LMFDB - Embedded newform 17.10.d.a.2.3

Newspace parameters

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	17.2
Dual form			17.10.d.a.9.3

$q$-expansion

$f(q)$	$=$	$q+(-22.5808 - 22.5808i) q^{2} +(147.205 - 60.9745i) q^{3} +507.789i q^{4} +(534.784 + 1291.08i) q^{5} +(-4700.88 - 1947.17i) q^{6} +(-3817.95 + 9217.34i) q^{7} +(-95.0916 + 95.0916i) q^{8} +(4033.58 - 4033.58i) q^{9} +O(q^{10})$	\(q+(-22.5808 - 22.5808i) q^{2} +(147.205 - 60.9745i) q^{3} +507.789i q^{4} +(534.784 + 1291.08i) q^{5} +(-4700.88 - 1947.17i) q^{6} +(-3817.95 + 9217.34i) q^{7} +(-95.0916 + 95.0916i) q^{8} +(4033.58 - 4033.58i) q^{9} +(17077.8 - 41229.6i) q^{10} +(46761.8 + 19369.4i) q^{11} +(30962.2 + 74749.3i) q^{12} +76005.9i q^{13} +(294348. - 121923. i) q^{14} +(157446. + 157446. i) q^{15} +264282. q^{16} +(-324117. - 116345. i) q^{17} -182163. q^{18} +(-460062. - 460062. i) q^{19} +(-655597. + 271557. i) q^{20} +1.58964e6i q^{21} +(-618544. - 1.49330e6i) q^{22} +(547050. + 226596. i) q^{23} +(-8199.84 + 19796.2i) q^{24} +(169.290 - 169.290i) q^{25} +(1.71628e6 - 1.71628e6i) q^{26} +(-852342. + 2.05773e6i) q^{27} +(-4.68046e6 - 1.93871e6i) q^{28} +(1.35186e6 + 3.26369e6i) q^{29} -7.11053e6i q^{30} +(3.15043e6 - 1.30495e6i) q^{31} +(-5.91903e6 - 5.91903e6i) q^{32} +8.06462e6 q^{33} +(4.69168e6 + 9.94599e6i) q^{34} -1.39421e7 q^{35} +(2.04821e6 + 2.04821e6i) q^{36} +(-5.75330e6 + 2.38309e6i) q^{37} +2.07772e7i q^{38} +(4.63442e6 + 1.11885e7i) q^{39} +(-173625. - 71917.6i) q^{40} +(-6432.62 + 15529.7i) q^{41} +(3.58954e7 - 3.58954e7i) q^{42} +(2.30025e7 - 2.30025e7i) q^{43} +(-9.83554e6 + 2.37451e7i) q^{44} +(7.36477e6 + 3.05059e6i) q^{45} +(-7.23613e6 - 1.74696e7i) q^{46} +5.02215e7i q^{47} +(3.89038e7 - 1.61145e7i) q^{48} +(-4.18484e7 - 4.18484e7i) q^{49} -7645.44 q^{50} +(-5.48058e7 + 2.63632e6i) q^{51} -3.85949e7 q^{52} +(1.10317e7 + 1.10317e7i) q^{53} +(6.57120e7 - 2.72188e7i) q^{54} +7.07317e7i q^{55} +(-513437. - 1.23955e6i) q^{56} +(-9.57757e7 - 3.96716e7i) q^{57} +(4.31706e7 - 1.04223e8i) q^{58} +(-1.14670e8 + 1.14670e8i) q^{59} +(-7.99494e7 + 7.99494e7i) q^{60} +(5.96668e7 - 1.44048e8i) q^{61} +(-1.00606e8 - 4.16725e7i) q^{62} +(2.17789e7 + 5.25789e7i) q^{63} +1.32001e8i q^{64} +(-9.81298e7 + 4.06467e7i) q^{65} +(-1.82106e8 - 1.82106e8i) q^{66} +2.74298e8 q^{67} +(5.90785e7 - 1.64583e8i) q^{68} +9.43453e7 q^{69} +(3.14825e8 + 3.14825e8i) q^{70} +(2.51521e8 - 1.04183e8i) q^{71} +767119. i q^{72} +(3.28100e6 + 7.92104e6i) q^{73} +(1.83727e8 + 7.61020e7i) q^{74} +(14598.1 - 35242.9i) q^{75} +(2.33614e8 - 2.33614e8i) q^{76} +(-3.57068e8 + 3.57068e8i) q^{77} +(1.47996e8 - 3.57295e8i) q^{78} +(-2.65406e8 - 1.09935e8i) q^{79} +(1.41334e8 + 3.41210e8i) q^{80} +4.67160e8i q^{81} +(495928. - 205420. i) q^{82} +(2.62900e8 + 2.62900e8i) q^{83} -8.07202e8 q^{84} +(-2.31221e7 - 4.80681e8i) q^{85} -1.03883e9 q^{86} +(3.98003e8 + 3.98003e8i) q^{87} +(-6.28852e6 + 2.60479e6i) q^{88} -4.29631e8i q^{89} +(-9.74179e7 - 2.35188e8i) q^{90} +(-7.00572e8 - 2.90187e8i) q^{91} +(-1.15063e8 + 2.77786e8i) q^{92} +(3.84192e8 - 3.84192e8i) q^{93} +(1.13404e9 - 1.13404e9i) q^{94} +(3.47944e8 - 8.40011e8i) q^{95} +(-1.23222e9 - 5.10404e8i) q^{96} +(3.90001e8 + 9.41546e8i) q^{97} +1.88994e9i q^{98} +(2.66745e8 - 1.10489e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) $ 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9	\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9 - 117636 * q^10 - 115768 * q^11 - 145528 * q^12 + 463660 * q^14 + 288244 * q^15 - 3407880 * q^16 - 271932 * q^17 + 2193336 * q^18 - 406700 * q^19 + 493564 * q^20 + 800964 * q^22 - 4172180 * q^23 + 15078440 * q^24 + 11946576 * q^25 - 14209012 * q^26 - 7973656 * q^27 + 13540804 * q^28 + 7833752 * q^29 + 5936252 * q^31 - 26730116 * q^32 - 1635208 * q^33 - 53493988 * q^34 + 46992776 * q^35 - 12761764 * q^36 + 74606796 * q^37 + 74096776 * q^39 - 69317672 * q^40 - 71362288 * q^41 - 308117664 * q^42 - 3765712 * q^43 + 163659820 * q^44 + 14167408 * q^45 + 72135428 * q^46 + 164621412 * q^48 - 284548508 * q^49 + 226223888 * q^50 - 406733132 * q^51 + 103553016 * q^52 - 244724728 * q^53 + 971226260 * q^54 + 470691652 * q^56 - 440646580 * q^57 - 308561768 * q^58 - 481734984 * q^59 + 379626176 * q^60 + 507966228 * q^61 + 358867236 * q^62 + 1070586456 * q^63 + 366263684 * q^65 - 2244715148 * q^66 - 311910088 * q^67 - 1839196668 * q^68 + 533688136 * q^69 + 34867672 * q^70 + 186006812 * q^71 + 487115192 * q^73 - 214149412 * q^74 + 533015920 * q^75 + 1104236912 * q^76 - 237869092 * q^77 - 2081523384 * q^78 - 136338052 * q^79 - 922534152 * q^80 + 1951892384 * q^82 + 1843663888 * q^83 - 2630025952 * q^84 - 395061976 * q^85 + 1538547296 * q^86 - 369395636 * q^87 - 3388839640 * q^88 + 874363684 * q^90 + 2087197720 * q^91 + 1061427500 * q^92 + 576415420 * q^93 + 6899365112 * q^94 + 5031766876 * q^95 + 490811364 * q^96 - 3419996368 * q^97 - 5630536112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−22.5808	−	22.5808i	−0.997942	−	0.997942i	0.00205624	−	0.999998i	$-0.499345\pi$
$2$	−22.5808	−	22.5808i	−0.997942	−	0.997942i	−0.999998	+	0.00205624i	$0.999345\pi$
$3$	147.205	−	60.9745i	1.04925	−	0.434613i	0.209625	−	0.977782i	$-0.432776\pi$
$3$	147.205	−	60.9745i	1.04925	−	0.434613i	0.839623	+	0.543169i	$0.182776\pi$
$4$			507.789i			0.991775i
$5$	534.784	+	1291.08i	0.382660	+	0.923823i	0.991449	+	0.130491i	$0.0416554\pi$
$5$	534.784	+	1291.08i	0.382660	+	0.923823i	−0.608790	+	0.793332i	$0.708345\pi$
$6$	−4700.88	−	1947.17i	−1.48081	−	0.613370i
$7$	−3817.95	+	9217.34i	−0.601020	+	1.45099i	0.271513	+	0.962435i	$0.412476\pi$
$7$	−3817.95	+	9217.34i	−0.601020	+	1.45099i	−0.872533	+	0.488556i	$0.837524\pi$
$8$	−95.0916	+	95.0916i	−0.00820800	+	0.00820800i
$9$	4033.58	−	4033.58i	0.204927	−	0.204927i
$10$	17077.8	−	41229.6i	0.540049	−	1.30379i
$11$	46761.8	+	19369.4i	0.962994	+	0.398885i	0.808100	−	0.589046i	$-0.200496\pi$
$11$	46761.8	+	19369.4i	0.962994	+	0.398885i	0.154895	+	0.987931i	$0.450496\pi$
$12$	30962.2	+	74749.3i	0.431038	+	1.04062i
$13$			76005.9i			0.738078i	0.929414	+	0.369039i	$0.120313\pi$
$13$			76005.9i			0.738078i	−0.929414	+	0.369039i	$0.879687\pi$
$14$	294348.	−	121923.i	2.04779	−	0.848221i
$15$	157446.	+	157446.i	0.803011	+	0.803011i
$16$	264282.			1.00816
$17$	−324117.	−	116345.i	−0.941199	−	0.337852i
$17$	−324117.	−	116345.i	−0.941199	−	0.337852i
$18$	−182163.			−0.409011
$19$	−460062.	−	460062.i	−0.809888	−	0.809888i	0.174728	−	0.984617i	$-0.444095\pi$
$19$	−460062.	−	460062.i	−0.809888	−	0.809888i	−0.984617	+	0.174728i	$0.944095\pi$
$20$	−655597.	+	271557.i	−0.916225	+	0.379513i
$21$			1.58964e6i			1.78366i
$22$	−618544.	−	1.49330e6i	−0.562948	−	1.35908i
$23$	547050.	+	226596.i	0.407617	+	0.168840i	0.577064	−	0.816699i	$-0.304198\pi$
$23$	547050.	+	226596.i	0.407617	+	0.168840i	−0.169447	+	0.985539i	$0.554198\pi$
$24$	−8199.84	+	19796.2i	−0.00504493	+	0.0121795i
$25$	169.290	−	169.290i	8.66767e−5	−	8.66767e-5i
$26$	1.71628e6	−	1.71628e6i	0.736559	−	0.736559i
$27$	−852342.	+	2.05773e6i	−0.308657	+	0.745165i
$28$	−4.68046e6	−	1.93871e6i	−1.43906	−	0.596077i
$29$	1.35186e6	+	3.26369e6i	0.354929	+	0.856875i	0.995997	+	0.0893904i	$0.0284919\pi$
$29$	1.35186e6	+	3.26369e6i	0.354929	+	0.856875i	−0.641067	+	0.767485i	$0.721508\pi$
$30$		−	7.11053e6i		−	1.60272i
$31$	3.15043e6	−	1.30495e6i	0.612692	−	0.253786i	−0.0546868	−	0.998504i	$-0.517416\pi$
$31$	3.15043e6	−	1.30495e6i	0.612692	−	0.253786i	0.667379	+	0.744718i	$0.267416\pi$
$32$	−5.91903e6	−	5.91903e6i	−0.997874	−	0.997874i
$33$	8.06462e6			1.18378
$34$	4.69168e6	+	9.94599e6i	0.602106	+	1.27642i
$35$	−1.39421e7			−1.57044
$36$	2.04821e6	+	2.04821e6i	0.203242	+	0.203242i
$37$	−5.75330e6	+	2.38309e6i	−0.504672	+	0.209042i	−0.620469	−	0.784231i	$-0.713058\pi$
