LMFDB - Embedded newform 17.10.d.a.2.5

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			2.5
Character	$\chi$	$=$	17.2
Dual form			17.10.d.a.9.5

$q$-expansion

$f(q)$	$=$	$q+(-10.5264 - 10.5264i) q^{2} +(-129.909 + 53.8103i) q^{3} -290.392i q^{4} +(-588.452 - 1420.65i) q^{5} +(1933.90 + 801.047i) q^{6} +(-818.389 + 1975.77i) q^{7} +(-8446.26 + 8446.26i) q^{8} +(62.9403 - 62.9403i) q^{9} +O(q^{10})$	\(q+(-10.5264 - 10.5264i) q^{2} +(-129.909 + 53.8103i) q^{3} -290.392i q^{4} +(-588.452 - 1420.65i) q^{5} +(1933.90 + 801.047i) q^{6} +(-818.389 + 1975.77i) q^{7} +(-8446.26 + 8446.26i) q^{8} +(62.9403 - 62.9403i) q^{9} +(-8760.00 + 21148.5i) q^{10} +(77662.6 + 32168.9i) q^{11} +(15626.1 + 37724.6i) q^{12} -12765.7i q^{13} +(29412.3 - 12183.0i) q^{14} +(152891. + 152891. i) q^{15} +29136.1 q^{16} +(-319104. + 129462. i) q^{17} -1325.06 q^{18} +(552253. + 552253. i) q^{19} +(-412545. + 170882. i) q^{20} -300708. i q^{21} +(-478883. - 1.15613e6i) q^{22} +(-1.22417e6 - 507067. i) q^{23} +(642754. - 1.55174e6i) q^{24} +(-290899. + 290899. i) q^{25} +(-134376. + 134376. i) q^{26} +(1.05436e6 - 2.54544e6i) q^{27} +(573746. + 237653. i) q^{28} +(836814. + 2.02025e6i) q^{29} -3.21877e6i q^{30} +(-2.69168e6 + 1.11493e6i) q^{31} +(4.01779e6 + 4.01779e6i) q^{32} -1.18201e7 q^{33} +(4.72177e6 + 1.99624e6i) q^{34} +3.28845e6 q^{35} +(-18277.3 - 18277.3i) q^{36} +(888857. - 368177. i) q^{37} -1.16264e7i q^{38} +(686926. + 1.65839e6i) q^{39} +(1.69694e7 + 7.02895e6i) q^{40} +(-1.11895e7 + 2.70139e7i) q^{41} +(-3.16536e6 + 3.16536e6i) q^{42} +(-6.88677e6 + 6.88677e6i) q^{43} +(9.34158e6 - 2.25526e7i) q^{44} +(-126453. - 52378.7i) q^{45} +(7.54846e6 + 1.82236e7i) q^{46} +1.22741e7i q^{47} +(-3.78506e6 + 1.56782e6i) q^{48} +(2.53004e7 + 2.53004e7i) q^{49} +6.12420e6 q^{50} +(3.44882e7 - 3.39894e7i) q^{51} -3.70706e6 q^{52} +(-3.83659e7 - 3.83659e7i) q^{53} +(-3.78928e7 + 1.56957e7i) q^{54} -1.29261e8i q^{55} +(-9.77551e6 - 2.36002e7i) q^{56} +(-1.01460e8 - 4.20260e7i) q^{57} +(1.24572e7 - 3.00744e7i) q^{58} +(-7.83688e7 + 7.83688e7i) q^{59} +(4.43983e7 - 4.43983e7i) q^{60} +(-3.25243e7 + 7.85206e7i) q^{61} +(4.00697e7 + 1.65974e7i) q^{62} +(72845.6 + 175865. i) q^{63} -9.95030e7i q^{64} +(-1.81356e7 + 7.51200e6i) q^{65} +(1.24423e8 + 1.24423e8i) q^{66} +1.27439e8 q^{67} +(3.75947e7 + 9.26652e7i) q^{68} +1.86317e8 q^{69} +(-3.46154e7 - 3.46154e7i) q^{70} +(-3.23928e8 + 1.34175e8i) q^{71} +1.06322e6i q^{72} +(9.63630e7 + 2.32641e8i) q^{73} +(-1.32320e7 - 5.48087e6i) q^{74} +(2.21371e7 - 5.34438e7i) q^{75} +(1.60370e8 - 1.60370e8i) q^{76} +(-1.27116e8 + 1.27116e8i) q^{77} +(1.02259e7 - 2.46876e7i) q^{78} +(1.51347e8 + 6.26901e7i) q^{79} +(-1.71452e7 - 4.13922e7i) q^{80} +3.89165e8i q^{81} +(4.02142e8 - 1.66573e8i) q^{82} +(-5.56409e8 - 5.56409e8i) q^{83} -8.73232e7 q^{84} +(3.71698e8 + 3.77153e8i) q^{85} +1.44985e8 q^{86} +(-2.17420e8 - 2.17420e8i) q^{87} +(-9.27665e8 + 3.84252e8i) q^{88} -2.83737e8i q^{89} +(779736. + 1.88245e6i) q^{90} +(2.52221e7 + 1.04473e7i) q^{91} +(-1.47248e8 + 3.55488e8i) q^{92} +(2.89680e8 - 2.89680e8i) q^{93} +(1.29202e8 - 1.29202e8i) q^{94} +(4.59583e8 - 1.10953e9i) q^{95} +(-7.38147e8 - 3.05750e8i) q^{96} +(-1.00334e8 - 2.42227e8i) q^{97} -5.32642e8i q^{98} +(6.91282e6 - 2.86339e6i) 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 $

$2$	−10.5264	−	10.5264i	−0.465204	−	0.465204i	0.435153	−	0.900357i	$-0.356694\pi$
$2$	−10.5264	−	10.5264i	−0.465204	−	0.465204i	−0.900357	+	0.435153i	$0.856694\pi$
$3$	−129.909	+	53.8103i	−0.925966	+	0.383548i	−0.794147	−	0.607726i	$-0.792082\pi$
$3$	−129.909	+	53.8103i	−0.925966	+	0.383548i	−0.131819	+	0.991274i	$0.542082\pi$
$4$		−	290.392i		−	0.567171i
$5$	−588.452	−	1420.65i	−0.421062	−	1.01653i	−0.982035	−	0.188699i	$-0.939573\pi$
$5$	−588.452	−	1420.65i	−0.421062	−	1.01653i	0.560973	−	0.827834i	$-0.310427\pi$
$6$	1933.90	+	801.047i	0.609191	+	0.252335i
$7$	−818.389	+	1975.77i	−0.128831	+	0.311024i	−0.975112	−	0.221711i	$-0.928836\pi$
$7$	−818.389	+	1975.77i	−0.128831	+	0.311024i	0.846282	+	0.532735i	$0.178836\pi$
$8$	−8446.26	+	8446.26i	−0.729054	+	0.729054i
$9$	62.9403	−	62.9403i	0.00319770	−	0.00319770i
$10$	−8760.00	+	21148.5i	−0.277015	+	0.668774i
$11$	77662.6	+	32168.9i	1.59935	+	0.662474i	0.991324	−	0.131439i	$-0.0419598\pi$
$11$	77662.6	+	32168.9i	1.59935	+	0.662474i	0.608031	+	0.793914i	$0.291960\pi$
$12$	15626.1	+	37724.6i	0.217537	+	0.525181i
$13$		−	12765.7i		−	0.123965i	−0.998077	−	0.0619826i	$-0.980258\pi$
$13$		−	12765.7i		−	0.123965i	0.998077	−	0.0619826i	$-0.0197423\pi$
$14$	29412.3	−	12183.0i	0.204622	−	0.0847572i
$15$	152891.	+	152891.i	0.779778	+	0.779778i
$16$	29136.1			0.111146
$17$	−319104.	+	129462.i	−0.926643	+	0.375944i
$17$	−319104.	+	129462.i	−0.926643	+	0.375944i
$18$	−1325.06			−0.00297516
$19$	552253.	+	552253.i	0.972181	+	0.972181i	0.999623	−	0.0274427i	$-0.00873638\pi$
$19$	552253.	+	552253.i	0.972181	+	0.972181i	−0.0274427	+	0.999623i	$0.508736\pi$
$20$	−412545.	+	170882.i	−0.576548	+	0.238814i
$21$		−	300708.i		−	0.337411i
$22$	−478883.	−	1.15613e6i	−0.435840	−	1.05221i
$23$	−1.22417e6	−	507067.i	−0.912149	−	0.377825i	−0.123270	−	0.992373i	$-0.539338\pi$
$23$	−1.22417e6	−	507067.i	−0.912149	−	0.377825i	−0.788879	+	0.614548i	$0.789338\pi$
$24$	642754.	−	1.55174e6i	0.395452	−	0.954706i
$25$	−290899.	+	290899.i	−0.148940	+	0.148940i
$26$	−134376.	+	134376.i	−0.0576691	+	0.0576691i
$27$	1.05436e6	−	2.54544e6i	0.381813	−	0.921779i
$28$	573746.	+	237653.i	0.176404	+	0.0730690i
$29$	836814.	+	2.02025e6i	0.219704	+	0.530412i	0.994849	−	0.101372i	$-0.0323231\pi$
$29$	836814.	+	2.02025e6i	0.219704	+	0.530412i	−0.775145	+	0.631784i	$0.782323\pi$
$30$		−	3.21877e6i		−	0.725511i
$31$	−2.69168e6	+	1.11493e6i	−0.523474	+	0.216830i	−0.628742	−	0.777614i	$-0.716430\pi$
$31$	−2.69168e6	+	1.11493e6i	−0.523474	+	0.216830i	0.105268	+	0.994444i	$0.466430\pi$
$32$	4.01779e6	+	4.01779e6i	0.677348	+	0.677348i
$33$	−1.18201e7			−1.73504
$34$	4.72177e6	+	1.99624e6i	0.605968	+	0.256187i
$35$	3.28845e6			0.370412
$36$	−18277.3	−	18277.3i	−0.00181364	−	0.00181364i
$37$	888857.	−	368177.i	0.0779694	−	0.0322960i	−0.343358	−	0.939205i	$-0.611564\pi$
$37$	888857.	−	368177.i	0.0779694	−	0.0322960i	0.421327	+	0.906909i	$0.361564\pi$
$38$		−	1.16264e7i		−	0.904524i
$39$	686926.	+	1.65839e6i	0.0475466	+	0.114788i
$40$	1.69694e7	+	7.02895e6i	1.04808	+	0.434131i
$41$	−1.11895e7	+	2.70139e7i	−0.618420	+	1.49300i	0.235117	+	0.971967i	$0.424453\pi$
$41$	−1.11895e7	+	2.70139e7i	−0.618420	+	1.49300i	−0.853538	+	0.521031i	$0.825547\pi$
$42$	−3.16536e6	+	3.16536e6i	−0.156965	+	0.156965i
$43$	−6.88677e6	+	6.88677e6i	−0.307190	+	0.307190i	−0.843819	−	0.536628i	$-0.819698\pi$
$43$	−6.88677e6	+	6.88677e6i	−0.307190	+	0.307190i	0.536628	+	0.843819i	$0.319698\pi$
$44$	9.34158e6	−	2.25526e7i	0.375736	−	0.907108i
$45$	−126453.	−	52378.7i	−0.00459699	−	0.00190414i
$46$	7.54846e6	+	1.82236e7i	0.248570	+	0.600101i
$47$			1.22741e7i			0.366902i	0.983029	+	0.183451i	$0.0587268\pi$
$47$			1.22741e7i			0.366902i	−0.983029	+	0.183451i	$0.941273\pi$
$48$	−3.78506e6	+	1.56782e6i	−0.102917	+	0.0426296i
$49$	2.53004e7	+	2.53004e7i	0.626968	+	0.626968i
$50$	6.12420e6			0.138575
$51$	3.44882e7	−	3.39894e7i	0.713847	−	0.703523i
$52$	−3.70706e6			−0.0703095
$53$	−3.83659e7	−	3.83659e7i	−0.667888	−	0.667888i	0.289339	−	0.957227i	$-0.406565\pi$
