LMFDB - Embedded newform 8.11.d.b.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,11,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	8.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08285802139$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 51x^{5} + 30855x^{4} - 121569x^{3} + 12144527x^{2} + 279415575x + 3348211684 $ x^8 - 3x^7 + 5x^6 - 51x^5 + 30855x^4 - 121569x^3 + 12144527x^2 + 279415575*x + 3348211684
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.4
Root			$4.83019 - 15.8950i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.11.d.b.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.66038 + 31.7900i) q^{2} -119.281 q^{3} +(-997.203 - 232.727i) q^{4} -948.910i q^{5} +(436.614 - 3791.94i) q^{6} -15458.1i q^{7} +(11048.5 - 30849.2i) q^{8} -44821.0 q^{9} +O(q^{10})$	\(q+(-3.66038 + 31.7900i) q^{2} -119.281 q^{3} +(-997.203 - 232.727i) q^{4} -948.910i q^{5} +(436.614 - 3791.94i) q^{6} -15458.1i q^{7} +(11048.5 - 30849.2i) q^{8} -44821.0 q^{9} +(30165.8 + 3473.37i) q^{10} -166691. q^{11} +(118948. + 27759.9i) q^{12} +349020. i q^{13} +(491413. + 56582.5i) q^{14} +113187. i q^{15} +(940253. + 464151. i) q^{16} -1.33948e6 q^{17} +(164062. - 1.42486e6i) q^{18} -1.84025e6 q^{19} +(-220837. + 946256. i) q^{20} +1.84386e6i q^{21} +(610153. - 5.29911e6i) q^{22} -9.06620e6i q^{23} +(-1.31788e6 + 3.67973e6i) q^{24} +8.86520e6 q^{25} +(-1.10953e7 - 1.27754e6i) q^{26} +1.23897e7 q^{27} +(-3.59751e6 + 1.54149e7i) q^{28} +3.86186e7i q^{29} +(-3.59821e6 - 414308. i) q^{30} -3.73975e7i q^{31} +(-1.81970e7 + 2.81916e7i) q^{32} +1.98831e7 q^{33} +(4.90299e6 - 4.25819e7i) q^{34} -1.46683e7 q^{35} +(4.46956e7 + 1.04310e7i) q^{36} +2.87741e6i q^{37} +(6.73600e6 - 5.85014e7i) q^{38} -4.16315e7i q^{39} +(-2.92731e7 - 1.04840e7i) q^{40} -1.14934e8 q^{41} +(-5.86163e7 - 6.74923e6i) q^{42} -1.12857e8 q^{43} +(1.66225e8 + 3.87935e7i) q^{44} +4.25311e7i q^{45} +(2.88214e8 + 3.31857e7i) q^{46} +2.25171e8i q^{47} +(-1.12154e8 - 5.53645e7i) q^{48} +4.35223e7 q^{49} +(-3.24500e7 + 2.81824e8i) q^{50} +1.59774e8 q^{51} +(8.12262e7 - 3.48044e8i) q^{52} -3.16175e8i q^{53} +(-4.53511e7 + 3.93869e8i) q^{54} +1.58175e8i q^{55} +(-4.76870e8 - 1.70789e8i) q^{56} +2.19507e8 q^{57} +(-1.22768e9 - 1.41359e8i) q^{58} +4.46702e8 q^{59} +(2.63416e7 - 1.12871e8i) q^{60} -1.42693e9i q^{61} +(1.18886e9 + 1.36889e8i) q^{62} +6.92848e8i q^{63} +(-8.29603e8 - 6.81675e8i) q^{64} +3.31188e8 q^{65} +(-7.27798e7 + 6.32084e8i) q^{66} -7.31834e7 q^{67} +(1.33573e9 + 3.11732e8i) q^{68} +1.08143e9i q^{69} +(5.36917e7 - 4.66306e8i) q^{70} +6.70175e8i q^{71} +(-4.95205e8 + 1.38269e9i) q^{72} -1.85303e9 q^{73} +(-9.14726e7 - 1.05324e7i) q^{74} -1.05745e9 q^{75} +(1.83510e9 + 4.28274e8i) q^{76} +2.57673e9i q^{77} +(1.32346e9 + 1.52387e8i) q^{78} -3.97541e9i q^{79} +(4.40438e8 - 8.92215e8i) q^{80} +1.16877e9 q^{81} +(4.20704e8 - 3.65376e9i) q^{82} -3.39373e9 q^{83} +(4.29116e8 - 1.83870e9i) q^{84} +1.27104e9i q^{85} +(4.13101e8 - 3.58773e9i) q^{86} -4.60647e9i q^{87} +(-1.84169e9 + 5.14229e9i) q^{88} -2.22429e9 q^{89} +(-1.35206e9 - 1.55680e8i) q^{90} +5.39518e9 q^{91} +(-2.10995e9 + 9.04085e9i) q^{92} +4.46081e9i q^{93} +(-7.15816e9 - 8.24210e8i) q^{94} +1.74623e9i q^{95} +(2.17056e9 - 3.36273e9i) q^{96} +1.09164e10 q^{97} +(-1.59308e8 + 1.38357e9i) q^{98} +7.47127e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9}+O(q^{10}) $ 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9	\( 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9} + 9120 q^{10} + 143328 q^{11} + 180120 q^{12} - 400320 q^{14} - 1987312 q^{16} - 370800 q^{17} + 3067758 q^{18} + 1753312 q^{19} + 2557440 q^{20} + 1549180 q^{22} - 19794288 q^{24} - 18792760 q^{25} + 1891680 q^{26} + 28949184 q^{27} + 18286080 q^{28} + 67026240 q^{30} - 64016928 q^{32} - 74308704 q^{33} - 115705388 q^{34} + 53736960 q^{35} + 50631516 q^{36} + 375128220 q^{38} - 357584640 q^{40} + 92669328 q^{41} - 576155520 q^{42} - 10190624 q^{43} + 727831512 q^{44} + 851947200 q^{46} - 1142760480 q^{48} - 80432248 q^{49} - 1669361190 q^{50} - 276714816 q^{51} + 2420759040 q^{52} + 1749768696 q^{54} - 2928529920 q^{56} + 1400712864 q^{57} - 3245264160 q^{58} - 965642016 q^{59} + 5250055680 q^{60} + 4060980480 q^{62} - 5804705728 q^{64} - 839028480 q^{65} - 5970262296 q^{66} - 1225582880 q^{67} + 5258111400 q^{68} + 7723829760 q^{70} - 4343608728 q^{72} + 2800072720 q^{73} - 7669373280 q^{74} + 4485554400 q^{75} + 3753451288 q^{76} + 7176312000 q^{78} - 6408629760 q^{80} - 11909065176 q^{81} - 3638778380 q^{82} + 1853422560 q^{83} - 2916218880 q^{84} + 3022180476 q^{86} + 5815578640 q^{88} + 6162596112 q^{89} + 12545940960 q^{90} + 7645985280 q^{91} - 8903892480 q^{92} - 14182177920 q^{94} + 7877525568 q^{96} - 9697863536 q^{97} + 34759868298 q^{98} - 13646747232 q^{99}+O(q^{100}) \) 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9 + 9120 * q^10 + 143328 * q^11 + 180120 * q^12 - 400320 * q^14 - 1987312 * q^16 - 370800 * q^17 + 3067758 * q^18 + 1753312 * q^19 + 2557440 * q^20 + 1549180 * q^22 - 19794288 * q^24 - 18792760 * q^25 + 1891680 * q^26 + 28949184 * q^27 + 18286080 * q^28 + 67026240 * q^30 - 64016928 * q^32 - 74308704 * q^33 - 115705388 * q^34 + 53736960 * q^35 + 50631516 * q^36 + 375128220 * q^38 - 357584640 * q^40 + 92669328 * q^41 - 576155520 * q^42 - 10190624 * q^43 + 727831512 * q^44 + 851947200 * q^46 - 1142760480 * q^48 - 80432248 * q^49 - 1669361190 * q^50 - 276714816 * q^51 + 2420759040 * q^52 + 1749768696 * q^54 - 2928529920 * q^56 + 1400712864 * q^57 - 3245264160 * q^58 - 965642016 * q^59 + 5250055680 * q^60 + 4060980480 * q^62 - 5804705728 * q^64 - 839028480 * q^65 - 5970262296 * q^66 - 1225582880 * q^67 + 5258111400 * q^68 + 7723829760 * q^70 - 4343608728 * q^72 + 2800072720 * q^73 - 7669373280 * q^74 + 4485554400 * q^75 + 3753451288 * q^76 + 7176312000 * q^78 - 6408629760 * q^80 - 11909065176 * q^81 - 3638778380 * q^82 + 1853422560 * q^83 - 2916218880 * q^84 + 3022180476 * q^86 + 5815578640 * q^88 + 6162596112 * q^89 + 12545940960 * q^90 + 7645985280 * q^91 - 8903892480 * q^92 - 14182177920 * q^94 + 7877525568 * q^96 - 9697863536 * q^97 + 34759868298 * q^98 - 13646747232 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−3.66038	+	31.7900i	−0.114387	+	0.993436i
$2$	−3.66038	+	31.7900i	−0.114387	+	0.993436i
$3$	−119.281			−0.490869			−0.245435	−	0.969413i	$-0.578931\pi$
$3$	−119.281			−0.490869			−0.245435	+	0.969413i	$0.578931\pi$
$4$	−997.203	−	232.727i	−0.973831	−	0.227272i
$5$		−	948.910i		−	0.303651i	−0.988407	−	0.151826i	$-0.951485\pi$
$5$		−	948.910i		−	0.303651i	0.988407	−	0.151826i	$-0.0485152\pi$
$6$	436.614	−	3791.94i	0.0561490	−	0.487647i
$7$		−	15458.1i		−	0.919742i	−0.887986	−	0.459871i	$-0.847896\pi$
$7$		−	15458.1i		−	0.919742i	0.887986	−	0.459871i	$-0.152104\pi$
$8$	11048.5	−	30849.2i	0.337174	−	0.941442i
$9$	−44821.0			−0.759048
$10$	30165.8	+	3473.37i	0.301658	+	0.0347337i
$11$	−166691.			−1.03502			−0.517511	−	0.855677i	$-0.673141\pi$
$11$	−166691.			−1.03502			−0.517511	+	0.855677i	$0.673141\pi$
$12$	118948.	+	27759.9i	0.478024	+	0.111561i
$13$			349020.i			0.940012i	0.882663	+	0.470006i	$0.155748\pi$
$13$			349020.i			0.940012i	−0.882663	+	0.470006i	$0.844252\pi$
$14$	491413.	+	56582.5i	0.913705	+	0.105206i
$15$			113187.i			0.149053i
$16$	940253.	+	464151.i	0.896695	+	0.442649i
$17$	−1.33948e6			−0.943388			−0.471694	−	0.881762i	$-0.656357\pi$
$17$	−1.33948e6			−0.943388			−0.471694	+	0.881762i	$0.656357\pi$
$18$	164062.	−	1.42486e6i	0.0868250	−	0.754065i
$19$	−1.84025e6			−0.743204			−0.371602	−	0.928392i	$-0.621191\pi$
$19$	−1.84025e6			−0.743204			−0.371602	+	0.928392i	$0.621191\pi$
$20$	−220837.	+	946256.i	−0.0690114	+	0.295705i
$21$			1.84386e6i			0.451473i
$22$	610153.	−	5.29911e6i	0.118393	−	1.02823i
$23$		−	9.06620e6i		−	1.40860i	−0.709905	−	0.704298i	$-0.751262\pi$
$23$		−	9.06620e6i		−	1.40860i	0.709905	−	0.704298i	$-0.248738\pi$
$24$	−1.31788e6	+	3.67973e6i	−0.165508	+	0.462125i
$25$	8.86520e6			0.907796
$26$	−1.10953e7	−	1.27754e6i	−0.933842	−	0.107525i
$27$	1.23897e7			0.863462
$28$	−3.59751e6	+	1.54149e7i	−0.209032	+	0.895674i
$29$			3.86186e7i			1.88281i	0.337278	+	0.941405i	$0.390494\pi$
$29$			3.86186e7i			1.88281i	−0.337278	+	0.941405i	$0.609506\pi$
$30$	−3.59821e6	−	414308.i	−0.148075	−	0.0170497i
$31$		−	3.73975e7i		−	1.30627i	−0.757241	−	0.653136i	$-0.773453\pi$
$31$		−	3.73975e7i		−	1.30627i	0.757241	−	0.653136i	$-0.226547\pi$
$32$	−1.81970e7	+	2.81916e7i	−0.542314	+	0.840176i
$33$	1.98831e7			0.508060
$34$	4.90299e6	−	4.25819e7i	0.107911	−	0.937196i
$35$	−1.46683e7			−0.279281
$36$	4.46956e7	+	1.04310e7i	0.739184	+	0.172510i
$37$			2.87741e6i			0.0414947i	0.999785	+	0.0207473i	$0.00660456\pi$
$37$			2.87741e6i			0.0414947i	−0.999785	+	0.0207473i	$0.993395\pi$
$38$	6.73600e6	−	5.85014e7i	0.0850128	−	0.738326i
$39$		−	4.16315e7i		−	0.461423i
$40$	−2.92731e7	−	1.04840e7i	−0.285870	−	0.102383i
$41$	−1.14934e8			−0.992044			−0.496022	−	0.868310i	$-0.665206\pi$
$41$	−1.14934e8			−0.992044			−0.496022	+	0.868310i	$0.665206\pi$
