LMFDB - Embedded newform 197.4.g.a.16.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(16,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(98))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("197.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.g (of order $49$, degree $42$, 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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$2058$
Relative dimension:	$49$ over $\Q(\zeta_{49})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{49}]$

Embedding invariants

Embedding label			16.8
Character	$\chi$	$=$	197.16
Dual form			197.4.g.a.37.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.27791 - 0.274651i) q^{2} +(-1.17628 + 1.68628i) q^{3} +(10.2908 + 1.32685i) q^{4} +(4.43621 - 2.88765i) q^{5} +(5.49515 - 6.89071i) q^{6} +(4.20983 - 0.270280i) q^{7} +(-9.99729 - 1.94697i) q^{8} +(7.86494 + 21.3716i) q^{9} +O(q^{10})$	\(q+(-4.27791 - 0.274651i) q^{2} +(-1.17628 + 1.68628i) q^{3} +(10.2908 + 1.32685i) q^{4} +(4.43621 - 2.88765i) q^{5} +(5.49515 - 6.89071i) q^{6} +(4.20983 - 0.270280i) q^{7} +(-9.99729 - 1.94697i) q^{8} +(7.86494 + 21.3716i) q^{9} +(-19.7708 + 11.1347i) q^{10} +(-0.707788 + 2.38477i) q^{11} +(-14.3423 + 15.7924i) q^{12} +(1.85783 - 57.9340i) q^{13} -18.0835 q^{14} +(-0.348817 + 10.8774i) q^{15} +(-38.0602 - 9.98055i) q^{16} +(-41.5430 - 40.2321i) q^{17} +(-27.7758 - 93.5858i) q^{18} +(12.5507 + 6.04409i) q^{19} +(49.4835 - 23.8300i) q^{20} +(-4.49617 + 7.41690i) q^{21} +(3.68283 - 10.0074i) q^{22} +(22.0195 + 136.198i) q^{23} +(15.0427 - 14.5681i) q^{24} +(-39.2565 + 88.6811i) q^{25} +(-23.8593 + 247.326i) q^{26} +(-98.9866 - 25.9574i) q^{27} +(43.6811 + 2.80442i) q^{28} +(161.858 - 178.223i) q^{29} +(4.47969 - 46.4367i) q^{30} +(78.5899 - 31.8175i) q^{31} +(237.407 + 78.8245i) q^{32} +(-3.18884 - 3.99868i) q^{33} +(166.667 + 183.519i) q^{34} +(17.8952 - 13.3556i) q^{35} +(52.5795 + 230.366i) q^{36} +(426.365 - 111.806i) q^{37} +(-52.0307 - 29.3031i) q^{38} +(95.5078 + 71.2793i) q^{39} +(-49.9723 + 20.2315i) q^{40} +(240.126 + 232.549i) q^{41} +(21.2713 - 30.4940i) q^{42} +(83.7011 - 282.017i) q^{43} +(-10.4479 + 23.6020i) q^{44} +(96.6042 + 72.0976i) q^{45} +(-56.7905 - 588.693i) q^{46} +(229.077 + 439.097i) q^{47} +(61.5994 - 52.4403i) q^{48} +(-322.534 + 41.5862i) q^{49} +(192.292 - 368.588i) q^{50} +(116.709 - 22.7290i) q^{51} +(95.9882 - 593.721i) q^{52} +(11.9311 + 123.678i) q^{53} +(416.327 + 138.230i) q^{54} +(3.74650 + 12.6232i) q^{55} +(-42.6132 - 5.49436i) q^{56} +(-24.9551 + 14.0545i) q^{57} +(-741.363 + 717.970i) q^{58} +(433.860 + 244.345i) q^{59} +(-18.0222 + 111.474i) q^{60} +(206.092 + 295.449i) q^{61} +(-344.939 + 114.528i) q^{62} +(38.8864 + 87.8450i) q^{63} +(-702.185 - 284.283i) q^{64} +(-159.051 - 262.372i) q^{65} +(12.5434 + 17.9818i) q^{66} +(-391.036 - 749.543i) q^{67} +(-374.128 - 469.141i) q^{68} +(-255.570 - 123.076i) q^{69} +(-80.2223 + 52.2190i) q^{70} +(228.770 + 621.642i) q^{71} +(-37.0182 - 228.971i) q^{72} +(489.997 - 128.492i) q^{73} +(-1854.66 + 361.195i) q^{74} +(-103.365 - 170.511i) q^{75} +(121.137 + 78.8512i) q^{76} +(-2.33511 + 10.2308i) q^{77} +(-388.997 - 331.158i) q^{78} +(310.589 + 202.171i) q^{79} +(-197.663 + 65.6287i) q^{80} +(-307.980 + 262.187i) q^{81} +(-963.368 - 1060.77i) q^{82} +(1147.97 - 552.834i) q^{83} +(-56.1102 + 70.3599i) q^{84} +(-300.470 - 58.5165i) q^{85} +(-435.522 + 1183.45i) q^{86} +(110.145 + 482.578i) q^{87} +(11.7190 - 22.4632i) q^{88} +(-901.193 - 364.853i) q^{89} +(-393.462 - 334.959i) q^{90} +(-7.83726 - 244.395i) q^{91} +(45.8832 + 1430.81i) q^{92} +(-38.7902 + 169.951i) q^{93} +(-859.372 - 1941.34i) q^{94} +(73.1306 - 9.42915i) q^{95} +(-412.177 + 307.616i) q^{96} +(373.891 - 616.772i) q^{97} +(1391.20 - 89.3177i) q^{98} +(-56.5330 + 3.62954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9}+O(q^{10}) $ 2058 * q - 42 * q^2 - 42 * q^3 - 84 * q^4 - 42 * q^5 - 119 * q^6 - 84 * q^7 - 98 * q^8 - 42 * q^9	\( 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9} + 168 q^{10} - 140 q^{11} + 14 q^{12} - 42 q^{13} - 812 q^{14} + 1638 q^{15} + 672 q^{16} - 42 q^{17} + 147 q^{18} - 567 q^{19} - 35 q^{20} - 42 q^{21} + 1302 q^{22} - 42 q^{23} - 434 q^{24} - 42 q^{25} + 364 q^{26} - 1596 q^{27} - 147 q^{28} + 4676 q^{29} - 847 q^{30} + 882 q^{31} + 910 q^{32} - 287 q^{33} - 882 q^{34} - 42 q^{35} - 17787 q^{36} - 1400 q^{37} + 14 q^{38} + 168 q^{39} + 3962 q^{40} - 392 q^{41} + 1764 q^{42} + 294 q^{43} - 12978 q^{44} + 2814 q^{45} + 840 q^{46} + 28 q^{47} + 3654 q^{48} + 1554 q^{49} - 4998 q^{50} - 98 q^{51} - 3703 q^{52} - 42 q^{53} - 1365 q^{54} + 4046 q^{55} - 3073 q^{56} + 14567 q^{57} - 10402 q^{58} + 4004 q^{59} - 4536 q^{60} - 1050 q^{61} + 210 q^{62} + 2254 q^{63} + 3822 q^{64} - 1106 q^{65} - 875 q^{66} - 3612 q^{67} + 819 q^{68} + 4333 q^{69} - 5292 q^{70} + 11424 q^{71} - 1876 q^{72} - 714 q^{73} + 1288 q^{74} - 1316 q^{75} + 8715 q^{76} + 6629 q^{77} + 13986 q^{78} - 1512 q^{79} + 406 q^{80} + 1078 q^{81} - 42 q^{82} - 5999 q^{83} - 7595 q^{84} + 30492 q^{85} + 7749 q^{86} - 35 q^{87} + 8897 q^{88} - 196 q^{89} - 14910 q^{90} - 8232 q^{91} - 7938 q^{92} - 2639 q^{93} - 11116 q^{94} + 3703 q^{95} + 14497 q^{96} - 2674 q^{97} - 10024 q^{98} + 6237 q^{99}+O(q^{100}) \) 2058 * q - 42 * q^2 - 42 * q^3 - 84 * q^4 - 42 * q^5 - 119 * q^6 - 84 * q^7 - 98 * q^8 - 42 * q^9 + 168 * q^10 - 140 * q^11 + 14 * q^12 - 42 * q^13 - 812 * q^14 + 1638 * q^15 + 672 * q^16 - 42 * q^17 + 147 * q^18 - 567 * q^19 - 35 * q^20 - 42 * q^21 + 1302 * q^22 - 42 * q^23 - 434 * q^24 - 42 * q^25 + 364 * q^26 - 1596 * q^27 - 147 * q^28 + 4676 * q^29 - 847 * q^30 + 882 * q^31 + 910 * q^32 - 287 * q^33 - 882 * q^34 - 42 * q^35 - 17787 * q^36 - 1400 * q^37 + 14 * q^38 + 168 * q^39 + 3962 * q^40 - 392 * q^41 + 1764 * q^42 + 294 * q^43 - 12978 * q^44 + 2814 * q^45 + 840 * q^46 + 28 * q^47 + 3654 * q^48 + 1554 * q^49 - 4998 * q^50 - 98 * q^51 - 3703 * q^52 - 42 * q^53 - 1365 * q^54 + 4046 * q^55 - 3073 * q^56 + 14567 * q^57 - 10402 * q^58 + 4004 * q^59 - 4536 * q^60 - 1050 * q^61 + 210 * q^62 + 2254 * q^63 + 3822 * q^64 - 1106 * q^65 - 875 * q^66 - 3612 * q^67 + 819 * q^68 + 4333 * q^69 - 5292 * q^70 + 11424 * q^71 - 1876 * q^72 - 714 * q^73 + 1288 * q^74 - 1316 * q^75 + 8715 * q^76 + 6629 * q^77 + 13986 * q^78 - 1512 * q^79 + 406 * q^80 + 1078 * q^81 - 42 * q^82 - 5999 * q^83 - 7595 * q^84 + 30492 * q^85 + 7749 * q^86 - 35 * q^87 + 8897 * q^88 - 196 * q^89 - 14910 * q^90 - 8232 * q^91 - 7938 * q^92 - 2639 * q^93 - 11116 * q^94 + 3703 * q^95 + 14497 * q^96 - 2674 * q^97 - 10024 * q^98 + 6237 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{49}\right)$

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 $

$2$	−4.27791	−	0.274651i	−1.51247	−	0.0971038i	−0.714430	−	0.699707i	$-0.753314\pi$
$2$	−4.27791	−	0.274651i	−1.51247	−	0.0971038i	−0.798041	+	0.602603i	$0.794130\pi$
$3$	−1.17628	+	1.68628i	−0.226375	+	0.324525i	−0.917148	−	0.398546i	$-0.869515\pi$
$3$	−1.17628	+	1.68628i	−0.226375	+	0.324525i	0.690774	+	0.723071i	$0.257270\pi$
$4$	10.2908	+	1.32685i	1.28635	+	0.165856i
$5$	4.43621	−	2.88765i	0.396787	−	0.258279i	−0.331636	−	0.943407i	$-0.607601\pi$
$5$	4.43621	−	2.88765i	0.396787	−	0.258279i	0.728423	+	0.685128i	$0.240254\pi$
$6$	5.49515	−	6.89071i	0.373898	−	0.468853i
$7$	4.20983	−	0.270280i	0.227310	−	0.0145938i	0.0500015	−	0.998749i	$-0.484077\pi$
$7$	4.20983	−	0.270280i	0.227310	−	0.0145938i	0.177308	+	0.984155i	$0.443261\pi$
$8$	−9.99729	−	1.94697i	−0.441822	−	0.0860449i
$9$	7.86494	+	21.3716i	0.291294	+	0.791540i
$10$	−19.7708	+	11.1347i	−0.625208	+	0.352111i
$11$	−0.707788	+	2.38477i	−0.0194005	+	0.0653669i	−0.967811	−	0.251679i	$-0.919017\pi$
$11$	−0.707788	+	2.38477i	−0.0194005	+	0.0653669i	0.948410	+	0.317046i	$0.102691\pi$
$12$	−14.3423	+	15.7924i	−0.345021	+	0.379907i
$13$	1.85783	−	57.9340i	0.0396361	−	1.23600i	−0.765706	−	0.643190i	$-0.777610\pi$
$13$	1.85783	−	57.9340i	0.0396361	−	1.23600i	0.805343	−	0.592810i	$-0.201981\pi$
$14$	−18.0835			−0.345216
$15$	−0.348817	+	10.8774i	−0.00600427	+	0.187235i
$16$	−38.0602	−	9.98055i	−0.594690	−	0.155946i
