LMFDB - Embedded newform 54.9.f.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	54.11
Dual form			54.9.f.a.5.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.27231 - 8.66680i) q^{2} +(30.8906 + 74.8784i) q^{3} +(-22.2270 - 126.055i) q^{4} +(187.067 - 513.962i) q^{5} +(873.602 + 276.817i) q^{6} +(-775.415 + 4397.60i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-4652.55 + 4626.07i) q^{9} +O(q^{10})$	\(q+(7.27231 - 8.66680i) q^{2} +(30.8906 + 74.8784i) q^{3} +(-22.2270 - 126.055i) q^{4} +(187.067 - 513.962i) q^{5} +(873.602 + 276.817i) q^{6} +(-775.415 + 4397.60i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-4652.55 + 4626.07i) q^{9} +(-3094.00 - 5358.96i) q^{10} +(-1403.39 - 3855.78i) q^{11} +(8752.22 - 5558.24i) q^{12} +(-14818.3 + 12434.0i) q^{13} +(32474.0 + 38701.1i) q^{14} +(44263.2 - 1869.31i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(89772.3 - 51830.0i) q^{17} +(6258.48 + 73964.9i) q^{18} +(-117491. + 203501. i) q^{19} +(-68945.6 - 12157.0i) q^{20} +(-353238. + 77782.4i) q^{21} +(-43623.1 - 15877.5i) q^{22} +(-139319. + 24565.7i) q^{23} +(15476.7 - 116275. i) q^{24} +(70073.2 + 58798.4i) q^{25} +218852. i q^{26} +(-490112. - 205473. i) q^{27} +571576. q^{28} +(-366403. + 436662. i) q^{29} +(305695. - 397215. i) q^{30} +(271967. + 1.54240e6i) q^{31} +(-63398.2 + 174185. i) q^{32} +(245363. - 224191. i) q^{33} +(203651. - 1.15496e6i) q^{34} +(2.11514e6 + 1.22118e6i) q^{35} +(686553. + 483655. i) q^{36} +(1.12829e6 + 1.95426e6i) q^{37} +(909268. + 2.49819e6i) q^{38} +(-1.38879e6 - 725477. i) q^{39} +(-606756. + 509129. i) q^{40} +(-3.31466e6 - 3.95026e6i) q^{41} +(-1.89473e6 + 3.62710e6i) q^{42} +(2.41971e6 - 880704. i) q^{43} +(-454848. + 262607. i) q^{44} +(1.50729e6 + 3.25662e6i) q^{45} +(-800264. + 1.38610e6i) q^{46} +(6.74662e6 + 1.18961e6i) q^{47} +(-895182. - 979722. i) q^{48} +(-1.33204e7 - 4.84825e6i) q^{49} +(1.01919e6 - 179710. i) q^{50} +(6.65406e6 + 5.12094e6i) q^{51} +(1.89674e6 + 1.59156e6i) q^{52} -9.71432e6i q^{53} +(-5.34505e6 + 2.75344e6i) q^{54} -2.24425e6 q^{55} +(4.15668e6 - 4.95374e6i) q^{56} +(-1.88672e7 - 2.51130e6i) q^{57} +(1.11987e6 + 6.35109e6i) q^{58} +(-2.73166e6 + 7.50518e6i) q^{59} +(-1.21947e6 - 5.53807e6i) q^{60} +(-374503. + 2.12391e6i) q^{61} +(1.53455e7 + 8.85975e6i) q^{62} +(-1.67359e7 - 2.40471e7i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(3.61861e6 + 9.94204e6i) q^{65} +(-158660. - 3.75690e6i) q^{66} +(8.75836e6 - 7.34913e6i) q^{67} +(-8.52882e6 - 1.01643e7i) q^{68} +(-6.14307e6 - 9.67312e6i) q^{69} +(2.59657e7 - 9.45074e6i) q^{70} +(5.23232e6 - 3.02088e6i) q^{71} +(9.18457e6 - 2.43293e6i) q^{72} +(1.90181e7 - 3.29404e7i) q^{73} +(2.51424e7 + 4.43329e6i) q^{74} +(-2.23813e6 + 7.06328e6i) q^{75} +(2.82638e7 + 1.02872e7i) q^{76} +(1.80444e7 - 3.18171e6i) q^{77} +(-1.63872e7 + 6.76045e6i) q^{78} +(-1.72779e7 - 1.44979e7i) q^{79} +8.96118e6i q^{80} +(245661. - 4.30460e7i) q^{81} -5.83413e7 q^{82} +(3.02233e6 - 3.60187e6i) q^{83} +(1.76563e7 + 4.27987e7i) q^{84} +(-9.84525e6 - 5.58352e7i) q^{85} +(9.96403e6 - 2.73759e7i) q^{86} +(-4.40150e7 - 1.39469e7i) q^{87} +(-1.03184e6 + 5.85184e6i) q^{88} +(-7.31545e6 - 4.22358e6i) q^{89} +(3.91859e7 + 1.06198e7i) q^{90} +(-4.31895e7 - 7.48065e7i) q^{91} +(6.19327e6 + 1.70159e7i) q^{92} +(-1.07091e8 + 6.80101e7i) q^{93} +(5.93736e7 - 4.98204e7i) q^{94} +(8.26129e7 + 9.84543e7i) q^{95} +(-1.50011e7 + 633520. i) q^{96} +(5.35437e7 - 1.94883e7i) q^{97} +(-1.38889e8 + 8.01878e7i) q^{98} +(2.43664e7 + 1.14470e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$3$	30.8906	+	74.8784i	0.381365	+	0.924425i
$3$	30.8906	+	74.8784i	0.381365	+	0.924425i
$4$	−22.2270	−	126.055i	−0.0868241	−	0.492404i
$5$	187.067	−	513.962i	0.299307	−	0.822339i	−0.695309	−	0.718711i	$-0.744733\pi$
$5$	187.067	−	513.962i	0.299307	−	0.822339i	0.994616	−	0.103628i	$-0.0330453\pi$
$6$	873.602	+	276.817i	0.674076	+	0.213593i
$7$	−775.415	+	4397.60i	−0.322955	+	1.83157i	0.200717	+	0.979649i	$0.435673\pi$
$7$	−775.415	+	4397.60i	−0.322955	+	1.83157i	−0.523672	+	0.851920i	$0.675438\pi$
$8$	−1254.14	−	724.077i	−0.306186	−	0.176777i
$9$	−4652.55	+	4626.07i	−0.709122	+	0.705086i
$10$	−3094.00	−	5358.96i	−0.309400	−	0.535896i
$11$	−1403.39	−	3855.78i	−0.0958533	−	0.263355i	0.882494	−	0.470323i	$-0.155863\pi$
$11$	−1403.39	−	3855.78i	−0.0958533	−	0.263355i	−0.978348	+	0.206968i	$0.933640\pi$
$12$	8752.22	−	5558.24i	0.422079	−	0.268048i
$13$	−14818.3	+	12434.0i	−0.518830	+	0.435350i	−0.864224	−	0.503108i	$-0.832190\pi$
$13$	−14818.3	+	12434.0i	−0.518830	+	0.435350i	0.345394	+	0.938458i	$0.387745\pi$
$14$	32474.0	+	38701.1i	0.845326	+	1.00742i
$15$	44263.2	−	1869.31i	0.874336	−	0.0369246i
$16$	−15395.9	+	5603.66i	−0.234923	+	0.0855050i
$17$	89772.3	−	51830.0i	1.07485	−	0.620563i	0.145345	−	0.989381i	$-0.453571\pi$
$17$	89772.3	−	51830.0i	1.07485	−	0.620563i	0.929502	+	0.368818i	$0.120237\pi$
$18$	6258.48	+	73964.9i	0.0596182	+	0.704589i
$19$	−117491.	+	203501.i	−0.901552	+	1.56153i	−0.0760730	+	0.997102i	$0.524238\pi$
$19$	−117491.	+	203501.i	−0.901552	+	1.56153i	−0.825479	+	0.564432i	$0.809095\pi$
$20$	−68945.6	−	12157.0i	−0.430910	−	0.0759811i
$21$	−353238.	+	77782.4i	−1.81631	+	0.399949i
$22$	−43623.1	−	15877.5i	−0.186220	−	0.0677785i
$23$	−139319.	+	24565.7i	−0.497850	+	0.0877844i	−0.416934	−	0.908937i	$-0.636895\pi$
$23$	−139319.	+	24565.7i	−0.497850	+	0.0877844i	−0.0809155	+	0.996721i	$0.525784\pi$
$24$	15476.7	−	116275.i	0.0466480	−	0.350462i
$25$	70073.2	+	58798.4i	0.179387	+	0.150524i
$26$			218852.i			0.478912i
$27$	−490112.	−	205473.i	−0.922233	−	0.386634i
$28$	571576.			0.929912
$29$	−366403.	+	436662.i	−0.518045	+	0.617382i	−0.960117	−	0.279598i	$-0.909799\pi$
$29$	−366403.	+	436662.i	−0.518045	+	0.617382i	0.442073	+	0.896979i	$0.354243\pi$
$30$	305695.	−	397215.i	0.377401	−	0.490389i
$31$	271967.	+	1.54240e6i	0.294489	+	1.67013i	0.669270	+	0.743019i	$0.266607\pi$
$31$	271967.	+	1.54240e6i	0.294489	+	1.67013i	−0.374781	+	0.927113i	$0.622282\pi$
$32$	−63398.2	+	174185.i	−0.0604612	+	0.166116i
$33$	245363.	−	224191.i	0.206896	−	0.189043i
$34$	203651.	−	1.15496e6i	0.152395	−	0.864276i
$35$	2.11514e6	+	1.22118e6i	1.40951	+	0.813780i
$36$	686553.	+	483655.i	0.408756	+	0.287956i
$37$	1.12829e6	+	1.95426e6i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$37$	1.12829e6	+	1.95426e6i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$38$	909268.	+	2.49819e6i	0.436071	+	1.19810i
$39$	−1.38879e6	−	725477.i	−0.600312	−	0.313592i
$40$	−606756.	+	509129.i	−0.237014	+	0.198878i
$41$	−3.31466e6	−	3.95026e6i	−1.17301	−	1.39794i	−0.899975	−	0.435942i	$-0.856415\pi$
$41$	−3.31466e6	−	3.95026e6i	−1.17301	−	1.39794i	−0.273040	−	0.962003i	$-0.588029\pi$
$42$	−1.89473e6	+	3.62710e6i	−0.608906	+	1.16564i
$43$	2.41971e6	−	880704.i	0.707767	−	0.257606i	0.0370436	−	0.999314i	$-0.488206\pi$
$43$	2.41971e6	−	880704.i	0.707767	−	0.257606i	0.670723	+	0.741707i	$0.265984\pi$
$44$	−454848.	+	262607.i	−0.121355	+	0.0700641i
$45$	1.50729e6	+	3.25662e6i	0.367575	+	0.794176i
$46$	−800264.	+	1.38610e6i	−0.178732	+	0.309573i
$47$	6.74662e6	+	1.18961e6i	1.38259	+	0.243789i	0.814972	−	0.579500i	$-0.196752\pi$
$47$	6.74662e6	+	1.18961e6i	1.38259	+	0.243789i	0.567622	+	0.823289i	$0.307863\pi$
$48$	−895182.	−	979722.i	−0.168634	−	0.184560i
$49$	−1.33204e7	−	4.84825e6i	−2.31065	−	0.841009i
$50$	1.01919e6	−	179710.i	0.163070	−	0.0287537i
$51$	6.65406e6	+	5.12094e6i	0.983572	+	0.756954i
$52$	1.89674e6	+	1.59156e6i	0.259415	+	0.217675i
$53$		−	9.71432e6i		−	1.23114i	−0.788080	−	0.615572i	$-0.788925\pi$
$53$		−	9.71432e6i		−	1.23114i	0.788080	−	0.615572i	$-0.211075\pi$
