LMFDB - Embedded newform 289.10.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

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:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$1$
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:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$119.947$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$-0.207029\pi$
$2$	36.0157	1.59168	0.795842	+	0.605504i	$0.207029\pi$
$3$	−119.947	−0.854955	−0.427478	−	0.904026i	$-0.640598\pi$
$3$	−119.947	−0.854955	−0.427478	+	0.904026i	$0.640598\pi$
$4$	785.131	1.53346
$5$	917.335	0.656391	0.328196	−	0.944610i	$-0.393559\pi$
$5$	917.335	0.656391	0.328196	+	0.944610i	$0.393559\pi$
$6$	−4319.97	−1.36082
$7$	−4193.73	−0.660175	−0.330087	−	0.943950i	$-0.607078\pi$
$7$	−4193.73	−0.660175	−0.330087	+	0.943950i	$0.607078\pi$
$8$	9837.00	0.849098
$9$	−5295.73	−0.269051
$10$	33038.5	1.04477
$11$	56024.5	1.15375	0.576874	−	0.816833i	$-0.304272\pi$
$11$	56024.5	1.15375	0.576874	+	0.816833i	$0.304272\pi$
$12$	−94174.0	−1.31104
$13$	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.	−1.05079
$15$	−110032.	−0.561185
$16$	−47700.5	−0.181963
$17$	0	0
$17$	0	0
$18$	−190730.	−0.428244
$19$	348672.	0.613798	0.306899	−	0.951742i	$-0.400709\pi$
$19$	348672.	0.613798	0.306899	+	0.951742i	$0.400709\pi$
$20$	720228.	1.00655
$21$	503025.	0.564420
$22$	2.01776e6	1.83640
$23$	287328.	0.214093	0.107046	−	0.994254i	$-0.465861\pi$
$23$	287328.	0.214093	0.107046	+	0.994254i	$0.465861\pi$
$24$	−1.17992e6	−0.725941
$25$	−1.11162e6	−0.569150
$26$	70090.0	0.0300799
$27$	2.99612e6	1.08498
$28$	−3.29262e6	−1.01235
$29$	−3.74448e6	−0.983107	−0.491554	−	0.870847i	$-0.663571\pi$
$29$	−3.74448e6	−0.983107	−0.491554	+	0.870847i	$0.663571\pi$
$30$	−3.96286e6	−0.893230
$31$	−3.22892e6	−0.627956	−0.313978	−	0.949430i	$-0.601662\pi$
$31$	−3.22892e6	−0.627956	−0.313978	+	0.949430i	$0.601662\pi$
$32$	−6.75451e6	−1.13873
$33$	−6.71997e6	−0.986403
$34$	0	0
$35$	−3.84705e6	−0.433333
$36$	−4.15784e6	−0.412579
$37$	7.92078e6	0.694801	0.347400	−	0.937717i	$-0.387064\pi$
$37$	7.92078e6	0.694801	0.347400	+	0.937717i	$0.387064\pi$
$38$	1.25576e7	0.976972
$39$	−233428.	−0.0161571
$40$	9.02382e6	0.557341
$41$	2.96386e7	1.63806	0.819030	−	0.573750i	$-0.194512\pi$
$41$	2.96386e7	1.63806	0.819030	+	0.573750i	$0.194512\pi$
$42$	1.81168e7	0.898379
$43$	−1.54310e7	−0.688314	−0.344157	−	0.938912i	$-0.611835\pi$
$43$	−1.54310e7	−0.688314	−0.344157	+	0.938912i	$0.611835\pi$
$44$	4.39866e7	1.76923
$45$	−4.85796e6	−0.176603
$46$	1.03483e7	0.340768
$47$	−2.94503e7	−0.880338	−0.440169	−	0.897915i	$-0.645081\pi$
$47$	−2.94503e7	−0.880338	−0.440169	+	0.897915i	$0.645081\pi$
$48$	5.72153e6	0.155570
$49$	−2.27663e7	−0.564169
$50$	−4.00358e7	−0.905908
$51$	0	0
$52$	1.52794e6	0.0289795
$53$	−1.12977e8	−1.96675	−0.983373	−	0.181596i	$-0.941874\pi$
$53$	−1.12977e8	−1.96675	−0.983373	+	0.181596i	$0.941874\pi$
$54$	1.07907e8	1.72695
$55$	5.13932e7	0.757310
