LMFDB - Embedded newform 430.2.q.c.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	430.31
Dual form			430.2.q.c.111.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(2.49243 - 1.69931i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.50830 - 2.61245i) q^{6} +(0.376122 + 0.651463i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.22854 - 5.67822i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(2.49243 - 1.69931i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.50830 - 2.61245i) q^{6} +(0.376122 + 0.651463i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.22854 - 5.67822i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(2.49732 + 3.13153i) q^{11} +(0.225431 - 3.00817i) q^{12} +(-6.45146 + 1.99001i) q^{13} +(0.621533 + 0.423754i) q^{14} +(-2.98291 - 0.449601i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-4.40696 + 4.08906i) q^{17} +(-0.455845 - 6.08282i) q^{18} +(0.741679 + 1.88977i) q^{19} +(-0.988831 + 0.149042i) q^{20} +(2.04450 + 0.984578i) q^{21} +(3.60873 + 1.73787i) q^{22} +(8.14749 - 1.22804i) q^{23} +(-1.10209 - 2.80807i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-4.94913 + 4.59213i) q^{26} +(-2.08081 - 9.11665i) q^{27} +(0.743842 + 0.112116i) q^{28} +(-2.97405 - 2.02767i) q^{29} +(-2.88258 + 0.889159i) q^{30} +(0.476570 - 6.35939i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(11.5458 + 3.56142i) q^{33} +(-2.19635 + 5.59622i) q^{34} +(0.167390 - 0.733384i) q^{35} +(-3.04994 - 5.28265i) q^{36} +(-2.47968 + 4.29494i) q^{37} +(1.48817 + 1.38082i) q^{38} +(-12.6982 + 15.9230i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(-4.39604 + 2.11702i) q^{41} +2.26922 q^{42} +(6.39389 + 1.45540i) q^{43} +4.00538 q^{44} +(-5.49580 + 2.64664i) q^{45} +(6.80781 - 4.64149i) q^{46} +(-0.700706 + 0.878657i) q^{47} +(-2.21132 - 2.05181i) q^{48} +(3.21706 - 5.57212i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.03546 + 17.6805i) q^{51} +(-2.46657 + 6.28471i) q^{52} +(-3.08922 - 0.952899i) q^{53} +(-5.83031 - 7.31098i) q^{54} +(0.299323 - 3.99418i) q^{55} +(0.718824 - 0.221728i) q^{56} +(5.05989 + 3.44977i) q^{57} +(-3.55930 - 0.536477i) q^{58} +(-2.92597 - 12.8195i) q^{59} +(-2.21132 + 2.05181i) q^{60} +(-0.330460 - 4.40968i) q^{61} +(-2.32986 - 5.93639i) q^{62} +(4.53735 - 0.683895i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(6.08281 + 2.92933i) q^{65} +(11.9477 - 1.80082i) q^{66} +(3.60087 + 9.17486i) q^{67} +(0.449262 + 5.99498i) q^{68} +(18.2203 - 16.9059i) q^{69} +(-0.167390 - 0.733384i) q^{70} +(-15.1231 - 2.27943i) q^{71} +(-5.03996 - 3.43618i) q^{72} +(12.2370 - 3.77463i) q^{73} +(-0.370614 + 4.94550i) q^{74} +(1.88082 + 2.35847i) q^{75} +(1.93991 + 0.598383i) q^{76} +(-1.10078 + 2.80475i) q^{77} +(-4.53193 + 19.8557i) q^{78} +(7.49410 + 12.9802i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.26373 - 6.73976i) q^{81} +(-3.04215 + 3.81474i) q^{82} +(-3.00656 + 2.04984i) q^{83} +(2.04450 - 0.984578i) q^{84} +6.01179 q^{85} +(6.39217 - 1.46294i) q^{86} -10.8583 q^{87} +(3.60873 - 1.73787i) q^{88} +(-2.56336 + 1.74767i) q^{89} +(-3.80321 + 4.76908i) q^{90} +(-3.72296 - 3.45440i) q^{91} +(4.11976 - 7.13563i) q^{92} +(-9.61876 - 16.6602i) q^{93} +(-0.250079 + 1.09567i) q^{94} +(0.741679 - 1.88977i) q^{95} +(-2.88258 - 0.889159i) q^{96} +(-0.603863 - 0.757220i) q^{97} +(0.480823 - 6.41614i) q^{98} +(23.3469 - 7.20156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	2.49243	−	1.69931i	1.43901	−	0.981098i	0.442572	−	0.896733i	$-0.354066\pi$
$3$	2.49243	−	1.69931i	1.43901	−	0.981098i	0.996435	−	0.0843648i	$-0.0268861\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−0.733052	−	0.680173i	−0.327831	−	0.304182i
$5$	−0.733052	−	0.680173i	−0.327831	−	0.304182i
$6$	1.50830	−	2.61245i	0.615761	−	1.06653i
$7$	0.376122	+	0.651463i	0.142161	+	0.246230i	0.928310	−	0.371807i	$-0.121262\pi$
$7$	0.376122	+	0.651463i	0.142161	+	0.246230i	−0.786149	+	0.618037i	$0.787928\pi$
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	2.22854	−	5.67822i	0.742845	−	1.89274i
$10$	−0.955573	−	0.294755i	−0.302179	−	0.0932098i
$11$	2.49732	+	3.13153i	0.752969	+	0.944193i	0.999690	−	0.0248932i	$-0.00792458\pi$
$11$	2.49732	+	3.13153i	0.752969	+	0.944193i	−0.246721	+	0.969087i	$0.579353\pi$
$12$	0.225431	−	3.00817i	0.0650763	−	0.868383i
$13$	−6.45146	+	1.99001i	−1.78931	+	0.551930i	−0.998213	−	0.0597550i	$-0.980968\pi$
$13$	−6.45146	+	1.99001i	−1.78931	+	0.551930i	−0.791101	+	0.611685i	$0.790492\pi$
$14$	0.621533	+	0.423754i	0.166112	+	0.113253i
$15$	−2.98291	−	0.449601i	−0.770183	−	0.116086i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−4.40696	+	4.08906i	−1.06884	+	0.991742i	−0.999983	−	0.00588427i	$-0.998127\pi$
$17$	−4.40696	+	4.08906i	−1.06884	+	0.991742i	−0.0688610	+	0.997626i	$0.521936\pi$
$18$	−0.455845	−	6.08282i	−0.107444	−	1.43374i
$19$	0.741679	+	1.88977i	0.170153	+	0.433542i	0.990359	−	0.138526i	$-0.0442364\pi$
$19$	0.741679	+	1.88977i	0.170153	+	0.433542i	−0.820206	+	0.572068i	$0.806141\pi$
$20$	−0.988831	+	0.149042i	−0.221109	+	0.0333269i
$21$	2.04450	+	0.984578i	0.446146	+	0.214852i
$22$	3.60873	+	1.73787i	0.769383	+	0.370515i
$23$	8.14749	−	1.22804i	1.69887	−	0.256063i	0.773136	−	0.634241i	$-0.218687\pi$
$23$	8.14749	−	1.22804i	1.69887	−	0.256063i	0.925733	+	0.378177i	$0.123449\pi$
$24$	−1.10209	−	2.80807i	−0.224963	−	0.573196i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	−4.94913	+	4.59213i	−0.970605	+	0.900590i
$27$	−2.08081	−	9.11665i	−0.400453	−	1.75450i
$28$	0.743842	+	0.112116i	0.140573	+	0.0211880i
$29$	−2.97405	−	2.02767i	−0.552266	−	0.376529i	0.254796	−	0.966995i	$-0.417992\pi$
$29$	−2.97405	−	2.02767i	−0.552266	−	0.376529i	−0.807063	+	0.590466i	$0.798944\pi$
$30$	−2.88258	+	0.889159i	−0.526285	+	0.162337i
$31$	0.476570	−	6.35939i	0.0855945	−	1.14218i	−0.774682	−	0.632351i	$-0.782090\pi$
$31$	0.476570	−	6.35939i	0.0855945	−	1.14218i	0.860276	−	0.509828i	$-0.170291\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	11.5458	+	3.56142i	2.00987	+	0.619964i
$34$	−2.19635	+	5.59622i	−0.376672	+	0.959744i
$35$	0.167390	−	0.733384i	0.0282941	−	0.123964i
$36$	−3.04994	−	5.28265i	−0.508323	−	0.880442i
$37$	−2.47968	+	4.29494i	−0.407657	+	0.706083i	−0.994627	−	0.103526i	$-0.966988\pi$
$37$	−2.47968	+	4.29494i	−0.407657	+	0.706083i	0.586969	+	0.809609i	$0.300321\pi$
$38$	1.48817	+	1.38082i	0.241413	+	0.223998i
$39$	−12.6982	+	15.9230i	−2.03334	+	2.54972i
$40$	−0.826239	+	0.563320i	−0.130640	+	0.0890687i
$41$	−4.39604	+	2.11702i	−0.686546	+	0.330623i	−0.744430	−	0.667700i	$-0.767279\pi$
$41$	−4.39604	+	2.11702i	−0.686546	+	0.330623i	0.0578846	+	0.998323i	$0.481564\pi$
$42$	2.26922			0.350148
$43$	6.39389	+	1.45540i	0.975059	+	0.221946i
$43$	6.39389	+	1.45540i	0.975059	+	0.221946i
$44$	4.00538			0.603834
$45$	−5.49580	+	2.64664i	−0.819266	+	0.394538i
$46$	6.80781	−	4.64149i	1.00376	−	0.684350i
$47$	−0.700706	+	0.878657i	−0.102208	+	0.128165i	−0.830305	−	0.557309i	$-0.811834\pi$
$47$	−0.700706	+	0.878657i	−0.102208	+	0.128165i	0.728097	+	0.685475i	$0.240405\pi$
$48$	−2.21132	−	2.05181i	−0.319177	−	0.296153i
$49$	3.21706	−	5.57212i	0.459581	−	0.796017i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−4.03546	+	17.6805i	−0.565077	+	2.47576i
$52$	−2.46657	+	6.28471i	−0.342051	+	0.871533i
$53$	−3.08922	−	0.952899i	−0.424337	−	0.130891i	0.0752292	−	0.997166i	$-0.476031\pi$
$53$	−3.08922	−	0.952899i	−0.424337	−	0.130891i	−0.499566	+	0.866276i	$0.666507\pi$
$54$	−5.83031	−	7.31098i	−0.793405	−	0.994899i
$55$	0.299323	−	3.99418i	0.0403607	−	0.538576i
$56$	0.718824	−	0.221728i	0.0960569	−	0.0296296i
$57$	5.05989	+	3.44977i	0.670199	+	0.456934i
$58$	−3.55930	−	0.536477i	−0.467358	−	0.0704429i
$59$	−2.92597	−	12.8195i	−0.380929	−	1.66896i	−0.694576	−	0.719419i	$-0.744408\pi$
$59$	−2.92597	−	12.8195i	−0.380929	−	1.66896i	0.313647	−	0.949540i	$-0.398449\pi$
$60$	−2.21132	+	2.05181i	−0.285481	+	0.264887i
$61$	−0.330460	−	4.40968i	−0.0423111	−	0.564602i	−0.977566	−	0.210628i	$-0.932449\pi$
$61$	−0.330460	−	4.40968i	−0.0423111	−	0.564602i	0.935255	−	0.353974i	$-0.115170\pi$
$62$	−2.32986	−	5.93639i	−0.295893	−	0.753922i
$63$	4.53735	−	0.683895i	0.571652	−	0.0861627i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	6.08281	+	2.92933i	0.754480	+	0.363338i
$66$	11.9477	−	1.80082i	1.47066	−	0.221666i
$67$	3.60087	+	9.17486i	0.439916	+	1.12089i	0.963213	+	0.268738i	$0.0866064\pi$
$67$	3.60087	+	9.17486i	0.439916	+	1.12089i	−0.523297	+	0.852150i	$0.675298\pi$
$68$	0.449262	+	5.99498i	0.0544810	+	0.726998i
$69$	18.2203	−	16.9059i	2.19346	−	2.03523i
$70$	−0.167390	−	0.733384i	−0.0200069	−	0.0876561i
$71$	−15.1231	−	2.27943i	−1.79478	−	0.270519i	−0.834791	−	0.550567i	$-0.814412\pi$
$71$	−15.1231	−	2.27943i	−1.79478	−	0.270519i	−0.959986	+	0.280048i	$0.909650\pi$
$72$	−5.03996	−	3.43618i	−0.593965	−	0.404958i
$73$	12.2370	−	3.77463i	1.43224	−	0.441787i	0.520961	−	0.853581i	$-0.325574\pi$
$73$	12.2370	−	3.77463i	1.43224	−	0.441787i	0.911277	+	0.411794i	$0.135098\pi$
$74$	−0.370614	+	4.94550i	−0.0430830	+	0.574903i
$75$	1.88082	+	2.35847i	0.217178	+	0.272333i
$76$	1.93991	+	0.598383i	0.222523	+	0.0686392i
$77$	−1.10078	+	2.80475i	−0.125446	+	0.319631i
$78$	−4.53193	+	19.8557i	−0.513140	+	2.24821i