$42$	−5.86163e7	−	6.74923e6i	−0.448510	−	0.0516426i
$43$	−1.12857e8			−0.767693			−0.383847	−	0.923397i	$-0.625401\pi$
$43$	−1.12857e8			−0.767693			−0.383847	+	0.923397i	$0.625401\pi$
$44$	1.66225e8	+	3.87935e7i	1.00794	+	0.235231i
$45$			4.25311e7i			0.230486i
$46$	2.88214e8	+	3.31857e7i	1.39935	+	0.161125i
$47$			2.25171e8i			0.981799i	0.871216	+	0.490899i	$0.163332\pi$
$47$			2.25171e8i			0.981799i	−0.871216	+	0.490899i	$0.836668\pi$
$48$	−1.12154e8	−	5.53645e7i	−0.440160	−	0.217283i
$49$	4.35223e7			0.154075
$50$	−3.24500e7	+	2.81824e8i	−0.103840	+	0.901837i
$51$	1.59774e8			0.463080
$52$	8.12262e7	−	3.48044e8i	0.213638	−	0.915413i
$53$		−	3.16175e8i		−	0.756046i	−0.925796	−	0.378023i	$-0.876604\pi$
$53$		−	3.16175e8i		−	0.756046i	0.925796	−	0.378023i	$-0.123396\pi$
$54$	−4.53511e7	+	3.93869e8i	−0.0987687	+	0.857795i
$55$			1.58175e8i			0.314285i
$56$	−4.76870e8	−	1.70789e8i	−0.865884	−	0.310113i
$57$	2.19507e8			0.364816
$58$	−1.22768e9	−	1.41359e8i	−1.87045	−	0.215369i
$59$	4.46702e8			0.624824			0.312412	−	0.949947i	$-0.398863\pi$
$59$	4.46702e8			0.624824			0.312412	+	0.949947i	$0.398863\pi$
$60$	2.63416e7	−	1.12871e8i	0.0338756	−	0.145152i
$61$		−	1.42693e9i		−	1.68948i	−0.535175	−	0.844741i	$-0.679754\pi$
$61$		−	1.42693e9i		−	1.68948i	0.535175	−	0.844741i	$-0.320246\pi$
$62$	1.18886e9	+	1.36889e8i	1.29770	+	0.149420i
$63$			6.92848e8i			0.698128i
$64$	−8.29603e8	−	6.81675e8i	−0.772628	−	0.634859i
$65$	3.31188e8			0.285436
$66$	−7.27798e7	+	6.32084e8i	−0.0581154	+	0.504725i
$67$	−7.31834e7			−0.0542049			−0.0271025	−	0.999633i	$-0.508628\pi$
$67$	−7.31834e7			−0.0542049			−0.0271025	+	0.999633i	$0.508628\pi$
$68$	1.33573e9	+	3.11732e8i	0.918701	+	0.214406i
$69$			1.08143e9i			0.691436i
$70$	5.36917e7	−	4.66306e8i	0.0319460	−	0.277448i
$71$			6.70175e8i			0.371446i	0.982602	+	0.185723i	$0.0594628\pi$
$71$			6.70175e8i			0.371446i	−0.982602	+	0.185723i	$0.940537\pi$
$72$	−4.95205e8	+	1.38269e9i	−0.255931	+	0.714600i
$73$	−1.85303e9			−0.893859			−0.446929	−	0.894569i	$-0.647483\pi$
$73$	−1.85303e9			−0.893859			−0.446929	+	0.894569i	$0.647483\pi$
$74$	−9.14726e7	−	1.05324e7i	−0.0412223	−	0.00474645i
$75$	−1.05745e9			−0.445609
$76$	1.83510e9	+	4.28274e8i	0.723756	+	0.168910i
$77$			2.57673e9i			0.951952i
$78$	1.32346e9	+	1.52387e8i	0.458394	+	0.0527807i
$79$		−	3.97541e9i		−	1.29195i	−0.763357	−	0.645977i	$-0.776450\pi$
$79$		−	3.97541e9i		−	1.29195i	0.763357	−	0.645977i	$-0.223550\pi$
$80$	4.40438e8	−	8.92215e8i	0.134411	−	0.272282i
$81$	1.16877e9			0.335201
$82$	4.20704e8	−	3.65376e9i	0.113477	−	0.985532i
$83$	−3.39373e9			−0.861563			−0.430782	−	0.902456i	$-0.641762\pi$
$83$	−3.39373e9			−0.861563			−0.430782	+	0.902456i	$0.641762\pi$
$84$	4.29116e8	−	1.83870e9i	0.102607	−	0.439659i
$85$			1.27104e9i			0.286461i
$86$	4.13101e8	−	3.58773e9i	0.0878140	−	0.762654i
$87$		−	4.60647e9i		−	0.924213i
$88$	−1.84169e9	+	5.14229e9i	−0.348982	+	0.974413i
$89$	−2.22429e9			−0.398328			−0.199164	−	0.979966i	$-0.563823\pi$
$89$	−2.22429e9			−0.398328			−0.199164	+	0.979966i	$0.563823\pi$
$90$	−1.35206e9	−	1.55680e8i	−0.228973	−	0.0263645i
$91$	5.39518e9			0.864568
$92$	−2.10995e9	+	9.04085e9i	−0.320134	+	1.37173i
$93$			4.46081e9i			0.641209i
$94$	−7.15816e9	−	8.24210e8i	−0.975354	−	0.112305i
$95$			1.74623e9i			0.225675i
$96$	2.17056e9	−	3.36273e9i	0.266205	−	0.412416i
$97$	1.09164e10			1.27122			0.635611	−	0.772010i	$-0.280748\pi$
$97$	1.09164e10			1.27122			0.635611	+	0.772010i	$0.280748\pi$
$98$	−1.59308e8	+	1.38357e9i	−0.0176241	+	0.153063i
$99$	7.47127e9			0.785630
$100$	−8.84040e9	−	2.06317e9i	−0.884040	−	0.206317i
$101$		−	4.73654e9i		−	0.450666i	−0.974282	−	0.225333i	$-0.927653\pi$
$101$		−	4.73654e9i		−	0.450666i	0.974282	−	0.225333i	$-0.0723470\pi$
$102$	−5.84834e8	+	5.07922e9i	−0.0529703	+	0.460040i
$103$			4.62081e9i			0.398595i	0.979939	+	0.199298i	$0.0638661\pi$
$103$			4.62081e9i			0.398595i	−0.979939	+	0.199298i	$0.936134\pi$
$104$	1.07670e10	+	3.85615e9i	0.884967	+	0.316947i
$105$	1.74966e9			0.137090
$106$	1.00512e10	+	1.15732e9i	0.751084	+	0.0864818i
$107$	−9.86064e9			−0.703050			−0.351525	−	0.936178i	$-0.614337\pi$
$107$	−9.86064e9			−0.703050			−0.351525	+	0.936178i	$0.614337\pi$
$108$	−1.23551e10	−	2.88342e9i	−0.840866	−	0.196241i
$109$		−	6.09092e9i		−	0.395868i	−0.980215	−	0.197934i	$-0.936577\pi$
$109$		−	6.09092e9i		−	0.395868i	0.980215	−	0.197934i	$-0.0634231\pi$
$110$	−5.02837e9	−	5.78980e8i	−0.312222	−	0.0359501i
$111$		−	3.43220e8i		−	0.0203685i
$112$	7.17490e9	−	1.45345e10i	0.407123	−	0.824728i
$113$	−2.78671e10			−1.51251			−0.756257	−	0.654275i	$-0.772974\pi$
$113$	−2.78671e10			−1.51251			−0.756257	+	0.654275i	$0.772974\pi$
$114$	−8.03478e8	+	6.97812e9i	−0.0417301	+	0.362421i
$115$	−8.60301e9			−0.427721
$116$	8.98758e9	−	3.85106e10i	0.427910	−	1.83354i
$117$		−	1.56434e10i		−	0.713514i
$118$	−1.63510e9	+	1.42006e10i	−0.0714716	+	0.620723i
$119$			2.07058e10i			0.867674i
$120$	3.49173e9	+	1.25055e9i	0.140325	+	0.0502567i
$121$	1.84853e9			0.0712687
$122$	4.53621e10	+	5.22311e9i	1.67839	+	0.193255i
$123$	1.37095e10			0.486964
$124$	−8.70338e9	+	3.72929e10i	−0.296879	+	1.27209i
$125$		−	1.76790e10i		−	0.579304i
$126$	−2.20256e10	−	2.53608e9i	−0.693546	−	0.0798566i
$127$			3.42457e10i			1.03654i	0.855216	+	0.518272i	$0.173424\pi$
$127$			3.42457e10i			1.03654i	−0.855216	+	0.518272i	$0.826576\pi$
$128$	2.47071e10	−	2.38778e10i	0.719071	−	0.694937i
$129$	1.34618e10			0.376837
$130$	−1.21227e9	+	1.05285e10i	−0.0326501	+	0.283562i
$131$	−3.67025e10			−0.951347			−0.475674	−	0.879622i	$-0.657796\pi$
$131$	−3.67025e10			−0.951347			−0.475674	+	0.879622i	$0.657796\pi$
$132$	−1.98275e10	−	4.62733e9i	−0.494765	−	0.115468i
$133$			2.84467e10i			0.683556i
$134$	2.67879e8	−	2.32650e9i	0.00620033	−	0.0538492i
$135$		−	1.17567e10i		−	0.262191i
$136$	−1.47992e10	+	4.13217e10i	−0.318086	+	0.888145i
$137$	−3.95010e9			−0.0818475			−0.0409238	−	0.999162i	$-0.513030\pi$
$137$	−3.95010e9			−0.0818475			−0.0409238	+	0.999162i	$0.513030\pi$
$138$	−3.43785e10	−	3.95843e9i	−0.686897	−	0.0790912i
$139$	7.83658e10			1.51026			0.755132	−	0.655573i	$-0.227573\pi$
$139$	7.83658e10			1.51026			0.755132	+	0.655573i	$0.227573\pi$
$140$	1.46273e10	+	3.41371e9i	0.271972	+	0.0634727i
$141$		−	2.68586e10i		−	0.481935i
$142$	−2.13048e10	−	2.45309e9i	−0.369008	−	0.0424886i
$143$		−	5.81785e10i		−	0.972932i
$144$	−4.21431e10	−	2.08037e10i	−0.680634	−	0.335992i
$145$	3.66456e10			0.571717
$146$	6.78280e9	−	5.89079e10i	0.102246	−	0.887992i
$147$	−5.19139e9			−0.0756305
$148$	6.69649e8	−	2.86936e9i	0.00943058	−	0.0404088i
$149$			4.99976e10i			0.680797i	0.940281	+	0.340398i	$0.110562\pi$
$149$			4.99976e10i			0.680797i	−0.940281	+	0.340398i	$0.889438\pi$
$150$	3.87067e9	−	3.36163e10i	0.0509718	−	0.442684i
$151$		−	1.30303e11i		−	1.65985i	−0.557875	−	0.829925i	$-0.688383\pi$
$151$		−	1.30303e11i		−	1.65985i	0.557875	−	0.829925i	$-0.311617\pi$
$152$	−2.03320e10	+	5.67701e10i	−0.250589	+	0.699684i
$153$	6.00366e10			0.716076
$154$	−8.19141e10	−	9.43181e9i	−0.945704	−	0.108891i
$155$	−3.54868e10			−0.396651
$156$	−9.68876e9	+	4.15151e10i	−0.104868	+	0.449348i
$157$			1.45881e11i			1.52933i	0.644426	+	0.764666i	$0.277096\pi$
$157$			1.45881e11i			1.52933i	−0.644426	+	0.764666i	$0.722904\pi$
$158$	1.26378e11	+	1.45515e10i	1.28347	+	0.147783i
$159$			3.77138e10i			0.371120i
$160$	2.67513e10	+	1.72673e10i	0.255120	+	0.164674i
$161$	−1.40146e11			−1.29554
$162$	−4.27815e9	+	3.71552e10i	−0.0383425	+	0.333000i
$163$	−8.99661e10			−0.781881			−0.390941	−	0.920416i	$-0.627850\pi$
$163$	−8.99661e10			−0.781881			−0.390941	+	0.920416i	$0.627850\pi$
$164$	1.14613e11	+	2.67483e10i	0.966083	+	0.225464i
$165$		−	1.88673e10i		−	0.154273i
$166$	1.24223e10	−	1.07887e11i	0.0985515	−	0.855908i
$167$			1.21120e11i			0.932467i	0.884662	+	0.466233i	$0.154389\pi$
$167$			1.21120e11i			0.932467i	−0.884662	+	0.466233i	$0.845611\pi$
$168$	5.68816e10	+	2.03719e10i	0.425036	+	0.152225i
$169$	1.60437e10			0.116378
$170$	−4.04064e10	−	4.65249e9i	−0.284581	−	0.0327673i
$171$	8.24817e10			0.564127
$172$	1.12542e11	+	2.62649e10i	0.747604	+	0.174475i
$173$		−	2.02689e10i		−	0.130797i	−0.997859	−	0.0653986i	$-0.979168\pi$
$173$		−	2.02689e10i		−	0.130797i	0.997859	−	0.0653986i	$-0.0208319\pi$
$174$	1.46440e11	+	1.68614e10i	0.918147	+	0.105718i
$175$		−	1.37039e11i		−	0.834938i
$176$	−1.56732e11	−	7.73700e10i	−0.928098	−	0.458151i
$177$	−5.32831e10			−0.306707
$178$	8.14174e9	−	7.07101e10i	0.0455635	−	0.395714i
$179$	−1.68938e11			−0.919311			−0.459656	−	0.888097i	$-0.652027\pi$
$179$	−1.68938e11			−0.919311			−0.459656	+	0.888097i	$0.652027\pi$
$180$	9.89811e9	−	4.24121e10i	0.0523829	−	0.224454i
$181$		−	1.77403e11i		−	0.913205i	−0.889671	−	0.456603i	$-0.849066\pi$
$181$		−	1.77403e11i		−	0.913205i	0.889671	−	0.456603i	$-0.150934\pi$
$182$	−1.97484e10	+	1.71513e11i	−0.0988952	+	0.858894i
$183$			1.70206e11i			0.829315i
$184$	−2.79685e11	−	1.00168e11i	−1.32611	−	0.474941i
$185$	2.73040e9			0.0125999
$186$	−1.41809e11	−	1.63283e10i	−0.637000	−	0.0733458i
$187$	2.23279e11			0.976426
