LMFDB - Embedded newform 84.12.b.a.55.6

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			55.6
Character	$\chi$	$=$	84.55
Dual form			84.12.b.a.55.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-40.8700 + 19.4330i) q^{2} -243.000 q^{3} +(1292.72 - 1588.45i) q^{4} +1211.18i q^{5} +(9931.41 - 4722.22i) q^{6} +(-25032.4 - 36752.0i) q^{7} +(-21964.9 + 90041.5i) q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+(-40.8700 + 19.4330i) q^{2} -243.000 q^{3} +(1292.72 - 1588.45i) q^{4} +1211.18i q^{5} +(9931.41 - 4722.22i) q^{6} +(-25032.4 - 36752.0i) q^{7} +(-21964.9 + 90041.5i) q^{8} +59049.0 q^{9} +(-23536.9 - 49501.0i) q^{10} -495487. i q^{11} +(-314130. + 385994. i) q^{12} +811.906i q^{13} +(1.73727e6 + 1.01560e6i) q^{14} -294317. i q^{15} +(-852072. - 4.10684e6i) q^{16} -4.23433e6i q^{17} +(-2.41333e6 + 1.14750e6i) q^{18} -1.72662e7 q^{19} +(1.92391e6 + 1.56571e6i) q^{20} +(6.08286e6 + 8.93073e6i) q^{21} +(9.62880e6 + 2.02505e7i) q^{22} -4.82401e7i q^{23} +(5.33747e6 - 2.18801e7i) q^{24} +4.73612e7 q^{25} +(-15777.8 - 33182.6i) q^{26} -1.43489e7 q^{27} +(-9.07386e7 - 7.74713e6i) q^{28} -3.74837e7 q^{29} +(5.71946e6 + 1.20287e7i) q^{30} +2.03149e8 q^{31} +(1.14633e8 + 1.51288e8i) q^{32} +1.20403e8i q^{33} +(8.22858e7 + 1.73057e8i) q^{34} +(4.45133e7 - 3.03187e7i) q^{35} +(7.63336e7 - 9.37967e7i) q^{36} +4.41964e8 q^{37} +(7.05671e8 - 3.35535e8i) q^{38} -197293. i q^{39} +(-1.09057e8 - 2.66035e7i) q^{40} -5.82689e8i q^{41} +(-4.22158e8 - 2.46791e8i) q^{42} +7.19229e8i q^{43} +(-7.87058e8 - 6.40524e8i) q^{44} +7.15190e7i q^{45} +(9.37451e8 + 1.97157e9i) q^{46} +2.68659e9 q^{47} +(2.07054e8 + 9.97963e8i) q^{48} +(-7.24089e8 + 1.83998e9i) q^{49} +(-1.93565e9 + 9.20370e8i) q^{50} +1.02894e9i q^{51} +(1.28968e6 + 1.04956e6i) q^{52} -3.24198e9 q^{53} +(5.86440e8 - 2.78842e8i) q^{54} +6.00124e8 q^{55} +(3.85904e9 - 1.44670e9i) q^{56} +4.19569e9 q^{57} +(1.53196e9 - 7.28421e8i) q^{58} -3.75912e9 q^{59} +(-4.67509e8 - 3.80468e8i) q^{60} -1.56573e9i q^{61} +(-8.30272e9 + 3.94780e9i) q^{62} +(-1.47814e9 - 2.17017e9i) q^{63} +(-7.62502e9 - 3.95551e9i) q^{64} -983365. q^{65} +(-2.33980e9 - 4.92088e9i) q^{66} -1.21311e10i q^{67} +(-6.72604e9 - 5.47379e9i) q^{68} +1.17224e10i q^{69} +(-1.23008e9 + 2.10415e9i) q^{70} -1.57657e10i q^{71} +(-1.29701e9 + 5.31686e9i) q^{72} -4.84329e9i q^{73} +(-1.80631e10 + 8.58870e9i) q^{74} -1.15088e10 q^{75} +(-2.23203e10 + 2.74266e10i) q^{76} +(-1.82101e10 + 1.24032e10i) q^{77} +(3.83400e6 + 8.06337e6i) q^{78} -2.24827e10i q^{79} +(4.97413e9 - 1.03201e9i) q^{80} +3.48678e9 q^{81} +(1.13234e10 + 2.38145e10i) q^{82} -5.78633e10 q^{83} +(2.20495e10 + 1.88255e9i) q^{84} +5.12854e9 q^{85} +(-1.39768e10 - 2.93949e10i) q^{86} +9.10854e9 q^{87} +(4.46144e10 + 1.08833e10i) q^{88} +6.72135e10i q^{89} +(-1.38983e9 - 2.92298e9i) q^{90} +(2.98391e7 - 2.03239e7i) q^{91} +(-7.66273e10 - 6.23608e10i) q^{92} -4.93653e10 q^{93} +(-1.09801e11 + 5.22086e10i) q^{94} -2.09125e10i q^{95} +(-2.78557e10 - 3.67631e10i) q^{96} +1.16526e11i q^{97} +(-6.16276e9 - 8.92711e10i) q^{98} -2.92580e10i 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 $

$2$	−40.8700	+	19.4330i	−0.903108	+	0.429413i
$2$	−40.8700	+	19.4330i	−0.903108	+	0.429413i
$3$	−243.000			−0.577350
$3$	−243.000			−0.577350
$4$	1292.72	−	1588.45i	0.631209	−	0.775613i
$5$			1211.18i			0.173330i	0.996238	+	0.0866651i	$0.0276210\pi$
$5$			1211.18i			0.173330i	−0.996238	+	0.0866651i	$0.972379\pi$
$6$	9931.41	−	4722.22i	0.521410	−	0.247922i
$7$	−25032.4	−	36752.0i	−0.562941	−	0.826497i
$7$	−25032.4	−	36752.0i	−0.562941	−	0.826497i
$8$	−21964.9	+	90041.5i	−0.236992	+	0.971512i
$9$	59049.0			0.333333
$10$	−23536.9	−	49501.0i	−0.0744302	−	0.156536i
$11$		−	495487.i		−	0.927625i	−0.885934	−	0.463812i	$-0.846481\pi$
$11$		−	495487.i		−	0.927625i	0.885934	−	0.463812i	$-0.153519\pi$
$12$	−314130.	+	385994.i	−0.364429	+	0.447800i
$13$			811.906i			0.000606481i	1.00000		0.000303241i	$9.65245e-5\pi$
$13$			811.906i			0.000606481i	−1.00000		0.000303241i	$0.999903\pi$
$14$	1.73727e6	+	1.01560e6i	0.863305	+	0.504683i
$15$		−	294317.i		−	0.100072i
$16$	−852072.	−	4.10684e6i	−0.203150	−	0.979148i
$17$		−	4.23433e6i		−	0.723296i	−0.932315	−	0.361648i	$-0.882214\pi$
$17$		−	4.23433e6i		−	0.723296i	0.932315	−	0.361648i	$-0.117786\pi$
$18$	−2.41333e6	+	1.14750e6i	−0.301036	+	0.143138i
$19$	−1.72662e7			−1.59975			−0.799876	−	0.600165i	$-0.795102\pi$
$19$	−1.72662e7			−1.59975			−0.799876	+	0.600165i	$0.795102\pi$
$20$	1.92391e6	+	1.56571e6i	0.134437	+	0.109408i
$21$	6.08286e6	+	8.93073e6i	0.325014	+	0.477179i
$22$	9.62880e6	+	2.02505e7i	0.398334	+	0.837745i
$23$		−	4.82401e7i		−	1.56281i	−0.624026	−	0.781404i	$-0.714504\pi$
$23$		−	4.82401e7i		−	1.56281i	0.624026	−	0.781404i	$-0.285496\pi$
$24$	5.33747e6	−	2.18801e7i	0.136828	−	0.560902i
$25$	4.73612e7			0.969957
$26$	−15777.8	−	33182.6i	−0.000260431	−	0.000547718i
$27$	−1.43489e7			−0.192450
$28$	−9.07386e7	−	7.74713e6i	−0.996375	−	0.0850690i
$29$	−3.74837e7			−0.339355			−0.169677	−	0.985500i	$-0.554273\pi$
$29$	−3.74837e7			−0.339355			−0.169677	+	0.985500i	$0.554273\pi$
$30$	5.71946e6	+	1.20287e7i	0.0429723	+	0.0903760i
$31$	2.03149e8			1.27446			0.637230	−	0.770674i	$-0.280080\pi$
$31$	2.03149e8			1.27446			0.637230	+	0.770674i	$0.280080\pi$
$32$	1.14633e8	+	1.51288e8i	0.603925	+	0.797041i
$33$			1.20403e8i			0.535564i
$34$	8.22858e7	+	1.73057e8i	0.310592	+	0.653214i
$35$	4.45133e7	−	3.03187e7i	0.143257	−	0.0975745i
$36$	7.63336e7	−	9.37967e7i	0.210403	−	0.258538i
$37$	4.41964e8			1.04780			0.523899	−	0.851780i	$-0.324477\pi$
$37$	4.41964e8			1.04780			0.523899	+	0.851780i	$0.324477\pi$
$38$	7.05671e8	−	3.35535e8i	1.44475	−	0.686954i
$39$		−	197293.i		−	0.000350152i
$40$	−1.09057e8	−	2.66035e7i	−0.168392	−	0.0410779i
$41$		−	5.82689e8i		−	0.785463i	−0.919653	−	0.392732i	$-0.871530\pi$
$41$		−	5.82689e8i		−	0.785463i	0.919653	−	0.392732i	$-0.128470\pi$
$42$	−4.22158e8	−	2.46791e8i	−0.498429	−	0.291379i
$43$			7.19229e8i			0.746089i	0.927813	+	0.373045i	$0.121686\pi$
$43$			7.19229e8i			0.746089i	−0.927813	+	0.373045i	$0.878314\pi$
$44$	−7.87058e8	−	6.40524e8i	−0.719477	−	0.585525i
$45$			7.15190e7i			0.0577767i
$46$	9.37451e8	+	1.97157e9i	0.671089	+	1.41138i
$47$	2.68659e9			1.70869			0.854345	−	0.519706i	$-0.173958\pi$
$47$	2.68659e9			1.70869			0.854345	+	0.519706i	$0.173958\pi$
$48$	2.07054e8	+	9.97963e8i	0.117289	+	0.565311i
$49$	−7.24089e8	+	1.83998e9i	−0.366196	+	0.930538i
$50$	−1.93565e9	+	9.20370e8i	−0.875976	+	0.416512i
$51$			1.02894e9i			0.417595i
$52$	1.28968e6	+	1.04956e6i	0.000470394	+	0.000382816i
$53$	−3.24198e9			−1.06486			−0.532430	−	0.846474i	$-0.678721\pi$
$53$	−3.24198e9			−1.06486			−0.532430	+	0.846474i	$0.678721\pi$
$54$	5.86440e8	−	2.78842e8i	0.173803	−	0.0826405i
$55$	6.00124e8			0.160785
$56$	3.85904e9	−	1.44670e9i	0.936364	−	0.351030i
$57$	4.19569e9			0.923618
$58$	1.53196e9	−	7.28421e8i	0.306474	−	0.145723i
$59$	−3.75912e9			−0.684541			−0.342271	−	0.939601i	$-0.611196\pi$
$59$	−3.75912e9			−0.684541			−0.342271	+	0.939601i	$0.611196\pi$
$60$	−4.67509e8	−	3.80468e8i	−0.0776173	−	0.0631665i
$61$		−	1.56573e9i		−	0.237357i	−0.992933	−	0.118678i	$-0.962134\pi$
$61$		−	1.56573e9i		−	0.237357i	0.992933	−	0.118678i	$-0.0378658\pi$
$62$	−8.30272e9	+	3.94780e9i	−1.15098	+	0.547269i
$63$	−1.47814e9	−	2.17017e9i	−0.187647	−	0.275499i
$64$	−7.62502e9	−	3.95551e9i	−0.887669	−	0.460481i
$65$	−983365.			−0.000105121
$66$	−2.33980e9	−	4.92088e9i	−0.229978	−	0.483673i
$67$		−	1.21311e10i		−	1.09771i	−0.835917	−	0.548857i	$-0.815063\pi$
$67$		−	1.21311e10i		−	1.09771i	0.835917	−	0.548857i	$-0.184937\pi$
$68$	−6.72604e9	−	5.47379e9i	−0.560997	−	0.456551i
$69$			1.17224e10i			0.902287i
$70$	−1.23008e9	+	2.10415e9i	−0.0874767	+	0.149637i
$71$		−	1.57657e10i		−	1.03703i	−0.855067	−	0.518517i	$-0.826484\pi$
$71$		−	1.57657e10i		−	1.03703i	0.855067	−	0.518517i	$-0.173516\pi$
$72$	−1.29701e9	+	5.31686e9i	−0.0789974	+	0.323837i
$73$		−	4.84329e9i		−	0.273442i	−0.990610	−	0.136721i	$-0.956344\pi$
$73$		−	4.84329e9i		−	0.273442i	0.990610	−	0.136721i	$-0.0436564\pi$
$74$	−1.80631e10	+	8.58870e9i	−0.946276	+	0.449938i
$75$	−1.15088e10			−0.560005
$76$	−2.23203e10	+	2.74266e10i	−1.00978	+	1.24079i
$77$	−1.82101e10	+	1.24032e10i	−0.766679	+	0.522197i
$78$	3.83400e6	+	8.06337e6i	0.000150360	+	0.000316225i
$79$		−	2.24827e10i		−	0.822054i	−0.911623	−	0.411027i	$-0.865170\pi$
$79$		−	2.24827e10i		−	0.822054i	0.911623	−	0.411027i	$-0.134830\pi$
$80$	4.97413e9	−	1.03201e9i	0.169716	−	0.0352120i
