LMFDB - Embedded newform 54.9.f.a.5.9

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			5.9
Character	$\chi$	$=$	54.5
Dual form			54.9.f.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.27231 - 8.66680i) q^{2} +(61.3803 + 52.8531i) q^{3} +(-22.2270 + 126.055i) q^{4} +(209.630 + 575.954i) q^{5} +(11.6907 - 916.336i) q^{6} +(358.863 + 2035.21i) q^{7} +(1254.14 - 724.077i) q^{8} +(974.093 + 6488.29i) q^{9} +O(q^{10})$	\(q+(-7.27231 - 8.66680i) q^{2} +(61.3803 + 52.8531i) q^{3} +(-22.2270 + 126.055i) q^{4} +(209.630 + 575.954i) q^{5} +(11.6907 - 916.336i) q^{6} +(358.863 + 2035.21i) q^{7} +(1254.14 - 724.077i) q^{8} +(974.093 + 6488.29i) q^{9} +(3467.19 - 6005.34i) q^{10} +(-1876.37 + 5155.27i) q^{11} +(-8026.72 + 6562.56i) q^{12} +(-427.513 - 358.726i) q^{13} +(15029.0 - 17910.9i) q^{14} +(-17573.8 + 46431.9i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-62437.1 - 36048.1i) q^{17} +(49148.8 - 55627.1i) q^{18} +(-75841.5 - 131361. i) q^{19} +(-77261.6 + 13623.3i) q^{20} +(-85540.2 + 143889. i) q^{21} +(58325.3 - 21228.7i) q^{22} +(-12116.4 - 2136.45i) q^{23} +(115249. + 21841.0i) q^{24} +(11457.8 - 9614.25i) q^{25} +6313.94i q^{26} +(-283136. + 449737. i) q^{27} -264526. q^{28} +(83917.4 + 100009. i) q^{29} +(530218. - 185358. i) q^{30} +(-173088. + 981632. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-387644. + 217261. i) q^{33} +(141640. + 803282. i) q^{34} +(-1.09696e6 + 633330. i) q^{35} +(-839535. - 21425.2i) q^{36} +(-1.08580e6 + 1.88067e6i) q^{37} +(-586940. + 1.61260e6i) q^{38} +(-7281.10 - 44614.1i) q^{39} +(679941. + 570538. i) q^{40} +(-1.67092e6 + 1.99132e6i) q^{41} +(1.86913e6 - 305046. i) q^{42} +(6.15302e6 + 2.23951e6i) q^{43} +(-608144. - 351112. i) q^{44} +(-3.53276e6 + 1.92117e6i) q^{45} +(69598.2 + 120548. i) q^{46} +(-4.51540e6 + 796186. i) q^{47} +(-648836. - 1.15768e6i) q^{48} +(1.40384e6 - 510956. i) q^{49} +(-166650. - 29384.8i) q^{50} +(-1.92716e6 - 5.51264e6i) q^{51} +(54721.7 - 45916.9i) q^{52} -8.48466e6i q^{53} +(5.95684e6 - 816744. i) q^{54} -3.36254e6 q^{55} +(1.92371e6 + 2.29259e6i) q^{56} +(2.28768e6 - 1.20715e7i) q^{57} +(256484. - 1.45459e6i) q^{58} +(-6.50099e6 - 1.78613e7i) q^{59} +(-5.46237e6 - 3.24731e6i) q^{60} +(2.29174e6 + 1.29971e7i) q^{61} +(9.76636e6 - 5.63861e6i) q^{62} +(-1.28555e7 + 4.31089e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(116990. - 321428. i) q^{65} +(4.70203e6 + 1.77965e6i) q^{66} +(-602495. - 505554. i) q^{67} +(5.93184e6 - 7.06929e6i) q^{68} +(-630792. - 771527. i) q^{69} +(1.34664e7 + 4.90136e6i) q^{70} +(1.88839e7 + 1.09027e7i) q^{71} +(5.91967e6 + 7.43189e6i) q^{72} +(7.76455e6 + 1.34486e7i) q^{73} +(2.41957e7 - 4.26635e6i) q^{74} +(1.21143e6 + 15455.5i) q^{75} +(1.82445e7 - 6.64046e6i) q^{76} +(-1.11654e7 - 1.96877e6i) q^{77} +(-333711. + 387552. i) q^{78} +(-926580. + 777493. i) q^{79} -1.00420e7i q^{80} +(-4.11490e7 + 1.26404e7i) q^{81} +2.94099e7 q^{82} +(-2.24413e7 - 2.67445e7i) q^{83} +(-1.62367e7 - 1.39810e7i) q^{84} +(7.67333e6 - 4.35176e7i) q^{85} +(-2.53372e7 - 6.96134e7i) q^{86} +(-134903. + 1.05739e7i) q^{87} +(1.37959e6 + 7.82406e6i) q^{88} +(-3.19449e7 + 1.84434e7i) q^{89} +(4.23417e7 + 1.66463e7i) q^{90} +(576665. - 998813. i) q^{91} +(538622. - 1.47985e6i) q^{92} +(-6.25065e7 + 5.11047e7i) q^{93} +(3.97378e7 + 3.33439e7i) q^{94} +(5.97594e7 - 7.12185e7i) q^{95} +(-5.31482e6 + 1.40423e7i) q^{96} +(1.53373e8 + 5.58232e7i) q^{97} +(-1.46375e7 - 8.45098e6i) q^{98} +(-3.52766e7 - 7.15268e6i) 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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
$3$	61.3803	+	52.8531i	0.757782	+	0.652508i
$3$	61.3803	+	52.8531i	0.757782	+	0.652508i
$4$	−22.2270	+	126.055i	−0.0868241	+	0.492404i
$5$	209.630	+	575.954i	0.335408	+	0.921527i	0.986679	+	0.162681i	$0.0520141\pi$
$5$	209.630	+	575.954i	0.335408	+	0.921527i	−0.651271	+	0.758846i	$0.725764\pi$
$6$	11.6907	−	916.336i	0.00902061	−	0.707049i
$7$	358.863	+	2035.21i	0.149464	+	0.847651i	0.963674	+	0.267081i	$0.0860592\pi$
$7$	358.863	+	2035.21i	0.149464	+	0.847651i	−0.814210	+	0.580570i	$0.802830\pi$
$8$	1254.14	−	724.077i	0.306186	−	0.176777i
$9$	974.093	+	6488.29i	0.148467	+	0.988917i
$10$	3467.19	−	6005.34i	0.346719	−	0.600534i
$11$	−1876.37	+	5155.27i	−0.128158	+	0.352112i	−0.987132	−	0.159908i	$-0.948880\pi$
$11$	−1876.37	+	5155.27i	−0.128158	+	0.352112i	0.858974	+	0.512020i	$0.171103\pi$
$12$	−8026.72	+	6562.56i	−0.387091	+	0.316481i
$13$	−427.513	−	358.726i	−0.0149684	−	0.0125600i	0.635273	−	0.772288i	$-0.280888\pi$
$13$	−427.513	−	358.726i	−0.0149684	−	0.0125600i	−0.650241	+	0.759728i	$0.725332\pi$
$14$	15029.0	−	17910.9i	0.391218	−	0.466235i
$15$	−17573.8	+	46431.9i	−0.347137	+	0.917173i
$16$	−15395.9	−	5603.66i	−0.234923	−	0.0855050i
$17$	−62437.1	−	36048.1i	−0.747561	−	0.431605i	0.0772508	−	0.997012i	$-0.475386\pi$
$17$	−62437.1	−	36048.1i	−0.747561	−	0.431605i	−0.824812	+	0.565407i	$0.808719\pi$
$18$	49148.8	−	55627.1i	0.468191	−	0.529903i
$19$	−75841.5	−	131361.i	−0.581959	−	1.00798i	−0.995247	−	0.0973821i	$-0.968953\pi$
$19$	−75841.5	−	131361.i	−0.581959	−	1.00798i	0.413288	−	0.910600i	$-0.364380\pi$
$20$	−77261.6	+	13623.3i	−0.482885	+	0.0851456i
$21$	−85540.2	+	143889.i	−0.439838	+	0.739861i
$22$	58325.3	−	21228.7i	0.248981	−	0.0906216i
$23$	−12116.4	−	2136.45i	−0.0432975	−	0.00763452i	0.151957	−	0.988387i	$-0.451442\pi$
$23$	−12116.4	−	2136.45i	−0.0432975	−	0.00763452i	−0.195255	+	0.980753i	$0.562553\pi$
$24$	115249.	+	21841.0i	0.347371	+	0.0658307i
$25$	11457.8	−	9614.25i	0.0293320	−	0.0246125i
$26$			6313.94i			0.0138168i
$27$	−283136.	+	449737.i	−0.532770	+	0.846260i
$28$	−264526.			−0.430364
$29$	83917.4	+	100009.i	0.118648	+	0.141399i	0.822099	−	0.569345i	$-0.192803\pi$
$29$	83917.4	+	100009.i	0.118648	+	0.141399i	−0.703451	+	0.710744i	$0.748359\pi$
$30$	530218.	−	185358.i	0.654590	−	0.228837i
$31$	−173088.	+	981632.i	−0.187422	+	1.06292i	0.735382	+	0.677653i	$0.237003\pi$
$31$	−173088.	+	981632.i	−0.187422	+	1.06292i	−0.922804	+	0.385270i	$0.874108\pi$
$32$	63398.2	+	174185.i	0.0604612	+	0.166116i
$33$	−387644.	+	217261.i	−0.326872	+	0.183200i
$34$	141640.	+	803282.i	0.105992	+	0.601108i
$35$	−1.09696e6	+	633330.i	−0.731002	+	0.422044i
$36$	−839535.	−	21425.2i	−0.499837	−	0.0127560i
$37$	−1.08580e6	+	1.88067e6i	−0.579355	+	1.00347i	0.416198	+	0.909274i	$0.363362\pi$
$37$	−1.08580e6	+	1.88067e6i	−0.579355	+	1.00347i	−0.995553	+	0.0941985i	$0.969971\pi$
$38$	−586940.	+	1.61260e6i	−0.281487	+	0.773380i
$39$	−7281.10	−	44614.1i	−0.00314730	−	0.0192848i
$40$	679941.	+	570538.i	0.265602	+	0.222866i
$41$	−1.67092e6	+	1.99132e6i	−0.591317	+	0.704704i	−0.975858	−	0.218404i	$-0.929915\pi$
$41$	−1.67092e6	+	1.99132e6i	−0.591317	+	0.704704i	0.384542	+	0.923108i	$0.374359\pi$
$42$	1.86913e6	−	305046.i	0.600679	−	0.0980319i
$43$	6.15302e6	+	2.23951e6i	1.79976	+	0.655058i	0.998380	+	0.0569009i	$0.0181219\pi$
$43$	6.15302e6	+	2.23951e6i	1.79976	+	0.655058i	0.801379	+	0.598158i	$0.204100\pi$
$44$	−608144.	−	351112.i	−0.162254	−	0.0936775i
$45$	−3.53276e6	+	1.92117e6i	−0.861516	+	0.468507i
$46$	69598.2	+	120548.i	0.0155441	+	0.0269232i
$47$	−4.51540e6	+	796186.i	−0.925347	+	0.163164i	−0.615964	−	0.787774i	$-0.711233\pi$
$47$	−4.51540e6	+	796186.i	−0.925347	+	0.163164i	−0.309383	+	0.950938i	$0.600122\pi$
$48$	−648836.	−	1.15768e6i	−0.122228	−	0.218083i
$49$	1.40384e6	−	510956.i	0.243519	−	0.0886338i
$50$	−166650.	−	29384.8i	−0.0266639	−	0.00470157i
$51$	−1.92716e6	−	5.51264e6i	−0.284863	−	0.814852i
$52$	54721.7	−	45916.9i	0.00748421	−	0.00628000i
$53$		−	8.48466e6i		−	1.07530i	−0.843167	−	0.537652i	$-0.819311\pi$
$53$		−	8.48466e6i		−	1.07530i	0.843167	−	0.537652i	$-0.180689\pi$
