LMFDB - Embedded newform 8.11.d.b.3.1

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			3.1
Root			$16.5295 + 8.54130i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.11.d.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-27.0589 - 17.0826i) q^{2} +203.867 q^{3} +(440.370 + 924.473i) q^{4} -2088.87i q^{5} +(-5516.42 - 3482.58i) q^{6} -25367.2i q^{7} +(3876.45 - 32537.9i) q^{8} -17487.2 q^{9} +O(q^{10})$	\(q+(-27.0589 - 17.0826i) q^{2} +203.867 q^{3} +(440.370 + 924.473i) q^{4} -2088.87i q^{5} +(-5516.42 - 3482.58i) q^{6} -25367.2i q^{7} +(3876.45 - 32537.9i) q^{8} -17487.2 q^{9} +(-35683.3 + 56522.5i) q^{10} +132418. q^{11} +(89777.0 + 188470. i) q^{12} -304071. i q^{13} +(-433337. + 686408. i) q^{14} -425852. i q^{15} +(-660724. + 814221. i) q^{16} +1.87886e6 q^{17} +(473185. + 298727. i) q^{18} -2.20249e6 q^{19} +(1.93110e6 - 919876. i) q^{20} -5.17153e6i q^{21} +(-3.58309e6 - 2.26204e6i) q^{22} +4.83836e6i q^{23} +(790281. - 6.63341e6i) q^{24} +5.40225e6 q^{25} +(-5.19431e6 + 8.22782e6i) q^{26} -1.56032e7 q^{27} +(2.34513e7 - 1.11709e7i) q^{28} +2.08912e7i q^{29} +(-7.27465e6 + 1.15231e7i) q^{30} +4.27897e7i q^{31} +(3.17875e7 - 1.07450e7i) q^{32} +2.69957e7 q^{33} +(-5.08398e7 - 3.20957e7i) q^{34} -5.29887e7 q^{35} +(-7.70084e6 - 1.61664e7i) q^{36} -1.24227e8i q^{37} +(5.95970e7 + 3.76242e7i) q^{38} -6.19900e7i q^{39} +(-6.79674e7 - 8.09740e6i) q^{40} +1.24377e8 q^{41} +(-8.83432e7 + 1.39936e8i) q^{42} +3.15891e7 q^{43} +(5.83129e7 + 1.22417e8i) q^{44} +3.65285e7i q^{45} +(8.26517e7 - 1.30921e8i) q^{46} -2.91858e7i q^{47} +(-1.34700e8 + 1.65993e8i) q^{48} -3.61018e8 q^{49} +(-1.46179e8 - 9.22844e7i) q^{50} +3.83037e8 q^{51} +(2.81105e8 - 1.33904e8i) q^{52} +5.07012e8i q^{53} +(4.22206e8 + 2.66543e8i) q^{54} -2.76604e8i q^{55} +(-8.25395e8 - 9.83346e7i) q^{56} -4.49015e8 q^{57} +(3.56876e8 - 5.65293e8i) q^{58} +1.64080e8 q^{59} +(3.93688e8 - 1.87532e8i) q^{60} -3.21644e7i q^{61} +(7.30959e8 - 1.15784e9i) q^{62} +4.43601e8i q^{63} +(-1.04369e9 - 2.52263e8i) q^{64} -6.35164e8 q^{65} +(-7.30473e8 - 4.61156e8i) q^{66} -3.70351e8 q^{67} +(8.27392e8 + 1.73695e9i) q^{68} +9.86382e8i q^{69} +(1.43382e9 + 9.05184e8i) q^{70} -3.20647e8i q^{71} +(-6.77883e7 + 5.68997e8i) q^{72} +2.69897e9 q^{73} +(-2.12211e9 + 3.36144e9i) q^{74} +1.10134e9 q^{75} +(-9.69910e8 - 2.03614e9i) q^{76} -3.35907e9i q^{77} +(-1.05895e9 + 1.67738e9i) q^{78} -1.89446e9i q^{79} +(1.70080e9 + 1.38017e9i) q^{80} -2.14838e9 q^{81} +(-3.36551e9 - 2.12468e9i) q^{82} -2.20629e9 q^{83} +(4.78094e9 - 2.27739e9i) q^{84} -3.92468e9i q^{85} +(-8.54767e8 - 5.39624e8i) q^{86} +4.25903e9i q^{87} +(5.13312e8 - 4.30860e9i) q^{88} +9.12704e9 q^{89} +(6.24001e8 - 9.88421e8i) q^{90} -7.71341e9 q^{91} +(-4.47293e9 + 2.13067e9i) q^{92} +8.72341e9i q^{93} +(-4.98569e8 + 7.89736e8i) q^{94} +4.60071e9i q^{95} +(6.48042e9 - 2.19056e9i) q^{96} -1.89466e9 q^{97} +(9.76876e9 + 6.16713e9i) q^{98} -2.31562e9 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 $

$2$	−27.0589	−	17.0826i	−0.845591	−	0.533831i
$2$	−27.0589	−	17.0826i	−0.845591	−	0.533831i
$3$	203.867			0.838959			0.419480	−	0.907765i	$-0.362213\pi$
$3$	203.867			0.838959			0.419480	+	0.907765i	$0.362213\pi$
$4$	440.370	+	924.473i	0.430049	+	0.902806i
$5$		−	2088.87i		−	0.668438i	−0.942495	−	0.334219i	$-0.891527\pi$
$5$		−	2088.87i		−	0.668438i	0.942495	−	0.334219i	$-0.108473\pi$
$6$	−5516.42	−	3482.58i	−0.709417	−	0.447862i
$7$		−	25367.2i		−	1.50932i	−0.656115	−	0.754661i	$-0.727801\pi$
$7$		−	25367.2i		−	1.50932i	0.656115	−	0.754661i	$-0.272199\pi$
$8$	3876.45	−	32537.9i	0.118300	−	0.992978i
$9$	−17487.2			−0.296147
$10$	−35683.3	+	56522.5i	−0.356833	+	0.565225i
$11$	132418.			0.822211			0.411106	−	0.911588i	$-0.365143\pi$
$11$	132418.			0.822211			0.411106	+	0.911588i	$0.365143\pi$
$12$	89777.0	+	188470.i	0.360794	+	0.757417i
$13$		−	304071.i		−	0.818951i	−0.912321	−	0.409475i	$-0.865712\pi$
$13$		−	304071.i		−	0.818951i	0.912321	−	0.409475i	$-0.134288\pi$
$14$	−433337.	+	686408.i	−0.805723	+	1.27627i
$15$		−	425852.i		−	0.560792i
$16$	−660724.	+	814221.i	−0.630116	+	0.776501i
$17$	1.87886e6			1.32327			0.661635	−	0.749826i	$-0.269863\pi$
$17$	1.87886e6			1.32327			0.661635	+	0.749826i	$0.269863\pi$
$18$	473185.	+	298727.i	0.250420	+	0.158093i
$19$	−2.20249e6			−0.889499			−0.444750	−	0.895655i	$-0.646707\pi$
$19$	−2.20249e6			−0.889499			−0.444750	+	0.895655i	$0.646707\pi$
$20$	1.93110e6	−	919876.i	0.603470	−	0.287461i
$21$		−	5.17153e6i		−	1.26626i
$22$	−3.58309e6	−	2.26204e6i	−0.695255	−	0.438922i
$23$			4.83836e6i			0.751724i	0.926676	+	0.375862i	$0.122653\pi$
$23$			4.83836e6i			0.751724i	−0.926676	+	0.375862i	$0.877347\pi$
$24$	790281.	−	6.63341e6i	0.0992488	−	0.833068i
$25$	5.40225e6			0.553190
$26$	−5.19431e6	+	8.22782e6i	−0.437181	+	0.692497i
$27$	−1.56032e7			−1.08741
$28$	2.34513e7	−	1.11709e7i	1.36262	−	0.649082i
$29$			2.08912e7i			1.01853i	0.860610	+	0.509265i	$0.170083\pi$
$29$			2.08912e7i			1.01853i	−0.860610	+	0.509265i	$0.829917\pi$
$30$	−7.27465e6	+	1.15231e7i	−0.299368	+	0.474201i
$31$			4.27897e7i			1.49462i	0.664476	+	0.747310i	$0.268655\pi$
$31$			4.27897e7i			1.49462i	−0.664476	+	0.747310i	$0.731345\pi$
$32$	3.17875e7	−	1.07450e7i	0.947341	−	0.320227i
$33$	2.69957e7			0.689802
$34$	−5.08398e7	−	3.20957e7i	−1.11895	−	0.706403i
$35$	−5.29887e7			−1.00889
$36$	−7.70084e6	−	1.61664e7i	−0.127358	−	0.267363i
$37$		−	1.24227e8i		−	1.79146i	−0.444602	−	0.895728i	$-0.646655\pi$
$37$		−	1.24227e8i		−	1.79146i	0.444602	−	0.895728i	$-0.353345\pi$
$38$	5.95970e7	+	3.76242e7i	0.752153	+	0.474842i
$39$		−	6.19900e7i		−	0.687066i
$40$	−6.79674e7	−	8.09740e6i	−0.663744	−	0.0790761i
$41$	1.24377e8			1.07355			0.536773	−	0.843727i	$-0.319643\pi$
$41$	1.24377e8			1.07355			0.536773	+	0.843727i	$0.319643\pi$
$42$	−8.83432e7	+	1.39936e8i	−0.675969	+	1.07074i
$43$	3.15891e7			0.214880			0.107440	−	0.994212i	$-0.465735\pi$
$43$	3.15891e7			0.214880			0.107440	+	0.994212i	$0.465735\pi$
$44$	5.83129e7	+	1.22417e8i	0.353591	+	0.742297i
$45$			3.65285e7i			0.197956i
$46$	8.26517e7	−	1.30921e8i	0.401294	−	0.635652i
$47$		−	2.91858e7i		−	0.127257i	−0.997974	−	0.0636286i	$-0.979733\pi$
$47$		−	2.91858e7i		−	0.127257i	0.997974	−	0.0636286i	$-0.0202673\pi$
$48$	−1.34700e8	+	1.65993e8i	−0.528641	+	0.651453i
$49$	−3.61018e8			−1.27805
$50$	−1.46179e8	−	9.22844e7i	−0.467773	−	0.295310i
$51$	3.83037e8			1.11017
$52$	2.81105e8	−	1.33904e8i	0.739353	−	0.352189i
$53$			5.07012e8i			1.21238i	0.795320	+	0.606190i	$0.207303\pi$
$53$			5.07012e8i			1.21238i	−0.795320	+	0.606190i	$0.792697\pi$
$54$	4.22206e8	+	2.66543e8i	0.919508	+	0.580496i
$55$		−	2.76604e8i		−	0.549597i
$56$	−8.25395e8	−	9.83346e7i	−1.49872	−	0.178553i
$57$	−4.49015e8			−0.746254
$58$	3.56876e8	−	5.65293e8i	0.543722	−	0.861259i
$59$	1.64080e8			0.229506			0.114753	−	0.993394i	$-0.463392\pi$
$59$	1.64080e8			0.229506			0.114753	+	0.993394i	$0.463392\pi$
$60$	3.93688e8	−	1.87532e8i	0.506287	−	0.241168i
$61$		−	3.21644e7i		−	0.0380826i	−0.999819	−	0.0190413i	$-0.993939\pi$
$61$		−	3.21644e7i		−	0.0380826i	0.999819	−	0.0190413i	$-0.00606140\pi$
$62$	7.30959e8	−	1.15784e9i	0.797874	−	1.26384i
$63$			4.43601e8i			0.446982i
$64$	−1.04369e9	−	2.52263e8i	−0.972010	−	0.234938i
$65$	−6.35164e8			−0.547418
$66$	−7.30473e8	−	4.61156e8i	−0.583290	−	0.368238i
$67$	−3.70351e8			−0.274309			−0.137154	−	0.990550i	$-0.543796\pi$
$67$	−3.70351e8			−0.274309			−0.137154	+	0.990550i	$0.543796\pi$
$68$	8.27392e8	+	1.73695e9i	0.569071	+	1.19466i
$69$			9.86382e8i			0.630666i
$70$	1.43382e9	+	9.05184e8i	0.853107	+	0.538576i
$71$		−	3.20647e8i		−	0.177719i	−0.996044	−	0.0888597i	$-0.971678\pi$
$71$		−	3.20647e8i		−	0.177719i	0.996044	−	0.0888597i	$-0.0283223\pi$
$72$	−6.77883e7	+	5.68997e8i	−0.0350342	+	0.294068i
$73$	2.69897e9			1.30192			0.650959	−	0.759113i	$-0.274367\pi$
$73$	2.69897e9			1.30192			0.650959	+	0.759113i	$0.274367\pi$
$74$	−2.12211e9	+	3.36144e9i	−0.956335	+	1.51484i
$75$	1.10134e9			0.464104
$76$	−9.69910e8	−	2.03614e9i	−0.382528	−	0.803045i
$77$		−	3.35907e9i		−	1.24098i
$78$	−1.05895e9	+	1.67738e9i	−0.366777	+	0.580977i
$79$		−	1.89446e9i		−	0.615673i	−0.951439	−	0.307837i	$-0.900395\pi$
$79$		−	1.89446e9i		−	0.615673i	0.951439	−	0.307837i	$-0.0996050\pi$
$80$	1.70080e9	+	1.38017e9i	0.519043	+	0.421193i
