LMFDB - Embedded newform 98.13.d.a.31.3

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			31.3
Root			$-272.613 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.31
Dual form			98.13.d.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-22.6274 - 39.1918i) q^{2} +(409.670 + 236.523i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18219.6 + 10519.1i) q^{5} -21407.6i q^{6} +92681.9 q^{8} +(-153834. - 266449. i) q^{9} +O(q^{10})$	\(q+(-22.6274 - 39.1918i) q^{2} +(409.670 + 236.523i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18219.6 + 10519.1i) q^{5} -21407.6i q^{6} +92681.9 q^{8} +(-153834. - 266449. i) q^{9} +(824525. + 476040. i) q^{10} +(-246520. + 426985. i) q^{11} +(-839004. + 484399. i) q^{12} -3.20567e6i q^{13} -9.95203e6 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(2.98777e7 + 1.72499e7i) q^{17} +(-6.96174e6 + 1.20581e7i) q^{18} +(1.84755e7 - 1.06668e7i) q^{19} -4.30862e7i q^{20} +2.23124e7 q^{22} +(-1.22901e8 - 2.12871e8i) q^{23} +(3.79690e7 + 2.19214e7i) q^{24} +(9.92324e7 - 1.71875e8i) q^{25} +(-1.25636e8 + 7.25360e7i) q^{26} -3.96937e8i q^{27} +8.71852e8 q^{29} +(2.25189e8 + 3.90038e8i) q^{30} +(6.16355e8 + 3.55853e8i) q^{31} +(-9.49063e7 + 1.64382e8i) q^{32} +(-2.01983e8 + 1.16615e8i) q^{33} -1.56128e9i q^{34} +6.30105e8 q^{36} +(1.22641e9 + 2.12420e9i) q^{37} +(-8.36106e8 - 4.82726e8i) q^{38} +(7.58214e8 - 1.31327e9i) q^{39} +(-1.68863e9 + 9.74930e8i) q^{40} +4.29341e9i q^{41} -8.71250e9 q^{43} +(-5.04873e8 - 8.74465e8i) q^{44} +(5.60560e9 + 3.23639e9i) q^{45} +(-5.56186e9 + 9.63343e9i) q^{46} +(4.94270e9 - 2.85367e9i) q^{47} -1.98410e9i q^{48} -8.98149e9 q^{50} +(8.15999e9 + 1.41335e10i) q^{51} +(5.68564e9 + 3.28260e9i) q^{52} +(-4.77915e9 + 8.27773e9i) q^{53} +(-1.55567e10 + 8.98167e9i) q^{54} -1.03727e10i q^{55} +1.00918e10 q^{57} +(-1.97278e10 - 3.41695e10i) q^{58} +(-4.83789e10 - 2.79316e10i) q^{59} +(1.01909e10 - 1.76511e10i) q^{60} +(-5.97865e10 + 3.45177e10i) q^{61} -3.22081e10i q^{62} +8.58993e9 q^{64} +(3.37207e10 + 5.84060e10i) q^{65} +(9.14073e9 + 5.27740e9i) q^{66} +(3.87174e10 - 6.70604e10i) q^{67} +(-6.11895e10 + 3.53278e10i) q^{68} -1.16276e11i q^{69} -1.07183e11 q^{71} +(-1.42577e10 - 2.46950e10i) q^{72} +(-2.07256e10 - 1.19659e10i) q^{73} +(5.55008e10 - 9.61301e10i) q^{74} +(8.13050e10 - 4.69415e10i) q^{75} +4.36914e10i q^{76} -6.86257e10 q^{78} +(1.59667e10 + 2.76551e10i) q^{79} +(7.64186e10 + 4.41203e10i) q^{80} +(1.21310e10 - 2.10115e10i) q^{81} +(1.68267e11 - 9.71488e10i) q^{82} +3.39427e11i q^{83} -7.25813e11 q^{85} +(1.97141e11 + 3.41459e11i) q^{86} +(3.57172e11 + 2.06213e11i) q^{87} +(-2.28479e10 + 3.95738e10i) q^{88} +(-7.24885e11 + 4.18513e11i) q^{89} -2.92925e11i q^{90} +5.03402e11 q^{92} +(1.68335e11 + 2.91564e11i) q^{93} +(-2.23681e11 - 1.29142e11i) q^{94} +(-2.24411e11 + 3.88691e11i) q^{95} +(-7.77605e10 + 4.48950e10i) q^{96} +9.93604e11i q^{97} +1.51693e11 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 $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	409.670	+	236.523i	0.561961	+	0.324449i	0.753932	−	0.656952i	$-0.228155\pi$
$3$	409.670	+	236.523i	0.561961	+	0.324449i	−0.191971	+	0.981401i	$0.561488\pi$
$4$	−1024.00	+	1773.62i	−0.250000	+	0.433013i
$5$	−18219.6	+	10519.1i	−1.16605	+	0.673222i	−0.952748	−	0.303763i	$-0.901757\pi$
$5$	−18219.6	+	10519.1i	−1.16605	+	0.673222i	−0.213307	+	0.976985i	$0.568424\pi$
$6$		−	21407.6i		−	0.458840i
$7$		0			0
$7$		0			0
$8$	92681.9			0.353553
$9$	−153834.	−	266449.i	−0.289466	−	0.501370i
$10$	824525.	+	476040.i	0.824525	+	0.476040i
$11$	−246520.	+	426985.i	−0.139154	+	0.241022i	−0.927177	−	0.374624i	$-0.877772\pi$
$11$	−246520.	+	426985.i	−0.139154	+	0.241022i	0.788023	+	0.615646i	$0.211105\pi$
$12$	−839004.	+	484399.i	−0.280981	+	0.162224i
$13$		−	3.20567e6i		−	0.664138i	−0.943255	−	0.332069i	$-0.892253\pi$
$13$		−	3.20567e6i		−	0.664138i	0.943255	−	0.332069i	$-0.107747\pi$
$14$		0			0
$15$	−9.95203e6			−0.873704
$16$	−2.09715e6	−	3.63237e6i	−0.125000	−	0.216506i
$17$	2.98777e7	+	1.72499e7i	1.23781	+	0.714649i	0.968646	−	0.248445i	$-0.0799196\pi$
$17$	2.98777e7	+	1.72499e7i	1.23781	+	0.714649i	0.269163	+	0.963095i	$0.413253\pi$
$18$	−6.96174e6	+	1.20581e7i	−0.204684	+	0.354522i
$19$	1.84755e7	−	1.06668e7i	0.392712	−	0.226733i	−0.290622	−	0.956838i	$-0.593862\pi$
$19$	1.84755e7	−	1.06668e7i	0.392712	−	0.226733i	0.683335	+	0.730105i	$0.260529\pi$
$20$		−	4.30862e7i		−	0.673222i
$21$		0			0
$22$	2.23124e7			0.196793
$23$	−1.22901e8	−	2.12871e8i	−0.830211	−	1.43797i	−0.897871	−	0.440259i	$-0.854887\pi$
$23$	−1.22901e8	−	2.12871e8i	−0.830211	−	1.43797i	0.0676600	−	0.997708i	$-0.478447\pi$
$24$	3.79690e7	+	2.19214e7i	0.198683	+	0.114710i
$25$	9.92324e7	−	1.71875e8i	0.406456	−	0.704002i
$26$	−1.25636e8	+	7.25360e7i	−0.406700	+	0.234808i
$27$		−	3.96937e8i		−	1.02456i
$28$		0			0
$29$	8.71852e8			1.46573			0.732867	−	0.680372i	$-0.238182\pi$
$29$	8.71852e8			1.46573			0.732867	+	0.680372i	$0.238182\pi$
$30$	2.25189e8	+	3.90038e8i	0.308901	+	0.535032i
$31$	6.16355e8	+	3.55853e8i	0.694482	+	0.400959i	0.805289	−	0.592883i	$-0.202010\pi$
$31$	6.16355e8	+	3.55853e8i	0.694482	+	0.400959i	−0.110807	+	0.993842i	$0.535344\pi$
$32$	−9.49063e7	+	1.64382e8i	−0.0883883	+	0.153093i
$33$	−2.01983e8	+	1.16615e8i	−0.156398	+	0.0902966i
$34$		−	1.56128e9i		−	1.01067i
$35$		0			0
$36$	6.30105e8			0.289466
$37$	1.22641e9	+	2.12420e9i	0.477995	+	0.827912i	0.999682	−	0.0252251i	$-0.00803026\pi$
$37$	1.22641e9	+	2.12420e9i	0.477995	+	0.827912i	−0.521687	+	0.853137i	$0.674697\pi$
$38$	−8.36106e8	−	4.82726e8i	−0.277690	−	0.160324i
$39$	7.58214e8	−	1.31327e9i	0.215479	−	0.373220i
$40$	−1.68863e9	+	9.74930e8i	−0.412263	+	0.238020i
$41$			4.29341e9i			0.903856i	0.892054	+	0.451928i	$0.149264\pi$
$41$			4.29341e9i			0.903856i	−0.892054	+	0.451928i	$0.850736\pi$
$42$		0			0
$43$	−8.71250e9			−1.37826			−0.689131	−	0.724637i	$-0.742008\pi$
$43$	−8.71250e9			−1.37826			−0.689131	+	0.724637i	$0.742008\pi$
$44$	−5.04873e8	−	8.74465e8i	−0.0695770	−	0.120511i
$45$	5.60560e9	+	3.23639e9i	0.675067	+	0.389750i
$46$	−5.56186e9	+	9.63343e9i	−0.587048	+	1.01680i
$47$	4.94270e9	−	2.85367e9i	0.458540	−	0.264738i	−0.252890	−	0.967495i	$-0.581381\pi$
$47$	4.94270e9	−	2.85367e9i	0.458540	−	0.264738i	0.711430	+	0.702757i	$0.248048\pi$
$48$		−	1.98410e9i		−	0.162224i
$49$		0			0
$50$	−8.98149e9			−0.574815
$51$	8.15999e9	+	1.41335e10i	0.463734	+	0.803211i
$52$	5.68564e9	+	3.28260e9i	0.287580	+	0.166035i
$53$	−4.77915e9	+	8.27773e9i	−0.215623	+	0.373470i	−0.953465	−	0.301503i	$-0.902512\pi$
$53$	−4.77915e9	+	8.27773e9i	−0.215623	+	0.373470i	0.737842	+	0.674973i	$0.235845\pi$
$54$	−1.55567e10	+	8.98167e9i	−0.627415	+	0.362238i
$55$		−	1.03727e10i		−	0.374726i
$56$		0			0
$57$	1.00918e10			0.294252
$58$	−1.97278e10	−	3.41695e10i	−0.518215	−	0.897575i
$59$	−4.83789e10	−	2.79316e10i	−1.14695	−	0.662191i	−0.198807	−	0.980039i	$-0.563707\pi$
$59$	−4.83789e10	−	2.79316e10i	−1.14695	−	0.662191i	−0.948142	+	0.317847i	$0.897040\pi$
$60$	1.01909e10	−	1.76511e10i	0.218426	−	0.378325i
$61$	−5.97865e10	+	3.45177e10i	−1.16044	+	0.669982i	−0.951410	−	0.307926i	$-0.900365\pi$
$61$	−5.97865e10	+	3.45177e10i	−1.16044	+	0.669982i	−0.209033	+	0.977909i	$0.567032\pi$
$62$		−	3.22081e10i		−	0.567042i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	3.37207e10	+	5.84060e10i	0.447112	+	0.774421i
$66$	9.14073e9	+	5.27740e9i	0.110590	+	0.0638494i
$67$	3.87174e10	−	6.70604e10i	0.428013	−	0.741340i	−0.568684	−	0.822556i	$-0.692547\pi$
$67$	3.87174e10	−	6.70604e10i	0.428013	−	0.741340i	0.996697	+	0.0812163i	$0.0258805\pi$
$68$	−6.11895e10	+	3.53278e10i	−0.618904	+	0.357325i
$69$		−	1.16276e11i		−	1.07744i
$70$		0			0
$71$	−1.07183e11			−0.836715			−0.418358	−	0.908282i	$-0.637394\pi$
$71$	−1.07183e11			−0.836715			−0.418358	+	0.908282i	$0.637394\pi$
$72$	−1.42577e10	−	2.46950e10i	−0.102342	−	0.177261i
$73$	−2.07256e10	−	1.19659e10i	−0.136953	−	0.0790696i	0.429958	−	0.902849i	$-0.358528\pi$
$73$	−2.07256e10	−	1.19659e10i	−0.136953	−	0.0790696i	−0.566911	+	0.823779i	$0.691862\pi$
$74$	5.55008e10	−	9.61301e10i	0.337994	−	0.585422i
$75$	8.13050e10	−	4.69415e10i	0.456825	−	0.263748i
$76$			4.36914e10i			0.226733i
$77$		0			0
$78$	−6.86257e10			−0.304733
$79$	1.59667e10	+	2.76551e10i	0.0656829	+	0.113766i	0.896997	−	0.442037i	$-0.145744\pi$
$79$	1.59667e10	+	2.76551e10i	0.0656829	+	0.113766i	−0.831314	+	0.555803i	$0.812411\pi$
$80$	7.64186e10	+	4.41203e10i	0.291514	+	0.168306i
