.269531	−	1.09353i	−0.667592	−	0.744527i	$-0.732675\pi$
$241$	4.18424	−	16.9761i	0.269531	−	1.09353i	0.937122	−	0.349001i	$-0.113479\pi$
$242$	−2.75146	+	3.10576i	−0.176871	+	0.199646i
$243$	−15.2442	+	3.75736i	−0.977916	+	0.241035i
$244$	−0.257691	−	0.228295i	−0.0164970	−	0.0146151i
$245$	3.18018	+	0.386143i	0.203174	+	0.0246698i
$246$	−0.527538	+	4.34467i	−0.0336346	+	0.277006i
$247$	−2.71583	+	4.67621i	−0.172804	+	0.297540i
$248$	−0.272320	−	2.24275i	−0.0172923	−	0.142415i
$249$		−	16.0868i		−	1.01946i
$250$	−0.0781829	+	0.643894i	−0.00494472	+	0.0407234i
$251$	7.16517	+	3.76057i	0.452261	+	0.237365i	0.675444	−	0.737412i	$-0.263952\pi$
$251$	7.16517	+	3.76057i	0.452261	+	0.237365i	−0.223182	+	0.974777i	$0.571644\pi$
$252$	8.89974	+	3.37523i	0.560631	+	0.212619i
$253$	−16.0738	+	18.1436i	−1.01055	+	1.14068i
$254$	7.62283	−	8.60440i	0.478299	−	0.539888i
$255$	5.55555	+	2.10694i	0.347902	+	0.131942i
$256$	−7.12636	−	3.74020i	−0.445397	−	0.233763i
$257$	0.294109	−	2.42221i	0.0183460	−	0.151093i	−0.980657	−	0.195734i	$-0.937291\pi$
$257$	0.294109	−	2.42221i	0.0183460	−	0.151093i	0.999003	+	0.0446406i	$0.0142143\pi$
$258$		−	4.00863i		−	0.249567i
$259$	−1.02567	−	8.44712i	−0.0637318	−	0.524879i
$260$	5.23281	+	2.24537i	0.324525	+	0.139252i
$261$	0.455824	−	3.75405i	0.0282148	−	0.232370i
$262$	2.89724	+	0.351789i	0.178992	+	0.0217336i
$263$	22.9009	+	20.2885i	1.41213	+	1.25104i	0.926194	+	0.377046i	$0.123060\pi$
$263$	22.9009	+	20.2885i	1.41213	+	1.25104i	0.485938	+	0.873994i	$0.338478\pi$
$264$	−9.91996	+	2.44505i	−0.610531	+	0.150482i
$265$	−4.66374	+	5.26428i	−0.286491	+	0.323382i
$266$	−0.743662	+	3.01716i	−0.0455969	+	0.184994i
$267$	14.3156	−	5.42919i	0.876100	−	0.332261i
$268$		−	18.2984i		−	1.11775i
$269$	3.02794	+	7.98403i	0.184617	+	0.486795i	0.995089	−	0.0989823i	$-0.0315587\pi$
$269$	3.02794	+	7.98403i	0.184617	+	0.486795i	−0.810472	+	0.585777i	$0.800789\pi$
$270$	−2.96123	+	1.55418i	−0.180215	+	0.0945841i
$271$	24.4345	−	2.96688i	1.48429	−	0.180225i	0.662090	−	0.749424i	$-0.269670\pi$
$271$	24.4345	−	2.96688i	1.48429	−	0.180225i	0.822200	+	0.569199i	$0.192747\pi$
$272$	−3.30038	−	8.70238i	−0.200115	−	0.527659i
$273$	5.18116	+	10.9918i	0.313578	+	0.665253i
$274$	−1.73731	+	4.58092i	−0.104955	+	0.276743i
$275$	0.998179	−	4.04977i	0.0601925	−	0.244210i
$276$	−9.40227	+	2.31745i	−0.565950	+	0.139494i
$277$	−6.19374	+	8.97318i	−0.372146	+	0.539146i	−0.963654	−	0.267153i	$-0.913917\pi$
$277$	−6.19374	+	8.97318i	−0.372146	+	0.539146i	0.591509	+	0.806299i	$0.298533\pi$
$278$	4.30181	+	8.19641i	0.258005	+	0.491588i
$279$	0.439403	+	1.78273i	0.0263064	+	0.106729i
$280$	7.36184	+	0.893889i	0.439954	+	0.0534201i
$281$	29.6768	−	11.2549i	1.77037	−	0.671412i	0.770965	−	0.636878i	$-0.219774\pi$
$281$	29.6768	−	11.2549i	1.77037	−	0.671412i	0.999404	−	0.0345345i	$-0.0109948\pi$
$282$	1.35052	−	3.56102i	0.0804222	−	0.212056i
$283$	13.0985	+	6.87463i	0.778626	+	0.408654i	0.806707	−	0.590951i	$-0.201248\pi$
$283$	13.0985	+	6.87463i	0.778626	+	0.408654i	−0.0280816	+	0.999606i	$0.508940\pi$
$284$	1.98323	+	8.04627i	0.117683	+	0.477458i
$285$	0.898928	+	1.30232i	0.0532479	+	0.0771429i
$286$	8.43504	+	4.89887i	0.498774	+	0.289676i
$287$	−11.6045	+	16.8120i	−0.684990	+	0.992380i
$288$	10.0826	+	3.82383i	0.594124	+	0.225322i
$289$	−5.21727	+	13.7568i	−0.306898	+	0.809224i
$290$	−0.156700	−	1.29054i	−0.00920171	−	0.0757829i
$291$	2.01411	−	0.244557i	0.118069	−	0.0143362i
$292$	7.19436	+	8.12075i	0.421018	+	0.475231i
$293$	8.26848	+	5.70732i	0.483050	+	0.333425i	0.784576	−	0.620033i	$-0.212881\pi$
$293$	8.26848	+	5.70732i	0.483050	+	0.333425i	−0.301526	+	0.953458i	$0.597496\pi$
$294$	1.45380	+	1.64100i	0.0847875	+	0.0957054i
$295$	7.37203	−	3.86914i	0.429216	−	0.225270i
$296$	−0.745453	−	6.13935i	−0.0433286	−	0.356843i
$297$	20.1080	−	7.62597i	1.16679	−	0.442504i
$298$	1.42618	+	1.26349i	0.0826166	+	0.0731919i
$299$	18.1195	+	10.5233i	1.04787	+	0.608581i
$300$	1.24724	−	1.10496i	0.0720093	−	0.0637947i
$301$	8.69527	−	16.5675i	0.501187	−	0.954933i
$302$	3.78301	+	5.48064i	0.217688	+	0.315376i
$303$	−5.70162	−	5.05119i	−0.327549	−	0.290184i
$304$	0.593211	−	2.40675i	0.0340230	−	0.138037i
$305$	0.203826	+	0.0773010i	0.0116710	+	0.00442624i
$306$	−3.20278	−	6.10238i	−0.183091	−	0.348850i
$307$	−9.65083	+	18.3881i	−0.550802	+	1.04947i	0.437823	+	0.899061i	$0.355750\pi$
$307$	−9.65083	+	18.3881i	−0.550802	+	1.04947i	−0.988625	+	0.150404i	$0.951943\pi$
$308$	−20.4299	−	5.03553i	−1.16410	−	0.286926i
$309$	−0.495372	+	0.438861i	−0.0281807	+	0.0249659i
$310$	0.293331	+	0.558895i	0.0166601	+	0.0317431i
$311$	−25.1922	−	13.2219i	−1.42852	−	0.749746i	−0.439601	−	0.898193i	$-0.644880\pi$
$311$	−25.1922	−	13.2219i	−1.42852	−	0.749746i	−0.988920	+	0.148447i	$0.952572\pi$
$312$	3.76566	+	7.98881i	0.213188	+	0.452277i
$313$	−25.9052	+	13.5961i	−1.46425	+	0.768497i	−0.993507	−	0.113773i	$-0.963706\pi$
$313$	−25.9052	+	13.5961i	−1.46425	+	0.768497i	−0.470743	+	0.882271i	$0.656014\pi$
$314$	3.86088	+	2.66497i	0.217882	+	0.150393i
$315$	−6.02694			−0.339580
$316$	−7.88308			−0.443458
$317$	−15.5951	−	10.7645i	−0.875908	−	0.604595i	0.0429969	−	0.999075i	$-0.486309\pi$
$317$	−15.5951	−	10.7645i	−0.875908	−	0.604595i	−0.918905	+	0.394480i	$0.870925\pi$
$318$	−4.77799	+	0.580153i	−0.267936	+	0.0325334i
$319$			8.35975i			0.468056i
$320$	0.398641	+	0.0484038i	0.0222847	+	0.00270586i
$321$	−7.74565	−	11.2215i	−0.432320	−	0.626324i
$322$	11.6909	+	2.88155i	0.651510	+	0.160583i
$323$	−6.95098	+	4.79792i	−0.386763	+	0.266963i
$324$	−0.337795	−	0.0832589i	−0.0187664	−	0.00462550i
$325$	−3.60224	−	0.154423i	−0.199816	−	0.00856585i
$326$	8.87278	−	2.18694i	0.491418	−	0.121124i
$327$	9.36707	−	10.5732i	0.518000	−	0.584701i
$328$	−8.43411	+	12.2189i	−0.465696	+	0.674677i
$329$	13.3060	−	11.7881i	0.733582	−	0.649897i
$330$	2.34915	−	1.62150i	0.129317	−	0.0892608i
$331$	−28.2697	+	19.5132i	−1.55384	+	1.07254i	−0.589540	+	0.807739i	$0.700691\pi$
$331$	−28.2697	+	19.5132i	−1.55384	+	1.07254i	−0.964303	+	0.264801i	$0.914694\pi$
$332$	11.1901	−	21.3210i	0.614138	−	1.17014i
$333$	1.20283	+	4.88008i	0.0659147	+	0.267427i
$334$	−1.00629	+	8.28753i	−0.0550617	+	0.453474i
$335$	4.10862	+	10.8335i	0.224478	+	0.591899i
$336$	−3.69369	−	4.16931i	−0.201507	−	0.227455i
$337$	−16.5100			−0.899358			−0.449679	−	0.893190i	$-0.648462\pi$
$337$	−16.5100			−0.899358			−0.449679	+	0.893190i	$0.648462\pi$
$338$	2.71118	−	7.98435i	0.147469	−	0.434291i
$339$	20.2228			1.09835
$340$	5.89757	+	6.65698i	0.319841	+	0.361026i
$341$	−1.43930	−	3.79513i	−0.0779427	−	0.205518i
$342$	0.221243	−	1.82210i	0.0119635	−	0.0985281i
$343$	−2.90219	−	11.7747i	−0.156704	−	0.635771i
$344$	6.31971	−	12.0412i	0.340736	−	0.649218i
$345$	5.04626	−	3.48318i	0.271681	−	0.187528i
$346$	−8.78028	+	6.06059i	−0.472031	+	0.325819i
