LMFDB - Embedded newform 8.30.b.a.5.13

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			5.13
Character	$\chi$	$=$	8.5
Dual form			8.30.b.a.5.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1176.52 - 23140.6i) q^{2} +9.62485e6i q^{3} +(-5.34103e8 - 5.44508e7i) q^{4} -1.90239e10i q^{5} +(2.22725e11 + 1.13238e10i) q^{6} -8.83863e11 q^{7} +(-1.88841e12 + 1.22954e13i) q^{8} -2.40073e13 q^{9} +(-4.40223e14 - 2.23820e13i) q^{10} +3.28805e14i q^{11} +(5.24080e14 - 5.14065e15i) q^{12} -2.13001e16i q^{13} +(-1.03988e15 + 2.04531e16i) q^{14} +1.83102e17 q^{15} +(2.82301e17 + 5.81646e16i) q^{16} -2.23580e17 q^{17} +(-2.82451e16 + 5.55543e17i) q^{18} -2.82601e18i q^{19} +(-1.03586e18 + 1.01607e19i) q^{20} -8.50704e18i q^{21} +(7.60875e18 + 3.86846e17i) q^{22} -6.13122e19 q^{23} +(-1.18341e20 - 1.81756e19i) q^{24} -1.75642e20 q^{25} +(-4.92898e20 - 2.50601e19i) q^{26} +4.29490e20i q^{27} +(4.72073e20 + 4.81270e19i) q^{28} +3.07074e21i q^{29} +(2.15423e20 - 4.23708e21i) q^{30} +3.36423e21 q^{31} +(1.67810e21 - 6.46417e21i) q^{32} -3.16470e21 q^{33} +(-2.63047e20 + 5.17377e21i) q^{34} +1.68145e22i q^{35} +(1.28224e22 + 1.30722e21i) q^{36} +3.38591e22i q^{37} +(-6.53954e22 - 3.32486e21i) q^{38} +2.05011e23 q^{39} +(2.33906e23 + 3.59248e22i) q^{40} -3.22602e23 q^{41} +(-1.96858e23 - 1.00087e22i) q^{42} +4.85007e23i q^{43} +(1.79037e22 - 1.75616e23i) q^{44} +4.56711e23i q^{45} +(-7.21351e22 + 1.41880e24i) q^{46} +8.09955e23 q^{47} +(-5.59825e23 + 2.71710e24i) q^{48} -2.43869e24 q^{49} +(-2.06647e23 + 4.06447e24i) q^{50} -2.15192e24i q^{51} +(-1.15981e24 + 1.13765e25i) q^{52} +5.47998e24i q^{53} +(9.93866e24 + 5.05304e23i) q^{54} +6.25515e24 q^{55} +(1.66909e24 - 1.08674e25i) q^{56} +2.71999e25 q^{57} +(7.10587e25 + 3.61279e24i) q^{58} +8.24495e25i q^{59} +(-9.77951e25 - 9.97003e24i) q^{60} +7.99491e25i q^{61} +(3.95809e24 - 7.78503e25i) q^{62} +2.12192e25 q^{63} +(-1.47610e26 - 4.64373e25i) q^{64} -4.05211e26 q^{65} +(-3.72334e24 + 7.32330e25i) q^{66} -3.20861e26i q^{67} +(1.19415e26 + 1.21741e25i) q^{68} -5.90120e26i q^{69} +(3.89097e26 + 1.97826e25i) q^{70} +1.21456e27 q^{71} +(4.53355e25 - 2.95179e26i) q^{72} -1.43208e27 q^{73} +(7.83518e26 + 3.98359e25i) q^{74} -1.69053e27i q^{75} +(-1.53878e26 + 1.50938e27i) q^{76} -2.90619e26i q^{77} +(2.41199e26 - 4.74407e27i) q^{78} +5.12226e26 q^{79} +(1.10651e27 - 5.37045e27i) q^{80} -5.78141e27 q^{81} +(-3.79549e26 + 7.46521e27i) q^{82} +6.16610e27i q^{83} +(-4.63215e26 + 4.54363e27i) q^{84} +4.25335e27i q^{85} +(1.12233e28 + 5.70621e26i) q^{86} -2.95554e28 q^{87} +(-4.04279e27 - 6.20918e26i) q^{88} +2.36585e28 q^{89} +(1.05686e28 + 5.37331e26i) q^{90} +1.88264e28i q^{91} +(3.27470e28 + 3.33850e27i) q^{92} +3.23802e28i q^{93} +(9.52930e26 - 1.87428e28i) q^{94} -5.37615e28 q^{95} +(6.22166e28 + 1.61514e28i) q^{96} -5.81609e28 q^{97} +(-2.86917e27 + 5.64328e28i) q^{98} -7.89373e27i 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 $

$2$	1176.52	−	23140.6i	0.0507767	−	0.998710i
$2$	1176.52	−	23140.6i	0.0507767	−	0.998710i
$3$			9.62485e6i			1.16181i	0.813971	+	0.580906i	$0.197302\pi$
$3$			9.62485e6i			1.16181i	−0.813971	+	0.580906i	$0.802698\pi$
$4$	−5.34103e8	−	5.44508e7i	−0.994843	−	0.101422i
$5$		−	1.90239e10i		−	1.39391i	−0.717117	−	0.696953i	$-0.754539\pi$
$5$		−	1.90239e10i		−	1.39391i	0.717117	−	0.696953i	$-0.245461\pi$
$6$	2.22725e11	+	1.13238e10i	1.16031	+	0.0589930i
$7$	−8.83863e11			−0.492565			−0.246282	−	0.969198i	$-0.579209\pi$
$7$	−8.83863e11			−0.492565			−0.246282	+	0.969198i	$0.579209\pi$
$8$	−1.88841e12	+	1.22954e13i	−0.151807	+	0.988410i
$9$	−2.40073e13			−0.349806
$10$	−4.40223e14	−	2.23820e13i	−1.39211	−	0.0707780i
$11$			3.28805e14i			0.261063i	0.991444	+	0.130531i	$0.0416683\pi$
$11$			3.28805e14i			0.261063i	−0.991444	+	0.130531i	$0.958332\pi$
$12$	5.24080e14	−	5.14065e15i	0.117834	−	1.15582i
$13$		−	2.13001e16i		−	1.50039i	−0.661217	−	0.750195i	$-0.729960\pi$
$13$		−	2.13001e16i		−	1.50039i	0.661217	−	0.750195i	$-0.270040\pi$
$14$	−1.03988e15	+	2.04531e16i	−0.0250108	+	0.491929i
$15$	1.83102e17			1.61946
$16$	2.82301e17	+	5.81646e16i	0.979427	+	0.201799i
$17$	−2.23580e17			−0.322050			−0.161025	−	0.986950i	$-0.551480\pi$
$17$	−2.23580e17			−0.322050			−0.161025	+	0.986950i	$0.551480\pi$
$18$	−2.82451e16	+	5.55543e17i	−0.0177620	+	0.349355i
$19$		−	2.82601e18i		−	0.811420i	−0.914002	−	0.405710i	$-0.867024\pi$
$19$		−	2.82601e18i		−	0.811420i	0.914002	−	0.405710i	$-0.132976\pi$
$20$	−1.03586e18	+	1.01607e19i	−0.141373	+	1.38672i
$21$		−	8.50704e18i		−	0.572267i
$22$	7.60875e18	+	3.86846e17i	0.260726	+	0.0132559i
$23$	−6.13122e19			−1.10279			−0.551395	−	0.834244i	$-0.685904\pi$
$23$	−6.13122e19			−1.10279			−0.551395	+	0.834244i	$0.685904\pi$
$24$	−1.18341e20	−	1.81756e19i	−1.14835	−	0.176371i
$25$	−1.75642e20			−0.942973
$26$	−4.92898e20	−	2.50601e19i	−1.49845	−	0.0761849i
$27$			4.29490e20i			0.755403i
$28$	4.72073e20	+	4.81270e19i	0.490025	+	0.0499571i
$29$			3.07074e21i			1.91634i	0.286205	+	0.958168i	$0.407606\pi$
$29$			3.07074e21i			1.91634i	−0.286205	+	0.958168i	$0.592394\pi$
$30$	2.15423e20	−	4.23708e21i	0.0822307	−	1.61737i
$31$	3.36423e21			0.798255			0.399127	−	0.916896i	$-0.369313\pi$
$31$	3.36423e21			0.798255			0.399127	+	0.916896i	$0.369313\pi$
$32$	1.67810e21	−	6.46417e21i	0.251271	−	0.967917i
$33$	−3.16470e21			−0.303306
$34$	−2.63047e20	+	5.17377e21i	−0.0163527	+	0.321635i
$35$			1.68145e22i			0.686589i
$36$	1.28224e22	+	1.30722e21i	0.348002	+	0.0354782i
$37$			3.38591e22i			0.617661i	0.951117	+	0.308830i	$0.0999375\pi$
$37$			3.38591e22i			0.617661i	−0.951117	+	0.308830i	$0.900062\pi$
$38$	−6.53954e22	−	3.32486e21i	−0.810373	−	0.0412013i
$39$	2.05011e23			1.74317
$40$	2.33906e23	+	3.59248e22i	1.37775	+	0.211604i
$41$	−3.22602e23			−1.32832			−0.664159	−	0.747592i	$-0.731210\pi$
$41$	−3.22602e23			−1.32832			−0.664159	+	0.747592i	$0.731210\pi$
$42$	−1.96858e23	−	1.00087e22i	−0.571529	−	0.0290579i
$43$			4.85007e23i			1.00105i	0.865722	+	0.500525i	$0.166860\pi$
$43$			4.85007e23i			1.00105i	−0.865722	+	0.500525i	$0.833140\pi$
$44$	1.79037e22	−	1.75616e23i	0.0264776	−	0.259717i
$45$			4.56711e23i			0.487596i
$46$	−7.21351e22	+	1.41880e24i	−0.0559961	+	1.10137i
$47$	8.09955e23			0.460301			0.230151	−	0.973155i	$-0.426078\pi$
$47$	8.09955e23			0.460301			0.230151	+	0.973155i	$0.426078\pi$
$48$	−5.59825e23	+	2.71710e24i	−0.234452	+	1.13791i
$49$	−2.43869e24			−0.757380
$50$	−2.06647e23	+	4.06447e24i	−0.0478811	+	0.941757i
$51$		−	2.15192e24i		−	0.374162i
$52$	−1.15981e24	+	1.13765e25i	−0.152173	+	1.49265i
$53$			5.47998e24i			0.545480i	0.962088	+	0.272740i	$0.0879299\pi$
$53$			5.47998e24i			0.545480i	−0.962088	+	0.272740i	$0.912070\pi$
$54$	9.93866e24	+	5.05304e23i	0.754429	+	0.0383569i
$55$	6.25515e24			0.363897
$56$	1.66909e24	−	1.08674e25i	0.0747745	−	0.486856i
$57$	2.71999e25			0.942717
$58$	7.10587e25	+	3.61279e24i	1.91386	+	0.0973053i
$59$			8.24495e25i			1.73314i	0.499054	+	0.866571i	$0.333681\pi$
$59$			8.24495e25i			1.73314i	−0.499054	+	0.866571i	$0.666319\pi$
$60$	−9.77951e25	−	9.97003e24i	−1.61110	−	0.164249i
$61$			7.99491e25i			1.03641i	0.855257	+	0.518205i	$0.173399\pi$
$61$			7.99491e25i			1.03641i	−0.855257	+	0.518205i	$0.826601\pi$
$62$	3.95809e24	−	7.78503e25i	0.0405328	−	0.797225i
$63$	2.12192e25			0.172302
$64$	−1.47610e26	−	4.64373e25i	−0.953910	−	0.300094i
$65$	−4.05211e26			−2.09140
$66$	−3.72334e24	+	7.32330e25i	−0.0154009	+	0.302914i
$67$		−	3.20861e26i		−	1.06717i	−0.845747	−	0.533583i	$-0.820845\pi$
$67$		−	3.20861e26i		−	1.06717i	0.845747	−	0.533583i	$-0.179155\pi$
$68$	1.19415e26	+	1.21741e25i	0.320390	+	0.0326631i
$69$		−	5.90120e26i		−	1.28123i
$70$	3.89097e26	+	1.97826e25i	0.685703	+	0.0348627i
$71$	1.21456e27			1.74250			0.871250	−	0.490840i	$-0.163310\pi$
$71$	1.21456e27			1.74250			0.871250	+	0.490840i	$0.163310\pi$
$72$	4.53355e25	−	2.95179e26i	0.0531028	−	0.345752i
$73$	−1.43208e27			−1.37336			−0.686681	−	0.726959i	$-0.740933\pi$
$73$	−1.43208e27			−1.37336			−0.686681	+	0.726959i	$0.740933\pi$
$74$	7.83518e26	+	3.98359e25i	0.616864	+	0.0313628i
$75$		−	1.69053e27i		−	1.09556i
$76$	−1.53878e26	+	1.50938e27i	−0.0822962	+	0.807236i
$77$		−	2.90619e26i		−	0.128590i
$78$	2.41199e26	−	4.74407e27i	0.0885124	−	1.74092i