$17$	−41.5430	−	40.2321i	−0.592685	−	0.573984i	0.337384	−	0.941367i	$-0.390458\pi$
$17$	−41.5430	−	40.2321i	−0.592685	−	0.573984i	−0.930070	+	0.367383i	$0.880254\pi$
$18$	−27.7758	−	93.5858i	−0.363712	−	1.22547i
$19$	12.5507	+	6.04409i	0.151543	+	0.0729794i	0.508118	−	0.861287i	$-0.330341\pi$
$19$	12.5507	+	6.04409i	0.151543	+	0.0729794i	−0.356575	+	0.934267i	$0.616056\pi$
$20$	49.4835	−	23.8300i	0.553243	−	0.266428i
$21$	−4.49617	+	7.41690i	−0.0467211	+	0.0770714i
$22$	3.68283	−	10.0074i	0.0356901	−	0.0969816i
$23$	22.0195	+	136.198i	0.199626	+	1.23475i	0.870120	+	0.492840i	$0.164041\pi$
$23$	22.0195	+	136.198i	0.199626	+	1.23475i	−0.670495	+	0.741914i	$0.733918\pi$
$24$	15.0427	−	14.5681i	0.127941	−	0.123904i
$25$	−39.2565	+	88.6811i	−0.314052	+	0.709449i
$26$	−23.8593	+	247.326i	−0.179969	+	1.86556i
$27$	−98.9866	−	25.9574i	−0.705555	−	0.185018i
$28$	43.6811	+	2.80442i	0.294820	+	0.0189281i
$29$	161.858	−	178.223i	1.03642	−	1.14122i	0.0465988	−	0.998914i	$-0.485162\pi$
$29$	161.858	−	178.223i	1.03642	−	1.14122i	0.989823	−	0.142302i	$-0.0454505\pi$
$30$	4.47969	−	46.4367i	0.0272625	−	0.282605i
$31$	78.5899	−	31.8175i	0.455328	−	0.184342i	−0.136108	−	0.990694i	$-0.543459\pi$
$31$	78.5899	−	31.8175i	0.455328	−	0.184342i	0.591436	+	0.806352i	$0.298561\pi$
$32$	237.407	+	78.8245i	1.31150	+	0.435448i
$33$	−3.18884	−	3.99868i	−0.0168214	−	0.0210934i
$34$	166.667	+	183.519i	0.840683	+	0.925685i
$35$	17.8952	−	13.3556i	0.0864242	−	0.0645000i
$36$	52.5795	+	230.366i	0.243424	+	1.06651i
$37$	426.365	−	111.806i	1.89443	−	0.496778i	0.895800	−	0.444458i	$-0.146604\pi$
$37$	426.365	−	111.806i	1.89443	−	0.496778i	0.998630	−	0.0523197i	$-0.0166615\pi$
$38$	−52.0307	−	29.3031i	−0.222118	−	0.125095i
$39$	95.5078	+	71.2793i	0.392141	+	0.292662i
$40$	−49.9723	+	20.2315i	−0.197533	+	0.0799721i
$41$	240.126	+	232.549i	0.914667	+	0.885806i	0.993814	−	0.111057i	$-0.0354236\pi$
$41$	240.126	+	232.549i	0.914667	+	0.885806i	−0.0791467	+	0.996863i	$0.525220\pi$
$42$	21.2713	−	30.4940i	0.0781483	−	0.112031i
$43$	83.7011	−	282.017i	0.296844	−	1.00017i	−0.669478	−	0.742832i	$-0.733482\pi$
$43$	83.7011	−	282.017i	0.296844	−	1.00017i	0.966322	−	0.257335i	$-0.0828443\pi$
$44$	−10.4479	+	23.6020i	−0.0357974	+	0.0808668i
$45$	96.6042	+	72.0976i	0.320020	+	0.238837i
$46$	−56.7905	−	588.693i	−0.182028	−	1.88691i
$47$	229.077	+	439.097i	0.710942	+	1.36274i	0.922737	+	0.385429i	$0.125947\pi$
$47$	229.077	+	439.097i	0.710942	+	1.36274i	−0.211795	+	0.977314i	$0.567931\pi$
$48$	61.5994	−	52.4403i	0.185231	−	0.157690i
$49$	−322.534	+	41.5862i	−0.940333	+	0.121243i
$50$	192.292	−	368.588i	0.543885	−	1.04253i
$51$	116.709	−	22.7290i	0.320441	−	0.0624059i
$52$	95.9882	−	593.721i	0.255984	−	1.58335i
$53$	11.9311	+	123.678i	0.0309219	+	0.320538i	0.997853	+	0.0654989i	$0.0208639\pi$
$53$	11.9311	+	123.678i	0.0309219	+	0.320538i	−0.966931	+	0.255039i	$0.917912\pi$
$54$	416.327	+	138.230i	1.04917	+	0.348347i
$55$	3.74650	+	12.6232i	0.00918504	+	0.0309475i
$56$	−42.6132	−	5.49436i	−0.101686	−	0.0131110i
$57$	−24.9551	+	14.0545i	−0.0579892	+	0.0326589i
$58$	−741.363	+	717.970i	−1.67837	+	1.62541i
$59$	433.860	+	244.345i	0.957352	+	0.539171i	0.888710	−	0.458471i	$-0.151603\pi$
$59$	433.860	+	244.345i	0.957352	+	0.539171i	0.0686426	+	0.997641i	$0.478133\pi$
$60$	−18.0222	+	111.474i	−0.0387777	+	0.239854i
$61$	206.092	+	295.449i	0.432580	+	0.620137i	0.975593	−	0.219588i	$-0.0704714\pi$
$61$	206.092	+	295.449i	0.432580	+	0.620137i	−0.543012	+	0.839725i	$0.682716\pi$
$62$	−344.939	+	114.528i	−0.706570	+	0.234597i
$63$	38.8864	+	87.8450i	0.0777655	+	0.175674i
$64$	−702.185	−	284.283i	−1.37146	−	0.555241i
$65$	−159.051	−	262.372i	−0.303506	−	0.500665i
$66$	12.5434	+	17.9818i	0.0233936	+	0.0335365i
$67$	−391.036	−	749.543i	−0.713024	−	1.36673i	−0.921373	−	0.388680i	$-0.872931\pi$
$67$	−391.036	−	749.543i	−0.713024	−	1.36673i	0.208348	−	0.978055i	$-0.433191\pi$
$68$	−374.128	−	469.141i	−0.667201	−	0.836643i
$69$	−255.570	−	123.076i	−0.445899	−	0.214734i
$70$	−80.2223	+	52.2190i	−0.136977	+	0.0891623i
$71$	228.770	+	621.642i	0.382395	+	1.03909i	0.972732	+	0.231933i	$0.0745049\pi$
$71$	228.770	+	621.642i	0.382395	+	1.03909i	−0.590337	+	0.807157i	$0.701005\pi$
$72$	−37.0182	−	228.971i	−0.0605922	−	0.374784i
$73$	489.997	−	128.492i	0.785613	−	0.206012i	0.161008	−	0.986953i	$-0.448525\pi$
$73$	489.997	−	128.492i	0.785613	−	0.206012i	0.624605	+	0.780941i	$0.285260\pi$
$74$	−1854.66	+	361.195i	−2.91351	+	0.567406i
$75$	−103.365	−	170.511i	−0.159141	−	0.262519i
$76$	121.137	+	78.8512i	0.182833	+	0.119011i
$77$	−2.33511	+	10.2308i	−0.00345598	+	0.0151417i
$78$	−388.997	−	331.158i	−0.564683	−	0.480721i
$79$	310.589	+	202.171i	0.442329	+	0.287925i	0.747362	−	0.664417i	$-0.231320\pi$
$79$	310.589	+	202.171i	0.442329	+	0.287925i	−0.305032	+	0.952342i	$0.598667\pi$
$80$	−197.663	+	65.6287i	−0.276243	+	0.0917189i
$81$	−307.980	+	262.187i	−0.422469	+	0.359653i
$82$	−963.368	−	1060.77i	−1.29739	−	1.42857i
$83$	1147.97	−	552.834i	1.51815	−	0.731102i	0.525349	−	0.850887i	$-0.323935\pi$
$83$	1147.97	−	552.834i	1.51815	−	0.731102i	0.992800	+	0.119785i	$0.0382206\pi$
$84$	−56.1102	+	70.3599i	−0.0728824	+	0.0913917i
$85$	−300.470	−	58.5165i	−0.383418	−	0.0746706i
$86$	−435.522	+	1183.45i	−0.546088	+	1.48390i
$87$	110.145	+	482.578i	0.135734	+	0.594688i
$88$	11.7190	−	22.4632i	0.0141961	−	0.0272112i
$89$	−901.193	−	364.853i	−1.07333	−	0.434543i	−0.230693	−	0.973027i	$-0.574099\pi$
$89$	−901.193	−	364.853i	−1.07333	−	0.434543i	−0.842636	+	0.538484i	$0.818997\pi$
$90$	−393.462	−	334.959i	−0.460829	−	0.392309i
$91$	−7.83726	−	244.395i	−0.00902822	−	0.281533i
$92$	45.8832	+	1430.81i	0.0519962	+	1.62143i
$93$	−38.7902	+	169.951i	−0.0432512	+	0.189496i
$94$	−859.372	−	1941.34i	−0.942952	−	2.13014i
$95$	73.1306	−	9.42915i	0.0789794	−	0.0101833i
$96$	−412.177	+	307.616i	−0.438204	+	0.327040i
$97$	373.891	−	616.772i	0.391370	−	0.645605i	−0.596191	−	0.802843i	$-0.703320\pi$
$97$	373.891	−	616.772i	0.391370	−	0.645605i	0.987561	+	0.157237i	$0.0502587\pi$
$98$	1391.20	−	89.3177i	1.43400	−	0.0920658i
$99$	−56.5330	+	3.62954i	−0.0573917	+	0.00368467i
$100$	−521.647	+	860.511i	−0.521647	+	0.860511i
$101$	−850.801	+	634.970i	−0.838197	+	0.625563i	−0.928906	−	0.370315i	$-0.879250\pi$
$101$	−850.801	+	634.970i	−0.838197	+	0.625563i	0.0907093	+	0.995877i	$0.471087\pi$
$102$	−505.513	+	65.1786i	−0.490718	+	0.0632711i
$103$	−68.3506	−	154.405i	−0.0653863	−	0.147709i	0.878732	−	0.477315i	$-0.158390\pi$
$103$	−68.3506	−	154.405i	−0.0653863	−	0.147709i	−0.944118	+	0.329607i	$0.893084\pi$
$104$	−131.369	+	575.566i	−0.123864	+	0.542682i
$105$	1.47148	+	45.8863i	0.00136764	+	0.0426480i
$106$	−17.0718	−	532.362i	−0.0156430	−	0.487807i
$107$	1157.55	+	985.438i	1.04584	+	0.890336i	0.994115	−	0.108326i	$-0.0345489\pi$
$107$	1157.55	+	985.438i	1.04584	+	0.890336i	0.0517235	+	0.998661i	$0.483529\pi$
$108$	−984.208	−	398.462i	−0.876903	−	0.355019i
$109$	678.238	−	1300.05i	0.595995	−	1.14241i	−0.380076	−	0.924955i	$-0.624102\pi$
$109$	678.238	−	1300.05i	0.595995	−	1.14241i	0.976070	−	0.217455i	$-0.0697754\pi$
$110$	−12.5602	−	55.0299i	−0.0108870	−	0.0476990i
$111$	−312.987	+	850.486i	−0.267634	+	0.727249i
$112$	−162.925	−	31.7296i	−0.137455	−	0.0267693i
$113$	−268.116	+	336.207i	−0.223206	+	0.279891i	−0.880808	−	0.473475i	$-0.843000\pi$
$113$	−268.116	+	336.207i	−0.223206	+	0.279891i	0.657602	+	0.753366i	$0.271571\pi$
$114$	110.616	−	53.2698i	0.0908783	−	0.0437647i
$115$	490.977	+	540.620i	0.398120	+	0.438375i
$116$	1902.12	−	1619.30i	1.52248	−	1.29610i
$117$	1252.75	−	415.942i	0.989889	−	0.328666i
$118$	−1788.91	−	1164.45i	−1.39561	−	0.908442i
$119$	−185.763	−	158.142i	−0.143100	−	0.121823i
$120$	24.6652	−	108.065i	0.0187635	−	0.0822080i
$121$	1110.31	+	722.731i	0.834192	+	0.542999i
$122$	−800.499	−	1320.51i	−0.594047	−	0.979943i
$123$	−674.598	+	131.378i	−0.494524	+	0.0963086i
$124$	850.969	−	223.150i	0.616284	−	0.161609i
$125$	187.530	+	1159.94i	0.134186	+	0.829987i
$126$	−142.226	−	386.474i	−0.100559	−	0.273252i
$127$	4.46306	−	2.90513i	0.00311836	−	0.00202983i	−0.543975	−	0.839102i	$-0.683081\pi$
$127$	4.46306	−	2.90513i	0.00311836	−	0.00202983i	0.547093	+	0.837072i	$0.315734\pi$
