LMFDB - Embedded newform 966.2.r.a.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.r (of order $22$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.3
Character	$\chi$	$=$	966.113
Dual form			966.2.r.a.701.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(-1.54004 + 0.792632i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-1.55379 - 0.456233i) q^{5} +(0.165806 - 1.72410i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.74347 - 2.44138i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(-1.54004 + 0.792632i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-1.55379 - 0.456233i) q^{5} +(0.165806 - 1.72410i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.74347 - 2.44138i) q^{9} +(1.22385 - 1.06047i) q^{10} +(0.974396 - 0.626207i) q^{11} +(1.36076 + 1.07160i) q^{12} +(3.83272 + 4.42320i) q^{13} +(0.959493 - 0.281733i) q^{14} +(2.75452 - 0.528963i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.484217 + 1.06029i) q^{17} +(1.11123 + 2.78661i) q^{18} +(2.15267 - 0.983092i) q^{19} +(0.230462 + 1.60290i) q^{20} +(1.68295 + 0.409483i) q^{21} +1.15827i q^{22} +(-4.60768 + 1.33016i) q^{23} +(-1.63717 + 0.565393i) q^{24} +(-2.00016 - 1.28543i) q^{25} +(-5.79316 + 0.832931i) q^{26} +(-0.749906 + 5.14175i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(2.28668 + 1.04429i) q^{29} +(-1.04422 + 2.60323i) q^{30} +(-0.129509 + 0.900755i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-1.00426 + 1.73672i) q^{33} +(-0.630183 - 0.980584i) q^{34} +(0.875505 + 1.36231i) q^{35} +(-2.94502 - 0.571731i) q^{36} +(-1.84956 - 6.29901i) q^{37} +(-0.336792 + 2.34244i) q^{38} +(-9.40853 - 3.77398i) q^{39} +(-1.47304 - 0.672716i) q^{40} +(-2.25044 + 7.66429i) q^{41} +(-1.25435 + 1.19441i) q^{42} +(-12.0652 + 1.73471i) q^{43} +(-0.974396 - 0.626207i) q^{44} +(-3.82282 + 2.99795i) q^{45} +(1.37210 - 4.59536i) q^{46} -3.54578i q^{47} +(0.409483 - 1.68295i) q^{48} +(0.142315 + 0.989821i) q^{49} +(2.16274 - 0.987690i) q^{50} +(-0.0947024 - 2.01670i) q^{51} +(2.43131 - 5.32383i) q^{52} +(-6.05890 + 6.99234i) q^{53} +(-3.92009 - 3.41070i) q^{54} +(-1.79970 + 0.528440i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(-2.53598 + 3.22028i) q^{57} +(-2.11479 + 1.35909i) q^{58} +(9.96582 - 8.63543i) q^{59} +(-1.62543 - 2.28586i) q^{60} +(1.56206 + 0.224590i) q^{61} +(-0.687746 - 0.595935i) q^{62} +(-2.91639 + 0.703339i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-3.93723 - 8.62133i) q^{65} +(-0.918080 - 1.78378i) q^{66} +(-3.15579 + 4.91051i) q^{67} +1.16562 q^{68} +(6.04169 - 5.70069i) q^{69} -1.61938 q^{70} +(1.69725 - 2.64097i) q^{71} +(2.07317 - 2.16840i) q^{72} +(0.0137313 + 0.0300673i) q^{73} +(6.29901 + 1.84956i) q^{74} +(4.09921 + 0.394220i) q^{75} +(-1.78850 - 1.54975i) q^{76} +(-1.14648 - 0.164839i) q^{77} +(8.26151 - 5.87459i) q^{78} +(-10.7279 + 9.29574i) q^{79} +(1.36231 - 0.875505i) q^{80} +(-2.92063 - 8.51293i) q^{81} +(-5.23093 - 6.03681i) q^{82} +(-13.9422 + 4.09379i) q^{83} +(-0.326644 - 1.70097i) q^{84} +(1.23611 - 1.42655i) q^{85} +(5.06361 - 11.0878i) q^{86} +(-4.34933 + 0.204241i) q^{87} +(1.05360 - 0.481162i) q^{88} +(1.13580 + 7.89963i) q^{89} +(-0.455266 - 4.83677i) q^{90} -5.85273i q^{91} +(3.12405 + 3.63872i) q^{92} +(-0.514518 - 1.48986i) q^{93} +(2.98290 + 1.91699i) q^{94} +(-3.79331 + 0.545396i) q^{95} +(1.19441 + 1.25435i) q^{96} +(-4.26555 + 14.5271i) q^{97} +(-0.909632 - 0.415415i) q^{98} +(0.170024 - 3.47064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} + 24 q^{14} + 18 q^{15} - 24 q^{16} + 32 q^{17} - 4 q^{18} + 4 q^{20} - 8 q^{23} + 12 q^{25} - 148 q^{27} + 40 q^{30} + 16 q^{31} + 42 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} + 154 q^{41} + 4 q^{42} + 22 q^{43} + 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} + 88 q^{50} + 24 q^{51} + 8 q^{52} - 108 q^{53} + 12 q^{54} - 16 q^{55} - 24 q^{56} - 62 q^{57} - 4 q^{58} + 22 q^{59} - 18 q^{60} - 4 q^{63} + 24 q^{64} - 100 q^{66} - 44 q^{67} - 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} - 16 q^{74} - 26 q^{75} - 78 q^{78} - 4 q^{80} + 52 q^{81} + 8 q^{82} + 16 q^{83} - 28 q^{85} + 16 q^{86} - 196 q^{87} + 24 q^{89} + 126 q^{90} + 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} + 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 + 24 * q^14 + 18 * q^15 - 24 * q^16 + 32 * q^17 - 4 * q^18 + 4 * q^20 - 8 * q^23 + 12 * q^25 - 148 * q^27 + 40 * q^30 + 16 * q^31 + 42 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 + 154 * q^41 + 4 * q^42 + 22 * q^43 + 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 + 88 * q^50 + 24 * q^51 + 8 * q^52 - 108 * q^53 + 12 * q^54 - 16 * q^55 - 24 * q^56 - 62 * q^57 - 4 * q^58 + 22 * q^59 - 18 * q^60 - 4 * q^63 + 24 * q^64 - 100 * q^66 - 44 * q^67 - 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 - 16 * q^74 - 26 * q^75 - 78 * q^78 - 4 * q^80 + 52 * q^81 + 8 * q^82 + 16 * q^83 - 28 * q^85 + 16 * q^86 - 196 * q^87 + 24 * q^89 + 126 * q^90 + 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	−1.54004	+	0.792632i	−0.889145	+	0.457626i
$3$	−1.54004	+	0.792632i	−0.889145	+	0.457626i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	−1.55379	−	0.456233i	−0.694875	−	0.204034i	−0.0848239	−	0.996396i	$-0.527033\pi$
$5$	−1.55379	−	0.456233i	−0.694875	−	0.204034i	−0.610051	+	0.792362i	$0.708851\pi$
$6$	0.165806	−	1.72410i	0.0676900	−	0.703859i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	1.74347	−	2.44138i	0.581156	−	0.813792i
$10$	1.22385	−	1.06047i	0.387015	−	0.335350i
$11$	0.974396	−	0.626207i	0.293792	−	0.188808i	−0.385439	−	0.922733i	$-0.625950\pi$
$11$	0.974396	−	0.626207i	0.293792	−	0.188808i	0.679231	+	0.733925i	$0.262314\pi$
$12$	1.36076	+	1.07160i	0.392818	+	0.309345i
$13$	3.83272	+	4.42320i	1.06301	+	1.22677i	0.972993	+	0.230834i	$0.0741456\pi$
$13$	3.83272	+	4.42320i	1.06301	+	1.22677i	0.0900135	+	0.995941i	$0.471309\pi$
$14$	0.959493	−	0.281733i	0.256435	−	0.0752962i
$15$	2.75452	−	0.528963i	0.711215	−	0.136578i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−0.484217	+	1.06029i	−0.117440	+	0.257157i	−0.959219	−	0.282665i	$-0.908781\pi$
$17$	−0.484217	+	1.06029i	−0.117440	+	0.257157i	0.841779	+	0.539823i	$0.181509\pi$
$18$	1.11123	+	2.78661i	0.261918	+	0.656810i
$19$	2.15267	−	0.983092i	0.493857	−	0.225537i	−0.152888	−	0.988244i	$-0.548857\pi$
$19$	2.15267	−	0.983092i	0.493857	−	0.225537i	0.646744	+	0.762707i	$0.276130\pi$
$20$	0.230462	+	1.60290i	0.0515329	+	0.358419i
$21$	1.68295	+	0.409483i	0.367250	+	0.0893565i
$22$			1.15827i			0.246943i
$23$	−4.60768	+	1.33016i	−0.960767	+	0.277357i
$23$	−4.60768	+	1.33016i	−0.960767	+	0.277357i
$24$	−1.63717	+	0.565393i	−0.334186	+	0.115410i
$25$	−2.00016	−	1.28543i	−0.400032	−	0.257085i
$26$	−5.79316	+	0.832931i	−1.13613	+	0.163351i
$27$	−0.749906	+	5.14175i	−0.144319	+	0.989531i
$28$	−0.281733	+	0.959493i	−0.0532424	+	0.181327i
$29$	2.28668	+	1.04429i	0.424626	+	0.193920i	0.616254	−	0.787547i	$-0.288649\pi$
$29$	2.28668	+	1.04429i	0.424626	+	0.193920i	−0.191628	+	0.981468i	$0.561377\pi$
$30$	−1.04422	+	2.60323i	−0.190647	+	0.475283i
$31$	−0.129509	+	0.900755i	−0.0232605	+	0.161780i	−0.998141	−	0.0609486i	$-0.980587\pi$
$31$	−0.129509	+	0.900755i	−0.0232605	+	0.161780i	0.974880	+	0.222729i	$0.0714965\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	−1.00426	+	1.73672i	−0.174820	+	0.302325i
$34$	−0.630183	−	0.980584i	−0.108076	−	0.168169i
$35$	0.875505	+	1.36231i	0.147987	+	0.230273i
$36$	−2.94502	−	0.571731i	−0.490836	−	0.0952885i
$37$	−1.84956	−	6.29901i	−0.304065	−	1.03555i	−0.959829	−	0.280585i	$-0.909471\pi$
$37$	−1.84956	−	6.29901i	−0.304065	−	1.03555i	0.655764	−	0.754966i	$-0.272347\pi$
$38$	−0.336792	+	2.34244i	−0.0546349	+	0.379994i
$39$	−9.40853	−	3.77398i	−1.50657	−	0.604321i
$40$	−1.47304	−	0.672716i	−0.232909	−	0.106366i
$41$	−2.25044	+	7.66429i	−0.351459	+	1.19696i	0.574236	+	0.818690i	$0.305299\pi$
$41$	−2.25044	+	7.66429i	−0.351459	+	1.19696i	−0.925695	+	0.378270i	$0.876519\pi$
$42$	−1.25435	+	1.19441i	−0.193551	+	0.184301i
$43$	−12.0652	+	1.73471i	−1.83993	+	0.264542i	−0.972480	−	0.232988i	$-0.925150\pi$
$43$	−12.0652	+	1.73471i	−1.83993	+	0.264542i	−0.867447	+	0.497529i	$0.834241\pi$
$44$	−0.974396	−	0.626207i	−0.146896	−	0.0944042i
$45$	−3.82282	+	2.99795i	−0.569872	+	0.446908i
$46$	1.37210	−	4.59536i	0.202305	−	0.677549i
$47$		−	3.54578i		−	0.517205i	−0.965984	−	0.258602i	$-0.916738\pi$
$47$		−	3.54578i		−	0.517205i	0.965984	−	0.258602i	$-0.0832619\pi$
$48$	0.409483	−	1.68295i	0.0591038	−	0.242913i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	2.16274	−	0.987690i	0.305857	−	0.139680i
$51$	−0.0947024	−	2.01670i	−0.0132610	−	0.282394i
$52$	2.43131	−	5.32383i	0.337162	−	0.738283i
$53$	−6.05890	+	6.99234i	−0.832254	+	0.960472i	−0.999677	−	0.0254128i	$-0.991910\pi$
$53$	−6.05890	+	6.99234i	−0.832254	+	0.960472i	0.167423	+	0.985885i	$0.446455\pi$
$54$	−3.92009	−	3.41070i	−0.533457	−	0.464138i
$55$	−1.79970	+	0.528440i	−0.242672	+	0.0712548i
$56$	−0.654861	−	0.755750i	−0.0875094	−	0.100991i
$57$	−2.53598	+	3.22028i	−0.335898	+	0.426537i
$58$	−2.11479	+	1.35909i	−0.277686	+	0.178458i
$59$	9.96582	−	8.63543i	1.29744	−	1.12424i	0.312766	−	0.949830i	$-0.398744\pi$
$59$	9.96582	−	8.63543i	1.29744	−	1.12424i	0.984674	−	0.174408i	$-0.0558010\pi$
$60$	−1.62543	−	2.28586i	−0.209842	−	0.295104i
$61$	1.56206	+	0.224590i	0.200001	+	0.0287558i	0.241587	−	0.970379i	$-0.422332\pi$
$61$	1.56206	+	0.224590i	0.200001	+	0.0287558i	−0.0415863	+	0.999135i	$0.513241\pi$
$62$	−0.687746	−	0.595935i	−0.0873438	−	0.0756838i
