LMFDB - Embedded newform 14.9.d.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,9,Mod(3,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, degree $2$, 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:	$5.70330054086$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 1771 x^{10} + 26038 x^{9} + 2442597 x^{8} + 26522276 x^{7} + 1175865280 x^{6} + \cdots + 36\!\cdots\!00 $ x^12 - 2x^11 + 1771x^10 + 26038x^9 + 2442597x^8 + 26522276x^7 + 1175865280x^6 + 6901058684x^5 + 370996492174x^4 + 1285719886320x^3 + 55526550982200x^2 - 240706289358000*x + 3600954063202500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{4}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.3
Root			$9.14374 + 15.8374i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.9.d.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 + 9.79796i) q^{2} +(123.742 - 71.4423i) q^{3} +(-64.0000 - 110.851i) q^{4} +(-758.365 - 437.842i) q^{5} +1616.56i q^{6} +(855.887 - 2243.27i) q^{7} +1448.15 q^{8} +(6927.51 - 11998.8i) q^{9} +O(q^{10})$	\(q+(-5.65685 + 9.79796i) q^{2} +(123.742 - 71.4423i) q^{3} +(-64.0000 - 110.851i) q^{4} +(-758.365 - 437.842i) q^{5} +1616.56i q^{6} +(855.887 - 2243.27i) q^{7} +1448.15 q^{8} +(6927.51 - 11998.8i) q^{9} +(8579.92 - 4953.62i) q^{10} +(6414.54 + 11110.3i) q^{11} +(-15838.9 - 9144.62i) q^{12} -3065.53i q^{13} +(17137.8 + 21075.8i) q^{14} -125122. q^{15} +(-8192.00 + 14189.0i) q^{16} +(62419.6 - 36038.0i) q^{17} +(78375.8 + 135751. i) q^{18} +(49079.6 + 28336.1i) q^{19} +112088. i q^{20} +(-54355.4 - 338733. i) q^{21} -145144. q^{22} +(-249593. + 432307. i) q^{23} +(179197. - 103460. i) q^{24} +(188099. + 325797. i) q^{25} +(30035.9 + 17341.3i) q^{26} -1.04220e6i q^{27} +(-303446. + 48693.1i) q^{28} -88328.5 q^{29} +(707796. - 1.22594e6i) q^{30} +(501813. - 289722. i) q^{31} +(-92681.9 - 160530. i) q^{32} +(1.58749e6 + 916539. i) q^{33} +815447. i q^{34} +(-1.63127e6 + 1.32647e6i) q^{35} -1.77344e6 q^{36} +(465050. - 805489. i) q^{37} +(-555272. + 320587. i) q^{38} +(-219009. - 379334. i) q^{39} +(-1.09823e6 - 634063. i) q^{40} +1.42277e6i q^{41} +(3.62637e6 + 1.38359e6i) q^{42} +2.95457e6 q^{43} +(821061. - 1.42212e6i) q^{44} +(-1.05072e7 + 6.06631e6i) q^{45} +(-2.82382e6 - 4.89099e6i) q^{46} +(6.92276e6 + 3.99685e6i) q^{47} +2.34102e6i q^{48} +(-4.29971e6 - 3.83997e6i) q^{49} -4.25620e6 q^{50} +(5.14928e6 - 8.91881e6i) q^{51} +(-339818. + 196194. i) q^{52} +(1.04248e6 + 1.80563e6i) q^{53} +(1.02115e7 + 5.89559e6i) q^{54} -1.12342e7i q^{55} +(1.23946e6 - 3.24860e6i) q^{56} +8.09759e6 q^{57} +(499661. - 865439. i) q^{58} +(7.60174e6 - 4.38887e6i) q^{59} +(8.00780e6 + 1.38699e7i) q^{60} +(-1.25971e7 - 7.27293e6i) q^{61} +6.55566e6i q^{62} +(-2.09874e7 - 2.58099e7i) q^{63} +2.09715e6 q^{64} +(-1.34222e6 + 2.32479e6i) q^{65} +(-1.79604e7 + 1.03695e7i) q^{66} +(7.05740e6 + 1.22238e7i) q^{67} +(-7.98971e6 - 4.61286e6i) q^{68} +7.13259e7i q^{69} +(-3.76886e6 - 2.34868e7i) q^{70} -3.34541e7 q^{71} +(1.00321e7 - 1.73761e7i) q^{72} +(1.12065e6 - 647007. i) q^{73} +(5.26143e6 + 9.11307e6i) q^{74} +(4.65514e7 + 2.68765e7i) q^{75} -7.25405e6i q^{76} +(3.04135e7 - 4.88037e6i) q^{77} +4.95560e6 q^{78} +(1.69458e7 - 2.93509e7i) q^{79} +(1.24251e7 - 7.17361e6i) q^{80} +(-2.90061e7 - 5.02400e7i) q^{81} +(-1.39402e7 - 8.04839e6i) q^{82} +7.65808e6i q^{83} +(-3.40702e7 + 2.77043e7i) q^{84} -6.31158e7 q^{85} +(-1.67136e7 + 2.89487e7i) q^{86} +(-1.09299e7 + 6.31039e6i) q^{87} +(9.28924e6 + 1.60894e7i) q^{88} +(8.82439e7 + 5.09476e7i) q^{89} -1.37265e8i q^{90} +(-6.87681e6 - 2.62375e6i) q^{91} +6.38957e7 q^{92} +(4.13968e7 - 7.17014e7i) q^{93} +(-7.83220e7 + 4.52192e7i) q^{94} +(-2.48135e7 - 4.29782e7i) q^{95} +(-2.29372e7 - 1.32428e7i) q^{96} +2.91159e7i q^{97} +(6.19467e7 - 2.04063e7i) q^{98} +1.77747e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9}+O(q^{10}) $ 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9	\( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9} + 17664 q^{10} + 10302 q^{11} - 20736 q^{12} + 56832 q^{14} - 255468 q^{15} - 98304 q^{16} + 173178 q^{17} + 16896 q^{18} + 405978 q^{19} - 656910 q^{21} - 941568 q^{22} + 158934 q^{23} + 98304 q^{24} + 838668 q^{25} + 1958400 q^{26} - 255744 q^{28} - 4355256 q^{29} + 916992 q^{30} + 4520250 q^{31} + 4954482 q^{33} - 5270790 q^{35} - 6042624 q^{36} + 134214 q^{37} + 1278720 q^{38} + 1335384 q^{39} - 2260992 q^{40} + 6660096 q^{42} - 12961896 q^{43} + 1318656 q^{44} - 8415396 q^{45} + 2345472 q^{46} + 18385002 q^{47} - 3659172 q^{49} + 2970624 q^{50} - 2673894 q^{51} - 3369984 q^{52} - 16540506 q^{53} - 19646208 q^{54} + 4325376 q^{56} + 100263780 q^{57} + 9176064 q^{58} + 31163922 q^{59} + 16349952 q^{60} - 85390158 q^{61} + 4361988 q^{63} + 25165824 q^{64} - 46506264 q^{65} - 111873024 q^{66} - 37750362 q^{67} - 22166784 q^{68} + 92031744 q^{70} + 45506424 q^{71} + 2162688 q^{72} + 9414786 q^{73} + 58837248 q^{74} + 9837540 q^{75} - 100614066 q^{77} - 25463808 q^{78} + 59730294 q^{79} - 27426816 q^{80} - 89677422 q^{81} - 93259776 q^{82} + 122616576 q^{84} - 64652220 q^{85} - 15144960 q^{86} + 334229724 q^{87} + 60260352 q^{88} + 323014482 q^{89} - 266861424 q^{91} - 40687104 q^{92} - 11119662 q^{93} - 443440128 q^{94} - 175918350 q^{95} - 12582912 q^{96} + 472166400 q^{98} - 346906296 q^{99}+O(q^{100}) \) 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9 + 17664 * q^10 + 10302 * q^11 - 20736 * q^12 + 56832 * q^14 - 255468 * q^15 - 98304 * q^16 + 173178 * q^17 + 16896 * q^18 + 405978 * q^19 - 656910 * q^21 - 941568 * q^22 + 158934 * q^23 + 98304 * q^24 + 838668 * q^25 + 1958400 * q^26 - 255744 * q^28 - 4355256 * q^29 + 916992 * q^30 + 4520250 * q^31 + 4954482 * q^33 - 5270790 * q^35 - 6042624 * q^36 + 134214 * q^37 + 1278720 * q^38 + 1335384 * q^39 - 2260992 * q^40 + 6660096 * q^42 - 12961896 * q^43 + 1318656 * q^44 - 8415396 * q^45 + 2345472 * q^46 + 18385002 * q^47 - 3659172 * q^49 + 2970624 * q^50 - 2673894 * q^51 - 3369984 * q^52 - 16540506 * q^53 - 19646208 * q^54 + 4325376 * q^56 + 100263780 * q^57 + 9176064 * q^58 + 31163922 * q^59 + 16349952 * q^60 - 85390158 * q^61 + 4361988 * q^63 + 25165824 * q^64 - 46506264 * q^65 - 111873024 * q^66 - 37750362 * q^67 - 22166784 * q^68 + 92031744 * q^70 + 45506424 * q^71 + 2162688 * q^72 + 9414786 * q^73 + 58837248 * q^74 + 9837540 * q^75 - 100614066 * q^77 - 25463808 * q^78 + 59730294 * q^79 - 27426816 * q^80 - 89677422 * q^81 - 93259776 * q^82 + 122616576 * q^84 - 64652220 * q^85 - 15144960 * q^86 + 334229724 * q^87 + 60260352 * q^88 + 323014482 * q^89 - 266861424 * q^91 - 40687104 * q^92 - 11119662 * q^93 - 443440128 * q^94 - 175918350 * q^95 - 12582912 * q^96 + 472166400 * q^98 - 346906296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−5.65685	+	9.79796i	−0.353553	+	0.612372i
$2$	−5.65685	+	9.79796i	−0.353553	+	0.612372i
$3$	123.742	−	71.4423i	1.52768	−	0.882004i	0.528217	−	0.849110i	$-0.322861\pi$
$3$	123.742	−	71.4423i	1.52768	−	0.882004i	0.999459	−	0.0328945i	$-0.0104725\pi$
$4$	−64.0000	−	110.851i	−0.250000	−	0.433013i
$5$	−758.365	−	437.842i	−1.21338	−	0.700547i	−0.249889	−	0.968274i	$-0.580394\pi$
$5$	−758.365	−	437.842i	−1.21338	−	0.700547i	−0.963495	+	0.267727i	$0.913727\pi$
$6$			1616.56i			1.24734i
$7$	855.887	−	2243.27i	0.356471	−	0.934306i
$7$	855.887	−	2243.27i	0.356471	−	0.934306i
$8$	1448.15			0.353553
$9$	6927.51	−	11998.8i	1.05586	−	1.82881i
$10$	8579.92	−	4953.62i	0.857992	−	0.495362i
$11$	6414.54	+	11110.3i	0.438121	+	0.758849i	0.997545	−	0.0700336i	$-0.0223106\pi$
$11$	6414.54	+	11110.3i	0.438121	+	0.758849i	−0.559423	+	0.828882i	$0.688977\pi$
$12$	−15838.9	−	9144.62i	−0.763838	−	0.441002i
$13$		−	3065.53i		−	0.107333i	−0.998559	−	0.0536664i	$-0.982909\pi$
$13$		−	3065.53i		−	0.107333i	0.998559	−	0.0536664i	$-0.0170907\pi$
$14$	17137.8	+	21075.8i	0.446112	+	0.548620i
$15$	−125122.			−2.47154
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	62419.6	−	36038.0i	0.747353	−	0.431484i	−0.0773839	−	0.997001i	$-0.524657\pi$
$17$	62419.6	−	36038.0i	0.747353	−	0.431484i	0.824737	+	0.565517i	$0.191323\pi$
$18$	78375.8	+	135751.i	0.746607	+	1.29316i
$19$	49079.6	+	28336.1i	0.376605	+	0.217433i	0.676340	−	0.736589i	$-0.263565\pi$
$19$	49079.6	+	28336.1i	0.376605	+	0.217433i	−0.299735	+	0.954023i	$0.596898\pi$
$20$			112088.i			0.700547i
$21$	−54355.4	−	338733.i	−0.279490	−	1.74173i
$22$	−145144.			−0.619597
$23$	−249593.	+	432307.i	−0.891908	+	1.54483i	−0.0543235	+	0.998523i	$0.517300\pi$
$23$	−249593.	+	432307.i	−0.891908	+	1.54483i	−0.837585	+	0.546307i	$0.816033\pi$
$24$	179197.	−	103460.i	0.540115	−	0.311835i
$25$	188099.	+	325797.i	0.481534	+	0.834041i
$26$	30035.9	+	17341.3i	0.0657276	+	0.0379479i
$27$		−	1.04220e6i		−	1.96109i
$28$	−303446.	+	48693.1i	−0.493684	+	0.0792200i
$29$	−88328.5			−0.124885			−0.0624423	−	0.998049i	$-0.519889\pi$
$29$	−88328.5			−0.124885			−0.0624423	+	0.998049i	$0.519889\pi$
$30$	707796.	−	1.22594e6i	0.873822	−	1.51350i
$31$	501813.	−	289722.i	0.543370	−	0.313715i	−0.203074	−	0.979163i	$-0.565093\pi$
$31$	501813.	−	289722.i	0.543370	−	0.313715i	0.746444	+	0.665449i	$0.231760\pi$
$32$	−92681.9	−	160530.i	−0.0883883	−	0.153093i
$33$	1.58749e6	+	916539.i	1.33862	+	0.772850i
$34$			815447.i			0.610211i
$35$	−1.63127e6	+	1.32647e6i	−1.08706	+	0.883947i
$36$	−1.77344e6			−1.05586
$37$	465050.	−	805489.i	0.248137	−	0.429787i	−0.714872	−	0.699256i	$-0.753515\pi$
$37$	465050.	−	805489.i	0.248137	−	0.429787i	0.963009	+	0.269469i	$0.0868482\pi$
$38$	−555272.	+	320587.i	−0.266300	+	0.153748i
$39$	−219009.	−	379334.i	−0.0946679	−	0.163970i
$40$	−1.09823e6	−	634063.i	−0.428996	−	0.247681i
$41$			1.42277e6i			0.503499i	0.967792	+	0.251749i	$0.0810059\pi$
$41$			1.42277e6i			0.503499i	−0.967792	+	0.251749i	$0.918994\pi$
$42$	3.62637e6	+	1.38359e6i	1.16540	+	0.444641i
$43$	2.95457e6			0.864211			0.432106	−	0.901823i	$-0.357771\pi$
$43$	2.95457e6			0.864211			0.432106	+	0.901823i	$0.357771\pi$
