LMFDB - Embedded newform 8.30.b.a.5.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8,30,Mod(5,8)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8.5"); S:= CuspForms(chi, 30); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 30, names="a")

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$42.6224339064$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	8.5
Dual form			8.30.b.a.5.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-21420.9 + 8832.69i) q^{2} +1.37657e7i q^{3} +(3.80838e8 - 3.78408e8i) q^{4} -3.24318e9i q^{5} +(-1.21588e11 - 2.94874e11i) q^{6} -1.14169e11 q^{7} +(-4.81553e12 + 1.14697e13i) q^{8} -1.20865e14 q^{9} +(2.86460e13 + 6.94719e13i) q^{10} -4.21982e14i q^{11} +(5.20906e15 + 5.24251e15i) q^{12} +4.79401e14i q^{13} +(2.44560e15 - 1.00842e15i) q^{14} +4.46447e16 q^{15} +(1.84499e15 - 2.88224e17i) q^{16} +1.01331e18 q^{17} +(2.58903e18 - 1.06756e18i) q^{18} -4.09766e18i q^{19} +(-1.22725e18 - 1.23513e18i) q^{20} -1.57162e18i q^{21} +(3.72723e18 + 9.03922e18i) q^{22} -6.46500e19 q^{23} +(-1.57888e20 - 6.62892e19i) q^{24} +1.75746e20 q^{25} +(-4.23440e18 - 1.02692e19i) q^{26} -7.19041e20i q^{27} +(-4.34799e19 + 4.32025e19i) q^{28} -2.46920e21i q^{29} +(-9.56330e20 + 3.94333e20i) q^{30} +7.94944e21 q^{31} +(2.50628e21 + 6.19032e21i) q^{32} +5.80888e21 q^{33} +(-2.17059e22 + 8.95022e21i) q^{34} +3.70271e20i q^{35} +(-4.60298e22 + 4.57361e22i) q^{36} -8.39842e21i q^{37} +(3.61933e22 + 8.77754e22i) q^{38} -6.59930e21 q^{39} +(3.71982e22 + 1.56176e22i) q^{40} +2.83744e23 q^{41} +(1.38816e22 + 3.36655e22i) q^{42} +3.51232e23i q^{43} +(-1.59681e23 - 1.60707e23i) q^{44} +3.91986e23i q^{45} +(1.38486e24 - 5.71034e23i) q^{46} -3.35752e23 q^{47} +(3.96762e24 + 2.53976e22i) q^{48} -3.20687e24 q^{49} +(-3.76464e24 + 1.55231e24i) q^{50} +1.39489e25i q^{51} +(1.81409e23 + 1.82574e23i) q^{52} +8.42388e24i q^{53} +(6.35107e24 + 1.54025e25i) q^{54} -1.36856e24 q^{55} +(5.49784e23 - 1.30948e24i) q^{56} +5.64072e25 q^{57} +(2.18097e25 + 5.28925e25i) q^{58} +2.16453e25i q^{59} +(1.70024e25 - 1.68939e25i) q^{60} -1.37965e26i q^{61} +(-1.70284e26 + 7.02149e25i) q^{62} +1.37990e25 q^{63} +(-1.08364e26 - 1.10465e26i) q^{64} +1.55479e24 q^{65} +(-1.24431e26 + 5.13080e25i) q^{66} +3.86937e26i q^{67} +(3.85906e26 - 3.83443e26i) q^{68} -8.89954e26i q^{69} +(-3.27049e24 - 7.93153e24i) q^{70} -8.00452e26 q^{71} +(5.82027e26 - 1.38628e27i) q^{72} +5.06347e26 q^{73} +(7.41806e25 + 1.79902e26i) q^{74} +2.41927e27i q^{75} +(-1.55059e27 - 1.56054e27i) q^{76} +4.81772e25i q^{77} +(1.41363e26 - 5.82896e25i) q^{78} -1.99534e27 q^{79} +(-9.34764e26 - 5.98364e24i) q^{80} +1.60314e27 q^{81} +(-6.07806e27 + 2.50623e27i) q^{82} -1.37572e27i q^{83} +(-5.94713e26 - 5.98532e26i) q^{84} -3.28634e27i q^{85} +(-3.10233e27 - 7.52371e27i) q^{86} +3.39903e28 q^{87} +(4.83999e27 + 2.03207e27i) q^{88} +1.72285e28 q^{89} +(-3.46229e27 - 8.39669e27i) q^{90} -5.47328e25i q^{91} +(-2.46212e28 + 2.44641e28i) q^{92} +1.09430e29i q^{93} +(7.19211e27 - 2.96560e27i) q^{94} -1.32894e28 q^{95} +(-8.52142e28 + 3.45007e28i) q^{96} -2.72276e27 q^{97} +(6.86940e28 - 2.83253e28i) q^{98} +5.10026e28i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 8642 q^{2} - 69796972 q^{4} - 35869200308 q^{6} + 1356446145696 q^{7} - 9960937476728 q^{8} - 594796603828988 q^{9} - 62453907924808 q^{10} - 73\!\cdots\!44 q^{12} + 78\!\cdots\!40 q^{14} - 11\!\cdots\!36 q^{15}+ \cdots + 15\!\cdots\!18 q^{98}+O(q^{100}) $ 28 * q - 8642 * q^2 - 69796972 * q^4 - 35869200308 * q^6 + 1356446145696 * q^7 - 9960937476728 * q^8 - 594796603828988 * q^9 - 62453907924808 * q^10 - 7307924809229144 * q^12 + 78078973393134640 * q^14 - 116634443346832736 * q^15 + 383700292994789136 * q^16 + 236508787823771000 * q^17 - 5463422025028232686 * q^18 + 8100282295034264464 * q^20 - 74241827096141255876 * q^22 + 149024448719096002016 * q^23 + 20712180656567708048 * q^24 - 985560523954733380084 * q^25 + 380313139658742379432 * q^26 - 1732909439174340048608 * q^28 + 7144801785073394672432 * q^30 - 7260046134127777257856 * q^31 + 6643977062920224197408 * q^32 - 2610896914152110428752 * q^33 - 2930192868202493524772 * q^34 - 28754573920484976067764 * q^36 + 252146488468191620775980 * q^38 + 74849868421738610351584 * q^39 + 820688210793094034561952 * q^40 - 80518000617380870331368 * q^41 - 1782819030248345808659744 * q^42 - 2294598007572934677578808 * q^44 + 4638427469402659794112144 * q^46 + 121247766087237335010240 * q^47 + 6184031365810992970795296 * q^48 + 8159536578855108935060412 * q^49 - 9220400966993622071721098 * q^50 - 22597445120917837888235600 * q^52 + 30818656788479461856375672 * q^54 + 48823262031438992129145632 * q^55 + 3128328639131527389044032 * q^56 - 36164170101969527032146832 * q^57 + 36177867997628119870848904 * q^58 + 329519076781799215890952992 * q^60 - 317074609885892335052163904 * q^62 - 493740527299257821299206560 * q^63 - 500218670532924741725109184 * q^64 + 275343801437622480199359040 * q^65 + 657604928464011122019443160 * q^66 - 106459616116586500235114136 * q^68 - 602966453165460640487523648 * q^70 + 1637917847840158826077048224 * q^71 - 556537060776134471328999112 * q^72 - 1631197084836886372704831464 * q^73 - 2073796425120249162662229896 * q^74 - 676347811772827416679548184 * q^76 + 4169403080301092166733125776 * q^78 - 2323214658985225396749618624 * q^79 + 13382509145726722749974633280 * q^80 + 3743945936405161605092781740 * q^81 - 12472627196010378834371800468 * q^82 - 30031545197634704679499565504 * q^84 + 24644722942495826507852746492 * q^86 - 23673763728982249679638339488 * q^87 + 6702747736581680058989669584 * q^88 - 3845720546264709069323947304 * q^89 + 34684748345566534013885745800 * q^90 + 106057936152291016342860027744 * q^92 - 115120233998779072244940565728 * q^94 + 120167370974924948019325601696 * q^95 - 107488627072203471026633280448 * q^96 - 6191808951720963836806076616 * q^97 + 159188980666085592813609483918 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−21420.9	+	8832.69i	−0.924491	+	0.381204i
$2$	−21420.9	+	8832.69i	−0.924491	+	0.381204i
$3$			1.37657e7i			1.66165i	0.556531	+	0.830827i	$0.312132\pi$
$3$			1.37657e7i			1.66165i	−0.556531	+	0.830827i	$0.687868\pi$
$4$	3.80838e8	−	3.78408e8i	0.709366	−	0.704840i
$5$		−	3.24318e9i		−	0.237633i	−0.992916	−	0.118816i	$-0.962090\pi$
$5$		−	3.24318e9i		−	0.237633i	0.992916	−	0.118816i	$-0.0379100\pi$
$6$	−1.21588e11	−	2.94874e11i	−0.633430	−	1.53618i
$7$	−1.14169e11			−0.0636248			−0.0318124	−	0.999494i	$-0.510128\pi$
$7$	−1.14169e11			−0.0636248			−0.0318124	+	0.999494i	$0.510128\pi$
$8$	−4.81553e12	+	1.14697e13i	−0.387114	+	0.922032i
$9$	−1.20865e14			−1.76109
$10$	2.86460e13	+	6.94719e13i	0.0905867	+	0.219689i
$11$		−	4.21982e14i		−	0.335042i	−0.985868	−	0.167521i	$-0.946424\pi$
$11$		−	4.21982e14i		−	0.335042i	0.985868	−	0.167521i	$-0.0535762\pi$
$12$	5.20906e15	+	5.24251e15i	1.17120	+	1.17872i
$13$			4.79401e14i			0.0337692i	0.999857	+	0.0168846i	$0.00537479\pi$
$13$			4.79401e14i			0.0337692i	−0.999857	+	0.0168846i	$0.994625\pi$
$14$	2.44560e15	−	1.00842e15i	0.0588206	−	0.0242541i
$15$	4.46447e16			0.394863
$16$	1.84499e15	−	2.88224e17i	0.00640110	−	0.999980i
$17$	1.01331e18			1.45959			0.729796	−	0.683665i	$-0.239615\pi$
$17$	1.01331e18			1.45959			0.729796	+	0.683665i	$0.239615\pi$
$18$	2.58903e18	−	1.06756e18i	1.62812	−	0.671337i
$19$		−	4.09766e18i		−	1.17654i	−0.808663	−	0.588272i	$-0.799808\pi$
$19$		−	4.09766e18i		−	1.17654i	0.808663	−	0.588272i	$-0.200192\pi$
$20$	−1.22725e18	−	1.23513e18i	−0.167493	−	0.168569i
$21$		−	1.57162e18i		−	0.105722i
$22$	3.72723e18	+	9.03922e18i	0.127720	+	0.309743i
$23$	−6.46500e19			−1.16283			−0.581413	−	0.813608i	$-0.697500\pi$
$23$	−6.46500e19			−1.16283			−0.581413	+	0.813608i	$0.697500\pi$
$24$	−1.57888e20	−	6.62892e19i	−1.53210	−	0.643250i
$25$	1.75746e20			0.943531
$26$	−4.23440e18	−	1.02692e19i	−0.0128730	−	0.0312193i
$27$		−	7.19041e20i		−	1.26468i
$28$	−4.34799e19	+	4.32025e19i	−0.0451333	+	0.0448453i
$29$		−	2.46920e21i		−	1.54094i	−0.637476	−	0.770470i	$-0.720022\pi$
$29$		−	2.46920e21i		−	1.54094i	0.637476	−	0.770470i	$-0.279978\pi$
$30$	−9.56330e20	+	3.94333e20i	−0.365048	+	0.150524i
$31$	7.94944e21			1.88622			0.943109	−	0.332484i	$-0.107887\pi$
$31$	7.94944e21			1.88622			0.943109	+	0.332484i	$0.107887\pi$
$32$	2.50628e21	+	6.19032e21i	0.375279	+	0.926912i
$33$	5.80888e21			0.556724
$34$	−2.17059e22	+	8.95022e21i	−1.34938	+	0.556403i
$35$			3.70271e20i			0.0151193i
$36$	−4.60298e22	+	4.57361e22i	−1.24926	+	1.24129i
$37$		−	8.39842e21i		−	0.153205i	−0.997062	−	0.0766024i	$-0.975593\pi$
$37$		−	8.39842e21i		−	0.153205i	0.997062	−	0.0766024i	$-0.0244072\pi$
$38$	3.61933e22	+	8.77754e22i	0.448504	+	1.08770i
$39$	−6.59930e21			−0.0561127
$40$	3.71982e22	+	1.56176e22i	0.219105	+	0.0919911i
$41$	2.83744e23			1.16832			0.584159	−	0.811639i	$-0.301424\pi$
$41$	2.83744e23			1.16832			0.584159	+	0.811639i	$0.301424\pi$
$42$	1.38816e22	+	3.36655e22i	0.0403019	+	0.0977394i
