LMFDB - Embedded newform 17.10.b.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,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, 10, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
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:	$8.75560921479$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 122690 x^{10} + 5157152560 x^{8} + 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 $ x^12 + 122690x^10 + 5157152560x^8 + 87983684680032x^6 + 612743619071665152x^4 + 1335826553351738886144*x^2 + 203949399568932198678528
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.1
Root			$-119.947i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.10.b.a.16.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-36.0157 q^{2} -119.947i q^{3} +785.131 q^{4} +917.335i q^{5} +4319.97i q^{6} +4193.73i q^{7} -9837.00 q^{8} +5295.73 q^{9} +O(q^{10})$	\(q-36.0157 q^{2} -119.947i q^{3} +785.131 q^{4} +917.335i q^{5} +4319.97i q^{6} +4193.73i q^{7} -9837.00 q^{8} +5295.73 q^{9} -33038.5i q^{10} -56024.5i q^{11} -94174.0i q^{12} +1946.10 q^{13} -151040. i q^{14} +110032. q^{15} -47700.5 q^{16} +(13639.9 - 344096. i) q^{17} -190730. q^{18} -348672. q^{19} +720228. i q^{20} +503025. q^{21} +2.01776e6i q^{22} -287328. i q^{23} +1.17992e6i q^{24} +1.11162e6 q^{25} -70090.0 q^{26} -2.99612e6i q^{27} +3.29262e6i q^{28} -3.74448e6i q^{29} -3.96286e6 q^{30} -3.22892e6i q^{31} +6.75451e6 q^{32} -6.71997e6 q^{33} +(-491252. + 1.23928e7i) q^{34} -3.84705e6 q^{35} +4.15784e6 q^{36} +7.92078e6i q^{37} +1.25576e7 q^{38} -233428. i q^{39} -9.02382e6i q^{40} -2.96386e7i q^{41} -1.81168e7 q^{42} +1.54310e7 q^{43} -4.39866e7i q^{44} +4.85796e6i q^{45} +1.03483e7i q^{46} -2.94503e7 q^{47} +5.72153e6i q^{48} +2.27663e7 q^{49} -4.00358e7 q^{50} +(-4.12732e7 - 1.63607e6i) q^{51} +1.52794e6 q^{52} +1.12977e8 q^{53} +1.07907e8i q^{54} +5.13932e7 q^{55} -4.12537e7i q^{56} +4.18221e7i q^{57} +1.34860e8i q^{58} -1.42908e8 q^{59} +8.63891e7 q^{60} -2.77387e7i q^{61} +1.16292e8i q^{62} +2.22089e7i q^{63} -2.18846e8 q^{64} +1.78522e6i q^{65} +2.42024e8 q^{66} -8.42027e7 q^{67} +(1.07091e7 - 2.70160e8i) q^{68} -3.44641e7 q^{69} +1.38554e8 q^{70} -3.54046e8i q^{71} -5.20941e7 q^{72} -2.56100e8i q^{73} -2.85273e8i q^{74} -1.33336e8i q^{75} -2.73753e8 q^{76} +2.34952e8 q^{77} +8.40709e6i q^{78} +3.39870e8i q^{79} -4.37573e7i q^{80} -2.55140e8 q^{81} +1.06745e9i q^{82} +5.29228e8 q^{83} +3.94940e8 q^{84} +(3.15651e8 + 1.25124e7i) q^{85} -5.55759e8 q^{86} -4.49139e8 q^{87} +5.51113e8i q^{88} -6.33877e8 q^{89} -1.74963e8i q^{90} +8.16140e6i q^{91} -2.25590e8i q^{92} -3.87299e8 q^{93} +1.06067e9 q^{94} -3.19849e8i q^{95} -8.10183e8i q^{96} +1.00489e9i q^{97} -8.19943e8 q^{98} -2.96691e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) $ 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9	$ 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9} - 63204 q^{13} - 243480 q^{15} + 38978 q^{16} - 105960 q^{17} + 547706 q^{18} + 1110672 q^{19} - 172580 q^{21} - 4441796 q^{25} + 1336332 q^{26} - 500496 q^{30} - 1934850 q^{32} - 6557404 q^{33} - 15085546 q^{34} + 3519864 q^{35} + 30244102 q^{36} + 28748136 q^{38} - 11901296 q^{42} + 10004616 q^{43} - 112552440 q^{47} + 121354720 q^{49} - 164889018 q^{50} - 52506472 q^{51} - 59093180 q^{52} + 76804272 q^{53} + 300732568 q^{55} + 11618904 q^{59} + 101609232 q^{60} - 260062974 q^{64} + 18429632 q^{66} - 304208752 q^{67} - 444301206 q^{68} - 211308236 q^{69} + 460311456 q^{70} + 493218954 q^{72} + 416024248 q^{76} + 138357828 q^{77} - 363335792 q^{81} - 845042136 q^{83} + 958037984 q^{84} - 388949632 q^{85} + 127952904 q^{86} + 610860648 q^{87} - 938223804 q^{89} + 1635779524 q^{93} - 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) $ 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9 - 63204 * q^13 - 243480 * q^15 + 38978 * q^16 - 105960 * q^17 + 547706 * q^18 + 1110672 * q^19 - 172580 * q^21 - 4441796 * q^25 + 1336332 * q^26 - 500496 * q^30 - 1934850 * q^32 - 6557404 * q^33 - 15085546 * q^34 + 3519864 * q^35 + 30244102 * q^36 + 28748136 * q^38 - 11901296 * q^42 + 10004616 * q^43 - 112552440 * q^47 + 121354720 * q^49 - 164889018 * q^50 - 52506472 * q^51 - 59093180 * q^52 + 76804272 * q^53 + 300732568 * q^55 + 11618904 * q^59 + 101609232 * q^60 - 260062974 * q^64 + 18429632 * q^66 - 304208752 * q^67 - 444301206 * q^68 - 211308236 * q^69 + 460311456 * q^70 + 493218954 * q^72 + 416024248 * q^76 + 138357828 * q^77 - 363335792 * q^81 - 845042136 * q^83 + 958037984 * q^84 - 388949632 * q^85 + 127952904 * q^86 + 610860648 * q^87 - 938223804 * q^89 + 1635779524 * q^93 - 238629952 * q^94 - 152046078 * 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 $

$2$	−36.0157			−1.59168			−0.795842	−	0.605504i	$-0.792971\pi$
$2$	−36.0157			−1.59168			−0.795842	+	0.605504i	$0.792971\pi$
$3$		−	119.947i		−	0.854955i	−0.904026	−	0.427478i	$-0.859402\pi$
$3$		−	119.947i		−	0.854955i	0.904026	−	0.427478i	$-0.140598\pi$
$4$	785.131			1.53346
$5$			917.335i			0.656391i	0.944610	+	0.328196i	$0.106441\pi$
$5$			917.335i			0.656391i	−0.944610	+	0.328196i	$0.893559\pi$
$6$			4319.97i			1.36082i
$7$			4193.73i			0.660175i	0.943950	+	0.330087i	$0.107078\pi$
$7$			4193.73i			0.660175i	−0.943950	+	0.330087i	$0.892922\pi$
$8$	−9837.00			−0.849098
$9$	5295.73			0.269051
$10$		−	33038.5i		−	1.04477i
$11$		−	56024.5i		−	1.15375i	−0.816833	−	0.576874i	$-0.804272\pi$
$11$		−	56024.5i		−	1.15375i	0.816833	−	0.576874i	$-0.195728\pi$
$12$		−	94174.0i		−	1.31104i
$13$	1946.10			0.0188982			0.00944908	−	0.999955i	$-0.496992\pi$
$13$	1946.10			0.0188982			0.00944908	+	0.999955i	$0.496992\pi$
$14$		−	151040.i		−	1.05079i
$15$	110032.			0.561185
$16$	−47700.5			−0.181963
$17$	13639.9	−	344096.i	0.0396089	−	0.999215i
$17$	13639.9	−	344096.i	0.0396089	−	0.999215i
$18$	−190730.			−0.428244
$19$	−348672.			−0.613798			−0.306899	−	0.951742i	$-0.599291\pi$
$19$	−348672.			−0.613798			−0.306899	+	0.951742i	$0.599291\pi$
$20$			720228.i			1.00655i
$21$	503025.			0.564420
$22$			2.01776e6i			1.83640i
$23$		−	287328.i		−	0.214093i	−0.994254	−	0.107046i	$-0.965861\pi$
$23$		−	287328.i		−	0.214093i	0.994254	−	0.107046i	$-0.0341393\pi$
$24$			1.17992e6i			0.725941i
$25$	1.11162e6			0.569150
$26$	−70090.0			−0.0300799
$27$		−	2.99612e6i		−	1.08498i
$28$			3.29262e6i			1.01235i
$29$		−	3.74448e6i		−	0.983107i	−0.870847	−	0.491554i	$-0.836429\pi$
$29$		−	3.74448e6i		−	0.983107i	0.870847	−	0.491554i	$-0.163571\pi$
$30$	−3.96286e6			−0.893230
$31$		−	3.22892e6i		−	0.627956i	−0.949430	−	0.313978i	$-0.898338\pi$
$31$		−	3.22892e6i		−	0.627956i	0.949430	−	0.313978i	$-0.101662\pi$
$32$	6.75451e6			1.13873
$33$	−6.71997e6			−0.986403
$34$	−491252.	+	1.23928e7i	−0.0630448	+	1.59044i
$35$	−3.84705e6			−0.433333
$36$	4.15784e6			0.412579
$37$			7.92078e6i			0.694801i	0.937717	+	0.347400i	$0.112936\pi$
$37$			7.92078e6i			0.694801i	−0.937717	+	0.347400i	$0.887064\pi$
$38$	1.25576e7			0.976972
$39$		−	233428.i		−	0.0161571i
$40$		−	9.02382e6i		−	0.557341i
$41$		−	2.96386e7i		−	1.63806i	−0.573750	−	0.819030i	$-0.694512\pi$
$41$		−	2.96386e7i		−	1.63806i	0.573750	−	0.819030i	$-0.305488\pi$
$42$	−1.81168e7			−0.898379
$43$	1.54310e7			0.688314			0.344157	−	0.938912i	$-0.388165\pi$
$43$	1.54310e7			0.688314			0.344157	+	0.938912i	$0.388165\pi$
$44$		−	4.39866e7i		−	1.76923i
$45$			4.85796e6i			0.176603i
