LMFDB - Embedded newform 98.13.d.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,13,Mod(19,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not 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:	$89.5713940931$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 2204556 x^{14} - 87623088 x^{13} + 1948666431190 x^{12} + 195028079162640 x^{11} + \cdots + 24\!\cdots\!25 $ x^16 - 8x^15 - 2204556x^14 - 87623088x^13 + 1948666431190x^12 + 195028079162640x^11 - 880028445307457796x^10 - 151849761581608663584x^9 + 211028190361269390536623x^8 + 54528516937299786222168960x^7 - 23832744423106572444860463196x^6 - 9141197551096679767843476458896x^5 + 523508549551073444838291611810734x^4 + 566732587460008152706924066069468392x^3 + 73514373627956541910802883627148139944x^2 + 2445664577552004486793879639585121170640*x + 24120197826518417347025654428599335187025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{8}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Root			$657.612 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.13.d.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.6274 - 39.1918i) q^{2} +(-985.668 + 569.076i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(12133.2 + 7005.11i) q^{5} +51506.9i q^{6} -92681.9 q^{8} +(381974. - 661598. i) q^{9} +O(q^{10})$	\(q+(22.6274 - 39.1918i) q^{2} +(-985.668 + 569.076i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(12133.2 + 7005.11i) q^{5} +51506.9i q^{6} -92681.9 q^{8} +(381974. - 661598. i) q^{9} +(549087. - 317015. i) q^{10} +(1.52051e6 + 2.63360e6i) q^{11} +(2.01865e6 + 1.16547e6i) q^{12} +8.06298e6i q^{13} -1.59458e7 q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(2.92560e6 - 1.68910e6i) q^{17} +(-1.72862e7 - 2.99405e7i) q^{18} +(1.38064e7 + 7.97110e6i) q^{19} -2.86929e7i q^{20} +1.37621e8 q^{22} +(6.09340e7 - 1.05541e8i) q^{23} +(9.13536e7 - 5.27430e7i) q^{24} +(-2.39271e7 - 4.14429e7i) q^{25} +(3.16003e8 + 1.82444e8i) q^{26} +2.64628e8i q^{27} +1.10751e9 q^{29} +(-3.60811e8 + 6.24944e8i) q^{30} +(1.49034e8 - 8.60447e7i) q^{31} +(9.49063e7 + 1.64382e8i) q^{32} +(-2.99743e9 - 1.73057e9i) q^{33} -1.52879e8i q^{34} -1.56457e9 q^{36} +(8.32019e8 - 1.44110e9i) q^{37} +(6.24804e8 - 3.60731e8i) q^{38} +(-4.58845e9 - 7.94742e9i) q^{39} +(-1.12453e9 - 6.49247e8i) q^{40} +2.84361e9i q^{41} +3.52303e9 q^{43} +(3.11400e9 - 5.39361e9i) q^{44} +(9.26915e9 - 5.35154e9i) q^{45} +(-2.75756e9 - 4.77623e9i) q^{46} +(4.75293e9 + 2.74410e9i) q^{47} -4.77375e9i q^{48} -2.16563e9 q^{50} +(-1.92245e9 + 3.32978e9i) q^{51} +(1.43007e10 - 8.25649e9i) q^{52} +(3.54944e9 + 6.14782e9i) q^{53} +(1.03713e10 + 5.98786e9i) q^{54} +4.26053e10i q^{55} -1.81446e10 q^{57} +(2.50602e10 - 4.34055e10i) q^{58} +(-2.94046e10 + 1.69768e10i) q^{59} +(1.63285e10 + 2.82817e10i) q^{60} +(-6.13008e10 - 3.53920e10i) q^{61} -7.78787e9i q^{62} +8.58993e9 q^{64} +(-5.64821e10 + 9.78299e10i) q^{65} +(-1.35648e11 + 7.83166e10i) q^{66} +(5.76089e10 + 9.97815e10i) q^{67} +(-5.99163e9 - 3.45927e9i) q^{68} +1.38704e11i q^{69} -5.03166e10 q^{71} +(-3.54021e10 + 6.13182e10i) q^{72} +(6.57596e10 - 3.79663e10i) q^{73} +(-3.76529e10 - 6.52167e10i) q^{74} +(4.71683e10 + 2.72326e10i) q^{75} -3.26496e10i q^{76} -4.15299e11 q^{78} +(-1.28534e11 + 2.22628e11i) q^{79} +(-5.08904e10 + 2.93816e10i) q^{80} +(5.24031e10 + 9.07648e10i) q^{81} +(1.11446e11 + 6.43435e10i) q^{82} -2.08263e9i q^{83} +4.73292e10 q^{85} +(7.97171e10 - 1.38074e11i) q^{86} +(-1.09164e12 + 6.30259e11i) q^{87} +(-1.40924e11 - 2.44087e11i) q^{88} +(7.55454e11 + 4.36162e11i) q^{89} -4.84366e11i q^{90} -2.49586e11 q^{92} +(-9.79319e10 + 1.69623e11i) q^{93} +(2.15093e11 - 1.24184e11i) q^{94} +(1.11677e11 + 1.93430e11i) q^{95} +(-1.87092e11 - 1.08018e11i) q^{96} +8.85916e11i q^{97} +2.32318e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9}+O(q^{10}) $ 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9} + 2290176 q^{10} + 2072088 q^{11} - 27163728 q^{15} - 33554432 q^{16} + 101561040 q^{17} - 4592640 q^{18} - 174931848 q^{19} + 62776320 q^{22} + 25630560 q^{23} - 242221056 q^{24} + 521205808 q^{25} + 1434682368 q^{26} + 532360944 q^{29} - 2151917568 q^{30} - 4583818344 q^{31} - 6054957720 q^{33} - 9675767808 q^{36} + 5764524040 q^{37} + 149506560 q^{38} + 10526083272 q^{39} - 4690280448 q^{40} - 66929432000 q^{43} + 4243636224 q^{44} - 57253352184 q^{45} + 7203213312 q^{46} - 18116171640 q^{47} - 99248080896 q^{50} - 23299256376 q^{51} - 8269578240 q^{52} + 39134161800 q^{53} - 105152205312 q^{54} - 328243960080 q^{57} + 29637396480 q^{58} - 201845459088 q^{59} + 27815657472 q^{60} - 336780254328 q^{61} + 137438953472 q^{64} + 158322703896 q^{65} - 268884080640 q^{66} + 107767119920 q^{67} - 207997009920 q^{68} - 1150259029344 q^{71} - 9405726720 q^{72} + 738414283320 q^{73} + 4902778368 q^{74} - 1537028640000 q^{75} - 786088888320 q^{78} + 227632064768 q^{79} + 76101451776 q^{80} - 391984178400 q^{81} + 302578053120 q^{82} + 710209696080 q^{85} - 38105192448 q^{86} - 1957017683880 q^{87} - 64282951680 q^{88} + 2485007442792 q^{89} - 104982773760 q^{92} - 458668768680 q^{93} + 2021298693120 q^{94} - 186503862960 q^{95} + 496068722688 q^{96} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9 + 2290176 * q^10 + 2072088 * q^11 - 27163728 * q^15 - 33554432 * q^16 + 101561040 * q^17 - 4592640 * q^18 - 174931848 * q^19 + 62776320 * q^22 + 25630560 * q^23 - 242221056 * q^24 + 521205808 * q^25 + 1434682368 * q^26 + 532360944 * q^29 - 2151917568 * q^30 - 4583818344 * q^31 - 6054957720 * q^33 - 9675767808 * q^36 + 5764524040 * q^37 + 149506560 * q^38 + 10526083272 * q^39 - 4690280448 * q^40 - 66929432000 * q^43 + 4243636224 * q^44 - 57253352184 * q^45 + 7203213312 * q^46 - 18116171640 * q^47 - 99248080896 * q^50 - 23299256376 * q^51 - 8269578240 * q^52 + 39134161800 * q^53 - 105152205312 * q^54 - 328243960080 * q^57 + 29637396480 * q^58 - 201845459088 * q^59 + 27815657472 * q^60 - 336780254328 * q^61 + 137438953472 * q^64 + 158322703896 * q^65 - 268884080640 * q^66 + 107767119920 * q^67 - 207997009920 * q^68 - 1150259029344 * q^71 - 9405726720 * q^72 + 738414283320 * q^73 + 4902778368 * q^74 - 1537028640000 * q^75 - 786088888320 * q^78 + 227632064768 * q^79 + 76101451776 * q^80 - 391984178400 * q^81 + 302578053120 * q^82 + 710209696080 * q^85 - 38105192448 * q^86 - 1957017683880 * q^87 - 64282951680 * q^88 + 2485007442792 * q^89 - 104982773760 * q^92 - 458668768680 * q^93 + 2021298693120 * q^94 - 186503862960 * q^95 + 496068722688 * q^96 + 3921180354576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	22.6274	−	39.1918i	0.353553	−	0.612372i
$2$	22.6274	−	39.1918i	0.353553	−	0.612372i
$3$	−985.668	+	569.076i	−1.35208	+	0.780625i	−0.988541	−	0.150953i	$-0.951766\pi$
$3$	−985.668	+	569.076i	−1.35208	+	0.780625i	−0.363542	+	0.931578i	$0.618433\pi$
$4$	−1024.00	−	1773.62i	−0.250000	−	0.433013i
$5$	12133.2	+	7005.11i	0.776526	+	0.448327i	0.835198	−	0.549950i	$-0.185353\pi$
$5$	12133.2	+	7005.11i	0.776526	+	0.448327i	−0.0586719	+	0.998277i	$0.518687\pi$
$6$			51506.9i			1.10397i
$7$		0			0
$7$		0			0
$8$	−92681.9			−0.353553
$9$	381974.	−	661598.i	0.718752	−	1.24491i
$10$	549087.	−	317015.i	0.549087	−	0.317015i
$11$	1.52051e6	+	2.63360e6i	0.858287	+	1.48660i	0.873561	+	0.486714i	$0.161805\pi$
$11$	1.52051e6	+	2.63360e6i	0.858287	+	1.48660i	−0.0152738	+	0.999883i	$0.504862\pi$
$12$	2.01865e6	+	1.16547e6i	0.676041	+	0.390313i
$13$			8.06298e6i			1.67046i	0.549902	+	0.835229i	$0.314665\pi$
$13$			8.06298e6i			1.67046i	−0.549902	+	0.835229i	$0.685335\pi$
$14$		0			0
$15$	−1.59458e7			−1.39990
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$	2.92560e6	−	1.68910e6i	0.121205	−	0.0699779i	−0.438172	−	0.898891i	$-0.644374\pi$
$17$	2.92560e6	−	1.68910e6i	0.121205	−	0.0699779i	0.559377	+	0.828913i	$0.311040\pi$
$18$	−1.72862e7	−	2.99405e7i	−0.508234	−	0.880287i
$19$	1.38064e7	+	7.97110e6i	0.293466	+	0.169433i	0.639504	−	0.768788i	$-0.279140\pi$
$19$	1.38064e7	+	7.97110e6i	0.293466	+	0.169433i	−0.346038	+	0.938221i	$0.612473\pi$
$20$		−	2.86929e7i		−	0.448327i
$21$		0			0
$22$	1.37621e8			1.21380
$23$	6.09340e7	−	1.05541e8i	0.411616	−	0.712940i	−0.583450	−	0.812149i	$-0.698298\pi$
$23$	6.09340e7	−	1.05541e8i	0.411616	−	0.712940i	0.995067	+	0.0992084i	$0.0316310\pi$
$24$	9.13536e7	−	5.27430e7i	0.478033	−	0.275993i
$25$	−2.39271e7	−	4.14429e7i	−0.0980052	−	0.169750i
$26$	3.16003e8	+	1.82444e8i	1.02294	+	0.590596i
$27$			2.64628e8i			0.683052i
$28$		0			0
$29$	1.10751e9			1.86192			0.930960	−	0.365122i	$-0.118973\pi$
$29$	1.10751e9			1.86192			0.930960	+	0.365122i	$0.118973\pi$
$30$	−3.60811e8	+	6.24944e8i	−0.494940	+	0.857262i
$31$	1.49034e8	−	8.60447e7i	0.167925	−	0.0969513i	−0.413682	−	0.910421i	$-0.635758\pi$
$31$	1.49034e8	−	8.60447e7i	0.167925	−	0.0969513i	0.581607	+	0.813470i	$0.302424\pi$
$32$	9.49063e7	+	1.64382e8i	0.0883883	+	0.153093i
$33$	−2.99743e9	−	1.73057e9i	−2.32095	−	1.34000i
$34$		−	1.52879e8i		−	0.0989637i
$35$		0			0
$36$	−1.56457e9			−0.718752
$37$	8.32019e8	−	1.44110e9i	0.324282	−	0.561673i	−0.657085	−	0.753817i	$-0.728211\pi$
$37$	8.32019e8	−	1.44110e9i	0.324282	−	0.561673i	0.981367	+	0.192144i	$0.0615440\pi$
$38$	6.24804e8	−	3.60731e8i	0.207512	−	0.119807i
