LMFDB - Embedded newform 8.30.b.a.5.19

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			5.19
Character	$\chi$	$=$	8.5
Dual form			8.30.b.a.5.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10885.6 - 20454.2i) q^{2} -7.14793e6i q^{3} +(-2.99879e8 - 4.45313e8i) q^{4} +6.52418e9i q^{5} +(-1.46205e11 - 7.78094e10i) q^{6} -3.17101e12 q^{7} +(-1.23729e13 + 1.28629e12i) q^{8} +1.75375e13 q^{9} +(1.33447e14 + 7.10196e13i) q^{10} -6.54138e13i q^{11} +(-3.18306e15 + 2.14351e15i) q^{12} +2.90650e14i q^{13} +(-3.45183e16 + 6.48605e16i) q^{14} +4.66344e16 q^{15} +(-1.08376e17 + 2.67079e17i) q^{16} +4.06364e17 q^{17} +(1.90906e17 - 3.58716e17i) q^{18} +1.33769e18i q^{19} +(2.90530e18 - 1.95646e18i) q^{20} +2.26661e19i q^{21} +(-1.33799e18 - 7.12068e17i) q^{22} -1.65536e19 q^{23} +(9.19428e18 + 8.84404e19i) q^{24} +1.43700e20 q^{25} +(5.94502e18 + 3.16390e18i) q^{26} -6.15922e20i q^{27} +(9.50917e20 + 1.41209e21i) q^{28} +2.01540e21i q^{29} +(5.07643e20 - 9.53869e20i) q^{30} -5.79042e21 q^{31} +(4.28316e21 + 5.12407e21i) q^{32} -4.67573e20 q^{33} +(4.42352e21 - 8.31186e21i) q^{34} -2.06882e22i q^{35} +(-5.25912e21 - 7.80967e21i) q^{36} -7.60304e22i q^{37} +(2.73614e22 + 1.45616e22i) q^{38} +2.07755e21 q^{39} +(-8.39196e21 - 8.07228e22i) q^{40} +9.81549e22 q^{41} +(4.63618e23 + 2.46734e23i) q^{42} +7.59746e23i q^{43} +(-2.91296e22 + 1.96162e22i) q^{44} +1.14418e23i q^{45} +(-1.80196e23 + 3.38592e23i) q^{46} +1.98369e24 q^{47} +(1.90906e24 + 7.74665e23i) q^{48} +6.83539e24 q^{49} +(1.56426e24 - 2.93926e24i) q^{50} -2.90466e24i q^{51} +(1.29430e23 - 8.71598e22i) q^{52} +7.10496e24i q^{53} +(-1.25982e25 - 6.70468e24i) q^{54} +4.26771e23 q^{55} +(3.92345e25 - 4.07883e24i) q^{56} +9.56172e24 q^{57} +(4.12235e25 + 2.19389e25i) q^{58} +8.43985e24i q^{59} +(-1.39846e25 - 2.07669e25i) q^{60} -9.24782e25i q^{61} +(-6.30321e25 + 1.18438e26i) q^{62} -5.56116e25 q^{63} +(1.51433e26 - 3.18301e25i) q^{64} -1.89625e24 q^{65} +(-5.08981e24 + 9.56384e24i) q^{66} +4.04147e26i q^{67} +(-1.21860e26 - 1.80959e26i) q^{68} +1.18324e26i q^{69} +(-4.23161e26 - 2.25204e26i) q^{70} -1.23370e27 q^{71} +(-2.16989e26 + 2.25583e25i) q^{72} +8.32250e26 q^{73} +(-1.55514e27 - 8.27636e26i) q^{74} -1.02715e27i q^{75} +(5.95691e26 - 4.01145e26i) q^{76} +2.07428e26i q^{77} +(2.26153e25 - 4.24946e25i) q^{78} -3.27763e27 q^{79} +(-1.74247e27 - 7.07065e26i) q^{80} -3.19896e27 q^{81} +(1.06847e27 - 2.00768e27i) q^{82} +1.06550e28i q^{83} +(1.00935e28 - 6.79709e27i) q^{84} +2.65119e27i q^{85} +(1.55400e28 + 8.27029e27i) q^{86} +1.44059e28 q^{87} +(8.41409e25 + 8.09357e26i) q^{88} -1.15593e28 q^{89} +(2.34033e27 + 1.24551e27i) q^{90} -9.21654e26i q^{91} +(4.96408e27 + 7.37154e27i) q^{92} +4.13895e28i q^{93} +(2.15936e28 - 4.05748e28i) q^{94} -8.72733e27 q^{95} +(3.66264e28 - 3.06157e28i) q^{96} -2.03878e28 q^{97} +(7.44072e28 - 1.39812e29i) q^{98} -1.14720e27i 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 $

$2$	10885.6	−	20454.2i	0.469805	−	0.882770i
$2$	10885.6	−	20454.2i	0.469805	−	0.882770i
$3$		−	7.14793e6i		−	0.862823i	−0.902155	−	0.431412i	$-0.858016\pi$
$3$		−	7.14793e6i		−	0.862823i	0.902155	−	0.431412i	$-0.141984\pi$
$4$	−2.99879e8	−	4.45313e8i	−0.558567	−	0.829459i
$5$			6.52418e9i			0.478036i	0.971015	+	0.239018i	$0.0768255\pi$
$5$			6.52418e9i			0.478036i	−0.971015	+	0.239018i	$0.923174\pi$
$6$	−1.46205e11	−	7.78094e10i	−0.761675	−	0.405358i
$7$	−3.17101e12			−1.76716			−0.883580	−	0.468281i	$-0.844874\pi$
$7$	−3.17101e12			−1.76716			−0.883580	+	0.468281i	$0.844874\pi$
$8$	−1.23729e13	+	1.28629e12i	−0.994640	+	0.103403i
$9$	1.75375e13			0.255536
$10$	1.33447e14	+	7.10196e13i	0.421996	+	0.224584i
$11$		−	6.54138e13i		−	0.0519368i	−0.999663	−	0.0259684i	$-0.991733\pi$
$11$		−	6.54138e13i		−	0.0519368i	0.999663	−	0.0259684i	$-0.00826693\pi$
$12$	−3.18306e15	+	2.14351e15i	−0.715677	+	0.481945i
$13$			2.90650e14i			0.0204735i	0.999948	+	0.0102367i	$0.00325852\pi$
$13$			2.90650e14i			0.0204735i	−0.999948	+	0.0102367i	$0.996741\pi$
$14$	−3.45183e16	+	6.48605e16i	−0.830220	+	1.56000i
$15$	4.66344e16			0.412461
$16$	−1.08376e17	+	2.67079e17i	−0.376005	+	0.926618i
$17$	4.06364e17			0.585338			0.292669	−	0.956214i	$-0.405457\pi$
$17$	4.06364e17			0.585338			0.292669	+	0.956214i	$0.405457\pi$
$18$	1.90906e17	−	3.58716e17i	0.120052	−	0.225579i
$19$			1.33769e18i			0.384086i	0.981387	+	0.192043i	$0.0615113\pi$
$19$			1.33769e18i			0.384086i	−0.981387	+	0.192043i	$0.938489\pi$
$20$	2.90530e18	−	1.95646e18i	0.396512	−	0.267015i
$21$			2.26661e19i			1.52475i
$22$	−1.33799e18	−	7.12068e17i	−0.0458483	−	0.0244002i
$23$	−1.65536e19			−0.297742			−0.148871	−	0.988857i	$-0.547564\pi$
$23$	−1.65536e19			−0.297742			−0.148871	+	0.988857i	$0.547564\pi$
$24$	9.19428e18	+	8.84404e19i	0.0892185	+	0.858198i
$25$	1.43700e20			0.771481
$26$	5.94502e18	+	3.16390e18i	0.0180734	+	0.00961854i
$27$		−	6.15922e20i		−	1.08331i
$28$	9.50917e20	+	1.41209e21i	0.987078	+	1.46579i
$29$			2.01540e21i			1.25774i	0.777511	+	0.628870i	$0.216482\pi$
$29$			2.01540e21i			1.25774i	−0.777511	+	0.628870i	$0.783518\pi$
$30$	5.07643e20	−	9.53869e20i	0.193776	−	0.364108i
$31$	−5.79042e21			−1.37393			−0.686966	−	0.726690i	$-0.741058\pi$
$31$	−5.79042e21			−1.37393			−0.686966	+	0.726690i	$0.741058\pi$
$32$	4.28316e21	+	5.12407e21i	0.641342	+	0.767255i
$33$	−4.67573e20			−0.0448123
$34$	4.42352e21	−	8.31186e21i	0.274994	−	0.516719i
$35$		−	2.06882e22i		−	0.844766i
$36$	−5.25912e21	−	7.80967e21i	−0.142734	−	0.211956i
$37$		−	7.60304e22i		−	1.38695i	−0.720478	−	0.693477i	$-0.756078\pi$
$37$		−	7.60304e22i		−	1.38695i	0.720478	−	0.693477i	$-0.243922\pi$
$38$	2.73614e22	+	1.45616e22i	0.339060	+	0.180445i
$39$	2.07755e21			0.0176650
$40$	−8.39196e21	−	8.07228e22i	−0.0494304	−	0.475474i
$41$	9.81549e22			0.404153			0.202077	−	0.979370i	$-0.435231\pi$
$41$	9.81549e22			0.404153			0.202077	+	0.979370i	$0.435231\pi$
$42$	4.63618e23	+	2.46734e23i	1.34600	+	0.716333i
$43$			7.59746e23i			1.56811i	0.620693	+	0.784054i	$0.286851\pi$
$43$			7.59746e23i			1.56811i	−0.620693	+	0.784054i	$0.713149\pi$
$44$	−2.91296e22	+	1.96162e22i	−0.0430795	+	0.0290102i
$45$			1.14418e23i			0.122155i
$46$	−1.80196e23	+	3.38592e23i	−0.139881	+	0.262838i
$47$	1.98369e24			1.12734			0.563669	−	0.826001i	$-0.309389\pi$
$47$	1.98369e24			1.12734			0.563669	+	0.826001i	$0.309389\pi$
$48$	1.90906e24	+	7.74665e23i	0.799507	+	0.324426i
$49$	6.83539e24			2.12285
$50$	1.56426e24	−	2.93926e24i	0.362446	−	0.681041i
$51$		−	2.90466e24i		−	0.505043i
$52$	1.29430e23	−	8.71598e22i	0.0169819	−	0.0114358i
$53$			7.10496e24i			0.707232i	0.935391	+	0.353616i	$0.115048\pi$
$53$			7.10496e24i			0.707232i	−0.935391	+	0.353616i	$0.884952\pi$
$54$	−1.25982e25	−	6.70468e24i	−0.956310	−	0.508942i
$55$	4.26771e23			0.0248277
$56$	3.92345e25	−	4.07883e24i	1.75769	−	0.182730i
$57$	9.56172e24			0.331398
$58$	4.12235e25	+	2.19389e25i	1.11030	+	0.590892i
$59$			8.43985e24i			0.177411i	0.996058	+	0.0887055i	$0.0282730\pi$
$59$			8.43985e24i			0.177411i	−0.996058	+	0.0887055i	$0.971727\pi$
$60$	−1.39846e25	−	2.07669e25i	−0.230387	−	0.342119i
$61$		−	9.24782e25i		−	1.19883i	−0.800439	−	0.599414i	$-0.795400\pi$
$61$		−	9.24782e25i		−	1.19883i	0.800439	−	0.599414i	$-0.204600\pi$
$62$	−6.30321e25	+	1.18438e26i	−0.645479	+	1.21287i
$63$	−5.56116e25			−0.451572
$64$	1.51433e26	−	3.18301e25i	0.978616	−	0.205697i
$65$	−1.89625e24			−0.00978707
$66$	−5.08981e24	+	9.56384e24i	−0.0210530	+	0.0395590i
$67$			4.04147e26i			1.34417i	0.740473	+	0.672086i	$0.234602\pi$
$67$			4.04147e26i			1.34417i	−0.740473	+	0.672086i	$0.765398\pi$
$68$	−1.21860e26	−	1.80959e26i	−0.326950	−	0.485514i
$69$			1.18324e26i			0.256899i
$70$	−4.23161e26	−	2.25204e26i	−0.745735	−	0.396875i
$71$	−1.23370e27			−1.76996			−0.884982	−	0.465624i	$-0.845830\pi$
$71$	−1.23370e27			−1.76996			−0.884982	+	0.465624i	$0.845830\pi$
$72$	−2.16989e26	+	2.25583e25i	−0.254166	+	0.0264232i
$73$	8.32250e26			0.798128			0.399064	−	0.916923i	$-0.369335\pi$
$73$	8.32250e26			0.798128			0.399064	+	0.916923i	$0.369335\pi$
$74$	−1.55514e27	−	8.27636e26i	−1.22436	−	0.651598i
$75$		−	1.02715e27i		−	0.665652i
$76$	5.95691e26	−	4.01145e26i	0.318584	−	0.214538i
$77$			2.07428e26i			0.0917807i
$78$	2.26153e25	−	4.24946e25i	0.00829910	−	0.0155942i
