LMFDB - Embedded newform 98.13.d.a.31.8

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			31.8
Root			$-773.618 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.31
Dual form			98.13.d.a.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.6274 + 39.1918i) q^{2} +(1161.18 + 670.406i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-14223.7 + 8212.03i) q^{5} +60678.2i q^{6} -92681.9 q^{8} +(633167. + 1.09668e6i) q^{9} +O(q^{10})$	\(q+(22.6274 + 39.1918i) q^{2} +(1161.18 + 670.406i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-14223.7 + 8212.03i) q^{5} +60678.2i q^{6} -92681.9 q^{8} +(633167. + 1.09668e6i) q^{9} +(-643689. - 371634. i) q^{10} +(-464134. + 803904. i) q^{11} +(-2.37809e6 + 1.37299e6i) q^{12} -8.24891e6i q^{13} -2.20216e7 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(-1.17285e7 - 6.77147e6i) q^{17} +(-2.86538e7 + 4.96299e7i) q^{18} +(-3.88828e7 + 2.24490e7i) q^{19} -3.36365e7i q^{20} -4.20086e7 q^{22} +(3.53913e7 + 6.12994e7i) q^{23} +(-1.07620e8 - 6.21345e7i) q^{24} +(1.28046e7 - 2.21782e7i) q^{25} +(3.23290e8 - 1.86652e8i) q^{26} +9.85352e8i q^{27} -5.34101e8 q^{29} +(-4.98291e8 - 8.63066e8i) q^{30} +(-1.14672e9 - 6.62060e8i) q^{31} +(9.49063e7 - 1.64382e8i) q^{32} +(-1.07788e9 + 6.22316e8i) q^{33} -6.12884e8i q^{34} -2.59345e9 q^{36} +(5.25480e8 + 9.10159e8i) q^{37} +(-1.75964e9 - 1.01593e9i) q^{38} +(5.53011e9 - 9.57844e9i) q^{39} +(1.31828e9 - 7.61107e8i) q^{40} -1.78011e9i q^{41} -4.20662e9 q^{43} +(-9.50546e8 - 1.64639e9i) q^{44} +(-1.80119e10 - 1.03992e10i) q^{45} +(-1.60163e9 + 2.77410e9i) q^{46} +(1.50464e10 - 8.68706e9i) q^{47} -5.62377e9i q^{48} +1.15894e9 q^{50} +(-9.07927e9 - 1.57258e10i) q^{51} +(1.46304e10 + 8.44688e9i) q^{52} +(2.46892e9 - 4.27630e9i) q^{53} +(-3.86177e10 + 2.22960e10i) q^{54} -1.52459e10i q^{55} -6.01997e10 q^{57} +(-1.20853e10 - 2.09324e10i) q^{58} +(-7.90727e9 - 4.56526e9i) q^{59} +(2.25501e10 - 3.90579e10i) q^{60} +(-1.85526e10 + 1.07113e10i) q^{61} -5.99229e10i q^{62} +8.58993e9 q^{64} +(6.77403e10 + 1.17330e11i) q^{65} +(-4.87794e10 - 2.81628e10i) q^{66} +(-3.21303e10 + 5.56512e10i) q^{67} +(2.40200e10 - 1.38680e10i) q^{68} +9.49060e10i q^{69} -9.11975e10 q^{71} +(-5.86831e10 - 1.01642e11i) q^{72} +(1.80214e11 + 1.04047e11i) q^{73} +(-2.37805e10 + 4.11891e10i) q^{74} +(2.97368e10 - 1.71686e10i) q^{75} -9.19511e10i q^{76} +5.00529e11 q^{78} +(1.52937e11 + 2.64895e11i) q^{79} +(5.96583e10 + 3.44438e10i) q^{80} +(-3.24094e11 + 5.61348e11i) q^{81} +(6.97656e10 - 4.02792e10i) q^{82} -2.37417e11i q^{83} +2.22430e11 q^{85} +(-9.51849e10 - 1.64865e11i) q^{86} +(-6.20185e11 - 3.58064e11i) q^{87} +(4.30168e10 - 7.45073e10i) q^{88} +(-9.71289e10 + 5.60774e10i) q^{89} -9.41225e11i q^{90} -1.44963e11 q^{92} +(-8.87698e11 - 1.53754e12i) q^{93} +(6.80923e11 + 3.93131e11i) q^{94} +(3.68704e11 - 6.38614e11i) q^{95} +(2.20406e11 - 1.27251e11i) q^{96} +9.61170e11i q^{97} -1.17550e12 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
$3$	1161.18	+	670.406i	1.59283	+	0.919623i	0.992818	+	0.119636i	$0.0381728\pi$
$3$	1161.18	+	670.406i	1.59283	+	0.919623i	0.600017	+	0.799987i	$0.295161\pi$
$4$	−1024.00	+	1773.62i	−0.250000	+	0.433013i
$5$	−14223.7	+	8212.03i	−0.910314	+	0.525570i	−0.880532	−	0.473986i	$-0.842815\pi$
$5$	−14223.7	+	8212.03i	−0.910314	+	0.525570i	−0.0297818	+	0.999556i	$0.509481\pi$
$6$			60678.2i			1.30054i
$7$		0			0
$7$		0			0
$8$	−92681.9			−0.353553
$9$	633167.	+	1.09668e6i	1.19141	+	2.06359i
$10$	−643689.	−	371634.i	−0.643689	−	0.371634i
$11$	−464134.	+	803904.i	−0.261992	+	0.453783i	−0.966771	−	0.255644i	$-0.917713\pi$
$11$	−464134.	+	803904.i	−0.261992	+	0.453783i	0.704780	+	0.709426i	$0.251046\pi$
$12$	−2.37809e6	+	1.37299e6i	−0.796417	+	0.459812i
$13$		−	8.24891e6i		−	1.70898i	−0.519470	−	0.854489i	$-0.673870\pi$
$13$		−	8.24891e6i		−	1.70898i	0.519470	−	0.854489i	$-0.326130\pi$
$14$		0			0
$15$	−2.20216e7			−1.93331
$16$	−2.09715e6	−	3.63237e6i	−0.125000	−	0.216506i
$17$	−1.17285e7	−	6.77147e6i	−0.485904	−	0.280537i	0.236970	−	0.971517i	$-0.423846\pi$
$17$	−1.17285e7	−	6.77147e6i	−0.485904	−	0.280537i	−0.722874	+	0.690980i	$0.757179\pi$
$18$	−2.86538e7	+	4.96299e7i	−0.842457	+	1.45918i
$19$	−3.88828e7	+	2.24490e7i	−0.826487	+	0.477173i	−0.852648	−	0.522485i	$-0.825005\pi$
$19$	−3.88828e7	+	2.24490e7i	−0.826487	+	0.477173i	0.0261613	+	0.999658i	$0.491672\pi$
$20$		−	3.36365e7i		−	0.525570i
$21$		0			0
$22$	−4.20086e7			−0.370512
$23$	3.53913e7	+	6.12994e7i	0.239072	+	0.414085i	0.960448	−	0.278458i	$-0.0898234\pi$
$23$	3.53913e7	+	6.12994e7i	0.239072	+	0.414085i	−0.721376	+	0.692543i	$0.756490\pi$
$24$	−1.07620e8	−	6.21345e7i	−0.563152	−	0.325136i
$25$	1.28046e7	−	2.21782e7i	0.0524477	−	0.0908420i
$26$	3.23290e8	−	1.86652e8i	1.04653	−	0.604215i
$27$			9.85352e8i			2.54336i
$28$		0			0
$29$	−5.34101e8			−0.897915			−0.448957	−	0.893553i	$-0.648205\pi$
$29$	−5.34101e8			−0.897915			−0.448957	+	0.893553i	$0.648205\pi$
$30$	−4.98291e8	−	8.63066e8i	−0.683527	−	1.18390i
$31$	−1.14672e9	−	6.62060e8i	−1.29208	−	0.745980i	−0.313054	−	0.949735i	$-0.601352\pi$
$31$	−1.14672e9	−	6.62060e8i	−1.29208	−	0.745980i	−0.979022	+	0.203755i	$0.934685\pi$
$32$	9.49063e7	−	1.64382e8i	0.0883883	−	0.153093i
$33$	−1.07788e9	+	6.22316e8i	−0.834618	+	0.481867i
$34$		−	6.12884e8i		−	0.396739i
$35$		0			0
$36$	−2.59345e9			−1.19141
$37$	5.25480e8	+	9.10159e8i	0.204808	+	0.354737i	0.950071	−	0.312032i	$-0.101010\pi$
$37$	5.25480e8	+	9.10159e8i	0.204808	+	0.354737i	−0.745264	+	0.666770i	$0.767676\pi$
$38$	−1.75964e9	−	1.01593e9i	−0.584415	−	0.337412i
$39$	5.53011e9	−	9.57844e9i	1.57162	−	2.72212i
$40$	1.31828e9	−	7.61107e8i	0.321845	−	0.185817i
$41$		−	1.78011e9i		−	0.374751i	−0.982288	−	0.187375i	$-0.940002\pi$
$41$		−	1.78011e9i		−	0.374751i	0.982288	−	0.187375i	$-0.0599981\pi$
$42$		0			0
$43$	−4.20662e9			−0.665461			−0.332730	−	0.943022i	$-0.607970\pi$
$43$	−4.20662e9			−0.665461			−0.332730	+	0.943022i	$0.607970\pi$
$44$	−9.50546e8	−	1.64639e9i	−0.130996	−	0.226891i
$45$	−1.80119e10	−	1.03992e10i	−2.16912	−	1.25234i
$46$	−1.60163e9	+	2.77410e9i	−0.169050	+	0.292802i
$47$	1.50464e10	−	8.68706e9i	1.39587	−	0.805908i	0.401916	−	0.915676i	$-0.368344\pi$
$47$	1.50464e10	−	8.68706e9i	1.39587	−	0.805908i	0.993957	+	0.109768i	$0.0350109\pi$
$48$		−	5.62377e9i		−	0.459812i
$49$		0			0
$50$	1.15894e9			0.0741722
$51$	−9.07927e9	−	1.57258e10i	−0.515976	−	0.893697i
$52$	1.46304e10	+	8.44688e9i	0.740009	+	0.427244i
$53$	2.46892e9	−	4.27630e9i	0.111392	−	0.192936i	−0.804940	−	0.593356i	$-0.797803\pi$
$53$	2.46892e9	−	4.27630e9i	0.111392	−	0.192936i	0.916332	+	0.400420i	$0.131136\pi$
$54$	−3.86177e10	+	2.22960e10i	−1.55749	+	0.899215i
$55$		−	1.52459e10i		−	0.550780i
$56$		0			0
$57$	−6.01997e10			−1.75528
$58$	−1.20853e10	−	2.09324e10i	−0.317461	−	0.549858i
$59$	−7.90727e9	−	4.56526e9i	−0.187463	−	0.108232i	0.403332	−	0.915054i	$-0.367852\pi$
$59$	−7.90727e9	−	4.56526e9i	−0.187463	−	0.108232i	−0.590794	+	0.806822i	$0.701185\pi$
$60$	2.25501e10	−	3.90579e10i	0.483327	−	0.837146i
$61$	−1.85526e10	+	1.07113e10i	−0.360101	+	0.207905i	−0.669125	−	0.743150i	$-0.733331\pi$
$61$	−1.85526e10	+	1.07113e10i	−0.360101	+	0.207905i	0.309024	+	0.951054i	$0.399998\pi$
$62$		−	5.99229e10i		−	1.05498i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	6.77403e10	+	1.17330e11i	0.898188	+	1.55571i
$66$	−4.87794e10	−	2.81628e10i	−0.590164	−	0.340731i
$67$	−3.21303e10	+	5.56512e10i	−0.355194	+	0.615214i	−0.987151	−	0.159790i	$-0.948918\pi$
$67$	−3.21303e10	+	5.56512e10i	−0.355194	+	0.615214i	0.631957	+	0.775003i	$0.282252\pi$
$68$	2.40200e10	−	1.38680e10i	0.242952	−	0.140268i
$69$			9.49060e10i			0.879425i
$70$		0			0
$71$	−9.11975e10			−0.711922			−0.355961	−	0.934501i	$-0.615846\pi$
$71$	−9.11975e10			−0.711922			−0.355961	+	0.934501i	$0.615846\pi$
$72$	−5.86831e10	−	1.01642e11i	−0.421229	−	0.729589i
$73$	1.80214e11	+	1.04047e11i	1.19083	+	0.687528i	0.958496	−	0.285107i	$-0.0920291\pi$
$73$	1.80214e11	+	1.04047e11i	1.19083	+	0.687528i	0.232338	+	0.972635i	$0.425362\pi$
$74$	−2.37805e10	+	4.11891e10i	−0.144821	+	0.250837i
$75$	2.97368e10	−	1.71686e10i	0.167081	−	0.0964642i
$76$		−	9.19511e10i		−	0.477173i
$77$		0			0
$78$	5.00529e11			2.22260
$79$	1.52937e11	+	2.64895e11i	0.629145	+	1.08971i	0.987724	+	0.156211i	$0.0499281\pi$
$79$	1.52937e11	+	2.64895e11i	0.629145	+	1.08971i	−0.358579	+	0.933499i	$0.616739\pi$
$80$	5.96583e10	+	3.44438e10i	0.227578	+	0.131393i
