LMFDB - Embedded newform 62.8.g.b.19.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,144] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	62.19
Dual form			62.8.g.b.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.47214 + 4.70228i) q^{2} +(-59.9156 - 26.6762i) q^{3} +(19.7771 + 60.8676i) q^{4} +(85.4015 - 147.920i) q^{5} +(-262.343 - 454.392i) q^{6} +(-1205.22 + 1338.54i) q^{7} +(-158.217 + 486.941i) q^{8} +(1414.88 + 1571.38i) q^{9} +(1248.29 - 555.775i) q^{10} +(4637.29 + 985.686i) q^{11} +(438.757 - 4174.50i) q^{12} +(-1579.62 - 15029.1i) q^{13} +(-14094.5 + 2995.89i) q^{14} +(-9062.81 + 6584.52i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(25388.9 - 5396.58i) q^{17} +(1768.20 + 16823.3i) q^{18} +(109.080 - 1037.83i) q^{19} +(10692.5 + 2272.76i) q^{20} +(107919. - 48048.5i) q^{21} +(25378.2 + 28185.3i) q^{22} +(17173.3 - 52853.9i) q^{23} +(22469.4 - 24954.8i) q^{24} +(24475.7 + 42393.1i) q^{25} +(60447.6 - 104698. i) q^{26} +(1469.38 + 4522.28i) q^{27} +(-105309. - 46886.7i) q^{28} +(154790. + 112461. i) q^{29} -89618.0 q^{30} +(111011. - 123244. i) q^{31} -32768.0 q^{32} +(-251552. - 182763. i) q^{33} +(189697. + 84458.4i) q^{34} +(95068.0 + 292589. i) q^{35} +(-67664.0 + 117197. i) q^{36} +(-132441. - 229394. i) q^{37} +(5586.13 - 6204.03i) q^{38} +(-306275. + 942618. i) q^{39} +(58516.2 + 64988.8i) q^{40} +(79220.3 - 35271.2i) q^{41} +(924402. + 196488. i) q^{42} +(48827.1 - 464559. i) q^{43} +(31715.7 + 301755. i) q^{44} +(353271. - 75090.0i) q^{45} +(359682. - 261324. i) q^{46} +(-479882. + 348654. i) q^{47} +(262769. - 55853.3i) q^{48} +(-253032. - 2.40743e6i) q^{49} +(-40934.5 + 389465. i) q^{50} +(-1.66515e6 - 353939. i) q^{51} +(883547. - 393380. i) q^{52} +(146348. + 162536. i) q^{53} +(-11755.0 + 36178.3i) q^{54} +(541834. - 601768. i) q^{55} +(-461101. - 798651. i) q^{56} +(-34220.8 + 59272.2i) q^{57} +(472995. + 1.45573e6i) q^{58} +(2.52494e6 + 1.12418e6i) q^{59} +(-580020. - 421409. i) q^{60} +631782. q^{61} +(1.29801e6 - 275648. i) q^{62} -3.80859e6 q^{63} +(-212079. - 154084. i) q^{64} +(-2.35801e6 - 1.04985e6i) q^{65} +(-768674. - 2.36574e6i) q^{66} +(-1.27867e6 + 2.21473e6i) q^{67} +(830595. + 1.43863e6i) q^{68} +(-2.43889e6 + 2.70866e6i) q^{69} +(-760544. + 2.34071e6i) q^{70} +(1.20904e6 + 1.34278e6i) q^{71} +(-989026. + 440343. i) q^{72} +(1.27060e6 + 270075. i) q^{73} +(221501. - 2.10744e6i) q^{74} +(-335590. - 3.19293e6i) q^{75} +(65327.3 - 13885.7i) q^{76} +(-6.90834e6 + 5.01921e6i) q^{77} +(-6.41471e6 + 4.66056e6i) q^{78} +(-5.11989e6 + 1.08827e6i) q^{79} +(73129.0 + 695776. i) q^{80} +(515981. - 4.90923e6i) q^{81} +(678580. + 144237. i) q^{82} +(1.35670e6 - 604041. i) q^{83} +(5.05891e6 + 5.61849e6i) q^{84} +(1.36999e6 - 4.21639e6i) q^{85} +(2.50050e6 - 2.77709e6i) q^{86} +(-6.27428e6 - 1.08674e7i) q^{87} +(-1.21367e6 + 2.10213e6i) q^{88} +(-678491. - 2.08818e6i) q^{89} +(2.63951e6 + 1.17519e6i) q^{90} +(2.20208e7 + 1.59991e7i) q^{91} +3.55673e6 q^{92} +(-9.93898e6 + 4.42291e6i) q^{93} -4.74533e6 q^{94} +(-144199. - 104767. i) q^{95} +(1.96332e6 + 874124. i) q^{96} +(-3.17944e6 - 9.78533e6i) q^{97} +(9.68278e6 - 1.67711e7i) q^{98} +(5.01230e6 + 8.68157e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) $ 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	6.47214	+	4.70228i	0.572061	+	0.415627i
$2$	6.47214	+	4.70228i	0.572061	+	0.415627i
$3$	−59.9156	−	26.6762i	−1.28120	−	0.570425i	−0.350618	−	0.936519i	$-0.614028\pi$
$3$	−59.9156	−	26.6762i	−1.28120	−	0.570425i	−0.930578	+	0.366093i	$0.880695\pi$
$4$	19.7771	+	60.8676i	0.154508	+	0.475528i
$5$	85.4015	−	147.920i	0.305542	−	0.529214i	−0.671840	−	0.740696i	$-0.734496\pi$
$5$	85.4015	−	147.920i	0.305542	−	0.529214i	0.977382	+	0.211483i	$0.0678291\pi$
$6$	−262.343	−	454.392i	−0.495839	−	0.858818i
$7$	−1205.22	+	1338.54i	−1.32808	+	1.47498i	−0.572545	+	0.819873i	$0.694044\pi$
$7$	−1205.22	+	1338.54i	−1.32808	+	1.47498i	−0.755535	+	0.655109i	$0.772623\pi$
$8$	−158.217	+	486.941i	−0.109254	+	0.336249i
$9$	1414.88	+	1571.38i	0.646948	+	0.718509i
$10$	1248.29	−	555.775i	0.394744	−	0.175751i
$11$	4637.29	+	985.686i	1.05049	+	0.223287i	0.700636	−	0.713519i	$-0.252900\pi$
$11$	4637.29	+	985.686i	1.05049	+	0.223287i	0.349849	+	0.936806i	$0.386233\pi$
$12$	438.757	−	4174.50i	0.0732977	−	0.697381i
$13$	−1579.62	−	15029.1i	−0.199412	−	1.89728i	−0.398293	−	0.917258i	$-0.630397\pi$
$13$	−1579.62	−	15029.1i	−0.199412	−	1.89728i	0.198880	−	0.980024i	$-0.436269\pi$
$14$	−14094.5	+	2995.89i	−1.37279	+	0.291795i
$15$	−9062.81	+	6584.52i	−0.693336	+	0.503738i
$16$	−3313.73	+	2407.57i	−0.202254	+	0.146946i
$17$	25388.9	−	5396.58i	1.25335	−	0.266408i	0.467038	−	0.884237i	$-0.345321\pi$
$17$	25388.9	−	5396.58i	1.25335	−	0.266408i	0.786312	+	0.617829i	$0.211988\pi$
$18$	1768.20	+	16823.3i	0.0714625	+	0.679921i
$19$	109.080	−	1037.83i	0.00364844	−	0.0347126i	−0.992546	−	0.121869i	$-0.961111\pi$
$19$	109.080	−	1037.83i	0.00364844	−	0.0347126i	0.996195	+	0.0871562i	$0.0277779\pi$
$20$	10692.5	+	2272.76i	0.298865	+	0.0635257i
$21$	107919.	−	48048.5i	2.54290	−	1.13217i
$22$	25378.2	+	28185.3i	0.508138	+	0.564344i
$23$	17173.3	−	52853.9i	0.294311	−	0.905795i	−0.689142	−	0.724627i	$-0.742012\pi$
$23$	17173.3	−	52853.9i	0.294311	−	0.905795i	0.983452	−	0.181168i	$-0.0579878\pi$
$24$	22469.4	−	24954.8i	0.331781	−	0.368480i
$25$	24475.7	+	42393.1i	0.313289	+	0.542632i
$26$	60447.6	−	104698.i	0.674485	−	1.16824i
$27$	1469.38	+	4522.28i	0.0143668	+	0.0442165i
$28$	−105309.	−	46886.7i	−0.906595	−	0.403642i
$29$	154790.	+	112461.i	1.17855	+	0.856268i	0.992008	−	0.126179i	$-0.0402713\pi$
$29$	154790.	+	112461.i	1.17855	+	0.856268i	0.186544	+	0.982447i	$0.440271\pi$
$30$	−89618.0			−0.605998
$31$	111011.	−	123244.i	0.669268	−	0.743021i
$31$	111011.	−	123244.i	0.669268	−	0.743021i
$32$	−32768.0			−0.176777
$33$	−251552.	−	182763.i	−1.21851	−	0.885298i
$34$	189697.	+	84458.4i	0.827720	+	0.368525i
$35$	95068.0	+	292589.i	0.374797	+	1.15351i
$36$	−67664.0	+	117197.i	−0.241712	+	0.418658i
$37$	−132441.	−	229394.i	−0.429849	−	0.744520i	0.567011	−	0.823710i	$-0.308100\pi$
$37$	−132441.	−	229394.i	−0.429849	−	0.744520i	−0.996860	+	0.0791904i	$0.974766\pi$
$38$	5586.13	−	6204.03i	0.0165146	−	0.0183413i
$39$	−306275.	+	942618.i	−0.826771	+	2.54454i
$40$	58516.2	+	64988.8i	0.144566	+	0.160557i
$41$	79220.3	−	35271.2i	0.179512	−	0.0799238i	−0.315013	−	0.949087i	$-0.602009\pi$
$41$	79220.3	−	35271.2i	0.179512	−	0.0799238i	0.494525	+	0.869164i	$0.335342\pi$
$42$	924402.	+	196488.i	1.92525	+	0.409226i
$43$	48827.1	−	464559.i	0.0936529	−	0.891048i	−0.842320	−	0.538977i	$-0.818811\pi$
$43$	48827.1	−	464559.i	0.0936529	−	0.891048i	0.935973	−	0.352071i	$-0.114522\pi$
$44$	31715.7	+	301755.i	0.0561294	+	0.534035i
$45$	353271.	−	75090.0i	0.577914	−	0.122840i
$46$	359682.	−	261324.i	0.544837	−	0.395847i
$47$	−479882.	+	348654.i	−0.674204	+	0.489838i	−0.871430	−	0.490520i	$-0.836807\pi$
$47$	−479882.	+	348654.i	−0.674204	+	0.489838i	0.197225	+	0.980358i	$0.436807\pi$
$48$	262769.	−	55853.3i	0.342949	−	0.0728961i
$49$	−253032.	−	2.40743e6i	−0.307248	−	2.92327i
$50$	−40934.5	+	389465.i	−0.0463121	+	0.440630i
$51$	−1.66515e6	−	353939.i	−1.75775	−	0.373622i
$52$	883547.	−	393380.i	0.871400	−	0.387972i
$53$	146348.	+	162536.i	0.135027	+	0.149963i	0.806866	−	0.590735i	$-0.201162\pi$
$53$	146348.	+	162536.i	0.135027	+	0.149963i	−0.671839	+	0.740697i	$0.734495\pi$
$54$	−11755.0	+	36178.3i	−0.0101589	+	0.0312658i
$55$	541834.	−	601768.i	0.439134	−	0.487707i
$56$	−461101.	−	798651.i	−0.350864	−	0.607714i
$57$	−34220.8	+	59272.2i	−0.0244753	+	0.0423925i
$58$	472995.	+	1.45573e6i	0.318316	+	0.979676i
$59$	2.52494e6	+	1.12418e6i	1.60055	+	0.712611i	0.996441	−	0.0842916i	$-0.0268627\pi$
$59$	2.52494e6	+	1.12418e6i	1.60055	+	0.712611i	0.604108	+	0.796902i	$0.293529\pi$
$60$	−580020.	−	421409.i	−0.346668	−	0.251869i
$61$	631782.			0.356379			0.178190	−	0.983996i	$-0.442976\pi$
$61$	631782.			0.356379			0.178190	+	0.983996i	$0.442976\pi$
$62$	1.29801e6	−	275648.i	0.691682	−	0.146887i
$63$	−3.80859e6			−1.91899
$64$	−212079.	−	154084.i	−0.101127	−	0.0734732i
$65$	−2.35801e6	−	1.04985e6i	−1.06500	−	0.474167i
$66$	−768674.	−	2.36574e6i	−0.329108	−	1.01289i
$67$	−1.27867e6	+	2.21473e6i	−0.519395	+	0.899619i	0.480351	+	0.877077i	$0.340509\pi$
$67$	−1.27867e6	+	2.21473e6i	−0.519395	+	0.899619i	−0.999746	+	0.0225424i	$0.992824\pi$
$68$	830595.	+	1.43863e6i	0.320338	+	0.554841i
$69$	−2.43889e6	+	2.70866e6i	−0.893758	+	0.992619i
$70$	−760544.	+	2.34071e6i	−0.265021	+	0.815652i
$71$	1.20904e6	+	1.34278e6i	0.400901	+	0.445245i	0.909466	−	0.415778i	$-0.136491\pi$
$71$	1.20904e6	+	1.34278e6i	0.400901	+	0.445245i	−0.508566	+	0.861023i	$0.669824\pi$
$72$	−989026.	+	440343.i	−0.312280	+	0.139036i
$73$	1.27060e6	+	270075.i	0.382278	+	0.0812557i	0.395043	−	0.918663i	$-0.370730\pi$
$73$	1.27060e6	+	270075.i	0.382278	+	0.0812557i	−0.0127644	+	0.999919i	$0.504063\pi$
$74$	221501.	−	2.10744e6i	0.0635427	−	0.604568i
$75$	−335590.	−	3.19293e6i	−0.0918533	−	0.873926i
$76$	65327.3	−	13885.7i	0.0170705	−	0.00362845i
$77$	−6.90834e6	+	5.01921e6i	−1.72447	+	1.25290i
$78$	−6.41471e6	+	4.66056e6i	−1.53054	+	1.11201i
$79$	−5.11989e6	+	1.08827e6i	−1.16833	+	0.248336i	−0.750927	−	0.660385i	$-0.770393\pi$
$79$	−5.11989e6	+	1.08827e6i	−1.16833	+	0.248336i	−0.417403	+	0.908721i	$0.637060\pi$
$80$	73129.0	+	695776.i	0.0159689	+	0.151934i
$81$	515981.	−	4.90923e6i	0.107879	−	1.02640i
$82$	678580.	+	144237.i	0.135910	+	0.0288886i
$83$	1.35670e6	−	604041.i	0.260441	−	0.115956i	−0.272363	−	0.962195i	$-0.587805\pi$
$83$	1.35670e6	−	604041.i	0.260441	−	0.115956i	0.532804	+	0.846239i	$0.321138\pi$
