LMFDB - Embedded newform 17.16.b.a.16.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,16,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	17.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.2578958670$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.17
Character	$\chi$	$=$	17.16
Dual form			17.16.b.a.16.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+210.994 q^{2} +3417.77i q^{3} +11750.3 q^{4} -46569.8i q^{5} +721128. i q^{6} +204211. i q^{7} -4.43460e6 q^{8} +2.66774e6 q^{9} +O(q^{10})$	\(q+210.994 q^{2} +3417.77i q^{3} +11750.3 q^{4} -46569.8i q^{5} +721128. i q^{6} +204211. i q^{7} -4.43460e6 q^{8} +2.66774e6 q^{9} -9.82593e6i q^{10} +1.19507e8i q^{11} +4.01598e7i q^{12} -2.11867e8 q^{13} +4.30872e7i q^{14} +1.59165e8 q^{15} -1.32071e9 q^{16} +(-1.59891e9 - 5.53087e8i) q^{17} +5.62876e8 q^{18} -5.73611e9 q^{19} -5.47208e8i q^{20} -6.97947e8 q^{21} +2.52152e10i q^{22} -1.86710e10i q^{23} -1.51565e10i q^{24} +2.83488e10 q^{25} -4.47025e10 q^{26} +5.81590e10i q^{27} +2.39954e9i q^{28} +1.73212e10i q^{29} +3.35828e10 q^{30} -3.41314e10i q^{31} -1.33347e11 q^{32} -4.08447e11 q^{33} +(-3.37360e11 - 1.16698e11i) q^{34} +9.51006e9 q^{35} +3.13467e10 q^{36} +7.99756e11i q^{37} -1.21028e12 q^{38} -7.24112e11i q^{39} +2.06519e11i q^{40} +1.95463e12i q^{41} -1.47262e11 q^{42} +2.45256e11 q^{43} +1.40424e12i q^{44} -1.24236e11i q^{45} -3.93946e12i q^{46} +1.54443e12 q^{47} -4.51387e12i q^{48} +4.70586e12 q^{49} +5.98142e12 q^{50} +(1.89032e12 - 5.46472e12i) q^{51} -2.48950e12 q^{52} +1.01766e13 q^{53} +1.22712e13i q^{54} +5.56541e12 q^{55} -9.05595e11i q^{56} -1.96047e13i q^{57} +3.65466e12i q^{58} -1.05892e13 q^{59} +1.87023e12 q^{60} +3.24766e13i q^{61} -7.20150e12i q^{62} +5.44782e11i q^{63} +1.51415e13 q^{64} +9.86659e12i q^{65} -8.61798e13 q^{66} -2.06491e12 q^{67} +(-1.87877e13 - 6.49893e12i) q^{68} +6.38131e13 q^{69} +2.00656e12 q^{70} -7.12668e13i q^{71} -1.18304e13 q^{72} -1.38066e14i q^{73} +1.68743e14i q^{74} +9.68898e13i q^{75} -6.74009e13 q^{76} -2.44046e13 q^{77} -1.52783e14i q^{78} +1.00832e12i q^{79} +6.15050e13i q^{80} -1.60495e14 q^{81} +4.12414e14i q^{82} +1.11101e14 q^{83} -8.20107e12 q^{84} +(-2.57571e13 + 7.44610e13i) q^{85} +5.17475e13 q^{86} -5.91999e13 q^{87} -5.29966e14i q^{88} -4.91732e14 q^{89} -2.62130e13i q^{90} -4.32655e13i q^{91} -2.19389e14i q^{92} +1.16653e14 q^{93} +3.25864e14 q^{94} +2.67129e14i q^{95} -4.55751e14i q^{96} +3.82439e14i q^{97} +9.92906e14 q^{98} +3.18814e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9}+O(q^{10}) $ 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9	$ 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9} + 702506672 q^{13} - 1787378376 q^{15} + 3524081474 q^{16} - 2245058454 q^{17} + 6803778314 q^{18} + 9958891784 q^{19} - 4168893668 q^{21} - 238696683970 q^{25} - 33467295588 q^{26} - 62541989808 q^{30} - 43445086338 q^{32} + 213283309748 q^{33} + 521524562854 q^{34} - 467785613304 q^{35} - 2300588654186 q^{36} + 3162083165688 q^{38} - 3011205093968 q^{42} - 2215728209008 q^{43} - 7793870107128 q^{47} - 1555224751482 q^{49} + 30118817411766 q^{50} - 21451923375880 q^{51} + 51163160044372 q^{52} - 6062965973460 q^{53} - 11679154373592 q^{55} + 22772194849344 q^{59} - 86295684546192 q^{60} - 28567749560318 q^{64} + 251781147903680 q^{66} + 153875904272808 q^{67} - 48849686100870 q^{68} + 60664072036996 q^{69} - 150925771647648 q^{70} - 293782759569702 q^{72} - 388479948338264 q^{76} - 622427249887884 q^{77} + 983865215787034 q^{81} - 15\!\cdots\!44 q^{83}+ \cdots + 26\!\cdots\!90 q^{98}+O(q^{100}) $ 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9 + 702506672 * q^13 - 1787378376 * q^15 + 3524081474 * q^16 - 2245058454 * q^17 + 6803778314 * q^18 + 9958891784 * q^19 - 4168893668 * q^21 - 238696683970 * q^25 - 33467295588 * q^26 - 62541989808 * q^30 - 43445086338 * q^32 + 213283309748 * q^33 + 521524562854 * q^34 - 467785613304 * q^35 - 2300588654186 * q^36 + 3162083165688 * q^38 - 3011205093968 * q^42 - 2215728209008 * q^43 - 7793870107128 * q^47 - 1555224751482 * q^49 + 30118817411766 * q^50 - 21451923375880 * q^51 + 51163160044372 * q^52 - 6062965973460 * q^53 - 11679154373592 * q^55 + 22772194849344 * q^59 - 86295684546192 * q^60 - 28567749560318 * q^64 + 251781147903680 * q^66 + 153875904272808 * q^67 - 48849686100870 * q^68 + 60664072036996 * q^69 - 150925771647648 * q^70 - 293782759569702 * q^72 - 388479948338264 * q^76 - 622427249887884 * q^77 + 983865215787034 * q^81 - 1541046988482144 * q^83 + 1542636638603936 * q^84 + 94526232685248 * q^85 + 102594718370712 * q^86 - 428830075363560 * q^87 - 894061425316800 * q^89 + 2342465228549812 * q^93 + 2620489835637760 * q^94 + 2662999543720290 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	210.994			1.16559			0.582793	−	0.812621i	$-0.301960\pi$
$2$	210.994			1.16559			0.582793	+	0.812621i	$0.301960\pi$
$3$			3417.77i			0.902264i	0.892457	+	0.451132i	$0.148980\pi$
$3$			3417.77i			0.902264i	−0.892457	+	0.451132i	$0.851020\pi$
$4$	11750.3			0.358590
$5$		−	46569.8i		−	0.266581i	−0.991077	−	0.133291i	$-0.957446\pi$
$5$		−	46569.8i		−	0.266581i	0.991077	−	0.133291i	$-0.0425543\pi$
$6$			721128.i			1.05167i
$7$			204211.i			0.0937225i	0.998901	+	0.0468612i	$0.0149219\pi$
$7$			204211.i			0.0937225i	−0.998901	+	0.0468612i	$0.985078\pi$
$8$	−4.43460e6			−0.747618
$9$	2.66774e6			0.185919
$10$		−	9.82593e6i		−	0.310723i
$11$			1.19507e8i			1.84905i	0.381125	+	0.924524i	$0.375537\pi$
$11$			1.19507e8i			1.84905i	−0.381125	+	0.924524i	$0.624463\pi$
$12$			4.01598e7i			0.323543i
$13$	−2.11867e8			−0.936457			−0.468228	−	0.883607i	$-0.655108\pi$
$13$	−2.11867e8			−0.936457			−0.468228	+	0.883607i	$0.655108\pi$
$14$			4.30872e7i			0.109242i
$15$	1.59165e8			0.240527
$16$	−1.32071e9			−1.23000
$17$	−1.59891e9	−	5.53087e8i	−0.945056	−	0.326909i
$17$	−1.59891e9	−	5.53087e8i	−0.945056	−	0.326909i
$18$	5.62876e8			0.216705
$19$	−5.73611e9			−1.47219			−0.736097	−	0.676876i	$-0.763333\pi$
$19$	−5.73611e9			−1.47219			−0.736097	+	0.676876i	$0.763333\pi$
$20$		−	5.47208e8i		−	0.0955934i
$21$	−6.97947e8			−0.0845624
$22$			2.52152e10i			2.15522i
$23$		−	1.86710e10i		−	1.14343i	−0.820453	−	0.571713i	$-0.806279\pi$
$23$		−	1.86710e10i		−	1.14343i	0.820453	−	0.571713i	$-0.193721\pi$
$24$		−	1.51565e10i		−	0.674549i
$25$	2.83488e10			0.928935
$26$	−4.47025e10			−1.09152
$27$			5.81590e10i			1.07001i
$28$			2.39954e9i			0.0336080i
$29$			1.73212e10i			0.186463i	0.995644	+	0.0932316i	$0.0297197\pi$
$29$			1.73212e10i			0.186463i	−0.995644	+	0.0932316i	$0.970280\pi$
$30$	3.35828e10			0.280354
$31$		−	3.41314e10i		−	0.222813i	−0.993775	−	0.111407i	$-0.964464\pi$
$31$		−	3.41314e10i		−	0.222813i	0.993775	−	0.111407i	$-0.0355356\pi$
$32$	−1.33347e11			−0.686056
$33$	−4.08447e11			−1.66833
$34$	−3.37360e11	−	1.16698e11i	−1.10154	−	0.381040i
$35$	9.51006e9			0.0249846
$36$	3.13467e10			0.0666689
$37$			7.99756e11i			1.38498i	0.721426	+	0.692492i	$0.243487\pi$
$37$			7.99756e11i			1.38498i	−0.721426	+	0.692492i	$0.756513\pi$
$38$	−1.21028e12			−1.71597
$39$		−	7.24112e11i		−	0.844931i
$40$			2.06519e11i			0.199301i
$41$			1.95463e12i			1.56742i	0.621126	+	0.783710i	$0.286675\pi$
$41$			1.95463e12i			1.56742i	−0.621126	+	0.783710i	$0.713325\pi$
$42$	−1.47262e11			−0.0985648
$43$	2.45256e11			0.137596			0.0687982	−	0.997631i	$-0.478084\pi$
$43$	2.45256e11			0.137596			0.0687982	+	0.997631i	$0.478084\pi$
$44$			1.40424e12i			0.663050i
