LMFDB - Embedded newform 430.2.q.c.111.4

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			111.4
Character	$\chi$	$=$	430.111
Dual form			430.2.q.c.31.4

$q$-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 $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

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	0.996435	+	0.0843648i	$0.0268861\pi$
$3$	2.49243	+	1.69931i	1.43901	+	0.981098i	0.442572	+	0.896733i	$0.354066\pi$
$4$	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	−0.786149	−	0.618037i	$-0.787928\pi$
$7$	0.376122	−	0.651463i	0.142161	−	0.246230i	0.928310	+	0.371807i	$0.121262\pi$
$8$	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	−0.246721	−	0.969087i	$-0.579353\pi$
$11$	2.49732	−	3.13153i	0.752969	−	0.944193i	0.999690	+	0.0248932i	$0.00792458\pi$
$12$	0.225431	+	3.00817i	0.0650763	+	0.868383i
$13$	−6.45146	−	1.99001i	−1.78931	−	0.551930i	−0.791101	−	0.611685i	$-0.790492\pi$
$13$	−6.45146	−	1.99001i	−1.78931	−	0.551930i	−0.998213	+	0.0597550i	$0.980968\pi$
$14$	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	−0.0688610	−	0.997626i	$-0.521936\pi$
$17$	−4.40696	−	4.08906i	−1.06884	−	0.991742i	−0.999983	+	0.00588427i	$0.998127\pi$
$18$	−0.455845	+	6.08282i	−0.107444	+	1.43374i
$19$	0.741679	−	1.88977i	0.170153	−	0.433542i	−0.820206	−	0.572068i	$-0.806141\pi$
$19$	0.741679	−	1.88977i	0.170153	−	0.433542i	0.990359	+	0.138526i	$0.0442364\pi$
$20$	−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	0.925733	−	0.378177i	$-0.123449\pi$
$23$	8.14749	+	1.22804i	1.69887	+	0.256063i	0.773136	+	0.634241i	$0.218687\pi$
$24$	−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	−0.807063	−	0.590466i	$-0.798944\pi$
$29$	−2.97405	+	2.02767i	−0.552266	+	0.376529i	0.254796	+	0.966995i	$0.417992\pi$
$30$	−2.88258	−	0.889159i	−0.526285	−	0.162337i
$31$	0.476570	+	6.35939i	0.0855945	+	1.14218i	0.860276	+	0.509828i	$0.170291\pi$
$31$	0.476570	+	6.35939i	0.0855945	+	1.14218i	−0.774682	+	0.632351i	$0.782090\pi$
$32$	−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	0.586969	−	0.809609i	$-0.300321\pi$
$37$	−2.47968	−	4.29494i	−0.407657	−	0.706083i	−0.994627	+	0.103526i	$0.966988\pi$
$38$	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	0.0578846	−	0.998323i	$-0.481564\pi$
$41$	−4.39604	−	2.11702i	−0.686546	−	0.330623i	−0.744430	+	0.667700i	$0.767279\pi$
$42$	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	0.728097	−	0.685475i	$-0.240405\pi$
$47$	−0.700706	−	0.878657i	−0.102208	−	0.128165i	−0.830305	+	0.557309i	$0.811834\pi$
$48$	−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	−0.499566	−	0.866276i	$-0.666507\pi$
$53$	−3.08922	+	0.952899i	−0.424337	+	0.130891i	0.0752292	+	0.997166i	$0.476031\pi$
$54$	−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	0.313647	+	0.949540i	$0.398449\pi$
$59$	−2.92597	+	12.8195i	−0.380929	+	1.66896i	−0.694576	+	0.719419i	$0.744408\pi$
$60$	−2.21132	−	2.05181i	−0.285481	−	0.264887i
$61$	−0.330460	+	4.40968i	−0.0423111	+	0.564602i	0.935255	+	0.353974i	$0.115170\pi$
$61$	−0.330460	+	4.40968i	−0.0423111	+	0.564602i	−0.977566	+	0.210628i	$0.932449\pi$
$62$	−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	−0.523297	−	0.852150i	$-0.675298\pi$
$67$	3.60087	−	9.17486i	0.439916	−	1.12089i	0.963213	−	0.268738i	$-0.0866064\pi$
$68$	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	−0.959986	−	0.280048i	$-0.909650\pi$
$71$	−15.1231	+	2.27943i	−1.79478	+	0.270519i	−0.834791	+	0.550567i	$0.814412\pi$
$72$	−5.03996	+	3.43618i	−0.593965	+	0.404958i
$73$	12.2370	+	3.77463i	1.43224	+	0.441787i	0.911277	−	0.411794i	$-0.135098\pi$
$73$	12.2370	+	3.77463i	1.43224	+	0.441787i	0.520961	+	0.853581i	$0.325574\pi$
$74$	−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	−0.0440644	−	0.999029i	$-0.514031\pi$