$188$	5.24032e10	−	2.24541e11i	0.223135	−	0.956106i
$189$		−	1.91522e11i		−	0.794162i
$190$	−5.55125e10	−	6.39186e9i	−0.224194	−	0.0258142i
$191$			1.62897e11i			0.640836i	0.947276	+	0.320418i	$0.103823\pi$
$191$			1.62897e11i			0.640836i	−0.947276	+	0.320418i	$0.896177\pi$
$192$	9.89560e10	+	8.13110e10i	0.379259	+	0.311633i
$193$	1.80721e11			0.674872			0.337436	−	0.941348i	$-0.390440\pi$
$193$	1.80721e11			0.674872			0.337436	+	0.941348i	$0.390440\pi$
$194$	−3.99582e10	+	3.47032e11i	−0.145411	+	1.26288i
$195$	−3.95045e10			−0.140112
$196$	−4.34005e10	−	1.01288e10i	−0.150043	−	0.0350168i
$197$		−	5.24880e10i		−	0.176900i	−0.996081	−	0.0884502i	$-0.971809\pi$
$197$		−	5.24880e10i		−	0.176900i	0.996081	−	0.0884502i	$-0.0281914\pi$
$198$	−2.73477e10	+	2.37511e11i	−0.0898657	+	0.780474i
$199$		−	1.05284e11i		−	0.337364i	−0.985671	−	0.168682i	$-0.946049\pi$
$199$		−	1.05284e11i		−	0.337364i	0.985671	−	0.168682i	$-0.0539510\pi$
$200$	9.79472e10	−	2.73484e11i	0.306085	−	0.854638i
$201$	8.72941e9			0.0266075
$202$	1.50575e11	+	1.73375e10i	0.447708	+	0.0515502i
$203$	5.96970e11			1.73170
$204$	−1.59327e11	−	3.71837e10i	−0.450962	−	0.105245i
$205$			1.09062e11i			0.301235i
$206$	−1.46896e11	−	1.69139e10i	−0.395979	−	0.0455941i
$207$			4.06356e11i			1.06919i
$208$	−1.61998e11	+	3.28167e11i	−0.416096	+	0.842904i
$209$	3.06753e11			0.769232
$210$	−6.40441e9	+	5.56216e10i	−0.0156813	+	0.136190i
$211$	−7.20888e11			−1.72367			−0.861837	−	0.507185i	$-0.830686\pi$
$211$	−7.20888e11			−1.72367			−0.861837	+	0.507185i	$0.830686\pi$
$212$	−7.35824e10	+	3.15291e11i	−0.171828	+	0.736262i
$213$		−	7.99392e10i		−	0.182332i
$214$	3.60937e10	−	3.13469e11i	0.0804197	−	0.698436i
$215$			1.07091e11i			0.233111i
$216$	1.36888e11	−	3.82213e11i	0.291137	−	0.812900i
$217$	−5.78094e11			−1.20143
$218$	1.93630e11	+	2.22951e10i	0.393269	+	0.0452821i
$219$	2.21032e11			0.438768
$220$	3.68115e10	−	1.57733e11i	0.0714283	−	0.306061i
$221$		−	4.67504e11i		−	0.886796i
$222$	1.09110e10	+	1.25632e9i	0.0202348	+	0.00232988i
$223$		−	7.99476e11i		−	1.44971i	−0.688901	−	0.724855i	$-0.741907\pi$
$223$		−	7.99476e11i		−	1.44971i	0.688901	−	0.724855i	$-0.258093\pi$
$224$	4.35789e11	+	2.81292e11i	0.772745	+	0.498789i
$225$	−3.97347e11			−0.689060
$226$	1.02004e11	−	8.85894e11i	0.173012	−	1.50259i
$227$	−5.94778e11			−0.986792			−0.493396	−	0.869805i	$-0.664245\pi$
$227$	−5.94778e11			−0.986792			−0.493396	+	0.869805i	$0.664245\pi$
$228$	−2.18893e11	−	5.10851e10i	−0.355269	−	0.0829125i
$229$			1.16902e12i			1.85628i	0.372235	+	0.928139i	$0.378592\pi$
$229$			1.16902e12i			1.85628i	−0.372235	+	0.928139i	$0.621408\pi$
$230$	3.14903e10	−	2.73489e11i	0.0489257	−	0.424914i
$231$		−	3.07355e11i		−	0.467284i
$232$	1.19135e12	+	4.26678e11i	1.77256	+	0.634834i
$233$	1.91770e11			0.279254			0.139627	−	0.990204i	$-0.455410\pi$
$233$	1.91770e11			0.279254			0.139627	+	0.990204i	$0.455410\pi$
$234$	4.97304e11	+	5.72608e10i	0.708830	+	0.0816166i
$235$	2.13667e11			0.298124
$236$	−4.45453e11	−	1.03959e11i	−0.608473	−	0.142005i
$237$			4.74192e11i			0.634180i
$238$	−6.58235e11	−	7.57909e10i	−0.861978	−	0.0992504i
$239$			6.84109e10i			0.0877275i	0.999038	+	0.0438638i	$0.0139667\pi$
$239$			6.84109e10i			0.0877275i	−0.999038	+	0.0438638i	$0.986033\pi$
$240$	−5.25359e10	+	1.06424e11i	−0.0659782	+	0.133655i
$241$	2.96983e11			0.365297			0.182649	−	0.983178i	$-0.441533\pi$
$241$	2.96983e11			0.365297			0.182649	+	0.983178i	$0.441533\pi$
$242$	−6.76631e9	+	5.87646e10i	−0.00815220	+	0.0708009i
$243$	−8.71014e11			−1.02800
$244$	−3.32085e11	+	1.42294e12i	−0.383972	+	1.64527i
$245$		−	4.12987e10i		−	0.0467849i
$246$	−5.01820e10	+	4.35825e11i	−0.0557022	+	0.483767i
$247$		−	6.42283e11i		−	0.698621i
$248$	−1.15368e12	−	4.13186e11i	−1.22978	−	0.440441i
$249$	4.04808e11			0.422915
$250$	5.62014e11	+	6.47117e10i	0.575502	+	0.0662648i
$251$	1.88895e12			1.89606			0.948029	−	0.318184i	$-0.103073\pi$
$251$	1.88895e12			1.89606			0.948029	+	0.318184i	$0.103073\pi$
$252$	1.61244e11	−	6.90910e11i	0.158665	−	0.679859i
$253$			1.51126e12i			1.45793i
$254$	−1.08867e12	−	1.25352e11i	−1.02974	−	0.118567i
$255$		−	1.51611e11i		−	0.140615i
$256$	6.68639e11	+	8.72839e11i	0.608123	+	0.793843i
$257$	6.09762e11			0.543869			0.271935	−	0.962316i	$-0.412337\pi$
$257$	6.09762e11			0.543869			0.271935	+	0.962316i	$0.412337\pi$
$258$	−4.92752e10	+	4.27949e11i	−0.0431052	+	0.374364i
$259$	4.44792e10			0.0381644
$260$	−3.30262e11	−	7.70763e10i	−0.277966	−	0.0648715i
$261$		−	1.73092e12i		−	1.42914i
$262$	1.34345e11	−	1.16677e12i	0.108822	−	0.945103i
$263$			1.25081e11i			0.0994063i	0.998764	+	0.0497032i	$0.0158275\pi$
$263$			1.25081e11i			0.0994063i	−0.998764	+	0.0497032i	$0.984172\pi$
$264$	2.19679e11	−	6.13378e11i	0.171304	−	0.478309i
$265$	−3.00022e11			−0.229574
$266$	−9.04321e11	−	1.04126e11i	−0.679070	−	0.0781898i
$267$	2.65316e11			0.195527
$268$	7.29788e10	+	1.70317e10i	0.0527865	+	0.0123193i
$269$		−	2.10964e12i		−	1.49778i	−0.662695	−	0.748890i	$-0.730587\pi$
$269$		−	2.10964e12i		−	1.49778i	0.662695	−	0.748890i	$-0.269413\pi$
$270$	3.73746e11	+	4.30341e10i	0.260470	+	0.0299912i
$271$			5.88668e11i			0.402739i	0.979515	+	0.201370i	$0.0645393\pi$
$271$			5.88668e11i			0.402739i	−0.979515	+	0.201370i	$0.935461\pi$
$272$	−1.25945e12	−	6.21720e11i	−0.845931	−	0.417590i
$273$	−6.43544e11			−0.424390
$274$	1.44589e10	−	1.25574e11i	0.00936228	−	0.0813103i
$275$	−1.47775e12			−0.939588
$276$	2.51677e11	−	1.07840e12i	0.157144	−	0.673342i
$277$			2.01749e11i			0.123712i	0.998085	+	0.0618561i	$0.0197020\pi$
$277$			2.01749e11i			0.123712i	−0.998085	+	0.0618561i	$0.980298\pi$
$278$	−2.86849e11	+	2.49125e12i	−0.172754	+	1.50035i
$279$			1.67619e12i			0.991523i
$280$	−1.62063e11	+	4.52507e11i	−0.0941661	+	0.262927i
$281$	2.14487e11			0.122425			0.0612123	−	0.998125i	$-0.480503\pi$
$281$	2.14487e11			0.122425			0.0612123	+	0.998125i	$0.480503\pi$
$282$	8.53834e11	+	9.83127e10i	0.478771	+	0.0551270i
$283$	4.46598e11			0.246028			0.123014	−	0.992405i	$-0.460744\pi$
$283$	4.46598e11			0.246028			0.123014	+	0.992405i	$0.460744\pi$
$284$	1.55967e11	−	6.68300e11i	0.0844194	−	0.361726i
$285$		−	2.08292e11i		−	0.110777i
$286$	1.84949e12	+	2.12955e11i	0.966546	+	0.111291i
$287$			1.77667e12i			0.912425i
$288$	8.15609e11	−	1.26358e12i	0.411642	−	0.637733i
$289$	−2.21798e11			−0.110019
$290$	−1.34137e11	+	1.16496e12i	−0.0653969	+	0.567965i
$291$	−1.30212e12			−0.624004
$292$	1.84785e12	+	4.31250e11i	0.870468	+	0.203149i
$293$		−	6.96014e11i		−	0.322315i	−0.986929	−	0.161157i	$-0.948477\pi$
$293$		−	6.96014e11i		−	0.322315i	0.986929	−	0.161157i	$-0.0515227\pi$
$294$	1.90024e10	−	1.65034e11i	0.00865113	−	0.0751340i
$295$		−	4.23880e11i		−	0.189729i
$296$	8.87656e10	+	3.17911e10i	0.0390649	+	0.0139909i
$297$	−2.06526e12			−0.893701
$298$	−1.58942e12	−	1.83010e11i	−0.676328	−	0.0778742i
$299$	3.16428e12			1.32410
$300$	1.05449e12	+	2.46097e11i	0.433948	+	0.101274i
$301$			1.74456e12i			0.706080i
$302$	4.14232e12	+	4.76957e11i	1.64896	+	0.189865i
$303$			5.64981e11i			0.221218i
$304$	−1.73030e12	−	8.54153e11i	−0.666427	−	0.328979i
$305$	−1.35403e12			−0.513013
$306$	−2.19757e11	+	1.90856e12i	−0.0819097	+	0.711376i
$307$	−4.60754e12			−1.68957			−0.844787	−	0.535102i	$-0.820273\pi$
$307$	−4.60754e12			−1.68957			−0.844787	+	0.535102i	$0.820273\pi$
$308$	5.99674e11	−	2.56952e12i	0.216352	−	0.927041i
$309$		−	5.51176e11i		−	0.195658i
$310$	1.29895e11	−	1.12812e12i	0.0453716	−	0.394047i
$311$			7.15890e11i			0.246062i	0.992403	+	0.123031i	$0.0392614\pi$
$311$			7.15890e11i			0.246062i	−0.992403	+	0.123031i	$0.960739\pi$
$312$	−1.28430e12	−	4.59966e11i	−0.434403	−	0.155580i
$313$	3.10996e12			1.03522			0.517610	−	0.855616i	$-0.326822\pi$
$313$	3.10996e12			1.03522			0.517610	+	0.855616i	$0.326822\pi$
$314$	−4.63757e12	−	5.33982e11i	−1.51929	−	0.174936i
$315$	6.57450e11			0.211987
$316$	−9.25185e11	+	3.96430e12i	−0.293625	+	1.25815i
$317$		−	2.51724e12i		−	0.786372i	−0.919459	−	0.393186i	$-0.871373\pi$
$317$		−	2.51724e12i		−	0.786372i	0.919459	−	0.393186i	$-0.128627\pi$
$318$	−1.19892e12	−	1.38047e11i	−0.368684	−	0.0424512i
$319$		−	6.43738e12i		−	1.94875i
$320$	−6.46848e11	+	7.87218e11i	−0.192776	+	0.234609i
$321$	1.17619e12			0.345106
$322$	5.12989e11	−	4.45525e12i	0.148193	−	1.28704i
$323$	2.46497e12			0.701130
$324$	−1.16550e12	−	2.72004e11i	−0.326429	−	0.0761817i
$325$			3.09413e12i			0.853339i
$326$	3.29310e11	−	2.86002e12i	0.0894369	−	0.776749i
$327$			7.26532e11i			0.194319i
$328$	−1.26985e12	+	3.54563e12i	−0.334491	+	0.933952i
$329$	3.48071e12			0.903001
$330$	5.99790e11	+	6.90614e10i	0.153260	+	0.0176468i
$331$	3.22572e12			0.811870			0.405935	−	0.913902i	$-0.366946\pi$
$331$	3.22572e12			0.811870			0.405935	+	0.913902i	$0.366946\pi$
$332$	3.38424e12	+	7.89812e11i	0.839017	+	0.195809i
$333$		−	1.28968e11i		−	0.0314964i
$334$	−3.85040e12	−	4.43345e11i	−0.926346	−	0.106662i
$335$			6.94445e10i			0.0164594i
$336$	−8.55831e11	+	1.73370e12i	−0.199844	+	0.404833i
$337$	−2.59871e12			−0.597872			−0.298936	−	0.954273i	$-0.596632\pi$
$337$	−2.59871e12			−0.597872			−0.298936	+	0.954273i	$0.596632\pi$