$63$	−2.91639	+	0.703339i	−0.367430	+	0.0886124i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−3.93723	−	8.62133i	−0.488353	−	1.06934i
$66$	−0.918080	−	1.78378i	−0.113008	−	0.219568i
$67$	−3.15579	+	4.91051i	−0.385541	+	0.599914i	−0.978731	−	0.205149i	$-0.934232\pi$
$67$	−3.15579	+	4.91051i	−0.385541	+	0.599914i	0.593189	+	0.805063i	$0.297869\pi$
$68$	1.16562			0.141352
$69$	6.04169	−	5.70069i	0.727335	−	0.686283i
$70$	−1.61938			−0.193553
$71$	1.69725	−	2.64097i	0.201427	−	0.313426i	−0.725815	−	0.687890i	$-0.758537\pi$
$71$	1.69725	−	2.64097i	0.201427	−	0.313426i	0.927241	+	0.374464i	$0.122173\pi$
$72$	2.07317	−	2.16840i	0.244325	−	0.255549i
$73$	0.0137313	+	0.0300673i	0.00160713	+	0.00351912i	0.910434	−	0.413655i	$-0.135748\pi$
$73$	0.0137313	+	0.0300673i	0.00160713	+	0.00351912i	−0.908827	+	0.417174i	$0.863021\pi$
$74$	6.29901	+	1.84956i	0.732246	+	0.215007i
$75$	4.09921	+	0.394220i	0.473336	+	0.0455206i
$76$	−1.78850	−	1.54975i	−0.205155	−	0.177768i
$77$	−1.14648	−	0.164839i	−0.130653	−	0.0187851i
$78$	8.26151	−	5.87459i	0.935432	−	0.665167i
$79$	−10.7279	+	9.29574i	−1.20698	+	1.04585i	−0.209293	+	0.977853i	$0.567116\pi$
$79$	−10.7279	+	9.29574i	−1.20698	+	1.04585i	−0.997685	+	0.0679996i	$0.978338\pi$
$80$	1.36231	−	0.875505i	0.152311	−	0.0978844i
$81$	−2.92063	−	8.51293i	−0.324515	−	0.945881i
$82$	−5.23093	−	6.03681i	−0.577659	−	0.666655i
$83$	−13.9422	+	4.09379i	−1.53035	+	0.449352i	−0.935159	−	0.354229i	$-0.884743\pi$
$83$	−13.9422	+	4.09379i	−1.53035	+	0.449352i	−0.595195	+	0.803582i	$0.702925\pi$
$84$	−0.326644	−	1.70097i	−0.0356398	−	0.185591i
$85$	1.23611	−	1.42655i	0.134075	−	0.154731i
$86$	5.06361	−	11.0878i	0.546023	−	1.19562i
$87$	−4.34933	+	0.204241i	−0.466297	+	0.0218970i
$88$	1.05360	−	0.481162i	0.112314	−	0.0512920i
$89$	1.13580	+	7.89963i	0.120394	+	0.837359i	0.957111	+	0.289723i	$0.0935631\pi$
$89$	1.13580	+	7.89963i	0.120394	+	0.837359i	−0.836717	+	0.547636i	$0.815528\pi$
$90$	−0.455266	−	4.83677i	−0.0479892	−	0.509840i
$91$		−	5.85273i		−	0.613533i
$92$	3.12405	+	3.63872i	0.325705	+	0.379363i
$93$	−0.514518	−	1.48986i	−0.0533530	−	0.154491i
$94$	2.98290	+	1.91699i	0.307662	+	0.197723i
$95$	−3.79331	+	0.545396i	−0.389186	+	0.0559564i
$96$	1.19441	+	1.25435i	0.121903	+	0.128022i
$97$	−4.26555	+	14.5271i	−0.433101	+	1.47501i	0.397221	+	0.917723i	$0.369975\pi$
$97$	−4.26555	+	14.5271i	−0.433101	+	1.47501i	−0.830322	+	0.557284i	$0.811844\pi$
$98$	−0.909632	−	0.415415i	−0.0918867	−	0.0419633i
$99$	0.170024	−	3.47064i	0.0170881	−	0.348812i
$100$	−0.338367	+	2.35340i	−0.0338367	+	0.235340i
$101$	1.53190	+	5.21717i	0.152430	+	0.519128i	0.999932	−	0.0116637i	$-0.00371276\pi$
$101$	1.53190	+	5.21717i	0.152430	+	0.519128i	−0.847502	+	0.530792i	$0.821895\pi$
$102$	1.74775	+	1.01064i	0.173053	+	0.100068i
$103$	−5.55666	−	8.64633i	−0.547514	−	0.851948i	0.451676	−	0.892182i	$-0.350826\pi$
$103$	−5.55666	−	8.64633i	−0.547514	−	0.851948i	−0.999190	+	0.0402334i	$0.987190\pi$
$104$	3.16423	+	4.92363i	0.310278	+	0.482802i
$105$	−2.42813	−	1.40407i	−0.236961	−	0.137023i
$106$	−2.60665	−	8.87742i	−0.253180	−	0.862251i
$107$	−0.378217	+	2.63056i	−0.0365636	+	0.254305i	−0.999902	−	0.0139830i	$-0.995549\pi$
$107$	−0.378217	+	2.63056i	−0.0365636	+	0.254305i	0.963339	+	0.268288i	$0.0864580\pi$
$108$	4.98863	−	1.45382i	0.480031	−	0.139894i
$109$	−5.29546	−	2.41835i	−0.507213	−	0.231636i	0.145337	−	0.989382i	$-0.453573\pi$
$109$	−5.29546	−	2.41835i	−0.507213	−	0.231636i	−0.652550	+	0.757746i	$0.726301\pi$
$110$	0.528440	−	1.79970i	0.0503848	−	0.171595i
$111$	7.84120	+	8.23474i	0.744254	+	0.781607i
$112$	0.989821	−	0.142315i	0.0935293	−	0.0134475i
$113$	7.15931	+	4.60101i	0.673491	+	0.432827i	0.832183	−	0.554502i	$-0.187091\pi$
$113$	7.15931	+	4.60101i	0.673491	+	0.432827i	−0.158691	+	0.987328i	$0.550727\pi$
$114$	−1.33802	−	3.87441i	−0.125317	−	0.362872i
$115$	7.76621	+	0.0353895i	0.724203	+	0.00330009i
$116$		−	2.51386i		−	0.233406i
$117$	17.4809	−	1.64541i	1.61611	−	0.152118i
$118$	1.87666	+	13.0525i	0.172760	+	1.20158i
$119$	1.06029	−	0.484217i	0.0971964	−	0.0443881i
$120$	2.80177	−	0.131569i	0.255765	−	0.0120105i
$121$	−4.01225	+	8.78561i	−0.364750	+	0.798691i
$122$	−1.03345	+	1.19266i	−0.0935640	+	0.107979i
$123$	−2.60919	−	13.5871i	−0.235262	−	1.22511i
$124$	0.873156	−	0.256382i	0.0784117	−	0.0230238i
$125$	7.82373	+	9.02906i	0.699775	+	0.807584i
$126$	0.985031	−	2.83367i	0.0877536	−	0.252444i
$127$	−5.68826	+	3.65562i	−0.504751	+	0.324384i	−0.768114	−	0.640313i	$-0.778805\pi$
$127$	−5.68826	+	3.65562i	−0.504751	+	0.324384i	0.263363	+	0.964697i	$0.415168\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	17.2060	−	12.2348i	1.51490	−	1.07721i
$130$	9.38135	+	1.34883i	0.822799	+	0.118301i
$131$	−14.2470	−	12.3451i	−1.24477	−	1.07860i	−0.993867	−	0.110586i	$-0.964727\pi$
$131$	−14.2470	−	12.3451i	−1.24477	−	1.07860i	−0.250903	−	0.968012i	$-0.580727\pi$
$132$	1.99696	+	0.192048i	0.173813	+	0.0167156i
$133$	−2.27067	−	0.666728i	−0.196892	−	0.0578127i
$134$	−2.42483	−	5.30964i	−0.209474	−	0.458683i
$135$	3.51103	−	7.64706i	0.302182	−	0.658154i
$136$	−0.630183	+	0.980584i	−0.0540378	+	0.0840844i
$137$	−16.1913			−1.38331			−0.691657	−	0.722226i	$-0.743119\pi$
$137$	−16.1913			−1.38331			−0.691657	+	0.722226i	$0.743119\pi$
$138$	1.52934	+	8.16463i	0.130186	+	0.695019i
$139$	−8.56225			−0.726240			−0.363120	−	0.931742i	$-0.618289\pi$
$139$	−8.56225			−0.726240			−0.363120	+	0.931742i	$0.618289\pi$
$140$	0.875505	−	1.36231i	0.0739937	−	0.115136i
$141$	2.81050	+	5.46065i	0.236687	+	0.459870i
$142$	1.30413	+	2.85564i	0.109440	+	0.239640i
$143$	6.50443	+	1.90987i	0.543928	+	0.159712i
$144$	0.703339	+	2.91639i	0.0586116	+	0.243032i
$145$	−3.07658	−	2.66587i	−0.255496	−	0.221388i
$146$	−0.0327179	−	0.00470413i	−0.00270776	−	0.000389317i
$147$	−1.00374	−	1.41156i	−0.0827867	−	0.116424i
$148$	−4.96145	+	4.29912i	−0.407829	+	0.353386i
$149$	0.883351	−	0.567695i	0.0723669	−	0.0465074i	−0.503957	−	0.863729i	$-0.668123\pi$
$149$	0.883351	−	0.567695i	0.0723669	−	0.0465074i	0.576324	+	0.817221i	$0.304487\pi$
$150$	−2.54784	+	3.23534i	−0.208030	+	0.264165i
$151$	−8.46043	−	9.76386i	−0.688500	−	0.794571i	0.298651	−	0.954362i	$-0.403463\pi$
$151$	−8.46043	−	9.76386i	−0.688500	−	0.794571i	−0.987151	+	0.159791i	$0.948918\pi$
$152$	2.27067	−	0.666728i	0.184176	−	0.0540788i
$153$	1.74434	+	3.03073i	0.141022	+	0.245020i
$154$	0.758504	−	0.875360i	0.0611220	−	0.0705385i
$155$	0.612184	−	1.34050i	0.0491718	−	0.107671i
$156$	0.475512	+	10.1261i	0.0380714	+	0.810735i
$157$	−8.91895	+	4.07315i	−0.711809	+	0.325072i	−0.738202	−	0.674579i	$-0.764325\pi$
$157$	−8.91895	+	4.07315i	−0.711809	+	0.325072i	0.0263931	+	0.999652i	$0.491598\pi$
$158$	−2.02016	−	14.0505i	−0.160715	−	1.11780i
$159$	3.78862	−	15.5710i	0.300457	−	1.23486i
$160$			1.61938i			0.128023i
$161$	4.35332	+	2.01212i	0.343090	+	0.158577i
$162$	8.74054	+	2.14544i	0.686722	+	0.168562i
$163$	5.28429	+	3.39601i	0.413898	+	0.265996i	0.730976	−	0.682404i	$-0.239065\pi$
$163$	5.28429	+	3.39601i	0.413898	+	0.265996i	−0.317078	+	0.948400i	$0.602702\pi$
$164$	7.90654	−	1.13679i	0.617397	−	0.0887683i
$165$	2.35276	−	2.24032i	0.183162	−	0.174409i
$166$	4.09379	−	13.9422i	0.317740	−	1.08212i
$167$	21.1480	+	9.65798i	1.63648	+	0.747357i	0.999719	−	0.0237016i	$-0.00754517\pi$
$167$	21.1480	+	9.65798i	1.63648	+	0.747357i	0.636764	+	0.771059i	$0.280272\pi$
$168$	1.60755	+	0.644824i	0.124025	+	0.0497492i
$169$	−3.02483	+	21.0381i	−0.232679	+	1.61832i
$170$	0.531795	+	1.81113i	0.0407868	+	0.138907i
$171$	1.35302	−	6.96947i	0.103468	−	0.532969i
$172$	6.59002	+	10.2543i	0.502484	+	0.781881i
$173$	3.11785	+	4.85147i	0.237046	+	0.368851i	0.939312	−	0.343064i	$-0.111465\pi$
$173$	3.11785	+	4.85147i	0.237046	+	0.368851i	−0.702266	+	0.711914i	$0.747828\pi$
$174$	2.17961	−	3.76931i	0.165236	−	0.285751i
$175$	0.669847	+	2.28129i	0.0506356	+	0.172449i
$176$	−0.164839	+	1.14648i	−0.0124252	+	0.0864190i
$177$	−8.50308	+	21.1982i	−0.639131	+	1.59335i
$178$	−7.25965	−	3.31537i	−0.544134	−	0.248497i
$179$	0.0217229	−	0.0739815i	0.00162365	−	0.00552964i	−0.958677	−	0.284496i	$-0.908174\pi$
$179$	0.0217229	−	0.0739815i	0.00162365	−	0.00552964i	0.960301	+	0.278967i	$0.0899919\pi$
$180$	4.31509	+	2.23196i	0.321628	+	0.166361i
$181$	15.3662	−	2.20932i	1.14216	−	0.164217i	0.454839	−	0.890574i	$-0.349697\pi$
$181$	15.3662	−	2.20932i	1.14216	−	0.164217i	0.687318	+	0.726356i	$0.258788\pi$
$182$	4.92363	+	3.16423i	0.364964	+	0.234548i
$183$	−2.58365	+	0.892257i	−0.190989	+	0.0659576i
$184$	−4.75008	+	0.660880i	−0.350180	+	0.0487207i
$185$			10.6312i			0.781618i
$186$	1.53152	+	0.372637i	0.112296	+	0.0273230i
$187$	0.192140	+	1.33636i	0.0140506	+	0.0977243i
$188$	−3.22535	+	1.47297i	−0.235233	+	0.107427i
$189$	3.93387	−	3.39480i	0.286147	−	0.246935i
$190$	1.59200	−	3.48600i	0.115496	−	0.252901i
$191$	−6.55339	+	7.56302i	−0.474187	+	0.547241i	−0.941571	−	0.336813i	$-0.890651\pi$
$191$	−6.55339	+	7.56302i	−0.474187	+	0.547241i	0.467385	+	0.884054i	$0.345196\pi$
$192$	−1.70097	+	0.326644i	−0.122757	+	0.0235735i
$193$	20.7239	−	6.08507i	1.49174	−	0.438013i	0.568641	−	0.822586i	$-0.307469\pi$
$193$	20.7239	−	6.08507i	1.49174	−	0.438013i	0.923095	+	0.384573i	$0.125651\pi$
$194$	−9.91487	−	11.4424i	−0.711846	−	0.821514i
$195$	12.8970	+	10.1564i	0.923576	+	0.727318i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	13.1043	−	11.3549i	0.933641	−	0.809005i	−0.0481747	−	0.998839i	$-0.515340\pi$
$197$	13.1043	−	11.3549i	0.933641	−	0.809005i	0.981816	+	0.189834i	$0.0607950\pi$
$198$	2.82777	+	2.01940i	0.200961	+	0.143513i
$199$	−3.90574	−	0.561561i	−0.276871	−	0.0398080i	0.00248065	−	0.999997i	$-0.499210\pi$