$81$	−3.24094e11	+	5.61348e11i	−1.14752	+	1.98757i
$82$	6.97656e10	−	4.02792e10i	0.229487	−	0.132494i
$83$		−	2.37417e11i		−	0.726178i	−0.931755	−	0.363089i	$-0.881722\pi$
$83$		−	2.37417e11i		−	0.726178i	0.931755	−	0.363089i	$-0.118278\pi$
$84$		0			0
$85$	2.22430e11			0.589767
$86$	−9.51849e10	−	1.64865e11i	−0.235276	−	0.407510i
$87$	−6.20185e11	−	3.58064e11i	−1.43023	−	0.825744i
$88$	4.30168e10	−	7.45073e10i	0.0926280	−	0.160436i
$89$	−9.71289e10	+	5.60774e10i	−0.195438	+	0.112836i	−0.594526	−	0.804077i	$-0.702660\pi$
$89$	−9.71289e10	+	5.60774e10i	−0.195438	+	0.112836i	0.399088	+	0.916913i	$0.369327\pi$
$90$		−	9.41225e11i		−	1.77108i
$91$		0			0
$92$	−1.44963e11			−0.239072
$93$	−8.87698e11	−	1.53754e12i	−1.37204	−	2.37645i
$94$	6.80923e11	+	3.93131e11i	0.987032	+	0.569863i
$95$	3.68704e11	−	6.38614e11i	0.501575	−	0.868754i
$96$	2.20406e11	−	1.27251e11i	0.281576	−	0.162568i
$97$			9.61170e11i			1.15390i	0.816778	+	0.576952i	$0.195758\pi$
$97$			9.61170e11i			1.15390i	−0.816778	+	0.576952i	$0.804242\pi$
$98$		0			0
$99$	−1.17550e12			−1.24856
$100$	2.62238e10	+	4.54210e10i	0.0262238	+	0.0454210i
$101$	−1.26919e12	−	7.32769e11i	−1.19564	−	0.690302i	−0.236058	−	0.971739i	$-0.575855\pi$
$101$	−1.26919e12	−	7.32769e11i	−1.19564	−	0.690302i	−0.959580	+	0.281438i	$0.909189\pi$
$102$	4.10881e11	−	7.11666e11i	0.364850	−	0.631939i
$103$	9.15674e11	−	5.28665e11i	0.766863	−	0.442748i	−0.0648917	−	0.997892i	$-0.520670\pi$
$103$	9.15674e11	−	5.28665e11i	0.766863	−	0.442748i	0.831754	+	0.555144i	$0.187337\pi$
$104$			7.64525e11i			0.604215i
$105$		0			0
$106$	2.23462e11			0.157532
$107$	−3.89941e11	−	6.75398e11i	−0.259834	−	0.450046i	0.706363	−	0.707850i	$-0.250335\pi$
$107$	−3.89941e11	−	6.75398e11i	−0.259834	−	0.450046i	−0.966197	+	0.257803i	$0.917001\pi$
$108$	−1.74764e12	−	1.00900e12i	−1.10131	−	0.635841i
$109$	−3.07392e11	+	5.32419e11i	−0.183288	+	0.317464i	−0.942998	−	0.332798i	$-0.892007\pi$
$109$	−3.07392e11	+	5.32419e11i	−0.183288	+	0.317464i	0.759710	+	0.650262i	$0.225341\pi$
$110$	5.97516e11	−	3.44976e11i	0.337282	−	0.194730i
$111$			1.40914e12i			0.753384i
$112$		0			0
$113$	2.34507e12			1.12638			0.563190	−	0.826328i	$-0.309574\pi$
$113$	2.34507e12			1.12638			0.563190	+	0.826328i	$0.309574\pi$
$114$	−1.36216e12	−	2.35934e12i	−0.620584	−	1.07488i
$115$	−1.00679e12	−	5.81268e11i	−0.435261	−	0.251298i
$116$	5.46919e11	−	9.47292e11i	0.224479	−	0.388809i
$117$	9.04639e12	−	5.22293e12i	3.52663	−	2.03610i
$118$		−	4.13201e11i		−	0.153063i
$119$		0			0
$120$	2.04100e12			0.683527
$121$	1.13837e12	+	1.97172e12i	0.362721	+	0.628251i
$122$	−8.39593e11	−	4.84739e11i	−0.254630	−	0.147011i
$123$	1.19339e12	−	2.06702e12i	0.344630	−	0.596916i
$124$	2.34849e12	−	1.35590e12i	0.646038	−	0.372990i
$125$		−	3.58917e12i		−	0.940880i
$126$		0			0
$127$	−4.49588e12			−1.07150			−0.535750	−	0.844377i	$-0.679971\pi$
$127$	−4.49588e12			−1.07150			−0.535750	+	0.844377i	$0.679971\pi$
$128$	1.94368e11	+	3.36655e11i	0.0441942	+	0.0765466i
$129$	−4.88463e12	−	2.82014e12i	−1.05997	−	0.611973i
$130$	−3.06558e12	+	5.30973e12i	−0.635114	+	1.10005i
$131$	−7.75211e12	+	4.47568e12i	−1.53388	+	0.885588i	−0.534705	+	0.845039i	$0.679577\pi$
$131$	−7.75211e12	+	4.47568e12i	−1.53388	+	0.885588i	−0.999178	+	0.0405491i	$0.987089\pi$
$132$		−	2.54901e12i		−	0.481867i
$133$		0			0
$134$	−2.90810e12			−0.502320
$135$	−8.09174e12	−	1.40153e13i	−1.33672	−	2.31526i
$136$	1.08702e12	+	6.27593e11i	0.171793	+	0.0991847i
$137$	−4.23307e12	+	7.33190e12i	−0.640225	+	1.10890i	0.345158	+	0.938545i	$0.387825\pi$
$137$	−4.23307e12	+	7.33190e12i	−0.640225	+	1.10890i	−0.985382	+	0.170357i	$0.945508\pi$
$138$	−3.71954e12	+	2.14748e12i	−0.538536	+	0.310924i
$139$		−	5.06800e12i		−	0.702664i	−0.936251	−	0.351332i	$-0.885729\pi$
$139$		−	5.06800e12i		−	0.702664i	0.936251	−	0.351332i	$-0.114271\pi$
$140$		0			0
$141$	2.32954e13			2.96453
$142$	−2.06356e12	−	3.57420e12i	−0.251703	−	0.435962i
$143$	6.63133e12	+	3.82860e12i	0.775504	+	0.447738i
$144$	2.65569e12	−	4.59980e12i	0.297854	−	0.515898i
$145$	7.59687e12	−	4.38605e12i	0.817385	−	0.471917i
$146$			9.41722e12i			0.972312i
$147$		0			0
$148$	−2.15237e12			−0.204808
$149$	−5.74237e12	−	9.94608e12i	−0.524775	−	0.908938i	−0.999584	−	0.0288486i	$-0.990816\pi$
$149$	−5.74237e12	−	9.94608e12i	−0.524775	−	0.908938i	0.474808	−	0.880089i	$-0.342517\pi$
$150$	1.34573e12	+	7.76960e11i	0.118144	+	0.0682105i
$151$	−6.13919e12	+	1.06334e13i	−0.517904	+	0.897036i	0.481880	+	0.876237i	$0.339954\pi$
$151$	−6.13919e12	+	1.06334e13i	−0.517904	+	0.897036i	−0.999784	+	0.0207985i	$0.993379\pi$
$152$	3.60373e12	−	2.08062e12i	0.292207	−	0.168706i
$153$		−	1.71499e13i		−	1.33694i
$154$		0			0
$155$	2.17474e13			1.56826
$156$	1.13257e13	+	1.96166e13i	0.785808	+	1.36106i
$157$	8.12188e11	+	4.68917e11i	0.0542324	+	0.0313111i	0.526871	−	0.849945i	$-0.323365\pi$
$157$	8.12188e11	+	4.68917e11i	0.0542324	+	0.0313111i	−0.472639	+	0.881256i	$0.656698\pi$
$158$	−6.92115e12	+	1.19878e13i	−0.444873	+	0.770542i
$159$	5.73371e12	−	3.31036e12i	0.354857	−	0.204877i
$160$			3.11749e12i			0.185817i
$161$		0			0
$162$	−2.93337e13			−1.62284
$163$	4.21550e12	+	7.30146e12i	0.224762	+	0.389300i	0.956248	−	0.292557i	$-0.0945061\pi$
$163$	4.21550e12	+	7.30146e12i	0.224762	+	0.389300i	−0.731486	+	0.681857i	$0.761173\pi$
$164$	3.15723e12	+	1.82283e12i	0.162272	+	0.0936877i
$165$	1.02210e13	−	1.77032e13i	0.506510	−	0.877301i
$166$	9.30480e12	−	5.37213e12i	0.444691	−	0.256743i
$167$			1.23904e12i			0.0571199i	0.999592	+	0.0285599i	$0.00909215\pi$
$167$			1.23904e12i			0.0571199i	−0.999592	+	0.0285599i	$0.990908\pi$
$168$		0			0
$169$	−4.47464e13			−1.92061
$170$	5.03302e12	+	8.71745e12i	0.208514	+	0.361157i
$171$	−4.92386e13	−	2.84279e13i	−1.96938	−	1.13702i
$172$	4.30758e12	−	7.46094e12i	0.166365	−	0.288153i
$173$	−3.41415e13	+	1.97116e13i	−1.27352	+	0.735267i	−0.975649	−	0.219339i	$-0.929610\pi$
$173$	−3.41415e13	+	1.97116e13i	−1.27352	+	0.735267i	−0.297871	+	0.954606i	$0.596277\pi$
$174$		−	3.24083e13i		−	1.16778i
$175$		0			0
$176$	3.89344e12			0.130996
$177$	−6.12116e12	−	1.06022e13i	−0.199065	−	0.344790i
$178$	−4.39555e12	−	2.53777e12i	−0.138195	−	0.0797871i
$179$	1.39781e12	−	2.42107e12i	0.0424941	−	0.0736019i	−0.843996	−	0.536349i	$-0.819803\pi$
$179$	1.39781e12	−	2.42107e12i	0.0424941	−	0.0736019i	0.886490	+	0.462747i	$0.153136\pi$
$180$	3.68883e13	−	2.12975e13i	1.08456	−	0.626172i
$181$		−	3.44578e13i		−	0.979976i	−0.871729	−	0.489988i	$-0.837001\pi$
$181$		−	3.44578e13i		−	0.979976i	0.871729	−	0.489988i	$-0.162999\pi$
$182$		0			0
$183$	−2.87237e13			−0.764776
$184$	−3.28013e12	−	5.68135e12i	−0.0845248	−	0.146401i
$185$	−1.49485e13	−	8.63052e12i	−0.372879	−	0.215282i
$186$	4.01726e13	−	6.95810e13i	0.970180	−	1.68040i
$187$	1.08872e13	−	6.28574e12i	0.254605	−	0.146996i
$188$			3.55822e13i			0.805908i
$189$		0			0
$190$	3.33713e13			0.709334
$191$	−1.21661e13	−	2.10724e13i	−0.250584	−	0.434024i	0.713103	−	0.701059i	$-0.247289\pi$
$191$	−1.21661e13	−	2.10724e13i	−0.250584	−	0.434024i	−0.963687	+	0.267036i	$0.913956\pi$
$192$	9.97443e12	+	5.75874e12i	0.199104	+	0.114953i
$193$	4.78420e12	−	8.28647e12i	0.0925689	−	0.160334i	−0.816022	−	0.578020i	$-0.803825\pi$
$193$	4.78420e12	−	8.28647e12i	0.0925689	−	0.160334i	0.908591	+	0.417686i	$0.137159\pi$
$194$	−3.76700e13	+	2.17488e13i	−0.706619	+	0.407967i
$195$			1.81654e14i			3.30398i
$196$		0			0
$197$	−3.14741e13			−0.538462			−0.269231	−	0.963076i	$-0.586770\pi$
$197$	−3.14741e13			−0.538462			−0.269231	+	0.963076i	$0.586770\pi$
$198$	−2.65984e13	−	4.60699e13i	−0.441433	−	0.764585i
$199$	9.28965e13	+	5.36338e13i	1.49582	+	0.863615i	0.999988	−	0.00480132i	$-0.00152831\pi$
$199$	9.28965e13	+	5.36338e13i	1.49582	+	0.863615i	0.495836	+	0.868416i	$0.334862\pi$
$200$	−1.18676e12	+	2.05552e12i	−0.0185430	+	0.0321175i
$201$	−7.46178e13	+	4.30806e13i	−1.13153	+	0.653289i
$202$		−	6.63227e13i		−	0.976234i
$203$		0			0
$204$	3.71887e13			0.515976
$205$	1.46183e13	+	2.53196e13i	0.196958	+	0.341141i
$206$	4.14387e13	+	2.39246e13i	0.542254	+	0.313070i
$207$	−4.48171e13	+	7.76255e13i	−0.569668	+	0.986694i
$208$	−2.99631e13	+	1.72992e13i	−0.370005	+	0.213622i
$209$		−	4.16774e13i		−	0.500061i
$210$		0			0
$211$	3.92422e13			0.444691			0.222346	−	0.974968i	$-0.428629\pi$
$211$	3.92422e13			0.444691			0.222346	+	0.974968i	$0.428629\pi$
$212$	5.05636e12	+	8.75787e12i	0.0556958	+	0.0964680i