$338$	−5.87259e10	+	5.10028e11i	−0.0133121	+	0.115614i
$339$	3.32402e12			0.742446
$340$	2.95805e11	−	1.26749e12i	0.0651045	−	0.278964i
$341$			6.23383e12i			1.35202i
$342$	−3.01914e11	+	2.62209e12i	−0.0645287	+	0.560425i
$343$		−	5.03930e12i		−	1.06145i
$344$	−1.24691e12	+	3.48156e12i	−0.258846	+	0.722739i
$345$	1.02618e12			0.209955
$346$	6.44346e11	+	7.41917e10i	0.129939	+	0.0149615i
$347$	−9.40440e12			−1.86932			−0.934660	−	0.355542i	$-0.884296\pi$
$347$	−9.40440e12			−1.86932			−0.934660	+	0.355542i	$0.884296\pi$
$348$	−1.07205e12	+	4.59359e12i	−0.210048	+	0.900028i
$349$			3.79523e12i			0.733012i	0.930416	+	0.366506i	$0.119446\pi$
$349$			3.79523e12i			0.733012i	−0.930416	+	0.366506i	$0.880554\pi$
$350$	4.35647e12	+	5.01615e11i	0.829458	+	0.0955059i
$351$			4.32426e12i			0.811665i
$352$	3.03329e12	−	4.69930e12i	0.561306	−	0.869600i
$353$	−2.01509e12			−0.367638			−0.183819	−	0.982960i	$-0.558846\pi$
$353$	−2.01509e12			−0.367638			−0.183819	+	0.982960i	$0.558846\pi$
$354$	1.95036e11	−	1.69387e12i	0.0350832	−	0.304694i
$355$	6.35935e11			0.112790
$356$	2.21807e12	+	5.17651e11i	0.387905	+	0.0905289i
$357$		−	2.46981e12i		−	0.425914i
$358$	6.18378e11	−	5.37054e12i	0.105157	−	0.913277i
$359$		−	2.64150e12i		−	0.442974i	−0.975163	−	0.221487i	$-0.928909\pi$
$359$		−	2.64150e12i		−	0.442974i	0.975163	−	0.221487i	$-0.0710911\pi$
$360$	1.31205e12	+	4.69905e11i	0.216989	+	0.0777137i
$361$	−2.74456e12			−0.447647
$362$	5.63964e12	+	6.49363e11i	0.907211	+	0.104459i
$363$	−2.20494e11			−0.0349836
$364$	−5.38010e12	−	1.25560e12i	−0.841944	−	0.196492i
$365$			1.75836e12i			0.271421i
$366$	−5.41084e12	−	6.23018e11i	−0.823872	−	0.0948627i
$367$		−	4.07835e12i		−	0.612568i	−0.951940	−	0.306284i	$-0.900914\pi$
$367$		−	4.07835e12i		−	0.612568i	0.951940	−	0.306284i	$-0.0990856\pi$
$368$	4.20809e12	−	8.52452e12i	0.623514	−	1.26308i
$369$	5.15148e12			0.753009
$370$	−9.99429e9	+	8.67993e10i	−0.00144126	+	0.0125172i
$371$	−4.88747e12			−0.695368
$372$	1.03815e12	−	4.44834e12i	0.145729	−	0.624429i
$373$		−	8.66480e12i		−	1.20009i	−0.799966	−	0.600046i	$-0.795149\pi$
$373$		−	8.66480e12i		−	1.20009i	0.799966	−	0.600046i	$-0.204851\pi$
$374$	−8.17285e11	+	7.09803e12i	−0.111690	+	0.970017i
$375$			2.10877e12i			0.284363i
$376$	6.94633e12	+	2.48780e12i	0.924307	+	0.331037i
$377$	−1.34787e13			−1.76986
$378$	6.08847e12	+	7.01042e11i	0.788950	+	0.0908417i
$379$	2.01091e12			0.257156			0.128578	−	0.991699i	$-0.458959\pi$
$379$	2.01091e12			0.257156			0.128578	+	0.991699i	$0.458959\pi$
$380$	4.06394e11	−	1.74134e12i	0.0512896	−	0.219769i
$381$		−	4.08487e12i		−	0.508807i
$382$	−5.17850e12	−	5.96266e11i	−0.636630	−	0.0733032i
$383$			1.22783e13i			1.48986i	0.667144	+	0.744929i	$0.267517\pi$
$383$			1.22783e13i			1.48986i	−0.667144	+	0.744929i	$0.732483\pi$
$384$	−2.94709e12	+	2.84818e12i	−0.352970	+	0.341123i
$385$	2.44508e12			0.289061
$386$	−6.61506e11	+	5.74511e12i	−0.0771965	+	0.670442i
$387$	5.05838e12			0.582716
$388$	−1.08859e13	−	2.54054e12i	−1.23796	−	0.288913i
$389$		−	5.07317e12i		−	0.569549i	−0.958595	−	0.284774i	$-0.908081\pi$
$389$		−	5.07317e12i		−	0.569549i	0.958595	−	0.284774i	$-0.0919187\pi$
$390$	1.44602e11	−	1.25585e12i	0.0160269	−	0.139192i
$391$			1.21440e13i			1.32885i
$392$	4.80856e11	−	1.34263e12i	0.0519499	−	0.145052i
$393$	4.37792e12			0.466987
$394$	1.66859e12	+	1.92126e11i	0.175739	+	0.0202351i
$395$	−3.77231e12			−0.392303
$396$	−7.45037e12	−	1.73876e12i	−0.765071	−	0.178552i
$397$		−	9.59987e10i		−	0.00973448i	−0.999988	−	0.00486724i	$-0.998451\pi$
$397$		−	9.59987e10i		−	0.00973448i	0.999988	−	0.00486724i	$-0.00154930\pi$
$398$	3.34698e12	+	3.85381e11i	0.335149	+	0.0385900i
$399$		−	3.39316e12i		−	0.335537i
$400$	8.33552e12	+	4.11479e12i	0.814016	+	0.401835i
$401$	6.27920e12			0.605595			0.302798	−	0.953055i	$-0.402079\pi$
$401$	6.27920e12			0.605595			0.302798	+	0.953055i	$0.402079\pi$
$402$	−3.19529e10	+	2.77508e11i	−0.00304355	+	0.0264329i
$403$	1.30525e13			1.22791
$404$	−1.10232e12	+	4.72330e12i	−0.102424	+	0.438873i
$405$		−	1.10906e12i		−	0.101784i
$406$	−2.18514e12	+	1.89777e13i	−0.198084	+	1.72033i
$407$		−	4.79638e11i		−	0.0429479i
$408$	1.76527e12	−	4.92891e12i	0.156138	−	0.435963i
$409$	1.46749e13			1.28221			0.641104	−	0.767454i	$-0.278477\pi$
$409$	1.46749e13			1.28221			0.641104	+	0.767454i	$0.278477\pi$
$410$	−3.46709e12	−	3.99210e11i	−0.299258	−	0.0344573i
$411$	4.71173e11			0.0401764
$412$	1.07539e12	−	4.60789e12i	0.0905896	−	0.388165i
$413$		−	6.90516e12i		−	0.574677i
$414$	−1.29180e13	−	1.48742e12i	−1.06217	−	0.122301i
$415$			3.22035e12i			0.261615i
$416$	−9.83944e12	−	6.35113e12i	−0.789775	−	0.509781i
$417$	−9.34757e12			−0.741342
$418$	−1.12283e12	+	9.75167e12i	−0.0879900	+	0.764183i
$419$	1.16491e13			0.902034			0.451017	−	0.892515i	$-0.351061\pi$
$419$	1.16491e13			0.902034			0.451017	+	0.892515i	$0.351061\pi$
$420$	−1.74476e12	−	4.07192e11i	−0.133503	−	0.0311568i
$421$			1.17116e11i			0.00885535i	0.999990	+	0.00442768i	$0.00140938\pi$
$421$			1.17116e11i			0.00885535i	−0.999990	+	0.00442768i	$0.998591\pi$
$422$	2.63872e12	−	2.29170e13i	0.197166	−	1.71236i
$423$		−	1.00924e13i		−	0.745232i
$424$	−9.75375e12	−	3.49327e12i	−0.711774	−	0.254919i
$425$	−1.18747e13			−0.856404
$426$	2.54127e12	+	2.92608e11i	0.181135	+	0.0208563i
$427$	−2.20576e13			−1.55389
$428$	9.83307e12	+	2.29483e12i	0.684652	+	0.159784i
$429$			6.93960e12i			0.477582i
$430$	−3.40443e12	−	3.91995e11i	−0.231581	−	0.0266648i
$431$		−	1.56309e13i		−	1.05099i	−0.850798	−	0.525493i	$-0.823881\pi$
$431$		−	1.56309e13i		−	1.05099i	0.850798	−	0.525493i	$-0.176119\pi$
$432$	1.16495e13	+	5.75071e12i	0.774262	+	0.382211i
$433$	2.69056e12			0.176768			0.0883838	−	0.996086i	$-0.471830\pi$
$433$	2.69056e12			0.176768			0.0883838	+	0.996086i	$0.471830\pi$
$434$	2.11604e12	−	1.83776e13i	0.137428	−	1.19355i
$435$	−4.37113e12			−0.280638
$436$	−1.41752e12	+	6.07388e12i	−0.0899697	+	0.385508i
$437$			1.66841e13i			1.04687i
$438$	−8.09061e11	+	7.02660e12i	−0.0501893	+	0.435888i
$439$			1.54140e12i			0.0945349i	0.998882	+	0.0472675i	$0.0150513\pi$
$439$			1.54140e12i			0.0945349i	−0.998882	+	0.0472675i	$0.984949\pi$
$440$	4.87957e12	+	1.74760e12i	0.295882	+	0.105969i
$441$	−1.95071e12			−0.116950
$442$	1.48619e13	+	1.71124e12i	0.880975	+	0.101438i
$443$	−1.49843e13			−0.878251			−0.439125	−	0.898426i	$-0.644712\pi$
$443$	−1.49843e13			−0.878251			−0.439125	+	0.898426i	$0.644712\pi$
$444$	−7.98765e10	+	3.42261e11i	−0.00462918	+	0.0198354i
$445$			2.11065e12i			0.120953i
$446$	2.54153e13	+	2.92639e12i	1.44020	+	0.165828i
$447$		−	5.96377e12i		−	0.334182i
$448$	−1.05374e13	+	1.28241e13i	−0.583907	+	0.710618i
$449$	1.34588e12			0.0737520			0.0368760	−	0.999320i	$-0.488259\pi$
$449$	1.34588e12			0.0737520			0.0368760	+	0.999320i	$0.488259\pi$
$450$	1.45444e12	−	1.26316e13i	0.0788194	−	0.684538i
$451$	1.91586e13			1.02679
$452$	2.77891e13	+	6.48541e12i	1.47293	+	0.343752i
$453$			1.55427e13i			0.814769i
$454$	2.17711e12	−	1.89080e13i	0.112876	−	0.980315i
$455$		−	5.11954e12i		−	0.262527i
$456$	2.42522e12	−	6.77161e12i	0.123006	−	0.343453i
$457$	−1.64027e13			−0.822874			−0.411437	−	0.911438i	$-0.634973\pi$
$457$	−1.64027e13			−0.822874			−0.411437	+	0.911438i	$0.634973\pi$
$458$	−3.71630e13	−	4.27904e12i	−1.84409	−	0.212334i
$459$	−1.65958e13			−0.814580
$460$	8.57895e12	+	2.00215e12i	0.416529	+	0.0972091i
$461$			2.18713e12i			0.105044i	0.998620	+	0.0525219i	$0.0167259\pi$
$461$			2.18713e12i			0.105044i	−0.998620	+	0.0525219i	$0.983274\pi$
$462$	9.77082e12	+	1.12504e12i	0.464217	+	0.0534511i
$463$			2.69444e13i			1.26638i	0.773997	+	0.633189i	$0.218255\pi$
$463$			2.69444e13i			1.26638i	−0.773997	+	0.633189i	$0.781745\pi$
$464$	−1.79249e13	+	3.63112e13i	−0.833425	+	1.68831i
$465$	4.23291e12			0.194704
$466$	−7.01949e11	+	6.09635e12i	−0.0319430	+	0.277421i
$467$	1.65679e13			0.745904			0.372952	−	0.927851i	$-0.378346\pi$
$467$	1.65679e13			0.745904			0.372952	+	0.927851i	$0.378346\pi$
$468$	−3.64064e12	+	1.55997e13i	−0.162162	+	0.694842i
$469$			1.13128e12i			0.0498546i
$470$	−7.82101e11	+	6.79245e12i	−0.0341015	+	0.296167i
$471$		−	1.74009e13i		−	0.750702i
$472$	4.93539e12	−	1.37804e13i	0.210674	−	0.588236i
$473$	1.88123e13			0.794579
$474$	−1.50746e13	−	1.73572e12i	−0.630018	−	0.0725419i
$475$	−1.63142e13			−0.674678
$476$	4.81878e12	−	2.06479e13i	0.197198	−	0.844968i
$477$			1.41713e13i			0.573875i
$478$	−2.17478e12	−	2.50410e11i	−0.0871517	−	0.0100349i
$479$		−	3.77578e13i		−	1.49737i	−0.662926	−	0.748685i	$-0.730686\pi$
$479$		−	3.77578e13i		−	1.49737i	0.662926	−	0.748685i	$-0.269314\pi$
$480$	−3.19093e12	−	2.05967e12i	−0.125231	−	0.0808335i
$481$	−1.00427e12			−0.0390055
$482$	−1.08707e12	+	9.44108e12i	−0.0417852	+	0.362899i
$483$	1.67168e13			0.635943
$484$	−1.84336e12	−	4.30201e11i	−0.0694037	−	0.0161974i
$485$		−	1.03587e13i		−	0.386008i
$486$	3.18824e12	−	2.76895e13i	0.117590	−	1.02125i
$487$			1.67338e13i			0.610871i	0.952213	+	0.305435i	$0.0988020\pi$
$487$			1.67338e13i			0.610871i	−0.952213	+	0.305435i	$0.901198\pi$