$79$	−3.27763e27			−0.999925			−0.499963	−	0.866047i	$-0.666653\pi$
$79$	−3.27763e27			−0.999925			−0.499963	+	0.866047i	$0.666653\pi$
$80$	−1.74247e27	−	7.07065e26i	−0.442957	−	0.179744i
$81$	−3.19896e27			−0.679166
$82$	1.06847e27	−	2.00768e27i	0.189873	−	0.356775i
$83$			1.06550e28i			1.58826i	0.607746	+	0.794131i	$0.292074\pi$
$83$			1.06550e28i			1.58826i	−0.607746	+	0.794131i	$0.707926\pi$
$84$	1.00935e28	−	6.79709e27i	1.26472	−	0.851674i
$85$			2.65119e27i			0.279813i
$86$	1.55400e28	+	8.27029e27i	1.38428	+	0.736704i
$87$	1.44059e28			1.08521
$88$	8.41409e25	+	8.09357e26i	0.00537042	+	0.0516584i
$89$	−1.15593e28			−0.626294			−0.313147	−	0.949705i	$-0.601383\pi$
$89$	−1.15593e28			−0.626294			−0.313147	+	0.949705i	$0.601383\pi$
$90$	2.34033e27	+	1.24551e27i	0.107835	+	0.0573891i
$91$		−	9.21654e26i		−	0.0361799i
$92$	4.96408e27	+	7.37154e27i	0.166309	+	0.246965i
$93$			4.13895e28i			1.18546i
$94$	2.15936e28	−	4.05748e28i	0.529629	−	0.995181i
$95$	−8.72733e27			−0.183607
$96$	3.66264e28	−	3.06157e28i	0.662006	−	0.553365i
$97$	−2.03878e28			−0.317089			−0.158544	−	0.987352i	$-0.550680\pi$
$97$	−2.03878e28			−0.317089			−0.158544	+	0.987352i	$0.550680\pi$
$98$	7.44072e28	−	1.39812e29i	0.997326	−	1.87399i
$99$		−	1.14720e27i		−	0.0132717i
$100$	−4.30924e28	−	6.39912e28i	−0.430924	−	0.639912i
$101$			1.75909e29i			1.52275i	0.648314	+	0.761373i	$0.275475\pi$
$101$			1.75909e29i			1.52275i	−0.648314	+	0.761373i	$0.724525\pi$
$102$	−5.94126e28	−	3.16190e28i	−0.445837	−	0.237271i
$103$	−2.69997e28			−0.175881			−0.0879407	−	0.996126i	$-0.528029\pi$
$103$	−2.69997e28			−0.175881			−0.0879407	+	0.996126i	$0.528029\pi$
$104$	−3.73859e26	−	3.59618e27i	−0.00211702	−	0.0203638i
$105$	−1.47878e29			−0.728884
$106$	1.45326e29	+	7.73417e28i	0.624323	+	0.332261i
$107$			5.07877e29i			1.90412i	0.305917	+	0.952058i	$0.401037\pi$
$107$			5.07877e29i			1.90412i	−0.305917	+	0.952058i	$0.598963\pi$
$108$	−2.74278e29	+	1.84702e29i	−0.898558	+	0.605099i
$109$		−	1.17154e28i		−	0.0335795i	−0.999859	−	0.0167898i	$-0.994655\pi$
$109$		−	1.17154e28i		−	0.0335795i	0.999859	−	0.0167898i	$-0.00534460\pi$
$110$	4.64566e27	−	8.72927e27i	0.0116642	−	0.0219171i
$111$	−5.43460e29			−1.19670
$112$	3.43661e29	−	8.46911e29i	0.664461	−	1.63748i
$113$	−8.70543e29			−1.47963			−0.739814	−	0.672811i	$-0.765087\pi$
$113$	−8.70543e29			−1.47963			−0.739814	+	0.672811i	$0.765087\pi$
$114$	1.04085e29	−	1.95577e29i	0.155693	−	0.292549i
$115$		−	1.07999e29i		−	0.142331i
$116$	8.97484e29	−	6.04376e29i	1.04324	−	0.702532i
$117$			5.09728e27i			0.00523171i
$118$	1.72631e29	+	9.18728e28i	0.156613	+	0.0833485i
$119$	−1.28858e30			−1.03438
$120$	−5.77001e29	+	5.99851e28i	−0.410250	+	0.0426497i
$121$	1.58203e30			0.997303
$122$	−1.89157e30	−	1.00668e30i	−1.05829	−	0.563215i
$123$		−	7.01604e29i		−	0.348713i
$124$	1.73642e30	+	2.57854e30i	0.767433	+	1.13962i
$125$			2.15274e30i			0.846832i
$126$	−6.05365e29	+	1.13749e30i	−0.212151	+	0.398635i
$127$	2.65719e30			0.830365			0.415182	−	0.909738i	$-0.363718\pi$
$127$	2.65719e30			0.830365			0.415182	+	0.909738i	$0.363718\pi$
$128$	9.97383e29	−	3.44394e30i	0.278175	−	0.960531i
$129$	5.43061e30			1.35300
$130$	−2.06419e28	+	3.87864e28i	−0.00459801	+	0.00863974i
$131$			3.89519e30i			0.776417i	0.921572	+	0.388208i	$0.126906\pi$
$131$			3.89519e30i			0.776417i	−0.921572	+	0.388208i	$0.873094\pi$
$132$	1.40215e29	+	2.08216e29i	0.0250307	+	0.0371700i
$133$		−	4.24183e30i		−	0.678741i
$134$	8.26651e30	+	4.39938e30i	1.18660	+	0.631498i
$135$	4.01838e30			0.517859
$136$	−5.02790e30	+	5.22701e29i	−0.582200	+	0.0605256i
$137$	−1.41589e29			−0.0147428			−0.00737140	−	0.999973i	$-0.502346\pi$
$137$	−1.41589e29			−0.0147428			−0.00737140	+	0.999973i	$0.502346\pi$
$138$	2.42023e30	+	1.28803e30i	0.226783	+	0.120692i
$139$		−	1.22834e31i		−	1.03658i	−0.855205	−	0.518290i	$-0.826569\pi$
$139$		−	1.22834e31i		−	1.03658i	0.855205	−	0.518290i	$-0.173431\pi$
$140$	−9.21272e30	+	6.20395e30i	−0.700699	+	0.471859i
$141$		−	1.41793e31i		−	0.972694i
$142$	−1.34296e31	+	2.52344e31i	−0.831538	+	1.56247i
$143$	1.90125e28			0.00106333
$144$	−1.90065e30	+	4.68391e30i	−0.0960828	+	0.236784i
$145$	−1.31488e31			−0.601245
$146$	9.05954e30	−	1.70230e31i	0.374964	−	0.704563i
$147$		−	4.88588e31i		−	1.83165i
$148$	−3.38573e31	+	2.27999e31i	−1.15042	+	0.774708i
$149$			2.41088e31i			0.742976i	0.928438	+	0.371488i	$0.121152\pi$
$149$			2.41088e31i			0.742976i	−0.928438	+	0.371488i	$0.878848\pi$
$150$	−2.10096e31	−	1.11812e31i	−0.587618	−	0.312726i
$151$	−4.09775e30			−0.104083			−0.0520415	−	0.998645i	$-0.516573\pi$
$151$	−4.09775e30			−0.104083			−0.0520415	+	0.998645i	$0.516573\pi$
$152$	−1.72065e30	−	1.65511e31i	−0.0397156	−	0.382027i
$153$	7.12662e30			0.149575
$154$	4.24277e30	+	2.25797e30i	0.0810213	+	0.0431190i
$155$		−	3.77777e31i		−	0.656789i
$156$	−6.23012e29	−	9.25157e29i	−0.00986710	−	0.0146524i
$157$			2.79248e31i			0.403130i	0.979475	+	0.201565i	$0.0646028\pi$
$157$			2.79248e31i			0.403130i	−0.979475	+	0.201565i	$0.935397\pi$
$158$	−3.56790e31	+	6.70414e31i	−0.469769	+	0.882704i
$159$	5.07858e31			0.610216
$160$	−3.34303e31	+	2.79441e31i	−0.366776	+	0.306585i
$161$	5.24917e31			0.526157
$162$	−3.48226e31	+	6.54322e31i	−0.319075	+	0.599547i
$163$			4.29874e31i			0.360264i	0.983642	+	0.180132i	$0.0576525\pi$
$163$			4.29874e31i			0.360264i	−0.983642	+	0.180132i	$0.942347\pi$
$164$	−2.94346e31	−	4.37096e31i	−0.225747	−	0.335229i
$165$		−	3.05053e30i		−	0.0214219i
$166$	2.17940e32	+	1.15986e32i	1.40207	+	0.746173i
$167$	−7.97480e31			−0.470252			−0.235126	−	0.971965i	$-0.575550\pi$
$167$	−7.97480e31			−0.470252			−0.235126	+	0.971965i	$0.575550\pi$
$168$	−2.91551e31	−	2.80445e32i	−0.157663	−	1.51657i
$169$	2.01454e32			0.999581
$170$	5.42281e31	+	2.88598e31i	0.247010	+	0.131457i
$171$			2.34598e31i			0.0981477i
$172$	3.38324e32	−	2.27831e32i	1.30068	−	0.875893i
$173$			1.59070e32i			0.562237i	0.959673	+	0.281118i	$0.0907054\pi$
$173$			1.59070e32i			0.562237i	−0.959673	+	0.281118i	$0.909295\pi$
$174$	1.56817e32	−	2.94662e32i	0.509835	−	0.957989i
$175$	−4.55673e32			−1.36333
$176$	1.74707e31	+	7.08929e30i	0.0481256	+	0.0195285i
$177$	6.03275e31			0.153074
$178$	−1.25830e32	+	2.36437e32i	−0.294236	+	0.552873i
$179$		−	4.67414e32i		−	1.00770i	−0.863790	−	0.503852i	$-0.831916\pi$
$179$		−	4.67414e32i		−	1.00770i	0.863790	−	0.503852i	$-0.168084\pi$
$180$	5.09517e31	−	3.43115e31i	0.101323	−	0.0682320i
$181$			8.29181e32i			1.52163i	0.648966	+	0.760817i	$0.275202\pi$
$181$			8.29181e32i			1.52163i	−0.648966	+	0.760817i	$0.724798\pi$
$182$	−1.88517e31	−	1.00328e31i	−0.0319386	−	0.0169975i
$183$	−6.61027e32			−1.03438
$184$	2.04816e32	−	2.12927e31i	0.296146	−	0.0307874i
$185$	4.96036e32			0.663015
$186$	8.46589e32	+	4.50549e32i	1.04649	+	0.556935i
$187$		−	2.65818e31i		−	0.0304006i
$188$	−5.94865e32	−	8.83361e32i	−0.629694	−	0.935081i
$189$			1.95309e33i			1.91437i
$190$	−9.50022e31	+	1.78511e32i	−0.0862594	+	0.162083i
$191$	−1.47033e32			−0.123717			−0.0618586	−	0.998085i	$-0.519703\pi$
$191$	−1.47033e32			−0.123717			−0.0618586	+	0.998085i	$0.519703\pi$
$192$	−2.27519e32	−	1.08244e33i	−0.177480	−	0.844373i
$193$	−2.51191e33			−1.81729			−0.908644	−	0.417571i	$-0.862882\pi$
$193$	−2.51191e33			−1.81729			−0.908644	+	0.417571i	$0.862882\pi$
$194$	−2.21934e32	+	4.17017e32i	−0.148970	+	0.279917i
$195$			1.35543e31i			0.00844452i
$196$	−2.04979e33	−	3.04388e33i	−1.18576	−	1.76082i
$197$			6.53511e32i			0.351150i	0.984466	+	0.175575i	$0.0561785\pi$
$197$			6.53511e32i			0.351150i	−0.984466	+	0.175575i	$0.943822\pi$
$198$	−2.34650e31	−	1.24879e31i	−0.0117159	−	0.00623511i
$199$	−3.12439e32			−0.145009			−0.0725047	−	0.997368i	$-0.523099\pi$
$199$	−3.12439e32			−0.145009			−0.0725047	+	0.997368i	$0.523099\pi$
$200$	−1.77798e33	+	1.84839e32i	−0.767346	+	0.0797735i
$201$	2.88881e33			1.15978
$202$	3.59808e33	+	1.91487e33i	1.34424	+	0.715393i
$203$		−	6.39086e33i		−	2.22263i
$204$	−1.29348e33	+	8.71046e32i	−0.418913	+	0.282100i
$205$			6.40380e32i			0.193200i
$206$	−2.93908e32	+	5.52258e32i	−0.0826299	+	0.155263i
$207$	−2.90310e32			−0.0760837
$208$	−7.76267e31	−	3.14995e31i	−0.0189711	−	0.00769814i
$209$	8.75034e31			0.0199482
$210$	−1.60974e33	+	3.02473e33i	−0.342433	+	0.643437i
$211$		−	5.23718e33i		−	1.03993i	−0.854189	−	0.519963i	$-0.825946\pi$