$128$	1122.79	+	540.705i	0.775321	+	0.373375i
$129$	377.104	+	472.874i	0.257381	+	0.322746i
$130$	608.348	+	1166.09i	0.410428	+	0.786713i
$131$	−586.242	−	840.422i	−0.390994	−	0.560519i	0.575306	−	0.817938i	$-0.304883\pi$
$131$	−586.242	−	840.422i	−0.390994	−	0.560519i	−0.966300	+	0.257419i	$0.917128\pi$
$132$	−27.5101	−	45.3807i	−0.0181397	−	0.0299234i
$133$	54.4699	+	22.0524i	0.0355123	+	0.0143773i
$134$	1466.95	+	3313.88i	0.945713	+	2.13638i
$135$	−514.081	+	170.687i	−0.327741	+	0.108818i
$136$	336.986	+	483.095i	0.212473	+	0.304596i
$137$	−15.5442	+	96.1464i	−0.00969366	+	0.0599587i	−0.991573	−	0.129547i	$-0.958648\pi$
$137$	−15.5442	+	96.1464i	−0.00969366	+	0.0599587i	0.981880	+	0.189506i	$0.0606885\pi$
$138$	1059.50	+	596.702i	0.653558	+	0.368077i
$139$	−144.393	+	139.837i	−0.0881097	+	0.0853295i	−0.738428	−	0.674332i	$-0.764431\pi$
$139$	−144.393	+	139.837i	−0.0881097	+	0.0853295i	0.650318	+	0.759662i	$0.274636\pi$
$140$	201.877	−	113.695i	0.121869	−	0.0686355i
$141$	−1009.90	−	130.212i	−0.603184	−	0.0777720i
$142$	−807.924	−	2722.16i	−0.477461	−	1.60872i
$143$	136.844	+	45.4355i	0.0800245	+	0.0265700i
$144$	−86.0407	−	891.902i	−0.0497921	−	0.516147i
$145$	203.388	−	1258.03i	0.116486	−	0.720506i
$146$	−2131.45	+	415.101i	−1.20822	+	0.235301i
$147$	309.264	−	592.801i	0.173522	−	0.332608i
$148$	4535.98	−	584.849i	2.51929	−	0.324826i
$149$	−1470.99	+	1252.28i	−0.808782	+	0.688526i	−0.953648	−	0.300925i	$-0.902705\pi$
$149$	−1470.99	+	1252.28i	−0.808782	+	0.688526i	0.144866	+	0.989451i	$0.453725\pi$
$150$	395.355	+	757.821i	0.215204	+	0.412506i
$151$	37.2783	+	386.429i	0.0200905	+	0.208259i	0.999963	+	0.00863343i	$0.00274814\pi$
$151$	37.2783	+	386.429i	0.0200905	+	0.208259i	−0.979872	+	0.199626i	$0.936027\pi$
$152$	−113.705	−	84.8603i	−0.0606757	−	0.0452834i
$153$	533.091	−	1204.26i	0.281685	−	0.636332i
$154$	12.7993	−	43.1251i	0.00669739	−	0.0225657i
$155$	256.763	−	368.089i	0.133056	−	0.190746i
$156$	888.273	+	860.244i	0.455889	+	0.441504i
$157$	2419.68	−	979.622i	1.23001	−	0.497977i	0.334239	−	0.942488i	$-0.391521\pi$
$157$	2419.68	−	979.622i	1.23001	−	0.497977i	0.895773	+	0.444512i	$0.146623\pi$
$158$	−1273.15	−	950.175i	−0.641052	−	0.478429i
$159$	−222.591	−	125.361i	−0.111023	−	0.0625268i
$160$	1280.80	−	335.866i	0.632853	−	0.165954i
$161$	129.510	+	567.422i	0.0633965	+	0.277758i
$162$	1389.52	−	1037.03i	0.673896	−	0.502942i
$163$	1927.07	+	2121.92i	0.926011	+	1.01964i	0.999750	+	0.0223635i	$0.00711911\pi$
$163$	1927.07	+	2121.92i	0.926011	+	1.01964i	−0.0737389	+	0.997278i	$0.523493\pi$
$164$	2162.53	+	2711.72i	1.02966	+	1.29116i
$165$	−25.6932	−	8.53073i	−0.0121225	−	0.00402495i
$166$	−5062.76	+	2049.69i	−2.36715	+	0.958352i
$167$	−63.8244	+	661.606i	−0.0295741	+	0.306567i	0.968719	+	0.248161i	$0.0798262\pi$
$167$	−63.8244	+	661.606i	−0.0295741	+	0.306567i	−0.998293	+	0.0584057i	$0.981398\pi$
$168$	59.3900	−	65.3950i	0.0272740	−	0.0300317i
$169$	−1160.41	−	74.5008i	−0.528179	−	0.0339102i
$170$	1269.31	+	332.853i	0.572657	+	0.150168i
$171$	−30.4614	+	315.764i	−0.0136225	+	0.141211i
$172$	1235.54	−	2791.11i	0.547729	−	1.23733i
$173$	1514.99	−	1467.19i	0.665796	−	0.644787i	−0.283573	−	0.958951i	$-0.591520\pi$
$173$	1514.99	−	1467.19i	0.665796	−	0.644787i	0.949369	+	0.314163i	$0.101724\pi$
$174$	−338.652	−	2094.68i	−0.147547	−	0.912628i
$175$	−141.295	+	383.943i	−0.0610335	+	0.165848i
$176$	50.7398	−	83.7007i	0.0217310	−	0.0358476i
$177$	−922.376	+	444.193i	−0.391695	+	0.188630i
$178$	3755.02	+	1808.32i	1.58118	+	0.761457i
$179$	1002.23	+	3376.86i	0.418495	+	1.41005i	0.858851	+	0.512225i	$0.171178\pi$
$179$	1002.23	+	3376.86i	0.418495	+	1.41005i	−0.440357	+	0.897823i	$0.645148\pi$
$180$	898.470	+	870.119i	0.372044	+	0.360305i
$181$	−3810.49	−	999.227i	−1.56481	−	0.410342i	−0.633258	−	0.773941i	$-0.718283\pi$
$181$	−3810.49	−	999.227i	−1.56481	−	0.410342i	−0.931556	+	0.363598i	$0.881548\pi$
$182$	−33.5961	+	1047.65i	−0.0136830	+	0.426687i
$183$	−740.632			−0.299175
$184$	45.0392	−	1404.49i	0.0180453	−	0.562719i
$185$	1568.59	−	1727.19i	0.623377	−	0.686407i
$186$	212.618	−	716.382i	0.0838169	−	0.282407i
$187$	125.348	−	70.5947i	0.0490179	−	0.0276064i
$188$	1774.76	+	4822.61i	0.688500	+	1.87088i
$189$	−423.733	−	82.5220i	−0.163080	−	0.0317598i
$190$	−315.436	+	20.2517i	−0.120443	+	0.00773269i
$191$	1738.88	−	2180.49i	0.658748	−	0.826044i	−0.334458	−	0.942411i	$-0.608553\pi$
$191$	1738.88	−	2180.49i	0.658748	−	0.826044i	0.993206	+	0.116367i	$0.0371248\pi$
$192$	1305.35	−	849.687i	0.490653	−	0.319380i
$193$	−3235.41	−	417.159i	−1.20668	−	0.155584i	−0.501847	−	0.864956i	$-0.667346\pi$
$193$	−3235.41	−	417.159i	−1.20668	−	0.155584i	−0.704834	+	0.709372i	$0.748979\pi$
$194$	−1768.87	+	2535.81i	−0.654626	+	0.938456i
$195$	629.522	+	40.4167i	0.231185	+	0.0148426i
$196$	−3374.31			−1.22970
$197$	817.791	−	2641.32i	0.295762	−	0.955262i
$197$	817.791	−	2641.32i	0.295762	−	0.955262i
$198$	242.840			0.0871611
$199$	850.583	+	54.6093i	0.302996	+	0.0194530i	0.214826	−	0.976652i	$-0.431082\pi$
$199$	850.583	+	54.6093i	0.302996	+	0.0194530i	0.0881705	+	0.996105i	$0.471898\pi$
$200$	565.119	−	810.140i	0.199800	−	0.286428i
$201$	1723.91	+	222.273i	0.604951	+	0.0779998i
$202$	3814.05	−	2482.67i	1.32849	−	0.864753i
$203$	633.224	−	794.038i	0.218934	−	0.274535i
$204$	1231.18	−	79.0446i	0.422549	−	0.0271286i
$205$	1736.77	+	338.236i	0.591713	+	0.115236i
$206$	249.990	+	679.305i	0.0845518	+	0.229754i
$207$	−2737.59	+	1541.78i	−0.919207	+	0.517688i
$208$	−648.922	+	2186.43i	−0.216321	+	0.728856i
$209$	−23.2970	+	25.6526i	−0.00771046	+	0.00849007i
$210$	6.30784	−	196.702i	0.00207277	−	0.0646367i
$211$	−4229.14			−1.37984			−0.689920	−	0.723886i	$-0.742354\pi$
$211$	−4229.14			−1.37984			−0.689920	+	0.723886i	$0.742354\pi$
$212$	−41.3222	+	1288.58i	−0.0133869	+	0.417452i
$213$	−1317.36	−	345.453i	−0.423775	−	0.111127i
$214$	−4681.25	−	4533.54i	−1.49535	−	1.44816i
$215$	−443.051	−	1492.78i	−0.140539	−	0.473521i
$216$	939.060	+	452.228i	0.295810	+	0.142455i
$217$	322.251	−	155.188i	0.100810	−	0.0485476i
$218$	−3258.50	+	5375.24i	−1.01236	+	1.66999i
$219$	−359.698	+	977.416i	−0.110987	+	0.301587i
$220$	21.8053	+	134.874i	0.00668233	+	0.0413326i
$221$	−2407.99	+	2332.01i	−0.732935	+	0.709808i
$222$	1572.52	−	3552.34i	0.475407	−	1.07395i
$223$	−185.963	+	1927.70i	−0.0558431	+	0.578872i	0.924447	+	0.381310i	$0.124527\pi$
$223$	−185.963	+	1927.70i	−0.0558431	+	0.578872i	−0.980290	+	0.197562i	$0.936698\pi$
$224$	1020.75	+	267.672i	0.304471	+	0.0798418i
$225$	−2204.00	−	141.502i	−0.653038	−	0.0419265i
$226$	1239.32	−	1364.63i	0.364771	−	0.401653i
$227$	252.822	−	2620.77i	0.0739225	−	0.766284i	−0.881724	−	0.471766i	$-0.843617\pi$
$227$	252.822	−	2620.77i	0.0739225	−	0.766284i	0.955646	−	0.294518i	$-0.0951589\pi$
$228$	−275.456	+	111.520i	−0.0800110	+	0.0323929i
$229$	−3622.96	−	1202.90i	−1.04547	−	0.347119i	−0.259730	−	0.965681i	$-0.583634\pi$
$229$	−3622.96	−	1202.90i	−1.04547	−	0.347119i	−0.785736	+	0.618563i	$0.787715\pi$
$230$	−1951.87	−	2447.57i	−0.559577	−	0.701688i
$231$	−14.5053	−	15.9719i	−0.00413150	−	0.00454924i
$232$	−1965.14	+	1466.62i	−0.556110	+	0.415036i
$233$	−924.002	−	4048.32i	−0.259800	−	1.13826i	−0.921466	−	0.388459i	$-0.873007\pi$
$233$	−924.002	−	4048.32i	−0.259800	−	1.13826i	0.661666	−	0.749799i	$-0.269850\pi$
$234$	−5473.40	+	1435.30i	−1.52909	+	0.400975i
$235$	2284.19	+	1286.43i	0.634061	+	0.357097i
$236$	4140.55	+	3090.17i	1.14206	+	0.852344i
$237$	−706.257	+	285.932i	−0.193571	+	0.0783682i
$238$	751.244	+	727.539i	0.204605	+	0.198149i
$239$	−3658.68	+	5245.00i	−0.990212	+	1.41954i	−0.0841233	+	0.996455i	$0.526809\pi$
$239$	−3658.68	+	5245.00i	−0.990212	+	1.41954i	−0.906089	+	0.423088i	$0.860946\pi$
$240$	121.838	−	410.514i	0.0327693	−	0.110411i
$241$	449.990	−	1016.54i	0.120276	−	0.271705i	−0.844127	−	0.536144i	$-0.819881\pi$
$241$	449.990	−	1016.54i	0.120276	−	0.271705i	0.964402	+	0.264439i	$0.0851867\pi$
$242$	−4551.31	−	3396.73i	−1.20896	−	0.902273i
$243$	−345.164	−	3577.98i	−0.0911204	−	0.944558i
$244$	1728.83	+	3313.85i	0.453595	+	0.869457i
$245$	−1310.74	+	1115.85i	−0.341797	+	0.290976i
