LMFDB - Embedded newform 10.19.c.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,19,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	10.c (of order $4$, degree $2$, 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:	$20.5386137710$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1012730x^{6} + 266454825649x^{4} + 6118030786524900x^{2} + 24596382356676000000 $ x^8 + 1012730x^6 + 266454825649x^4 + 6118030786524900*x^2 + 24596382356676000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.3
Root			$735.343i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.19.c.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(256.000 + 256.000i) q^{2} +(10752.0 - 10752.0i) q^{3} +131072. i q^{4} +(1.75470e6 + 857742. i) q^{5} +5.50503e6 q^{6} +(-4.02524e6 - 4.02524e6i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +1.56209e8i q^{9} +O(q^{10})$	\(q+(256.000 + 256.000i) q^{2} +(10752.0 - 10752.0i) q^{3} +131072. i q^{4} +(1.75470e6 + 857742. i) q^{5} +5.50503e6 q^{6} +(-4.02524e6 - 4.02524e6i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +1.56209e8i q^{9} +(2.29622e8 + 6.68785e8i) q^{10} +1.03954e9 q^{11} +(1.40929e9 + 1.40929e9i) q^{12} +(6.67687e9 - 6.67687e9i) q^{13} -2.06092e9i q^{14} +(2.80890e10 - 9.64413e9i) q^{15} -1.71799e10 q^{16} +(7.11595e10 + 7.11595e10i) q^{17} +(-3.99894e10 + 3.99894e10i) q^{18} +2.17531e11i q^{19} +(-1.12426e11 + 2.29992e11i) q^{20} -8.65589e10 q^{21} +(2.66121e11 + 2.66121e11i) q^{22} +(5.11245e11 - 5.11245e11i) q^{23} +7.21556e11i q^{24} +(2.34326e12 + 3.01016e12i) q^{25} +3.41856e12 q^{26} +(5.84511e12 + 5.84511e12i) q^{27} +(5.27596e11 - 5.27596e11i) q^{28} +1.96961e13i q^{29} +(9.65969e12 + 4.72190e12i) q^{30} +1.66999e13 q^{31} +(-4.39805e12 - 4.39805e12i) q^{32} +(1.11771e13 - 1.11771e13i) q^{33} +3.64337e13i q^{34} +(-3.61048e12 - 1.05157e13i) q^{35} -2.04746e13 q^{36} +(-1.60627e14 - 1.60627e14i) q^{37} +(-5.56879e13 + 5.56879e13i) q^{38} -1.43580e14i q^{39} +(-8.76590e13 + 3.00970e13i) q^{40} -3.31732e13 q^{41} +(-2.21591e13 - 2.21591e13i) q^{42} +(3.83404e14 - 3.83404e14i) q^{43} +1.36254e14i q^{44} +(-1.33987e14 + 2.74099e14i) q^{45} +2.61758e14 q^{46} +(-1.26531e15 - 1.26531e15i) q^{47} +(-1.84718e14 + 1.84718e14i) q^{48} -1.59601e15i q^{49} +(-1.70727e14 + 1.37047e15i) q^{50} +1.53022e15 q^{51} +(8.75151e14 + 8.75151e14i) q^{52} +(-9.46206e14 + 9.46206e14i) q^{53} +2.99270e15i q^{54} +(1.82408e15 + 8.91654e14i) q^{55} +2.70129e14 q^{56} +(2.33890e15 + 2.33890e15i) q^{57} +(-5.04219e15 + 5.04219e15i) q^{58} -4.59400e15i q^{59} +(1.26408e15 + 3.68169e15i) q^{60} +1.10082e16 q^{61} +(4.27517e15 + 4.27517e15i) q^{62} +(6.28777e14 - 6.28777e14i) q^{63} -2.25180e15i q^{64} +(1.74429e16 - 5.98889e15i) q^{65} +5.72268e15 q^{66} +(-2.22736e16 - 2.22736e16i) q^{67} +(-9.32702e15 + 9.32702e15i) q^{68} -1.09938e16i q^{69} +(1.76774e15 - 3.61630e15i) q^{70} -8.76720e16 q^{71} +(-5.24149e15 - 5.24149e15i) q^{72} +(-4.04287e16 + 4.04287e16i) q^{73} -8.22412e16i q^{74} +(5.75600e16 + 7.17057e15i) q^{75} -2.85122e16 q^{76} +(-4.18438e15 - 4.18438e15i) q^{77} +(3.67564e16 - 3.67564e16i) q^{78} -3.77215e16i q^{79} +(-3.01455e16 - 1.47359e16i) q^{80} +6.51751e16 q^{81} +(-8.49234e15 - 8.49234e15i) q^{82} +(3.05964e15 - 3.05964e15i) q^{83} -1.13455e16i q^{84} +(6.38272e16 + 1.85900e17i) q^{85} +1.96303e17 q^{86} +(2.11772e17 + 2.11772e17i) q^{87} +(-3.48811e16 + 3.48811e16i) q^{88} +5.34526e17i q^{89} +(-1.04470e17 + 3.58689e16i) q^{90} -5.37520e16 q^{91} +(6.70100e16 + 6.70100e16i) q^{92} +(1.79558e17 - 1.79558e17i) q^{93} -6.47840e17i q^{94} +(-1.86585e17 + 3.81702e17i) q^{95} -9.45758e16 q^{96} +(-3.98072e17 - 3.98072e17i) q^{97} +(4.08578e17 - 4.08578e17i) q^{98} +1.62385e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8}+O(q^{10}) $ 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8	$ 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8} - 361676800 q^{10} - 2678523284 q^{11} + 4853071872 q^{12} - 13618988004 q^{13} - 44901376950 q^{15} - 137438953472 q^{16} + 131385428404 q^{17} + 219304891392 q^{18} + 225397964800 q^{20} - 2519443347204 q^{21} - 685701960704 q^{22} + 2992780401346 q^{23} + 5025487502500 q^{25} - 6972921858048 q^{26} - 36827718166440 q^{27} + 5712087089152 q^{28} - 6097905484800 q^{30} - 41290623629644 q^{31} - 35184372088832 q^{32} + 3721928304252 q^{33} + 259024770537850 q^{35} + 112284104392704 q^{36} - 191725492483296 q^{37} + 93053262223360 q^{38} + 162809459507200 q^{40} + 538572935041756 q^{41} - 644977496884224 q^{42} + 278176126066386 q^{43} - 649523899006350 q^{45} + 15\!\cdots\!52 q^{46}+ \cdots + 14\!\cdots\!68 q^{98}+O(q^{100}) $ 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8 - 361676800 * q^10 - 2678523284 * q^11 + 4853071872 * q^12 - 13618988004 * q^13 - 44901376950 * q^15 - 137438953472 * q^16 + 131385428404 * q^17 + 219304891392 * q^18 + 225397964800 * q^20 - 2519443347204 * q^21 - 685701960704 * q^22 + 2992780401346 * q^23 + 5025487502500 * q^25 - 6972921858048 * q^26 - 36827718166440 * q^27 + 5712087089152 * q^28 - 6097905484800 * q^30 - 41290623629644 * q^31 - 35184372088832 * q^32 + 3721928304252 * q^33 + 259024770537850 * q^35 + 112284104392704 * q^36 - 191725492483296 * q^37 + 93053262223360 * q^38 + 162809459507200 * q^40 + 538572935041756 * q^41 - 644977496884224 * q^42 + 278176126066386 * q^43 - 649523899006350 * q^45 + 1532303565489152 * q^46 - 634311997628766 * q^47 - 636101836406784 * q^48 + 190733484160000 * q^50 + 8385208158427476 * q^51 - 1785067995660288 * q^52 - 12985998337176064 * q^53 + 7061537235641100 * q^55 + 2924588589645824 * q^56 - 14364945328494720 * q^57 - 3324209031454720 * q^58 + 2763185671372800 * q^60 + 6032452171830396 * q^61 - 10570399649188864 * q^62 - 67339871781169614 * q^63 + 116629895397895800 * q^65 + 1905627291777024 * q^66 - 43112377024267886 * q^67 - 17220950871769088 * q^68 + 57331386108262400 * q^70 - 20683118221989964 * q^71 + 28744730724532224 * q^72 - 85903701564675544 * q^73 + 487247617377746250 * q^75 + 47643270258360320 * q^76 - 31041870745561732 * q^77 - 251885813313555456 * q^78 + 53815081225420800 * q^80 - 598065530496252012 * q^81 + 137874671370689536 * q^82 + 247117472833336746 * q^83 - 265705533435464900 * q^85 + 142426176545989632 * q^86 - 431292883391162160 * q^87 + 89876327393394688 * q^88 - 1156199666753126400 * q^90 - 346988460443022684 * q^91 + 392269712765222912 * q^92 + 2117557938231099132 * q^93 - 1658756785135297000 * q^95 - 325684140240273408 * q^96 + 1905016584439493544 * q^97 + 1418620057223277568 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	256.000	+	256.000i	0.500000	+	0.500000i
$2$	256.000	+	256.000i	0.500000	+	0.500000i
$3$	10752.0	−	10752.0i	0.546259	−	0.546259i	−0.379097	−	0.925357i	$-0.623765\pi$
$3$	10752.0	−	10752.0i	0.546259	−	0.546259i	0.925357	+	0.379097i	$0.123765\pi$
$4$			131072.i			0.500000i
$5$	1.75470e6	+	857742.i	0.898407	+	0.439164i
$5$	1.75470e6	+	857742.i	0.898407	+	0.439164i
$6$	5.50503e6			0.546259
$7$	−4.02524e6	−	4.02524e6i	−0.0997492	−	0.0997492i	0.655471	−	0.755220i	$-0.272470\pi$
$7$	−4.02524e6	−	4.02524e6i	−0.0997492	−	0.0997492i	−0.755220	+	0.655471i	$0.772470\pi$
$8$	−3.35544e7	+	3.35544e7i	−0.250000	+	0.250000i
$9$			1.56209e8i			0.403202i
$10$	2.29622e8	+	6.68785e8i	0.229622	+	0.668785i
$11$	1.03954e9			0.440865			0.220432	−	0.975402i	$-0.429253\pi$
$11$	1.03954e9			0.440865			0.220432	+	0.975402i	$0.429253\pi$
$12$	1.40929e9	+	1.40929e9i	0.273130	+	0.273130i
$13$	6.67687e9	−	6.67687e9i	0.629626	−	0.629626i	−0.318348	−	0.947974i	$-0.603128\pi$
$13$	6.67687e9	−	6.67687e9i	0.629626	−	0.629626i	0.947974	+	0.318348i	$0.103128\pi$
$14$		−	2.06092e9i		−	0.0997492i
$15$	2.80890e10	−	9.64413e9i	0.730660	−	0.250866i
$16$	−1.71799e10			−0.250000
$17$	7.11595e10	+	7.11595e10i	0.600057	+	0.600057i	0.940328	−	0.340271i	$-0.110519\pi$
$17$	7.11595e10	+	7.11595e10i	0.600057	+	0.600057i	−0.340271	+	0.940328i	$0.610519\pi$
$18$	−3.99894e10	+	3.99894e10i	−0.201601	+	0.201601i
$19$			2.17531e11i			0.674122i	0.941483	+	0.337061i	$0.109433\pi$
$19$			2.17531e11i			0.674122i	−0.941483	+	0.337061i	$0.890567\pi$
$20$	−1.12426e11	+	2.29992e11i	−0.219582	+	0.449204i
$21$	−8.65589e10			−0.108978
$22$	2.66121e11	+	2.66121e11i	0.220432	+	0.220432i
$23$	5.11245e11	−	5.11245e11i	0.283843	−	0.283843i	−0.550796	−	0.834640i	$-0.685676\pi$
$23$	5.11245e11	−	5.11245e11i	0.283843	−	0.283843i	0.834640	+	0.550796i	$0.185676\pi$
$24$			7.21556e11i			0.273130i
$25$	2.34326e12	+	3.01016e12i	0.614271	+	0.789095i
$26$	3.41856e12			0.629626
$27$	5.84511e12	+	5.84511e12i	0.766512	+	0.766512i
$28$	5.27596e11	−	5.27596e11i	0.0498746	−	0.0498746i
$29$			1.96961e13i			1.35768i	0.734286	+	0.678840i	$0.237517\pi$
$29$			1.96961e13i			1.35768i	−0.734286	+	0.678840i	$0.762483\pi$
$30$	9.65969e12	+	4.72190e12i	0.490763	+	0.239897i
$31$	1.66999e13			0.631624			0.315812	−	0.948822i	$-0.397723\pi$
$31$	1.66999e13			0.631624			0.315812	+	0.948822i	$0.397723\pi$
$32$	−4.39805e12	−	4.39805e12i	−0.125000	−	0.125000i
$33$	1.11771e13	−	1.11771e13i	0.240827	−	0.240827i
$34$			3.64337e13i			0.600057i
$35$	−3.61048e12	−	1.05157e13i	−0.0458092	−	0.133422i
$36$	−2.04746e13			−0.201601
$37$	−1.60627e14	−	1.60627e14i	−1.23596	−	1.23596i	−0.961638	−	0.274321i	$-0.911547\pi$
$37$	−1.60627e14	−	1.60627e14i	−1.23596	−	1.23596i	−0.274321	−	0.961638i	$-0.588453\pi$
$38$	−5.56879e13	+	5.56879e13i	−0.337061	+	0.337061i
$39$		−	1.43580e14i		−	0.687879i
$40$	−8.76590e13	+	3.00970e13i	−0.334393	+	0.114811i
$41$	−3.31732e13			−0.101329			−0.0506644	−	0.998716i	$-0.516134\pi$
$41$	−3.31732e13			−0.101329			−0.0506644	+	0.998716i	$0.516134\pi$