$81$	1.21310e10	−	2.10115e10i	0.0429523	−	0.0743955i
$82$	1.68267e11	−	9.71488e10i	0.553497	−	0.319561i
$83$			3.39427e11i			1.03819i	0.854716	+	0.519097i	$0.173731\pi$
$83$			3.39427e11i			1.03819i	−0.854716	+	0.519097i	$0.826269\pi$
$84$		0			0
$85$	−7.25813e11			−1.92447
$86$	1.97141e11	+	3.41459e11i	0.487289	+	0.844010i
$87$	3.57172e11	+	2.06213e11i	0.823685	+	0.475555i
$88$	−2.28479e10	+	3.95738e10i	−0.0491984	+	0.0852141i
$89$	−7.24885e11	+	4.18513e11i	−1.45858	+	0.842110i	−0.998942	−	0.0459978i	$-0.985353\pi$
$89$	−7.24885e11	+	4.18513e11i	−1.45858	+	0.842110i	−0.459635	+	0.888108i	$0.652020\pi$
$90$		−	2.92925e11i		−	0.551190i
$91$		0			0
$92$	5.03402e11			0.830211
$93$	1.68335e11	+	2.91564e11i	0.260181	+	0.450647i
$94$	−2.23681e11	−	1.29142e11i	−0.324236	−	0.187198i
$95$	−2.24411e11	+	3.88691e11i	−0.305283	+	0.528765i
$96$	−7.77605e10	+	4.48950e10i	−0.0993417	+	0.0573549i
$97$			9.93604e11i			1.19284i	0.802672	+	0.596421i	$0.203411\pi$
$97$			9.93604e11i			1.19284i	−0.802672	+	0.596421i	$0.796589\pi$
$98$		0			0
$99$	1.51693e11			0.161122
$100$	2.03228e11	+	3.52001e11i	0.203228	+	0.352001i
$101$	2.43625e11	+	1.40657e11i	0.229506	+	0.132505i	0.610344	−	0.792136i	$-0.291031\pi$
$101$	2.43625e11	+	1.40657e11i	0.229506	+	0.132505i	−0.380838	+	0.924642i	$0.624365\pi$
$102$	3.69279e11	−	6.39610e11i	0.327909	−	0.567956i
$103$	−7.84748e11	+	4.53075e11i	−0.657214	+	0.379443i	−0.791215	−	0.611538i	$-0.790551\pi$
$103$	−7.84748e11	+	4.53075e11i	−0.657214	+	0.379443i	0.134001	+	0.990981i	$0.457218\pi$
$104$		−	2.97107e11i		−	0.234808i
$105$		0			0
$106$	4.32559e11			0.304937
$107$	6.82690e11	+	1.18245e12i	0.454905	+	0.787919i	0.998683	−	0.0513106i	$-0.0163398\pi$
$107$	6.82690e11	+	1.18245e12i	0.454905	+	0.787919i	−0.543778	+	0.839229i	$0.683006\pi$
$108$	7.04016e11	+	4.06464e11i	0.443650	+	0.256141i
$109$	1.63912e9	−	2.83903e9i	0.000977352	−	0.00169282i	−0.865536	−	0.500846i	$-0.833022\pi$
$109$	1.63912e9	−	2.83903e9i	0.000977352	−	0.00169282i	0.866514	+	0.499153i	$0.166356\pi$
$110$	−4.06524e11	+	2.34707e11i	−0.229472	+	0.132486i
$111$			1.16029e12i			0.620340i
$112$		0			0
$113$	3.90063e12			1.87354			0.936772	−	0.349941i	$-0.113798\pi$
$113$	3.90063e12			1.87354			0.936772	+	0.349941i	$0.113798\pi$
$114$	−2.28352e11	−	3.95516e11i	−0.104034	−	0.180192i
$115$	4.47842e12	+	2.58561e12i	1.93614	+	1.11783i
$116$	−8.92777e11	+	1.54633e12i	−0.366433	+	0.634681i
$117$	−8.54146e11	+	4.93141e11i	−0.332979	+	0.192246i
$118$			2.52808e12i			0.936480i
$119$		0			0
$120$	−9.22373e11			−0.308901
$121$	1.44767e12	+	2.50744e12i	0.461272	+	0.798947i
$122$	2.70563e12	+	1.56209e12i	0.820557	+	0.473749i
$123$	−1.01549e12	+	1.75888e12i	−0.293255	+	0.507932i
$124$	−1.26230e12	+	7.28786e11i	−0.347241	+	0.200480i
$125$		−	9.60938e11i		−	0.251904i
$126$		0			0
$127$	−5.55734e12			−1.32448			−0.662239	−	0.749293i	$-0.730393\pi$
$127$	−5.55734e12			−1.32448			−0.662239	+	0.749293i	$0.730393\pi$
$128$	−1.94368e11	−	3.36655e11i	−0.0441942	−	0.0765466i
$129$	−3.56925e12	−	2.06071e12i	−0.774530	−	0.447175i
$130$	1.52603e12	−	2.64315e12i	0.316156	−	0.547599i
$131$	1.32531e12	−	7.65171e11i	0.262235	−	0.151402i	−0.363119	−	0.931743i	$-0.618288\pi$
$131$	1.32531e12	−	7.65171e11i	0.262235	−	0.151402i	0.625354	+	0.780341i	$0.284955\pi$
$132$		−	4.77656e11i		−	0.0902966i
$133$		0			0
$134$	−3.50429e12			−0.605302
$135$	4.17542e12	+	7.23204e12i	0.689760	+	1.19470i
$136$	2.76912e12	+	1.59875e12i	0.437632	+	0.252667i
$137$	4.48361e12	−	7.76583e12i	0.678116	−	1.17453i	−0.297432	−	0.954743i	$-0.596130\pi$
$137$	4.48361e12	−	7.76583e12i	0.678116	−	1.17453i	0.975548	−	0.219788i	$-0.0705367\pi$
$138$	−4.55706e12	+	2.63102e12i	−0.659796	+	0.380934i
$139$			1.16471e13i			1.61484i	0.589978	+	0.807419i	$0.299136\pi$
$139$			1.16471e13i			1.61484i	−0.589978	+	0.807419i	$0.700864\pi$
$140$		0			0
$141$	2.69983e12			0.343575
$142$	2.42529e12	+	4.20072e12i	0.295824	+	0.512381i
$143$	1.36877e12	+	7.90261e11i	0.160072	+	0.0924175i
$144$	−6.45228e11	+	1.11757e12i	−0.0723666	+	0.125343i
$145$	−1.58848e13	+	9.17110e12i	−1.70913	+	0.986764i
$146$			1.08303e12i			0.111821i
$147$		0			0
$148$	−5.02336e12			−0.477995
$149$	5.91457e12	+	1.02443e13i	0.540512	+	0.936195i	0.998875	+	0.0474295i	$0.0151030\pi$
$149$	5.91457e12	+	1.02443e13i	0.540512	+	0.936195i	−0.458362	+	0.888766i	$0.651564\pi$
$150$	−3.67944e12	−	2.12433e12i	−0.323024	−	0.186498i
$151$	−3.48253e11	+	6.03192e11i	−0.0293788	+	0.0508855i	−0.880341	−	0.474341i	$-0.842686\pi$
$151$	−3.48253e11	+	6.03192e11i	−0.0293788	+	0.0508855i	0.850962	+	0.525227i	$0.176020\pi$
$152$	1.71234e12	−	9.88623e11i	0.138845	−	0.0801621i
$153$		−	1.06145e13i		−	0.827468i
$154$		0			0
$155$	−1.49730e13			−1.07974
$156$	1.55282e12	+	2.68957e12i	0.107739	+	0.186610i
$157$	1.31986e13	+	7.62023e12i	0.881314	+	0.508827i	0.871091	−	0.491121i	$-0.163413\pi$
$157$	1.31986e13	+	7.62023e12i	0.881314	+	0.508827i	0.0102224	+	0.999948i	$0.496746\pi$
$158$	7.22570e11	−	1.25153e12i	0.0464448	−	0.0804448i
$159$	−3.91575e12	+	2.26076e12i	−0.242344	+	0.139917i
$160$		−	3.99331e12i		−	0.238020i
$161$		0			0
$162$	−1.09797e12			−0.0607437
$163$	−1.51249e13	−	2.61971e13i	−0.806430	−	1.39678i	−0.915321	−	0.402724i	$-0.868063\pi$
$163$	−1.51249e13	−	2.61971e13i	−0.806430	−	1.39678i	0.108891	−	0.994054i	$-0.465270\pi$
$164$	−7.61488e12	−	4.39645e12i	−0.391381	−	0.225964i
$165$	2.45337e12	−	4.24937e12i	0.121579	−	0.210582i
$166$	1.33028e13	−	7.68036e12i	0.635761	−	0.367057i
$167$		−	2.30730e12i		−	0.106367i	−0.998585	−	0.0531834i	$-0.983063\pi$
$167$		−	2.30730e12i		−	0.106367i	0.998585	−	0.0531834i	$-0.0169368\pi$
$168$		0			0
$169$	1.30218e13			0.558921
$170$	1.64233e13	+	2.84459e13i	0.680403	+	1.17849i
$171$	−5.68433e12	−	3.28185e12i	−0.227354	−	0.131263i
$172$	8.92160e12	−	1.54527e13i	0.344566	−	0.596805i
$173$	−1.76692e13	+	1.02013e13i	−0.659082	+	0.380521i	−0.791927	−	0.610615i	$-0.790922\pi$
$173$	−1.76692e13	+	1.02013e13i	−0.659082	+	0.380521i	0.132845	+	0.991137i	$0.457589\pi$
$174$		−	1.86643e13i		−	0.672536i
$175$		0			0
$176$	2.06796e12			0.0695770
$177$	−1.32129e13	−	2.28855e13i	−0.429694	−	0.744252i
$178$	3.28046e13	+	1.89397e13i	1.03137	+	0.595462i
$179$	−1.72380e13	+	2.98571e13i	−0.524046	+	0.907674i	0.475563	+	0.879682i	$0.342245\pi$
$179$	−1.72380e13	+	2.98571e13i	−0.524046	+	0.907674i	−0.999608	+	0.0279917i	$0.991089\pi$
$180$	−1.14803e13	+	6.62813e12i	−0.337534	+	0.194875i
$181$		−	6.96878e12i		−	0.198192i	−0.995078	−	0.0990958i	$-0.968405\pi$
$181$		−	6.96878e12i		−	0.198192i	0.995078	−	0.0990958i	$-0.0315950\pi$
$182$		0			0
$183$	−3.26569e13			−0.869499
$184$	−1.13907e13	−	1.97293e13i	−0.293524	−	0.508398i
$185$	−4.46892e13	−	2.58013e13i	−1.11474	−	0.643594i
$186$	7.61796e12	−	1.31947e13i	0.183976	−	0.318656i
$187$	−1.47309e13	+	8.50488e12i	−0.344492	+	0.198893i
$188$			1.16886e13i			0.264738i
$189$		0			0
$190$	2.03114e13			0.431735
$191$	3.54982e13	+	6.14847e13i	0.731149	+	1.26639i	0.956392	+	0.292085i	$0.0943491\pi$
$191$	3.54982e13	+	6.14847e13i	0.731149	+	1.26639i	−0.225243	+	0.974303i	$0.572318\pi$
$192$	3.51904e12	+	2.03172e12i	0.0702452	+	0.0405561i
$193$	−2.96152e13	+	5.12951e13i	−0.573022	+	0.992503i	0.423231	+	0.906022i	$0.360896\pi$
$193$	−2.96152e13	+	5.12951e13i	−0.573022	+	0.992503i	−0.996253	+	0.0864816i	$0.972438\pi$
$194$	3.89411e13	−	2.24827e13i	0.730463	−	0.421733i
$195$			3.19029e13i			0.580260i
$196$		0			0
$197$	9.54694e13			1.63330			0.816651	−	0.577132i	$-0.195828\pi$
$197$	9.54694e13			1.63330			0.816651	+	0.577132i	$0.195828\pi$
$198$	−3.43242e12	−	5.94512e12i	−0.0569651	−	0.0986664i
$199$	−2.20483e13	−	1.27296e13i	−0.355023	−	0.204973i	0.311872	−	0.950124i	$-0.399044\pi$
$199$	−2.20483e13	−	1.27296e13i	−0.355023	−	0.204973i	−0.666895	+	0.745151i	$0.732377\pi$
$200$	9.19704e12	−	1.59297e13i	0.143704	−	0.248902i
$201$	3.17227e13	−	1.83151e13i	0.481053	−	0.277736i
$202$		−	1.27308e13i		−	0.187391i
$203$		0			0
$204$	−3.34233e13			−0.463734
$205$	−4.51628e13	−	7.82243e13i	−0.608496	−	1.05395i
$206$	3.55136e13	+	2.05038e13i	0.464721	+	0.268307i
$207$	−3.78128e13	+	6.54936e13i	−0.480636	+	0.832486i
$208$	−1.16442e13	+	6.72277e12i	−0.143790	+	0.0830173i
$209$			1.05183e13i			0.126203i
$210$		0			0
$211$	−6.19581e12			−0.0702107			−0.0351054	−	0.999384i	$-0.511177\pi$
$211$	−6.19581e12			−0.0702107			−0.0351054	+	0.999384i	$0.511177\pi$
$212$	−9.78770e12	−	1.69528e13i	−0.107812	−	0.186735i