$81$	−2.14838e9			−0.616150
$82$	−3.36551e9	−	2.12468e9i	−0.907781	−	0.573092i
$83$	−2.20629e9			−0.560108			−0.280054	−	0.959984i	$-0.590352\pi$
$83$	−2.20629e9			−0.560108			−0.280054	+	0.959984i	$0.590352\pi$
$84$	4.78094e9	−	2.27739e9i	1.14319	−	0.544554i
$85$		−	3.92468e9i		−	0.884525i
$86$	−8.54767e8	−	5.39624e8i	−0.181700	−	0.114709i
$87$			4.25903e9i			0.854504i
$88$	5.13312e8	−	4.30860e9i	0.0972675	−	0.816438i
$89$	9.12704e9			1.63448			0.817241	−	0.576296i	$-0.195503\pi$
$89$	9.12704e9			1.63448			0.817241	+	0.576296i	$0.195503\pi$
$90$	6.24001e8	−	9.88421e8i	0.105675	−	0.167390i
$91$	−7.71341e9			−1.23606
$92$	−4.47293e9	+	2.13067e9i	−0.678661	+	0.323278i
$93$			8.72341e9i			1.25392i
$94$	−4.98569e8	+	7.89736e8i	−0.0679338	+	0.107608i
$95$			4.60071e9i			0.594575i
$96$	6.48042e9	−	2.19056e9i	0.794780	−	0.268658i
$97$	−1.89466e9			−0.220634			−0.110317	−	0.993896i	$-0.535187\pi$
$97$	−1.89466e9			−0.220634			−0.110317	+	0.993896i	$0.535187\pi$
$98$	9.76876e9	+	6.16713e9i	1.08071	+	0.682264i
$99$	−2.31562e9			−0.243496
$100$	2.37899e9	+	4.99423e9i	0.237899	+	0.499423i
$101$		−	5.17098e9i		−	0.492001i	−0.969270	−	0.246000i	$-0.920884\pi$
$101$		−	5.17098e9i		−	0.492001i	0.969270	−	0.246000i	$-0.0791165\pi$
$102$	−1.03646e10	−	6.54326e9i	−0.938750	−	0.592643i
$103$			9.68439e9i			0.835384i	0.908589	+	0.417692i	$0.137161\pi$
$103$			9.68439e9i			0.835384i	−0.908589	+	0.417692i	$0.862839\pi$
$104$	−9.89382e9	−	1.17871e9i	−0.813200	−	0.0968817i
$105$	−1.08027e10			−0.846416
$106$	8.66107e9	−	1.37192e10i	0.647206	−	1.02518i
$107$	1.63929e10			1.16879			0.584394	−	0.811470i	$-0.301332\pi$
$107$	1.63929e10			1.16879			0.584394	+	0.811470i	$0.301332\pi$
$108$	−6.87119e9	−	1.44247e10i	−0.467642	−	0.981724i
$109$			8.06193e9i			0.523970i	0.965072	+	0.261985i	$0.0843771\pi$
$109$			8.06193e9i			0.523970i	−0.965072	+	0.261985i	$0.915623\pi$
$110$	−4.72511e9	+	7.48460e9i	−0.293392	+	0.464735i
$111$		−	2.53257e10i		−	1.50296i
$112$	2.06545e10	+	1.67607e10i	1.17199	+	0.951047i
$113$	−7.36232e9			−0.399597			−0.199799	−	0.979837i	$-0.564029\pi$
$113$	−7.36232e9			−0.399597			−0.199799	+	0.979837i	$0.564029\pi$
$114$	1.21499e10	+	7.67034e9i	0.631026	+	0.398373i
$115$	1.01067e10			0.502481
$116$	−1.93133e10	+	9.19986e9i	−0.919534	+	0.438017i
$117$			5.31734e9i			0.242530i
$118$	−4.43982e9	−	2.80291e9i	−0.194069	−	0.122518i
$119$		−	4.76612e10i		−	1.99724i
$120$	−1.38563e10	−	1.65079e9i	−0.556855	−	0.0663417i
$121$	−8.40292e9			−0.323969
$122$	−5.49452e8	+	8.70335e8i	−0.0203297	+	0.0322023i
$123$	2.53564e10			0.900662
$124$	−3.95579e10	+	1.88433e10i	−1.34935	+	0.642760i
$125$		−	3.16837e10i		−	1.03821i
$126$	7.57785e9	−	1.20034e10i	0.238613	−	0.377964i
$127$			5.32119e10i			1.61061i	0.592861	+	0.805305i	$0.297998\pi$
$127$			5.32119e10i			1.61061i	−0.592861	+	0.805305i	$0.702002\pi$
$128$	2.39318e10	+	2.46549e10i	0.696506	+	0.717551i
$129$	6.43998e9			0.180275
$130$	1.71868e10	+	1.08502e10i	0.462892	+	0.292229i
$131$	−1.66260e10			−0.430955			−0.215477	−	0.976509i	$-0.569131\pi$
$131$	−1.66260e10			−0.430955			−0.215477	+	0.976509i	$0.569131\pi$
$132$	1.18881e10	+	2.49568e10i	0.296649	+	0.622757i
$133$			5.58709e10i			1.34254i
$134$	1.00213e10	+	6.32655e9i	0.231953	+	0.146434i
$135$			3.25931e10i			0.726870i
$136$	7.28329e9	−	6.11340e10i	0.156543	−	1.31398i
$137$	−8.03849e9			−0.166560			−0.0832802	−	0.996526i	$-0.526540\pi$
$137$	−8.03849e9			−0.166560			−0.0832802	+	0.996526i	$0.526540\pi$
$138$	1.68500e10	−	2.66904e10i	0.336669	−	0.533286i
$139$	−2.95171e10			−0.568852			−0.284426	−	0.958698i	$-0.591803\pi$
$139$	−2.95171e10			−0.568852			−0.284426	+	0.958698i	$0.591803\pi$
$140$	−2.33346e10	−	4.89866e10i	−0.433871	−	0.910830i
$141$		−	5.95003e9i		−	0.106764i
$142$	−5.47747e9	+	8.67635e9i	−0.0948721	+	0.150278i
$143$		−	4.02644e10i		−	0.673350i
$144$	1.15542e10	−	1.42384e10i	0.186607	−	0.229959i
$145$	4.36390e10			0.680824
$146$	−7.30312e10	−	4.61054e10i	−1.10089	−	0.695004i
$147$	−7.35998e10			−1.07223
$148$	1.14844e11	−	5.47057e10i	1.61734	−	0.770414i
$149$		−	4.99611e10i		−	0.680301i	−0.940371	−	0.340150i	$-0.889522\pi$
$149$		−	4.99611e10i		−	0.680301i	0.940371	−	0.340150i	$-0.110478\pi$
$150$	−2.98011e10	−	1.88138e10i	−0.392442	−	0.247753i
$151$			2.89845e10i			0.369217i	0.982812	+	0.184608i	$0.0591016\pi$
$151$			2.89845e10i			0.369217i	−0.982812	+	0.184608i	$0.940898\pi$
$152$	−8.53784e9	+	7.16644e10i	−0.105228	+	0.883253i
$153$	−3.28559e10			−0.391883
$154$	−5.73816e10	+	9.08928e10i	−0.662474	+	1.04936i
$155$	8.93820e10			0.999061
$156$	5.73081e10	−	2.72985e10i	0.620287	−	0.295472i
$157$			7.19130e8i			0.00753892i	0.999993	+	0.00376946i	$0.00119986\pi$
$157$			7.19130e8i			0.00753892i	−0.999993	+	0.00376946i	$0.998800\pi$
$158$	−3.23623e10	+	5.12621e10i	−0.328665	+	0.520608i
$159$			1.03363e11i			1.01714i
$160$	−2.24450e10	−	6.63999e10i	−0.214052	−	0.633239i
$161$	1.22735e11			1.13459
$162$	5.81329e10	+	3.66999e10i	0.521011	+	0.328920i
$163$	−1.44355e11			−1.25456			−0.627281	−	0.778793i	$-0.715832\pi$
$163$	−1.44355e11			−1.25456			−0.627281	+	0.778793i	$0.715832\pi$
$164$	5.47719e10	+	1.14983e11i	0.461677	+	0.969203i
$165$		−	5.63904e10i		−	0.461090i
$166$	5.96998e10	+	3.76891e10i	0.473622	+	0.299003i
$167$		−	6.02212e10i		−	0.463625i	−0.972760	−	0.231813i	$-0.925534\pi$
$167$		−	6.02212e10i		−	0.463625i	0.972760	−	0.231813i	$-0.0744656\pi$
$168$	−1.68271e11	−	2.00472e10i	−1.25737	−	0.149798i
$169$	4.53996e10			0.329320
$170$	−6.70437e10	+	1.06198e11i	−0.472187	+	0.747946i
$171$	3.85154e10			0.263423
$172$	1.39109e10	+	2.92033e10i	0.0924087	+	0.193994i
$173$		−	9.37427e9i		−	0.0604932i	−0.999542	−	0.0302466i	$-0.990371\pi$
$173$		−	9.37427e9i		−	0.0604932i	0.999542	−	0.0302466i	$-0.00962926\pi$
$174$	7.27552e10	−	1.15245e11i	0.456161	−	0.722561i
$175$		−	1.37040e11i		−	0.834942i
$176$	−8.74917e10	+	1.07817e11i	−0.518088	+	0.638448i
$177$	3.34504e10			0.192546
$178$	−2.46968e11	−	1.55914e11i	−1.38210	−	0.872537i
$179$	4.54078e10			0.247096			0.123548	−	0.992339i	$-0.460573\pi$
$179$	4.54078e10			0.247096			0.123548	+	0.992339i	$0.460573\pi$
$180$	−3.37696e10	+	1.60861e10i	−0.178716	+	0.0851308i
$181$		−	2.09295e11i		−	1.07737i	−0.842506	−	0.538686i	$-0.818921\pi$
$181$		−	2.09295e11i		−	1.07737i	0.842506	−	0.538686i	$-0.181079\pi$
$182$	2.08717e11	+	1.31765e11i	1.04520	+	0.659847i
$183$		−	6.55727e9i		−	0.0319498i
$184$	1.57430e11	+	1.87556e10i	0.746446	+	0.0889289i
$185$	−2.59493e11			−1.19748
$186$	1.49018e11	−	2.36046e11i	0.669384	−	1.06031i
$187$	2.48794e11			1.08801
$188$	2.69815e10	−	1.28526e10i	0.114889	−	0.0547268i
$189$			3.95809e11i			1.64126i
$190$	7.85921e10	−	1.24490e11i	0.317403	−	0.502768i
$191$		−	9.24953e10i		−	0.363876i	−0.983310	−	0.181938i	$-0.941763\pi$
$191$		−	9.24953e10i		−	0.363876i	0.983310	−	0.181938i	$-0.0582370\pi$
$192$	−2.12774e11	−	5.14281e10i	−0.815477	−	0.197104i
$193$	−2.90187e11			−1.08366			−0.541828	−	0.840490i	$-0.682268\pi$
$193$	−2.90187e11			−1.08366			−0.541828	+	0.840490i	$0.682268\pi$
$194$	5.12675e10	+	3.23657e10i	0.186566	+	0.117781i
$195$	−1.29489e11			−0.459261
$196$	−1.58982e11	−	3.33752e11i	−0.549625	−	1.15383i
$197$			5.37709e11i			1.81224i	0.423019	+	0.906121i	$0.360970\pi$
$197$			5.37709e11i			1.81224i	−0.423019	+	0.906121i	$0.639030\pi$
$198$	6.26581e10	+	3.95568e10i	0.205898	+	0.129985i
$199$			2.72659e11i			0.873683i	0.899539	+	0.436841i	$0.143903\pi$
$199$			2.72659e11i			0.873683i	−0.899539	+	0.436841i	$0.856097\pi$
$200$	2.09416e10	−	1.75778e11i	0.0654424	−	0.549306i
$201$	−7.55024e10			−0.230134
$202$	−8.83337e10	+	1.39921e11i	−0.262645	+	0.416032i
$203$	5.29951e11			1.53729
$204$	1.68678e11	+	3.54107e11i	0.477428	+	1.00227i
$205$		−	2.59807e11i		−	0.717599i
$206$	1.65434e11	−	2.62049e11i	0.445954	−	0.706393i
$207$		−	8.46093e10i		−	0.222621i
$208$	2.47581e11	+	2.00907e11i	0.635916	+	0.516034i
$209$	−2.91649e11			−0.731356
$210$	2.92308e11	+	1.84537e11i	0.715722	+	0.451843i
$211$	−6.55845e11			−1.56815			−0.784077	−	0.620664i	$-0.786863\pi$
$211$	−6.55845e11			−1.56815			−0.784077	+	0.620664i	$0.786863\pi$
$212$	−4.68719e11	+	2.23273e11i	−1.09454	+	0.521383i
$213$		−	6.53693e10i		−	0.149099i
$214$	−4.43573e11	−	2.80033e11i	−0.988317	−	0.623935i
$215$		−	6.59855e10i		−	0.143634i