$79$	7.49410	+	12.9802i	0.843152	+	1.46038i	0.887216	+	0.461354i	$0.152636\pi$
$79$	7.49410	+	12.9802i	0.843152	+	1.46038i	−0.0440644	+	0.999029i	$0.514031\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−7.26373	−	6.73976i	−0.807081	−	0.748862i
$82$	−3.04215	+	3.81474i	−0.335949	+	0.421267i
$83$	−3.00656	+	2.04984i	−0.330013	+	0.224999i	−0.716979	−	0.697095i	$-0.754476\pi$
$83$	−3.00656	+	2.04984i	−0.330013	+	0.224999i	0.386966	+	0.922094i	$0.373523\pi$
$84$	2.04450	−	0.984578i	0.223073	−	0.107426i
$85$	6.01179			0.652070
$86$	6.39217	−	1.46294i	0.689285	−	0.157752i
$87$	−10.8583			−1.16413
$88$	3.60873	−	1.73787i	0.384691	−	0.185258i
$89$	−2.56336	+	1.74767i	−0.271715	+	0.185252i	−0.691510	−	0.722367i	$-0.743054\pi$
$89$	−2.56336	+	1.74767i	−0.271715	+	0.185252i	0.419795	+	0.907619i	$0.362102\pi$
$90$	−3.80321	+	4.76908i	−0.400894	+	0.502705i
$91$	−3.72296	−	3.45440i	−0.390272	−	0.362119i
$92$	4.11976	−	7.13563i	0.429515	−	0.743941i
$93$	−9.61876	−	16.6602i	−0.997419	−	1.72758i
$94$	−0.250079	+	1.09567i	−0.0257937	+	0.113009i
$95$	0.741679	−	1.88977i	0.0760947	−	0.193886i
$96$	−2.88258	−	0.889159i	−0.294202	−	0.0907494i
$97$	−0.603863	−	0.757220i	−0.0613130	−	0.0768841i	0.750229	−	0.661178i	$-0.229943\pi$
$97$	−0.603863	−	0.757220i	−0.0613130	−	0.0768841i	−0.811542	+	0.584294i	$0.801372\pi$
$98$	0.480823	−	6.41614i	0.0485705	−	0.648128i
$99$	23.3469	−	7.20156i	2.34645	−	0.723784i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	−6.29615	−	0.948992i	−0.626490	−	0.0944282i	−0.171879	−	0.985118i	$-0.554984\pi$
$101$	−6.29615	−	0.948992i	−0.626490	−	0.0944282i	−0.454612	+	0.890690i	$0.650222\pi$
$102$	4.03546	+	17.6805i	0.399570	+	1.75063i
$103$	−4.25487	+	3.94794i	−0.419245	+	0.389002i	−0.861393	−	0.507940i	$-0.830407\pi$
$103$	−4.25487	+	3.94794i	−0.419245	+	0.389002i	0.442148	+	0.896942i	$0.354217\pi$
$104$	0.504534	+	6.73253i	0.0494736	+	0.660179i
$105$	−0.829039	−	2.11236i	−0.0809059	−	0.206145i
$106$	−3.19674	+	0.481831i	−0.310495	+	0.0467996i
$107$	1.97081	+	0.949093i	0.190526	+	0.0917523i	0.526714	−	0.850042i	$-0.323424\pi$
$107$	1.97081	+	0.949093i	0.190526	+	0.0917523i	−0.336189	+	0.941795i	$0.609138\pi$
$108$	−8.42505	−	4.05729i	−0.810701	−	0.390413i
$109$	−2.29859	+	0.346456i	−0.220165	+	0.0331845i	−0.258198	−	0.966092i	$-0.583129\pi$
$109$	−2.29859	+	0.346456i	−0.220165	+	0.0331845i	0.0380334	+	0.999276i	$0.487891\pi$
$110$	−1.46333	−	3.72851i	−0.139523	−	0.355499i
$111$	1.11799	+	14.9186i	0.106115	+	1.41601i
$112$	0.551434	−	0.511656i	0.0521056	−	0.0483469i
$113$	−0.906499	−	3.97163i	−0.0852763	−	0.373620i	0.914225	−	0.405208i	$-0.132801\pi$
$113$	−0.906499	−	3.97163i	−0.0852763	−	0.373620i	−0.999501	+	0.0315878i	$0.989944\pi$
$114$	6.05560	+	0.912735i	0.567159	+	0.0854855i
$115$	−6.80781	−	4.64149i	−0.634832	−	0.432821i
$116$	−3.43958	+	1.06097i	−0.319357	+	0.0985087i
$117$	−3.07759	+	41.0676i	−0.284524	+	3.79670i
$118$	−8.19839	−	10.2805i	−0.754723	−	0.946393i
$119$	−4.32142	−	1.33298i	−0.396144	−	0.122194i
$120$	−1.10209	+	2.80807i	−0.100606	+	0.256341i
$121$	−1.12219	+	4.91666i	−0.102018	+	0.446969i
$122$	−2.21102	−	3.82961i	−0.200177	−	0.346716i
$123$	−7.35935	+	12.7468i	−0.663570	+	1.14934i
$124$	−4.67483	−	4.33761i	−0.419812	−	0.389529i
$125$	0.623490	−	0.781831i	0.0557666	−	0.0699291i
$126$	3.79128	−	2.58485i	0.337754	−	0.230277i
$127$	5.75196	−	2.77000i	0.510404	−	0.245798i	−0.160912	−	0.986969i	$-0.551444\pi$
$127$	5.75196	−	2.77000i	0.510404	−	0.245798i	0.671316	+	0.741171i	$0.265729\pi$
$128$	−1.00000			−0.0883883
$129$	18.4095	−	7.23773i	1.62087	−	0.637246i
$130$	6.75141			0.592138
$131$	4.07889	−	1.96429i	0.356375	−	0.171621i	−0.247126	−	0.968983i	$-0.579486\pi$
$131$	4.07889	−	1.96429i	0.356375	−	0.171621i	0.603501	+	0.797362i	$0.293772\pi$
$132$	9.98315	−	6.80639i	0.868921	−	0.592421i
$133$	−0.952151	+	1.19396i	−0.0825619	+	0.103529i
$134$	7.22509	+	6.70391i	0.624153	+	0.579129i
$135$	−4.67555	+	8.09829i	−0.402407	+	0.696990i
$136$	3.00590	+	5.20636i	0.257753	+	0.446442i
$137$	−2.15792	+	9.45449i	−0.184364	+	0.807751i	0.795156	+	0.606405i	$0.207389\pi$
$137$	−2.15792	+	9.45449i	−0.184364	+	0.807751i	−0.979520	+	0.201347i	$0.935468\pi$
$138$	9.08067	−	23.1372i	0.772998	−	1.96957i
$139$	−0.467896	−	0.144327i	−0.0396865	−	0.0122417i	0.274848	−	0.961488i	$-0.411372\pi$
$139$	−0.467896	−	0.144327i	−0.0396865	−	0.0122417i	−0.314535	+	0.949246i	$0.601849\pi$
$140$	−0.469017	−	0.588128i	−0.0396391	−	0.0497059i
$141$	−0.253349	+	3.38071i	−0.0213359	+	0.284707i
$142$	−14.6144	+	4.50795i	−1.22641	+	0.378299i
$143$	−22.3431	−	15.2333i	−1.86843	−	1.27387i
$144$	−6.03175	−	0.909140i	−0.502646	−	0.0757617i
$145$	0.800964	+	3.50925i	0.0665164	+	0.291428i
$146$	9.38745	−	8.71028i	0.776911	−	0.720868i
$147$	−1.45045	−	19.3549i	−0.119631	−	1.59637i
$148$	1.81186	+	4.61654i	0.148934	+	0.379478i
$149$	−6.29019	+	0.948093i	−0.515312	+	0.0776708i	−0.401550	−	0.915837i	$-0.631528\pi$
$149$	−6.29019	+	0.948093i	−0.515312	+	0.0776708i	−0.113762	+	0.993508i	$0.536290\pi$
$150$	2.71786	+	1.30885i	0.221913	+	0.106867i
$151$	−10.0015	−	4.81646i	−0.813909	−	0.391958i	−0.0198530	−	0.999803i	$-0.506320\pi$
$151$	−10.0015	−	4.81646i	−0.813909	−	0.391958i	−0.794056	+	0.607845i	$0.792034\pi$
$152$	2.00743	−	0.302571i	0.162824	−	0.0245417i
$153$	13.3975	+	34.1363i	1.08312	+	2.75975i
$154$	0.225164	+	3.00460i	0.0181442	+	0.242118i
$155$	−4.67483	+	4.33761i	−0.375492	+	0.348405i
$156$	4.53193	+	19.8557i	0.362845	+	1.58973i
$157$	−12.0018	−	1.80898i	−0.957845	−	0.144372i	−0.348528	−	0.937298i	$-0.613318\pi$
$157$	−12.0018	−	1.80898i	−0.957845	−	0.144372i	−0.609317	+	0.792926i	$0.708556\pi$
$158$	12.3838	+	8.44315i	0.985205	+	0.671701i
$159$	−9.31895	+	2.87452i	−0.739041	+	0.227964i
$160$	−0.0747301	+	0.997204i	−0.00590793	+	0.0788359i
$161$	3.86447	+	4.84589i	0.304563	+	0.381910i
$162$	−9.46866	−	2.92070i	−0.743929	−	0.229472i
$163$	−1.88036	+	4.79107i	−0.147281	+	0.375265i	−0.985408	−	0.170210i	$-0.945556\pi$
$163$	−1.88036	+	4.79107i	−0.147281	+	0.375265i	0.838127	+	0.545475i	$0.183651\pi$
$164$	−1.08573	+	4.75690i	−0.0847814	+	0.371451i
$165$	−6.04132	−	10.4639i	−0.470316	−	0.814612i
$166$	−1.81943	+	3.15134i	−0.141215	+	0.244591i
$167$	−6.80155	−	6.31092i	−0.526320	−	0.488354i	0.371673	−	0.928364i	$-0.378784\pi$
$167$	−6.80155	−	6.31092i	−0.526320	−	0.488354i	−0.897993	+	0.440010i	$0.854975\pi$
$168$	1.41484	−	1.77415i	0.109157	−	0.136878i
$169$	26.9201	−	18.3538i	2.07078	−	1.41183i
$170$	5.41644	−	2.60842i	0.415422	−	0.200057i
$171$	12.3834			0.946980
$172$	5.12440	−	4.09152i	0.390732	−	0.311975i
$173$	12.0620			0.917060			0.458530	−	0.888679i	$-0.348376\pi$
$173$	12.0620			0.917060			0.458530	+	0.888679i	$0.348376\pi$
$174$	−9.78295	+	4.71122i	−0.741643	+	0.357157i
$175$	−0.621533	+	0.423754i	−0.0469835	+	0.0320328i
$176$	2.49732	−	3.13153i	0.188242	−	0.236048i
$177$	−29.0771	−	26.9796i	−2.18557	−	2.02791i
$178$	−1.55122	+	2.68679i	−0.116269	+	0.201384i
$179$	7.69982	+	13.3365i	0.575512	+	0.996815i	0.995986	+	0.0895109i	$0.0285304\pi$
$179$	7.69982	+	13.3365i	0.575512	+	0.996815i	−0.420474	+	0.907304i	$0.638136\pi$
$180$	−1.35735	+	5.94694i	−0.101171	+	0.443259i
$181$	−1.58464	+	4.03758i	−0.117785	+	0.300111i	−0.977592	−	0.210507i	$-0.932488\pi$
$181$	−1.58464	+	4.03758i	−0.117785	+	0.300111i	0.859807	+	0.510619i	$0.170584\pi$
$182$	−4.85308	−	1.49698i	−0.359734	−	0.110963i
$183$	−8.31708	−	10.4293i	−0.614816	−	0.770955i
$184$	0.615740	−	8.21648i	0.0453930	−	0.605727i
$185$	4.73904	−	1.46180i	0.348421	−	0.107474i
$186$	−15.8948	−	10.8369i	−1.16546	−	0.794599i
$187$	−23.8106	−	3.58887i	−1.74120	−	0.262444i
$188$	0.250079	+	1.09567i	0.0182389	+	0.0799098i
$189$	5.15651	−	4.78454i	0.375081	−	0.348024i
$190$	−0.151710	−	2.02442i	−0.0110062	−	0.146867i
$191$	−5.48989	−	13.9880i	−0.397234	−	1.01214i	−0.979912	−	0.199433i	$-0.936090\pi$
$191$	−5.48989	−	13.9880i	−0.397234	−	1.01214i	0.582677	−	0.812704i	$-0.302005\pi$
$192$	−2.98291	+	0.449601i	−0.215273	+	0.0324472i
$193$	1.62783	+	0.783921i	0.117174	+	0.0564279i	0.491552	−	0.870848i	$-0.336430\pi$
$193$	1.62783	+	0.783921i	0.117174	+	0.0564279i	−0.374379	+	0.927276i	$0.622144\pi$
$194$	−0.872608	−	0.420226i	−0.0626496	−	0.0301704i
$195$	20.1388	−	3.03544i	1.44217	−	0.217372i
$196$	−2.35065	−	5.98936i	−0.167904	−	0.427812i
$197$	0.816875	+	10.9004i	0.0581999	+	0.776624i	0.947593	+	0.319480i	$0.103508\pi$
$197$	0.816875	+	10.9004i	0.0581999	+	0.776624i	−0.889393	+	0.457143i	$0.848873\pi$
$198$	17.9102	−	16.6182i	1.27282	−	1.18101i
$199$	−3.59146	−	15.7352i	−0.254592	−	1.11544i	−0.926941	−	0.375207i	$-0.877572\pi$
$199$	−3.59146	−	15.7352i	−0.254592	−	1.11544i	0.672349	−	0.740234i	$-0.265285\pi$
$200$	0.988831	+	0.149042i	0.0699209	+	0.0105389i
$201$	24.5659	+	16.7487i	1.73274	+	1.18136i
$202$	−6.08439	+	1.87679i	−0.428096	+	0.132050i
$203$	0.202347	−	2.70013i	0.0142020	−	0.189512i
$204$	11.3071	+	14.1787i	0.791655	+	0.992704i
$205$	4.66246	+	1.43818i	0.325640	+	0.100447i
$206$	−2.12056	+	5.40309i	−0.147746	+	0.376451i
$207$	11.1839	−	48.9999i	0.777336	−	3.40573i
$208$	3.37571	+	5.84689i	0.234063	+	0.405409i
$209$	−4.06567	+	7.04194i	−0.281228	+	0.487101i
$210$	−1.66346	−	1.54346i	−0.114789	−	0.106509i