$213$	−1.05896e14	−	6.11393e13i	−1.13397	−	0.654701i
$214$	1.76467e13	−	3.05650e13i	0.183731	−	0.318231i
$215$	5.98335e13	−	3.45449e13i	0.605778	−	0.349746i
$216$		−	9.13243e13i		−	0.899215i
$217$		0			0
$218$	−2.78220e13			−0.259208
$219$	1.39507e14	+	2.41633e14i	1.26453	+	2.19024i
$220$	2.70405e13	+	1.56118e13i	0.238495	+	0.137695i
$221$	−5.58573e13	+	9.67476e13i	−0.479431	+	0.830399i
$222$	−5.52268e13	+	3.18852e13i	−0.461351	+	0.266361i
$223$			1.59588e14i			1.29769i	0.760920	+	0.648845i	$0.224748\pi$
$223$			1.59588e14i			1.29769i	−0.760920	+	0.648845i	$0.775252\pi$
$224$		0			0
$225$	3.24298e13			0.249948
$226$	5.30628e13	+	9.19075e13i	0.398235	+	0.689764i
$227$	4.04200e13	+	2.33365e13i	0.295421	+	0.170561i	0.640384	−	0.768055i	$-0.278775\pi$
$227$	4.04200e13	+	2.33365e13i	0.295421	+	0.170561i	−0.344963	+	0.938616i	$0.612109\pi$
$228$	6.16445e13	−	1.06771e14i	0.438819	−	0.760057i
$229$	2.27382e13	−	1.31279e13i	0.157668	−	0.0910297i	−0.419090	−	0.907945i	$-0.637651\pi$
$229$	2.27382e13	−	1.31279e13i	0.157668	−	0.0910297i	0.576758	+	0.816915i	$0.304318\pi$
$230$		−	5.26104e13i		−	0.355389i
$231$		0			0
$232$	4.95015e13			0.317461
$233$	2.33179e13	+	4.03879e13i	0.145732	+	0.252415i	0.929646	−	0.368455i	$-0.120113\pi$
$233$	2.33179e13	+	4.03879e13i	0.145732	+	0.252415i	−0.783914	+	0.620870i	$0.786780\pi$
$234$	4.09393e14	+	2.36363e14i	2.49370	+	1.43974i
$235$	−1.42677e14	+	2.47123e14i	−0.847122	+	1.46726i
$236$	1.61941e13	−	9.34966e12i	0.0937313	−	0.0541158i
$237$			4.10120e14i			2.31431i
$238$		0			0
$239$	9.36225e13			0.502334			0.251167	−	0.967944i	$-0.419186\pi$
$239$	9.36225e13			0.502334			0.251167	+	0.967944i	$0.419186\pi$
$240$	4.61826e13	+	7.99906e13i	0.241663	+	0.418573i
$241$	6.74741e13	+	3.89562e13i	0.344378	+	0.198826i	0.662206	−	0.749322i	$-0.269620\pi$
$241$	6.74741e13	+	3.89562e13i	0.344378	+	0.198826i	−0.317829	+	0.948148i	$0.602954\pi$
$242$	−5.15169e13	+	8.92299e13i	−0.256482	+	0.444241i
$243$	−2.99162e14	+	1.72721e14i	−1.45301	+	0.838896i
$244$		−	4.38736e13i		−	0.207905i
$245$		0			0
$246$	1.08014e14			0.487380
$247$	1.85180e14	+	3.20741e14i	0.815477	+	1.41245i
$248$	1.06280e14	+	6.13610e13i	0.456818	+	0.263744i
$249$	1.59166e14	−	2.75683e14i	0.667810	−	1.15668i
$250$	1.40666e14	−	8.12137e13i	0.576169	−	0.332651i
$251$			1.06944e13i			0.0427675i	0.999771	+	0.0213837i	$0.00680717\pi$
$251$			1.06944e13i			0.0427675i	−0.999771	+	0.0213837i	$0.993193\pi$
$252$		0			0
$253$	−6.57051e13			−0.250539
$254$	−1.01730e14	−	1.76202e14i	−0.378832	−	0.656157i
$255$	2.58281e14	+	1.49118e14i	0.939401	+	0.542363i
$256$	−8.79609e12	+	1.52353e13i	−0.0312500	+	0.0541266i
$257$	−3.40707e14	+	1.96707e14i	−1.18245	+	0.682686i	−0.956579	−	0.291472i	$-0.905855\pi$
$257$	−3.40707e14	+	1.96707e14i	−1.18245	+	0.682686i	−0.225868	+	0.974158i	$0.572522\pi$
$258$		−	2.55250e14i		−	0.865461i
$259$		0			0
$260$	−2.77464e14			−0.898188
$261$	−3.38175e14	−	5.85736e14i	−1.06979	−	1.85293i
$262$	−3.50820e14	−	2.02546e14i	−1.08462	−	0.626205i
$263$	−1.57223e14	+	2.72319e14i	−0.475098	+	0.822893i	−0.999593	−	0.0285199i	$-0.990921\pi$
$263$	−1.57223e14	+	2.72319e14i	−0.475098	+	0.822893i	0.524496	+	0.851413i	$0.324254\pi$
$264$	9.99002e13	−	5.76774e13i	0.295082	−	0.170366i
$265$			8.10995e13i			0.234176i
$266$		0			0
$267$	−1.50378e14			−0.415067
$268$	−6.58028e13	−	1.13974e14i	−0.177597	−	0.307607i
$269$	−3.82229e14	−	2.20680e14i	−1.00881	−	0.582437i	−0.0979679	−	0.995190i	$-0.531234\pi$
$269$	−3.82229e14	−	2.20680e14i	−1.00881	−	0.582437i	−0.910843	+	0.412752i	$0.864568\pi$
$270$	3.66190e14	−	6.34260e14i	0.945201	−	1.63714i
$271$	−4.27273e14	+	2.46686e14i	−1.07867	+	0.622772i	−0.930538	−	0.366195i	$-0.880660\pi$
$271$	−4.27273e14	+	2.46686e14i	−1.07867	+	0.622772i	−0.148135	+	0.988967i	$0.547327\pi$
$272$			5.68032e13i			0.140268i
$273$		0			0
$274$	−3.83134e14			−0.905414
$275$	1.18861e13	+	2.05873e13i	0.0274817	+	0.0475997i
$276$	−1.68327e14	−	9.71837e13i	−0.380802	−	0.219856i
$277$	3.44803e14	−	5.97216e14i	0.763295	−	1.32207i	−0.177849	−	0.984058i	$-0.556914\pi$
$277$	3.44803e14	−	5.97216e14i	0.763295	−	1.32207i	0.941143	−	0.338008i	$-0.109753\pi$
$278$	1.98624e14	−	1.14676e14i	0.430292	−	0.248429i
$279$		−	1.67678e15i		−	3.55509i
$280$		0			0
$281$	−4.08440e14			−0.829641			−0.414820	−	0.909903i	$-0.636156\pi$
$281$	−4.08440e14			−0.829641			−0.414820	+	0.909903i	$0.636156\pi$
$282$	5.27115e14	+	9.12990e14i	1.04812	+	1.81540i
$283$	−8.31069e14	−	4.79818e14i	−1.61778	−	0.934023i	−0.987494	−	0.157657i	$-0.949606\pi$
$283$	−8.31069e14	−	4.79818e14i	−1.61778	−	0.934023i	−0.630282	−	0.776366i	$-0.717061\pi$
$284$	9.33862e13	−	1.61750e14i	0.177981	−	0.308271i
$285$	8.56260e14	−	4.94362e14i	1.59785	−	0.922520i
$286$			3.46525e14i			0.633197i
$287$		0			0
$288$	2.40366e14			0.421229
$289$	−1.99605e14	−	3.45727e14i	−0.342598	−	0.593398i
$290$	3.43795e14	+	1.98490e14i	0.577978	+	0.333696i
$291$	−6.44373e14	+	1.11609e15i	−1.06116	+	1.83798i
$292$	−3.69078e14	+	2.13087e14i	−0.595417	+	0.343764i
$293$			9.48005e14i			1.49832i	0.662388	+	0.749161i	$0.269543\pi$
$293$			9.48005e14i			1.49832i	−0.662388	+	0.749161i	$0.730457\pi$
$294$		0			0
$295$	1.49960e14			0.227533
$296$	−4.87025e13	−	8.43552e13i	−0.0724104	−	0.125419i
$297$	−7.92128e14	−	4.57335e14i	−1.15413	−	0.666340i
$298$	2.59870e14	−	4.50108e14i	0.371072	−	0.642716i
$299$	5.05654e14	−	2.91939e14i	0.707662	−	0.408569i
$300$			7.03224e13i			0.0964642i
$301$		0			0
$302$	−5.55656e14			−0.732427
$303$	−9.82505e14	−	1.70175e15i	−1.26963	−	2.19907i
$304$	1.63086e14	+	9.41579e13i	0.206622	+	0.119293i
$305$	1.75923e14	−	3.04708e14i	0.218537	−	0.378517i
$306$	6.72135e14	−	3.88058e14i	0.818706	−	0.472680i
$307$			8.39849e14i			1.00316i	0.865111	+	0.501581i	$0.167248\pi$
$307$			8.39849e14i			1.00316i	−0.865111	+	0.501581i	$0.832752\pi$
$308$		0			0
$309$	1.41768e15			1.62865
$310$	4.92088e14	+	8.52322e14i	0.554463	+	0.960359i
$311$	3.30007e13	+	1.90529e13i	0.0364721	+	0.0210572i	0.518125	−	0.855305i	$-0.326630\pi$
$311$	3.30007e13	+	1.90529e13i	0.0364721	+	0.0210572i	−0.481653	+	0.876362i	$0.659963\pi$
$312$	−5.12542e14	+	8.87748e14i	−0.555650	+	0.962414i
$313$	−2.59337e13	+	1.49728e13i	−0.0275803	+	0.0159235i	−0.513727	−	0.857954i	$-0.671735\pi$
$313$	−2.59337e13	+	1.49728e13i	−0.0275803	+	0.0159235i	0.486146	+	0.873877i	$0.338402\pi$
$314$			4.24415e13i			0.0442805i
$315$		0			0
$316$	−6.26431e14			−0.629145
$317$	1.81719e14	+	3.14746e14i	0.179079	+	0.310174i	0.941565	−	0.336831i	$-0.109355\pi$
$317$	1.81719e14	+	3.14746e14i	0.179079	+	0.310174i	−0.762486	+	0.647004i	$0.776022\pi$
$318$	2.59478e14	+	1.49810e14i	0.250922	+	0.144870i
$319$	2.47894e14	−	4.29366e14i	0.235246	−	0.407458i
$320$	−1.22180e14	+	7.05408e13i	−0.113789	+	0.0656963i
$321$		−	1.04568e15i		−	0.955799i
$322$		0			0
$323$	6.08051e14			0.535458
$324$	−6.63745e14	−	1.14964e15i	−0.573762	−	0.993784i
$325$	−1.82946e14	−	1.05624e14i	−0.155247	−	0.0896319i
$326$	−1.90772e14	+	3.30426e14i	−0.158931	+	0.275276i
$327$	−7.13873e14	+	4.12155e14i	−0.583895	+	0.337112i
$328$			1.64984e14i			0.132494i
$329$		0			0
$330$	9.25095e14			0.716313
$331$	3.42754e14	+	5.93667e14i	0.260624	+	0.451414i	0.966408	−	0.257013i	$-0.0827384\pi$
$331$	3.42754e14	+	5.93667e14i	0.260624	+	0.451414i	−0.705784	+	0.708427i	$0.749405\pi$
$332$	4.21087e14	+	2.43115e14i	0.314444	+	0.181544i
$333$	−6.65433e14	+	1.15256e15i	−0.488022	+	0.845278i
$334$	−4.85603e13	+	2.80363e13i	−0.0349786	+	0.0201949i
$335$		−	1.05542e15i		−	0.746717i
$336$		0			0
$337$	−2.02273e15			−1.38089			−0.690445	−	0.723385i	$-0.742585\pi$
$337$	−2.02273e15			−1.38089			−0.690445	+	0.723385i	$0.742585\pi$
$338$	−1.01250e15	−	1.75369e15i	−0.679037	−	1.17613i
$339$	2.72304e15	+	1.57215e15i	1.79414	+	1.03584i
$340$	−2.27769e14	+	3.94507e14i	−0.147442	+	0.255376i
$341$	1.06447e15	−	6.14569e14i	0.677026	−	0.390881i
$342$		−	2.57300e15i		−	1.60799i
$343$		0			0
$344$	3.89877e14			0.235276
$345$	−7.79371e14	−	1.34991e15i	−0.462200	−	0.800553i
$346$	−1.54507e15	−	8.92045e14i	−0.900514	−	0.519912i
$347$	−1.30801e15	+	2.26554e15i	−0.749263	+	1.29776i	0.198913	+	0.980017i	$0.436259\pi$
$347$	−1.30801e15	+	2.26554e15i	−0.749263	+	1.29776i	−0.948176	+	0.317745i	$0.897074\pi$
$348$	1.27014e15	−	7.33315e14i	0.715115	−	0.412872i
$349$			2.07896e14i			0.115052i	0.998344	+	0.0575260i	$0.0183212\pi$
$349$			2.07896e14i			0.115052i	−0.998344	+	0.0575260i	$0.981679\pi$
$350$		0			0
$351$	8.12808e15			4.34655