$54$	5.95684e6	−	816744.i	0.700553	−	0.0960530i
$55$	−3.36254e6			−0.367466
$56$	1.92371e6	+	2.29259e6i	0.195609	+	0.233117i
$57$	2.28768e6	−	1.20715e7i	0.216718	−	1.14356i
$58$	256484.	−	1.45459e6i	0.0226646	−	0.128537i
$59$	−6.50099e6	−	1.78613e7i	−0.536502	−	1.47403i	−0.851203	−	0.524837i	$-0.824126\pi$
$59$	−6.50099e6	−	1.78613e7i	−0.536502	−	1.47403i	0.314700	−	0.949191i	$-0.398096\pi$
$60$	−5.46237e6	−	3.24731e6i	−0.421480	−	0.250564i
$61$	2.29174e6	+	1.29971e7i	0.165519	+	0.938703i	0.948528	+	0.316693i	$0.102572\pi$
$61$	2.29174e6	+	1.29971e7i	0.165519	+	0.938703i	−0.783009	+	0.622010i	$0.786316\pi$
$62$	9.76636e6	−	5.63861e6i	0.660946	−	0.381597i
$63$	−1.28555e7	+	4.31089e6i	−0.816067	+	0.273656i
$64$	1.04858e6	−	1.81619e6i	0.0625000	−	0.108253i
$65$	116990.	−	321428.i	0.00655384	−	0.0180065i
$66$	4.70203e6	+	1.77965e6i	0.247805	+	0.0937905i
$67$	−602495.	−	505554.i	−0.0298988	−	0.0250881i	0.627716	−	0.778443i	$-0.283990\pi$
$67$	−602495.	−	505554.i	−0.0298988	−	0.0250881i	−0.657615	+	0.753355i	$0.728434\pi$
$68$	5.93184e6	−	7.06929e6i	0.277430	−	0.330628i
$69$	−630792.	−	771527.i	−0.0278285	−	0.0340373i
$70$	1.34664e7	+	4.90136e6i	0.560865	+	0.204138i
$71$	1.88839e7	+	1.09027e7i	0.743121	+	0.429041i	0.823203	−	0.567747i	$-0.192185\pi$
$71$	1.88839e7	+	1.09027e7i	0.743121	+	0.429041i	−0.0800822	+	0.996788i	$0.525518\pi$
$72$	5.91967e6	+	7.43189e6i	0.220276	+	0.276547i
$73$	7.76455e6	+	1.34486e7i	0.273416	+	0.473571i	0.969734	−	0.244162i	$-0.0785130\pi$
$73$	7.76455e6	+	1.34486e7i	0.273416	+	0.473571i	−0.696318	+	0.717733i	$0.745180\pi$
$74$	2.41957e7	−	4.26635e6i	0.806884	−	0.142275i
$75$	1.21143e6	+	15455.5i	0.0382871	+	0.000488471i
$76$	1.82445e7	−	6.64046e6i	0.546863	−	0.199042i
$77$	−1.11654e7	−	1.96877e6i	−0.317623	−	0.0560056i
$78$	−333711.	+	387552.i	−0.00901556	+	0.0104701i
$79$	−926580.	+	777493.i	−0.0237889	+	0.0199613i	−0.654605	−	0.755971i	$-0.727165\pi$
$79$	−926580.	+	777493.i	−0.0237889	+	0.0199613i	0.630816	+	0.775933i	$0.282720\pi$
$80$		−	1.00420e7i		−	0.245167i
$81$	−4.11490e7	+	1.26404e7i	−0.955915	+	0.293644i
$82$	2.94099e7			0.650486
$83$	−2.24413e7	−	2.67445e7i	−0.472862	−	0.563536i	0.475911	−	0.879494i	$-0.342119\pi$
$83$	−2.24413e7	−	2.67445e7i	−0.472862	−	0.563536i	−0.948773	+	0.315958i	$0.897674\pi$
$84$	−1.62367e7	−	1.39810e7i	−0.326122	−	0.280816i
$85$	7.67333e6	−	4.35176e7i	0.146997	−	0.833661i
$86$	−2.53372e7	−	6.96134e7i	−0.463196	−	1.27262i
$87$	−134903.	+	1.05739e7i	−0.00235474	+	0.184568i
$88$	1.37959e6	+	7.82406e6i	0.0230049	+	0.130467i
$89$	−3.19449e7	+	1.84434e7i	−0.509146	+	0.293955i	−0.732482	−	0.680786i	$-0.761638\pi$
$89$	−3.19449e7	+	1.84434e7i	−0.509146	+	0.293955i	0.223337	+	0.974741i	$0.428305\pi$
$90$	4.23417e7	+	1.66463e7i	0.645355	+	0.253716i
$91$	576665.	−	998813.i	0.00840926	−	0.0145653i
$92$	538622.	−	1.47985e6i	0.00751853	−	0.0206570i
$93$	−6.25065e7	+	5.11047e7i	−0.835591	+	0.683170i
$94$	3.97378e7	+	3.33439e7i	0.508970	+	0.427076i
$95$	5.97594e7	−	7.12185e7i	0.733689	−	0.874376i
$96$	−5.31482e6	+	1.40423e7i	−0.0625754	+	0.165331i
$97$	1.53373e8	+	5.58232e7i	1.73246	+	0.630563i	0.998801	−	0.0489589i	$-0.0155903\pi$
$97$	1.53373e8	+	5.58232e7i	1.73246	+	0.630563i	0.733656	+	0.679521i	$0.237813\pi$
$98$	−1.46375e7	−	8.45098e6i	−0.158695	−	0.0916226i
$99$	−3.52766e7	−	7.15268e6i	−0.367237	−	0.0744609i
$100$	957255.	+	1.65801e6i	0.00957255	+	0.0165801i
$101$	6.04415e7	−	1.06575e7i	0.580831	−	0.102416i	0.124489	−	0.992221i	$-0.460271\pi$
$101$	6.04415e7	−	1.06575e7i	0.580831	−	0.102416i	0.456341	+	0.889805i	$0.349160\pi$
$102$	−3.37621e7	+	5.67919e7i	−0.311909	+	0.524669i
$103$	−1.36149e8	+	4.95541e7i	−1.20966	+	0.440282i	−0.866587	−	0.499026i	$-0.833691\pi$
$103$	−1.36149e8	+	4.95541e7i	−1.20966	+	0.440282i	−0.343077	+	0.939307i	$0.611469\pi$
$104$	−795906.	−	140340.i	−0.00680344	−	0.00119963i
$105$	−1.00805e8	−	1.91037e7i	−0.829327	−	0.157167i
$106$	−7.35349e7	+	6.17031e7i	−0.582465	+	0.488747i
$107$		−	3.13078e7i		−	0.238846i	−0.992843	−	0.119423i	$-0.961896\pi$
$107$		−	3.13078e7i		−	0.238846i	0.992843	−	0.119423i	$-0.0381044\pi$
$108$	−5.03985e7	−	4.56871e7i	−0.370444	−	0.335814i
$109$	3.10455e7			0.219934			0.109967	−	0.993935i	$-0.464925\pi$
$109$	3.10455e7			0.219934			0.109967	+	0.993935i	$0.464925\pi$
$110$	2.44535e7	+	2.91425e7i	0.167020	+	0.199047i
$111$	−1.66046e8	+	5.80479e7i	−1.09380	+	0.382380i
$112$	5.87960e6	−	3.33449e7i	0.0373659	−	0.211913i
$113$	−5.73174e6	−	1.57478e7i	−0.0351539	−	0.0965844i	0.920874	−	0.389860i	$-0.127477\pi$
$113$	−5.73174e6	−	1.57478e7i	−0.0351539	−	0.0965844i	−0.956028	+	0.293276i	$0.905255\pi$
$114$	−1.21258e8	+	6.79605e7i	−0.717943	+	0.402381i
$115$	−1.30947e6	−	7.42636e6i	−0.00748693	−	0.0424605i
$116$	−1.44719e7	+	8.35535e6i	−0.0799269	+	0.0461458i
$117$	1.91108e6	−	3.12326e6i	0.0101985	−	0.0166673i
$118$	−1.07523e8	+	1.86236e8i	−0.554594	+	0.960585i
$119$	5.09591e7	−	1.40009e8i	0.254117	−	0.698181i
$120$	1.15803e7	+	7.09568e7i	0.0558462	+	0.342191i
$121$	1.41152e8	+	1.18441e8i	0.658486	+	0.552535i
$122$	9.59773e7	−	1.14381e8i	0.433241	−	0.516316i
$123$	−2.07809e8	+	3.39148e7i	−0.907914	+	0.148173i
$124$	−1.19893e8	−	4.36374e7i	−0.507115	−	0.184575i
$125$	2.15284e8	+	1.24294e8i	0.881803	+	0.509109i
$126$	1.30851e8	+	8.00657e7i	0.519151	+	0.317661i
$127$	8.11111e7	+	1.40489e8i	0.311792	+	0.540040i	0.978750	−	0.205055i	$-0.0657374\pi$
$127$	8.11111e7	+	1.40489e8i	0.311792	+	0.540040i	−0.666958	+	0.745095i	$0.732404\pi$
$128$	−2.33661e7	+	4.12008e6i	−0.0870455	+	0.0153485i
$129$	2.59309e8	+	4.62668e8i	0.936394	+	1.67075i
$130$	−3.63654e6	+	1.32359e6i	−0.0127325	+	0.00463426i
$131$	2.88786e8	+	5.09207e7i	0.980597	+	0.172906i	0.640896	−	0.767628i	$-0.278563\pi$
$131$	2.88786e8	+	5.09207e7i	0.980597	+	0.172906i	0.339701	+	0.940533i	$0.389674\pi$
$132$	−1.87707e7	−	5.36937e7i	−0.0618280	−	0.176859i
$133$	2.40131e8	−	2.01494e8i	0.767436	−	0.643955i
$134$			8.89825e6i			0.0275985i
$135$	−3.18382e8	−	6.87949e7i	−0.958546	−	0.207120i
$136$	−1.04406e8			−0.305191
$137$	−2.71128e8	−	3.23118e8i	−0.769649	−	0.917232i	0.228768	−	0.973481i	$-0.426530\pi$
$137$	−2.71128e8	−	3.23118e8i	−0.769649	−	0.917232i	−0.998417	+	0.0562489i	$0.982086\pi$
$138$	−2.09936e6	+	1.10777e7i	−0.00578855	+	0.0305446i
$139$	−2.61714e7	+	1.48426e8i	−0.0701081	+	0.397603i	0.929479	+	0.368875i	$0.120257\pi$
$139$	−2.61714e7	+	1.48426e8i	−0.0701081	+	0.397603i	−0.999587	+	0.0287282i	$0.990854\pi$
$140$	−5.54526e7	−	1.52355e8i	−0.144348	−	0.396592i
$141$	−3.19238e8	−	1.89783e8i	−0.807677	−	0.480154i
$142$	−4.28388e7	−	2.42951e8i	−0.105362	−	0.597538i
$143$	2.65150e6	−	1.53085e6i	0.00634085	−	0.00366089i
$144$	2.13611e7	−	1.05352e8i	0.0496790	−	0.245014i
$145$	−4.00089e7	+	6.92974e7i	−0.0905075	+	0.156764i
$146$	6.00901e7	−	1.65096e8i	0.132249	−	0.363350i
$147$	1.13174e8	+	4.28347e7i	0.242369	+	0.0917332i
$148$	−2.12934e8	−	1.78673e8i	−0.443812	−	0.372402i
$149$	2.35050e7	−	2.80122e7i	0.0476887	−	0.0568332i	−0.741673	−	0.670762i	$-0.765967\pi$
$149$	2.35050e7	−	2.80122e7i	0.0476887	−	0.0568332i	0.789362	+	0.613929i	$0.210412\pi$
$150$	−8.67593e6	−	1.06116e7i	−0.0171376	−	0.0209612i
$151$	7.92027e8	+	2.88274e8i	1.52346	+	0.554496i	0.962011	−	0.273012i	$-0.0880200\pi$
$151$	7.92027e8	+	2.88274e8i	1.52346	+	0.554496i	0.561454	+	0.827508i	$0.310242\pi$
$152$	−1.90231e8	−	1.09830e8i	−0.356376	−	0.205754i
$153$	1.73071e8	−	4.40224e8i	0.315833	−	0.803355i
$154$	6.41355e7	+	1.11086e8i	0.114029	+	0.197504i
$155$	−6.01659e8	+	1.06089e8i	−1.04237	+	0.183799i
$156$	5.78569e6	+	73814.4i	0.00976915	+	0.000124636i
$157$	9.55069e8	−	3.47617e8i	1.57194	−	0.572139i	0.598509	−	0.801116i	$-0.295760\pi$