$211$	13.6559	−	17.1240i	0.940112	−	1.17886i	−0.0435886	−	0.999050i	$-0.513879\pi$
$211$	13.6559	−	17.1240i	0.940112	−	1.17886i	0.983701	−	0.179814i	$-0.0575495\pi$
$212$	−2.67110	+	1.82113i	−0.183452	+	0.125076i
$213$	−41.5667	+	20.0175i	−2.84810	+	1.37157i
$214$	2.18744			0.149530
$215$	−3.69713	−	5.41583i	−0.252142	−	0.369357i
$216$	−9.35110			−0.636262
$217$	4.32215	−	2.08144i	0.293407	−	0.141297i
$218$	−1.92063	+	1.30947i	−0.130082	+	0.0886883i
$219$	24.0857	−	30.2026i	1.62756	−	2.04090i
$220$	−2.93615	−	2.72435i	−0.197955	−	0.183676i
$221$	20.2940	−	35.1503i	1.36512	−	2.36447i
$222$	7.48021	+	12.9561i	0.502039	+	0.869557i
$223$	−1.95780	+	8.57767i	−0.131104	+	0.574403i	0.866113	+	0.499848i	$0.166611\pi$
$223$	−1.95780	+	8.57767i	−0.131104	+	0.574403i	−0.997217	+	0.0745552i	$0.976246\pi$
$224$	0.274826	−	0.700244i	0.0183626	−	0.0467870i
$225$	5.82888	+	1.79797i	0.388592	+	0.119865i
$226$	−2.53995	−	3.18500i	−0.168955	−	0.211863i
$227$	−1.28841	+	17.1927i	−0.0855149	+	1.14112i	0.775093	+	0.631848i	$0.217703\pi$
$227$	−1.28841	+	17.1927i	−0.0855149	+	1.14112i	−0.860607	+	0.509269i	$0.829916\pi$
$228$	5.85193	−	1.80508i	0.387554	−	0.119544i
$229$	4.54351	+	3.09771i	0.300243	+	0.204703i	0.704065	−	0.710135i	$-0.251366\pi$
$229$	4.54351	+	3.09771i	0.300243	+	0.204703i	−0.403822	+	0.914838i	$0.632319\pi$
$230$	−8.14749	−	1.22804i	−0.537230	−	0.0809743i
$231$	2.02251	+	8.86121i	0.133072	+	0.583025i
$232$	−2.63862	+	2.44828i	−0.173234	+	0.160738i
$233$	−1.95680	−	26.1117i	−0.128194	−	1.71063i	−0.576786	−	0.816895i	$-0.695693\pi$
$233$	−1.95680	−	26.1117i	−0.128194	−	1.71063i	0.448592	−	0.893737i	$-0.351926\pi$
$234$	15.0458	+	38.3360i	0.983572	+	2.50610i
$235$	1.11129	−	0.167500i	0.0724927	−	0.0109265i
$236$	−11.8470	−	5.70522i	−0.771175	−	0.371378i
$237$	40.7359	+	19.6174i	2.64608	+	1.27428i
$238$	−4.47182	+	0.674019i	−0.289865	+	0.0436902i
$239$	−5.56486	−	14.1790i	−0.359961	−	0.917166i	−0.990059	−	0.140650i	$-0.955081\pi$
$239$	−5.56486	−	14.1790i	−0.359961	−	0.917166i	0.630098	−	0.776515i	$-0.283015\pi$
$240$	0.225431	+	3.00817i	0.0145515	+	0.194176i
$241$	5.88948	−	5.46464i	0.379374	−	0.352008i	−0.467319	−	0.884089i	$-0.654780\pi$
$241$	5.88948	−	5.46464i	0.379374	−	0.352008i	0.846694	+	0.532081i	$0.178590\pi$
$242$	1.12219	+	4.91666i	0.0721374	+	0.316055i
$243$	−1.81734	−	0.273920i	−0.116582	−	0.0175720i
$244$	−3.65367	−	2.49103i	−0.233902	−	0.159472i
$245$	−6.14828	+	1.89649i	−0.392799	+	0.121162i
$246$	−1.09993	+	14.6775i	−0.0701289	+	0.935806i
$247$	−8.54558	−	10.7158i	−0.543742	−	0.681831i
$248$	−6.09390	−	1.87972i	−0.386963	−	0.119362i
$249$	−4.01033	+	10.2182i	−0.254145	+	0.647550i
$250$	0.222521	−	0.974928i	0.0140735	−	0.0616599i
$251$	−8.15591	−	14.1265i	−0.514797	−	0.891654i	−0.999853	−	0.0171708i	$-0.994534\pi$
$251$	−8.15591	−	14.1265i	−0.514797	−	0.891654i	0.485056	−	0.874483i	$-0.338799\pi$
$252$	2.29430	−	3.97384i	0.144527	−	0.250329i
$253$	24.1925	+	22.4474i	1.52097	+	1.41125i
$254$	3.98048	−	4.99137i	0.249758	−	0.313186i
$255$	14.9840	−	10.2159i	0.938334	−	0.639745i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−13.9490			−0.870115			−0.435058	−	0.900403i	$-0.643272\pi$
$257$	−13.9490			−0.870115			−0.435058	+	0.900403i	$0.643272\pi$
$258$	13.4461	−	14.5086i	0.837115	−	0.903263i
$259$	−3.73065			−0.231812
$260$	6.08281	−	2.92933i	0.377240	−	0.181669i
$261$	−18.1413	+	12.3685i	−1.12292	+	0.765594i
$262$	2.82268	−	3.53953i	0.174386	−	0.218673i
$263$	−7.78013	−	7.21891i	−0.479744	−	0.445137i	0.402855	−	0.915264i	$-0.368018\pi$
$263$	−7.78013	−	7.21891i	−0.479744	−	0.445137i	−0.882599	+	0.470127i	$0.844208\pi$
$264$	6.04132	−	10.4639i	0.371818	−	0.644007i
$265$	1.61642	+	2.79973i	0.0992962	+	0.171986i
$266$	−0.339819	+	1.48884i	−0.0208356	+	0.0912868i
$267$	−3.41916	+	8.71188i	−0.209249	+	0.533159i
$268$	9.41830	+	2.90516i	0.575314	+	0.177461i
$269$	7.62315	+	9.55913i	0.464792	+	0.582831i	0.957887	−	0.287145i	$-0.0927061\pi$
$269$	7.62315	+	9.55913i	0.464792	+	0.582831i	−0.493095	+	0.869975i	$0.664135\pi$
$270$	−0.698808	+	9.32495i	−0.0425281	+	0.567498i
$271$	13.5293	−	4.17323i	0.821845	−	0.253506i	0.144813	−	0.989459i	$-0.453742\pi$
$271$	13.5293	−	4.17323i	0.821845	−	0.253506i	0.677032	+	0.735953i	$0.263266\pi$
$272$	4.96718	+	3.38656i	0.301179	+	0.205341i
$273$	−15.1493	−	2.28339i	−0.916879	−	0.138197i
$274$	2.15792	+	9.45449i	0.130365	+	0.571166i
$275$	−2.93615	+	2.72435i	−0.177057	+	0.164285i
$276$	−1.85744	−	24.7858i	−0.111805	−	1.49193i
$277$	7.23266	+	18.4285i	0.434568	+	1.10726i	0.965628	+	0.259928i	$0.0836988\pi$
$277$	7.23266	+	18.4285i	0.434568	+	1.10726i	−0.531060	+	0.847334i	$0.678206\pi$
$278$	−0.484181	+	0.0729786i	−0.0290393	+	0.00437696i
$279$	−35.0479	−	16.8782i	−2.09826	−	1.01047i
$280$	−0.677749	−	0.326386i	−0.0405032	−	0.0195053i
$281$	−25.5043	+	3.84416i	−1.52146	+	0.229323i	−0.855947	−	0.517063i	$-0.827025\pi$
$281$	−25.5043	+	3.84416i	−1.52146	+	0.229323i	−0.665513	+	0.746386i	$0.731787\pi$
$282$	1.23858	+	3.15584i	0.0737561	+	0.187927i
$283$	0.130164	+	1.73691i	0.00773742	+	0.103249i	0.999735	−	0.0230055i	$-0.00732353\pi$
$283$	0.130164	+	1.73691i	0.00773742	+	0.103249i	−0.991998	+	0.126254i	$0.959704\pi$
$284$	−11.2112	+	10.4025i	−0.665263	+	0.617274i
$285$	−1.36272	−	5.97046i	−0.0807205	−	0.353660i
$286$	−26.7400	−	4.03040i	−1.58117	−	0.238322i
$287$	−3.03261	−	2.06760i	−0.179009	−	0.122046i
$288$	−5.82888	+	1.79797i	−0.343470	+	0.105946i
$289$	1.43046	−	19.0881i	0.0841445	−	1.12283i
$290$	2.24425	+	2.81420i	0.131787	+	0.165256i
$291$	−2.79184	−	0.861169i	−0.163661	−	0.0504826i
$292$	4.67855	−	11.9208i	0.273791	−	0.697609i
$293$	6.58643	−	28.8570i	0.384783	−	1.68585i	−0.297470	−	0.954731i	$-0.596143\pi$
$293$	6.58643	−	28.8570i	0.384783	−	1.68585i	0.682254	−	0.731115i	$-0.261000\pi$
$294$	−9.70460	−	16.8089i	−0.565984	−	0.980312i
$295$	−6.57460	+	11.3875i	−0.382788	+	0.663008i
$296$	3.63547	+	3.37323i	0.211308	+	0.196065i
$297$	23.3526	−	29.2833i	1.35506	−	1.69919i
$298$	−5.25590	+	3.58341i	−0.304466	+	0.207581i
$299$	−50.1194	+	24.1362i	−2.89848	+	1.39584i
$300$	3.01660			0.174164
$301$	1.45675	+	4.71279i	0.0839654	+	0.271640i
$302$	−11.1008			−0.638779
$303$	−17.3054	+	8.33382i	−0.994167	+	0.478766i
$304$	1.67735	−	1.14360i	0.0962025	−	0.0655898i
$305$	−2.75710	+	3.45730i	−0.157871	+	0.197964i
$306$	26.8819	+	24.9428i	1.53674	+	1.42588i
$307$	−5.20936	+	9.02288i	−0.297314	+	0.514963i	−0.975521	−	0.219908i	$-0.929424\pi$
$307$	−5.20936	+	9.02288i	−0.297314	+	0.514963i	0.678206	+	0.734871i	$0.262758\pi$
$308$	1.50651	+	2.60936i	0.0858415	+	0.148682i
$309$	−3.89619	+	17.0703i	−0.221647	+	0.971097i
$310$	−2.32986	+	5.93639i	−0.132327	+	0.337164i
$311$	20.0420	+	6.18215i	1.13648	+	0.350557i	0.805216	−	0.592981i	$-0.202049\pi$
$311$	20.0420	+	6.18215i	1.13648	+	0.350557i	0.331263	+	0.943539i	$0.392525\pi$
$312$	12.6982	+	15.9230i	0.718893	+	0.901464i
$313$	1.20083	−	16.0240i	0.0678752	−	0.905732i	−0.854504	−	0.519445i	$-0.826139\pi$
$313$	1.20083	−	16.0240i	0.0678752	−	0.905732i	0.922379	−	0.386286i	$-0.126242\pi$
$314$	−11.5981	+	3.57754i	−0.654519	+	0.201892i
$315$	−3.79128	−	2.58485i	−0.213614	−	0.145640i
$316$	14.8208	+	2.23388i	0.833735	+	0.125665i
$317$	0.0437199	+	0.191549i	0.00245556	+	0.0107585i	0.976141	−	0.217138i	$-0.0696723\pi$
$317$	0.0437199	+	0.191549i	0.00245556	+	0.0107585i	−0.973685	+	0.227897i	$0.926815\pi$
$318$	−7.14888	+	6.63319i	−0.400889	+	0.371971i
$319$	−1.07741	−	14.3771i	−0.0603235	−	0.804961i
$320$	0.365341	+	0.930874i	0.0204232	+	0.0520374i
$321$	6.52492	−	0.983473i	0.364185	−	0.0548921i
$322$	5.58432	+	2.68927i	0.311202	+	0.149867i
$323$	−10.9959	−	5.29535i	−0.611829	−	0.294641i
$324$	−9.79822	+	1.47684i	−0.544345	+	0.0820468i
$325$	−2.46657	−	6.28471i	−0.136821	−	0.348613i
$326$	0.384625	+	5.13246i	0.0213024	+	0.284261i
$327$	−5.14034	+	4.76954i	−0.284261	+	0.263756i
$328$	1.08573	+	4.75690i	0.0599495	+	0.262656i
$329$	−0.835963	−	0.126001i	−0.0460881	−	0.00694667i
$330$	−9.98315	−	6.80639i	−0.549554	−	0.374680i
$331$	11.4771	−	3.54022i	0.630839	−	0.194588i	0.0371851	−	0.999308i	$-0.488161\pi$
$331$	11.4771	−	3.54022i	0.630839	−	0.194588i	0.593654	+	0.804720i	$0.297685\pi$
$332$	−0.271932	+	3.62868i	−0.0149242	+	0.199150i
$333$	18.8615	+	23.6516i	1.03361	+	1.29610i
$334$	−8.86619	−	2.73486i	−0.485136	−	0.149645i
$335$	3.60087	−	9.17486i	0.196736	−	0.501276i
$336$	0.504949	−	2.21233i	0.0275472	−	0.120692i
$337$	9.59542	+	16.6198i	0.522696	+	0.905336i	0.999651	+	0.0264083i	$0.00840699\pi$
$337$	9.59542	+	16.6198i	0.522696	+	0.905336i	−0.476955	+	0.878927i	$0.658260\pi$
$338$	16.2908	−	28.2164i	0.886101	−	1.53477i
$339$	−9.00843	−	8.35860i	−0.489271	−	0.453977i
$340$	3.74829	−	4.70021i	0.203280	−	0.254905i
$341$	21.1048	−	14.3890i	1.14289	−	0.779208i
$342$	11.1570	−	5.37294i	0.603303	−	0.290535i
$343$	10.1057			0.545659
$344$	2.84168	−	5.90972i	0.153213	−	0.318631i
$345$	−24.8553			−1.33817
$346$	10.8675	−	5.23352i	0.584241	−	0.281356i
$347$	6.18833	−	4.21914i	0.332207	−	0.226495i	−0.385716	−	0.922618i	$-0.626045\pi$
$347$	6.18833	−	4.21914i	0.332207	−	0.226495i	0.717923	+	0.696123i	$0.245093\pi$
$348$	−6.77001	+	8.48932i	−0.362911	+	0.455075i