$44$	821061.	−	1.42212e6i	0.219061	−	0.379424i
$45$	−1.05072e7	+	6.06631e6i	−2.56233	+	1.47936i
$46$	−2.82382e6	−	4.89099e6i	−0.630674	−	1.09236i
$47$	6.92276e6	+	3.99685e6i	1.41869	+	0.819081i	0.996184	−	0.0872789i	$-0.0278171\pi$
$47$	6.92276e6	+	3.99685e6i	1.41869	+	0.819081i	0.422506	+	0.906360i	$0.361150\pi$
$48$			2.34102e6i			0.441002i
$49$	−4.29971e6	−	3.83997e6i	−0.745857	−	0.666107i
$50$	−4.25620e6			−0.680991
$51$	5.14928e6	−	8.91881e6i	0.761142	−	1.31834i
$52$	−339818.	+	196194.i	−0.0464764	+	0.0268332i
$53$	1.04248e6	+	1.80563e6i	0.132119	+	0.228837i	0.924493	−	0.381199i	$-0.124489\pi$
$53$	1.04248e6	+	1.80563e6i	0.132119	+	0.228837i	−0.792374	+	0.610035i	$0.791155\pi$
$54$	1.02115e7	+	5.89559e6i	1.20092	+	0.693350i
$55$		−	1.12342e7i		−	1.22770i
$56$	1.23946e6	−	3.24860e6i	0.126032	−	0.330327i
$57$	8.09759e6			0.767108
$58$	499661.	−	865439.i	0.0441534	−	0.0764759i
$59$	7.60174e6	−	4.38887e6i	0.627343	−	0.362197i	−0.152379	−	0.988322i	$-0.548693\pi$
$59$	7.60174e6	−	4.38887e6i	0.627343	−	0.362197i	0.779722	+	0.626125i	$0.215360\pi$
$60$	8.00780e6	+	1.38699e7i	0.617886	+	1.07021i
$61$	−1.25971e7	−	7.27293e6i	−0.909810	−	0.525279i	−0.0294401	−	0.999567i	$-0.509372\pi$
$61$	−1.25971e7	−	7.27293e6i	−0.909810	−	0.525279i	−0.880370	+	0.474287i	$0.842706\pi$
$62$			6.55566e6i			0.443660i
$63$	−2.09874e7	−	2.58099e7i	−1.33228	−	1.63842i
$64$	2.09715e6			0.125000
$65$	−1.34222e6	+	2.32479e6i	−0.0751917	+	0.130236i
$66$	−1.79604e7	+	1.03695e7i	−0.946544	+	0.546487i
$67$	7.05740e6	+	1.22238e7i	0.350224	+	0.606605i	0.986288	−	0.165030i	$-0.0527722\pi$
$67$	7.05740e6	+	1.22238e7i	0.350224	+	0.606605i	−0.636065	+	0.771636i	$0.719439\pi$
$68$	−7.98971e6	−	4.61286e6i	−0.373676	−	0.215742i
$69$			7.13259e7i			3.14667i
$70$	−3.76886e6	−	2.34868e7i	−0.156970	−	0.978209i
$71$	−3.34541e7			−1.31649			−0.658243	−	0.752806i	$-0.728700\pi$
$71$	−3.34541e7			−1.31649			−0.658243	+	0.752806i	$0.728700\pi$
$72$	1.00321e7	−	1.73761e7i	0.373304	−	0.646581i
$73$	1.12065e6	−	647007.i	0.0394619	−	0.0227833i	−0.480139	−	0.877192i	$-0.659414\pi$
$73$	1.12065e6	−	647007.i	0.0394619	−	0.0227833i	0.519601	+	0.854409i	$0.326081\pi$
$74$	5.26143e6	+	9.11307e6i	0.175460	+	0.303905i
$75$	4.65514e7	+	2.68765e7i	1.47125	+	0.849429i
$76$		−	7.25405e6i		−	0.217433i
$77$	3.04135e7	−	4.88037e6i	0.865175	−	0.138832i
$78$	4.95560e6			0.133881
$79$	1.69458e7	−	2.93509e7i	0.435063	−	0.753552i	−0.562237	−	0.826976i	$-0.690059\pi$
$79$	1.69458e7	−	2.93509e7i	0.435063	−	0.753552i	0.997301	+	0.0734239i	$0.0233926\pi$
$80$	1.24251e7	−	7.17361e6i	0.303346	−	0.175137i
$81$	−2.90061e7	−	5.02400e7i	−0.673827	−	1.16710i
$82$	−1.39402e7	−	8.04839e6i	−0.308329	−	0.178014i
$83$			7.65808e6i			0.161364i	0.996740	+	0.0806821i	$0.0257099\pi$
$83$			7.65808e6i			0.161364i	−0.996740	+	0.0806821i	$0.974290\pi$
$84$	−3.40702e7	+	2.77043e7i	−0.684317	+	0.556454i
$85$	−6.31158e7			−1.20910
$86$	−1.67136e7	+	2.89487e7i	−0.305545	+	0.529219i
$87$	−1.09299e7	+	6.31039e6i	−0.190783	+	0.110149i
$88$	9.28924e6	+	1.60894e7i	0.154899	+	0.268294i
$89$	8.82439e7	+	5.09476e7i	1.40645	+	0.812015i	0.995044	−	0.0994374i	$-0.0317043\pi$
$89$	8.82439e7	+	5.09476e7i	1.40645	+	0.812015i	0.411407	+	0.911452i	$0.365038\pi$
$90$		−	1.37265e8i		−	2.09214i
$91$	−6.87681e6	−	2.62375e6i	−0.100282	−	0.0382610i
$92$	6.38957e7			0.891908
$93$	4.13968e7	−	7.17014e7i	0.553395	−	0.958509i
$94$	−7.83220e7	+	4.52192e7i	−1.00317	+	0.579178i
$95$	−2.48135e7	−	4.29782e7i	−0.304645	−	0.527660i
$96$	−2.29372e7	−	1.32428e7i	−0.270057	−	0.155918i
$97$			2.91159e7i			0.328884i	0.986387	+	0.164442i	$0.0525824\pi$
$97$			2.91159e7i			0.328884i	−0.986387	+	0.164442i	$0.947418\pi$
$98$	6.19467e7	−	2.04063e7i	0.671605	−	0.221238i
$99$	1.77747e8			1.85038
$100$	2.40767e7	−	4.17020e7i	0.240767	−	0.417020i
$101$	−3.14578e7	+	1.81622e7i	−0.302304	+	0.174535i	−0.643477	−	0.765465i	$-0.722509\pi$
$101$	−3.14578e7	+	1.81622e7i	−0.302304	+	0.174535i	0.341174	+	0.940000i	$0.389176\pi$
$102$	5.82574e7	+	1.00905e8i	0.538208	+	0.932204i
$103$	−1.41753e8	−	8.18412e7i	−1.25946	−	0.727149i	−0.286489	−	0.958083i	$-0.592488\pi$
$103$	−1.41753e8	−	8.18412e7i	−1.25946	−	0.727149i	−0.972969	+	0.230935i	$0.925822\pi$
$104$		−	4.43936e6i		−	0.0379479i
$105$	−1.07090e8	+	2.80682e8i	−0.881034	+	2.30918i
$106$	−2.35887e7			−0.186844
$107$	−1.00138e8	+	1.73443e8i	−0.763945	+	1.32319i	0.176858	+	0.984236i	$0.443407\pi$
$107$	−1.00138e8	+	1.73443e8i	−0.763945	+	1.32319i	−0.940803	+	0.338954i	$0.889927\pi$
$108$	−1.15530e8	+	6.67010e7i	−0.849177	+	0.490273i
$109$	−7.45243e7	−	1.29080e8i	−0.527949	−	0.914435i	−0.999469	−	0.0325795i	$-0.989628\pi$
$109$	−7.45243e7	−	1.29080e8i	−0.527949	−	0.914435i	0.471520	−	0.881855i	$-0.343706\pi$
$110$	1.10072e8	+	6.35503e7i	0.751809	+	0.434057i
$111$		−	1.32897e8i		−	0.875433i
$112$	2.48182e7	+	3.05210e7i	0.157724	+	0.193967i
$113$	−2.00627e8			−1.23048			−0.615242	−	0.788338i	$-0.710942\pi$
$113$	−2.00627e8			−1.23048			−0.615242	+	0.788338i	$0.710942\pi$
$114$	−4.58069e7	+	7.93399e7i	−0.271214	+	0.469756i
$115$	3.78564e8	−	2.18564e8i	2.16445	−	1.24965i
$116$	5.65302e6	+	9.79132e6i	0.0312211	+	0.0540766i
$117$	−3.67827e7	−	2.12365e7i	−0.196291	−	0.113329i
$118$			9.93088e7i			0.512224i
$119$	−2.74188e7	−	1.70869e8i	−0.136729	−	0.852068i
$120$	−1.81196e8			−0.873822
$121$	2.48869e7	−	4.31053e7i	0.116099	−	0.201090i
$122$	1.42520e8	−	8.22838e7i	0.643333	−	0.371428i
$123$	1.01646e8	+	1.76056e8i	0.444088	+	0.769183i
$124$	−6.42321e7	−	3.70844e7i	−0.271685	−	0.156857i
$125$			1.26335e7i			0.0517466i
$126$	3.71607e8	−	5.96306e7i	1.47435	−	0.236585i
$127$	8.46459e6			0.0325380			0.0162690	−	0.999868i	$-0.494821\pi$
$127$	8.46459e6			0.0325380			0.0162690	+	0.999868i	$0.494821\pi$
$128$	−1.18633e7	+	2.05478e7i	−0.0441942	+	0.0765466i
$129$	3.65603e8	−	2.11081e8i	1.32023	−	0.762238i
$130$	−1.51855e7	−	2.63020e7i	−0.0531686	−	0.0920906i
$131$	−2.13575e8	−	1.23307e8i	−0.725212	−	0.418701i	0.0914562	−	0.995809i	$-0.470848\pi$
$131$	−2.13575e8	−	1.23307e8i	−0.725212	−	0.418701i	−0.816668	+	0.577108i	$0.804181\pi$
$132$		−	2.34634e8i		−	0.772850i
$133$	1.05572e8	−	8.58462e7i	0.337398	−	0.274356i
$134$	−1.59691e8			−0.495291
$135$	−4.56321e8	+	7.90371e8i	−1.37384	+	2.37955i
$136$	9.03933e7	−	5.21886e7i	0.264229	−	0.152553i
$137$	−2.09994e8	−	3.63721e8i	−0.596109	−	1.03249i	−0.993389	−	0.114794i	$-0.963379\pi$
$137$	−2.09994e8	−	3.63721e8i	−0.596109	−	1.03249i	0.397280	−	0.917697i	$-0.369954\pi$
$138$	−6.98848e8	−	4.03480e8i	−1.92693	−	1.11251i
$139$			6.41408e8i			1.71820i	0.511804	+	0.859102i	$0.328977\pi$
$139$			6.41408e8i			1.71820i	−0.511804	+	0.859102i	$0.671023\pi$
$140$	2.51443e8	+	9.59343e7i	0.654526	+	0.249725i
$141$	1.14218e9			2.88973
$142$	1.89245e8	−	3.27782e8i	0.465448	−	0.806179i
$143$	3.40590e7	−	1.96640e7i	0.0814493	−	0.0470248i
$144$	1.13500e8	+	1.96588e8i	0.263966	+	0.457202i
$145$	6.69852e7	+	3.86739e7i	0.151533	+	0.0874876i
$146$			1.46401e7i			0.0322205i
$147$	−8.06391e8	−	1.67983e8i	−1.72694	−	0.359746i
$148$	−1.19053e8			−0.248137
$149$	−1.15983e8	+	2.00889e8i	−0.235315	+	0.407578i	−0.959364	−	0.282170i	$-0.908946\pi$
$149$	−1.15983e8	+	2.00889e8i	−0.235315	+	0.407578i	0.724049	+	0.689749i	$0.242279\pi$
$150$	−5.26669e8	+	3.04072e8i	−1.04033	+	0.600637i
$151$	2.83226e8	+	4.90561e8i	0.544784	+	0.943594i	0.998620	+	0.0525090i	$0.0167218\pi$
$151$	2.83226e8	+	4.90561e8i	0.544784	+	0.943594i	−0.453836	+	0.891085i	$0.649945\pi$
$152$	7.10748e7	+	4.10351e7i	0.133150	+	0.0768742i
$153$		−	9.98614e8i		−	1.82235i
$154$	−1.24227e8	+	3.25598e8i	−0.220869	+	0.578894i
$155$	−5.07410e8			−0.879088
$156$	−2.80331e7	+	4.85548e7i	−0.0473340	+	0.0819848i
$157$	−6.98264e8	+	4.03143e8i	−1.14927	+	0.663530i	−0.948709	−	0.316152i	$-0.897609\pi$
$157$	−6.98264e8	+	4.03143e8i	−1.14927	+	0.663530i	−0.200559	+	0.979682i	$0.564276\pi$
$158$	1.91719e8	+	3.32068e8i	0.307636	+	0.532842i
$159$	2.57997e8	+	1.48955e8i	0.403669	+	0.233059i
$160$			1.62320e8i			0.247681i
$161$	7.56158e8	+	9.29909e8i	1.12541	+	1.38400i
$162$	6.56332e8			0.952936
$163$	−2.01244e7	+	3.48565e7i	−0.0285084	+	0.0493780i	−0.879928	−	0.475108i	$-0.842409\pi$
$163$	−2.01244e7	+	3.48565e7i	−0.0285084	+	0.0493780i	0.851419	+	0.524486i	$0.175742\pi$
$164$	1.57716e8	−	9.10571e7i	0.218021	−	0.125875i
$165$	−8.02599e8	−	1.39014e9i	−1.08284	−	1.87553i
$166$	−7.50335e7	−	4.33206e7i	−0.0988150	−	0.0570509i
$167$		−	2.59671e6i		−	0.00333854i	−0.999999	−	0.00166927i	$-0.999469\pi$
$167$		−	2.59671e6i		−	0.00333854i	0.999999	−	0.00166927i	$-0.000531346\pi$
$168$	−7.87150e7	−	4.90537e8i	−0.0988145	−	0.615793i
$169$	8.06333e8			0.988480
$170$	3.57037e8	−	6.18406e8i	0.427482	−	0.740420i
$171$	6.79999e8	−	3.92597e8i	0.795287	−	0.459159i
$172$	−1.89092e8	−	3.27517e8i	−0.216053	−	0.374214i
$173$	−1.93829e8	−	1.11907e8i	−0.216388	−	0.124932i	0.387889	−	0.921706i	$-0.373205\pi$
$173$	−1.93829e8	−	1.11907e8i	−0.216388	−	0.124932i	−0.604277	+	0.796774i	$0.706538\pi$
$174$		−	1.42788e8i		−	0.155774i
$175$	8.91842e8	−	1.43111e8i	0.950902	−	0.152588i
$176$	−2.10192e8			−0.219061
$177$	6.27102e8	−	1.08617e9i	0.638918	−	1.10664i
$178$	−9.98365e8	+	5.76406e8i	−0.994511	+	0.574181i
$179$	−6.89778e8	−	1.19473e9i	−0.671889	−	1.16375i	−0.977368	−	0.211547i	$-0.932150\pi$
$179$	−6.89778e8	−	1.19473e9i	−0.671889	−	1.16375i	0.305479	−	0.952199i	$-0.401183\pi$
$180$	1.34492e9	+	7.76488e8i	1.28117	+	0.739681i
$181$			1.75868e9i			1.63860i	0.573368	+	0.819298i	$0.305636\pi$
$181$			1.75868e9i			1.63860i	−0.573368	+	0.819298i	$0.694364\pi$
$182$	6.46085e7	−	5.25366e7i	0.0588849	−	0.0478824i
$183$	−2.07838e9			−1.85319
$184$	−3.61449e8	+	6.26047e8i	−0.315337	+	0.546180i
$185$	−7.05354e8	+	4.07237e8i	−0.602172	+	0.347664i
$186$	4.68352e8	+	8.11209e8i	0.391309	+	0.677768i
$187$	8.00786e8	+	4.62334e8i	0.654862	+	0.378085i
$188$		−	1.02319e9i		−	0.819081i
$189$	−2.33794e9	−	8.92009e8i	−1.83226	−	0.699072i
$190$	5.61465e8			0.430832