$54$	−5.34505e6	+	2.75344e6i	−0.628603	+	0.323818i
$55$	−2.24425e6			−0.245256
$56$	4.15668e6	−	4.95374e6i	0.422663	−	0.503710i
$57$	−1.88672e7	−	2.51130e6i	−1.78734	−	0.237903i
$58$	1.11987e6	+	6.35109e6i	0.0989589	+	0.561224i
$59$	−2.73166e6	+	7.50518e6i	−0.225434	+	0.619374i	−0.999913	−	0.0132257i	$-0.995790\pi$
$59$	−2.73166e6	+	7.50518e6i	−0.225434	+	0.619374i	0.774479	+	0.632600i	$0.218012\pi$
$60$	−1.21947e6	−	5.53807e6i	−0.0940952	−	0.427320i
$61$	−374503.	+	2.12391e6i	−0.0270480	+	0.153397i	−0.995341	−	0.0964223i	$-0.969260\pi$
$61$	−374503.	+	2.12391e6i	−0.0270480	+	0.153397i	0.968292	+	0.249819i	$0.0803712\pi$
$62$	1.53455e7	+	8.85975e6i	1.03852	+	0.599590i
$63$	−1.67359e7	−	2.40471e7i	−1.06240	−	1.52652i
$64$	1.04858e6	+	1.81619e6i	0.0625000	+	0.108253i
$65$	3.61861e6	+	9.94204e6i	0.202716	+	0.556958i
$66$	−158660.	−	3.75690e6i	−0.00836163	−	0.197995i
$67$	8.75836e6	−	7.34913e6i	0.434634	−	0.364701i	−0.399063	−	0.916923i	$-0.630665\pi$
$67$	8.75836e6	−	7.34913e6i	0.434634	−	0.364701i	0.833697	+	0.552223i	$0.186220\pi$
$68$	−8.52882e6	−	1.01643e7i	−0.398890	−	0.475379i
$69$	−6.14307e6	−	9.67312e6i	−0.271012	−	0.426747i
$70$	2.59657e7	−	9.45074e6i	1.08145	−	0.393617i
$71$	5.23232e6	−	3.02088e6i	0.205902	−	0.118878i	−0.393503	−	0.919323i	$-0.628737\pi$
$71$	5.23232e6	−	3.02088e6i	0.205902	−	0.118878i	0.599405	+	0.800446i	$0.295404\pi$
$72$	9.18457e6	−	2.43293e6i	0.341766	−	0.0905315i
$73$	1.90181e7	−	3.29404e7i	0.669694	−	1.15994i	−0.308296	−	0.951291i	$-0.599759\pi$
$73$	1.90181e7	−	3.29404e7i	0.669694	−	1.15994i	0.977990	−	0.208654i	$-0.0669081\pi$
$74$	2.51424e7	+	4.43329e6i	0.838457	+	0.147843i
$75$	−2.23813e6	+	7.06328e6i	−0.0707359	+	0.223235i
$76$	2.82638e7	+	1.02872e7i	0.847182	+	0.308349i
$77$	1.80444e7	−	3.18171e6i	0.513309	−	0.0905102i
$78$	−1.63872e7	+	6.76045e6i	−0.442718	+	0.182640i
$79$	−1.72779e7	−	1.44979e7i	−0.443591	−	0.372217i	0.393460	−	0.919342i	$-0.371278\pi$
$79$	−1.72779e7	−	1.44979e7i	−0.443591	−	0.372217i	−0.837051	+	0.547125i	$0.815722\pi$
$80$			8.96118e6i			0.218779i
$81$	245661.	−	4.30460e7i	0.00570686	−	0.999984i
$82$	−5.83413e7			−1.29039
$83$	3.02233e6	−	3.60187e6i	0.0636838	−	0.0758954i	−0.733262	−	0.679946i	$-0.762003\pi$
$83$	3.02233e6	−	3.60187e6i	0.0636838	−	0.0758954i	0.796946	+	0.604051i	$0.206448\pi$
$84$	1.76563e7	+	4.27987e7i	0.354636	+	0.859633i
$85$	−9.84525e6	−	5.58352e7i	−0.188604	−	1.06963i
$86$	9.96403e6	−	2.73759e7i	0.182155	−	0.500467i
$87$	−4.40150e7	−	1.39469e7i	−0.768287	−	0.243446i
$88$	−1.03184e6	+	5.85184e6i	−0.0172060	+	0.0975802i
$89$	−7.31545e6	−	4.22358e6i	−0.116595	−	0.0673164i	0.440568	−	0.897719i	$-0.354777\pi$
$89$	−7.31545e6	−	4.22358e6i	−0.116595	−	0.0673164i	−0.557164	+	0.830403i	$0.688110\pi$
$90$	3.91859e7	+	1.06198e7i	0.597255	+	0.161862i
$91$	−4.31895e7	−	7.48065e7i	−0.629815	−	1.09087i
$92$	6.19327e6	+	1.70159e7i	0.0864507	+	0.237521i
$93$	−1.07091e8	+	6.80101e7i	−1.43160	+	0.909163i
$94$	5.93736e7	−	4.98204e7i	0.760470	−	0.638110i
$95$	8.26129e7	+	9.84543e7i	1.01427	+	1.20876i
$96$	−1.50011e7	+	633520.i	−0.176619	+	0.00745891i
$97$	5.35437e7	−	1.94883e7i	0.604814	−	0.220134i	−0.0214186	−	0.999771i	$-0.506818\pi$
$97$	5.35437e7	−	1.94883e7i	0.604814	−	0.220134i	0.626233	+	0.779636i	$0.284596\pi$
$98$	−1.38889e8	+	8.01878e7i	−1.50579	+	0.869368i
$99$	2.43664e7	+	1.14470e7i	0.253659	+	0.119166i
$100$	5.85434e6	−	1.01400e7i	0.0585434	−	0.101400i
$101$	−1.38889e7	−	2.44899e6i	−0.133470	−	0.0235343i	0.106514	−	0.994311i	$-0.466031\pi$
$101$	−1.38889e7	−	2.44899e6i	−0.133470	−	0.0235343i	−0.239984	+	0.970777i	$0.577142\pi$
$102$	9.27726e7	−	2.04284e7i	0.857076	−	0.188727i
$103$	−6.72075e6	−	2.44615e6i	−0.0597130	−	0.0217338i	0.311991	−	0.950085i	$-0.399004\pi$
$103$	−6.72075e6	−	2.44615e6i	−0.0597130	−	0.0217338i	−0.371704	+	0.928351i	$0.621226\pi$
$104$	2.75874e7	−	4.86441e6i	0.235818	−	0.0415811i
$105$	−2.61019e7	+	1.96101e8i	−0.214741	+	1.61333i
$106$	−8.41921e7	−	7.06456e7i	−0.666881	−	0.559579i
$107$			1.44822e7i			0.110484i	0.998473	+	0.0552419i	$0.0175930\pi$
$107$			1.44822e7i			0.110484i	−0.998473	+	0.0552419i	$0.982407\pi$
$108$	−1.50073e7	+	6.63484e7i	−0.110308	+	0.487680i
$109$	1.00650e8			0.713030			0.356515	−	0.934290i	$-0.383965\pi$
$109$	1.00650e8			0.713030			0.356515	+	0.934290i	$0.383965\pi$
$110$	−1.63209e7	+	1.94505e7i	−0.111474	+	0.132849i
$111$	−1.11478e8	+	1.44853e8i	−0.734341	+	0.954190i
$112$	−1.27044e7	−	7.20502e7i	−0.0807388	−	0.457892i
$113$	−5.75487e7	+	1.58114e8i	−0.352957	+	0.969742i	0.628458	+	0.777844i	$0.283687\pi$
$113$	−5.75487e7	+	1.58114e8i	−0.352957	+	0.969742i	−0.981415	+	0.191898i	$0.938536\pi$
$114$	−1.58973e8	+	1.45255e8i	−0.941247	+	0.860027i
$115$	−1.34361e7	+	7.62000e7i	−0.0768214	+	0.435676i
$116$	6.31877e7	+	3.64814e7i	0.348980	+	0.201484i
$117$	1.14221e7	−	1.26400e8i	0.0609542	−	0.674536i
$118$	4.51804e7	+	7.82548e7i	0.233036	+	0.403630i
$119$	1.58317e8	+	4.34972e8i	0.789477	+	2.16907i
$120$	−5.68658e7	−	2.97056e7i	−0.274237	−	0.143256i
$121$	1.51311e8	−	1.26965e8i	0.705877	−	0.592301i
$122$	1.56840e7	+	1.86915e7i	0.0707975	+	0.0843731i
$123$	1.93397e8	−	3.70222e8i	0.844948	−	1.61749i
$124$	1.88383e8	−	6.85659e7i	0.796811	−	0.290015i
$125$	2.28356e8	−	1.31841e8i	0.935345	−	0.540022i
$126$	−3.30121e8	−	2.98313e7i	−1.30976	−	0.118356i
$127$	−5.77688e7	+	1.00059e8i	−0.222064	+	0.384627i	−0.955435	−	0.295203i	$-0.904613\pi$
$127$	−5.77688e7	+	1.00059e8i	−0.222064	+	0.384627i	0.733370	+	0.679829i	$0.237946\pi$
$128$	2.33661e7	+	4.12008e6i	0.0870455	+	0.0153485i
$129$	1.40692e8	+	1.53979e8i	0.508055	+	0.556035i
$130$	1.12481e8	+	4.09399e7i	0.393829	+	0.143342i
$131$	2.23259e8	−	3.93666e7i	0.758095	−	0.133673i	0.218777	−	0.975775i	$-0.429793\pi$
$131$	2.23259e8	−	3.93666e7i	0.758095	−	0.133673i	0.539318	+	0.842102i	$0.318682\pi$
$132$	−3.37141e7	−	2.59462e7i	−0.111049	−	0.0854631i
$133$	−8.03810e8	−	6.74476e8i	−2.56890	−	2.15556i
$134$		−	1.29352e8i		−	0.401194i
$135$	−1.97289e8	+	2.13462e8i	−0.593975	+	0.642666i
$136$	−1.50116e8			−0.438804
$137$	−2.36828e8	+	2.82241e8i	−0.672282	+	0.801194i	−0.989093	−	0.147294i	$-0.952944\pi$
$137$	−2.36828e8	+	2.82241e8i	−0.672282	+	0.801194i	0.316811	+	0.948489i	$0.397388\pi$
$138$	−1.28509e8	−	1.71051e7i	−0.354339	−	0.0471640i
$139$	3.49906e7	+	1.98442e8i	0.0937330	+	0.531586i	0.995128	+	0.0985891i	$0.0314329\pi$
$139$	3.49906e7	+	1.98442e8i	0.0937330	+	0.531586i	−0.901395	+	0.432997i	$0.857456\pi$
$140$	1.06923e8	−	2.93768e8i	0.278329	−	0.764703i
$141$	1.19331e8	+	5.41924e8i	0.301909	+	1.37108i
$142$	1.18697e7	−	6.73163e7i	0.0291934	−	0.165564i
$143$	6.87387e7	+	3.96863e7i	0.164383	+	0.0949066i
$144$	4.57073e7	−	9.72939e7i	0.106301	−	0.226275i
$145$	1.55886e8	+	2.70002e8i	0.352643	+	0.610795i
$146$	−1.47182e8	−	4.04379e8i	−0.323924	−	0.889974i
$147$	−4.84472e7	−	1.14718e9i	−0.103753	−	2.45675i
$148$	2.21266e8	−	1.85664e8i	0.461178	−	0.386974i
$149$	−2.28680e8	−	2.72530e8i	−0.463963	−	0.552930i	0.482435	−	0.875932i	$-0.339752\pi$
$149$	−2.28680e8	−	2.72530e8i	−0.463963	−	0.552930i	−0.946398	+	0.323002i	$0.895308\pi$
$150$	4.49397e7	+	7.07638e7i	0.0887698	+	0.139780i
$151$	2.21820e8	−	8.07358e7i	0.426670	−	0.155295i	−0.119754	−	0.992804i	$-0.538211\pi$
$151$	2.21820e8	−	8.07358e7i	0.426670	−	0.155295i	0.546425	+	0.837508i	$0.315988\pi$
$152$	2.94701e8	−	1.70145e8i	0.552086	−	0.318747i
$153$	−1.77900e8	+	6.56434e8i	−0.324647	+	1.19791i
$154$	1.03649e8	−	1.79525e8i	0.184282	−	0.319185i
$155$	8.43612e8	+	1.48752e8i	1.46156	+	0.257712i
$156$	−6.05817e7	+	1.91189e8i	−0.102292	+	0.322823i
$157$	4.12962e8	+	1.50306e8i	0.679690	+	0.247387i	0.658715	−	0.752393i	$-0.271101\pi$