$45$		−	1.24236e11i		−	0.0495626i
$46$		−	3.93946e12i		−	1.33276i
$47$	1.54443e12			0.444666			0.222333	−	0.974971i	$-0.428633\pi$
$47$	1.54443e12			0.444666			0.222333	+	0.974971i	$0.428633\pi$
$48$		−	4.51387e12i		−	1.10979i
$49$	4.70586e12			0.991216
$50$	5.98142e12			1.08275
$51$	1.89032e12	−	5.46472e12i	0.294958	−	0.852690i
$52$	−2.48950e12			−0.335804
$53$	1.01766e13			1.18996			0.594981	−	0.803740i	$-0.297160\pi$
$53$	1.01766e13			1.18996			0.594981	+	0.803740i	$0.297160\pi$
$54$			1.22712e13i			1.24719i
$55$	5.56541e12			0.492921
$56$		−	9.05595e11i		−	0.0700686i
$57$		−	1.96047e13i		−	1.32831i
$58$			3.65466e12i			0.217339i
$59$	−1.05892e13			−0.553953			−0.276977	−	0.960877i	$-0.589332\pi$
$59$	−1.05892e13			−0.553953			−0.276977	+	0.960877i	$0.589332\pi$
$60$	1.87023e12			0.0862505
$61$			3.24766e13i			1.32311i	0.749895	+	0.661557i	$0.230104\pi$
$61$			3.24766e13i			1.32311i	−0.749895	+	0.661557i	$0.769896\pi$
$62$		−	7.20150e12i		−	0.259708i
$63$			5.44782e11i			0.0174248i
$64$	1.51415e13			0.430346
$65$			9.86659e12i			0.249642i
$66$	−8.61798e13			−1.94458
$67$	−2.06491e12			−0.0416237			−0.0208118	−	0.999783i	$-0.506625\pi$
$67$	−2.06491e12			−0.0416237			−0.0208118	+	0.999783i	$0.506625\pi$
$68$	−1.87877e13	−	6.49893e12i	−0.338888	−	0.117226i
$69$	6.38131e13			1.03167
$70$	2.00656e12			0.0291217
$71$		−	7.12668e13i		−	0.929928i	−0.885330	−	0.464964i	$-0.846067\pi$
$71$		−	7.12668e13i		−	0.929928i	0.885330	−	0.464964i	$-0.153933\pi$
$72$	−1.18304e13			−0.138997
$73$		−	1.38066e14i		−	1.46273i	−0.681987	−	0.731365i	$-0.738884\pi$
$73$		−	1.38066e14i		−	1.46273i	0.681987	−	0.731365i	$-0.261116\pi$
$74$			1.68743e14i			1.61432i
$75$			9.68898e13i			0.838144i
$76$	−6.74009e13			−0.527915
$77$	−2.44046e13			−0.173297
$78$		−	1.52783e14i		−	0.984840i
$79$			1.00832e12i			0.00590741i	0.999996	+	0.00295370i	$0.000940195\pi$
$79$			1.00832e12i			0.00590741i	−0.999996	+	0.00295370i	$0.999060\pi$
$80$			6.15050e13i			0.327896i
$81$	−1.60495e14			−0.779514
$82$			4.12414e14i			1.82696i
$83$	1.11101e14			0.449398			0.224699	−	0.974428i	$-0.427860\pi$
$83$	1.11101e14			0.449398			0.224699	+	0.974428i	$0.427860\pi$
$84$	−8.20107e12			−0.0303233
$85$	−2.57571e13	+	7.44610e13i	−0.0871476	+	0.251934i
$86$	5.17475e13			0.160380
$87$	−5.91999e13			−0.168239
$88$		−	5.29966e14i		−	1.38238i
$89$	−4.91732e14			−1.17843			−0.589215	−	0.807977i	$-0.700563\pi$
$89$	−4.91732e14			−1.17843			−0.589215	+	0.807977i	$0.700563\pi$
$90$		−	2.62130e13i		−	0.0577695i
$91$		−	4.32655e13i		−	0.0877671i
$92$		−	2.19389e14i		−	0.410022i
$93$	1.16653e14			0.201036
$94$	3.25864e14			0.518296
$95$			2.67129e14i			0.392459i
$96$		−	4.55751e14i		−	0.619004i
$97$			3.82439e14i			0.480589i	0.970700	+	0.240295i	$0.0772441\pi$
$97$			3.82439e14i			0.480589i	−0.970700	+	0.240295i	$0.922756\pi$
$98$	9.92906e14			1.15535
$99$			3.18814e14i			0.343774i
$100$	3.33107e14			0.333107
$101$	9.36739e14			0.869377			0.434688	−	0.900581i	$-0.356858\pi$
$101$	9.36739e14			0.869377			0.434688	+	0.900581i	$0.356858\pi$
$102$	3.98846e14	−	1.15302e15i	0.343799	−	0.993883i
$103$	−8.06495e14			−0.646134			−0.323067	−	0.946376i	$-0.604714\pi$
$103$	−8.06495e14			−0.646134			−0.323067	+	0.946376i	$0.604714\pi$
$104$	9.39545e14			0.700112
$105$			3.25032e13i			0.0225427i
$106$	2.14719e15			1.38700
$107$		−	2.36180e15i		−	1.42188i	−0.703251	−	0.710942i	$-0.748269\pi$
$107$		−	2.36180e15i		−	1.42188i	0.703251	−	0.710942i	$-0.251731\pi$
$108$			6.83385e14i			0.383696i
$109$			3.69884e15i			1.93806i	0.246951	+	0.969028i	$0.420571\pi$
$109$			3.69884e15i			1.93806i	−0.246951	+	0.969028i	$0.579429\pi$
$110$	1.17427e15			0.574542
$111$	−2.73338e15			−1.24962
$112$		−	2.69703e14i		−	0.115279i
$113$			1.48553e15i			0.594010i	0.954876	+	0.297005i	$0.0959878\pi$
$113$			1.48553e15i			0.594010i	−0.954876	+	0.297005i	$0.904012\pi$
$114$		−	4.13647e15i		−	1.54826i
$115$	−8.69504e14			−0.304816
$116$			2.03529e14i			0.0668639i
$117$	−5.65206e14			−0.174106
$118$	−2.23425e15			−0.645680
$119$	1.12946e14	−	3.26515e14i	0.0306387	−	0.0885730i
$120$	−7.05833e14			−0.179822
$121$	−1.01047e16			−2.41897
$122$			6.85236e15i			1.54220i
$123$	−6.68048e15			−1.41423
$124$		−	4.01053e14i		−	0.0798987i
$125$		−	2.74140e15i		−	0.514217i
$126$			1.14945e14i			0.0203101i
$127$	−3.74828e14			−0.0624172			−0.0312086	−	0.999513i	$-0.509936\pi$
$127$	−3.74828e14			−0.0624172			−0.0312086	+	0.999513i	$0.509936\pi$
$128$	7.56428e15			1.18766
$129$			8.38230e14i			0.124148i
$130$			2.08179e15i			0.290979i
$131$			5.33098e15i			0.703514i	0.936091	+	0.351757i	$0.114416\pi$
$131$			5.33098e15i			0.703514i	−0.936091	+	0.351757i	$0.885584\pi$
$132$	−4.79937e15			−0.598246
$133$		−	1.17138e15i		−	0.137978i
$134$	−4.35683e14			−0.0485160
$135$	2.70845e15			0.285245
$136$	7.09054e15	+	2.45272e15i	0.706541	+	0.244403i
$137$	5.83582e15			0.550424			0.275212	−	0.961384i	$-0.411252\pi$
$137$	5.83582e15			0.550424			0.275212	+	0.961384i	$0.411252\pi$
$138$	1.34642e16			1.20250
$139$			2.44003e14i			0.0206435i	0.999947	+	0.0103218i	$0.00328558\pi$
$139$			2.44003e14i			0.0206435i	−0.999947	+	0.0103218i	$0.996714\pi$
$140$	1.11746e14			0.00895925
$141$			5.27850e15i			0.401206i
$142$		−	1.50368e16i		−	1.08391i
$143$		−	2.53196e16i		−	1.73155i
$144$	−3.52330e15			−0.228682
$145$	8.06645e14			0.0497076
$146$		−	2.91309e16i		−	1.70494i
$147$			1.60836e16i			0.894339i
$148$			9.39736e15i			0.496642i
$149$	1.69353e16			0.850936			0.425468	−	0.904974i	$-0.360110\pi$
$149$	1.69353e16			0.850936			0.425468	+	0.904974i	$0.360110\pi$
$150$			2.04431e16i			0.976929i
$151$	−1.58011e15			−0.0718391			−0.0359195	−	0.999355i	$-0.511436\pi$
$151$	−1.58011e15			−0.0718391			−0.0359195	+	0.999355i	$0.511436\pi$
$152$	2.54374e16			1.10064
$153$	−4.26548e15	−	1.47549e15i	−0.175704	−	0.0607787i
$154$	−5.14922e15			−0.201993
$155$	−1.58949e15			−0.0593978
$156$		−	8.50853e15i		−	0.302984i
$157$	−1.51406e16			−0.513921			−0.256960	−	0.966422i	$-0.582721\pi$
$157$	−1.51406e16			−0.513921			−0.256960	+	0.966422i	$0.582721\pi$
$158$			2.12750e14i			0.00688559i
$159$			3.47813e16i			1.07366i
$160$			6.20996e15i			0.182890i
$161$	3.81282e15			0.107165
$162$	−3.38634e16			−0.908591
$163$		−	5.61450e16i		−	1.43848i	−0.694762	−	0.719240i	$-0.744490\pi$
$163$		−	5.61450e16i		−	1.43848i	0.694762	−	0.719240i	$-0.255510\pi$
$164$			2.29675e16i			0.562062i
$165$			1.90213e16i			0.444745i
$166$	2.34415e16			0.523811
$167$		−	1.57276e16i		−	0.335961i	−0.985790	−	0.167981i	$-0.946275\pi$
$167$		−	1.57276e16i		−	0.335961i	0.985790	−	0.167981i	$-0.0537246\pi$
$168$	3.09512e15			0.0632204
$169$	−6.29835e15			−0.123049
$170$	−5.43459e15	+	1.57108e16i	−0.101578	+	0.293651i
$171$	−1.53024e16			−0.273710
$172$	2.88183e15			0.0493407
$173$			9.04694e16i			1.48305i	0.670925	+	0.741525i	$0.265897\pi$
$173$			9.04694e16i			1.48305i	−0.670925	+	0.741525i	$0.734103\pi$
$174$	−1.24908e16			−0.196097
$175$			5.78914e15i			0.0870620i
$176$		−	1.57834e17i		−	2.27433i
$177$		−	3.61915e16i		−	0.499812i
$178$	−1.03752e17			−1.37356
$179$	8.56648e16			1.08744			0.543719	−	0.839267i	$-0.317016\pi$
$179$	8.56648e16			1.08744			0.543719	+	0.839267i	$0.317016\pi$
$180$		−	1.45981e15i		−	0.0177727i
$181$			1.04695e17i			1.22275i	0.791342	+	0.611374i	$0.209383\pi$
$181$			1.04695e17i			1.22275i	−0.791342	+	0.611374i	$0.790617\pi$
$182$		−	9.12875e15i		−	0.102300i
$183$	−1.10998e17			−1.19380
