LMFDB - Embedded newform 930.2.bs.a.107.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			107.12
Character	$\chi$	$=$	930.107
Dual form			930.2.bs.a.113.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(-0.695665 - 1.58621i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.24127 + 1.85990i) q^{5} +(-1.09749 + 1.33996i) q^{6} +(3.78072 - 3.06157i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.03210 + 2.20694i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.695665 - 1.58621i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.24127 + 1.85990i) q^{5} +(-1.09749 + 1.33996i) q^{6} +(3.78072 - 3.06157i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.03210 + 2.20694i) q^{9} +(1.09366 - 1.95036i) q^{10} +(0.770724 + 1.73108i) q^{11} +(1.69217 + 0.369543i) q^{12} +(-0.836980 + 0.543541i) q^{13} +(-4.44428 - 1.97872i) q^{14} +(2.08668 - 3.26279i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.60634 - 0.616615i) q^{17} +(2.88895 + 0.808685i) q^{18} +(1.08529 + 5.10588i) q^{19} +(-2.23430 - 0.0890114i) q^{20} +(-7.48639 - 3.86717i) q^{21} +(1.19250 - 1.47261i) q^{22} +(7.95034 + 1.25921i) q^{23} +(-0.438963 - 1.67550i) q^{24} +(-1.91848 + 4.61730i) q^{25} +(0.864279 + 0.498992i) q^{26} +(4.91432 + 1.68804i) q^{27} +(0.254608 + 4.85821i) q^{28} +(-2.21251 + 6.80941i) q^{29} +(-3.85450 - 0.377969i) q^{30} +(4.23292 - 3.61695i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.20968 - 2.42678i) q^{33} +(-1.27867 - 1.15132i) q^{34} +(10.3871 + 3.23153i) q^{35} +(-0.591012 - 2.94121i) q^{36} +(1.24334 - 4.64021i) q^{37} +(4.05666 - 3.28502i) q^{38} +(1.44443 + 0.949500i) q^{39} +(0.935039 + 2.03118i) q^{40} +(3.78232 - 3.40562i) q^{41} +(-0.0469271 + 8.42608i) q^{42} +(-2.27243 + 3.49924i) q^{43} +(-1.85349 - 0.393971i) q^{44} +(-6.62708 - 1.04009i) q^{45} +(-2.48741 - 7.65547i) q^{46} +(-7.19111 - 3.66405i) q^{47} +(-1.29360 + 1.15178i) q^{48} +(3.46527 - 16.3028i) q^{49} +(4.98501 - 0.386835i) q^{50} +(-2.09555 - 2.11902i) q^{51} +(0.0522304 - 0.996616i) q^{52} +(-2.36179 + 2.91657i) q^{53} +(-0.727001 - 5.14504i) q^{54} +(-2.26295 + 3.58221i) q^{55} +(4.21311 - 2.43244i) q^{56} +(7.34398 - 5.27348i) q^{57} +(7.07169 - 1.12005i) q^{58} +(-1.43182 + 1.59020i) q^{59} +(1.41313 + 3.60598i) q^{60} +6.55747 q^{61} +(-5.14444 - 2.12950i) q^{62} +(-0.926111 + 14.5652i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.04985 - 0.882017i) q^{65} +(-3.16545 - 0.867102i) q^{66} +(-2.69030 + 0.720864i) q^{67} +(-0.445329 + 1.66199i) q^{68} +(-3.53341 - 13.4869i) q^{69} +(-1.83634 - 10.7221i) q^{70} +(-10.5517 + 1.10903i) q^{71} +(-2.35232 + 1.86188i) q^{72} +(5.35409 - 13.9479i) q^{73} +(-4.69892 + 0.998786i) q^{74} +(8.65860 - 0.168997i) q^{75} +(-4.76866 - 2.12314i) q^{76} +(8.21369 + 4.18508i) q^{77} +(0.190255 - 1.71806i) q^{78} +(4.13270 - 9.28219i) q^{79} +(1.38530 - 1.75526i) q^{80} +(-0.741146 - 8.96943i) q^{81} +(-4.75156 - 1.82395i) q^{82} +(0.146806 - 2.80122i) q^{83} +(7.52900 - 3.78355i) q^{84} +(3.14075 + 2.22224i) q^{85} +(4.14951 + 0.436131i) q^{86} +(12.3403 - 1.22757i) q^{87} +(0.490436 + 1.83033i) q^{88} +(-3.79996 - 2.76083i) q^{89} +(2.08190 + 6.37696i) q^{90} +(-1.50030 + 4.61744i) q^{91} +(-5.69181 + 5.69181i) q^{92} +(-8.68193 - 4.19810i) q^{93} +8.07077i q^{94} +(-8.14930 + 8.35633i) q^{95} +(1.61353 + 0.629707i) q^{96} +(0.720618 + 4.54980i) q^{97} +(-16.0991 + 4.31374i) q^{98} +(-5.38656 - 1.81678i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	−0.695665	−	1.58621i	−0.401643	−	0.915796i
$3$	−0.695665	−	1.58621i	−0.401643	−	0.915796i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	1.24127	+	1.85990i	0.555115	+	0.831774i
$5$	1.24127	+	1.85990i	0.555115	+	0.831774i
$6$	−1.09749	+	1.33996i	−0.448050	+	0.547038i
$7$	3.78072	−	3.06157i	1.42898	−	1.15716i	0.466925	−	0.884297i	$-0.345362\pi$
$7$	3.78072	−	3.06157i	1.42898	−	1.15716i	0.962052	−	0.272866i	$-0.0879715\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	−2.03210	+	2.20694i	−0.677366	+	0.735646i
$10$	1.09366	−	1.95036i	0.345845	−	0.616759i
$11$	0.770724	+	1.73108i	0.232382	+	0.521939i	0.991668	−	0.128818i	$-0.0411184\pi$
$11$	0.770724	+	1.73108i	0.232382	+	0.521939i	−0.759286	+	0.650757i	$0.774452\pi$
$12$	1.69217	+	0.369543i	0.488487	+	0.106678i
$13$	−0.836980	+	0.543541i	−0.232136	+	0.150751i	−0.655466	−	0.755225i	$-0.727528\pi$
$13$	−0.836980	+	0.543541i	−0.232136	+	0.150751i	0.423330	+	0.905976i	$0.360861\pi$
$14$	−4.44428	−	1.97872i	−1.18778	−	0.528836i
$15$	2.08668	−	3.26279i	0.538778	−	0.842448i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.60634	−	0.616615i	0.389594	−	0.149551i	−0.155683	−	0.987807i	$-0.549758\pi$
$17$	1.60634	−	0.616615i	0.389594	−	0.149551i	0.545277	+	0.838256i	$0.316424\pi$
$18$	2.88895	+	0.808685i	0.680932	+	0.190609i
$19$	1.08529	+	5.10588i	0.248982	+	1.17137i	0.907911	+	0.419164i	$0.137677\pi$
$19$	1.08529	+	5.10588i	0.248982	+	1.17137i	−0.658928	+	0.752206i	$0.728990\pi$
$20$	−2.23430	−	0.0890114i	−0.499604	−	0.0199036i
$21$	−7.48639	−	3.86717i	−1.63366	−	0.843886i
$22$	1.19250	−	1.47261i	0.254241	−	0.313962i
$23$	7.95034	+	1.25921i	1.65776	+	0.262563i	0.913950	−	0.405827i	$-0.133017\pi$
$23$	7.95034	+	1.25921i	1.65776	+	0.262563i	0.743810	+	0.668391i	$0.233017\pi$
$24$	−0.438963	−	1.67550i	−0.0896030	−	0.342011i
$25$	−1.91848	+	4.61730i	−0.383695	+	0.923460i
$26$	0.864279	+	0.498992i	0.169499	+	0.0978604i
$27$	4.91432	+	1.68804i	0.945761	+	0.324863i
$28$	0.254608	+	4.85821i	0.0481164	+	0.918115i
$29$	−2.21251	+	6.80941i	−0.410853	+	1.26448i	0.505054	+	0.863088i	$0.331472\pi$
$29$	−2.21251	+	6.80941i	−0.410853	+	1.26448i	−0.915908	+	0.401389i	$0.868528\pi$
$30$	−3.85450	−	0.377969i	−0.703731	−	0.0690074i
$31$	4.23292	−	3.61695i	0.760255	−	0.649624i
$31$	4.23292	−	3.61695i	0.760255	−	0.649624i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.20968	−	2.42678i	0.384655	−	0.422448i
$34$	−1.27867	−	1.15132i	−0.219290	−	0.197450i
$35$	10.3871	+	3.23153i	1.75574	+	0.546228i
$36$	−0.591012	−	2.94121i	−0.0985020	−	0.490201i
$37$	1.24334	−	4.64021i	0.204404	−	0.762845i	−0.785227	−	0.619208i	$-0.787454\pi$
$37$	1.24334	−	4.64021i	0.204404	−	0.762845i	0.989630	−	0.143637i	$-0.0458797\pi$
$38$	4.05666	−	3.28502i	0.658077	−	0.532901i
$39$	1.44443	+	0.949500i	0.231293	+	0.152042i
$40$	0.935039	+	2.03118i	0.147843	+	0.321158i
$41$	3.78232	−	3.40562i	0.590699	−	0.531868i	−0.318666	−	0.947867i	$-0.603235\pi$
$41$	3.78232	−	3.40562i	0.590699	−	0.531868i	0.909365	+	0.415999i	$0.136568\pi$
$42$	−0.0469271	+	8.42608i	−0.00724102	+	1.30017i
$43$	−2.27243	+	3.49924i	−0.346543	+	0.533629i	−0.968368	−	0.249527i	$-0.919725\pi$
$43$	−2.27243	+	3.49924i	−0.346543	+	0.533629i	0.621825	+	0.783156i	$0.286392\pi$
$44$	−1.85349	−	0.393971i	−0.279424	−	0.0593934i
$45$	−6.62708	−	1.04009i	−0.987907	−	0.155048i
$46$	−2.48741	−	7.65547i	−0.366749	−	1.12874i
$47$	−7.19111	−	3.66405i	−1.04893	−	0.534457i	−0.157456	−	0.987526i	$-0.550329\pi$
$47$	−7.19111	−	3.66405i	−1.04893	−	0.534457i	−0.891476	+	0.453069i	$0.850329\pi$
$48$	−1.29360	+	1.15178i	−0.186715	+	0.166245i
$49$	3.46527	−	16.3028i	0.495038	−	2.32897i
$50$	4.98501	−	0.386835i	0.704987	−	0.0547067i
$51$	−2.09555	−	2.11902i	−0.293436	−	0.296723i
$52$	0.0522304	−	0.996616i	0.00724306	−	0.138206i
$53$	−2.36179	+	2.91657i	−0.324417	+	0.400622i	−0.913096	−	0.407745i	$-0.866315\pi$
$53$	−2.36179	+	2.91657i	−0.324417	+	0.400622i	0.588678	+	0.808367i	$0.299648\pi$
$54$	−0.727001	−	5.14504i	−0.0989323	−	0.700152i
$55$	−2.26295	+	3.58221i	−0.305136	+	0.483025i
$56$	4.21311	−	2.43244i	0.563000	−	0.325048i
$57$	7.34398	−	5.27348i	0.972734	−	0.698489i
$58$	7.07169	−	1.12005i	0.928559	−	0.147069i
$59$	−1.43182	+	1.59020i	−0.186407	+	0.207026i	−0.829104	−	0.559095i	$-0.811149\pi$
$59$	−1.43182	+	1.59020i	−0.186407	+	0.207026i	0.642697	+	0.766121i	$0.277816\pi$
$60$	1.41313	+	3.60598i	0.182435	+	0.465529i
$61$	6.55747			0.839598			0.419799	−	0.907617i	$-0.362101\pi$
$61$	6.55747			0.839598			0.419799	+	0.907617i	$0.362101\pi$
$62$	−5.14444	−	2.12950i	−0.653344	−	0.270447i
$63$	−0.926111	+	14.5652i	−0.116679	+	1.83504i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−2.04985	−	0.882017i	−0.254253	−	0.109401i
$66$	−3.16545	−	0.867102i	−0.389639	−	0.106733i
$67$	−2.69030	+	0.720864i	−0.328673	+	0.0880676i	−0.419382	−	0.907810i	$-0.637753\pi$
$67$	−2.69030	+	0.720864i	−0.328673	+	0.0880676i	0.0907094	+	0.995877i	$0.471087\pi$
$68$	−0.445329	+	1.66199i	−0.0540041	+	0.201546i
$69$	−3.53341	−	13.4869i	−0.425373	−	1.62363i
$70$	−1.83634	−	10.7221i	−0.219485	−	1.28153i
$71$	−10.5517	+	1.10903i	−1.25226	+	0.131617i	−0.707340	−	0.706873i	$-0.750105\pi$
$71$	−10.5517	+	1.10903i	−1.25226	+	0.131617i	−0.544916	+	0.838491i	$0.683439\pi$
$72$	−2.35232	+	1.86188i	−0.277224	+	0.219424i
$73$	5.35409	−	13.9479i	0.626648	−	1.63248i	−0.139808	−	0.990179i	$-0.544649\pi$
$73$	5.35409	−	13.9479i	0.626648	−	1.63248i	0.766456	−	0.642296i	$-0.222018\pi$
$74$	−4.69892	+	0.998786i	−0.546238	+	0.116106i
$75$	8.65860	−	0.168997i	0.999810	−	0.0195140i
$76$	−4.76866	−	2.12314i	−0.547003	−	0.243541i
$77$	8.21369	+	4.18508i	0.936037	+	0.476935i
$78$	0.190255	−	1.71806i	0.0215421	−	0.194532i
$79$	4.13270	−	9.28219i	0.464965	−	1.04433i	−0.517124	−	0.855910i	$-0.672998\pi$
$79$	4.13270	−	9.28219i	0.464965	−	1.04433i	0.982089	−	0.188417i	$-0.0603358\pi$