$56$	−4.12537e7	−0.560553
$57$	−4.18221e7	−0.524770
$58$	−1.34860e8	−1.56480
$59$	1.42908e8	1.53540	0.767700	−	0.640809i	$-0.221401\pi$
$59$	1.42908e8	1.53540	0.767700	+	0.640809i	$0.221401\pi$
$60$	−8.63891e7	−0.860555
$61$	2.77387e7	0.256508	0.128254	−	0.991741i	$-0.459063\pi$
$61$	2.77387e7	0.256508	0.128254	+	0.991741i	$0.459063\pi$
$62$	−1.16292e8	−0.999508
$63$	2.22089e7	0.177621
$64$	−2.18846e8	−1.63053
$65$	1.78522e6	0.0124046
$66$	−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	$0.582157\pi$
$68$	0	0
$69$	−3.44641e7	−0.183040
$70$	−1.38554e8	−0.689730
$71$	−3.54046e8	−1.65347	−0.826736	−	0.562590i	$-0.809805\pi$
$71$	−3.54046e8	−1.65347	−0.826736	+	0.562590i	$0.809805\pi$
$72$	−5.20941e7	−0.228451
$73$	−2.56100e8	−1.05550	−0.527748	−	0.849401i	$-0.676963\pi$
$73$	−2.56100e8	−1.05550	−0.527748	+	0.849401i	$0.676963\pi$
$74$	2.85273e8	1.10590
$75$	1.33336e8	0.486598
$76$	2.73753e8	0.941233
$77$	−2.34952e8	−0.761676
$78$	−8.40709e6	−0.0257170
$79$	−3.39870e8	−0.981728	−0.490864	−	0.871236i	$-0.663319\pi$
$79$	−3.39870e8	−0.981728	−0.490864	+	0.871236i	$0.663319\pi$
$80$	−4.37573e7	−0.119439
$81$	−2.55140e8	−0.658560
$82$	1.06745e9	2.60727
$83$	−5.29228e8	−1.22403	−0.612014	−	0.790847i	$-0.709640\pi$
$83$	−5.29228e8	−1.22403	−0.612014	+	0.790847i	$0.709640\pi$
$84$	3.94940e8	0.865515
$85$	0	0
$86$	−5.55759e8	−1.09558
$87$	4.49139e8	0.840513
$88$	5.51113e8	0.979645
$89$	−6.33877e8	−1.07090	−0.535451	−	0.844566i	$-0.679858\pi$
$89$	−6.33877e8	−1.07090	−0.535451	+	0.844566i	$0.679858\pi$
$90$	−1.74963e8	−0.281096
$91$	−8.16140e6	−0.0124761
$92$	2.25590e8	0.328303
$93$	3.87299e8	0.536874
$94$	−1.06067e9	−1.40122
$95$	3.19849e8	0.402892
$96$	8.10183e8	0.973560
$97$	1.00489e9	1.15252	0.576259	−	0.817267i	$-0.304512\pi$
$97$	1.00489e9	1.15252	0.576259	+	0.817267i	$0.304512\pi$
$98$	−8.19943e8	−0.897979
$99$	−2.96691e8	−0.310417
$100$	−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	$0.239303\pi$
$102$	0	0
$103$	−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
$105$	4.61442e8	0.370481
$106$	−4.06894e9	−3.13044
$107$	2.37895e9	1.75452	0.877258	−	0.480019i	$-0.159370\pi$
$107$	2.37895e9	1.75452	0.877258	+	0.480019i	$0.159370\pi$
$108$	2.35235e9	1.66378
$109$	−9.33309e7	−0.0633295	−0.0316648	−	0.999499i	$-0.510081\pi$
$109$	−9.33309e7	−0.0633295	−0.0316648	+	0.999499i	$0.510081\pi$
$110$	1.85096e9	1.20540
$111$	−9.50073e8	−0.594024
$112$	2.00043e8	0.120127
$113$	−1.71780e9	−0.991104	−0.495552	−	0.868578i	$-0.665034\pi$
$113$	−1.71780e9	−0.991104	−0.495552	+	0.868578i	$0.665034\pi$
$114$	−1.50625e9	−0.835268
$115$	2.63576e8	0.140529
$116$	−2.93991e9	−1.50755
$117$	−1.03060e7	−0.00508457
$118$	5.14692e9	2.44387
$119$	0	0
$120$	−1.08238e9	−0.476501
$121$	7.80799e8	0.331135
$122$	9.99028e8	0.408280
$123$	−3.55506e9	−1.40047
$124$	−2.53512e9	−0.962945
$125$	−2.81140e9	−1.02998
$126$	7.99868e8	0.282716
$127$	2.30615e9	0.786629	0.393315	−	0.919404i	$-0.371328\pi$