$246$	2921.95	−	376.744i	0.757305	−	0.0976437i
$247$	373.475	−	715.882i	0.0962091	−	0.184415i
$248$	−847.634	+	165.077i	−0.217036	+	0.0422677i
$249$	−418.100	+	2586.09i	−0.106410	+	0.658181i
$250$	−483.659	−	5013.64i	−0.122357	−	1.26836i
$251$	−609.434	−	202.346i	−0.153255	−	0.0508843i	0.237452	−	0.971399i	$-0.423688\pi$
$251$	−609.434	−	202.346i	−0.153255	−	0.0508843i	−0.390707	+	0.920515i	$0.627769\pi$
$252$	283.614	+	955.591i	0.0708969	+	0.238875i
$253$	−340.387	−	43.8881i	−0.0845849	−	0.0109060i
$254$	−19.8905	+	11.2021i	−0.00491354	+	0.00276725i
$255$	452.111	−	437.845i	0.111029	−	0.107525i
$256$	625.864	+	352.480i	0.152799	+	0.0860546i
$257$	810.392	−	5012.56i	0.196696	−	1.21663i	−0.679134	−	0.734014i	$-0.737644\pi$
$257$	810.392	−	5012.56i	0.196696	−	1.21663i	0.875830	−	0.482620i	$-0.160315\pi$
$258$	−1483.34	−	2126.49i	−0.357942	−	0.513136i
$259$	1764.71	−	585.923i	0.423372	−	0.140569i
$260$	−1288.64	−	2911.05i	−0.307376	−	0.694368i
$261$	5081.92	+	2057.44i	1.20522	+	0.487940i
$262$	2277.07	+	3756.27i	0.536938	+	0.885736i
$263$	558.177	+	800.189i	0.130869	+	0.187611i	0.880225	−	0.474557i	$-0.157392\pi$
$263$	558.177	+	800.189i	0.130869	+	0.187611i	−0.749355	+	0.662168i	$0.769637\pi$
$264$	24.0945	+	46.1846i	0.00561710	+	0.0107669i
$265$	410.069	+	514.210i	0.0950578	+	0.119199i
$266$	−226.961	−	109.298i	−0.0523152	−	0.0251937i
$267$	1675.30	−	1090.50i	0.383995	−	0.249953i
$268$	−3029.54	−	8232.23i	−0.690516	−	1.87636i
$269$	−329.497	−	2038.06i	−0.0746833	−	0.461943i	−0.997123	−	0.0758014i	$-0.975849\pi$
$269$	−329.497	−	2038.06i	−0.0746833	−	0.461943i	0.922440	−	0.386141i	$-0.126192\pi$
$270$	2246.07	−	588.990i	0.506265	−	0.132758i
$271$	−372.237	+	72.4931i	−0.0834383	+	0.0162496i	−0.232705	−	0.972547i	$-0.574758\pi$
$271$	−372.237	+	72.4931i	−0.0834383	+	0.0162496i	0.149267	+	0.988797i	$0.452309\pi$
$272$	1179.59	+	1945.86i	0.262953	+	0.433769i
$273$	421.337	+	274.260i	0.0934084	+	0.0608021i
$274$	92.9035	−	407.037i	0.0204836	−	0.0897445i
$275$	−183.699	−	156.385i	−0.0402817	−	0.0342923i
$276$	−2466.71	−	1605.65i	−0.537967	−	0.350177i
$277$	−6196.44	+	2057.36i	−1.34407	+	0.446263i	−0.894534	−	0.446999i	$-0.852493\pi$
$277$	−6196.44	+	2057.36i	−1.34407	+	0.446263i	−0.449537	+	0.893262i	$0.648411\pi$
$278$	656.106	−	558.552i	0.141549	−	0.120503i
$279$	1298.09	+	1429.35i	0.278548	+	0.306712i
$280$	−204.907	+	98.6779i	−0.0437340	+	0.0210612i
$281$	−1222.75	+	1533.27i	−0.259583	+	0.325507i	−0.894495	−	0.447077i	$-0.852465\pi$
$281$	−1222.75	+	1533.27i	−0.259583	+	0.325507i	0.634912	+	0.772584i	$0.281036\pi$
$282$	4284.50	+	834.407i	0.904746	+	0.176199i
$283$	1224.12	−	3326.33i	0.257125	−	0.698692i	−0.742460	−	0.669890i	$-0.766341\pi$
$283$	1224.12	−	3326.33i	0.257125	−	0.698692i	0.999585	−	0.0288017i	$-0.00916912\pi$
$284$	1529.40	+	6700.73i	0.319553	+	1.40005i
$285$	−70.1217	+	134.410i	−0.0145742	+	0.0279361i
$286$	−572.929	−	231.953i	−0.118455	−	0.0479570i
$287$	1073.74	+	914.091i	0.220840	+	0.188004i
$288$	182.586	+	5693.71i	0.0373576	+	1.16495i
$289$	−50.2748	−	1567.75i	−0.0102330	−	0.319103i
$290$	−1215.59	+	5325.86i	−0.246145	+	1.07843i
$291$	600.253	+	1355.98i	0.120919	+	0.273158i
$292$	5212.94	−	672.134i	1.04474	−	0.134704i
$293$	−5541.67	+	4135.85i	−1.10494	+	0.824639i	−0.985747	−	0.168232i	$-0.946194\pi$
$293$	−5541.67	+	4135.85i	−1.10494	+	0.824639i	−0.119193	+	0.992871i	$0.538031\pi$
$294$	−1485.82	+	2451.01i	−0.294744	+	0.486211i
$295$	2630.28	−	168.870i	0.519121	−	0.0333287i
$296$	−4480.18	+	287.637i	−0.879746	+	0.0564816i
$297$	131.964	−	217.688i	0.0257822	−	0.0425305i
$298$	6636.72	−	4953.11i	1.29012	−	0.962840i
$299$	7931.43	−	1022.64i	1.53407	−	0.197796i
$300$	−837.463	−	1891.84i	−0.161170	−	0.364086i
$301$	276.144	−	1209.87i	0.0528794	−	0.231680i
$302$	−53.3403	−	1663.35i	−0.0101635	−	0.316937i
$303$	−69.9594	−	2181.59i	−0.0132642	−	0.413628i
$304$	−417.357	−	355.302i	−0.0787404	−	0.0670327i
$305$	1767.42	+	715.549i	0.331811	+	0.134335i
$306$	−2611.27	+	5005.31i	−0.487831	+	0.935080i
$307$	−456.399	−	1999.62i	−0.0848472	−	0.371740i	0.914622	−	0.404309i	$-0.132488\pi$
$307$	−456.399	−	1999.62i	−0.0848472	−	0.371740i	−0.999469	+	0.0325696i	$0.989631\pi$
$308$	−37.6049	+	102.185i	−0.00695693	+	0.0189042i
$309$	340.770	+	66.3650i	0.0627371	+	0.0122180i
$310$	−1199.51	+	1504.13i	−0.219766	+	0.275578i
$311$	9079.67	−	4372.54i	1.65550	−	0.797248i	0.656420	−	0.754395i	$-0.272070\pi$
$311$	9079.67	−	4372.54i	1.65550	−	0.797248i	0.999081	−	0.0428523i	$-0.0136445\pi$
$312$	−816.041	−	898.551i	−0.148074	−	0.163046i
$313$	−5164.88	+	4396.92i	−0.932703	+	0.794022i	−0.978780	−	0.204916i	$-0.934308\pi$
$313$	−5164.88	+	4396.92i	−0.932703	+	0.794022i	0.0460762	+	0.998938i	$0.485328\pi$
$314$	−10620.3	+	3526.17i	−1.90871	+	0.633736i
$315$	426.174	+	277.409i	0.0762292	+	0.0496197i
$316$	2927.96	+	2492.61i	0.521235	+	0.443734i
$317$	2327.58	−	10197.8i	0.412397	−	1.80683i	−0.160306	−	0.987067i	$-0.551248\pi$
$317$	2327.58	−	10197.8i	0.412397	−	1.80683i	0.572703	−	0.819763i	$-0.305895\pi$
$318$	917.794	+	597.418i	0.161847	+	0.105351i
$319$	310.461	+	512.138i	0.0544906	+	0.0898879i
$320$	−3935.95	+	766.526i	−0.687582	+	0.133907i
$321$	−3023.33	+	792.811i	−0.525688	+	0.137852i
$322$	−398.191	−	2462.95i	−0.0689140	−	0.426257i
$323$	−278.226	−	756.029i	−0.0479285	−	0.130237i
$324$	−3517.24	+	2289.47i	−0.603093	+	0.392570i
$325$	5064.72	+	2439.04i	0.864431	+	0.416288i
$326$	−7661.05	−	9606.65i	−1.30155	−	1.63210i
$327$	1394.46	+	2672.93i	0.235823	+	0.452028i
$328$	−1947.84	−	2792.38i	−0.327901	−	0.470071i
$329$	1083.06	+	1786.61i	0.181492	+	0.299389i
$330$	107.570	+	43.5504i	0.0179441	+	0.00726475i
$331$	2107.67	+	4761.26i	0.349994	+	0.790642i	0.999540	+	0.0303202i	$0.00965271\pi$
$331$	2107.67	+	4761.26i	0.349994	+	0.790642i	−0.649546	+	0.760322i	$0.725041\pi$
$332$	12547.1	−	4165.91i	2.07412	−	0.688657i
$333$	5742.80	+	8232.73i	0.945055	+	1.35481i
$334$	454.746	−	2812.76i	0.0744988	−	0.460801i
$335$	−3899.14	−	2195.95i	−0.635918	−	0.358142i
$336$	245.150	−	237.414i	0.0398036	−	0.0385476i
$337$	−332.733	+	187.392i	−0.0537838	+	0.0302904i	−0.517376	−	0.855758i	$-0.673091\pi$
$337$	−332.733	+	187.392i	−0.0537838	+	0.0302904i	0.463592	+	0.886049i	$0.346560\pi$
$338$	4943.67	+	637.416i	0.795563	+	0.102576i
$339$	−251.561	−	847.593i	−0.0403036	−	0.135796i
$340$	−3014.42	−	1000.86i	−0.480824	−	0.159645i
$341$	20.2526	+	209.939i	0.00321624	+	0.0333397i
$342$	217.036	−	1342.44i	0.0343157	−	0.212255i
$343$	−2766.84	+	538.842i	−0.435555	+	0.0848243i
$344$	−1385.86	+	2656.44i	−0.217211	+	0.416354i
$345$	−1489.16	+	192.006i	−0.232388	+	0.0299631i
$346$	−6883.96	+	5860.40i	−1.06961	+	0.910570i
$347$	−4137.11	−	7930.07i	−0.640034	−	1.22682i	−0.960160	−	0.279450i	$-0.909848\pi$
$347$	−4137.11	−	7930.07i	−0.640034	−	1.22682i	0.320127	−	0.947375i	$-0.396275\pi$
$348$	493.173	+	5112.26i	0.0759680	+	0.787488i
$349$	471.276	+	351.722i	0.0722832	+	0.0539463i	0.633644	−	0.773625i	$-0.281559\pi$
$349$	471.276	+	351.722i	0.0722832	+	0.0539463i	−0.561360	+	0.827571i	$0.689722\pi$
$350$	709.896	−	1603.67i	0.108416	−	0.244913i
$351$	−1687.71	+	5686.47i	−0.256648	+	0.864732i
$352$	−356.012	+	510.370i	−0.0539077	+	0.0772807i
$353$	−1744.44	−	1689.39i	−0.263023	−	0.254723i	0.552413	−	0.833570i	$-0.313707\pi$
$353$	−1744.44	−	1689.39i	−0.263023	−	0.254723i	−0.815436	+	0.578847i	$0.803503\pi$
$354$	4067.84	−	1646.89i	0.610744	−	0.247263i
$355$	2809.96	+	2097.13i	0.420104	+	0.313532i
$356$	−8789.88	−	4950.37i	−1.30860	−	0.736991i
$357$	485.182	−	127.230i	0.0719287	−	0.0188619i
$358$	−3360.01	−	14721.2i	−0.496040	−	2.17329i
$359$	−3128.92	+	2335.17i	−0.459995	+	0.343303i	−0.802948	−	0.596050i	$-0.796736\pi$
$359$	−3128.92	+	2335.17i	−0.459995	+	0.343303i	0.342953	+	0.939353i	$0.388573\pi$
$360$	−825.408	−	908.866i	−0.120841	−	0.133060i
$361$	−4155.53	−	5210.87i	−0.605850	−	0.759712i
$362$	16026.5	+	5321.16i	2.32689	+	0.772580i
$363$	−2524.76	+	1022.16i	−0.365057	+	0.147795i
$364$	243.623	−	2525.41i	0.0350806	−	0.363647i
$365$	1802.69	−	1984.96i	0.258512	−	0.284651i
$366$	3168.36	+	203.415i	0.452494	+	0.0290511i
$367$	−3275.16	−	858.849i	−0.465837	−	0.122157i	0.0132728	−	0.999912i	$-0.495775\pi$