$37$	−5.75330e6	+	2.38309e6i	−0.504672	+	0.209042i	0.115797	+	0.993273i	$0.463058\pi$
$38$			2.07772e7i			1.61644i
$39$	4.63442e6	+	1.11885e7i	0.320778	+	0.774427i
$40$	−173625.	−	71917.6i	−0.0107236	−	0.00444187i
$41$	−6432.62	+	15529.7i	−0.000355517	+	0.000858294i	−0.924057	−	0.382254i	$-0.875148\pi$
$41$	−6432.62	+	15529.7i	−0.000355517	+	0.000858294i	0.923702	+	0.383113i	$0.125148\pi$
$42$	3.58954e7	−	3.58954e7i	1.77999	−	1.77999i
$43$	2.30025e7	−	2.30025e7i	1.02605	−	1.02605i	0.0263957	−	0.999652i	$-0.491597\pi$
$43$	2.30025e7	−	2.30025e7i	1.02605	−	1.02605i	0.999652	−	0.0263957i	$-0.00840299\pi$
$44$	−9.83554e6	+	2.37451e7i	−0.395605	+	0.955074i
$45$	7.36477e6	+	3.05059e6i	0.267734	+	0.110899i
$46$	−7.23613e6	−	1.74696e7i	−0.238285	−	0.575270i
$47$			5.02215e7i			1.50124i	0.660736	+	0.750619i	$0.270244\pi$
$47$			5.02215e7i			1.50124i	−0.660736	+	0.750619i	$0.729756\pi$
$48$	3.89038e7	−	1.61145e7i	1.05781	−	0.438158i
$49$	−4.18484e7	−	4.18484e7i	−1.03704	−	1.03704i
$50$	−7645.44			−0.000172997
$51$	−5.48058e7	+	2.63632e6i	−1.13439	+	0.0545672i
$52$	−3.85949e7			−0.732007
$53$	1.10317e7	+	1.10317e7i	0.192045	+	0.192045i	0.796579	−	0.604534i	$-0.206641\pi$
$53$	1.10317e7	+	1.10317e7i	0.192045	+	0.192045i	−0.604534	+	0.796579i	$0.706641\pi$
$54$	6.57120e7	−	2.72188e7i	1.05165	−	0.435609i
$55$			7.07317e7i			1.04227i
$56$	−513437.	−	1.23955e6i	−0.00697656	−	0.0168429i
$57$	−9.57757e7	−	3.96716e7i	−1.20176	−	0.497786i
$58$	4.31706e7	−	1.04223e8i	0.500912	−	1.20931i
$59$	−1.14670e8	+	1.14670e8i	−1.23201	+	1.23201i	−0.268824	+	0.963189i	$0.586635\pi$
$59$	−1.14670e8	+	1.14670e8i	−1.23201	+	1.23201i	−0.963189	+	0.268824i	$0.913365\pi$
$60$	−7.99494e7	+	7.99494e7i	−0.796406	+	0.796406i
$61$	5.96668e7	−	1.44048e8i	0.551758	−	1.33206i	−0.364400	−	0.931243i	$-0.618726\pi$
$61$	5.96668e7	−	1.44048e8i	0.551758	−	1.33206i	0.916157	−	0.400818i	$-0.131274\pi$
$62$	−1.00606e8	−	4.16725e7i	−0.864694	−	0.358168i
$63$	2.17789e7	+	5.25789e7i	0.174182	+	0.420513i
$64$			1.32001e8i			0.983483i
$65$	−9.81298e7	+	4.06467e7i	−0.681853	+	0.282433i
$66$	−1.82106e8	−	1.82106e8i	−1.18134	−	1.18134i
$67$	2.74298e8			1.66298			0.831488	−	0.555542i	$-0.187489\pi$
$67$	2.74298e8			1.66298			0.831488	+	0.555542i	$0.187489\pi$
$68$	5.90785e7	−	1.64583e8i	0.335073	−	0.933458i
$69$	9.43453e7			0.501071
$70$	3.14825e8	+	3.14825e8i	1.56721	+	1.56721i
$71$	2.51521e8	−	1.04183e8i	1.17466	−	0.486560i	0.291929	−	0.956440i	$-0.405703\pi$
$71$	2.51521e8	−	1.04183e8i	1.17466	−	0.486560i	0.882730	+	0.469880i	$0.155703\pi$
$72$			767119.i			0.00336408i
$73$	3.28100e6	+	7.92104e6i	0.0135224	+	0.0326459i	0.930497	−	0.366301i	$-0.119376\pi$
$73$	3.28100e6	+	7.92104e6i	0.0135224	+	0.0326459i	−0.916974	+	0.398947i	$0.869376\pi$
$74$	1.83727e8	+	7.61020e7i	0.712245	+	0.295021i
$75$	14598.1	−	35242.9i	5.32746e−5	−	0.000128616i
$76$	2.33614e8	−	2.33614e8i	0.803227	−	0.803227i
$77$	−3.57068e8	+	3.57068e8i	−1.15756	+	1.15756i
$78$	1.47996e8	−	3.57295e8i	0.452715	−	1.09295i
$79$	−2.65406e8	−	1.09935e8i	−0.766634	−	0.317550i	−0.0351260	−	0.999383i	$-0.511183\pi$
$79$	−2.65406e8	−	1.09935e8i	−0.766634	−	0.317550i	−0.731508	+	0.681833i	$0.761183\pi$
$80$	1.41334e8	+	3.41210e8i	0.385781	+	0.931359i
$81$			4.67160e8i			1.20582i
$82$	495928.	−	205420.i	0.00121131	−	0.000501742i
$83$	2.62900e8	+	2.62900e8i	0.608050	+	0.608050i	0.942436	−	0.334386i	$-0.108529\pi$
$83$	2.62900e8	+	2.62900e8i	0.608050	+	0.608050i	−0.334386	+	0.942436i	$0.608529\pi$
$84$	−8.07202e8			−1.76899
$85$	−2.31221e7	−	4.80681e8i	−0.0480443	−	0.998784i
$86$	−1.03883e9			−2.04787
$87$	3.98003e8	+	3.98003e8i	0.744818	+	0.744818i
$88$	−6.28852e6	+	2.60479e6i	−0.0111783	+	0.00463021i
$89$		−	4.29631e8i		−	0.725839i	−0.931821	−	0.362919i	$-0.881780\pi$
$89$		−	4.29631e8i		−	0.725839i	0.931821	−	0.362919i	$-0.118220\pi$
$90$	−9.74179e7	−	2.35188e8i	−0.156512	−	0.377853i
$91$	−7.00572e8	−	2.90187e8i	−1.07094	−	0.443600i
$92$	−1.15063e8	+	2.77786e8i	−0.167452	+	0.404264i
$93$	3.84192e8	−	3.84192e8i	0.532568	−	0.532568i
$94$	1.13404e9	−	1.13404e9i	1.49815	−	1.49815i
$95$	3.47944e8	−	8.40011e8i	0.438282	−	1.05811i
$96$	−1.23222e9	−	5.10404e8i	−1.48071	−	0.613329i
$97$	3.90001e8	+	9.41546e8i	0.447294	+	1.07986i	0.973332	+	0.229402i	$0.0736770\pi$
$97$	3.90001e8	+	9.41546e8i	0.447294	+	1.07986i	−0.526038	+	0.850461i	$0.676323\pi$
$98$			1.88994e9i			2.06981i
$99$	2.66745e8	−	1.10489e8i	0.279086	−	0.115601i
$100$	85963.8	+	85963.8i	8.59638e−5	+	8.59638e-5i
$101$	5.60377e8			0.535838			0.267919	−	0.963441i	$-0.413664\pi$
$101$	5.60377e8			0.535838			0.267919	+	0.963441i	$0.413664\pi$
$102$	1.29709e9	+	1.17803e9i	1.18651	+	1.07760i
$103$	−1.44725e8			−0.126699			−0.0633497	−	0.997991i	$-0.520178\pi$
$103$	−1.44725e8			−0.126699			−0.0633497	+	0.997991i	$0.520178\pi$
$104$	−7.22753e6	−	7.22753e6i	−0.00605814	−	0.00605814i
$105$	−2.05236e9	+	8.50114e8i	−1.64779	+	0.682535i
$106$		−	4.98212e8i		−	0.383299i
$107$	−7.31531e8	−	1.76607e9i	−0.539518	−	1.30251i	−0.925060	−	0.379821i	$-0.875986\pi$
$107$	−7.31531e8	−	1.76607e9i	−0.539518	−	1.30251i	0.385542	−	0.922690i	$-0.374014\pi$
$108$	−1.04489e9	−	4.32810e8i	−0.739036	−	0.306119i
$109$	9.27654e8	−	2.23955e9i	0.629458	−	1.51965i	−0.210840	−	0.977521i	$-0.567620\pi$
$109$	9.27654e8	−	2.23955e9i	0.629458	−	1.51965i	0.840298	−	0.542125i	$-0.182380\pi$
$110$	1.59718e9	−	1.59718e9i	1.04013	−	1.04013i
$111$	−7.01609e8	+	7.01609e8i	−0.438674	+	0.438674i
$112$	−1.00902e9	+	2.43598e9i	−0.605923	+	1.46283i
$113$	−1.05934e9	−	4.38792e8i	−0.611197	−	0.253166i	0.0555433	−	0.998456i	$-0.482311\pi$
$113$	−1.05934e9	−	4.38792e8i	−0.611197	−	0.253166i	−0.666740	+	0.745290i	$0.732311\pi$
$114$	1.26688e9	+	3.05851e9i	0.702527	+	1.69605i
$115$			8.27466e8i			0.441174i
$116$	−1.65726e9	+	6.86461e8i	−0.849827	+	0.352010i
$117$	3.06576e8	+	3.06576e8i	0.151252	+	0.151252i
$118$	5.17869e9			2.45895
$119$	2.30985e9	−	2.54330e9i	1.05590	−	1.16262i
$120$	−2.99436e7			−0.0131822
$121$	1.44169e8	+	1.44169e8i	0.0611419	+	0.0611419i
$122$	−4.60006e9	+	1.90541e9i	−1.87994	+	0.778697i
$123$			2.67828e6i			0.00105508i
$124$	6.62640e8	+	1.59975e9i	0.251698	+	0.607653i
$125$	2.52195e9	+	1.04463e9i	0.923936	+	0.382707i
$126$	6.95490e8	−	1.67906e9i	0.245824	−	0.593470i
$127$	−1.75016e9	+	1.75016e9i	−0.596982	+	0.596982i	−0.939508	−	0.342526i	$-0.888717\pi$
$127$	−1.75016e9	+	1.75016e9i	−0.596982	+	0.596982i	0.342526	+	0.939508i	$0.388717\pi$
$128$	−4.98537e7	+	4.98537e7i	−0.0164154	+	0.0164154i
$129$	1.98353e9	−	4.78866e9i	0.630645	−	1.52251i
$130$	3.13369e9	+	1.29802e9i	0.962301	+	0.398598i
$131$	−7.70757e8	−	1.86077e9i	−0.228663	−	0.552042i	0.767352	−	0.641226i	$-0.221574\pi$
$131$	−7.70757e8	−	1.86077e9i	−0.228663	−	0.552042i	−0.996015	+	0.0891841i	$0.971574\pi$
$132$			4.09513e9i			1.17404i
$133$	5.99704e9	−	2.48406e9i	1.66190	−	0.688381i
$134$	−6.19388e9	−	6.19388e9i	−1.65955	−	1.65955i
$135$	−3.11252e9			−0.806511
$136$	4.18842e7	−	1.97574e7i	0.0104985	−	0.00495228i
$137$	2.91545e9			0.707070			0.353535	−	0.935421i	$-0.384979\pi$
$137$	2.91545e9			0.707070			0.353535	+	0.935421i	$0.384979\pi$
$138$	−2.13040e9	−	2.13040e9i	−0.500040	−	0.500040i
$139$	−6.95579e9	+	2.88118e9i	−1.58045	+	0.654642i	−0.988484	−	0.151323i	$-0.951647\pi$
$139$	−6.95579e9	+	2.88118e9i	−1.58045	+	0.654642i	−0.591962	+	0.805966i	$0.701647\pi$
$140$		−	7.07965e9i		−	1.55753i
$141$	3.06223e9	+	7.39288e9i	0.652457	+	1.57517i
$142$	−8.03211e9	−	3.32701e9i	−1.65780	−	0.686683i
$143$	−1.47219e9	+	3.55417e9i	−0.294408	+	0.710765i
$144$	1.06600e9	−	1.06600e9i	0.206599	−	0.206599i
$145$	−3.49073e9	+	3.49073e9i	−0.655783	+	0.655783i
$146$	1.04776e8	−	2.52951e8i	0.0190842	−	0.0460733i
$147$	−8.71199e9	−	3.60863e9i	−1.53883	−	0.637403i
