LMFDB - Embedded newform 197.4.g.a.16.3

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			16.3
Character	$\chi$	$=$	197.16
Dual form			197.4.g.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.92908 - 0.316457i) q^{2} +(4.70953 - 6.75146i) q^{3} +(16.2613 + 2.09667i) q^{4} +(6.63060 - 4.31604i) q^{5} +(-25.3502 + 31.7881i) q^{6} +(4.33945 - 0.278602i) q^{7} +(-40.7048 - 7.92726i) q^{8} +(-14.0777 - 38.2538i) q^{9} +O(q^{10})$	\(q+(-4.92908 - 0.316457i) q^{2} +(4.70953 - 6.75146i) q^{3} +(16.2613 + 2.09667i) q^{4} +(6.63060 - 4.31604i) q^{5} +(-25.3502 + 31.7881i) q^{6} +(4.33945 - 0.278602i) q^{7} +(-40.7048 - 7.92726i) q^{8} +(-14.0777 - 38.2538i) q^{9} +(-34.0486 + 19.1758i) q^{10} +(8.49702 - 28.6293i) q^{11} +(90.7388 - 99.9135i) q^{12} +(0.892088 - 27.8186i) q^{13} -21.4776 q^{14} +(2.08740 - 65.0927i) q^{15} +(71.2506 + 18.6841i) q^{16} +(20.1806 + 19.5438i) q^{17} +(57.2846 + 193.011i) q^{18} +(80.5898 + 38.8100i) q^{19} +(116.872 - 56.2825i) q^{20} +(18.5558 - 30.6097i) q^{21} +(-50.9424 + 138.427i) q^{22} +(-14.0692 - 87.0228i) q^{23} +(-245.221 + 237.483i) q^{24} +(-25.2613 + 57.0657i) q^{25} +(-13.2006 + 136.838i) q^{26} +(-109.580 - 28.7352i) q^{27} +(71.1494 + 4.56794i) q^{28} +(150.601 - 165.828i) q^{29} +(-30.8880 + 320.187i) q^{30} +(-68.3505 + 27.6721i) q^{31} +(-30.4321 - 10.1042i) q^{32} +(-153.273 - 192.198i) q^{33} +(-93.2869 - 102.719i) q^{34} +(27.5707 - 20.5765i) q^{35} +(-148.717 - 651.574i) q^{36} +(27.2570 - 7.14762i) q^{37} +(-384.952 - 216.801i) q^{38} +(-183.615 - 137.035i) q^{39} +(-304.111 + 123.121i) q^{40} +(-295.899 - 286.562i) q^{41} +(-101.150 + 145.005i) q^{42} +(-16.3071 + 54.9439i) q^{43} +(198.199 - 447.735i) q^{44} +(-258.449 - 192.885i) q^{45} +(41.8090 + 433.394i) q^{46} +(-1.17965 - 2.26117i) q^{47} +(461.702 - 393.053i) q^{48} +(-321.431 + 41.4439i) q^{49} +(142.574 - 273.287i) q^{50} +(226.990 - 44.2064i) q^{51} +(72.8329 - 450.497i) q^{52} +(36.6583 + 380.002i) q^{53} +(531.033 + 176.315i) q^{54} +(-67.2248 - 226.503i) q^{55} +(-178.845 - 23.0595i) q^{56} +(641.564 - 361.322i) q^{57} +(-794.802 + 769.723i) q^{58} +(-637.432 - 358.995i) q^{59} +(170.422 - 1054.12i) q^{60} +(119.983 + 172.005i) q^{61} +(345.662 - 114.768i) q^{62} +(-71.7471 - 162.078i) q^{63} +(-399.406 - 161.702i) q^{64} +(-114.151 - 188.304i) q^{65} +(694.670 + 995.862i) q^{66} +(379.049 + 726.566i) q^{67} +(287.187 + 360.120i) q^{68} +(-653.790 - 314.849i) q^{69} +(-142.410 + 92.6983i) q^{70} +(212.793 + 578.226i) q^{71} +(269.784 + 1668.71i) q^{72} +(-534.631 + 140.197i) q^{73} +(-136.614 + 26.6055i) q^{74} +(266.308 + 439.303i) q^{75} +(1229.13 + 800.073i) q^{76} +(28.8962 - 126.603i) q^{77} +(861.686 + 733.564i) q^{78} +(-153.592 - 99.9772i) q^{79} +(553.076 - 183.634i) q^{80} +(127.952 - 108.927i) q^{81} +(1367.82 + 1506.13i) q^{82} +(429.939 - 207.048i) q^{83} +(365.920 - 458.849i) q^{84} +(218.161 + 42.4869i) q^{85} +(97.7662 - 265.662i) q^{86} +(-410.325 - 1797.75i) q^{87} +(-572.821 + 1097.99i) q^{88} +(-318.409 - 128.910i) q^{89} +(1212.87 + 1032.53i) q^{90} +(-3.87914 - 120.966i) q^{91} +(-46.3257 - 1444.61i) q^{92} +(-135.072 + 591.788i) q^{93} +(5.09902 + 11.5188i) q^{94} +(701.864 - 90.4954i) q^{95} +(-211.539 + 157.876i) q^{96} +(-918.381 + 1514.97i) q^{97} +(1597.47 - 102.561i) q^{98} +(-1214.80 + 77.9925i) 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 $

$2$	−4.92908	−	0.316457i	−1.74269	−	0.111885i	−0.840114	−	0.542410i	$-0.817512\pi$
$2$	−4.92908	−	0.316457i	−1.74269	−	0.111885i	−0.902578	+	0.430526i	$0.858328\pi$
$3$	4.70953	−	6.75146i	0.906349	−	1.29932i	−0.0474497	−	0.998874i	$-0.515109\pi$
$3$	4.70953	−	6.75146i	0.906349	−	1.29932i	0.953799	−	0.300446i	$-0.0971355\pi$
$4$	16.2613	+	2.09667i	2.03267	+	0.262084i
$5$	6.63060	−	4.31604i	0.593059	−	0.386038i	−0.213718	−	0.976895i	$-0.568557\pi$
$5$	6.63060	−	4.31604i	0.593059	−	0.386038i	0.806776	+	0.590857i	$0.201210\pi$
$6$	−25.3502	+	31.7881i	−1.72486	+	2.16291i
$7$	4.33945	−	0.278602i	0.234308	−	0.0150431i	0.0535268	−	0.998566i	$-0.482954\pi$
$7$	4.33945	−	0.278602i	0.234308	−	0.0150431i	0.180781	+	0.983523i	$0.442137\pi$
$8$	−40.7048	−	7.92726i	−1.79891	−	0.350339i
$9$	−14.0777	−	38.2538i	−0.521398	−	1.41681i
$10$	−34.0486	+	19.1758i	−1.07671	+	0.606392i
$11$	8.49702	−	28.6293i	0.232904	−	0.784732i	−0.758244	−	0.651971i	$-0.773942\pi$
$11$	8.49702	−	28.6293i	0.232904	−	0.784732i	0.991148	−	0.132761i	$-0.0423843\pi$
$12$	90.7388	−	99.9135i	2.18284	−	2.40355i
$13$	0.892088	−	27.8186i	0.0190324	−	0.593499i	−0.944901	−	0.327356i	$-0.893842\pi$
$13$	0.892088	−	27.8186i	0.0190324	−	0.593499i	0.963934	−	0.266143i	$-0.0857494\pi$
$14$	−21.4776			−0.410010
$15$	2.08740	−	65.0927i	0.0359309	−	1.12046i
$16$	71.2506	+	18.6841i	1.11329	+	0.291939i
$17$	20.1806	+	19.5438i	0.287912	+	0.278828i	0.825526	−	0.564363i	$-0.190878\pi$
$17$	20.1806	+	19.5438i	0.287912	+	0.278828i	−0.537614	+	0.843191i	$0.680674\pi$
$18$	57.2846	+	193.011i	0.750117	+	2.52739i
$19$	80.5898	+	38.8100i	0.973083	+	0.468612i	0.851721	−	0.523996i	$-0.175559\pi$
$19$	80.5898	+	38.8100i	0.973083	+	0.468612i	0.121362	+	0.992608i	$0.461274\pi$
$20$	116.872	−	56.2825i	1.30667	−	0.629257i
$21$	18.5558	−	30.6097i	0.192819	−	0.318075i
$22$	−50.9424	+	138.427i	−0.493680	+	1.34149i
$23$	−14.0692	−	87.0228i	−0.127549	−	0.788935i	−0.968718	−	0.248163i	$-0.920173\pi$
$23$	−14.0692	−	87.0228i	−0.127549	−	0.788935i	0.841169	−	0.540772i	$-0.181868\pi$
$24$	−245.221	+	237.483i	−2.08565	+	2.01984i
$25$	−25.2613	+	57.0657i	−0.202090	+	0.456526i
$26$	−13.2006	+	136.838i	−0.0995709	+	1.03216i
$27$	−109.580	−	28.7352i	−0.781060	−	0.204818i
$28$	71.1494	+	4.56794i	0.480213	+	0.0308307i
$29$	150.601	−	165.828i	0.964342	−	1.06185i	−0.0337087	−	0.999432i	$-0.510732\pi$
$29$	150.601	−	165.828i	0.964342	−	1.06185i	0.998050	−	0.0624156i	$-0.0198804\pi$
$30$	−30.8880	+	320.187i	−0.187978	+	1.94859i
$31$	−68.3505	+	27.6721i	−0.396004	+	0.160324i	−0.564607	−	0.825360i	$-0.690972\pi$
$31$	−68.3505	+	27.6721i	−0.396004	+	0.160324i	0.168603	+	0.985684i	$0.446074\pi$
$32$	−30.4321	−	10.1042i	−0.168115	−	0.0558181i
$33$	−153.273	−	192.198i	−0.808525	−	1.01386i
$34$	−93.2869	−	102.719i	−0.470546	−	0.518124i
$35$	27.5707	−	20.5765i	0.133151	−	0.0993733i
$36$	−148.717	−	651.574i	−0.688507	−	3.01655i
$37$	27.2570	−	7.14762i	0.121109	−	0.0317584i	−0.192603	−	0.981277i	$-0.561693\pi$
$37$	27.2570	−	7.14762i	0.121109	−	0.0317584i	0.313711	+	0.949518i	$0.398428\pi$
$38$	−384.952	−	216.801i	−1.64335	−	0.925519i
$39$	−183.615	−	137.035i	−0.753895	−	0.562646i
$40$	−304.111	+	123.121i	−1.20211	+	0.486679i
$41$	−295.899	−	286.562i	−1.12711	−	1.09155i	−0.994955	−	0.100320i	$-0.968013\pi$
$41$	−295.899	−	286.562i	−1.12711	−	1.09155i	−0.132159	−	0.991229i	$-0.542191\pi$
$42$	−101.150	+	145.005i	−0.371612	+	0.532734i
$43$	−16.3071	+	54.9439i	−0.0578326	+	0.194857i	−0.982621	−	0.185626i	$-0.940569\pi$
$43$	−16.3071	+	54.9439i	−0.0578326	+	0.194857i	0.924788	+	0.380483i	$0.124242\pi$
$44$	198.199	−	447.735i	0.679083	−	1.53406i
$45$	−258.449	−	192.885i	−0.856161	−	0.638969i
$46$	41.8090	+	433.394i	0.134009	+	1.38914i
$47$	−1.17965	−	2.26117i	−0.00366105	−	0.00701755i	0.884762	−	0.466043i	$-0.154321\pi$
$47$	−1.17965	−	2.26117i	−0.00366105	−	0.00701755i	−0.888423	+	0.459026i	$0.848199\pi$
$48$	461.702	−	393.053i	1.38835	−	1.18192i