$42$	−2.21591e13	−	2.21591e13i	−0.0544889	−	0.0544889i
$43$	3.83404e14	−	3.83404e14i	0.762853	−	0.762853i	−0.213984	−	0.976837i	$-0.568644\pi$
$43$	3.83404e14	−	3.83404e14i	0.762853	−	0.762853i	0.976837	+	0.213984i	$0.0686441\pi$
$44$			1.36254e14i			0.220432i
$45$	−1.33987e14	+	2.74099e14i	−0.177072	+	0.362239i
$46$	2.61758e14			0.283843
$47$	−1.26531e15	−	1.26531e15i	−1.13062	−	1.13062i	−0.990074	−	0.140548i	$-0.955114\pi$
$47$	−1.26531e15	−	1.26531e15i	−1.13062	−	1.13062i	−0.140548	−	0.990074i	$-0.544886\pi$
$48$	−1.84718e14	+	1.84718e14i	−0.136565	+	0.136565i
$49$		−	1.59601e15i		−	0.980100i
$50$	−1.70727e14	+	1.37047e15i	−0.0874125	+	0.701683i
$51$	1.53022e15			0.655573
$52$	8.75151e14	+	8.75151e14i	0.314813	+	0.314813i
$53$	−9.46206e14	+	9.46206e14i	−0.286750	+	0.286750i	−0.835794	−	0.549044i	$-0.814992\pi$
$53$	−9.46206e14	+	9.46206e14i	−0.286750	+	0.286750i	0.549044	+	0.835794i	$0.314992\pi$
$54$			2.99270e15i			0.766512i
$55$	1.82408e15	+	8.91654e14i	0.396076	+	0.193612i
$56$	2.70129e14			0.0498746
$57$	2.33890e15	+	2.33890e15i	0.368245	+	0.368245i
$58$	−5.04219e15	+	5.04219e15i	−0.678840	+	0.678840i
$59$		−	4.59400e15i		−	0.530302i	−0.964207	−	0.265151i	$-0.914578\pi$
$59$		−	4.59400e15i		−	0.530302i	0.964207	−	0.265151i	$-0.0854218\pi$
$60$	1.26408e15	+	3.68169e15i	0.125433	+	0.365330i
$61$	1.10082e16			0.941344			0.470672	−	0.882308i	$-0.344012\pi$
$61$	1.10082e16			0.941344			0.470672	+	0.882308i	$0.344012\pi$
$62$	4.27517e15	+	4.27517e15i	0.315812	+	0.315812i
$63$	6.28777e14	−	6.28777e14i	0.0402190	−	0.0402190i
$64$		−	2.25180e15i		−	0.125000i
$65$	1.74429e16	−	5.98889e15i	0.842170	−	0.289152i
$66$	5.72268e15			0.240827
$67$	−2.22736e16	−	2.22736e16i	−0.818684	−	0.818684i	0.167233	−	0.985917i	$-0.446517\pi$
$67$	−2.22736e16	−	2.22736e16i	−0.818684	−	0.818684i	−0.985917	+	0.167233i	$0.946517\pi$
$68$	−9.32702e15	+	9.32702e15i	−0.300029	+	0.300029i
$69$		−	1.09938e16i		−	0.310104i
$70$	1.76774e15	−	3.61630e15i	0.0438062	−	0.0896154i
$71$	−8.76720e16			−1.91221			−0.956105	−	0.293023i	$-0.905339\pi$
$71$	−8.76720e16			−1.91221			−0.956105	+	0.293023i	$0.905339\pi$
$72$	−5.24149e15	−	5.24149e15i	−0.100800	−	0.100800i
$73$	−4.04287e16	+	4.04287e16i	−0.686727	+	0.686727i	−0.961507	−	0.274780i	$-0.911395\pi$
$73$	−4.04287e16	+	4.04287e16i	−0.686727	+	0.686727i	0.274780	+	0.961507i	$0.411395\pi$
$74$		−	8.22412e16i		−	1.23596i
$75$	5.75600e16	+	7.17057e15i	0.766602	+	0.0954997i
$76$	−2.85122e16			−0.337061
$77$	−4.18438e15	−	4.18438e15i	−0.0439759	−	0.0439759i
$78$	3.67564e16	−	3.67564e16i	0.343939	−	0.343939i
$79$		−	3.77215e16i		−	0.314735i	−0.987540	−	0.157367i	$-0.949699\pi$
$79$		−	3.77215e16i		−	0.314735i	0.987540	−	0.157367i	$-0.0503007\pi$
$80$	−3.01455e16	−	1.47359e16i	−0.224602	−	0.109791i
$81$	6.51751e16			0.434227
$82$	−8.49234e15	−	8.49234e15i	−0.0506644	−	0.0506644i
$83$	3.05964e15	−	3.05964e15i	0.0163669	−	0.0163669i	−0.698876	−	0.715243i	$-0.746316\pi$
$83$	3.05964e15	−	3.05964e15i	0.0163669	−	0.0163669i	0.715243	+	0.698876i	$0.246316\pi$
$84$		−	1.13455e16i		−	0.0544889i
$85$	6.38272e16	+	1.85900e17i	0.275572	+	0.802619i
$86$	1.96303e17			0.762853
$87$	2.11772e17	+	2.11772e17i	0.741645	+	0.741645i
$88$	−3.48811e16	+	3.48811e16i	−0.110216	+	0.110216i
$89$			5.34526e17i			1.52566i	0.646597	+	0.762832i	$0.276192\pi$
$89$			5.34526e17i			1.52566i	−0.646597	+	0.762832i	$0.723808\pi$
$90$	−1.04470e17	+	3.58689e16i	−0.269655	+	0.0925838i
$91$	−5.37520e16			−0.125609
$92$	6.70100e16	+	6.70100e16i	0.141922	+	0.141922i
$93$	1.79558e17	−	1.79558e17i	0.345030	−	0.345030i
$94$		−	6.47840e17i		−	1.13062i
$95$	−1.86585e17	+	3.81702e17i	−0.296050	+	0.605636i
$96$	−9.45758e16			−0.136565
$97$	−3.98072e17	−	3.98072e17i	−0.523619	−	0.523619i	0.395043	−	0.918662i	$-0.370730\pi$
$97$	−3.98072e17	−	3.98072e17i	−0.523619	−	0.523619i	−0.918662	+	0.395043i	$0.870730\pi$
$98$	4.08578e17	−	4.08578e17i	0.490050	−	0.490050i
$99$			1.62385e17i			0.177757i
$100$	−3.94548e17	+	3.07135e17i	−0.394548	+	0.307135i
$101$	−1.28125e18			−1.17150			−0.585749	−	0.810492i	$-0.699200\pi$
$101$	−1.28125e18			−1.17150			−0.585749	+	0.810492i	$0.699200\pi$
$102$	3.91735e17	+	3.91735e17i	0.327787	+	0.327787i
$103$	1.49938e18	−	1.49938e18i	1.14915	−	1.14915i	0.162429	−	0.986720i	$-0.448067\pi$
$103$	1.49938e18	−	1.49938e18i	1.14915	−	1.14915i	0.986720	−	0.162429i	$-0.0519328\pi$
$104$			4.48077e17i			0.314813i
$105$	−1.51885e17	−	7.42452e16i	−0.0979065	−	0.0478591i
$106$	−4.84458e17			−0.286750
$107$	2.98044e17	+	2.98044e17i	0.162116	+	0.162116i	0.783504	−	0.621387i	$-0.213431\pi$
$107$	2.98044e17	+	2.98044e17i	0.162116	+	0.162116i	−0.621387	+	0.783504i	$0.713431\pi$
$108$	−7.66130e17	+	7.66130e17i	−0.383256	+	0.383256i
$109$		−	3.06644e18i		−	1.41188i	−0.708274	−	0.705938i	$-0.750526\pi$
$109$		−	3.06644e18i		−	1.41188i	0.708274	−	0.705938i	$-0.249474\pi$
$110$	2.38700e17	+	6.95227e17i	0.101232	+	0.294844i
$111$	−3.45414e18			−1.35031
$112$	6.91531e16	+	6.91531e16i	0.0249373	+	0.0249373i
$113$	2.47280e18	−	2.47280e18i	0.823158	−	0.823158i	−0.163402	−	0.986560i	$-0.552247\pi$
$113$	2.47280e18	−	2.47280e18i	0.823158	−	0.823158i	0.986560	+	0.163402i	$0.0522467\pi$
$114$			1.19752e18i			0.368245i
$115$	1.33560e18	−	4.58567e17i	0.379661	−	0.130353i
$116$	−2.58160e18			−0.678840
$117$	1.04298e18	+	1.04298e18i	0.253866	+	0.253866i
$118$	1.17606e18	−	1.17606e18i	0.265151	−	0.265151i
$119$		−	5.72868e17i		−	0.119710i
$120$	−6.18908e17	+	1.26612e18i	−0.119949	+	0.245382i
$121$	−4.47928e18			−0.805638
$122$	2.81810e18	+	2.81810e18i	0.470672	+	0.470672i
$123$	−3.56679e17	+	3.56679e17i	−0.0553518	+	0.0553518i
$124$			2.18889e18i			0.315812i
$125$	1.52978e18	+	7.29184e18i	0.205323	+	0.978694i
$126$	3.21934e17			0.0402190
$127$	8.86039e18	+	8.86039e18i	1.03091	+	1.03091i	0.999507	+	0.0314002i	$0.00999665\pi$
$127$	8.86039e18	+	8.86039e18i	1.03091	+	1.03091i	0.0314002	+	0.999507i	$0.490003\pi$
$128$	5.76461e17	−	5.76461e17i	0.0625000	−	0.0625000i
$129$		−	8.24474e18i		−	0.833431i
$130$	5.99855e18	+	2.93224e18i	0.565661	+	0.276509i
$131$	−8.05096e17			−0.0708608			−0.0354304	−	0.999372i	$-0.511280\pi$
$131$	−8.05096e17			−0.0708608			−0.0354304	+	0.999372i	$0.511280\pi$
$132$	1.46501e18	+	1.46501e18i	0.120413	+	0.120413i
$133$	8.75614e17	−	8.75614e17i	0.0672431	−	0.0672431i
$134$		−	1.14041e19i		−	0.818684i
$135$	5.24283e18	+	1.52700e19i	0.352016	+	1.02526i
$136$	−4.77543e18			−0.300029
$137$	5.43663e18	+	5.43663e18i	0.319775	+	0.319775i	0.848681	−	0.528906i	$-0.177397\pi$
$137$	5.43663e18	+	5.43663e18i	0.319775	+	0.319775i	−0.528906	+	0.848681i	$0.677397\pi$
$138$	2.81442e18	−	2.81442e18i	0.155052	−	0.155052i
$139$		−	2.55528e19i		−	1.31918i	−0.751624	−	0.659592i	$-0.770729\pi$
$139$		−	2.55528e19i		−	1.31918i	0.751624	−	0.659592i	$-0.229271\pi$
$140$	1.37831e18	−	4.73233e17i	0.0667108	−	0.0229046i
$141$	−2.72093e19			−1.23523
$142$	−2.24440e19	−	2.24440e19i	−0.956105	−	0.956105i
$143$	6.94085e18	−	6.94085e18i	0.277580	−	0.277580i
$144$		−	2.68364e18i		−	0.100800i
$145$	−1.68941e19	+	3.45607e19i	−0.596243	+	1.21975i
$146$	−2.06995e19			−0.686727
$147$	−1.71603e19	−	1.71603e19i	−0.535389	−	0.535389i
$148$	2.10538e19	−	2.10538e19i	0.617979	−	0.617979i
$149$		−	1.53286e19i		−	0.423474i	−0.977327	−	0.211737i	$-0.932088\pi$
$149$		−	1.53286e19i		−	0.423474i	0.977327	−	0.211737i	$-0.0679120\pi$
$150$	1.28997e19	+	1.65710e19i	0.335551	+	0.431051i
$151$	−8.79708e18			−0.215549			−0.107774	−	0.994175i	$-0.534372\pi$
$151$	−8.79708e18			−0.215549			−0.107774	+	0.994175i	$0.534372\pi$
$152$	−7.29913e18	−	7.29913e18i	−0.168531	−	0.168531i
$153$	−1.11157e19	+	1.11157e19i	−0.241944	+	0.241944i
$154$		−	2.14240e18i		−	0.0439759i
$155$	2.93033e19	+	1.43242e19i	0.567456	+	0.277386i
$156$	1.88193e19			0.343939
$157$	1.09193e19	+	1.09193e19i	0.188407	+	0.188407i	0.795007	−	0.606600i	$-0.207467\pi$
$157$	1.09193e19	+	1.09193e19i	0.188407	+	0.188407i	−0.606600	+	0.795007i	$0.707467\pi$
$158$	9.65670e18	−	9.65670e18i	0.157367	−	0.157367i
$159$			2.03473e19i			0.313279i
$160$	−3.94487e18	−	1.14896e19i	−0.0574054	−	0.167196i
$161$	−4.11577e18			−0.0566263
$162$	1.66848e19	+	1.66848e19i	0.217113	+	0.217113i
$163$	1.68085e19	−	1.68085e19i	0.206938	−	0.206938i	−0.596027	−	0.802964i	$-0.703255\pi$
$163$	1.68085e19	−	1.68085e19i	0.206938	−	0.206938i	0.802964	+	0.596027i	$0.203255\pi$
$164$		−	4.34808e18i		−	0.0506644i
$165$	2.91996e19	−	1.00254e19i	0.322123	−	0.110598i
$166$	1.56653e18			0.0163669
$167$	9.86790e19	+	9.86790e19i	0.976734	+	0.976734i	0.999735	−	0.0230014i	$-0.00732222\pi$
$167$	9.86790e19	+	9.86790e19i	0.976734	+	0.976734i	−0.0230014	+	0.999735i	$0.507322\pi$
$168$	2.90444e18	−	2.90444e18i	0.0272445	−	0.0272445i
$169$			2.32941e19i			0.207141i
$170$	−3.12507e19	+	6.39302e19i	−0.263523	+	0.539096i
$171$	−3.39802e19			−0.271807
$172$	5.02536e19	+	5.02536e19i	0.381426	+	0.381426i
$173$	4.36719e19	−	4.36719e19i	0.314621	−	0.314621i	−0.532076	−	0.846697i	$-0.678588\pi$
$173$	4.36719e19	−	4.36719e19i	0.314621	−	0.314621i	0.846697	+	0.532076i	$0.178588\pi$
$174$			1.08427e20i			0.741645i
$175$	2.68445e18	−	2.15488e19i	0.0174386	−	0.139985i
$176$	−1.78591e19			−0.110216
$177$	−4.93948e19	−	4.93948e19i	−0.289682	−	0.289682i
$178$	−1.36839e20	+	1.36839e20i	−0.762832	+	0.762832i
$179$		−	1.50473e20i		−	0.797590i	−0.917040	−	0.398795i	$-0.869428\pi$
$179$		−	1.50473e20i		−	0.797590i	0.917040	−	0.398795i	$-0.130572\pi$
$180$	−3.59268e19	−	1.75619e19i	−0.181120	−	0.0885358i
$181$	−2.46461e20			−1.18207			−0.591033	−	0.806647i	$-0.701280\pi$
$181$	−2.46461e20			−1.18207			−0.591033	+	0.806647i	$0.701280\pi$
$182$	−1.37605e19	−	1.37605e19i	−0.0628047	−	0.0628047i
