LMFDB - Embedded newform 197.4.g.a.37.8

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			37.8
Character	$\chi$	$=$	197.37
Dual form			197.4.g.a.16.8

$q$-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 $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{48}{49}\right)$

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	−0.798041	−	0.602603i	$-0.794130\pi$
$2$	−4.27791	+	0.274651i	−1.51247	+	0.0971038i	−0.714430	+	0.699707i	$0.753314\pi$
$3$	−1.17628	−	1.68628i	−0.226375	−	0.324525i	0.690774	−	0.723071i	$-0.257270\pi$
$3$	−1.17628	−	1.68628i	−0.226375	−	0.324525i	−0.917148	+	0.398546i	$0.869515\pi$
$4$	10.2908	−	1.32685i	1.28635	−	0.165856i
$5$	4.43621	+	2.88765i	0.396787	+	0.258279i	0.728423	−	0.685128i	$-0.240254\pi$
$5$	4.43621	+	2.88765i	0.396787	+	0.258279i	−0.331636	+	0.943407i	$0.607601\pi$
$6$	5.49515	+	6.89071i	0.373898	+	0.468853i
$7$	4.20983	+	0.270280i	0.227310	+	0.0145938i	0.177308	−	0.984155i	$-0.443261\pi$
$7$	4.20983	+	0.270280i	0.227310	+	0.0145938i	0.0500015	+	0.998749i	$0.484077\pi$
$8$	−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	0.948410	−	0.317046i	$-0.102691\pi$
$11$	−0.707788	−	2.38477i	−0.0194005	−	0.0653669i	−0.967811	+	0.251679i	$0.919017\pi$
$12$	−14.3423	−	15.7924i	−0.345021	−	0.379907i
$13$	1.85783	+	57.9340i	0.0396361	+	1.23600i	0.805343	+	0.592810i	$0.201981\pi$
$13$	1.85783	+	57.9340i	0.0396361	+	1.23600i	−0.765706	+	0.643190i	$0.777610\pi$
$14$	−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	−0.930070	−	0.367383i	$-0.880254\pi$
$17$	−41.5430	+	40.2321i	−0.592685	+	0.573984i	0.337384	+	0.941367i	$0.390458\pi$
$18$	−27.7758	+	93.5858i	−0.363712	+	1.22547i
$19$	12.5507	−	6.04409i	0.151543	−	0.0729794i	−0.356575	−	0.934267i	$-0.616056\pi$
$19$	12.5507	−	6.04409i	0.151543	−	0.0729794i	0.508118	+	0.861287i	$0.330341\pi$
$20$	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	−0.670495	−	0.741914i	$-0.733918\pi$
$23$	22.0195	−	136.198i	0.199626	−	1.23475i	0.870120	−	0.492840i	$-0.164041\pi$
$24$	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	0.989823	+	0.142302i	$0.0454505\pi$
$29$	161.858	+	178.223i	1.03642	+	1.14122i	0.0465988	+	0.998914i	$0.485162\pi$
$30$	4.47969	+	46.4367i	0.0272625	+	0.282605i
$31$	78.5899	+	31.8175i	0.455328	+	0.184342i	0.591436	−	0.806352i	$-0.298561\pi$
$31$	78.5899	+	31.8175i	0.455328	+	0.184342i	−0.136108	+	0.990694i	$0.543459\pi$
$32$	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	0.998630	+	0.0523197i	$0.0166615\pi$
$37$	426.365	+	111.806i	1.89443	+	0.496778i	0.895800	+	0.444458i	$0.146604\pi$
$38$	−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	−0.0791467	−	0.996863i	$-0.525220\pi$
$41$	240.126	−	232.549i	0.914667	−	0.885806i	0.993814	+	0.111057i	$0.0354236\pi$
$42$	21.2713	+	30.4940i	0.0781483	+	0.112031i
$43$	83.7011	+	282.017i	0.296844	+	1.00017i	0.966322	+	0.257335i	$0.0828443\pi$
$43$	83.7011	+	282.017i	0.296844	+	1.00017i	−0.669478	+	0.742832i	$0.733482\pi$
$44$	−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	−0.211795	−	0.977314i	$-0.567931\pi$
$47$	229.077	−	439.097i	0.710942	−	1.36274i	0.922737	−	0.385429i	$-0.125947\pi$