$53$	−3.83659e7	−	3.83659e7i	−0.667888	−	0.667888i	−0.957227	+	0.289339i	$0.906565\pi$
$54$	−3.78928e7	+	1.56957e7i	−0.606436	+	0.251194i
$55$		−	1.29261e8i		−	1.90474i
$56$	−9.77551e6	−	2.36002e7i	−0.132829	−	0.320678i
$57$	−1.01460e8	−	4.20260e7i	−1.27308	−	0.527329i
$58$	1.24572e7	−	3.00744e7i	0.144543	−	0.348957i
$59$	−7.83688e7	+	7.83688e7i	−0.841995	+	0.841995i	−0.989118	−	0.147124i	$-0.952999\pi$
$59$	−7.83688e7	+	7.83688e7i	−0.841995	+	0.841995i	0.147124	+	0.989118i	$0.452999\pi$
$60$	4.43983e7	−	4.43983e7i	0.442268	−	0.442268i
$61$	−3.25243e7	+	7.85206e7i	−0.300762	+	0.726105i	0.699175	+	0.714950i	$0.253551\pi$
$61$	−3.25243e7	+	7.85206e7i	−0.300762	+	0.726105i	−0.999938	+	0.0111544i	$0.996449\pi$
$62$	4.00697e7	+	1.65974e7i	0.344392	+	0.142652i
$63$	72845.6	+	175865.i	0.000582601	+	0.00140652i
$64$		−	9.95030e7i		−	0.741355i
$65$	−1.81356e7	+	7.51200e6i	−0.126015	+	0.0521970i
$66$	1.24423e8	+	1.24423e8i	0.807146	+	0.807146i
$67$	1.27439e8			0.772619			0.386310	−	0.922369i	$-0.373750\pi$
$67$	1.27439e8			0.772619			0.386310	+	0.922369i	$0.373750\pi$
$68$	3.75947e7	+	9.26652e7i	0.213224	+	0.525565i
$69$	1.86317e8			0.989533
$70$	−3.46154e7	−	3.46154e7i	−0.172317	−	0.172317i
$71$	−3.23928e8	+	1.34175e8i	−1.51282	+	0.626629i	−0.976136	−	0.217158i	$-0.930321\pi$
$71$	−3.23928e8	+	1.34175e8i	−1.51282	+	0.626629i	−0.536679	+	0.843787i	$0.680321\pi$
$72$			1.06322e6i			0.00466259i
$73$	9.63630e7	+	2.32641e8i	0.397153	+	0.958811i	0.988338	+	0.152275i	$0.0486601\pi$
$73$	9.63630e7	+	2.32641e8i	0.397153	+	0.958811i	−0.591186	+	0.806536i	$0.701340\pi$
$74$	−1.32320e7	−	5.48087e6i	−0.0512959	−	0.0212474i
$75$	2.21371e7	−	5.34438e7i	0.0807878	−	0.195039i
$76$	1.60370e8	−	1.60370e8i	0.551393	−	0.551393i
$77$	−1.27116e8	+	1.27116e8i	−0.412091	+	0.412091i
$78$	1.02259e7	−	2.46876e7i	0.0312808	−	0.0755184i
$79$	1.51347e8	+	6.26901e7i	0.437173	+	0.181083i	0.590405	−	0.807107i	$-0.298968\pi$
$79$	1.51347e8	+	6.26901e7i	0.437173	+	0.181083i	−0.153232	+	0.988190i	$0.548968\pi$
$80$	−1.71452e7	−	4.13922e7i	−0.0467991	−	0.112983i
$81$			3.89165e8i			1.00450i
$82$	4.02142e8	−	1.66573e8i	0.982239	−	0.406857i
$83$	−5.56409e8	−	5.56409e8i	−1.28689	−	1.28689i	−0.936664	−	0.350230i	$-0.886103\pi$
$83$	−5.56409e8	−	5.56409e8i	−1.28689	−	1.28689i	−0.350230	−	0.936664i	$-0.613897\pi$
$84$	−8.73232e7			−0.191370
$85$	3.71698e8	+	3.77153e8i	0.772333	+	0.783668i
$86$	1.44985e8			0.285812
$87$	−2.17420e8	−	2.17420e8i	−0.406877	−	0.406877i
$88$	−9.27665e8	+	3.84252e8i	−1.64900	+	0.683036i
$89$		−	2.83737e8i		−	0.479360i	−0.970852	−	0.239680i	$-0.922958\pi$
$89$		−	2.83737e8i		−	0.479360i	0.970852	−	0.239680i	$-0.0770425\pi$
$90$	779736.	+	1.88245e6i	0.00125273	+	0.00302435i
$91$	2.52221e7	+	1.04473e7i	0.0385562	+	0.0159705i
$92$	−1.47248e8	+	3.55488e8i	−0.214291	+	0.517345i
$93$	2.89680e8	−	2.89680e8i	0.401555	−	0.401555i
$94$	1.29202e8	−	1.29202e8i	0.170684	−	0.170684i
$95$	4.59583e8	−	1.10953e9i	0.578906	−	1.39760i
$96$	−7.38147e8	−	3.05750e8i	−0.886997	−	0.367406i
$97$	−1.00334e8	−	2.42227e8i	−0.115073	−	0.277811i	0.855841	−	0.517239i	$-0.173040\pi$
$97$	−1.00334e8	−	2.42227e8i	−0.115073	−	0.277811i	−0.970914	+	0.239428i	$0.923040\pi$
$98$		−	5.32642e8i		−	0.583335i
$99$	6.91282e6	−	2.86339e6i	0.00723264	−	0.00299586i
$100$	8.44745e7	+	8.44745e7i	0.0844745	+	0.0844745i
$101$	1.01701e9			0.972477			0.486238	−	0.873826i	$-0.338369\pi$
$101$	1.01701e9			0.972477			0.486238	+	0.873826i	$0.338369\pi$
$102$	−7.20820e8	−	5.25072e6i	−0.659366	−	0.00480306i
$103$	1.11236e9			0.973814			0.486907	−	0.873454i	$-0.338125\pi$
$103$	1.11236e9			0.973814			0.486907	+	0.873454i	$0.338125\pi$
$104$	1.07822e8	+	1.07822e8i	0.0903773	+	0.0903773i
$105$	−4.27201e8	+	1.76952e8i	−0.342989	+	0.142071i
$106$			8.07706e8i			0.621408i
$107$	4.49497e8	+	1.08518e9i	0.331512	+	0.800342i	0.998473	+	0.0552485i	$0.0175951\pi$
$107$	4.49497e8	+	1.08518e9i	0.331512	+	0.800342i	−0.666960	+	0.745093i	$0.732405\pi$
$108$	−7.39176e8	−	3.06177e8i	−0.522806	−	0.216554i
$109$	4.34048e8	−	1.04789e9i	0.294523	−	0.711041i	−0.705475	−	0.708735i	$-0.749266\pi$
$109$	4.34048e8	−	1.04789e9i	0.294523	−	0.711041i	0.999997	−	0.00230568i	$-0.000733922\pi$
$110$	−1.36065e9	+	1.36065e9i	−0.886092	+	0.886092i
$111$	−9.56593e7	+	9.56593e7i	−0.0598100	+	0.0598100i
$112$	−2.38447e7	+	5.75662e7i	−0.0143189	+	0.0345690i
$113$	−1.27036e9	−	5.26199e8i	−0.732948	−	0.303597i	−0.0151850	−	0.999885i	$-0.504834\pi$
$113$	−1.27036e9	−	5.26199e8i	−0.732948	−	0.303597i	−0.717763	+	0.696288i	$0.754834\pi$
$114$	6.25621e8	+	1.51038e9i	0.346928	+	0.837558i
$115$			2.03750e9i			1.08632i
$116$	5.86663e8	−	2.43004e8i	0.300835	−	0.124610i
$117$	−803477.	−	803477.i	−0.000396403	−	0.000396403i
$118$	1.64988e9			0.783398
$119$	5.36440e6	−	7.36426e8i	0.00245222	−	0.336641i
$120$	−2.58271e9			−1.13700
$121$	3.32932e9	+	3.32932e9i	1.41196	+	1.41196i
$122$	1.16890e9	−	4.84173e8i	0.477702	−	0.197871i
$123$		−	4.11147e9i		−	1.61966i
$124$	3.23766e8	+	7.81641e8i	0.122980	+	0.296900i
$125$	−2.19026e9	−	9.07235e8i	−0.802418	−	0.332372i
$126$	1.08442e6	−	2.61802e6i	0.000383291	−	0.000925347i
$127$	1.15794e9	−	1.15794e9i	0.394974	−	0.394974i	−0.481482	−	0.876456i	$-0.659901\pi$
$127$	1.15794e9	−	1.15794e9i	0.394974	−	0.394974i	0.876456	+	0.481482i	$0.159901\pi$
$128$	1.00970e9	−	1.00970e9i	0.332467	−	0.332467i
$129$	5.24078e8	−	1.26524e9i	0.166626	−	0.402270i
$130$	2.69976e8	+	1.11828e8i	0.0829048	+	0.0343403i
$131$	1.87492e9	+	4.52645e9i	0.556239	+	1.34288i	0.912723	+	0.408579i	$0.133976\pi$
$131$	1.87492e9	+	4.52645e9i	0.556239	+	1.34288i	−0.356484	+	0.934302i	$0.616024\pi$
$132$			3.43247e9i			0.984064i
$133$	−1.54308e9	+	6.39165e8i	−0.427618	+	0.177125i
$134$	−1.34147e9	−	1.34147e9i	−0.359425	−	0.359425i
$135$	−4.23662e9			−1.09779
$136$	1.60177e9	−	3.78871e9i	0.401489	−	0.949655i
$137$	−3.10441e9			−0.752899			−0.376449	−	0.926437i	$-0.622855\pi$
$137$	−3.10441e9			−0.752899			−0.376449	+	0.926437i	$0.622855\pi$
$138$	−1.96123e9	−	1.96123e9i	−0.460334	−	0.460334i
$139$	2.60628e8	−	1.07956e8i	0.0592181	−	0.0245289i	−0.352878	−	0.935669i	$-0.614797\pi$
$139$	2.60628e8	−	1.07956e8i	0.0592181	−	0.0245289i	0.412096	+	0.911140i	$0.364797\pi$
$140$		−	9.54939e8i		−	0.210087i
$141$	−6.60473e8	−	1.59452e9i	−0.140724	−	0.339738i
$142$	4.82216e9	+	1.99740e9i	0.995277	+	0.412257i
$143$	4.10659e8	−	9.91418e8i	0.0821238	−	0.198264i
$144$	1.83384e6	−	1.83384e6i	0.000355410	−	0.000355410i
$145$	2.37764e9	−	2.37764e9i	0.446673	−	0.446673i
$146$	1.43451e9	−	3.46321e9i	0.261286	−	0.630799i
$147$	−4.64819e9	−	1.92534e9i	−0.821023	−	0.340079i
$148$	−1.06915e8	−	2.58117e8i	−0.0183174	−	0.0442220i
$149$			1.55842e9i			0.259028i	0.991578	+	0.129514i	$0.0413417\pi$
$149$			1.55842e9i			0.259028i	−0.991578	+	0.129514i	$0.958658\pi$
$150$	−7.95592e8	+	3.29545e8i	−0.128316	+	0.0531501i
$151$	−5.92882e9	−	5.92882e9i	−0.928051	−	0.928051i	0.0695289	−	0.997580i	$-0.477850\pi$
$151$	−5.92882e9	−	5.92882e9i	−0.928051	−	0.928051i	−0.997580	+	0.0695289i	$0.977850\pi$
$152$	−9.32895e9			−1.41754
$153$	−1.19361e7	+	2.82329e7i	−0.00176097	+	0.00416528i
$154$	2.67615e9			0.383413
$155$	3.16785e9	+	3.16785e9i	0.440830	+	0.440830i
$156$	4.81582e8	−	1.99478e8i	0.0651042	−	0.0269671i
$157$			8.18273e9i			1.07486i	0.843310	+	0.537428i	$0.180604\pi$
$157$			8.18273e9i			1.07486i	−0.843310	+	0.537428i	$0.819396\pi$