$488$	−4.40197e13	−	1.57655e13i	−1.59055	−	0.569649i
$489$	1.07313e13			0.383801
$490$	1.31288e12	+	1.51169e11i	0.0464778	+	0.00535158i
$491$	−8.96254e11			−0.0314068			−0.0157034	−	0.999877i	$-0.504999\pi$
$491$	−8.96254e11			−0.0314068			−0.0157034	+	0.999877i	$0.504999\pi$
$492$	−1.36712e13	−	3.19057e12i	−0.474221	−	0.110673i
$493$		−	5.17287e13i		−	1.77622i
$494$	2.04181e13	+	2.35100e12i	0.694035	+	0.0799130i
$495$		−	7.08956e12i		−	0.238557i
$496$	1.73581e13	−	3.51631e13i	0.578220	−	1.17133i
$497$	1.03596e13			0.341635
$498$	−1.48175e12	+	1.28688e13i	−0.0483759	+	0.420139i
$499$	2.95103e13			0.953829			0.476914	−	0.878950i	$-0.341755\pi$
$499$	2.95103e13			0.953829			0.476914	+	0.878950i	$0.341755\pi$
$500$	−4.11437e12	+	1.76295e13i	−0.131660	+	0.564145i
$501$		−	1.44473e13i		−	0.457719i
$502$	−6.91427e12	+	6.00496e13i	−0.216884	+	1.88361i
$503$			3.32549e13i			1.03280i	0.856348	+	0.516399i	$0.172728\pi$
$503$			3.32549e13i			1.03280i	−0.856348	+	0.516399i	$0.827272\pi$
$504$	2.13738e13	+	7.65493e12i	0.657247	+	0.235390i
$505$	−4.49455e12			−0.136845
$506$	−4.80428e13	−	5.53177e12i	−1.44836	−	0.166768i
$507$	−1.91371e12			−0.0571263
$508$	7.96988e12	−	3.41499e13i	0.235577	−	1.00942i
$509$			4.22636e13i			1.23702i	0.785776	+	0.618511i	$0.212264\pi$
$509$			4.22636e13i			1.23702i	−0.785776	+	0.618511i	$0.787736\pi$
$510$	4.81972e12	+	5.54955e11i	0.139692	+	0.0160845i
$511$			2.86444e13i			0.822120i
$512$	−3.01950e13	+	1.80611e13i	−0.858193	+	0.513327i
$513$	−2.28002e13			−0.641729
$514$	−2.23196e12	+	1.93843e13i	−0.0622115	+	0.540300i
$515$	4.38474e12			0.121034
$516$	−1.34241e13	−	3.13291e12i	−0.366976	−	0.0856445i
$517$		−	3.75340e13i		−	1.01618i
$518$	−1.62811e11	+	1.41399e12i	−0.00436551	+	0.0379139i
$519$			2.41769e12i			0.0642043i
$520$	3.65914e12	−	1.02169e13i	0.0962414	−	0.268721i
$521$	1.83180e13			0.477187			0.238593	−	0.971120i	$-0.423314\pi$
$521$	1.83180e13			0.477187			0.238593	+	0.971120i	$0.423314\pi$
$522$	5.50260e13	+	6.33584e12i	1.41976	+	0.163475i
$523$	−1.70396e13			−0.435463			−0.217731	−	0.976009i	$-0.569866\pi$
$523$	−1.70396e13			−0.435463			−0.217731	+	0.976009i	$0.569866\pi$
$524$	3.65998e13	+	8.54164e12i	0.926452	+	0.216215i
$525$			1.63462e13i			0.409845i
$526$	−3.97633e12	−	4.57845e11i	−0.0987539	−	0.0113708i
$527$			5.00930e13i			1.23232i
$528$	1.86952e13	+	9.22878e12i	0.455575	+	0.224892i
$529$	−4.07695e13			−0.984140
$530$	1.09819e12	−	9.53768e12i	0.0262603	−	0.228067i
$531$	−2.00216e13			−0.474271
$532$	6.62031e12	−	2.83672e13i	0.155353	−	0.665668i
$533$		−	4.01144e13i		−	0.932533i
$534$	−9.71157e11	+	8.43438e12i	−0.0223657	+	0.194244i
$535$			9.35686e12i			0.213482i
$536$	−8.08568e11	+	2.25765e12i	−0.0182765	+	0.0510308i
$537$	2.01511e13			0.451262
$538$	6.70655e13	+	7.72210e12i	1.48795	+	0.171326i
$539$	−7.25478e12			−0.159470
$540$	−2.73611e12	+	1.17239e13i	−0.0595887	+	0.255330i
$541$		−	6.13265e13i		−	1.32331i	−0.749808	−	0.661655i	$-0.769854\pi$
$541$		−	6.13265e13i		−	1.32331i	0.749808	−	0.661655i	$-0.230146\pi$
$542$	−1.87137e13	−	2.15475e12i	−0.400096	−	0.0460681i
$543$			2.11609e13i			0.448264i
$544$	2.43745e13	−	3.77620e13i	0.511612	−	0.792612i
$545$	−5.77973e12			−0.120206
$546$	2.35561e12	−	2.04582e13i	0.0485446	−	0.421604i
$547$	−4.66636e13			−0.952887			−0.476444	−	0.879205i	$-0.658074\pi$
$547$	−4.66636e13			−0.952887			−0.476444	+	0.879205i	$0.658074\pi$
$548$	3.93906e12	+	9.19294e11i	0.0797057	+	0.0186017i
$549$			6.39565e13i			1.28240i
$550$	5.40912e12	−	4.69776e13i	0.107476	−	0.933421i
$551$		−	7.10678e13i		−	1.39931i
$552$	3.33612e13	+	1.19482e13i	0.650947	+	0.233134i
$553$	−6.14524e13			−1.18826
$554$	−6.41360e12	−	7.38478e11i	−0.122900	−	0.0141511i
$555$	−3.25685e11			−0.00618491
$556$	−7.81467e13	−	1.82378e13i	−1.47074	−	0.343241i
$557$			4.12628e13i			0.769631i	0.922994	+	0.384815i	$0.125735\pi$
$557$			4.12628e13i			0.769631i	−0.922994	+	0.384815i	$0.874265\pi$
$558$	−5.32861e13	−	6.13550e12i	−0.985015	−	0.113417i
$559$		−	3.93895e13i		−	0.721641i
$560$	−1.37920e13	−	6.80833e12i	−0.250430	−	0.123623i
$561$	−2.66330e13			−0.479298
$562$	−7.85102e11	+	6.81852e12i	−0.0140038	+	0.121621i
$563$	7.81706e13			1.38198			0.690989	−	0.722865i	$-0.257175\pi$
$563$	7.81706e13			1.38198			0.690989	+	0.722865i	$0.257175\pi$
$564$	−6.25071e12	+	2.67835e13i	−0.109530	+	0.469323i
$565$			2.64433e13i			0.459276i
$566$	−1.63472e12	+	1.41973e13i	−0.0281423	+	0.244413i
$567$		−	1.80670e13i		−	0.308298i
$568$	2.06743e13	+	7.40443e12i	0.349695	+	0.125242i
$569$	7.01252e13			1.17574			0.587872	−	0.808954i	$-0.299966\pi$
$569$	7.01252e13			1.17574			0.587872	+	0.808954i	$0.299966\pi$
$570$	6.62160e12	+	7.62428e11i	0.110050	+	0.0126714i
$571$	−3.98236e12			−0.0656084			−0.0328042	−	0.999462i	$-0.510444\pi$
$571$	−3.98236e12			−0.0656084			−0.0328042	+	0.999462i	$0.510444\pi$
$572$	−1.35397e13	+	5.80158e13i	−0.221120	+	0.947472i
$573$		−	1.94306e13i		−	0.314567i
$574$	−5.64802e13	−	6.50328e12i	−0.906436	−	0.104369i
$575$		−	8.03737e13i		−	1.27872i
$576$	3.71836e13	+	3.05534e13i	0.586461	+	0.481888i
$577$	1.05066e14			1.64279			0.821394	−	0.570361i	$-0.193197\pi$
$577$	1.05066e14			1.64279			0.821394	+	0.570361i	$0.193197\pi$
$578$	8.11865e11	−	7.05095e12i	0.0125848	−	0.109297i
$579$	−2.15566e13			−0.331274
$580$	−3.65431e13	−	8.52840e12i	−0.556756	−	0.129935i
$581$			5.24607e13i			0.792416i
$582$	4.76626e12	−	4.13944e13i	0.0713778	−	0.619908i
$583$			5.27036e13i			0.782524i
$584$	−2.04733e13	+	5.71646e13i	−0.301386	+	0.841517i
$585$	−1.48442e13			−0.216659
$586$	2.21263e13	+	2.54768e12i	0.320199	+	0.0368686i
$587$	4.34059e13			0.622814			0.311407	−	0.950277i	$-0.399200\pi$
$587$	4.34059e13			0.622814			0.311407	+	0.950277i	$0.399200\pi$
$588$	5.17687e12	+	1.20817e12i	0.0736513	+	0.0171887i
$589$			6.88206e13i			0.970827i
$590$	1.34751e13	+	1.55156e12i	0.188483	+	0.0217024i
$591$			6.26083e12i			0.0868349i
$592$	−1.33555e12	+	2.70549e12i	−0.0183676	+	0.0372081i
$593$	5.27341e13			0.719147			0.359574	−	0.933117i	$-0.382922\pi$
$593$	5.27341e13			0.719147			0.359574	+	0.933117i	$0.382922\pi$
$594$	7.55963e12	−	6.56545e13i	0.102228	−	0.887835i
$595$	1.96479e13			0.263470
$596$	1.16358e13	−	4.98577e13i	0.154726	−	0.662981i
$597$			1.25584e13i			0.165601i
$598$	−1.15825e13	+	1.00592e14i	−0.151459	+	1.31541i
$599$		−	5.55584e13i		−	0.720470i	−0.932862	−	0.360235i	$-0.882697\pi$
$599$		−	5.55584e13i		−	0.720470i	0.932862	−	0.360235i	$-0.117303\pi$
$600$	−1.16833e13	+	3.26215e13i	−0.150248	+	0.419515i
$601$	−1.13300e13			−0.144497			−0.0722485	−	0.997387i	$-0.523017\pi$
$601$	−1.13300e13			−0.144497			−0.0722485	+	0.997387i	$0.523017\pi$
$602$	−5.54595e13	−	6.38576e12i	−0.701445	−	0.0807662i
$603$	3.28015e12			0.0411441
$604$	−3.03249e13	+	1.29938e14i	−0.377238	+	1.61641i
$605$		−	1.75409e12i		−	0.0216408i
$606$	−1.79607e13	−	2.06804e12i	−0.219766	−	0.0253044i
$607$		−	1.08707e13i		−	0.131921i	−0.997822	−	0.0659606i	$-0.978989\pi$
$607$		−	1.08707e13i		−	0.131921i	0.997822	−	0.0659606i	$-0.0210112\pi$
$608$	3.34870e13	−	5.18796e13i	0.403050	−	0.624422i
$609$	−7.12073e13			−0.850038
$610$	4.95626e12	−	4.30445e13i	0.0586820	−	0.509646i
$611$	−7.85890e13			−0.922902
$612$	−5.98687e13	−	1.39721e13i	−0.697337	−	0.162744i
$613$		−	3.54339e13i		−	0.409371i	−0.978828	−	0.204685i	$-0.934383\pi$
$613$		−	3.54339e13i		−	0.409371i	0.978828	−	0.204685i	$-0.0656171\pi$
$614$	1.68653e13	−	1.46474e14i	0.193265	−	1.67848i
$615$		−	1.30091e13i		−	0.147867i
$616$	7.94900e13	+	2.84690e13i	0.896208	+	0.320973i
$617$	−1.30704e14			−1.46171			−0.730857	−	0.682530i	$-0.760879\pi$
$617$	−1.30704e14			−1.46171			−0.730857	+	0.682530i	$0.760879\pi$
$618$	1.75219e13	+	2.01751e12i	0.194374	+	0.0223807i
$619$	3.87987e13			0.426937			0.213468	−	0.976950i	$-0.431524\pi$
$619$	3.87987e13			0.426937			0.213468	+	0.976950i	$0.431524\pi$
$620$	3.53876e13	+	8.25873e12i	0.386271	+	0.0901477i
$621$		−	1.12328e14i		−	1.21627i
$622$	−2.27581e13	−	2.62043e12i	−0.244447	−	0.0281462i
$623$			3.43833e13i			0.366359i
$624$	1.93233e13	−	3.91441e13i	0.204248	−	0.413755i
$625$	6.97984e13			0.731890
$626$	−1.13836e13	+	9.88655e13i	−0.118416	+	1.02843i
$627$	−3.65899e13			−0.377592
$628$	3.39505e13	−	1.45474e14i	0.347575	−	1.48931i
$629$		−	3.85422e12i		−	0.0391456i
$630$	−2.40652e12	+	2.09003e13i	−0.0242486	+	0.210596i
$631$			9.35111e13i			0.934795i	0.884047	+	0.467397i	$0.154808\pi$
$631$			9.35111e13i			0.934795i	−0.884047	+	0.467397i	$0.845192\pi$
$632$	−1.22638e14	−	4.39224e13i	−1.21630	−	0.435613i
$633$	8.59883e13			0.846099
$634$	8.00230e13	+	9.21405e12i	0.781211	+	0.0899506i
$635$	3.24961e13			0.314748
$636$	8.77699e12	−	3.76083e13i	0.0843452	−	0.361408i
$637$			1.51901e13i			0.144832i
$638$	2.04644e14	+	2.35633e13i	1.93596	+	0.222911i
$639$		−	3.00379e13i		−	0.281946i
$640$	−2.26579e13	−	2.34448e13i	−0.211018	−	0.218347i
$641$	−1.26314e14			−1.16724			−0.583622	−	0.812025i	$-0.698365\pi$
$641$	−1.26314e14			−1.16724			−0.583622	+	0.812025i	$0.698365\pi$
$642$	−4.30530e12	+	3.73910e13i	−0.0394755	+	0.342840i
$643$	−1.48134e14			−1.34772			−0.673862	−	0.738858i	$-0.735366\pi$