$48$	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	−0.966931	−	0.255039i	$-0.917912\pi$
$53$	11.9311	−	123.678i	0.0309219	−	0.320538i	0.997853	−	0.0654989i	$-0.0208639\pi$
$54$	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	0.0686426	−	0.997641i	$-0.478133\pi$
$59$	433.860	−	244.345i	0.957352	−	0.539171i	0.888710	+	0.458471i	$0.151603\pi$
$60$	−18.0222	−	111.474i	−0.0387777	−	0.239854i
$61$	206.092	−	295.449i	0.432580	−	0.620137i	−0.543012	−	0.839725i	$-0.682716\pi$
$61$	206.092	−	295.449i	0.432580	−	0.620137i	0.975593	+	0.219588i	$0.0704714\pi$
$62$	−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	0.208348	+	0.978055i	$0.433191\pi$
$67$	−391.036	+	749.543i	−0.713024	+	1.36673i	−0.921373	+	0.388680i	$0.872931\pi$
$68$	−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	−0.590337	−	0.807157i	$-0.701005\pi$
$71$	228.770	−	621.642i	0.382395	−	1.03909i	0.972732	−	0.231933i	$-0.0745049\pi$
$72$	−37.0182	+	228.971i	−0.0605922	+	0.374784i
$73$	489.997	+	128.492i	0.785613	+	0.206012i	0.624605	−	0.780941i	$-0.285260\pi$
$73$	489.997	+	128.492i	0.785613	+	0.206012i	0.161008	+	0.986953i	$0.448525\pi$
$74$	−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	−0.305032	−	0.952342i	$-0.598667\pi$
$79$	310.589	−	202.171i	0.442329	−	0.287925i	0.747362	+	0.664417i	$0.231320\pi$
$80$	−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	0.992800	−	0.119785i	$-0.0382206\pi$
$83$	1147.97	+	552.834i	1.51815	+	0.731102i	0.525349	+	0.850887i	$0.323935\pi$
$84$	−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	−0.842636	−	0.538484i	$-0.818997\pi$
$89$	−901.193	+	364.853i	−1.07333	+	0.434543i	−0.230693	+	0.973027i	$0.574099\pi$
$90$	−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	0.987561	−	0.157237i	$-0.0502587\pi$
$97$	373.891	+	616.772i	0.391370	+	0.645605i	−0.596191	+	0.802843i	$0.703320\pi$
$98$	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	0.0907093	−	0.995877i	$-0.471087\pi$
$101$	−850.801	−	634.970i	−0.838197	−	0.625563i	−0.928906	+	0.370315i	$0.879250\pi$
$102$	−505.513	−	65.1786i	−0.490718	−	0.0632711i
$103$	−68.3506	+	154.405i	−0.0653863	+	0.147709i	−0.944118	−	0.329607i	$-0.893084\pi$
$103$	−68.3506	+	154.405i	−0.0653863	+	0.147709i	0.878732	+	0.477315i	$0.158390\pi$
$104$	−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	0.0517235	−	0.998661i	$-0.483529\pi$
$107$	1157.55	−	985.438i	1.04584	−	0.890336i	0.994115	+	0.108326i	$0.0345489\pi$
$108$	−984.208	+	398.462i	−0.876903	+	0.355019i
$109$	678.238	+	1300.05i	0.595995	+	1.14241i	0.976070	+	0.217455i	$0.0697754\pi$
$109$	678.238	+	1300.05i	0.595995	+	1.14241i	−0.380076	+	0.924955i	$0.624102\pi$
$110$	−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	0.657602	−	0.753366i	$-0.271571\pi$
$113$	−268.116	−	336.207i	−0.223206	−	0.279891i	−0.880808	+	0.473475i	$0.843000\pi$
$114$	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	0.547093	−	0.837072i	$-0.315734\pi$
$127$	4.46306	+	2.90513i	0.00311836	+	0.00202983i	−0.543975	+	0.839102i	$0.683081\pi$
$128$	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	−0.966300	−	0.257419i	$-0.917128\pi$
$131$	−586.242	+	840.422i	−0.390994	+	0.560519i	0.575306	+	0.817938i	$0.304883\pi$