$81$	3.48678e9			0.111111
$82$	1.13234e10	+	2.38145e10i	0.337288	+	0.709358i
$83$	−5.78633e10			−1.61240			−0.806202	−	0.591640i	$-0.798481\pi$
$83$	−5.78633e10			−1.61240			−0.806202	+	0.591640i	$0.798481\pi$
$84$	2.20495e10	+	1.88255e9i	0.575257	+	0.0491146i
$85$	5.12854e9			0.125369
$86$	−1.39768e10	−	2.93949e10i	−0.320380	−	0.673799i
$87$	9.10854e9			0.195926
$88$	4.46144e10	+	1.08833e10i	0.901198	+	0.219840i
$89$			6.72135e10i			1.27589i	0.770084	+	0.637943i	$0.220214\pi$
$89$			6.72135e10i			1.27589i	−0.770084	+	0.637943i	$0.779786\pi$
$90$	−1.38983e9	−	2.92298e9i	−0.0248101	−	0.0521786i
$91$	2.98391e7	−	2.03239e7i	0.000501255	−	0.000341413i
$92$	−7.66273e10	−	6.23608e10i	−1.21213	−	0.986458i
$93$	−4.93653e10			−0.735810
$94$	−1.09801e11	+	5.22086e10i	−1.54313	+	0.733734i
$95$		−	2.09125e10i		−	0.277285i
$96$	−2.78557e10	−	3.67631e10i	−0.348676	−	0.460172i
$97$			1.16526e11i			1.37777i	0.724869	+	0.688887i	$0.241900\pi$
$97$			1.16526e11i			1.37777i	−0.724869	+	0.688887i	$0.758100\pi$
$98$	−6.16276e9	−	8.92711e10i	−0.0688702	−	0.997626i
$99$		−	2.92580e10i		−	0.309208i
$100$	6.12246e10	−	7.52311e10i	0.612246	−	0.752311i
$101$		−	2.49783e10i		−	0.236480i	−0.992985	−	0.118240i	$-0.962275\pi$
$101$		−	2.49783e10i		−	0.236480i	0.992985	−	0.118240i	$-0.0377253\pi$
$102$	−1.99954e10	−	4.20529e10i	−0.179321	−	0.377133i
$103$	−1.98339e11			−1.68579			−0.842894	−	0.538080i	$-0.819150\pi$
$103$	−1.98339e11			−1.68579			−0.842894	+	0.538080i	$0.819150\pi$
$104$	−7.31052e7	−	1.78334e7i	−0.000589203	−	0.000143731i
$105$	−1.08167e10	+	7.36745e9i	−0.0827094	+	0.0563347i
$106$	1.32500e11	−	6.30014e10i	0.961684	−	0.457265i
$107$			3.13969e10i			0.216410i	0.994129	+	0.108205i	$0.0345102\pi$
$107$			3.13969e10i			0.216410i	−0.994129	+	0.108205i	$0.965490\pi$
$108$	−1.85491e10	+	2.27926e10i	−0.121476	+	0.149267i
$109$	−1.09821e11			−0.683660			−0.341830	−	0.939762i	$-0.611047\pi$
$109$	−1.09821e11			−0.683660			−0.341830	+	0.939762i	$0.611047\pi$
$110$	−2.45271e10	+	1.16622e10i	−0.145207	+	0.0690433i
$111$	−1.07397e11			−0.604947
$112$	−1.29605e11	+	1.34119e11i	−0.694902	+	0.719105i
$113$	−2.62005e11			−1.33776			−0.668879	−	0.743371i	$-0.733226\pi$
$113$	−2.62005e11			−1.33776			−0.668879	+	0.743371i	$0.733226\pi$
$114$	−1.71478e11	+	8.15350e10i	−0.834127	+	0.396613i
$115$	5.84275e10			0.270882
$116$	−4.84558e10	+	5.95412e10i	−0.214204	+	0.263208i
$117$			4.79422e7i			0.000202160i
$118$	1.53635e11	−	7.30509e10i	0.618215	−	0.293951i
$119$	−1.55620e11	+	1.05995e11i	−0.597802	+	0.407172i
$120$	2.65008e10	+	6.46464e9i	0.0972213	+	0.0237163i
$121$	3.98046e10			0.139513
$122$	3.04268e10	+	6.39913e10i	0.101924	+	0.214359i
$123$			1.41593e11i			0.453487i
$124$	2.62615e11	−	3.22694e11i	0.804451	−	0.988487i
$125$			1.16503e11i			0.341453i
$126$	1.02584e11	+	5.99702e10i	0.287768	+	0.168228i
$127$		−	3.60186e11i		−	0.967401i	−0.875234	−	0.483700i	$-0.839292\pi$
$127$		−	3.60186e11i		−	0.967401i	0.875234	−	0.483700i	$-0.160708\pi$
$128$	3.88502e11	+	1.34845e10i	0.999398	+	0.0346881i
$129$		−	1.74773e11i		−	0.430755i
$130$	4.01901e7	−	1.91097e7i	9.49360e−5	−	4.51405e-5i
$131$	1.40420e11			0.318007			0.159004	−	0.987278i	$-0.449172\pi$
$131$	1.40420e11			0.318007			0.159004	+	0.987278i	$0.449172\pi$
$132$	1.91255e11	+	1.55647e11i	0.415390	+	0.338053i
$133$	4.32214e11	+	6.34568e11i	0.900565	+	1.32219i
$134$	2.35744e11	+	4.95798e11i	0.471372	+	0.991354i
$135$		−	1.73791e10i		−	0.0333574i
$136$	3.81266e11	+	9.30066e10i	0.702690	+	0.171415i
$137$	7.28759e10			0.129009			0.0645046	−	0.997917i	$-0.479453\pi$
$137$	7.28759e10			0.129009			0.0645046	+	0.997917i	$0.479453\pi$
$138$	−2.27801e11	−	4.79093e11i	−0.387454	−	0.814863i
$139$	2.66940e11			0.436348			0.218174	−	0.975910i	$-0.429990\pi$
$139$	2.66940e11			0.436348			0.218174	+	0.975910i	$0.429990\pi$
$140$	9.38317e9	−	1.09901e11i	0.0147450	−	0.172702i
$141$	−6.52842e11			−0.986513
$142$	3.06376e11	+	6.44346e11i	0.445316	+	0.936554i
$143$	4.02289e8			0.000562587
$144$	−5.03140e10	−	2.42505e11i	−0.0677166	−	0.326383i
$145$		−	4.53996e10i		−	0.0588204i
$146$	9.41197e10	+	1.97945e11i	0.117419	+	0.246948i
$147$	1.75954e11	−	4.47114e11i	0.211423	−	0.537246i
$148$	5.71335e11	−	7.02040e11i	0.661380	−	0.812686i
$149$	−3.79530e11			−0.423371			−0.211686	−	0.977338i	$-0.567895\pi$
$149$	−3.79530e11			−0.423371			−0.211686	+	0.977338i	$0.567895\pi$
$150$	4.70363e11	−	2.23650e11i	0.505745	−	0.240473i
$151$			1.15765e12i			1.20007i	0.799976	+	0.600033i	$0.204846\pi$
$151$			1.15765e12i			1.20007i	−0.799976	+	0.600033i	$0.795154\pi$
$152$	3.79251e11	−	1.55468e12i	0.379129	−	1.55418i
$153$		−	2.50033e11i		−	0.241099i
$154$	5.03216e11	−	8.60796e11i	0.468156	−	0.800823i
$155$			2.46051e11i			0.220902i
$156$	−3.13391e8	−	2.55044e8i	−0.000271582	−	0.000221019i
$157$			1.90744e12i			1.59589i	0.602733	+	0.797943i	$0.294078\pi$
$157$			1.90744e12i			1.59589i	−0.602733	+	0.797943i	$0.705922\pi$
$158$	4.36907e11	+	9.18870e11i	0.353000	+	0.742403i
$159$	7.87801e11			0.614798
$160$	−1.83238e11	+	1.38841e11i	−0.138151	+	0.104678i
$161$	−1.77292e12	+	1.20756e12i	−1.29166	+	0.879767i
$162$	−1.42505e11	+	6.77587e10i	−0.100345	+	0.0477125i
$163$		−	1.28458e12i		−	0.874435i	−0.899356	−	0.437218i	$-0.855964\pi$
$163$		−	1.28458e12i		−	0.874435i	0.899356	−	0.437218i	$-0.144036\pi$
$164$	−9.25575e11	−	7.53252e11i	−0.609215	−	0.495792i
$165$	−1.45830e11			−0.0928294
$166$	2.36488e12	−	1.12446e12i	1.45618	−	0.692387i
$167$	−1.10424e12			−0.657843			−0.328921	−	0.944357i	$-0.606685\pi$
$167$	−1.10424e12			−0.657843			−0.328921	+	0.944357i	$0.606685\pi$
$168$	−9.37746e11	+	3.51548e11i	−0.540610	+	0.202667i
$169$	1.79216e12			1.00000
$170$	−2.09604e11	+	9.96630e10i	−0.113222	+	0.0538350i
$171$	−1.01955e12			−0.533251
$172$	1.14246e12	+	9.29759e11i	0.578676	+	0.470938i
$173$		−	2.89632e12i		−	1.42100i	−0.703698	−	0.710499i	$-0.748469\pi$
$173$		−	2.89632e12i		−	1.42100i	0.703698	−	0.710499i	$-0.251531\pi$
$174$	−3.72266e11	+	1.77006e11i	−0.176943	+	0.0841333i
$175$	−1.18556e12	−	1.74062e12i	−0.546028	−	0.801667i
$176$	−2.03489e12	+	4.22190e11i	−0.908281	+	0.188447i
$177$	9.13465e11			0.395220
$178$	−1.30616e12	−	2.74702e12i	−0.547882	−	1.15226i
$179$		−	3.73432e12i		−	1.51887i	−0.650584	−	0.759434i	$-0.725476\pi$
$179$		−	3.73432e12i		−	1.51887i	0.650584	−	0.759434i	$-0.274524\pi$
$180$	1.13605e11	+	9.24538e10i	0.0448123	+	0.0364692i
$181$			3.30958e12i			1.26631i	0.774024	+	0.633156i	$0.218241\pi$
$181$			3.30958e12i			1.26631i	−0.774024	+	0.633156i	$0.781759\pi$
$182$	−8.24572e8	+	1.41050e9i	−0.000306081	+	0.000523578i
$183$			3.80471e11i			0.137038i
$184$	4.34362e12	+	1.05959e12i	1.51829	+	0.370373i
$185$			5.35299e11i			0.181615i
$186$	2.01756e12	−	9.59316e11i	0.664516	−	0.315966i
$187$	−2.09805e12			−0.670947
$188$	3.47300e12	−	4.26753e12i	1.07854	−	1.32528i
$189$	3.59187e11	+	5.27351e11i	0.108338	+	0.159060i
$190$	4.06393e11	+	8.54696e11i	0.119070	+	0.250419i
$191$			5.43520e12i			1.54715i	0.633706	+	0.773574i	$0.281533\pi$
$191$			5.43520e12i			1.54715i	−0.633706	+	0.773574i	$0.718467\pi$
$192$	1.85288e12	+	9.61188e11i	0.512496	+	0.265859i
$193$	−3.03104e12			−0.814755			−0.407377	−	0.913260i	$-0.633557\pi$
$193$	−3.03104e12			−0.814755			−0.407377	+	0.913260i	$0.633557\pi$
$194$	−2.26445e12	−	4.76242e12i	−0.591634	−	1.24428i
$195$	2.38958e8			6.06919e−5
$196$	1.98668e12	+	3.52875e12i	0.490591	+	0.871390i
$197$	−5.20245e12			−1.24923			−0.624617	−	0.780931i	$-0.714745\pi$
$197$	−5.20245e12			−1.24923			−0.624617	+	0.780931i	$0.714745\pi$
$198$	5.68571e11	+	1.19577e12i	0.132778	+	0.279248i
$199$	6.42699e12			1.45987			0.729937	−	0.683514i	$-0.239549\pi$
$199$	6.42699e12			1.45987			0.729937	+	0.683514i	$0.239549\pi$
$200$	−1.04028e12	+	4.26447e12i	−0.229872	+	0.942324i
$201$			2.94786e12i			0.633765i
$202$	4.85403e11	+	1.02086e12i	0.101548	+	0.213567i
$203$	9.38306e11	+	1.37760e12i	0.191036	+	0.280476i
$204$	1.63443e12	+	1.33013e12i	0.323892	+	0.263590i
$205$	7.05742e11			0.136144
$206$	8.10611e12	−	3.85432e12i	1.52245	−	0.723899i
$207$		−	2.84853e12i		−	0.520936i
$208$	3.33437e9	−	6.91802e8i	0.000593834	−	0.000123207i
$209$			8.55519e12i			1.48397i
$210$	2.98908e11	−	5.11309e11i	0.0505047	−	0.0863928i
$211$		−	1.60347e11i		−	0.0263940i	−0.999913	−	0.0131970i	$-0.995799\pi$
$211$		−	1.60347e11i		−	0.0263940i	0.999913	−	0.0131970i	$-0.00420087\pi$
$212$	−4.19096e12	+	5.14973e12i	−0.672150	+	0.825919i
$213$			3.83107e12i			0.598732i
$214$	−6.10137e11	−	1.28319e12i	−0.0929290	−	0.195441i