$347$	22.2637	−	19.7239i	1.19518	−	1.05883i	0.198278	−	0.980146i	$-0.436465\pi$
$347$	22.2637	−	19.7239i	1.19518	−	1.05883i	0.996899	−	0.0786883i	$-0.0250732\pi$
$348$	−1.89717	+	2.74852i	−0.101699	+	0.147336i
$349$	−9.11491	+	10.2886i	−0.487910	+	0.550737i	−0.939973	−	0.341249i	$-0.889150\pi$
$349$	−9.11491	+	10.2886i	−0.487910	+	0.550737i	0.452063	+	0.891986i	$0.350688\pi$
$350$	−2.01169	+	0.495837i	−0.107529	+	0.0265036i
$351$	−9.89550	−	15.7377i	−0.528183	−	0.840017i
$352$	−23.1453	−	5.70481i	−1.23365	−	0.304067i
$353$	25.8436	−	17.8385i	1.37551	−	0.949448i	0.375772	−	0.926712i	$-0.377378\pi$
$353$	25.8436	−	17.8385i	1.37551	−	0.949448i	0.999741	−	0.0227364i	$-0.00723783\pi$
$354$	5.53218	+	1.36356i	0.294032	+	0.0724723i
$355$	−2.98084	−	4.31849i	−0.158206	−	0.229201i
$356$	22.7501	+	2.76236i	1.20575	+	0.146405i
$357$			18.9794i			1.00450i
$358$	−6.39106	+	0.776016i	−0.337778	+	0.0410137i
$359$	6.84531	+	4.72498i	0.361282	+	0.249375i	0.734853	−	0.678227i	$-0.237251\pi$
$359$	6.84531	+	4.72498i	0.361282	+	0.249375i	−0.373571	+	0.927602i	$0.621867\pi$
$360$	−4.38037			−0.230866
$361$	16.7506			0.881609
$362$	−7.28927	−	5.03142i	−0.383116	−	0.264446i
$363$	−5.97633	+	3.13662i	−0.313676	+	0.164630i
$364$	−0.779020	+	18.1723i	−0.0408317	+	0.952487i
$365$	−6.08281	−	3.19250i	−0.318389	−	0.167103i
$366$	0.0693294	+	0.132096i	0.00362390	+	0.00690477i
$367$	−7.54541	+	6.68465i	−0.393867	+	0.348936i	−0.836693	−	0.547671i	$-0.815514\pi$
$367$	−7.54541	+	6.68465i	−0.393867	+	0.348936i	0.442826	+	0.896608i	$0.353976\pi$
$368$	−9.32571	−	2.29858i	−0.486136	−	0.119822i
$369$	5.60749	−	10.6842i	0.291914	−	0.556196i
$370$	0.802968	+	1.52993i	0.0417443	+	0.0795372i
$371$	−21.0056	−	7.96637i	−1.09056	−	0.413594i
$372$	0.388055	−	1.57440i	0.0201197	−	0.0816288i
$373$	−14.9536	−	13.2478i	−0.774270	−	0.685943i	0.180405	−	0.983592i	$-0.442259\pi$
$373$	−14.9536	−	13.2478i	−0.774270	−	0.685943i	−0.954675	+	0.297649i	$0.903798\pi$
$374$	8.65457	+	12.5383i	0.447517	+	0.648341i
$375$	−0.490325	+	0.934237i	−0.0253203	+	0.0482438i
$376$	9.67075	−	8.56754i	0.498731	−	0.441837i
$377$	7.08414	−	1.42731i	0.364852	−	0.0735105i
$378$	−7.99611	−	7.08394i	−0.411276	−	0.364358i
$379$	16.3705	−	6.20850i	0.840894	−	0.318909i	0.103715	−	0.994607i	$-0.466927\pi$
$379$	16.3705	−	6.20850i	0.840894	−	0.318909i	0.737179	+	0.675698i	$0.236158\pi$
$380$	0.285507	+	2.35137i	0.0146462	+	0.120622i
$381$	16.5572	−	8.68989i	0.848251	−	0.445197i
$382$	−0.910280	−	1.02749i	−0.0465740	−	0.0525711i
$383$	−4.30478	−	2.97137i	−0.219964	−	0.151830i	0.452987	−	0.891517i	$-0.350358\pi$
$383$	−4.30478	−	2.97137i	−0.219964	−	0.151830i	−0.672951	+	0.739687i	$0.734974\pi$
$384$	−7.81512	−	8.82145i	−0.398814	−	0.450168i
$385$	13.2262	−	1.60595i	0.674069	−	0.0818468i
$386$	1.10611	+	9.10961i	0.0562993	+	0.463667i
$387$	−3.91904	+	10.3337i	−0.199216	+	0.525290i
$388$	2.83956	+	1.07690i	0.144157	+	0.0546716i
$389$	7.59417	−	11.0021i	0.385040	−	0.557826i	−0.581760	−	0.813360i	$-0.697636\pi$
$389$	7.59417	−	11.0021i	0.385040	−	0.557826i	0.966800	+	0.255534i	$0.0822513\pi$
$390$	−1.77516	−	1.71385i	−0.0898889	−	0.0867840i
$391$	18.5910	+	26.9338i	0.940189	+	1.36210i
$392$	1.77987	+	7.22124i	0.0898973	+	0.364728i
$393$	4.20366	+	2.20625i	0.212047	+	0.111291i
$394$	−5.02413	+	13.2476i	−0.253112	+	0.667402i
$395$	4.66717	−	1.77003i	0.234831	−	0.0890597i
$396$	12.3379	+	1.49810i	0.620004	+	0.0752822i
$397$	−8.99928	−	36.5115i	−0.451661	−	1.83246i	−0.547157	−	0.837030i	$-0.684290\pi$
$397$	−8.99928	−	36.5115i	−0.451661	−	1.83246i	0.0954962	−	0.995430i	$-0.469556\pi$
$398$	3.53359	+	6.73269i	0.177123	+	0.337479i
$399$	−2.87144	+	4.16000i	−0.143752	+	0.208261i
$400$	1.60470	−	0.395523i	0.0802350	−	0.0197762i
$401$	2.86064	−	11.6061i	0.142854	−	0.579580i	−0.855261	−	0.518198i	$-0.826603\pi$
$401$	2.86064	−	11.6061i	0.142854	−	0.579580i	0.998114	−	0.0613819i	$-0.0195508\pi$
$402$	−2.81176	+	7.41401i	−0.140238	+	0.369777i
$403$	−2.97029	+	1.86765i	−0.147961	+	0.0930342i
$404$	−4.04311	−	10.6608i	−0.201152	−	0.530395i
$405$	0.218686	−	0.0265532i	0.0108666	−	0.00131944i
$406$	3.67698	−	1.92983i	0.182485	−	0.0957757i
$407$	−3.93998	−	10.3889i	−0.195297	−	0.514957i
$408$			13.7942i			0.682916i
$409$	13.4479	−	5.10011i	0.664955	−	0.252184i	0.00104810	−	0.999999i	$-0.499666\pi$
$409$	13.4479	−	5.10011i	0.664955	−	0.252184i	0.663907	+	0.747815i	$0.268897\pi$
$410$	0.992695	−	4.02752i	0.0490257	−	0.198905i
$411$	−5.28475	+	5.96525i	−0.260678	+	0.294244i
$412$	−0.961828	+	0.237069i	−0.0473859	+	0.0116796i
$413$	19.9064	+	17.6356i	0.979532	+	0.867789i
$414$	−7.06031	−	0.857277i	−0.346996	−	0.0421329i
$415$	−1.83780	+	15.1357i	−0.0902142	+	0.742980i
$416$	−0.882561	+	20.5876i	−0.0432711	+	1.00939i
$417$	1.81499	+	14.9478i	0.0888802	+	0.731995i
$418$			4.05758i			0.198463i
$419$	−2.98958	+	24.6214i	−0.146051	+	1.20283i	0.716765	+	0.697315i	$0.245622\pi$
$419$	−2.98958	+	24.6214i	−0.146051	+	1.20283i	−0.862815	+	0.505519i	$0.831301\pi$
$420$	4.71296	+	2.47355i	0.229969	+	0.120697i
$421$	4.89797	+	1.85756i	0.238713	+	0.0905317i	0.471060	−	0.882101i	$-0.343871\pi$
$421$	4.89797	+	1.85756i	0.238713	+	0.0905317i	−0.232348	+	0.972633i	$0.574641\pi$
$422$	−0.383087	+	0.432416i	−0.0186484	+	0.0210497i
$423$	−6.96287	+	7.85946i	−0.338547	+	0.382140i
$424$	−15.2668	−	5.78995i	−0.741423	−	0.281185i
$425$	−4.98638	−	2.61705i	−0.241875	−	0.126946i
$426$	0.432855	−	3.56488i	0.0209719	−	0.172719i
$427$			0.696331i			0.0336978i
$428$	−2.46009	−	20.2606i	−0.118913	−	0.979335i
$429$	10.0035	+	12.3165i	0.482976	+	0.594645i
$430$	−0.457958	+	3.77162i	−0.0220847	+	0.181884i
$431$	−11.7726	−	1.42945i	−0.567065	−	0.0688541i	−0.168017	−	0.985784i	$-0.553736\pi$
$431$	−11.7726	−	1.42945i	−0.567065	−	0.0688541i	−0.399048	+	0.916930i	$0.630659\pi$
$432$	6.37840	+	5.65077i	0.306881	+	0.271873i
$433$	3.10921	−	0.766351i	0.149419	−	0.0368285i	−0.163897	−	0.986478i	$-0.552406\pi$
$433$	3.10921	−	0.766351i	0.149419	−	0.0368285i	0.313316	+	0.949649i	$0.398560\pi$
$434$	−1.33700	+	1.50916i	−0.0641782	+	0.0724422i
$435$	0.506078	−	2.05324i	0.0242646	−	0.0984452i
$436$	19.7697	−	7.49766i	0.946797	−	0.359073i
$437$			8.71615i			0.416950i
$438$	−1.66711	−	4.39581i	−0.0796576	−	0.210040i
$439$	19.9118	−	10.4505i	0.950340	−	0.498777i	0.0830308	−	0.996547i	$-0.473540\pi$
$439$	19.9118	−	10.4505i	0.950340	−	0.498777i	0.867309	+	0.497770i	$0.165848\pi$
$440$	9.61277	−	1.16720i	0.458271	−	0.0556441i
$441$	−2.14336	−	5.65158i	−0.102065	−	0.269123i
$442$	9.14744	−	9.47472i	0.435099	−	0.450667i
$443$	13.5218	−	35.6541i	0.642440	−	1.69398i	−0.0748441	−	0.997195i	$-0.523846\pi$
$443$	13.5218	−	35.6541i	0.642440	−	1.69398i	0.717284	−	0.696781i	$-0.245385\pi$
$444$	1.06227	−	4.30979i	0.0504130	−	0.204534i
$445$	−14.0894	+	3.47273i	−0.667903	+	0.164623i