$157$	9.55069e8	−	3.47617e8i	1.57194	−	0.572139i	0.973432	+	0.228977i	$0.0735380\pi$
$158$	1.34768e7	+	2.37632e6i	0.0216250	+	0.00381308i
$159$	4.48441e8	−	5.20792e8i	0.701644	−	0.814846i
$160$	−8.70324e7	+	7.30288e7i	−0.132801	+	0.111433i
$161$		−	2.54262e7i		−	0.0378423i
$162$	4.08800e8	+	2.64705e8i	0.593541	+	0.384329i
$163$	4.35974e6			0.00617605			0.00308802	−	0.999995i	$-0.499017\pi$
$163$	4.35974e6			0.00617605			0.00308802	+	0.999995i	$0.499017\pi$
$164$	−2.13878e8	−	2.54890e8i	−0.295658	−	0.352352i
$165$	−2.06394e8	−	1.77721e8i	−0.278459	−	0.239774i
$166$	−6.85891e7	+	3.88988e8i	−0.0903280	+	0.512276i
$167$	−5.83854e7	−	1.60412e8i	−0.0750651	−	0.206240i	0.896485	−	0.443074i	$-0.146112\pi$
$167$	−5.83854e7	−	1.60412e8i	−0.0750651	−	0.206240i	−0.971550	+	0.236835i	$0.923890\pi$
$168$	−3.09249e6	+	2.42394e8i	−0.00388214	+	0.304288i
$169$	−1.41596e8	−	8.03031e8i	−0.173582	−	0.984432i
$170$	−4.32962e8	+	2.49971e8i	−0.518387	+	0.299291i
$171$	7.78433e8	−	6.20039e8i	0.910409	−	0.725162i
$172$	−4.19066e8	+	7.25843e8i	−0.478816	+	0.829333i
$173$	−2.83342e8	+	7.78475e8i	−0.316320	+	0.869081i	0.675025	+	0.737795i	$0.264133\pi$
$173$	−2.83342e8	+	7.78475e8i	−0.316320	+	0.869081i	−0.991345	+	0.131286i	$0.958089\pi$
$174$	9.26227e7	−	7.57273e7i	0.101046	−	0.0826144i
$175$	2.36788e7	+	1.98689e7i	0.0252469	+	0.0211846i
$176$	5.77768e7	−	6.88557e7i	0.0602147	−	0.0717611i
$177$	5.44994e8	−	1.43993e9i	0.555263	−	1.46706i
$178$	3.92159e8	+	1.42734e8i	0.390645	+	0.142183i
$179$	1.50419e9	+	8.68446e8i	1.46518	+	0.845923i	0.999243	−	0.0388952i	$-0.0123838\pi$
$179$	1.50419e9	+	8.68446e8i	1.46518	+	0.845923i	0.465937	+	0.884818i	$0.345717\pi$
$180$	−1.63652e8	−	4.88025e8i	−0.155895	−	0.464892i
$181$	−5.94377e8	−	1.02949e9i	−0.553793	−	0.959197i	−0.997996	−	0.0632715i	$-0.979847\pi$
$181$	−5.94377e8	−	1.02949e9i	−0.553793	−	0.959197i	0.444203	−	0.895926i	$-0.353487\pi$
$182$	−1.28502e7	+	2.26584e6i	−0.0117118	+	0.00206511i
$183$	−5.46271e8	+	9.18894e8i	−0.487084	+	0.819334i
$184$	−1.67426e7	+	6.09382e6i	−0.0146067	+	0.00531641i
$185$	−1.31080e9	−	2.31129e8i	−1.11905	−	0.197318i
$186$	8.97481e8	+	1.70083e8i	0.749849	+	0.142105i
$187$	3.02992e8	−	2.54241e8i	0.247779	−	0.207912i
$188$		−	5.86887e8i		−	0.469811i
$189$	−1.01692e9	−	4.14848e8i	−0.796963	−	0.325118i
$190$	−1.05183e9			−0.807104
$191$	1.50409e9	+	1.79250e9i	1.13016	+	1.34687i	0.930195	+	0.367066i	$0.119638\pi$
$191$	1.50409e9	+	1.79250e9i	1.13016	+	1.34687i	0.199963	+	0.979803i	$0.435918\pi$
$192$	1.60353e8	−	5.60577e7i	0.117997	−	0.0412506i
$193$	1.94286e8	−	1.10185e9i	0.140027	−	0.794132i	−0.831200	−	0.555974i	$-0.812345\pi$
$193$	1.94286e8	−	1.10185e9i	0.140027	−	0.794132i	0.971226	−	0.238158i	$-0.0765435\pi$
$194$	−6.31568e8	−	1.73522e9i	−0.445875	−	1.22503i
$195$	2.41694e7	−	1.35460e7i	0.0167158	−	0.00936859i
$196$	3.32057e7	+	1.88319e8i	0.0225003	+	0.127605i
$197$	−2.12594e9	+	1.22741e9i	−1.41152	+	0.814940i	−0.995531	−	0.0944317i	$-0.969897\pi$
$197$	−2.12594e9	+	1.22741e9i	−1.41152	+	0.814940i	−0.415985	+	0.909371i	$0.636563\pi$
$198$	1.94552e8	+	3.57752e8i	0.126583	+	0.232767i
$199$	−1.09908e9	+	1.90366e9i	−0.700837	+	1.21389i	0.267336	+	0.963603i	$0.413857\pi$
$199$	−1.09908e9	+	1.90366e9i	−0.700837	+	1.21389i	−0.968173	+	0.250282i	$0.919477\pi$
$200$	7.40823e6	−	2.03539e7i	0.00463014	−	0.0127212i
$201$	−1.02613e7	−	6.28748e7i	−0.00628662	−	0.0385205i
$202$	−5.31915e8	−	4.46330e8i	−0.319475	−	0.268072i
$203$	−1.73424e8	+	2.06679e8i	−0.102124	+	0.121706i
$204$	7.37732e8	−	1.20399e8i	0.425969	−	0.0695189i
$205$	−1.49719e9	−	5.44931e8i	−0.847736	−	0.308551i
$206$	1.41959e9	+	8.19602e8i	0.788305	+	0.455128i
$207$	2.05939e6	−	8.06959e7i	0.00112165	−	0.0439511i
$208$	4.57178e6	+	7.91856e6i	0.00244249	+	0.00423051i
$209$	8.19510e8	−	1.44502e8i	0.429506	−	0.0757334i
$210$	5.67519e8	+	1.01259e9i	0.291812	+	0.520661i
$211$	−1.46917e8	+	5.34735e7i	−0.0741213	+	0.0269779i	−0.378815	−	0.925473i	$-0.623668\pi$
$211$	−1.46917e8	+	5.34735e7i	−0.0741213	+	0.0269779i	0.304693	+	0.952450i	$0.401446\pi$
$212$	1.06954e9	+	1.88588e8i	0.529484	+	0.0933623i
$213$	5.82864e8	+	1.66728e9i	0.283171	+	0.810012i
$214$	−2.71339e8	+	2.27680e8i	−0.129377	+	0.108560i
$215$			4.01332e9i			1.87824i
$216$	−2.94475e7	+	7.69045e8i	−0.0135280	+	0.353294i
$217$	−2.05994e9			−0.929001
$218$	−2.25772e8	−	2.69065e8i	−0.0999643	−	0.119133i
$219$	−2.34209e8	+	1.23586e9i	−0.101819	+	0.537270i
$220$	7.47391e7	−	4.23867e8i	0.0319049	−	0.180942i
$221$	1.37613e7	+	3.78088e7i	0.00576886	+	0.0158498i
$222$	1.71063e9	+	1.01695e9i	0.704278	+	0.418684i
$223$	1.31016e7	+	7.43029e7i	0.00529792	+	0.0300460i	0.987342	−	0.158605i	$-0.0506996\pi$
$223$	1.31016e7	+	7.43029e7i	0.00529792	+	0.0300460i	−0.982044	+	0.188651i	$0.939589\pi$
$224$	−3.31752e8	+	1.91537e8i	−0.131771	+	0.0760783i
$225$	7.35410e7	+	6.49764e7i	0.0286945	+	0.0253528i
$226$	−9.48004e7	+	1.64199e8i	−0.0363393	+	0.0629415i
$227$	−1.18038e9	+	3.24306e9i	−0.444546	+	1.22138i	0.491925	+	0.870637i	$0.336293\pi$
$227$	−1.18038e9	+	3.24306e9i	−0.444546	+	1.22138i	−0.936472	+	0.350744i	$0.885929\pi$
$228$	1.47082e9	+	5.56686e8i	0.544279	+	0.206002i
$229$	−2.28950e8	−	1.92112e8i	−0.0832528	−	0.0698574i	0.600211	−	0.799841i	$-0.295083\pi$
$229$	−2.28950e8	−	1.92112e8i	−0.0832528	−	0.0698574i	−0.683464	+	0.729984i	$0.739528\pi$
$230$	−5.48400e7	+	6.53557e7i	−0.0195968	+	0.0233546i
$231$	−5.81282e8	−	7.10971e8i	−0.204145	−	0.249692i
$232$	1.77658e8	+	6.46623e7i	0.0613244	+	0.0223203i
$233$	6.83338e8	+	3.94525e8i	0.231853	+	0.133860i	0.611426	−	0.791301i	$-0.290596\pi$
$233$	6.83338e8	+	3.94525e8i	0.231853	+	0.133860i	−0.379574	+	0.925161i	$0.623929\pi$
$234$	−4.09666e7	+	6.15037e6i	−0.0136637	+	0.00205134i
$235$	−1.40513e9	−	2.43376e9i	−0.460729	−	0.798005i
$236$	2.39601e9	−	4.22482e8i	0.772399	−	0.136195i
$237$	−9.79667e7	−	1.24987e6i	−0.0310517	−	0.000396161i
$238$	−1.58402e9	+	5.76536e8i	−0.493688	+	0.179688i
$239$	−3.90748e9	−	6.88994e8i	−1.19758	−	0.211166i	−0.460928	−	0.887437i	$-0.652483\pi$
$239$	−3.90748e9	−	6.88994e8i	−1.19758	−	0.211166i	−0.736652	+	0.676272i	$0.763595\pi$
$240$	5.30753e8	−	6.16384e8i	0.159973	−	0.185783i
$241$	3.42039e9	−	2.87004e9i	1.01393	−	0.850786i	0.0250751	−	0.999686i	$-0.492018\pi$
$241$	3.42039e9	−	2.87004e9i	1.01393	−	0.850786i	0.988852	+	0.148899i	$0.0475731\pi$
$242$		−	2.08468e9i		−	0.607824i
$243$	−3.19382e9	−	1.39898e9i	−0.915980	−	0.401224i
$244$	−1.68930e9			−0.476592
$245$	5.88574e8	+	7.01436e8i	0.163357	+	0.194681i
$246$	1.80519e9	+	1.55440e9i	0.492926	+	0.424447i
$247$	−1.46995e7	+	8.33650e7i	−0.00394925	+	0.0223973i
$248$	4.93701e8	+	1.35643e9i	0.130514	+	0.358584i
$249$	3.60758e7	−	2.82767e9i	0.00938465	−	0.735584i
$250$	−4.88378e8	−	2.76973e9i	−0.125025	−	0.709051i
$251$	−5.78760e9	+	3.34147e9i	−1.45815	+	0.841865i	−0.998921	−	0.0464503i	$-0.985209\pi$
$251$	−5.78760e9	+	3.34147e9i	−1.45815	+	0.841865i	−0.459233	+	0.888316i	$0.651876\pi$
$252$	−2.57673e8	−	1.71632e9i	−0.0638949	−	0.425594i
$253$	3.37488e7	−	5.84547e7i	0.00823714	−	0.0142671i
$254$	6.27721e8	−	1.72465e9i	0.150811	−	0.414349i
$255$	2.77104e9	−	2.26557e9i	0.655362	−	0.535817i
$256$	2.05633e8	+	1.72547e8i	0.0478778	+	0.0401742i
$257$	3.45809e9	−	4.12119e9i	0.792690	−	0.944691i	−0.206742	−	0.978396i	$-0.566286\pi$
$257$	3.45809e9	−	4.12119e9i	0.792690	−	0.944691i	0.999432	+	0.0337043i	$0.0107304\pi$
$258$	2.12408e9	−	5.61205e9i	0.479394	−	1.26661i
$259$	−4.21721e9	−	1.53494e9i	−0.937187	−	0.341108i
$260$	3.79174e7	+	2.18916e7i	0.00829745	+	0.00479054i
$261$	−5.67143e8	+	6.41898e8i	−0.122217	+	0.138326i
$262$	−1.65882e9	−	2.87316e9i	−0.352042	−	0.609754i
$263$	8.07348e9	−	1.42357e9i	1.68748	−	0.297548i	0.754183	−	0.656664i	$-0.228033\pi$