$211$		−	5.23718e33i		−	1.03993i	0.854189	−	0.519963i	$-0.174054\pi$
$212$	3.16393e33	−	2.13063e33i	0.586620	−	0.395036i
$213$			8.81842e33i			1.52717i
$214$	1.03882e34	+	5.52854e33i	1.68090	+	0.894563i
$215$	−4.95672e33			−0.749612
$216$	7.92252e32	+	7.62072e33i	0.112017	+	1.07750i
$217$	1.83615e34			2.42796
$218$	−2.39630e32	−	1.27530e32i	−0.0296430	−	0.0157758i
$219$		−	5.94886e33i		−	0.688643i
$220$	−1.27980e32	−	1.90047e32i	−0.0138679	−	0.0205936i
$221$			1.18110e32i			0.0119839i
$222$	−5.91588e33	+	1.11160e34i	−0.562214	+	1.05641i
$223$	6.54272e33			0.582556			0.291278	−	0.956638i	$-0.405920\pi$
$223$	6.54272e33			0.582556			0.291278	+	0.956638i	$0.405920\pi$
$224$	−1.35819e34	−	1.62485e34i	−1.13335	−	1.35586i
$225$	2.52013e33			0.197141
$226$	−9.47638e33	+	1.78063e34i	−0.695136	+	1.30617i
$227$		−	1.74891e34i		−	1.20335i	−0.798740	−	0.601677i	$-0.794500\pi$
$227$		−	1.74891e34i		−	1.20335i	0.798740	−	0.601677i	$-0.205500\pi$
$228$	−2.86735e33	−	4.25795e33i	−0.185108	−	0.274882i
$229$		−	1.82562e34i		−	1.10610i	−0.833147	−	0.553051i	$-0.813463\pi$
$229$		−	1.82562e34i		−	1.10610i	0.833147	−	0.553051i	$-0.186537\pi$
$230$	−2.20903e33	−	1.17563e33i	−0.125646	−	0.0668680i
$231$	1.48268e33			0.0791905
$232$	−2.59238e33	−	2.49363e34i	−0.130054	−	1.25100i
$233$	1.64664e34			0.776134			0.388067	−	0.921631i	$-0.373143\pi$
$233$	1.64664e34			0.776134			0.388067	+	0.921631i	$0.373143\pi$
$234$	1.04261e32	+	5.54870e31i	0.00461840	+	0.00245788i
$235$			1.29419e34i			0.538909i
$236$	3.75837e33	−	2.53093e33i	0.147155	−	0.0990960i
$237$			2.34283e34i			0.862759i
$238$	−1.40270e34	+	2.63570e34i	−0.485959	+	0.913124i
$239$	−5.13848e34			−1.67519			−0.837597	−	0.546288i	$-0.816040\pi$
$239$	−5.13848e34			−1.67519			−0.837597	+	0.546288i	$0.816040\pi$
$240$	−5.05405e33	+	1.24551e34i	−0.155087	+	0.382193i
$241$	−6.31154e34			−1.82343			−0.911713	−	0.410828i	$-0.865240\pi$
$241$	−6.31154e34			−1.82343			−0.911713	+	0.410828i	$0.865240\pi$
$242$	1.72213e34	−	3.23592e34i	0.468537	−	0.880389i
$243$		−	1.94050e34i		−	0.497306i
$244$	−4.11817e34	+	2.77322e34i	−0.994379	+	0.669626i
$245$			4.45953e34i			1.01480i
$246$	−1.43508e34	−	7.63738e33i	−0.307834	−	0.163827i
$247$	−3.88800e32			−0.00786359
$248$	7.16441e34	−	7.44813e33i	1.36657	−	0.142069i
$249$	7.61614e34			1.37039
$250$	4.40327e34	+	2.34339e34i	0.747558	+	0.397846i
$251$		−	6.50797e34i		−	1.04274i	−0.853330	−	0.521371i	$-0.825421\pi$
$251$		−	6.50797e34i		−	1.04274i	0.853330	−	0.521371i	$-0.174579\pi$
$252$	1.66767e34	+	2.47645e34i	0.252234	+	0.374561i
$253$			1.08284e33i			0.0154638i
$254$	2.89251e34	−	5.43507e34i	0.390109	−	0.733021i
$255$	1.89505e34			0.241429
$256$	−5.95860e34	−	5.78900e34i	−0.717240	−	0.696826i
$257$	−1.24762e35			−1.41923			−0.709613	−	0.704592i	$-0.751130\pi$
$257$	−1.24762e35			−1.41923			−0.709613	+	0.704592i	$0.751130\pi$
$258$	5.91154e34	−	1.11079e35i	0.635645	−	1.19439i
$259$			2.41093e35i			2.45097i
$260$	5.68646e32	+	8.44426e32i	0.00546674	+	0.00811798i
$261$			3.53451e34i			0.321397i
$262$	7.96730e34	+	4.24015e34i	0.685398	+	0.364764i
$263$	8.57356e34			0.697916			0.348958	−	0.937138i	$-0.386536\pi$
$263$	8.57356e34			0.697916			0.348958	+	0.937138i	$0.386536\pi$
$264$	5.78522e33	−	6.01433e32i	0.0445721	−	0.00463373i
$265$	−4.63540e34			−0.338082
$266$	−8.67633e34	−	4.61748e34i	−0.599173	−	0.318876i
$267$			8.26253e34i			0.540381i
$268$	1.79972e35	−	1.21195e35i	1.11494	−	0.750811i
$269$		−	8.60250e34i		−	0.504913i	−0.967608	−	0.252457i	$-0.918762\pi$
$269$		−	8.60250e34i		−	0.504913i	0.967608	−	0.252457i	$-0.0812385\pi$
$270$	4.37425e34	−	8.21929e34i	0.243293	−	0.457151i
$271$	1.74216e35			0.918402			0.459201	−	0.888332i	$-0.348136\pi$
$271$	1.74216e35			0.918402			0.459201	+	0.888332i	$0.348136\pi$
$272$	−4.40402e34	+	1.08532e35i	−0.220090	+	0.542384i
$273$	−6.58792e33			−0.0312169
$274$	−1.54128e33	+	2.89608e33i	−0.00692624	+	0.0130145i
$275$		−	9.39994e33i		−	0.0400683i
$276$	5.26913e34	−	3.54829e34i	0.213087	−	0.143495i
$277$		−	2.34566e35i		−	0.900137i	−0.892994	−	0.450068i	$-0.851400\pi$
$277$		−	2.34566e35i		−	0.900137i	0.892994	−	0.450068i	$-0.148600\pi$
$278$	−2.51247e35	−	1.33712e35i	−0.915063	−	0.486990i
$279$	−1.01549e35			−0.351089
$280$	2.66110e34	+	2.55973e35i	0.0873513	+	0.840238i
$281$	5.63658e34			0.175701			0.0878505	−	0.996134i	$-0.472000\pi$
$281$	5.63658e34			0.175701			0.0878505	+	0.996134i	$0.472000\pi$
$282$	−2.90025e35	−	1.54350e35i	−0.858666	−	0.456976i
$283$			2.73525e35i			0.769297i	0.923063	+	0.384649i	$0.125677\pi$
$283$			2.73525e35i			0.769297i	−0.923063	+	0.384649i	$0.874323\pi$
$284$	3.69961e35	+	5.49384e35i	0.988645	+	1.46811i
$285$			6.23824e34i			0.158420i
$286$	2.06963e32	−	3.88886e32i	0.000499557	−	0.000938675i
$287$	−3.11250e35			−0.714204
$288$	7.51160e34	+	8.98634e34i	0.163886	+	0.196061i
$289$	−3.16836e35			−0.657380
$290$	−1.43133e35	+	2.68949e35i	−0.282468	+	0.530761i
$291$			1.45731e35i			0.273592i
$292$	−2.49574e35	−	3.70611e35i	−0.445808	−	0.662014i
$293$		−	8.49726e35i		−	1.44444i	−0.691665	−	0.722218i	$-0.743123\pi$
$293$		−	8.49726e35i		−	1.44444i	0.691665	−	0.722218i	$-0.256877\pi$
$294$	−9.99369e35	−	5.31858e35i	−1.61692	−	0.860516i
$295$	−5.50631e34			−0.0848089
$296$	9.77969e34	+	9.40715e35i	0.143415	+	1.37952i
$297$	−4.02898e34			−0.0562635
$298$	4.93127e35	+	2.62439e35i	0.655877	+	0.349054i
$299$		−	4.81132e33i		−	0.00609582i
$300$	−4.57405e35	+	3.08022e35i	−0.552131	+	0.371812i
$301$		−	2.40916e36i		−	2.77110i
$302$	−4.46065e34	+	8.38163e34i	−0.0488987	+	0.0918815i
$303$	1.25738e36			1.31386
$304$	−3.57270e35	−	1.44974e35i	−0.355901	−	0.144418i
$305$	6.03344e35			0.573083
$306$	7.75775e34	−	1.45769e35i	0.0702709	−	0.132040i
$307$			8.74059e35i			0.755152i	0.925979	+	0.377576i	$0.123242\pi$
$307$			8.74059e35i			0.755152i	−0.925979	+	0.377576i	$0.876758\pi$
$308$	9.23701e34	−	6.22031e34i	0.0761283	−	0.0512657i
$309$			1.92992e35i			0.151755i
$310$	−7.72713e35	−	4.11233e35i	−0.579794	−	0.308563i
$311$	2.05111e36			1.46880			0.734401	−	0.678716i	$-0.237463\pi$
$311$	2.05111e36			1.46880			0.734401	+	0.678716i	$0.237463\pi$
$312$	−2.57052e34	+	2.67232e33i	−0.0175703	+	0.00182661i
$313$	−1.53011e36			−0.998458			−0.499229	−	0.866470i	$-0.666383\pi$
$313$	−1.53011e36			−0.998458			−0.499229	+	0.866470i	$0.666383\pi$
$314$	5.71180e35	+	3.03978e35i	0.355872	+	0.189393i
$315$		−	3.62820e35i		−	0.215868i
$316$	9.82892e35	+	1.45957e36i	0.558525	+	0.829397i
$317$			3.20073e36i			1.73736i	0.495374	+	0.868680i	$0.335031\pi$
$317$			3.20073e36i			1.73736i	−0.495374	+	0.868680i	$0.664969\pi$
$318$	5.52833e35	−	1.03878e36i	0.286682	−	0.538681i
$319$	1.31835e35			0.0653230
$320$	2.07665e35	+	9.87979e35i	0.0983308	+	0.467814i
$321$	3.63027e36			1.64292
$322$	5.71404e35	−	1.07368e36i	0.247191	−	0.464476i
$323$			5.43590e35i			0.224820i
$324$	9.59299e35	+	1.42454e36i	0.379360	+	0.563340i
$325$			4.17663e34i			0.0157949i
$326$	8.79274e35	+	4.67944e35i	0.318031	+	0.169254i
$327$	−8.37411e34			−0.0289732
$328$	−1.21446e36	+	1.26255e35i	−0.401987	+	0.0417907i
$329$	−6.29029e36			−1.99219
$330$	−6.23962e34	−	3.32068e34i	−0.0189106	−	0.0100641i
$331$		−	4.75365e36i		−	1.37886i	−0.724350	−	0.689432i	$-0.757860\pi$
$331$		−	4.75365e36i		−	1.37886i	0.724350	−	0.689432i	$-0.242140\pi$
$332$	4.74482e36	−	3.19521e36i	1.31740	−	0.887151i
$333$		−	1.33338e36i		−	0.354417i
$334$	−8.68104e35	+	1.63118e36i	−0.220927	+	0.415125i
$335$	−2.63673e36			−0.642563
$336$	−6.05366e36	−	2.45647e36i	−1.41286	−	0.573313i
$337$	−7.16871e35			−0.160253			−0.0801267	−	0.996785i	$-0.525532\pi$
$337$	−7.16871e35			−0.160253			−0.0801267	+	0.996785i	$0.525532\pi$
$338$	2.19294e36	−	4.12058e36i	0.469608	−	0.882400i
$339$			6.22258e36i			1.27666i
$340$	1.18061e36	−	7.95036e35i	0.232093	−	0.156294i
$341$			3.78773e35i			0.0713577i
$342$	4.79851e35	+	2.55374e35i	0.0866419	+	0.0461102i
$343$	−1.14647e37			−1.98426
$344$	−9.77251e35	−	9.40024e36i	−0.162147	−	1.55970i
$345$	−7.71968e35			−0.122807
$346$	3.25365e36	+	1.73157e36i	0.496326	+	0.264141i
$347$			5.85907e36i			0.857140i	0.903509	+	0.428570i	$0.140982\pi$
$347$			5.85907e36i			0.857140i	−0.903509	+	0.428570i	$0.859018\pi$
$348$	−4.32003e36	−	6.41515e36i	−0.606161	−	0.900135i