$215$	−8.71116e11			−0.129320
$216$	3.15172e11	−	1.29200e12i	0.0456092	−	0.186967i
$217$	−5.08531e12	−	7.46614e12i	−0.717445	−	1.05334i
$218$	4.48839e12	−	2.13416e12i	0.617419	−	0.293573i
$219$			1.17692e12i			0.157872i
$220$	7.75790e11	−	9.53270e11i	0.101489	−	0.124707i
$221$	3.43788e9			0.000438665
$222$	4.38933e12	−	2.08705e12i	0.546332	−	0.259772i
$223$	−5.11461e12			−0.621064			−0.310532	−	0.950563i	$-0.600507\pi$
$223$	−5.11461e12			−0.621064			−0.310532	+	0.950563i	$0.600507\pi$
$224$	2.69063e12	−	8.00008e12i	0.318779	−	0.947829i
$225$	2.79663e12			0.323319
$226$	1.07081e13	−	5.09154e12i	1.20814	−	0.574451i
$227$	−1.50549e13			−1.65781			−0.828905	−	0.559389i	$-0.811036\pi$
$227$	−1.50549e13			−1.65781			−0.828905	+	0.559389i	$0.811036\pi$
$228$	5.42384e12	−	6.66467e12i	0.582996	−	0.716369i
$229$		−	1.27546e12i		−	0.133836i	−0.997758	−	0.0669179i	$-0.978683\pi$
$229$		−	1.27546e12i		−	0.133836i	0.997758	−	0.0669179i	$-0.0213166\pi$
$230$	−2.38793e12	+	1.13542e12i	−0.244635	+	0.116320i
$231$	4.42506e12	−	3.01398e12i	0.442642	−	0.301491i
$232$	8.23326e11	−	3.37509e12i	0.0804244	−	0.329687i
$233$	−1.09965e13			−1.04905			−0.524525	−	0.851395i	$-0.675757\pi$
$233$	−1.09965e13			−1.04905			−0.524525	+	0.851395i	$0.675757\pi$
$234$	−9.31662e8	−	1.95940e9i	−8.68102e−5	−	0.000182573i
$235$			3.25395e12i			0.296168i
$236$	−4.85947e12	+	5.97119e12i	−0.432089	+	0.530939i
$237$			5.46330e12i			0.474613i
$238$	4.30039e12	−	7.35619e12i	0.365035	−	0.624425i
$239$		−	2.76724e12i		−	0.229540i	−0.993392	−	0.114770i	$-0.963387\pi$
$239$		−	2.76724e12i		−	0.229540i	0.993392	−	0.114770i	$-0.0366131\pi$
$240$	−1.20871e12	+	2.50779e11i	−0.0979855	+	0.0203296i
$241$			2.15507e13i			1.70753i	0.520661	+	0.853764i	$0.325686\pi$
$241$			2.15507e13i			1.70753i	−0.520661	+	0.853764i	$0.674314\pi$
$242$	−1.62681e12	+	7.73523e11i	−0.125995	+	0.0599085i
$243$	−8.47289e11			−0.0641500
$244$	−2.48708e12	−	2.02404e12i	−0.184097	−	0.149822i
$245$	−2.22855e12	−	8.77003e11i	−0.161290	−	0.0634728i
$246$	−2.75159e12	−	5.78693e12i	−0.194733	−	0.409548i
$247$		−	1.40186e10i		−	0.000970220i
$248$	−4.46215e12	+	1.82919e13i	−0.302037	+	1.23815i
$249$	1.40608e13			0.930922
$250$	−2.26400e12	−	4.76147e12i	−0.146624	−	0.308369i
$251$	−7.40890e12			−0.469406			−0.234703	−	0.972067i	$-0.575412\pi$
$251$	−7.40890e12			−0.469406			−0.234703	+	0.972067i	$0.575412\pi$
$252$	−5.35802e12	−	4.57460e11i	−0.332125	−	0.0283563i
$253$	−2.39023e13			−1.44970
$254$	6.99950e12	+	1.47208e13i	0.415414	+	0.873668i
$255$	−1.24624e12			−0.0723818
$256$	−1.61401e13	+	6.99865e12i	−0.917460	+	0.397827i
$257$		−	8.02831e12i		−	0.446675i	−0.974741	−	0.223338i	$-0.928305\pi$
$257$		−	8.02831e12i		−	0.446675i	0.974741	−	0.223338i	$-0.0716952\pi$
$258$	3.39636e12	+	7.14296e12i	0.184972	+	0.389018i
$259$	−1.10634e13	−	1.62431e13i	−0.589848	−	0.866003i
$260$	−1.27121e9	+	1.56203e9i	−6.63536e−5	+	8.15335e-5i
$261$	−2.21338e12			−0.113118
$262$	−5.73897e12	+	2.72878e12i	−0.287195	+	0.136556i
$263$			1.80266e13i			0.883401i	0.897163	+	0.441701i	$0.145625\pi$
$263$			1.80266e13i			0.883401i	−0.897163	+	0.441701i	$0.854375\pi$
$264$	−1.08413e13	−	2.64465e12i	−0.520307	−	0.126925i
$265$		−	3.92662e12i		−	0.184572i
$266$	−2.99962e13	−	1.75356e13i	−1.38107	−	0.807368i
$267$		−	1.63329e13i		−	0.736633i
$268$	−1.92697e13	−	1.56821e13i	−0.851400	−	0.692887i
$269$			2.45573e13i			1.06302i	0.847051	+	0.531511i	$0.178376\pi$
$269$			2.45573e13i			1.06302i	−0.847051	+	0.531511i	$0.821624\pi$
$270$	3.37729e11	+	7.10285e11i	0.0143241	+	0.0301253i
$271$	−1.69197e13			−0.703171			−0.351586	−	0.936156i	$-0.614357\pi$
$271$	−1.69197e13			−0.703171			−0.351586	+	0.936156i	$0.614357\pi$
$272$	−1.73897e13	+	3.60796e12i	−0.708213	+	0.146937i
$273$	−7.25091e9	+	4.93871e9i	−0.000289400	+	0.000197115i
$274$	−2.97844e12	+	1.41620e12i	−0.116509	+	0.0553982i
$275$		−	2.34668e13i		−	0.899756i
$276$	1.86204e13	+	1.51537e13i	0.699825	+	0.569532i
$277$	3.65497e12			0.134662			0.0673309	−	0.997731i	$-0.478552\pi$
$277$	3.65497e12			0.134662			0.0673309	+	0.997731i	$0.478552\pi$
$278$	−1.09099e13	+	5.18746e12i	−0.394070	+	0.187373i
$279$	1.19958e13			0.424820
$280$	1.75221e12	+	4.67399e12i	0.0608440	+	0.162300i
$281$	−4.22188e12			−0.143754			−0.0718772	−	0.997413i	$-0.522899\pi$
$281$	−4.22188e12			−0.143754			−0.0718772	+	0.997413i	$0.522899\pi$
$282$	2.66817e13	−	1.26867e13i	0.890928	−	0.423621i
$283$	−3.91328e12			−0.128149			−0.0640746	−	0.997945i	$-0.520410\pi$
$283$	−3.91328e12			−0.128149			−0.0640746	+	0.997945i	$0.520410\pi$
$284$	−2.50431e13	−	2.03806e13i	−0.804337	−	0.654586i
$285$			5.08175e12i			0.160091i
$286$	−1.64415e10	+	7.81768e9i	−0.000508077	+	0.000241582i
$287$	−2.14150e13	+	1.45861e13i	−0.649183	+	0.442169i
$288$	6.76893e12	+	8.93343e12i	0.201308	+	0.265680i
$289$	1.63423e13			0.476844
$290$	8.82250e11	+	1.85548e12i	0.0252582	+	0.0531212i
$291$		−	2.83158e13i		−	0.795458i
$292$	−7.69335e12	−	6.26100e12i	−0.212085	−	0.172599i
$293$		−	5.17504e13i		−	1.40004i	−0.714121	−	0.700022i	$-0.753173\pi$
$293$		−	5.17504e13i		−	1.40004i	0.714121	−	0.700022i	$-0.246827\pi$
$294$	1.49755e12	+	2.16929e13i	0.0397623	+	0.575979i
$295$		−	4.55297e12i		−	0.118652i
$296$	−9.70770e12	+	3.97952e13i	−0.248320	+	1.01795i
$297$			7.10969e12i			0.178521i
$298$	1.55114e13	−	7.37540e12i	0.382350	−	0.181801i
$299$	3.91664e10			0.000947813
$300$	−1.48776e13	+	1.82811e13i	−0.353480	+	0.434347i
$301$	2.64331e13	−	1.80040e13i	0.616641	−	0.420004i
$302$	−2.24967e13	−	4.73133e13i	−0.515323	−	1.08379i
$303$			6.06972e12i			0.136532i
$304$	1.47121e13	+	7.09097e13i	0.324989	+	1.56639i
$305$	1.89638e12			0.0411411
$306$	4.85889e12	+	1.02189e13i	0.103531	+	0.217738i
$307$	5.17255e13			1.08254			0.541269	−	0.840849i	$-0.317944\pi$
$307$	5.17255e13			1.08254			0.541269	+	0.840849i	$0.317944\pi$
$308$	−3.83860e12	+	4.49598e13i	−0.0789121	+	0.924262i
$309$	4.81963e13			0.973290
$310$	−4.78150e12	−	1.00561e13i	−0.0948583	−	0.199499i
$311$	8.23553e13			1.60513			0.802564	−	0.596567i	$-0.203469\pi$
$311$	8.23553e13			1.60513			0.802564	+	0.596567i	$0.203469\pi$
$312$	1.77646e10	+	4.33352e9i	0.000340177	+	8.29833e-5i
$313$		−	1.08163e13i		−	0.203509i	−0.994810	−	0.101755i	$-0.967554\pi$
$313$		−	1.08163e13i		−	0.203509i	0.994810	−	0.101755i	$-0.0324456\pi$
$314$	−3.70672e13	−	7.79569e13i	−0.685294	−	1.44126i
$315$	2.62847e12	−	1.79029e12i	0.0477523	−	0.0325248i
$316$	−3.57128e13	−	2.90638e13i	−0.637595	−	0.518888i
$317$	3.00106e13			0.526561			0.263281	−	0.964719i	$-0.415195\pi$
$317$	3.00106e13			0.526561			0.263281	+	0.964719i	$0.415195\pi$
$318$	−3.21974e13	+	1.53093e13i	−0.555229	+	0.264002i
$319$			1.85727e13i			0.314794i
$320$	4.79083e12	−	9.23528e12i	0.0798153	−	0.153860i
$321$		−	7.62945e12i		−	0.124944i
$322$	4.89927e13	−	8.38063e13i	0.788722	−	1.34918i
$323$			7.31110e13i			1.15709i
$324$	4.50742e12	−	5.53860e12i	0.0701344	−	0.0861792i
$325$			3.84528e10i			0.000588260i
$326$	2.49632e13	+	5.25006e13i	0.375494	+	0.789710i
$327$	2.66866e13			0.394712
$328$	5.24662e13	+	1.27987e13i	0.763086	+	0.186149i
$329$	−6.72517e13	−	9.87376e13i	−0.961891	−	1.41223i
$330$	5.96008e12	−	2.83392e12i	0.0838350	−	0.0398621i
$331$			9.62657e13i			1.33174i	0.746070	+	0.665868i	$0.231938\pi$
$331$			9.62657e13i			1.33174i	−0.746070	+	0.665868i	$0.768062\pi$
$332$	−7.48009e13	+	9.19133e13i	−1.01776	+	1.25060i
$333$	2.60976e13			0.349266
$334$	4.51302e13	−	2.14587e13i	0.594103	−	0.282486i
$335$	1.46930e13			0.190267
$336$	3.14941e13	−	3.25910e13i	0.401202	−	0.415175i
$337$	1.08714e14			1.36245			0.681227	−	0.732073i	$-0.261447\pi$
$337$	1.08714e14			1.36245			0.681227	+	0.732073i	$0.261447\pi$
$338$	−7.32456e13	+	3.48271e13i	−0.903108	+	0.429413i
$339$	6.36671e13			0.772355
$340$	6.62975e12	−	8.14646e12i	0.0791340	−	0.0972377i
$341$		−	1.00658e14i		−	1.18222i
$342$	4.16692e13	−	1.98130e13i	0.481583	−	0.228985i
$343$	8.57485e13	−	1.94473e13i	0.975234	−	0.221177i
$344$	−6.47605e13	−	1.57978e13i	−0.724834	−	0.176817i
$345$	−1.41979e13			−0.156394
$346$	5.62843e13	+	1.18373e14i	0.610195	+	1.28331i
$347$			1.09973e14i			1.17347i	0.809778	+	0.586736i	$0.199588\pi$
$347$			1.09973e14i			1.17347i	−0.809778	+	0.586736i	$0.800412\pi$
$348$	1.17748e13	−	1.44685e13i	0.123671	−	0.151963i
$349$		−	1.16282e14i		−	1.20219i	−0.799177	−	0.601095i	$-0.794731\pi$
$349$		−	1.16282e14i		−	1.20219i	0.799177	−	0.601095i	$-0.205269\pi$
$350$	8.22793e13	+	4.81000e13i	0.837368	+	0.489520i
$351$		−	1.16500e10i		−	0.000116717i