$183$	1.18361e20	−	1.18361e20i	0.514218	−	0.514218i
$184$			3.43091e19i			0.141922i
$185$	−1.44076e20	−	4.19630e20i	−0.567606	−	1.65318i
$186$	9.19335e19			0.345030
$187$	7.39729e19	+	7.39729e19i	0.264544	+	0.264544i
$188$	1.65847e20	−	1.65847e20i	0.565311	−	0.565311i
$189$		−	4.70559e19i		−	0.152918i
$190$	−1.45481e20	+	4.99498e19i	−0.450843	+	0.154793i
$191$	4.55758e20			1.34721			0.673603	−	0.739093i	$-0.264746\pi$
$191$	4.55758e20			1.34721			0.673603	+	0.739093i	$0.264746\pi$
$192$	−2.42114e19	−	2.42114e19i	−0.0682824	−	0.0682824i
$193$	−3.74197e20	+	3.74197e20i	−1.00713	+	1.00713i	−0.00715402	+	0.999974i	$0.502277\pi$
$193$	−3.74197e20	+	3.74197e20i	−1.00713	+	1.00713i	−0.999974	+	0.00715402i	$0.997723\pi$
$194$		−	2.03813e20i		−	0.523619i
$195$	1.23154e20	−	2.51940e20i	0.302091	−	0.617995i
$196$	2.09192e20			0.490050
$197$	−2.80595e20	−	2.80595e20i	−0.627891	−	0.627891i	0.319646	−	0.947537i	$-0.396436\pi$
$197$	−2.80595e20	−	2.80595e20i	−0.627891	−	0.627891i	−0.947537	+	0.319646i	$0.896436\pi$
$198$	−4.15704e19	+	4.15704e19i	−0.0888787	+	0.0888787i
$199$			8.70870e20i			1.77941i	0.456538	+	0.889704i	$0.349089\pi$
$199$			8.70870e20i			1.77941i	−0.456538	+	0.889704i	$0.650911\pi$
$200$	−1.79631e20	−	2.23776e19i	−0.350842	−	0.0437062i
$201$	−4.78971e20			−0.894427
$202$	−3.28000e20	−	3.28000e20i	−0.585749	−	0.585749i
$203$	7.92813e19	−	7.92813e19i	0.135427	−	0.135427i
$204$			2.00569e20i			0.327787i
$205$	−5.82091e19	−	2.84540e19i	−0.0910345	−	0.0444999i
$206$	7.67682e20			1.14915
$207$	7.98609e19	+	7.98609e19i	0.114446	+	0.114446i
$208$	−1.14708e20	+	1.14708e20i	−0.157407	+	0.157407i
$209$			2.26131e20i			0.297197i
$210$	−1.98758e19	−	5.78893e19i	−0.0250237	−	0.0728828i
$211$	1.48759e21			1.79449			0.897245	−	0.441532i	$-0.145565\pi$
$211$	1.48759e21			1.79449			0.897245	+	0.441532i	$0.145565\pi$
$212$	−1.24021e20	−	1.24021e20i	−0.143375	−	0.143375i
$213$	−9.42651e20	+	9.42651e20i	−1.04456	+	1.04456i
$214$			1.52599e20i			0.162116i
$215$	1.00162e21	−	3.43898e20i	1.02037	−	0.350335i
$216$	−3.92259e20			−0.383256
$217$	−6.72211e19	−	6.72211e19i	−0.0630040	−	0.0630040i
$218$	7.85009e20	−	7.85009e20i	0.705938	−	0.705938i
$219$			8.69380e20i			0.750262i
$220$	−1.16871e20	+	2.39085e20i	−0.0968059	+	0.198038i
$221$	9.50246e20			0.755624
$222$	−8.84259e20	−	8.84259e20i	−0.675154	−	0.675154i
$223$	−1.10204e21	+	1.10204e21i	−0.808076	+	0.808076i	−0.984342	−	0.176267i	$-0.943598\pi$
$223$	−1.10204e21	+	1.10204e21i	−0.808076	+	0.808076i	0.176267	+	0.984342i	$0.443598\pi$
$224$			3.54064e19i			0.0249373i
$225$	−4.70213e20	+	3.66037e20i	−0.318165	+	0.247675i
$226$	1.26607e21			0.823158
$227$	9.64303e20	+	9.64303e20i	0.602533	+	0.602533i	0.940984	−	0.338451i	$-0.109903\pi$
$227$	9.64303e20	+	9.64303e20i	0.602533	+	0.602533i	−0.338451	+	0.940984i	$0.609903\pi$
$228$	−3.06564e20	+	3.06564e20i	−0.184123	+	0.184123i
$229$		−	1.06105e21i		−	0.612659i	−0.951926	−	0.306329i	$-0.900899\pi$
$229$		−	1.06105e21i		−	0.612659i	0.951926	−	0.306329i	$-0.0991009\pi$
$230$	4.59306e20	+	2.24520e20i	0.255007	+	0.124654i
$231$	−8.99812e19			−0.0480445
$232$	−6.60890e20	−	6.60890e20i	−0.339420	−	0.339420i
$233$	−4.92367e20	+	4.92367e20i	−0.243268	+	0.243268i	−0.818201	−	0.574932i	$-0.805028\pi$
$233$	−4.92367e20	+	4.92367e20i	−0.243268	+	0.243268i	0.574932	+	0.818201i	$0.305028\pi$
$234$			5.34008e20i			0.253866i
$235$	−1.13494e21	−	3.30556e21i	−0.519231	−	1.51229i
$236$	6.02145e20			0.265151
$237$	−4.05582e20	−	4.05582e20i	−0.171927	−	0.171927i
$238$	1.46654e20	−	1.46654e20i	0.0598552	−	0.0598552i
$239$		−	5.06100e21i		−	1.98909i	−0.104292	−	0.994547i	$-0.533258\pi$
$239$		−	5.06100e21i		−	1.98909i	0.104292	−	0.994547i	$-0.466742\pi$
$240$	−4.82566e20	+	1.65685e20i	−0.182665	+	0.0627165i
$241$	−4.74446e21			−1.72995			−0.864974	−	0.501816i	$-0.832665\pi$
$241$	−4.74446e21			−1.72995			−0.864974	+	0.501816i	$0.832665\pi$
$242$	−1.14670e21	−	1.14670e21i	−0.402819	−	0.402819i
$243$	−1.56375e21	+	1.56375e21i	−0.529311	+	0.529311i
$244$			1.44287e21i			0.470672i
$245$	1.36896e21	−	2.80052e21i	0.430424	−	0.880529i
$246$	−1.82620e20			−0.0553518
$247$	1.45243e21	+	1.45243e21i	0.424445	+	0.424445i
$248$	−5.60356e20	+	5.60356e20i	−0.157906	+	0.157906i
$249$		−	6.57945e19i		−	0.0178812i
$250$	−1.47509e21	+	2.25833e21i	−0.386686	+	0.592009i
$251$	2.89788e21			0.732852			0.366426	−	0.930447i	$-0.380581\pi$
$251$	2.89788e21			0.732852			0.366426	+	0.930447i	$0.380581\pi$
$252$	8.24151e19	+	8.24151e19i	0.0201095	+	0.0201095i
$253$	5.31458e20	−	5.31458e20i	0.125137	−	0.125137i
$254$			4.53652e21i			1.03091i
$255$	2.68507e21	+	1.31253e21i	0.588972	+	0.287904i
$256$	2.95148e20			0.0625000
$257$	3.31053e21	+	3.31053e21i	0.676862	+	0.676862i	0.959289	−	0.282427i	$-0.0911395\pi$
$257$	3.31053e21	+	3.31053e21i	0.676862	+	0.676862i	−0.282427	+	0.959289i	$0.591140\pi$
$258$	2.11065e21	−	2.11065e21i	0.416715	−	0.416715i
$259$			1.29313e21i			0.246572i
$260$	7.84975e20	+	2.28628e21i	0.144576	+	0.421085i
$261$	−3.07669e21			−0.547419
$262$	−2.06104e20	−	2.06104e20i	−0.0354304	−	0.0354304i
$263$	6.82868e21	−	6.82868e21i	1.13432	−	1.13432i	0.144868	−	0.989451i	$-0.453724\pi$
$263$	6.82868e21	−	6.82868e21i	1.13432	−	1.13432i	0.989451	−	0.144868i	$-0.0462758\pi$
$264$			7.50084e20i			0.120413i
$265$	−2.47191e21	+	8.48709e20i	−0.383548	+	0.131688i
$266$	4.48314e20			0.0672431
$267$	5.74724e21	+	5.74724e21i	0.833408	+	0.833408i
$268$	2.91944e21	−	2.91944e21i	0.409342	−	0.409342i
$269$		−	3.02167e21i		−	0.409710i	−0.978792	−	0.204855i	$-0.934328\pi$
$269$		−	3.02167e21i		−	0.409710i	0.978792	−	0.204855i	$-0.0656723\pi$
$270$	−2.56696e21	+	5.25129e21i	−0.336624	+	0.688640i
$271$	−8.21335e21			−1.04183			−0.520915	−	0.853609i	$-0.674409\pi$
$271$	−8.21335e21			−1.04183			−0.520915	+	0.853609i	$0.674409\pi$
$272$	−1.22251e21	−	1.22251e21i	−0.150014	−	0.150014i
$273$	−5.77943e20	+	5.77943e20i	−0.0686153	+	0.0686153i
$274$			2.78355e21i			0.319775i
$275$	2.43590e21	+	3.12917e21i	0.270810	+	0.347885i
$276$	1.44098e21			0.155052
$277$	1.43723e21	+	1.43723e21i	0.149695	+	0.149695i	0.777982	−	0.628287i	$-0.216244\pi$
$277$	1.43723e21	+	1.43723e21i	0.149695	+	0.149695i	−0.628287	+	0.777982i	$0.716244\pi$
$278$	6.54151e21	−	6.54151e21i	0.659592	−	0.659592i
$279$			2.60867e21i			0.254672i
$280$	4.73996e20	+	2.31701e20i	0.0448077	+	0.0219031i
$281$	−1.63065e22			−1.49281			−0.746404	−	0.665493i	$-0.768221\pi$
$281$	−1.63065e22			−1.49281			−0.746404	+	0.665493i	$0.768221\pi$
$282$	−6.96559e21	−	6.96559e21i	−0.617613	−	0.617613i
$283$	−5.37987e21	+	5.37987e21i	−0.462055	+	0.462055i	−0.899329	−	0.437273i	$-0.855944\pi$
$283$	−5.37987e21	+	5.37987e21i	−0.462055	+	0.462055i	0.437273	+	0.899329i	$0.355944\pi$
$284$		−	1.14913e22i		−	0.956105i
$285$	2.09790e21	+	6.11023e21i	0.169114	+	0.492554i
$286$	3.55372e21			0.277580
$287$	1.33530e20	+	1.33530e20i	0.0101075	+	0.0101075i
$288$	6.87013e20	−	6.87013e20i	0.0504002	−	0.0504002i
$289$		−	3.93574e21i		−	0.279863i
$290$	−1.31724e22	+	4.52264e21i	−0.907996	+	0.311753i
$291$	−8.56015e21			−0.572064
$292$	−5.29907e21	−	5.29907e21i	−0.343363	−	0.343363i
$293$	1.37140e22	−	1.37140e22i	0.861697	−	0.861697i	−0.129838	−	0.991535i	$-0.541446\pi$
$293$	1.37140e22	−	1.37140e22i	0.861697	−	0.861697i	0.991535	+	0.129838i	$0.0414458\pi$
$294$		−	8.78608e21i		−	0.535389i
$295$	3.94047e21	−	8.06110e21i	0.232889	−	0.476427i
$296$	1.07795e22			0.617979
$297$	6.07621e21	+	6.07621e21i	0.337928	+	0.337928i
$298$	3.92413e21	−	3.92413e21i	0.211737	−	0.211737i
$299$		−	6.82704e21i		−	0.357431i
$300$	−9.39861e20	+	7.54451e21i	−0.0477499	+	0.383301i
$301$	−3.08659e21			−0.152188
$302$	−2.25205e21	−	2.25205e21i	−0.107774	−	0.107774i
$303$	−1.37760e22	+	1.37760e22i	−0.639942	+	0.639942i
$304$		−	3.73715e21i		−	0.168531i
$305$	1.93161e22	+	9.44220e21i	0.845710	+	0.413404i
$306$	−5.69125e21			−0.241944
$307$	2.44360e21	+	2.44360e21i	0.100875	+	0.100875i	0.755743	−	0.654868i	$-0.227276\pi$
$307$	2.44360e21	+	2.44360e21i	0.100875	+	0.100875i	−0.654868	+	0.755743i	$0.727276\pi$
$308$	5.48456e20	−	5.48456e20i	0.0219880	−	0.0219880i
$309$		−	3.22427e22i		−	1.25547i
$310$	3.83466e21	+	1.11686e22i	0.145035	+	0.422421i
$311$	−2.64985e22			−0.973595			−0.486797	−	0.873515i	$-0.661835\pi$
$311$	−2.64985e22			−0.973595			−0.486797	+	0.873515i	$0.661835\pi$
$312$	4.81774e21	+	4.81774e21i	0.171970	+	0.171970i
$313$	−1.31947e22	+	1.31947e22i	−0.457614	+	0.457614i	−0.897872	−	0.440257i	$-0.854887\pi$
$313$	−1.31947e22	+	1.31947e22i	−0.457614	+	0.457614i	0.440257	+	0.897872i	$0.354887\pi$
$314$			5.59067e21i			0.188407i
$315$	1.64264e21	−	5.63988e20i	0.0537958	−	0.0184703i
$316$	4.94423e21			0.157367
$317$	3.89757e22	+	3.89757e22i	1.20576	+	1.20576i	0.972387	+	0.233373i	$0.0749764\pi$
$317$	3.89757e22	+	3.89757e22i	1.20576	+	1.20576i	0.233373	+	0.972387i	$0.425024\pi$
$318$	−5.20890e21	+	5.20890e21i	−0.156640	+	0.156640i
$319$			2.04748e22i			0.598553i
$320$	1.93146e21	−	3.95124e21i	0.0548955	−	0.112301i
$321$	6.40916e21			0.177115
$322$	−1.05364e21	−	1.05364e21i	−0.0283132	−	0.0283132i
$323$	−1.54794e22	+	1.54794e22i	−0.404512	+	0.404512i
$324$			8.54263e21i			0.217113i
$325$	3.57441e22	+	4.45283e21i	0.883596	+	0.110074i
$326$	8.60593e21			0.206938
$327$	−3.29705e22	−	3.29705e22i	−0.771250	−	0.771250i
$328$	1.11311e21	−	1.11311e21i	0.0253322	−	0.0253322i
$329$			1.01864e22i			0.225557i
$330$	1.00416e22	+	4.90858e21i	0.216360	+	0.105762i
$331$	2.60635e22			0.546489			0.273244	−	0.961945i	$-0.411903\pi$
$331$	2.60635e22			0.546489			0.273244	+	0.961945i	$0.411903\pi$
$332$	4.01033e20	+	4.01033e20i	0.00818346	+	0.00818346i
$333$	2.50914e22	−	2.50914e22i	0.498341	−	0.498341i