$191$	1.03184e9	−	1.78720e9i	0.775316	−	1.34289i	−0.159301	−	0.987230i	$-0.550924\pi$
$191$	1.03184e9	−	1.78720e9i	0.775316	−	1.34289i	0.934617	−	0.355656i	$-0.115743\pi$
$192$	2.59505e8	−	1.49825e8i	0.190959	−	0.110250i
$193$	5.13097e8	+	8.88711e8i	0.369803	+	0.640518i	0.989535	−	0.144296i	$-0.0460918\pi$
$193$	5.13097e8	+	8.88711e8i	0.369803	+	0.640518i	−0.619732	+	0.784814i	$0.712759\pi$
$194$	−2.85276e8	−	1.64704e8i	−0.201400	−	0.116278i
$195$			3.83565e8i			0.265277i
$196$	−1.50484e8	+	7.22387e8i	−0.101968	+	0.489492i
$197$	−1.22831e9			−0.815536			−0.407768	−	0.913086i	$-0.633693\pi$
$197$	−1.22831e9			−0.815536			−0.407768	+	0.913086i	$0.633693\pi$
$198$	−1.00549e9	+	1.74156e9i	−0.654209	+	1.13312i
$199$	2.14905e9	−	1.24076e9i	1.37036	−	0.791178i	0.379387	−	0.925238i	$-0.376135\pi$
$199$	2.14905e9	−	1.24076e9i	1.37036	−	0.791178i	0.990973	+	0.134060i	$0.0428015\pi$
$200$	2.72396e8	+	4.71805e8i	0.170248	+	0.294878i
$201$	1.74659e9	+	1.00839e9i	1.07006	+	0.617797i
$202$		−	4.10964e8i		−	0.246830i
$203$	−7.55992e7	+	1.98145e8i	−0.0445178	+	0.116680i
$204$	−1.31821e9			−0.761142
$205$	6.22948e8	−	1.07898e9i	0.352725	−	0.610937i
$206$	1.60375e9	−	9.25928e8i	0.890572	−	0.514172i
$207$	3.45811e9	+	5.98962e9i	1.88346	+	3.26226i
$208$	4.34967e7	+	2.51128e7i	0.0232382	+	0.0134166i
$209$			7.27052e8i			0.381049i
$210$	−2.14432e9	−	2.63704e9i	−1.10258	−	1.35594i
$211$	−3.39729e9			−1.71397			−0.856984	−	0.515343i	$-0.827665\pi$
$211$	−3.39729e9			−1.71397			−0.856984	+	0.515343i	$0.827665\pi$
$212$	1.33438e8	−	2.31121e8i	0.0660594	−	0.114418i
$213$	−4.13967e9	+	2.39004e9i	−2.01116	+	1.16115i
$214$	−1.13293e9	−	1.96229e9i	−0.540190	−	0.935637i
$215$	−2.24064e9	−	1.29363e9i	−1.04862	−	0.605421i
$216$		−	1.50927e9i		−	0.693350i
$217$	−2.20429e8	−	1.37367e9i	−0.0994100	−	0.619504i
$218$	1.68629e9			0.746633
$219$	9.24473e7	−	1.60123e8i	0.0401900	−	0.0696111i
$220$	−1.24533e9	+	7.18990e8i	−0.531610	+	0.306925i
$221$	−1.10476e8	−	1.91349e8i	−0.0463124	−	0.0802154i
$222$	1.30212e9	+	7.51778e8i	0.536091	+	0.309512i
$223$		−	2.09206e8i		−	0.0845971i	−0.999105	−	0.0422986i	$-0.986532\pi$
$223$		−	2.09206e8i		−	0.0845971i	0.999105	−	0.0422986i	$-0.0134681\pi$
$224$	−4.39437e8	+	7.05151e7i	−0.174544	+	0.0280085i
$225$	5.21223e9			2.03373
$226$	1.13492e9	−	1.96574e9i	0.435042	−	0.753515i
$227$	1.09121e9	−	6.30012e8i	0.410966	−	0.237271i	−0.280239	−	0.959930i	$-0.590414\pi$
$227$	1.09121e9	−	6.30012e8i	0.410966	−	0.237271i	0.691205	+	0.722659i	$0.257080\pi$
$228$	−5.18246e8	−	8.97628e8i	−0.191777	−	0.332167i
$229$	2.99386e9	+	1.72850e9i	1.08865	+	0.628534i	0.933217	−	0.359312i	$-0.116989\pi$
$229$	2.99386e9	+	1.72850e9i	1.08865	+	0.628534i	0.155435	+	0.987846i	$0.450322\pi$
$230$			4.94554e9i			1.76727i
$231$	3.41476e9	−	2.77672e9i	1.19926	−	0.975178i
$232$	−1.27913e8			−0.0441534
$233$	−9.17713e8	+	1.58953e9i	−0.311375	+	0.539316i	−0.978660	−	0.205485i	$-0.934123\pi$
$233$	−9.17713e8	+	1.58953e9i	−0.311375	+	0.539316i	0.667286	+	0.744802i	$0.267456\pi$
$234$	4.16149e8	−	2.40264e8i	0.138799	−	0.0801354i
$235$	−3.49998e9	−	6.06215e9i	−1.14761	−	1.98772i
$236$	−9.73023e8	−	5.61775e8i	−0.313672	−	0.181098i
$237$		−	4.84258e9i		−	1.53491i
$238$	1.82927e9	+	6.97930e8i	0.570124	+	0.217523i
$239$	2.30067e9			0.705120			0.352560	−	0.935789i	$-0.385311\pi$
$239$	2.30067e9			0.705120			0.352560	+	0.935789i	$0.385311\pi$
$240$	1.02500e9	−	1.77535e9i	0.308943	−	0.535105i
$241$	−1.26558e9	+	7.30684e8i	−0.375165	+	0.216602i	−0.675713	−	0.737165i	$-0.736164\pi$
$241$	−1.26558e9	+	7.30684e8i	−0.375165	+	0.216602i	0.300548	+	0.953767i	$0.402831\pi$
$242$	2.81563e8	+	4.87681e8i	0.0820945	+	0.142192i
$243$	−1.25672e9	−	7.25570e8i	−0.360425	−	0.208091i
$244$			1.86187e9i			0.525279i
$245$	1.57945e9	+	4.79470e9i	0.438371	+	1.33075i
$246$	−2.29998e9			−0.628035
$247$	8.68652e7	−	1.50455e8i	0.0233377	−	0.0404221i
$248$	7.26703e8	−	4.19562e8i	0.192110	−	0.110915i
$249$	5.47111e8	+	9.47624e8i	0.142324	+	0.246512i
$250$	−1.23782e8	−	7.14656e7i	−0.0316882	−	0.0182952i
$251$			1.53360e9i			0.386381i	0.981161	+	0.193191i	$0.0618836\pi$
$251$			1.53360e9i			0.386381i	−0.981161	+	0.193191i	$0.938116\pi$
$252$	−1.51787e9	+	3.97831e9i	−0.376384	+	0.986499i
$253$	−6.40408e9			−1.56306
$254$	−4.78830e7	+	8.29357e7i	−0.0115039	+	0.0199254i
$255$	−7.81006e9	+	4.50914e9i	−1.84711	+	1.06643i
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	−2.50705e9	−	1.44744e9i	−0.574685	−	0.331795i	0.184333	−	0.982864i	$-0.440987\pi$
$257$	−2.50705e9	−	1.44744e9i	−0.574685	−	0.331795i	−0.759018	+	0.651069i	$0.774321\pi$
$258$			4.77622e9i			1.07797i
$259$	−1.40890e9	−	1.73264e9i	−0.313099	−	0.385043i
$260$	3.43608e8			0.0751917
$261$	−6.11897e8	+	1.05984e9i	−0.131861	+	0.228390i
$262$	2.41632e9	−	1.39506e9i	0.512802	−	0.296066i
$263$	2.71973e8	+	4.71071e8i	0.0568464	+	0.0984609i	0.893048	−	0.449961i	$-0.148562\pi$
$263$	2.71973e8	+	4.71071e8i	0.0568464	+	0.0984609i	−0.836202	+	0.548422i	$0.815229\pi$
$264$	2.29893e9	+	1.32729e9i	0.473272	+	0.273244i
$265$		−	1.82577e9i		−	0.370222i
$266$	2.43912e8	+	1.52001e9i	0.0487198	+	0.303613i
$267$	1.45593e10			2.86480
$268$	9.03347e8	−	1.56464e9i	0.175112	−	0.303303i
$269$	−6.55960e8	+	3.78719e8i	−0.125276	+	0.0723282i	−0.561328	−	0.827593i	$-0.689710\pi$
$269$	−6.55960e8	+	3.78719e8i	−0.125276	+	0.0723282i	0.436052	+	0.899921i	$0.356376\pi$
$270$	−5.16268e9	−	8.94202e9i	−0.971449	−	1.68260i
$271$	−2.65727e9	−	1.53417e9i	−0.492672	−	0.284444i	0.233010	−	0.972474i	$-0.425142\pi$
$271$	−2.65727e9	−	1.53417e9i	−0.492672	−	0.284444i	−0.725682	+	0.688030i	$0.758476\pi$
$272$			1.18089e9i			0.215742i
$273$	−1.03840e9	+	1.66628e8i	−0.186944	+	0.0299984i
$274$	4.75163e9			0.843025
$275$	−2.41314e9	+	4.17967e9i	−0.421940	+	0.730822i
$276$	7.90656e9	−	4.56486e9i	1.36255	−	0.786667i
$277$	2.87053e9	+	4.97190e9i	0.487576	+	0.844506i	0.999898	−	0.0142870i	$-0.00454786\pi$
$277$	2.87053e9	+	4.97190e9i	0.487576	+	0.844506i	−0.512322	+	0.858793i	$0.671215\pi$
$278$	−6.28448e9	−	3.62835e9i	−1.05218	−	0.607477i
$279$		−	8.02821e9i		−	1.32496i
$280$	−2.36234e9	+	1.92094e9i	−0.384335	+	0.312523i
$281$	1.97804e9			0.317256			0.158628	−	0.987338i	$-0.449293\pi$
$281$	1.97804e9			0.317256			0.158628	+	0.987338i	$0.449293\pi$
$282$	−6.46114e9	+	1.11910e10i	−1.02167	+	1.76959i
$283$	5.52235e9	−	3.18833e9i	0.860951	−	0.497070i	−0.00337979	−	0.999994i	$-0.501076\pi$
$283$	5.52235e9	−	3.18833e9i	0.860951	−	0.497070i	0.864331	+	0.502924i	$0.167742\pi$
$284$	2.14106e9	+	3.70843e9i	0.329121	+	0.570055i
$285$	−6.14093e9	−	3.54547e9i	−0.930796	−	0.537395i
$286$			4.44945e8i			0.0665031i
$287$	3.19165e9	+	1.21773e9i	0.470422	+	0.179483i
$288$	−2.56822e9			−0.373304
$289$	−8.90405e8	+	1.54223e9i	−0.127643	+	0.221084i
$290$	−7.57851e8	+	4.37546e8i	−0.107150	+	0.0618631i
$291$	2.08011e9	+	3.60285e9i	0.290077	+	0.502429i
$292$	−1.43443e8	−	8.28169e7i	−0.0197309	−	0.0113917i
$293$		−	7.38690e9i		−	1.00229i	−0.865364	−	0.501143i	$-0.832913\pi$
$293$		−	7.38690e9i		−	1.00229i	0.865364	−	0.501143i	$-0.167087\pi$
$294$	6.20753e9	−	6.95073e9i	0.830863	−	0.930338i
$295$	−7.68653e9			−1.01494
$296$	6.73464e8	−	1.16647e9i	0.0877298	−	0.151953i
$297$	1.15792e10	−	6.68525e9i	1.48817	−	0.859196i
$298$	−1.31220e9	−	2.27280e9i	−0.166393	−	0.288201i
$299$	1.32525e9	+	7.65134e8i	0.165811	+	0.0957310i
$300$		−	6.88037e9i		−	0.849429i
$301$	2.52878e9	−	6.62789e9i	0.308066	−	0.807438i
$302$	−6.40866e9			−0.770441
$303$	−2.59510e9	+	4.49484e9i	−0.307881	+	0.533266i
$304$	−8.04120e8	+	4.64259e8i	−0.0941513	+	0.0543583i
$305$	6.36879e9	+	1.10311e10i	0.735966	+	1.27473i
$306$	9.78438e9	+	5.64902e9i	1.11596	+	0.644298i
$307$		−	2.19092e9i		−	0.246645i	−0.992367	−	0.123322i	$-0.960645\pi$
$307$		−	2.19092e9i		−	0.246645i	0.992367	−	0.123322i	$-0.0393549\pi$
$308$	−2.48746e9	−	3.05903e9i	−0.276410	−	0.339924i
$309$	−2.33877e10			−2.56539
$310$	2.87035e9	−	4.97158e9i	0.310805	−	0.538329i
$311$	7.20343e9	−	4.15890e9i	0.770013	−	0.444567i	−0.0628665	−	0.998022i	$-0.520024\pi$
$311$	7.20343e9	−	4.15890e9i	0.770013	−	0.444567i	0.832879	+	0.553455i	$0.186691\pi$
$312$	−3.17158e8	−	5.49334e8i	−0.0334702	−	0.0579720i
$313$	7.36210e8	+	4.25051e8i	0.0767051	+	0.0442857i	0.537862	−	0.843033i	$-0.319232\pi$
$313$	7.36210e8	+	4.25051e8i	0.0767051	+	0.0442857i	−0.461157	+	0.887319i	$0.652565\pi$
$314$		−	9.12208e9i		−	0.938373i
$315$	4.61543e9	+	2.87625e10i	0.468781	+	2.92135i
$316$	−4.33811e9			−0.435063
$317$	−2.14375e8	+	3.71309e8i	−0.0212294	+	0.0367704i	−0.876445	−	0.481502i	$-0.840091\pi$
$317$	−2.14375e8	+	3.71309e8i	−0.0212294	+	0.0367704i	0.855216	+	0.518272i	$0.173425\pi$
$318$	−2.91890e9	+	1.68523e9i	−0.285437	+	0.164797i
$319$	−5.66586e8	−	9.81356e8i	−0.0547146	−	0.0947685i
$320$	−1.59041e9	−	9.18222e8i	−0.151673	−	0.0875684i
$321$			2.86162e10i			2.69521i
$322$	−1.33887e10	+	2.14844e9i	−1.24542	+	0.199848i
$323$	4.08471e9			0.375276
$324$	−3.71277e9	+	6.43071e9i	−0.336914	+	0.583551i
$325$	9.98741e8	−	5.76623e8i	0.0895199	−	0.0516843i
$326$	−2.27682e8	−	3.94357e8i	−0.0201585	−	0.0349155i
$327$	−1.84435e10	−	1.06484e10i	−1.61307	−	0.931307i
$328$			2.06039e9i			0.178014i
$329$	1.48911e10	−	1.21087e10i	1.27099	−	1.03351i
$330$	1.81607e10			1.53136
$331$	−3.98245e9	+	6.89781e9i	−0.331771	+	0.574645i	−0.982859	−	0.184358i	$-0.940980\pi$
$331$	−3.98245e9	+	6.89781e9i	−0.331771	+	0.574645i	0.651088	+	0.759002i	$0.274313\pi$
$332$	8.48908e8	−	4.90117e8i	0.0698728	−	0.0403411i
$333$	−6.44327e9	−	1.11601e10i	−0.523998	−	0.907591i
$334$	2.54424e7	+	1.46892e7i	0.00204443	+	0.00118035i
$335$		−	1.23601e10i		−	0.981393i
$336$	5.25154e9	+	2.00365e9i	0.412031	+	0.157204i
$337$	1.30470e10			1.01156			0.505779	−	0.862663i	$-0.331205\pi$
$337$	1.30470e10			1.01156			0.505779	+	0.862663i	$0.331205\pi$
$338$	−4.56131e9	+	7.90042e9i	−0.349480	+	0.605318i
$339$	−2.48260e10	+	1.43333e10i	−1.87978	+	1.08529i
$340$	4.03941e9	+	6.99647e9i	0.302275	+	0.523556i
$341$	6.43780e9	+	3.71687e9i	0.476124	+	0.274890i