$349$			9.84226e36i			1.32473i	0.749183	+	0.662363i	$0.230446\pi$
$349$			9.84226e36i			1.32473i	−0.749183	+	0.662363i	$0.769554\pi$
$350$	−4.96027e36	+	9.32042e36i	−0.640499	+	1.20351i
$351$	1.79018e35			0.0221791
$352$	3.35185e35	−	2.80178e35i	0.0398488	−	0.0333093i
$353$	1.11571e37			1.27297			0.636486	−	0.771288i	$-0.280387\pi$
$353$	1.11571e37			1.27297			0.636486	+	0.771288i	$0.280387\pi$
$354$	6.56700e35	−	1.23395e36i	0.0719151	−	0.135130i
$355$		−	8.04890e36i		−	0.846107i
$356$	3.46640e36	+	5.14752e36i	0.349827	+	0.519485i
$357$			9.21071e36i			0.892491i
$358$	−9.56058e36	−	5.08808e36i	−0.889571	−	0.473424i
$359$	1.80642e36			0.161417			0.0807083	−	0.996738i	$-0.474282\pi$
$359$	1.80642e36			0.161417			0.0807083	+	0.996738i	$0.474282\pi$
$360$	−1.47174e35	−	1.41568e36i	−0.0126312	−	0.121501i
$361$	1.03404e37			0.852478
$362$	1.69603e37	+	9.02613e36i	1.34325	+	0.714871i
$363$		−	1.13082e37i		−	0.860496i
$364$	−4.10424e35	+	2.76384e35i	−0.0300098	+	0.0202089i
$365$			5.42975e36i			0.381534i
$366$	−7.19568e36	+	1.35208e37i	−0.485955	+	0.913117i
$367$	−1.54580e37			−1.00345			−0.501724	−	0.865028i	$-0.667301\pi$
$367$	−1.54580e37			−1.00345			−0.501724	+	0.865028i	$0.667301\pi$
$368$	1.79402e36	−	4.42114e36i	0.111952	−	0.275893i
$369$	1.72139e36			0.103276
$370$	5.39965e36	−	1.01460e37i	0.311487	−	0.585290i
$371$		−	2.25299e37i		−	1.24979i
$372$	1.84312e37	−	1.24118e37i	0.983291	−	0.662159i
$373$			9.96234e36i			0.511191i	0.966784	+	0.255596i	$0.0822716\pi$
$373$			9.96234e36i			0.511191i	−0.966784	+	0.255596i	$0.917728\pi$
$374$	−5.43711e35	−	2.89359e35i	−0.0268367	−	0.0142823i
$375$	1.53877e37			0.730667
$376$	−2.45439e37	+	2.55159e36i	−1.12130	+	0.116570i
$377$	−5.85777e35			−0.0257503
$378$	3.99490e37	+	2.12606e37i	1.68995	+	0.899382i
$379$		−	2.96859e37i		−	1.20860i	−0.796758	−	0.604299i	$-0.793453\pi$
$379$		−	2.96859e37i		−	1.20860i	0.796758	−	0.604299i	$-0.206547\pi$
$380$	2.61714e36	+	3.88639e36i	0.102557	+	0.152295i
$381$		−	1.89934e37i		−	0.716458i
$382$	−1.60054e36	+	3.00744e36i	−0.0581229	+	0.109214i
$383$	3.57287e37			1.24921			0.624603	−	0.780942i	$-0.285261\pi$
$383$	3.57287e37			1.24921			0.624603	+	0.780942i	$0.285261\pi$
$384$	−2.46170e37	−	7.12922e36i	−0.828768	−	0.240016i
$385$	−1.35330e36			−0.0438745
$386$	−2.73437e37	+	5.13792e37i	−0.853771	+	1.60425i
$387$			1.33241e37i			0.400707i
$388$	6.11388e36	+	9.07896e36i	0.177116	+	0.263012i
$389$		−	2.28110e37i		−	0.636612i	−0.947988	−	0.318306i	$-0.896886\pi$
$389$		−	2.28110e37i		−	0.636612i	0.947988	−	0.318306i	$-0.103114\pi$
$390$	2.77242e35	+	1.47546e35i	0.00745457	+	0.00396727i
$391$	−6.72681e36			−0.174280
$392$	−8.45734e37	+	8.79227e36i	−2.11147	+	0.219509i
$393$	2.78425e37			0.669911
$394$	1.33671e37	+	7.11386e36i	0.309985	+	0.164972i
$395$		−	2.13839e37i		−	0.478000i
$396$	−5.10860e35	+	3.44019e35i	−0.0110083	+	0.00741315i
$397$			6.55086e37i			1.36093i	0.732781	+	0.680465i	$0.238222\pi$
$397$			6.55086e37i			1.36093i	−0.732781	+	0.680465i	$0.761778\pi$
$398$	−3.40109e36	+	6.39070e36i	−0.0681261	+	0.128010i
$399$	−3.03203e37			−0.585634
$400$	−1.55736e37	+	3.83792e37i	−0.290081	+	0.714868i
$401$	−3.62232e37			−0.650720			−0.325360	−	0.945590i	$-0.605485\pi$
$401$	−3.62232e37			−0.650720			−0.325360	+	0.945590i	$0.605485\pi$
$402$	3.14465e37	−	5.90884e37i	0.544871	−	1.02382i
$403$		−	1.68299e36i		−	0.0281292i
$404$	7.83344e37	−	5.27513e37i	1.26306	−	0.850557i
$405$		−	2.08706e37i		−	0.324666i
$406$	−1.30720e38	−	6.95683e37i	−1.96207	−	1.04420i
$407$	−4.97344e36			−0.0720340
$408$	3.73623e36	+	3.59390e37i	0.0522229	+	0.502336i
$409$	4.11429e37			0.555018			0.277509	−	0.960723i	$-0.410491\pi$
$409$	4.11429e37			0.555018			0.277509	+	0.960723i	$0.410491\pi$
$410$	1.30985e37	+	6.97092e36i	0.170551	+	0.0907662i
$411$			1.01207e36i			0.0127204i
$412$	8.09664e36	+	1.20233e37i	0.0982416	+	0.145886i
$413$		−	2.67628e37i		−	0.313514i
$414$	−3.16019e36	+	5.93806e36i	−0.0357445	+	0.0671644i
$415$	−6.95153e37			−0.759247
$416$	−1.48931e36	+	1.24490e36i	−0.0157084	+	0.0131305i
$417$	−8.78006e37			−0.894386
$418$	9.52527e35	−	1.78981e36i	0.00937176	−	0.0176097i
$419$			5.28940e37i			0.502693i	0.967897	+	0.251347i	$0.0808734\pi$
$419$			5.28940e37i			0.502693i	−0.967897	+	0.251347i	$0.919127\pi$
$420$	4.43454e37	+	6.58519e37i	0.407131	+	0.604580i
$421$		−	1.01760e38i		−	0.902583i	−0.892377	−	0.451292i	$-0.850963\pi$
$421$		−	1.01760e38i		−	0.902583i	0.892377	−	0.451292i	$-0.149037\pi$
$422$	−1.07122e38	−	5.70099e37i	−0.918016	−	0.488562i
$423$	3.47889e37			0.288075
$424$	−9.13902e36	−	8.79088e37i	−0.0731298	−	0.703440i
$425$	5.83944e37			0.451577
$426$	1.80374e38	+	9.59938e37i	1.34814	+	0.717470i
$427$			2.93249e38i			2.11852i
$428$	2.26164e38	−	1.52301e38i	1.57939	−	1.06358i
$429$		−	1.35900e35i		−	0.000917465i
$430$	−5.39568e37	+	1.01386e38i	−0.352171	+	0.661735i
$431$	1.12901e38			0.712485			0.356242	−	0.934394i	$-0.384058\pi$
$431$	1.12901e38			0.712485			0.356242	+	0.934394i	$0.384058\pi$
$432$	1.64500e38	+	6.67512e37i	1.00381	+	0.407329i
$433$	−2.41009e38			−1.42220			−0.711098	−	0.703093i	$-0.751802\pi$
$433$	−2.41009e38			−1.42220			−0.711098	+	0.703093i	$0.751802\pi$
$434$	1.99875e38	−	3.75569e38i	1.14067	−	2.14333i
$435$			9.39870e37i			0.518768i
$436$	−5.21703e36	+	3.51321e36i	−0.0278528	+	0.0187564i
$437$		−	2.21437e37i		−	0.114359i
$438$	−1.21679e38	−	6.47569e37i	−0.607914	−	0.323528i
$439$	−6.94692e36			−0.0335781			−0.0167891	−	0.999859i	$-0.505344\pi$
$439$	−6.94692e36			−0.0335781			−0.0167891	+	0.999859i	$0.505344\pi$
$440$	−5.28039e36	+	5.48950e35i	−0.0246946	+	0.00256726i
$441$	1.19876e38			0.542465
$442$	2.41585e36	+	1.28570e36i	0.0105790	+	0.00563009i
$443$			2.22067e38i			0.941086i	0.882377	+	0.470543i	$0.155942\pi$
$443$			2.22067e38i			0.941086i	−0.882377	+	0.470543i	$0.844058\pi$
$444$	1.62972e38	+	2.42009e38i	0.668436	+	0.992611i
$445$		−	7.54152e37i		−	0.299391i
$446$	7.12214e37	−	1.33826e38i	0.273688	−	0.514263i
$447$	1.72328e38			0.641057
$448$	−4.80197e38	+	1.00934e38i	−1.72937	+	0.363500i
$449$	1.00503e38			0.350436			0.175218	−	0.984530i	$-0.443937\pi$
$449$	1.00503e38			0.350436			0.175218	+	0.984530i	$0.443937\pi$
$450$	2.74332e37	−	5.15473e37i	0.0926178	−	0.174030i
$451$		−	6.42069e36i		−	0.0209904i
$452$	2.61057e38	+	3.87664e38i	0.826472	+	1.22729i
$453$			2.92904e37i			0.0898053i
$454$	−3.57726e38	−	1.90380e38i	−1.06228	−	0.565341i
$455$	6.01304e36			0.0172953
$456$	−1.18306e38	+	1.22991e37i	−0.329622	+	0.0342676i
$457$	−4.68163e38			−1.26361			−0.631804	−	0.775128i	$-0.717685\pi$
$457$	−4.68163e38			−1.26361			−0.631804	+	0.775128i	$0.717685\pi$
$458$	−3.73416e38	−	1.98729e38i	−0.976434	−	0.519652i
$459$		−	2.50289e38i		−	0.634099i
$460$	−4.80933e37	+	3.23866e37i	−0.118058	+	0.0795017i
$461$			1.91135e38i			0.454649i	0.973819	+	0.227325i	$0.0729979\pi$
$461$			1.91135e38i			0.454649i	−0.973819	+	0.227325i	$0.927002\pi$
$462$	1.61398e37	−	3.03270e37i	0.0372041	−	0.0699070i
$463$	−9.47814e37			−0.211738			−0.105869	−	0.994380i	$-0.533762\pi$
$463$	−9.47814e37			−0.211738			−0.105869	+	0.994380i	$0.533762\pi$
$464$	−5.38272e38	−	2.18421e38i	−1.16544	−	0.472917i
$465$	−2.70032e38			−0.566693
$466$	1.79246e38	−	3.36806e38i	0.364631	−	0.685148i
$467$		−	1.77344e38i		−	0.349721i	−0.984593	−	0.174861i	$-0.944053\pi$
$467$		−	1.77344e38i		−	0.349721i	0.984593	−	0.174861i	$-0.0559475\pi$
$468$	2.26988e36	−	1.52857e36i	0.00433949	−	0.00292226i
$469$		−	1.28155e39i		−	2.37537i
$470$	2.64717e38	+	1.40881e38i	0.475733	+	0.253182i
$471$	1.99605e38			0.347830
$472$	−1.08561e37	−	1.04425e38i	−0.0183448	−	0.176460i
$473$	4.96979e37			0.0814425
$474$	4.79207e38	+	2.55031e38i	0.761618	+	0.405328i
$475$			1.92226e38i			0.296315i
$476$	3.86419e38	+	5.73823e38i	0.577774	+	0.857980i
$477$			1.24603e38i			0.180723i
$478$	−5.59354e38	+	1.05104e39i	−0.787014	+	1.47881i
$479$	4.97161e38			0.678629			0.339314	−	0.940673i	$-0.389805\pi$
$479$	4.97161e38			0.678629			0.339314	+	0.940673i	$0.389805\pi$
$480$	1.99742e38	+	2.38957e38i	0.264528	+	0.316463i
$481$	2.20983e37			0.0283958
$482$	−6.87049e38	+	1.29098e39i	−0.856654	+	1.60967i
$483$		−	3.75207e38i		−	0.453981i
$484$	−4.74417e38	−	7.04498e38i	−0.557061	−	0.827222i
$485$		−	1.33014e38i		−	0.151580i
$486$	−3.96915e38	−	2.11235e38i	−0.439007	−	0.233636i