$79$	7.49410	−	12.9802i	0.843152	−	1.46038i	0.887216	−	0.461354i	$-0.152636\pi$
$80$	−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	0.386966	−	0.922094i	$-0.373523\pi$
$83$	−3.00656	−	2.04984i	−0.330013	−	0.224999i	−0.716979	+	0.697095i	$0.754476\pi$
$84$	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	0.419795	−	0.907619i	$-0.362102\pi$
$89$	−2.56336	−	1.74767i	−0.271715	−	0.185252i	−0.691510	+	0.722367i	$0.743054\pi$
$90$	−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	−0.811542	−	0.584294i	$-0.801372\pi$
$97$	−0.603863	+	0.757220i	−0.0613130	+	0.0768841i	0.750229	+	0.661178i	$0.229943\pi$
$98$	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	−0.454612	−	0.890690i	$-0.650222\pi$
$101$	−6.29615	+	0.948992i	−0.626490	+	0.0944282i	−0.171879	+	0.985118i	$0.554984\pi$
$102$	4.03546	−	17.6805i	0.399570	−	1.75063i
$103$	−4.25487	−	3.94794i	−0.419245	−	0.389002i	0.442148	−	0.896942i	$-0.354217\pi$
$103$	−4.25487	−	3.94794i	−0.419245	−	0.389002i	−0.861393	+	0.507940i	$0.830407\pi$
$104$	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	−0.336189	−	0.941795i	$-0.609138\pi$
$107$	1.97081	−	0.949093i	0.190526	−	0.0917523i	0.526714	+	0.850042i	$0.323424\pi$
$108$	−8.42505	+	4.05729i	−0.810701	+	0.390413i
$109$	−2.29859	−	0.346456i	−0.220165	−	0.0331845i	0.0380334	−	0.999276i	$-0.487891\pi$
$109$	−2.29859	−	0.346456i	−0.220165	−	0.0331845i	−0.258198	+	0.966092i	$0.583129\pi$
$110$	−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	−0.999501	−	0.0315878i	$-0.989944\pi$
$113$	−0.906499	+	3.97163i	−0.0852763	+	0.373620i	0.914225	+	0.405208i	$0.132801\pi$
$114$	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	0.671316	−	0.741171i	$-0.265729\pi$
$127$	5.75196	+	2.77000i	0.510404	+	0.245798i	−0.160912	+	0.986969i	$0.551444\pi$
$128$	−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	0.603501	−	0.797362i	$-0.293772\pi$
$131$	4.07889	+	1.96429i	0.356375	+	0.171621i	−0.247126	+	0.968983i	$0.579486\pi$
$132$	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	−0.979520	−	0.201347i	$-0.935468\pi$
$137$	−2.15792	−	9.45449i	−0.184364	−	0.807751i	0.795156	−	0.606405i	$-0.207389\pi$
$138$	9.08067	+	23.1372i	0.772998	+	1.96957i
$139$	−0.467896	+	0.144327i	−0.0396865	+	0.0122417i	−0.314535	−	0.949246i	$-0.601849\pi$
$139$	−0.467896	+	0.144327i	−0.0396865	+	0.0122417i	0.274848	+	0.961488i	$0.411372\pi$
$140$	−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	−0.113762	−	0.993508i	$-0.536290\pi$
$149$	−6.29019	−	0.948093i	−0.515312	−	0.0776708i	−0.401550	+	0.915837i	$0.631528\pi$
$150$	2.71786	−	1.30885i	0.221913	−	0.106867i
$151$	−10.0015	+	4.81646i	−0.813909	+	0.391958i	−0.794056	−	0.607845i	$-0.792034\pi$
$151$	−10.0015	+	4.81646i	−0.813909	+	0.391958i	−0.0198530	+	0.999803i	$0.506320\pi$
$152$	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	−0.609317	−	0.792926i	$-0.708556\pi$
$157$	−12.0018	+	1.80898i	−0.957845	+	0.144372i	−0.348528	+	0.937298i	$0.613318\pi$
$158$	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	0.838127	−	0.545475i	$-0.183651\pi$
$163$	−1.88036	−	4.79107i	−0.147281	−	0.375265i	−0.985408	+	0.170210i	$0.945556\pi$
$164$	−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	−0.897993	−	0.440010i	$-0.854975\pi$
$167$	−6.80155	+	6.31092i	−0.526320	+	0.488354i	0.371673	+	0.928364i	$0.378784\pi$
$168$	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	−0.420474	−	0.907304i	$-0.638136\pi$
$179$	7.69982	−	13.3365i	0.575512	−	0.996815i	0.995986	−	0.0895109i	$-0.0285304\pi$
$180$	−1.35735	−	5.94694i	−0.101171	−	0.443259i
$181$	−1.58464	−	4.03758i	−0.117785	−	0.300111i	0.859807	−	0.510619i	$-0.170584\pi$
$181$	−1.58464	−	4.03758i	−0.117785	−	0.300111i	−0.977592	+	0.210507i	$0.932488\pi$
$182$	−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	0.582677	+	0.812704i	$0.302005\pi$