$132$	−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	0.981880	−	0.189506i	$-0.0606885\pi$
$137$	−15.5442	−	96.1464i	−0.00969366	−	0.0599587i	−0.991573	+	0.129547i	$0.958648\pi$
$138$	1059.50	−	596.702i	0.653558	−	0.368077i
$139$	−144.393	−	139.837i	−0.0881097	−	0.0853295i	0.650318	−	0.759662i	$-0.274636\pi$
$139$	−144.393	−	139.837i	−0.0881097	−	0.0853295i	−0.738428	+	0.674332i	$0.764431\pi$
$140$	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	0.144866	−	0.989451i	$-0.453725\pi$
$149$	−1470.99	−	1252.28i	−0.808782	−	0.688526i	−0.953648	+	0.300925i	$0.902705\pi$
$150$	395.355	−	757.821i	0.215204	−	0.412506i
$151$	37.2783	−	386.429i	0.0200905	−	0.208259i	−0.979872	−	0.199626i	$-0.936027\pi$
$151$	37.2783	−	386.429i	0.0200905	−	0.208259i	0.999963	−	0.00863343i	$-0.00274814\pi$
$152$	−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	0.895773	−	0.444512i	$-0.146623\pi$
$157$	2419.68	+	979.622i	1.23001	+	0.497977i	0.334239	+	0.942488i	$0.391521\pi$
$158$	−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	−0.0737389	−	0.997278i	$-0.523493\pi$
$163$	1927.07	−	2121.92i	0.926011	−	1.01964i	0.999750	−	0.0223635i	$-0.00711911\pi$
$164$	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	−0.998293	−	0.0584057i	$-0.981398\pi$
$167$	−63.8244	−	661.606i	−0.0295741	−	0.306567i	0.968719	−	0.248161i	$-0.0798262\pi$
$168$	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	0.949369	−	0.314163i	$-0.101724\pi$
$173$	1514.99	+	1467.19i	0.665796	+	0.644787i	−0.283573	+	0.958951i	$0.591520\pi$
$174$	−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	−0.440357	−	0.897823i	$-0.645148\pi$
$179$	1002.23	−	3376.86i	0.418495	−	1.41005i	0.858851	−	0.512225i	$-0.171178\pi$
$180$	898.470	−	870.119i	0.372044	−	0.360305i
$181$	−3810.49	+	999.227i	−1.56481	+	0.410342i	−0.931556	−	0.363598i	$-0.881548\pi$
$181$	−3810.49	+	999.227i	−1.56481	+	0.410342i	−0.633258	+	0.773941i	$0.718283\pi$
$182$	−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	0.993206	−	0.116367i	$-0.0371248\pi$
$191$	1738.88	+	2180.49i	0.658748	+	0.826044i	−0.334458	+	0.942411i	$0.608553\pi$
$192$	1305.35	+	849.687i	0.490653	+	0.319380i
$193$	−3235.41	+	417.159i	−1.20668	+	0.155584i	−0.704834	−	0.709372i	$-0.748979\pi$
$193$	−3235.41	+	417.159i	−1.20668	+	0.155584i	−0.501847	+	0.864956i	$0.667346\pi$
$194$	−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	0.0881705	−	0.996105i	$-0.471898\pi$
$199$	850.583	−	54.6093i	0.302996	−	0.0194530i	0.214826	+	0.976652i	$0.431082\pi$
$200$	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	−0.980290	−	0.197562i	$-0.936698\pi$
$223$	−185.963	−	1927.70i	−0.0558431	−	0.578872i	0.924447	−	0.381310i	$-0.124527\pi$
$224$	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	0.955646	+	0.294518i	$0.0951589\pi$
$227$	252.822	+	2620.77i	0.0739225	+	0.766284i	−0.881724	+	0.471766i	$0.843617\pi$
$228$	−275.456	−	111.520i	−0.0800110	−	0.0323929i
$229$	−3622.96	+	1202.90i	−1.04547	+	0.347119i	−0.785736	−	0.618563i	$-0.787715\pi$
$229$	−3622.96	+	1202.90i	−1.04547	+	0.347119i	−0.259730	+	0.965681i	$0.583634\pi$
$230$	−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	0.661666	+	0.749799i	$0.269850\pi$