$46$			1.03483e7i			0.340768i
$47$	−2.94503e7			−0.880338			−0.440169	−	0.897915i	$-0.645081\pi$
$47$	−2.94503e7			−0.880338			−0.440169	+	0.897915i	$0.645081\pi$
$48$			5.72153e6i			0.155570i
$49$	2.27663e7			0.564169
$50$	−4.00358e7			−0.905908
$51$	−4.12732e7	−	1.63607e6i	−0.854285	−	0.0338638i
$52$	1.52794e6			0.0289795
$53$	1.12977e8			1.96675			0.983373	−	0.181596i	$-0.0581263\pi$
$53$	1.12977e8			1.96675			0.983373	+	0.181596i	$0.0581263\pi$
$54$			1.07907e8i			1.72695i
$55$	5.13932e7			0.757310
$56$		−	4.12537e7i		−	0.560553i
$57$			4.18221e7i			0.524770i
$58$			1.34860e8i			1.56480i
$59$	−1.42908e8			−1.53540			−0.767700	−	0.640809i	$-0.778599\pi$
$59$	−1.42908e8			−1.53540			−0.767700	+	0.640809i	$0.778599\pi$
$60$	8.63891e7			0.860555
$61$		−	2.77387e7i		−	0.256508i	−0.991741	−	0.128254i	$-0.959063\pi$
$61$		−	2.77387e7i		−	0.256508i	0.991741	−	0.128254i	$-0.0409373\pi$
$62$			1.16292e8i			0.999508i
$63$			2.22089e7i			0.177621i
$64$	−2.18846e8			−1.63053
$65$			1.78522e6i			0.0124046i
$66$	2.42024e8			1.57004
$67$	−8.42027e7			−0.510493			−0.255246	−	0.966876i	$-0.582157\pi$
$67$	−8.42027e7			−0.510493			−0.255246	+	0.966876i	$0.582157\pi$
$68$	1.07091e7	−	2.70160e8i	0.0607386	−	1.53226i
$69$	−3.44641e7			−0.183040
$70$	1.38554e8			0.689730
$71$		−	3.54046e8i		−	1.65347i	−0.562590	−	0.826736i	$-0.690195\pi$
$71$		−	3.54046e8i		−	1.65347i	0.562590	−	0.826736i	$-0.309805\pi$
$72$	−5.20941e7			−0.228451
$73$		−	2.56100e8i		−	1.05550i	−0.849401	−	0.527748i	$-0.823037\pi$
$73$		−	2.56100e8i		−	1.05550i	0.849401	−	0.527748i	$-0.176963\pi$
$74$		−	2.85273e8i		−	1.10590i
$75$		−	1.33336e8i		−	0.486598i
$76$	−2.73753e8			−0.941233
$77$	2.34952e8			0.761676
$78$			8.40709e6i			0.0257170i
$79$			3.39870e8i			0.981728i	0.871236	+	0.490864i	$0.163319\pi$
$79$			3.39870e8i			0.981728i	−0.871236	+	0.490864i	$0.836681\pi$
$80$		−	4.37573e7i		−	0.119439i
$81$	−2.55140e8			−0.658560
$82$			1.06745e9i			2.60727i
$83$	5.29228e8			1.22403			0.612014	−	0.790847i	$-0.290360\pi$
$83$	5.29228e8			1.22403			0.612014	+	0.790847i	$0.290360\pi$
$84$	3.94940e8			0.865515
$85$	3.15651e8	+	1.25124e7i	0.655876	+	0.0259989i
$86$	−5.55759e8			−1.09558
$87$	−4.49139e8			−0.840513
$88$			5.51113e8i			0.979645i
$89$	−6.33877e8			−1.07090			−0.535451	−	0.844566i	$-0.679858\pi$
$89$	−6.33877e8			−1.07090			−0.535451	+	0.844566i	$0.679858\pi$
$90$		−	1.74963e8i		−	0.281096i
$91$			8.16140e6i			0.0124761i
$92$		−	2.25590e8i		−	0.328303i
$93$	−3.87299e8			−0.536874
$94$	1.06067e9			1.40122
$95$		−	3.19849e8i		−	0.402892i
$96$		−	8.10183e8i		−	0.973560i
$97$			1.00489e9i			1.15252i	0.817267	+	0.576259i	$0.195488\pi$
$97$			1.00489e9i			1.15252i	−0.817267	+	0.576259i	$0.804512\pi$
$98$	−8.19943e8			−0.897979
$99$		−	2.96691e8i		−	0.310417i
$100$	8.72768e8			0.872768
$101$	1.52783e9			1.46093			0.730465	−	0.682950i	$-0.239303\pi$
$101$	1.52783e9			1.46093			0.730465	+	0.682950i	$0.239303\pi$
$102$	1.48648e9	+	5.89242e7i	1.35975	+	0.0539005i
$103$	−1.79886e8			−0.157482			−0.0787409	−	0.996895i	$-0.525090\pi$
$103$	−1.79886e8			−0.157482			−0.0787409	+	0.996895i	$0.525090\pi$
$104$	−1.91438e7			−0.0160464
$105$			4.61442e8i			0.370481i
$106$	−4.06894e9			−3.13044
$107$			2.37895e9i			1.75452i	0.480019	+	0.877258i	$0.340630\pi$
$107$			2.37895e9i			1.75452i	−0.480019	+	0.877258i	$0.659370\pi$
$108$		−	2.35235e9i		−	1.66378i
$109$			9.33309e7i			0.0633295i	0.999499	+	0.0316648i	$0.0100809\pi$
$109$			9.33309e7i			0.0633295i	−0.999499	+	0.0316648i	$0.989919\pi$
$110$	−1.85096e9			−1.20540
$111$	9.50073e8			0.594024
$112$		−	2.00043e8i		−	0.120127i
$113$			1.71780e9i			0.991104i	0.868578	+	0.495552i	$0.165034\pi$
$113$			1.71780e9i			0.991104i	−0.868578	+	0.495552i	$0.834966\pi$
$114$		−	1.50625e9i		−	0.835268i
$115$	2.63576e8			0.140529
$116$		−	2.93991e9i		−	1.50755i
$117$	1.03060e7			0.00508457
$118$	5.14692e9			2.44387
$119$	1.44304e9	+	5.72022e7i	0.659657	+	0.0261488i
$120$	−1.08238e9			−0.476501
$121$	−7.80799e8			−0.331135
$122$			9.99028e8i			0.408280i
$123$	−3.55506e9			−1.40047
$124$		−	2.53512e9i		−	0.962945i
$125$			2.81140e9i			1.02998i
$126$		−	7.99868e8i		−	0.282716i
$127$	−2.30615e9			−0.786629			−0.393315	−	0.919404i	$-0.628672\pi$
$127$	−2.30615e9			−0.786629			−0.393315	+	0.919404i	$0.628672\pi$
$128$	4.42358e9			1.45656
$129$		−	1.85090e9i		−	0.588478i
$130$		−	6.42960e7i		−	0.0197442i
$131$		−	2.35000e9i		−	0.697183i	−0.937275	−	0.348591i	$-0.886660\pi$
$131$		−	2.35000e9i		−	0.697183i	0.937275	−	0.348591i	$-0.113340\pi$
$132$	−5.27606e9			−1.51261
$133$		−	1.46223e9i		−	0.405214i
$134$	3.03262e9			0.812543
$135$	2.74845e9			0.712173
$136$	−1.34176e8	+	3.38487e9i	−0.0336318	+	0.848432i
$137$	−2.35491e9			−0.571127			−0.285563	−	0.958360i	$-0.592181\pi$
$137$	−2.35491e9			−0.571127			−0.285563	+	0.958360i	$0.592181\pi$
$138$	1.24125e9			0.291342
$139$		−	5.15857e9i		−	1.17209i	−0.810277	−	0.586047i	$-0.800683\pi$
$139$		−	5.15857e9i		−	1.17209i	0.810277	−	0.586047i	$-0.199317\pi$
$140$	−3.02044e9			−0.664499
$141$			3.53247e9i			0.752649i
$142$			1.27512e10i			2.63181i
$143$		−	1.09029e8i		−	0.0218037i
$144$	−2.52609e8			−0.0489573
$145$	3.43495e9			0.645303
$146$			9.22361e9i			1.68002i
$147$		−	2.73074e9i		−	0.482339i
$148$			6.21885e9i			1.06545i
$149$	−6.04226e9			−1.00429			−0.502147	−	0.864782i	$-0.667457\pi$
$149$	−6.04226e9			−1.00429			−0.502147	+	0.864782i	$0.667457\pi$
$150$			4.80218e9i			0.774511i
$151$	7.56844e9			1.18471			0.592353	−	0.805679i	$-0.298199\pi$
$151$	7.56844e9			1.18471			0.592353	+	0.805679i	$0.298199\pi$
$152$	3.42988e9			0.521174
$153$	7.22335e7	−	1.82224e9i	0.0106568	−	0.268840i
$154$	−8.46195e9			−1.21235
$155$	2.96200e9			0.412185
$156$		−	1.83272e8i		−	0.0247762i
$157$	3.59797e9			0.472616			0.236308	−	0.971678i	$-0.424062\pi$
$157$	3.59797e9			0.472616			0.236308	+	0.971678i	$0.424062\pi$
$158$		−	1.22407e10i		−	1.56260i
$159$		−	1.35512e10i		−	1.68148i
$160$			6.19615e9i			0.747450i
$161$	1.20497e9			0.141339
$162$	9.18904e9			1.04822
$163$		−	2.46020e9i		−	0.272977i	−0.990642	−	0.136488i	$-0.956418\pi$
$163$		−	2.46020e9i		−	0.272977i	0.990642	−	0.136488i	$-0.0435816\pi$
$164$		−	2.32702e10i		−	2.51190i
$165$		−	6.16446e9i		−	0.647467i
$166$	−1.90605e10			−1.94827
$167$		−	6.06431e9i		−	0.603333i	−0.953414	−	0.301667i	$-0.902457\pi$
$167$		−	6.06431e9i		−	0.603333i	0.953414	−	0.301667i	$-0.0975429\pi$
$168$	−4.94825e9			−0.479248
$169$	−1.06007e10			−0.999643
$170$	−1.13684e10	−	4.50643e8i	−1.04395	−	0.0413821i
$171$	−1.84647e9			−0.165143
$172$	1.21154e10			1.05550
$173$		−	7.56160e9i		−	0.641810i	−0.947111	−	0.320905i	$-0.896013\pi$
$173$		−	7.56160e9i		−	0.641810i	0.947111	−	0.320905i	$-0.103987\pi$
$174$	1.61761e10			1.33783
$175$			4.66184e9i			0.375739i
$176$			2.67240e9i			0.209939i
$177$			1.71413e10i			1.31270i
$178$	2.28295e10			1.70454
$179$	−1.98968e9			−0.144859			−0.0724293	−	0.997374i	$-0.523075\pi$
$179$	−1.98968e9			−0.144859			−0.0724293	+	0.997374i	$0.523075\pi$
$180$			3.81414e9i			0.270813i
$181$			2.17900e10i			1.50905i	0.656272	+	0.754525i	$0.272133\pi$
$181$			2.17900e10i			1.50905i	−0.656272	+	0.754525i	$0.727867\pi$
$182$		−	2.93939e8i		−	0.0198580i
$183$	−3.32717e9			−0.219303
$184$			2.82644e9i			0.181786i
$185$	−7.26601e9			−0.456061
$186$	1.39488e10			0.854535
$187$	−1.92778e10	−	7.64172e8i	−1.15284	−	0.0456987i