$446$	4.63685	−	6.71764i	0.219561	−	0.318090i
$447$	1.44035	+	2.74437i	0.0681264	+	0.129804i
$448$	0.306978	+	1.24546i	0.0145033	+	0.0588424i
$449$	38.8002	+	4.71119i	1.83109	+	0.222335i	0.962139	−	0.272558i	$-0.0878695\pi$
$449$	38.8002	+	4.71119i	1.83109	+	0.222335i	0.868954	+	0.494893i	$0.164793\pi$
$450$	1.14428	−	0.433969i	0.0539420	−	0.0204575i
$451$	−9.45876	+	24.9407i	−0.445396	+	1.17441i
$452$	26.8027	+	14.0672i	1.26069	+	0.661663i
$453$	2.59244	+	10.5179i	0.121804	+	0.494176i
$454$	2.77290	+	4.01724i	0.130139	+	0.188538i
$455$	−3.61909	−	10.9338i	−0.169666	−	0.512585i
$456$	−2.08696	+	3.02348i	−0.0977308	+	0.141588i
$457$	11.0801	+	4.20211i	0.518304	+	0.196567i	0.599864	−	0.800102i	$-0.295221\pi$
$457$	11.0801	+	4.20211i	0.518304	+	0.196567i	−0.0815607	+	0.996668i	$0.525990\pi$
$458$	−5.75475	+	15.1740i	−0.268902	+	0.709035i
$459$	−3.49986	−	28.8239i	−0.163359	−	1.34539i
$460$	9.11111	−	1.10629i	0.424808	−	0.0515810i
$461$	23.5694	+	26.6044i	1.09774	+	1.23909i	0.968908	+	0.247421i	$0.0795832\pi$
$461$	23.5694	+	26.6044i	1.09774	+	1.23909i	0.128828	+	0.991667i	$0.458878\pi$
$462$	7.50389	+	5.17956i	0.349113	+	0.240975i
$463$	5.71137	+	6.44680i	0.265430	+	0.299608i	0.866082	−	0.499902i	$-0.166631\pi$
$463$	5.71137	+	6.44680i	0.265430	+	0.299608i	−0.600652	+	0.799511i	$0.705092\pi$
$464$	−2.93308	+	1.53940i	−0.136165	+	0.0714648i
$465$	0.123760	+	1.01925i	0.00573923	+	0.0472668i
$466$	2.90539	−	1.10187i	0.134589	−	0.0510430i
$467$	−18.0964	−	16.0320i	−0.837400	−	0.741872i	0.130971	−	0.991386i	$-0.458191\pi$
$467$	−18.0964	−	16.0320i	−0.837400	−	0.741872i	−0.968371	+	0.249514i	$0.919729\pi$
$468$	−0.837034	−	10.7111i	−0.0386919	−	0.495119i
$469$	−27.7029	+	24.5426i	−1.27920	+	1.13327i
$470$	−1.67749	+	3.19619i	−0.0773768	+	0.147429i
$471$	4.33502	+	6.28036i	0.199747	+	0.289383i
$472$	14.4680	+	12.8175i	0.665942	+	0.589973i
$473$	5.84685	−	23.7216i	0.268839	−	1.09072i
$474$	3.19401	+	1.21133i	0.146706	+	0.0556382i
$475$	−0.696997	−	1.32802i	−0.0319804	−	0.0609336i
$476$	−13.2023	+	25.1548i	−0.605126	+	1.15297i
$477$	12.8841	+	3.17566i	0.589925	+	0.145403i
$478$	6.07283	−	5.38006i	0.277765	−	0.246078i
$479$	−4.10195	−	7.81561i	−0.187423	−	0.357104i	0.773555	−	0.633729i	$-0.218476\pi$
$479$	−4.10195	−	7.81561i	−0.187423	−	0.357104i	−0.960978	+	0.276624i	$0.910784\pi$
$480$	5.33937	+	2.80232i	0.243708	+	0.127908i
$481$	−8.13093	+	5.11254i	−0.370739	+	0.233112i
$482$	−10.0416	+	5.27026i	−0.457384	+	0.240054i
$483$	16.1192	+	11.1263i	0.733451	+	0.506265i
$484$	−10.1027			−0.459215
$485$	−1.92296			−0.0873173
$486$	8.38099	+	5.78498i	0.380170	+	0.262412i
$487$	−10.5923	+	1.28614i	−0.479983	+	0.0582805i	−0.356953	−	0.934122i	$-0.616184\pi$
$487$	−10.5923	+	1.28614i	−0.479983	+	0.0582805i	−0.123030	+	0.992403i	$0.539261\pi$
$488$			0.506092i			0.0229097i
$489$	14.7566	+	1.79177i	0.667316	+	0.0810268i
$490$	−1.18037	−	1.71007i	−0.0533239	−	0.0772529i
$491$	9.61874	+	2.37081i	0.434088	+	0.106993i	0.450304	−	0.892875i	$-0.351316\pi$
$491$	9.61874	+	2.37081i	0.434088	+	0.106993i	−0.0162158	+	0.999869i	$0.505162\pi$
$492$	−8.76991	+	6.05343i	−0.395378	+	0.272910i
$493$	10.9589	+	2.70113i	0.493564	+	0.121653i
$494$	3.43843	−	0.692776i	0.154702	−	0.0311695i
$495$	−7.64104	+	1.88335i	−0.343439	+	0.0846501i
$496$	1.06651	−	1.20384i	0.0478877	−	0.0540541i
$497$	9.52168	−	13.7945i	0.427105	−	0.618769i
$498$	−7.81016	+	6.91920i	−0.349982	+	0.310057i
$499$	26.5255	−	18.3092i	1.18744	−	0.819633i	0.200342	−	0.979726i	$-0.435795\pi$
$499$	26.5255	−	18.3092i	1.18744	−	0.819633i	0.987102	+	0.160093i	$0.0511794\pi$
$500$	−1.29973	+	0.897138i	−0.0581256	+	0.0401212i
$501$	−6.31096	+	12.0245i	−0.281953	+	0.537216i
$502$	−1.25610	−	5.09618i	−0.0560623	−	0.227454i
$503$	3.27733	−	26.9912i	0.146129	−	1.20348i	−0.716480	−	0.697608i	$-0.754248\pi$
$503$	3.27733	−	26.9912i	0.146129	−	1.20348i	0.862609	−	0.505872i	$-0.168829\pi$
$504$	−4.96170	−	13.0829i	−0.221012	−	0.582760i
$505$	4.78745	+	5.40391i	0.213039	+	0.240471i
$506$	15.7224			0.698944
$507$	8.72914	−	10.5800i	0.387675	−	0.469873i
$508$	27.9892			1.24182
$509$	−19.1157	−	21.5772i	−0.847289	−	0.956392i	0.152200	−	0.988350i	$-0.451364\pi$
$509$	−19.1157	−	21.5772i	−0.847289	−	0.956392i	−0.999489	+	0.0319579i	$0.989826\pi$
$510$	−1.36661	−	3.60346i	−0.0605146	−	0.159564i
$511$	2.64504	−	21.7838i	0.117009	−	0.963660i
$512$	−4.09700	−	16.6222i	−0.181064	−	0.734604i
$513$	3.59372	−	6.84726i	0.158667	−	0.302314i
$514$	−1.30249	+	0.899041i	−0.0574502	+	0.0396550i
$515$	0.516219	−	0.356321i	0.0227473	−	0.0157014i
$516$	7.30572	−	6.47230i	0.321616	−	0.284927i
$517$	13.1859	−	19.1030i	0.579913	−	0.840149i
$518$	−3.65993	+	4.13121i	−0.160808	+	0.181515i
$519$	−16.8503	+	4.15323i	−0.739647	+	0.182307i
$520$	−2.63035	−	7.94667i	−0.115348	−	0.348485i
$521$	−5.19636	−	1.28079i	−0.227657	−	0.0561123i	0.123837	−	0.992303i	$-0.460480\pi$
$521$	−5.19636	−	1.28079i	−0.227657	−	0.0561123i	−0.351494	+	0.936190i	$0.614326\pi$
$522$	−2.01865	+	1.39338i	−0.0883540	+	0.0609864i
$523$	1.27716	+	0.314792i	0.0558464	+	0.0137649i	0.267140	−	0.963658i	$-0.413921\pi$
$523$	1.27716	+	0.314792i	0.0558464	+	0.0137649i	−0.211293	+	0.977423i	$0.567768\pi$
$524$	4.03673	+	5.84821i	0.176345	+	0.255480i
$525$	−3.34570	−	0.406242i	−0.146018	−	0.0177298i
$526$		−	19.8448i		−	0.865276i
$527$	−5.44014	+	0.660553i	−0.236976	+	0.0287741i
$528$	−5.98577	−	4.13168i	−0.260497	−	0.179808i
$529$	10.7735			0.468412
$530$	4.56177			0.198151
$531$	−12.9281	−	8.92359i	−0.561030	−	0.387251i
$532$	−6.69947	+	3.51615i	−0.290459	+	0.152445i
$533$	22.7500	+	3.75716i	0.985410	+	0.162741i
$534$	−8.79325	−	4.61506i	−0.380521	−	0.199713i
$535$	6.00571	+	11.4429i	0.259649	+	0.494721i
$536$	−20.1344	+	17.8375i	−0.869673	+	0.770463i
$537$	−10.1682	−	2.50622i	−0.438788	−	0.108152i
$538$	2.57389	−	4.90413i	0.110968	−	0.211432i
$539$	6.20956	+	11.8313i	0.267465	+	0.509611i
$540$	−7.61366	−	2.88748i	−0.327640	−	0.124257i
$541$	1.06976	−	4.34019i	0.0459927	−	0.186600i	−0.943452	−	0.331508i	$-0.892443\pi$
$541$	1.06976	−	4.34019i	0.0459927	−	0.186600i	0.989445	+	0.144908i	$0.0462888\pi$
$542$	−11.9501	−	10.5869i	−0.513301	−	0.454745i
$543$	−8.18443	−	11.8572i	−0.351227	−	0.508841i
$544$	−14.9570	+	28.4982i	−0.641277	+	1.22185i
$545$	−10.0212	+	8.87797i	−0.429259	+	0.380290i
$546$	3.10803	−	7.24321i	0.133011	−	0.309981i
$547$	1.74175	+	1.54305i	0.0744717	+	0.0659762i	0.699538	−	0.714596i	$-0.253389\pi$
$547$	1.74175	+	1.54305i	0.0744717	+	0.0659762i	−0.625066	+	0.780572i	$0.714928\pi$
$548$	−11.1538	+	4.23006i	−0.476465	+	0.180699i
$549$	−0.0495771	−	0.408304i	−0.00211590	−	0.0174260i
$550$	−2.39550	+	1.25726i	−0.102145	+	0.0536096i
$551$	1.99336	+	2.25004i	0.0849202	+	0.0958551i
$552$	11.7154	+	8.08658i	0.498642	+	0.344188i
$553$	10.5731	+	11.9346i	0.449616	+	0.507511i
$554$	7.02052	−	0.852446i	0.298273	−	0.0362169i