$342$			8.88347e9i			0.649349i
$343$	−1.22942e10	+	6.35884e9i	−0.888224	+	0.459411i
$344$	4.27867e9			0.305545
$345$	3.12295e10	−	5.40910e10i	2.20439	−	3.81811i
$346$	2.19292e9	−	1.26608e9i	0.153010	−	0.0883402i
$347$	−1.30853e10	−	2.26643e10i	−0.902535	−	1.56324i	−0.824192	−	0.566310i	$-0.808370\pi$
$347$	−1.30853e10	−	2.26643e10i	−0.902535	−	1.56324i	−0.0783432	−	0.996926i	$-0.524963\pi$
$348$	1.39903e9	+	8.07730e8i	0.0953916	+	0.0550744i
$349$			7.96331e9i			0.536775i	0.963311	+	0.268387i	$0.0864907\pi$
$349$			7.96331e9i			0.536775i	−0.963311	+	0.268387i	$0.913509\pi$
$350$	−3.64282e9	+	9.54779e9i	−0.242754	+	0.636254i
$351$	−3.19491e9			−0.210489
$352$	1.18902e9	−	2.05945e9i	0.0774497	−	0.134147i
$353$	2.48989e9	−	1.43754e9i	0.160354	−	0.0925806i	−0.417675	−	0.908596i	$-0.637155\pi$
$353$	2.48989e9	−	1.43754e9i	0.160354	−	0.0925806i	0.578030	+	0.816016i	$0.303822\pi$
$354$	7.09485e9	+	1.22886e10i	0.451783	+	0.782512i
$355$	2.53704e10	+	1.46476e10i	1.59740	+	0.922261i
$356$		−	1.30426e10i		−	0.812015i
$357$	−1.56001e10	−	1.91847e10i	−0.960405	−	1.18109i
$358$	1.56079e10			0.950194
$359$	−1.24261e10	+	2.15226e10i	−0.748094	+	1.29574i	0.200641	+	0.979665i	$0.435698\pi$
$359$	−1.24261e10	+	2.15226e10i	−0.748094	+	1.29574i	−0.948735	+	0.316072i	$0.897636\pi$
$360$	−1.52160e10	+	8.78496e9i	−0.905921	+	0.523034i
$361$	−6.88591e9	−	1.19267e10i	−0.405446	−	0.702252i
$362$	−1.72314e10	−	9.94858e9i	−1.00343	−	0.579331i
$363$		−	7.11191e9i		−	0.409600i
$364$	1.49270e8	+	9.30223e8i	0.00850290	+	0.0529885i
$365$	−1.13315e9			−0.0638432
$366$	1.17571e10	−	2.03639e10i	0.655203	−	1.13484i
$367$	2.24815e8	−	1.29797e8i	0.0123925	−	0.00715484i	−0.493791	−	0.869581i	$-0.664389\pi$
$367$	2.24815e8	−	1.29797e8i	0.0123925	−	0.00715484i	0.506183	+	0.862426i	$0.331056\pi$
$368$	−4.08932e9	−	7.08292e9i	−0.222977	−	0.386208i
$369$	1.70715e10	+	9.85624e9i	0.920802	+	0.531625i
$370$		−	9.21471e9i		−	0.491671i
$371$	4.94276e9	−	7.93150e8i	0.260900	−	0.0418658i
$372$	−1.05976e10			−0.553395
$373$	−1.72152e10	+	2.98176e10i	−0.889359	+	1.54042i	−0.0487248	+	0.998812i	$0.515516\pi$
$373$	−1.72152e10	+	2.98176e10i	−0.889359	+	1.54042i	−0.840634	+	0.541603i	$0.817818\pi$
$374$	−9.05986e9	+	5.23071e9i	−0.463058	+	0.267346i
$375$	9.02563e8	+	1.56329e9i	0.0456407	+	0.0790520i
$376$	1.00252e10	+	5.78806e9i	0.501583	+	0.289589i
$377$			2.70774e8i			0.0134042i
$378$	2.19653e10	−	1.78611e10i	1.07589	−	0.874865i
$379$	3.06189e10			1.48400			0.741998	−	0.670402i	$-0.233878\pi$
$379$	3.06189e10			1.48400			0.741998	+	0.670402i	$0.233878\pi$
$380$	−3.17613e9	+	5.50121e9i	−0.152322	+	0.263830i
$381$	1.04742e9	−	6.04730e8i	0.0497075	−	0.0286987i
$382$	1.16739e10	+	2.02198e10i	0.548231	+	0.949564i
$383$	1.73217e10	+	1.00007e10i	0.804999	+	0.464766i	0.845216	−	0.534425i	$-0.179472\pi$
$383$	1.73217e10	+	1.00007e10i	0.804999	+	0.464766i	−0.0402172	+	0.999191i	$0.512805\pi$
$384$			3.39016e9i			0.155918i
$385$	−2.52014e10	−	9.61522e9i	−1.14705	−	0.437640i
$386$	−1.16101e10			−0.522980
$387$	2.04678e10	−	3.54512e10i	0.912488	−	1.58048i
$388$	3.22753e9	−	1.86342e9i	0.142411	−	0.0822211i
$389$	6.06521e9	+	1.05052e10i	0.264879	+	0.458784i	0.967532	−	0.252749i	$-0.0813347\pi$
$389$	6.06521e9	+	1.05052e10i	0.264879	+	0.458784i	−0.702653	+	0.711533i	$0.748001\pi$
$390$	−3.75815e9	−	2.16977e9i	−0.162449	−	0.0937897i
$391$			3.59793e10i			1.53938i
$392$	−6.22665e9	−	5.56087e9i	−0.263700	−	0.235504i
$393$	−3.52375e10			−1.47718
$394$	6.94837e9	−	1.20349e10i	0.288335	−	0.499412i
$395$	−2.57021e10	+	1.48391e10i	−1.05580	+	0.609565i
$396$	−1.13758e10	−	1.97035e10i	−0.462596	−	0.801239i
$397$	−5.98646e9	−	3.45628e9i	−0.240995	−	0.139139i	0.374639	−	0.927171i	$-0.377767\pi$
$397$	−5.98646e9	−	3.45628e9i	−0.240995	−	0.139139i	−0.615634	+	0.788032i	$0.711100\pi$
$398$			2.80751e10i			1.11889i
$399$	6.93063e9	−	1.81651e10i	0.273452	−	0.716714i
$400$	−6.16363e9			−0.240767
$401$	−1.26426e10	+	2.18976e10i	−0.488944	+	0.846875i	−0.999919	−	0.0127200i	$-0.995951\pi$
$401$	−1.26426e10	+	2.18976e10i	−0.488944	+	0.846875i	0.510975	+	0.859595i	$0.329284\pi$
$402$	−1.97604e10	+	1.14087e10i	−0.756644	+	0.436849i
$403$	−8.88152e8	−	1.53832e9i	−0.0336719	−	0.0583214i
$404$	4.02660e9	+	2.32476e9i	0.151152	+	0.0872676i
$405$			5.08003e10i			1.88819i
$406$	−1.51376e9	−	1.86159e9i	−0.0557125	−	0.0685142i
$407$	1.19323e10			0.434857
$408$	7.45695e9	−	1.29158e10i	0.269104	−	0.466102i
$409$	6.79049e9	−	3.92049e9i	0.242666	−	0.140103i	−0.373736	−	0.927535i	$-0.621923\pi$
$409$	6.79049e9	−	3.92049e9i	0.242666	−	0.140103i	0.616401	+	0.787432i	$0.288590\pi$
$410$	7.04785e9	+	1.22072e10i	0.249414	+	0.431998i
$411$	−5.19702e10	−	3.00050e10i	−1.82132	−	1.05154i
$412$			2.09514e10i			0.727149i
$413$	−3.33918e9	−	2.08091e10i	−0.114773	−	0.715244i
$414$	−7.82481e10			−2.66362
$415$	3.35303e9	−	5.80762e9i	0.113043	−	0.195797i
$416$	−4.92109e8	+	2.84119e8i	−0.0164319	+	0.00948696i
$417$	4.58236e10	+	7.93689e10i	1.51546	+	2.62486i
$418$	−7.12363e9	−	4.11283e9i	−0.233344	−	0.134721i
$419$		−	4.39321e10i		−	1.42536i	−0.701488	−	0.712682i	$-0.747480\pi$
$419$		−	4.39321e10i		−	1.42536i	0.701488	−	0.712682i	$-0.252520\pi$
$420$	3.79677e10	−	6.09257e9i	1.22016	−	0.195796i
$421$	5.72195e9			0.182144			0.0910721	−	0.995844i	$-0.470971\pi$
$421$	5.72195e9			0.182144			0.0910721	+	0.995844i	$0.470971\pi$
$422$	1.92180e10	−	3.32865e10i	0.605979	−	1.04959i
$423$	9.59149e10	−	5.53765e10i	2.99588	−	1.72967i
$424$	1.50967e9	+	2.61483e9i	0.0467111	+	0.0809059i
$425$	2.34821e10	+	1.35574e10i	0.719751	+	0.415548i
$426$		−	5.40804e10i		−	1.64211i
$427$	−2.70968e10	+	2.20339e10i	−0.815093	+	0.662795i
$428$	2.56352e10			0.763945
$429$	2.80968e9	−	4.86650e9i	0.0829521	−	0.143677i
$430$	2.53499e10	−	1.46358e10i	0.741486	−	0.428097i
$431$	−6.82833e9	−	1.18270e10i	−0.197882	−	0.342741i	0.749960	−	0.661483i	$-0.230073\pi$
$431$	−6.82833e9	−	1.18270e10i	−0.197882	−	0.342741i	−0.947841	+	0.318743i	$0.896739\pi$
$432$	1.47878e10	+	8.53773e9i	0.424588	+	0.245136i
$433$		−	5.05551e10i		−	1.43818i	−0.694917	−	0.719090i	$-0.744559\pi$
$433$		−	5.05551e10i		−	1.43818i	0.694917	−	0.719090i	$-0.255441\pi$
$434$	1.47061e10	+	5.61091e9i	0.414514	+	0.158152i
$435$	1.10518e10			0.308658
$436$	−9.53912e9	+	1.65222e10i	−0.263975	+	0.457217i
$437$	−2.44998e10	+	1.41450e10i	−0.671795	+	0.387861i
$438$	1.04592e9	+	1.81159e9i	0.0284186	+	0.0492225i
$439$	3.81030e10	+	2.19988e10i	1.02589	+	0.592298i	0.915805	−	0.401624i	$-0.131554\pi$
$439$	3.81030e10	+	2.19988e10i	1.02589	+	0.592298i	0.110086	+	0.993922i	$0.464887\pi$
$440$		−	1.62689e10i		−	0.434057i
$441$	−7.58614e10	+	2.49900e10i	−2.00570	+	0.660711i
$442$	2.49978e9			0.0654956
$443$	−2.48510e9	+	4.30432e9i	−0.0645252	+	0.111761i	−0.896483	−	0.443078i	$-0.853887\pi$
$443$	−2.48510e9	+	4.30432e9i	−0.0645252	+	0.111761i	0.831958	+	0.554839i	$0.187220\pi$
$444$	−1.47318e10	+	8.50540e9i	−0.379074	+	0.218858i
$445$	−4.46140e10	−	7.72738e10i	−1.13771	−	1.97057i
$446$	2.04980e9	+	1.18345e9i	0.0518049	+	0.0299096i
$447$			3.31445e10i			0.830197i
$448$	1.79493e9	−	4.70448e9i	0.0445589	−	0.116788i
$449$	−1.19199e10			−0.293284			−0.146642	−	0.989190i	$-0.546846\pi$
$449$	−1.19199e10			−0.293284			−0.146642	+	0.989190i	$0.546846\pi$
$450$	−2.94848e10	+	5.10692e10i	−0.719033	+	1.24540i
$451$	−1.58074e10	+	9.12639e9i	−0.382079	+	0.220594i
$452$	1.28401e10	+	2.22398e10i	0.307621	+	0.532816i
$453$	7.00936e10	+	4.04686e10i	1.66451	+	0.961004i
$454$			1.42555e10i			0.335552i
$455$	4.06634e9	+	5.00072e9i	0.0948765	+	0.116677i
$456$	1.17266e10			0.271214
$457$	2.45068e10	−	4.24470e10i	0.561852	−	0.973155i	−0.435483	−	0.900197i	$-0.643423\pi$
$457$	2.45068e10	−	4.24470e10i	0.561852	−	0.973155i	0.997335	−	0.0729587i	$-0.0232441\pi$
$458$	−3.38716e10	+	1.95558e10i	−0.769794	+	0.444441i
$459$	−3.75589e10	−	6.50540e10i	−0.846179	−	1.46563i
$460$	−4.84562e10	−	2.79762e10i	−1.08223	−	0.624824i
$461$		−	5.59070e10i		−	1.23784i	−0.785456	−	0.618918i	$-0.787571\pi$
$461$		−	5.59070e10i		−	1.23784i	0.785456	−	0.618918i	$-0.212429\pi$
$462$	7.88938e9	+	4.91651e10i	0.173171	+	1.07917i
$463$	1.00933e10			0.219638			0.109819	−	0.993952i	$-0.464973\pi$
$463$	1.00933e10			0.219638			0.109819	+	0.993952i	$0.464973\pi$
$464$	7.23587e8	−	1.25329e9i	0.0156106	−	0.0270383i
$465$	−6.27878e10	+	3.62506e10i	−1.34296	+	0.775359i
$466$	−1.03827e10	−	1.79834e10i	−0.220175	−	0.381354i
$467$	−7.53687e10	−	4.35142e10i	−1.58461	−	0.914878i	−0.994173	−	0.107797i	$-0.965620\pi$
$467$	−7.53687e10	−	4.35142e10i	−1.58461	−	0.914878i	−0.590442	−	0.807080i	$-0.701046\pi$
$468$			5.43654e9i			0.113329i
$469$	3.34616e10	−	5.36948e9i	0.691600	−	0.110979i
$470$	7.91956e10			1.62297
$471$	−5.76029e10	+	9.97712e10i	−1.17047	+	2.02732i
$472$	1.10085e10	−	6.35576e9i	0.221799	−	0.128056i
$473$	1.89522e10	+	3.28261e10i	0.378629	+	0.655806i
$474$	4.74474e10	+	2.73937e10i	0.939937	+	0.542673i
$475$			2.13200e10i			0.418806i
$476$	−1.71862e10	+	1.39750e10i	−0.334774	+	0.272222i
$477$	2.88872e10			0.557997
$478$	−1.30146e10	+	2.25419e10i	−0.249298	+	0.431796i
$479$	5.19458e10	−	2.99909e10i	0.986752	−	0.569701i	0.0824501	−	0.996595i	$-0.473725\pi$
$479$	5.19458e10	−	2.99909e10i	0.986752	−	0.569701i	0.904302	+	0.426894i	$0.140392\pi$
$480$	1.15965e10	+	2.00858e10i	0.218456	+	0.378376i
$481$	−2.46925e9	−	1.42562e9i	−0.0461302	−	0.0266333i
$482$		−	1.65335e10i		−	0.306321i
$483$	1.60003e11	+	6.10469e10i	2.93995	+	1.12170i
$484$	−6.37104e9			−0.116099
$485$	1.27482e10	−	2.20805e10i	0.230399	−	0.399063i
$486$	1.42182e10	−	8.20889e9i	0.254859	−	0.147143i
$487$	−2.90910e10	−	5.03871e10i	−0.517182	−	0.895785i	−0.999801	−	0.0199548i	$-0.993648\pi$
$487$	−2.90910e10	−	5.03871e10i	−0.517182	−	0.895785i	0.482619	−	0.875830i	$-0.339686\pi$
$488$	−1.82425e10	−	1.05323e10i	−0.321666	−	0.185714i
$489$			5.75094e9i			0.100578i
$490$	−5.59130e10	−	1.16475e10i	−0.969903	−	0.202045i
$491$	−7.31652e10			−1.25886			−0.629432	−	0.777056i	$-0.716712\pi$