$349$	0.722011	+	0.669928i	0.0386484	+	0.0358604i	0.699261	−	0.714867i	$-0.253513\pi$
$349$	0.722011	+	0.669928i	0.0386484	+	0.0358604i	−0.660612	+	0.750727i	$0.729703\pi$
$350$	−0.376122	+	0.651463i	−0.0201046	+	0.0348221i
$351$	31.5665	+	54.6749i	1.68490	+	2.91833i
$352$	0.891282	−	3.90496i	0.0475055	−	0.208135i
$353$	−3.67167	+	9.35526i	−0.195423	+	0.497930i	−0.994674	−	0.103067i	$-0.967134\pi$
$353$	−3.67167	+	9.35526i	−0.195423	+	0.497930i	0.799251	+	0.600997i	$0.205230\pi$
$354$	−37.9036	−	11.6917i	−2.01456	−	0.621408i
$355$	9.53558	+	11.9572i	0.506096	+	0.634624i
$356$	−0.231846	+	3.09377i	−0.0122878	+	0.163969i
$357$	−13.0360	+	4.02107i	−0.689938	+	0.212818i
$358$	12.7238	+	8.67493i	0.672473	+	0.458484i
$359$	26.1632	+	3.94347i	1.38084	+	0.208128i	0.797118	−	0.603824i	$-0.206357\pi$
$359$	26.1632	+	3.94347i	1.38084	+	0.208128i	0.583724	+	0.811952i	$0.301595\pi$
$360$	1.35735	+	5.94694i	0.0715387	+	0.313431i
$361$	10.9069	−	10.1201i	0.574045	−	0.532636i
$362$	0.324135	+	4.32529i	0.0170362	+	0.227332i
$363$	5.55794	+	14.1614i	0.291716	+	0.743280i
$364$	−5.02198	+	0.756942i	−0.263223	+	0.0396746i
$365$	−11.5378	−	5.55631i	−0.603915	−	0.290830i
$366$	−12.0185	−	5.78781i	−0.628218	−	0.302534i
$367$	31.5983	−	4.76268i	1.64942	−	0.248610i	0.742479	−	0.669869i	$-0.233650\pi$
$367$	31.5983	−	4.76268i	1.64942	−	0.248610i	0.906940	+	0.421259i	$0.138412\pi$
$368$	−3.01023	−	7.66995i	−0.156919	−	0.399824i
$369$	2.22417	+	29.6795i	0.115786	+	1.54505i
$370$	3.63547	−	3.37323i	0.188999	−	0.175366i
$371$	−0.541147	−	2.37092i	−0.0280949	−	0.123092i
$372$	−19.0227	−	2.86720i	−0.986279	−	0.148658i
$373$	−9.30088	−	6.34123i	−0.481581	−	0.328337i	0.298077	−	0.954542i	$-0.403655\pi$
$373$	−9.30088	−	6.34123i	−0.481581	−	0.328337i	−0.779658	+	0.626205i	$0.784607\pi$
$374$	−23.0097	+	7.09757i	−1.18981	+	0.367006i
$375$	0.225431	−	3.00817i	0.0116412	−	0.155341i
$376$	0.700706	+	0.878657i	0.0361361	+	0.0453133i
$377$	23.2220	+	7.16305i	1.19600	+	0.368916i
$378$	2.56992	−	6.54805i	0.132182	−	0.336795i
$379$	−6.28633	+	27.5422i	−0.322907	+	1.41475i	0.509445	+	0.860503i	$0.329851\pi$
$379$	−6.28633	+	27.5422i	−0.322907	+	1.41475i	−0.832353	+	0.554246i	$0.813007\pi$
$380$	−1.01505	−	1.75812i	−0.0520710	−	0.0901896i
$381$	9.62929	−	16.6784i	0.493323	−	0.854461i
$382$	−11.0154	−	10.2208i	−0.563596	−	0.522941i
$383$	−4.64660	+	5.82665i	−0.237430	+	0.297728i	−0.886244	−	0.463219i	$-0.846694\pi$
$383$	−4.64660	+	5.82665i	−0.237430	+	0.297728i	0.648813	+	0.760948i	$0.275266\pi$
$384$	−2.49243	+	1.69931i	−0.127191	+	0.0867176i
$385$	2.71464	−	1.30730i	0.138351	−	0.0666263i
$386$	1.80675			0.0919613
$387$	22.5131	−	33.0625i	1.14440	−	1.68066i
$388$	−0.968521			−0.0491692
$389$	−7.17669	+	3.45611i	−0.363873	+	0.175232i	−0.606882	−	0.794792i	$-0.707580\pi$
$389$	−7.17669	+	3.45611i	−0.363873	+	0.175232i	0.243009	+	0.970024i	$0.421866\pi$
$390$	16.8274	−	11.4728i	0.852090	−	0.580945i
$391$	−30.8841	+	38.7275i	−1.56188	+	1.95853i
$392$	−4.71655	−	4.37632i	−0.238222	−	0.221037i
$393$	6.82842	−	11.8272i	0.344448	−	0.596602i
$394$	5.46550	+	9.46652i	0.275348	+	0.476916i
$395$	3.33519	−	14.6124i	0.167812	−	0.735230i
$396$	8.92614	−	22.7434i	0.448555	−	1.14290i
$397$	30.7368	+	9.48106i	1.54264	+	0.475841i	0.945315	−	0.326160i	$-0.105755\pi$
$397$	30.7368	+	9.48106i	1.54264	+	0.475841i	0.597323	+	0.802001i	$0.296231\pi$
$398$	−10.0631	−	12.6187i	−0.504416	−	0.632517i
$399$	−0.344262	+	4.59386i	−0.0172347	+	0.229981i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	−11.1907	−	7.62969i	−0.558837	−	0.381008i	0.250712	−	0.968062i	$-0.419335\pi$
$401$	−11.1907	−	7.62969i	−0.558837	−	0.381008i	−0.809548	+	0.587054i	$0.800288\pi$
$402$	29.4001	+	4.43135i	1.46634	+	0.221016i
$403$	9.58069	+	41.9757i	0.477248	+	2.09096i
$404$	−4.66754	+	4.33084i	−0.232219	+	0.215467i
$405$	0.740492	+	9.88118i	0.0367954	+	0.491000i
$406$	−0.989235	−	2.52053i	−0.0490949	−	0.125092i
$407$	−19.6423	+	2.96060i	−0.973633	+	0.146751i
$408$	16.3392	+	7.86856i	0.808912	+	0.389552i
$409$	−35.7881	−	17.2346i	−1.76961	−	0.852199i	−0.966624	−	0.256198i	$-0.917530\pi$
$409$	−35.7881	−	17.2346i	−1.76961	−	0.852199i	−0.802984	−	0.596000i	$-0.796756\pi$
$410$	4.82474	−	0.727212i	0.238277	−	0.0359144i
$411$	10.6876	+	27.2317i	0.527182	+	1.34324i
$412$	0.433758	+	5.78809i	0.0213697	+	0.285159i
$413$	7.25091	−	6.72786i	0.356794	−	0.331057i
$414$	−11.1839	−	48.9999i	−0.549660	−	2.40822i
$415$	3.59821	+	0.542343i	0.176629	+	0.0266226i
$416$	5.57828	+	3.80320i	0.273498	+	0.186467i
$417$	−1.41146	+	0.435377i	−0.0691193	+	0.0213205i
$418$	−0.607655	+	8.10859i	−0.0297214	+	0.396604i
$419$	−5.99882	−	7.52229i	−0.293062	−	0.367488i	0.613402	−	0.789771i	$-0.289800\pi$
$419$	−5.99882	−	7.52229i	−0.293062	−	0.367488i	−0.906464	+	0.422283i	$0.861229\pi$
$420$	−2.16840	−	0.668864i	−0.105807	−	0.0326372i
$421$	−0.0324626	+	0.0827133i	−0.00158213	+	0.00403120i	−0.931663	−	0.363325i	$-0.881642\pi$
$421$	−0.0324626	+	0.0827133i	−0.00158213	+	0.00403120i	0.930081	+	0.367356i	$0.119737\pi$
$422$	4.87374	−	21.3533i	0.237250	−	1.03946i
$423$	3.42766	+	5.93688i	0.166658	+	0.288661i
$424$	−1.61642	+	2.79973i	−0.0785005	+	0.135967i
$425$	−4.40696	−	4.08906i	−0.213769	−	0.198348i
$426$	−28.7650	+	36.0702i	−1.39367	+	1.74761i
$427$	2.74845	−	1.87386i	0.133007	−	0.0906825i
$428$	1.97081	−	0.949093i	0.0952628	−	0.0458761i
$429$	−81.5749			−3.93847
$430$	−5.68084	−	3.27537i	−0.273954	−	0.157952i
$431$	24.5399			1.18205			0.591023	−	0.806655i	$-0.298724\pi$
$431$	24.5399			1.18205			0.591023	+	0.806655i	$0.298724\pi$
$432$	−8.42505	+	4.05729i	−0.405350	+	0.195206i
$433$	−18.9803	+	12.9405i	−0.912134	+	0.621882i	−0.925796	−	0.378024i	$-0.876604\pi$
$433$	−18.9803	+	12.9405i	−0.912134	+	0.621882i	0.0136618	+	0.999907i	$0.495651\pi$
$434$	2.99102	−	3.75062i	0.143574	−	0.180036i
$435$	7.95966	+	7.38549i	0.381637	+	0.354107i
$436$	−1.16228	+	2.01312i	−0.0556629	+	0.0964110i
$437$	8.36353	+	14.4861i	0.400082	+	0.692962i
$438$	8.59610	−	37.6620i	0.410738	−	1.79956i
$439$	−11.1170	+	28.3257i	−0.530585	+	1.35191i	0.374716	+	0.927140i	$0.377740\pi$
$439$	−11.1170	+	28.3257i	−0.530585	+	1.35191i	−0.905301	+	0.424770i	$0.860355\pi$
$440$	−3.82744	−	1.18061i	−0.182466	−	0.0562833i
$441$	−24.4704	−	30.6849i	−1.16526	−	1.46118i
$442$	3.03315	−	40.4746i	0.144272	−	1.92518i
$443$	−17.4770	+	5.39094i	−0.830358	+	0.256131i	−0.680659	−	0.732600i	$-0.738306\pi$
$443$	−17.4770	+	5.39094i	−0.830358	+	0.256131i	−0.149698	+	0.988732i	$0.547830\pi$
$444$	12.3609	+	8.42751i	0.586622	+	0.399952i
$445$	3.06779	+	0.462395i	0.145427	+	0.0219196i
$446$	1.95780	+	8.57767i	0.0927044	+	0.406164i
$447$	−14.0668	+	13.0520i	−0.665335	+	0.617340i
$448$	−0.0562153	−	0.750141i	−0.00265592	−	0.0354408i
$449$	11.0051	+	28.0405i	0.519361	+	1.32331i	0.914461	+	0.404673i	$0.132615\pi$
$449$	11.0051	+	28.0405i	0.519361	+	1.32331i	−0.395100	+	0.918638i	$0.629290\pi$
$450$	6.03175	−	0.909140i	0.284339	−	0.0428573i
$451$	−17.6078	−	8.47948i	−0.829119	−	0.399283i
$452$	−3.67034	−	1.76754i	−0.172638	−	0.0831382i
$453$	−33.1127	+	4.99093i	−1.55577	+	0.234494i
$454$	6.29879	+	16.0491i	0.295617	+	0.753220i
$455$	0.379532	+	5.06451i	0.0177928	+	0.237428i
$456$	4.48921	−	4.16538i	0.210227	−	0.195062i
$457$	1.16623	+	5.10958i	0.0545538	+	0.239016i	0.994852	−	0.101335i	$-0.0323113\pi$
$457$	1.16623	+	5.10958i	0.0545538	+	0.239016i	−0.940299	+	0.340351i	$0.889454\pi$
$458$	5.43761	+	0.819587i	0.254083	+	0.0382968i
$459$	46.4485	+	31.6681i	2.16803	+	1.47814i
$460$	−7.87346	+	2.42864i	−0.367102	+	0.113236i
$461$	−2.71877	+	36.2794i	−0.126626	+	1.68970i	0.466445	+	0.884550i	$0.345534\pi$
$461$	−2.71877	+	36.2794i	−0.126626	+	1.68970i	−0.593071	+	0.805150i	$0.702085\pi$
$462$	5.66696	+	7.10614i	0.263651	+	0.330608i
$463$	−3.03115	−	0.934984i	−0.140869	−	0.0434524i	0.223519	−	0.974700i	$-0.428246\pi$
$463$	−3.03115	−	0.934984i	−0.140869	−	0.0434524i	−0.364388	+	0.931247i	$0.618722\pi$
$464$	−1.31504	+	3.35068i	−0.0610494	+	0.155551i
$465$	−4.28075	+	18.7552i	−0.198515	+	0.869752i
$466$	−13.0924	−	22.6768i	−0.606496	−	1.05048i
$467$	17.0147	−	29.4704i	0.787348	−	1.36373i	−0.140238	−	0.990118i	$-0.544787\pi$
$467$	17.0147	−	29.4704i	0.787348	−	1.36373i	0.927586	−	0.373609i	$-0.121880\pi$
$468$	30.1891	+	28.0114i	1.39549	+	1.29483i
$469$	−4.62271	+	5.79670i	−0.213457	+	0.267667i
$470$	0.928564	−	0.633084i	0.0428315	−	0.0292020i
$471$	−32.9876	+	15.8860i	−1.51999	+	0.731988i
$472$	−13.1492			−0.605241
$473$	11.4099	+	23.6573i	0.524629	+	1.08776i
$474$	45.2134			2.07672
$475$	−1.82906	+	0.880828i	−0.0839229	+	0.0404151i
$476$	−3.73653	+	2.54752i	−0.171264	+	0.116765i
$477$	−12.2952	+	15.4177i	−0.562959	+	0.705928i
$478$	−11.1658	−	10.3604i	−0.510713	−	0.473872i
$479$	0.955435	−	1.65486i	0.0436549	−	0.0756126i	−0.843372	−	0.537330i	$-0.819433\pi$
$479$	0.955435	−	1.65486i	0.0436549	−	0.0756126i	0.887027	+	0.461717i	$0.152766\pi$
$480$	1.50830	+	2.61245i	0.0688442	+	0.119242i
$481$	7.45061	−	32.6432i	0.339718	−	1.48840i
$482$	2.93522	−	7.47881i	0.133696	−	0.340651i
$483$	17.8666	+	5.51112i	0.812959	+	0.250765i
$484$	3.14432	+	3.94285i	0.142924	+	0.179221i
$485$	−0.0723777	+	0.965813i	−0.00328650	+	0.0438553i