$188$	−2.31223e10			−1.34996
$189$	1.25649e10			0.716278
$190$			1.15196e10i			0.641276i
$191$	1.55821e10			0.847180			0.423590	−	0.905854i	$-0.360770\pi$
$191$	1.55821e10			0.847180			0.423590	+	0.905854i	$0.360770\pi$
$192$			2.62499e10i			1.39403i
$193$		−	3.56806e9i		−	0.185108i	−0.995708	−	0.0925538i	$-0.970497\pi$
$193$		−	3.56806e9i		−	0.185108i	0.995708	−	0.0925538i	$-0.0295030\pi$
$194$		−	3.61920e10i		−	1.83444i
$195$	2.14132e8			0.0106054
$196$	1.78745e10			0.865130
$197$			3.07563e10i			1.45491i	0.686155	+	0.727456i	$0.259297\pi$
$197$			3.07563e10i			1.45491i	−0.686155	+	0.727456i	$0.740703\pi$
$198$			1.06855e10i			0.494086i
$199$		−	1.48762e10i		−	0.672441i	−0.941783	−	0.336220i	$-0.890851\pi$
$199$		−	1.48762e10i		−	0.672441i	0.941783	−	0.336220i	$-0.109149\pi$
$200$	−1.09350e10			−0.483264
$201$			1.00999e10i			0.436449i
$202$	−5.50260e10			−2.32534
$203$	1.57033e10			0.649023
$204$	−3.24049e10	−	1.28453e9i	−1.31001	−	0.0519288i
$205$	2.71885e10			1.07521
$206$	6.47873e9			0.250661
$207$		−	1.52161e9i		−	0.0576019i
$208$	−9.28298e7			−0.00343876
$209$			1.95342e10i			0.708168i
$210$		−	1.66192e10i		−	0.589688i
$211$		−	3.47123e10i		−	1.20562i	−0.797883	−	0.602812i	$-0.794047\pi$
$211$		−	3.47123e10i		−	1.20562i	0.797883	−	0.602812i	$-0.205953\pi$
$212$	8.87017e10			3.01592
$213$	−4.24667e10			−1.41364
$214$		−	8.56794e10i		−	2.79264i
$215$			1.41554e10i			0.451803i
$216$			2.94729e10i			0.921256i
$217$	1.35412e10			0.414561
$218$		−	3.36138e9i		−	0.100801i
$219$	−3.07184e10			−0.902401
$220$	4.03504e10			1.16130
$221$	2.65447e7	−	6.69643e8i	0.000748535	−	0.0188833i
$222$	−3.42176e10			−0.945498
$223$	−3.59058e10			−0.972283			−0.486142	−	0.873880i	$-0.661596\pi$
$223$	−3.59058e10			−0.972283			−0.486142	+	0.873880i	$0.661596\pi$
$224$			2.83266e10i			0.751758i
$225$	5.88685e9			0.153131
$226$		−	6.18677e10i		−	1.57753i
$227$			5.61479e9i			0.140352i	0.997535	+	0.0701758i	$0.0223560\pi$
$227$			5.61479e9i			0.140352i	−0.997535	+	0.0701758i	$0.977644\pi$
$228$			3.28358e10i			0.804713i
$229$	7.90733e10			1.90007			0.950036	−	0.312139i	$-0.101046\pi$
$229$	7.90733e10			1.90007			0.950036	+	0.312139i	$0.101046\pi$
$230$	−9.49286e9			−0.223677
$231$		−	2.81817e10i		−	0.651199i
$232$			3.68345e10i			0.834754i
$233$			6.81753e10i			1.51539i	0.652607	+	0.757697i	$0.273675\pi$
$233$			6.81753e10i			1.51539i	−0.652607	+	0.757697i	$0.726325\pi$
$234$	−3.71178e8			−0.00809303
$235$		−	2.70158e10i		−	0.577846i
$236$	−1.12201e11			−2.35447
$237$	4.07664e10			0.839334
$238$	−5.19722e10	−	2.06018e9i	−1.04997	−	0.0416206i
$239$	−3.19952e10			−0.634300			−0.317150	−	0.948375i	$-0.602726\pi$
$239$	−3.19952e10			−0.634300			−0.317150	+	0.948375i	$0.602726\pi$
$240$	−5.24856e9			−0.102115
$241$		−	4.21107e9i		−	0.0804111i	−0.999191	−	0.0402056i	$-0.987199\pi$
$241$		−	4.21107e9i		−	0.0804111i	0.999191	−	0.0402056i	$-0.0128013\pi$
$242$	2.81210e10			0.527062
$243$		−	2.83694e10i		−	0.521942i
$244$		−	2.17785e10i		−	0.393345i
$245$			2.08843e10i			0.370316i
$246$	1.28038e11			2.22910
$247$	−6.78548e8			−0.0115996
$248$			3.17629e10i			0.533196i
$249$		−	6.34793e10i		−	1.04649i
$250$		−	1.01255e11i		−	1.63940i
$251$	1.26806e10			0.201654			0.100827	−	0.994904i	$-0.467851\pi$
$251$	1.26806e10			0.201654			0.100827	+	0.994904i	$0.467851\pi$
$252$			1.74369e10i			0.272374i
$253$	−1.60974e10			−0.247009
$254$	8.30575e10			1.25207
$255$	1.50082e9	−	3.78614e10i	0.0222279	−	0.560745i
$256$	−4.72692e10			−0.687857
$257$	−8.11867e10			−1.16088			−0.580438	−	0.814304i	$-0.697119\pi$
$257$	−8.11867e10			−1.16088			−0.580438	+	0.814304i	$0.697119\pi$
$258$			6.66616e10i			0.936671i
$259$	−3.32176e10			−0.458690
$260$			1.40163e9i			0.0190219i
$261$		−	1.98298e10i		−	0.264506i
$262$			8.46368e10i			1.10969i
$263$	4.36957e10			0.563168			0.281584	−	0.959537i	$-0.409140\pi$
$263$	4.36957e10			0.563168			0.281584	+	0.959537i	$0.409140\pi$
$264$	6.61043e10			0.837553
$265$			1.03638e11i			1.29096i
$266$			5.26634e10i			0.644972i
$267$			7.60316e10i			0.915574i
$268$	−6.61102e10			−0.782819
$269$			1.52414e11i			1.77476i	0.461042	+	0.887378i	$0.347476\pi$
$269$			1.52414e11i			1.77476i	−0.461042	+	0.887378i	$0.652524\pi$
$270$	−9.89873e10			−1.13355
$271$	1.41824e10			0.159731			0.0798655	−	0.996806i	$-0.474551\pi$
$271$	1.41824e10			0.159731			0.0798655	+	0.996806i	$0.474551\pi$
$272$	−6.50632e8	+	1.64135e10i	−0.00720735	+	0.181820i
$273$	9.78935e8			0.0106665
$274$	8.48139e10			0.909053
$275$		−	6.22781e10i		−	0.656656i
$276$	−2.70588e10			−0.280684
$277$		−	7.86224e10i		−	0.802394i	−0.915992	−	0.401197i	$-0.868594\pi$
$277$		−	7.86224e10i		−	0.802394i	0.915992	−	0.401197i	$-0.131406\pi$
$278$			1.85789e11i			1.86560i
$279$		−	1.70995e10i		−	0.168952i
$280$	3.78435e10			0.367942
$281$	−3.72134e10			−0.356058			−0.178029	−	0.984025i	$-0.556972\pi$
$281$	−3.72134e10			−0.356058			−0.178029	+	0.984025i	$0.556972\pi$
$282$		−	1.27224e11i		−	1.19798i
$283$			7.37798e9i			0.0683752i	0.999415	+	0.0341876i	$0.0108844\pi$
$283$			7.37798e9i			0.0683752i	−0.999415	+	0.0341876i	$0.989116\pi$
$284$		−	2.77972e11i		−	2.53553i
$285$	−3.83649e10			−0.344454
$286$			3.92676e9i			0.0347046i
$287$	1.24296e11			1.08141
$288$	3.57701e10			0.306375
$289$	−1.18216e11	−	9.38689e9i	−0.996862	−	0.0791556i
$290$	−1.23712e11			−1.02712
$291$	1.20534e11			0.985351
$292$		−	2.01072e11i		−	1.61856i
$293$	9.58955e10			0.760140			0.380070	−	0.924958i	$-0.375900\pi$
$293$	9.58955e10			0.760140			0.380070	+	0.924958i	$0.375900\pi$
$294$			9.83496e10i			0.767732i
$295$		−	1.31094e11i		−	1.00782i
$296$		−	7.79167e10i		−	0.589954i
$297$	−1.67856e11			−1.25180
$298$	2.17616e11			1.59852
$299$		−	5.59167e8i		−	0.00404596i
$300$		−	1.04686e11i		−	0.746178i
$301$			6.47135e10i			0.454407i
$302$	−2.72583e11			−1.88568
$303$		−	1.83259e11i		−	1.24903i
$304$	1.66318e10			0.111688
$305$	2.54457e10			0.168370
$306$	−2.60154e9	+	6.56292e10i	−0.0169623	+	0.427908i
$307$	1.36312e11			0.875814			0.437907	−	0.899020i	$-0.355720\pi$
$307$	1.36312e11			0.875814			0.437907	+	0.899020i	$0.355720\pi$
$308$	1.84468e11			1.16800
$309$			2.15768e10i			0.134640i
$310$	−1.06678e11			−0.656068
$311$			1.33880e11i			0.811507i	0.913983	+	0.405754i	$0.132991\pi$
$311$			1.33880e11i			0.811507i	−0.913983	+	0.405754i	$0.867009\pi$
$312$			2.29623e9i			0.0137189i
$313$		−	8.69004e10i		−	0.511767i	−0.966708	−	0.255883i	$-0.917634\pi$
$313$		−	8.69004e10i		−	0.511767i	0.966708	−	0.255883i	$-0.0823663\pi$
$314$	−1.29583e11			−0.752256
$315$	−2.03730e10			−0.116589
$316$			2.66843e11i			1.50544i
$317$		−	2.48261e11i		−	1.38083i	−0.723412	−	0.690417i	$-0.757427\pi$
$317$		−	2.48261e11i		−	1.38083i	0.723412	−	0.690417i	$-0.242573\pi$
$318$			4.88057e11i			2.67639i
$319$	−2.09783e11			−1.13426
$320$		−	2.00755e11i		−	1.07026i
$321$	2.85347e11			1.50003
$322$	−4.33980e10			−0.224967
$323$	−4.75586e9	+	1.19976e11i	−0.0243118	+	0.613316i
$324$	−2.00318e11			−1.00988
$325$	2.16332e9			0.0107559
$326$			8.86057e10i			0.434493i
$327$	1.11948e10			0.0541439
$328$			2.91555e11i			1.39087i
$329$		−	1.23506e11i		−	0.581177i
$330$			2.22017e11i			1.03056i
$331$	−2.88811e11			−1.32248			−0.661239	−	0.750175i	$-0.729969\pi$
$331$	−2.88811e11			−1.32248			−0.661239	+	0.750175i	$0.729969\pi$
$332$	4.15513e11			1.87700
$333$			4.19463e10i			0.186937i
$334$			2.18410e11i			0.960316i