$158$	−9.33237e8	−	2.25303e9i	−0.119134	−	0.287615i
$159$	7.04857e9	+	2.91961e9i	0.874609	+	0.362275i
$160$	3.34359e9	−	8.07214e9i	0.403342	−	0.973753i
$161$	2.00369e9	−	2.00369e9i	0.235025	−	0.235025i
$162$	4.09648e9	−	4.09648e9i	0.467298	−	0.467298i
$163$	−3.53544e9	+	8.53531e9i	−0.392283	+	0.947055i	0.597159	+	0.802123i	$0.296296\pi$
$163$	−3.53544e9	+	8.53531e9i	−0.392283	+	0.947055i	−0.989442	+	0.144932i	$0.953704\pi$
$164$	7.84460e9	+	3.24934e9i	0.846786	+	0.350750i
$165$	6.95557e9	+	1.67922e10i	0.730559	+	1.76373i
$166$			1.17139e10i			1.19734i
$167$	−9.94146e9	+	4.11789e9i	−0.989067	+	0.409685i	−0.817777	−	0.575535i	$-0.804794\pi$
$167$	−9.94146e9	+	4.11789e9i	−0.989067	+	0.409685i	−0.171291	+	0.985221i	$0.554794\pi$
$168$	2.53986e9	+	2.53986e9i	0.245990	+	0.245990i
$169$	1.04415e10			0.984633
$170$	5.74202e7	−	7.88266e9i	0.00527284	−	0.723857i
$171$	6.95179e7			0.00621748
$172$	1.99986e9	+	1.99986e9i	0.174230	+	0.174230i
$173$	−1.52806e10	+	6.32944e9i	−1.29698	+	0.537227i	−0.921059	−	0.389424i	$-0.872674\pi$
$173$	−1.52806e10	+	6.32944e9i	−1.29698	+	0.537227i	−0.375922	+	0.926651i	$0.622674\pi$
$174$			4.57728e9i			0.378561i
$175$	−3.36679e8	−	8.12816e8i	−0.0271360	−	0.0655120i
$176$	2.26279e9	+	9.37277e8i	0.177761	+	0.0736311i
$177$	5.96380e9	−	1.43979e10i	0.456713	−	1.10260i
$178$	−2.98672e9	+	2.98672e9i	−0.223000	+	0.223000i
$179$	8.52450e9	−	8.52450e9i	0.620627	−	0.620627i	−0.325065	−	0.945692i	$-0.605386\pi$
$179$	8.52450e9	−	8.52450e9i	0.620627	−	0.620627i	0.945692	+	0.325065i	$0.105386\pi$
$180$	−1.52103e7	+	3.67210e7i	−0.00107997	+	0.00260728i
$181$	−1.89837e10	−	7.86330e9i	−1.31470	−	0.544567i	−0.388448	−	0.921471i	$-0.626989\pi$
$181$	−1.89837e10	−	7.86330e9i	−1.31470	−	0.544567i	−0.926252	+	0.376904i	$0.876989\pi$
$182$	−1.55524e8	−	3.75468e8i	−0.0105069	−	0.0253660i
$183$		−	1.19507e10i		−	0.787705i
$184$	1.46225e10	−	6.05682e9i	0.940460	−	0.389551i
$185$	−1.04610e9	−	1.04610e9i	−0.0656599	−	0.0656599i
$186$	−6.09854e9			−0.373610
$187$	−2.89471e10	−	2.10862e8i	−1.73108	−	0.0126099i
$188$	3.56430e9			0.208096
$189$	4.16633e9	+	4.16633e9i	0.237506	+	0.237506i
$190$	−1.65171e10	+	6.84159e9i	−0.919479	+	0.380861i
$191$		−	3.26529e10i		−	1.77530i	−0.460517	−	0.887651i	$-0.652336\pi$
$191$		−	3.26529e10i		−	1.77530i	0.460517	−	0.887651i	$-0.347664\pi$
$192$	5.35428e9	+	1.29264e10i	0.284345	+	0.686470i
$193$	2.57010e10	+	1.06457e10i	1.33334	+	0.552289i	0.931607	−	0.363467i	$-0.118407\pi$
$193$	2.57010e10	+	1.06457e10i	1.33334	+	0.552289i	0.401736	+	0.915756i	$0.368407\pi$
$194$	−1.49362e9	+	3.60592e9i	−0.0757064	+	0.182771i
$195$	1.95176e9	−	1.95176e9i	0.0966654	−	0.0966654i
$196$	7.34703e9	−	7.34703e9i	0.355598	−	0.355598i
$197$	−1.05700e10	+	2.55183e10i	−0.500009	+	1.20713i	0.449469	+	0.893296i	$0.351613\pi$
$197$	−1.05700e10	+	2.55183e10i	−0.500009	+	1.20713i	−0.949478	+	0.313833i	$0.898387\pi$
$198$	−1.02908e8	−	4.26258e7i	−0.00475834	−	0.00197097i
$199$	−1.43774e10	−	3.47100e10i	−0.649891	−	1.56897i	−0.812934	−	0.582356i	$-0.802131\pi$
$199$	−1.43774e10	−	3.47100e10i	−0.649891	−	1.56897i	0.163043	−	0.986619i	$-0.447869\pi$
$200$		−	4.91401e9i		−	0.217171i
$201$	−1.65555e10	+	6.85752e9i	−0.715419	+	0.296336i
$202$	−1.07054e10	−	1.07054e10i	−0.452400	−	0.452400i
$203$	−4.67638e9			−0.193276
$204$	−9.87025e9	−	1.00151e10i	−0.399018	−	0.404874i
$205$	4.49617e10			1.77808
$206$	−1.17091e10	−	1.17091e10i	−0.453022	−	0.453022i
$207$	−1.08964e8	+	4.51346e7i	−0.00412495	+	0.00170861i
$208$		−	3.71943e8i		−	0.0137782i
$209$	2.51240e10	+	6.06548e10i	0.910817	+	2.19891i
$210$	6.35953e9	+	2.63421e9i	0.225652	+	0.0934680i
$211$	1.41079e9	−	3.40596e9i	0.0489996	−	0.118296i	−0.897484	−	0.441046i	$-0.854608\pi$
$211$	1.41079e9	−	3.40596e9i	0.0489996	−	0.118296i	0.946484	+	0.322751i	$0.104608\pi$
$212$	−1.11411e10	+	1.11411e10i	−0.378807	+	0.378807i
$213$	3.48613e10	−	3.48613e10i	1.16047	−	1.16047i
$214$	6.69144e9	−	1.61546e10i	0.218101	−	0.526543i
$215$	1.38362e10	+	5.73115e9i	0.441615	+	0.182923i
$216$	1.25941e10	+	3.04049e10i	0.393664	+	0.950389i
$217$		−	6.23057e9i		−	0.190748i
$218$	−1.55994e10	+	6.46147e9i	−0.467792	+	0.193766i
$219$	−2.50369e10	−	2.50369e10i	−0.735500	−	0.735500i
$220$	−3.75363e10			−1.08031
$221$	1.65268e9	+	4.07359e9i	0.0466039	+	0.114871i
$222$	2.01389e9			0.0556477
$223$	−8.94485e9	−	8.94485e9i	−0.242215	−	0.242215i	0.575551	−	0.817766i	$-0.304788\pi$
$223$	−8.94485e9	−	8.94485e9i	−0.242215	−	0.242215i	−0.817766	+	0.575551i	$0.804788\pi$
$224$	−1.12263e10	+	4.65010e9i	−0.297935	+	0.123409i
$225$			3.66185e7i			0.000952530i
$226$	7.83327e9	+	1.89112e10i	0.199736	+	0.482204i
$227$	4.09024e10	+	1.69423e10i	1.02243	+	0.423503i	0.829973	−	0.557803i	$-0.188356\pi$
$227$	4.09024e10	+	1.69423e10i	1.02243	+	0.423503i	0.192453	+	0.981306i	$0.438356\pi$
$228$	−1.22040e10	+	2.94631e10i	−0.299086	+	0.722057i
$229$	−4.72078e10	+	4.72078e10i	−1.13437	+	1.13437i	−0.144925	+	0.989443i	$0.546294\pi$
$229$	−4.72078e10	+	4.72078e10i	−1.13437	+	1.13437i	−0.989443	+	0.144925i	$0.953706\pi$
$230$	2.14474e10	−	2.14474e10i	0.505359	−	0.505359i
$231$	9.67346e9	−	2.33538e10i	0.223526	−	0.539639i
$232$	−2.41315e10	−	9.99558e9i	−0.546875	−	0.226523i
$233$	2.38301e10	+	5.75309e10i	0.529692	+	1.27879i	0.931725	+	0.363165i	$0.118304\pi$
$233$	2.38301e10	+	5.75309e10i	0.529692	+	1.27879i	−0.402033	+	0.915625i	$0.631696\pi$
$234$			1.69154e7i			0.000368816i
$235$	1.74372e10	−	7.22272e9i	0.372968	−	0.154488i
$236$	2.27577e10	+	2.27577e10i	0.477555	+	0.477555i
$237$	−2.30348e10			−0.474261
$238$	−7.80834e9	+	7.69541e9i	−0.157748	+	0.155466i
$239$	6.82772e10			1.35358			0.676792	−	0.736174i	$-0.263370\pi$
$239$	6.82772e10			1.35358			0.676792	+	0.736174i	$0.263370\pi$
$240$	4.45465e9	+	4.45465e9i	0.0866688	+	0.0866688i
$241$	−5.72975e10	+	2.37334e10i	−1.09410	+	0.453193i	−0.855436	−	0.517908i	$-0.826711\pi$
$241$	−5.72975e10	+	2.37334e10i	−1.09410	+	0.453193i	−0.238668	+	0.971101i	$0.576711\pi$
$242$		−	7.00912e10i		−	1.31369i
$243$	−1.88125e8	−	4.54174e8i	−0.00346114	−	0.00835592i
$244$	2.28017e10	+	9.44478e9i	0.411826	+	0.170584i
$245$	2.10549e10	−	5.08311e10i	0.373341	−	0.901326i
$246$	−4.32788e10	+	4.32788e10i	−0.753471	+	0.753471i
$247$	7.04990e9	−	7.04990e9i	0.120517	−	0.120517i
$248$	1.33176e10	−	3.21516e10i	0.223560	−	0.539722i
$249$	1.02223e11	+	4.23423e10i	1.68521	+	0.698035i
$250$	1.35056e10	+	3.26053e10i	0.218667	+	0.527908i
$251$		−	8.72683e10i		−	1.38779i	−0.720074	−	0.693897i	$-0.755892\pi$
$251$		−	8.72683e10i		−	1.38779i	0.720074	−	0.693897i	$-0.244108\pi$
$252$	5.10697e7	−	2.11538e7i	0.000797739	−	0.000330434i
$253$	−7.87603e10	−	7.87603e10i	−1.20855	−	1.20855i
$254$	−2.43777e10			−0.367486
$255$	−6.85817e10	−	2.89945e10i	−1.01573	−	0.429423i
$256$	−7.22025e10			−1.05069
$257$	−1.64355e10	−	1.64355e10i	−0.235009	−	0.235009i	0.579771	−	0.814780i	$-0.303142\pi$
$257$	−1.64355e10	−	1.64355e10i	−0.235009	−	0.235009i	−0.814780	+	0.579771i	$0.803142\pi$
$258$	−1.88350e10	+	7.80169e9i	−0.264652	+	0.109623i
$259$			2.05749e9i			0.0284111i
$260$	2.18142e9	+	5.26642e9i	0.0296047	+	0.0714719i
$261$	1.79824e8	+	7.44856e7i	0.00239864	+	0.000993551i
$262$	2.79110e10	−	6.73831e10i	0.365948	−	0.883477i
$263$	−1.80017e10	+	1.80017e10i	−0.232014	+	0.232014i	−0.813533	−	0.581519i	$-0.802459\pi$
$263$	−1.80017e10	+	1.80017e10i	−0.232014	+	0.232014i	0.581519	+	0.813533i	$0.302459\pi$