$84$	5.05891e6	+	5.61849e6i	0.931279	+	1.03429i
$85$	1.36999e6	−	4.21639e6i	0.241964	−	0.744689i
$86$	2.50050e6	−	2.77709e6i	0.423919	−	0.470810i
$87$	−6.27428e6	−	1.08674e7i	−1.02152	−	1.76932i
$88$	−1.21367e6	+	2.10213e6i	−0.189850	+	0.328830i
$89$	−678491.	−	2.08818e6i	−0.102019	−	0.313981i	0.887001	−	0.461768i	$-0.152785\pi$
$89$	−678491.	−	2.08818e6i	−0.102019	−	0.313981i	−0.989019	+	0.147788i	$0.952785\pi$
$90$	2.63951e6	+	1.17519e6i	0.381658	+	0.169925i
$91$	2.20208e7	+	1.59991e7i	3.06329	+	2.22561i
$92$	3.55673e6			0.476205
$93$	−9.93898e6	+	4.42291e6i	−1.28130	+	0.570188i
$94$	−4.74533e6			−0.589276
$95$	−144199.	−	104767.i	−0.0172556	−	0.0125369i
$96$	1.96332e6	+	874124.i	0.226486	+	0.100838i
$97$	−3.17944e6	−	9.78533e6i	−0.353712	−	1.08861i	−0.956752	−	0.290904i	$-0.906044\pi$
$97$	−3.17944e6	−	9.78533e6i	−0.353712	−	1.08861i	0.603040	−	0.797711i	$-0.293956\pi$
$98$	9.68278e6	−	1.67711e7i	1.03922	−	1.79999i
$99$	5.01230e6	+	8.68157e6i	0.519176	+	0.899239i
$100$	−2.09631e6	+	2.32819e6i	−0.209631	+	0.232819i
$101$	823310.	−	2.53389e6i	0.0795131	−	0.244716i	−0.903396	−	0.428807i	$-0.858934\pi$
$101$	823310.	−	2.53389e6i	0.0795131	−	0.244716i	0.982909	+	0.184091i	$0.0589341\pi$
$102$	−9.11277e6	−	1.01208e7i	−0.850256	−	0.944305i
$103$	1.27769e7	−	5.68863e6i	1.15211	−	0.512953i	0.260375	−	0.965508i	$-0.416154\pi$
$103$	1.27769e7	−	5.68863e6i	1.15211	−	0.512953i	0.891737	+	0.452555i	$0.149487\pi$
$104$	7.56822e6	+	1.60867e6i	0.659746	+	0.140233i
$105$	2.10910e6	−	2.00667e7i	0.177801	−	1.69166i
$106$	182894.	+	1.74012e6i	0.0149152	+	0.141909i
$107$	1.04513e7	−	2.22148e6i	0.824756	−	0.175307i	0.223846	−	0.974624i	$-0.428139\pi$
$107$	1.04513e7	−	2.22148e6i	0.824756	−	0.175307i	0.600909	+	0.799317i	$0.294805\pi$
$108$	−246201.	+	178875.i	−0.0188064	+	0.0136637i
$109$	−1.13494e7	+	8.24584e6i	−0.839424	+	0.609877i	−0.922210	−	0.386690i	$-0.873618\pi$
$109$	−1.13494e7	+	8.24584e6i	−0.839424	+	0.609877i	0.0827859	+	0.996567i	$0.473618\pi$
$110$	6.33650e6	−	1.34687e6i	0.453916	−	0.0964828i
$111$	1.81592e6	+	1.72773e7i	0.126028	+	1.19907i
$112$	771171.	−	7.33721e6i	0.0518666	−	0.493478i
$113$	1.21734e7	+	2.58754e6i	0.793667	+	0.168699i	0.586866	−	0.809684i	$-0.300361\pi$
$113$	1.21734e7	+	2.58754e6i	0.793667	+	0.168699i	0.206801	+	0.978383i	$0.433695\pi$
$114$	−500196.	+	222702.i	−0.0316208	+	0.0140785i
$115$	−6.35151e6	−	7.05407e6i	−0.389435	−	0.432511i
$116$	−3.78396e6	+	1.16458e7i	−0.225083	+	0.692735i
$117$	2.13815e7	−	2.37465e7i	1.23420	−	1.37072i
$118$	1.10556e7	+	1.91488e7i	0.619432	+	1.07289i
$119$	−2.33758e7	+	4.04880e7i	−1.27160	+	2.20248i
$120$	−1.77238e6	−	5.45484e6i	−0.0936318	−	0.288169i
$121$	2.73047e6	+	1.21568e6i	0.140116	+	0.0623837i
$122$	4.08898e6	+	2.97081e6i	0.203871	+	0.148121i
$123$	−5.68743e6			−0.275580
$124$	9.69706e6	+	4.31957e6i	0.456735	+	0.203453i
$125$	2.17050e7			0.993974
$126$	−2.46497e7	−	1.79091e7i	−1.09778	−	0.797583i
$127$	−4.95796e6	−	2.20742e6i	−0.214778	−	0.0956253i	0.296528	−	0.955024i	$-0.404171\pi$
$127$	−4.95796e6	−	2.20742e6i	−0.214778	−	0.0956253i	−0.511306	+	0.859399i	$0.670838\pi$
$128$	−648056.	−	1.99451e6i	−0.0273135	−	0.0840623i
$129$	−1.53182e7	+	2.65318e7i	−0.628264	+	1.08819i
$130$	−1.03246e7	−	1.78828e7i	−0.412167	−	0.713894i
$131$	1.62543e7	−	1.80522e7i	0.631710	−	0.701585i	−0.339286	−	0.940683i	$-0.610185\pi$
$131$	1.62543e7	−	1.80522e7i	0.631710	−	0.701585i	0.970995	+	0.239099i	$0.0768519\pi$
$132$	6.14939e6	−	1.89259e7i	0.232714	−	0.716222i
$133$	1.25770e6	+	1.39682e6i	0.0463550	+	0.0514825i
$134$	−1.86900e7	+	8.32134e6i	−0.671032	+	0.298763i
$135$	794422.	+	168860.i	0.0277896	+	0.00590687i
$136$	−1.38913e6	+	1.32167e7i	−0.0473541	+	0.450544i
$137$	−4.96521e6	−	4.72408e7i	−0.164974	−	1.56962i	−0.693343	−	0.720608i	$-0.743863\pi$
$137$	−4.96521e6	−	4.72408e7i	−0.164974	−	1.56962i	0.528369	−	0.849015i	$-0.322804\pi$
$138$	−2.85217e7	+	6.06247e6i	−0.923844	+	0.196369i
$139$	1.35267e7	−	9.82776e6i	0.427210	−	0.310386i	−0.353322	−	0.935502i	$-0.614948\pi$
$139$	1.35267e7	−	9.82776e6i	0.427210	−	0.310386i	0.780532	+	0.625115i	$0.214948\pi$
$140$	−1.59290e7	+	1.15731e7i	−0.490616	+	0.356453i
$141$	3.80532e7	−	8.08845e6i	1.14320	−	0.242996i
$142$	1.51097e6	+	1.43759e7i	0.0442838	+	0.421333i
$143$	7.48883e6	−	7.12514e7i	0.214160	−	2.03759i
$144$	−8.47173e6	−	1.80072e6i	−0.236430	−	0.0502548i
$145$	2.98545e7	−	1.32921e7i	0.813245	−	0.362080i
$146$	6.95354e6	+	7.72269e6i	0.184915	+	0.205368i
$147$	−4.90606e7	+	1.50993e8i	−1.27386	+	3.92054i
$148$	1.13434e7	−	1.25981e7i	0.287625	−	0.319440i
$149$	1.21689e7	+	2.10772e7i	0.301371	+	0.521989i	0.976447	−	0.215759i	$-0.0692226\pi$
$149$	1.21689e7	+	2.10772e7i	0.301371	+	0.521989i	−0.675076	+	0.737748i	$0.735889\pi$
$150$	1.28421e7	−	2.22431e7i	0.310681	−	0.538116i
$151$	4.77951e6	+	1.47098e7i	0.112970	+	0.347686i	0.991518	−	0.129968i	$-0.0414873\pi$
$151$	4.77951e6	+	1.47098e7i	0.112970	+	0.347686i	−0.878548	+	0.477654i	$0.841487\pi$
$152$	488102.	+	217317.i	0.0112735	+	0.00501928i
$153$	4.44022e7	+	3.22601e7i	1.00227	+	0.728192i
$154$	−6.83135e7			−1.50724
$155$	−8.74975e6	−	2.69460e7i	−0.188727	−	0.581210i
$156$	−6.34321e7			−1.33774
$157$	−2.66247e6	−	1.93440e6i	−0.0549080	−	0.0398930i	0.559993	−	0.828498i	$-0.310804\pi$
$157$	−2.66247e6	−	1.93440e6i	−0.0549080	−	0.0398930i	−0.614901	+	0.788605i	$0.710804\pi$
$158$	−3.82539e7	−	1.70318e7i	−0.771572	−	0.343526i
$159$	−4.43270e6	−	1.36424e7i	−0.0874537	−	0.269155i
$160$	−2.79844e6	+	4.84703e6i	−0.0540126	+	0.0935526i
$161$	5.00492e7	+	8.66878e7i	0.945163	+	1.63707i
$162$	2.64241e7	−	2.93469e7i	0.488312	−	0.542325i
$163$	−2.77145e6	+	8.52966e6i	−0.0501246	+	0.154268i	−0.972986	−	0.230865i	$-0.925844\pi$
$163$	−2.77145e6	+	8.52966e6i	−0.0501246	+	0.154268i	0.922861	+	0.385133i	$0.125844\pi$
$164$	3.71362e6	+	4.12439e6i	0.0657421	+	0.0730140i
$165$	−4.85172e7	+	2.16012e7i	−0.840817	+	0.374356i
$166$	1.16211e7	+	2.47014e6i	0.197183	+	0.0419125i
$167$	7.39318e6	−	7.03414e7i	0.122835	−	1.16870i	−0.743323	−	0.668932i	$-0.766752\pi$
$167$	7.39318e6	−	7.03414e7i	0.122835	−	1.16870i	0.866159	−	0.499769i	$-0.166582\pi$
$168$	6.32224e6	+	6.01521e7i	0.102870	+	0.978742i
$169$	−1.62002e8	+	3.44346e7i	−2.58177	+	0.548771i
$170$	2.86934e7	−	2.08470e7i	0.447931	−	0.325441i
$171$	1.78515e6	−	1.29699e6i	0.0273017	−	0.0198358i
$172$	2.92423e7	−	6.21563e6i	0.438189	−	0.0931399i
$173$	2.12565e6	+	2.02242e7i	0.0312126	+	0.296968i	0.998981	+	0.0451273i	$0.0143694\pi$
$173$	2.12565e6	+	2.02242e7i	0.0312126	+	0.296968i	−0.967769	+	0.251841i	$0.918964\pi$
$174$	1.04935e7	−	9.98385e7i	0.151007	−	1.43673i
$175$	−8.62433e7	−	1.83316e7i	−1.21644	−	0.258563i
$176$	−1.77399e7	+	7.89829e6i	−0.245276	+	0.109204i
$177$	−1.21295e8	−	1.34711e8i	−1.64413	−	1.82599i
$178$	5.42793e6	−	1.67054e7i	0.0721380	−	0.222018i
$179$	4.70878e7	−	5.22963e7i	0.613653	−	0.681531i	−0.353585	−	0.935403i	$-0.615037\pi$
$179$	4.70878e7	−	5.22963e7i	0.613653	−	0.681531i	0.967238	+	0.253871i	$0.0817040\pi$
$180$	1.15572e7	+	2.00177e7i	0.147706	+	0.255835i
$181$	−6.32640e6	+	1.09576e7i	−0.0793016	+	0.137354i	−0.902949	−	0.429748i	$-0.858602\pi$
$181$	−6.32640e6	+	1.09576e7i	−0.0793016	+	0.137354i	0.823647	+	0.567103i	$0.191936\pi$
$182$	6.72896e7	+	2.07096e8i	0.827367	+	2.54637i
$183$	−3.78536e7	−	1.68535e7i	−0.456592	−	0.203288i
$184$	2.30196e7	+	1.67247e7i	0.272418	+	0.197923i
$185$	−4.52426e7			−0.525347
$186$	−8.51242e7	−	1.81102e7i	−0.969969	−	0.206361i
$187$	1.23055e8			1.37611
$188$	−3.07124e7	−	2.23139e7i	−0.337102	−	0.244919i
$189$	−7.82416e6	−	3.48354e6i	−0.0842988	−	0.0375323i
$190$	−440634.	−	1.35613e6i	−0.00466059	−	0.0143438i
$191$	1.73234e6	−	3.00051e6i	0.0179894	−	0.0311586i	−0.856891	−	0.515498i	$-0.827607\pi$
$191$	1.73234e6	−	3.00051e6i	0.0179894	−	0.0311586i	0.874880	+	0.484340i	$0.160940\pi$
$192$	8.59646e6	+	1.48895e7i	0.0876528	+	0.151819i
$193$	6.21997e7	−	6.90798e7i	0.622784	−	0.691672i	−0.346378	−	0.938095i	$-0.612589\pi$
$193$	6.21997e7	−	6.90798e7i	0.622784	−	0.691672i	0.969162	+	0.246423i	$0.0792552\pi$
$194$	2.54356e7	−	7.82826e7i	0.250112	−	0.769767i
$195$	1.13275e8	+	1.25805e8i	1.09399	+	1.21500i
$196$	1.41531e8	−	6.30135e7i	1.34262	−	0.597774i
$197$	1.24828e8	+	2.65330e7i	1.16327	+	0.247261i	0.748796	−	0.662800i	$-0.230632\pi$
$197$	1.24828e8	+	2.65330e7i	1.16327	+	0.247261i	0.414474	+	0.910061i	$0.363965\pi$
$198$	−8.38286e6	+	7.97575e7i	−0.0767474	+	0.730203i
$199$	1.39946e7	+	1.33149e8i	0.125885	+	1.19772i	0.856947	+	0.515405i	$0.172358\pi$
$199$	1.39946e7	+	1.33149e8i	0.125885	+	1.19772i	−0.731062	+	0.682311i	$0.760975\pi$
$200$	−2.45154e7	+	5.21091e6i	−0.216688	+	0.0460584i
$201$	1.35693e8	−	9.85867e7i	1.17861	−	0.856312i
$202$	1.72436e7	−	1.25282e7i	0.147197	−	0.106945i
$203$	−3.37089e8	+	7.16505e7i	−2.82819	+	0.601150i
$204$	−1.13884e7	−	1.08354e8i	−0.0939200	−	0.893589i
$205$	1.54823e6	−	1.47305e7i	0.0125516	−	0.119420i
$206$	1.09443e8	+	2.32629e7i	0.872276	+	0.185408i
$207$	1.07352e8	−	4.77960e7i	0.841226	−	0.374538i
$208$	4.14181e7	+	4.59995e7i	0.319131	+	0.354430i
$209$	1.52881e6	−	4.70518e6i	0.0115835	−	0.0356504i
$210$	1.08010e8	−	1.19957e8i	0.804813	−	0.893836i
$211$	3.44447e6	+	5.96599e6i	0.0252426	+	0.0437214i	0.878371	−	0.477980i	$-0.158631\pi$
$211$	3.44447e6	+	5.96599e6i	0.0252426	+	0.0437214i	−0.853128	+	0.521701i	$0.825298\pi$
$212$	−6.99883e6	+	1.21223e7i	−0.0504487	+	0.0873797i
$213$	−3.66203e7	−	1.12706e8i	−0.259653	−	0.799130i
$214$	7.80880e7	+	3.47670e7i	0.544673	+	0.242504i
$215$	−6.45475e7	−	4.68965e7i	−0.442940	−	0.321815i
$216$	−2.43456e6			−0.0164374
$217$	3.11738e7	+	2.97129e8i	0.207100	+	1.97395i
