LMFDB - Embedded newform 84.12.b.a.55.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(55,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("84.55");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.b (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:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.16
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-23.3606 + 38.7593i) q^{2} -243.000 q^{3} +(-956.568 - 1810.88i) q^{4} +7022.22i q^{5} +(5676.62 - 9418.51i) q^{6} +(-17991.9 - 40664.7i) q^{7} +(92534.4 + 5227.27i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-23.3606 + 38.7593i) q^{2} -243.000 q^{3} +(-956.568 - 1810.88i) q^{4} +7022.22i q^{5} +(5676.62 - 9418.51i) q^{6} +(-17991.9 - 40664.7i) q^{7} +(92534.4 + 5227.27i) q^{8} +59049.0 q^{9} +(-272177. - 164043. i) q^{10} +197179. i q^{11} +(232446. + 440044. i) q^{12} -1.63530e6i q^{13} +(1.99644e6 + 252597. i) q^{14} -1.70640e6i q^{15} +(-2.36426e6 + 3.46446e6i) q^{16} -1.21139e6i q^{17} +(-1.37942e6 + 2.28870e6i) q^{18} +3.44328e6 q^{19} +(1.27164e7 - 6.71723e6i) q^{20} +(4.37203e6 + 9.88152e6i) q^{21} +(-7.64252e6 - 4.60622e6i) q^{22} +4.70358e7i q^{23} +(-2.24859e7 - 1.27023e6i) q^{24} -483514. q^{25} +(6.33829e7 + 3.82014e7i) q^{26} -1.43489e7 q^{27} +(-5.64284e7 + 7.14797e7i) q^{28} +2.09529e8 q^{29} +(6.61389e7 + 3.98625e7i) q^{30} -2.19236e8 q^{31} +(-7.90494e7 - 1.72569e8i) q^{32} -4.79145e7i q^{33} +(4.69527e7 + 2.82988e7i) q^{34} +(2.85557e8 - 1.26343e8i) q^{35} +(-5.64844e7 - 1.06931e8i) q^{36} +6.89880e7 q^{37} +(-8.04370e7 + 1.33459e8i) q^{38} +3.97377e8i q^{39} +(-3.67070e7 + 6.49797e8i) q^{40} +1.46028e9i q^{41} +(-4.85134e8 - 6.13810e7i) q^{42} -5.23297e7i q^{43} +(3.57067e8 - 1.88615e8i) q^{44} +4.14655e8i q^{45} +(-1.82308e9 - 1.09878e9i) q^{46} -1.19926e9 q^{47} +(5.74515e8 - 8.41863e8i) q^{48} +(-1.32991e9 + 1.46327e9i) q^{49} +(1.12952e7 - 1.87407e7i) q^{50} +2.94368e8i q^{51} +(-2.96132e9 + 1.56427e9i) q^{52} -4.16512e8 q^{53} +(3.35199e8 - 5.56154e8i) q^{54} -1.38464e9 q^{55} +(-1.45230e9 - 3.85693e9i) q^{56} -8.36718e8 q^{57} +(-4.89472e9 + 8.12121e9i) q^{58} +2.99821e9 q^{59} +(-3.09008e9 + 1.63229e9i) q^{60} -1.47652e9i q^{61} +(5.12148e9 - 8.49744e9i) q^{62} +(-1.06240e9 - 2.40121e9i) q^{63} +(8.53529e9 + 9.67403e8i) q^{64} +1.14834e10 q^{65} +(1.85713e9 + 1.11931e9i) q^{66} -1.59032e10i q^{67} +(-2.19368e9 + 1.15878e9i) q^{68} -1.14297e10i q^{69} +(-1.77379e9 + 1.40194e10i) q^{70} -1.73490e10i q^{71} +(5.46406e9 + 3.08665e8i) q^{72} -7.51561e9i q^{73} +(-1.61160e9 + 2.67393e9i) q^{74} +1.17494e8 q^{75} +(-3.29373e9 - 6.23537e9i) q^{76} +(8.01823e9 - 3.54763e9i) q^{77} +(-1.54020e10 - 9.28295e9i) q^{78} -9.12224e8i q^{79} +(-2.43282e10 - 1.66024e10i) q^{80} +3.48678e9 q^{81} +(-5.65994e10 - 3.41129e10i) q^{82} -5.01431e10 q^{83} +(1.37121e10 - 1.73696e10i) q^{84} +8.50666e9 q^{85} +(2.02826e9 + 1.22245e9i) q^{86} -5.09156e10 q^{87} +(-1.03071e9 + 1.82458e10i) q^{88} -6.78142e9i q^{89} +(-1.60718e10 - 9.68658e9i) q^{90} +(-6.64988e10 + 2.94221e10i) q^{91} +(8.51762e10 - 4.49930e10i) q^{92} +5.32744e10 q^{93} +(2.80153e10 - 4.64823e10i) q^{94} +2.41795e10i q^{95} +(1.92090e10 + 4.19342e10i) q^{96} -1.49341e11i q^{97} +(-2.56479e10 - 8.57292e10i) q^{98} +1.16432e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) $ 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−23.3606	+	38.7593i	−0.516201	+	0.856468i
$2$	−23.3606	+	38.7593i	−0.516201	+	0.856468i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	−956.568	−	1810.88i	−0.467074	−	0.884218i
$5$			7022.22i			1.00494i	0.864595	+	0.502469i	$0.167575\pi$
$5$			7022.22i			1.00494i	−0.864595	+	0.502469i	$0.832425\pi$
$6$	5676.62	−	9418.51i	0.298029	−	0.494482i
$7$	−17991.9	−	40664.7i	−0.404611	−	0.914489i
$7$	−17991.9	−	40664.7i	−0.404611	−	0.914489i
$8$	92534.4	+	5227.27i	0.998408	+	0.0564001i
$9$	59049.0			0.333333
$10$	−272177.	−	164043.i	−0.860698	−	0.518750i
$11$			197179.i			0.369148i	0.982819	+	0.184574i	$0.0590906\pi$
$11$			197179.i			0.369148i	−0.982819	+	0.184574i	$0.940909\pi$
$12$	232446.	+	440044.i	0.269665	+	0.510504i
$13$		−	1.63530e6i		−	1.22154i	−0.791808	−	0.610770i	$-0.790860\pi$
$13$		−	1.63530e6i		−	1.22154i	0.791808	−	0.610770i	$-0.209140\pi$
$14$	1.99644e6	+	252597.i	0.992091	+	0.125523i
$15$		−	1.70640e6i		−	0.580202i
$16$	−2.36426e6	+	3.46446e6i	−0.563684	+	0.825991i
$17$		−	1.21139e6i		−	0.206926i	−0.994633	−	0.103463i	$-0.967008\pi$
$17$		−	1.21139e6i		−	0.206926i	0.994633	−	0.103463i	$-0.0329924\pi$
$18$	−1.37942e6	+	2.28870e6i	−0.172067	+	0.285489i
$19$	3.44328e6			0.319027			0.159514	−	0.987196i	$-0.449007\pi$
$19$	3.44328e6			0.319027			0.159514	+	0.987196i	$0.449007\pi$
$20$	1.27164e7	−	6.71723e6i	0.888585	−	0.469381i
$21$	4.37203e6	+	9.88152e6i	0.233602	+	0.527980i
$22$	−7.64252e6	−	4.60622e6i	−0.316164	−	0.190555i
$23$			4.70358e7i			1.52379i	0.647699	+	0.761896i	$0.275731\pi$
$23$			4.70358e7i			1.52379i	−0.647699	+	0.761896i	$0.724269\pi$
$24$	−2.24859e7	−	1.27023e6i	−0.576431	−	0.0325626i
$25$	−483514.			−0.00990237
$26$	6.33829e7	+	3.82014e7i	1.04621	+	0.630560i
$27$	−1.43489e7			−0.192450
$28$	−5.64284e7	+	7.14797e7i	−0.619624	+	0.784899i
$29$	2.09529e8			1.89695			0.948474	−	0.316854i	$-0.102627\pi$
$29$	2.09529e8			1.89695			0.948474	+	0.316854i	$0.102627\pi$
$30$	6.61389e7	+	3.98625e7i	0.496924	+	0.299500i
$31$	−2.19236e8			−1.37538			−0.687690	−	0.726005i	$-0.741375\pi$
$31$	−2.19236e8			−1.37538			−0.687690	+	0.726005i	$0.741375\pi$
$32$	−7.90494e7	−	1.72569e8i	−0.416461	−	0.909154i
$33$		−	4.79145e7i		−	0.213128i
$34$	4.69527e7	+	2.82988e7i	0.177226	+	0.106815i
$35$	2.85557e8	−	1.26343e8i	0.919005	−	0.406610i
$36$	−5.64844e7	−	1.06931e8i	−0.155691	−	0.294739i
$37$	6.89880e7			0.163555			0.0817776	−	0.996651i	$-0.473940\pi$
$37$	6.89880e7			0.163555			0.0817776	+	0.996651i	$0.473940\pi$
$38$	−8.04370e7	+	1.33459e8i	−0.164682	+	0.273237i
$39$			3.97377e8i			0.705256i
$40$	−3.67070e7	+	6.49797e8i	−0.0566786	+	1.00334i
$41$			1.46028e9i			1.96845i	0.176920	+	0.984225i	$0.443387\pi$
$41$			1.46028e9i			1.96845i	−0.176920	+	0.984225i	$0.556613\pi$
$42$	−4.85134e8	−	6.13810e7i	−0.572784	−	0.0724707i
$43$		−	5.23297e7i		−	0.0542840i	−0.999632	−	0.0271420i	$-0.991359\pi$
$43$		−	5.23297e7i		−	0.0542840i	0.999632	−	0.0271420i	$-0.00864063\pi$
$44$	3.57067e8	−	1.88615e8i	0.326408	−	0.172420i
$45$			4.14655e8i			0.334980i
$46$	−1.82308e9	−	1.09878e9i	−1.30508	−	0.786583i
$47$	−1.19926e9			−0.762735			−0.381368	−	0.924423i	$-0.624547\pi$
$47$	−1.19926e9			−0.762735			−0.381368	+	0.924423i	$0.624547\pi$
$48$	5.74515e8	−	8.41863e8i	0.325443	−	0.476886i
$49$	−1.32991e9	+	1.46327e9i	−0.672579	+	0.740025i
$50$	1.12952e7	−	1.87407e7i	0.00511161	−	0.00848106i
$51$			2.94368e8i			0.119469i
$52$	−2.96132e9	+	1.56427e9i	−1.08011	+	0.570550i
$53$	−4.16512e8			−0.136808			−0.0684038	−	0.997658i	$-0.521791\pi$
$53$	−4.16512e8			−0.136808			−0.0684038	+	0.997658i	$0.521791\pi$
$54$	3.35199e8	−	5.56154e8i	0.0993428	−	0.164827i
$55$	−1.38464e9			−0.370972
$56$	−1.45230e9	−	3.85693e9i	−0.352390	−	0.935853i
$57$	−8.36718e8			−0.184190
$58$	−4.89472e9	+	8.12121e9i	−0.979206	+	1.62468i
$59$	2.99821e9			0.545979			0.272990	−	0.962017i	$-0.411988\pi$
$59$	2.99821e9			0.545979			0.272990	+	0.962017i	$0.411988\pi$
$60$	−3.09008e9	+	1.63229e9i	−0.513025	+	0.270997i
$61$		−	1.47652e9i		−	0.223834i	−0.993718	−	0.111917i	$-0.964301\pi$
$61$		−	1.47652e9i		−	0.223834i	0.993718	−	0.111917i	$-0.0356990\pi$
$62$	5.12148e9	−	8.49744e9i	0.709972	−	1.17797i
$63$	−1.06240e9	−	2.40121e9i	−0.134870	−	0.304830i
$64$	8.53529e9	+	9.67403e8i	0.993638	+	0.112621i
$65$	1.14834e10			1.22757
$66$	1.85713e9	+	1.11931e9i	0.182537	+	0.110017i
$67$		−	1.59032e10i		−	1.43904i	−0.694470	−	0.719522i	$-0.744361\pi$
$67$		−	1.59032e10i		−	1.43904i	0.694470	−	0.719522i	$-0.255639\pi$
$68$	−2.19368e9	+	1.15878e9i	−0.182968	+	0.0966498i
$69$		−	1.14297e10i		−	0.879762i
$70$	−1.77379e9	+	1.40194e10i	−0.126143	+	0.996991i
$71$		−	1.73490e10i		−	1.14118i	−0.821237	−	0.570588i	$-0.806715\pi$
$71$		−	1.73490e10i		−	1.14118i	0.821237	−	0.570588i	$-0.193285\pi$
$72$	5.46406e9	+	3.08665e8i	0.332803	+	0.0188000i
$73$		−	7.51561e9i		−	0.424315i	−0.977236	−	0.212157i	$-0.931951\pi$
$73$		−	7.51561e9i		−	0.424315i	0.977236	−	0.212157i	$-0.0680490\pi$
$74$	−1.61160e9	+	2.67393e9i	−0.0844273	+	0.140080i
$75$	1.17494e8			0.00571714
$76$	−3.29373e9	−	6.23537e9i	−0.149009	−	0.282090i
$77$	8.01823e9	−	3.54763e9i	0.337582	−	0.149362i
$78$	−1.54020e10	−	9.28295e9i	−0.604029	−	0.364054i
$79$		−	9.12224e8i		−	0.0333544i	−0.999861	−	0.0166772i	$-0.994691\pi$
$79$		−	9.12224e8i		−	0.0333544i	0.999861	−	0.0166772i	$-0.00530876\pi$
$80$	−2.43282e10	−	1.66024e10i	−0.830070	−	0.566468i
$81$	3.48678e9			0.111111
$82$	−5.65994e10	−	3.41129e10i	−1.68591	−	1.01612i
$83$	−5.01431e10			−1.39728			−0.698638	−	0.715476i	$-0.746210\pi$