$39$	−4.58845e9	−	7.94742e9i	−1.30400	−	2.25860i
$40$	−1.12453e9	−	6.49247e8i	−0.274543	−	0.158508i
$41$			2.84361e9i			0.598641i	0.954153	+	0.299321i	$0.0967600\pi$
$41$			2.84361e9i			0.598641i	−0.954153	+	0.299321i	$0.903240\pi$
$42$		0			0
$43$	3.52303e9			0.557321			0.278661	−	0.960390i	$-0.410110\pi$
$43$	3.52303e9			0.557321			0.278661	+	0.960390i	$0.410110\pi$
$44$	3.11400e9	−	5.39361e9i	0.429144	−	0.743299i
$45$	9.26915e9	−	5.35154e9i	1.11626	−	0.644472i
$46$	−2.75756e9	−	4.77623e9i	−0.291057	−	0.504125i
$47$	4.75293e9	+	2.74410e9i	0.440934	+	0.254574i	0.703994	−	0.710206i	$-0.251398\pi$
$47$	4.75293e9	+	2.74410e9i	0.440934	+	0.254574i	−0.263059	+	0.964780i	$0.584732\pi$
$48$		−	4.77375e9i		−	0.390313i
$49$		0			0
$50$	−2.16563e9			−0.138600
$51$	−1.92245e9	+	3.32978e9i	−0.109253	+	0.189232i
$52$	1.43007e10	−	8.25649e9i	0.723330	−	0.417614i
$53$	3.54944e9	+	6.14782e9i	0.160142	+	0.277374i	0.934919	−	0.354860i	$-0.115471\pi$
$53$	3.54944e9	+	6.14782e9i	0.160142	+	0.277374i	−0.774778	+	0.632234i	$0.782138\pi$
$54$	1.03713e10	+	5.98786e9i	0.418282	+	0.241495i
$55$			4.26053e10i			1.53917i
$56$		0			0
$57$	−1.81446e10			−0.529053
$58$	2.50602e10	−	4.34055e10i	0.658288	−	1.14019i
$59$	−2.94046e10	+	1.69768e10i	−0.697114	+	0.402479i	−0.806272	−	0.591545i	$-0.798518\pi$
$59$	−2.94046e10	+	1.69768e10i	−0.697114	+	0.402479i	0.109158	+	0.994024i	$0.465185\pi$
$60$	1.63285e10	+	2.82817e10i	0.349976	+	0.606176i
$61$	−6.13008e10	−	3.53920e10i	−1.18984	−	0.686952i	−0.231567	−	0.972819i	$-0.574385\pi$
$61$	−6.13008e10	−	3.53920e10i	−1.18984	−	0.686952i	−0.958269	+	0.285867i	$0.907719\pi$
$62$		−	7.78787e9i		−	0.137110i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	−5.64821e10	+	9.78299e10i	−0.748912	+	1.29715i
$66$	−1.35648e11	+	7.83166e10i	−1.64116	+	0.947524i
$67$	5.76089e10	+	9.97815e10i	0.636855	+	1.10307i	0.986119	+	0.166041i	$0.0530985\pi$
$67$	5.76089e10	+	9.97815e10i	0.636855	+	1.10307i	−0.349264	+	0.937025i	$0.613568\pi$
$68$	−5.99163e9	−	3.45927e9i	−0.0606026	−	0.0349889i
$69$			1.38704e11i			1.28527i
$70$		0			0
$71$	−5.03166e10			−0.392791			−0.196395	−	0.980525i	$-0.562924\pi$
$71$	−5.03166e10			−0.392791			−0.196395	+	0.980525i	$0.562924\pi$
$72$	−3.54021e10	+	6.13182e10i	−0.254117	+	0.440144i
$73$	6.57596e10	−	3.79663e10i	0.434532	−	0.250877i	−0.266743	−	0.963768i	$-0.585948\pi$
$73$	6.57596e10	−	3.79663e10i	0.434532	−	0.250877i	0.701276	+	0.712890i	$0.252614\pi$
$74$	−3.76529e10	−	6.52167e10i	−0.229302	−	0.397163i
$75$	4.71683e10	+	2.72326e10i	0.265022	+	0.153011i
$76$		−	3.26496e10i		−	0.169433i
$77$		0			0
$78$	−4.15299e11			−1.84414
$79$	−1.28534e11	+	2.22628e11i	−0.528757	+	0.915835i	0.470680	+	0.882304i	$0.344009\pi$
$79$	−1.28534e11	+	2.22628e11i	−0.528757	+	0.915835i	−0.999438	+	0.0335308i	$0.989325\pi$
$80$	−5.08904e10	+	2.93816e10i	−0.194131	+	0.112082i
$81$	5.24031e10	+	9.07648e10i	0.185544	+	0.321372i
$82$	1.11446e11	+	6.43435e10i	0.366591	+	0.211652i
$83$		−	2.08263e9i		−	0.00637006i	−0.999995	−	0.00318503i	$-0.998986\pi$
$83$		−	2.08263e9i		−	0.00637006i	0.999995	−	0.00318503i	$-0.00101383\pi$
$84$		0			0
$85$	4.73292e10			0.125492
$86$	7.97171e10	−	1.38074e11i	0.197043	−	0.341288i
$87$	−1.09164e12	+	6.30259e11i	−2.51747	+	1.45346i
$88$	−1.40924e11	−	2.44087e11i	−0.303450	−	0.525592i
$89$	7.55454e11	+	4.36162e11i	1.52009	+	0.877622i	0.999720	+	0.0236790i	$0.00753797\pi$
$89$	7.55454e11	+	4.36162e11i	1.52009	+	0.877622i	0.520366	+	0.853943i	$0.325795\pi$
$90$		−	4.84366e11i		−	0.911421i
$91$		0			0
$92$	−2.49586e11			−0.411616
$93$	−9.79319e10	+	1.69623e11i	−0.151365	+	0.262172i
$94$	2.15093e11	−	1.24184e11i	0.311788	−	0.180011i
$95$	1.11677e11	+	1.93430e11i	0.151922	+	0.263137i
$96$	−1.87092e11	−	1.08018e11i	−0.239017	−	0.137996i
$97$			8.85916e11i			1.06356i	0.846882	+	0.531780i	$0.178477\pi$
$97$			8.85916e11i			1.06356i	−0.846882	+	0.531780i	$0.821523\pi$
$98$		0			0
$99$	2.32318e12			2.46758
$100$	−4.90026e10	+	8.48750e10i	−0.0490026	+	0.0848750i
$101$	1.00057e12	−	5.77677e11i	0.942579	−	0.544198i	0.0518111	−	0.998657i	$-0.483501\pi$
$101$	1.00057e12	−	5.77677e11i	0.942579	−	0.544198i	0.890768	+	0.454459i	$0.150167\pi$
$102$	8.70000e10	+	1.50688e11i	0.0772535	+	0.133807i
$103$	−5.71960e11	−	3.30221e11i	−0.479007	−	0.276555i	0.240995	−	0.970526i	$-0.422526\pi$
$103$	−5.71960e11	−	3.30221e11i	−0.479007	−	0.276555i	−0.720003	+	0.693971i	$0.755859\pi$
$104$		−	7.47292e11i		−	0.590596i
$105$		0			0
$106$	3.21259e11			0.226475
$107$	−6.00582e11	+	1.04024e12i	−0.400193	+	0.693155i	−0.993749	−	0.111638i	$-0.964390\pi$
$107$	−6.00582e11	+	1.04024e12i	−0.400193	+	0.693155i	0.593556	+	0.804793i	$0.297724\pi$
$108$	4.69350e11	−	2.70979e11i	0.295770	−	0.170763i
$109$	−9.97053e11	−	1.72695e12i	−0.594510	−	1.02972i	−0.993616	−	0.112817i	$-0.964013\pi$
$109$	−9.97053e11	−	1.72695e12i	−0.594510	−	1.02972i	0.399106	−	0.916905i	$-0.369321\pi$
$110$	1.66978e12	+	9.64049e11i	0.942548	+	0.544181i
$111$			1.89393e12i			1.01257i
$112$		0			0
$113$	2.93470e12			1.40959			0.704796	−	0.709410i	$-0.251038\pi$
$113$	2.93470e12			1.40959			0.704796	+	0.709410i	$0.251038\pi$
$114$	−4.10567e11	+	7.11122e11i	−0.187049	+	0.323978i
$115$	1.47865e12	−	8.53699e11i	0.639261	−	0.369078i
$116$	−1.13409e12	−	1.96431e12i	−0.465480	−	0.806235i
$117$	5.33446e12	+	3.07985e12i	2.07958	+	1.20064i
$118$			1.53656e12i			0.569191i
$119$		0			0
$120$	1.47788e12			0.494940
$121$	−3.05468e12	+	5.29086e12i	−0.973315	+	1.68583i
$122$	−2.77416e12	+	1.60166e12i	−0.841341	+	0.485749i
$123$	−1.61823e12	−	2.80286e12i	−0.467315	−	0.809413i
$124$	−3.05221e11	−	1.76219e11i	−0.0839623	−	0.0484757i
$125$		−	4.09091e12i		−	1.07241i
$126$		0			0
$127$	−4.33664e12			−1.03355			−0.516775	−	0.856122i	$-0.672867\pi$
$127$	−4.33664e12			−1.03355			−0.516775	+	0.856122i	$0.672867\pi$
$128$	1.94368e11	−	3.36655e11i	0.0441942	−	0.0765466i
$129$	−3.47254e12	+	2.00487e12i	−0.753544	+	0.435059i
$130$	2.55609e12	+	4.42728e12i	0.529561	+	0.917226i
$131$	−1.55731e12	−	8.99112e11i	−0.308139	−	0.177904i	0.337954	−	0.941162i	$-0.390265\pi$
$131$	−1.55731e12	−	8.99112e11i	−0.308139	−	0.177904i	−0.646093	+	0.763258i	$0.723598\pi$
$132$			7.08841e12i			1.34000i
$133$		0			0
$134$	5.21416e12			0.900649
$135$	−1.85375e12	+	3.21079e12i	−0.306231	+	0.530407i
$136$	−2.71150e11	+	1.56549e11i	−0.0428525	+	0.0247409i
$137$	−6.12087e11	−	1.06017e12i	−0.0925742	−	0.160343i	0.816019	−	0.578025i	$-0.196176\pi$
$137$	−6.12087e11	−	1.06017e12i	−0.0925742	−	0.160343i	−0.908594	+	0.417681i	$0.862843\pi$
$138$	5.43607e12	+	3.13852e12i	0.787065	+	0.454412i
$139$		−	4.36570e12i		−	0.605292i	−0.953103	−	0.302646i	$-0.902130\pi$
$139$		−	4.36570e12i		−	0.605292i	0.953103	−	0.302646i	$-0.0978700\pi$
$140$		0			0
$141$	−6.24641e12			−0.794906
$142$	−1.13853e12	+	1.97200e12i	−0.138872	+	0.240534i
$143$	−2.12347e13	+	1.22598e13i	−2.48330	+	1.43373i
$144$	1.60212e12	+	2.77495e12i	0.179688	+	0.311229i
$145$	1.34377e13	+	7.75826e12i	1.44583	+	0.834749i
$146$		−	3.43632e12i		−	0.354794i
$147$		0			0
$148$	−3.40795e12			−0.324282
$149$	2.76244e12	−	4.78468e12i	0.252450	−	0.437256i	−0.711750	−	0.702433i	$-0.752097\pi$
$149$	2.76244e12	−	4.78468e12i	0.252450	−	0.437256i	0.964200	+	0.265177i	$0.0854304\pi$
$150$	2.13459e12	−	1.23241e12i	0.187399	−	0.108195i
$151$	8.50548e12	+	1.47319e13i	0.717525	+	1.24279i	0.961977	+	0.273129i	$0.0880585\pi$
$151$	8.50548e12	+	1.47319e13i	0.717525	+	1.24279i	−0.244452	+	0.969661i	$0.578608\pi$
$152$	−1.27960e12	−	7.38777e11i	−0.103756	−	0.0599035i
$153$		−	2.58076e12i		−	0.201187i
$154$		0			0
$155$	2.41101e12			0.173864
$156$	−9.39714e12	+	1.62763e13i	−0.652001	+	1.12930i
$157$	−1.55451e13	+	8.97495e12i	−1.03799	+	0.599286i	−0.919264	−	0.393641i	$-0.871215\pi$
$157$	−1.55451e13	+	8.97495e12i	−1.03799	+	0.599286i	−0.118729	+	0.992927i	$0.537882\pi$
$158$	5.81680e12	+	1.00750e13i	0.373888	+	0.647593i
$159$	−6.99715e12	−	4.03981e12i	−0.433050	−	0.250022i
$160$			2.65932e12i			0.158508i
$161$		0			0
$162$	4.74299e12			0.262399
$163$	−1.34370e13	+	2.32736e13i	−0.716435	+	1.24090i	0.245969	+	0.969278i	$0.420894\pi$
$163$	−1.34370e13	+	2.32736e13i	−0.716435	+	1.24090i	−0.962404	+	0.271624i	$0.912439\pi$
$164$	5.04348e12	−	2.91186e12i	0.259219	−	0.149660i
$165$	−2.42457e13	−	4.19947e13i	−1.20152	−	2.08109i
$166$	−8.16221e10	−	4.71245e10i	−0.00390085	−	0.00225216i
$167$			3.87671e13i			1.78716i	0.448900	+	0.893582i	$0.351816\pi$
$167$			3.87671e13i			1.78716i	−0.448900	+	0.893582i	$0.648184\pi$
$168$		0			0
$169$	−4.17136e13			−1.79043
$170$	1.07094e12	−	1.85492e12i	0.0443681	−	0.0768478i
$171$	1.05473e13	−	6.08951e12i	0.421858	−	0.243560i
$172$	−3.60758e12	−	6.24852e12i	−0.139330	−	0.241327i
$173$	−6.48299e12	−	3.74296e12i	−0.241824	−	0.139617i	0.374191	−	0.927352i	$-0.377920\pi$
$173$	−6.48299e12	−	3.74296e12i	−0.241824	−	0.139617i	−0.616015	+	0.787735i	$0.711254\pi$
$174$			5.70445e13i			2.05550i
$175$		0			0
$176$	−1.27550e13			−0.429144
$177$	1.93221e13	−	3.34669e13i	0.628371	−	1.08837i
$178$	3.41880e13	−	1.97384e13i	1.07486	−	0.620573i
$179$	1.68741e13	+	2.92267e13i	0.512981	+	0.888509i	0.999887	+	0.0150546i	$0.00479222\pi$
$179$	1.68741e13	+	2.92267e13i	0.512981	+	0.888509i	−0.486906	+	0.873455i	$0.661874\pi$
$180$	−1.89832e13	−	1.09600e13i	−0.558129	−	0.322236i