$199$	−3.90574	−	0.561561i	−0.276871	−	0.0398080i	−0.279352	+	0.960189i	$0.590119\pi$
$200$	−1.79687	−	1.55700i	−0.127058	−	0.110096i
$201$	0.967831	−	10.0638i	0.0682656	−	0.709844i
$202$	−5.21717	−	1.53190i	−0.367079	−	0.107784i
$203$	−1.04429	−	2.28668i	−0.0732950	−	0.160494i
$204$	−1.79511	+	0.923910i	−0.125683	+	0.0646866i
$205$	6.99340	−	10.8819i	0.488440	−	0.760028i
$206$	10.2779			0.716096
$207$	−4.78592	+	13.5682i	−0.332644	+	0.943052i
$208$	−5.85273			−0.405814
$209$	1.48194	−	2.30594i	0.102508	−	0.159505i
$210$	2.49392	−	1.28358i	0.172097	−	0.0885751i
$211$	1.66474	+	3.64528i	0.114606	+	0.250951i	0.958239	−	0.285968i	$-0.0923152\pi$
$211$	1.66474	+	3.64528i	0.114606	+	0.250951i	−0.843634	+	0.536919i	$0.819588\pi$
$212$	8.87742	+	2.60665i	0.609704	+	0.179025i
$213$	−0.520520	+	5.41251i	−0.0356654	+	0.370859i
$214$	−2.00849	−	1.74036i	−0.137297	−	0.118969i
$215$	19.5382	+	2.80917i	1.33249	+	0.191584i
$216$	−1.47402	+	4.98270i	−0.100294	+	0.339030i
$217$	0.687746	−	0.595935i	0.0466872	−	0.0404547i
$218$	4.89739	−	3.14736i	0.331693	−	0.213166i
$219$	−0.0449791	−	0.0354211i	−0.00303941	−	0.00239354i
$220$	1.22831	+	1.41754i	0.0828125	+	0.0955708i
$221$	−6.54573	+	1.92200i	−0.440314	+	0.129288i
$222$	−11.1668	+	2.14440i	−0.749465	+	0.143923i
$223$	−16.3002	+	18.8114i	−1.09154	+	1.25970i	−0.128105	+	0.991761i	$0.540889\pi$
$223$	−16.3002	+	18.8114i	−1.09154	+	1.25970i	−0.963435	+	0.267943i	$0.913656\pi$
$224$	−0.415415	+	0.909632i	−0.0277561	+	0.0607773i
$225$	−6.62543	+	2.64205i	−0.441695	+	0.176136i
$226$	−7.74123	+	3.53530i	−0.514939	+	0.235165i
$227$	2.81873	+	19.6047i	0.187085	+	1.30121i	0.839506	+	0.543350i	$0.182845\pi$
$227$	2.81873	+	19.6047i	0.187085	+	1.30121i	−0.652421	+	0.757857i	$0.726246\pi$
$228$	3.98275	+	0.969053i	0.263764	+	0.0641771i
$229$		−	1.98077i		−	0.130893i	−0.997856	−	0.0654465i	$-0.979153\pi$
$229$		−	1.98077i		−	0.130893i	0.997856	−	0.0654465i	$-0.0208472\pi$
$230$	−4.22850	+	6.51422i	−0.278819	+	0.429535i
$231$	1.89628	−	0.654876i	0.124766	−	0.0430877i
$232$	2.11479	+	1.35909i	0.138843	+	0.0892288i
$233$	−4.91266	+	0.706334i	−0.321839	+	0.0462735i	−0.301341	−	0.953516i	$-0.597434\pi$
$233$	−4.91266	+	0.706334i	−0.321839	+	0.0462735i	−0.0204980	+	0.999790i	$0.506525\pi$
$234$	−8.06670	+	15.5955i	−0.527337	+	1.01951i
$235$	−1.61770	+	5.50938i	−0.105527	+	0.359392i
$236$	−11.9950	−	5.47794i	−0.780809	−	0.356584i
$237$	9.15327	−	22.8191i	0.594569	−	1.48226i
$238$	−0.165885	+	1.15376i	−0.0107528	+	0.0747870i
$239$	−3.79789	−	12.9344i	−0.245665	−	0.836659i	−0.986330	−	0.164784i	$-0.947307\pi$
$239$	−3.79789	−	12.9344i	−0.245665	−	0.836659i	0.740664	−	0.671875i	$-0.234511\pi$
$240$	−1.40407	+	2.42813i	−0.0906321	+	0.156735i
$241$	7.51199	+	11.6889i	0.483890	+	0.752947i	0.994258	−	0.107009i	$-0.0341273\pi$
$241$	7.51199	+	11.6889i	0.483890	+	0.752947i	−0.510368	+	0.859956i	$0.670491\pi$
$242$	−5.22173	−	8.12518i	−0.335666	−	0.522306i
$243$	11.2455	+	10.7953i	0.721400	+	0.692518i
$244$	−0.444607	−	1.51419i	−0.0284631	−	0.0969363i
$245$	0.230462	−	1.60290i	0.0147237	−	0.102406i
$246$	12.8408	+	5.15076i	0.818701	+	0.328400i
$247$	12.5990	+	5.75377i	0.801656	+	0.366104i
$248$	−0.256382	+	0.873156i	−0.0162803	+	0.0554454i
$249$	18.2267	−	17.3556i	1.15507	−	1.09987i
$250$	−11.8256	+	1.70026i	−0.747914	+	0.107534i
$251$	8.78380	+	5.64500i	0.554428	+	0.356309i	0.787658	−	0.616112i	$-0.211293\pi$
$251$	8.78380	+	5.64500i	0.554428	+	0.356309i	−0.233230	+	0.972422i	$0.574930\pi$
$252$	1.85129	+	2.36066i	0.116620	+	0.148708i
$253$	−3.65675	+	4.18146i	−0.229898	+	0.262886i
$254$		−	6.76165i		−	0.424263i
$255$	−0.772936	+	3.17672i	−0.0484031	+	0.198934i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−0.217244	+	0.0992121i	−0.0135513	+	0.00618868i	−0.422179	−	0.906512i	$-0.638735\pi$
$257$	−0.217244	+	0.0992121i	−0.0135513	+	0.00618868i	0.408628	+	0.912701i	$0.366007\pi$
$258$	0.990332	+	21.0892i	0.0616554	+	1.31296i
$259$	−2.72717	+	5.97168i	−0.169458	+	0.371062i
$260$	−6.20665	+	7.16286i	−0.384920	+	0.444221i
$261$	6.53627	−	3.76196i	0.404585	−	0.232860i
$262$	18.0879	−	5.31109i	1.11747	−	0.328120i
$263$	−1.41812	−	1.63660i	−0.0874452	−	0.100917i	0.710341	−	0.703858i	$-0.248541\pi$
$263$	−1.41812	−	1.63660i	−0.0874452	−	0.100917i	−0.797786	+	0.602941i	$0.793995\pi$
$264$	−1.24120	+	1.57612i	−0.0763907	+	0.0970038i
$265$	12.6044	−	8.10034i	0.774281	−	0.497600i
$266$	1.78850	−	1.54975i	0.109660	−	0.0950211i
$267$	−8.01067	−	11.2655i	−0.490245	−	0.689438i
$268$	5.77772	+	0.830711i	0.352930	+	0.0507437i
$269$	−16.9289	−	14.6690i	−1.03217	−	0.894382i	−0.0376899	−	0.999289i	$-0.512000\pi$
$269$	−16.9289	−	14.6690i	−1.03217	−	0.894382i	−0.994482	+	0.104907i	$0.966545\pi$
$270$	4.53491	+	7.08798i	0.275986	+	0.431361i
$271$	−17.0214	−	4.99794i	−1.03398	−	0.303603i	−0.279650	−	0.960102i	$-0.590219\pi$
$271$	−17.0214	−	4.99794i	−1.03398	−	0.303603i	−0.754327	+	0.656499i	$0.772037\pi$
$272$	−0.484217	−	1.06029i	−0.0293600	−	0.0642894i
$273$	4.63906	+	9.01346i	0.280769	+	0.545520i
$274$	8.75366	−	13.6210i	0.528828	−	0.822872i
$275$	−2.75389			−0.166066
$276$	−7.69535	−	3.12756i	−0.463205	−	0.188257i
$277$	20.8575			1.25321			0.626603	−	0.779338i	$-0.284445\pi$
$277$	20.8575			1.25321			0.626603	+	0.779338i	$0.284445\pi$
$278$	4.62910	−	7.20302i	0.277635	−	0.432009i
$279$	1.97329	+	1.88662i	0.118138	+	0.112949i
$280$	0.672716	+	1.47304i	0.0402025	+	0.0880311i
$281$	19.1306	+	5.61725i	1.14124	+	0.335097i	0.797115	−	0.603828i	$-0.206359\pi$
$281$	19.1306	+	5.61725i	1.14124	+	0.335097i	0.344122	+	0.938925i	$0.388177\pi$
$282$	−6.11326	−	0.587911i	−0.364039	−	0.0350096i
$283$	−19.0114	−	16.4735i	−1.13011	−	0.979246i	−0.130185	−	0.991490i	$-0.541557\pi$
$283$	−19.0114	−	16.4735i	−1.13011	−	0.979246i	−0.999925	+	0.0122437i	$0.996103\pi$
$284$	−3.10738	−	0.446774i	−0.184389	−	0.0265111i
$285$	5.40957	−	3.84663i	0.320435	−	0.227855i
$286$	−5.12325	+	4.43932i	−0.302944	+	0.262502i
$287$	6.71981	−	4.31856i	0.396658	−	0.254916i
$288$	−2.83367	−	0.985031i	−0.166976	−	0.0580435i
$289$	10.2429	+	11.8209i	0.602523	+	0.695348i
$290$	3.90600	−	1.14690i	0.229368	−	0.0673485i
$291$	−4.94554	−	25.7534i	−0.289912	−	1.50969i
$292$	0.0216460	−	0.0249808i	0.00126674	−	0.00146189i
$293$	4.69216	−	10.2744i	0.274119	−	0.600237i	−0.721637	−	0.692272i	$-0.756610\pi$
$293$	4.69216	−	10.2744i	0.274119	−	0.600237i	0.995756	+	0.0920348i	$0.0293371\pi$
$294$	1.73014	−	0.0812462i	0.100904	−	0.00473837i
$295$	−19.4245	+	8.87089i	−1.13094	+	0.516483i
$296$	−0.934288	−	6.49812i	−0.0543044	−	0.377696i
$297$	2.48910	+	5.47970i	0.144432	+	0.317965i
$298$			1.05004i			0.0608272i
$299$	−23.5435	−	15.2825i	−1.36156	−	0.883812i
$300$	−1.34428	−	3.89254i	−0.0776119	−	0.224736i
$301$	10.2543	+	6.59002i	0.591046	+	0.379842i
$302$	12.7879	−	1.83863i	0.735863	−	0.105801i
$303$	−6.49449	−	6.82044i	−0.373099	−	0.391824i
$304$	−0.666728	+	2.27067i	−0.0382395	+	0.130232i
$305$	−2.32464	−	1.06163i	−0.133108	−	0.0607885i
$306$	−3.49268	−	0.171104i	−0.199663	−	0.00978137i
$307$	1.54465	−	10.7433i	0.0881581	−	0.613153i	−0.897068	−	0.441893i	$-0.854307\pi$
$307$	1.54465	−	10.7433i	0.0881581	−	0.613153i	0.985226	−	0.171260i	$-0.0547838\pi$
$308$	0.326322	+	1.11135i	0.0185939	+	0.0633250i
$309$	15.4109	+	8.91134i	0.876693	+	0.506949i
$310$	0.796725	+	1.23973i	0.0452509	+	0.0704118i
$311$	10.1260	+	15.7564i	0.574196	+	0.893466i	0.999935	−	0.0113799i	$-0.00362242\pi$
$311$	10.1260	+	15.7564i	0.574196	+	0.893466i	−0.425740	+	0.904846i	$0.639986\pi$
$312$	−8.77567	−	5.07454i	−0.496825	−	0.287289i
$313$	1.50997	+	5.14247i	0.0853483	+	0.290670i	0.991096	−	0.133147i	$-0.0425083\pi$
$313$	1.50997	+	5.14247i	0.0853483	+	0.290670i	−0.905748	+	0.423817i	$0.860690\pi$
$314$	1.39540	−	9.70520i	0.0787468	−	0.547696i
$315$	4.85233	+	0.237713i	0.273398	+	0.0133936i
$316$	12.9122	+	5.89681i	0.726369	+	0.331722i
$317$	1.19649	−	4.07487i	0.0672015	−	0.228867i	−0.919044	−	0.394155i	$-0.871037\pi$
$317$	1.19649	−	4.07487i	0.0672015	−	0.228867i	0.986245	+	0.165288i	$0.0528554\pi$
$318$	11.0509	+	11.6055i	0.619702	+	0.650804i
$319$	2.88208	−	0.414380i	0.161365	−	0.0232009i
$320$	−1.36231	−	0.875505i	−0.0761556	−	0.0489422i
$321$	−1.50259	−	4.35096i	−0.0838665	−	0.242847i
$322$	−4.04628	+	2.57441i	−0.225491	+	0.143466i
$323$			2.75848i			0.153486i
$324$	−6.53036	+	6.19310i	−0.362798	+	0.344061i
$325$	−1.98037	−	13.7738i	−0.109851	−	0.764033i
$326$	−5.71381	+	2.60941i	−0.316459	+	0.144522i
$327$	10.0721	−	0.472978i	0.556988	−	0.0261557i
$328$	−3.31827	+	7.26600i	−0.183221	+	0.401198i
$329$	−2.32199	+	2.67972i	−0.128015	+	0.147738i
$330$	0.612680	+	3.19048i	0.0337269	+	0.175630i
$331$	23.3508	−	6.85642i	1.28348	−	0.376863i	0.432295	−	0.901732i	$-0.357704\pi$
$331$	23.3508	−	6.85642i	1.28348	−	0.376863i	0.851183	+	0.524869i	$0.175886\pi$
$332$	9.51564	+	10.9816i	0.522238	+	0.602695i
$333$	−18.6029	−	6.46667i	−1.01943	−	0.354371i
$334$	−19.5583	+	12.5694i	−1.07018	+	0.687764i
$335$	7.14376	−	6.19011i	0.390306	−	0.338202i
$336$	−1.41156	+	1.00374i	−0.0770072	+	0.0547582i
$337$	−12.0643	−	1.73459i	−0.657186	−	0.0944890i	−0.194349	−	0.980933i	$-0.562259\pi$
$337$	−12.0643	−	1.73459i	−0.657186	−	0.0944890i	−0.462837	+	0.886443i	$0.653168\pi$
$338$	−16.0631	−	13.9187i	−0.873715	−	0.757079i
$339$	−14.6726	−	1.41106i	−0.796904	−	0.0766381i
$340$	−1.81113	−	0.531795i	−0.0982223	−	0.0288407i
$341$	0.437866	+	0.958792i	0.0237118	+	0.0519215i
$342$	5.13159	+	4.90621i	0.277485	+	0.265298i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	−12.1893			−0.657202
$345$	−11.9884	+	6.10124i	−0.645431	+	0.328480i