$487$	−1.78929e38			−0.192093			−0.0960466	−	0.995377i	$-0.530620\pi$
$487$	−1.78929e38			−0.192093			−0.0960466	+	0.995377i	$0.530620\pi$
$488$	1.18953e38	+	1.14422e39i	0.123962	+	1.19240i
$489$	3.07271e38			0.310845
$490$	9.12161e38	+	4.85446e38i	0.895836	+	0.476758i
$491$		−	1.36069e38i		−	0.129742i	−0.997894	−	0.0648708i	$-0.979336\pi$
$491$		−	1.36069e38i		−	0.129742i	0.997894	−	0.0648708i	$-0.0206635\pi$
$492$	−3.12433e38	+	2.10396e38i	−0.289243	+	0.194780i
$493$			8.18988e38i			0.736202i
$494$	−4.23232e36	+	7.95260e36i	−0.00369435	+	0.00694174i
$495$	7.48451e36			0.00634436
$496$	6.27543e38	−	1.54650e39i	0.516605	−	1.27311i
$497$	3.91208e39			3.12781
$498$	8.29062e38	−	1.55782e39i	0.643815	−	1.20974i
$499$		−	6.43698e38i		−	0.485539i	−0.970084	−	0.242770i	$-0.921944\pi$
$499$		−	6.43698e38i		−	0.485539i	0.970084	−	0.242770i	$-0.0780559\pi$
$500$	9.58644e38	−	6.45562e38i	0.702413	−	0.473013i
$501$			5.70033e38i			0.405745i
$502$	−1.33115e39	−	7.08431e38i	−0.920501	−	0.489885i
$503$	−5.24902e38			−0.352649			−0.176324	−	0.984332i	$-0.556421\pi$
$503$	−5.24902e38			−0.352649			−0.176324	+	0.984332i	$0.556421\pi$
$504$	6.88075e38	−	7.15325e37i	0.449152	−	0.0466939i
$505$	−1.14766e39			−0.727928
$506$	2.21486e37	+	1.17873e37i	0.0136510	+	0.00726495i
$507$		−	1.43998e39i		−	0.862462i
$508$	−7.96835e38	−	1.18328e39i	−0.463815	−	0.688754i
$509$			1.65456e39i			0.935995i	0.883730	+	0.467998i	$0.155024\pi$
$509$			1.65456e39i			0.935995i	−0.883730	+	0.467998i	$0.844976\pi$
$510$	2.06288e38	−	3.87618e38i	0.113424	−	0.213126i
$511$	−2.63907e39			−1.41042
$512$	−1.83272e39	+	5.88617e38i	−0.952100	+	0.305786i
$513$	8.23913e38			0.416083
$514$	−1.35811e39	+	2.55191e39i	−0.666759	+	1.25285i
$515$		−	1.76151e38i		−	0.0840776i
$516$	−1.62852e39	−	2.41832e39i	−0.755741	−	1.12226i
$517$		−	1.29761e38i		−	0.0585504i
$518$	4.93137e39	+	2.62444e39i	2.16364	+	1.15148i
$519$	1.13702e39			0.485111
$520$	2.34621e37	−	2.43913e36i	0.00973461	−	0.00101201i
$521$	−2.41225e39			−0.973362			−0.486681	−	0.873580i	$-0.661793\pi$
$521$	−2.41225e39			−0.973362			−0.486681	+	0.873580i	$0.661793\pi$
$522$	7.22957e38	+	3.84753e38i	0.283720	+	0.150994i
$523$			1.44931e39i			0.553206i	0.960984	+	0.276603i	$0.0892086\pi$
$523$			1.44931e39i			0.553206i	−0.960984	+	0.276603i	$0.910791\pi$
$524$	1.73458e39	−	1.16808e39i	0.644006	−	0.433681i
$525$			3.25711e39i			1.17631i
$526$	9.33283e38	−	1.75365e39i	0.327884	−	0.616099i
$527$	−2.35302e39			−0.804214
$528$	5.06737e37	−	1.24879e38i	0.0168497	−	0.0415239i
$529$	−2.81704e39			−0.911350
$530$	−5.04591e38	+	9.48135e38i	−0.158833	+	0.298449i
$531$			1.48014e38i			0.0453349i
$532$	−1.88894e39	+	1.27203e39i	−0.562988	+	0.379123i
$533$			2.85288e37i			0.00827443i
$534$	1.69004e39	+	8.99426e38i	0.477032	+	0.253873i
$535$	−3.31348e39			−0.910237
$536$	−5.19849e38	−	5.00046e39i	−0.138991	−	1.33697i
$537$	−3.34104e39			−0.869470
$538$	−1.75957e39	−	9.36433e38i	−0.445722	−	0.237211i
$539$		−	4.47129e38i		−	0.110254i
$540$	−1.20503e39	−	1.78944e39i	−0.289259	−	0.429543i
$541$			7.65834e39i			1.78968i	0.446391	+	0.894838i	$0.352709\pi$
$541$			7.65834e39i			1.78968i	−0.446391	+	0.894838i	$0.647291\pi$
$542$	1.89644e39	−	3.56345e39i	0.431470	−	0.810738i
$543$	5.92693e39			1.31290
$544$	1.74052e39	+	2.08224e39i	0.375401	+	0.449103i
$545$	7.64337e37			0.0160522
$546$	−7.17134e37	+	1.34751e38i	−0.0146658	+	0.0275574i
$547$		−	7.17574e39i		−	1.42906i	−0.699605	−	0.714530i	$-0.746640\pi$
$547$		−	7.17574e39i		−	1.42906i	0.699605	−	0.714530i	$-0.253360\pi$
$548$	4.24594e37	+	6.30512e37i	0.00823485	+	0.0122286i
$549$		−	1.62184e39i		−	0.306343i
$550$	−1.92268e38	−	1.02324e38i	−0.0353711	−	0.0188243i
$551$	−2.69599e39			−0.483080
$552$	−1.52199e38	−	1.46401e39i	−0.0265641	−	0.255522i
$553$	1.03934e40			1.76703
$554$	−4.79786e39	−	2.55339e39i	−0.794614	−	0.422888i
$555$		−	3.54563e39i		−	0.572065i
$556$	−5.46994e39	+	3.68352e39i	−0.859801	+	0.579000i
$557$		−	2.19393e39i		−	0.335987i	−0.985788	−	0.167994i	$-0.946271\pi$
$557$		−	2.19393e39i		−	0.335987i	0.985788	−	0.167994i	$-0.0537288\pi$
$558$	−1.10543e39	+	2.07711e39i	−0.164943	+	0.309931i
$559$	−2.20820e38			−0.0321046
$560$	5.52540e39	+	2.24211e39i	0.782775	+	0.317636i
$561$	−1.90005e38			−0.0262303
$562$	6.13575e38	−	1.15292e39i	0.0825451	−	0.155104i
$563$			1.02319e40i			1.34148i	0.741690	+	0.670742i	$0.234024\pi$
$563$			1.02319e40i			1.34148i	−0.741690	+	0.670742i	$0.765976\pi$
$564$	−6.31420e39	+	4.25205e39i	−0.806810	+	0.543315i
$565$		−	5.67958e39i		−	0.707316i
$566$	5.59474e39	+	2.97749e39i	0.679113	+	0.361419i
$567$	1.01439e40			1.20019
$568$	1.52645e40	−	1.58690e39i	1.76048	−	0.183020i
$569$	5.66712e39			0.637140			0.318570	−	0.947899i	$-0.396797\pi$
$569$	5.66712e39			0.637140			0.318570	+	0.947899i	$0.396797\pi$
$570$	1.27598e39	+	6.79069e38i	0.139849	+	0.0744267i
$571$			1.62421e38i			0.0173548i	0.999962	+	0.00867740i	$0.00276214\pi$
$571$			1.62421e38i			0.0173548i	−0.999962	+	0.00867740i	$0.997238\pi$
$572$	−5.70145e36	−	8.46652e36i	−0.000593941	−	0.000881988i
$573$			1.05098e39i			0.106746i
$574$	−3.38814e39	+	6.36638e39i	−0.335536	+	0.630478i
$575$	−2.37875e39			−0.229702
$576$	2.65577e39	−	5.58221e38i	0.250071	−	0.0525630i
$577$	−1.26117e38			−0.0115804			−0.00579019	−	0.999983i	$-0.501843\pi$
$577$	−1.26117e38			−0.0115804			−0.00579019	+	0.999983i	$0.501843\pi$
$578$	−3.44895e39	+	6.48064e39i	−0.308840	+	0.580316i
$579$			1.79550e40i			1.56800i
$580$	3.94306e39	+	5.85534e39i	0.335836	+	0.498708i
$581$		−	3.37872e40i		−	2.80671i
$582$	2.98081e39	+	1.58637e39i	0.241519	+	0.128535i
$583$	4.64763e38			0.0367314
$584$	−1.02973e40	+	1.07051e39i	−0.793849	+	0.0825287i
$585$	−3.32556e37			−0.00250095
$586$	−1.73805e40	−	9.24977e39i	−1.27511	−	0.678603i
$587$		−	1.14108e40i		−	0.816705i	−0.912824	−	0.408353i	$-0.866103\pi$
$587$		−	1.14108e40i		−	0.816705i	0.912824	−	0.408353i	$-0.133897\pi$
$588$	−2.17575e40	+	1.46517e40i	−1.51928	+	1.02310i
$589$		−	7.74579e39i		−	0.527708i
$590$	−5.99395e38	+	1.12627e39i	−0.0398436	+	0.0748668i
$591$	4.67125e39			0.302981
$592$	2.03062e40	+	8.23988e39i	1.28518	+	0.521502i
$593$	−1.71476e40			−1.05904			−0.529519	−	0.848298i	$-0.677628\pi$
$593$	−1.71476e40			−1.05904			−0.529519	+	0.848298i	$0.677628\pi$
$594$	−4.38578e38	+	8.24096e38i	−0.0264328	+	0.0496677i
$595$		−	8.40696e39i		−	0.494473i
$596$	1.07360e40	−	7.22971e39i	0.616268	−	0.415002i
$597$			2.23329e39i			0.125117i
$598$	−9.84118e37	−	5.23741e37i	−0.00538121	−	0.00286384i
$599$	−4.38460e38			−0.0234014			−0.0117007	−	0.999932i	$-0.503725\pi$
$599$	−4.38460e38			−0.0234014			−0.0117007	+	0.999932i	$0.503725\pi$
$600$	1.32121e39	+	1.27088e40i	0.0688304	+	0.662084i
$601$	7.92587e39			0.403058			0.201529	−	0.979483i	$-0.435409\pi$
$601$	7.92587e39			0.403058			0.201529	+	0.979483i	$0.435409\pi$
$602$	−4.92775e40	−	2.62251e40i	−2.44624	−	1.30187i
$603$			7.08774e39i			0.343484i
$604$	1.22883e39	+	1.82478e39i	0.0581374	+	0.0863327i
$605$			1.03214e40i			0.476747i
$606$	1.36874e40	−	2.57188e40i	0.617258	−	1.15984i
$607$	−4.09531e39			−0.180323			−0.0901614	−	0.995927i	$-0.528738\pi$
$607$	−4.09531e39			−0.180323			−0.0901614	+	0.995927i	$0.528738\pi$
$608$	−6.85442e39	+	5.72954e39i	−0.294692	+	0.246330i
$609$	−4.56814e40			−1.91773
$610$	6.56776e39	−	1.23409e40i	0.269237	−	0.505901i
$611$			5.76559e38i			0.0230806i
$612$	−2.13712e39	−	3.17357e39i	−0.0835475	−	0.124066i
$613$			3.67421e39i			0.140277i	0.997537	+	0.0701387i	$0.0223442\pi$
$613$			3.67421e39i			0.140277i	−0.997537	+	0.0701387i	$0.977656\pi$
$614$	1.78782e40	+	9.51466e39i	0.666626	+	0.354774i
$615$	4.57739e39			0.166697
$616$	−2.66811e38	−	2.56648e39i	−0.00949039	−	0.0912887i
$617$	8.01951e39			0.278621			0.139310	−	0.990249i	$-0.455511\pi$
$617$	8.01951e39			0.278621			0.139310	+	0.990249i	$0.455511\pi$
$618$	3.94750e39	+	2.10083e39i	0.133964	+	0.0712950i
$619$			5.69660e40i			1.88843i	0.329328	+	0.944216i	$0.393178\pi$
$619$			5.69660e40i			1.88843i	−0.329328	+	0.944216i	$0.606822\pi$
$620$	−1.68229e40	+	1.13287e40i	−0.544780	+	0.366861i
$621$			1.01958e40i			0.322546i
$622$	2.23276e40	−	4.19538e40i	0.690050	−	1.29662i
$623$	3.66548e40			1.10676
$624$	−2.25156e38	+	5.54870e38i	−0.00664214	+	0.0163687i
$625$	1.27212e40			0.366665