$555$	0.338783	+	2.79013i	0.0143805	+	0.118434i
$556$	−7.99227	+	21.0739i	−0.338948	+	0.893731i
$557$	−23.7503	−	9.00730i	−1.00633	−	0.381651i	−0.204284	−	0.978912i	$-0.565487\pi$
$557$	−23.7503	−	9.00730i	−1.00633	−	0.381651i	−0.802048	+	0.597260i	$0.796256\pi$
$558$	0.676523	−	0.980113i	0.0286395	−	0.0414915i
$559$	−21.1002	−	0.904536i	−0.892444	−	0.0382578i
$560$	2.99898	+	4.34478i	0.126730	+	0.183600i
$561$	5.93085	+	24.0624i	0.250401	+	1.01591i
$562$	−18.2288	−	9.56719i	−0.768934	−	0.403568i
$563$	6.55461	−	17.2831i	0.276244	−	0.728395i	−0.723049	−	0.690797i	$-0.757260\pi$
$563$	6.55461	−	17.2831i	0.276244	−	0.728395i	0.999293	−	0.0375986i	$-0.0119708\pi$
$564$	8.67049	−	3.28828i	0.365093	−	0.138462i
$565$	−19.0271	−	2.31031i	−0.800476	−	0.0971954i
$566$	−2.29625	−	9.31624i	−0.0965184	−	0.391591i
$567$	0.327015	+	0.623076i	0.0137334	+	0.0261667i
$568$	6.92034	−	10.0258i	0.290371	−	0.420675i
$569$	−4.08341	+	1.00647i	−0.171185	+	0.0421934i	−0.323977	−	0.946065i	$-0.605020\pi$
$569$	−4.08341	+	1.00647i	−0.171185	+	0.0421934i	0.152791	+	0.988258i	$0.451174\pi$
$570$	0.245635	−	0.996581i	0.0102885	−	0.0417422i
$571$	10.4141	−	27.4597i	0.435816	−	1.14915i	−0.519736	−	0.854327i	$-0.673970\pi$
$571$	10.4141	−	27.4597i	0.435816	−	1.14915i	0.955551	−	0.294825i	$-0.0952612\pi$
$572$	4.69097	+	23.2825i	0.196139	+	0.973490i
$573$	−0.791814	−	2.08784i	−0.0330785	−	0.0872209i
$574$	13.1535	−	1.59713i	0.549017	−	0.0666628i
$575$	−5.14582	+	2.70074i	−0.214596	+	0.112629i
$576$	−0.268675	−	0.708437i	−0.0111948	−	0.0295182i
$577$			6.24605i			0.260026i	0.991512	+	0.130013i	$0.0415020\pi$
$577$			6.24605i			0.260026i	−0.991512	+	0.130013i	$0.958498\pi$
$578$	8.92298	−	3.38404i	0.371147	−	0.140758i
$579$	−3.57229	+	14.4933i	−0.148459	+	0.602323i
$580$	2.09899	−	2.36927i	0.0871560	−	0.0983788i
$581$	−47.2877	+	11.6554i	−1.96182	+	0.483546i
$582$	−0.985036	−	0.872665i	−0.0408310	−	0.0361731i
$583$	−29.1206	−	3.53588i	−1.20605	−	0.146441i
$584$	1.92241	−	15.8324i	0.0795498	−	0.655151i
$585$	2.90057	+	6.15353i	0.119924	+	0.254417i
$586$	−0.785500	−	6.46918i	−0.0324487	−	0.267239i
$587$			1.92274i			0.0793601i	0.999212	+	0.0396801i	$0.0126339\pi$
$587$			1.92274i			0.0793601i	−0.999212	+	0.0396801i	$0.987366\pi$
$588$	−0.643428	+	5.29911i	−0.0265345	+	0.218531i
$589$	−1.29233	−	0.678268i	−0.0532496	−	0.0279476i
$590$	−5.04931	−	1.91495i	−0.207877	−	0.0788372i
$591$	−15.2830	+	17.2509i	−0.628658	+	0.709608i
$592$	2.91949	−	3.29542i	0.119990	−	0.135441i
$593$	3.56828	+	1.35327i	0.146532	+	0.0555722i	0.426781	−	0.904355i	$-0.359648\pi$
$593$	3.56828	+	1.35327i	0.146532	+	0.0555722i	−0.280249	+	0.959927i	$0.590417\pi$
$594$	−12.3512	−	6.48242i	−0.506777	−	0.265977i
$595$	2.16827	−	17.8573i	0.0888902	−	0.732077i
$596$			4.63923i			0.190030i
$597$	1.49086	+	12.2784i	0.0610170	+	0.502521i
$598$	−2.68438	−	13.3233i	−0.109773	−	0.544830i
$599$	−1.78642	+	14.7125i	−0.0729912	+	0.601137i	0.909617	+	0.415447i	$0.136375\pi$
$599$	−1.78642	+	14.7125i	−0.0729912	+	0.601137i	−0.982608	+	0.185690i	$0.940548\pi$
$600$	−2.43165	−	0.295256i	−0.0992717	−	0.0120538i
$601$	7.35329	+	6.51445i	0.299947	+	0.265730i	0.799649	−	0.600467i	$-0.205019\pi$
$601$	7.35329	+	6.51445i	0.299947	+	0.265730i	−0.499702	+	0.866197i	$0.666557\pi$
$602$	−11.7835	+	2.90437i	−0.480260	+	0.118373i
$603$	14.4966	−	16.3633i	0.590348	−	0.666365i
$604$	−3.88043	+	15.7435i	−0.157893	+	0.640595i
$605$	5.98131	−	2.26841i	0.243175	−	0.0922241i
$606$			4.94075i			0.200704i
$607$	−8.69825	−	22.9354i	−0.353051	−	0.930919i	−0.987453	−	0.157915i	$-0.949523\pi$
$607$	−8.69825	−	22.9354i	−0.353051	−	0.930919i	0.634402	−	0.773003i	$-0.281247\pi$
$608$	−7.58991	+	3.98349i	−0.307811	+	0.161552i
$609$	6.70569	−	0.814218i	0.271728	−	0.0329938i
$610$	−0.0501392	−	0.132206i	−0.00203008	−	0.00535287i
$611$	−18.4394	−	7.91224i	−0.745978	−	0.320095i
$612$	5.95039	−	15.6899i	0.240530	−	0.634227i
$613$	2.17888	−	8.84004i	0.0880039	−	0.357046i	−0.910387	−	0.413759i	$-0.864216\pi$
$613$	2.17888	−	8.84004i	0.0880039	−	0.357046i	0.998391	+	0.0567126i	$0.0180619\pi$
$614$	13.0784	−	3.22355i	0.527803	−	0.130092i
$615$	3.83301	−	5.55308i	0.154562	−	0.223922i
$616$	14.3746	+	27.3885i	0.579170	+	1.10352i
$617$	−6.66003	−	27.0208i	−0.268123	−	1.08782i	−0.938357	−	0.345667i	$-0.887653\pi$
$617$	−6.66003	−	27.0208i	−0.268123	−	1.08782i	0.670234	−	0.742150i	$-0.266194\pi$
$618$	0.426135	+	0.0517422i	0.0171417	+	0.00208138i
$619$	34.2174	−	12.9769i	1.37531	−	0.521587i	0.447383	−	0.894342i	$-0.352356\pi$
$619$	34.2174	−	12.9769i	1.37531	−	0.521587i	0.927930	+	0.372755i	$0.121587\pi$
$620$	−0.544975	+	1.43698i	−0.0218867	+	0.0577105i
$621$	−26.5319	−	13.9250i	−1.06469	−	0.558791i
$622$	4.41635	+	17.9178i	0.177080	+	0.718440i
$623$	−26.3314	−	38.1475i	−1.05494	−	1.52835i
$624$	−2.47923	+	5.77782i	−0.0992488	+	0.231298i
$625$	0.568065	−	0.822984i	0.0227226	−	0.0329194i
$626$	17.7432	+	6.72911i	0.709161	+	0.268949i
$627$	−2.34050	+	6.17140i	−0.0934707	+	0.246462i
$628$	1.37684	+	11.3393i	0.0549419	+	0.452487i
$629$	−14.8920	+	1.80821i	−0.593781	+	0.0720981i
$630$	2.59229	+	2.92609i	0.103279	+	0.116578i
$631$	−27.0816	−	18.6931i	−1.07810	−	0.744159i	−0.109801	−	0.993954i	$-0.535021\pi$
$631$	−27.0816	−	18.6931i	−1.07810	−	0.744159i	−0.968299	+	0.249795i	$0.919637\pi$
$632$	7.68454	+	8.67405i	0.305675	+	0.345035i
$633$	−0.832085	+	0.436712i	−0.0330724	+	0.0173577i
$634$	1.48152	+	12.2014i	0.0588388	+	0.484581i
$635$	−16.5710	+	6.28456i	−0.657601	+	0.249395i
$636$	−8.77183	−	7.77116i	−0.347826	−	0.308147i
$637$	8.96579	−	7.28208i	0.355237	−	0.288527i
$638$	4.05867	−	3.59567i	0.160684	−	0.142354i
$639$	−4.60104	+	8.76655i	−0.182014	+	0.346800i
$640$	6.34526	+	9.19270i	0.250819	+	0.363373i
$641$	9.45644	+	8.37767i	0.373507	+	0.330898i	0.828905	−	0.559390i	$-0.188965\pi$
$641$	9.45644	+	8.37767i	0.373507	+	0.330898i	−0.455398	+	0.890288i	$0.650503\pi$
$642$	−2.11653	+	8.58708i	−0.0835326	+	0.338905i
$643$	15.1235	+	5.73561i	0.596415	+	0.226190i	0.634294	−	0.773092i	$-0.281291\pi$
$643$	15.1235	+	5.73561i	0.596415	+	0.226190i	−0.0378792	+	0.999282i	$0.512060\pi$
$644$	13.6244	+	25.9592i	0.536878	+	1.02294i
$645$	−2.87209	+	5.47231i	−0.113088	+	0.215472i
$646$	5.31913	+	1.31105i	0.209278	+	0.0515825i
$647$	−34.0466	+	30.1626i	−1.33851	+	1.18581i	−0.372282	+	0.928120i	$0.621424\pi$
$647$	−34.0466	+	30.1626i	−1.33851	+	1.18581i	−0.966226	+	0.257695i	$0.917037\pi$
$648$	0.237674	+	0.452850i	0.00933672	+	0.0177896i
$649$	30.7485	+	16.1381i	1.20699	+	0.633475i
$650$	1.47441	+	1.81531i	0.0578312	+	0.0712025i
$651$	−2.90404	+	1.52416i	−0.113818	+	0.0597365i
$652$	18.3116	+	12.6396i	0.717138	+	0.495005i
$653$	33.7703			1.32153			0.660767	−	0.750591i	$-0.270231\pi$
$653$	33.7703			1.32153			0.660767	+	0.750591i	$0.270231\pi$