$83$	−5.01431e10			−1.39728			−0.698638	+	0.715476i	$0.746210\pi$
$84$	1.37121e10	−	1.73696e10i	0.357740	−	0.453161i
$85$	8.50666e9			0.207948
$86$	2.02826e9	+	1.22245e9i	0.0464925	+	0.0280214i
$87$	−5.09156e10			−1.09520
$88$	−1.03071e9	+	1.82458e10i	−0.0208200	+	0.368561i
$89$		−	6.78142e9i		−	0.128729i	−0.997926	−	0.0643643i	$-0.979498\pi$
$89$		−	6.78142e9i		−	0.128729i	0.997926	−	0.0643643i	$-0.0205020\pi$
$90$	−1.60718e10	−	9.68658e9i	−0.286899	−	0.172917i
$91$	−6.64988e10	+	2.94221e10i	−1.11708	+	0.494249i
$92$	8.51762e10	−	4.49930e10i	1.34737	−	0.711724i
$93$	5.32744e10			0.794076
$94$	2.80153e10	−	4.64823e10i	0.393724	−	0.653258i
$95$			2.41795e10i			0.320603i
$96$	1.92090e10	+	4.19342e10i	0.240444	+	0.524900i
$97$		−	1.49341e11i		−	1.76577i	−0.469591	−	0.882884i	$-0.655599\pi$
$97$		−	1.49341e11i		−	1.76577i	0.469591	−	0.882884i	$-0.344401\pi$
$98$	−2.56479e10	−	8.57292e10i	−0.286622	−	0.958044i
$99$			1.16432e10i			0.123049i
$100$	4.62514e8	+	8.75586e8i	0.00462514	+	0.00875586i
$101$			9.99819e10i			0.946572i	0.880909	+	0.473286i	$0.156932\pi$
$101$			9.99819e10i			0.946572i	−0.880909	+	0.473286i	$0.843068\pi$
$102$	−1.14095e10	−	6.87661e9i	−0.102321	−	0.0616699i
$103$	9.17767e9			0.0780060			0.0390030	−	0.999239i	$-0.487582\pi$
$103$	9.17767e9			0.0780060			0.0390030	+	0.999239i	$0.487582\pi$
$104$	8.54812e9	−	1.51321e11i	0.0688949	−	1.21960i
$105$	−6.93903e10	+	3.07014e10i	−0.530588	+	0.234756i
$106$	9.72996e9	−	1.61437e10i	0.0706202	−	0.117171i
$107$		−	1.34817e11i		−	0.929250i	−0.885507	−	0.464625i	$-0.846189\pi$
$107$		−	1.34817e11i		−	0.929250i	0.885507	−	0.464625i	$-0.153811\pi$
$108$	1.37257e10	+	2.59841e10i	0.0898884	+	0.170168i
$109$	−5.23092e10			−0.325636			−0.162818	−	0.986656i	$-0.552058\pi$
$109$	−5.23092e10			−0.325636			−0.162818	+	0.986656i	$0.552058\pi$
$110$	3.23459e10	−	5.36675e10i	0.191496	−	0.317725i
$111$	−1.67641e10			−0.0944286
$112$	1.83419e11	+	3.38098e10i	0.983432	+	0.181277i
$113$	−1.94555e11			−0.993367			−0.496684	−	0.867932i	$-0.665449\pi$
$113$	−1.94555e11			−0.993367			−0.496684	+	0.867932i	$0.665449\pi$
$114$	1.95462e10	−	3.24306e10i	0.0950792	−	0.157753i
$115$	−3.30296e11			−1.53132
$116$	−2.00429e11	−	3.79432e11i	−0.886015	−	1.67732i
$117$		−	9.65625e10i		−	0.407180i
$118$	−7.00399e10	+	1.16209e11i	−0.281835	+	0.467614i
$119$	−4.92609e10	+	2.17952e10i	−0.189232	+	0.0837247i
$120$	8.91981e9	−	1.57901e11i	0.0327234	−	0.579278i
$121$	2.46432e11			0.863729
$122$	5.72289e10	+	3.44924e10i	0.191706	+	0.115543i
$123$		−	3.54848e11i		−	1.13649i
$124$	2.09714e11	+	3.97010e11i	0.642404	+	1.21614i
$125$			3.39487e11i			0.994988i
$126$	1.17888e11	+	1.49156e10i	0.330697	+	0.0418410i
$127$			2.91847e11i			0.783852i	0.919997	+	0.391926i	$0.128191\pi$
$127$			2.91847e11i			0.783852i	−0.919997	+	0.391926i	$0.871809\pi$
$128$	−2.36885e11	+	3.08223e11i	−0.609372	+	0.792884i
$129$			1.27161e10i			0.0313409i
$130$	−2.68259e11	+	4.45089e11i	−0.633674	+	1.05138i
$131$	−9.33635e10			−0.211439			−0.105720	−	0.994396i	$-0.533715\pi$
$131$	−9.33635e10			−0.211439			−0.105720	+	0.994396i	$0.533715\pi$
$132$	−8.67674e10	+	4.58335e10i	−0.188452	+	0.0995465i
$133$	−6.19512e10	−	1.40020e11i	−0.129082	−	0.291747i
$134$	6.16398e11	+	3.71509e11i	1.23249	+	0.742835i
$135$		−	1.00761e11i		−	0.193401i
$136$	6.33226e9	−	1.12095e11i	0.0116707	−	0.206597i
$137$	−1.05278e12			−1.86369			−0.931843	−	0.362863i	$-0.881799\pi$
$137$	−1.05278e12			−1.86369			−0.931843	+	0.362863i	$0.881799\pi$
$138$	4.43008e11	+	2.67005e11i	0.753488	+	0.454134i
$139$	−1.03261e12			−1.68793			−0.843964	−	0.536399i	$-0.819784\pi$
$139$	−1.03261e12			−1.68793			−0.843964	+	0.536399i	$0.819784\pi$
$140$	−5.01947e11	−	3.96253e11i	−0.788775	−	0.622684i
$141$	2.91419e11			0.440365
$142$	6.72434e11	+	4.05282e11i	0.977380	+	0.589076i
$143$	3.22446e11			0.450930
$144$	−1.39607e11	+	2.04573e11i	−0.187895	+	0.275330i
$145$			1.47136e12i			1.90632i
$146$	2.91300e11	+	1.75569e11i	0.363412	+	0.219032i
$147$	3.23168e11	−	3.55575e11i	0.388314	−	0.427254i
$148$	−6.59917e10	−	1.24929e11i	−0.0763924	−	0.144618i
$149$	−4.08137e11			−0.455283			−0.227641	−	0.973745i	$-0.573101\pi$
$149$	−4.08137e11			−0.455283			−0.227641	+	0.973745i	$0.573101\pi$
$150$	−2.74473e9	+	4.55399e9i	−0.00295119	+	0.00489654i
$151$		−	5.49821e11i		−	0.569965i	−0.958533	−	0.284982i	$-0.908012\pi$
$151$		−	5.49821e11i		−	0.569965i	0.958533	−	0.284982i	$-0.0919877\pi$
$152$	3.18622e11	+	1.79989e10i	0.318519	+	0.0179932i
$153$		−	7.15315e10i		−	0.0689754i
$154$	−4.98068e10	+	3.93656e11i	−0.0463366	+	0.366229i
$155$		−	1.53952e12i		−	1.38217i
$156$	7.19601e11	−	3.80118e11i	0.623601	−	0.329407i
$157$			1.36601e12i			1.14290i	0.820638	+	0.571448i	$0.193618\pi$
$157$			1.36601e12i			1.14290i	−0.820638	+	0.571448i	$0.806382\pi$
$158$	3.53572e10	+	2.13101e10i	0.0285669	+	0.0172175i
$159$	1.01212e11			0.0789859
$160$	1.21182e12	−	5.55103e11i	0.913644	−	0.418517i
$161$	1.91270e12	−	8.46265e11i	1.39349	−	0.616544i
$162$	−8.14533e10	+	1.35145e11i	−0.0573556	+	0.0951631i
$163$			2.65490e12i			1.80724i	0.428331	+	0.903622i	$0.359102\pi$
$163$			2.65490e12i			1.80724i	−0.428331	+	0.903622i	$0.640898\pi$
$164$	2.64439e12	−	1.39686e12i	1.74054	−	0.919412i
$165$	3.36466e11			0.214181
$166$	1.17137e12	−	1.94351e12i	0.721274	−	1.19672i
$167$	−6.60485e11			−0.393480			−0.196740	−	0.980456i	$-0.563035\pi$
$167$	−6.60485e11			−0.393480			−0.196740	+	0.980456i	$0.563035\pi$
$168$	3.52910e11	+	9.37234e11i	0.203452	+	0.540315i
$169$	−8.82030e11			−0.492160
$170$	−1.98720e11	+	3.29712e11i	−0.107343	+	0.178101i
$171$	2.03322e11			0.106342
$172$	−9.47628e10	+	5.00569e10i	−0.0479989	+	0.0253547i
$173$			1.87269e12i			0.918783i	0.888234	+	0.459391i	$0.151932\pi$
$173$			1.87269e12i			0.918783i	−0.888234	+	0.459391i	$0.848068\pi$
$174$	1.18942e12	−	1.97345e12i	0.565345	−	0.938007i
$175$	8.69935e9	+	1.96620e10i	0.00400661	+	0.00905561i
$176$	−6.83118e11	−	4.66183e11i	−0.304913	−	0.208083i
$177$	−7.28565e11			−0.315221
$178$	2.62843e11	+	1.58418e11i	0.110252	+	0.0664498i
$179$			4.16752e11i			0.169507i	0.996402	+	0.0847533i	$0.0270102\pi$
$179$			4.16752e11i			0.169507i	−0.996402	+	0.0847533i	$0.972990\pi$
$180$	7.50891e11	−	3.96646e11i	0.296195	−	0.156460i
$181$		−	6.95597e11i		−	0.266150i	−0.991106	−	0.133075i	$-0.957515\pi$
$181$		−	6.95597e11i		−	0.266150i	0.991106	−	0.133075i	$-0.0424850\pi$
$182$	4.13070e11	−	3.26476e12i	0.153331	−	1.21188i
$183$			3.58795e11i			0.129230i
$184$	−2.45869e11	+	4.35243e12i	−0.0859420	+	1.52137i
$185$			4.84449e11i			0.164363i
$186$	−1.24452e12	+	2.06488e12i	−0.409902	+	0.680100i
$187$	2.38861e11			0.0763865
$188$	1.14717e12	+	2.17171e12i	0.356254	+	0.674424i
$189$	2.58164e11	+	5.83494e11i	0.0778675	+	0.175993i
$190$	−9.37181e11	−	5.64847e11i	−0.274586	−	0.165495i
$191$		−	1.66618e12i		−	0.474285i	−0.971475	−	0.237143i	$-0.923789\pi$
$191$		−	1.66618e12i		−	0.474285i	0.971475	−	0.237143i	$-0.0762108\pi$
$192$	−2.07407e12	−	2.35079e11i	−0.573677	−	0.0650215i
$193$	5.25950e12			1.41377			0.706886	−	0.707327i	$-0.250099\pi$
$193$	5.25950e12			1.41377			0.706886	+	0.707327i	$0.250099\pi$
$194$	5.78834e12	+	3.48868e12i	1.51232	+	0.911491i
$195$	−2.79047e12			−0.708740
$196$	3.92196e12	+	1.00859e12i	0.968488	+	0.249060i
$197$	−4.69249e12			−1.12678			−0.563390	−	0.826191i	$-0.690503\pi$
$197$	−4.69249e12			−1.12678			−0.563390	+	0.826191i	$0.690503\pi$
$198$	−4.51283e11	−	2.71992e11i	−0.105388	−	0.0635182i
$199$	−7.00587e12			−1.59137			−0.795683	−	0.605713i	$-0.792888\pi$
$199$	−7.00587e12			−1.59137			−0.795683	+	0.605713i	$0.792888\pi$
$200$	−4.47417e10	−	2.52746e9i	−0.00988661	−	0.000558495i
$201$			3.86449e12i			0.830832i
$202$	−3.87523e12	−	2.33563e12i	−0.810708	−	0.488621i
$203$	−3.76983e12	−	8.52044e12i	−0.767527	−	1.73474i
$204$	5.33065e11	−	2.81583e11i	0.105637	−	0.0558008i
$205$	−1.02544e13			−1.97817
$206$	−2.14396e11	+	3.55720e11i	−0.0402667	+	0.0668096i
$207$			2.77742e12i			0.507931i
$208$	5.66541e12	+	3.86626e12i	1.00898	+	0.688562i
$209$			6.78943e11i			0.117768i
$210$	4.31031e11	−	3.40672e12i	0.0728287	−	0.575613i
$211$		−	4.35070e12i		−	0.716153i	−0.933692	−	0.358077i	$-0.883433\pi$
$211$		−	4.35070e12i		−	0.716153i	0.933692	−	0.358077i	$-0.116567\pi$
$212$	3.98422e11	+	7.54253e11i	0.0638993	+	0.120968i
$213$			4.21580e12i			0.658858i
$214$	5.22540e12	+	3.14939e12i	0.795873	+	0.479679i
$215$	3.67471e11			0.0545521
$216$	−1.32777e12	−	7.50055e10i	−0.192144	−	0.0108542i
$217$	3.94447e12	+	8.91517e12i	0.556494	+	1.25777i
$218$	1.22197e12	−	2.02747e12i	0.168094	−	0.278897i
$219$			1.82629e12i			0.244978i
$220$	1.32450e12	+	2.50741e12i	0.173271	+	0.328020i
$221$	−1.98098e12			−0.252769
$222$	3.91619e11	−	6.49764e11i	0.0487441	−	0.0808751i
$223$	5.05960e12			0.614384			0.307192	−	0.951648i	$-0.400611\pi$
$223$	5.05960e12			0.614384			0.307192	+	0.951648i	$0.400611\pi$
$224$	−5.59521e12	+	6.31936e12i	−0.662906	+	0.748702i