$213$	−4.39098e13	−	2.53514e13i	−0.470202	−	0.271471i
$214$	3.08950e13	−	5.35117e13i	0.321666	−	0.557143i
$215$	1.58738e14	−	9.16476e13i	1.60713	−	0.927877i
$216$		−	3.67889e13i		−	0.362238i
$217$		0			0
$218$	−1.48356e11			−0.00138218
$219$	−5.66044e12	−	9.80417e12i	−0.0513081	−	0.0888681i
$220$	1.83972e13	+	1.06216e13i	0.162261	+	0.0936815i
$221$	5.52974e13	−	9.57780e13i	0.474626	−	0.822076i
$222$	4.54740e13	−	2.62544e13i	0.379879	−	0.219323i
$223$			1.24687e14i			1.01389i	0.861977	+	0.506947i	$0.169226\pi$
$223$			1.24687e14i			1.01389i	−0.861977	+	0.506947i	$0.830774\pi$
$224$		0			0
$225$	−6.10613e13			−0.470621
$226$	−8.82611e13	−	1.52873e14i	−0.662398	−	1.14731i
$227$	−1.47962e14	−	8.54259e13i	−1.08142	−	0.624359i	−0.150142	−	0.988664i	$-0.547973\pi$
$227$	−1.47962e14	−	8.54259e13i	−1.08142	−	0.624359i	−0.931279	+	0.364306i	$0.881306\pi$
$228$	−1.03340e13	+	1.78990e13i	−0.0735631	+	0.127415i
$229$	1.77873e14	−	1.02695e14i	1.23338	−	0.712094i	0.265650	−	0.964070i	$-0.414413\pi$
$229$	1.77873e14	−	1.02695e14i	1.23338	−	0.712094i	0.967734	+	0.251975i	$0.0810801\pi$
$230$		−	2.34023e14i		−	1.58085i
$231$		0			0
$232$	8.08049e13			0.518215
$233$	−1.31093e14	−	2.27060e14i	−0.819302	−	1.41907i	−0.906197	−	0.422855i	$-0.861028\pi$
$233$	−1.31093e14	−	2.27060e14i	−0.819302	−	1.41907i	0.0868957	−	0.996217i	$-0.472305\pi$
$234$	3.86542e13	+	2.23170e13i	0.235452	+	0.135938i
$235$	−6.00360e13	+	1.03985e14i	−0.356455	+	0.617398i
$236$	9.90800e13	−	5.72039e13i	0.573475	−	0.331096i
$237$			1.51060e13i			0.0852429i
$238$		0			0
$239$	2.57036e14			1.37914			0.689568	−	0.724221i	$-0.257800\pi$
$239$	2.57036e14			1.37914			0.689568	+	0.724221i	$0.257800\pi$
$240$	2.08709e13	+	3.61495e13i	0.109213	+	0.189162i
$241$	−1.19687e14	−	6.91013e13i	−0.610864	−	0.352683i	0.162439	−	0.986719i	$-0.448064\pi$
$241$	−1.19687e14	−	6.91013e13i	−0.610864	−	0.352683i	−0.773304	+	0.634036i	$0.781397\pi$
$242$	6.55141e13	−	1.13474e14i	0.326169	−	0.564941i
$243$	−1.72748e14	+	9.97359e13i	−0.839024	+	0.484411i
$244$		−	1.41385e14i		−	0.669982i
$245$		0			0
$246$	9.19117e13			0.414725
$247$	−3.41943e13	−	5.92263e13i	−0.150582	−	0.260815i
$248$	5.71250e13	+	3.29811e13i	0.245536	+	0.141760i
$249$	−8.02823e13	+	1.39053e14i	−0.336840	+	0.583424i
$250$	−3.76609e13	+	2.17436e13i	−0.154259	+	0.0890616i
$251$			1.98023e14i			0.791904i	0.918271	+	0.395952i	$0.129585\pi$
$251$			1.98023e14i			0.791904i	−0.918271	+	0.395952i	$0.870415\pi$
$252$		0			0
$253$	1.21190e14			0.462109
$254$	1.25748e14	+	2.17802e14i	0.468273	+	0.811073i
$255$	−2.97344e14	−	1.71671e14i	−1.08148	−	0.624392i
$256$	−8.79609e12	+	1.52353e13i	−0.0312500	+	0.0541266i
$257$	8.73651e11	−	5.04403e11i	0.00303207	−	0.00175057i	−0.498483	−	0.866899i	$-0.666109\pi$
$257$	8.73651e11	−	5.04403e11i	0.00303207	−	0.00175057i	0.501515	+	0.865149i	$0.332776\pi$
$258$			1.86514e14i			0.632401i
$259$		0			0
$260$	−1.38120e14			−0.447112
$261$	−1.34121e14	−	2.32304e14i	−0.424280	−	0.734875i
$262$	−5.99769e13	−	3.46277e13i	−0.185428	−	0.107057i
$263$	−1.48779e13	+	2.57693e13i	−0.0449580	+	0.0778695i	−0.887629	−	0.460560i	$-0.847649\pi$
$263$	−1.48779e13	+	2.57693e13i	−0.0449580	+	0.0778695i	0.842671	+	0.538429i	$0.180982\pi$
$264$	−1.87202e13	+	1.08081e13i	−0.0552952	+	0.0319247i
$265$		−	2.01089e14i		−	0.580649i
$266$		0			0
$267$	−3.95952e14			−1.09289
$268$	7.92931e13	+	1.37340e14i	0.214006	+	0.370670i
$269$	−6.78960e13	−	3.91998e13i	−0.179197	−	0.103459i	0.407718	−	0.913108i	$-0.366325\pi$
$269$	−6.78960e13	−	3.91998e13i	−0.179197	−	0.103459i	−0.586915	+	0.809648i	$0.699658\pi$
$270$	1.88958e14	−	3.27285e14i	0.487734	−	0.844779i
$271$	−2.35729e14	+	1.36098e14i	−0.595109	+	0.343586i	−0.767115	−	0.641509i	$-0.778309\pi$
$271$	−2.35729e14	+	1.36098e14i	−0.595109	+	0.343586i	0.172006	+	0.985096i	$0.444975\pi$
$272$		−	1.44703e14i		−	0.357325i
$273$		0			0
$274$	−4.05810e14			−0.959001
$275$	4.89255e13	+	8.47414e13i	0.113120	+	0.195929i
$276$	2.06229e14	+	1.19066e14i	0.466546	+	0.269361i
$277$	−3.85418e14	+	6.67564e14i	−0.853205	+	1.47779i	0.0250951	+	0.999685i	$0.492011\pi$
$277$	−3.85418e14	+	6.67564e14i	−0.853205	+	1.47779i	−0.878300	+	0.478110i	$0.841322\pi$
$278$	4.56471e14	−	2.63544e14i	0.988882	−	0.570931i
$279$		−	2.18969e14i		−	0.464257i
$280$		0			0
$281$	−5.71699e14			−1.16126			−0.580630	−	0.814168i	$-0.697194\pi$
$281$	−5.71699e14			−1.16126			−0.580630	+	0.814168i	$0.697194\pi$
$282$	−6.10902e13	−	1.05811e14i	−0.121472	−	0.210396i
$283$	1.36757e14	+	7.89569e13i	0.266215	+	0.153699i	0.627166	−	0.778885i	$-0.284215\pi$
$283$	1.36757e14	+	7.89569e13i	0.266215	+	0.153699i	−0.360951	+	0.932585i	$0.617548\pi$
$284$	1.09756e14	−	1.90103e14i	0.209179	−	0.362308i
$285$	−1.83869e14	+	1.06157e14i	−0.343114	+	0.198097i
$286$		−	7.15262e13i		−	0.130698i
$287$		0			0
$288$	5.83993e13			0.102342
$289$	3.03807e14	+	5.26209e14i	0.521447	+	0.903173i
$290$	7.18864e14	+	4.15036e14i	1.20853	+	0.697747i
$291$	−2.35010e14	+	4.07049e14i	−0.387016	+	0.670331i
$292$	4.24461e13	−	2.45062e13i	0.0684763	−	0.0395348i
$293$			3.53680e14i			0.558991i	0.960147	+	0.279496i	$0.0901673\pi$
$293$			3.53680e14i			0.558991i	−0.960147	+	0.279496i	$0.909833\pi$
$294$		0			0
$295$	1.17526e15			1.78321
$296$	1.13666e14	+	1.96875e14i	0.168997	+	0.292711i
$297$	1.69486e14	+	9.78529e13i	0.246942	+	0.142572i
$298$	2.67663e14	−	4.63606e14i	0.382200	−	0.661990i
$299$	−6.82393e14	+	3.93980e14i	−0.955009	+	0.551375i
$300$			1.92272e14i			0.263748i
$301$		0			0
$302$	3.15203e13			0.0415478
$303$	6.65372e13	+	1.15246e14i	0.0859823	+	0.148926i
$304$	−7.74919e13	−	4.47400e13i	−0.0981781	−	0.0566832i
$305$	7.26190e14	−	1.25780e15i	0.902093	−	1.56247i
$306$	−4.16002e14	+	2.40179e14i	−0.506718	+	0.292554i
$307$		−	6.29037e14i		−	0.751356i	−0.926750	−	0.375678i	$-0.877410\pi$
$307$		−	6.29037e14i		−	0.751356i	0.926750	−	0.375678i	$-0.122590\pi$
$308$		0			0
$309$	−4.28650e14			−0.492439
$310$	3.38800e14	+	5.86819e14i	0.381745	+	0.661202i
$311$	1.73042e14	+	9.99060e13i	0.191245	+	0.110415i	0.592565	−	0.805522i	$-0.298115\pi$
$311$	1.73042e14	+	9.99060e13i	0.191245	+	0.110415i	−0.401320	+	0.915938i	$0.631449\pi$
$312$	7.02727e13	−	1.21716e14i	0.0761832	−	0.131953i
$313$	−7.58277e14	+	4.37791e14i	−0.806421	+	0.465587i	−0.845711	−	0.533641i	$-0.820823\pi$
$313$	−7.58277e14	+	4.37791e14i	−0.806421	+	0.465587i	0.0392907	+	0.999228i	$0.487490\pi$
$314$		−	6.89704e14i		−	0.719590i
$315$		0			0
$316$	−6.53995e13			−0.0656829
$317$	−1.60157e14	−	2.77400e14i	−0.157830	−	0.273370i	0.776256	−	0.630418i	$-0.217116\pi$
$317$	−1.60157e14	−	2.77400e14i	−0.157830	−	0.273370i	−0.934086	+	0.357048i	$0.883783\pi$
$318$	1.77206e14	+	1.02310e14i	0.171363	+	0.0989364i
$319$	−2.14929e14	+	3.72268e14i	−0.203963	+	0.353274i
$320$	−1.56505e14	+	9.03583e13i	−0.145757	+	0.0841528i
$321$			6.45887e14i			0.590373i
$322$		0			0
$323$	7.36007e14			0.648137
$324$	2.48443e13	+	4.30315e13i	0.0214761	+	0.0371978i
$325$	−5.50976e14	−	3.18106e14i	−0.467554	−	0.269943i
$326$	−6.84475e14	+	1.18554e15i	−0.570232	+	0.987671i
$327$	1.34299e12	−	7.75377e11i	0.00109847	−	0.000634201i
$328$			3.97922e14i			0.319561i
$329$		0			0
$330$	−2.22054e14			−0.171939
$331$	2.45663e14	+	4.25501e14i	0.186798	+	0.323543i	0.944181	−	0.329428i	$-0.106856\pi$
$331$	2.45663e14	+	4.25501e14i	0.186798	+	0.323543i	−0.757383	+	0.652971i	$0.773522\pi$
$332$	−6.02015e14	−	3.47573e14i	−0.449551	−	0.259548i
$333$	3.77326e14	−	6.53548e14i	0.276727	−	0.479305i
$334$	−9.04275e13	+	5.22083e13i	−0.0651361	+	0.0376063i
$335$			1.62909e15i			1.15259i
$336$		0			0
$337$	−1.16473e15			−0.795147			−0.397573	−	0.917570i	$-0.630148\pi$
$337$	−1.16473e15			−0.795147			−0.397573	+	0.917570i	$0.630148\pi$
$338$	−2.94649e14	−	5.10348e14i	−0.197608	−	0.342268i
$339$	1.59797e15	+	9.22588e14i	1.05286	+	0.607868i
$340$	7.43233e14	−	1.28732e15i	0.481118	−	0.833320i
$341$	−3.03888e14	+	1.75450e14i	−0.193280	+	0.111590i
$342$			2.97039e14i			0.185634i
$343$		0			0
$344$	−8.07491e14			−0.487289
$345$	1.22311e15	+	2.11850e15i	0.725358	+	1.25636i
$346$	7.99616e14	+	4.61658e14i	0.466042	+	0.269069i
$347$	−1.70099e14	+	2.94619e14i	−0.0974370	+	0.168766i	−0.910623	−	0.413238i	$-0.864398\pi$
$347$	−1.70099e14	+	2.94619e14i	−0.0974370	+	0.168766i	0.813186	+	0.582004i	$0.197731\pi$
$348$	−7.31487e14	+	4.22324e14i	−0.411843	+	0.237778i
$349$			3.45573e15i			1.91244i	0.292656	+	0.956218i	$0.405461\pi$
$349$			3.45573e15i			1.91244i	−0.292656	+	0.956218i	$0.594539\pi$