$626$	−1.66562e40	+	3.12972e40i	−0.469080	+	0.881409i
$627$		−	6.25468e38i		−	0.0172118i
$628$	1.24353e40	−	8.37406e39i	0.334380	−	0.225175i
$629$		−	3.08961e40i		−	0.811837i
$630$	−7.42120e39	−	3.94951e39i	−0.190562	−	0.101416i
$631$	2.98605e40			0.749326			0.374663	−	0.927161i	$-0.377758\pi$
$631$	2.98605e40			0.749326			0.374663	+	0.927161i	$0.377758\pi$
$632$	4.05537e40	−	4.21598e39i	0.994565	−	0.103395i
$633$	−3.74350e40			−0.897272
$634$	6.54684e40	+	3.48418e40i	1.53369	+	0.816219i
$635$			1.73360e40i			0.396944i
$636$	−1.52296e40	−	2.26155e40i	−0.340847	−	0.506149i
$637$			1.98671e39i			0.0434622i
$638$	1.43510e39	−	2.69658e39i	0.0306890	−	0.0576652i
$639$	−2.16361e40			−0.452289
$640$	2.24689e40	+	6.50711e39i	0.459168	+	0.132978i
$641$	3.06343e40			0.612022			0.306011	−	0.952028i	$-0.401006\pi$
$641$	3.06343e40			0.612022			0.306011	+	0.952028i	$0.401006\pi$
$642$	3.95176e40	−	7.42542e40i	0.771850	−	1.45032i
$643$			6.79168e40i			1.29693i	0.761242	+	0.648467i	$0.224590\pi$
$643$			6.79168e40i			1.29693i	−0.761242	+	0.648467i	$0.775410\pi$
$644$	−1.57411e40	−	2.33752e40i	−0.293894	−	0.436426i
$645$			3.54303e40i			0.646783i
$646$	1.11187e40	+	5.91730e39i	0.198464	+	0.105621i
$647$	−1.01776e41			−1.77638			−0.888188	−	0.459480i	$-0.848036\pi$
$647$	−1.01776e41			−1.77638			−0.888188	+	0.459480i	$0.848036\pi$
$648$	3.95803e40	−	4.11478e39i	0.675525	−	0.0702277i
$649$	5.52083e38			0.00921417
$650$	8.54297e38	+	4.54651e38i	0.0139433	+	0.00742053i
$651$		−	1.31246e41i		−	2.09490i
$652$	1.91428e40	−	1.28910e40i	0.298825	−	0.201232i
$653$			8.39578e40i			1.28180i	0.767625	+	0.640899i	$0.221438\pi$
$653$			8.39578e40i			1.28180i	−0.767625	+	0.640899i	$0.778562\pi$
$654$	−9.11572e38	+	1.71286e39i	−0.0136117	+	0.0255767i
$655$	−2.54129e40			−0.371155
$656$	−1.06377e40	+	2.62152e40i	−0.151964	+	0.374496i
$657$	1.45956e40			0.203950
$658$	−6.84735e40	+	1.28663e41i	−0.935939	+	1.75864i
$659$		−	3.82158e40i		−	0.510981i	−0.966812	−	0.255491i	$-0.917763\pi$
$659$		−	3.82158e40i		−	0.510981i	0.966812	−	0.255491i	$-0.0822370\pi$
$660$	−1.35844e39	+	9.14788e38i	−0.0177686	+	0.0119656i
$661$		−	4.65389e40i		−	0.595518i	−0.954641	−	0.297759i	$-0.903761\pi$
$661$		−	4.65389e40i		−	0.595518i	0.954641	−	0.297759i	$-0.0962393\pi$
$662$	−9.72322e40	−	5.17463e40i	−1.21722	−	0.647797i
$663$	8.44241e38			0.0103400
$664$	−1.37054e40	−	1.31833e41i	−0.164231	−	1.57975i
$665$	2.76744e40			0.324463
$666$	−2.72733e40	−	1.45147e40i	−0.312868	−	0.166507i
$667$		−	3.33622e40i		−	0.374482i
$668$	2.39147e40	+	3.55128e40i	0.262668	+	0.390055i
$669$		−	4.67669e40i		−	0.502643i
$670$	−2.87024e40	+	5.39322e40i	−0.301879	+	0.567236i
$671$	−6.04935e39			−0.0622633
$672$	−1.16143e41	+	9.70826e40i	−1.16987	+	0.977884i
$673$	1.76559e41			1.74049			0.870243	−	0.492624i	$-0.163962\pi$
$673$	1.76559e41			1.74049			0.870243	+	0.492624i	$0.163962\pi$
$674$	−7.80357e39	+	1.46630e40i	−0.0752878	+	0.141467i
$675$		−	8.85077e40i		−	0.835750i
$676$	−6.04116e40	−	8.97098e40i	−0.558333	−	0.829112i
$677$			1.38750e41i			1.25515i	0.778555	+	0.627577i	$0.215953\pi$
$677$			1.38750e41i			1.25515i	−0.778555	+	0.627577i	$0.784047\pi$
$678$	1.27278e41	+	6.77364e40i	1.12700	+	0.599780i
$679$	6.46500e40			0.560347
$680$	−3.41020e39	−	3.28029e40i	−0.0289334	−	0.278313i
$681$	−1.25011e41			−1.03828
$682$	7.74750e39	+	4.12317e39i	0.0629924	+	0.0335242i
$683$			1.06021e41i			0.843900i	0.906619	+	0.421950i	$0.138654\pi$
$683$			1.06021e41i			0.843900i	−0.906619	+	0.421950i	$0.861346\pi$
$684$	1.04469e40	−	7.03508e39i	0.0814095	−	0.0548221i
$685$		−	9.23750e38i		−	0.00704759i
$686$	−1.24800e41	+	2.34502e41i	−0.932214	+	1.75165i
$687$	−1.30494e41			−0.954371
$688$	−2.02912e41	−	8.23383e40i	−1.45304	−	0.589616i
$689$	−2.06506e39			−0.0144795
$690$	−8.40334e39	+	1.57900e40i	−0.0576952	+	0.108410i
$691$		−	9.35943e40i		−	0.629242i	−0.949217	−	0.314621i	$-0.898123\pi$
$691$		−	9.35943e40i		−	0.629242i	0.949217	−	0.314621i	$-0.101877\pi$
$692$	7.08358e40	−	4.77016e40i	0.466352	−	0.314047i
$693$			3.63777e39i			0.0234532i
$694$	1.19843e41	+	6.37795e40i	0.756658	+	0.402688i
$695$	8.01389e40			0.495523
$696$	−1.78243e41	+	1.85302e40i	−1.07939	+	0.112214i
$697$	3.98867e40			0.236566
$698$	2.01316e41	+	1.07139e41i	1.16943	+	0.622362i
$699$		−	1.17700e41i		−	0.669666i
$700$	1.36646e41	+	2.02917e41i	0.761512	+	1.13083i
$701$		−	1.54919e41i		−	0.845657i	−0.906210	−	0.422828i	$-0.861037\pi$
$701$		−	1.54919e41i		−	0.845657i	0.906210	−	0.422828i	$-0.138963\pi$
$702$	1.94872e39	−	3.66167e39i	0.0104198	−	0.0195790i
$703$	1.01705e41			0.532710
$704$	−2.08213e39	−	9.90584e39i	−0.0106833	−	0.0508262i
$705$	9.25080e40			0.464983
$706$	1.21452e41	−	2.28210e41i	0.598048	−	1.12374i
$707$		−	5.57808e41i		−	2.69094i
$708$	−1.80909e40	−	2.68646e40i	−0.0855024	−	0.126969i
$709$		−	2.65495e40i		−	0.122938i	−0.998109	−	0.0614690i	$-0.980421\pi$
$709$		−	2.65495e40i		−	0.122938i	0.998109	−	0.0614690i	$-0.0195785\pi$
$710$	−1.64634e41	−	8.76171e40i	−0.746919	−	0.397505i
$711$	−5.74815e40			−0.255517
$712$	1.43022e41	−	1.48686e40i	0.622936	−	0.0647606i
$713$	9.58525e40			0.409077
$714$	1.88398e41	+	1.00264e41i	0.787865	+	0.419297i
$715$			1.24041e38i			0.000508310i
$716$	−2.08145e41	+	1.40167e41i	−0.835849	+	0.562870i
$717$			3.67295e41i			1.44540i
$718$	1.96639e40	−	3.69488e40i	0.0758343	−	0.142494i
$719$	9.53555e39			0.0360393			0.0180197	−	0.999838i	$-0.494264\pi$
$719$	9.53555e39			0.0360393			0.0180197	+	0.999838i	$0.494264\pi$
$720$	−3.05586e40	−	1.24002e40i	−0.113191	−	0.0459310i
$721$	8.56164e40			0.310810
$722$	1.12561e41	−	2.11505e41i	0.400498	−	0.752542i
$723$			4.51144e41i			1.57329i
$724$	3.69245e41	−	2.48654e41i	1.26213	−	0.849935i
$725$			2.89612e41i			0.970323i
$726$	−2.31301e41	−	1.23097e41i	−0.759620	−	0.404265i
$727$	2.93044e39			0.00943373			0.00471687	−	0.999989i	$-0.498499\pi$
$727$	2.93044e39			0.00943373			0.00471687	+	0.999989i	$0.498499\pi$
$728$	1.18551e39	+	1.14035e40i	0.00374111	+	0.0359860i
$729$	−3.58251e41			−1.10825
$730$	1.11061e41	+	5.91060e40i	0.336807	+	0.179246i
$731$			3.08734e41i			0.917872i
$732$	1.98228e41	+	2.94364e41i	0.577769	+	0.857973i
$733$			6.25117e40i			0.178630i	0.996003	+	0.0893148i	$0.0284677\pi$
$733$			6.25117e40i			0.178630i	−0.996003	+	0.0893148i	$0.971532\pi$
$734$	−1.68269e41	+	3.16181e41i	−0.471424	+	0.885814i
$735$	3.18764e41			0.875594
$736$	−7.09019e40	−	8.48220e40i	−0.190954	−	0.228444i
$737$	2.64368e40			0.0698120
$738$	1.87384e40	−	3.52097e40i	0.0485194	−	0.0911687i
$739$			5.00173e41i			1.26992i	0.772545	+	0.634959i	$0.218983\pi$
$739$			5.00173e41i			1.26992i	−0.772545	+	0.634959i	$0.781017\pi$
$740$	−1.48751e41	−	2.20891e41i	−0.370338	−	0.549944i
$741$			2.77912e39i			0.00678489i
$742$	−4.60831e41	−	2.45251e41i	−1.10328	−	0.587158i
$743$	−1.94900e41			−0.457588			−0.228794	−	0.973475i	$-0.573478\pi$
$743$	−1.94900e41			−0.457588			−0.228794	+	0.973475i	$0.573478\pi$
$744$	−5.32387e40	−	5.12107e41i	−0.122580	−	1.17911i
$745$	−1.57290e41			−0.355169
$746$	2.03772e41	+	1.08446e41i	0.451265	+	0.240160i
$747$			1.86863e41i			0.405858i
$748$	−1.18372e40	+	7.97132e39i	−0.0252160	+	0.0169808i
$749$		−	1.61048e42i		−	3.36488i
$750$	1.67504e41	−	3.14743e41i	0.343271	−	0.645011i
$751$	−6.83822e41			−1.37456			−0.687280	−	0.726392i	$-0.741196\pi$
$751$	−6.83822e41			−1.37456			−0.687280	+	0.726392i	$0.741196\pi$
$752$	−2.14984e41	+	5.29802e41i	−0.423885	+	1.04461i
$753$	−4.65185e41			−0.899702
$754$	−6.37653e39	+	1.19816e40i	−0.0120976	+	0.0227316i
$755$		−	2.67345e40i		−	0.0497555i
$756$	8.69737e41	−	5.85691e41i	1.58790	−	1.06931i
$757$			7.04397e41i			1.26162i	0.775939	+	0.630808i	$0.217277\pi$
$757$			7.04397e41i			1.26162i	−0.775939	+	0.630808i	$0.782723\pi$
$758$	−6.07202e41	−	3.23149e41i	−1.06691	−	0.567805i
$759$	7.74004e39			0.0133425
$760$	1.07982e41	−	1.12259e40i	0.182623	−	0.0189855i
$761$	1.55438e41			0.257917			0.128959	−	0.991650i	$-0.458837\pi$
$761$	1.55438e41			0.257917			0.128959	+	0.991650i	$0.458837\pi$
$762$	−3.88495e41	−	2.06755e41i	−0.632468	−	0.336595i
$763$			3.71498e40i			0.0593404i
$764$	4.40920e40	+	6.54755e40i	0.0691044	+	0.102618i
$765$			4.64954e40i			0.0715021i
$766$	3.88928e41	−	7.30801e41i	0.586883	−	1.10276i
$767$	−2.45304e39			−0.00363222