$264$	9.98358e10	−	9.98358e10i	1.26494	−	1.26494i
$265$	−3.19280e10	+	7.70809e10i	−0.397708	+	0.960153i
$266$	2.29711e10	+	9.51494e9i	0.281329	+	0.116530i
$267$	1.52680e10	+	3.68602e10i	0.183857	+	0.443871i
$268$		−	3.70072e10i		−	0.438207i
$269$	1.53860e10	−	6.37307e9i	0.179159	−	0.0742102i	−0.291301	−	0.956632i	$-0.594088\pi$
$269$	1.53860e10	−	6.37307e9i	0.179159	−	0.0742102i	0.470460	+	0.882421i	$0.344088\pi$
$270$	4.45962e10	+	4.45962e10i	0.510694	+	0.510694i
$271$	−7.55383e10			−0.850756			−0.425378	−	0.905016i	$-0.639859\pi$
$271$	−7.55383e10			−0.850756			−0.425378	+	0.905016i	$0.639859\pi$
$272$	−9.29746e9	+	3.77203e9i	−0.102992	+	0.0417844i
$273$	−3.83876e9			−0.0418272
$274$	3.26781e10	+	3.26781e10i	0.350251	+	0.350251i
$275$	−3.19498e10	+	1.32341e10i	−0.336877	+	0.139539i
$276$		−	5.41048e10i		−	0.561235i
$277$	1.18144e10	+	2.85226e10i	0.120574	+	0.291092i	0.972630	−	0.232359i	$-0.0746444\pi$
$277$	1.18144e10	+	2.85226e10i	0.120574	+	0.291092i	−0.852056	+	0.523451i	$0.824644\pi$
$278$	−3.87984e9	−	1.60708e9i	−0.0389594	−	0.0161375i
$279$	−9.92410e7	+	2.39589e8i	−0.000980555	+	0.00236727i
$280$	−2.77751e10	+	2.77751e10i	−0.270050	+	0.270050i
$281$	4.17258e10	−	4.17258e10i	0.399233	−	0.399233i	−0.478729	−	0.877962i	$-0.658903\pi$
$281$	4.17258e10	−	4.17258e10i	0.399233	−	0.399233i	0.877962	+	0.478729i	$0.158903\pi$
$282$	−9.83214e9	+	2.37369e10i	−0.0925821	+	0.223513i
$283$	−1.69623e11	−	7.02599e10i	−1.57197	−	0.651132i	−0.584855	−	0.811138i	$-0.698849\pi$
$283$	−1.69623e11	−	7.02599e10i	−1.57197	−	0.651132i	−0.987116	+	0.160006i	$0.948849\pi$
$284$	3.89634e10	+	9.40660e10i	0.355406	+	0.858025i
$285$			1.68869e11i			1.51617i
$286$	−1.47588e10	+	6.11328e9i	−0.130438	+	0.0540290i
$287$	−4.42157e10	−	4.42157e10i	−0.384687	−	0.384687i
$288$	5.05761e8			0.00433191
$289$	8.50670e10	−	8.26238e10i	0.717333	−	0.696731i
$290$	−5.00557e10			−0.415587
$291$	2.60686e10	+	2.60686e10i	0.213108	+	0.213108i
$292$	6.75570e10	−	2.79830e10i	0.543810	−	0.225253i
$293$			8.80276e10i			0.697774i	0.937165	+	0.348887i	$0.113440\pi$
$293$			8.80276e10i			0.697774i	−0.937165	+	0.348887i	$0.886560\pi$
$294$	2.86616e10	+	6.91953e10i	0.223737	+	0.540149i
$295$	1.57451e11	+	6.52183e10i	1.21045	+	0.501384i
$296$	−4.39780e9	+	1.06172e10i	−0.0332984	+	0.0803894i
$297$	1.63768e11	−	1.63768e11i	1.22131	−	1.22131i
$298$	1.64045e10	−	1.64045e10i	0.120501	−	0.120501i
$299$	−6.47307e9	+	1.56274e10i	−0.0468371	+	0.113075i
$300$	−1.55196e10	−	6.42844e9i	−0.110621	−	0.0458205i
$301$	−7.97059e9	−	1.92427e10i	−0.0559682	−	0.135119i
$302$			1.24818e11i			0.863465i
$303$	−1.32119e11	+	5.47256e10i	−0.900481	+	0.372991i
$304$	1.60905e10	+	1.60905e10i	0.108054	+	0.108054i
$305$	1.30689e11			0.864749
$306$	4.22833e8	−	1.71546e8i	0.00275691	−	0.00111849i
$307$	1.25066e11			0.803558			0.401779	−	0.915737i	$-0.368392\pi$
$307$	1.25066e11			0.803558			0.401779	+	0.915737i	$0.368392\pi$
$308$	3.69136e10	+	3.69136e10i	0.233726	+	0.233726i
$309$	−1.44506e11	+	5.98561e10i	−0.901719	+	0.373504i
$310$		−	6.66917e10i		−	0.410152i
$311$	4.73166e10	+	1.14232e11i	0.286808	+	0.692416i	0.999963	−	0.00859042i	$-0.00273445\pi$
$311$	4.73166e10	+	1.14232e11i	0.286808	+	0.692416i	−0.713155	+	0.701006i	$0.752734\pi$
$312$	−1.98091e10	−	8.20520e9i	−0.118350	−	0.0490223i
$313$	−1.88470e10	+	4.55007e10i	−0.110992	+	0.267959i	−0.969609	−	0.244658i	$-0.921324\pi$
$313$	−1.88470e10	+	4.55007e10i	−0.110992	+	0.267959i	0.858617	+	0.512618i	$0.171324\pi$
$314$	8.61344e10	−	8.61344e10i	0.500027	−	0.500027i
$315$	2.06976e8	−	2.06976e8i	0.00118447	−	0.00118447i
$316$	1.82047e10	−	4.39500e10i	0.102705	−	0.247952i
$317$	−2.71663e11	−	1.12526e11i	−1.51100	−	0.625875i	−0.535233	−	0.844705i	$-0.679776\pi$
$317$	−2.71663e11	−	1.12526e11i	−1.51100	−	0.625875i	−0.975763	+	0.218829i	$0.929776\pi$
$318$	−4.34629e10	−	1.04929e11i	−0.238340	−	0.575403i
$319$			1.83817e11i			0.993865i
$320$	−1.41359e11	+	5.85527e10i	−0.753612	+	0.312156i
$321$	−1.16788e11	−	1.16788e11i	−0.613939	−	0.613939i
$322$	−4.21832e10			−0.218669
$323$	−2.47722e11	−	1.04730e11i	−1.26635	−	0.535379i
$324$	1.13010e11			0.569725
$325$	3.71353e9	+	3.71353e9i	0.0184634	+	0.0184634i
$326$	1.27061e11	−	5.26304e10i	0.623065	−	0.258082i
$327$			1.59487e11i			0.771363i
$328$	−1.33657e11	−	3.22676e11i	−0.637614	−	1.53934i
$329$	−2.42508e10	−	1.00450e10i	−0.114115	−	0.0472681i
$330$	1.03544e11	−	2.49978e11i	0.480633	−	1.16035i
$331$	−2.17162e10	+	2.17162e10i	−0.0994395	+	0.0994395i	−0.755076	−	0.655637i	$-0.772400\pi$
$331$	−2.17162e10	+	2.17162e10i	−0.0994395	+	0.0994395i	0.655637	+	0.755076i	$0.272400\pi$
$332$	−1.61577e11	+	1.61577e11i	−0.729889	+	0.729889i
$333$	3.27718e7	−	7.91181e7i	0.000146050	−	0.000352595i
$334$	1.47994e11	+	6.13010e10i	0.650705	+	0.269531i
$335$	−7.49917e10	−	1.81046e11i	−0.325321	−	0.785393i
$336$		−	8.76148e9i		−	0.0375017i
$337$	3.94971e11	−	1.63602e11i	1.66813	−	0.690963i	0.669479	−	0.742831i	$-0.266518\pi$
$337$	3.94971e11	−	1.63602e11i	1.66813	−	0.690963i	0.998654	+	0.0518683i	$0.0165176\pi$
$338$	−1.09911e11	−	1.09911e11i	−0.458055	−	0.458055i
$339$	1.93346e11			0.795129
$340$	1.09522e11	−	1.07938e11i	0.444474	−	0.438045i
$341$	−2.44909e11			−0.980866
$342$	−7.31770e8	−	7.31770e8i	−0.00289239	−	0.00289239i
$343$	−1.50423e11	+	6.23071e10i	−0.586799	+	0.243060i
$344$		−	1.16335e11i		−	0.447917i
$345$	−1.09638e11	−	2.64690e11i	−0.416655	−	1.00589i
$346$	2.27475e11	+	9.42233e10i	0.853280	+	0.353440i
$347$	5.02641e10	−	1.21348e11i	0.186112	−	0.449315i	−0.803093	−	0.595854i	$-0.796814\pi$
$347$	5.02641e10	−	1.21348e11i	0.186112	−	0.449315i	0.989205	+	0.146540i	$0.0468136\pi$
$348$	−6.31370e10	+	6.31370e10i	−0.230769	+	0.230769i
$349$	−1.34700e11	+	1.34700e11i	−0.486018	+	0.486018i	−0.907047	−	0.421029i	$-0.861669\pi$
$349$	−1.34700e11	+	1.34700e11i	−0.486018	+	0.486018i	0.421029	+	0.907047i	$0.361669\pi$
$350$	−5.01198e9	+	1.21000e10i	−0.0178527	+	0.0431002i
$351$	−3.24944e10	−	1.34596e10i	−0.114268	−	0.0473316i
$352$	1.82784e11	+	4.41280e11i	0.634594	+	1.53205i
$353$			5.20746e10i			0.178501i	0.996009	+	0.0892503i	$0.0284471\pi$
$353$			5.20746e10i			0.178501i	−0.996009	+	0.0892503i	$0.971553\pi$
$354$	−2.14335e11	+	8.87803e10i	−0.725400	+	0.300470i
$355$	3.81232e11	+	3.81232e11i	1.27398	+	1.27398i
$356$	−8.23950e10			−0.271879
$357$	3.89304e10	+	9.59573e10i	0.126847	+	0.312659i
$358$	−1.79464e11			−0.577435
$359$	4.35039e11	+	4.35039e11i	1.38230	+	1.38230i	0.840515	+	0.541788i	$0.182253\pi$
$359$	4.35039e11	+	4.35039e11i	1.38230	+	1.38230i	0.541788	+	0.840515i	$0.317747\pi$
$360$	1.51046e9	−	6.25654e8i	0.00473967	−	0.00196324i
$361$			2.87279e11i			0.890271i
$362$	1.17057e11	+	2.82601e11i	0.358269	+	0.864938i
$363$	−6.11662e11	−	2.53359e11i	−1.84898	−	0.765871i
$364$	3.03381e9	−	7.32427e9i	0.00905801	−	0.0218680i
$365$	2.73796e11	−	2.73796e11i	0.807438	−	0.807438i
$366$	−1.25797e11	+	1.25797e11i	−0.366443	+	0.366443i
$367$	2.14315e11	−	5.17401e11i	0.616672	−	1.48878i	−0.238873	−	0.971051i	$-0.576778\pi$
$367$	2.14315e11	−	5.17401e11i	0.616672	−	1.48878i	0.855545	−	0.517728i	$-0.173222\pi$
$368$	−3.56675e10	−	1.47740e10i	−0.101381	−	0.0419935i
$369$	9.95989e8	+	2.40453e9i	0.00279664	+	0.00675168i
$370$			2.20232e10i			0.0610904i
$371$	1.07200e11	−	4.44038e10i	0.293774	−	0.121685i
$372$	−8.41206e10	−	8.41206e10i	−0.227750	−	0.227750i
$373$	2.00817e10			0.0537169			0.0268585	−	0.999639i	$-0.491450\pi$