$184$			8.27984e16i			0.854846i
$185$	3.72445e16			0.369210
$186$	2.46131e16			0.234325
$187$	6.60977e16	−	1.91081e17i	0.604469	−	1.74745i
$188$	1.81475e16			0.159453
$189$	−1.18767e16			−0.100284
$190$			5.63626e16i			0.457445i
$191$	−2.04404e17			−1.59492			−0.797461	−	0.603370i	$-0.793824\pi$
$191$	−2.04404e17			−1.59492			−0.797461	+	0.603370i	$0.793824\pi$
$192$			5.17500e16i			0.388286i
$193$		−	3.68063e16i		−	0.265609i	−0.991142	−	0.132804i	$-0.957602\pi$
$193$		−	3.68063e16i		−	0.265609i	0.991142	−	0.132804i	$-0.0423982\pi$
$194$			8.06922e16i			0.560168i
$195$	−3.37218e16			−0.225243
$196$	5.52952e16			0.355440
$197$			1.91623e17i			1.18563i	0.805338	+	0.592816i	$0.201984\pi$
$197$			1.91623e17i			1.18563i	−0.805338	+	0.592816i	$0.798016\pi$
$198$			6.72676e16i			0.400698i
$199$			3.45316e16i			0.198070i	0.995084	+	0.0990351i	$0.0315756\pi$
$199$			3.45316e16i			0.198070i	−0.995084	+	0.0990351i	$0.968424\pi$
$200$	−1.25716e17			−0.694488
$201$		−	7.05740e15i		−	0.0375556i
$202$	1.97646e17			1.01333
$203$	−3.53718e15			−0.0174758
$204$	2.22118e16	−	6.42120e16i	0.105769	−	0.305766i
$205$	9.10267e16			0.417845
$206$	−1.70165e17			−0.753125
$207$		−	4.98093e16i		−	0.212585i
$208$	2.79814e17			1.15184
$209$		−	6.85505e17i		−	2.72216i
$210$			6.85797e15i			0.0262755i
$211$			1.44706e17i			0.535018i	0.963555	+	0.267509i	$0.0862005\pi$
$211$			1.44706e17i			0.535018i	−0.963555	+	0.267509i	$0.913800\pi$
$212$	1.19578e17			0.426709
$213$	2.43574e17			0.839041
$214$		−	4.98324e17i		−	1.65733i
$215$		−	1.14215e16i		−	0.0366806i
$216$		−	2.57912e17i		−	0.799961i
$217$	6.97000e15			0.0208826
$218$			7.80431e17i			2.25897i
$219$	4.71877e17			1.31977
$220$	6.53952e16			0.176757
$221$	3.38756e17	+	1.17181e17i	0.885004	+	0.306136i
$222$	−5.76726e17			−1.45654
$223$	5.58278e17			1.36321			0.681607	−	0.731718i	$-0.261281\pi$
$223$	5.58278e17			1.36321			0.681607	+	0.731718i	$0.261281\pi$
$224$		−	2.72310e16i		−	0.0642989i
$225$	7.56273e16			0.172707
$226$			3.13438e17i			0.692370i
$227$		−	1.30188e17i		−	0.278213i	−0.990277	−	0.139107i	$-0.955577\pi$
$227$		−	1.30188e17i		−	0.278213i	0.990277	−	0.139107i	$-0.0444231\pi$
$228$		−	2.30361e17i		−	0.476318i
$229$	−8.11827e17			−1.62442			−0.812208	−	0.583368i	$-0.801735\pi$
$229$	−8.11827e17			−1.62442			−0.812208	+	0.583368i	$0.801735\pi$
$230$	−1.83460e17			−0.355289
$231$		−	8.34094e16i		−	0.156360i
$232$		−	7.68127e16i		−	0.139403i
$233$			1.11003e18i			1.95058i	0.220929	+	0.975290i	$0.429091\pi$
$233$			1.11003e18i			1.95058i	−0.220929	+	0.975290i	$0.570909\pi$
$234$	−1.19255e17			−0.202935
$235$		−	7.19237e16i		−	0.118539i
$236$	−1.24426e17			−0.198642
$237$	−3.44622e15			−0.00533004
$238$	2.38310e16	−	6.88926e16i	0.0357120	−	0.103239i
$239$	−3.59209e17			−0.521630			−0.260815	−	0.965389i	$-0.583991\pi$
$239$	−3.59209e17			−0.521630			−0.260815	+	0.965389i	$0.583991\pi$
$240$	−2.10210e17			−0.295848
$241$		−	5.98315e17i		−	0.816210i	−0.912935	−	0.408105i	$-0.866190\pi$
$241$		−	5.98315e17i		−	0.816210i	0.912935	−	0.408105i	$-0.133810\pi$
$242$	−2.13202e18			−2.81952
$243$			2.85983e17i			0.366685i
$244$			3.81610e17i			0.474456i
$245$		−	2.19151e17i		−	0.264239i
$246$	−1.40954e18			−1.64840
$247$	1.21529e18			1.37865
$248$			1.51359e17i			0.166579i
$249$			3.79717e17i			0.405475i
$250$		−	5.78417e17i		−	0.599365i
$251$	−1.47840e18			−1.48675			−0.743375	−	0.668875i	$-0.766776\pi$
$251$	−1.47840e18			−1.48675			−0.743375	+	0.668875i	$0.766776\pi$
$252$			6.40134e15i			0.00624837i
$253$	2.23131e18			2.11425
$254$	−7.90863e16			−0.0727526
$255$	−2.54491e17	−	8.80320e16i	−0.227311	−	0.0786302i
$256$	1.09986e18			0.953975
$257$	2.07255e17			0.174585			0.0872924	−	0.996183i	$-0.472179\pi$
$257$	2.07255e17			0.174585			0.0872924	+	0.996183i	$0.472179\pi$
$258$			1.76861e17i			0.144705i
$259$	−1.63319e17			−0.129804
$260$			1.15935e17i			0.0895191i
$261$			4.62085e16i			0.0346671i
$262$			1.12480e18i			0.820006i
$263$	−1.39958e18			−0.991584			−0.495792	−	0.868441i	$-0.665122\pi$
$263$	−1.39958e18			−0.991584			−0.495792	+	0.868441i	$0.665122\pi$
$264$	1.81130e18			1.24727
$265$		−	4.73922e17i		−	0.317221i
$266$		−	2.47153e17i		−	0.160825i
$267$		−	1.68063e18i		−	1.06325i
$268$	−2.42633e16			−0.0149258
$269$		−	2.10596e18i		−	1.25982i	−0.776670	−	0.629908i	$-0.783092\pi$
$269$		−	2.10596e18i		−	1.25982i	0.776670	−	0.629908i	$-0.216908\pi$
$270$	5.71466e17			0.332478
$271$	2.37668e18			1.34493			0.672467	−	0.740127i	$-0.265235\pi$
$271$	2.37668e18			1.34493			0.672467	+	0.740127i	$0.265235\pi$
$272$	2.11169e18	+	7.30465e17i	1.16242	+	0.402099i
$273$	1.47872e17			0.0791891
$274$	1.23132e18			0.641567
$275$			3.38788e18i			1.71764i
$276$	7.49823e17			0.369948
$277$		−	2.76401e17i		−	0.132721i	−0.997796	−	0.0663607i	$-0.978861\pi$
$277$		−	2.76401e17i		−	0.132721i	0.997796	−	0.0663607i	$-0.0211388\pi$
$278$			5.14831e16i			0.0240618i
$279$		−	9.10537e16i		−	0.0414253i
$280$	−4.21734e16			−0.0186790
$281$	−1.27251e18			−0.548736			−0.274368	−	0.961625i	$-0.588469\pi$
$281$	−1.27251e18			−0.548736			−0.274368	+	0.961625i	$0.588469\pi$
$282$			1.11373e18i			0.467640i
$283$		−	1.31430e18i		−	0.537397i	−0.963224	−	0.268698i	$-0.913407\pi$
$283$		−	1.31430e18i		−	0.537397i	0.963224	−	0.268698i	$-0.0865935\pi$
$284$		−	8.37405e17i		−	0.333463i
$285$	−9.12987e17			−0.354102
$286$		−	5.34226e18i		−	2.01827i
$287$	−3.99157e17			−0.146903
$288$	−3.55736e17			−0.127551
$289$	2.25061e18	+	1.76867e18i	0.786262	+	0.617894i
$290$	1.70197e17			0.0579384
$291$	−1.30709e18			−0.433619
$292$		−	1.62231e18i		−	0.524520i
$293$	−5.60518e18			−1.76637			−0.883187	−	0.469022i	$-0.844607\pi$
$293$	−5.60518e18			−1.76637			−0.883187	+	0.469022i	$0.844607\pi$
$294$			3.39353e18i			1.04243i
$295$			4.93137e17i			0.147673i
$296$		−	3.54660e18i		−	1.03544i
$297$	−6.95041e18			−1.97850
$298$	3.57325e18			0.991838
$299$			3.95576e18i			1.07077i
$300$			1.13848e18i			0.300550i
$301$			5.00840e16i			0.0128959i
$302$	−3.33393e17			−0.0837346
$303$			3.20156e18i			0.784408i
$304$	7.57571e18			1.81080
$305$	1.51243e18			0.352717
$306$	−8.99989e17	−	3.11319e17i	−0.204798	−	0.0708428i
$307$	−5.36399e18			−1.19111			−0.595553	−	0.803316i	$-0.703067\pi$
$307$	−5.36399e18			−1.19111			−0.595553	+	0.803316i	$0.703067\pi$
$308$	−2.86761e17			−0.0621427
$309$		−	2.75642e18i		−	0.582984i
$310$	−3.35372e17			−0.0692332
$311$			3.90638e18i			0.787175i	0.919287	+	0.393588i	$0.128766\pi$
$311$			3.90638e18i			0.787175i	−0.919287	+	0.393588i	$0.871234\pi$
$312$			3.21115e18i			0.631686i
$313$		−	9.48415e17i		−	0.182144i	−0.995844	−	0.0910722i	$-0.970971\pi$
$313$		−	9.48415e17i		−	0.182144i	0.995844	−	0.0910722i	$-0.0290294\pi$
$314$	−3.19457e18			−0.599018
$315$	2.53704e16			0.00464513
$316$			1.18481e16i			0.00211834i
$317$		−	7.44731e18i		−	1.30033i	−0.759792	−	0.650167i	$-0.774699\pi$
$317$		−	7.44731e18i		−	1.30033i	0.759792	−	0.650167i	$-0.225301\pi$
$318$			7.33862e18i			1.25144i
$319$	−2.07000e18			−0.344779
$320$		−	7.05134e17i		−	0.114722i
$321$	8.07208e18			1.28291
$322$	8.04480e17			0.124910
$323$	9.17153e18	+	3.17256e18i	1.39131	+	0.481273i
$324$	−1.88586e18			−0.279526
$325$	−6.00618e18			−0.869907
$326$		−	1.18462e19i		−	1.67667i
$327$	−1.26418e19			−1.74864
$328$		−	8.66801e18i		−	1.17183i
$329$			3.15389e17i			0.0416752i
$330$			4.01338e18i			0.518388i
$331$	−3.59914e17			−0.0454453			−0.0227227	−	0.999742i	$-0.507233\pi$
$331$	−3.59914e17			−0.0454453			−0.0227227	+	0.999742i	$0.507233\pi$