$643$	−1.48134e14			−1.34772			−0.673862	+	0.738858i	$0.735366\pi$
$644$	1.39754e14	+	3.26158e13i	1.26164	+	0.294441i
$645$		−	1.27740e13i		−	0.114427i
$646$	−9.02271e12	+	7.83612e13i	−0.0802000	+	0.696528i
$647$			8.22868e13i			0.725787i	0.931831	+	0.362893i	$0.118211\pi$
$647$			8.22868e13i			0.725787i	−0.931831	+	0.362893i	$0.881789\pi$
$648$	1.29132e13	−	3.60557e13i	0.113021	−	0.315572i
$649$	−7.44613e13			−0.646706
$650$	−9.83622e13	−	1.13257e13i	−0.847738	−	0.0976107i
$651$	6.89557e13			0.589747
$652$	8.97145e13	+	2.09375e13i	0.761421	+	0.177700i
$653$		−	1.92857e13i		−	0.162431i	−0.996697	−	0.0812155i	$-0.974120\pi$
$653$		−	1.92857e13i		−	0.162431i	0.996697	−	0.0812155i	$-0.0258802\pi$
$654$	−2.30964e13	−	2.65938e12i	−0.193044	−	0.0222276i
$655$			3.48273e13i			0.288878i
$656$	−1.08067e14	−	5.33470e13i	−0.889561	−	0.439128i
$657$	8.30548e13			0.678481
$658$	−1.27407e13	+	1.10652e14i	−0.103291	+	0.897074i
$659$	−2.18050e14			−1.75440			−0.877202	−	0.480122i	$-0.840593\pi$
$659$	−2.18050e14			−1.75440			−0.877202	+	0.480122i	$0.840593\pi$
$660$	−4.39092e12	+	1.88145e13i	−0.0350619	+	0.150236i
$661$		−	2.98437e13i		−	0.236508i	−0.992983	−	0.118254i	$-0.962270\pi$
$661$		−	2.98437e13i		−	0.236508i	0.992983	−	0.118254i	$-0.0377297\pi$
$662$	−1.18073e13	+	1.02545e14i	−0.0928672	+	0.806541i
$663$			5.57644e13i			0.435301i
$664$	−3.74957e13	+	1.04694e14i	−0.290497	+	0.811112i
$665$	2.69934e13			0.207563
$666$	4.09989e12	+	4.72073e11i	0.0312897	+	0.00360278i
$667$	3.50124e14			2.65212
$668$	2.81878e13	−	1.20781e14i	0.211924	−	0.908065i
$669$			9.53625e13i			0.711618i
$670$	−2.20764e12	−	2.54193e11i	−0.0163514	−	0.00188274i
$671$			2.37857e14i			1.74865i
$672$	−5.19814e13	−	3.35528e13i	−0.379317	−	0.244840i
$673$	−5.31918e13			−0.385274			−0.192637	−	0.981270i	$-0.561704\pi$
$673$	−5.31918e13			−0.385274			−0.192637	+	0.981270i	$0.561704\pi$
$674$	9.51227e12	−	8.26129e13i	0.0683887	−	0.593948i
$675$	1.09837e14			0.783847
$676$	−1.59988e13	−	3.73379e12i	−0.113332	−	0.0264494i
$677$		−	2.44151e14i		−	1.71678i	−0.512996	−	0.858391i	$-0.671465\pi$
$677$		−	2.44151e14i		−	1.71678i	0.512996	−	0.858391i	$-0.328535\pi$
$678$	−1.21672e13	+	1.05670e14i	−0.0849261	+	0.737573i
$679$		−	1.68747e14i		−	1.16920i
$680$	3.92106e13	+	1.40431e13i	0.269686	+	0.0965871i
$681$	7.09458e13			0.484386
$682$	−1.98173e14	−	2.28182e13i	−1.34315	−	0.154653i
$683$	−4.30287e13			−0.289504			−0.144752	−	0.989468i	$-0.546238\pi$
$683$	−4.30287e13			−0.289504			−0.144752	+	0.989468i	$0.546238\pi$
$684$	−8.22510e13	−	1.91957e13i	−0.549365	−	0.128210i
$685$			3.74829e12i			0.0248531i
$686$	1.60199e14	+	1.84458e13i	1.05448	+	0.121416i
$687$		−	1.39442e14i		−	0.911189i
$688$	−1.06114e14	−	5.23829e13i	−0.688387	−	0.339819i
$689$	1.10351e14			0.710693
$690$	−3.75620e12	+	3.26221e13i	−0.0240161	+	0.208577i
$691$	1.32035e13			0.0838105			0.0419053	−	0.999122i	$-0.486657\pi$
$691$	1.32035e13			0.0838105			0.0419053	+	0.999122i	$0.486657\pi$
$692$	−4.71710e12	+	2.02122e13i	−0.0297266	+	0.127374i
$693$		−	1.15492e14i		−	0.722577i
$694$	3.44237e13	−	2.98966e14i	0.213826	−	1.85705i
$695$		−	7.43621e13i		−	0.458593i
$696$	−1.42106e14	−	5.08947e13i	−0.870094	−	0.311621i
$697$	1.53952e14			0.935882
$698$	−1.20650e14	−	1.38920e13i	−0.728201	−	0.0838470i
$699$	−2.28745e13			−0.137077
$700$	−3.18926e13	+	1.36656e14i	−0.189758	+	0.813089i
$701$		−	3.23737e13i		−	0.191250i	−0.995417	−	0.0956252i	$-0.969515\pi$
$701$		−	3.23737e13i		−	0.191250i	0.995417	−	0.0956252i	$-0.0304850\pi$
$702$	−1.37468e14	−	1.58284e13i	−0.806337	−	0.0928437i
$703$		−	5.29514e12i		−	0.0308390i
$704$	1.38287e14	+	1.13629e14i	0.799686	+	0.657093i
$705$	−2.54864e13			−0.146340
$706$	7.37599e12	−	6.40596e13i	0.0420530	−	0.365225i
$707$	−7.32180e13			−0.414496
$708$	5.31341e13	+	1.24004e13i	0.298681	+	0.0697059i
$709$			3.04892e14i			1.70182i	0.525310	+	0.850911i	$0.323950\pi$
$709$			3.04892e14i			1.70182i	−0.525310	+	0.850911i	$0.676050\pi$
$710$	−2.32776e12	+	2.02164e13i	−0.0129017	+	0.112050i
$711$			1.78182e14i			0.980654i
$712$	−2.45751e13	+	6.86175e13i	−0.134306	+	0.375003i
$713$	−3.39053e14			−1.84001
$714$	7.85151e13	+	9.04043e12i	0.423119	+	0.0487190i
$715$	−5.52062e13			−0.295432
$716$	1.68466e14	+	3.93164e13i	0.895254	+	0.208934i
$717$		−	8.16013e12i		−	0.0430627i
$718$	8.39732e13	+	9.66890e12i	0.440067	+	0.0506704i
$719$		−	2.13041e14i		−	1.10871i	−0.832280	−	0.554356i	$-0.812965\pi$
$719$		−	2.13041e14i		−	1.10871i	0.832280	−	0.554356i	$-0.187035\pi$
$720$	−1.97409e13	+	3.99900e13i	−0.102024	+	0.206675i
$721$	7.14290e13			0.366605
$722$	1.00461e13	−	8.72493e13i	0.0512050	−	0.444709i
$723$	−3.54245e13			−0.179313
$724$	−4.12864e13	+	1.76907e14i	−0.207546	+	0.889308i
$725$			3.42361e14i			1.70921i
$726$	8.07093e11	−	7.00951e12i	0.00400166	−	0.0347540i
$727$		−	2.39997e14i		−	1.18177i	−0.806756	−	0.590885i	$-0.798779\pi$
$727$		−	2.39997e14i		−	1.18177i	0.806756	−	0.590885i	$-0.201221\pi$
$728$	5.96088e13	−	1.66437e14i	0.291510	−	0.813941i
$729$	3.48808e13			0.169414
$730$	−5.58982e13	−	6.43627e12i	−0.269640	−	0.0310470i
$731$	1.51170e14			0.724233
$732$	3.96115e13	−	1.69730e14i	0.188480	−	0.807613i
$733$			2.98350e13i			0.140996i	0.997512	+	0.0704979i	$0.0224588\pi$
$733$			2.98350e13i			0.140996i	−0.997512	+	0.0704979i	$0.977541\pi$
$734$	1.29651e14	+	1.49283e13i	0.608547	+	0.0700697i
$735$			4.92616e12i			0.0229653i
$736$	2.55591e14	+	1.64978e14i	1.18347	+	0.763901i
$737$	1.21990e13			0.0561033
$738$	−1.88564e13	+	1.63765e14i	−0.0861343	+	0.748066i
$739$	−3.24729e14			−1.47333			−0.736664	−	0.676259i	$-0.763600\pi$
$739$	−3.24729e14			−1.47333			−0.736664	+	0.676259i	$0.763600\pi$
$740$	−2.72276e12	−	6.35436e11i	−0.0122702	−	0.00286361i
$741$			7.66123e13i			0.342931i
$742$	1.78900e13	−	1.55372e14i	0.0795409	−	0.690803i
$743$			1.59567e14i			0.704691i	0.935870	+	0.352345i	$0.114616\pi$
$743$			1.59567e14i			0.704691i	−0.935870	+	0.352345i	$0.885384\pi$
$744$	1.37612e14	+	4.92854e13i	0.603661	+	0.216199i
$745$	4.74432e13			0.206725
$746$	2.75454e14	+	3.17164e13i	1.19221	+	0.137275i
$747$	1.52110e14			0.653967
$748$	−2.22654e14	−	5.19629e13i	−0.950875	−	0.221914i
$749$			1.52427e14i			0.646625i
$750$	−6.70377e13	−	7.71889e12i	−0.282496	−	0.0325273i
$751$		−	1.28853e14i		−	0.539381i	−0.962947	−	0.269691i	$-0.913079\pi$
$751$		−	1.28853e14i		−	0.539381i	0.962947	−	0.269691i	$-0.0869215\pi$
$752$	−1.04513e14	+	2.11717e14i	−0.434592	+	0.880374i
$753$	−2.25316e14			−0.930716
$754$	4.93370e13	−	4.28486e14i	0.202449	−	1.75825i
$755$	−1.23646e14			−0.504015
$756$	−4.45722e13	+	1.90986e14i	−0.180491	+	0.773380i
$757$		−	8.36867e12i		−	0.0336649i	−0.999858	−	0.0168324i	$-0.994642\pi$
$757$		−	8.36867e12i		−	0.0336649i	0.999858	−	0.0168324i	$-0.00535819\pi$
$758$	−7.36069e12	+	6.39268e13i	−0.0294153	+	0.255468i
$759$		−	1.80264e14i		−	0.715651i
$760$	5.38697e13	+	1.92932e13i	0.212460	+	0.0760916i
$761$	2.38978e14			0.936343			0.468171	−	0.883638i	$-0.344913\pi$
$761$	2.38978e14			0.936343			0.468171	+	0.883638i	$0.344913\pi$
$762$	1.29858e14	+	1.49522e13i	0.505467	+	0.0582008i
$763$	−9.41540e13			−0.364096
$764$	3.79105e13	−	1.62442e14i	0.145644	−	0.624066i
$765$		−	5.69694e13i		−	0.217437i
$766$	−3.90327e14	−	4.49433e13i	−1.48008	−	0.170420i
$767$			1.55908e14i			0.587342i
$768$	−7.97560e13	−	1.04113e14i	−0.298509	−	0.389673i
$769$	−3.54539e14			−1.31836			−0.659178	−	0.751987i	$-0.729096\pi$
$769$	−3.54539e14			−1.31836			−0.659178	+	0.751987i	$0.729096\pi$
$770$	−8.94993e12	+	7.77291e13i	−0.0330648	+	0.287164i
$771$	−7.27331e13			−0.266969
$772$	−1.80215e14	−	4.20585e13i	−0.657212	−	0.153380i
$773$		−	3.99219e14i		−	1.44649i	−0.690594	−	0.723243i	$-0.742651\pi$
$773$		−	3.99219e14i		−	1.44649i	0.690594	−	0.723243i	$-0.257349\pi$
$774$	−1.85156e13	+	1.60806e14i	−0.0666550	+	0.578891i
$775$		−	3.31536e14i		−	1.18583i
$776$	1.20610e14	−	3.36762e14i	0.428623	−	1.19678i
$777$	−5.30554e12			−0.0187337
$778$	1.61276e14	+	1.85697e13i	0.565811	+	0.0651489i
$779$	2.11508e14			0.737291
$780$	3.93940e13	+	9.19375e12i	0.136445	+	0.0318434i
$781$		−	1.11712e14i		−	0.384455i
$782$	−3.86056e14	−	4.44515e13i	−1.32013	−	0.152003i
$783$			4.78474e14i			1.62574i
$784$	4.09219e13	+	2.02009e13i	0.138158	+	0.0682010i
$785$	1.38428e14			0.464384
$786$	−1.60248e13	+	1.39174e14i	−0.0534172	+	0.463922i
$787$	2.36206e14			0.782380			0.391190	−	0.920310i	$-0.372064\pi$
$787$	2.36206e14			0.782380			0.391190	+	0.920310i	$0.372064\pi$
$788$	−1.22154e13	+	5.23412e13i	−0.0402045	+	0.172271i
$789$		−	1.49199e13i		−	0.0487955i
$790$	1.38081e13	−	1.19922e14i	0.0448743	−	0.389728i
$791$			4.30772e14i			1.39112i
$792$	8.25464e13	−	2.30482e14i	0.264894	−	0.739626i
$793$	4.98027e14			1.58813
$794$	3.05179e12	+	3.51392e11i	0.00967059	+	0.00111350i
$795$	3.57869e13			0.112691
$796$	−2.45025e13	+	1.04990e14i	−0.0766733	+	0.328535i
$797$		−	3.83919e14i		−	1.19384i	−0.802299	−	0.596922i	$-0.796390\pi$
$797$		−	3.83919e14i		−	1.19384i	0.802299	−	0.596922i	$-0.203610\pi$
$798$	1.07868e14	+	1.24203e13i	0.333334	+	0.0383810i