$191$	−5.48989	+	13.9880i	−0.397234	+	1.01214i	−0.979912	+	0.199433i	$0.936090\pi$
$192$	−2.98291	−	0.449601i	−0.215273	−	0.0324472i
$193$	1.62783	−	0.783921i	0.117174	−	0.0564279i	−0.374379	−	0.927276i	$-0.622144\pi$
$193$	1.62783	−	0.783921i	0.117174	−	0.0564279i	0.491552	+	0.870848i	$0.336430\pi$
$194$	−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	−0.889393	−	0.457143i	$-0.848873\pi$
$197$	0.816875	−	10.9004i	0.0581999	−	0.776624i	0.947593	−	0.319480i	$-0.103508\pi$
$198$	17.9102	+	16.6182i	1.27282	+	1.18101i
$199$	−3.59146	+	15.7352i	−0.254592	+	1.11544i	0.672349	+	0.740234i	$0.265285\pi$
$199$	−3.59146	+	15.7352i	−0.254592	+	1.11544i	−0.926941	+	0.375207i	$0.877572\pi$
$200$	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	0.983701	+	0.179814i	$0.0575495\pi$
$211$	13.6559	+	17.1240i	0.940112	+	1.17886i	−0.0435886	+	0.999050i	$0.513879\pi$
$212$	−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	−0.997217	−	0.0745552i	$-0.976246\pi$
$223$	−1.95780	−	8.57767i	−0.131104	−	0.574403i	0.866113	−	0.499848i	$-0.166611\pi$
$224$	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	−0.860607	−	0.509269i	$-0.829916\pi$
$227$	−1.28841	−	17.1927i	−0.0855149	−	1.14112i	0.775093	−	0.631848i	$-0.217703\pi$
$228$	5.85193	+	1.80508i	0.387554	+	0.119544i
$229$	4.54351	−	3.09771i	0.300243	−	0.204703i	−0.403822	−	0.914838i	$-0.632319\pi$
$229$	4.54351	−	3.09771i	0.300243	−	0.204703i	0.704065	+	0.710135i	$0.251366\pi$
$230$	−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	0.448592	+	0.893737i	$0.351926\pi$
$233$	−1.95680	+	26.1117i	−0.128194	+	1.71063i	−0.576786	+	0.816895i	$0.695693\pi$
$234$	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	0.630098	+	0.776515i	$0.283015\pi$
$239$	−5.56486	+	14.1790i	−0.359961	+	0.917166i	−0.990059	+	0.140650i	$0.955081\pi$
$240$	0.225431	−	3.00817i	0.0145515	−	0.194176i
$241$	5.88948	+	5.46464i	0.379374	+	0.352008i	0.846694	−	0.532081i	$-0.178590\pi$
$241$	5.88948	+	5.46464i	0.379374	+	0.352008i	−0.467319	+	0.884089i	$0.654780\pi$
$242$	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	0.485056	+	0.874483i	$0.338799\pi$
$251$	−8.15591	+	14.1265i	−0.514797	+	0.891654i	−0.999853	+	0.0171708i	$0.994534\pi$
$252$	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	−0.882599	−	0.470127i	$-0.844208\pi$
$263$	−7.78013	+	7.21891i	−0.479744	+	0.445137i	0.402855	+	0.915264i	$0.368018\pi$
$264$	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	−0.493095	−	0.869975i	$-0.664135\pi$
$269$	7.62315	−	9.55913i	0.464792	−	0.582831i	0.957887	+	0.287145i	$0.0927061\pi$
$270$	−0.698808	−	9.32495i	−0.0425281	−	0.567498i
$271$	13.5293	+	4.17323i	0.821845	+	0.253506i	0.677032	−	0.735953i	$-0.263266\pi$
$271$	13.5293	+	4.17323i	0.821845	+	0.253506i	0.144813	+	0.989459i	$0.453742\pi$
$272$	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	−0.531060	−	0.847334i	$-0.678206\pi$
$277$	7.23266	−	18.4285i	0.434568	−	1.10726i	0.965628	−	0.259928i	$-0.0836988\pi$
$278$	−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	−0.665513	−	0.746386i	$-0.731787\pi$
$281$	−25.5043	−	3.84416i	−1.52146	−	0.229323i	−0.855947	+	0.517063i	$0.827025\pi$
$282$	1.23858	−	3.15584i	0.0737561	−	0.187927i
$283$	0.130164	−	1.73691i	0.00773742	−	0.103249i	−0.991998	−	0.126254i	$-0.959704\pi$
$283$	0.130164	−	1.73691i	0.00773742	−	0.103249i	0.999735	+	0.0230055i	$0.00732353\pi$
$284$	−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	0.682254	+	0.731115i	$0.261000\pi$
$293$	6.58643	+	28.8570i	0.384783	+	1.68585i	−0.297470	+	0.954731i	$0.596143\pi$
$294$	−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	0.678206	−	0.734871i	$-0.262758\pi$
$307$	−5.20936	−	9.02288i	−0.297314	−	0.514963i	−0.975521	+	0.219908i	$0.929424\pi$
$308$	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	0.331263	−	0.943539i	$-0.392525\pi$