$127$	2.30615e9	0.786629	0.393315	+	0.919404i	$0.371328\pi$
$128$	−4.42358e9	−1.45656
$129$	1.85090e9	0.588478
$130$	6.42960e7	0.0197442
$131$	−2.35000e9	−0.697183	−0.348591	−	0.937275i	$-0.613340\pi$
$131$	−2.35000e9	−0.697183	−0.348591	+	0.937275i	$0.613340\pi$
$132$	−5.27606e9	−1.51261
$133$	−1.46223e9	−0.405214
$134$	−3.03262e9	−0.812543
$135$	2.74845e9	0.712173
$136$	0	0
$137$	−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
$139$	−5.15857e9	−1.17209	−0.586047	−	0.810277i	$-0.699317\pi$
$139$	−5.15857e9	−1.17209	−0.586047	+	0.810277i	$0.699317\pi$
$140$	−3.02044e9	−0.664499
$141$	3.53247e9	0.752649
$142$	−1.27512e10	−2.63181
$143$	1.09029e8	0.0218037
$144$	2.52609e8	0.0489573
$145$	−3.43495e9	−0.645303
$146$	−9.22361e9	−1.68002
$147$	2.73074e9	0.482339
$148$	6.21885e9	1.06545
$149$	−6.04226e9	−1.00429	−0.502147	−	0.864782i	$-0.667457\pi$
$149$	−6.04226e9	−1.00429	−0.502147	+	0.864782i	$0.667457\pi$
$150$	4.80218e9	0.774511
$151$	−7.56844e9	−1.18471	−0.592353	−	0.805679i	$-0.701801\pi$
$151$	−7.56844e9	−1.18471	−0.592353	+	0.805679i	$0.701801\pi$
$152$	3.42988e9	0.521174
$153$	0	0
$154$	−8.46195e9	−1.21235
$155$	−2.96200e9	−0.412185
$156$	−1.83272e8	−0.0247762
$157$	3.59797e9	0.472616	0.236308	−	0.971678i	$-0.424062\pi$
$157$	3.59797e9	0.472616	0.236308	+	0.971678i	$0.424062\pi$
$158$	−1.22407e10	−1.56260
$159$	1.35512e10	1.68148
$160$	−6.19615e9	−0.747450
$161$	−1.20497e9	−0.141339
$162$	−9.18904e9	−1.04822
$163$	2.46020e9	0.272977	0.136488	−	0.990642i	$-0.456418\pi$
$163$	2.46020e9	0.272977	0.136488	+	0.990642i	$0.456418\pi$
$164$	2.32702e10	2.51190
$165$	−6.16446e9	−0.647467
$166$	−1.90605e10	−1.94827
$167$	−6.06431e9	−0.603333	−0.301667	−	0.953414i	$-0.597543\pi$
$167$	−6.06431e9	−0.603333	−0.301667	+	0.953414i	$0.597543\pi$
$168$	4.94825e9	0.479248
$169$	−1.06007e10	−0.999643
$170$	0	0
$171$	−1.84647e9	−0.165143
$172$	−1.21154e10	−1.05550
$173$	−7.56160e9	−0.641810	−0.320905	−	0.947111i	$-0.603987\pi$
$173$	−7.56160e9	−0.641810	−0.320905	+	0.947111i	$0.603987\pi$
$174$	1.61761e10	1.33783
$175$	4.66184e9	0.375739
$176$	−2.67240e9	−0.209939
$177$	−1.71413e10	−1.31270
$178$	−2.28295e10	−1.70454
$179$	1.98968e9	0.144859	0.0724293	−	0.997374i	$-0.476925\pi$
$179$	1.98968e9	0.144859	0.0724293	+	0.997374i	$0.476925\pi$
$180$	−3.81414e9	−0.270813
$181$	−2.17900e10	−1.50905	−0.754525	−	0.656272i	$-0.772133\pi$
$181$	−2.17900e10	−1.50905	−0.754525	+	0.656272i	$0.772133\pi$
$182$	−2.93939e8	−0.0198580
$183$	−3.32717e9	−0.219303
$184$	2.82644e9	0.181786
$185$	7.26601e9	0.456061
$186$	1.39488e10	0.854535
$187$	0	0
$188$	−2.31223e10	−1.34996
$189$	−1.25649e10	−0.716278
$190$	1.15196e10	0.641276
$191$	1.55821e10	0.847180	0.423590	−	0.905854i	$-0.360770\pi$
$191$	1.55821e10	0.847180	0.423590	+	0.905854i	$0.360770\pi$
$192$	2.62499e10	1.39403
$193$	3.56806e9	0.185108	0.0925538	−	0.995708i	$-0.470497\pi$
$193$	3.56806e9	0.185108	0.0925538	+	0.995708i	$0.470497\pi$
$194$	3.61920e10	1.83444
$195$	−2.14132e8	−0.0106054