$218$	−1.12229e8			−0.733683
$219$	−6.89244e7	−	5.00765e7i	−0.443423	−	0.322166i
$220$	4.73441e7	+	2.10789e7i	0.299769	+	0.133466i
$221$	−1.21211e8	−	3.73048e8i	−0.755385	−	2.32483i
$222$	−6.94899e7	+	1.20360e8i	−0.426272	+	0.738324i
$223$	−7.09711e7	−	1.22926e8i	−0.428563	−	0.742293i	0.568183	−	0.822902i	$-0.307647\pi$
$223$	−7.09711e7	−	1.22926e8i	−0.428563	−	0.742293i	−0.996746	+	0.0806098i	$0.974313\pi$
$224$	3.94927e7	−	4.38611e7i	0.234774	−	0.260742i
$225$	−3.19856e7	+	9.84416e7i	−0.187204	+	0.576156i
$226$	6.66207e7	+	7.39898e7i	0.383910	+	0.426376i
$227$	−1.56397e8	+	6.96323e7i	−0.887436	+	0.395112i	−0.799255	−	0.600992i	$-0.794772\pi$
$227$	−1.56397e8	+	6.96323e7i	−0.887436	+	0.395112i	−0.0881815	+	0.996104i	$0.528106\pi$
$228$	−4.28455e6	−	910708.i	−0.0239405	−	0.00508870i
$229$	−6.51064e6	+	6.19446e7i	−0.0358261	+	0.340863i	0.961897	+	0.273413i	$0.0881527\pi$
$229$	−6.51064e6	+	6.19446e7i	−0.0358261	+	0.340863i	−0.997723	+	0.0674492i	$0.978514\pi$
$230$	−7.93763e6	−	7.55215e7i	−0.0430173	−	0.409283i
$231$	5.47811e8	−	1.16441e8i	2.92408	−	0.621532i
$232$	−7.92522e7	+	5.75801e7i	−0.416681	+	0.302736i
$233$	1.64414e8	−	1.19454e8i	0.851516	−	0.618662i	−0.0740479	−	0.997255i	$-0.523592\pi$
$233$	1.64414e8	−	1.19454e8i	0.851516	−	0.618662i	0.925564	+	0.378592i	$0.123592\pi$
$234$	2.50047e8	−	5.31491e7i	1.27575	−	0.271169i
$235$	1.05903e7	+	1.00760e8i	0.0532315	+	0.506464i
$236$	−1.84899e7	+	1.75920e8i	−0.0915680	+	0.871211i
$237$	3.35792e8	+	7.13748e7i	1.63852	+	0.348278i
$238$	−3.41677e8	+	1.52124e8i	−1.64284	+	0.731442i
$239$	1.96151e7	+	2.17848e7i	0.0929389	+	0.103219i	0.787820	−	0.615906i	$-0.211210\pi$
$239$	1.96151e7	+	2.17848e7i	0.0929389	+	0.103219i	−0.694881	+	0.719125i	$0.744543\pi$
$240$	1.41791e7	−	4.36387e7i	0.0662077	−	0.203766i
$241$	9.02946e7	−	1.00282e8i	0.415530	−	0.461493i	−0.498649	−	0.866804i	$-0.666170\pi$
$241$	9.02946e7	−	1.00282e8i	0.415530	−	0.461493i	0.914179	+	0.405311i	$0.132837\pi$
$242$	1.19555e7	+	2.07075e7i	0.0542267	+	0.0939234i
$243$	−1.56675e8	+	2.71369e8i	−0.700451	+	1.21322i
$244$	1.24948e7	+	3.84550e7i	0.0550636	+	0.169468i
$245$	−3.77716e8	−	1.68170e8i	−1.64091	−	0.730580i
$246$	−3.68098e7	−	2.67439e7i	−0.157649	−	0.114539i
$247$	−1.57699e7			−0.0665871
$248$	4.24489e7	+	7.35551e7i	0.176720	+	0.306219i
$249$	−9.74008e7			−0.399820
$250$	1.40478e8	+	1.02063e8i	0.568614	+	0.413122i
$251$	−3.78676e8	−	1.68597e8i	−1.51150	−	0.672965i	−0.527248	−	0.849711i	$-0.676776\pi$
$251$	−3.78676e8	−	1.68597e8i	−1.51150	−	0.672965i	−0.984257	+	0.176746i	$0.943443\pi$
$252$	−7.53228e7	−	2.31820e8i	−0.296500	−	0.912533i
$253$	1.31735e8	−	2.28172e8i	0.511422	−	0.885808i
$254$	−2.17086e7	−	3.76005e7i	−0.0831217	−	0.143971i
$255$	−1.94561e8	+	2.16082e8i	−0.734793	+	0.816070i
$256$	5.18444e6	−	1.59561e7i	0.0193136	−	0.0594410i
$257$	8.45166e7	+	9.38651e7i	0.310582	+	0.344936i	0.878146	−	0.478393i	$-0.158781\pi$
$257$	8.45166e7	+	9.38651e7i	0.310582	+	0.344936i	−0.567564	+	0.823329i	$0.692114\pi$
$258$	−2.23901e8	+	9.96873e7i	−0.811685	+	0.361385i
$259$	4.66673e8	+	9.91944e7i	1.66903	+	0.354763i
$260$	1.72675e7	−	1.64289e8i	0.0609288	−	0.579699i
$261$	4.22889e7	+	4.02352e8i	0.147226	+	1.40076i
$262$	1.90086e8	−	4.04041e7i	0.652974	−	0.138794i
$263$	−2.01163e8	+	1.46154e8i	−0.681873	+	0.495410i	−0.873979	−	0.485964i	$-0.838468\pi$
$263$	−2.01163e8	+	1.46154e8i	−0.681873	+	0.495410i	0.192105	+	0.981374i	$0.438468\pi$
$264$	1.28795e8	−	9.35747e7i	0.430808	−	0.313000i
$265$	3.65406e7	−	7.76694e6i	0.120619	−	0.0256383i
$266$	1.57178e6	+	1.49545e7i	0.00512042	+	0.0487175i
$267$	−1.50524e7	+	1.43214e8i	−0.0483968	+	0.460465i
$268$	−1.60094e8	−	3.40290e7i	−0.508045	−	0.107988i
$269$	1.35639e8	−	6.03903e7i	0.424865	−	0.189162i	−0.183154	−	0.983084i	$-0.558631\pi$
$269$	1.35639e8	−	6.03903e7i	0.424865	−	0.189162i	0.608020	+	0.793922i	$0.291964\pi$
$270$	4.34758e6	+	4.82848e6i	0.0134423	+	0.0149292i
$271$	−8.67044e7	+	2.66849e8i	−0.264636	+	0.814465i	0.727141	+	0.686488i	$0.240848\pi$
$271$	−8.67044e7	+	2.66849e8i	−0.264636	+	0.814465i	−0.991777	+	0.127977i	$0.959152\pi$
$272$	−7.11394e7	+	7.90083e7i	−0.214348	+	0.238057i
$273$	−8.92597e8	−	1.54602e9i	−2.65513	−	4.59883i
$274$	1.90004e8	−	3.29097e8i	0.558002	−	0.966488i
$275$	7.17145e7	+	2.20714e8i	0.207942	+	0.639980i
$276$	−2.13104e8	−	9.48799e7i	−0.610112	−	0.271639i
$277$	−3.10047e8	−	2.25262e8i	−0.876493	−	0.636809i	0.0558285	−	0.998440i	$-0.482220\pi$
$277$	−3.10047e8	−	2.25262e8i	−0.876493	−	0.636809i	−0.932321	+	0.361631i	$0.882220\pi$
$278$	1.33760e8			0.373395
$279$	3.50730e8	+	65067.4i	0.966849	+	0.000179370i
$280$	−1.57515e8			−0.428814
$281$	2.57954e8	+	1.87415e8i	0.693538	+	0.503885i	0.877821	−	0.478988i	$-0.158996\pi$
$281$	2.57954e8	+	1.87415e8i	0.693538	+	0.503885i	−0.184283	+	0.982873i	$0.558996\pi$
$282$	2.84319e8	+	1.26587e8i	0.754979	+	0.336138i
$283$	1.36804e6	+	4.21041e6i	0.00358796	+	0.0110426i	0.952834	−	0.303490i	$-0.0981521\pi$
$283$	1.36804e6	+	4.21041e6i	0.00358796	+	0.0110426i	−0.949247	+	0.314533i	$0.898152\pi$
$284$	−5.78203e7	+	1.00148e8i	−0.149784	+	0.259434i
$285$	5.84502e6	+	1.01239e7i	0.0149565	+	0.0259053i
$286$	3.83513e8	−	4.25934e8i	0.969391	−	1.07662i
$287$	−4.82664e7	+	1.48549e8i	−0.120520	+	0.370922i
$288$	−4.63627e7	−	5.14910e7i	−0.114365	−	0.127016i
$289$	2.40610e8	−	1.07126e8i	0.586369	−	0.261068i
$290$	2.55725e8	+	5.43561e7i	0.615716	+	0.130875i
$291$	−7.05364e7	+	6.71109e8i	−0.167798	+	1.59650i
$292$	8.69000e6	+	8.26798e7i	0.0204258	+	0.194339i
$293$	1.09740e7	−	2.33259e6i	0.0254875	−	0.00541753i	−0.195150	−	0.980773i	$-0.562519\pi$
$293$	1.09740e7	−	2.33259e6i	0.0254875	−	0.00541753i	0.220638	+	0.975356i	$0.429186\pi$
$294$	−1.02754e9	+	7.46550e8i	−2.35821	+	1.71334i
$295$	3.81921e8	−	2.77482e8i	0.866158	−	0.629300i
$296$	1.32656e8	−	2.81969e7i	0.297307	−	0.0631946i
$297$	2.35638e6	+	2.24195e7i	0.00521913	+	0.0496567i
$298$	−2.03520e7	+	1.93636e8i	−0.0445503	+	0.423867i
$299$	−8.21476e8	−	1.74610e8i	−1.77724	−	0.377764i
$300$	1.87709e8	−	8.35734e7i	0.401384	−	0.178708i
$301$	5.62981e8	+	6.25254e8i	1.18990	+	1.32152i
$302$	−3.82360e7	+	1.17678e8i	−0.0798819	+	0.245851i
$303$	−1.16924e8	+	1.29857e8i	−0.241464	+	0.268173i
$304$	2.13718e6	+	3.70170e6i	0.00436298	+	0.00755690i
$305$	5.39551e7	−	9.34529e7i	0.108889	−	0.188601i
$306$	1.35681e8	+	4.17583e8i	0.270704	+	0.833141i
$307$	−1.25026e8	−	5.56650e7i	−0.246612	−	0.109799i	0.279708	−	0.960085i	$-0.409762\pi$
$307$	−1.25026e8	−	5.56650e7i	−0.246612	−	0.109799i	−0.526321	+	0.850286i	$0.676429\pi$
$308$	−4.42134e8	−	3.21229e8i	−0.862236	−	0.626451i
$309$	−9.17286e8			−1.76868
$310$	7.00780e7	−	2.15542e8i	0.133603	−	0.410928i
$311$	1.80105e8			0.339520			0.169760	−	0.985485i	$-0.445701\pi$
$311$	1.80105e8			0.339520			0.169760	+	0.985485i	$0.445701\pi$
$312$	−4.10541e8	−	2.98276e8i	−0.765272	−	0.556003i
$313$	−7.61690e8	−	3.39126e8i	−1.40402	−	0.625109i	−0.441732	−	0.897147i	$-0.645636\pi$
$313$	−7.61690e8	−	3.39126e8i	−1.40402	−	0.625109i	−0.962287	+	0.272038i	$0.912303\pi$
$314$	−8.13578e6	−	2.50394e7i	−0.0148302	−	0.0456425i
$315$	−3.25259e8	+	5.63365e8i	−0.586330	+	1.01555i
$316$	−1.67497e8	−	2.90113e8i	−0.298608	−	0.517204i
$317$	−5.09091e8	+	5.65403e8i	−0.897611	+	0.996898i	0.102387	+	0.994745i	$0.467352\pi$
$317$	−5.09091e8	+	5.65403e8i	−0.897611	+	0.996898i	−0.999998	+	0.00215304i	$0.999315\pi$
$318$	3.54616e7	−	1.09139e8i	0.0618391	−	0.190321i
$319$	6.06953e8	+	6.74089e8i	1.04686	+	1.16265i
$320$	−4.09040e7	+	1.82116e7i	−0.0697815	+	0.0310687i
$321$	−6.85454e8	−	1.45698e8i	−1.15667	−	0.245859i
$322$	−8.37051e7	+	7.96401e8i	−0.139719	+	1.32934i
$323$	−2.83129e6	−	2.69379e7i	−0.00467493	−	0.0444790i
$324$	3.09018e8	−	6.56837e7i	0.504749	−	0.107288i
$325$	5.98469e8	−	4.34813e8i	0.967052	−	0.702604i
$326$	−5.80461e7	+	4.21729e7i	−0.0927921	+	0.0674174i
$327$	8.99975e8	−	1.91296e8i	1.42336	−	0.302544i
$328$	4.64099e6	+	4.41561e7i	0.00726194	+	0.0690927i
$329$	1.11678e8	−	1.06254e9i	0.172895	−	1.64498i
$330$	−4.15585e8	−	8.83353e7i	−0.636591	−	0.135312i
$331$	1.45014e8	−	6.45644e7i	0.219792	−	0.0978577i	−0.293887	−	0.955840i	$-0.594949\pi$
$331$	1.45014e8	−	6.45644e7i	0.219792	−	0.0978577i	0.513679	+	0.857982i	$0.328282\pi$
$332$	6.35980e7	+	7.06328e7i	0.0953807	+	0.105931i
$333$	1.73078e8	−	5.32679e8i	0.256854	−	0.790516i
$334$	3.78615e8	−	4.20494e8i	0.556013	−	0.617515i
$335$	2.18401e8	+	3.78282e8i	0.317394	+	0.549742i
$336$	−2.41934e8	+	4.19041e8i	−0.347944	+	0.602656i
$337$	3.54949e8	+	1.09242e9i	0.505198	+	1.55484i	0.800437	+	0.599416i	$0.204601\pi$
$337$	3.54949e8	+	1.09242e9i	0.505198	+	1.55484i	−0.295239	+	0.955423i	$0.595399\pi$
$338$	−1.21042e9	−	5.38914e8i	−1.70501	−	0.759121i
$339$	−6.60353e8	−	4.79774e8i	−0.920613	−	0.668864i
$340$	2.83736e8			0.391506
$341$	6.36271e8	−	4.62097e8i	0.868964	−	0.631093i
$342$	1.76526e7			0.0238625
$343$	2.32734e9	+	1.69091e9i	3.11409	+	2.26252i
$344$	2.18487e8	+	9.72769e7i	0.289382	+	0.128841i
$345$	1.92379e8	+	5.92083e8i	0.252227	+	0.776275i
$346$	−8.13424e7	+	1.40889e8i	−0.105573	+	0.182857i
$347$	−5.07470e7	−	8.78964e7i	−0.0652015	−	0.112932i	0.831582	−	0.555402i	$-0.187436\pi$
$347$	−5.07470e7	−	8.78964e7i	−0.0652015	−	0.112932i	−0.896783	+	0.442470i	$0.854102\pi$
$348$	5.37384e8	−	5.96825e8i	0.683530	−	0.759137i
$349$	−7.55963e7	+	2.32661e8i	−0.0951944	+	0.292978i	−0.987304	−	0.158840i	$-0.949225\pi$
$349$	−7.55963e7	+	2.32661e8i	−0.0951944	+	0.292978i	0.892110	+	0.451818i	$0.149225\pi$
$350$	−4.71978e8	−	5.24185e8i	−0.588415	−	0.653501i
$351$	6.56449e7	−	2.92270e7i	0.0810263	−	0.0360752i
$352$	−1.51955e8	−	3.22990e7i	−0.185701	−	0.0394720i