$216$	−6.04851e10	+	5.07696e11i	−0.128641	+	1.07978i
$217$	1.08545e12			2.25586
$218$	1.37719e11	−	2.18147e11i	0.279711	−	0.443064i
$219$	5.50231e11			1.09226
$220$	2.55713e11	−	1.21808e11i	0.496180	−	0.236354i
$221$		−	5.71305e11i		−	1.08369i
$222$	−4.32629e11	+	6.85287e11i	−0.802326	+	1.27089i
$223$		−	1.20654e11i		−	0.218784i	−0.993999	−	0.109392i	$-0.965110\pi$
$223$		−	1.20654e11i		−	0.218784i	0.993999	−	0.109392i	$-0.0348904\pi$
$224$	−2.72572e11	−	8.06359e11i	−0.483326	−	1.42984i
$225$	−9.44702e10			−0.163826
$226$	1.99216e11	+	1.25767e11i	0.337896	+	0.213317i
$227$	−1.01745e12			−1.68805			−0.844024	−	0.536305i	$-0.819820\pi$
$227$	−1.01745e12			−1.68805			−0.844024	+	0.536305i	$0.819820\pi$
$228$	−1.97733e11	−	4.15102e11i	−0.320926	−	0.673722i
$229$		−	4.00233e11i		−	0.635529i	−0.948170	−	0.317764i	$-0.897068\pi$
$229$		−	4.00233e11i		−	0.635529i	0.948170	−	0.317764i	$-0.102932\pi$
$230$	−2.73476e11	−	1.72648e11i	−0.424894	−	0.268240i
$231$		−	6.84804e11i		−	1.04113i
$232$	6.79756e11	+	8.09837e10i	1.01138	+	0.120492i
$233$	−2.50256e8			−0.000364422			−0.000182211	−	1.00000i	$-0.500058\pi$
$233$	−2.50256e8			−0.000364422			−0.000182211		1.00000i	$0.500058\pi$
$234$	9.08340e10	−	1.43882e11i	0.129470	−	0.205081i
$235$	−6.09653e10			−0.0850636
$236$	7.22558e10	+	1.51687e11i	0.0986990	+	0.207200i
$237$		−	3.86218e11i		−	0.516525i
$238$	−8.14178e11	+	1.28966e12i	−1.06619	+	1.68885i
$239$			1.38040e12i			1.77017i	0.465427	+	0.885086i	$0.345901\pi$
$239$			1.38040e12i			1.77017i	−0.465427	+	0.885086i	$0.654099\pi$
$240$	3.46737e11	+	2.81371e11i	0.435456	+	0.353364i
$241$	8.00760e11			0.984957			0.492479	−	0.870325i	$-0.336091\pi$
$241$	8.00760e11			0.984957			0.492479	+	0.870325i	$0.336091\pi$
$242$	2.27374e11	+	1.43544e11i	0.273945	+	0.172945i
$243$	4.83370e11			0.570490
$244$	2.97351e10	−	1.41643e10i	0.0343812	−	0.0163774i
$245$			7.54120e11i			0.854299i
$246$	−6.86116e11	−	4.33153e11i	−0.761591	−	0.480801i
$247$			6.69712e11i			0.728456i
$248$	1.39229e12	+	1.65872e11i	1.48412	+	0.176813i
$249$	−4.49790e11			−0.469908
$250$	−5.41240e11	+	8.57327e11i	−0.554230	+	0.877903i
$251$	4.85659e11			0.487486			0.243743	−	0.969840i	$-0.421625\pi$
$251$	4.85659e11			0.487486			0.243743	+	0.969840i	$0.421625\pi$
$252$	−4.10097e11	+	1.95349e11i	−0.403537	+	0.192224i
$253$			6.40685e11i			0.618076i
$254$	9.08997e11	−	1.43986e12i	0.859793	−	1.36192i
$255$		−	8.00114e11i		−	0.742080i
$256$	−2.26399e11	−	1.07595e12i	−0.205908	−	0.978571i
$257$	−5.41553e11			−0.483031			−0.241516	−	0.970397i	$-0.577644\pi$
$257$	−5.41553e11			−0.483031			−0.241516	+	0.970397i	$0.577644\pi$
$258$	−1.74259e11	−	1.10012e11i	−0.152439	−	0.0962365i
$259$	−3.15128e12			−2.70389
$260$	−2.79707e11	−	5.87192e11i	−0.235416	−	0.494212i
$261$		−	3.65329e11i		−	0.301635i
$262$	4.49882e11	+	2.84015e11i	0.364411	+	0.230057i
$263$		−	1.04908e11i		−	0.0833736i	−0.999131	−	0.0416868i	$-0.986727\pi$
$263$		−	1.04908e11i		−	0.0833736i	0.999131	−	0.0416868i	$-0.0132732\pi$
$264$	1.04647e11	−	8.78382e11i	0.0816035	−	0.684958i
$265$	1.05908e12			0.810401
$266$	9.54420e11	−	1.51181e12i	0.716690	−	1.13524i
$267$	1.86070e12			1.37126
$268$	−1.63092e11	−	3.42379e11i	−0.117966	−	0.247647i
$269$			1.43692e12i			1.02017i	0.860125	+	0.510083i	$0.170385\pi$
$269$			1.43692e12i			1.02017i	−0.860125	+	0.510083i	$0.829615\pi$
$270$	5.56774e11	−	8.81933e11i	0.388025	−	0.614635i
$271$			1.21213e12i			0.829280i	0.909985	+	0.414640i	$0.136093\pi$
$271$			1.21213e12i			0.829280i	−0.909985	+	0.414640i	$0.863907\pi$
$272$	−1.24140e12	+	1.52980e12i	−0.833814	+	1.02752i
$273$	−1.57251e12			−1.03700
$274$	2.17513e11	+	1.37318e11i	0.140842	+	0.0889151i
$275$	7.15355e11			0.454839
$276$	−9.11883e11	+	4.34373e11i	−0.569369	+	0.271217i
$277$		−	2.87127e12i		−	1.76066i	−0.474362	−	0.880330i	$-0.657321\pi$
$277$		−	2.87127e12i		−	1.76066i	0.474362	−	0.880330i	$-0.342679\pi$
$278$	7.98700e11	+	5.04228e11i	0.481016	+	0.303671i
$279$		−	7.48272e11i		−	0.442627i
$280$	−2.05408e11	+	1.72414e12i	−0.119351	+	1.00180i
$281$	−1.27196e12			−0.726007			−0.363004	−	0.931788i	$-0.618249\pi$
$281$	−1.27196e12			−0.726007			−0.363004	+	0.931788i	$0.618249\pi$
$282$	−1.01642e11	+	1.61001e11i	−0.0569937	+	0.0902784i
$283$	2.45158e12			1.35056			0.675279	−	0.737562i	$-0.264023\pi$
$283$	2.45158e12			1.35056			0.675279	+	0.737562i	$0.264023\pi$
$284$	2.96429e11	−	1.41203e11i	0.160446	−	0.0764281i
$285$			9.37934e11i			0.498825i
$286$	−6.87820e11	+	1.08951e12i	−0.359455	+	0.569379i
$287$		−	3.15509e12i		−	1.62033i
$288$	−5.55874e11	+	1.87901e11i	−0.280552	+	0.0948345i
$289$	1.51410e12			0.751045
$290$	−1.18082e12	−	7.45467e11i	−0.575699	−	0.363445i
$291$	−3.86259e11			−0.185103
$292$	1.18855e12	+	2.49512e12i	0.559888	+	1.17538i
$293$			2.61648e12i			1.21165i	0.795596	+	0.605827i	$0.207158\pi$
$293$			2.61648e12i			1.21165i	−0.795596	+	0.605827i	$0.792842\pi$
$294$	1.99153e12	+	1.25727e12i	0.906672	+	0.572392i
$295$		−	3.42741e11i		−	0.153411i
$296$	−4.04208e12	−	4.81559e11i	−1.77888	−	0.211929i
$297$	−2.06615e12			−0.894085
$298$	−8.53466e11	+	1.35189e12i	−0.363166	+	0.575256i
$299$	1.47120e12			0.615625
$300$	4.84998e11	+	1.01816e12i	0.199588	+	0.418996i
$301$		−	8.01326e11i		−	0.324322i
$302$	4.95130e11	−	7.84289e11i	0.197099	−	0.312206i
$303$		−	1.05419e12i		−	0.412769i
$304$	1.45524e12	−	1.79331e12i	0.560488	−	0.690697i
$305$	−6.71873e10			−0.0254559
$306$	8.89046e11	+	5.61264e11i	0.331373	+	0.209199i
$307$	−4.14347e11			−0.151940			−0.0759700	−	0.997110i	$-0.524205\pi$
$307$	−4.14347e11			−0.151940			−0.0759700	+	0.997110i	$0.524205\pi$
$308$	3.10537e12	−	1.47923e12i	1.12036	−	0.533683i
$309$			1.97433e12i			0.700853i
$310$	−2.41858e12	−	1.52688e12i	−0.844797	−	0.533329i
$311$			1.73263e12i			0.595530i	0.954639	+	0.297765i	$0.0962413\pi$
$311$			1.73263e12i			0.595530i	−0.954639	+	0.297765i	$0.903759\pi$
$312$	−2.01702e12	−	2.40301e11i	−0.682242	−	0.0812798i
$313$	−5.44579e11			−0.181276			−0.0906378	−	0.995884i	$-0.528891\pi$
$313$	−5.44579e11			−0.181276			−0.0906378	+	0.995884i	$0.528891\pi$
$314$	1.22846e10	−	1.94589e10i	0.00402451	−	0.00637485i
$315$	9.26624e11			0.298780
$316$	1.75138e12	−	8.34264e11i	0.555833	−	0.264770i
$317$		−	5.23802e12i		−	1.63633i	−0.574985	−	0.818164i	$-0.694992\pi$
$317$		−	5.23802e12i		−	1.63633i	0.574985	−	0.818164i	$-0.305008\pi$
$318$	1.76571e12	−	2.79689e12i	0.542979	−	0.860082i
$319$			2.76637e12i			0.837446i
$320$	−5.26945e11	+	2.18013e12i	−0.157042	+	0.649729i
$321$	3.34197e12			0.980566
$322$	−3.32109e12	−	2.09664e12i	−0.959403	−	0.605681i
$323$	−4.13816e12			−1.17705
$324$	−9.46083e11	−	1.98612e12i	−0.264975	−	0.556263i
$325$		−	1.64267e12i		−	0.453036i
$326$	3.90608e12	+	2.46595e12i	1.06085	+	0.669724i
$327$			1.64356e12i			0.439589i
$328$	4.82141e11	−	4.04697e12i	0.127000	−	1.06601i
$329$	−7.40361e11			−0.192072
$330$	−9.63294e11	+	1.52586e12i	−0.246144	+	0.389893i
$331$	−6.72784e12			−1.69331			−0.846653	−	0.532145i	$-0.821386\pi$
$331$	−6.72784e12			−1.69331			−0.846653	+	0.532145i	$0.821386\pi$
$332$	−9.71583e11	−	2.03965e12i	−0.240874	−	0.505669i
$333$			2.17238e12i			0.530535i
$334$	−1.02873e12	+	1.62952e12i	−0.247497	+	0.392037i
$335$			7.73615e11i			0.183358i
$336$	4.21077e12	+	3.41696e12i	0.983252	+	0.797890i
$337$	5.42632e12			1.24841			0.624203	−	0.781262i	$-0.285424\pi$
$337$	5.42632e12			1.24841			0.624203	+	0.781262i	$0.285424\pi$
$338$	−1.22846e12	−	7.75542e11i	−0.278470	−	0.175801i
$339$	−1.50093e12			−0.335246
$340$	3.62826e12	−	1.72831e12i	0.798554	−	0.380389i
$341$			5.66612e12i			1.22889i
$342$	−1.04218e12	−	6.57942e11i	−0.222748	−	0.140623i
$343$			1.99242e12i			0.419671i
$344$	1.22454e11	−	1.02784e12i	0.0254202	−	0.213371i
$345$	2.06042e12			0.421561
$346$	−1.60137e11	+	2.53657e11i	−0.0322932	+	0.0511525i
$347$	5.28169e12			1.04985			0.524923	−	0.851149i	$-0.324094\pi$
$347$	5.28169e12			1.04985			0.524923	+	0.851149i	$0.324094\pi$
$348$	−3.93736e12	+	1.87555e12i	−0.771451	+	0.367479i
$349$			4.86322e11i			0.0939283i	0.998897	+	0.0469641i	$0.0149547\pi$
$349$			4.86322e11i			0.0939283i	−0.998897	+	0.0469641i	$0.985045\pi$
$350$	−2.34100e12	+	3.70815e12i	−0.445718	+	0.706020i
$351$			4.74448e12i			0.890539i
$352$	4.20923e12	−	1.42284e12i	0.778914	−	0.263295i
$353$	−3.75886e12			−0.685777			−0.342888	−	0.939376i	$-0.611405\pi$