$79$	5.12226e26			0.156268			0.0781338	−	0.996943i	$-0.475104\pi$
$79$	5.12226e26			0.156268			0.0781338	+	0.996943i	$0.475104\pi$
$80$	1.10651e27	−	5.37045e27i	0.281289	−	1.36523i
$81$	−5.78141e27			−1.22744
$82$	−3.79549e26	+	7.46521e27i	−0.0674476	+	1.32660i
$83$			6.16610e27i			0.919132i	0.888144	+	0.459566i	$0.151995\pi$
$83$			6.16610e27i			0.919132i	−0.888144	+	0.459566i	$0.848005\pi$
$84$	−4.63215e26	+	4.54363e27i	−0.0580407	+	0.569316i
$85$			4.25335e27i			0.448908i
$86$	1.12233e28	+	5.70621e26i	0.999758	+	0.0508300i
$87$	−2.95554e28			−2.22642
$88$	−4.04279e27	−	6.20918e26i	−0.258037	−	0.0396310i
$89$	2.36585e28			1.28184			0.640918	−	0.767609i	$-0.278554\pi$
$89$	2.36585e28			1.28184			0.640918	+	0.767609i	$0.278554\pi$
$90$	1.05686e28	+	5.37331e26i	0.486967	+	0.0247586i
$91$			1.88264e28i			0.739039i
$92$	3.27470e28	+	3.33850e27i	1.09710	+	0.111848i
$93$			3.23802e28i			0.927421i
$94$	9.52930e26	−	1.87428e28i	0.0233726	−	0.459707i
$95$	−5.37615e28			−1.13104
$96$	6.22166e28	+	1.61514e28i	1.12454	+	0.291929i
$97$	−5.81609e28			−0.904567			−0.452284	−	0.891874i	$-0.649391\pi$
$97$	−5.81609e28			−0.904567			−0.452284	+	0.891874i	$0.649391\pi$
$98$	−2.86917e27	+	5.64328e28i	−0.0384573	+	0.756403i
$99$		−	7.89373e27i		−	0.0913213i
$100$	9.38111e28	+	9.56387e27i	0.938111	+	0.0956387i
$101$		−	8.15047e28i		−	0.705542i	−0.935710	−	0.352771i	$-0.885240\pi$
$101$		−	8.15047e28i		−	0.705542i	0.935710	−	0.352771i	$-0.114760\pi$
$102$	−4.97968e28	−	2.53178e27i	−0.373679	−	0.0189987i
$103$	−1.63097e29			−1.06245			−0.531224	−	0.847232i	$-0.678268\pi$
$103$	−1.63097e29			−1.06245			−0.531224	+	0.847232i	$0.678268\pi$
$104$	2.61893e29	+	4.02233e28i	1.48300	+	0.227769i
$105$	−1.61837e29			−0.797686
$106$	1.26810e29	+	6.44732e27i	0.544777	+	0.0276977i
$107$		−	3.01419e29i		−	1.13007i	−0.825066	−	0.565036i	$-0.808862\pi$
$107$		−	3.01419e29i		−	1.13007i	0.825066	−	0.565036i	$-0.191138\pi$
$108$	2.33861e28	−	2.29392e29i	0.0766148	−	0.751508i
$109$		−	6.71724e28i		−	0.192534i	−0.995356	−	0.0962668i	$-0.969310\pi$
$109$		−	6.71724e28i		−	0.192534i	0.995356	−	0.0962668i	$-0.0306902\pi$
$110$	7.35931e27	−	1.44748e29i	0.0184775	−	0.363428i
$111$	−3.25888e29			−0.717605
$112$	−2.49515e29	−	5.14095e28i	−0.482431	−	0.0993990i
$113$	−1.01616e30			−1.72713			−0.863563	−	0.504241i	$-0.831772\pi$
$113$	−1.01616e30			−1.72713			−0.863563	+	0.504241i	$0.831772\pi$
$114$	3.20012e28	−	6.29421e29i	0.0478681	−	0.941501i
$115$			1.16639e30i			1.53719i
$116$	1.67204e29	−	1.64009e30i	0.194360	−	1.90645i
$117$			5.11359e29i			0.524845i
$118$	1.90793e30	+	9.70036e28i	1.73091	+	0.0880033i
$119$	1.97614e29			0.158631
$120$	−3.45770e29	+	2.25131e30i	−0.245844	+	1.60069i
$121$	1.47820e30			0.931846
$122$	1.85007e30	+	9.40619e28i	1.03507	+	0.0526255i
$123$		−	3.10500e30i		−	1.54325i
$124$	−1.79685e30	−	1.83185e29i	−0.794138	−	0.0809610i
$125$		−	2.02072e29i		−	0.0794896i
$126$	2.49648e28	−	4.91024e29i	0.00874893	−	0.172080i
$127$	1.04639e30			0.326993			0.163497	−	0.986544i	$-0.447723\pi$
$127$	1.04639e30			0.326993			0.163497	+	0.986544i	$0.447723\pi$
$128$	−1.24825e30	+	3.36116e30i	−0.348144	+	0.937441i
$129$	−4.66812e30			−1.16303
$130$	−4.76739e29	+	9.37682e30i	−0.106195	+	2.08870i
$131$			4.16860e30i			0.830914i	0.909613	+	0.415457i	$0.136378\pi$
$131$			4.16860e30i			0.830914i	−0.909613	+	0.415457i	$0.863622\pi$
$132$	1.69028e30	+	1.72320e29i	0.301742	+	0.0307620i
$133$			2.49780e30i			0.399677i
$134$	−7.42491e30	−	3.77500e29i	−1.06579	−	0.0541873i
$135$	8.17056e30			1.05296
$136$	4.22210e29	−	2.74900e30i	0.0488893	−	0.318318i
$137$	2.45574e30			0.255702			0.127851	−	0.991793i	$-0.459192\pi$
$137$	2.45574e30			0.255702			0.127851	+	0.991793i	$0.459192\pi$
$138$	−1.36557e31	−	6.94289e29i	−1.27958	−	0.0650569i
$139$			5.21558e29i			0.0440137i	0.999758	+	0.0220069i	$0.00700556\pi$
$139$			5.21558e29i			0.0440137i	−0.999758	+	0.0220069i	$0.992994\pi$
$140$	9.15561e29	−	8.98065e30i	0.0696355	−	0.683048i
$141$			7.79570e30i			0.534783i
$142$	1.42895e30	−	2.81056e31i	0.0884784	−	1.74025i
$143$	7.00360e30			0.391696
$144$	−6.77728e30	−	1.39638e30i	−0.342609	−	0.0705904i
$145$	5.84173e31			2.67119
$146$	−1.68487e30	+	3.31391e31i	−0.0697348	+	1.37159i
$147$		−	2.34720e31i		−	0.879933i
$148$	1.84365e30	−	1.80842e31i	0.0626447	−	0.614476i
$149$		−	2.32169e31i		−	0.715491i	−0.933819	−	0.357746i	$-0.883546\pi$
$149$		−	2.32169e31i		−	0.715491i	0.933819	−	0.357746i	$-0.116454\pi$
$150$	−3.91199e31	−	1.98895e30i	−1.09414	−	0.0556288i
$151$	−2.50339e31			−0.635862			−0.317931	−	0.948114i	$-0.602988\pi$
$151$	−2.50339e31			−0.635862			−0.317931	+	0.948114i	$0.602988\pi$
$152$	3.47468e31	+	5.33665e30i	0.802016	+	0.123179i
$153$	5.36755e30			0.112655
$154$	−6.72509e30	−	3.41919e29i	−0.128424	−	0.00652940i
$155$		−	6.40007e31i		−	1.11269i
$156$	−1.09497e32	−	1.11630e31i	−1.73418	−	0.176797i
$157$			4.01159e31i			0.579124i	0.957159	+	0.289562i	$0.0935097\pi$
$157$			4.01159e31i			0.579124i	−0.957159	+	0.289562i	$0.906490\pi$
$158$	6.02645e29	−	1.18532e31i	0.00793476	−	0.156066i
$159$	−5.27440e31			−0.633745
$160$	−1.22973e32	−	3.19238e31i	−1.34918	−	0.350248i
$161$	5.41915e31			0.543196
$162$	−6.80195e30	+	1.33785e32i	−0.0623255	+	1.22586i
$163$		−	1.31193e31i		−	0.109949i	−0.998488	−	0.0549743i	$-0.982492\pi$
$163$		−	1.31193e31i		−	0.109949i	0.998488	−	0.0549743i	$-0.0175077\pi$
$164$	1.72303e32	+	1.75660e31i	1.32147	+	0.134721i
$165$			6.02048e31i			0.422780i
$166$	1.42687e32	+	7.25454e30i	0.917946	+	0.0466705i
$167$	2.47573e32			1.45987			0.729935	−	0.683517i	$-0.239550\pi$
$167$	2.47573e32			1.45987			0.729935	+	0.683517i	$0.239550\pi$
$168$	1.04597e32	+	1.60647e31i	0.565635	+	0.0868739i
$169$	−2.52158e32			−1.25117
$170$	9.84251e31	+	5.00416e30i	0.448329	+	0.0227941i
$171$			6.78448e31i			0.283839i
$172$	2.64090e31	−	2.59043e32i	0.101529	−	0.995887i
$173$			3.67765e32i			1.29988i	0.759987	+	0.649939i	$0.225205\pi$
$173$			3.67765e32i			1.29988i	−0.759987	+	0.649939i	$0.774795\pi$
$174$	−3.47725e31	+	6.83929e32i	−0.113050	+	2.22355i
$175$	1.55244e32			0.464475
$176$	−1.91248e31	+	9.28220e31i	−0.0526822	+	0.255692i
$177$	−7.93564e32			−2.01358
$178$	2.78348e31	−	5.47472e32i	0.0650875	−	1.28018i
$179$		−	6.72769e32i		−	1.45043i	−0.688522	−	0.725216i	$-0.741740\pi$
$179$		−	6.72769e32i		−	1.45043i	0.688522	−	0.725216i	$-0.258260\pi$
$180$	2.48683e31	−	2.43931e32i	0.0494532	−	0.485082i
$181$			1.01211e33i			1.85733i	0.370926	+	0.928663i	$0.379040\pi$
$181$			1.01211e33i			1.85733i	−0.370926	+	0.928663i	$0.620960\pi$
$182$	4.35654e32	+	2.21497e31i	0.738085	+	0.0375260i
$183$	−7.69498e32			−1.20411
$184$	1.15782e32	−	7.53857e32i	0.167411	−	1.09001i
$185$	6.44130e32			0.860961
$186$	7.49297e32	+	3.80960e31i	0.926225	+	0.0470914i
$187$		−	7.35143e31i		−	0.0840754i
$188$	−4.32599e32	−	4.41027e31i	−0.457928	−	0.0466849i
$189$		−	3.79610e32i		−	0.372085i
$190$	−6.32516e31	+	1.24407e33i	−0.0574307	+	1.12958i
$191$	−1.94764e33			−1.63879			−0.819397	−	0.573226i	$-0.805692\pi$
$191$	−1.94764e33			−1.63879			−0.819397	+	0.573226i	$0.805692\pi$
$192$	4.46952e32	−	1.42073e33i	0.348653	−	1.10826i
$193$	−4.51090e32			−0.326349			−0.163174	−	0.986597i	$-0.552173\pi$
$193$	−4.51090e32			−0.326349			−0.163174	+	0.986597i	$0.552173\pi$
$194$	−6.84275e31	+	1.34588e33i	−0.0459310	+	0.903400i
$195$		−	3.90009e33i		−	2.42981i
$196$	1.30251e33	+	1.32789e32i	0.753475	+	0.0768154i
$197$		−	1.97989e32i		−	0.106385i	−0.998584	−	0.0531925i	$-0.983060\pi$
$197$		−	1.97989e32i		−	0.106385i	0.998584	−	0.0531925i	$-0.0169397\pi$
$198$	−1.82666e32	−	9.28714e30i	−0.0912035	−	0.00463700i
$199$	−6.23363e32			−0.289315			−0.144658	−	0.989482i	$-0.546208\pi$
$199$	−6.23363e32			−0.289315			−0.144658	+	0.989482i	$0.546208\pi$
$200$	3.31684e32	−	2.15959e33i	0.143150	−	0.932045i
$201$	3.08824e33			1.23985
$202$	−1.88607e33	−	9.58920e31i	−0.704632	−	0.0358251i
$203$		−	2.71411e33i		−	0.943919i
$204$	−1.17174e32	+	1.14935e33i	−0.0379484	+	0.372232i
$205$			6.13714e33i			1.85155i
$206$	−1.91888e32	+	3.77417e33i	−0.0539476	+	1.06108i
$207$	1.47194e33			0.385763
$208$	1.23891e33	−	6.01304e33i	0.302777	−	1.46952i
$209$	9.29206e32			0.211832
$210$	−1.90404e32	+	3.74500e33i	−0.0405039	+	0.796657i
$211$			4.37250e33i			0.868229i	0.900858	+	0.434114i	$0.142939\pi$