$233$	−924.002	+	4048.32i	−0.259800	+	1.13826i	−0.921466	+	0.388459i	$0.873007\pi$
$234$	−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	−0.906089	−	0.423088i	$-0.860946\pi$
$239$	−3658.68	−	5245.00i	−0.990212	−	1.41954i	−0.0841233	−	0.996455i	$-0.526809\pi$
$240$	121.838	+	410.514i	0.0327693	+	0.110411i
$241$	449.990	+	1016.54i	0.120276	+	0.271705i	0.964402	−	0.264439i	$-0.0851867\pi$
$241$	449.990	+	1016.54i	0.120276	+	0.271705i	−0.844127	+	0.536144i	$0.819881\pi$
$242$	−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	−0.390707	−	0.920515i	$-0.627769\pi$
$251$	−609.434	+	202.346i	−0.153255	+	0.0508843i	0.237452	+	0.971399i	$0.423688\pi$
$252$	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	0.875830	+	0.482620i	$0.160315\pi$
$257$	810.392	+	5012.56i	0.196696	+	1.21663i	−0.679134	+	0.734014i	$0.737644\pi$
$258$	−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	−0.749355	−	0.662168i	$-0.769637\pi$
$263$	558.177	−	800.189i	0.130869	−	0.187611i	0.880225	+	0.474557i	$0.157392\pi$
$264$	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	0.922440	+	0.386141i	$0.126192\pi$
$269$	−329.497	+	2038.06i	−0.0746833	+	0.461943i	−0.997123	+	0.0758014i	$0.975849\pi$
$270$	2246.07	+	588.990i	0.506265	+	0.132758i
$271$	−372.237	−	72.4931i	−0.0834383	−	0.0162496i	0.149267	−	0.988797i	$-0.452309\pi$
$271$	−372.237	−	72.4931i	−0.0834383	−	0.0162496i	−0.232705	+	0.972547i	$0.574758\pi$
$272$	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	−0.449537	−	0.893262i	$-0.648411\pi$
$277$	−6196.44	−	2057.36i	−1.34407	−	0.446263i	−0.894534	+	0.446999i	$0.852493\pi$
$278$	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	0.634912	−	0.772584i	$-0.281036\pi$
$281$	−1222.75	−	1533.27i	−0.259583	−	0.325507i	−0.894495	+	0.447077i	$0.852465\pi$
$282$	4284.50	−	834.407i	0.904746	−	0.176199i
$283$	1224.12	+	3326.33i	0.257125	+	0.698692i	0.999585	+	0.0288017i	$0.00916912\pi$
$283$	1224.12	+	3326.33i	0.257125	+	0.698692i	−0.742460	+	0.669890i	$0.766341\pi$
$284$	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	−0.119193	−	0.992871i	$-0.538031\pi$
$293$	−5541.67	−	4135.85i	−1.10494	−	0.824639i	−0.985747	+	0.168232i	$0.946194\pi$
$294$	−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	−0.999469	−	0.0325696i	$-0.989631\pi$
$307$	−456.399	+	1999.62i	−0.0848472	+	0.371740i	0.914622	+	0.404309i	$0.132488\pi$
$308$	−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	0.999081	+	0.0428523i	$0.0136445\pi$
$311$	9079.67	+	4372.54i	1.65550	+	0.797248i	0.656420	+	0.754395i	$0.272070\pi$
$312$	−816.041	+	898.551i	−0.148074	+	0.163046i
$313$	−5164.88	−	4396.92i	−0.932703	−	0.794022i	0.0460762	−	0.998938i	$-0.485328\pi$
$313$	−5164.88	−	4396.92i	−0.932703	−	0.794022i	−0.978780	+	0.204916i	$0.934308\pi$
$314$	−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	0.572703	+	0.819763i	$0.305895\pi$
$317$	2327.58	+	10197.8i	0.412397	+	1.80683i	−0.160306	+	0.987067i	$0.551248\pi$
$318$	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	−0.649546	−	0.760322i	$-0.725041\pi$
$331$	2107.67	−	4761.26i	0.349994	−	0.790642i	0.999540	−	0.0303202i	$-0.00965271\pi$