$654$	−9.16225			−0.358272
$655$	−3.70307	−	2.55604i	−0.144691	−	0.0998729i
$656$	−10.4924	+	1.27401i	−0.409660	+	0.0497417i
$657$			12.9616i			0.505680i
$658$	−11.4462	−	1.38982i	−0.446221	−	0.0541810i
$659$	22.9072	+	33.1869i	0.892339	+	1.29278i	0.955566	+	0.294777i	$0.0952454\pi$
$659$	22.9072	+	33.1869i	0.892339	+	1.29278i	−0.0632271	+	0.997999i	$0.520139\pi$
$660$	6.74811	+	1.66326i	0.262670	+	0.0647423i
$661$	−18.4265	+	12.7189i	−0.716706	+	0.494707i	−0.869737	−	0.493515i	$-0.835712\pi$
$661$	−18.4265	+	12.7189i	−0.716706	+	0.494707i	0.153031	+	0.988221i	$0.451097\pi$
$662$	21.6329	+	5.33204i	0.840788	+	0.207236i
$663$	19.3781	−	9.13419i	0.752583	−	0.354742i
$664$	−34.3686	+	8.47110i	−1.33376	+	0.328742i
$665$	3.17692	−	3.58600i	0.123196	−	0.139059i
$666$	1.85193	−	2.68298i	0.0717607	−	0.103963i
$667$	8.71850	−	7.72392i	0.337582	−	0.299071i
$668$	−16.7288	+	11.5470i	−0.647255	+	0.446768i
$669$	10.9273	−	7.54260i	0.422475	−	0.291614i
$670$	3.49251	−	6.65443i	0.134928	−	0.257083i
$671$	0.217595	+	0.882817i	0.00840016	+	0.0340808i
$672$	−2.32176	+	19.1214i	−0.0895638	+	0.737624i
$673$	−8.83702	−	23.3013i	−0.340642	−	0.898200i	−0.990422	−	0.138077i	$-0.955908\pi$
$673$	−8.83702	−	23.3013i	−0.340642	−	0.898200i	0.649779	−	0.760123i	$-0.274861\pi$
$674$	7.10123	+	8.01564i	0.273529	+	0.308751i
$675$	5.15600			0.198455
$676$	18.9289	−	7.95035i	0.728035	−	0.305783i
$677$	14.1893			0.545341			0.272670	−	0.962108i	$-0.412093\pi$
$677$	14.1893			0.545341			0.272670	+	0.962108i	$0.412093\pi$
$678$	−8.69815	−	9.81819i	−0.334051	−	0.377065i
$679$	−2.17817	−	5.74336i	−0.0835904	−	0.220410i
$680$	1.57589	−	12.9786i	0.0604327	−	0.497708i
$681$	1.90022	+	7.70951i	0.0728168	+	0.295429i
$682$	−1.22347	+	2.33113i	−0.0468492	+	0.0892637i
$683$	−8.96301	+	6.18672i	−0.342960	+	0.236728i	−0.727077	−	0.686556i	$-0.759121\pi$
$683$	−8.96301	+	6.18672i	−0.342960	+	0.236728i	0.384116	+	0.923285i	$0.374506\pi$
$684$	3.67800	−	2.53874i	0.140632	−	0.0970710i
$685$	5.65378	−	5.00881i	0.216020	−	0.191377i
$686$	−4.46833	+	6.47349i	−0.170602	+	0.247159i
$687$	−17.5054	+	19.7595i	−0.667874	+	0.753874i
$688$	9.39956	−	2.31678i	0.358355	−	0.0883266i
$689$	1.97561	+	25.2808i	0.0752646	+	0.963121i
$690$	−3.86157	−	0.951791i	−0.147007	−	0.0362341i
$691$	33.1436	−	22.8774i	1.26084	−	0.870297i	0.265259	−	0.964177i	$-0.414543\pi$
$691$	33.1436	−	22.8774i	1.26084	−	0.870297i	0.995583	+	0.0938807i	$0.0299272\pi$
$692$	−25.2220	−	6.21666i	−0.958796	−	0.236322i
$693$	−14.2801	−	20.6883i	−0.542457	−	0.785885i
$694$	−19.1520	−	2.32547i	−0.726999	−	0.0882736i
$695$		−	14.2713i		−	0.541342i
$696$	4.87368	−	0.591772i	0.184736	−	0.0224311i
$697$	29.6389	+	20.4582i	1.12265	+	0.774911i
$698$	8.91561			0.337461
$699$	5.05455			0.191181
$700$	−4.15172	−	2.86572i	−0.156920	−	0.108314i
$701$	4.36981	−	2.29345i	0.165045	−	0.0866225i	−0.380178	−	0.924913i	$-0.624137\pi$
$701$	4.36981	−	2.29345i	0.165045	−	0.0866225i	0.545223	+	0.838291i	$0.316445\pi$
$702$	−3.38446	+	11.5733i	−0.127738	+	0.436807i
$703$	−3.53766	−	1.85670i	−0.133425	−	0.0700269i
$704$	0.778381	+	1.48308i	0.0293363	+	0.0558957i
$705$	−4.39502	+	3.89365i	−0.165526	+	0.146643i
$706$	−19.7764	−	4.87444i	−0.744294	−	0.183452i
$707$	−10.7172	+	20.4198i	−0.403060	+	0.767967i
$708$	6.44712	+	12.2840i	0.242298	+	0.461660i
$709$	−30.9109	−	11.7230i	−1.16088	−	0.440265i	−0.302437	−	0.953169i	$-0.597800\pi$
$709$	−30.9109	−	11.7230i	−1.16088	−	0.440265i	−0.858446	+	0.512904i	$0.828570\pi$
$710$	−0.814524	+	3.30465i	−0.0305685	+	0.124021i
$711$	−7.04944	−	6.24526i	−0.264375	−	0.234216i
$712$	−19.1376	−	27.7256i	−0.717211	−	1.03906i
$713$	−2.62817	+	5.00755i	−0.0984256	+	0.187534i
$714$	9.21455	−	8.16338i	0.344846	−	0.305507i
$715$	−8.00501	−	12.7311i	−0.299370	−	0.476116i
$716$	−11.7332	−	10.3947i	−0.438492	−	0.388470i
$717$	12.3398	−	4.67989i	0.460840	−	0.174774i
$718$	−0.650300	−	5.35570i	−0.0242690	−	0.199873i
$719$	9.99121	−	5.24379i	0.372609	−	0.195560i	−0.268015	−	0.963415i	$-0.586368\pi$
$719$	9.99121	−	5.24379i	0.372609	−	0.195560i	0.640625	+	0.767854i	$0.278675\pi$
$720$	−2.06784	−	2.33411i	−0.0770638	−	0.0869870i
$721$	1.64896	+	1.13819i	0.0614104	+	0.0423885i
$722$	−7.20470	−	8.13242i	−0.268131	−	0.302657i
$723$	−18.3129	+	2.22359i	−0.681065	+	0.0826962i
$724$	−2.59945	−	21.4084i	−0.0966077	−	0.795636i
$725$	−0.710724	+	1.87402i	−0.0263956	+	0.0695995i
$726$	4.09335	+	1.55240i	0.151919	+	0.0576151i
$727$	−14.0320	+	20.3289i	−0.520419	+	0.753957i	−0.991776	−	0.127986i	$-0.959149\pi$
$727$	−14.0320	+	20.3289i	−0.520419	+	0.753957i	0.471357	+	0.881942i	$0.343764\pi$
$728$	20.7550	−	16.8574i	0.769233	−	0.624777i
$729$	9.03480	+	13.0892i	0.334622	+	0.484784i
$730$	1.06635	+	4.32636i	0.0394675	+	0.160126i
$731$	−29.2078	−	15.3294i	−1.08029	−	0.566979i
$732$	−0.128806	+	0.339634i	−0.00476081	+	0.0125532i
$733$	−10.0941	+	3.82818i	−0.372833	+	0.141397i	−0.533902	−	0.845546i	$-0.679275\pi$
$733$	−10.0941	+	3.82818i	−0.372833	+	0.141397i	0.161069	+	0.986943i	$0.448506\pi$
$734$	6.49082	+	0.788128i	0.239580	+	0.0290903i
$735$	−0.808892	−	3.28180i	−0.0298364	−	0.121051i
$736$	15.4353	+	29.4095i	0.568952	+	1.08405i
$737$	−27.4528	+	39.7722i	−1.01124	+	1.46503i
$738$	−7.59906	+	1.87300i	−0.279725	+	0.0689461i
$739$	11.9342	−	48.4189i	0.439007	−	1.78112i	−0.167319	−	0.985903i	$-0.553511\pi$
$739$	11.9342	−	48.4189i	0.439007	−	1.78112i	0.606325	−	0.795217i	$-0.292643\pi$
$740$	−1.49182	+	3.93362i	−0.0548406	+	0.144603i
$741$	5.62931	+	0.929682i	0.206798	+	0.0341527i
$742$	5.16718	+	13.6247i	0.189693	+	0.500179i
$743$	−4.20606	+	0.510709i	−0.154306	+	0.0187361i	−0.197325	−	0.980338i	$-0.563225\pi$
$743$	−4.20606	+	0.510709i	−0.154306	+	0.0187361i	0.0430193	+	0.999074i	$0.486302\pi$
$744$	−2.11065	+	1.10776i	−0.0773803	+	0.0406123i
$745$	−1.04167	−	2.74665i	−0.0381638	−	0.100630i
$746$			12.9581i			0.474430i
$747$	26.8980	−	10.2011i	0.984147	−	0.373238i
$748$	−8.87744	+	36.0172i	−0.324591	+	1.31692i
$749$	−27.3741	+	30.8989i	−1.00023	+	1.12902i
$750$	0.664471	−	0.163777i	0.0242630	−	0.00598030i
$751$	−19.2411	−	17.0461i	−0.702118	−	0.622022i	0.234606	−	0.972090i	$-0.424620\pi$
$751$	−19.2411	−	17.0461i	−0.702118	−	0.622022i	−0.936724	+	0.350068i	$0.886158\pi$
$752$	9.13053	+	1.10865i	0.332956	+	0.0404282i
$753$	1.02913	−	8.47562i	0.0375035	−	0.308869i
$754$	−3.73997	−	2.82545i	−0.136202	−	0.102897i
$755$	−1.23756	−	10.1922i	−0.0450395	−	0.370934i
$756$		−	26.0106i		−	0.945995i
$757$	−1.50225	+	12.3721i	−0.0546002	+	0.449673i	0.939612	+	0.342241i	$0.111186\pi$
$757$	−1.50225	+	12.3721i	−0.0546002	+	0.449673i	−0.994212	+	0.107432i	$0.965737\pi$
$758$	−10.0554	−	5.27750i	−0.365230	−	0.191688i
$759$	23.9130	+	9.06901i	0.867988	+	0.329184i
$760$	2.30898	−	2.60630i	0.0837554	−	0.0945404i
$761$	4.77821	−	5.39348i	0.173210	−	0.195514i	−0.655495	−	0.755200i	$-0.727540\pi$