$352$	8.80984e13	+	1.52591e14i	0.0463140	+	0.0802182i
$353$	−3.14047e15	−	1.81315e15i	−1.62310	−	0.937100i	−0.986083	−	0.166253i	$-0.946833\pi$
$353$	−3.14047e15	−	1.81315e15i	−1.62310	−	0.937100i	−0.637021	−	0.770846i	$-0.719834\pi$
$354$	2.77012e14	−	4.79799e14i	0.140760	−	0.243803i
$355$	1.29716e15	−	7.48916e14i	0.648073	−	0.374165i
$356$		−	2.29693e14i		−	0.112836i
$357$		0			0
$358$	1.26515e14			0.0600957
$359$	1.62351e15	+	2.81200e15i	0.758381	+	1.31355i	0.943676	+	0.330872i	$0.107343\pi$
$359$	1.62351e15	+	2.81200e15i	0.758381	+	1.31355i	−0.185295	+	0.982683i	$0.559324\pi$
$360$	1.66938e15	+	9.63815e14i	0.766901	+	0.442770i
$361$	−9.87422e13	+	1.71026e14i	−0.0446128	+	0.0772716i
$362$	1.35046e15	−	7.79690e14i	0.600110	−	0.346474i
$363$			3.05269e15i			1.33427i
$364$		0			0
$365$	−3.41773e15			−1.44538
$366$	−6.49944e14	−	1.12574e15i	−0.270389	−	0.468328i
$367$	2.99836e15	+	1.73110e15i	1.22712	+	0.708478i	0.966426	−	0.256944i	$-0.0827156\pi$
$367$	2.99836e15	+	1.73110e15i	1.22712	+	0.708478i	0.260693	+	0.965422i	$0.416049\pi$
$368$	1.48442e14	−	2.57109e14i	0.0597680	−	0.103521i
$369$	1.95220e15	−	1.12710e15i	0.773332	−	0.446484i
$370$		−	7.81146e14i		−	0.304454i
$371$		0			0
$372$	3.63601e15			1.37204
$373$	2.35425e13	+	4.07768e13i	0.00874176	+	0.0151412i	0.870363	−	0.492410i	$-0.163884\pi$
$373$	2.35425e13	+	4.07768e13i	0.00874176	+	0.0151412i	−0.861621	+	0.507551i	$0.830551\pi$
$374$	4.92699e14	+	2.84460e14i	0.180033	+	0.103942i
$375$	2.40620e15	−	4.16766e15i	0.865256	−	1.49867i
$376$	−1.39453e15	+	8.05133e14i	−0.493516	+	0.284932i
$377$			4.40575e15i			1.53452i
$378$		0			0
$379$	−4.47743e15			−1.51075			−0.755376	−	0.655292i	$-0.772546\pi$
$379$	−4.47743e15			−1.51075			−0.755376	+	0.655292i	$0.772546\pi$
$380$	7.55105e14	+	1.30788e15i	0.250788	+	0.434377i
$381$	−5.22050e15	−	3.01406e15i	−1.70672	−	0.985376i
$382$	5.50577e14	−	9.53627e14i	0.177189	−	0.306901i
$383$	2.32729e15	−	1.34366e15i	0.737322	−	0.425693i	−0.0837726	−	0.996485i	$-0.526697\pi$
$383$	2.32729e15	−	1.34366e15i	0.737322	−	0.425693i	0.821095	+	0.570792i	$0.193364\pi$
$384$			5.21222e14i			0.162568i
$385$		0			0
$386$	4.33016e14			0.130912
$387$	−2.66349e15	−	4.61330e15i	−0.792840	−	1.37324i
$388$	−1.70475e15	−	9.84238e14i	−0.499655	−	0.288476i
$389$	2.47330e15	−	4.28388e15i	0.713804	−	1.23634i	−0.249615	−	0.968345i	$-0.580304\pi$
$389$	2.47330e15	−	4.28388e15i	0.713804	−	1.23634i	0.963419	−	0.268000i	$-0.0863626\pi$
$390$	−7.11935e15	+	4.11036e15i	−2.02326	+	1.16813i
$391$		−	9.58604e14i		−	0.268274i
$392$		0			0
$393$	−1.20021e16			−3.25763
$394$	−7.12177e14	−	1.23353e15i	−0.190375	−	0.329740i
$395$	−4.35065e15	−	2.51185e15i	−1.14544	−	0.661319i
$396$	1.20371e15	−	2.08488e15i	0.312141	−	0.540643i
$397$	−1.19397e15	+	6.89338e14i	−0.304965	+	0.176072i	−0.644671	−	0.764460i	$-0.723006\pi$
$397$	−1.19397e15	+	6.89338e14i	−0.304965	+	0.176072i	0.339706	+	0.940532i	$0.389672\pi$
$398$			4.85438e15i			1.22134i
$399$		0			0
$400$	−1.07413e14			−0.0262238
$401$	9.83427e14	+	1.70335e15i	0.236524	+	0.409672i	0.959715	−	0.280977i	$-0.0906583\pi$
$401$	9.83427e14	+	1.70335e15i	0.236524	+	0.409672i	−0.723190	+	0.690649i	$0.757325\pi$
$402$	−3.37682e15	−	1.94961e15i	−0.800112	−	0.461945i
$403$	−5.46128e15	+	9.45921e15i	−1.27486	+	2.20813i
$404$	2.59931e15	−	1.50071e15i	0.597819	−	0.345151i
$405$		−	1.06459e16i		−	2.41241i
$406$		0			0
$407$	−9.75573e14			−0.214631
$408$	8.41484e14	+	1.45749e15i	0.182425	+	0.315970i
$409$	2.87201e15	+	1.65816e15i	0.613545	+	0.354230i	0.774351	−	0.632756i	$-0.218076\pi$
$409$	2.87201e15	+	1.65816e15i	0.613545	+	0.354230i	−0.160807	+	0.986986i	$0.551410\pi$
$410$	−6.61548e14	+	1.14583e15i	−0.139270	+	0.241223i
$411$	−9.83069e15	+	5.67575e15i	−2.03954	+	1.17753i
$412$			2.16541e15i			0.442748i
$413$		0			0
$414$	−4.05638e15			−0.805632
$415$	1.94967e15	+	3.37693e15i	0.381657	+	0.661050i
$416$	−1.35598e15	−	7.82873e14i	−0.261633	−	0.151054i
$417$	3.39762e15	−	5.88484e15i	0.646186	−	1.11923i
$418$	1.63341e15	−	9.43051e14i	0.306223	−	0.176798i
$419$			3.45895e15i			0.639235i	0.947547	+	0.319618i	$0.103554\pi$
$419$			3.45895e15i			0.639235i	−0.947547	+	0.319618i	$0.896446\pi$
$420$		0			0
$421$	2.52314e15			0.453156			0.226578	−	0.973993i	$-0.427246\pi$
$421$	2.52314e15			0.453156			0.226578	+	0.973993i	$0.427246\pi$
$422$	8.87949e14	+	1.53797e15i	0.157222	+	0.272317i
$423$	1.90538e16	+	1.10007e16i	3.32613	+	1.92034i
$424$	−2.28825e14	+	3.96336e14i	−0.0393829	+	0.0682132i
$425$	−3.00359e14	+	1.73412e14i	−0.0509690	+	0.0294270i
$426$		−	5.53370e15i		−	0.925886i
$427$		0			0
$428$	1.59720e15			0.259834
$429$	5.13343e15	+	8.89136e15i	0.823500	+	1.42634i
$430$	2.70775e15	+	1.56332e15i	0.428350	+	0.247308i
$431$	2.86010e15	−	4.95384e15i	0.446188	−	0.772820i	−0.551946	−	0.833880i	$-0.686115\pi$
$431$	2.86010e15	−	4.95384e15i	0.446188	−	0.772820i	0.998134	+	0.0610596i	$0.0194480\pi$
$432$	3.57917e15	−	2.06643e15i	0.550655	−	0.317921i
$433$			5.07252e15i			0.769656i	0.922988	+	0.384828i	$0.125739\pi$
$433$			5.07252e15i			0.769656i	−0.922988	+	0.384828i	$0.874261\pi$
$434$		0			0
$435$	1.17617e16			1.73594
$436$	−6.29539e14	−	1.09039e15i	−0.0916439	−	0.158732i
$437$	−2.75222e15	−	1.58900e15i	−0.395180	−	0.228157i
$438$	−6.31336e15	+	1.09351e16i	−0.894161	+	1.54873i
$439$	1.41167e14	−	8.15027e13i	0.0197217	−	0.0113864i	−0.490107	−	0.871662i	$-0.663042\pi$
$439$	1.41167e14	−	8.15027e13i	0.0197217	−	0.0113864i	0.509828	+	0.860276i	$0.329709\pi$
$440$			1.41302e15i			0.194730i
$441$		0			0
$442$	−5.05562e15			−0.678018
$443$	1.03892e15	+	1.79945e15i	0.137454	+	0.238077i	0.926532	−	0.376215i	$-0.122775\pi$
$443$	1.03892e15	+	1.79945e15i	0.137454	+	0.238077i	−0.789078	+	0.614293i	$0.789441\pi$
$444$	−2.49928e15	−	1.44296e15i	−0.326225	−	0.188346i
$445$	9.21019e14	−	1.59525e15i	0.118606	−	0.205432i
$446$	−6.25455e15	+	3.61106e15i	−0.794670	+	0.458803i
$447$		−	1.53989e16i		−	1.93038i
$448$		0			0
$449$	8.24719e15			1.00653			0.503267	−	0.864131i	$-0.332131\pi$
$449$	8.24719e15			1.00653			0.503267	+	0.864131i	$0.332131\pi$
$450$	7.33802e14	+	1.27098e15i	0.0883698	+	0.153061i
$451$	1.43103e15	+	8.26207e14i	0.170055	+	0.0981815i
$452$	−2.40135e15	+	4.15926e15i	−0.281595	+	0.487736i
$453$	−1.42574e16	+	8.23149e15i	−1.64987	+	0.952553i
$454$			2.11218e15i			0.241210i
$455$		0			0
$456$	5.57943e15			0.620584
$457$	4.87326e15	+	8.44074e15i	0.534962	+	0.926581i	0.999165	+	0.0408521i	$0.0130072\pi$
$457$	4.87326e15	+	8.44074e15i	0.534962	+	0.926581i	−0.464204	+	0.885728i	$0.653659\pi$
$458$	1.02902e15	+	5.94102e14i	0.111488	+	0.0643677i
$459$	6.67228e15	−	1.15567e16i	0.713507	−	1.23583i
$460$	2.06190e15	−	1.19044e15i	0.217631	−	0.125649i
$461$		−	5.11431e15i		−	0.532821i	−0.963860	−	0.266410i	$-0.914162\pi$
$461$		−	5.11431e15i		−	0.532821i	0.963860	−	0.266410i	$-0.0858377\pi$
$462$		0			0
$463$	−1.08295e16			−1.09931			−0.549656	−	0.835391i	$-0.685241\pi$
$463$	−1.08295e16			−1.09931			−0.549656	+	0.835391i	$0.685241\pi$
$464$	1.12009e15	+	1.94005e15i	0.112239	+	0.194404i
$465$	2.52526e16	+	1.45796e16i	2.49798	+	1.44221i
$466$	−1.05525e15	+	1.82775e15i	−0.103048	+	0.178484i
$467$	2.91927e15	−	1.68544e15i	0.281432	−	0.162485i	−0.352640	−	0.935759i	$-0.614716\pi$
$467$	2.91927e15	−	1.68544e15i	0.281432	−	0.162485i	0.634072	+	0.773274i	$0.281382\pi$
$468$			2.13931e16i			2.03610i
$469$		0			0
$470$	−1.29136e16			−1.19801
$471$	6.28729e14	+	1.08899e15i	0.0575888	+	0.0997467i
$472$	7.32861e14	+	4.23117e14i	0.0662780	+	0.0382656i
$473$	1.95243e15	−	3.38172e15i	0.174345	−	0.301974i
$474$	−1.60733e16	+	9.27995e15i	−1.41722	+	0.818231i
$475$			1.14980e15i			0.100106i
$476$		0			0
$477$	6.25296e15			0.530854
$478$	2.11843e15	+	3.66924e15i	0.177602	+	0.307616i
$479$	−1.01311e15	−	5.84921e14i	−0.0838773	−	0.0484266i	0.457475	−	0.889223i	$-0.348754\pi$
$479$	−1.01311e15	−	5.84921e14i	−0.0838773	−	0.0484266i	−0.541352	+	0.840796i	$0.682087\pi$
$480$	−2.08998e15	+	3.61996e15i	−0.170882	+	0.295976i
$481$	7.50782e15	−	4.33464e15i	0.606238	−	0.350012i
$482$			3.52591e15i			0.281183i
$483$		0			0
$484$	−4.66278e15			−0.362721
$485$	−7.89315e15	−	1.36713e16i	−0.606457	−	1.05041i
$486$	−1.35385e16	−	7.81647e15i	−1.02743	−	0.593189i
$487$	−4.21224e15	+	7.29582e15i	−0.315747	+	0.546890i	−0.979596	−	0.200976i	$-0.935589\pi$
$487$	−4.21224e15	+	7.29582e15i	−0.315747	+	0.546890i	0.663849	+	0.747867i	$0.268922\pi$