$181$		−	2.44112e13i		−	0.694252i	−0.937819	−	0.347126i	$-0.887158\pi$
$181$		−	2.44112e13i		−	0.694252i	0.937819	−	0.347126i	$-0.112842\pi$
$182$		0			0
$183$	8.05630e13			2.14501
$184$	−5.64748e12	+	9.78172e12i	−0.145528	+	0.252063i
$185$	2.01901e13	−	1.16568e13i	0.503627	−	0.290769i
$186$	4.43189e12	+	7.67626e12i	0.107031	+	0.185384i
$187$	8.89680e12	+	5.13657e12i	0.208058	+	0.120122i
$188$		−	1.12399e13i		−	0.254574i
$189$		0			0
$190$	1.01078e13			0.214851
$191$	2.73396e13	−	4.73536e13i	0.563109	−	0.975334i	−0.434114	−	0.900858i	$-0.642938\pi$
$191$	2.73396e13	−	4.73536e13i	0.563109	−	0.975334i	0.997223	−	0.0744756i	$-0.0237283\pi$
$192$	−8.46683e12	+	4.88832e12i	−0.169010	+	0.0975782i
$193$	−1.73142e13	−	2.99890e13i	−0.335010	−	0.580254i	0.648477	−	0.761234i	$-0.275406\pi$
$193$	−1.73142e13	−	2.99890e13i	−0.335010	−	0.580254i	−0.983487	+	0.180980i	$0.942073\pi$
$194$	3.47207e13	+	2.00460e13i	0.651295	+	0.376025i
$195$		−	1.28570e14i		−	2.33848i
$196$		0			0
$197$	2.42879e13			0.415521			0.207761	−	0.978180i	$-0.433383\pi$
$197$	2.42879e13			0.415521			0.207761	+	0.978180i	$0.433383\pi$
$198$	5.25675e13	−	9.10497e13i	0.872422	−	1.51108i
$199$	2.96893e13	−	1.71411e13i	0.478059	−	0.276008i	−0.241548	−	0.970389i	$-0.577655\pi$
$199$	2.96893e13	−	1.71411e13i	0.478059	−	0.276008i	0.719607	+	0.694381i	$0.244322\pi$
$200$	2.21760e12	+	3.84100e12i	0.0346501	+	0.0600157i
$201$	−1.13567e14	−	6.55677e13i	−1.72216	−	0.994291i
$202$		−	5.22854e13i		−	0.769612i
$203$		0			0
$204$	7.87434e12			0.109253
$205$	−1.99198e13	+	3.45021e13i	−0.268387	+	0.464860i
$206$	−2.58839e13	+	1.49441e13i	−0.338709	+	0.195554i
$207$	−4.65504e13	−	8.06277e13i	−0.591700	−	1.02485i
$208$	−2.92878e13	−	1.69093e13i	−0.361665	−	0.208807i
$209$			4.84805e13i			0.581687i
$210$		0			0
$211$	−4.46496e13			−0.505967			−0.252984	−	0.967471i	$-0.581412\pi$
$211$	−4.46496e13			−0.505967			−0.252984	+	0.967471i	$0.581412\pi$
$212$	7.26926e12	−	1.25907e13i	0.0800710	−	0.138687i
$213$	4.95955e13	−	2.86340e13i	0.531085	−	0.306622i
$214$	2.71793e13	+	4.70759e13i	0.282980	+	0.490135i
$215$	4.27457e13	+	2.46792e13i	0.432774	+	0.249862i
$216$		−	2.45263e13i		−	0.241495i
$217$		0			0
$218$	−9.02430e13			−0.840764
$219$	−4.32114e13	+	7.48444e13i	−0.391682	+	0.678414i
$220$	7.55657e13	−	4.36279e13i	0.666482	−	0.384794i
$221$	1.36191e13	+	2.35891e13i	0.116895	+	0.202468i
$222$	7.42265e13	+	4.28547e13i	0.620071	+	0.357998i
$223$			9.08410e13i			0.738674i	0.929296	+	0.369337i	$0.120415\pi$
$223$			9.08410e13i			0.738674i	−0.929296	+	0.369337i	$0.879585\pi$
$224$		0			0
$225$	−3.65580e13			−0.281766
$226$	6.64048e13	−	1.15016e14i	0.498366	−	0.863195i
$227$	−1.25149e14	+	7.22549e13i	−0.914688	+	0.528095i	−0.881936	−	0.471368i	$-0.843760\pi$
$227$	−1.25149e14	+	7.22549e13i	−0.914688	+	0.528095i	−0.0327514	+	0.999464i	$0.510427\pi$
$228$	1.85801e13	+	3.21817e13i	0.132263	+	0.229087i
$229$	−1.31986e14	−	7.62024e13i	−0.915201	−	0.528391i	−0.0330999	−	0.999452i	$-0.510538\pi$
$229$	−1.31986e14	−	7.62024e13i	−0.915201	−	0.528391i	−0.882101	+	0.471061i	$0.843871\pi$
$230$		−	7.72680e13i		−	0.521955i
$231$		0			0
$232$	−1.02646e14			−0.658288
$233$	6.44584e12	−	1.11645e13i	0.0402851	−	0.0697758i	−0.845180	−	0.534482i	$-0.820507\pi$
$233$	6.44584e12	−	1.11645e13i	0.0402851	−	0.0697758i	0.885465	+	0.464706i	$0.153840\pi$
$234$	2.41410e14	−	1.39378e14i	1.47048	−	0.848984i
$235$	3.84455e13	+	6.65896e13i	0.228265	+	0.395366i
$236$	6.02207e13	+	3.47684e13i	0.348557	+	0.201240i
$237$		−	2.92583e14i		−	1.65105i
$238$		0			0
$239$	1.47682e14			0.792392			0.396196	−	0.918166i	$-0.370330\pi$
$239$	1.47682e14			0.792392			0.396196	+	0.918166i	$0.370330\pi$
$240$	3.34407e13	−	5.79210e13i	0.174988	−	0.303088i
$241$	−1.38929e14	+	8.02104e13i	−0.709070	+	0.409382i	−0.810717	−	0.585439i	$-0.800922\pi$
$241$	−1.38929e14	+	8.02104e13i	−0.709070	+	0.409382i	0.101647	+	0.994821i	$0.467589\pi$
$242$	1.38239e14	+	2.39437e14i	0.688237	+	1.19206i
$243$	−2.25097e14	−	1.29960e14i	−1.09328	−	0.631207i
$244$			1.44966e14i			0.686952i
$245$		0			0
$246$	−1.46465e14			−0.660883
$247$	−6.42709e13	+	1.11320e14i	−0.283030	+	0.490222i
$248$	−1.38127e13	+	7.97478e12i	−0.0593703	+	0.0342775i
$249$	1.18517e12	+	2.05278e12i	0.00497263	+	0.00861285i
$250$	−1.60330e14	−	9.25668e13i	−0.656713	−	0.379154i
$251$		−	1.81669e14i		−	0.726504i	−0.931691	−	0.363252i	$-0.881666\pi$
$251$		−	1.81669e14i		−	0.726504i	0.931691	−	0.363252i	$-0.118334\pi$
$252$		0			0
$253$	3.70603e14			1.41314
$254$	−9.81270e13	+	1.69961e14i	−0.365415	+	0.632917i
$255$	−4.66509e13	+	2.69339e13i	−0.169676	+	0.0979622i
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	1.16893e14	+	6.74882e13i	0.405686	+	0.234223i	0.688934	−	0.724824i	$-0.258079\pi$
$257$	1.16893e14	+	6.74882e13i	0.405686	+	0.234223i	−0.283249	+	0.959046i	$0.591412\pi$
$258$			1.81460e14i			0.615266i
$259$		0			0
$260$	2.31351e14			0.748912
$261$	4.23041e14	−	7.32729e14i	1.33826	−	2.31793i
$262$	−7.04757e13	+	4.06891e13i	−0.217887	+	0.125797i
$263$	−1.75536e13	−	3.04037e13i	−0.0530433	−	0.0918737i	0.838285	−	0.545233i	$-0.183559\pi$
$263$	−1.75536e13	−	3.04037e13i	−0.0530433	−	0.0918737i	−0.891328	+	0.453359i	$0.850225\pi$
$264$	2.77808e14	+	1.60392e14i	0.820580	+	0.473762i
$265$			9.94570e13i			0.287184i
$266$		0			0
$267$	−9.92836e14			−2.74038
$268$	1.17983e14	−	2.04353e14i	0.318428	−	0.551533i
$269$	5.49523e14	−	3.17267e14i	1.45035	−	0.837358i	0.451846	−	0.892096i	$-0.350766\pi$
$269$	5.49523e14	−	3.17267e14i	1.45035	−	0.837358i	0.998501	+	0.0547375i	$0.0174322\pi$
$270$	8.38912e13	+	1.45304e14i	0.216538	+	0.375055i
$271$	−2.48989e14	−	1.43754e14i	−0.628587	−	0.362915i	0.151618	−	0.988439i	$-0.451552\pi$
$271$	−2.48989e14	−	1.43754e14i	−0.628587	−	0.362915i	−0.780205	+	0.625525i	$0.784885\pi$
$272$			1.41692e13i			0.0349889i
$273$		0			0
$274$	−5.53998e13			−0.130920
$275$	7.27626e13	−	1.26028e14i	0.168233	−	0.291389i
$276$	2.46009e14	−	1.42033e14i	0.556539	−	0.321318i
$277$	−3.35788e14	−	5.81602e14i	−0.743338	−	1.28750i	−0.950967	−	0.309292i	$-0.899908\pi$
$277$	−3.35788e14	−	5.81602e14i	−0.743338	−	1.28750i	0.207629	−	0.978208i	$-0.433425\pi$
$278$	−1.71100e14	−	9.87845e13i	−0.370664	−	0.214003i
$279$		−	1.31467e14i		−	0.278736i
$280$		0			0
$281$	3.07036e14			0.623665			0.311832	−	0.950137i	$-0.399057\pi$
$281$	3.07036e14			0.623665			0.311832	+	0.950137i	$0.399057\pi$
$282$	−1.41340e14	+	2.44808e14i	−0.281042	+	0.486779i
$283$	−5.60549e14	+	3.23633e14i	−1.09118	+	0.629991i	−0.933889	−	0.357562i	$-0.883608\pi$
$283$	−5.60549e14	+	3.23633e14i	−1.09118	+	0.629991i	−0.157286	+	0.987553i	$0.550275\pi$
$284$	5.15242e13	+	8.92425e13i	0.0981977	+	0.170083i
$285$	−2.20153e14	−	1.27105e14i	−0.410824	−	0.237189i
$286$			1.10963e15i			2.02760i
$287$		0			0
$288$	1.45007e14			0.254117
$289$	−2.85605e14	+	4.94682e14i	−0.490206	+	0.849062i
$290$	6.08121e14	−	3.51099e14i	1.02236	−	0.590257i
$291$	−5.04153e14	−	8.73219e14i	−0.830242	−	1.43802i
$292$	−1.34676e14	−	7.77550e13i	−0.217266	−	0.125439i
$293$		−	4.60155e14i		−	0.727275i	−0.931541	−	0.363638i	$-0.881535\pi$
$293$		−	4.60155e14i		−	0.727275i	0.931541	−	0.363638i	$-0.118465\pi$
$294$		0			0
$295$	−4.75697e14			−0.721769
$296$	−7.71131e13	+	1.33564e14i	−0.114651	+	0.198581i
$297$	−6.96925e14	+	4.02370e14i	−1.01542	+	0.586255i
$298$	−1.25014e14	−	2.16530e14i	−0.178509	−	0.309187i
$299$	8.50973e14	+	4.91310e14i	1.19094	+	0.687588i
$300$		−	1.11545e14i		−	0.153011i
$301$		0			0
$302$	7.69828e14			1.01473
$303$	−6.57484e14	+	1.13880e15i	−0.849630	+	1.47160i
$304$	−5.79081e13	+	3.34332e13i	−0.0733664	+	0.0423581i
$305$	−4.95851e14	−	8.58838e14i	−0.615959	−	1.06687i
$306$	−1.01145e14	−	5.83960e13i	−0.123201	−	0.0711303i
$307$			3.97752e14i			0.475097i	0.971376	+	0.237548i	$0.0763438\pi$
$307$			3.97752e14i			0.475097i	−0.971376	+	0.237548i	$0.923656\pi$
$308$		0			0
$309$	7.51683e14			0.863543
$310$	5.45549e13	−	9.44919e13i	0.0614701	−	0.106469i
$311$	−9.44605e14	+	5.45368e14i	−1.04397	+	0.602736i	−0.920955	−	0.389668i	$-0.872590\pi$
$311$	−9.44605e14	+	5.45368e14i	−1.04397	+	0.602736i	−0.123015	+	0.992405i	$0.539256\pi$
$312$	4.25266e14	+	7.36582e14i	0.461034	+	0.798535i
$313$	−4.92556e14	−	2.84377e14i	−0.523829	−	0.302433i	0.214671	−	0.976686i	$-0.431132\pi$
$313$	−4.92556e14	−	2.84377e14i	−0.523829	−	0.302433i	−0.738500	+	0.674254i	$0.764465\pi$
$314$			8.12320e14i			0.847518i
$315$		0			0
$316$	5.26476e14			0.528757
$317$	−1.19437e14	+	2.06870e14i	−0.117701	+	0.203865i	−0.918856	−	0.394592i	$-0.870886\pi$
$317$	−1.19437e14	+	2.06870e14i	−0.117701	+	0.203865i	0.801155	+	0.598457i	$0.204219\pi$
$318$	−3.16655e14	+	1.82821e14i	−0.306213	+	0.176792i
$319$	1.68398e15	+	2.91674e15i	1.59806	+	2.76792i
$320$	1.04224e14	+	6.01735e13i	0.0970657	+	0.0560409i
$321$		−	1.36711e15i		−	1.24960i
$322$		0			0
$323$	5.38558e13			0.0474261
$324$	1.07322e14	−	1.85886e14i	0.0927720	−	0.160686i
$325$	3.34153e14	−	1.92923e14i	0.283560	−	0.163714i
$326$	6.08089e14	+	1.05324e15i	0.506596	+	0.877450i
$327$	1.96553e15	+	1.13480e15i	1.60765	+	0.928179i
$328$		−	2.63551e14i		−	0.211652i
$329$		0			0
$330$	−2.19447e15			−1.69920
$331$	3.64766e14	−	6.31793e14i	0.277362	−	0.480405i	−0.693367	−	0.720585i	$-0.743873\pi$