$353$	−6.03148e7	+	5.73857e8i	−0.0729814	+	0.694372i	0.895462	+	0.445138i	$0.146845\pi$
$353$	−6.03148e7	+	5.73857e8i	−0.0729814	+	0.694372i	−0.968443	+	0.249234i	$0.919821\pi$
$354$	−1.51585e8	−	1.44223e9i	−0.181612	−	1.72792i
$355$	3.01877e8	−	6.41659e7i	0.358122	−	0.0761211i
$356$	1.13684e8	−	8.25962e7i	0.133544	−	0.0970254i
$357$	2.48064e9	−	1.80229e9i	2.88552	−	2.09646i
$358$	5.50671e8	−	1.17049e8i	0.634310	−	0.134827i
$359$	−7.98881e7	−	7.60084e8i	−0.0911279	−	0.867024i	−0.940629	−	0.339437i	$-0.889763\pi$
$359$	−7.98881e7	−	7.60084e8i	−0.0911279	−	0.867024i	0.849501	−	0.527587i	$-0.176903\pi$
$360$	−1.93289e7	+	1.83902e8i	−0.0218348	+	0.207744i
$361$	8.73273e8	+	1.85620e8i	0.976956	+	0.207658i
$362$	−9.24713e7	+	4.11709e7i	−0.102454	+	0.0456153i
$363$	−1.31168e8	−	1.45677e8i	−0.143931	−	0.159852i
$364$	−5.38317e8	+	1.65677e9i	−0.585037	+	1.80056i
$365$	1.48461e8	−	1.64882e8i	0.159804	−	0.177480i
$366$	−1.65744e8	−	2.87076e8i	−0.176707	−	0.306065i
$367$	1.28109e8	−	2.21891e8i	0.135285	−	0.234320i	−0.790421	−	0.612563i	$-0.790138\pi$
$367$	1.28109e8	−	2.21891e8i	0.135285	−	0.234320i	0.925706	+	0.378243i	$0.123472\pi$
$368$	7.03418e7	+	2.16490e8i	0.0735777	+	0.226449i
$369$	1.67511e8	+	7.45808e7i	0.173561	+	0.0772743i
$370$	−2.92816e8	−	2.12743e8i	−0.300531	−	0.218348i
$371$	−3.93942e8			−0.400519
$372$	−4.65776e8	−	5.17490e8i	−0.469112	−	0.521197i
$373$	−6.50956e8			−0.649487			−0.324744	−	0.945802i	$-0.605278\pi$
$373$	−6.50956e8			−0.649487			−0.324744	+	0.945802i	$0.605278\pi$
$374$	7.96429e8	+	5.78639e8i	0.787220	+	0.571949i
$375$	−1.30047e9	−	5.79006e8i	−1.27348	−	0.566988i
$376$	−9.38488e7	−	2.88837e8i	−0.0910482	−	0.280218i
$377$	1.44568e9	−	2.50400e9i	1.38956	−	2.40680i
$378$	−3.42585e7	−	5.93374e7i	−0.0326247	−	0.0565076i
$379$	−2.40770e8	+	2.67402e8i	−0.227177	+	0.252306i	−0.845948	−	0.533266i	$-0.820964\pi$
$379$	−2.40770e8	+	2.67402e8i	−0.227177	+	0.252306i	0.618770	+	0.785572i	$0.287631\pi$
$380$	3.52507e6	−	1.08491e7i	0.00329553	−	0.0101426i
$381$	2.38173e8	+	2.64518e8i	0.220626	+	0.245030i
$382$	2.53212e7	−	1.12737e7i	0.0232414	−	0.0103477i
$383$	4.92757e8	+	1.04739e8i	0.448164	+	0.0952603i	0.426465	−	0.904504i	$-0.359759\pi$
$383$	4.92757e8	+	1.04739e8i	0.448164	+	0.0952603i	0.0216998	+	0.999765i	$0.493092\pi$
$384$	−1.43772e7	+	1.36790e8i	−0.0129573	+	0.123281i
$385$	1.52457e8	+	1.45053e9i	0.136155	+	1.29543i
$386$	7.27397e8	−	1.54613e8i	0.643748	−	0.136833i
$387$	7.99083e8	−	5.80567e8i	0.700815	−	0.509172i
$388$	5.32729e8	−	3.87050e8i	0.463015	−	0.336400i
$389$	−6.90296e8	+	1.46727e8i	−0.594582	+	0.126382i	−0.495367	−	0.868684i	$-0.664966\pi$
$389$	−6.90296e8	+	1.46727e8i	−0.594582	+	0.126382i	−0.0992147	+	0.995066i	$0.531633\pi$
$390$	1.41563e8	+	1.34688e9i	0.120843	+	1.14975i
$391$	1.50780e8	−	1.43458e9i	0.127563	−	1.21369i
$392$	1.21231e9	+	2.57685e8i	1.01651	+	0.216067i
$393$	−1.45545e9	+	6.48007e8i	−1.20955	+	0.538525i
$394$	6.83139e8	+	7.58703e8i	0.562694	+	0.624935i
$395$	−2.76270e8	+	8.50272e8i	−0.225551	+	0.694173i
$396$	−4.29297e8	+	4.76783e8i	−0.347396	+	0.385823i
$397$	−4.56274e8	−	7.90290e8i	−0.365981	−	0.633899i	0.622952	−	0.782260i	$-0.285933\pi$
$397$	−4.56274e8	−	7.90290e8i	−0.365981	−	0.633899i	−0.988933	+	0.148362i	$0.952600\pi$
$398$	−5.35532e8	+	9.27568e8i	−0.425789	+	0.737488i
$399$	−3.80942e7	−	1.17242e8i	−0.0300230	−	0.0924013i
$400$	−1.83170e8	−	8.15526e7i	−0.143102	−	0.0637130i
$401$	6.16966e8	+	4.48252e8i	0.477811	+	0.347150i	0.800478	−	0.599363i	$-0.204579\pi$
$401$	6.16966e8	+	4.48252e8i	0.477811	+	0.347150i	−0.322667	+	0.946513i	$0.604579\pi$
$402$	1.34181e9			1.03015
$403$	−2.02761e9	−	1.47372e9i	−1.54318	−	1.12162i
$404$	1.70514e8			0.128655
$405$	−6.82106e8	−	4.95579e8i	−0.510222	−	0.370698i
$406$	−2.51861e9	−	1.12136e9i	−1.86775	−	0.831577i
$407$	−3.88056e8	−	1.19431e9i	−0.285308	−	0.878087i
$408$	4.35802e8	−	7.54831e8i	0.317672	−	0.550224i
$409$	1.01843e9	+	1.76397e9i	0.736036	+	1.27485i	0.954267	+	0.298954i	$0.0966378\pi$
$409$	1.01843e9	+	1.76397e9i	0.736036	+	1.27485i	−0.218232	+	0.975897i	$0.570029\pi$
$410$	7.92871e7	−	8.80573e7i	0.0568145	−	0.0630989i
$411$	−9.62710e8	+	2.96292e9i	−0.683989	+	2.10510i
$412$	5.98943e8	+	6.65194e8i	0.421935	+	0.468606i
$413$	−4.54786e9	+	2.02484e9i	−3.17675	+	1.41438i
$414$	9.19545e8	+	1.95455e8i	0.636901	+	0.135377i
$415$	2.65145e7	−	2.52268e8i	0.0182102	−	0.173258i
$416$	5.17611e7	+	4.92474e8i	0.0352515	+	0.335395i
$417$	−1.07263e9	+	2.27995e8i	−0.724392	+	0.153974i
$418$	3.20197e7	−	2.32637e7i	0.0214438	−	0.0155798i
$419$	−1.98696e8	+	1.44361e8i	−0.131959	+	0.0958741i	−0.651807	−	0.758385i	$-0.725989\pi$
$419$	−1.98696e8	+	1.44361e8i	−0.131959	+	0.0958741i	0.519848	+	0.854259i	$0.325989\pi$
$420$	1.26312e9	−	2.68485e8i	0.831905	−	0.176827i
$421$	−3.47749e7	−	3.30861e8i	−0.0227132	−	0.216102i	−0.999991	−	0.00414132i	$-0.998682\pi$
$421$	−3.47749e7	−	3.30861e8i	−0.0227132	−	0.216102i	0.977278	−	0.211961i	$-0.0679849\pi$
$422$	−5.76072e6	+	5.48095e7i	−0.00373149	+	0.0355028i
$423$	−1.22684e9	−	2.60773e8i	−0.788129	−	0.167522i
$424$	−1.02300e8	+	4.55469e7i	−0.0651771	+	0.0290187i
$425$	8.50188e8	+	9.44229e8i	0.537222	+	0.596645i
$426$	2.92963e8	−	9.01646e8i	0.183603	−	0.565071i
$427$	−7.61437e8	+	8.45662e8i	−0.473300	+	0.525653i
$428$	3.41912e8	+	5.92209e8i	0.210795	+	0.365108i
$429$	−2.34941e9	+	4.06930e9i	−1.43668	+	2.48839i
$430$	−1.97240e8	−	6.07041e8i	−0.119634	−	0.368196i
$431$	−2.99315e9	−	1.33264e9i	−1.80077	−	0.801755i	−0.969175	−	0.246372i	$-0.920761\pi$
$431$	−2.99315e9	−	1.33264e9i	−1.80077	−	0.801755i	−0.831595	−	0.555382i	$-0.812572\pi$
$432$	−1.57568e7	−	1.14480e7i	−0.00940320	−	0.00683183i
$433$	1.94812e9			1.15321			0.576606	−	0.817022i	$-0.304377\pi$
$433$	1.94812e9			1.15321			0.576606	+	0.817022i	$0.304377\pi$
$434$	−1.19542e9	+	2.06965e9i	−0.701953	+	1.21530i
$435$	−2.14333e9			−1.24847
$436$	−7.26363e8	−	5.27734e8i	−0.419712	−	0.304938i
$437$	−5.29800e7	−	2.35882e7i	−0.0303687	−	0.0135210i
$438$	−2.10614e8	−	6.48203e8i	−0.119764	−	0.368597i
$439$	−3.11575e8	+	5.39663e8i	−0.175767	+	0.304437i	−0.940426	−	0.339998i	$-0.889574\pi$
$439$	−3.11575e8	+	5.39663e8i	−0.175767	+	0.304437i	0.764660	+	0.644434i	$0.222907\pi$
$440$	2.07298e8	+	3.59051e8i	0.116014	+	0.200942i
$441$	3.42498e9	−	3.80383e9i	1.90162	−	2.11196i
$442$	9.69686e8	−	2.98439e9i	0.534138	−	1.64391i
$443$	1.19617e9	+	1.32848e9i	0.653703	+	0.726011i	0.975304	−	0.220865i	$-0.0708879\pi$
$443$	1.19617e9	+	1.32848e9i	0.653703	+	0.726011i	−0.321602	+	0.946875i	$0.604221\pi$
$444$	−1.01572e9	+	4.52225e8i	−0.550721	+	0.245197i
$445$	−3.66827e8	−	7.79715e7i	−0.197334	−	0.0419446i
$446$	1.18696e8	−	1.12932e9i	0.0633525	−	0.602759i
$447$	−1.66850e8	−	1.58748e9i	−0.0883590	−	0.840680i
$448$	4.61850e8	−	9.81692e7i	0.242676	−	0.0515825i
$449$	1.50018e9	−	1.08994e9i	0.782134	−	0.568254i	−0.123485	−	0.992346i	$-0.539407\pi$
$449$	1.50018e9	−	1.08994e9i	0.782134	−	0.568254i	0.905619	+	0.424093i	$0.139407\pi$
$450$	−6.69915e8	+	4.86722e8i	−0.346558	+	0.251789i
$451$	4.02134e8	−	8.54762e7i	0.206420	−	0.0438760i
$452$	8.32574e7	+	7.92142e8i	0.0424071	+	0.403477i
$453$	1.06034e8	−	1.00885e9i	0.0535922	−	0.509895i
$454$	−1.33965e9	−	2.84752e8i	−0.671887	−	0.142814i
$455$	4.24719e9	−	1.89097e9i	2.11379	−	0.941119i
$456$	−2.34478e7	−	2.60414e7i	−0.0115804	−	0.0128614i
$457$	−1.01666e9	+	3.12895e9i	−0.498274	+	1.53353i	0.313517	+	0.949583i	$0.398493\pi$
$457$	−1.01666e9	+	3.12895e9i	−0.498274	+	1.53353i	−0.811791	+	0.583948i	$0.801507\pi$
$458$	−3.33419e8	+	3.70299e8i	−0.162166	+	0.180104i
$459$	6.17107e7	+	1.06886e8i	0.0297863	+	0.0515914i
$460$	3.03750e8	−	5.26111e8i	0.145500	−	0.252014i
$461$	−7.41157e7	−	2.28105e8i	−0.0352336	−	0.108438i	0.931893	−	0.362733i	$-0.118156\pi$
$461$	−7.41157e7	−	2.28105e8i	−0.0352336	−	0.108438i	−0.967127	+	0.254296i	$0.918156\pi$
$462$	4.09304e9	+	1.82234e9i	1.93108	+	0.859771i
$463$	−1.01666e9	−	7.38644e8i	−0.476037	−	0.345861i	0.323752	−	0.946142i	$-0.395056\pi$
$463$	−1.01666e9	−	7.38644e8i	−0.476037	−	0.345861i	−0.799789	+	0.600281i	$0.795056\pi$
$464$	−7.83689e8			−0.364192
$465$	−1.94568e8	+	1.84789e9i	−0.0897401	+	0.852299i
$466$	1.62581e9			0.744252
$467$	−6.11807e8	−	4.44504e8i	−0.277975	−	0.201961i	0.440059	−	0.897969i	$-0.354958\pi$
$467$	−6.11807e8	−	4.44504e8i	−0.277975	−	0.201961i	−0.718034	+	0.696008i	$0.754958\pi$
$468$	1.86826e9	+	8.31802e8i	0.842513	+	0.375111i
$469$	−1.42341e9	−	4.38079e9i	−0.637123	−	1.96086i
$470$	−4.05258e8	+	7.01928e8i	−0.180048	+	0.311853i
$471$	1.07921e8	+	1.86925e8i	0.0475920	+	0.0824317i
$472$	−9.46895e8	+	1.05163e9i	−0.414481	+	0.460328i
$473$	6.84335e8	−	2.10617e9i	0.297341	−	0.915121i
$474$	1.83767e9	+	2.04094e9i	0.792579	+	0.880248i
$475$	4.66665e7	−	2.07773e7i	0.0199792	−	0.00889530i
$476$	−2.92671e9	−	6.22092e8i	−1.24382	−	0.264381i
$477$	−4.83412e7	+	4.59936e8i	−0.0203940	+	0.194036i
$478$	2.45134e7	+	2.33229e8i	0.0102661	+	0.0976755i
$479$	1.68655e9	−	3.58487e8i	0.701172	−	0.149039i	0.156488	−	0.987680i	$-0.449983\pi$
$479$	1.68655e9	−	3.58487e8i	0.701172	−	0.149039i	0.544684	+	0.838641i	$0.316650\pi$
$480$	2.96970e8	−	2.15762e8i	0.122566	−	0.0890491i
$481$	−3.23839e9	+	2.35283e9i	−1.32685	+	0.964011i
$482$	1.05596e9	−	2.24450e8i	0.429517	−	0.0912968i
$483$	−6.86233e8	−	6.52907e9i	−0.277113	−	2.63655i
$484$	−1.99950e7	+	1.90240e8i	−0.00801609	+	0.0762680i
$485$	−1.71897e9	−	3.65379e8i	−0.684184	−	0.145428i
$486$	−2.29008e9	+	1.01961e9i	−0.904947	+	0.402908i
$487$	−1.88884e9	−	2.09777e9i	−0.741042	−	0.823011i	0.248290	−	0.968686i	$-0.420131\pi$
$487$	−1.88884e9	−	2.09777e9i	−0.741042	−	0.823011i	−0.989333	+	0.145675i	$0.953465\pi$