$225$	−2.85510e10			−0.00330079
$226$	4.54490e12	−	7.54080e12i	0.512777	−	0.850787i
$227$	−9.72796e12			−1.07122			−0.535611	−	0.844465i	$-0.679919\pi$
$227$	−9.72796e12			−1.07122			−0.535611	+	0.844465i	$0.679919\pi$
$228$	8.00377e11	+	1.51519e12i	0.0860306	+	0.162865i
$229$		−	4.71071e12i		−	0.494301i	−0.968977	−	0.247150i	$-0.920506\pi$
$229$		−	4.71071e12i		−	0.494301i	0.968977	−	0.247150i	$-0.0794941\pi$
$230$	7.71591e12	−	1.28021e13i	0.790467	−	1.31152i
$231$	−1.94843e12	+	8.62074e11i	−0.194903	+	0.0862340i
$232$	1.93887e13	+	1.09526e12i	1.89393	+	0.106988i
$233$	−7.15250e12			−0.682339			−0.341170	−	0.940002i	$-0.610823\pi$
$233$	−7.15250e12			−0.682339			−0.341170	+	0.940002i	$0.610823\pi$
$234$	3.74270e12	+	2.25576e12i	0.348737	+	0.210187i
$235$		−	8.42145e12i		−	0.766502i
$236$	−2.86799e12	−	5.42940e12i	−0.255013	−	0.482765i
$237$			2.21671e11i			0.0192571i
$238$	3.05993e11	−	2.41847e12i	0.0259740	−	0.205290i
$239$			1.34337e13i			1.11431i	0.830408	+	0.557156i	$0.188108\pi$
$239$			1.34337e13i			1.11431i	−0.830408	+	0.557156i	$0.811892\pi$
$240$	5.91175e12	+	4.03438e12i	0.479241	+	0.327050i
$241$			4.44043e12i			0.351829i	0.984405	+	0.175914i	$0.0562882\pi$
$241$			4.44043e12i			0.351829i	−0.984405	+	0.175914i	$0.943712\pi$
$242$	−5.75679e12	+	9.55154e12i	−0.445858	+	0.739756i
$243$	−8.47289e11			−0.0641500
$244$	−2.67380e12	+	1.41239e12i	−0.197918	+	0.104547i
$245$	−1.02754e13	−	9.33892e12i	−0.743680	−	0.675901i
$246$	1.37537e13	+	8.28944e12i	0.973363	+	0.586654i
$247$		−	5.63078e12i		−	0.389705i
$248$	−2.02869e13	−	1.14600e12i	−1.37319	−	0.0775715i
$249$	1.21848e13			0.806717
$250$	−1.31583e13	−	7.93060e12i	−0.852175	−	0.513613i
$251$	−2.70575e13			−1.71428			−0.857140	−	0.515084i	$-0.827761\pi$
$251$	−2.70575e13			−1.71428			−0.857140	+	0.515084i	$0.827761\pi$
$252$	−3.33204e12	+	4.22081e12i	−0.206541	+	0.261633i
$253$	−9.27448e12			−0.562506
$254$	−1.13118e13	−	6.81770e12i	−0.671344	−	0.404625i
$255$	−2.06712e12			−0.120059
$256$	−6.41273e12	−	1.63818e13i	−0.364521	−	0.931195i
$257$		−	7.58270e12i		−	0.421883i	−0.977499	−	0.210941i	$-0.932347\pi$
$257$		−	7.58270e12i		−	0.421883i	0.977499	−	0.210941i	$-0.0676529\pi$
$258$	−4.92868e11	−	2.97056e11i	−0.0268425	−	0.0161782i
$259$	−1.24123e12	−	2.80538e12i	−0.0661763	−	0.149569i
$260$	−1.09847e13	−	2.07951e13i	−0.573368	−	1.08544i
$261$	1.23725e13			0.632316
$262$	2.18103e12	−	3.61871e12i	0.109145	−	0.181091i
$263$		−	1.38094e13i		−	0.676735i	−0.941014	−	0.338367i	$-0.890125\pi$
$263$		−	1.38094e13i		−	0.676735i	0.941014	−	0.338367i	$-0.109875\pi$
$264$	2.50462e11	−	4.43374e12i	0.0120204	−	0.212789i
$265$		−	2.92484e12i		−	0.137483i
$266$	6.87430e12	+	8.69761e11i	0.316504	+	0.0400453i
$267$			1.64788e12i			0.0743215i
$268$	−2.87988e13	+	1.52125e13i	−1.27243	+	0.672140i
$269$		−	2.68542e13i		−	1.16245i	−0.813742	−	0.581226i	$-0.802573\pi$
$269$		−	2.68542e13i		−	1.16245i	0.813742	−	0.581226i	$-0.197427\pi$
$270$	3.90544e12	+	2.35384e12i	0.165641	+	0.0998335i
$271$	−1.55602e13			−0.646673			−0.323336	−	0.946284i	$-0.604805\pi$
$271$	−1.55602e13			−0.646673			−0.323336	+	0.946284i	$0.604805\pi$
$272$	4.19681e12	+	2.86405e12i	0.170919	+	0.116641i
$273$	1.61592e13	−	7.14957e12i	0.644949	−	0.285355i
$274$	2.45934e13	−	4.08048e13i	0.962035	−	1.59619i
$275$		−	9.53389e10i		−	0.00365545i
$276$	−2.06978e13	+	1.09333e13i	−0.777902	+	0.410914i
$277$	3.56247e13			1.31254			0.656269	−	0.754527i	$-0.272134\pi$
$277$	3.56247e13			1.31254			0.656269	+	0.754527i	$0.272134\pi$
$278$	2.41223e13	−	4.00232e13i	0.871310	−	1.44566i
$279$	−1.29457e13			−0.458460
$280$	2.70842e13	−	1.01984e13i	0.940475	−	0.354131i
$281$	−1.57562e13			−0.536495			−0.268248	−	0.963350i	$-0.586445\pi$
$281$	−1.57562e13			−0.536495			−0.268248	+	0.963350i	$0.586445\pi$
$282$	−6.80772e12	+	1.12952e13i	−0.227317	+	0.377159i
$283$	−4.74231e13			−1.55297			−0.776487	−	0.630133i	$-0.783000\pi$
$283$	−4.74231e13			−1.55297			−0.776487	+	0.630133i	$0.783000\pi$
$284$	−3.14169e13	+	1.65955e13i	−1.00905	+	0.533014i
$285$		−	5.87562e12i		−	0.185100i
$286$	−7.53252e12	+	1.24978e13i	−0.232770	+	0.386207i
$287$	5.93818e13	−	2.62732e13i	1.80013	−	0.796457i
$288$	−4.66779e12	−	1.01900e13i	−0.138820	−	0.303051i
$289$	3.28044e13			0.957182
$290$	−5.70289e13	−	3.43718e13i	−1.63270	−	0.984042i
$291$			3.62898e13i			1.01947i
$292$	−1.36099e13	+	7.18918e12i	−0.375187	+	0.198186i
$293$			2.40859e13i			0.651615i	0.945436	+	0.325808i	$0.105636\pi$
$293$			2.40859e13i			0.651615i	−0.945436	+	0.325808i	$0.894364\pi$
$294$	6.23245e12	+	2.08322e13i	0.165481	+	0.553127i
$295$			2.10541e13i			0.548676i
$296$	6.38376e12	+	3.60619e11i	0.163295	+	0.00922452i
$297$		−	2.82930e12i		−	0.0710427i
$298$	9.53431e12	−	1.58191e13i	0.235017	−	0.389935i
$299$	7.69175e13			1.86137
$300$	−1.12391e11	−	2.12767e11i	−0.00267033	−	0.00505520i
$301$	−2.12797e12	+	9.41512e11i	−0.0496421	+	0.0219639i
$302$	2.13107e13	+	1.28441e13i	0.488156	+	0.294216i
$303$		−	2.42956e13i		−	0.546504i
$304$	−8.14082e12	+	1.19291e13i	−0.179830	+	0.263514i
$305$	1.03685e13			0.224939
$306$	2.77251e12	+	1.67102e12i	0.0590752	+	0.0356051i
$307$	8.79126e13			1.83988			0.919942	−	0.392055i	$-0.128236\pi$
$307$	8.79126e13			1.83988			0.919942	+	0.392055i	$0.128236\pi$
$308$	−1.40943e13	−	1.11265e13i	−0.289744	−	0.228733i
$309$	−2.23017e12			−0.0450368
$310$	5.96709e13	+	3.59642e13i	1.18379	+	0.713478i
$311$	−1.82280e13			−0.355269			−0.177634	−	0.984097i	$-0.556844\pi$
$311$	−1.82280e13			−0.355269			−0.177634	+	0.984097i	$0.556844\pi$
$312$	−2.07719e12	+	3.67710e13i	−0.0397765	+	0.704134i
$313$		−	5.06236e13i		−	0.952487i	−0.879313	−	0.476243i	$-0.841998\pi$
$313$		−	5.06236e13i		−	0.952487i	0.879313	−	0.476243i	$-0.158002\pi$
$314$	−5.29457e13	−	3.19108e13i	−0.978853	−	0.589963i
$315$	1.68618e13	−	7.46044e12i	0.306335	−	0.135537i
$316$	−1.65193e12	+	8.72604e11i	−0.0294925	+	0.0155790i
$317$	−9.23104e13			−1.61966			−0.809831	−	0.586663i	$-0.800441\pi$
$317$	−9.23104e13			−1.61966			−0.809831	+	0.586663i	$0.800441\pi$
$318$	−2.36438e12	+	3.92292e12i	−0.0407726	+	0.0676489i
$319$			4.13148e13i			0.700256i
$320$	−6.79332e12	+	5.99367e13i	−0.113177	+	0.998546i
$321$			3.27604e13i			0.536503i
$322$	−1.18811e13	+	9.39041e13i	−0.191271	+	1.51174i
$323$		−	4.17116e12i		−	0.0660151i
$324$	−3.33535e12	−	6.31414e12i	−0.0518971	−	0.0982465i
$325$			7.90689e11i			0.0120961i
$326$	−1.02902e14	−	6.20200e13i	−1.54785	−	0.932900i
$327$	1.27111e13			0.188006
$328$	−7.63326e12	+	1.35126e14i	−0.111021	+	1.96532i
$329$	2.15769e13	+	4.87674e13i	0.308611	+	0.697513i
$330$	−7.86005e12	+	1.30412e13i	−0.110560	+	0.183439i
$331$			8.27090e13i			1.14419i	0.820187	+	0.572096i	$0.193870\pi$
$331$			8.27090e13i			1.14419i	−0.820187	+	0.572096i	$0.806130\pi$
$332$	4.79653e13	+	9.08032e13i	0.652631	+	1.23550i
$333$	4.07367e12			0.0545184
$334$	1.54293e13	−	2.55999e13i	0.203114	−	0.337003i
$335$	1.11676e14			1.44615
$336$	−4.45707e13	−	8.21578e12i	−0.567785	−	0.104660i
$337$	−3.21523e13			−0.402947			−0.201473	−	0.979494i	$-0.564573\pi$
$337$	−3.21523e13			−0.402947			−0.201473	+	0.979494i	$0.564573\pi$
$338$	2.06047e13	−	3.41869e13i	0.254053	−	0.421519i
$339$	4.72767e13			0.573521
$340$	−8.13720e12	−	1.54045e13i	−0.0971272	−	0.183872i
$341$		−	4.32288e13i		−	0.507719i
$342$	−4.74973e12	+	7.88063e12i	−0.0548940	+	0.0910789i
$343$	8.34311e13	+	2.77533e13i	0.948878	+	0.315644i
$344$	2.73541e11	−	4.84230e12i	0.00306162	−	0.0541976i
$345$	8.02620e13			0.884107
$346$	−7.25842e13	−	4.37472e13i	−0.786908	−	0.474276i
$347$		−	7.48344e12i		−	0.0798526i	−0.999203	−	0.0399263i	$-0.987288\pi$
$347$		−	7.48344e12i		−	0.0798526i	0.999203	−	0.0399263i	$-0.0127123\pi$
$348$	4.87042e13	+	9.22020e13i	0.511541	+	0.968399i
$349$		−	4.49400e13i		−	0.464615i	−0.972642	−	0.232308i	$-0.925372\pi$
$349$		−	4.49400e13i		−	0.464615i	0.972642	−	0.232308i	$-0.0746276\pi$
$350$	−9.65306e11	−	1.22134e11i	−0.00982405	−	0.00124298i
$351$			2.34647e13i			0.235085i
$352$	3.40270e13	−	1.55869e13i	0.335613	−	0.153736i
$353$			1.05093e14i			1.02050i	0.860026	+	0.510250i	$0.170447\pi$
$353$			1.05093e14i			1.02050i	−0.860026	+	0.510250i	$0.829553\pi$
$354$	1.70197e13	−	2.82387e13i	0.162717	−	0.269977i
$355$	1.21828e14			1.14681
$356$	−1.22803e13	+	6.48688e12i	−0.113824	+	0.0601258i
$357$	1.19704e13	−	5.29624e12i	0.109253	−	0.0483385i
$358$	−1.61530e13	−	9.73557e12i	−0.145177	−	0.0874994i
$359$		−	4.41274e12i		−	0.0390561i	−0.999809	−	0.0195280i	$-0.993784\pi$
$359$		−	4.41274e12i		−	0.0390561i	0.999809	−	0.0195280i	$-0.00621636\pi$
$360$	−2.16751e12	+	3.83699e13i	−0.0188929	+	0.334446i
$361$	−1.04634e14			−0.898222
$362$	2.69609e13	+	1.62495e13i	0.227948	+	0.137387i
$363$	−5.98830e13			−0.498674
$364$	1.16890e14	+	9.22770e13i	0.958785	+	0.756896i
$365$	5.27763e13			0.426411
$366$	−1.39066e13	−	8.38164e12i	−0.110682	−	0.0667088i
$367$	−1.23668e14			−0.969603			−0.484802	−	0.874624i	$-0.661108\pi$