$332$	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	0.463592	−	0.886049i	$-0.346560\pi$
$337$	−332.733	−	187.392i	−0.0537838	−	0.0302904i	−0.517376	+	0.855758i	$0.673091\pi$
$338$	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	0.320127	+	0.947375i	$0.396275\pi$
$347$	−4137.11	+	7930.07i	−0.640034	+	1.22682i	−0.960160	+	0.279450i	$0.909848\pi$
$348$	493.173	−	5112.26i	0.0759680	−	0.787488i
$349$	471.276	−	351.722i	0.0722832	−	0.0539463i	−0.561360	−	0.827571i	$-0.689722\pi$
$349$	471.276	−	351.722i	0.0722832	−	0.0539463i	0.633644	+	0.773625i	$0.281559\pi$
$350$	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	−0.815436	−	0.578847i	$-0.803503\pi$
$353$	−1744.44	+	1689.39i	−0.263023	+	0.254723i	0.552413	+	0.833570i	$0.313707\pi$
$354$	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	0.342953	−	0.939353i	$-0.388573\pi$
$359$	−3128.92	−	2335.17i	−0.459995	−	0.343303i	−0.802948	+	0.596050i	$0.796736\pi$
$360$	−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	−0.479109	−	0.877755i	$-0.659040\pi$
$367$	−3275.16	+	858.849i	−0.465837	+	0.122157i	0.0132728	+	0.999912i	$0.495775\pi$
$368$	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	−0.955388	−	0.295354i	$-0.904562\pi$
$373$	−5585.45	−	9213.79i	−0.775345	−	1.27901i	0.180042	−	0.983659i	$-0.442376\pi$
$374$	−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	−0.978840	−	0.204626i	$-0.934402\pi$
$379$	−111.572	−	3479.24i	−0.0151216	−	0.471547i	0.963719	−	0.266921i	$-0.0860061\pi$
$380$	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	−0.998364	−	0.0571717i	$-0.981792\pi$
$383$	−1445.40	−	4870.02i	−0.192836	−	0.649729i	0.805528	−	0.592558i	$-0.201882\pi$
$384$	−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	−0.994529	−	0.104461i	$-0.966688\pi$
$389$	−11451.8	−	7454.29i	−1.49262	−	0.971587i	−0.498089	−	0.867126i	$-0.665965\pi$
$390$	−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	0.938307	+	0.345804i	$0.112394\pi$
$397$	7425.86	+	10645.5i	0.938774	+	1.34580i	0.000467259		1.00000i	$0.499851\pi$
$398$	−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	0.357970	−	0.933733i	$-0.383469\pi$
$401$	4766.61	+	306.026i	0.593599	+	0.0381103i	0.235628	+	0.971843i	$0.424285\pi$
$402$	−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	0.963750	+	0.266808i	$0.0859688\pi$
$409$	157.775	+	4920.02i	0.0190745	+	0.594815i	−0.944675	+	0.328007i	$0.893623\pi$
$410$	−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	0.932365	−	0.361518i	$-0.117741\pi$
$419$	325.156	+	734.533i	0.0379115	+	0.0856427i	−0.894454	+	0.447161i	$0.852435\pi$
$420$	−45.7415	−	474.158i	−0.00531418	−	0.0550870i
$421$	692.600	−	181.621i	0.0801787	−	0.0210253i	−0.213347	−	0.976976i	$-0.568437\pi$
$421$	692.600	−	181.621i	0.0801787	−	0.0210253i	0.293526	+	0.955951i	$0.405171\pi$
$422$	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	0.764211	−	0.644966i	$-0.223129\pi$
$431$	9964.14	+	2612.91i	1.11359	+	0.292017i	0.349375	+	0.936983i	$0.386394\pi$
$432$	3508.38	−	1975.88i	0.390734	−	0.220057i
$433$	3181.43	−	2374.36i	0.353094	−	0.263521i	−0.406870	−	0.913486i	$-0.633380\pi$
$433$	3181.43	−	2374.36i	0.353094	−	0.263521i	0.759964	+	0.649965i	$0.225216\pi$