$43$			3.51232e23i			0.724940i	0.931996	+	0.362470i	$0.118066\pi$
$43$			3.51232e23i			0.724940i	−0.931996	+	0.362470i	$0.881934\pi$
$44$	−1.59681e23	−	1.60707e23i	−0.236151	−	0.237668i
$45$			3.91986e23i			0.418494i
$46$	1.38486e24	−	5.71034e23i	1.07502	−	0.443275i
$47$	−3.35752e23			−0.190810			−0.0954048	−	0.995439i	$-0.530415\pi$
$47$	−3.35752e23			−0.190810			−0.0954048	+	0.995439i	$0.530415\pi$
$48$	3.96762e24	+	2.53976e22i	1.66162	+	0.0106364i
$49$	−3.20687e24			−0.995952
$50$	−3.76464e24	+	1.55231e24i	−0.872285	+	0.359678i
$51$			1.39489e25i			2.42534i
$52$	1.81409e23	+	1.82574e23i	0.0238019	+	0.0239547i
$53$			8.42388e24i			0.838517i	0.907867	+	0.419259i	$0.137710\pi$
$53$			8.42388e24i			0.838517i	−0.907867	+	0.419259i	$0.862290\pi$
$54$	6.35107e24	+	1.54025e25i	0.482100	+	1.16918i
$55$	−1.36856e24			−0.0796170
$56$	5.49784e23	−	1.30948e24i	0.0246301	−	0.0586641i
$57$	5.64072e25			1.95501
$58$	2.18097e25	+	5.28925e25i	0.587413	+	1.42458i
$59$			2.16453e25i			0.454997i	0.973778	+	0.227499i	$0.0730547\pi$
$59$			2.16453e25i			0.454997i	−0.973778	+	0.227499i	$0.926945\pi$
$60$	1.70024e25	−	1.68939e25i	0.280103	−	0.278316i
$61$		−	1.37965e26i		−	1.78849i	−0.447580	−	0.894244i	$-0.647714\pi$
$61$		−	1.37965e26i		−	1.78849i	0.447580	−	0.894244i	$-0.352286\pi$
$62$	−1.70284e26	+	7.02149e25i	−1.74379	+	0.719035i
$63$	1.37990e25			0.112049
$64$	−1.08364e26	−	1.10465e26i	−0.700285	−	0.713864i
$65$	1.55479e24			0.00802467
$66$	−1.24431e26	+	5.13080e25i	−0.514686	+	0.212226i
$67$			3.86937e26i			1.28693i	0.765475	+	0.643465i	$0.222504\pi$
$67$			3.86937e26i			1.28693i	−0.765475	+	0.643465i	$0.777496\pi$
$68$	3.85906e26	−	3.83443e26i	1.03539	−	1.02878i
$69$		−	8.89954e26i		−	1.93222i
$70$	−3.27049e24	−	7.93153e24i	−0.00576356	−	0.0139777i
$71$	−8.00452e26			−1.14839			−0.574195	−	0.818718i	$-0.694685\pi$
$71$	−8.00452e26			−1.14839			−0.574195	+	0.818718i	$0.694685\pi$
$72$	5.82027e26	−	1.38628e27i	0.681745	−	1.62378i
$73$	5.06347e26			0.485587			0.242793	−	0.970078i	$-0.421936\pi$
$73$	5.06347e26			0.485587			0.242793	+	0.970078i	$0.421936\pi$
$74$	7.41806e25	+	1.79902e26i	0.0584024	+	0.141636i
$75$			2.41927e27i			1.56782i
$76$	−1.55059e27	−	1.56054e27i	−0.829276	−	0.834601i
$77$			4.81772e25i			0.0213170i
$78$	1.41363e26	−	5.82896e25i	0.0518757	−	0.0213904i
$79$	−1.99534e27			−0.608728			−0.304364	−	0.952556i	$-0.598444\pi$
$79$	−1.99534e27			−0.608728			−0.304364	+	0.952556i	$0.598444\pi$
$80$	−9.34764e26	−	5.98364e24i	−0.237628	−	0.00152111i
$81$	1.60314e27			0.340359
$82$	−6.07806e27	+	2.50623e27i	−1.08010	+	0.445368i
$83$		−	1.37572e27i		−	0.205068i	−0.994730	−	0.102534i	$-0.967305\pi$
$83$		−	1.37572e27i		−	0.205068i	0.994730	−	0.102534i	$-0.0326950\pi$
$84$	−5.94713e26	−	5.98532e26i	−0.0745174	−	0.0749960i
$85$		−	3.28634e27i		−	0.346847i
$86$	−3.10233e27	−	7.52371e27i	−0.276350	−	0.670200i
$87$	3.39903e28			2.56051
$88$	4.83999e27	+	2.03207e27i	0.308920	+	0.129700i
$89$	1.72285e28			0.933453			0.466727	−	0.884402i	$-0.345433\pi$
$89$	1.72285e28			0.933453			0.466727	+	0.884402i	$0.345433\pi$
$90$	−3.46229e27	−	8.39669e27i	−0.159532	−	0.386894i
$91$		−	5.47328e25i		−	0.00214856i
$92$	−2.46212e28	+	2.44641e28i	−0.824870	+	0.819607i
$93$			1.09430e29i			3.13424i
$94$	7.19211e27	−	2.96560e27i	0.176402	−	0.0727374i
$95$	−1.32894e28			−0.279585
$96$	−8.52142e28	+	3.45007e28i	−1.54021	+	0.623584i
$97$	−2.72276e27			−0.0423467			−0.0211733	−	0.999776i	$-0.506740\pi$
$97$	−2.72276e27			−0.0423467			−0.0211733	+	0.999776i	$0.506740\pi$
$98$	6.86940e28	−	2.83253e28i	0.920748	−	0.379661i
$99$			5.10026e28i			0.590041i
$100$	6.69309e28	−	6.65038e28i	0.669309	−	0.665038i
$101$			1.88983e29i			1.63592i	0.575276	+	0.817960i	$0.304895\pi$
$101$			1.88983e29i			1.63592i	−0.575276	+	0.817960i	$0.695105\pi$
$102$	−1.23206e29	−	2.98798e29i	−0.924549	−	2.24220i
$103$	2.21195e29			1.44090			0.720452	−	0.693505i	$-0.243934\pi$
$103$	2.21195e29			1.44090			0.720452	+	0.693505i	$0.243934\pi$
$104$	−5.49857e27	−	2.30857e27i	−0.0311363	−	0.0130725i
$105$	−5.09704e27			−0.0251231
$106$	−7.44055e28	−	1.80447e29i	−0.319647	−	0.775201i
$107$		−	8.17979e28i		−	0.306674i	−0.988174	−	0.153337i	$-0.950998\pi$
$107$		−	8.17979e28i		−	0.306674i	0.988174	−	0.153337i	$-0.0490021\pi$
$108$	−2.72091e29	−	2.73838e29i	−0.891394	−	0.897118i
$109$		−	3.84074e29i		−	1.10086i	−0.834882	−	0.550428i	$-0.814464\pi$
$109$		−	3.84074e29i		−	1.10086i	0.834882	−	0.550428i	$-0.185536\pi$
$110$	2.93158e28	−	1.20881e28i	0.0736052	−	0.0303504i
$111$	1.15610e29			0.254574
$112$	−2.10641e26	+	3.29063e28i	−0.000407269	+	0.0636235i
$113$	6.31098e29			1.07265			0.536326	−	0.844011i	$-0.319812\pi$
$113$	6.31098e29			1.07265			0.536326	+	0.844011i	$0.319812\pi$
$114$	−1.20829e30	+	4.98227e29i	−1.80739	+	0.745258i
$115$			2.09672e29i			0.276326i
$116$	−9.34366e29	−	9.40366e29i	−1.08612	−	1.09309i
$117$		−	5.79426e28i		−	0.0594707i
$118$	−1.91186e29	−	4.63661e29i	−0.173447	−	0.420641i
$119$	−1.15688e29			−0.0928663
$120$	−2.14988e29	+	5.12060e29i	−0.152857	+	0.364077i
$121$	1.40824e30			0.887747
$122$	1.21860e30	+	2.95533e30i	0.681780	+	1.65344i
$123$			3.90595e30i			1.94134i
$124$	3.02745e30	−	3.00813e30i	1.33802	−	1.32948i
$125$		−	1.17407e30i		−	0.461847i
$126$	−2.95587e29	+	1.21882e29i	−0.103589	+	0.0427137i
$127$	−4.06201e29			−0.126937			−0.0634684	−	0.997984i	$-0.520216\pi$
$127$	−4.06201e29			−0.126937			−0.0634684	+	0.997984i	$0.520216\pi$
$128$	3.29695e30	+	1.40912e30i	0.919535	+	0.393009i
$129$	−4.83496e30			−1.20460
$130$	−3.33049e28	+	1.37329e28i	−0.00741873	+	0.00305904i
$131$			3.24993e30i			0.647799i	0.946092	+	0.323899i	$0.104994\pi$
$131$			3.24993e30i			0.647799i	−0.946092	+	0.323899i	$0.895006\pi$
$132$	2.21224e30	−	2.19813e30i	0.394921	−	0.392402i
$133$			4.67825e29i			0.0748574i
$134$	−3.41769e30	−	8.28853e30i	−0.490584	−	1.18976i
$135$	−2.33198e30			−0.300528
$136$	−4.87961e30	+	1.16223e31i	−0.565029	+	1.34579i
$137$	−4.38666e29			−0.0456757			−0.0228379	−	0.999739i	$-0.507270\pi$
$137$	−4.38666e29			−0.0456757			−0.0228379	+	0.999739i	$0.507270\pi$
$138$	7.86069e30	+	1.90636e31i	0.736569	+	1.78632i
$139$		−	1.95300e31i		−	1.64811i	−0.566508	−	0.824056i	$-0.691706\pi$
$139$		−	1.95300e31i		−	1.64811i	0.566508	−	0.824056i	$-0.308294\pi$
$140$	1.40114e29	+	1.41013e29i	0.0106567	+	0.0107252i
$141$		−	4.62187e30i		−	0.317059i
$142$	1.71464e31	−	7.07015e30i	1.06168	−	0.437772i
$143$	2.02299e29			0.0113141
$144$	−2.22994e29	+	3.48361e31i	−0.0112729	+	1.76106i
$145$	−8.00807e30			−0.366178
$146$	−1.08464e31	+	4.47241e30i	−0.448921	+	0.185108i
$147$		−	4.41449e31i		−	1.65493i
$148$	−3.17803e30	−	3.19844e30i	−0.107985	−	0.108678i
$149$		−	8.70799e30i		−	0.268360i	−0.990957	−	0.134180i	$-0.957160\pi$
$149$		−	8.70799e30i		−	0.268360i	0.990957	−	0.134180i	$-0.0428400\pi$
$150$	−2.13687e31	−	5.18230e31i	−0.597661	−	1.44944i
$151$	3.89435e31			0.989166			0.494583	−	0.869130i	$-0.335321\pi$
$151$	3.89435e31			0.989166			0.494583	+	0.869130i	$0.335321\pi$
$152$	4.69987e31	+	1.97324e31i	1.08481	+	0.455457i
$153$	−1.22473e32			−2.57048
$154$	−4.25534e29	−	1.03200e30i	−0.00812614	−	0.0197074i
$155$		−	2.57815e31i		−	0.448227i
$156$	−2.51327e30	+	2.49723e30i	−0.0398045	+	0.0395505i
$157$		−	8.53107e30i		−	0.123157i	−0.998102	−	0.0615784i	$-0.980387\pi$
$157$		−	8.53107e30i		−	0.123157i	0.998102	−	0.0615784i	$-0.0196134\pi$
$158$	4.27419e31	−	1.76242e31i	0.562763	−	0.232050i
$159$	−1.15961e32			−1.39333
$160$	2.00763e31	−	8.12831e30i	0.220265	−	0.0891786i
$161$	7.38103e30			0.0739847
$162$	−3.43406e31	+	1.41600e31i	−0.314659	+	0.129746i
$163$			1.05806e32i			0.886724i	0.896343	+	0.443362i	$0.146214\pi$
$163$			1.05806e32i			0.886724i	−0.896343	+	0.443362i	$0.853786\pi$
$164$	1.08061e32	−	1.07371e32i	0.828766	−	0.823478i
$165$		−	1.88393e31i		−	0.132296i
$166$	1.21513e31	+	2.94692e31i	0.0781728	+	0.189583i
$167$	3.04895e32			1.79788			0.898942	−	0.438069i	$-0.144337\pi$
$167$	3.04895e32			1.79788			0.898942	+	0.438069i	$0.144337\pi$
$168$	1.80259e31	+	7.56818e30i	0.0974795	+	0.0409267i
$169$	2.01308e32			0.998860
$170$	2.90272e31	+	7.03963e31i	0.132220	+	0.320657i
$171$			4.95261e32i			2.07201i
$172$	1.32909e32	+	1.33763e32i	0.510966	+	0.514248i
$173$		−	1.88662e32i		−	0.666832i	−0.942780	−	0.333416i	$-0.891799\pi$
$173$		−	1.88662e32i		−	0.666832i	0.942780	−	0.333416i	$-0.108201\pi$
$174$	−7.28103e32	+	3.00226e32i	−2.36717	+	0.976078i
$175$	−2.00648e31			−0.0600320
$176$	−1.21625e32	−	7.78552e29i	−0.335035	−	0.00214464i
$177$	−2.97963e32			−0.756048
$178$	−3.69050e32	+	1.52174e32i	−0.862969	+	0.355837i
$179$			5.35796e32i			1.15513i	0.816345	+	0.577565i	$0.195997\pi$
$179$			5.35796e32i			1.15513i	−0.816345	+	0.577565i	$0.804003\pi$
$180$	1.48331e32	+	1.49283e32i	0.294971	+	0.296865i
$181$		−	3.04526e32i		−	0.558838i	−0.960169	−	0.279419i	$-0.909858\pi$
$181$		−	3.04526e32i		−	0.558838i	0.960169	−	0.279419i	$-0.0901418\pi$
$182$	4.83438e29	+	1.17242e30i	0.000819040	+	0.00198632i
$183$	1.89919e33			2.97185