$263$	8.07348e9	−	1.42357e9i	1.68748	−	0.297548i	0.933293	+	0.359116i	$0.116922\pi$
$264$	−3.28846e8	+	5.53159e8i	−0.0676982	+	0.113877i
$265$	4.88678e9	−	1.77864e9i	0.990921	−	0.360666i
$266$	−3.49262e9	−	6.15843e8i	−0.697629	−	0.123011i
$267$	−2.93558e9	−	5.56327e8i	−0.577630	−	0.109467i
$268$	7.71194e7	−	6.47109e7i	0.0149494	−	0.0125441i
$269$			2.57842e8i			0.0492431i	0.999697	+	0.0246215i	$0.00783807\pi$
$269$			2.57842e8i			0.0492431i	−0.999697	+	0.0246215i	$0.992162\pi$
$270$	1.71914e9	+	3.25965e9i	0.323486	+	0.613361i
$271$	3.57905e9			0.663575			0.331788	−	0.943354i	$-0.392348\pi$
$271$	3.57905e9			0.663575			0.331788	+	0.943354i	$0.392348\pi$
$272$	7.59275e8	+	9.04869e8i	0.138715	+	0.165314i
$273$	8.81862e7	−	3.08289e7i	0.0158763	−	0.00555019i
$274$	−8.28672e8	+	4.69963e9i	−0.147021	+	0.833800i
$275$	2.80650e7	+	7.71080e7i	0.00490721	+	0.0134824i
$276$	1.11276e8	−	6.23660e7i	0.0191763	−	0.0107476i
$277$	−1.13222e9	−	6.42112e9i	−0.192314	−	1.09067i	−0.916193	−	0.400738i	$-0.868754\pi$
$277$	−1.13222e9	−	6.42112e9i	−0.192314	−	1.09067i	0.723879	−	0.689927i	$-0.242357\pi$
$278$	1.47670e9	−	8.52574e8i	0.247237	−	0.142742i
$279$	−6.53771e9	−	1.66845e8i	−1.07897	−	0.0275357i
$280$	−9.17160e8	+	1.58857e9i	−0.149215	+	0.258448i
$281$	1.75169e9	−	4.81272e9i	0.280952	−	0.771908i	−0.716298	−	0.697794i	$-0.754165\pi$
$281$	1.75169e9	−	4.81272e9i	0.280952	−	0.771908i	0.997250	−	0.0741139i	$-0.0236128\pi$
$282$	6.76786e8	+	4.14693e9i	0.107018	+	0.655738i
$283$	9.09122e9	+	7.62844e9i	1.41735	+	1.18930i	0.952743	+	0.303777i	$0.0982478\pi$
$283$	9.09122e9	+	7.62844e9i	1.41735	+	1.18930i	0.464604	+	0.885519i	$0.346197\pi$
$284$	−1.79407e9	+	2.13809e9i	−0.275782	+	0.328664i
$285$	7.43217e9	−	1.21294e9i	1.12651	−	0.183849i
$286$	−3.25501e7	−	1.18473e7i	−0.00486506	−	0.00177074i
$287$	−4.65240e9	−	2.68606e9i	−0.685724	−	0.395903i
$288$	−1.06841e9	+	5.81018e8i	−0.155298	+	0.0844539i
$289$	−8.88954e8	−	1.53971e9i	−0.127435	−	0.220724i
$290$	8.91544e8	−	1.57203e8i	0.126052	−	0.0222264i
$291$	6.46366e9	+	1.15327e10i	0.901377	+	1.60827i
$292$	−1.86785e9	+	6.79842e8i	−0.256927	+	0.0935139i
$293$	5.81364e9	+	1.02510e9i	0.788820	+	0.139090i	0.553524	−	0.832834i	$-0.313283\pi$
$293$	5.81364e9	+	1.02510e9i	0.788820	+	0.139090i	0.235296	+	0.971924i	$0.424394\pi$
$294$	−4.51795e8	−	1.29236e9i	−0.0604718	−	0.172980i
$295$	8.92450e9	−	7.48855e9i	1.17841	−	0.988803i
$296$			3.14483e9i			0.409666i
$297$	−1.78725e9	−	2.30352e9i	−0.229699	−	0.296050i
$298$	−4.13712e8			−0.0524606
$299$	4.41353e6	+	5.25984e6i	0.000552206	+	0.000658093i
$300$	−2.88746e7	+	1.52363e8i	−0.00356477	+	0.0188103i
$301$	−2.34980e9	+	1.33264e10i	−0.286262	+	1.62348i
$302$	−3.26145e9	−	8.96076e9i	−0.392088	−	1.07725i
$303$	4.27320e9	+	2.54036e9i	0.506970	+	0.301387i
$304$	4.31546e8	+	2.44742e9i	0.0505281	+	0.286559i
$305$	−7.00533e9	+	4.04453e9i	−0.809523	+	0.467378i
$306$	−5.07396e9	+	1.70148e9i	−0.578710	+	0.194062i
$307$	−2.23954e9	+	3.87900e9i	−0.252119	+	0.436683i	−0.964109	−	0.265507i	$-0.914461\pi$
$307$	−2.23954e9	+	3.87900e9i	−0.252119	+	0.436683i	0.711990	+	0.702190i	$0.247794\pi$
$308$	4.96347e8	−	1.36370e9i	0.0551547	−	0.151536i
$309$	−1.09759e10	−	4.15424e9i	−1.20395	−	0.455678i
$310$	5.29491e9	+	4.44295e9i	0.573339	+	0.481089i
$311$	4.06207e9	−	4.84099e9i	0.434216	−	0.517479i	−0.503918	−	0.863752i	$-0.668109\pi$
$311$	4.06207e9	−	4.84099e9i	0.434216	−	0.517479i	0.938134	+	0.346273i	$0.112553\pi$
$312$	−4.14356e7	−	5.06802e7i	−0.00437276	−	0.00534835i
$313$	−8.65906e9	−	3.15164e9i	−0.902180	−	0.328367i	−0.151054	−	0.988525i	$-0.548267\pi$
$313$	−8.65906e9	−	3.15164e9i	−0.902180	−	0.328367i	−0.751126	+	0.660159i	$0.770489\pi$
$314$	−9.95828e9	−	5.74942e9i	−1.02439	−	0.591433i
$315$	−5.17777e9	−	6.50047e9i	−0.525896	−	0.660241i
$316$	−7.74121e7	−	1.34082e8i	−0.00776355	−	0.0134469i
$317$	1.52319e10	−	2.68580e9i	1.50840	−	0.265972i	0.642540	−	0.766252i	$-0.277881\pi$
$317$	1.52319e10	−	2.68580e9i	1.50840	−	0.265972i	0.865864	+	0.500280i	$0.166769\pi$
$318$	−7.77480e9	−	9.91917e7i	−0.760293	−	0.00969989i
$319$	−6.73033e8	+	2.44964e8i	−0.0649940	+	0.0236559i
$320$	1.26585e9	+	2.23204e8i	0.120721	+	0.0212864i
$321$	1.65472e9	−	1.92168e9i	0.155849	−	0.180993i
$322$	−2.20363e8	+	1.84907e8i	−0.0204982	+	0.0172000i
$323$			1.09357e10i			1.00470i
$324$	−6.78772e8	−	5.46801e9i	−0.0615948	−	0.496192i
$325$	−8.34724e6			−0.000748186
$326$	−3.17054e7	−	3.77850e7i	−0.00280713	−	0.00334541i
$327$	1.90558e9	+	1.64085e9i	0.166662	+	0.143509i
$328$	−6.53692e8	+	3.70727e9i	−0.0564778	+	0.320302i
$329$	−3.24081e9	−	8.90406e9i	−0.276612	−	0.759984i
$330$	−3.93105e7	+	3.08122e9i	−0.00331477	+	0.259817i
$331$	1.08256e9	+	6.13950e9i	0.0901861	+	0.511471i	0.996117	+	0.0880443i	$0.0280617\pi$
$331$	1.08256e9	+	6.13950e9i	0.0901861	+	0.511471i	−0.905930	+	0.423427i	$0.860827\pi$
$332$	3.87008e9	−	2.23439e9i	0.318543	−	0.183911i
$333$	−1.32600e10	−	5.21306e9i	−1.07837	−	0.423952i
$334$	−9.65667e8	+	1.67258e9i	−0.0775964	+	0.134401i
$335$	1.64874e8	−	4.52989e8i	0.0130910	−	0.0359673i
$336$	2.12327e9	−	1.73597e9i	0.166590	−	0.136202i
$337$	1.73679e10	+	1.45734e10i	1.34657	+	1.12990i	0.979886	+	0.199557i	$0.0639501\pi$
$337$	1.73679e10	+	1.45734e10i	1.34657	+	1.12990i	0.366680	+	0.930347i	$0.380494\pi$
$338$	−5.92998e9	+	7.06708e9i	−0.454346	+	0.541468i
$339$	4.80506e8	−	1.26955e9i	0.0363831	−	0.0961281i
$340$	5.31508e9	+	1.93453e9i	0.397735	+	0.144764i
$341$	−4.73580e9	−	2.73422e9i	−0.350248	−	0.202216i
$342$	−1.10348e10	−	2.23741e9i	−0.806601	−	0.163546i
$343$	7.50048e9	+	1.29912e10i	0.541892	+	0.938584i
$344$	9.33832e9	−	1.64660e9i	0.666860	−	0.117585i
$345$	3.12131e8	−	5.25042e8i	0.0220323	−	0.0370611i
$346$	8.80744e9	−	3.20565e9i	0.614533	−	0.223672i
$347$	−2.57563e10	−	4.54153e9i	−1.77650	−	0.313245i	−0.813264	−	0.581895i	$-0.802312\pi$
$347$	−2.57563e10	−	4.54153e9i	−1.77650	−	0.313245i	−0.963238	+	0.268650i	$0.913423\pi$
$348$	−1.32990e9	−	2.52030e8i	−0.0906777	−	0.0171845i
$349$	−1.55726e9	+	1.30670e9i	−0.104969	+	0.0880793i	−0.693762	−	0.720205i	$-0.744048\pi$
$349$	−1.55726e9	+	1.30670e9i	−0.104969	+	0.0880793i	0.588793	+	0.808284i	$0.299603\pi$
$350$		−	3.49712e8i		−	0.0233044i
$351$	2.82377e8	−	9.07002e7i	0.0186038	−	0.00597558i
$352$	−1.01693e9			−0.0662400
$353$	−4.86605e9	−	5.79914e9i	−0.313385	−	0.373478i	0.586243	−	0.810135i	$-0.300606\pi$
$353$	−4.86605e9	−	5.79914e9i	−0.313385	−	0.373478i	−0.899628	+	0.436658i	$0.856162\pi$
$354$	−1.64430e10	+	5.74828e9i	−1.04705	+	0.366037i
$355$	−2.32078e9	+	1.31618e10i	−0.146124	+	0.828709i
$356$	−1.61485e9	−	4.43677e9i	−0.100539	−	0.276228i
$357$	1.05278e10	−	5.90045e9i	0.648133	−	0.363255i
$358$	−3.41231e9	−	1.93521e10i	−0.207738	−	1.17814i
$359$	6.51994e9	−	3.76429e9i	0.392524	−	0.226624i	−0.290729	−	0.956805i	$-0.593898\pi$
$359$	6.51994e9	−	3.76429e9i	0.392524	−	0.226624i	0.683253	+	0.730182i	$0.260565\pi$
$360$	−3.03949e9	+	4.96741e9i	−0.180963	+	0.295747i
$361$	−3.01208e9	+	5.21707e9i	−0.177352	+	0.307183i
$362$	−4.59990e9	+	1.26381e10i	−0.267864	+	0.735950i
$363$	2.40401e9	+	1.47303e10i	0.138455	+	0.848369i
$364$	1.13088e8	+	9.48923e7i	0.00644187	+	0.00540537i
$365$	−6.11809e9	+	7.29125e9i	−0.344702	+	0.410800i
$366$	1.19365e10	−	1.94806e9i	0.665202	−	0.108562i
$367$	−1.37482e9	−	5.00394e8i	−0.0757848	−	0.0275834i	0.303850	−	0.952720i	$-0.401728\pi$
$367$	−1.37482e9	−	5.00394e8i	−0.0757848	−	0.0275834i	−0.379634	+	0.925137i	$0.623950\pi$
$368$	1.74571e8	+	1.00789e8i	0.00951880	+	0.00549568i
$369$	−1.45479e10	−	8.90167e9i	−0.784685	−	0.480138i
$370$	7.52937e9	+	1.30413e10i	0.401746	+	0.695845i
$371$	1.72681e10	−	3.04483e9i	0.911483	−	0.160719i
$372$	−5.05269e9	−	9.01519e9i	−0.263846	−	0.470764i