$148$	−1.21011e9	−	2.92146e9i	−0.207323	−	0.500521i
$149$			8.08087e9i			1.34314i	0.740943	+	0.671568i	$0.234379\pi$
$149$			8.08087e9i			1.34314i	−0.740943	+	0.671568i	$0.765621\pi$
$150$	−1.12545e6	+	466177.i	−0.000181516	+	7.51865e-5i
$151$	2.25623e9	+	2.25623e9i	0.353172	+	0.353172i	0.861288	−	0.508116i	$-0.169658\pi$
$151$	2.25623e9	+	2.25623e9i	0.353172	+	0.353172i	−0.508116	+	0.861288i	$0.669658\pi$
$152$	8.74961e7			0.0132951
$153$	−1.77664e9	+	8.38067e8i	−0.262112	+	0.123642i
$154$	1.61258e10			2.31035
$155$	3.36960e9	+	3.36960e9i	0.468906	+	0.468906i
$156$	−5.68139e9	+	2.35331e9i	−0.768058	+	0.318140i
$157$		−	2.16958e9i		−	0.284988i	−0.989796	−	0.142494i	$-0.954488\pi$
$157$		−	2.16958e9i		−	0.284988i	0.989796	−	0.142494i	$-0.0455122\pi$
$158$	3.51067e9	+	8.47550e9i	0.448160	+	1.08195i
$159$	2.29659e9	+	9.51278e8i	0.284968	+	0.118038i
$160$	4.47655e9	−	1.08074e10i	0.540012	−	1.30371i
$161$	−4.17722e9	+	4.17722e9i	−0.489971	+	0.489971i
$162$	1.05489e10	−	1.05489e10i	1.20334	−	1.20334i
$163$	6.17014e9	−	1.48960e10i	0.684622	−	1.65282i	−0.0707222	−	0.997496i	$-0.522530\pi$
$163$	6.17014e9	−	1.48960e10i	0.684622	−	1.65282i	0.755344	−	0.655328i	$-0.227470\pi$
$164$	−7.88581e6	−	3.26641e6i	−0.000851234	−	0.000352593i
$165$	4.31283e9	+	1.04121e10i	0.452986	+	1.09360i
$166$		−	1.18730e10i		−	1.21360i
$167$	−1.02730e10	+	4.25523e9i	−1.02206	+	0.423350i	−0.829839	−	0.558003i	$-0.811568\pi$
$167$	−1.02730e10	+	4.25523e9i	−1.02206	+	0.423350i	−0.192218	+	0.981352i	$0.561568\pi$
$168$	−1.51162e8	−	1.51162e8i	−0.0146403	−	0.0146403i
$169$	4.82760e9			0.455241
$170$	−1.03321e10	+	1.13763e10i	−0.948783	+	1.04467i
$171$	−3.71139e9			−0.331936
$172$	1.16804e10	+	1.16804e10i	1.01761	+	1.01761i
$173$	1.37526e10	−	5.69650e9i	1.16728	−	0.483504i	0.286989	−	0.957934i	$-0.407346\pi$
$173$	1.37526e10	−	5.69650e9i	1.16728	−	0.483504i	0.880294	+	0.474429i	$0.157346\pi$
$174$		−	1.79745e10i		−	1.48657i
$175$	914066.	+	2.20675e6i	7.36726e−5	+	0.000177861i
$176$	1.23583e10	+	5.11898e9i	0.970850	+	0.402139i
$177$	−9.88810e9	+	2.38720e10i	−0.757239	+	1.82814i
$178$	−9.70142e9	+	9.70142e9i	−0.724345	+	0.724345i
$179$	1.03071e10	−	1.03071e10i	0.750408	−	0.750408i	−0.224147	−	0.974555i	$-0.571960\pi$
$179$	1.03071e10	−	1.03071e10i	0.750408	−	0.750408i	0.974555	+	0.224147i	$0.0719597\pi$
$180$	−1.54906e9	+	3.73975e9i	−0.109987	+	0.265532i
$181$	2.68335e9	+	1.11148e9i	0.185833	+	0.0769747i	0.473660	−	0.880708i	$-0.342933\pi$
$181$	2.68335e9	+	1.11148e9i	0.185833	+	0.0769747i	−0.287826	+	0.957683i	$0.592933\pi$
$182$	9.26686e9	+	2.23722e10i	0.626053	+	1.51143i
$183$		−	2.48429e10i		−	1.63746i
$184$	−7.35672e7	+	3.04725e7i	−0.00473156	+	0.00195988i
$185$	−6.15354e9	−	6.15354e9i	−0.386235	−	0.386235i
$186$	−1.73508e10			−1.06294
$187$	−1.29028e10	−	1.17184e10i	−0.771606	−	0.700780i
$188$	−2.55019e10			−1.48889
$189$	−1.57127e10	−	1.57127e10i	−0.895718	−	0.895718i
$190$	−2.68250e10	+	1.11113e10i	−1.49331	+	0.618548i
$191$			1.67129e10i			0.908658i	0.890834	+	0.454329i	$0.150121\pi$
$191$			1.67129e10i			0.908658i	−0.890834	+	0.454329i	$0.849879\pi$
$192$	8.04869e9	+	1.94312e10i	0.427434	+	1.03192i
$193$	9.28945e9	+	3.84782e9i	0.481928	+	0.199621i	0.610402	−	0.792092i	$-0.291008\pi$
$193$	9.28945e9	+	3.84782e9i	0.481928	+	0.199621i	−0.128474	+	0.991713i	$0.541008\pi$
$194$	1.24543e10	−	3.00674e10i	0.631267	−	1.52401i
$195$	−1.19668e10	+	1.19668e10i	−0.592685	+	0.592685i
$196$	2.12501e10	−	2.12501e10i	1.02851	−	1.02851i
$197$	−2.48261e9	+	5.99355e9i	−0.117439	+	0.283522i	−0.971658	−	0.236391i	$-0.924035\pi$
$197$	−2.48261e9	+	5.99355e9i	−0.117439	+	0.283522i	0.854220	+	0.519912i	$0.174035\pi$
$198$	−8.51827e9	−	3.52838e9i	−0.393875	−	0.163148i
$199$	−1.78596e8	−	4.31168e8i	−0.00807295	−	0.0194898i	0.919792	−	0.392407i	$-0.128358\pi$
$199$	−1.78596e8	−	4.31168e8i	−0.00807295	−	0.0194898i	−0.927865	+	0.372917i	$0.878358\pi$
$200$			32196.2i			1.42288e-6i
$201$	4.03782e10	−	1.67252e10i	1.74488	−	0.722751i
$202$	−1.26538e10	−	1.26538e10i	−0.534735	−	0.534735i
$203$	−3.52439e10			−1.45664
$204$	−1.33869e9	−	2.78298e10i	−0.0541184	−	1.12506i
$205$	−2.34902e7			−0.000928954
$206$	3.26800e9	+	3.26800e9i	0.126439	+	0.126439i
$207$	3.12056e9	−	1.29258e9i	0.118132	−	0.0489317i
$208$			2.00870e10i			0.744099i
$209$	−1.26022e10	−	3.04244e10i	−0.456865	−	1.10297i
$210$	6.55402e10	+	2.71476e10i	2.32553	+	0.963264i
$211$	4.06743e8	−	9.81965e8i	0.0141270	−	0.0341055i	−0.916659	−	0.399671i	$-0.869124\pi$
$211$	4.06743e8	−	9.81965e8i	0.0141270	−	0.0341055i	0.930786	+	0.365565i	$0.119124\pi$
$212$	−5.60179e9	+	5.60179e9i	−0.190465	+	0.190465i
$213$	3.06728e10	−	3.06728e10i	1.02104	−	1.02104i
$214$	−2.33608e10	+	5.63980e10i	−0.761423	+	1.83824i
$215$	4.19995e10	+	1.73968e10i	1.34051	+	0.555259i
$216$	−1.14623e8	−	2.76724e8i	−0.00358285	−	0.00864978i
$217$			3.40208e10i			1.04154i
$218$	−7.15182e10	+	2.96238e10i	−2.14468	+	0.888356i
$219$	9.65963e8	+	9.65963e8i	0.0283767	+	0.0283767i
$220$	−3.59167e10			−1.03370
$221$	8.84287e9	−	2.46348e10i	0.249361	−	0.694679i
$222$	3.16858e10			0.875542
$223$	−3.39091e10	−	3.39091e10i	−0.918214	−	0.918214i	0.0786853	−	0.996900i	$-0.474928\pi$
$223$	−3.39091e10	−	3.39091e10i	−0.918214	−	0.918214i	−0.996900	+	0.0786853i	$0.974928\pi$
$224$	7.71563e10	−	3.19592e10i	2.04765	−	0.848164i
$225$		−	1.36569e6i		−	3.55248e-5i
$226$	1.40124e10	+	3.38290e10i	0.357294	+	0.862584i
$227$	1.94473e10	+	8.05532e9i	0.486118	+	0.201357i	0.612262	−	0.790655i	$-0.290260\pi$
$227$	1.94473e10	+	8.05532e9i	0.486118	+	0.201357i	−0.126143	+	0.992012i	$0.540260\pi$
$228$	2.01448e10	−	4.86338e10i	0.493692	−	1.19188i
$229$	1.13634e10	−	1.13634e10i	0.273054	−	0.273054i	−0.557275	−	0.830328i	$-0.688153\pi$
$229$	1.13634e10	−	1.13634e10i	0.273054	−	0.273054i	0.830328	+	0.557275i	$0.188153\pi$
$230$	1.86849e10	−	1.86849e10i	0.440266	−	0.440266i
$231$	−3.07903e10	+	7.43344e10i	−0.711476	+	1.71765i
$232$	−4.38900e8	−	1.81798e8i	−0.00994649	−	0.00411997i
$233$	2.32763e10	+	5.61939e10i	0.517382	+	1.24907i	0.939506	+	0.342533i	$0.111285\pi$
$233$	2.32763e10	+	5.61939e10i	0.517382	+	1.24907i	−0.422124	+	0.906538i	$0.638715\pi$
$234$		−	1.38455e10i		−	0.301882i
$235$	−6.48401e10	+	2.68576e10i	−1.38688	+	0.574463i
$236$	−5.82281e10	−	5.82281e10i	−1.22188	−	1.22188i
$237$	−4.57724e10			−0.942401
$238$	−1.09588e11	+	5.27150e9i	−2.21395	+	0.106497i
$239$	4.66769e10			0.925362			0.462681	−	0.886525i	$-0.346887\pi$
$239$	4.66769e10			0.925362			0.462681	+	0.886525i	$0.346887\pi$
$240$	4.16102e10	+	4.16102e10i	0.809561	+	0.809561i
$241$	−9.08976e9	+	3.76510e9i	−0.173570	+	0.0718952i	−0.467777	−	0.883847i	$-0.654945\pi$
$241$	−9.08976e9	+	3.76510e9i	−0.173570	+	0.0718952i	0.294206	+	0.955742i	$0.404945\pi$
$242$		−	6.51093e9i		−	0.122032i
$243$	1.17082e10	+	2.82661e10i	0.215408	+	0.520040i
$244$	7.31462e10	+	3.02981e10i	1.32111	+	0.547220i
$245$	3.16498e10	−	7.64095e10i	0.561208	−	1.35488i
$246$	6.04779e7	−	6.04779e7i	0.00105290	−	0.00105290i
$247$	3.49674e10	−	3.49674e10i	0.597761	−	0.597761i
$248$	−1.75490e8	+	4.23670e8i	−0.00294591	+	0.00711205i
$249$	5.47305e10	+	2.26701e10i	0.902262	+	0.373729i
$250$	−3.33593e10	−	8.05364e10i	−0.540115	−	1.30395i
$251$		−	5.71571e10i		−	0.908947i	−0.890760	−	0.454473i	$-0.849827\pi$
$251$		−	5.71571e10i		−	0.908947i	0.890760	−	0.454473i	$-0.150173\pi$
$252$	−2.66990e10	+	1.10591e10i	−0.417054	+	0.172749i
$253$	2.11920e10	+	2.11920e10i	0.325185	+	0.325185i
$254$	7.90402e10			1.19151
$255$	−3.27130e10	−	6.93490e10i	−0.484495	−	1.02709i
$256$	6.98359e10			1.01625
$257$	6.08016e10	+	6.08016e10i	0.869392	+	0.869392i	0.992405	−	0.123013i	$-0.0392556\pi$
$257$	6.08016e10	+	6.08016e10i	0.869392	+	0.869392i	−0.123013	+	0.992405i	$0.539256\pi$
$258$	−1.52922e11	+	6.33423e10i	−2.14873	+	0.890031i