$352$	7.49614e13	−	5.67989e13i	0.739355	−	0.560216i
$353$		−	5.22570e13i		−	0.507439i	−0.967278	−	0.253719i	$-0.918346\pi$
$353$		−	5.22570e13i		−	0.507439i	0.967278	−	0.253719i	$-0.0816540\pi$
$354$	−3.73333e13	+	1.77514e13i	−0.356927	+	0.169713i
$355$	1.90952e13			0.179749
$356$	1.06766e14	+	8.68880e13i	0.989593	+	0.805351i
$357$	3.78157e13	−	2.57569e13i	0.345141	−	0.235081i
$358$	7.25691e13	+	1.52622e14i	0.652222	+	1.37170i
$359$		−	1.30626e14i		−	1.15614i	−0.815988	−	0.578069i	$-0.803807\pi$
$359$		−	1.30626e14i		−	1.15614i	0.815988	−	0.578069i	$-0.196193\pi$
$360$	−6.43968e12	−	1.57091e12i	−0.0561307	−	0.0136926i
$361$	1.81633e14			1.55921
$362$	−6.43151e13	−	1.35263e14i	−0.543771	−	1.14362i
$363$	−9.67252e12			−0.0805477
$364$	6.28994e9	−	7.36712e10i	5.15928e−5	−	0.000604283i
$365$	5.86610e12			0.0473957
$366$	−7.39370e12	−	1.55499e13i	−0.0588459	−	0.123760i
$367$	1.51120e12			0.0118484			0.00592418	−	0.999982i	$-0.498114\pi$
$367$	1.51120e12			0.0118484			0.00592418	+	0.999982i	$0.498114\pi$
$368$	−1.98115e14	+	4.11041e13i	−1.53022	+	0.317484i
$369$		−	3.44072e13i		−	0.261821i
$370$	−1.04025e13	−	2.18777e13i	−0.0779878	−	0.164018i
$371$	8.11543e13	+	1.19149e14i	0.599453	+	0.880104i
$372$	−6.38153e13	+	7.84145e13i	−0.464450	+	0.570703i
$373$	−1.23043e14			−0.882385			−0.441193	−	0.897412i	$-0.645444\pi$
$373$	−1.23043e14			−0.882385			−0.441193	+	0.897412i	$0.645444\pi$
$374$	8.57475e13	−	4.07715e13i	0.605938	−	0.288113i
$375$		−	2.83101e13i		−	0.197138i
$376$	−5.90107e13	+	2.41905e14i	−0.404946	+	1.66001i
$377$		−	3.04333e10i		−	0.000205812i
$378$	−2.49280e13	−	1.45728e13i	−0.166143	−	0.0971263i
$379$			2.06465e14i			1.35622i	0.734960	+	0.678111i	$0.237201\pi$
$379$			2.06465e14i			1.35622i	−0.734960	+	0.678111i	$0.762799\pi$
$380$	−3.32186e13	−	2.70340e13i	−0.215066	−	0.175025i
$381$			8.75252e13i			0.558529i
$382$	−1.05622e14	−	2.22137e14i	−0.664365	−	1.39724i
$383$	−8.61224e13			−0.533977			−0.266989	−	0.963700i	$-0.586029\pi$
$383$	−8.61224e13			−0.533977			−0.266989	+	0.963700i	$0.586029\pi$
$384$	−9.44060e13	−	3.27673e12i	−0.577003	−	0.0200272i
$385$	−1.50225e13	−	2.20557e13i	−0.0905125	−	0.132889i
$386$	1.23879e14	−	5.89023e13i	0.735812	−	0.349866i
$387$			4.24697e13i			0.248696i
$388$	1.85096e14	+	1.50635e14i	1.06862	+	0.869664i
$389$	5.93145e13			0.337627			0.168814	−	0.985648i	$-0.446006\pi$
$389$	5.93145e13			0.337627			0.168814	+	0.985648i	$0.446006\pi$
$390$	−9.76620e9	+	4.64367e9i	−5.48113e−5	+	2.60619e-5i
$391$	−2.04265e14			−1.13037
$392$	−1.49770e14	−	1.05613e14i	−0.817243	−	0.576294i
$393$	−3.41221e13			−0.183602
$394$	2.12624e14	−	1.01099e14i	1.12819	−	0.536437i
$395$	2.72307e13			0.142487
$396$	−4.64750e13	−	3.78223e13i	−0.239826	−	0.195175i
$397$		−	2.29477e14i		−	1.16786i	−0.811803	−	0.583932i	$-0.801513\pi$
$397$		−	2.29477e14i		−	1.16786i	0.811803	−	0.583932i	$-0.198487\pi$
$398$	−2.62671e14	+	1.24896e14i	−1.31842	+	0.626889i
$399$	−1.05028e14	−	1.54200e14i	−0.519942	−	0.763368i
$400$	−4.03551e13	−	1.94505e14i	−0.197047	−	0.949731i
$401$	−2.42600e13			−0.116842			−0.0584208	−	0.998292i	$-0.518607\pi$
$401$	−2.42600e13			−0.116842			−0.0584208	+	0.998292i	$0.518607\pi$
$402$	−5.72857e13	−	1.20479e14i	−0.272147	−	0.572358i
$403$			1.64938e11i			0.000772936i
$404$	−3.96769e13	−	3.22898e13i	−0.183417	−	0.149269i
$405$			4.22313e12i			0.0192589i
$406$	−6.51195e13	−	3.80685e13i	−0.292966	−	0.171266i
$407$		−	2.18987e14i		−	0.971964i
$408$	−9.26476e13	−	2.26006e13i	−0.405698	−	0.0989668i
$409$			1.22760e14i			0.530369i	0.964198	+	0.265185i	$0.0854329\pi$
$409$			1.22760e14i			0.530369i	−0.964198	+	0.265185i	$0.914567\pi$
$410$	−2.88437e13	+	1.37147e13i	−0.122953	+	0.0584622i
$411$	−1.77088e13			−0.0744835
$412$	−2.56396e14	+	3.15052e14i	−1.06408	+	1.30752i
$413$	9.40995e13	+	1.38155e14i	0.385356	+	0.565772i
$414$	5.53555e13	+	1.16420e14i	0.223696	+	0.470461i
$415$		−	7.00830e13i		−	0.279478i
$416$	−1.22832e11	+	9.30708e10i	−0.000483390	+	0.000366269i
$417$	−6.48665e13			−0.251926
$418$	−1.66253e14	−	3.49651e14i	−0.637236	−	1.34019i
$419$	−1.00346e14			−0.379599			−0.189799	−	0.981823i	$-0.560784\pi$
$419$	−1.00346e14			−0.379599			−0.189799	+	0.981823i	$0.560784\pi$
$420$	−2.28011e12	+	2.67059e13i	−0.00851305	+	0.0997094i
$421$	−1.50401e14			−0.554243			−0.277121	−	0.960835i	$-0.589380\pi$
$421$	−1.50401e14			−0.554243			−0.277121	+	0.960835i	$0.589380\pi$
$422$	3.11601e12	+	6.55336e12i	0.0113339	+	0.0238367i
$423$	1.58641e14			0.569564
$424$	7.12097e13	−	2.91913e14i	0.252364	−	1.03452i
$425$		−	2.00543e14i		−	0.701565i
$426$	−7.44493e13	−	1.56576e14i	−0.257103	−	0.540720i
$427$	−5.75435e13	+	3.91938e13i	−0.196175	+	0.133618i
$428$	4.98726e13	+	4.05873e13i	0.167850	+	0.136600i
$429$	−9.77561e10			−0.000324810
$430$	3.56025e13	−	1.69284e13i	0.116790	−	0.0555315i
$431$		−	1.41120e14i		−	0.457048i	−0.973538	−	0.228524i	$-0.926610\pi$
$431$		−	1.41120e14i		−	0.457048i	0.973538	−	0.228524i	$-0.0733900\pi$
$432$	1.22263e13	+	5.89287e13i	0.0390962	+	0.188437i
$433$			2.43929e14i			0.770158i	0.922884	+	0.385079i	$0.125826\pi$
$433$			2.43929e14i			0.770158i	−0.922884	+	0.385079i	$0.874174\pi$
$434$	3.52926e14	+	2.06319e14i	1.10025	+	0.643198i
$435$			1.10321e13i			0.0339600i
$436$	−1.41968e14	+	1.74446e14i	−0.431533	+	0.530256i
$437$			8.32925e14i			2.50010i
$438$	−2.28711e13	−	4.81007e13i	−0.0677921	−	0.142575i
$439$	−7.84321e13			−0.229583			−0.114791	−	0.993390i	$-0.536620\pi$
$439$	−7.84321e13			−0.229583			−0.114791	+	0.993390i	$0.536620\pi$
$440$	−1.31817e13	+	5.40361e13i	−0.0381049	+	0.156205i
$441$	−4.27567e13	+	1.08649e14i	−0.122065	+	0.310179i
$442$	−1.40506e11	+	6.68083e10i	−0.000396162	+	0.000188368i
$443$		−	4.58531e14i		−	1.27688i	−0.769673	−	0.638438i	$-0.779581\pi$
$443$		−	4.58531e14i		−	1.27688i	0.769673	−	0.638438i	$-0.220419\pi$
$444$	−1.38834e14	+	1.70596e14i	−0.381848	+	0.469204i
$445$	−8.14078e13			−0.221149
$446$	2.09034e14	−	9.93923e13i	0.560888	−	0.266693i
$447$	9.22257e13			0.244433
$448$	4.54996e13	+	3.79250e14i	0.119118	+	0.992880i
$449$	3.57670e14			0.924970			0.462485	−	0.886627i	$-0.346958\pi$
$449$	3.57670e14			0.924970			0.462485	+	0.886627i	$0.346958\pi$
$450$	−1.14298e14	+	5.43469e13i	−0.291992	+	0.138837i
$451$	−2.88715e14			−0.728615
$452$	−3.38698e14	+	4.16183e14i	−0.844405	+	1.03758i
$453$		−	2.81309e14i		−	0.692858i
$454$	6.15293e14	−	2.92562e14i	1.49718	−	0.711885i
$455$	2.46159e10	+	3.61406e10i	5.91771e−5	+	8.68826e-5i
$456$	−9.21580e13	+	3.77787e14i	−0.218890	+	0.897305i
$457$	−6.10405e14			−1.43245			−0.716224	−	0.697870i	$-0.754131\pi$
$457$	−6.10405e14			−1.43245			−0.716224	+	0.697870i	$0.754131\pi$
$458$	2.47861e13	+	5.21281e13i	0.0574708	+	0.120868i
$459$			6.07580e13i			0.139198i
$460$	7.55302e13	−	9.28095e13i	0.170983	−	0.210099i
$461$		−	6.56071e12i		−	0.0146756i	−0.999973	−	0.00733780i	$-0.997664\pi$
$461$		−	6.56071e12i		−	0.0146756i	0.999973	−	0.00733780i	$-0.00233571\pi$
$462$	−1.22282e14	+	2.09173e14i	−0.270290	+	0.462355i
$463$			2.00722e14i			0.438429i	0.975677	+	0.219215i	$0.0703495\pi$
$463$			2.00722e14i			0.438429i	−0.975677	+	0.219215i	$0.929651\pi$
$464$	3.19388e13	+	1.53940e14i	0.0689398	+	0.332278i
$465$		−	5.97903e13i		−	0.127538i
$466$	4.49426e14	−	2.13695e14i	0.947406	−	0.450476i
$467$	1.24443e14			0.259255			0.129628	−	0.991563i	$-0.458622\pi$
$467$	1.24443e14			0.259255			0.129628	+	0.991563i	$0.458622\pi$
$468$	7.61541e10	+	6.19757e10i	0.000156798	+	0.000127605i
$469$	−4.45842e14	+	3.03670e14i	−0.907257	+	0.617947i
$470$	−6.32340e13	−	1.32989e14i	−0.127178	−	0.267471i
$471$		−	4.63507e14i		−	0.921385i
$472$	8.25686e13	−	3.38477e14i	0.162231	−	0.665040i
$473$	3.56368e14			0.692090
$474$	−1.06168e14	−	2.23285e14i	−0.203805	−	0.428627i
$475$	−8.17749e14			−1.55169
$476$	−3.28039e13	+	3.84217e14i	−0.0615301	+	0.720674i
$477$	−1.91436e14			−0.354954
$478$	5.37758e13	+	1.13097e14i	0.0985675	+	0.207300i
$479$	3.97194e14			0.719710			0.359855	−	0.933008i	$-0.382826\pi$
$479$	3.97194e14			0.719710			0.359855	+	0.933008i	$0.382826\pi$
$480$	4.45268e13	−	3.37383e13i	0.0797617	−	0.0604361i
$481$			3.58833e11i			0.000635470i
$482$	−4.18795e14	−	8.80778e14i	−0.733234	−	1.54208i
$483$	4.30820e14	−	2.93438e14i	0.745738	−	0.507934i
$484$	5.14561e13	−	6.32278e13i	0.0880617	−	0.108208i
$485$	−1.41134e14			−0.238810
$486$	3.46287e13	−	1.64654e13i	0.0579344	−	0.0275468i
$487$			6.65349e14i			1.10063i	0.834958	+	0.550313i	$0.185492\pi$
$487$			6.65349e14i			1.10063i	−0.834958	+	0.550313i	$0.814508\pi$