$157$	4.12962e8	+	1.50306e8i	0.679690	+	0.247387i	0.0209757	+	0.999780i	$0.493323\pi$
$158$	−2.51301e8	+	4.43111e7i	−0.403242	+	0.0711024i
$159$	7.27393e8	−	3.00081e8i	1.13810	−	0.469515i
$160$	7.76648e7	+	6.51685e7i	0.118507	+	0.0994392i
$161$		−	6.31716e8i		−	0.940197i
$162$	−3.71285e8	−	3.15173e8i	−0.539073	−	0.457603i
$163$	−1.82731e8			−0.258858			−0.129429	−	0.991589i	$-0.541314\pi$
$163$	−1.82731e8			−0.258858			−0.129429	+	0.991589i	$0.541314\pi$
$164$	−4.24276e8	+	5.05633e8i	−0.586507	+	0.698972i
$165$	−6.93261e7	−	1.68046e8i	−0.0935322	−	0.226721i
$166$	−9.23738e6	−	5.23878e7i	−0.0121651	−	0.0689919i
$167$	1.02272e8	−	2.80989e8i	0.131489	−	0.361263i	−0.856424	−	0.516273i	$-0.827319\pi$
$167$	1.02272e8	−	2.80989e8i	0.131489	−	0.361263i	0.987913	+	0.155010i	$0.0495411\pi$
$168$	4.99330e8	+	1.58222e8i	0.626831	+	0.198623i
$169$	−7.66732e7	+	4.34835e8i	−0.0939933	+	0.533062i
$170$	−5.55511e8	−	3.20724e8i	−0.665115	−	0.384004i
$171$	−3.94775e8	−	1.49032e9i	−0.461706	−	1.74299i
$172$	−1.64800e8	−	2.85443e8i	−0.188297	−	0.326141i
$173$	2.89556e8	+	7.95549e8i	0.323258	+	0.888143i	0.989773	+	0.142652i	$0.0455628\pi$
$173$	2.89556e8	+	7.95549e8i	0.323258	+	0.888143i	−0.666515	+	0.745491i	$0.732215\pi$
$174$	−4.40966e8	+	2.80043e8i	−0.481070	+	0.305511i
$175$	−3.12907e8	+	2.62560e8i	−0.333629	+	0.279948i
$176$	4.32129e7	+	5.14991e7i	0.0450363	+	0.0536722i
$177$	−6.46358e8	+	2.72967e7i	−0.658537	+	0.0278111i
$178$	−8.98052e7	+	3.26864e7i	−0.0894585	+	0.0325602i
$179$	−1.66412e9	+	9.60781e8i	−1.62096	+	0.935863i	−0.634300	+	0.773087i	$0.718712\pi$
$179$	−1.66412e9	+	9.60781e8i	−1.62096	+	0.935863i	−0.986663	+	0.162777i	$0.947955\pi$
$180$	3.77012e8	−	2.62386e8i	0.359141	−	0.249949i
$181$	−1.29079e8	+	2.23571e8i	−0.120266	+	0.208306i	−0.919872	−	0.392218i	$-0.871708\pi$
$181$	−1.29079e8	+	2.23571e8i	−0.120266	+	0.208306i	0.799607	+	0.600524i	$0.205041\pi$
$182$	−9.62421e8	−	1.69701e8i	−0.877161	−	0.154667i
$183$	−1.70604e8	+	3.75666e7i	−0.152119	+	0.0334964i
$184$	1.92513e8	+	7.00688e7i	0.167953	+	0.0611299i
$185$	1.21548e9	−	2.14322e8i	1.03767	−	0.182970i
$186$	−1.89372e8	+	1.42273e9i	−0.158221	+	1.18870i
$187$	−3.25830e8	−	2.73404e8i	−0.266456	−	0.223583i
$188$		−	8.76889e8i		−	0.701962i
$189$	1.28363e9	−	1.99599e9i	1.00599	−	1.56427i
$190$	1.45407e9			1.11576
$191$	6.03614e8	−	7.19360e8i	0.453551	−	0.540521i	−0.490011	−	0.871716i	$-0.663007\pi$
$191$	6.03614e8	−	7.19360e8i	0.453551	−	0.540521i	0.943562	+	0.331195i	$0.107452\pi$
$192$	−1.03602e8	+	1.34619e8i	−0.0762366	+	0.0990605i
$193$	4.17008e8	+	2.36497e9i	0.300549	+	1.70450i	0.643751	+	0.765235i	$0.277377\pi$
$193$	4.17008e8	+	2.36497e9i	0.300549	+	1.70450i	−0.343202	+	0.939261i	$0.611512\pi$
$194$	2.20485e8	−	6.05778e8i	0.155658	−	0.427668i
$195$	−6.32663e8	+	5.78071e8i	−0.437557	+	0.399800i
$196$	−3.15074e8	+	1.78688e9i	−0.213496	+	1.21079i
$197$	1.29146e9	+	7.45628e8i	0.857468	+	0.495059i	0.863163	−	0.504925i	$-0.168480\pi$
$197$	1.29146e9	+	7.45628e8i	0.857468	+	0.495059i	−0.00569590	+	0.999984i	$0.501813\pi$
$198$	2.76409e8	−	1.27933e8i	0.179842	−	0.0832379i
$199$	−3.80506e8	−	6.59056e8i	−0.242633	−	0.420252i	0.718831	−	0.695185i	$-0.244678\pi$
$199$	−3.80506e8	−	6.59056e8i	−0.242633	−	0.420252i	−0.961463	+	0.274933i	$0.911344\pi$
$200$	−4.53069e7	−	1.24480e8i	−0.0283168	−	0.0777998i
$201$	8.20842e8	+	4.28793e8i	0.502893	+	0.262702i
$202$	−1.22229e8	+	1.02563e8i	−0.0734126	+	0.0616005i
$203$	−1.63615e9	−	1.94989e9i	−0.963472	−	1.14822i
$204$	4.97623e8	−	9.52604e8i	0.287329	−	0.550037i
$205$	−2.65034e9	+	9.64647e8i	−1.50068	+	0.546201i
$206$	−7.00758e7	+	4.04583e7i	−0.0389134	+	0.0224666i
$207$	5.34545e8	−	7.58791e8i	0.291141	−	0.413277i
$208$	1.58465e8	−	2.74470e8i	0.0846606	−	0.146636i
$209$	9.49539e8	+	1.67429e8i	0.497654	+	0.0877499i
$210$	1.50975e9	+	1.65233e9i	0.776297	+	0.849610i
$211$	2.31751e9	+	8.43506e8i	1.16921	+	0.425558i	0.852379	−	0.522924i	$-0.175159\pi$
$211$	2.31751e9	+	8.43506e8i	1.16921	+	0.425558i	0.316831	+	0.948482i	$0.397381\pi$
$212$	−1.22454e9	+	2.15920e8i	−0.606220	+	0.106893i
$213$	3.87828e8	+	2.98471e8i	0.188417	+	0.145005i
$214$	1.25514e8	+	1.05319e8i	0.0598463	+	0.0502170i
$215$		−	1.40839e9i		−	0.659128i
$216$	4.65891e8	+	6.12571e8i	0.214027	+	0.281411i
$217$	−6.99375e9			−3.15407
$218$	7.31958e8	−	8.72314e8i	0.324086	−	0.386231i
$219$	3.05400e9	+	4.06501e8i	1.32768	+	0.176720i
$220$	4.98829e7	+	2.82900e8i	0.0212942	+	0.120765i
$221$	−6.85816e8	+	1.88426e9i	−0.287501	+	0.789901i
$222$	4.44707e8	+	2.01957e9i	0.183089	+	0.831472i
$223$	−2.24459e8	+	1.27297e9i	−0.0907649	+	0.514753i	0.905198	+	0.424990i	$0.139722\pi$
$223$	−2.24459e8	+	1.27297e9i	−0.0907649	+	0.514753i	−0.995963	+	0.0897637i	$0.971389\pi$
$224$	−7.16836e8	−	4.13865e8i	−0.284726	−	0.164387i
$225$	−5.98024e8	+	5.06013e7i	−0.233340	+	0.0197438i
$226$	9.51829e8	+	1.64862e9i	0.364859	+	0.631955i
$227$	−1.79178e8	−	4.92288e8i	−0.0674811	−	0.185403i	0.901368	−	0.433053i	$-0.142564\pi$
$227$	−1.79178e8	−	4.92288e8i	−0.0674811	−	0.185403i	−0.968849	+	0.247650i	$0.920342\pi$
$228$	1.02797e8	+	2.43413e9i	0.0380401	+	0.900749i
$229$	−3.80334e8	+	3.19139e8i	−0.138301	+	0.116048i	−0.709314	−	0.704893i	$-0.750995\pi$
$229$	−3.80334e8	+	3.19139e8i	−0.138301	+	0.116048i	0.571013	+	0.820941i	$0.306551\pi$
$230$	5.62699e8	+	6.70598e8i	0.201078	+	0.239635i
$231$	7.95641e8	+	1.25285e9i	0.279428	+	0.439998i
$232$	7.75698e8	−	2.82331e8i	0.267757	−	0.0974555i
$233$	−1.96042e9	+	1.13185e9i	−0.665158	+	0.384029i	−0.794239	−	0.607605i	$-0.792130\pi$
$233$	−1.96042e9	+	1.13185e9i	−0.665158	+	0.384029i	0.129082	+	0.991634i	$0.458797\pi$
$234$	−1.01242e9	−	1.01822e9i	−0.337675	−	0.339607i
$235$	1.87348e9	−	3.24497e9i	0.614297	−	1.06399i
$236$	1.00679e9	+	1.77523e8i	0.324555	+	0.0572279i
$237$	5.51854e8	−	1.74159e9i	0.174917	−	0.552017i
$238$	4.92115e9	+	1.79115e9i	1.53376	+	0.558244i
$239$	−5.65186e9	+	9.96575e8i	−1.73221	+	0.305435i	−0.948754	−	0.316016i	$-0.897655\pi$
$239$	−5.65186e9	+	9.96575e8i	−1.73221	+	0.305435i	−0.783453	+	0.621451i	$0.786543\pi$
$240$	−6.70999e8	+	2.76816e8i	−0.202244	+	0.0834346i
$241$	3.35116e9	+	2.81196e9i	0.993408	+	0.833568i	0.986058	−	0.166405i	$-0.0532158\pi$
$241$	3.35116e9	+	2.81196e9i	0.993408	+	0.833568i	0.00735037	+	0.999973i	$0.497660\pi$
$242$		−	2.23471e9i		−	0.651568i
$243$	3.23081e9	−	1.31132e9i	0.926586	−	0.376083i
$244$	2.76054e8			0.0778817
$245$	−4.98363e9	+	5.93926e9i	−1.38319	+	1.64842i
$246$	−1.80220e9	−	4.36851e9i	−0.492109	−	1.19287i
$247$	−7.89315e8	−	4.47643e9i	−0.212062	−	1.20266i
$248$	7.75734e8	−	2.13131e9i	0.205072	−	0.563430i
$249$	3.63063e8	+	1.15043e8i	0.0944463	+	0.0299270i
$250$	5.18032e8	−	2.93791e9i	0.132616	−	0.752104i
$251$	1.32733e9	+	7.66332e8i	0.334413	+	0.193073i	0.657798	−	0.753194i	$-0.271488\pi$
$251$	1.32733e9	+	7.66332e8i	0.334413	+	0.193073i	−0.323386	+	0.946267i	$0.604821\pi$
$252$	−2.65928e9	+	2.64415e9i	−0.659421	+	0.655668i
$253$	2.90238e8	+	5.02707e8i	0.0708390	+	0.122697i
$254$	4.47075e8	+	1.22833e9i	0.107410	+	0.295107i
$255$	3.87673e9	−	2.46198e9i	0.916863	−	0.582269i
$256$	2.05633e8	−	1.72547e8i	0.0478778	−	0.0401742i
$257$	−2.21844e9	−	2.64383e9i	−0.508527	−	0.606039i	0.449301	−	0.893381i	$-0.351673\pi$
$257$	−2.21844e9	−	2.64383e9i	−0.508527	−	0.606039i	−0.957828	+	0.287341i	$0.907229\pi$
$258$	2.35766e9	−	9.95678e7i	0.532111	−	0.0224719i
$259$	−9.46893e9	+	3.44641e9i	−2.10427	+	0.765892i
$260$	1.17282e9	−	6.77126e8i	0.256647	−	0.148175i
$261$	−3.15323e8	−	3.72660e9i	−0.0679506	−	0.803065i
$262$	1.28243e9	−	2.22123e9i	0.272162	−	0.471398i
$263$	1.02595e9	+	1.80903e8i	0.214439	+	0.0378114i	0.279836	−	0.960048i	$-0.409720\pi$
$263$	1.02595e9	+	1.80903e8i	0.214439	+	0.0378114i	−0.0653964	+	0.997859i	$0.520831\pi$