$335$		−	7.72421e10i		−	0.335083i
$336$	−2.39945e10			−0.102704
$337$			9.17448e10i			0.387478i	0.981053	+	0.193739i	$0.0620615\pi$
$337$			9.17448e10i			0.387478i	−0.981053	+	0.193739i	$0.937939\pi$
$338$	3.81792e11			1.59112
$339$	2.06045e11			0.847350
$340$	2.47827e11	+	9.82387e9i	1.00576	+	0.0398683i
$341$	−1.80898e11			−0.724503
$342$	6.65020e10			0.262855
$343$			2.64708e11i			1.03263i
$344$	−1.51795e11			−0.584446
$345$		−	3.16151e10i		−	0.120146i
$346$			2.72336e11i			1.02156i
$347$		−	4.84910e11i		−	1.79547i	−0.440534	−	0.897736i	$-0.645211\pi$
$347$		−	4.84910e11i		−	1.79547i	0.440534	−	0.897736i	$-0.354789\pi$
$348$	−3.52633e11			−1.28889
$349$	−6.43524e9			−0.0232194			−0.0116097	−	0.999933i	$-0.503696\pi$
$349$	−6.43524e9			−0.0232194			−0.0116097	+	0.999933i	$0.503696\pi$
$350$		−	1.67899e11i		−	0.598057i
$351$		−	5.83074e9i		−	0.0205042i
$352$		−	3.78418e11i		−	1.31380i
$353$	−1.83629e11			−0.629440			−0.314720	−	0.949185i	$-0.601911\pi$
$353$	−1.83629e11			−0.629440			−0.314720	+	0.949185i	$0.601911\pi$
$354$		−	6.17357e11i		−	2.08940i
$355$	3.24779e11			1.08532
$356$	−4.97676e11			−1.64218
$357$	6.86123e9	−	1.73089e11i	0.0223561	−	0.563977i
$358$	7.16596e10			0.230569
$359$	−4.45051e11			−1.41412			−0.707058	−	0.707155i	$-0.749978\pi$
$359$	−4.45051e11			−1.41412			−0.707058	+	0.707155i	$0.749978\pi$
$360$		−	4.77878e10i		−	0.149953i
$361$	−2.01116e11			−0.623252
$362$		−	7.84782e11i		−	2.40193i
$363$			9.36544e10i			0.283106i
$364$			6.40777e9i			0.0191316i
$365$	2.34929e11			0.692818
$366$	1.19830e11			0.349061
$367$			4.05760e11i			1.16754i	0.811919	+	0.583770i	$0.198423\pi$
$367$			4.05760e11i			1.16754i	−0.811919	+	0.583770i	$0.801577\pi$
$368$			1.37057e10i			0.0389570i
$369$		−	1.56958e11i		−	0.440722i
$370$	2.61690e11			0.725906
$371$			4.73794e11i			1.29840i
$372$	−3.04080e11			−0.823275
$373$	4.07694e11			1.09055			0.545274	−	0.838258i	$-0.316426\pi$
$373$	4.07694e11			1.09055			0.545274	+	0.838258i	$0.316426\pi$
$374$	6.94303e11	+	2.75222e10i	1.83496	+	0.0727379i
$375$	3.37219e11			0.880584
$376$	2.89703e11			0.747493
$377$		−	7.28713e9i		−	0.0185789i
$378$	−4.52534e11			−1.14009
$379$			6.72982e11i			1.67543i	0.546105	+	0.837717i	$0.316110\pi$
$379$			6.72982e11i			1.67543i	−0.546105	+	0.837717i	$0.683890\pi$
$380$		−	2.51123e11i		−	0.617818i
$381$			2.76615e11i			0.672533i
$382$	−5.61200e11			−1.34844
$383$	−3.49592e11			−0.830170			−0.415085	−	0.909783i	$-0.636248\pi$
$383$	−3.49592e11			−0.830170			−0.415085	+	0.909783i	$0.636248\pi$
$384$		−	5.30594e11i		−	1.24529i
$385$			2.15529e11i			0.499957i
$386$			1.28506e11i			0.294633i
$387$	8.17185e10			0.185192
$388$			7.88973e11i			1.76734i
$389$	4.97423e11			1.10142			0.550709	−	0.834697i	$-0.314357\pi$
$389$	4.97423e11			1.10142			0.550709	+	0.834697i	$0.314357\pi$
$390$	−7.71211e9			−0.0168804
$391$	−9.88682e10	−	3.91913e9i	−0.213925	−	0.00847998i
$392$	−2.23952e11			−0.479035
$393$	−2.81875e11			−0.596060
$394$		−	1.10771e12i		−	2.31576i
$395$	−3.11775e11			−0.644398
$396$		−	2.32941e11i		−	0.476012i
$397$			1.58244e11i			0.319721i	0.987140	+	0.159860i	$0.0511044\pi$
$397$			1.58244e11i			0.319721i	−0.987140	+	0.159860i	$0.948896\pi$
$398$			5.35778e11i			1.07031i
$399$	−1.75390e11			−0.346440
$400$	−5.30249e10			−0.103564
$401$		−	9.10311e10i		−	0.175809i	−0.996129	−	0.0879043i	$-0.971983\pi$
$401$		−	9.10311e10i		−	0.175809i	0.996129	−	0.0879043i	$-0.0280170\pi$
$402$		−	3.63754e11i		−	0.694688i
$403$		−	6.28378e9i		−	0.0118672i
$404$	1.19955e12			2.24028
$405$		−	2.34049e11i		−	0.432273i
$406$	−5.65567e11			−1.03304
$407$	4.43758e11			0.801625
$408$	4.06005e11	+	1.60940e10i	0.725371	+	0.0287537i
$409$	4.23339e11			0.748055			0.374027	−	0.927418i	$-0.377977\pi$
$409$	4.23339e11			0.748055			0.374027	+	0.927418i	$0.377977\pi$
$410$	−9.79213e11			−1.71139
$411$			2.82465e11i			0.488288i
$412$	−1.41234e11			−0.241492
$413$		−	5.99316e11i		−	1.01363i
$414$			5.48019e10i			0.0916841i
$415$			4.85479e11i			0.803442i
$416$	1.31449e10			0.0215198
$417$	−6.18754e11			−1.00209
$418$		−	7.03536e11i		−	1.12718i
$419$			6.22425e11i			0.986561i	0.869870	+	0.493280i	$0.164202\pi$
$419$			6.22425e11i			0.986561i	−0.869870	+	0.493280i	$0.835798\pi$
$420$			3.62292e11i			0.568117i
$421$	4.67294e11			0.724971			0.362486	−	0.931989i	$-0.381928\pi$
$421$	4.67294e11			0.724971			0.362486	+	0.931989i	$0.381928\pi$
$422$			1.25019e12i			1.91897i
$423$	−1.55961e11			−0.236856
$424$	−1.11135e12			−1.66996
$425$	1.51625e10	−	3.82504e11i	0.0225434	−	0.568704i
$426$	1.52947e12			2.25008
$427$	1.16328e11			0.169340
$428$			1.86778e12i			2.69048i
$429$	−1.30777e10			−0.0186412
$430$		−	5.09817e11i		−	0.719128i
$431$		−	2.57969e11i		−	0.360097i	−0.983658	−	0.180049i	$-0.942374\pi$
$431$		−	2.57969e11i		−	0.360097i	0.983658	−	0.180049i	$-0.0576255\pi$
$432$			1.42917e11i			0.197427i
$433$	−2.74180e11			−0.374836			−0.187418	−	0.982280i	$-0.560012\pi$
$433$	−2.74180e11			−0.374836			−0.187418	+	0.982280i	$0.560012\pi$
$434$	−4.87696e11			−0.659850
$435$		−	4.12011e11i		−	0.551705i
$436$			7.32770e10i			0.0971132i
$437$			1.00183e11i			0.131410i
$438$	1.10634e12			1.43634
$439$		−	7.90421e11i		−	1.01571i	−0.861444	−	0.507853i	$-0.830439\pi$
$439$		−	7.90421e11i		−	1.01571i	0.861444	−	0.507853i	$-0.169561\pi$
$440$	−5.05555e11			−0.643031
$441$	1.20564e11			0.151790
$442$	−9.56024e8	+	2.41177e10i	−0.00119143	+	0.0300563i
$443$	−6.58883e10			−0.0812815			−0.0406407	−	0.999174i	$-0.512940\pi$
$443$	−6.58883e10			−0.0812815			−0.0406407	+	0.999174i	$0.512940\pi$
$444$	7.45932e11			0.910911
$445$		−	5.81477e11i		−	0.702931i
$446$	1.29317e12			1.54757
$447$			7.24751e11i			0.858627i
$448$		−	9.17780e11i		−	1.07643i
$449$		−	8.66534e11i		−	1.00618i	−0.864233	−	0.503092i	$-0.832196\pi$
$449$		−	8.66534e11i		−	1.00618i	0.864233	−	0.503092i	$-0.167804\pi$
$450$	−2.12019e11			−0.243735
$451$	−1.66049e12			−1.88991
$452$			1.34870e12i			1.51982i
$453$		−	9.07811e11i		−	1.01287i
$454$		−	2.02221e11i		−	0.223395i
$455$	−7.48674e9			−0.00818920
$456$		−	4.11404e11i		−	0.445581i
$457$	6.25354e11			0.670661			0.335330	−	0.942101i	$-0.391152\pi$
$457$	6.25354e11			0.670661			0.335330	+	0.942101i	$0.391152\pi$
$458$	−2.84788e12			−3.02432
$459$	−1.03095e12	−	4.08670e10i	−1.08413	−	0.0429749i
$460$	2.06941e11			0.215495
$461$	−1.45870e12			−1.50422			−0.752110	−	0.659038i	$-0.770964\pi$
$461$	−1.45870e12			−1.50422			−0.752110	+	0.659038i	$0.770964\pi$
$462$			1.01498e12i			1.03650i
$463$	1.55507e12			1.57266			0.786330	−	0.617807i	$-0.211979\pi$
$463$	1.55507e12			1.57266			0.786330	+	0.617807i	$0.211979\pi$
$464$			1.78614e11i			0.178889i
$465$		−	3.55283e11i		−	0.352400i
$466$		−	2.45538e12i		−	2.41203i
$467$	1.93889e12			1.88638			0.943188	−	0.332260i	$-0.107811\pi$
$467$	1.93889e12			1.88638			0.943188	+	0.332260i	$0.107811\pi$
$468$	8.09157e9			0.00779698
$469$		−	3.53123e11i		−	0.337014i
$470$			9.72992e11i			0.919748i
$471$		−	4.31565e11i		−	0.404066i
$472$	1.40578e12			1.30370
$473$		−	8.64515e11i		−	0.794141i
$474$	−1.46823e12			−1.33595
$475$	−3.87591e11			−0.349343
$476$	1.13298e12	+	4.49112e10i	1.01156	+	0.0400981i
$477$	5.98296e11			0.529155
$478$	1.15233e12			1.00960
$479$		−	1.79275e12i		−	1.55600i	−0.628266	−	0.777998i	$-0.716235\pi$
$479$		−	1.79275e12i		−	1.55600i	0.628266	−	0.777998i	$-0.283765\pi$
$480$	7.43209e11			0.639036