$486$	−1.75622	+	0.541721i	−0.0796636	+	0.0245730i
$487$	−10.1324	−	6.90815i	−0.459143	−	0.313038i	0.311567	−	0.950224i	$-0.399146\pi$
$487$	−10.1324	−	6.90815i	−0.459143	−	0.313038i	−0.770710	+	0.637186i	$0.780098\pi$
$488$	−4.37266	−	0.659072i	−0.197941	−	0.0298348i
$489$	3.45486	+	15.1367i	0.156234	+	0.684506i
$490$	−4.71655	+	4.37632i	−0.213072	+	0.197702i
$491$	1.23761	+	16.5148i	0.0558526	+	0.745301i	0.952884	+	0.303334i	$0.0980999\pi$
$491$	1.23761	+	16.5148i	0.0558526	+	0.745301i	−0.897032	+	0.441966i	$0.854281\pi$
$492$	5.37734	+	13.7012i	0.242429	+	0.617700i
$493$	21.3977	−	3.22519i	0.963706	−	0.145255i
$494$	−12.3487	−	5.94683i	−0.555595	−	0.267560i
$495$	−22.0128	−	10.6008i	−0.989401	−	0.476471i
$496$	−6.30599	+	0.950475i	−0.283147	+	0.0426776i
$497$	−4.20315	−	10.7095i	−0.188537	−	0.480385i
$498$	0.820309	+	10.9463i	0.0367589	+	0.490514i
$499$	16.8882	−	15.6700i	0.756020	−	0.701484i	−0.204755	−	0.978813i	$-0.565640\pi$
$499$	16.8882	−	15.6700i	0.756020	−	0.701484i	0.960775	+	0.277329i	$0.0894493\pi$
$500$	−0.222521	−	0.974928i	−0.00995144	−	0.0436001i
$501$	−27.6766	−	4.17158i	−1.23650	−	0.186372i
$502$	−13.4775	−	9.18878i	−0.601529	−	0.410115i
$503$	−8.05237	+	2.48383i	−0.359037	+	0.110748i	−0.469026	−	0.883185i	$-0.655395\pi$
$503$	−8.05237	+	2.48383i	−0.359037	+	0.110748i	0.109988	+	0.993933i	$0.464919\pi$
$504$	0.342906	−	4.57577i	0.0152743	−	0.203821i
$505$	3.96993	+	4.97813i	0.176659	+	0.221524i
$506$	31.5362	+	9.72764i	1.40196	+	0.432446i
$507$	35.9077	−	91.4914i	1.59472	−	4.06328i
$508$	1.42062	−	6.22413i	0.0630297	−	0.276151i
$509$	4.15947	+	7.20442i	0.184365	+	0.319330i	0.943362	−	0.331764i	$-0.107644\pi$
$509$	4.15947	+	7.20442i	0.184365	+	0.319330i	−0.758997	+	0.651094i	$0.774310\pi$
$510$	9.06759	−	15.7055i	0.401520	−	0.695452i
$511$	7.06165	+	6.55226i	0.312389	+	0.289855i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	15.6850	−	10.6939i	0.692512	−	0.472146i
$514$	−12.5676	+	6.05225i	−0.554334	+	0.266953i
$515$	5.80432			0.255769
$516$	5.81946	−	18.9058i	0.256187	−	0.832281i
$517$	−4.50143			−0.197973
$518$	−3.36120	+	1.61867i	−0.147683	+	0.0711203i
$519$	30.0638	−	20.4972i	1.31965	−	0.899725i
$520$	4.20944	−	5.27847i	0.184596	−	0.231476i
$521$	−9.64207	−	8.94653i	−0.422427	−	0.391955i	0.440114	−	0.897942i	$-0.354938\pi$
$521$	−9.64207	−	8.94653i	−0.422427	−	0.391955i	−0.862541	+	0.505987i	$0.831128\pi$
$522$	−10.9783	+	19.0149i	−0.480505	+	0.832259i
$523$	13.0441	+	22.5931i	0.570380	+	0.987927i	0.996527	+	0.0832727i	$0.0265372\pi$
$523$	13.0441	+	22.5931i	0.570380	+	0.987927i	−0.426147	+	0.904654i	$0.640129\pi$
$524$	1.00740	−	4.41372i	0.0440086	−	0.192814i
$525$	−0.829039	+	2.11236i	−0.0361822	+	0.0921908i
$526$	−10.1418	−	3.12834i	−0.442205	−	0.136402i
$527$	23.9037	+	29.9743i	1.04126	+	1.30570i
$528$	0.902937	−	12.0489i	0.0392953	−	0.524359i
$529$	42.8953	−	13.2315i	1.86501	−	0.575281i
$530$	2.67110	+	1.82113i	0.116025	+	0.0791048i
$531$	−79.3126	−	11.9545i	−3.44188	−	0.518779i
$532$	0.339819	+	1.48884i	0.0147330	+	0.0645495i
$533$	24.1480	−	22.4060i	1.04596	−	0.970514i
$534$	0.699386	+	9.33266i	0.0302654	+	0.403864i
$535$	−0.799160	−	2.03623i	−0.0345507	−	0.0880338i
$536$	9.74610	−	1.46899i	0.420967	−	0.0634506i
$537$	41.8541	+	20.1559i	1.80614	+	0.869790i
$538$	11.0158	+	5.30492i	0.474924	+	0.228711i
$539$	25.4833	−	3.84099i	1.09764	−	0.165443i
$540$	3.41634	+	8.70469i	0.147016	+	0.374590i
$541$	−2.90902	−	38.8182i	−0.125068	−	1.66892i	−0.608510	−	0.793546i	$-0.708232\pi$
$541$	−2.90902	−	38.8182i	−0.125068	−	1.66892i	0.483442	−	0.875377i	$-0.339387\pi$
$542$	10.3788	−	9.63009i	0.445806	−	0.413648i
$543$	2.91152	+	12.7562i	0.124945	+	0.547421i
$544$	5.94465	+	0.896011i	0.254875	+	0.0384162i
$545$	1.92063	+	1.30947i	0.0822710	+	0.0560914i
$546$	−14.6398	+	4.51578i	−0.626525	+	0.193257i
$547$	−1.41946	+	18.9414i	−0.0606917	+	0.809874i	0.880940	+	0.473228i	$0.156912\pi$
$547$	−1.41946	+	18.9414i	−0.0606917	+	0.809874i	−0.941631	+	0.336646i	$0.890708\pi$
$548$	6.04637	+	7.58191i	0.258288	+	0.323883i
$549$	−25.7756	−	7.95071i	−1.10008	−	0.339328i
$550$	−1.46333	+	3.72851i	−0.0623966	+	0.158984i
$551$	1.62604	−	7.12413i	0.0692715	−	0.303498i
$552$	−12.4277	−	21.5254i	−0.528957	−	0.916180i
$553$	−5.63739	+	9.76425i	−0.239726	+	0.415218i
$554$	14.5122	+	13.4654i	0.616566	+	0.572089i
$555$	9.32767	−	11.6965i	0.395938	−	0.496490i
$556$	−0.404568	+	0.275830i	−0.0171575	+	0.0116978i
$557$	−20.3074	+	9.77954i	−0.860453	+	0.414372i	−0.811447	−	0.584426i	$-0.801320\pi$
$557$	−20.3074	+	9.77954i	−0.860453	+	0.414372i	−0.0490062	+	0.998798i	$0.515605\pi$
$558$	−38.9003			−1.64678
$559$	−44.1462	+	3.33447i	−1.86719	+	0.141033i
$560$	−0.752244			−0.0317881
$561$	−65.4449	+	31.5166i	−2.76308	+	1.33063i
$562$	−21.3107	+	14.5294i	−0.898937	+	0.612885i
$563$	−18.5750	+	23.2923i	−0.782843	+	0.981654i	0.217142	+	0.976140i	$0.430326\pi$
$563$	−18.5750	+	23.2923i	−0.782843	+	0.981654i	−0.999985	+	0.00551353i	$0.998245\pi$
$564$	2.48519	+	2.30591i	0.104645	+	0.0970965i
$565$	−2.03689	+	3.52799i	−0.0856924	+	0.148424i
$566$	0.870892	+	1.50843i	0.0366063	+	0.0634040i
$567$	1.65865	−	7.26702i	0.0696567	−	0.305186i
$568$	−5.58748	+	14.2367i	−0.234446	+	0.597358i
$569$	−21.4381	−	6.61278i	−0.898732	−	0.277222i	−0.189236	−	0.981932i	$-0.560601\pi$
$569$	−21.4381	−	6.61278i	−0.898732	−	0.277222i	−0.709496	+	0.704709i	$0.751077\pi$
$570$	−3.81825	−	4.78794i	−0.159929	−	0.200545i
$571$	−0.00105218	+	0.0140404i	−4.40325e−5	+	0.000587572i	−0.997226	−	0.0744363i	$-0.976284\pi$
$571$	−0.00105218	+	0.0140404i	−4.40325e−5	+	0.000587572i	0.997182	+	0.0750239i	$0.0239033\pi$
$572$	−25.8406	+	7.97077i	−1.08045	+	0.333274i
$573$	−37.4532	−	25.5351i	−1.56463	−	1.06675i
$574$	−3.62938	−	0.547041i	−0.151487	−	0.0228330i
$575$	1.83347	+	8.03294i	0.0764608	+	0.334997i
$576$	−4.47153	+	4.14897i	−0.186314	+	0.172874i
$577$	0.927504	+	12.3767i	0.0386125	+	0.515248i	0.982657	+	0.185431i	$0.0593681\pi$
$577$	0.927504	+	12.3767i	0.0386125	+	0.515248i	−0.944045	+	0.329817i	$0.893013\pi$
$578$	−6.99323	−	17.8185i	−0.290880	−	0.741150i
$579$	5.38938	−	0.812318i	0.223975	−	0.0337588i
$580$	3.24304	+	1.56176i	0.134660	+	0.0648487i
$581$	−2.46623	−	1.18767i	−0.102316	−	0.0492729i
$582$	−2.88901	+	0.435448i	−0.119753	+	0.0180499i
$583$	−4.73073	−	12.0537i	−0.195927	−	0.499213i
$584$	−0.956992	−	12.7702i	−0.0396006	−	0.528433i
$585$	30.1891	−	28.0114i	1.24817	−	1.15813i
$586$	−6.58643	−	28.8570i	−0.272083	−	1.19207i
$587$	−4.98210	−	0.750930i	−0.205633	−	0.0309942i	0.0454178	−	0.998968i	$-0.485538\pi$
$587$	−4.98210	−	0.750930i	−0.205633	−	0.0309942i	−0.251051	+	0.967974i	$0.580776\pi$
$588$	−16.0366	−	10.9336i	−0.661340	−	0.450894i
$589$	12.3712	−	3.81602i	0.509747	−	0.157236i
$590$	−0.982641	+	13.1124i	−0.0404547	+	0.539830i
$591$	20.5592	+	25.7805i	0.845694	+	1.06047i
$592$	4.73904	+	1.46180i	0.194773	+	0.0600796i
$593$	−7.39781	+	18.8493i	−0.303791	+	0.774048i	0.694708	+	0.719292i	$0.255533\pi$
$593$	−7.39781	+	18.8493i	−0.303791	+	0.774048i	−0.998500	+	0.0547565i	$0.982562\pi$
$594$	8.33446	−	36.5157i	0.341967	−	1.49826i
$595$	2.26117	+	3.91646i	0.0926988	+	0.160559i
$596$	−3.18062	+	5.50899i	−0.130283	+	0.225657i
$597$	−35.6905	−	33.1160i	−1.46072	−	1.35535i
$598$	−34.6837	+	43.4920i	−1.41832	+	1.77852i
$599$	31.6095	−	21.5510i	1.29153	−	0.880550i	0.294357	−	0.955696i	$-0.404895\pi$
$599$	31.6095	−	21.5510i	1.29153	−	0.880550i	0.997173	+	0.0751458i	$0.0239422\pi$
$600$	2.71786	−	1.30885i	0.110956	−	0.0534337i
$601$	46.7539			1.90713			0.953565	−	0.301188i	$-0.0973832\pi$
$601$	46.7539			1.90713			0.953565	+	0.301188i	$0.0973832\pi$
$602$	3.35728	+	3.61402i	0.136833	+	0.147296i
$603$	60.1215			2.44834
$604$	−10.0015	+	4.81646i	−0.406954	+	0.195979i
$605$	4.16680	−	2.84088i	0.169405	−	0.115498i
$606$	−11.9757	+	15.0170i	−0.486479	+	0.610025i
$607$	−11.2077	−	10.3992i	−0.454907	−	0.422092i	0.419149	−	0.907918i	$-0.362329\pi$
$607$	−11.2077	−	10.3992i	−0.454907	−	0.422092i	−0.874056	+	0.485825i	$0.838519\pi$
$608$	1.01505	−	1.75812i	0.0411657	−	0.0713011i
$609$	−4.08403	−	7.07374i	−0.165493	−	0.286643i
$610$	−0.983998	+	4.31118i	−0.0398409	+	0.174554i
$611$	2.77204	−	7.06304i	0.112145	−	0.285740i
$612$	35.0420	+	10.8090i	1.41649	+	0.436929i
$613$	13.4681	+	16.8885i	0.543972	+	0.682119i	0.975505	−	0.219978i	$-0.0705986\pi$
$613$	13.4681	+	16.8885i	0.543972	+	0.682119i	−0.431533	+	0.902097i	$0.642027\pi$
$614$	−0.778593	+	10.3896i	−0.0314214	+	0.419290i
$615$	14.0648	−	4.33841i	0.567147	−	0.174942i
$616$	2.48948	+	1.69730i	0.100304	+	0.0683861i
$617$	33.7284	+	5.08374i	1.35785	+	0.204664i	0.787287	−	0.616587i	$-0.211485\pi$
$617$	33.7284	+	5.08374i	1.35785	+	0.204664i	0.570568	+	0.821251i	$0.306723\pi$
$618$	3.89619	+	17.0703i	0.156728	+	0.686669i
$619$	−8.30196	+	7.70309i	−0.333684	+	0.309613i	−0.829163	−	0.559006i	$-0.811183\pi$
$619$	−8.30196	+	7.70309i	−0.333684	+	0.309613i	0.495480	+	0.868620i	$0.334992\pi$
$620$	0.476570	+	6.35939i	0.0191395	+	0.255399i
$621$	−28.1490	−	71.7225i	−1.12958	−	2.87812i
$622$	20.7396	−	3.12599i	0.831581	−	0.125341i
$623$	−2.10267	−	1.01259i	−0.0842419	−	0.0405688i
$624$	18.3494	+	8.83661i	0.734564	+	0.353748i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	−5.87065	−	14.9582i	−0.234638	−	0.597849i