$346$	−5.76696			−0.310034
$347$	12.1783	−	18.9497i	0.653763	−	1.01727i	−0.343190	−	0.939266i	$-0.611507\pi$
$347$	12.1783	−	18.9497i	0.653763	−	1.01727i	0.996953	−	0.0780087i	$-0.0248562\pi$
$348$	1.99256	+	3.87145i	0.106813	+	0.207531i
$349$	−9.34652	−	20.4660i	−0.500308	−	1.09552i	−0.976369	−	0.216109i	$-0.930663\pi$
$349$	−9.34652	−	20.4660i	−0.500308	−	1.09552i	0.476061	−	0.879412i	$-0.342064\pi$
$350$	−2.28129	−	0.669847i	−0.121940	−	0.0358048i
$351$	−25.6172	+	16.3899i	−1.36734	+	0.874831i
$352$	−0.875360	−	0.758504i	−0.0466568	−	0.0404284i
$353$	−9.73773	−	1.40007i	−0.518287	−	0.0745184i	−0.121793	−	0.992556i	$-0.538864\pi$
$353$	−9.73773	−	1.40007i	−0.518287	−	0.0745184i	−0.396494	+	0.918037i	$0.629773\pi$
$354$	−13.2359	−	18.6138i	−0.703482	−	0.989315i
$355$	−3.84207	+	3.32917i	−0.203916	+	0.176694i
$356$	6.71393	−	4.31478i	0.355837	−	0.228683i
$357$	−1.24908	+	1.58613i	−0.0661085	+	0.0839471i
$358$	0.0504929	+	0.0582719i	0.00266863	+	0.00307977i
$359$	−13.4692	+	3.95492i	−0.710878	+	0.208733i	−0.617128	−	0.786863i	$-0.711704\pi$
$359$	−13.4692	+	3.95492i	−0.710878	+	0.208733i	−0.0937507	+	0.995596i	$0.529886\pi$
$360$	−4.21056	+	2.42339i	−0.221916	+	0.127724i
$361$	−8.77483	+	10.1267i	−0.461833	+	0.532984i
$362$	−6.44897	+	14.1213i	−0.338951	+	0.742198i
$363$	−0.784709	−	16.7105i	−0.0411866	−	0.877071i
$364$	−5.32383	+	2.43131i	−0.279045	+	0.127435i
$365$	−0.00761779	−	0.0529829i	−0.000398733	−	0.00277325i
$366$	0.646212	−	2.65590i	0.0337781	−	0.138826i
$367$			15.4580i			0.806899i	0.915002	+	0.403449i	$0.132189\pi$
$367$			15.4580i			0.806899i	−0.915002	+	0.403449i	$0.867811\pi$
$368$	2.01212	−	4.35332i	0.104889	−	0.226932i
$369$	14.7878	+	18.8566i	0.769824	+	0.981636i
$370$	−8.94350	−	5.74764i	−0.464950	−	0.298805i
$371$	9.15802	−	1.31672i	0.475461	−	0.0683610i
$372$	−1.14148	+	1.08693i	−0.0591831	+	0.0563547i
$373$	10.5650	−	35.9810i	0.547033	−	1.86302i	0.0434907	−	0.999054i	$-0.486152\pi$
$373$	10.5650	−	35.9810i	0.547033	−	1.86302i	0.503543	−	0.863970i	$-0.332030\pi$
$374$	−1.22810	−	0.560853i	−0.0635034	−	0.0290010i
$375$	−19.2056	−	7.70381i	−0.991773	−	0.397823i
$376$	0.504617	−	3.50969i	0.0260236	−	0.180998i
$377$	4.14511	+	14.1169i	0.213484	+	0.727060i
$378$	0.729070	+	5.14475i	0.0374993	+	0.264617i
$379$	−0.0705089	−	0.109714i	−0.00362180	−	0.00563563i	0.839438	−	0.543456i	$-0.182884\pi$
$379$	−0.0705089	−	0.109714i	−0.00362180	−	0.00563563i	−0.843060	+	0.537820i	$0.819248\pi$
$380$	2.07191	+	3.22395i	0.106287	+	0.165385i
$381$	5.86260	−	10.1385i	0.300350	−	0.519412i
$382$	−2.81938	−	9.60194i	−0.144252	−	0.491278i
$383$	0.471683	−	3.28063i	0.0241019	−	0.167632i	−0.974215	−	0.225620i	$-0.927559\pi$
$383$	0.471683	−	3.28063i	0.0241019	−	0.167632i	0.998317	+	0.0579875i	$0.0184684\pi$
$384$	0.644824	−	1.60755i	0.0329060	−	0.0820347i
$385$	1.70618	+	0.779185i	0.0869549	+	0.0397110i
$386$	−6.08507	+	20.7239i	−0.309722	+	1.05482i
$387$	−16.8002	+	32.4801i	−0.854003	+	1.65106i
$388$	14.9863	−	2.15471i	0.760815	−	0.109389i
$389$	−25.0703	−	16.1117i	−1.27112	−	0.816896i	−0.281351	−	0.959605i	$-0.590782\pi$
$389$	−25.0703	−	16.1117i	−1.27112	−	0.816896i	−0.989765	+	0.142709i	$0.954419\pi$
$390$	−15.5168	+	5.35869i	−0.785724	+	0.271348i
$391$	0.820764	−	5.52955i	0.0415078	−	0.279641i
$392$			1.00000i			0.0505076i
$393$	31.7262	+	7.71938i	1.60038	+	0.389391i
$394$	2.46766	+	17.1630i	0.124319	+	0.864657i
$395$	20.9098	−	9.54920i	1.05209	−	0.480472i
$396$	−3.22764	+	1.28710i	−0.162195	+	0.0646790i
$397$	−7.86489	+	17.2217i	−0.394728	+	0.864333i	0.603050	+	0.797703i	$0.293952\pi$
$397$	−7.86489	+	17.2217i	−0.394728	+	0.864333i	−0.997778	+	0.0666297i	$0.978775\pi$
$398$	2.58402	−	2.98212i	0.129525	−	0.149480i
$399$	4.02540	−	0.773014i	0.201522	−	0.0386991i
$400$	2.28129	−	0.669847i	0.114064	−	0.0334923i
$401$	5.43209	+	6.26896i	0.271266	+	0.313057i	0.874995	−	0.484132i	$-0.160865\pi$
$401$	5.43209	+	6.26896i	0.271266	+	0.313057i	−0.603729	+	0.797189i	$0.706319\pi$
$402$	7.94294	+	6.25508i	0.396158	+	0.311975i
$403$	−4.48059	+	2.87950i	−0.223194	+	0.143438i
$404$	4.10933	−	3.56076i	0.204447	−	0.177154i
$405$	0.654162	+	14.5598i	0.0325056	+	0.723480i
$406$	2.48827	+	0.357759i	0.123491	+	0.0177553i
$407$	−5.74669	−	4.97953i	−0.284853	−	0.246826i
$408$	0.193267	−	2.00965i	0.00956815	−	0.0994923i
$409$	−0.894294	−	0.262589i	−0.0442200	−	0.0129842i	0.259548	−	0.965730i	$-0.416427\pi$
$409$	−0.894294	−	0.262589i	−0.0442200	−	0.0129842i	−0.303768	+	0.952746i	$0.598245\pi$
$410$	5.37356	+	11.7664i	0.265381	+	0.581103i
$411$	24.9353	−	12.8337i	1.22997	−	0.633041i
$412$	−5.55666	+	8.64633i	−0.273757	+	0.425974i
$413$	−13.1867			−0.648874
$414$	−8.82680	−	11.3617i	−0.433813	−	0.558396i
$415$	23.5309			1.15509
$416$	3.16423	−	4.92363i	0.155139	−	0.241401i
$417$	13.1862	−	6.78671i	0.645733	−	0.332347i
$418$	1.13868	+	2.49337i	0.0556948	+	0.121955i
$419$	4.22665	+	1.24106i	0.206485	+	0.0606295i	0.383339	−	0.923608i	$-0.374774\pi$
$419$	4.22665	+	1.24106i	0.206485	+	0.0606295i	−0.176854	+	0.984237i	$0.556592\pi$
$420$	−0.268503	+	2.79197i	−0.0131016	+	0.136234i
$421$	−18.8085	−	16.2976i	−0.916669	−	0.794298i	0.0623528	−	0.998054i	$-0.480140\pi$
$421$	−18.8085	−	16.2976i	−0.916669	−	0.794298i	−0.979022	+	0.203756i	$0.934685\pi$
$422$	−3.96663	−	0.570315i	−0.193092	−	0.0277625i
$423$	−8.65657	−	6.18195i	−0.420897	−	0.300577i
$424$	−6.99234	+	6.05890i	−0.339578	+	0.294246i
$425$	2.33143	−	1.49832i	0.113091	−	0.0726793i
$426$	−4.27188	−	3.36411i	−0.206973	−	0.162992i
$427$	−1.03345	−	1.19266i	−0.0500120	−	0.0577170i
$428$	2.54995	−	0.748734i	0.123257	−	0.0361914i
$429$	−11.5309	+	2.21433i	−0.556719	+	0.106909i
$430$	−12.9264	+	14.9178i	−0.623365	+	0.719401i
$431$	−6.59219	+	14.4349i	−0.317535	+	0.695304i	−0.999344	−	0.0362261i	$-0.988466\pi$
$431$	−6.59219	+	14.4349i	−0.317535	+	0.695304i	0.681809	+	0.731530i	$0.261194\pi$
$432$	−3.39480	−	3.93387i	−0.163332	−	0.189269i
$433$	33.1847	−	15.1549i	1.59476	−	0.728300i	0.597467	−	0.801894i	$-0.296174\pi$
$433$	33.1847	−	15.1549i	1.59476	−	0.728300i	0.997288	+	0.0735932i	$0.0234466\pi$
$434$	0.129509	+	0.900755i	0.00621663	+	0.0432376i
$435$	6.85112	+	1.66696i	0.328486	+	0.0799247i
$436$			5.82154i			0.278801i
$437$	−8.61114	+	7.39316i	−0.411927	+	0.353663i
$438$	0.0541157	−	0.0186887i	0.00258575	−	0.000892982i
$439$	−25.5951	−	16.4490i	−1.22159	−	0.785066i	−0.239027	−	0.971013i	$-0.576829\pi$
$439$	−25.5951	−	16.4490i	−1.22159	−	0.785066i	−0.982560	+	0.185946i	$0.940465\pi$
$440$	−1.85659	+	0.266937i	−0.0885093	+	0.0127257i
$441$	2.66465	+	1.37828i	0.126888	+	0.0656323i
$442$	1.92200	−	6.54573i	0.0914203	−	0.311349i
$443$	−34.0019	−	15.5282i	−1.61548	−	0.737766i	−0.616704	−	0.787195i	$-0.711532\pi$
$443$	−34.0019	−	15.5282i	−1.61548	−	0.737766i	−0.998778	+	0.0494297i	$0.984260\pi$
$444$	4.23323	−	10.5534i	0.200900	−	0.500844i
$445$	1.83929	−	12.7925i	0.0871906	−	0.606424i
$446$	−7.01261	−	23.8828i	−0.332057	−	1.13088i
$447$	−0.910425	+	1.57445i	−0.0430616	+	0.0744688i
$448$	−0.540641	−	0.841254i	−0.0255429	−	0.0397455i
$449$	2.16768	+	3.37298i	0.102299	+	0.159181i	0.888630	−	0.458625i	$-0.151658\pi$
$449$	2.16768	+	3.37298i	0.102299	+	0.159181i	−0.786330	+	0.617806i	$0.788022\pi$
$450$	1.35935	−	7.00206i	0.0640802	−	0.330081i
$451$	2.60661	+	8.87729i	0.122740	+	0.418015i
$452$	1.21114	−	8.42367i	0.0569673	−	0.396216i
$453$	20.7686	+	8.33076i	0.975793	+	0.391413i
$454$	−18.0164	−	8.22782i	−0.845552	−	0.386151i
$455$	−2.67021	+	9.09390i	−0.125181	+	0.426329i
$456$	−2.96846	+	2.82660i	−0.139011	+	0.132367i
$457$	12.2165	−	1.75647i	0.571465	−	0.0821643i	0.149476	−	0.988765i	$-0.452241\pi$
$457$	12.2165	−	1.75647i	0.571465	−	0.0821643i	0.421989	+	0.906601i	$0.361332\pi$
$458$	1.66633	+	1.07088i	0.0778625	+	0.0500392i
$459$	−5.08862	−	3.28484i	−0.237516	−	0.153323i
$460$	−3.19401	−	7.07909i	−0.148921	−	0.330064i
$461$		−	0.728891i		−	0.0339478i	−0.999856	−	0.0169739i	$-0.994597\pi$
$461$		−	0.728891i		−	0.0339478i	0.999856	−	0.0169739i	$-0.00540323\pi$
$462$	−0.474291	+	1.94931i	−0.0220660	+	0.0906900i
$463$	−3.82012	−	26.5695i	−0.177536	−	1.23479i	−0.862440	−	0.506158i	$-0.831065\pi$
$463$	−3.82012	−	26.5695i	−0.177536	−	1.23479i	0.684904	−	0.728633i	$-0.259844\pi$
$464$	−2.28668	+	1.04429i	−0.106157	+	0.0484801i
$465$	0.119730	+	2.54966i	0.00555234	+	0.118238i
$466$	2.06178	−	4.51467i	0.0955101	−	0.209138i
$467$	−12.0345	+	13.8885i	−0.556888	+	0.642683i	−0.962474	−	0.271374i	$-0.912522\pi$
$467$	−12.0345	+	13.8885i	−0.556888	+	0.642683i	0.405586	+	0.914057i	$0.367067\pi$
$468$	−8.75856	−	15.2177i	−0.404864	−	0.703438i
$469$	5.60069	−	1.64451i	0.258616	−	0.0759364i
$470$	−3.76019	−	4.33949i	−0.173445	−	0.200166i
$471$	10.5071	−	13.3423i	0.484140	−	0.614779i
$472$	11.0933	−	7.12925i	0.510612	−	0.328150i
$473$	−10.6700	+	9.24561i	−0.490607	+	0.425114i
$474$	14.2480	+	20.0371i	0.654433	+	0.920337i
$475$	−5.56938	−	0.800757i	−0.255541	−	0.0367412i
$476$	−0.880919	−	0.763320i	−0.0403768	−	0.0349867i
$477$	6.50743	+	26.9830i	0.297955	+	1.23547i
$478$	12.9344	+	3.79789i	0.591607	+	0.173712i
$479$	1.70988	+	3.74411i	0.0781263	+	0.171073i	0.944665	−	0.328038i	$-0.106387\pi$
$479$	1.70988	+	3.74411i	0.0781263	+	0.171073i	−0.866538	+	0.499111i	$0.833660\pi$
$480$	−1.28358	−	2.49392i	−0.0585869	−	0.113831i
$481$	20.7730	−	32.3234i	0.947165	−	1.47382i
$482$	−13.8946			−0.632882
$483$	−8.29917	+	0.351829i	−0.377625	+	0.0160088i
$484$	9.65842			0.439019
$485$	13.2555	−	20.6260i	0.601902	−	0.936578i
$486$	−15.1614	+	3.62396i	−0.687733	+	0.164386i
$487$	1.62829	+	3.56545i	0.0737848	+	0.161566i	0.942930	−	0.332991i	$-0.108058\pi$