$434$	−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	0.381799	−	0.924245i	$-0.375305\pi$
$439$	12660.9	−	9449.09i	1.37648	−	1.02729i	0.994677	−	0.103045i	$-0.0328586\pi$
$440$	−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	−0.327994	−	0.944680i	$-0.606372\pi$
$443$	−8250.71	−	1063.81i	−0.884883	−	0.114093i	−0.556889	+	0.830587i	$0.688005\pi$
$444$	−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	−0.965464	−	0.260536i	$-0.916101\pi$
$449$	−134.994	+	454.840i	−0.0141888	+	0.0478067i	0.951275	+	0.308342i	$0.0997743\pi$
$450$	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	−0.467090	−	0.884210i	$-0.654698\pi$
$457$	4899.39	−	11067.8i	0.501496	−	1.13289i	0.968586	−	0.248678i	$-0.0799962\pi$
$458$	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	−0.881389	−	0.472391i	$-0.843391\pi$
$461$	102.048	−	195.607i	0.0103099	−	0.0197621i	0.891699	+	0.452628i	$0.149514\pi$
$462$	57.6656	−	72.3104i	0.00580703	−	0.00728178i
$463$	11.8398	−	5.70175i	0.00118843	−	0.000572317i	−0.433289	−	0.901255i	$-0.642647\pi$
$463$	11.8398	−	5.70175i	0.00118843	−	0.000572317i	0.434478	+	0.900683i	$0.356933\pi$
$464$	−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	0.439884	−	0.898055i	$-0.355020\pi$
$467$	3859.89	+	1012.18i	0.382472	+	0.100296i	−0.0574120	+	0.998351i	$0.518285\pi$
$468$	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	−0.0878194	−	0.996136i	$-0.527990\pi$
$479$	2144.87	−	417.714i	0.204596	−	0.0398451i	0.292416	+	0.956291i	$0.405541\pi$
$480$	−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	0.915982	+	0.401218i	$0.131413\pi$
$487$	2845.77	+	12468.1i	0.264793	+	1.16013i	−0.651189	+	0.758915i	$0.725730\pi$
$488$	−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	0.533038	−	0.846091i	$-0.321050\pi$
$491$	−5044.50	−	8321.44i	−0.463656	−	0.764850i	−0.996694	+	0.0812415i	$0.974111\pi$
$492$	−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	−0.985482	−	0.169781i	$-0.945694\pi$
$499$	98.6841	−	3077.33i	0.00885312	−	0.276073i	0.994335	−	0.106292i	$-0.0338978\pi$
$500$	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	0.999475	+	0.0323921i	$0.0103125\pi$
$503$	5124.17	+	9822.08i	0.454226	+	0.870666i	−0.545249	+	0.838274i	$0.683565\pi$
$504$	−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	−0.923529	−	0.383527i	$-0.874709\pi$
$509$	−5203.14	+	5729.23i	−0.453094	+	0.498907i	0.470435	+	0.882435i	$0.344097\pi$
$510$	−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	0.645444	−	0.763807i	$-0.276672\pi$
$521$	2476.81	+	1612.23i	0.208275	+	0.135572i	−0.437170	+	0.899379i	$0.644019\pi$
$522$	−21174.9	+	10197.3i	−1.77548	+	0.855026i
$523$	10455.9	−	13111.3i	0.874197	−	1.09621i	−0.120434	−	0.992721i	$-0.538429\pi$
$523$	10455.9	−	13111.3i	0.874197	−	1.09621i	0.994631	−	0.103487i	$-0.0329999\pi$
$524$	−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	0.968944	+	0.247281i	$0.0795369\pi$
$541$	7769.05	+	14891.8i	0.617408	+	1.18345i	−0.351536	+	0.936174i	$0.614341\pi$
$542$	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	0.692700	−	0.721226i	$-0.256421\pi$
$547$	−3926.38	−	8869.77i	−0.306910	−	0.693316i	−0.999610	+	0.0279099i	$0.991115\pi$