$49$	−321.431	+	41.4439i	−0.937116	+	0.120828i
$50$	142.574	−	273.287i	0.403260	−	0.772973i
$51$	226.990	−	44.2064i	0.623235	−	0.121375i
$52$	72.8329	−	450.497i	0.194233	−	1.20140i
$53$	36.6583	+	380.002i	0.0950077	+	0.984854i	0.912544	+	0.408978i	$0.134115\pi$
$53$	36.6583	+	380.002i	0.0950077	+	0.984854i	−0.817537	+	0.575876i	$0.804661\pi$
$54$	531.033	+	176.315i	1.33823	+	0.444323i
$55$	−67.2248	−	226.503i	−0.164811	−	0.555302i
$56$	−178.845	−	23.0595i	−0.426770	−	0.0550259i
$57$	641.564	−	361.322i	1.49083	−	0.839619i
$58$	−794.802	+	769.723i	−1.79935	+	1.74258i
$59$	−637.432	−	358.995i	−1.40655	−	0.792155i	−0.413575	−	0.910470i	$-0.635720\pi$
$59$	−637.432	−	358.995i	−1.40655	−	0.792155i	−0.992976	+	0.118315i	$0.962251\pi$
$60$	170.422	−	1054.12i	0.366689	−	2.26810i
$61$	119.983	+	172.005i	0.251841	+	0.361033i	0.925981	−	0.377571i	$-0.123241\pi$
$61$	119.983	+	172.005i	0.251841	+	0.361033i	−0.674140	+	0.738604i	$0.735486\pi$
$62$	345.662	−	114.768i	0.708050	−	0.235089i
$63$	−71.7471	−	162.078i	−0.143481	−	0.324126i
$64$	−399.406	−	161.702i	−0.780091	−	0.315824i
$65$	−114.151	−	188.304i	−0.217826	−	0.359327i
$66$	694.670	+	995.862i	1.29558	+	1.85731i
$67$	379.049	+	726.566i	0.691167	+	1.32484i	0.934871	+	0.354988i	$0.115515\pi$
$67$	379.049	+	726.566i	0.691167	+	1.32484i	−0.243704	+	0.969850i	$0.578362\pi$
$68$	287.187	+	360.120i	0.512154	+	0.642221i
$69$	−653.790	−	314.849i	−1.14068	−	0.549324i
$70$	−142.410	+	92.6983i	−0.243160	+	0.158280i
$71$	212.793	+	578.226i	0.355688	+	0.966519i	0.982321	+	0.187204i	$0.0599426\pi$
$71$	212.793	+	578.226i	0.355688	+	0.966519i	−0.626633	+	0.779314i	$0.715568\pi$
$72$	269.784	+	1668.71i	0.441588	+	2.73138i
$73$	−534.631	+	140.197i	−0.857175	+	0.224778i	−0.655985	−	0.754774i	$-0.727746\pi$
$73$	−534.631	+	140.197i	−0.857175	+	0.224778i	−0.201191	+	0.979552i	$0.564481\pi$
$74$	−136.614	+	26.6055i	−0.214608	+	0.0417950i
$75$	266.308	+	439.303i	0.410008	+	0.676352i
$76$	1229.13	+	800.073i	1.85514	+	1.20756i
$77$	28.8962	−	126.603i	0.0427666	−	0.187373i
$78$	861.686	+	733.564i	1.25086	+	1.06487i
$79$	−153.592	−	99.9772i	−0.218740	−	0.142384i	0.431500	−	0.902113i	$-0.357985\pi$
$79$	−153.592	−	99.9772i	−0.218740	−	0.142384i	−0.650240	+	0.759729i	$0.725331\pi$
$80$	553.076	−	183.634i	0.772947	−	0.256636i
$81$	127.952	−	108.927i	0.175518	−	0.149420i
$82$	1367.82	+	1506.13i	1.84209	+	2.02834i
$83$	429.939	−	207.048i	0.568578	−	0.273812i	−0.127429	−	0.991848i	$-0.540673\pi$
$83$	429.939	−	207.048i	0.568578	−	0.273812i	0.696007	+	0.718035i	$0.254958\pi$
$84$	365.920	−	458.849i	0.475300	−	0.596007i
$85$	218.161	+	42.4869i	0.278387	+	0.0542159i
$86$	97.7662	−	265.662i	0.122586	−	0.333106i
$87$	−410.325	−	1797.75i	−0.505649	−	2.21539i
$88$	−572.821	+	1097.99i	−0.693897	+	1.33007i
$89$	−318.409	−	128.910i	−0.379228	−	0.153533i	0.177717	−	0.984082i	$-0.443129\pi$
$89$	−318.409	−	128.910i	−0.379228	−	0.153533i	−0.556945	+	0.830549i	$0.688027\pi$
$90$	1212.87	+	1032.53i	1.42053	+	1.20932i
$91$	−3.87914	−	120.966i	−0.00446862	−	0.139348i
$92$	−46.3257	−	1444.61i	−0.0524977	−	1.63707i
$93$	−135.072	+	591.788i	−0.150605	+	0.659845i
$94$	5.09902	+	11.5188i	0.00559493	+	0.0126391i
$95$	701.864	−	90.4954i	0.757997	−	0.0977329i
$96$	−211.539	+	157.876i	−0.224897	+	0.167845i
$97$	−918.381	+	1514.97i	−0.961314	+	1.58579i	−0.160364	+	0.987058i	$0.551267\pi$
$97$	−918.381	+	1514.97i	−0.961314	+	1.58579i	−0.800950	+	0.598731i	$0.795672\pi$
$98$	1597.47	−	102.561i	1.64662	−	0.105717i
$99$	−1214.80	+	77.9925i	−1.23325	+	0.0791772i
$100$	−530.431	+	875.001i	−0.530431	+	0.875001i
$101$	956.442	−	713.811i	0.942273	−	0.703236i	−0.0127035	−	0.999919i	$-0.504044\pi$
$101$	956.442	−	713.811i	0.942273	−	0.703236i	0.954976	+	0.296683i	$0.0958805\pi$
$102$	−1132.84	+	146.064i	−1.09969	+	0.141789i
$103$	−119.428	−	269.790i	−0.114248	−	0.258089i	0.848137	−	0.529777i	$-0.177724\pi$
$103$	−119.428	−	269.790i	−0.114248	−	0.258089i	−0.962385	+	0.271688i	$0.912418\pi$
$104$	−256.837	+	1125.28i	−0.242163	+	1.06099i
$105$	−9.07680	−	283.048i	−0.00843624	−	0.263073i
$106$	−60.4374	−	1884.66i	−0.0553792	−	1.72693i
$107$	−222.112	−	189.087i	−0.200676	−	0.170838i	0.542238	−	0.840225i	$-0.317577\pi$
$107$	−222.112	−	189.087i	−0.200676	−	0.170838i	−0.742914	+	0.669387i	$0.766557\pi$
$108$	−1721.67	−	697.025i	−1.53396	−	0.621030i
$109$	692.507	−	1327.41i	0.608534	−	1.16645i	−0.363498	−	0.931595i	$-0.618418\pi$
$109$	692.507	−	1327.41i	0.608534	−	1.16645i	0.972032	−	0.234850i	$-0.0754599\pi$
$110$	259.678	+	1137.72i	0.225085	+	0.986161i
$111$	80.1106	−	217.686i	0.0685024	−	0.186143i
$112$	314.394	+	61.2282i	0.265245	+	0.0516564i
$113$	822.491	−	1031.37i	0.684721	−	0.858613i	−0.311059	−	0.950391i	$-0.600684\pi$
$113$	822.491	−	1031.37i	0.684721	−	0.858613i	0.995780	+	0.0917778i	$0.0292549\pi$
$114$	−3276.66	+	1577.96i	−2.69200	+	1.29640i
$115$	−468.881	−	516.290i	−0.380203	−	0.418646i
$116$	2796.66	−	2380.83i	2.23848	−	1.90564i
$117$	−1076.72	+	357.497i	−0.850796	+	0.282484i
$118$	3028.34	+	1971.23i	2.36256	+	1.53785i
$119$	93.0175	+	79.1869i	0.0716546	+	0.0610005i
$120$	−600.974	+	2633.04i	−0.457176	+	2.00302i
$121$	368.059	+	239.580i	0.276528	+	0.180000i
$122$	−536.975	−	885.796i	−0.398487	−	0.657346i
$123$	−3328.26	+	648.178i	−2.43983	+	0.475157i
$124$	−1169.49	+	306.677i	−0.846962	+	0.222100i
$125$	236.636	+	1463.68i	0.169323	+	1.04732i
$126$	302.356	+	821.600i	0.213778	+	0.580904i
$127$	−1366.87	+	889.734i	−0.955041	+	0.621663i	−0.925842	−	0.377911i	$-0.876643\pi$
$127$	−1366.87	+	889.734i	−0.955041	+	0.621663i	−0.0291988	+	0.999574i	$0.509296\pi$
$128$	2148.65	+	1034.74i	1.48372	+	0.714521i
$129$	294.153	+	368.856i	0.200765	+	0.251752i
$130$	503.069	+	964.290i	0.339401	+	0.650568i
$131$	815.668	+	1169.32i	0.544009	+	0.779878i	0.993552	−	0.113381i	$-0.0361680\pi$
$131$	815.668	+	1169.32i	0.544009	+	0.779878i	−0.449542	+	0.893259i	$0.648413\pi$
$132$	−2089.44	−	3446.76i	−1.37775	−	2.27274i
$133$	360.528	+	145.961i	0.235050	+	0.0951614i
$134$	−1638.43	−	3701.25i	−1.05626	−	2.38612i
$135$	−850.601	+	282.419i	−0.542282	+	0.180050i
$136$	−666.517	−	955.503i	−0.420246	−	0.602454i
$137$	221.638	−	1370.91i	0.138218	−	0.854926i	−0.820724	−	0.571324i	$-0.806430\pi$
$137$	221.638	−	1370.91i	0.138218	−	0.854926i	0.958942	−	0.283602i	$-0.0915294\pi$
$138$	3122.95	+	1758.81i	1.92640	+	1.08493i
$139$	1356.78	−	1313.97i	0.827918	−	0.801794i	−0.154597	−	0.987978i	$-0.549408\pi$
$139$	1356.78	−	1313.97i	0.827918	−	0.801794i	0.982515	+	0.186184i	$0.0596120\pi$
$140$	491.478	−	276.795i	0.296696	−	0.167096i
$141$	−20.8218	−	2.68467i	−0.0124362	−	0.00160348i
$142$	−865.887	−	2917.46i	−0.511716	−	1.72414i
$143$	−788.846	−	261.915i	−0.461305	−	0.153164i
$144$	−288.310	−	2988.63i	−0.166846	−	1.72953i
$145$	282.852	−	1749.54i	0.161997	−	1.00201i
$146$	2679.60	−	521.853i	1.51894	−	0.295814i
$147$	−1233.98	+	2365.31i	−0.692360	+	1.32713i
$148$	458.221	−	59.0811i	0.254497	−	0.0328138i
$149$	1744.43	−	1485.06i	0.959124	−	0.816514i	−0.0239518	−	0.999713i	$-0.507625\pi$
$149$	1744.43	−	1485.06i	0.959124	−	0.816514i	0.983076	+	0.183199i	$0.0586452\pi$
$150$	−1173.63	−	2249.64i	−0.638845	−	1.22455i
$151$	−91.2203	−	945.593i	−0.0491616	−	0.509611i	−0.986794	−	0.161982i	$-0.948211\pi$
$151$	−91.2203	−	945.593i	−0.0491616	−	0.509611i	0.937632	−	0.347629i	$-0.113013\pi$