$80$	1.38530	−	1.75526i	0.154881	−	0.196244i
$81$	−0.741146	−	8.96943i	−0.0823495	−	0.996604i
$82$	−4.75156	−	1.82395i	−0.524722	−	0.201422i
$83$	0.146806	−	2.80122i	0.0161140	−	0.307474i	−0.978668	−	0.205449i	$-0.934134\pi$
$83$	0.146806	−	2.80122i	0.0161140	−	0.307474i	0.994782	−	0.102025i	$-0.0325322\pi$
$84$	7.52900	−	3.78355i	0.821481	−	0.412819i
$85$	3.14075	+	2.22224i	0.340662	+	0.241036i
$86$	4.14951	+	0.436131i	0.447453	+	0.0470292i
$87$	12.3403	−	1.22757i	1.32302	−	0.131610i
$88$	0.490436	+	1.83033i	0.0522806	+	0.195114i
$89$	−3.79996	−	2.76083i	−0.402794	−	0.292647i	0.367884	−	0.929872i	$-0.380082\pi$
$89$	−3.79996	−	2.76083i	−0.402794	−	0.292647i	−0.770678	+	0.637224i	$0.780082\pi$
$90$	2.08190	+	6.37696i	0.219452	+	0.672191i
$91$	−1.50030	+	4.61744i	−0.157274	+	0.484040i
$92$	−5.69181	+	5.69181i	−0.593413	+	0.593413i
$93$	−8.68193	−	4.19810i	−0.900275	−	0.435323i
$94$			8.07077i			0.832437i
$95$	−8.14930	+	8.35633i	−0.836101	+	0.857341i
$96$	1.61353	+	0.629707i	0.164680	+	0.0642692i
$97$	0.720618	+	4.54980i	0.0731676	+	0.461962i	0.996884	+	0.0788846i	$0.0251358\pi$
$97$	0.720618	+	4.54980i	0.0731676	+	0.461962i	−0.923716	+	0.383078i	$0.874864\pi$
$98$	−16.0991	+	4.31374i	−1.62625	+	0.435753i
$99$	−5.38656	−	1.81678i	−0.541370	−	0.182593i
$100$	−2.60782	−	4.26606i	−0.260782	−	0.426606i
$101$	0.631870	+	0.869695i	0.0628734	+	0.0865378i	0.839296	−	0.543675i	$-0.182968\pi$
$101$	0.631870	+	0.869695i	0.0628734	+	0.0865378i	−0.776422	+	0.630213i	$0.782968\pi$
$102$	−0.936704	+	2.82917i	−0.0927475	+	0.280129i
$103$	−8.63289	−	0.452430i	−0.850623	−	0.0445793i	−0.377960	−	0.925822i	$-0.623374\pi$
$103$	−8.63289	−	0.452430i	−0.850623	−	0.0445793i	−0.472664	+	0.881243i	$0.656708\pi$
$104$	−0.911704	+	0.405917i	−0.0893999	+	0.0398034i
$105$	−2.10010	−	18.7242i	−0.204948	−	1.82729i
$106$	3.67092	+	0.780278i	0.356551	+	0.0757873i
$107$	10.4188	−	3.99941i	1.00722	−	0.386637i	0.201858	−	0.979415i	$-0.435302\pi$
$107$	10.4188	−	3.99941i	1.00722	−	0.386637i	0.805366	+	0.592778i	$0.201969\pi$
$108$	−4.25422	+	2.98356i	−0.409362	+	0.287094i
$109$	−14.7989	+	4.80846i	−1.41748	+	0.460567i	−0.914800	−	0.403906i	$-0.867652\pi$
$109$	−14.7989	+	4.80846i	−1.41748	+	0.460567i	−0.502679	+	0.864473i	$0.667652\pi$
$110$	4.21913	+	0.390014i	0.402278	+	0.0371864i
$111$	−8.22527	+	1.25584i	−0.780708	+	0.119199i
$112$	−4.08003	−	2.64960i	−0.385526	−	0.250364i
$113$	−3.36195	−	1.29053i	−0.316266	−	0.121403i	0.195057	−	0.980792i	$-0.437511\pi$
$113$	−3.36195	−	1.29053i	−0.316266	−	0.121403i	−0.511323	+	0.859389i	$0.670844\pi$
$114$	−8.03280	−	4.14943i	−0.752340	−	0.388629i
$115$	7.52654	+	16.3499i	0.701854	+	1.52463i
$116$	−4.20845	−	5.79243i	−0.390745	−	0.537814i
$117$	0.501265	−	2.95169i	0.0463420	−	0.272884i
$118$	2.06691	+	0.553827i	0.190274	+	0.0509839i
$119$	4.18530	−	7.24916i	0.383666	−	0.664529i
$120$	2.57140	−	2.89619i	0.234736	−	0.264385i
$121$	4.95783	−	5.50623i	0.450712	−	0.500566i
$122$	−2.97703	−	5.84275i	−0.269528	−	0.528978i
$123$	−8.03324	−	3.63037i	−0.724333	−	0.327339i
$124$	0.438128	+	5.55050i	0.0393450	+	0.498450i
$125$	−10.9691	+	2.16316i	−0.981105	+	0.193478i
$126$	13.3981	−	5.78730i	1.19360	−	0.515573i
$127$	−0.306371	+	0.0160562i	−0.0271861	+	0.00142476i	−0.0659241	−	0.997825i	$-0.521000\pi$
$127$	−0.306371	+	0.0160562i	−0.0271861	+	0.00142476i	0.0387381	+	0.999249i	$0.487666\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	7.13137	+	1.17025i	0.627882	+	0.103035i
$130$	0.144731	+	2.22686i	0.0126938	+	0.195309i
$131$	4.87207	+	0.512075i	0.425675	+	0.0447402i	0.314944	−	0.949110i	$-0.398014\pi$
$131$	4.87207	+	0.512075i	0.425675	+	0.0447402i	0.110731	+	0.993850i	$0.464681\pi$
$132$	0.664489	+	3.21409i	0.0578363	+	0.279751i
$133$	19.7352	+	15.9812i	1.71125	+	1.38575i
$134$	1.86367	+	2.06981i	0.160996	+	0.178804i
$135$	2.96043	+	11.2355i	0.254793	+	0.966996i
$136$	1.68302	−	0.357737i	0.144318	−	0.0306757i
$137$	−8.36079	+	5.42956i	−0.714310	+	0.463878i	−0.849939	−	0.526881i	$-0.823361\pi$
$137$	−8.36079	+	5.42956i	−0.714310	+	0.463878i	0.135629	+	0.990760i	$0.456695\pi$
$138$	−10.4127	+	9.27120i	−0.886392	+	0.789217i
$139$	13.1994	−	4.28875i	1.11956	−	0.363767i	0.309960	−	0.950749i	$-0.399684\pi$
$139$	13.1994	−	4.28875i	1.11956	−	0.363767i	0.809600	+	0.586982i	$0.199684\pi$
$140$	−8.71976	+	6.50391i	−0.736954	+	0.549681i
$141$	−0.809337	+	13.9555i	−0.0681585	+	1.17527i
$142$	5.77852	+	8.89815i	0.484923	+	0.746716i
$143$	−1.58599	−	1.02995i	−0.132627	−	0.0861291i
$144$	2.72688	+	1.25066i	0.227240	+	0.104222i
$145$	−15.4112	+	4.33729i	−1.27983	+	0.360193i
$146$	−14.8584	+	1.56168i	−1.22969	+	0.129245i
$147$	−28.2703	+	5.84467i	−2.33169	+	0.482060i
$148$	3.02319	+	3.73333i	0.248505	+	0.306878i
$149$	−11.3104	−	19.5902i	−0.926586	−	1.60489i	−0.788990	−	0.614406i	$-0.789396\pi$
$149$	−11.3104	−	19.5902i	−0.926586	−	1.60489i	−0.137596	−	0.990488i	$-0.543938\pi$
$150$	−4.08150	−	7.63815i	−0.333253	−	0.623652i
$151$	16.4803	+	11.9737i	1.34115	+	0.974403i	0.999401	+	0.0346117i	$0.0110195\pi$
$151$	16.4803	+	11.9737i	1.34115	+	0.974403i	0.341750	+	0.939791i	$0.388981\pi$
$152$	0.273191	+	5.21279i	0.0221587	+	0.422814i
$153$	−1.90341	+	4.79811i	−0.153881	+	0.387904i
$154$		−	9.21844i		−	0.742843i
$155$	11.9814	+	3.38319i	0.962369	+	0.271745i
$156$	−1.61717	+	0.610463i	−0.129478	+	0.0488762i
$157$	4.31954	−	2.20091i	0.344737	−	0.175652i	−0.273046	−	0.962001i	$-0.588031\pi$
$157$	4.31954	−	2.20091i	0.344737	−	0.175652i	0.617783	+	0.786349i	$0.288031\pi$
$158$	−10.1467	+	0.531766i	−0.807228	+	0.0423050i
$159$	6.26930	+	1.71733i	0.497188	+	0.136193i
$160$	−2.19286	−	0.437436i	−0.173361	−	0.0345824i
$161$	33.9131	−	19.5798i	2.67273	−	1.54310i
$162$	−7.65535	+	4.73240i	−0.601461	+	0.371813i
$163$	2.10150	−	13.2684i	0.164602	−	1.03926i	−0.757648	−	0.652664i	$-0.773651\pi$
$163$	2.10150	−	13.2684i	0.164602	−	1.03926i	0.922250	−	0.386594i	$-0.126349\pi$
$164$	0.532009	+	5.06173i	0.0415430	+	0.395255i
$165$	7.25638	+	1.09749i	0.564909	+	0.0854392i
$166$	−2.56256	+	1.14092i	−0.198893	+	0.0885529i
$167$	−9.11259	+	14.0322i	−0.705154	+	1.08584i	0.286646	+	0.958037i	$0.407460\pi$
$167$	−9.11259	+	14.0322i	−0.705154	+	1.08584i	−0.991799	+	0.127805i	$0.959207\pi$
$168$	−6.78926	−	4.99069i	−0.523803	−	0.385040i
$169$	−4.88248	+	10.9662i	−0.375575	+	0.843556i
$170$	0.554162	−	3.80731i	0.0425023	−	0.292007i
$171$	−13.4738	−	7.98049i	−1.03037	−	0.610283i
$172$	−1.49524	−	3.89524i	−0.114011	−	0.297009i
$173$	12.9947	+	20.0100i	0.987967	+	1.52134i	0.847187	+	0.531295i	$0.178294\pi$
$173$	12.9947	+	20.0100i	0.987967	+	1.52134i	0.140780	+	0.990041i	$0.455039\pi$
$174$	−6.69616	−	10.4380i	−0.507634	−	0.791302i
$175$	6.88294	+	23.3302i	0.520302	+	1.76360i
$176$	1.40818	−	1.26793i	0.106146	−	0.0955741i
$177$	3.51845	+	1.16492i	0.264463	+	0.0875605i
$178$	−0.734773	+	4.63918i	−0.0550736	+	0.347721i
$179$	0.203721	−	1.93827i	0.0152268	−	0.144873i	−0.984267	−	0.176688i	$-0.943462\pi$
$179$	0.203721	−	1.93827i	0.0152268	−	0.144873i	0.999494	+	0.0318142i	$0.0101285\pi$
$180$	4.73675	−	4.75007i	0.353057	−	0.354049i
$181$	−8.49155	+	14.7078i	−0.631172	+	1.09322i	0.356141	+	0.934432i	$0.384092\pi$
$181$	−8.49155	+	14.7078i	−0.631172	+	1.09322i	−0.987313	+	0.158789i	$0.949241\pi$
$182$	4.79529	−	0.759500i	0.355451	−	0.0562979i
$183$	−4.56181	−	10.4015i	−0.337218	−	0.768901i
$184$	7.65547	+	2.48741i	0.564369	+	0.183375i
$185$	10.1737	−	3.44728i	0.747982	−	0.253449i
$186$	0.200982	+	9.64156i	0.0147367	+	0.706953i
$187$	2.30545	+	2.30545i	0.168591	+	0.168591i
$188$	7.19111	−	3.66405i	0.524466	−	0.267229i
$189$	23.7477	−	8.66351i	1.72739	−	0.630178i
$190$	11.1452	+	3.46739i	0.808561	+	0.251551i
$191$	4.47714	+	2.58488i	0.323954	+	0.187035i	0.653154	−	0.757225i	$-0.273446\pi$
$191$	4.47714	+	2.58488i	0.323954	+	0.187035i	−0.329200	+	0.944260i	$0.606779\pi$
$192$	−0.171453	−	1.72354i	−0.0123735	−	0.124386i
$193$	12.1140	+	14.9595i	0.871985	+	1.07681i	0.996416	+	0.0845833i	$0.0269559\pi$
$193$	12.1140	+	14.9595i	0.871985	+	1.07681i	−0.124432	+	0.992228i	$0.539711\pi$
$194$	3.72675	−	2.70764i	0.267565	−	0.194397i
$195$	0.0269518	+	3.86508i	0.00193006	+	0.276784i
$196$	11.1524	+	12.3860i	0.796600	+	0.884714i
$197$	4.82684	−	12.5744i	0.343898	−	0.895886i	−0.647148	−	0.762365i	$-0.724038\pi$
$197$	4.82684	−	12.5744i	0.343898	−	0.895886i	0.991046	−	0.133521i	$-0.0426284\pi$
$198$	0.826689	+	5.62426i	0.0587502	+	0.399699i
$199$	1.40593	−	6.61438i	0.0996637	−	0.468881i	−0.899805	−	0.436292i	$-0.856291\pi$
$199$	1.40593	−	6.61438i	0.0996637	−	0.468881i	0.999469	−	0.0325889i	$-0.0103752\pi$
$200$	−2.61716	+	4.26034i	−0.185061	+	0.301251i
$201$	3.01499	+	3.76589i	0.212661	+	0.265626i
$202$	0.488041	−	0.957833i	0.0343384	−	0.0673929i
$203$	12.4826	+	32.5182i	0.876105	+	2.28233i
$204$	2.94606	−	0.449806i	0.206266	−	0.0314927i
$205$	11.0290	+	2.80744i	0.770299	+	0.196080i
$206$	3.51613	+	7.89736i	0.244980	+	0.550235i
$207$	−18.9349	+	14.9871i	−1.31606	+	1.04167i
$208$	0.775579	+	0.628052i	0.0537767	+	0.0435475i
$209$	−8.00220	+	5.81394i	−0.553524	+	0.402159i
$210$	−15.7299	+	10.3718i	−1.08547	+	0.715722i
$211$	0.252489	+	0.437324i	0.0173821	+	0.0301066i	0.874586	−	0.484871i	$-0.161133\pi$
$211$	0.252489	+	0.437324i	0.0173821	+	0.0301066i	−0.857204	+	0.514978i	$0.827800\pi$
$212$	−0.971329	−	3.62505i	−0.0667112	−	0.248969i