$211$			4.37250e33i			0.868229i	−0.900858	+	0.434114i	$0.857061\pi$
$212$	2.98389e32	−	2.92687e33i	0.0553240	−	0.542668i
$213$			1.16899e34i			2.02446i
$214$	−6.97501e33	−	3.54626e32i	−1.12861	−	0.0573814i
$215$	9.22670e33			1.39537
$216$	−5.28075e33	−	8.11052e32i	−0.746648	−	0.114675i
$217$	−2.97352e33			−0.393192
$218$	−1.55441e33	−	7.90298e31i	−0.192285	−	0.00977623i
$219$		−	1.37835e34i		−	1.59559i
$220$	−3.34089e33	−	3.40598e32i	−0.362021	−	0.0369073i
$221$			4.76229e33i			0.483201i
$222$	−3.83414e32	+	7.54125e33i	−0.0364376	+	0.716679i
$223$	4.70134e33			0.418602			0.209301	−	0.977851i	$-0.432881\pi$
$223$	4.70134e33			0.418602			0.209301	+	0.977851i	$0.432881\pi$
$224$	−1.48321e33	+	5.71344e33i	−0.123767	+	0.476762i
$225$	4.21670e33			0.329858
$226$	−1.19553e33	+	2.35145e34i	−0.0876978	+	1.72490i
$227$		−	1.35870e34i		−	0.934863i	−0.884029	−	0.467432i	$-0.845179\pi$
$227$		−	1.35870e34i		−	0.934863i	0.884029	−	0.467432i	$-0.154821\pi$
$228$	−1.45275e34	−	1.48105e33i	−0.937856	−	0.0956127i
$229$		−	9.03222e33i		−	0.547243i	−0.961837	−	0.273622i	$-0.911778\pi$
$229$		−	9.03222e33i		−	0.547243i	0.961837	−	0.273622i	$-0.0882216\pi$
$230$	2.69910e34	+	1.37229e33i	1.53520	+	0.0780533i
$231$	2.79716e33			0.149398
$232$	−3.77559e34	−	5.79880e33i	−1.89413	−	0.290912i
$233$	2.07998e34			0.980387			0.490193	−	0.871614i	$-0.336926\pi$
$233$	2.07998e34			0.980387			0.490193	+	0.871614i	$0.336926\pi$
$234$	1.18331e34	+	6.01625e32i	0.524168	+	0.0266499i
$235$		−	1.54085e34i		−	0.641617i
$236$	4.48944e33	−	4.40365e34i	0.175780	−	1.72420i
$237$			4.93010e33i			0.181554i
$238$	2.32497e32	−	4.57290e33i	0.00805474	−	0.158426i
$239$	1.38859e34			0.452695			0.226348	−	0.974047i	$-0.427321\pi$
$239$	1.38859e34			0.452695			0.226348	+	0.974047i	$0.427321\pi$
$240$	5.16897e34	+	1.06500e34i	1.58614	+	0.326804i
$241$	−1.88340e34			−0.544121			−0.272060	−	0.962280i	$-0.587705\pi$
$241$	−1.88340e34			−0.544121			−0.272060	+	0.962280i	$0.587705\pi$
$242$	1.73913e33	−	3.42063e34i	0.0473161	−	0.930644i
$243$		−	2.61691e34i		−	0.670653i
$244$	4.35329e33	−	4.27010e34i	0.105115	−	1.03106i
$245$			4.63933e34i			1.05572i
$246$	−7.18515e34	−	3.65310e33i	−1.54126	−	0.0783614i
$247$	−6.01943e34			−1.21745
$248$	−6.35304e33	+	4.13645e34i	−0.121180	+	0.789003i
$249$	−5.93477e34			−1.06786
$250$	−4.67606e33	−	2.37742e32i	−0.0793871	−	0.00403622i
$251$			7.43104e34i			1.19064i	0.803488	+	0.595320i	$0.202975\pi$
$251$			7.43104e34i			1.19064i	−0.803488	+	0.595320i	$0.797025\pi$
$252$	−1.13332e34	−	1.15540e33i	−0.171413	−	0.0174753i
$253$		−	2.01598e34i		−	0.287898i
$254$	1.23110e33	−	2.42140e34i	0.0166036	−	0.326571i
$255$	−4.09379e34			−0.521546
$256$	7.63105e34	+	3.28398e34i	0.918554	+	0.395295i
$257$	3.82520e33			0.0435134			0.0217567	−	0.999763i	$-0.493074\pi$
$257$	3.82520e33			0.0435134			0.0217567	+	0.999763i	$0.493074\pi$
$258$	−5.49214e33	+	1.08023e35i	−0.0590549	+	1.16153i
$259$		−	2.99268e34i		−	0.304238i
$260$	2.16424e35	+	2.20640e34i	2.08062	+	0.212115i
$261$		−	7.37201e34i		−	0.670346i
$262$	9.64638e34	+	4.90444e33i	0.829842	+	0.0421911i
$263$	−4.35018e34			−0.354119			−0.177059	−	0.984200i	$-0.556658\pi$
$263$	−4.35018e34			−0.354119			−0.177059	+	0.984200i	$0.556658\pi$
$264$	5.97624e33	−	3.89112e34i	0.0460438	−	0.299791i
$265$	1.04250e35			0.760348
$266$	5.78006e34	+	2.93872e33i	0.399161	+	0.0202943i
$267$			2.27710e35i			1.48925i
$268$	−1.74711e34	+	1.71373e35i	−0.108235	+	1.06166i
$269$			4.15101e34i			0.243638i	0.992552	+	0.121819i	$0.0388728\pi$
$269$			4.15101e34i			0.243638i	−0.992552	+	0.121819i	$0.961127\pi$
$270$	9.61284e33	−	1.89072e35i	0.0534659	−	1.05160i
$271$	−8.75805e34			−0.461693			−0.230846	−	0.972990i	$-0.574149\pi$
$271$	−8.75805e34			−0.461693			−0.230846	+	0.972990i	$0.574149\pi$
$272$	−6.31168e34	−	1.30044e34i	−0.315425	−	0.0649894i
$273$	−1.81201e35			−0.858623
$274$	2.88923e33	−	5.68273e34i	0.0129837	−	0.255372i
$275$		−	5.77522e34i		−	0.246175i
$276$	−3.21325e34	+	3.15185e35i	−0.129946	+	1.27463i
$277$		−	2.55175e35i		−	0.979225i	−0.871940	−	0.489612i	$-0.837138\pi$
$277$		−	2.55175e35i		−	0.979225i	0.871940	−	0.489612i	$-0.162862\pi$
$278$	1.20692e34	+	6.13624e32i	0.0439569	+	0.00223487i
$279$	−8.07661e34			−0.279234
$280$	−2.06740e35	−	3.17525e34i	−0.678631	−	0.104229i
$281$	1.60037e35			0.498861			0.249430	−	0.968393i	$-0.419757\pi$
$281$	1.60037e35			0.498861			0.249430	+	0.968393i	$0.419757\pi$
$282$	1.80397e35	+	9.17180e33i	0.534093	+	0.0271545i
$283$			5.79320e35i			1.62935i	0.579915	+	0.814677i	$0.303086\pi$
$283$			5.79320e35i			1.62935i	−0.579915	+	0.814677i	$0.696914\pi$
$284$	−6.48699e35	−	6.61337e34i	−1.73351	−	0.176729i
$285$		−	5.17446e35i		−	1.31406i
$286$	8.23989e33	−	1.62067e35i	0.0198890	−	0.391191i
$287$	2.85136e35			0.654282
$288$	−4.02865e34	+	1.55187e35i	−0.0878960	+	0.338583i
$289$	−4.31981e35			−0.896284
$290$	6.87292e34	−	1.35181e36i	0.135634	−	2.66775i
$291$		−	5.59790e35i		−	1.05094i
$292$	7.64876e35	+	7.79777e34i	1.36628	+	0.139290i
$293$		−	1.62529e35i		−	0.276281i	−0.990413	−	0.138140i	$-0.955887\pi$
$293$		−	1.62529e35i		−	0.276281i	0.990413	−	0.138140i	$-0.0441125\pi$
$294$	−5.43157e35	−	2.76154e34i	−0.878798	−	0.0446801i
$295$	1.56851e36			2.41584
$296$	−4.16310e35	−	6.39396e34i	−0.610502	−	0.0937649i
$297$	−1.41219e35			−0.197208
$298$	−5.37254e35	−	2.73152e34i	−0.714568	−	0.0363303i
$299$			1.30596e36i			1.65462i
$300$	−9.20508e34	+	9.02917e35i	−0.111114	+	1.08991i
$301$		−	4.28680e35i		−	0.493081i
$302$	−2.94529e34	+	5.79299e35i	−0.0322870	+	0.635042i
$303$	7.84470e35			0.819706
$304$	1.64373e35	−	7.97783e35i	0.163744	−	0.794727i
$305$	1.52094e36			1.44466
$306$	6.31504e33	−	1.24208e35i	0.00572026	−	0.112510i
$307$			5.67386e35i			0.490199i	0.969498	+	0.245099i	$0.0788206\pi$
$307$			5.67386e35i			0.490199i	−0.969498	+	0.245099i	$0.921179\pi$
$308$	−1.58244e34	+	1.55220e35i	−0.0130419	+	0.127927i
$309$		−	1.56979e36i		−	1.23436i
$310$	−1.48101e36	−	7.52981e34i	−1.11126	−	0.0564989i
$311$	−2.67675e36			−1.91683			−0.958413	−	0.285383i	$-0.907879\pi$
$311$	−2.67675e36			−1.91683			−0.958413	+	0.285383i	$0.907879\pi$
$312$	−3.87143e35	+	2.52068e36i	−0.264625	+	1.72297i
$313$	−2.60015e35			−0.169670			−0.0848350	−	0.996395i	$-0.527036\pi$
$313$	−2.60015e35			−0.169670			−0.0848350	+	0.996395i	$0.527036\pi$
$314$	9.28306e35	+	4.71972e34i	0.578377	+	0.0294060i
$315$		−	4.03670e35i		−	0.240173i
$316$	−2.73581e35	−	2.78911e34i	−0.155462	−	0.0158491i
$317$		−	8.09502e34i		−	0.0439399i	−0.999759	−	0.0219699i	$-0.993006\pi$
$317$		−	8.09502e34i		−	0.0439399i	0.999759	−	0.0219699i	$-0.00699381\pi$
$318$	−6.20544e34	+	1.22053e36i	−0.0321795	+	0.632928i
$319$	−1.00968e36			−0.500284
$320$	−8.83417e35	+	2.80812e36i	−0.418303	+	1.32966i
$321$	2.90111e36			1.31293
$322$	6.37575e34	−	1.25402e36i	0.0275817	−	0.542495i
$323$			6.31838e35i			0.261318i
$324$	3.08786e36	+	3.14802e35i	1.22111	+	0.124490i
$325$			3.74121e36i			1.41483i
$326$	−3.03588e35	−	1.54351e34i	−0.109807	−	0.00558283i
$327$	6.46524e35			0.223688
$328$	6.09204e35	−	3.96652e36i	0.201647	−	1.31292i
$329$	−7.15889e35			−0.226728
$330$	1.39317e36	+	7.08322e34i	0.422234	+	0.0214674i
$331$			4.71233e36i			1.36688i	0.730007	+	0.683439i	$0.239517\pi$
$331$			4.71233e36i			1.36688i	−0.730007	+	0.683439i	$0.760483\pi$
$332$	3.35749e35	−	3.29333e36i	0.0932207	−	0.914393i
$333$		−	8.12865e35i		−	0.216061i
$334$	2.91275e35	−	5.72898e36i	0.0741274	−	1.45799i
$335$	−6.10401e36			−1.48753
$336$	4.94809e35	−	2.40154e36i	0.115483	−	0.560494i
$337$	−2.87343e36			−0.642344			−0.321172	−	0.947021i	$-0.604077\pi$
$337$	−2.87343e36			−0.642344			−0.321172	+	0.947021i	$0.604077\pi$
$338$	−2.96669e35	+	5.83508e36i	−0.0635302	+	1.24955i
$339$		−	9.78037e36i		−	2.00660i
$340$	2.31598e35	−	2.27173e36i	0.0455293	−	0.446593i
$341$			1.10618e36i			0.208395i
$342$	1.56997e36	+	7.98208e34i	0.283473	+	0.0144124i
$343$	5.00142e36			0.865623
$344$	−5.96335e36	−	9.15890e35i	−0.989447	−	0.151966i
$345$	−1.12264e37			−1.78592
$346$	8.51030e36	+	4.32684e35i	1.29820	+	0.0660035i
$347$		−	2.25013e35i		−	0.0329177i	−0.999865	−	0.0164589i	$-0.994761\pi$
$347$		−	2.25013e35i		−	0.0329177i	0.999865	−	0.0164589i	$-0.00523926\pi$
$348$	1.57856e37	+	1.60931e36i	2.21494	+	0.225809i