$367$	−3275.16	−	858.849i	−0.465837	−	0.122157i	−0.479109	+	0.877755i	$0.659040\pi$
$368$	521.270	−	5403.50i	0.0738398	−	0.765427i
$369$	−3081.36	+	6960.85i	−0.434714	+	0.982025i
$370$	−7184.65	+	6957.94i	−1.00949	+	0.977638i
$371$	83.6558	+	517.440i	0.0117067	+	0.0724102i
$372$	−624.681	+	1697.46i	−0.0870651	+	0.236584i
$373$	−5585.45	+	9213.79i	−0.775345	+	1.27901i	0.180042	+	0.983659i	$0.442376\pi$
$373$	−5585.45	+	9213.79i	−0.775345	+	1.27901i	−0.955388	+	0.295354i	$0.904562\pi$
$374$	−555.617	+	267.571i	−0.0768189	+	0.0369940i
$375$	−2176.58	−	1048.18i	−0.299728	−	0.144341i
$376$	−1435.24	−	4835.79i	−0.196853	−	0.663263i
$377$	−10024.5	−	9708.18i	−1.36946	−	1.32625i
$378$	1790.03	+	469.401i	0.243569	+	0.0638713i
$379$	−111.572	+	3479.24i	−0.0151216	+	0.471547i	0.963719	+	0.266921i	$0.0860061\pi$
$379$	−111.572	+	3479.24i	−0.0151216	+	0.471547i	−0.978840	+	0.204626i	$0.934402\pi$
$380$	765.083			0.103284
$381$	−0.350928	+	10.9432i	−4.71878e−5	+	0.00147149i
$382$	−8037.64	+	8850.34i	−1.07655	+	1.18540i
$383$	−1445.40	+	4870.02i	−0.192836	+	0.649729i	0.805528	+	0.592558i	$0.201882\pi$
$383$	−1445.40	+	4870.02i	−0.192836	+	0.649729i	−0.998364	+	0.0571717i	$0.981792\pi$
$384$	−2232.49	+	1257.31i	−0.296683	+	0.167089i
$385$	19.1839	+	52.1289i	0.00253949	+	0.00690061i
$386$	13726.2	+	2673.18i	1.80996	+	0.352490i
$387$	6685.45	−	429.220i	0.878140	−	0.0563785i
$388$	4665.99	−	5850.97i	0.610515	−	0.765562i
$389$	−11451.8	+	7454.29i	−1.49262	+	0.971587i	−0.498089	+	0.867126i	$0.665965\pi$
$389$	−11451.8	+	7454.29i	−1.49262	+	0.971587i	−0.994529	+	0.104461i	$0.966688\pi$
$390$	−2681.94	−	345.798i	−0.348219	−	0.0448979i
$391$	4564.80	−	6543.98i	0.590414	−	0.846402i
$392$	3305.44	+	212.216i	0.425892	+	0.0273432i
$393$	2106.77			0.270414
$394$	−4223.88	+	11074.7i	−0.540091	+	1.41609i
$395$	1961.64			0.249875
$396$	−586.585	−	37.6600i	−0.0744369	−	0.00477901i
$397$	7425.86	−	10645.5i	0.938774	−	1.34580i	0.000467259	−	1.00000i	$-0.499851\pi$
$397$	7425.86	−	10645.5i	0.938774	−	1.34580i	0.938307	−	0.345804i	$-0.112394\pi$
$398$	−3623.72	−	467.227i	−0.456384	−	0.0588442i
$399$	−101.258	+	65.9119i	−0.0127049	+	0.00826997i
$400$	2379.20	−	2983.42i	0.297399	−	0.372927i
$401$	4766.61	−	306.026i	0.593599	−	0.0381103i	0.235628	−	0.971843i	$-0.424285\pi$
$401$	4766.61	−	306.026i	0.593599	−	0.0381103i	0.357970	+	0.933733i	$0.383469\pi$
$402$	−7313.68	−	1424.34i	−0.907396	−	0.176715i
$403$	−1697.31	−	4612.14i	−0.209799	−	0.570092i
$404$	−9597.92	+	5405.45i	−1.18197	+	0.665671i
$405$	−609.158	+	2052.46i	−0.0747391	+	0.251821i
$406$	−2926.96	+	3222.91i	−0.357790	+	0.393966i
$407$	−35.1439	+	1095.92i	−0.00428015	+	0.133471i
$408$	−1211.03			−0.146948
$409$	157.775	−	4920.02i	0.0190745	−	0.594815i	−0.944675	−	0.328007i	$-0.893623\pi$
$409$	157.775	−	4920.02i	0.0190745	−	0.594815i	0.963750	−	0.266808i	$-0.0859688\pi$
$410$	−7336.85	−	1923.95i	−0.883759	−	0.231749i
$411$	−143.846	−	139.307i	−0.0172637	−	0.0167190i
$412$	−498.509	−	1679.64i	−0.0596111	−	0.200850i
$413$	1892.52	+	911.390i	0.225484	+	0.108587i
$414$	12134.6	−	5843.73i	1.44054	−	0.693729i
$415$	3496.25	−	5767.43i	0.413552	−	0.682198i
$416$	5007.68	−	13607.5i	0.590196	−	1.60375i
$417$	−65.9581	−	407.974i	−0.00774576	−	0.0479103i
$418$	106.708	−	103.341i	0.0124863	−	0.0120923i
$419$	325.156	−	734.533i	0.0379115	−	0.0856427i	−0.894454	−	0.447161i	$-0.852435\pi$
$419$	325.156	−	734.533i	0.0379115	−	0.0856427i	0.932365	+	0.361518i	$0.117741\pi$
$420$	−45.7415	+	474.158i	−0.00531418	+	0.0550870i
$421$	692.600	+	181.621i	0.0801787	+	0.0210253i	0.293526	−	0.955951i	$-0.405171\pi$
$421$	692.600	+	181.621i	0.0801787	+	0.0210253i	−0.213347	+	0.976976i	$0.568437\pi$
$422$	18091.9	+	1161.54i	2.08697	+	0.133988i
$423$	−7582.53	+	8349.21i	−0.871572	+	0.959698i
$424$	121.520	−	1259.68i	0.0139187	−	0.144282i
$425$	5198.66	−	2104.70i	0.593346	−	0.240219i
$426$	5540.68	+	1839.63i	0.630157	+	0.209226i
$427$	947.468	+	1188.09i	0.107380	+	0.134650i
$428$	10604.6	+	11676.8i	1.19765	+	1.31874i
$429$	−237.584	+	177.314i	−0.0267382	+	0.0199552i
$430$	1485.34	+	6507.69i	0.166580	+	0.729834i
$431$	9964.14	−	2612.91i	1.11359	−	0.292017i	0.349375	−	0.936983i	$-0.386394\pi$
$431$	9964.14	−	2612.91i	1.11359	−	0.292017i	0.764211	+	0.644966i	$0.223129\pi$
$432$	3508.38	+	1975.88i	0.390734	+	0.220057i
$433$	3181.43	+	2374.36i	0.353094	+	0.263521i	0.759964	−	0.649965i	$-0.225216\pi$
$433$	3181.43	+	2374.36i	0.353094	+	0.263521i	−0.406870	+	0.913486i	$0.633380\pi$
$434$	−1421.18	+	575.373i	−0.157187	+	0.0636378i
$435$	1882.15	+	1822.76i	0.207453	+	0.200907i
$436$	8704.58	−	12478.7i	0.956132	−	1.37069i
$437$	−546.836	+	1842.47i	−0.0598597	+	0.201687i
$438$	1807.21	−	4082.51i	0.197150	−	0.445365i
$439$	12660.9	+	9449.09i	1.37648	+	1.02729i	0.994677	+	0.103045i	$0.0328586\pi$
$439$	12660.9	+	9449.09i	1.37648	+	1.02729i	0.381799	+	0.924245i	$0.375305\pi$
$440$	−12.8778	−	133.492i	−0.00139529	−	0.0144636i
$441$	−3425.47	−	6565.99i	−0.369882	−	0.708994i
$442$	10941.6	−	9314.76i	1.17747	−	1.00239i
$443$	−8250.71	+	1063.81i	−0.884883	+	0.114093i	−0.556889	−	0.830587i	$-0.688005\pi$
$443$	−8250.71	+	1063.81i	−0.884883	+	0.114093i	−0.327994	+	0.944680i	$0.606372\pi$
$444$	−4349.35	+	8336.88i	−0.464889	+	0.891106i
$445$	−5051.45	+	983.769i	−0.538116	+	0.104798i
$446$	1324.98	−	8195.47i	0.140672	−	0.870105i
$447$	−381.393	−	3953.54i	−0.0403563	−	0.418335i
$448$	−3032.92	−	1007.00i	−0.319848	−	0.106197i
$449$	−134.994	−	454.840i	−0.0141888	−	0.0478067i	0.951275	−	0.308342i	$-0.0997743\pi$
$449$	−134.994	−	454.840i	−0.0141888	−	0.0478067i	−0.965464	+	0.260536i	$0.916101\pi$
$450$	9389.68	+	1210.66i	0.983630	+	0.126825i
$451$	−724.534	+	408.050i	−0.0756474	+	0.0426038i
$452$	−3205.22	+	3104.09i	−0.333542	+	0.323018i
$453$	−695.478	−	391.686i	−0.0721334	−	0.0406248i
$454$	−1801.35	+	11142.0i	−0.186215	+	1.15180i
$455$	−740.494	−	1061.55i	−0.0762965	−	0.109377i
$456$	276.847	−	91.9197i	0.0284311	−	0.00943976i
$457$	4899.39	+	11067.8i	0.501496	+	1.13289i	0.968586	+	0.248678i	$0.0799962\pi$
$457$	4899.39	+	11067.8i	0.501496	+	1.13289i	−0.467090	+	0.884210i	$0.654698\pi$
$458$	15168.3	+	6140.97i	1.54753	+	0.626525i
$459$	3067.88	+	5060.79i	0.311975	+	0.514635i
$460$	4335.22	+	6214.86i	0.439414	+	0.629933i
$461$	102.048	+	195.607i	0.0103099	+	0.0197621i	0.891699	−	0.452628i	$-0.149514\pi$
$461$	102.048	+	195.607i	0.0103099	+	0.0197621i	−0.881389	+	0.472391i	$0.843391\pi$
$462$	57.6656	+	72.3104i	0.00580703	+	0.00728178i
$463$	11.8398	+	5.70175i	0.00118843	+	0.000572317i	0.434478	−	0.900683i	$-0.356933\pi$
$463$	11.8398	+	5.70175i	0.00118843	+	0.000572317i	−0.433289	+	0.901255i	$0.642647\pi$
$464$	−7939.10	+	5167.78i	−0.794318	+	0.517044i
$465$	318.678	+	865.951i	0.0317814	+	0.0863603i
$466$	2840.93	+	17572.1i	0.282411	+	1.74681i
$467$	3859.89	−	1012.18i	0.382472	−	0.100296i	−0.0574120	−	0.998351i	$-0.518285\pi$
$467$	3859.89	−	1012.18i	0.382472	−	0.100296i	0.439884	+	0.898055i	$0.355020\pi$
$468$	13443.7	−	2618.16i	1.32785	−	0.258599i
$469$	−1848.78	−	3049.76i	−0.182023	−	0.300266i
$470$	−9418.26	−	6130.61i	−0.924323	−	0.601668i
$471$	−1194.30	+	5232.58i	−0.116838	+	0.511899i
$472$	−3861.69	−	3287.51i	−0.376587	−	0.320593i
$473$	613.303	+	399.216i	0.0596188	+	0.0388075i
$474$	3099.84	−	1029.22i	0.300380	−	0.0997332i
$475$	−1028.69	+	875.738i	−0.0993676	+	0.0845929i
$476$	−1701.82	−	1873.89i	−0.163871	−	0.180440i
$477$	−2549.36	+	1227.71i	−0.244711	+	0.117847i
$478$	17092.1	−	21432.8i	1.63551	−	2.05086i
$479$	2144.87	+	417.714i	0.204596	+	0.0398451i	0.292416	−	0.956291i	$-0.405541\pi$
$479$	2144.87	+	417.714i	0.204596	+	0.0398451i	−0.0878194	+	0.996136i	$0.527990\pi$
$480$	−940.216	+	2554.87i	−0.0894058	+	0.242944i
$481$	−5685.25	−	24908.7i	−0.538930	−	2.36121i
$482$	−2204.21	+	4225.06i	−0.208297	+	0.399266i
$483$	−1109.17	−	449.055i	−0.104491	−	0.0423037i
$484$	10467.0	+	8910.68i	0.983001	+	0.836841i
$485$	−122.365	−	3815.80i	−0.0114563	−	0.357250i
$486$	493.883	+	15401.1i	0.0460967	+	1.43746i
$487$	2845.77	−	12468.1i	0.264793	−	1.16013i	−0.651189	−	0.758915i	$-0.725730\pi$
$487$	2845.77	−	12468.1i	0.264793	−	1.16013i	0.915982	−	0.401218i	$-0.131413\pi$