$213$	9.09960	+	15.9657i	0.623494	+	1.09395i
$214$	−8.29354	−	7.46754i	−0.566935	−	0.510470i
$215$	−9.32896	+	0.117012i	−0.636230	+	0.00798017i
$216$	4.58975	+	2.43602i	0.312293	+	0.165750i
$217$	4.92995	−	26.6341i	0.334667	−	1.80804i
$218$	11.0029	+	11.0029i	0.745213	+	0.745213i
$219$	−25.8489	+	1.21037i	−1.74670	+	0.0817891i
$220$	−1.56794	−	3.93634i	−0.105711	−	0.265388i
$221$	−1.00932	+	1.38920i	−0.0678940	+	0.0934480i
$222$	4.85316	+	6.75863i	0.325722	+	0.453610i
$223$	3.17840	+	0.851649i	0.212841	+	0.0570306i	0.363664	−	0.931530i	$-0.381526\pi$
$223$	3.17840	+	0.851649i	0.212841	+	0.0570306i	−0.150823	+	0.988561i	$0.548192\pi$
$224$	−0.508518	+	4.83822i	−0.0339768	+	0.323267i
$225$	−6.29156	−	13.6168i	−0.419437	−	0.907784i
$226$	0.376422	+	3.58141i	0.0250392	+	0.238232i
$227$	−26.3407	−	1.38046i	−1.74829	−	0.0916241i	−0.848842	−	0.528647i	$-0.822700\pi$
$227$	−26.3407	−	1.38046i	−1.74829	−	0.0916241i	−0.899451	+	0.437023i	$0.856033\pi$
$228$	−0.0503522	+	9.04108i	−0.00333466	+	0.598760i
$229$	−0.485280	−	2.28307i	−0.0320682	−	0.150869i	0.959200	−	0.282727i	$-0.0912391\pi$
$229$	−0.485280	−	2.28307i	−0.0320682	−	0.150869i	−0.991269	+	0.131858i	$0.957906\pi$
$230$	11.1509	−	14.1289i	0.735267	−	0.931631i
$231$	0.924425	−	15.9400i	0.0608227	−	1.04878i
$232$	−3.25050	+	6.37947i	−0.213406	+	0.418832i
$233$	−3.05586	+	5.99747i	−0.200196	+	0.392907i	−0.969177	−	0.246364i	$-0.920764\pi$
$233$	−3.05586	+	5.99747i	−0.200196	+	0.392907i	0.768981	+	0.639272i	$0.220764\pi$
$234$	−2.85755	+	0.893410i	−0.186804	+	0.0584040i
$235$	−2.11136	−	17.9229i	−0.137730	−	1.16916i
$236$	−0.444894	−	2.09306i	−0.0289601	−	0.136247i
$237$	−17.5984	−	0.0980105i	−1.14314	−	0.00636647i
$238$	−8.35913	−	0.438084i	−0.541842	−	0.0283967i
$239$	0.450939	+	4.29039i	0.0291688	+	0.277523i	0.999378	+	0.0352552i	$0.0112244\pi$
$239$	0.450939	+	4.29039i	0.0291688	+	0.277523i	−0.970210	+	0.242267i	$0.922109\pi$
$240$	−3.74791	−	0.976291i	−0.241927	−	0.0630193i
$241$	−1.16820	+	11.1147i	−0.0752505	+	0.715960i	0.890235	+	0.455502i	$0.150540\pi$
$241$	−1.16820	+	11.1147i	−0.0752505	+	0.715960i	−0.965485	+	0.260458i	$0.916126\pi$
$242$	−7.15690	−	1.91768i	−0.460063	−	0.123273i
$243$	−13.7118	+	7.41533i	−0.879611	+	0.475694i
$244$	−3.85439	+	5.30511i	−0.246752	+	0.339625i
$245$	34.6230	−	13.7912i	2.21198	−	0.881086i
$246$	0.412331	+	8.80582i	0.0262893	+	0.561439i
$247$	−3.68362	−	3.68362i	−0.234383	−	0.234383i
$248$	4.74663	−	2.91025i	0.301411	−	0.184801i
$249$	−4.54545	+	1.71585i	−0.288056	+	0.108738i
$250$	6.90724	+	8.79147i	0.436852	+	0.556021i
$251$	2.51486	+	2.26439i	0.158737	+	0.142927i	0.744672	−	0.667431i	$-0.232606\pi$
$251$	2.51486	+	2.26439i	0.158737	+	0.142927i	−0.585935	+	0.810358i	$0.699273\pi$
$252$	−11.2391	−	9.31046i	−0.708000	−	0.586504i
$253$	3.94773	+	14.7331i	0.248192	+	0.926264i
$254$	0.153396	+	0.265689i	0.00962491	+	0.0166708i
$255$	1.34002	−	6.52781i	0.0839156	−	0.408788i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.4273	−	9.25361i	−0.712813	−	0.577224i	0.202832	−	0.979214i	$-0.434986\pi$
$257$	−11.4273	−	9.25361i	−0.712813	−	0.577224i	−0.915644	+	0.401989i	$0.868319\pi$
$258$	−2.19488	−	6.88538i	−0.136647	−	0.428665i
$259$	−9.50558	−	21.3499i	−0.590648	−	1.32662i
$260$	1.91844	−	1.13993i	0.118977	−	0.0706955i
$261$	−10.5319	−	18.7203i	−0.651909	−	1.15876i
$262$	−1.75561	−	4.57352i	−0.108462	−	0.282553i
$263$	−2.81883	+	5.53226i	−0.173816	+	0.341134i	−0.961436	−	0.275028i	$-0.911313\pi$
$263$	−2.81883	+	5.53226i	−0.173816	+	0.341134i	0.787620	+	0.616161i	$0.211313\pi$
$264$	2.56210	−	2.05123i	0.157686	−	0.126244i
$265$	−8.35618	−	0.772440i	−0.513316	−	0.0474506i
$266$	5.27979	−	24.8395i	0.323725	−	1.52301i
$267$	−1.73575	+	7.94813i	−0.106226	+	0.486417i
$268$	0.998128	−	2.60021i	0.0609704	−	0.158833i
$269$	−6.76883	−	7.51755i	−0.412703	−	0.458353i	0.500573	−	0.865694i	$-0.333123\pi$
$269$	−6.76883	−	7.51755i	−0.412703	−	0.458353i	−0.913276	+	0.407341i	$0.866456\pi$
$270$	8.66687	−	7.73856i	0.527449	−	0.470954i
$271$	−21.8475	+	15.8732i	−1.32714	+	0.964226i	−0.327330	+	0.944910i	$0.606149\pi$
$271$	−21.8475	+	15.8732i	−1.32714	+	0.964226i	−0.999813	+	0.0193158i	$0.993851\pi$
$272$	−1.08282	−	1.33717i	−0.0656557	−	0.0810780i
$273$	8.36792	−	0.832414i	0.506450	−	0.0503800i
$274$	8.63349	+	4.98455i	0.521568	+	0.301127i
$275$	−9.47151	+	0.237638i	−0.571153	+	0.0143301i
$276$	12.9880	+	5.06879i	0.781785	+	0.305105i
$277$	9.50697	−	4.84404i	0.571218	−	0.291050i	−0.144425	−	0.989516i	$-0.546133\pi$
$277$	9.50697	−	4.84404i	0.571218	−	0.291050i	0.715644	+	0.698465i	$0.246133\pi$
$278$	−9.81372	−	9.81372i	−0.588588	−	0.588588i
$279$	−0.619328	+	16.6918i	−0.0370782	+	0.999312i
$280$	9.75372	+	4.81664i	0.582896	+	0.287850i
$281$	−25.2038	−	8.18922i	−1.50353	−	0.488528i	−0.562488	−	0.826805i	$-0.690156\pi$
$281$	−25.2038	−	8.18922i	−1.50353	−	0.488528i	−0.941046	+	0.338278i	$0.890156\pi$
$282$	12.8019	−	5.61456i	0.762343	−	0.334342i
$283$	−22.9139	+	3.62921i	−1.36209	+	0.215734i	−0.794343	−	0.607469i	$-0.792185\pi$
$283$	−22.9139	+	3.62921i	−1.36209	+	0.215734i	−0.567747	+	0.823203i	$0.692185\pi$
$284$	5.30491	−	9.18838i	0.314789	−	0.545230i
$285$	18.9240	+	7.11326i	1.12096	+	0.421353i
$286$	−0.197671	+	1.88072i	−0.0116886	+	0.111209i
$287$	3.87337	−	24.4555i	0.228638	−	1.44356i
$288$	−0.123629	−	2.99745i	−0.00728493	−	0.176627i
$289$	−10.4334	+	9.39424i	−0.613727	+	0.552602i
$290$	10.8611	+	11.7624i	0.637785	+	0.690710i
$291$	6.71561	−	4.30819i	0.393676	−	0.252550i
$292$	8.13701	+	12.5299i	0.476183	+	0.733257i
$293$	−9.29195	−	24.2064i	−0.542842	−	1.41415i	−0.881025	−	0.473071i	$-0.843146\pi$
$293$	−9.29195	−	24.2064i	−0.542842	−	1.41415i	0.338183	−	0.941080i	$-0.390188\pi$
$294$	18.0421	+	22.5356i	1.05223	+	1.31430i
$295$	−4.73489	−	0.689175i	−0.275676	−	0.0401253i
$296$	1.95392	−	4.38858i	0.113569	−	0.255081i
$297$	0.865464	+	9.80807i	0.0502193	+	0.569122i
$298$	−12.3202	+	18.9714i	−0.713690	+	1.09899i
$299$	−7.33871	+	3.26740i	−0.424408	+	0.188959i
$300$	−4.95268	+	7.10429i	−0.285943	+	0.410167i
$301$	2.12172	+	20.1869i	0.122294	+	1.16355i
$302$	3.18670	−	20.1200i	0.183374	−	1.15778i
$303$	0.939945	−	1.60729i	0.0539984	−	0.0923365i
$304$	4.52061	−	2.60997i	0.259275	−	0.149692i
$305$	8.13962	+	12.1963i	0.466073	+	0.698356i
$306$	5.13928	−	0.482349i	0.293793	−	0.0275741i
$307$	0.910792	−	0.0477326i	0.0519816	−	0.00272424i	−0.0263274	−	0.999653i	$-0.508381\pi$
$307$	0.910792	−	0.0477326i	0.0519816	−	0.00272424i	0.0783090	+	0.996929i	$0.475048\pi$
$308$	−8.21369	+	4.18508i	−0.468018	+	0.238467i
$309$	5.28795	+	14.0083i	0.300821	+	0.796903i
$310$	−2.42500	−	12.2114i	−0.137731	−	0.693563i
$311$			7.99499i			0.453354i	0.973970	+	0.226677i	$0.0727862\pi$
$311$			7.99499i			0.453354i	−0.973970	+	0.226677i	$0.927214\pi$
$312$	1.27811	+	1.16377i	0.0723586	+	0.0658854i
$313$	−1.63608	−	31.2182i	−0.0924766	−	1.76456i	−0.514046	−	0.857762i	$-0.671854\pi$
$313$	−1.63608	−	31.2182i	−0.0924766	−	1.76456i	0.421570	−	0.906796i	$-0.361479\pi$
$314$	−3.92206	−	2.84954i	−0.221334	−	0.160809i
$315$	−28.2394	+	16.3569i	−1.59111	+	0.921610i
$316$	5.08031	+	8.79936i	0.285790	+	0.495002i
$317$	0.591752	+	0.730753i	0.0332361	+	0.0410432i	0.793493	−	0.608579i	$-0.208260\pi$
$317$	0.591752	+	0.730753i	0.0332361	+	0.0410432i	−0.760257	+	0.649623i	$0.774927\pi$
$318$	−1.31605	−	6.36564i	−0.0738004	−	0.356968i
$319$	−13.4928	+	1.41816i	−0.755454	+	0.0794014i
$320$	0.605780	+	2.15245i	0.0338642	+	0.120325i
$321$	−13.5919	−	13.7441i	−0.758625	−	0.767123i
$322$	−32.8419	−	21.3278i	−1.83021	−	1.18855i
$323$	4.89170	+	7.53256i	0.272182	+	0.419123i
$324$	7.69206	+	4.67250i	0.427337	+	0.259583i
$325$	−0.903966	−	4.90736i	−0.0501430	−	0.272211i
$326$	−12.7763	+	4.15126i	−0.707611	+	0.229917i
$327$	17.9223	+	20.1291i	0.991106	+	1.11314i
$328$	4.26851	−	2.77200i	0.235689	−	0.153058i
$329$	−38.4053	+	8.16330i	−2.11735	+	0.450057i
$330$	−2.31646	−	6.96373i	−0.127517	−	0.383341i
$331$	6.04050	+	6.70865i	0.332016	+	0.368741i	0.885919	−	0.463840i	$-0.153529\pi$
$331$	6.04050	+	6.70865i	0.332016	+	0.368741i	−0.553903	+	0.832581i	$0.686862\pi$
$332$	2.17995	+	1.76529i	0.119640	+	0.0968827i
$333$	7.71406	+	12.1733i	0.422728	+	0.667094i
$334$	16.6398	+	1.74891i	0.910488	+	0.0956962i
$335$	−4.68014	−	4.10891i	−0.255703	−	0.224494i
$336$	−1.36448	+	8.31500i	−0.0744384	+	0.453620i
$337$	4.45793	+	28.1463i	0.242839	+	1.53322i	0.744183	+	0.667976i	$0.232839\pi$
$337$	4.45793	+	28.1463i	0.242839	+	1.53322i	−0.501344	+	0.865248i	$0.667161\pi$
$338$	11.9876	−	0.628242i	0.652038	−	0.0341719i
$339$	0.291744	+	6.23053i	0.0158453	+	0.338396i
$340$	−3.64392	+	1.23472i	−0.197619	+	0.0669620i
$341$	9.52364	+	4.53983i	0.515734	+	0.245846i
$342$	−0.993706	+	15.6283i	−0.0537334	+	0.845081i
$343$	−21.3506	−	41.9030i	−1.15283	−	2.26255i
$344$	−2.79186	+	3.10067i	−0.150527	+	0.167177i
$345$	20.6983	−	23.3127i	1.11436	−	1.25511i
$346$	11.9296	−	20.6627i	0.641340	−	1.11083i
$347$	14.1885	+	3.80181i	0.761681	+	0.204092i	0.618693	−	0.785633i	$-0.287662\pi$
$347$	14.1885	+	3.80181i	0.761681	+	0.204092i	0.142988	+	0.989724i	$0.454329\pi$
$348$	−6.26032	+	10.7051i	−0.335588	+	0.573852i
$349$	−12.1600	−	16.7368i	−0.650910	−	0.895901i	0.348228	−	0.937410i	$-0.386784\pi$
$349$	−12.1600	−	16.7368i	−0.650910	−	0.895901i	−0.999138	+	0.0415086i	$0.986784\pi$
$350$	17.6626	−	16.7245i	0.944106	−	0.893960i