$487$	1.62829	+	3.56545i	0.0737848	+	0.161566i	−0.869145	+	0.494557i	$0.835330\pi$
$488$	1.51419	+	0.444607i	0.0685443	+	0.0201264i
$489$	−10.8298	−	1.04150i	−0.489742	−	0.0470984i
$490$	1.22385	+	1.06047i	0.0552878	+	0.0479072i
$491$	−19.6253	−	2.82169i	−0.885678	−	0.127341i	−0.315561	−	0.948905i	$-0.602193\pi$
$491$	−19.6253	−	2.82169i	−0.885678	−	0.127341i	−0.570116	+	0.821564i	$0.693102\pi$
$492$	−11.2754	+	8.01769i	−0.508333	+	0.361465i
$493$	−2.21450	+	1.91888i	−0.0997362	+	0.0864219i
$494$	−11.6519	+	7.48823i	−0.524245	+	0.336912i
$495$	−1.84760	+	5.31506i	−0.0830435	+	0.238894i
$496$	−0.595935	−	0.687746i	−0.0267583	−	0.0308807i
$497$	−3.01217	+	0.884452i	−0.135114	+	0.0396731i
$498$	4.74640	+	24.7164i	0.212691	+	1.10757i
$499$	26.1285	−	30.1539i	1.16967	−	1.34987i	0.244812	−	0.969571i	$-0.421274\pi$
$499$	26.1285	−	30.1539i	1.16967	−	1.34987i	0.924861	−	0.380304i	$-0.124181\pi$
$500$	4.96303	−	10.8675i	0.221953	−	0.486010i
$501$	−40.2241	+	1.88889i	−1.79708	+	0.0843895i
$502$	−9.49776	+	4.33748i	−0.423906	+	0.193591i
$503$	2.17690	+	15.1407i	0.0970634	+	0.675091i	0.979021	+	0.203761i	$0.0653166\pi$
$503$	2.17690	+	15.1407i	0.0970634	+	0.675091i	−0.881957	+	0.471329i	$0.843774\pi$
$504$	−2.98680	+	0.281135i	−0.133043	+	0.0125228i
$505$		−	8.80528i		−	0.391830i
$506$	−1.54068	−	5.33692i	−0.0684916	−	0.237255i
$507$	−12.0171	−	34.7972i	−0.533700	−	1.54540i
$508$	5.68826	+	3.65562i	0.252376	+	0.162192i
$509$	−13.9859	+	2.01086i	−0.619912	+	0.0891299i	−0.445113	−	0.895474i	$-0.646837\pi$
$509$	−13.9859	+	2.01086i	−0.619912	+	0.0891299i	−0.174799	+	0.984604i	$0.555927\pi$
$510$	−2.25455	−	2.36770i	−0.0998330	−	0.104844i
$511$	0.00931250	−	0.0317155i	0.000411961	−	0.00140301i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	3.44052	+	11.8057i	0.151903	+	0.521236i
$514$	0.0339885	−	0.236395i	0.00149917	−	0.0104270i
$515$	4.68912	+	15.9697i	0.206628	+	0.703709i
$516$	−18.2768	−	10.5686i	−0.804591	−	0.465255i
$517$	−2.22039	−	3.45499i	−0.0976526	−	0.151950i
$518$	−3.54927	−	5.52278i	−0.155946	−	0.242657i
$519$	−8.64706	−	5.00017i	−0.379564	−	0.219483i
$520$	−2.67021	−	9.09390i	−0.117096	−	0.398794i
$521$	−5.72412	+	39.8121i	−0.250778	+	1.74420i	0.342787	+	0.939413i	$0.388629\pi$
$521$	−5.72412	+	39.8121i	−0.250778	+	1.74420i	−0.593565	+	0.804786i	$0.702280\pi$
$522$	−0.369014	+	7.53253i	−0.0161513	+	0.329690i
$523$	22.9188	+	10.4667i	1.00217	+	0.457676i	0.847788	−	0.530335i	$-0.177934\pi$
$523$	22.9188	+	10.4667i	1.00217	+	0.457676i	0.154382	+	0.988011i	$0.450661\pi$
$524$	−5.31109	+	18.0879i	−0.232016	+	0.790174i
$525$	−2.83982	−	2.98234i	−0.123940	−	0.130160i
$526$	2.14349	−	0.308188i	0.0934607	−	0.0134376i
$527$	−0.892349	−	0.573478i	−0.0388713	−	0.0249811i
$528$	−0.654876	−	1.89628i	−0.0284998	−	0.0825251i
$529$	19.4614	−	12.2579i	0.846146	−	0.532952i
$530$			14.9829i			0.650814i
$531$	−3.70724	−	39.3859i	−0.160880	−	1.70920i
$532$	0.336792	+	2.34244i	0.0146018	+	0.101558i
$533$	−42.5260	+	19.4210i	−1.84200	+	0.841215i
$534$	13.8080	−	0.648415i	0.597532	−	0.0280596i
$535$	1.78781	−	3.91477i	0.0772940	−	0.169250i
$536$	−3.82251	+	4.41141i	−0.165107	+	0.190544i
$537$	0.0251859	+	0.131153i	0.00108685	+	0.00565967i
$538$	21.4928	−	6.31084i	0.926618	−	0.272080i
$539$	0.758504	+	0.875360i	0.0326711	+	0.0377044i
$540$	−8.41455	−	0.0170436i	−0.362104	−	0.000733441i
$541$	7.38511	−	4.74612i	0.317511	−	0.204052i	−0.372171	−	0.928164i	$-0.621387\pi$
$541$	7.38511	−	4.74612i	0.317511	−	0.204052i	0.689682	+	0.724112i	$0.257750\pi$
$542$	13.4070	−	11.6172i	0.575880	−	0.499003i
$543$	−21.9134	+	15.5822i	−0.940393	+	0.668694i
$544$	1.15376	+	0.165885i	0.0494670	+	0.00711228i
$545$	7.12468	+	6.17357i	0.305188	+	0.264447i
$546$	−10.0907	−	0.970418i	−0.431841	−	0.0415301i
$547$	14.8115	+	4.34906i	0.633295	+	0.185952i	0.582596	−	0.812762i	$-0.302037\pi$
$547$	14.8115	+	4.34906i	0.633295	+	0.185952i	0.0506990	+	0.998714i	$0.483855\pi$
$548$	6.72610	+	14.7281i	0.287325	+	0.629153i
$549$	3.27170	−	3.42200i	0.139633	−	0.146047i
$550$	1.48887	−	2.31672i	0.0634855	−	0.0987854i
$551$	5.94911			0.253441
$552$	6.79149	−	4.78285i	0.289065	−	0.203571i
$553$	14.1950			0.603632
$554$	−11.2764	+	17.5465i	−0.479089	+	0.745478i
$555$	−8.42659	−	16.3724i	−0.357689	−	0.694972i
$556$	3.55689	+	7.78849i	0.150846	+	0.330306i
$557$	−16.8516	−	4.94807i	−0.714025	−	0.209657i	−0.0955084	−	0.995429i	$-0.530448\pi$
$557$	−16.8516	−	4.94807i	−0.714025	−	0.209657i	−0.618516	+	0.785772i	$0.712266\pi$
$558$	−2.65396	+	0.640051i	−0.112351	+	0.0270955i
$559$	−53.9156	−	46.7181i	−2.28039	−	1.97597i
$560$	−1.60290	−	0.230462i	−0.0677349	−	0.00973881i
$561$	−1.35515	−	1.90576i	−0.0572143	−	0.0804611i
$562$	−15.0683	+	13.0568i	−0.635619	+	0.550767i
$563$	−5.32418	+	3.42164i	−0.224387	+	0.144205i	−0.648005	−	0.761636i	$-0.724396\pi$
$563$	−5.32418	+	3.42164i	−0.224387	+	0.144205i	0.423618	+	0.905841i	$0.360760\pi$
$564$	3.79966	−	4.82495i	0.159995	−	0.203167i
$565$	−9.02491	−	10.4153i	−0.379681	−	0.438175i
$566$	24.1367	−	7.08717i	1.01454	−	0.297896i
$567$	−3.36751	+	8.34625i	−0.141422	+	0.350509i
$568$	2.05583	−	2.37255i	0.0862605	−	0.0995499i
$569$	−8.09161	+	17.7181i	−0.339218	+	0.742783i	−0.999969	−	0.00782135i	$-0.997510\pi$
$569$	−8.09161	+	17.7181i	−0.339218	+	0.742783i	0.660752	+	0.750605i	$0.270238\pi$
$570$	0.311361	+	6.63046i	0.0130415	+	0.277720i
$571$	8.14590	−	3.72011i	0.340895	−	0.155682i	−0.237609	−	0.971361i	$-0.576364\pi$
$571$	8.14590	−	3.72011i	0.340895	−	0.155682i	0.578504	+	0.815679i	$0.303637\pi$
$572$	−0.964756	−	6.71003i	−0.0403385	−	0.280560i
$573$	4.09782	−	16.8418i	0.171189	−	0.703576i
$574$			7.98785i			0.333406i
$575$	10.9259	+	3.26229i	0.455642	+	0.136047i
$576$	2.36066	−	1.85129i	0.0983609	−	0.0771371i
$577$	17.0015	+	10.9262i	0.707784	+	0.454865i	0.844368	−	0.535763i	$-0.179976\pi$
$577$	17.0015	+	10.9262i	0.707784	+	0.454865i	−0.136584	+	0.990628i	$0.543612\pi$
$578$	−15.4821	+	2.22599i	−0.643971	+	0.0925891i
$579$	−27.0924	+	25.7977i	−1.12592	+	1.07211i
$580$	−1.14690	+	3.90600i	−0.0476226	+	0.162188i
$581$	13.2177	+	6.03630i	0.548361	+	0.250428i
$582$	24.3389	+	9.76291i	1.00888	+	0.404685i
$583$	−1.52512	+	10.6074i	−0.0631640	+	0.439315i
$584$	0.00931250	+	0.0317155i	0.000385354	+	0.00131239i
$585$	−27.9123	−	5.41876i	−1.15403	−	0.224038i
$586$	6.10661	+	9.50206i	0.252262	+	0.392527i
$587$	16.5217	+	25.7082i	0.681923	+	1.06109i	0.993823	+	0.110978i	$0.0353982\pi$
$587$	16.5217	+	25.7082i	0.681923	+	1.06109i	−0.311900	+	0.950115i	$0.600965\pi$
$588$	−0.867038	+	1.49941i	−0.0357560	+	0.0618348i
$589$	0.606735	+	2.06635i	0.0250001	+	0.0851424i
$590$	3.03903	−	21.1369i	0.125115	−	0.870193i
$591$	−11.1809	+	27.8740i	−0.459920	+	1.14658i
$592$	5.97168	+	2.72717i	0.245435	+	0.112086i
$593$	1.39535	−	4.75212i	0.0573001	−	0.195146i	−0.925869	−	0.377845i	$-0.876665\pi$
$593$	1.39535	−	4.75212i	0.0573001	−	0.195146i	0.983169	+	0.182699i	$0.0584834\pi$
$594$	−5.95553	−	0.868591i	−0.244358	−	0.0356387i
$595$	−1.86838	+	0.268632i	−0.0765960	+	0.0110128i
$596$	−0.883351	−	0.567695i	−0.0361835	−	0.0232537i
$597$	6.46013	−	2.23099i	0.264395	−	0.0913083i
$598$	25.5851	−	11.5437i	1.04625	−	0.472057i
$599$		−	5.29081i		−	0.216177i	−0.994141	−	0.108088i	$-0.965527\pi$
$599$		−	5.29081i		−	0.216177i	0.994141	−	0.108088i	$-0.0344730\pi$
$600$	4.00138	+	0.973585i	0.163356	+	0.0397465i
$601$	2.66602	+	18.5426i	0.108749	+	0.756368i	0.969100	+	0.246667i	$0.0793352\pi$
$601$	2.66602	+	18.5426i	0.108749	+	0.756368i	−0.860351	+	0.509702i	$0.829756\pi$
$602$	−11.0878	+	5.06361i	−0.451903	+	0.206377i
$603$	6.48637	+	16.2658i	0.264145	+	0.662394i
$604$	−5.36693	+	11.7519i	−0.218377	+	0.478179i
$605$	10.2425	−	11.8204i	0.416415	−	0.480569i
$606$	9.24891	−	1.77611i	0.375711	−	0.0721493i
$607$	18.1043	−	5.31590i	0.734831	−	0.215766i	0.107157	−	0.994242i	$-0.465825\pi$
$607$	18.1043	−	5.31590i	0.734831	−	0.215766i	0.627674	+	0.778476i	$0.284007\pi$
$608$	−1.54975	−	1.78850i	−0.0628506	−	0.0725334i
$609$	3.42076	+	2.69385i	0.138616	+	0.109160i
$610$	2.14989	−	1.38165i	0.0870465	−	0.0559414i
$611$	15.6837	−	13.5900i	0.634494	−	0.549792i
$612$	2.03223	−	2.84572i	0.0821479	−	0.115032i
$613$	−28.3426	−	4.07505i	−1.14475	−	0.164590i	−0.456265	−	0.889844i	$-0.650813\pi$
$613$	−28.3426	−	4.07505i	−1.14475	−	0.164590i	−0.688481	+	0.725254i	$0.741722\pi$
$614$	8.20274	+	7.10772i	0.331036	+	0.286844i
$615$	−2.14477	+	22.3019i	−0.0864853	+	0.899298i
$616$	−1.11135	−	0.326322i	−0.0447775	−	0.0131479i
$617$	−2.87023	−	6.28494i	−0.115551	−	0.253022i	0.843016	−	0.537889i	$-0.180778\pi$
$617$	−2.87023	−	6.28494i	−0.115551	−	0.253022i	−0.958567	+	0.284867i	$0.908051\pi$
$618$	−15.8284	+	8.14660i	−0.636713	+	0.327705i
$619$	−4.68286	+	7.28667i	−0.188220	+	0.292876i	−0.922520	−	0.385949i	$-0.873874\pi$
$619$	−4.68286	+	7.28667i	−0.188220	+	0.292876i	0.734300	+	0.678825i	$0.237510\pi$
$620$	−1.47367			−0.0591839
$621$	−3.38403	−	24.6890i	−0.135796	−	0.990737i
$622$	−18.7297			−0.750993
$623$	4.31478	−	6.71393i	0.172868	−	0.268988i
$624$	9.01346	−	4.63906i	0.360827	−	0.185711i
$625$	−3.09860	−	6.78498i	−0.123944	−	0.271399i
$626$	−5.14247	−	1.50997i	−0.205534	−	0.0603503i
$627$	−0.454486	+	4.72588i	−0.0181504	+	0.188733i
$628$	7.41013	+	6.42091i	0.295696	+	0.256222i
$629$	7.57435	+	1.08903i	0.302009	+	0.0434224i
$630$	−2.82334	+	3.95352i	−0.112485	+	0.157512i
$631$	−11.7112	+	10.1478i	−0.466216	+	0.403978i	−0.856039	−	0.516912i	$-0.827082\pi$
$631$	−11.7112	+	10.1478i	−0.466216	+	0.403978i	0.389823	+	0.920890i	$0.372536\pi$
$632$	−11.9416	+	7.67439i	−0.475011	+	0.305271i