$332$	1.30546e18			0.161150
$333$			2.13354e18i			0.257495i
$334$		−	3.31843e18i		−	0.391592i
$335$			9.61625e16i			0.0110961i
$336$	9.21782e17			0.104012
$337$			6.99316e18i			0.771702i	0.922561	+	0.385851i	$0.126092\pi$
$337$			6.99316e18i			0.771702i	−0.922561	+	0.385851i	$0.873908\pi$
$338$	−1.32891e18			−0.143424
$339$	−5.07721e18			−0.535954
$340$	−3.02654e17	+	8.74938e17i	−0.0312503	+	0.0903411i
$341$	4.07894e18			0.411992
$342$	−3.22872e18			−0.319032
$343$			1.93049e18i			0.186622i
$344$	−1.08761e18			−0.102870
$345$		−	2.97177e18i		−	0.275024i
$346$			1.90885e19i			1.72862i
$347$			8.13530e18i			0.720946i	0.932770	+	0.360473i	$0.117385\pi$
$347$			8.13530e18i			0.720946i	−0.932770	+	0.360473i	$0.882615\pi$
$348$	−6.95616e17			−0.0603289
$349$	1.29759e19			1.10140			0.550702	−	0.834702i	$-0.314360\pi$
$349$	1.29759e19			1.10140			0.550702	+	0.834702i	$0.314360\pi$
$350$			1.22147e18i			0.101478i
$351$		−	1.23220e19i		−	1.00202i
$352$		−	1.59359e19i		−	1.26855i
$353$	7.82086e18			0.609459			0.304729	−	0.952439i	$-0.401434\pi$
$353$	7.82086e18			0.609459			0.304729	+	0.952439i	$0.401434\pi$
$354$		−	7.63617e18i		−	0.582574i
$355$	−3.31888e18			−0.247901
$356$	−5.77799e18			−0.422573
$357$	1.11595e18	+	3.86025e17i	0.0799162	+	0.0276442i
$358$	1.80747e19			1.26750
$359$	1.70470e19			1.17068			0.585342	−	0.810787i	$-0.300960\pi$
$359$	1.70470e19			1.17068			0.585342	+	0.810787i	$0.300960\pi$
$360$			5.50938e17i			0.0370539i
$361$	1.77218e19			1.16736
$362$			2.20900e19i			1.42522i
$363$		−	3.45354e19i		−	2.18255i
$364$		−	5.08382e17i		−	0.0314724i
$365$	−6.42969e18			−0.389936
$366$	−2.34198e19			−1.39147
$367$			8.24828e18i			0.480140i	0.970756	+	0.240070i	$0.0771704\pi$
$367$			8.24828e18i			0.480140i	−0.970756	+	0.240070i	$0.922830\pi$
$368$			2.46589e19i			1.40642i
$369$			5.21445e18i			0.291414i
$370$	7.85834e18			0.430346
$371$			2.07817e18i			0.111526i
$372$	1.37071e18			0.0720897
$373$	1.39843e19			0.720817			0.360408	−	0.932795i	$-0.382637\pi$
$373$	1.39843e19			0.720817			0.360408	+	0.932795i	$0.382637\pi$
$374$	1.39462e19	−	4.03169e19i	0.704561	−	2.03681i
$375$	9.36947e18			0.463960
$376$	−6.84892e18			−0.332440
$377$		−	3.66979e18i		−	0.174615i
$378$	−2.50591e18			−0.116890
$379$		−	3.25143e19i		−	1.48689i	−0.668795	−	0.743447i	$-0.733189\pi$
$379$		−	3.25143e19i		−	1.48689i	0.668795	−	0.743447i	$-0.266811\pi$
$380$			3.13885e18i			0.140732i
$381$		−	1.28108e18i		−	0.0563168i
$382$	−4.31280e19			−1.85902
$383$	−4.53256e18			−0.191581			−0.0957906	−	0.995402i	$-0.530538\pi$
$383$	−4.53256e18			−0.191581			−0.0957906	+	0.995402i	$0.530538\pi$
$384$			2.58530e19i			1.07158i
$385$			1.13652e18i			0.0461978i
$386$		−	7.76590e18i		−	0.309590i
$387$	6.54280e17			0.0255818
$388$			4.49377e18i			0.172335i
$389$	3.57677e18			0.134545			0.0672727	−	0.997735i	$-0.478570\pi$
$389$	3.57677e18			0.134545			0.0672727	+	0.997735i	$0.478570\pi$
$390$	−7.11508e18			−0.262540
$391$	−1.03267e19	+	2.98532e19i	−0.373796	+	1.08060i
$392$	−2.08686e19			−0.741051
$393$	−1.82201e19			−0.634755
$394$			4.04311e19i			1.38196i
$395$	4.69575e16			0.00157480
$396$			3.74615e18i			0.123274i
$397$			1.32106e19i			0.426572i	0.976990	+	0.213286i	$0.0684166\pi$
$397$			1.32106e19i			0.426572i	−0.976990	+	0.213286i	$0.931583\pi$
$398$			7.28595e18i			0.230868i
$399$	4.00350e18			0.124492
$400$	−3.74405e19			−1.14259
$401$		−	2.48332e19i		−	0.743790i	−0.928275	−	0.371895i	$-0.878708\pi$
$401$		−	2.48332e19i		−	0.743790i	0.928275	−	0.371895i	$-0.121292\pi$
$402$		−	1.48907e18i		−	0.0437742i
$403$			7.23131e18i			0.208655i
$404$	1.10069e19			0.311750
$405$			7.47423e18i			0.207804i
$406$	−7.46322e17			−0.0203695
$407$	−9.55764e19			−2.56090
$408$	−8.38284e18	+	2.42338e19i	−0.220516	+	0.637487i
$409$	3.19731e19			0.825771			0.412886	−	0.910783i	$-0.364521\pi$
$409$	3.19731e19			0.825771			0.412886	+	0.910783i	$0.364521\pi$
$410$	1.92061e19			0.487034
$411$			1.99455e19i			0.496628i
$412$	−9.47655e18			−0.231697
$413$		−	2.16243e18i		−	0.0519179i
$414$		−	1.05094e19i		−	0.247786i
$415$		−	5.17393e18i		−	0.119801i
$416$	2.82519e19			0.642462
$417$	−8.33946e17			−0.0186259
$418$		−	1.44637e20i		−	3.17291i
$419$			4.44369e19i			0.957500i	0.877951	+	0.478750i	$0.158910\pi$
$419$			4.44369e19i			0.957500i	−0.877951	+	0.478750i	$0.841090\pi$
$420$			3.81922e17i			0.00808361i
$421$	8.11320e19			1.68685			0.843425	−	0.537247i	$-0.180536\pi$
$421$	8.11320e19			1.68685			0.843425	+	0.537247i	$0.180536\pi$
$422$			3.05320e19i			0.623609i
$423$	4.12013e18			0.0826720
$424$	−4.51291e19			−0.889637
$425$	−4.53273e19	−	1.56794e19i	−0.877895	−	0.303677i
$426$	5.13925e19			0.977974
$427$	−6.63208e18			−0.124005
$428$		−	2.77518e19i		−	0.509873i
$429$	8.65365e19			1.56232
$430$		−	2.40987e18i		−	0.0427544i
$431$		−	4.27732e19i		−	0.745749i	−0.927882	−	0.372874i	$-0.878372\pi$
$431$		−	4.27732e19i		−	0.745749i	0.927882	−	0.372874i	$-0.121628\pi$
$432$		−	7.68110e19i		−	1.31612i
$433$	5.21848e19			0.878790			0.439395	−	0.898294i	$-0.355193\pi$
$433$	5.21848e19			0.878790			0.439395	+	0.898294i	$0.355193\pi$
$434$	1.47063e18			0.0243405
$435$			2.75693e18i			0.0448493i
$436$			4.34624e19i			0.694968i
$437$			1.07099e20i			1.68335i
$438$	9.95629e19			1.53830
$439$		−	6.16271e19i		−	0.936026i	−0.883722	−	0.468013i	$-0.844970\pi$
$439$		−	6.16271e19i		−	0.936026i	0.883722	−	0.468013i	$-0.155030\pi$
$440$	−2.46804e19			−0.368517
$441$	1.25540e19			0.184286
$442$	7.14754e19	+	2.47244e19i	1.03155	+	0.356828i
$443$	7.12278e19			1.01070			0.505349	−	0.862915i	$-0.331364\pi$
$443$	7.12278e19			1.01070			0.505349	+	0.862915i	$0.331364\pi$
$444$	−3.21180e19			−0.448102
$445$			2.28999e19i			0.314147i
$446$	1.17793e20			1.58894
$447$			5.78811e19i			0.767769i
$448$			3.09205e18i			0.0403331i
$449$		−	9.14405e19i		−	1.17298i	−0.809956	−	0.586491i	$-0.800509\pi$
$449$		−	9.14405e19i		−	1.17298i	0.809956	−	0.586491i	$-0.199491\pi$
$450$	1.59569e19			0.201305
$451$	−2.33592e20			−2.89823
$452$			1.74554e19i			0.213006i
$453$		−	5.40046e18i		−	0.0648178i
$454$		−	2.74689e19i		−	0.324281i
$455$	−2.01487e18			−0.0233970
$456$			8.69391e19i			0.993067i
$457$	−3.64721e19			−0.409817			−0.204908	−	0.978781i	$-0.565690\pi$
$457$	−3.64721e19			−0.409817			−0.204908	+	0.978781i	$0.565690\pi$
$458$	−1.71290e20			−1.89340
$459$	3.21670e19	−	9.29911e19i	0.349796	−	1.01122i
$460$	−1.02169e19			−0.109304
$461$	−4.67304e19			−0.491861			−0.245931	−	0.969287i	$-0.579094\pi$
$461$	−4.67304e19			−0.491861			−0.245931	+	0.969287i	$0.579094\pi$
$462$		−	1.75989e19i		−	0.182251i
$463$	6.11036e19			0.622600			0.311300	−	0.950312i	$-0.399236\pi$
$463$	6.11036e19			0.622600			0.311300	+	0.950312i	$0.399236\pi$
$464$		−	2.28762e19i		−	0.229350i
$465$		−	5.43252e18i		−	0.0535925i
$466$			2.34208e20i			2.27357i
$467$	−6.11265e19			−0.583919			−0.291960	−	0.956431i	$-0.594307\pi$
$467$	−6.11265e19			−0.583919			−0.291960	+	0.956431i	$0.594307\pi$
$468$	−6.64133e18			−0.0624325
$469$		−	4.21678e17i		−	0.00390107i
$470$		−	1.51754e19i		−	0.138168i
$471$		−	5.17472e19i		−	0.463692i
$472$	4.69589e19			0.414146
$473$			2.93098e19i			0.254422i
$474$	−7.27131e17			−0.00621262
$475$	−1.62612e20			−1.36757
$476$	1.32715e18	−	3.83665e18i	0.0109867	−	0.0317614i
$477$	2.71485e19			0.221237
$478$	−7.57907e19			−0.608004
$479$			1.28415e20i			1.01414i	0.861904	+	0.507071i	$0.169272\pi$