$548$	−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	−0.984473	−	0.175537i	$-0.943834\pi$
$557$	−9401.98	+	10352.6i	−0.715214	+	0.787531i	0.269258	+	0.963068i	$0.413221\pi$
$558$	−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	−0.455792	−	0.890086i	$-0.650644\pi$
$563$	−10607.0	+	680.995i	−0.794020	+	0.0509778i	−0.338228	+	0.941064i	$0.609828\pi$
$564$	−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	0.877487	−	0.479600i	$-0.159218\pi$
$569$	−1378.48	−	3745.78i	−0.101562	−	0.275977i	−0.979049	+	0.203623i	$0.934728\pi$
$570$	336.891	+	555.736i	0.0247558	+	0.0408372i
$571$	−19975.7	−	9619.79i	−1.46402	−	0.705036i	−0.479057	−	0.877784i	$-0.659021\pi$
$571$	−19975.7	−	9619.79i	−1.46402	−	0.705036i	−0.984966	+	0.172747i	$0.944736\pi$
$572$	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	−0.636315	−	0.771430i	$-0.719542\pi$
$587$	−15020.3	+	1936.66i	−1.05614	+	0.136174i	−0.419827	+	0.907604i	$0.637909\pi$
$588$	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	−0.407294	−	0.913297i	$-0.633528\pi$
$593$	−10028.3	+	643.836i	−0.694455	+	0.0445855i	−0.287161	+	0.957882i	$0.592711\pi$
$594$	−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	−0.926131	−	0.377202i	$-0.876886\pi$
$599$	−24087.1	+	4690.96i	−1.64303	+	0.319979i	−0.716895	+	0.697181i	$0.754437\pi$
$600$	701.389	−	1905.90i	0.0477235	−	0.129680i
$601$	−5581.78	−	3143.60i	−0.378844	−	0.213361i	0.289559	−	0.957160i	$-0.406491\pi$
$601$	−5581.78	−	3143.60i	−0.378844	−	0.213361i	−0.668403	+	0.743799i	$0.733022\pi$
$602$	−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	0.742822	−	0.669489i	$-0.233487\pi$
$607$	25701.3	−	6739.67i	1.71859	−	0.450667i	0.975765	+	0.218822i	$0.0702215\pi$
$608$	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	−0.998954	−	0.0457269i	$-0.985440\pi$
$613$	−4066.66	−	11050.4i	−0.267946	−	0.728096i	0.731008	−	0.682369i	$-0.239050\pi$
$614$	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	−0.836678	−	0.547696i	$-0.815505\pi$
$617$	−1841.04	−	19084.3i	−0.120126	−	1.24523i	0.716552	−	0.697534i	$-0.245719\pi$
$618$	−1439.56	+	377.497i	−0.0937015	+	0.0245714i
$619$	−5906.18	+	379.189i	−0.383505	+	0.0246218i	−0.254629	−	0.967039i	$-0.581953\pi$
$619$	−5906.18	+	379.189i	−0.383505	+	0.0246218i	−0.128876	+	0.991661i	$0.541137\pi$
$620$	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	0.800395	−	0.599473i	$-0.204623\pi$
$631$	15189.8	+	6149.68i	0.958315	+	0.387979i	0.157920	+	0.987452i	$0.449521\pi$
$632$	−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	0.692696	−	0.721229i	$-0.256423\pi$
$641$	−4789.76	−	9181.08i	−0.295139	−	0.565727i	−0.987835	+	0.155503i	$0.950300\pi$
$642$	13151.3	+	2561.21i	0.808474	+	0.157450i
$643$	−2146.26	−	13275.4i	−0.131633	−	0.814197i	−0.965149	−	0.261702i	$-0.915716\pi$
$643$	−2146.26	−	13275.4i	−0.131633	−	0.814197i	0.833516	−	0.552496i	$-0.186324\pi$
$644$	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	0.785357	−	0.619043i	$-0.212479\pi$
$647$	28011.0	−	3611.62i	1.70205	−	0.219455i	0.916695	+	0.399587i	$0.130847\pi$
$648$	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	0.251385	−	0.967887i	$-0.419114\pi$