$491$	−7.31652e10			−1.25886			−0.629432	+	0.777056i	$0.716712\pi$
$492$	1.30107e10	−	2.25351e10i	0.222044	−	0.384591i
$493$	−5.51343e9	+	3.18318e9i	−0.0933328	+	0.0538857i
$494$	9.82768e8	+	1.70220e9i	0.0165022	+	0.0285827i
$495$	−1.34797e11	−	7.78252e10i	−2.24523	−	1.29628i
$496$			9.49361e9i			0.156857i
$497$	−2.86329e10	+	7.50466e10i	−0.469289	+	1.23000i
$498$	−1.23797e10			−0.201276
$499$	−3.13183e10	+	5.42448e10i	−0.505121	+	0.874895i	0.494861	+	0.868972i	$0.335219\pi$
$499$	−3.13183e10	+	5.42448e10i	−0.505121	+	0.874895i	−0.999982	+	0.00592344i	$0.998115\pi$
$500$	1.40043e9	−	8.08541e8i	0.0224069	−	0.0129367i
$501$	−1.85515e8	−	3.21321e8i	−0.00294461	−	0.00510021i
$502$	−1.50261e10	−	8.67533e9i	−0.236609	−	0.136606i
$503$			1.86966e10i			0.292072i	0.989279	+	0.146036i	$0.0466515\pi$
$503$			1.86966e10i			0.292072i	−0.989279	+	0.146036i	$0.953348\pi$
$504$	−3.03930e10	−	3.73767e10i	−0.471033	−	0.579267i
$505$	3.18087e10			0.489081
$506$	3.62270e10	−	6.27469e10i	0.552624	−	0.957173i
$507$	9.97771e10	−	5.76063e10i	1.51008	−	0.871843i
$508$	−5.41734e8	−	9.38311e8i	−0.00813451	−	0.0140894i
$509$	6.80948e10	+	3.93145e10i	1.01448	+	0.585709i	0.912500	−	0.409078i	$-0.134149\pi$
$509$	6.80948e10	+	3.93145e10i	1.01448	+	0.585709i	0.101978	+	0.994787i	$0.467483\pi$
$510$		−	1.02030e11i		−	1.50816i
$511$	−4.92262e8	−	3.06768e9i	−0.00721959	−	0.0449911i
$512$	3.03700e9			0.0441942
$513$	2.95320e10	−	5.11509e10i	0.426406	−	0.738557i
$514$	2.83640e10	−	1.63760e10i	0.406364	−	0.234614i
$515$	7.16671e10	+	1.24131e11i	1.01880	+	1.76462i
$516$	−4.67972e10	−	2.70184e10i	−0.660117	−	0.381119i
$517$			1.02552e11i			1.43543i
$518$	2.49463e10	−	4.00305e9i	0.346487	−	0.0555997i
$519$	−3.19796e10			−0.440762
$520$	−1.94374e9	+	3.36666e9i	−0.0265843	+	0.0460453i
$521$	−2.52432e10	+	1.45742e10i	−0.342605	+	0.197803i	−0.661423	−	0.750013i	$-0.730047\pi$
$521$	−2.52432e10	+	1.45742e10i	−0.342605	+	0.197803i	0.318818	+	0.947816i	$0.396714\pi$
$522$	−6.92282e9	−	1.19907e10i	−0.0932397	−	0.161496i
$523$	−5.31017e9	−	3.06583e9i	−0.0709744	−	0.0409771i	0.464093	−	0.885787i	$-0.346380\pi$
$523$	−5.31017e9	−	3.06583e9i	−0.0709744	−	0.0409771i	−0.535067	+	0.844809i	$0.679714\pi$
$524$			3.15667e10i			0.418701i
$525$	1.00134e11	−	8.14241e10i	1.31809	−	1.07181i
$526$	−6.15405e9			−0.0803930
$527$	2.08820e10	−	3.61687e10i	0.270726	−	0.468911i
$528$	−2.60095e10	+	1.50166e10i	−0.334654	+	0.193212i
$529$	−8.54374e10	−	1.47982e11i	−1.09100	−	1.88967i
$530$	1.78888e10	+	1.03281e10i	0.226714	+	0.130893i
$531$		−	1.21616e11i		−	1.52972i
$532$	−1.62728e10	−	6.20864e9i	−0.203149	−	0.0775087i
$533$	4.36154e9			0.0540419
$534$	−8.23596e10	+	1.42651e11i	−1.01286	+	1.75432i
$535$	1.51882e11	−	8.76889e10i	1.85392	−	1.07036i
$536$	1.02202e10	+	1.77019e10i	0.123823	+	0.214467i
$537$	−1.70709e11	−	9.85587e10i	−2.05286	−	1.18522i
$538$		−	8.56942e9i		−	0.102287i
$539$	1.50826e10	−	7.24028e10i	0.178698	−	0.857828i
$540$	1.16818e11			1.37384
$541$	−6.25770e10	+	1.08386e11i	−0.730509	+	1.26528i	0.226157	+	0.974091i	$0.427384\pi$
$541$	−6.25770e10	+	1.08386e11i	−0.730509	+	1.26528i	−0.956666	+	0.291188i	$0.905950\pi$
$542$	3.00635e10	−	1.73572e10i	0.348372	−	0.201132i
$543$	1.25644e11	+	2.17622e11i	1.44525	+	2.50324i
$544$	−1.15703e10	−	6.68014e9i	−0.132115	−	0.0762764i
$545$			1.30520e11i			1.47941i
$546$	4.24143e9	−	1.11167e10i	0.0477246	−	0.125086i
$547$	−8.08478e9			−0.0903064			−0.0451532	−	0.998980i	$-0.514378\pi$
$547$	−8.08478e9			−0.0903064			−0.0451532	+	0.998980i	$0.514378\pi$
$548$	−2.68793e10	+	4.65563e10i	−0.298054	+	0.516245i
$549$	−1.74533e11	+	1.00767e11i	−1.92127	+	1.10924i
$550$	−2.73015e10	−	4.72876e10i	−0.298357	−	0.516769i
$551$	−4.33513e9	−	2.50289e9i	−0.0470322	−	0.0271541i
$552$			1.03291e11i			1.11251i
$553$	−5.13383e10	−	6.31350e10i	−0.548961	−	0.675102i
$554$	−6.49526e10			−0.689537
$555$	−5.81879e10	+	1.00784e11i	−0.613282	+	1.06224i
$556$	7.11008e10	−	4.10501e10i	0.744004	−	0.429551i
$557$	2.26100e10	+	3.91616e10i	0.234898	+	0.406855i	0.959243	−	0.282583i	$-0.0911911\pi$
$557$	2.26100e10	+	3.91616e10i	0.234898	+	0.406855i	−0.724345	+	0.689438i	$0.757858\pi$
$558$	7.86601e10	+	4.54144e10i	0.811368	+	0.468443i
$559$		−	9.05731e9i		−	0.0927582i
$560$	−5.45789e9	−	3.40125e10i	−0.0554974	−	0.345849i
$561$	1.32121e11			1.33389
$562$	−1.11895e10	+	1.93807e10i	−0.112167	+	0.194279i
$563$	−1.60535e11	+	9.26851e10i	−1.59785	+	0.922521i	−0.605953	+	0.795500i	$0.707208\pi$
$563$	−1.60535e11	+	9.26851e10i	−1.59785	+	0.922521i	−0.991900	+	0.127021i	$0.959459\pi$
$564$	−7.30994e10	−	1.26612e11i	−0.722433	−	1.25129i
$565$	1.52149e11	+	8.78431e10i	1.49305	+	0.862013i
$566$			7.21437e10i			0.702963i
$567$	−1.37528e11	+	2.20687e10i	−1.33063	+	0.213522i
$568$	−4.84467e10			−0.465448
$569$	1.00436e11	−	1.73960e11i	0.958164	−	1.65959i	0.231207	−	0.972905i	$-0.425733\pi$
$569$	1.00436e11	−	1.73960e11i	0.958164	−	1.65959i	0.726957	−	0.686683i	$-0.240934\pi$
$570$	6.94767e10	−	4.01124e10i	0.658172	−	0.379996i
$571$	1.50052e10	+	2.59897e10i	0.141155	+	0.244488i	0.927932	−	0.372750i	$-0.121585\pi$
$571$	1.50052e10	+	2.59897e10i	0.141155	+	0.244488i	−0.786777	+	0.617238i	$0.788252\pi$
$572$	−4.35955e9	−	2.51699e9i	−0.0407247	−	0.0235124i
$573$		−	2.94868e11i		−	2.73533i
$574$	−2.99860e10	+	2.43831e10i	−0.276230	+	0.224617i
$575$	−1.87792e11			−1.71794
$576$	1.45280e10	−	2.51633e10i	0.131983	−	0.228601i
$577$	7.61972e10	−	4.39925e10i	0.687442	−	0.396895i	−0.115211	−	0.993341i	$-0.536754\pi$
$577$	7.61972e10	−	4.39925e10i	0.687442	−	0.396895i	0.802653	+	0.596446i	$0.203421\pi$
$578$	−1.00738e10	−	1.74483e10i	−0.0902570	−	0.156330i
$579$	1.26983e11	+	7.33137e10i	1.12988	+	0.652335i
$580$		−	9.90053e9i		−	0.0874876i
$581$	1.71791e10	+	6.55445e9i	0.150764	+	0.0575217i
$582$	−4.70675e10			−0.410231
$583$	−1.33741e10	+	2.31646e10i	−0.115768	+	0.200516i
$584$	1.62287e9	−	9.36966e8i	0.0139519	−	0.00805513i
$585$	1.85965e10	+	3.22100e10i	0.158784	+	0.275022i
$586$	7.23766e10	+	4.17866e10i	0.613773	+	0.354362i
$587$		−	4.35775e10i		−	0.367037i	−0.983016	−	0.183519i	$-0.941251\pi$
$587$		−	4.35775e10i		−	0.367037i	0.983016	−	0.183519i	$-0.0587487\pi$
$588$	3.29879e10	+	1.00140e11i	0.275959	+	0.837722i
$589$	3.28384e10			0.272848
$590$	4.34816e10	−	7.53123e10i	0.358837	−	0.621524i
$591$	−1.51993e11	+	8.77533e10i	−1.24587	+	0.719306i
$592$	7.61937e9	+	1.31971e10i	0.0620344	+	0.107447i
$593$	−1.49827e11	−	8.65027e10i	−1.21163	−	0.699537i	−0.248519	−	0.968627i	$-0.579944\pi$
$593$	−1.49827e11	−	8.65027e10i	−1.21163	−	0.699537i	−0.963115	+	0.269090i	$0.913277\pi$
$594$			1.51270e11i			1.21509i
$595$	−5.40200e10	+	1.41586e11i	−0.431010	+	1.12967i
$596$	2.96917e10			0.235315
$597$	1.77285e11	−	3.07067e11i	1.39564	−	2.41733i
$598$	−1.49935e10	+	8.65650e9i	−0.117246	+	0.0676920i
$599$	−7.79310e10	−	1.34981e11i	−0.605345	−	1.04849i	−0.991997	−	0.126263i	$-0.959702\pi$
$599$	−7.79310e10	−	1.34981e11i	−0.605345	−	1.04849i	0.386652	−	0.922226i	$-0.373632\pi$
$600$	6.74136e10	+	3.89213e10i	0.520167	+	0.300318i
$601$			1.42951e11i			1.09569i	0.836580	+	0.547845i	$0.184552\pi$
$601$			1.42951e11i			1.09569i	−0.836580	+	0.547845i	$0.815448\pi$
$602$	5.06349e10	+	6.22698e10i	0.385535	+	0.474124i
$603$	1.95561e11			1.47915
$604$	3.62529e10	−	6.27918e10i	0.272392	−	0.471797i
$605$	−3.77467e10	+	2.17931e10i	−0.281746	+	0.162666i
$606$	−2.93602e10	−	5.08533e10i	−0.217705	−	0.377076i
$607$	−1.53187e11	−	8.84427e10i	−1.12841	−	0.651489i	−0.184877	−	0.982762i	$-0.559189\pi$
$607$	−1.53187e11	−	8.84427e10i	−1.12841	−	0.651489i	−0.943535	+	0.331272i	$0.892522\pi$
$608$		−	1.05050e10i		−	0.0768742i
$609$	4.80113e9	+	2.99197e10i	0.0349039	+	0.217515i
$610$	−1.44109e11			−1.04081
$611$	1.22525e10	−	2.12219e10i	0.0879142	−	0.152272i
$612$	−1.10698e11	+	6.39113e10i	−0.789101	+	0.455588i
$613$	−6.87312e10	−	1.19046e11i	−0.486757	−	0.843088i	0.513127	−	0.858313i	$-0.328487\pi$
$613$	−6.87312e10	−	1.19046e11i	−0.486757	−	0.843088i	−0.999884	+	0.0152246i	$0.995154\pi$
$614$	2.14665e10	+	1.23937e10i	0.151039	+	0.0872022i
$615$		−	1.78019e11i		−	1.24442i
$616$	4.40435e10	−	7.06753e9i	0.305885	−	0.0490845i
$617$	−1.18079e10			−0.0814761			−0.0407381	−	0.999170i	$-0.512971\pi$
$617$	−1.18079e10			−0.0814761			−0.0407381	+	0.999170i	$0.512971\pi$
$618$	1.32301e11	−	2.29152e11i	0.907003	−	1.57098i
$619$	1.06013e11	−	6.12069e10i	0.722102	−	0.416906i	−0.0934240	−	0.995626i	$-0.529781\pi$
$619$	1.06013e11	−	6.12069e10i	0.722102	−	0.416906i	0.815526	+	0.578721i	$0.196448\pi$
$620$	3.24743e10	+	5.62471e10i	0.219772	+	0.380656i
$621$	4.50552e11	+	2.60126e11i	3.02955	+	1.74911i
$622$			9.41052e10i			0.628713i
$623$	1.89816e11	−	1.54349e11i	1.26003	−	1.02460i
$624$	7.17647e9			0.0473340
$625$	7.90076e10	−	1.36845e11i	0.517784	−	0.896829i
$626$	−8.32926e9	+	4.80890e9i	−0.0542387	+	0.0313147i
$627$	5.19423e10	+	8.99667e10i	0.336086	+	0.582119i
$628$	8.93778e10	+	5.16023e10i	0.574634	+	0.331765i
$629$		−	6.70378e10i		−	0.428270i
$630$	−3.07922e11	−	1.17483e11i	−1.95470	−	0.745786i
$631$	6.31617e10			0.398416			0.199208	−	0.979957i	$-0.436163\pi$
$631$	6.31617e10			0.398416			0.199208	+	0.979957i	$0.436163\pi$
$632$	2.45401e10	−	4.25047e10i	0.153818	−	0.266421i
$633$	−4.20387e11	+	2.42710e11i	−2.61839	+	1.51173i
$634$	−2.42538e9	−	4.20088e9i	−0.0150114	−	0.0260006i
$635$	−6.41925e9	−	3.70616e9i	−0.0394811	−	0.0227944i
$636$		−	3.81324e10i		−	0.233059i
$637$	−1.17716e10	+	1.31809e10i	−0.0714950	+	0.0800548i
$638$	1.28204e10			0.0773782
$639$	−2.31754e11	+	4.01409e11i	−1.39003	+	2.40760i
$640$	1.79934e10	−	1.03885e10i	0.107249	−	0.0619202i
$641$	1.41683e11	+	2.45402e11i	0.839239	+	1.45360i	0.890532	+	0.454921i	$0.150333\pi$
$641$	1.41683e11	+	2.45402e11i	0.839239	+	1.45360i	−0.0512925	+	0.998684i	$0.516334\pi$
$642$	−2.80381e11	−	1.61878e11i	−1.65047	−	0.952900i
$643$			1.63523e11i			0.956608i	0.878194	+	0.478304i	$0.158748\pi$
$643$			1.63523e11i			0.956608i	−0.878194	+	0.478304i	$0.841252\pi$