$152$	−2972.73	−	2218.61i	−1.58632	−	1.18390i
$153$	463.527	−	1047.12i	0.244928	−	0.553296i
$154$	−182.496	+	614.889i	−0.0954931	+	0.321748i
$155$	−333.771	+	478.486i	−0.172962	+	0.247954i
$156$	−2698.51	−	2613.36i	−1.38496	−	1.34126i
$157$	1727.63	−	699.440i	0.878216	−	0.355550i	0.108621	−	0.994083i	$-0.465356\pi$
$157$	1727.63	−	699.440i	0.878216	−	0.355550i	0.769594	+	0.638533i	$0.220458\pi$
$158$	725.428	+	541.401i	0.365265	+	0.272605i
$159$	2738.21	+	1542.13i	1.36575	+	0.769176i
$160$	−245.393	+	64.3497i	−0.121250	+	0.0317955i
$161$	−85.2971	−	373.711i	−0.0417537	−	0.182935i
$162$	−665.158	+	496.420i	−0.322591	+	0.240756i
$163$	1709.17	+	1881.98i	0.821303	+	0.904346i	0.996784	−	0.0801371i	$-0.0255358\pi$
$163$	1709.17	+	1881.98i	0.821303	+	0.904346i	−0.175481	+	0.984483i	$0.556148\pi$
$164$	−4210.89	−	5280.29i	−2.00497	−	2.51415i
$165$	−1845.82	−	612.855i	−0.870891	−	0.289156i
$166$	−2184.72	+	884.497i	−1.02149	+	0.413556i
$167$	−245.681	+	2546.74i	−0.113840	+	1.18007i	0.744725	+	0.667371i	$0.232581\pi$
$167$	−245.681	+	2546.74i	−0.113840	+	1.18007i	−0.858566	+	0.512704i	$0.828644\pi$
$168$	−997.960	+	1098.86i	−0.458299	+	0.504638i
$169$	1419.41	+	91.1290i	0.646067	+	0.0414789i
$170$	−1061.89	−	278.460i	−0.479077	−	0.125629i
$171$	350.107	−	3629.22i	0.156569	−	1.62300i
$172$	−380.374	+	859.271i	−0.168623	+	0.380923i
$173$	−1664.53	+	1612.00i	−0.731512	+	0.708430i	−0.964510	−	0.264047i	$-0.914943\pi$
$173$	−1664.53	+	1612.00i	−0.731512	+	0.708430i	0.232997	+	0.972477i	$0.425147\pi$
$174$	1453.61	+	8991.10i	0.633322	+	3.91732i
$175$	−93.7214	+	254.671i	−0.0404839	+	0.110008i
$176$	1140.33	−	1881.10i	0.488385	−	0.805642i
$177$	−5425.74	+	2612.90i	−2.30409	+	1.10959i
$178$	1528.67	+	736.169i	0.643700	+	0.309990i
$179$	−438.522	−	1477.52i	−0.183110	−	0.616958i	−0.999236	−	0.0390838i	$-0.987556\pi$
$179$	−438.522	−	1477.52i	−0.183110	−	0.616958i	0.816126	−	0.577874i	$-0.196117\pi$
$180$	−3798.30	−	3678.45i	−1.57283	−	1.52320i
$181$	1883.19	+	493.830i	0.773350	+	0.202796i	0.619181	−	0.785248i	$-0.287465\pi$
$181$	1883.19	+	493.830i	0.773350	+	0.202796i	0.154169	+	0.988045i	$0.450730\pi$
$182$	−19.1599	+	597.477i	−0.00780345	+	0.243340i
$183$	1726.35			0.697352
$184$	−117.169	+	3653.77i	−0.0469448	+	1.46391i
$185$	149.881	−	165.035i	0.0595645	−	0.0655872i
$186$	853.055	−	2874.23i	0.336285	−	1.13306i
$187$	731.000	−	411.692i	0.285861	−	0.160994i
$188$	−14.4418	−	39.2429i	−0.00560252	−	0.0152239i
$189$	−483.521	−	94.1657i	−0.186090	−	0.0362410i
$190$	−3488.18	+	223.949i	−1.33189	+	0.0855102i
$191$	−2346.14	+	2941.96i	−0.888798	+	1.11452i	0.103984	+	0.994579i	$0.466841\pi$
$191$	−2346.14	+	2941.96i	−0.888798	+	1.11452i	−0.992781	+	0.119938i	$0.961730\pi$
$192$	−2972.74	+	1935.04i	−1.11739	+	0.727340i
$193$	4082.31	+	526.356i	1.52255	+	0.196311i	0.843237	−	0.537542i	$-0.180647\pi$
$193$	4082.31	+	526.356i	1.52255	+	0.196311i	0.679309	+	0.733852i	$0.262280\pi$
$194$	5006.20	−	7176.76i	1.85270	−	2.65599i
$195$	−1808.93	−	116.137i	−0.664307	−	0.0426499i
$196$	−5313.79			−1.93651
$197$	690.172	+	2677.51i	0.249608	+	0.968347i
$197$	690.172	+	2677.51i	0.249608	+	0.968347i
$198$	6012.51			2.15803
$199$	−5274.63	−	338.642i	−1.87894	−	0.120632i	−0.917858	−	0.396908i	$-0.870083\pi$
$199$	−5274.63	−	338.642i	−1.87894	−	0.120632i	−0.961078	+	0.276277i	$0.910899\pi$
$200$	1480.63	−	2122.60i	0.523482	−	0.750451i
$201$	6690.52	+	862.648i	2.34783	+	0.302719i
$202$	−4940.27	+	3215.76i	−1.72077	+	1.12010i
$203$	607.325	−	761.561i	0.209980	−	0.263306i
$204$	3783.85	−	242.931i	1.29864	−	0.0833755i
$205$	−3198.80	−	622.967i	−1.08982	−	0.212243i
$206$	503.293	+	1367.61i	0.170224	+	0.462553i
$207$	−3130.89	+	1763.28i	−1.05126	+	0.592061i
$208$	583.327	−	1965.42i	0.194454	−	0.655181i
$209$	1795.88	−	1977.46i	0.594370	−	0.654468i
$210$	−44.8324	+	1398.04i	−0.0147320	+	0.459399i
$211$	4496.44			1.46705			0.733526	−	0.679662i	$-0.237873\pi$
$211$	4496.44			1.46705			0.733526	+	0.679662i	$0.237873\pi$
$212$	−200.624	+	6256.20i	−0.0649949	+	2.02678i
$213$	4906.03	+	1286.51i	1.57819	+	0.413851i
$214$	1034.97	+	1002.31i	0.330603	+	0.320171i
$215$	129.015	+	434.693i	0.0409243	+	0.137887i
$216$	4232.63	+	2038.33i	1.33330	+	0.642086i
$217$	−288.894	+	139.124i	−0.0903751	+	0.0435224i
$218$	−3833.49	+	6323.74i	−1.19099	+	1.96467i
$219$	−1571.33	+	4269.80i	−0.484842	+	1.31747i
$220$	−618.265	−	3824.19i	−0.189470	−	1.17194i
$221$	561.684	−	543.960i	0.170964	−	0.165569i
$222$	−463.760	+	1047.64i	−0.140205	+	0.316726i
$223$	−21.7634	+	225.600i	−0.00653535	+	0.0677457i	−0.998070	−	0.0620945i	$-0.980222\pi$
$223$	−21.7634	+	225.600i	−0.00653535	+	0.0677457i	0.991535	+	0.129840i	$0.0414465\pi$
$224$	−134.874	−	35.3680i	−0.0402305	−	0.0105497i
$225$	2538.60	+	162.984i	0.752178	+	0.0482914i
$226$	−4380.51	+	4823.43i	−1.28932	+	1.41969i
$227$	181.516	−	1881.60i	0.0530733	−	0.550160i	−0.930077	−	0.367363i	$-0.880261\pi$
$227$	181.516	−	1881.60i	0.0530733	−	0.550160i	0.983151	−	0.182797i	$-0.0585150\pi$
$228$	11190.3	−	4530.44i	3.25041	−	1.31595i
$229$	4328.34	+	1437.11i	1.24902	+	0.414702i	0.861781	−	0.507280i	$-0.169349\pi$
$229$	4328.34	+	1437.11i	1.24902	+	0.414702i	0.387234	+	0.921982i	$0.373431\pi$
$230$	2147.77	+	2693.21i	0.615737	+	0.772110i
$231$	−718.665	−	791.330i	−0.204696	−	0.225393i
$232$	−7444.75	+	5556.16i	−2.10677	+	1.57233i
$233$	−112.216	−	491.649i	−0.0315515	−	0.138236i	0.956699	−	0.291079i	$-0.0940143\pi$
$233$	−112.216	−	491.649i	−0.0315515	−	0.138236i	−0.988250	+	0.152843i	$0.951157\pi$
$234$	5420.39	−	1421.39i	1.51428	−	0.397091i
$235$	−17.5811	−	9.90147i	−0.00488026	−	0.00274851i
$236$	−9612.80	−	7174.22i	−2.65144	−	1.97882i
$237$	−1398.34	+	566.124i	−0.383256	+	0.155163i
$238$	−433.431	−	419.755i	−0.118047	−	0.114322i
$239$	−666.590	+	955.606i	−0.180410	+	0.258632i	−0.900119	−	0.435645i	$-0.856520\pi$
$239$	−666.590	+	955.606i	−0.180410	+	0.258632i	0.719708	+	0.694277i	$0.244276\pi$
$240$	1364.93	−	4598.90i	0.367107	−	1.23691i
$241$	−1016.71	+	2296.77i	−0.271751	+	0.613891i	−0.997232	−	0.0743516i	$-0.976311\pi$
$241$	−1016.71	+	2296.77i	−0.271751	+	0.613891i	0.725481	+	0.688242i	$0.241617\pi$
$242$	−1738.37	−	1297.38i	−0.461764	−	0.344623i
$243$	−426.529	−	4421.42i	−0.112600	−	1.16722i
$244$	1590.45	+	3048.60i	0.417288	+	0.799863i
$245$	−1952.40	+	1662.11i	−0.509121	+	0.433421i
$246$	16610.4	−	2141.67i	4.30503	−	0.555073i
$247$	1151.53	−	2207.27i	0.296641	−	0.568605i
$248$	3001.56	−	584.553i	0.768545	−	0.149674i
$249$	626.935	−	3877.81i	0.159560	−	0.986934i
$250$	−703.207	−	7289.47i	−0.177899	−	1.84411i
$251$	2545.07	+	845.022i	0.640014	+	0.212499i	0.616662	−	0.787228i	$-0.288484\pi$
$251$	2545.07	+	845.022i	0.640014	+	0.212499i	0.0233521	+	0.999727i	$0.492566\pi$
$252$	−826.881	−	2786.04i	−0.206701	−	0.696444i
$253$	−2610.95	−	336.644i	−0.648809	−	0.0836547i
$254$	7018.98	−	3953.01i	1.73390	−	0.976512i
$255$	1314.28	−	1272.81i	0.322760	−	0.312575i
$256$	−7259.84	−	4088.67i	−1.77242	−	0.998210i
$257$	751.164	−	4646.22i	0.182320	−	1.12772i	−0.719143	−	0.694862i	$-0.755466\pi$
$257$	751.164	−	4646.22i	0.182320	−	1.12772i	0.901464	−	0.432854i	$-0.142494\pi$
$258$	−1333.18	−	1911.21i	−0.321705	−	0.461189i
$259$	116.289	−	38.6105i	0.0278990	−	0.00926310i
$260$	−1461.44	−	3301.41i	−0.348594	−	0.787481i
$261$	−8463.68	−	3426.57i	−2.00724	−	0.812640i