$481$			1.54146e10i			0.0131304i
$482$			1.51665e11i			0.127989i
$483$		−	1.44533e11i		−	0.120838i
$484$	−6.13029e11			−0.507782
$485$	−9.21824e11			−0.756502
$486$			1.02175e12i			0.830768i
$487$			1.88154e12i			1.51577i	0.652386	+	0.757887i	$0.273768\pi$
$487$			1.88154e12i			1.51577i	−0.652386	+	0.757887i	$0.726232\pi$
$488$			2.72865e11i			0.217801i
$489$	−2.95093e11			−0.233383
$490$		−	7.52162e11i		−	0.589426i
$491$	2.04604e12			1.58872			0.794359	−	0.607448i	$-0.207807\pi$
$491$	2.04604e12			1.58872			0.794359	+	0.607448i	$0.207807\pi$
$492$	−2.79118e12			−2.14756
$493$	−1.28846e12	−	5.10746e10i	−0.982336	−	0.0389398i
$494$	2.44384e10			0.0184630
$495$	2.72165e11			0.203755
$496$			1.54021e11i			0.114265i
$497$	1.48477e12			1.09158
$498$			2.28625e12i			1.66568i
$499$			2.49934e12i			1.80457i	0.431141	+	0.902284i	$0.358111\pi$
$499$			2.49934e12i			1.80457i	−0.431141	+	0.902284i	$0.641889\pi$
$500$			2.20732e12i			1.57943i
$501$	−7.27395e11			−0.515823
$502$	−4.56701e11			−0.320970
$503$		−	1.26660e12i		−	0.882231i	−0.897450	−	0.441115i	$-0.854583\pi$
$503$		−	1.26660e12i		−	0.882231i	0.897450	−	0.441115i	$-0.145417\pi$
$504$		−	2.18469e11i		−	0.150817i
$505$			1.40153e12i			0.958942i
$506$	5.79759e11			0.393161
$507$			1.27152e12i			0.854650i
$508$	−1.81063e12			−1.20626
$509$	−9.24061e11			−0.610198			−0.305099	−	0.952321i	$-0.598690\pi$
$509$	−9.24061e11			−0.610198			−0.305099	+	0.952321i	$0.598690\pi$
$510$	−5.40532e10	+	1.36360e12i	−0.0353798	+	0.892529i
$511$	1.07401e12			0.696811
$512$	−5.62439e11			−0.361710
$513$			1.04466e12i			0.665960i
$514$	2.92400e12			1.84775
$515$		−	1.65016e11i		−	0.103370i
$516$		−	1.45320e12i		−	0.902406i
$517$			1.64994e12i			1.01569i
$518$	1.19636e12			0.730090
$519$	−9.06991e11			−0.548719
$520$		−	1.75612e10i		−	0.0105327i
$521$		−	1.78556e12i		−	1.06171i	−0.847464	−	0.530853i	$-0.821872\pi$
$521$		−	1.78556e12i		−	1.06171i	0.847464	−	0.530853i	$-0.178128\pi$
$522$			7.14184e11i			0.421010i
$523$	1.92158e11			0.112306			0.0561528	−	0.998422i	$-0.482117\pi$
$523$	1.92158e11			0.112306			0.0561528	+	0.998422i	$0.482117\pi$
$524$		−	1.84506e12i		−	1.06910i
$525$	5.59173e11			0.321240
$526$	−1.57373e12			−0.896386
$527$	−1.11106e12	−	4.40423e10i	−0.627463	−	0.0248726i
$528$	3.20546e11			0.179489
$529$	1.71860e12			0.954164
$530$		−	3.73258e12i		−	2.05479i
$531$	−7.56801e11			−0.413101
$532$		−	1.14804e12i		−	0.621379i
$533$		−	5.76795e10i		−	0.0309563i
$534$		−	2.73833e12i		−	1.45730i
$535$	−2.18229e12			−1.15165
$536$	8.28302e11			0.433458
$537$			2.38656e11i			0.123848i
$538$		−	5.48929e12i		−	2.82485i
$539$		−	1.27547e12i		−	0.650909i
$540$	2.15789e12			1.09209
$541$			1.86552e12i			0.936294i	0.883651	+	0.468147i	$0.155078\pi$
$541$			1.86552e12i			0.936294i	−0.883651	+	0.468147i	$0.844922\pi$
$542$	−5.10791e11			−0.254241
$543$	2.61364e12			1.29017
$544$	9.21312e10	−	2.32420e12i	0.0451036	−	1.13783i
$545$	−8.56157e10			−0.0415690
$546$	−3.52570e10			−0.0169777
$547$		−	7.99617e11i		−	0.381891i	−0.981601	−	0.190945i	$-0.938845\pi$
$547$		−	7.99617e11i		−	0.381891i	0.981601	−	0.190945i	$-0.0611554\pi$
$548$	−1.84892e12			−0.875799
$549$		−	1.46897e11i		−	0.0690138i
$550$			2.24299e12i			1.04519i
$551$			1.30559e12i			0.603429i
$552$	3.39023e11			0.155419
$553$	−1.42532e12			−0.648112
$554$			2.83164e12i			1.27716i
$555$			8.71536e11i			0.389912i
$556$		−	4.05015e12i		−	1.79736i
$557$	−9.85166e11			−0.433672			−0.216836	−	0.976208i	$-0.569574\pi$
$557$	−9.85166e11			−0.433672			−0.216836	+	0.976208i	$0.569574\pi$
$558$			6.15850e11i			0.268919i
$559$	3.00302e10			0.0130079
$560$	1.83506e11			0.0788506
$561$	−9.16600e10	+	2.31231e12i	−0.0390703	+	0.985629i
$562$	1.34027e12			0.566733
$563$	−2.98482e12			−1.25207			−0.626037	−	0.779793i	$-0.715324\pi$
$563$	−2.98482e12			−1.25207			−0.626037	+	0.779793i	$0.715324\pi$
$564$			2.77345e12i			1.15416i
$565$	−1.57580e12			−0.650552
$566$		−	2.65723e11i		−	0.108832i
$567$		−	1.06999e12i		−	0.434765i
$568$			3.48275e12i			1.40396i
$569$	2.16083e12			0.864202			0.432101	−	0.901825i	$-0.357772\pi$
$569$	2.16083e12			0.864202			0.432101	+	0.901825i	$0.357772\pi$
$570$	1.38174e12			0.548263
$571$			2.50099e12i			0.984576i	0.870432	+	0.492288i	$0.163839\pi$
$571$			2.50099e12i			0.984576i	−0.870432	+	0.492288i	$0.836161\pi$
$572$		−	8.56021e10i		−	0.0334351i
$573$		−	1.86902e12i		−	0.724301i
$574$	−4.47661e12			−1.72126
$575$		−	3.19400e11i		−	0.121851i
$576$	−1.15895e12			−0.438696
$577$	3.98607e12			1.49711			0.748556	−	0.663072i	$-0.230748\pi$
$577$	3.98607e12			1.49711			0.748556	+	0.663072i	$0.230748\pi$
$578$	4.25762e12	+	3.38076e11i	1.58669	+	0.125991i
$579$	−4.27978e11			−0.158259
$580$	2.69688e12			0.989546
$581$			2.21944e12i			0.808073i
$582$	−4.34111e12			−1.56837
$583$		−	6.32948e12i		−	2.26913i
$584$			2.51925e12i			0.896219i
$585$			9.45406e9i			0.00333747i
$586$	−3.45374e12			−1.20990
$587$	3.85772e11			0.134110			0.0670548	−	0.997749i	$-0.478640\pi$
$587$	3.85772e11			0.134110			0.0670548	+	0.997749i	$0.478640\pi$
$588$		−	2.14399e12i		−	0.739648i
$589$			1.12583e12i			0.385438i
$590$			4.72145e12i			1.60414i
$591$	3.68913e12			1.24388
$592$		−	3.77825e11i		−	0.126428i
$593$	3.33499e12			1.10751			0.553755	−	0.832679i	$-0.313194\pi$
$593$	3.33499e12			1.10751			0.553755	+	0.832679i	$0.313194\pi$
$594$	6.04546e12			1.99246
$595$	−5.24736e10	+	1.32375e12i	−0.0171638	+	0.432993i
$596$	−4.74397e12			−1.54004
$597$	−1.78436e12			−0.574907
$598$			2.01388e10i			0.00643989i
$599$	−3.02329e12			−0.959531			−0.479766	−	0.877397i	$-0.659278\pi$
$599$	−3.02329e12			−0.959531			−0.479766	+	0.877397i	$0.659278\pi$
$600$			1.31162e12i			0.413169i
$601$		−	1.33418e12i		−	0.417137i	−0.978008	−	0.208568i	$-0.933120\pi$
$601$		−	1.33418e12i		−	0.417137i	0.978008	−	0.208568i	$-0.0668804\pi$
$602$		−	2.33070e12i		−	0.723273i
$603$	−4.45915e11			−0.137349
$604$	5.94222e12			1.81670
$605$		−	7.16254e11i		−	0.217354i
$606$			6.60020e12i			1.98806i
$607$		−	8.24460e11i		−	0.246502i	−0.992376	−	0.123251i	$-0.960668\pi$
$607$		−	8.24460e11i		−	0.246502i	0.992376	−	0.123251i	$-0.0393320\pi$
$608$	−2.35511e12			−0.698947
$609$		−	1.88357e12i		−	0.554886i
$610$	−9.16443e11			−0.267992
$611$	−5.73131e10			−0.0166368
$612$	5.67128e10	−	1.43070e12i	0.0163418	−	0.412255i
$613$	−2.33330e12			−0.667419			−0.333709	−	0.942676i	$-0.608300\pi$
$613$	−2.33330e12			−0.667419			−0.333709	+	0.942676i	$0.608300\pi$
$614$	−4.90938e12			−1.39402
$615$		−	3.26118e12i		−	0.919256i
$616$	−2.31122e12			−0.646737
$617$			3.34499e12i			0.929206i	0.885519	+	0.464603i	$0.153803\pi$
$617$			3.34499e12i			0.929206i	−0.885519	+	0.464603i	$0.846197\pi$
$618$		−	7.77104e11i		−	0.214304i
$619$			3.20260e12i			0.876788i	0.898783	+	0.438394i	$0.144453\pi$
$619$			3.20260e12i			0.876788i	−0.898783	+	0.438394i	$0.855547\pi$
$620$	2.32556e12			0.632069
$621$	−8.60869e11			−0.232287
$622$		−	4.82176e12i		−	1.29166i
$623$		−	2.65831e12i		−	0.706983i
$624$			1.11346e10i			0.00293999i
$625$	−4.07859e11			−0.106918
$626$			3.12978e12i			0.814571i
$627$	2.34306e12			0.605452
$628$	2.82488e12			0.724738
$629$	2.72551e12	+	1.08039e11i	0.694255	+	0.0275203i
$630$	7.33747e11			0.185573
$631$	1.11507e12			0.280007			0.140004	−	0.990151i	$-0.455289\pi$
$631$	1.11507e12			0.280007			0.140004	+	0.990151i	$0.455289\pi$