$373$	2.96376e10	−	1.07872e10i	1.53112	−	0.557280i	0.567221	−	0.823566i	$-0.308019\pi$
$373$	2.96376e10	−	1.07872e10i	1.53112	−	0.557280i	0.963894	+	0.266285i	$0.0857963\pi$
$374$	−4.40691e9	−	7.77057e8i	−0.225241	−	0.0397161i
$375$	6.64486e9	+	1.90076e10i	0.336017	+	0.961177i
$376$	−5.08643e9	+	4.26803e9i	−0.254485	+	0.213538i
$377$		−	7.28584e7i		−	0.00360674i
$378$	3.79993e9	+	1.18303e10i	0.186127	+	0.579468i
$379$	−2.49091e10			−1.20726			−0.603631	−	0.797264i	$-0.706280\pi$
$379$	−2.49091e10			−1.20726			−0.603631	+	0.797264i	$0.706280\pi$
$380$	7.64920e9	+	9.11597e9i	0.366844	+	0.437188i
$381$	−2.44663e9	+	1.29102e10i	−0.116110	+	0.612680i
$382$	4.59706e9	−	2.60712e10i	0.215887	−	1.22436i
$383$	−9.16902e9	−	2.51917e10i	−0.426116	−	1.17074i	−0.948151	−	0.317820i	$-0.897049\pi$
$383$	−9.16902e9	−	2.51917e10i	−0.426116	−	1.17074i	0.522035	−	0.852924i	$-0.325173\pi$
$384$	−1.65198e9	−	9.82080e8i	−0.0759765	−	0.0451671i
$385$	−1.20669e9	−	6.84348e9i	−0.0549229	−	0.311483i
$386$	−1.09624e10	+	6.32915e9i	−0.493806	+	0.285099i
$387$	−8.53700e9	+	4.21040e10i	−0.380594	+	1.87707i
$388$	−1.04458e10	+	1.80927e10i	−0.460910	+	0.798320i
$389$	6.46268e9	−	1.77561e10i	0.282237	−	0.775441i	−0.714858	−	0.699270i	$-0.753508\pi$
$389$	6.46268e9	−	1.77561e10i	0.282237	−	0.775441i	0.997095	−	0.0761704i	$-0.0242693\pi$
$390$	−2.93168e8	−	1.10960e8i	−0.0126724	−	0.00479632i
$391$	6.79499e8	+	5.70167e8i	0.0290724	+	0.0243947i
$392$	1.39064e9	−	1.65730e9i	0.0588939	−	0.0701870i
$393$	1.50345e10	+	1.83888e10i	0.630257	+	0.770872i
$394$	2.60982e10	+	9.49898e9i	1.08299	+	0.394178i
$395$	−6.42039e8	−	3.70682e8i	−0.0263738	−	0.0152269i
$396$	1.68573e9	−	4.28783e9i	0.0685499	−	0.174364i
$397$	−1.89328e10	−	3.27925e10i	−0.762171	−	1.32012i	−0.941729	−	0.336372i	$-0.890800\pi$
$397$	−1.89328e10	−	3.27925e10i	−0.762171	−	1.32012i	0.179558	−	0.983747i	$-0.442533\pi$
$398$	2.44915e10	−	4.31852e9i	0.976076	−	0.172108i
$399$	2.53889e10	+	3.23915e8i	1.00173	+	0.0127802i
$400$	−2.30279e8	+	8.38145e7i	−0.00899526	+	0.00327401i
$401$	1.86431e10	+	3.28728e9i	0.721008	+	0.127133i	0.522099	−	0.852885i	$-0.325149\pi$
$401$	1.86431e10	+	3.28728e9i	0.721008	+	0.127133i	0.198909	+	0.980018i	$0.436260\pi$
$402$	−4.70300e8	+	5.46178e8i	−0.0180082	+	0.0209136i
$403$	4.26134e8	−	3.57569e8i	0.0161557	−	0.0135563i
$404$			7.85586e9i			0.294896i
$405$	−1.59064e10	−	2.10501e10i	−0.591222	−	0.782411i
$406$	3.05244e9			0.112342
$407$	−7.65799e9	−	9.12644e9i	−0.279086	−	0.332601i
$408$	−6.40850e9	−	5.51820e9i	−0.231268	−	0.199139i
$409$	−2.30423e9	+	1.30680e10i	−0.0823443	+	0.466998i	0.915554	+	0.402195i	$0.131753\pi$
$409$	−2.30423e9	+	1.30680e10i	−0.0823443	+	0.466998i	−0.997898	+	0.0648022i	$0.979358\pi$
$410$	6.16519e9	+	1.69387e10i	0.218178	+	0.599440i
$411$	4.35856e8	−	3.41631e10i	0.0152748	−	1.19726i
$412$	−3.22039e9	−	1.82637e10i	−0.111768	−	0.633870i
$413$	3.40186e10	−	1.96407e10i	1.16927	−	0.675081i
$414$	−7.14352e8	+	5.68997e8i	−0.0243170	+	0.0193691i
$415$	1.06992e10	−	1.85316e10i	0.360711	−	0.624770i
$416$	3.53812e7	−	9.72089e7i	0.00118140	−	0.00324588i
$417$	−9.45117e9	+	7.72717e9i	−0.312566	+	0.255550i
$418$	−7.21210e9	−	6.05167e9i	−0.236242	−	0.198230i
$419$	3.02319e10	−	3.60290e10i	0.980865	−	1.16895i	−0.00475730	−	0.999989i	$-0.501514\pi$
$419$	3.02319e10	−	3.60290e10i	0.980865	−	1.16895i	0.985623	−	0.168961i	$-0.0540413\pi$
$420$	4.64872e9	−	1.22824e10i	0.149395	−	0.394718i
$421$	−2.18560e10	−	7.95494e9i	−0.695733	−	0.253226i	−0.0301450	−	0.999546i	$-0.509597\pi$
$421$	−2.18560e10	−	7.95494e9i	−0.695733	−	0.253226i	−0.665588	+	0.746319i	$0.731819\pi$
$422$	1.53187e9	+	8.84427e8i	0.0483029	+	0.0278877i
$423$	−9.56430e9	−	2.85216e10i	−0.298739	−	0.890867i
$424$	−6.14355e9	−	1.06409e10i	−0.190089	−	0.329243i
$425$	−1.06197e9	+	1.87253e8i	−0.0325503	+	0.00573950i
$426$	1.02113e10	−	1.71766e10i	0.310056	−	0.521553i
$427$	−2.56295e10	+	9.32837e9i	−0.770954	+	0.280604i
$428$	3.94652e9	+	6.95878e8i	0.117609	+	0.0207376i
$429$	2.43660e8	+	4.61764e7i	0.00719375	+	0.00136330i
$430$	3.47827e10	−	2.91861e10i	1.01739	−	0.853695i
$431$			1.75369e10i			0.508211i	0.967177	+	0.254105i	$0.0817810\pi$
$431$			1.75369e10i			0.508211i	−0.967177	+	0.254105i	$0.918219\pi$
$432$	6.87931e9	−	5.33752e9i	0.197520	−	0.153251i
$433$	−4.92821e10			−1.40197			−0.700983	−	0.713178i	$-0.747255\pi$
$433$	−4.92821e10			−1.40197			−0.700983	+	0.713178i	$0.747255\pi$
$434$	1.49805e10	+	1.78531e10i	0.422249	+	0.503217i
$435$	−6.11835e9	+	2.13890e9i	−0.170874	+	0.0597358i
$436$	−6.90047e8	+	3.91345e9i	−0.0190956	+	0.108296i
$437$	6.38280e8	+	1.75366e9i	0.0175019	+	0.0480861i
$438$	1.24142e10	−	6.95771e9i	0.337304	−	0.189047i
$439$	−2.23872e9	−	1.26964e10i	−0.0602756	−	0.341840i	0.939724	−	0.341933i	$-0.111082\pi$
$439$	−2.23872e9	−	1.26964e10i	−0.0602756	−	0.341840i	−1.00000		9.29709e-5i	$0.999970\pi$
$440$	−4.21710e9	+	2.43474e9i	−0.112513	+	0.0649594i
$441$	4.68270e9	+	8.61080e9i	0.123806	+	0.227661i
$442$	2.27605e8	−	3.94224e8i	0.00596339	−	0.0103289i
$443$	−1.94414e10	+	5.34149e10i	−0.504793	+	1.38691i	0.381751	+	0.924265i	$0.375321\pi$
$443$	−1.94414e10	+	5.34149e10i	−0.504793	+	1.38691i	−0.886545	+	0.462643i	$0.846901\pi$
$444$	−3.62655e9	−	2.22213e10i	−0.0933172	−	0.571790i
$445$	−1.73192e10	−	1.45325e10i	−0.441659	−	0.370596i
$446$	5.48690e8	−	6.53903e8i	0.0138672	−	0.0165262i
$447$	2.92328e9	−	4.77084e8i	0.0732217	−	0.0119499i
$448$	4.07262e9	+	1.48231e9i	0.101102	+	0.0367983i
$449$	−8.87105e9	−	5.12170e9i	−0.218268	−	0.126017i	0.386880	−	0.922130i	$-0.373553\pi$
$449$	−8.87105e9	−	5.12170e9i	−0.218268	−	0.126017i	−0.605148	+	0.796113i	$0.706886\pi$
$450$	2.83249e7	−	1.10989e9i	0.000690746	−	0.0270665i
$451$	−7.13056e9	−	1.23505e10i	−0.172353	−	0.298523i
$452$	2.11250e9	−	3.72491e8i	0.0506108	−	0.00892404i
$453$	3.33787e10	+	5.95555e10i	0.792641	+	1.41426i
$454$	3.66910e10	−	1.33544e10i	0.863647	−	0.314342i
$455$	6.96156e8	+	1.22751e8i	0.0162428	+	0.00286405i
$456$	−5.87160e9	−	1.67957e10i	−0.135799	−	0.388454i
$457$	−1.81131e10	+	1.51987e10i	−0.415268	+	0.348451i	−0.826359	−	0.563143i	$-0.809592\pi$
$457$	−1.81131e10	+	1.51987e10i	−0.415268	+	0.348451i	0.411092	+	0.911594i	$0.365148\pi$
$458$			3.38136e9i			0.0768475i
$459$	3.38903e10	−	1.78738e10i	0.763528	−	0.402685i
$460$	9.65239e8			0.0215578
$461$	−3.27293e10	−	3.90053e10i	−0.724659	−	0.863615i	0.270416	−	0.962744i	$-0.412839\pi$
$461$	−3.27293e10	−	3.90053e10i	−0.724659	−	0.863615i	−0.995075	+	0.0991290i	$0.968394\pi$
$462$	−1.93458e9	+	1.02083e10i	−0.0424638	+	0.224070i
$463$	−1.23618e10	+	7.01075e10i	−0.269004	+	1.52560i	0.488381	+	0.872630i	$0.337588\pi$
$463$	−1.23618e10	+	7.01075e10i	−0.269004	+	1.52560i	−0.757385	+	0.652968i	$0.773524\pi$
$464$	−7.31570e8	−	2.00997e9i	−0.0157828	−	0.0433629i
$465$	−4.25372e10	−	2.52878e10i	−0.909823	−	0.540878i
$466$	−1.55017e9	−	8.79147e9i	−0.0328728	−	0.186431i
$467$	−6.07992e10	+	3.51025e10i	−1.27829	+	0.738023i	−0.976534	−	0.215361i	$-0.930907\pi$
$467$	−6.07992e10	+	3.51025e10i	−1.27829	+	0.738023i	−0.301759	+	0.953384i	$0.597574\pi$
$468$	3.51226e8	+	3.10323e8i	0.00732156	+	0.00646889i
$469$	8.12695e8	−	1.40763e9i	0.0167972	−	0.0290936i
$470$	−1.08743e10	+	2.98770e10i	−0.222850	+	0.612274i
$471$	7.69951e10	+	2.91415e10i	1.56451	+	0.592146i
$472$	−2.10861e10	−	1.76934e10i	−0.424844	−	0.356486i
$473$	−2.30906e10	+	2.75183e10i	−0.461308	+	0.549765i
$474$	7.01612e8	+	8.58148e8i	0.0138990	+	0.0170000i
$475$	−2.13192e9	−	7.75954e8i	−0.0418790	−	0.0152427i
$476$	1.65162e10	+	9.53564e9i	0.321723	+	0.185747i
$477$	5.50509e10	−	8.26485e9i	1.06339	−	0.159647i
$478$	2.24450e10	+	3.88759e10i	0.429941	+	0.744679i