$349$		−	1.76856e36i		−	0.238040i	−0.992892	−	0.119020i	$-0.962025\pi$
$349$		−	1.76856e36i		−	0.238040i	0.992892	−	0.119020i	$-0.0379753\pi$
$350$	1.82648e35	−	3.59243e36i	0.0235845	−	0.463876i
$351$	9.14820e36			1.13340
$352$	2.12545e36	+	5.51767e35i	0.252687	+	0.0655974i
$353$	−8.56861e36			−0.977636			−0.488818	−	0.872386i	$-0.662572\pi$
$353$	−8.56861e36			−0.977636			−0.488818	+	0.872386i	$0.662572\pi$
$354$	−9.33645e35	+	1.83635e37i	−0.102243	+	2.01099i
$355$		−	2.31056e37i		−	2.42888i
$356$	−1.26361e37	−	1.28822e36i	−1.27523	−	0.130007i
$357$			1.90200e36i			0.184299i
$358$	−1.55683e37	−	7.91527e35i	−1.44856	−	0.0736482i
$359$	−9.72956e36			−0.869408			−0.434704	−	0.900573i	$-0.643147\pi$
$359$	−9.72956e36			−0.869408			−0.434704	+	0.900573i	$0.643147\pi$
$360$	−5.61544e36	−	8.62456e35i	−0.481945	−	0.0740203i
$361$	4.14351e36			0.341597
$362$	2.34208e37	+	1.19077e36i	1.85493	+	0.0943089i
$363$			1.42274e37i			1.08263i
$364$	1.02511e36	−	1.00552e37i	0.0749551	−	0.735228i
$365$			2.72436e37i			1.91434i
$366$	−9.05331e35	+	1.78066e37i	−0.0611409	+	1.20256i
$367$	−6.02886e36			−0.391361			−0.195680	−	0.980668i	$-0.562691\pi$
$367$	−6.02886e36			−0.391361			−0.195680	+	0.980668i	$0.562691\pi$
$368$	−1.73085e37	−	3.56620e36i	−1.08010	−	0.222542i
$369$	7.74482e36			0.464653
$370$	7.57832e35	−	1.49055e37i	0.0437168	−	0.859850i
$371$		−	4.84355e36i		−	0.268684i
$372$	1.76313e36	−	1.72944e37i	0.0940614	−	0.922639i
$373$			2.35890e37i			1.21041i	0.796071	+	0.605203i	$0.206908\pi$
$373$			2.35890e37i			1.21041i	−0.796071	+	0.605203i	$0.793092\pi$
$374$	−1.70116e36	−	8.64912e34i	−0.0839669	−	0.00426907i
$375$	1.94491e36			0.0923520
$376$	−1.52952e36	+	9.95871e36i	−0.0698767	+	0.454966i
$377$	6.54072e37			2.87525
$378$	−8.78441e36	−	4.46620e35i	−0.371605	−	0.0188933i
$379$		−	9.52431e36i		−	0.387762i	−0.981025	−	0.193881i	$-0.937892\pi$
$379$		−	9.52431e36i		−	0.387762i	0.981025	−	0.193881i	$-0.0621075\pi$
$380$	2.87142e37	+	2.92736e36i	1.12521	+	0.114713i
$381$			1.00713e37i			0.379904i
$382$	−2.29144e36	+	4.50695e37i	−0.0832126	+	1.63668i
$383$	1.71587e37			0.599934			0.299967	−	0.953950i	$-0.403024\pi$
$383$	1.71587e37			0.599934			0.299967	+	0.953950i	$0.403024\pi$
$384$	−3.23506e37	−	1.20143e37i	−1.08913	−	0.404477i
$385$	−5.52869e36			−0.179243
$386$	−5.30717e35	+	1.04385e37i	−0.0165709	+	0.325928i
$387$		−	1.16437e37i		−	0.350173i
$388$	3.10639e37	+	3.16691e36i	0.899903	+	0.0917435i
$389$		−	2.18945e37i		−	0.611036i	−0.952186	−	0.305518i	$-0.901170\pi$
$389$		−	2.18945e37i		−	0.611036i	0.952186	−	0.305518i	$-0.0988296\pi$
$390$	−9.02504e37	−	4.58854e36i	−2.42668	−	0.123378i
$391$	1.37082e37			0.355154
$392$	4.60524e36	−	2.99847e37i	0.114975	−	0.748602i
$393$	−4.01221e37			−0.965366
$394$	−4.58158e36	−	2.32938e35i	−0.106248	−	0.00540189i
$395$		−	9.74452e36i		−	0.217822i
$396$	−4.29820e35	+	4.21606e36i	−0.00926203	+	0.0908504i
$397$		−	7.13583e37i		−	1.48246i	−0.671252	−	0.741229i	$-0.734243\pi$
$397$		−	7.13583e37i		−	1.48246i	0.671252	−	0.741229i	$-0.265757\pi$
$398$	−7.33399e35	+	1.44250e37i	−0.0146905	+	0.288942i
$399$	−2.40409e37			−0.464349
$400$	−4.95840e37	−	1.02162e37i	−0.923574	−	0.190291i
$401$	6.14640e37			1.10415			0.552075	−	0.833795i	$-0.313836\pi$
$401$	6.14640e37			1.10415			0.552075	+	0.833795i	$0.313836\pi$
$402$	3.63338e36	−	7.14636e37i	0.0629554	−	1.23825i
$403$		−	7.16586e37i		−	1.19769i
$404$	−4.43799e36	+	4.35319e37i	−0.0715578	+	0.701904i
$405$			1.09985e38i			1.71094i
$406$	−6.28061e37	−	3.19321e36i	−0.942702	−	0.0479292i
$407$	−1.11330e37			−0.161248
$408$	2.64587e37	+	4.06371e36i	0.369825	+	0.0568002i
$409$	−1.03330e38			−1.39392			−0.696958	−	0.717112i	$-0.745464\pi$
$409$	−1.03330e38			−1.39392			−0.696958	+	0.717112i	$0.745464\pi$
$410$	1.42017e38	+	7.22048e36i	1.84916	+	0.0940156i
$411$			2.36361e37i			0.297078i
$412$	8.71108e37	+	8.88078e36i	1.05697	+	0.107756i
$413$		−	7.28741e37i		−	0.853684i
$414$	1.73177e36	−	3.40615e37i	0.0195878	−	0.385265i
$415$	1.17303e38			1.28118
$416$	−1.37688e38	−	3.57437e37i	−1.45225	−	0.377004i
$417$	−5.01992e36			−0.0511356
$418$	1.09323e36	−	2.15024e37i	0.0107561	−	0.211558i
$419$			1.90772e38i			1.81306i	0.422145	+	0.906529i	$0.361277\pi$
$419$			1.90772e38i			1.81306i	−0.422145	+	0.906529i	$0.638723\pi$
$420$	8.64374e37	+	8.81214e36i	0.793573	+	0.0809033i
$421$		−	1.50473e38i		−	1.33465i	−0.744765	−	0.667327i	$-0.767438\pi$
$421$		−	1.50473e38i		−	1.33465i	0.744765	−	0.667327i	$-0.232562\pi$
$422$	1.01182e38	+	5.14434e36i	0.867109	+	0.0440858i
$423$	−1.94448e37			−0.161016
$424$	−6.73785e37	−	1.03484e37i	−0.539158	−	0.0828075i
$425$	3.92702e37			0.303685
$426$	2.70512e38	+	1.37535e37i	2.02184	+	0.102795i
$427$		−	7.06641e37i		−	0.510498i
$428$	−1.64125e37	+	1.60989e38i	−0.114615	+	1.12424i
$429$			6.74086e37i			0.455077i
$430$	1.08554e37	−	2.13511e38i	0.0708522	−	1.39357i
$431$	−2.59137e38			−1.63535			−0.817673	−	0.575683i	$-0.804736\pi$
$431$	−2.59137e38			−1.63535			−0.817673	+	0.575683i	$0.804736\pi$
$432$	−2.49811e37	+	1.21245e38i	−0.152440	+	0.739862i
$433$	−2.66221e38			−1.57097			−0.785485	−	0.618880i	$-0.787587\pi$
$433$	−2.66221e38			−1.57097			−0.785485	+	0.618880i	$0.787587\pi$
$434$	−3.49841e36	+	6.88090e37i	−0.0199650	+	0.392685i
$435$			5.62257e38i			3.10342i
$436$	−3.65759e36	+	3.58770e37i	−0.0195272	+	0.191541i
$437$			1.73269e38i			0.894827i
$438$	−3.18959e38	−	1.62166e37i	−1.59353	−	0.0810187i
$439$	−1.23290e38			−0.595926			−0.297963	−	0.954577i	$-0.596307\pi$
$439$	−1.23290e38			−0.595926			−0.297963	+	0.954577i	$0.596307\pi$
$440$	−1.18123e37	+	7.69094e37i	−0.0552419	+	0.359679i
$441$	5.85464e37			0.264936
$442$	1.10202e38	+	5.60293e36i	0.482577	+	0.0245354i
$443$		−	1.36502e38i		−	0.578477i	−0.957257	−	0.289239i	$-0.906598\pi$
$443$		−	1.36502e38i		−	0.578477i	0.957257	−	0.289239i	$-0.0934021\pi$
$444$	1.74058e38	+	1.77449e37i	0.713905	+	0.0727813i
$445$		−	4.50076e38i		−	1.78676i
$446$	5.53123e36	−	1.08792e38i	0.0212553	−	0.418062i
$447$	2.23460e38			0.831266
$448$	1.30467e38	+	4.10442e37i	0.469862	+	0.147816i
$449$	−2.56625e38			−0.894804			−0.447402	−	0.894333i	$-0.647651\pi$
$449$	−2.56625e38			−0.894804			−0.447402	+	0.894333i	$0.647651\pi$
$450$	4.96104e36	−	9.75770e37i	0.0167491	−	0.329432i
$451$		−	1.06073e38i		−	0.346774i
$452$	5.42733e38	+	5.53306e37i	1.71822	+	0.175169i
$453$		−	2.40947e38i		−	0.738752i
$454$	−3.14411e38	−	1.59854e37i	−0.933657	−	0.0474693i
$455$	3.58151e38			1.03015
$456$	−5.13644e37	+	3.34433e38i	−0.143111	+	0.931791i
$457$	3.91078e38			1.05555			0.527774	−	0.849385i	$-0.323027\pi$
$457$	3.91078e38			1.05555			0.527774	+	0.849385i	$0.323027\pi$
$458$	−2.09011e38	−	1.06266e37i	−0.546537	−	0.0277872i
$459$		−	9.60255e37i		−	0.243278i
$460$	6.35110e37	−	6.22974e38i	0.155905	−	1.52926i
$461$		−	4.73334e38i		−	1.12591i	−0.826487	−	0.562956i	$-0.809664\pi$
$461$		−	4.73334e38i		−	1.12591i	0.826487	−	0.562956i	$-0.190336\pi$
$462$	3.29092e36	−	6.47280e37i	0.00758593	−	0.149205i
$463$	−5.14380e38			−1.14910			−0.574552	−	0.818468i	$-0.694824\pi$
$463$	−5.14380e38			−1.14910			−0.574552	+	0.818468i	$0.694824\pi$
$464$	−1.78608e38	+	8.66871e38i	−0.386715	+	1.87691i
$465$	6.15997e38			1.29274
$466$	2.44714e37	−	4.81319e38i	0.0497808	−	0.979122i
$467$			4.04731e37i			0.0798127i	0.999203	+	0.0399063i	$0.0127060\pi$
$467$			4.04731e37i			0.0798127i	−0.999203	+	0.0399063i	$0.987294\pi$
$468$	2.78439e37	−	2.73118e38i	0.0532311	−	0.522138i
$469$			2.83597e38i			0.525649i
$470$	−3.56561e38	−	1.81284e37i	−0.640789	−	0.0325792i
$471$	−3.86110e38			−0.672833
$472$	−1.01375e39	−	1.55698e38i	−1.71306	−	0.263102i
$473$	−1.59473e38			−0.261337
$474$	1.14085e38	+	5.80037e36i	0.181319	+	0.00921870i
$475$			4.96367e38i			0.765148i
$476$	−1.05546e38	−	1.07602e37i	−0.157813	−	0.0160887i
$477$		−	1.31560e38i		−	0.190812i
$478$	1.63371e37	−	3.21329e38i	0.0229864	−	0.452111i
$479$	7.56268e38			1.03231			0.516156	−	0.856495i	$-0.327362\pi$
$479$	7.56268e38			1.03231			0.516156	+	0.856495i	$0.327362\pi$
$480$	3.07262e38	−	1.18360e39i	0.406922	−	1.56750i
$481$	7.21203e38			0.926731
$482$	−2.21586e37	+	4.35830e38i	−0.0276287	+	0.543419i
$483$			5.21585e38i			0.631091i
$484$	−7.89508e38	−	8.04889e37i	−0.927041	−	0.0945101i
$485$			1.10644e39i			1.26088i