$653$	−2103.44	−	698.389i	−0.126055	−	0.0418531i	−0.377440	+	0.926034i	$0.623196\pi$
$654$	−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	−0.231123	−	0.972925i	$-0.574240\pi$
$659$	13006.6	−	16309.7i	0.768838	−	0.964092i	0.999961	+	0.00883224i	$0.00281143\pi$
$660$	−253.084	+	121.879i	−0.0149262	+	0.00718807i
$661$	4423.62	+	2879.46i	0.260301	+	0.169437i	0.669067	−	0.743202i	$-0.266694\pi$
$661$	4423.62	+	2879.46i	0.260301	+	0.169437i	−0.408766	+	0.912639i	$0.634041\pi$
$662$	−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	−0.936337	−	0.351104i	$-0.885806\pi$
$673$	−8676.23	+	9553.50i	−0.496945	+	0.547192i	0.439391	+	0.898296i	$0.355194\pi$
$674$	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	−0.988199	−	0.153178i	$-0.951049\pi$
$677$	−5901.61	−	16036.6i	−0.335033	−	0.910393i	0.653166	−	0.757215i	$-0.273441\pi$
$678$	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	0.899317	+	0.437297i	$0.144064\pi$
$683$	−467.127	+	14566.7i	−0.0261700	+	0.816077i	−0.925487	+	0.378779i	$0.876344\pi$
$684$	−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	0.950162	−	0.311755i	$-0.100917\pi$
$691$	4255.41	+	7019.74i	0.234274	+	0.386459i	−0.715888	+	0.698215i	$0.753978\pi$
$692$	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	0.859412	+	0.511284i	$0.170830\pi$
$701$	−2537.69	+	11118.3i	−0.136729	+	0.599050i	−0.996141	+	0.0877662i	$0.972027\pi$
$702$	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	−0.757254	−	0.653120i	$-0.773460\pi$
$709$	−8807.94	+	5733.33i	−0.466557	+	0.303695i	0.290697	+	0.956815i	$0.406113\pi$
$710$	−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	0.325778	−	0.945446i	$-0.394374\pi$
$719$	24447.8	−	11773.4i	1.26808	−	0.610674i	0.942299	+	0.334772i	$0.108659\pi$
$720$	−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	−0.933245	−	0.359242i	$-0.883035\pi$
$727$	−5367.00	+	7693.99i	−0.273798	+	0.392510i	0.659447	+	0.751751i	$0.270791\pi$
$728$	−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	−0.602576	−	0.798061i	$-0.705859\pi$
$733$	6703.83	−	22587.4i	0.337806	−	1.13818i	0.940382	−	0.340119i	$-0.110467\pi$
$734$	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	0.463812	−	0.885934i	$-0.346481\pi$
$739$	13816.1	+	1781.39i	0.687733	+	0.0886733i	0.223921	+	0.974607i	$0.428114\pi$
$740$	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	−0.682477	−	0.730907i	$-0.739097\pi$
$743$	−3563.75	+	2659.69i	−0.175964	+	0.131325i	0.506513	+	0.862232i	$0.330934\pi$
$744$	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	0.655019	−	0.755612i	$-0.272661\pi$
$751$	17595.6	+	4614.11i	0.854957	+	0.224196i	0.199938	+	0.979809i	$0.435926\pi$
$752$	−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	0.615404	−	0.788212i	$-0.288993\pi$
$757$	10604.2	+	4293.15i	0.509134	+	0.206126i	−0.106270	+	0.994337i	$0.533891\pi$
$758$	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	0.199846	−	0.979827i	$-0.435956\pi$
$761$	17944.8	−	4705.67i	0.854793	−	0.224153i	0.654948	+	0.755674i	$0.272691\pi$
$762$	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	+

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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