$334$			5.05236e22i			0.976734i
$335$	−1.99785e22	−	5.81884e22i	−0.375975	−	1.09505i
$336$	1.48707e21			0.0272445
$337$	−2.53790e21	−	2.53790e21i	−0.0452694	−	0.0452694i	0.684110	−	0.729379i	$-0.260191\pi$
$337$	−2.53790e21	−	2.53790e21i	−0.0452694	−	0.0452694i	−0.729379	+	0.684110i	$0.760191\pi$
$338$	−5.96330e21	+	5.96330e21i	−0.103571	+	0.103571i
$339$		−	5.31752e22i		−	0.899315i
$340$	−2.43663e22	+	8.36596e21i	−0.401309	+	0.137786i
$341$	1.73602e22			0.278461
$342$	−8.69893e21	−	8.69893e21i	−0.135904	−	0.135904i
$343$	−1.29791e22	+	1.29791e22i	−0.197513	+	0.197513i
$344$			2.57298e22i			0.381426i
$345$	9.42988e21	−	1.92909e22i	0.136187	−	0.278600i
$346$	2.23600e22			0.314621
$347$	−5.95167e22	−	5.95167e22i	−0.815969	−	0.815969i	0.169552	−	0.985521i	$-0.445768\pi$
$347$	−5.95167e22	−	5.95167e22i	−0.815969	−	0.815969i	−0.985521	+	0.169552i	$0.945768\pi$
$348$	−2.77574e22	+	2.77574e22i	−0.370822	+	0.370822i
$349$			1.07931e22i			0.140514i	0.997529	+	0.0702568i	$0.0223819\pi$
$349$			1.07931e22i			0.140514i	−0.997529	+	0.0702568i	$0.977618\pi$
$350$	6.20371e21	−	4.82927e21i	0.0787116	−	0.0612730i
$351$	7.80541e22			0.965232
$352$	−4.57193e21	−	4.57193e21i	−0.0551081	−	0.0551081i
$353$	3.71467e21	−	3.71467e21i	0.0436463	−	0.0436463i	−0.684947	−	0.728593i	$-0.740175\pi$
$353$	3.71467e21	−	3.71467e21i	0.0436463	−	0.0436463i	0.728593	+	0.684947i	$0.240175\pi$
$354$		−	2.52901e22i		−	0.289682i
$355$	−1.53838e23	−	7.51999e22i	−1.71794	−	0.839773i
$356$	−7.00614e22			−0.762832
$357$	−6.15949e21	−	6.15949e21i	−0.0653929	−	0.0653929i
$358$	3.85210e22	−	3.85210e22i	0.398795	−	0.398795i
$359$			1.24074e23i			1.25265i	0.779562	+	0.626325i	$0.215442\pi$
$359$			1.24074e23i			1.25265i	−0.779562	+	0.626325i	$0.784558\pi$
$360$	−4.70141e21	−	1.36931e22i	−0.0462919	−	0.134828i
$361$	5.68077e22			0.545559
$362$	−6.30941e22	−	6.30941e22i	−0.591033	−	0.591033i
$363$	−4.81613e22	+	4.81613e22i	−0.440087	+	0.440087i
$364$		−	7.04539e21i		−	0.0628047i
$365$	−1.05618e23	+	3.62629e22i	−0.918546	+	0.315375i
$366$	6.06006e22			0.514218
$367$	−1.44670e22	−	1.44670e22i	−0.119780	−	0.119780i	0.644676	−	0.764456i	$-0.276992\pi$
$367$	−1.44670e22	−	1.44670e22i	−0.119780	−	0.119780i	−0.764456	+	0.644676i	$0.776992\pi$
$368$	−8.78313e21	+	8.78313e21i	−0.0709609	+	0.0709609i
$369$		−	5.18194e21i		−	0.0408559i
$370$	7.05417e22	−	1.44309e23i	0.542788	−	1.11039i
$371$	7.61741e21			0.0572061
$372$	2.35350e22	+	2.35350e22i	0.172515	+	0.172515i
$373$	7.35531e22	−	7.35531e22i	0.526286	−	0.526286i	−0.393177	−	0.919463i	$-0.628624\pi$
$373$	7.35531e22	−	7.35531e22i	0.526286	−	0.526286i	0.919463	+	0.393177i	$0.128624\pi$
$374$			3.78741e22i			0.264544i
$375$	9.48502e22	+	6.19538e22i	0.646780	+	0.422461i
$376$	8.49137e22			0.565311
$377$	1.31508e23	+	1.31508e23i	0.854831	+	0.854831i
$378$	1.20463e22	−	1.20463e22i	0.0764589	−	0.0764589i
$379$			1.43624e23i			0.890170i	0.895488	+	0.445085i	$0.146827\pi$
$379$			1.43624e23i			0.890170i	−0.895488	+	0.445085i	$0.853173\pi$
$380$	−5.00304e22	−	2.44561e22i	−0.302818	−	0.148025i
$381$	1.90534e23			1.12629
$382$	1.16674e23	+	1.16674e23i	0.673603	+	0.673603i
$383$	−1.49147e23	+	1.49147e23i	−0.841059	+	0.841059i	−0.988997	−	0.147938i	$-0.952736\pi$
$383$	−1.49147e23	+	1.49147e23i	−0.841059	+	0.841059i	0.147938	+	0.988997i	$0.452736\pi$
$384$		−	1.23962e22i		−	0.0682824i
$385$	−3.75322e21	−	1.09315e22i	−0.0201957	−	0.0588209i
$386$	−1.91589e23			−1.00713
$387$	5.98910e22	+	5.98910e22i	0.307584	+	0.307584i
$388$	5.21760e22	−	5.21760e22i	0.261810	−	0.261810i
$389$			2.15296e23i			1.05558i	0.849376	+	0.527788i	$0.176978\pi$
$389$			2.15296e23i			1.05558i	−0.849376	+	0.527788i	$0.823022\pi$
$390$	9.60240e22	−	3.29690e22i	0.460043	−	0.157952i
$391$	7.27599e22			0.340645
$392$	5.35532e22	+	5.35532e22i	0.245025	+	0.245025i
$393$	−8.65641e21	+	8.65641e21i	−0.0387083	+	0.0387083i
$394$		−	1.43665e23i		−	0.627891i
$395$	3.23553e22	−	6.61899e22i	0.138220	−	0.282760i
$396$	−2.12841e22			−0.0888787
$397$	−2.63471e23	−	2.63471e23i	−1.07552	−	1.07552i	−0.996905	−	0.0786156i	$-0.974950\pi$
$397$	−2.63471e23	−	2.63471e23i	−1.07552	−	1.07552i	−0.0786156	−	0.996905i	$-0.525050\pi$
$398$	−2.22943e23	+	2.22943e23i	−0.889704	+	0.889704i
$399$		−	1.88292e22i		−	0.0734644i
$400$	−4.02568e22	−	5.17142e22i	−0.153568	−	0.197274i
$401$	−1.66124e23			−0.619630			−0.309815	−	0.950797i	$-0.600267\pi$
$401$	−1.66124e23			−0.619630			−0.309815	+	0.950797i	$0.600267\pi$
$402$	−1.22617e23	−	1.22617e23i	−0.447214	−	0.447214i
$403$	1.11503e23	−	1.11503e23i	0.397687	−	0.397687i
$404$		−	1.67936e23i		−	0.585749i
$405$	1.14363e23	+	5.59034e22i	0.390112	+	0.190697i
$406$	4.05920e22			0.135427
$407$	−1.66978e23	−	1.66978e23i	−0.544891	−	0.544891i
$408$	−5.13456e22	+	5.13456e22i	−0.163893	+	0.163893i
$409$		−	3.08765e23i		−	0.964091i	−0.876146	−	0.482046i	$-0.839894\pi$
$409$		−	3.08765e23i		−	0.964091i	0.876146	−	0.482046i	$-0.160106\pi$
$410$	−7.61729e21	−	2.21858e22i	−0.0232673	−	0.0677672i
$411$	1.16910e23			0.349360
$412$	1.96527e23	+	1.96527e23i	0.574575	+	0.574575i
$413$	−1.84920e22	+	1.84920e22i	−0.0528972	+	0.0528972i
$414$			4.08888e22i			0.114446i
$415$	7.99312e21	−	2.74437e21i	0.0218919	−	0.00751640i
$416$	−5.87304e22			−0.157407
$417$	−2.74744e23	−	2.74744e23i	−0.720616	−	0.720616i
$418$	−5.78896e22	+	5.78896e22i	−0.148598	+	0.148598i
$419$		−	1.65948e23i		−	0.416914i	−0.978032	−	0.208457i	$-0.933156\pi$
$419$		−	1.65948e23i		−	0.416914i	0.978032	−	0.208457i	$-0.0668441\pi$
$420$	9.73146e21	−	1.99079e22i	0.0239296	−	0.0489532i
$421$	−6.59831e23			−1.58816			−0.794079	−	0.607814i	$-0.792047\pi$
$421$	−6.59831e23			−1.58816			−0.794079	+	0.607814i	$0.792047\pi$
$422$	3.80823e23	+	3.80823e23i	0.897245	+	0.897245i
$423$	1.97653e23	−	1.97653e23i	0.455869	−	0.455869i
$424$		−	6.34988e22i		−	0.143375i
$425$	−4.74566e22	+	3.80946e23i	−0.104905	+	0.842100i
$426$	−4.82637e23			−1.04456
$427$	−4.43107e22	−	4.43107e22i	−0.0938983	−	0.0938983i
$428$	−3.90653e22	+	3.90653e22i	−0.0810582	+	0.0810582i
$429$		−	1.49256e23i		−	0.303262i
$430$	3.44453e23	+	1.68377e23i	0.685352	+	0.335017i
$431$	4.75355e23			0.926237			0.463119	−	0.886296i	$-0.346730\pi$
$431$	4.75355e23			0.926237			0.463119	+	0.886296i	$0.346730\pi$
$432$	−1.00418e23	−	1.00418e23i	−0.191628	−	0.191628i
$433$	3.86355e23	−	3.86355e23i	0.722097	−	0.722097i	−0.246935	−	0.969032i	$-0.579423\pi$
$433$	3.86355e23	−	3.86355e23i	0.722097	−	0.722097i	0.969032	+	0.246935i	$0.0794235\pi$
$434$		−	3.44172e22i		−	0.0630040i
$435$	1.89951e23	+	5.53243e23i	0.340596	+	0.992003i
$436$	4.01925e23			0.705938
$437$	1.11212e23	+	1.11212e23i	0.191345	+	0.191345i
$438$	−2.22561e23	+	2.22561e23i	−0.375131	+	0.375131i
$439$		−	1.81590e23i		−	0.299854i	−0.988697	−	0.149927i	$-0.952096\pi$
$439$		−	1.81590e23i		−	0.299854i	0.988697	−	0.149927i	$-0.0479039\pi$
$440$	−9.11248e22	+	3.12869e22i	−0.147422	+	0.0506161i
$441$	2.49310e23			0.395178
$442$	2.43263e23	+	2.43263e23i	0.377812	+	0.377812i
$443$	5.16837e23	−	5.16837e23i	0.786538	−	0.786538i	−0.194387	−	0.980925i	$-0.562272\pi$
$443$	5.16837e23	−	5.16837e23i	0.786538	−	0.786538i	0.980925	+	0.194387i	$0.0622717\pi$
$444$		−	4.52741e23i		−	0.675154i
$445$	−4.58485e23	+	9.37934e23i	−0.670016	+	1.37067i
$446$	−5.64243e23			−0.808076
$447$	−1.64814e23	−	1.64814e23i	−0.231327	−	0.231327i
$448$	−9.06403e21	+	9.06403e21i	−0.0124686	+	0.0124686i
$449$			1.16875e23i			0.157581i	0.996891	+	0.0787907i	$0.0251059\pi$
$449$			1.16875e23i			0.157581i	−0.996891	+	0.0787907i	$0.974894\pi$
$450$	−2.14080e23	−	2.66691e22i	−0.282920	−	0.0352448i
$451$	−3.44848e22			−0.0446723
$452$	3.24115e23	+	3.24115e23i	0.411579	+	0.411579i
$453$	−9.45864e22	+	9.45864e22i	−0.117746	+	0.117746i
$454$			4.93723e23i			0.602533i
$455$	−9.43188e22	−	4.61053e22i	−0.112848	−	0.0551631i
$456$	−1.56961e23			−0.184123
$457$	9.98727e21	+	9.98727e21i	0.0114869	+	0.0114869i	0.712827	−	0.701340i	$-0.247415\pi$
$457$	9.98727e21	+	9.98727e21i	0.0114869	+	0.0114869i	−0.701340	+	0.712827i	$0.747415\pi$
$458$	2.71630e23	−	2.71630e23i	0.306329	−	0.306329i
$459$			8.31870e23i			0.919902i
$460$	6.01052e22	+	1.75060e23i	0.0651766	+	0.189830i
$461$	−7.48766e23			−0.796228			−0.398114	−	0.917336i	$-0.630335\pi$
$461$	−7.48766e23			−0.796228			−0.398114	+	0.917336i	$0.630335\pi$
$462$	−2.30352e22	−	2.30352e22i	−0.0240223	−	0.0240223i
$463$	1.09536e23	−	1.09536e23i	0.112028	−	0.112028i	−0.648870	−	0.760899i	$-0.724758\pi$
$463$	1.09536e23	−	1.09536e23i	0.112028	−	0.112028i	0.760899	+	0.648870i	$0.224758\pi$
$464$		−	3.38376e23i		−	0.339420i
$465$	4.69084e23	−	1.61056e23i	0.461503	−	0.158453i
$466$	−2.52092e23			−0.243268
$467$	8.32742e23	+	8.32742e23i	0.788240	+	0.788240i	0.981206	−	0.192966i	$-0.0618106\pi$
$467$	8.32742e23	+	8.32742e23i	0.788240	+	0.788240i	−0.192966	+	0.981206i	$0.561811\pi$
$468$	−1.36706e23	+	1.36706e23i	−0.126933	+	0.126933i
$469$			1.79313e23i			0.163326i
$470$	5.55680e23	−	1.13677e24i	0.496528	−	1.01576i
$471$	2.34809e23			0.205838
$472$	1.54149e23	+	1.54149e23i	0.132575	+	0.132575i
$473$	3.98563e23	−	3.98563e23i	0.336315	−	0.336315i
$474$		−	2.07658e23i		−	0.171927i
$475$	−6.54803e23	+	5.09731e23i	−0.531947	+	0.414093i
$476$	7.50870e22			0.0598552
$477$	−1.47806e23	−	1.47806e23i	−0.115618	−	0.115618i
$478$	1.29562e24	−	1.29562e24i	0.994547	−	0.994547i
$479$		−	1.05746e24i		−	0.796608i	−0.917253	−	0.398304i	$-0.869599\pi$
$479$		−	1.05746e24i		−	0.796608i	0.917253	−	0.398304i	$-0.130401\pi$
$480$	−1.65952e23	−	8.11216e22i	−0.122691	−	0.0599743i
$481$	−2.14498e24			−1.55638
$482$	−1.21458e24	−	1.21458e24i	−0.864974	−	0.864974i
$483$	−4.42529e22	+	4.42529e22i	−0.0309326	+	0.0309326i