$761$	4.77821	−	5.39348i	0.173210	−	0.195514i	0.828705	+	0.559686i	$0.189078\pi$
$762$	−11.3405	−	4.30088i	−0.410822	−	0.155804i
$763$	−37.8671	−	19.8742i	−1.37088	−	0.719494i
$764$	0.402874	−	3.31796i	0.0145755	−	0.120040i
$765$			10.6253i			0.384157i
$766$	0.408951	+	3.36801i	0.0147760	+	0.121691i
$767$	8.42567	−	28.8120i	0.304233	−	1.04034i
$768$	−1.02355	+	8.42971i	−0.0369343	+	0.304181i
$769$	−31.3043	−	3.80103i	−1.12886	−	0.137069i	−0.465274	−	0.885167i	$-0.654044\pi$
$769$	−31.3043	−	3.80103i	−1.12886	−	0.137069i	−0.663588	+	0.748098i	$0.730967\pi$
$770$	−6.46849	−	5.73059i	−0.233108	−	0.206516i
$771$	−2.49961	+	0.616099i	−0.0900213	+	0.0221883i
$772$	−14.8163	+	16.7242i	−0.533251	+	0.601916i
$773$	−4.01422	+	16.2863i	−0.144382	+	0.585779i	0.853522	+	0.521057i	$0.174462\pi$
$773$	−4.01422	+	16.2863i	−0.144382	+	0.585779i	−0.997903	+	0.0647218i	$0.979384\pi$
$774$	6.70266	−	2.54198i	0.240922	−	0.0913697i
$775$		−	0.973129i		−	0.0349558i
$776$	−1.58309	−	4.17426i	−0.0568296	−	0.149847i
$777$	−7.94958	+	4.17226i	−0.285190	+	0.149679i
$778$	−8.60789	+	1.04519i	−0.308608	+	0.0374718i
$779$	3.40121	+	8.96826i	0.121861	+	0.321321i
$780$	0.257314	−	6.00239i	0.00921332	−	0.214920i
$781$	7.76108	−	20.4643i	0.277713	−	0.732270i
$782$	5.08007	−	20.6106i	0.181663	−	0.737035i
$783$	−10.0337	+	2.47309i	−0.358576	+	0.0883811i
$784$	−3.00765	+	4.35734i	−0.107416	+	0.155619i
$785$	−3.36122	−	6.40427i	−0.119967	−	0.228578i
$786$	−0.736927	−	2.98983i	−0.0262853	−	0.106644i
$787$	−4.94436	−	0.600354i	−0.176247	−	0.0214003i	0.0319371	−	0.999490i	$-0.489832\pi$
$787$	−4.94436	−	0.600354i	−0.176247	−	0.0214003i	−0.208185	+	0.978090i	$0.566755\pi$
$788$	−32.2556	+	12.2329i	−1.14906	+	0.435780i
$789$	11.4470	−	30.1831i	0.407522	−	1.07455i
$790$	−2.86678	−	1.50460i	−0.101995	−	0.0535313i
$791$	−14.6520	−	59.4455i	−0.520965	−	2.11364i
$792$	−10.3788	−	15.0363i	−0.368794	−	0.534290i
$793$	0.710957	−	0.335121i	0.0252468	−	0.0119005i
$794$	−13.8556	+	20.0734i	−0.491719	+	0.712377i
$795$	6.93825	+	2.63133i	0.246074	+	0.0933237i
$796$	−6.56500	+	17.3105i	−0.232690	+	0.613554i
$797$	4.88801	+	40.2564i	0.173142	+	1.42595i	0.777321	+	0.629105i	$0.216578\pi$
$797$	4.88801	+	40.2564i	0.173142	+	1.42595i	−0.604179	+	0.796849i	$0.706499\pi$
$798$	3.25474	−	0.395197i	0.115217	−	0.0139898i
$799$	−20.7819	−	23.4579i	−0.735210	−	0.829881i
$800$	−4.70353	−	3.24661i	−0.166295	−	0.114785i
$801$	18.1558	+	20.4937i	0.641504	+	0.724108i
$802$	−6.86518	+	3.60312i	−0.242418	+	0.127231i
$803$	−3.45377	−	28.4444i	−0.121881	−	1.00378i
$804$	−18.0519	+	6.84616i	−0.636640	+	0.241446i
$805$	−13.8951	−	12.3100i	−0.489737	−	0.433870i
$806$	2.18432	+	0.638774i	0.0769393	+	0.0224999i
$807$	6.74359	−	5.97430i	0.237385	−	0.210305i
$808$	−7.78921	+	14.8411i	−0.274024	+	0.522108i
$809$	−26.3296	−	38.1450i	−0.925700	−	1.34111i	−0.939987	−	0.341210i	$-0.889163\pi$
$809$	−26.3296	−	38.1450i	−0.925700	−	1.34111i	0.0142871	−	0.999898i	$-0.495452\pi$
$810$	−0.106952	−	0.0947512i	−0.00375791	−	0.00332922i
$811$	−1.35615	+	5.50210i	−0.0476207	+	0.193205i	−0.989935	−	0.141526i	$-0.954799\pi$
$811$	−1.35615	+	5.50210i	−0.0476207	+	0.193205i	0.942314	+	0.334731i	$0.108645\pi$
$812$	9.45392	+	3.58540i	0.331767	+	0.125823i
$813$	−12.0688	−	22.9953i	−0.423273	−	0.806479i
$814$	−3.34916	+	6.38129i	−0.117388	+	0.223664i
$815$	−13.6794	−	3.37167i	−0.479168	−	0.118104i
$816$	−7.35033	+	6.51183i	−0.257313	+	0.227960i
$817$	−4.08268	−	7.77889i	−0.142835	−	0.272149i
$818$	−8.26027	−	4.33532i	−0.288814	−	0.151581i
$819$	−15.0934	+	15.6334i	−0.527405	+	0.546275i
$820$	8.94294	−	4.69362i	0.312301	−	0.163908i
$821$	26.9436	+	18.5979i	0.940340	+	0.649070i	0.936404	−	0.350923i	$-0.114132\pi$
$821$	26.9436	+	18.5979i	0.940340	+	0.649070i	0.00393513	+	0.999992i	$0.498747\pi$
$822$	5.16920			0.180297
$823$	15.1785			0.529091			0.264545	−	0.964373i	$-0.414778\pi$
$823$	15.1785			0.529091			0.264545	+	0.964373i	$0.414778\pi$
$824$	1.19846	+	0.827237i	0.0417503	+	0.0288182i
$825$	−4.36867	+	0.530453i	−0.152098	+	0.0184680i
$826$		−	17.2500i		−	0.600203i
$827$	33.6368	+	4.08424i	1.16966	+	0.142023i	0.682231	−	0.731137i	$-0.261010\pi$
$827$	33.6368	+	4.08424i	1.16966	+	0.142023i	0.487434	+	0.873160i	$0.337933\pi$
$828$	−9.83714	−	14.2516i	−0.341864	−	0.495276i
$829$	52.0076	+	12.8187i	1.80630	+	0.445213i	0.991004	−	0.133832i	$-0.0427283\pi$
$829$	52.0076	+	12.8187i	1.80630	+	0.445213i	0.815296	+	0.579045i	$0.196574\pi$
$830$	8.13886	−	5.61785i	0.282504	−	0.194998i
$831$	11.1696	+	2.75306i	0.387470	+	0.0955027i
$832$	1.12388	−	0.912824i	0.0389635	−	0.0316465i
$833$	17.5162	−	4.31736i	0.606901	−	0.149588i
$834$	6.47650	−	7.31046i	0.224263	−	0.253140i
$835$	7.31154	−	10.5926i	0.253026	−	0.366572i
$836$	−7.39492	+	6.55133i	−0.255759	+	0.226582i
$837$	4.12928	−	2.85024i	0.142729	−	0.0985187i
$838$	13.2396	−	9.13864i	0.457354	−	0.315689i
$839$	−6.97969	+	13.2987i	−0.240966	+	0.459122i	−0.975664	−	0.219273i	$-0.929632\pi$
$839$	−6.97969	+	13.2987i	−0.240966	+	0.459122i	0.734698	+	0.678394i	$0.237324\pi$
$840$	−1.87252	−	7.59710i	−0.0646080	−	0.262125i
$841$	−3.01136	+	24.8008i	−0.103840	+	0.855198i
$842$	−1.20485	−	3.17694i	−0.0415220	−	0.109485i
$843$	−22.2066	−	25.0660i	−0.764835	−	0.863320i
$844$	−1.40660			−0.0484173
$845$	−9.42172	+	8.95719i	−0.324117	+	0.308137i
$846$	6.81063			0.234154
$847$	13.5502	+	15.2950i	0.465591	+	0.525544i
$848$	−4.12179	−	10.8683i	−0.141543	−	0.373218i
$849$	1.88133	−	15.4941i	0.0645670	−	0.531757i
$850$	0.874141	+	3.54653i	0.0299828	+	0.121645i
$851$	−7.19439	+	13.7078i	−0.246620	+	0.469896i
$852$	7.19586	−	4.96695i	0.246526	−	0.170165i
$853$	8.91757	−	6.15535i	0.305332	−	0.210755i	−0.405539	−	0.914078i	$-0.632916\pi$
$853$	8.91757	−	6.15535i	0.305332	−	0.210755i	0.710871	+	0.703322i	$0.248301\pi$
$854$	0.338070	−	0.299504i	0.0115685	−	0.0102488i
$855$	−1.60752	+	2.32889i	−0.0549760	+	0.0796465i
$856$	−19.8954	+	22.4573i	−0.680011	+	0.767574i
$857$	−19.7942	+	4.87884i	−0.676157	+	0.166658i	−0.562418	−	0.826853i	$-0.690129\pi$
$857$	−19.7942	+	4.87884i	−0.676157	+	0.166658i	−0.113739	+	0.993511i	$0.536283\pi$
$858$	1.67698	−	10.1543i	0.0572511	−	0.346661i
$859$	−45.1455	−	11.1274i	−1.54034	−	0.379661i	−0.624445	−	0.781069i	$-0.714675\pi$
$859$	−45.1455	−	11.1274i	−1.54034	−	0.379661i	−0.915899	+	0.401408i	$0.868521\pi$
$860$	−7.61318	+	5.25500i	−0.259607	+	0.179194i
$861$	20.9272	+	5.15809i	0.713197	+	0.175787i
$862$	4.36958	+	6.33043i	0.148829	+	0.215615i
$863$	32.7857	+	3.98091i	1.11604	+	0.135512i	0.657711	−	0.753271i	$-0.271525\pi$
$863$	32.7857	+	3.98091i	1.11604	+	0.135512i	0.458329	+	0.888783i	$0.348448\pi$
$864$		−	29.4677i		−	1.00251i
$865$	16.3285	−	1.98264i	0.555186	−	0.0674118i
$866$	−1.70939	−	1.17990i	−0.0580873	−	0.0400948i
$867$	15.5235			0.527204
$868$	−4.90916			−0.166628