$184$	3.11324e32	−	7.41514e32i	0.450147	−	1.07216i
$185$	−2.72376e31			−0.0364065
$186$	−9.66559e32	−	2.34408e33i	−1.19479	−	2.89758i
$187$		−	4.27597e32i		−	0.489025i
$188$	−1.27867e32	+	1.27051e32i	−0.135354	+	0.134490i
$189$			8.20922e31i			0.0804648i
$190$	2.84672e32	−	1.17382e32i	0.258474	−	0.106579i
$191$	−1.08538e33			−0.913263			−0.456632	−	0.889656i	$-0.650944\pi$
$191$	−1.08538e33			−0.913263			−0.456632	+	0.889656i	$0.650944\pi$
$192$	1.52063e33	−	1.49171e33i	1.18619	−	1.16363i
$193$	−1.53434e33			−1.11004			−0.555021	−	0.831836i	$-0.687290\pi$
$193$	−1.53434e33			−1.11004			−0.555021	+	0.831836i	$0.687290\pi$
$194$	5.83239e31	−	2.40493e31i	0.0391491	−	0.0161427i
$195$			2.14027e31i			0.0133342i
$196$	−1.22130e33	+	1.21351e33i	−0.706495	+	0.701987i
$197$			2.36971e33i			1.27331i	0.771147	+	0.636657i	$0.219683\pi$
$197$			2.36971e33i			1.27331i	−0.771147	+	0.636657i	$0.780317\pi$
$198$	−4.50490e32	−	1.09252e33i	−0.224926	−	0.545487i
$199$	3.05454e33			1.41767			0.708836	−	0.705373i	$-0.249221\pi$
$199$	3.05454e33			1.41767			0.708836	+	0.705373i	$0.249221\pi$
$200$	−8.46312e32	+	2.01575e33i	−0.365254	+	0.869965i
$201$	−5.32646e33			−2.13843
$202$	−1.66922e33	−	4.04817e33i	−0.623620	−	1.51239i
$203$			2.81906e32i			0.0980420i
$204$	5.27837e33	+	5.31227e33i	1.70947	+	1.72045i
$205$		−	9.20235e32i		−	0.277631i
$206$	−4.73819e33	+	1.95374e33i	−1.33210	+	0.549279i
$207$	7.81390e33			2.04785
$208$	1.38175e32	+	8.84491e29i	0.0337685	+	0.000216160i
$209$	−1.72914e33			−0.394192
$210$	1.09183e32	−	4.50206e31i	0.0232261	−	0.00957705i
$211$		−	3.49674e33i		−	0.694332i	−0.937804	−	0.347166i	$-0.887144\pi$
$211$		−	3.49674e33i		−	0.694332i	0.937804	−	0.347166i	$-0.112856\pi$
$212$	3.18766e33	+	3.20813e33i	0.591021	+	0.594816i
$213$		−	1.10188e34i		−	1.90823i
$214$	7.22496e32	+	1.75218e33i	0.116906	+	0.283518i
$215$	1.13911e33			0.172269
$216$	8.24716e33	+	3.46256e33i	1.16607	+	0.489574i
$217$	−9.07580e32			−0.120010
$218$	3.39241e33	+	8.22721e33i	0.419651	+	1.01773i
$219$			6.97023e33i			0.806877i
$220$	−5.21201e32	+	5.17875e32i	−0.0564776	+	0.0561172i
$221$			4.85780e32i			0.0492892i
$222$	−2.47647e33	+	1.02115e33i	−0.235351	+	0.0970446i
$223$	−8.80242e33			−0.783758			−0.391879	−	0.920017i	$-0.628175\pi$
$223$	−8.80242e33			−0.783758			−0.391879	+	0.920017i	$0.628175\pi$
$224$	−2.86139e32	−	7.06743e32i	−0.0238771	−	0.0589746i
$225$	−2.12415e34			−1.66165
$226$	−1.35187e34	+	5.57429e33i	−0.991658	+	0.408900i
$227$			2.06625e34i			1.42170i	0.703343	+	0.710850i	$0.251690\pi$
$227$			2.06625e34i			1.42170i	−0.703343	+	0.710850i	$0.748310\pi$
$228$	2.14820e34	−	2.13449e34i	1.38682	−	1.37797i
$229$		−	1.68240e34i		−	1.01933i	−0.860372	−	0.509666i	$-0.829769\pi$
$229$		−	1.68240e34i		−	1.01933i	0.860372	−	0.509666i	$-0.170231\pi$
$230$	−1.85197e33	−	4.49136e33i	−0.105337	−	0.255461i
$231$	−6.63194e32			−0.0354215
$232$	2.83209e34	+	1.18905e34i	1.42080	+	0.596520i
$233$	−1.81414e34			−0.855089			−0.427544	−	0.903994i	$-0.640621\pi$
$233$	−1.81414e34			−0.855089			−0.427544	+	0.903994i	$0.640621\pi$
$234$	5.11789e32	+	1.24118e33i	0.0226705	+	0.0549801i
$235$			1.08891e33i			0.0453426i
$236$	8.19075e33	+	8.24335e33i	0.320700	+	0.322760i
$237$		−	2.74672e34i		−	1.01150i
$238$	2.47814e33	−	1.02184e33i	0.0858540	−	0.0354010i
$239$	3.29285e34			1.07350			0.536751	−	0.843741i	$-0.319652\pi$
$239$	3.29285e34			1.07350			0.536751	+	0.843741i	$0.319652\pi$
$240$	8.23692e31	−	1.28677e34i	0.00252756	−	0.394855i
$241$	8.73698e33			0.252415			0.126207	−	0.992004i	$-0.459720\pi$
$241$	8.73698e33			0.252415			0.126207	+	0.992004i	$0.459720\pi$
$242$	−3.01658e34	+	1.24386e34i	−0.820714	+	0.338413i
$243$		−	2.72798e34i		−	0.699117i
$244$	−5.22070e34	−	5.25423e34i	−1.26060	−	1.26869i
$245$			1.04005e34i			0.236671i
$246$	−3.45000e34	−	8.36688e34i	−0.740048	−	1.79475i
$247$	1.96442e33			0.0397309
$248$	−3.82808e34	+	9.11774e34i	−0.730182	+	1.73915i
$249$	1.89378e34			0.340752
$250$	1.03702e34	+	2.51496e34i	0.176058	+	0.426973i
$251$		−	4.36459e34i		−	0.699318i	−0.936877	−	0.349659i	$-0.886297\pi$
$251$		−	4.36459e34i		−	0.699318i	0.936877	−	0.349659i	$-0.113703\pi$
$252$	5.25518e33	−	5.22165e33i	0.0794840	−	0.0789769i
$253$			2.72811e34i			0.389596i
$254$	8.70119e33	−	3.58785e33i	0.117352	−	0.0483889i
$255$	4.52388e34			0.576339
$256$	−8.30699e34	−	1.06354e33i	−0.999918	−	0.0128019i
$257$	6.14746e34			0.699303			0.349651	−	0.936880i	$-0.386300\pi$
$257$	6.14746e34			0.699303			0.349651	+	0.936880i	$0.386300\pi$
$258$	1.03569e35	−	4.27057e34i	1.11364	−	0.459198i
$259$			9.58839e32i			0.00974764i
$260$	5.92122e32	−	5.88344e32i	0.00569243	−	0.00565611i
$261$			2.98439e35i			2.71374i
$262$	−2.87056e34	−	6.96164e34i	−0.246944	−	0.598884i
$263$	4.94009e33			0.0402140			0.0201070	−	0.999798i	$-0.493599\pi$
$263$	4.94009e33			0.0402140			0.0201070	+	0.999798i	$0.493599\pi$
$264$	−2.79728e34	+	6.66259e34i	−0.215516	+	0.513317i
$265$	2.73202e34			0.199259
$266$	−4.13216e33	−	1.00212e34i	−0.0285360	−	0.0692050i
$267$			2.37163e35i			1.55108i
$268$	1.46420e35	+	1.47360e35i	0.907080	+	0.912905i
$269$			1.35457e35i			0.795048i	0.917592	+	0.397524i	$0.130130\pi$
$269$			1.35457e35i			0.795048i	−0.917592	+	0.397524i	$0.869870\pi$
$270$	4.99531e34	−	2.05977e34i	0.277836	−	0.114563i
$271$	1.62610e35			0.857223			0.428611	−	0.903489i	$-0.359003\pi$
$271$	1.62610e35			0.857223			0.428611	+	0.903489i	$0.359003\pi$
$272$	1.86954e33	−	2.92060e35i	0.00934299	−	1.45956i
$273$	7.53436e32			0.00357016
$274$	9.39661e33	−	3.87460e33i	0.0422268	−	0.0174118i
$275$		−	7.41617e34i		−	0.316123i
$276$	−3.36766e35	−	3.38928e35i	−1.36190	−	1.37065i
$277$		−	2.93992e35i		−	1.12818i	−0.825713	−	0.564090i	$-0.809227\pi$
$277$		−	2.93992e35i		−	1.12818i	0.825713	−	0.564090i	$-0.190773\pi$
$278$	1.72502e35	+	4.18349e35i	0.628268	+	1.52366i
$279$	−9.60805e35			−3.32181
$280$	−4.24688e33	−	1.78305e33i	−0.0139405	−	0.00585292i
$281$	5.20455e35			1.62234			0.811170	−	0.584811i	$-0.198831\pi$
$281$	5.20455e35			1.62234			0.811170	+	0.584811i	$0.198831\pi$
$282$	4.08235e34	+	9.90046e34i	0.120864	+	0.293118i
$283$		−	4.42786e35i		−	1.24535i	−0.782482	−	0.622673i	$-0.786047\pi$
$283$		−	4.42786e35i		−	1.24535i	0.782482	−	0.622673i	$-0.213953\pi$
$284$	−3.04843e35	+	3.02898e35i	−0.814629	+	0.809431i
$285$		−	1.82939e35i		−	0.464574i
$286$	−4.33341e33	+	1.78684e33i	−0.0104598	+	0.00431299i
$287$	−3.23948e34			−0.0743341
$288$	−3.02920e35	−	7.48191e35i	−0.660902	−	1.63238i
$289$	5.44821e35			1.13041
$290$	1.71540e35	−	7.07328e34i	0.338528	−	0.139589i
$291$		−	3.74807e34i		−	0.0703655i
$292$	1.92836e35	−	1.91606e35i	0.344459	−	0.342261i
$293$		−	1.04317e36i		−	1.77327i	−0.462473	−	0.886633i	$-0.653038\pi$
$293$		−	1.04317e36i		−	1.77327i	0.462473	−	0.886633i	$-0.346962\pi$
$294$	3.89918e35	+	9.45623e35i	0.630866	+	1.52997i
$295$	7.01996e34			0.108122
$296$	9.63271e34	+	4.04429e34i	0.141260	+	0.0593078i
$297$	−3.03422e35			−0.423720
$298$	7.69150e34	+	1.86533e35i	0.102300	+	0.248096i
$299$		−	3.09933e34i		−	0.0392677i
$300$	9.15473e35	+	9.21352e35i	1.10506	+	1.11216i
$301$		−	4.00998e34i		−	0.0461242i
$302$	−8.34204e35	+	3.43976e35i	−0.914475	+	0.377074i
$303$	−2.60148e36			−2.71833
$304$	−1.18104e36	−	7.56014e33i	−1.17652	−	0.00753118i
$305$	−4.47445e35			−0.425003
$306$	2.62348e36	−	1.08176e36i	2.37638	−	0.979878i
$307$		−	5.22110e35i		−	0.451082i	−0.974234	−	0.225541i	$-0.927585\pi$
$307$		−	5.22110e35i		−	0.451082i	0.974234	−	0.225541i	$-0.0724149\pi$
$308$	1.82306e34	+	1.83477e34i	0.0150251	+	0.0151216i
$309$			3.04490e36i			2.39428i
$310$	2.27720e35	+	5.52262e35i	0.170866	+	0.414382i
$311$	8.42163e35			0.603074			0.301537	−	0.953454i	$-0.402500\pi$
$311$	8.42163e35			0.603074			0.301537	+	0.953454i	$0.402500\pi$
$312$	3.17791e34	−	7.56918e34i	0.0217220	−	0.0517377i
$313$	4.21587e35			0.275103			0.137551	−	0.990495i	$-0.456077\pi$
$313$	4.21587e35			0.275103			0.137551	+	0.990495i	$0.456077\pi$
$314$	7.53523e34	+	1.82743e35i	0.0469480	+	0.113857i
$315$		−	4.47526e34i		−	0.0266266i
$316$	−7.59900e35	+	7.55051e35i	−0.431811	+	0.429056i
$317$			7.19524e35i			0.390558i	0.980748	+	0.195279i	$0.0625613\pi$
$317$			7.19524e35i			0.390558i	−0.980748	+	0.195279i	$0.937439\pi$
$318$	2.48398e36	−	1.02425e36i	1.28812	−	0.531142i
$319$	−1.04196e36			−0.516280
$320$	−3.58258e35	+	3.51444e35i	−0.169637	+	0.166411i
$321$	1.12601e36			0.509587
$322$	−1.58108e35	+	6.51943e34i	−0.0683981	+	0.0282033i
$323$		−	4.15218e36i		−	1.71727i
$324$	6.10535e35	−	6.06639e35i	0.241439	−	0.239899i
$325$			8.42530e34i			0.0318623i
$326$	−9.34548e35	−	2.26645e36i	−0.338023	−	0.819768i
$327$	5.28705e36			1.82924
$328$	−1.36638e36	+	3.25445e36i	−0.452273	+	1.07723i
$329$	3.83325e34			0.0121402
$330$	1.66401e35	+	4.03554e35i	0.0504318	+	0.122306i
$331$			1.22217e36i			0.354509i	0.984165	+	0.177254i	$0.0567215\pi$
$331$			1.22217e36i			0.354509i	−0.984165	+	0.177254i	$0.943278\pi$
$332$	−5.20584e35	−	5.23927e35i	−0.144540	−	0.145468i
$333$			1.01507e36i			0.269808i