$262$	−3650.45	−	6021.80i	−0.860784	−	1.41995i
$263$	−2689.04	−	3854.94i	−0.630469	−	0.903825i	0.369205	−	0.929348i	$-0.379630\pi$
$263$	−2689.04	−	3854.94i	−0.630469	−	0.903825i	−0.999674	+	0.0255230i	$0.991875\pi$
$264$	4715.33	+	9038.40i	1.09927	+	2.10710i
$265$	1883.17	+	2361.42i	0.436537	+	0.547400i
$266$	−1730.88	−	833.547i	−0.398974	−	0.192136i
$267$	−2369.89	+	1542.63i	−0.543201	+	0.353585i
$268$	4640.48	+	12609.7i	1.05770	+	2.87410i
$269$	54.9895	+	340.129i	0.0124638	+	0.0770932i	0.992661	−	0.120932i	$-0.0385882\pi$
$269$	54.9895	+	340.129i	0.0124638	+	0.0770932i	−0.980197	+	0.198025i	$0.936547\pi$
$270$	4282.05	−	1122.89i	0.965176	−	0.253099i
$271$	3345.00	−	651.440i	0.749795	−	0.146023i	0.198231	−	0.980155i	$-0.436480\pi$
$271$	3345.00	−	651.440i	0.749795	−	0.146023i	0.551564	+	0.834133i	$0.314031\pi$
$272$	1072.72	+	1769.56i	0.239130	+	0.394469i
$273$	−834.965	−	543.502i	−0.185108	−	0.120492i
$274$	−1526.31	+	6687.19i	−0.336524	+	1.47441i
$275$	1419.11	+	1208.10i	0.311183	+	0.264914i
$276$	−9971.37	−	6490.64i	−2.17466	−	1.41555i
$277$	−3469.80	+	1152.05i	−0.752636	+	0.249892i	−0.665596	−	0.746313i	$-0.731822\pi$
$277$	−3469.80	+	1152.05i	−0.752636	+	0.249892i	−0.0870401	+	0.996205i	$0.527741\pi$
$278$	−7103.49	+	6047.29i	−1.53251	+	1.30465i
$279$	2020.78	+	2225.10i	0.433624	+	0.477468i
$280$	−1285.37	+	619.003i	−0.274342	+	0.132116i
$281$	571.524	−	716.668i	0.121332	−	0.152145i	−0.717456	−	0.696604i	$-0.754693\pi$
$281$	571.524	−	716.668i	0.121332	−	0.152145i	0.838788	+	0.544459i	$0.183265\pi$
$282$	101.783	+	19.8222i	0.0214931	+	0.00418579i
$283$	2471.26	−	6715.20i	0.519084	−	1.41052i	−0.359595	−	0.933108i	$-0.617085\pi$
$283$	2471.26	−	6715.20i	0.519084	−	1.41052i	0.878680	−	0.477412i	$-0.158425\pi$
$284$	2247.94	+	9848.89i	0.469687	+	2.05783i
$285$	2694.47	−	5164.80i	0.560024	−	1.07346i
$286$	3805.40	+	1540.64i	0.786776	+	0.318530i
$287$	−1363.87	−	1161.08i	−0.280512	−	0.238803i
$288$	41.8933	+	1306.39i	0.00857148	+	0.267290i
$289$	−132.174	−	4121.67i	−0.0269029	−	0.838930i
$290$	−1947.86	+	8534.12i	−0.394421	+	1.72807i
$291$	5903.09	+	13335.2i	1.18916	+	2.68633i
$292$	−8987.76	+	1158.84i	−1.80126	+	0.232247i
$293$	835.319	−	623.415i	0.166552	−	0.124301i	−0.511596	−	0.859226i	$-0.670946\pi$
$293$	835.319	−	623.415i	0.166552	−	0.124301i	0.678149	+	0.734925i	$0.262782\pi$
$294$	6830.90	−	11268.3i	1.35506	−	2.23531i
$295$	−5775.99	+	370.831i	−1.13997	+	0.0731885i
$296$	−1166.15	+	74.8693i	−0.228990	+	0.0147017i
$297$	−1753.77	+	2893.03i	−0.342640	+	0.565220i
$298$	−9068.40	+	6767.92i	−1.76281	+	1.31562i
$299$	−2433.40	+	313.752i	−0.470660	+	0.0606848i
$300$	3409.46	+	7702.02i	0.656150	+	1.48226i
$301$	−55.4562	+	242.969i	−0.0106194	+	0.0465266i
$302$	150.392	+	4689.77i	0.0286559	+	0.893596i
$303$	−314.879	−	9819.10i	−0.0597008	−	1.86169i
$304$	5016.94	+	4270.99i	0.946518	+	0.805783i
$305$	1537.94	+	622.644i	0.288729	+	0.116893i
$306$	−2616.13	+	5014.63i	−0.488739	+	0.936821i
$307$	−171.618	−	751.907i	−0.0319047	−	0.139784i	0.956467	−	0.291840i	$-0.0942676\pi$
$307$	−171.618	−	751.907i	−0.0319047	−	0.139784i	−0.988372	+	0.152057i	$0.951410\pi$
$308$	735.334	−	1998.14i	0.136038	−	0.369658i
$309$	−2383.93	−	464.270i	−0.438889	−	0.0854737i
$310$	1796.60	−	2252.87i	0.329162	−	0.412756i
$311$	923.588	−	444.777i	0.168398	−	0.0810964i	−0.347786	−	0.937574i	$-0.613066\pi$
$311$	923.588	−	444.777i	0.168398	−	0.0810964i	0.516184	+	0.856478i	$0.327352\pi$
$312$	6387.69	+	7033.55i	1.15908	+	1.27627i
$313$	6146.08	−	5232.24i	1.10990	−	0.944867i	0.111093	−	0.993810i	$-0.464565\pi$
$313$	6146.08	−	5232.24i	1.10990	−	0.944867i	0.998802	+	0.0489425i	$0.0155851\pi$
$314$	−8736.96	+	2900.87i	−1.57024	+	0.521356i
$315$	−1175.26	−	765.011i	−0.210217	−	0.136836i
$316$	−2287.99	−	1947.79i	−0.407309	−	0.346747i
$317$	−2363.66	+	10355.9i	−0.418789	+	1.83484i	0.120498	+	0.992714i	$0.461551\pi$
$317$	−2363.66	+	10355.9i	−0.418789	+	1.83484i	−0.539288	+	0.842122i	$0.681306\pi$
$318$	−13008.8	−	8467.81i	−2.29402	−	1.49324i
$319$	−3467.89	−	5720.65i	−0.608666	−	1.00406i
$320$	−3346.21	+	651.675i	−0.584559	+	0.113843i
$321$	−2322.65	+	609.071i	−0.403856	+	0.105904i
$322$	302.172	+	1869.04i	0.0522963	+	0.323471i
$323$	867.854	+	2358.24i	0.149501	+	0.406241i
$324$	2309.06	−	1503.03i	0.395930	−	0.257722i
$325$	1564.95	+	753.641i	0.267101	+	0.128629i
$326$	−7829.05	−	9817.32i	−1.33010	−	1.66789i
$327$	−5700.56	−	10926.9i	−0.964041	−	1.84789i
$328$	9772.86	+	14010.1i	1.64517	+	2.35847i
$329$	−5.74899	−	9.48356i	−0.000963380	−	0.00158920i
$330$	8904.26	+	3604.93i	1.48534	+	0.601349i
$331$	−2324.69	−	5251.52i	−0.386032	−	0.872053i	−0.996777	−	0.0802252i	$-0.974436\pi$
$331$	−2324.69	−	5251.52i	−0.386032	−	0.872053i	0.610745	−	0.791827i	$-0.290870\pi$
$332$	7425.50	−	2465.43i	1.22749	−	0.407555i
$333$	−657.140	−	942.059i	−0.108141	−	0.155029i
$334$	2016.91	−	12475.3i	0.330421	−	2.04377i
$335$	5649.21	+	3181.57i	0.921341	+	0.518890i
$336$	1894.03	−	1834.26i	0.307522	−	0.297819i
$337$	2614.43	−	1472.42i	0.422603	−	0.238006i	−0.264768	−	0.964312i	$-0.585295\pi$
$337$	2614.43	−	1472.42i	0.422603	−	0.238006i	0.687371	+	0.726307i	$0.258765\pi$
$338$	−6967.54	−	898.364i	−1.12125	−	0.144570i
$339$	−3089.72	−	10410.3i	−0.495016	−	1.66787i
$340$	3458.51	+	1148.31i	0.551659	+	0.183164i
$341$	211.455	+	2191.96i	0.0335805	+	0.348097i
$342$	−2874.20	+	17777.9i	−0.454441	+	2.81088i
$343$	−2847.28	+	554.507i	−0.448217	+	0.0872902i
$344$	1099.33	−	2107.21i	0.172302	−	0.330271i
$345$	−5693.92	+	734.150i	−0.888552	+	0.114566i
$346$	8714.71	−	7418.94i	1.35406	−	1.15273i
$347$	5646.47	+	10823.2i	0.873540	+	1.67441i	0.728565	+	0.684977i	$0.240188\pi$
$347$	5646.47	+	10823.2i	0.873540	+	1.67441i	0.144975	+	0.989435i	$0.453690\pi$
$348$	−2903.15	−	30094.2i	−0.447198	−	4.63568i
$349$	6494.27	+	4846.80i	0.996075	+	0.743390i	0.966630	−	0.256176i	$-0.0824628\pi$
$349$	6494.27	+	4846.80i	0.996075	+	0.743390i	0.0294448	+	0.999566i	$0.490626\pi$
$350$	542.553	−	1225.64i	0.0828591	−	0.187180i
$351$	−897.127	+	3022.72i	−0.136425	+	0.459660i
$352$	−547.857	+	785.395i	−0.0829571	+	0.118925i
$353$	643.054	+	622.763i	0.0969583	+	0.0938989i	0.742576	−	0.669762i	$-0.233604\pi$
$353$	643.054	+	622.763i	0.0969583	+	0.0938989i	−0.645617	+	0.763661i	$0.723400\pi$
$354$	27570.8	−	11162.2i	4.13946	−	1.67588i
$355$	3906.59	+	2915.56i	0.584057	+	0.435893i
$356$	−4907.48	−	2763.84i	−0.730607	−	0.411470i
$357$	972.696	−	255.071i	0.144203	−	0.0378145i
$358$	1693.93	+	7421.61i	0.250076	+	1.09565i
$359$	−5354.53	+	3996.19i	−0.787191	+	0.587496i	−0.914602	−	0.404354i	$-0.867496\pi$
$359$	−5354.53	+	3996.19i	−0.787191	+	0.587496i	0.127412	+	0.991850i	$0.459333\pi$
$360$	8991.04	+	9900.14i	1.31630	+	1.44940i
$361$	711.985	+	892.801i	0.103803	+	0.130165i
$362$	−9126.11	−	3030.08i	−1.32502	−	0.439937i
$363$	3350.89	−	1356.63i	0.484508	−	0.196155i
$364$	190.545	−	1975.20i	0.0274376	−	0.284419i
$365$	−2939.83	+	3237.08i	−0.421582	+	0.464209i
$366$	−8509.31	−	546.316i	−1.21527	−	0.0780230i
$367$	5585.22	+	1464.62i	0.794403	+	0.208317i	0.628484	−	0.777822i	$-0.283676\pi$
$367$	5585.22	+	1464.62i	0.794403	+	0.208317i	0.165919	+	0.986139i	$0.446941\pi$
$368$	623.507	−	6463.30i	0.0883221	−	0.915551i
$369$	−6796.49	+	15353.4i	−0.958838	+	2.16603i
$370$	−791.000	+	766.041i	−0.111141	+	0.107634i
$371$	264.946	+	1638.78i	0.0370763	+	0.229330i