$627$	1.83305	+	24.4604i	0.0732051	+	0.976854i
$628$	−8.89729	+	8.25548i	−0.355041	+	0.329430i
$629$	−6.63439	−	29.0672i	−0.264530	−	1.15898i
$630$	−4.53735	−	0.683895i	−0.180772	−	0.0272470i
$631$	30.3527	+	20.6941i	1.20832	+	0.823820i	0.988426	−	0.151704i	$-0.0484760\pi$
$631$	30.3527	+	20.6941i	1.20832	+	0.823820i	0.219895	+	0.975523i	$0.429428\pi$
$632$	14.3223	−	4.41785i	0.569711	−	0.175733i
$633$	4.93747	−	65.8860i	0.196247	−	2.61873i
$634$	0.122500	+	0.153611i	0.00486512	+	0.00610066i
$635$	−6.10057	−	1.88178i	−0.242094	−	0.0746760i
$636$	−3.56288	+	9.07808i	−0.141278	+	0.359969i
$637$	−9.66619	+	42.3503i	−0.382988	+	1.67798i
$638$	−7.20869	−	12.4858i	−0.285395	−	0.494318i
$639$	−46.6454	+	80.7922i	−1.84526	+	3.19609i
$640$	0.733052	+	0.680173i	0.0289764	+	0.0268862i
$641$	19.5456	−	24.5094i	0.772003	−	0.968062i	−0.227981	−	0.973666i	$-0.573212\pi$
$641$	19.5456	−	24.5094i	0.772003	−	0.968062i	0.999984	+	0.00560405i	$0.00178383\pi$
$642$	5.45204	−	3.71714i	0.215175	−	0.146704i
$643$	29.2105	−	14.0670i	1.15195	−	0.554750i	0.242331	−	0.970194i	$-0.422088\pi$
$643$	29.2105	−	14.0670i	1.15195	−	0.554750i	0.909619	+	0.415444i	$0.136374\pi$
$644$	6.19813			0.244241
$645$	−18.4180	−	7.21602i	−0.725209	−	0.284130i
$646$	−12.2045			−0.480181
$647$	0.133047	−	0.0640720i	0.00523062	−	0.00251893i	−0.431267	−	0.902225i	$-0.641933\pi$
$647$	0.133047	−	0.0640720i	0.00523062	−	0.00251893i	0.436497	+	0.899706i	$0.356219\pi$
$648$	−8.18711	+	5.58188i	−0.321620	+	0.219277i
$649$	32.8377	−	41.1772i	1.28899	−	1.61635i
$650$	−4.94913	−	4.59213i	−0.194121	−	0.180118i
$651$	7.23566	−	12.5325i	0.283588	−	0.491188i
$652$	2.57343	+	4.45730i	0.100783	+	0.174561i
$653$	−8.17451	+	35.8149i	−0.319893	+	1.40154i	0.517846	+	0.855474i	$0.326734\pi$
$653$	−8.17451	+	35.8149i	−0.319893	+	1.40154i	−0.837739	+	0.546070i	$0.816123\pi$
$654$	−2.56186	+	6.52751i	−0.100177	+	0.255246i
$655$	−4.32610	−	1.33442i	−0.169035	−	0.0521403i
$656$	3.04215	+	3.81474i	0.118776	+	0.148940i
$657$	5.83754	−	77.8965i	0.227744	−	3.03903i
$658$	−0.807846	+	0.249188i	−0.0314931	+	0.00971434i
$659$	13.1214	+	8.94601i	0.511137	+	0.348487i	0.791263	−	0.611476i	$-0.209424\pi$
$659$	13.1214	+	8.94601i	0.511137	+	0.348487i	−0.280126	+	0.959963i	$0.590376\pi$
$660$	−11.9477	−	1.80082i	−0.465063	−	0.0700970i
$661$	9.38824	+	41.1326i	0.365160	+	1.59987i	0.739884	+	0.672735i	$0.234881\pi$
$661$	9.38824	+	41.1326i	0.365160	+	1.59987i	−0.374723	+	0.927137i	$0.622262\pi$
$662$	8.80448	−	8.16936i	0.342196	−	0.317511i
$663$	−9.14980	−	122.096i	−0.355349	−	4.74180i
$664$	1.32942	+	3.38731i	0.0515916	+	0.131453i
$665$	1.51007	−	0.227607i	0.0585582	−	0.00882622i
$666$	27.2557	+	13.1256i	1.05614	+	0.508609i
$667$	−26.7211	−	12.8682i	−1.03464	−	0.498258i
$668$	−9.17477	+	1.38287i	−0.354983	+	0.0535050i
$669$	9.69646	+	24.7062i	0.374887	+	0.955196i
$670$	−0.736553	−	9.82862i	−0.0284555	−	0.379713i
$671$	12.9838	−	12.0472i	0.501235	−	0.465078i
$672$	−0.504949	−	2.21233i	−0.0194788	−	0.0853423i
$673$	−12.5470	−	1.89116i	−0.483652	−	0.0728988i	−0.0973095	−	0.995254i	$-0.531024\pi$
$673$	−12.5470	−	1.89116i	−0.483652	−	0.0728988i	−0.386343	+	0.922355i	$0.626262\pi$
$674$	15.8562	+	10.8106i	0.610759	+	0.416408i
$675$	8.93565	−	2.75628i	0.343934	−	0.106089i
$676$	2.43482	−	32.4904i	0.0936470	−	1.24963i
$677$	−12.2568	−	15.3696i	−0.471067	−	0.590700i	0.488365	−	0.872640i	$-0.337594\pi$
$677$	−12.2568	−	15.3696i	−0.471067	−	0.590700i	−0.959432	+	0.281940i	$0.909022\pi$
$678$	−11.7430	−	3.62223i	−0.450986	−	0.139111i
$679$	0.266174	−	0.678202i	0.0102148	−	0.0260270i
$680$	1.33775	−	5.86106i	0.0513004	−	0.224762i
$681$	26.0044	+	45.0409i	0.996491	+	1.72597i
$682$	12.7716	−	22.1211i	0.489050	−	0.847059i
$683$	−26.4310	−	24.5244i	−1.01135	−	0.938400i	−0.0132479	−	0.999912i	$-0.504217\pi$
$683$	−26.4310	−	24.5244i	−1.01135	−	0.938400i	−0.998106	+	0.0615127i	$0.980408\pi$
$684$	7.72090	−	9.68171i	0.295216	−	0.370189i
$685$	8.01255	−	5.46287i	0.306144	−	0.208725i
$686$	9.10496	−	4.38472i	0.347629	−	0.167409i
$687$	16.5884			0.632886
$688$	−0.00386573	−	6.55744i	−0.000147380	−	0.250000i
$689$	21.8263			0.831515
$690$	−22.3939	+	10.7843i	−0.852521	+	0.410552i
$691$	6.18766	−	4.21868i	0.235390	−	0.160486i	−0.439881	−	0.898056i	$-0.644979\pi$
$691$	6.18766	−	4.21868i	0.235390	−	0.160486i	0.675271	+	0.737570i	$0.264027\pi$
$692$	7.52056	−	9.43048i	0.285889	−	0.358493i
$693$	13.4728	+	12.5010i	0.511791	+	0.474872i
$694$	3.74488	−	6.48633i	0.142154	−	0.246218i
$695$	0.244825	+	0.424050i	0.00928675	+	0.0160851i
$696$	−2.41619	+	10.5860i	−0.0915854	+	0.401262i
$697$	10.7165	−	27.3053i	0.405917	−	1.03426i
$698$	0.941181	+	0.290316i	0.0356242	+	0.0109886i
$699$	−49.2490	−	61.7563i	−1.86277	−	2.33584i
$700$	−0.0562153	+	0.750141i	−0.00212474	+	0.0283527i
$701$	−27.1688	+	8.38047i	−1.02615	+	0.316526i	−0.761739	−	0.647883i	$-0.775654\pi$
$701$	−27.1688	+	8.38047i	−1.02615	+	0.316526i	−0.264413	+	0.964410i	$0.585178\pi$
$702$	52.1630	+	35.5641i	1.96877	+	1.34228i
$703$	−9.95556	−	1.50056i	−0.375481	−	0.0565947i
$704$	−0.891282	−	3.90496i	−0.0335914	−	0.147174i
$705$	2.48519	−	2.30591i	0.0935975	−	0.0868458i
$706$	0.751036	+	10.0219i	0.0282656	+	0.377178i
$707$	−1.74989	−	4.45864i	−0.0658113	−	0.167685i
$708$	−39.2228	+	5.91189i	−1.47408	+	0.222182i
$709$	3.45912	+	1.66582i	0.129910	+	0.0625613i	0.497710	−	0.867344i	$-0.334175\pi$
$709$	3.45912	+	1.66582i	0.129910	+	0.0625613i	−0.367800	+	0.929905i	$0.619889\pi$
$710$	13.7793	+	6.63577i	0.517128	+	0.249036i
$711$	90.4050	−	13.6264i	3.39045	−	0.511029i
$712$	1.13345	+	2.88798i	0.0424778	+	0.108232i
$713$	−3.92671	−	52.3983i	−0.147056	−	1.96233i
$714$	−10.0004	+	9.27897i	−0.374254	+	0.347257i
$715$	6.01741	+	26.3640i	0.225038	+	0.985957i
$716$	15.2276	+	2.29520i	0.569084	+	0.0857756i
$717$	−37.9646	−	25.8839i	−1.41782	−	0.966650i
$718$	25.2832	−	7.79885i	0.943562	−	0.291050i
$719$	−2.35735	+	31.4567i	−0.0879144	+	1.17314i	0.762487	+	0.647003i	$0.223978\pi$
$719$	−2.35735	+	31.4567i	−0.0879144	+	1.17314i	−0.850402	+	0.526134i	$0.823641\pi$
$720$	3.80321	+	4.76908i	0.141737	+	0.177733i
$721$	−4.17229	−	1.28698i	−0.155384	−	0.0479297i
$722$	5.43580	−	13.8502i	0.202299	−	0.515450i
$723$	5.39300	−	23.6283i	0.200568	−	0.878745i
$724$	2.16871	+	3.75631i	0.0805994	+	0.139602i
$725$	1.79975	−	3.11726i	0.0668410	−	0.115772i
$726$	11.1519	+	10.3475i	0.413887	+	0.384031i
$727$	18.0648	−	22.6526i	0.669987	−	0.840137i	−0.324402	−	0.945919i	$-0.605163\pi$
$727$	18.0648	−	22.6526i	0.669987	−	0.840137i	0.994389	+	0.105782i	$0.0337346\pi$
$728$	−4.19623	+	2.86094i	−0.155522	+	0.106033i
$729$	21.7877	−	10.4924i	0.806953	−	0.388608i
$730$	−12.8060			−0.473971
$731$	−34.1288	+	19.7311i	−1.26230	+	0.729781i
$732$	−13.3396			−0.493044
$733$	−23.4224	+	11.2796i	−0.865125	+	0.416622i	−0.813169	−	0.582027i	$-0.802260\pi$
$733$	−23.4224	+	11.2796i	−0.865125	+	0.416622i	−0.0519559	+	0.998649i	$0.516546\pi$
$734$	26.4027	−	18.0010i	0.974540	−	0.664430i
$735$	−12.1014	+	15.1747i	−0.446368	+	0.559728i
$736$	−6.03999	−	5.60430i	−0.222637	−	0.206577i
$737$	−19.7389	+	34.1888i	−0.727091	+	1.25936i
$738$	14.8814	+	25.7753i	0.547791	+	0.948801i
$739$	−2.01060	+	8.80903i	−0.0739612	+	0.324045i	−0.998351	−	0.0574039i	$-0.981718\pi$
$739$	−2.01060	+	8.80903i	−0.0739612	+	0.324045i	0.924390	+	0.381449i	$0.124575\pi$
$740$	1.81186	−	4.61654i	0.0666053	−	0.169708i
$741$	−39.5088	−	12.1868i	−1.45139	−	0.447695i
$742$	−1.51626	−	1.90133i	−0.0556636	−	0.0698000i
$743$	2.54139	−	33.9125i	0.0932347	−	1.24413i	−0.732773	−	0.680473i	$-0.761775\pi$
$743$	2.54139	−	33.9125i	0.0932347	−	1.24413i	0.826008	−	0.563658i	$-0.190606\pi$
$744$	−18.3829	+	5.67036i	−0.673948	+	0.207885i
$745$	5.25590	+	3.58341i	0.192561	+	0.131286i
$746$	−11.1312	−	1.67775i	−0.407541	−	0.0614269i
$747$	4.93920	+	21.6400i	0.180716	+	0.791768i
$748$	−17.6515	+	16.3782i	−0.645404	+	0.598848i
$749$	0.122967	+	1.64088i	0.00449313	+	0.0599566i
$750$	−1.10209	−	2.80807i	−0.0402426	−	0.102536i
$751$	−39.6262	+	5.97269i	−1.44598	+	0.217946i	−0.824668	−	0.565617i	$-0.808638\pi$
$751$	−39.6262	+	5.97269i	−1.44598	+	0.217946i	−0.621312	+	0.783563i	$0.713400\pi$
$752$	1.01255	+	0.487618i	0.0369239	+	0.0177816i
$753$	−44.3333	−	21.3498i	−1.61560	−	0.778030i
$754$	24.0303	−	3.62198i	0.875131	−	0.131905i
$755$	4.05558	+	10.3334i	0.147598	+	0.376073i
$756$	−0.525675	−	7.01464i	−0.0191186	−	0.255120i
$757$	34.0036	−	31.5507i	1.23588	−	1.14673i	0.252033	−	0.967719i	$-0.418901\pi$
$757$	34.0036	−	31.5507i	1.23588	−	1.14673i	0.983847	−	0.179011i	$-0.0572897\pi$
$758$	6.28633	+	27.5422i	0.228330	+	1.00038i
$759$	98.4432	+	14.8379i	3.57326	+	0.538583i
$760$	−1.67735	−	1.14360i	−0.0608438	−	0.0414826i
$761$	8.71766	−	2.68904i	0.316015	−	0.0974777i	−0.132690	−	0.991158i	$-0.542362\pi$
$761$	8.71766	−	2.68904i	0.316015	−	0.0974777i	0.448705	+	0.893680i	$0.351885\pi$
$762$	1.43920	−	19.2047i	0.0521365	−	0.695714i
$763$	−1.09025	−	1.36713i	−0.0394698	−	0.0494936i
$764$	−14.3592	−	4.42921i	−0.519496	−	0.160243i
$765$	13.3975	−	34.1363i	0.484387	−	1.23420i
$766$	−1.65835	+	7.26572i	−0.0599187	+	0.262521i
$767$	44.3878	+	76.8819i	1.60275	+	2.77605i