$367$	−1.23668e14			−0.969603			−0.484802	+	0.874624i	$0.661108\pi$
$368$	−1.62954e14	−	1.11205e14i	−1.25864	−	0.858937i
$369$			8.62280e13i			0.656150i
$370$	−1.87769e13	−	1.13170e13i	−0.140772	−	0.0848442i
$371$	7.49385e12	+	1.69373e13i	0.0553539	+	0.125109i
$372$	−5.09605e13	−	9.64734e13i	−0.370892	−	0.702136i
$373$	−9.78230e13			−0.701524			−0.350762	−	0.936465i	$-0.614077\pi$
$373$	−9.78230e13			−0.701524			−0.350762	+	0.936465i	$0.614077\pi$
$374$	−5.57993e12	+	9.25809e12i	−0.0394307	+	0.0654226i
$375$		−	8.24953e13i		−	0.574456i
$376$	−1.10972e14	−	6.26883e12i	−0.761521	−	0.0430183i
$377$		−	3.42642e14i		−	2.31720i
$378$	−2.86467e13	−	3.62449e12i	−0.190928	−	0.0241569i
$379$			2.24292e14i			1.47332i	0.676262	+	0.736661i	$0.263599\pi$
$379$			2.24292e14i			1.47332i	−0.676262	+	0.736661i	$0.736401\pi$
$380$	4.37861e13	−	2.31293e13i	0.283483	−	0.149745i
$381$		−	7.09187e13i		−	0.452557i
$382$	6.45801e13	+	3.89230e13i	0.406210	+	0.244826i
$383$	1.50722e14			0.934508			0.467254	−	0.884123i	$-0.345243\pi$
$383$	1.50722e14			0.934508			0.467254	+	0.884123i	$0.345243\pi$
$384$	5.75631e13	−	7.48981e13i	0.351821	−	0.457772i
$385$	2.49122e13	+	5.63058e13i	0.150099	+	0.339249i
$386$	−1.22865e14	+	2.03855e14i	−0.729790	+	1.21085i
$387$		−	3.09002e12i		−	0.0180947i
$388$	−2.70438e14	+	1.42855e14i	−1.56132	+	0.824745i
$389$	4.71676e13			0.268486			0.134243	−	0.990948i	$-0.457140\pi$
$389$	4.71676e13			0.268486			0.134243	+	0.990948i	$0.457140\pi$
$390$	6.51869e13	−	1.08157e14i	0.365852	−	0.607013i
$391$	5.69788e13			0.315313
$392$	−1.30711e14	+	1.28451e14i	−0.713246	+	0.700914i
$393$	2.26873e13			0.122074
$394$	1.09619e14	−	1.81878e14i	0.581644	−	0.965051i
$395$	6.40584e12			0.0335191
$396$	2.10845e13	−	1.11375e13i	0.108803	−	0.0574732i
$397$		−	1.35330e14i		−	0.688727i	−0.938836	−	0.344364i	$-0.888095\pi$
$397$		−	1.35330e14i		−	0.688727i	0.938836	−	0.344364i	$-0.111905\pi$
$398$	1.63661e14	−	2.71543e14i	0.821464	−	1.36295i
$399$	1.50541e13	+	3.40249e13i	0.0745256	+	0.168440i
$400$	1.14315e12	−	1.67511e12i	0.00558181	−	0.00817927i
$401$	1.56175e14			0.752174			0.376087	−	0.926584i	$-0.377269\pi$
$401$	1.56175e14			0.752174			0.376087	+	0.926584i	$0.377269\pi$
$402$	−1.49785e14	−	9.02766e13i	−0.711581	−	0.428876i
$403$			3.58516e14i			1.68008i
$404$	1.81055e14	−	9.56394e13i	0.836976	−	0.442119i
$405$			2.44850e13i			0.111660i
$406$	4.18312e14	+	5.29264e13i	1.88195	+	0.238111i
$407$			1.36030e13i			0.0603761i
$408$	−1.53874e12	+	2.72392e13i	−0.00673805	+	0.119279i
$409$			3.58770e13i			0.155002i	0.996992	+	0.0775012i	$0.0246942\pi$
$409$			3.58770e13i			0.155002i	−0.996992	+	0.0775012i	$0.975306\pi$
$410$	2.39549e14	−	3.97454e14i	1.02113	−	1.69424i
$411$	2.55824e14			1.07600
$412$	−8.77906e12	−	1.66197e13i	−0.0364346	−	0.0689743i
$413$	−5.39436e13	−	1.21921e14i	−0.220909	−	0.499292i
$414$	−1.07651e14	−	6.48821e13i	−0.435026	−	0.262194i
$415$		−	3.52116e14i		−	1.40418i
$416$	−2.82201e14	+	1.29269e14i	−1.11057	+	0.508723i
$417$	2.50924e14			0.974526
$418$	−2.63154e13	−	1.58605e13i	−0.100865	−	0.0607921i
$419$	−3.73085e14			−1.41134			−0.705668	−	0.708543i	$-0.749353\pi$
$419$	−3.73085e14			−1.41134			−0.705668	+	0.708543i	$0.749353\pi$
$420$	1.21973e14	+	9.62894e13i	0.455400	+	0.359507i
$421$	−1.06682e14			−0.393133			−0.196566	−	0.980491i	$-0.562979\pi$
$421$	−1.06682e14			−0.393133			−0.196566	+	0.980491i	$0.562979\pi$
$422$	1.68630e14	+	1.01635e14i	0.613362	+	0.369679i
$423$	−7.08149e13			−0.254245
$424$	−3.85417e13	−	2.17722e12i	−0.136590	−	0.00771596i
$425$			5.85725e11i			0.00204906i
$426$	−1.63401e14	−	9.84834e13i	−0.564291	−	0.340103i
$427$	−6.00423e13	+	2.65654e13i	−0.204693	+	0.0905656i
$428$	−2.44137e14	+	1.28961e14i	−0.821660	+	0.434029i
$429$	−7.83544e13			−0.260344
$430$	−8.58434e12	+	1.42429e13i	−0.0281598	+	0.0467222i
$431$		−	3.71990e13i		−	0.120477i	−0.998184	−	0.0602387i	$-0.980814\pi$
$431$		−	3.71990e13i		−	0.120477i	0.998184	−	0.0602387i	$-0.0191862\pi$
$432$	3.39246e13	−	4.97112e13i	0.108481	−	0.158962i
$433$		−	2.78304e14i		−	0.878690i	−0.898318	−	0.439345i	$-0.855211\pi$
$433$		−	2.78304e14i		−	0.878690i	0.898318	−	0.439345i	$-0.144789\pi$
$434$	−4.37691e14	−	5.53783e13i	−1.36450	−	0.172642i
$435$		−	3.57541e14i		−	1.10061i
$436$	5.00373e13	+	9.47257e13i	0.152096	+	0.287933i
$437$			1.61958e14i			0.486131i
$438$	−7.07858e13	−	4.26632e13i	−0.209816	−	0.126458i
$439$	−5.08374e14			−1.48809			−0.744044	−	0.668131i	$-0.767095\pi$
$439$	−5.08374e14			−1.48809			−0.744044	+	0.668131i	$0.767095\pi$
$440$	−1.28126e14	−	7.23786e12i	−0.370381	−	0.0209228i
$441$	−7.85298e13	+	8.64047e13i	−0.224193	+	0.246675i
$442$	4.62769e13	−	7.67815e13i	0.130479	−	0.216488i
$443$		−	3.53256e14i		−	0.983715i	−0.870676	−	0.491858i	$-0.836318\pi$
$443$		−	3.53256e14i		−	0.983715i	0.870676	−	0.491858i	$-0.163682\pi$
$444$	1.60360e13	+	3.03577e13i	0.0441052	+	0.0834955i
$445$	4.76206e13			0.129364
$446$	−1.18195e14	+	1.96107e14i	−0.317145	+	0.526200i
$447$	9.91773e13			0.262858
$448$	−1.14227e14	−	3.64490e14i	−0.299047	−	0.954238i
$449$	5.47696e14			1.41640			0.708198	−	0.706014i	$-0.249508\pi$
$449$	5.47696e14			1.41640			0.708198	+	0.706014i	$0.249508\pi$
$450$	6.66969e11	−	1.10662e12i	0.00170387	−	0.00282702i
$451$	−2.87936e14			−0.726651
$452$	1.86105e14	+	3.52315e14i	0.463976	+	0.878353i
$453$			1.33606e14i			0.329069i
$454$	2.27251e14	−	3.77049e14i	0.552965	−	0.917467i
$455$	−2.06608e14	−	4.66969e14i	−0.496690	−	1.12260i
$456$	−7.74251e13	−	4.37374e12i	−0.183897	−	0.0103884i
$457$	−4.45195e14			−1.04475			−0.522373	−	0.852717i	$-0.674953\pi$
$457$	−4.45195e14			−1.04475			−0.522373	+	0.852717i	$0.674953\pi$
$458$	1.82584e14	+	1.10045e14i	0.423353	+	0.255158i
$459$			1.73821e13i			0.0398230i
$460$	3.15951e14	+	5.98127e14i	0.715239	+	1.35402i
$461$			4.03499e14i			0.902583i	0.892376	+	0.451292i	$0.149037\pi$
$461$			4.03499e14i			0.902583i	−0.892376	+	0.451292i	$0.850963\pi$
$462$	1.21030e13	−	9.56583e13i	0.0267525	−	0.211442i
$463$		−	5.24422e14i		−	1.14548i	−0.819739	−	0.572738i	$-0.805881\pi$
$463$		−	5.24422e14i		−	1.14548i	0.819739	−	0.572738i	$-0.194119\pi$
$464$	−4.95382e14	+	7.25905e14i	−1.06928	+	1.56686i
$465$			3.74105e14i			0.797998i
$466$	1.67086e14	−	2.77226e14i	0.352224	−	0.584401i
$467$	−6.15087e13			−0.128143			−0.0640713	−	0.997945i	$-0.520409\pi$
$467$	−6.15087e13			−0.128143			−0.0640713	+	0.997945i	$0.520409\pi$
$468$	−1.74863e14	+	9.23686e13i	−0.360036	+	0.190183i
$469$	−6.46700e14	+	2.86130e14i	−1.31599	+	0.582253i
$470$	3.26409e14	+	1.96730e14i	0.656484	+	0.395669i
$471$		−	3.31941e14i		−	0.659851i
$472$	2.77438e14	+	1.56724e13i	0.545110	+	0.0307933i
$473$	1.03183e13			0.0200389
$474$	−8.59179e12	−	5.17835e12i	−0.0164931	−	0.00994055i
$475$	−1.66488e12			−0.00315913
$476$	8.65899e13	+	6.83569e13i	0.162416	+	0.128216i
$477$	−2.45946e13			−0.0456026
$478$	−5.20681e14	−	3.13819e14i	−0.954373	−	0.575209i
$479$	−5.99164e14			−1.08568			−0.542838	−	0.839837i	$-0.682650\pi$
$479$	−5.99164e14			−1.08568			−0.542838	+	0.839837i	$0.682650\pi$
$480$	−2.94471e14	+	1.34890e14i	−0.527493	+	0.241631i
$481$		−	1.12816e14i		−	0.199789i
$482$	−1.72108e14	−	1.03731e14i	−0.301330	−	0.181614i
$483$	−4.64786e14	+	2.05642e14i	−0.804532	+	0.355962i
$484$	−2.35729e14	−	4.46259e14i	−0.403426	−	0.763725i
$485$	1.04870e15			1.77449
$486$	1.97931e13	−	3.28403e13i	0.0331143	−	0.0549424i
$487$			6.90147e14i			1.14165i	0.821072	+	0.570824i	$0.193376\pi$
$487$			6.90147e14i			1.14165i	−0.821072	+	0.570824i	$0.806624\pi$
$488$	7.71817e12	−	1.36629e14i	0.0126242	−	0.223477i
$489$		−	6.45141e14i		−	1.04341i
$490$	6.02010e14	−	1.80106e14i	0.962776	−	0.288037i
$491$			9.21835e14i			1.45782i	0.684608	+	0.728912i	$0.259974\pi$
$491$			9.21835e14i			1.45782i	−0.684608	+	0.728912i	$0.740026\pi$
$492$	−6.42586e14	+	3.39436e14i	−1.00490	+	0.530823i
$493$		−	2.53822e14i		−	0.392528i
$494$	2.18245e14	+	1.31538e14i	0.333769	+	0.201166i
$495$	−8.17614e13			−0.123657
$496$	5.18331e14	−	7.59534e14i	0.775279	−	1.13605i
$497$	−7.05490e14	+	3.12141e14i	−1.04359	+	0.461733i
$498$	−2.84644e14	+	4.72274e14i	−0.416428	+	0.690927i
$499$		−	9.95593e13i		−	0.144055i	−0.997403	−	0.0720276i	$-0.977053\pi$
$499$		−	9.95593e13i		−	0.144055i	0.997403	−	0.0720276i	$-0.0229470\pi$
$500$	6.14769e14	−	3.24742e14i	0.879786	−	0.464733i
$501$	1.60498e14			0.227175
$502$	6.32078e14	−	1.04873e15i	0.884912	−	1.46822i
$503$	3.51570e14			0.486841			0.243421	−	0.969921i	$-0.421730\pi$
$503$	3.51570e14			0.486841			0.243421	+	0.969921i	$0.421730\pi$
$504$	−8.57572e13	−	2.27748e14i	−0.117463	−	0.311951i
$505$	−7.02095e14			−0.951247
$506$	2.16657e14	−	3.59473e14i	0.290366	−	0.481768i
$507$	2.14333e14			0.284149
$508$	5.28499e14	−	2.79171e14i	0.693096	−	0.366117i
$509$			1.13520e15i			1.47274i	0.676579	+	0.736370i	$0.263462\pi$
$509$			1.13520e15i			1.47274i	−0.676579	+	0.736370i	$0.736538\pi$