$479$			1.28415e20i			1.01414i	−0.861904	+	0.507071i	$0.830728\pi$
$480$	−2.12242e19			−0.165015
$481$		−	1.69442e20i		−	1.29698i
$482$		−	1.26241e20i		−	0.951363i
$483$			1.30313e19i			0.0966909i
$484$	−1.18733e20			−0.867421
$485$	1.78101e19			0.128116
$486$			6.03405e19i			0.427402i
$487$			7.26913e19i			0.507008i	0.967334	+	0.253504i	$0.0815831\pi$
$487$			7.26913e19i			0.507008i	−0.967334	+	0.253504i	$0.918417\pi$
$488$		−	1.44021e20i		−	0.989184i
$489$	1.91891e20			1.29789
$490$		−	4.62394e19i		−	0.307994i
$491$	−1.26347e20			−0.828810			−0.414405	−	0.910093i	$-0.636010\pi$
$491$	−1.26347e20			−0.828810			−0.414405	+	0.910093i	$0.636010\pi$
$492$	−7.84975e19			−0.507128
$493$	9.58013e18	−	2.76951e19i	0.0609564	−	0.176218i
$494$	2.56418e20			1.60693
$495$	1.48471e19			0.0916436
$496$			4.50775e19i			0.274061i
$497$	1.45535e19			0.0871552
$498$			8.01177e19i			0.472616i
$499$			2.43740e20i			1.41636i	0.706033	+	0.708179i	$0.250483\pi$
$499$			2.43740e20i			1.41636i	−0.706033	+	0.708179i	$0.749517\pi$
$500$		−	3.22122e19i		−	0.184393i
$501$	5.37534e19			0.303126
$502$	−3.11932e20			−1.73293
$503$			2.08924e20i			1.14348i	0.820435	+	0.571739i	$0.193731\pi$
$503$			2.08924e20i			1.14348i	−0.820435	+	0.571739i	$0.806269\pi$
$504$		−	2.41589e18i		−	0.0130271i
$505$		−	4.36237e19i		−	0.231759i
$506$	4.70792e20			2.46434
$507$		−	2.15263e19i		−	0.111022i
$508$	−4.40434e18			−0.0223822
$509$	−1.08950e19			−0.0545562			−0.0272781	−	0.999628i	$-0.508684\pi$
$509$	−1.08950e19			−0.0545562			−0.0272781	+	0.999628i	$0.508684\pi$
$510$	−5.36959e19	−	1.85742e19i	−0.264951	−	0.0916502i
$511$	2.81945e19			0.137091
$512$	−1.58031e19			−0.0757214
$513$		−	3.33606e20i		−	1.57527i
$514$	4.37295e19			0.203494
$515$			3.75583e19i			0.172247i
$516$			9.84944e18i			0.0445183i
$517$			1.84570e20i			0.822208i
$518$	−3.44592e19			−0.151298
$519$	−3.09204e20			−1.33810
$520$		−	4.37544e19i		−	0.186637i
$521$		−	2.07731e20i		−	0.873410i	−0.899605	−	0.436705i	$-0.856145\pi$
$521$		−	2.07731e20i		−	0.873410i	0.899605	−	0.436705i	$-0.143855\pi$
$522$			9.74969e18i			0.0404075i
$523$	1.82294e20			0.744747			0.372374	−	0.928083i	$-0.378544\pi$
$523$	1.82294e20			0.744747			0.372374	+	0.928083i	$0.378544\pi$
$524$			6.26406e19i			0.252273i
$525$	−1.97860e19			−0.0785530
$526$	−2.95302e20			−1.15578
$527$	−1.88776e19	+	5.45731e19i	−0.0728396	+	0.210571i
$528$	5.39439e20			2.05205
$529$	−8.19702e19			−0.307424
$530$		−	9.99944e19i		−	0.369749i
$531$	−2.82493e19			−0.102991
$532$		−	1.37640e19i		−	0.0494775i
$533$		−	4.14121e20i		−	1.46782i
$534$		−	3.54602e20i		−	1.23931i
$535$	−1.09988e20			−0.379047
$536$	9.15706e18			0.0311186
$537$			2.92783e20i			0.981156i
$538$		−	4.44343e20i		−	1.46842i
$539$			5.62383e20i			1.83281i
$540$	3.18251e19			0.102286
$541$			1.00103e20i			0.317298i	0.987335	+	0.158649i	$0.0507137\pi$
$541$			1.00103e20i			0.317298i	−0.987335	+	0.158649i	$0.949286\pi$
$542$	5.01464e20			1.56764
$543$	−3.57824e20			−1.10324
$544$	2.13211e20	+	7.37527e19i	0.648361	+	0.224278i
$545$	1.72254e20			0.516649
$546$	3.12000e19			0.0923016
$547$		−	2.91955e20i		−	0.851943i	−0.904737	−	0.425971i	$-0.859932\pi$
$547$		−	2.91955e20i		−	0.851943i	0.904737	−	0.425971i	$-0.140068\pi$
$548$	6.85725e19			0.197377
$549$			8.66392e19i			0.245993i
$550$			7.14821e20i			2.00206i
$551$		−	9.93563e19i		−	0.274510i
$552$	−2.82986e20			−0.771297
$553$	−2.05911e17			−0.000553657
$554$		−	5.83188e19i		−	0.154698i
$555$			1.27293e20i			0.333125i
$556$			2.86710e18i			0.00740257i
$557$	6.35909e20			1.61987			0.809937	−	0.586517i	$-0.199501\pi$
$557$	6.35909e20			1.61987			0.809937	+	0.586517i	$0.199501\pi$
$558$		−	1.92117e19i		−	0.0482848i
$559$	−5.19617e19			−0.128853
$560$	−1.25600e19			−0.0307312
$561$	6.53071e20	+	2.25907e20i	1.57666	+	0.545391i
$562$	−2.68491e20			−0.639599
$563$	−4.05594e20			−0.953406			−0.476703	−	0.879064i	$-0.658168\pi$
$563$	−4.05594e20			−0.953406			−0.476703	+	0.879064i	$0.658168\pi$
$564$			6.20239e19i			0.143869i
$565$	6.91809e19			0.158352
$566$		−	2.77308e20i		−	0.626382i
$567$		−	3.27749e19i		−	0.0730580i
$568$			3.16040e20i			0.695231i
$569$	−6.97011e20			−1.51320			−0.756602	−	0.653875i	$-0.773142\pi$
$569$	−6.97011e20			−1.51320			−0.756602	+	0.653875i	$0.773142\pi$
$570$	−1.92634e20			−0.412736
$571$		−	5.09913e20i		−	1.07826i	−0.842221	−	0.539132i	$-0.818752\pi$
$571$		−	5.09913e20i		−	1.07826i	0.842221	−	0.539132i	$-0.181248\pi$
$572$		−	2.97512e20i		−	0.620918i
$573$		−	6.98607e20i		−	1.43904i
$574$	−8.42195e19			−0.171228
$575$		−	5.29300e20i		−	1.06217i
$576$	4.03935e19			0.0800097
$577$	6.60915e19			0.129219			0.0646096	−	0.997911i	$-0.479420\pi$
$577$	6.60915e19			0.129219			0.0646096	+	0.997911i	$0.479420\pi$
$578$	4.74865e20	+	3.73179e20i	0.916455	+	0.720208i
$579$	1.25796e20			0.239649
$580$	9.47831e18			0.0178246
$581$			2.26880e19i			0.0421187i
$582$	−2.75787e20			−0.505420
$583$			1.21617e21i			2.20030i
$584$			6.12266e20i			1.09356i
$585$			2.63215e19i			0.0464132i
$586$	−1.18266e21			−2.05886
$587$	−3.12962e20			−0.537905			−0.268953	−	0.963153i	$-0.586677\pi$
$587$	−3.12962e20			−0.537905			−0.268953	+	0.963153i	$0.586677\pi$
$588$			1.88986e20i			0.320701i
$589$			1.95781e20i			0.328025i
$590$			1.04049e20i			0.172126i
$591$	−6.54922e20			−1.06975
$592$		−	1.05624e21i		−	1.70353i
$593$	8.01166e20			1.27589			0.637944	−	0.770083i	$-0.279785\pi$
$593$	8.01166e20			1.27589			0.637944	+	0.770083i	$0.279785\pi$
$594$	−1.46649e21			−2.30612
$595$	−1.52058e19	−	5.25989e18i	−0.0236119	−	0.00816769i
$596$	1.98995e20			0.305137
$597$	−1.18021e20			−0.178712
$598$			8.34640e20i			1.24807i
$599$	−2.74198e20			−0.404914			−0.202457	−	0.979291i	$-0.564893\pi$
$599$	−2.74198e20			−0.404914			−0.202457	+	0.979291i	$0.564893\pi$
$600$		−	4.29668e20i		−	0.626612i
$601$		−	4.68601e20i		−	0.674908i	−0.941342	−	0.337454i	$-0.890434\pi$
$601$		−	4.68601e20i		−	0.674908i	0.941342	−	0.337454i	$-0.109566\pi$
$602$			1.05674e19i			0.0150312i
$603$	−5.50865e18			−0.00773865
$604$	−1.85668e19			−0.0257608
$605$			4.70572e20i			0.644853i
$606$			6.75508e20i			0.914294i
$607$		−	6.63189e20i		−	0.886588i	−0.896376	−	0.443294i	$-0.853810\pi$
$607$		−	6.63189e20i		−	0.886588i	0.896376	−	0.443294i	$-0.146190\pi$
$608$	7.64895e20			1.01001
$609$		−	1.20893e19i		−	0.0157678i
$610$	3.19113e20			0.411122
$611$	−3.27213e20			−0.416410
$612$	−5.01206e19	−	1.73375e19i	−0.0630058	−	0.0217946i
$613$	9.10398e20			1.13052			0.565259	−	0.824913i	$-0.308776\pi$
$613$	9.10398e20			1.13052			0.565259	+	0.824913i	$0.308776\pi$
$614$	−1.13177e21			−1.38834
$615$			3.11109e20i			0.377006i
$616$	1.08225e20			0.129560
$617$			7.26028e20i			0.858647i	0.903151	+	0.429323i	$0.141248\pi$
$617$			7.26028e20i			0.858647i	−0.903151	+	0.429323i	$0.858752\pi$
$618$		−	5.81586e20i		−	0.679517i
$619$		−	1.07213e21i		−	1.23757i	−0.785561	−	0.618785i	$-0.787625\pi$
$619$		−	1.07213e21i		−	1.23757i	0.785561	−	0.618785i	$-0.212375\pi$
$620$	−1.86770e19			−0.0212995
$621$	1.08589e21			1.22348
$622$			8.24221e20i			0.917521i
$623$		−	1.00417e20i		−	0.110445i
$624$			9.56340e20i			1.03927i
$625$	7.37471e20			0.791854
$626$		−	2.00109e20i		−	0.212305i
$627$	2.34290e21			2.45610
$628$	−1.77906e20			−0.184287
$629$	4.42334e20	−	1.27874e21i	0.452763	−	1.30889i
$630$	5.35299e18			0.00541430
$631$	1.44214e21			1.44140			0.720702	−	0.693245i	$-0.243820\pi$
$631$	1.44214e21			1.44140			0.720702	+	0.693245i	$0.243820\pi$
$632$		−	4.47152e18i		−	0.00441649i