$353$	−3.75886e12			−0.685777			−0.342888	+	0.939376i	$0.611405\pi$
$354$	−9.05133e11	−	5.71420e11i	−0.162816	−	0.102787i
$355$	−6.69789e11			−0.118794
$356$	4.01928e12	+	8.43770e12i	0.702907	+	1.47562i
$357$		−	9.71656e12i		−	1.67560i
$358$	−1.22869e12	−	7.75682e11i	−0.208942	−	0.131907i
$359$		−	4.14060e12i		−	0.694370i	−0.937797	−	0.347185i	$-0.887138\pi$
$359$		−	4.14060e12i		−	0.694370i	0.937797	−	0.347185i	$-0.112862\pi$
$360$	1.18856e12	+	1.41601e11i	0.196566	+	0.0234182i
$361$	−1.28011e12			−0.208791
$362$	−3.57530e12	+	5.66330e12i	−0.575135	+	0.911017i
$363$	−1.71308e12			−0.271797
$364$	−3.39676e12	−	7.13084e12i	−0.531566	−	1.11592i
$365$		−	5.63779e12i		−	0.870251i
$366$	−1.12015e11	+	1.77433e11i	−0.0170558	+	0.0270164i
$367$		−	1.27382e13i		−	1.91328i	−0.291272	−	0.956640i	$-0.594079\pi$
$367$		−	1.27382e13i		−	1.91328i	0.291272	−	0.956640i	$-0.405921\pi$
$368$	−3.93949e12	−	3.19682e12i	−0.583715	−	0.473673i
$369$	−2.17500e12			−0.317928
$370$	7.02161e12	+	4.43282e12i	1.01258	+	0.639251i
$371$	1.28615e13			1.82987
$372$	−8.06455e12	+	3.84153e12i	−1.13205	+	0.539249i
$373$			1.97372e11i			0.0273364i	0.999907	+	0.0136682i	$0.00435085\pi$
$373$			1.97372e11i			0.0273364i	−0.999907	+	0.0136682i	$0.995649\pi$
$374$	−6.73210e12	−	4.25005e12i	−0.920010	−	0.580812i
$375$		−	6.45927e12i		−	0.871017i
$376$	−9.49645e11	−	1.13137e11i	−0.126364	−	0.0150545i
$377$	6.35240e12			0.834125
$378$	6.76145e12	−	1.07102e13i	0.876155	−	1.38783i
$379$	−4.09437e12			−0.523590			−0.261795	−	0.965124i	$-0.584314\pi$
$379$	−4.09437e12			−0.523590			−0.261795	+	0.965124i	$0.584314\pi$
$380$	−4.25323e12	+	2.02602e12i	−0.536786	+	0.255697i
$381$			1.08482e13i			1.35124i
$382$	−1.58006e12	+	2.50282e12i	−0.194248	+	0.307690i
$383$			4.76814e12i			0.578569i	0.957243	+	0.289285i	$0.0934174\pi$
$383$			4.76814e12i			0.578569i	−0.957243	+	0.289285i	$0.906583\pi$
$384$	4.87890e12	+	5.02632e12i	0.584340	+	0.601996i
$385$	−7.01666e12			−0.829519
$386$	7.85214e12	+	4.95714e12i	0.916330	+	0.578489i
$387$	−5.52405e11			−0.0636360
$388$	−8.34352e11	−	1.75156e12i	−0.0948835	−	0.199190i
$389$		−	9.35450e11i		−	0.105020i	−0.998620	−	0.0525101i	$-0.983278\pi$
$389$		−	9.35450e11i		−	0.105020i	0.998620	−	0.0525101i	$-0.0167222\pi$
$390$	3.50383e12	+	2.21201e12i	0.388347	+	0.245168i
$391$			9.09057e12i			0.994735i
$392$	−1.39947e12	+	1.17468e13i	−0.151193	+	1.26908i
$393$	−3.38950e12			−0.361553
$394$	9.18546e12	−	1.45498e13i	0.967431	−	1.53242i
$395$	−3.95728e12			−0.411540
$396$	−1.01973e12	−	2.14073e12i	−0.104715	−	0.219829i
$397$			1.13676e13i			1.15270i	0.817203	+	0.576351i	$0.195524\pi$
$397$			1.13676e13i			1.15270i	−0.817203	+	0.576351i	$0.804476\pi$
$398$	4.65771e12	−	7.37785e12i	0.466399	−	0.738778i
$399$			1.13902e13i			1.12634i
$400$	−3.56940e12	+	4.39862e12i	−0.348574	+	0.429553i
$401$	−6.60693e12			−0.637203			−0.318601	−	0.947889i	$-0.603213\pi$
$401$	−6.60693e12			−0.637203			−0.318601	+	0.947889i	$0.603213\pi$
$402$	2.04301e12	+	1.28978e12i	0.194599	+	0.122853i
$403$	1.30111e13			1.22402
$404$	4.78043e12	−	2.27714e12i	0.444181	−	0.211584i
$405$			4.48769e12i			0.411858i
$406$	−1.43399e13	−	9.05293e12i	−1.29992	−	0.820652i
$407$		−	1.64498e13i		−	1.47296i
$408$	1.48482e12	−	1.24632e13i	0.131333	−	1.10237i
$409$	−3.26755e12			−0.285500			−0.142750	−	0.989759i	$-0.545594\pi$
$409$	−3.26755e12			−0.285500			−0.142750	+	0.989759i	$0.545594\pi$
$410$	−4.43818e12	+	7.03010e12i	−0.383077	+	0.606796i
$411$	−1.63878e12			−0.139737
$412$	−8.95295e12	+	4.26471e12i	−0.754189	+	0.359256i
$413$		−	4.16224e12i		−	0.346399i
$414$	−1.44535e12	+	2.28944e12i	−0.118842	+	0.188246i
$415$			4.60865e12i			0.374398i
$416$	−3.26725e12	−	9.66564e12i	−0.262250	−	0.775825i
$417$	−6.01756e12			−0.477244
$418$	7.89171e12	+	4.98212e12i	0.618429	+	0.390421i
$419$	−2.06044e12			−0.159548			−0.0797738	−	0.996813i	$-0.525420\pi$
$419$	−2.06044e12			−0.159548			−0.0797738	+	0.996813i	$0.525420\pi$
$420$	−4.75717e12	−	9.98676e12i	−0.364001	−	0.764149i
$421$			5.83555e12i			0.441237i	0.975360	+	0.220618i	$0.0708075\pi$
$421$			5.83555e12i			0.441237i	−0.975360	+	0.220618i	$0.929192\pi$
$422$	1.77464e13	+	1.12035e13i	1.32602	+	0.837129i
$423$			5.10378e11i			0.0376869i
$424$	1.64971e13	+	1.96541e12i	1.20387	+	0.143424i
$425$	1.01500e13			0.732021
$426$	−1.11668e12	+	1.76882e12i	−0.0795939	+	0.126077i
$427$	−8.15921e11			−0.0574789
$428$	7.21893e12	+	1.51548e13i	0.502636	+	1.05519i
$429$		−	8.20859e12i		−	0.564914i
$430$	−1.12720e12	+	1.78550e12i	−0.0766761	+	0.121455i
$431$		−	1.85492e13i		−	1.24720i	−0.781742	−	0.623602i	$-0.785668\pi$
$431$		−	1.85492e13i		−	1.24720i	0.781742	−	0.623602i	$-0.214332\pi$
$432$	1.03094e13	−	1.27045e13i	0.685197	−	0.844379i
$433$	−4.60728e11			−0.0302695			−0.0151347	−	0.999885i	$-0.504818\pi$
$433$	−4.60728e11			−0.0302695			−0.0151347	+	0.999885i	$0.504818\pi$
$434$	−2.93712e13	−	1.85424e13i	−1.90754	−	1.20425i
$435$	8.89655e12			0.571183
$436$	−7.45303e12	+	3.55023e12i	−0.473043	+	0.225333i
$437$		−	1.06564e13i		−	0.668658i
$438$	−1.48887e13	−	9.39937e12i	−0.923602	−	0.583080i
$439$			2.12657e13i			1.30424i	0.758115	+	0.652121i	$0.226121\pi$
$439$			2.12657e13i			1.30424i	−0.758115	+	0.652121i	$0.773879\pi$
$440$	−9.00011e12	−	1.07224e12i	−0.545738	−	0.0650173i
$441$	6.31320e12			0.378492
$442$	−9.75936e12	+	1.54589e13i	−0.578509	+	0.916361i
$443$	−3.22811e13			−1.89203			−0.946017	−	0.324116i	$-0.894933\pi$
$443$	−3.22811e13			−1.89203			−0.946017	+	0.324116i	$0.894933\pi$
$444$	2.34130e13	−	1.11527e13i	1.35688	−	0.646346i
$445$		−	1.90652e13i		−	1.09255i
$446$	−2.06108e12	+	3.26476e12i	−0.116794	+	0.185002i
$447$		−	1.01854e13i		−	0.570745i
$448$	−6.39920e12	+	2.64754e13i	−0.354598	+	1.46708i
$449$	2.25683e13			1.23671			0.618353	−	0.785900i	$-0.287800\pi$
$449$	2.25683e13			1.23671			0.618353	+	0.785900i	$0.287800\pi$
$450$	2.55626e12	+	1.61380e12i	0.138530	+	0.0874553i
$451$	1.64697e13			0.882682
$452$	−3.24215e12	−	6.80626e12i	−0.171846	−	0.360758i
$453$			5.90899e12i			0.309758i
$454$	2.75312e13	+	1.73807e13i	1.42740	+	0.901133i
$455$			1.61123e13i			0.826230i
$456$	−1.74058e12	+	1.46100e13i	−0.0882817	+	0.741014i
$457$	1.06357e13			0.533563			0.266782	−	0.963757i	$-0.414040\pi$
$457$	1.06357e13			0.533563			0.266782	+	0.963757i	$0.414040\pi$
$458$	−6.83701e12	+	1.08299e13i	−0.339265	+	0.537398i
$459$	−2.93162e13			−1.43894
$460$	4.45069e12	+	9.34336e12i	0.216092	+	0.453643i
$461$		−	1.15452e13i		−	0.554494i	−0.960799	−	0.277247i	$-0.910578\pi$
$461$		−	1.15452e13i		−	0.554494i	0.960799	−	0.277247i	$-0.0894221\pi$
$462$	−1.16982e13	+	1.85300e13i	−0.555789	+	0.880373i
$463$		−	2.23021e12i		−	0.104819i	−0.998626	−	0.0524097i	$-0.983310\pi$
$463$		−	2.23021e12i		−	0.104819i	0.998626	−	0.0524097i	$-0.0166902\pi$
$464$	−1.70100e13	−	1.38033e13i	−0.790889	−	0.641791i
$465$	1.82221e13			0.838171
$466$	6.77166e9	+	4.27502e9i	0.000308152	+	0.000194540i
$467$	6.67938e12			0.300712			0.150356	−	0.988632i	$-0.451958\pi$
$467$	6.67938e12			0.300712			0.150356	+	0.988632i	$0.451958\pi$
$468$	−4.91574e12	+	2.34160e12i	−0.218957	+	0.104300i
$469$			9.39476e12i			0.414020i
$470$	1.64966e12	+	1.04145e12i	0.0719290	+	0.0454096i
$471$			1.46607e11i			0.00632485i
$472$	6.36047e11	−	5.33881e12i	0.0271506	−	0.227895i
$473$	4.18296e12			0.176676
$474$	−6.59761e12	+	1.04507e13i	−0.275737	+	0.436769i
$475$	−1.18984e13			−0.492063
$476$	4.40615e13	−	2.09886e13i	1.80312	−	0.858912i
$477$		−	8.86621e12i		−	0.359043i
$478$	2.35808e13	−	3.73521e13i	0.944973	−	1.49684i
$479$			3.25794e13i			1.29201i	0.763334	+	0.646004i	$0.223561\pi$
$479$			3.25794e13i			1.29201i	−0.763334	+	0.646004i	$0.776439\pi$
$480$	−4.57580e12	−	1.35368e13i	−0.179581	−	0.531261i
$481$	−3.77737e13			−1.46711
$482$	−2.16677e13	−	1.36791e13i	−0.832871	−	0.525801i
$483$	2.50217e13			0.951878
$484$	−3.70039e12	−	7.76827e12i	−0.139322	−	0.292481i
$485$			3.95770e12i			0.147480i
$486$	−1.30795e13	−	8.25721e12i	−0.482402	−	0.304545i
$487$		−	3.47745e13i		−	1.26945i	−0.772738	−	0.634726i	$-0.781113\pi$
$487$		−	3.47745e13i		−	1.26945i	0.772738	−	0.634726i	$-0.218887\pi$
$488$	−1.04656e12	−	1.24684e11i	−0.0378152	−	0.00450517i
$489$	−2.94291e13			−1.05253
$490$	1.28823e13	−	2.04057e13i	0.456051	−	0.722388i