$350$		0			0
$351$	−1.27245e15			−0.680452
$352$	−4.67926e13	−	8.10471e13i	−0.0245992	−	0.0426070i
$353$	−1.19841e15	−	6.91900e14i	−0.619378	−	0.357598i	0.157249	−	0.987559i	$-0.449738\pi$
$353$	−1.19841e15	−	6.91900e14i	−0.619378	−	0.357598i	−0.776627	+	0.629961i	$0.783071\pi$
$354$	−5.97949e14	+	1.03568e15i	−0.303840	+	0.526266i
$355$	1.95284e15	−	1.12747e15i	0.975656	−	0.563295i
$356$		−	1.71423e15i		−	0.842110i
$357$		0			0
$358$	1.56021e15			0.741112
$359$	−4.99594e14	−	8.65322e14i	−0.233373	−	0.404214i	0.725426	−	0.688300i	$-0.241643\pi$
$359$	−4.99594e14	−	8.65322e14i	−0.233373	−	0.404214i	−0.958799	+	0.284087i	$0.908310\pi$
$360$	5.19538e14	+	2.99955e14i	0.238672	+	0.137797i
$361$	−8.79095e14	+	1.52264e15i	−0.397185	+	0.687944i
$362$	−2.73119e14	+	1.57685e14i	−0.121367	+	0.0700713i
$363$			1.36963e15i			0.598637i
$364$		0			0
$365$	5.03483e14			0.212926
$366$	7.38942e14	+	1.27989e15i	0.307414	+	0.532457i
$367$	3.32044e15	+	1.91706e15i	1.35894	+	0.784583i	0.989481	−	0.144665i	$-0.0462104\pi$
$367$	3.32044e15	+	1.91706e15i	1.35894	+	0.784583i	0.369457	+	0.929248i	$0.379544\pi$
$368$	−5.15484e14	+	8.92845e14i	−0.207553	+	0.359492i
$369$	1.14397e15	−	6.60474e14i	0.453167	−	0.261636i
$370$			2.33527e15i			0.910179i
$371$		0			0
$372$	−6.89499e14			−0.260181
$373$	7.48211e14	+	1.29594e15i	0.277825	+	0.481207i	0.970844	−	0.239712i	$-0.0770531\pi$
$373$	7.48211e14	+	1.29594e15i	0.277825	+	0.481207i	−0.693019	+	0.720919i	$0.743720\pi$
$374$	6.66644e14	+	3.84887e14i	0.243593	+	0.140638i
$375$	2.27284e14	−	3.93667e14i	0.0817300	−	0.141560i
$376$	4.58099e14	−	2.64483e14i	0.162118	−	0.0935990i
$377$		−	2.79487e15i		−	0.973449i
$378$		0			0
$379$	2.15636e15			0.727587			0.363794	−	0.931480i	$-0.381481\pi$
$379$	2.15636e15			0.727587			0.363794	+	0.931480i	$0.381481\pi$
$380$	−4.59594e14	−	7.96039e14i	−0.152641	−	0.264383i
$381$	−2.27667e15	−	1.31444e15i	−0.744305	−	0.429725i
$382$	1.60647e15	−	2.78248e15i	0.517001	−	0.895472i
$383$	−4.03701e15	+	2.33077e15i	−1.27899	+	0.738425i	−0.976663	−	0.214779i	$-0.931097\pi$
$383$	−4.03701e15	+	2.33077e15i	−1.27899	+	0.738425i	−0.302328	+	0.953204i	$0.597764\pi$
$384$		−	1.83890e14i		−	0.0573549i
$385$		0			0
$386$	2.68046e15			0.810375
$387$	1.34028e15	+	2.32143e15i	0.398960	+	0.691020i
$388$	−1.76228e15	−	1.01745e15i	−0.516516	−	0.298210i
$389$	1.18748e15	−	2.05677e15i	0.342710	−	0.593592i	−0.642225	−	0.766516i	$-0.721988\pi$
$389$	1.18748e15	−	2.05677e15i	0.342710	−	0.593592i	0.984935	+	0.172925i	$0.0553217\pi$
$390$	1.25033e15	−	7.21880e14i	0.355335	−	0.205153i
$391$		−	8.48012e15i		−	2.37324i
$392$		0			0
$393$	7.23922e14			0.196488
$394$	−2.16022e15	−	3.74162e15i	−0.577460	−	1.00019i
$395$	−5.81813e14	−	3.35910e14i	−0.153180	−	0.0884383i
$396$	−1.55333e14	+	2.69045e14i	−0.0402804	+	0.0697677i
$397$	−1.85783e15	+	1.07262e15i	−0.474529	+	0.273969i	−0.718134	−	0.695905i	$-0.755003\pi$
$397$	−1.85783e15	+	1.07262e15i	−0.474529	+	0.273969i	0.243605	+	0.969875i	$0.421670\pi$
$398$			1.15215e15i			0.289875i
$399$		0			0
$400$	−8.32421e14			−0.203228
$401$	−1.77790e15	−	3.07941e15i	−0.427602	−	0.740629i	0.569057	−	0.822298i	$-0.307308\pi$
$401$	−1.77790e15	−	3.07941e15i	−0.427602	−	0.740629i	−0.996660	+	0.0816691i	$0.973975\pi$
$402$	−1.43560e15	−	8.28846e14i	−0.340156	−	0.196389i
$403$	1.14075e15	−	1.97583e15i	0.266292	−	0.461232i
$404$	−4.98944e14	+	2.88066e14i	−0.114753	+	0.0662526i
$405$			5.10428e14i			0.115666i
$406$		0			0
$407$	−1.20933e15			−0.266060
$408$	7.56284e14	+	1.30992e15i	0.163955	+	0.283978i
$409$	4.16545e15	+	2.40492e15i	0.889861	+	0.513761i	0.873897	−	0.486111i	$-0.161585\pi$
$409$	4.16545e15	+	2.40492e15i	0.889861	+	0.513761i	0.0159638	+	0.999873i	$0.494918\pi$
$410$	−2.04384e15	+	3.54003e15i	−0.430272	+	0.745252i
$411$	3.67360e15	−	2.12095e15i	0.762150	−	0.440028i
$412$		−	1.85579e15i		−	0.379443i
$413$		0			0
$414$	3.42242e15			0.679722
$415$	−3.57047e15	−	6.18423e15i	−0.698934	−	1.21059i
$416$	5.26956e14	+	3.04238e14i	0.101675	+	0.0587021i
$417$	−2.75481e15	+	4.77147e15i	−0.523932	+	0.907477i
$418$	4.12233e14	−	2.38003e14i	0.0772833	−	0.0446195i
$419$		−	6.30850e15i		−	1.16585i	−0.812527	−	0.582924i	$-0.801908\pi$
$419$		−	6.30850e15i		−	1.16585i	0.812527	−	0.582924i	$-0.198092\pi$
$420$		0			0
$421$	−1.94961e15			−0.350150			−0.175075	−	0.984555i	$-0.556017\pi$
$421$	−1.94961e15			−0.350150			−0.175075	+	0.984555i	$0.556017\pi$
$422$	1.40195e14	+	2.42825e14i	0.0248232	+	0.0429951i
$423$	−1.52071e15	−	8.77984e14i	−0.265463	−	0.153265i
$424$	−4.42941e14	+	7.67196e14i	−0.0762343	+	0.132042i
$425$	5.92967e15	−	3.42350e15i	1.00623	−	0.580947i
$426$			2.29454e15i			0.383918i
$427$		0			0
$428$	−2.79630e15			−0.454905
$429$	3.73830e14	+	6.47492e14i	0.0599694	+	0.103870i
$430$	−7.18367e15	−	4.14750e15i	−1.13641	−	0.656108i
$431$	−2.83913e15	+	4.91751e15i	−0.442916	+	0.767153i	−0.997904	−	0.0647051i	$-0.979389\pi$
$431$	−2.83913e15	+	4.91751e15i	−0.442916	+	0.767153i	0.554988	+	0.831858i	$0.312723\pi$
$432$	−1.44182e15	+	8.32438e14i	−0.221825	+	0.128071i
$433$			3.15969e15i			0.479421i	0.970844	+	0.239711i	$0.0770526\pi$
$433$			3.15969e15i			0.479421i	−0.970844	+	0.239711i	$0.922947\pi$
$434$		0			0
$435$	−8.67670e15			−1.28062
$436$	3.35691e12	+	5.81434e12i	0.000488676	+	0.000846411i
$437$	−4.54132e15	−	2.62193e15i	−0.652068	−	0.376472i
$438$	−2.56162e14	+	4.43686e14i	−0.0362803	+	0.0628393i
$439$	3.54688e15	−	2.04779e15i	0.495517	−	0.286087i	−0.231343	−	0.972872i	$-0.574312\pi$
$439$	3.54688e15	−	2.04779e15i	0.495517	−	0.286087i	0.726860	+	0.686785i	$0.240979\pi$
$440$		−	9.61358e14i		−	0.132486i
$441$		0			0
$442$	−5.00495e15			−0.671222
$443$	−5.22014e15	−	9.04155e15i	−0.690653	−	1.19625i	−0.971624	−	0.236530i	$-0.923990\pi$
$443$	−5.22014e15	−	9.04155e15i	−0.690653	−	1.19625i	0.280971	−	0.959716i	$-0.409343\pi$
$444$	−2.05792e15	−	1.18814e15i	−0.268615	−	0.155085i
$445$	8.80475e15	−	1.52503e16i	1.13385	−	1.96389i
$446$	4.88672e15	−	2.82135e15i	0.620881	−	0.358466i
$447$			5.59573e15i			0.701474i
$448$		0			0
$449$	−2.06032e15			−0.251452			−0.125726	−	0.992065i	$-0.540126\pi$
$449$	−2.06032e15			−0.251452			−0.125726	+	0.992065i	$0.540126\pi$
$450$	1.38166e15	+	2.39311e15i	0.166390	+	0.288195i
$451$	−1.83322e15	−	1.05841e15i	−0.217849	−	0.125775i
$452$	−3.99424e15	+	6.91823e15i	−0.468386	+	0.811268i
$453$	−2.85338e14	+	1.64740e14i	−0.0330195	+	0.0190638i
$454$			7.73187e15i			0.882977i
$455$		0			0
$456$	9.35328e14			0.104034
$457$	2.67562e15	+	4.63431e15i	0.293716	+	0.508731i	0.974685	−	0.223581i	$-0.0717748\pi$
$457$	2.67562e15	+	4.63431e15i	0.293716	+	0.508731i	−0.680970	+	0.732312i	$0.738441\pi$
$458$	−8.04963e15	−	4.64746e15i	−0.872134	−	0.503527i
$459$	6.84713e15	−	1.18596e16i	0.732204	−	1.26822i
$460$	−9.17179e15	+	5.29534e15i	−0.968071	+	0.558916i
$461$		−	1.28741e16i		−	1.34126i	−0.741794	−	0.670628i	$-0.766025\pi$
$461$		−	1.28741e16i		−	1.34126i	0.741794	−	0.670628i	$-0.233975\pi$
$462$		0			0
$463$	1.65577e16			1.68079			0.840397	−	0.541972i	$-0.182322\pi$
$463$	1.65577e16			1.68079			0.840397	+	0.541972i	$0.182322\pi$
$464$	−1.82841e15	−	3.16689e15i	−0.183217	−	0.317341i
$465$	−6.13398e15	−	3.54146e15i	−0.606771	−	0.350320i
$466$	−5.93259e15	+	1.02755e16i	−0.579334	+	1.00344i
$467$	1.10442e16	−	6.37638e15i	1.06471	−	0.614713i	0.137982	−	0.990435i	$-0.455938\pi$
$467$	1.10442e16	−	6.37638e15i	1.06471	−	0.614713i	0.926733	+	0.375721i	$0.122605\pi$
$468$		−	2.01991e15i		−	0.192246i
$469$		0			0
$470$	5.43384e15			0.504103
$471$	3.60472e15	+	6.24355e15i	0.330176	+	0.571882i
$472$	−4.48385e15	−	2.58875e15i	−0.405508	−	0.234120i
$473$	2.14780e15	−	3.72010e15i	0.191791	−	0.332191i
$474$	5.92030e14	−	3.41809e14i	0.0522004	−	0.0301379i
$475$		−	4.23398e15i		−	0.368627i
$476$		0			0
$477$	2.94079e15			0.249663
$478$	−5.81607e15	−	1.00737e16i	−0.487598	−	0.844545i
$479$	1.62969e15	+	9.40903e14i	0.134925	+	0.0778990i	0.565943	−	0.824444i	$-0.308512\pi$
$479$	1.62969e15	+	9.40903e14i	0.134925	+	0.0778990i	−0.431018	+	0.902343i	$0.641846\pi$
$480$	9.44510e14	−	1.63594e15i	0.0772252	−	0.133758i
$481$	6.80947e15	−	3.93145e15i	0.549848	−	0.317455i
$482$			6.25434e15i			0.498769i
$483$		0			0
$484$	−5.92966e15			−0.461272
$485$	−1.04518e16	−	1.81031e16i	−0.803047	−	1.39092i
$486$	7.81766e15	+	4.51353e15i	0.593280	+	0.342530i
$487$	−7.89345e15	+	1.36719e16i	−0.591689	+	1.02483i	0.402316	+	0.915501i	$0.368205\pi$