$488$	1.71949e15	−	9.92746e14i	0.127315	−	0.0735054i
$489$			1.13044e16i			0.826787i
$490$		0			0
$491$	4.07478e15			0.290814			0.145407	−	0.989372i	$-0.453551\pi$
$491$	4.07478e15			0.290814			0.145407	+	0.989372i	$0.453551\pi$
$492$	2.44407e15	+	4.23325e15i	0.172315	+	0.298458i
$493$	6.26422e15	+	3.61665e15i	0.436300	+	0.251898i
$494$	−8.38028e15	+	1.45151e16i	−0.576629	+	0.998752i
$495$	1.67199e16	−	9.65321e15i	1.13658	−	0.656207i
$496$			5.55376e15i			0.372990i
$497$		0			0
$498$	1.44060e16			0.944426
$499$	4.14150e15	+	7.17329e15i	0.268259	+	0.464639i	0.968412	−	0.249354i	$-0.0802183\pi$
$499$	4.14150e15	+	7.17329e15i	0.268259	+	0.464639i	−0.700153	+	0.713993i	$0.746885\pi$
$500$	6.36583e15	+	3.67531e15i	0.407413	+	0.235220i
$501$	−8.30661e14	+	1.43875e15i	−0.0525288	+	0.0909825i
$502$	−4.19132e14	+	2.41986e14i	−0.0261896	+	0.0151206i
$503$		−	1.35321e16i		−	0.835519i	−0.908558	−	0.417759i	$-0.862815\pi$
$503$		−	1.35321e16i		−	0.835519i	0.908558	−	0.417759i	$-0.137185\pi$
$504$		0			0
$505$	2.40701e16			1.45121
$506$	−1.48674e15	−	2.57510e15i	−0.0885791	−	0.153423i
$507$	−5.19585e16	−	2.99983e16i	−3.05921	−	1.76623i
$508$	4.60378e15	−	7.97398e15i	0.267875	−	0.463973i
$509$	1.73828e16	−	1.00360e16i	0.999571	−	0.577102i	0.0914495	−	0.995810i	$-0.470850\pi$
$509$	1.73828e16	−	1.00360e16i	0.999571	−	0.577102i	0.908121	+	0.418707i	$0.137517\pi$
$510$			1.34967e16i			0.767017i
$511$		0			0
$512$	−7.96131e14			−0.0441942
$513$	−2.21202e16	−	3.83132e16i	−1.21362	−	2.10206i
$514$	−1.54186e16	−	8.90195e15i	−0.836117	−	0.482732i
$515$	−8.68282e15	+	1.50391e16i	−0.465390	+	0.806080i
$516$	1.00037e16	−	5.77565e15i	0.529984	−	0.305987i
$517$			1.61278e16i			0.844564i
$518$		0			0
$519$	−5.28590e16			−2.70467
$520$	−6.27830e15	−	1.08743e16i	−0.317557	−	0.550025i
$521$	1.45168e16	+	8.38128e15i	0.725846	+	0.419067i	0.816901	−	0.576778i	$-0.195690\pi$
$521$	1.45168e16	+	8.38128e15i	0.725846	+	0.419067i	−0.0910545	+	0.995846i	$0.529024\pi$
$522$	1.53040e16	−	2.65074e16i	0.756455	−	1.31022i
$523$	−8.42692e15	+	4.86529e15i	−0.411774	+	0.237738i	−0.691552	−	0.722327i	$-0.743073\pi$
$523$	−8.42692e15	+	4.86529e15i	−0.411774	+	0.237738i	0.279778	+	0.960065i	$0.409739\pi$
$524$		−	1.83324e16i		−	0.885588i
$525$		0			0
$526$	−1.42302e16			−0.671890
$527$	8.96625e15	+	1.55300e16i	0.418550	+	0.724949i
$528$	4.52097e15	+	2.61018e15i	0.208655	+	0.120467i
$529$	8.45223e15	−	1.46397e16i	0.385689	−	0.668033i
$530$	−3.17844e15	+	1.83507e15i	−0.143403	+	0.0827939i
$531$		−	1.15623e16i		−	0.515795i
$532$		0			0
$533$	−1.46839e16			−0.640441
$534$	−3.40267e15	−	5.89361e15i	−0.146748	−	0.254175i
$535$	1.10928e16	+	6.40442e15i	0.473062	+	0.273122i
$536$	2.97789e15	−	5.15786e15i	0.125580	−	0.217511i
$537$	3.24620e15	−	1.87419e15i	0.135372	−	0.0781571i
$538$		−	1.99737e16i		−	0.823691i
$539$		0			0
$540$	3.31438e16			1.33672
$541$	1.23841e16	+	2.14499e16i	0.493949	+	0.855545i	0.999976	−	0.00697320i	$-0.00221966\pi$
$541$	1.23841e16	+	2.14499e16i	0.493949	+	0.855545i	−0.506027	+	0.862518i	$0.668886\pi$
$542$	−1.93362e16	−	1.11637e16i	−0.762737	−	0.440367i
$543$	2.31007e16	−	4.00115e16i	0.901209	−	1.56094i
$544$	−2.22622e15	+	1.28531e15i	−0.0858965	+	0.0495923i
$545$		−	1.00973e16i		−	0.385322i
$546$		0			0
$547$	1.37294e16			0.512540			0.256270	−	0.966605i	$-0.417506\pi$
$547$	1.37294e16			0.512540			0.256270	+	0.966605i	$0.417506\pi$
$548$	−8.66933e15	−	1.50157e16i	−0.320112	−	0.554451i
$549$	−2.34937e16	−	1.35641e16i	−0.858060	−	0.495401i
$550$	−5.37904e14	+	9.31676e14i	−0.0194325	+	0.0336581i
$551$	2.07673e16	−	1.19900e16i	0.742115	−	0.428460i
$552$		−	8.79607e15i		−	0.310924i
$553$		0			0
$554$	3.12080e16			1.07946
$555$	−1.15719e16	−	2.00431e16i	−0.395956	−	0.685816i
$556$	8.98871e15	+	5.18963e15i	0.304263	+	0.175666i
$557$	−8.51626e14	+	1.47506e15i	−0.0285179	+	0.0493945i	−0.879932	−	0.475099i	$-0.842412\pi$
$557$	−8.51626e14	+	1.47506e15i	−0.0285179	+	0.0493945i	0.851414	+	0.524494i	$0.175745\pi$
$558$	6.57160e16	−	3.79412e16i	2.17704	−	1.25691i
$559$			3.47000e16i			1.13726i
$560$		0			0
$561$	1.68560e16			0.540726
$562$	−9.24193e15	−	1.60075e16i	−0.293322	−	0.508049i
$563$	−1.36940e16	−	7.90624e15i	−0.430012	−	0.248267i	0.269340	−	0.963045i	$-0.413195\pi$
$563$	−1.36940e16	−	7.90624e15i	−0.430012	−	0.248267i	−0.699352	+	0.714778i	$0.746528\pi$
$564$	−2.38545e16	+	4.13172e16i	−0.741132	+	1.28368i
$565$	−3.33554e16	+	1.92578e16i	−1.02536	+	0.591991i
$566$		−	4.34282e16i		−	1.32091i
$567$		0			0
$568$	8.45235e15			0.251703
$569$	−2.79471e16	−	4.84058e16i	−0.823499	−	1.42634i	−0.903061	−	0.429512i	$-0.858686\pi$
$569$	−2.79471e16	−	4.84058e16i	−0.823499	−	1.42634i	0.0795628	−	0.996830i	$-0.474648\pi$
$570$	3.87499e16	+	2.23723e16i	1.12985	+	0.652320i
$571$	5.96106e15	−	1.03249e16i	0.171991	−	0.297898i	−0.767125	−	0.641498i	$-0.778313\pi$
$571$	5.96106e15	−	1.03249e16i	0.171991	−	0.297898i	0.939116	+	0.343600i	$0.111647\pi$
$572$	−1.35810e16	+	7.84097e15i	−0.387752	+	0.223869i
$573$		−	3.26250e16i		−	0.921771i
$574$		0			0
$575$	1.81268e15			0.0501551
$576$	5.43886e15	+	9.42038e15i	0.148927	+	0.257949i
$577$	3.21626e16	+	1.85691e16i	0.871558	+	0.503194i	0.867866	−	0.496799i	$-0.165491\pi$
$577$	3.21626e16	+	1.85691e16i	0.871558	+	0.503194i	0.00369242	+	0.999993i	$0.498825\pi$
$578$	9.03311e15	−	1.56458e16i	0.242254	−	0.419596i
$579$	1.11106e16	−	6.41470e15i	0.294894	−	0.170257i
$580$			1.79653e16i			0.471917i
$581$		0			0
$582$	−5.83220e16			−1.50070
$583$	2.29182e15	+	3.96955e15i	0.0583673	+	0.101095i
$584$	−1.67026e16	−	9.64323e15i	−0.421023	−	0.243078i
$585$	−8.57818e16	+	1.48578e17i	−2.14023	+	3.70698i
$586$	−3.71541e16	+	2.14509e16i	−0.917531	+	0.529737i
$587$			5.00677e16i			1.22385i	0.790915	+	0.611926i	$0.209605\pi$
$587$			5.00677e16i			1.22385i	−0.790915	+	0.611926i	$0.790395\pi$
$588$		0			0
$589$	5.94504e16			1.42385
$590$	3.39322e15	+	5.87722e15i	0.0804451	+	0.139335i
$591$	−3.65469e16	−	2.11004e16i	−0.857682	−	0.495183i
$592$	2.20402e15	−	3.81748e15i	0.0512019	−	0.0886843i
$593$	−3.80381e15	+	2.19613e15i	−0.0874763	+	0.0505045i	−0.543100	−	0.839668i	$-0.682750\pi$
$593$	−3.80381e15	+	2.19613e15i	−0.0874763	+	0.0505045i	0.455624	+	0.890172i	$0.349416\pi$
$594$		−	4.13932e16i		−	0.942347i
$595$		0			0
$596$	2.35207e16			0.524775
$597$	7.19128e16	+	1.24557e17i	1.58840	+	2.75119i
$598$	2.28833e16	+	1.32117e16i	0.500393	+	0.288902i
$599$	−3.95640e16	+	6.85269e16i	−0.856524	+	1.48354i	0.0186994	+	0.999825i	$0.494047\pi$
$599$	−3.95640e16	+	6.85269e16i	−0.856524	+	1.48354i	−0.875224	+	0.483718i	$0.839286\pi$
$600$	−2.75606e15	+	1.59121e15i	−0.0590720	+	0.0341052i
$601$		−	7.67076e16i		−	1.62776i	−0.581030	−	0.813882i	$-0.697350\pi$
$601$		−	7.67076e16i		−	1.62776i	0.581030	−	0.813882i	$-0.302650\pi$
$602$		0			0
$603$	−8.13752e16			−1.69273
$604$	−1.25731e16	−	2.17772e16i	−0.258952	−	0.448518i
$605$	−3.23837e16	−	1.86967e16i	−0.660380	−	0.381270i
$606$	4.44631e16	−	7.70123e16i	0.897767	−	1.55498i
$607$	4.78581e16	−	2.76309e16i	0.956804	−	0.552411i	0.0616161	−	0.998100i	$-0.480375\pi$
$607$	4.78581e16	−	2.76309e16i	0.956804	−	0.552411i	0.895188	+	0.445689i	$0.147041\pi$
$608$			8.52220e15i			0.168706i
$609$		0			0
$610$	1.59228e16			0.309058
$611$	−7.16587e16	−	1.24117e17i	−1.37728	−	2.38552i
$612$	3.04174e16	+	1.75615e16i	0.578913	+	0.334236i
$613$	2.08176e16	−	3.60571e16i	0.392344	−	0.679560i	−0.600414	−	0.799689i	$-0.704998\pi$
$613$	2.08176e16	−	3.60571e16i	0.392344	−	0.679560i	0.992758	+	0.120129i	$0.0383309\pi$
$614$	−3.29152e16	+	1.90036e16i	−0.614308	+	0.354671i
$615$			3.92007e16i			0.724508i
$616$		0			0
$617$	−8.46408e16			−1.53415			−0.767077	−	0.641556i	$-0.778289\pi$
$617$	−8.46408e16			−1.53415			−0.767077	+	0.641556i	$0.778289\pi$
$618$	3.20784e16	+	5.55614e16i	0.575814	+	0.997339i
$619$	−6.27977e16	−	3.62563e16i	−1.11635	−	0.644525i	−0.175883	−	0.984411i	$-0.556278\pi$
$619$	−6.27977e16	−	3.62563e16i	−1.11635	−	0.644525i	−0.940466	+	0.339886i	$0.889611\pi$
$620$	−2.22694e16	+	3.85717e16i	−0.392065	+	0.679076i
$621$	−6.04015e16	+	3.48728e16i	−1.05317	+	0.608048i
$622$			1.72448e15i			0.0297793i
$623$		0			0
$624$	−4.63900e16			−0.785808
$625$	3.26005e16	+	5.64658e16i	0.546946	+	0.947339i
$626$	−1.17363e15	−	6.77594e14i	−0.0195022	−	0.0112596i
$627$	2.79407e16	−	4.83948e16i	0.459867	−	0.796514i
$628$	−1.66336e15	+	9.60341e14i	−0.0271162	+	0.0156555i
$629$		−	1.42331e16i		−	0.229824i
$630$		0			0