$799$		−	3.01611e14i		−	0.926217i
$800$	−1.61320e14	+	2.49924e14i	−0.492310	+	0.762708i
$801$	9.96949e13			0.302350
$802$	−2.29842e13	+	1.99615e14i	−0.0692721	+	0.601620i
$803$	3.08884e14			0.925163
$804$	−8.70499e12	−	2.03157e12i	−0.0259112	−	0.00604715i
$805$			1.32986e14i			0.393393i
$806$	−4.77769e13	+	4.14937e14i	−0.140457	+	1.21985i
$807$			2.51641e14i			0.735214i
$808$	−1.46119e14	−	5.23317e13i	−0.424276	−	0.151953i
$809$	−3.59859e14			−1.03846			−0.519229	−	0.854635i	$-0.673781\pi$
$809$	−3.59859e14			−1.03846			−0.519229	+	0.854635i	$0.673781\pi$
$810$	3.52570e13	+	4.05958e12i	0.101116	+	0.0116428i
$811$	9.53522e13			0.271786			0.135893	−	0.990724i	$-0.456610\pi$
$811$	9.53522e13			0.271786			0.135893	+	0.990724i	$0.456610\pi$
$812$	−5.95301e14	−	1.38931e14i	−1.68638	−	0.393567i
$813$		−	7.02171e13i		−	0.197692i
$814$	1.52477e13	+	1.75566e12i	0.0426660	+	0.00491267i
$815$			8.53697e13i			0.237419i
$816$	1.50228e14	+	7.41595e13i	0.415241	+	0.204982i
$817$	2.07686e14			0.570553
$818$	−5.37157e13	+	4.66515e14i	−0.146668	+	1.27379i
$819$	−2.41818e14			−0.656248
$820$	2.53817e13	−	1.08757e14i	0.0684624	−	0.293352i
$821$		−	1.35922e14i		−	0.364396i	−0.983262	−	0.182198i	$-0.941679\pi$
$821$		−	1.35922e14i		−	0.364396i	0.983262	−	0.182198i	$-0.0583212\pi$
$822$	−1.72467e12	+	1.49786e13i	−0.00459565	+	0.0399127i
$823$			3.60746e14i			0.955437i	0.878513	+	0.477718i	$0.158536\pi$
$823$			3.60746e14i			0.955437i	−0.878513	+	0.477718i	$0.841464\pi$
$824$	1.42548e14	+	5.10531e13i	0.375255	+	0.134396i
$825$	1.76268e14			0.461215
$826$	2.19515e14	+	2.52755e13i	0.570905	+	0.0657355i
$827$	−2.66016e14			−0.687671			−0.343836	−	0.939030i	$-0.611726\pi$
$827$	−2.66016e14			−0.687671			−0.343836	+	0.939030i	$0.611726\pi$
$828$	9.45699e13	−	4.05220e14i	0.242997	−	1.04121i
$829$			5.41661e14i			1.38342i	0.722174	+	0.691712i	$0.243143\pi$
$829$			5.41661e14i			1.38342i	−0.722174	+	0.691712i	$0.756857\pi$
$830$	−1.02375e14	−	1.17877e13i	−0.259897	−	0.0299253i
$831$		−	2.40649e13i		−	0.0607265i
$832$	2.37918e14	−	2.89548e14i	0.596775	−	0.726279i
$833$	−5.82970e13			−0.145352
$834$	3.42157e13	−	2.97159e14i	0.0847997	−	0.736476i
$835$	1.14932e14			0.283145
$836$	−3.05895e14	−	7.13896e13i	−0.749102	−	0.174825i
$837$		−	4.63345e14i		−	1.12792i
$838$	−4.26402e13	+	3.70325e14i	−0.103181	+	0.896113i
$839$		−	2.32397e14i		−	0.559012i	−0.960144	−	0.279506i	$-0.909829\pi$
$839$		−	2.32397e14i		−	0.559012i	0.960144	−	0.279506i	$-0.0901707\pi$
$840$	1.93311e13	−	5.39755e13i	0.0462232	−	0.129063i
$841$	−1.07069e15			−2.54498
$842$	−3.72311e12	−	4.28689e11i	−0.00879723	−	0.00101294i
$843$	−2.55842e13			−0.0600944
$844$	7.18871e14	+	1.67770e14i	1.67857	+	0.391743i
$845$		−	1.52240e13i		−	0.0353383i
$846$	3.20836e14	+	3.69419e13i	0.740340	+	0.0852447i
$847$		−	2.85747e13i		−	0.0655488i
$848$	1.46753e14	−	2.97285e14i	0.334663	−	0.677943i
$849$	−5.32707e13			−0.120767
$850$	4.34660e13	−	3.77497e14i	0.0979613	−	0.850783i
$851$	2.60871e13			0.0584492
$852$	−1.86040e13	+	7.97157e13i	−0.0414389	+	0.177560i
$853$		−	2.28671e14i		−	0.506367i	−0.967418	−	0.253183i	$-0.918522\pi$
$853$		−	2.28671e14i		−	0.506367i	0.967418	−	0.253183i	$-0.0814776\pi$
$854$	8.07393e13	−	7.01212e14i	0.177744	−	1.54369i
$855$		−	7.82677e13i		−	0.171298i
$856$	−1.08945e14	+	3.04193e14i	−0.237050	+	0.661881i
$857$	5.66367e14			1.22516			0.612582	−	0.790407i	$-0.290131\pi$
$857$	5.66367e14			1.22516			0.612582	+	0.790407i	$0.290131\pi$
$858$	−2.20610e14	−	2.54016e13i	−0.474448	−	0.0546291i
$859$	−6.49958e14			−1.38970			−0.694848	−	0.719157i	$-0.744528\pi$
$859$	−6.49958e14			−1.38970			−0.694848	+	0.719157i	$0.744528\pi$
$860$	2.49230e13	−	1.06792e14i	0.0529796	−	0.227011i
$861$		−	2.11923e14i		−	0.447881i
$862$	4.96905e14	+	5.72149e13i	1.04409	+	0.120219i
$863$		−	3.72753e14i		−	0.778695i	−0.921091	−	0.389348i	$-0.872700\pi$
$863$		−	3.72753e14i		−	0.778695i	0.921091	−	0.389348i	$-0.127300\pi$
$864$	−2.25456e14	+	3.49287e14i	−0.468268	+	0.725460i
$865$	−1.92333e13			−0.0397167
$866$	−9.84846e12	+	8.55327e13i	−0.0202199	+	0.175607i
$867$	2.64563e13			0.0540050
$868$	5.76477e14	+	1.34538e14i	1.16999	+	0.273052i
$869$			6.62667e14i			1.33720i
$870$	1.60000e13	−	1.38958e14i	0.0321013	−	0.278796i
$871$		−	2.55425e13i		−	0.0509533i
$872$	−1.87900e14	−	6.72956e13i	−0.372687	−	0.133476i
$873$	−4.89285e14			−0.964918
$874$	−5.30385e14	−	6.10700e13i	−1.04000	−	0.119749i
$875$	−2.73283e14			−0.532811
$876$	−2.20414e14	−	5.14400e13i	−0.427286	−	0.0997196i
$877$			7.44427e14i			1.43491i	0.696606	+	0.717454i	$0.254693\pi$
$877$			7.44427e14i			1.43491i	−0.696606	+	0.717454i	$0.745307\pi$
$878$	−4.90010e13	−	5.64210e12i	−0.0939144	−	0.0108136i
$879$			8.30214e13i			0.158214i
$880$	−7.34171e13	+	1.48724e14i	−0.139118	+	0.281818i
$881$	4.26107e14			0.802859			0.401429	−	0.915890i	$-0.368514\pi$
$881$	4.26107e14			0.802859			0.401429	+	0.915890i	$0.368514\pi$
$882$	7.14034e12	−	6.20130e13i	0.0133775	−	0.116182i
$883$	2.78444e14			0.518721			0.259361	−	0.965781i	$-0.416488\pi$
$883$	2.78444e14			0.518721			0.259361	+	0.965781i	$0.416488\pi$
$884$	−1.08801e14	+	4.66196e14i	−0.201544	+	0.863589i
$885$			5.05609e13i			0.0931319i
$886$	5.48483e13	−	4.76351e14i	0.100460	−	0.872486i
$887$		−	1.26454e14i		−	0.230311i	−0.993347	−	0.115155i	$-0.963263\pi$
$887$		−	1.26454e14i		−	0.230311i	0.993347	−	0.115155i	$-0.0367366\pi$
$888$	−1.05881e13	−	3.79207e12i	−0.0191757	−	0.00686771i
$889$	5.29374e14			0.953352
$890$	−6.70975e13	−	7.72578e12i	−0.120159	−	0.0138354i
$891$	−1.94824e14			−0.346940
$892$	−1.86059e14	+	7.97240e14i	−0.329479	+	1.41177i
$893$		−	4.14370e14i		−	0.729677i
$894$	1.89588e14	+	2.18297e13i	0.331989	+	0.0382260i
$895$			1.60307e14i			0.279150i
$896$	−3.69106e14	−	3.81925e14i	−0.639163	−	0.661360i
$897$	−3.77440e14			−0.649958
$898$	−4.92642e12	+	4.27854e13i	−0.00843625	+	0.0732679i
$899$	1.44424e15			2.45946
$900$	3.96236e14	+	9.24732e13i	0.671028	+	0.156604i
$901$			4.23509e14i			0.713245i
$902$	−7.01276e13	+	6.09050e14i	−0.117451	+	1.02005i
$903$		−	2.08093e14i		−	0.346593i
$904$	−3.07890e14	+	8.59677e14i	−0.509980	+	1.42394i
$905$	−1.68340e14			−0.277296
$906$	−4.94101e14	−	5.68920e13i	−0.809421	−	0.0931989i
$907$	−3.18754e14			−0.519301			−0.259650	−	0.965703i	$-0.583607\pi$
$907$	−3.18754e14			−0.519301			−0.259650	+	0.965703i	$0.583607\pi$
$908$	5.93115e14	+	1.38421e14i	0.960969	+	0.224270i
$909$			2.12297e14i			0.342077i
$910$	1.62750e14	+	1.87395e13i	0.260804	+	0.0300296i
$911$		−	4.42124e14i		−	0.704616i	−0.935884	−	0.352308i	$-0.885397\pi$
$911$		−	4.42124e14i		−	0.704616i	0.935884	−	0.352308i	$-0.114603\pi$
$912$	2.06392e14	+	1.01884e14i	0.327129	+	0.161486i
$913$	5.65705e14			0.891736
$914$	6.00400e13	−	5.21440e14i	0.0941260	−	0.817473i
$915$	1.61510e14			0.251822
$916$	2.72061e14	−	1.16575e15i	0.421880	−	1.80770i
$917$			5.67351e14i			0.874994i
$918$	6.07467e13	−	5.27578e14i	0.0931772	−	0.809233i
$919$		−	8.59042e14i		−	1.31050i	−0.755412	−	0.655250i	$-0.772563\pi$
$919$		−	8.59042e14i		−	1.31050i	0.755412	−	0.655250i	$-0.227437\pi$
$920$	−9.50504e13	+	2.65396e14i	−0.144216	+	0.402675i
$921$	5.49593e14			0.829360
$922$	−6.95289e13	−	8.00574e12i	−0.104354	−	0.0120156i
$923$	−2.33904e14			−0.349164
$924$	−7.15298e13	+	3.06496e14i	−0.106201	+	0.455056i
$925$			2.55088e13i			0.0376687i
$926$	−8.56561e14	−	9.86267e13i	−1.25807	−	0.144857i
$927$		−	2.07109e14i		−	0.302553i
$928$	−1.08872e15	−	7.02744e14i	−1.58189	−	1.02107i
$929$	3.15994e14			0.456667			0.228334	−	0.973583i	$-0.426672\pi$
$929$	3.15994e14			0.456667			0.228334	+	0.973583i	$0.426672\pi$
$930$	−1.54941e13	+	1.34564e14i	−0.0222715	+	0.193426i
$931$	−8.00917e13			−0.114509
$932$	−1.91233e14	−	4.46299e13i	−0.271947	−	0.0634667i
$933$		−	8.53922e13i		−	0.120784i
$934$	−6.06448e13	+	5.26693e14i	−0.0853216	+	0.741008i
$935$		−	2.11871e14i		−	0.296493i
$936$	−4.82587e14	−	1.72836e14i	−0.671732	−	0.240578i
$937$	−7.43539e14			−1.02945			−0.514725	−	0.857355i	$-0.672106\pi$
$937$	−7.43539e14			−1.02945			−0.514725	+	0.857355i	$0.672106\pi$
$938$	−3.59633e13	−	4.14090e12i	−0.0495273	−	0.00570270i
$939$	−3.70960e14			−0.508158
$940$	−2.13069e14	−	4.97259e13i	−0.290323	−	0.0677553i
$941$		−	1.14117e15i		−	1.54669i	−0.633987	−	0.773344i	$-0.718583\pi$
$941$		−	1.14117e15i		−	1.54669i	0.633987	−	0.773344i	$-0.281417\pi$
$942$	5.53175e14	+	6.36940e13i	0.745775	+	0.0858704i
$943$			1.04202e15i			1.39739i
$944$	4.20013e14	+	2.07337e14i	0.560276	+	0.276578i
$945$	−1.81737e14			−0.241148
$946$	−6.88603e13	+	5.98043e14i	−0.0908894	+	0.789363i
$947$	−1.75638e14			−0.230605			−0.115303	−	0.993330i	$-0.536784\pi$
$947$	−1.75638e14			−0.230605			−0.115303	+	0.993330i	$0.536784\pi$
$948$	1.10357e14	−	4.72866e14i	0.144131	−	0.617585i
$949$		−	6.46745e14i		−	0.840238i
$950$	5.97160e13	−	5.18626e14i	0.0771743	−	0.670249i
$951$			3.00259e14i			0.386006i
$952$	6.38756e14	+	2.28768e14i	0.816865	+	0.292557i
$953$	3.39856e14			0.432345			0.216173	−	0.976355i	$-0.430643\pi$
$953$	3.39856e14			0.432345			0.216173	+	0.976355i	$0.430643\pi$
$954$	−4.50505e14	−	5.18723e13i	−0.570108	−	0.0656438i