$632$		−	3.34330e12i		−	0.833583i
$633$	−4.16363e12			−1.03076
$634$			8.94129e12i			2.19785i
$635$		−	2.11551e12i		−	0.516337i
$636$		−	1.06395e13i		−	2.57848i
$637$	4.43053e10			0.0106618
$638$	7.55548e12			1.80538
$639$		−	1.87493e12i		−	0.444868i
$640$			4.05790e12i			0.956074i
$641$			4.56993e12i			1.06917i	0.845113	+	0.534587i	$0.179533\pi$
$641$			4.56993e12i			1.06917i	−0.845113	+	0.534587i	$0.820467\pi$
$642$	−1.02770e13			−2.38758
$643$		−	2.30320e12i		−	0.531351i	−0.964062	−	0.265676i	$-0.914405\pi$
$643$		−	2.30320e12i		−	0.531351i	0.964062	−	0.265676i	$-0.0855950\pi$
$644$	9.46062e11			0.216737
$645$	1.69790e12			0.386272
$646$	1.71286e11	−	4.32103e12i	0.0386968	−	0.976205i
$647$	−5.60809e12			−1.25819			−0.629094	−	0.777329i	$-0.716574\pi$
$647$	−5.60809e12			−1.25819			−0.629094	+	0.777329i	$0.716574\pi$
$648$	2.50981e12			0.559182
$649$			8.00633e12i			1.77146i
$650$	−7.79136e10			−0.0171200
$651$		−	1.62422e12i		−	0.354431i
$652$		−	1.93158e12i		−	0.418598i
$653$			1.27396e12i			0.274186i	0.990558	+	0.137093i	$0.0437759\pi$
$653$			1.27396e12i			0.274186i	−0.990558	+	0.137093i	$0.956224\pi$
$654$	−4.03187e11			−0.0861800
$655$	2.15574e12			0.457625
$656$			1.41377e12i			0.298066i
$657$		−	1.35624e12i		−	0.283982i
$658$			4.44817e12i			0.925050i
$659$	−2.22728e12			−0.460035			−0.230017	−	0.973187i	$-0.573878\pi$
$659$	−2.22728e12			−0.460035			−0.230017	+	0.973187i	$0.573878\pi$
$660$		−	4.83991e12i		−	0.992864i
$661$	5.98094e12			1.21860			0.609302	−	0.792938i	$-0.291450\pi$
$661$	5.98094e12			1.21860			0.609302	+	0.792938i	$0.291450\pi$
$662$	1.04017e13			2.10497
$663$	−8.03217e10	−	3.18395e9i	−0.0161444	−	0.000639964i
$664$	−5.20602e12			−1.03932
$665$	1.34136e12			0.265979
$666$		−	1.51073e12i		−	0.297545i
$667$	−1.07589e12			−0.210476
$668$		−	4.76128e12i		−	0.925186i
$669$			4.30679e12i			0.831259i
$670$			2.78193e12i			0.533346i
$671$	−1.55405e12			−0.295946
$672$	3.39769e12			0.642720
$673$		−	6.43719e12i		−	1.20956i	−0.796392	−	0.604781i	$-0.793261\pi$
$673$		−	6.43719e12i		−	1.20956i	0.796392	−	0.604781i	$-0.206739\pi$
$674$		−	3.30425e12i		−	0.616742i
$675$		−	3.33055e12i		−	0.617518i
$676$	−8.32295e12			−1.53291
$677$		−	7.34022e11i		−	0.134295i	−0.997743	−	0.0671476i	$-0.978610\pi$
$677$		−	7.34022e11i		−	0.134295i	0.997743	−	0.0671476i	$-0.0213898\pi$
$678$	−7.42085e12			−1.34871
$679$	−4.21425e12			−0.760863
$680$	−3.10506e12	−	1.23085e11i	−0.556903	−	0.0220756i
$681$	6.73477e11			0.119994
$682$	6.51519e12			1.15318
$683$			4.45334e12i			0.783057i	0.920166	+	0.391528i	$0.128053\pi$
$683$			4.45334e12i			0.783057i	−0.920166	+	0.391528i	$0.871947\pi$
$684$	−1.44972e12			−0.253240
$685$		−	2.16024e12i		−	0.374883i
$686$		−	9.53363e12i		−	1.64361i
$687$		−	9.48460e12i		−	1.62448i
$688$	−7.36067e11			−0.125248
$689$	2.19864e11			0.0371679
$690$			1.13864e12i			0.191234i
$691$			1.18066e12i			0.197004i	0.995137	+	0.0985019i	$0.0314051\pi$
$691$			1.18066e12i			0.197004i	−0.995137	+	0.0985019i	$0.968595\pi$
$692$		−	5.93685e12i		−	0.984189i
$693$	1.24424e12			0.204930
$694$			1.74644e13i			2.85782i
$695$	4.73213e12			0.769352
$696$	4.41818e12			0.713678
$697$	−1.01985e13	−	4.04269e11i	−1.63677	−	0.0648817i
$698$	2.31770e11			0.0369579
$699$	8.17742e12			1.29559
$700$			3.66015e12i			0.576180i
$701$	5.00732e11			0.0783202			0.0391601	−	0.999233i	$-0.487532\pi$
$701$	5.00732e11			0.0783202			0.0391601	+	0.999233i	$0.487532\pi$
$702$			2.09998e11i			0.0326361i
$703$		−	2.76175e12i		−	0.426467i
$704$			1.22607e13i			1.88122i
$705$	−3.24046e12			−0.494033
$706$	6.61352e12			1.00187
$707$			6.40731e12i			0.964470i
$708$			1.34582e13i			2.01297i
$709$			4.45528e12i			0.662166i	0.943602	+	0.331083i	$0.107414\pi$
$709$			4.45528e12i			0.662166i	−0.943602	+	0.331083i	$0.892586\pi$
$710$	−1.16971e13			−1.72749
$711$			1.79986e12i			0.264135i
$712$	6.23545e12			0.909301
$713$	−9.27757e11			−0.134441
$714$	−2.47112e11	+	6.23391e12i	−0.0355838	+	0.897674i
$715$	1.00016e11			0.0143118
$716$	−1.56216e12			−0.222135
$717$			3.83773e12i			0.542298i
$718$	1.60288e13			2.25083
$719$		−	2.07009e12i		−	0.288874i	−0.989514	−	0.144437i	$-0.953863\pi$
$719$		−	2.07009e12i		−	0.288874i	0.989514	−	0.144437i	$-0.0461372\pi$
$720$		−	2.31727e11i		−	0.0321352i
$721$		−	7.54394e11i		−	0.103966i
$722$	7.24333e12			0.992021
$723$	−5.05105e11			−0.0687479
$724$			1.71080e13i			2.31407i
$725$		−	4.16245e12i		−	0.559536i
$726$		−	3.37303e12i		−	0.450615i
$727$	−5.41864e12			−0.719425			−0.359713	−	0.933063i	$-0.617125\pi$
$727$	−5.41864e12			−0.719425			−0.359713	+	0.933063i	$0.617125\pi$
$728$		−	8.02837e10i		−	0.0105934i
$729$	−8.42474e12			−1.10480
$730$	−8.46114e12			−1.10275
$731$	2.10478e11	−	5.30975e12i	0.0272633	−	0.687774i
$732$	−2.61226e12			−0.336292
$733$	1.11750e13			1.42982			0.714909	−	0.699218i	$-0.246468\pi$
$733$	1.11750e13			1.42982			0.714909	+	0.699218i	$0.246468\pi$
$734$		−	1.46137e13i		−	1.85836i
$735$	2.50501e12			0.316603
$736$		−	1.94076e12i		−	0.243793i
$737$			4.71742e12i			0.588980i
$738$			5.65295e12i			0.701490i
$739$	5.17452e12			0.638219			0.319110	−	0.947718i	$-0.396616\pi$
$739$	5.17452e12			0.638219			0.319110	+	0.947718i	$0.396616\pi$
$740$	−5.70477e12			−0.699351
$741$			8.13898e10i			0.00991718i
$742$		−	1.70640e13i		−	2.06664i
$743$		−	6.63620e12i		−	0.798859i	−0.916764	−	0.399429i	$-0.869208\pi$
$743$		−	6.63620e12i		−	0.798859i	0.916764	−	0.399429i	$-0.130792\pi$
$744$	3.80986e12			0.455859
$745$		−	5.54278e12i		−	0.659211i
$746$	−1.46834e13			−1.73581
$747$	2.80265e12			0.329326
$748$	−1.51356e13	−	5.99975e11i	−1.76784	−	0.0700770i
$749$	−9.97665e12			−1.15829
$750$	−1.21452e13			−1.40161
$751$		−	1.50960e13i		−	1.73173i	−0.500275	−	0.865866i	$-0.666768\pi$
$751$		−	1.50960e13i		−	1.73173i	0.500275	−	0.865866i	$-0.333232\pi$
$752$	1.40479e12			0.160189
$753$		−	1.52100e12i		−	0.172406i
$754$			2.62451e11i			0.0295718i
$755$			6.94280e12i			0.777630i
$756$	9.86511e12			1.09838
$757$	3.33377e12			0.368981			0.184491	−	0.982834i	$-0.440936\pi$
$757$	3.33377e12			0.368981			0.184491	+	0.982834i	$0.440936\pi$
$758$		−	2.42379e13i		−	2.66676i
$759$			1.93083e12i			0.211182i
$760$			3.14635e12i			0.342094i
$761$	1.76503e13			1.90774			0.953872	−	0.300213i	$-0.0970579\pi$
$761$	1.76503e13			1.90774			0.953872	+	0.300213i	$0.0970579\pi$
$762$		−	9.96249e12i		−	1.07046i
$763$	−3.91404e11			−0.0418086
$764$	1.22340e13			1.29912
$765$	1.67160e12	+	6.62623e10i	0.176464	+	0.00699504i
$766$	1.25908e13			1.32137
$767$	−2.78112e11			−0.0290162
$768$			5.66979e12i			0.588087i
$769$	1.65629e12			0.170793			0.0853963	−	0.996347i	$-0.472784\pi$
$769$	1.65629e12			0.170793			0.0853963	+	0.996347i	$0.472784\pi$
$770$		−	7.76244e12i		−	0.795774i
$771$			9.73810e12i			0.992497i
$772$		−	2.80139e12i		−	0.283855i
$773$	9.98087e12			1.00545			0.502725	−	0.864446i	$-0.332331\pi$
$773$	9.98087e12			1.00545			0.502725	+	0.864446i	$0.332331\pi$
$774$	−2.94315e12			−0.294767
$775$		−	3.58933e12i		−	0.357401i
$776$		−	9.88514e12i		−	0.978600i
$777$			3.98435e12i			0.392160i
$778$	−1.79150e13			−1.75311
$779$			1.03341e13i			1.00544i
$780$	1.68122e11			0.0162629
$781$	−1.98352e13			−1.90769
$782$	3.56081e12	+	1.41150e11i	0.340501	+	0.0134974i
$783$	−1.12189e13			−1.06665
$784$	−1.08596e12			−0.102658
$785$			3.30054e12i			0.310221i
$786$	1.01519e13			0.948740