$631$	9.77355e16			1.54838			0.774188	−	0.632956i	$-0.218159\pi$
$631$	9.77355e16			1.54838			0.774188	+	0.632956i	$0.218159\pi$
$632$	−1.41745e16	−	2.45510e16i	−0.222436	−	0.385271i
$633$	4.55671e16	+	2.63082e16i	0.708319	+	0.408948i
$634$	−8.22365e15	+	1.42438e16i	−0.126628	+	0.219326i
$635$	6.39478e16	−	3.69203e16i	0.975401	−	0.563148i
$636$			1.35592e16i			0.204877i
$637$		0			0
$638$	2.24368e16			0.332688
$639$	−5.77432e16	−	1.00014e17i	−0.848195	−	1.46912i
$640$	−5.52925e15	−	3.19231e15i	−0.0804611	−	0.0464543i
$641$	4.48773e16	−	7.77298e16i	0.646962	−	1.12057i	−0.336883	−	0.941546i	$-0.609373\pi$
$641$	4.48773e16	−	7.77298e16i	0.646962	−	1.12057i	0.983845	−	0.179024i	$-0.0572939\pi$
$642$	4.09819e16	−	2.36609e16i	0.585305	−	0.337926i
$643$		−	5.41761e16i		−	0.766553i	−0.923634	−	0.383276i	$-0.874796\pi$
$643$		−	5.41761e16i		−	0.766553i	0.923634	−	0.383276i	$-0.125204\pi$
$644$		0			0
$645$	9.26363e16			1.28654
$646$	1.37586e16	+	2.38306e16i	0.189313	+	0.327899i
$647$	−2.85506e16	−	1.64837e16i	−0.389215	−	0.224713i	0.292605	−	0.956233i	$-0.405478\pi$
$647$	−2.85506e16	−	1.64837e16i	−0.389215	−	0.224713i	−0.681820	+	0.731520i	$0.738811\pi$
$648$	3.00377e16	−	5.20268e16i	0.405711	−	0.702712i
$649$	7.34006e15	−	4.23779e15i	0.0982272	−	0.0567115i
$650$		−	9.56000e15i		−	0.126759i
$651$		0			0
$652$	−1.72667e16			−0.224762
$653$	2.33522e16	+	4.04472e16i	0.301196	+	0.521686i	0.976407	−	0.215938i	$-0.0692810\pi$
$653$	2.33522e16	+	4.04472e16i	0.301196	+	0.521686i	−0.675212	+	0.737624i	$0.735948\pi$
$654$	−3.23062e16	−	1.86520e16i	−0.412876	−	0.238374i
$655$	7.35089e16	−	1.27321e17i	0.930877	−	1.61233i
$656$	−6.46601e15	+	3.73315e15i	−0.0811359	+	0.0468438i
$657$			2.63515e17i			3.27653i
$658$		0			0
$659$	5.21979e16			0.637295			0.318648	−	0.947873i	$-0.396771\pi$
$659$	5.21979e16			0.637295			0.318648	+	0.947873i	$0.396771\pi$
$660$	2.09325e16	+	3.62562e16i	0.253255	+	0.438650i
$661$	6.25653e16	+	3.61221e16i	0.750109	+	0.433076i	0.825733	−	0.564061i	$-0.190762\pi$
$661$	6.25653e16	+	3.61221e16i	0.750109	+	0.433076i	−0.0756241	+	0.997136i	$0.524095\pi$
$662$	−1.55113e16	+	2.68663e16i	−0.184289	+	0.319198i
$663$	−1.29720e17	+	7.48940e16i	−1.52731	+	0.881792i
$664$			2.20042e16i			0.256743i
$665$		0			0
$666$	−6.02281e16			−0.690167
$667$	−1.89025e16	−	3.27401e16i	−0.214666	−	0.371813i
$668$	−2.19759e15	−	1.26878e15i	−0.0247336	−	0.0142800i
$669$	−1.06989e17	+	1.85310e17i	−1.19339	+	2.06701i
$670$	4.13638e16	−	2.38814e16i	0.457269	−	0.264004i
$671$		−	1.98860e16i		−	0.217877i
$672$		0			0
$673$	−1.64285e17			−1.76810			−0.884051	−	0.467391i	$-0.845194\pi$
$673$	−1.64285e17			−1.76810			−0.884051	+	0.467391i	$0.845194\pi$
$674$	−4.57692e16	−	7.92746e16i	−0.488218	−	0.845619i
$675$	2.18534e16	+	1.26170e16i	0.231044	+	0.133394i
$676$	4.58203e16	−	7.93632e16i	0.480151	−	0.831647i
$677$	3.84461e16	−	2.21969e16i	0.399320	−	0.230547i	−0.286871	−	0.957969i	$-0.592615\pi$
$677$	3.84461e16	−	2.21969e16i	0.399320	−	0.230547i	0.686190	+	0.727422i	$0.259282\pi$
$678$			1.42294e17i			1.46491i
$679$		0			0
$680$	−2.06153e16			−0.208514
$681$	3.12899e16	+	5.41956e16i	0.313705	+	0.543352i
$682$	4.81722e16	+	2.78122e16i	0.478730	+	0.276395i
$683$	6.92043e16	−	1.19865e17i	0.681725	−	1.18078i	−0.292729	−	0.956195i	$-0.594563\pi$
$683$	6.92043e16	−	1.19865e17i	0.681725	−	1.18078i	0.974454	−	0.224587i	$-0.0721032\pi$
$684$	1.00841e17	−	5.82204e16i	0.984689	−	0.568510i
$685$		−	1.39049e17i		−	1.34593i
$686$		0			0
$687$	3.52041e16			0.334852
$688$	8.82192e15	+	1.52800e16i	0.0831826	+	0.144076i
$689$	−3.52748e16	−	2.03659e16i	−0.329723	−	0.190366i
$690$	3.52703e16	−	6.10899e16i	0.326824	−	0.566077i
$691$	2.79880e16	−	1.61589e16i	0.257101	−	0.148437i	−0.365910	−	0.930650i	$-0.619242\pi$
$691$	2.79880e16	−	1.61589e16i	0.257101	−	0.148437i	0.623011	+	0.782213i	$0.285909\pi$
$692$		−	8.07387e16i		−	0.735267i
$693$		0			0
$694$	−1.18388e17			−1.05962
$695$	4.16186e16	+	7.20855e16i	0.369299	+	0.639645i
$696$	5.74799e16	+	3.31861e16i	0.505663	+	0.291944i
$697$	−1.20539e16	+	2.08780e16i	−0.105131	+	0.182093i
$698$	−8.14784e15	+	4.70416e15i	−0.0704547	+	0.0406771i
$699$			6.25299e16i			0.536074i
$700$		0			0
$701$	1.88144e17			1.58556			0.792780	−	0.609508i	$-0.208633\pi$
$701$	1.88144e17			1.58556			0.792780	+	0.609508i	$0.208633\pi$
$702$	1.83917e17	+	3.18554e17i	1.53674	+	2.66171i
$703$	−4.08643e16	−	2.35930e16i	−0.338542	−	0.195457i
$704$	−3.98688e15	+	6.90548e15i	−0.0327489	+	0.0567228i
$705$	−3.31346e17	+	1.91303e17i	−2.69865	+	1.55807i
$706$		−	1.64108e17i		−	1.32526i
$707$		0			0
$708$	2.50723e16			0.199065
$709$	−3.87369e16	−	6.70943e16i	−0.304963	−	0.528212i	0.672290	−	0.740288i	$-0.265311\pi$
$709$	−3.87369e16	−	6.70943e16i	−0.304963	−	0.528212i	−0.977253	+	0.212076i	$0.931978\pi$
$710$	5.87028e16	+	3.38921e16i	0.458257	+	0.264575i
$711$	−1.93669e17	+	3.35445e17i	−1.49914	+	2.59660i
$712$	9.00209e15	−	5.19736e15i	0.0690977	−	0.0398936i
$713$		−	9.37246e16i		−	0.713372i
$714$		0			0
$715$	−1.25762e17			−0.941270
$716$	2.86270e15	+	4.95835e15i	0.0212470	+	0.0368010i
$717$	1.08712e17	+	6.27650e16i	0.800135	+	0.461958i
$718$	−7.34715e16	+	1.27256e17i	−0.536256	+	0.928823i
$719$	−1.84792e17	+	1.06689e17i	−1.33755	+	0.772233i	−0.986443	−	0.164104i	$-0.947527\pi$
$719$	−1.84792e17	+	1.06689e17i	−1.33755	+	0.772233i	−0.351103	+	0.936337i	$0.614193\pi$
$720$			8.72345e16i			0.626172i
$721$		0			0
$722$	−8.93712e15			−0.0630920
$723$	5.22329e16	+	9.04700e16i	0.365691	+	0.633395i
$724$	6.11150e16	+	3.52847e16i	0.424342	+	0.244994i
$725$	−6.83895e15	+	1.18454e16i	−0.0470935	+	0.0815684i
$726$	−1.19640e17	+	6.90744e16i	−0.817068	+	0.471734i
$727$			9.14145e16i			0.619168i	0.950872	+	0.309584i	$0.100190\pi$
$727$			9.14145e16i			0.619168i	−0.950872	+	0.309584i	$0.899810\pi$
$728$		0			0
$729$	−1.18699e17			−0.790828
$730$	−7.73345e16	−	1.33947e17i	−0.511018	−	0.885109i
$731$	4.93375e16	+	2.84850e16i	0.323350	+	0.186686i
$732$	2.94131e16	−	5.09450e16i	0.191194	−	0.331158i
$733$	6.33849e16	−	3.65953e16i	0.408660	−	0.235940i	−0.281554	−	0.959545i	$-0.590850\pi$
$733$	6.33849e16	−	3.65953e16i	0.408660	−	0.235940i	0.690214	+	0.723605i	$0.257516\pi$
$734$			1.56681e17i			1.00194i
$735$		0			0
$736$	1.34354e16			0.0845248
$737$	−2.98255e16	−	5.16593e16i	−0.186116	−	0.322362i
$738$	8.83465e16	+	5.10069e16i	0.546828	+	0.315712i
$739$	9.29953e16	−	1.61073e17i	0.570945	−	0.988906i	−0.425524	−	0.904947i	$-0.639910\pi$
$739$	9.29953e16	−	1.61073e17i	0.570945	−	0.988906i	0.996469	−	0.0839586i	$-0.0267563\pi$
$740$	3.06145e16	−	1.76753e16i	0.186439	−	0.107641i
$741$			4.96582e17i			2.99973i
$742$		0			0
$743$	3.21389e17			1.91028			0.955141	−	0.296150i	$-0.0957029\pi$
$743$	3.21389e17			1.91028			0.955141	+	0.296150i	$0.0957029\pi$
$744$	8.22735e16	+	1.42502e17i	0.485090	+	0.840201i
$745$	1.63355e17	+	9.43130e16i	0.955421	+	0.551613i
$746$	−1.06541e15	+	1.84535e15i	−0.00618136	+	0.0107064i
$747$	2.60369e17	−	1.50324e17i	1.49853	−	0.865179i
$748$			2.57464e16i			0.146996i
$749$		0			0
$750$	2.17785e17			1.22366
$751$	2.41775e16	+	4.18766e16i	0.134763	+	0.233417i	0.925507	−	0.378731i	$-0.123639\pi$
$751$	2.41775e16	+	4.18766e16i	0.134763	+	0.233417i	−0.790744	+	0.612147i	$0.790306\pi$
$752$	−6.31093e16	−	3.64362e16i	−0.348968	−	0.201477i
$753$	−7.16957e15	+	1.24181e16i	−0.0393300	+	0.0681215i
$754$	−1.72669e17	+	9.96907e16i	−0.939696	+	0.542534i
$755$		−	2.01661e17i		−	1.08878i
$756$		0			0
$757$	1.00275e17			0.532867			0.266433	−	0.963853i	$-0.414155\pi$
$757$	1.00275e17			0.532867			0.266433	+	0.963853i	$0.414155\pi$
$758$	−1.01313e17	−	1.75479e17i	−0.534131	−	0.925143i
$759$	−7.62952e16	−	4.40491e16i	−0.399068	−	0.230402i
$760$	−3.41722e16	+	5.91879e16i	−0.177334	+	0.307151i
$761$	2.59668e17	−	1.49920e17i	1.33694	−	0.771881i	0.350586	−	0.936531i	$-0.385983\pi$
$761$	2.59668e17	−	1.49920e17i	1.33694	−	0.771881i	0.986352	+	0.164649i	$0.0526492\pi$
$762$		−	2.72802e17i		−	1.39353i
$763$		0			0
$764$	4.98325e16			0.250584
$765$	1.40835e17	+	2.43934e17i	0.702657	+	1.21704i
$766$	1.05321e17	+	6.08071e16i	0.521366	+	0.301011i
$767$	−3.76585e16	+	6.52264e16i	−0.184965	+	0.320369i
$768$	−2.04276e16	+	1.17939e16i	−0.0995522	+	0.0574765i
$769$		−	1.29642e17i		−	0.626886i	−0.949607	−	0.313443i	$-0.898517\pi$
$769$		−	1.29642e17i		−	0.626886i	0.949607	−	0.313443i	$-0.101483\pi$
$770$		0			0
$771$	−5.27494e17			−2.51126
$772$	9.79804e15	+	1.69707e16i	0.0462845	+	0.0801670i