$372$	−3437.23	+	9340.07i	−0.479065	+	1.30177i
$373$	−2037.55	+	3361.15i	−0.282842	+	0.466578i	−0.964127	−	0.265440i	$-0.914483\pi$
$373$	−2037.55	+	3361.15i	−0.282842	+	0.466578i	0.681285	+	0.732018i	$0.261421\pi$
$374$	−3733.44	+	1797.93i	−0.516181	+	0.248579i
$375$	10996.4	+	5295.60i	1.51427	+	0.729236i
$376$	30.0925	+	101.392i	0.00412740	+	0.0139066i
$377$	−4478.76	−	4337.44i	−0.611852	−	0.592545i
$378$	2353.51	+	617.164i	0.320242	+	0.0839774i
$379$	−98.8266	+	3081.78i	−0.0133942	+	0.417679i	0.970727	+	0.240184i	$0.0772076\pi$
$379$	−98.8266	+	3081.78i	−0.0133942	+	0.417679i	−0.984122	+	0.177495i	$0.943201\pi$
$380$	11603.0			1.56637
$381$	−430.309	+	13418.6i	−0.0578619	+	1.80435i
$382$	12495.3	−	13758.7i	1.67360	−	1.84282i
$383$	−2657.01	+	8952.36i	−0.354483	+	1.19437i	0.572701	+	0.819764i	$0.305896\pi$
$383$	−2657.01	+	8952.36i	−0.354483	+	1.19437i	−0.927184	+	0.374606i	$0.877778\pi$
$384$	17105.1	−	9633.44i	2.27316	−	1.28022i
$385$	−354.823	−	964.167i	−0.0469700	−	0.127633i
$386$	−19955.5	−	3886.33i	−2.63137	−	0.512458i
$387$	2331.38	−	149.679i	0.306229	−	0.0196605i
$388$	−18110.5	+	22709.8i	−2.36964	+	2.97144i
$389$	−8511.03	+	5540.06i	−1.10932	+	0.722088i	−0.963630	−	0.267242i	$-0.913888\pi$
$389$	−8511.03	+	5540.06i	−1.10932	+	0.722088i	−0.145692	+	0.989330i	$0.546541\pi$
$390$	8879.58	+	1144.90i	1.15291	+	0.148651i
$391$	1416.83	−	2031.14i	0.183254	−	0.262708i
$392$	13412.3	+	861.099i	1.72812	+	0.110949i
$393$	11736.0			1.50637
$394$	−2554.60	−	13416.0i	−0.326647	−	1.71546i
$395$	−1449.91			−0.184691
$396$	−19917.8	−	1278.76i	−2.52754	−	0.162273i
$397$	−6871.40	+	9850.67i	−0.868679	+	1.24532i	0.0994947	+	0.995038i	$0.468277\pi$
$397$	−6871.40	+	9850.67i	−0.868679	+	1.24532i	−0.968174	+	0.250279i	$0.919478\pi$
$398$	25891.9	+	3338.39i	3.26091	+	0.420448i
$399$	2683.37	−	1746.68i	0.336683	−	0.219156i
$400$	−2866.11	+	3593.98i	−0.358263	+	0.449248i
$401$	12472.1	−	800.738i	1.55319	−	0.0997181i	0.736357	−	0.676593i	$-0.236544\pi$
$401$	12472.1	−	800.738i	1.55319	−	0.0997181i	0.816832	+	0.576875i	$0.195728\pi$
$402$	−32705.1	−	6369.32i	−4.05767	−	0.790231i
$403$	708.823	+	1926.10i	0.0876153	+	0.238079i
$404$	17049.7	−	9602.19i	2.09963	−	1.18249i
$405$	378.265	−	1274.50i	0.0464103	−	0.156372i
$406$	−3234.55	+	3561.60i	−0.395390	+	0.435368i
$407$	26.9718	−	841.081i	0.00328488	−	0.102435i
$408$	−9590.03			−1.16367
$409$	−420.483	+	13112.2i	−0.0508351	+	1.58522i	0.583465	+	0.812138i	$0.301696\pi$
$409$	−420.483	+	13112.2i	−0.0508351	+	1.58522i	−0.634300	+	0.773087i	$0.718712\pi$
$410$	15570.0	+	4082.94i	1.87548	+	0.491809i
$411$	−8211.85	−	7952.73i	−0.985549	−	0.954451i
$412$	−1376.40	−	4637.55i	−0.164588	−	0.554552i
$413$	−2866.12	−	1380.25i	−0.341483	−	0.164449i
$414$	15990.4	−	7700.56i	1.89827	−	0.914160i
$415$	1957.13	−	3228.48i	0.231498	−	0.381880i
$416$	−308.232	+	837.565i	−0.0363276	+	0.0987139i
$417$	−2481.41	−	15348.4i	−0.291404	−	1.80244i
$418$	−9477.80	+	9178.73i	−1.10903	+	1.07403i
$419$	3492.59	−	7889.83i	0.407218	−	0.919912i	−0.586702	−	0.809803i	$-0.699574\pi$
$419$	3492.59	−	7889.83i	0.407218	−	0.919912i	0.993920	−	0.110109i	$-0.0351200\pi$
$420$	445.857	−	4621.77i	0.0517990	−	0.536951i
$421$	−5617.91	−	1473.19i	−0.650357	−	0.170544i	−0.0862865	−	0.996270i	$-0.527500\pi$
$421$	−5617.91	−	1473.19i	−0.650357	−	0.170544i	−0.564070	+	0.825727i	$0.690765\pi$
$422$	−22163.3	−	1422.93i	−2.55662	−	0.164140i
$423$	−69.8913	+	76.9581i	−0.00803365	+	0.00884594i
$424$	1520.20	−	15758.5i	0.174122	−	1.80495i
$425$	−1625.07	+	657.918i	−0.185476	+	0.0750910i
$426$	−23775.1	−	7893.86i	−2.70400	−	0.897791i
$427$	568.582	+	712.979i	0.0644393	+	0.0808044i
$428$	−3215.38	−	3540.50i	−0.363134	−	0.399851i
$429$	−5483.40	+	4092.37i	−0.617112	+	0.460563i
$430$	−498.361	−	2183.46i	−0.0558909	−	0.244874i
$431$	−3195.71	+	838.015i	−0.357151	+	0.0936561i	−0.427870	−	0.903840i	$-0.640736\pi$
$431$	−3195.71	+	838.015i	−0.357151	+	0.0936561i	0.0707190	+	0.997496i	$0.477471\pi$
$432$	−7270.73	−	4094.80i	−0.809753	−	0.456044i
$433$	3011.80	+	2247.77i	0.334268	+	0.249470i	0.752093	−	0.659057i	$-0.229044\pi$
$433$	3011.80	+	2247.77i	0.334268	+	0.249470i	−0.417825	+	0.908527i	$0.637208\pi$
$434$	1468.01	−	594.330i	0.162365	−	0.0657345i
$435$	−10479.9	−	10149.2i	−1.15511	−	1.11866i
$436$	14044.2	−	20133.5i	1.54265	−	2.21151i
$437$	2243.52	−	7559.17i	0.245589	−	0.827470i
$438$	9096.40	−	20548.9i	0.992335	−	2.24170i
$439$	−555.801	−	414.805i	−0.0604259	−	0.0450970i	0.567472	−	0.823392i	$-0.307921\pi$
$439$	−555.801	−	414.805i	−0.0604259	−	0.0450970i	−0.627898	+	0.778295i	$0.716085\pi$
$440$	940.827	+	9752.65i	0.101937	+	1.05668i
$441$	6110.40	+	11712.5i	0.659800	+	1.26471i
$442$	−2940.72	+	2503.47i	−0.316461	+	0.269408i
$443$	−1324.08	+	170.721i	−0.142007	+	0.0183098i	−0.198552	−	0.980090i	$-0.563624\pi$
$443$	−1324.08	+	170.721i	−0.142007	+	0.0183098i	0.0565456	+	0.998400i	$0.481991\pi$
$444$	1759.12	−	3371.91i	0.188028	−	0.360414i
$445$	−2667.62	+	519.520i	−0.284174	+	0.0553429i
$446$	178.666	−	1105.11i	0.0189688	−	0.117329i
$447$	−1810.85	−	18771.4i	−0.191612	−	1.98626i
$448$	−1778.25	−	590.421i	−0.187532	−	0.0622651i
$449$	898.657	+	3027.87i	0.0944549	+	0.318250i	0.992597	−	0.121456i	$-0.0387563\pi$
$449$	898.657	+	3027.87i	0.0944549	+	0.318250i	−0.898142	+	0.439706i	$0.855083\pi$
$450$	−12461.4	−	1606.72i	−1.30541	−	0.168314i
$451$	−10718.3	+	6036.45i	−1.11908	+	0.630256i
$452$	15537.3	−	15047.0i	1.61684	−	1.56582i
$453$	−6813.74	−	3837.43i	−0.706705	−	0.398009i
$454$	−1490.15	+	9217.12i	−0.154045	+	0.952822i
$455$	−547.814	−	785.333i	−0.0564438	−	0.0809164i
$456$	−28979.0	+	9621.70i	−2.97603	+	0.988108i
$457$	6831.18	+	15431.7i	0.699232	+	1.57958i	0.810468	+	0.585783i	$0.199213\pi$
$457$	6831.18	+	15431.7i	0.699232	+	1.57958i	−0.111236	+	0.993794i	$0.535481\pi$
$458$	−20879.9	−	8453.34i	−2.13025	−	0.862443i
$459$	−1649.79	−	2721.50i	−0.167768	−	0.276751i
$460$	−6542.14	−	9378.65i	−0.663107	−	0.950613i
$461$	910.658	+	1745.56i	0.0920034	+	0.176353i	0.928205	−	0.372068i	$-0.121351\pi$
$461$	910.658	+	1745.56i	0.0920034	+	0.176353i	−0.836202	+	0.548422i	$0.815229\pi$
$462$	3291.93	+	4127.95i	0.331503	+	0.415692i
$463$	−2050.24	−	987.342i	−0.205794	−	0.0991051i	0.328148	−	0.944626i	$-0.393576\pi$
$463$	−2050.24	−	987.342i	−0.205794	−	0.0991051i	−0.533942	+	0.845521i	$0.679290\pi$
$464$	13828.8	−	9001.54i	1.38359	−	0.900616i
$465$	1658.58	+	4506.89i	0.165408	+	0.449466i
$466$	397.534	+	2458.89i	0.0395180	+	0.244433i
$467$	−11045.1	+	2896.36i	−1.09445	+	0.286997i	−0.756385	−	0.654127i	$-0.773036\pi$
$467$	−11045.1	+	2896.36i	−1.09445	+	0.286997i	−0.338061	+	0.941124i	$0.609771\pi$
$468$	−18258.5	+	3555.85i	−1.80342	+	0.351216i
$469$	1847.28	+	3047.29i	0.181876	+	0.300023i
$470$	83.5250	+	54.3688i	0.00819728	+	0.00533584i
$471$	3414.08	−	14958.1i	0.333997	−	1.46334i
$472$	23100.7	+	19665.9i	2.25274	+	1.91779i
$473$	1434.44	+	933.719i	0.139441	+	0.0907663i
$474$	7071.67	−	2347.96i	0.685258	−	0.227521i
$475$	−4250.53	+	3618.53i	−0.410584	+	0.349535i
$476$	1346.56	+	1482.71i	0.129663	+	0.142773i
$477$	14020.4	−	6751.88i	1.34581	−	0.648108i
$478$	3588.08	−	4499.31i	0.343337	−	0.430531i
$479$	−514.693	−	100.236i	−0.0490958	−	0.00956141i	0.166551	−	0.986033i	$-0.446737\pi$
$479$	−514.693	−	100.236i	−0.0490958	−	0.00956141i	−0.215647	+	0.976471i	$0.569186\pi$