$869$	17.1342	+	11.8269i	0.581238	+	0.401199i
$870$	−1.21452	+	0.637431i	−0.0411762	+	0.0216109i
$871$	38.3906	+	16.4732i	1.30081	+	0.558173i
$872$	−27.5217	−	14.4445i	−0.932004	−	0.489153i
$873$	1.68612	+	3.21262i	0.0570664	+	0.108731i
$874$	4.23170	−	3.74896i	0.143140	−	0.126811i
$875$	3.10148	+	0.764445i	0.104849	+	0.0258430i
$876$	5.31965	−	10.1357i	0.179734	−	0.342455i
$877$	−21.7308	−	41.4045i	−0.733796	−	1.39813i	−0.910349	−	0.413840i	$-0.864187\pi$
$877$	−21.7308	−	41.4045i	−0.733796	−	1.39813i	0.176554	−	0.984291i	$-0.443505\pi$
$878$	−13.6382	−	5.17227i	−0.460266	−	0.174556i
$879$	2.53686	−	10.2924i	0.0855660	−	0.347155i
$880$	5.15984	+	4.57122i	0.173938	+	0.154096i
$881$	−12.1815	−	17.6479i	−0.410404	−	0.594573i	0.562211	−	0.826994i	$-0.309951\pi$
$881$	−12.1815	−	17.6479i	−0.410404	−	0.594573i	−0.972615	+	0.232421i	$0.925335\pi$
$882$	−1.82196	+	3.47145i	−0.0613484	+	0.116890i
$883$	25.1569	−	22.2871i	0.846597	−	0.750020i	−0.123601	−	0.992332i	$-0.539444\pi$
$883$	25.1569	−	22.2871i	0.846597	−	0.750020i	0.970198	+	0.242312i	$0.0779059\pi$
$884$	32.0370	+	1.37338i	1.07752	+	0.0461918i
$885$	−6.57519	−	5.82511i	−0.221023	−	0.195809i
$886$	−23.1261	+	8.77056i	−0.776935	+	0.294653i
$887$	1.76633	+	14.5471i	0.0593076	+	0.488442i	0.991853	+	0.127389i	$0.0406597\pi$
$887$	1.76633	+	14.5471i	0.0593076	+	0.488442i	−0.932545	+	0.361053i	$0.882417\pi$
$888$	−5.77774	+	3.03239i	−0.193888	+	0.101760i
$889$	−37.5404	−	42.3744i	−1.25907	−	1.42119i
$890$	7.74611	+	5.34676i	0.259650	+	0.179224i
$891$	0.609298	+	0.687755i	0.0204122	+	0.0230407i
$892$	19.7295	−	2.39560i	0.660593	−	0.0802105i
$893$	−1.00607	−	8.28575i	−0.0336669	−	0.277272i
$894$	0.712873	−	1.87969i	0.0238420	−	0.0628663i
$895$	9.28064	+	3.51968i	0.310218	+	0.117650i
$896$	−20.2687	+	29.3642i	−0.677128	+	0.980989i
$897$	3.60235	−	21.8125i	0.120279	−	0.728300i
$898$	−14.4013	−	20.8639i	−0.480578	−	0.696238i
$899$	0.466764	+	1.89374i	0.0155675	+	0.0631597i
$900$	2.63846	+	1.38477i	0.0879486	+	0.0461590i
$901$	−14.0444	+	37.0321i	−0.467887	+	1.23372i
$902$	16.1771	−	6.13517i	0.538639	−	0.204279i
$903$	−19.5975	−	2.37957i	−0.652164	−	0.0791871i
$904$	−10.6490	−	43.2049i	−0.354182	−	1.43697i
$905$	6.34592	+	12.0911i	0.210946	+	0.401923i
$906$	3.99143	−	5.78258i	0.132606	−	0.192113i
$907$	23.5490	−	5.80430i	0.781931	−	0.192729i	0.171909	−	0.985113i	$-0.445007\pi$
$907$	23.5490	−	5.80430i	0.781931	−	0.192729i	0.610022	+	0.792384i	$0.291160\pi$
$908$	−2.84430	+	11.5398i	−0.0943916	+	0.382962i
$909$	4.83033	−	12.7365i	0.160212	−	0.422444i
$910$	−3.75175	+	6.45989i	−0.124369	+	0.214143i
$911$	4.70346	+	12.4020i	0.155833	+	0.410897i	0.990082	−	0.140491i	$-0.0448680\pi$
$911$	4.70346	+	12.4020i	0.155833	+	0.410897i	−0.834249	+	0.551387i	$0.814099\pi$
$912$	−2.59627	+	0.315244i	−0.0859711	+	0.0104388i
$913$	−56.3098	+	29.5537i	−1.86358	+	0.978083i
$914$	−2.72559	−	7.18679i	−0.0901545	−	0.237718i
$915$		−	0.230001i		−	0.00760361i
$916$	−36.9462	+	14.0118i	−1.22074	+	0.462964i
$917$	3.43967	−	13.9553i	0.113588	−	0.460844i
$918$	−12.4887	+	14.0968i	−0.412189	+	0.465265i
$919$	26.0706	−	6.42583i	0.859990	−	0.211968i	0.215427	−	0.976520i	$-0.430886\pi$
$919$	26.0706	−	6.42583i	0.859990	−	0.211968i	0.644563	+	0.764551i	$0.277039\pi$
$920$	−10.0989	−	8.94687i	−0.332952	−	0.294969i
$921$	21.7512	+	2.64107i	0.716725	+	0.0870262i
$922$	2.77886	−	22.8860i	0.0915168	−	0.753709i
$923$	−18.6667	−	3.08282i	−0.614423	−	0.101472i
$924$	2.67598	+	22.0387i	0.0880334	+	0.725020i
$925$		−	2.66386i		−	0.0875872i
$926$	0.673377	−	5.54576i	0.0221285	−	0.182245i
$927$	−1.04793	−	0.549995i	−0.0344185	−	0.0180642i
$928$	10.7105	+	4.06194i	0.351588	+	0.133340i
$929$	−2.12511	+	2.39875i	−0.0697225	+	0.0787005i	−0.782337	−	0.622855i	$-0.785972\pi$
$929$	−2.12511	+	2.39875i	−0.0697225	+	0.0787005i	0.712614	+	0.701556i	$0.247511\pi$
$930$	0.441618	−	0.498484i	0.0144812	−	0.0163459i
$931$	4.49247	+	1.70377i	0.147235	+	0.0558388i
$932$	6.69916	+	3.51599i	0.219438	+	0.115170i
$933$	−3.61834	+	29.7997i	−0.118459	+	0.975599i
$934$			15.6814i			0.513112i
$935$	−2.83123	−	23.3172i	−0.0925910	−	0.762556i
$936$	−10.9698	+	11.3623i	−0.358560	+	0.371389i
$937$	−4.28046	+	35.2528i	−0.139837	+	1.15166i	0.738718	+	0.674015i	$0.235432\pi$
$937$	−4.28046	+	35.2528i	−0.139837	+	1.15166i	−0.878554	+	0.477642i	$0.841491\pi$
$938$	23.8309	+	2.89360i	0.778107	+	0.0944793i
$939$	23.1051	+	20.4694i	0.754007	+	0.667992i
$940$	−8.53351	+	2.10332i	−0.278332	+	0.0686027i
$941$	−14.2525	+	16.0877i	−0.464618	+	0.524446i	−0.933385	−	0.358876i	$-0.883160\pi$
$941$	−14.2525	+	16.0877i	−0.464618	+	0.524446i	0.468767	+	0.883322i	$0.344698\pi$
$942$	1.18456	−	4.80594i	0.0385950	−	0.156586i
$943$	34.7504	−	13.1791i	1.13163	−	0.429170i
$944$			13.7601i			0.447853i
$945$	5.84027	+	15.3995i	0.189984	+	0.500947i
$946$	−14.0317	+	7.36441i	−0.456210	+	0.239438i
$947$	−22.8739	+	2.77740i	−0.743303	+	0.0902533i	−0.483422	−	0.875387i	$-0.660606\pi$
$947$	−22.8739	+	2.77740i	−0.743303	+	0.0902533i	−0.259881	+	0.965641i	$0.583683\pi$
$948$	2.94938	+	7.77688i	0.0957915	+	0.252581i
$949$	−23.5144	+	7.78325i	−0.763308	+	0.252655i
$950$	−0.344964	+	0.909596i	−0.0111921	+	0.0295112i
$951$	−4.78474	+	19.4124i	−0.155156	+	0.629491i
$952$	40.5486	−	9.99433i	1.31419	−	0.323918i
$953$	−5.91685	+	8.57203i	−0.191666	+	0.277675i	−0.907021	−	0.421085i	$-0.861649\pi$
$953$	−5.91685	+	8.57203i	−0.191666	+	0.277675i	0.715356	+	0.698761i	$0.246265\pi$
$954$	−3.99990	−	7.62117i	−0.129502	−	0.246745i
$955$	0.506477	+	2.05486i	0.0163892	+	0.0664936i
$956$	19.6103	+	2.38112i	0.634242	+	0.0770109i
$957$	8.24713	−	3.12772i	0.266592	−	0.101105i
$958$	−2.03017	+	5.35313i	−0.0655919	+	0.172952i
$959$	21.3640	+	11.2127i	0.689880	+	0.362077i
$960$	−0.101396	−	0.411381i	−0.00327255	−	0.0132773i
$961$	17.0721	+	24.7332i	0.550712	+	0.797844i
$962$	5.97939	+	1.74859i	0.192783	+	0.0563769i
$963$	13.8513	−	20.0670i	0.446351	−	0.646651i
$964$	−25.8182	−	9.79155i	−0.831548	−	0.315365i
$965$	5.01684	−	13.2283i	0.161498	−	0.425834i
$966$	−1.53132	−	12.6115i	−0.0492693	−	0.405769i
$967$	−23.2440	+	2.82234i	−0.747477	+	0.0907602i	−0.485407	−	0.874288i	$-0.661328\pi$
$967$	−23.2440	+	2.82234i	−0.747477	+	0.0907602i	−0.262071	+	0.965049i	$0.584405\pi$
$968$	9.84828	+	11.1164i	0.316536	+	0.357295i
$969$	7.33392	+	5.06224i	0.235600	+	0.162623i
$970$	0.827099	+	0.933602i	0.0265566	+	0.0299762i
$971$	3.00633	−	1.57784i	0.0964778	−	0.0506354i	−0.415794	−	0.909459i	$-0.636496\pi$
$971$	3.00633	−	1.57784i	0.0964778	−	0.0506354i	0.512272	+	0.858823i	$0.328804\pi$
$972$	2.98877	+	24.6147i	0.0958648	+	0.789517i
$973$	42.6244	−	16.1653i	1.36648	−	0.518236i
$974$	5.18035	+	4.58939i	0.165989	+	0.147053i
$975$	1.19540	+	3.61149i	0.0382835	+	0.115660i
$976$	−0.269674	+	0.238910i	−0.00863206	+	0.00764734i