$264$	−4.70050e8	+	1.03504e8i	−0.0967673	+	0.0213080i
$265$	−4.99279e9	−	1.81723e9i	−1.01242	−	0.368490i
$266$	−1.16911e10	+	2.06146e9i	−2.33523	+	0.411764i
$267$	9.02764e7	−	6.78238e8i	0.0177635	−	0.133456i
$268$	−1.12107e9	−	9.40689e8i	−0.217317	−	0.182350i
$269$		−	9.62236e9i		−	1.83769i	−0.394618	−	0.918845i	$-0.629123\pi$
$269$		−	9.62236e9i		−	1.83769i	0.394618	−	0.918845i	$-0.370877\pi$
$270$	4.15284e8	+	3.26223e9i	0.0781429	+	0.613846i
$271$	8.58528e9			1.59176			0.795880	−	0.605455i	$-0.207009\pi$
$271$	8.58528e9			1.59176			0.795880	+	0.605455i	$0.207009\pi$
$272$	−1.09169e9	+	1.30102e9i	−0.199445	+	0.237689i
$273$	4.26724e9	−	5.54478e9i	0.768239	−	0.998237i
$274$	7.23838e8	+	4.10509e9i	0.128422	+	0.728317i
$275$	1.28374e8	−	3.52703e8i	0.0224463	−	0.0616707i
$276$	−1.08281e9	+	9.89372e8i	−0.186601	+	0.170499i
$277$	6.55062e8	−	3.71504e9i	0.111266	−	0.631023i	−0.877265	−	0.480006i	$-0.840634\pi$
$277$	6.55062e8	−	3.71504e9i	0.111266	−	0.631023i	0.988531	−	0.151016i	$-0.0482545\pi$
$278$	1.97432e9	+	1.13987e9i	0.330551	+	0.190844i
$279$	−8.40060e9	−	5.91796e9i	−1.38642	−	0.976687i
$280$	−1.76846e9	−	3.06305e9i	−0.287715	−	0.498336i
$281$	3.15354e9	+	8.66429e9i	0.505794	+	1.38966i	0.885538	+	0.464566i	$0.153790\pi$
$281$	3.15354e9	+	8.66429e9i	0.505794	+	1.38966i	−0.379744	+	0.925091i	$0.623988\pi$
$282$	5.56456e9	+	2.90682e9i	0.879902	+	0.459645i
$283$	1.42610e9	−	1.19664e9i	0.222332	−	0.186559i	−0.524817	−	0.851215i	$-0.675866\pi$
$283$	1.42610e9	−	1.19664e9i	0.222332	−	0.186559i	0.747150	+	0.664656i	$0.231422\pi$
$284$	−4.97097e8	−	5.92417e8i	−0.0764131	−	0.0910655i
$285$	−4.82014e9	+	9.22723e9i	−0.730600	+	1.39859i
$286$	8.43843e8	−	3.07134e8i	0.126124	−	0.0459053i
$287$	1.99419e10	−	1.15134e10i	2.93926	−	1.69698i
$288$	−5.10829e8	−	1.10369e9i	−0.0742516	−	0.160427i
$289$	1.88483e9	−	3.26462e9i	0.270197	−	0.467994i
$290$	3.47371e9	+	6.12509e8i	0.491136	+	0.0866005i
$291$	3.11325e9	+	3.40726e9i	0.434152	+	0.475153i
$292$	−4.57503e9	−	1.66517e9i	−0.629307	−	0.229049i
$293$	7.09871e9	−	1.25169e9i	0.963183	−	0.169835i	0.330123	−	0.943938i	$-0.392910\pi$
$293$	7.09871e9	−	1.25169e9i	0.963183	−	0.169835i	0.633060	+	0.774103i	$0.281799\pi$
$294$	−1.02947e10	−	7.92276e9i	−1.37792	−	1.06044i
$295$	3.34637e9	+	2.80794e9i	0.441862	+	0.370766i
$296$		−	3.26788e9i		−	0.425696i
$297$	−1.04441e8	+	2.17812e9i	−0.0134229	+	0.279935i
$298$	−4.02500e9			−0.510388
$299$	1.75902e9	−	2.09632e9i	0.220083	−	0.262284i
$300$	9.40112e8	+	1.25133e8i	0.116063	+	0.0154485i
$301$	1.99670e9	+	1.13238e10i	0.243246	+	1.37952i
$302$	9.13421e8	−	2.50960e9i	0.109810	−	0.301701i
$303$	−2.45660e8	−	1.11563e9i	−0.0291450	−	0.132358i
$304$	6.68537e8	−	3.79146e9i	0.0782765	−	0.443928i
$305$	1.02155e9	+	5.89793e8i	0.118049	+	0.0681554i
$306$	4.39544e9	+	6.31562e9i	0.501322	+	0.720328i
$307$	−2.91794e9	−	5.05402e9i	−0.328491	−	0.568962i	0.653722	−	0.756735i	$-0.273207\pi$
$307$	−2.91794e9	−	5.05402e9i	−0.328491	−	0.568962i	−0.982213	+	0.187772i	$0.939873\pi$
$308$	−8.02143e8	−	2.20387e9i	−0.0891351	−	0.244897i
$309$	−2.44437e7	−	5.78802e8i	−0.00268123	−	0.0634887i
$310$	7.42421e9	−	6.22965e9i	0.803903	−	0.674555i
$311$	−7.82473e8	−	9.32515e8i	−0.0836426	−	0.0996814i	0.722600	−	0.691266i	$-0.242947\pi$
$311$	−7.82473e8	−	9.32515e8i	−0.0836426	−	0.0996814i	−0.806243	+	0.591585i	$0.798502\pi$
$312$	1.21643e9	+	1.91544e9i	0.128371	+	0.202139i
$313$	−9.24559e9	+	3.36512e9i	−0.963291	+	0.350609i	−0.775322	−	0.631566i	$-0.782413\pi$
$313$	−9.24559e9	+	3.36512e9i	−0.963291	+	0.350609i	−0.187969	+	0.982175i	$0.560190\pi$
$314$	4.30586e9	−	2.48599e9i	0.442936	−	0.255729i
$315$	−1.54901e10	+	4.10321e9i	−1.57330	+	0.416756i
$316$	−1.44350e9	+	2.50022e9i	−0.144767	+	0.250743i
$317$	8.06192e9	+	1.42153e9i	0.798365	+	0.140773i	0.557926	−	0.829891i	$-0.311597\pi$
$317$	8.06192e9	+	1.42153e9i	0.798365	+	0.140773i	0.240439	+	0.970664i	$0.422709\pi$
$318$	2.68909e9	−	8.48645e9i	0.262964	−	0.829885i
$319$	2.19788e9	+	7.99962e8i	0.212247	+	0.0772515i
$320$	1.12960e9	−	1.99180e8i	0.107728	−	0.0189953i
$321$	−1.08440e9	+	4.47362e8i	−0.102134	+	0.0421346i
$322$	−5.47496e9	−	4.59404e9i	−0.509281	−	0.427338i
$323$			2.43583e10i			2.23788i
$324$	−5.43164e9	+	9.25816e8i	−0.492891	+	0.0840126i
$325$	−1.76947e9			−0.158602
$326$	−1.32887e9	+	1.58369e9i	−0.117656	+	0.140217i
$327$	3.10913e9	+	7.53651e9i	0.271925	+	0.659142i
$328$	1.29675e9	+	7.35424e9i	0.112037	+	0.635393i
$329$	−1.04629e10	+	2.87465e10i	−0.893032	+	2.45358i
$330$	−1.96058e9	−	6.21246e8i	−0.165321	−	0.0523851i
$331$	−2.68734e9	+	1.52407e10i	−0.223877	+	1.26967i	0.640942	+	0.767589i	$0.278544\pi$
$331$	−2.68734e9	+	1.52407e10i	−0.223877	+	1.26967i	−0.864820	+	0.502083i	$0.832567\pi$
$332$	−5.21212e8	−	3.00922e8i	−0.0429005	−	0.0247686i
$333$	−1.42900e10	−	3.87272e9i	−1.16213	−	0.314948i
$334$	−1.69153e9	−	2.92981e9i	−0.135923	−	0.235425i
$335$	−2.13878e9	−	5.87624e9i	−0.169819	−	0.466574i
$336$	5.00256e9	−	3.17696e9i	0.392496	−	0.249261i
$337$	9.85509e9	−	8.26940e9i	0.764084	−	0.641142i	−0.175103	−	0.984550i	$-0.556026\pi$
$337$	9.85509e9	−	8.26940e9i	0.764084	−	0.641142i	0.939186	+	0.343408i	$0.111581\pi$
$338$	3.21104e9	+	3.82677e9i	0.246025	+	0.293201i
$339$	−1.36170e10	+	5.75069e8i	−1.03106	+	0.0435433i
$340$	−6.81950e9	+	2.48209e9i	−0.510313	+	0.185739i
$341$	5.56548e9	−	3.21323e9i	0.411610	−	0.237643i
$342$	−1.57872e10	−	7.41663e9i	−1.15399	−	0.542128i
$343$	1.87783e10	−	3.25250e10i	1.35669	−	2.34986i
$344$	−3.67236e9	−	6.47535e8i	−0.262247	−	0.0462413i
$345$	−6.12078e9	+	1.34779e9i	−0.432047	+	0.0951359i
$346$	9.00062e9	+	3.27596e9i	0.628012	+	0.228578i
$347$	5.95662e8	−	1.05031e8i	0.0410849	−	0.00724437i	−0.153068	−	0.988216i	$-0.548915\pi$
$347$	5.95662e8	−	1.05031e8i	0.0410849	−	0.00724437i	0.194153	+	0.980971i	$0.437804\pi$
$348$	−7.79767e8	+	5.85832e9i	−0.0531677	+	0.399444i
$349$	1.42674e10	+	1.19718e10i	0.961709	+	0.806970i	0.981230	−	0.192839i	$-0.0617696\pi$
$349$	1.42674e10	+	1.19718e10i	0.961709	+	0.806970i	−0.0195209	+	0.999809i	$0.506214\pi$
$350$			4.62133e9i			0.307960i
$351$	9.81750e9	−	3.04931e9i	0.646804	−	0.200897i
$352$	7.60591e8			0.0495428
$353$	−1.40018e10	+	1.66867e10i	−0.901747	+	1.07466i	0.0951125	+	0.995467i	$0.469679\pi$
$353$	−1.40018e10	+	1.66867e10i	−0.901747	+	1.07466i	−0.996859	+	0.0791934i	$0.974766\pi$
$354$	−4.46394e9	+	5.80037e9i	−0.284253	+	0.369354i
$355$	−5.73824e8	−	3.25432e9i	−0.0361298	−	0.204902i
$356$	−3.69805e8	+	1.01603e9i	−0.0230236	+	0.0632567i
$357$	−2.76795e10	+	2.52910e10i	−1.70406	+	1.55702i
$358$	−3.77511e9	+	2.14097e10i	−0.229825	+	1.30340i
$359$	1.26537e9	+	7.30559e8i	0.0761795	+	0.0439823i	0.537606	−	0.843196i	$-0.319329\pi$
$359$	1.26537e9	+	7.30559e8i	0.0761795	+	0.0439823i	−0.461426	+	0.887178i	$0.652662\pi$
$360$	4.67695e8	−	5.17564e9i	0.0278454	−	0.308144i
$361$	−1.91166e10	−	3.31109e10i	−1.12559	−	1.94958i
$362$	9.98946e8	+	2.74458e9i	0.0581712	+	0.159824i
$363$	1.41810e10	+	7.40790e9i	0.816734	+	0.426647i
$364$	−8.46979e9	+	7.10699e9i	−0.482466	+	0.404837i
$365$	−1.33724e10	−	1.59367e10i	−0.753423	−	0.897895i
$366$	−9.15100e8	+	1.75178e9i	−0.0509969	+	0.0976239i
$367$	−1.83108e10	+	6.66458e9i	−1.00935	+	0.367374i	−0.793184	−	0.608982i	$-0.791578\pi$
$367$	−1.83108e10	+	6.66458e9i	−1.00935	+	0.367374i	−0.216168	+	0.976356i	$0.569356\pi$
$368$	2.00728e9	−	1.15891e9i	0.109450	−	0.0631912i
$369$	3.36958e10	+	3.04491e9i	1.81748	+	0.164236i
$370$	6.98186e9	−	1.20929e10i	0.372533	−	0.645246i
$371$	4.27197e10	+	7.53263e9i	2.25493	+	0.397604i
$372$	1.09534e10	+	1.19878e10i	0.571973	+	0.625990i