$484$		−	5.87108e23i		−	0.402819i
$485$	−3.57054e23	−	1.03994e24i	−0.240469	−	0.700378i
$486$	−8.00641e23			−0.529311
$487$	2.04206e23	+	2.04206e23i	0.132528	+	0.132528i	0.770259	−	0.637731i	$-0.220127\pi$
$487$	2.04206e23	+	2.04206e23i	0.132528	+	0.132528i	−0.637731	+	0.770259i	$0.720127\pi$
$488$	−3.69374e23	+	3.69374e23i	−0.235336	+	0.235336i
$489$		−	3.61450e23i		−	0.226083i
$490$	1.06739e24	−	3.66478e23i	0.655477	−	0.225052i
$491$	5.10148e22			0.0307584			0.0153792	−	0.999882i	$-0.495104\pi$
$491$	5.10148e22			0.0307584			0.0153792	+	0.999882i	$0.495104\pi$
$492$	−4.67506e22	−	4.67506e22i	−0.0276759	−	0.0276759i
$493$	−1.40156e24	+	1.40156e24i	−0.814685	+	0.814685i
$494$			7.43642e23i			0.424445i
$495$	−1.39284e23	+	2.84936e23i	−0.0780646	+	0.159699i
$496$	−2.86902e23			−0.157906
$497$	3.52901e23	+	3.52901e23i	0.190741	+	0.190741i
$498$	1.68434e22	−	1.68434e22i	0.00894058	−	0.00894058i
$499$			1.50079e24i			0.782373i	0.920312	+	0.391186i	$0.127935\pi$
$499$			1.50079e24i			0.782373i	−0.920312	+	0.391186i	$0.872065\pi$
$500$	−9.55756e23	+	2.00511e23i	−0.489347	+	0.102661i
$501$	2.12200e24			1.06710
$502$	7.41856e23	+	7.41856e23i	0.366426	+	0.366426i
$503$	1.02193e24	−	1.02193e24i	0.495803	−	0.495803i	−0.414325	−	0.910129i	$-0.635982\pi$
$503$	1.02193e24	−	1.02193e24i	0.495803	−	0.495803i	0.910129	+	0.414325i	$0.135982\pi$
$504$			4.21965e22i			0.0201095i
$505$	−2.24821e24	−	1.09898e24i	−1.05248	−	0.514480i
$506$	2.72107e23			0.125137
$507$	2.50459e23	+	2.50459e23i	0.113153	+	0.113153i
$508$	−1.16135e24	+	1.16135e24i	−0.515454	+	0.515454i
$509$		−	8.52837e23i		−	0.371883i	−0.982561	−	0.185941i	$-0.940467\pi$
$509$		−	8.52837e23i		−	0.371883i	0.982561	−	0.185941i	$-0.0595334\pi$
$510$	3.51371e23	+	1.02339e24i	0.150534	+	0.438438i
$511$	3.25470e23			0.137001
$512$	7.55579e22	+	7.55579e22i	0.0312500	+	0.0312500i
$513$	−1.27149e24	+	1.27149e24i	−0.516723	+	0.516723i
$514$			1.69499e24i			0.676862i
$515$	3.91704e24	−	1.34488e24i	1.53707	−	0.527739i
$516$	1.08065e24			0.416715
$517$	−1.31534e24	−	1.31534e24i	−0.498452	−	0.498452i
$518$	−3.31041e23	+	3.31041e23i	−0.123286	+	0.123286i
$519$		−	9.39123e23i		−	0.343729i
$520$	−3.84335e23	+	7.86242e23i	−0.138255	+	0.282830i
$521$	5.47907e24			1.93717			0.968584	−	0.248687i	$-0.0799989\pi$
$521$	5.47907e24			1.93717			0.968584	+	0.248687i	$0.0799989\pi$
$522$	−7.87633e23	−	7.87633e23i	−0.273709	−	0.273709i
$523$	−1.38385e24	+	1.38385e24i	−0.472688	+	0.472688i	−0.902784	−	0.430095i	$-0.858480\pi$
$523$	−1.38385e24	+	1.38385e24i	−0.472688	+	0.472688i	0.430095	+	0.902784i	$0.358480\pi$
$524$		−	1.05526e23i		−	0.0354304i
$525$	−2.02830e23	−	2.60556e23i	−0.0669419	−	0.0859939i
$526$	3.49629e24			1.13432
$527$	1.18836e24	+	1.18836e24i	0.379010	+	0.379010i
$528$	−1.92021e23	+	1.92021e23i	−0.0602066	+	0.0602066i
$529$			2.72141e24i			0.838866i
$530$	−8.50078e23	−	4.15539e23i	−0.257618	−	0.125930i
$531$	7.17623e23			0.213819
$532$	1.14768e23	+	1.14768e23i	0.0336216	+	0.0336216i
$533$	−2.21493e23	+	2.21493e23i	−0.0637993	+	0.0637993i
$534$			2.94258e24i			0.833408i
$535$	2.67334e23	+	7.78624e23i	0.0744509	+	0.216842i
$536$	1.49475e24			0.409342
$537$	−1.61788e24	−	1.61788e24i	−0.435691	−	0.435691i
$538$	7.73548e23	−	7.73548e23i	0.204855	−	0.204855i
$539$		−	1.65911e24i		−	0.432092i
$540$	−2.00147e24	+	6.87188e23i	−0.512632	+	0.176008i
$541$	−1.50493e23			−0.0379090			−0.0189545	−	0.999820i	$-0.506034\pi$
$541$	−1.50493e23			−0.0379090			−0.0189545	+	0.999820i	$0.506034\pi$
$542$	−2.10262e24	−	2.10262e24i	−0.520915	−	0.520915i
$543$	−2.64996e24	+	2.64996e24i	−0.645715	+	0.645715i
$544$		−	6.25926e23i		−	0.150014i
$545$	2.63022e24	−	5.38069e24i	0.620044	−	1.26844i
$546$	−2.95907e23			−0.0686153
$547$	−5.76237e24	−	5.76237e24i	−1.31436	−	1.31436i	−0.918165	−	0.396198i	$-0.870329\pi$
$547$	−5.76237e24	−	5.76237e24i	−1.31436	−	1.31436i	−0.396198	−	0.918165i	$-0.629671\pi$
$548$	−7.12590e23	+	7.12590e23i	−0.159888	+	0.159888i
$549$			1.71958e24i			0.379551i
$550$	−1.77477e23	+	1.42466e24i	−0.0385371	+	0.309347i
$551$	−4.28450e24			−0.915242
$552$	3.68892e23	+	3.68892e23i	0.0775261	+	0.0775261i
$553$	−1.51838e23	+	1.51838e23i	−0.0313946	+	0.0313946i
$554$			7.35860e23i			0.149695i
$555$	−6.06098e24	−	2.96276e24i	−1.21313	−	0.593006i
$556$	3.34925e24			0.659592
$557$	3.37859e24	+	3.37859e24i	0.654695	+	0.654695i	0.954120	−	0.299425i	$-0.0967947\pi$
$557$	3.37859e24	+	3.37859e24i	0.654695	+	0.654695i	−0.299425	+	0.954120i	$0.596795\pi$
$558$	−6.67819e23	+	6.67819e23i	−0.127336	+	0.127336i
$559$		−	5.11988e24i		−	0.960625i
$560$	6.20275e22	+	1.80659e23i	0.0114523	+	0.0333554i
$561$	1.59072e24			0.289019
$562$	−4.17446e24	−	4.17446e24i	−0.746404	−	0.746404i
$563$	−2.51171e24	+	2.51171e24i	−0.441971	+	0.441971i	−0.892674	−	0.450703i	$-0.851173\pi$
$563$	−2.51171e24	+	2.51171e24i	−0.441971	+	0.441971i	0.450703	+	0.892674i	$0.351173\pi$
$564$		−	3.56638e24i		−	0.617613i
$565$	6.46005e24	−	2.21800e24i	1.10103	−	0.378030i
$566$	−2.75449e24			−0.462055
$567$	−2.62345e23	−	2.62345e23i	−0.0433138	−	0.0433138i
$568$	2.94178e24	−	2.94178e24i	0.478053	−	0.478053i
$569$			2.70435e24i			0.432567i	0.976331	+	0.216283i	$0.0693935\pi$
$569$			2.70435e24i			0.432567i	−0.976331	+	0.216283i	$0.930606\pi$
$570$	−1.02716e24	+	2.10128e24i	−0.161720	+	0.330834i
$571$	−5.82157e24			−0.902225			−0.451113	−	0.892467i	$-0.648973\pi$
$571$	−5.82157e24			−0.902225			−0.451113	+	0.892467i	$0.648973\pi$
$572$	9.09752e23	+	9.09752e23i	0.138790	+	0.138790i
$573$	4.90032e24	−	4.90032e24i	0.735924	−	0.735924i
$574$			6.83674e22i			0.0101075i
$575$	2.73691e24	+	3.40952e23i	0.398336	+	0.0496229i
$576$	3.51750e23			0.0504002
$577$	4.60052e24	+	4.60052e24i	0.648969	+	0.648969i	0.952744	−	0.303775i	$-0.0982470\pi$
$577$	4.60052e24	+	4.60052e24i	0.648969	+	0.648969i	−0.303775	+	0.952744i	$0.598247\pi$
$578$	1.00755e24	−	1.00755e24i	0.139932	−	0.139932i
$579$			8.04675e24i			1.10031i
$580$	−4.52994e24	−	2.21435e24i	−0.609874	−	0.298122i
$581$	−2.46315e22			−0.00326517
$582$	−2.19140e24	−	2.19140e24i	−0.286032	−	0.286032i
$583$	−9.83616e23	+	9.83616e23i	−0.126418	+	0.126418i
$584$		−	2.71312e24i		−	0.343363i
$585$	9.35515e23	+	2.72474e24i	0.116586	+	0.339564i
$586$	7.02155e24			0.861697
$587$	9.65969e24	+	9.65969e24i	1.16740	+	1.16740i	0.982816	+	0.184585i	$0.0590942\pi$
$587$	9.65969e24	+	9.65969e24i	1.16740	+	1.16740i	0.184585	+	0.982816i	$0.440906\pi$
$588$	2.24924e24	−	2.24924e24i	0.267694	−	0.267694i
$589$			3.63274e24i			0.425792i
$590$	3.07240e24	−	1.05488e24i	0.354658	−	0.121769i
$591$	−6.03393e24			−0.685983
$592$	2.75956e24	+	2.75956e24i	0.308990	+	0.308990i
$593$	−8.45555e24	+	8.45555e24i	−0.932501	+	0.932501i	−0.997862	−	0.0653603i	$-0.979180\pi$
$593$	−8.45555e24	+	8.45555e24i	−0.932501	+	0.932501i	0.0653603	+	0.997862i	$0.479180\pi$
$594$			3.11102e24i			0.337928i
$595$	4.91373e23	−	1.00521e24i	0.0525725	−	0.107549i
$596$	2.00915e24			0.211737
$597$	9.36361e24	+	9.36361e24i	0.972018	+	0.972018i
$598$	1.74772e24	−	1.74772e24i	0.178715	−	0.178715i
$599$		−	5.33481e24i		−	0.537375i	−0.963227	−	0.268688i	$-0.913410\pi$
$599$		−	5.33481e24i		−	0.537375i	0.963227	−	0.268688i	$-0.0865899\pi$
$600$	−2.17200e24	+	1.69079e24i	−0.215525	+	0.167775i
$601$	8.93643e23			0.0873562			0.0436781	−	0.999046i	$-0.486092\pi$
$601$	8.93643e23			0.0873562			0.0436781	+	0.999046i	$0.486092\pi$
$602$	−7.90167e23	−	7.90167e23i	−0.0760940	−	0.0760940i
$603$	3.47932e24	−	3.47932e24i	0.330095	−	0.330095i
$604$		−	1.15305e24i		−	0.107774i
$605$	−7.85980e24	−	3.84207e24i	−0.723791	−	0.353807i
$606$	−7.05333e24			−0.639942
$607$	−2.49857e23	−	2.49857e23i	−0.0223354	−	0.0223354i	0.695851	−	0.718186i	$-0.255027\pi$
$607$	−2.49857e23	−	2.49857e23i	−0.0223354	−	0.0223354i	−0.718186	+	0.695851i	$0.755027\pi$
$608$	9.56711e23	−	9.56711e23i	0.0842653	−	0.0842653i
$609$		−	1.70487e24i		−	0.147957i
$610$	2.52772e24	+	7.36213e24i	0.216153	+	0.629557i
$611$	−1.68967e25			−1.42374
$612$	−1.45696e24	−	1.45696e24i	−0.120972	−	0.120972i
$613$	5.07841e24	−	5.07841e24i	0.415512	−	0.415512i	−0.468142	−	0.883653i	$-0.655076\pi$
$613$	5.07841e24	−	5.07841e24i	0.415512	−	0.415512i	0.883653	+	0.468142i	$0.155076\pi$
$614$			1.25112e24i			0.100875i
$615$	−9.31803e23	+	3.19927e23i	−0.0740369	+	0.0254199i
$616$	2.80809e23			0.0219880
$617$	−1.32795e24	−	1.32795e24i	−0.102474	−	0.102474i	0.654011	−	0.756485i	$-0.273085\pi$
$617$	−1.32795e24	−	1.32795e24i	−0.102474	−	0.102474i	−0.756485	+	0.654011i	$0.773085\pi$
$618$	8.25413e24	−	8.25413e24i	0.627733	−	0.627733i
$619$		−	1.05329e25i		−	0.789465i	−0.918796	−	0.394732i	$-0.870837\pi$
$619$		−	1.05329e25i		−	0.789465i	0.918796	−	0.394732i	$-0.129163\pi$
$620$	−1.87750e24	+	3.84085e24i	−0.138693	+	0.283728i
$621$	5.97657e24			0.435139
$622$	−6.78362e24	−	6.78362e24i	−0.486797	−	0.486797i
$623$	2.15160e24	−	2.15160e24i	0.152184	−	0.152184i
$624$			2.46668e24i			0.171970i
$625$	−3.57022e24	+	1.41072e25i	−0.245343	+	0.969436i
$626$	−6.75567e24			−0.457614
$627$	2.43137e24	+	2.43137e24i	0.162347	+	0.162347i
$628$	−1.43121e24	+	1.43121e24i	−0.0942036	+	0.0942036i
$629$		−	2.28603e25i		−	1.48329i
$630$	5.64898e23	+	2.76136e23i	0.0361331	+	0.0176627i
$631$	5.76618e24			0.363600			0.181800	−	0.983336i	$-0.441808\pi$
$631$	5.76618e24			0.363600			0.181800	+	0.983336i	$0.441808\pi$
$632$	1.26572e24	+	1.26572e24i	0.0786837	+	0.0786837i
$633$	1.59946e25	−	1.59946e25i	0.980257	−	0.980257i
$634$			1.99556e25i			1.20576i
$635$	7.94742e24	+	2.31473e25i	0.473437	+	1.37891i
$636$	−2.66696e24			−0.156640
$637$	−1.06563e25	−	1.06563e25i	−0.617097	−	0.617097i
$638$	−5.24154e24	+	5.24154e24i	−0.299277	+	0.299277i