$259$		−	6.21286e10i		−	0.857912i
$260$	−2.06399e10	−	4.98292e10i	−0.280110	−	0.676245i
$261$	1.86172e10	+	7.71149e9i	0.248331	+	0.102862i
$262$	−2.46135e10	+	5.94221e10i	−0.322713	+	0.779099i
$263$	−1.84881e10	+	1.84881e10i	−0.238282	+	0.238282i	−0.816138	−	0.577856i	$-0.803889\pi$
$263$	−1.84881e10	+	1.84881e10i	−0.238282	+	0.238282i	0.577856	+	0.816138i	$0.303889\pi$
$264$	−7.66878e8	+	7.66878e8i	−0.00971648	+	0.00971648i
$265$	−8.34328e9	+	2.01425e10i	−0.103928	+	0.250903i
$266$	−1.91510e11	−	7.93262e10i	−2.34544	−	0.971514i
$267$	−2.61965e10	−	6.32440e10i	−0.315459	−	0.761585i
$268$			1.39285e11i			1.64930i
$269$	1.98411e10	−	8.21845e9i	0.231036	−	0.0956983i	−0.264162	−	0.964478i	$-0.585095\pi$
$269$	1.98411e10	−	8.21845e9i	0.231036	−	0.0956983i	0.495198	+	0.868780i	$0.335095\pi$
$270$	7.02834e10	+	7.02834e10i	0.804851	+	0.804851i
$271$	−1.61241e11			−1.81599			−0.907997	−	0.418976i	$-0.862389\pi$
$271$	−1.61241e11			−1.81599			−0.907997	+	0.418976i	$0.862389\pi$
$272$	−8.56584e10	−	3.07478e10i	−0.948877	−	0.340608i
$273$	−1.20822e11			−1.31648
$274$	−6.58332e10	−	6.58332e10i	−0.705615	−	0.705615i
$275$	1.11954e7	−	4.63727e6i	0.000118043	−	4.88951e-5i
$276$			4.79075e10i			0.496950i
$277$	1.81719e10	+	4.38710e10i	0.185457	+	0.447732i	0.989075	−	0.147413i	$-0.0470946\pi$
$277$	1.81719e10	+	4.38710e10i	0.185457	+	0.447732i	−0.803618	+	0.595145i	$0.797095\pi$
$278$	2.22127e11	+	9.20081e10i	2.23049	+	0.923898i
$279$	7.44389e9	−	1.79711e10i	0.0735498	−	0.177565i
$280$	1.32578e9	−	1.32578e9i	0.0128902	−	0.0128902i
$281$	1.92745e9	−	1.92745e9i	0.0184419	−	0.0184419i	−0.697826	−	0.716268i	$-0.745849\pi$
$281$	1.92745e9	−	1.92745e9i	0.0184419	−	0.0184419i	0.716268	+	0.697826i	$0.245849\pi$
$282$	9.77897e10	−	2.36085e11i	0.920815	−	2.22304i
$283$	−3.92533e10	−	1.62592e10i	−0.363778	−	0.150682i	0.193304	−	0.981139i	$-0.438079\pi$
$283$	−3.92533e10	−	1.62592e10i	−0.363778	−	0.150682i	−0.557083	+	0.830457i	$0.688079\pi$
$284$	5.29032e10	+	1.27720e11i	0.482558	+	1.16500i
$285$		−	1.44870e11i		−	1.30070i
$286$	1.13499e11	−	4.70130e10i	1.00310	−	0.415499i
$287$	−1.18583e8	−	1.18583e8i	−0.00103170	−	0.00103170i
$288$	−4.77498e10			−0.408983
$289$	9.15158e10	+	7.54185e10i	0.771713	+	0.635971i
$290$	1.57647e11			1.30887
$291$	1.14821e11	+	1.14821e11i	0.938645	+	0.938645i
$292$	−4.02221e9	+	1.66606e9i	−0.0323774	+	0.0134112i
$293$			6.93631e9i			0.0549825i	0.999622	+	0.0274912i	$0.00875183\pi$
$293$			6.93631e9i			0.0549825i	−0.999622	+	0.0274912i	$0.991248\pi$
$294$	1.15238e11	+	2.78210e11i	0.899568	+	2.17175i
$295$	−2.09372e11	−	8.67246e10i	−1.60960	−	0.666720i
$296$	3.20478e8	−	7.73703e8i	0.00242653	−	0.00585816i
$297$	−7.97140e10	+	7.97140e10i	−0.594471	+	0.594471i
$298$	1.82473e11	−	1.82473e11i	1.34037	−	1.34037i
$299$	−1.72226e10	+	4.15790e10i	−0.124617	+	0.300853i
$300$	1.78959e7	+	7.41274e6i	0.000127558	+	5.28364e-5i
$301$	1.24200e11	+	2.99845e11i	0.872110	+	2.10546i
$302$		−	1.01895e11i		−	0.704891i
$303$	8.24905e10	−	3.41687e10i	0.562228	−	0.232882i
$304$	−1.21586e11	−	1.21586e11i	−0.816495	−	0.816495i
$305$	2.17887e11			1.44172
$306$	5.90422e10	+	2.11937e10i	0.384961	+	0.138185i
$307$	1.64410e10			0.105635			0.0528173	−	0.998604i	$-0.483180\pi$
$307$	1.64410e10			0.105635			0.0528173	+	0.998604i	$0.483180\pi$
$308$	−1.81315e11	−	1.81315e11i	−1.14804	−	1.14804i
$309$	−2.13042e10	+	8.82451e9i	−0.132939	+	0.0550652i
$310$		−	1.52177e11i		−	0.935881i
$311$	−4.68694e10	−	1.13153e11i	−0.284098	−	0.685872i	0.715826	−	0.698279i	$-0.246051\pi$
$311$	−4.68694e10	−	1.13153e11i	−0.284098	−	0.685872i	−0.999923	+	0.0124071i	$0.996051\pi$
$312$	−1.50463e9	−	6.23237e8i	−0.00898945	−	0.00372355i
$313$	−9.05020e10	+	2.18491e11i	−0.532977	+	1.28672i	0.396565	+	0.918006i	$0.370202\pi$
$313$	−9.05020e10	+	2.18491e11i	−0.532977	+	1.28672i	−0.929543	+	0.368715i	$0.879798\pi$
$314$	−4.89909e10	+	4.89909e10i	−0.284402	+	0.284402i
$315$	−5.62367e10	+	5.62367e10i	−0.321827	+	0.321827i
$316$	5.58236e10	−	1.34770e11i	0.314938	−	0.760329i
$317$	4.00600e10	+	1.65934e10i	0.222815	+	0.0922930i	0.491298	−	0.870991i	$-0.336522\pi$
$317$	4.00600e10	+	1.65934e10i	0.222815	+	0.0922930i	−0.268483	+	0.963284i	$0.586522\pi$
$318$	−3.03782e10	−	7.33395e10i	−0.166587	−	0.402176i
$319$			1.78800e11i			0.966742i
$320$	−1.70424e11	+	7.05919e10i	−0.908564	+	0.376340i
$321$	−2.15371e11	−	2.15371e11i	−1.13218	−	1.13218i
$322$	1.88650e11			0.977926
$323$	9.55882e10	+	2.02640e11i	0.488644	+	1.03589i
$324$	−2.37218e11			−1.19590
$325$	1.28671e7	+	1.28671e7i	6.39741e−5	+	6.39741e-5i
$326$	−4.75692e11	+	1.97038e11i	−2.33263	+	0.966209i
$327$		−	3.86238e11i		−	1.86806i
$328$	−865057.	−	2.08843e6i	−4.12679e−6	−	9.96296e-6i
$329$	−4.62909e11	−	1.91743e11i	−2.17828	−	0.902274i
$330$	1.37726e11	−	3.32501e11i	0.639300	−	1.54341i
$331$	1.20201e11	−	1.20201e11i	0.550406	−	0.550406i	−0.376152	−	0.926558i	$-0.622753\pi$
$331$	1.20201e11	−	1.20201e11i	0.550406	−	0.550406i	0.926558	+	0.376152i	$0.122753\pi$
$332$	−1.33498e11	+	1.33498e11i	−0.603049	+	0.603049i
$333$	−1.35940e10	+	3.28188e10i	−0.0605826	+	0.146259i
$334$	3.28061e11	+	1.35887e11i	1.44243	+	0.597475i
$335$	1.46690e11	+	3.54141e11i	0.636355	+	1.53630i
$336$			4.20114e11i			1.79821i
$337$	−9.48238e9	+	3.92773e9i	−0.0400482	+	0.0165885i	−0.402618	−	0.915368i	$-0.631900\pi$
$337$	−9.48238e9	+	3.92773e9i	−0.0400482	+	0.0165885i	0.362569	+	0.931957i	$0.381900\pi$
$338$	−1.09011e11	−	1.09011e11i	−0.454304	−	0.454304i
$339$	−1.82695e11			−0.751327
$340$	2.44084e11	−	1.17411e10i	0.990569	−	0.0476492i
$341$	1.72596e11			0.691251
$342$	8.38064e10	+	8.38064e10i	0.331253	+	0.331253i
$343$	1.73553e11	−	7.18878e10i	0.677029	−	0.280435i
$344$			4.37469e9i			0.0168436i
$345$	5.04543e10	+	1.21808e11i	0.191740	+	0.462901i
$346$	−4.39176e11	−	1.81913e11i	−1.64739	−	0.682371i
$347$	−5.75630e10	+	1.38969e11i	−0.213138	+	0.514561i	−0.993902	−	0.110265i	$-0.964830\pi$
$347$	−5.75630e10	+	1.38969e11i	−0.213138	+	0.514561i	0.780764	+	0.624826i	$0.214830\pi$
$348$	−2.02102e11	+	2.02102e11i	−0.738692	+	0.738692i
$349$	3.10027e11	−	3.10027e11i	1.11862	−	1.11862i	0.126681	−	0.991943i	$-0.459567\pi$
$349$	3.10027e11	−	3.10027e11i	1.11862	−	1.11862i	0.991943	−	0.126681i	$-0.0404326\pi$
$350$	2.91899e7	−	7.04706e7i	0.000103974	−	0.000251016i
$351$	−1.56400e11	−	6.47830e10i	−0.549990	−	0.227813i
$352$	−1.62137e11	−	3.91432e11i	−0.562910	−	1.35898i
$353$		−	3.32465e10i		−	0.113962i	−0.998375	−	0.0569810i	$-0.981853\pi$
$353$		−	3.32465e10i		−	0.113962i	0.998375	−	0.0569810i	$-0.0181475\pi$
$354$	7.62331e11	−	3.15768e11i	2.58005	−	1.06869i
$355$	2.69019e11	+	2.69019e11i	0.898990	+	0.898990i
$356$	2.18162e11			0.719869
$357$	1.84946e11	−	5.15230e11i	0.602612	−	1.67878i
$358$	−4.65485e11			−1.49773
$359$	1.44809e11	+	1.44809e11i	0.460119	+	0.460119i	0.898695	−	0.438575i	$-0.144517\pi$
$359$	1.44809e11	+	1.44809e11i	0.460119	+	0.460119i	−0.438575	+	0.898695i	$0.644517\pi$
$360$	−9.90414e8	+	4.10243e8i	−0.00310782	+	0.00128730i
$361$			1.00627e11i			0.311839i
$362$	−3.54941e10	−	8.56905e10i	−0.108635	−	0.262267i
$363$	3.00132e10	+	1.24319e10i	0.0907260	+	0.0375800i
$364$	1.47354e11	−	3.55743e11i	0.439951	−	1.06214i
$365$	−8.47208e9	+	8.47208e9i	−0.0249846	+	0.0249846i
$366$	−5.60973e11	+	5.60973e11i	−1.63409	+	1.63409i
$367$	1.22419e11	−	2.95545e11i	0.352249	−	0.850405i	−0.644092	−	0.764948i	$-0.722765\pi$
$367$	1.22419e11	−	2.95545e11i	0.352249	−	0.850405i	0.996342	−	0.0854576i	$-0.0272352\pi$
$368$	1.44576e11	+	5.98852e10i	0.410942	+	0.170218i
$369$	3.66939e7	+	8.85868e7i	0.000103033	+	0.000248743i
$370$			2.77904e11i			0.770881i
$371$	−1.43802e11	+	5.95647e10i	−0.394078	+	0.163232i
$372$	1.95088e11	+	1.95088e11i	0.528188	+	0.528188i
$373$	1.73495e11			0.464084			0.232042	−	0.972706i	$-0.425459\pi$