$334$	−6.53112e36	+	2.69304e36i	−1.66213	+	0.685361i
$335$	1.25491e36			0.305817
$336$	−4.52979e35	−	2.89962e33i	−0.105720	−	0.000676740i
$337$	−3.01311e35			−0.0673568			−0.0336784	−	0.999433i	$-0.510722\pi$
$337$	−3.01311e35			−0.0673568			−0.0336784	+	0.999433i	$0.510722\pi$
$338$	−4.31220e36	+	1.77809e36i	−0.923437	+	0.380770i
$339$			8.68751e36i			1.78238i
$340$	−1.24358e36	−	1.25156e36i	−0.244472	−	0.246041i
$341$		−	3.35452e36i		−	0.631963i
$342$	−4.37449e36	−	1.06089e37i	−0.789858	−	1.91555i
$343$	7.33739e35			0.126992
$344$	−4.02852e36	−	1.69137e36i	−0.668417	−	0.280635i
$345$	−2.88628e36			−0.459158
$346$	1.66639e36	+	4.04131e36i	0.254199	+	0.616480i
$347$			2.35759e36i			0.344898i	0.985018	+	0.172449i	$0.0551681\pi$
$347$			2.35759e36i			0.344898i	−0.985018	+	0.172449i	$0.944832\pi$
$348$	1.29448e37	−	1.28622e37i	1.81634	−	1.80475i
$349$		−	7.13478e36i		−	0.960311i	−0.877184	−	0.480155i	$-0.840580\pi$
$349$		−	7.13478e36i		−	0.960311i	0.877184	−	0.480155i	$-0.159420\pi$
$350$	4.29805e35	−	1.77226e35i	0.0554990	−	0.0228845i
$351$	3.44709e35			0.0427071
$352$	2.61220e36	−	1.05760e36i	0.310555	−	0.125734i
$353$	3.84271e36			0.438434			0.219217	−	0.975676i	$-0.429650\pi$
$353$	3.84271e36			0.438434			0.219217	+	0.975676i	$0.429650\pi$
$354$	6.38263e36	−	2.63181e36i	0.698960	−	0.288209i
$355$			2.59601e36i			0.272895i
$356$	6.56127e36	−	6.51941e36i	0.662160	−	0.657935i
$357$		−	1.59253e36i		−	0.154312i
$358$	−4.73252e36	−	1.14772e37i	−0.440341	−	1.06791i
$359$	−1.64126e36			−0.146659			−0.0733294	−	0.997308i	$-0.523362\pi$
$359$	−1.64126e36			−0.146659			−0.0733294	+	0.997308i	$0.523362\pi$
$360$	−4.49595e36	−	1.88762e36i	−0.385864	−	0.162005i
$361$	−4.66097e36			−0.384257
$362$	2.68979e36	+	6.52323e36i	0.213031	+	0.516640i
$363$			1.93854e37i			1.47513i
$364$	−2.07113e34	−	2.08443e34i	−0.00151439	−	0.00152412i
$365$		−	1.64218e36i		−	0.115391i
$366$	−4.06822e37	+	1.67749e37i	−2.74745	+	1.13288i
$367$	2.31471e37			1.50259			0.751293	−	0.659969i	$-0.229430\pi$
$367$	2.31471e37			1.50259			0.751293	+	0.659969i	$0.229430\pi$
$368$	−1.19279e35	+	1.86337e37i	−0.00744337	+	1.16280i
$369$	−3.42946e37			−2.05752
$370$	5.83454e35	−	2.40581e35i	0.0336575	−	0.0138783i
$371$		−	9.61746e35i		−	0.0533505i
$372$	4.14091e37	+	4.16750e37i	2.20914	+	2.22333i
$373$		−	2.37633e36i		−	0.121935i	−0.998140	−	0.0609675i	$-0.980581\pi$
$373$		−	2.37633e36i		−	0.121935i	0.998140	−	0.0609675i	$-0.0194186\pi$
$374$	3.77683e36	+	9.15950e36i	0.186418	+	0.452099i
$375$	1.61619e37			0.767429
$376$	1.61683e36	−	3.85097e36i	0.0738651	−	0.175932i
$377$	1.18374e36			0.0520363
$378$	−7.25095e35	−	1.75849e36i	−0.0306735	−	0.0743889i
$379$		−	3.24594e37i		−	1.32151i	−0.750600	−	0.660757i	$-0.770235\pi$
$379$		−	3.24594e37i		−	1.32151i	0.750600	−	0.660757i	$-0.229765\pi$
$380$	−5.06113e36	+	5.02883e36i	−0.198329	+	0.197063i
$381$		−	5.59165e36i		−	0.210925i
$382$	2.32497e37	−	9.58678e36i	0.844304	−	0.348140i
$383$	2.82063e37			0.986196			0.493098	−	0.869974i	$-0.335864\pi$
$383$	2.82063e37			0.986196			0.493098	+	0.869974i	$0.335864\pi$
$384$	−1.93975e37	+	4.53849e37i	−0.653044	+	1.52795i
$385$	1.56248e35			0.00506562
$386$	3.28668e37	−	1.35523e37i	1.02622	−	0.423153i
$387$		−	4.24515e37i		−	1.27669i
$388$	−1.03693e36	+	1.03031e36i	−0.0300393	+	0.0298476i
$389$			4.69170e37i			1.30936i	0.755904	+	0.654682i	$0.227198\pi$
$389$			4.69170e37i			1.30936i	−0.755904	+	0.654682i	$0.772802\pi$
$390$	−1.89044e35	−	4.58466e35i	−0.00508306	−	0.0123274i
$391$	−6.55103e37			−1.69725
$392$	1.54428e37	−	3.67817e37i	0.385547	−	0.918299i
$393$	−4.47376e37			−1.07642
$394$	−2.09309e37	−	5.07614e37i	−0.485393	−	1.17717i
$395$			6.47124e36i			0.144654i
$396$	1.92998e37	+	1.94237e37i	0.415884	+	0.418555i
$397$		−	7.02748e37i		−	1.45995i	−0.683476	−	0.729973i	$-0.739532\pi$
$397$		−	7.02748e37i		−	1.45995i	0.683476	−	0.729973i	$-0.260468\pi$
$398$	−6.54309e37	+	2.69798e37i	−1.31062	+	0.540423i
$399$	−6.43995e36			−0.124387
$400$	3.24250e35	−	5.06544e37i	0.00603963	−	0.943511i
$401$	−5.35873e37			−0.962650			−0.481325	−	0.876542i	$-0.659844\pi$
$401$	−5.35873e37			−0.962650			−0.481325	+	0.876542i	$0.659844\pi$
$402$	1.14098e38	−	4.70470e37i	1.97696	−	0.815181i
$403$			3.81097e36i			0.0636961i
$404$	7.15125e37	+	7.19718e37i	1.15306	+	1.16047i
$405$		−	5.19926e36i		−	0.0808805i
$406$	−2.48999e36	−	6.03869e36i	−0.0373741	−	0.0906390i
$407$	−3.54398e36			−0.0513301
$408$	−1.59989e38	−	6.71713e37i	−2.23624	−	0.938883i
$409$	−2.41408e37			−0.325659			−0.162830	−	0.986654i	$-0.552062\pi$
$409$	−2.41408e37			−0.325659			−0.162830	+	0.986654i	$0.552062\pi$
$410$	8.12815e36	+	1.97122e37i	0.105834	+	0.256667i
$411$		−	6.03855e36i		−	0.0758972i
$412$	8.42394e37	−	8.37019e37i	1.02213	−	1.01561i
$413$		−	2.47122e36i		−	0.0289491i
$414$	−1.67381e38	+	6.90177e37i	−1.89322	+	0.780649i
$415$	−4.46171e36			−0.0487309
$416$	−2.96765e36	+	1.20151e36i	−0.0313011	+	0.0126729i
$417$	2.68844e38			2.73859
$418$	3.70396e37	−	1.52729e37i	0.364427	−	0.150268i
$419$			1.65339e38i			1.57135i	0.618641	+	0.785674i	$0.287683\pi$
$419$			1.65339e38i			1.57135i	−0.618641	+	0.785674i	$0.712317\pi$
$420$	−1.94115e36	+	1.92876e36i	−0.0178215	+	0.0177078i
$421$			6.84156e36i			0.0606827i	0.999540	+	0.0303414i	$0.00965943\pi$
$421$			6.84156e36i			0.0606827i	−0.999540	+	0.0303414i	$0.990341\pi$
$422$	3.08856e37	+	7.49032e37i	0.264682	+	0.641904i
$423$	4.05806e37			0.336034
$424$	−9.66191e37	−	4.05655e37i	−0.773140	−	0.324602i
$425$	1.78085e38			1.37717
$426$	9.73256e37	+	2.36033e38i	0.727425	+	1.76414i
$427$			1.57513e37i			0.113792i
$428$	−3.09530e37	−	3.11518e37i	−0.216156	−	0.217545i
$429$			2.78478e36i			0.0188001i
$430$	−2.44008e37	+	1.00614e37i	−0.159261	+	0.0656699i
$431$	−1.72652e38			−1.08956			−0.544780	−	0.838579i	$-0.683387\pi$
$431$	−1.72652e38			−1.08956			−0.544780	+	0.838579i	$0.683387\pi$
$432$	−2.07245e38	−	1.32662e36i	−1.26465	−	0.00809532i
$433$	−1.30681e37			−0.0771149			−0.0385575	−	0.999256i	$-0.512276\pi$
$433$	−1.30681e37			−0.0771149			−0.0385575	+	0.999256i	$0.512276\pi$
$434$	1.94412e37	−	8.01637e36i	0.110948	−	0.0457485i
$435$		−	1.10237e38i		−	0.608461i
$436$	−1.45337e38	−	1.46270e38i	−0.775928	−	0.780911i
$437$			2.64914e38i			1.36812i
$438$	−6.15659e37	−	1.49309e38i	−0.307585	−	0.745951i
$439$	−1.01815e38			−0.492125			−0.246062	−	0.969254i	$-0.579137\pi$
$439$	−1.01815e38			−0.492125			−0.246062	+	0.969254i	$0.579137\pi$
$440$	6.59036e36	−	1.56970e37i	0.0308209	−	0.0734094i
$441$	3.87597e38			1.75397
$442$	−4.29075e36	−	1.04058e37i	−0.0187893	−	0.0455674i
$443$			2.22084e38i			0.941159i	0.882358	+	0.470580i	$0.155955\pi$
$443$			2.22084e38i			0.941159i	−0.882358	+	0.470580i	$0.844045\pi$
$444$	4.40288e37	−	4.37479e37i	0.180586	−	0.179434i
$445$		−	5.58752e37i		−	0.221819i
$446$	1.88556e38	−	7.77491e37i	0.724577	−	0.298772i
$447$	1.19872e38			0.445921
$448$	1.23718e37	+	1.26117e37i	0.0445555	+	0.0454194i
$449$	−2.50697e38			−0.874132			−0.437066	−	0.899429i	$-0.643982\pi$
$449$	−2.50697e38			−0.874132			−0.437066	+	0.899429i	$0.643982\pi$
$450$	4.55012e38	−	1.87620e38i	1.53618	−	0.633427i
$451$		−	1.19735e38i		−	0.391436i
$452$	2.40346e38	−	2.38812e38i	0.760904	−	0.756049i
$453$			5.36085e38i			1.64365i
$454$	−1.82505e38	−	4.42609e38i	−0.541959	−	1.31435i
$455$	−1.77508e35			−0.000510568
$456$	−2.71630e38	+	6.46971e38i	−0.756812	+	1.80258i
$457$	−3.49852e38			−0.944276			−0.472138	−	0.881525i	$-0.656518\pi$
$457$	−3.49852e38			−0.944276			−0.472138	+	0.881525i	$0.656518\pi$
$458$	1.48602e38	+	3.60386e38i	0.388574	+	0.942364i
$459$		−	7.28609e38i		−	1.84591i
$460$	7.93415e37	+	7.98510e37i	0.194765	+	0.196016i
$461$		−	6.75286e37i		−	0.160629i	−0.996770	−	0.0803145i	$-0.974408\pi$
$461$		−	6.75286e37i		−	0.160629i	0.996770	−	0.0803145i	$-0.0255925\pi$
$462$	1.42062e37	−	5.85779e36i	0.0327468	−	0.0135028i
$463$	−7.80167e38			−1.74286			−0.871431	−	0.490517i	$-0.836808\pi$
$463$	−7.80167e38			−1.74286			−0.871431	+	0.490517i	$0.836808\pi$
$464$	−7.11685e38	−	4.55566e36i	−1.54091	−	0.00986371i
$465$	3.54900e38			0.744798
$466$	3.88606e38	−	1.60238e38i	0.790521	−	0.325964i
$467$		−	2.65997e38i		−	0.524544i	−0.964994	−	0.262272i	$-0.915528\pi$
$467$		−	2.65997e38i		−	0.524544i	0.964994	−	0.262272i	$-0.0844717\pi$
$468$	−2.19260e37	−	2.20668e37i	−0.0419174	−	0.0421865i
$469$		−	4.41762e37i		−	0.0818808i
$470$	−9.61797e36	−	2.33253e37i	−0.0172848	−	0.0419188i
$471$	1.17436e38			0.204644
$472$	−2.48264e38	−	1.04233e38i	−0.419522	−	0.176136i
$473$	1.48214e38			0.242885
$474$	2.42610e38	+	5.88373e38i	0.385587	+	0.935118i
$475$		−	7.20148e38i		−	1.11011i
$476$	−4.40585e37	+	4.37774e37i	−0.0658762	+	0.0654559i
$477$		−	1.01815e39i		−	1.47671i
$478$	−7.05358e38	+	2.90847e38i	−0.992442	+	0.409224i
$479$	−1.68529e38			−0.230043			−0.115022	−	0.993363i	$-0.536694\pi$
$479$	−1.68529e38			−0.230043			−0.115022	+	0.993363i	$0.536694\pi$
$480$	1.11892e38	+	2.76365e38i	0.148184	+	0.366004i
$481$	4.02621e36			0.00517360
$482$	−1.87154e38	+	7.71710e37i	−0.233355	+	0.0962215i