$479$	−1.40431e10	+	2.47618e9i	−0.266760	+	0.0470371i	−0.305428	−	0.952215i	$-0.598800\pi$
$479$	−1.40431e10	+	2.47618e9i	−0.266760	+	0.0470371i	0.0386679	+	0.999252i	$0.487689\pi$
$480$	−9.20188e9	−	1.17399e8i	−0.173345	−	0.00221156i
$481$	1.13884e9	−	4.14504e8i	0.0212756	−	0.00774370i
$482$	−4.97482e10	−	8.77195e9i	−0.921700	−	0.162520i
$483$	1.34385e9	−	1.56067e9i	0.0246924	−	0.0286762i
$484$	−1.80675e10	+	1.51604e10i	−0.329243	+	0.276268i
$485$			1.00038e11i			1.80800i
$486$	1.11018e10	+	3.78541e10i	0.198998	+	0.678528i
$487$	3.07686e10			0.547005			0.273503	−	0.961871i	$-0.411818\pi$
$487$	3.07686e10			0.547005			0.273503	+	0.961871i	$0.411818\pi$
$488$	1.22851e10	+	1.46408e10i	0.216620	+	0.258158i
$489$	2.67603e8	+	2.30426e8i	0.00468010	+	0.00402992i
$490$	1.79891e9	−	1.02021e10i	0.0312050	−	0.176973i
$491$	−1.40875e9	−	3.87051e9i	−0.0242387	−	0.0665951i	0.926983	−	0.375103i	$-0.122393\pi$
$491$	−1.40875e9	−	3.87051e9i	−0.0242387	−	0.0665951i	−0.951222	+	0.308508i	$0.900170\pi$
$492$	3.43822e8	−	2.69493e10i	0.00586777	−	0.459925i
$493$	−1.63443e9	−	9.26932e9i	−0.0276681	−	0.156913i
$494$	8.29407e8	−	4.78858e8i	0.0139271	−	0.00804080i
$495$	−3.27543e9	−	2.18171e10i	−0.0545566	−	0.363393i
$496$	8.16558e9	−	1.41432e10i	0.134915	−	0.233680i
$497$	−1.54125e10	+	4.23454e10i	−0.252607	+	0.694033i
$498$	−2.47693e10	+	2.02511e10i	−0.402713	+	0.329254i
$499$	−6.20527e10	−	5.20684e10i	−1.00083	−	0.839792i	−0.0137269	−	0.999906i	$-0.504370\pi$
$499$	−6.20527e10	−	5.20684e10i	−1.00083	−	0.839792i	−0.987099	+	0.160113i	$0.948814\pi$
$500$	−2.04531e10	+	2.43750e10i	−0.327249	+	0.390000i
$501$	4.89459e9	−	1.29320e10i	0.0776900	−	0.205265i
$502$	7.10491e10	+	2.58597e10i	1.11878	+	0.407202i
$503$	1.09420e10	+	6.31738e9i	0.170933	+	0.0986881i	0.583026	−	0.812454i	$-0.301869\pi$
$503$	1.09420e10	+	6.31738e9i	0.170933	+	0.0986881i	−0.412093	+	0.911142i	$0.635202\pi$
$504$	−1.30011e10	+	1.47148e10i	−0.201492	+	0.228051i
$505$	1.88086e10	+	3.25774e10i	0.289195	+	0.500900i
$506$	−7.52047e8	+	1.32606e8i	−0.0114721	+	0.00202284i
$507$	3.37515e10	−	5.67741e10i	0.510812	−	0.859248i
$508$	−1.95122e10	+	7.10186e9i	−0.292989	+	0.106639i
$509$	5.12441e10	+	9.03572e9i	0.763436	+	0.134614i	0.541791	−	0.840513i	$-0.317746\pi$
$509$	5.12441e10	+	9.03572e9i	0.763436	+	0.134614i	0.221645	+	0.975127i	$0.428857\pi$
$510$	−3.97871e10	−	7.54010e9i	−0.588114	−	0.111454i
$511$	−2.45843e10	+	2.06287e10i	−0.360557	+	0.302544i
$512$		−	3.03700e9i		−	0.0441942i
$513$	8.05515e10	+	3.08439e9i	1.16307	+	0.0445349i
$514$	−6.08658e10			−0.872009
$515$	−5.70818e10	−	6.80274e10i	−0.811462	−	0.967063i
$516$	−6.40855e10	+	2.24036e10i	−0.903984	+	0.316023i
$517$	4.36798e9	−	2.47720e10i	0.0611390	−	0.346737i
$518$	1.73659e10	+	4.77123e10i	0.241200	+	0.662691i
$519$	−5.85364e10	+	3.28076e10i	−0.806783	+	0.452173i
$520$	−8.60167e7	−	4.87825e8i	−0.00117644	−	0.00667192i
$521$	−3.25987e10	+	1.88208e10i	−0.442434	+	0.255440i	−0.704630	−	0.709575i	$-0.748887\pi$
$521$	−3.25987e10	+	1.88208e10i	−0.442434	+	0.255440i	0.262195	+	0.965015i	$0.415554\pi$
$522$	9.68764e9	+	2.47232e8i	0.130478	+	0.00332984i
$523$	1.37783e10	−	2.38647e10i	0.184157	−	0.318969i	−0.759135	−	0.650933i	$-0.774378\pi$
$523$	1.37783e10	−	2.38647e10i	0.184157	−	0.318969i	0.943292	+	0.331964i	$0.107711\pi$
$524$	−1.28377e10	+	3.52712e10i	−0.170279	+	0.467837i
$525$	4.03281e8	+	2.47106e9i	0.00530848	+	0.0325271i
$526$	−7.10507e10	−	5.96186e10i	−0.928165	−	0.778823i
$527$	4.61930e10	−	5.50507e10i	0.598872	−	0.713708i
$528$	7.18560e9	−	1.17270e9i	0.0924543	−	0.0150887i
$529$	−7.34460e10	−	2.67322e10i	−0.937876	−	0.341359i
$530$	−5.09533e10	−	2.94179e10i	−0.645757	−	0.372828i
$531$	1.09557e11	−	5.95789e10i	1.37804	−	0.749401i
$532$	2.00620e10	+	3.47484e10i	0.250454	+	0.433799i
$533$	1.42868e9	−	2.51915e8i	0.0177022	−	0.00312137i
$534$	1.65269e10	+	2.94879e10i	0.203248	+	0.362643i
$535$	1.80319e10	−	6.56306e9i	0.220103	−	0.0801109i
$536$	−1.12167e9	−	1.97781e8i	−0.0135896	−	0.00239621i
$537$	4.64278e10	+	1.32807e11i	0.558317	+	1.59707i
$538$	2.23467e9	−	1.87511e9i	0.0266738	−	0.0223819i
$539$			8.19592e9i			0.0971052i
$540$	1.57486e10	−	3.86046e10i	0.185211	−	0.454009i
$541$	4.57596e10			0.534186			0.267093	−	0.963671i	$-0.413937\pi$
$541$	4.57596e10			0.534186			0.267093	+	0.963671i	$0.413937\pi$
$542$	−2.60279e10	−	3.10189e10i	−0.301608	−	0.359442i
$543$	1.79288e10	−	9.46051e10i	0.206229	−	1.08822i
$544$	2.32064e9	−	1.31610e10i	0.0264979	−	0.150277i
$545$	6.50807e9	+	1.78808e10i	0.0737677	+	0.202675i
$546$	−9.08506e8	−	5.40095e8i	−0.0102225	−	0.00607715i
$547$	2.44999e10	+	1.38946e11i	0.273662	+	1.55201i	0.743180	+	0.669091i	$0.233317\pi$
$547$	2.44999e10	+	1.38946e11i	0.273662	+	1.55201i	−0.469518	+	0.882923i	$0.655572\pi$
$548$	4.67572e10	−	2.69953e10i	0.518473	−	0.299340i
$549$	−8.20967e10	+	2.75299e10i	−0.903725	+	0.303051i
$550$	4.64182e8	−	8.03987e8i	0.00507268	−	0.00878615i
$551$	6.77287e9	−	1.86083e10i	0.0734795	−	0.201883i
$552$	−1.34975e9	−	5.10860e8i	−0.0145377	−	0.00550231i
$553$	−1.91488e9	−	1.60677e9i	−0.0204758	−	0.0171812i
$554$	−4.74167e10	+	5.65091e10i	−0.503376	+	0.599900i
$555$	−6.82412e10	−	8.34664e10i	−0.719242	−	0.879711i
$556$	−1.81281e10	−	6.59810e9i	−0.189694	−	0.0690430i
$557$	1.33034e11	+	7.68070e10i	1.38210	+	0.797958i	0.992408	−	0.122986i	$-0.0392470\pi$
$557$	1.33034e11	+	7.68070e10i	1.38210	+	0.797958i	0.389695	+	0.920944i	$0.372580\pi$
$558$	4.60983e10	+	5.78744e10i	0.475497	+	0.596966i
$559$	−1.82712e9	−	3.16467e9i	−0.0187120	−	0.0324101i
$560$	2.04377e10	−	3.60371e9i	0.207816	−	0.0366436i
$561$	3.20352e10	+	4.08708e8i	0.323427	+	0.00412631i
$562$	−5.44498e10	+	1.98181e10i	−0.545822	+	0.198663i
$563$	8.51046e10	+	1.50062e10i	0.847071	+	0.149361i	0.580304	−	0.814400i	$-0.302934\pi$
$563$	8.51046e10	+	1.50062e10i	0.847071	+	0.149361i	0.266766	+	0.963761i	$0.414045\pi$
$564$	3.10188e10	−	3.60233e10i	0.306555	−	0.356014i
$565$	7.86849e9	−	6.60244e9i	0.0772142	−	0.0647904i
$566$		−	1.34268e11i		−	1.30830i
$567$	−4.04927e10	−	7.92107e10i	−0.391782	−	0.766394i
$568$	3.15775e10			0.303378
$569$	−7.55986e10	−	9.00949e10i	−0.721215	−	0.859510i	0.273534	−	0.961862i	$-0.411808\pi$
$569$	−7.55986e10	−	9.00949e10i	−0.721215	−	0.859510i	−0.994748	+	0.102352i	$0.967363\pi$
$570$	−6.45614e10	−	5.55923e10i	−0.611609	−	0.526641i
$571$	2.33331e10	−	1.32329e11i	0.219497	−	1.24483i	−0.653434	−	0.756984i	$-0.726672\pi$
$571$	2.33331e10	−	1.32329e11i	0.219497	−	1.24483i	0.872930	−	0.487845i	$-0.162217\pi$
$572$	1.34036e8	+	3.68262e8i	0.00125210	+	0.00344011i
$573$	−2.41791e9	+	1.89520e11i	−0.0224296	+	1.75807i
$574$	1.05541e10	+	5.98553e10i	0.0972240	+	0.551385i
$575$	−1.59368e8	+	9.20112e7i	−0.00145791	+	0.000841723i
$576$	1.28054e10	+	5.03433e9i	0.116333	+	0.0457353i
$577$	2.60646e10	−	4.51452e10i	0.235151	−	0.407294i	−0.724165	−	0.689626i	$-0.757775\pi$
$577$	2.60646e10	−	4.51452e10i	0.235151	−	0.407294i	0.959317	+	0.282332i	$0.0911081\pi$
$578$	−6.87965e9	+	1.89017e10i	−0.0616389	+	0.169351i
$579$	7.01615e10	−	5.73632e10i	0.624287	−	0.510410i
$580$	−7.84604e9	−	6.58361e9i	−0.0693327	−	0.0581771i
$581$	4.63773e10	−	5.52703e10i	0.407006	−	0.485051i
$582$	5.29459e10	−	1.39889e11i	0.461467	−	1.21924i
$583$	4.37408e10	+	1.59203e10i	0.378627	+	0.137809i
$584$	1.94756e10	+	1.12443e10i	0.167433	+	0.0966673i
$585$	2.19947e9	+	4.45965e8i	0.0187800	+	0.00380783i
$586$	−3.33943e10	−	5.78405e10i	−0.283192	−	0.490503i
$587$	−2.02163e10	+	3.56468e9i	−0.170275	+	0.0300240i	−0.258135	−	0.966109i	$-0.583108\pi$
$587$	−2.02163e10	+	3.56468e9i	−0.170275	+	0.0300240i	0.0878608	+	0.996133i	$0.471997\pi$
$588$	−7.91506e9	+	1.33141e10i	−0.0662132	+	0.111379i
$589$	1.42076e11	−	5.17113e10i	1.18048	−	0.429660i