$373$	1.73495e11			0.464084			0.232042	+	0.972706i	$0.425459\pi$
$374$	2.67436e10	+	5.55967e11i	0.0706801	+	1.46935i
$375$	4.34941e11			1.13577
$376$	−4.77565e9	−	4.77565e9i	−0.0123222	−	0.0123222i
$377$	−2.48059e11	+	1.02750e11i	−0.632440	+	0.261965i
$378$			7.09610e11i			1.78775i
$379$	−5.13111e10	−	1.23876e11i	−0.127742	−	0.308397i	0.847049	−	0.531514i	$-0.178377\pi$
$379$	−5.13111e10	−	1.23876e11i	−0.127742	−	0.308397i	−0.974792	+	0.223117i	$0.928377\pi$
$380$	4.26548e11	+	1.76682e11i	1.04940	+	0.434677i
$381$	−1.50918e11	+	3.64348e11i	−0.366926	+	0.885838i
$382$	3.77390e11	−	3.77390e11i	0.906788	−	0.906788i
$383$	−4.09179e11	+	4.09179e11i	−0.971669	+	0.971669i	−0.999610	−	0.0279404i	$-0.991105\pi$
$383$	−4.09179e11	+	4.09179e11i	−0.971669	+	0.971669i	0.0279404	+	0.999610i	$0.491105\pi$
$384$	−4.29893e9	+	1.03785e10i	−0.0100895	+	0.0243582i
$385$	−6.51958e11	−	2.70050e11i	−1.51233	−	0.626427i
$386$	−1.22877e11	−	2.96651e11i	−0.281726	−	0.680146i
$387$		−	1.85565e11i		−	0.420530i
$388$	−4.78106e11	+	1.98038e11i	−1.07098	+	0.443615i
$389$	−2.40690e11	−	2.40690e11i	−0.532948	−	0.532948i	0.388500	−	0.921449i	$-0.372993\pi$
$389$	−2.40690e11	−	2.40690e11i	−0.532948	−	0.532948i	−0.921449	+	0.388500i	$0.872993\pi$
$390$	5.40442e11			1.18293
$391$	−1.50945e11	−	1.37090e11i	−0.326605	−	0.296626i
$392$	7.95886e9			0.0170241
$393$	−2.26919e11	−	2.26919e11i	−0.479849	−	0.479849i
$394$	1.91399e11	−	7.92800e10i	0.400135	−	0.165741i
$395$		−	4.01452e11i		−	0.829748i
$396$	5.61053e10	+	1.35450e11i	0.114650	+	0.276791i
$397$	3.12258e11	+	1.29341e11i	0.630893	+	0.261324i	0.675132	−	0.737697i	$-0.264086\pi$
$397$	3.12258e11	+	1.29341e11i	0.630893	+	0.261324i	−0.0442395	+	0.999021i	$0.514086\pi$
$398$	−5.70330e9	+	1.37690e10i	−0.0113934	+	0.0275060i
$399$	7.31333e11	−	7.31333e11i	1.44457	−	1.44457i
$400$	4.47405e7	−	4.47405e7i	8.73837e−5	−	8.73837e-5i
$401$	2.59597e11	−	6.26723e11i	0.501361	−	1.21039i	−0.447382	−	0.894343i	$-0.647643\pi$
$401$	2.59597e11	−	6.26723e11i	0.501361	−	1.21039i	0.948743	−	0.316049i	$-0.102357\pi$
$402$	−1.28944e12	−	5.34104e11i	−2.46255	−	1.02002i
$403$	9.91840e10	+	2.39451e11i	0.187313	+	0.452215i
$404$			2.84553e11i			0.531431i
$405$	−6.03141e11	+	2.49829e11i	−1.11396	+	0.461419i
$406$	7.95836e11	+	7.95836e11i	1.45364	+	1.45364i
$407$	−3.15193e11			−0.569380
$408$	4.96089e9	−	5.46227e9i	0.00886316	−	0.00975893i
$409$	3.79922e11			0.671336			0.335668	−	0.941980i	$-0.391038\pi$
$409$	3.79922e11			0.671336			0.335668	+	0.941980i	$0.391038\pi$
$410$	5.30428e8	+	5.30428e8i	0.000927042	+	0.000927042i
$411$	4.29170e11	−	1.77768e11i	0.741892	−	0.307302i
$412$		−	7.34895e10i		−	0.125657i
$413$	−6.19148e11	−	1.49476e12i	−1.04717	−	2.52810i
$414$	−9.96524e10	−	4.12774e10i	−0.166719	−	0.0690575i
$415$	−1.98831e11	+	4.80020e11i	−0.329054	+	0.794407i
$416$	4.49881e11	−	4.49881e11i	0.736509	−	0.736509i
$417$	−8.48252e11	+	8.48252e11i	−1.37376	+	1.37376i
$418$	−4.02441e11	+	9.71577e11i	−0.644775	+	1.55663i
$419$	5.82365e11	+	2.41224e11i	0.923065	+	0.382346i	0.793043	−	0.609165i	$-0.208495\pi$
$419$	5.82365e11	+	2.41224e11i	0.923065	+	0.382346i	0.130022	+	0.991511i	$0.458495\pi$
$420$	−4.31678e11	−	1.04216e12i	−0.676922	−	1.63423i
$421$		−	3.36779e11i		−	0.522488i	−0.965273	−	0.261244i	$-0.915867\pi$
$421$		−	3.36779e11i		−	0.522488i	0.965273	−	0.261244i	$-0.0841327\pi$
$422$	−3.13582e10	+	1.29890e10i	−0.0481332	+	0.0199374i
$423$	2.02572e11	+	2.02572e11i	0.307644	+	0.307644i
$424$	−2.09805e9			−0.00315261
$425$	−7.45659e7	+	3.51739e7i	−0.000110864	+	5.22962e-5i
$426$	−1.38523e12			−2.03788
$427$	1.09994e12	+	1.09994e12i	1.60119	+	1.60119i
$428$	8.96792e11	−	3.71463e11i	1.29180	−	0.535080i
$429$			6.12959e11i			0.873723i
$430$	−5.55551e11	−	1.34122e12i	−0.783638	−	1.89187i
$431$	−1.91658e11	−	7.93872e10i	−0.267534	−	0.110816i	0.244884	−	0.969552i	$-0.421250\pi$
$431$	−1.91658e11	−	7.93872e10i	−0.267534	−	0.110816i	−0.512418	+	0.858736i	$0.671250\pi$
$432$	−2.25259e11	+	5.43823e11i	−0.311175	+	0.751244i
$433$	−4.61492e11	+	4.61492e11i	−0.630911	+	0.630911i	−0.948297	−	0.317385i	$-0.897195\pi$
$433$	−4.61492e11	+	4.61492e11i	−0.630911	+	0.630911i	0.317385	+	0.948297i	$0.397195\pi$
$434$	7.68219e11	−	7.68219e11i	1.03940	−	1.03940i
$435$	−3.01009e11	+	7.26700e11i	−0.403068	+	0.973092i
$436$	1.13722e12	+	4.71052e11i	1.50715	+	0.624281i
$437$	−1.47429e11	−	3.55925e11i	−0.193382	−	0.466866i
$438$		−	4.36245e10i		−	0.0566366i
$439$	5.53757e11	−	2.29374e11i	0.711589	−	0.294750i	0.00262700	−	0.999997i	$-0.499164\pi$
$439$	5.53757e11	−	2.29374e11i	0.711589	−	0.294750i	0.708962	+	0.705247i	$0.249164\pi$
$440$	−6.72599e9	−	6.72599e9i	−0.00855498	−	0.00855498i
$441$	−3.37597e11			−0.425036
$442$	−7.55954e11	+	3.56595e11i	−0.942096	+	0.444401i
$443$	1.38710e11			0.171117			0.0855583	−	0.996333i	$-0.472733\pi$
$443$	1.38710e11			0.171117			0.0855583	+	0.996333i	$0.472733\pi$
$444$	−3.56269e11	−	3.56269e11i	−0.435066	−	0.435066i
$445$	5.54688e11	−	2.29759e11i	0.670546	−	0.277749i
$446$			1.53139e12i			1.83265i
$447$	4.92727e11	+	1.18955e12i	0.583745	+	1.40928i
$448$	−1.21670e12	−	5.03972e11i	−1.42702	−	0.591093i
$449$	−6.81450e10	+	1.64517e11i	−0.0791271	+	0.191030i	−0.958492	−	0.285118i	$-0.907967\pi$
$449$	−6.81450e10	+	1.64517e11i	−0.0791271	+	0.191030i	0.879365	+	0.476148i	$0.157967\pi$
$450$	−3.08385e7	+	3.08385e7i	−3.54517e−5	+	3.54517e-5i
$451$	−6.01601e8	+	6.01601e8i	−0.000684722	+	0.000684722i
$452$	2.22814e11	−	5.37919e11i	0.251084	−	0.606170i
$453$	4.69701e11	+	1.94557e11i	0.524059	+	0.217072i
$454$	−2.57240e11	−	6.21031e11i	−0.284175	−	0.686060i
$455$		−	1.05968e12i		−	1.15911i
$456$	1.28799e10	−	5.33503e9i	0.0139499	−	0.00577824i
$457$	1.15093e11	+	1.15093e11i	0.123431	+	0.123431i	0.766124	−	0.642693i	$-0.222183\pi$
$457$	1.15093e11	+	1.15093e11i	0.123431	+	0.123431i	−0.642693	+	0.766124i	$0.722183\pi$
$458$	−5.13189e11			−0.544983
$459$	5.15665e11	−	5.67781e11i	0.542263	−	0.597068i
$460$	−4.20178e11			−0.437545
$461$	−1.01437e12	−	1.01437e12i	−1.04602	−	1.04602i	−0.998889	−	0.0471320i	$-0.984992\pi$
$461$	−1.01437e12	−	1.01437e12i	−1.04602	−	1.04602i	−0.0471320	−	0.998889i	$-0.515008\pi$
$462$	2.37380e12	−	9.83262e11i	2.42413	−	1.00411i
$463$			8.05823e11i			0.814939i	0.913219	+	0.407470i	$0.133589\pi$
$463$			8.05823e11i			0.814939i	−0.913219	+	0.407470i	$0.866411\pi$
$464$	3.57274e11	+	8.62535e11i	0.357824	+	0.863865i
$465$	7.01483e11	+	2.90564e11i	0.695791	+	0.288206i
$466$	7.43307e11	−	1.79450e12i	0.730183	−	1.76282i
$467$	−6.52494e11	+	6.52494e11i	−0.634820	+	0.634820i	−0.949273	−	0.314453i	$-0.898179\pi$
$467$	−6.52494e11	+	6.52494e11i	−0.634820	+	0.634820i	0.314453	+	0.949273i	$0.398179\pi$
$468$	−1.55676e11	+	1.55676e11i	−0.150008	+	0.150008i
$469$	−1.04726e12	+	2.52830e12i	−0.999482	+	2.41296i
$470$	2.07061e12	+	8.57675e11i	1.95730	+	0.810742i
$471$	−1.32289e11	−	3.19374e11i	−0.123860	−	0.299023i
$472$		−	2.18083e10i		−	0.0202247i
$473$	1.52118e12	−	6.30094e11i	1.39735	−	0.578803i
$474$	1.03358e12	+	1.03358e12i	0.940461	+	0.940461i
$475$	−1.55768e8			−0.000140397
$476$	1.29146e12	+	1.17292e12i	1.15305	+	1.04721i
$477$	8.89948e10			0.0787104
$478$	−1.05400e12	−	1.05400e12i	−0.923458	−	0.923458i
$479$	−3.79472e11	+	1.57182e11i	−0.329359	+	0.136425i	−0.541235	−	0.840872i	$-0.682043\pi$
$479$	−3.79472e11	+	1.57182e11i	−0.329359	+	0.136425i	0.211875	+	0.977297i	$0.432043\pi$
$480$		−	1.86386e12i		−	1.60261i
$481$	−1.81129e11	−	4.37285e11i	−0.154289	−	0.372487i
$482$	2.90274e11	+	1.20235e11i	0.244960	+	0.101466i
$483$	−3.60206e11	+	8.69613e11i	−0.301154	+	0.727050i
$484$	−7.32076e10	+	7.32076e10i	−0.0606390	+	0.0606390i
$485$	−1.00705e12	+	1.00705e12i	−0.826441	+	0.826441i
$486$	3.73891e11	−	9.02652e11i	0.304005	−	0.733934i