$311$	20.0420	−	6.18215i	1.13648	−	0.350557i	0.805216	+	0.592981i	$0.202049\pi$
$312$	12.6982	−	15.9230i	0.718893	−	0.901464i
$313$	1.20083	+	16.0240i	0.0678752	+	0.905732i	0.922379	+	0.386286i	$0.126242\pi$
$313$	1.20083	+	16.0240i	0.0678752	+	0.905732i	−0.854504	+	0.519445i	$0.826139\pi$
$314$	−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	−0.973685	−	0.227897i	$-0.926815\pi$
$317$	0.0437199	−	0.191549i	0.00245556	−	0.0107585i	0.976141	+	0.217138i	$0.0696723\pi$
$318$	−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	0.593654	−	0.804720i	$-0.297685\pi$
$331$	11.4771	+	3.54022i	0.630839	+	0.194588i	0.0371851	+	0.999308i	$0.488161\pi$
$332$	−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	−0.476955	−	0.878927i	$-0.658260\pi$
$337$	9.59542	−	16.6198i	0.522696	−	0.905336i	0.999651	−	0.0264083i	$-0.00840699\pi$
$338$	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	0.717923	−	0.696123i	$-0.245093\pi$
$347$	6.18833	+	4.21914i	0.332207	+	0.226495i	−0.385716	+	0.922618i	$0.626045\pi$
$348$	−6.77001	−	8.48932i	−0.362911	−	0.455075i
$349$	0.722011	−	0.669928i	0.0386484	−	0.0358604i	−0.660612	−	0.750727i	$-0.729703\pi$
$349$	0.722011	−	0.669928i	0.0386484	−	0.0358604i	0.699261	+	0.714867i	$0.253513\pi$
$350$	−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	0.799251	−	0.600997i	$-0.205230\pi$
$353$	−3.67167	−	9.35526i	−0.195423	−	0.497930i	−0.994674	+	0.103067i	$0.967134\pi$
$354$	−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	0.583724	−	0.811952i	$-0.301595\pi$
$359$	26.1632	−	3.94347i	1.38084	−	0.208128i	0.797118	+	0.603824i	$0.206357\pi$
$360$	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	0.906940	−	0.421259i	$-0.138412\pi$
$367$	31.5983	+	4.76268i	1.64942	+	0.248610i	0.742479	+	0.669869i	$0.233650\pi$
$368$	−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	−0.779658	−	0.626205i	$-0.784607\pi$
$373$	−9.30088	+	6.34123i	−0.481581	+	0.328337i	0.298077	+	0.954542i	$0.403655\pi$
$374$	−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	−0.832353	−	0.554246i	$-0.813007\pi$
$379$	−6.28633	−	27.5422i	−0.322907	−	1.41475i	0.509445	−	0.860503i	$-0.329851\pi$
$380$	−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	0.648813	−	0.760948i	$-0.275266\pi$
$383$	−4.64660	−	5.82665i	−0.237430	−	0.297728i	−0.886244	+	0.463219i	$0.846694\pi$
$384$	−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	0.243009	−	0.970024i	$-0.421866\pi$
$389$	−7.17669	−	3.45611i	−0.363873	−	0.175232i	−0.606882	+	0.794792i	$0.707580\pi$
$390$	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	0.597323	−	0.802001i	$-0.296231\pi$
$397$	30.7368	−	9.48106i	1.54264	−	0.475841i	0.945315	+	0.326160i	$0.105755\pi$
$398$	−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	−0.809548	−	0.587054i	$-0.800288\pi$
$401$	−11.1907	+	7.62969i	−0.558837	+	0.381008i	0.250712	+	0.968062i	$0.419335\pi$
$402$	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	−0.802984	+	0.596000i	$0.796756\pi$
$409$	−35.7881	+	17.2346i	−1.76961	+	0.852199i	−0.966624	+	0.256198i	$0.917530\pi$
$410$	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	−0.906464	−	0.422283i	$-0.861229\pi$
$419$	−5.99882	+	7.52229i	−0.293062	+	0.367488i	0.613402	+	0.789771i	$0.289800\pi$
$420$	−2.16840	+	0.668864i	−0.105807	+	0.0326372i
$421$	−0.0324626	−	0.0827133i	−0.00158213	−	0.00403120i	0.930081	−	0.367356i	$-0.119737\pi$
$421$	−0.0324626	−	0.0827133i	−0.00158213	−	0.00403120i	−0.931663	+	0.363325i	$0.881642\pi$
$422$	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	0.0136618	−	0.999907i	$-0.495651\pi$
$433$	−18.9803	−	12.9405i	−0.912134	−	0.621882i	−0.925796	+	0.378024i	$0.876604\pi$
$434$	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	−0.905301	−	0.424770i	$-0.860355\pi$