$510$	4.82891e13	−	8.01201e13i	0.0619745	−	0.102827i
$511$	−3.05620e14	+	1.35220e14i	−0.388031	+	0.171683i
$512$	7.84750e14	+	1.34134e14i	0.985705	+	0.168483i
$513$	−4.94073e13			−0.0613968
$514$	2.93900e14	+	1.77136e14i	0.361329	+	0.217776i
$515$			6.44477e13i			0.0783912i
$516$	2.30274e13	−	1.21638e13i	0.0277122	−	0.0146385i
$517$		−	2.36468e14i		−	0.281562i
$518$	1.37730e14	+	1.74261e13i	0.162262	+	0.0205299i
$519$		−	4.55064e14i		−	0.530459i
$520$	1.06261e15	+	6.00268e13i	1.22562	+	0.0692352i
$521$			1.41004e15i			1.60925i	0.593784	+	0.804625i	$0.297633\pi$
$521$			1.41004e15i			1.60925i	−0.593784	+	0.804625i	$0.702367\pi$
$522$	−2.89028e14	+	4.79549e14i	−0.326402	+	0.541558i
$523$	−1.00683e15			−1.12511			−0.562555	−	0.826760i	$-0.690182\pi$
$523$	−1.00683e15			−1.12511			−0.562555	+	0.826760i	$0.690182\pi$
$524$	8.93085e13	+	1.69070e14i	0.0987577	+	0.186958i
$525$	−2.11394e12	−	4.77786e12i	−0.00231322	−	0.00522826i
$526$	5.35243e14	+	3.22596e14i	0.579602	+	0.349331i
$527$			2.65581e14i			0.284602i
$528$	1.65998e14	+	1.13282e14i	0.176042	+	0.120137i
$529$	−1.25956e15			−1.32194
$530$	1.13365e14	+	6.83260e13i	0.117750	+	0.0709690i
$531$	1.77041e14			0.181993
$532$	−1.94299e14	+	2.46125e14i	−0.197677	+	0.250404i
$533$	2.38799e15			2.40454
$534$	−6.38708e13	−	3.84955e13i	−0.0636540	−	0.0383648i
$535$	9.46713e14			0.933840
$536$	8.31304e13	−	1.47160e15i	0.0811622	−	1.43675i
$537$		−	1.01271e14i		−	0.0978647i
$538$	1.04085e15	+	6.27330e14i	0.995603	+	0.600059i
$539$	−2.88526e14	−	2.62230e14i	−0.273179	−	0.248282i
$540$	−1.82466e14	+	9.63849e13i	−0.171008	+	0.0903324i
$541$	−1.85333e15			−1.71936			−0.859682	−	0.510829i	$-0.829339\pi$
$541$	−1.85333e15			−1.71936			−0.859682	+	0.510829i	$0.829339\pi$
$542$	3.63495e14	−	6.03103e14i	0.333813	−	0.553854i
$543$			1.69030e14i			0.153662i
$544$	−2.09048e14	+	9.57598e13i	−0.188128	+	0.0861766i
$545$		−	3.67327e14i		−	0.327244i
$546$	−1.00376e14	+	7.93337e14i	−0.0885259	+	0.699678i
$547$		−	8.02017e14i		−	0.700251i	−0.936703	−	0.350125i	$-0.886139\pi$
$547$		−	8.02017e14i		−	0.700251i	0.936703	−	0.350125i	$-0.113861\pi$
$548$	1.00705e15	+	1.90645e15i	0.870479	+	1.64790i
$549$		−	8.71871e13i		−	0.0746112i
$550$	3.69527e12	+	2.22717e12i	0.00313077	+	0.00188694i
$551$	7.21468e14			0.605178
$552$	5.97461e13	−	1.05764e15i	0.0496186	−	0.878362i
$553$	−3.70953e13	+	1.64127e13i	−0.0305022	+	0.0134956i
$554$	−8.32212e14	+	1.38079e15i	−0.677533	+	1.12415i
$555$		−	1.17721e14i		−	0.0948950i
$556$	9.87759e14	+	1.86993e15i	0.788388	+	1.49250i
$557$	1.51461e14			0.119701			0.0598504	−	0.998207i	$-0.480938\pi$
$557$	1.51461e14			0.119701			0.0598504	+	0.998207i	$0.480938\pi$
$558$	3.02418e14	−	5.01765e14i	0.236657	−	0.392656i
$559$	−8.55746e13			−0.0663101
$560$	−2.37420e14	+	1.28801e15i	−0.182173	+	0.988289i
$561$	−5.80432e13			−0.0441018
$562$	3.68073e14	−	6.10698e14i	0.276939	−	0.459491i
$563$	−1.46207e15			−1.08936			−0.544680	−	0.838644i	$-0.683349\pi$
$563$	−1.46207e15			−1.08936			−0.544680	+	0.838644i	$0.683349\pi$
$564$	−2.78762e14	−	5.27725e14i	−0.205683	−	0.389379i
$565$		−	1.36621e15i		−	0.998274i
$566$	1.10783e15	−	1.83809e15i	0.801646	−	1.33007i
$567$	−6.27339e13	−	1.41789e14i	−0.0449568	−	0.101610i
$568$	9.06876e13	−	1.60538e15i	0.0643624	−	1.13936i
$569$	−8.50879e14			−0.598067			−0.299034	−	0.954243i	$-0.596664\pi$
$569$	−8.50879e14			−0.598067			−0.299034	+	0.954243i	$0.596664\pi$
$570$	2.27735e14	+	1.37258e14i	0.158532	+	0.0955488i
$571$			7.44357e14i			0.513195i	0.966518	+	0.256598i	$0.0826015\pi$
$571$			7.44357e14i			0.513195i	−0.966518	+	0.256598i	$0.917398\pi$
$572$	−3.08441e14	−	5.83911e14i	−0.210618	−	0.398720i
$573$			4.04883e14i			0.273829i
$574$	−3.68861e14	+	2.91535e15i	−0.247086	+	1.95288i
$575$		−	2.27425e13i		−	0.0150892i
$576$	5.04000e14	+	5.71242e13i	0.331213	+	0.0375402i
$577$			6.31578e13i			0.0411112i	0.999789	+	0.0205556i	$0.00654351\pi$
$577$			6.31578e13i			0.0411112i	−0.999789	+	0.0205556i	$0.993456\pi$
$578$	−7.66330e14	+	1.27148e15i	−0.494098	+	0.819795i
$579$	−1.27806e15			−0.816242
$580$	2.66446e15	−	1.40746e15i	1.68560	−	0.890391i
$581$	9.02171e14	+	2.03906e15i	0.565354	+	1.27779i
$582$	−1.40657e15	−	8.47750e14i	−0.873140	−	0.526249i
$583$		−	8.21275e13i		−	0.0505023i
$584$	3.92861e13	−	6.95452e14i	0.0239314	−	0.423639i
$585$	6.78084e14			0.409191
$586$	−9.33553e14	−	5.62661e14i	−0.558087	−	0.336364i
$587$	2.96092e15			1.75355			0.876774	−	0.480903i	$-0.159691\pi$
$587$	2.96092e15			1.75355			0.876774	+	0.480903i	$0.159691\pi$
$588$	−9.53035e14	−	2.45087e14i	−0.559157	−	0.143795i
$589$	−7.54892e14			−0.438784
$590$	−8.16043e14	−	4.91836e14i	−0.469923	−	0.283227i
$591$	1.14028e15			0.650547
$592$	−1.63106e14	+	2.39006e14i	−0.0921934	+	0.135095i
$593$		−	3.11573e15i		−	1.74486i	−0.488743	−	0.872428i	$-0.662545\pi$
$593$		−	3.11573e15i		−	1.74486i	0.488743	−	0.872428i	$-0.337455\pi$
$594$	1.09662e14	+	6.60942e13i	0.0608457	+	0.0366723i
$595$	−1.53051e14	−	3.45921e14i	−0.0841382	−	0.190166i
$596$	3.90411e14	+	7.39087e14i	0.212651	+	0.402570i
$597$	1.70243e15			0.918776
$598$	−1.79684e15	+	2.98127e15i	−0.960842	+	1.59421i
$599$		−	1.04652e15i		−	0.554496i	−0.960798	−	0.277248i	$-0.910578\pi$
$599$		−	1.04652e15i		−	0.554496i	0.960798	−	0.277248i	$-0.0894223\pi$
$600$	1.08722e13	+	6.14172e11i	0.00570804	+	0.000322447i
$601$		−	1.90421e15i		−	0.990614i	−0.868718	−	0.495307i	$-0.835056\pi$
$601$		−	1.90421e15i		−	0.990614i	0.868718	−	0.495307i	$-0.164944\pi$
$602$	1.32183e13	−	1.04473e14i	0.00681390	−	0.0538547i
$603$		−	9.39070e14i		−	0.479681i
$604$	−9.95659e14	+	5.25941e14i	−0.503973	+	0.266216i
$605$			1.73050e15i			0.867995i
$606$	9.41680e14	+	5.67559e14i	0.468063	+	0.282105i
$607$	−3.57948e14			−0.176312			−0.0881562	−	0.996107i	$-0.528097\pi$
$607$	−3.57948e14			−0.176312			−0.0881562	+	0.996107i	$0.528097\pi$
$608$	−2.72190e14	−	5.94203e14i	−0.132862	−	0.290045i
$609$	9.16069e14	+	2.07047e15i	0.443132	+	1.00155i
$610$	−2.42213e14	+	4.01874e14i	−0.116114	+	0.192653i
$611$			1.96114e15i			0.931711i
$612$	−1.29535e14	+	6.84247e13i	−0.0609893	+	0.0322166i
$613$	−2.40508e15			−1.12227			−0.561136	−	0.827724i	$-0.689635\pi$
$613$	−2.40508e15			−1.12227			−0.561136	+	0.827724i	$0.689635\pi$
$614$	−2.05369e15	+	3.40743e15i	−0.949749	+	1.57580i
$615$	2.49182e15			1.14210
$616$	7.60506e14	−	2.86364e14i	0.345469	−	0.130084i
$617$	−1.84284e15			−0.829697			−0.414849	−	0.909890i	$-0.636165\pi$
$617$	−1.84284e15			−0.829697			−0.414849	+	0.909890i	$0.636165\pi$
$618$	5.20981e13	−	8.64400e13i	0.0232480	−	0.0385725i
$619$	1.57794e15			0.697897			0.348948	−	0.937142i	$-0.386539\pi$
$619$	1.57794e15			0.697897			0.348948	+	0.937142i	$0.386539\pi$
$620$	−2.78789e15	+	1.47266e15i	−1.22214	+	0.645577i
$621$		−	6.74913e14i		−	0.293254i
$622$	4.25817e14	−	7.06505e14i	0.183390	−	0.304276i
$623$	−2.75764e14	+	1.22011e14i	−0.117721	+	0.0520851i
$624$	−1.37669e15	−	9.39502e14i	−0.582535	−	0.397542i
$625$	−2.40756e15			−1.00980
$626$	1.96213e15	+	1.18260e15i	0.815774	+	0.491674i
$627$		−	1.64983e14i		−	0.0679936i
$628$	2.47368e15	−	1.30668e15i	1.01057	−	0.533817i
$629$		−	8.35715e13i		−	0.0338438i
$630$	−1.04741e14	+	8.27833e14i	−0.0420477	+	0.332330i
$631$			3.33751e15i			1.32819i	0.747647	+	0.664097i	$0.231184\pi$
$631$			3.33751e15i			1.32819i	−0.747647	+	0.664097i	$0.768816\pi$
$632$	4.76844e12	−	8.44121e13i	0.00188119	−	0.0333013i
$633$			1.05722e15i			0.413471i
$634$	2.15642e15	−	3.57789e15i	0.836071	−	1.38719i
$635$	−2.04941e15			−0.787724
$636$	−9.68166e13	−	1.83284e14i	−0.0368923	−	0.0698408i
$637$	2.39288e15	+	2.17479e15i	0.903970	+	0.821583i
$638$	−1.60133e15	−	9.65137e14i	−0.599746	−	0.361472i
$639$		−	1.02444e15i		−	0.380392i
$640$	−2.16441e15	−	1.66346e15i	−0.796800	−	0.612382i
$641$	3.75614e15			1.37095			0.685477	−	0.728094i	$-0.259594\pi$
$641$	3.75614e15			1.37095			0.685477	+	0.728094i	$0.259594\pi$
$642$	−1.26977e15	−	7.65303e14i	−0.459497	−	0.276943i
$643$	8.44470e14			0.302987			0.151493	−	0.988458i	$-0.451592\pi$
$643$	8.44470e14			0.302987			0.151493	+	0.988458i	$0.451592\pi$
$644$	−3.36211e15	−	2.65416e15i	−1.19602	−	0.944179i
$645$	−8.92955e13			−0.0314957
$646$	1.61671e14	+	9.74407e13i	0.0565398	+	0.0340770i
$647$	5.43882e14			0.188596			0.0942978	−	0.995544i	$-0.469939\pi$
$647$	5.43882e14			0.188596			0.0942978	+	0.995544i	$0.469939\pi$
$648$	3.22647e14	+	1.82263e13i	0.110934	+	0.00626667i
$649$			5.91185e14i			0.201547i
$650$	−3.06465e13	−	1.84709e13i	−0.0103600	−	0.00624404i
$651$	−9.58507e14	−	2.16639e15i	−0.321292	−	0.726173i
$652$	4.80771e15	−	2.53959e15i	1.59800	−	0.844117i
$653$	3.56762e15			1.17586			0.587930	−	0.808912i	$-0.299943\pi$
$653$	3.56762e15			1.17586			0.587930	+	0.808912i	$0.299943\pi$
$654$	−2.96940e14	+	4.92675e14i	−0.0970489	+	0.161021i
$655$		−	6.55620e14i		−	0.212483i
$656$	−5.05907e15	−	3.45248e15i	−1.62592	−	1.10958i
$657$		−	4.43789e14i		−	0.141438i