$773$	−1.18545e17	−	6.84421e16i	−0.555657	−	0.320809i	0.195743	−	0.980655i	$-0.437288\pi$
$773$	−1.18545e17	−	6.84421e16i	−0.555657	−	0.320809i	−0.751401	+	0.659846i	$0.770621\pi$
$774$	1.20536e17	−	2.08774e17i	0.560622	−	0.971026i
$775$	−2.93666e16	+	1.69548e16i	−0.135533	+	0.0782499i
$776$		−	8.90830e16i		−	0.407967i
$777$		0			0
$778$	2.23857e17			1.00947
$779$	3.99616e16	+	6.92155e16i	0.178821	+	0.309727i
$780$	−3.22185e17	−	1.86014e17i	−1.43066	−	0.825994i
$781$	4.23278e16	−	7.33140e16i	0.186518	−	0.323058i
$782$	3.75694e16	−	2.16907e16i	0.164284	−	0.0948492i
$783$		−	5.26277e17i		−	2.28373i
$784$		0			0
$785$	−1.54030e16			−0.0658246
$786$	−2.71576e17	−	4.70384e17i	−1.15175	−	1.99488i
$787$	−1.61112e16	−	9.30179e15i	−0.0678077	−	0.0391488i	0.465713	−	0.884936i	$-0.345798\pi$
$787$	−1.61112e16	−	9.30179e15i	−0.0678077	−	0.0391488i	−0.533521	+	0.845787i	$0.679131\pi$
$788$	3.22294e16	−	5.58230e16i	0.134616	−	0.233161i
$789$	−3.65128e17	+	2.10807e17i	−1.51350	+	0.873822i
$790$		−	2.27347e17i		−	0.935247i
$791$		0			0
$792$	1.08947e17			0.441433
$793$	8.83567e16	+	1.53038e17i	0.355304	+	0.615405i
$794$	−5.40329e16	−	3.11959e16i	−0.215643	−	0.124501i
$795$	−5.43696e16	+	9.41709e16i	−0.215354	+	0.373004i
$796$	−1.90252e17	+	1.09842e17i	−0.747912	+	0.431807i
$797$			3.64359e17i			1.42161i	0.703390	+	0.710804i	$0.251669\pi$
$797$			3.64359e17i			1.42161i	−0.703390	+	0.710804i	$0.748331\pi$
$798$		0			0
$799$	−2.35297e17			−0.904347
$800$	−2.43047e15	−	4.20971e15i	−0.00927152	−	0.0160588i
$801$	−1.22998e17	−	7.10127e16i	−0.465695	−	0.268869i
$802$	−4.45048e16	+	7.70846e16i	−0.167248	+	0.289682i
$803$	−1.67287e17	+	9.65831e16i	−0.623977	+	0.360253i
$804$		−	1.76458e17i		−	0.653289i
$805$		0			0
$806$	−4.94298e17			−1.80293
$807$	−2.95890e17	−	5.12497e17i	−1.07125	−	1.85545i
$808$	1.17631e17	+	6.79144e16i	0.422722	+	0.244058i
$809$	7.96501e16	−	1.37958e17i	0.284116	−	0.492103i	−0.688279	−	0.725446i	$-0.741633\pi$
$809$	7.96501e16	−	1.37958e17i	0.284116	−	0.492103i	0.972394	+	0.233344i	$0.0749667\pi$
$810$	4.17232e17	−	2.40889e17i	1.47730	−	0.852917i
$811$		−	1.20080e17i		−	0.422031i	−0.977483	−	0.211015i	$-0.932323\pi$
$811$		−	1.20080e17i		−	0.422031i	0.977483	−	0.211015i	$-0.0676770\pi$
$812$		0			0
$813$	−6.61519e17			−2.29086
$814$	−2.20747e16	−	3.82345e16i	−0.0758837	−	0.131434i
$815$	−1.19920e17	−	6.92356e16i	−0.409209	−	0.236257i
$816$	−3.80812e16	+	6.59586e16i	−0.128994	+	0.223424i
$817$	1.63565e17	−	9.44344e16i	0.549995	−	0.317540i
$818$			1.50079e17i			0.500957i
$819$		0			0
$820$	−5.98765e16			−0.196958
$821$	1.56110e17	+	2.70391e17i	0.509768	+	0.882944i	0.999936	+	0.0113161i	$0.00360211\pi$
$821$	1.56110e17	+	2.70391e17i	0.509768	+	0.882944i	−0.490168	+	0.871628i	$0.663065\pi$
$822$	−4.44886e17	−	2.56855e17i	−1.44218	−	0.832640i
$823$	−1.41648e17	+	2.45341e17i	−0.455838	+	0.789534i	−0.998736	−	0.0502644i	$-0.983994\pi$
$823$	−1.41648e17	+	2.45341e17i	−0.455838	+	0.789534i	0.542898	+	0.839798i	$0.317327\pi$
$824$	−8.48664e16	+	4.89976e16i	−0.271127	+	0.156535i
$825$			3.18740e16i			0.101091i
$826$		0			0
$827$	4.70648e17			1.47117			0.735585	−	0.677433i	$-0.236907\pi$
$827$	4.70648e17			1.47117			0.735585	+	0.677433i	$0.236907\pi$
$828$	−9.17855e16	−	1.58977e17i	−0.284834	−	0.493347i
$829$	−2.99170e16	−	1.72726e16i	−0.0921702	−	0.0532145i	0.453206	−	0.891406i	$-0.350280\pi$
$829$	−2.99170e16	−	1.72726e16i	−0.0921702	−	0.0532145i	−0.545377	+	0.838191i	$0.683613\pi$
$830$	−8.82322e16	+	1.52823e17i	−0.269872	+	0.467433i
$831$	8.00754e17	−	4.62316e17i	2.43160	−	1.40389i
$832$		−	7.08576e16i		−	0.213622i
$833$		0			0
$834$	3.07517e17			0.913846
$835$	−1.01751e16	−	1.76237e16i	−0.0300205	−	0.0519970i
$836$	7.39198e16	+	4.26776e16i	0.216533	+	0.125015i
$837$	6.52362e17	−	1.12992e18i	1.89730	−	3.28622i
$838$	−1.35563e17	+	7.82672e16i	−0.391450	+	0.226004i
$839$			1.99771e17i			0.572745i	0.958118	+	0.286373i	$0.0924495\pi$
$839$			1.99771e17i			0.572745i	−0.958118	+	0.286373i	$0.907551\pi$
$840$		0			0
$841$	−6.85511e16			−0.193749
$842$	5.70920e16	+	9.88863e16i	0.160215	+	0.277500i
$843$	−4.74270e17	−	2.73820e17i	−1.32148	−	0.762957i
$844$	−4.01840e16	+	6.96007e16i	−0.111173	+	0.192557i
$845$	6.36458e17	−	3.67459e17i	1.74835	−	1.00941i
$846$			9.95670e17i			2.71577i
$847$		0			0
$848$	−2.07108e16			−0.0556958
$849$	−6.43345e17	−	1.11431e18i	−1.71790	−	2.97549i
$850$	−1.35927e16	−	7.84774e15i	−0.0360406	−	0.0208080i
$851$	−3.71948e16	+	6.44233e16i	−0.0979276	+	0.169616i
$852$	2.16876e17	−	1.25213e17i	0.566987	−	0.327350i
$853$			9.66293e16i			0.250850i	0.992103	+	0.125425i	$0.0400295\pi$
$853$			9.66293e16i			0.250850i	−0.992103	+	0.125425i	$0.959971\pi$
$854$		0			0
$855$	9.33804e17			2.39034
$856$	3.61405e16	+	6.25972e16i	0.0918653	+	0.159115i
$857$	−5.28665e16	−	3.05225e16i	−0.133443	−	0.0770434i	0.431792	−	0.901973i	$-0.357881\pi$
$857$	−5.28665e16	−	3.05225e16i	−0.133443	−	0.0770434i	−0.565235	+	0.824930i	$0.691215\pi$
$858$	−2.32312e17	+	4.02377e17i	−0.582303	+	1.00858i
$859$	4.50874e17	−	2.60312e17i	1.12227	−	0.647941i	0.180288	−	0.983614i	$-0.442297\pi$
$859$	4.50874e17	−	2.60312e17i	1.12227	−	0.647941i	0.941978	+	0.335673i	$0.108964\pi$
$860$			1.41496e17i			0.349746i
$861$		0			0
$862$	2.58867e17			0.631005
$863$	8.43872e16	+	1.46163e17i	0.204273	+	0.353812i	0.949901	−	0.312551i	$-0.101184\pi$
$863$	8.43872e16	+	1.46163e17i	0.204273	+	0.353812i	−0.745628	+	0.666363i	$0.767850\pi$
$864$	1.61975e17	+	9.35160e16i	0.389372	+	0.224804i
$865$	3.23744e17	−	5.60742e17i	0.772868	−	1.33865i
$866$	−1.98801e17	+	1.14778e17i	−0.471316	+	0.272114i
$867$		−	5.35266e17i		−	1.26025i
$868$		0			0
$869$	−2.83933e17			−0.659322
$870$	2.66138e17	+	4.60964e17i	0.613749	+	1.06304i
$871$	4.59062e17	+	2.65040e17i	1.05139	+	0.607018i
$872$	2.84897e16	−	4.93456e16i	0.0648021	−	0.112240i
$873$	−1.05409e18	+	6.08580e17i	−2.38119	+	1.37478i
$874$		−	1.43820e17i		−	0.322663i
$875$		0			0
$876$	−5.71420e17			−1.26453
$877$	1.06935e17	+	1.85217e17i	0.235030	+	0.407084i	0.959281	−	0.282452i	$-0.0911479\pi$
$877$	1.06935e17	+	1.85217e17i	0.235030	+	0.407084i	−0.724251	+	0.689536i	$0.757815\pi$
$878$	6.38848e15	+	3.68839e15i	0.0139454	+	0.00805137i
$879$	−6.35548e17	+	1.10080e18i	−1.37789	+	2.38658i
$880$	−5.53789e16	+	3.19730e16i	−0.119247	+	0.0688474i
$881$		−	2.38082e17i		−	0.509180i	−0.967049	−	0.254590i	$-0.918059\pi$
$881$		−	2.38082e17i		−	0.509180i	0.967049	−	0.254590i	$-0.0819406\pi$
$882$		0			0
$883$	5.50929e17			1.16233			0.581167	−	0.813784i	$-0.302596\pi$
$883$	5.50929e17			1.16233			0.581167	+	0.813784i	$0.302596\pi$
$884$	−1.14396e17	−	1.98139e17i	−0.239715	−	0.415199i
$885$	1.74130e17	+	1.00534e17i	0.362422	+	0.209245i
$886$	−4.70159e16	+	8.14340e16i	−0.0971947	+	0.168346i
$887$	−1.90550e16	+	1.10014e16i	−0.0391262	+	0.0225895i	−0.519435	−	0.854510i	$-0.673858\pi$
$887$	−1.90550e16	+	1.10014e16i	−0.0391262	+	0.0225895i	0.480309	+	0.877099i	$0.340524\pi$
$888$		−	1.30602e17i		−	0.266361i
$889$		0			0
$890$	8.33611e16			0.167735
$891$	−3.00846e17	−	5.21081e17i	−0.601283	−	1.04145i
$892$	−2.83049e17	−	1.63418e17i	−0.561916	−	0.324423i
$893$	−3.90031e17	+	6.75554e17i	−0.769114	+	1.33215i
$894$	6.03510e17	−	3.48437e17i	1.18211	−	0.682494i
$895$			4.59153e16i			0.0893345i
$896$		0			0
$897$	7.82871e17			1.50292
$898$	1.86613e17	+	3.23223e17i	0.355863	+	0.616373i
$899$	6.12465e17	+	3.53607e17i	1.16017	+	0.669827i
$900$	−3.32081e16	+	5.75181e16i	−0.0624869	+	0.108231i
$901$	−5.79137e16	+	3.34365e16i	−0.108251	+	0.0624989i
$902$			7.47797e16i			0.138850i
$903$		0			0
$904$	−2.17345e17			−0.398235
$905$	2.82968e17	+	4.90115e17i	0.515046	+	0.892086i
$906$	−6.45214e17	−	3.72515e17i	−1.16663	−	0.673557i
$907$	4.01056e17	−	6.94649e17i	0.720379	−	1.24773i	−0.240468	−	0.970657i	$-0.577301\pi$
$907$	4.01056e17	−	6.94649e17i	0.720379	−	1.24773i	0.960848	−	0.277077i	$-0.0893657\pi$
$908$	−8.27802e16	+	4.77932e16i	−0.147711	+	0.0852807i
$909$		−	1.85586e18i		−	3.28974i
$910$		0			0
$911$	2.18794e17			0.382759			0.191379	−	0.981516i	$-0.438704\pi$
$911$	2.18794e17			0.382759			0.191379	+	0.981516i	$0.438704\pi$
$912$	1.26248e17	+	2.18668e17i	0.219410	+	0.380028i
$913$	1.90860e17	+	1.10193e17i	0.329527	+	0.190252i
$914$	−2.20539e17	+	3.81984e17i	−0.378275	+	0.655191i
$915$	4.08556e17	−	2.35880e17i	0.696186	−	0.401943i
$916$			5.37720e16i			0.0910297i
$917$		0			0
$918$	6.03906e17			1.00905