$439$	−11.1170	−	28.3257i	−0.530585	−	1.35191i	0.374716	−	0.927140i	$-0.377740\pi$
$440$	−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	−0.149698	−	0.988732i	$-0.547830\pi$
$443$	−17.4770	−	5.39094i	−0.830358	−	0.256131i	−0.680659	+	0.732600i	$0.738306\pi$
$444$	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	−0.395100	−	0.918638i	$-0.629290\pi$
$449$	11.0051	−	28.0405i	0.519361	−	1.32331i	0.914461	−	0.404673i	$-0.132615\pi$
$450$	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	−0.940299	−	0.340351i	$-0.889454\pi$
$457$	1.16623	−	5.10958i	0.0545538	−	0.239016i	0.994852	+	0.101335i	$0.0323113\pi$
$458$	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	−0.593071	−	0.805150i	$-0.702085\pi$
$461$	−2.71877	−	36.2794i	−0.126626	−	1.68970i	0.466445	−	0.884550i	$-0.345534\pi$
$462$	5.66696	−	7.10614i	0.263651	−	0.330608i
$463$	−3.03115	+	0.934984i	−0.140869	+	0.0434524i	−0.364388	−	0.931247i	$-0.618722\pi$
$463$	−3.03115	+	0.934984i	−0.140869	+	0.0434524i	0.223519	+	0.974700i	$0.428246\pi$
$464$	−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	0.927586	+	0.373609i	$0.121880\pi$
$467$	17.0147	+	29.4704i	0.787348	+	1.36373i	−0.140238	+	0.990118i	$0.544787\pi$
$468$	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	0.887027	−	0.461717i	$-0.152766\pi$
$479$	0.955435	+	1.65486i	0.0436549	+	0.0756126i	−0.843372	+	0.537330i	$0.819433\pi$
$480$	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	−0.770710	−	0.637186i	$-0.780098\pi$
$487$	−10.1324	+	6.90815i	−0.459143	+	0.313038i	0.311567	+	0.950224i	$0.399146\pi$
$488$	−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	−0.897032	−	0.441966i	$-0.854281\pi$
$491$	1.23761	−	16.5148i	0.0558526	−	0.745301i	0.952884	−	0.303334i	$-0.0980999\pi$
$492$	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	0.960775	−	0.277329i	$-0.0894493\pi$
$499$	16.8882	+	15.6700i	0.756020	+	0.701484i	−0.204755	+	0.978813i	$0.565640\pi$
$500$	−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	0.109988	−	0.993933i	$-0.464919\pi$
$503$	−8.05237	−	2.48383i	−0.359037	−	0.110748i	−0.469026	+	0.883185i	$0.655395\pi$
$504$	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	−0.758997	−	0.651094i	$-0.774310\pi$
$509$	4.15947	−	7.20442i	0.184365	−	0.319330i	0.943362	+	0.331764i	$0.107644\pi$
$510$	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	−0.862541	−	0.505987i	$-0.831128\pi$
$521$	−9.64207	+	8.94653i	−0.422427	+	0.391955i	0.440114	+	0.897942i	$0.354938\pi$
$522$	−10.9783	−	19.0149i	−0.480505	−	0.832259i
$523$	13.0441	−	22.5931i	0.570380	−	0.987927i	−0.426147	−	0.904654i	$-0.640129\pi$
$523$	13.0441	−	22.5931i	0.570380	−	0.987927i	0.996527	−	0.0832727i	$-0.0265372\pi$
$524$	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	0.483442	+	0.875377i	$0.339387\pi$
$541$	−2.90902	+	38.8182i	−0.125068	+	1.66892i	−0.608510	+	0.793546i	$0.708232\pi$
$542$	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	−0.941631	−	0.336646i	$-0.890708\pi$
$547$	−1.41946	−	18.9414i	−0.0606917	−	0.809874i	0.880940	−	0.473228i	$-0.156912\pi$
$548$	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	−0.0490062	−	0.998798i	$-0.515605\pi$
$557$	−20.3074	−	9.77954i	−0.860453	−	0.414372i	−0.811447	+	0.584426i	$0.801320\pi$
$558$	−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	−0.999985	−	0.00551353i	$-0.998245\pi$
$563$	−18.5750	−	23.2923i	−0.782843	−	0.981654i	0.217142	−	0.976140i	$-0.430326\pi$
$564$	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	−0.709496	−	0.704709i	$-0.751077\pi$
$569$	−21.4381	+	6.61278i	−0.898732	+	0.277222i	−0.189236	+	0.981932i	$0.560601\pi$
$570$	−3.81825	+	4.78794i	−0.159929	+	0.200545i
$571$	−0.00105218	−	0.0140404i	−4.40325e−5	−	0.000587572i	0.997182	−	0.0750239i	$-0.0239033\pi$