$351$	−5.03070	+	1.25828i	−0.268519	+	0.0671620i
$352$	−1.76904	−	0.679071i	−0.0942901	−	0.0361946i
$353$	23.9486	+	15.5524i	1.27466	+	0.827772i	0.991348	−	0.131256i	$-0.0419011\pi$
$353$	23.9486	+	15.5524i	1.27466	+	0.827772i	0.283309	+	0.959029i	$0.408568\pi$
$354$	−0.559394	−	3.66382i	−0.0297315	−	0.194730i
$355$	−15.1602	−	18.2485i	−0.804622	−	0.968531i
$356$	4.46712	−	1.45145i	0.236757	−	0.0769269i
$357$	−14.4102	−	1.59576i	−0.762670	−	0.0844568i
$358$	−1.81950	+	0.698441i	−0.0961636	+	0.0369138i
$359$	9.35934	+	1.98939i	0.493967	+	0.104996i	0.448158	−	0.893954i	$-0.352080\pi$
$359$	9.35934	+	1.98939i	0.493967	+	0.104996i	0.0458089	+	0.998950i	$0.485413\pi$
$360$	−6.38278	−	2.06399i	−0.336402	−	0.108782i
$361$	−7.53480	+	3.35471i	−0.396568	+	0.176564i
$362$	16.9598	+	0.888826i	0.891388	+	0.0467157i
$363$	−12.1830	−	4.03365i	−0.639442	−	0.211712i
$364$	−2.85374	−	3.92783i	−0.149576	−	0.205874i
$365$	32.5876	−	7.35506i	1.70571	−	0.384981i
$366$	−7.19679	+	8.78678i	−0.376182	+	0.459292i
$367$	10.2751	−	2.75322i	0.536358	−	0.143717i	0.0195355	−	0.999809i	$-0.493781\pi$
$367$	10.2751	−	2.75322i	0.536358	−	0.143717i	0.516823	+	0.856092i	$0.327115\pi$
$368$	−1.25921	−	7.95034i	−0.0656409	−	0.414440i
$369$	−0.170067	+	15.2679i	−0.00885336	+	0.794815i
$370$	−7.69029	−	7.49976i	−0.399799	−	0.389894i
$371$			18.2575i			0.947883i
$372$	8.49945	−	4.55625i	0.440676	−	0.236231i
$373$	−3.62820	+	3.62820i	−0.187861	+	0.187861i	−0.794771	−	0.606910i	$-0.792409\pi$
$373$	−3.62820	+	3.62820i	−0.187861	+	0.187861i	0.606910	+	0.794771i	$0.292409\pi$
$374$	1.00752	−	3.10082i	0.0520976	−	0.160340i
$375$	11.0620	+	15.8944i	0.571240	+	0.820783i
$376$	−6.52939	−	4.74388i	−0.336728	−	0.244647i
$377$	−1.84937	−	6.90193i	−0.0952473	−	0.355468i
$378$	−18.5005	−	17.2262i	−0.951562	−	0.886020i
$379$	−22.5536	−	2.37048i	−1.15850	−	0.121763i	−0.494281	−	0.869302i	$-0.664569\pi$
$379$	−22.5536	−	2.37048i	−1.15850	−	0.121763i	−0.664218	+	0.747539i	$0.731235\pi$
$380$	−1.97037	−	11.5046i	−0.101078	−	0.590176i
$381$	0.238600	+	0.474798i	0.0122239	+	0.0243247i
$382$	0.270564	−	5.16267i	0.0138432	−	0.264145i
$383$	13.8015	+	5.29789i	0.705223	+	0.270710i	0.684435	−	0.729074i	$-0.260049\pi$
$383$	13.8015	+	5.29789i	0.705223	+	0.270710i	0.0207880	+	0.999784i	$0.493382\pi$
$384$	−1.45785	+	0.935238i	−0.0743957	+	0.0477262i
$385$	2.41159	+	20.4715i	0.122906	+	1.04332i
$386$	7.82941	−	17.5851i	0.398506	−	0.895060i
$387$	−3.10480	−	12.1259i	−0.157826	−	0.616395i
$388$	−4.10443	−	2.09131i	−0.208371	−	0.106170i
$389$	−29.2374	−	13.0173i	−1.48239	−	0.660004i	−0.503430	−	0.864036i	$-0.667929\pi$
$389$	−29.2374	−	13.0173i	−1.48239	−	0.660004i	−0.978964	+	0.204032i	$0.934595\pi$
$390$	3.43158	−	1.77872i	0.173765	−	0.0900692i
$391$	13.5474	−	2.87958i	0.685120	−	0.145627i
$392$	5.97292	−	15.5600i	0.301678	−	0.785898i
$393$	−2.57707	−	8.08434i	−0.129996	−	0.407801i
$394$	−13.3952	+	1.40789i	−0.674839	+	0.0709285i
$395$	22.3938	−	3.83533i	1.12675	−	0.192976i
$396$	4.63594	−	3.28995i	0.232965	−	0.165326i
$397$	1.20100	−	4.48219i	0.0602765	−	0.224955i	−0.929217	−	0.369536i	$-0.879517\pi$
$397$	1.20100	−	4.48219i	0.0602765	−	0.224955i	0.989493	+	0.144581i	$0.0461834\pi$
$398$	−6.53173	+	1.75017i	−0.327406	+	0.0877282i
$399$	11.6204	−	42.4216i	0.581749	−	2.12374i
$400$	4.98415	+	0.397756i	0.249208	+	0.0198878i
$401$	−12.2103	−	3.96736i	−0.609752	−	0.198120i	−0.0121670	−	0.999926i	$-0.503873\pi$
$401$	−12.2103	−	3.96736i	−0.609752	−	0.198120i	−0.597585	+	0.801806i	$0.703873\pi$
$402$	1.98666	−	4.39605i	0.0990855	−	0.219255i
$403$	−1.57691	+	5.32809i	−0.0785514	+	0.265411i
$404$	−1.07500			−0.0534833
$405$	15.7623	−	12.5120i	0.783235	−	0.621725i
$406$	23.3070	−	25.8850i	1.15671	−	1.28465i
$407$	8.99082	−	1.42401i	0.445658	−	0.0705853i
$408$	−1.73826	−	2.42075i	−0.0860569	−	0.119845i
$409$	23.3278	−	13.4683i	1.15348	−	0.665964i	0.203750	−	0.979023i	$-0.434687\pi$
$409$	23.3278	−	13.4683i	1.15348	−	0.665964i	0.949734	+	0.313059i	$0.101354\pi$
$410$	−2.50562	−	11.1015i	−0.123744	−	0.548263i
$411$	14.4287	+	9.48477i	0.711716	+	0.467849i
$412$	5.44031	−	6.71822i	0.268025	−	0.330983i
$413$	−0.544815	+	10.3957i	−0.0268086	+	0.511539i
$414$	21.9498	+	10.0671i	1.07877	+	0.494772i
$415$	5.39223	−	3.20404i	0.264694	−	0.157280i
$416$	0.207493	−	0.976176i	0.0101732	−	0.0478609i
$417$	−15.9852	−	17.9535i	−0.782800	−	0.879185i
$418$	8.81318	+	4.49054i	0.431067	+	0.219640i
$419$	10.0081	+	30.8018i	0.488928	+	1.50476i	0.826211	+	0.563361i	$0.190492\pi$
$419$	10.0081	+	30.8018i	0.488928	+	1.50476i	−0.337283	+	0.941403i	$0.609508\pi$
$420$	16.3826	+	9.30678i	0.799388	+	0.454124i
$421$	−36.4697	−	7.75187i	−1.77742	−	0.377803i	−0.801859	−	0.597513i	$-0.796155\pi$
$421$	−36.4697	−	7.75187i	−1.77742	−	0.377803i	−0.975565	+	0.219710i	$0.929489\pi$
$422$	0.275031	−	0.423511i	0.0133883	−	0.0206162i
$423$	22.6994	−	8.42461i	1.10368	−	0.409619i
$424$	−2.78897	+	2.51120i	−0.135444	+	0.121955i
$425$	−0.234624	+	8.59990i	−0.0113809	+	0.417157i
$426$	10.0944	−	15.3561i	0.489074	−	0.744004i
$427$	24.7920	−	20.0761i	1.19977	−	0.971552i
$428$	−2.88844	+	10.7798i	−0.139618	+	0.521061i
$429$	−0.530401	+	3.23221i	−0.0256080	+	0.156053i
$430$	4.33952	+	8.25904i	0.209270	+	0.398286i
$431$	−18.6992	−	16.8368i	−0.900707	−	0.811000i	0.0819110	−	0.996640i	$-0.473898\pi$
$431$	−18.6992	−	16.8368i	−0.900707	−	0.811000i	−0.982618	+	0.185639i	$0.940564\pi$
$432$	0.0868114	−	5.19543i	0.00417672	−	0.249965i
$433$	16.9683	−	16.9683i	0.815446	−	0.815446i	−0.169998	−	0.985444i	$-0.554376\pi$
$433$	16.9683	−	16.9683i	0.815446	−	0.815446i	0.985444	+	0.169998i	$0.0543762\pi$
$434$	−25.9693	+	7.69899i	−1.24656	+	0.369563i
$435$	17.6009	+	21.4280i	0.843897	+	1.02739i
$436$	4.80846	−	14.7989i	0.230283	−	0.708740i
$437$	2.19903	+	41.9601i	0.105194	+	2.00722i
$438$	12.8136	+	22.4820i	0.612257	+	1.07423i
$439$	30.4311	+	17.5694i	1.45240	+	0.838543i	0.998617	−	0.0525695i	$-0.0167411\pi$
$439$	30.4311	+	17.5694i	1.45240	+	0.838543i	0.453782	+	0.891113i	$0.350074\pi$
$440$	−2.79547	+	3.18410i	−0.133269	+	0.151796i
$441$	28.9375	+	40.7765i	1.37798	+	1.94174i
$442$	1.69601	+	0.268622i	0.0806710	+	0.0127770i
$443$	6.79870	−	8.39569i	0.323016	−	0.398891i	−0.589609	−	0.807688i	$-0.700718\pi$
$443$	6.79870	−	8.39569i	0.323016	−	0.398891i	0.912625	+	0.408797i	$0.134052\pi$
$444$	3.81870	−	7.39255i	0.181227	−	0.350835i
$445$	0.418087	−	10.4945i	0.0198192	−	0.497487i
$446$	−0.684137	−	3.21861i	−0.0323948	−	0.152406i
$447$	−23.2059	+	31.5689i	−1.09760	+	1.49316i
$448$	4.54175	−	1.74342i	0.214578	−	0.0823686i
$449$	0.183304	+	0.564150i	0.00865063	+	0.0266239i	0.955289	−	0.295675i	$-0.0955445\pi$
$449$	0.183304	+	0.564150i	0.00865063	+	0.0266239i	−0.946638	+	0.322299i	$0.895544\pi$
$450$	−9.27632	+	11.7877i	−0.437290	+	0.555677i
$451$	8.81050	+	3.92269i	0.414870	+	0.184712i
$452$	3.02017	−	1.96132i	0.142057	−	0.0922528i
$453$	7.52790	−	34.4709i	0.353691	−	1.61958i
$454$	10.7284	+	24.0964i	0.503510	+	1.13090i
$455$	−10.4503	+	2.94110i	−0.489917	+	0.137881i
$456$	8.07852	−	4.05970i	0.378311	−	0.190113i
$457$	−22.1318	−	3.50534i	−1.03528	−	0.163973i	−0.384413	−	0.923161i	$-0.625596\pi$
$457$	−22.1318	−	3.50534i	−1.03528	−	0.163973i	−0.650871	+	0.759189i	$0.725596\pi$
$458$	−1.81391	+	1.46888i	−0.0847586	+	0.0686362i
$459$	8.93493	−	0.318685i	0.417047	−	0.0148749i
$460$	−17.6513	−	3.52112i	−0.822997	−	0.164173i
$461$	−1.66937	+	2.29769i	−0.0777504	+	0.107014i	−0.846121	−	0.532991i	$-0.821068\pi$
$461$	−1.66937	+	2.29769i	−0.0777504	+	0.107014i	0.768370	+	0.640005i	$0.221068\pi$
$462$	−14.6223	+	6.41295i	−0.680293	+	0.298357i
$463$	−0.796991	−	1.56418i	−0.0370393	−	0.0726938i	0.871745	−	0.489959i	$-0.162988\pi$
$463$	−0.796991	−	1.56418i	−0.0370393	−	0.0726938i	−0.908785	+	0.417266i	$0.862988\pi$
$464$	7.15984			0.332387
$465$	−2.96861	−	21.3585i	−0.137666	−	0.990479i
$466$	6.73111			0.311813
$467$	3.29293	+	6.46273i	0.152378	+	0.299059i	0.954559	−	0.298022i	$-0.0963269\pi$
$467$	3.29293	+	6.46273i	0.152378	+	0.299059i	−0.802181	+	0.597082i	$0.796327\pi$
$468$	2.09333	+	2.14049i	0.0967643	+	0.0989443i
$469$	−7.96430	+	10.9619i	−0.367757	+	0.506174i
$470$	−15.0109	+	10.0180i	−0.692399	+	0.462098i
$471$	−6.49606	−	5.32058i	−0.299322	−	0.245159i
$472$	−1.66295	+	1.34663i	−0.0765437	+	0.0619838i
$473$	−7.80887	−	1.23680i	−0.359052	−	0.0568683i
$474$	7.90220	+	15.7248i	0.362960	+	0.722265i
$475$	−25.6575	−	4.78441i	−1.17725	−	0.219524i
$476$	3.40463	+	7.64693i	0.156051	+	0.350496i
$477$	−1.63729	−	11.1391i	−0.0749665	−	0.510024i
$478$	3.61805	−	2.34959i	0.165486	−	0.107468i
$479$	−9.28164	−	4.13245i	−0.424089	−	0.188817i	0.183584	−	0.983004i	$-0.441230\pi$
$479$	−9.28164	−	4.13245i	−0.424089	−	0.188817i	−0.607673	+	0.794187i	$0.707897\pi$
$480$	0.831635	+	3.78264i	0.0379588	+	0.172653i
$481$	1.48149	+	4.55956i	0.0675502	+	0.207898i
$482$	10.4336	−	4.00509i	0.475238	−	0.182427i
$483$	−54.6497	−	40.1723i	−2.48665	−	1.82790i
$484$	1.54049	+	7.24745i	0.0700224	+	0.329430i
$485$	−7.56770	+	6.98783i	−0.343632	+	0.317301i
$486$	12.8321	+	8.85079i	0.582077	+	0.401480i
$487$	10.5760	−	13.0602i	0.479242	−	0.591815i	−0.478985	−	0.877823i	$-0.658995\pi$
$487$	10.5760	−	13.0602i	0.479242	−	0.591815i	0.958227	+	0.286008i	$0.0923285\pi$
$488$	6.47674	+	1.02581i	0.293188	+	0.0464364i
$489$	−22.5083	+	5.89693i	−1.01786	+	0.266668i