$639$		−	1.36951e25i		−	0.771006i
$640$	1.50597e24	−	5.17062e23i	0.0835982	−	0.0287027i
$641$	−2.40274e25			−1.31518			−0.657590	−	0.753376i	$-0.728424\pi$
$641$	−2.40274e25			−1.31518			−0.657590	+	0.753376i	$0.728424\pi$
$642$	1.64074e24	+	1.64074e24i	0.0885576	+	0.0885576i
$643$	3.15464e24	−	3.15464e24i	0.167900	−	0.167900i	−0.618156	−	0.786056i	$-0.712120\pi$
$643$	3.15464e24	−	3.15464e24i	0.167900	−	0.167900i	0.786056	+	0.618156i	$0.212120\pi$
$644$		−	5.39462e23i		−	0.0283132i
$645$	7.07186e24	−	1.44671e25i	0.366013	−	0.748760i
$646$	−7.92545e24			−0.404512
$647$	−1.29599e25	−	1.29599e25i	−0.652325	−	0.652325i	0.301227	−	0.953552i	$-0.402604\pi$
$647$	−1.29599e25	−	1.29599e25i	−0.652325	−	0.652325i	−0.953552	+	0.301227i	$0.902604\pi$
$648$	−2.18691e24	+	2.18691e24i	−0.108557	+	0.108557i
$649$		−	4.77563e24i		−	0.233792i
$650$	8.01056e24	+	1.02904e25i	0.386761	+	0.496835i
$651$	−1.44553e24			−0.0688330
$652$	2.20312e24	+	2.20312e24i	0.103469	+	0.103469i
$653$	−7.52591e24	+	7.52591e24i	−0.348610	+	0.348610i	−0.859592	−	0.510981i	$-0.829282\pi$
$653$	−7.52591e24	+	7.52591e24i	−0.348610	+	0.348610i	0.510981	+	0.859592i	$0.329282\pi$
$654$		−	1.68809e25i		−	0.771250i
$655$	−1.41270e24	−	6.90564e23i	−0.0636618	−	0.0311195i
$656$	5.69911e23			0.0253322
$657$	−6.31531e24	−	6.31531e24i	−0.276889	−	0.276889i
$658$	−2.60771e24	+	2.60771e24i	−0.112779	+	0.112779i
$659$			4.92136e24i			0.209950i	0.994475	+	0.104975i	$0.0334763\pi$
$659$			4.92136e24i			0.209950i	−0.994475	+	0.104975i	$0.966524\pi$
$660$	1.31405e24	+	3.82725e24i	0.0552990	+	0.161061i
$661$	8.79030e23			0.0364914			0.0182457	−	0.999834i	$-0.494192\pi$
$661$	8.79030e23			0.0364914			0.0182457	+	0.999834i	$0.494192\pi$
$662$	6.67226e24	+	6.67226e24i	0.273244	+	0.273244i
$663$	1.02171e25	−	1.02171e25i	0.412766	−	0.412766i
$664$			2.05329e23i			0.00818346i
$665$	2.28749e24	−	7.85391e23i	0.0899424	−	0.0308810i
$666$	1.28468e25			0.498341
$667$	1.00695e25	+	1.00695e25i	0.385368	+	0.385368i
$668$	−1.29340e25	+	1.29340e25i	−0.488367	+	0.488367i
$669$			2.36982e25i			0.882838i
$670$	9.78173e24	−	2.00107e25i	0.359536	−	0.735511i
$671$	1.14434e25			0.415005
$672$	3.80690e23	+	3.80690e23i	0.0136222	+	0.0136222i
$673$	−1.02235e25	+	1.02235e25i	−0.360965	+	0.360965i	−0.864168	−	0.503203i	$-0.832155\pi$
$673$	−1.02235e25	+	1.02235e25i	−0.360965	+	0.360965i	0.503203	+	0.864168i	$0.332155\pi$
$674$		−	1.29940e24i		−	0.0452694i
$675$	−3.89813e24	+	3.12913e25i	−0.134005	+	1.07570i
$676$	−3.05321e24			−0.103571
$677$	2.30687e25	+	2.30687e25i	0.772190	+	0.772190i	0.978489	−	0.206299i	$-0.0661419\pi$
$677$	2.30687e25	+	2.30687e25i	0.772190	+	0.772190i	−0.206299	+	0.978489i	$0.566142\pi$
$678$	1.36129e25	−	1.36129e25i	0.449658	−	0.449658i
$679$			3.20467e24i			0.104461i
$680$	−8.37946e24	−	4.09609e24i	−0.269548	−	0.131762i
$681$	2.07364e25			0.658278
$682$	4.44420e24	+	4.44420e24i	0.139230	+	0.139230i
$683$	−3.83034e25	+	3.83034e25i	−1.18427	+	1.18427i	−0.205643	+	0.978627i	$0.565928\pi$
$683$	−3.83034e25	+	3.83034e25i	−1.18427	+	1.18427i	−0.978627	+	0.205643i	$0.934072\pi$
$684$		−	4.45385e24i		−	0.135904i
$685$	4.87644e24	+	1.42029e25i	0.146855	+	0.427722i
$686$	−6.64528e24			−0.197513
$687$	−1.14085e25	−	1.14085e25i	−0.334670	−	0.334670i
$688$	−6.58684e24	+	6.58684e24i	−0.190713	+	0.190713i
$689$			1.26354e25i			0.361090i
$690$	7.35252e24	−	2.52442e24i	0.207393	−	0.0712067i
$691$	6.42774e25			1.78960			0.894799	−	0.446468i	$-0.147318\pi$
$691$	6.42774e25			1.78960			0.894799	+	0.446468i	$0.147318\pi$
$692$	5.72417e24	+	5.72417e24i	0.157310	+	0.157310i
$693$	6.53637e23	−	6.53637e23i	0.0177312	−	0.0177312i
$694$		−	3.04726e25i		−	0.815969i
$695$	2.19177e25	−	4.48375e25i	0.579337	−	1.18516i
$696$	−1.42118e25			−0.370822
$697$	−2.36059e24	−	2.36059e24i	−0.0608030	−	0.0608030i
$698$	−2.76304e24	+	2.76304e24i	−0.0702568	+	0.0702568i
$699$			1.05879e25i			0.265775i
$700$	2.82444e24	+	3.51856e23i	0.0699923	+	0.00871932i
$701$	−5.35454e25			−1.30997			−0.654983	−	0.755644i	$-0.727324\pi$
$701$	−5.35454e25			−1.30997			−0.654983	+	0.755644i	$0.727324\pi$
$702$	1.99819e25	+	1.99819e25i	0.482616	+	0.482616i
$703$	3.49414e25	−	3.49414e25i	0.833187	−	0.833187i
$704$		−	2.34083e24i		−	0.0551081i
$705$	−4.77443e25	−	2.33386e25i	−1.10974	−	0.542466i
$706$	1.90191e24			0.0436463
$707$	5.15734e24	+	5.15734e24i	0.116856	+	0.116856i
$708$	6.47428e24	−	6.47428e24i	0.144841	−	0.144841i
$709$			1.82152e25i			0.402364i	0.979554	+	0.201182i	$0.0644782\pi$
$709$			1.82152e25i			0.402364i	−0.979554	+	0.201182i	$0.935522\pi$
$710$	−2.01314e25	−	5.86337e25i	−0.439085	−	1.27886i
$711$	5.89242e24			0.126902
$712$	−1.79357e25	−	1.79357e25i	−0.381416	−	0.381416i
$713$	8.53775e24	−	8.53775e24i	0.179282	−	0.179282i
$714$		−	3.15366e24i		−	0.0653929i
$715$	1.81326e25	−	6.22567e24i	0.371283	−	0.127477i
$716$	1.97227e25			0.398795
$717$	−5.44160e25	−	5.44160e25i	−1.08656	−	1.08656i
$718$	−3.17629e25	+	3.17629e25i	−0.626325	+	0.626325i
$719$			4.43566e24i			0.0863770i	0.999067	+	0.0431885i	$0.0137516\pi$
$719$			4.43566e24i			0.0863770i	−0.999067	+	0.0431885i	$0.986248\pi$
$720$	2.30187e24	−	4.70899e24i	0.0442679	−	0.0905598i
$721$	−1.20707e25			−0.229253
$722$	1.45428e25	+	1.45428e25i	0.272780	+	0.272780i
$723$	−5.10125e25	+	5.10125e25i	−0.945000	+	0.945000i
$724$		−	3.23042e25i		−	0.591033i
$725$	−5.92883e25	+	4.61529e25i	−1.07134	+	0.833983i
$726$	−2.46586e25			−0.440087
$727$	−4.56295e25	−	4.56295e25i	−0.804333	−	0.804333i	0.179436	−	0.983770i	$-0.442573\pi$
$727$	−4.56295e25	−	4.56295e25i	−0.804333	−	0.804333i	−0.983770	+	0.179436i	$0.942573\pi$
$728$	1.80362e24	−	1.80362e24i	0.0314024	−	0.0314024i
$729$			5.88772e25i			1.01251i
$730$	−3.63214e25	−	1.77548e25i	−0.616960	−	0.301585i
$731$	5.45657e25			0.915511
$732$	1.55137e25	+	1.55137e25i	0.257109	+	0.257109i
$733$	2.22989e25	−	2.22989e25i	0.365045	−	0.365045i	−0.500621	−	0.865666i	$-0.666895\pi$
$733$	2.22989e25	−	2.22989e25i	0.365045	−	0.365045i	0.865666	+	0.500621i	$0.166895\pi$
$734$		−	7.40710e24i		−	0.119780i
$735$	−1.53921e25	−	4.48303e25i	−0.245874	−	0.716120i
$736$	−4.49696e24			−0.0709609
$737$	−2.31542e25	−	2.31542e25i	−0.360929	−	0.360929i
$738$	1.32658e24	−	1.32658e24i	0.0204280	−	0.0204280i
$739$			1.03811e26i			1.57923i	0.613605	+	0.789613i	$0.289719\pi$
$739$			1.03811e26i			1.57923i	−0.613605	+	0.789613i	$0.710281\pi$
$740$	5.50017e25	−	1.88844e25i	0.826591	−	0.283803i
$741$	3.12330e25			0.463714
$742$	1.95006e24	+	1.95006e24i	0.0286031	+	0.0286031i
$743$	5.48078e25	−	5.48078e25i	0.794224	−	0.794224i	−0.187954	−	0.982178i	$-0.560186\pi$
$743$	5.48078e25	−	5.48078e25i	0.794224	−	0.794224i	0.982178	+	0.187954i	$0.0601856\pi$
$744$			1.20499e25i			0.172515i
$745$	1.31480e25	−	2.68972e25i	0.185974	−	0.380452i
$746$	3.76592e25			0.526286
$747$	4.77941e23	+	4.77941e23i	0.00659917	+	0.00659917i
$748$	−9.69578e24	+	9.69578e24i	−0.132272	+	0.132272i
$749$		−	2.39940e24i		−	0.0323419i
$750$	8.42147e24	+	4.01418e25i	0.112160	+	0.534621i
$751$	1.01713e26			1.33849			0.669247	−	0.743040i	$-0.266617\pi$
$751$	1.01713e26			1.33849			0.669247	+	0.743040i	$0.266617\pi$
$752$	2.17379e25	+	2.17379e25i	0.282655	+	0.282655i
$753$	3.11580e25	−	3.11580e25i	0.400327	−	0.400327i
$754$			6.73321e25i			0.854831i
$755$	−1.54362e25	−	7.54562e24i	−0.193651	−	0.0946613i
$756$	6.16772e24			0.0764589
$757$	1.14042e25	+	1.14042e25i	0.139702	+	0.139702i	0.773499	−	0.633797i	$-0.218505\pi$
$757$	1.14042e25	+	1.14042e25i	0.139702	+	0.139702i	−0.633797	+	0.773499i	$0.718505\pi$
$758$	−3.67676e25	+	3.67676e25i	−0.445085	+	0.445085i
$759$		−	1.14285e25i		−	0.136714i
$760$	−6.54702e24	−	1.90685e25i	−0.0773965	−	0.225421i
$761$	3.88248e25			0.453573			0.226786	−	0.973945i	$-0.427178\pi$
$761$	3.88248e25			0.453573			0.226786	+	0.973945i	$0.427178\pi$
$762$	4.87768e25	+	4.87768e25i	0.563143	+	0.563143i
$763$	−1.23432e25	+	1.23432e25i	−0.140833	+	0.140833i
$764$			5.97371e25i			0.673603i
$765$	−2.90392e25	+	9.97036e24i	−0.323617	+	0.111111i
$766$	−7.63634e25			−0.841059
$767$	−3.06736e25	−	3.06736e25i	−0.333892	−	0.333892i
$768$	3.17344e24	−	3.17344e24i	0.0341412	−	0.0341412i
$769$		−	3.02079e25i		−	0.321206i	−0.987019	−	0.160603i	$-0.948656\pi$
$769$		−	3.02079e25i		−	0.321206i	0.987019	−	0.160603i	$-0.0513439\pi$
$770$	1.83763e24	−	3.75928e24i	0.0193126	−	0.0395083i
$771$	7.11899e25			0.739484
$772$	−4.90468e25	−	4.90468e25i	−0.503564	−	0.503564i
$773$	9.75011e24	−	9.75011e24i	0.0989450	−	0.0989450i	−0.655901	−	0.754846i	$-0.727711\pi$
$773$	9.75011e24	−	9.75011e24i	0.0989450	−	0.0989450i	0.754846	+	0.655901i	$0.227711\pi$
$774$			3.06642e25i			0.307584i
$775$	3.91321e25	+	5.02694e25i	0.387988	+	0.498412i
$776$	2.67141e25			0.261810
$777$	1.39037e25	+	1.39037e25i	0.134692	+	0.134692i
$778$	−5.51158e25	+	5.51158e25i	−0.527788	+	0.527788i
$779$		−	7.21620e24i		−	0.0683079i
$780$	3.30222e25	+	1.61421e25i	0.308997	+	0.151046i
$781$	−9.11382e25			−0.843027
$782$	1.86265e25	+	1.86265e25i	0.170322	+	0.170322i
$783$	−1.15126e26	+	1.15126e26i	−1.04068	+	1.04068i
$784$			2.74192e25i			0.245025i
$785$	9.79416e24	+	2.85260e25i	0.0865247	+	0.252008i
$786$	−4.43208e24			−0.0387083
$787$	1.75293e25	+	1.75293e25i	0.151353	+	0.151353i	0.778722	−	0.627369i	$-0.215868\pi$
$787$	1.75293e25	+	1.75293e25i	0.151353	+	0.151353i	−0.627369	+	0.778722i	$0.715868\pi$
$788$	3.67782e25	−	3.67782e25i	0.313946	−	0.313946i
$789$		−	1.46844e26i		−	1.23926i
$790$	2.52276e25	−	8.66167e24i	0.210490	−	0.0722700i
$791$	−1.99072e25			−0.164219
$792$	−5.44872e24	−	5.44872e24i	−0.0444394	−	0.0444394i
$793$	7.35004e25	−	7.35004e25i	0.592695	−	0.592695i
$794$		−	1.34897e26i		−	1.07552i
$795$	−1.74527e25	+	3.57034e25i	−0.137581	+	0.281452i