$373$	2.22272e10	+	8.09003e9i	1.14828	+	0.417941i	0.844898	−	0.534927i	$-0.179661\pi$
$373$	2.22272e10	+	8.09003e9i	1.14828	+	0.417941i	0.303385	+	0.952868i	$0.401883\pi$
$374$	−4.73908e9	+	8.35628e8i	−0.242219	+	0.0427097i
$375$	1.69261e10	+	1.30263e10i	0.855918	+	0.658711i
$376$	−7.59983e9	−	6.37701e9i	−0.380235	−	0.319055i
$377$		−	1.10265e10i		−	0.545847i
$378$	−7.96390e9	−	2.56404e10i	−0.390084	−	1.25591i
$379$	1.99960e10			0.969141			0.484570	−	0.874752i	$-0.338976\pi$
$379$	1.99960e10			0.969141			0.484570	+	0.874752i	$0.338976\pi$
$380$	1.05745e10	−	1.26021e10i	0.507135	−	0.604380i
$381$	−9.27673e9	−	1.23477e9i	−0.440246	−	0.0585986i
$382$	−1.84488e9	−	1.04628e10i	−0.0866391	−	0.491355i
$383$	8.87781e9	−	2.43916e10i	0.412582	−	1.13356i	−0.543230	−	0.839584i	$-0.682799\pi$
$383$	8.87781e9	−	2.43916e10i	0.412582	−	1.13356i	0.955813	−	0.293977i	$-0.0949788\pi$
$384$	4.13288e8	+	1.87689e9i	0.0190076	+	0.0863204i
$385$	1.74023e9	−	9.86931e9i	0.0792068	−	0.449204i
$386$	2.35293e10	+	1.35847e10i	1.05989	+	0.611927i
$387$	−7.18364e9	+	1.52913e10i	−0.320258	+	0.681711i
$388$	−3.64672e9	−	6.31631e9i	−0.160907	−	0.278700i
$389$	−9.48835e8	−	2.60690e9i	−0.0414374	−	0.113848i	0.917248	−	0.398316i	$-0.130405\pi$
$389$	−9.48835e8	−	2.60690e9i	−0.0414374	−	0.113848i	−0.958686	+	0.284468i	$0.908183\pi$
$390$	4.09101e8	+	9.68708e9i	0.0176836	+	0.418730i
$391$	−1.12337e10	+	9.42621e9i	−0.480636	+	0.403302i
$392$	1.31952e10	+	1.57254e10i	0.558819	+	0.665975i
$393$	9.84430e9	+	1.55012e10i	0.412681	+	0.649824i
$394$	1.58541e10	−	5.77044e9i	0.657897	−	0.239455i
$395$	−1.06835e10	+	6.16812e9i	−0.438859	+	0.253375i
$396$	9.01366e8	−	3.32595e9i	0.0366539	−	0.135249i
$397$	−6.95581e8	+	1.20478e9i	−0.0280018	+	0.0485005i	−0.879687	−	0.475554i	$-0.842248\pi$
$397$	−6.95581e8	+	1.20478e9i	−0.0280018	+	0.0485005i	0.851685	+	0.524054i	$0.175581\pi$
$398$	−8.47907e9	−	1.49509e9i	−0.337921	−	0.0595847i
$399$	2.56736e10	−	8.10229e10i	1.01297	−	3.19681i
$400$	−1.40833e9	−	5.12589e8i	−0.0550128	−	0.0200230i
$401$	−3.51801e10	+	6.20321e9i	−1.36057	+	0.239905i	−0.805843	−	0.592129i	$-0.798287\pi$
$401$	−3.51801e10	+	6.20321e9i	−1.36057	+	0.239905i	−0.554724	+	0.832034i	$0.687176\pi$
$402$	9.68568e9	−	3.99576e9i	0.370874	−	0.153001i
$403$	−2.32084e10	−	1.94741e10i	−0.879882	−	0.738309i
$404$			1.80521e9i			0.0677644i
$405$	−2.20781e10	−	8.17874e9i	−0.820618	−	0.303995i
$406$	−2.87979e10			−1.05988
$407$	5.95175e9	−	7.09302e9i	0.216904	−	0.258496i
$408$	−4.63716e9	−	1.12404e10i	−0.167345	−	0.405641i
$409$	2.12549e9	+	1.20543e10i	0.0759567	+	0.430772i	0.998944	+	0.0459416i	$0.0146288\pi$
$409$	2.12549e9	+	1.20543e10i	0.0759567	+	0.430772i	−0.922987	+	0.384830i	$0.874260\pi$
$410$	−1.09137e10	+	2.99852e10i	−0.386223	+	1.06114i
$411$	−2.84495e10	−	9.01474e9i	−0.997029	−	0.315927i
$412$	−1.58969e8	+	9.01558e8i	−0.00551726	+	0.0312899i
$413$	−3.08866e10	−	1.78324e10i	−1.06162	−	0.612928i
$414$	−2.68892e9	−	1.01510e10i	−0.0915328	−	0.345546i
$415$	−1.28585e9	−	2.22715e9i	−0.0433507	−	0.0750857i
$416$	−1.22637e9	−	3.36942e9i	−0.0409494	−	0.112508i
$417$	−1.37781e10	+	8.75002e9i	−0.455665	+	0.289378i
$418$	8.35642e9	−	7.01187e9i	0.273725	−	0.229683i
$419$	−3.59351e10	−	4.28257e10i	−1.16590	−	1.38947i	−0.905702	−	0.423914i	$-0.860656\pi$
$419$	−3.59351e10	−	4.28257e10i	−1.16590	−	1.38947i	−0.260200	−	0.965555i	$-0.583789\pi$
$420$	2.52998e10	−	1.06845e9i	0.813055	−	0.0343366i
$421$	5.55688e10	−	2.02254e10i	1.76890	−	0.643826i	0.768908	−	0.639360i	$-0.220801\pi$
$421$	5.55688e10	−	2.02254e10i	1.76890	−	0.643826i	0.999990	−	0.00446628i	$-0.00142167\pi$
$422$	2.41642e10	−	1.39512e10i	0.761943	−	0.439908i
$423$	−3.68922e10	+	2.56756e10i	−1.15232	+	0.801972i
$424$	−7.03392e9	+	1.21831e10i	−0.217638	+	0.376960i
$425$	9.33815e9	+	1.64657e9i	0.286223	+	0.0504689i
$426$	5.40719e9	−	1.19065e9i	0.164185	−	0.0361533i
$427$	−9.04970e9	−	3.29382e9i	−0.272222	−	0.0990806i
$428$	1.82555e9	−	3.21894e8i	0.0544026	−	0.00959265i
$429$	−8.48270e8	+	6.37297e9i	−0.0250441	+	0.188154i
$430$	−1.22063e10	−	1.02423e10i	−0.357033	−	0.299586i
$431$		−	3.32089e10i		−	0.962377i	−0.876617	−	0.481188i	$-0.840205\pi$
$431$		−	3.32089e10i		−	0.962377i	0.876617	−	0.481188i	$-0.159795\pi$
$432$	8.69714e9	+	4.17029e8i	0.249713	+	0.0119738i
$433$	2.26292e10			0.643750			0.321875	−	0.946782i	$-0.395687\pi$
$433$	2.26292e10			0.643750			0.321875	+	0.946782i	$0.395687\pi$
$434$	−5.08607e10	+	6.06135e10i	−1.43359	+	1.70848i
$435$	−1.54019e10	+	2.00130e10i	−0.430148	+	0.558927i
$436$	−2.23714e9	−	1.26875e10i	−0.0619082	−	0.351099i
$437$	1.13696e10	−	3.12377e10i	0.311759	−	0.856552i
$438$	2.57327e10	−	2.35122e10i	0.699181	−	0.638848i
$439$	−3.62286e9	+	2.05462e10i	−0.0975423	+	0.553190i	0.896396	+	0.443253i	$0.146176\pi$
$439$	−3.62286e9	+	2.05462e10i	−0.0975423	+	0.553190i	−0.993939	+	0.109936i	$0.964935\pi$
$440$	2.81460e9	+	1.62501e9i	0.0750942	+	0.0433556i
$441$	8.44023e10	−	3.90646e10i	2.23152	−	1.03283i
$442$	1.13431e10	+	1.96468e10i	0.297195	+	0.514757i
$443$	3.18743e9	+	8.75739e9i	0.0827610	+	0.227384i	0.974170	−	0.225816i	$-0.0725047\pi$
$443$	3.18743e9	+	8.75739e9i	0.0827610	+	0.227384i	−0.891409	+	0.453200i	$0.850282\pi$
$444$	2.07373e10	+	1.08328e10i	0.533605	+	0.278746i
$445$	−3.53924e9	+	2.96977e9i	−0.0902547	+	0.0757327i
$446$	9.40026e9	+	1.12028e10i	0.237575	+	0.283131i
$447$	1.33426e10	−	2.55418e10i	0.334202	−	0.639767i
$448$	−8.79994e9	+	3.20292e9i	−0.218458	+	0.0795121i
$449$	1.15933e10	−	6.69341e9i	0.285248	−	0.164688i	−0.350549	−	0.936544i	$-0.614005\pi$
$449$	1.15933e10	−	6.69341e9i	0.285248	−	0.164688i	0.635797	+	0.771856i	$0.280672\pi$
$450$	−3.91047e9	+	5.55095e9i	−0.0953627	+	0.135368i
$451$	−1.05796e10	+	1.83243e10i	−0.255718	+	0.442916i
$452$	2.12102e10	+	3.73994e9i	0.508150	+	0.0896005i
$453$	1.28975e10	+	1.41155e10i	0.306276	+	0.335200i
$454$	−5.56961e9	−	2.02717e9i	−0.131099	−	0.0477163i
$455$	−4.65270e10	+	8.20397e9i	−1.08557	+	0.191416i
$456$	2.18437e10	+	1.68108e10i	0.505204	+	0.388803i
$457$	−4.61233e10	−	3.87020e10i	−1.05744	−	0.887296i	−0.0635826	−	0.997977i	$-0.520253\pi$
$457$	−4.61233e10	−	3.87020e10i	−1.05744	−	0.887296i	−0.993856	+	0.110680i	$0.964697\pi$
$458$			5.61716e9i			0.127660i
$459$	−5.46482e10	+	6.95675e9i	−1.23119	+	0.156731i
$460$	9.90406e9			0.221198
$461$	−3.30535e10	+	3.93916e10i	−0.731836	+	0.872168i	−0.995723	−	0.0923857i	$-0.970551\pi$
$461$	−3.30535e10	+	3.93916e10i	−0.731836	+	0.872168i	0.263888	+	0.964553i	$0.414995\pi$
$462$	1.66443e10	+	2.21543e9i	0.365341	+	0.0486285i
$463$	7.44793e9	+	4.22393e10i	0.162073	+	0.919163i	0.952031	+	0.306002i	$0.0989913\pi$
$463$	7.44793e9	+	4.22393e10i	0.162073	+	0.919163i	−0.789958	+	0.613161i	$0.789898\pi$
$464$	3.19421e9	−	8.77602e9i	0.0689115	−	0.189333i
$465$	1.49214e10	+	6.77634e10i	0.319152	+	1.44938i
$466$	−4.44726e9	+	2.52217e10i	−0.0943081	+	0.534848i
$467$	−1.83204e10	−	1.05773e10i	−0.385184	−	0.222386i	0.294887	−	0.955532i	$-0.404718\pi$
$467$	−1.83204e10	−	1.05773e10i	−0.385184	−	0.222386i	−0.680071	+	0.733146i	$0.738051\pi$
$468$	−1.61873e10	+	1.36968e9i	−0.337436	+	0.0285519i
$469$	2.55272e10	+	4.42143e10i	0.527608	+	0.913843i
$470$	−1.44990e10	−	3.98355e10i	−0.297129	−	0.816356i
$471$	1.50196e9	+	3.55649e10i	0.0305194	+	0.722667i
$472$	8.86022e9	−	7.43460e9i	0.178516	−	0.149792i
$473$	−6.79160e9	−	8.09391e9i	−0.135684	−	0.161701i
$474$	−1.10808e10	−	1.74482e10i	−0.219511	−	0.345651i
$475$	−2.01985e10	+	7.35165e9i	−0.396775	+	0.144414i
$476$	5.13117e10	−	2.96248e10i	0.999513	−	0.577069i
$477$	4.49392e10	+	4.51963e10i	0.868063	+	0.873031i
$478$	−3.24650e10	+	5.62310e10i	−0.621875	+	1.07712i
$479$	−2.39841e10	−	4.22904e9i	−0.455598	−	0.0803341i	−0.0588601	−	0.998266i	$-0.518747\pi$