$483$			1.01605e38i			0.122937i
$484$	5.36312e38	−	5.32890e38i	0.629738	−	0.625719i
$485$			8.83041e36i			0.0100630i
$486$	2.40954e38	+	5.84357e38i	0.266506	+	0.646327i
$487$	7.84258e38			0.841955			0.420977	−	0.907071i	$-0.361687\pi$
$487$	7.84258e38			0.841955			0.420977	+	0.907071i	$0.361687\pi$
$488$	1.58241e39	+	6.64374e38i	1.64904	+	0.692349i
$489$	−1.45649e39			−1.47343
$490$	−9.18641e37	−	2.22787e38i	−0.0902200	−	0.218800i
$491$			1.22291e39i			1.16604i	0.812459	+	0.583019i	$0.198129\pi$
$491$			1.22291e39i			1.16604i	−0.812459	+	0.583019i	$0.801871\pi$
$492$	1.47804e39	+	1.48753e39i	1.36834	+	1.37712i
$493$		−	2.50206e39i		−	2.24914i
$494$	−4.20797e37	+	1.73511e37i	−0.0367309	+	0.0151456i
$495$	1.65411e38			0.140213
$496$	1.46666e37	−	2.29122e39i	0.0120739	−	1.88618i
$497$	9.13869e37			0.0730661
$498$	−4.05664e38	+	1.67271e38i	−0.315022	+	0.129896i
$499$			2.11284e39i			1.59371i	0.604171	+	0.796855i	$0.293505\pi$
$499$			2.11284e39i			1.59371i	−0.604171	+	0.796855i	$0.706495\pi$
$500$	−4.44276e38	−	4.47129e38i	−0.325528	−	0.327618i
$501$			4.19710e39i			2.98746i
$502$	3.85511e38	+	9.34934e38i	0.266583	+	0.646513i
$503$	−7.58018e38			−0.509265			−0.254632	−	0.967038i	$-0.581954\pi$
$503$	−7.58018e38			−0.509265			−0.254632	+	0.967038i	$0.581954\pi$
$504$	−6.64495e37	+	1.58270e38i	−0.0433759	+	0.103313i
$505$	6.12905e38			0.388748
$506$	−2.40966e38	−	5.84386e38i	−0.148516	−	0.360178i
$507$			2.77115e39i			1.65976i
$508$	−1.54697e38	+	1.53710e38i	−0.0900447	+	0.0894701i
$509$		−	2.72877e39i		−	1.54369i	−0.635812	−	0.771844i	$-0.719334\pi$
$509$		−	2.72877e39i		−	1.54369i	0.635812	−	0.771844i	$-0.280666\pi$
$510$	−9.69055e38	+	3.99580e38i	−0.532821	+	0.219703i
$511$	−5.78092e37			−0.0308954
$512$	1.78883e39	−	7.10949e38i	0.929295	−	0.369338i
$513$	−2.94638e39			−1.48795
$514$	−1.31684e39	+	5.42986e38i	−0.646499	+	0.266577i
$515$		−	7.17375e38i		−	0.342406i
$516$	−1.84134e39	+	1.82959e39i	−0.854502	+	0.849049i
$517$			1.41681e38i			0.0639292i
$518$	−8.46913e36	−	2.05392e37i	−0.00371584	−	0.00901160i
$519$	2.59707e39			1.10804
$520$	−7.48712e36	+	1.78329e37i	−0.00310646	+	0.00739900i
$521$	2.15784e39			0.870706			0.435353	−	0.900260i	$-0.356623\pi$
$521$	2.15784e39			0.870706			0.435353	+	0.900260i	$0.356623\pi$
$522$	−2.63602e39	−	6.39283e39i	−1.03449	−	2.50883i
$523$		−	3.92591e39i		−	1.49853i	−0.662270	−	0.749265i	$-0.730407\pi$
$523$		−	3.92591e39i		−	1.49853i	0.662270	−	0.749265i	$-0.269593\pi$
$524$	1.22980e39	+	1.23770e39i	0.456594	+	0.459527i
$525$		−	2.76206e38i		−	0.0997524i
$526$	−1.05821e38	+	4.36343e37i	−0.0371774	+	0.0153297i
$527$	8.05522e39			2.75311
$528$	1.07173e37	−	1.67426e39i	0.00356365	−	0.556713i
$529$	1.08857e39			0.352166
$530$	−5.85222e38	+	2.41311e38i	−0.184213	+	0.0759585i
$531$		−	2.61615e39i		−	0.801293i
$532$	1.77029e38	+	1.78166e38i	0.0527625	+	0.0531013i
$533$			1.36027e38i			0.0394532i
$534$	−2.09479e39	−	5.08024e39i	−0.591277	−	1.43396i
$535$	−2.65286e38			−0.0728759
$536$	−4.43803e39	−	1.86331e39i	−1.18659	−	0.498189i
$537$	−7.37562e39			−1.91943
$538$	−1.19645e39	−	2.90161e39i	−0.303076	−	0.735014i
$539$			1.35324e39i			0.333686i
$540$	−8.88107e38	+	8.82441e38i	−0.213185	+	0.211824i
$541$		−	1.73611e39i		−	0.405711i	−0.979209	−	0.202856i	$-0.934978\pi$
$541$		−	1.73611e39i		−	0.405711i	0.979209	−	0.202856i	$-0.0650222\pi$
$542$	−3.48326e39	+	1.43629e39i	−0.792494	+	0.326777i
$543$	4.19202e39			0.928595
$544$	2.53963e39	+	6.27269e39i	0.547754	+	1.35291i
$545$	−1.24562e39			−0.261600
$546$	−1.61393e37	+	6.65486e36i	−0.00330058	+	0.00136096i
$547$			2.96690e39i			0.590863i	0.955364	+	0.295432i	$0.0954634\pi$
$547$			2.96690e39i			0.590863i	−0.955364	+	0.295432i	$0.904537\pi$
$548$	−1.67061e38	+	1.65995e38i	−0.0324008	+	0.0321941i
$549$			1.66751e40i			3.14970i
$550$	6.55047e38	+	1.58861e39i	0.120507	+	0.292252i
$551$	−1.01179e40			−1.81298
$552$	1.02075e40	+	4.28560e39i	1.78156	+	0.747989i
$553$	2.27806e38			0.0387302
$554$	2.59674e39	+	6.29757e39i	0.430068	+	1.04299i
$555$		−	3.74945e38i		−	0.0604950i
$556$	−7.39030e39	−	7.43775e39i	−1.16166	−	1.16912i
$557$		−	7.94415e39i		−	1.21660i	−0.793708	−	0.608299i	$-0.791852\pi$
$557$		−	7.94415e39i		−	1.21660i	0.793708	−	0.608299i	$-0.208148\pi$
$558$	2.05813e40	−	8.48650e39i	3.07098	−	1.26629i
$559$	−1.68381e38			−0.0244806
$560$	1.06721e38	+	6.83147e35i	0.0151190	+	9.67804e-5i
$561$	5.88617e39			0.812590
$562$	−1.11486e40	+	4.59702e39i	−1.49984	+	0.618443i
$563$			6.98747e39i			0.916112i	0.888923	+	0.458056i	$0.151454\pi$
$563$			6.98747e39i			0.916112i	−0.888923	+	0.458056i	$0.848546\pi$
$564$	−1.74895e39	−	1.76018e39i	−0.223476	−	0.224911i
$565$		−	2.04676e39i		−	0.254897i
$566$	3.91099e39	+	9.48486e39i	0.474732	+	1.15131i
$567$	−1.83028e38			−0.0216553
$568$	3.85460e39	−	9.18092e39i	0.444558	−	1.05885i
$569$	8.37978e39			0.942117			0.471058	−	0.882102i	$-0.343872\pi$
$569$	8.37978e39			0.942117			0.471058	+	0.882102i	$0.343872\pi$
$570$	1.61584e39	+	3.91871e39i	0.177098	+	0.429495i
$571$			5.14234e39i			0.549462i	0.961521	+	0.274731i	$0.0885888\pi$
$571$			5.14234e39i			0.549462i	−0.961521	+	0.274731i	$0.911411\pi$
$572$	7.70430e37	−	7.65514e37i	0.00802584	−	0.00797463i
$573$		−	1.49410e40i		−	1.51753i
$574$	6.93926e38	−	2.86133e38i	0.0687212	−	0.0283365i
$575$	−1.13620e40			−1.09716
$576$	1.30973e40	+	1.33513e40i	1.23327	+	1.25718i
$577$	−8.17029e39			−0.750219			−0.375110	−	0.926980i	$-0.622395\pi$
$577$	−8.17029e39			−0.750219			−0.375110	+	0.926980i	$0.622395\pi$
$578$	−1.16706e40	+	4.81224e39i	−1.04505	+	0.430917i
$579$		−	2.11212e40i		−	1.84451i
$580$	−3.04978e39	+	3.03032e39i	−0.259754	+	0.258097i
$581$			1.57065e38i			0.0130474i
$582$	3.31056e38	+	8.02871e38i	0.0268236	+	0.0650523i
$583$	3.55472e39			0.280939
$584$	−2.43833e39	+	5.80763e39i	−0.187978	+	0.447726i
$585$	−1.87919e38			−0.0141322
$586$	9.21398e39	+	2.23456e40i	0.675977	+	1.63937i
$587$			8.92282e39i			0.638631i	0.947649	+	0.319315i	$0.103453\pi$
$587$			8.92282e39i			0.638631i	−0.947649	+	0.319315i	$0.896547\pi$
$588$	−1.67048e40	−	1.68121e40i	−1.16646	−	1.17395i
$589$		−	3.25741e40i		−	2.21922i
$590$	−1.50374e39	+	6.20051e38i	−0.0999580	+	0.0412167i
$591$	−3.26208e40			−2.11581
$592$	−2.42063e39	−	1.54950e37i	−0.153202	−	0.000980680i
$593$	1.10815e40			0.684392			0.342196	−	0.939629i	$-0.388829\pi$
$593$	1.10815e40			0.684392			0.342196	+	0.939629i	$0.388829\pi$
$594$	6.49957e39	−	2.68003e39i	0.391725	−	0.161524i
$595$			3.75198e38i			0.0220681i
$596$	−3.29517e39	−	3.31633e39i	−0.189151	−	0.190365i
$597$			4.20479e40i			2.35568i
$598$	2.73754e38	+	6.63904e38i	0.0149690	+	0.0363026i
$599$	8.92959e39			0.476588			0.238294	−	0.971193i	$-0.423412\pi$
$599$	8.92959e39			0.476588			0.238294	+	0.971193i	$0.423412\pi$
$600$	−2.77483e40	−	1.16501e40i	−1.44558	−	0.606926i
$601$	3.42402e40			1.74123			0.870614	−	0.491966i	$-0.163722\pi$
$601$	3.42402e40			1.74123			0.870614	+	0.491966i	$0.163722\pi$
$602$	3.54189e38	+	8.58974e38i	0.0175827	+	0.0426414i
$603$		−	4.67669e40i		−	2.26641i
$604$	1.48312e40	−	1.47365e40i	0.701681	−	0.697204i
$605$		−	4.56718e39i		−	0.210958i
$606$	5.57260e40	−	2.29781e40i	2.51307	−	1.03624i
$607$	−2.59227e40			−1.14142			−0.570709	−	0.821152i	$-0.693332\pi$
$607$	−2.59227e40			−1.14142			−0.570709	+	0.821152i	$0.693332\pi$
$608$	2.53658e40	−	1.02699e40i	1.09055	−	0.441532i
$609$	−3.88064e39			−0.162912
$610$	9.58468e39	−	3.95214e39i	0.392912	−	0.162013i
$611$		−	1.60960e38i		−	0.00644348i
$612$	−4.66423e40	+	4.63447e40i	−1.82341	+	1.81178i
$613$			3.58625e40i			1.36919i	0.728923	+	0.684595i	$0.240021\pi$
$613$			3.58625e40i			1.36919i	−0.728923	+	0.684595i	$0.759979\pi$
$614$	4.61163e39	+	1.11841e40i	0.171954	+	0.417021i
$615$	1.26677e40			0.461326
$616$	−5.52576e38	−	2.31999e38i	−0.0196550	−	0.00825212i
$617$	−5.48134e40			−1.90437			−0.952186	−	0.305518i	$-0.901170\pi$
$617$	−5.48134e40			−1.90437			−0.952186	+	0.305518i	$0.901170\pi$
$618$	−2.68947e40	−	6.52246e40i	−0.912712	−	2.21349i
$619$			3.31033e40i			1.09738i	0.836026	+	0.548690i	$0.184873\pi$
$619$			3.31033e40i			1.09738i	−0.836026	+	0.548690i	$0.815127\pi$
$620$	−9.75592e39	−	9.81857e39i	−0.315928	−	0.317957i
$621$			4.64860e40i			1.47060i
$622$	−1.80399e40	+	7.43856e39i	−0.557536	+	0.229894i
$623$	−1.96696e39			−0.0593908
$624$	−1.21757e37	+	1.90208e39i	−0.000359183	+	0.0561116i
$625$	2.89276e40			0.833781
$626$	−9.03077e39	+	3.72375e39i	−0.254330	+	0.104870i
$627$		−	2.38028e40i		−	0.655011i
$628$	−3.22823e39	−	3.24896e39i	−0.0868059	−	0.0873633i
$629$		−	8.51017e39i		−	0.223617i
$630$	3.95286e38	+	9.58641e38i	0.0101502	+	0.0246160i
$631$	1.64765e40			0.413465			0.206733	−	0.978397i	$-0.433717\pi$
$631$	1.64765e40			0.413465			0.206733	+	0.978397i	$0.433717\pi$
$632$	9.60860e39	−	2.28858e40i	0.235647	−	0.561267i
$633$	4.81351e40			1.15374
$634$	−6.35533e39	−	1.54128e40i	−0.148883	−	0.361068i
$635$			1.31739e39i			0.0301643i
$636$	−4.41623e40	+	4.38805e40i	−0.988378	+	0.982072i
$637$		−	1.53738e39i		−	0.0336325i