$658$	−2.39424e15	−	3.02928e14i	−0.756702	−	0.0957408i
$659$		−	3.64445e15i		−	1.14225i	−0.820862	−	0.571127i	$-0.806506\pi$
$659$		−	3.64445e15i		−	1.14225i	0.820862	−	0.571127i	$-0.193494\pi$
$660$	−3.21853e14	−	6.09300e14i	−0.100038	−	0.189382i
$661$			1.07326e14i			0.0330825i	0.999863	+	0.0165412i	$0.00526548\pi$
$661$			1.07326e14i			0.0330825i	−0.999863	+	0.0165412i	$0.994735\pi$
$662$	−3.20574e15	−	1.93213e15i	−0.979964	−	0.590633i
$663$	4.81379e14			0.145936
$664$	−4.63996e15	−	2.62112e14i	−1.39505	−	0.0788064i
$665$	9.83252e14	−	4.35035e14i	0.293188	−	0.129720i
$666$	−9.51633e13	+	1.57893e14i	−0.0281424	+	0.0466932i
$667$			9.85538e15i			2.89056i
$668$	6.31798e14	+	1.19606e15i	0.183784	+	0.347922i
$669$	−1.22948e15			−0.354715
$670$	−2.60882e15	+	4.32849e15i	−0.746504	+	1.23858i
$671$	2.91139e14			0.0826279
$672$	1.35964e15	−	1.53561e15i	0.382729	−	0.432264i
$673$	1.67325e15			0.467174			0.233587	−	0.972336i	$-0.424954\pi$
$673$	1.67325e15			0.467174			0.233587	+	0.972336i	$0.424954\pi$
$674$	7.51097e14	−	1.24620e15i	0.208001	−	0.345111i
$675$	6.93790e12			0.00190571
$676$	8.43721e14	+	1.59725e15i	0.229875	+	0.435177i
$677$		−	5.85764e15i		−	1.58301i	−0.611160	−	0.791507i	$-0.709297\pi$
$677$		−	5.85764e15i		−	1.58301i	0.611160	−	0.791507i	$-0.290703\pi$
$678$	−1.10441e15	+	1.83241e15i	−0.296052	+	0.491202i
$679$	−6.07290e15	+	2.68692e15i	−1.61478	+	0.714450i
$680$	7.87159e14	+	4.44666e13i	0.207617	+	0.0117283i
$681$	2.36389e15			0.618470
$682$	1.67552e15	+	1.00985e15i	0.434845	+	0.262085i
$683$		−	1.74795e15i		−	0.450003i	−0.974358	−	0.225002i	$-0.927761\pi$
$683$		−	1.74795e15i		−	0.450003i	0.974358	−	0.225002i	$-0.0722387\pi$
$684$	−1.94492e14	−	3.68192e14i	−0.0496698	−	0.0940299i
$685$		−	7.39283e15i		−	1.87289i
$686$	−3.02470e15	+	2.58540e15i	−0.760150	+	0.649748i
$687$			1.14470e15i			0.285385i
$688$	1.81294e14	+	1.23721e14i	0.0448381	+	0.0305990i
$689$			6.81120e14i			0.167116i
$690$	−1.87497e15	+	3.11090e15i	−0.456377	+	0.757209i
$691$	−3.24942e14			−0.0784652			−0.0392326	−	0.999230i	$-0.512491\pi$
$691$	−3.24942e14			−0.0784652			−0.0392326	+	0.999230i	$0.512491\pi$
$692$	3.39122e15	−	1.79136e15i	0.812404	−	0.429140i
$693$	4.73468e14	−	2.09484e14i	0.112527	−	0.0497872i
$694$	2.90053e14	+	1.74817e14i	0.0683912	+	0.0412200i
$695$		−	7.25121e15i		−	1.69627i
$696$	−4.71144e15	−	2.66149e14i	−1.09346	−	0.0617696i
$697$	1.76897e15			0.407324
$698$	1.74184e15	+	1.04982e15i	0.397928	+	0.239835i
$699$	1.73806e15			0.393949
$700$	2.72839e13	−	3.45615e13i	0.00613575	−	0.00777236i
$701$	−4.68794e15			−1.04600			−0.523001	−	0.852332i	$-0.675188\pi$
$701$	−4.68794e15			−1.04600			−0.523001	+	0.852332i	$0.675188\pi$
$702$	−9.09475e14	−	5.48149e14i	−0.201343	−	0.121351i
$703$	2.37545e14			0.0521786
$704$	−1.90752e14	+	1.68298e15i	−0.0415737	+	0.366800i
$705$			2.04641e15i			0.442540i
$706$	−4.07333e15	−	2.45503e15i	−0.874025	−	0.526782i
$707$	4.06573e15	−	1.79886e15i	0.865629	−	0.382994i
$708$	6.96922e14	+	1.31934e15i	0.147232	+	0.278724i
$709$	−3.09004e15			−0.647753			−0.323877	−	0.946099i	$-0.604986\pi$
$709$	−3.09004e15			−0.647753			−0.323877	+	0.946099i	$0.604986\pi$
$710$	−2.84598e15	+	4.72198e15i	−0.591985	+	0.982208i
$711$		−	5.38659e13i		−	0.0111181i
$712$	3.54483e13	−	6.27514e14i	0.00726031	−	0.128524i
$713$		−	1.03120e16i		−	2.09579i
$714$	−7.43564e13	+	5.87687e14i	−0.0149961	+	0.118524i
$715$			2.26429e15i			0.453157i
$716$	7.54688e14	−	3.98652e14i	0.149881	−	0.0791721i
$717$		−	3.26439e15i		−	0.643349i
$718$	1.71035e14	+	1.03084e14i	0.0334503	+	0.0201608i
$719$	6.06739e15			1.17759			0.588793	−	0.808284i	$-0.299603\pi$
$719$	6.06739e15			1.17759			0.588793	+	0.808284i	$0.299603\pi$
$720$	−1.43656e15	−	9.80353e14i	−0.276690	−	0.188823i
$721$	−1.65124e14	−	3.73207e14i	−0.0315621	−	0.0713356i
$722$	2.44431e15	−	4.05554e15i	0.463662	−	0.769298i
$723$		−	1.07902e15i		−	0.203128i
$724$	−1.25964e15	+	6.65386e14i	−0.235334	+	0.124312i
$725$	−1.01310e14			−0.0187843
$726$	1.39890e15	−	2.32102e15i	0.257416	−	0.427099i
$727$	3.26289e15			0.595886			0.297943	−	0.954584i	$-0.403699\pi$
$727$	3.26289e15			0.595886			0.297943	+	0.954584i	$0.403699\pi$
$728$	−6.30722e15	+	2.37495e15i	−1.14318	+	0.430459i
$729$	2.05891e14			0.0370370
$730$	−1.23288e15	+	2.04557e15i	−0.220113	+	0.365207i
$731$	−6.33918e13			−0.0112328
$732$	6.49733e14	−	3.43211e14i	0.114268	−	0.0603602i
$733$		−	3.44450e15i		−	0.601249i	−0.953743	−	0.300625i	$-0.902805\pi$
$733$		−	3.44450e15i		−	0.601249i	0.953743	−	0.300625i	$-0.0971951\pi$
$734$	2.88896e15	−	4.79329e15i	0.500510	−	0.830434i
$735$	2.49693e15	+	2.26936e15i	0.429364	+	0.390232i
$736$	8.11692e15	−	3.71816e15i	1.38536	−	0.634600i
$737$	3.13579e15			0.531221
$738$	−3.34214e15	−	2.01434e15i	−0.561971	−	0.338705i
$739$		−	4.48735e14i		−	0.0748937i	−0.999299	−	0.0374469i	$-0.988078\pi$
$739$		−	4.48735e14i		−	0.0748937i	0.999299	−	0.0374469i	$-0.0119225\pi$
$740$	8.77279e14	−	4.63409e14i	0.145333	−	0.0767697i
$741$			1.36828e15i			0.224996i
$742$	−8.31540e14	−	1.05210e14i	−0.135726	−	0.0171725i
$743$			8.44211e15i			1.36777i	0.729591	+	0.683884i	$0.239711\pi$
$743$			8.44211e15i			1.36777i	−0.729591	+	0.683884i	$0.760289\pi$
$744$	4.92971e15	+	2.78479e14i	0.792812	+	0.0447859i
$745$		−	2.86603e15i		−	0.457532i
$746$	2.28520e15	−	3.79155e15i	0.362127	−	0.600832i
$747$	−2.96090e15			−0.465759
$748$	−2.28487e14	−	4.32548e14i	−0.0356781	−	0.0675423i
$749$	−5.48228e15	+	2.42561e15i	−0.849789	+	0.375985i
$750$	3.19746e15	+	1.92714e15i	0.492003	+	0.296535i
$751$		−	6.90240e15i		−	1.05434i	−0.849760	−	0.527170i	$-0.823253\pi$
$751$		−	6.90240e15i		−	1.05434i	0.849760	−	0.527170i	$-0.176747\pi$
$752$	2.83535e15	−	4.15477e15i	0.429941	−	0.630012i
$753$	6.57496e15			0.989740
$754$	1.32806e16	+	8.00431e15i	1.98461	+	1.19614i
$755$	3.86096e15			0.572780
$756$	8.09685e14	−	1.02566e15i	0.119247	−	0.151054i
$757$	−6.86465e15			−1.00367			−0.501835	−	0.864963i	$-0.667342\pi$
$757$	−6.86465e15			−1.00367			−0.501835	+	0.864963i	$0.667342\pi$
$758$	−8.69340e15	−	5.23959e15i	−1.26185	−	0.760530i
$759$	2.25370e15			0.324763
$760$	−1.26393e14	+	2.23743e15i	−0.0180820	+	0.320093i
$761$		−	3.39973e13i		−	0.00482869i	−0.999997	−	0.00241434i	$-0.999231\pi$
$761$		−	3.39973e13i		−	0.00482869i	0.999997	−	0.00241434i	$-0.000768511\pi$
$762$	2.74876e15	+	1.65670e15i	0.387601	+	0.233610i
$763$	9.41143e14	+	2.12714e15i	0.131756	+	0.297791i
$764$	−3.01726e15	+	1.59382e15i	−0.419372	+	0.221526i
$765$	5.02310e14			0.0693161
$766$	−3.52095e15	+	5.84188e15i	−0.482394	+	0.800376i
$767$		−	4.90296e15i		−	0.666936i
$768$	1.55829e15	+	3.98077e15i	0.210457	+	0.537626i
$769$			5.25477e15i			0.704627i	0.935882	+	0.352313i	$0.114605\pi$
$769$			5.25477e15i			0.704627i	−0.935882	+	0.352313i	$0.885395\pi$
$770$	−2.76434e15	−	3.49754e14i	−0.368038	−	0.0465655i
$771$			1.84260e15i			0.243574i
$772$	−5.03107e15	−	9.52432e15i	−0.660336	−	1.25008i
$773$			1.10205e16i			1.43619i	0.695944	+	0.718096i	$0.254986\pi$
$773$			1.10205e16i			1.43619i	−0.695944	+	0.718096i	$0.745014\pi$
$774$	1.19767e14	+	7.21846e13i	0.0154975	+	0.00934048i
$775$	1.06004e14			0.0136195
$776$	7.80644e14	−	1.38192e16i	0.0995895	−	1.76296i
$777$	3.01618e14	+	6.81707e14i	0.0382069	+	0.0863539i
$778$	−1.10186e15	+	1.82818e15i	−0.138592	+	0.229949i
$779$			5.02815e15i			0.627989i
$780$	2.66927e15	+	5.05320e15i	0.331034	+	0.626681i
$781$	3.42085e15			0.421263
$782$	−1.33106e15	+	2.20846e15i	−0.162765	+	0.270055i
$783$	−3.00652e15			−0.365068
$784$	−1.92519e15	−	8.06697e15i	−0.232132	−	0.972684i
$785$	−9.59245e15			−1.14854
$786$	−5.29989e14	+	8.79346e14i	−0.0630149	+	0.104553i
$787$	1.16032e14			0.0136999			0.00684994	−	0.999977i	$-0.497820\pi$
$787$	1.16032e14			0.0136999			0.00684994	+	0.999977i	$0.497820\pi$
$788$	4.48868e15	+	8.49753e15i	0.526290	+	0.996319i
$789$			3.35569e15i			0.390713i
$790$	−1.49644e14	+	2.48286e14i	−0.0173026	+	0.0287080i
$791$	3.50041e15	+	7.91150e15i	0.401928	+	0.908423i
$792$	−6.08622e13	+	1.07740e15i	−0.00694000	+	0.122854i
$793$	−2.41455e15			−0.273422
$794$	5.24531e15	+	3.16139e15i	0.589873	+	0.355521i
$795$			7.10737e14i			0.0793761i
$796$	6.70159e15	+	1.26868e16i	0.743286	+	1.40712i
$797$			5.12945e15i			0.565002i	0.959267	+	0.282501i	$0.0911640\pi$
$797$			5.12945e15i			0.565002i	−0.959267	+	0.282501i	$0.908836\pi$
$798$	−1.67045e15	−	2.11352e14i	−0.182734	−	0.0231201i
$799$			1.45277e15i			0.157830i
$800$	3.82215e13	+	8.34395e13i	0.00412395	+	0.00900278i
$801$		−	4.00436e14i		−	0.0429096i
$802$	−3.64834e15	+	6.05325e15i	−0.388273	+	0.644213i
$803$	1.48192e15			0.156635
$804$	6.99812e15	−	3.69664e15i	0.734637	−	0.388060i
$805$	5.94266e15	+	1.34314e16i	0.619589	+	1.40037i
$806$	−1.38958e16	−	8.37513e15i	−1.43894	−	0.867259i
$807$			6.52558e15i			0.671142i
$808$	−5.22632e14	+	9.25176e15i	−0.0533867	+	0.945065i
$809$	−1.13574e16			−1.15229			−0.576143	−	0.817349i	$-0.695443\pi$