$590$	−1.29804e11	−	2.28879e10i	−1.07122	−	0.188885i
$591$	−1.95363e11	−	3.70236e10i	−1.60138	−	0.303479i
$592$	2.72556e10	−	2.28702e10i	0.221906	−	0.186201i
$593$		−	1.69568e11i		−	1.37128i	−0.727943	−	0.685638i	$-0.759523\pi$
$593$		−	1.69568e11i		−	1.37128i	0.727943	−	0.685638i	$-0.240477\pi$
$594$	−6.96667e9	+	3.22416e10i	−0.0559602	+	0.258983i
$595$	9.13212e10			0.728625
$596$	3.00864e9	+	3.58556e9i	0.0238443	+	0.0284166i
$597$	−1.68076e11	+	5.87576e10i	−1.32315	+	0.462559i
$598$	1.34894e7	−	7.65023e7i	0.000105485	−	0.000598232i
$599$	−2.99353e10	−	8.22467e10i	−0.232529	−	0.638868i	0.767469	−	0.641086i	$-0.221516\pi$
$599$	−2.99353e10	−	8.22467e10i	−0.232529	−	0.638868i	−0.999998	+	0.00221858i	$0.999294\pi$
$600$	1.53049e9	−	8.57784e8i	0.0118093	−	0.00661870i
$601$	−6.33839e9	−	3.59468e10i	−0.0485826	−	0.275526i	0.950833	−	0.309704i	$-0.100230\pi$
$601$	−6.33839e9	−	3.59468e10i	−0.0485826	−	0.275526i	−0.999416	+	0.0341779i	$0.989119\pi$
$602$	1.32585e11	−	7.65482e10i	1.00951	−	0.582840i
$603$	2.69329e9	−	4.40162e9i	0.0203711	−	0.0332922i
$604$	−5.39429e10	+	9.34318e10i	−0.405309	+	0.702016i
$605$	−3.86267e10	+	1.06126e11i	−0.288314	+	0.792137i
$606$	−9.05921e9	−	5.55093e10i	−0.0671738	−	0.411600i
$607$	7.27875e10	+	6.10760e10i	0.536169	+	0.449900i	0.870225	−	0.492654i	$-0.163973\pi$
$607$	7.27875e10	+	6.10760e10i	0.536169	+	0.449900i	−0.334056	+	0.942553i	$0.608417\pi$
$608$	1.80730e10	−	2.15385e10i	0.132256	−	0.157616i
$609$	−2.15685e10	+	3.52001e9i	−0.156802	+	0.0255903i
$610$	8.59981e10	+	3.13007e10i	0.621111	+	0.226066i
$611$	2.21600e9	+	1.27941e9i	0.0159003	+	0.00918005i
$612$	5.16457e10	+	3.16013e10i	0.368153	+	0.225268i
$613$	3.10433e10	+	5.37686e10i	0.219850	+	0.380791i	0.954762	−	0.297371i	$-0.0961099\pi$
$613$	3.10433e10	+	5.37686e10i	0.219850	+	0.380791i	−0.734912	+	0.678162i	$0.762777\pi$
$614$	4.99052e10	−	8.79963e9i	0.351133	−	0.0619143i
$615$	−6.30965e10	−	1.12579e11i	−0.441067	−	0.786968i
$616$	−1.54285e10	+	5.61553e9i	−0.107152	+	0.0390003i
$617$	2.13904e11	+	3.77171e10i	1.47597	+	0.260254i	0.852968	−	0.521964i	$-0.174800\pi$
$617$	2.13904e11	+	3.77171e10i	1.47597	+	0.260254i	0.623005	+	0.782218i	$0.285911\pi$
$618$	4.38165e10	+	1.25337e11i	0.300389	+	0.859263i
$619$	−5.01793e10	+	4.21054e10i	−0.341792	+	0.286797i	−0.797484	−	0.603340i	$-0.793836\pi$
$619$	−5.01793e10	+	4.21054e10i	−0.341792	+	0.286797i	0.455692	+	0.890137i	$0.349392\pi$
$620$		−	7.82005e10i		−	0.529228i
$621$	4.39144e9	−	4.84430e9i	0.0295284	−	0.0325735i
$622$	−7.14965e10			−0.477665
$623$	−4.90001e10	−	5.83960e10i	−0.325270	−	0.387642i
$624$	−1.37903e8	+	7.27677e8i	−0.000909569	+	0.00479954i
$625$	−2.54432e10	+	1.44296e11i	−0.166745	+	0.945655i
$626$	3.56567e10	+	9.79661e10i	0.232190	+	0.637938i
$627$	5.79391e10	+	3.44441e10i	0.374888	+	0.222866i
$628$	2.25907e10	+	1.28118e11i	0.145241	+	0.823705i
$629$	1.35589e11	−	7.82823e10i	0.866207	−	0.500105i
$630$	−1.86839e10	+	9.21481e10i	−0.118606	+	0.584957i
$631$	7.02657e10	−	1.21704e11i	0.443227	−	0.767691i	−0.554700	−	0.832050i	$-0.687167\pi$
$631$	7.02657e10	−	1.21704e11i	0.443227	−	0.767691i	0.997927	+	0.0643593i	$0.0205004\pi$
$632$	−5.99095e8	+	1.64600e9i	−0.00375515	+	0.0103172i
$633$	−1.18441e10	−	4.48281e9i	−0.0737711	−	0.0279213i
$634$	−1.34049e11	−	1.12480e11i	−0.829670	−	0.696175i
$635$	−6.39116e10	+	7.61669e10i	−0.393084	+	0.468459i
$636$	5.56811e10	+	6.81040e10i	0.340314	+	0.416241i
$637$	−7.83453e8	−	2.85154e8i	−0.00475834	−	0.00173189i
$638$	7.01756e9	+	4.05159e9i	0.0423549	+	0.0244536i
$639$	−5.23448e10	+	1.33145e11i	−0.313957	+	0.798583i
$640$	−7.27121e9	−	1.25941e10i	−0.0433398	−	0.0750668i
$641$	−2.48613e11	+	4.38372e10i	−1.47262	+	0.259663i	−0.851626	−	0.524150i	$-0.824383\pi$
$641$	−2.48613e11	+	4.38372e10i	−1.47262	+	0.259663i	−0.620997	+	0.783813i	$0.713272\pi$
$642$	−2.86885e10	−	3.66011e8i	−0.168876	−	0.00215453i
$643$	5.79071e10	−	2.10765e10i	0.338757	−	0.123297i	−0.167040	−	0.985950i	$-0.553421\pi$
$643$	5.79071e10	−	2.10765e10i	0.338757	−	0.123297i	0.505797	+	0.862653i	$0.331199\pi$
$644$	3.20510e9	+	5.65146e8i	0.0186337	+	0.00328562i
$645$	−2.12117e11	+	2.46339e11i	−1.22556	+	1.42329i
$646$	9.47780e10	−	7.95282e10i	0.544224	−	0.456658i
$647$		−	2.86294e11i		−	1.63378i	−0.576791	−	0.816892i	$-0.695695\pi$
$647$		−	2.86294e11i		−	1.63378i	0.576791	−	0.816892i	$-0.304305\pi$
$648$	−4.24539e10	+	4.56479e10i	−0.240779	+	0.258893i
$649$	1.04278e11			0.587780
$650$	6.07038e7	+	7.23439e7i	0.000340065	+	0.000405274i
$651$	−1.26440e11	−	1.08874e11i	−0.703980	−	0.606181i
$652$	−9.69039e7	+	5.49569e8i	−0.000536230	+	0.00304111i
$653$	1.01407e11	+	2.78614e11i	0.557720	+	1.53232i	0.822935	+	0.568135i	$0.192335\pi$
$653$	1.01407e11	+	2.78614e11i	0.557720	+	1.53232i	−0.265215	+	0.964189i	$0.585443\pi$
$654$	3.62944e8	−	2.84481e10i	0.00198394	−	0.155504i
$655$	3.12102e10	+	1.77002e11i	0.169563	+	0.961640i
$656$	3.68841e10	−	2.12950e10i	0.199170	−	0.114991i
$657$	−7.96949e10	+	6.34788e10i	−0.427729	+	0.340696i
$658$	−5.36016e10	+	9.28406e10i	−0.285939	+	0.495261i
$659$	3.98751e9	−	1.09556e10i	0.0211427	−	0.0580890i	−0.928672	−	0.370901i	$-0.879049\pi$
$659$	3.98751e9	−	1.09556e10i	0.0211427	−	0.0580890i	0.949815	+	0.312812i	$0.101271\pi$
$660$	2.69902e10	−	2.20669e10i	0.142243	−	0.116296i
$661$	−1.90914e11	−	1.60196e11i	−1.00007	−	0.839160i	−0.0130777	−	0.999914i	$-0.504163\pi$
$661$	−1.90914e11	−	1.60196e11i	−1.00007	−	0.839160i	−0.986994	+	0.160754i	$0.948607\pi$
$662$	4.53371e10	−	5.40307e10i	0.236060	−	0.281325i
$663$	−1.15364e9	+	3.04805e9i	−0.00597059	+	0.0157749i
$664$	−4.75095e10	−	1.72920e10i	−0.244404	−	0.0889558i
$665$	1.66390e11	+	9.60653e10i	0.850826	+	0.491225i
$666$	5.12502e10	+	1.52833e11i	0.260495	+	0.776819i
$667$	−8.03114e8	−	1.39103e9i	−0.00405764	−	0.00702804i
$668$	2.15186e10	−	3.79431e9i	0.108071	−	0.0190558i
$669$	−3.12296e9	+	5.25320e9i	−0.0155906	+	0.0262252i
$670$	−5.12498e9	+	1.86534e9i	−0.0254327	+	0.00925676i
$671$	−7.13039e10	−	1.25728e10i	−0.351741	−	0.0620215i
$672$	−3.04864e10	−	5.77752e9i	−0.149496	−	0.0283311i
$673$	−1.49719e11	+	1.25629e11i	−0.729820	+	0.612392i	−0.930083	−	0.367351i	$-0.880265\pi$
$673$	−1.49719e11	+	1.25629e11i	−0.729820	+	0.612392i	0.200263	+	0.979742i	$0.435820\pi$
$674$		−	2.56507e11i		−	1.24296i
$675$	1.07976e9	+	7.87514e9i	0.00520132	+	0.0379353i
$676$	1.04374e11			0.499809
$677$	5.25533e9	+	6.26306e9i	0.0250176	+	0.0298148i	0.778408	−	0.627758i	$-0.216027\pi$
$677$	5.25533e9	+	6.26306e9i	0.0250176	+	0.0298148i	−0.753391	+	0.657573i	$0.771583\pi$
$678$	−1.44973e10	+	5.06810e9i	−0.0686071	+	0.0239843i
$679$	−5.85722e10	+	3.32180e11i	−0.275558	+	1.56277i
$680$	−2.18867e10	−	6.01332e10i	−0.102363	−	0.281241i
$681$	−2.43858e11	+	1.36673e11i	−1.13383	+	0.635471i
$682$	1.07433e10	+	6.09284e10i	0.0496593	+	0.281632i
$683$	−2.10590e11	+	1.21584e11i	−0.967730	+	0.558719i	−0.898543	−	0.438885i	$-0.855374\pi$
$683$	−2.10590e11	+	1.21584e11i	−0.967730	+	0.558719i	−0.0691862	+	0.997604i	$0.522040\pi$
$684$	6.08571e10	+	1.11907e11i	0.278027	+	0.511251i
$685$	1.29265e11	−	2.23893e11i	0.587107	−	1.01690i
$686$	5.80464e10	−	1.59481e11i	0.262107	−	0.720134i
$687$	−3.89932e9	−	2.38926e10i	−0.0175050	−	0.107260i
$688$	−8.21819e10	−	6.89588e10i	−0.366794	−	0.307777i
$689$	−3.04367e9	+	3.62730e9i	−0.0135058	+	0.0160956i
$690$	−6.82035e9	+	1.11309e9i	−0.0300892	+	0.00491061i
$691$	−1.92368e11	−	7.00161e10i	−0.843761	−	0.307104i	−0.116267	−	0.993218i	$-0.537093\pi$
$691$	−1.92368e11	−	7.00161e10i	−0.843761	−	0.307104i	−0.727494	+	0.686114i	$0.759315\pi$
$692$	−9.18331e10	−	5.30199e10i	−0.400475	−	0.231214i
$693$	1.89775e9	−	7.43622e10i	0.00822823	−	0.322418i