$633$	−4.94572e20			−0.482727
$634$		−	1.57133e21i		−	1.51565i
$635$			1.74557e19i			0.0166392i
$636$			4.08690e20i			0.385004i
$637$	−9.97015e20			−0.928231
$638$	−4.36757e20			−0.401870
$639$		−	1.90121e20i		−	0.172892i
$640$		−	3.52267e20i		−	0.316608i
$641$		−	1.13948e21i		−	1.01221i	−0.862472	−	0.506105i	$-0.831085\pi$
$641$		−	1.13948e21i		−	1.01221i	0.862472	−	0.506105i	$-0.168915\pi$
$642$	1.70316e21			1.49535
$643$			1.15760e21i			1.00456i	0.864705	+	0.502280i	$0.167505\pi$
$643$			1.15760e21i			1.00456i	−0.864705	+	0.502280i	$0.832495\pi$
$644$	4.48017e19			0.0384282
$645$	3.90362e19			0.0330956
$646$	1.93513e21	+	6.69391e20i	1.62169	+	0.560965i
$647$	3.12009e20			0.258455			0.129228	−	0.991615i	$-0.458750\pi$
$647$	3.12009e20			0.258455			0.129228	+	0.991615i	$0.458750\pi$
$648$	7.11732e20			0.582779
$649$		−	1.26548e21i		−	1.02429i
$650$	−1.26726e21			−1.01395
$651$			2.38219e19i			0.0188416i
$652$		−	6.59719e20i		−	0.515825i
$653$			1.75559e21i			1.35698i	0.734607	+	0.678492i	$0.237366\pi$
$653$			1.75559e21i			1.35698i	−0.734607	+	0.678492i	$0.762634\pi$
$654$	−2.66733e21			−2.03819
$655$	2.48263e20			0.187543
$656$		−	2.58149e21i		−	1.92793i
$657$		−	3.68323e20i		−	0.271950i
$658$			6.65451e19i			0.0485760i
$659$	−2.63854e21			−1.90424			−0.952122	−	0.305719i	$-0.901103\pi$
$659$	−2.63854e21			−1.90424			−0.952122	+	0.305719i	$0.901103\pi$
$660$			2.23506e20i			0.159481i
$661$	1.86081e21			1.31278			0.656389	−	0.754423i	$-0.272083\pi$
$661$	1.86081e21			1.31278			0.656389	+	0.754423i	$0.272083\pi$
$662$	−7.59396e19			−0.0529704
$663$	−4.00497e20	+	1.15779e21i	−0.276215	+	0.798507i
$664$	−4.92687e20			−0.335978
$665$	−5.45507e19			−0.0367823
$666$			4.50164e20i			0.300133i
$667$	3.23404e20			0.213207
$668$		−	1.84804e20i		−	0.120472i
$669$			1.90807e21i			1.22998i
$670$			2.02897e19i			0.0129334i
$671$	−3.88118e21			−2.44650
$672$	9.30693e19			0.0580146
$673$		−	1.35743e19i		−	0.00836766i	−0.999991	−	0.00418383i	$-0.998668\pi$
$673$		−	1.35743e19i		−	0.00836766i	0.999991	−	0.00418383i	$-0.00133176\pi$
$674$			1.47551e21i			0.899485i
$675$			1.64874e21i			0.993972i
$676$	−7.40074e19			−0.0441240
$677$			2.69137e21i			1.58693i	0.608613	+	0.793467i	$0.291726\pi$
$677$			2.69137e21i			1.58693i	−0.608613	+	0.793467i	$0.708274\pi$
$678$	−1.07126e21			−0.624700
$679$	−7.80982e19			−0.0450420
$680$	1.14223e20	−	3.30205e20i	0.0651532	−	0.188350i
$681$	4.44954e20			0.251022
$682$	8.60629e20			0.480212
$683$		−	1.57044e20i		−	0.0866693i	−0.999061	−	0.0433346i	$-0.986202\pi$
$683$		−	1.57044e20i		−	0.0866693i	0.999061	−	0.0433346i	$-0.0137982\pi$
$684$	−1.79808e20			−0.0981496
$685$		−	2.71773e20i		−	0.146733i
$686$			4.07321e20i			0.217524i
$687$		−	2.77464e21i		−	1.46565i
$688$	−3.23912e20			−0.169244
$689$	−2.15608e21			−1.11435
$690$		−	6.27023e20i		−	0.320565i
$691$			4.10933e19i			0.0207819i	0.999946	+	0.0103910i	$0.00330760\pi$
$691$			4.10933e19i			0.0207819i	−0.999946	+	0.0103910i	$0.996692\pi$
$692$			1.06304e21i			0.531807i
$693$	−6.51052e19			−0.0322193
$694$			1.71650e21i			0.840324i
$695$	1.13632e19			0.00550318
$696$	2.62528e20			0.125779
$697$	1.08108e21	−	3.12528e21i	0.512403	−	1.48130i
$698$	2.73783e21			1.28378
$699$	−3.79382e21			−1.75994
$700$			6.80241e19i			0.0312196i
$701$	−3.12194e21			−1.41755			−0.708776	−	0.705434i	$-0.750752\pi$
$701$	−3.12194e21			−1.41755			−0.708776	+	0.705434i	$0.750752\pi$
$702$		−	2.59986e21i		−	1.16794i
$703$		−	4.58749e21i		−	2.03897i
$704$			1.80951e21i			0.795730i
$705$	2.45819e20			0.106954
$706$	1.65015e21			0.710377
$707$			1.91292e20i			0.0814802i
$708$		−	4.25260e20i		−	0.179228i
$709$			4.55049e21i			1.89763i	0.315833	+	0.948815i	$0.397716\pi$
$709$			4.55049e21i			1.89763i	−0.315833	+	0.948815i	$0.602284\pi$
$710$	−7.00262e20			−0.288950
$711$			2.68995e18i			0.00109830i
$712$	2.18064e21			0.881015
$713$	−6.37266e20			−0.254771
$714$	2.35459e20	+	8.14488e19i	0.0931492	+	0.0322217i
$715$	−1.17913e21			−0.461599
$716$	1.00659e21			0.389945
$717$		−	1.22769e21i		−	0.470648i
$718$	3.59681e21			1.36453
$719$			1.72404e21i			0.647263i	0.946183	+	0.323631i	$0.104904\pi$
$719$			1.72404e21i			0.647263i	−0.946183	+	0.323631i	$0.895096\pi$
$720$			1.64079e20i			0.0609622i
$721$		−	1.64695e20i		−	0.0605573i
$722$	3.73918e21			1.36065
$723$	2.04490e21			0.736437
$724$			1.23020e21i			0.438465i
$725$			4.91036e20i			0.173212i
$726$		−	7.28675e21i		−	2.54395i
$727$	4.94200e21			1.70763			0.853817	−	0.520574i	$-0.174282\pi$
$727$	4.94200e21			1.70763			0.853817	+	0.520574i	$0.174282\pi$
$728$			1.91865e20i			0.0656162i
$729$	−3.28035e21			−1.11036
$730$	−1.35662e21			−0.454504
$731$	−3.92143e20	−	1.35648e20i	−0.130036	−	0.0449814i
$732$	−1.30425e21			−0.428084
$733$	−1.34477e21			−0.436886			−0.218443	−	0.975850i	$-0.570098\pi$
$733$	−1.34477e21			−0.436886			−0.218443	+	0.975850i	$0.570098\pi$
$734$			1.74033e21i			0.559644i
$735$	7.49008e20			0.238414
$736$			2.48973e21i			0.784455i
$737$		−	2.46771e20i		−	0.0769641i
$738$			1.10021e21i			0.339668i
$739$	5.30890e20			0.162245			0.0811225	−	0.996704i	$-0.474149\pi$
$739$	5.30890e20			0.162245			0.0811225	+	0.996704i	$0.474149\pi$
$740$	4.37633e20			0.132395
$741$			4.15359e21i			1.24390i
$742$			4.38481e20i			0.129993i
$743$		−	8.20160e20i		−	0.240704i	−0.992731	−	0.120352i	$-0.961598\pi$
$743$		−	8.20160e20i		−	0.240704i	0.992731	−	0.120352i	$-0.0384023\pi$
$744$	−5.17311e20			−0.150298
$745$		−	7.88675e20i		−	0.226843i
$746$	2.95060e21			0.840174
$747$	2.96388e20			0.0835518
$748$	7.76667e20	−	2.24526e21i	0.216757	−	0.626619i
$749$	4.82305e20			0.133262
$750$	1.97690e21			0.540785
$751$			2.25967e21i			0.611992i	0.952033	+	0.305996i	$0.0989894\pi$
$751$			2.25967e21i			0.611992i	−0.952033	+	0.305996i	$0.901011\pi$
$752$	−2.03974e21			−0.546940
$753$		−	5.05282e21i		−	1.34144i
$754$		−	7.74302e20i		−	0.203528i
$755$			7.35855e19i			0.0191509i
$756$	−1.39555e20			−0.0359609
$757$	−3.67737e21			−0.938250			−0.469125	−	0.883132i	$-0.655431\pi$
$757$	−3.67737e21			−0.938250			−0.469125	+	0.883132i	$0.655431\pi$
$758$		−	6.86030e21i		−	1.73310i
$759$			7.62611e21i			1.90761i
$760$		−	1.18461e21i		−	0.293410i
$761$	−1.72047e21			−0.421952			−0.210976	−	0.977491i	$-0.567664\pi$
$761$	−1.72047e21			−0.421952			−0.210976	+	0.977491i	$0.567664\pi$
$762$		−	2.70299e20i		−	0.0656420i
$763$	−7.55343e20			−0.181639
$764$	−2.40181e21			−0.571924
$765$	−6.87134e19	+	1.98643e20i	−0.0162024	+	0.0468394i
$766$	−9.56341e20			−0.223304
$767$	2.24350e21			0.518753
$768$			3.75907e21i			0.860738i
$769$	−1.33781e21			−0.303353			−0.151676	−	0.988430i	$-0.548467\pi$
$769$	−1.33781e21			−0.303353			−0.151676	+	0.988430i	$0.548467\pi$
$770$			2.39798e20i			0.0538475i
$771$			7.08350e20i			0.157522i
$772$		−	4.32485e20i		−	0.0952448i
$773$	5.15657e21			1.12464			0.562321	−	0.826919i	$-0.309908\pi$
$773$	5.15657e21			1.12464			0.562321	+	0.826919i	$0.309908\pi$
$774$	1.38049e20			0.0298178
$775$		−	9.67585e20i		−	0.206979i
$776$		−	1.69597e21i		−	0.359297i
$777$		−	5.58187e20i		−	0.117118i
$778$	7.54675e20			0.156824
$779$		−	1.12120e22i		−	2.30755i
$780$	−3.96240e20			−0.0807698
$781$	8.51687e21			1.71948
$782$	−2.17886e21	+	6.29884e21i	−0.435691	+	1.25953i
$783$	−1.00738e21			−0.199518
$784$	−6.21506e21			−1.21920
$785$			7.05095e20i			0.137001i
$786$	−3.84432e21			−0.739862
$787$			1.00238e22i			1.91083i	0.295269	+	0.955414i	$0.404591\pi$