$490$	−28.0065	−	24.5882i	−1.26521	−	1.11078i
$491$	−7.71111	−	4.45201i	−0.347998	−	0.200917i	0.315805	−	0.948824i	$-0.397725\pi$
$491$	−7.71111	−	4.45201i	−0.347998	−	0.200917i	−0.663803	+	0.747907i	$0.731059\pi$
$492$	7.65885	−	4.36515i	0.345288	−	0.196796i
$493$	0.644746	+	12.3025i	0.0290379	+	0.554076i
$494$	−1.60980	+	4.95446i	−0.0724284	+	0.222912i
$495$	−3.30718	−	12.2736i	−0.148646	−	0.551657i
$496$	−4.74797	−	2.90805i	−0.213190	−	0.130575i
$497$	−36.4976	+	36.4976i	−1.63714	+	1.63714i
$498$	3.59242	+	3.27104i	0.160980	+	0.146579i
$499$	7.45470	+	6.71224i	0.333718	+	0.300481i	0.818905	−	0.573930i	$-0.194582\pi$
$499$	7.45470	+	6.71224i	0.333718	+	0.300481i	−0.485187	+	0.874411i	$0.661248\pi$
$500$	4.69744	−	10.1456i	0.210076	−	0.453727i
$501$	28.5972	+	4.69276i	1.27763	+	0.209657i
$502$	0.875864	−	3.26877i	0.0390917	−	0.145892i
$503$	−18.4401	+	14.9325i	−0.822203	+	0.665807i	−0.945161	−	0.326605i	$-0.894095\pi$
$503$	−18.4401	+	14.9325i	−0.822203	+	0.665807i	0.122958	+	0.992412i	$0.460762\pi$
$504$	−3.19321	+	14.2410i	−0.142237	+	0.634345i
$505$	−0.833223	+	2.25475i	−0.0370779	+	0.100335i
$506$	11.3351	−	10.2062i	0.503906	−	0.453719i
$507$	20.7913	+	0.115792i	0.923372	+	0.00514251i
$508$	0.167091	−	0.257297i	0.00741345	−	0.0114157i
$509$	4.44422	+	0.944648i	0.196986	+	0.0418708i	0.305348	−	0.952241i	$-0.401227\pi$
$509$	4.44422	+	0.944648i	0.196986	+	0.0418708i	−0.108362	+	0.994112i	$0.534560\pi$
$510$	−6.42468	+	1.76960i	−0.284490	+	0.0783590i
$511$	−22.4600	−	69.1249i	−0.993573	−	3.05790i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−3.28547	+	26.9239i	−0.145057	+	1.18872i
$514$	−3.05716	+	14.3828i	−0.134846	+	0.634399i
$515$	−9.87430	−	16.6179i	−0.435114	−	0.732273i
$516$	−5.13847	+	5.08155i	−0.226208	+	0.223703i
$517$	0.800389	−	15.2723i	0.0352011	−	0.671676i
$518$	−14.7074	+	18.1622i	−0.646208	+	0.798000i
$519$	22.7001	−	34.5325i	0.996424	−	1.51581i
$520$	−1.88664	−	1.19183i	−0.0827346	−	0.0522650i
$521$	22.0362	−	12.7226i	0.965424	−	0.557388i	0.0675862	−	0.997713i	$-0.478470\pi$
$521$	22.0362	−	12.7226i	0.965424	−	0.557388i	0.897838	+	0.440325i	$0.145137\pi$
$522$	−11.8985	+	17.8828i	−0.520784	+	0.782710i
$523$	−34.9172	+	5.53034i	−1.52682	+	0.241825i	−0.862668	−	0.505771i	$-0.831208\pi$
$523$	−34.9172	+	5.53034i	−1.52682	+	0.241825i	−0.664154	+	0.747596i	$0.731208\pi$
$524$	−3.27801	+	3.64060i	−0.143200	+	0.159040i
$525$	32.2183	−	27.1478i	1.40612	−	1.18483i
$526$	6.20900			0.270725
$527$	4.56924	−	8.42014i	0.199039	−	0.366787i
$528$	−2.99083	−	1.35161i	−0.130159	−	0.0588213i
$529$	39.7480	+	12.9149i	1.72817	+	0.561517i
$530$	3.10537	+	7.79609i	0.134889	+	0.338640i
$531$	−0.599866	−	6.39138i	−0.0260319	−	0.277362i
$532$	−24.5291	+	6.57255i	−1.06347	+	0.284956i
$533$	−1.31463	+	4.90628i	−0.0569431	+	0.212514i
$534$	7.86984	−	2.06181i	0.340561	−	0.0892233i
$535$	20.3711	+	14.4136i	0.880720	+	0.623155i
$536$	−2.76995	+	0.291133i	−0.119643	+	0.0125750i
$537$	−3.21622	+	1.02525i	−0.138790	+	0.0442427i
$538$	−3.62520	+	9.44397i	−0.156293	+	0.407158i
$539$	30.8921	−	6.56632i	1.33062	−	0.282832i
$540$	−10.8298	−	4.20901i	−0.466040	−	0.181127i
$541$	9.65301	+	4.29780i	0.415015	+	0.184777i	0.603613	−	0.797278i	$-0.293727\pi$
$541$	9.65301	+	4.29780i	0.415015	+	0.184777i	−0.188597	+	0.982055i	$0.560394\pi$
$542$	24.0617	+	12.2600i	1.03354	+	0.526613i
$543$	29.2369	+	3.23764i	1.25467	+	0.138940i
$544$	−0.699839	+	1.57187i	−0.0300054	+	0.0673932i
$545$	−27.3128	−	21.5559i	−1.16995	−	0.923355i
$546$	−4.54064	−	7.07797i	−0.194322	−	0.302909i
$547$	−18.3314	−	7.03676i	−0.783793	−	0.300870i	−0.0666324	−	0.997778i	$-0.521225\pi$
$547$	−18.3314	−	7.03676i	−0.783793	−	0.300870i	−0.717161	+	0.696907i	$0.754559\pi$
$548$	0.521742	−	9.95543i	0.0222877	−	0.425275i
$549$	−13.3254	+	14.4719i	−0.568716	+	0.617647i
$550$	4.51171	+	8.33129i	0.192380	+	0.355247i
$551$	−37.1693	−	3.90665i	−1.58346	−	0.166429i
$552$	−1.38010	−	13.8736i	−0.0587408	−	0.590498i
$553$	−12.7935	−	47.7459i	−0.544033	−	2.03036i
$554$	−8.63215	−	6.27162i	−0.366745	−	0.266456i
$555$	−12.5456	−	13.7394i	−0.532529	−	0.583204i
$556$	−4.28875	+	13.1994i	−0.181884	+	0.559780i
$557$	24.7406	−	24.7406i	1.04829	−	1.04829i	0.0495216	−	0.998773i	$-0.484230\pi$
$557$	24.7406	−	24.7406i	1.04829	−	1.04829i	0.998773	−	0.0495216i	$-0.0157697\pi$
$558$	15.1537	−	7.02610i	0.641506	−	0.297438i
$559$		−	4.16396i		−	0.176117i
$560$	−0.136433	−	10.8773i	−0.00576536	−	0.459651i
$561$	2.05310	−	5.26074i	0.0866818	−	0.222109i
$562$	4.14565	+	26.1746i	0.174874	+	1.10411i
$563$	15.8762	−	4.25402i	0.669102	−	0.179285i	0.0917519	−	0.995782i	$-0.470753\pi$
$563$	15.8762	−	4.25402i	0.669102	−	0.179285i	0.577350	+	0.816496i	$0.304087\pi$
$564$	−10.8146	−	8.85763i	−0.455375	−	0.372973i
$565$	−1.77284	−	7.85481i	−0.0745840	−	0.330454i
$566$	13.6363	+	18.7688i	0.573178	+	0.788912i
$567$	−30.2626	−	31.6418i	−1.27091	−	1.32883i
$568$	−10.5953	−	0.555275i	−0.444568	−	0.0232988i
$569$	−41.0818	+	18.2908i	−1.72224	+	0.766790i	−0.725316	+	0.688417i	$0.758306\pi$
$569$	−41.0818	+	18.2908i	−1.72224	+	0.766790i	−0.996924	+	0.0783739i	$0.975027\pi$
$570$	−2.25338	−	20.0908i	−0.0943835	−	0.841511i
$571$	28.6058	+	6.08035i	1.19712	+	0.254455i	0.762998	−	0.646401i	$-0.223727\pi$
$571$	28.6058	+	6.08035i	1.19712	+	0.254455i	0.434118	+	0.900856i	$0.357060\pi$
$572$	1.76547	−	0.677702i	0.0738181	−	0.0283361i
$573$	0.985556	−	8.89987i	0.0411722	−	0.371797i
$574$	−23.5485	+	7.65136i	−0.982894	+	0.319362i
$575$	−21.0667	+	34.2933i	−0.878542	+	1.43013i
$576$	−2.61462	+	1.47097i	−0.108943	+	0.0612904i
$577$	7.88360	+	5.11967i	0.328198	+	0.213135i	0.698211	−	0.715892i	$-0.253980\pi$
$577$	7.88360	+	5.11967i	0.328198	+	0.213135i	−0.370012	+	0.929027i	$0.620647\pi$
$578$	13.1070	+	5.03129i	0.545178	+	0.209274i
$579$	15.3016	−	29.6221i	0.635914	−	1.23105i
$580$	5.54952	−	15.0173i	0.230431	−	0.623560i
$581$	−8.02110	−	11.0401i	−0.332771	−	0.458020i
$582$	−6.88745	−	4.02778i	−0.285494	−	0.166957i
$583$	−6.86910	−	1.84057i	−0.284489	−	0.0762286i
$584$	7.47010	−	12.9386i	0.309115	−	0.535403i
$585$	6.11207	−	2.73155i	0.252703	−	0.112936i
$586$	−17.3496	+	19.2687i	−0.716704	+	0.795981i
$587$	12.8979	+	25.3135i	0.532352	+	1.04480i	0.987973	+	0.154626i	$0.0494171\pi$
$587$	12.8979	+	25.3135i	0.532352	+	1.04480i	−0.455621	+	0.890174i	$0.650583\pi$
$588$	11.8884	−	26.3065i	0.490270	−	1.08486i
$589$	23.0617	+	17.6874i	0.950240	+	0.728795i
$590$	1.53554	+	4.53170i	0.0632171	+	0.186567i
$591$	−23.3034	+	1.09118i	−0.958573	+	0.0448850i
$592$	−4.79731	+	0.251416i	−0.197168	+	0.0103332i
$593$	−5.72384	−	36.1389i	−0.235050	−	1.48405i	−0.769391	−	0.638778i	$-0.779440\pi$
$593$	−5.72384	−	36.1389i	−0.235050	−	1.48405i	0.534341	−	0.845269i	$-0.320560\pi$
$594$	8.34614	−	5.22390i	0.342446	−	0.214339i
$595$	18.6778	−	1.21394i	0.765716	−	0.0497665i
$596$	22.4969	+	2.36452i	0.921510	+	0.0968546i
$597$	−11.4698	+	2.37130i	−0.469429	+	0.0970509i
$598$	6.24298	+	5.05546i	0.255294	+	0.206733i
$599$	7.46336	+	8.28890i	0.304945	+	0.338675i	0.876067	−	0.482190i	$-0.160158\pi$
$599$	7.46336	+	8.28890i	0.304945	+	0.338675i	−0.571122	+	0.820865i	$0.693492\pi$
$600$	8.57844	+	1.18759i	0.350213	+	0.0484831i
$601$	−20.3551	+	4.32661i	−0.830303	+	0.176486i	−0.603408	−	0.797433i	$-0.706191\pi$
$601$	−20.3551	+	4.32661i	−0.830303	+	0.176486i	−0.226895	+	0.973919i	$0.572857\pi$
$602$	17.0234	−	11.0551i	0.693821	−	0.450573i
$603$	3.87606	−	7.40219i	0.157845	−	0.301441i
$604$	−19.3738	+	6.29493i	−0.788308	+	0.256137i
$605$	16.3951	+	2.38634i	0.666555	+	0.0970186i
$606$	−1.85883	−	0.107801i	−0.0755100	−	0.00437912i
$607$	1.00266	+	1.54396i	0.0406967	+	0.0626675i	0.858433	−	0.512925i	$-0.171438\pi$
$607$	1.00266	+	1.54396i	0.0406967	+	0.0626675i	−0.817737	+	0.575593i	$0.804771\pi$
$608$	−4.37782	−	2.84299i	−0.177544	−	0.115298i
$609$	42.8969	−	42.4217i	1.73827	−	1.71902i
$610$	7.17164	−	12.7894i	0.290371	−	0.517829i
$611$	8.01038	−	0.841925i	0.324065	−	0.0340606i
$612$	−2.76296	−	4.36015i	−0.111686	−	0.176248i
$613$	27.0600	+	33.4163i	1.09294	+	1.34967i	0.931897	+	0.362724i	$0.118153\pi$
$613$	27.0600	+	33.4163i	1.09294	+	1.34967i	0.161045	+	0.986947i	$0.448514\pi$
$614$	−0.456021	−	0.789851i	−0.0184035	−	0.0318758i
$615$	−3.21932	−	19.4473i	−0.129815	−	0.784192i
$616$	7.45787	+	5.41846i	0.300486	+	0.218316i
$617$	−1.23564	−	23.5774i	−0.0497450	−	0.949192i	−0.903519	−	0.428548i	$-0.859025\pi$
$617$	−1.23564	−	23.5774i	−0.0497450	−	0.949192i	0.853774	−	0.520644i	$-0.174308\pi$
$618$	10.0808	−	11.0712i	0.405509	−	0.445350i
$619$		−	5.10094i		−	0.205024i	−0.994732	−	0.102512i	$-0.967312\pi$
$619$		−	5.10094i		−	0.205024i	0.994732	−	0.102512i	$-0.0326880\pi$
$620$	−9.77955	+	7.70457i	−0.392756	+	0.309423i
$621$	36.9449	+	19.6086i	1.48255	+	0.786867i
$622$	7.12359	−	3.62965i	0.285630	−	0.145536i
$623$	−22.8190	+	1.19589i	−0.914225	+	0.0479125i
$624$	0.456676	−	1.66714i	0.0182817	−	0.0667391i
$625$	−17.6389	−	17.7164i	−0.705556	−	0.708654i
$626$	−27.0729	+	15.6305i	−1.08205	+	0.624722i
$627$	14.7890	+	8.64859i	0.590614	+	0.345391i
$628$	−0.758383	+	4.78824i	−0.0302628	+	0.191072i
$629$	−0.863999	−	8.22040i	−0.0344499	−	0.327769i
$630$	27.3946	+	17.7356i	1.09143	+	0.706604i
$631$	−6.57162	+	2.92587i	−0.261612	+	0.116477i	−0.533352	−	0.845894i	$-0.679068\pi$
$631$	−6.57162	+	2.92587i	−0.261612	+	0.116477i	0.271740	+	0.962371i	$0.412401\pi$