$487$	−7.89345e15	+	1.36719e16i	−0.591689	+	1.02483i	−0.994005	+	0.109334i	$0.965128\pi$
$488$	−5.54112e15	+	3.19917e15i	−0.410279	+	0.236874i
$489$		−	1.43095e16i		−	1.04658i
$490$		0			0
$491$	1.42083e16			1.01404			0.507018	−	0.861935i	$-0.330748\pi$
$491$	1.42083e16			1.01404			0.507018	+	0.861935i	$0.330748\pi$
$492$	−2.07972e15	−	3.60219e15i	−0.146627	−	0.253966i
$493$	2.60489e16	+	1.50394e16i	1.81430	+	1.04749i
$494$	−1.54746e15	+	2.68028e15i	−0.106477	+	0.184424i
$495$	−2.76378e15	+	1.59567e15i	−0.187877	+	0.108471i
$496$		−	2.98511e15i		−	0.200480i
$497$		0			0
$498$	7.26633e15			0.476364
$499$	1.08211e16	+	1.87427e16i	0.700919	+	1.21403i	0.968144	+	0.250394i	$0.0805601\pi$
$499$	1.08211e16	+	1.87427e16i	0.700919	+	1.21403i	−0.267225	+	0.963634i	$0.586107\pi$
$500$	1.70434e15	+	9.84001e14i	0.109078	+	0.0629761i
$501$	5.45731e14	−	9.45233e14i	0.0345106	−	0.0597740i
$502$	7.76087e15	−	4.48074e15i	0.484940	−	0.279980i
$503$			8.39579e15i			0.518387i	0.965825	+	0.259193i	$0.0834567\pi$
$503$			8.39579e15i			0.518387i	−0.965825	+	0.259193i	$0.916543\pi$
$504$		0			0
$505$	−5.91834e15			−0.356822
$506$	−2.74222e15	−	4.74966e15i	−0.163380	−	0.282983i
$507$	5.33463e15	+	3.07995e15i	0.314092	+	0.181341i
$508$	5.69071e15	−	9.85661e15i	0.331119	−	0.573515i
$509$	6.22140e15	−	3.59193e15i	0.357752	−	0.206548i	−0.310342	−	0.950625i	$-0.600444\pi$
$509$	6.22140e15	−	3.59193e15i	0.357752	−	0.206548i	0.668094	+	0.744077i	$0.267110\pi$
$510$			1.55379e16i			0.883023i
$511$		0			0
$512$	7.96131e14			0.0441942
$513$	−4.23407e15	−	7.33362e15i	−0.232302	−	0.402359i
$514$	−3.95370e13	−	2.28267e13i	−0.00214400	−	0.00123784i
$515$	9.53187e15	−	1.65097e16i	0.510898	−	0.884902i
$516$	7.30982e15	−	4.22033e15i	0.387265	−	0.223588i
$517$			2.81394e15i			0.147357i
$518$		0			0
$519$	−9.65137e15			−0.493838
$520$	3.12530e15	+	5.41318e15i	0.158078	+	0.273799i
$521$	1.71082e16	+	9.87744e15i	0.855418	+	0.493876i	0.862475	−	0.506099i	$-0.168913\pi$
$521$	1.71082e16	+	9.87744e15i	0.855418	+	0.493876i	−0.00705697	+	0.999975i	$0.502246\pi$
$522$	−6.06961e15	+	1.05129e16i	−0.300012	+	0.519635i
$523$	−2.08364e16	+	1.20299e16i	−1.01815	+	0.587831i	−0.913568	−	0.406685i	$-0.866685\pi$
$523$	−2.08364e16	+	1.20299e16i	−1.01815	+	0.587831i	−0.104585	+	0.994516i	$0.533351\pi$
$524$			3.13414e15i			0.151402i
$525$		0			0
$526$	1.34659e15			0.0635802
$527$	1.22768e16	+	2.12641e16i	0.573090	+	0.992622i
$528$	8.47180e14	+	4.89120e14i	0.0390996	+	0.0225742i
$529$	−1.92520e16	+	3.33454e16i	−0.878500	+	1.52161i
$530$	−7.88106e15	+	4.55013e15i	−0.355573	+	0.205290i
$531$			1.71873e16i			0.766728i
$532$		0			0
$533$	1.37632e16			0.600285
$534$	8.95936e15	+	1.55181e16i	0.386393	+	0.669253i
$535$	−2.48767e16	−	1.43626e16i	−1.06089	−	0.612504i
$536$	3.58840e15	−	6.21529e15i	0.151325	−	0.262103i
$537$	−1.41238e16	+	8.15437e15i	−0.588987	+	0.340052i
$538$			3.54796e15i			0.146314i
$539$		0			0
$540$	−1.71025e16			−0.689760
$541$	1.19235e16	+	2.06521e16i	0.475575	+	0.823721i	0.999609	−	0.0279771i	$-0.00890654\pi$
$541$	1.19235e16	+	2.06521e16i	0.475575	+	0.823721i	−0.524033	+	0.851698i	$0.675573\pi$
$542$	1.06679e16	+	6.15909e15i	0.420806	+	0.242952i
$543$	1.64828e15	−	2.85490e15i	0.0643030	−	0.111376i
$544$	−5.67116e15	+	3.27425e15i	−0.218816	+	0.126333i
$545$			6.89681e13i			0.00263190i
$546$		0			0
$547$	−3.24286e16			−1.21061			−0.605305	−	0.795993i	$-0.706949\pi$
$547$	−3.24286e16			−1.21061			−0.605305	+	0.795993i	$0.706949\pi$
$548$	9.18243e15	+	1.59044e16i	0.339058	+	0.587266i
$549$	1.83944e16	+	1.06200e16i	0.671818	+	0.387874i
$550$	2.21411e15	−	3.83496e15i	0.0799878	−	0.138543i
$551$	1.61079e16	−	9.29991e15i	0.575612	−	0.332330i
$552$		−	1.07766e16i		−	0.380934i
$553$		0			0
$554$	3.48841e16			1.20661
$555$	−1.22052e16	−	2.11401e16i	−0.417626	−	0.723350i
$556$	−2.06575e16	−	1.19266e16i	−0.699245	−	0.403709i
$557$	5.91971e15	−	1.02532e16i	0.198230	−	0.343344i	−0.749725	−	0.661750i	$-0.769814\pi$
$557$	5.91971e15	−	1.02532e16i	0.198230	−	0.343344i	0.947955	+	0.318406i	$0.103147\pi$
$558$	−8.58181e15	+	4.95471e15i	−0.284298	+	0.164140i
$559$			2.79294e16i			0.915356i
$560$		0			0
$561$	−8.04640e15			−0.258122
$562$	1.29361e16	+	2.24059e16i	0.410567	+	0.711124i
$563$	−2.21804e16	−	1.28059e16i	−0.696498	−	0.402123i	0.109544	−	0.993982i	$-0.465061\pi$
$563$	−2.21804e16	−	1.28059e16i	−0.696498	−	0.402123i	−0.806042	+	0.591859i	$0.798394\pi$
$564$	−2.76463e15	+	4.78848e15i	−0.0858938	+	0.148772i
$565$	−7.10679e16	+	4.10311e16i	−2.18465	+	1.26131i
$566$		−	7.14637e15i		−	0.217364i
$567$		0			0
$568$	−9.93397e15			−0.295824
$569$	1.94844e16	+	3.37479e16i	0.574133	+	0.994427i	0.996135	+	0.0878326i	$0.0279940\pi$
$569$	1.94844e16	+	3.37479e16i	0.574133	+	0.994427i	−0.422002	+	0.906595i	$0.638673\pi$
$570$	8.32095e15	+	4.80410e15i	0.242618	+	0.140076i
$571$	2.35800e15	−	4.08417e15i	0.0680341	−	0.117839i	−0.830002	−	0.557761i	$-0.811661\pi$
$571$	2.35800e15	−	4.08417e15i	0.0680341	−	0.117839i	0.898036	+	0.439922i	$0.144994\pi$
$572$	−2.80324e15	+	1.61845e15i	−0.0800359	+	0.0462087i
$573$			3.35846e16i			0.948882i
$574$		0			0
$575$	−4.87830e16			−1.34978
$576$	−1.32143e15	−	2.28878e15i	−0.0361833	−	0.0626713i
$577$	2.14410e16	+	1.23789e16i	0.581017	+	0.335451i	0.761538	−	0.648121i	$-0.224445\pi$
$577$	2.14410e16	+	1.23789e16i	0.581017	+	0.335451i	−0.180520	+	0.983571i	$0.557778\pi$
$578$	1.37487e16	−	2.38135e16i	0.368719	−	0.638640i
$579$	−2.42649e16	+	1.40094e16i	−0.644032	+	0.371832i
$580$		−	3.75648e16i		−	0.986764i
$581$		0			0
$582$	2.12707e16			0.547323
$583$	−2.35631e15	−	4.08125e15i	−0.0600097	−	0.103940i
$584$	−1.92089e15	−	1.10903e15i	−0.0484201	−	0.0279553i
$585$	1.03748e16	−	1.79697e16i	0.258848	−	0.448338i
$586$	1.38614e16	−	8.00287e15i	0.342311	−	0.197633i
$587$		−	1.29127e16i		−	0.315636i	−0.987468	−	0.157818i	$-0.949554\pi$
$587$		−	1.29127e16i		−	0.315636i	0.987468	−	0.157818i	$-0.0504460\pi$
$588$		0			0
$589$	1.51833e16			0.363642
$590$	−2.65931e16	−	4.60606e16i	−0.630459	−	1.09199i
$591$	3.91109e16	+	2.25807e16i	0.917853	+	0.529923i
$592$	5.14392e15	−	8.90952e15i	0.119499	−	0.206978i
$593$	5.03855e16	−	2.90901e16i	1.15872	−	0.668985i	0.207720	−	0.978188i	$-0.433396\pi$
$593$	5.03855e16	−	2.90901e16i	1.15872	−	0.668985i	0.950996	+	0.309203i	$0.100062\pi$
$594$		−	8.85664e15i		−	0.201628i
$595$		0			0
$596$	−2.42261e16			−0.540512
$597$	−6.02168e15	−	1.04299e16i	−0.133006	−	0.230374i
$598$	3.08816e16	+	1.78295e16i	0.675293	+	0.389881i
$599$	−7.72257e15	+	1.33759e16i	−0.167186	+	0.289575i	−0.937430	−	0.348175i	$-0.886802\pi$
$599$	−7.72257e15	+	1.33759e16i	−0.167186	+	0.289575i	0.770243	+	0.637750i	$0.220135\pi$
$600$	7.53550e15	−	4.35062e15i	0.161512	−	0.0932490i
$601$		−	5.16840e16i		−	1.09675i	−0.836231	−	0.548377i	$-0.815246\pi$
$601$		−	5.16840e16i		−	1.09675i	0.836231	−	0.548377i	$-0.184754\pi$
$602$		0			0
$603$	−2.38242e16			−0.495581
$604$	−7.13222e14	−	1.23534e15i	−0.0146894	−	0.0254427i
$605$	−5.27520e16	−	3.04564e16i	−1.07574	−	0.621077i
$606$	3.01113e15	−	5.21543e15i	0.0607986	−	0.105306i
$607$	−1.25871e16	+	7.26718e15i	−0.251648	+	0.145289i	−0.620519	−	0.784192i	$-0.713078\pi$
$607$	−1.25871e16	+	7.26718e15i	−0.251648	+	0.145289i	0.368870	+	0.929481i	$0.379745\pi$
$608$			4.04940e15i			0.0801621i
$609$		0			0
$610$	−6.57273e16			−1.27575
$611$	−9.14791e15	−	1.58446e16i	−0.175823	−	0.304534i
$612$	1.88261e16	+	1.08692e16i	0.358304	+	0.206867i
$613$	9.48835e15	−	1.64343e16i	0.178825	−	0.309734i	−0.762654	−	0.646807i	$-0.776104\pi$
$613$	9.48835e15	−	1.64343e16i	0.178825	−	0.309734i	0.941478	+	0.337074i	$0.109437\pi$
$614$	−2.46531e16	+	1.42335e16i	−0.460110	+	0.265645i
$615$		−	4.27282e16i		−	0.789703i
$616$		0			0
$617$	−5.51530e15			−0.0999674			−0.0499837	−	0.998750i	$-0.515917\pi$
$617$	−5.51530e15			−0.0999674			−0.0499837	+	0.998750i	$0.515917\pi$
$618$	9.69925e15	+	1.67996e16i	0.174103	+	0.301556i
$619$	−3.22376e16	−	1.86124e16i	−0.573084	−	0.330870i	0.185296	−	0.982683i	$-0.440676\pi$
$619$	−3.22376e16	−	1.86124e16i	−0.573084	−	0.330870i	−0.758380	+	0.651812i	$0.774009\pi$
$620$	1.53323e16	−	2.65564e16i	0.269935	−	0.467540i
$621$	−8.44964e16	+	4.87840e16i	−1.47329	+	0.850605i
$622$		−	9.04246e15i		−	0.156151i
$623$		0			0
$624$	−6.36036e15			−0.107739
$625$	3.43349e16	+	5.94697e16i	0.576043	+	0.997736i
$626$	3.43157e16	+	1.98122e16i	0.570225	+	0.329220i
$627$	−2.48783e15	+	4.30905e15i	−0.0409464	+	0.0709212i
$628$	−2.70308e16	+	1.56062e16i	−0.440657	+	0.254413i