$331$	3.64766e14	−	6.31793e14i	0.277362	−	0.480405i	0.970728	+	0.240181i	$0.0772066\pi$
$332$	−3.69379e12	+	2.13261e12i	−0.00275832	+	0.00159252i
$333$	−6.35619e14	−	1.10093e15i	−0.466156	−	0.807407i
$334$	1.51935e15	+	8.77199e14i	1.09441	+	0.631858i
$335$			1.61423e15i			1.14208i
$336$		0			0
$337$	1.36845e15			0.934218			0.467109	−	0.884200i	$-0.345296\pi$
$337$	1.36845e15			0.934218			0.467109	+	0.884200i	$0.345296\pi$
$338$	−9.43871e14	+	1.63483e15i	−0.633013	+	1.09641i
$339$	−2.89264e15	+	1.67007e15i	−1.90589	+	1.10036i
$340$	−4.84651e13	−	8.39441e13i	−0.0313730	−	0.0543396i
$341$	4.53214e14	+	2.61663e14i	0.288255	+	0.166424i
$342$		−	5.51160e14i		−	0.344446i
$343$		0			0
$344$	−3.26521e14			−0.197043
$345$	−9.71639e14	+	1.68293e15i	−0.576223	+	0.998047i
$346$	−2.93387e14	+	1.69387e14i	−0.170995	+	0.0987241i
$347$	−5.31356e14	−	9.20335e14i	−0.304375	−	0.527192i	0.672747	−	0.739872i	$-0.265114\pi$
$347$	−5.31356e14	−	9.20335e14i	−0.304375	−	0.527192i	−0.977122	+	0.212680i	$0.931781\pi$
$348$	2.23568e15	+	1.29077e15i	1.25873	+	0.726731i
$349$			2.28786e15i			1.26613i	0.774100	+	0.633063i	$0.218202\pi$
$349$			2.28786e15i			1.26613i	−0.774100	+	0.633063i	$0.781798\pi$
$350$		0			0
$351$	−2.13369e15			−1.14101
$352$	−2.88612e14	+	4.99890e14i	−0.151725	+	0.262796i
$353$	7.89328e14	−	4.55719e14i	0.407952	−	0.235531i	−0.281957	−	0.959427i	$-0.590984\pi$
$353$	7.89328e14	−	4.55719e14i	0.407952	−	0.235531i	0.689910	+	0.723896i	$0.257650\pi$
$354$	−8.74421e14	−	1.51454e15i	−0.444325	−	0.769594i
$355$	−6.10502e14	−	3.52474e14i	−0.305012	−	0.176099i
$356$		−	1.78652e15i		−	0.877622i
$357$		0			0
$358$	1.52727e15			0.725465
$359$	−1.06968e15	+	1.85274e15i	−0.499675	+	0.865462i	−1.00000		0.000375531i	$-0.999880\pi$
$359$	−1.06968e15	+	1.85274e15i	−0.499675	+	0.865462i	0.500325	+	0.865838i	$0.333214\pi$
$360$	−8.59082e14	+	4.95991e14i	−0.394657	+	0.227855i
$361$	−9.79580e14	−	1.69668e15i	−0.442585	−	0.766580i
$362$	−9.56718e14	−	5.52361e14i	−0.425141	−	0.245455i
$363$		−	6.95337e15i		−	3.03918i
$364$		0			0
$365$	1.06383e15			0.449901
$366$	1.82293e15	−	3.15741e15i	0.758375	−	1.31354i
$367$	1.59545e15	−	9.21136e14i	0.652962	−	0.376988i	−0.136628	−	0.990622i	$-0.543627\pi$
$367$	1.59545e15	−	9.21136e14i	0.652962	−	0.376988i	0.789590	+	0.613635i	$0.210293\pi$
$368$	2.55576e14	+	4.42670e14i	0.102904	+	0.178235i
$369$	1.88133e15	+	1.08618e15i	0.745257	+	0.430274i
$370$		−	1.05505e15i		−	0.411210i
$371$		0			0
$372$	4.01129e14			0.151365
$373$	−4.78263e14	+	8.28376e14i	−0.177588	+	0.307592i	−0.941054	−	0.338257i	$-0.890163\pi$
$373$	−4.78263e14	+	8.28376e14i	−0.177588	+	0.307592i	0.763466	+	0.645848i	$0.223496\pi$
$374$	4.02623e14	−	2.32455e14i	0.147119	−	0.0849393i
$375$	2.32804e15	+	4.03228e15i	0.837149	+	1.44998i
$376$	−4.40510e14	−	2.54329e14i	−0.155894	−	0.0900054i
$377$			8.92986e15i			3.11026i
$378$		0			0
$379$	3.65431e15			1.23302			0.616510	−	0.787347i	$-0.288546\pi$
$379$	3.65431e15			1.23302			0.616510	+	0.787347i	$0.288546\pi$
$380$	2.28714e14	−	3.96145e14i	0.0759612	−	0.131569i
$381$	4.27449e15	−	2.46788e15i	1.39744	−	0.806815i
$382$	−1.23725e15	−	2.14298e15i	−0.398178	−	0.689665i
$383$	−2.55844e15	−	1.47712e15i	−0.810555	−	0.467974i	0.0365933	−	0.999330i	$-0.488349\pi$
$383$	−2.55844e15	−	1.47712e15i	−0.810555	−	0.467974i	−0.847149	+	0.531356i	$0.821683\pi$
$384$			4.42441e14i			0.137996i
$385$		0			0
$386$	−1.56710e15			−0.473776
$387$	1.34571e15	−	2.33083e15i	0.400576	−	0.693817i
$388$	1.57128e15	−	9.07178e14i	0.460535	−	0.265890i
$389$	−1.22210e15	−	2.11674e15i	−0.352703	−	0.610900i	0.634019	−	0.773318i	$-0.281404\pi$
$389$	−1.22210e15	−	2.11674e15i	−0.352703	−	0.610900i	−0.986722	+	0.162418i	$0.948071\pi$
$390$	−5.03891e15	−	2.90922e15i	−1.43202	−	0.826777i
$391$		−	4.11693e14i		−	0.115216i
$392$		0			0
$393$	2.04665e15			0.555506
$394$	5.49573e14	−	9.51889e14i	0.146909	−	0.254454i
$395$	−3.11907e15	+	1.80079e15i	−0.821187	+	0.474113i
$396$	−2.37894e15	−	4.12044e15i	−0.616895	−	1.06849i
$397$	−1.35832e15	−	7.84227e14i	−0.346944	−	0.200308i	0.316395	−	0.948628i	$-0.397528\pi$
$397$	−1.35832e15	−	7.84227e14i	−0.346944	−	0.200308i	−0.663338	+	0.748320i	$0.730861\pi$
$398$		−	1.55144e15i		−	0.390334i
$399$		0			0
$400$	2.00715e14			0.0490026
$401$	−5.72742e14	+	9.92019e14i	−0.137750	+	0.238591i	−0.926645	−	0.375938i	$-0.877321\pi$
$401$	−5.72742e14	+	9.92019e14i	−0.137750	+	0.238591i	0.788894	+	0.614529i	$0.210654\pi$
$402$	−5.13943e15	+	2.96725e15i	−1.21775	+	0.703070i
$403$	6.93776e14	+	1.20166e15i	0.161953	+	0.280511i
$404$	−2.04916e15	−	1.18308e15i	−0.471289	−	0.272099i
$405$			1.46836e15i			0.332738i
$406$		0			0
$407$	5.06037e15			1.11331
$408$	1.78176e14	−	3.08610e14i	0.0386268	−	0.0669035i
$409$	7.56565e15	−	4.36803e15i	1.61624	−	0.933138i	0.628362	−	0.777921i	$-0.283726\pi$
$409$	7.56565e15	−	4.36803e15i	1.61624	−	0.933138i	0.987880	−	0.155216i	$-0.0496075\pi$
$410$	9.01468e14	+	1.56139e15i	0.189778	+	0.328706i
$411$	1.20663e15	+	6.96648e14i	0.250336	+	0.144532i
$412$			1.35259e15i			0.276555i
$413$		0			0
$414$	−4.21326e15			−0.836790
$415$	1.45891e13	−	2.52690e13i	0.00285587	−	0.00494652i
$416$	−1.32541e15	+	7.65227e14i	−0.255736	+	0.147649i
$417$	2.48441e15	+	4.30313e15i	0.472506	+	0.818405i
$418$	1.90004e15	+	1.09699e15i	0.356209	+	0.205658i
$419$			1.57572e15i			0.291203i	0.989343	+	0.145601i	$0.0465117\pi$
$419$			1.57572e15i			0.291203i	−0.989343	+	0.145601i	$0.953488\pi$
$420$		0			0
$421$	−8.93849e15			−1.60536			−0.802678	−	0.596413i	$-0.796592\pi$
$421$	−8.93849e15			−1.60536			−0.802678	+	0.596413i	$0.796592\pi$
$422$	−1.01030e15	+	1.74990e15i	−0.178887	+	0.309841i
$423$	3.63099e15	−	2.09635e15i	0.633845	−	0.365950i
$424$	−3.28969e14	−	5.69791e14i	−0.0566187	−	0.0980665i
$425$	−1.40002e14	−	8.08302e13i	−0.0237575	−	0.0137164i
$426$		−	2.59165e15i		−	0.433629i
$427$		0			0
$428$	2.45999e15			0.400193
$429$	1.39535e16	−	2.41683e16i	2.23842	−	3.87705i
$430$	1.93445e15	−	1.11685e15i	0.306018	−	0.176679i
$431$	−7.11093e14	−	1.23165e15i	−0.110933	−	0.192142i	0.805213	−	0.592985i	$-0.202051\pi$
$431$	−7.11093e14	−	1.23165e15i	−0.110933	−	0.192142i	−0.916147	+	0.400843i	$0.868717\pi$
$432$	−9.61229e14	−	5.54966e14i	−0.147885	−	0.0853815i
$433$		−	7.63274e15i		−	1.15812i	−0.815286	−	0.579059i	$-0.803420\pi$
$433$		−	7.63274e15i		−	1.15812i	0.815286	−	0.579059i	$-0.196580\pi$
$434$		0			0
$435$	−1.76601e16			−2.60651
$436$	−2.04197e15	+	3.53679e15i	−0.297255	+	0.514861i
$437$	1.68255e15	−	9.71422e14i	0.241591	−	0.139482i
$438$	1.95553e15	+	3.38707e15i	0.276961	+	0.479711i
$439$	−1.23220e15	−	7.11414e14i	−0.172145	−	0.0993882i	0.411452	−	0.911432i	$-0.365022\pi$
$439$	−1.23220e15	−	7.11414e14i	−0.172145	−	0.0993882i	−0.583597	+	0.812043i	$0.698355\pi$
$440$		−	3.94874e15i		−	0.544181i
$441$		0			0
$442$	1.23266e15			0.165315
$443$	−4.15114e15	+	7.18999e15i	−0.549219	+	0.951275i	0.449110	+	0.893477i	$0.351741\pi$
$443$	−4.15114e15	+	7.18999e15i	−0.549219	+	0.951275i	−0.998328	+	0.0577979i	$0.981592\pi$
$444$	3.35911e15	−	1.93938e15i	0.438456	−	0.253143i
$445$	6.11073e15	+	1.05841e16i	0.786924	+	1.36299i
$446$	3.56022e15	+	2.05550e15i	0.452343	+	0.261161i
$447$			6.28815e15i			0.788275i
$448$		0			0
$449$	5.42464e14			0.0662053			0.0331026	−	0.999452i	$-0.489461\pi$
$449$	5.42464e14			0.0662053			0.0331026	+	0.999452i	$0.489461\pi$
$450$	−8.27214e14	+	1.43278e15i	−0.0996192	+	0.172545i
$451$	−7.48892e15	+	4.32373e15i	−0.889939	+	0.513806i
$452$	−3.00514e15	−	5.20505e15i	−0.352398	−	0.610371i
$453$	−1.67672e16	−	9.68053e15i	−1.94031	−	1.12024i
$454$			6.53977e15i			0.746839i
$455$		0			0
$456$	1.68168e15			0.187049
$457$	−2.66405e15	+	4.61428e15i	−0.292446	+	0.506532i	−0.974388	−	0.224875i	$-0.927803\pi$
$457$	−2.66405e15	+	4.61428e15i	−0.292446	+	0.506532i	0.681941	+	0.731407i	$0.261136\pi$
$458$	−5.97302e15	+	3.44853e15i	−0.647145	+	0.373629i
$459$	4.46983e14	+	7.74197e14i	0.0477985	+	0.0827895i
$460$	−3.02828e15	−	1.74838e15i	−0.319631	−	0.184539i
$461$			1.29900e15i			0.135333i	0.997708	+	0.0676663i	$0.0215553\pi$
$461$			1.29900e15i			0.135333i	−0.997708	+	0.0676663i	$0.978445\pi$
$462$		0			0
$463$	−1.49560e16			−1.51820			−0.759101	−	0.650973i	$-0.774361\pi$
$463$	−1.49560e16			−1.51820			−0.759101	+	0.650973i	$0.774361\pi$
$464$	−2.32262e15	+	4.02290e15i	−0.232740	+	0.403117i
$465$	−2.37646e15	+	1.37205e15i	−0.235078	+	0.135722i
$466$	−2.91706e14	−	5.05249e14i	−0.0284858	−	0.0493389i
$467$	−5.32993e15	−	3.07724e15i	−0.513831	−	0.296661i	0.220576	−	0.975370i	$-0.429206\pi$
$467$	−5.32993e15	−	3.07724e15i	−0.513831	−	0.296661i	−0.734407	+	0.678709i	$0.762540\pi$
$468$		−	1.26151e16i		−	1.20064i
$469$		0			0
$470$	3.47969e15			0.322815
$471$	1.02149e16	−	1.76926e16i	0.935635	−	1.62057i
$472$	2.72528e15	−	1.57344e15i	0.246467	−	0.142298i
$473$	5.35680e15	+	9.27825e15i	0.478342	+	0.828512i
$474$	−1.14669e16	−	6.62040e15i	−1.01105	−	0.583733i
$475$		−	7.62900e14i		−	0.0664211i
$476$		0			0
$477$	5.42318e15			0.460409
$478$	3.34166e15	−	5.78793e15i	0.280153	−	0.485239i
$479$	8.13481e15	−	4.69664e15i	0.673495	−	0.388843i	−0.123905	−	0.992294i	$-0.539542\pi$
$479$	8.13481e15	−	4.69664e15i	0.673495	−	0.388843i	0.797400	+	0.603452i	$0.206208\pi$