$768$	−1.50830	+	2.61245i	−0.0544261	+	0.0942688i
$769$	4.82516	+	4.47709i	0.174000	+	0.161448i	0.762365	−	0.647147i	$-0.224038\pi$
$769$	4.82516	+	4.47709i	0.174000	+	0.161448i	−0.588366	+	0.808595i	$0.700228\pi$
$770$	1.87859	−	2.35568i	0.0676997	−	0.0848928i
$771$	−34.7670	+	23.7037i	−1.25210	+	0.853669i
$772$	1.62783	−	0.783921i	0.0585868	−	0.0282139i
$773$	−7.70623			−0.277174			−0.138587	−	0.990350i	$-0.544256\pi$
$773$	−7.70623			−0.277174			−0.138587	+	0.990350i	$0.544256\pi$
$774$	5.93831	−	39.5563i	0.213448	−	1.42182i
$775$	6.37722			0.229076
$776$	−0.872608	+	0.420226i	−0.0313248	+	0.0150852i
$777$	−9.29840	+	6.33954i	−0.333578	+	0.227430i
$778$	−4.96642	+	6.22770i	−0.178055	+	0.223274i
$779$	−7.26112	−	6.73734i	−0.260157	−	0.241390i
$780$	10.1832	−	17.6377i	0.364615	−	0.631532i
$781$	−30.6289	−	53.0509i	−1.09599	−	1.89831i
$782$	−11.0224	+	48.2923i	−0.394161	+	1.72693i
$783$	−12.2971	+	31.3325i	−0.439463	+	1.11973i
$784$	−6.14828	−	1.89649i	−0.219581	−	0.0677319i
$785$	7.56750	+	9.48935i	0.270096	+	0.338689i
$786$	1.02058	−	13.6187i	0.0364028	−	0.485761i
$787$	−43.2341	+	13.3360i	−1.54113	+	0.475375i	−0.944878	−	0.327422i	$-0.893820\pi$
$787$	−43.2341	+	13.3360i	−1.54113	+	0.475375i	−0.596251	+	0.802798i	$0.703344\pi$
$788$	9.03161	+	6.15765i	0.321738	+	0.219357i
$789$	−31.6586	−	4.77177i	−1.12708	−	0.169880i
$790$	−3.33519	−	14.6124i	−0.118661	−	0.519886i
$791$	2.24642	−	2.08437i	0.0798733	−	0.0741116i
$792$	−1.82583	−	24.3640i	−0.0648781	−	0.865738i
$793$	10.9073	+	27.7913i	0.387329	+	0.986898i
$794$	31.8066	−	4.79408i	1.12877	−	0.170135i
$795$	8.78644	+	4.23133i	0.311623	+	0.150070i
$796$	−14.5415	−	7.00284i	−0.515411	−	0.248209i
$797$	2.06629	−	0.311443i	0.0731917	−	0.0110319i	−0.112344	−	0.993669i	$-0.535836\pi$
$797$	2.06629	−	0.311443i	0.0731917	−	0.0110319i	0.185536	+	0.982637i	$0.440598\pi$
$798$	1.68303	+	4.28830i	0.0595787	+	0.151804i
$799$	−0.504900	−	6.73743i	−0.0178621	−	0.238353i
$800$	0.733052	−	0.680173i	0.0259173	−	0.0240477i
$801$	4.21110	+	18.4500i	0.148792	+	0.651900i
$802$	−13.3929	−	2.01865i	−0.472918	−	0.0712810i
$803$	42.3801	+	28.8943i	1.49556	+	1.01966i
$804$	28.4112	−	8.76371i	1.00199	−	0.309072i
$805$	0.463187	−	6.18080i	0.0163252	−	0.217845i
$806$	26.8445	+	33.6619i	0.945557	+	1.18569i
$807$	35.2441	+	10.8714i	1.24065	+	0.382691i
$808$	−2.32622	+	5.92712i	−0.0818363	+	0.208515i
$809$	−4.90762	+	21.5017i	−0.172543	+	0.755959i	0.812403	+	0.583096i	$0.198159\pi$
$809$	−4.90762	+	21.5017i	−0.172543	+	0.755959i	−0.984946	+	0.172863i	$0.944698\pi$
$810$	4.95444	+	8.58135i	0.174081	+	0.301518i
$811$	2.08286	−	3.60761i	0.0731390	−	0.126680i	−0.827136	−	0.562001i	$-0.810032\pi$
$811$	2.08286	−	3.60761i	0.0731390	−	0.126680i	0.900275	+	0.435321i	$0.143365\pi$
$812$	−1.98489	−	1.84170i	−0.0696558	−	0.0646312i
$813$	26.6292	−	33.3920i	0.933927	−	1.17111i
$814$	−16.4125	+	11.1899i	−0.575259	+	0.392205i
$815$	4.63715	−	2.23313i	0.162432	−	0.0782233i
$816$	18.1352			0.634858
$817$	1.99185	+	13.1624i	0.0696860	+	0.460494i
$818$	−39.7218			−1.38884
$819$	−27.9116	+	13.4415i	−0.975309	+	0.469684i
$820$	4.03141	−	2.74857i	0.140783	−	0.0959842i
$821$	5.78574	−	7.25508i	0.201924	−	0.253204i	−0.670551	−	0.741863i	$-0.733942\pi$
$821$	5.78574	−	7.25508i	0.201924	−	0.253204i	0.872475	+	0.488659i	$0.162514\pi$
$822$	21.4446	+	19.8977i	0.747966	+	0.694011i
$823$	−8.21699	+	14.2322i	−0.286426	+	0.496105i	−0.972954	−	0.230999i	$-0.925801\pi$
$823$	−8.21699	+	14.2322i	−0.286426	+	0.496105i	0.686528	+	0.727104i	$0.259134\pi$
$824$	2.90216	+	5.02669i	0.101102	+	0.175113i
$825$	−2.68864	+	11.7797i	−0.0936065	+	0.410117i
$826$	3.61374	−	9.20765i	0.125738	−	0.320375i
$827$	−18.8982	−	5.82932i	−0.657154	−	0.202705i	−0.0517951	−	0.998658i	$-0.516494\pi$
$827$	−18.8982	−	5.82932i	−0.657154	−	0.202705i	−0.605359	+	0.795952i	$0.706970\pi$
$828$	−31.3366	−	39.2949i	−1.08902	−	1.36559i
$829$	1.63500	−	21.8175i	0.0567858	−	0.757754i	−0.894032	−	0.448003i	$-0.852135\pi$
$829$	1.63500	−	21.8175i	0.0567858	−	0.757754i	0.950818	−	0.309751i	$-0.100246\pi$
$830$	3.47719	−	1.07257i	0.120695	−	0.0372295i
$831$	49.3427	+	33.6413i	1.71168	+	1.16700i
$832$	6.67600	+	1.00625i	0.231449	+	0.0348853i
$833$	8.60725	+	37.7108i	0.298224	+	1.30660i
$834$	−1.08278	+	1.00467i	−0.0374935	+	0.0347888i
$835$	0.693376	+	9.25246i	0.0239953	+	0.320195i
$836$	2.97071	+	7.56924i	0.102744	+	0.261788i
$837$	−58.9679	+	8.88799i	−2.03823	+	0.307214i
$838$	−8.66855	−	4.17456i	−0.299450	−	0.144208i
$839$	43.7922	+	21.0892i	1.51187	+	0.728080i	0.992009	−	0.126168i	$-0.0402680\pi$
$839$	43.7922	+	21.0892i	1.51187	+	0.728080i	0.519865	+	0.854248i	$0.325982\pi$
$840$	−2.24387	+	0.338210i	−0.0774210	+	0.0116693i
$841$	−5.86139	−	14.9346i	−0.202117	−	0.514985i
$842$	0.00664019	+	0.0886071i	0.000228836	+	0.00305360i
$843$	−57.0354	+	52.9211i	−1.96440	+	1.82270i
$844$	−4.87374	−	21.3533i	−0.167761	−	0.735009i
$845$	−32.2176	−	4.85603i	−1.10832	−	0.167052i
$846$	5.66413	+	3.86174i	0.194737	+	0.132769i
$847$	−3.62510	+	1.11819i	−0.124560	+	0.0384216i
$848$	−0.241591	+	3.22381i	−0.00829627	+	0.110706i
$849$	3.27598	+	4.10795i	0.112431	+	0.140984i
$850$	−5.74470	−	1.77201i	−0.197042	−	0.0607793i
$851$	−14.9289	+	38.0381i	−0.511754	+	1.30393i
$852$	−10.2661	+	44.9788i	−0.351712	+	1.54095i
$853$	−14.5554	−	25.2107i	−0.498367	−	0.863197i	0.501631	−	0.865082i	$-0.332733\pi$
$853$	−14.5554	−	25.2107i	−0.498367	−	0.863197i	−0.999998	+	0.00188451i	$0.999400\pi$
$854$	1.66323	−	2.88080i	0.0569146	−	0.0985789i
$855$	−9.07765	−	8.42283i	−0.310449	−	0.288055i
$856$	1.36384	−	1.71021i	0.0466152	−	0.0584536i
$857$	27.8801	−	19.0083i	0.952367	−	0.649313i	0.0158274	−	0.999875i	$-0.494962\pi$
$857$	27.8801	−	19.0083i	0.952367	−	0.649313i	0.936540	+	0.350562i	$0.114009\pi$
$858$	−73.4964	+	35.3940i	−2.50913	+	1.20833i
$859$	−26.9358			−0.919037			−0.459518	−	0.888168i	$-0.651978\pi$
$859$	−26.9358			−0.919037			−0.459518	+	0.888168i	$0.651978\pi$
$860$	−6.53939	−	0.486183i	−0.222991	−	0.0165787i
$861$	−11.0721			−0.377335
$862$	22.1097	−	10.6475i	0.753059	−	0.362654i
$863$	20.8427	−	14.2103i	0.709494	−	0.483725i	−0.154008	−	0.988070i	$-0.549218\pi$
$863$	20.8427	−	14.2103i	0.709494	−	0.483725i	0.863502	+	0.504345i	$0.168266\pi$
$864$	−5.83031	+	7.31098i	−0.198351	+	0.248725i
$865$	−8.84210	−	8.20427i	−0.300640	−	0.278953i
$866$	−11.4860	+	19.8943i	−0.390309	+	0.676034i
$867$	−28.8713	−	50.0066i	−0.980522	−	1.69831i
$868$	1.06748	−	4.67695i	0.0362327	−	0.158746i
$869$	−21.9327	+	55.8836i	−0.744016	+	1.89572i
$870$	10.3758	+	3.20053i	0.351774	+	0.108508i
$871$	−41.4890	−	52.0255i	−1.40580	−	1.76282i
$872$	−0.173714	+	2.31805i	−0.00588270	+	0.0784991i
$873$	−5.64539	+	1.74137i	−0.191068	+	0.0589366i
$874$	13.8205	+	9.42268i	0.467487	+	0.318727i
$875$	0.743842	+	0.112116i	0.0251465	+	0.00379022i
$876$	−8.59610	−	37.6620i	−0.290435	−	1.27248i
$877$	14.9489	−	13.8705i	0.504788	−	0.468375i	−0.386191	−	0.922419i	$-0.626210\pi$
$877$	14.9489	−	13.8705i	0.504788	−	0.468375i	0.890979	+	0.454044i	$0.150019\pi$
$878$	2.27397	+	30.3440i	0.0767428	+	1.02406i
$879$	−32.6209	−	83.1166i	−1.10027	−	2.80345i
$880$	−3.96065	+	0.596971i	−0.133513	+	0.0201239i
$881$	0.0528121	+	0.0254330i	0.00177928	+	0.000856858i	0.434773	−	0.900540i	$-0.356829\pi$
$881$	0.0528121	+	0.0254330i	0.00177928	+	0.000856858i	−0.432994	+	0.901397i	$0.642543\pi$
$882$	−35.3607	−	17.0288i	−1.19066	−	0.573390i
$883$	−6.50064	+	0.979813i	−0.218764	+	0.0329733i	−0.257510	−	0.966276i	$-0.582902\pi$
$883$	−6.50064	+	0.979813i	−0.218764	+	0.0329733i	0.0387457	+	0.999249i	$0.487664\pi$
$884$	−14.8285	−	37.7824i	−0.498736	−	1.27076i
$885$	2.96423	+	39.5550i	0.0996416	+	1.32963i
$886$	−13.4072	+	12.4401i	−0.450424	+	0.417932i
$887$	5.37293	+	23.5403i	0.180405	+	0.790408i	0.981437	+	0.191785i	$0.0614277\pi$
$887$	5.37293	+	23.5403i	0.180405	+	0.790408i	−0.801032	+	0.598622i	$0.795715\pi$
$888$	14.7933	+	2.22974i	0.496432	+	0.0748250i
$889$	3.96799	+	2.70533i	0.133082	+	0.0907339i
$890$	2.96461	−	0.914461i	0.0993739	−	0.0306528i
$891$	2.96596	−	39.5779i	0.0993632	−	1.32591i
$892$	5.48563	+	6.87876i	0.183672	+	0.230318i
$893$	−2.18016	−	0.672489i	−0.0729561	−	0.0225040i
$894$	−7.01064	+	17.8628i	−0.234471	+	0.597422i
$895$	3.42674	−	15.0135i	0.114543	−	0.501847i
$896$	−0.376122	−	0.651463i	−0.0125654	−	0.0217638i
$897$	−83.9043	+	145.326i	−2.80148	+	4.85231i
$898$	22.0815	+	20.4887i	0.736870	+	0.683715i
$899$	−14.3121	+	17.9468i	−0.477335	+	0.598559i
$900$	5.03996	−	3.43618i	0.167999	−	0.114539i
$901$	17.5105	−	8.43262i	0.583360	−	0.280931i
$902$	−19.5432			−0.650717
$903$	11.6393	+	9.27084i	0.387333	+	0.308514i
$904$	−4.07377			−0.135492
$905$	3.90787	−	1.88193i	0.129902	−	0.0625576i
$906$	−27.6680	+	18.8637i	−0.919208	+	0.626705i
$907$	−23.4414	+	29.3946i	−0.778359	+	0.976031i	0.221641	+	0.975128i	$0.428859\pi$
$907$	−23.4414	+	29.3946i	−0.778359	+	0.976031i	−1.00000		0.000902958i	$0.999713\pi$
$908$	12.6384	+	11.7268i	0.419422	+	0.389166i
$909$	−19.4198	+	33.6361i	−0.644114	+	1.11564i
$910$	2.53935	+	4.39829i	0.0841788	+	0.145802i
$911$	−6.50888	+	28.5173i	−0.215649	+	0.944819i	0.745003	+	0.667062i	$0.232448\pi$