$480$	−721.232	+	1959.82i	−0.0685824	+	0.186361i
$481$	−174.521	−	764.627i	−0.0165436	−	0.0724823i
$482$	5738.27	−	10999.2i	0.542264	−	1.03942i
$483$	−2924.80	−	1184.12i	−0.275535	−	0.111552i
$484$	5482.81	+	4667.58i	0.514914	+	0.438353i
$485$	449.238	+	14008.9i	0.0420595	+	1.31157i
$486$	703.204	+	21928.5i	0.0656337	+	2.04670i
$487$	4147.87	−	18173.0i	0.385951	−	1.69096i	−0.292459	−	0.956278i	$-0.594474\pi$
$487$	4147.87	−	18173.0i	0.385951	−	1.69096i	0.678410	−	0.734683i	$-0.262669\pi$
$488$	−3520.37	−	7952.57i	−0.326556	−	0.737696i
$489$	20755.5	−	2676.13i	1.91942	−	0.247482i
$490$	10149.5	−	7574.80i	0.935734	−	0.698356i
$491$	10106.9	−	16672.4i	0.928958	−	1.53241i	0.0847480	−	0.996402i	$-0.472991\pi$
$491$	10106.9	−	16672.4i	0.928958	−	1.53241i	0.844211	−	0.536012i	$-0.180070\pi$
$492$	−55481.0	+	3562.00i	−5.08389	+	0.326397i
$493$	6280.13	−	403.198i	0.573718	−	0.0368339i
$494$	−6374.50	+	10515.4i	−0.580572	+	0.957714i
$495$	−7718.21	+	5760.25i	−0.700824	+	0.523038i
$496$	−5387.05	+	694.583i	−0.487672	+	0.0628784i
$497$	1084.50	+	2449.90i	0.0978799	+	0.221112i
$498$	−4317.37	+	18915.6i	−0.388486	+	1.70207i
$499$	−503.592	−	15703.8i	−0.0451781	−	1.40882i	−0.731659	−	0.681671i	$-0.761254\pi$
$499$	−503.592	−	15703.8i	−0.0451781	−	1.40882i	0.686481	−	0.727148i	$-0.259155\pi$
$500$	779.175	+	24297.5i	0.0696915	+	2.17324i
$501$	16037.2	+	13652.6i	1.43012	+	1.21747i
$502$	−12277.4	−	4970.59i	−1.09157	−	0.441929i
$503$	1239.08	−	2375.08i	0.109836	−	0.210536i	−0.825410	−	0.564534i	$-0.809056\pi$
$503$	1239.08	−	2375.08i	0.109836	−	0.210536i	0.935246	+	0.353999i	$0.115178\pi$
$504$	1635.62	+	7166.11i	0.144556	+	0.633341i
$505$	3260.94	−	8861.04i	0.287347	−	0.780814i
$506$	12763.0	+	2485.60i	1.12132	+	0.218376i
$507$	7300.00	−	9153.91i	0.639456	−	0.801853i
$508$	−24092.6	+	11602.4i	−2.10421	+	1.01333i
$509$	5683.94	+	6258.65i	0.494963	+	0.545010i	0.935779	−	0.352588i	$-0.114698\pi$
$509$	5683.94	+	6258.65i	0.494963	+	0.545010i	−0.440815	+	0.897598i	$0.645311\pi$
$510$	−6881.00	+	5857.88i	−0.597443	+	0.508611i
$511$	−2280.94	+	757.325i	−0.197462	+	0.0655618i
$512$	18500.9	+	12042.7i	1.59694	+	1.03949i
$513$	−7715.80	−	6568.55i	−0.664056	−	0.565319i
$514$	−5172.88	+	22663.9i	−0.443902	+	1.94486i
$515$	−1956.30	−	1273.41i	−0.167388	−	0.108958i
$516$	4009.96	+	6614.84i	0.342109	+	0.564345i
$517$	−74.7591	+	14.5593i	−0.00635958	+	0.00123853i
$518$	−585.415	+	153.514i	−0.0496557	+	0.0130213i
$519$	3044.25	+	18829.8i	0.257472	+	1.59255i
$520$	3153.76	+	8569.78i	0.265964	+	0.722711i
$521$	−8324.84	+	5418.87i	−0.700034	+	0.455672i	−0.845698	−	0.533662i	$-0.820815\pi$
$521$	−8324.84	+	5418.87i	−0.700034	+	0.455672i	0.145663	+	0.989334i	$0.453468\pi$
$522$	40633.8	+	19568.2i	3.40707	+	1.64076i
$523$	−1229.37	−	1541.58i	−0.102785	−	0.128889i	0.727778	−	0.685812i	$-0.240553\pi$
$523$	−1229.37	−	1541.58i	−0.102785	−	0.128889i	−0.830564	+	0.556924i	$0.811982\pi$
$524$	10812.2	+	20724.9i	0.901397	+	1.72781i
$525$	1278.02	+	1832.14i	0.106243	+	0.152307i
$526$	12034.6	+	19852.3i	0.997590	+	1.64563i
$527$	−1920.17	−	777.391i	−0.158717	−	0.0642575i
$528$	−7329.72	−	16558.0i	−0.604139	−	1.36476i
$529$	4172.14	−	1385.25i	0.342906	−	0.113853i
$530$	−8535.00	−	12235.6i	−0.699503	−	1.00279i
$531$	−4759.31	+	29438.0i	−0.388957	+	2.40584i
$532$	5556.63	+	3129.44i	0.452839	+	0.255034i
$533$	−8235.72	+	7975.85i	−0.669285	+	0.648166i
$534$	12169.5	−	6853.75i	0.986193	−	0.555414i
$535$	−2288.84	−	295.113i	−0.184963	−	0.0238483i
$536$	−9669.43	−	32579.5i	−0.779209	−	2.62541i
$537$	−12040.7	−	3997.78i	−0.967586	−	0.321261i
$538$	−163.411	−	1693.93i	−0.0130951	−	0.135744i
$539$	−1544.69	+	9554.48i	−0.123441	+	0.763527i
$540$	−14424.1	+	2809.08i	−1.14947	+	0.223859i
$541$	10908.5	−	20909.6i	0.866902	−	1.66169i	0.124006	−	0.992281i	$-0.460426\pi$
$541$	10908.5	−	20909.6i	0.866902	−	1.66169i	0.742896	−	0.669407i	$-0.233452\pi$
$542$	−16693.9	+	2152.45i	−1.32300	+	0.170582i
$543$	12203.0	−	10388.6i	0.964422	−	0.821025i
$544$	−416.664	−	798.667i	−0.0328388	−	0.0629459i
$545$	−1137.40	−	11790.4i	−0.0893964	−	0.926688i
$546$	3943.61	+	2943.19i	0.309104	+	0.230691i
$547$	7311.68	−	16517.2i	0.571527	−	1.29109i	−0.361865	−	0.932230i	$-0.617860\pi$
$547$	7311.68	−	16517.2i	0.571527	−	1.29109i	0.933392	−	0.358858i	$-0.116834\pi$
$548$	6478.48	−	21828.2i	0.505013	−	1.70156i
$549$	4890.75	−	7011.25i	0.380204	−	0.545051i
$550$	−6612.57	−	6403.91i	−0.512656	−	0.496480i
$551$	18572.7	−	7519.26i	1.43598	−	0.581363i
$552$	24116.5	+	17998.6i	1.85954	+	1.38781i
$553$	−694.357	−	391.055i	−0.0533943	−	0.0300711i
$554$	17467.5	−	4580.52i	1.33957	−	0.351277i
$555$	−408.362	−	1789.15i	−0.0312324	−	0.136838i
$556$	24818.0	−	18522.2i	1.89302	−	1.41280i
$557$	8977.29	+	9884.99i	0.682908	+	0.751958i	0.979146	−	0.203156i	$-0.0651200\pi$
$557$	8977.29	+	9884.99i	0.682908	+	0.751958i	−0.296238	+	0.955114i	$0.595732\pi$
$558$	−9256.44	−	11607.2i	−0.702251	−	0.880595i
$559$	1513.91	+	502.654i	0.114547	+	0.0380322i
$560$	2348.88	−	950.957i	0.177247	−	0.0717594i
$561$	663.145	−	6874.19i	0.0499073	−	0.517342i
$562$	−3043.88	+	3351.65i	−0.228467	+	0.251567i
$563$	−14082.5	−	904.129i	−1.05419	−	0.0676811i	−0.472690	−	0.881229i	$-0.656717\pi$
$563$	−14082.5	−	904.129i	−1.05419	−	0.0676811i	−0.581498	+	0.813548i	$0.697533\pi$
$564$	−332.961	−	87.3127i	−0.0248585	−	0.00651867i
$565$	1002.17	−	10388.5i	0.0746221	−	0.773536i
$566$	−14306.1	+	32317.7i	−1.06242	+	2.40003i
$567$	524.895	−	508.332i	0.0388775	−	0.0376507i
$568$	−4077.93	−	25223.4i	−0.301243	−	1.86330i
$569$	2721.30	−	7394.65i	0.200497	−	0.544815i	−0.797814	−	0.602903i	$-0.794011\pi$
$569$	2721.30	−	7394.65i	0.200497	−	0.544815i	0.998311	+	0.0580877i	$0.0185003\pi$
$570$	−14915.7	+	24605.0i	−1.09605	+	1.80805i
$571$	−19638.7	+	9457.49i	−1.43932	+	0.693141i	−0.980705	−	0.195493i	$-0.937369\pi$
$571$	−19638.7	+	9457.49i	−1.43932	+	0.693141i	−0.458617	+	0.888634i	$0.651655\pi$
$572$	−12278.5	−	5913.04i	−0.897538	−	0.432232i
$573$	8813.35	+	29695.1i	0.642553	+	2.16497i
$574$	6355.21	+	6154.68i	0.462128	+	0.447546i
$575$	5321.42	+	1395.44i	0.385946	+	0.101207i
$576$	−562.961	+	17555.2i	−0.0407234	+	1.26991i
$577$	−8453.13			−0.609894			−0.304947	−	0.952369i	$-0.598639\pi$
$577$	−8453.13			−0.609894			−0.304947	+	0.952369i	$0.598639\pi$
$578$	−652.836	+	20357.8i	−0.0469799	+	1.46501i
$579$	22779.4	−	25082.7i	1.63503	−	1.80035i
$580$	8267.77	−	27856.9i	0.591897	−	1.99430i
$581$	1808.01	−	1018.25i	0.129103	−	0.0727096i
$582$	−24876.8	−	67598.3i	−1.77178	−	4.81450i
$583$	11190.7	+	2179.38i	0.794974	+	0.154821i
$584$	22873.4	−	1468.52i	1.62073	−	0.104055i
$585$	−5596.35	+	7017.60i	−0.395522	+	0.495969i
$586$	−4314.64	+	2808.52i	−0.304157	+	0.197984i
$587$	−4764.73	−	614.344i	−0.335028	−	0.0431971i	−0.0414740	−	0.999140i	$-0.513205\pi$
$587$	−4764.73	−	614.344i	−0.335028	−	0.0431971i	−0.293554	+	0.955943i	$0.594838\pi$
$588$	−25025.4	+	35875.9i	−1.75516	+	2.51615i
$589$	−6582.31	−	422.598i	−0.460474	−	0.0295634i
$590$	28587.6			1.99480
$591$	21327.5	+	7950.11i	1.48442	+	0.553340i
$592$	2075.62			0.144101
$593$	−10861.9	−	697.360i	−0.752187	−	0.0482920i	−0.316747	−	0.948510i	$-0.602591\pi$
$593$	−10861.9	−	697.360i	−0.752187	−	0.0482920i	−0.435439	+	0.900218i	$0.643407\pi$
$594$	9559.98	−	13705.0i	0.660355	−	0.946669i