$488$	1.40980e14	+	3.43910e13i	0.230595	+	0.0562517i
$489$			3.12152e14i			0.504855i
$490$	1.08123e14	−	7.46421e12i	0.172919	−	0.0119373i
$491$		−	9.09612e14i		−	1.43849i	−0.694754	−	0.719247i	$-0.744487\pi$
$491$		−	9.09612e14i		−	1.43849i	0.694754	−	0.719247i	$-0.255513\pi$
$492$	2.24915e14	+	1.83040e14i	0.351730	+	0.286245i
$493$			1.58718e14i			0.245454i
$494$	2.72423e11	+	5.72939e11i	0.000416625	+	0.000876213i
$495$	3.54367e13			0.0535951
$496$	−1.73098e14	−	8.34303e14i	−0.258906	−	1.24788i
$497$	−5.79422e14	+	3.94653e14i	−0.857106	+	0.583789i
$498$	−5.74665e14	+	2.73243e14i	−0.840724	+	0.399750i
$499$			1.26979e15i			1.83730i	0.395076	+	0.918649i	$0.370718\pi$
$499$			1.26979e15i			1.83730i	−0.395076	+	0.918649i	$0.629282\pi$
$500$	1.85059e14	+	1.50605e14i	0.264835	+	0.215528i
$501$	2.68330e14			0.379806
$502$	3.02802e14	−	1.43977e14i	0.423924	−	0.201569i
$503$	2.46651e14			0.341554			0.170777	−	0.985310i	$-0.445372\pi$
$503$	2.46651e14			0.341554			0.170777	+	0.985310i	$0.445372\pi$
$504$	2.27872e14	−	8.54261e13i	0.312121	−	0.117010i
$505$	3.02532e13			0.0409892
$506$	9.76889e14	−	4.64494e14i	1.30923	−	0.622519i
$507$	−4.35495e14			−0.577350
$508$	−5.72139e14	−	4.65618e14i	−0.750328	−	0.610632i
$509$			1.25189e15i			1.62412i	0.583572	+	0.812061i	$0.301655\pi$
$509$			1.25189e15i			1.62412i	−0.583572	+	0.812061i	$0.698345\pi$
$510$	5.09337e13	−	2.42181e13i	0.0653686	−	0.0310817i
$511$	−1.78001e14	+	1.21239e14i	−0.225999	+	0.153932i
$512$	5.23643e14	−	5.99686e14i	0.657734	−	0.753250i
$513$	2.47752e14			0.307873
$514$	1.56014e14	+	3.28117e14i	0.191808	+	0.403396i
$515$		−	2.40224e14i		−	0.292198i
$516$	−2.77618e14	−	2.25931e14i	−0.334099	−	0.271896i
$517$		−	1.33117e15i		−	1.58502i
$518$	7.67813e14	+	4.48859e14i	0.904570	+	0.528806i
$519$			7.03806e14i			0.820413i
$520$	2.15995e10	−	8.85437e10i	2.49130e−5	−	0.000102127i
$521$		−	3.22040e14i		−	0.367538i	−0.982969	−	0.183769i	$-0.941170\pi$
$521$		−	3.22040e14i		−	0.367538i	0.982969	−	0.183769i	$-0.0588298\pi$
$522$	9.04607e13	−	4.30126e13i	0.102158	−	0.0485744i
$523$	−1.50967e15			−1.68702			−0.843512	−	0.537110i	$-0.819516\pi$
$523$	−1.50967e15			−1.68702			−0.843512	+	0.537110i	$0.819516\pi$
$524$	1.81523e14	−	2.23051e14i	0.200729	−	0.246651i
$525$	2.88091e14	+	4.22970e14i	0.315249	+	0.462842i
$526$	−3.50312e14	−	7.36749e14i	−0.379344	−	0.797807i
$527$		−	8.60202e14i		−	0.921811i
$528$	4.94477e14	−	1.02592e14i	0.524397	−	0.108800i
$529$	−1.37430e15			−1.44237
$530$	7.63061e13	+	1.60481e14i	0.0792578	+	0.166689i
$531$	−2.21972e14			−0.228180
$532$	1.56671e15	+	1.33764e14i	1.59395	+	0.136089i
$533$	4.73089e11			0.000476368
$534$	3.17397e14	+	6.67525e14i	0.316320	+	0.665259i
$535$	−3.80274e13			−0.0375103
$536$	1.09230e15	+	2.66458e14i	1.06644	+	0.260150i
$537$			9.07440e14i			0.876919i
$538$	−4.77222e14	−	1.00366e15i	−0.456476	−	0.960024i
$539$	9.11684e14	+	3.58777e14i	0.863190	+	0.339692i
$540$	−2.76059e13	−	2.24663e13i	−0.0258724	−	0.0210555i
$541$	−6.30398e14			−0.584830			−0.292415	−	0.956291i	$-0.594459\pi$
$541$	−6.30398e14			−0.584830			−0.292415	+	0.956291i	$0.594459\pi$
$542$	6.91508e14	−	3.28800e14i	0.635040	−	0.301951i
$543$		−	8.04229e14i		−	0.731106i
$544$	6.40605e14	−	4.85392e14i	0.576496	−	0.436816i
$545$		−	1.33013e14i		−	0.118499i
$546$	2.00371e11	−	3.42752e11i	0.000176716	−	0.000302288i
$547$			5.63290e14i			0.491815i	0.969293	+	0.245907i	$0.0790859\pi$
$547$			5.63290e14i			0.491815i	−0.969293	+	0.245907i	$0.920914\pi$
$548$	9.42079e13	−	1.15760e14i	0.0814318	−	0.100061i
$549$		−	9.24546e13i		−	0.0791189i
$550$	4.56031e14	+	9.59090e14i	0.386367	+	0.812577i
$551$	6.47203e14			0.542883
$552$	−1.05550e15	−	2.57480e14i	−0.876582	−	0.213835i
$553$	−8.26285e14	+	5.62796e14i	−0.679425	+	0.462767i
$554$	−1.49379e14	+	7.10270e13i	−0.121614	+	0.0578255i
$555$		−	1.30078e14i		−	0.104855i
$556$	3.45078e14	−	4.24023e14i	0.275427	−	0.338437i
$557$	1.56348e15			1.23563			0.617814	−	0.786324i	$-0.288019\pi$
$557$	1.56348e15			1.23563			0.617814	+	0.786324i	$0.288019\pi$
$558$	−4.90267e14	+	2.33114e14i	−0.383658	+	0.182423i
$559$	−5.83946e11			−0.000452489
$560$	−1.62443e14	−	1.56975e14i	−0.124643	−	0.120447i
$561$	5.09827e14			0.387371
$562$	1.72548e14	−	8.20438e13i	0.129826	−	0.0617300i
$563$	3.59241e13			0.0267664			0.0133832	−	0.999910i	$-0.495740\pi$
$563$	3.59241e13			0.0267664			0.0133832	+	0.999910i	$0.495740\pi$
$564$	−8.43939e14	+	1.03701e15i	−0.622696	+	0.765152i
$565$		−	3.17335e14i		−	0.231874i
$566$	1.59936e14	−	7.60468e13i	0.115733	−	0.0550289i
$567$	−8.72824e13	−	1.28146e14i	−0.0625489	−	0.0918330i
$568$	1.41957e15	+	3.46293e14i	1.00749	+	0.245769i
$569$	9.67003e14			0.679689			0.339845	−	0.940482i	$-0.389626\pi$
$569$	9.67003e14			0.679689			0.339845	+	0.940482i	$0.389626\pi$
$570$	−9.87536e13	−	2.07691e14i	−0.0687450	−	0.144579i
$571$			1.15637e15i			0.797254i	0.917113	+	0.398627i	$0.130513\pi$
$571$			1.15637e15i			0.797254i	−0.917113	+	0.398627i	$0.869487\pi$
$572$	5.20045e11	−	6.39017e11i	0.000355110	−	0.000436349i
$573$		−	1.32075e15i		−	0.893246i
$574$	5.91779e14	−	1.01229e15i	0.396410	−	0.678094i
$575$		−	2.28471e15i		−	1.51586i
$576$	−4.50250e14	−	2.33569e14i	−0.295890	−	0.153494i
$577$		−	1.26741e15i		−	0.824991i	−0.910960	−	0.412496i	$-0.864657\pi$
$577$		−	1.26741e15i		−	0.824991i	0.910960	−	0.412496i	$-0.135343\pi$
$578$	−6.67912e14	+	3.17581e14i	−0.430641	+	0.204763i
$579$	7.36544e14			0.470399
$580$	−7.21152e13	−	5.86888e13i	−0.0456218	−	0.0371280i
$581$	1.44846e15	+	2.12659e15i	0.907688	+	1.33265i
$582$	5.50261e14	+	1.15727e15i	0.341580	+	0.718385i
$583$			1.60636e15i			0.987791i
$584$	4.36098e14	+	1.06382e14i	0.265652	+	0.0648036i
$585$	−5.80667e10			−3.50405e−5
$586$	1.00567e15	+	2.11504e15i	0.601197	+	1.26439i
$587$	−1.16708e15			−0.691181			−0.345591	−	0.938385i	$-0.612321\pi$
$587$	−1.16708e15			−0.691181			−0.345591	+	0.938385i	$0.612321\pi$
$588$	−4.82763e14	−	8.57487e14i	−0.283243	−	0.503097i
$589$	−3.50762e15			−2.03882
$590$	8.84779e13	+	1.86080e14i	0.0509505	+	0.107155i
$591$	1.26420e15			0.721245
$592$	−3.76586e14	−	1.81508e15i	−0.212860	−	1.02595i
$593$			5.39604e14i			0.302186i	0.988520	+	0.151093i	$0.0482793\pi$
$593$			5.39604e14i			0.302186i	−0.988520	+	0.151093i	$0.951721\pi$
$594$	−1.38163e14	−	2.90573e14i	−0.0766594	−	0.161224i
$595$	−1.28379e14	−	1.88484e14i	−0.0705752	−	0.103617i
$596$	−4.90624e14	+	6.02866e14i	−0.267236	+	0.328372i
$597$	−1.56176e15			−0.842859
$598$	−1.60073e12	+	7.61122e11i	−0.000855978	+	0.000407003i
$599$			1.92745e15i			1.02126i	0.859801	+	0.510629i	$0.170587\pi$
$599$			1.92745e15i			1.02126i	−0.859801	+	0.510629i	$0.829413\pi$
$600$	2.52789e14	−	1.03627e15i	0.132717	−	0.544051i
$601$		−	3.03815e15i		−	1.58052i	−0.612772	−	0.790260i	$-0.709946\pi$
$601$		−	3.03815e15i		−	1.58052i	0.612772	−	0.790260i	$-0.290054\pi$
$602$	−7.30449e14	+	1.24950e15i	−0.376538	+	0.644102i
$603$		−	7.16329e14i		−	0.365904i
$604$	1.83888e15	+	1.49652e15i	0.930786	+	0.757492i
$605$			4.82106e13i			0.0241818i
$606$	−1.17953e14	−	2.48070e14i	−0.0586286	−	0.123303i
$607$	−1.95316e15			−0.962055			−0.481027	−	0.876706i	$-0.659736\pi$
$607$	−1.95316e15			−0.962055			−0.481027	+	0.876706i	$0.659736\pi$
$608$	−1.97927e15	−	2.61218e15i	−0.966130	−	1.27507i
$609$	−2.28008e14	−	3.34757e14i	−0.110295	−	0.161933i
$610$	−7.75050e13	+	3.68523e13i	−0.0371549	+	0.0176665i
$611$			2.18126e12i			0.00103629i
$612$	−3.97166e14	−	3.23222e14i	−0.186999	−	0.152184i
$613$	3.13686e15			1.46373			0.731867	−	0.681447i	$-0.238649\pi$
$613$	3.13686e15			1.46373			0.731867	+	0.681447i	$0.238649\pi$
$614$	−2.11402e15	+	1.00518e15i	−0.977649	+	0.464856i
$615$	−1.71495e14			−0.0786030
$616$	−7.16820e14	−	1.91210e15i	−0.325624	−	0.868595i
$617$	2.34841e15			1.05732			0.528660	−	0.848834i	$-0.322695\pi$
$617$	2.34841e15			1.05732			0.528660	+	0.848834i	$0.322695\pi$
$618$	−1.96978e15	+	9.36599e14i	−0.878986	+	0.417943i
$619$	2.71378e15			1.20026			0.600131	−	0.799902i	$-0.295115\pi$
$619$	2.71378e15			1.20026			0.600131	+	0.799902i	$0.295115\pi$
$620$	3.90840e14	+	3.18074e14i	0.171335	+	0.139436i
$621$			6.92193e14i			0.300762i
$622$	−3.36586e15	+	1.60041e15i	−1.44960	+	0.689262i
$623$	2.47023e15	−	1.68251e15i	1.05452	−	0.718248i
$624$	−8.10252e11	+	1.68108e11i	−0.000342850	+	7.11333e-5i
$625$	2.17145e15			0.910773
$626$	2.10193e14	+	4.42061e14i	0.0873894	+	0.183791i
$627$		−	2.07891e15i		−	0.856770i
$628$	3.02987e15	+	2.46577e15i	1.23779	+	1.00734i
$629$		−	1.87142e15i		−	0.757868i