$629$			8.46214e16i			1.36640i
$630$		0			0
$631$	7.95855e16			1.26083			0.630417	−	0.776257i	$-0.282884\pi$
$631$	7.95855e16			1.26083			0.630417	+	0.776257i	$0.282884\pi$
$632$	1.47982e15	+	2.56313e15i	0.0232224	+	0.0402224i
$633$	−2.53824e15	−	1.46545e15i	−0.0394557	−	0.0227798i
$634$	−7.24787e15	+	1.25537e16i	−0.111603	+	0.193302i
$635$	1.01252e17	−	5.84582e16i	1.54441	−	0.891667i
$636$		−	9.26006e15i		−	0.139917i
$637$		0			0
$638$	1.94531e16			0.288447
$639$	1.64885e16	+	2.85589e16i	0.242201	+	0.419504i
$640$	7.08262e15	+	4.08915e15i	0.103066	+	0.0595050i
$641$	−3.48282e16	+	6.03242e16i	−0.502091	+	0.869648i	0.497906	+	0.867231i	$0.334103\pi$
$641$	−3.48282e16	+	6.03242e16i	−0.502091	+	0.869648i	−0.999997	+	0.00241656i	$0.999231\pi$
$642$	2.53135e16	−	1.46148e16i	0.361528	−	0.208728i
$643$			3.39087e16i			0.479784i	0.970800	+	0.239892i	$0.0771120\pi$
$643$			3.39087e16i			0.479784i	−0.970800	+	0.239892i	$0.922888\pi$
$644$		0			0
$645$	8.67070e16			1.20419
$646$	−1.66539e16	−	2.88455e16i	−0.229151	−	0.396901i
$647$	−2.81289e16	−	1.62402e16i	−0.383466	−	0.221394i	0.295859	−	0.955232i	$-0.404394\pi$
$647$	−2.81289e16	−	1.62402e16i	−0.383466	−	0.221394i	−0.679325	+	0.733837i	$0.737727\pi$
$648$	1.12432e15	−	1.94738e15i	0.0151859	−	0.0263028i
$649$	2.38527e16	−	1.37714e16i	0.319205	−	0.184293i
$650$			2.87917e16i			0.381757i
$651$		0			0
$652$	6.19516e16			0.806430
$653$	2.76124e16	+	4.78261e16i	0.356144	+	0.616859i	0.987313	−	0.158786i	$-0.0507580\pi$
$653$	2.76124e16	+	4.78261e16i	0.356144	+	0.616859i	−0.631169	+	0.775645i	$0.717425\pi$
$654$	−6.07769e13	−	3.50896e13i	−0.000776734	−	0.000448448i
$655$	−1.60978e16	+	2.78822e16i	−0.203854	+	0.353085i
$656$	1.55953e16	−	9.00394e15i	0.195691	−	0.112982i
$657$			7.36309e15i			0.0915520i
$658$		0			0
$659$	−1.23419e16			−0.150685			−0.0753426	−	0.997158i	$-0.524005\pi$
$659$	−1.23419e16			−0.150685			−0.0753426	+	0.997158i	$0.524005\pi$
$660$	5.02451e15	+	8.70270e15i	0.0607897	+	0.105291i
$661$	−5.94936e16	−	3.43486e16i	−0.713282	−	0.411814i	0.0989930	−	0.995088i	$-0.468438\pi$
$661$	−5.94936e16	−	3.43486e16i	−0.713282	−	0.411814i	−0.812275	+	0.583275i	$0.801771\pi$
$662$	1.11174e16	−	1.92560e16i	0.132086	−	0.228780i
$663$	4.53074e16	−	2.61582e16i	0.533443	−	0.307983i
$664$			3.14588e16i			0.367057i
$665$		0			0
$666$	−3.41517e16			−0.391351
$667$	−1.07152e17	−	1.85592e17i	−1.21687	−	2.10768i
$668$	4.09228e15	+	2.36268e15i	0.0460582	+	0.0265917i
$669$	−2.94914e16	+	5.10806e16i	−0.328957	+	0.569770i
$670$	6.38469e16	−	3.68620e16i	0.705815	−	0.407502i
$671$		−	3.40372e16i		−	0.372923i
$672$		0			0
$673$	−2.37216e16			−0.255301			−0.127651	−	0.991819i	$-0.540744\pi$
$673$	−2.37216e16			−0.255301			−0.127651	+	0.991819i	$0.540744\pi$
$674$	2.63549e16	+	4.56481e16i	0.281127	+	0.486926i
$675$	−6.82238e16	−	3.93890e16i	−0.721296	−	0.416440i
$676$	−1.33343e16	+	2.30957e16i	−0.139730	+	0.242020i
$677$	4.24573e15	−	2.45127e15i	0.0440981	−	0.0254601i	−0.477789	−	0.878475i	$-0.658562\pi$
$677$	4.24573e15	−	2.45127e15i	0.0440981	−	0.0254601i	0.521887	+	0.853015i	$0.325228\pi$
$678$		−	8.35031e16i		−	0.859656i
$679$		0			0
$680$	−6.72697e16			−0.680403
$681$	−4.04104e16	−	6.99928e16i	−0.405145	−	0.701731i
$682$	1.37524e16	+	7.93994e15i	0.136669	+	0.0789062i
$683$	−3.56599e16	+	6.17648e16i	−0.351282	+	0.608438i	−0.986474	−	0.163916i	$-0.947588\pi$
$683$	−3.56599e16	+	6.17648e16i	−0.351282	+	0.608438i	0.635192	+	0.772354i	$0.280921\pi$
$684$	1.16415e16	−	6.72123e15i	0.113677	−	0.0656314i
$685$			1.88654e17i			1.82609i
$686$		0			0
$687$	9.71592e16			0.924152
$688$	1.82714e16	+	3.16470e16i	0.172283	+	0.298403i
$689$	2.65356e16	+	1.53204e16i	0.248036	+	0.143204i
$690$	5.53518e16	−	9.58722e16i	0.512906	−	0.888379i
$691$	2.36455e16	−	1.36517e16i	0.217210	−	0.125406i	−0.387448	−	0.921892i	$-0.626643\pi$
$691$	2.36455e16	−	1.36517e16i	0.217210	−	0.125406i	0.604658	+	0.796485i	$0.293310\pi$
$692$		−	4.17845e16i		−	0.380521i
$693$		0			0
$694$	1.53956e16			0.137797
$695$	−1.22517e17	−	2.12206e17i	−1.08714	−	1.88299i
$696$	3.31033e16	+	1.91122e16i	0.291217	+	0.168134i
$697$	−7.40609e16	+	1.28277e17i	−0.645940	+	1.11880i
$698$	1.35436e17	−	7.81942e16i	1.17112	−	0.676148i
$699$		−	1.24026e17i		−	1.06329i
$700$		0			0
$701$	7.58708e16			0.639391			0.319695	−	0.947520i	$-0.396419\pi$
$701$	7.58708e16			0.639391			0.319695	+	0.947520i	$0.396419\pi$
$702$	2.87922e16	+	4.98696e16i	0.240576	+	0.416690i
$703$	4.53169e16	+	2.61637e16i	0.375429	+	0.216754i
$704$	−2.11759e15	+	3.66777e15i	−0.0173943	+	0.0301277i
$705$	−4.91899e16	+	2.83998e16i	−0.400628	+	0.231302i
$706$			6.26237e16i			0.505720i
$707$		0			0
$708$	5.41201e16			0.429694
$709$	−3.17487e16	−	5.49903e16i	−0.249947	−	0.432921i	0.713564	−	0.700590i	$-0.247080\pi$
$709$	−3.17487e16	−	5.49903e16i	−0.249947	−	0.432921i	−0.963511	+	0.267669i	$0.913747\pi$
$710$	−8.83755e16	−	5.10236e16i	−0.689893	−	0.398310i
$711$	4.91245e15	−	8.50861e15i	0.0380260	−	0.0658629i
$712$	−6.71838e16	+	3.87886e16i	−0.515685	+	0.297731i
$713$		−	1.74939e17i		−	1.33152i
$714$		0			0
$715$	−3.32513e16			−0.248870
$716$	−3.53035e16	−	6.11474e16i	−0.262023	−	0.453837i
$717$	1.05300e17	+	6.07950e16i	0.775021	+	0.447459i
$718$	−2.26090e16	+	3.91600e16i	−0.165020	+	0.285822i
$719$	−2.29564e16	+	1.32539e16i	−0.166162	+	0.0959334i	−0.580775	−	0.814064i	$-0.697250\pi$
$719$	−2.29564e16	+	1.32539e16i	−0.166162	+	0.0959334i	0.414613	+	0.909998i	$0.363917\pi$
$720$		−	2.71488e16i		−	0.194875i
$721$		0			0
$722$	7.95666e16			0.561704
$723$	−3.26881e16	−	5.66175e16i	−0.228855	−	0.396388i
$724$	1.23600e16	+	7.13603e15i	0.0858195	+	0.0495479i
$725$	8.65160e16	−	1.49850e17i	0.595756	−	1.03188i
$726$	5.36783e16	−	3.09912e16i	0.366589	−	0.211650i
$727$			9.07684e16i			0.614792i	0.951582	+	0.307396i	$0.0994576\pi$
$727$			9.07684e16i			0.614792i	−0.951582	+	0.307396i	$0.900542\pi$
$728$		0			0
$729$	−1.07253e17			−0.714570
$730$	−1.13925e16	−	1.97324e16i	−0.0752806	−	0.130390i
$731$	−2.60309e17	−	1.50290e17i	−1.70603	−	0.984974i
$732$	3.34407e16	−	5.79210e16i	0.217375	−	0.376504i
$733$	1.30636e17	−	7.54227e16i	0.842246	−	0.486271i	−0.0157811	−	0.999875i	$-0.505023\pi$
$733$	1.30636e17	−	7.54227e16i	0.842246	−	0.486271i	0.858027	+	0.513605i	$0.171690\pi$
$734$		−	1.73512e17i		−	1.10957i
$735$		0			0
$736$	4.66563e16			0.293524
$737$	1.90892e16	+	3.30634e16i	0.119119	+	0.206321i
$738$	−5.17704e16	−	2.98896e16i	−0.320437	−	0.185005i
$739$	1.07535e17	−	1.86257e17i	0.660213	−	1.14352i	−0.320346	−	0.947301i	$-0.603799\pi$
$739$	1.07535e17	−	1.86257e17i	0.660213	−	1.14352i	0.980559	−	0.196222i	$-0.0628674\pi$
$740$	9.15236e16	−	5.28411e16i	0.557369	−	0.321797i
$741$		−	3.23510e16i		−	0.195424i
$742$		0			0
$743$	1.73261e17			1.02984			0.514919	−	0.857239i	$-0.327822\pi$
$743$	1.73261e17			1.02984			0.514919	+	0.857239i	$0.327822\pi$
$744$	1.56016e16	+	2.70227e16i	0.0919880	+	0.159328i
$745$	−2.15522e17	−	1.24432e17i	−1.26053	−	0.727770i
$746$	3.38602e16	−	5.86476e16i	0.196452	−	0.340265i
$747$	9.04400e16	−	5.22155e16i	0.520519	−	0.300522i
$748$		−	3.48360e16i		−	0.198893i
$749$		0			0
$750$	−2.05714e16			−0.115584
$751$	8.30820e16	+	1.43902e17i	0.463092	+	0.802099i	0.999113	−	0.0421056i	$-0.0134066\pi$
$751$	8.30820e16	+	1.43902e17i	0.463092	+	0.802099i	−0.536021	+	0.844205i	$0.680073\pi$
$752$	−2.07312e16	−	1.19691e16i	−0.114635	−	0.0661845i
$753$	−4.68369e16	+	8.11239e16i	−0.256932	+	0.445020i
$754$	−1.09536e17	+	6.32407e16i	−0.596113	+	0.344166i
$755$		−	1.46532e16i		−	0.0791137i
$756$		0			0
$757$	−2.91105e17			−1.54694			−0.773471	−	0.633832i	$-0.781481\pi$
$757$	−2.91105e17			−1.54694			−0.773471	+	0.633832i	$0.781481\pi$
$758$	−4.87928e16	−	8.45115e16i	−0.257241	−	0.445554i
$759$	4.96479e16	+	2.86643e16i	0.259687	+	0.149930i
$760$	−2.07988e16	+	3.60246e16i	−0.107934	+	0.186947i
$761$	−2.05180e17	+	1.18461e17i	−1.05640	+	0.609911i	−0.924433	−	0.381344i	$-0.875461\pi$
$761$	−2.05180e17	+	1.18461e17i	−1.05640	+	0.609911i	−0.131963	+	0.991255i	$0.542128\pi$
$762$			1.18969e17i			0.607722i
$763$		0			0
$764$	−1.45401e17			−0.731149
$765$	1.11655e17	+	1.93392e17i	0.557069	+	0.964872i
$766$	1.82694e17	+	1.05479e17i	0.904383	+	0.522146i
$767$	−8.95394e16	+	1.55087e17i	−0.439786	+	0.761732i
$768$	−7.20699e15	+	4.16096e15i	−0.0351226	+	0.0202780i
$769$			2.91008e17i			1.40717i	0.710611	+	0.703585i	$0.248419\pi$
$769$			2.91008e17i			1.40717i	−0.710611	+	0.703585i	$0.751581\pi$
$770$		0			0