$638$	2.23197e40	−	9.20329e39i	0.477296	−	0.196808i
$639$	9.67464e40			2.02242
$640$	4.57002e39	−	1.06926e40i	0.0933917	−	0.218512i
$641$	4.99522e40			0.997960			0.498980	−	0.866613i	$-0.333708\pi$
$641$	4.99522e40			0.997960			0.498980	+	0.866613i	$0.333708\pi$
$642$	−2.41201e40	+	9.94567e39i	−0.471108	+	0.194257i
$643$			6.77502e40i			1.29375i	0.762594	+	0.646877i	$0.223925\pi$
$643$			6.77502e40i			1.29375i	−0.762594	+	0.646877i	$0.776075\pi$
$644$	2.81098e39	−	2.79304e39i	0.0524822	−	0.0521474i
$645$			1.56807e40i			0.286252i
$646$	3.66749e40	+	8.89434e40i	0.654633	+	1.58760i
$647$	−5.39524e40			−0.941671			−0.470835	−	0.882221i	$-0.656047\pi$
$647$	−5.39524e40			−0.941671			−0.470835	+	0.882221i	$0.656047\pi$
$648$	−7.71995e39	+	1.83874e40i	−0.131758	+	0.313822i
$649$	9.13391e39			0.152443
$650$	−7.44181e38	−	1.80477e39i	−0.0121460	−	0.0294564i
$651$		−	1.24935e40i		−	0.199416i
$652$	4.00377e40	+	4.02948e40i	0.624999	+	0.629012i
$653$		−	8.85444e40i		−	1.35182i	−0.736982	−	0.675912i	$-0.763750\pi$
$653$		−	8.85444e40i		−	1.35182i	0.736982	−	0.675912i	$-0.236250\pi$
$654$	−1.13253e41	+	4.66989e40i	−1.69112	+	0.697316i
$655$	1.05401e40			0.153938
$656$	5.23506e38	−	8.17821e40i	0.00747853	−	1.16829i
$657$	−6.11994e40			−0.855164
$658$	−8.21116e38	+	3.38579e38i	−0.0112235	+	0.00462791i
$659$			3.18393e40i			0.425720i	0.977083	+	0.212860i	$0.0682779\pi$
$659$			3.18393e40i			0.425720i	−0.977083	+	0.212860i	$0.931722\pi$
$660$	−7.12893e39	−	7.17471e39i	−0.0932475	−	0.0938463i
$661$			4.63696e40i			0.593352i	0.954978	+	0.296676i	$0.0958781\pi$
$661$			4.63696e40i			0.593352i	−0.954978	+	0.296676i	$0.904122\pi$
$662$	−1.07951e40	−	2.61800e40i	−0.135140	−	0.327740i
$663$	−6.68712e39			−0.0819017
$664$	1.57790e40	+	6.62482e39i	0.189079	+	0.0793848i
$665$	1.51724e39			0.0177886
$666$	−8.96581e39	−	2.17437e40i	−0.102852	−	0.249435i
$667$			1.59634e41i			1.79185i
$668$	1.16116e41	−	1.15375e41i	1.27536	−	1.26722i
$669$		−	1.21172e41i		−	1.30233i
$670$	−2.68812e40	+	1.10842e40i	−0.282725	+	0.116579i
$671$	−5.82186e40			−0.599219
$672$	9.72882e39	−	3.93891e39i	0.0979954	−	0.0396754i
$673$	−1.68526e41			−1.66131			−0.830653	−	0.556791i	$-0.812033\pi$
$673$	−1.68526e41			−1.66131			−0.830653	+	0.556791i	$0.812033\pi$
$674$	6.45435e39	−	2.66139e39i	0.0622707	−	0.0256767i
$675$		−	1.26369e41i		−	1.19326i
$676$	7.66659e40	−	7.61767e40i	0.708557	−	0.704036i
$677$		−	1.84000e41i		−	1.66449i	−0.554407	−	0.832245i	$-0.687055\pi$
$677$		−	1.84000e41i		−	1.66449i	0.554407	−	0.832245i	$-0.312945\pi$
$678$	−7.67341e40	−	1.86094e41i	−0.679450	−	1.64779i
$679$	3.10855e38			0.00269430
$680$	3.76932e40	+	1.58255e40i	0.319804	+	0.134269i
$681$	−2.84434e41			−2.36237
$682$	2.96294e40	+	7.18567e40i	0.240907	+	0.584244i
$683$		−	1.19209e41i		−	0.948875i	−0.880289	−	0.474438i	$-0.842651\pi$
$683$		−	1.19209e41i		−	0.948875i	0.880289	−	0.474438i	$-0.157349\pi$
$684$	1.87411e41	+	1.88614e41i	1.46043	+	1.46981i
$685$			1.42267e39i			0.0108540i
$686$	−1.57173e40	+	6.48089e39i	−0.117403	+	0.0484100i
$687$	2.31595e41			1.69378
$688$	1.01234e41	+	6.48021e38i	0.724925	+	0.00464041i
$689$	−4.03842e39			−0.0283160
$690$	6.18267e40	−	2.54936e40i	0.424487	−	0.175033i
$691$			1.20596e41i			0.810778i	0.914144	+	0.405389i	$0.132864\pi$
$691$			1.20596e41i			0.810778i	−0.914144	+	0.405389i	$0.867136\pi$
$692$	−7.13913e40	−	7.18498e40i	−0.470010	−	0.473028i
$693$		−	5.82292e39i		−	0.0375413i
$694$	−2.08239e40	−	5.05017e40i	−0.131477	−	0.318855i
$695$	−6.33392e40			−0.391645
$696$	−1.63682e41	+	3.89858e41i	−0.991210	+	2.36087i
$697$	2.87520e41			1.70527
$698$	6.30193e40	+	1.52833e41i	0.366075	+	0.887798i
$699$		−	2.49730e41i		−	1.42086i
$700$	−7.64143e39	+	7.59268e39i	−0.0425847	+	0.0423129i
$701$			2.28136e41i			1.24533i	0.782490	+	0.622663i	$0.213949\pi$
$701$			2.28136e41i			1.24533i	−0.782490	+	0.622663i	$0.786051\pi$
$702$	−7.38398e39	+	3.04471e39i	−0.0394823	+	0.0162801i
$703$	−3.44138e40			−0.180252
$704$	−4.66142e40	+	4.57275e40i	−0.239174	+	0.234625i
$705$	−1.49896e40			−0.0753437
$706$	−8.23143e40	+	3.39415e40i	−0.405329	+	0.167133i
$707$		−	2.15760e40i		−	0.104085i
$708$	−1.13476e41	+	1.12751e41i	−0.536315	+	0.532893i
$709$		−	6.78082e40i		−	0.313987i	−0.987600	−	0.156994i	$-0.949820\pi$
$709$		−	6.78082e40i		−	0.313987i	0.987600	−	0.156994i	$-0.0501802\pi$
$710$	−2.29298e40	−	5.56089e40i	−0.104029	−	0.252289i
$711$	2.41165e41			1.07203
$712$	−8.29644e40	+	1.97605e41i	−0.361353	+	0.860674i
$713$	−5.13931e41			−2.19334
$714$	1.40663e40	+	3.41134e40i	0.0588243	+	0.142660i
$715$		−	6.56091e38i		−	0.00268860i
$716$	2.02750e41	+	2.04052e41i	0.814182	+	0.819410i
$717$			4.53285e41i			1.78379i
$718$	3.51573e40	−	1.44968e40i	0.135585	−	0.0559070i
$719$	1.40163e41			0.529744			0.264872	−	0.964284i	$-0.414670\pi$
$719$	1.40163e41			0.529744			0.264872	+	0.964284i	$0.414670\pi$
$720$	1.12980e41	+	7.23211e38i	0.418485	+	0.00267882i
$721$	−2.52536e40			−0.0916773
$722$	9.98420e40	−	4.11689e40i	0.355242	−	0.146480i
$723$			1.20271e41i			0.419426i
$724$	−1.15235e41	−	1.15975e41i	−0.393891	−	0.396421i
$725$		−	4.33953e41i		−	1.45392i
$726$	−1.71226e41	−	4.15253e41i	−0.562325	−	1.36374i
$727$	1.03870e41			0.334381			0.167191	−	0.985925i	$-0.446530\pi$
$727$	1.03870e41			0.334381			0.167191	+	0.985925i	$0.446530\pi$
$728$	6.27767e38	+	2.63567e38i	0.00198104	+	0.000831738i
$729$	4.85549e41			1.50205
$730$	1.45048e40	+	3.51769e40i	0.0439877	+	0.106678i
$731$			3.55906e41i			1.05812i
$732$	7.23282e41	−	7.18667e41i	2.10813	−	2.09468i
$733$			2.98404e41i			0.852702i	0.904558	+	0.426351i	$0.140201\pi$
$733$			2.98404e41i			0.852702i	−0.904558	+	0.426351i	$0.859799\pi$
$734$	−4.95832e41	+	2.04452e41i	−1.38913	+	0.572793i
$735$	−1.43170e41			−0.393265
$736$	−1.62031e41	−	4.00204e41i	−0.436384	−	1.07784i
$737$	1.63280e41			0.431176
$738$	7.34622e41	−	3.02914e41i	1.90216	−	0.784336i
$739$		−	6.69506e40i		−	0.169985i	−0.996382	−	0.0849924i	$-0.972913\pi$
$739$		−	6.69506e40i		−	0.169985i	0.996382	−	0.0849924i	$-0.0270866\pi$
$740$	−1.03731e40	+	1.03069e40i	−0.0258255	+	0.0256608i
$741$			2.70417e40i			0.0660191i
$742$	8.49480e39	+	2.06015e40i	0.0203375	+	0.0493221i
$743$	−4.55132e41			−1.06856			−0.534280	−	0.845307i	$-0.679417\pi$
$743$	−4.55132e41			−1.06856			−0.534280	+	0.845307i	$0.679417\pi$
$744$	−1.25512e42	−	5.26962e41i	−2.88987	−	1.21331i
$745$	−2.82416e40			−0.0637710
$746$	2.09894e40	+	5.09031e40i	0.0464822	+	0.112728i
$747$			1.66276e41i			0.361144i
$748$	−1.61806e41	−	1.62845e41i	−0.344684	−	0.346898i
$749$			9.33879e39i			0.0195121i
$750$	−3.46202e41	+	1.42753e41i	−0.709481	+	0.292547i
$751$	−4.46363e41			−0.897240			−0.448620	−	0.893723i	$-0.648084\pi$
$751$	−4.46363e41			−0.897240			−0.448620	+	0.893723i	$0.648084\pi$
$752$	−6.19460e38	+	9.67720e40i	−0.00122139	+	0.190806i
$753$	6.00817e41			1.16202
$754$	−2.53567e40	+	1.04556e40i	−0.0481071	+	0.0198365i
$755$		−	1.26301e41i		−	0.235058i
$756$	3.10644e40	+	3.12638e40i	0.0567148	+	0.0570790i
$757$		−	6.39830e41i		−	1.14597i	−0.819565	−	0.572986i	$-0.805785\pi$
$757$		−	6.39830e41i		−	1.14597i	0.819565	−	0.572986i	$-0.194215\pi$
$758$	2.86704e41	+	6.95309e41i	0.503767	+	1.22173i
$759$	−3.75544e41			−0.647374
$760$	6.39957e40	−	1.52425e41i	0.108232	−	0.257787i
$761$	7.31055e41			1.21303			0.606516	−	0.795071i	$-0.292567\pi$
$761$	7.31055e41			1.21303			0.606516	+	0.795071i	$0.292567\pi$
$762$	4.93893e40	+	1.19778e41i	0.0804055	+	0.194998i
$763$			4.38494e40i			0.0700418i
$764$	−4.13352e41	+	4.10715e41i	−0.647838	+	0.643705i
$765$			3.97202e41i			0.610830i
$766$	−6.04203e41	+	2.49137e41i	−0.911729	+	0.375942i
$767$	−1.03768e40			−0.0153649
$768$	1.46404e40	−	1.14352e42i	0.0212724	−	1.66152i
$769$	4.14817e41			0.591459			0.295729	−	0.955272i	$-0.404437\pi$
$769$	4.14817e41			0.591459			0.295729	+	0.955272i	$0.404437\pi$
$770$	−3.34696e39	+	1.38009e39i	−0.00468312	+	0.00193104i
$771$			8.46242e41i			1.16200i
$772$	−5.84334e41	+	5.80605e41i	−0.787427	+	0.782402i
$773$		−	4.54331e41i		−	0.600855i	−0.953805	−	0.300428i	$-0.902871\pi$
$773$		−	4.54331e41i		−	0.600855i	0.953805	−	0.300428i	$-0.0971294\pi$
$774$	3.74961e41	+	9.09350e41i	0.486679	+	1.18029i
$775$	1.39708e42			1.77970
$776$	1.31115e40	−	3.12291e40i	0.0163930	−	0.0390450i
$777$	−1.31991e40			−0.0161972
$778$	−4.14403e41	−	1.00500e42i	−0.499136	−	1.21050i
$779$		−	1.16269e42i		−	1.37458i
$780$	8.09897e39	+	8.15098e39i	0.00939849	+	0.00945885i
$781$			3.37776e41i			0.384759i
$782$	1.40329e42	−	5.78632e41i	1.56909	−	0.647000i
$783$	−1.77546e42			−1.94879
$784$	−5.91665e39	+	9.24299e41i	−0.00637519	+	0.995931i
$785$	−2.76678e40			−0.0292661
$786$	9.58319e41	−	3.95153e41i	0.995138	−	0.410335i
$787$		−	1.60400e42i		−	1.63520i	−0.575785	−	0.817601i	$-0.695304\pi$
$787$		−	1.60400e42i		−	1.63520i	0.575785	−	0.817601i	$-0.304696\pi$
$788$	8.96719e41	+	9.02477e41i	0.897483	+	0.903246i
$789$			6.80039e40i			0.0668217i
$790$	−5.71584e40	−	1.38620e41i	−0.0551426	−	0.133731i
$791$	−7.20518e40			−0.0682474