$633$	−5.45314	−	4.29436i	−0.216743	−	0.170685i
$634$	2.78113	+	3.20959i	0.110453	+	0.127469i
$635$	10.5062	−	3.08489i	0.416924	−	0.122420i
$636$	−15.7377	+	3.02218i	−0.624041	+	0.119837i
$637$	−3.83272	+	4.42320i	−0.151858	+	0.175254i
$638$	−1.20957	+	2.64859i	−0.0478874	+	0.104859i
$639$	−3.48851	−	8.74808i	−0.138003	−	0.346069i
$640$	1.47304	−	0.672716i	0.0582271	−	0.0265914i
$641$	−6.10577	−	42.4666i	−0.241164	−	1.67733i	−0.646308	−	0.763077i	$-0.723688\pi$
$641$	−6.10577	−	42.4666i	−0.241164	−	1.67733i	0.405145	−	0.914253i	$-0.367221\pi$
$642$	4.47262	+	1.08824i	0.176520	+	0.0429496i
$643$			35.9678i			1.41843i	0.704991	+	0.709217i	$0.250951\pi$
$643$			35.9678i			1.41843i	−0.704991	+	0.709217i	$0.749049\pi$
$644$	0.0218537	−	4.79578i	0.000861156	−	0.188980i
$645$	−32.3163	+	11.1604i	−1.27245	+	0.439439i
$646$	−2.32058	−	1.49135i	−0.0913020	−	0.0586763i
$647$	13.1583	−	1.89188i	0.517307	−	0.0743776i	0.121284	−	0.992618i	$-0.461299\pi$
$647$	13.1583	−	1.89188i	0.517307	−	0.0743776i	0.396024	+	0.918240i	$0.370390\pi$
$648$	−1.67939	−	8.84193i	−0.0659726	−	0.347344i
$649$	4.30310	−	14.6550i	0.168911	−	0.575259i
$650$	12.6579	+	5.78068i	0.496485	+	0.226737i
$651$	−0.586801	+	1.46289i	−0.0229985	+	0.0573354i
$652$	0.893944	−	6.21752i	0.0350095	−	0.243497i
$653$	9.70914	+	33.0663i	0.379948	+	1.29398i	0.898513	+	0.438946i	$0.144648\pi$
$653$	9.70914	+	33.0663i	0.379948	+	1.29398i	−0.518565	+	0.855038i	$0.673534\pi$
$654$	−5.04749	+	8.72890i	−0.197373	+	0.341327i
$655$	16.5046	+	25.6817i	0.644888	+	1.00347i
$656$	−4.31856	−	6.71981i	−0.168611	−	0.262364i
$657$	0.0973457	+	0.0188982i	0.00379782	+	0.000737290i
$658$	−0.998961	−	3.40215i	−0.0389436	−	0.132630i
$659$	2.05545	−	14.2960i	0.0800690	−	0.556892i	−0.909815	−	0.415014i	$-0.863777\pi$
$659$	2.05545	−	14.2960i	0.0800690	−	0.556892i	0.989884	−	0.141878i	$-0.0453141\pi$
$660$	−3.01524	−	1.20948i	−0.117368	−	0.0470790i
$661$	17.0371	+	7.78057i	0.662665	+	0.302629i	0.718209	−	0.695827i	$-0.244962\pi$
$661$	17.0371	+	7.78057i	0.662665	+	0.302629i	−0.0555439	+	0.998456i	$0.517689\pi$
$662$	−6.85642	+	23.3508i	−0.266482	+	0.907556i
$663$	8.55728	−	8.14832i	0.332337	−	0.316455i
$664$	−14.3829	+	2.06795i	−0.558164	+	0.0802519i
$665$	3.22395	+	2.07191i	0.125019	+	0.0803451i
$666$	15.4976	−	12.1536i	0.600520	−	0.470943i
$667$	−11.9254	−	1.77011i	−0.461752	−	0.0685390i
$668$		−	23.2490i		−	0.899530i
$669$	10.1925	−	41.8904i	0.394063	−	1.61958i
$670$	1.34524	+	9.35634i	0.0519711	+	0.361467i
$671$	1.66270	−	0.759330i	0.0641879	−	0.0293136i
$672$	−0.0812462	−	1.73014i	−0.00313414	−	0.0667418i
$673$	−20.3246	+	44.5047i	−0.783456	+	1.71553i	−0.0889563	+	0.996036i	$0.528353\pi$
$673$	−20.3246	+	44.5047i	−0.783456	+	1.71553i	−0.694499	+	0.719493i	$0.744374\pi$
$674$	7.98169	−	9.21137i	0.307443	−	0.354809i
$675$	8.10928	−	9.32040i	0.312126	−	0.358742i
$676$	20.3935	−	5.98808i	0.784366	−	0.230311i
$677$	7.21857	+	8.33067i	0.277432	+	0.320174i	0.877316	−	0.479913i	$-0.159332\pi$
$677$	7.21857	+	8.33067i	0.277432	+	0.320174i	−0.599884	+	0.800087i	$0.704786\pi$
$678$	9.11964	−	11.5805i	0.350238	−	0.444745i
$679$	12.7369	−	8.18553i	0.488799	−	0.314132i
$680$	1.42655	−	1.23611i	0.0547055	−	0.0474026i
$681$	−19.8802	−	27.9578i	−0.761813	−	1.07135i
$682$	−1.04332	−	0.150006i	−0.0399506	−	0.00574403i
$683$	−21.4702	−	18.6041i	−0.821536	−	0.711865i	0.138918	−	0.990304i	$-0.455637\pi$
$683$	−21.4702	−	18.6041i	−0.821536	−	0.711865i	−0.960454	+	0.278439i	$0.910183\pi$
$684$	−6.90172	+	1.66447i	−0.263894	+	0.0636427i
$685$	25.1578	+	7.38699i	0.961229	+	0.282242i
$686$	0.415415	+	0.909632i	0.0158606	+	0.0347299i
$687$	1.57002	+	3.05047i	0.0599000	+	0.116383i
$688$	6.59002	−	10.2543i	0.251242	−	0.390940i
$689$	−54.1506			−2.06297
$690$	1.34870	−	13.3838i	0.0513441	−	0.509514i
$691$	32.5159			1.23696			0.618481	−	0.785800i	$-0.287748\pi$
$691$	32.5159			1.23696			0.618481	+	0.785800i	$0.287748\pi$
$692$	3.11785	−	4.85147i	0.118523	−	0.184425i
$693$	−2.40128	+	2.51159i	−0.0912171	+	0.0954075i
$694$	9.35747	+	20.4900i	0.355205	+	0.777790i
$695$	13.3039	+	3.90638i	0.504646	+	0.148177i
$696$	−4.33413	−	0.416812i	−0.164285	−	0.0157992i
$697$	−7.03665	−	6.09729i	−0.266532	−	0.230951i
$698$	22.2702	+	3.20198i	0.842941	+	0.121197i
$699$	7.00585	−	4.98172i	0.264986	−	0.188426i
$700$	1.79687	−	1.55700i	0.0679152	−	0.0588489i
$701$	17.1475	−	11.0201i	0.647653	−	0.416222i	−0.175155	−	0.984541i	$-0.556043\pi$
$701$	17.1475	−	11.0201i	0.647653	−	0.416222i	0.822808	+	0.568319i	$0.192406\pi$
$702$	0.0615986	−	30.4116i	0.00232489	−	1.14781i
$703$	−10.1740	−	11.7414i	−0.383720	−	0.442836i
$704$	1.11135	−	0.326322i	0.0418856	−	0.0122987i
$705$	−1.87558	−	9.76693i	−0.0706386	−	0.367844i
$706$	6.44243	−	7.43496i	0.242464	−	0.279819i
$707$	2.25879	−	4.94606i	0.0849505	−	0.186016i
$708$	22.8148	−	1.07137i	0.857434	−	0.0402644i
$709$	−18.7268	+	8.55222i	−0.703298	+	0.321185i	−0.734767	−	0.678319i	$-0.762709\pi$
$709$	−18.7268	+	8.55222i	−0.703298	+	0.321185i	0.0314693	+	0.999505i	$0.489981\pi$
$710$	−0.723498	−	5.03204i	−0.0271524	−	0.188849i
$711$	3.99071	+	42.3976i	0.149663	+	1.59003i
$712$			7.98086i			0.299095i
$713$	−0.601412	−	4.32266i	−0.0225231	−	0.161885i
$714$	−0.659035	−	1.90832i	−0.0246638	−	0.0714172i
$715$	−9.23515	−	5.93507i	−0.345375	−	0.221959i
$716$	−0.0763200	+	0.0109732i	−0.00285221	+	0.000410086i
$717$	16.1012	+	16.9093i	0.601309	+	0.631488i
$718$	3.95492	−	13.4692i	0.147596	−	0.502667i
$719$	−24.6525	−	11.2584i	−0.919385	−	0.419869i	−0.101227	−	0.994863i	$-0.532277\pi$
$719$	−24.6525	−	11.2584i	−0.919385	−	0.419869i	−0.818157	+	0.574994i	$0.805004\pi$
$720$	0.237713	−	4.85233i	0.00885902	−	0.180836i
$721$	−1.46270	+	10.1733i	−0.0544738	+	0.378874i
$722$	−3.77509	−	12.8568i	−0.140494	−	0.478479i
$723$	−20.8338	−	12.0471i	−0.774816	−	0.448038i
$724$	−8.39300	−	13.0598i	−0.311923	−	0.485362i
$725$	−3.23138	−	5.02812i	−0.120010	−	0.186740i
$726$	14.4820	+	8.37421i	0.537476	+	0.310796i
$727$	3.64606	+	12.4173i	0.135225	+	0.460533i	0.999065	−	0.0432326i	$-0.0137657\pi$
$727$	3.64606	+	12.4173i	0.135225	+	0.460533i	−0.863840	+	0.503766i	$0.831947\pi$
$728$	0.832931	−	5.79316i	0.0308705	−	0.214709i
$729$	−25.8753	−	7.71166i	−0.958344	−	0.285617i
$730$	0.0486905	+	0.0222362i	0.00180212	+	0.000823000i
$731$	4.00288	−	13.6326i	0.148052	−	0.504219i
$732$	1.88491	+	1.97951i	0.0696684	+	0.0731650i
$733$	−9.45652	+	1.35964i	−0.349285	+	0.0502195i	−0.314724	−	0.949183i	$-0.601912\pi$
$733$	−9.45652	+	1.35964i	−0.349285	+	0.0502195i	−0.0345601	+	0.999403i	$0.511003\pi$
$734$	−13.0041	−	8.35720i	−0.479989	−	0.308470i
$735$	0.915588	+	2.65121i	0.0337720	+	0.0977913i
$736$	2.57441	+	4.04628i	0.0948940	+	0.149148i
$737$			6.76096i			0.249043i
$738$	−23.8581	+	2.24567i	−0.878229	+	0.0826641i
$739$	4.65579	+	32.3817i	0.171266	+	1.19118i	0.876214	+	0.481922i	$0.160061\pi$
$739$	4.65579	+	32.3817i	0.171266	+	1.19118i	−0.704948	+	0.709259i	$0.749030\pi$
$740$	9.67044	−	4.41634i	0.355492	−	0.162348i
$741$	−23.9636	+	1.12531i	−0.880327	+	0.0413394i
$742$	−3.84350	+	8.41609i	−0.141099	+	0.308965i
$743$	14.9771	−	17.2845i	0.549456	−	0.634106i	−0.411300	−	0.911500i	$-0.634925\pi$
$743$	14.9771	−	17.2845i	0.549456	−	0.634106i	0.960756	+	0.277394i	$0.0894707\pi$
$744$	−0.297252	−	1.54791i	−0.0108978	−	0.0567493i
$745$	−1.63154	+	0.479063i	−0.0597750	+	0.0175515i
$746$	24.5573	+	28.3406i	0.899106	+	1.03762i
$747$	−14.3133	+	41.1755i	−0.523695	+	1.50653i
$748$	1.13578	−	0.729920i	0.0415282	−	0.0266885i
$749$	2.00849	−	1.74036i	0.0733884	−	0.0635915i
$750$	16.8642	−	11.9918i	0.615793	−	0.437878i
$751$	−11.8983	−	1.71072i	−0.434176	−	0.0624251i	−0.0782381	−	0.996935i	$-0.524929\pi$
$751$	−11.8983	−	1.71072i	−0.434176	−	0.0624251i	−0.355938	+	0.934510i	$0.615839\pi$
$752$	2.67972	+	2.32199i	0.0977193	+	0.0846743i
$753$	−18.0018	−	1.73123i	−0.656024	−	0.0630897i
$754$	−14.1169	−	4.14511i	−0.514109	−	0.150956i
$755$	8.69111	+	19.0309i	0.316302	+	0.692605i
$756$	−4.72220	−	2.16813i	−0.171745	−	0.0788541i
$757$	14.3425	−	22.3173i	0.521286	−	0.811136i	−0.476393	−	0.879232i	$-0.658056\pi$
$757$	14.3425	−	22.3173i	0.521286	−	0.811136i	0.997679	+	0.0680960i	$0.0216924\pi$
$758$	0.130417			0.00473697
$759$	2.31719	−	9.33809i	0.0841088	−	0.338951i
$760$	−3.83232			−0.139013
$761$	−23.6578	+	36.8122i	−0.857594	+	1.33444i	0.0835741	+	0.996502i	$0.473366\pi$
$761$	−23.6578	+	36.8122i	−0.857594	+	1.33444i	−0.941168	+	0.337940i	$0.890270\pi$
$762$	5.35950	+	10.4132i	0.194154	+	0.377232i
$763$	2.41835	+	5.29546i	0.0875503	+	0.191708i
$764$	9.60194	+	2.81938i	0.347386	+	0.102002i
$765$	−1.32762	−	5.50494i	−0.0480001	−	0.199032i
$766$	2.50483	+	2.17045i	0.0905032	+	0.0784215i
$767$	76.3925	+	10.9836i	2.75837	+	0.396594i
$768$	1.00374	+	1.41156i	0.0362192	+	0.0509355i
$769$	11.6104	−	10.0604i	0.418680	−	0.362788i	−0.419897	−	0.907572i	$-0.637934\pi$
$769$	11.6104	−	10.0604i	0.418680	−	0.362788i	0.838577	+	0.544784i	$0.183388\pi$
$770$	−1.57792	+	1.01407i	−0.0568643	+	0.0365445i
$771$	0.255927	−	0.324986i	0.00921698	−	0.0117041i
$772$	−14.1442	−	16.3233i	−0.509060	−	0.587487i
$773$	−39.3646	+	11.5585i	−1.41585	+	0.415730i	−0.898095	−	0.439801i	$-0.855049\pi$
$773$	−39.3646	+	11.5585i	−1.41585	+	0.415730i	−0.517751	+	0.855531i	$0.673231\pi$
$774$	−18.2411	−	31.6933i	−0.655664	−	1.13919i
$775$	1.41689	−	1.63518i	0.0508963	−	0.0587375i
$776$	−6.28956	+	13.7722i	−0.225782	+	0.494394i
$777$	−0.533376	−	11.3583i	−0.0191348	−	0.407477i
$778$	27.1081	−	12.3798i	0.971871	−	0.443839i
$779$	2.69025	+	18.7111i	0.0963881	+	0.670394i
$780$	3.88100	−	15.9507i	0.138962	−	0.571127i
$781$		−	3.63619i		−	0.130113i