$373$	2.00817e10			0.0537169			0.0268585	+	0.999639i	$0.491450\pi$
$374$	3.02488e11	+	3.06927e11i	0.799440	+	0.811172i
$375$	3.33354e11			0.870492
$376$	−1.03670e11	−	1.03670e11i	−0.267491	−	0.267491i
$377$	2.57899e10	−	1.06825e10i	0.0657526	−	0.0272356i
$378$		−	8.77125e10i		−	0.220978i
$379$	8.50937e9	+	2.05434e10i	0.0211846	+	0.0511442i	0.934118	−	0.356965i	$-0.116188\pi$
$379$	8.50937e9	+	2.05434e10i	0.0211846	+	0.0511442i	−0.912933	+	0.408109i	$0.866188\pi$
$380$	−3.22199e11	−	1.33459e11i	−0.792680	−	0.328339i
$381$	−8.81181e10	+	2.12736e11i	−0.214241	+	0.517223i
$382$	−3.43717e11	+	3.43717e11i	−0.825877	+	0.825877i
$383$	7.48749e10	−	7.48749e10i	0.177804	−	0.177804i	−0.612594	−	0.790398i	$-0.709874\pi$
$383$	7.48749e10	−	7.48749e10i	0.177804	−	0.177804i	0.790398	+	0.612594i	$0.209874\pi$
$384$	−7.68376e10	+	1.85502e11i	−0.180336	+	0.435370i
$385$	2.55390e11	+	1.05786e11i	0.592421	+	0.245389i
$386$	−1.58477e11	−	3.82598e11i	−0.363349	−	0.877203i
$387$			8.66911e8i			0.00196460i
$388$	−7.03407e10	+	2.91361e10i	−0.157567	+	0.0652662i
$389$	−4.53778e10	−	4.53778e10i	−0.100478	−	0.100478i	0.655081	−	0.755559i	$-0.272635\pi$
$389$	−4.53778e10	−	4.53778e10i	−0.100478	−	0.100478i	−0.755559	+	0.655081i	$0.772635\pi$
$390$	−4.10899e10			−0.0899381
$391$	4.56283e11	+	3.32374e9i	0.987277	+	0.00719169i
$392$	−4.27388e11			−0.914187
$393$	−4.87139e11	−	4.87139e11i	−1.03012	−	1.03012i
$394$	3.79878e11	−	1.57351e11i	0.794166	−	0.328955i
$395$		−	2.51902e11i		−	0.520648i
$396$	−8.31503e8	−	2.00743e9i	−0.00169917	−	0.00410215i
$397$	−1.26626e11	−	5.24501e10i	−0.255838	−	0.105971i	0.251079	−	0.967967i	$-0.419215\pi$
$397$	−1.26626e11	−	5.24501e10i	−0.255838	−	0.105971i	−0.506916	+	0.861995i	$0.669215\pi$
$398$	−2.14029e11	+	5.16711e11i	−0.427561	+	1.03222i
$399$	1.66067e11	−	1.66067e11i	0.328024	−	0.328024i
$400$	−8.47566e9	+	8.47566e9i	−0.0165540	+	0.0165540i
$401$	−1.84954e11	+	4.46519e11i	−0.357202	+	0.862363i	0.638489	+	0.769631i	$0.279560\pi$
$401$	−1.84954e11	+	4.46519e11i	−0.357202	+	0.862363i	−0.995691	+	0.0927318i	$0.970440\pi$
$402$	2.46454e11	+	1.02085e11i	0.470672	+	0.194959i
$403$	1.42329e10	+	3.43612e10i	0.0268794	+	0.0648926i
$404$		−	2.95331e11i		−	0.551561i
$405$	5.52866e11	−	2.29005e11i	1.02111	−	0.422957i
$406$	4.92252e10	+	4.92252e10i	0.0899125	+	0.0899125i
$407$	8.08748e10			0.146096
$408$	−4.21314e9	+	5.78380e11i	−0.00752722	+	1.03334i
$409$	−2.08768e11			−0.368900			−0.184450	−	0.982842i	$-0.559050\pi$
$409$	−2.08768e11			−0.368900			−0.184450	+	0.982842i	$0.559050\pi$
$410$	−4.73283e11	−	4.73283e11i	−0.827167	−	0.827167i
$411$	4.03292e11	−	1.67049e11i	0.697159	−	0.288773i
$412$		−	3.23019e11i		−	0.552319i
$413$	−9.07023e10	−	2.18975e11i	−0.153406	−	0.370355i
$414$	1.62210e9	+	6.71896e8i	0.00271379	+	0.00112409i
$415$	−4.63042e11	+	1.11788e12i	−0.766309	+	1.85003i
$416$	5.12899e10	−	5.12899e10i	0.0839676	−	0.0839676i
$417$	−2.80489e10	+	2.80489e10i	−0.0454259	+	0.0454259i
$418$	3.74009e11	−	9.02938e11i	0.599224	−	1.44665i
$419$	1.66284e11	+	6.88770e10i	0.263564	+	0.109172i	0.510553	−	0.859847i	$-0.329441\pi$
$419$	1.66284e11	+	6.88770e10i	0.263564	+	0.109172i	−0.246988	+	0.969018i	$0.579441\pi$
$420$	5.13855e10	+	1.24056e11i	0.0805785	+	0.194534i
$421$		−	1.24378e12i		−	1.92963i	−0.262937	−	0.964813i	$-0.584691\pi$
$421$		−	1.24378e12i		−	1.92963i	0.262937	−	0.964813i	$-0.415309\pi$
$422$	−5.07029e10	+	2.10018e10i	−0.0778263	+	0.0322367i
$423$	7.72536e8	+	7.72536e8i	0.00117324	+	0.00117324i
$424$	6.48097e11			0.973853
$425$	5.51666e10	−	1.30487e11i	0.0820211	−	0.194007i
$426$	−7.33925e11			−1.07971
$427$	−1.28521e11	−	1.28521e11i	−0.187089	−	0.187089i
$428$	3.15128e11	−	1.30530e11i	0.453931	−	0.188024i
$429$			1.50892e11i			0.215084i
$430$	−8.53168e10	−	2.05973e11i	−0.120345	−	0.290538i
$431$	−7.85580e11	−	3.25398e11i	−1.09659	−	0.454221i	−0.240288	−	0.970702i	$-0.577242\pi$
$431$	−7.85580e11	−	3.25398e11i	−1.09659	−	0.454221i	−0.856299	+	0.516481i	$0.827242\pi$
$432$	3.07199e10	−	7.41644e10i	0.0424368	−	0.102452i
$433$	−4.88725e11	+	4.88725e11i	−0.668142	+	0.668142i	−0.957286	−	0.289144i	$-0.906629\pi$
$433$	−4.88725e11	+	4.88725e11i	−0.668142	+	0.668142i	0.289144	+	0.957286i	$0.406629\pi$
$434$	−6.55852e10	+	6.55852e10i	−0.0887365	+	0.0887365i
$435$	−1.80936e11	+	4.36819e11i	−0.242283	+	0.584924i
$436$	−3.04297e11	−	1.26044e11i	−0.403282	−	0.167045i
$437$	−3.96021e11	−	9.56080e11i	−0.519460	−	1.25409i
$438$			5.27095e11i			0.684314i
$439$	−1.83436e11	+	7.59816e10i	−0.235719	+	0.0976378i	−0.497416	−	0.867512i	$-0.665718\pi$
$439$	−1.83436e11	+	7.59816e10i	−0.235719	+	0.0976378i	0.261697	+	0.965150i	$0.415718\pi$
$440$	1.09177e12	+	1.09177e12i	1.38866	+	1.38866i
$441$	3.18483e9			0.00400971
$442$	2.54834e10	−	6.02767e10i	0.0317583	−	0.0751189i
$443$	1.17901e12			1.45445			0.727227	−	0.686397i	$-0.240809\pi$
$443$	1.17901e12			1.45445			0.727227	+	0.686397i	$0.240809\pi$
$444$	2.77787e10	+	2.77787e10i	0.0339225	+	0.0339225i
$445$	−4.03091e11	+	1.66966e11i	−0.487285	+	0.201840i
$446$			1.88313e11i			0.225359i
$447$	−8.38591e10	−	2.02454e11i	−0.0993496	−	0.239851i
$448$	1.96595e11	+	8.14322e10i	0.230580	+	0.0955092i
$449$	2.95767e10	−	7.14045e10i	0.0343432	−	0.0829119i	−0.905777	−	0.423754i	$-0.860712\pi$
$449$	2.95767e10	−	7.14045e10i	0.0343432	−	0.0829119i	0.940121	+	0.340842i	$0.110712\pi$
$450$	3.85459e8	−	3.85459e8i	0.000443120	−	0.000443120i
$451$	−1.73801e12	+	1.73801e12i	−1.97815	+	1.97815i
$452$	−1.52804e11	+	3.68901e11i	−0.172191	+	0.415707i
$453$	1.08924e12	+	4.51178e11i	1.21530	+	0.503392i
$454$	−2.52212e11	−	6.08893e11i	−0.278621	−	0.672651i
$455$		−	4.19794e10i		−	0.0459182i
$456$	1.21192e12	−	5.01993e11i	1.31260	−	0.543696i
$457$	1.85350e11	+	1.85350e11i	0.198778	+	0.198778i	0.799476	−	0.600698i	$-0.205110\pi$
$457$	1.85350e11	+	1.85350e11i	0.198778	+	0.198778i	−0.600698	+	0.799476i	$0.705110\pi$
$458$	9.93851e11			1.05542
$459$	−6.91113e9	+	9.48761e11i	−0.00726762	+	0.997700i
$460$	5.91672e11			0.616128
$461$	5.55612e11	+	5.55612e11i	0.572951	+	0.572951i	0.932952	−	0.360001i	$-0.117224\pi$
$461$	5.55612e11	+	5.55612e11i	0.572951	+	0.572951i	−0.360001	+	0.932952i	$0.617224\pi$
$462$	−3.47657e11	+	1.44004e11i	−0.355027	+	0.147057i
$463$			1.23202e12i			1.24596i	0.782237	+	0.622981i	$0.214079\pi$
$463$			1.23202e12i			1.24596i	−0.782237	+	0.622981i	$0.785921\pi$
$464$	2.43815e10	+	5.88622e10i	0.0244191	+	0.0589529i
$465$	−5.81996e11	−	2.41071e11i	−0.577273	−	0.239114i
$466$	3.54747e11	−	8.56434e11i	0.348483	−	0.841313i
$467$	−3.93738e10	+	3.93738e10i	−0.0383073	+	0.0383073i	−0.726001	−	0.687694i	$-0.758623\pi$
$467$	−3.93738e10	+	3.93738e10i	−0.0383073	+	0.0383073i	0.687694	+	0.726001i	$0.258623\pi$
$468$	−2.33323e8	+	2.33323e8i	−0.000224828	+	0.000224828i
$469$	−1.04295e11	+	2.51790e11i	−0.0995369	+	0.240303i
$470$	−2.59579e11	−	1.07521e11i	−0.245374	−	0.101637i
$471$	−4.40315e11	−	1.06301e12i	−0.412258	−	0.995280i
$472$		−	1.32385e12i		−	1.22772i
$473$	−7.56385e11	+	3.13305e11i	−0.694812	+	0.287801i
$474$	2.42473e11	+	2.42473e11i	0.220628	+	0.220628i
$475$	−3.21299e11			−0.289593
$476$	−2.13852e11	−	1.55778e9i	−0.190933	−	0.00139083i
$477$	−4.82952e9			−0.00427141
$478$	−7.18710e11	−	7.18710e11i	−0.629692	−	0.629692i
$479$	1.50881e12	−	6.24968e11i	1.30955	−	0.542435i	0.384800	−	0.923000i	$-0.374270\pi$