$919$	−1.68122e17	−	2.91195e17i	−0.279081	−	0.483382i	0.692076	−	0.721825i	$-0.256696\pi$
$919$	−1.68122e17	−	2.91195e17i	−0.279081	−	0.483382i	−0.971157	+	0.238443i	$0.923363\pi$
$920$	9.33108e16	+	5.38730e16i	0.153888	+	0.0888474i
$921$	−5.63039e17	+	9.75212e17i	−0.922531	+	1.59787i
$922$	2.00439e17	−	1.15724e17i	0.326285	−	0.188381i
$923$			7.52280e17i			1.21666i
$924$		0			0
$925$	2.69143e16			0.0429667
$926$	−2.45043e17	−	4.24427e17i	−0.388665	−	0.673188i
$927$	1.15955e18	+	6.69466e17i	1.82730	+	1.05499i
$928$	−5.06895e16	+	8.77968e16i	−0.0793652	+	0.137465i
$929$	−7.48828e17	+	4.32336e17i	−1.16490	+	0.672554i	−0.952473	−	0.304623i	$-0.901469\pi$
$929$	−7.48828e17	+	4.32336e17i	−1.16490	+	0.672554i	−0.212425	+	0.977177i	$0.568136\pi$
$930$			1.31960e18i			2.03959i
$931$		0			0
$932$	−9.55103e16			−0.145732
$933$	2.55464e16	+	4.42477e16i	0.0387293	+	0.0670811i
$934$	1.32111e17	+	7.62745e16i	0.199002	+	0.114894i
$935$	−1.03237e17	+	1.78812e17i	−0.154514	+	0.267626i
$936$	−8.38436e17	+	4.84071e17i	−1.24685	+	0.719871i
$937$		−	1.98208e17i		−	0.292876i	−0.989220	−	0.146438i	$-0.953219\pi$
$937$		−	1.98208e17i		−	0.292876i	0.989220	−	0.146438i	$-0.0467808\pi$
$938$		0			0
$939$	−4.01515e16			−0.0585745
$940$	−2.92202e17	−	5.06109e17i	−0.423561	−	0.733629i
$941$	−3.68004e17	−	2.12467e17i	−0.530047	−	0.306023i	0.210988	−	0.977489i	$-0.432332\pi$
$941$	−3.68004e17	−	2.12467e17i	−0.530047	−	0.306023i	−0.741036	+	0.671466i	$0.765665\pi$
$942$	−2.84530e16	+	4.92821e16i	−0.0407214	+	0.0705316i
$943$	1.09119e17	−	6.30001e16i	0.155179	−	0.0895925i
$944$			3.82962e16i			0.0541158i
$945$		0			0
$946$	1.76714e17			0.246561
$947$	3.93367e17	+	6.81331e17i	0.545378	+	0.944623i	0.998583	+	0.0532163i	$0.0169473\pi$
$947$	3.93367e17	+	6.81331e17i	0.545378	+	0.944623i	−0.453205	+	0.891406i	$0.649719\pi$
$948$	−7.27397e17	−	4.19963e17i	−1.00212	−	0.578576i
$949$	8.58271e17	−	1.48657e18i	1.17497	−	2.03511i
$950$	−4.50629e16	+	2.60171e16i	−0.0613024	+	0.0353929i
$951$			4.87301e17i			0.658740i
$952$		0			0
$953$	−1.19506e18			−1.59526			−0.797631	−	0.603146i	$-0.793914\pi$
$953$	−1.19506e18			−1.59526			−0.797631	+	0.603146i	$0.793914\pi$
$954$	1.41488e17	+	2.45065e17i	0.187685	+	0.325081i
$955$	3.46094e17	+	1.99818e17i	0.456220	+	0.263399i
$956$	−9.58694e16	+	1.66051e17i	−0.125584	+	0.217517i
$957$	5.75698e17	−	3.32379e17i	0.749416	−	0.432676i
$958$		−	5.29410e16i		−	0.0684855i
$959$		0			0
$960$	−1.89164e17			−0.241663
$961$	4.82816e17	+	8.36262e17i	0.612973	+	1.06170i
$962$	3.39765e17	+	1.96163e17i	0.428675	+	0.247496i
$963$	4.93796e17	−	8.55279e17i	0.619141	−	1.07238i
$964$	−1.38187e17	+	7.97823e16i	−0.172189	+	0.0994132i
$965$			1.57152e17i			0.194606i
$966$		0			0
$967$	−4.45589e17			−0.544974			−0.272487	−	0.962159i	$-0.587846\pi$
$967$	−4.45589e17			−0.544974			−0.272487	+	0.962159i	$0.587846\pi$
$968$	−1.05507e17	−	1.82743e17i	−0.128241	−	0.222120i
$969$	7.06055e17	+	4.07641e17i	0.852895	+	0.492419i
$970$	3.57203e17	−	6.18694e17i	0.428830	−	0.742755i
$971$	−8.53152e17	+	4.92567e17i	−1.01791	+	0.587693i	−0.913499	−	0.406841i	$-0.866630\pi$
$971$	−8.53152e17	+	4.92567e17i	−1.01791	+	0.587693i	−0.104415	+	0.994534i	$0.533297\pi$
$972$		−	7.07466e17i		−	0.838896i
$973$		0			0
$974$	−3.81249e17			−0.446534
$975$	−1.41622e17	−	2.45296e17i	−0.164855	−	0.285538i
$976$	7.78151e16	+	4.49265e16i	0.0900253	+	0.0519762i
$977$	3.30254e17	−	5.72017e17i	0.379735	−	0.657720i	−0.611288	−	0.791408i	$-0.709348\pi$
$977$	3.30254e17	−	5.72017e17i	0.379735	−	0.657720i	0.991024	+	0.133687i	$0.0426818\pi$
$978$	−4.43039e17	+	2.55789e17i	−0.506301	+	0.292313i
$979$		−	1.04110e17i		−	0.118248i
$980$		0			0
$981$	−7.78522e17			−0.873488
$982$	9.22016e16	+	1.59698e17i	0.102818	+	0.178086i
$983$	−1.43457e18	−	8.28251e17i	−1.59002	−	0.917996i	−0.993303	−	0.115541i	$-0.963140\pi$
$983$	−1.43457e18	−	8.28251e17i	−1.59002	−	0.917996i	−0.596713	−	0.802455i	$-0.703527\pi$
$984$	−1.10606e17	+	1.91575e17i	−0.121845	+	0.211042i
$985$	4.47676e17	−	2.58466e17i	0.490170	−	0.283000i
$986$			3.27342e17i			0.356238i
$987$		0			0
$988$	−7.58496e17			−0.815477
$989$	−1.48877e17	−	2.57863e17i	−0.159093	−	0.275557i
$990$	7.56654e17	+	4.36855e17i	0.803686	+	0.464008i
$991$	2.17086e17	−	3.76005e17i	0.229187	−	0.396964i	−0.728380	−	0.685173i	$-0.759726\pi$
$991$	2.17086e17	−	3.76005e17i	0.229187	−	0.396964i	0.957568	+	0.288209i	$0.0930598\pi$
$992$	−2.17662e17	+	1.25667e17i	−0.228409	+	0.131872i
$993$			9.19136e17i			0.958704i
$994$		0			0
$995$	−1.76177e18			−1.81556
$996$	3.25971e17	+	5.64598e17i	0.333905	+	0.578340i
$997$	−8.52632e17	−	4.92267e17i	−0.868142	−	0.501222i	−0.00141159	−	0.999999i	$-0.500449\pi$
$997$	−8.52632e17	−	4.92267e17i	−0.868142	−	0.501222i	−0.866730	+	0.498777i	$0.833783\pi$
$998$	−1.87423e17	+	3.24626e17i	−0.189688	+	0.328549i
$999$	−8.96826e17	+	5.17783e17i	−0.902226	+	0.520901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.a.31.8		16
7.2	even	3		14.13.d.a.5.5	yes	16
7.3	odd	6		98.13.b.c.97.8		16
7.4	even	3		98.13.b.c.97.1		16
7.5	odd	6	inner	98.13.d.a.19.8		16
7.6	odd	2		14.13.d.a.3.5	✓	16
21.2	odd	6		126.13.n.a.19.1		16
21.20	even	2		126.13.n.a.73.1		16
28.23	odd	6		112.13.s.c.33.8		16
28.27	even	2		112.13.s.c.17.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.d.a.3.5	✓	16	7.6	odd	2
14.13.d.a.5.5	yes	16	7.2	even	3
98.13.b.c.97.1		16	7.4	even	3
98.13.b.c.97.8		16	7.3	odd	6
98.13.d.a.19.8		16	7.5	odd	6	inner
98.13.d.a.31.8		16	1.1	even	1	trivial
112.13.s.c.17.8		16	28.27	even	2
112.13.s.c.33.8		16	28.23	odd	6
126.13.n.a.19.1		16	21.2	odd	6
126.13.n.a.73.1		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)

\(f(q)\)	\(=\)	\(q+(22.6274 + 39.1918i) q^{2} +(1161.18 + 670.406i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-14223.7 + 8212.03i) q^{5} +60678.2i q^{6} -92681.9 q^{8} +(633167. + 1.09668e6i) q^{9} +O(q^{10})\)	\(q+(22.6274 + 39.1918i) q^{2} +(1161.18 + 670.406i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(-14223.7 + 8212.03i) q^{5} +60678.2i q^{6} -92681.9 q^{8} +(633167. + 1.09668e6i) q^{9} +(-643689. - 371634. i) q^{10} +(-464134. + 803904. i) q^{11} +(-2.37809e6 + 1.37299e6i) q^{12} -8.24891e6i q^{13} -2.20216e7 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(-1.17285e7 - 6.77147e6i) q^{17} +(-2.86538e7 + 4.96299e7i) q^{18} +(-3.88828e7 + 2.24490e7i) q^{19} -3.36365e7i q^{20} -4.20086e7 q^{22} +(3.53913e7 + 6.12994e7i) q^{23} +(-1.07620e8 - 6.21345e7i) q^{24} +(1.28046e7 - 2.21782e7i) q^{25} +(3.23290e8 - 1.86652e8i) q^{26} +9.85352e8i q^{27} -5.34101e8 q^{29} +(-4.98291e8 - 8.63066e8i) q^{30} +(-1.14672e9 - 6.62060e8i) q^{31} +(9.49063e7 - 1.64382e8i) q^{32} +(-1.07788e9 + 6.22316e8i) q^{33} -6.12884e8i q^{34} -2.59345e9 q^{36} +(5.25480e8 + 9.10159e8i) q^{37} +(-1.75964e9 - 1.01593e9i) q^{38} +(5.53011e9 - 9.57844e9i) q^{39} +(1.31828e9 - 7.61107e8i) q^{40} -1.78011e9i q^{41} -4.20662e9 q^{43} +(-9.50546e8 - 1.64639e9i) q^{44} +(-1.80119e10 - 1.03992e10i) q^{45} +(-1.60163e9 + 2.77410e9i) q^{46} +(1.50464e10 - 8.68706e9i) q^{47} -5.62377e9i q^{48} +1.15894e9 q^{50} +(-9.07927e9 - 1.57258e10i) q^{51} +(1.46304e10 + 8.44688e9i) q^{52} +(2.46892e9 - 4.27630e9i) q^{53} +(-3.86177e10 + 2.22960e10i) q^{54} -1.52459e10i q^{55} -6.01997e10 q^{57} +(-1.20853e10 - 2.09324e10i) q^{58} +(-7.90727e9 - 4.56526e9i) q^{59} +(2.25501e10 - 3.90579e10i) q^{60} +(-1.85526e10 + 1.07113e10i) q^{61} -5.99229e10i q^{62} +8.58993e9 q^{64} +(6.77403e10 + 1.17330e11i) q^{65} +(-4.87794e10 - 2.81628e10i) q^{66} +(-3.21303e10 + 5.56512e10i) q^{67} +(2.40200e10 - 1.38680e10i) q^{68} +9.49060e10i q^{69} -9.11975e10 q^{71} +(-5.86831e10 - 1.01642e11i) q^{72} +(1.80214e11 + 1.04047e11i) q^{73} +(-2.37805e10 + 4.11891e10i) q^{74} +(2.97368e10 - 1.71686e10i) q^{75} -9.19511e10i q^{76} +5.00529e11 q^{78} +(1.52937e11 + 2.64895e11i) q^{79} +(5.96583e10 + 3.44438e10i) q^{80} +(-3.24094e11 + 5.61348e11i) q^{81} +(6.97656e10 - 4.02792e10i) q^{82} -2.37417e11i q^{83} +2.22430e11 q^{85} +(-9.51849e10 - 1.64865e11i) q^{86} +(-6.20185e11 - 3.58064e11i) q^{87} +(4.30168e10 - 7.45073e10i) q^{88} +(-9.71289e10 + 5.60774e10i) q^{89} -9.41225e11i q^{90} -1.44963e11 q^{92} +(-8.87698e11 - 1.53754e12i) q^{93} +(6.80923e11 + 3.93131e11i) q^{94} +(3.68704e11 - 6.38614e11i) q^{95} +(2.20406e11 - 1.27251e11i) q^{96} +9.61170e11i q^{97} -1.17550e12 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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