$488$	−1485.13	−	3354.94i	−0.137764	−	0.311211i
$489$	−5844.93	+	753.620i	−0.540525	+	0.0696930i
$490$	5913.71	−	4413.52i	0.545213	−	0.406903i
$491$	−5044.50	+	8321.44i	−0.463656	+	0.764850i	−0.996694	−	0.0812415i	$-0.974111\pi$
$491$	−5044.50	+	8321.44i	−0.463656	+	0.764850i	0.533038	+	0.846091i	$0.321050\pi$
$492$	−7116.46	+	456.892i	−0.652103	+	0.0418664i
$493$	−13894.4	+	892.047i	−1.26931	+	0.0814925i
$494$	−1794.31	+	2959.90i	−0.163421	+	0.269580i
$495$	−240.311	+	179.349i	−0.0218206	+	0.0162851i
$496$	−3308.70	+	426.610i	−0.299526	+	0.0386196i
$497$	1131.10	+	2555.18i	0.102086	+	0.230615i
$498$	2498.87	−	10948.2i	0.224853	−	0.985146i
$499$	98.6841	+	3077.33i	0.00885312	+	0.276073i	0.994335	+	0.106292i	$0.0338978\pi$
$499$	98.6841	+	3077.33i	0.00885312	+	0.276073i	−0.985482	+	0.169781i	$0.945694\pi$
$500$	390.766	+	12185.5i	0.0349512	+	1.08991i
$501$	−1040.58	−	885.859i	−0.0927938	−	0.0789965i
$502$	2551.53	+	1033.00i	0.226853	+	0.0918427i
$503$	5124.17	−	9822.08i	0.454226	−	0.870666i	−0.545249	−	0.838274i	$-0.683565\pi$
$503$	5124.17	−	9822.08i	0.454226	−	0.870666i	0.999475	−	0.0323921i	$-0.0103125\pi$
$504$	−217.727	−	953.924i	−0.0192427	−	0.0843078i
$505$	−1940.76	+	5273.68i	−0.171015	+	0.464704i
$506$	1444.09	+	281.237i	0.126873	+	0.0247085i
$507$	1490.59	−	1869.15i	0.130571	−	0.163731i
$508$	49.7830	−	23.9742i	0.00434796	−	0.00209387i
$509$	−5203.14	−	5729.23i	−0.453094	−	0.498907i	0.470435	−	0.882435i	$-0.344097\pi$
$509$	−5203.14	−	5729.23i	−0.453094	−	0.498907i	−0.923529	+	0.383527i	$0.874709\pi$
$510$	−2054.35	+	1748.89i	−0.178369	+	0.151847i
$511$	2028.08	−	673.368i	0.175571	−	0.0582936i
$512$	−10936.0	−	7118.53i	−0.943957	−	0.614448i
$513$	−1085.46	−	924.066i	−0.0934196	−	0.0795293i
$514$	−4843.49	+	21220.7i	−0.415637	+	1.82102i
$515$	−749.086	−	487.601i	−0.0640945	−	0.0417209i
$516$	3253.27	+	5366.60i	0.277552	+	0.457852i
$517$	−1209.28	+	235.508i	−0.102871	+	0.0200341i
$518$	−7710.18	+	2021.85i	−0.653988	+	0.171496i
$519$	692.042	+	4280.52i	0.0585304	+	0.362031i
$520$	1079.25	+	2932.68i	0.0910161	+	0.247320i
$521$	2476.81	−	1612.23i	0.208275	−	0.135572i	−0.437170	−	0.899379i	$-0.644019\pi$
$521$	2476.81	−	1612.23i	0.208275	−	0.135572i	0.645444	+	0.763807i	$0.276672\pi$
$522$	−21174.9	−	10197.3i	−1.77548	−	0.855026i
$523$	10455.9	+	13111.3i	0.874197	+	1.09621i	0.994631	+	0.103487i	$0.0329999\pi$
$523$	10455.9	+	13111.3i	0.874197	+	1.09621i	−0.120434	+	0.992721i	$0.538429\pi$
$524$	−4917.78	−	9426.46i	−0.409989	−	0.785872i
$525$	−481.235	−	689.887i	−0.0400054	−	0.0573507i
$526$	−2168.06	−	3576.44i	−0.179718	−	0.296464i
$527$	−4544.94	−	1840.04i	−0.375675	−	0.152094i
$528$	81.4589	+	184.017i	0.00671410	+	0.0151673i
$529$	−6518.01	+	2164.13i	−0.535712	+	0.177869i
$530$	−1613.01	−	2312.37i	−0.132197	−	0.189515i
$531$	−1809.76	+	11194.0i	−0.147904	+	0.914839i
$532$	531.277	+	299.210i	0.0432966	+	0.0243842i
$533$	13918.6	−	13479.4i	1.13111	−	1.09542i
$534$	−7466.29	+	4204.93i	−0.605052	+	0.340759i
$535$	7980.75	+	1029.00i	0.644930	+	0.0831546i
$536$	2449.96	+	8254.73i	0.197430	+	0.665206i
$537$	−6873.25	−	2282.08i	−0.552333	−	0.183387i
$538$	849.806	+	8809.13i	0.0680999	+	0.705927i
$539$	129.112	−	798.605i	0.0103177	−	0.0638188i
$540$	−5516.77	+	1074.39i	−0.439637	+	0.0856193i
$541$	7769.05	−	14891.8i	0.617408	−	1.18345i	−0.351536	−	0.936174i	$-0.614341\pi$
$541$	7769.05	−	14891.8i	0.617408	−	1.18345i	0.968944	−	0.247281i	$-0.0795369\pi$
$542$	1612.31	−	207.884i	0.127776	−	0.0164749i
$543$	6167.17	−	5250.19i	0.487401	−	0.414930i
$544$	−6691.31	−	12826.0i	−0.527367	−	1.01086i
$545$	−745.302	−	7725.83i	−0.0585784	−	0.607226i
$546$	−1727.12	−	1288.98i	−0.135373	−	0.101032i
$547$	−3926.38	+	8869.77i	−0.306910	+	0.693316i	−0.999610	−	0.0279099i	$-0.991115\pi$
$547$	−3926.38	+	8869.77i	−0.306910	+	0.693316i	0.692700	+	0.721226i	$0.256421\pi$
$548$	−287.534	+	968.797i	−0.0224139	+	0.0755200i
$549$	−4693.30	+	6728.20i	−0.364855	+	0.523047i
$550$	742.897	+	719.455i	0.0575949	+	0.0557776i
$551$	3108.62	−	1258.54i	0.240348	−	0.0973061i
$552$	2315.39	+	1728.02i	0.178531	+	0.133241i
$553$	1362.17	+	767.161i	0.104748	+	0.0589928i
$554$	27072.9	−	7099.34i	2.07620	−	0.544444i
$555$	1067.43	+	4676.73i	0.0816397	+	0.357687i
$556$	−1671.46	+	1247.44i	−0.127492	+	0.0951498i
$557$	−9401.98	−	10352.6i	−0.715214	−	0.787531i	0.269258	−	0.963068i	$-0.413221\pi$
$557$	−9401.98	−	10352.6i	−0.715214	−	0.787531i	−0.984473	+	0.175537i	$0.943834\pi$
$558$	−5160.57	−	6471.14i	−0.391513	−	0.490942i
$559$	−16182.9	−	5373.08i	−1.22444	−	0.406542i
$560$	−814.391	+	329.710i	−0.0614541	+	0.0248800i
$561$	−28.4015	+	294.411i	−0.00213745	+	0.0221570i
$562$	5651.92	−	6223.39i	0.424220	−	0.467113i
$563$	−10607.0	−	680.995i	−0.794020	−	0.0509778i	−0.338228	−	0.941064i	$-0.609828\pi$
$563$	−10607.0	−	680.995i	−0.794020	−	0.0509778i	−0.455792	+	0.890086i	$0.650644\pi$
$564$	−10219.9	−	2679.97i	−0.763006	−	0.200084i
$565$	−218.571	+	2265.71i	−0.0162749	+	0.168707i
$566$	−6150.26	+	13893.5i	−0.456740	+	1.03178i
$567$	−1225.68	+	1187.01i	−0.0907827	+	0.0879181i
$568$	−1076.76	−	6660.15i	−0.0795421	−	0.491996i
$569$	−1378.48	+	3745.78i	−0.101562	+	0.275977i	−0.979049	−	0.203623i	$-0.934728\pi$
$569$	−1378.48	+	3745.78i	−0.101562	+	0.275977i	0.877487	+	0.479600i	$0.159218\pi$
$570$	336.891	−	555.736i	0.0247558	−	0.0408372i
$571$	−19975.7	+	9619.79i	−1.46402	+	0.705036i	−0.984966	−	0.172747i	$-0.944736\pi$
$571$	−19975.7	+	9619.79i	−1.46402	+	0.705036i	−0.479057	+	0.877784i	$0.659021\pi$
$572$	1347.95	+	649.138i	0.0985325	+	0.0474508i
$573$	1631.51	+	5497.10i	0.118948	+	0.400776i
$574$	−4342.33	−	4205.31i	−0.315758	−	0.305795i
$575$	−12942.6	−	3393.96i	−0.938688	−	0.246153i
$576$	552.939	−	17242.7i	0.0399985	−	1.24730i
$577$	−7061.29			−0.509472			−0.254736	−	0.967011i	$-0.581989\pi$
$577$	−7061.29			−0.509472			−0.254736	+	0.967011i	$0.581989\pi$
$578$	−215.514	+	6720.52i	−0.0155090	+	0.483628i
$579$	4509.19	−	4965.11i	0.323653	−	0.356378i
$580$	3762.23	−	12676.2i	0.269342	−	0.907501i
$581$	4683.35	−	2637.62i	0.334420	−	0.188342i
$582$	−2195.41	−	5965.63i	−0.156362	−	0.424885i
$583$	−303.389	−	59.0850i	−0.0215525	−	0.00419734i
$584$	−5148.81	+	330.565i	−0.364828	+	0.0234227i
$585$	4356.37	−	5462.72i	0.307887	−	0.386078i
$586$	24842.7	−	16170.8i	1.75127	−	1.13995i
$587$	−15020.3	−	1936.66i	−1.05614	−	0.136174i	−0.419827	−	0.907604i	$-0.637909\pi$
$587$	−15020.3	−	1936.66i	−1.05614	−	0.136174i	−0.636315	+	0.771430i	$0.719542\pi$
$588$	3969.13	−	5690.04i	0.278374	−	0.399070i
$589$	1178.66	+	75.6727i	0.0824550	+	0.00529379i
$590$	−11298.5			−0.788392
$591$	3492.07	+	4485.96i	0.243053	+	0.312230i
$592$	−17343.4			−1.20407
$593$	−10028.3	−	643.836i	−0.694455	−	0.0445855i	−0.287161	−	0.957882i	$-0.592711\pi$
$593$	−10028.3	−	643.836i	−0.694455	−	0.0445855i	−0.407294	+	0.913297i	$0.633528\pi$
$594$	−624.318	+	895.007i	−0.0431247	+	0.0618225i
$595$	−1280.74	−	165.134i	−0.0882443	−	0.0113778i
$596$	−16799.3	+	10935.1i	−1.15457	+	0.751543i
$597$	−1092.61	+	1370.09i	−0.0749037	+	0.0939263i
$598$	−34210.8	+	2196.41i	−2.33944	+	0.150197i
$599$	−24087.1	−	4690.96i	−1.64303	−	0.319979i	−0.716895	−	0.697181i	$-0.754437\pi$
$599$	−24087.1	−	4690.96i	−1.64303	−	0.319979i	−0.926131	+	0.377202i	$0.876886\pi$
$600$	701.389	+	1905.90i	0.0477235	+	0.129680i
$601$	−5581.78	+	3143.60i	−0.378844	+	0.213361i	−0.668403	−	0.743799i	$-0.733022\pi$
$601$	−5581.78	+	3143.60i	−0.378844	+	0.213361i	0.289559	+	0.957160i	$0.406491\pi$
$602$	−1513.61	+	5099.86i	−0.102475	+	0.345274i
$603$	12943.4	−	14252.2i	0.874125	−	0.962509i
$604$	−129.110	+	4026.12i	−0.00869769	+	0.271226i
$605$	7012.56			0.471241
$606$	−299.897	+	9351.88i	−0.0201031	+	0.626888i
$607$	25701.3	+	6739.67i	1.71859	+	0.450667i	0.975765	−	0.218822i	$-0.0702215\pi$
$607$	25701.3	+	6739.67i	1.71859	+	0.450667i	0.742822	+	0.669489i	$0.233487\pi$
$608$	2503.19	+	2424.21i	0.166970	+	0.161702i
$609$	594.125	+	2001.81i	0.0395323	+	0.133197i
$610$	−7364.35	−	3546.48i	−0.488809	−	0.235398i
$611$	25864.3	−	12455.6i	1.71253	−	0.824711i
$612$	7083.80	−	11685.5i	0.467885	−	0.771825i