$479$	1.50881e12	−	6.24968e11i	1.30955	−	0.542435i	0.924754	+	0.380565i	$0.124270\pi$
$480$			1.22857e12i			1.05636i
$481$	−4.70004e9	−	1.13469e10i	−0.00400358	−	0.00966550i
$482$	8.52960e11	+	3.53307e11i	0.719808	+	0.298154i
$483$	−1.52479e11	+	3.68118e11i	−0.127482	+	0.307769i
$484$	9.66807e11	−	9.66807e11i	0.800821	−	0.800821i
$485$	−2.85078e11	+	2.85078e11i	−0.233952	+	0.233952i
$486$	−2.80053e9	+	6.76107e9i	−0.00227707	+	0.00549734i
$487$	6.43277e11	+	2.66454e11i	0.518224	+	0.214656i	0.626437	−	0.779472i	$-0.284513\pi$
$487$	6.43277e11	+	2.66454e11i	0.518224	+	0.214656i	−0.108212	+	0.994128i	$0.534513\pi$
$488$	−3.88497e11	−	9.37914e11i	−0.310097	−	0.748641i
$489$		−	1.29906e12i		−	1.02740i
$490$	−7.56698e11	+	3.13434e11i	−0.592980	+	0.245620i
$491$	−5.22311e10	−	5.22311e10i	−0.0405567	−	0.0405567i	0.686538	−	0.727094i	$-0.259130\pi$
$491$	−5.22311e10	−	5.22311e10i	−0.0405567	−	0.0405567i	−0.727094	+	0.686538i	$0.759130\pi$
$492$	−1.19394e12			−0.918624
$493$	−5.28576e11	−	5.36333e11i	−0.402992	−	0.408906i
$494$	−1.48420e11			−0.112129
$495$	−8.13573e9	−	8.13573e9i	−0.00609078	−	0.00609078i
$496$	−7.84251e10	+	3.24847e10i	−0.0581818	+	0.0240997i
$497$		−	7.49814e11i		−	0.551251i
$498$	−6.30329e11	−	1.52175e12i	−0.459235	−	1.10869i
$499$	4.08981e11	+	1.69406e11i	0.295291	+	0.122314i	0.525411	−	0.850849i	$-0.323912\pi$
$499$	4.08981e11	+	1.69406e11i	0.295291	+	0.122314i	−0.230119	+	0.973162i	$0.573912\pi$
$500$	−2.63454e11	+	6.36033e11i	−0.188512	+	0.455108i
$501$	1.06990e12	−	1.06990e12i	0.758709	−	0.758709i
$502$	−9.18617e11	+	9.18617e11i	−0.645607	+	0.645607i
$503$	−2.93709e11	+	7.09076e11i	−0.204579	+	0.493898i	−0.992553	−	0.121810i	$-0.961130\pi$
$503$	−2.93709e11	+	7.09076e11i	−0.204579	+	0.493898i	0.787974	+	0.615708i	$0.211130\pi$
$504$	−2.10067e9	−	8.70128e8i	−0.00145018	−	0.000600683i
$505$	−5.98462e11	−	1.44481e12i	−0.409473	−	0.988555i
$506$			1.65812e12i			1.12444i
$507$	−1.35645e12	+	5.61862e11i	−0.911737	+	0.377654i
$508$	−3.36255e11	−	3.36255e11i	−0.224018	−	0.224018i
$509$	−1.23640e12			−0.816452			−0.408226	−	0.912881i	$-0.633852\pi$
$509$	−1.23640e12			−0.816452			−0.408226	+	0.912881i	$0.633852\pi$
$510$	4.16709e11	+	1.02712e12i	0.272751	+	0.672289i
$511$	−5.38506e11			−0.349379
$512$	2.43062e11	+	2.43062e11i	0.156315	+	0.156315i
$513$	1.98800e12	−	8.23457e11i	1.26733	−	0.524944i
$514$			3.46012e11i			0.218654i
$515$	−6.54568e11	−	1.58027e12i	−0.410036	−	0.989915i
$516$	−3.67414e11	−	1.52188e11i	−0.228156	−	0.0945053i
$517$	−3.94845e11	+	9.53239e11i	−0.243063	+	0.586806i
$518$	2.16578e10	−	2.16578e10i	0.0132169	−	0.0132169i
$519$	1.64451e12	−	1.64451e12i	0.994908	−	0.994908i
$520$	8.97295e10	−	2.16626e11i	0.0538171	−	0.129926i
$521$	−6.25988e11	−	2.59293e11i	−0.372217	−	0.154177i	0.188730	−	0.982029i	$-0.439563\pi$
$521$	−6.25988e11	−	2.59293e11i	−0.372217	−	0.154177i	−0.560947	+	0.827852i	$0.689563\pi$
$522$	−1.10883e9	−	2.67695e9i	−0.000653654	−	0.00157806i
$523$			1.65170e12i			0.965324i	0.875807	+	0.482662i	$0.160330\pi$
$523$			1.65170e12i			0.965324i	−0.875807	+	0.482662i	$0.839670\pi$
$524$	1.31444e12	−	5.44461e11i	0.761643	−	0.315483i
$525$	8.74757e10	+	8.74757e10i	0.0502540	+	0.0502540i
$526$	3.78985e11			0.215867
$527$	7.14584e11	−	7.04249e11i	0.403558	−	0.397721i
$528$	−3.44393e11			−0.192842
$529$	−3.21356e10	−	3.21356e10i	−0.0178417	−	0.0178417i
$530$	1.14747e12	−	4.75296e11i	0.631682	−	0.261651i
$531$			9.86511e9i			0.00538489i
$532$	1.85608e11	+	4.48098e11i	0.100460	+	0.242533i
$533$	3.44851e11	+	1.42842e11i	0.185080	+	0.0766626i
$534$	2.27287e11	−	5.48719e11i	0.120959	−	0.292021i
$535$	1.27715e12	−	1.27715e12i	0.673987	−	0.673987i
$536$	−1.07638e12	+	1.07638e12i	−0.563281	+	0.563281i
$537$	−6.48708e11	+	1.56612e12i	−0.336639	+	0.812719i
$538$	−2.29043e11	−	9.48728e10i	−0.117868	−	0.0488227i
$539$	1.15101e12	+	2.77878e12i	0.587394	+	1.41809i
$540$			1.23028e12i			0.622633i
$541$	−9.10224e10	+	3.77027e10i	−0.0456836	+	0.0189228i	−0.405408	−	0.914136i	$-0.632871\pi$
$541$	−9.10224e10	+	3.77027e10i	−0.0456836	+	0.0189228i	0.359725	+	0.933059i	$0.382871\pi$
$542$	7.95143e11	+	7.95143e11i	0.395775	+	0.395775i
$543$	2.88929e12			1.42624
$544$	−1.80224e12	−	7.61941e11i	−0.882305	−	0.373015i
$545$	−1.74409e12			−0.846809
$546$	4.04081e10	+	4.04081e10i	0.0194582	+	0.0194582i
$547$	−1.46845e11	+	6.08251e10i	−0.0701319	+	0.0290496i	−0.417474	−	0.908689i	$-0.637084\pi$
$547$	−1.46845e11	+	6.08251e10i	−0.0701319	+	0.0290496i	0.347342	+	0.937739i	$0.387084\pi$
$548$			9.01495e11i			0.427022i
$549$	2.89502e9	+	6.98919e9i	0.00136012	+	0.00328361i
$550$	4.75622e11	+	1.97009e11i	0.221630	+	0.0918023i
$551$	−6.53555e11	+	1.57782e12i	−0.302065	+	0.729248i
$552$	−1.57368e12	+	1.57368e12i	−0.721423	+	0.721423i
$553$	−2.47722e11	+	2.47722e11i	−0.112642	+	0.112642i
$554$	1.75876e11	−	4.24602e11i	0.0793254	−	0.191509i
$555$	1.92189e11	+	7.96073e10i	0.0859826	+	0.0356151i
$556$	−3.13494e10	−	7.56842e10i	−0.0139121	−	0.0335868i
$557$		−	2.80868e12i		−	1.23639i	−0.786026	−	0.618194i	$-0.787865\pi$
$557$		−	2.80868e12i		−	1.23639i	0.786026	−	0.618194i	$-0.212135\pi$
$558$	3.56664e9	−	1.47735e9i	0.00155742	−	0.000645105i
$559$	8.79145e10	+	8.79145e10i	0.0380809	+	0.0380809i
$560$	9.58128e10			0.0411697
$561$	3.77185e12	−	1.53026e12i	1.60776	−	0.652277i
$562$	−8.78442e11			−0.371449
$563$	2.12265e11	+	2.12265e11i	0.0890412	+	0.0890412i	0.750224	−	0.661183i	$-0.229945\pi$
$563$	2.12265e11	+	2.12265e11i	0.0890412	+	0.0890412i	−0.661183	+	0.750224i	$0.729945\pi$
$564$	−4.63036e11	+	1.91796e11i	−0.192690	+	0.0798148i
$565$			2.11437e12i			0.872899i
$566$	1.04593e12	+	2.52509e12i	0.428378	+	1.03420i
$567$	−7.68898e11	−	3.18488e11i	−0.312425	−	0.129410i
$568$	1.60270e12	−	3.86926e12i	0.646078	−	1.55977i
$569$	−3.03201e12	+	3.03201e12i	−1.21262	+	1.21262i	−0.242461	+	0.970161i	$0.577955\pi$
$569$	−3.03201e12	+	3.03201e12i	−1.21262	+	1.21262i	−0.970161	+	0.242461i	$0.922045\pi$
$570$	1.77757e12	−	1.77757e12i	0.705328	−	0.705328i
$571$	6.42120e10	−	1.55021e11i	0.0252786	−	0.0610280i	−0.910736	−	0.412989i	$-0.864485\pi$
$571$	6.42120e10	−	1.55021e11i	0.0252786	−	0.0610280i	0.936015	+	0.351961i	$0.114485\pi$
$572$	−2.87900e11	−	1.19252e11i	−0.112450	−	0.0465782i
$573$	1.75706e12	+	4.24193e12i	0.680913	+	1.64387i
$574$			9.30860e11i			0.357916i
$575$	5.03614e11	−	2.08604e11i	0.192129	−	0.0795824i
$576$	−6.26275e9	−	6.26275e9i	−0.00237063	−	0.00237063i
$577$	−7.33555e11			−0.275513			−0.137756	−	0.990466i	$-0.543989\pi$
$577$	−7.33555e11			−0.275513			−0.137756	+	0.990466i	$0.543989\pi$
$578$	−1.76517e12	−	2.57177e10i	−0.657827	−	0.00958423i
$579$	−3.91165e12			−1.44646
$580$	−6.90446e11	−	6.90446e11i	−0.253340	−	0.253340i
$581$	1.55469e12	−	6.43975e11i	0.566047	−	0.234464i
$582$		−	5.48815e11i		−	0.198277i
$583$	−1.74541e12	−	4.21378e12i	−0.625731	−	1.51065i
$584$	−2.77885e12	−	1.15104e12i	−0.988570	−	0.409479i
$585$	−6.68651e8	+	1.61427e9i	−0.000236047	+	0.000569867i
$586$	9.26610e11	−	9.26610e11i	0.324607	−	0.324607i
$587$	2.62755e12	−	2.62755e12i	0.913439	−	0.913439i	−0.0831023	−	0.996541i	$-0.526483\pi$
$587$	2.62755e12	−	2.62755e12i	0.913439	−	0.913439i	0.996541	+	0.0831023i	$0.0264828\pi$
$588$	−5.59103e11	+	1.34979e12i	−0.192883	+	0.465661i
$589$	−2.10221e12	−	8.70764e11i	−0.719710	−	0.298114i
$590$	−9.70873e11	−	2.34389e12i	−0.329859	−	0.796350i
$591$		−	3.88384e12i		−	1.30954i