$491$	−4.94642e12			−0.173334			−0.0866669	−	0.996237i	$-0.527622\pi$
$491$	−4.94642e12			−0.173334			−0.0866669	+	0.996237i	$0.527622\pi$
$492$	1.11662e13	+	2.34413e13i	0.387329	+	0.813122i
$493$			3.92515e13i			1.34779i
$494$	1.14404e13	−	1.81217e13i	0.388872	−	0.615976i
$495$			4.83702e12i			0.162762i
$496$	−3.48402e13	−	2.82722e13i	−1.16057	−	0.941783i
$497$	−8.13390e12			−0.268236
$498$	1.21708e13	+	7.68357e12i	0.397350	+	0.250851i
$499$	6.33777e12			0.204849			0.102425	−	0.994741i	$-0.467340\pi$
$499$	6.33777e12			0.204849			0.102425	+	0.994741i	$0.467340\pi$
$500$	2.92907e13	−	1.39526e13i	0.937303	−	0.446482i
$501$		−	1.22771e13i		−	0.388963i
$502$	−1.31414e13	−	8.29631e12i	−0.412214	−	0.260235i
$503$			1.72088e13i			0.534455i	0.963633	+	0.267228i	$0.0861075\pi$
$503$			1.72088e13i			0.534455i	−0.963633	+	0.267228i	$0.913892\pi$
$504$	1.44338e13	+	1.71960e12i	0.443843	+	0.0528779i
$505$	−1.08015e13			−0.328872
$506$	1.09446e13	−	1.73362e13i	0.329948	−	0.522640i
$507$	9.25548e12			0.276286
$508$	−4.91930e13	+	2.34329e13i	−1.45407	+	0.692641i
$509$			5.81472e13i			1.70192i	0.525229	+	0.850961i	$0.323980\pi$
$509$			5.81472e13i			1.70192i	−0.525229	+	0.850961i	$0.676020\pi$
$510$	−1.36680e13	+	2.16502e13i	−0.396145	+	0.627496i
$511$		−	6.84652e13i		−	1.96501i
$512$	−1.22539e13	+	3.29815e13i	−0.348277	+	0.937392i
$513$	3.43659e13			0.967255
$514$	1.46538e13	+	9.25112e12i	0.408447	+	0.257857i
$515$	2.02294e13			0.558402
$516$	2.83598e12	+	5.95359e12i	0.0775272	+	0.162753i
$517$		−	3.86472e12i		−	0.104632i
$518$	8.52702e13	+	5.38320e13i	2.28638	+	1.44342i
$519$		−	1.91110e12i		−	0.0507514i
$520$	−2.46218e12	+	2.06669e13i	−0.0647595	+	0.543574i
$521$	−5.26939e13			−1.37269			−0.686344	−	0.727277i	$-0.740786\pi$
$521$	−5.26939e13			−1.37269			−0.686344	+	0.727277i	$0.740786\pi$
$522$	−6.24076e12	+	9.88540e12i	−0.161022	+	0.255060i
$523$	4.02928e13			1.02972			0.514859	−	0.857275i	$-0.327844\pi$
$523$	4.02928e13			1.02972			0.514859	+	0.857275i	$0.327844\pi$
$524$	−7.32160e12	−	1.53703e13i	−0.185332	−	0.389068i
$525$		−	2.79379e13i		−	0.700483i
$526$	−1.79209e12	+	2.83869e12i	−0.0445074	+	0.0705000i
$527$			8.03956e13i			1.97779i
$528$	−1.78367e13	+	2.19804e13i	−0.434655	+	0.535632i
$529$	1.80168e13			0.434910
$530$	−2.86576e13	−	1.80918e13i	−0.685268	−	0.432617i
$531$	−2.86929e12			−0.0679677
$532$	−5.16511e13	+	2.46039e13i	−1.21205	+	0.577358i
$533$		−	3.78194e13i		−	0.879181i
$534$	−5.03486e13	−	3.17856e13i	−1.15953	−	0.732023i
$535$		−	3.42425e13i		−	0.781263i
$536$	−1.43565e12	+	1.20504e13i	−0.0324507	+	0.272382i
$537$	9.25715e12			0.207303
$538$	2.45463e13	−	3.88815e13i	0.544597	−	0.862644i
$539$	−4.78053e13			−1.05083
$540$	−3.01314e13	+	1.43530e13i	−0.656222	+	0.312590i
$541$		−	2.22804e13i		−	0.480769i	−0.970678	−	0.240385i	$-0.922726\pi$
$541$		−	2.22804e13i		−	0.480769i	0.970678	−	0.240385i	$-0.0772736\pi$
$542$	2.07063e13	−	3.27988e13i	0.442695	−	0.701232i
$543$		−	4.26684e13i		−	0.903872i
$544$	5.97241e13	−	2.01884e13i	1.25359	−	0.423748i
$545$	1.68403e13			0.350241
$546$	4.25505e13	+	2.68626e13i	0.876882	+	0.553585i
$547$	6.41889e13			1.31076			0.655380	−	0.755299i	$-0.272508\pi$
$547$	6.41889e13			1.31076			0.655380	+	0.755299i	$0.272508\pi$
$548$	−3.53991e12	−	7.43137e12i	−0.0716291	−	0.150372i
$549$			5.62466e11i			0.0112781i
$550$	−1.93567e13	−	1.22201e13i	−0.384608	−	0.242807i
$551$		−	4.60126e13i		−	0.905981i
$552$	3.20948e13	+	3.82366e12i	0.626238	+	0.0746077i
$553$	−4.80571e13			−0.929249
$554$	−4.90487e13	+	7.76935e13i	−0.939894	+	1.48880i
$555$	−5.29022e13			−1.00464
$556$	−1.29984e13	−	2.72877e13i	−0.244634	−	0.513563i
$557$			1.84305e13i			0.343764i	0.985118	+	0.171882i	$0.0549849\pi$
$557$			1.84305e13i			0.343764i	−0.985118	+	0.171882i	$0.945015\pi$
$558$	−1.27824e13	+	2.02474e13i	−0.236288	+	0.374282i
$559$		−	9.60532e12i		−	0.175976i
$560$	3.50109e13	−	4.31445e13i	0.635716	−	0.783403i
$561$	5.07209e13			0.912794
$562$	3.44178e13	+	2.17283e13i	0.613905	+	0.387565i
$563$	−3.43128e13			−0.606617			−0.303309	−	0.952892i	$-0.598091\pi$
$563$	−3.43128e13			−0.606617			−0.303309	+	0.952892i	$0.598091\pi$
$564$	5.50064e12	−	2.62021e12i	0.0963868	−	0.0459136i
$565$			1.53789e13i			0.267106i
$566$	−6.63371e13	−	4.18793e13i	−1.14202	−	0.720970i
$567$			5.44983e13i			0.929968i
$568$	−1.04332e13	−	1.24297e12i	−0.176471	−	0.0210242i
$569$	9.76085e13			1.63654			0.818269	−	0.574835i	$-0.194934\pi$
$569$	9.76085e13			1.63654			0.818269	+	0.574835i	$0.194934\pi$
$570$	1.60223e13	−	2.53795e13i	0.266288	−	0.421802i
$571$	4.78352e13			0.788073			0.394037	−	0.919095i	$-0.371078\pi$
$571$	4.78352e13			0.788073			0.394037	+	0.919095i	$0.371078\pi$
$572$	3.72233e13	−	1.77312e13i	0.607904	−	0.289574i
$573$		−	1.88568e13i		−	0.305277i
$574$	−5.38972e13	+	8.53734e13i	−0.864981	+	1.37013i
$575$			2.61380e13i			0.415847i
$576$	1.82512e13	+	4.41138e12i	0.287858	+	0.0695763i
$577$	−9.82519e13			−1.53625			−0.768125	−	0.640300i	$-0.778810\pi$
$577$	−9.82519e13			−1.53625			−0.768125	+	0.640300i	$0.778810\pi$
$578$	−4.09700e13	−	2.58648e13i	−0.635077	−	0.400931i
$579$	−5.91596e13			−0.909143
$580$	1.92173e13	+	4.03431e13i	0.292788	+	0.614651i
$581$			5.59673e13i			0.845383i
$582$	1.04517e13	+	6.59830e12i	0.156522	+	0.0988137i
$583$			6.71374e13i			0.996832i
$584$	1.04624e13	−	8.78188e13i	0.154017	−	1.29278i
$585$	1.11072e13			0.162116
$586$	4.46962e13	−	7.07990e13i	0.646819	−	1.02456i
$587$	−6.65454e12			−0.0954834			−0.0477417	−	0.998860i	$-0.515202\pi$
$587$	−6.65454e12			−0.0954834			−0.0477417	+	0.998860i	$0.515202\pi$
$588$	−3.24111e13	−	6.80410e13i	−0.461113	−	0.968019i
$589$		−	9.42438e13i		−	1.32946i
$590$	−5.85490e12	+	9.27420e12i	−0.0818954	+	0.129723i
$591$			1.09621e14i			1.52040i
$592$	1.01148e14	+	8.20796e13i	1.39107	+	1.12883i
$593$	−5.14742e13			−0.701967			−0.350983	−	0.936382i	$-0.614153\pi$
$593$	−5.14742e13			−0.701967			−0.350983	+	0.936382i	$0.614153\pi$
$594$	5.59077e13	+	3.52951e13i	0.756030	+	0.477290i
$595$	−9.95581e13			−1.33503
$596$	4.61877e13	−	2.20014e13i	0.614179	−	0.292563i
$597$			5.55861e13i			0.732984i
$598$	−3.98091e13	−	2.51319e13i	−0.520567	−	0.328640i
$599$			1.31771e13i			0.170878i	0.996343	+	0.0854390i	$0.0272293\pi$
$599$			1.31771e13i			0.170878i	−0.996343	+	0.0854390i	$0.972771\pi$
$600$	4.26929e12	−	3.58353e13i	0.0549035	−	0.460845i
$601$	9.02087e13			1.15047			0.575236	−	0.817988i	$-0.304910\pi$
$601$	9.02087e13			1.15047			0.575236	+	0.817988i	$0.304910\pi$
$602$	−1.36887e13	+	2.16830e13i	−0.173133	+	0.274244i
$603$	6.47640e12			0.0812357
$604$	−2.67954e13	+	1.27639e13i	−0.333331	+	0.158781i
$605$			1.75526e13i			0.216553i
$606$	−1.80083e13	+	2.85253e13i	−0.220349	+	0.349034i
$607$			2.75800e12i			0.0334696i	0.999860	+	0.0167348i	$0.00532710\pi$
$607$			2.75800e12i			0.0334696i	−0.999860	+	0.0167348i	$0.994673\pi$
$608$	−7.00116e13	+	2.36658e13i	−0.842659	+	0.284842i
$609$	1.08040e14			1.28972
$610$	1.81802e12	+	1.14773e12i	0.0215253	+	0.0135891i
$611$	−8.87455e12			−0.104217
$612$	−1.44688e13	−	3.03744e13i	−0.168529	−	0.353794i
$613$			4.06668e13i			0.469826i	0.972016	+	0.234913i	$0.0754806\pi$
$613$			4.06668e13i			0.469826i	−0.972016	+	0.234913i	$0.924519\pi$
$614$	1.12118e13	+	7.07812e12i	0.128479	+	0.0811103i
$615$		−	5.29662e13i		−	0.602037i
$616$	−1.09297e14	−	1.30213e13i	−1.23227	−	0.146808i
$617$	2.79773e13			0.312882			0.156441	−	0.987687i	$-0.449998\pi$
$617$	2.79773e13			0.312882			0.156441	+	0.987687i	$0.449998\pi$
$618$	3.37266e13	−	5.34232e13i	0.374137	−	0.592635i
$619$	3.72952e13			0.410393			0.205197	−	0.978721i	$-0.434217\pi$
$619$	3.72952e13			0.410393			0.205197	+	0.978721i	$0.434217\pi$
$620$	3.93612e13	+	8.26313e13i	0.429645	+	0.901957i
$621$		−	7.54939e13i		−	0.817436i
$622$	2.95978e13	−	4.68831e13i	0.317913	−	0.503575i
$623$		−	2.31527e14i		−	2.46696i
$624$	5.04735e13	+	4.09583e13i	0.533508	+	0.432931i
$625$	−1.34268e13			−0.140790
$626$	1.47357e13	+	9.30283e12i	0.153285	+	0.0967706i
$627$	−5.94576e13			−0.613578
$628$	−6.64816e11	+	3.16684e11i	−0.00680618	+	0.00324211i
$629$		−	2.33404e14i		−	2.37058i
$630$	−2.50734e13	−	1.58291e13i	−0.252645	−	0.159498i
$631$		−	2.81208e13i		−	0.281113i	−0.990073	−	0.140557i	$-0.955111\pi$
$631$		−	2.81208e13i		−	0.281113i	0.990073	−	0.140557i	$-0.0448892\pi$
$632$	−6.16418e13	−	7.34379e12i	−0.611350	−	0.0728341i