$632$	5.53387	−	8.52141i	0.220126	−	0.338964i
$633$	0.518038	−	0.704732i	0.0205902	−	0.0280106i
$634$	0.382456	−	0.859010i	0.0151893	−	0.0341157i
$635$	−0.410154	−	0.549891i	−0.0162765	−	0.0218217i
$636$	−5.07436	+	4.06255i	−0.201211	+	0.161091i
$637$	5.96088	+	15.5286i	0.236179	+	0.615266i
$638$	7.38921	+	11.3784i	0.292542	+	0.450475i
$639$	18.9945	−	25.5406i	0.751413	−	1.01037i
$640$	1.64283	−	1.51695i	0.0649384	−	0.0599625i
$641$	−3.60572	+	3.24661i	−0.142418	+	0.128233i	−0.737260	−	0.675609i	$-0.763881\pi$
$641$	−3.60572	+	3.24661i	−0.142418	+	0.128233i	0.594843	+	0.803842i	$0.297214\pi$
$642$	−6.07552	+	18.3502i	−0.239782	+	0.724223i
$643$	4.42158	−	27.9168i	0.174370	−	1.10093i	−0.732886	−	0.680351i	$-0.761827\pi$
$643$	4.42158	−	27.9168i	0.174370	−	1.10093i	0.907256	−	0.420578i	$-0.138173\pi$
$644$	−4.09328	+	38.9450i	−0.161298	+	1.53465i
$645$	6.67544	+	14.7163i	0.262845	+	0.579452i
$646$	4.49078	−	7.77825i	0.176687	−	0.306031i
$647$	20.3746	−	3.22703i	0.801010	−	0.126867i	0.257509	−	0.966276i	$-0.417098\pi$
$647$	20.3746	−	3.22703i	0.801010	−	0.126867i	0.543501	+	0.839409i	$0.317098\pi$
$648$	0.671107	−	8.97494i	0.0263636	−	0.352569i
$649$	−3.85629	−	1.25298i	−0.151373	−	0.0491839i
$650$	−3.96209	+	3.03333i	−0.155406	+	0.118977i
$651$	−45.6767	+	10.7085i	−1.79021	+	0.419698i
$652$	9.49910	+	9.49910i	0.372013	+	0.372013i
$653$	23.5838	−	12.0166i	0.922906	−	0.470244i	0.0730913	−	0.997325i	$-0.476714\pi$
$653$	23.5838	−	12.0166i	0.922906	−	0.470244i	0.849815	+	0.527081i	$0.176714\pi$
$654$	9.79856	−	25.1073i	0.383154	−	0.981773i
$655$	5.09516	+	9.69720i	0.199084	+	0.378901i
$656$	−4.40773	−	2.54481i	−0.172093	−	0.0993580i
$657$	19.9020	+	40.1596i	0.776453	+	1.56678i
$658$	24.7092	+	30.5133i	0.963265	+	1.18953i
$659$	8.95261	−	6.50445i	0.348744	−	0.253377i	−0.399598	−	0.916691i	$-0.630850\pi$
$659$	8.95261	−	6.50445i	0.348744	−	0.253377i	0.748342	+	0.663313i	$0.230850\pi$
$660$	−5.15308	+	5.22545i	−0.200583	+	0.203400i
$661$	−26.8619	−	29.8332i	−1.04481	−	1.16038i	−0.986781	−	0.162060i	$-0.948186\pi$
$661$	−26.8619	−	29.8332i	−1.04481	−	1.16038i	−0.0580256	−	0.998315i	$-0.518481\pi$
$662$	3.23512	−	8.42779i	0.125737	−	0.327555i
$663$	2.90571	+	0.634562i	0.112849	+	0.0246443i
$664$	0.583207	−	2.74377i	0.0226328	−	0.106479i
$665$	−5.22676	+	56.5425i	−0.202685	+	2.19263i
$666$	7.34441	−	12.3999i	0.284590	−	0.480484i
$667$	−26.1647	+	51.3511i	−1.01310	+	1.98832i
$668$	−5.99601	−	15.6201i	−0.231993	−	0.604361i
$669$	−0.860210	−	5.63405i	−0.0332576	−	0.217825i
$670$	−1.53633	+	6.03544i	−0.0593534	+	0.233169i
$671$	5.05400	+	11.3515i	0.195108	+	0.438219i
$672$	8.02818	−	2.55917i	0.309694	−	0.0987222i
$673$	−36.9300	−	29.9053i	−1.42355	−	1.15276i	−0.964414	−	0.264396i	$-0.914828\pi$
$673$	−36.9300	−	29.9053i	−1.42355	−	1.15276i	−0.459131	−	0.888369i	$-0.651839\pi$
$674$	23.0546	−	16.7502i	0.888032	−	0.645193i
$675$	−17.2222	+	19.4524i	−0.662882	+	0.748724i
$676$	−6.00201	−	10.3958i	−0.230847	−	0.399838i
$677$	−1.97193	−	7.35934i	−0.0757874	−	0.282843i	0.917623	−	0.397451i	$-0.130105\pi$
$677$	−1.97193	−	7.35934i	−0.0757874	−	0.282843i	−0.993411	+	0.114609i	$0.963439\pi$
$678$	5.41899	−	3.08855i	0.208115	−	0.118615i
$679$	16.6540	+	14.9953i	0.639120	+	0.575467i
$680$	2.75445	+	2.68621i	0.105628	+	0.103011i
$681$	16.1346	+	42.7421i	0.618280	+	1.63788i
$682$	−0.278619	−	10.5467i	−0.0106689	−	0.403853i
$683$	17.7440	+	17.7440i	0.678957	+	0.678957i	0.959764	−	0.280807i	$-0.0906021\pi$
$683$	17.7440	+	17.7440i	0.678957	+	0.678957i	−0.280807	+	0.959764i	$0.590602\pi$
$684$	14.3760	−	6.20970i	0.549682	−	0.237434i
$685$	−20.4765	−	8.81068i	−0.782366	−	0.336639i
$686$	−27.6428	+	38.0471i	−1.05541	+	1.45264i
$687$	−3.28382	+	2.35800i	−0.125286	+	0.0899635i
$688$	4.03020	+	1.07989i	0.153650	+	0.0411703i
$689$	0.391497	−	3.72484i	0.0149148	−	0.141905i
$690$	−30.1686	−	7.85860i	−1.14850	−	0.299172i
$691$	1.99601	+	18.9907i	0.0759317	+	0.722442i	0.964569	+	0.263831i	$0.0849861\pi$
$691$	1.99601	+	18.9907i	0.0759317	+	0.722442i	−0.888637	+	0.458611i	$0.848347\pi$
$692$	−23.8265	−	1.24870i	−0.905749	−	0.0474683i
$693$	−25.9273	+	9.62259i	−0.984895	+	0.365532i
$694$	−3.05403	−	14.3681i	−0.115929	−	0.545404i
$695$	24.3608	+	19.2261i	0.924056	+	0.729288i
$696$	12.3804	+	0.717989i	0.469278	+	0.0272153i
$697$	3.97573	−	7.80280i	0.150591	−	0.295552i
$698$	−9.39209	+	18.4330i	−0.355496	+	0.697700i
$699$	11.6391	+	0.674996i	0.440230	+	0.0255307i
$700$	−22.9203	−	8.14476i	−0.866304	−	0.307843i
$701$	−9.69246	−	45.5995i	−0.366079	−	1.72227i	−0.646959	−	0.762525i	$-0.723959\pi$
$701$	−9.69246	−	45.5995i	−0.366079	−	1.72227i	0.280880	−	0.959743i	$-0.409374\pi$
$702$	3.40503	+	3.91114i	0.128514	+	0.147617i
$703$	25.0417	+	1.31238i	0.944466	+	0.0494974i
$704$	0.198071	+	1.88452i	0.00746507	+	0.0710254i
$705$	−26.9606	+	15.8174i	−1.01539	+	0.595716i
$706$	2.98486	−	28.3990i	0.112337	−	1.06881i
$707$	5.05155	+	1.35356i	0.189983	+	0.0509058i
$708$	−3.01053	+	2.16176i	−0.113143	+	0.0812441i
$709$	−5.61535	+	7.72886i	−0.210889	+	0.290263i	−0.901337	−	0.433118i	$-0.857413\pi$
$709$	−5.61535	+	7.72886i	−0.210889	+	0.290263i	0.690448	+	0.723382i	$0.257413\pi$
$710$	−9.37695	+	21.7925i	−0.351911	+	0.817859i
$711$	12.0872	+	27.9829i	0.453304	+	1.04944i
$712$	−3.32128	−	3.32128i	−0.124470	−	0.124470i
$713$	38.2077	−	23.4259i	1.43089	−	0.877306i
$714$	5.12027	+	13.5641i	0.191621	+	0.507622i
$715$	−0.0530345	−	4.22825i	−0.00198338	−	0.158127i
$716$	1.44835	+	1.30410i	0.0541275	+	0.0487366i
$717$	6.49175	−	3.69996i	0.242439	−	0.138178i
$718$	−2.47649	−	9.24240i	−0.0924219	−	0.344923i
$719$	−18.3364	−	31.7595i	−0.683831	−	1.18443i	−0.973803	−	0.227394i	$-0.926979\pi$
$719$	−18.3364	−	31.7595i	−0.683831	−	1.18443i	0.289972	−	0.957035i	$-0.406354\pi$
$720$	1.05869	+	6.62414i	0.0394552	+	0.246867i
$721$	−34.0236	+	24.7196i	−1.26711	+	0.920607i
$722$	6.40979	+	5.19055i	0.238548	+	0.193172i
$723$	18.4429	−	5.87910i	0.685898	−	0.218646i
$724$	−6.90765	−	15.5148i	−0.256721	−	0.576604i
$725$	−27.1964	−	23.2795i	−1.01005	−	0.864580i
$726$	1.93696	+	12.6864i	0.0718874	+	0.470836i
$727$	−4.81468	−	12.5427i	−0.178567	−	0.465182i	0.814859	−	0.579659i	$-0.196814\pi$
$727$	−4.81468	−	12.5427i	−0.178567	−	0.465182i	−0.993426	+	0.114477i	$0.963481\pi$
$728$	−2.20415	+	4.32590i	−0.0816914	+	0.160328i
$729$	21.3011	+	16.5911i	0.788928	+	0.614486i
$730$	−21.3479	−	25.6966i	−0.790119	−	0.951075i
$731$	−1.49261	+	7.02218i	−0.0552062	+	0.259725i
$732$	11.0964	+	2.42327i	0.410133	+	0.0895666i
$733$	−4.75043	+	12.3753i	−0.175461	+	0.457091i	−0.992904	−	0.118918i	$-0.962057\pi$
$733$	−4.75043	+	12.3753i	−0.175461	+	0.457091i	0.817443	+	0.576009i	$0.195391\pi$
$734$	−7.11795	−	7.90529i	−0.262729	−	0.291790i
$735$	−45.9617	−	45.3251i	−1.69532	−	1.67184i
$736$	−6.51213	+	4.73134i	−0.240040	+	0.174400i
$737$	−3.32135	−	4.10153i	−0.122344	−	0.151082i
$738$	13.6810	−	6.77995i	0.503605	−	0.249573i
$739$	14.1014	+	8.14147i	0.518730	+	0.299489i	0.736415	−	0.676530i	$-0.236517\pi$
$739$	14.1014	+	8.14147i	0.518730	+	0.299489i	−0.217685	+	0.976019i	$0.569851\pi$
$740$	−3.19102	+	10.2569i	−0.117304	+	0.377052i
$741$	−3.28041	+	8.40555i	−0.120509	+	0.308785i
$742$	16.2676	−	8.28874i	0.597201	−	0.304289i
$743$	−19.3688	−	19.3688i	−0.710573	−	0.710573i	0.256082	−	0.966655i	$-0.417568\pi$
$743$	−19.3688	−	19.3688i	−0.710573	−	0.710573i	−0.966655	+	0.256082i	$0.917568\pi$
$744$	−7.91832	−	5.50457i	−0.290300	−	0.201807i
$745$	22.3966	−	45.3531i	0.820548	−	1.66161i
$746$	4.87992	+	1.58558i	0.178667	+	0.0580523i
$747$	5.88380	+	6.01636i	0.215277	+	0.220127i
$748$	−3.22026	+	0.510039i	−0.117744	+	0.0186489i
$749$	27.1461	−	47.0185i	0.991898	−	1.71802i
$750$	9.13995	−	17.0722i	0.333744	−	0.623390i
$751$	−3.78644	+	36.0256i	−0.138169	+	1.31459i	0.677264	+	0.735740i	$0.263165\pi$
$751$	−3.78644	+	36.0256i	−0.138169	+	1.31459i	−0.815433	+	0.578851i	$0.803501\pi$
$752$	−1.26255	+	7.97141i	−0.0460403	+	0.290687i
$753$	1.84229	−	5.56434i	0.0671367	−	0.202776i
$754$	−5.31007	+	4.78121i	−0.193381	+	0.174121i
$755$	−1.81323	+	45.5144i	−0.0659904	+	1.65644i
$756$	−6.94961	+	24.3046i	−0.252755	+	0.883949i
$757$	7.84992	+	12.0878i	0.285310	+	0.439339i	0.952046	−	0.305955i	$-0.0989757\pi$
$757$	7.84992	+	12.0878i	0.285310	+	0.439339i	−0.666736	+	0.745294i	$0.732309\pi$
$758$	8.12700	+	21.1716i	0.295186	+	0.768985i
$759$	20.6235	−	16.5113i	0.748585	−	0.599320i
$760$	−9.35619	+	6.97862i	−0.339385	+	0.253141i
$761$	4.80164	−	10.7847i	0.174059	−	0.390944i	−0.805358	−	0.592788i	$-0.798027\pi$
$761$	4.80164	−	10.7847i	0.174059	−	0.390944i	0.979418	+	0.201845i	$0.0646937\pi$
$762$	0.314726	−	0.428148i	0.0114013	−	0.0155102i
$763$	−41.2291	+	63.4873i	−1.49259	+	2.29839i
$764$	−4.72280	+	2.10273i	−0.170865	+	0.0760740i
$765$	−11.2867	+	2.41562i	−0.408070	+	0.0873369i
$766$	−1.54528	−	14.7024i	−0.0558334	−	0.531219i
$767$	0.334067	−	2.10922i	0.0120625	−	0.0761594i
$768$	1.49515	+	0.874366i	0.0539517	+	0.0315510i
$769$	−30.2740	+	17.4787i	−1.09171	+	0.630298i	−0.934031	−	0.357193i	$-0.883734\pi$
$769$	−30.2740	+	17.4787i	−1.09171	+	0.630298i	−0.157677	+	0.987491i	$0.550401\pi$
$770$	17.1454	−	11.4426i	0.617877	−	0.412363i
$771$	−6.72858	+	24.5634i	−0.242324	+	0.884629i
$772$	−19.2230	+	1.00743i	−0.691849	+	0.0362583i
$773$	−32.9395	+	16.7835i	−1.18475	+	0.603662i	−0.931501	−	0.363738i	$-0.881500\pi$