$480$	−1.51335e15	−	2.62120e15i	−0.123735	−	0.214315i
$481$	1.16196e16	+	6.70855e15i	0.938251	+	0.541700i
$482$			7.25982e15i			0.578953i
$483$		0			0
$484$	1.25120e16			0.973315
$485$	−6.20594e15	+	1.07490e16i	−0.476823	+	0.825882i
$486$	−1.01867e16	+	5.88131e15i	−0.773067	+	0.446330i
$487$	4.10445e15	+	7.10912e15i	0.307667	+	0.532895i	0.977852	−	0.209299i	$-0.0671183\pi$
$487$	4.10445e15	+	7.10912e15i	0.307667	+	0.532895i	−0.670184	+	0.742195i	$0.733785\pi$
$488$	5.68148e15	+	3.28020e15i	0.420671	+	0.242874i
$489$		−	3.05867e16i		−	2.23707i
$490$		0			0
$491$	1.70306e16			1.21546			0.607730	−	0.794144i	$-0.292080\pi$
$491$	1.70306e16			1.21546			0.607730	+	0.794144i	$0.292080\pi$
$492$	−3.31413e15	+	5.74025e15i	−0.233657	+	0.404706i
$493$	3.24014e15	−	1.87070e15i	0.225674	−	0.130293i
$494$	2.90857e15	+	5.03779e15i	0.200132	+	0.346640i
$495$	2.81876e16	+	1.62741e16i	1.91614	+	1.10628i
$496$			7.21795e14i			0.0484757i
$497$		0			0
$498$	1.07270e14			0.00703236
$499$	−3.47566e15	+	6.02003e15i	−0.225131	+	0.389938i	−0.956359	−	0.292195i	$-0.905614\pi$
$499$	−3.47566e15	+	6.02003e15i	−0.225131	+	0.389938i	0.731228	+	0.682133i	$0.238948\pi$
$500$	−7.25573e15	+	4.18909e15i	−0.464366	+	0.268102i
$501$	−2.20614e16	−	3.82115e16i	−1.39511	−	2.41639i
$502$	−7.11993e15	−	4.11069e15i	−0.444891	−	0.256858i
$503$			1.04626e16i			0.645996i	0.946400	+	0.322998i	$0.104691\pi$
$503$			1.04626e16i			0.645996i	−0.946400	+	0.322998i	$0.895309\pi$
$504$		0			0
$505$	1.61868e16			0.975916
$506$	8.38578e15	−	1.45246e16i	0.499621	−	0.865368i
$507$	4.11158e16	−	2.37382e16i	2.42081	−	1.39765i
$508$	4.44072e15	+	7.69155e15i	0.258387	+	0.447540i
$509$	1.63453e16	+	9.43694e15i	0.939908	+	0.542656i	0.889931	−	0.456094i	$-0.150752\pi$
$509$	1.63453e16	+	9.43694e15i	0.939908	+	0.542656i	0.0499765	+	0.998750i	$0.484085\pi$
$510$			2.43778e15i			0.138539i
$511$		0			0
$512$	−7.96131e14			−0.0441942
$513$	−2.10938e15	+	3.65355e15i	−0.115731	+	0.200452i
$514$	5.28997e15	−	3.05417e15i	0.286863	−	0.165620i
$515$	−4.62647e15	−	8.01329e15i	−0.247974	−	0.429504i
$516$	7.11176e15	+	4.10598e15i	0.376772	+	0.217530i
$517$			1.66897e16i			0.873989i
$518$		0			0
$519$	8.52011e15			0.435954
$520$	5.23487e15	−	9.06706e15i	0.264780	−	0.458613i
$521$	−3.28541e15	+	1.89683e15i	−0.164272	+	0.0948423i	−0.579882	−	0.814700i	$-0.696901\pi$
$521$	−3.28541e15	+	1.89683e15i	−0.164272	+	0.0948423i	0.415610	+	0.909543i	$0.363568\pi$
$522$	−1.91447e16	−	3.31595e16i	−0.946291	−	1.63902i
$523$	−1.44767e16	−	8.35814e15i	−0.707392	−	0.408413i	0.102702	−	0.994712i	$-0.467251\pi$
$523$	−1.44767e16	−	8.35814e15i	−0.707392	−	0.408413i	−0.810095	+	0.586299i	$0.800584\pi$
$524$			3.68276e15i			0.177904i
$525$		0			0
$526$	−1.58877e15			−0.0750146
$527$	2.90675e14	−	5.03464e14i	0.0135689	−	0.0235020i
$528$	1.25721e16	−	7.25853e15i	0.580238	−	0.335000i
$529$	3.53141e15	+	6.11658e15i	0.161144	+	0.279110i
$530$	3.89790e15	+	2.25046e15i	0.175864	+	0.101535i
$531$			2.59388e16i			1.15713i
$532$		0			0
$533$	−2.29280e16			−1.00001
$534$	−2.24653e16	+	3.89111e16i	−0.968869	+	1.67813i
$535$	−1.45740e16	+	8.41430e15i	−0.621521	+	0.358835i
$536$	−5.33930e15	−	9.24794e15i	−0.225162	−	0.389993i
$537$	−3.32644e16	−	1.92052e16i	−1.38719	−	0.800892i
$538$		−	2.87157e16i		−	1.18420i
$539$		0			0
$540$	7.59297e15			0.306231
$541$	5.85969e15	−	1.01493e16i	0.233717	−	0.404810i	−0.725182	−	0.688558i	$-0.758244\pi$
$541$	5.85969e15	−	1.01493e16i	0.233717	−	0.404810i	0.958899	+	0.283747i	$0.0915776\pi$
$542$	−1.12680e16	+	6.50557e15i	−0.444478	+	0.256619i
$543$	1.38918e16	+	2.40613e16i	0.541950	+	0.938685i
$544$	5.55315e14	+	3.20612e14i	0.0214263	+	0.0123705i
$545$		−	2.79379e16i		−	1.06614i
$546$		0			0
$547$	3.62257e16			1.35236			0.676181	−	0.736736i	$-0.263634\pi$
$547$	3.62257e16			1.35236			0.676181	+	0.736736i	$0.263634\pi$
$548$	−1.25355e15	+	2.17122e15i	−0.0462871	+	0.0801716i
$549$	−4.68306e16	+	2.70377e16i	−1.71039	+	0.987496i
$550$	−3.29286e15	−	5.70340e15i	−0.118959	−	0.206043i
$551$	1.52907e16	+	8.82810e15i	0.546410	+	0.315470i
$552$		−	1.28554e16i		−	0.454412i
$553$		0			0
$554$	−3.03921e16			−1.05124
$555$	−1.32672e16	+	2.29794e16i	−0.453963	+	0.786287i
$556$	−7.74309e15	+	4.47048e15i	−0.262099	+	0.151323i
$557$	1.92509e16	+	3.33435e16i	0.644643	+	1.11656i	0.984384	+	0.176036i	$0.0563275\pi$
$557$	1.92509e16	+	3.33435e16i	0.644643	+	1.11656i	−0.339740	+	0.940519i	$0.610339\pi$
$558$	−5.15244e15	−	2.97477e15i	−0.170690	−	0.0985479i
$559$			2.84061e16i			0.930982i
$560$		0			0
$561$	−1.16924e16			−0.375082
$562$	6.94743e15	−	1.20333e16i	0.220499	−	0.381915i
$563$	−8.79162e15	+	5.07584e15i	−0.276069	+	0.159389i	−0.631643	−	0.775260i	$-0.717619\pi$
$563$	−8.79162e15	+	5.07584e15i	−0.276069	+	0.159389i	0.355573	+	0.934648i	$0.384286\pi$
$564$	6.39633e15	+	1.10788e16i	0.198727	+	0.344205i
$565$	3.56074e16	+	2.05579e16i	1.09458	+	0.631959i
$566$			2.92919e16i			0.890941i
$567$		0			0
$568$	4.66344e15			0.138872
$569$	−1.72786e16	+	2.99274e16i	−0.509137	+	0.881852i	0.490807	+	0.871269i	$0.336702\pi$
$569$	−1.72786e16	+	2.99274e16i	−0.509137	+	0.881852i	−0.999944	+	0.0105833i	$0.996631\pi$
$570$	−9.96298e15	+	5.75213e15i	−0.290496	+	0.167718i
$571$	−2.59825e16	−	4.50030e16i	−0.749659	−	1.29845i	−0.947986	−	0.318312i	$-0.896884\pi$
$571$	−2.59825e16	−	4.50030e16i	−0.749659	−	1.29845i	0.198327	−	0.980136i	$-0.436449\pi$
$572$	4.34886e16	+	2.51081e16i	1.24165	+	0.716867i
$573$			6.22333e16i			1.75831i
$574$		0			0
$575$	−5.83188e15			−0.161362
$576$	3.28113e15	−	5.68309e15i	0.0898439	−	0.155614i
$577$	−4.62325e14	+	2.66924e14i	−0.0125283	+	0.00723323i	−0.506251	−	0.862386i	$-0.668969\pi$
$577$	−4.62325e14	+	2.66924e14i	−0.0125283	+	0.00723323i	0.493723	+	0.869619i	$0.335636\pi$
$578$	1.29250e16	+	2.23868e16i	0.346628	+	0.600378i
$579$	3.41321e16	+	1.97061e16i	0.905922	+	0.523035i
$580$		−	3.17778e16i		−	0.834749i
$581$		0			0
$582$	−4.56307e16			−1.17414
$583$	−1.07939e16	+	1.86956e16i	−0.274896	+	0.476133i
$584$	−6.09473e15	+	3.51879e15i	−0.153630	+	0.0886985i
$585$	4.31494e16	+	7.47370e16i	1.07656	+	1.86466i
$586$	−1.80343e16	−	1.04121e16i	−0.445363	−	0.257131i
$587$			6.77758e15i			0.165671i	0.996563	+	0.0828354i	$0.0263976\pi$
$587$			6.77758e15i			0.165671i	−0.996563	+	0.0828354i	$0.973602\pi$
$588$		0			0
$589$	2.74348e15			0.0657068
$590$	−1.07638e16	+	1.86434e16i	−0.255184	+	0.441992i
$591$	−2.39398e16	+	1.38217e16i	−0.561819	+	0.324366i
$592$	3.48974e15	+	6.04441e15i	0.0810705	+	0.140418i
$593$	2.12563e15	+	1.22723e15i	0.0488832	+	0.0282227i	0.524242	−	0.851569i	$-0.324349\pi$
$593$	2.12563e15	+	1.22723e15i	0.0488832	+	0.0282227i	−0.475359	+	0.879792i	$0.657682\pi$
$594$			3.64183e16i			0.829090i
$595$		0			0
$596$	−1.13149e16			−0.252450
$597$	−1.95092e16	+	3.37910e16i	−0.430917	+	0.746371i
$598$	3.85107e16	−	2.22341e16i	0.842120	−	0.486198i
$599$	−3.73685e16	−	6.47241e16i	−0.808993	−	1.40122i	−0.913562	−	0.406699i	$-0.866680\pi$
$599$	−3.73685e16	−	6.47241e16i	−0.808993	−	1.40122i	0.104569	−	0.994518i	$-0.466654\pi$
$600$	−4.37164e15	−	2.52397e15i	−0.0936995	−	0.0540974i
$601$		−	2.12849e16i		−	0.451674i	−0.974165	−	0.225837i	$-0.927488\pi$
$601$		−	2.12849e16i		−	0.451674i	0.974165	−	0.225837i	$-0.0725116\pi$
$602$		0			0
$603$	8.80204e16			1.83096
$604$	1.74192e16	−	3.01710e16i	0.358763	−	0.621395i
$605$	−7.41261e16	+	4.27967e16i	−1.51161	+	0.872727i
$606$	2.97543e16	+	5.15360e16i	0.600779	+	1.04058i
$607$	−4.83175e16	−	2.78961e16i	−0.965990	−	0.557714i	−0.0679784	−	0.997687i	$-0.521655\pi$
$607$	−4.83175e16	−	2.78961e16i	−0.965990	−	0.557714i	−0.898011	+	0.439972i	$0.854988\pi$
$608$			3.02603e15i			0.0599035i
$609$		0			0
$610$	−4.48793e16			−0.871098
$611$	−2.21257e16	+	3.83228e16i	−0.425255	+	0.736563i
$612$	−4.57729e15	+	2.64270e15i	−0.0871165	+	0.0502967i
$613$	−1.41029e16	−	2.44269e16i	−0.265794	−	0.460369i	0.701977	−	0.712199i	$-0.252301\pi$
$613$	−1.41029e16	−	2.44269e16i	−0.265794	−	0.460369i	−0.967771	+	0.251830i	$0.918968\pi$
$614$	1.55886e16	+	9.00009e15i	0.290936	+	0.167972i
$615$		−	4.53435e16i		−	0.838040i
$616$		0			0
$617$	−9.54280e16			−1.72968			−0.864838	−	0.502051i	$-0.832579\pi$
$617$	−9.54280e16			−1.72968			−0.864838	+	0.502051i	$0.832579\pi$
$618$	1.70087e16	−	2.94599e16i	0.305309	−	0.528810i
$619$	−2.46755e16	+	1.42464e16i	−0.438653	+	0.253257i	−0.703026	−	0.711164i	$-0.748168\pi$
$619$	−2.46755e16	+	1.42464e16i	−0.438653	+	0.253257i	0.264373	+	0.964421i	$0.414835\pi$
$620$	−2.46887e15	−	4.27622e15i	−0.0434659	−	0.0752852i
$621$	2.79291e16	+	1.61249e16i	0.486975	+	0.281155i
$622$			4.93611e16i			0.852398i
$623$		0			0
$624$	3.84907e16			0.652001
$625$	2.28157e16	−	3.95180e16i	0.382785	−	0.663003i
$626$	−2.22905e16	+	1.28694e16i	−0.370403	+	0.213852i
$627$	−2.75891e16	−	4.77857e16i	−0.454080	−	0.786489i
$628$	3.18363e16	+	1.83807e16i	0.518997	+	0.299643i
$629$		−	5.62144e15i		−	0.0907703i
$630$		0			0
$631$	−7.69031e16			−1.21834			−0.609169	−	0.793041i	$-0.708497\pi$
$631$	−7.69031e16			−1.21834			−0.609169	+	0.793041i	$0.708497\pi$
$632$	1.19128e16	−	2.06336e16i	0.186944	−	0.323796i
$633$	4.40097e16	−	2.54090e16i	0.684110	−	0.394971i
$634$	5.40508e15	+	9.36188e15i	0.0832275	+	0.144154i
$635$	−5.26174e16	−	3.03787e16i	−0.802578	−	0.463368i