$809$	−1.13574e16			−1.15229			−0.576143	+	0.817349i	$0.695443\pi$
$810$	−9.49021e14	−	5.71983e14i	−0.0956331	−	0.0576389i
$811$	9.89804e15			0.990683			0.495341	−	0.868698i	$-0.335043\pi$
$811$	9.89804e15			0.990683			0.495341	+	0.868698i	$0.335043\pi$
$812$	−1.18234e16	+	1.49771e16i	−1.17540	+	1.48891i
$813$	3.78113e15			0.373357
$814$	−5.27243e14	−	3.17774e14i	−0.0517102	−	0.0311662i
$815$	−1.86433e16			−1.81617
$816$	−1.01983e15	−	6.95963e14i	−0.0986802	−	0.0673427i
$817$		−	1.80186e14i		−	0.0173181i
$818$	−1.39057e15	−	8.38108e14i	−0.132755	−	0.0800123i
$819$	−3.92669e15	+	1.73734e15i	−0.372362	+	0.164750i
$820$	9.80903e15	+	1.85695e16i	0.923953	+	1.74914i
$821$	−3.90780e15			−0.365633			−0.182817	−	0.983147i	$-0.558521\pi$
$821$	−3.90780e15			−0.365633			−0.182817	+	0.983147i	$0.558521\pi$
$822$	−5.97620e15	+	9.91558e15i	−0.555431	+	0.921559i
$823$		−	5.94287e15i		−	0.548652i	−0.961637	−	0.274326i	$-0.911545\pi$
$823$		−	5.94287e15i		−	0.548652i	0.961637	−	0.274326i	$-0.0884548\pi$
$824$	8.49250e14	+	4.79741e13i	0.0778818	+	0.00439954i
$825$			2.31674e13i			0.00211047i
$826$	5.98574e15	+	7.57338e14i	0.541661	+	0.0685330i
$827$		−	6.60502e15i		−	0.593737i	−0.954918	−	0.296868i	$-0.904058\pi$
$827$		−	6.60502e15i		−	0.593737i	0.954918	−	0.296868i	$-0.0959422\pi$
$828$	5.02957e15	−	2.65679e15i	0.449122	−	0.237241i
$829$			1.89974e16i			1.68518i	0.538559	+	0.842588i	$0.318969\pi$
$829$			1.89974e16i			1.68518i	−0.538559	+	0.842588i	$0.681031\pi$
$830$	1.36478e16	+	8.22564e15i	1.20263	+	0.724837i
$831$	−8.65679e15			−0.757794
$832$	1.58199e15	−	1.39577e16i	0.137571	−	1.21377i
$833$	1.77259e15	+	1.61104e15i	0.153131	+	0.139174i
$834$	−5.86172e15	+	9.72563e15i	−0.503051	+	0.834650i
$835$		−	4.63807e15i		−	0.395423i
$836$	1.22948e15	−	6.49455e14i	0.104133	−	0.0550066i
$837$	3.14580e15			0.264692
$838$	8.71547e15	−	1.44605e16i	0.728532	−	1.20876i
$839$	2.90779e15			0.241475			0.120738	−	0.992684i	$-0.461474\pi$
$839$	2.90779e15			0.241475			0.120738	+	0.992684i	$0.461474\pi$
$840$	−6.58147e15	+	2.47821e15i	−0.542984	+	0.204457i
$841$	3.17020e16			2.59841
$842$	2.49215e15	−	4.13492e15i	0.202935	−	0.336706i
$843$	3.82875e15			0.309746
$844$	−7.87860e15	+	4.16174e15i	−0.633236	+	0.334497i
$845$		−	6.19381e15i		−	0.494591i
$846$	1.65428e15	−	2.74474e15i	0.131241	−	0.217753i
$847$	−4.43378e15	−	1.00211e16i	−0.349475	−	0.789871i
$848$	9.84743e14	−	1.44299e15i	0.0771163	−	0.113002i
$849$	1.15238e16			0.896610
$850$	−2.27023e13	−	1.36829e13i	−0.00175495	−	0.00105773i
$851$			3.24491e15i			0.249224i
$852$	7.63430e15	−	4.03270e15i	0.582574	−	0.307736i
$853$		−	1.97818e16i		−	1.49985i	−0.661525	−	0.749923i	$-0.730090\pi$
$853$		−	1.97818e16i		−	1.49985i	0.661525	−	0.749923i	$-0.269910\pi$
$854$	3.72964e14	−	2.94778e15i	0.0280963	−	0.222063i
$855$			1.42778e15i			0.106868i
$856$	7.04722e14	−	1.24752e16i	0.0524098	−	0.927771i
$857$			7.61599e15i			0.562771i	0.959595	+	0.281386i	$0.0907940\pi$
$857$			7.61599e15i			0.562771i	−0.959595	+	0.281386i	$0.909206\pi$
$858$	1.83040e15	−	3.03696e15i	0.134390	−	0.222977i
$859$	2.26405e16			1.65167			0.825837	−	0.563909i	$-0.190703\pi$
$859$	2.26405e16			1.65167			0.825837	+	0.563909i	$0.190703\pi$
$860$	−3.51511e14	−	6.65446e14i	−0.0254799	−	0.0482360i
$861$	−1.44298e16	+	6.38439e15i	−1.03930	+	0.459835i
$862$	1.44181e15	+	8.68989e14i	0.103185	+	0.0621905i
$863$			5.05455e15i			0.359437i	0.983718	+	0.179719i	$0.0575187\pi$
$863$			5.05455e15i			0.359437i	−0.983718	+	0.179719i	$0.942481\pi$
$864$	1.13427e15	+	2.47617e15i	0.0801479	+	0.174967i
$865$	−1.31505e16			−0.923321
$866$	1.07869e16	+	6.50134e15i	0.752570	+	0.453580i
$867$	−7.97148e15			−0.552629
$868$	1.23711e16	−	1.56709e16i	0.852219	−	1.07953i
$869$	1.79872e14			0.0123127
$870$	1.38580e16	+	8.35236e15i	0.942640	+	0.568137i
$871$	−2.60065e16			−1.75785
$872$	−4.84040e15	−	2.73434e14i	−0.325118	−	0.0183659i
$873$		−	8.81842e15i		−	0.588589i
$874$	−6.27737e15	−	3.78342e15i	−0.416356	−	0.250941i
$875$	1.38051e16	−	6.10801e15i	0.909905	−	0.402583i
$876$	3.30719e15	−	1.74697e15i	0.216614	−	0.114423i
$877$	−1.53334e16			−0.998025			−0.499012	−	0.866595i	$-0.666304\pi$
$877$	−1.53334e16			−0.998025			−0.499012	+	0.866595i	$0.666304\pi$
$878$	1.18759e16	−	1.97042e16i	0.768151	−	1.27450i
$879$		−	5.85288e15i		−	0.376210i
$880$	3.27364e15	−	4.79701e15i	0.209111	−	0.306419i
$881$			1.39349e16i			0.884578i	0.896873	+	0.442289i	$0.145833\pi$
$881$			1.39349e16i			0.884578i	−0.896873	+	0.442289i	$0.854167\pi$
$882$	−1.51449e15	−	5.06222e15i	−0.0955406	−	0.319348i
$883$		−	2.06613e16i		−	1.29531i	−0.761933	−	0.647655i	$-0.775750\pi$
$883$		−	2.06613e16i		−	1.29531i	0.761933	−	0.647655i	$-0.224250\pi$
$884$	1.89494e15	+	3.58732e15i	0.118062	+	0.223503i
$885$		−	5.11615e15i		−	0.316778i
$886$	1.36920e16	+	8.25227e15i	0.842520	+	0.507794i
$887$	1.02896e16			0.629246			0.314623	−	0.949217i	$-0.398122\pi$
$887$	1.02896e16			0.629246			0.314623	+	0.949217i	$0.398122\pi$
$888$	−1.55125e15	−	8.76303e13i	−0.0942783	−	0.00532578i
$889$	1.18679e16	−	5.25088e15i	0.716824	−	0.317156i
$890$	−1.11245e15	+	1.84574e15i	−0.0667780	+	0.110797i
$891$			6.87521e14i			0.0410165i
$892$	−4.83985e15	−	9.16233e15i	−0.286963	−	0.543249i
$893$	−4.12938e15			−0.243333
$894$	−2.31684e15	+	3.84404e15i	−0.135687	+	0.225129i
$895$	−2.92653e15			−0.170344
$896$	1.67958e16	+	4.08734e15i	0.971643	+	0.236454i
$897$	−1.86909e16			−1.07466
$898$	−1.27945e16	+	2.12283e16i	−0.731144	+	1.21310i
$899$	−4.59364e16			−2.60902
$900$	2.73110e13	+	5.17025e13i	0.00154171	+	0.00291862i
$901$			5.04559e14i			0.0283091i
$902$	6.72636e15	−	1.11602e16i	0.375097	−	0.622353i
$903$	5.17098e14	−	2.28787e14i	0.0286609	−	0.0126809i
$904$	−1.80030e16	−	1.01699e15i	−0.991786	−	0.0560260i
$905$	4.88464e15			0.267464
$906$	−5.17849e15	−	3.12112e15i	−0.281837	−	0.169866i
$907$		−	1.06325e16i		−	0.575170i	−0.957755	−	0.287585i	$-0.907148\pi$
$907$		−	1.06325e16i		−	0.575170i	0.957755	−	0.287585i	$-0.0928524\pi$
$908$	9.30545e15	+	1.76162e16i	0.500340	+	0.947194i
$909$			5.90383e15i			0.315524i
$910$	2.29259e16	+	2.90067e15i	1.21786	+	0.154089i
$911$		−	2.22900e16i		−	1.17695i	−0.808514	−	0.588476i	$-0.799728\pi$
$911$		−	2.22900e16i		−	1.17695i	0.808514	−	0.588476i	$-0.200272\pi$
$912$	1.97822e15	−	2.89877e15i	0.103825	−	0.152140i
$913$		−	9.88718e15i		−	0.515802i
$914$	1.04000e16	−	1.72554e16i	0.539299	−	0.894791i
$915$	−2.51954e15			−0.129869
$916$	−8.53052e15	+	4.50611e15i	−0.437070	+	0.230875i
$917$	1.67979e15	+	3.79660e15i	0.0855506	+	0.193359i
$918$	−6.73720e14	−	4.06057e14i	−0.0341071	−	0.0205566i
$919$		−	2.92078e15i		−	0.146982i	−0.997296	−	0.0734909i	$-0.976586\pi$
$919$		−	2.92078e15i		−	0.146982i	0.997296	−	0.0734909i	$-0.0234140\pi$
$920$	−3.05638e16	−	1.72655e15i	−1.52888	−	0.0863665i
$921$	−2.13628e16			−1.06226
$922$	−1.56393e16	−	9.42597e15i	−0.773034	−	0.465914i
$923$	−2.83707e16			−1.39399
$924$	3.42492e15	+	2.70374e15i	0.167284	+	0.132059i
$925$	−3.33567e13			−0.00161958
$926$	2.03263e16	+	1.22508e16i	0.981063	+	0.591295i
$927$	5.41932e14			0.0260020
$928$	−1.65632e16	−	3.61582e16i	−0.790004	−	1.72462i
$929$		−	3.54157e16i		−	1.67923i	−0.543183	−	0.839614i	$-0.682781\pi$
$929$		−	3.54157e16i		−	1.67923i	0.543183	−	0.839614i	$-0.317219\pi$
$930$	−1.45000e16	−	8.73929e15i	−0.683459	−	0.411927i
$931$	−4.57925e15	+	5.03846e15i	−0.214571	+	0.236088i
$932$	6.84185e15	+	1.29523e16i	0.318703	+	0.603337i
$933$	4.42940e15			0.205114
$934$	1.43688e15	−	2.38404e15i	0.0661473	−	0.109750i
$935$			1.67734e15i			0.0767638i
$936$	5.04758e14	−	8.93535e15i	0.0229650	−	0.406532i
$937$			4.05065e16i			1.83213i	0.401027	+	0.916066i	$0.368653\pi$
$937$			4.05065e16i			1.83213i	−0.401027	+	0.916066i	$0.631347\pi$
$938$	4.01710e15	−	3.17498e16i	0.180633	−	1.42766i
$939$			1.23015e16i			0.549919i
$940$	−1.52502e16	+	8.05568e15i	−0.677755	+	0.358013i
$941$		−	3.39879e16i		−	1.50170i	−0.660476	−	0.750848i	$-0.729645\pi$
$941$		−	3.39879e16i		−	1.50170i	0.660476	−	0.750848i	$-0.270355\pi$
$942$	1.28658e16	+	7.75433e15i	0.565141	+	0.340615i
$943$	−6.86854e16			−2.99951
$944$	−7.08855e15	+	1.03872e16i	−0.307760	+	0.450974i
$945$	−4.09743e15	+	1.81289e15i	−0.176863	+	0.0782521i
$946$	−2.41042e14	+	3.99931e14i	−0.0103441	+	0.0171626i
$947$		−	3.55412e15i		−	0.151638i	−0.997122	−	0.0758189i	$-0.975843\pi$
$947$		−	3.55412e15i		−	0.151638i	0.997122	−	0.0758189i	$-0.0241571\pi$
$948$	4.01418e14	−	2.12043e14i	0.0170275	−	0.00899451i
$949$	−1.22902e16			−0.518318
$950$	3.88925e13	−	6.45294e13i	0.00163074	−	0.00270569i
$951$	2.24314e16			0.935113
$952$	−4.67225e15	+	1.75931e15i	−0.193653	+	0.0729187i
$953$	−8.24521e15			−0.339775			−0.169887	−	0.985464i	$-0.554340\pi$
$953$	−8.24521e15			−0.339775			−0.169887	+	0.985464i	$0.554340\pi$
$954$	5.74545e14	−	9.53271e14i	0.0235401	−	0.0390571i
$955$	1.17003e16			0.476628
$956$	2.43268e16	−	1.28502e16i	0.985295	−	0.520466i