$486$	−6.05568e38	−	3.07885e37i	−0.669788	−	0.0340536i
$487$	8.73684e38			0.937961			0.468980	−	0.883209i	$-0.344622\pi$
$487$	8.73684e38			0.937961			0.468980	+	0.883209i	$0.344622\pi$
$488$	−9.83005e38	−	1.50976e38i	−1.02440	−	0.157334i
$489$	1.26271e38			0.127740
$490$	1.07357e39	+	5.45827e37i	1.05435	+	0.0536058i
$491$		−	8.37636e38i		−	0.798682i	−0.916802	−	0.399341i	$-0.869239\pi$
$491$		−	8.37636e38i		−	0.798682i	0.916802	−	0.399341i	$-0.130761\pi$
$492$	−1.69070e38	+	1.65839e39i	−0.156521	+	1.53530i
$493$		−	6.86556e38i		−	0.617157i
$494$	−7.08199e37	+	1.39293e39i	−0.0618179	+	1.21588i
$495$	−1.50169e38			−0.127293
$496$	9.49725e38	+	1.95679e38i	0.781832	+	0.161087i
$497$	−1.07350e39			−0.858293
$498$	−6.98239e37	+	1.37334e39i	−0.0542224	+	1.06648i
$499$		−	1.52796e39i		−	1.15253i	−0.817262	−	0.576267i	$-0.804509\pi$
$499$		−	1.52796e39i		−	1.15253i	0.817262	−	0.576267i	$-0.195491\pi$
$500$	−1.10030e37	+	1.07927e38i	−0.00806204	+	0.0790798i
$501$			2.38285e39i			1.69609i
$502$	1.71959e39	+	8.74278e37i	1.18910	+	0.0604569i
$503$	1.09859e39			0.738075			0.369038	−	0.929414i	$-0.379687\pi$
$503$	1.09859e39			0.738075			0.369038	+	0.929414i	$0.379687\pi$
$504$	−4.00704e37	+	2.60898e38i	−0.0261566	+	0.170305i
$505$	−1.55053e39			−0.983459
$506$	−4.66509e38	−	2.37184e37i	−0.287526	−	0.0146185i
$507$		−	2.42698e39i		−	1.45362i
$508$	−5.58878e38	−	5.69766e37i	−0.325307	−	0.0331644i
$509$		−	2.36219e38i		−	0.133631i	−0.997765	−	0.0668155i	$-0.978716\pi$
$509$		−	2.36219e38i		−	0.133631i	0.997765	−	0.0668155i	$-0.0212839\pi$
$510$	−4.81643e37	+	9.47327e38i	−0.0264824	+	0.520873i
$511$	1.26576e39			0.676469
$512$	8.49713e38	−	1.72723e39i	0.441426	−	0.897298i
$513$	1.21374e39			0.612949
$514$	4.50042e36	−	8.85173e37i	0.00220947	−	0.0434573i
$515$			3.10274e39i			1.48095i
$516$	2.49325e39	+	2.54183e38i	1.15703	+	0.117957i
$517$			2.66318e38i			0.120168i
$518$	−6.92523e38	−	3.52095e37i	−0.303845	−	0.0154482i
$519$	−3.53968e39			−1.51021
$520$	7.65202e38	−	4.98222e39i	0.317488	−	2.06716i
$521$	−3.61394e39			−1.45826			−0.729129	−	0.684376i	$-0.760075\pi$
$521$	−3.61394e39			−1.45826			−0.729129	+	0.684376i	$0.760075\pi$
$522$	−1.70593e39	−	8.67333e37i	−0.669481	−	0.0340380i
$523$		−	2.68571e39i		−	1.02514i	−0.858645	−	0.512571i	$-0.828693\pi$
$523$		−	2.68571e39i		−	1.02514i	0.858645	−	0.512571i	$-0.171307\pi$
$524$	2.26983e38	−	2.22646e39i	0.0842734	−	0.826630i
$525$			1.49420e39i			0.539633i
$526$	−5.11808e37	+	1.00666e39i	−0.0179810	+	0.353662i
$527$	−7.52175e38			−0.257078
$528$	−8.93397e38	−	1.84074e38i	−0.297066	−	0.0612068i
$529$	6.68123e38			0.216147
$530$	1.22653e38	−	2.41242e39i	0.0386080	−	0.759368i
$531$		−	1.97939e39i		−	0.606263i
$532$	1.36007e38	−	1.33408e39i	0.0405362	−	0.397616i
$533$			6.87148e39i			1.99299i
$534$	5.26933e39	+	2.67905e38i	1.48733	+	0.0756194i
$535$	−5.73415e39			−1.57521
$536$	3.94511e39	+	6.05916e38i	1.05480	+	0.162003i
$537$	6.47530e39			1.68513
$538$	9.60568e38	+	4.88375e37i	0.243324	+	0.0123712i
$539$		−	8.01855e38i		−	0.197724i
$540$	−4.36392e39	−	4.44893e38i	−1.04753	−	0.106794i
$541$		−	6.68726e39i		−	1.56274i	−0.624066	−	0.781372i	$-0.714520\pi$
$541$		−	6.68726e39i		−	1.56274i	0.624066	−	0.781372i	$-0.285480\pi$
$542$	−1.03040e38	+	2.02667e39i	−0.0234432	+	0.461097i
$543$	−9.74139e39			−2.15786
$544$	−3.75189e38	+	1.44526e39i	−0.0809218	+	0.311718i
$545$	−1.27788e39			−0.268374
$546$	−2.13187e38	+	4.19310e39i	−0.0435981	+	0.857516i
$547$		−	5.78187e39i		−	1.15147i	−0.817637	−	0.575734i	$-0.804716\pi$
$547$		−	5.78187e39i		−	1.15147i	0.817637	−	0.575734i	$-0.195284\pi$
$548$	−1.31162e39	−	1.33717e38i	−0.254384	−	0.0259340i
$549$		−	1.91936e39i		−	0.362542i
$550$	−1.33642e39	−	6.79467e37i	−0.245858	−	0.0125000i
$551$	8.67792e39			1.55495
$552$	7.25575e39	+	1.11439e39i	1.26639	+	0.194500i
$553$	−4.52738e38			−0.0769719
$554$	−5.90491e39	−	3.00219e38i	−0.977961	−	0.0497218i
$555$			6.19965e39i			1.00027i
$556$	2.83992e37	−	2.78565e38i	0.00446398	−	0.0437867i
$557$		−	1.31892e39i		−	0.201985i	−0.994887	−	0.100992i	$-0.967798\pi$
$557$		−	1.31892e39i		−	0.201985i	0.994887	−	0.100992i	$-0.0322018\pi$
$558$	−9.50231e37	+	1.86898e39i	−0.0141786	+	0.278874i
$559$	1.03307e40			1.50196
$560$	−9.78007e38	+	4.74674e39i	−0.138553	+	0.672463i
$561$	7.07564e38			0.0976797
$562$	1.88287e38	−	3.70336e39i	0.0253305	−	0.498217i
$563$		−	1.87016e39i		−	0.245193i	−0.992457	−	0.122596i	$-0.960878\pi$
$563$		−	1.87016e39i		−	0.245193i	0.992457	−	0.122596i	$-0.0391221\pi$
$564$	4.24482e38	−	4.16370e39i	0.0542390	−	0.532026i
$565$			1.93313e40i			2.40745i
$566$	1.34058e40	+	6.81583e38i	1.62725	+	0.0827333i
$567$	5.10997e39			0.604594
$568$	−2.29358e39	+	1.49335e40i	−0.264523	+	1.72230i
$569$	−1.68278e39			−0.189190			−0.0945952	−	0.995516i	$-0.530156\pi$
$569$	−1.68278e39			−0.189190			−0.0945952	+	0.995516i	$0.530156\pi$
$570$	−1.19740e40	−	6.08787e38i	−1.31236	−	0.0667236i
$571$			1.58324e40i			1.69170i	0.533422	+	0.845849i	$0.320906\pi$
$571$			1.58324e40i			1.69170i	−0.533422	+	0.845849i	$0.679094\pi$
$572$	−3.74064e39	−	3.81352e38i	−0.389676	−	0.0397268i
$573$		−	1.87457e40i		−	1.90397i
$574$	3.35469e38	−	6.59822e39i	0.0332223	−	0.653438i
$575$	1.07690e40			1.03990
$576$	3.54373e39	+	1.11484e39i	0.333683	+	0.104975i
$577$	−1.42227e40			−1.30596			−0.652982	−	0.757373i	$-0.726482\pi$
$577$	−1.42227e40			−1.30596			−0.652982	+	0.757373i	$0.726482\pi$
$578$	−5.08234e38	+	9.99628e39i	−0.0455104	+	0.895127i
$579$		−	4.34167e39i		−	0.379156i
$580$	−3.12008e40	−	3.18087e39i	−2.65742	−	0.270919i
$581$		−	5.44998e39i		−	0.452732i
$582$	−1.29539e40	−	6.58604e38i	−1.04958	−	0.0533631i
$583$	−1.80185e39			−0.142405
$584$	2.70434e39	−	1.76079e40i	0.208485	−	1.35744i
$585$	9.72802e39			0.731584
$586$	−3.76102e39	−	1.91219e38i	−0.275924	−	0.0140286i
$587$			1.44590e40i			1.03487i	0.855722	+	0.517436i	$0.173113\pi$
$587$			1.44590e40i			1.03487i	−0.855722	+	0.517436i	$0.826887\pi$
$588$	−1.27807e39	+	1.25365e40i	−0.0892450	+	0.875395i
$589$		−	9.50734e39i		−	0.647720i
$590$	1.84538e39	−	3.62962e40i	0.122668	−	2.41272i
$591$	1.90561e39			0.123599
$592$	−1.96940e39	+	9.55843e39i	−0.124643	+	0.604953i
$593$	6.57957e39			0.406354			0.203177	−	0.979142i	$-0.434873\pi$
$593$	6.57957e39			0.406354			0.203177	+	0.979142i	$0.434873\pi$
$594$	−1.66147e38	+	3.26788e39i	−0.0100136	+	0.196953i
$595$		−	3.75938e39i		−	0.221116i
$596$	−1.26418e39	+	1.24002e40i	−0.0725669	+	0.711802i
$597$		−	5.99977e39i		−	0.336130i
$598$	3.02206e40	+	1.53649e39i	1.65248	+	0.0840160i
$599$	1.36922e40			0.730775			0.365387	−	0.930856i	$-0.380937\pi$
$599$	1.36922e40			0.730775			0.365387	+	0.930856i	$0.380937\pi$
$600$	2.07857e40	+	3.19241e39i	1.08286	+	0.166313i
$601$	1.46323e40			0.744104			0.372052	−	0.928212i	$-0.378654\pi$
$601$	1.46323e40			0.744104			0.372052	+	0.928212i	$0.378654\pi$
$602$	−9.91990e39	−	5.04351e38i	−0.492445	−	0.0250371i
$603$			7.70301e39i			0.373301i
$604$	1.33707e40	+	1.36312e39i	0.632583	+	0.0644907i
$605$		−	2.81210e40i		−	1.29891i
$606$	9.22946e38	−	1.81531e40i	0.0416220	−	0.818649i
$607$	−1.86909e40			−0.822987			−0.411494	−	0.911413i	$-0.634993\pi$
$607$	−1.86909e40			−0.822987			−0.411494	+	0.911413i	$0.634993\pi$
$608$	−1.82678e40	−	4.74231e39i	−0.785387	−	0.203886i
$609$	2.61229e40			1.09666
$610$	1.78942e39	−	3.51955e40i	0.0733549	−	1.44279i
$611$		−	1.72522e40i		−	0.690631i
$612$	−2.86682e39	−	2.92267e38i	−0.112074	−	0.0114258i
$613$			3.10819e39i			0.118667i	0.998238	+	0.0593337i	$0.0188976\pi$
$613$			3.10819e39i			0.118667i	−0.998238	+	0.0593337i	$0.981102\pi$
$614$	1.31296e40	+	6.67541e38i	0.489566	+	0.0248907i
$615$	−5.90691e40			−2.15115
$616$	3.57327e39	+	5.48806e38i	0.127100	+	0.0195208i
$617$	−2.01435e40			−0.699842			−0.349921	−	0.936779i	$-0.613792\pi$
$617$	−2.01435e40			−0.699842			−0.349921	+	0.936779i	$0.613792\pi$
$618$	−3.63258e40	−	1.84689e39i	−1.23277	−	0.0626770i
$619$			4.43240e40i			1.46935i	0.678421	+	0.734674i	$0.262665\pi$
$619$			4.43240e40i			1.46935i	−0.678421	+	0.734674i	$0.737335\pi$
$620$	−3.48489e39	+	3.41829e40i	−0.112852	+	1.10695i
$621$		−	2.63330e40i		−	0.833051i
$622$	−3.14926e39	+	6.19417e40i	−0.0973302	+	1.91435i
$623$	−2.09109e40			−0.631387
$624$	5.78746e40	+	1.19244e40i	1.70731	+	0.351770i
$625$	−3.65601e40			−1.05377