$636$			1.65470e16i			0.250022i
$637$		0			0
$638$	1.52417e17			2.26000
$639$	−1.92196e16	+	3.32894e16i	−0.282319	+	0.488991i
$640$	4.71662e15	−	2.72314e15i	0.0686358	−	0.0396269i
$641$	5.28270e15	+	9.14990e15i	0.0761566	+	0.131907i	0.901589	−	0.432594i	$-0.142402\pi$
$641$	5.28270e15	+	9.14990e15i	0.0761566	+	0.131907i	−0.825432	+	0.564501i	$0.809068\pi$
$642$	−5.35795e16	−	3.09341e16i	−0.765223	−	0.441802i
$643$		−	3.09940e16i		−	0.438543i	−0.975664	−	0.219272i	$-0.929632\pi$
$643$		−	3.09940e16i		−	0.438543i	0.975664	−	0.219272i	$-0.0703681\pi$
$644$		0			0
$645$	−5.61774e16			−0.780195
$646$	1.21862e15	−	2.11071e15i	0.0167677	−	0.0290424i
$647$	2.77746e16	−	1.60357e16i	0.378637	−	0.218606i	−0.298588	−	0.954382i	$-0.596516\pi$
$647$	2.77746e16	−	1.60357e16i	0.378637	−	0.218606i	0.677225	+	0.735776i	$0.263182\pi$
$648$	−4.85682e15	−	8.41225e15i	−0.0655997	−	0.113622i
$649$	−8.94200e16	−	5.16267e16i	−1.19665	−	0.690885i
$650$		−	1.74614e16i		−	0.231526i
$651$		0			0
$652$	5.50380e16			0.716435
$653$	3.25065e16	−	5.63029e16i	0.419267	−	0.726193i	−0.576599	−	0.817028i	$-0.695620\pi$
$653$	3.25065e16	−	5.63029e16i	0.419267	−	0.726193i	0.995866	+	0.0908351i	$0.0289536\pi$
$654$	8.89496e16	−	5.13551e16i	1.13678	−	0.656322i
$655$	−1.25968e16	−	2.18182e16i	−0.159519	−	0.276294i
$656$	−1.03291e16	−	5.96348e15i	−0.129610	−	0.0748302i
$657$		−	5.80086e16i		−	0.721274i
$658$		0			0
$659$	1.60030e17			1.95385			0.976923	−	0.213594i	$-0.0685168\pi$
$659$	1.60030e17			1.95385			0.976923	+	0.213594i	$0.0685168\pi$
$660$	−4.96551e16	+	8.60052e16i	−0.600759	+	1.04055i
$661$	1.31451e17	−	7.58935e16i	1.57600	−	0.909904i	0.580591	−	0.814196i	$-0.302822\pi$
$661$	1.31451e17	−	7.58935e16i	1.57600	−	0.909904i	0.995409	−	0.0957083i	$-0.0305116\pi$
$662$	−1.65074e16	−	2.85917e16i	−0.196124	−	0.339697i
$663$	−2.68479e16	−	1.55007e16i	−0.316104	−	0.182503i
$664$			1.93022e14i			0.00225216i
$665$		0			0
$666$	−5.75297e16			−0.659245
$667$	6.74852e16	−	1.16888e17i	0.766396	−	1.32744i
$668$	6.87581e16	−	3.96975e16i	0.773865	−	0.446791i
$669$	−5.16954e16	−	8.95391e16i	−0.576627	−	0.998748i
$670$	6.32645e16	+	3.65258e16i	0.699377	+	0.403786i
$671$		−	2.15256e17i		−	2.35841i
$672$		0			0
$673$	−7.64122e16			−0.822380			−0.411190	−	0.911550i	$-0.634887\pi$
$673$	−7.64122e16			−0.822380			−0.411190	+	0.911550i	$0.634887\pi$
$674$	3.09644e16	−	5.36319e16i	0.330296	−	0.572090i
$675$	1.09670e16	−	6.33178e15i	0.115948	−	0.0669426i
$676$	4.27147e16	+	7.39841e16i	0.447607	+	0.775279i
$677$	3.90256e16	+	2.25314e16i	0.405338	+	0.234022i	0.688785	−	0.724966i	$-0.258145\pi$
$677$	3.90256e16	+	2.25314e16i	0.405338	+	0.234022i	−0.283447	+	0.958988i	$0.591478\pi$
$678$			1.51157e17i			1.55615i
$679$		0			0
$680$	−4.38656e15			−0.0443681
$681$	8.22371e16	−	1.42439e17i	0.824489	−	1.42806i
$682$	2.05101e16	−	1.18415e16i	0.203827	−	0.117680i
$683$	−6.42829e16	−	1.11341e17i	−0.633244	−	1.09681i	−0.986884	−	0.161429i	$-0.948390\pi$
$683$	−6.42829e16	−	1.11341e17i	−0.633244	−	1.09681i	0.353640	−	0.935381i	$-0.384944\pi$
$684$	−2.16010e16	−	1.24713e16i	−0.210929	−	0.121780i
$685$		−	1.71510e16i		−	0.166014i
$686$		0			0
$687$	1.73460e17			1.64990
$688$	−7.38833e15	+	1.27970e16i	−0.0696652	+	0.120664i
$689$	−4.95697e16	+	2.86191e16i	−0.463342	+	0.267510i
$690$	4.39714e16	+	7.61606e16i	0.407451	+	0.705726i
$691$	3.41126e16	+	1.96949e16i	0.313362	+	0.180920i	0.648430	−	0.761274i	$-0.275426\pi$
$691$	3.41126e16	+	1.96949e16i	0.313362	+	0.180920i	−0.335068	+	0.942194i	$0.608759\pi$
$692$			1.53312e16i			0.139617i
$693$		0			0
$694$	−4.80928e16			−0.430451
$695$	3.05822e16	−	5.29700e16i	0.271369	−	0.470025i
$696$	1.01175e17	−	5.84136e16i	0.890060	−	0.513876i
$697$	4.80313e15	+	8.31926e15i	0.0418917	+	0.0725585i
$698$	8.96654e16	+	5.17683e16i	0.775340	+	0.447643i
$699$			1.46727e16i			0.125790i
$700$		0			0
$701$	5.18834e16			0.437241			0.218620	−	0.975810i	$-0.429844\pi$
$701$	5.18834e16			0.437241			0.218620	+	0.975810i	$0.429844\pi$
$702$	−4.82800e16	+	8.36234e16i	−0.403408	+	0.698723i
$703$	2.29743e16	−	1.32642e16i	0.190331	−	0.109888i
$704$	1.30611e16	+	2.26224e16i	0.107286	+	0.185825i
$705$	−7.57891e16	−	4.37568e16i	−0.617265	−	0.356378i
$706$		−	4.12470e16i		−	0.333092i
$707$		0			0
$708$	−7.91435e16			−0.628371
$709$	−2.92719e16	+	5.07003e16i	−0.230448	+	0.399148i	−0.957940	−	0.286969i	$-0.907352\pi$
$709$	−2.92719e16	+	5.07003e16i	−0.230448	+	0.399148i	0.727492	+	0.686116i	$0.240686\pi$
$710$	−2.76282e16	+	1.59511e16i	−0.215676	+	0.124521i
$711$	9.81935e16	+	1.70076e17i	0.760090	+	1.31652i
$712$	−7.00169e16	−	4.04243e16i	−0.537432	−	0.310286i
$713$		−	2.09722e16i		−	0.159627i
$714$		0			0
$715$	−3.43526e17			−2.57113
$716$	3.45581e16	−	5.98563e16i	0.256491	−	0.444255i
$717$	−1.45565e17	+	8.40423e16i	−1.07138	+	0.618561i
$718$	4.84082e16	+	8.38455e16i	0.353323	+	0.611974i
$719$	9.50918e16	+	5.49013e16i	0.688287	+	0.397383i	0.802970	−	0.596019i	$-0.203252\pi$
$719$	9.50918e16	+	5.49013e16i	0.688287	+	0.397383i	−0.114683	+	0.993402i	$0.536585\pi$
$720$			4.48920e16i			0.322236i
$721$		0			0
$722$	−8.86615e16			−0.625910
$723$	9.12916e16	−	1.58122e17i	0.639147	−	1.10704i
$724$	−4.32961e16	+	2.49970e16i	−0.300620	+	0.173563i
$725$	−2.64995e16	−	4.58985e16i	−0.182478	−	0.316061i
$726$	−2.72516e17	−	1.57337e17i	−1.86111	−	1.07451i
$727$			6.97698e16i			0.472565i	0.971684	+	0.236282i	$0.0759290\pi$
$727$			6.97698e16i			0.472565i	−0.971684	+	0.236282i	$0.924071\pi$
$728$		0			0
$729$	2.40130e17			1.59986
$730$	2.40718e16	−	4.16936e16i	0.159064	−	0.275507i
$731$	1.03070e16	−	5.95074e15i	0.0675503	−	0.0390002i
$732$	−8.24965e16	−	1.42888e17i	−0.536252	−	0.928816i
$733$	−1.25691e17	−	7.25679e16i	−0.810366	−	0.467865i	0.0367169	−	0.999326i	$-0.488310\pi$
$733$	−1.25691e17	−	7.25679e16i	−0.810366	−	0.467865i	−0.847083	+	0.531461i	$0.821643\pi$
$734$		−	8.33717e16i		−	0.533141i
$735$		0			0
$736$	2.31321e16			0.145528
$737$	−1.75190e17	+	3.03437e17i	−1.09321	+	1.89349i
$738$	8.51392e16	−	4.91551e16i	0.526976	−	0.304250i
$739$	1.27126e17	+	2.20188e17i	0.780489	+	1.35185i	0.931657	+	0.363338i	$0.118363\pi$
$739$	1.27126e17	+	2.20188e17i	0.780489	+	1.35185i	−0.151169	+	0.988508i	$0.548304\pi$
$740$	−4.13494e16	−	2.38731e16i	−0.251813	−	0.145385i
$741$		−	1.46300e17i		−	0.883761i
$742$		0			0
$743$	−1.89108e17			−1.12403			−0.562013	−	0.827128i	$-0.689973\pi$
$743$	−1.89108e17			−1.12403			−0.562013	+	0.827128i	$0.689973\pi$
$744$	9.07651e15	−	1.57210e16i	0.0535157	−	0.0926919i
$745$	6.70345e16	−	3.87024e16i	0.392067	−	0.226360i
$746$	2.16437e16	+	3.74880e16i	0.125574	+	0.217500i
$747$	−1.37787e15	−	7.95511e14i	−0.00793018	−	0.00457849i
$748$		−	2.10394e16i		−	0.120122i
$749$		0			0
$750$	2.10710e17			1.18391
$751$	−8.78442e16	+	1.52151e17i	−0.489636	+	0.848074i	−0.999929	−	0.0119263i	$-0.996204\pi$
$751$	−8.78442e16	+	1.52151e17i	−0.489636	+	0.848074i	0.510293	+	0.860001i	$0.329537\pi$
$752$	−1.99352e16	+	1.15096e16i	−0.110234	+	0.0636434i
$753$	1.03383e17	+	1.79065e17i	0.567127	+	0.982293i
$754$	3.49978e17	+	2.02060e17i	1.90464	+	1.09964i
$755$			2.38327e17i			1.28674i
$756$		0			0
$757$	7.95370e16			0.422663			0.211331	−	0.977414i	$-0.432220\pi$
$757$	7.95370e16			0.422663			0.211331	+	0.977414i	$0.432220\pi$
$758$	8.26876e16	−	1.43219e17i	0.435938	−	0.755067i
$759$	−3.65291e17	+	2.10901e17i	−1.91068	+	1.10313i
$760$	−1.03504e16	−	1.79275e16i	−0.0537127	−	0.0930331i
$761$	−2.38900e17	−	1.37929e17i	−1.23001	−	0.710147i	−0.262978	−	0.964802i	$-0.584705\pi$
$761$	−2.38900e17	−	1.37929e17i	−1.23001	−	0.710147i	−0.967032	+	0.254655i	$0.918038\pi$
$762$		−	2.23367e17i		−	1.14101i
$763$		0			0
$764$	−1.11983e17			−0.563109
$765$	1.80785e16	−	3.13130e16i	0.0901976	−	0.156227i
$766$	−1.15782e17	+	6.68467e16i	−0.573149	+	0.330908i
$767$	−1.36883e17	−	2.37089e17i	−0.672324	−	1.16450i
$768$	1.73401e16	+	1.00113e16i	0.0845052	+	0.0487891i
$769$		−	1.76448e17i		−	0.853217i	−0.904436	−	0.426609i	$-0.859708\pi$
$769$		−	1.76448e17i		−	0.853217i	0.904436	−	0.426609i	$-0.140292\pi$
$770$		0			0
$771$	−1.53624e17			−0.731361
$772$	−3.54594e16	+	6.14175e16i	−0.167505	+	0.290127i
$773$	−1.95408e16	+	1.12819e16i	−0.0915937	+	0.0528817i	−0.545097	−	0.838373i	$-0.683507\pi$
$773$	−1.95408e16	+	1.12819e16i	−0.0915937	+	0.0528817i	0.453504	+	0.891254i	$0.350174\pi$
$774$	−6.08997e16	−	1.05481e17i	−0.283250	−	0.490603i
$775$	−7.13187e15	−	4.11759e15i	−0.0329150	−	0.0190035i
$776$		−	8.21084e16i		−	0.376025i
$777$		0			0
$778$	−1.10612e17			−0.498798
$779$	−2.26667e16	+	3.92599e16i	−0.101429	+	0.175681i
$780$	−2.28035e17	+	1.31656e17i	−1.01259	+	0.584620i
$781$	−7.65068e16	−	1.32514e17i	−0.337127	−	0.583922i
$782$	−1.61350e16	−	9.31556e15i	−0.0705552	−	0.0407351i
$783$			2.93079e17i			1.27179i
$784$		0			0
$785$	−2.51482e17			−1.07470
$786$	4.63104e16	−	8.02120e16i	0.196401	−	0.340176i
$787$	3.74906e17	−	2.16452e17i	1.57788	−	0.910990i	0.582726	−	0.812669i	$-0.301986\pi$
$787$	3.74906e17	−	2.16452e17i	1.57788	−	0.910990i	0.995155	−	0.0983211i	$-0.0313472\pi$
$788$	−2.48708e16	−	4.30776e16i	−0.103880	−	0.179926i
$789$	3.46040e16	+	1.99786e16i	0.143438	+	0.0828139i
$790$			1.62989e17i			0.670497i
$791$		0			0
$792$	−2.15317e17			−0.872422