$487$	6.74522e11	+	2.79396e11i	0.543395	+	0.225082i	0.637459	−	0.770484i	$-0.279986\pi$
$487$	6.74522e11	+	2.79396e11i	0.543395	+	0.225082i	−0.0940634	+	0.995566i	$0.529986\pi$
$488$	8.02398e9	+	1.93716e10i	0.00640473	+	0.0154624i
$489$		−	2.56900e12i		−	2.03177i
$490$	−2.44007e12	+	1.01071e12i	−1.91214	+	0.792035i
$491$	−1.55074e12	−	1.55074e12i	−1.20413	−	1.20413i	−0.972900	−	0.231227i	$-0.925726\pi$
$491$	−1.55074e12	−	1.55074e12i	−1.20413	−	1.20413i	−0.231227	−	0.972900i	$-0.574274\pi$
$492$	−1.36000e9			−0.00104640
$493$	−5.84496e10	−	1.21510e12i	−0.0445626	−	0.926404i
$494$	−1.57919e12			−1.19306
$495$	2.85302e11	+	2.85302e11i	0.213590	+	0.213590i
$496$	8.32604e11	−	3.44876e11i	0.617690	−	0.255856i
$497$			2.71612e12i			1.99685i
$498$	−7.23951e11	−	1.74777e12i	−0.527445	−	1.27336i
$499$	−1.94673e12	−	8.06362e11i	−1.40557	−	0.582207i	−0.454381	−	0.890807i	$-0.650140\pi$
$499$	−1.94673e12	−	8.06362e11i	−1.40557	−	0.582207i	−0.951192	+	0.308600i	$0.900140\pi$
$500$	−5.30450e11	+	1.28062e12i	−0.379559	+	0.916337i
$501$	−1.25279e12	+	1.25279e12i	−0.888398	+	0.888398i
$502$	−1.29066e12	+	1.29066e12i	−0.907076	+	0.907076i
$503$	1.11753e11	−	2.69795e11i	0.0778400	−	0.187922i	−0.880169	−	0.474660i	$-0.842571\pi$
$503$	1.11753e11	−	2.69795e11i	0.0778400	−	0.187922i	0.958009	+	0.286738i	$0.0925709\pi$
$504$	−7.07080e9	−	2.92882e9i	−0.00488125	−	0.00202188i
$505$	2.99680e11	+	7.23492e11i	0.205044	+	0.495020i
$506$		−	9.57067e11i		−	0.649030i
$507$	7.10650e11	−	2.94361e11i	0.477661	−	0.197854i
$508$	−8.88712e11	−	8.88712e11i	−0.592072	−	0.592072i
$509$	3.27240e11			0.216091			0.108045	−	0.994146i	$-0.465541\pi$
$509$	3.27240e11			0.216091			0.108045	+	0.994146i	$0.465541\pi$
$510$	−8.27272e11	+	2.30464e12i	−0.541480	+	1.50848i
$511$	−8.55376e10			−0.0554962
$512$	−1.55143e12	−	1.55143e12i	−0.997739	−	0.997739i
$513$	1.33882e12	−	5.54556e11i	0.853479	−	0.353522i
$514$		−	2.74590e12i		−	1.73521i
$515$	−7.73963e10	−	1.86851e11i	−0.0484828	−	0.117048i
$516$	2.43163e12	+	1.00721e12i	1.50999	+	0.625458i
$517$	−9.72758e11	+	2.34845e12i	−0.598822	+	1.44568i
$518$	−1.40292e12	+	1.40292e12i	−0.856147	+	0.856147i
$519$	1.67711e12	−	1.67711e12i	1.01463	−	1.01463i
$520$	5.46616e9	−	1.31965e10i	0.00327844	−	0.00791486i
$521$	4.23798e11	+	1.75543e11i	0.251994	+	0.104379i	0.505105	−	0.863058i	$-0.331454\pi$
$521$	4.23798e11	+	1.75543e11i	0.251994	+	0.104379i	−0.253111	+	0.967437i	$0.581454\pi$
$522$	−2.46260e11	−	5.94524e11i	−0.145170	−	0.350471i
$523$		−	2.19925e11i		−	0.128534i	−0.997933	−	0.0642669i	$-0.979529\pi$
$523$		−	2.19925e11i		−	0.128534i	0.997933	−	0.0642669i	$-0.0204709\pi$
$524$	9.44879e11	−	3.91382e11i	0.547502	−	0.226783i
$525$	2.69111e8	+	2.69111e8i	0.000154602	+	0.000154602i
$526$	8.34954e11			0.475583
$527$	−1.17293e12	+	5.64214e10i	−0.662408	+	0.0318637i
$528$	2.13134e12			1.19344
$529$	−1.02569e12	−	1.02569e12i	−0.569463	−	0.569463i
$530$	6.43232e11	−	2.66436e11i	0.354100	−	0.146673i
$531$			9.25060e11i			0.504946i
$532$	1.26138e12	+	3.04523e12i	0.682719	+	1.64823i
$533$	−1.18035e9	−	4.88917e8i	−0.000633488	−	0.000262399i
$534$	−8.36563e11	+	2.01964e12i	−0.445208	+	1.07483i
$535$	1.88893e12	−	1.88893e12i	0.996838	−	0.996838i
$536$	−2.60834e10	+	2.60834e10i	−0.0136497	+	0.0136497i
$537$	8.88790e11	−	2.14573e12i	0.461227	−	1.11350i
$538$	−6.33608e11	−	2.62449e11i	−0.326062	−	0.135059i
$539$	−1.14633e12	−	2.76748e12i	−0.585004	−	1.41233i
$540$		−	1.58050e12i		−	0.799878i
$541$	1.46492e12	−	6.06791e11i	0.735237	−	0.304545i	0.0165348	−	0.999863i	$-0.494737\pi$
$541$	1.46492e12	−	6.06791e11i	0.735237	−	0.304545i	0.718702	+	0.695318i	$0.244737\pi$
$542$	3.64096e12	+	3.64096e12i	1.81226	+	1.81226i
$543$	4.62776e11			0.228440
$544$	1.22981e12	+	2.60711e12i	0.602065	+	1.27633i
$545$	3.38754e12			1.64475
$546$	2.72826e12	+	2.72826e12i	1.31377	+	1.31377i
$547$	−3.38579e12	+	1.40244e12i	−1.61702	+	0.669793i	−0.993690	−	0.112163i	$-0.964222\pi$
$547$	−3.38579e12	+	1.40244e12i	−1.61702	+	0.669793i	−0.623334	+	0.781956i	$0.714222\pi$
$548$			1.48043e12i			0.701255i
$549$	−3.40360e11	−	8.21702e11i	−0.159905	−	0.386046i
$550$	−3.57514e8	−	1.48087e8i	−0.000166595	−	6.90058e-5i
$551$	8.79557e11	−	2.12344e12i	0.406520	−	0.981426i
$552$	−8.97145e9	+	8.97145e9i	−0.00411279	+	0.00411279i
$553$	2.02661e12	−	2.02661e12i	0.921525	−	0.921525i
$554$	5.80305e11	−	1.40098e12i	0.261736	−	0.631885i
$555$	−1.28104e12	−	5.30626e11i	−0.573120	−	0.237394i
$556$	−1.46303e12	−	3.53207e12i	−0.649258	−	1.56745i
$557$			1.44850e12i			0.637632i	0.947817	+	0.318816i	$0.103285\pi$
$557$			1.44850e12i			0.637632i	−0.947817	+	0.318816i	$0.896715\pi$
$558$	−5.73893e11	+	2.37714e11i	−0.250598	+	0.103801i
$559$	1.74833e12	+	1.74833e12i	0.757303	+	0.757303i
$560$	−3.68466e12			−1.58326
$561$	−2.61388e12	−	9.38275e11i	−1.11417	−	0.399942i
$562$	−8.70470e10			−0.0368079
$563$	2.43763e12	+	2.43763e12i	1.02254	+	1.02254i	0.999740	+	0.0228010i	$0.00725841\pi$
$563$	2.43763e12	+	2.43763e12i	1.02254	+	1.02254i	0.0228010	+	0.999740i	$0.492742\pi$
$564$	−3.75402e12	+	1.55497e12i	−1.56222	+	0.647091i
$565$		−	1.60235e12i		−	0.661514i
$566$	5.19225e11	+	1.25352e12i	0.212658	+	0.513402i
$567$	−4.30597e12	−	1.78359e12i	−1.74963	−	0.724722i
$568$	−1.40106e10	+	3.38245e10i	−0.00564792	+	0.0136353i
$569$	2.07409e12	−	2.07409e12i	0.829513	−	0.829513i	−0.157936	−	0.987449i	$-0.550484\pi$
$569$	2.07409e12	−	2.07409e12i	0.829513	−	0.829513i	0.987449	+	0.157936i	$0.0504841\pi$
$570$	−3.27129e12	+	3.27129e12i	−1.29802	+	1.29802i
$571$	−1.85799e12	+	4.48559e12i	−0.731444	+	1.76586i	−0.0937195	+	0.995599i	$0.529876\pi$
$571$	−1.85799e12	+	4.48559e12i	−0.731444	+	1.76586i	−0.637725	+	0.770264i	$0.720124\pi$
$572$	−1.80477e12	−	7.47559e11i	−0.704919	−	0.291987i
$573$	1.01906e12	+	2.46022e12i	0.394915	+	0.953408i
$574$			5.35542e9i			0.00205916i
$575$	1.30971e8	−	5.42499e7i	4.99654e−5	−	2.06963e-5i
$576$	5.32436e11	+	5.32436e11i	0.201542	+	0.201542i
$577$	3.14368e12			1.18072			0.590360	−	0.807140i	$-0.298986\pi$
$577$	3.14368e12			1.18072			0.590360	+	0.807140i	$0.298986\pi$
$578$	−3.63490e11	−	3.76952e12i	−0.135462	−	1.40479i
$579$	1.60208e12			0.592420
$580$	−1.77255e12	−	1.77255e12i	−0.650390	−	0.650390i
$581$	−3.42698e12	+	1.41950e12i	−1.24773	+	0.516825i
$582$		−	5.18549e12i		−	1.87343i
$583$	3.02186e11	+	7.29541e11i	0.108334	+	0.261542i
$584$	−1.06522e9	−	4.41229e8i	−0.000378950	−	0.000156966i
$585$	−2.31863e11	+	5.59766e11i	−0.0818521	+	0.197608i
$586$	1.56628e11	−	1.56628e11i	0.0548693	−	0.0548693i
$587$	3.74660e11	−	3.74660e11i	0.130246	−	0.130246i	−0.638978	−	0.769225i	$-0.720643\pi$
$587$	3.74660e11	−	3.74660e11i	0.130246	−	0.130246i	0.769225	+	0.638978i	$0.220643\pi$
$588$	1.83242e12	−	4.42385e12i	0.632160	−	1.52617i
$589$	−2.04975e12	−	8.49036e11i	−0.701750	−	0.290675i
$590$	2.76948e12	+	6.68611e12i	0.940943	+	2.27164i
$591$			1.03366e12i			0.348525i
$592$	−1.52050e12	+	6.29810e11i	−0.508789	+	0.210747i
$593$	−1.30887e12	−	1.30887e12i	−0.434660	−	0.434660i	0.455550	−	0.890210i	$-0.349443\pi$
$593$	−1.30887e12	−	1.30887e12i	−0.434660	−	0.434660i	−0.890210	+	0.455550i	$0.849443\pi$
$594$	3.60002e12			1.18649
$595$	4.51888e12	+	1.62209e12i	1.47810	+	0.530577i
$596$	−4.10338e12			−1.33209
$597$	−5.25806e10	−	5.25806e10i	−0.0169411	−	0.0169411i
$598$	1.32779e12	−	5.49989e11i	0.424594	−	0.175873i
$599$			9.54735e11i			0.303014i	0.988456	+	0.151507i	$0.0484126\pi$
$599$			9.54735e11i			0.303014i	−0.988456	+	0.151507i	$0.951587\pi$
$600$	1.96315e6	+	4.73946e6i	6.18404e−7	+	1.49296e-6i
$601$	4.89651e12	+	2.02820e12i	1.53092	+	0.634126i	0.979742	−	0.200264i	$-0.0641800\pi$
$601$	4.89651e12	+	2.02820e12i	1.53092	+	0.634126i	0.551174	+	0.834390i	$0.314180\pi$
$602$	3.96621e12	−	9.57528e12i	1.23081	−	2.97144i