$796$	−1.14147e26			−0.889704
$797$	3.27012e25	+	3.27012e25i	0.252022	+	0.252022i	0.821799	−	0.569777i	$-0.192971\pi$
$797$	3.27012e25	+	3.27012e25i	0.252022	+	0.252022i	−0.569777	+	0.821799i	$0.692971\pi$
$798$	4.82029e24	−	4.82029e24i	0.0367322	−	0.0367322i
$799$		−	1.80078e26i		−	1.35688i
$800$	2.93308e24	−	2.35446e25i	0.0218531	−	0.175421i
$801$	−8.34976e25			−0.615150
$802$	−4.25277e25	−	4.25277e25i	−0.309815	−	0.309815i
$803$	−4.20271e25	+	4.20271e25i	−0.302754	+	0.302754i
$804$		−	6.27797e25i		−	0.447214i
$805$	−7.22195e24	−	3.53027e24i	−0.0508735	−	0.0248682i
$806$	5.70896e25			0.397687
$807$	−3.24891e25	−	3.24891e25i	−0.223808	−	0.223808i
$808$	4.29916e25	−	4.29916e25i	0.292875	−	0.292875i
$809$		−	9.27570e25i		−	0.624899i	−0.949934	−	0.312450i	$-0.898850\pi$
$809$		−	9.27570e25i		−	0.624899i	0.949934	−	0.312450i	$-0.101150\pi$
$810$	1.49656e25	+	4.35882e25i	0.0997079	+	0.290405i
$811$	−2.05117e26			−1.35149			−0.675747	−	0.737134i	$-0.736179\pi$
$811$	−2.05117e26			−1.35149			−0.675747	+	0.737134i	$0.736179\pi$
$812$	1.03916e25	+	1.03916e25i	0.0677137	+	0.0677137i
$813$	−8.83101e25	+	8.83101e25i	−0.569109	+	0.569109i
$814$		−	8.54928e25i		−	0.544891i
$815$	4.39111e25	−	1.50765e25i	0.276794	−	0.0950347i
$816$	−2.62889e25			−0.163893
$817$	8.34023e25	+	8.34023e25i	0.514256	+	0.514256i
$818$	7.90438e25	−	7.90438e25i	0.482046	−	0.482046i
$819$		−	8.39653e24i		−	0.0506459i
$820$	3.72953e24	−	7.62958e24i	0.0222500	−	0.0455172i
$821$	6.54870e25			0.386427			0.193213	−	0.981157i	$-0.438109\pi$
$821$	6.54870e25			0.386427			0.193213	+	0.981157i	$0.438109\pi$
$822$	2.99288e25	+	2.99288e25i	0.174680	+	0.174680i
$823$	3.03455e25	−	3.03455e25i	0.175185	−	0.175185i	−0.614068	−	0.789253i	$-0.710468\pi$
$823$	3.03455e25	−	3.03455e25i	0.175185	−	0.175185i	0.789253	+	0.614068i	$0.210468\pi$
$824$			1.00622e26i			0.574575i
$825$	5.98358e25	+	7.45407e24i	0.337968	+	0.0421025i
$826$	−9.46788e24			−0.0528972
$827$	−1.91855e25	−	1.91855e25i	−0.106029	−	0.106029i	0.652102	−	0.758131i	$-0.273887\pi$
$827$	−1.91855e25	−	1.91855e25i	−0.106029	−	0.106029i	−0.758131	+	0.652102i	$0.773887\pi$
$828$	−1.04675e25	+	1.04675e25i	−0.0572231	+	0.0572231i
$829$			3.69347e26i			1.99730i	0.0519126	+	0.998652i	$0.483468\pi$
$829$			3.69347e26i			1.99730i	−0.0519126	+	0.998652i	$0.516532\pi$
$830$	2.74880e24	+	1.34368e24i	0.0147042	+	0.00718776i
$831$	3.09062e25			0.163545
$832$	−1.50350e25	−	1.50350e25i	−0.0787033	−	0.0787033i
$833$	1.13571e26	−	1.13571e26i	0.588116	−	0.588116i
$834$		−	1.40669e26i		−	0.720616i
$835$	8.85111e25	+	2.57793e26i	0.448559	+	1.30645i
$836$	−2.96395e25			−0.148598
$837$	9.76128e25	+	9.76128e25i	0.484147	+	0.484147i
$838$	4.24827e25	−	4.24827e25i	0.208457	−	0.208457i
$839$		−	2.86001e26i		−	1.38838i	−0.719790	−	0.694192i	$-0.755762\pi$
$839$		−	2.86001e26i		−	1.38838i	0.719790	−	0.694192i	$-0.244238\pi$
$840$	7.58767e24	−	2.60516e24i	0.0364414	−	0.0125118i
$841$	−1.77477e26			−0.843294
$842$	−1.68917e26	−	1.68917e26i	−0.794079	−	0.794079i
$843$	−1.75328e26	+	1.75328e26i	−0.815460	+	0.815460i
$844$			1.94981e26i			0.897245i
$845$	−1.99804e25	+	4.08743e25i	−0.0909689	+	0.186097i
$846$	1.01198e26			0.455869
$847$	1.80302e25	+	1.80302e25i	0.0803617	+	0.0803617i
$848$	1.62557e25	−	1.62557e25i	0.0716874	−	0.0716874i
$849$			1.15689e26i			0.504804i
$850$	−1.09671e26	+	8.53734e25i	−0.473502	+	0.368597i
$851$	−1.64240e26			−0.701638
$852$	−1.23555e26	−	1.23555e26i	−0.522281	−	0.522281i
$853$	2.62622e26	−	2.62622e26i	1.09848	−	1.09848i	0.103887	−	0.994589i	$-0.466872\pi$
$853$	2.62622e26	−	2.62622e26i	1.09848	−	1.09848i	0.994589	−	0.103887i	$-0.0331280\pi$
$854$		−	2.26871e25i		−	0.0938983i
$855$	−5.96251e25	−	2.91462e25i	−0.244193	−	0.119368i
$856$	−2.00014e25			−0.0810582
$857$	2.79490e26	+	2.79490e26i	1.12083	+	1.12083i	0.991617	+	0.129211i	$0.0412444\pi$
$857$	2.79490e26	+	2.79490e26i	1.12083	+	1.12083i	0.129211	+	0.991617i	$0.458756\pi$
$858$	3.82096e25	−	3.82096e25i	0.151631	−	0.151631i
$859$			1.89534e26i			0.744300i	0.928173	+	0.372150i	$0.121379\pi$
$859$			1.89534e26i			0.744300i	−0.928173	+	0.372150i	$0.878621\pi$
$860$	4.50754e25	+	1.31285e26i	0.175168	+	0.510185i
$861$	2.87144e24			0.0110426
$862$	1.21691e26	+	1.21691e26i	0.463119	+	0.463119i
$863$	1.70345e26	−	1.70345e26i	0.641552	−	0.641552i	−0.309385	−	0.950937i	$-0.600123\pi$
$863$	1.70345e26	−	1.70345e26i	0.641552	−	0.641552i	0.950937	+	0.309385i	$0.100123\pi$
$864$		−	5.14141e25i		−	0.191628i
$865$	1.14090e26	−	3.91720e25i	0.420828	−	0.144488i
$866$	1.97814e26			0.722097
$867$	−4.23171e25	−	4.23171e25i	−0.152878	−	0.152878i
$868$	8.81080e24	−	8.81080e24i	0.0315020	−	0.0315020i
$869$		−	3.92129e25i		−	0.138756i
$870$	−9.30027e25	+	1.90258e26i	−0.325704	+	0.666299i
$871$	−2.97435e26			−1.03093
$872$	1.02893e26	+	1.02893e26i	0.352969	+	0.352969i
$873$	6.21822e25	−	6.21822e25i	0.211124	−	0.211124i
$874$			5.69404e25i			0.191345i
$875$	2.31937e25	−	3.55091e25i	0.0771432	−	0.118105i
$876$	−1.13951e26			−0.375131
$877$	1.79784e26	+	1.79784e26i	0.585807	+	0.585807i	0.936493	−	0.350686i	$-0.114052\pi$
$877$	1.79784e26	+	1.79784e26i	0.585807	+	0.585807i	−0.350686	+	0.936493i	$0.614052\pi$
$878$	4.64870e25	−	4.64870e25i	0.149927	−	0.149927i
$879$		−	2.94906e26i		−	0.941420i
$880$	−3.13374e25	−	1.53185e25i	−0.0990191	−	0.0484030i
$881$	5.75150e25			0.179886			0.0899431	−	0.995947i	$-0.471331\pi$
$881$	5.75150e25			0.179886			0.0899431	+	0.995947i	$0.471331\pi$
$882$	6.38234e25	+	6.38234e25i	0.197589	+	0.197589i
$883$	−3.09372e26	+	3.09372e26i	−0.948057	+	0.948057i	−0.998716	−	0.0506591i	$-0.983868\pi$
$883$	−3.09372e26	+	3.09372e26i	−0.948057	+	0.948057i	0.0506591	+	0.998716i	$0.483868\pi$
$884$			1.24551e26i			0.377812i
$885$	−4.43052e25	−	1.29041e26i	−0.133035	−	0.387471i
$886$	2.64620e26			0.786538
$887$	−3.71318e26	−	3.71318e26i	−1.09253	−	1.09253i	−0.995258	−	0.0972739i	$-0.968988\pi$
$887$	−3.71318e26	−	3.71318e26i	−1.09253	−	1.09253i	−0.0972739	−	0.995258i	$-0.531012\pi$
$888$	1.15902e26	−	1.15902e26i	0.337577	−	0.337577i
$889$		−	7.13304e25i		−	0.205664i
$890$	−3.57483e26	+	1.22739e26i	−1.02034	+	0.350325i
$891$	6.77519e25			0.191435
$892$	−1.44446e26	−	1.44446e26i	−0.404038	−	0.404038i
$893$	2.75245e26	−	2.75245e26i	0.762177	−	0.762177i
$894$		−	8.43846e25i		−	0.231327i
$895$	1.29067e26	−	2.64034e26i	0.350273	−	0.716561i
$896$	−4.64079e24			−0.0124686
$897$	−7.34045e25	−	7.34045e25i	−0.195250	−	0.195250i
$898$	−2.99200e25	+	2.99200e25i	−0.0787907	+	0.0787907i
$899$			3.28922e26i			0.857543i
$900$	−4.79772e25	−	6.16317e25i	−0.123837	−	0.159082i
$901$	−1.34663e26			−0.344132
$902$	−8.82810e24	−	8.82810e24i	−0.0223361	−	0.0223361i
$903$	−3.31871e25	+	3.31871e25i	−0.0831341	+	0.0831341i
$904$			1.65947e26i			0.411579i
$905$	−4.32466e26	−	2.11400e26i	−1.06198	−	0.519121i
$906$	−4.84282e25			−0.117746
$907$	−2.51976e25	−	2.51976e25i	−0.0606587	−	0.0606587i	0.676127	−	0.736785i	$-0.263657\pi$
$907$	−2.51976e25	−	2.51976e25i	−0.0606587	−	0.0606587i	−0.736785	+	0.676127i	$0.763657\pi$
$908$	−1.26393e26	+	1.26393e26i	−0.301266	+	0.301266i
$909$		−	2.00142e26i		−	0.472350i
$910$	−1.23426e25	−	3.59486e25i	−0.0288427	−	0.0840058i
$911$	−1.16243e26			−0.268968			−0.134484	−	0.990916i	$-0.542938\pi$
$911$	−1.16243e26			−0.268968			−0.134484	+	0.990916i	$0.542938\pi$
$912$	−4.01819e25	−	4.01819e25i	−0.0920614	−	0.0920614i
$913$	3.18060e24	−	3.18060e24i	0.00721560	−	0.00721560i
$914$			5.11348e24i			0.0114869i
$915$	3.09210e26	−	1.06165e26i	0.687803	−	0.236151i
$916$	1.39075e26			0.306329
$917$	3.24070e24	+	3.24070e24i	0.00706830	+	0.00706830i
$918$	−2.12959e26	+	2.12959e26i	−0.459951	+	0.459951i
$919$		−	8.66154e26i		−	1.85249i	−0.376923	−	0.926244i	$-0.623018\pi$
$919$		−	8.66154e26i		−	1.85249i	0.376923	−	0.926244i	$-0.376982\pi$
$920$	−2.94283e25	+	6.02022e25i	−0.0623269	+	0.127503i
$921$	5.25473e25			0.110208
$922$	−1.91684e26	−	1.91684e26i	−0.398114	−	0.398114i
$923$	−5.85375e26	+	5.85375e26i	−1.20398	+	1.20398i
$924$		−	1.17940e25i		−	0.0240223i
$925$	1.07123e26	−	8.59905e26i	0.216076	−	1.73450i
$926$	5.60824e25			0.112028
$927$	2.34216e26	+	2.34216e26i	0.463339	+	0.463339i
$928$	8.66242e25	−	8.66242e25i	0.169710	−	0.169710i
$929$			5.84258e26i			1.13361i	0.823852	+	0.566805i	$0.191821\pi$
$929$			5.84258e26i			1.13361i	−0.823852	+	0.566805i	$0.808179\pi$
$930$	1.61316e26	+	7.88552e25i	0.309978	+	0.151525i
$931$	3.47181e26			0.660707
$932$	−6.45355e25	−	6.45355e25i	−0.121634	−	0.121634i
$933$	−2.84913e26	+	2.84913e26i	−0.531835	+	0.531835i
$934$			4.26364e26i			0.788240i
$935$	6.63507e25	+	1.93250e26i	0.121490	+	0.353847i
$936$	−6.99935e25			−0.126933
$937$	−2.75920e25	−	2.75920e25i	−0.0495594	−	0.0495594i	0.681893	−	0.731452i	$-0.261157\pi$
$937$	−2.75920e25	−	2.75920e25i	−0.0495594	−	0.0495594i	−0.731452	+	0.681893i	$0.761157\pi$
$938$	−4.59041e25	+	4.59041e25i	−0.0816631	+	0.0816631i
$939$			2.83739e26i			0.499952i
$940$	4.33266e26	−	1.48758e26i	0.756143	−	0.259615i
$941$	4.04959e26			0.700011			0.350005	−	0.936748i	$-0.386180\pi$
$941$	4.04959e26			0.700011			0.350005	+	0.936748i	$0.386180\pi$
$942$	6.01110e25	+	6.01110e25i	0.102919	+	0.102919i
$943$	−1.69596e25	+	1.69596e25i	−0.0287615	+	0.0287615i
$944$			7.89244e25i			0.132575i
$945$	4.03618e25	−	8.25691e25i	0.0671560	−	0.137383i
$946$	2.04064e26			0.336315
$947$	6.83274e26	+	6.83274e26i	1.11544	+	1.11544i	0.992402	+	0.123034i	$0.0392625\pi$
$947$	6.83274e26	+	6.83274e26i	1.11544	+	1.11544i	0.123034	+	0.992402i	$0.460737\pi$
$948$	5.31605e25	−	5.31605e25i	0.0859634	−	0.0859634i
$949$			5.39875e26i			0.864763i
$950$	−2.98121e26	−	3.71385e25i	−0.473020	−	0.0589267i