$592$	2.58979e10	−	1.07272e10i	0.00866595	−	0.00358955i
$593$	−1.99919e11	−	1.99919e11i	−0.0663910	−	0.0663910i	0.673132	−	0.739523i	$-0.264949\pi$
$593$	−1.99919e11	−	1.99919e11i	−0.0663910	−	0.0663910i	−0.739523	+	0.673132i	$0.764949\pi$
$594$	−3.44777e12			−1.13632
$595$	−1.04936e12	+	4.25730e11i	−0.343240	+	0.139254i
$596$	4.52553e11			0.146913
$597$	3.73551e12	+	3.73551e12i	1.20355	+	1.20355i
$598$	2.32637e11	−	9.63615e10i	0.0743916	−	0.0308140i
$599$		−	5.50565e12i		−	1.74738i	−0.486482	−	0.873691i	$-0.661720\pi$
$599$		−	5.50565e12i		−	1.74738i	0.486482	−	0.873691i	$-0.338280\pi$
$600$	2.64424e11	+	6.38376e11i	0.0832953	+	0.201093i
$601$	1.42529e12	+	5.90373e11i	0.445622	+	0.184583i	0.594199	−	0.804318i	$-0.297469\pi$
$601$	1.42529e12	+	5.90373e11i	0.445622	+	0.184583i	−0.148577	+	0.988901i	$0.547469\pi$
$602$	−1.18654e11	+	2.86457e11i	−0.0368213	+	0.0888945i
$603$	8.02104e9	−	8.02104e9i	0.00247060	−	0.00247060i
$604$	−1.72168e12	+	1.72168e12i	−0.526364	+	0.526364i
$605$	2.77065e12	−	6.68894e12i	0.840780	−	2.02982i
$606$	1.96680e12	+	8.14673e11i	0.592424	+	0.245390i
$607$	1.37442e12	+	3.31815e12i	0.410933	+	0.992079i	0.984888	+	0.173192i	$0.0554083\pi$
$607$	1.37442e12	+	3.31815e12i	0.410933	+	0.992079i	−0.573955	+	0.818887i	$0.694592\pi$
$608$			4.43767e12i			1.31701i
$609$	6.07505e11	−	2.51637e11i	0.178967	−	0.0741304i
$610$	−1.37568e12	−	1.37568e12i	−0.402284	−	0.402284i
$611$	1.56688e11			0.0454830
$612$	8.19859e9	+	3.46615e9i	0.00236242	+	0.000998771i
$613$	5.79969e12			1.65895			0.829474	−	0.558546i	$-0.188641\pi$
$613$	5.79969e12			1.65895			0.829474	+	0.558546i	$0.188641\pi$
$614$	−1.31649e12	−	1.31649e12i	−0.373818	−	0.373818i
$615$	−5.84095e12	+	2.41940e12i	−1.64644	+	0.681977i
$616$		−	2.14732e12i		−	0.600873i
$617$	1.96784e12	+	4.75079e12i	0.546647	+	1.31972i	0.919958	+	0.392017i	$0.128222\pi$
$617$	1.96784e12	+	4.75079e12i	0.546647	+	1.31972i	−0.373311	+	0.927706i	$0.621778\pi$
$618$	2.15118e12	+	8.91049e11i	0.593238	+	0.245727i
$619$	−6.35351e10	+	1.53387e11i	−0.0173943	+	0.0419934i	−0.932338	−	0.361588i	$-0.882235\pi$
$619$	−6.35351e10	+	1.53387e11i	−0.0173943	+	0.0419934i	0.914944	+	0.403581i	$0.132235\pi$
$620$	9.19916e11	−	9.19916e11i	0.250026	−	0.250026i
$621$	−2.58142e12	+	2.58142e12i	−0.696541	+	0.696541i
$622$	7.04379e11	−	1.70052e12i	0.188690	−	0.455539i
$623$	5.60599e11	+	2.32208e11i	0.149093	+	0.0617561i
$624$	2.00144e10	+	4.83189e10i	0.00528459	+	0.0127581i
$625$			4.44895e12i			1.16627i
$626$	6.77347e11	−	2.80566e11i	0.176290	−	0.0730216i
$627$	−6.52770e12	−	6.52770e12i	−1.68677	−	1.68677i
$628$	2.37620e12			0.609627
$629$	−2.35973e11	+	2.32560e11i	−0.0601083	+	0.0592389i
$630$	−4.35741e9			−0.00110204
$631$	1.51720e12	+	1.51720e12i	0.380986	+	0.380986i	0.871457	−	0.490471i	$-0.163175\pi$
$631$	1.51720e12	+	1.51720e12i	0.380986	+	0.380986i	−0.490471	+	0.871457i	$0.663175\pi$
$632$	−1.80782e12	+	7.48822e11i	−0.450741	+	0.186703i
$633$			5.18382e11i			0.128331i
$634$	1.67513e12	+	4.04411e12i	0.411761	+	0.994080i
$635$	−2.32641e12	−	9.63631e11i	−0.567812	−	0.235195i
$636$	8.47831e11	−	2.04685e12i	0.205472	−	0.496053i
$637$	3.22978e11	−	3.22978e11i	0.0777222	−	0.0777222i
$638$	1.93492e12	−	1.93492e12i	0.462350	−	0.462350i
$639$	−1.19431e10	+	2.88331e10i	−0.00283376	+	0.00684129i
$640$	−2.02860e12	−	8.40272e11i	−0.477953	−	0.197975i
$641$	−2.43313e11	−	5.87409e11i	−0.0569251	−	0.137429i	0.892858	−	0.450338i	$-0.148697\pi$
$641$	−2.43313e11	−	5.87409e11i	−0.0569251	−	0.137429i	−0.949783	+	0.312909i	$0.898697\pi$
$642$			2.45870e12i			0.571213i
$643$	−4.03076e12	+	1.66959e12i	−0.929902	+	0.385178i	−0.795641	−	0.605768i	$-0.792866\pi$
$643$	−4.03076e12	+	1.66959e12i	−0.929902	+	0.385178i	−0.134261	+	0.990946i	$0.542866\pi$
$644$	−5.81856e11	−	5.81856e11i	−0.133300	−	0.133300i
$645$	−2.10585e12			−0.479081
$646$	1.50518e12	+	3.71004e12i	0.340050	+	0.838170i
$647$	5.37030e12			1.20484			0.602419	−	0.798180i	$-0.294204\pi$
$647$	5.37030e12			1.20484			0.602419	+	0.798180i	$0.294204\pi$
$648$	−3.28699e12	−	3.28699e12i	−0.732336	−	0.732336i
$649$	−8.60737e12	+	3.56529e12i	−1.90445	+	0.788848i
$650$		−	7.81798e10i		−	0.0171785i
$651$	3.35269e11	+	8.09410e11i	0.0731608	+	0.176626i
$652$	2.47858e12	+	1.02666e12i	0.537142	+	0.222492i
$653$	−7.31072e11	+	1.76496e12i	−0.157344	+	0.379862i	−0.982818	−	0.184578i	$-0.940908\pi$
$653$	−7.31072e11	+	1.76496e12i	−0.157344	+	0.379862i	0.825474	+	0.564441i	$0.190908\pi$
$654$	1.67881e12	−	1.67881e12i	0.358841	−	0.358841i
$655$	5.32720e12	−	5.32720e12i	1.13087	−	1.13087i
$656$	−3.26019e11	+	7.87079e11i	−0.0687346	+	0.165940i
$657$	2.07076e10	+	8.57736e9i	0.00433596	+	0.00179601i
$658$	1.49535e11	+	3.61009e11i	0.0310976	+	0.0750762i
$659$			4.74561e11i			0.0980184i	0.998798	+	0.0490092i	$0.0156064\pi$
$659$			4.74561e11i			0.0980184i	−0.998798	+	0.0490092i	$0.984394\pi$
$660$	4.87633e12	−	2.01984e12i	1.00033	−	0.414352i
$661$	4.66928e12	+	4.66928e12i	0.951356	+	0.951356i	0.998871	−	0.0475145i	$-0.0151300\pi$
$661$	4.66928e12	+	4.66928e12i	0.951356	+	0.951356i	−0.0475145	+	0.998871i	$0.515130\pi$
$662$	4.57186e11			0.0925192
$663$	−4.33899e11	−	4.40267e11i	−0.0872123	−	0.0884922i
$664$	9.39915e12			1.87643
$665$	1.81606e12	+	1.81606e12i	0.360108	+	0.360108i
$666$	−1.17779e9	+	4.87858e8i	−0.000231972	+	9.60857e-5i
$667$		−	2.89744e12i		−	0.566825i
$668$	1.19580e12	+	2.88692e12i	0.232362	+	0.560971i
$669$	1.64334e12	+	6.80696e11i	0.317184	+	0.131382i
$670$	−1.11636e12	+	2.69514e12i	−0.214027	+	0.516708i
$671$	−5.05184e12	+	5.05184e12i	−0.962051	+	0.962051i
$672$	1.20818e12	−	1.20818e12i	0.228545	−	0.228545i
$673$	1.05048e12	−	2.53609e12i	0.197388	−	0.476537i	−0.793932	−	0.608006i	$-0.791969\pi$
$673$	1.05048e12	−	2.53609e12i	0.197388	−	0.476537i	0.991320	+	0.131469i	$0.0419695\pi$
$674$	−5.87974e12	−	2.43547e12i	−1.09746	−	0.454583i
$675$	4.33755e11	+	1.04718e12i	0.0804225	+	0.194157i
$676$		−	3.03214e12i		−	0.558455i
$677$	−1.06996e12	+	4.43192e11i	−0.195758	+	0.0810855i	−0.478409	−	0.878137i	$-0.658786\pi$
$677$	−1.06996e12	+	4.43192e11i	−0.195758	+	0.0810855i	0.282651	+	0.959223i	$0.408786\pi$
$678$	−2.03523e12	−	2.03523e12i	−0.369897	−	0.369897i
$679$	5.60696e11			0.101231
$680$	−6.32498e12	−	4.60735e10i	−1.13441	−	0.00826345i
$681$	−6.22527e12			−1.10917
$682$	2.57800e12	+	2.57800e12i	0.456302	+	0.456302i
$683$	−5.65216e12	+	2.34120e12i	−0.993852	+	0.411667i	−0.819539	−	0.573023i	$-0.805770\pi$
$683$	−5.65216e12	+	2.34120e12i	−0.993852	+	0.411667i	−0.174313	+	0.984690i	$0.555770\pi$
$684$		−	2.01874e10i		−	0.00352637i
$685$	1.82680e12	+	4.41027e12i	0.317017	+	0.765346i
$686$	2.23927e12	+	9.27535e11i	0.386054	+	0.159909i
$687$	3.59247e12	−	8.67300e12i	0.615302	−	1.48547i
$688$	−2.00654e11	+	2.00654e11i	−0.0341428	+	0.0341428i
$689$	−4.89768e11	+	4.89768e11i	−0.0827949	+	0.0827949i
$690$	−1.63213e12	+	3.94032e12i	−0.274116	+	0.661775i
$691$	2.20254e12	+	9.12323e11i	0.367513	+	0.152229i	0.558794	−	0.829306i	$-0.311264\pi$
$691$	2.20254e12	+	9.12323e11i	0.367513	+	0.152229i	−0.191281	+	0.981535i	$0.561264\pi$
$692$	1.83802e12	+	4.43737e12i	0.304700	+	0.735610i
$693$			1.60015e10i			0.00263549i
$694$	−1.80645e12	+	7.48257e11i	−0.295603	+	0.122443i
$695$	−3.06734e11	−	3.06734e11i	−0.0498690	−	0.0498690i
$696$	3.67277e12			0.593270
$697$	7.33453e10	−	1.00689e13i	0.0117713	−	1.61597i
$698$	2.83579e12			0.452194