$955$	1.54575e14			0.194591
$956$	1.59210e13	−	6.82196e13i	0.0199380	−	0.0854318i
$957$			7.67858e14i			0.956580i
$958$	1.20032e15	+	1.38208e14i	1.48754	+	0.171279i
$959$			6.10611e13i			0.0752786i
$960$	7.71568e13	−	9.39003e13i	0.0946277	−	0.115162i
$961$	−5.78942e14			−0.706347
$962$	3.67601e12	−	3.19258e13i	0.00446172	−	0.0387495i
$963$	4.41964e14			0.533649
$964$	−2.96152e14	−	6.91158e13i	−0.355738	−	0.0830218i
$965$		−	1.71488e14i		−	0.204926i
$966$	−6.11899e13	+	5.31427e14i	−0.0727435	+	0.631769i
$967$			1.00951e15i			1.19392i	0.802270	+	0.596961i	$0.203625\pi$
$967$			1.00951e15i			1.19392i	−0.802270	+	0.596961i	$0.796375\pi$
$968$	2.04235e13	−	5.70255e13i	0.0240299	−	0.0670954i
$969$	−2.94024e14			−0.344163
$970$	3.29302e14	+	3.79167e13i	0.383474	+	0.0441542i
$971$	−5.94588e14			−0.688843			−0.344422	−	0.938815i	$-0.611925\pi$
$971$	−5.94588e14			−0.688843			−0.344422	+	0.938815i	$0.611925\pi$
$972$	8.68578e14	+	2.02708e14i	1.00110	+	0.233636i
$973$		−	1.21139e15i		−	1.38905i
$974$	−5.31966e14	−	6.12520e13i	−0.606861	−	0.0698756i
$975$		−	3.69071e14i		−	0.418878i
$976$	6.62312e14	−	1.34168e15i	0.747848	−	1.51495i
$977$	−5.12453e14			−0.575680			−0.287840	−	0.957678i	$-0.592937\pi$
$977$	−5.12453e14			−0.575680			−0.287840	+	0.957678i	$0.592937\pi$
$978$	−3.92805e13	+	3.41146e14i	−0.0439018	+	0.381282i
$979$	3.70769e14			0.412278
$980$	−9.61130e12	+	4.11832e13i	−0.0106329	+	0.0455606i
$981$			2.73001e14i			0.300482i
$982$	3.28063e12	−	2.84919e13i	0.00359252	−	0.0312007i
$983$			1.49515e15i			1.62899i	0.580171	+	0.814495i	$0.302986\pi$
$983$			1.49515e15i			1.62899i	−0.580171	+	0.814495i	$0.697014\pi$
$984$	1.51470e14	−	4.22927e14i	0.164191	−	0.458448i
$985$	−4.98064e13			−0.0537160
$986$	1.64445e15	+	1.89347e14i	1.76456	+	0.203176i
$987$	−4.15183e14			−0.443256
$988$	−1.49476e14	+	6.40486e14i	−0.158777	+	0.680339i
$989$			1.02319e15i			1.08137i
$990$	2.25377e14	+	2.59505e13i	0.236992	+	0.0272878i
$991$			5.29183e14i			0.553653i	0.960920	+	0.276827i	$0.0892827\pi$
$991$			5.29183e14i			0.553653i	−0.960920	+	0.276827i	$0.910717\pi$
$992$	1.05430e15	+	6.80523e14i	1.09750	+	0.708410i
$993$	−3.84767e14			−0.398522
$994$	−3.79202e13	+	3.29332e14i	−0.0390785	+	0.339393i
$995$	−9.99053e13			−0.102441
$996$	−4.03676e14	−	9.42097e13i	−0.411848	−	0.0961167i
$997$		−	1.34451e15i		−	1.36486i	−0.730953	−	0.682428i	$-0.760924\pi$
$997$		−	1.34451e15i		−	1.36486i	0.730953	−	0.682428i	$-0.239076\pi$
$998$	−1.08019e14	+	9.38130e14i	−0.109105	+	0.947568i
$999$			3.56503e13i			0.0358291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.11.d.b.3.4	yes	8
3.2	odd	2		72.11.b.b.19.5		8
4.3	odd	2		32.11.d.b.15.5		8
8.3	odd	2	inner	8.11.d.b.3.3	✓	8
8.5	even	2		32.11.d.b.15.6		8
12.11	even	2		288.11.b.b.271.5		8
16.3	odd	4		256.11.c.m.255.9		16
16.5	even	4		256.11.c.m.255.10		16
16.11	odd	4		256.11.c.m.255.8		16
16.13	even	4		256.11.c.m.255.7		16
24.5	odd	2		288.11.b.b.271.4		8
24.11	even	2		72.11.b.b.19.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.11.d.b.3.3	✓	8	8.3	odd	2	inner
8.11.d.b.3.4	yes	8	1.1	even	1	trivial
32.11.d.b.15.5		8	4.3	odd	2
32.11.d.b.15.6		8	8.5	even	2
72.11.b.b.19.5		8	3.2	odd	2
72.11.b.b.19.6		8	24.11	even	2
256.11.c.m.255.7		16	16.13	even	4
256.11.c.m.255.8		16	16.11	odd	4
256.11.c.m.255.9		16	16.3	odd	4
256.11.c.m.255.10		16	16.5	even	4
288.11.b.b.271.4		8	24.5	odd	2
288.11.b.b.271.5		8	12.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.66038 + 31.7900i) q^{2} -119.281 q^{3} +(-997.203 - 232.727i) q^{4} -948.910i q^{5} +(436.614 - 3791.94i) q^{6} -15458.1i q^{7} +(11048.5 - 30849.2i) q^{8} -44821.0 q^{9} +O(q^{10})\)	\(q+(-3.66038 + 31.7900i) q^{2} -119.281 q^{3} +(-997.203 - 232.727i) q^{4} -948.910i q^{5} +(436.614 - 3791.94i) q^{6} -15458.1i q^{7} +(11048.5 - 30849.2i) q^{8} -44821.0 q^{9} +(30165.8 + 3473.37i) q^{10} -166691. q^{11} +(118948. + 27759.9i) q^{12} +349020. i q^{13} +(491413. + 56582.5i) q^{14} +113187. i q^{15} +(940253. + 464151. i) q^{16} -1.33948e6 q^{17} +(164062. - 1.42486e6i) q^{18} -1.84025e6 q^{19} +(-220837. + 946256. i) q^{20} +1.84386e6i q^{21} +(610153. - 5.29911e6i) q^{22} -9.06620e6i q^{23} +(-1.31788e6 + 3.67973e6i) q^{24} +8.86520e6 q^{25} +(-1.10953e7 - 1.27754e6i) q^{26} +1.23897e7 q^{27} +(-3.59751e6 + 1.54149e7i) q^{28} +3.86186e7i q^{29} +(-3.59821e6 - 414308. i) q^{30} -3.73975e7i q^{31} +(-1.81970e7 + 2.81916e7i) q^{32} +1.98831e7 q^{33} +(4.90299e6 - 4.25819e7i) q^{34} -1.46683e7 q^{35} +(4.46956e7 + 1.04310e7i) q^{36} +2.87741e6i q^{37} +(6.73600e6 - 5.85014e7i) q^{38} -4.16315e7i q^{39} +(-2.92731e7 - 1.04840e7i) q^{40} -1.14934e8 q^{41} +(-5.86163e7 - 6.74923e6i) q^{42} -1.12857e8 q^{43} +(1.66225e8 + 3.87935e7i) q^{44} +4.25311e7i q^{45} +(2.88214e8 + 3.31857e7i) q^{46} +2.25171e8i q^{47} +(-1.12154e8 - 5.53645e7i) q^{48} +4.35223e7 q^{49} +(-3.24500e7 + 2.81824e8i) q^{50} +1.59774e8 q^{51} +(8.12262e7 - 3.48044e8i) q^{52} -3.16175e8i q^{53} +(-4.53511e7 + 3.93869e8i) q^{54} +1.58175e8i q^{55} +(-4.76870e8 - 1.70789e8i) q^{56} +2.19507e8 q^{57} +(-1.22768e9 - 1.41359e8i) q^{58} +4.46702e8 q^{59} +(2.63416e7 - 1.12871e8i) q^{60} -1.42693e9i q^{61} +(1.18886e9 + 1.36889e8i) q^{62} +6.92848e8i q^{63} +(-8.29603e8 - 6.81675e8i) q^{64} +3.31188e8 q^{65} +(-7.27798e7 + 6.32084e8i) q^{66} -7.31834e7 q^{67} +(1.33573e9 + 3.11732e8i) q^{68} +1.08143e9i q^{69} +(5.36917e7 - 4.66306e8i) q^{70} +6.70175e8i q^{71} +(-4.95205e8 + 1.38269e9i) q^{72} -1.85303e9 q^{73} +(-9.14726e7 - 1.05324e7i) q^{74} -1.05745e9 q^{75} +(1.83510e9 + 4.28274e8i) q^{76} +2.57673e9i q^{77} +(1.32346e9 + 1.52387e8i) q^{78} -3.97541e9i q^{79} +(4.40438e8 - 8.92215e8i) q^{80} +1.16877e9 q^{81} +(4.20704e8 - 3.65376e9i) q^{82} -3.39373e9 q^{83} +(4.29116e8 - 1.83870e9i) q^{84} +1.27104e9i q^{85} +(4.13101e8 - 3.58773e9i) q^{86} -4.60647e9i q^{87} +(-1.84169e9 + 5.14229e9i) q^{88} -2.22429e9 q^{89} +(-1.35206e9 - 1.55680e8i) q^{90} +5.39518e9 q^{91} +(-2.10995e9 + 9.04085e9i) q^{92} +4.46081e9i q^{93} +(-7.15816e9 - 8.24210e8i) q^{94} +1.74623e9i q^{95} +(2.17056e9 - 3.36273e9i) q^{96} +1.09164e10 q^{97} +(-1.59308e8 + 1.38357e9i) q^{98} +7.47127e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9}+O(q^{10}) \) 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9	\( 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9} + 9120 q^{10} + 143328 q^{11} + 180120 q^{12} - 400320 q^{14} - 1987312 q^{16} - 370800 q^{17} + 3067758 q^{18} + 1753312 q^{19} + 2557440 q^{20} + 1549180 q^{22} - 19794288 q^{24} - 18792760 q^{25} + 1891680 q^{26} + 28949184 q^{27} + 18286080 q^{28} + 67026240 q^{30} - 64016928 q^{32} - 74308704 q^{33} - 115705388 q^{34} + 53736960 q^{35} + 50631516 q^{36} + 375128220 q^{38} - 357584640 q^{40} + 92669328 q^{41} - 576155520 q^{42} - 10190624 q^{43} + 727831512 q^{44} + 851947200 q^{46} - 1142760480 q^{48} - 80432248 q^{49} - 1669361190 q^{50} - 276714816 q^{51} + 2420759040 q^{52} + 1749768696 q^{54} - 2928529920 q^{56} + 1400712864 q^{57} - 3245264160 q^{58} - 965642016 q^{59} + 5250055680 q^{60} + 4060980480 q^{62} - 5804705728 q^{64} - 839028480 q^{65} - 5970262296 q^{66} - 1225582880 q^{67} + 5258111400 q^{68} + 7723829760 q^{70} - 4343608728 q^{72} + 2800072720 q^{73} - 7669373280 q^{74} + 4485554400 q^{75} + 3753451288 q^{76} + 7176312000 q^{78} - 6408629760 q^{80} - 11909065176 q^{81} - 3638778380 q^{82} + 1853422560 q^{83} - 2916218880 q^{84} + 3022180476 q^{86} + 5815578640 q^{88} + 6162596112 q^{89} + 12545940960 q^{90} + 7645985280 q^{91} - 8903892480 q^{92} - 14182177920 q^{94} + 7877525568 q^{96} - 9697863536 q^{97} + 34759868298 q^{98} - 13646747232 q^{99}+O(q^{100}) \) 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9 + 9120 * q^10 + 143328 * q^11 + 180120 * q^12 - 400320 * q^14 - 1987312 * q^16 - 370800 * q^17 + 3067758 * q^18 + 1753312 * q^19 + 2557440 * q^20 + 1549180 * q^22 - 19794288 * q^24 - 18792760 * q^25 + 1891680 * q^26 + 28949184 * q^27 + 18286080 * q^28 + 67026240 * q^30 - 64016928 * q^32 - 74308704 * q^33 - 115705388 * q^34 + 53736960 * q^35 + 50631516 * q^36 + 375128220 * q^38 - 357584640 * q^40 + 92669328 * q^41 - 576155520 * q^42 - 10190624 * q^43 + 727831512 * q^44 + 851947200 * q^46 - 1142760480 * q^48 - 80432248 * q^49 - 1669361190 * q^50 - 276714816 * q^51 + 2420759040 * q^52 + 1749768696 * q^54 - 2928529920 * q^56 + 1400712864 * q^57 - 3245264160 * q^58 - 965642016 * q^59 + 5250055680 * q^60 + 4060980480 * q^62 - 5804705728 * q^64 - 839028480 * q^65 - 5970262296 * q^66 - 1225582880 * q^67 + 5258111400 * q^68 + 7723829760 * q^70 - 4343608728 * q^72 + 2800072720 * q^73 - 7669373280 * q^74 + 4485554400 * q^75 + 3753451288 * q^76 + 7176312000 * q^78 - 6408629760 * q^80 - 11909065176 * q^81 - 3638778380 * q^82 + 1853422560 * q^83 - 2916218880 * q^84 + 3022180476 * q^86 + 5815578640 * q^88 + 6162596112 * q^89 + 12545940960 * q^90 + 7645985280 * q^91 - 8903892480 * q^92 - 14182177920 * q^94 + 7877525568 * q^96 - 9697863536 * q^97 + 34759868298 * q^98 - 13646747232 * q^99

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