$787$			8.71656e12i			0.809951i	0.914328	+	0.404975i	$0.132720\pi$
$787$			8.71656e12i			0.809951i	−0.914328	+	0.404975i	$0.867280\pi$
$788$			2.41478e13i			2.23105i
$789$		−	5.24117e12i		−	0.481484i
$790$	1.12288e13			1.02568
$791$	−7.20398e12			−0.654302
$792$			2.91855e12i			0.263575i
$793$		−	5.39821e10i		−	0.00484753i
$794$		−	5.69928e12i		−	0.508895i
$795$	1.24310e13			1.10371
$796$		−	1.16798e13i		−	1.03116i
$797$	−1.27804e13			−1.12197			−0.560987	−	0.827825i	$-0.689578\pi$
$797$	−1.27804e13			−1.12197			−0.560987	+	0.827825i	$0.689578\pi$
$798$	6.31681e12			0.551423
$799$	−4.01700e11	+	1.01337e13i	−0.0348692	+	0.879647i
$800$	7.50846e12			0.648106
$801$	−3.35684e12			−0.288127
$802$			3.27855e12i			0.279832i
$803$	−1.43479e13			−1.21778
$804$			7.92971e12i			0.669276i
$805$			1.10536e12i			0.0927735i
$806$			2.26315e11i			0.0188888i
$807$	1.82816e13			1.51734
$808$	−1.50293e13			−1.24047
$809$			3.13377e12i			0.257216i	0.991695	+	0.128608i	$0.0410509\pi$
$809$			3.13377e12i			0.257216i	−0.991695	+	0.128608i	$0.958949\pi$
$810$			8.42943e12i			0.688043i
$811$			9.63303e12i			0.781932i	0.920405	+	0.390966i	$0.127859\pi$
$811$			9.63303e12i			0.781932i	−0.920405	+	0.390966i	$0.872141\pi$
$812$	1.23292e13			0.995250
$813$		−	1.70114e12i		−	0.136563i
$814$	−1.59823e13			−1.27593
$815$	2.25682e12			0.179180
$816$	1.96875e12	+	7.80413e10i	0.155448	+	0.00616196i
$817$	−5.38036e12			−0.422485
$818$	−1.52469e13			−1.19067
$819$			4.32206e10i			0.00335670i
$820$	2.13465e13			1.64879
$821$			2.49670e13i			1.91788i	0.283602	+	0.958942i	$0.408471\pi$
$821$			2.49670e13i			1.91788i	−0.283602	+	0.958942i	$0.591529\pi$
$822$		−	1.01732e13i		−	0.777200i
$823$		−	4.54640e12i		−	0.345437i	−0.984971	−	0.172718i	$-0.944745\pi$
$823$		−	4.54640e12i		−	0.345437i	0.984971	−	0.172718i	$-0.0552551\pi$
$824$	1.76954e12			0.133718
$825$	−7.47006e12			−0.561412
$826$			2.15848e13i			1.61338i
$827$			2.42269e13i			1.80104i	0.434819	+	0.900518i	$0.356812\pi$
$827$			2.42269e13i			1.80104i	−0.434819	+	0.900518i	$0.643188\pi$
$828$		−	1.19466e12i		−	0.0883302i
$829$	1.77633e13			1.30626			0.653130	−	0.757246i	$-0.273456\pi$
$829$	1.77633e13			1.30626			0.653130	+	0.757246i	$0.273456\pi$
$830$		−	1.74849e13i		−	1.27883i
$831$	−9.43052e12			−0.686011
$832$	−4.25895e11			−0.0308140
$833$	3.10531e11	−	7.83377e12i	0.0223461	−	0.563726i
$834$	2.22849e13			1.59501
$835$	5.56300e12			0.396023
$836$			1.53369e13i			1.08595i
$837$	−9.67423e12			−0.681321
$838$		−	2.24171e13i		−	1.57029i
$839$		−	1.27875e13i		−	0.890955i	−0.895293	−	0.445477i	$-0.853034\pi$
$839$		−	1.27875e13i		−	0.890955i	0.895293	−	0.445477i	$-0.146966\pi$
$840$		−	4.53921e12i		−	0.314574i
$841$	4.85991e11			0.0335001
$842$	−1.68299e13			−1.15393
$843$			4.46364e12i			0.304414i
$844$		−	2.72537e13i		−	1.84878i
$845$		−	9.72440e12i		−	0.656157i
$846$	5.61704e12			0.377000
$847$		−	3.27446e12i		−	0.218607i
$848$	−5.38906e12			−0.357875
$849$	8.84966e11			0.0584577
$850$	−5.46087e11	+	1.37762e13i	−0.0358820	+	0.905197i
$851$	2.27586e12			0.148752
$852$	−3.33419e13			−2.16777
$853$		−	1.39538e13i		−	0.902450i	−0.892410	−	0.451225i	$-0.850987\pi$
$853$		−	1.39538e13i		−	0.902450i	0.892410	−	0.451225i	$-0.149013\pi$
$854$	−4.18965e12			−0.269536
$855$		−	1.69383e12i		−	0.108398i
$856$		−	2.34017e13i		−	1.48976i
$857$		−	1.46381e13i		−	0.926984i	−0.886101	−	0.463492i	$-0.846596\pi$
$857$		−	1.46381e13i		−	0.926984i	0.886101	−	0.463492i	$-0.153404\pi$
$858$	4.71003e11			0.0296709
$859$	1.39610e13			0.874876			0.437438	−	0.899249i	$-0.355886\pi$
$859$	1.39610e13			0.874876			0.437438	+	0.899249i	$0.355886\pi$
$860$			1.11138e13i			0.692822i
$861$		−	1.49089e13i		−	0.924554i
$862$			9.29093e12i			0.573161i
$863$	3.05848e13			1.87697			0.938485	−	0.345321i	$-0.112230\pi$
$863$	3.05848e13			1.87697			0.938485	+	0.345321i	$0.112230\pi$
$864$		−	2.02373e13i		−	1.23550i
$865$	6.93652e12			0.421278
$866$	9.87480e12			0.596620
$867$	−1.12593e12	+	1.41796e13i	−0.0676745	+	0.852273i
$868$	1.06316e13			0.635712
$869$	1.90411e13			1.13267
$870$			1.48389e13i			0.878141i
$871$	−1.63867e11			−0.00964737
$872$		−	9.18096e11i		−	0.0537730i
$873$			5.32165e12i			0.310086i
$874$		−	3.60816e12i		−	0.209163i
$875$	−1.17902e13			−0.679965
$876$	−2.41179e13			−1.38380
$877$		−	1.08401e13i		−	0.618781i	−0.950935	−	0.309391i	$-0.899875\pi$
$877$		−	1.08401e13i		−	0.618781i	0.950935	−	0.309391i	$-0.100125\pi$
$878$			2.84676e13i			1.61668i
$879$		−	1.15024e13i		−	0.649886i
$880$	−2.45148e12			−0.137802
$881$			2.25641e13i			1.26190i	0.775822	+	0.630952i	$0.217335\pi$
$881$			2.25641e13i			1.26190i	−0.775822	+	0.630952i	$0.782665\pi$
$882$	−4.34220e12			−0.241602
$883$	−2.69045e13			−1.48937			−0.744684	−	0.667417i	$-0.767400\pi$
$883$	−2.69045e13			−1.48937			−0.744684	+	0.667417i	$0.767400\pi$
$884$	2.08410e10	−	5.25758e11i	0.00114785	−	0.0289568i
$885$	−1.57243e13			−0.861644
$886$	2.37301e12			0.129374
$887$		−	1.58992e12i		−	0.0862422i	−0.999070	−	0.0431211i	$-0.986270\pi$
$887$		−	1.58992e12i		−	0.0862422i	0.999070	−	0.0431211i	$-0.0137301\pi$
$888$	−9.34587e12			−0.504384
$889$		−	9.67135e12i		−	0.519313i
$890$			2.09423e13i			1.11884i
$891$			1.42941e13i			0.759813i
$892$	−2.81908e13			−1.49096
$893$	1.02685e13			0.540349
$894$		−	2.61024e13i		−	1.36666i
$895$		−	1.82520e12i		−	0.0950839i
$896$			1.85513e13i			0.961585i
$897$	−6.70704e10			−0.00345911
$898$			3.12088e13i			1.60153i
$899$	−1.20906e13			−0.617348
$900$	4.62195e12			0.234819
$901$	1.54100e12	−	3.88749e13i	0.0779006	−	1.96520i
$902$	5.98036e13			3.00814
$903$	7.76218e12			0.388498
$904$		−	1.68980e13i		−	0.841545i
$905$	−1.99887e13			−0.990527
$906$			3.26955e13i			1.61217i
$907$		−	1.69740e13i		−	0.832821i	−0.909177	−	0.416411i	$-0.863288\pi$
$907$		−	1.69740e13i		−	0.832821i	0.909177	−	0.416411i	$-0.136712\pi$
$908$			4.40834e12i			0.215223i
$909$	8.09099e12			0.393065
$910$	2.69640e11			0.0130346
$911$			7.56497e12i			0.363894i	0.983308	+	0.181947i	$0.0582399\pi$
$911$			7.56497e12i			0.363894i	−0.983308	+	0.181947i	$0.941760\pi$
$912$		−	1.99493e12i		−	0.0954886i
$913$		−	2.96497e13i		−	1.41222i
$914$	−2.25226e13			−1.06748
$915$		−	3.05213e12i		−	0.143949i
$916$	6.20829e13			2.91368
$917$	9.85525e12			0.460263
$918$	3.71305e13	+	1.47185e12i	1.72559	+	0.0684025i
$919$	−3.81894e13			−1.76613			−0.883065	−	0.469251i	$-0.844524\pi$
$919$	−3.81894e13			−1.76613			−0.883065	+	0.469251i	$0.844524\pi$
$920$	−2.59279e12			−0.119323
$921$		−	1.63502e13i		−	0.748782i
$922$	5.25360e13			2.39424
$923$		−	6.89007e11i		−	0.0312476i
$924$		−	2.21263e13i		−	0.998586i
$925$			8.80491e12i			0.395446i
$926$	−5.60068e13			−2.50318
$927$	−9.52630e11			−0.0423707
$928$		−	2.52922e13i		−	1.11949i
$929$		−	3.31874e13i		−	1.46185i	−0.682457	−	0.730925i	$-0.739089\pi$
$929$		−	3.31874e13i		−	1.46185i	0.682457	−	0.730925i	$-0.260911\pi$
$930$			1.27958e13i			0.560909i
$931$	−7.93795e12			−0.346286
$932$			5.35265e13i			2.32379i
$933$	1.60584e13			0.693803
$934$	−6.98306e13			−3.00251
$935$	7.01001e11	−	1.76842e13i	0.0299962	−	0.756716i
$936$	−1.01380e11			−0.00431730
$937$	1.99592e13			0.845891			0.422945	−	0.906155i	$-0.360996\pi$
$937$	1.99592e13			0.845891			0.422945	+	0.906155i	$0.360996\pi$
$938$			1.27180e13i			0.536421i
$939$	−1.04234e13			−0.437538
$940$		−	2.12109e13i		−	0.886103i
$941$		−	9.88180e12i		−	0.410849i	−0.978673	−	0.205425i	$-0.934142\pi$