$787$			1.00238e22i			1.91083i	−0.295269	+	0.955414i	$0.595409\pi$
$788$			2.25162e21i			0.425156i
$789$		−	4.78345e21i		−	0.894671i
$790$	9.90772e18			0.00183557
$791$	−3.03362e20			−0.0556721
$792$		−	1.41381e21i		−	0.257012i
$793$		−	6.88072e21i		−	1.23904i
$794$			2.78734e21i			0.497207i
$795$	1.61976e21			0.286217
$796$			4.05756e20i			0.0710260i
$797$	−3.38385e21			−0.586777			−0.293389	−	0.955993i	$-0.594783\pi$
$797$	−3.38385e21			−0.586777			−0.293389	+	0.955993i	$0.594783\pi$
$798$	8.44712e20			0.145107
$799$	−2.46940e21	−	8.54203e20i	−0.420234	−	0.145365i
$800$	−3.78024e21			−0.637301
$801$	−1.31181e21			−0.219093
$802$		−	5.23965e21i		−	0.866951i
$803$	1.64998e22			2.70466
$804$		−	8.29264e19i		−	0.0134671i
$805$		−	1.77562e20i		−	0.0285681i
$806$			1.52576e21i			0.243205i
$807$	7.19768e21			1.13669
$808$	−4.15406e21			−0.649962
$809$			7.46643e21i			1.15744i	0.815526	+	0.578721i	$0.196448\pi$
$809$			7.46643e21i			1.15744i	−0.815526	+	0.578721i	$0.803552\pi$
$810$			1.57701e21i			0.242213i
$811$			8.30946e21i			1.26449i	0.774767	+	0.632247i	$0.217867\pi$
$811$			8.30946e21i			1.26449i	−0.774767	+	0.632247i	$0.782133\pi$
$812$	−4.15629e19			−0.00626665
$813$			8.12295e21i			1.21349i
$814$	−2.01660e22			−2.98495
$815$	−2.61466e21			−0.383472
$816$	−2.49656e21	+	7.21728e21i	−0.362799	+	1.04881i
$817$	−1.40682e21			−0.202569
$818$	6.74611e21			0.962507
$819$		−	1.15421e20i		−	0.0163176i
$820$	1.06959e21			0.149835
$821$		−	6.58567e21i		−	0.914168i	−0.889423	−	0.457084i	$-0.848894\pi$
$821$		−	6.58567e21i		−	0.914168i	0.889423	−	0.457084i	$-0.151106\pi$
$822$			4.20837e21i			0.578863i
$823$		−	5.96579e21i		−	0.813147i	−0.913618	−	0.406574i	$-0.866723\pi$
$823$		−	5.96579e21i		−	0.813147i	0.913618	−	0.406574i	$-0.133277\pi$
$824$	3.57649e21			0.483062
$825$	−1.15790e22			−1.54977
$826$		−	4.56259e20i		−	0.0605147i
$827$		−	1.02066e22i		−	1.34150i	−0.741682	−	0.670751i	$-0.765972\pi$
$827$		−	1.02066e22i		−	1.34150i	0.741682	−	0.670751i	$-0.234028\pi$
$828$		−	5.85274e20i		−	0.0762310i
$829$	−1.04079e22			−1.34340			−0.671698	−	0.740825i	$-0.734435\pi$
$829$	−1.04079e22			−1.34340			−0.671698	+	0.740825i	$0.734435\pi$
$830$		−	1.09167e21i		−	0.139638i
$831$	9.44675e20			0.119750
$832$	−3.20797e21			−0.403000
$833$	−7.52425e21	−	2.60275e21i	−0.936755	−	0.324037i
$834$	−1.75957e20			−0.0217101
$835$	−7.32432e20			−0.0895610
$836$		−	8.05487e21i		−	0.976139i
$837$	1.98505e21			0.238413
$838$			9.37591e21i			1.11605i
$839$		−	1.00697e21i		−	0.118796i	−0.998234	−	0.0593982i	$-0.981082\pi$
$839$		−	1.00697e21i		−	0.118796i	0.998234	−	0.0593982i	$-0.0189182\pi$
$840$		−	1.44139e20i		−	0.0168534i
$841$	8.32916e21			0.965231
$842$	1.71183e22			1.96617
$843$		−	4.34915e21i		−	0.495105i
$844$			1.70034e21i			0.191852i
$845$			2.93313e20i			0.0328024i
$846$	8.69322e20			0.0963613
$847$		−	2.06348e21i		−	0.226712i
$848$	−1.34403e22			−1.46366
$849$	4.49197e21			0.484874
$850$	−9.56376e21	−	3.30824e21i	−1.02326	−	0.353961i
$851$	1.49322e22			1.58363
$852$	2.86206e21			0.300872
$853$		−	7.19853e21i		−	0.750112i	−0.927002	−	0.375056i	$-0.877623\pi$
$853$		−	7.19853e21i		−	0.750112i	0.927002	−	0.375056i	$-0.122377\pi$
$854$	−1.39933e21			−0.144539
$855$			7.12632e20i			0.0729658i
$856$			1.04736e22i			1.06303i
$857$			8.59452e21i			0.864700i	0.901706	+	0.432350i	$0.142315\pi$
$857$			8.59452e21i			0.864700i	−0.901706	+	0.432350i	$0.857685\pi$
$858$	1.82586e22			1.82102
$859$	2.81235e21			0.278048			0.139024	−	0.990289i	$-0.455603\pi$
$859$	2.81235e21			0.278048			0.139024	+	0.990289i	$0.455603\pi$
$860$		−	1.34206e20i		−	0.0131533i
$861$		−	1.36423e21i		−	0.132545i
$862$		−	9.02488e21i		−	0.869234i
$863$	8.90990e21			0.850730			0.425365	−	0.905022i	$-0.360146\pi$
$863$	8.90990e21			0.850730			0.425365	+	0.905022i	$0.360146\pi$
$864$		−	7.75535e21i		−	0.734089i
$865$	4.21314e21			0.395353
$866$	1.10107e22			1.02430
$867$	−6.04492e21	+	7.69208e21i	−0.557503	+	0.709416i
$868$	8.18995e19			0.00748830
$869$	−1.20502e20			−0.0109231
$870$			5.81694e20i			0.0522758i
$871$	4.37486e20			0.0389788
$872$		−	1.64029e22i		−	1.44893i
$873$			1.02025e21i			0.0893509i
$874$			2.25971e22i			1.96208i
$875$	5.59823e20			0.0481937
$876$	5.54469e21			0.473256
$877$			8.59019e21i			0.726952i	0.931604	+	0.363476i	$0.118410\pi$
$877$			8.59019e21i			0.726952i	−0.931604	+	0.363476i	$0.881590\pi$
$878$		−	1.30029e22i		−	1.09102i
$879$		−	1.91572e22i		−	1.59374i
$880$	−7.35027e21			−0.606294
$881$			7.99455e21i			0.653845i	0.945051	+	0.326922i	$0.106012\pi$
$881$			7.99455e21i			0.653845i	−0.945051	+	0.326922i	$0.893988\pi$
$882$	2.64882e21			0.214802
$883$	1.00885e22			0.811185			0.405593	−	0.914054i	$-0.367065\pi$
$883$	1.00885e22			0.811185			0.405593	+	0.914054i	$0.367065\pi$
$884$	3.98048e21	+	1.37691e21i	0.317354	+	0.109777i
$885$	−1.68543e21			−0.133240
$886$	1.50286e22			1.17805
$887$			1.86593e22i			1.45034i	0.688572	+	0.725168i	$0.258238\pi$
$887$			1.86593e22i			1.45034i	−0.688572	+	0.725168i	$0.741762\pi$
$888$	1.21215e22			0.934239
$889$		−	7.65440e19i		−	0.00584989i
$890$			4.83172e21i			0.366165i
$891$		−	1.91803e22i		−	1.44136i
$892$	6.55993e21			0.488835
$893$	−8.85900e21			−0.654635
$894$			1.22125e22i			0.894900i
$895$		−	3.98939e21i		−	0.289890i
$896$			1.54471e21i			0.111311i
$897$	−1.35199e22			−0.966117
$898$		−	1.92934e22i		−	1.36721i
$899$	5.91197e20			0.0415465
$900$	8.88643e20			0.0619310
$901$	−1.62715e22	−	5.62854e21i	−1.12458	−	0.389009i
$902$	−4.92864e22			−3.37814
$903$	−1.71176e20			−0.0116355
$904$		−	6.58775e21i		−	0.444093i
$905$	4.87563e21			0.325961
$906$		−	1.13946e21i		−	0.0755507i
$907$		−	1.25032e22i		−	0.822178i	−0.911595	−	0.411089i	$-0.865149\pi$
$907$		−	1.25032e22i		−	0.822178i	0.911595	−	0.411089i	$-0.134851\pi$
$908$		−	1.52975e21i		−	0.0997646i
$909$	2.49898e21			0.161634
$910$	−4.25124e20			−0.0272713
$911$			2.47909e22i			1.57727i	0.614865	+	0.788633i	$0.289211\pi$
$911$			2.47909e22i			1.57727i	−0.614865	+	0.788633i	$0.710789\pi$
$912$			2.58921e22i			1.63382i
$913$			1.32773e22i			0.830957i
$914$	−7.69539e21			−0.477677
$915$			5.16914e21i			0.318244i
$916$	−9.53920e21			−0.582500
$917$	−1.08865e21			−0.0659351
$918$	6.78703e21	−	1.96205e22i	0.407718	−	1.17867i
$919$	−1.80309e22			−1.07437			−0.537183	−	0.843466i	$-0.680512\pi$
$919$	−1.80309e22			−1.07437			−0.537183	+	0.843466i	$0.680512\pi$
$920$	3.85590e21			0.227886
$921$		−	1.83329e22i		−	1.07469i
$922$	−9.85981e21			−0.573306
$923$			1.50991e22i			0.870838i
$924$		−	9.80085e20i		−	0.0560691i
$925$			2.26721e22i			1.28656i
$926$	1.28925e22			0.725694
$927$	−2.15152e21			−0.120129
$928$		−	2.30974e21i		−	0.127924i
$929$		−	1.11152e22i		−	0.610660i	−0.952247	−	0.305330i	$-0.901233\pi$
$929$		−	1.11152e22i		−	0.610660i	0.952247	−	0.305330i	$-0.0987668\pi$
$930$		−	1.14623e21i		−	0.0624667i
$931$	−2.69933e22			−1.45926
$932$			1.30431e22i			0.699459i
$933$	−1.33511e22			−0.710240
$934$	−1.28973e22			−0.680608
$935$	−8.89860e21	−	3.07816e21i	−0.465838	−	0.161140i
$936$	2.50646e21			0.130164
$937$	−1.81126e22			−0.933113			−0.466557	−	0.884491i	$-0.654506\pi$
$937$	−1.81126e22			−0.933113			−0.466557	+	0.884491i	$0.654506\pi$
$938$		−	8.89713e19i		−	0.00454704i
$939$	3.24147e21			0.164342
$940$		−	8.45124e20i		−	0.0425071i
$941$		−	1.63943e22i		−	0.818034i	−0.912527	−	0.409017i	$-0.865872\pi$
$941$		−	1.63943e22i		−	0.818034i	0.912527	−	0.409017i	$-0.134128\pi$
$942$		−	1.09183e22i		−	0.540473i