$957$		−	1.00395e16i		−	0.404293i
$958$	1.39968e16	−	2.32232e16i	0.560427	−	0.929847i
$959$	1.89414e16	+	4.28108e16i	0.754068	+	1.70432i
$960$	1.65078e15	−	1.45646e16i	0.0653427	−	0.576511i
$961$	2.26560e16			0.891669
$962$	4.37266e15	+	2.63544e15i	0.171113	+	0.103131i
$963$		−	7.96079e15i		−	0.309750i
$964$	8.04108e15	−	4.24757e15i	0.311093	−	0.164330i
$965$			3.69334e16i			1.42075i
$966$	2.88711e15	−	2.28187e16i	0.110430	−	0.872804i
$967$			1.86755e16i			0.710274i	0.934814	+	0.355137i	$0.115566\pi$
$967$			1.86755e16i			0.710274i	−0.934814	+	0.355137i	$0.884434\pi$
$968$	2.28034e16	+	1.28817e15i	0.862355	+	0.0487144i
$969$			1.01359e15i			0.0381138i
$970$	−2.44983e16	+	4.06470e16i	−0.915992	+	1.51979i
$971$	−3.88125e16			−1.44300			−0.721500	−	0.692414i	$-0.756547\pi$
$971$	−3.88125e16			−1.44300			−0.721500	+	0.692414i	$0.756547\pi$
$972$	8.10489e14	+	1.53434e15i	0.0299628	+	0.0567226i
$973$	1.85786e16	+	4.19907e16i	0.682955	+	1.54359i
$974$	−2.67496e16	−	1.61222e16i	−0.977785	−	0.589319i
$975$		−	1.92137e14i		−	0.00698371i
$976$	5.11534e15	+	3.49088e15i	0.184885	+	0.126171i
$977$	3.87782e16			1.39369			0.696847	−	0.717220i	$-0.254586\pi$
$977$	3.87782e16			1.39369			0.696847	+	0.717220i	$0.254586\pi$
$978$	2.50052e16	+	1.50709e16i	0.893649	+	0.538610i
$979$	1.33715e15			0.0475200
$980$	−7.08252e15	+	2.75408e16i	−0.250291	+	0.973271i
$981$	−3.08881e15			−0.108545
$982$	−3.57297e16	−	2.15346e16i	−1.24858	−	0.752529i
$983$	6.92122e15			0.240513			0.120256	−	0.992743i	$-0.461628\pi$
$983$	6.92122e15			0.240513			0.120256	+	0.992743i	$0.461628\pi$
$984$	1.85488e15	−	3.28356e16i	0.0640979	−	1.13468i
$985$		−	3.29517e16i		−	1.13235i
$986$	9.83796e15	+	5.92942e15i	0.336188	+	0.202623i
$987$	−5.24319e15	−	1.18505e16i	−0.178177	−	0.402709i
$988$	−1.01967e16	+	5.38622e15i	−0.344584	+	0.182021i
$989$	2.46137e15			0.0827176
$990$	1.90999e15	−	3.16901e15i	0.0638319	−	0.105908i
$991$			2.07356e16i			0.689145i	0.938760	+	0.344573i	$0.111976\pi$
$991$			2.07356e16i			0.689145i	−0.938760	+	0.344573i	$0.888024\pi$
$992$	1.73305e16	+	3.78333e16i	0.572791	+	1.25043i
$993$		−	2.00983e16i		−	0.660600i
$994$	4.38229e15	−	3.46361e16i	0.143244	−	1.13215i
$995$		−	4.91968e16i		−	1.59923i
$996$	−1.16556e16	−	2.20652e16i	−0.376797	−	0.713314i
$997$		−	1.72816e16i		−	0.555597i	−0.960639	−	0.277799i	$-0.910395\pi$
$997$		−	1.72816e16i		−	0.555597i	0.960639	−	0.277799i	$-0.0896048\pi$
$998$	3.85885e15	+	2.32576e15i	0.123379	+	0.0743614i
$999$	−9.89903e14			−0.0314762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.16	yes	44
4.3	odd	2		84.12.b.b.55.15	yes	44
7.6	odd	2		84.12.b.b.55.16	yes	44
28.27	even	2	inner	84.12.b.a.55.15	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.15	✓	44	28.27	even	2	inner
84.12.b.a.55.16	yes	44	1.1	even	1	trivial
84.12.b.b.55.15	yes	44	4.3	odd	2
84.12.b.b.55.16	yes	44	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-23.3606 + 38.7593i) q^{2} -243.000 q^{3} +(-956.568 - 1810.88i) q^{4} +7022.22i q^{5} +(5676.62 - 9418.51i) q^{6} +(-17991.9 - 40664.7i) q^{7} +(92534.4 + 5227.27i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-23.3606 + 38.7593i) q^{2} -243.000 q^{3} +(-956.568 - 1810.88i) q^{4} +7022.22i q^{5} +(5676.62 - 9418.51i) q^{6} +(-17991.9 - 40664.7i) q^{7} +(92534.4 + 5227.27i) q^{8} +59049.0 q^{9} +(-272177. - 164043. i) q^{10} +197179. i q^{11} +(232446. + 440044. i) q^{12} -1.63530e6i q^{13} +(1.99644e6 + 252597. i) q^{14} -1.70640e6i q^{15} +(-2.36426e6 + 3.46446e6i) q^{16} -1.21139e6i q^{17} +(-1.37942e6 + 2.28870e6i) q^{18} +3.44328e6 q^{19} +(1.27164e7 - 6.71723e6i) q^{20} +(4.37203e6 + 9.88152e6i) q^{21} +(-7.64252e6 - 4.60622e6i) q^{22} +4.70358e7i q^{23} +(-2.24859e7 - 1.27023e6i) q^{24} -483514. q^{25} +(6.33829e7 + 3.82014e7i) q^{26} -1.43489e7 q^{27} +(-5.64284e7 + 7.14797e7i) q^{28} +2.09529e8 q^{29} +(6.61389e7 + 3.98625e7i) q^{30} -2.19236e8 q^{31} +(-7.90494e7 - 1.72569e8i) q^{32} -4.79145e7i q^{33} +(4.69527e7 + 2.82988e7i) q^{34} +(2.85557e8 - 1.26343e8i) q^{35} +(-5.64844e7 - 1.06931e8i) q^{36} +6.89880e7 q^{37} +(-8.04370e7 + 1.33459e8i) q^{38} +3.97377e8i q^{39} +(-3.67070e7 + 6.49797e8i) q^{40} +1.46028e9i q^{41} +(-4.85134e8 - 6.13810e7i) q^{42} -5.23297e7i q^{43} +(3.57067e8 - 1.88615e8i) q^{44} +4.14655e8i q^{45} +(-1.82308e9 - 1.09878e9i) q^{46} -1.19926e9 q^{47} +(5.74515e8 - 8.41863e8i) q^{48} +(-1.32991e9 + 1.46327e9i) q^{49} +(1.12952e7 - 1.87407e7i) q^{50} +2.94368e8i q^{51} +(-2.96132e9 + 1.56427e9i) q^{52} -4.16512e8 q^{53} +(3.35199e8 - 5.56154e8i) q^{54} -1.38464e9 q^{55} +(-1.45230e9 - 3.85693e9i) q^{56} -8.36718e8 q^{57} +(-4.89472e9 + 8.12121e9i) q^{58} +2.99821e9 q^{59} +(-3.09008e9 + 1.63229e9i) q^{60} -1.47652e9i q^{61} +(5.12148e9 - 8.49744e9i) q^{62} +(-1.06240e9 - 2.40121e9i) q^{63} +(8.53529e9 + 9.67403e8i) q^{64} +1.14834e10 q^{65} +(1.85713e9 + 1.11931e9i) q^{66} -1.59032e10i q^{67} +(-2.19368e9 + 1.15878e9i) q^{68} -1.14297e10i q^{69} +(-1.77379e9 + 1.40194e10i) q^{70} -1.73490e10i q^{71} +(5.46406e9 + 3.08665e8i) q^{72} -7.51561e9i q^{73} +(-1.61160e9 + 2.67393e9i) q^{74} +1.17494e8 q^{75} +(-3.29373e9 - 6.23537e9i) q^{76} +(8.01823e9 - 3.54763e9i) q^{77} +(-1.54020e10 - 9.28295e9i) q^{78} -9.12224e8i q^{79} +(-2.43282e10 - 1.66024e10i) q^{80} +3.48678e9 q^{81} +(-5.65994e10 - 3.41129e10i) q^{82} -5.01431e10 q^{83} +(1.37121e10 - 1.73696e10i) q^{84} +8.50666e9 q^{85} +(2.02826e9 + 1.22245e9i) q^{86} -5.09156e10 q^{87} +(-1.03071e9 + 1.82458e10i) q^{88} -6.78142e9i q^{89} +(-1.60718e10 - 9.68658e9i) q^{90} +(-6.64988e10 + 2.94221e10i) q^{91} +(8.51762e10 - 4.49930e10i) q^{92} +5.32744e10 q^{93} +(2.80153e10 - 4.64823e10i) q^{94} +2.41795e10i q^{95} +(1.92090e10 + 4.19342e10i) q^{96} -1.49341e11i q^{97} +(-2.56479e10 - 8.57292e10i) q^{98} +1.16432e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9}+O(q^{10}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9	\( 44 q - 23 q^{2} - 10692 q^{3} + 1541 q^{4} + 5589 q^{6} - 134 q^{7} - 18695 q^{8} + 2598156 q^{9} - 828424 q^{10} - 374463 q^{12} + 4198365 q^{14} - 4412759 q^{16} - 1358127 q^{18} + 6983052 q^{19} - 44417108 q^{20} + 32562 q^{21} - 17991462 q^{22} + 4542885 q^{24} - 453628696 q^{25} - 98243700 q^{26} - 631351908 q^{27} + 197028053 q^{28} - 77673208 q^{29} + 201307032 q^{30} + 363408768 q^{31} - 193132863 q^{32} + 244149820 q^{34} - 387281676 q^{35} + 90994509 q^{36} + 341371884 q^{37} - 414182420 q^{38} - 770410876 q^{40} - 1020202695 q^{42} - 880133666 q^{44} - 1775052978 q^{46} - 1792699304 q^{47} + 1072300437 q^{48} - 819617000 q^{49} + 2158233149 q^{50} - 4514138716 q^{52} + 1914807152 q^{53} + 330024861 q^{54} + 1785927092 q^{55} - 16112780167 q^{56} - 1696881636 q^{57} + 5084833750 q^{58} + 3729062416 q^{59} + 10793357244 q^{60} - 18353275776 q^{62} - 7912566 q^{63} - 12067108399 q^{64} - 5624825000 q^{65} + 4371925266 q^{66} + 885261520 q^{68} + 34763977928 q^{70} - 1103921055 q^{72} - 40922634778 q^{74} + 110231773128 q^{75} + 82420472236 q^{76} - 2093349112 q^{77} + 23873219100 q^{78} - 62176412340 q^{80} + 153418513644 q^{81} - 5083269068 q^{82} + 34205636344 q^{83} - 47877816879 q^{84} + 105152127628 q^{85} + 242964863598 q^{86} + 18874589544 q^{87} + 218894674838 q^{88} - 48917608776 q^{90} - 6678724880 q^{91} + 101339859530 q^{92} - 88308330624 q^{93} + 220283048096 q^{94} + 46931285709 q^{96} + 222198095305 q^{98}+O(q^{100}) \) 44 * q - 23 * q^2 - 10692 * q^3 + 1541 * q^4 + 5589 * q^6 - 134 * q^7 - 18695 * q^8 + 2598156 * q^9 - 828424 * q^10 - 374463 * q^12 + 4198365 * q^14 - 4412759 * q^16 - 1358127 * q^18 + 6983052 * q^19 - 44417108 * q^20 + 32562 * q^21 - 17991462 * q^22 + 4542885 * q^24 - 453628696 * q^25 - 98243700 * q^26 - 631351908 * q^27 + 197028053 * q^28 - 77673208 * q^29 + 201307032 * q^30 + 363408768 * q^31 - 193132863 * q^32 + 244149820 * q^34 - 387281676 * q^35 + 90994509 * q^36 + 341371884 * q^37 - 414182420 * q^38 - 770410876 * q^40 - 1020202695 * q^42 - 880133666 * q^44 - 1775052978 * q^46 - 1792699304 * q^47 + 1072300437 * q^48 - 819617000 * q^49 + 2158233149 * q^50 - 4514138716 * q^52 + 1914807152 * q^53 + 330024861 * q^54 + 1785927092 * q^55 - 16112780167 * q^56 - 1696881636 * q^57 + 5084833750 * q^58 + 3729062416 * q^59 + 10793357244 * q^60 - 18353275776 * q^62 - 7912566 * q^63 - 12067108399 * q^64 - 5624825000 * q^65 + 4371925266 * q^66 + 885261520 * q^68 + 34763977928 * q^70 - 1103921055 * q^72 - 40922634778 * q^74 + 110231773128 * q^75 + 82420472236 * q^76 - 2093349112 * q^77 + 23873219100 * q^78 - 62176412340 * q^80 + 153418513644 * q^81 - 5083269068 * q^82 + 34205636344 * q^83 - 47877816879 * q^84 + 105152127628 * q^85 + 242964863598 * q^86 + 18874589544 * q^87 + 218894674838 * q^88 - 48917608776 * q^90 - 6678724880 * q^91 + 101339859530 * q^92 - 88308330624 * q^93 + 220283048096 * q^94 + 46931285709 * q^96 + 222198095305 * q^98

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