$911$	−6.50888	+	28.5173i	−0.215649	+	0.944819i	−0.960651	+	0.277757i	$0.910409\pi$
$912$	2.23735	−	5.70067i	0.0740860	−	0.188768i
$913$	−13.9275	−	4.29606i	−0.460932	−	0.142179i
$914$	3.26770	+	4.09756i	0.108086	+	0.135535i
$915$	−0.996866	+	13.3023i	−0.0329554	+	0.439759i
$916$	5.25472	−	1.62087i	0.173621	−	0.0535549i
$917$	2.81382	+	1.91843i	0.0929207	+	0.0633522i
$918$	55.5890	+	8.37869i	1.83471	+	0.276538i
$919$	0.705115	+	3.08931i	0.0232596	+	0.101907i	0.985225	−	0.171263i	$-0.0547849\pi$
$919$	0.705115	+	3.08931i	0.0232596	+	0.101907i	−0.961966	+	0.273170i	$0.911928\pi$
$920$	−6.03999	+	5.60430i	−0.199133	+	0.184768i
$921$	2.34870	+	31.3413i	0.0773924	+	1.03273i
$922$	13.2915	+	33.8662i	0.437733	+	1.11533i
$923$	102.102	−	15.3894i	3.36073	−	0.506548i
$924$	8.18899	+	3.94361i	0.269398	+	0.129735i
$925$	−4.46823	−	2.15179i	−0.146915	−	0.0707504i
$926$	−3.13664	+	0.472773i	−0.103076	+	0.0155363i
$927$	12.9351	+	32.9582i	0.424846	+	1.08249i
$928$	0.268991	+	3.58943i	0.00883006	+	0.117829i
$929$	−27.7860	+	25.7817i	−0.911630	+	0.845869i	−0.988508	−	0.151172i	$-0.951695\pi$
$929$	−27.7860	+	25.7817i	−0.911630	+	0.845869i	0.0768778	+	0.997041i	$0.475505\pi$
$930$	4.28075	+	18.7552i	0.140371	+	0.615007i
$931$	12.9160	+	1.94678i	0.423306	+	0.0638031i
$932$	−21.6350	−	14.7505i	−0.708677	−	0.483168i
$933$	60.4588	−	18.6491i	1.97933	−	0.610543i
$934$	2.54303	−	33.9343i	0.0832103	−	1.11036i
$935$	15.0133	+	18.8261i	0.490989	+	0.615680i
$936$	39.3532	+	12.1388i	1.28630	+	0.396770i
$937$	18.9899	−	48.3854i	0.620372	−	1.58068i	−0.181634	−	0.983366i	$-0.558139\pi$
$937$	18.9899	−	48.3854i	0.620372	−	1.58068i	0.802006	−	0.597316i	$-0.203766\pi$
$938$	−1.64983	+	7.22836i	−0.0538688	+	0.236014i
$939$	−24.2368	−	41.9794i	−0.790939	−	1.36995i
$940$	0.561922	−	0.973278i	0.0183279	−	0.0317448i
$941$	23.3733	+	21.6873i	0.761948	+	0.706984i	0.962075	−	0.272786i	$-0.0879450\pi$
$941$	23.3733	+	21.6873i	0.761948	+	0.706984i	−0.200127	+	0.979770i	$0.564135\pi$
$942$	−22.8281	+	28.6256i	−0.743781	+	0.932671i
$943$	−33.2169	+	22.6469i	−1.08169	+	0.737484i
$944$	−11.8470	+	5.70522i	−0.385588	+	0.185689i
$945$	−7.03431			−0.228826
$946$	20.5445	+	16.3639i	0.667959	+	0.532036i
$947$	−6.63876			−0.215731			−0.107865	−	0.994166i	$-0.534402\pi$
$947$	−6.63876			−0.215731			−0.107865	+	0.994166i	$0.534402\pi$
$948$	40.7359	−	19.6174i	1.32304	−	0.637142i
$949$	−71.4353	+	48.7038i	−2.31889	+	1.58099i
$950$	−1.26575	+	1.58720i	−0.0410663	+	0.0514955i
$951$	0.434471	+	0.403130i	0.0140887	+	0.0130724i
$952$	−2.26117	+	3.91646i	−0.0732849	+	0.126933i
$953$	4.42187	+	7.65891i	0.143239	+	0.248096i	0.928714	−	0.370796i	$-0.120915\pi$
$953$	4.42187	+	7.65891i	0.143239	+	0.248096i	−0.785476	+	0.618892i	$0.787582\pi$
$954$	−4.38811	+	19.2256i	−0.142070	+	0.622451i
$955$	−5.48989	+	13.9880i	−0.177649	+	0.452641i
$956$	−14.5553	−	4.48970i	−0.470751	−	0.145207i
$957$	−27.1165	−	34.0030i	−0.876551	−	1.09916i
$958$	0.142799	−	1.90553i	0.00461364	−	0.0615648i
$959$	−6.97089	+	2.15023i	−0.225102	+	0.0694347i
$960$	2.49243	+	1.69931i	0.0804429	+	0.0548450i
$961$	−9.56093	−	1.44108i	−0.308417	−	0.0464864i
$962$	−7.45061	−	32.6432i	−0.240217	−	1.05246i
$963$	9.78118	−	9.07561i	0.315194	−	0.292457i
$964$	−0.600396	−	8.01172i	−0.0193374	−	0.258040i
$965$	−0.660081	−	1.68186i	−0.0212488	−	0.0541410i
$966$	18.4884	−	2.78668i	0.594856	−	0.0896601i
$967$	−41.7992	−	20.1294i	−1.34417	−	0.647319i	−0.383122	−	0.923698i	$-0.625151\pi$
$967$	−41.7992	−	20.1294i	−1.34417	−	0.647319i	−0.961049	+	0.276379i	$0.910865\pi$
$968$	4.54367	+	2.18812i	0.146039	+	0.0703288i
$969$	−36.4050	+	5.48717i	−1.16950	+	0.176273i
$970$	0.353841	+	0.901571i	0.0113611	+	0.0289477i
$971$	−1.66601	−	22.2314i	−0.0534648	−	0.713438i	−0.957950	−	0.286934i	$-0.907364\pi$
$971$	−1.66601	−	22.2314i	−0.0534648	−	0.713438i	0.904486	−	0.426504i	$-0.140255\pi$
$972$	−1.34725	+	1.25007i	−0.0432131	+	0.0400959i
$973$	−0.0819626	−	0.359102i	−0.00262760	−	0.0115123i
$974$	−12.1263	−	1.82775i	−0.388552	−	0.0585648i
$975$	−16.8274	−	11.4728i	−0.538909	−	0.367422i
$976$	−4.22559	+	1.30342i	−0.135258	+	0.0417215i
$977$	−1.50621	+	20.0989i	−0.0481878	+	0.643022i	0.919858	+	0.392250i	$0.128303\pi$
$977$	−1.50621	+	20.0989i	−0.0481878	+	0.643022i	−0.968046	+	0.250772i	$0.919316\pi$
$978$	9.68030	+	12.1387i	0.309542	+	0.388153i
$979$	−11.8744	−	3.66277i	−0.379507	−	0.117062i
$980$	−2.35065	+	5.98936i	−0.0750888	+	0.191323i
$981$	−3.15523	+	13.8240i	−0.100739	+	0.441366i
$982$	8.28054	+	14.3423i	0.264243	+	0.457681i
$983$	11.4415	−	19.8172i	0.364926	−	0.632070i	−0.623839	−	0.781553i	$-0.714428\pi$
$983$	11.4415	−	19.8172i	0.364926	−	0.632070i	0.988764	+	0.149483i	$0.0477611\pi$
$984$	10.7896	+	10.0113i	0.343959	+	0.319147i
$985$	6.81537	−	8.54620i	0.217156	−	0.272305i
$986$	17.8793	−	12.1899i	0.569394	−	0.388206i
$987$	−2.29770	+	1.10651i	−0.0731365	+	0.0352207i
$988$	−13.7060			−0.436047
$989$	53.8814	+	4.00591i	1.71333	+	0.127381i
$990$	−24.4324			−0.776511
$991$	49.2865	−	23.7351i	1.56564	−	0.753972i	0.568024	−	0.823012i	$-0.307708\pi$
$991$	49.2865	−	23.7351i	1.56564	−	0.753972i	0.997614	+	0.0690404i	$0.0219937\pi$
$992$	−5.26911	+	3.59242i	−0.167294	+	0.114059i
$993$	22.5900	−	28.3270i	0.716872	−	0.898929i
$994$	−8.43357	−	7.82521i	−0.267496	−	0.248200i
$995$	−8.06995	+	13.9776i	−0.255835	+	0.443118i
$996$	5.48848	+	9.50633i	0.173909	+	0.301220i
$997$	−2.14958	+	9.41793i	−0.0680779	+	0.298269i	−0.997493	−	0.0707676i	$-0.977455\pi$
$997$	−2.14958	+	9.41793i	−0.0680779	+	0.298269i	0.929415	+	0.369037i	$0.120312\pi$
$998$	8.41680	−	21.4457i	0.266429	−	0.678851i
$999$	44.3152	+	13.6694i	1.40207	+	0.432481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.31.4	✓	48
43.25	even	21	inner	430.2.q.c.111.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.31.4	✓	48	1.1	even	1	trivial
430.2.q.c.111.4	yes	48	43.25	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(2.49243 - 1.69931i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.50830 - 2.61245i) q^{6} +(0.376122 + 0.651463i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.22854 - 5.67822i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(2.49243 - 1.69931i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.50830 - 2.61245i) q^{6} +(0.376122 + 0.651463i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.22854 - 5.67822i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(2.49732 + 3.13153i) q^{11} +(0.225431 - 3.00817i) q^{12} +(-6.45146 + 1.99001i) q^{13} +(0.621533 + 0.423754i) q^{14} +(-2.98291 - 0.449601i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-4.40696 + 4.08906i) q^{17} +(-0.455845 - 6.08282i) q^{18} +(0.741679 + 1.88977i) q^{19} +(-0.988831 + 0.149042i) q^{20} +(2.04450 + 0.984578i) q^{21} +(3.60873 + 1.73787i) q^{22} +(8.14749 - 1.22804i) q^{23} +(-1.10209 - 2.80807i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-4.94913 + 4.59213i) q^{26} +(-2.08081 - 9.11665i) q^{27} +(0.743842 + 0.112116i) q^{28} +(-2.97405 - 2.02767i) q^{29} +(-2.88258 + 0.889159i) q^{30} +(0.476570 - 6.35939i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(11.5458 + 3.56142i) q^{33} +(-2.19635 + 5.59622i) q^{34} +(0.167390 - 0.733384i) q^{35} +(-3.04994 - 5.28265i) q^{36} +(-2.47968 + 4.29494i) q^{37} +(1.48817 + 1.38082i) q^{38} +(-12.6982 + 15.9230i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(-4.39604 + 2.11702i) q^{41} +2.26922 q^{42} +(6.39389 + 1.45540i) q^{43} +4.00538 q^{44} +(-5.49580 + 2.64664i) q^{45} +(6.80781 - 4.64149i) q^{46} +(-0.700706 + 0.878657i) q^{47} +(-2.21132 - 2.05181i) q^{48} +(3.21706 - 5.57212i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.03546 + 17.6805i) q^{51} +(-2.46657 + 6.28471i) q^{52} +(-3.08922 - 0.952899i) q^{53} +(-5.83031 - 7.31098i) q^{54} +(0.299323 - 3.99418i) q^{55} +(0.718824 - 0.221728i) q^{56} +(5.05989 + 3.44977i) q^{57} +(-3.55930 - 0.536477i) q^{58} +(-2.92597 - 12.8195i) q^{59} +(-2.21132 + 2.05181i) q^{60} +(-0.330460 - 4.40968i) q^{61} +(-2.32986 - 5.93639i) q^{62} +(4.53735 - 0.683895i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(6.08281 + 2.92933i) q^{65} +(11.9477 - 1.80082i) q^{66} +(3.60087 + 9.17486i) q^{67} +(0.449262 + 5.99498i) q^{68} +(18.2203 - 16.9059i) q^{69} +(-0.167390 - 0.733384i) q^{70} +(-15.1231 - 2.27943i) q^{71} +(-5.03996 - 3.43618i) q^{72} +(12.2370 - 3.77463i) q^{73} +(-0.370614 + 4.94550i) q^{74} +(1.88082 + 2.35847i) q^{75} +(1.93991 + 0.598383i) q^{76} +(-1.10078 + 2.80475i) q^{77} +(-4.53193 + 19.8557i) q^{78} +(7.49410 + 12.9802i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.26373 - 6.73976i) q^{81} +(-3.04215 + 3.81474i) q^{82} +(-3.00656 + 2.04984i) q^{83} +(2.04450 - 0.984578i) q^{84} +6.01179 q^{85} +(6.39217 - 1.46294i) q^{86} -10.8583 q^{87} +(3.60873 - 1.73787i) q^{88} +(-2.56336 + 1.74767i) q^{89} +(-3.80321 + 4.76908i) q^{90} +(-3.72296 - 3.45440i) q^{91} +(4.11976 - 7.13563i) q^{92} +(-9.61876 - 16.6602i) q^{93} +(-0.250079 + 1.09567i) q^{94} +(0.741679 - 1.88977i) q^{95} +(-2.88258 - 0.889159i) q^{96} +(-0.603863 - 0.757220i) q^{97} +(0.480823 - 6.41614i) q^{98} +(23.3469 - 7.20156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

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