$977$	−18.3060	+	34.8791i	−0.585660	+	1.11588i	0.394727	+	0.918798i	$0.370839\pi$
$977$	−18.3060	+	34.8791i	−0.585660	+	1.11588i	−0.980387	+	0.197083i	$0.936853\pi$
$978$	−5.47715	−	7.93502i	−0.175140	−	0.253734i
$979$	−45.3039	−	40.1357i	−1.44792	−	1.28274i
$980$	1.21077	−	4.91229i	0.0386766	−	0.156917i
$981$	23.6189	+	8.95749i	0.754095	+	0.285991i
$982$	−2.98615	−	5.68964i	−0.0952920	−	0.181564i
$983$	−21.3026	+	40.5887i	−0.679447	+	1.29458i	0.264469	+	0.964394i	$0.414803\pi$
$983$	−21.3026	+	40.5887i	−0.679447	+	1.29458i	−0.943916	+	0.330184i	$0.892889\pi$
$984$	15.2098	+	3.74889i	0.484872	+	0.119510i
$985$	16.3502	−	14.4850i	0.520960	−	0.461530i
$986$	−3.40221	−	6.48237i	−0.108348	−	0.206441i
$987$	−16.6075	−	8.71631i	−0.528624	−	0.277443i
$988$	6.81424	+	5.14798i	0.216790	+	0.163779i
$989$	−30.1418	+	15.8196i	−0.958452	+	0.503034i
$990$	4.20091	+	2.89968i	0.133514	+	0.0921577i
$991$	33.2836			1.05729			0.528644	−	0.848844i	$-0.322701\pi$
$991$	33.2836			1.05729			0.528644	+	0.848844i	$0.322701\pi$
$992$	−5.56164			−0.176582
$993$	29.8271	+	20.5882i	0.946535	+	0.653346i
$994$	−10.7927	+	1.31047i	−0.342324	+	0.0415656i
$995$		−	11.7227i		−	0.371636i
$996$	−25.2205	−	3.06232i	−0.799141	−	0.0970332i
$997$	−14.5460	−	21.0736i	−0.460677	−	0.667406i	0.521954	−	0.852973i	$-0.325203\pi$
$997$	−14.5460	−	21.0736i	−0.460677	−	0.667406i	−0.982632	+	0.185567i	$0.940588\pi$
$998$	−20.2982	−	5.00306i	−0.642528	−	0.158369i
$999$	11.3036	−	7.80230i	0.357629	−	0.246854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.w.a.116.25	yes	744
169.51	even	26	inner	845.2.w.a.51.25	✓	744

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.w.a.51.25	✓	744	169.51	even	26	inner
845.2.w.a.116.25	yes	744	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.w (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.430117 - 0.485501i) q^{2} +(-0.374141 - 0.986528i) q^{3} +(0.190362 - 1.56777i) q^{4} +(0.239316 + 0.970942i) q^{5} +(-0.318036 + 0.605968i) q^{6} +(-2.62885 + 1.81457i) q^{7} +(-1.91065 + 1.31882i) q^{8} +(1.41228 - 1.25117i) q^{9} +O(q^{10})\)	\(q+(-0.430117 - 0.485501i) q^{2} +(-0.374141 - 0.986528i) q^{3} +(0.190362 - 1.56777i) q^{4} +(0.239316 + 0.970942i) q^{5} +(-0.318036 + 0.605968i) q^{6} +(-2.62885 + 1.81457i) q^{7} +(-1.91065 + 1.31882i) q^{8} +(1.41228 - 1.25117i) q^{9} +(0.368460 - 0.533806i) q^{10} +(-2.76587 + 3.12202i) q^{11} +(-1.61787 + 0.398770i) q^{12} +(3.11786 + 1.81078i) q^{13} +(2.01169 + 0.495837i) q^{14} +(0.868323 - 0.599360i) q^{15} +(-1.60470 - 0.395523i) q^{16} +(3.19901 + 4.63457i) q^{17} +(-1.21489 - 0.147514i) q^{18} +1.49981i q^{19} +(1.56777 - 0.190362i) q^{20} +(2.77368 + 1.91453i) q^{21} +2.70539 q^{22} +5.81150 q^{23} +(2.01591 + 1.39148i) q^{24} +(-0.885456 + 0.464723i) q^{25} +(-0.461909 - 2.29257i) q^{26} +(-4.56541 - 2.39611i) q^{27} +(2.34440 + 4.46687i) q^{28} +(1.50022 - 1.32908i) q^{29} +(-0.664471 - 0.163777i) q^{30} +(-0.452236 + 0.861663i) q^{31} +(2.65599 + 5.06057i) q^{32} +(4.11478 + 1.56053i) q^{33} +(0.874141 - 3.54653i) q^{34} +(-2.39097 - 2.11821i) q^{35} +(-1.69270 - 2.45230i) q^{36} +(-1.23796 + 2.35873i) q^{37} +(0.728161 - 0.645094i) q^{38} +(0.619866 - 3.75335i) q^{39} +(-1.73775 - 1.53951i) q^{40} +(5.97959 - 2.26776i) q^{41} +(-0.263498 - 2.17010i) q^{42} +(-5.18658 + 2.72212i) q^{43} +(4.36810 + 4.93057i) q^{44} +(1.55279 + 1.07181i) q^{45} +(-2.49962 - 2.82149i) q^{46} +(-5.52452 + 0.670799i) q^{47} +(0.210189 + 1.73106i) q^{48} +(1.13599 - 2.99536i) q^{49} +(0.606473 + 0.230005i) q^{50} +(3.37525 - 4.88989i) q^{51} +(3.43242 - 4.54340i) q^{52} +(3.99520 + 5.78805i) q^{53} +(0.800344 + 3.24712i) q^{54} +(-3.69321 - 1.93835i) q^{55} +(2.62972 - 6.93400i) q^{56} +(1.47961 - 0.561141i) q^{57} +(-1.29054 - 0.156700i) q^{58} +(-1.99247 - 8.08376i) q^{59} +(-0.774365 - 1.47543i) q^{60} +(0.123834 - 0.179404i) q^{61} +(0.612853 - 0.151055i) q^{62} +(-1.44234 + 5.85181i) q^{63} +(0.142398 - 0.375474i) q^{64} +(-1.01201 + 3.46061i) q^{65} +(-1.01220 - 2.66894i) q^{66} +(11.5020 - 1.39659i) q^{67} +(7.87492 - 4.13308i) q^{68} +(-2.17432 - 5.73320i) q^{69} +2.07190i q^{70} +(-4.90636 + 1.86074i) q^{71} +(-1.04829 + 4.25308i) q^{72} +(-4.55544 + 5.14203i) q^{73} +(1.67763 - 0.413500i) q^{74} +(0.789747 + 0.699655i) q^{75} +(2.35137 + 0.285507i) q^{76} +(1.60595 - 13.2262i) q^{77} +(-2.08887 + 1.31343i) q^{78} +(-0.601664 - 4.95515i) q^{79} -1.65273i q^{80} +(0.0265532 - 0.218686i) q^{81} +(-3.67292 - 1.92770i) q^{82} +(14.2560 + 5.40660i) q^{83} +(3.52956 - 3.98405i) q^{84} +(-3.73432 + 4.21518i) q^{85} +(3.55243 + 1.34726i) q^{86} +(-1.87246 - 0.982744i) q^{87} +(1.16720 - 9.61277i) q^{88} +14.5111i q^{89} +(-0.147514 - 1.21489i) q^{90} +(-11.4822 + 0.897295i) q^{91} +(1.10629 - 9.11111i) q^{92} +(1.01925 + 0.123760i) q^{93} +(2.70186 + 2.39364i) q^{94} +(-1.45623 + 0.358929i) q^{95} +(3.99868 - 4.51358i) q^{96} +(-0.460196 + 1.86709i) q^{97} +(-1.94286 + 0.736829i) q^{98} +7.86972i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9}+O(q^{10}) \) 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9	\( 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9} - 2 q^{10} - 122 q^{13} - 4 q^{14} - 66 q^{16} - 12 q^{17} - 78 q^{18} - 24 q^{22} + 140 q^{23} + 156 q^{24} + 62 q^{25} - 14 q^{26} + 28 q^{27} + 8 q^{29} - 20 q^{30} - 52 q^{31} - 26 q^{32} - 130 q^{34} + 4 q^{35} + 70 q^{36} + 126 q^{38} + 16 q^{39} + 6 q^{40} - 24 q^{42} - 24 q^{43} - 78 q^{47} - 94 q^{48} - 32 q^{49} - 12 q^{51} + 110 q^{52} - 156 q^{54} + 16 q^{55} + 16 q^{56} - 78 q^{57} - 104 q^{58} - 104 q^{59} + 28 q^{61} + 106 q^{62} + 14 q^{64} - 2 q^{65} - 308 q^{66} - 104 q^{67} - 18 q^{68} + 20 q^{69} - 78 q^{71} - 338 q^{72} - 4 q^{75} - 286 q^{76} - 52 q^{77} + 312 q^{78} - 12 q^{79} - 78 q^{81} + 268 q^{82} + 12 q^{87} - 72 q^{88} + 26 q^{90} - 136 q^{91} + 52 q^{92} - 130 q^{93} + 124 q^{94} - 16 q^{95} + 338 q^{96}+O(q^{100}) \) 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9 - 2 * q^10 - 122 * q^13 - 4 * q^14 - 66 * q^16 - 12 * q^17 - 78 * q^18 - 24 * q^22 + 140 * q^23 + 156 * q^24 + 62 * q^25 - 14 * q^26 + 28 * q^27 + 8 * q^29 - 20 * q^30 - 52 * q^31 - 26 * q^32 - 130 * q^34 + 4 * q^35 + 70 * q^36 + 126 * q^38 + 16 * q^39 + 6 * q^40 - 24 * q^42 - 24 * q^43 - 78 * q^47 - 94 * q^48 - 32 * q^49 - 12 * q^51 + 110 * q^52 - 156 * q^54 + 16 * q^55 + 16 * q^56 - 78 * q^57 - 104 * q^58 - 104 * q^59 + 28 * q^61 + 106 * q^62 + 14 * q^64 - 2 * q^65 - 308 * q^66 - 104 * q^67 - 18 * q^68 + 20 * q^69 - 78 * q^71 - 338 * q^72 - 4 * q^75 - 286 * q^76 - 52 * q^77 + 312 * q^78 - 12 * q^79 - 78 * q^81 + 268 * q^82 + 12 * q^87 - 72 * q^88 + 26 * q^90 - 136 * q^91 + 52 * q^92 - 130 * q^93 + 124 * q^94 - 16 * q^95 + 338 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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