$488$	−9.99584e7	+	3.07640e8i	−0.0389359	+	0.119832i
$489$	3.93592e8	−	4.37128e8i	0.152218	−	0.169055i
$490$	−1.65385e9	−	2.86455e9i	−0.635052	−	1.09994i
$491$	−4.85131e8	+	8.40271e8i	−0.184958	+	0.320357i	−0.943562	−	0.331195i	$-0.892548\pi$
$491$	−4.85131e8	+	8.40271e8i	−0.184958	+	0.320357i	0.758604	+	0.651552i	$0.225882\pi$
$492$	−1.12481e8	−	3.46181e8i	−0.0425795	−	0.131046i
$493$	4.53684e9	+	2.01993e9i	1.70525	+	0.759228i
$494$	−1.02065e8	−	7.41546e7i	−0.0380919	−	0.0276754i
$495$	1.71223e9			0.634519
$496$	−7.11420e7	+	6.75666e8i	−0.0261782	+	0.248626i
$497$	−3.25452e9			−1.18916
$498$	−6.30392e8	−	4.58006e8i	−0.228722	−	0.166176i
$499$	2.53216e9	+	1.12739e9i	0.912303	+	0.406183i	0.808555	−	0.588420i	$-0.200250\pi$
$499$	2.53216e9	+	1.12739e9i	0.912303	+	0.406183i	0.103748	+	0.994604i	$0.466917\pi$
$500$	4.29262e8	+	1.32113e9i	0.153577	+	0.472663i
$501$	−2.31941e9	+	4.01733e9i	−0.824033	+	1.42727i
$502$	−1.65805e9	−	2.87183e9i	−0.584971	−	1.01320i
$503$	−6.37413e8	+	7.07919e8i	−0.223323	+	0.248025i	−0.844386	−	0.535735i	$-0.820034\pi$
$503$	−6.37413e8	+	7.07919e8i	−0.223323	+	0.248025i	0.621063	+	0.783761i	$0.286701\pi$
$504$	6.02582e8	−	1.85456e9i	0.209657	−	0.645258i
$505$	−3.04500e8	−	3.38182e8i	−0.105213	−	0.116850i
$506$	1.92553e9	−	8.57303e8i	0.660730	−	0.294176i
$507$	1.06250e10	+	2.25842e9i	3.62078	+	0.769621i
$508$	3.63067e7	−	3.45435e8i	0.0122875	−	0.116908i
$509$	2.81471e8	+	2.67802e9i	0.0946067	+	0.900123i	0.934162	+	0.356849i	$0.116149\pi$
$509$	2.81471e8	+	2.67802e9i	0.0946067	+	0.900123i	−0.839555	+	0.543274i	$0.817185\pi$
$510$	−2.27530e9	+	4.83630e8i	−0.759527	+	0.161443i
$511$	−1.89286e9	+	1.37525e9i	−0.627547	+	0.455939i
$512$	1.08584e8	−	7.88912e7i	0.0357538	−	0.0259767i
$513$	4.85362e6	−	1.03167e6i	0.00158729	−	0.000337388i
$514$	1.05622e8	+	1.00493e9i	0.0343071	+	0.326411i
$515$	2.49703e8	−	2.37577e9i	0.0805563	−	0.766442i
$516$	−1.91788e9	−	4.07657e8i	−0.614535	−	0.130623i
$517$	−2.56901e9	+	1.14380e9i	−0.817617	+	0.364026i
$518$	2.55393e9	+	2.83643e9i	0.807337	+	0.896639i
$519$	4.12145e8	−	1.26845e9i	0.129409	−	0.398279i
$520$	8.84292e8	−	9.82105e8i	0.275793	−	0.306300i
$521$	2.34566e9	+	4.06280e9i	0.726663	+	1.25862i	0.958286	+	0.285811i	$0.0922631\pi$
$521$	2.34566e9	+	4.06280e9i	0.726663	+	1.25862i	−0.231623	+	0.972806i	$0.574404\pi$
$522$	−1.61827e9	+	2.80293e9i	−0.497972	+	0.862512i
$523$	4.02836e8	+	1.23980e9i	0.123133	+	0.378963i	0.993556	−	0.113340i	$-0.0361551\pi$
$523$	4.02836e8	+	1.23980e9i	0.123133	+	0.378963i	−0.870424	+	0.492303i	$0.836155\pi$
$524$	1.42026e9	+	6.32338e8i	0.431228	+	0.191995i
$525$	4.67831e9	+	3.39899e9i	1.41101	+	1.02516i
$526$	−1.98921e9			−0.595979
$527$	2.15335e9	−	3.72812e9i	0.640881	−	1.10956i
$528$	1.27359e9			0.376540
$529$	2.55945e8	+	1.85955e8i	0.0751713	+	0.0546151i
$530$	2.73018e8	+	1.21555e8i	0.0796573	+	0.0354657i
$531$	1.80597e9	+	5.55821e9i	0.523456	+	1.61103i
$532$	−6.01474e7	+	1.04178e8i	−0.0173191	+	0.0299976i
$533$	−6.55233e8	−	1.13490e9i	−0.187435	−	0.324647i
$534$	−7.70855e8	+	8.56121e8i	−0.219068	+	0.243299i
$535$	5.63952e8	−	1.73566e9i	0.159222	−	0.490036i
$536$	−8.76134e8	−	9.73046e8i	−0.245750	−	0.272933i
$537$	−4.21636e9	+	1.87725e9i	−1.17497	+	0.523132i
$538$	1.16185e9	+	2.46958e8i	0.321670	+	0.0683731i
$539$	1.19959e9	−	1.14134e10i	0.329970	−	3.13945i
$540$	5.43327e6	+	5.16941e7i	0.00148485	+	0.0141274i
$541$	3.41536e9	−	7.25957e8i	0.927355	−	0.197115i	0.280610	−	0.959822i	$-0.409463\pi$
$541$	3.41536e9	−	7.25957e8i	0.927355	−	0.197115i	0.646745	+	0.762707i	$0.276130\pi$
$542$	−1.81596e9	+	1.31937e9i	−0.489901	+	0.355934i
$543$	6.71358e8	−	4.87770e8i	0.179951	−	0.130742i
$544$	−8.31943e8	+	1.76835e8i	−0.221563	+	0.0470947i
$545$	2.50465e8	+	2.38301e9i	0.0662763	+	0.630577i
$546$	1.49283e9	−	1.42033e10i	0.392497	−	3.73436i
$547$	−7.24878e9	−	1.54078e9i	−1.89369	−	0.402516i	−0.894669	−	0.446730i	$-0.852589\pi$
$547$	−7.24878e9	−	1.54078e9i	−1.89369	−	0.402516i	−0.999022	+	0.0442134i	$0.985922\pi$
$548$	2.77724e9	−	1.23651e9i	0.720910	−	0.320970i
$549$	8.93893e8	+	9.92768e8i	0.230559	+	0.256062i
$550$	−5.73716e8	+	1.76572e9i	−0.147037	+	0.452534i
$551$	1.33600e8	−	1.48377e8i	0.0340232	−	0.0377865i
$552$	−9.33084e8	−	1.61615e9i	−0.236121	−	0.408973i
$553$	4.71392e9	−	8.16475e9i	1.18534	−	2.05308i
$554$	−9.47419e8	−	2.91586e9i	−0.236733	−	0.728588i
$555$	2.71074e9	+	1.20690e9i	0.673073	+	0.299671i
$556$	8.65712e8	+	6.28976e8i	0.213605	+	0.155193i
$557$	6.35036e9			1.55706			0.778530	−	0.627607i	$-0.215966\pi$
$557$	6.35036e9			1.55706			0.778530	+	0.627607i	$0.215966\pi$
$558$	2.26967e9	+	1.64965e9i	0.553023	+	0.401951i
$559$	−7.05904e9			−1.70925
$560$	−1.01946e9	−	7.40680e8i	−0.245308	−	0.178227i
$561$	−7.37292e9	−	3.28263e9i	−1.76307	−	0.784969i
$562$	7.88238e8	+	2.42595e9i	0.187318	+	0.576506i
$563$	−2.57900e9	+	4.46696e9i	−0.609077	+	1.05495i	0.382316	+	0.924032i	$0.375127\pi$
$563$	−2.57900e9	+	4.46696e9i	−0.609077	+	1.05495i	−0.991393	+	0.130921i	$0.958207\pi$
$564$	1.24491e9	+	2.15624e9i	0.292186	+	0.506081i
$565$	1.42238e9	−	1.57971e9i	0.331776	−	0.368475i
$566$	−1.09444e7	+	3.36833e7i	−0.00253707	+	0.00780830i
$567$	5.94931e9	+	6.60737e9i	1.37065	+	1.52226i
$568$	−8.45143e8	+	3.76282e8i	−0.193513	+	0.0861577i
$569$	9.59046e8	+	2.03851e8i	0.218246	+	0.0463896i	0.315737	−	0.948847i	$-0.397748\pi$
$569$	9.59046e8	+	2.03851e8i	0.218246	+	0.0463896i	−0.0974908	+	0.995236i	$0.531082\pi$
$570$	−9.77553e6	+	9.30080e7i	−0.00221095	+	0.0210358i
$571$	−4.32978e7	−	4.11951e8i	−0.00973285	−	0.0926019i	0.988577	−	0.150716i	$-0.0481579\pi$
$571$	−4.32978e7	−	4.11951e8i	−0.00973285	−	0.0926019i	−0.998310	+	0.0581142i	$0.981491\pi$
$572$	4.48501e9	−	9.53319e8i	1.00202	−	0.212986i
$573$	−1.83837e8	+	1.33565e8i	−0.0408217	+	0.0296587i
$574$	−1.01091e9	+	7.34466e8i	−0.223110	+	0.162099i
$575$	2.66097e9	−	5.65607e8i	0.583717	−	0.124073i
$576$	−5.79405e7	−	5.51267e8i	−0.0126329	−	0.120194i
$577$	−4.98395e8	+	4.74191e9i	−0.108009	+	1.02763i	0.797504	+	0.603313i	$0.206153\pi$
$577$	−4.98395e8	+	4.74191e9i	−0.108009	+	1.02763i	−0.905513	+	0.424319i	$0.860514\pi$
$578$	2.06100e9	+	4.38079e8i	0.443946	+	0.0943636i
$579$	−5.56952e9	+	2.47971e9i	−1.19246	+	0.530916i
$580$	1.39949e9	+	1.55429e9i	0.297833	+	0.330777i
$581$	−8.26593e8	+	2.54399e9i	−0.174854	+	0.538145i
$582$	−3.61227e9	+	4.01183e9i	−0.759538	+	0.843552i
$583$	5.18448e8	+	8.97979e8i	0.108359	+	0.187684i
$584$	−3.32541e8	+	5.75978e8i	−0.0690876	+	0.119663i
$585$	−1.68657e9	−	5.19073e9i	−0.348305	−	1.07197i
$586$	8.19935e7	+	3.65059e7i	0.0168321	+	0.00749413i
$587$	5.36178e8	+	3.89556e8i	0.109415	+	0.0794944i	0.641147	−	0.767418i	$-0.278459\pi$
$587$	5.36178e8	+	3.89556e8i	0.109415	+	0.0794944i	−0.531732	+	0.846912i	$0.678459\pi$
$588$	−1.01609e10			−2.06115
$589$	−1.15797e8	−	1.28654e8i	−0.0233504	−	0.0259429i
$590$	3.77665e9			0.757050
$591$	−6.77136e9	−	4.91968e9i	−1.34933	−	0.980349i
$592$	9.91156e8	+	4.41291e8i	0.196343	+	0.0874176i
$593$	−2.09986e8	−	6.46270e8i	−0.0413522	−	0.127269i	0.928249	−	0.371959i	$-0.121314\pi$
$593$	−2.09986e8	−	6.46270e8i	−0.0413522	−	0.127269i	−0.969601	+	0.244690i	$0.921314\pi$
$594$	−9.01719e7	+	1.56182e8i	−0.0176530	+	0.0305759i
$595$	3.99265e9	+	6.91547e9i	0.777055	+	1.34590i
$596$	−1.04225e9	+	1.15754e9i	−0.201656	+	0.223962i
$597$	2.71342e9	−	8.35106e9i	0.521924	−	1.60632i
$598$	−4.49564e9	−	4.99291e9i	−0.859680	−	0.954772i
$599$	−7.82554e9	+	3.48416e9i	−1.48772	+	0.662375i	−0.979973	−	0.199133i	$-0.936188\pi$
$599$	−7.82554e9	+	3.48416e9i	−1.48772	+	0.662375i	−0.507745	+	0.861507i	$0.669521\pi$
$600$	1.60786e9	+	3.41762e8i	0.303892	+	0.0645943i
$601$	−7.53633e7	+	7.17034e8i	−0.0141612	+	0.134735i	−0.999318	−	0.0369211i	$-0.988245\pi$
$601$	−7.53633e7	+	7.17034e8i	−0.0141612	+	0.134735i	0.985157	+	0.171656i	$0.0549117\pi$
$602$	7.03570e8	+	6.69402e9i	0.131438	+	1.25055i
$603$	−5.28934e9	+	1.12428e9i	−0.982406	+	0.208817i
$604$	−8.00826e8	+	5.81834e8i	−0.147880	+	0.107441i
$605$	4.13009e8	−	3.00069e8i	0.0758256	−	0.0550905i
$606$	−1.36737e9	+	2.90643e8i	−0.249592	+	0.0530525i
$607$	−2.76185e8	−	2.62773e9i	−0.0501234	−	0.476892i	−0.990576	−	0.136966i	$-0.956265\pi$
$607$	−2.76185e8	−	2.62773e9i	−0.0501234	−	0.476892i	0.940452	−	0.339926i	$-0.110402\pi$
$608$	−3.57433e6	+	3.40075e7i	−0.000644959	+	0.00613638i
$609$	2.21083e10	+	4.69926e9i	3.96638	+	0.843080i
$610$	7.88647e8	−	3.51128e8i	0.140679	−	0.0626341i
$611$	5.99800e9	+	6.66146e9i	1.06381	+	1.18148i
$612$	−1.08545e9	+	3.34067e9i	−0.191416	+	0.589119i
$613$	2.25944e9	−	2.50936e9i	0.396177	−	0.439999i	−0.511746	−	0.859137i	$-0.671001\pi$
$613$	2.25944e9	−	2.50936e9i	0.396177	−	0.439999i	0.907922	+	0.419138i	$0.137668\pi$
$614$	−5.47430e8	−	9.48177e8i	−0.0954420	−	0.165310i
$615$	−4.85715e8	+	8.41283e8i	−0.0842013	+	0.145841i
$616$	−1.35104e9	−	4.15808e9i	−0.232882	−	0.716737i
$617$	−7.45695e9	−	3.32005e9i	−1.27809	−	0.569045i	−0.348390	−	0.937350i	$-0.613272\pi$
$617$	−7.45695e9	−	3.32005e9i	−1.27809	−	0.569045i	−0.929705	+	0.368305i	$0.879938\pi$
$618$	−5.93680e9	−	4.31334e9i	−1.01179	−	0.735112i
$619$	7.56709e9			1.28236			0.641182	−	0.767389i	$-0.278444\pi$
$619$	7.56709e9			1.28236			0.641182	+	0.767389i	$0.278444\pi$
$620$	1.46709e9	−	1.06549e9i	0.247222	−	0.179547i
$621$	2.64254e8			0.0442794
$622$	1.16567e9	+	8.46907e8i	0.194226	+	0.141114i
$623$	3.61284e9	+	1.60854e9i	0.598605	+	0.266516i
$624$	−1.25450e9	−	3.86096e9i	−0.206693	−	0.636135i
$625$	−5.85213e7	+	1.01362e8i	−0.00958813	+	0.0166071i
$626$	−3.33509e9	−	5.77655e9i	−0.543373	−	0.941149i
$627$	−2.17116e8	+	2.41131e8i	−0.0351767	+	0.0390677i
$628$	6.50863e7	−	2.00315e8i	0.0104865	−	0.0322741i