$626$	−3.05913e38	+	6.01689e39i	−0.00861528	+	0.169451i
$627$			8.94346e39i			0.246108i
$628$	2.18434e39	−	2.14260e40i	0.0587362	−	0.576138i
$629$		−	7.57021e39i		−	0.198918i
$630$	−9.34116e39	−	4.74926e38i	−0.239863	−	0.0121952i
$631$	5.97903e40			1.50039			0.750196	−	0.661216i	$-0.229959\pi$
$631$	5.97903e40			1.50039			0.750196	+	0.661216i	$0.229959\pi$
$632$	−9.67291e38	+	6.29802e39i	−0.0237225	+	0.154457i
$633$	−4.20846e40			−1.00872
$634$	−1.87323e39	−	9.52396e37i	−0.0438832	−	0.00223112i
$635$		−	1.99063e40i		−	0.455798i
$636$	2.81707e40	+	2.87195e39i	0.630477	+	0.0642760i
$637$			5.19445e40i			1.13636i
$638$	−1.18790e39	+	2.33645e40i	−0.0254028	+	0.499639i
$639$	−2.91583e40			−0.609536
$640$	6.39421e40	+	2.37466e40i	1.30670	+	0.485279i
$641$	1.60831e40			0.321313			0.160656	−	0.987010i	$-0.448639\pi$
$641$	1.60831e40			0.321313			0.160656	+	0.987010i	$0.448639\pi$
$642$	3.41322e39	−	6.71334e40i	0.0666663	−	1.31124i
$643$			7.11498e40i			1.35867i	0.733827	+	0.679336i	$0.237732\pi$
$643$			7.11498e40i			1.35867i	−0.733827	+	0.679336i	$0.762268\pi$
$644$	−2.89438e40	−	2.95077e39i	−0.540395	−	0.0550922i
$645$			8.88056e40i			1.62115i
$646$	1.46211e40	+	7.43371e38i	0.260981	+	0.0132689i
$647$	−3.73785e39			−0.0652394			−0.0326197	−	0.999468i	$-0.510385\pi$
$647$	−3.73785e39			−0.0652394			−0.0326197	+	0.999468i	$0.510385\pi$
$648$	1.09176e40	−	7.10846e40i	0.186334	−	1.21322i
$649$	−2.71099e40			−0.452459
$650$	8.65738e40	+	4.40161e39i	1.41300	+	0.0718403i
$651$		−	2.86197e40i		−	0.456815i
$652$	−7.14355e38	+	7.00704e39i	−0.0111513	+	0.109382i
$653$		−	2.76054e40i		−	0.421456i	−0.977545	−	0.210728i	$-0.932417\pi$
$653$		−	2.76054e40i		−	0.421456i	0.977545	−	0.210728i	$-0.0675834\pi$
$654$	7.60649e38	−	1.49609e40i	0.0113581	−	0.223399i
$655$	7.93028e40			1.15822
$656$	−9.10709e40	−	1.87640e40i	−1.30099	−	0.268053i
$657$	3.43803e40			0.480410
$658$	−8.42259e38	+	1.65661e40i	−0.0115125	+	0.226436i
$659$		−	1.59094e40i		−	0.212723i	−0.994328	−	0.106362i	$-0.966080\pi$
$659$		−	1.59094e40i		−	0.212723i	0.994328	−	0.106362i	$-0.0339201\pi$
$660$	3.27820e39	−	3.21555e40i	0.0428794	−	0.420600i
$661$		−	3.78843e40i		−	0.484772i	−0.970180	−	0.242386i	$-0.922070\pi$
$661$		−	3.78843e40i		−	0.484772i	0.970180	−	0.242386i	$-0.0779301\pi$
$662$	1.09046e41	+	5.54416e39i	1.36512	+	0.0694056i
$663$	−4.58363e40			−0.561388
$664$	−7.58145e40	−	1.16441e40i	−0.908480	−	0.139530i
$665$	4.75178e40			0.557112
$666$	−1.88102e40	−	9.56352e38i	−0.215783	−	0.0109709i
$667$		−	1.88274e41i		−	2.11332i
$668$	−1.32229e41	−	1.34805e40i	−1.45234	−	0.148064i
$669$			4.52497e40i			0.486337i
$670$	−7.18150e39	+	1.41250e41i	−0.0755319	+	1.48561i
$671$	−2.62877e40			−0.270568
$672$	−5.49910e40	−	1.42756e40i	−0.553907	−	0.143794i
$673$	−1.49068e41			−1.46949			−0.734745	−	0.678343i	$-0.762698\pi$
$673$	−1.49068e41			−1.46949			−0.734745	+	0.678343i	$0.762698\pi$
$674$	−3.38066e39	+	6.64930e40i	−0.0326161	+	0.641516i
$675$		−	7.54367e40i		−	0.712325i
$676$	1.34678e41	+	1.37302e40i	1.24472	+	0.126897i
$677$			3.51871e40i			0.318309i	0.987254	+	0.159154i	$0.0508767\pi$
$677$			3.51871e40i			0.318309i	−0.987254	+	0.159154i	$0.949123\pi$
$678$	−2.26324e41	−	1.15068e40i	−2.00401	−	0.101888i
$679$	5.14062e40			0.445558
$680$	−5.22966e40	−	8.03206e39i	−0.443705	−	0.0681471i
$681$	1.30773e41			1.08613
$682$	2.55976e40	+	1.30144e39i	0.208126	+	0.0105816i
$683$		−	1.74206e41i		−	1.38664i	−0.720631	−	0.693319i	$-0.756148\pi$
$683$		−	1.74206e41i		−	1.38664i	0.720631	−	0.693319i	$-0.243852\pi$
$684$	3.69420e39	−	3.62361e40i	0.0287877	−	0.282376i
$685$		−	4.67177e40i		−	0.356425i
$686$	5.88428e39	−	1.15736e41i	0.0439535	−	0.864507i
$687$	8.69338e40			0.635793
$688$	−2.82102e40	+	1.36918e41i	−0.202011	+	0.980455i
$689$	1.16724e41			0.818433
$690$	−1.32081e40	+	2.59785e41i	−0.0906832	+	1.78362i
$691$			4.29117e40i			0.288499i	0.989541	+	0.144249i	$0.0460767\pi$
$691$			4.29117e40i			0.288499i	−0.989541	+	0.144249i	$0.953923\pi$
$692$	2.00251e40	−	1.96424e41i	0.131837	−	1.29317i
$693$			6.97697e39i			0.0449816i
$694$	−5.20693e39	−	2.64732e38i	−0.0328753	−	0.00167146i
$695$	9.92204e39			0.0613510
$696$	5.58126e40	−	3.63395e41i	0.337985	−	2.20062i
$697$	7.21275e40			0.427785
$698$	−4.09254e40	−	2.08074e39i	−0.237733	−	0.0120869i
$699$			2.00195e41i			1.13902i
$700$	−8.29161e40	−	8.45315e39i	−0.462080	−	0.0471082i
$701$			2.86416e41i			1.56346i	0.623617	+	0.781730i	$0.285662\pi$
$701$			2.86416e41i			1.56346i	−0.623617	+	0.781730i	$0.714338\pi$
$702$	1.07631e40	−	2.11695e41i	0.0575503	−	1.13194i
$703$	9.56859e40			0.501182
$704$	1.52688e40	−	4.85351e40i	0.0783435	−	0.249030i
$705$	1.48304e41			0.745437
$706$	−1.00812e40	+	1.98283e41i	−0.0496412	+	0.976375i
$707$			7.20389e40i			0.347525i
$708$	4.23845e41	+	4.32102e40i	2.00320	+	0.204223i
$709$			2.94727e41i			1.36474i	0.731007	+	0.682370i	$0.239051\pi$
$709$			2.94727e41i			1.36474i	−0.731007	+	0.682370i	$0.760949\pi$
$710$	−5.34677e41	−	2.71842e40i	−2.42575	−	0.123331i
$711$	−1.22972e40			−0.0546633
$712$	−4.46769e40	+	2.90891e41i	−0.194591	+	1.26698i
$713$	−2.06268e41			−0.880308
$714$	4.40135e40	+	2.23775e39i	0.184061	+	0.00935809i
$715$		−	1.33235e41i		−	0.545987i
$716$	−3.66328e40	+	3.59328e41i	−0.147106	+	1.44295i
$717$			1.33650e41i			0.525947i
$718$	−1.14470e40	+	2.25148e41i	−0.0441457	+	0.868286i
$719$	−1.01924e41			−0.385218			−0.192609	−	0.981276i	$-0.561695\pi$
$719$	−1.01924e41			−0.385218			−0.192609	+	0.981276i	$0.561695\pi$
$720$	−2.65644e40	+	1.28930e41i	−0.0983964	+	0.477565i
$721$	1.44156e41			0.523324
$722$	4.87493e39	−	9.58833e40i	0.0173452	−	0.341157i
$723$		−	1.81274e41i		−	0.632166i
$724$	5.51101e40	−	5.40570e41i	0.188375	−	1.84775i
$725$		−	5.39352e41i		−	1.80705i
$726$	3.29231e41	+	1.67389e40i	1.08123	+	0.0549724i
$727$	−3.42460e41			−1.10246			−0.551228	−	0.834355i	$-0.685841\pi$
$727$	−3.42460e41			−1.10246			−0.551228	+	0.834355i	$0.685841\pi$
$728$	−2.31478e41	−	3.55519e40i	−0.730473	−	0.112191i
$729$	−1.44907e41			−0.448270
$730$	6.30433e41	+	3.20527e40i	1.91187	+	0.0972037i
$731$		−	1.08438e41i		−	0.322388i
$732$	4.10991e41	+	4.18998e40i	1.19790	+	0.122124i
$733$		−	2.64335e39i		−	0.00755349i	−0.999993	−	0.00377675i	$-0.998798\pi$
$733$		−	2.64335e39i		−	0.00755349i	0.999993	−	0.00377675i	$-0.00120218\pi$
$734$	−7.09308e39	+	1.39511e41i	−0.0198720	+	0.390856i
$735$	−4.46529e41			−1.22654
$736$	−1.02888e41	+	3.96332e41i	−0.277099	+	1.06741i
$737$	1.05501e41			0.278598
$738$	9.11194e39	−	1.79220e41i	0.0235936	−	0.464054i
$739$			5.43454e41i			1.37981i	0.723901	+	0.689904i	$0.242347\pi$
$739$			5.43454e41i			1.37981i	−0.723901	+	0.689904i	$0.757653\pi$
$740$	−3.44031e41	−	3.50734e40i	−0.856521	−	0.0873208i
$741$		−	5.79361e41i		−	1.41444i
$742$	−1.12083e41	−	5.69854e39i	−0.268338	−	0.0136429i
$743$	4.19754e41			0.985502			0.492751	−	0.870170i	$-0.335991\pi$
$743$	4.19754e41			0.985502			0.492751	+	0.870170i	$0.335991\pi$
$744$	−3.98127e41	−	6.11470e40i	−0.916673	−	0.140789i
$745$	−4.41676e41			−0.997327
$746$	5.45862e41	+	2.77529e40i	1.20884	+	0.0614604i
$747$		−	1.48031e41i		−	0.321518i
$748$	−4.00291e39	+	3.92642e40i	−0.00852713	+	0.0836418i
$749$			2.66413e41i			0.556633i
$750$	2.28823e39	−	4.50064e40i	0.00468933	−	0.0922328i
$751$	−3.51877e41			−0.707313			−0.353656	−	0.935375i	$-0.615062\pi$
$751$	−3.51877e41			−0.707313			−0.353656	+	0.935375i	$0.615062\pi$
$752$	2.28651e41	+	4.71107e40i	0.450831	+	0.0928883i
$753$	−7.15226e41			−1.38330
$754$	7.69529e40	−	1.51356e42i	0.145996	−	2.87154i
$755$			4.76241e41i			0.886332i
$756$	−2.06701e40	+	2.02751e41i	−0.0377378	+	0.370166i
$757$		−	4.60813e41i		−	0.825343i	−0.910880	−	0.412671i	$-0.864596\pi$
$757$		−	4.60813e41i		−	0.825343i	0.910880	−	0.412671i	$-0.135404\pi$
$758$	−2.20398e41	−	1.12056e40i	−0.387261	−	0.0196893i
$759$	1.94035e41			0.334483
$760$	1.01524e41	−	6.61018e41i	0.171700	−	1.11793i
$761$	3.95139e40			0.0655651			0.0327826	−	0.999463i	$-0.489563\pi$
$761$	3.95139e40			0.0655651			0.0327826	+	0.999463i	$0.489563\pi$
$762$	2.33056e41	+	1.18491e40i	0.379414	+	0.0192903i
$763$			5.93712e40i			0.0948353i
$764$	1.04024e42	+	1.06050e41i	1.63034	+	0.166211i
$765$		−	1.02112e41i		−	0.157031i
$766$	2.01876e40	−	3.97063e41i	0.0304627	−	0.599160i
$767$	1.75619e42			2.60039