$196$	−1.78745e10	−0.865130
$197$	−3.07563e10	−1.45491	−0.727456	−	0.686155i	$-0.759297\pi$
$197$	−3.07563e10	−1.45491	−0.727456	+	0.686155i	$0.759297\pi$
$198$	−1.06855e10	−0.494086
$199$	−1.48762e10	−0.672441	−0.336220	−	0.941783i	$-0.609149\pi$
$199$	−1.48762e10	−0.672441	−0.336220	+	0.941783i	$0.609149\pi$
$200$	−1.09350e10	−0.483264
$201$	1.00999e10	0.436449
$202$	5.50260e10	2.32534
$203$	1.57033e10	0.649023
$204$	0	0
$205$	2.71885e10	1.07521
$206$	−6.47873e9	−0.250661
$207$	−1.52161e9	−0.0576019
$208$	−9.28298e7	−0.00343876
$209$	1.95342e10	0.708168
$210$	1.66192e10	0.589688
$211$	3.47123e10	1.20562	0.602812	−	0.797883i	$-0.294047\pi$
$211$	3.47123e10	1.20562	0.602812	+	0.797883i	$0.294047\pi$
$212$	−8.87017e10	−3.01592
$213$	4.24667e10	1.41364
$214$	8.56794e10	2.79264
$215$	−1.41554e10	−0.451803
$216$	2.94729e10	0.921256
$217$	1.35412e10	0.414561
$218$	−3.36138e9	−0.100801
$219$	3.07184e10	0.902401
$220$	4.03504e10	1.16130
$221$	0	0
$222$	−3.42176e10	−0.945498
$223$	3.59058e10	0.972283	0.486142	−	0.873880i	$-0.338404\pi$
$223$	3.59058e10	0.972283	0.486142	+	0.873880i	$0.338404\pi$
$224$	2.83266e10	0.751758
$225$	5.88685e9	0.153131
$226$	−6.18677e10	−1.57753
$227$	−5.61479e9	−0.140352	−0.0701758	−	0.997535i	$-0.522356\pi$
$227$	−5.61479e9	−0.140352	−0.0701758	+	0.997535i	$0.522356\pi$
$228$	−3.28358e10	−0.804713
$229$	−7.90733e10	−1.90007	−0.950036	−	0.312139i	$-0.898954\pi$
$229$	−7.90733e10	−1.90007	−0.950036	+	0.312139i	$0.898954\pi$
$230$	9.49286e9	0.223677
$231$	2.81817e10	0.651199
$232$	−3.68345e10	−0.834754
$233$	6.81753e10	1.51539	0.757697	−	0.652607i	$-0.226325\pi$
$233$	6.81753e10	1.51539	0.757697	+	0.652607i	$0.226325\pi$
$234$	−3.71178e8	−0.00809303
$235$	−2.70158e10	−0.577846
$236$	1.12201e11	2.35447
$237$	4.07664e10	0.839334
$238$	0	0
$239$	−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
$241$	−4.21107e9	−0.0804111	−0.0402056	−	0.999191i	$-0.512801\pi$
$241$	−4.21107e9	−0.0804111	−0.0402056	+	0.999191i	$0.512801\pi$
$242$	2.81210e10	0.527062
$243$	−2.83694e10	−0.521942
$244$	2.17785e10	0.393345
$245$	−2.08843e10	−0.370316
$246$	−1.28038e11	−2.22910
$247$	6.78548e8	0.0115996
$248$	−3.17629e10	−0.533196
$249$	6.34793e10	1.04649
$250$	−1.01255e11	−1.63940
$251$	1.26806e10	0.201654	0.100827	−	0.994904i	$-0.467851\pi$
$251$	1.26806e10	0.201654	0.100827	+	0.994904i	$0.467851\pi$
$252$	1.74369e10	0.272374
$253$	1.60974e10	0.247009
$254$	8.30575e10	1.25207
$255$	0	0
$256$	−4.72692e10	−0.687857
$257$	8.11867e10	1.16088	0.580438	−	0.814304i	$-0.302881\pi$
$257$	8.11867e10	1.16088	0.580438	+	0.814304i	$0.302881\pi$
$258$	6.66616e10	0.936671
$259$	−3.32176e10	−0.458690
$260$	1.40163e9	0.0190219
$261$	1.98298e10	0.264506
$262$	−8.46368e10	−1.10969
$263$	−4.36957e10	−0.563168	−0.281584	−	0.959537i	$-0.590860\pi$
$263$	−4.36957e10	−0.563168	−0.281584	+	0.959537i	$0.590860\pi$
$264$	−6.61043e10	−0.837553
$265$	−1.03638e11	−1.29096
$266$	−5.26634e10	−0.644972
$267$	7.60316e10	0.915574