$793$	2.85365e17	−	4.94267e17i	1.14752	−	1.98757i
$794$	−6.14706e16	+	3.54901e16i	−0.245326	+	0.141639i
$795$	−5.65986e16	−	9.80316e16i	−0.224183	−	0.388297i
$796$	−6.08037e16	−	3.51051e16i	−0.239030	−	0.138004i
$797$			2.73462e17i			1.06696i	0.845813	+	0.533479i	$0.179116\pi$
$797$			2.73462e17i			1.06696i	−0.845813	+	0.533479i	$0.820884\pi$
$798$		0			0
$799$	1.85402e16			0.0712581
$800$	4.54165e15	−	7.86638e15i	0.0173250	−	0.0300078i
$801$	5.77128e17	−	3.33205e17i	2.18513	−	1.26158i
$802$	2.59194e16	+	4.48937e16i	0.0974043	+	0.168709i
$803$	1.99976e17	+	1.15456e17i	0.745907	+	0.430650i
$804$			2.68565e17i			0.994291i
$805$		0			0
$806$	6.27935e16			0.229036
$807$	−3.61098e17	+	6.25440e17i	−1.30733	+	2.26436i
$808$	−9.27344e16	+	5.35402e16i	−0.333252	+	0.192403i
$809$	8.57211e16	+	1.48473e17i	0.305771	+	0.529611i	0.977433	−	0.211247i	$-0.0677524\pi$
$809$	8.57211e16	+	1.48473e17i	0.305771	+	0.529611i	−0.671662	+	0.740858i	$0.734419\pi$
$810$	5.75477e16	+	3.32252e16i	0.203759	+	0.117641i
$811$			2.32308e17i			0.816466i	0.912878	+	0.408233i	$0.133855\pi$
$811$			2.32308e17i			0.816466i	−0.912878	+	0.408233i	$0.866145\pi$
$812$		0			0
$813$	3.27228e17			1.13320
$814$	1.14503e17	−	1.98325e17i	0.393614	−	0.681760i
$815$	−3.26068e17	+	1.88255e17i	−1.11266	+	0.642395i
$816$	−8.06333e15	−	1.39661e16i	−0.0273132	−	0.0473079i
$817$	4.86402e16	+	2.80824e16i	0.163555	+	0.0944284i
$818$		−	3.95349e17i		−	1.31966i
$819$		0			0
$820$	8.15915e16			0.268387
$821$	1.51474e16	−	2.62360e16i	0.0494627	−	0.0856719i	−0.840234	−	0.542224i	$-0.817582\pi$
$821$	1.51474e16	−	2.62360e16i	0.0494627	−	0.0856719i	0.889697	+	0.456552i	$0.150916\pi$
$822$	5.46058e16	−	3.15267e16i	0.177014	−	0.102199i
$823$	8.12445e16	+	1.40720e17i	0.261454	+	0.452851i	0.966628	−	0.256182i	$-0.0824648\pi$
$823$	8.12445e16	+	1.40720e17i	0.261454	+	0.452851i	−0.705175	+	0.709034i	$0.749131\pi$
$824$	5.30103e16	+	3.06055e16i	0.169355	+	0.0977770i
$825$			1.65630e17i			0.525309i
$826$		0			0
$827$	4.54389e17			1.42035			0.710174	−	0.704026i	$-0.248616\pi$
$827$	4.54389e17			1.42035			0.710174	+	0.704026i	$0.248616\pi$
$828$	−9.53352e16	+	1.65125e17i	−0.295850	+	0.512427i
$829$	3.63717e17	−	2.09992e17i	1.12056	−	0.646957i	0.179018	−	0.983846i	$-0.442708\pi$
$829$	3.63717e17	−	2.09992e17i	1.12056	−	0.646957i	0.941544	+	0.336889i	$0.109375\pi$
$830$	−6.60226e14	−	1.14354e15i	−0.00201941	−	0.00349772i
$831$	6.61951e17	+	3.82178e17i	2.01011	+	1.16054i
$832$			6.92605e16i			0.208807i
$833$		0			0
$834$	2.24864e17			0.668225
$835$	−2.71568e17	+	4.70369e17i	−0.801234	+	1.38778i
$836$	8.59860e16	−	4.96441e16i	0.251878	−	0.145422i
$837$	2.27699e16	+	3.94385e16i	0.0662228	+	0.114701i
$838$	6.17554e16	+	3.56545e16i	0.178324	+	0.102956i
$839$			2.11535e16i			0.0606473i	0.999540	+	0.0303236i	$0.00965379\pi$
$839$			2.11535e16i			0.0606473i	−0.999540	+	0.0303236i	$0.990346\pi$
$840$		0			0
$841$	8.72771e17			2.46674
$842$	−2.02255e17	+	3.50316e17i	−0.567579	+	0.983076i
$843$	−3.02635e17	+	1.74727e17i	−0.843246	+	0.486848i
$844$	4.57212e16	+	7.91914e16i	0.126492	+	0.219090i
$845$	−5.06120e17	−	2.92208e17i	−1.39031	−	0.802699i
$846$		−	1.89740e17i		−	0.517532i
$847$		0			0
$848$	−2.97749e16			−0.0800710
$849$	3.68343e17	−	6.37989e17i	0.983573	−	1.70360i
$850$	−6.33576e15	+	3.65796e15i	−0.0167991	+	0.00969895i
$851$	−1.01396e17	−	1.75624e17i	−0.266960	−	0.462388i
$852$	−1.01572e17	−	5.86423e16i	−0.265543	−	0.153311i
$853$			3.17413e17i			0.824006i	0.911183	+	0.412003i	$0.135171\pi$
$853$			3.17413e17i			0.824006i	−0.911183	+	0.412003i	$0.864829\pi$
$854$		0			0
$855$	1.70631e17			0.436778
$856$	5.56631e16	−	9.64114e16i	0.141490	−	0.245067i
$857$	−3.22966e17	+	1.86465e17i	−0.815215	+	0.470665i	−0.848764	−	0.528773i	$-0.822652\pi$
$857$	−3.22966e17	+	1.86465e17i	−0.815215	+	0.470665i	0.0335487	+	0.999437i	$0.489319\pi$
$858$	−6.31466e17	−	1.09373e18i	−1.58280	−	2.74149i
$859$	3.62991e17	+	2.09573e17i	0.903519	+	0.521647i	0.878340	−	0.478036i	$-0.158651\pi$
$859$	3.62991e17	+	2.09573e17i	0.903519	+	0.521647i	0.0251784	+	0.999683i	$0.491985\pi$
$860$		−	1.01086e17i		−	0.249862i
$861$		0			0
$862$	−6.43608e16			−0.156884
$863$	−1.67121e17	+	2.89462e17i	−0.404545	+	0.700692i	−0.994268	−	0.106913i	$-0.965903\pi$
$863$	−1.67121e17	+	2.89462e17i	−0.404545	+	0.700692i	0.589724	+	0.807605i	$0.299237\pi$
$864$	−4.35003e16	+	2.51149e16i	−0.104571	+	0.0603738i
$865$	−5.24397e16	−	9.08282e16i	−0.125188	−	0.216832i
$866$	−2.99141e17	−	1.72709e17i	−0.709200	−	0.409457i
$867$		−	6.50124e17i		−	1.53067i
$868$		0			0
$869$	−7.81750e17			−1.81530
$870$	−3.99603e17	+	6.92133e17i	−0.921539	+	1.59615i
$871$	−8.04537e17	+	4.64499e17i	−1.84262	+	1.06384i
$872$	9.24088e16	+	1.60057e17i	0.210191	+	0.364062i
$873$	5.86121e17	+	3.38397e17i	1.32404	+	0.764436i
$874$		−	8.79231e16i		−	0.197258i
$875$		0			0
$876$	1.76994e17			0.391682
$877$	−1.04169e17	+	1.80426e17i	−0.228950	+	0.396553i	−0.957497	−	0.288443i	$-0.906863\pi$
$877$	−1.04169e17	+	1.80426e17i	−0.228950	+	0.396553i	0.728547	+	0.684996i	$0.240196\pi$
$878$	−5.57632e16	+	3.21949e16i	−0.121725	+	0.0702781i
$879$	2.61863e17	+	4.53560e17i	0.567729	+	0.983336i
$880$	−1.54759e17	−	8.93499e16i	−0.333241	−	0.192397i
$881$			1.11446e16i			0.0238347i	0.999929	+	0.0119174i	$0.00379350\pi$
$881$			1.11446e16i			0.0238347i	−0.999929	+	0.0119174i	$0.996206\pi$
$882$		0			0
$883$	−4.76939e17			−1.00623			−0.503117	−	0.864218i	$-0.667813\pi$
$883$	−4.76939e17			−1.00623			−0.503117	+	0.864218i	$0.667813\pi$
$884$	2.78920e16	−	4.83104e16i	0.0584476	−	0.101234i
$885$	4.68880e17	−	2.70708e17i	0.975892	−	0.563431i
$886$	1.87859e17	+	3.25382e17i	0.388356	+	0.672653i
$887$	−3.47506e17	−	2.00632e17i	−0.713543	−	0.411964i	0.0988285	−	0.995104i	$-0.468490\pi$
$887$	−3.47506e17	−	2.00632e17i	−0.713543	−	0.411964i	−0.812372	+	0.583140i	$0.801824\pi$
$888$		−	1.75533e17i		−	0.357998i
$889$		0			0
$890$	5.53080e17			1.11288
$891$	−1.59359e17	+	2.76017e17i	−0.318500	+	0.551658i
$892$	1.61117e17	−	9.30212e16i	0.319855	−	0.184668i
$893$	4.37471e16	+	7.57722e16i	0.0862661	+	0.149417i
$894$	2.46444e17	+	1.42285e17i	0.482718	+	0.278697i
$895$			4.72819e17i			0.919934i
$896$		0			0
$897$	−1.11837e18			−2.14699
$898$	1.22746e16	−	2.12601e16i	0.0234071	−	0.0405423i
$899$	1.65057e17	−	9.52956e16i	0.312662	−	0.180516i
$900$	3.74354e16	+	6.48401e16i	0.0704414	+	0.122008i
$901$	2.07685e16	+	1.19907e16i	0.0388201	+	0.0224128i
$902$			3.91340e17i			0.726632i
$903$		0			0
$904$	−2.71994e17			−0.498366
$905$	1.71003e17	−	2.96186e17i	0.311252	−	0.539104i
$906$	−7.58795e17	+	4.38091e17i	−1.37200	+	0.792127i
$907$	2.11727e17	+	3.66722e17i	0.380305	+	0.658708i	0.991106	−	0.133077i	$-0.0424856\pi$
$907$	2.11727e17	+	3.66722e17i	0.380305	+	0.658708i	−0.610801	+	0.791784i	$0.709152\pi$
$908$	2.56306e17	+	1.47978e17i	0.457344	+	0.264048i
$909$		−	8.82631e17i		−	1.56457i
$910$		0			0
$911$	−3.15441e16			−0.0551834			−0.0275917	−	0.999619i	$-0.508784\pi$
$911$	−3.15441e16			−0.0551834			−0.0275917	+	0.999619i	$0.508784\pi$
$912$	3.80521e16	−	6.59082e16i	0.0661317	−	0.114543i
$913$	5.48481e15	−	3.16666e15i	0.00946972	−	0.00546734i
$914$	1.20561e17	+	2.08818e17i	0.206791	+	0.358172i
$915$	9.77488e17	+	5.64353e17i	1.66565	+	0.961666i
$916$			3.12125e17i			0.528391i
$917$		0			0
$918$	4.04562e16			0.0675973
$919$	1.78384e17	−	3.08971e17i	0.296117	−	0.512890i	−0.679127	−	0.734021i	$-0.737641\pi$
$919$	1.78384e17	−	3.08971e17i	0.296117	−	0.512890i	0.975244	+	0.221131i	$0.0709748\pi$
$920$	−1.37044e17	+	7.91225e16i	−0.226013	+	0.130489i
$921$	−2.26351e17	−	3.92051e17i	−0.370872	−	0.642370i
$922$	5.09101e16	+	2.93929e16i	0.0828740	+	0.0478473i
$923$		−	4.05702e17i		−	0.656140i
$924$		0			0
$925$	−7.96310e16			−0.127125
$926$	−3.38416e17	+	5.86153e17i	−0.536765	+	0.929705i
$927$	−4.36948e17	+	2.52272e17i	−0.688575	+	0.397549i
$928$	1.05110e17	+	1.82056e17i	0.164572	+	0.285047i
$929$	7.87030e17	+	4.54392e17i	1.22433	+	0.706864i	0.965837	−	0.259150i	$-0.0834424\pi$
$929$	7.87030e17	+	4.54392e17i	1.22433	+	0.706864i	0.258488	+	0.966014i	$0.416776\pi$
$930$			1.24184e17i			0.191940i
$931$		0			0
$932$	−2.64022e16			−0.0402851
$933$	6.20712e17	−	1.07510e18i	0.941023	−	1.62990i
$934$	−2.41205e17	+	1.39260e17i	−0.363334	+	0.209771i
$935$	7.19645e16	+	1.24646e17i	0.107708	+	0.186556i
$936$	−4.94408e17	−	2.85446e17i	−0.735241	−	0.424492i
$937$		−	7.52418e16i		−	0.111179i	−0.998454	−	0.0555894i	$-0.982296\pi$
$937$		−	7.52418e16i		−	0.111179i	0.998454	−	0.0555894i	$-0.0177038\pi$
$938$		0			0
$939$	6.47329e17			0.944346
$940$	7.87364e16	−	1.36376e17i	0.114132	−	0.197683i
$941$	1.16129e18	−	6.70472e17i	1.67264	−	0.965701i	0.706494	−	0.707719i	$-0.250276\pi$
$941$	1.16129e18	−	6.70472e17i	1.67264	−	0.965701i	0.966150	−	0.257982i	$-0.0830577\pi$
$942$	−4.62271e17	−	8.00678e17i	−0.661594	−	1.14591i
$943$	3.00117e17	+	1.73272e17i	0.426796	+	0.246411i
$944$		−	1.42412e17i		−	0.201240i
$945$		0			0
$946$	4.84842e17			0.676478
$947$	5.24027e16	−	9.07641e16i	0.0726530	−	0.125839i	−0.827410	−	0.561598i	$-0.810187\pi$
$947$	5.24027e16	−	9.07641e16i	0.0726530	−	0.125839i	0.900063	+	0.435759i	$0.143520\pi$
$948$	−5.18931e17	+	2.99605e17i	−0.714924	+	0.412761i
$949$	3.06122e17	+	5.30218e17i	0.419080	+	0.725868i