$771$	4.77212e14			0.00227188
$772$	−6.06520e16	−	1.05052e17i	−0.286511	−	0.496252i
$773$	1.30017e17	+	7.50656e16i	0.609431	+	0.351855i	0.772743	−	0.634719i	$-0.218884\pi$
$773$	1.30017e17	+	7.50656e16i	0.609431	+	0.351855i	−0.163312	+	0.986575i	$0.552218\pi$
$774$	6.06542e16	−	1.05056e17i	0.282108	−	0.488625i
$775$	1.22325e17	−	7.06242e16i	0.564552	−	0.325944i
$776$			9.20891e16i			0.421733i
$777$		0			0
$778$	−1.07478e17			−0.484666
$779$	4.57971e16	+	7.93229e16i	0.204934	+	0.354956i
$780$	−5.65836e16	−	3.26686e16i	−0.251260	−	0.145065i
$781$	2.64229e16	−	4.57657e16i	0.116432	−	0.201667i
$782$	−3.32351e17	+	1.91883e17i	−1.45331	+	0.839066i
$783$		−	3.46071e17i		−	1.50174i
$784$		0			0
$785$	−3.20631e17			−1.37021
$786$	−1.63805e16	−	2.83718e16i	−0.0694690	−	0.120324i
$787$	−2.19495e17	−	1.26725e17i	−0.923796	−	0.533354i	−0.0389516	−	0.999241i	$-0.512402\pi$
$787$	−2.19495e17	−	1.26725e17i	−0.923796	−	0.533354i	−0.884844	+	0.465887i	$0.845735\pi$
$788$	−9.77606e16	+	1.69326e17i	−0.408326	+	0.707241i
$789$	−1.21900e16	+	7.03792e15i	−0.0505293	+	0.0291731i
$790$			3.04031e16i			0.125071i
$791$		0			0
$792$	1.40592e16			0.0569651
$793$	1.10652e17	+	1.91656e17i	0.444961	+	0.770694i
$794$	8.40757e16	+	4.85412e16i	0.335543	+	0.193726i
$795$	4.75622e16	−	8.23802e16i	0.188391	−	0.326302i
$796$	4.51549e16	−	2.60702e16i	0.177512	−	0.102486i
$797$		−	1.10228e17i		−	0.430074i	−0.976606	−	0.215037i	$-0.931013\pi$
$797$		−	1.10228e17i		−	0.430074i	0.976606	−	0.215037i	$-0.0689873\pi$
$798$		0			0
$799$	1.96902e17			0.756779
$800$	1.88355e16	+	3.26241e16i	0.0718519	+	0.124451i
$801$	2.23024e17	+	1.28763e17i	0.844418	+	0.487525i
$802$	−8.04584e16	+	1.39358e17i	−0.302360	+	0.523704i
$803$	1.02186e16	−	5.89968e15i	0.0381150	−	0.0220057i
$804$			7.50186e16i			0.277736i
$805$		0			0
$806$	−1.03249e17			−0.376594
$807$	−1.85433e16	−	3.21179e16i	−0.0671345	−	0.116280i
$808$	2.25796e16	+	1.30364e16i	0.0811426	+	0.0468477i
$809$	6.77826e16	−	1.17403e17i	0.241784	−	0.418782i	−0.719439	−	0.694556i	$-0.755601\pi$
$809$	6.77826e16	−	1.17403e17i	0.241784	−	0.418782i	0.961222	+	0.275774i	$0.0889342\pi$
$810$	2.00046e16	−	1.15497e16i	0.0708305	−	0.0408940i
$811$			2.24423e17i			0.788755i	0.918949	+	0.394378i	$0.129040\pi$
$811$			2.24423e17i			0.788755i	−0.918949	+	0.394378i	$0.870960\pi$
$812$		0			0
$813$	−1.28761e17			−0.445905
$814$	2.73641e16	+	4.73960e16i	0.0940664	+	0.162928i
$815$	5.51139e17	+	3.18200e17i	1.88068	+	1.08581i
$816$	3.42255e16	−	5.92803e16i	0.115933	−	0.200803i
$817$	−1.60968e17	+	9.29348e16i	−0.541261	+	0.312497i
$818$		−	2.17669e17i		−	0.726568i
$819$		0			0
$820$	1.84987e17			0.608496
$821$	9.74377e16	+	1.68767e17i	0.318177	+	0.551098i	0.980108	−	0.198467i	$-0.0635962\pi$
$821$	9.74377e16	+	1.68767e17i	0.318177	+	0.551098i	−0.661931	+	0.749565i	$0.730263\pi$
$822$	−1.66248e17	−	9.59833e16i	−0.538921	−	0.311146i
$823$	−2.13166e17	+	3.69215e17i	−0.685993	+	1.18817i	0.287131	+	0.957891i	$0.407299\pi$
$823$	−2.13166e17	+	3.69215e17i	−0.685993	+	1.18817i	−0.973124	+	0.230283i	$0.926035\pi$
$824$	−7.27319e16	+	4.19918e16i	−0.232360	+	0.134153i
$825$			4.62880e16i			0.146806i
$826$		0			0
$827$	6.48259e15			0.0202635			0.0101318	−	0.999949i	$-0.496775\pi$
$827$	6.48259e15			0.0202635			0.0101318	+	0.999949i	$0.496775\pi$
$828$	−7.74405e16	−	1.34131e17i	−0.240318	−	0.416243i
$829$	1.99010e17	+	1.14899e17i	0.613123	+	0.353987i	0.774187	−	0.632957i	$-0.218159\pi$
$829$	1.99010e17	+	1.14899e17i	0.613123	+	0.353987i	−0.161064	+	0.986944i	$0.551492\pi$
$830$	−1.61581e17	+	2.79866e17i	−0.494221	+	0.856016i
$831$	−3.15788e17	+	1.82320e17i	−0.958937	+	0.553642i
$832$		−	2.75365e16i		−	0.0830173i
$833$		0			0
$834$	2.49337e17			0.740952
$835$	2.42708e16	+	4.20382e16i	0.0716085	+	0.124030i
$836$	−1.86555e16	−	1.07708e16i	−0.0546475	−	0.0315508i
$837$	1.41251e17	−	2.44654e17i	0.410809	−	0.711541i
$838$	−2.47242e17	+	1.42745e17i	−0.713933	+	0.412190i
$839$		−	1.09927e17i		−	0.315162i	−0.987506	−	0.157581i	$-0.949630\pi$
$839$		−	1.09927e17i		−	0.315162i	0.987506	−	0.157581i	$-0.0503696\pi$
$840$		0			0
$841$	4.06312e17			1.14837
$842$	4.41145e16	+	7.64086e16i	0.123797	+	0.214422i
$843$	−2.34208e17	−	1.35220e17i	−0.652583	−	0.376769i
$844$	6.34451e15	−	1.09890e16i	0.0175527	−	0.0304021i
$845$	−2.37252e17	+	1.36977e17i	−0.651732	+	0.376278i
$846$			7.94660e16i			0.216750i
$847$		0			0
$848$	4.00904e16			0.107812
$849$	3.73503e16	+	6.46926e16i	0.0997350	+	0.172746i
$850$	−2.68346e17	−	1.54930e17i	−0.711511	−	0.410791i
$851$	3.01453e17	−	5.22132e17i	0.793674	−	1.37468i
$852$	8.99274e16	−	5.19196e16i	0.235101	−	0.135736i
$853$		−	8.03866e16i		−	0.208684i	−0.994541	−	0.104342i	$-0.966726\pi$
$853$		−	8.03866e16i		−	0.208684i	0.994541	−	0.104342i	$-0.0332737\pi$
$854$		0			0
$855$	1.38088e17			0.353476
$856$	6.32730e16	+	1.09592e17i	0.160833	+	0.278571i
$857$	5.93030e17	+	3.42386e17i	1.49690	+	0.864233i	0.999994	−	0.00357323i	$-0.00113740\pi$
$857$	5.93030e17	+	3.42386e17i	1.49690	+	0.864233i	0.496902	+	0.867806i	$0.334471\pi$
$858$	1.69176e16	−	2.93021e16i	0.0424048	−	0.0734473i
$859$	7.81106e16	−	4.50972e16i	0.194425	−	0.112251i	−0.399628	−	0.916678i	$-0.630861\pi$
$859$	7.81106e16	−	4.50972e16i	0.194425	−	0.112251i	0.594052	+	0.804426i	$0.297527\pi$
$860$			3.75388e17i			0.927877i
$861$		0			0
$862$	2.56969e17			0.626378
$863$	2.14933e16	+	3.72275e16i	0.0520281	+	0.0901154i	0.890867	−	0.454265i	$-0.150098\pi$
$863$	2.14933e16	+	3.72275e16i	0.0520281	+	0.0901154i	−0.838838	+	0.544380i	$0.816765\pi$
$864$	6.52495e16	+	3.76718e16i	0.156854	+	0.0905596i
$865$	2.14617e17	−	3.71727e17i	0.512351	−	0.887417i
$866$	1.23834e17	−	7.14957e16i	0.293584	−	0.169501i
$867$			2.87429e17i			0.676731i
$868$		0			0
$869$	−1.57444e16			−0.0365602
$870$	1.96331e17	+	3.40056e17i	0.452766	+	0.784214i
$871$	−2.14973e17	−	1.24115e17i	−0.492352	−	0.284260i
$872$	1.51916e14	−	2.63127e14i	0.000345546	−	0.000598503i
$873$	2.64744e17	−	1.52850e17i	0.598055	−	0.345287i
$874$			2.37310e17i			0.532411i
$875$		0			0
$876$	2.31852e16			0.0513081
$877$	2.72381e14	+	4.71778e14i	0.000598659	+	0.00103691i	0.866325	−	0.499481i	$-0.166476\pi$
$877$	2.72381e14	+	4.71778e14i	0.000598659	+	0.00103691i	−0.865726	+	0.500518i	$0.833143\pi$
$878$	−1.60513e17	−	9.26724e16i	−0.350384	−	0.202294i
$879$	−8.36535e16	+	1.44892e17i	−0.181364	+	0.314132i
$880$	−3.76774e16	+	2.17530e16i	−0.0811306	+	0.0468408i
$881$			4.51410e17i			0.965419i	0.875781	+	0.482709i	$0.160347\pi$
$881$			4.51410e17i			0.965419i	−0.875781	+	0.482709i	$0.839653\pi$
$882$		0			0
$883$	−5.11454e17			−1.07905			−0.539526	−	0.841969i	$-0.681397\pi$
$883$	−5.11454e17			−1.07905			−0.539526	+	0.841969i	$0.681397\pi$
$884$	1.13249e17	+	1.96153e17i	0.237313	+	0.411038i
$885$	4.81469e17	+	2.77976e17i	1.00209	+	0.578559i
$886$	−2.36237e17	+	4.09174e17i	−0.488365	+	0.845874i
$887$	1.33233e16	−	7.69219e15i	0.0273570	−	0.0157946i	−0.486259	−	0.873815i	$-0.661639\pi$
$887$	1.33233e16	−	7.69219e15i	0.0273570	−	0.0157946i	0.513616	+	0.858020i	$0.328306\pi$
$888$			1.07538e17i			0.219323i
$889$		0			0
$890$	−7.96915e17			−1.60351
$891$	5.98106e15	+	1.03595e16i	0.0119540	+	0.0207049i
$892$	−2.21148e17	−	1.27680e17i	−0.439029	−	0.253474i
$893$	6.08792e16	−	1.05446e17i	0.120049	−	0.207932i
$894$	2.19307e17	−	1.26617e17i	0.429563	−	0.248008i
$895$		−	7.25313e17i		−	1.41120i
$896$		0			0
$897$	−3.72741e17			−0.715571
$898$	4.66196e16	+	8.07476e16i	0.0889019	+	0.153983i
$899$	5.37371e17	+	3.10251e17i	1.01792	+	0.587699i
$900$	6.25268e16	−	1.08300e17i	0.117655	−	0.203785i
$901$	−2.85580e17	+	1.64880e17i	−0.533801	+	0.308190i
$902$			9.57964e16i			0.177873i
$903$		0			0
$904$	3.61518e17			0.662398
$905$	7.33052e16	+	1.26968e17i	0.133427	+	0.231102i
$906$	1.29129e16	+	7.45527e15i	0.0233483	+	0.0134801i
$907$	−3.51591e17	+	6.08974e17i	−0.631531	+	1.09384i	0.355708	+	0.934597i	$0.384240\pi$
$907$	−3.51591e17	+	6.08974e17i	−0.631531	+	1.09384i	−0.987239	+	0.159246i	$0.949094\pi$
$908$	3.03026e17	−	1.74952e17i	0.540711	−	0.312179i
$909$		−	8.65515e16i		−	0.153423i
$910$		0			0
$911$	−6.13291e16			−0.107289			−0.0536446	−	0.998560i	$-0.517084\pi$
$911$	−6.13291e16			−0.107289			−0.0536446	+	0.998560i	$0.517084\pi$
$912$	−2.11641e16	−	3.66572e16i	−0.0367815	−	0.0637075i
$913$	−1.44930e17	−	8.36755e16i	−0.250227	−	0.144469i
$914$	1.21085e17	−	2.09725e17i	0.207688	−	0.359727i
$915$	5.94997e17	−	3.43521e17i	1.01388	−	0.585366i
$916$			4.20640e17i			0.712094i