$630$	−7.26347e13	+	1.24248e14i	−0.0291589	+	0.0498789i
$631$			2.86363e15i			1.13961i	0.821780	+	0.569805i	$0.192981\pi$
$631$			2.86363e15i			1.13961i	−0.821780	+	0.569805i	$0.807019\pi$
$632$	2.02438e15	+	4.93831e14i	0.798634	+	0.194820i
$633$			3.89642e13i			0.0152386i
$634$	−1.22653e15	+	5.83197e14i	−0.475542	+	0.226112i
$635$	4.36251e14			0.167680
$636$	1.01840e15	−	1.25139e15i	0.388066	−	0.476845i
$637$	−1.49389e12	−	5.87892e11i	−0.000564353	−	0.000222091i
$638$	−3.60923e14	−	7.59066e14i	−0.135176	−	0.284293i
$639$		−	9.30951e14i		−	0.345678i
$640$	−1.63322e13	+	4.70546e14i	−0.00601248	+	0.173226i
$641$	−4.03073e15			−1.47117			−0.735587	−	0.677430i	$-0.763094\pi$
$641$	−4.03073e15			−1.47117			−0.735587	+	0.677430i	$0.763094\pi$
$642$	1.48263e14	+	3.11816e14i	0.0536526	+	0.112838i
$643$	−2.73534e15			−0.981412			−0.490706	−	0.871325i	$-0.663261\pi$
$643$	−2.73534e15			−0.981412			−0.490706	+	0.871325i	$0.663261\pi$
$644$	−3.73722e14	+	4.37724e15i	−0.132947	+	1.55714i
$645$	2.11681e14			0.0746628
$646$	−1.42077e15	−	2.98805e15i	−0.496871	−	1.04498i
$647$	1.24307e15			0.431046			0.215523	−	0.976499i	$-0.430854\pi$
$647$	1.24307e15			0.431046			0.215523	+	0.976499i	$0.430854\pi$
$648$	−7.65869e13	+	3.13955e14i	−0.0263325	+	0.107946i
$649$			1.86259e15i			0.634997i
$650$	−7.47254e11	−	1.57157e12i	−0.000252607	−	0.000531263i
$651$	1.23573e15	+	1.81427e15i	0.414217	+	0.608145i
$652$	−2.04049e15	−	1.66059e15i	−0.678223	−	0.551952i
$653$	5.49631e14			0.181154			0.0905772	−	0.995889i	$-0.471129\pi$
$653$	5.49631e14			0.181154			0.0905772	+	0.995889i	$0.471129\pi$
$654$	−1.09068e15	+	5.18600e14i	−0.356467	+	0.169494i
$655$			1.70074e14i			0.0551203i
$656$	−2.39301e15	+	4.96493e14i	−0.769084	+	0.159567i
$657$		−	2.85992e14i		−	0.0911473i
$658$	4.66735e15	+	2.72850e15i	1.47512	+	0.862347i
$659$			8.09334e14i			0.253664i	0.991924	+	0.126832i	$0.0404808\pi$
$659$			8.09334e14i			0.253664i	−0.991924	+	0.126832i	$0.959519\pi$
$660$	−1.88517e14	+	2.31645e14i	−0.0585948	+	0.0719997i
$661$			1.42093e15i			0.437992i	0.975726	+	0.218996i	$0.0702781\pi$
$661$			1.42093e15i			0.437992i	−0.975726	+	0.218996i	$0.929722\pi$
$662$	−1.87073e15	−	3.93438e15i	−0.571864	−	1.20270i
$663$	−8.35404e11			−0.000253263
$664$	1.27096e15	−	5.21010e15i	0.382127	−	1.56647i
$665$	−7.68577e14	+	5.23490e14i	−0.229176	+	0.156095i
$666$	−1.06661e15	+	5.07154e14i	−0.315425	+	0.149979i
$667$			1.80822e15i			0.530346i
$668$	−1.42747e15	+	1.75403e15i	−0.415236	+	0.510231i
$669$	1.24285e15			0.358571
$670$	−6.00502e14	+	2.85528e14i	−0.171831	+	0.0817030i
$671$	−7.75796e14			−0.220178
$672$	−6.53822e14	+	1.94402e15i	−0.184047	+	0.547229i
$673$	2.59896e15			0.725633			0.362816	−	0.931861i	$-0.381815\pi$
$673$	2.59896e15			0.725633			0.362816	+	0.931861i	$0.381815\pi$
$674$	−4.44315e15	+	2.11264e15i	−1.23044	+	0.585055i
$675$	−6.79581e14			−0.186668
$676$	2.31675e15	−	2.84676e15i	0.631209	−	0.775612i
$677$		−	5.09684e15i		−	1.37741i	−0.725042	−	0.688705i	$-0.758180\pi$
$677$		−	5.09684e15i		−	1.37741i	0.725042	−	0.688705i	$-0.241820\pi$
$678$	−2.60208e15	+	1.23724e15i	−0.697520	+	0.331659i
$679$	4.28256e15	−	2.91692e15i	1.13873	−	0.775605i
$680$	−1.12648e14	+	4.61782e14i	−0.0297115	+	0.121797i
$681$	3.65833e15			0.957138
$682$	1.95608e15	+	4.11389e15i	0.507661	+	1.06767i
$683$		−	3.23473e15i		−	0.832769i	−0.909189	−	0.416384i	$-0.863297\pi$
$683$		−	3.23473e15i		−	0.832769i	0.909189	−	0.416384i	$-0.136703\pi$
$684$	−1.31799e15	+	1.61951e15i	−0.336593	+	0.413596i
$685$			8.82659e13i			0.0223612i
$686$	−3.12662e15	+	2.46116e15i	−0.785765	+	0.618525i
$687$			3.09937e14i			0.0772701i
$688$	2.95376e15	−	6.12835e14i	0.730531	−	0.151568i
$689$		−	2.63218e12i		−	0.000645818i
$690$	5.80268e14	−	2.75908e14i	0.141240	−	0.0671574i
$691$	−1.14923e15			−0.277509			−0.138755	−	0.990327i	$-0.544310\pi$
$691$	−1.14923e15			−0.277509			−0.138755	+	0.990327i	$0.544310\pi$
$692$	−4.60068e15	−	3.74412e15i	−1.10214	−	0.896947i
$693$	−1.07529e15	+	7.32397e14i	−0.255560	+	0.174066i
$694$	−2.13710e15	−	4.49459e15i	−0.503904	−	1.05977i
$695$			3.23313e14i			0.0756323i
$696$	−2.00068e14	+	8.20147e14i	−0.0464331	+	0.190345i
$697$	−2.46730e15			−0.568122
$698$	2.25971e15	+	4.75246e15i	0.516236	+	1.08571i
$699$	2.67215e15			0.605669
$700$	−4.29749e15	−	3.66913e14i	−0.966441	−	0.0825133i
$701$	−1.26750e15			−0.282812			−0.141406	−	0.989952i	$-0.545162\pi$
$701$	−1.26750e15			−0.282812			−0.141406	+	0.989952i	$0.545162\pi$
$702$	2.26394e11	+	4.76134e11i	5.01199e−5	+	0.000105408i
$703$	−7.63106e15			−1.67622
$704$	−1.95990e15	+	3.77810e15i	−0.427154	+	0.823424i
$705$		−	7.90710e14i		−	0.170992i
$706$	1.01551e15	+	2.13574e15i	0.217901	+	0.458272i
$707$	−9.18001e14	+	6.25265e14i	−0.195450	+	0.133124i
$708$	1.18085e15	−	1.45100e15i	0.249467	−	0.306538i
$709$	2.31841e15			0.486000			0.243000	−	0.970026i	$-0.421869\pi$
$709$	2.31841e15			0.486000			0.243000	+	0.970026i	$0.421869\pi$
$710$	−7.80419e14	+	3.71076e14i	−0.162333	+	0.0771867i
$711$		−	1.32758e15i		−	0.274018i
$712$	−6.05201e15	−	1.47634e15i	−1.23954	−	0.302375i
$713$		−	9.79995e15i		−	1.99173i
$714$	−1.04499e15	+	1.78756e15i	−0.210753	+	0.360512i
$715$			4.87244e11i			9.75132e-5i
$716$	−5.93180e15	−	4.82742e15i	−1.17805	−	0.958724i
$717$			6.72440e14i			0.132525i
$718$	2.53845e15	+	5.33868e15i	0.496460	+	1.04412i
$719$	−5.67615e15			−1.10165			−0.550827	−	0.834620i	$-0.685688\pi$
$719$	−5.67615e15			−1.10165			−0.550827	+	0.834620i	$0.685688\pi$
$720$	2.93717e14	−	6.09394e13i	0.0565719	−	0.0117373i
$721$	4.96488e15	+	7.28934e15i	0.948998	+	1.39330i
$722$	−7.42333e15	+	3.52967e15i	−1.40813	+	0.669544i
$723$		−	5.23682e15i		−	0.985841i
$724$	5.25712e15	+	4.27835e15i	0.982168	+	0.799308i
$725$	−1.77527e15			−0.329159
$726$	3.95316e14	−	1.87966e14i	0.0727433	−	0.0345882i
$727$	−5.53672e15			−1.01114			−0.505572	−	0.862784i	$-0.668719\pi$
$727$	−5.53672e15			−1.01114			−0.505572	+	0.862784i	$0.668719\pi$
$728$	1.17458e12	+	3.13318e12i	0.000212893	+	0.000567887i
$729$	2.05891e14			0.0370370
$730$	−2.39748e14	+	1.13996e14i	−0.0428035	+	0.0203523i
$731$	3.04545e15			0.539643
$732$	6.04362e14	+	4.91842e14i	0.106288	+	0.0864997i
$733$		−	5.96837e15i		−	1.04180i	−0.853618	−	0.520900i	$-0.825597\pi$
$733$		−	5.96837e15i		−	1.04180i	0.853618	−	0.520900i	$-0.174403\pi$
$734$	−6.17627e13	+	2.93671e13i	−0.0107003	+	0.00508783i
$735$	5.41537e14	+	2.13112e14i	0.0931210	+	0.0366460i
$736$	7.29817e15	−	5.52989e15i	1.24562	−	0.943818i
$737$	−6.01080e15			−1.01827
$738$	6.68636e14	+	1.40622e15i	0.112429	+	0.236453i
$739$			4.23156e15i			0.706246i	0.935577	+	0.353123i	$0.114880\pi$
$739$			4.23156e15i			0.706246i	−0.935577	+	0.353123i	$0.885120\pi$
$740$	8.50298e14	+	6.91990e14i	0.140863	+	0.114637i
$741$			3.40651e12i			0.000560157i
$742$	−5.63220e15	−	3.29255e15i	−0.919299	−	0.537417i
$743$			1.66451e15i			0.269680i	0.990867	+	0.134840i	$0.0430520\pi$
$743$			1.66451e15i			0.269680i	−0.990867	+	0.134840i	$0.956948\pi$
$744$	1.08430e15	−	4.44493e15i	0.174381	−	0.714848i
$745$		−	4.59679e14i		−	0.0733830i
$746$	5.02877e15	−	2.39110e15i	0.796889	−	0.378908i
$747$	−3.41677e15			−0.537468
$748$	−2.71219e15	+	3.33266e15i	−0.423508	+	0.520395i
$749$	1.15390e15	−	7.85939e14i	0.178862	−	0.121826i
$750$	5.50151e14	+	1.15704e15i	0.0846535	+	0.178037i
$751$			3.76217e15i			0.574670i	0.957830	+	0.287335i	$0.0927693\pi$
$751$			3.76217e15i			0.574670i	−0.957830	+	0.287335i	$0.907231\pi$
$752$	−2.28917e15	−	1.10334e16i	−0.347120	−	1.67306i
$753$	1.80036e15			0.271011
$754$	5.91410e11	+	1.24381e12i	8.83784e−5	+	0.000185871i
$755$	−1.40213e15			−0.208007
$756$	1.30200e15	+	1.11163e14i	0.191752	+	0.0163715i
$757$	1.95060e15			0.285195			0.142597	−	0.989781i	$-0.454455\pi$
$757$	1.95060e15			0.285195			0.142597	+	0.989781i	$0.454455\pi$
$758$	−4.01223e15	−	8.43822e15i	−0.582379	−	1.22481i
$759$	5.80827e15			0.836984
$760$	1.88300e15	+	4.59342e14i	0.269386	+	0.0657145i
$761$		−	7.62489e15i		−	1.08297i	−0.840709	−	0.541487i	$-0.817862\pi$
$761$		−	7.62489e15i		−	1.08297i	0.840709	−	0.541487i	$-0.182138\pi$
$762$	−1.70088e15	−	3.57716e15i	−0.239840	−	0.504412i
$763$	2.74908e15	+	4.03615e15i	0.384860	+	0.565044i
$764$	8.63356e15	+	7.02617e15i	1.19999	+	0.976574i
$765$	3.02835e14			0.0417896
$766$	3.51982e15	−	1.67362e15i	0.482239	−	0.229297i
$767$		−	3.05205e12i		−	0.000415161i
$768$	3.92205e15	−	1.70067e15i	0.529696	−	0.229686i
$769$		−	9.15314e15i		−	1.22737i	−0.789551	−	0.613685i	$-0.789687\pi$