$479$	−2.39841e10	−	4.22904e9i	−0.455598	−	0.0803341i	−0.396738	+	0.917932i	$0.629858\pi$
$480$	−2.48060e9	+	7.82850e9i	−0.0467296	+	0.147473i
$481$	−4.10187e10	−	1.49296e10i	−0.766304	−	0.278912i
$482$	4.87414e10	−	8.59443e9i	0.903046	−	0.159231i
$483$	4.73019e10	−	1.95141e10i	0.869141	−	0.358558i
$484$	−1.93678e10	−	1.62515e10i	−0.352938	−	0.296150i
$485$		−	3.11651e10i		−	0.563250i
$486$	1.21305e10	−	3.75371e10i	0.217436	−	0.672846i
$487$	2.63816e9			0.0469014			0.0234507	−	0.999725i	$-0.492535\pi$
$487$	2.63816e9			0.0469014			0.0234507	+	0.999725i	$0.492535\pi$
$488$	2.00755e9	−	2.39251e9i	0.0353987	−	0.0421866i
$489$	−5.64465e9	−	1.36826e10i	−0.0987192	−	0.239294i
$490$	1.52319e10	+	8.63843e10i	0.264222	+	1.49848i
$491$	2.38970e10	−	6.56564e10i	0.411165	−	1.12967i	−0.545406	−	0.838172i	$-0.683625\pi$
$491$	2.38970e10	−	6.56564e10i	0.411165	−	1.12967i	0.956572	−	0.291496i	$-0.0941531\pi$
$492$	−5.09671e10	−	1.61498e10i	−0.869820	−	0.275618i
$493$	−1.02606e10	+	5.81909e10i	−0.173694	+	0.985070i
$494$	−4.45364e10	−	2.57131e10i	−0.747838	−	0.431765i
$495$	1.04415e10	−	1.03821e10i	0.173917	−	0.172927i
$496$	−1.28303e10	−	2.22227e10i	−0.211987	−	0.367173i
$497$	9.22740e9	+	2.53521e10i	0.151235	+	0.415516i
$498$	3.63737e9	−	2.30997e9i	0.0591384	−	0.0375568i
$499$	5.55057e10	−	4.65748e10i	0.895232	−	0.751189i	−0.0740204	−	0.997257i	$-0.523583\pi$
$499$	5.55057e10	−	4.65748e10i	0.895232	−	0.751189i	0.969253	+	0.246068i	$0.0791386\pi$
$500$	−2.16950e10	−	2.58551e10i	−0.347119	−	0.413681i
$501$	2.41992e10	−	1.02197e9i	0.384106	−	0.0162214i
$502$	1.62944e10	−	5.93067e9i	0.256580	−	0.0933875i
$503$	−9.77733e10	+	5.64495e10i	−1.52739	+	0.881836i	−0.527915	+	0.849297i	$0.677026\pi$
$503$	−9.77733e10	+	5.64495e10i	−1.52739	+	0.881836i	−0.999470	+	0.0325387i	$0.989641\pi$
$504$	3.57719e9	+	4.22766e10i	0.0554396	+	0.655206i
$505$	−3.85684e9	+	6.68025e9i	−0.0593016	+	0.102713i
$506$	6.46756e9	+	1.14041e9i	0.0986594	+	0.0173963i
$507$	−3.49282e10	+	7.69114e9i	−0.528622	+	0.116402i
$508$	1.38969e10	+	5.05807e9i	0.208672	+	0.0759504i
$509$	6.78014e10	−	1.19552e10i	1.01011	−	0.178109i	0.355980	−	0.934494i	$-0.384147\pi$
$509$	6.78014e10	−	1.19552e10i	1.01011	−	0.178109i	0.654127	+	0.756385i	$0.273036\pi$
$510$	6.85528e9	−	5.15031e10i	0.101331	−	0.761294i
$511$	1.30112e11	+	1.09177e11i	1.90824	+	1.60120i
$512$		−	3.03700e9i		−	0.0441942i
$513$	9.93979e10	−	7.55969e10i	1.43518	−	1.09153i
$514$	−3.90467e10			−0.559412
$515$	−2.51446e9	+	2.99662e9i	−0.0357451	+	0.0425993i
$516$	1.62827e10	−	2.11575e10i	0.229683	−	0.298446i
$517$	−4.88125e9	−	2.76829e10i	−0.0683233	−	0.387481i
$518$	−3.89917e10	+	1.07129e11i	−0.541568	+	1.48794i
$519$	−5.06249e10	+	4.62565e10i	−0.697742	+	0.637534i
$520$	2.66057e9	−	1.50889e10i	0.0363883	−	0.206368i
$521$	−7.65721e10	−	4.42089e10i	−1.03925	−	0.600011i	−0.119629	−	0.992819i	$-0.538170\pi$
$521$	−7.65721e10	−	4.42089e10i	−1.03925	−	0.600011i	−0.919621	+	0.392808i	$0.871504\pi$
$522$	−3.45908e10	−	2.43681e10i	−0.465885	−	0.328201i
$523$	4.45812e10	+	7.72169e10i	0.595861	+	1.03206i	0.993425	+	0.114487i	$0.0365224\pi$
$523$	4.45812e10	+	7.72169e10i	0.595861	+	1.03206i	−0.397564	+	0.917575i	$0.630144\pi$
$524$	−9.92474e9	−	2.72680e10i	−0.131642	−	0.361683i
$525$	−2.93260e10	−	1.53194e10i	−0.386025	−	0.201652i
$526$	9.02889e9	−	7.57614e9i	0.117948	−	0.0989703i
$527$	1.04358e11	+	1.24369e11i	1.35295	+	1.61239i
$528$	−2.52130e9	+	4.82655e9i	−0.0324406	+	0.0621014i
$529$	−5.47820e10	+	1.99390e10i	−0.699544	+	0.254613i
$530$	−5.20587e10	+	3.00561e10i	−0.659766	+	0.380916i
$531$	−2.20103e10	−	4.75551e10i	−0.276852	−	0.598162i
$532$	−6.71551e10	+	1.16316e11i	−0.838364	+	1.45209i
$533$	9.82353e10	+	1.73215e10i	1.21719	+	0.214624i
$534$	−5.22164e9	−	5.71477e9i	−0.0642158	−	0.0702803i
$535$	7.44328e9	+	2.70913e9i	0.0908551	+	0.0330685i
$536$	−1.63055e10	+	2.87511e9i	−0.197549	+	0.0348333i
$537$	−1.23347e11	−	9.49277e10i	−1.48331	−	1.14155i
$538$	−8.33951e10	−	6.99768e10i	−0.995431	−	0.835266i
$539$			5.81646e10i			0.689135i
$540$	3.12932e10	+	2.01248e10i	0.368023	+	0.236677i
$541$	−5.98821e10			−0.699050			−0.349525	−	0.936927i	$-0.613657\pi$
$541$	−5.98821e10			−0.699050			−0.349525	+	0.936927i	$0.613657\pi$
$542$	6.24348e10	−	7.44069e10i	0.723485	−	0.862216i
$543$	−2.07280e10	−	2.75898e9i	−0.238428	−	0.0317358i
$544$	3.33662e9	+	1.89229e10i	0.0380988	+	0.216069i
$545$	1.88283e10	−	5.17303e10i	0.213415	−	0.586352i
$546$	−1.70228e10	−	7.73067e10i	−0.191540	−	0.869854i
$547$	−2.43016e9	+	1.37821e10i	−0.0271448	+	0.153946i	−0.995367	−	0.0961441i	$-0.969349\pi$
$547$	−2.43016e9	+	1.37821e10i	−0.0271448	+	0.153946i	0.968223	+	0.250090i	$0.0804601\pi$
$548$	4.08420e10	+	2.35801e10i	0.452882	+	0.261471i
$549$	−8.08297e9	−	1.16141e10i	−0.0889777	−	0.127848i
$550$	−2.12324e9	−	3.67756e9i	−0.0232032	−	0.0401891i
$551$	−4.58120e10	−	1.25867e11i	−0.497018	−	1.36555i
$552$	7.00178e8	+	1.65795e10i	0.00754141	+	0.178573i
$553$	7.71534e10	−	6.47394e10i	0.825001	−	0.692258i
$554$	−2.74337e10	−	3.26943e10i	−0.291237	−	0.347082i
$555$	5.35949e10	+	8.43927e10i	0.564874	+	0.889473i
$556$	2.42369e10	−	8.82152e9i	0.253617	−	0.0923090i
$557$	8.60416e9	−	4.96761e9i	0.0893897	−	0.0516092i	−0.454639	−	0.890676i	$-0.650232\pi$
$557$	8.60416e9	−	4.96761e9i	0.0893897	−	0.0516092i	0.544029	+	0.839067i	$0.316898\pi$
$558$	−1.12382e11	+	2.97691e10i	−1.15920	+	0.307064i
$559$	−2.49054e10	+	4.31374e10i	−0.255062	+	0.441780i
$560$	−3.94077e10	−	6.94863e9i	−0.400708	−	0.0706557i
$561$	1.04070e10	−	3.28433e10i	0.105069	−	0.331585i
$562$	9.80253e10	+	3.56783e10i	0.982636	+	0.357650i
$563$	1.23181e11	−	2.17201e10i	1.22605	−	0.216186i	0.477125	−	0.878836i	$-0.341679\pi$
$563$	1.23181e11	−	2.17201e10i	1.22605	−	0.216186i	0.748930	+	0.662649i	$0.230568\pi$
$564$	6.56601e10	−	2.70876e10i	0.648911	−	0.267704i
$565$	7.04991e10	+	5.91557e10i	0.691814	+	0.580501i
$566$		−	2.10620e10i		−	0.205227i
$567$	1.89109e11	+	3.44588e10i	1.82970	+	0.333402i
$568$	−8.74940e9			−0.0840592
$569$	−3.69250e10	+	4.40055e10i	−0.352267	+	0.419815i	−0.912858	−	0.408277i	$-0.866130\pi$
$569$	−3.69250e10	+	4.40055e10i	−0.352267	+	0.419815i	0.560591	+	0.828093i	$0.310574\pi$
$570$	4.49171e10	+	1.08878e11i	0.425512	+	1.03144i
$571$	−9.70275e8	−	5.50271e9i	−0.00912747	−	0.0517645i	0.979904	−	0.199470i	$-0.0639222\pi$
$571$	−9.70275e8	−	5.50271e9i	−0.00912747	−	0.0517645i	−0.989031	+	0.147706i	$0.952811\pi$
$572$	3.47482e9	−	9.54699e9i	0.0324600	−	0.0891830i
$573$	7.25105e10	+	2.29763e10i	0.672639	+	0.213138i
$574$	4.52387e10	−	2.56562e11i	0.416738	−	2.36344i
$575$	−1.12069e10	−	6.47033e9i	−0.102522	−	0.0591909i
$576$	−1.32804e10	−	3.59911e9i	−0.120648	−	0.0326968i
$577$	−6.94546e10	−	1.20299e11i	−0.626610	−	1.08532i	−0.988227	−	0.152994i	$-0.951108\pi$
$577$	−6.94546e10	−	1.20299e11i	−0.626610	−	1.08532i	0.361617	−	0.932327i	$-0.382225\pi$
$578$	−1.45867e10	−	4.00767e10i	−0.130691	−	0.359071i
$579$	−1.64203e11	+	1.04280e11i	−1.46106	+	0.927870i
$580$	3.05704e10	−	2.56516e10i	0.270140	−	0.226674i
$581$	1.34960e10	+	1.60839e10i	0.118441	+	0.141152i
$582$	5.21706e10	−	2.20325e9i	0.454709	−	0.0192031i
$583$	−3.74563e10	+	1.36330e10i	−0.324228	+	0.118009i
$584$	−4.77028e10	+	2.75412e10i	−0.410102	+	0.236773i
$585$	−6.28283e10	−	2.95159e10i	−0.536453	−	0.252018i
$586$	4.07758e10	−	7.06258e10i	0.345790	−	0.598926i
$587$	−5.91204e10	−	1.04245e10i	−0.497949	−	0.0878019i	−0.0809676	−	0.996717i	$-0.525801\pi$
$587$	−5.91204e10	−	1.04245e10i	−0.497949	−	0.0878019i	−0.416982	+	0.908915i	$0.636912\pi$
$588$	−1.43531e11	+	3.16053e10i	−1.20071	+	0.264394i
$589$	−3.45834e11	−	1.25873e11i	−2.87347	−	1.04586i