$792$	−5.84983e41	−	2.45605e41i	−0.544036	−	0.228413i
$793$	6.61406e40			0.0603958
$794$	6.20715e41	+	1.50535e42i	0.556538	+	1.34971i
$795$			3.76082e41i			0.331100i
$796$	1.16328e42	−	1.15586e42i	1.00565	−	0.999232i
$797$			2.29358e42i			1.94701i	0.228664	+	0.973505i	$0.426564\pi$
$797$			2.29358e42i			1.94701i	−0.228664	+	0.973505i	$0.573436\pi$
$798$	1.37949e41	−	5.68821e40i	0.114995	−	0.0474169i
$799$	−3.40220e41			−0.278504
$800$	4.40469e41	+	1.08793e42i	0.354087	+	0.874570i
$801$	−2.08232e42			−1.64390
$802$	1.14789e42	−	4.73320e41i	0.889961	−	0.366967i
$803$		−	2.13669e41i		−	0.162692i
$804$	−2.02852e42	+	2.01558e42i	−1.51693	+	1.50725i
$805$		−	2.39380e40i		−	0.0175812i
$806$	−3.36611e40	−	8.16344e40i	−0.0242812	−	0.0588864i
$807$	−1.86466e42			−1.32109
$808$	−2.16757e42	−	9.10051e41i	−1.50837	−	0.633288i
$809$	−4.57189e41			−0.312495			−0.156247	−	0.987718i	$-0.549940\pi$
$809$	−4.57189e41			−0.312495			−0.156247	+	0.987718i	$0.549940\pi$
$810$	4.59234e40	+	1.11373e41i	0.0308320	+	0.0747733i
$811$		−	4.43371e41i		−	0.292391i	−0.989256	−	0.146196i	$-0.953297\pi$
$811$		−	4.43371e41i		−	0.292391i	0.989256	−	0.146196i	$-0.0467029\pi$
$812$	1.06676e41	+	1.07361e41i	0.0691040	+	0.0695477i
$813$			2.23845e42i			1.42441i
$814$	7.59152e40	−	3.13029e40i	0.0474542	−	0.0195673i
$815$	3.43147e41			0.210715
$816$	4.02041e42	+	2.57356e40i	2.42529	+	0.0155248i
$817$	1.43923e42			0.852924
$818$	5.17117e41	−	2.13228e41i	0.301069	−	0.124143i
$819$			6.61525e39i			0.00378382i
$820$	−3.48224e41	−	3.50461e41i	−0.195685	−	0.196942i
$821$		−	2.96133e42i		−	1.63497i	−0.575947	−	0.817487i	$-0.695367\pi$
$821$		−	2.96133e42i		−	1.63497i	0.575947	−	0.817487i	$-0.304633\pi$
$822$	5.33366e40	+	1.29351e41i	0.0289324	+	0.0701663i
$823$	7.66432e41			0.408485			0.204242	−	0.978920i	$-0.434527\pi$
$823$	7.66432e41			0.408485			0.204242	+	0.978920i	$0.434527\pi$
$824$	−1.06517e42	+	2.53703e42i	−0.557795	+	1.32856i
$825$	1.02089e42			0.525286
$826$	2.18275e40	+	5.29357e40i	0.0110355	+	0.0267632i
$827$		−	1.81453e42i		−	0.901434i	−0.892667	−	0.450717i	$-0.851168\pi$
$827$		−	1.81453e42i		−	0.901434i	0.892667	−	0.450717i	$-0.148832\pi$
$828$	2.97583e42	−	2.95684e42i	1.45267	−	1.44341i
$829$		−	2.10567e42i		−	1.01007i	−0.863100	−	0.505034i	$-0.831480\pi$
$829$		−	2.10567e42i		−	1.01007i	0.863100	−	0.505034i	$-0.168520\pi$
$830$	9.55738e40	−	3.94089e40i	0.0450512	−	0.0185764i
$831$	4.04701e42			1.87465
$832$	5.29571e40	−	5.19498e40i	0.0241066	−	0.0236481i
$833$	−3.24954e42			−1.45368
$834$	−5.75888e42	+	2.37461e42i	−2.53180	+	1.04396i
$835$		−	9.88830e41i		−	0.427236i
$836$	−6.58521e41	+	6.54319e41i	−0.279627	+	0.277842i
$837$		−	5.71597e42i		−	2.38545i
$838$	−1.46039e42	−	3.54171e42i	−0.599005	−	1.45270i
$839$	−6.95115e41			−0.280226			−0.140113	−	0.990136i	$-0.544747\pi$
$839$	−6.95115e41			−0.280226			−0.140113	+	0.990136i	$0.544747\pi$
$840$	2.45450e40	−	5.84614e40i	0.00972552	−	0.0231643i
$841$	−3.52927e42			−1.37450
$842$	−6.04294e40	−	1.46552e41i	−0.0231325	−	0.0561006i
$843$			7.16444e42i			2.69577i
$844$	−1.32319e42	−	1.33169e42i	−0.489393	−	0.492536i
$845$		−	6.52880e41i		−	0.237362i
$846$	−8.69272e41	+	3.58435e41i	−0.310660	+	0.128097i
$847$	−1.60777e41			−0.0564827
$848$	2.42797e42	+	1.55420e40i	0.838500	+	0.00536743i
$849$	6.09526e42			2.06934
$850$	−3.81474e42	+	1.57297e42i	−1.27318	+	0.524983i
$851$			5.42958e41i			0.178151i
$852$	−4.16960e42	−	4.19638e42i	−1.34500	−	1.35363i
$853$			3.94730e42i			1.25181i	0.779898	+	0.625907i	$0.215271\pi$
$853$			3.94730e42i			1.25181i	−0.779898	+	0.625907i	$0.784729\pi$
$854$	−1.39126e41	−	3.37407e41i	−0.0433781	−	0.105200i
$855$	1.60622e42			0.492376
$856$	9.38195e41	+	3.93901e41i	0.282764	+	0.118718i
$857$	−5.52862e41			−0.163831			−0.0819153	−	0.996639i	$-0.526104\pi$
$857$	−5.52862e41			−0.163831			−0.0819153	+	0.996639i	$0.526104\pi$
$858$	−2.45971e40	−	5.96526e40i	−0.00716669	−	0.0173805i
$859$		−	6.40845e41i		−	0.183591i	−0.995778	−	0.0917957i	$-0.970739\pi$
$859$		−	6.40845e41i		−	0.183591i	0.995778	−	0.0917957i	$-0.0292607\pi$
$860$	4.33817e41	−	4.31049e41i	0.122202	−	0.121422i
$861$		−	4.45938e41i		−	0.123518i
$862$	3.69836e42	−	1.52498e42i	1.00729	−	0.415345i
$863$	−9.82926e41			−0.263247			−0.131624	−	0.991300i	$-0.542019\pi$
$863$	−9.82926e41			−0.263247			−0.131624	+	0.991300i	$0.542019\pi$
$864$	4.45110e42	−	1.80212e42i	1.17224	−	0.474606i
$865$	−6.11866e41			−0.158461
$866$	2.79931e41	−	1.15427e41i	0.0712920	−	0.0293966i
$867$			7.49986e42i			1.87835i
$868$	−3.45641e41	+	3.43435e41i	−0.0851313	+	0.0845881i
$869$			8.41995e41i			0.203950i
$870$	9.73688e41	+	2.36137e42i	0.231948	+	0.562516i
$871$	−1.85498e41			−0.0434586
$872$	4.40520e42	+	1.84952e42i	1.01502	+	0.426157i
$873$	3.29085e41			0.0745765
$874$	−2.33990e42	−	5.67468e42i	−0.521532	−	1.26481i
$875$			1.34042e41i			0.0293849i
$876$	2.63759e42	+	2.65453e42i	0.568719	+	0.572372i
$877$			6.20493e42i			1.31596i	0.753035	+	0.657980i	$0.228589\pi$
$877$			6.20493e42i			1.31596i	−0.753035	+	0.657980i	$0.771411\pi$
$878$	2.18096e42	−	8.99298e41i	0.454965	−	0.187600i
$879$	1.43600e43			2.94656
$880$	−2.52499e39	+	3.94453e41i	−0.000509636	+	0.0796154i
$881$	−8.64463e42			−1.71631			−0.858155	−	0.513390i	$-0.828389\pi$
$881$	−8.64463e42			−1.71631			−0.858155	+	0.513390i	$0.828389\pi$
$882$	−8.30268e42	+	3.42352e42i	−1.62152	+	0.668619i
$883$			5.85471e42i			1.12480i	0.826866	+	0.562400i	$0.190122\pi$
$883$			5.85471e42i			1.12480i	−0.826866	+	0.562400i	$0.809878\pi$
$884$	1.83823e41	+	1.85004e41i	0.0347410	+	0.0349641i
$885$			9.66347e41i			0.179662i
$886$	−1.96160e42	−	4.75724e42i	−0.358774	−	0.870093i
$887$	−1.50284e42			−0.270409			−0.135204	−	0.990818i	$-0.543169\pi$
$887$	−1.50284e42			−0.270409			−0.135204	+	0.990818i	$0.543169\pi$
$888$	−5.56725e41	+	1.32601e42i	−0.0985491	+	0.234725i
$889$	4.63756e40			0.00807633
$890$	4.93528e41	+	1.19690e42i	0.0845584	+	0.205070i
$891$		−	6.76494e41i		−	0.114035i
$892$	−3.35230e42	+	3.33091e42i	−0.555971	+	0.552424i
$893$			1.37580e42i			0.224496i
$894$	−2.56776e42	+	1.05879e42i	−0.412250	+	0.169987i
$895$	1.73769e42			0.274497
$896$	−3.76410e41	−	1.60877e41i	−0.0585053	−	0.0250051i
$897$	4.26645e41			0.0652494
$898$	5.37015e42	−	2.21433e42i	0.808127	−	0.333223i
$899$		−	1.96288e43i		−	2.90655i
$900$	−8.08957e42	+	8.03796e42i	−1.17872	+	1.17120i
$901$			8.53597e42i			1.22389i
$902$	1.05758e42	+	2.56483e42i	0.149217	+	0.361879i
$903$	5.52003e41			0.0766424
$904$	−3.03907e42	+	7.23848e42i	−0.415239	+	0.989020i
$905$	−9.87635e41			−0.132798
$906$	−4.73507e42	−	1.14834e43i	−0.626567	−	1.51954i
$907$		−	8.50845e42i		−	1.10801i	−0.832512	−	0.554006i	$-0.813098\pi$
$907$		−	8.50845e42i		−	1.10801i	0.832512	−	0.554006i	$-0.186902\pi$
$908$	7.81886e42	+	7.86907e42i	1.00207	+	1.00851i
$909$		−	2.28413e43i		−	2.88101i
$910$	3.80239e39	−	1.56788e39i	0.000472015	−	0.000194631i
$911$	−1.06878e43			−1.30579			−0.652893	−	0.757451i	$-0.726445\pi$
$911$	−1.06878e43			−1.30579			−0.652893	+	0.757451i	$0.726445\pi$
$912$	1.04071e41	−	1.62579e43i	0.0125142	−	1.95497i
$913$	−5.80529e41			−0.0687064
$914$	7.49413e42	−	3.09013e42i	0.872974	−	0.359962i
$915$		−	6.15940e42i		−	0.706208i
$916$	−6.36636e42	−	6.40724e42i	−0.718467	−	0.723080i
$917$		−	3.71041e41i		−	0.0412161i
$918$	6.43558e42	+	1.56075e43i	0.703669	+	1.70653i
$919$	1.00358e43			1.08013			0.540067	−	0.841622i	$-0.318399\pi$
$919$	1.00358e43			1.08013			0.540067	+	0.841622i	$0.318399\pi$
$920$	−2.40487e42	−	1.00968e42i	−0.254781	−	0.106970i
$921$	7.18721e42			0.749542
$922$	5.96459e41	+	1.44652e42i	0.0612325	+	0.148500i
$923$		−	3.83738e41i		−	0.0387802i
$924$	−2.52570e41	+	2.50958e41i	−0.0251268	+	0.0249665i
$925$		−	1.47599e42i		−	0.144554i
$926$	1.67119e43	−	6.89097e42i	1.61126	−	0.664387i
$927$	−2.67346e43			−2.53757
$928$	1.52852e43	−	6.18850e42i	1.42832	−	0.578282i
$929$	1.73649e42			0.159751			0.0798756	−	0.996805i	$-0.474548\pi$
$929$	1.73649e42			0.159751			0.0798756	+	0.996805i	$0.474548\pi$
$930$	−7.60228e42	+	3.13473e42i	−0.688559	+	0.283921i
$931$			1.31407e43i			1.17178i
$932$	−6.90895e42	+	6.86487e42i	−0.606571	+	0.602701i
$933$			1.15930e43i			1.00210i
$934$	2.34947e42	+	5.69789e42i	0.199958	+	0.484936i
$935$	−1.38677e42			−0.116208
$936$	6.64583e41	+	2.79025e41i	0.0548339	+	0.0230220i
$937$	−5.82762e42			−0.473442			−0.236721	−	0.971578i	$-0.576073\pi$
$937$	−5.82762e42			−0.473442			−0.236721	+	0.971578i	$0.576073\pi$
$938$	3.90194e41	+	9.46293e41i	0.0312133	+	0.0756980i
$939$			5.80345e42i			0.457125i
$940$	4.12051e41	+	4.14697e41i	0.0319593	+	0.0321645i
$941$		−	5.73768e42i		−	0.438215i	−0.975701	−	0.219107i	$-0.929686\pi$
$941$		−	5.73768e42i		−	0.438215i	0.975701	−	0.219107i	$-0.0703145\pi$
$942$	−2.51559e42	+	1.03728e42i	−0.189192	+	0.0780113i
$943$	−1.83441e43			−1.35855
$944$	6.23870e42	+	3.99353e40i	0.454988	+	0.00291248i
$945$	2.66240e41			0.0191211
$946$	−3.17487e42	+	1.30912e42i	−0.224545	+	0.0925890i
$947$			3.51594e42i			0.244887i	0.992475	+	0.122444i	$0.0390731\pi$