$768$	−4.13794e41	+	4.25916e41i	−0.601238	+	0.618852i
$769$	−1.21075e42			−1.72632			−0.863160	−	0.504930i	$-0.831518\pi$
$769$	−1.21075e42			−1.72632			−0.863160	+	0.504930i	$0.831518\pi$
$770$	−1.47314e40	+	2.76806e40i	−0.0206124	+	0.0387311i
$771$			8.91789e41i			1.22454i
$772$	7.53269e41	+	1.11859e42i	1.01508	+	1.50737i
$773$		−	5.36588e41i		−	0.709641i	−0.934935	−	0.354820i	$-0.884542\pi$
$773$		−	5.36588e41i		−	0.709641i	0.934935	−	0.354820i	$-0.115458\pi$
$774$	2.72533e41	+	1.45040e41i	0.353733	+	0.188254i
$775$	−8.32080e41			−1.05996
$776$	2.52256e41	−	2.62246e40i	0.315389	−	0.0327879i
$777$	1.72332e42			2.11475
$778$	−4.66581e41	−	2.48311e41i	−0.561983	−	0.299083i
$779$			1.31301e41i			0.155230i
$780$	6.03589e39	−	4.06464e39i	0.00700438	−	0.00471683i
$781$			8.07012e40i			0.0919264i
$782$	−7.32254e40	+	1.37592e41i	−0.0818773	+	0.153849i
$783$	1.24133e42			1.36252
$784$	−7.40793e41	+	1.82559e42i	−0.798204	+	1.96707i
$785$	−1.82187e41			−0.192711
$786$	3.03083e41	−	5.69497e41i	0.314727	−	0.591377i
$787$		−	9.27051e41i		−	0.945083i	−0.881308	−	0.472542i	$-0.843337\pi$
$787$		−	9.27051e41i		−	0.945083i	0.881308	−	0.472542i	$-0.156663\pi$
$788$	2.91017e41	−	1.95974e41i	0.291265	−	0.196141i
$789$		−	6.12832e41i		−	0.602178i
$790$	−4.37390e41	−	2.32776e41i	−0.421965	−	0.224567i
$791$	2.76050e42			2.61474
$792$	1.47562e39	+	1.41941e40i	0.00137233	+	0.0132006i
$793$	2.68788e40			0.0245442
$794$	1.33993e42	+	7.13100e41i	1.20139	+	0.639371i
$795$			3.31335e41i			0.291705i
$796$	9.36939e40	+	1.39133e41i	0.0809975	+	0.120279i
$797$		−	8.18415e41i		−	0.694749i	−0.937726	−	0.347374i	$-0.887073\pi$
$797$		−	8.18415e41i		−	0.694749i	0.937726	−	0.347374i	$-0.112927\pi$
$798$	−3.30054e41	+	6.20177e41i	−0.275134	+	0.516980i
$799$	8.06100e41			0.659874
$800$	6.15488e41	+	7.36326e41i	0.494783	+	0.591923i
$801$	−2.02722e41			−0.160040
$802$	−3.94312e41	+	7.40918e41i	−0.305711	+	0.574436i
$803$		−	5.44406e40i		−	0.0414522i
$804$	−8.66293e41	−	1.28643e42i	−0.647817	−	0.961993i
$805$			3.42465e41i			0.251522i
$806$	−3.44241e40	−	1.83203e40i	−0.0248316	−	0.0132152i
$807$	−6.14901e41			−0.435651
$808$	−2.26269e41	−	2.17650e42i	−0.157457	−	1.51458i
$809$	−2.01413e41			−0.137668			−0.0688342	−	0.997628i	$-0.521928\pi$
$809$	−2.01413e41			−0.137668			−0.0688342	+	0.997628i	$0.521928\pi$
$810$	−4.26891e41	−	2.27189e41i	−0.286605	−	0.152529i
$811$			5.24879e40i			0.0346144i	0.999850	+	0.0173072i	$0.00550933\pi$
$811$			5.24879e40i			0.0346144i	−0.999850	+	0.0173072i	$0.994491\pi$
$812$	−2.84593e42	+	1.91648e42i	−1.84358	+	1.24149i
$813$		−	1.24528e42i		−	0.792419i
$814$	−5.41388e40	+	1.01728e41i	−0.0338419	+	0.0635895i
$815$	−2.80458e41			−0.172219
$816$	7.75776e41	+	3.14796e41i	0.467982	+	0.189899i
$817$	−1.01631e42			−0.602288
$818$	4.47865e41	−	8.41545e41i	0.260750	−	0.489953i
$819$		−	1.61635e40i		−	0.00924527i
$820$	2.85169e41	−	1.92036e41i	0.160251	−	0.107915i
$821$			6.34456e41i			0.350288i	0.984543	+	0.175144i	$0.0560392\pi$
$821$			6.34456e41i			0.350288i	−0.984543	+	0.175144i	$0.943961\pi$
$822$	2.07010e40	+	1.10169e40i	0.0112292	+	0.00597612i
$823$	8.33082e41			0.444007			0.222004	−	0.975046i	$-0.428740\pi$
$823$	8.33082e41			0.444007			0.222004	+	0.975046i	$0.428740\pi$
$824$	3.34064e41	−	3.47294e40i	0.174939	−	0.0181866i
$825$	−6.71901e40			−0.0345719
$826$	−5.47413e41	−	2.91329e41i	−0.276761	−	0.147290i
$827$		−	3.26159e42i		−	1.62031i	−0.586213	−	0.810157i	$-0.699382\pi$
$827$		−	3.26159e42i		−	1.62031i	0.586213	−	0.810157i	$-0.300618\pi$
$828$	8.70577e40	+	1.29279e41i	0.0424979	+	0.0631083i
$829$		−	8.04864e41i		−	0.386084i	−0.981191	−	0.193042i	$-0.938165\pi$
$829$		−	8.04864e41i		−	0.386084i	0.981191	−	0.193042i	$-0.0618353\pi$
$830$	−7.56715e41	+	1.42188e42i	−0.356698	+	0.670241i
$831$	−1.67666e42			−0.776659
$832$	9.25143e39	+	4.40142e40i	0.00421134	+	0.0200357i
$833$	2.77766e42			1.24259
$834$	−9.55762e41	+	1.79589e42i	−0.420187	+	0.789537i
$835$		−	5.20290e41i		−	0.224798i
$836$	−2.62404e40	−	3.89664e40i	−0.0111424	−	0.0165462i
$837$			3.56644e42i			1.48839i
$838$	1.08191e42	+	5.75783e41i	0.443763	+	0.236168i
$839$	−4.28529e42			−1.72755			−0.863777	−	0.503874i	$-0.831907\pi$
$839$	−4.28529e42			−1.72755			−0.863777	+	0.503874i	$0.831907\pi$
$840$	1.82967e42	−	1.90213e41i	0.724977	−	0.0753688i
$841$	−1.49416e42			−0.581909
$842$	−2.08142e42	−	1.10772e42i	−0.796774	−	0.424038i
$843$		−	4.02899e41i		−	0.151599i
$844$	−2.33218e42	+	1.57052e42i	−0.862576	+	0.580868i
$845$			1.31432e42i			0.477836i
$846$	3.78698e41	−	7.11580e41i	0.135339	−	0.254304i
$847$	−5.01663e42			−1.76239
$848$	−1.89759e42	−	7.70008e41i	−0.655333	−	0.265923i
$849$	1.95514e42			0.663768
$850$	6.35658e41	−	1.19441e42i	0.212153	−	0.398639i
$851$			1.25858e42i			0.412955i
$852$	3.92695e42	−	2.64446e42i	1.26672	−	0.853026i
$853$			1.11623e42i			0.353992i	0.984212	+	0.176996i	$0.0566379\pi$
$853$			1.11623e42i			0.353992i	−0.984212	+	0.176996i	$0.943362\pi$
$854$	5.99818e42	+	3.19219e42i	1.87017	+	0.995290i
$855$	−1.53056e41			−0.0469182
$856$	−6.53275e41	−	6.28389e42i	−0.196891	−	1.89391i
$857$	1.21535e42			0.360148			0.180074	−	0.983653i	$-0.442366\pi$
$857$	1.21535e42			0.360148			0.180074	+	0.983653i	$0.442366\pi$
$858$	−2.77973e39	−	1.47935e39i	−0.000809911	−	0.000431029i
$859$			2.86320e42i			0.820259i	0.912027	+	0.410129i	$0.134516\pi$
$859$			2.86320e42i			0.820259i	−0.912027	+	0.410129i	$0.865484\pi$
$860$	1.48641e42	+	2.20729e42i	0.418709	+	0.621773i
$861$			2.22479e42i			0.616232i
$862$	1.22899e42	−	2.30929e42i	0.334729	−	0.628961i
$863$	6.08211e42			1.62891			0.814456	−	0.580225i	$-0.197035\pi$
$863$	6.08211e42			1.62891			0.814456	+	0.580225i	$0.197035\pi$
$864$	3.15602e42	−	2.63809e42i	0.831172	−	0.694769i
$865$	−1.03780e42			−0.268770
$866$	−2.62353e42	+	4.92965e42i	−0.668154	+	1.25547i
$867$			2.26472e42i			0.567203i
$868$	−5.50621e42	−	8.17659e42i	−1.35618	−	2.01389i
$869$			2.14402e41i			0.0519329i
$870$	1.92243e42	+	1.02310e42i	0.457953	+	0.243720i
$871$	−1.17465e41			−0.0275199
$872$	1.50694e40	+	1.44954e41i	0.00347222	+	0.0333995i
$873$	−3.57552e41			−0.0810276
$874$	−4.52931e41	−	2.41047e41i	−0.100952	−	0.0537262i
$875$		−	6.82637e42i		−	1.49649i
$876$	−2.64910e42	+	1.78394e42i	−0.571201	+	0.384654i
$877$			4.22279e42i			0.895582i	0.894138	+	0.447791i	$0.147789\pi$
$877$			4.22279e42i			0.895582i	−0.894138	+	0.447791i	$0.852211\pi$
$878$	−7.56213e40	+	1.42094e41i	−0.0157752	+	0.0296418i
$879$	−6.07378e42			−1.24629
$880$	−4.62518e40	+	1.13982e41i	−0.00933534	+	0.0230058i
$881$	8.23397e42			1.63478			0.817389	−	0.576086i	$-0.195421\pi$
$881$	8.23397e42			1.63478			0.817389	+	0.576086i	$0.195421\pi$
$882$	1.30492e42	−	2.45196e42i	0.254852	−	0.478872i
$883$			7.58624e41i			0.145746i	0.997341	+	0.0728729i	$0.0232168\pi$
$883$			7.58624e41i			0.145746i	−0.997341	+	0.0728729i	$0.976783\pi$
$884$	5.25958e40	−	3.54186e40i	0.00994016	−	0.00669382i
$885$			3.93587e41i			0.0731751i
$886$	4.54220e42	+	2.41733e42i	0.830763	+	0.442127i
$887$	9.70941e42			1.74703			0.873515	−	0.486798i	$-0.161835\pi$
$887$	9.70941e42			1.74703			0.873515	+	0.486798i	$0.161835\pi$
$888$	6.72416e42	−	6.99045e41i	1.19028	−	0.123742i
$889$	−8.42597e42			−1.46739
$890$	−1.54256e42	−	8.20939e41i	−0.264294	−	0.140655i
$891$			2.09256e41i			0.0352737i
$892$	−1.96202e42	−	2.91355e42i	−0.325397	−	0.483206i
$893$			2.65356e42i			0.432995i
$894$	1.87589e42	−	3.52483e42i	0.301172	−	0.565906i
$895$	3.04949e42			0.481719
$896$	−3.16271e42	+	1.09208e43i	−0.491579	+	1.69741i
$897$	−3.43910e40			−0.00525961
$898$	1.09404e42	−	2.05572e42i	0.164636	−	0.309355i
$899$		−	1.16700e43i		−	1.72805i
$900$	−7.55734e41	−	1.12225e42i	−0.110117	−	0.163520i
$901$			2.88720e42i			0.413969i
$902$	−1.31330e41	−	6.98930e40i	−0.0185297	−	0.00986141i
$903$	−1.72205e43			−2.39097
$904$	1.07711e43	−	1.11977e42i	1.47170	−	0.152998i
$905$	−5.40973e42			−0.727396
$906$	5.99113e41	+	3.18844e41i	0.0792775	+	0.0421909i
$907$			5.41372e42i			0.705002i	0.935811	+	0.352501i	$0.114669\pi$
$907$			5.41372e42i			0.705002i	−0.935811	+	0.352501i	$0.885331\pi$
$908$	−7.78813e42	+	5.24461e42i	−0.998133	+	0.672154i
$909$			3.08500e42i			0.389116i
$910$	6.54555e40	−	1.22992e41i	0.00812542	−	0.0152678i
$911$	4.92035e42			0.601146			0.300573	−	0.953759i	$-0.402822\pi$