$595$	958.535	+	123.589i	0.0660439	+	0.00851542i
$596$	31480.5	−	20491.5i	2.16358	−	1.40833i
$597$	−27127.3	+	34016.6i	−1.85971	+	2.33200i
$598$	12093.7	−	776.442i	0.827005	−	0.0530955i
$599$	−16253.0	−	3165.28i	−1.10865	−	0.215909i	−0.396567	−	0.918006i	$-0.629799\pi$
$599$	−16253.0	−	3165.28i	−1.10865	−	0.215909i	−0.712082	+	0.702096i	$0.752248\pi$
$600$	−7357.55	−	19992.8i	−0.500618	−	1.36034i
$601$	7821.73	−	4405.12i	0.530874	−	0.298982i	−0.201956	−	0.979395i	$-0.564730\pi$
$601$	7821.73	−	4405.12i	0.530874	−	0.298982i	0.732830	+	0.680412i	$0.238199\pi$
$602$	350.237	−	1180.06i	0.0237120	−	0.0798935i
$603$	22457.7	−	24728.4i	1.51667	−	1.67002i
$604$	499.232	−	15567.9i	0.0336315	−	1.04875i
$605$	3474.48			0.233484
$606$	−1555.26	+	48498.7i	−0.104254	+	3.25103i
$607$	5362.40	+	1406.19i	0.358572	+	0.0940287i	0.428546	−	0.903520i	$-0.359026\pi$
$607$	5362.40	+	1406.19i	0.358572	+	0.0940287i	−0.0699735	+	0.997549i	$0.522291\pi$
$608$	−2060.38	−	1995.36i	−0.137433	−	0.133097i
$609$	−2281.44	−	7686.92i	−0.151804	−	0.511478i
$610$	−7383.59	−	3555.75i	−0.490087	−	0.236013i
$611$	−63.9548	+	30.7990i	−0.00423459	+	0.00203927i
$612$	9733.03	−	16055.6i	0.642866	−	1.06048i
$613$	−6397.44	+	17383.9i	−0.421518	+	1.14540i	0.532705	+	0.846301i	$0.321176\pi$
$613$	−6397.44	+	17383.9i	−0.421518	+	1.14540i	−0.954222	+	0.299098i	$0.903314\pi$
$614$	607.972	+	3760.52i	0.0399605	+	0.247170i
$615$	−19270.8	+	18662.7i	−1.26353	+	1.22366i
$616$	−2179.82	+	4924.26i	−0.142577	+	0.322085i
$617$	−1628.48	+	16880.9i	−0.106256	+	1.10146i	0.776015	+	0.630714i	$0.217238\pi$
$617$	−1628.48	+	16880.9i	−0.106256	+	1.10146i	−0.882271	+	0.470741i	$0.843987\pi$
$618$	11603.6	+	3042.83i	0.755286	+	0.198059i
$619$	−10561.7	−	678.085i	−0.685802	−	0.0440300i	−0.282732	−	0.959199i	$-0.591241\pi$
$619$	−10561.7	−	678.085i	−0.685802	−	0.0440300i	−0.403070	+	0.915169i	$0.632057\pi$
$620$	−6430.79	+	7081.02i	−0.416559	+	0.458678i
$621$	−958.920	+	9940.21i	−0.0619648	+	0.642330i
$622$	−4693.19	+	1900.06i	−0.302540	+	0.122485i
$623$	−1417.63	−	470.687i	−0.0911659	−	0.0302691i
$624$	−10522.3	−	13194.5i	−0.675046	−	0.846481i
$625$	2641.80	+	2908.92i	0.169075	+	0.186171i
$626$	−31950.3	+	23845.1i	−2.03992	+	1.52243i
$627$	−4893.01	−	21437.7i	−0.311656	−	1.36545i
$628$	29560.1	−	7751.56i	1.87830	−	0.492549i
$629$	689.753	+	388.462i	0.0437238	+	0.0246248i
$630$	5550.86	+	4142.72i	0.351034	+	0.261984i
$631$	−5132.70	+	2078.00i	−0.323818	+	0.131100i	−0.531407	−	0.847117i	$-0.678336\pi$
$631$	−5132.70	+	2078.00i	−0.323818	+	0.131100i	0.207589	+	0.978216i	$0.433439\pi$
$632$	5459.38	+	5287.11i	0.343611	+	0.332769i
$633$	21176.1	−	30357.6i	1.32966	−	1.90617i
$634$	14927.8	−	50296.8i	0.935110	−	3.15070i
$635$	−5223.04	+	11798.9i	−0.326409	+	0.737365i
$636$	41293.7	+	30818.3i	2.57453	+	1.92142i
$637$	866.166	+	8978.72i	0.0538756	+	0.558477i
$638$	15283.2	+	29295.0i	0.948379	+	1.81787i
$639$	19123.7	−	16280.2i	1.18391	−	1.00788i
$640$	18712.8	−	2412.75i	1.15577	−	0.149019i
$641$	−12545.4	+	24047.2i	−0.773033	+	1.48176i	0.100469	+	0.994940i	$0.467966\pi$
$641$	−12545.4	+	24047.2i	−0.773033	+	1.48176i	−0.873502	+	0.486820i	$0.838157\pi$
$642$	11641.3	−	2267.14i	0.715646	−	0.139372i
$643$	−2575.83	+	15932.4i	−0.157980	+	0.977159i	0.778808	+	0.627262i	$0.215824\pi$
$643$	−2575.83	+	15932.4i	−0.157980	+	0.977159i	−0.936788	+	0.349898i	$0.886216\pi$
$644$	−603.497	−	6255.88i	−0.0369272	−	0.382789i
$645$	3542.41	+	1176.16i	0.216252	+	0.0718005i
$646$	−3531.44	−	11898.6i	−0.215081	−	0.724681i
$647$	−25964.4	−	3347.74i	−1.57769	−	0.203421i	−0.711337	−	0.702851i	$-0.751910\pi$
$647$	−25964.4	−	3347.74i	−1.57769	−	0.203421i	−0.866354	+	0.499430i	$0.833543\pi$
$648$	−6071.77	+	3419.56i	−0.368089	+	0.207304i
$649$	−15694.0	+	15198.8i	−0.949222	+	0.919270i
$650$	−7475.28	−	4210.00i	−0.451084	−	0.254046i
$651$	−421.264	+	2605.66i	−0.0253619	+	0.156873i
$652$	23847.5	+	34187.1i	1.43242	+	2.05348i
$653$	1793.18	−	595.377i	0.107462	−	0.0356798i	−0.260872	−	0.965373i	$-0.584010\pi$
$653$	1793.18	−	595.377i	0.107462	−	0.0356798i	0.368334	+	0.929694i	$0.379928\pi$
$654$	24640.6	+	55663.5i	1.47328	+	3.32816i
$655$	10455.2	+	4232.84i	0.623692	+	0.252505i
$656$	−15728.8	−	25946.4i	−0.936140	−	1.54426i
$657$	12889.4	+	18478.0i	0.765396	+	1.09725i
$658$	25.3361	+	48.5645i	0.00150107	+	0.00287727i
$659$	−10615.8	−	13311.7i	−0.627514	−	0.786877i	0.361866	−	0.932230i	$-0.382140\pi$
$659$	−10615.8	−	13311.7i	−0.627514	−	0.786877i	−0.989380	+	0.145353i	$0.953568\pi$
$660$	−28730.6	−	13835.9i	−1.69445	−	0.816004i
$661$	1351.17	−	879.516i	0.0795076	−	0.0517537i	−0.505167	−	0.863022i	$-0.668569\pi$
$661$	1351.17	−	879.516i	0.0795076	−	0.0517537i	0.584675	+	0.811268i	$0.301222\pi$
$662$	9796.70	+	26620.8i	0.575165	+	1.56291i
$663$	−1027.26	−	6353.98i	−0.0601743	−	0.372200i
$664$	−19141.9	+	5019.60i	−1.11875	+	0.293371i
$665$	3020.49	−	588.240i	0.176135	−	0.0343022i
$666$	2940.97	+	4851.44i	0.171112	+	0.282267i
$667$	−16549.7	−	10772.6i	−0.960729	−	0.625365i
$668$	−9334.76	+	40898.3i	−0.540678	+	2.36886i
$669$	1420.64	+	1209.40i	0.0821001	+	0.0698928i
$670$	−26838.6	−	17470.0i	−1.54756	−	1.00735i
$671$	5943.88	−	1973.50i	0.341969	−	0.113541i
$672$	−873.977	+	744.027i	−0.0501702	+	0.0427105i
$673$	−17605.3	−	19385.4i	−1.00837	−	1.11033i	−0.993884	−	0.110433i	$-0.964776\pi$
$673$	−17605.3	−	19385.4i	−1.00837	−	1.11033i	−0.0144871	−	0.999895i	$-0.504612\pi$
$674$	−13352.7	+	6430.32i	−0.763096	+	0.367488i
$675$	4407.92	−	5527.36i	0.251350	−	0.315182i
$676$	22890.4	+	4457.91i	1.30237	+	0.253636i
$677$	−1649.52	+	4482.29i	−0.0936430	+	0.254458i	−0.976626	−	0.214947i	$-0.931042\pi$
$677$	−1649.52	+	4482.29i	−0.0936430	+	0.254458i	0.882983	+	0.469406i	$0.155532\pi$
$678$	11935.1	+	52290.9i	0.676052	+	2.96198i
$679$	−3563.19	+	6829.98i	−0.201389	+	0.386024i
$680$	−8543.40	−	3458.84i	−0.481801	−	0.195059i
$681$	−11848.7	−	10087.0i	−0.666731	−	0.567596i
$682$	−348.620	−	10871.2i	−0.0195738	−	0.610383i
$683$	−148.048	−	4616.69i	−0.00829416	−	0.258643i	−0.995232	−	0.0975391i	$-0.968903\pi$
$683$	−148.048	−	4616.69i	−0.00829416	−	0.258643i	0.986938	−	0.161103i	$-0.0515053\pi$
$684$	13302.5	−	58281.9i	0.743615	−	3.25799i
$685$	−4447.32	−	10046.6i	−0.248063	−	0.560379i
$686$	14209.9	−	1832.17i	0.790871	−	0.101971i
$687$	30087.0	−	22454.5i	1.67087	−	1.24701i
$688$	−2188.47	+	3610.11i	−0.121271	+	0.200049i
$689$	10603.8	−	680.787i	0.586318	−	0.0376429i
$690$	28298.1	−	1816.80i	1.56129	−	0.100238i
$691$	−14043.0	+	23165.3i	−0.773110	+	1.27533i	0.183230	+	0.983070i	$0.441345\pi$
$691$	−14043.0	+	23165.3i	−0.773110	+	1.27533i	−0.956340	+	0.292256i	$0.905594\pi$
$692$	−30447.3	+	22723.4i	−1.67259	+	1.24829i
$693$	−5249.82	+	676.889i	−0.287769	+	0.0371037i
$694$	−24406.8	−	55135.4i	−1.33497	−	3.01572i
$695$	3325.12	−	14568.3i	0.181481	−	0.795119i
$696$	2450.96	+	76429.8i	0.133482	+	4.16245i
$697$	−370.899	−	11566.0i	−0.0201561	−	0.628541i
$698$	−30476.9	−	25945.4i	−1.65268	−	1.40695i
$699$	−3847.83	−	1557.81i	−0.208209	−	0.0842946i
$700$	−2058.00	+	3944.80i	−0.111121	+	0.212999i
$701$	−4314.41	−	18902.7i	−0.232458	−	1.01846i	−0.947593	−	0.319479i	$-0.896492\pi$
$701$	−4314.41	−	18902.7i	−0.232458	−	1.01846i	0.715135	−	0.698986i	$-0.246365\pi$
$702$	5378.57	−	14615.3i	0.289175	−	0.785783i
$703$	2474.03	+	481.818i	0.132731	+	0.0258494i