$633$	−1.33705e14			−1.31562
$634$	−8.94789e13	+	1.41735e14i	−0.873523	+	1.38367i
$635$	1.11153e14			1.07659
$636$	−9.55563e13	+	4.55180e13i	−0.918277	+	0.437419i
$637$			1.09775e14i			1.04666i
$638$	4.72568e13	−	7.48550e13i	0.447055	−	0.708137i
$639$			5.60721e12i			0.0526311i
$640$	5.15008e13	−	4.99903e13i	0.479638	−	0.465571i
$641$	−1.42063e14			−1.31278			−0.656388	−	0.754423i	$-0.727917\pi$
$641$	−1.42063e14			−1.31278			−0.656388	+	0.754423i	$0.727917\pi$
$642$	−9.04300e13	−	5.70894e13i	−0.829158	−	0.523456i
$643$	1.42601e14			1.29738			0.648691	−	0.761052i	$-0.275317\pi$
$643$	1.42601e14			1.29738			0.648691	+	0.761052i	$0.275317\pi$
$644$	5.40490e13	+	1.13466e14i	0.487931	+	1.02432i
$645$		−	1.34523e13i		−	0.120503i
$646$	1.11974e14	+	7.06904e13i	0.995302	+	0.628345i
$647$			9.36509e13i			0.826020i	0.910727	+	0.413010i	$0.135522\pi$
$647$			9.36509e13i			0.826020i	−0.910727	+	0.413010i	$0.864478\pi$
$648$	−8.32809e12	+	6.99038e13i	−0.0728904	+	0.611823i
$649$	2.17271e13			0.188703
$650$	−2.80610e13	+	4.44488e13i	−0.241844	+	0.383083i
$651$	2.21288e14			1.89258
$652$	−6.35694e13	−	1.33452e14i	−0.539523	−	1.13263i
$653$			1.86286e14i			1.56897i	0.620147	+	0.784485i	$0.287073\pi$
$653$			1.86286e14i			1.56897i	−0.620147	+	0.784485i	$0.712927\pi$
$654$	2.80763e13	−	4.44730e13i	0.234666	−	0.371713i
$655$			3.47296e13i			0.288067i
$656$	−8.21789e13	+	1.01270e14i	−0.676458	+	0.833610i
$657$	−4.71974e13			−0.385559
$658$	2.00334e13	+	1.26473e13i	0.162414	+	0.102534i
$659$	−1.00559e14			−0.809082			−0.404541	−	0.914520i	$-0.632569\pi$
$659$	−1.00559e14			−0.809082			−0.404541	+	0.914520i	$0.632569\pi$
$660$	5.21314e13	−	2.48327e13i	0.416274	−	0.198291i
$661$			2.07976e14i			1.64819i	0.566454	+	0.824094i	$0.308315\pi$
$661$			2.07976e14i			1.64819i	−0.566454	+	0.824094i	$0.691685\pi$
$662$	1.82048e14	+	1.14929e14i	1.43185	+	0.903940i
$663$		−	1.16470e14i		−	0.909175i
$664$	−8.55257e12	+	7.17880e13i	−0.0662607	+	0.556175i
$665$	1.16707e14			0.897406
$666$	3.71098e13	−	5.87822e13i	0.283216	−	0.448616i
$667$	−1.01079e14			−0.765653
$668$	5.56728e13	−	2.65196e13i	0.418563	−	0.199381i
$669$		−	2.45973e13i		−	0.183551i
$670$	1.32153e13	−	2.09332e13i	0.0978824	−	0.155046i
$671$		−	4.25915e12i		−	0.0313119i
$672$	−5.55684e13	−	1.64390e14i	−0.405491	−	1.19958i
$673$	−1.30742e14			−0.946977			−0.473488	−	0.880800i	$-0.657005\pi$
$673$	−1.30742e14			−0.946977			−0.473488	+	0.880800i	$0.657005\pi$
$674$	−1.46830e14	−	9.26956e13i	−1.05564	−	0.666438i
$675$	−8.42925e13			−0.601547
$676$	1.99926e13	+	4.19707e13i	0.141624	+	0.297312i
$677$		−	1.03511e14i		−	0.727853i	−0.931428	−	0.363927i	$-0.881436\pi$
$677$		−	1.03511e14i		−	0.727853i	0.931428	−	0.363927i	$-0.118564\pi$
$678$	4.06137e13	+	2.56398e13i	0.283481	+	0.178965i
$679$			4.80622e13i			0.333008i
$680$	−1.27701e14	−	1.52138e13i	−0.878313	−	0.104639i
$681$	−2.07425e14			−1.41620
$682$	9.67920e13	−	1.53319e14i	0.656021	−	1.03914i
$683$	2.77817e14			1.86920			0.934600	−	0.355699i	$-0.115757\pi$
$683$	2.77817e14			1.86920			0.934600	+	0.355699i	$0.115757\pi$
$684$	1.69610e13	+	3.56064e13i	0.113285	+	0.237820i
$685$			1.67914e13i			0.111335i
$686$	3.40356e13	−	5.39126e13i	0.224034	−	0.354870i
$687$		−	8.15943e13i		−	0.533183i
$688$	−2.08717e13	+	2.57205e13i	−0.135399	+	0.166854i
$689$	1.54167e14			0.992879
$690$	−5.57528e13	−	3.51974e13i	−0.356469	−	0.225042i
$691$	−3.03259e14			−1.92497			−0.962483	−	0.271341i	$-0.912533\pi$
$691$	−3.03259e14			−1.92497			−0.962483	+	0.271341i	$0.912533\pi$
$692$	8.66625e12	−	4.12815e12i	0.0546136	−	0.0260151i
$693$			5.87407e13i			0.367513i
$694$	−1.42917e14	−	9.02250e13i	−0.887741	−	0.560441i
$695$			6.16573e13i			0.380242i
$696$	1.38580e14	+	1.65099e13i	0.848504	+	0.101088i
$697$	2.33686e14			1.42059
$698$	8.30763e12	−	1.31593e13i	0.0501418	−	0.0794249i
$699$	−5.10190e10			−0.000305736
$700$	1.26690e14	−	6.03483e13i	0.753791	−	0.359066i
$701$		−	1.61408e14i		−	0.953533i	−0.879030	−	0.476766i	$-0.841809\pi$
$701$		−	1.61408e14i		−	0.953533i	0.879030	−	0.476766i	$-0.158191\pi$
$702$	8.10480e13	−	1.28380e14i	0.475397	−	0.753032i
$703$			2.73608e14i			1.59350i
$704$	−1.38203e14	−	3.34042e13i	−0.799198	−	0.193169i
$705$	−1.24288e13			−0.0713649
$706$	1.01711e14	+	6.42111e13i	0.579887	+	0.366089i
$707$	−1.31173e14			−0.742588
$708$	1.47306e13	+	3.09240e13i	0.0828044	+	0.173832i
$709$		−	2.45219e14i		−	1.36874i	−0.729133	−	0.684372i	$-0.760076\pi$
$709$		−	2.45219e14i		−	1.36874i	0.729133	−	0.684372i	$-0.239924\pi$
$710$	1.81238e13	+	1.14417e13i	0.100452	+	0.0634162i
$711$			3.31288e13i			0.182330i
$712$	3.53805e13	−	2.96975e14i	0.193359	−	1.62300i
$713$	−2.07032e14			−1.12354
$714$	−1.65984e14	+	2.62920e14i	−0.894489	+	1.41688i
$715$	−8.41071e13			−0.450093
$716$	1.99962e13	+	4.19783e13i	0.106263	+	0.223079i
$717$			2.81418e14i			1.48510i
$718$	−7.07322e13	+	1.12040e14i	−0.370676	+	0.587153i
$719$		−	5.06378e13i		−	0.263530i	−0.991281	−	0.131765i	$-0.957936\pi$
$719$		−	5.06378e13i		−	0.263530i	0.991281	−	0.131765i	$-0.0420645\pi$
$720$	−2.97422e13	−	2.41352e13i	−0.153713	−	0.124735i
$721$	2.45665e14			1.26086
$722$	3.46384e13	+	2.18676e13i	0.176552	+	0.111459i
$723$	1.63249e14			0.826339
$724$	1.93488e14	−	9.21673e13i	0.972658	−	0.463323i
$725$			1.12859e14i			0.563440i
$726$	4.63540e13	+	2.92638e13i	0.229829	+	0.145093i
$727$		−	1.14938e14i		−	0.565968i	−0.959125	−	0.282984i	$-0.908676\pi$
$727$		−	1.14938e14i		−	0.565968i	0.959125	−	0.282984i	$-0.0913243\pi$
$728$	−2.99007e13	+	2.50978e14i	−0.146226	+	1.22738i
$729$	2.25403e14			1.09477
$730$	−9.63081e13	+	1.52553e14i	−0.464567	+	0.735877i
$731$	5.93514e13			0.284344
$732$	6.06202e12	−	2.88763e12i	0.0288444	−	0.0137400i
$733$		−	2.84996e14i		−	1.34685i	−0.739256	−	0.673425i	$-0.764823\pi$
$733$		−	2.84996e14i		−	1.34685i	0.739256	−	0.673425i	$-0.235177\pi$
$734$	−2.17602e14	+	3.44683e14i	−1.02137	+	1.61785i
$735$			1.53740e14i			0.716722i
$736$	5.19884e13	+	1.53799e14i	0.240723	+	0.712139i
$737$	−4.90411e13			−0.225540
$738$	5.88533e13	+	3.71547e13i	0.268837	+	0.169720i
$739$	−2.54337e14			−1.15395			−0.576976	−	0.816761i	$-0.695767\pi$
$739$	−2.54337e14			−1.15395			−0.576976	+	0.816761i	$0.695767\pi$
$740$	−1.14273e14	−	2.39895e14i	−0.514974	−	1.08109i
$741$			1.36532e14i			0.611145i
$742$	−3.48017e14	−	2.19707e14i	−1.54732	−	0.976842i
$743$		−	3.38292e14i		−	1.49399i	−0.664830	−	0.746995i	$-0.731496\pi$
$743$		−	3.38292e14i		−	1.49399i	0.664830	−	0.746995i	$-0.268504\pi$
$744$	2.83841e14	+	3.38159e13i	1.24512	+	0.148339i
$745$	−1.04362e14			−0.454739
$746$	3.37162e12	−	5.34066e12i	0.0145930	−	0.0231154i
$747$	3.85818e13			0.165874
$748$	1.09562e14	+	2.30003e14i	0.467897	+	0.982260i
$749$		−	4.15841e14i		−	1.76408i
$750$	−1.10341e14	+	1.74781e14i	−0.464976	+	0.736525i
$751$			3.25526e13i			0.136266i	0.997676	+	0.0681329i	$0.0217042\pi$
$751$			3.25526e13i			0.136266i	−0.997676	+	0.0681329i	$0.978296\pi$
$752$	2.37637e13	+	1.92838e13i	0.0988154	+	0.0801868i
$753$	9.90098e13			0.408981
$754$	−1.71889e14	−	1.08515e14i	−0.705329	−	0.445282i
$755$	6.05448e13			0.246798
$756$	−3.65915e14	+	1.74303e14i	−1.48174	+	0.705822i
$757$		−	1.45864e14i		−	0.586772i	−0.955994	−	0.293386i	$-0.905218\pi$
$757$		−	1.45864e14i		−	0.586772i	0.955994	−	0.293386i	$-0.0947821\pi$
$758$	1.10789e14	+	6.99425e13i	0.442743	+	0.279508i
$759$			1.30615e14i			0.518541i
$760$	1.49697e14	+	1.78344e13i	0.590400	+	0.0703382i
$761$	1.60409e14			0.628500			0.314250	−	0.949340i	$-0.398247\pi$
$761$	1.60409e14			0.628500			0.314250	+	0.949340i	$0.398247\pi$
$762$	1.85315e14	−	2.93539e14i	0.721331	−	1.14259i
$763$	2.04508e14			0.790839
$764$	8.55094e13	−	4.07322e13i	0.328509	−	0.156484i
$765$			6.86317e13i			0.261950i
$766$	8.14522e13	−	1.29021e14i	0.308858	−	0.489233i
$767$		−	4.98918e13i		−	0.187954i
$768$	−4.61553e13	−	2.19351e14i	−0.172749	−	0.820981i
$769$	2.82478e14			1.05040			0.525199	−	0.850980i	$-0.323991\pi$
$769$	2.82478e14			1.05040			0.525199	+	0.850980i	$0.323991\pi$
$770$	1.89863e14	+	1.19863e14i	0.701434	+	0.442823i
$771$	−1.10405e14			−0.405243
$772$	−1.27790e14	−	2.68270e14i	−0.466025	−	0.978330i
$773$			3.90458e14i			1.41474i	0.706843	+	0.707370i	$0.250119\pi$
$773$			3.90458e14i			1.41474i	−0.706843	+	0.707370i	$0.749881\pi$