$603$	1.10640e12	−	1.10640e12i	0.340789	−	0.340789i
$604$	−1.14569e12	+	1.14569e12i	−0.350267	+	0.350267i
$605$	−1.09035e11	+	2.63234e11i	−0.0330877	+	0.0798808i
$606$	−2.63426e12	−	1.09115e12i	−0.793473	−	0.328667i
$607$	−1.05947e12	−	2.55778e12i	−0.316765	−	0.764739i	−0.999422	−	0.0339997i	$-0.989175\pi$
$607$	−1.05947e12	−	2.55778e12i	−0.316765	−	0.764739i	0.682657	−	0.730739i	$-0.260825\pi$
$608$			5.44624e12i			1.61633i
$609$	−5.18809e12	+	2.14898e12i	−1.52837	+	0.633073i
$610$	−4.92007e12	−	4.92007e12i	−1.43876	−	1.43876i
$611$	−3.81713e12			−1.10803
$612$	−4.25561e11	−	9.02156e11i	−0.122625	−	0.259956i
$613$	6.26290e11			0.179144			0.0895722	−	0.995980i	$-0.471450\pi$
$613$	6.26290e11			0.179144			0.0895722	+	0.995980i	$0.471450\pi$
$614$	−3.71252e11	−	3.71252e11i	−0.105417	−	0.105417i
$615$	−3.45788e9	+	1.43230e9i	−0.000974703	+	0.000403735i
$616$		−	6.79083e10i		−	0.0190025i
$617$	−1.44420e12	−	3.48661e12i	−0.401184	−	0.968545i	−0.987379	−	0.158375i	$-0.949375\pi$
$617$	−1.44420e12	−	3.48661e12i	−0.401184	−	0.968545i	0.586195	−	0.810170i	$-0.300625\pi$
$618$	6.80332e11	+	2.81803e11i	0.187617	+	0.0777137i
$619$	−5.69735e11	+	1.37546e12i	−0.155979	+	0.376566i	−0.982480	−	0.186369i	$-0.940328\pi$
$619$	−5.69735e11	+	1.37546e12i	−0.155979	+	0.376566i	0.826501	+	0.562935i	$0.190328\pi$
$620$	−1.71104e12	+	1.71104e12i	−0.465049	+	0.465049i
$621$	−9.32547e11	+	9.32547e11i	−0.251628	+	0.251628i
$622$	−1.49673e12	+	3.61343e12i	−0.400948	+	0.967973i
$623$	3.96005e12	+	1.64031e12i	1.05318	+	0.436244i
$624$	1.22480e12	+	2.95692e12i	0.323395	+	0.780744i
$625$			3.81423e12i			0.999877i
$626$	6.97733e12	−	2.89010e12i	1.81595	−	0.752192i
$627$	−3.71023e12	−	3.71023e12i	−0.958731	−	0.958731i
$628$	1.10169e12			0.282644
$629$	2.14200e12	−	1.03036e11i	0.545622	−	0.0262460i
$630$	2.53974e12			0.642328
$631$	−5.79226e10	−	5.79226e10i	−0.0145451	−	0.0145451i	0.699797	−	0.714342i	$-0.253274\pi$
$631$	−5.79226e10	−	5.79226e10i	−0.0145451	−	0.0145451i	−0.714342	+	0.699797i	$0.753274\pi$
$632$	3.56917e10	−	1.47840e10i	0.00889899	−	0.00368608i
$633$		−	1.69352e11i		−	0.0419249i
$634$	−5.29896e11	−	1.27928e12i	−0.130253	−	0.314459i
$635$	−3.19556e12	−	1.32364e12i	−0.779946	−	0.323064i
$636$	−4.83048e11	+	1.16618e12i	−0.117067	+	0.282624i
$637$	3.18072e12	−	3.18072e12i	0.765417	−	0.765417i
$638$	4.03746e12	−	4.03746e12i	0.964752	−	0.964752i
$639$	5.94298e11	−	1.43476e12i	0.141010	−	0.340429i
$640$	−9.10262e10	−	3.77043e10i	−0.0214465	−	0.00888343i
$641$	−3.33558e11	−	8.05280e11i	−0.0780387	−	0.188402i	0.880045	−	0.474890i	$-0.157512\pi$
$641$	−3.33558e11	−	8.05280e11i	−0.0780387	−	0.188402i	−0.958084	+	0.286488i	$0.907512\pi$
$642$			9.72650e12i			2.25969i
$643$	6.48078e11	−	2.68443e11i	0.149513	−	0.0619302i	−0.306672	−	0.951815i	$-0.599216\pi$
$643$	6.48078e11	−	2.68443e11i	0.149513	−	0.0619302i	0.456185	+	0.889885i	$0.349216\pi$
$644$	−2.12114e12	−	2.12114e12i	−0.485941	−	0.485941i
$645$	7.24332e12			1.64785
$646$	2.41731e12	−	6.73424e12i	0.546118	−	1.52140i
$647$	−6.30742e12			−1.41509			−0.707543	−	0.706671i	$-0.750196\pi$
$647$	−6.30742e12			−1.41509			−0.707543	+	0.706671i	$0.750196\pi$
$648$	−4.44230e10	−	4.44230e10i	−0.00989737	−	0.00989737i
$649$	−7.58325e12	+	3.14108e12i	−1.67785	+	0.694990i
$650$		−	5.81098e8i		−	0.000127685i
$651$	2.07440e12	+	5.00806e12i	0.452667	+	1.09284i
$652$	7.56404e12	+	3.13313e12i	1.63923	+	0.678991i
$653$	−7.96043e11	+	1.92182e12i	−0.171328	+	0.413622i	−0.986099	−	0.166161i	$-0.946863\pi$
$653$	−7.96043e11	+	1.92182e12i	−0.171328	+	0.413622i	0.814771	+	0.579783i	$0.196863\pi$
$654$	−8.72158e12	+	8.72158e12i	−1.86421	+	1.86421i
$655$	1.99022e12	−	1.99022e12i	0.422489	−	0.422489i
$656$	−1.70003e9	+	4.10423e9i	−0.000358417	+	0.000865295i
$657$	4.51843e10	+	1.87160e10i	0.00946114	+	0.00391893i
$658$	6.12315e12	+	1.47826e13i	1.27338	+	3.07421i
$659$			1.77225e12i			0.366051i	0.983108	+	0.183025i	$0.0585890\pi$
$659$			1.77225e12i			0.366051i	−0.983108	+	0.183025i	$0.941411\pi$
$660$	−5.28714e12	+	2.19001e12i	−1.08461	+	0.449260i
$661$	9.39346e11	+	9.39346e11i	0.191390	+	0.191390i	0.796296	−	0.604907i	$-0.206790\pi$
$661$	9.39346e11	+	9.39346e11i	0.191390	+	0.191390i	−0.604907	+	0.796296i	$0.706790\pi$
$662$	−5.42849e12			−1.09855
$663$	−2.00376e11	−	4.16557e12i	−0.0402748	−	0.837266i
$664$	−4.99992e10			−0.00998175
$665$	6.41424e12	+	6.41424e12i	1.27188	+	1.27188i
$666$	1.04804e12	−	4.34112e11i	0.206416	−	0.0855004i
$667$			2.09173e12i			0.409203i
$668$	−2.16076e12	−	5.21654e12i	−0.419868	−	1.01365i
$669$	−7.05919e12	−	2.92401e12i	−1.36250	−	0.564367i
$670$	4.68442e12	−	1.13092e13i	0.898089	−	2.16818i
$671$	5.58025e12	−	5.58025e12i	1.06268	−	1.06268i
$672$	9.40913e12	−	9.40913e12i	1.77987	−	1.77987i
$673$	2.71863e12	−	6.56336e12i	0.510838	−	1.23327i	−0.432559	−	0.901605i	$-0.642389\pi$
$673$	2.71863e12	−	6.56336e12i	0.510838	−	1.23327i	0.943397	−	0.331666i	$-0.107611\pi$
$674$	3.02812e11	+	1.25429e11i	0.0565201	+	0.0234114i
$675$	2.04061e8	+	4.92648e8i	3.78350e−5	+	9.13418e-5i
$676$			2.45140e12i			0.451497i
$677$	1.04359e11	−	4.32271e10i	0.0190934	−	0.00790874i	−0.373116	−	0.927785i	$-0.621711\pi$
$677$	1.04359e11	−	4.32271e10i	0.0190934	−	0.00790874i	0.392210	+	0.919876i	$0.371711\pi$
$678$	4.12541e12	+	4.12541e12i	0.749780	+	0.749780i
$679$	−1.01676e13			−1.83570
$680$	4.79074e10	+	4.35100e10i	0.00859237	+	0.00780367i
$681$	3.35391e12			0.597571
$682$	−3.89736e12	−	3.89736e12i	−0.689828	−	0.689828i
$683$	3.09603e12	−	1.28242e12i	0.544392	−	0.225495i	−0.0935014	−	0.995619i	$-0.529806\pi$
$683$	3.09603e12	−	1.28242e12i	0.544392	−	0.225495i	0.637894	+	0.770125i	$0.279806\pi$
$684$		−	1.88460e12i		−	0.329206i
$685$	1.55913e12	+	3.76408e12i	0.270567	+	0.653208i
$686$	−5.54225e12	−	2.29568e12i	−0.955493	−	0.395778i
$687$	9.79875e11	−	2.36563e12i	0.167828	−	0.405174i
$688$	6.07916e12	−	6.07916e12i	1.03442	−	1.03442i
$689$	−8.38477e11	+	8.38477e11i	−0.141744	+	0.141744i
$690$	1.61122e12	−	3.88982e12i	0.270603	−	0.653293i
$691$	−6.97270e12	−	2.88819e12i	−1.16346	−	0.481919i	−0.284432	−	0.958696i	$-0.591805\pi$
$691$	−6.97270e12	−	2.88819e12i	−1.16346	−	0.481919i	−0.879024	+	0.476777i	$0.841805\pi$
$692$	2.89262e12	+	6.98340e12i	0.479528	+	1.15768i
$693$			2.88052e12i			0.474430i
$694$	4.43787e12	−	1.83823e12i	0.726201	−	0.300802i
$695$	−7.43968e12	−	7.43968e12i	−1.20955	−	1.20955i
$696$	−7.56936e10			−0.0122269
$697$	3.89172e9	−	4.28504e9i	0.000624588	−	0.000687714i
$698$	−1.40013e13			−2.23264
$699$	6.85278e12	+	6.85278e12i	1.08572	+	1.08572i
$700$	−1.12056e9	+	4.64152e8i	−0.000176399	+	7.30667e-5i
$701$			1.61959e12i			0.253323i	0.991946	+	0.126662i	$0.0404262\pi$
$701$			1.61959e12i			0.253323i	−0.991946	+	0.126662i	$0.959574\pi$
$702$	2.06879e12	+	4.99450e12i	0.321513	+	0.776202i
$703$	3.74325e12	+	1.55050e12i	0.578029	+	0.239427i
$704$	−2.55677e12	+	6.17259e12i	−0.392297	+	0.947089i
$705$	−7.90718e12	+	7.90718e12i	−1.20551	+	1.20551i
$706$	−7.50735e11	+	7.50735e11i	−0.113727	+	0.113727i
$707$	−2.13949e12	+	5.16518e12i	−0.322050	+	0.777496i
$708$	−1.21219e13	−	5.02106e12i	−1.81310	−	0.751011i
$709$	−6.57643e11	−	1.58769e12i	−0.0977422	−	0.235971i	0.867444	−	0.497535i	$-0.165761\pi$
$709$	−6.57643e11	−	1.58769e12i	−0.0977422	−	0.235971i	−0.965186	+	0.261565i	$0.915761\pi$
$710$		−	1.21493e13i		−	1.79428i
$711$	−1.51396e12	+	6.27105e11i	−0.222179	+	0.0920295i
$712$	4.08543e10	+	4.08543e10i	0.00595768	+	0.00595768i
$713$	2.01914e12			0.292593
$714$	−1.58106e13	+	7.45808e12i	−2.27670	+	1.07395i
$715$	−5.37602e12			−0.769279
$716$	5.23382e12	+	5.23382e12i	0.744236	+	0.744236i
$717$	6.87110e12	−	2.84610e12i	0.970935	−	0.402175i
$718$		−	6.53982e12i		−	0.918345i
$719$	5.14369e12	+	1.24180e13i	0.717786	+	1.73289i	0.679561	+	0.733619i	$0.262170\pi$