$917$		0			0
$918$	−6.19731e17			−1.03549
$919$	−6.94627e16	−	1.20313e17i	−0.115308	−	0.199719i	0.802595	−	0.596524i	$-0.203452\pi$
$919$	−6.94627e16	−	1.20313e17i	−0.115308	−	0.199719i	−0.917903	+	0.396805i	$0.870119\pi$
$920$	4.15068e17	+	2.39640e17i	0.684530	+	0.395213i
$921$	1.48782e17	−	2.57697e17i	0.243776	−	0.422233i
$922$	−5.04560e17	+	2.91308e17i	−0.821348	+	0.474205i
$923$			3.43595e17i			0.555695i
$924$		0			0
$925$	4.86796e17			0.777136
$926$	−3.74658e17	−	6.48927e17i	−0.594250	−	1.02927i
$927$	2.41442e17	+	1.39397e17i	0.380483	+	0.219672i
$928$	−8.27443e16	+	1.43317e17i	−0.129554	+	0.224394i
$929$	−5.02250e17	+	2.89974e17i	−0.781314	+	0.451092i	−0.836896	−	0.547362i	$-0.815632\pi$
$929$	−5.02250e17	+	2.89974e17i	−0.781314	+	0.451092i	0.0555818	+	0.998454i	$0.482299\pi$
$930$			3.20536e17i			0.495427i
$931$		0			0
$932$	5.36957e17			0.819302
$933$	4.72601e16	+	8.18569e16i	0.0716482	+	0.124098i
$934$	−4.99804e17	−	2.88562e17i	−0.752867	−	0.434668i
$935$	1.78927e17	−	3.09911e17i	0.267798	−	0.463839i
$936$	−7.91639e16	+	4.57053e16i	−0.117726	+	0.0679691i
$937$		−	6.26473e17i		−	0.925688i	−0.886440	−	0.462844i	$-0.846829\pi$
$937$		−	6.26473e17i		−	0.925688i	0.886440	−	0.462844i	$-0.153171\pi$
$938$		0			0
$939$	−4.14191e17			−0.604236
$940$	−1.22954e17	−	2.12962e17i	−0.178227	−	0.308699i
$941$	−1.05310e18	−	6.08010e17i	−1.51682	−	0.875736i	−0.999805	−	0.0197585i	$-0.993710\pi$
$941$	−1.05310e18	−	6.08010e17i	−1.51682	−	0.875736i	−0.517014	−	0.855977i	$-0.672956\pi$
$942$	1.63131e17	−	2.82551e17i	0.233470	−	0.404382i
$943$	9.13942e17	−	5.27665e17i	1.29972	−	0.750391i
$944$			2.34307e17i			0.331096i
$945$		0			0
$946$	−1.94397e17			−0.271233
$947$	−3.19688e17	−	5.53716e17i	−0.443227	−	0.767692i	0.554699	−	0.832051i	$-0.312833\pi$
$947$	−3.19688e17	−	5.53716e17i	−0.443227	−	0.767692i	−0.997927	+	0.0643584i	$0.979500\pi$
$948$	−2.67922e16	−	1.54685e16i	−0.0369112	−	0.0213107i
$949$	−3.83588e16	+	6.64394e16i	−0.0525131	+	0.0909554i
$950$	−1.65937e17	+	9.58041e16i	−0.225737	+	0.130329i
$951$		−	1.51523e17i		−	0.204831i
$952$		0			0
$953$	9.80104e17			1.30832			0.654161	−	0.756355i	$-0.273022\pi$
$953$	9.80104e17			1.30832			0.654161	+	0.756355i	$0.273022\pi$
$954$	−6.65424e16	−	1.15255e17i	−0.0882690	−	0.152886i
$955$	−1.29353e18	−	7.46818e17i	−1.70512	−	0.984452i
$956$	−2.63205e17	+	4.55885e17i	−0.344784	+	0.597183i
$957$	−1.76100e17	+	1.01671e17i	−0.229238	+	0.132351i
$958$		−	8.51608e16i		−	0.110166i
$959$		0			0
$960$	−8.54873e16			−0.109213
$961$	−1.40569e17	−	2.43473e17i	−0.178463	−	0.309108i
$962$	−3.08161e17	−	1.77917e17i	−0.388801	−	0.224474i
$963$	2.10042e17	−	3.63804e17i	0.263359	−	0.456152i
$964$	2.45119e17	−	1.41520e17i	0.305432	−	0.176341i
$965$		−	1.24610e18i		−	1.54308i
$966$		0			0
$967$	3.33540e17			0.407933			0.203967	−	0.978978i	$-0.434617\pi$
$967$	3.33540e17			0.407933			0.203967	+	0.978978i	$0.434617\pi$
$968$	1.34173e17	+	2.32394e17i	0.163084	+	0.282470i
$969$	3.01520e17	+	1.74083e17i	0.364228	+	0.210287i
$970$	−4.72995e17	+	8.19251e17i	−0.567840	+	0.983528i
$971$	9.47801e17	−	5.47213e17i	1.13084	−	0.652892i	0.186695	−	0.982418i	$-0.440222\pi$
$971$	9.47801e17	−	5.47213e17i	1.13084	−	0.652892i	0.944146	+	0.329526i	$0.106889\pi$
$972$		−	4.08518e17i		−	0.484411i
$973$		0			0
$974$	7.14434e17			0.836774
$975$	−1.50479e17	−	2.60637e17i	−0.175165	−	0.303395i
$976$	2.50763e17	+	1.44778e17i	0.290111	+	0.167496i
$977$	4.05037e17	−	7.01545e17i	0.465723	−	0.806655i	−0.533511	−	0.845793i	$-0.679128\pi$
$977$	4.05037e17	−	7.01545e17i	0.465723	−	0.806655i	0.999234	+	0.0391378i	$0.0124611\pi$
$978$	−5.60817e17	+	3.23788e17i	−0.640897	+	0.370022i
$979$		−	4.12687e17i		−	0.468732i
$980$		0			0
$981$	−1.00861e15			−0.00113164
$982$	−3.21498e17	−	5.56850e17i	−0.358516	−	0.620968i
$983$	6.13657e17	+	3.54295e17i	0.680150	+	0.392685i	0.799911	−	0.600118i	$-0.204880\pi$
$983$	6.13657e17	+	3.54295e17i	0.680150	+	0.392685i	−0.119762	+	0.992803i	$0.538213\pi$
$984$	−9.41176e16	+	1.63016e17i	−0.103681	+	0.179581i
$985$	−1.73941e18	+	1.00425e18i	−1.90452	+	1.09958i
$986$		−	1.36121e18i		−	1.48137i
$987$		0			0
$988$	1.40060e17			0.150582
$989$	1.07077e18	+	1.85464e18i	1.14425	+	1.98190i
$990$	1.25075e17	+	7.22118e16i	0.132849	+	0.0767003i
$991$	−5.69566e17	+	9.86517e17i	−0.601315	+	1.04151i	0.391307	+	0.920260i	$0.372023\pi$
$991$	−5.69566e17	+	9.86517e17i	−0.601315	+	1.04151i	−0.992622	+	0.121248i	$0.961310\pi$
$992$	−1.16992e17	+	6.75453e16i	−0.122768	+	0.0708802i
$993$			2.32420e17i			0.242425i
$994$		0			0
$995$	5.35615e17			0.551969
$996$	−1.64418e17	−	2.84781e17i	−0.168420	−	0.291712i
$997$	2.79166e17	+	1.61177e17i	0.284244	+	0.164109i	0.635343	−	0.772230i	$-0.280859\pi$
$997$	2.79166e17	+	1.61177e17i	0.284244	+	0.164109i	−0.351099	+	0.936338i	$0.614192\pi$
$998$	4.89707e17	−	8.48197e17i	0.495625	−	0.858447i
$999$	8.43173e17	−	4.86806e17i	0.848250	−	0.489737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.a.31.3		16
7.2	even	3		14.13.d.a.5.2	yes	16
7.3	odd	6		98.13.b.c.97.13		16
7.4	even	3		98.13.b.c.97.12		16
7.5	odd	6	inner	98.13.d.a.19.3		16
7.6	odd	2		14.13.d.a.3.2	✓	16
21.2	odd	6		126.13.n.a.19.6		16
21.20	even	2		126.13.n.a.73.6		16
28.23	odd	6		112.13.s.c.33.5		16
28.27	even	2		112.13.s.c.17.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.2	✓	16	7.6	odd	2
14.13.d.a.5.2	yes	16	7.2	even	3
98.13.b.c.97.12		16	7.4	even	3
98.13.b.c.97.13		16	7.3	odd	6
98.13.d.a.19.3		16	7.5	odd	6	inner
98.13.d.a.31.3		16	1.1	even	1	trivial
112.13.s.c.17.5		16	28.27	even	2
112.13.s.c.33.5		16	28.23	odd	6
126.13.n.a.19.6		16	21.2	odd	6
126.13.n.a.73.6		16	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-22.6274 - 39.1918i) q^{2} +(409.670 + 236.523i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18219.6 + 10519.1i) q^{5} -21407.6i q^{6} +92681.9 q^{8} +(-153834. - 266449. i) q^{9} +O(q^{10})\)	\(q+(-22.6274 - 39.1918i) q^{2} +(409.670 + 236.523i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-18219.6 + 10519.1i) q^{5} -21407.6i q^{6} +92681.9 q^{8} +(-153834. - 266449. i) q^{9} +(824525. + 476040. i) q^{10} +(-246520. + 426985. i) q^{11} +(-839004. + 484399. i) q^{12} -3.20567e6i q^{13} -9.95203e6 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(2.98777e7 + 1.72499e7i) q^{17} +(-6.96174e6 + 1.20581e7i) q^{18} +(1.84755e7 - 1.06668e7i) q^{19} -4.30862e7i q^{20} +2.23124e7 q^{22} +(-1.22901e8 - 2.12871e8i) q^{23} +(3.79690e7 + 2.19214e7i) q^{24} +(9.92324e7 - 1.71875e8i) q^{25} +(-1.25636e8 + 7.25360e7i) q^{26} -3.96937e8i q^{27} +8.71852e8 q^{29} +(2.25189e8 + 3.90038e8i) q^{30} +(6.16355e8 + 3.55853e8i) q^{31} +(-9.49063e7 + 1.64382e8i) q^{32} +(-2.01983e8 + 1.16615e8i) q^{33} -1.56128e9i q^{34} +6.30105e8 q^{36} +(1.22641e9 + 2.12420e9i) q^{37} +(-8.36106e8 - 4.82726e8i) q^{38} +(7.58214e8 - 1.31327e9i) q^{39} +(-1.68863e9 + 9.74930e8i) q^{40} +4.29341e9i q^{41} -8.71250e9 q^{43} +(-5.04873e8 - 8.74465e8i) q^{44} +(5.60560e9 + 3.23639e9i) q^{45} +(-5.56186e9 + 9.63343e9i) q^{46} +(4.94270e9 - 2.85367e9i) q^{47} -1.98410e9i q^{48} -8.98149e9 q^{50} +(8.15999e9 + 1.41335e10i) q^{51} +(5.68564e9 + 3.28260e9i) q^{52} +(-4.77915e9 + 8.27773e9i) q^{53} +(-1.55567e10 + 8.98167e9i) q^{54} -1.03727e10i q^{55} +1.00918e10 q^{57} +(-1.97278e10 - 3.41695e10i) q^{58} +(-4.83789e10 - 2.79316e10i) q^{59} +(1.01909e10 - 1.76511e10i) q^{60} +(-5.97865e10 + 3.45177e10i) q^{61} -3.22081e10i q^{62} +8.58993e9 q^{64} +(3.37207e10 + 5.84060e10i) q^{65} +(9.14073e9 + 5.27740e9i) q^{66} +(3.87174e10 - 6.70604e10i) q^{67} +(-6.11895e10 + 3.53278e10i) q^{68} -1.16276e11i q^{69} -1.07183e11 q^{71} +(-1.42577e10 - 2.46950e10i) q^{72} +(-2.07256e10 - 1.19659e10i) q^{73} +(5.55008e10 - 9.61301e10i) q^{74} +(8.13050e10 - 4.69415e10i) q^{75} +4.36914e10i q^{76} -6.86257e10 q^{78} +(1.59667e10 + 2.76551e10i) q^{79} +(7.64186e10 + 4.41203e10i) q^{80} +(1.21310e10 - 2.10115e10i) q^{81} +(1.68267e11 - 9.71488e10i) q^{82} +3.39427e11i q^{83} -7.25813e11 q^{85} +(1.97141e11 + 3.41459e11i) q^{86} +(3.57172e11 + 2.06213e11i) q^{87} +(-2.28479e10 + 3.95738e10i) q^{88} +(-7.24885e11 + 4.18513e11i) q^{89} -2.92925e11i q^{90} +5.03402e11 q^{92} +(1.68335e11 + 2.91564e11i) q^{93} +(-2.23681e11 - 1.29142e11i) q^{94} +(-2.24411e11 + 3.88691e11i) q^{95} +(-7.77605e10 + 4.48950e10i) q^{96} +9.93604e11i q^{97} +1.51693e11 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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