$629$	−4.60047e9	−	5.10934e9i	−0.737097	−	0.818630i
$630$	−4.75422e9	+	2.11672e9i	−0.757509	+	0.337265i
$631$	−1.19402e10	−	2.53798e9i	−1.89195	−	0.402147i	−0.893093	−	0.449872i	$-0.851470\pi$
$631$	−1.19402e10	−	2.53798e9i	−1.89195	−	0.402147i	−0.998861	+	0.0477250i	$0.984803\pi$
$632$	2.80131e8	−	2.66526e9i	0.0441419	−	0.419982i
$633$	−4.72277e7	−	4.49341e8i	−0.00740088	−	0.0704147i
$634$	−5.95359e9	+	1.26547e9i	−0.927826	+	0.197215i
$635$	−7.49938e8	+	5.44862e8i	−0.116230	+	0.0844459i
$636$	7.42717e8	−	5.39615e8i	0.114478	−	0.0831734i
$637$	−3.57819e10	+	7.60569e9i	−5.48499	+	1.16587i
$638$	7.58522e8	+	7.21686e9i	0.115637	+	1.10021i
$639$	−3.99367e8	+	3.79972e9i	−0.0605507	+	0.576101i
$640$	−3.50372e8	−	7.44739e7i	−0.0528323	−	0.0112299i
$641$	−4.43419e9	+	1.97423e9i	−0.664985	+	0.296070i	−0.711333	−	0.702855i	$-0.751908\pi$
$641$	−4.43419e9	+	1.97423e9i	−0.664985	+	0.296070i	0.0463485	+	0.998925i	$0.485242\pi$
$642$	−3.75124e9	−	4.16617e9i	−0.559503	−	0.621391i
$643$	2.41734e9	−	7.43981e9i	0.358591	−	1.10363i	−0.595307	−	0.803498i	$-0.702969\pi$
$643$	2.41734e9	−	7.43981e9i	0.358591	−	1.10363i	0.953898	−	0.300131i	$-0.0970305\pi$
$644$	−4.28665e9	+	4.76081e9i	−0.632438	+	0.702393i
$645$	2.61639e9	+	4.53171e9i	0.383922	+	0.664972i
$646$	1.08345e8	−	1.87659e8i	0.0158123	−	0.0273878i
$647$	−5.38833e8	−	1.65836e9i	−0.0782148	−	0.240721i	0.904302	−	0.426893i	$-0.140392\pi$
$647$	−5.38833e8	−	1.65836e9i	−0.0782148	−	0.240721i	−0.982517	+	0.186172i	$0.940392\pi$
$648$	2.30887e9	+	1.02797e9i	0.333339	+	0.148412i
$649$	1.06008e10	+	7.70193e9i	1.52224	+	1.10597i
$650$	5.91799e9			0.845234
$651$	6.05846e9	−	1.86343e10i	0.860655	−	2.64715i
$652$	−5.73991e8			−0.0811033
$653$	1.93290e9	+	1.40434e9i	0.271653	+	0.197367i	0.715268	−	0.698850i	$-0.246304\pi$
$653$	1.93290e9	+	1.40434e9i	0.271653	+	0.197367i	−0.443616	+	0.896217i	$0.646304\pi$
$654$	6.72429e9	+	2.99385e9i	0.939992	+	0.418512i
$655$	−1.28214e9	−	3.94601e9i	−0.178275	−	0.548673i
$656$	−1.77597e8	+	3.07608e8i	−0.0245625	+	0.0425435i
$657$	1.37335e9	+	2.37872e9i	0.188931	+	0.327239i
$658$	5.71918e9	−	6.35179e9i	0.782606	−	0.869172i
$659$	2.66295e9	−	8.19573e9i	0.362464	−	1.11555i	−0.589090	−	0.808067i	$-0.700514\pi$
$659$	2.66295e9	−	8.19573e9i	0.362464	−	1.11555i	0.951554	−	0.307482i	$-0.0994864\pi$
$660$	−2.27434e9	−	2.52591e9i	−0.307930	−	0.341991i
$661$	1.23387e9	−	5.49354e8i	0.166174	−	0.0739856i	−0.321964	−	0.946752i	$-0.604343\pi$
$661$	1.23387e9	−	5.49354e8i	0.166174	−	0.0739856i	0.488138	+	0.872766i	$0.337676\pi$
$662$	1.24215e9	+	2.64027e8i	0.166407	+	0.0353709i
$663$	−2.68908e9	+	2.55849e10i	−0.358349	+	3.40946i
$664$	7.94799e7	+	7.56201e8i	0.0105358	+	0.100242i
$665$	3.14027e8	−	6.67484e7i	0.0414086	−	0.00880168i
$666$	3.62499e9	−	2.63371e9i	0.475496	−	0.345468i
$667$	8.60226e9	−	6.24991e9i	1.12246	−	0.815517i
$668$	4.42773e9	−	9.41143e8i	0.574729	−	0.122163i
$669$	9.73097e8	+	9.25840e9i	0.125651	+	1.19549i
$670$	−3.65266e8	+	3.47528e9i	−0.0469189	+	0.446404i
$671$	2.92975e9	+	6.22738e8i	0.374371	+	0.0795750i
$672$	−3.53628e9	+	1.57445e9i	−0.449525	+	0.200141i
$673$	−6.63301e9	−	7.36670e9i	−0.838799	−	0.931580i	0.159655	−	0.987173i	$-0.448962\pi$
$673$	−6.63301e9	−	7.36670e9i	−0.838799	−	0.931580i	−0.998454	+	0.0555925i	$0.982295\pi$
$674$	−2.83959e9	+	8.73937e9i	−0.357229	+	1.09944i
$675$	−1.55750e8	+	1.72977e8i	−0.0194923	+	0.0216484i
$676$	−5.29988e9	−	9.17966e9i	−0.659861	−	1.14291i
$677$	2.10179e9	−	3.64041e9i	0.260333	−	0.450911i	−0.705997	−	0.708215i	$-0.749501\pi$
$677$	2.10179e9	−	3.64041e9i	0.260333	−	0.450911i	0.966330	+	0.257304i	$0.0828342\pi$
$678$	−2.01786e9	−	6.21033e9i	−0.248649	−	0.765263i
$679$	1.69299e10	+	7.53770e9i	2.07545	+	0.924048i
$680$	1.83638e9	+	1.33421e9i	0.223966	+	0.162720i
$681$	1.12281e10			1.36236
$682$	6.29094e9	+	1.16709e6i	0.759400	+	0.000140884i
$683$	3.46537e9			0.416176			0.208088	−	0.978110i	$-0.433276\pi$
$683$	3.46537e9			0.416176			0.208088	+	0.978110i	$0.433276\pi$
$684$	1.14250e8	+	8.30074e7i	0.0136508	+	0.00991791i
$685$	−7.41188e9	−	3.29998e9i	−0.881072	−	0.392279i
$686$	7.11173e9	+	2.18876e10i	0.841087	+	2.58860i
$687$	2.04253e9	−	3.53777e9i	0.240337	−	0.416276i
$688$	9.56657e8	+	1.65698e9i	0.111995	+	0.193980i
$689$	2.21160e9	−	2.45623e9i	0.257596	−	0.286089i
$690$	−1.53904e9	+	4.73666e9i	−0.178352	+	0.548910i
$691$	−6.60453e9	−	7.33507e9i	−0.761498	−	0.845729i	0.230356	−	0.973106i	$-0.426011\pi$
$691$	−6.60453e9	−	7.33507e9i	−0.761498	−	0.845729i	−0.991854	+	0.127377i	$0.959344\pi$
$692$	−1.18896e9	+	5.29359e8i	−0.136394	+	0.0607266i
$693$	−1.76615e10	−	3.75407e9i	−2.01587	−	0.428486i
$694$	8.48721e7	−	8.07504e8i	0.00963844	−	0.0917036i
$695$	−2.98515e8	−	2.84018e9i	−0.0337302	−	0.320921i
$696$	6.28446e9	−	1.33580e9i	0.706539	−	0.150179i
$697$	1.82097e9	−	1.32301e9i	0.203699	−	0.147996i
$698$	−1.58331e9	+	1.15034e9i	−0.176227	+	0.128036i
$699$	−1.30375e10	+	2.77121e9i	−1.44386	+	0.306902i
$700$	−5.89842e8	−	5.61197e9i	−0.0649969	−	0.618404i
$701$	−1.65931e8	+	1.57873e9i	−0.0181934	+	0.173099i	−0.999845	−	0.0175825i	$-0.994403\pi$
$701$	−1.65931e8	+	1.57873e9i	−0.0181934	+	0.173099i	0.981652	+	0.190681i	$0.0610697\pi$
$702$	5.62296e8	+	1.19520e8i	0.0613459	+	0.0130395i
$703$	−2.52518e8	+	1.12428e8i	−0.0274125	+	0.0122048i
$704$	−8.31593e8	−	9.23577e8i	−0.0898269	−	0.0997629i
$705$	2.05336e9	−	6.31958e9i	0.220700	−	0.679245i
$706$	−3.08880e9	+	3.43046e9i	−0.330349	+	0.366890i
$707$	2.39943e9	+	4.15593e9i	0.255352	+	0.442283i
$708$	5.80071e9	−	1.00471e10i	0.614277	−	1.06396i
$709$	1.63500e9	+	5.03203e9i	0.172289	+	0.530251i	0.999499	−	0.0316417i	$-0.0100735\pi$
$709$	1.63500e9	+	5.03203e9i	0.172289	+	0.530251i	−0.827210	+	0.561892i	$0.810074\pi$
$710$	2.25551e9	+	1.00422e9i	0.236506	+	0.105299i
$711$	−8.95408e9	−	6.50552e9i	−0.934281	−	0.678795i
$712$	1.12417e9			0.116722
$713$	−4.60752e9	−	7.98388e9i	−0.476052	−	0.824899i
$714$	2.45299e10			2.52204
$715$	−9.89993e9	−	7.19272e9i	−1.01289	−	0.735906i
$716$	4.11441e9	+	1.83186e9i	0.418902	+	0.186507i
$717$	−5.94116e8	−	1.82850e9i	−0.0601942	−	0.185259i
$718$	3.05708e9	−	5.29503e9i	0.308228	−	0.533866i
$719$	−5.61714e9	−	9.72918e9i	−0.563592	−	0.976169i	−0.997179	−	0.0750577i	$-0.976086\pi$
$719$	−5.61714e9	−	9.72918e9i	−0.563592	−	0.976169i	0.433588	−	0.901111i	$-0.357247\pi$
$720$	−9.89860e8	+	1.09935e9i	−0.0988348	+	0.109767i
$721$	−7.78455e9	+	2.39584e10i	−0.773499	+	2.38059i
$722$	4.77911e9	+	5.30774e9i	0.472570	+	0.524843i
$723$	−8.08521e9	+	3.59977e9i	−0.795623	+	0.354234i
$724$	−7.92084e8	−	1.68363e8i	−0.0775686	−	0.0164877i
$725$	−9.79001e8	+	9.31457e9i	−0.0954114	+	0.907779i
$726$	−1.63924e8	−	1.55963e9i	−0.0158988	−	0.151267i
$727$	−1.23868e9	+	2.63290e8i	−0.119561	+	0.0254134i	−0.267303	−	0.963612i	$-0.586133\pi$
$727$	−1.23868e9	+	2.63290e8i	−0.119561	+	0.0254134i	0.147743	+	0.989026i	$0.452799\pi$
$728$	−1.12747e10	+	8.19152e9i	−1.08304	+	0.786873i
$729$	7.89253e9	−	5.73426e9i	0.754518	−	0.548190i
$730$	1.73618e9	−	3.69037e8i	0.165183	−	0.0351107i
$731$	−1.26736e9	−	1.20581e10i	−0.120002	−	1.14175i
$732$	2.77199e8	−	2.63737e9i	0.0261218	−	0.248532i
$733$	8.87836e9	+	1.88715e9i	0.832662	+	0.176988i	0.604470	−	0.796628i	$-0.293385\pi$
$733$	8.87836e9	+	1.88715e9i	0.832662	+	0.176988i	0.228193	+	0.973616i	$0.426718\pi$
$734$	1.87254e9	−	8.33707e8i	0.174781	−	0.0778175i
$735$	1.81450e10	+	2.01520e10i	1.68559	+	1.87203i
$736$	−5.62734e8	+	1.73192e9i	−0.0520273	+	0.160123i
$737$	−8.11261e9	+	9.00997e9i	−0.746491	+	0.829062i
$738$	7.33456e8	+	1.27038e9i	0.0671702	+	0.116342i
$739$	6.82175e9	−	1.18156e10i	0.621785	−	1.07696i	−0.367369	−	0.930075i	$-0.619741\pi$
$739$	6.82175e9	−	1.18156e10i	0.621785	−	1.07696i	0.989153	−	0.146887i	$-0.0469254\pi$
$740$	−8.94766e8	−	2.75381e9i	−0.0811706	−	0.249817i
$741$	9.44865e8	+	4.20681e8i	0.0853112	+	0.0379830i
$742$	−2.54964e9	−	1.85243e9i	−0.229122	−	0.166467i
$743$	−2.76571e9			−0.247369			−0.123685	−	0.992322i	$-0.539471\pi$
$743$	−2.76571e9			−0.247369			−0.123685	+	0.992322i	$0.539471\pi$
$744$	−5.81183e8	−	5.53948e9i	−0.0517378	−	0.493132i
$745$	4.15698e9			0.368325
$746$	−4.21307e9	−	3.06098e9i	−0.371546	−	0.269944i
$747$	2.86874e9	+	1.27724e9i	0.251807	+	0.112112i
$748$	2.43367e9	+	7.49006e9i	0.212621	+	0.654380i
$749$	−9.62256e9	+	1.66668e10i	−0.836766	+	1.44932i
$750$	−5.69417e9	−	9.86258e9i	−0.492851	−	0.853643i
$751$	3.65181e9	−	4.05575e9i	0.314607	−	0.349407i	−0.565014	−	0.825081i	$-0.691129\pi$
$751$	3.65181e9	−	4.05575e9i	0.314607	−	0.349407i	0.879621	+	0.475675i	$0.157796\pi$
$752$	7.50791e8	−	2.31070e9i	0.0643808	−	0.198144i
$753$	1.81911e10	+	2.02032e10i	1.55266	+	1.72440i
$754$	2.11312e10	−	9.40820e9i	1.79524	−	0.799295i
$755$	2.58405e9	+	5.49256e8i	0.218517	+	0.0464473i
$756$	5.72957e7	−	5.45133e8i	0.00482276	−	0.0458855i
$757$	−8.01831e8	−	7.62891e9i	−0.0671811	−	0.639186i	−0.975362	−	0.220609i	$-0.929196\pi$
$757$	−8.01831e8	−	7.62891e9i	−0.0671811	−	0.639186i	0.908181	−	0.418577i	$-0.137471\pi$
$758$	−2.81569e9	+	5.98494e8i	−0.234824	+	0.0499135i
$759$	−1.39797e10	+	1.01569e10i	−1.16052	+	0.843166i
$760$	7.38301e7	−	5.36407e7i	0.00610079	−	0.00443248i
$761$	2.01098e10	−	4.27448e9i	1.65410	−	0.351590i	0.716041	−	0.698058i	$-0.245952\pi$
$761$	2.01098e10	−	4.27448e9i	1.65410	−	0.351590i	0.938062	+	0.346468i	$0.112619\pi$
$762$	2.97651e8	+	2.83196e9i	0.0243705	+	0.231870i
$763$	2.64124e9	−	2.51297e10i	0.215264	−	2.04810i
$764$	2.16895e8	+	4.61024e7i	0.0175963	+	0.00374021i
$765$	8.56392e9	−	3.81290e9i	0.691604	−	0.307922i
$766$	2.69668e9	+	2.99497e9i	0.216785	+	0.240764i
$767$	1.29069e10	−	3.97234e10i	1.03285	−	3.17880i
$768$	−7.36276e8	+	8.17717e8i	−0.0586511	+	0.0651387i