$769$		−	9.15314e15i		−	1.22737i	0.789551	−	0.613685i	$-0.210313\pi$
$770$	1.04258e15	+	6.09486e14i	0.138807	+	0.0811456i
$771$			1.95088e15i			0.257888i
$772$	−3.91828e15	+	4.81468e15i	−0.514281	+	0.631934i
$773$			9.67601e15i			1.26098i	0.776197	+	0.630491i	$0.217146\pi$
$773$			9.67601e15i			1.26098i	−0.776197	+	0.630491i	$0.782854\pi$
$774$	−8.25315e14	−	1.73574e15i	−0.106793	−	0.224600i
$775$	9.62139e15			1.23617
$776$	−1.04922e16	−	2.55948e15i	−1.33852	−	0.326522i
$777$	2.68841e15	+	3.94706e15i	0.340549	+	0.499987i
$778$	−2.42418e15	+	1.15266e15i	−0.304914	+	0.144982i
$779$			1.00608e16i			1.25655i
$780$	3.08905e11	−	3.79573e11i	3.83093e−5	−	4.70734e-5i
$781$	−7.81171e15			−0.961979
$782$	8.34830e15	−	3.96948e15i	1.02085	−	0.485396i
$783$	5.37850e14			0.0653088
$784$	8.17347e15	+	1.40593e15i	0.985527	+	0.169521i
$785$	−2.31025e15			−0.276615
$786$	1.39457e15	−	6.63095e14i	0.165812	−	0.0788409i
$787$	1.01634e16			1.19999			0.599994	−	0.800004i	$-0.295169\pi$
$787$	1.01634e16			1.19999			0.599994	+	0.800004i	$0.295169\pi$
$788$	−6.72529e15	+	8.26385e15i	−0.788528	+	0.968921i
$789$		−	4.38047e15i		−	0.510032i
$790$	−1.11292e15	+	5.29174e14i	−0.128681	+	0.0611856i
$791$	6.55860e15	+	9.62919e15i	0.753078	+	1.10565i
$792$	2.63443e15	+	6.42649e14i	0.300399	+	0.0732800i
$793$	1.27122e12			0.000143952
$794$	4.45944e15	+	9.37875e15i	0.501496	+	1.05471i
$795$			9.54169e14i			0.106563i
$796$	8.30827e15	−	1.02090e16i	0.921486	−	1.13230i
$797$			1.11186e16i			1.22470i	0.790587	+	0.612350i	$0.209776\pi$
$797$			1.11186e16i			1.22470i	−0.790587	+	0.612350i	$0.790224\pi$
$798$	7.28907e15	+	4.26115e15i	0.797363	+	0.466134i
$799$		−	1.13759e16i		−	1.23589i
$800$	5.42913e15	+	7.16520e15i	0.585781	+	0.773095i
$801$			3.96889e15i			0.425295i
$802$	9.91508e14	−	4.71445e14i	0.105521	−	0.0501733i
$803$	−2.39979e15			−0.253651
$804$	4.68254e15	+	3.81074e15i	0.491556	+	0.400038i
$805$	−1.46258e15	−	2.14733e15i	−0.152490	−	0.223883i
$806$	−3.20524e12	−	6.74103e12i	−0.000331909	−	0.000698045i
$807$		−	5.96742e15i		−	0.613736i
$808$	2.24908e15	+	5.48645e14i	0.229743	+	0.0560440i
$809$	1.32449e16			1.34379			0.671896	−	0.740646i	$-0.265480\pi$
$809$	1.32449e16			1.34379			0.671896	+	0.740646i	$0.265480\pi$
$810$	−8.20681e13	−	1.72599e14i	−0.00827002	−	0.0173929i
$811$	8.19982e15			0.820710			0.410355	−	0.911926i	$-0.365405\pi$
$811$	8.19982e15			0.820710			0.410355	+	0.911926i	$0.365405\pi$
$812$	3.40122e15	+	2.90391e14i	0.338124	+	0.0288686i
$813$	4.11148e15			0.405976
$814$	4.25559e15	+	8.95002e15i	0.417374	+	0.877788i
$815$	1.55585e15			0.151566
$816$	4.22571e15	−	8.76733e14i	0.408887	−	0.0848343i
$817$		−	1.24184e16i		−	1.19356i
$818$	−2.38559e15	−	5.01720e15i	−0.227747	−	0.478981i
$819$	1.76197e12	−	1.20011e12i	0.000167085	−	0.000113804i
$820$	9.12325e14	−	1.12104e15i	0.0859356	−	0.105595i
$821$	3.64874e15			0.341393			0.170697	−	0.985324i	$-0.445398\pi$
$821$	3.64874e15			0.341393			0.170697	+	0.985324i	$0.445398\pi$
$822$	7.23761e14	−	3.44136e14i	0.0672667	−	0.0319842i
$823$		−	2.77704e15i		−	0.256380i	−0.991750	−	0.128190i	$-0.959083\pi$
$823$		−	2.77704e15i		−	0.256380i	0.991750	−	0.128190i	$-0.0409167\pi$
$824$	4.35649e15	−	1.78587e16i	0.399519	−	1.63776i
$825$			5.70244e15i			0.519474i
$826$	−6.53062e15	−	3.81776e15i	−0.590968	−	0.345476i
$827$			1.15483e16i			1.03810i	0.854744	+	0.519050i	$0.173714\pi$
$827$			1.15483e16i			1.03810i	−0.854744	+	0.519050i	$0.826286\pi$
$828$	−4.52476e15	−	3.68234e15i	−0.404044	−	0.328819i
$829$			1.31645e13i			0.00116776i	1.00000		0.000583880i	$0.000185855\pi$
$829$			1.31645e13i			0.00116776i	−1.00000		0.000583880i	$0.999814\pi$
$830$	1.36192e15	+	2.86429e15i	0.120012	+	0.252399i
$831$	−8.88157e14			−0.0777471
$832$	3.21150e12	−	6.19080e12i	0.000279273	−	0.000538355i
$833$	7.79107e15	+	3.06603e15i	0.673054	+	0.264868i
$834$	2.65110e15	−	1.26055e15i	0.227516	−	0.108180i
$835$		−	1.33743e15i		−	0.114024i
$836$	1.35895e16	+	1.10594e16i	1.15099	+	0.936695i
$837$	−2.91497e15			−0.245270
$838$	4.10116e15	−	1.95003e15i	0.342819	−	0.163004i
$839$	1.22372e15			0.101623			0.0508113	−	0.998708i	$-0.483819\pi$
$839$	1.22372e15			0.101623			0.0508113	+	0.998708i	$0.483819\pi$
$840$	−4.25788e14	−	1.13578e15i	−0.0351283	−	0.0937040i
$841$	−1.07955e16			−0.884838
$842$	6.14690e15	−	2.92275e15i	0.500541	−	0.237999i
$843$	1.02592e15			0.0829966
$844$	−2.54703e14	−	2.07283e14i	−0.0204716	−	0.0166602i
$845$			2.17063e15i			0.173330i
$846$	−6.48364e15	+	3.08286e15i	−0.514378	+	0.244578i
$847$	−9.96403e14	−	1.46290e15i	−0.0785374	−	0.115307i
$848$	2.76240e15	+	1.33143e16i	0.216326	+	1.04266i
$849$	9.50927e14			0.0739869
$850$	3.89715e15	+	8.19619e15i	0.301261	+	0.633589i
$851$		−	2.13204e16i		−	1.63751i
$852$	6.08548e15	+	4.95249e15i	0.464384	+	0.377925i
$853$			1.85999e16i			1.41024i	0.709090	+	0.705118i	$0.249106\pi$
$853$			1.85999e16i			1.41024i	−0.709090	+	0.705118i	$0.750894\pi$
$854$	1.59015e15	−	2.72010e15i	0.119790	−	0.204911i
$855$		−	1.23486e15i		−	0.0924284i
$856$	−2.82703e15	−	6.89630e14i	−0.210244	−	0.0512874i
$857$		−	4.77513e15i		−	0.352851i	−0.984314	−	0.176425i	$-0.943547\pi$
$857$		−	4.77513e15i		−	0.352851i	0.984314	−	0.176425i	$-0.0564534\pi$
$858$	3.99529e12	−	1.89970e12i	0.000293338	−	0.000139477i
$859$	−2.45789e16			−1.79309			−0.896543	−	0.442958i	$-0.853929\pi$
$859$	−2.45789e16			−1.79309			−0.896543	+	0.442958i	$0.853929\pi$
$860$	−1.12611e15	+	1.38373e15i	−0.0816278	+	0.100302i
$861$	5.20384e15	−	3.54442e15i	0.374806	−	0.255286i
$862$	2.74238e15	+	5.76756e15i	0.196262	+	0.412764i
$863$		−	1.75527e16i		−	1.24820i	−0.781345	−	0.624100i	$-0.785466\pi$
$863$		−	1.75527e16i		−	1.24820i	0.781345	−	0.624100i	$-0.214534\pi$
$864$	−1.64485e15	−	2.17082e15i	−0.116225	−	0.153391i
$865$	3.50797e15			0.246302
$866$	−4.74027e15	−	9.96938e15i	−0.330716	−	0.695536i
$867$	−3.97119e15			−0.275306
$868$	−1.84335e16	−	1.57382e15i	−1.26984	−	0.108417i
$869$	−1.11399e16			−0.762557
$870$	−2.14387e14	−	4.50882e14i	−0.0145828	−	0.0306695i
$871$	9.84931e12			0.000665742
$872$	2.41221e15	−	9.88847e15i	0.162022	−	0.664184i
$873$			6.88074e15i			0.459258i
$874$	−1.61862e16	−	3.40417e16i	−1.07358	−	2.25787i
$875$	4.28170e15	−	2.91634e15i	0.282210	−	0.192218i
$876$	1.86948e15	+	1.52142e15i	0.122447	+	0.0996501i
$877$	−3.59018e14			−0.0233678			−0.0116839	−	0.999932i	$-0.503719\pi$
$877$	−3.59018e14			−0.0233678			−0.0116839	+	0.999932i	$0.503719\pi$
$878$	3.20552e15	−	1.52417e15i	0.207338	−	0.0985857i
$879$			1.25753e16i			0.808316i
$880$	−5.11349e14	−	2.46462e15i	−0.0326635	−	0.157433i
$881$			2.03463e15i			0.129157i	0.997913	+	0.0645786i	$0.0205703\pi$
$881$			2.03463e15i			0.129157i	−0.997913	+	0.0645786i	$0.979430\pi$
$882$	−3.63905e14	−	5.27137e15i	−0.0229567	−	0.332542i
$883$		−	2.71105e16i		−	1.69963i	−0.527082	−	0.849815i	$-0.676714\pi$
$883$		−	2.71105e16i		−	1.69963i	0.527082	−	0.849815i	$-0.323286\pi$
$884$	4.44420e12	−	5.46091e12i	0.000276889	−	0.000340234i
$885$			1.10637e15i			0.0685036i
$886$	8.91065e15	+	1.87402e16i	0.548307	+	1.15316i
$887$	−2.71093e16			−1.65782			−0.828911	−	0.559381i	$-0.811039\pi$
$887$	−2.71093e16			−1.65782			−0.828911	+	0.559381i	$0.811039\pi$
$888$	2.35897e15	−	9.67022e15i	0.143368	−	0.587713i
$889$	−1.32376e16	+	9.01631e15i	−0.799554	+	0.544589i
$890$	3.32714e15	−	1.58200e15i	0.199722	−	0.0949644i
$891$		−	1.72766e15i		−	0.103069i
$892$	−6.61175e15	+	8.12433e15i	−0.392021	+	0.481705i
$893$	−4.63873e16			−2.73348
$894$	−3.76927e15	+	1.79222e15i	−0.220750	+	0.104963i
$895$	4.52294e15			0.263266
$896$	−9.22954e15	−	1.46158e16i	−0.533932	−	0.845527i
$897$	−9.51745e12			−0.000547220
$898$	−1.46180e16	+	6.95060e15i	−0.835348	+	0.397194i
$899$	−7.61479e15			−0.432494
$900$	3.61525e15	−	4.44232e15i	0.204082	−	0.250770i
$901$			1.37276e16i			0.770209i
$902$	1.17998e16	−	5.61060e15i	0.658018	−	0.312877i
$903$	−6.42324e15	+	4.37497e15i	−0.356018	+	0.242489i
$904$	5.75491e15	−	2.35913e16i	0.317038	−	1.29965i
$905$	−4.00850e15			−0.219490
$906$	5.46669e15	+	1.14971e16i	0.297522	+	0.625726i
$907$			3.95568e15i			0.213984i	0.994260	+	0.106992i	$0.0341219\pi$
$907$			3.95568e15i			0.213984i	−0.994260	+	0.106992i	$0.965878\pi$
$908$	−1.94617e16	+	2.39140e16i	−1.04643	+	1.28582i
$909$		−	1.47494e15i		−	0.0788268i
$910$	−1.70837e12	−	9.98705e11i	−9.07518e−5	−	5.30530e-5i
$911$			3.39057e16i			1.79029i	0.445780	+	0.895143i	$0.352926\pi$
$911$			3.39057e16i			1.79029i	−0.445780	+	0.895143i	$0.647074\pi$
$912$	−3.57503e15	−	1.72311e16i	−0.187633	−	0.904358i
$913$			2.86705e16i			1.49571i