$644$	5.46875e10	−	1.43335e11i	0.317940	−	0.833316i
$645$	−3.69681e11			−2.13593
$646$	−2.31066e10	+	4.00218e10i	−0.132680	+	0.229809i
$647$	−7.92369e10	+	4.57474e10i	−0.452179	+	0.261066i	−0.708750	−	0.705460i	$-0.750741\pi$
$647$	−7.92369e10	+	4.57474e10i	−0.452179	+	0.261066i	0.256571	+	0.966525i	$0.417407\pi$
$648$	−4.20052e10	−	7.27552e10i	−0.238234	−	0.412633i
$649$	9.75233e10	+	5.63051e10i	0.549705	+	0.317372i
$650$			1.30475e10i			0.0730927i
$651$	−1.25415e11	−	1.54233e11i	−0.698271	−	0.858721i
$652$	5.15185e9			0.0285084
$653$	−7.72477e10	+	1.33797e11i	−0.424847	+	0.735857i	−0.996406	−	0.0847040i	$-0.973006\pi$
$653$	−7.72477e10	+	1.33797e11i	−0.424847	+	0.735857i	0.571559	+	0.820561i	$0.306339\pi$
$654$	2.08665e11	−	1.20473e11i	1.14061	−	0.658533i
$655$	1.07978e11	+	1.87024e11i	0.586640	+	1.01609i
$656$	−2.01876e10	−	1.16553e10i	−0.109011	−	0.0629374i
$657$		−	1.79286e10i		−	0.0962242i
$658$	3.44041e10	+	2.14400e11i	0.183530	+	1.14372i
$659$	−6.38574e9			−0.0338586			−0.0169293	−	0.999857i	$-0.505389\pi$
$659$	−6.38574e9			−0.0338586			−0.0169293	+	0.999857i	$0.505389\pi$
$660$	−1.02733e11	+	1.77938e11i	−0.541418	+	0.937763i
$661$	1.84299e11	−	1.06405e11i	0.965423	−	0.557387i	0.0675854	−	0.997713i	$-0.478470\pi$
$661$	1.84299e11	−	1.06405e11i	0.965423	−	0.557387i	0.897838	+	0.440326i	$0.145137\pi$
$662$	−4.50563e10	−	7.80398e10i	−0.234598	−	0.406335i
$663$	−2.73409e10	−	1.57853e10i	−0.141501	−	0.0816954i
$664$			1.10901e10i			0.0570509i
$665$	−1.17649e11	+	1.88788e10i	−0.601593	+	0.0965358i
$666$	1.45795e11			0.741045
$667$	2.20461e10	−	3.81850e10i	0.111386	−	0.192926i
$668$	−2.87848e8	+	1.66189e8i	−0.00144563	+	0.000834636i
$669$	−1.49462e10	−	2.58876e10i	−0.0746150	−	0.129237i
$670$	1.21104e11	+	6.99193e10i	0.600978	+	0.346975i
$671$		−	1.86610e11i		−	0.920544i
$672$	−4.93389e10	+	4.01200e10i	−0.241943	+	0.196736i
$673$	−3.32635e11			−1.62147			−0.810734	−	0.585415i	$-0.800932\pi$
$673$	−3.32635e11			−1.62147			−0.810734	+	0.585415i	$0.800932\pi$
$674$	−7.38049e10	+	1.27834e11i	−0.357639	+	0.619450i
$675$	3.39547e11	−	1.96037e11i	1.63563	−	0.944331i
$676$	−5.16053e10	−	8.93830e10i	−0.247120	−	0.428024i
$677$	3.35630e11	+	1.93776e11i	1.59774	+	0.922456i	0.991922	+	0.126853i	$0.0404876\pi$
$677$	3.35630e11	+	1.93776e11i	1.59774	+	0.922456i	0.605819	+	0.795603i	$0.292846\pi$
$678$		−	3.24325e11i		−	1.53484i
$679$	6.53148e10	+	2.49199e10i	0.307279	+	0.117238i
$680$	−9.14015e10			−0.427482
$681$	9.00190e10	−	1.55918e11i	0.418549	−	0.724947i
$682$	−7.28354e10	+	4.20515e10i	−0.336670	+	0.194377i
$683$	−1.26032e11	−	2.18293e11i	−0.579157	−	1.00313i	−0.995576	−	0.0939571i	$-0.970048\pi$
$683$	−1.26032e11	−	2.18293e11i	−0.579157	−	1.00313i	0.416419	−	0.909173i	$-0.363285\pi$
$684$	−8.70398e10	−	5.02525e10i	−0.397643	−	0.229579i
$685$			3.67778e11i			1.67041i
$686$	7.24267e9	−	1.56429e11i	0.0327041	−	0.706350i
$687$	4.93954e11			2.21748
$688$	−2.42038e10	+	4.19222e10i	−0.108026	+	0.187107i
$689$	5.53522e9	−	3.19576e9i	0.0245617	−	0.0141807i
$690$	3.53321e11	+	6.11970e11i	1.55874	+	2.69981i
$691$	−2.42724e11	−	1.40137e11i	−1.06463	−	0.614666i	−0.137923	−	0.990443i	$-0.544043\pi$
$691$	−2.42724e11	−	1.40137e11i	−1.06463	−	0.614666i	−0.926710	+	0.375777i	$0.877376\pi$
$692$			2.86482e10i			0.124932i
$693$	1.52131e11	−	3.98735e11i	0.659608	−	1.72882i
$694$	2.96085e11			1.27638
$695$	2.80835e11	−	4.86421e11i	1.20368	−	2.08484i
$696$	−1.58282e10	+	9.13842e9i	−0.0674520	+	0.0389434i
$697$	5.12737e10	+	8.88086e10i	0.217252	+	0.376291i
$698$	−7.80242e10	−	4.50473e10i	−0.328706	−	0.189778i
$699$			2.62254e11i			1.09853i
$700$	−7.29420e10	−	8.97027e10i	−0.303798	−	0.373606i
$701$	−1.30623e11			−0.540939			−0.270469	−	0.962729i	$-0.587179\pi$
$701$	−1.30623e11			−0.540939			−0.270469	+	0.962729i	$0.587179\pi$
$702$	1.80731e10	−	3.13036e10i	0.0744192	−	0.128898i
$703$	4.56489e10	−	2.63554e10i	0.186900	−	0.107907i
$704$	1.34523e10	+	2.33000e10i	0.0547652	+	0.0948561i
$705$	−8.66188e11	−	5.00094e11i	−3.50635	−	2.02439i
$706$			3.25277e10i			0.130929i
$707$	1.38183e10	+	8.61132e10i	0.0553067	+	0.344661i
$708$	−1.60538e11			−0.638918
$709$	−1.43526e11	+	2.48595e11i	−0.567997	+	0.983800i	0.428767	+	0.903415i	$0.358948\pi$
$709$	−1.43526e11	+	2.48595e11i	−0.567997	+	0.983800i	−0.996764	+	0.0803847i	$0.974385\pi$
$710$	−2.87034e11	+	1.65719e11i	−1.12953	+	0.652137i
$711$	−2.34784e11	−	4.06657e11i	−0.918734	−	1.59129i
$712$	1.27791e11	+	7.37800e10i	0.497255	+	0.287090i
$713$			2.89250e11i			1.11922i
$714$	2.76218e11	−	4.43239e10i	1.06282	−	0.170548i
$715$	−3.44388e10			−0.131772
$716$	−8.82916e10	+	1.52926e11i	−0.335944	+	0.581873i
$717$	2.84689e11	−	1.64365e11i	1.07720	−	0.621919i
$718$	−1.40585e11	−	2.43500e11i	−0.528982	−	0.916224i
$719$	3.30933e10	+	1.91064e10i	0.123830	+	0.0714931i	0.560635	−	0.828063i	$-0.310557\pi$
$719$	3.30933e10	+	1.91064e10i	0.123830	+	0.0714931i	−0.436806	+	0.899556i	$0.643890\pi$
$720$		−	1.98781e11i		−	0.739681i
$721$	−3.04917e11	+	2.47944e11i	−1.12834	+	0.917513i
$722$	1.55810e11			0.573387
$723$	−1.04404e11	+	1.80832e11i	−0.382087	+	0.661794i
$724$	1.94952e11	−	1.12555e11i	0.709533	−	0.409649i
$725$	−1.66145e10	−	2.87772e10i	−0.0601361	−	0.104159i
$726$	6.96822e10	+	4.02310e10i	0.250828	+	0.144815i
$727$			1.60138e11i			0.573268i	0.958040	+	0.286634i	$0.0925364\pi$
$727$			1.60138e11i			0.573268i	−0.958040	+	0.286634i	$0.907464\pi$
$728$	−9.95869e9	−	3.79959e9i	−0.0354549	−	0.0135273i
$729$	1.73272e11			0.613504
$730$	6.41005e9	−	1.11025e10i	0.0225720	−	0.0390958i
$731$	1.84423e11	−	1.06477e11i	0.645871	−	0.372894i
$732$	1.33016e11	+	2.30391e11i	0.463298	+	0.802456i
$733$	−2.36694e11	−	1.36655e11i	−0.819920	−	0.473381i	0.0304686	−	0.999536i	$-0.490300\pi$
$733$	−2.36694e11	−	1.36655e11i	−0.819920	−	0.473381i	−0.850389	+	0.526154i	$0.823633\pi$
$734$			2.93697e9i			0.0101185i
$735$	5.37988e11	+	4.80464e11i	1.84342	+	1.64631i
$736$	9.25308e10			0.315337
$737$	−9.05399e10	+	1.56820e11i	−0.306881	+	0.531534i
$738$	−1.93142e11	+	1.11511e11i	−0.651105	+	0.375916i
$739$	−2.04395e11	−	3.54022e11i	−0.685317	−	1.18700i	−0.973337	−	0.229380i	$-0.926330\pi$
$739$	−2.04395e11	−	3.54022e11i	−0.685317	−	1.18700i	0.288020	−	0.957624i	$-0.407003\pi$
$740$	9.02854e10	+	5.21263e10i	0.301086	+	0.173832i
$741$		−	2.48234e10i		−	0.0823358i
$742$	−2.01892e10	+	5.29157e10i	−0.0666046	+	0.174570i
$743$	−3.69962e10			−0.121395			−0.0606977	−	0.998156i	$-0.519333\pi$
$743$	−3.69962e10			−0.121395			−0.0606977	+	0.998156i	$0.519333\pi$
$744$	5.99490e10	−	1.03835e11i	0.195655	−	0.338884i
$745$	1.75915e11	−	1.01565e11i	0.571056	−	0.329699i
$746$	−1.94768e11	−	3.37348e11i	−0.628872	−	1.08924i
$747$	9.18878e10	+	5.30514e10i	0.295104	+	0.170378i
$748$		−	1.18358e11i		−	0.378085i
$749$	3.03374e11	+	3.73083e11i	0.963941	+	1.18544i
$750$	−2.04227e10			−0.0645457
$751$	1.71650e11	−	2.97307e11i	0.539616	−	0.934642i	−0.459309	−	0.888277i	$-0.651903\pi$
$751$	1.71650e11	−	2.97307e11i	0.539616	−	0.934642i	0.998925	−	0.0463654i	$-0.0147639\pi$
$752$	−1.13422e11	+	6.54845e10i	−0.354673	+	0.204770i
$753$	1.09564e11	+	1.89770e11i	0.340790	+	0.590266i
$754$	−2.65303e9	−	1.53173e9i	−0.00820837	−	0.00473910i
$755$		−	4.96032e11i		−	1.52659i
$756$	5.07481e10	+	3.16253e11i	0.155358	+	0.968159i
$757$	3.19344e11			0.972468			0.486234	−	0.873829i	$-0.338370\pi$
$757$	3.19344e11			0.972468			0.486234	+	0.873829i	$0.338370\pi$
$758$	−1.73207e11	+	3.00003e11i	−0.524672	+	0.908759i
$759$	−7.92452e11	+	4.57522e11i	−2.38784	+	1.37862i
$760$	−3.59338e10	−	6.22391e10i	−0.107708	−	0.186556i
$761$	3.31461e11	+	1.91369e11i	0.988312	+	0.570602i	0.904769	−	0.425902i	$-0.140043\pi$
$761$	3.31461e11	+	1.91369e11i	0.988312	+	0.570602i	0.0835424	+	0.996504i	$0.473377\pi$
$762$			1.36835e10i			0.0405860i
$763$	−3.53346e11	+	5.67003e10i	−1.04256	+	0.167297i
$764$	−2.64151e11			−0.775316
$765$	−4.37235e11	+	7.57314e11i	−1.27664	+	2.21121i
$766$	−1.95973e11	+	1.13145e11i	−0.569220	+	0.328639i
$767$	−1.34542e10	−	2.33034e10i	−0.0388756	−	0.0673345i
$768$	−3.32167e10	−	1.91777e10i	−0.0954797	−	0.0551252i
$769$		−	6.74904e11i		−	1.92991i	−0.262417	−	0.964955i	$-0.584520\pi$
$769$		−	6.74904e11i		−	1.92991i	0.262417	−	0.964955i	$-0.415480\pi$
$770$	2.36770e11	−	1.92530e11i	0.673541	−	0.547691i
$771$	−4.13635e11			−1.17058
$772$	6.56764e10	−	1.13755e11i	0.184902	−	0.320259i
$773$	1.92323e10	−	1.11038e10i	0.0538658	−	0.0310994i	−0.472825	−	0.881156i	$-0.656766\pi$
$773$	1.92323e10	−	1.11038e10i	0.0538658	−	0.0310994i	0.526691	+	0.850057i	$0.323432\pi$
$774$	2.31567e11	+	4.01085e11i	0.645226	+	1.11756i
$775$	1.88781e11	+	1.08993e11i	0.523301	+	0.302128i
$776$			4.21643e10i			0.116278i
$777$	−2.98124e11	−	1.13745e11i	−0.817922	−	0.312067i
$778$	−1.37240e11			−0.374595
$779$	−4.03157e10	+	6.98288e10i	−0.109477	+	0.189620i
$780$	4.25186e10	−	2.45482e10i	0.114869	−	0.0663194i
$781$	−2.14593e11	−	3.71685e11i	−0.576781	−	0.999013i
$782$	−3.52523e11	−	2.03529e11i	−0.942672	−	0.544252i
$783$			9.20563e10i			0.244910i
$784$	8.97085e10	−	2.95514e10i	0.237448	−	0.0782194i
$785$	7.06052e11			1.85934
$786$	1.99333e11	−	3.45255e11i	0.522264	−	0.904587i
$787$	9.20770e10	−	5.31607e10i	0.240023	−	0.138577i	−0.375165	−	0.926958i	$-0.622414\pi$
$787$	9.20770e10	−	5.31607e10i	0.240023	−	0.138577i	0.615187	+	0.788381i	$0.289080\pi$
$788$	7.86118e10	+	1.36160e11i	0.203884	+	0.353137i
$789$	6.73089e10	+	3.88608e10i	0.173686	+	0.100278i
$790$		−	3.35771e11i		−	0.862055i
$791$	−1.71714e11	+	4.50061e11i	−0.438632	+	1.14965i
$792$	2.57405e11			0.654209
$793$	−2.22954e10	+	3.86168e10i	−0.0563797	+	0.0976524i
$794$	6.77291e10	−	3.91034e10i	0.170409	−	0.0983858i
$795$	−1.30437e11	−	2.25924e11i	−0.326537	−	0.565579i
$796$	−2.75079e11	−	1.58817e11i	−0.685180	−	0.395589i
$797$		−	4.77766e10i		−	0.118408i	−0.998246	−	0.0592041i	$-0.981144\pi$
$797$		−	4.77766e10i		−	0.118408i	0.998246	−	0.0592041i	$-0.0188563\pi$