$768$	−3.16078e41	+	7.34477e41i	−0.459258	+	1.06719i
$769$	−6.35782e41			−0.906517			−0.453259	−	0.891379i	$-0.649739\pi$
$769$	−6.35782e41			−0.906517			−0.453259	+	0.891379i	$0.649739\pi$
$770$	−6.50462e39	+	1.27937e41i	−0.00910136	+	0.179012i
$771$			3.68169e40i			0.0505544i
$772$	2.40928e41	+	2.45622e40i	0.324666	+	0.0330991i
$773$		−	6.47564e41i		−	0.856407i	−0.903682	−	0.428204i	$-0.859147\pi$
$773$		−	6.47564e41i		−	0.856407i	0.903682	−	0.428204i	$-0.140853\pi$
$774$	−2.69442e41	−	1.36991e40i	−0.349721	−	0.0177806i
$775$	−5.90902e41			−0.752733
$776$	1.09831e41	−	7.15110e41i	0.137319	−	0.894084i
$777$	2.88040e41			0.353467
$778$	−5.06652e41	−	2.57594e40i	−0.610247	−	0.0310264i
$779$			9.11676e41i			1.07782i
$780$	−2.12363e41	+	2.08305e42i	−0.246438	+	2.41728i
$781$			3.99354e41i			0.454902i
$782$	1.61280e40	−	3.17215e41i	0.0180336	−	0.354696i
$783$	−1.31885e42			−1.44761
$784$	−6.88444e41	−	1.41846e41i	−0.741799	−	0.152839i
$785$	7.63159e41			0.807245
$786$	−4.72045e40	+	9.28449e41i	−0.0490181	+	0.964120i
$787$			3.05128e41i			0.311063i	0.987831	+	0.155531i	$0.0497090\pi$
$787$			3.05128e41i			0.311063i	−0.987831	+	0.155531i	$0.950291\pi$
$788$	−1.07806e40	+	1.05746e41i	−0.0107898	+	0.105836i
$789$		−	4.18698e41i		−	0.411419i
$790$	−2.25494e41	−	1.14646e40i	−0.217541	−	0.0110603i
$791$	8.98145e41			0.850721
$792$	9.70564e40	+	1.49066e40i	0.0902629	+	0.0138632i
$793$	1.70293e42			1.55502
$794$	−1.65127e42	−	8.39546e40i	−1.48055	−	0.0752744i
$795$			1.00339e42i			0.883381i
$796$	3.32939e41	+	3.39426e40i	0.287823	+	0.0293431i
$797$			6.16253e41i			0.523134i	0.965185	+	0.261567i	$0.0842393\pi$
$797$			6.16253e41i			0.523134i	−0.965185	+	0.261567i	$0.915761\pi$
$798$	−2.82847e40	+	5.56322e41i	−0.0235781	+	0.463750i
$799$	−1.81090e41			−0.148240
$800$	−2.94745e41	+	1.13538e42i	−0.236942	+	0.912720i
$801$	−5.67977e41			−0.448394
$802$	7.23137e40	−	1.42231e42i	0.0560651	−	1.10272i
$803$		−	4.70875e41i		−	0.358534i
$804$	−1.64944e42	−	1.68157e41i	−1.23345	−	0.125748i
$805$		−	1.03093e42i		−	0.757163i
$806$	−1.65822e42	−	8.43079e40i	−1.19615	−	0.0608149i
$807$	−3.99528e41			−0.283062
$808$	1.00213e42	+	1.53914e41i	0.697365	+	0.107106i
$809$	1.78449e42			1.21972			0.609861	−	0.792508i	$-0.291225\pi$
$809$	1.78449e42			1.21972			0.609861	+	0.792508i	$0.291225\pi$
$810$	2.54511e42	+	1.29399e41i	1.70873	+	0.0868759i
$811$		−	2.48437e41i		−	0.163838i	−0.996639	−	0.0819188i	$-0.973895\pi$
$811$		−	2.48437e41i		−	0.163838i	0.996639	−	0.0819188i	$-0.0261048\pi$
$812$	−1.47785e41	+	1.44961e42i	−0.0957346	+	0.939052i
$813$		−	8.42949e41i		−	0.536400i
$814$	−1.30983e40	+	2.57625e41i	−0.00818766	+	0.161040i
$815$	−2.49579e41			−0.153258
$816$	1.25166e41	−	6.07489e41i	0.0755054	−	0.366464i
$817$	1.37063e42			0.812271
$818$	−1.21569e41	+	2.39111e42i	−0.0707785	+	1.39212i
$819$		−	4.51971e41i		−	0.258520i
$820$	3.34172e41	−	3.27786e42i	0.187789	−	1.84200i
$821$		−	5.44083e41i		−	0.300393i	−0.988656	−	0.150196i	$-0.952009\pi$
$821$		−	5.44083e41i		−	0.300393i	0.988656	−	0.150196i	$-0.0479906\pi$
$822$	5.46954e41	+	2.78084e40i	0.296695	+	0.0150846i
$823$	−2.71634e40			−0.0144773			−0.00723864	−	0.999974i	$-0.502304\pi$
$823$	−2.71634e40			−0.0144773			−0.00723864	+	0.999974i	$0.502304\pi$
$824$	3.07994e41	−	2.00535e42i	0.161286	−	1.05013i
$825$	5.55856e41			0.286009
$826$	−1.68635e42	−	8.57379e40i	−0.852583	−	0.0433473i
$827$		−	1.30138e41i		−	0.0646506i	−0.999477	−	0.0323253i	$-0.989709\pi$
$827$		−	1.30138e41i		−	0.0646506i	0.999477	−	0.0323253i	$-0.0102913\pi$
$828$	−7.86167e41	−	8.01483e40i	−0.383773	−	0.0391250i
$829$			1.48286e42i			0.711313i	0.934617	+	0.355656i	$0.115743\pi$
$829$			1.48286e42i			0.711313i	−0.934617	+	0.355656i	$0.884257\pi$
$830$	1.38009e41	−	2.71446e42i	0.0650543	−	1.27953i
$831$	2.45602e42			1.13767
$832$	−9.89122e41	+	3.14412e42i	−0.450258	+	1.43124i
$833$	5.45243e41			0.243914
$834$	−5.90604e39	+	1.16164e41i	−0.00259650	+	0.0510697i
$835$		−	4.70979e42i		−	2.03492i
$836$	−4.96291e41	−	5.05960e40i	−0.210739	−	0.0214845i
$837$			1.44491e42i			0.603004i
$838$	4.41458e42	+	2.24447e41i	1.81072	+	0.0920611i
$839$	5.99866e41			0.241828			0.120914	−	0.992663i	$-0.461418\pi$
$839$	5.99866e41			0.241828			0.120914	+	0.992663i	$0.461418\pi$
$840$	3.05613e41	−	1.98984e42i	0.121094	−	0.788441i
$841$	−6.86175e42			−2.67235
$842$	−3.48204e42	−	1.77035e41i	−1.33293	−	0.0677694i
$843$			1.54033e42i			0.579582i
$844$	2.38086e41	−	2.33536e42i	0.0880579	−	0.863752i
$845$			4.79702e42i			1.74401i
$846$	−2.28773e40	+	4.49965e41i	−0.00817587	+	0.160808i
$847$	−1.30652e42			−0.458994
$848$	−3.18741e41	+	1.54700e42i	−0.110077	+	0.534258i
$849$	−5.57587e42			−1.89300
$850$	4.62022e40	−	9.08734e41i	0.0154201	−	0.303293i
$851$		−	2.07597e42i		−	0.681150i
$852$	6.36527e41	−	6.24363e42i	0.205325	−	2.01402i
$853$		−	2.07615e42i		−	0.658412i	−0.944258	−	0.329206i	$-0.893219\pi$
$853$		−	2.07615e42i		−	0.658412i	0.944258	−	0.329206i	$-0.106781\pi$
$854$	−1.63521e42	−	8.31378e40i	−0.509840	−	0.0259214i
$855$	1.29067e42			0.395646
$856$	3.70606e42	+	5.69202e41i	1.11697	+	0.171552i
$857$	−3.50501e42			−1.03865			−0.519323	−	0.854578i	$-0.673816\pi$
$857$	−3.50501e42			−1.03865			−0.519323	+	0.854578i	$0.673816\pi$
$858$	1.55987e42	+	7.93076e40i	0.454490	+	0.0231073i
$859$			2.46041e42i			0.704866i	0.935837	+	0.352433i	$0.114646\pi$
$859$			2.46041e42i			0.704866i	−0.935837	+	0.352433i	$0.885354\pi$
$860$	−4.92800e42	−	5.02401e41i	−1.38817	−	0.141522i
$861$			2.74439e42i			0.760152i
$862$	−3.04881e41	+	5.99659e42i	−0.0830375	+	1.63324i
$863$	3.72820e41			0.0998488			0.0499244	−	0.998753i	$-0.484102\pi$
$863$	3.72820e41			0.0998488			0.0499244	+	0.998753i	$0.484102\pi$
$864$	2.77630e42	+	7.20726e41i	0.731167	+	0.189811i
$865$	6.99631e42			1.81191
$866$	−3.13215e41	+	6.16051e42i	−0.0797688	+	1.56894i
$867$		−	4.15775e42i		−	1.04131i
$868$	1.58816e42	+	1.61910e41i	0.391164	+	0.0398785i
$869$			1.68423e41i			0.0407957i
$870$	1.30110e43	+	6.61508e41i	3.09942	+	0.157582i
$871$	−6.83439e42			−1.60117
$872$	8.25911e41	+	1.26849e41i	0.190302	+	0.0292279i
$873$	1.39629e42			0.316423
$874$	4.00954e42	+	2.03854e41i	0.893672	+	0.0454364i
$875$			1.78604e41i			0.0391538i
$876$	−7.50523e41	+	7.36181e42i	−0.161828	+	1.58736i
$877$		−	5.21568e42i		−	1.10616i	−0.833129	−	0.553079i	$-0.813453\pi$
$877$		−	5.21568e42i		−	1.10616i	0.833129	−	0.553079i	$-0.186547\pi$
$878$	−1.45053e41	+	2.85300e42i	−0.0302592	+	0.595157i
$879$	1.56432e42			0.320986
$880$	1.76583e42	+	3.63828e41i	0.356410	+	0.0734340i
$881$	6.59223e42			1.30883			0.654413	−	0.756137i	$-0.272916\pi$
$881$	6.59223e42			1.30883			0.654413	+	0.756137i	$0.272916\pi$
$882$	6.88811e40	−	1.35480e42i	0.0134526	−	0.264594i
$883$		−	5.29616e42i		−	1.01749i	−0.860917	−	0.508746i	$-0.830109\pi$
$883$		−	5.29616e42i		−	1.01749i	0.860917	−	0.508746i	$-0.169891\pi$
$884$	2.59310e41	−	2.54355e42i	0.0490074	−	0.480709i
$885$			1.50967e43i			2.80675i
$886$	−3.15874e42	−	1.60598e41i	−0.577731	−	0.0293732i
$887$	−1.64758e42			−0.296451			−0.148226	−	0.988954i	$-0.547356\pi$
$887$	−1.64758e42			−0.296451			−0.148226	+	0.988954i	$0.547356\pi$
$888$	6.15409e41	−	4.00692e42i	0.108937	−	0.709288i
$889$	−9.24863e41			−0.161065
$890$	−1.04150e43	−	5.29524e41i	−1.78445	−	0.0907258i
$891$		−	1.90096e42i		−	0.320439i
$892$	−2.51100e42	−	2.55992e41i	−0.416444	−	0.0424557i
$893$		−	2.28894e42i		−	0.373498i
$894$	2.62905e41	−	5.17099e42i	0.0422090	−	0.830193i
$895$	−1.27987e43			−2.02176
$896$	1.10328e42	−	2.97080e42i	0.171483	−	0.461750i
$897$	−1.25696e43			−1.92235
$898$	−3.01925e41	+	5.93846e42i	−0.0454352	+	0.893650i
$899$			1.03307e43i			1.52972i
$900$	−2.25215e42	−	2.29603e41i	−0.328157	−	0.0334550i
$901$		−	1.22522e42i		−	0.175672i
$902$	−2.45460e42	−	1.24798e41i	−0.346327	−	0.0176081i
$903$	4.12597e42			0.572868
$904$	1.91892e42	−	1.24941e43i	0.262189	−	1.70711i
$905$	1.92542e43			2.58894
$906$	−5.57567e42	−	2.83480e41i	−0.737799	−	0.0375114i
$907$		−	2.82474e42i		−	0.367852i	−0.982940	−	0.183926i	$-0.941119\pi$
$907$		−	2.82474e42i		−	0.367852i	0.982940	−	0.183926i	$-0.0588807\pi$
$908$	−7.39822e41	+	7.25684e42i	−0.0948161	+	0.930042i
$909$			1.95671e42i			0.246803i
$910$	4.21372e41	−	8.28782e42i	0.0523077	−	1.02882i