$951$	8.38136e26			1.31732
$952$	1.92223e25	+	1.92223e25i	0.0299276	+	0.0299276i
$953$	−6.05913e26	+	6.05913e26i	−0.934488	+	0.934488i	−0.997982	−	0.0634940i	$-0.979776\pi$
$953$	−6.05913e26	+	6.05913e26i	−0.934488	+	0.934488i	0.0634940	+	0.997982i	$0.479776\pi$
$954$		−	7.56764e25i		−	0.115618i
$955$	7.99719e26	+	3.90923e26i	1.21034	+	0.591644i
$956$	6.63355e26			0.994547
$957$	2.20145e26	+	2.20145e26i	0.326965	+	0.326965i
$958$	2.70710e26	−	2.70710e26i	0.398304	−	0.398304i
$959$		−	4.37675e25i		−	0.0637946i
$960$	−2.17167e25	−	6.32509e25i	−0.0313582	−	0.0913326i
$961$	−4.20167e26			−0.601051
$962$	−5.49114e26	−	5.49114e26i	−0.778192	−	0.778192i
$963$	−4.65571e25	+	4.65571e25i	−0.0653656	+	0.0653656i
$964$		−	6.21866e26i		−	0.864974i
$965$	−9.77569e26	+	3.35640e26i	−1.34711	+	0.462517i
$966$	−2.26575e25			−0.0309326
$967$	−7.67425e26	−	7.67425e26i	−1.03800	−	1.03800i	−0.999249	−	0.0387519i	$-0.987662\pi$
$967$	−7.67425e26	−	7.67425e26i	−1.03800	−	1.03800i	−0.0387519	−	0.999249i	$-0.512338\pi$
$968$	1.50300e26	−	1.50300e26i	0.201410	−	0.201410i
$969$			3.32869e26i			0.441936i
$970$	1.74819e26	−	3.57630e26i	0.229955	−	0.470423i
$971$	1.60397e26			0.209037			0.104519	−	0.994523i	$-0.466670\pi$
$971$	1.60397e26			0.209037			0.104519	+	0.994523i	$0.466670\pi$
$972$	−2.04964e26	−	2.04964e26i	−0.264656	−	0.264656i
$973$	−1.02856e26	+	1.02856e26i	−0.131587	+	0.131587i
$974$			1.04554e26i			0.132528i
$975$	4.32198e26	−	3.36444e26i	0.542802	−	0.422544i
$976$	−1.89120e26			−0.235336
$977$	−5.47273e26	−	5.47273e26i	−0.674766	−	0.674766i	0.284045	−	0.958811i	$-0.408323\pi$
$977$	−5.47273e26	−	5.47273e26i	−0.674766	−	0.674766i	−0.958811	+	0.284045i	$0.908323\pi$
$978$	9.25311e25	−	9.25311e25i	0.113042	−	0.113042i
$979$			5.55659e26i			0.672612i
$980$	3.67070e26	+	1.79433e26i	0.440264	+	0.215212i
$981$	4.79005e26			0.569271
$982$	1.30598e25	+	1.30598e25i	0.0153792	+	0.0153792i
$983$	−2.62584e26	+	2.62584e26i	−0.306399	+	0.306399i	−0.843511	−	0.537112i	$-0.819515\pi$
$983$	−2.62584e26	+	2.62584e26i	−0.306399	+	0.306399i	0.537112	+	0.843511i	$0.319515\pi$
$984$		−	2.39363e25i		−	0.0276759i
$985$	−2.51683e26	−	7.33039e26i	−0.288355	−	0.839849i
$986$	−7.17599e26			−0.814685
$987$	1.09524e26	+	1.09524e26i	0.123213	+	0.123213i
$988$	−1.90372e26	+	1.90372e26i	−0.212223	+	0.212223i
$989$		−	3.92027e26i		−	0.433062i
$990$	−1.08600e26	+	3.72870e25i	−0.118882	+	0.0408170i
$991$	1.05306e25			0.0114232			0.00571162	−	0.999984i	$-0.498182\pi$
$991$	1.05306e25			0.0114232			0.00571162	+	0.999984i	$0.498182\pi$
$992$	−7.34469e25	−	7.34469e25i	−0.0789530	−	0.0789530i
$993$	2.80236e26	−	2.80236e26i	0.298525	−	0.298525i
$994$			1.80685e26i			0.190741i
$995$	−7.46981e26	+	1.52812e27i	−0.781451	+	1.59863i
$996$	8.62382e24			0.00894058
$997$	−5.23985e26	−	5.23985e26i	−0.538347	−	0.538347i	0.384696	−	0.923043i	$-0.374306\pi$
$997$	−5.23985e26	−	5.23985e26i	−0.538347	−	0.538347i	−0.923043	+	0.384696i	$0.874306\pi$
$998$	−3.84201e26	+	3.84201e26i	−0.391186	+	0.391186i
$999$		−	1.87777e27i		−	1.89475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.19.c.a.7.3	yes	8
3.2	odd	2		90.19.g.a.37.1		8
5.2	odd	4		50.19.c.c.43.2		8
5.3	odd	4	inner	10.19.c.a.3.3	✓	8
5.4	even	2		50.19.c.c.7.2		8
15.8	even	4		90.19.g.a.73.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.19.c.a.3.3	✓	8	5.3	odd	4	inner
10.19.c.a.7.3	yes	8	1.1	even	1	trivial
50.19.c.c.7.2		8	5.4	even	2
50.19.c.c.43.2		8	5.2	odd	4
90.19.g.a.37.1		8	3.2	odd	2
90.19.g.a.73.1		8	15.8	even	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(256.000 + 256.000i) q^{2} +(10752.0 - 10752.0i) q^{3} +131072. i q^{4} +(1.75470e6 + 857742. i) q^{5} +5.50503e6 q^{6} +(-4.02524e6 - 4.02524e6i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +1.56209e8i q^{9} +O(q^{10})\)	\(q+(256.000 + 256.000i) q^{2} +(10752.0 - 10752.0i) q^{3} +131072. i q^{4} +(1.75470e6 + 857742. i) q^{5} +5.50503e6 q^{6} +(-4.02524e6 - 4.02524e6i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +1.56209e8i q^{9} +(2.29622e8 + 6.68785e8i) q^{10} +1.03954e9 q^{11} +(1.40929e9 + 1.40929e9i) q^{12} +(6.67687e9 - 6.67687e9i) q^{13} -2.06092e9i q^{14} +(2.80890e10 - 9.64413e9i) q^{15} -1.71799e10 q^{16} +(7.11595e10 + 7.11595e10i) q^{17} +(-3.99894e10 + 3.99894e10i) q^{18} +2.17531e11i q^{19} +(-1.12426e11 + 2.29992e11i) q^{20} -8.65589e10 q^{21} +(2.66121e11 + 2.66121e11i) q^{22} +(5.11245e11 - 5.11245e11i) q^{23} +7.21556e11i q^{24} +(2.34326e12 + 3.01016e12i) q^{25} +3.41856e12 q^{26} +(5.84511e12 + 5.84511e12i) q^{27} +(5.27596e11 - 5.27596e11i) q^{28} +1.96961e13i q^{29} +(9.65969e12 + 4.72190e12i) q^{30} +1.66999e13 q^{31} +(-4.39805e12 - 4.39805e12i) q^{32} +(1.11771e13 - 1.11771e13i) q^{33} +3.64337e13i q^{34} +(-3.61048e12 - 1.05157e13i) q^{35} -2.04746e13 q^{36} +(-1.60627e14 - 1.60627e14i) q^{37} +(-5.56879e13 + 5.56879e13i) q^{38} -1.43580e14i q^{39} +(-8.76590e13 + 3.00970e13i) q^{40} -3.31732e13 q^{41} +(-2.21591e13 - 2.21591e13i) q^{42} +(3.83404e14 - 3.83404e14i) q^{43} +1.36254e14i q^{44} +(-1.33987e14 + 2.74099e14i) q^{45} +2.61758e14 q^{46} +(-1.26531e15 - 1.26531e15i) q^{47} +(-1.84718e14 + 1.84718e14i) q^{48} -1.59601e15i q^{49} +(-1.70727e14 + 1.37047e15i) q^{50} +1.53022e15 q^{51} +(8.75151e14 + 8.75151e14i) q^{52} +(-9.46206e14 + 9.46206e14i) q^{53} +2.99270e15i q^{54} +(1.82408e15 + 8.91654e14i) q^{55} +2.70129e14 q^{56} +(2.33890e15 + 2.33890e15i) q^{57} +(-5.04219e15 + 5.04219e15i) q^{58} -4.59400e15i q^{59} +(1.26408e15 + 3.68169e15i) q^{60} +1.10082e16 q^{61} +(4.27517e15 + 4.27517e15i) q^{62} +(6.28777e14 - 6.28777e14i) q^{63} -2.25180e15i q^{64} +(1.74429e16 - 5.98889e15i) q^{65} +5.72268e15 q^{66} +(-2.22736e16 - 2.22736e16i) q^{67} +(-9.32702e15 + 9.32702e15i) q^{68} -1.09938e16i q^{69} +(1.76774e15 - 3.61630e15i) q^{70} -8.76720e16 q^{71} +(-5.24149e15 - 5.24149e15i) q^{72} +(-4.04287e16 + 4.04287e16i) q^{73} -8.22412e16i q^{74} +(5.75600e16 + 7.17057e15i) q^{75} -2.85122e16 q^{76} +(-4.18438e15 - 4.18438e15i) q^{77} +(3.67564e16 - 3.67564e16i) q^{78} -3.77215e16i q^{79} +(-3.01455e16 - 1.47359e16i) q^{80} +6.51751e16 q^{81} +(-8.49234e15 - 8.49234e15i) q^{82} +(3.05964e15 - 3.05964e15i) q^{83} -1.13455e16i q^{84} +(6.38272e16 + 1.85900e17i) q^{85} +1.96303e17 q^{86} +(2.11772e17 + 2.11772e17i) q^{87} +(-3.48811e16 + 3.48811e16i) q^{88} +5.34526e17i q^{89} +(-1.04470e17 + 3.58689e16i) q^{90} -5.37520e16 q^{91} +(6.70100e16 + 6.70100e16i) q^{92} +(1.79558e17 - 1.79558e17i) q^{93} -6.47840e17i q^{94} +(-1.86585e17 + 3.81702e17i) q^{95} -9.45758e16 q^{96} +(-3.98072e17 - 3.98072e17i) q^{97} +(4.08578e17 - 4.08578e17i) q^{98} +1.62385e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8}+O(q^{10}) \) 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8	\( 8 q + 2048 q^{2} + 37026 q^{3} - 3132450 q^{5} + 18957312 q^{6} - 43579766 q^{7} - 268435456 q^{8} - 361676800 q^{10} - 2678523284 q^{11} + 4853071872 q^{12} - 13618988004 q^{13} - 44901376950 q^{15} - 137438953472 q^{16} + 131385428404 q^{17} + 219304891392 q^{18} + 225397964800 q^{20} - 2519443347204 q^{21} - 685701960704 q^{22} + 2992780401346 q^{23} + 5025487502500 q^{25} - 6972921858048 q^{26} - 36827718166440 q^{27} + 5712087089152 q^{28} - 6097905484800 q^{30} - 41290623629644 q^{31} - 35184372088832 q^{32} + 3721928304252 q^{33} + 259024770537850 q^{35} + 112284104392704 q^{36} - 191725492483296 q^{37} + 93053262223360 q^{38} + 162809459507200 q^{40} + 538572935041756 q^{41} - 644977496884224 q^{42} + 278176126066386 q^{43} - 649523899006350 q^{45} + 15\!\cdots\!52 q^{46}+ \cdots + 14\!\cdots\!68 q^{98}+O(q^{100}) \) 8 * q + 2048 * q^2 + 37026 * q^3 - 3132450 * q^5 + 18957312 * q^6 - 43579766 * q^7 - 268435456 * q^8 - 361676800 * q^10 - 2678523284 * q^11 + 4853071872 * q^12 - 13618988004 * q^13 - 44901376950 * q^15 - 137438953472 * q^16 + 131385428404 * q^17 + 219304891392 * q^18 + 225397964800 * q^20 - 2519443347204 * q^21 - 685701960704 * q^22 + 2992780401346 * q^23 + 5025487502500 * q^25 - 6972921858048 * q^26 - 36827718166440 * q^27 + 5712087089152 * q^28 - 6097905484800 * q^30 - 41290623629644 * q^31 - 35184372088832 * q^32 + 3721928304252 * q^33 + 259024770537850 * q^35 + 112284104392704 * q^36 - 191725492483296 * q^37 + 93053262223360 * q^38 + 162809459507200 * q^40 + 538572935041756 * q^41 - 644977496884224 * q^42 + 278176126066386 * q^43 - 649523899006350 * q^45 + 1532303565489152 * q^46 - 634311997628766 * q^47 - 636101836406784 * q^48 + 190733484160000 * q^50 + 8385208158427476 * q^51 - 1785067995660288 * q^52 - 12985998337176064 * q^53 + 7061537235641100 * q^55 + 2924588589645824 * q^56 - 14364945328494720 * q^57 - 3324209031454720 * q^58 + 2763185671372800 * q^60 + 6032452171830396 * q^61 - 10570399649188864 * q^62 - 67339871781169614 * q^63 + 116629895397895800 * q^65 + 1905627291777024 * q^66 - 43112377024267886 * q^67 - 17220950871769088 * q^68 + 57331386108262400 * q^70 - 20683118221989964 * q^71 + 28744730724532224 * q^72 - 85903701564675544 * q^73 + 487247617377746250 * q^75 + 47643270258360320 * q^76 - 31041870745561732 * q^77 - 251885813313555456 * q^78 + 53815081225420800 * q^80 - 598065530496252012 * q^81 + 137874671370689536 * q^82 + 247117472833336746 * q^83 - 265705533435464900 * q^85 + 142426176545989632 * q^86 - 431292883391162160 * q^87 + 89876327393394688 * q^88 - 1156199666753126400 * q^90 - 346988460443022684 * q^91 + 392269712765222912 * q^92 + 2117557938231099132 * q^93 - 1658756785135297000 * q^95 - 325684140240273408 * q^96 + 1905016584439493544 * q^97 + 1418620057223277568 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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