$769$	−1.19139e9	−	2.06356e9i	−0.0944743	−	0.163634i	0.814915	−	0.579581i	$-0.196784\pi$
$769$	−1.19139e9	−	2.06356e9i	−0.0944743	−	0.163634i	−0.909389	+	0.415947i	$0.863450\pi$
$770$	−5.83407e9	+	1.01049e10i	−0.460526	+	0.797654i
$771$	−2.55990e9	−	7.87857e9i	−0.201156	−	0.619094i
$772$	5.43485e9	+	2.41975e9i	0.425135	+	0.189282i
$773$	−1.76723e10	−	1.28397e10i	−1.37615	−	0.999828i	−0.997229	−	0.0743973i	$-0.976297\pi$
$773$	−1.76723e10	−	1.28397e10i	−1.37615	−	0.999828i	−0.378917	−	0.925431i	$-0.623703\pi$
$774$	7.90176e9			0.612535
$775$	7.94178e9	+	1.68962e9i	0.612861	+	0.130386i
$776$	5.26792e9			0.404690
$777$	−2.53149e10	−	1.83923e10i	−1.93599	−	1.40658i
$778$	−5.15764e9	−	2.29633e9i	−0.392665	−	0.174826i
$779$	−2.79640e7	−	8.60643e7i	−0.00211943	−	0.00652292i
$780$	−5.41720e9	+	9.38286e9i	−0.408737	+	0.707953i
$781$	4.28312e9	+	7.41858e9i	0.321722	+	0.557240i
$782$	7.72167e9	−	8.57578e9i	0.577414	−	0.641284i
$783$	−2.81137e8	+	8.65250e8i	−0.0209291	+	0.0644133i
$784$	6.63454e9	+	7.36841e9i	0.491705	+	0.546094i
$785$	−5.13514e8	+	2.28631e8i	−0.0378886	+	0.0168691i
$786$	−1.24670e10	−	2.64993e9i	−0.915760	−	0.194651i
$787$	−2.10706e9	+	2.00473e10i	−0.154086	+	1.46603i	0.595087	+	0.803661i	$0.297117\pi$
$787$	−2.10706e9	+	2.00473e10i	−0.154086	+	1.46603i	−0.749174	+	0.662373i	$0.769549\pi$
$788$	8.53734e8	+	8.12274e9i	0.0621557	+	0.591372i
$789$	1.59516e10	−	3.39063e9i	1.15621	−	0.245760i
$790$	−5.78627e9	+	4.20397e9i	−0.417546	+	0.303365i
$791$	−1.81352e10	+	1.31760e10i	−1.30288	+	0.946599i
$792$	−5.02044e9	+	1.06713e9i	−0.359090	+	0.0763270i
$793$	−9.97978e8	−	9.49512e9i	−0.0710665	−	0.676152i
$794$	7.63098e8	−	7.26039e9i	0.0541014	−	0.514741i
$795$	−2.39654e9	−	5.09401e8i	−0.169161	−	0.0359563i
$796$	−7.82772e9	+	3.48513e9i	−0.550097	+	0.244919i
$797$	1.10005e9	+	1.22173e9i	0.0769678	+	0.0854814i	0.780399	−	0.625282i	$-0.215016\pi$
$797$	1.10005e9	+	1.22173e9i	0.0769678	+	0.0854814i	−0.703431	+	0.710764i	$0.748350\pi$
$798$	3.04754e8	−	9.37936e8i	0.0212295	−	0.0653376i
$799$	−1.03021e10	+	1.14417e10i	−0.714518	+	0.793552i
$800$	−8.02019e8	−	1.38914e9i	−0.0553821	−	0.0959247i
$801$	2.32134e9	−	4.02068e9i	0.159597	−	0.276431i
$802$	1.88528e9	+	5.80230e9i	0.129052	+	0.397182i
$803$	5.62594e9	+	2.50483e9i	0.383434	+	0.170716i
$804$	8.68435e9	+	6.30955e9i	0.589306	+	0.428156i
$805$	1.70971e10			1.15515
$806$	−6.19312e9	−	1.90725e10i	−0.416617	−	1.28302i
$807$	−9.73787e9			−0.652239
$808$	1.10359e9	+	8.01807e8i	0.0735985	+	0.0534724i
$809$	1.59102e10	+	7.08369e9i	1.05647	+	0.470370i	0.860082	−	0.510156i	$-0.170412\pi$
$809$	1.59102e10	+	7.08369e9i	1.05647	+	0.470370i	0.196387	+	0.980526i	$0.437079\pi$
$810$	−2.08433e9	−	6.41491e9i	−0.137806	−	0.424124i
$811$	−1.23257e9	+	2.13488e9i	−0.0811407	+	0.140540i	−0.903740	−	0.428081i	$-0.859190\pi$
$811$	−1.23257e9	+	2.13488e9i	−0.0811407	+	0.140540i	0.822599	+	0.568621i	$0.192523\pi$
$812$	−1.10278e10	−	1.91008e10i	−0.722843	−	1.25200i
$813$	1.23134e10	−	1.36755e10i	0.803642	−	0.892535i
$814$	3.10445e9	−	9.55450e9i	0.201743	−	0.620901i
$815$	1.02502e9	+	1.13840e9i	0.0663254	+	0.0736618i
$816$	6.37000e9	−	2.83611e9i	0.410416	−	0.182729i
$817$	−4.76805e8	−	1.01348e8i	−0.0305889	−	0.00650187i
$818$	−1.70328e9	+	1.62056e10i	−0.108805	+	1.03521i
$819$	6.01614e9	+	5.72397e10i	0.382670	+	3.64086i
$820$	9.27227e8	−	1.97088e8i	0.0587270	−	0.0124828i
$821$	3.19948e9	−	2.32455e9i	0.201780	−	0.146602i	−0.482307	−	0.876002i	$-0.660201\pi$
$821$	3.19948e9	−	2.32455e9i	0.201780	−	0.146602i	0.684087	+	0.729401i	$0.260201\pi$
$822$	−2.01633e10	+	1.46495e10i	−1.26622	+	0.919963i
$823$	−2.47658e10	+	5.26412e9i	−1.54865	+	0.329175i	−0.901359	−	0.433072i	$-0.857430\pi$
$823$	−2.47658e10	+	5.26412e9i	−1.54865	+	0.329175i	−0.647286	+	0.762247i	$0.724096\pi$
$824$	7.48513e8	+	7.12162e9i	0.0466073	+	0.443439i
$825$	1.59100e9	−	1.51373e10i	0.0986462	−	0.938556i
$826$	−3.89558e10	−	8.28030e9i	−2.40515	−	0.511230i
$827$	7.96977e9	−	3.54837e9i	0.489978	−	0.218152i	−0.146849	−	0.989159i	$-0.546913\pi$
$827$	7.96977e9	−	3.54837e9i	0.489978	−	0.218152i	0.636827	+	0.771007i	$0.280247\pi$
$828$	5.03233e9	+	5.58897e9i	0.308080	+	0.342157i
$829$	−7.89131e9	+	2.42870e10i	−0.481070	+	1.48058i	0.356523	+	0.934287i	$0.383962\pi$
$829$	−7.89131e9	+	2.42870e10i	−0.481070	+	1.48058i	−0.837593	+	0.546295i	$0.816038\pi$
$830$	1.35784e9	−	1.50804e9i	0.0824282	−	0.0915458i
$831$	1.25675e10	+	2.17676e10i	0.759707	+	1.31585i
$832$	−1.98075e9	+	3.43076e9i	−0.119233	+	0.206518i
$833$	−1.94161e10	−	5.97566e10i	−1.16387	−	3.58202i
$834$	−8.01430e9	−	3.56820e9i	−0.478393	−	0.212994i
$835$	−9.77349e9	−	7.10086e9i	−0.580961	−	0.422093i
$836$	3.16629e8			0.0187425
$837$	7.20463e8	+	3.20931e8i	0.0424690	+	0.0189179i
$838$	−1.96482e9			−0.115337
$839$	1.50781e10	+	1.09549e10i	0.881412	+	0.640384i	0.933625	−	0.358252i	$-0.116627\pi$
$839$	1.50781e10	+	1.09549e10i	0.881412	+	0.640384i	−0.0522124	+	0.998636i	$0.516627\pi$
$840$	9.43761e9	+	4.20189e9i	0.549395	+	0.244606i
$841$	5.98178e9	+	1.84100e10i	0.346772	+	1.06726i
$842$	1.33074e9	−	2.30490e9i	0.0768245	−	0.133064i
$843$	−1.04560e10	−	1.81103e10i	−0.601130	−	1.04119i
$844$	−2.95014e8	+	3.27646e8i	−0.0168906	+	0.0187589i
$845$	−8.74166e9	+	2.69041e10i	−0.498420	+	1.53398i
$846$	−6.71406e9	−	7.45671e9i	−0.381231	−	0.423400i
$847$	−4.91805e9	+	2.18966e9i	−0.278100	+	0.123818i
$848$	−8.76274e8	−	1.86258e8i	−0.0493463	−	0.0104889i
$849$	3.03502e7	−	2.88763e8i	0.00170210	−	0.0161944i
$850$	1.06250e9	+	1.01090e10i	0.0593420	+	0.564602i
$851$	−1.43988e10	+	3.06057e9i	−0.800892	+	0.170235i
$852$	6.13589e9	−	4.45799e9i	0.339890	−	0.246945i
$853$	2.77173e9	−	2.01378e9i	0.152907	−	0.111094i	−0.508701	−	0.860943i	$-0.669874\pi$
$853$	2.77173e9	−	2.01378e9i	0.152907	−	0.111094i	0.661608	+	0.749849i	$0.269874\pi$
$854$	−8.90467e9	+	1.89275e9i	−0.489232	+	0.103990i
$855$	−3.93956e7	−	3.74824e8i	−0.00215559	−	0.0205091i
$856$	−5.71832e8	+	5.44062e9i	−0.0311609	+	0.296476i
$857$	−1.59645e10	−	3.39336e9i	−0.866408	−	0.184161i	−0.246795	−	0.969068i	$-0.579377\pi$
$857$	−1.59645e10	−	3.39336e9i	−0.866408	−	0.184161i	−0.619614	+	0.784907i	$0.712711\pi$
$858$	−3.43407e10	+	1.52895e10i	−1.85611	+	0.826394i
$859$	1.88250e10	+	2.09073e10i	1.01335	+	1.12544i	0.992073	+	0.125664i	$0.0401060\pi$
$859$	1.88250e10	+	2.09073e10i	1.01335	+	1.12544i	0.0212754	+	0.999774i	$0.493227\pi$
$860$	1.57792e9	−	4.85633e9i	0.0845940	−	0.260354i
$861$	6.85462e9	−	7.61283e9i	0.365993	−	0.406476i
$862$	−1.31057e10	−	2.26997e10i	−0.696920	−	1.20710i
$863$	−1.68948e10	+	2.92627e10i	−0.894779	+	1.54980i	−0.0607014	+	0.998156i	$0.519334\pi$
$863$	−1.68948e10	+	2.92627e10i	−0.894779	+	1.54980i	−0.834078	+	0.551647i	$0.814000\pi$
$864$	−4.81486e7	−	1.48186e8i	−0.00253972	−	0.00781645i
$865$	3.17309e9	+	1.41275e9i	0.166696	+	0.0742181i
$866$	1.26085e10	+	9.16063e9i	0.659708	+	0.479306i
$867$	−1.72740e10			−0.900174
$868$	−1.74690e10	+	7.77382e9i	−0.906670	+	0.403474i
$869$	−2.48151e10			−1.28276
$870$	−1.38719e10	−	1.00785e10i	−0.714200	−	0.518896i
$871$	3.53052e10	+	1.57189e10i	1.81040	+	0.806044i
$872$	−2.21957e9	−	6.83113e9i	−0.113360	−	0.348887i
$873$	1.08779e10	−	1.88411e10i	0.553346	−	0.958423i
$874$	−2.31975e8	−	4.01793e8i	−0.0117531	−	0.0203569i
$875$	−2.61594e10	+	2.90529e10i	−1.32008	+	1.46609i
$876$	1.68491e9	−	5.18563e9i	0.0846863	−	0.260638i
$877$	−1.75526e10	−	1.94942e10i	−0.878706	−	0.975902i	0.121154	−	0.992634i	$-0.461340\pi$
$877$	−1.75526e10	−	1.94942e10i	−0.878706	−	0.975902i	−0.999860	+	0.0167322i	$0.994674\pi$
$878$	−4.55420e9	+	2.02766e9i	−0.227081	+	0.101103i
$879$	−7.19737e8	−	1.52985e8i	−0.0357448	−	0.00759779i
$880$	−3.46697e8	+	3.29860e9i	−0.0171499	+	0.163170i
$881$	−3.63783e9	−	3.46116e10i	−0.179237	−	1.70532i	−0.601520	−	0.798858i	$-0.705438\pi$
$881$	−3.63783e9	−	3.46116e10i	−0.179237	−	1.70532i	0.422283	−	0.906464i	$-0.361229\pi$
$882$	4.00537e10	−	8.51367e9i	1.96563	−	0.417808i
$883$	1.76404e10	−	1.28165e10i	0.862274	−	0.626479i	−0.0662285	−	0.997804i	$-0.521097\pi$
$883$	1.76404e10	−	1.28165e10i	0.862274	−	0.626479i	0.928503	+	0.371326i	$0.121097\pi$
$884$	2.03094e10	−	1.47556e10i	0.988811	−	0.718413i
$885$	−3.02852e10	+	6.43732e9i	−1.46869	+	0.312179i
$886$	1.49488e9	+	1.42229e10i	0.0722086	+	0.687019i
$887$	−2.35682e9	+	2.24236e10i	−0.113395	+	1.07888i	0.778813	+	0.627256i	$0.215822\pi$
$887$	−2.35682e9	+	2.24236e10i	−0.113395	+	1.07888i	−0.892208	+	0.451625i	$0.850845\pi$
$888$	−8.70034e9	−	1.84931e9i	−0.416956	−	0.0886268i
$889$	8.93016e9	−	3.97596e9i	0.426288	−	0.189796i
$890$	−2.00751e9	−	2.22957e9i	−0.0954537	−	0.106012i
$891$	7.23171e9	−	2.22569e10i	0.342507	−	1.05413i
$892$	6.07858e9	−	6.75095e9i	0.286764	−	0.318484i
$893$	3.09497e8	+	5.36065e8i	0.0145438	+	0.0251905i
$894$	6.38488e9	−	1.10589e10i	0.298862	−	0.517645i
$895$	−3.71429e9	−	1.14314e10i	−0.173179	−	0.532990i
$896$	3.45077e9	+	1.53638e9i	0.160265	+	0.0713545i
$897$	4.45613e10	+	3.23757e10i	2.06150	+	1.49777i
$898$	1.48346e10			0.683610
$899$	3.10436e10	−	6.59249e9i	1.42499	−	0.302615i
$900$	−6.62449e9			−0.302903
$901$	4.59275e9	+	3.33683e9i	0.209188	+	0.151984i
$902$	3.00460e9	+	1.33773e9i	0.136321	+	0.0606941i
$903$	−1.70520e10	−	5.24806e10i	−0.770669	−	2.37188i
$904$	−3.18602e9	+	5.51835e9i	−0.143436	+	0.248439i
$905$	1.08057e9	+	1.87160e9i	0.0484599	+	0.0839349i
$906$	5.43014e9	−	6.03079e9i	0.242584	−	0.269417i
$907$	2.59906e9	−	7.99908e9i	0.115662	−	0.355971i	−0.876423	−	0.481543i	$-0.840077\pi$
$907$	2.59906e9	−	7.99908e9i	0.115662	−	0.355971i	0.992085	+	0.125572i	$0.0400765\pi$
$908$	−7.33143e9	−	8.14237e9i	−0.325003	−	0.360953i