$773$	−32.9395	+	16.7835i	−1.18475	+	0.603662i	−0.253252	+	0.967400i	$0.581500\pi$
$774$	−9.39473	+	8.27145i	−0.337687	+	0.297311i
$775$	8.57980	+	26.4837i	0.308195	+	0.951323i
$776$			4.60651i			0.165364i
$777$	−27.2526	+	29.9302i	−0.977682	+	1.07374i
$778$	1.67498	+	31.9604i	0.0600508	+	1.14584i
$779$	21.4936	+	15.6160i	0.770087	+	0.559501i
$780$	−3.14276	−	2.25003i	−0.112529	−	0.0805641i
$781$	−10.0523	−	17.4110i	−0.359698	−	0.623016i
$782$	−8.71611	−	10.7635i	−0.311687	−	0.384902i
$783$	−22.3675	+	29.7288i	−0.799351	+	1.06242i
$784$	−16.5757	+	1.74218i	−0.591989	+	0.0622206i
$785$	9.45522	+	5.30198i	0.337471	+	0.189236i
$786$	−6.03323	+	5.96640i	−0.215198	+	0.212814i
$787$	26.7906	+	17.3980i	0.954981	+	0.620172i	0.925239	−	0.379386i	$-0.123865\pi$
$787$	26.7906	+	17.3980i	0.954981	+	0.620172i	0.0297425	+	0.999558i	$0.490531\pi$
$788$	7.33572	+	11.2960i	0.261324	+	0.402404i
$789$	10.7363	+	0.622639i	0.382221	+	0.0221665i
$790$	−13.5839	−	18.2118i	−0.483292	−	0.647947i
$791$	−16.6616	+	5.41370i	−0.592420	+	0.192489i
$792$	−5.03604	−	2.63705i	−0.178948	−	0.0937036i
$793$	−5.48847	+	3.56425i	−0.194901	+	0.126570i
$794$	−4.53891	+	0.964774i	−0.161080	+	0.0342386i
$795$	4.58785	+	13.7920i	0.162714	+	0.489151i
$796$	4.52476	+	5.02526i	0.160376	+	0.178115i
$797$	0.0714438	+	0.0578541i	0.00253067	+	0.00204930i	0.630585	−	0.776120i	$-0.282815\pi$
$797$	0.0714438	+	0.0578541i	0.00253067	+	0.00204930i	−0.628054	+	0.778170i	$0.716148\pi$
$798$	−43.0735	+	8.90512i	−1.52478	+	0.315238i
$799$	−13.8107	−	1.45156i	−0.488586	−	0.0513525i
$800$	−1.90836	−	4.62149i	−0.0674706	−	0.163394i
$801$	13.8149	−	2.77598i	0.488124	−	0.0980846i
$802$	2.00841	+	12.6806i	0.0709193	+	0.447767i
$803$	28.2713	−	1.48164i	0.997674	−	0.0522859i
$804$	−4.81884	+	0.225641i	−0.169947	+	0.00795775i
$805$	78.5120	+	38.7713i	2.76718	+	1.36651i
$806$	5.46326	−	1.01386i	0.192435	−	0.0357119i
$807$	−7.21554	+	15.9665i	−0.253999	+	0.562046i
$808$	0.488041	+	0.957833i	0.0171692	+	0.0336965i
$809$	−1.76467	+	1.95987i	−0.0620425	+	0.0689052i	−0.773367	−	0.633959i	$-0.781429\pi$
$809$	−1.76467	+	1.95987i	−0.0620425	+	0.0689052i	0.711325	+	0.702864i	$0.248096\pi$
$810$	−18.3042	−	8.36399i	−0.643144	−	0.293881i
$811$	−27.6389	+	47.8721i	−0.970535	+	1.68102i	−0.276588	+	0.960988i	$0.589204\pi$
$811$	−27.6389	+	47.8721i	−0.970535	+	1.68102i	−0.693946	+	0.720027i	$0.744129\pi$
$812$	−33.6449	−	9.01512i	−1.18070	−	0.316369i
$813$	40.3767	+	23.6123i	1.41607	+	0.828119i
$814$	−5.35054	−	7.36439i	−0.187536	−	0.258122i
$815$	27.2864	−	12.5611i	0.955801	−	0.439996i
$816$	−1.36775	+	2.64780i	−0.0478809	+	0.0926917i
$817$	−20.3330	−	7.80509i	−0.711360	−	0.273066i
$818$	−22.5909	−	14.6707i	−0.789873	−	0.512950i
$819$	−7.14165	−	12.6942i	−0.249550	−	0.443570i
$820$	−8.75396	+	7.27248i	−0.305701	+	0.253966i
$821$	−8.02392	+	2.60713i	−0.280037	+	0.0909895i	−0.445668	−	0.895198i	$-0.647034\pi$
$821$	−8.02392	+	2.60713i	−0.280037	+	0.0909895i	0.165631	+	0.986188i	$0.447034\pi$
$822$	1.90050	−	17.1621i	0.0662875	−	0.598596i
$823$	−18.5870	+	7.13487i	−0.647902	+	0.248706i	−0.660052	−	0.751220i	$-0.729466\pi$
$823$	−18.5870	+	7.13487i	−0.647902	+	0.248706i	0.0121503	+	0.999926i	$0.496132\pi$
$824$	−8.45582	−	1.79734i	−0.294573	−	0.0626133i
$825$	6.96594	+	14.8584i	0.242523	+	0.517305i
$826$	9.50998	−	4.23411i	0.330894	−	0.147324i
$827$	52.1719	+	2.73422i	1.81420	+	0.0950780i	0.928986	−	0.370114i	$-0.120681\pi$
$827$	52.1719	+	2.73422i	1.81420	+	0.0950780i	0.885210	+	0.465192i	$0.154015\pi$
$828$	−0.995147	−	24.1278i	−0.0345837	−	0.838499i
$829$	−13.4028	−	18.4473i	−0.465498	−	0.640703i	0.510140	−	0.860091i	$-0.329594\pi$
$829$	−13.4028	−	18.4473i	−0.465498	−	0.640703i	−0.975637	+	0.219389i	$0.929594\pi$
$830$	−5.30284	−	3.34991i	−0.184064	−	0.116277i
$831$	−14.2973	−	11.7102i	−0.495969	−	0.406222i
$832$	−0.963978	+	0.258297i	−0.0334199	+	0.00895485i
$833$	−4.48616	−	28.3245i	−0.155436	−	0.981387i
$834$	−8.73951	+	22.3936i	−0.302625	+	0.775428i
$835$	−37.4097	+	0.469226i	−1.29462	+	0.0162382i
$836$		−	9.89127i		−	0.342097i
$837$	26.9075	−	10.6295i	0.930059	−	0.367410i
$838$	22.9010	−	22.9010i	0.791101	−	0.791101i
$839$	−15.4277	+	47.4814i	−0.532622	+	1.63924i	0.216111	+	0.976369i	$0.430663\pi$
$839$	−15.4277	+	47.4814i	−0.532622	+	1.63924i	−0.748732	+	0.662872i	$0.769337\pi$
$840$	0.854866	−	18.8222i	0.0294957	−	0.649427i
$841$	−18.0114	−	13.0861i	−0.621083	−	0.451244i
$842$	9.64993	+	36.0140i	0.332558	+	1.24112i
$843$	4.54364	+	45.6754i	0.156491	+	1.57315i
$844$	−0.502212	−	0.0527846i	−0.0172869	−	0.00181692i
$845$	−26.4566	+	4.53116i	−0.910135	+	0.155877i
$846$	−17.8117	−	16.4006i	−0.612378	−	0.563865i
$847$	1.88648	−	35.9962i	0.0648203	−	1.23684i
$848$	3.50366	+	1.34493i	0.120316	+	0.0461851i
$849$	21.6971	+	33.8215i	0.744642	+	1.16075i
$850$	7.76909	−	3.69522i	0.266477	−	0.126745i
$851$	15.7280	−	35.3256i	0.539148	−	1.21095i
$852$	−18.2651	−	2.02265i	−0.625752	−	0.0692947i
$853$	20.4396	+	10.4145i	0.699839	+	0.356586i	0.767435	−	0.641127i	$-0.221533\pi$
$853$	20.4396	+	10.4145i	0.699839	+	0.356586i	−0.0675958	+	0.997713i	$0.521533\pi$
$854$	−29.1433	−	12.9754i	−0.997262	−	0.444010i
$855$	−1.88171	−	34.9659i	−0.0643531	−	1.19581i
$856$	10.9162	−	2.32031i	0.373107	−	0.0793064i
$857$	9.89810	−	25.7854i	0.338113	−	0.880813i	−0.654117	−	0.756393i	$-0.726960\pi$
$857$	9.89810	−	25.7854i	0.338113	−	0.880813i	0.992230	−	0.124420i	$-0.0397070\pi$
$858$	3.12072	−	0.994803i	0.106540	−	0.0339620i
$859$	−8.60766	+	0.904701i	−0.293689	+	0.0308680i	−0.250227	−	0.968187i	$-0.580505\pi$
$859$	−8.60766	+	0.904701i	−0.293689	+	0.0308680i	−0.0434620	+	0.999055i	$0.513839\pi$
$860$	5.38876	−	7.61607i	0.183755	−	0.259706i
$861$	−41.4860	+	10.8689i	−1.41384	+	0.370410i
$862$	−6.51246	+	24.3048i	−0.221815	+	0.827826i
$863$	23.3504	−	6.25673i	0.794858	−	0.212982i	0.161533	−	0.986867i	$-0.448356\pi$
$863$	23.3504	−	6.25673i	0.794858	−	0.212982i	0.633325	+	0.773886i	$0.281690\pi$
$864$	−4.66857	+	2.28133i	−0.158828	+	0.0776123i
$865$	−21.0868	+	49.0068i	−0.716972	+	1.66628i
$866$	−22.8224	−	7.41543i	−0.775535	−	0.251987i
$867$	22.1593	+	10.0142i	0.752570	+	0.340100i
$868$	18.6497	+	19.6435i	0.633010	+	0.666744i
$869$	19.2533			0.653125
$870$	11.1019	−	25.4106i	0.376389	−	0.861500i
$871$	1.85991	−	2.06564i	0.0630206	−	0.0699915i
$872$	−15.3689	+	2.43420i	−0.520458	+	0.0824324i
$873$	−11.5055	−	7.65529i	−0.389402	−	0.259092i
$874$	36.3884	−	21.0088i	1.23085	−	0.710634i
$875$	−34.8484	+	41.7608i	−1.17809	+	1.41177i
$876$	14.2144	−	21.6236i	0.480259	−	0.730594i
$877$	−10.8783	+	13.4336i	−0.367333	+	0.453619i	−0.926979	−	0.375113i	$-0.877604\pi$
$877$	−10.8783	+	13.4336i	−0.367333	+	0.453619i	0.559646	+	0.828732i	$0.310937\pi$
$878$	1.83903	−	35.0907i	0.0620641	−	1.18425i
$879$	−31.9322	+	31.5785i	−1.07705	+	1.06512i
$880$	4.10618	+	1.04523i	0.138419	+	0.0352347i
$881$	−12.0269	+	56.5821i	−0.405197	+	1.90630i	0.0171217	+	0.999853i	$0.494550\pi$
$881$	−12.0269	+	56.5821i	−0.405197	+	1.90630i	−0.422318	+	0.906448i	$0.638784\pi$
$882$	23.1948	−	44.2956i	0.781010	−	1.49151i
$883$	−28.6666	−	14.6064i	−0.964707	−	0.491543i	−0.100642	−	0.994923i	$-0.532090\pi$
$883$	−28.6666	−	14.6064i	−0.964707	−	0.491543i	−0.864065	+	0.503380i	$0.832090\pi$
$884$	−0.530629	−	1.63311i	−0.0178470	−	0.0549274i
$885$	2.20073	+	7.98995i	0.0739767	+	0.268579i
$886$	−10.5672	−	2.24612i	−0.355011	−	0.0754598i
$887$	12.3848	−	19.0709i	0.415840	−	0.640338i	−0.567232	−	0.823558i	$-0.691986\pi$
$887$	12.3848	−	19.0709i	0.415840	−	0.640338i	0.983072	+	0.183221i	$0.0586523\pi$
$888$	−8.32046	−	0.0463389i	−0.279216	−	0.00155503i
$889$	−1.10915	+	0.998680i	−0.0371996	+	0.0334946i
$890$	−9.54047	+	4.39188i	−0.319797	+	0.147216i
$891$	14.9555	−	8.19594i	0.501029	−	0.274574i
$892$	−2.55721	+	2.07079i	−0.0856218	+	0.0693352i
$893$	10.9038	−	40.6935i	0.364881	−	1.36176i
$894$	38.6634	+	6.34460i	1.29310	+	0.212195i
$895$	3.85787	−	2.02703i	0.128954	−	0.0677561i
$896$	−3.61531	−	3.25524i	−0.120779	−	0.108750i
$897$	10.2881	+	9.36768i	0.343508	+	0.312778i
$898$	0.419443	−	0.419443i	0.0139970	−	0.0139970i
$899$	15.2639	+	36.8263i	0.509081	+	1.22823i
$900$	14.7143	+	2.91376i	0.490476	+	0.0971253i
$901$	−1.99544	+	6.14132i	−0.0664776	+	0.204597i
$902$	−0.504743	−	9.63108i	−0.0168061	−	0.320680i
$903$	30.5445	−	17.4088i	1.01646	−	0.579328i
$904$	−3.11868	−	1.80057i	−0.103726	−	0.0598861i
$905$	−37.8954	+	2.46295i	−1.25969	+	0.0818713i
$906$	−34.1314	+	8.94204i	−1.13394	+	0.297079i
$907$	−20.6380	−	3.26874i	−0.685274	−	0.108537i	−0.195917	−	0.980620i	$-0.562768\pi$
$907$	−20.6380	−	3.26874i	−0.685274	−	0.108537i	−0.489357	+	0.872084i	$0.662768\pi$
$908$	16.5995	−	20.4986i	0.550873	−	0.680271i
$909$	−3.20338	−	0.372808i	−0.106250	−	0.0123653i
$910$	7.36487	+	7.97603i	0.244143	+	0.264403i
$911$	−11.8170	−	55.5948i	−0.391516	−	1.84194i	−0.525288	−	0.850924i	$-0.676043\pi$
$911$	−11.8170	−	55.5948i	−0.391516	−	1.84194i	0.133773	−	0.991012i	$-0.457291\pi$
$912$	−7.28479	−	5.35495i	−0.241223	−	0.177320i
$913$	4.96228	−	1.90484i	0.164227	−	0.0630410i
$914$	6.92436	+	21.3110i	0.229038	+	0.704905i
$915$	13.6833	−	21.3956i	0.452357	−	0.707318i
$916$	2.13228	+	0.949352i	0.0704525	+	0.0313675i
$917$	19.9877	−	12.9801i	0.660051	−	0.428642i
$918$	−4.34032	−	7.81640i	−0.143252	−	0.257980i