$590$	4.86718e10	−	8.58214e9i	0.401670	−	0.0708252i
$591$	−1.59373e10	+	1.19736e11i	−0.130637	+	0.981462i
$592$	−2.83221e10	−	2.37650e10i	−0.230589	−	0.193487i
$593$			1.18478e11i			0.958117i	0.877783	+	0.479058i	$0.159022\pi$
$593$			1.18478e11i			0.958117i	−0.877783	+	0.479058i	$0.840978\pi$
$594$	1.81178e10	+	1.67452e10i	0.145533	+	0.134507i
$595$	2.53175e11			2.02001
$596$	−2.92711e10	+	3.48839e10i	−0.231982	+	0.276465i
$597$	3.75950e10	−	4.88503e10i	0.295960	−	0.384565i
$598$	−5.37623e9	−	3.04901e10i	−0.0420410	−	0.238426i
$599$	5.17275e10	−	1.42120e11i	0.401804	−	1.10395i	−0.559589	−	0.828770i	$-0.689041\pi$
$599$	5.17275e10	−	1.42120e11i	0.401804	−	1.10395i	0.961393	−	0.275178i	$-0.0887367\pi$
$600$	7.92129e9	−	7.23776e9i	0.0611210	−	0.0558469i
$601$	3.48933e10	−	1.97890e11i	0.267451	−	1.51679i	−0.494512	−	0.869171i	$-0.664653\pi$
$601$	3.48933e10	−	1.97890e11i	0.267451	−	1.51679i	0.761964	−	0.647620i	$-0.224236\pi$
$602$	1.12662e11	+	6.50455e10i	0.857812	+	0.495258i
$603$	−6.75105e9	+	7.47090e10i	−0.0510625	+	0.565071i
$604$	−1.51076e10	−	2.61671e10i	−0.113513	−	0.196611i
$605$	−3.69499e10	−	1.01519e11i	−0.275798	−	0.757750i
$606$	−1.14555e10	−	5.98413e9i	−0.0849420	−	0.0443721i
$607$	−1.81601e11	+	1.52381e11i	−1.33771	+	1.12248i	−0.355507	+	0.934674i	$0.615692\pi$
$607$	−1.81601e11	+	1.52381e11i	−1.33771	+	1.12248i	−0.982207	+	0.187801i	$0.939864\pi$
$608$	−2.79980e10	−	3.33668e10i	−0.204887	−	0.244174i
$609$	9.54629e10	−	1.82745e11i	0.694009	−	1.32855i
$610$	1.25407e10	−	4.56443e9i	0.0905735	−	0.0329661i
$611$	−1.14765e11	+	6.62597e10i	−0.823465	+	0.475428i
$612$	8.67013e10	+	7.83473e9i	0.618045	+	0.0558494i
$613$	2.53376e10	−	4.38861e10i	0.179442	−	0.310803i	−0.762248	−	0.647286i	$-0.775904\pi$
$613$	2.53376e10	−	4.38861e10i	0.179442	−	0.310803i	0.941690	+	0.336483i	$0.109237\pi$
$614$	−6.50224e10	−	1.14652e10i	−0.457498	−	0.0806693i
$615$	−1.54102e11	−	1.68655e11i	−1.07723	−	1.17896i
$616$	−2.49339e10	−	9.07521e9i	−0.173168	−	0.0630280i
$617$	−6.52087e9	+	1.14980e9i	−0.0449950	+	0.00793384i	−0.196100	−	0.980584i	$-0.562828\pi$
$617$	−6.52087e9	+	1.14980e9i	−0.0449950	+	0.00793384i	0.151105	+	0.988518i	$0.451717\pi$
$618$	−5.19413e9	−	3.99738e9i	−0.0356089	−	0.0274045i
$619$	1.08800e10	+	9.12943e9i	0.0741084	+	0.0621844i	0.679089	−	0.734056i	$-0.262375\pi$
$619$	1.08800e10	+	9.12943e9i	0.0741084	+	0.0621844i	−0.604981	+	0.796240i	$0.706819\pi$
$620$		−	1.09648e11i		−	0.742053i
$621$	7.33295e10	+	1.65864e10i	0.493074	+	0.111528i
$622$	−1.37723e10			−0.0920121
$623$	2.42461e10	−	2.88954e10i	0.160950	−	0.191812i
$624$	2.54470e10	+	3.38710e9i	0.167841	+	0.0223403i
$625$	−1.88388e10	−	1.06840e11i	−0.123462	−	0.700188i
$626$	−3.80720e10	+	1.04602e11i	−0.247918	+	0.681149i
$627$	1.67950e10	+	7.62719e10i	0.108670	+	0.493509i
$628$	9.76796e9	−	5.53969e10i	0.0628008	−	0.356161i
$629$	2.02578e11	+	1.16959e11i	1.29417	+	0.747188i
$630$	−7.70868e10	+	1.64089e11i	−0.489348	+	1.04164i
$631$	−2.33984e10	−	4.05272e10i	−0.147594	−	0.255640i	0.782744	−	0.622344i	$-0.213820\pi$
$631$	−2.33984e10	−	4.05272e10i	−0.147594	−	0.255640i	−0.930338	+	0.366704i	$0.880486\pi$
$632$	1.11713e10	+	3.06929e10i	0.0700222	+	0.192384i
$633$	8.42892e9	+	1.99588e11i	0.0524997	+	1.24314i
$634$	7.09489e10	−	5.95332e10i	0.439126	−	0.368470i
$635$	4.06197e10	+	4.84086e10i	0.249828	+	0.297734i
$636$	−5.39946e10	−	8.50219e10i	−0.330006	−	0.519640i
$637$	2.57670e11	−	9.37841e10i	1.56497	−	0.569602i
$638$	2.29168e10	−	1.32310e10i	0.138315	−	0.0798565i
$639$	−1.03688e10	+	3.82599e10i	−0.0621906	+	0.229477i
$640$	6.48859e9	−	1.12386e10i	0.0386750	−	0.0669870i
$641$	2.62489e11	+	4.62839e10i	1.55482	+	0.274156i	0.884007	−	0.467473i	$-0.154835\pi$
$641$	2.62489e11	+	4.62839e10i	1.55482	+	0.274156i	0.670810	+	0.741629i	$0.265947\pi$
$642$	−4.00890e9	+	1.26516e10i	−0.0235986	+	0.0744744i
$643$	−2.59456e11	−	9.44343e10i	−1.51782	−	0.552441i	−0.557217	−	0.830367i	$-0.688131\pi$
$643$	−2.59456e11	−	9.44343e10i	−1.51782	−	0.552441i	−0.960602	+	0.277926i	$0.910353\pi$
$644$	−7.96313e10	+	1.40411e10i	−0.462956	+	0.0816317i
$645$	1.05458e11	−	4.35060e10i	0.609314	−	0.251368i
$646$	2.11109e11	+	1.77141e11i	1.21220	+	1.01716i
$647$			2.64839e11i			1.51135i	0.654949	+	0.755673i	$0.272690\pi$
$647$			2.64839e11i			1.51135i	−0.654949	+	0.755673i	$0.727310\pi$
$648$	−3.14767e10	+	5.38078e10i	−0.178521	+	0.305172i
$649$	3.27719e10			0.184724
$650$	−1.28681e10	+	1.53356e10i	−0.0720878	+	0.0859108i
$651$	−2.16041e11	−	5.23681e11i	−1.20285	−	2.91570i
$652$	4.06155e9	+	2.30342e10i	0.0224751	+	0.127462i
$653$	4.17773e9	−	1.14782e10i	0.0229767	−	0.0631280i	−0.927674	−	0.373391i	$-0.878195\pi$
$653$	4.17773e9	−	1.14782e10i	0.0229767	−	0.0631280i	0.950651	+	0.310263i	$0.100417\pi$
$654$	8.79280e10	+	2.78616e10i	0.480636	+	0.152298i
$655$	2.15314e10	−	1.22111e11i	0.116979	−	0.663420i
$656$	7.31681e10	+	4.22436e10i	0.395100	+	0.228111i
$657$	6.39017e10	+	2.41236e11i	0.342966	+	1.29473i
$658$	1.73051e11	+	2.99733e11i	0.923145	+	1.59893i
$659$	8.75157e10	+	2.40447e11i	0.464028	+	1.27491i	0.922431	+	0.386162i	$0.126200\pi$
$659$	8.75157e10	+	2.40447e11i	0.464028	+	1.27491i	−0.458403	+	0.888745i	$0.651578\pi$
$660$	−1.96422e10	+	1.24741e10i	−0.103518	+	0.0657405i
$661$	1.54679e11	−	1.29791e11i	0.810262	−	0.679891i	−0.140408	−	0.990094i	$-0.544841\pi$
$661$	1.54679e11	−	1.29791e11i	0.810262	−	0.679891i	0.950670	+	0.310203i	$0.100397\pi$
$662$	1.12545e11	+	1.34125e11i	0.585993	+	0.698359i
$663$	−1.62276e11	+	6.85317e9i	−0.839847	+	0.0354681i
$664$	−6.39845e9	+	2.32884e9i	−0.0329156	+	0.0119803i
$665$	−4.97021e11	+	2.86955e11i	−2.54149	+	1.46733i
$666$	−1.37485e11	+	9.56846e10i	−0.698810	+	0.486346i
$667$	4.03200e10	−	6.98362e10i	0.203712	−	0.352840i
$668$	−3.76934e10	−	6.64636e9i	−0.189304	−	0.0333793i
$669$	−1.02252e11	+	2.25157e10i	−0.510465	+	0.112404i
$670$	−6.64821e10	−	2.41975e10i	−0.329918	−	0.120080i
$671$	8.71489e9	−	1.53667e9i	0.0429905	−	0.00758038i
$672$	8.84611e9	−	6.64600e10i	0.0433786	−	0.325899i
$673$	4.31162e10	+	3.61788e10i	0.210174	+	0.176357i	0.741798	−	0.670624i	$-0.233973\pi$
$673$	4.31162e10	+	3.61788e10i	0.210174	+	0.176357i	−0.531623	+	0.846981i	$0.678418\pi$
$674$		−	1.45550e11i		−	0.705297i
$675$	−2.22622e10	−	4.32160e10i	−0.107239	−	0.208175i
$676$	5.65175e10			0.270643
$677$	−2.86897e10	+	3.41911e10i	−0.136575	+	0.162764i	−0.829997	−	0.557768i	$-0.811658\pi$
$677$	−2.86897e10	+	3.41911e10i	−0.136575	+	0.162764i	0.693422	+	0.720532i	$0.256102\pi$
$678$	−9.40432e10	+	1.22198e11i	−0.445050	+	0.578290i
$679$	4.41832e10	+	2.50575e11i	0.207863	+	1.17885i
$680$	−2.80817e10	+	7.71538e10i	−0.131337	+	0.360846i
$681$	3.13268e10	−	2.86236e10i	0.145656	−	0.133087i
$682$	1.26255e10	−	7.16026e10i	0.0583593	−	0.330972i
$683$	6.58181e10	+	3.80001e10i	0.302456	+	0.174623i	0.643546	−	0.765408i	$-0.277463\pi$
$683$	6.58181e10	+	3.80001e10i	0.302456	+	0.174623i	−0.341089	+	0.940031i	$0.610796\pi$
$684$	−1.79088e11	+	8.28889e10i	−0.818168	+	0.378679i
$685$	1.00758e11	+	1.74519e11i	0.457635	+	0.792647i
$686$	−1.45326e11	−	3.99280e11i	−0.656217	−	1.80294i
$687$	−3.56453e10	−	1.86205e10i	−0.160021	−	0.0835918i
$688$	−3.23186e10	+	2.71185e10i	−0.144244	+	0.121035i
$689$	1.20788e11	+	1.43950e11i	0.535979	+	0.638755i
$690$	−3.28312e10	+	6.28491e10i	−0.144841	+	0.277270i
$691$	−1.55480e10	+	5.65901e9i	−0.0681965	+	0.0248215i	−0.375893	−	0.926663i	$-0.622664\pi$
$691$	−1.55480e10	+	5.65901e9i	−0.0681965	+	0.0248215i	0.307697	+	0.951485i	$0.400442\pi$
$692$	9.38473e10	−	5.41828e10i	0.409258	−	0.236285i
$693$	−6.92334e10	+	9.82775e10i	−0.300181	+	0.426110i
$694$	3.42155e9	−	5.92630e9i	0.0147498	−	0.0255474i