$782$	4.20801	+	3.67997i	0.150478	+	0.131595i
$783$	−7.08430	+	10.9744i	−0.253172	+	0.392195i
$784$	−0.841254	−	0.540641i	−0.0300448	−	0.0193086i
$785$	15.7164	−	2.25968i	0.560944	−	0.0806516i
$786$	−23.6464	+	22.5164i	−0.843440	+	0.803132i
$787$	−5.37326	+	18.2997i	−0.191536	+	0.652312i	0.806589	+	0.591112i	$0.201311\pi$
$787$	−5.37326	+	18.2997i	−0.191536	+	0.652312i	−0.998126	+	0.0612002i	$0.980507\pi$
$788$	−15.7725	−	7.20307i	−0.561873	−	0.256599i
$789$	3.48119	+	1.39639i	0.123934	+	0.0497127i
$790$	−3.27141	+	22.7532i	−0.116392	+	0.809521i
$791$	−2.39763	−	8.16556i	−0.0852498	−	0.290334i
$792$	0.662217	−	3.41112i	0.0235309	−	0.121209i
$793$	4.99352	+	7.77007i	0.177325	+	0.275923i
$794$	−10.2357	−	15.9271i	−0.363253	−	0.565233i
$795$	−12.9907	+	22.4655i	−0.460733	+	0.796770i
$796$	1.11169	+	3.78607i	0.0394028	+	0.134194i
$797$	−1.55421	+	10.8098i	−0.0550529	+	0.382902i	0.943603	+	0.331078i	$0.107412\pi$
$797$	−1.55421	+	10.8098i	−0.0550529	+	0.382902i	−0.998656	+	0.0518234i	$0.983497\pi$
$798$	−1.52599	+	3.80430i	−0.0540196	+	0.134671i
$799$	3.75954	+	1.71693i	0.133003	+	0.0607405i
$800$	−0.669847	+	2.28129i	−0.0236827	+	0.0806557i
$801$	21.2662	+	10.9999i	0.751404	+	0.388661i
$802$	−8.21060	+	1.18051i	−0.289926	+	0.0416851i
$803$	0.0322081	+	0.0206989i	0.00113660	+	0.000730448i
$804$	−9.55639	+	3.30027i	−0.337028	+	0.116392i
$805$	−5.84613	−	5.11253i	−0.206049	−	0.180193i
$806$		−	5.32609i		−	0.187604i
$807$	37.6983	+	9.17246i	1.32704	+	0.322886i
$808$	0.773827	+	5.38208i	0.0272231	+	0.189341i
$809$	44.3304	−	20.2450i	1.55857	−	0.711777i	0.565015	−	0.825081i	$-0.308871\pi$
$809$	44.3304	−	20.2450i	1.55857	−	0.711777i	0.993560	+	0.113304i	$0.0361433\pi$
$810$	−12.6021	−	7.32129i	−0.442793	−	0.257244i
$811$	17.5182	−	38.3596i	0.615149	−	1.34699i	−0.303847	−	0.952721i	$-0.598271\pi$
$811$	17.5182	−	38.3596i	0.615149	−	1.34699i	0.918996	−	0.394267i	$-0.129001\pi$
$812$	−1.64623	+	1.89985i	−0.0577712	+	0.0666715i
$813$	30.1753	−	5.79468i	1.05829	−	0.203228i
$814$	7.29594	−	2.14228i	0.255723	−	0.0750869i
$815$	−6.66129	−	7.68754i	−0.233335	−	0.269283i
$816$	1.58613	+	1.24908i	0.0555258	+	0.0437267i
$817$	−24.2670	+	15.5955i	−0.848996	+	0.545617i
$818$	0.704396	−	0.610362i	0.0246286	−	0.0213408i
$819$	−14.2887	−	10.2041i	−0.499288	−	0.356559i
$820$	−12.8037	−	1.84090i	−0.447126	−	0.0642869i
$821$	−10.6200	−	9.20227i	−0.370640	−	0.321161i	0.449547	−	0.893257i	$-0.351585\pi$
$821$	−10.6200	−	9.20227i	−0.370640	−	0.321161i	−0.820187	+	0.572095i	$0.806131\pi$
$822$	−2.68461	+	27.9153i	−0.0936365	+	0.973658i
$823$	51.9413	+	15.2514i	1.81056	+	0.531629i	0.998640	−	0.0521384i	$-0.0166037\pi$
$823$	51.9413	+	15.2514i	1.81056	+	0.531629i	0.811921	+	0.583767i	$0.198422\pi$
$824$	−4.26960	−	9.34912i	−0.148739	−	0.325692i
$825$	4.24112	−	2.18282i	0.147657	−	0.0759962i
$826$	7.12925	−	11.0933i	0.248058	−	0.385986i
$827$	49.3450			1.71589			0.857947	−	0.513738i	$-0.171740\pi$
$827$	49.3450			1.71589			0.857947	+	0.513738i	$0.171740\pi$
$828$	14.3302	−	1.28299i	0.498008	−	0.0445870i
$829$	49.8378			1.73094			0.865469	−	0.500963i	$-0.167021\pi$
$829$	49.8378			1.73094			0.865469	+	0.500963i	$0.167021\pi$
$830$	−12.7218	+	19.7955i	−0.441579	+	0.687110i
$831$	−32.1215	+	16.5323i	−1.11428	+	0.573500i
$832$	2.43131	+	5.32383i	0.0842906	+	0.184571i
$833$	−1.11841	−	0.328394i	−0.0387505	−	0.0113782i
$834$	−1.41967	+	14.7621i	−0.0491592	+	0.511171i
$835$	−28.4532	−	24.6549i	−0.984665	−	0.853217i
$836$	−2.71317	−	0.390095i	−0.0938371	−	0.0134917i
$837$	−4.53434	−	1.34139i	−0.156730	−	0.0463651i
$838$	−3.32914	+	2.88472i	−0.115003	+	0.0996509i
$839$	21.0003	−	13.4961i	0.725011	−	0.465937i	−0.125365	−	0.992111i	$-0.540010\pi$
$839$	21.0003	−	13.4961i	0.725011	−	0.465937i	0.850377	+	0.526174i	$0.176374\pi$
$840$	−2.20359	−	1.73533i	−0.0760312	−	0.0598747i
$841$	−14.8526	−	17.1408i	−0.512158	−	0.591062i
$842$	23.8791	−	7.01153i	0.822927	−	0.241633i
$843$	−33.9144	+	6.51272i	−1.16807	+	0.224310i
$844$	2.62430	−	3.02860i	0.0903322	−	0.104249i
$845$	14.2982	−	31.3088i	0.491874	−	1.07705i
$846$	9.88069	−	3.94016i	0.339705	−	0.135465i
$847$	8.78561	−	4.01225i	0.301877	−	0.137863i
$848$	−1.31672	−	9.15802i	−0.0452165	−	0.314488i
$849$	42.3358	+	10.3008i	1.45296	+	0.353523i
$850$			2.77138i			0.0950576i
$851$	16.9009	+	26.5636i	0.579354	+	0.910589i
$852$	5.13962	−	1.77496i	0.176081	−	0.0608090i
$853$	−42.1606	−	27.0950i	−1.44355	−	0.927714i	−0.999497	−	0.0317132i	$-0.989904\pi$
$853$	−42.1606	−	27.0950i	−1.44355	−	0.927714i	−0.444053	−	0.896000i	$-0.646460\pi$
$854$	1.56206	−	0.224590i	0.0534524	−	0.00768530i
$855$	−5.28200	+	10.2118i	−0.180641	+	0.349235i
$856$	−0.748734	+	2.54995i	−0.0255912	+	0.0871557i
$857$	−15.3871	−	7.02703i	−0.525612	−	0.240039i	0.134894	−	0.990860i	$-0.456931\pi$
$857$	−15.3871	−	7.02703i	−0.525612	−	0.240039i	−0.660506	+	0.750821i	$0.729658\pi$
$858$	4.37128	−	10.8976i	0.149233	−	0.372038i
$859$	−4.35769	+	30.3084i	−0.148683	+	1.03411i	0.769697	+	0.638409i	$0.220407\pi$
$859$	−4.35769	+	30.3084i	−0.148683	+	1.03411i	−0.918380	+	0.395701i	$0.870502\pi$
$860$	−5.56115	−	18.9395i	−0.189634	−	0.645833i
$861$	−6.92577	+	11.9771i	−0.236030	+	0.408179i
$862$	−8.57939	−	13.3498i	−0.292215	−	0.454696i
$863$	−4.99946	−	7.77931i	−0.170184	−	0.264811i	0.745677	−	0.666308i	$-0.232126\pi$
$863$	−4.99946	−	7.77931i	−0.170184	−	0.264811i	−0.915860	+	0.401497i	$0.868490\pi$
$864$	5.14475	−	0.729070i	0.175028	−	0.0248035i
$865$	−2.63108	−	8.96062i	−0.0894593	−	0.304670i
$866$	−5.19185	+	36.1101i	−0.176426	+	1.22707i
$867$	−25.1441	−	10.0859i	−0.853940	−	0.342535i
$868$	−0.827781	−	0.378035i	−0.0280967	−	0.0128313i
$869$	−4.63213	+	15.7756i	−0.157134	+	0.535150i
$870$	−5.10633	+	4.86230i	−0.173121	+	0.164847i
$871$	−33.8154	+	4.86193i	−1.14579	+	0.164740i
$872$	−4.89739	−	3.14736i	−0.165846	−	0.106583i
$873$	28.0293	+	35.7414i	0.948649	+	1.20966i
$874$	−1.56399	−	11.2412i	−0.0529028	−	0.380239i
$875$		−	11.9472i		−	0.403888i
$876$	−0.0135352	+	0.0556289i	−0.000457312	+	0.00187953i
$877$	5.38538	+	37.4561i	0.181851	+	1.26480i	0.852381	+	0.522921i	$0.175158\pi$
$877$	5.38538	+	37.4561i	0.181851	+	1.26480i	−0.670530	+	0.741883i	$0.733933\pi$
$878$	27.6755	−	12.6390i	0.934003	−	0.426545i
$879$	0.917686	+	19.5422i	0.0309528	+	0.659142i
$880$	0.779185	−	1.70618i	0.0262663	−	0.0575152i
$881$	20.9616	−	24.1910i	0.706215	−	0.815015i	−0.283363	−	0.959013i	$-0.591450\pi$
$881$	20.9616	−	24.1910i	0.706215	−	0.815015i	0.989578	+	0.143997i	$0.0459957\pi$
$882$	−2.60010	+	1.49649i	−0.0875499	+	0.0503895i
$883$	26.9116	−	7.90196i	0.905648	−	0.265922i	0.204440	−	0.978879i	$-0.434463\pi$
$883$	26.9116	−	7.90196i	0.905648	−	0.265922i	0.701208	+	0.712957i	$0.252644\pi$
$884$	4.46751	+	5.15578i	0.150259	+	0.173408i
$885$	22.8833	−	29.0581i	0.769213	−	0.976776i
$886$	31.4460	−	20.2091i	1.05645	−	0.678938i
$887$	20.3236	−	17.6105i	0.682400	−	0.591303i	−0.243122	−	0.969996i	$-0.578172\pi$
$887$	20.3236	−	17.6105i	0.682400	−	0.591303i	0.925523	+	0.378693i	$0.123626\pi$
$888$	6.58946	+	9.26684i	0.221128	+	0.310975i
$889$	6.69282	+	0.962283i	0.224470	+	0.0322739i
$890$	9.76736	+	8.46347i	0.327403	+	0.283696i
$891$	−8.17670	−	6.46605i	−0.273930	−	0.216621i
$892$	23.8828	+	7.01261i	0.799654	+	0.234800i
$893$	−3.48583	−	7.63289i	−0.116649	−	0.255425i
$894$	−0.832296	−	1.61711i	−0.0278361	−	0.0540842i
$895$	−0.0675056	+	0.105041i	−0.00225646	+	0.00351113i
$896$	1.00000			0.0334077
$897$	48.3715	+	4.87443i	1.61508	+	0.162753i
$898$	−4.00947			−0.133798
$899$	−1.23680	+	1.92450i	−0.0412495	+	0.0641855i
$900$	5.15559	+	4.92916i	0.171853	+	0.164305i
$901$	−4.48007	−	9.80999i	−0.149253	−	0.326818i
$902$	−8.87729	−	2.60661i	−0.295581	−	0.0867905i
$903$	−21.0155	−	2.02105i	−0.699352	−	0.0672565i
$904$	6.43165	+	5.57305i	0.213913	+	0.185357i
$905$	−24.8837	−	3.57774i	−0.827162	−	0.118928i
$906$	−18.2366	+	12.9677i	−0.605871	+	0.430823i
$907$	1.99153	−	1.72567i	0.0661278	−	0.0573001i	−0.621170	−	0.783676i	$-0.713342\pi$
$907$	1.99153	−	1.72567i	0.0661278	−	0.0573001i	0.687298	+	0.726376i	$0.258797\pi$
$908$	16.6621	−	10.7081i	0.552951	−	0.355360i
$909$	15.4079	+	5.35604i	0.511048	+	0.177648i
$910$	−6.20665	−	7.16286i	−0.205748	−	0.237446i
$911$	−14.2983	+	4.19835i	−0.473723	+	0.139098i	−0.509875	−	0.860249i	$-0.670308\pi$
$911$	−14.2983	+	4.19835i	−0.473723	+	0.139098i	0.0361518	+	0.999346i	$0.488490\pi$
$912$	−0.773014	−	4.02540i	−0.0255970	−	0.133294i
$913$	−11.0217	+	12.7197i	−0.364763	+	0.420959i
$914$	−5.12712	+	11.2268i	−0.169590	+	0.371350i
$915$	4.42152	−	0.207631i	0.146171	−	0.00686407i
$916$	−1.80177	+	0.822841i	−0.0595322	+	0.0271874i
$917$	2.68285	+	18.6596i	0.0885956	+	0.616196i
$918$	5.51450	−	2.50490i	0.182006	−	0.0826741i
$919$			20.0849i			0.662541i	0.943536	+	0.331270i	$0.107477\pi$
$919$			20.0849i			0.662541i	−0.943536	+	0.331270i	$0.892523\pi$
$920$	7.68212	+	1.14028i	0.253272	+	0.0375938i
$921$	6.13666	+	17.7695i	0.202210	+	0.585525i
$922$	0.613182	+	0.394068i	0.0201941	+	0.0129779i
$923$	18.1867	−	2.61485i	0.598621	−	0.0860687i
$924$	−1.38344	−	1.45287i	−0.0455119	−	0.0477960i
$925$	−4.39750	+	14.9765i	−0.144589	+	0.492425i
$926$	24.4170	+	11.1509i	0.802394	+	0.366441i
$927$	−30.7968	−	1.50872i	−1.01150	−	0.0495527i
$928$	0.357759	−	2.48827i	0.0117440	−	0.0816814i
$929$	9.93847	+	33.8473i	0.326071	+	1.11049i	0.945549	+	0.325481i	$0.105526\pi$
$929$	9.93847	+	33.8473i	0.326071	+	1.11049i	−0.619478	+	0.785014i	$0.712656\pi$
$930$	−2.20964	−	1.27773i	−0.0724569	−	0.0418983i
$931$	1.27944	+	1.99085i	0.0419320	+	0.0652475i
$932$	2.68330	+	4.17529i	0.0878943	+	0.136766i