$911$	4.92035e42			0.601146			0.300573	+	0.953759i	$0.402822\pi$
$912$	−1.03626e42	+	2.55374e42i	−0.124608	+	0.307080i
$913$	6.96986e41			0.0824893
$914$	−5.09623e42	+	9.57591e42i	−0.593649	+	1.11548i
$915$		−	4.31266e42i		−	0.494469i
$916$	−8.12970e42	+	5.47463e42i	−0.917467	+	0.617833i
$917$		−	1.23517e43i		−	1.37205i
$918$	−5.11946e42	−	2.72454e42i	−0.559764	−	0.297903i
$919$	9.78187e42			1.05280			0.526401	−	0.850236i	$-0.323541\pi$
$919$	9.78187e42			1.05280			0.526401	+	0.850236i	$0.323541\pi$
$920$	1.38918e41	+	1.33626e42i	0.0147175	+	0.141568i
$921$	6.24771e42			0.651563
$922$	3.90951e42	+	2.08062e42i	0.401351	+	0.213596i
$923$		−	3.58576e41i		−	0.0362374i
$924$	−4.44623e41	−	6.60255e41i	−0.0442332	−	0.0656853i
$925$		−	1.09255e43i		−	1.07001i
$926$	−1.03175e42	+	1.93868e42i	−0.0994755	+	0.186916i
$927$	−4.73508e41			−0.0449440
$928$	−1.03271e43	+	8.63229e42i	−0.965007	+	0.806641i
$929$	−3.18939e42			−0.293414			−0.146707	−	0.989180i	$-0.546867\pi$
$929$	−3.18939e42			−0.293414			−0.146707	+	0.989180i	$0.546867\pi$
$930$	−2.93946e42	+	5.52330e42i	−0.266235	+	0.500260i
$931$			9.14363e42i			0.815358i
$932$	−4.93791e42	−	7.33267e42i	−0.433523	−	0.643771i
$933$		−	1.46612e43i		−	1.26732i
$934$	−3.62743e42	−	1.93050e42i	−0.308724	−	0.164301i
$935$	1.73425e41			0.0145326
$936$	−6.55657e39	−	6.30680e40i	−0.000540974	−	0.00520367i
$937$	3.74440e42			0.304199			0.152100	−	0.988365i	$-0.451397\pi$
$937$	3.74440e42			0.304199			0.152100	+	0.988365i	$0.451397\pi$
$938$	−2.62132e43	−	1.39505e43i	−2.09690	−	1.11596i
$939$			1.09371e43i			0.861493i
$940$	5.76320e42	−	3.88101e42i	0.447003	−	0.301017i
$941$		−	8.92329e42i		−	0.681515i	−0.940151	−	0.340758i	$-0.889316\pi$
$941$		−	8.92329e42i		−	0.681515i	0.940151	−	0.340758i	$-0.110684\pi$
$942$	2.17282e42	−	4.08276e42i	0.163412	−	0.307054i
$943$	−1.62482e42			−0.120333
$944$	−2.25411e42	−	9.14678e41i	−0.164392	−	0.0667075i
$945$	−1.27423e43			−0.915140
$946$	5.40991e41	−	1.01653e42i	0.0382621	−	0.0718950i
$947$			5.34734e42i			0.372446i	0.982508	+	0.186223i	$0.0596246\pi$
$947$			5.34734e42i			0.372446i	−0.982508	+	0.186223i	$0.940375\pi$
$948$	1.04329e43	−	7.02564e42i	0.715623	−	0.481909i
$949$			2.41894e41i			0.0163405i
$950$	3.93182e42	+	2.09249e42i	0.261578	+	0.139210i
$951$	2.28786e43			1.49903
$952$	1.59435e43	−	1.65749e42i	1.02884	−	0.106958i
$953$	1.28495e43			0.816657			0.408328	−	0.912835i	$-0.366112\pi$
$953$	1.28495e43			0.816657			0.408328	+	0.912835i	$0.366112\pi$
$954$	2.54866e42	+	1.35638e42i	0.159537	+	0.0849045i
$955$		−	9.59268e41i		−	0.0591413i
$956$	1.54092e43	+	2.28823e43i	0.935709	+	1.38951i
$957$		−	9.42348e41i		−	0.0563622i
$958$	5.41190e42	−	1.01690e43i	0.318823	−	0.599073i
$959$	4.48979e41			0.0260529
$960$	7.06200e42	−	1.48438e42i	0.403641	−	0.0848421i
$961$	1.57670e43			0.887689
$962$	2.40553e41	−	4.52002e41i	0.0133405	−	0.0250670i
$963$			8.90689e42i			0.486570i
$964$	1.89270e43	+	2.81061e43i	1.01851	+	1.51246i
$965$		−	1.63882e43i		−	0.868730i
$966$	−7.67457e42	−	4.08435e42i	−0.400761	−	0.213282i
$967$	−1.82842e43			−0.940571			−0.470285	−	0.882514i	$-0.655849\pi$
$967$	−1.82842e43			−0.940571			−0.470285	+	0.882514i	$0.655849\pi$
$968$	−1.95743e43	+	2.03494e42i	−0.991957	+	0.103124i
$969$	3.88554e42			0.193980
$970$	−2.72069e42	−	1.44794e42i	−0.133810	−	0.0712130i
$971$		−	3.58308e42i		−	0.173611i	−0.996225	−	0.0868056i	$-0.972334\pi$
$971$		−	3.58308e42i		−	0.173611i	0.996225	−	0.0868056i	$-0.0276659\pi$
$972$	−8.64130e42	+	5.81915e42i	−0.412495	+	0.277779i
$973$			3.89507e43i			1.83180i
$974$	−1.94775e42	+	3.65986e42i	−0.0902463	+	0.169574i
$975$	2.98543e41			0.0136282
$976$	2.46990e43	+	1.00224e43i	1.11085	+	0.450765i
$977$	−3.59500e43			−1.59304			−0.796522	−	0.604610i	$-0.793329\pi$
$977$	−3.59500e43			−1.59304			−0.796522	+	0.604610i	$0.793329\pi$
$978$	3.34483e42	−	6.28499e42i	0.146036	−	0.274404i
$979$			7.56140e41i			0.0325277i
$980$	1.98588e43	−	1.33732e43i	0.841736	−	0.566834i
$981$		−	2.05460e41i		−	0.00858077i
$982$	−2.78319e42	−	1.48120e42i	−0.114532	−	0.0609532i
$983$	1.90710e43			0.773299			0.386650	−	0.922227i	$-0.373632\pi$
$983$	1.90710e43			0.773299			0.386650	+	0.922227i	$0.373632\pi$
$984$	9.02464e41	+	8.68086e42i	0.0360580	+	0.346844i
$985$	−4.26363e42			−0.167862
$986$	1.67517e43	+	8.91517e42i	0.649898	+	0.345871i
$987$			4.49625e43i			1.71891i
$988$	1.16593e41	+	1.73138e41i	0.00439234	+	0.00652252i
$989$		−	1.25766e43i		−	0.466891i
$990$	8.14733e40	−	1.53090e41i	0.00298061	−	0.00560061i
$991$	1.10529e43			0.398481			0.199240	−	0.979951i	$-0.436153\pi$
$991$	1.10529e43			0.398481			0.199240	+	0.979951i	$0.436153\pi$
$992$	−2.48013e43	−	2.96705e43i	−0.881160	−	1.05416i
$993$	−3.39788e43			−1.18972
$994$	4.25854e43	−	8.00186e43i	1.46946	−	2.76114i
$995$		−	2.03841e42i		−	0.0693197i
$996$	−2.28392e43	−	3.39156e43i	−0.765455	−	1.13668i
$997$		−	2.14333e43i		−	0.707960i	−0.935253	−	0.353980i	$-0.884828\pi$
$997$		−	2.14333e43i		−	0.707960i	0.935253	−	0.353980i	$-0.115172\pi$
$998$	−1.31663e43	−	7.00704e42i	−0.428620	−	0.228109i
$999$	−4.68288e43			−1.50250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.30.b.a.5.19	✓	28
4.3	odd	2		32.30.b.a.17.21		28
8.3	odd	2		32.30.b.a.17.8		28
8.5	even	2	inner	8.30.b.a.5.20	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.30.b.a.5.19	✓	28	1.1	even	1	trivial
8.30.b.a.5.20	yes	28	8.5	even	2	inner
32.30.b.a.17.8		28	8.3	odd	2
32.30.b.a.17.21		28	4.3	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+(10885.6 - 20454.2i) q^{2} -7.14793e6i q^{3} +(-2.99879e8 - 4.45313e8i) q^{4} +6.52418e9i q^{5} +(-1.46205e11 - 7.78094e10i) q^{6} -3.17101e12 q^{7} +(-1.23729e13 + 1.28629e12i) q^{8} +1.75375e13 q^{9} +(1.33447e14 + 7.10196e13i) q^{10} -6.54138e13i q^{11} +(-3.18306e15 + 2.14351e15i) q^{12} +2.90650e14i q^{13} +(-3.45183e16 + 6.48605e16i) q^{14} +4.66344e16 q^{15} +(-1.08376e17 + 2.67079e17i) q^{16} +4.06364e17 q^{17} +(1.90906e17 - 3.58716e17i) q^{18} +1.33769e18i q^{19} +(2.90530e18 - 1.95646e18i) q^{20} +2.26661e19i q^{21} +(-1.33799e18 - 7.12068e17i) q^{22} -1.65536e19 q^{23} +(9.19428e18 + 8.84404e19i) q^{24} +1.43700e20 q^{25} +(5.94502e18 + 3.16390e18i) q^{26} -6.15922e20i q^{27} +(9.50917e20 + 1.41209e21i) q^{28} +2.01540e21i q^{29} +(5.07643e20 - 9.53869e20i) q^{30} -5.79042e21 q^{31} +(4.28316e21 + 5.12407e21i) q^{32} -4.67573e20 q^{33} +(4.42352e21 - 8.31186e21i) q^{34} -2.06882e22i q^{35} +(-5.25912e21 - 7.80967e21i) q^{36} -7.60304e22i q^{37} +(2.73614e22 + 1.45616e22i) q^{38} +2.07755e21 q^{39} +(-8.39196e21 - 8.07228e22i) q^{40} +9.81549e22 q^{41} +(4.63618e23 + 2.46734e23i) q^{42} +7.59746e23i q^{43} +(-2.91296e22 + 1.96162e22i) q^{44} +1.14418e23i q^{45} +(-1.80196e23 + 3.38592e23i) q^{46} +1.98369e24 q^{47} +(1.90906e24 + 7.74665e23i) q^{48} +6.83539e24 q^{49} +(1.56426e24 - 2.93926e24i) q^{50} -2.90466e24i q^{51} +(1.29430e23 - 8.71598e22i) q^{52} +7.10496e24i q^{53} +(-1.25982e25 - 6.70468e24i) q^{54} +4.26771e23 q^{55} +(3.92345e25 - 4.07883e24i) q^{56} +9.56172e24 q^{57} +(4.12235e25 + 2.19389e25i) q^{58} +8.43985e24i q^{59} +(-1.39846e25 - 2.07669e25i) q^{60} -9.24782e25i q^{61} +(-6.30321e25 + 1.18438e26i) q^{62} -5.56116e25 q^{63} +(1.51433e26 - 3.18301e25i) q^{64} -1.89625e24 q^{65} +(-5.08981e24 + 9.56384e24i) q^{66} +4.04147e26i q^{67} +(-1.21860e26 - 1.80959e26i) q^{68} +1.18324e26i q^{69} +(-4.23161e26 - 2.25204e26i) q^{70} -1.23370e27 q^{71} +(-2.16989e26 + 2.25583e25i) q^{72} +8.32250e26 q^{73} +(-1.55514e27 - 8.27636e26i) q^{74} -1.02715e27i q^{75} +(5.95691e26 - 4.01145e26i) q^{76} +2.07428e26i q^{77} +(2.26153e25 - 4.24946e25i) q^{78} -3.27763e27 q^{79} +(-1.74247e27 - 7.07065e26i) q^{80} -3.19896e27 q^{81} +(1.06847e27 - 2.00768e27i) q^{82} +1.06550e28i q^{83} +(1.00935e28 - 6.79709e27i) q^{84} +2.65119e27i q^{85} +(1.55400e28 + 8.27029e27i) q^{86} +1.44059e28 q^{87} +(8.41409e25 + 8.09357e26i) q^{88} -1.15593e28 q^{89} +(2.34033e27 + 1.24551e27i) q^{90} -9.21654e26i q^{91} +(4.96408e27 + 7.37154e27i) q^{92} +4.13895e28i q^{93} +(2.15936e28 - 4.05748e28i) q^{94} -8.72733e27 q^{95} +(3.66264e28 - 3.06157e28i) q^{96} -2.03878e28 q^{97} +(7.44072e28 - 1.39812e29i) q^{98} -1.14720e27i 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

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