$268$	−6.61102e10	−0.782819
$269$	1.52414e11	1.77476	0.887378	−	0.461042i	$-0.152524\pi$
$269$	1.52414e11	1.77476	0.887378	+	0.461042i	$0.152524\pi$
$270$	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	$0.474551\pi$
$272$	0	0
$273$	9.78935e8	0.0106665
$274$	−8.48139e10	−0.909053
$275$	−6.22781e10	−0.656656
$276$	−2.70588e10	−0.280684
$277$	−7.86224e10	−0.802394	−0.401197	−	0.915992i	$-0.631406\pi$
$277$	−7.86224e10	−0.802394	−0.401197	+	0.915992i	$0.631406\pi$
$278$	−1.85789e11	−1.86560
$279$	1.70995e10	0.168952
$280$	−3.78435e10	−0.367942
$281$	3.72134e10	0.356058	0.178029	−	0.984025i	$-0.443028\pi$
$281$	3.72134e10	0.356058	0.178029	+	0.984025i	$0.443028\pi$
$282$	1.27224e11	1.19798
$283$	−7.37798e9	−0.0683752	−0.0341876	−	0.999415i	$-0.510884\pi$
$283$	−7.37798e9	−0.0683752	−0.0341876	+	0.999415i	$0.510884\pi$
$284$	−2.77972e11	−2.53553
$285$	−3.83649e10	−0.344454
$286$	3.92676e9	0.0347046
$287$	−1.24296e11	−1.08141
$288$	3.57701e10	0.306375
$289$	0	0
$290$	−1.23712e11	−1.02712
$291$	−1.20534e11	−0.985351
$292$	−2.01072e11	−1.61856
$293$	9.58955e10	0.760140	0.380070	−	0.924958i	$-0.375900\pi$
$293$	9.58955e10	0.760140	0.380070	+	0.924958i	$0.375900\pi$
$294$	9.83496e10	0.767732
$295$	1.31094e11	1.00782
$296$	7.79167e10	0.589954
$297$	1.67856e11	1.25180
$298$	−2.17616e11	−1.59852
$299$	5.59167e8	0.00404596
$300$	1.04686e11	0.746178
$301$	6.47135e10	0.454407
$302$	−2.72583e11	−1.88568
$303$	−1.83259e11	−1.24903
$304$	−1.66318e10	−0.111688
$305$	2.54457e10	0.168370
$306$	0	0
$307$	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
$309$	2.15768e10	0.134640
$310$	−1.06678e11	−0.656068
$311$	1.33880e11	0.811507	0.405754	−	0.913983i	$-0.367009\pi$
$311$	1.33880e11	0.811507	0.405754	+	0.913983i	$0.367009\pi$
$312$	−2.29623e9	−0.0137189
$313$	8.69004e10	0.511767	0.255883	−	0.966708i	$-0.417634\pi$
$313$	8.69004e10	0.511767	0.255883	+	0.966708i	$0.417634\pi$
$314$	1.29583e11	0.752256
$315$	2.03730e10	0.116589
$316$	−2.66843e11	−1.50544
$317$	2.48261e11	1.38083	0.690417	−	0.723412i	$-0.257427\pi$
$317$	2.48261e11	1.38083	0.690417	+	0.723412i	$0.257427\pi$
$318$	4.88057e11	2.67639
$319$	−2.09783e11	−1.13426
$320$	−2.00755e11	−1.07026
$321$	−2.85347e11	−1.50003
$322$	−4.33980e10	−0.224967
$323$	0	0
$324$	−2.00318e11	−1.00988
$325$	−2.16332e9	−0.0107559
$326$	8.86057e10	0.434493
$327$	1.11948e10	0.0541439
$328$	2.91555e11	1.39087
$329$	1.23506e11	0.581177
$330$	−2.22017e11	−1.03056
$331$	2.88811e11	1.32248	0.661239	−	0.750175i	$-0.270031\pi$
$331$	2.88811e11	1.32248	0.661239	+	0.750175i	$0.270031\pi$
$332$	−4.15513e11	−1.87700
$333$	−4.19463e10	−0.186937
$334$	−2.18410e11	−0.960316
$335$	−7.72421e10	−0.335083
$336$	−2.39945e10	−0.102704
$337$	9.17448e10	0.387478	0.193739	−	0.981053i	$-0.437939\pi$
$337$	9.17448e10	0.387478	0.193739	+	0.981053i	$0.437939\pi$
$338$	−3.81792e11	−1.59112
$339$	2.06045e11	0.847350
$340$	0	0
$341$	−1.80898e11	−0.724503
$342$	−6.65020e10	−0.262855