$774$	1.49475e13	+	9.43651e12i	0.0538100	+	0.0339709i
$775$			2.31161e14i			0.826809i
$776$	−7.34456e12	+	6.16483e13i	−0.0261010	+	0.219085i
$777$	−6.42442e14			−2.26845
$778$	−1.59799e13	+	2.53123e13i	−0.0560630	+	0.0888041i
$779$	−2.73939e14			−0.954919
$780$	−5.70231e13	−	1.19709e14i	−0.197505	−	0.414624i
$781$		−	4.24594e13i		−	0.146123i
$782$	1.55290e14	−	2.45981e14i	0.531020	−	0.841139i
$783$		−	3.25970e14i		−	1.10756i
$784$	2.38534e14	−	2.93949e14i	0.805321	−	0.992410i
$785$	1.50217e12			0.00503930
$786$	9.17161e13	+	5.79014e13i	0.305726	+	0.193008i
$787$	−1.96267e14			−0.650089			−0.325045	−	0.945699i	$-0.605379\pi$
$787$	−1.96267e14			−0.650089			−0.325045	+	0.945699i	$0.605379\pi$
$788$	−4.97097e14	+	2.36791e14i	−1.63610	+	0.779353i
$789$		−	2.13872e13i		−	0.0699470i
$790$	1.07080e14	+	6.76006e13i	0.347994	+	0.219693i
$791$			1.86761e14i			0.603121i
$792$	−8.97638e12	+	7.53454e13i	−0.0288055	+	0.241786i
$793$	−9.78026e12			−0.0311878
$794$	1.94188e14	−	3.07595e14i	0.615348	−	0.974714i
$795$	2.15912e14			0.679893
$796$	−2.52065e14	+	1.20071e14i	−0.788766	+	0.375726i
$797$			4.02234e14i			1.25080i	0.780306	+	0.625398i	$0.215063\pi$
$797$			4.02234e14i			1.25080i	−0.780306	+	0.625398i	$0.784937\pi$
$798$	1.94575e14	−	3.08208e14i	0.601274	−	0.952421i
$799$		−	5.48359e13i		−	0.168396i
$800$	1.71724e14	−	5.80474e13i	0.524060	−	0.177147i
$801$	−1.59606e14			−0.484047
$802$	1.78776e14	+	1.12863e14i	0.538813	+	0.340159i
$803$	3.57392e14			1.07045
$804$	−3.32490e13	−	6.97999e13i	−0.0989688	−	0.207766i
$805$		−	2.56378e14i		−	0.758406i
$806$	−3.52066e14	−	2.22263e14i	−1.03502	−	0.653419i
$807$			2.92941e14i			0.855879i
$808$	−1.68253e14	−	2.00450e13i	−0.488546	−	0.0582036i
$809$	−2.08977e14			−0.603053			−0.301527	−	0.953458i	$-0.597496\pi$
$809$	−2.08977e14			−0.603053			−0.301527	+	0.953458i	$0.597496\pi$
$810$	7.66613e13	−	1.21432e14i	0.219862	−	0.348263i
$811$	2.46451e14			0.702468			0.351234	−	0.936288i	$-0.385762\pi$
$811$	2.46451e14			0.702468			0.351234	+	0.936288i	$0.385762\pi$
$812$	2.33375e14	+	4.89925e14i	0.661109	+	1.38787i
$813$			2.47113e14i			0.695732i
$814$	−2.81006e14	+	4.45115e14i	−0.786309	+	1.24552i
$815$			3.01538e14i			0.838598i
$816$	−2.53082e14	+	3.11876e14i	−0.699536	+	0.862049i
$817$	−6.95747e13			−0.191135
$818$	8.84163e13	+	5.58182e13i	0.241416	+	0.152409i
$819$	1.34886e14			0.366056
$820$	2.40185e14	−	1.14411e14i	0.647853	−	0.308603i
$821$			4.81499e14i			1.29086i	0.763819	+	0.645431i	$0.223322\pi$
$821$			4.81499e14i			1.29086i	−0.763819	+	0.645431i	$0.776678\pi$
$822$	4.43437e13	+	2.79947e13i	0.118161	+	0.0745961i
$823$		−	4.66519e14i		−	1.23558i	−0.786344	−	0.617789i	$-0.788029\pi$
$823$		−	4.66519e14i		−	1.23558i	0.786344	−	0.617789i	$-0.211971\pi$
$824$	3.15110e14	+	3.75410e13i	0.829517	+	0.0988258i
$825$	1.45837e14			0.381592
$826$	−7.11018e13	+	1.12626e14i	−0.184918	+	0.292912i
$827$	2.28021e14			0.589450			0.294725	−	0.955582i	$-0.404772\pi$
$827$	2.28021e14			0.589450			0.294725	+	0.955582i	$0.404772\pi$
$828$	7.82190e13	−	3.72594e13i	0.200984	−	0.0957380i
$829$			4.42704e14i			1.13068i	0.824857	+	0.565342i	$0.191256\pi$
$829$			4.42704e14i			1.13068i	−0.824857	+	0.565342i	$0.808744\pi$
$830$	7.87276e13	−	1.24705e14i	0.199865	−	0.316587i
$831$		−	5.85358e14i		−	1.47712i
$832$	−7.67058e13	+	3.17355e14i	−0.192403	+	0.796028i
$833$	−6.78301e14			−1.69121
$834$	1.62829e14	+	1.02795e14i	0.403553	+	0.254767i
$835$	−1.25794e14			−0.309905
$836$	−1.28434e14	−	2.69622e14i	−0.314519	−	0.660273i
$837$		−	6.67657e14i		−	1.62527i
$838$	5.57533e13	+	3.51977e13i	0.134912	+	0.0851715i
$839$		−	2.87447e14i		−	0.691429i	−0.938340	−	0.345715i	$-0.887637\pi$
$839$		−	2.87447e14i		−	0.691429i	0.938340	−	0.345715i	$-0.112363\pi$
$840$	−4.18760e13	+	3.51496e14i	−0.100131	+	0.840473i
$841$	−1.57350e13			−0.0374014
$842$	9.96864e13	−	1.57904e14i	0.235546	−	0.373106i
$843$	−2.59310e14			−0.609090
$844$	−2.88814e14	−	6.06311e14i	−0.674383	−	1.41574i
$845$		−	9.48337e13i		−	0.220130i
$846$	8.71858e12	−	1.38103e13i	0.0201184	−	0.0318677i
$847$			2.13158e14i			0.488973i
$848$	−4.12819e14	−	3.34995e14i	−0.941414	−	0.763939i
$849$	4.99796e14			1.13306
$850$	−2.74649e14	−	1.73389e14i	−0.618990	−	0.390775i
$851$	6.01053e14			1.34668
$852$	6.04321e13	−	2.87867e13i	0.134608	−	0.0641200i
$853$		−	3.23468e14i		−	0.716286i	−0.933667	−	0.358143i	$-0.883410\pi$
$853$		−	3.23468e14i		−	0.716286i	0.933667	−	0.358143i	$-0.116590\pi$
$854$	2.20779e13	+	1.39380e13i	0.0486037	+	0.0306840i
$855$		−	8.04536e13i		−	0.176082i
$856$	6.35461e13	−	5.33389e14i	0.138268	−	1.16058i
$857$	5.02722e14			1.08749			0.543743	−	0.839252i	$-0.317007\pi$
$857$	5.02722e14			1.08749			0.543743	+	0.839252i	$0.317007\pi$
$858$	−1.40224e14	+	2.22115e14i	−0.301568	+	0.477686i
$859$	−6.31840e14			−1.35096			−0.675478	−	0.737380i	$-0.736063\pi$
$859$	−6.31840e14			−1.35096			−0.675478	+	0.737380i	$0.736063\pi$
$860$	6.10018e13	−	2.90581e13i	0.129673	−	0.0617695i
$861$		−	6.43220e14i		−	1.35939i
$862$	−3.16868e14	+	5.01920e14i	−0.665796	+	1.05463i
$863$		−	1.69445e14i		−	0.353976i	−0.984213	−	0.176988i	$-0.943365\pi$
$863$		−	1.69445e14i		−	0.353976i	0.984213	−	0.176988i	$-0.0566353\pi$
$864$	−4.95987e14	+	1.67657e14i	−1.03015	+	0.348220i
$865$	−1.95816e13			−0.0404360
$866$	1.24668e13	+	7.87043e12i	0.0255956	+	0.0161588i
$867$	3.08676e14			0.630096
$868$	4.78001e14	+	1.00347e15i	0.970131	+	2.03660i
$869$		−	2.50861e14i		−	0.506214i
$870$	−2.40731e14	−	1.51976e14i	−0.482988	−	0.304915i
$871$			1.12613e14i			0.224645i
$872$	2.62318e14	+	3.12517e13i	0.520291	+	0.0619856i
$873$	3.31323e13			0.0653402
$874$	−1.82039e14	+	2.88351e14i	−0.356951	+	0.565412i
$875$	−8.03726e14			−1.56700
$876$	2.42305e14	+	5.08673e14i	0.469724	+	0.986095i
$877$			7.57672e13i			0.146044i	0.997330	+	0.0730219i	$0.0232643\pi$
$877$			7.57672e13i			0.146044i	−0.997330	+	0.0730219i	$0.976736\pi$
$878$	3.63274e14	−	5.75428e14i	0.696245	−	1.10286i
$879$			5.33414e14i			1.01653i
$880$	2.25216e14	+	1.82759e14i	0.426763	+	0.346310i
$881$	−3.19549e14			−0.602085			−0.301042	−	0.953611i	$-0.597335\pi$
$881$	−3.19549e14			−0.602085			−0.301042	+	0.953611i	$0.597335\pi$
$882$	−1.70828e14	−	1.07846e14i	−0.320049	−	0.202051i
$883$	4.13607e14			0.770522			0.385261	−	0.922808i	$-0.374112\pi$
$883$	4.13607e14			0.770522			0.385261	+	0.922808i	$0.374112\pi$
$884$	5.28156e14	−	2.51586e14i	0.978364	−	0.466041i
$885$		−	6.98736e13i		−	0.128705i
$886$	8.73490e14	+	5.51444e14i	1.59989	+	1.01003i
$887$			7.76606e14i			1.41443i	0.706997	+	0.707217i	$0.250050\pi$
$887$			7.76606e14i			1.41443i	−0.706997	+	0.707217i	$0.749950\pi$
$888$	−8.24046e14	−	9.81740e13i	−1.49241	−	0.177800i
$889$	1.34984e15			2.43093
$890$	−3.25683e14	+	5.15884e14i	−0.583237	+	0.923851i
$891$	−2.84484e14			−0.506605
$892$	1.11541e14	−	5.31322e13i	0.197520	−	0.0940879i
$893$			6.42814e13i			0.113195i
$894$	−1.73994e14	+	2.75607e14i	−0.304681	+	0.482617i
$895$		−	9.48509e13i		−	0.165168i
$896$	6.25424e14	−	6.07081e14i	1.08302	−	1.05125i
$897$	2.99930e14			0.516484
$898$	−6.10673e14	−	3.85524e14i	−1.04575	−	0.660192i
$899$	−8.93928e14			−1.52231
$900$	−4.16019e13	−	8.73352e13i	−0.0704531	−	0.147903i
$901$			9.52601e14i			1.60431i
$902$	−4.45653e14	−	2.81346e14i	−0.746388	−	0.471203i
$903$		−	1.63364e14i		−	0.272093i
$904$	−2.85397e13	+	2.39554e14i	−0.0472723	+	0.396791i
$905$	−4.37190e14			−0.720157
$906$	1.00941e14	−	1.59891e14i	0.165358	−	0.261928i
$907$	−2.38403e14			−0.388396			−0.194198	−	0.980962i	$-0.562210\pi$
$907$	−2.38403e14			−0.388396			−0.194198	+	0.980962i	$0.562210\pi$
$908$	−4.48056e14	−	9.40607e14i	−0.725944	−	1.52398i
$909$			9.04259e13i			0.145705i
$910$	2.75240e14	−	4.35982e14i	0.441067	−	0.698653i
$911$			1.97185e14i			0.314255i	0.987578	+	0.157128i	$0.0502234\pi$
$911$			1.97185e14i			0.314255i	−0.987578	+	0.157128i	$0.949777\pi$
$912$	2.96675e14	−	3.65597e14i	0.470226	−	0.579467i
$913$	−2.92152e14			−0.460527
$914$	−2.87791e14	−	1.81686e14i	−0.451176	−	0.284833i
$915$	−1.36973e13			−0.0213564
$916$	3.70004e14	−	1.76251e14i	0.573759	−	0.273309i
$917$			4.21755e14i			0.650449i
$918$	7.93264e14	+	5.00796e14i	1.21676	+	0.768153i
$919$			6.18802e14i			0.944005i	0.881597	+	0.472003i	$0.156469\pi$
$919$			6.18802e14i			0.944005i	−0.881597	+	0.472003i	$0.843531\pi$