$798$	1.38775e11	+	1.70663e11i	0.342216	+	0.420851i
$799$	5.76155e11			1.41368
$800$	3.48668e10	−	6.03910e10i	0.0851239	−	0.147439i
$801$	1.22262e12	−	7.05880e11i	2.97004	−	1.71475i
$802$	−1.43035e11	−	2.47743e11i	−0.345735	−	0.598831i
$803$	1.43769e10	+	8.30050e9i	0.0345782	+	0.0199637i
$804$		−	2.58149e11i		−	0.617797i
$805$	−1.66290e11	−	1.03629e12i	−0.395989	−	2.46773i
$806$	2.00966e10			0.0476192
$807$	−5.41131e10	+	9.37266e10i	−0.127587	+	0.220988i
$808$	−4.55558e10	+	2.63017e10i	−0.106880	+	0.0617075i
$809$	4.04920e11	+	7.01341e11i	0.945311	+	1.63733i	0.755128	+	0.655578i	$0.227575\pi$
$809$	4.04920e11	+	7.01341e11i	0.945311	+	1.63733i	0.190183	+	0.981749i	$0.439092\pi$
$810$	−4.97739e11	−	2.87370e11i	−1.15628	−	0.667577i
$811$			3.75704e11i			0.868484i	0.900796	+	0.434242i	$0.142984\pi$
$811$			3.75704e11i			0.868484i	−0.900796	+	0.434242i	$0.857016\pi$
$812$	2.68029e10	−	4.30099e9i	0.0616536	−	0.00989336i
$813$	−4.38419e11			−1.00352
$814$	−6.74993e10	+	1.16912e11i	−0.153745	+	0.266295i
$815$	3.05233e10	−	1.76226e10i	0.0691833	−	0.0399430i
$816$	8.43657e10	+	1.46126e11i	0.190285	+	0.329584i
$817$	1.45009e11	+	8.37209e10i	0.325467	+	0.187908i
$818$			8.87106e10i			0.198136i
$819$	−7.91210e10	+	6.43374e10i	−0.175856	+	0.142997i
$820$	−1.59475e11			−0.352725
$821$	−1.38321e11	+	2.39579e11i	−0.304450	+	0.527323i	−0.977139	−	0.212603i	$-0.931806\pi$
$821$	−1.38321e11	+	2.39579e11i	−0.304450	+	0.527323i	0.672689	+	0.739926i	$0.265139\pi$
$822$	5.87975e11	−	3.39468e11i	1.28787	−	0.743552i
$823$	1.99482e11	+	3.45513e11i	0.434814	+	0.753121i	0.997280	−	0.0736996i	$-0.0234806\pi$
$823$	1.99482e11	+	3.45513e11i	0.434814	+	0.753121i	−0.562466	+	0.826820i	$0.690147\pi$
$824$	−2.05281e11	−	1.18519e11i	−0.445286	−	0.257086i
$825$			6.89600e11i			1.48861i
$826$	2.22776e11	+	8.49971e10i	0.478574	+	0.182593i
$827$	−4.78161e11			−1.02224			−0.511119	−	0.859510i	$-0.670769\pi$
$827$	−4.78161e11			−1.02224			−0.511119	+	0.859510i	$0.670769\pi$
$828$	4.42638e11	−	7.66672e11i	0.941732	−	1.63113i
$829$	−4.13580e11	+	2.38780e11i	−0.875671	+	0.505569i	−0.869229	−	0.494410i	$-0.835384\pi$
$829$	−4.13580e11	+	2.38780e11i	−0.875671	+	0.505569i	−0.00644231	+	0.999979i	$0.502051\pi$
$830$	3.79352e10	+	6.57057e10i	0.0799337	+	0.138449i
$831$	7.10408e11	+	4.10154e11i	1.48972	+	0.860088i
$832$		−	6.42888e9i		−	0.0134166i
$833$	−4.06772e11	−	8.47365e10i	−0.844832	−	0.175991i
$834$	−1.03687e12			−2.14319
$835$	−1.13695e9	+	1.96925e9i	−0.00233881	+	0.00405094i
$836$	8.05946e10	−	4.65313e10i	0.164999	−	0.0952622i
$837$	−3.01949e11	−	5.22992e11i	−0.615223	−	1.06560i
$838$	4.30445e11	+	2.48517e11i	0.872853	+	0.503942i
$839$		−	4.93131e11i		−	0.995209i	−0.867404	−	0.497604i	$-0.834213\pi$
$839$		−	4.93131e11i		−	0.995209i	0.867404	−	0.497604i	$-0.165787\pi$
$840$	−1.55083e11	+	4.06471e11i	−0.311492	+	0.816418i
$841$	−4.92444e11			−0.984404
$842$	−3.23682e10	+	5.60634e10i	−0.0643977	+	0.111540i
$843$	2.44766e11	−	1.41316e11i	0.484664	−	0.279821i
$844$	2.17427e11	+	3.76594e11i	0.428492	+	0.742170i
$845$	−6.11495e11	−	3.53047e11i	−1.19941	−	0.692477i
$846$			1.25303e12i			2.44613i
$847$	−7.53965e10	−	9.27213e10i	−0.146493	−	0.180155i
$848$	−3.41600e10			−0.0660594
$849$	4.55564e11	−	7.89059e11i	0.876836	−	1.51872i
$850$	−2.65670e11	+	1.53385e11i	−0.508941	+	0.293837i
$851$	2.32146e11	+	4.02088e11i	0.442632	+	0.766661i
$852$	5.29878e11	+	3.05925e11i	1.00558	+	0.580573i
$853$		−	6.24713e11i		−	1.18001i	−0.807401	−	0.590004i	$-0.799126\pi$
$853$		−	6.24713e11i		−	1.18001i	0.807401	−	0.590004i	$-0.200874\pi$
$854$	−6.26039e10	−	3.90136e11i	−0.117698	−	0.733474i
$855$	−6.87583e11			−1.28665
$856$	−1.45015e11	+	2.51173e11i	−0.270095	+	0.467819i
$857$	−7.96567e10	+	4.59898e10i	−0.147672	+	0.0852587i	−0.572016	−	0.820243i	$-0.693838\pi$
$857$	−7.96567e10	+	4.59898e10i	−0.147672	+	0.0852587i	0.424343	+	0.905501i	$0.360505\pi$
$858$	3.17879e10	+	5.50582e10i	0.0586560	+	0.101595i
$859$	−3.04542e11	−	1.75827e11i	−0.559338	−	0.322934i	0.193541	−	0.981092i	$-0.438003\pi$
$859$	−3.04542e11	−	1.75827e11i	−0.559338	−	0.322934i	−0.752880	+	0.658158i	$0.771336\pi$
$860$			3.31170e11i			0.605421i
$861$	4.81938e11	−	7.73351e10i	0.876957	−	0.140723i
$862$	1.54507e11			0.279847
$863$	−1.79901e11	+	3.11598e11i	−0.324333	+	0.561762i	−0.981377	−	0.192091i	$-0.938473\pi$
$863$	−1.79901e11	+	3.11598e11i	−0.324333	+	0.561762i	0.657044	+	0.753852i	$0.271807\pi$
$864$	−1.67305e11	+	9.65934e10i	−0.300229	+	0.173338i
$865$	9.79953e10	+	1.69733e11i	0.175041	+	0.303181i
$866$	4.95336e11	+	2.85983e11i	0.880701	+	0.508473i
$867$			2.54450e11i			0.450326i
$868$	−1.38166e11	+	1.12350e11i	−0.243401	+	0.197922i
$869$	4.34797e11			0.762442
$870$	−6.25186e10	+	1.08285e11i	−0.109127	+	0.189013i
$871$	3.74724e10	−	2.16347e10i	0.0651086	−	0.0375905i
$872$	−1.07923e11	−	1.86928e11i	−0.186658	−	0.323302i
$873$	3.49356e11	+	2.01701e11i	0.601466	+	0.347257i
$874$		−	3.20064e11i		−	0.548518i
$875$	2.83402e10	+	1.08128e10i	0.0483472	+	0.0184462i
$876$	−2.36665e10			−0.0401900
$877$	−5.31314e11	+	9.20263e11i	−0.898158	+	1.55566i	−0.0683115	+	0.997664i	$0.521761\pi$
$877$	−5.31314e11	+	9.20263e11i	−0.898158	+	1.55566i	−0.829847	+	0.557991i	$0.811572\pi$
$878$	−4.31086e11	+	2.48888e11i	−0.725414	+	0.418818i
$879$	−5.27738e11	−	9.14068e11i	−0.884021	−	1.53117i
$880$	1.59402e11	+	9.20307e10i	0.265805	+	0.153462i
$881$		−	3.25470e11i		−	0.540266i	−0.962823	−	0.270133i	$-0.912932\pi$
$881$		−	3.25470e11i		−	0.540266i	0.962823	−	0.270133i	$-0.0870677\pi$
$882$	1.84286e11	−	8.84651e11i	0.304521	−	1.46183i
$883$	4.60107e11			0.756861			0.378431	−	0.925630i	$-0.376464\pi$
$883$	4.60107e11			0.756861			0.378431	+	0.925630i	$0.376464\pi$
$884$	−1.41409e10	+	2.44927e10i	−0.0231562	+	0.0401077i
$885$	−9.51144e11	+	5.49143e11i	−1.55051	+	0.895185i
$886$	−2.81157e10	−	4.86979e10i	−0.0456262	−	0.0790269i
$887$	−4.83578e11	−	2.79194e11i	−0.781217	−	0.451036i	0.0556445	−	0.998451i	$-0.482279\pi$
$887$	−4.83578e11	−	2.79194e11i	−0.781217	−	0.451036i	−0.836861	+	0.547415i	$0.815612\pi$
$888$		−	1.92455e11i		−	0.309512i
$889$	7.24474e9	−	1.89884e10i	0.0115989	−	0.0304005i
$890$	1.00950e12			1.60896
$891$	3.72121e11	−	6.44532e11i	0.590436	−	1.02267i
$892$	−2.31908e10	+	1.33892e10i	−0.0366316	+	0.0211493i
$893$	2.26511e11	+	3.92328e11i	0.356191	+	0.616941i
$894$	−3.24748e11	−	1.87493e11i	−0.508389	−	0.293519i
$895$			1.20806e12i			1.88276i
$896$	3.59406e10	+	4.41991e10i	0.0557640	+	0.0685775i
$897$	2.18652e11			0.337740
$898$	6.74293e10	−	1.16791e11i	0.103691	−	0.179599i
$899$	−4.43244e10	+	2.55907e10i	−0.0678585	+	0.0391781i
$900$	−3.33583e11	−	5.77782e11i	−0.508433	−	0.880632i
$901$	1.30143e11	+	7.51379e10i	0.197479	+	0.114014i
$902$		−	2.06507e11i		−	0.311967i
$903$	−1.60597e11	−	1.00081e12i	−0.241538	−	1.50522i
$904$	−2.90539e11			−0.435042
$905$	7.70023e11	−	1.33372e12i	1.14791	−	1.98825i
$906$	−7.93019e11	+	4.57850e11i	−1.17698	+	0.679532i
$907$	2.39788e11	+	4.15326e11i	0.354323	+	0.613705i	0.987002	−	0.160709i	$-0.0513781\pi$
$907$	2.39788e11	+	4.15326e11i	0.354323	+	0.613705i	−0.632679	+	0.774414i	$0.718045\pi$
$908$	−1.39675e11	−	8.06415e10i	−0.205483	−	0.118636i
$909$			5.03275e11i			0.737140i
$910$	−7.19995e10	+	1.15535e10i	−0.104994	+	0.0168481i
$911$	5.85058e11			0.849426			0.424713	−	0.905328i	$-0.360375\pi$
$911$	5.85058e11			0.849426			0.424713	+	0.905328i	$0.360375\pi$
$912$	−6.63355e10	+	1.14896e11i	−0.0958885	+	0.166084i
$913$	−8.50836e10	+	4.91230e10i	−0.122451	+	0.0706972i
$914$	2.77263e11	+	4.80233e11i	0.397289	+	0.688125i
$915$	1.57617e12	+	9.10003e11i	2.24863	+	1.29825i
$916$		−	4.42497e11i		−	0.628534i
$917$	−4.59408e11	+	3.73569e11i	−0.649712	+	0.528315i
$918$	8.49862e11			1.19668
$919$	6.64889e11	−	1.15162e12i	0.932152	−	1.61454i	0.152517	−	0.988301i	$-0.451262\pi$
$919$	6.64889e11	−	1.15162e12i	0.932152	−	1.61454i	0.779635	−	0.626234i	$-0.215405\pi$
$920$	5.48220e11	−	3.16515e11i	0.765250	−	0.441817i
$921$	−1.56524e11	−	2.71108e11i	−0.217542	−	0.376793i
$922$	5.47775e11	+	3.16258e11i	0.758016	+	0.437641i
$923$			1.02555e11i			0.141302i
$924$	−5.26347e11	−	2.00820e11i	−0.722078	−	0.275499i
$925$	3.49901e11			0.477946
$926$	−5.70962e10	+	9.88936e10i	−0.0776539	+	0.134501i
$927$	−1.96399e12	+	1.13391e12i	−2.65963	+	1.53554i
$928$	8.18645e9	+	1.41794e10i	0.0110383	+	0.0191190i
$929$	−6.13628e11	−	3.54278e11i	−0.823839	−	0.475644i	0.0278995	−	0.999611i	$-0.491118\pi$
$929$	−6.13628e11	−	3.54278e11i	−0.823839	−	0.475644i	−0.851739	+	0.523967i	$0.824451\pi$
$930$		−	8.20257e11i		−	1.09652i
$931$	−1.02218e11	−	3.10301e11i	−0.136060	−	0.413033i
$932$	2.34934e11			0.311375
$933$	5.94243e11	−	1.02926e12i	0.784220	−	1.35831i
$934$	8.52700e11	−	4.92306e11i	1.12049	−	0.646916i
$935$	−4.04859e11	−	7.01236e11i	−0.529733	−	0.917524i
$936$	−5.32670e10	−	3.07537e10i	−0.0693993	−	0.0400677i
$937$		−	2.84697e11i		−	0.369338i	−0.982801	−	0.184669i	$-0.940879\pi$
$937$		−	2.84697e11i		−	0.369338i	0.982801	−	0.184669i	$-0.0591213\pi$
$938$	−1.36677e11	+	3.58229e11i	−0.176557	+	0.462754i
$939$	1.21467e11			0.156241
$940$	−4.47998e11	+	7.75955e11i	−0.573805	+	0.993860i
$941$	9.65681e11	−	5.57536e11i	1.23162	−	0.711073i	0.264249	−	0.964455i	$-0.414876\pi$
$941$	9.65681e11	−	5.57536e11i	1.23162	−	0.711073i	0.967366	+	0.253381i	$0.0815427\pi$
$942$	−6.51703e11	−	1.12878e12i	−0.827648	−	1.43353i
$943$	−6.15072e11	−	3.55112e11i	−0.777820	−	0.449075i
$944$			1.43814e11i			0.181098i
$945$	1.38246e12	+	1.70012e12i	1.73350	+	2.13183i
$946$	−4.28839e11			−0.535463
$947$	−2.79065e11	+	4.83354e11i	−0.346981	+	0.600988i	−0.985712	−	0.168442i	$-0.946126\pi$
$947$	−2.79065e11	+	4.83354e11i	−0.346981	+	0.600988i	0.638731	+	0.769430i	$0.279460\pi$
$948$	−5.36806e11	+	3.09925e11i	−0.664636	+	0.383728i
$949$	−1.98342e9	−	3.43538e9i	−0.00244540	−	0.00423555i
$950$	−2.08892e11	−	1.20604e11i	−0.256465	−	0.148070i
$951$			6.12618e10i			0.0748976i
$952$	−3.97066e10	−	2.47444e11i	−0.0483409	−	0.301252i