$919$	−22.2942	−	50.0736i	−0.735418	−	1.65178i	−0.758189	−	0.652035i	$-0.773916\pi$
$919$	−22.2942	−	50.0736i	−0.735418	−	1.65178i	0.0227715	−	0.999741i	$-0.492751\pi$
$920$	4.87619	+	17.3260i	0.160763	+	0.571221i
$921$	−0.709320	−	1.41150i	−0.0233729	−	0.0465104i
$922$	2.80514	+	0.444290i	0.0923823	+	0.0146319i
$923$	8.22876	−	6.66352i	0.270853	−	0.219332i
$924$	12.3524	+	10.1172i	0.406364	+	0.332831i
$925$	19.0399	+	14.6430i	0.626028	+	0.481459i
$926$	−1.03187	+	1.42025i	−0.0339094	+	0.0466723i
$927$	18.5414	−	18.1329i	0.608978	−	0.595561i
$928$	−3.25050	−	6.37947i	−0.106703	−	0.209416i
$929$	25.9906			0.852726			0.426363	−	0.904552i	$-0.359795\pi$
$929$	25.9906			0.852726			0.426363	+	0.904552i	$0.359795\pi$
$930$	−17.6829	+	12.3416i	−0.579845	+	0.404698i
$931$	87.0009			2.85134
$932$	−3.05586	−	5.99747i	−0.100098	−	0.196454i
$933$	12.6817	−	5.56184i	0.415180	−	0.182086i
$934$	4.26338	−	5.86804i	0.139502	−	0.192008i
$935$	−1.42622	+	7.14961i	−0.0466423	+	0.233817i
$936$	0.956840	−	2.83694i	0.0312753	−	0.0927282i
$937$	−1.24302	+	1.00658i	−0.0406076	+	0.0328834i	−0.649409	−	0.760439i	$-0.724984\pi$
$937$	−1.24302	+	1.00658i	−0.0406076	+	0.0328834i	0.608802	+	0.793322i	$0.291650\pi$
$938$	13.3829	+	2.11964i	0.436966	+	0.0692086i
$939$	−48.3804	+	24.3126i	−1.57883	+	0.793412i
$940$	15.7409	+	8.82667i	0.513412	+	0.287894i
$941$	−8.94495	−	20.0907i	−0.291597	−	0.654938i	0.707038	−	0.707176i	$-0.250031\pi$
$941$	−8.94495	−	20.0907i	−0.291597	−	0.654938i	−0.998635	+	0.0522383i	$0.983364\pi$
$942$	−1.79152	+	8.20352i	−0.0583709	+	0.267285i
$943$	34.3591	−	22.3131i	1.11889	−	0.726613i
$944$	1.95482	+	0.870344i	0.0636241	+	0.0283273i
$945$	45.5907	+	33.4146i	1.48307	+	1.08698i
$946$	2.44315	+	7.51925i	0.0794338	+	0.244472i
$947$	−5.98548	+	2.29761i	−0.194502	+	0.0746623i	−0.453669	−	0.891170i	$-0.649885\pi$
$947$	−5.98548	+	2.29761i	−0.194502	+	0.0746623i	0.259167	+	0.965832i	$0.416552\pi$
$948$	10.4234	−	14.1798i	0.338536	−	0.460539i
$949$	3.09998	+	14.5843i	0.100630	+	0.473425i
$950$	7.38531	+	25.0331i	0.239611	+	0.812180i
$951$	0.747464	−	1.44700i	0.0242382	−	0.0469222i
$952$	5.26779	−	6.50518i	0.170730	−	0.210834i
$953$	−31.9586	−	5.06175i	−1.03524	−	0.163966i	−0.384390	−	0.923171i	$-0.625588\pi$
$953$	−31.9586	−	5.06175i	−1.03524	−	0.163966i	−0.650852	+	0.759205i	$0.725588\pi$
$954$	−9.18169	+	6.51588i	−0.297268	+	0.210960i
$955$	0.749736	+	11.5356i	0.0242609	+	0.373282i
$956$	−3.73606	−	2.15701i	−0.120833	−	0.0697628i
$957$	11.6360	+	20.4159i	0.376138	+	0.659951i
$958$	0.531734	+	10.1461i	0.0171796	+	0.327806i
$959$	−14.9868	+	46.1247i	−0.483950	+	1.48944i
$960$	2.99280	−	2.45828i	0.0965924	−	0.0793405i
$961$	4.83528	−	30.6206i	0.155977	−	0.987761i
$962$	3.39002	−	3.39002i	0.109299	−	0.109299i
$963$	−12.3456	+	31.1209i	−0.397832	+	1.00286i
$964$	−8.30532	−	7.47815i	−0.267496	−	0.240855i
$965$	−12.7865	+	41.0998i	−0.411612	+	1.32305i
$966$	−10.9833	+	66.9311i	−0.353382	+	2.15347i
$967$	4.53529	−	16.9259i	0.145845	−	0.544302i	−0.853871	−	0.520484i	$-0.825751\pi$
$967$	4.53529	−	16.9259i	0.145845	−	0.544302i	0.999716	−	0.0238172i	$-0.00758196\pi$
$968$	5.75816	−	4.66286i	0.185074	−	0.149870i
$969$	8.54521	−	12.9994i	0.274512	−	0.417601i
$970$	9.66187	+	3.57046i	0.310224	+	0.114641i
$971$	−3.31069	+	2.98096i	−0.106245	+	0.0956636i	−0.720541	−	0.693412i	$-0.756107\pi$
$971$	−3.31069	+	2.98096i	−0.106245	+	0.0956636i	0.614296	+	0.789076i	$0.289440\pi$
$972$	2.06045	−	15.4517i	0.0660889	−	0.495613i
$973$	36.7730	−	56.6254i	1.17889	−	1.81533i
$974$	−16.4381	−	3.49403i	−0.526711	−	0.111956i
$975$	−7.15522	+	4.84775i	−0.229150	+	0.155252i
$976$	−2.02637	−	6.23653i	−0.0648625	−	0.199626i
$977$	−36.5633	−	18.6299i	−1.16976	−	0.596025i	−0.242397	−	0.970177i	$-0.577934\pi$
$977$	−36.5633	−	18.6299i	−1.16976	−	0.596025i	−0.927367	+	0.374152i	$0.877934\pi$
$978$	15.4728	+	17.3779i	0.494764	+	0.555684i
$979$	1.85048	−	8.70585i	0.0591417	−	0.278240i
$980$	−9.19356	+	36.1168i	−0.293678	+	1.15371i
$981$	19.4609	−	42.4316i	0.621339	−	1.35474i
$982$	−0.466001	+	8.89182i	−0.0148707	+	0.283750i
$983$	24.2161	−	29.9044i	0.772373	−	0.953801i	−0.227427	−	0.973795i	$-0.573031\pi$
$983$	24.2161	−	29.9044i	0.772373	−	0.953801i	0.999800	+	0.0199937i	$0.00636462\pi$
$984$	−7.36642	−	4.84235i	−0.234833	−	0.154368i
$985$	29.3785	−	6.63077i	0.936078	−	0.211274i
$986$	10.6689	−	6.15969i	0.339767	−	0.196164i
$987$	39.6659	+	55.2398i	1.26258	+	1.75830i
$988$	5.14529	−	0.814934i	0.163693	−	0.0259265i
$989$	−22.4729	+	24.9587i	−0.714597	+	0.793640i
$990$	−9.43443	+	8.51881i	−0.299846	+	0.270746i
$991$	30.6133			0.972463			0.486232	−	0.873830i	$-0.338371\pi$
$991$	30.6133			0.972463			0.486232	+	0.873830i	$0.338371\pi$
$992$	−0.435556	+	5.55070i	−0.0138289	+	0.176235i
$993$	6.43914	−	14.2485i	0.204340	−	0.452161i
$994$	49.0892	+	15.9501i	1.55702	+	0.505905i
$995$	14.0472	−	5.59537i	0.445328	−	0.177385i
$996$	1.28359	−	4.68590i	0.0406722	−	0.148478i
$997$	−23.5241	+	6.30327i	−0.745017	+	0.199627i	−0.611307	−	0.791394i	$-0.709356\pi$
$997$	−23.5241	+	6.30327i	−0.745017	+	0.199627i	−0.133710	+	0.991020i	$0.542689\pi$
$998$	2.59629	−	9.68948i	0.0821840	−	0.306715i
$999$	13.9430	−	20.7046i	0.441137	−	0.655066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.107.12	✓	1024
3.2	odd	2	inner	930.2.bs.a.107.53	yes	1024
5.3	odd	4	inner	930.2.bs.a.293.27	yes	1024
15.8	even	4	inner	930.2.bs.a.293.60	yes	1024
31.20	even	15	inner	930.2.bs.a.857.60	yes	1024
93.20	odd	30	inner	930.2.bs.a.857.27	yes	1024
155.113	odd	60	inner	930.2.bs.a.113.53	yes	1024
465.113	even	60	inner	930.2.bs.a.113.12	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.12	✓	1024	1.1	even	1	trivial
930.2.bs.a.107.53	yes	1024	3.2	odd	2	inner
930.2.bs.a.113.12	yes	1024	465.113	even	60	inner
930.2.bs.a.113.53	yes	1024	155.113	odd	60	inner
930.2.bs.a.293.27	yes	1024	5.3	odd	4	inner
930.2.bs.a.293.60	yes	1024	15.8	even	4	inner
930.2.bs.a.857.27	yes	1024	93.20	odd	30	inner
930.2.bs.a.857.60	yes	1024	31.20	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.695665 - 1.58621i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.24127 + 1.85990i) q^{5} +(-1.09749 + 1.33996i) q^{6} +(3.78072 - 3.06157i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.03210 + 2.20694i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.695665 - 1.58621i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.24127 + 1.85990i) q^{5} +(-1.09749 + 1.33996i) q^{6} +(3.78072 - 3.06157i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.03210 + 2.20694i) q^{9} +(1.09366 - 1.95036i) q^{10} +(0.770724 + 1.73108i) q^{11} +(1.69217 + 0.369543i) q^{12} +(-0.836980 + 0.543541i) q^{13} +(-4.44428 - 1.97872i) q^{14} +(2.08668 - 3.26279i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.60634 - 0.616615i) q^{17} +(2.88895 + 0.808685i) q^{18} +(1.08529 + 5.10588i) q^{19} +(-2.23430 - 0.0890114i) q^{20} +(-7.48639 - 3.86717i) q^{21} +(1.19250 - 1.47261i) q^{22} +(7.95034 + 1.25921i) q^{23} +(-0.438963 - 1.67550i) q^{24} +(-1.91848 + 4.61730i) q^{25} +(0.864279 + 0.498992i) q^{26} +(4.91432 + 1.68804i) q^{27} +(0.254608 + 4.85821i) q^{28} +(-2.21251 + 6.80941i) q^{29} +(-3.85450 - 0.377969i) q^{30} +(4.23292 - 3.61695i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.20968 - 2.42678i) q^{33} +(-1.27867 - 1.15132i) q^{34} +(10.3871 + 3.23153i) q^{35} +(-0.591012 - 2.94121i) q^{36} +(1.24334 - 4.64021i) q^{37} +(4.05666 - 3.28502i) q^{38} +(1.44443 + 0.949500i) q^{39} +(0.935039 + 2.03118i) q^{40} +(3.78232 - 3.40562i) q^{41} +(-0.0469271 + 8.42608i) q^{42} +(-2.27243 + 3.49924i) q^{43} +(-1.85349 - 0.393971i) q^{44} +(-6.62708 - 1.04009i) q^{45} +(-2.48741 - 7.65547i) q^{46} +(-7.19111 - 3.66405i) q^{47} +(-1.29360 + 1.15178i) q^{48} +(3.46527 - 16.3028i) q^{49} +(4.98501 - 0.386835i) q^{50} +(-2.09555 - 2.11902i) q^{51} +(0.0522304 - 0.996616i) q^{52} +(-2.36179 + 2.91657i) q^{53} +(-0.727001 - 5.14504i) q^{54} +(-2.26295 + 3.58221i) q^{55} +(4.21311 - 2.43244i) q^{56} +(7.34398 - 5.27348i) q^{57} +(7.07169 - 1.12005i) q^{58} +(-1.43182 + 1.59020i) q^{59} +(1.41313 + 3.60598i) q^{60} +6.55747 q^{61} +(-5.14444 - 2.12950i) q^{62} +(-0.926111 + 14.5652i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-2.04985 - 0.882017i) q^{65} +(-3.16545 - 0.867102i) q^{66} +(-2.69030 + 0.720864i) q^{67} +(-0.445329 + 1.66199i) q^{68} +(-3.53341 - 13.4869i) q^{69} +(-1.83634 - 10.7221i) q^{70} +(-10.5517 + 1.10903i) q^{71} +(-2.35232 + 1.86188i) q^{72} +(5.35409 - 13.9479i) q^{73} +(-4.69892 + 0.998786i) q^{74} +(8.65860 - 0.168997i) q^{75} +(-4.76866 - 2.12314i) q^{76} +(8.21369 + 4.18508i) q^{77} +(0.190255 - 1.71806i) q^{78} +(4.13270 - 9.28219i) q^{79} +(1.38530 - 1.75526i) q^{80} +(-0.741146 - 8.96943i) q^{81} +(-4.75156 - 1.82395i) q^{82} +(0.146806 - 2.80122i) q^{83} +(7.52900 - 3.78355i) q^{84} +(3.14075 + 2.22224i) q^{85} +(4.14951 + 0.436131i) q^{86} +(12.3403 - 1.22757i) q^{87} +(0.490436 + 1.83033i) q^{88} +(-3.79996 - 2.76083i) q^{89} +(2.08190 + 6.37696i) q^{90} +(-1.50030 + 4.61744i) q^{91} +(-5.69181 + 5.69181i) q^{92} +(-8.68193 - 4.19810i) q^{93} +8.07077i q^{94} +(-8.14930 + 8.35633i) q^{95} +(1.61353 + 0.629707i) q^{96} +(0.720618 + 4.54980i) q^{97} +(-16.0991 + 4.31374i) q^{98} +(-5.38656 - 1.81678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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