$571$	−0.00105218	−	0.0140404i	−4.40325e−5	−	0.000587572i	−0.997226	+	0.0744363i	$0.976284\pi$
$572$	−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	−0.944045	−	0.329817i	$-0.893013\pi$
$577$	0.927504	−	12.3767i	0.0386125	−	0.515248i	0.982657	−	0.185431i	$-0.0593681\pi$
$578$	−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	−0.251051	−	0.967974i	$-0.580776\pi$
$587$	−4.98210	+	0.750930i	−0.205633	+	0.0309942i	0.0454178	+	0.998968i	$0.485538\pi$
$588$	−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	−0.998500	−	0.0547565i	$-0.982562\pi$
$593$	−7.39781	−	18.8493i	−0.303791	−	0.774048i	0.694708	−	0.719292i	$-0.255533\pi$
$594$	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	0.997173	−	0.0751458i	$-0.0239422\pi$
$599$	31.6095	+	21.5510i	1.29153	+	0.880550i	0.294357	+	0.955696i	$0.404895\pi$
$600$	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	−0.874056	−	0.485825i	$-0.838519\pi$
$607$	−11.2077	+	10.3992i	−0.454907	+	0.422092i	0.419149	+	0.907918i	$0.362329\pi$
$608$	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	−0.431533	−	0.902097i	$-0.642027\pi$
$613$	13.4681	−	16.8885i	0.543972	−	0.682119i	0.975505	+	0.219978i	$0.0705986\pi$
$614$	−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	0.570568	−	0.821251i	$-0.306723\pi$
$617$	33.7284	−	5.08374i	1.35785	−	0.204664i	0.787287	+	0.616587i	$0.211485\pi$
$618$	3.89619	−	17.0703i	0.156728	−	0.686669i
$619$	−8.30196	−	7.70309i	−0.333684	−	0.309613i	0.495480	−	0.868620i	$-0.334992\pi$
$619$	−8.30196	−	7.70309i	−0.333684	−	0.309613i	−0.829163	+	0.559006i	$0.811183\pi$
$620$	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	0.219895	−	0.975523i	$-0.429428\pi$
$631$	30.3527	−	20.6941i	1.20832	−	0.823820i	0.988426	+	0.151704i	$0.0484760\pi$
$632$	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	0.999984	−	0.00560405i	$-0.00178383\pi$
$641$	19.5456	+	24.5094i	0.772003	+	0.968062i	−0.227981	+	0.973666i	$0.573212\pi$
$642$	5.45204	+	3.71714i	0.215175	+	0.146704i
$643$	29.2105	+	14.0670i	1.15195	+	0.554750i	0.909619	−	0.415444i	$-0.136374\pi$
$643$	29.2105	+	14.0670i	1.15195	+	0.554750i	0.242331	+	0.970194i	$0.422088\pi$
$644$	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	0.436497	−	0.899706i	$-0.356219\pi$
$647$	0.133047	+	0.0640720i	0.00523062	+	0.00251893i	−0.431267	+	0.902225i	$0.641933\pi$
$648$	−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	−0.837739	−	0.546070i	$-0.816123\pi$
$653$	−8.17451	−	35.8149i	−0.319893	−	1.40154i	0.517846	−	0.855474i	$-0.326734\pi$
$654$	−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	−0.280126	−	0.959963i	$-0.590376\pi$
$659$	13.1214	−	8.94601i	0.511137	−	0.348487i	0.791263	+	0.611476i	$0.209424\pi$
$660$	−11.9477	+	1.80082i	−0.465063	+	0.0700970i
$661$	9.38824	−	41.1326i	0.365160	−	1.59987i	−0.374723	−	0.927137i	$-0.622262\pi$
$661$	9.38824	−	41.1326i	0.365160	−	1.59987i	0.739884	−	0.672735i	$-0.234881\pi$
$662$	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	−0.386343	−	0.922355i	$-0.626262\pi$
$673$	−12.5470	+	1.89116i	−0.483652	+	0.0728988i	−0.0973095	+	0.995254i	$0.531024\pi$
$674$	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	−0.959432	−	0.281940i	$-0.909022\pi$
$677$	−12.2568	+	15.3696i	−0.471067	+	0.590700i	0.488365	+	0.872640i	$0.337594\pi$
$678$	−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	−0.998106	−	0.0615127i	$-0.980408\pi$
$683$	−26.4310	+	24.5244i	−1.01135	+	0.938400i	−0.0132479	+	0.999912i	$0.504217\pi$
$684$	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	0.675271	−	0.737570i	$-0.264027\pi$
$691$	6.18766	+	4.21868i	0.235390	+	0.160486i	−0.439881	+	0.898056i	$0.644979\pi$
$692$	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	−0.264413	−	0.964410i	$-0.585178\pi$
$701$	−27.1688	−	8.38047i	−1.02615	−	0.316526i	−0.761739	+	0.647883i	$0.775654\pi$