$947$			3.51594e42i			0.244887i	−0.992475	+	0.122444i	$0.960927\pi$
$948$	−1.03938e43	−	1.04606e43i	−0.712942	−	0.717521i
$949$			2.42743e41i			0.0163979i
$950$	6.36084e42	+	1.54262e43i	0.423177	+	1.02628i
$951$	−9.90477e42			−0.648973
$952$	5.57100e41	−	1.32690e42i	0.0359499	−	0.0856257i
$953$	−1.99198e43			−1.26602			−0.633008	−	0.774146i	$-0.718180\pi$
$953$	−1.99198e43			−1.26602			−0.633008	+	0.774146i	$0.718180\pi$
$954$	8.99299e42	+	2.18096e43i	0.562928	+	1.36520i
$955$			3.52007e42i			0.217021i
$956$	1.25404e43	−	1.24604e43i	0.761506	−	0.756647i
$957$		−	1.43433e43i		−	0.857879i
$958$	3.61004e42	−	1.48856e42i	0.212673	−	0.0876935i
$959$	5.00820e40			0.00290611
$960$	−4.83787e42	−	4.93168e42i	−0.276517	−	0.281879i
$961$	4.54317e43			2.55782
$962$	−8.62451e40	+	3.55623e40i	−0.00478295	+	0.00197220i
$963$			9.88647e42i			0.540083i
$964$	3.32738e42	−	3.30614e42i	0.179054	−	0.177912i
$965$			4.97613e42i			0.263782i
$966$	−8.97447e41	−	2.17647e42i	−0.0468641	−	0.113654i
$967$	2.48039e43			1.27596			0.637979	−	0.770053i	$-0.279770\pi$
$967$	2.48039e43			1.27596			0.637979	+	0.770053i	$0.279770\pi$
$968$	−6.78143e42	+	1.61520e43i	−0.343660	+	0.818531i
$969$	5.71578e43			2.85352
$970$	−7.79962e40	−	1.89155e41i	−0.00383604	−	0.00930311i
$971$		−	2.18437e43i		−	1.05840i	−0.848499	−	0.529198i	$-0.822493\pi$
$971$		−	2.18437e43i		−	1.05840i	0.848499	−	0.529198i	$-0.177507\pi$
$972$	−1.03229e43	−	1.03892e43i	−0.492765	−	0.495930i
$973$			2.22972e42i			0.104861i
$974$	−1.67995e43	+	6.92710e42i	−0.778379	+	0.320957i
$975$	−1.15980e42			−0.0529441
$976$	−3.97649e43	−	2.54544e41i	−1.78845	−	0.0114483i
$977$	−1.50763e43			−0.668071			−0.334035	−	0.942561i	$-0.608411\pi$
$977$	−1.50763e43			−0.668071			−0.334035	+	0.942561i	$0.608411\pi$
$978$	3.11993e43	−	1.28647e43i	1.36217	−	0.561678i
$979$		−	7.27011e42i		−	0.312746i
$980$	3.93562e42	+	3.96089e42i	0.166815	+	0.167886i
$981$			4.64209e43i			1.93871i
$982$	−1.08016e43	−	2.61958e43i	−0.444499	−	1.07799i
$983$	−2.75985e43			−1.11908			−0.559538	−	0.828805i	$-0.689021\pi$
$983$	−2.75985e43			−1.11908			−0.559538	+	0.828805i	$0.689021\pi$
$984$	−4.47999e43	−	1.88092e43i	−1.78998	−	0.751521i
$985$	7.68541e42			0.302581
$986$	2.20999e43	+	5.35963e43i	0.857383	+	2.07931i
$987$			5.27674e41i			0.0201729i
$988$	7.48127e41	−	7.43353e41i	0.0281838	−	0.0280040i
$989$		−	2.27072e43i		−	0.842979i
$990$	−3.54325e42	+	1.46102e42i	−0.129626	+	0.0534498i
$991$	2.56224e43			0.923743			0.461872	−	0.886947i	$-0.347178\pi$
$991$	2.56224e43			0.923743			0.461872	+	0.886947i	$0.347178\pi$
$992$	1.99235e43	+	4.92096e43i	0.707858	+	1.74836i
$993$	−1.68241e43			−0.589071
$994$	−1.95759e42	+	8.07192e41i	−0.0675490	+	0.0278531i
$995$		−	9.90642e42i		−	0.336885i
$996$	7.21223e42	−	7.16621e42i	0.241718	−	0.240176i
$997$			3.92004e43i			1.29482i	0.762140	+	0.647412i	$0.224149\pi$
$997$			3.92004e43i			1.29482i	−0.762140	+	0.647412i	$0.775851\pi$
$998$	−1.86621e43	−	4.52590e43i	−0.607529	−	1.47337i
$999$	−6.03881e42			−0.193754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.30.b.a.5.4	yes	28
4.3	odd	2		32.30.b.a.17.3		28
8.3	odd	2		32.30.b.a.17.26		28
8.5	even	2	inner	8.30.b.a.5.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.30.b.a.5.3	✓	28	8.5	even	2	inner
8.30.b.a.5.4	yes	28	1.1	even	1	trivial
32.30.b.a.17.3		28	4.3	odd	2
32.30.b.a.17.26		28	8.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-21420.9 + 8832.69i) q^{2} +1.37657e7i q^{3} +(3.80838e8 - 3.78408e8i) q^{4} -3.24318e9i q^{5} +(-1.21588e11 - 2.94874e11i) q^{6} -1.14169e11 q^{7} +(-4.81553e12 + 1.14697e13i) q^{8} -1.20865e14 q^{9} +(2.86460e13 + 6.94719e13i) q^{10} -4.21982e14i q^{11} +(5.20906e15 + 5.24251e15i) q^{12} +4.79401e14i q^{13} +(2.44560e15 - 1.00842e15i) q^{14} +4.46447e16 q^{15} +(1.84499e15 - 2.88224e17i) q^{16} +1.01331e18 q^{17} +(2.58903e18 - 1.06756e18i) q^{18} -4.09766e18i q^{19} +(-1.22725e18 - 1.23513e18i) q^{20} -1.57162e18i q^{21} +(3.72723e18 + 9.03922e18i) q^{22} -6.46500e19 q^{23} +(-1.57888e20 - 6.62892e19i) q^{24} +1.75746e20 q^{25} +(-4.23440e18 - 1.02692e19i) q^{26} -7.19041e20i q^{27} +(-4.34799e19 + 4.32025e19i) q^{28} -2.46920e21i q^{29} +(-9.56330e20 + 3.94333e20i) q^{30} +7.94944e21 q^{31} +(2.50628e21 + 6.19032e21i) q^{32} +5.80888e21 q^{33} +(-2.17059e22 + 8.95022e21i) q^{34} +3.70271e20i q^{35} +(-4.60298e22 + 4.57361e22i) q^{36} -8.39842e21i q^{37} +(3.61933e22 + 8.77754e22i) q^{38} -6.59930e21 q^{39} +(3.71982e22 + 1.56176e22i) q^{40} +2.83744e23 q^{41} +(1.38816e22 + 3.36655e22i) q^{42} +3.51232e23i q^{43} +(-1.59681e23 - 1.60707e23i) q^{44} +3.91986e23i q^{45} +(1.38486e24 - 5.71034e23i) q^{46} -3.35752e23 q^{47} +(3.96762e24 + 2.53976e22i) q^{48} -3.20687e24 q^{49} +(-3.76464e24 + 1.55231e24i) q^{50} +1.39489e25i q^{51} +(1.81409e23 + 1.82574e23i) q^{52} +8.42388e24i q^{53} +(6.35107e24 + 1.54025e25i) q^{54} -1.36856e24 q^{55} +(5.49784e23 - 1.30948e24i) q^{56} +5.64072e25 q^{57} +(2.18097e25 + 5.28925e25i) q^{58} +2.16453e25i q^{59} +(1.70024e25 - 1.68939e25i) q^{60} -1.37965e26i q^{61} +(-1.70284e26 + 7.02149e25i) q^{62} +1.37990e25 q^{63} +(-1.08364e26 - 1.10465e26i) q^{64} +1.55479e24 q^{65} +(-1.24431e26 + 5.13080e25i) q^{66} +3.86937e26i q^{67} +(3.85906e26 - 3.83443e26i) q^{68} -8.89954e26i q^{69} +(-3.27049e24 - 7.93153e24i) q^{70} -8.00452e26 q^{71} +(5.82027e26 - 1.38628e27i) q^{72} +5.06347e26 q^{73} +(7.41806e25 + 1.79902e26i) q^{74} +2.41927e27i q^{75} +(-1.55059e27 - 1.56054e27i) q^{76} +4.81772e25i q^{77} +(1.41363e26 - 5.82896e25i) q^{78} -1.99534e27 q^{79} +(-9.34764e26 - 5.98364e24i) q^{80} +1.60314e27 q^{81} +(-6.07806e27 + 2.50623e27i) q^{82} -1.37572e27i q^{83} +(-5.94713e26 - 5.98532e26i) q^{84} -3.28634e27i q^{85} +(-3.10233e27 - 7.52371e27i) q^{86} +3.39903e28 q^{87} +(4.83999e27 + 2.03207e27i) q^{88} +1.72285e28 q^{89} +(-3.46229e27 - 8.39669e27i) q^{90} -5.47328e25i q^{91} +(-2.46212e28 + 2.44641e28i) q^{92} +1.09430e29i q^{93} +(7.19211e27 - 2.96560e27i) q^{94} -1.32894e28 q^{95} +(-8.52142e28 + 3.45007e28i) q^{96} -2.72276e27 q^{97} +(6.86940e28 - 2.83253e28i) q^{98} +5.10026e28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 8642 q^{2} - 69796972 q^{4} - 35869200308 q^{6} + 1356446145696 q^{7} - 9960937476728 q^{8} - 594796603828988 q^{9} - 62453907924808 q^{10} - 73\!\cdots\!44 q^{12} + 78\!\cdots\!40 q^{14} - 11\!\cdots\!36 q^{15}+ \cdots + 15\!\cdots\!18 q^{98}+O(q^{100}) \) 28 * q - 8642 * q^2 - 69796972 * q^4 - 35869200308 * q^6 + 1356446145696 * q^7 - 9960937476728 * q^8 - 594796603828988 * q^9 - 62453907924808 * q^10 - 7307924809229144 * q^12 + 78078973393134640 * q^14 - 116634443346832736 * q^15 + 383700292994789136 * q^16 + 236508787823771000 * q^17 - 5463422025028232686 * q^18 + 8100282295034264464 * q^20 - 74241827096141255876 * q^22 + 149024448719096002016 * q^23 + 20712180656567708048 * q^24 - 985560523954733380084 * q^25 + 380313139658742379432 * q^26 - 1732909439174340048608 * q^28 + 7144801785073394672432 * q^30 - 7260046134127777257856 * q^31 + 6643977062920224197408 * q^32 - 2610896914152110428752 * q^33 - 2930192868202493524772 * q^34 - 28754573920484976067764 * q^36 + 252146488468191620775980 * q^38 + 74849868421738610351584 * q^39 + 820688210793094034561952 * q^40 - 80518000617380870331368 * q^41 - 1782819030248345808659744 * q^42 - 2294598007572934677578808 * q^44 + 4638427469402659794112144 * q^46 + 121247766087237335010240 * q^47 + 6184031365810992970795296 * q^48 + 8159536578855108935060412 * q^49 - 9220400966993622071721098 * q^50 - 22597445120917837888235600 * q^52 + 30818656788479461856375672 * q^54 + 48823262031438992129145632 * q^55 + 3128328639131527389044032 * q^56 - 36164170101969527032146832 * q^57 + 36177867997628119870848904 * q^58 + 329519076781799215890952992 * q^60 - 317074609885892335052163904 * q^62 - 493740527299257821299206560 * q^63 - 500218670532924741725109184 * q^64 + 275343801437622480199359040 * q^65 + 657604928464011122019443160 * q^66 - 106459616116586500235114136 * q^68 - 602966453165460640487523648 * q^70 + 1637917847840158826077048224 * q^71 - 556537060776134471328999112 * q^72 - 1631197084836886372704831464 * q^73 - 2073796425120249162662229896 * q^74 - 676347811772827416679548184 * q^76 + 4169403080301092166733125776 * q^78 - 2323214658985225396749618624 * q^79 + 13382509145726722749974633280 * q^80 + 3743945936405161605092781740 * q^81 - 12472627196010378834371800468 * q^82 - 30031545197634704679499565504 * q^84 + 24644722942495826507852746492 * q^86 - 23673763728982249679638339488 * q^87 + 6702747736581680058989669584 * q^88 - 3845720546264709069323947304 * q^89 + 34684748345566534013885745800 * q^90 + 106057936152291016342860027744 * q^92 - 115120233998779072244940565728 * q^94 + 120167370974924948019325601696 * q^95 - 107488627072203471026633280448 * q^96 - 6191808951720963836806076616 * q^97 + 159188980666085592813609483918 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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