$343$	2.64708e11	1.03263
$344$	−1.51795e11	−0.584446
$345$	−3.16151e10	−0.120146
$346$	−2.72336e11	−1.02156
$347$	4.84910e11	1.79547	0.897736	−	0.440534i	$-0.145211\pi$
$347$	4.84910e11	1.79547	0.897736	+	0.440534i	$0.145211\pi$
$348$	3.52633e11	1.28889
$349$	6.43524e9	0.0232194	0.0116097	−	0.999933i	$-0.496304\pi$
$349$	6.43524e9	0.0232194	0.0116097	+	0.999933i	$0.496304\pi$
$350$	1.67899e11	0.598057
$351$	5.83074e9	0.0205042
$352$	−3.78418e11	−1.31380
$353$	−1.83629e11	−0.629440	−0.314720	−	0.949185i	$-0.601911\pi$
$353$	−1.83629e11	−0.629440	−0.314720	+	0.949185i	$0.601911\pi$
$354$	−6.17357e11	−2.08940
$355$	−3.24779e11	−1.08532
$356$	−4.97676e11	−1.64218
$357$	0	0
$358$	7.16596e10	0.230569
$359$	4.45051e11	1.41412	0.707058	−	0.707155i	$-0.250022\pi$
$359$	4.45051e11	1.41412	0.707058	+	0.707155i	$0.250022\pi$
$360$	−4.77878e10	−0.149953
$361$	−2.01116e11	−0.623252
$362$	−7.84782e11	−2.40193
$363$	−9.36544e10	−0.283106
$364$	−6.40777e9	−0.0191316
$365$	−2.34929e11	−0.692818
$366$	−1.19830e11	−0.349061
$367$	−4.05760e11	−1.16754	−0.583770	−	0.811919i	$-0.698423\pi$
$367$	−4.05760e11	−1.16754	−0.583770	+	0.811919i	$0.698423\pi$
$368$	−1.37057e10	−0.0389570
$369$	−1.56958e11	−0.440722
$370$	2.61690e11	0.725906
$371$	4.73794e11	1.29840
$372$	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	$0.316426\pi$
$374$	0	0
$375$	3.37219e11	0.880584
$376$	−2.89703e11	−0.747493
$377$	−7.28713e9	−0.0185789
$378$	−4.52534e11	−1.14009
$379$	6.72982e11	1.67543	0.837717	−	0.546105i	$-0.183890\pi$
$379$	6.72982e11	1.67543	0.837717	+	0.546105i	$0.183890\pi$
$380$	2.51123e11	0.617818
$381$	−2.76615e11	−0.672533
$382$	5.61200e11	1.34844
$383$	3.49592e11	0.830170	0.415085	−	0.909783i	$-0.363752\pi$
$383$	3.49592e11	0.830170	0.415085	+	0.909783i	$0.363752\pi$
$384$	5.30594e11	1.24529
$385$	−2.15529e11	−0.499957
$386$	1.28506e11	0.294633
$387$	8.17185e10	0.185192
$388$	7.88973e11	1.76734
$389$	−4.97423e11	−1.10142	−0.550709	−	0.834697i	$-0.685643\pi$
$389$	−4.97423e11	−1.10142	−0.550709	+	0.834697i	$0.685643\pi$
$390$	−7.71211e9	−0.0168804
$391$	0	0
$392$	−2.23952e11	−0.479035
$393$	2.81875e11	0.596060
$394$	−1.10771e12	−2.31576
$395$	−3.11775e11	−0.644398
$396$	−2.32941e11	−0.476012
$397$	−1.58244e11	−0.319721	−0.159860	−	0.987140i	$-0.551104\pi$
$397$	−1.58244e11	−0.319721	−0.159860	+	0.987140i	$0.551104\pi$
$398$	−5.35778e11	−1.07031
$399$	1.75390e11	0.346440
$400$	5.30249e10	0.103564
$401$	9.10311e10	0.175809	0.0879043	−	0.996129i	$-0.471983\pi$
$401$	9.10311e10	0.175809	0.0879043	+	0.996129i	$0.471983\pi$
$402$	3.63754e11	0.694688
$403$	−6.28378e9	−0.0118672
$404$	1.19955e12	2.24028
$405$	−2.34049e11	−0.432273
$406$	5.65567e11	1.03304
$407$	4.43758e11	0.801625
$408$	0	0
$409$	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
$411$	2.82465e11	0.488288
$412$	−1.41234e11	−0.241492
$413$	−5.99316e11	−1.01363
$414$	−5.48019e10	−0.0916841
$415$	−4.85479e11	−0.803442
$416$	−1.31449e10	−0.0215198
$417$	6.18754e11	1.00209