$941$		−	9.88180e12i		−	0.410849i	0.978673	−	0.205425i	$-0.0658576\pi$
$942$			1.55431e13i			0.643146i
$943$	−8.51598e12			−0.350697
$944$	6.81677e12			0.279386
$945$			1.15262e13i			0.470159i
$946$			3.11361e13i			1.26402i
$947$			4.35997e13i			1.76161i	0.473482	+	0.880803i	$0.342997\pi$
$947$			4.35997e13i			1.76161i	−0.473482	+	0.880803i	$0.657003\pi$
$948$	3.20069e13			1.28708
$949$		−	4.98395e11i		−	0.0199469i
$950$	1.39594e13			0.556044
$951$	−2.97781e13			−1.18055
$952$	−1.41952e13	−	5.62698e11i	−0.560113	−	0.0222029i
$953$	−8.78631e12			−0.345055			−0.172528	−	0.985005i	$-0.555193\pi$
$953$	−8.78631e12			−0.345055			−0.172528	+	0.985005i	$0.555193\pi$
$954$	−2.15480e13			−0.842248
$955$			1.42940e13i			0.556082i
$956$	−2.51204e13			−0.972672
$957$			2.51628e13i			0.969740i
$958$			6.45670e13i			2.47666i
$959$		−	9.87587e12i		−	0.377043i
$960$	−2.40799e13			−0.915029
$961$	1.60137e13			0.605671
$962$		−	5.55168e11i		−	0.0208995i
$963$			1.25983e13i			0.472055i
$964$		−	3.30624e12i		−	0.123307i
$965$	3.27310e12			0.121503
$966$			5.20545e12i			0.192336i
$967$	5.16213e13			1.89850			0.949249	−	0.314525i	$-0.101845\pi$
$967$	5.16213e13			1.89850			0.949249	+	0.314525i	$0.101845\pi$
$968$	7.68072e12			0.281166
$969$	1.43908e13	+	5.70451e11i	0.524358	+	0.0207855i
$970$	3.32001e13			1.20411
$971$	2.90086e13			1.04722			0.523612	−	0.851957i	$-0.324584\pi$
$971$	2.90086e13			1.04722			0.523612	+	0.851957i	$0.324584\pi$
$972$		−	2.22737e13i		−	0.800377i
$973$	2.16336e13			0.773787
$974$		−	6.77651e13i		−	2.41263i
$975$		−	2.59484e11i		−	0.00919581i
$976$			1.32315e12i			0.0466750i
$977$	−3.35721e13			−1.17883			−0.589417	−	0.807829i	$-0.700642\pi$
$977$	−3.35721e13			−1.17883			−0.589417	+	0.807829i	$0.700642\pi$
$978$	1.06280e13			0.371472
$979$			3.55126e13i			1.23555i
$980$			1.63969e13i			0.567864i
$981$			4.94256e11i			0.0170389i
$982$	−7.36895e13			−2.52874
$983$		−	3.00685e13i		−	1.02712i	−0.858054	−	0.513559i	$-0.828327\pi$
$983$		−	3.00685e13i		−	1.02712i	0.858054	−	0.513559i	$-0.171673\pi$
$984$	3.49711e13			1.18914
$985$	−2.82139e13			−0.954991
$986$	4.64048e13	+	1.83949e12i	1.56357	+	0.0619798i
$987$	−1.48142e13			−0.496880
$988$	−5.32749e11			−0.0177876
$989$		−	4.43376e12i		−	0.147363i
$990$	−9.80221e12			−0.324314
$991$		−	2.45476e13i		−	0.808494i	−0.914650	−	0.404247i	$-0.867534\pi$
$991$		−	2.45476e13i		−	0.808494i	0.914650	−	0.404247i	$-0.132466\pi$
$992$		−	2.18098e13i		−	0.715069i
$993$			3.46420e13i			1.13066i
$994$	−5.34751e13			−1.73745
$995$	1.36465e13			0.441384
$996$		−	4.98395e13i		−	1.60475i
$997$			4.26106e13i			1.36581i	0.730509	+	0.682904i	$0.239283\pi$
$997$			4.26106e13i			1.36581i	−0.730509	+	0.682904i	$0.760717\pi$
$998$		−	9.00156e13i		−	2.87230i
$999$	2.37316e13			0.753846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.b.a.16.1	✓	12
3.2	odd	2		153.10.d.b.118.11		12
4.3	odd	2		272.10.b.c.33.10		12
17.4	even	4		289.10.a.c.1.11		12
17.13	even	4		289.10.a.c.1.12		12
17.16	even	2	inner	17.10.b.a.16.2	yes	12
51.50	odd	2		153.10.d.b.118.12		12
68.67	odd	2		272.10.b.c.33.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.1	✓	12	1.1	even	1	trivial
17.10.b.a.16.2	yes	12	17.16	even	2	inner
153.10.d.b.118.11		12	3.2	odd	2
153.10.d.b.118.12		12	51.50	odd	2
272.10.b.c.33.3		12	68.67	odd	2
272.10.b.c.33.10		12	4.3	odd	2
289.10.a.c.1.11		12	17.4	even	4
289.10.a.c.1.12		12	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-36.0157 q^{2} -119.947i q^{3} +785.131 q^{4} +917.335i q^{5} +4319.97i q^{6} +4193.73i q^{7} -9837.00 q^{8} +5295.73 q^{9} +O(q^{10})\)	\(q-36.0157 q^{2} -119.947i q^{3} +785.131 q^{4} +917.335i q^{5} +4319.97i q^{6} +4193.73i q^{7} -9837.00 q^{8} +5295.73 q^{9} -33038.5i q^{10} -56024.5i q^{11} -94174.0i q^{12} +1946.10 q^{13} -151040. i q^{14} +110032. q^{15} -47700.5 q^{16} +(13639.9 - 344096. i) q^{17} -190730. q^{18} -348672. q^{19} +720228. i q^{20} +503025. q^{21} +2.01776e6i q^{22} -287328. i q^{23} +1.17992e6i q^{24} +1.11162e6 q^{25} -70090.0 q^{26} -2.99612e6i q^{27} +3.29262e6i q^{28} -3.74448e6i q^{29} -3.96286e6 q^{30} -3.22892e6i q^{31} +6.75451e6 q^{32} -6.71997e6 q^{33} +(-491252. + 1.23928e7i) q^{34} -3.84705e6 q^{35} +4.15784e6 q^{36} +7.92078e6i q^{37} +1.25576e7 q^{38} -233428. i q^{39} -9.02382e6i q^{40} -2.96386e7i q^{41} -1.81168e7 q^{42} +1.54310e7 q^{43} -4.39866e7i q^{44} +4.85796e6i q^{45} +1.03483e7i q^{46} -2.94503e7 q^{47} +5.72153e6i q^{48} +2.27663e7 q^{49} -4.00358e7 q^{50} +(-4.12732e7 - 1.63607e6i) q^{51} +1.52794e6 q^{52} +1.12977e8 q^{53} +1.07907e8i q^{54} +5.13932e7 q^{55} -4.12537e7i q^{56} +4.18221e7i q^{57} +1.34860e8i q^{58} -1.42908e8 q^{59} +8.63891e7 q^{60} -2.77387e7i q^{61} +1.16292e8i q^{62} +2.22089e7i q^{63} -2.18846e8 q^{64} +1.78522e6i q^{65} +2.42024e8 q^{66} -8.42027e7 q^{67} +(1.07091e7 - 2.70160e8i) q^{68} -3.44641e7 q^{69} +1.38554e8 q^{70} -3.54046e8i q^{71} -5.20941e7 q^{72} -2.56100e8i q^{73} -2.85273e8i q^{74} -1.33336e8i q^{75} -2.73753e8 q^{76} +2.34952e8 q^{77} +8.40709e6i q^{78} +3.39870e8i q^{79} -4.37573e7i q^{80} -2.55140e8 q^{81} +1.06745e9i q^{82} +5.29228e8 q^{83} +3.94940e8 q^{84} +(3.15651e8 + 1.25124e7i) q^{85} -5.55759e8 q^{86} -4.49139e8 q^{87} +5.51113e8i q^{88} -6.33877e8 q^{89} -1.74963e8i q^{90} +8.16140e6i q^{91} -2.25590e8i q^{92} -3.87299e8 q^{93} +1.06067e9 q^{94} -3.19849e8i q^{95} -8.10183e8i q^{96} +1.00489e9i q^{97} -8.19943e8 q^{98} -2.96691e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) \) 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9} - 63204 q^{13} - 243480 q^{15} + 38978 q^{16} - 105960 q^{17} + 547706 q^{18} + 1110672 q^{19} - 172580 q^{21} - 4441796 q^{25} + 1336332 q^{26} - 500496 q^{30} - 1934850 q^{32} - 6557404 q^{33} - 15085546 q^{34} + 3519864 q^{35} + 30244102 q^{36} + 28748136 q^{38} - 11901296 q^{42} + 10004616 q^{43} - 112552440 q^{47} + 121354720 q^{49} - 164889018 q^{50} - 52506472 q^{51} - 59093180 q^{52} + 76804272 q^{53} + 300732568 q^{55} + 11618904 q^{59} + 101609232 q^{60} - 260062974 q^{64} + 18429632 q^{66} - 304208752 q^{67} - 444301206 q^{68} - 211308236 q^{69} + 460311456 q^{70} + 493218954 q^{72} + 416024248 q^{76} + 138357828 q^{77} - 363335792 q^{81} - 845042136 q^{83} + 958037984 q^{84} - 388949632 q^{85} + 127952904 q^{86} + 610860648 q^{87} - 938223804 q^{89} + 1635779524 q^{93} - 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9 - 63204 * q^13 - 243480 * q^15 + 38978 * q^16 - 105960 * q^17 + 547706 * q^18 + 1110672 * q^19 - 172580 * q^21 - 4441796 * q^25 + 1336332 * q^26 - 500496 * q^30 - 1934850 * q^32 - 6557404 * q^33 - 15085546 * q^34 + 3519864 * q^35 + 30244102 * q^36 + 28748136 * q^38 - 11901296 * q^42 + 10004616 * q^43 - 112552440 * q^47 + 121354720 * q^49 - 164889018 * q^50 - 52506472 * q^51 - 59093180 * q^52 + 76804272 * q^53 + 300732568 * q^55 + 11618904 * q^59 + 101609232 * q^60 - 260062974 * q^64 + 18429632 * q^66 - 304208752 * q^67 - 444301206 * q^68 - 211308236 * q^69 + 460311456 * q^70 + 493218954 * q^72 + 416024248 * q^76 + 138357828 * q^77 - 363335792 * q^81 - 845042136 * q^83 + 958037984 * q^84 - 388949632 * q^85 + 127952904 * q^86 + 610860648 * q^87 - 938223804 * q^89 + 1635779524 * q^93 - 238629952 * q^94 - 152046078 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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