$719$	5.14369e12	+	1.24180e13i	0.717786	+	1.73289i	0.0382249	+	0.999269i	$0.487830\pi$
$720$	1.94638e12	+	8.06217e11i	0.269918	+	0.111804i
$721$	5.52551e11	−	1.33398e12i	0.0761489	−	0.183840i
$722$	2.27223e12	−	2.27223e12i	0.311197	−	0.311197i
$723$	−1.10849e12	+	1.10849e12i	−0.150872	+	0.150872i
$724$	−5.64397e11	+	1.36258e12i	−0.0763416	+	0.184305i
$725$	7.81368e8	+	3.23653e8i	0.000105035	+	4.35070e-5i
$726$	−3.97001e11	−	9.58444e11i	−0.0530367	−	0.128042i
$727$		−	1.27527e13i		−	1.69316i	−0.532263	−	0.846579i	$-0.678658\pi$
$727$		−	1.27527e13i		−	1.69316i	0.532263	−	0.846579i	$-0.321342\pi$
$728$	9.42129e10	−	3.90243e10i	0.0124314	−	0.00514924i
$729$	−3.05490e12	−	3.05490e12i	−0.400611	−	0.400611i
$730$	3.82614e11			0.0498663
$731$	−1.01317e13	+	4.77929e12i	−1.31237	+	0.619063i
$732$	1.26149e13			1.62400
$733$	8.09689e12	+	8.09689e12i	1.03598	+	1.03598i	0.999328	+	0.0366492i	$0.0116684\pi$
$733$	8.09689e12	+	8.09689e12i	1.03598	+	1.03598i	0.0366492	+	0.999328i	$0.488332\pi$
$734$	−9.43796e12	+	3.90933e12i	−1.20018	+	0.497130i
$735$		−	1.31777e13i		−	1.66551i
$736$	−1.89678e12	−	4.57923e12i	−0.238269	−	0.575231i
$737$	1.28267e13	+	5.31298e12i	1.60144	+	0.663337i
$738$	1.17179e9	−	2.82894e9i	0.000145410	−	0.000351051i
$739$	−9.02381e12	+	9.02381e12i	−1.11299	+	1.11299i	−0.120242	+	0.992745i	$0.538367\pi$
$739$	−9.02381e12	+	9.02381e12i	−1.11299	+	1.11299i	−0.992745	+	0.120242i	$0.961633\pi$
$740$	3.12470e12	−	3.12470e12i	0.383059	−	0.383059i
$741$	3.01528e12	−	7.27952e12i	0.367405	−	0.886994i
$742$	4.59219e12	+	1.90215e12i	0.556163	+	0.230370i
$743$	−1.73861e12	−	4.19739e12i	−0.209292	−	0.505277i	0.784020	−	0.620736i	$-0.213166\pi$
$743$	−1.73861e12	−	4.19739e12i	−0.209292	−	0.505277i	−0.993312	+	0.115459i	$0.963166\pi$
$744$			7.30669e10i			0.00874264i
$745$	−1.04331e13	+	4.32152e12i	−1.24082	+	0.513965i
$746$	−3.91766e12	−	3.91766e12i	−0.463129	−	0.463129i
$747$	2.12086e12			0.249212
$748$	5.95048e12	−	6.55188e12i	0.695016	−	0.765259i
$749$	1.90714e13			2.21419
$750$	−9.82133e12	−	9.82133e12i	−1.13343	−	1.13343i
$751$	−8.21191e12	+	3.40149e12i	−0.942030	+	0.390202i	−0.800230	−	0.599694i	$-0.795289\pi$
$751$	−8.21191e12	+	3.40149e12i	−0.942030	+	0.390202i	−0.141800	+	0.989895i	$0.545289\pi$
$752$			1.32727e13i			1.51348i
$753$	−3.48513e12	−	8.41384e12i	−0.395040	−	0.953711i
$754$	7.92156e12	+	3.28122e12i	0.892565	+	0.369712i
$755$	−1.70638e12	+	4.11957e12i	−0.191124	+	0.461413i
$756$	7.97871e12	−	7.97871e12i	0.888351	−	0.888351i
$757$	4.45431e12	−	4.45431e12i	0.493003	−	0.493003i	−0.416248	−	0.909251i	$-0.636655\pi$
$757$	4.45431e12	−	4.45431e12i	0.493003	−	0.493003i	0.909251	+	0.416248i	$0.136655\pi$
$758$	−1.63858e12	+	3.95587e12i	−0.180283	+	0.435242i
$759$	4.41175e12	+	1.82741e12i	0.482529	+	0.199870i
$760$	4.67915e10	+

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.5808 - 22.5808i) q^{2} +(147.205 - 60.9745i) q^{3} +507.789i q^{4} +(534.784 + 1291.08i) q^{5} +(-4700.88 - 1947.17i) q^{6} +(-3817.95 + 9217.34i) q^{7} +(-95.0916 + 95.0916i) q^{8} +(4033.58 - 4033.58i) q^{9} +O(q^{10})\)	\(q+(-22.5808 - 22.5808i) q^{2} +(147.205 - 60.9745i) q^{3} +507.789i q^{4} +(534.784 + 1291.08i) q^{5} +(-4700.88 - 1947.17i) q^{6} +(-3817.95 + 9217.34i) q^{7} +(-95.0916 + 95.0916i) q^{8} +(4033.58 - 4033.58i) q^{9} +(17077.8 - 41229.6i) q^{10} +(46761.8 + 19369.4i) q^{11} +(30962.2 + 74749.3i) q^{12} +76005.9i q^{13} +(294348. - 121923. i) q^{14} +(157446. + 157446. i) q^{15} +264282. q^{16} +(-324117. - 116345. i) q^{17} -182163. q^{18} +(-460062. - 460062. i) q^{19} +(-655597. + 271557. i) q^{20} +1.58964e6i q^{21} +(-618544. - 1.49330e6i) q^{22} +(547050. + 226596. i) q^{23} +(-8199.84 + 19796.2i) q^{24} +(169.290 - 169.290i) q^{25} +(1.71628e6 - 1.71628e6i) q^{26} +(-852342. + 2.05773e6i) q^{27} +(-4.68046e6 - 1.93871e6i) q^{28} +(1.35186e6 + 3.26369e6i) q^{29} -7.11053e6i q^{30} +(3.15043e6 - 1.30495e6i) q^{31} +(-5.91903e6 - 5.91903e6i) q^{32} +8.06462e6 q^{33} +(4.69168e6 + 9.94599e6i) q^{34} -1.39421e7 q^{35} +(2.04821e6 + 2.04821e6i) q^{36} +(-5.75330e6 + 2.38309e6i) q^{37} +2.07772e7i q^{38} +(4.63442e6 + 1.11885e7i) q^{39} +(-173625. - 71917.6i) q^{40} +(-6432.62 + 15529.7i) q^{41} +(3.58954e7 - 3.58954e7i) q^{42} +(2.30025e7 - 2.30025e7i) q^{43} +(-9.83554e6 + 2.37451e7i) q^{44} +(7.36477e6 + 3.05059e6i) q^{45} +(-7.23613e6 - 1.74696e7i) q^{46} +5.02215e7i q^{47} +(3.89038e7 - 1.61145e7i) q^{48} +(-4.18484e7 - 4.18484e7i) q^{49} -7645.44 q^{50} +(-5.48058e7 + 2.63632e6i) q^{51} -3.85949e7 q^{52} +(1.10317e7 + 1.10317e7i) q^{53} +(6.57120e7 - 2.72188e7i) q^{54} +7.07317e7i q^{55} +(-513437. - 1.23955e6i) q^{56} +(-9.57757e7 - 3.96716e7i) q^{57} +(4.31706e7 - 1.04223e8i) q^{58} +(-1.14670e8 + 1.14670e8i) q^{59} +(-7.99494e7 + 7.99494e7i) q^{60} +(5.96668e7 - 1.44048e8i) q^{61} +(-1.00606e8 - 4.16725e7i) q^{62} +(2.17789e7 + 5.25789e7i) q^{63} +1.32001e8i q^{64} +(-9.81298e7 + 4.06467e7i) q^{65} +(-1.82106e8 - 1.82106e8i) q^{66} +2.74298e8 q^{67} +(5.90785e7 - 1.64583e8i) q^{68} +9.43453e7 q^{69} +(3.14825e8 + 3.14825e8i) q^{70} +(2.51521e8 - 1.04183e8i) q^{71} +767119. i q^{72} +(3.28100e6 + 7.92104e6i) q^{73} +(1.83727e8 + 7.61020e7i) q^{74} +(14598.1 - 35242.9i) q^{75} +(2.33614e8 - 2.33614e8i) q^{76} +(-3.57068e8 + 3.57068e8i) q^{77} +(1.47996e8 - 3.57295e8i) q^{78} +(-2.65406e8 - 1.09935e8i) q^{79} +(1.41334e8 + 3.41210e8i) q^{80} +4.67160e8i q^{81} +(495928. - 205420. i) q^{82} +(2.62900e8 + 2.62900e8i) q^{83} -8.07202e8 q^{84} +(-2.31221e7 - 4.80681e8i) q^{85} -1.03883e9 q^{86} +(3.98003e8 + 3.98003e8i) q^{87} +(-6.28852e6 + 2.60479e6i) q^{88} -4.29631e8i q^{89} +(-9.74179e7 - 2.35188e8i) q^{90} +(-7.00572e8 - 2.90187e8i) q^{91} +(-1.15063e8 + 2.77786e8i) q^{92} +(3.84192e8 - 3.84192e8i) q^{93} +(1.13404e9 - 1.13404e9i) q^{94} +(3.47944e8 - 8.40011e8i) q^{95} +(-1.23222e9 - 5.10404e8i) q^{96} +(3.90001e8 + 9.41546e8i) q^{97} +1.88994e9i q^{98} +(2.66745e8 - 1.10489e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) \) 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9	\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) 52 * q - 4 * q^2 - 4 * q^3 - 1140 * q^5 + 12308 * q^6 - 4 * q^7 + 2044 * q^8 - 83224 * q^9 - 117636 * q^10 - 115768 * q^11 - 145528 * q^12 + 463660 * q^14 + 288244 * q^15 - 3407880 * q^16 - 271932 * q^17 + 2193336 * q^18 - 406700 * q^19 + 493564 * q^20 + 800964 * q^22 - 4172180 * q^23 + 15078440 * q^24 + 11946576 * q^25 - 14209012 * q^26 - 7973656 * q^27 + 13540804 * q^28 + 7833752 * q^29 + 5936252 * q^31 - 26730116 * q^32 - 1635208 * q^33 - 53493988 * q^34 + 46992776 * q^35 - 12761764 * q^36 + 74606796 * q^37 + 74096776 * q^39 - 69317672 * q^40 - 71362288 * q^41 - 308117664 * q^42 - 3765712 * q^43 + 163659820 * q^44 + 14167408 * q^45 + 72135428 * q^46 + 164621412 * q^48 - 284548508 * q^49 + 226223888 * q^50 - 406733132 * q^51 + 103553016 * q^52 - 244724728 * q^53 + 971226260 * q^54 + 470691652 * q^56 - 440646580 * q^57 - 308561768 * q^58 - 481734984 * q^59 + 379626176 * q^60 + 507966228 * q^61 + 358867236 * q^62 + 1070586456 * q^63 + 366263684 * q^65 - 2244715148 * q^66 - 311910088 * q^67 - 1839196668 * q^68 + 533688136 * q^69 + 34867672 * q^70 + 186006812 * q^71 + 487115192 * q^73 - 214149412 * q^74 + 533015920 * q^75 + 1104236912 * q^76 - 237869092 * q^77 - 2081523384 * q^78 - 136338052 * q^79 - 922534152 * q^80 + 1951892384 * q^82 + 1843663888 * q^83 - 2630025952 * q^84 - 395061976 * q^85 + 1538547296 * q^86 - 369395636 * q^87 - 3388839640 * q^88 + 874363684 * q^90 + 2087197720 * q^91 + 1061427500 * q^92 + 576415420 * q^93 + 6899365112 * q^94 + 5031766876 * q^95 + 490811364 * q^96 - 3419996368 * q^97 - 5630536112 * q^99

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