$699$	−6.19150e12	−	6.19150e12i	−0.980954	−	0.980954i
$700$	−2.36035e11	+	9.77689e10i	−0.0371565	+	0.0153907i
$701$		−	3.30170e12i		−	0.516424i	−0.966088	−	0.258212i	$-0.916867\pi$
$701$		−	3.30170e12i		−	0.516424i	0.966088	−	0.258212i	$-0.0831334\pi$
$702$	2.00367e11	+	4.83728e11i	0.0311393	+	0.0751769i
$703$	6.94201e11	+	2.87548e11i	0.107198	+	0.0444028i
$704$	3.20090e12	−	7.72766e12i	0.491129	−	1.18569i
$705$	−1.87660e12	+	1.87660e12i	−0.286102	+	0.286102i
$706$	5.48156e11	−	5.48156e11i	0.0830391	−	0.0830391i
$707$	−8.32310e11	+	2.00937e12i	−0.125285	+	0.302464i
$708$	−4.18103e12	−	1.73184e12i	−0.625365	−	0.259035i
$709$	−2.48788e12	−	6.00628e12i	−0.369762	−	0.892684i	−0.993789	−	0.111281i	$-0.964505\pi$
$709$	−2.48788e12	−	6.00628e12i	−0.369762	−	0.892684i	0.624027	−	0.781403i	$-0.285495\pi$
$710$		−	8.02597e12i		−	1.18532i
$711$	1.34716e10	−	5.58011e9i	0.00197699	−	0.000818897i
$712$	2.39652e12	+	2.39652e12i	0.349479	+	0.349479i
$713$	3.86041e12			0.559411
$714$	6.00286e11	−	1.41988e12i	0.0864403	−	0.204460i
$715$	−1.65011e12			−0.236122
$716$	−2.47544e12	−	2.47544e12i	−0.352002	−	0.352002i
$717$	−8.86985e12	+	3.67401e12i	−1.25337	+	0.519164i
$718$		−	9.15875e12i		−	1.28610i
$719$	−9.07004e11	−	2.18970e12i	−0.126570	−	0.305566i	0.847874	−	0.530197i	$-0.177882\pi$
$719$	−9.07004e11	−	2.18970e12i	−0.126570	−	0.305566i	−0.974444	+	0.224631i	$0.927882\pi$
$720$	−3.68436e9	−	1.52611e9i	−0.000510935	−	0.000211636i
$721$	−9.10340e11	+	2.19775e12i	−0.125457	+	0.302880i
$722$	3.02400e12	−	3.02400e12i	0.414157	−	0.414157i
$723$	6.16638e12	−	6.16638e12i	0.839283	−	0.839283i
$724$	−2.28344e12	+	5.51270e12i	−0.308863	+	0.745660i
$725$	−8.31115e11	−	3.44259e11i	−0.111722	−	0.0462769i
$726$	3.77163e12	+	9.10551e12i	0.503865	+	1.21644i
$727$			6.84668e12i			0.909023i	0.890741	+	0.454512i	$0.150186\pi$
$727$			6.84668e12i			0.909023i	−0.890741	+	0.454512i	$0.849814\pi$
$728$	−3.01273e11	+	1.24791e11i	−0.0397529	+	0.0164662i
$729$	−5.36751e12	−	5.36751e12i	−0.703880	−	0.703880i
$730$	−5.76414e12			−0.751246
$731$	1.30602e12	−	3.08917e12i	0.169169	−	0.400142i
$732$	−3.47039e12			−0.446764
$733$	8.62793e12	+	8.62793e12i	1.10392	+	1.10392i	0.993933	+	0.109991i	$0.0350821\pi$
$733$	8.62793e12	+	8.62793e12i	1.10392	+	1.10392i	0.109991	+	0.993933i	$0.464918\pi$
$734$	−7.70230e12	+	3.19040e12i	−0.979463	+	0.405707i
$735$			7.73641e12i			0.977792i
$736$	−2.88116e12	−	6.95574e12i	−0.361924	−	0.873762i
$737$	9.89724e12	+	4.09957e12i	1.23569	+	0.511841i
$738$	1.48268e10	−	3.57951e10i	0.00183990	−	0.00444191i
$739$	−4.53771e12	+	4.53771e12i	−0.559676	+	0.559676i	−0.929215	−	0.369539i	$-0.879516\pi$
$739$	−4.53771e12	+	4.53771e12i	−0.559676	+	0.559676i	0.369539	+	0.929215i	$0.379516\pi$
$740$	−3.03779e11	+	3.03779e11i	−0.0372404	+	0.0372404i
$741$	−5.36492e11	+	1.29521e12i	−0.0653704	+	0.157818i
$742$	−1.59584e12	−	6.61018e11i	−0.193273	−	0.0800563i
$743$	7.16314e10	+	1.72933e11i	0.00862291	+	0.0208175i	0.928132	−	0.372250i	$-0.121414\pi$
$743$	7.16314e10	+	1.72933e11i	0.00862291	+	0.0208175i	−0.919509	+	0.393068i	$0.871414\pi$
$744$			4.89342e12i			0.585510i
$745$	2.21397e12	−	9.17056e11i	0.263311	−	0.109067i
$746$	−2.11387e11	−	2.11387e11i	−0.0249893	−	0.0249893i
$747$	−7.00411e10			−0.00823019
$748$	−6.12324e10	+	8.40600e12i	−0.00715195	+	0.981821i
$749$	−2.51193e12			−0.291635
$750$	−3.50900e12	−	3.50900e12i	−0.404956	−	0.404956i
$751$	1.36617e13	−	5.65886e12i	1.56720	−	0.649156i	0.580880	−	0.813989i	$-0.302709\pi$
$751$	1.36617e13	−	5.65886e12i	1.56720	−	0.649156i	0.986321	+	0.164834i	$0.0527087\pi$
$752$			3.57620e11i			0.0407795i
$753$	4.69593e12	+	1.13370e13i	0.532285	+	1.28505i
$754$	−3.83921e11	−	1.59025e11i	−0.0432585	−	0.0179183i
$755$	−4.93394e12	+	1.19116e13i	−0.552628	+	1.33416i
$756$	1.20987e12	−	1.20987e12i	0.134707	−	0.134707i
$757$	1.00156e13	−	1.00156e13i	1.10853	−	1.10853i	0.115185	−	0.993344i	$-0.463254\pi$
$757$	1.00156e13	−	1.00156e13i	1.10853	−	1.10853i	0.993344	−	0.115185i	$-0.0367461\pi$
$758$	1.26675e11	−	3.05820e11i	0.0139373	−	0.0336477i
$759$	1.44698e13	+	5.99360e12i	1.58261	+	0.655541i
$760$

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)

\(f(q)\)	\(=\)	\(q+(-10.5264 - 10.5264i) q^{2} +(-129.909 + 53.8103i) q^{3} -290.392i q^{4} +(-588.452 - 1420.65i) q^{5} +(1933.90 + 801.047i) q^{6} +(-818.389 + 1975.77i) q^{7} +(-8446.26 + 8446.26i) q^{8} +(62.9403 - 62.9403i) q^{9} +O(q^{10})\)	\(q+(-10.5264 - 10.5264i) q^{2} +(-129.909 + 53.8103i) q^{3} -290.392i q^{4} +(-588.452 - 1420.65i) q^{5} +(1933.90 + 801.047i) q^{6} +(-818.389 + 1975.77i) q^{7} +(-8446.26 + 8446.26i) q^{8} +(62.9403 - 62.9403i) q^{9} +(-8760.00 + 21148.5i) q^{10} +(77662.6 + 32168.9i) q^{11} +(15626.1 + 37724.6i) q^{12} -12765.7i q^{13} +(29412.3 - 12183.0i) q^{14} +(152891. + 152891. i) q^{15} +29136.1 q^{16} +(-319104. + 129462. i) q^{17} -1325.06 q^{18} +(552253. + 552253. i) q^{19} +(-412545. + 170882. i) q^{20} -300708. i q^{21} +(-478883. - 1.15613e6i) q^{22} +(-1.22417e6 - 507067. i) q^{23} +(642754. - 1.55174e6i) q^{24} +(-290899. + 290899. i) q^{25} +(-134376. + 134376. i) q^{26} +(1.05436e6 - 2.54544e6i) q^{27} +(573746. + 237653. i) q^{28} +(836814. + 2.02025e6i) q^{29} -3.21877e6i q^{30} +(-2.69168e6 + 1.11493e6i) q^{31} +(4.01779e6 + 4.01779e6i) q^{32} -1.18201e7 q^{33} +(4.72177e6 + 1.99624e6i) q^{34} +3.28845e6 q^{35} +(-18277.3 - 18277.3i) q^{36} +(888857. - 368177. i) q^{37} -1.16264e7i q^{38} +(686926. + 1.65839e6i) q^{39} +(1.69694e7 + 7.02895e6i) q^{40} +(-1.11895e7 + 2.70139e7i) q^{41} +(-3.16536e6 + 3.16536e6i) q^{42} +(-6.88677e6 + 6.88677e6i) q^{43} +(9.34158e6 - 2.25526e7i) q^{44} +(-126453. - 52378.7i) q^{45} +(7.54846e6 + 1.82236e7i) q^{46} +1.22741e7i q^{47} +(-3.78506e6 + 1.56782e6i) q^{48} +(2.53004e7 + 2.53004e7i) q^{49} +6.12420e6 q^{50} +(3.44882e7 - 3.39894e7i) q^{51} -3.70706e6 q^{52} +(-3.83659e7 - 3.83659e7i) q^{53} +(-3.78928e7 + 1.56957e7i) q^{54} -1.29261e8i q^{55} +(-9.77551e6 - 2.36002e7i) q^{56} +(-1.01460e8 - 4.20260e7i) q^{57} +(1.24572e7 - 3.00744e7i) q^{58} +(-7.83688e7 + 7.83688e7i) q^{59} +(4.43983e7 - 4.43983e7i) q^{60} +(-3.25243e7 + 7.85206e7i) q^{61} +(4.00697e7 + 1.65974e7i) q^{62} +(72845.6 + 175865. i) q^{63} -9.95030e7i q^{64} +(-1.81356e7 + 7.51200e6i) q^{65} +(1.24423e8 + 1.24423e8i) q^{66} +1.27439e8 q^{67} +(3.75947e7 + 9.26652e7i) q^{68} +1.86317e8 q^{69} +(-3.46154e7 - 3.46154e7i) q^{70} +(-3.23928e8 + 1.34175e8i) q^{71} +1.06322e6i q^{72} +(9.63630e7 + 2.32641e8i) q^{73} +(-1.32320e7 - 5.48087e6i) q^{74} +(2.21371e7 - 5.34438e7i) q^{75} +(1.60370e8 - 1.60370e8i) q^{76} +(-1.27116e8 + 1.27116e8i) q^{77} +(1.02259e7 - 2.46876e7i) q^{78} +(1.51347e8 + 6.26901e7i) q^{79} +(-1.71452e7 - 4.13922e7i) q^{80} +3.89165e8i q^{81} +(4.02142e8 - 1.66573e8i) q^{82} +(-5.56409e8 - 5.56409e8i) q^{83} -8.73232e7 q^{84} +(3.71698e8 + 3.77153e8i) q^{85} +1.44985e8 q^{86} +(-2.17420e8 - 2.17420e8i) q^{87} +(-9.27665e8 + 3.84252e8i) q^{88} -2.83737e8i q^{89} +(779736. + 1.88245e6i) q^{90} +(2.52221e7 + 1.04473e7i) q^{91} +(-1.47248e8 + 3.55488e8i) q^{92} +(2.89680e8 - 2.89680e8i) q^{93} +(1.29202e8 - 1.29202e8i) q^{94} +(4.59583e8 - 1.10953e9i) q^{95} +(-7.38147e8 - 3.05750e8i) q^{96} +(-1.00334e8 - 2.42227e8i) q^{97} -5.32642e8i q^{98} +(6.91282e6 - 2.86339e6i) 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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