$953$	−8.07374e11			−0.978821			−0.489410	−	0.872054i	$-0.662788\pi$
$953$	−8.07374e11			−0.978821			−0.489410	+	0.872054i	$0.662788\pi$
$954$	−1.63411e11	+	2.83036e11i	−0.197282	+	0.341702i
$955$	−1.56502e12	+	9.03566e11i	−1.88151	+	1.08629i
$956$	−1.47243e11	−	2.55032e11i	−0.176280	−	0.305326i
$957$	−1.40221e11	−	8.09565e10i	−0.167172	−	0.0965170i
$958$			6.78616e11i			0.805680i
$959$	−9.95656e11	+	1.59770e11i	−1.17716	+	0.188895i
$960$	−2.62400e11			−0.308943
$961$	−2.58568e11	+	4.47852e11i	−0.303166	+	0.525099i
$962$	2.79364e10	−	1.61291e10i	0.0326190	−	0.0188326i
$963$	1.38741e12	+	2.40306e12i	1.61324	+	2.79421i
$964$	1.61995e11	+	9.35276e10i	0.187582	+	0.108301i
$965$		−	8.98622e11i		−	1.03626i
$966$	−1.50325e12	+	1.22237e12i	−1.72633	+	1.40377i
$967$	−1.26699e10			−0.0144899			−0.00724495	−	0.999974i	$-0.502306\pi$
$967$	−1.26699e10			−0.0144899			−0.00724495	+	0.999974i	$0.502306\pi$
$968$	3.60401e10	−	6.24232e10i	0.0410472	−	0.0710959i
$969$	5.05449e11	−	2.91821e11i	0.573300	−	0.330995i
$970$	1.44229e11	+	2.49812e11i	0.162917	+	0.282180i
$971$	3.00011e11	+	1.73212e11i	0.337490	+	0.194850i	0.659161	−	0.752001i	$-0.270911\pi$
$971$	3.00011e11	+	1.73212e11i	0.337490	+	0.194850i	−0.321672	+	0.946851i	$0.604245\pi$
$972$			1.85746e11i			0.208091i
$973$	1.43885e12	+	5.48973e11i	1.60533	+	0.612490i
$974$	6.58255e11			0.731405
$975$	8.23906e10	−	1.42705e11i	0.0911715	−	0.157914i
$976$	2.06391e11	−	1.19160e11i	0.227453	−	0.131320i
$977$	−3.56249e11	−	6.17041e11i	−0.390999	−	0.677230i	0.601583	−	0.798810i	$-0.294537\pi$
$977$	−3.56249e11	−	6.17041e11i	−0.390999	−	0.677230i	−0.992582	+	0.121581i	$0.961204\pi$
$978$	−5.63475e10	−	3.25322e10i	−0.0615913	−	0.0355597i
$979$			1.30722e12i			1.42304i
$980$	4.30413e11	−	4.81945e11i	0.466639	−	0.522508i
$981$	−2.06507e12			−2.22977
$982$	4.13885e11	−	7.16870e11i	0.445076	−	0.770893i
$983$	1.36181e12	−	7.86241e11i	1.45849	−	0.842058i	0.459549	−	0.888152i	$-0.348011\pi$
$983$	1.36181e12	−	7.86241e11i	1.45849	−	0.842058i	0.998937	+	0.0460947i	$0.0146776\pi$
$984$	1.47199e11	+	2.54956e11i	0.157009	+	0.271947i
$985$	9.31507e11	+	5.37806e11i	0.989558	+	0.571321i
$986$		−	7.20272e10i		−	0.0762059i
$987$	9.77576e11	−	2.56221e12i	1.03011	−	2.69989i
$988$	−2.22375e10			−0.0233377
$989$	−7.37438e11	+	1.27728e12i	−0.770797	+	1.33506i
$990$	1.52506e12	−	8.80491e11i	1.58761	−	0.916609i
$991$	1.68912e11	+	2.92564e11i	0.175132	+	0.303338i	0.940207	−	0.340604i	$-0.110631\pi$
$991$	1.68912e11	+	2.92564e11i	0.175132	+	0.303338i	−0.765075	+	0.643941i	$0.777298\pi$
$992$	−9.30180e10	−	5.37040e10i	−0.0960551	−	0.0554574i
$993$			1.13806e12i			1.17049i
$994$	−5.73331e11	−	7.05072e11i	−0.587300	−	0.722251i
$995$	−2.17302e12			−2.21703
$996$	7.00302e10	−	1.21296e11i	0.0711620	−	0.123256i
$997$	−2.01610e10	+	1.16400e10i	−0.0204048	+	0.0117807i	−0.510168	−	0.860075i	$-0.670417\pi$
$997$	−2.01610e10	+	1.16400e10i	−0.0204048	+	0.0117807i	0.489763	+	0.871856i	$0.337083\pi$
$998$	−3.54326e11	−	6.13710e11i	−0.357175	−	0.618644i
$999$	−8.39484e11	−	4.84676e11i	−0.842850	−	0.486620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.9.d.a.5.3	yes	12
3.2	odd	2		126.9.n.b.19.6		12
4.3	odd	2		112.9.s.c.33.2		12
7.2	even	3		98.9.b.c.97.12		12
7.3	odd	6	inner	14.9.d.a.3.3	✓	12
7.4	even	3		98.9.d.b.31.1		12
7.5	odd	6		98.9.b.c.97.7		12
7.6	odd	2		98.9.d.b.19.1		12
21.17	even	6		126.9.n.b.73.6		12
28.3	even	6		112.9.s.c.17.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.9.d.a.3.3	✓	12	7.3	odd	6	inner
14.9.d.a.5.3	yes	12	1.1	even	1	trivial
98.9.b.c.97.7		12	7.5	odd	6
98.9.b.c.97.12		12	7.2	even	3
98.9.d.b.19.1		12	7.6	odd	2
98.9.d.b.31.1		12	7.4	even	3
112.9.s.c.17.2		12	28.3	even	6
112.9.s.c.33.2		12	4.3	odd	2
126.9.n.b.19.6		12	3.2	odd	2
126.9.n.b.73.6		12	21.17	even	6

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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 + 9.79796i) q^{2} +(123.742 - 71.4423i) q^{3} +(-64.0000 - 110.851i) q^{4} +(-758.365 - 437.842i) q^{5} +1616.56i q^{6} +(855.887 - 2243.27i) q^{7} +1448.15 q^{8} +(6927.51 - 11998.8i) q^{9} +O(q^{10})\)	\(q+(-5.65685 + 9.79796i) q^{2} +(123.742 - 71.4423i) q^{3} +(-64.0000 - 110.851i) q^{4} +(-758.365 - 437.842i) q^{5} +1616.56i q^{6} +(855.887 - 2243.27i) q^{7} +1448.15 q^{8} +(6927.51 - 11998.8i) q^{9} +(8579.92 - 4953.62i) q^{10} +(6414.54 + 11110.3i) q^{11} +(-15838.9 - 9144.62i) q^{12} -3065.53i q^{13} +(17137.8 + 21075.8i) q^{14} -125122. q^{15} +(-8192.00 + 14189.0i) q^{16} +(62419.6 - 36038.0i) q^{17} +(78375.8 + 135751. i) q^{18} +(49079.6 + 28336.1i) q^{19} +112088. i q^{20} +(-54355.4 - 338733. i) q^{21} -145144. q^{22} +(-249593. + 432307. i) q^{23} +(179197. - 103460. i) q^{24} +(188099. + 325797. i) q^{25} +(30035.9 + 17341.3i) q^{26} -1.04220e6i q^{27} +(-303446. + 48693.1i) q^{28} -88328.5 q^{29} +(707796. - 1.22594e6i) q^{30} +(501813. - 289722. i) q^{31} +(-92681.9 - 160530. i) q^{32} +(1.58749e6 + 916539. i) q^{33} +815447. i q^{34} +(-1.63127e6 + 1.32647e6i) q^{35} -1.77344e6 q^{36} +(465050. - 805489. i) q^{37} +(-555272. + 320587. i) q^{38} +(-219009. - 379334. i) q^{39} +(-1.09823e6 - 634063. i) q^{40} +1.42277e6i q^{41} +(3.62637e6 + 1.38359e6i) q^{42} +2.95457e6 q^{43} +(821061. - 1.42212e6i) q^{44} +(-1.05072e7 + 6.06631e6i) q^{45} +(-2.82382e6 - 4.89099e6i) q^{46} +(6.92276e6 + 3.99685e6i) q^{47} +2.34102e6i q^{48} +(-4.29971e6 - 3.83997e6i) q^{49} -4.25620e6 q^{50} +(5.14928e6 - 8.91881e6i) q^{51} +(-339818. + 196194. i) q^{52} +(1.04248e6 + 1.80563e6i) q^{53} +(1.02115e7 + 5.89559e6i) q^{54} -1.12342e7i q^{55} +(1.23946e6 - 3.24860e6i) q^{56} +8.09759e6 q^{57} +(499661. - 865439. i) q^{58} +(7.60174e6 - 4.38887e6i) q^{59} +(8.00780e6 + 1.38699e7i) q^{60} +(-1.25971e7 - 7.27293e6i) q^{61} +6.55566e6i q^{62} +(-2.09874e7 - 2.58099e7i) q^{63} +2.09715e6 q^{64} +(-1.34222e6 + 2.32479e6i) q^{65} +(-1.79604e7 + 1.03695e7i) q^{66} +(7.05740e6 + 1.22238e7i) q^{67} +(-7.98971e6 - 4.61286e6i) q^{68} +7.13259e7i q^{69} +(-3.76886e6 - 2.34868e7i) q^{70} -3.34541e7 q^{71} +(1.00321e7 - 1.73761e7i) q^{72} +(1.12065e6 - 647007. i) q^{73} +(5.26143e6 + 9.11307e6i) q^{74} +(4.65514e7 + 2.68765e7i) q^{75} -7.25405e6i q^{76} +(3.04135e7 - 4.88037e6i) q^{77} +4.95560e6 q^{78} +(1.69458e7 - 2.93509e7i) q^{79} +(1.24251e7 - 7.17361e6i) q^{80} +(-2.90061e7 - 5.02400e7i) q^{81} +(-1.39402e7 - 8.04839e6i) q^{82} +7.65808e6i q^{83} +(-3.40702e7 + 2.77043e7i) q^{84} -6.31158e7 q^{85} +(-1.67136e7 + 2.89487e7i) q^{86} +(-1.09299e7 + 6.31039e6i) q^{87} +(9.28924e6 + 1.60894e7i) q^{88} +(8.82439e7 + 5.09476e7i) q^{89} -1.37265e8i q^{90} +(-6.87681e6 - 2.62375e6i) q^{91} +6.38957e7 q^{92} +(4.13968e7 - 7.17014e7i) q^{93} +(-7.83220e7 + 4.52192e7i) q^{94} +(-2.48135e7 - 4.29782e7i) q^{95} +(-2.29372e7 - 1.32428e7i) q^{96} +2.91159e7i q^{97} +(6.19467e7 - 2.04063e7i) q^{98} +1.77747e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9}+O(q^{10}) \) 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9	\( 12 q + 162 q^{3} - 768 q^{4} + 1674 q^{5} - 1308 q^{7} + 23604 q^{9} + 17664 q^{10} + 10302 q^{11} - 20736 q^{12} + 56832 q^{14} - 255468 q^{15} - 98304 q^{16} + 173178 q^{17} + 16896 q^{18} + 405978 q^{19} - 656910 q^{21} - 941568 q^{22} + 158934 q^{23} + 98304 q^{24} + 838668 q^{25} + 1958400 q^{26} - 255744 q^{28} - 4355256 q^{29} + 916992 q^{30} + 4520250 q^{31} + 4954482 q^{33} - 5270790 q^{35} - 6042624 q^{36} + 134214 q^{37} + 1278720 q^{38} + 1335384 q^{39} - 2260992 q^{40} + 6660096 q^{42} - 12961896 q^{43} + 1318656 q^{44} - 8415396 q^{45} + 2345472 q^{46} + 18385002 q^{47} - 3659172 q^{49} + 2970624 q^{50} - 2673894 q^{51} - 3369984 q^{52} - 16540506 q^{53} - 19646208 q^{54} + 4325376 q^{56} + 100263780 q^{57} + 9176064 q^{58} + 31163922 q^{59} + 16349952 q^{60} - 85390158 q^{61} + 4361988 q^{63} + 25165824 q^{64} - 46506264 q^{65} - 111873024 q^{66} - 37750362 q^{67} - 22166784 q^{68} + 92031744 q^{70} + 45506424 q^{71} + 2162688 q^{72} + 9414786 q^{73} + 58837248 q^{74} + 9837540 q^{75} - 100614066 q^{77} - 25463808 q^{78} + 59730294 q^{79} - 27426816 q^{80} - 89677422 q^{81} - 93259776 q^{82} + 122616576 q^{84} - 64652220 q^{85} - 15144960 q^{86} + 334229724 q^{87} + 60260352 q^{88} + 323014482 q^{89} - 266861424 q^{91} - 40687104 q^{92} - 11119662 q^{93} - 443440128 q^{94} - 175918350 q^{95} - 12582912 q^{96} + 472166400 q^{98} - 346906296 q^{99}+O(q^{100}) \) 12 * q + 162 * q^3 - 768 * q^4 + 1674 * q^5 - 1308 * q^7 + 23604 * q^9 + 17664 * q^10 + 10302 * q^11 - 20736 * q^12 + 56832 * q^14 - 255468 * q^15 - 98304 * q^16 + 173178 * q^17 + 16896 * q^18 + 405978 * q^19 - 656910 * q^21 - 941568 * q^22 + 158934 * q^23 + 98304 * q^24 + 838668 * q^25 + 1958400 * q^26 - 255744 * q^28 - 4355256 * q^29 + 916992 * q^30 + 4520250 * q^31 + 4954482 * q^33 - 5270790 * q^35 - 6042624 * q^36 + 134214 * q^37 + 1278720 * q^38 + 1335384 * q^39 - 2260992 * q^40 + 6660096 * q^42 - 12961896 * q^43 + 1318656 * q^44 - 8415396 * q^45 + 2345472 * q^46 + 18385002 * q^47 - 3659172 * q^49 + 2970624 * q^50 - 2673894 * q^51 - 3369984 * q^52 - 16540506 * q^53 - 19646208 * q^54 + 4325376 * q^56 + 100263780 * q^57 + 9176064 * q^58 + 31163922 * q^59 + 16349952 * q^60 - 85390158 * q^61 + 4361988 * q^63 + 25165824 * q^64 - 46506264 * q^65 - 111873024 * q^66 - 37750362 * q^67 - 22166784 * q^68 + 92031744 * q^70 + 45506424 * q^71 + 2162688 * q^72 + 9414786 * q^73 + 58837248 * q^74 + 9837540 * q^75 - 100614066 * q^77 - 25463808 * q^78 + 59730294 * q^79 - 27426816 * q^80 - 89677422 * q^81 - 93259776 * q^82 + 122616576 * q^84 - 64652220 * q^85 - 15144960 * q^86 + 334229724 * q^87 + 60260352 * q^88 + 323014482 * q^89 - 266861424 * q^91 - 40687104 * q^92 - 11119662 * q^93 - 443440128 * q^94 - 175918350 * q^95 - 12582912 * q^96 + 472166400 * q^98 - 346906296 * q^99

Introduction

L-functions

Modular forms

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Database

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