$695$	1.08537e11	+	1.91380e10i	0.465199	+	0.0820272i
$696$	4.51022e10	+	4.93616e10i	0.192203	+	0.210355i
$697$	−5.02306e11	−	1.82825e11i	−2.12832	−	0.774646i
$698$	2.07514e11	−	3.65904e10i	0.874231	−	0.154151i
$699$	−1.45309e11	−	1.11829e11i	−0.608674	−	0.468433i
$700$	4.00521e10	+	3.36077e10i	0.166814	+	0.139974i
$701$			1.93876e10i			0.0802881i	0.999194	+	0.0401441i	$0.0127817\pi$
$701$			1.93876e10i			0.0802881i	−0.999194	+	0.0401441i	$0.987218\pi$
$702$	4.49681e10	−	1.07262e11i	0.185164	−	0.441669i
$703$	−5.30257e11			−2.17103
$704$	5.53125e9	−	6.59189e9i	0.0225182	−	0.0268361i
$705$	3.00851e11	+	4.00445e10i	1.21785	+	0.162101i
$706$	4.27948e10	+	2.42701e11i	0.172255	+	0.976908i
$707$	2.15394e10	−	5.91789e10i	0.0862095	−	0.236859i
$708$	1.78075e10	+	8.08702e10i	0.0708712	+	0.321852i
$709$	−3.95597e10	+	2.24354e11i	−0.156555	+	0.887869i	0.800795	+	0.598939i	$0.204411\pi$
$709$	−3.95597e10	+	2.24354e11i	−0.156555	+	0.887869i	−0.957350	+	0.288930i	$0.906700\pi$
$710$	−3.23776e10	−	1.86932e10i	−0.127412	−	0.0735614i
$711$	1.47455e11	−	1.24767e10i	0.577005	−	0.0488228i
$712$	6.11640e9	+	1.05939e10i	0.0237999	+	0.0412227i
$713$	−7.57803e10	−	2.08205e11i	−0.293223	−	0.805624i
$714$	1.78985e10	+	4.23817e11i	0.0688689	+	1.63074i
$715$	3.32560e10	−	2.79051e10i	0.127246	−	0.106772i
$716$	1.58100e11	+	1.88416e11i	0.601561	+	0.716913i
$717$	−2.49211e11	−	3.92417e11i	−0.942954	−	1.48481i
$718$	1.55337e10	−	5.65382e9i	0.0584492	−	0.0212738i
$719$	4.26363e11	−	2.46161e11i	1.59538	−	0.921092i	0.603016	−	0.797729i	$-0.293965\pi$
$719$	4.26363e11	−	2.46161e11i	1.59538	−	0.921092i	0.992362	−	0.123363i	$-0.0393679\pi$
$720$	−4.14550e10	−	4.16923e10i	−0.154258	−	0.155141i
$721$	1.59686e10	−	2.76584e10i	0.0590915	−	0.102350i
$722$	−4.25987e11	−	7.51131e10i	−1.56765	−	0.276418i
$723$	−1.07036e11	+	3.37793e11i	−0.391720	+	1.23622i
$724$	3.10514e10	+	1.13018e10i	0.113013	+	0.0411332i
$725$	−5.13501e10	+	9.05440e9i	−0.185861	+	0.0327724i
$726$	1.67332e11	−	6.90315e10i	0.602326	−	0.248485i
$727$	−2.62089e10	−	2.19919e10i	−0.0938233	−	0.0787271i	0.594670	−	0.803970i	$-0.297283\pi$
$727$	−2.62089e10	−	2.19919e10i	−0.0938233	−	0.0787271i	−0.688493	+	0.725243i	$0.741727\pi$
$728$			1.25090e11i			0.445346i
$729$	1.97991e11	+	2.01410e11i	0.701028	+	0.713134i
$730$	−2.35368e11			−0.828813
$731$	1.71576e11	−	2.04477e11i	0.600880	−	0.716101i
$732$	8.52747e9	+	2.06705e10i	0.0297013	+	0.0719957i
$733$	−4.60198e10	−	2.60992e11i	−0.159415	−	0.904088i	−0.954638	−	0.297770i	$-0.903757\pi$
$733$	−4.60198e10	−	2.60992e11i	−0.159415	−	0.904088i	0.795223	−	0.606318i	$-0.207354\pi$
$734$	−7.54012e10	+	2.07163e11i	−0.259773	+	0.713720i
$735$	−5.98669e11	−	1.89699e11i	−2.05134	−	0.650004i
$736$	4.55358e9	−	2.58247e10i	0.0155182	−	0.0880082i
$737$	−4.06280e10	−	2.34566e10i	−0.137707	−	0.0795050i
$738$	2.71436e11	−	2.69891e11i	0.915043	−	0.909836i
$739$	5.01162e10	+	8.68039e10i	0.168035	+	0.291046i	0.937729	−	0.347368i	$-0.112924\pi$
$739$	5.01162e10	+	8.68039e10i	0.168035	+	0.291046i	−0.769694	+	0.638413i	$0.779591\pi$
$740$	−5.40329e10	−	1.48454e11i	−0.180190	−	0.495068i
$741$	3.10805e11	−	1.97382e11i	1.03090	−	0.654688i
$742$	3.75955e11	−	3.15463e11i	1.24028	−	1.04072i
$743$	−9.10204e10	−	1.08474e11i	−0.298664	−	0.355934i	0.595753	−	0.803168i	$-0.296854\pi$
$743$	−9.10204e10	−	1.08474e11i	−0.298664	−	0.355934i	−0.894417	+	0.447233i	$0.852409\pi$
$744$	1.83552e11	−	7.75170e9i	0.599056	−	0.0252991i
$745$	−1.82849e11	+	6.65515e10i	−0.593563	+	0.216039i
$746$	2.31758e11	−	1.33805e11i	0.748306	−	0.432034i
$747$	2.60098e9	+	3.07393e10i	0.00835324	+	0.0987216i
$748$	−2.72218e10	+	4.71496e10i	−0.0869583	+	0.150616i
$749$	−6.36867e10	−	1.12297e10i	−0.202359	−	0.0356813i
$750$	2.35988e11	−	5.19642e10i	0.745839	−	0.164232i
$751$	8.08239e10	+	2.94175e10i	0.254086	+	0.0924796i	0.465923	−	0.884825i	$-0.345722\pi$
$751$	8.08239e10	+	2.94175e10i	0.254086	+	0.0924796i	−0.211837	+	0.977305i	$0.567945\pi$
$752$	−1.10537e11	+	1.94906e10i	−0.345649	+	0.0609472i
$753$	−1.63799e10	+	1.23060e11i	−0.0509484	+	0.382771i
$754$	−9.55642e10	−	8.01879e10i	−0.295672	−	0.248098i
$755$		−	1.29110e11i		−	0.397349i
$756$

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.27231 - 8.66680i) q^{2} +(30.8906 + 74.8784i) q^{3} +(-22.2270 - 126.055i) q^{4} +(187.067 - 513.962i) q^{5} +(873.602 + 276.817i) q^{6} +(-775.415 + 4397.60i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-4652.55 + 4626.07i) q^{9} +O(q^{10})\)	\(q+(7.27231 - 8.66680i) q^{2} +(30.8906 + 74.8784i) q^{3} +(-22.2270 - 126.055i) q^{4} +(187.067 - 513.962i) q^{5} +(873.602 + 276.817i) q^{6} +(-775.415 + 4397.60i) q^{7} +(-1254.14 - 724.077i) q^{8} +(-4652.55 + 4626.07i) q^{9} +(-3094.00 - 5358.96i) q^{10} +(-1403.39 - 3855.78i) q^{11} +(8752.22 - 5558.24i) q^{12} +(-14818.3 + 12434.0i) q^{13} +(32474.0 + 38701.1i) q^{14} +(44263.2 - 1869.31i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(89772.3 - 51830.0i) q^{17} +(6258.48 + 73964.9i) q^{18} +(-117491. + 203501. i) q^{19} +(-68945.6 - 12157.0i) q^{20} +(-353238. + 77782.4i) q^{21} +(-43623.1 - 15877.5i) q^{22} +(-139319. + 24565.7i) q^{23} +(15476.7 - 116275. i) q^{24} +(70073.2 + 58798.4i) q^{25} +218852. i q^{26} +(-490112. - 205473. i) q^{27} +571576. q^{28} +(-366403. + 436662. i) q^{29} +(305695. - 397215. i) q^{30} +(271967. + 1.54240e6i) q^{31} +(-63398.2 + 174185. i) q^{32} +(245363. - 224191. i) q^{33} +(203651. - 1.15496e6i) q^{34} +(2.11514e6 + 1.22118e6i) q^{35} +(686553. + 483655. i) q^{36} +(1.12829e6 + 1.95426e6i) q^{37} +(909268. + 2.49819e6i) q^{38} +(-1.38879e6 - 725477. i) q^{39} +(-606756. + 509129. i) q^{40} +(-3.31466e6 - 3.95026e6i) q^{41} +(-1.89473e6 + 3.62710e6i) q^{42} +(2.41971e6 - 880704. i) q^{43} +(-454848. + 262607. i) q^{44} +(1.50729e6 + 3.25662e6i) q^{45} +(-800264. + 1.38610e6i) q^{46} +(6.74662e6 + 1.18961e6i) q^{47} +(-895182. - 979722. i) q^{48} +(-1.33204e7 - 4.84825e6i) q^{49} +(1.01919e6 - 179710. i) q^{50} +(6.65406e6 + 5.12094e6i) q^{51} +(1.89674e6 + 1.59156e6i) q^{52} -9.71432e6i q^{53} +(-5.34505e6 + 2.75344e6i) q^{54} -2.24425e6 q^{55} +(4.15668e6 - 4.95374e6i) q^{56} +(-1.88672e7 - 2.51130e6i) q^{57} +(1.11987e6 + 6.35109e6i) q^{58} +(-2.73166e6 + 7.50518e6i) q^{59} +(-1.21947e6 - 5.53807e6i) q^{60} +(-374503. + 2.12391e6i) q^{61} +(1.53455e7 + 8.85975e6i) q^{62} +(-1.67359e7 - 2.40471e7i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(3.61861e6 + 9.94204e6i) q^{65} +(-158660. - 3.75690e6i) q^{66} +(8.75836e6 - 7.34913e6i) q^{67} +(-8.52882e6 - 1.01643e7i) q^{68} +(-6.14307e6 - 9.67312e6i) q^{69} +(2.59657e7 - 9.45074e6i) q^{70} +(5.23232e6 - 3.02088e6i) q^{71} +(9.18457e6 - 2.43293e6i) q^{72} +(1.90181e7 - 3.29404e7i) q^{73} +(2.51424e7 + 4.43329e6i) q^{74} +(-2.23813e6 + 7.06328e6i) q^{75} +(2.82638e7 + 1.02872e7i) q^{76} +(1.80444e7 - 3.18171e6i) q^{77} +(-1.63872e7 + 6.76045e6i) q^{78} +(-1.72779e7 - 1.44979e7i) q^{79} +8.96118e6i q^{80} +(245661. - 4.30460e7i) q^{81} -5.83413e7 q^{82} +(3.02233e6 - 3.60187e6i) q^{83} +(1.76563e7 + 4.27987e7i) q^{84} +(-9.84525e6 - 5.58352e7i) q^{85} +(9.96403e6 - 2.73759e7i) q^{86} +(-4.40150e7 - 1.39469e7i) q^{87} +(-1.03184e6 + 5.85184e6i) q^{88} +(-7.31545e6 - 4.22358e6i) q^{89} +(3.91859e7 + 1.06198e7i) q^{90} +(-4.31895e7 - 7.48065e7i) q^{91} +(6.19327e6 + 1.70159e7i) q^{92} +(-1.07091e8 + 6.80101e7i) q^{93} +(5.93736e7 - 4.98204e7i) q^{94} +(8.26129e7 + 9.84543e7i) q^{95} +(-1.50011e7 + 633520. i) q^{96} +(5.35437e7 - 1.94883e7i) q^{97} +(-1.38889e8 + 8.01878e7i) q^{98} +(2.43664e7 + 1.14470e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

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