$933$	−28.0836	−	16.2394i	−0.919416	−	0.531653i
$934$	−5.17743	−	17.6327i	−0.169411	−	0.576960i
$935$	0.311148	−	2.16408i	0.0101756	−	0.0707730i
$936$	17.5372	+	0.859134i	0.573220	+	0.0280817i
$937$	37.6353	+	17.1875i	1.22949	+	0.561490i	0.920935	−	0.389717i	$-0.127427\pi$
$937$	37.6353	+	17.1875i	1.22949	+	0.561490i	0.308556	+	0.951206i	$0.400154\pi$
$938$	−1.64451	+	5.60069i	−0.0536952	+	0.182869i
$939$	−6.40150	−	6.72278i	−0.208905	−	0.219390i
$940$	5.68353	−	0.817168i	0.185376	−	0.0266531i
$941$	27.4094	+	17.6150i	0.893521	+	0.574231i	0.904862	−	0.425704i	$-0.139974\pi$
$941$	27.4094	+	17.6150i	0.893521	+	0.574231i	−0.0113409	+	0.999936i	$0.503610\pi$
$942$	5.54368	+	16.0525i	0.180623	+	0.523018i
$943$	0.174564	−	38.3080i	0.00568459	−	1.24748i
$944$			13.1867i			0.429190i
$945$	−7.66122	+	3.48003i	−0.249219	+	0.113205i
$946$	−2.00926	−	13.9747i	−0.0653268	−	0.454358i
$947$	37.1466	−	16.9643i	1.20710	−	0.551265i	0.292751	−	0.956189i	$-0.405429\pi$
$947$	37.1466	−	16.9643i	1.20710	−	0.551265i	0.914350	+	0.404924i	$0.132702\pi$
$948$	−24.5594	+	1.15329i	−0.797652	+	0.0374571i
$949$	−0.0803656	+	0.175976i	−0.00260878	+	0.00571242i
$950$	3.68468	−	4.25234i	0.119547	−	0.137964i
$951$	1.38723	+	7.22385i	0.0449839	+	0.234249i
$952$	1.11841	−	0.328394i	0.0362478	−	0.0106433i
$953$	−22.6477	−	26.1368i	−0.733631	−	0.846655i	0.259245	−	0.965812i	$-0.416526\pi$
$953$	−22.6477	−	26.1368i	−0.733631	−	0.846655i	−0.992875	+	0.119156i	$0.961981\pi$
$954$	−26.2177	−	9.11370i	−0.848830	−	0.295067i
$955$	13.6331	−	8.76144i	0.441156	−	0.283514i
$956$	−10.1879	+	8.82785i	−0.329499	+	0.285513i
$957$	−4.11008	+	2.92259i	−0.132860	+	0.0944740i
$958$	−4.07418	−	0.585778i	−0.131631	−	0.0189256i
$959$	12.2365	+	10.6030i	0.395139	+	0.342390i
$960$	2.79197	+	0.268503i	0.0901105	+	0.00866591i
$961$	28.9497	+	8.50040i	0.933861	+	0.274206i
$962$	15.9614	+	34.9506i	0.514617	+	1.12685i
$963$	5.76277	+	5.50966i	0.185703	+	0.177546i
$964$	7.51199	−	11.6889i	0.241945	−	0.376473i
$965$	−34.9767			−1.12594
$966$	4.19089	−	7.17192i	0.134840	−	0.230753i
$967$	−22.6772			−0.729248			−0.364624	−	0.931155i	$-0.618803\pi$
$967$	−22.6772			−0.729248			−0.364624	+	0.931155i	$0.618803\pi$
$968$	−5.22173	+	8.12518i	−0.167833	+	0.261153i
$969$	−2.18646	−	4.24818i	−0.0702392	−	0.136471i
$970$	10.1852	+	22.3025i	0.327027	+	0.716090i
$971$	18.2585	+	5.36116i	0.585942	+	0.172048i	0.561249	−	0.827647i	$-0.310321\pi$
$971$	18.2585	+	5.36116i	0.585942	+	0.172048i	0.0246927	+	0.999695i	$0.492139\pi$
$972$	5.14819	−	14.7138i	0.165128	−	0.471946i
$973$	6.47092	+	5.60708i	0.207448	+	0.179755i
$974$	−3.87977	−	0.557826i	−0.124316	−	0.0178739i
$975$	13.9674	+	19.6426i	0.447315	+	0.629065i
$976$	−1.19266	+	1.03345i	−0.0381762	+	0.0330799i
$977$	39.2784	−	25.2427i	1.25663	−	0.807585i	0.268808	−	0.963194i	$-0.413370\pi$
$977$	39.2784	−	25.2427i	1.25663	−	0.807585i	0.987819	+	0.155609i	$0.0497338\pi$
$978$	6.73121	−	8.54755i	0.215241	−	0.273321i
$979$	6.05351	+	6.98613i	0.193471	+	0.223278i
$980$	−1.55379	+	0.456233i	−0.0496339	+	0.0145738i
$981$	−15.1366	+	8.71187i	−0.483274	+	0.278149i
$982$	12.9840	−	14.9843i	0.414336	−	0.478169i
$983$	−4.57185	+	10.0110i	−0.145820	+	0.319300i	−0.968422	−	0.249317i	$-0.919794\pi$
$983$	−4.57185	+	10.0110i	−0.145820	+	0.319300i	0.822603	+	0.568617i	$0.192521\pi$
$984$	−0.648982	−	13.8201i	−0.0206888	−	0.440570i
$985$	−25.5418	+	11.6645i	−0.813828	+	0.371663i
$986$	−0.417012	−	2.90038i	−0.0132804	−	0.0923670i
$987$	1.45193	−	5.96737i	0.0462156	−	0.189943i
$988$		−	13.8507i		−	0.440648i
$989$	53.2851	−	24.0417i	1.69437	−	0.764480i
$990$	−3.47243	−	4.42784i	−0.110361	−	0.140726i
$991$	31.2322	+	20.0717i	0.992125	+	0.637600i	0.932708	−	0.360633i	$-0.117439\pi$
$991$	31.2322	+	20.0717i	0.992125	+	0.637600i	0.0594170	+	0.998233i	$0.481076\pi$
$992$	0.900755	−	0.129509i	0.0285990	−	0.00411192i
$993$	−30.5267	+	29.0678i	−0.968735	+	0.922439i
$994$	0.884452	−	3.01217i	0.0280531	−	0.0955401i
$995$	5.81249	+	2.65448i	0.184268	+	0.0841525i
$996$	−23.3589	−	9.36979i	−0.740155	−	0.296893i
$997$	−0.534326	+	3.71632i	−0.0169223	+	0.117697i	−0.996532	−	0.0832146i	$-0.973481\pi$
$997$	−0.534326	+	3.71632i	−0.0169223	+	0.117697i	0.979609	+	0.200912i	$0.0643904\pi$
$998$	11.2409	+	38.2832i	0.355826	+	1.21183i
$999$	33.7750	−	4.78630i	1.06859	−	0.151432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.a.113.3	✓	240
3.2	odd	2		966.2.r.b.113.24	yes	240
23.11	odd	22		966.2.r.b.701.24	yes	240
69.11	even	22	inner	966.2.r.a.701.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.3	✓	240	1.1	even	1	trivial
966.2.r.a.701.3	yes	240	69.11	even	22	inner
966.2.r.b.113.24	yes	240	3.2	odd	2
966.2.r.b.701.24	yes	240	23.11	odd	22

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(-1.54004 + 0.792632i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-1.55379 - 0.456233i) q^{5} +(0.165806 - 1.72410i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.74347 - 2.44138i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(-1.54004 + 0.792632i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-1.55379 - 0.456233i) q^{5} +(0.165806 - 1.72410i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.74347 - 2.44138i) q^{9} +(1.22385 - 1.06047i) q^{10} +(0.974396 - 0.626207i) q^{11} +(1.36076 + 1.07160i) q^{12} +(3.83272 + 4.42320i) q^{13} +(0.959493 - 0.281733i) q^{14} +(2.75452 - 0.528963i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.484217 + 1.06029i) q^{17} +(1.11123 + 2.78661i) q^{18} +(2.15267 - 0.983092i) q^{19} +(0.230462 + 1.60290i) q^{20} +(1.68295 + 0.409483i) q^{21} +1.15827i q^{22} +(-4.60768 + 1.33016i) q^{23} +(-1.63717 + 0.565393i) q^{24} +(-2.00016 - 1.28543i) q^{25} +(-5.79316 + 0.832931i) q^{26} +(-0.749906 + 5.14175i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(2.28668 + 1.04429i) q^{29} +(-1.04422 + 2.60323i) q^{30} +(-0.129509 + 0.900755i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-1.00426 + 1.73672i) q^{33} +(-0.630183 - 0.980584i) q^{34} +(0.875505 + 1.36231i) q^{35} +(-2.94502 - 0.571731i) q^{36} +(-1.84956 - 6.29901i) q^{37} +(-0.336792 + 2.34244i) q^{38} +(-9.40853 - 3.77398i) q^{39} +(-1.47304 - 0.672716i) q^{40} +(-2.25044 + 7.66429i) q^{41} +(-1.25435 + 1.19441i) q^{42} +(-12.0652 + 1.73471i) q^{43} +(-0.974396 - 0.626207i) q^{44} +(-3.82282 + 2.99795i) q^{45} +(1.37210 - 4.59536i) q^{46} -3.54578i q^{47} +(0.409483 - 1.68295i) q^{48} +(0.142315 + 0.989821i) q^{49} +(2.16274 - 0.987690i) q^{50} +(-0.0947024 - 2.01670i) q^{51} +(2.43131 - 5.32383i) q^{52} +(-6.05890 + 6.99234i) q^{53} +(-3.92009 - 3.41070i) q^{54} +(-1.79970 + 0.528440i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(-2.53598 + 3.22028i) q^{57} +(-2.11479 + 1.35909i) q^{58} +(9.96582 - 8.63543i) q^{59} +(-1.62543 - 2.28586i) q^{60} +(1.56206 + 0.224590i) q^{61} +(-0.687746 - 0.595935i) q^{62} +(-2.91639 + 0.703339i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-3.93723 - 8.62133i) q^{65} +(-0.918080 - 1.78378i) q^{66} +(-3.15579 + 4.91051i) q^{67} +1.16562 q^{68} +(6.04169 - 5.70069i) q^{69} -1.61938 q^{70} +(1.69725 - 2.64097i) q^{71} +(2.07317 - 2.16840i) q^{72} +(0.0137313 + 0.0300673i) q^{73} +(6.29901 + 1.84956i) q^{74} +(4.09921 + 0.394220i) q^{75} +(-1.78850 - 1.54975i) q^{76} +(-1.14648 - 0.164839i) q^{77} +(8.26151 - 5.87459i) q^{78} +(-10.7279 + 9.29574i) q^{79} +(1.36231 - 0.875505i) q^{80} +(-2.92063 - 8.51293i) q^{81} +(-5.23093 - 6.03681i) q^{82} +(-13.9422 + 4.09379i) q^{83} +(-0.326644 - 1.70097i) q^{84} +(1.23611 - 1.42655i) q^{85} +(5.06361 - 11.0878i) q^{86} +(-4.34933 + 0.204241i) q^{87} +(1.05360 - 0.481162i) q^{88} +(1.13580 + 7.89963i) q^{89} +(-0.455266 - 4.83677i) q^{90} -5.85273i q^{91} +(3.12405 + 3.63872i) q^{92} +(-0.514518 - 1.48986i) q^{93} +(2.98290 + 1.91699i) q^{94} +(-3.79331 + 0.545396i) q^{95} +(1.19441 + 1.25435i) q^{96} +(-4.26555 + 14.5271i) q^{97} +(-0.909632 - 0.415415i) q^{98} +(0.170024 - 3.47064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} + 24 q^{14} + 18 q^{15} - 24 q^{16} + 32 q^{17} - 4 q^{18} + 4 q^{20} - 8 q^{23} + 12 q^{25} - 148 q^{27} + 40 q^{30} + 16 q^{31} + 42 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} + 154 q^{41} + 4 q^{42} + 22 q^{43} + 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} + 88 q^{50} + 24 q^{51} + 8 q^{52} - 108 q^{53} + 12 q^{54} - 16 q^{55} - 24 q^{56} - 62 q^{57} - 4 q^{58} + 22 q^{59} - 18 q^{60} - 4 q^{63} + 24 q^{64} - 100 q^{66} - 44 q^{67} - 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} - 16 q^{74} - 26 q^{75} - 78 q^{78} - 4 q^{80} + 52 q^{81} + 8 q^{82} + 16 q^{83} - 28 q^{85} + 16 q^{86} - 196 q^{87} + 24 q^{89} + 126 q^{90} + 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} + 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 + 24 * q^14 + 18 * q^15 - 24 * q^16 + 32 * q^17 - 4 * q^18 + 4 * q^20 - 8 * q^23 + 12 * q^25 - 148 * q^27 + 40 * q^30 + 16 * q^31 + 42 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 + 154 * q^41 + 4 * q^42 + 22 * q^43 + 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 + 88 * q^50 + 24 * q^51 + 8 * q^52 - 108 * q^53 + 12 * q^54 - 16 * q^55 - 24 * q^56 - 62 * q^57 - 4 * q^58 + 22 * q^59 - 18 * q^60 - 4 * q^63 + 24 * q^64 - 100 * q^66 - 44 * q^67 - 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 - 16 * q^74 - 26 * q^75 - 78 * q^78 - 4 * q^80 + 52 * q^81 + 8 * q^82 + 16 * q^83 - 28 * q^85 + 16 * q^86 - 196 * q^87 + 24 * q^89 + 126 * q^90 + 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 + 172 * q^99

Introduction

L-functions

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