$702$	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	−0.367800	−	0.929905i	$-0.619889\pi$
$709$	3.45912	−	1.66582i	0.129910	−	0.0625613i	0.497710	+	0.867344i	$0.334175\pi$
$710$	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	−0.850402	−	0.526134i	$-0.823641\pi$
$719$	−2.35735	−	31.4567i	−0.0879144	−	1.17314i	0.762487	−	0.647003i	$-0.223978\pi$
$720$	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	0.994389	−	0.105782i	$-0.0337346\pi$
$727$	18.0648	+	22.6526i	0.669987	+	0.840137i	−0.324402	+	0.945919i	$0.605163\pi$
$728$	−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	−0.0519559	−	0.998649i	$-0.516546\pi$
$733$	−23.4224	−	11.2796i	−0.865125	−	0.416622i	−0.813169	+	0.582027i	$0.802260\pi$
$734$	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	0.924390	−	0.381449i	$-0.124575\pi$
$739$	−2.01060	−	8.80903i	−0.0739612	−	0.324045i	−0.998351	+	0.0574039i	$0.981718\pi$
$740$	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	0.826008	+	0.563658i	$0.190606\pi$
$743$	2.54139	+	33.9125i	0.0932347	+	1.24413i	−0.732773	+	0.680473i	$0.761775\pi$
$744$	−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	−0.621312	−	0.783563i	$-0.713400\pi$
$751$	−39.6262	−	5.97269i	−1.44598	−	0.217946i	−0.824668	+	0.565617i	$0.808638\pi$
$752$	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	0.983847	+	0.179011i	$0.0572897\pi$
$757$	34.0036	+	31.5507i	1.23588	+	1.14673i	0.252033	+	0.967719i	$0.418901\pi$
$758$	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	0.448705	−	0.893680i	$-0.351885\pi$
$761$	8.71766	+	2.68904i	0.316015	+	0.0974777i	−0.132690	+	0.991158i	$0.542362\pi$
$762$	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	−0.588366	−	0.808595i	$-0.700228\pi$
$769$	4.82516	−	4.47709i	0.174000	−	0.161448i	0.762365	+	0.647147i	$0.224038\pi$
$770$	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	−0.596251	−	0.802798i	$-0.703344\pi$
$787$	−43.2341	−	13.3360i	−1.54113	−	0.475375i	−0.944878	+	0.327422i	$0.893820\pi$
$788$	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	0.185536	−	0.982637i	$-0.440598\pi$
$797$	2.06629	+	0.311443i	0.0731917	+	0.0110319i	−0.112344	+	0.993669i	$0.535836\pi$
$798$	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	−0.984946	−	0.172863i	$-0.944698\pi$
$809$	−4.90762	−	21.5017i	−0.172543	−	0.755959i	0.812403	−	0.583096i	$-0.198159\pi$
$810$	4.95444	−	8.58135i	0.174081	−	0.301518i
$811$	2.08286	+	3.60761i	0.0731390	+	0.126680i	0.900275	−	0.435321i	$-0.143365\pi$
$811$	2.08286	+	3.60761i	0.0731390	+	0.126680i	−0.827136	+	0.562001i	$0.810032\pi$
$812$	−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	0.872475	−	0.488659i	$-0.162514\pi$
$821$	5.78574	+	7.25508i	0.201924	+	0.253204i	−0.670551	+	0.741863i	$0.733942\pi$
$822$	21.4446	−	19.8977i	0.747966	−	0.694011i
$823$	−8.21699	−	14.2322i	−0.286426	−	0.496105i	0.686528	−	0.727104i	$-0.259134\pi$
$823$	−8.21699	−	14.2322i	−0.286426	−	0.496105i	−0.972954	+	0.230999i	$0.925801\pi$
$824$	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	−0.605359	−	0.795952i	$-0.706970\pi$
$827$	−18.8982	+	5.82932i	−0.657154	+	0.202705i	−0.0517951	+	0.998658i	$0.516494\pi$
$828$	−31.3366	+	39.2949i	−1.08902	+	1.36559i
$829$	1.63500	+	21.8175i	0.0567858	+	0.757754i	0.950818	+	0.309751i	$0.100246\pi$
$829$	1.63500	+	21.8175i	0.0567858	+	0.757754i	−0.894032	+	0.448003i	$0.852135\pi$
$830$	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	0.519865	−	0.854248i	$-0.325982\pi$
$839$	43.7922	−	21.0892i	1.51187	−	0.728080i	0.992009	+	0.126168i	$0.0402680\pi$
$840$	−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	−0.999998	−	0.00188451i	$-0.999400\pi$
$853$	−14.5554	+	25.2107i	−0.498367	+	0.863197i	0.501631	+	0.865082i	$0.332733\pi$
$854$	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	0.936540	−	0.350562i	$-0.114009\pi$