$909$	5.14658e9	−	2.29141e9i	0.227272	−	0.101188i
$910$	3.63802e10	+	7.73286e9i	1.60037	+	0.340169i
$911$	−8.43148e8	+	8.02201e9i	−0.0369479	+	0.351535i	0.960393	+	0.278651i	$0.0898872\pi$
$911$	−8.43148e8	+	8.02201e9i	−0.0369479	+	0.351535i	−0.997340	+	0.0728847i	$0.976779\pi$
$912$	−2.93032e7	−	2.78801e8i	−0.00127918	−	0.0121706i
$913$	6.88679e9	−	1.46383e9i	0.299481	−	0.0636567i
$914$	−2.12932e10	+	1.54704e10i	−0.922420	+	0.670177i
$915$	−5.72572e9	+	4.15998e9i	−0.247091	+	0.179522i
$916$	−3.89918e9	+	8.28797e8i	−0.167625	+	0.0356299i
$917$	4.57348e9	+	4.35138e10i	0.195864	+	1.86352i
$918$	−1.03208e8	+	9.81963e8i	−0.00440317	+	0.0418934i
$919$	−4.11838e10	−	8.75389e9i	−1.75034	−	0.372046i	−0.782311	−	0.622888i	$-0.785959\pi$
$919$	−4.11838e10	−	8.75389e9i	−1.75034	−	0.372046i	−0.968028	+	0.250842i	$0.919293\pi$
$920$	4.43983e9	−	1.97674e9i	0.187979	−	0.0836936i
$921$	6.00606e9	+	6.67041e9i	0.253327	+	0.281348i
$922$	5.92926e8	−	1.82484e9i	0.0249139	−	0.0766771i
$923$	1.82709e10	−	2.02919e10i	0.764811	−	0.849409i
$924$	1.79216e10	+	3.10411e10i	0.747350	+	1.29445i
$925$	6.48316e9	−	1.12292e10i	0.269334	−	0.466499i
$926$	−3.10663e9	−	9.56121e9i	−0.128573	−	0.395708i
$927$	2.70167e10	+	1.20286e10i	1.11392	+	0.495948i
$928$	−5.07214e9	−	3.68513e9i	−0.208340	−	0.151368i
$929$	1.53878e10			0.629682			0.314841	−	0.949144i	$-0.398049\pi$
$929$	1.53878e10			0.629682			0.314841	+	0.949144i	$0.398049\pi$
$930$	−9.94859e9	+	1.10449e10i	−0.405575	+	0.450269i
$931$	−2.52610e9			−0.102595
$932$	1.05225e10	+	7.64503e9i	0.425758	+	0.309331i
$933$	−1.07911e10	−	4.80452e9i	−0.434992	−	0.193671i
$934$	−1.86952e9	−	5.75378e9i	−0.0750785	−	0.231068i
$935$	1.05091e10	−	1.82023e10i	0.420459	−	0.728257i
$936$	8.18026e9	+	1.41686e10i	0.326063	+	0.564757i
$937$	2.91609e10	−	3.23865e10i	1.15801	−	1.28610i	0.206515	−	0.978443i	$-0.433788\pi$
$937$	2.91609e10	−	3.23865e10i	1.15801	−	1.28610i	0.951497	−	0.307659i	$-0.0995456\pi$
$938$	1.13872e10	−	3.50463e10i	0.450514	−	1.38654i
$939$	3.65905e10	+	4.06379e10i	1.44225	+	1.60178i
$940$	−5.92355e9	+	2.63733e9i	−0.232613	+	0.103566i
$941$	−2.95669e10	−	6.28464e9i	−1.15676	−	0.245876i	−0.410707	−	0.911767i	$-0.634718\pi$
$941$	−2.95669e10	−	6.28464e9i	−1.15676	−	0.245876i	−0.746049	+	0.665891i	$0.768052\pi$
$942$	−1.80493e8	+	1.71728e9i	−0.00703531	+	0.0669365i
$943$	−5.03746e8	−	4.79283e9i	−0.0195623	−	0.186123i
$944$	−1.10735e10	+	2.35375e9i	−0.428433	+	0.0910663i
$945$	−1.18348e9	+	8.59848e8i	−0.0456194	+	0.0331444i
$946$	1.43329e10	−	1.04135e10i	0.550446	−	0.399923i
$947$	−8.57267e8	+	1.82218e8i	−0.0328013	+	0.00697214i	−0.224283	−	0.974524i	$-0.572004\pi$
$947$	−8.57267e8	+	1.82218e8i	−0.0328013	+	0.00697214i	0.191482	+	0.981496i	$0.438671\pi$
$948$	2.29657e9	+	2.18504e10i	0.0875490	+	0.832973i
$949$	2.05191e9	−	1.95227e10i	0.0779341	−	0.741493i
$950$	3.99732e8	+	8.49658e7i	0.0151264	+	0.00321522i
$951$	4.55853e10	−	2.02959e10i	1.71867	−	0.765202i
$952$	−1.60168e10	−	1.77885e10i	−0.601655	−	0.668205i
$953$	−2.27024e9	+	6.98707e9i	−0.0849662	+	0.261499i	−0.984509	−	0.175333i	$-0.943900\pi$
$953$	−2.27024e9	+	6.98707e9i	−0.0849662	+	0.261499i	0.899543	+	0.436832i	$0.143900\pi$
$954$	−2.47562e9	+	2.74945e9i	−0.0923134	+	0.102524i
$955$	−2.95890e8	−	5.12496e8i	−0.0109930	−	0.0190405i
$956$	−9.38057e8	+	1.62476e9i	−0.0347237	+	0.0601433i
$957$	−1.83838e10	−	5.65796e10i	−0.678023	−	2.08674i
$958$	1.26013e10	+	5.61045e9i	0.463058	+	0.206167i
$959$	6.92177e10	+	5.02896e10i	2.53426	+	1.84125i
$960$	2.93660e9			0.107126
$961$	−2.86570e9	−	2.73630e10i	−0.104159	−	0.994561i
$962$	−3.20229e10			−1.15971
$963$	1.82780e10	+	1.32798e10i	0.659534	+	0.479180i
$964$	7.88971e9	+	3.51273e9i	0.283656	+	0.126292i
$965$	−4.90631e9	−	1.51001e10i	−0.175756	−	0.540921i
$966$	2.62602e10	−	4.54839e10i	0.937297	−	1.62345i
$967$	8.47449e9	+	1.46782e10i	0.301384	+	0.522013i	0.976450	−	0.215745i	$-0.0692179\pi$
$967$	8.47449e9	+	1.46782e10i	0.301384	+	0.522013i	−0.675065	+	0.737758i	$0.735885\pi$
$968$	−1.02397e9	+	1.13724e9i	−0.0362847	+	0.0402983i
$969$	−5.48962e8	+	1.68953e9i	−0.0193825	+	0.0596531i
$970$	−9.40731e9	−	1.04479e10i	−0.330951	−	0.367559i
$971$	−4.52327e10	+	2.01389e10i	−1.58557	+	0.705942i	−0.994890	−	0.100964i	$-0.967807\pi$
$971$	−4.52327e10	+	2.01389e10i	−1.58557	+	0.705942i	−0.590681	+	0.806905i	$0.701141\pi$
$972$	−1.96162e10	−	4.16955e9i	−0.685145	−	0.145632i
$973$	−3.14794e9	+	2.99507e10i	−0.109555	+	1.04234i
$974$	−2.36052e9	−	2.24589e10i	−0.0818562	−	0.778810i
$975$	−4.74568e10	+	1.00873e10i	−1.63977	+	0.348543i
$976$	−2.09356e9	+	1.52106e9i	−0.0720792	+	0.0523686i
$977$	3.73400e10	−	2.71291e10i	1.28098	−	0.930688i	0.281400	−	0.959590i	$-0.409201\pi$
$977$	3.73400e10	−	2.71291e10i	1.28098	−	0.930688i	0.999582	+	0.0289021i	$0.00920111\pi$
$978$	4.60288e9	−	9.78372e8i	0.157342	−	0.0334440i
$979$	−1.08807e9	−	1.03523e10i	−0.0370610	−	0.352611i
$980$	2.76599e9	−	2.63166e10i	0.0938769	−	0.893179i
$981$	−2.90154e10	−	6.16741e9i	−0.981266	−	0.208575i
$982$	−7.09102e9	+	3.15713e9i	−0.238956	+	0.106390i
$983$	−3.60923e10	−	4.00845e10i	−1.21193	−	1.34598i	−0.921158	−	0.389189i	$-0.872755\pi$
$983$	−3.60923e10	−	4.00845e10i	−1.21193	−	1.34598i	−0.290770	−	0.956793i	$-0.593911\pi$
$984$	8.99847e8	−	2.76944e9i	0.0301083	−	0.0926637i
$985$	1.45853e10	−	1.61986e10i	0.486281	−	0.540070i
$986$	1.98648e10	+	3.44068e10i	0.659955	+	1.14308i
$987$	−3.50359e10	+	6.06839e10i	−1.15985	+	2.00892i
$988$	−3.11883e8	−	9.59878e8i	−0.0102883	−	0.0316641i
$989$	−2.37152e10	−	1.05587e10i	−0.779544	−	0.347075i
$990$	1.10818e10	+	8.05140e9i	0.362984	+	0.263723i
$991$	−1.99473e10			−0.651068			−0.325534	−	0.945530i	$-0.605544\pi$
$991$	−1.99473e10			−0.651068			−0.325534	+	0.945530i	$0.605544\pi$
$992$	−3.63761e9	+	4.03847e9i	−0.118311	+	0.131349i
$993$	−1.04109e10			−0.337417
$994$	−2.10637e10	−	1.53037e10i	−0.680271	−	0.494246i
$995$	2.08906e10	+	9.30109e9i	0.672311	+	0.299332i
$996$	−1.92631e9	−	5.92856e9i	−0.0617757	−	0.190126i
$997$	−2.22610e10	+	3.85571e10i	−0.711395	+	1.23217i	0.252938	+	0.967482i	$0.418603\pi$
$997$	−2.22610e10	+	3.85571e10i	−0.711395	+	1.23217i	−0.964333	+	0.264690i	$0.914730\pi$
$998$	1.10872e10	+	1.92035e10i	0.353073	+	0.611540i
$999$	8.42780e8	−	9.36002e8i	0.0267445	−	0.0297028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.g.b.19.2	✓	72
31.18	even	15	inner	62.8.g.b.49.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.g.b.19.2	✓	72	1.1	even	1	trivial
62.8.g.b.49.2	yes	72	31.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(6.47214 + 4.70228i) q^{2} +(-59.9156 - 26.6762i) q^{3} +(19.7771 + 60.8676i) q^{4} +(85.4015 - 147.920i) q^{5} +(-262.343 - 454.392i) q^{6} +(-1205.22 + 1338.54i) q^{7} +(-158.217 + 486.941i) q^{8} +(1414.88 + 1571.38i) q^{9} +(1248.29 - 555.775i) q^{10} +(4637.29 + 985.686i) q^{11} +(438.757 - 4174.50i) q^{12} +(-1579.62 - 15029.1i) q^{13} +(-14094.5 + 2995.89i) q^{14} +(-9062.81 + 6584.52i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(25388.9 - 5396.58i) q^{17} +(1768.20 + 16823.3i) q^{18} +(109.080 - 1037.83i) q^{19} +(10692.5 + 2272.76i) q^{20} +(107919. - 48048.5i) q^{21} +(25378.2 + 28185.3i) q^{22} +(17173.3 - 52853.9i) q^{23} +(22469.4 - 24954.8i) q^{24} +(24475.7 + 42393.1i) q^{25} +(60447.6 - 104698. i) q^{26} +(1469.38 + 4522.28i) q^{27} +(-105309. - 46886.7i) q^{28} +(154790. + 112461. i) q^{29} -89618.0 q^{30} +(111011. - 123244. i) q^{31} -32768.0 q^{32} +(-251552. - 182763. i) q^{33} +(189697. + 84458.4i) q^{34} +(95068.0 + 292589. i) q^{35} +(-67664.0 + 117197. i) q^{36} +(-132441. - 229394. i) q^{37} +(5586.13 - 6204.03i) q^{38} +(-306275. + 942618. i) q^{39} +(58516.2 + 64988.8i) q^{40} +(79220.3 - 35271.2i) q^{41} +(924402. + 196488. i) q^{42} +(48827.1 - 464559. i) q^{43} +(31715.7 + 301755. i) q^{44} +(353271. - 75090.0i) q^{45} +(359682. - 261324. i) q^{46} +(-479882. + 348654. i) q^{47} +(262769. - 55853.3i) q^{48} +(-253032. - 2.40743e6i) q^{49} +(-40934.5 + 389465. i) q^{50} +(-1.66515e6 - 353939. i) q^{51} +(883547. - 393380. i) q^{52} +(146348. + 162536. i) q^{53} +(-11755.0 + 36178.3i) q^{54} +(541834. - 601768. i) q^{55} +(-461101. - 798651. i) q^{56} +(-34220.8 + 59272.2i) q^{57} +(472995. + 1.45573e6i) q^{58} +(2.52494e6 + 1.12418e6i) q^{59} +(-580020. - 421409. i) q^{60} +631782. q^{61} +(1.29801e6 - 275648. i) q^{62} -3.80859e6 q^{63} +(-212079. - 154084. i) q^{64} +(-2.35801e6 - 1.04985e6i) q^{65} +(-768674. - 2.36574e6i) q^{66} +(-1.27867e6 + 2.21473e6i) q^{67} +(830595. + 1.43863e6i) q^{68} +(-2.43889e6 + 2.70866e6i) q^{69} +(-760544. + 2.34071e6i) q^{70} +(1.20904e6 + 1.34278e6i) q^{71} +(-989026. + 440343. i) q^{72} +(1.27060e6 + 270075. i) q^{73} +(221501. - 2.10744e6i) q^{74} +(-335590. - 3.19293e6i) q^{75} +(65327.3 - 13885.7i) q^{76} +(-6.90834e6 + 5.01921e6i) q^{77} +(-6.41471e6 + 4.66056e6i) q^{78} +(-5.11989e6 + 1.08827e6i) q^{79} +(73129.0 + 695776. i) q^{80} +(515981. - 4.90923e6i) q^{81} +(678580. + 144237. i) q^{82} +(1.35670e6 - 604041. i) q^{83} +(5.05891e6 + 5.61849e6i) q^{84} +(1.36999e6 - 4.21639e6i) q^{85} +(2.50050e6 - 2.77709e6i) q^{86} +(-6.27428e6 - 1.08674e7i) q^{87} +(-1.21367e6 + 2.10213e6i) q^{88} +(-678491. - 2.08818e6i) q^{89} +(2.63951e6 + 1.17519e6i) q^{90} +(2.20208e7 + 1.59991e7i) q^{91} +3.55673e6 q^{92} +(-9.93898e6 + 4.42291e6i) q^{93} -4.74533e6 q^{94} +(-144199. - 104767. i) q^{95} +(1.96332e6 + 874124. i) q^{96} +(-3.17944e6 - 9.78533e6i) q^{97} +(9.68278e6 - 1.67711e7i) q^{98} +(5.01230e6 + 8.68157e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) \) 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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