$694$	1.47947e11	+	2.56252e11i	0.637778	+	1.10466i
$695$	−9.09726e10	+	1.60409e10i	−0.389916	+	0.0687528i
$696$	7.48712e9	+	1.33588e10i	0.0319064	+	0.0569285i
$697$	1.76111e11	−	6.40991e10i	0.746199	−	0.271594i
$698$	2.26498e10	+	3.99377e9i	0.0954208	+	0.0168253i
$699$	2.10916e10	+	6.03327e10i	0.0883489	+	0.252722i
$700$	−3.03089e9	+	2.54322e9i	−0.0126234	+	0.0105923i
$701$			6.11409e10i			0.253198i	0.991954	+	0.126599i	$0.0404061\pi$
$701$			6.11409e10i			0.253198i	−0.991954	+	0.126599i	$0.959594\pi$
$702$	−2.83961e9	−	1.78770e9i	−0.0116926	−	0.00736118i
$703$	3.29396e11			1.34864
$704$	7.39543e9	+	8.81353e9i	0.0301074	+	0.0358805i
$705$	4.23843e10	−	2.23650e11i	0.171573	−	0.905343i
$706$	−1.48725e10	+	8.43463e10i	−0.0598640	+	0.339506i
$707$	4.33804e10	+	1.19187e11i	0.173626	+	0.477034i
$708$	1.69398e11	+	1.00705e11i	0.674178	+	0.400790i
$709$	1.73375e9	+	9.83258e9i	0.00686122	+	0.0389119i	0.988046	−	0.154158i	$-0.0492666\pi$
$709$	1.73375e9	+	9.83258e9i	0.00686122	+	0.0389119i	−0.981185	+	0.193070i	$0.938155\pi$
$710$	1.30948e11	−	7.56030e10i	0.515307	−	0.297513i
$711$	−5.94717e9	−	5.25457e9i	−0.0232719	−	0.0205617i
$712$	−2.67089e10	+	4.62612e10i	−0.103929	+	0.180010i
$713$	4.19442e9	−	1.15241e10i	0.0162298	−	0.0445911i
$714$	−1.27699e11	−	4.83324e10i	−0.491356	−	0.185971i
$715$	1.43753e9	+	1.20623e9i	0.00550039	+	0.00461537i
$716$	−1.42906e11	+	1.70309e11i	−0.543749	+	0.648014i
$717$	−2.03427e11	−	2.48813e11i	−0.769718	−	0.941448i
$718$	−8.00394e10	−	2.91320e10i	−0.301166	−	0.109616i
$719$	−1.16250e11	−	6.71170e10i	−0.434989	−	0.251141i	0.266481	−	0.963840i	$-0.414139\pi$
$719$	−1.16250e11	−	6.71170e10i	−0.434989	−	0.251141i	−0.701470	+	0.712699i	$0.747472\pi$
$720$	6.51556e10	−	9.78188e9i	0.242450	−	0.0363993i
$721$	−1.49712e11	−	2.59308e11i	−0.554006	−	0.959567i
$722$	6.71200e10	−	1.18351e10i	0.247004	−	0.0435534i
$723$	3.61635e11	+	4.61378e9i	1.32348	+	0.0168851i
$724$	1.42984e11	−	5.20419e10i	0.520395	−	0.189408i
$725$	1.92302e9	+	3.39080e8i	0.00696036	+	0.00122730i
$726$	1.10182e11	−	1.27958e11i	0.396610	−	0.460598i
$727$	−3.18134e11	+	2.66946e11i	−1.13887	+	0.955622i	−0.999401	−	0.0346055i	$-0.988983\pi$
$727$	−3.18134e11	+	2.66946e11i	−1.13887	+	0.955622i	−0.139464	+	0.990227i	$0.544538\pi$
$728$		−	1.67020e9i		−	0.00594625i
$729$	−1.22097e11	−	2.54674e11i	−0.432311	−	0.901724i
$730$	1.07684e11			0.379194
$731$	−3.03446e11	−	3.61633e11i	−1.06270	−	1.26648i
$732$	−1.03690e11	−	8.92846e10i	−0.361153	−	0.310980i
$733$	−6.37458e10	+	3.61520e11i	−0.220819	+	1.25232i	0.649701	+	0.760190i	$0.274894\pi$
$733$	−6.37458e10	+	3.61520e11i	−0.220819	+	1.25232i	−0.870519	+	0.492134i	$0.836217\pi$
$734$	5.66132e9	+	1.55543e10i	0.0195044	+	0.0535880i
$735$	−9.46171e8	+	7.41624e10i	−0.00324206	+	0.254117i
$736$	−3.96021e8	−	2.24595e9i	−0.00134960	−	0.00765399i
$737$	3.73677e9	−	2.15742e9i	0.0126656	−	0.00731249i
$738$	2.86480e10	+	1.90820e11i	0.0965758	+	0.643276i
$739$	2.31041e11	−	4.00175e11i	0.774661	−	1.34175i	−0.160324	−	0.987064i	$-0.551254\pi$
$739$	2.31041e11	−	4.00175e11i	0.774661	−	1.34175i	0.934985	−	0.354688i	$-0.115413\pi$
$740$	5.82700e10	−	1.60096e11i	0.194320	−	0.533891i
$741$	−5.30836e9	+	4.34006e9i	−0.0176071	+	0.0143954i
$742$	−1.51968e11	−	1.27516e11i	−0.501344	−	0.420678i
$743$	−2.16327e11	+	2.57808e11i	−0.709832	+	0.845944i	−0.993601	−	0.112948i	$-0.963971\pi$
$743$	−2.16327e11	+	2.57808e11i	−0.709832	+	0.845944i	0.283769	+	0.958893i	$0.408415\pi$
$744$	−4.13881e10	+	1.09352e11i	−0.135078	+	0.356890i
$745$	2.10611e10	+	7.66561e9i	0.0683684	+	0.0248841i
$746$	−3.09025e11	−	1.78415e11i	−0.997787	−	0.576072i
$747$	1.51666e11	−	1.71657e11i	0.487086	−	0.551288i
$748$	2.53138e10	+	4.38448e10i	0.0808633	+	0.140059i
$749$	6.37180e10	−	1.12352e10i	0.202458	−	0.0356988i
$750$	1.16412e11	−	1.95819e11i	0.367920	−	0.618885i
$751$	3.30825e11	−	1.20410e11i	1.04001	−	0.378534i	0.235128	−	0.971965i	$-0.424449\pi$
$751$	3.30825e11	−	1.20410e11i	1.04001	−	0.378534i	0.804885	+	0.593431i	$0.202227\pi$
$752$	7.39803e10	+	1.30447e10i	0.231337	+	0.0407909i
$753$	−5.31852e11	−	1.00792e11i	−1.65429	−	0.313506i
$754$	−6.31450e8	+	5.29849e8i	−0.00195368	+	0.00163933i
$755$			5.16602e11i			1.58990i

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)

\(f(q)\)	\(=\)	\(q+(-7.27231 - 8.66680i) q^{2} +(61.3803 + 52.8531i) q^{3} +(-22.2270 + 126.055i) q^{4} +(209.630 + 575.954i) q^{5} +(11.6907 - 916.336i) q^{6} +(358.863 + 2035.21i) q^{7} +(1254.14 - 724.077i) q^{8} +(974.093 + 6488.29i) q^{9} +O(q^{10})\)	\(q+(-7.27231 - 8.66680i) q^{2} +(61.3803 + 52.8531i) q^{3} +(-22.2270 + 126.055i) q^{4} +(209.630 + 575.954i) q^{5} +(11.6907 - 916.336i) q^{6} +(358.863 + 2035.21i) q^{7} +(1254.14 - 724.077i) q^{8} +(974.093 + 6488.29i) q^{9} +(3467.19 - 6005.34i) q^{10} +(-1876.37 + 5155.27i) q^{11} +(-8026.72 + 6562.56i) q^{12} +(-427.513 - 358.726i) q^{13} +(15029.0 - 17910.9i) q^{14} +(-17573.8 + 46431.9i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-62437.1 - 36048.1i) q^{17} +(49148.8 - 55627.1i) q^{18} +(-75841.5 - 131361. i) q^{19} +(-77261.6 + 13623.3i) q^{20} +(-85540.2 + 143889. i) q^{21} +(58325.3 - 21228.7i) q^{22} +(-12116.4 - 2136.45i) q^{23} +(115249. + 21841.0i) q^{24} +(11457.8 - 9614.25i) q^{25} +6313.94i q^{26} +(-283136. + 449737. i) q^{27} -264526. q^{28} +(83917.4 + 100009. i) q^{29} +(530218. - 185358. i) q^{30} +(-173088. + 981632. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-387644. + 217261. i) q^{33} +(141640. + 803282. i) q^{34} +(-1.09696e6 + 633330. i) q^{35} +(-839535. - 21425.2i) q^{36} +(-1.08580e6 + 1.88067e6i) q^{37} +(-586940. + 1.61260e6i) q^{38} +(-7281.10 - 44614.1i) q^{39} +(679941. + 570538. i) q^{40} +(-1.67092e6 + 1.99132e6i) q^{41} +(1.86913e6 - 305046. i) q^{42} +(6.15302e6 + 2.23951e6i) q^{43} +(-608144. - 351112. i) q^{44} +(-3.53276e6 + 1.92117e6i) q^{45} +(69598.2 + 120548. i) q^{46} +(-4.51540e6 + 796186. i) q^{47} +(-648836. - 1.15768e6i) q^{48} +(1.40384e6 - 510956. i) q^{49} +(-166650. - 29384.8i) q^{50} +(-1.92716e6 - 5.51264e6i) q^{51} +(54721.7 - 45916.9i) q^{52} -8.48466e6i q^{53} +(5.95684e6 - 816744. i) q^{54} -3.36254e6 q^{55} +(1.92371e6 + 2.29259e6i) q^{56} +(2.28768e6 - 1.20715e7i) q^{57} +(256484. - 1.45459e6i) q^{58} +(-6.50099e6 - 1.78613e7i) q^{59} +(-5.46237e6 - 3.24731e6i) q^{60} +(2.29174e6 + 1.29971e7i) q^{61} +(9.76636e6 - 5.63861e6i) q^{62} +(-1.28555e7 + 4.31089e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(116990. - 321428. i) q^{65} +(4.70203e6 + 1.77965e6i) q^{66} +(-602495. - 505554. i) q^{67} +(5.93184e6 - 7.06929e6i) q^{68} +(-630792. - 771527. i) q^{69} +(1.34664e7 + 4.90136e6i) q^{70} +(1.88839e7 + 1.09027e7i) q^{71} +(5.91967e6 + 7.43189e6i) q^{72} +(7.76455e6 + 1.34486e7i) q^{73} +(2.41957e7 - 4.26635e6i) q^{74} +(1.21143e6 + 15455.5i) q^{75} +(1.82445e7 - 6.64046e6i) q^{76} +(-1.11654e7 - 1.96877e6i) q^{77} +(-333711. + 387552. i) q^{78} +(-926580. + 777493. i) q^{79} -1.00420e7i q^{80} +(-4.11490e7 + 1.26404e7i) q^{81} +2.94099e7 q^{82} +(-2.24413e7 - 2.67445e7i) q^{83} +(-1.62367e7 - 1.39810e7i) q^{84} +(7.67333e6 - 4.35176e7i) q^{85} +(-2.53372e7 - 6.96134e7i) q^{86} +(-134903. + 1.05739e7i) q^{87} +(1.37959e6 + 7.82406e6i) q^{88} +(-3.19449e7 + 1.84434e7i) q^{89} +(4.23417e7 + 1.66463e7i) q^{90} +(576665. - 998813. i) q^{91} +(538622. - 1.47985e6i) q^{92} +(-6.25065e7 + 5.11047e7i) q^{93} +(3.97378e7 + 3.33439e7i) q^{94} +(5.97594e7 - 7.12185e7i) q^{95} +(-5.31482e6 + 1.40423e7i) q^{96} +(1.53373e8 + 5.58232e7i) q^{97} +(-1.46375e7 - 8.45098e6i) q^{98} +(-3.52766e7 - 7.15268e6i) 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

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