$950$	−2.98995e16	−	1.72625e16i	−0.0406744	−	0.0234834i
$951$		−	2.71874e17i		−	0.367523i
$952$		0			0
$953$	6.53447e17			0.872274			0.436137	−	0.899880i	$-0.356346\pi$
$953$	6.53447e17			0.872274			0.436137	+	0.899880i	$0.356346\pi$
$954$	1.22713e17	−	2.12544e17i	0.162779	−	0.281942i
$955$	6.63435e17	−	3.83035e17i	0.874537	−	0.504914i
$956$	−1.51226e17	−	2.61932e17i	−0.198098	−	0.343116i
$957$	−3.31970e18	−	1.91663e18i	−4.32142	−	2.49498i
$958$		−	4.25091e17i		−	0.549906i
$959$		0			0
$960$	−1.36973e17			−0.174988
$961$	−3.79024e17	+	6.56489e17i	−0.481201	+	0.833464i
$962$	5.25841e17	−	3.03595e17i	0.663444	−	0.383039i
$963$	4.58814e17	+	7.94689e17i	0.575279	+	0.996413i
$964$	2.84526e17	+	1.64271e17i	0.354535	+	0.204691i
$965$		−	4.85151e17i		−	0.600777i
$966$		0			0
$967$	−2.98974e17			−0.365658			−0.182829	−	0.983145i	$-0.558525\pi$
$967$	−2.98974e17			−0.365658			−0.182829	+	0.983145i	$0.558525\pi$
$968$	2.83113e17	−	4.90367e17i	0.344119	−	0.596031i
$969$	−5.30840e16	+	3.06481e16i	−0.0641240	+	0.0370220i
$970$	2.80849e17	+	4.86445e17i	0.337165	+	0.583987i
$971$	−5.60125e17	−	3.23388e17i	−0.668297	−	0.385841i	0.127134	−	0.991886i	$-0.459422\pi$
$971$	−5.60125e17	−	3.23388e17i	−0.668297	−	0.385841i	−0.795431	+	0.606044i	$0.792755\pi$
$972$			5.32315e17i			0.631207i
$973$		0			0
$974$	3.71493e17			0.435107
$975$	−2.19576e17	+	3.80317e17i	−0.255598	+	0.442709i
$976$	2.57114e17	−	1.48445e17i	0.297459	−	0.171738i
$977$	−7.29729e17	−	1.26393e18i	−0.839062	−	1.45330i	−0.890680	−	0.454631i	$-0.849771\pi$
$977$	−7.29729e17	−	1.26393e18i	−0.839062	−	1.45330i	0.0516180	−	0.998667i	$-0.483562\pi$
$978$	−1.19875e18	−	6.92098e17i	−1.36992	−	0.790923i
$979$			2.65275e18i			3.01301i
$980$		0			0
$981$	−1.52339e18			−1.70922
$982$	3.85358e17	−	6.67460e17i	0.429730	−	0.744314i
$983$	4.19576e16	−	2.42242e16i	0.0465039	−	0.0268490i	−0.476568	−	0.879138i	$-0.658119\pi$
$983$	4.19576e16	−	2.42242e16i	0.0465039	−	0.0268490i	0.523072	+	0.852289i	$0.324786\pi$
$984$	1.49981e17	+	2.59774e17i	0.165221	+	0.286171i
$985$	2.94691e17	+	1.70140e17i	0.322663	+	0.186289i
$986$		−	1.69316e17i		−	0.184262i
$987$		0			0
$988$	2.63253e17			0.283030
$989$	2.14672e17	−	3.71823e17i	0.229403	−	0.397337i
$990$	1.27563e18	−	7.36483e17i	1.35492	−	0.782261i
$991$	6.04866e17	+	1.04766e18i	0.638583	+	1.10606i	0.985744	+	0.168252i	$0.0538123\pi$
$991$	6.04866e17	+	1.04766e18i	0.638583	+	1.10606i	−0.347161	+	0.937805i	$0.612854\pi$
$992$	2.82885e16	+	1.63324e16i	0.0296852	+	0.0171387i
$993$			8.30318e17i			0.866062i
$994$		0			0
$995$	4.80303e17			0.494967
$996$	2.42724e15	−	4.20410e15i	0.00248632	−	0.00430642i
$997$	1.50455e18	−	8.68652e17i	1.53192	−	0.884454i	0.532645	−	0.846339i	$-0.321198\pi$
$997$	1.50455e18	−	8.68652e17i	1.53192	−	0.884454i	0.999273	−	0.0381148i	$-0.0121352\pi$
$998$	1.57291e17	+	2.72435e17i	0.159191	+	0.275728i
$999$	3.81356e17	+	2.20176e17i	0.383652	+	0.221502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.a.19.5		16
7.2	even	3		98.13.b.c.97.2		16
7.3	odd	6	inner	98.13.d.a.31.5		16
7.4	even	3		14.13.d.a.3.8	✓	16
7.5	odd	6		98.13.b.c.97.7		16
7.6	odd	2		14.13.d.a.5.8	yes	16
21.11	odd	6		126.13.n.a.73.3		16
21.20	even	2		126.13.n.a.19.3		16
28.11	odd	6		112.13.s.c.17.2		16
28.27	even	2		112.13.s.c.33.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.8	✓	16	7.4	even	3
14.13.d.a.5.8	yes	16	7.6	odd	2
98.13.b.c.97.2		16	7.2	even	3
98.13.b.c.97.7		16	7.5	odd	6
98.13.d.a.19.5		16	1.1	even	1	trivial
98.13.d.a.31.5		16	7.3	odd	6	inner
112.13.s.c.17.2		16	28.11	odd	6
112.13.s.c.33.2		16	28.27	even	2
126.13.n.a.19.3		16	21.20	even	2
126.13.n.a.73.3		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(22.6274 - 39.1918i) q^{2} +(-985.668 + 569.076i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(12133.2 + 7005.11i) q^{5} +51506.9i q^{6} -92681.9 q^{8} +(381974. - 661598. i) q^{9} +O(q^{10})\)	\(q+(22.6274 - 39.1918i) q^{2} +(-985.668 + 569.076i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(12133.2 + 7005.11i) q^{5} +51506.9i q^{6} -92681.9 q^{8} +(381974. - 661598. i) q^{9} +(549087. - 317015. i) q^{10} +(1.52051e6 + 2.63360e6i) q^{11} +(2.01865e6 + 1.16547e6i) q^{12} +8.06298e6i q^{13} -1.59458e7 q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(2.92560e6 - 1.68910e6i) q^{17} +(-1.72862e7 - 2.99405e7i) q^{18} +(1.38064e7 + 7.97110e6i) q^{19} -2.86929e7i q^{20} +1.37621e8 q^{22} +(6.09340e7 - 1.05541e8i) q^{23} +(9.13536e7 - 5.27430e7i) q^{24} +(-2.39271e7 - 4.14429e7i) q^{25} +(3.16003e8 + 1.82444e8i) q^{26} +2.64628e8i q^{27} +1.10751e9 q^{29} +(-3.60811e8 + 6.24944e8i) q^{30} +(1.49034e8 - 8.60447e7i) q^{31} +(9.49063e7 + 1.64382e8i) q^{32} +(-2.99743e9 - 1.73057e9i) q^{33} -1.52879e8i q^{34} -1.56457e9 q^{36} +(8.32019e8 - 1.44110e9i) q^{37} +(6.24804e8 - 3.60731e8i) q^{38} +(-4.58845e9 - 7.94742e9i) q^{39} +(-1.12453e9 - 6.49247e8i) q^{40} +2.84361e9i q^{41} +3.52303e9 q^{43} +(3.11400e9 - 5.39361e9i) q^{44} +(9.26915e9 - 5.35154e9i) q^{45} +(-2.75756e9 - 4.77623e9i) q^{46} +(4.75293e9 + 2.74410e9i) q^{47} -4.77375e9i q^{48} -2.16563e9 q^{50} +(-1.92245e9 + 3.32978e9i) q^{51} +(1.43007e10 - 8.25649e9i) q^{52} +(3.54944e9 + 6.14782e9i) q^{53} +(1.03713e10 + 5.98786e9i) q^{54} +4.26053e10i q^{55} -1.81446e10 q^{57} +(2.50602e10 - 4.34055e10i) q^{58} +(-2.94046e10 + 1.69768e10i) q^{59} +(1.63285e10 + 2.82817e10i) q^{60} +(-6.13008e10 - 3.53920e10i) q^{61} -7.78787e9i q^{62} +8.58993e9 q^{64} +(-5.64821e10 + 9.78299e10i) q^{65} +(-1.35648e11 + 7.83166e10i) q^{66} +(5.76089e10 + 9.97815e10i) q^{67} +(-5.99163e9 - 3.45927e9i) q^{68} +1.38704e11i q^{69} -5.03166e10 q^{71} +(-3.54021e10 + 6.13182e10i) q^{72} +(6.57596e10 - 3.79663e10i) q^{73} +(-3.76529e10 - 6.52167e10i) q^{74} +(4.71683e10 + 2.72326e10i) q^{75} -3.26496e10i q^{76} -4.15299e11 q^{78} +(-1.28534e11 + 2.22628e11i) q^{79} +(-5.08904e10 + 2.93816e10i) q^{80} +(5.24031e10 + 9.07648e10i) q^{81} +(1.11446e11 + 6.43435e10i) q^{82} -2.08263e9i q^{83} +4.73292e10 q^{85} +(7.97171e10 - 1.38074e11i) q^{86} +(-1.09164e12 + 6.30259e11i) q^{87} +(-1.40924e11 - 2.44087e11i) q^{88} +(7.55454e11 + 4.36162e11i) q^{89} -4.84366e11i q^{90} -2.49586e11 q^{92} +(-9.79319e10 + 1.69623e11i) q^{93} +(2.15093e11 - 1.24184e11i) q^{94} +(1.11677e11 + 1.93430e11i) q^{95} +(-1.87092e11 - 1.08018e11i) q^{96} +8.85916e11i q^{97} +2.32318e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9}+O(q^{10}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9	\( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9} + 2290176 q^{10} + 2072088 q^{11} - 27163728 q^{15} - 33554432 q^{16} + 101561040 q^{17} - 4592640 q^{18} - 174931848 q^{19} + 62776320 q^{22} + 25630560 q^{23} - 242221056 q^{24} + 521205808 q^{25} + 1434682368 q^{26} + 532360944 q^{29} - 2151917568 q^{30} - 4583818344 q^{31} - 6054957720 q^{33} - 9675767808 q^{36} + 5764524040 q^{37} + 149506560 q^{38} + 10526083272 q^{39} - 4690280448 q^{40} - 66929432000 q^{43} + 4243636224 q^{44} - 57253352184 q^{45} + 7203213312 q^{46} - 18116171640 q^{47} - 99248080896 q^{50} - 23299256376 q^{51} - 8269578240 q^{52} + 39134161800 q^{53} - 105152205312 q^{54} - 328243960080 q^{57} + 29637396480 q^{58} - 201845459088 q^{59} + 27815657472 q^{60} - 336780254328 q^{61} + 137438953472 q^{64} + 158322703896 q^{65} - 268884080640 q^{66} + 107767119920 q^{67} - 207997009920 q^{68} - 1150259029344 q^{71} - 9405726720 q^{72} + 738414283320 q^{73} + 4902778368 q^{74} - 1537028640000 q^{75} - 786088888320 q^{78} + 227632064768 q^{79} + 76101451776 q^{80} - 391984178400 q^{81} + 302578053120 q^{82} + 710209696080 q^{85} - 38105192448 q^{86} - 1957017683880 q^{87} - 64282951680 q^{88} + 2485007442792 q^{89} - 104982773760 q^{92} - 458668768680 q^{93} + 2021298693120 q^{94} - 186503862960 q^{95} + 496068722688 q^{96} + 3921180354576 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 - 18144 * q^5 + 2362248 * q^9 + 2290176 * q^10 + 2072088 * q^11 - 27163728 * q^15 - 33554432 * q^16 + 101561040 * q^17 - 4592640 * q^18 - 174931848 * q^19 + 62776320 * q^22 + 25630560 * q^23 - 242221056 * q^24 + 521205808 * q^25 + 1434682368 * q^26 + 532360944 * q^29 - 2151917568 * q^30 - 4583818344 * q^31 - 6054957720 * q^33 - 9675767808 * q^36 + 5764524040 * q^37 + 149506560 * q^38 + 10526083272 * q^39 - 4690280448 * q^40 - 66929432000 * q^43 + 4243636224 * q^44 - 57253352184 * q^45 + 7203213312 * q^46 - 18116171640 * q^47 - 99248080896 * q^50 - 23299256376 * q^51 - 8269578240 * q^52 + 39134161800 * q^53 - 105152205312 * q^54 - 328243960080 * q^57 + 29637396480 * q^58 - 201845459088 * q^59 + 27815657472 * q^60 - 336780254328 * q^61 + 137438953472 * q^64 + 158322703896 * q^65 - 268884080640 * q^66 + 107767119920 * q^67 - 207997009920 * q^68 - 1150259029344 * q^71 - 9405726720 * q^72 + 738414283320 * q^73 + 4902778368 * q^74 - 1537028640000 * q^75 - 786088888320 * q^78 + 227632064768 * q^79 + 76101451776 * q^80 - 391984178400 * q^81 + 302578053120 * q^82 + 710209696080 * q^85 - 38105192448 * q^86 - 1957017683880 * q^87 - 64282951680 * q^88 + 2485007442792 * q^89 - 104982773760 * q^92 - 458668768680 * q^93 + 2021298693120 * q^94 - 186503862960 * q^95 + 496068722688 * q^96 + 3921180354576 * q^99

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