$857$	27.8801	+	19.0083i	0.952367	+	0.649313i	0.0158274	+	0.999875i	$0.494962\pi$
$858$	−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	0.863502	−	0.504345i	$-0.168266\pi$
$863$	20.8427	+	14.2103i	0.709494	+	0.483725i	−0.154008	+	0.988070i	$0.549218\pi$
$864$	−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	0.890979	−	0.454044i	$-0.150019\pi$
$877$	14.9489	+	13.8705i	0.504788	+	0.468375i	−0.386191	+	0.922419i	$0.626210\pi$
$878$	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	−0.432994	−	0.901397i	$-0.642543\pi$
$881$	0.0528121	−	0.0254330i	0.00177928	−	0.000856858i	0.434773	+	0.900540i	$0.356829\pi$
$882$	−35.3607	+	17.0288i	−1.19066	+	0.573390i
$883$	−6.50064	−	0.979813i	−0.218764	−	0.0329733i	0.0387457	−	0.999249i	$-0.487664\pi$
$883$	−6.50064	−	0.979813i	−0.218764	−	0.0329733i	−0.257510	+	0.966276i	$0.582902\pi$
$884$	−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	−0.801032	−	0.598622i	$-0.795715\pi$
$887$	5.37293	−	23.5403i	0.180405	−	0.790408i	0.981437	−	0.191785i	$-0.0614277\pi$
$888$	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	−1.00000		0.000902958i	$-0.999713\pi$
$907$	−23.4414	−	29.3946i	−0.778359	−	0.976031i	0.221641	−	0.975128i	$-0.428859\pi$
$908$	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	−0.960651	−	0.277757i	$-0.910409\pi$
$911$	−6.50888	−	28.5173i	−0.215649	−	0.944819i	0.745003	−	0.667062i	$-0.232448\pi$
$912$	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	−0.961966	−	0.273170i	$-0.911928\pi$
$919$	0.705115	−	3.08931i	0.0232596	−	0.101907i	0.985225	+	0.171263i	$0.0547849\pi$
$920$	−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	0.0768778	−	0.997041i	$-0.475505\pi$
$929$	−27.7860	−	25.7817i	−0.911630	−	0.845869i	−0.988508	+	0.151172i	$0.951695\pi$
$930$	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	0.802006	+	0.597316i	$0.203766\pi$
$937$	18.9899	+	48.3854i	0.620372	+	1.58068i	−0.181634	+	0.983366i	$0.558139\pi$
$938$	−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	−0.200127	−	0.979770i	$-0.564135\pi$
$941$	23.3733	−	21.6873i	0.761948	−	0.706984i	0.962075	+	0.272786i	$0.0879450\pi$
$942$	−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	−0.785476	−	0.618892i	$-0.787582\pi$
$953$	4.42187	−	7.65891i	0.143239	−	0.248096i	0.928714	+	0.370796i	$0.120915\pi$
$954$	−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	−0.961049	−	0.276379i	$-0.910865\pi$
$967$	−41.7992	+	20.1294i	−1.34417	+	0.647319i	−0.383122	+	0.923698i	$0.625151\pi$
$968$	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	0.904486	+	0.426504i	$0.140255\pi$
$971$	−1.66601	+	22.2314i	−0.0534648	+	0.713438i	−0.957950	+	0.286934i	$0.907364\pi$
$972$	−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	−0.968046	−	0.250772i	$-0.919316\pi$
$977$	−1.50621	−	20.0989i	−0.0481878	−	0.643022i	0.919858	−	0.392250i	$-0.128303\pi$
$978$	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	0.988764	−	0.149483i	$-0.0477611\pi$
$983$	11.4415	+	19.8172i	0.364926	+	0.632070i	−0.623839	+	0.781553i	$0.714428\pi$
$984$	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	0.997614	−	0.0690404i	$-0.0219937\pi$
$991$	49.2865	+	23.7351i	1.56564	+	0.753972i	0.568024	+	0.823012i	$0.307708\pi$
$992$	−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	0.929415	−	0.369037i	$-0.120312\pi$
$997$	−2.14958	−	9.41793i	−0.0680779	−	0.298269i	−0.997493	+	0.0707676i	$0.977455\pi$
$998$	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.111.4	yes	48
43.31	even	21	inner	430.2.q.c.31.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.31.4	✓	48	43.31	even	21	inner
430.2.q.c.111.4	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
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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