$613$	−4066.66	+	11050.4i	−0.267946	+	0.728096i	0.731008	+	0.682369i	$0.239050\pi$
$613$	−4066.66	+	11050.4i	−0.267946	+	0.728096i	−0.998954	+	0.0457269i	$0.985440\pi$
$614$	1403.24	+	8679.53i	0.0922315	+	0.570484i
$615$	−2613.28	+	2530.82i	−0.171346	+	0.165939i
$616$	43.2639	−	97.7339i	0.00282979	−	0.00639255i
$617$	−1841.04	+	19084.3i	−0.120126	+	1.24523i	0.716552	+	0.697534i	$0.245719\pi$
$617$	−1841.04	+	19084.3i	−0.120126	+	1.24523i	−0.836678	+	0.547696i	$0.815505\pi$
$618$	−1439.56	−	377.497i	−0.0937015	−	0.0245714i
$619$	−5906.18	−	379.189i	−0.383505	−	0.0246218i	−0.128876	−	0.991661i	$-0.541137\pi$
$619$	−5906.18	−	379.189i	−0.383505	−	0.0246218i	−0.254629	+	0.967039i	$0.581953\pi$
$620$	3130.69	−	3447.24i	0.202793	−	0.223298i
$621$	1355.71	−	14053.4i	0.0876054	−	0.908122i
$622$	−40043.0	+	16211.6i	−2.58131	+	1.04506i
$623$	−3892.49	−	1292.39i	−0.250320	−	0.0831119i
$624$	−2923.64	−	3666.12i	−0.187563	−	0.235196i
$625$	−3968.66	−	4369.94i	−0.253994	−	0.279676i
$626$	23302.5	−	17391.1i	1.48779	−	1.11037i
$627$	−15.8538	−	69.4598i	−0.00100979	−	0.00442418i
$628$	26200.3	−	6870.52i	1.66482	−	0.436566i
$629$	−22210.6	−	12508.8i	−1.40794	−	0.792939i
$630$	−1746.94	−	1303.78i	−0.110476	−	0.0824505i
$631$	15189.8	−	6149.68i	0.958315	−	0.387979i	0.157920	−	0.987452i	$-0.449521\pi$
$631$	15189.8	−	6149.68i	0.958315	−	0.387979i	0.800395	+	0.599473i	$0.204623\pi$
$632$	−2711.43	−	2625.87i	−0.170657	−	0.165272i
$633$	4974.65	−	7131.53i	0.312361	−	0.447793i
$634$	−12758.0	+	42986.0i	−0.799189	+	2.69273i
$635$	11.4101	−	25.7755i	0.000713061	−	0.00161082i
$636$	−2124.30	−	1585.41i	−0.132443	−	0.0988450i
$637$	1810.04	+	18763.0i	0.112585	+	1.16706i
$638$	−1187.47	−	2276.15i	−0.0736869	−	0.141244i
$639$	−11486.2	+	9778.35i	−0.711091	+	0.605361i
$640$	6542.28	−	843.533i	0.404072	−	0.0520993i
$641$	−4789.76	+	9181.08i	−0.295139	+	0.565727i	−0.987835	−	0.155503i	$-0.950300\pi$
$641$	−4789.76	+	9181.08i	−0.295139	+	0.565727i	0.692696	+	0.721229i	$0.256423\pi$
$642$	13151.3	−	2561.21i	0.808474	−	0.157450i
$643$	−2146.26	+	13275.4i	−0.131633	+	0.814197i	0.833516	+	0.552496i	$0.186324\pi$
$643$	−2146.26	+	13275.4i	−0.131633	+	0.814197i	−0.965149	+	0.261702i	$0.915716\pi$
$644$	579.879	+	6011.05i	0.0354821	+	0.367809i
$645$	3038.41	+	1008.82i	0.185484	+	0.0615850i
$646$	982.581	+	3310.64i	0.0598439	+	0.201634i
$647$	28011.0	+	3611.62i	1.70205	+	0.219455i	0.916695	−	0.399587i	$-0.130847\pi$
$647$	28011.0	+	3611.62i	1.70205	+	0.219455i	0.785357	+	0.619043i	$0.212479\pi$
$648$	3589.44	−	2021.53i	0.217603	−	0.122551i
$649$	−889.789	+	861.713i	−0.0538171	+	0.0521189i
$650$	−20996.5	−	11825.0i	−1.26700	−	0.713563i
$651$	−117.366	+	725.950i	−0.00706595	+	0.0437054i
$652$	17015.6	+	24393.1i	1.02206	+	1.46520i
$653$	−2103.44	+	698.389i	−0.126055	+	0.0418531i	−0.377440	−	0.926034i	$-0.623196\pi$
$653$	−2103.44	+	698.389i	−0.126055	+	0.0418531i	0.251385	+	0.967887i	$0.419114\pi$
$654$	−5231.27	−	11817.5i	−0.312781	−	0.706579i
$655$	−5027.54	−	2035.43i	−0.299912	−	0.121421i
$656$	−6818.26	−	11247.4i	−0.405806	−	0.669419i
$657$	6599.87	+	9461.42i	0.391911	+	0.561834i
$658$	−4142.52	−	7940.43i	−0.245429	−	0.470441i
$659$	13006.6	+	16309.7i	0.768838	+	0.964092i	0.999961	−	0.00883224i	$-0.00281143\pi$
$659$	13006.6	+	16309.7i	0.768838	+	0.964092i	−0.231123	+	0.972925i	$0.574240\pi$
$660$	−253.084	−	121.879i	−0.0149262	−	0.00718807i
$661$	4423.62	−	2879.46i	0.260301	−	0.169437i	−0.408766	−	0.912639i	$-0.634041\pi$
$661$	4423.62	−	2879.46i	0.260301	−	0.169437i	0.669067	+	0.743202i	$0.266694\pi$
$662$	−7708.74	−	20947.1i	−0.452581	−	1.22981i
$663$	−1099.96	−	6803.63i	−0.0644327	−	0.398539i
$664$	−12553.0	+	3291.78i	−0.733659	+	0.192388i
$665$	305.319	−	59.4609i	0.0178042	−	0.00346736i
$666$	−22306.1	−	36796.2i	−1.29781	−	2.14088i
$667$	27837.8	+	18120.4i	1.61602	+	1.05191i
$668$	−1534.65	+	6723.76i	−0.0888886	+	0.389446i
$669$	−3031.91	−	2581.10i	−0.175217	−	0.149165i
$670$	16077.0	+	10465.0i	0.927030	+	0.603430i
$671$	−850.447	+	282.368i	−0.0489287	+	0.0162454i
$672$	−1652.05	+	1406.41i	−0.0948354	+	0.0807345i
$673$	−8676.23	−	9553.50i	−0.496945	−	0.547192i	0.439391	−	0.898296i	$-0.355194\pi$
$673$	−8676.23	−	9553.50i	−0.496945	−	0.547192i	−0.936337	+	0.351104i	$0.885806\pi$
$674$	1474.87	−	710.260i	0.0842877	−	0.0405908i
$675$	6187.80	−	7759.25i	0.352842	−	0.442450i
$676$	−11842.7	−	2306.36i	−0.673798	−	0.131222i
$677$	−5901.61	+	16036.6i	−0.335033	+	0.910393i	0.653166	+	0.757215i	$0.273441\pi$
$677$	−5901.61	+	16036.6i	−0.335033	+	0.910393i	−0.988199	+	0.153178i	$0.951049\pi$
$678$	843.365	+	3695.02i	0.0477717	+	0.209302i
$679$	1407.32	−	2697.56i	0.0795403	−	0.152464i
$680$	2889.95	+	1170.01i	0.162977	+	0.0659822i
$681$	4121.97	+	3509.08i	0.231944	+	0.197457i
$682$	−28.9787	−	903.663i	−0.00162706	−	0.0507376i
$683$	−467.127	−	14566.7i	−0.0261700	−	0.816077i	−0.925487	−	0.378779i	$-0.876344\pi$
$683$	−467.127	−	14566.7i	−0.0261700	−	0.816077i	0.899317	−	0.437297i	$-0.144064\pi$
$684$	−732.443	+	3209.04i	−0.0409439	+	0.179387i
$685$	208.680	+	471.412i	0.0116398	+	0.0262945i
$686$	11984.3	−	1545.20i	0.667001	−	0.0860002i
$687$	6290.04	−	4694.38i	0.349316	−	0.260701i
$688$	−6000.36	+	9898.22i	−0.332502	+	0.548497i
$689$	7187.34	−	461.443i	0.397411	−	0.0255146i
$690$	6423.25	−	412.386i	0.354390	−	0.0227526i
$691$	4255.41	−	7019.74i	0.234274	−	0.386459i	−0.715888	−	0.698215i	$-0.753978\pi$
$691$	4255.41	−	7019.74i	0.234274	−	0.386459i	0.950162	+	0.311755i	$0.100917\pi$
$692$	17537.2	−	13088.3i	0.963387	−	0.718994i
$693$	−237.014	+	30.5595i	−0.0129919	+	0.00167512i
$694$	15520.2	+	35060.4i	0.848903	+	1.91769i
$695$	−236.757	+	1037.30i	−0.0129219	+	0.0566145i
$696$	−161.589	−	5038.93i	−0.00880029	−	0.274425i
$697$	−619.604	−	19321.5i	−0.0336717	−	1.05001i
$698$	−1919.48	−	1634.07i	−0.104088	−	0.0886112i
$699$	7913.49	+	3203.82i	0.428206	+	0.173361i
$700$	−1963.47	+	3763.60i	−0.106017	+	0.203215i
$701$	−2537.69	−	11118.3i	−0.136729	−	0.599050i	−0.996141	−	0.0877662i	$-0.972027\pi$
$701$	−2537.69	−	11118.3i	−0.136729	−	0.599050i	0.859412	−	0.511284i	$-0.170830\pi$
$702$	8781.68	−	23862.7i	0.472141	−	1.28296i
$703$	6026.93	+	1173.74i	0.323343	+	0.0629710i
$704$	1174.95	−	1473.34i	0.0629013	−	0.0788758i
$705$	−4856.14	+	2338.59i	−0.259422	+	0.124931i
$706$	6998.56	+	7706.19i	0.373080	+	0.410802i
$707$	−3410.11	+	2903.07i	−0.181401	+	0.154429i
$708$	−10081.3	+	3347.24i	−0.535142	+	0.177679i
$709$	−8807.94	−	5733.33i	−0.466557	−	0.303695i	0.290697	−	0.956815i	$-0.406113\pi$
$709$	−8807.94	−	5733.33i	−0.466557	−	0.303695i	−0.757254	+	0.653120i	$0.773460\pi$
$710$	−11444.8	−	9743.08i	−0.604950	−	0.515002i
$711$	−1877.95	+	8227.85i	−0.0990558	+	0.433992i
$712$	8299.13	+	5402.14i	0.436830	+	0.284345i
$713$	6064.01	+	10003.2i	0.318512	+	0.525419i
$714$	−2110.51	+	411.021i	−0.110622	+	0.0215435i
$715$	738.272	−	193.598i	0.0386151	−	0.0101261i
$716$	5833.19	+	36080.4i	0.304465	+	1.88322i
$717$	−4540.92	−	12339.2i	−0.236519	−	0.642698i
$718$	14026.6	−	9130.31i	0.729064	−	0.474568i
$719$	24447.8	+	11773.4i	1.26808	+	0.610674i	0.942299	−	0.334772i	$-0.108659\pi$
$719$	24447.8	+	11773.4i	1.26808	+	0.610674i	0.325778	+	0.945446i	$0.394374\pi$
$720$	−2957.20	−	3708.21i	−0.153067	−	0.191940i
$721$	−329.478	−	631.547i	−0.0170186	−	0.0326214i
$722$	16345.8	+	23433.0i	0.842560	+	1.20787i
$723$	1184.85	+	1954.54i	0.0609477	+	0.100540i
$724$	−37887.1	−	15338.8i	−1.94484	−	0.787377i
$725$	9451.08	+	21350.2i	0.484144	+	1.09369i
$726$	11081.4	−	3679.29i	0.566489	−	0.188087i
$727$	−5367.00	−	7693.99i	−0.273798	−	0.392510i	0.659447	−	0.751751i	$-0.270791\pi$
$727$	−5367.00	−	7693.99i	−0.273798	−	0.392510i	−0.933245	+	0.359242i	$0.883035\pi$
$728$	−397.478	+	2458.54i	−0.0202356	+	0.125164i
$729$	−3075.84	−	1732.28i	−0.156269	−	0.0880090i
$730$	−8256.91	+	7996.37i	−0.418633	+	0.405423i
$731$	−14823.3	+	8348.34i	−0.750014	+	0.422400i
$732$	−7621.68	−	982.707i	−0.384844	−	0.0496201i
$733$	6703.83	+	22587.4i	0.337806	+	1.13818i	0.940382	+	0.340119i	$0.110467\pi$
$733$	6703.83	+	22587.4i	0.337806	+	1.13818i	−0.602576	+	0.798061i	$0.705859\pi$
$734$	13775.0	+	4573.61i	0.692702	+	0.229993i
$735$	−339.844	−	3522.84i	−0.0170549	−	0.176792i