$943$	3.64949e22			1.79223
$944$	1.39852e22			0.681364
$945$			5.53096e20i			0.0267339i
$946$			6.18419e21i			0.296551i
$947$			7.77498e21i			0.369892i	0.982749	+	0.184946i	$0.0592109\pi$
$947$			7.77498e21i			0.369892i	−0.982749	+	0.184946i	$0.940789\pi$
$948$	−4.04941e19			−0.00191130
$949$			2.92515e22i			1.36978i
$950$	−3.43101e22			−1.59402
$951$	2.54532e22			1.17324
$952$	−5.00872e20	+	1.44797e21i	−0.0229060	+	0.0662188i
$953$	9.62643e21			0.436786			0.218393	−	0.975861i	$-0.429919\pi$
$953$	9.62643e21			0.436786			0.218393	+	0.975861i	$0.429919\pi$
$954$	5.72816e21			0.257871
$955$			9.51906e21i			0.425176i
$956$	−4.22080e21			−0.187051
$957$		−	7.07480e21i		−	0.311082i
$958$			2.70947e22i			1.18207i
$959$			1.19174e21i			0.0515871i
$960$	2.40999e21			0.103510
$961$	2.23003e22			0.950354
$962$		−	3.57511e22i		−	1.51174i
$963$		−	6.30066e21i		−	0.264356i
$964$		−	7.03037e21i		−	0.292685i
$965$	−1.71406e21			−0.0708063
$966$			2.74953e21i			0.112702i
$967$	3.49000e22			1.41947			0.709737	−	0.704467i	$-0.248814\pi$
$967$	3.49000e22			1.41947			0.709737	+	0.704467i	$0.248814\pi$
$968$	4.48101e22			1.80847
$969$	−1.08431e22	+	3.13462e22i	−0.434235	+	1.25533i
$970$	3.75782e21			0.149330
$971$	1.97300e21			0.0778005			0.0389003	−	0.999243i	$-0.487615\pi$
$971$	1.97300e21			0.0778005			0.0389003	+	0.999243i	$0.487615\pi$
$972$			3.36038e21i			0.131490i
$973$	−4.98281e19			−0.00193476
$974$			1.53374e22i			0.590962i
$975$		−	2.05277e22i		−	0.784886i
$976$		−	4.28921e22i		−	1.62743i
$977$	−2.48666e22			−0.936284			−0.468142	−	0.883653i	$-0.655077\pi$
$977$	−2.48666e22			−0.936284			−0.468142	+	0.883653i	$0.655077\pi$
$978$	4.04877e22			1.51280
$979$		−	5.87654e22i		−	2.17897i
$980$		−	2.57509e21i		−	0.0947537i
$981$			9.86754e21i			0.360322i
$982$	−2.66585e22			−0.966049
$983$		−	4.51617e22i		−	1.62412i	−0.583572	−	0.812062i	$-0.698345\pi$
$983$		−	4.51617e22i		−	1.62412i	0.583572	−	0.812062i	$-0.301655\pi$
$984$	2.96253e22			1.05730
$985$	8.92383e21			0.316067
$986$	2.02135e21	−	5.84348e21i	0.0710499	−	0.205397i
$987$	−1.07793e21			−0.0376020
$988$	1.42800e22			0.494369
$989$		−	4.57918e21i		−	0.157331i
$990$	3.13264e21			0.106818
$991$		−	2.95987e22i		−	1.00166i	−0.865546	−	0.500830i	$-0.833028\pi$
$991$		−	2.95987e22i		−	1.00166i	0.865546	−	0.500830i	$-0.166972\pi$
$992$			4.55133e21i			0.152862i
$993$		−	1.23011e21i		−	0.0410037i
$994$	3.07069e21			0.101587
$995$	1.60813e21			0.0528018
$996$			4.46178e21i			0.145399i
$997$			3.11272e22i			1.00676i	0.864065	+	0.503380i	$0.167910\pi$
$997$			3.11272e22i			1.00676i	−0.864065	+	0.503380i	$0.832090\pi$
$998$			5.14276e22i			1.65089i
$999$	−4.65130e22			−1.48195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.16.b.a.16.17	✓	22
17.16	even	2	inner	17.16.b.a.16.18	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.16.b.a.16.17	✓	22	1.1	even	1	trivial
17.16.b.a.16.18	yes	22	17.16	even	2	inner

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+210.994 q^{2} +3417.77i q^{3} +11750.3 q^{4} -46569.8i q^{5} +721128. i q^{6} +204211. i q^{7} -4.43460e6 q^{8} +2.66774e6 q^{9} +O(q^{10})\)	\(q+210.994 q^{2} +3417.77i q^{3} +11750.3 q^{4} -46569.8i q^{5} +721128. i q^{6} +204211. i q^{7} -4.43460e6 q^{8} +2.66774e6 q^{9} -9.82593e6i q^{10} +1.19507e8i q^{11} +4.01598e7i q^{12} -2.11867e8 q^{13} +4.30872e7i q^{14} +1.59165e8 q^{15} -1.32071e9 q^{16} +(-1.59891e9 - 5.53087e8i) q^{17} +5.62876e8 q^{18} -5.73611e9 q^{19} -5.47208e8i q^{20} -6.97947e8 q^{21} +2.52152e10i q^{22} -1.86710e10i q^{23} -1.51565e10i q^{24} +2.83488e10 q^{25} -4.47025e10 q^{26} +5.81590e10i q^{27} +2.39954e9i q^{28} +1.73212e10i q^{29} +3.35828e10 q^{30} -3.41314e10i q^{31} -1.33347e11 q^{32} -4.08447e11 q^{33} +(-3.37360e11 - 1.16698e11i) q^{34} +9.51006e9 q^{35} +3.13467e10 q^{36} +7.99756e11i q^{37} -1.21028e12 q^{38} -7.24112e11i q^{39} +2.06519e11i q^{40} +1.95463e12i q^{41} -1.47262e11 q^{42} +2.45256e11 q^{43} +1.40424e12i q^{44} -1.24236e11i q^{45} -3.93946e12i q^{46} +1.54443e12 q^{47} -4.51387e12i q^{48} +4.70586e12 q^{49} +5.98142e12 q^{50} +(1.89032e12 - 5.46472e12i) q^{51} -2.48950e12 q^{52} +1.01766e13 q^{53} +1.22712e13i q^{54} +5.56541e12 q^{55} -9.05595e11i q^{56} -1.96047e13i q^{57} +3.65466e12i q^{58} -1.05892e13 q^{59} +1.87023e12 q^{60} +3.24766e13i q^{61} -7.20150e12i q^{62} +5.44782e11i q^{63} +1.51415e13 q^{64} +9.86659e12i q^{65} -8.61798e13 q^{66} -2.06491e12 q^{67} +(-1.87877e13 - 6.49893e12i) q^{68} +6.38131e13 q^{69} +2.00656e12 q^{70} -7.12668e13i q^{71} -1.18304e13 q^{72} -1.38066e14i q^{73} +1.68743e14i q^{74} +9.68898e13i q^{75} -6.74009e13 q^{76} -2.44046e13 q^{77} -1.52783e14i q^{78} +1.00832e12i q^{79} +6.15050e13i q^{80} -1.60495e14 q^{81} +4.12414e14i q^{82} +1.11101e14 q^{83} -8.20107e12 q^{84} +(-2.57571e13 + 7.44610e13i) q^{85} +5.17475e13 q^{86} -5.91999e13 q^{87} -5.29966e14i q^{88} -4.91732e14 q^{89} -2.62130e13i q^{90} -4.32655e13i q^{91} -2.19389e14i q^{92} +1.16653e14 q^{93} +3.25864e14 q^{94} +2.67129e14i q^{95} -4.55751e14i q^{96} +3.82439e14i q^{97} +9.92906e14 q^{98} +3.18814e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9}+O(q^{10}) \) 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9	\( 22 q - 258 q^{2} + 414386 q^{4} - 12648450 q^{8} - 78109330 q^{9} + 702506672 q^{13} - 1787378376 q^{15} + 3524081474 q^{16} - 2245058454 q^{17} + 6803778314 q^{18} + 9958891784 q^{19} - 4168893668 q^{21} - 238696683970 q^{25} - 33467295588 q^{26} - 62541989808 q^{30} - 43445086338 q^{32} + 213283309748 q^{33} + 521524562854 q^{34} - 467785613304 q^{35} - 2300588654186 q^{36} + 3162083165688 q^{38} - 3011205093968 q^{42} - 2215728209008 q^{43} - 7793870107128 q^{47} - 1555224751482 q^{49} + 30118817411766 q^{50} - 21451923375880 q^{51} + 51163160044372 q^{52} - 6062965973460 q^{53} - 11679154373592 q^{55} + 22772194849344 q^{59} - 86295684546192 q^{60} - 28567749560318 q^{64} + 251781147903680 q^{66} + 153875904272808 q^{67} - 48849686100870 q^{68} + 60664072036996 q^{69} - 150925771647648 q^{70} - 293782759569702 q^{72} - 388479948338264 q^{76} - 622427249887884 q^{77} + 983865215787034 q^{81} - 15\!\cdots\!44 q^{83}+ \cdots + 26\!\cdots\!90 q^{98}+O(q^{100}) \) 22 * q - 258 * q^2 + 414386 * q^4 - 12648450 * q^8 - 78109330 * q^9 + 702506672 * q^13 - 1787378376 * q^15 + 3524081474 * q^16 - 2245058454 * q^17 + 6803778314 * q^18 + 9958891784 * q^19 - 4168893668 * q^21 - 238696683970 * q^25 - 33467295588 * q^26 - 62541989808 * q^30 - 43445086338 * q^32 + 213283309748 * q^33 + 521524562854 * q^34 - 467785613304 * q^35 - 2300588654186 * q^36 + 3162083165688 * q^38 - 3011205093968 * q^42 - 2215728209008 * q^43 - 7793870107128 * q^47 - 1555224751482 * q^49 + 30118817411766 * q^50 - 21451923375880 * q^51 + 51163160044372 * q^52 - 6062965973460 * q^53 - 11679154373592 * q^55 + 22772194849344 * q^59 - 86295684546192 * q^60 - 28567749560318 * q^64 + 251781147903680 * q^66 + 153875904272808 * q^67 - 48849686100870 * q^68 + 60664072036996 * q^69 - 150925771647648 * q^70 - 293782759569702 * q^72 - 388479948338264 * q^76 - 622427249887884 * q^77 + 983865215787034 * q^81 - 1541046988482144 * q^83 + 1542636638603936 * q^84 + 94526232685248 * q^85 + 102594718370712 * q^86 - 428830075363560 * q^87 - 894061425316800 * q^89 + 2342465228549812 * q^93 + 2620489835637760 * q^94 + 2662999543720290 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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