$920$	3.91781e13	−	3.28851e14i	0.0594435	−	0.498953i
$921$	−8.44717e13			−0.127471
$922$	−1.97222e14	+	3.12401e14i	−0.296006	+	0.468875i
$923$	−9.74992e13			−0.145543
$924$	6.33082e14	−	3.01567e14i	0.939941	−	0.447738i
$925$		−	6.71104e14i		−	0.991017i
$926$	−3.80978e13	+	6.03472e13i	−0.0559558	+	0.0886344i
$927$		−	1.69353e14i		−	0.247397i
$928$	2.24477e14	+	6.64079e14i	0.326161	+	0.964894i
$929$	−3.05402e14			−0.441360			−0.220680	−	0.975346i	$-0.570828\pi$
$929$	−3.05402e14			−0.441360			−0.220680	+	0.975346i	$0.570828\pi$
$930$	−4.93069e14	−	3.11280e14i	−0.708750	−	0.447442i
$931$	7.95139e14			1.13683
$932$	−1.10205e11	−	2.31355e11i	−0.000156719	−	0.000329003i
$933$			3.53226e14i			0.499626i
$934$	−1.80737e14	−	1.14101e14i	−0.254280	−	0.160530i
$935$		−	5.19698e14i		−	0.727266i
$936$	1.73015e14	+	2.06124e13i	0.240827	+	0.0286913i
$937$	−1.24962e15			−1.73013			−0.865066	−	0.501658i	$-0.832724\pi$
$937$	−1.24962e15			−1.73013			−0.865066	+	0.501658i	$0.832724\pi$
$938$	1.60487e14	−	2.54212e14i	0.221017	−	0.350092i
$939$	−1.11022e14			−0.152083
$940$	−2.68473e13	−	5.63608e13i	−0.0365815	−	0.0767959i
$941$		−	8.67444e14i		−	1.17569i	−0.808973	−	0.587846i	$-0.799976\pi$
$941$		−	8.67444e14i		−	1.17569i	0.808973	−	0.587846i	$-0.200024\pi$
$942$	2.50443e12	−	3.96703e12i	0.00337640	−	0.00534824i
$943$			6.01780e14i			0.807011i
$944$	−1.08411e14	+	1.33597e14i	−0.144616	+	0.178212i
$945$	8.26794e14			1.09708
$946$	−1.13187e14	−	7.14559e13i	−0.149396	−	0.0943153i
$947$	1.24423e15			1.63362			0.816812	−	0.576904i	$-0.195739\pi$
$947$	1.24423e15			1.63362			0.816812	+	0.576904i	$0.195739\pi$
$948$	3.57048e14	−	1.70079e14i	0.466322	−	0.222131i
$949$		−	8.20677e14i		−	1.06621i
$950$	3.21958e14	+	2.03255e14i	0.416084	+	0.262678i
$951$		−	1.06786e15i		−	1.37281i
$952$	−1.55080e15	−	1.84756e14i	−1.98322	−	0.236273i
$953$	1.19147e15			1.51572			0.757860	−	0.652417i	$-0.226245\pi$
$953$	1.19147e15			1.51572			0.757860	+	0.652417i	$0.226245\pi$
$954$	−1.51458e14	+	2.39910e14i	−0.191668	+	0.303604i
$955$	−1.93211e14			−0.243228
$956$	−1.27614e15	+	6.07887e14i	−1.59812	+	0.761261i
$957$			5.63972e14i			0.702583i
$958$	5.56541e14	−	8.81563e14i	0.689714	−	1.09251i
$959$			2.03914e14i			0.251393i
$960$	−1.07427e14	+	4.44456e14i	−0.131752	+	0.545096i
$961$	−1.01133e15			−1.23389
$962$	1.02212e15	+	6.45272e14i	1.24058	+	0.783191i
$963$	−2.86665e14			−0.346134
$964$	3.52631e14	+	7.40281e14i	0.423580	+	0.889225i
$965$			6.06163e14i			0.724357i
$966$	−6.77061e14	−	4.27436e14i	−0.804900	−	0.508142i
$967$		−	1.37316e15i		−	1.62401i	−0.583652	−	0.812004i	$-0.698377\pi$
$967$		−	1.37316e15i		−	1.62401i	0.583652	−	0.812004i	$-0.301623\pi$
$968$	−3.25735e13	+	2.73413e14i	−0.0383255	+	0.321694i
$969$	−8.43634e14			−0.987496
$970$	6.76077e13	−	1.07091e14i	0.0787295	−	0.124708i
$971$	−7.44459e14			−0.862471			−0.431235	−	0.902239i	$-0.641922\pi$
$971$	−7.44459e14			−0.862471			−0.431235	+	0.902239i	$0.641922\pi$
$972$	2.12862e14	+	4.46862e14i	0.245339	+	0.515042i
$973$			7.48765e14i			0.858581i
$974$	−5.94038e14	+	9.40960e14i	−0.677672	+	1.07344i
$975$		−	3.34885e14i		−	0.380078i
$976$	2.61889e13	+	2.12518e13i	0.0295712	+	0.0239964i
$977$	8.44024e14			0.948161			0.474081	−	0.880482i	$-0.342781\pi$
$977$	8.44024e14			0.948161			0.474081	+	0.880482i	$0.342781\pi$
$978$	7.96321e14	+	5.02726e14i	0.890008	+	0.561872i
$979$	1.20858e15			1.34389
$980$	−6.97164e14	+	3.32092e14i	−0.771266	+	0.367391i
$981$		−	1.40981e14i		−	0.155172i
$982$	1.33845e14	+	8.44976e13i	0.146569	+	0.0925309i
$983$			6.75786e14i			0.736277i	0.929771	+	0.368139i	$0.120005\pi$
$983$			6.75786e14i			0.736277i	−0.929771	+	0.368139i	$0.879995\pi$
$984$	9.82927e13	−	8.25043e14i	0.106548	−	0.894337i
$985$	1.12320e15			1.21137
$986$	6.70518e14	−	1.06210e15i	0.719492	−	1.13968i
$987$	−1.50935e14			−0.161141
$988$	−6.19131e14	+	2.94921e14i	−0.657654	+	0.313272i
$989$			1.52839e14i			0.161530i
$990$	8.26289e13	−	1.30885e14i	0.0868873	−	0.137630i
$991$		−	5.73477e14i		−	0.599995i	−0.953940	−	0.299998i	$-0.903014\pi$
$991$		−	5.73477e14i		−	0.599995i	0.953940	−	0.299998i	$-0.0969859\pi$
$992$	4.59777e14	+	1.36018e15i	0.478618	+	1.41591i
$993$	−1.37159e15			−1.42062
$994$	2.20094e14	+	1.38948e14i	0.226818	+	0.143193i
$995$	5.69548e14			0.584003
$996$	−1.98074e14	−	4.15818e14i	−0.202083	−	0.424235i
$997$		−	4.15346e14i		−	0.421633i	−0.977526	−	0.210816i	$-0.932388\pi$
$997$		−	4.15346e14i		−	0.421633i	0.977526	−	0.210816i	$-0.0676122\pi$
$998$	−1.71493e14	−	1.08266e14i	−0.173219	−	0.109355i
$999$			1.93834e15i			1.94806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.11.d.b.3.1	✓	8
3.2	odd	2		72.11.b.b.19.8		8
4.3	odd	2		32.11.d.b.15.3		8
8.3	odd	2	inner	8.11.d.b.3.2	yes	8
8.5	even	2		32.11.d.b.15.4		8
12.11	even	2		288.11.b.b.271.6		8
16.3	odd	4		256.11.c.m.255.3		16
16.5	even	4		256.11.c.m.255.4		16
16.11	odd	4		256.11.c.m.255.14		16
16.13	even	4		256.11.c.m.255.13		16
24.5	odd	2		288.11.b.b.271.3		8
24.11	even	2		72.11.b.b.19.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.11.d.b.3.1	✓	8	1.1	even	1	trivial
8.11.d.b.3.2	yes	8	8.3	odd	2	inner
32.11.d.b.15.3		8	4.3	odd	2
32.11.d.b.15.4		8	8.5	even	2
72.11.b.b.19.7		8	24.11	even	2
72.11.b.b.19.8		8	3.2	odd	2
256.11.c.m.255.3		16	16.3	odd	4
256.11.c.m.255.4		16	16.5	even	4
256.11.c.m.255.13		16	16.13	even	4
256.11.c.m.255.14		16	16.11	odd	4
288.11.b.b.271.3		8	24.5	odd	2
288.11.b.b.271.6		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)

\(f(q)\)	\(=\)	\(q+(-27.0589 - 17.0826i) q^{2} +203.867 q^{3} +(440.370 + 924.473i) q^{4} -2088.87i q^{5} +(-5516.42 - 3482.58i) q^{6} -25367.2i q^{7} +(3876.45 - 32537.9i) q^{8} -17487.2 q^{9} +O(q^{10})\)	\(q+(-27.0589 - 17.0826i) q^{2} +203.867 q^{3} +(440.370 + 924.473i) q^{4} -2088.87i q^{5} +(-5516.42 - 3482.58i) q^{6} -25367.2i q^{7} +(3876.45 - 32537.9i) q^{8} -17487.2 q^{9} +(-35683.3 + 56522.5i) q^{10} +132418. q^{11} +(89777.0 + 188470. i) q^{12} -304071. i q^{13} +(-433337. + 686408. i) q^{14} -425852. i q^{15} +(-660724. + 814221. i) q^{16} +1.87886e6 q^{17} +(473185. + 298727. i) q^{18} -2.20249e6 q^{19} +(1.93110e6 - 919876. i) q^{20} -5.17153e6i q^{21} +(-3.58309e6 - 2.26204e6i) q^{22} +4.83836e6i q^{23} +(790281. - 6.63341e6i) q^{24} +5.40225e6 q^{25} +(-5.19431e6 + 8.22782e6i) q^{26} -1.56032e7 q^{27} +(2.34513e7 - 1.11709e7i) q^{28} +2.08912e7i q^{29} +(-7.27465e6 + 1.15231e7i) q^{30} +4.27897e7i q^{31} +(3.17875e7 - 1.07450e7i) q^{32} +2.69957e7 q^{33} +(-5.08398e7 - 3.20957e7i) q^{34} -5.29887e7 q^{35} +(-7.70084e6 - 1.61664e7i) q^{36} -1.24227e8i q^{37} +(5.95970e7 + 3.76242e7i) q^{38} -6.19900e7i q^{39} +(-6.79674e7 - 8.09740e6i) q^{40} +1.24377e8 q^{41} +(-8.83432e7 + 1.39936e8i) q^{42} +3.15891e7 q^{43} +(5.83129e7 + 1.22417e8i) q^{44} +3.65285e7i q^{45} +(8.26517e7 - 1.30921e8i) q^{46} -2.91858e7i q^{47} +(-1.34700e8 + 1.65993e8i) q^{48} -3.61018e8 q^{49} +(-1.46179e8 - 9.22844e7i) q^{50} +3.83037e8 q^{51} +(2.81105e8 - 1.33904e8i) q^{52} +5.07012e8i q^{53} +(4.22206e8 + 2.66543e8i) q^{54} -2.76604e8i q^{55} +(-8.25395e8 - 9.83346e7i) q^{56} -4.49015e8 q^{57} +(3.56876e8 - 5.65293e8i) q^{58} +1.64080e8 q^{59} +(3.93688e8 - 1.87532e8i) q^{60} -3.21644e7i q^{61} +(7.30959e8 - 1.15784e9i) q^{62} +4.43601e8i q^{63} +(-1.04369e9 - 2.52263e8i) q^{64} -6.35164e8 q^{65} +(-7.30473e8 - 4.61156e8i) q^{66} -3.70351e8 q^{67} +(8.27392e8 + 1.73695e9i) q^{68} +9.86382e8i q^{69} +(1.43382e9 + 9.05184e8i) q^{70} -3.20647e8i q^{71} +(-6.77883e7 + 5.68997e8i) q^{72} +2.69897e9 q^{73} +(-2.12211e9 + 3.36144e9i) q^{74} +1.10134e9 q^{75} +(-9.69910e8 - 2.03614e9i) q^{76} -3.35907e9i q^{77} +(-1.05895e9 + 1.67738e9i) q^{78} -1.89446e9i q^{79} +(1.70080e9 + 1.38017e9i) q^{80} -2.14838e9 q^{81} +(-3.36551e9 - 2.12468e9i) q^{82} -2.20629e9 q^{83} +(4.78094e9 - 2.27739e9i) q^{84} -3.92468e9i q^{85} +(-8.54767e8 - 5.39624e8i) q^{86} +4.25903e9i q^{87} +(5.13312e8 - 4.30860e9i) q^{88} +9.12704e9 q^{89} +(6.24001e8 - 9.88421e8i) q^{90} -7.71341e9 q^{91} +(-4.47293e9 + 2.13067e9i) q^{92} +8.72341e9i q^{93} +(-4.98569e8 + 7.89736e8i) q^{94} +4.60071e9i q^{95} +(6.48042e9 - 2.19056e9i) q^{96} -1.89466e9 q^{97} +(9.76876e9 + 6.16713e9i) q^{98} -2.31562e9 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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