$704$	−8023.17	+	10060.7i	−0.429524	+	0.538605i
$705$	−149.648	+	72.0666i	−0.00799442	+	0.00384991i
$706$	−2972.58	−	3273.15i	−0.158463	−	0.174485i
$707$	3951.56	−	3364.01i	0.210203	−	0.178949i
$708$	−93708.2	+	31113.3i	−4.97425	+	1.65157i
$709$	2385.44	+	1552.75i	0.126357	+	0.0822494i	0.607161	−	0.794579i	$-0.292308\pi$
$709$	2385.44	+	1552.75i	0.126357	+	0.0822494i	−0.480804	+	0.876828i	$0.659655\pi$
$710$	−18333.2	−	15607.3i	−0.969062	−	0.824974i
$711$	−1662.28	+	7282.92i	−0.0876798	+	0.384150i
$712$	11938.9	+	7771.35i	0.628411	+	0.409050i
$713$	3369.73	+	5558.73i	0.176995	+	0.291972i
$714$	−4875.21	+	949.448i	−0.255533	+	0.0497650i
$715$	−6360.96	+	1668.04i	−0.332708	+	0.0872463i
$716$	−4033.07	−	24946.0i	−0.210507	−	1.30206i
$717$	3312.42	+	9000.91i	0.172531	+	0.468822i
$718$	27657.5	−	18003.1i	1.43756	−	0.935750i
$719$	7338.87	+	3534.21i	0.380659	+	0.183316i	0.614421	−	0.788978i	$-0.289390\pi$
$719$	7338.87	+	3534.21i	0.380659	+	0.183316i	−0.233763	+	0.972294i	$0.575104\pi$
$720$	−14810.7	−	18572.1i	−0.766616	−	0.961306i
$721$	−593.415	−	1137.47i	−0.0306518	−	0.0587537i
$722$	−3226.90	−	4626.00i	−0.166333	−	0.238451i
$723$	10718.3	+	17681.0i	0.551339	+	0.909491i
$724$	29587.8	+	11978.8i	1.51881	+	0.614900i
$725$	5658.74	+	12783.2i	0.289876	+	0.654836i
$726$	−16946.1	+	5626.50i	−0.866295	+	0.287630i
$727$	6700.34	+	9605.44i	0.341818	+	0.490022i	0.953630	−	0.300981i	$-0.0973141\pi$
$727$	6700.34	+	9605.44i	0.341818	+	0.490022i	−0.611812	+	0.791003i	$0.709559\pi$
$728$	−801.027	+	4954.64i	−0.0407803	+	0.252240i
$729$	−27906.6	−	15716.7i	−1.41780	−	0.798490i
$730$	15515.0	−	15025.5i	0.786626	−	0.761805i
$731$	−1402.90	+	790.098i	−0.0709823	+	0.0399765i
$732$	28072.8	+	3619.58i	1.41749	+	0.182765i
$733$	7784.70	+	26229.2i	0.392271	+	1.32169i	0.890634	+	0.454721i	$0.150261\pi$
$733$	7784.70	+	26229.2i	0.392271	+	1.32169i	−0.498363	+	0.866968i	$0.666065\pi$
$734$	−27066.5	−	8986.69i	−1.36109	−	0.451914i
$735$	2026.74	+	21009.3i	0.101711	+	1.05434i
$736$	−451.138	+	2790.45i	−0.0225940	+	0.139752i
$737$	24021.8	−	4678.25i	1.20062	−	0.233821i
$738$	38359.1	−	73527.3i	1.91331	−	3.66745i
$739$	−10872.5	+	1401.85i	−0.541204	+	0.0697805i	−0.393627	−	0.919270i	$-0.628780\pi$
$739$	−10872.5	+	1401.85i	−0.541204	+	0.0697805i	−0.147577	+	0.989051i	$0.547147\pi$
$740$	2783.28	−	2369.44i	0.138264	−	0.117706i
$741$	−9479.14	−	18169.7i	−0.469939	−	0.900786i
$742$	−787.334	−	8161.54i	−0.0389541	−	0.403800i
$743$	−19666.3	−	14677.3i	−0.971045	−	0.724710i	−0.00967068	−	0.999953i	$-0.503078\pi$
$743$	−19666.3	−	14677.3i	−0.971045	−	0.724710i	−0.961375	+	0.275243i	$0.911242\pi$
$744$	10189.3	−	23017.9i	0.502095	−	1.13424i
$745$	5157.06	−	17375.9i	0.253611	−	0.854500i
$746$	11106.9	−	15922.6i	0.545110	−	0.781456i
$747$	−13972.9	−	13532.0i	−0.684394	−	0.662799i
$748$	12750.2	−	5161.99i	0.623254	−	0.252328i
$749$	−1016.52	−	758.650i	−0.0495900	−	0.0370100i
$750$	−52526.4	−	29582.3i	−2.55732	−	1.44026i
$751$	−14918.8	+	3912.17i	−0.724893	+	0.190089i	−0.597621	−	0.801779i	$-0.703887\pi$
$751$	−14918.8	+	3912.17i	−0.724893	+	0.190089i	−0.127272	+	0.991868i	$0.540622\pi$
$752$	−41.8028	−	183.150i	−0.00202712	−	0.00888139i
$753$	17691.2	−	13203.3i	0.856181	−	0.638984i
$754$	20703.6	+	22796.9i	0.999972	+	1.10108i
$755$	−4686.06	−	5876.14i	−0.225885	−	0.283251i
$756$	−7665.26	−	2545.04i	−0.368761	−	0.122437i
$757$	−5725.49	+	2317.99i	−0.274896	+	0.111293i	−0.508566	−	0.861023i	$-0.669824\pi$
$757$	−5725.49	+	2317.99i	−0.274896	+	0.111293i	0.233670	+	0.972316i	$0.424926\pi$
$758$	1462.38	−	15159.1i	0.0700737	−	0.726387i
$759$	−14569.2	+	16042.3i	−0.696742	+	0.767190i
$760$	−29286.6	−	1880.26i	−1.39781	−	0.0897425i
$761$	18744.6	+	4915.40i	0.892891	+	0.234144i	0.671467	−	0.741034i	$-0.265664\pi$
$761$	18744.6	+	4915.40i	0.892891	+	0.234144i	0.221424	+	0.975178i	$0.428930\pi$
$762$	6367.44	−	66005.2i	0.302714	−	3.13795i
$763$	2635.28	−	5953.14i	0.125037	−	0.282462i
$764$	−44319.6	+	42921.2i	−2.09873	+	2.03250i
$765$	−1445.93	−	8943.60i	−0.0683370	−

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)

\(f(q)\)	\(=\)	\(q+(-4.92908 - 0.316457i) q^{2} +(4.70953 - 6.75146i) q^{3} +(16.2613 + 2.09667i) q^{4} +(6.63060 - 4.31604i) q^{5} +(-25.3502 + 31.7881i) q^{6} +(4.33945 - 0.278602i) q^{7} +(-40.7048 - 7.92726i) q^{8} +(-14.0777 - 38.2538i) q^{9} +O(q^{10})\)	\(q+(-4.92908 - 0.316457i) q^{2} +(4.70953 - 6.75146i) q^{3} +(16.2613 + 2.09667i) q^{4} +(6.63060 - 4.31604i) q^{5} +(-25.3502 + 31.7881i) q^{6} +(4.33945 - 0.278602i) q^{7} +(-40.7048 - 7.92726i) q^{8} +(-14.0777 - 38.2538i) q^{9} +(-34.0486 + 19.1758i) q^{10} +(8.49702 - 28.6293i) q^{11} +(90.7388 - 99.9135i) q^{12} +(0.892088 - 27.8186i) q^{13} -21.4776 q^{14} +(2.08740 - 65.0927i) q^{15} +(71.2506 + 18.6841i) q^{16} +(20.1806 + 19.5438i) q^{17} +(57.2846 + 193.011i) q^{18} +(80.5898 + 38.8100i) q^{19} +(116.872 - 56.2825i) q^{20} +(18.5558 - 30.6097i) q^{21} +(-50.9424 + 138.427i) q^{22} +(-14.0692 - 87.0228i) q^{23} +(-245.221 + 237.483i) q^{24} +(-25.2613 + 57.0657i) q^{25} +(-13.2006 + 136.838i) q^{26} +(-109.580 - 28.7352i) q^{27} +(71.1494 + 4.56794i) q^{28} +(150.601 - 165.828i) q^{29} +(-30.8880 + 320.187i) q^{30} +(-68.3505 + 27.6721i) q^{31} +(-30.4321 - 10.1042i) q^{32} +(-153.273 - 192.198i) q^{33} +(-93.2869 - 102.719i) q^{34} +(27.5707 - 20.5765i) q^{35} +(-148.717 - 651.574i) q^{36} +(27.2570 - 7.14762i) q^{37} +(-384.952 - 216.801i) q^{38} +(-183.615 - 137.035i) q^{39} +(-304.111 + 123.121i) q^{40} +(-295.899 - 286.562i) q^{41} +(-101.150 + 145.005i) q^{42} +(-16.3071 + 54.9439i) q^{43} +(198.199 - 447.735i) q^{44} +(-258.449 - 192.885i) q^{45} +(41.8090 + 433.394i) q^{46} +(-1.17965 - 2.26117i) q^{47} +(461.702 - 393.053i) q^{48} +(-321.431 + 41.4439i) q^{49} +(142.574 - 273.287i) q^{50} +(226.990 - 44.2064i) q^{51} +(72.8329 - 450.497i) q^{52} +(36.6583 + 380.002i) q^{53} +(531.033 + 176.315i) q^{54} +(-67.2248 - 226.503i) q^{55} +(-178.845 - 23.0595i) q^{56} +(641.564 - 361.322i) q^{57} +(-794.802 + 769.723i) q^{58} +(-637.432 - 358.995i) q^{59} +(170.422 - 1054.12i) q^{60} +(119.983 + 172.005i) q^{61} +(345.662 - 114.768i) q^{62} +(-71.7471 - 162.078i) q^{63} +(-399.406 - 161.702i) q^{64} +(-114.151 - 188.304i) q^{65} +(694.670 + 995.862i) q^{66} +(379.049 + 726.566i) q^{67} +(287.187 + 360.120i) q^{68} +(-653.790 - 314.849i) q^{69} +(-142.410 + 92.6983i) q^{70} +(212.793 + 578.226i) q^{71} +(269.784 + 1668.71i) q^{72} +(-534.631 + 140.197i) q^{73} +(-136.614 + 26.6055i) q^{74} +(266.308 + 439.303i) q^{75} +(1229.13 + 800.073i) q^{76} +(28.8962 - 126.603i) q^{77} +(861.686 + 733.564i) q^{78} +(-153.592 - 99.9772i) q^{79} +(553.076 - 183.634i) q^{80} +(127.952 - 108.927i) q^{81} +(1367.82 + 1506.13i) q^{82} +(429.939 - 207.048i) q^{83} +(365.920 - 458.849i) q^{84} +(218.161 + 42.4869i) q^{85} +(97.7662 - 265.662i) q^{86} +(-410.325 - 1797.75i) q^{87} +(-572.821 + 1097.99i) q^{88} +(-318.409 - 128.910i) q^{89} +(1212.87 + 1032.53i) q^{90} +(-3.87914 - 120.966i) q^{91} +(-46.3257 - 1444.61i) q^{92} +(-135.072 + 591.788i) q^{93} +(5.09902 + 11.5188i) q^{94} +(701.864 - 90.4954i) q^{95} +(-211.539 + 157.876i) q^{96} +(-918.381 + 1514.97i) q^{97} +(1597.47 - 102.561i) q^{98} +(-1214.80 + 77.9925i) 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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