$418$	7.03536e11	1.12718
$419$	−6.22425e11	−0.986561	−0.493280	−	0.869870i	$-0.664202\pi$
$419$	−6.22425e11	−0.986561	−0.493280	+	0.869870i	$0.664202\pi$
$420$	3.62292e11	0.568117
$421$	4.67294e11	0.724971	0.362486	−	0.931989i	$-0.381928\pi$
$421$	4.67294e11	0.724971	0.362486	+	0.931989i	$0.381928\pi$
$422$	1.25019e12	1.91897
$423$	1.55961e11	0.236856
$424$	−1.11135e12	−1.66996
$425$	0	0
$426$	1.52947e12	2.25008
$427$	−1.16328e11	−0.169340
$428$	1.86778e12	2.69048
$429$	−1.30777e10	−0.0186412
$430$	−5.09817e11	−0.719128
$431$	2.57969e11	0.360097	0.180049	−	0.983658i	$-0.442374\pi$
$431$	2.57969e11	0.360097	0.180049	+	0.983658i	$0.442374\pi$
$432$	−1.42917e11	−0.197427
$433$	2.74180e11	0.374836	0.187418	−	0.982280i	$-0.439988\pi$
$433$	2.74180e11	0.374836	0.187418	+	0.982280i	$0.439988\pi$
$434$	4.87696e11	0.659850
$435$	4.12011e11	0.551705
$436$	−7.32770e10	−0.0971132
$437$	1.00183e11	0.131410
$438$	1.10634e12	1.43634
$439$	−7.90421e11	−1.01571	−0.507853	−	0.861444i	$-0.669561\pi$
$439$	−7.90421e11	−1.01571	−0.507853	+	0.861444i	$0.669561\pi$
$440$	5.05555e11	0.643031
$441$	1.20564e11	0.151790
$442$	0	0
$443$	−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
$445$	−5.81477e11	−0.702931
$446$	1.29317e12	1.54757
$447$	7.24751e11	0.858627
$448$	9.17780e11	1.07643
$449$	8.66534e11	1.00618	0.503092	−	0.864233i	$-0.332196\pi$
$449$	8.66534e11	1.00618	0.503092	+	0.864233i	$0.332196\pi$
$450$	2.12019e11	0.243735
$451$	1.66049e12	1.88991
$452$	−1.34870e12	−1.51982
$453$	9.07811e11	1.01287
$454$	−2.02221e11	−0.223395
$455$	−7.48674e9	−0.00818920
$456$	−4.11404e11	−0.445581
$457$	−6.25354e11	−0.670661	−0.335330	−	0.942101i	$-0.608848\pi$
$457$	−6.25354e11	−0.670661	−0.335330	+	0.942101i	$0.608848\pi$
$458$	−2.84788e12	−3.02432
$459$	0	0
$460$	2.06941e11	0.215495
$461$	1.45870e12	1.50422	0.752110	−	0.659038i	$-0.229036\pi$
$461$	1.45870e12	1.50422	0.752110	+	0.659038i	$0.229036\pi$
$462$	1.01498e12	1.03650
$463$	1.55507e12	1.57266	0.786330	−	0.617807i	$-0.211979\pi$
$463$	1.55507e12	1.57266	0.786330	+	0.617807i	$0.211979\pi$
$464$	1.78614e11	0.178889
$465$	3.55283e11	0.352400
$466$	2.45538e12	2.41203
$467$	−1.93889e12	−1.88638	−0.943188	−	0.332260i	$-0.892189\pi$
$467$	−1.93889e12	−1.88638	−0.943188	+	0.332260i	$0.892189\pi$
$468$	−8.09157e9	−0.00779698
$469$	3.53123e11	0.337014
$470$	−9.72992e11	−0.919748
$471$	−4.31565e11	−0.404066
$472$	1.40578e12	1.30370
$473$	−8.64515e11	−0.794141
$474$	1.46823e12	1.33595
$475$	−3.87591e11	−0.349343
$476$	0	0
$477$	5.98296e11	0.529155
$478$	−1.15233e12	−1.00960
$479$	−1.79275e12	−1.55600	−0.777998	−	0.628266i	$-0.783765\pi$
$479$	−1.79275e12	−1.55600	−0.777998	+	0.628266i	$0.783765\pi$
$480$	7.43209e11	0.639036
$481$	1.54146e10	0.0131304
$482$	−1.51665e11	−0.127989
$483$	1.44533e11	0.120838
$484$	6.13029e11	0.507782
$485$	9.21824e11	0.756502
$486$	−1.02175e12	−0.830768
$487$	−1.88154e12	−1.51577	−0.757887	−	0.652386i	$-0.773768\pi$