$911$	5.16810e42			0.631415			0.315707	−	0.948857i	$-0.397758\pi$
$911$	5.16810e42			0.631415			0.315707	+	0.948857i	$0.397758\pi$
$912$	7.67854e42	+	1.58207e42i	0.923323	+	0.190239i
$913$	−2.02745e42			−0.239951
$914$	4.60111e41	−	9.04977e42i	0.0535973	−	1.05419i
$915$			1.46388e43i			1.67842i
$916$	−4.91812e41	+	4.82413e42i	−0.0555027	+	0.544421i
$917$		−	3.68447e42i		−	0.409279i
$918$	−2.22209e42	−	1.12976e41i	−0.242964	−	0.0123529i
$919$	1.34321e43			1.44567			0.722836	−	0.691020i	$-0.242838\pi$
$919$	1.34321e43			1.44567			0.722836	+	0.691020i	$0.242838\pi$
$920$	−1.43413e43	−	2.20262e42i	−1.51937	−	0.233355i
$921$	−5.46100e42			−0.569518
$922$	−1.09532e43	−	5.56887e41i	−1.12446	−	0.0571701i
$923$		−	2.58703e43i		−	2.61443i
$924$	−1.49397e42	−	1.52308e41i	−0.148627	−	0.0151523i
$925$		−	5.94709e42i		−	0.582438i
$926$	−6.05179e41	+	1.19030e43i	−0.0583478	+	1.14762i
$927$	3.91553e42			0.371650
$928$	1.98498e43	+	5.15299e42i	1.85485	+	0.481519i
$929$	1.41624e43			1.30289			0.651446	−	0.758695i	$-0.274163\pi$
$929$	1.41624e43			1.30289			0.651446	+	0.758695i	$0.274163\pi$
$930$	7.24733e41	−	1.42545e43i	0.0656410	−	1.29107i
$931$			6.89176e42i			0.614554i
$932$	−1.11092e43	−	1.13256e42i	−0.975331	−	0.0994333i
$933$		−	2.57634e43i		−	2.22699i
$934$	9.36572e41	+	4.76175e40i	0.0797097	+	0.00405263i
$935$	−1.39853e42			−0.117193
$936$	−6.28735e42	−	9.65653e41i	−0.518762	−	0.0796749i
$937$	−1.52563e43			−1.23944			−0.619721	−	0.784822i	$-0.712754\pi$
$937$	−1.52563e43			−1.23944			−0.619721	+	0.784822i	$0.712754\pi$
$938$	6.56260e42	+	3.33658e41i	0.524971	+	0.0266907i
$939$		−	2.50260e42i		−	0.197124i
$940$	−8.39003e41	+	8.22970e42i	−0.0650743	+	0.638308i
$941$		−	1.89999e43i		−	1.45111i	−0.688162	−	0.725557i	$-0.741582\pi$
$941$		−	1.89999e43i		−	1.45111i	0.688162	−	0.725557i	$-0.258418\pi$
$942$	−4.54266e41	+	8.93480e42i	−0.0341643	+	0.671965i
$943$	1.97795e43			1.46486
$944$	−4.79564e42	+	2.32756e43i	−0.349746	+	1.69749i
$945$	−7.22165e42			−0.518651
$946$	−1.87623e41	+	3.69030e42i	−0.0132698	+	0.261000i
$947$			6.91205e42i			0.481429i	0.970596	+	0.240714i	$0.0773817\pi$
$947$			6.91205e42i			0.481429i	−0.970596	+	0.240714i	$0.922618\pi$
$948$	2.68448e41	−	2.63318e42i	0.0184136	−	0.180617i
$949$			3.05034e43i			2.06058i
$950$	1.14862e43	+	5.83986e41i	0.764161	+	0.0388517i
$951$	7.79133e41			0.0510498
$952$	−3.73175e41	+	2.42974e42i	−0.0240812	+	0.156792i
$953$	1.34173e43			0.852742			0.426371	−	0.904548i	$-0.359792\pi$
$953$	1.34173e43			0.852742			0.426371	+	0.904548i	$0.359792\pi$
$954$	−3.04437e42	−	1.54783e41i	−0.190566	−	0.00968882i
$955$			3.70516e43i			2.28432i
$956$	−7.41652e42	−	7.56101e41i	−0.450361	−	0.0459135i
$957$		−	9.71797e42i		−	0.581236i
$958$	8.89766e41	−	1.75005e43i	0.0524174	−	1.03098i
$959$	−2.17054e42			−0.125950
$960$	−2.70277e43	−	8.50276e42i	−1.54481	−	0.485989i
$961$	−6.44383e42			−0.362790
$962$	8.48510e41	−	1.66891e43i	0.0470564	−	0.925536i
$963$			7.23626e42i			0.395306i
$964$	1.00593e43	+	1.02553e42i	0.541315	+	0.0551861i
$965$			8.58146e42i			0.454899i
$966$	1.20698e43	+	6.13656e41i	0.630277	+	0.0320447i
$967$	−1.88957e43			−0.972030			−0.486015	−	0.873950i	$-0.661550\pi$
$967$	−1.88957e43			−0.972030			−0.486015	+	0.873950i	$0.661550\pi$
$968$	−2.79143e42	+	1.81750e43i	−0.141460	+	0.921046i
$969$	−6.08135e42			−0.303602
$970$	2.56038e43	+	1.30176e42i	1.25926	+	0.0640235i
$971$			7.68996e42i			0.372602i	0.982493	+	0.186301i	$0.0596500\pi$
$971$			7.68996e42i			0.372602i	−0.982493	+	0.186301i	$0.940350\pi$
$972$	−1.42493e42	+	1.39770e43i	−0.0680193	+	0.667194i
$973$		−	4.60986e41i		−	0.0216796i
$974$	1.02791e42	−	2.02176e43i	0.0476266	−	0.936751i
$975$	−3.60086e43			−1.64376
$976$	−4.65021e42	+	2.25697e43i	−0.209146	+	1.01509i
$977$	1.73941e43			0.770781			0.385391	−	0.922754i	$-0.374067\pi$
$977$	1.73941e43			0.770781			0.385391	+	0.922754i	$0.374067\pi$
$978$	1.48561e41	−	2.92199e42i	0.00648620	−	0.127575i
$979$			7.77905e42i			0.334640i
$980$	2.52615e42	−	2.47788e43i	0.107073	−	1.05027i
$981$			1.61263e42i			0.0673494i
$982$	−1.93834e43	−	9.85497e41i	−0.797652	−	0.0405545i
$983$	3.04906e43			1.23635			0.618174	−	0.786042i	$-0.287873\pi$
$983$	3.04906e43			1.23635			0.618174	+	0.786042i	$0.287873\pi$
$984$	3.81772e43	+	5.86350e42i	1.52537	+	0.234276i
$985$	−3.76651e42			−0.148291
$986$	−1.58873e43	−	8.07747e41i	−0.616361	−	0.0313372i
$987$		−	6.89032e42i		−	0.263415i
$988$	3.21499e43	+	3.27763e42i	1.21117	+	0.123476i
$989$		−	2.97368e43i		−	1.10395i
$990$	−1.76677e41	+	3.47500e42i	−0.00646354	+	0.127129i
$991$	−1.30647e43			−0.471012			−0.235506	−	0.971873i	$-0.575675\pi$
$991$	−1.30647e43			−0.471012			−0.235506	+	0.971873i	$0.575675\pi$
$992$	5.64550e42	−	2.17470e43i	0.200578	−	0.772644i
$993$	−4.53555e43			−1.58806
$994$	−1.26300e42	+	2.48415e43i	−0.0435813	+	0.857186i
$995$			1.18588e43i			0.403278i
$996$	3.16978e43	+	3.23153e42i	1.06235	+	0.108305i
$997$			1.23304e43i			0.407286i	0.979045	+	0.203643i	$0.0652781\pi$
$997$			1.23304e43i			0.407286i	−0.979045	+	0.203643i	$0.934722\pi$
$998$	−3.53579e43	−	1.79768e42i	−1.15105	−	0.0585219i
$999$	−1.45421e43			−0.466583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.30.b.a.5.13	✓	28
4.3	odd	2		32.30.b.a.17.6		28
8.3	odd	2		32.30.b.a.17.23		28
8.5	even	2	inner	8.30.b.a.5.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.30.b.a.5.13	✓	28	1.1	even	1	trivial
8.30.b.a.5.14	yes	28	8.5	even	2	inner
32.30.b.a.17.6		28	4.3	odd	2
32.30.b.a.17.23		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+(1176.52 - 23140.6i) q^{2} +9.62485e6i q^{3} +(-5.34103e8 - 5.44508e7i) q^{4} -1.90239e10i q^{5} +(2.22725e11 + 1.13238e10i) q^{6} -8.83863e11 q^{7} +(-1.88841e12 + 1.22954e13i) q^{8} -2.40073e13 q^{9} +(-4.40223e14 - 2.23820e13i) q^{10} +3.28805e14i q^{11} +(5.24080e14 - 5.14065e15i) q^{12} -2.13001e16i q^{13} +(-1.03988e15 + 2.04531e16i) q^{14} +1.83102e17 q^{15} +(2.82301e17 + 5.81646e16i) q^{16} -2.23580e17 q^{17} +(-2.82451e16 + 5.55543e17i) q^{18} -2.82601e18i q^{19} +(-1.03586e18 + 1.01607e19i) q^{20} -8.50704e18i q^{21} +(7.60875e18 + 3.86846e17i) q^{22} -6.13122e19 q^{23} +(-1.18341e20 - 1.81756e19i) q^{24} -1.75642e20 q^{25} +(-4.92898e20 - 2.50601e19i) q^{26} +4.29490e20i q^{27} +(4.72073e20 + 4.81270e19i) q^{28} +3.07074e21i q^{29} +(2.15423e20 - 4.23708e21i) q^{30} +3.36423e21 q^{31} +(1.67810e21 - 6.46417e21i) q^{32} -3.16470e21 q^{33} +(-2.63047e20 + 5.17377e21i) q^{34} +1.68145e22i q^{35} +(1.28224e22 + 1.30722e21i) q^{36} +3.38591e22i q^{37} +(-6.53954e22 - 3.32486e21i) q^{38} +2.05011e23 q^{39} +(2.33906e23 + 3.59248e22i) q^{40} -3.22602e23 q^{41} +(-1.96858e23 - 1.00087e22i) q^{42} +4.85007e23i q^{43} +(1.79037e22 - 1.75616e23i) q^{44} +4.56711e23i q^{45} +(-7.21351e22 + 1.41880e24i) q^{46} +8.09955e23 q^{47} +(-5.59825e23 + 2.71710e24i) q^{48} -2.43869e24 q^{49} +(-2.06647e23 + 4.06447e24i) q^{50} -2.15192e24i q^{51} +(-1.15981e24 + 1.13765e25i) q^{52} +5.47998e24i q^{53} +(9.93866e24 + 5.05304e23i) q^{54} +6.25515e24 q^{55} +(1.66909e24 - 1.08674e25i) q^{56} +2.71999e25 q^{57} +(7.10587e25 + 3.61279e24i) q^{58} +8.24495e25i q^{59} +(-9.77951e25 - 9.97003e24i) q^{60} +7.99491e25i q^{61} +(3.95809e24 - 7.78503e25i) q^{62} +2.12192e25 q^{63} +(-1.47610e26 - 4.64373e25i) q^{64} -4.05211e26 q^{65} +(-3.72334e24 + 7.32330e25i) q^{66} -3.20861e26i q^{67} +(1.19415e26 + 1.21741e25i) q^{68} -5.90120e26i q^{69} +(3.89097e26 + 1.97826e25i) q^{70} +1.21456e27 q^{71} +(4.53355e25 - 2.95179e26i) q^{72} -1.43208e27 q^{73} +(7.83518e26 + 3.98359e25i) q^{74} -1.69053e27i q^{75} +(-1.53878e26 + 1.50938e27i) q^{76} -2.90619e26i q^{77} +(2.41199e26 - 4.74407e27i) q^{78} +5.12226e26 q^{79} +(1.10651e27 - 5.37045e27i) q^{80} -5.78141e27 q^{81} +(-3.79549e26 + 7.46521e27i) q^{82} +6.16610e27i q^{83} +(-4.63215e26 + 4.54363e27i) q^{84} +4.25335e27i q^{85} +(1.12233e28 + 5.70621e26i) q^{86} -2.95554e28 q^{87} +(-4.04279e27 - 6.20918e26i) q^{88} +2.36585e28 q^{89} +(1.05686e28 + 5.37331e26i) q^{90} +1.88264e28i q^{91} +(3.27470e28 + 3.33850e27i) q^{92} +3.23802e28i q^{93} +(9.52930e26 - 1.87428e28i) q^{94} -5.37615e28 q^{95} +(6.22166e28 + 1.61514e28i) q^{96} -5.81609e28 q^{97} +(-2.86917e27 + 5.64328e28i) q^{98} -7.89373e27i 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

Learn more