$736$	−5508.19	+	34070.1i	−0.275862	+	1.70631i
$737$	2064.26	−	402.014i	0.103172	−	0.0200928i
$738$	15093.6	−	28931.6i	0.752850	−	1.44307i
$739$	13816.1	−	1781.39i	0.687733	−	0.0886733i	0.223921	−	0.974607i	$-0.428114\pi$
$739$	13816.1	−	1781.39i	0.687733	−	0.0886733i	0.463812	+	0.885934i	$0.346481\pi$
$740$	18433.7	−	15692.8i	0.915724	−	0.779567i
$741$	767.869	+	1471.86i	0.0380680	+	0.0729692i
$742$	−215.756	−	2236.54i	−0.0106748	−	0.110655i
$743$	−3563.75	−	2659.69i	−0.175964	−	0.131325i	0.506513	−	0.862232i	$-0.330934\pi$
$743$	−3563.75	−	2659.69i	−0.175964	−	0.131325i	−0.682477	+	0.730907i	$0.739097\pi$
$744$	718.687	−	1623.53i	0.0354145	−	0.0800019i
$745$	−2909.50	+	9803.07i	−0.143082	+	0.482090i
$746$	26424.7	−	37881.7i	1.29688	−	1.85918i
$747$	20843.7	+	20186.0i	1.02092	+	0.988709i
$748$	1383.60	−	560.157i	0.0676328	−	0.0273815i
$749$	5139.45	+	3835.67i	0.250723	+	0.187119i
$750$	9023.33	+	5081.84i	0.439314	+	0.247417i
$751$	17595.6	−	4614.11i	0.854957	−	0.224196i	0.199938	−	0.979809i	$-0.435926\pi$
$751$	17595.6	−	4614.11i	0.854957	−	0.224196i	0.655019	+	0.755612i	$0.272661\pi$
$752$	−4336.27	−	18998.4i	−0.210276	−	0.921279i
$753$	1058.08	−	789.663i	0.0512064	−	0.0382163i
$754$	40217.5	+	44284.0i	1.94249	+	2.13890i
$755$	1281.25	+	1606.63i	0.0617607	+	0.0774455i
$756$	−4251.05	−	1411.45i	−0.204510	−	0.0679019i
$757$	10604.2	−	4293.15i	0.509134	−	0.206126i	−0.106270	−	0.994337i	$-0.533891\pi$
$757$	10604.2	−	4293.15i	0.509134	−	0.206126i	0.615404	+	0.788212i	$0.288993\pi$
$758$	1432.87	−	14853.2i	0.0686600	−	0.711733i
$759$	474.398	−	522.365i	0.0226872	−	0.0249811i
$760$	−749.467	−	48.1174i	−0.0357711	−	0.00229658i
$761$	17944.8	+	4705.67i	0.854793	+	0.224153i	0.654948	−	0.755674i	$-0.272691\pi$
$761$	17944.8	+	4705.67i	0.854793	+	0.224153i	0.199846	+	0.979827i	$0.435956\pi$
$762$	4.50680	−	46.7177i	0.000214258	−	0.00222100i
$763$	2503.89	−	5656.33i	0.118803	−	0.268379i
$764$	20787.6	−	20131.7i	0.984383	−	0.953322i
$765$	−1112.59	−	6881.74i	−0.0525825

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.g (of order \(49\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.27791 - 0.274651i) q^{2} +(-1.17628 + 1.68628i) q^{3} +(10.2908 + 1.32685i) q^{4} +(4.43621 - 2.88765i) q^{5} +(5.49515 - 6.89071i) q^{6} +(4.20983 - 0.270280i) q^{7} +(-9.99729 - 1.94697i) q^{8} +(7.86494 + 21.3716i) q^{9} +O(q^{10})\)	\(q+(-4.27791 - 0.274651i) q^{2} +(-1.17628 + 1.68628i) q^{3} +(10.2908 + 1.32685i) q^{4} +(4.43621 - 2.88765i) q^{5} +(5.49515 - 6.89071i) q^{6} +(4.20983 - 0.270280i) q^{7} +(-9.99729 - 1.94697i) q^{8} +(7.86494 + 21.3716i) q^{9} +(-19.7708 + 11.1347i) q^{10} +(-0.707788 + 2.38477i) q^{11} +(-14.3423 + 15.7924i) q^{12} +(1.85783 - 57.9340i) q^{13} -18.0835 q^{14} +(-0.348817 + 10.8774i) q^{15} +(-38.0602 - 9.98055i) q^{16} +(-41.5430 - 40.2321i) q^{17} +(-27.7758 - 93.5858i) q^{18} +(12.5507 + 6.04409i) q^{19} +(49.4835 - 23.8300i) q^{20} +(-4.49617 + 7.41690i) q^{21} +(3.68283 - 10.0074i) q^{22} +(22.0195 + 136.198i) q^{23} +(15.0427 - 14.5681i) q^{24} +(-39.2565 + 88.6811i) q^{25} +(-23.8593 + 247.326i) q^{26} +(-98.9866 - 25.9574i) q^{27} +(43.6811 + 2.80442i) q^{28} +(161.858 - 178.223i) q^{29} +(4.47969 - 46.4367i) q^{30} +(78.5899 - 31.8175i) q^{31} +(237.407 + 78.8245i) q^{32} +(-3.18884 - 3.99868i) q^{33} +(166.667 + 183.519i) q^{34} +(17.8952 - 13.3556i) q^{35} +(52.5795 + 230.366i) q^{36} +(426.365 - 111.806i) q^{37} +(-52.0307 - 29.3031i) q^{38} +(95.5078 + 71.2793i) q^{39} +(-49.9723 + 20.2315i) q^{40} +(240.126 + 232.549i) q^{41} +(21.2713 - 30.4940i) q^{42} +(83.7011 - 282.017i) q^{43} +(-10.4479 + 23.6020i) q^{44} +(96.6042 + 72.0976i) q^{45} +(-56.7905 - 588.693i) q^{46} +(229.077 + 439.097i) q^{47} +(61.5994 - 52.4403i) q^{48} +(-322.534 + 41.5862i) q^{49} +(192.292 - 368.588i) q^{50} +(116.709 - 22.7290i) q^{51} +(95.9882 - 593.721i) q^{52} +(11.9311 + 123.678i) q^{53} +(416.327 + 138.230i) q^{54} +(3.74650 + 12.6232i) q^{55} +(-42.6132 - 5.49436i) q^{56} +(-24.9551 + 14.0545i) q^{57} +(-741.363 + 717.970i) q^{58} +(433.860 + 244.345i) q^{59} +(-18.0222 + 111.474i) q^{60} +(206.092 + 295.449i) q^{61} +(-344.939 + 114.528i) q^{62} +(38.8864 + 87.8450i) q^{63} +(-702.185 - 284.283i) q^{64} +(-159.051 - 262.372i) q^{65} +(12.5434 + 17.9818i) q^{66} +(-391.036 - 749.543i) q^{67} +(-374.128 - 469.141i) q^{68} +(-255.570 - 123.076i) q^{69} +(-80.2223 + 52.2190i) q^{70} +(228.770 + 621.642i) q^{71} +(-37.0182 - 228.971i) q^{72} +(489.997 - 128.492i) q^{73} +(-1854.66 + 361.195i) q^{74} +(-103.365 - 170.511i) q^{75} +(121.137 + 78.8512i) q^{76} +(-2.33511 + 10.2308i) q^{77} +(-388.997 - 331.158i) q^{78} +(310.589 + 202.171i) q^{79} +(-197.663 + 65.6287i) q^{80} +(-307.980 + 262.187i) q^{81} +(-963.368 - 1060.77i) q^{82} +(1147.97 - 552.834i) q^{83} +(-56.1102 + 70.3599i) q^{84} +(-300.470 - 58.5165i) q^{85} +(-435.522 + 1183.45i) q^{86} +(110.145 + 482.578i) q^{87} +(11.7190 - 22.4632i) q^{88} +(-901.193 - 364.853i) q^{89} +(-393.462 - 334.959i) q^{90} +(-7.83726 - 244.395i) q^{91} +(45.8832 + 1430.81i) q^{92} +(-38.7902 + 169.951i) q^{93} +(-859.372 - 1941.34i) q^{94} +(73.1306 - 9.42915i) q^{95} +(-412.177 + 307.616i) q^{96} +(373.891 - 616.772i) q^{97} +(1391.20 - 89.3177i) q^{98} +(-56.5330 + 3.62954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9}+O(q^{10}) \) 2058 * q - 42 * q^2 - 42 * q^3 - 84 * q^4 - 42 * q^5 - 119 * q^6 - 84 * q^7 - 98 * q^8 - 42 * q^9	\( 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9} + 168 q^{10} - 140 q^{11} + 14 q^{12} - 42 q^{13} - 812 q^{14} + 1638 q^{15} + 672 q^{16} - 42 q^{17} + 147 q^{18} - 567 q^{19} - 35 q^{20} - 42 q^{21} + 1302 q^{22} - 42 q^{23} - 434 q^{24} - 42 q^{25} + 364 q^{26} - 1596 q^{27} - 147 q^{28} + 4676 q^{29} - 847 q^{30} + 882 q^{31} + 910 q^{32} - 287 q^{33} - 882 q^{34} - 42 q^{35} - 17787 q^{36} - 1400 q^{37} + 14 q^{38} + 168 q^{39} + 3962 q^{40} - 392 q^{41} + 1764 q^{42} + 294 q^{43} - 12978 q^{44} + 2814 q^{45} + 840 q^{46} + 28 q^{47} + 3654 q^{48} + 1554 q^{49} - 4998 q^{50} - 98 q^{51} - 3703 q^{52} - 42 q^{53} - 1365 q^{54} + 4046 q^{55} - 3073 q^{56} + 14567 q^{57} - 10402 q^{58} + 4004 q^{59} - 4536 q^{60} - 1050 q^{61} + 210 q^{62} + 2254 q^{63} + 3822 q^{64} - 1106 q^{65} - 875 q^{66} - 3612 q^{67} + 819 q^{68} + 4333 q^{69} - 5292 q^{70} + 11424 q^{71} - 1876 q^{72} - 714 q^{73} + 1288 q^{74} - 1316 q^{75} + 8715 q^{76} + 6629 q^{77} + 13986 q^{78} - 1512 q^{79} + 406 q^{80} + 1078 q^{81} - 42 q^{82} - 5999 q^{83} - 7595 q^{84} + 30492 q^{85} + 7749 q^{86} - 35 q^{87} + 8897 q^{88} - 196 q^{89} - 14910 q^{90} - 8232 q^{91} - 7938 q^{92} - 2639 q^{93} - 11116 q^{94} + 3703 q^{95} + 14497 q^{96} - 2674 q^{97} - 10024 q^{98} + 6237 q^{99}+O(q^{100}) \) 2058 * q - 42 * q^2 - 42 * q^3 - 84 * q^4 - 42 * q^5 - 119 * q^6 - 84 * q^7 - 98 * q^8 - 42 * q^9 + 168 * q^10 - 140 * q^11 + 14 * q^12 - 42 * q^13 - 812 * q^14 + 1638 * q^15 + 672 * q^16 - 42 * q^17 + 147 * q^18 - 567 * q^19 - 35 * q^20 - 42 * q^21 + 1302 * q^22 - 42 * q^23 - 434 * q^24 - 42 * q^25 + 364 * q^26 - 1596 * q^27 - 147 * q^28 + 4676 * q^29 - 847 * q^30 + 882 * q^31 + 910 * q^32 - 287 * q^33 - 882 * q^34 - 42 * q^35 - 17787 * q^36 - 1400 * q^37 + 14 * q^38 + 168 * q^39 + 3962 * q^40 - 392 * q^41 + 1764 * q^42 + 294 * q^43 - 12978 * q^44 + 2814 * q^45 + 840 * q^46 + 28 * q^47 + 3654 * q^48 + 1554 * q^49 - 4998 * q^50 - 98 * q^51 - 3703 * q^52 - 42 * q^53 - 1365 * q^54 + 4046 * q^55 - 3073 * q^56 + 14567 * q^57 - 10402 * q^58 + 4004 * q^59 - 4536 * q^60 - 1050 * q^61 + 210 * q^62 + 2254 * q^63 + 3822 * q^64 - 1106 * q^65 - 875 * q^66 - 3612 * q^67 + 819 * q^68 + 4333 * q^69 - 5292 * q^70 + 11424 * q^71 - 1876 * q^72 - 714 * q^73 + 1288 * q^74 - 1316 * q^75 + 8715 * q^76 + 6629 * q^77 + 13986 * q^78 - 1512 * q^79 + 406 * q^80 + 1078 * q^81 - 42 * q^82 - 5999 * q^83 - 7595 * q^84 + 30492 * q^85 + 7749 * q^86 - 35 * q^87 + 8897 * q^88 - 196 * q^89 - 14910 * q^90 - 8232 * q^91 - 7938 * q^92 - 2639 * q^93 - 11116 * q^94 + 3703 * q^95 + 14497 * q^96 - 2674 * q^97 - 10024 * q^98 + 6237 * q^99

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