$914$	2.49473e16	−	1.18620e16i	1.29366	−	0.615112i
$915$	−4.60820e14			−0.0237528
$916$	−2.02601e15	−	1.64881e15i	−0.103805	−	0.0844784i
$917$	−3.51505e15	−	5.16072e15i	−0.179019	−	0.262832i
$918$	−1.18071e15	−	2.48318e15i	−0.0597735	−	0.125711i
$919$			2.92165e16i			1.47026i	0.677928	+	0.735128i	$0.262878\pi$
$919$			2.92165e16i			1.47026i	−0.677928	+	0.735128i	$0.737122\pi$
$920$	−1.28335e15	+	5.26090e15i	−0.0641968	+	0.263165i
$921$	−1.25693e16			−0.625004
$922$	1.27494e14	+	2.68136e14i	0.00630189	+	0.0132536i
$923$	1.28003e13			0.000628942
$924$	9.32780e14	−	1.09252e16i	0.0455599	−	0.533623i
$925$	2.09319e16			1.01632
$926$	−3.90063e15	−	8.20351e15i	−0.188267	−	0.395949i
$927$	−1.17117e16			−0.561929
$928$	−4.29685e15	−	5.67085e15i	−0.204945	−	0.270480i
$929$			1.27705e15i			0.0605511i	0.999542	+	0.0302756i	$0.00963849\pi$
$929$			1.27705e15i			0.0605511i	−0.999542	+	0.0302756i	$0.990362\pi$
$930$	1.16191e15	+	2.44363e15i	0.0547665	+	0.115181i
$931$	1.25023e16	−	3.17695e16i	0.585823	−	1.48863i
$932$	−1.42153e16	+	1.74674e16i	−0.662170	+	0.813657i
$933$	−2.00123e16			−0.926721
$934$	−5.08598e15	+	2.41830e15i	−0.234135	+	0.111327i
$935$		−	2.54112e15i		−	0.116295i
$936$	−4.31679e12	−	1.05305e12i	−0.000196401	−	4.79104e-5i
$937$			4.83786e15i			0.218819i	0.993997	+	0.109410i	$0.0348960\pi$
$937$			4.83786e15i			0.218819i	−0.993997	+	0.109410i	$0.965104\pi$
$938$	1.23203e16	−	2.10751e16i	0.553997	−	0.947661i
$939$			2.62835e15i			0.117496i
$940$	5.16875e15	+	4.20643e15i	0.229711	+	0.186944i
$941$			4.15914e16i			1.83764i	0.394675	+	0.918821i	$0.370857\pi$
$941$			4.15914e16i			1.83764i	−0.394675	+	0.918821i	$0.629143\pi$
$942$	9.00733e15	+	1.89435e16i	0.395655	+	0.832110i
$943$	−2.81090e16			−1.22753
$944$	3.20304e15	+	1.54381e16i	0.139064	+	0.670267i
$945$	−6.38717e14	+	4.35040e14i	−0.0275698	+	0.0187782i
$946$	−1.45648e16	+	6.92531e15i	−0.625033	+	0.297193i
$947$		−	2.56071e16i		−	1.09253i	−0.837611	−	0.546267i	$-0.816048\pi$
$947$		−	2.56071e16i		−	1.09253i	0.837611	−	0.546267i	$-0.183952\pi$
$948$	8.67821e15	+	7.06250e15i	0.368116	+	0.299580i
$949$	3.93230e12			0.000165837
$950$	3.34214e16	−	1.58913e16i	1.40134	−	0.666316i
$951$	−7.29258e15			−0.304010
$952$	−6.12580e15	−	1.63404e16i	−0.253898	−	0.677268i
$953$	2.92620e15			0.120585			0.0602924	−	0.998181i	$-0.480797\pi$
$953$	2.92620e15			0.120585			0.0602924	+	0.998181i	$0.480797\pi$
$954$	7.82397e15	−	3.72017e15i	0.320561	−	0.152422i
$955$	−6.58301e15			−0.268167
$956$	−4.39564e15	−	3.57726e15i	−0.178034	−	0.144888i
$957$		−	4.51316e15i		−	0.181746i
$958$	−1.62333e16	+	7.71867e15i	−0.649976	+	0.309053i
$959$	−1.82426e15	−	2.67833e15i	−0.0726245	−	0.106626i
$960$	−1.16417e15	+	2.24417e15i	−0.0460814	+	0.0888310i
$961$	1.58612e16			0.624248
$962$	−6.97321e12	−	1.46655e13i	−0.000272879	−	0.000573898i
$963$			1.85396e15i			0.0721365i
$964$	3.42323e16	+	2.78589e16i	1.32438	+	1.07781i
$965$		−	3.67114e15i		−	0.141222i
$966$	−1.19052e16	+	2.03649e16i	−0.455369	+	0.778949i
$967$		−	3.14977e16i		−	1.19794i	−0.800773	−	0.598968i	$-0.795578\pi$
$967$		−	3.14977e16i		−	1.19794i	0.800773	−	0.598968i	$-0.204422\pi$
$968$	−8.74304e14	+	3.58407e15i	−0.0330634	+	0.135538i
$969$		−	1.77660e16i		−	0.668048i
$970$	5.76815e15	−	2.74266e15i	0.215671	−	0.102548i
$971$	−5.70074e15			−0.211946			−0.105973	−	0.994369i	$-0.533796\pi$
$971$	−5.70074e15			−0.211946			−0.105973	+	0.994369i	$0.533796\pi$
$972$	−1.09530e15	+	1.34588e15i	−0.0404921	+	0.0497556i
$973$	−6.68215e15	−	9.81059e15i	−0.245638	−	0.360641i
$974$	−1.29297e16	−	2.71928e16i	−0.472623	−	0.993985i
$975$		−	9.34403e12i		−	0.000339632i
$976$	−6.43019e15	+	1.33411e15i	−0.232407	+	0.0482190i
$977$	6.89481e15			0.247800			0.123900	−	0.992295i	$-0.460460\pi$
$977$	6.89481e15			0.247800			0.123900	+	0.992295i	$0.460460\pi$
$978$	−6.06605e15	−	1.27576e16i	−0.216791	−	0.455939i
$979$	3.33034e16			1.18354
$980$	−4.27396e15	+	2.40623e15i	−0.151038	+	0.0850341i
$981$	−6.48483e15			−0.227887
$982$	1.76765e16	+	3.71759e16i	0.617708	+	1.29912i
$983$	−4.76936e16			−1.65736			−0.828678	−	0.559725i	$-0.810907\pi$
$983$	−4.76936e16			−1.65736			−0.828678	+	0.559725i	$0.810907\pi$
$984$	−1.27493e16	−	3.11009e15i	−0.440568	−	0.107473i
$985$		−	6.30111e15i		−	0.216530i
$986$	−3.08438e15	−	6.48683e15i	−0.105401	−	0.221671i
$987$	1.63422e16	+	2.39932e16i	0.555348	+	0.815350i
$988$	−2.22678e13	−	1.81220e13i	−0.000752515	−	0.000612412i
$989$	3.46957e16			1.16599
$990$	−1.44830e15	+	6.88642e14i	−0.0484022	+	0.0230144i
$991$		−	2.56370e16i		−	0.852044i	−0.904713	−	0.426022i	$-0.859915\pi$
$991$		−	2.56370e16i		−	0.852044i	0.904713	−	0.426022i	$-0.140085\pi$
$992$	2.32875e16	+	3.07341e16i	0.769678	+	1.01580i
$993$		−	2.33926e16i		−	0.768878i
$994$	1.60117e16	−	2.73894e16i	0.523373	−	0.895277i
$995$			7.78424e15i			0.253040i
$996$	1.81766e16	−	2.23349e16i	0.587607	−	0.722035i
$997$			3.14188e16i			1.01010i	0.863089	+	0.505051i	$0.168527\pi$
$997$			3.14188e16i			1.01010i	−0.863089	+	0.505051i	$0.831473\pi$
$998$	−2.46759e16	−	5.18964e16i	−0.788959	−	1.65928i
$999$	−6.34171e15			−0.201649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.b.a.55.6	yes	44
4.3	odd	2		84.12.b.b.55.5	yes	44
7.6	odd	2		84.12.b.b.55.6	yes	44
28.27	even	2	inner	84.12.b.a.55.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.b.a.55.5	✓	44	28.27	even	2	inner
84.12.b.a.55.6	yes	44	1.1	even	1	trivial
84.12.b.b.55.5	yes	44	4.3	odd	2
84.12.b.b.55.6	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)

\(f(q)\)	\(=\)	\(q+(-40.8700 + 19.4330i) q^{2} -243.000 q^{3} +(1292.72 - 1588.45i) q^{4} +1211.18i q^{5} +(9931.41 - 4722.22i) q^{6} +(-25032.4 - 36752.0i) q^{7} +(-21964.9 + 90041.5i) q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+(-40.8700 + 19.4330i) q^{2} -243.000 q^{3} +(1292.72 - 1588.45i) q^{4} +1211.18i q^{5} +(9931.41 - 4722.22i) q^{6} +(-25032.4 - 36752.0i) q^{7} +(-21964.9 + 90041.5i) q^{8} +59049.0 q^{9} +(-23536.9 - 49501.0i) q^{10} -495487. i q^{11} +(-314130. + 385994. i) q^{12} +811.906i q^{13} +(1.73727e6 + 1.01560e6i) q^{14} -294317. i q^{15} +(-852072. - 4.10684e6i) q^{16} -4.23433e6i q^{17} +(-2.41333e6 + 1.14750e6i) q^{18} -1.72662e7 q^{19} +(1.92391e6 + 1.56571e6i) q^{20} +(6.08286e6 + 8.93073e6i) q^{21} +(9.62880e6 + 2.02505e7i) q^{22} -4.82401e7i q^{23} +(5.33747e6 - 2.18801e7i) q^{24} +4.73612e7 q^{25} +(-15777.8 - 33182.6i) q^{26} -1.43489e7 q^{27} +(-9.07386e7 - 7.74713e6i) q^{28} -3.74837e7 q^{29} +(5.71946e6 + 1.20287e7i) q^{30} +2.03149e8 q^{31} +(1.14633e8 + 1.51288e8i) q^{32} +1.20403e8i q^{33} +(8.22858e7 + 1.73057e8i) q^{34} +(4.45133e7 - 3.03187e7i) q^{35} +(7.63336e7 - 9.37967e7i) q^{36} +4.41964e8 q^{37} +(7.05671e8 - 3.35535e8i) q^{38} -197293. i q^{39} +(-1.09057e8 - 2.66035e7i) q^{40} -5.82689e8i q^{41} +(-4.22158e8 - 2.46791e8i) q^{42} +7.19229e8i q^{43} +(-7.87058e8 - 6.40524e8i) q^{44} +7.15190e7i q^{45} +(9.37451e8 + 1.97157e9i) q^{46} +2.68659e9 q^{47} +(2.07054e8 + 9.97963e8i) q^{48} +(-7.24089e8 + 1.83998e9i) q^{49} +(-1.93565e9 + 9.20370e8i) q^{50} +1.02894e9i q^{51} +(1.28968e6 + 1.04956e6i) q^{52} -3.24198e9 q^{53} +(5.86440e8 - 2.78842e8i) q^{54} +6.00124e8 q^{55} +(3.85904e9 - 1.44670e9i) q^{56} +4.19569e9 q^{57} +(1.53196e9 - 7.28421e8i) q^{58} -3.75912e9 q^{59} +(-4.67509e8 - 3.80468e8i) q^{60} -1.56573e9i q^{61} +(-8.30272e9 + 3.94780e9i) q^{62} +(-1.47814e9 - 2.17017e9i) q^{63} +(-7.62502e9 - 3.95551e9i) q^{64} -983365. q^{65} +(-2.33980e9 - 4.92088e9i) q^{66} -1.21311e10i q^{67} +(-6.72604e9 - 5.47379e9i) q^{68} +1.17224e10i q^{69} +(-1.23008e9 + 2.10415e9i) q^{70} -1.57657e10i q^{71} +(-1.29701e9 + 5.31686e9i) q^{72} -4.84329e9i q^{73} +(-1.80631e10 + 8.58870e9i) q^{74} -1.15088e10 q^{75} +(-2.23203e10 + 2.74266e10i) q^{76} +(-1.82101e10 + 1.24032e10i) q^{77} +(3.83400e6 + 8.06337e6i) q^{78} -2.24827e10i q^{79} +(4.97413e9 - 1.03201e9i) q^{80} +3.48678e9 q^{81} +(1.13234e10 + 2.38145e10i) q^{82} -5.78633e10 q^{83} +(2.20495e10 + 1.88255e9i) q^{84} +5.12854e9 q^{85} +(-1.39768e10 - 2.93949e10i) q^{86} +9.10854e9 q^{87} +(4.46144e10 + 1.08833e10i) q^{88} +6.72135e10i q^{89} +(-1.38983e9 - 2.92298e9i) q^{90} +(2.98391e7 - 2.03239e7i) q^{91} +(-7.66273e10 - 6.23608e10i) q^{92} -4.93653e10 q^{93} +(-1.09801e11 + 5.22086e10i) q^{94} -2.09125e10i q^{95} +(-2.78557e10 - 3.67631e10i) q^{96} +1.16526e11i q^{97} +(-6.16276e9 - 8.92711e10i) q^{98} -2.92580e10i 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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