$487$	−1.88154e12	−1.51577	−0.757887	+	0.652386i	$0.773768\pi$
$488$	2.72865e11	0.217801
$489$	−2.95093e11	−0.233383
$490$	−7.52162e11	−0.589426
$491$	−2.04604e12	−1.58872	−0.794359	−	0.607448i	$-0.792193\pi$
$491$	−2.04604e12	−1.58872	−0.794359	+	0.607448i	$0.792193\pi$
$492$	−2.79118e12	−2.14756
$493$	0	0
$494$	2.44384e10	0.0184630
$495$	−2.72165e11	−0.203755
$496$	1.54021e11	0.114265
$497$	1.48477e12	1.09158
$498$	2.28625e12	1.66568
$499$	−2.49934e12	−1.80457	−0.902284	−	0.431141i	$-0.858111\pi$
$499$	−2.49934e12	−1.80457	−0.902284	+	0.431141i	$0.858111\pi$
$500$	−2.20732e12	−1.57943
$501$	7.27395e11	0.515823
$502$	4.56701e11	0.320970
$503$	1.26660e12	0.882231	0.441115	−	0.897450i	$-0.354583\pi$
$503$	1.26660e12	0.882231	0.441115	+	0.897450i	$0.354583\pi$
$504$	2.18469e11	0.150817
$505$	1.40153e12	0.958942
$506$	5.79759e11	0.393161
$507$	1.27152e12	0.854650
$508$	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	$0.598690\pi$
$510$	0	0
$511$	1.07401e12	0.696811
$512$	5.62439e11	0.361710
$513$	1.04466e12	0.665960
$514$	2.92400e12	1.84775
$515$	−1.65016e11	−0.103370
$516$	1.45320e12	0.902406
$517$	−1.64994e12	−1.01569
$518$	−1.19636e12	−0.730090
$519$	9.06991e11	0.548719
$520$	1.75612e10	0.0105327
$521$	1.78556e12	1.06171	0.530853	−	0.847464i	$-0.321872\pi$
$521$	1.78556e12	1.06171	0.530853	+	0.847464i	$0.321872\pi$
$522$	7.14184e11	0.421010
$523$	1.92158e11	0.112306	0.0561528	−	0.998422i	$-0.482117\pi$
$523$	1.92158e11	0.112306	0.0561528	+	0.998422i	$0.482117\pi$
$524$	−1.84506e12	−1.06910
$525$	−5.59173e11	−0.321240
$526$	−1.57373e12	−0.896386
$527$	0	0
$528$	3.20546e11	0.179489
$529$	−1.71860e12	−0.954164
$530$	−3.73258e12	−2.05479
$531$	−7.56801e11	−0.413101
$532$	−1.14804e12	−0.621379
$533$	5.76795e10	0.0309563
$534$	2.73833e12	1.45730
$535$	2.18229e12	1.15165
$536$	−8.28302e11	−0.433458
$537$	−2.38656e11	−0.123848
$538$	5.48929e12	2.82485
$539$	−1.27547e12	−0.650909
$540$	2.15789e12	1.09209
$541$	1.86552e12	0.936294	0.468147	−	0.883651i	$-0.344922\pi$
$541$	1.86552e12	0.936294	0.468147	+	0.883651i	$0.344922\pi$
$542$	5.10791e11	0.254241
$543$	2.61364e12	1.29017
$544$	0	0
$545$	−8.56157e10	−0.0415690
$546$	3.52570e10	0.0169777
$547$	−7.99617e11	−0.381891	−0.190945	−	0.981601i	$-0.561155\pi$
$547$	−7.99617e11	−0.381891	−0.190945	+	0.981601i	$0.561155\pi$
$548$	−1.84892e12	−0.875799
$549$	−1.46897e11	−0.0690138
$550$	−2.24299e12	−1.04519
$551$	−1.30559e12	−0.603429
$552$	−3.39023e11	−0.155419
$553$	1.42532e12	0.648112
$554$	−2.83164e12	−1.27716
$555$	−8.71536e11	−0.389912
$556$	−4.05015e12	−1.79736
$557$	−9.85166e11	−0.433672	−0.216836	−	0.976208i	$-0.569574\pi$
$557$	−9.85166e11	−0.433672	−0.216836	+	0.976208i	$0.569574\pi$
$558$	6.15850e11	0.268919
$559$	−3.00302e10	−0.0130079
$560$	1.83506e11	0.0788506
$561$	0	0
$562$	1.34027e12	0.566733
$563$	2.98482e12	1.25207	0.626037	−	0.779793i	$-0.284676\pi$
$563$	2.98482e12	1.25207	0.626037	+	0.779793i	$0.284676\pi$
$564$	2.77345e12	1.15416
$565$	−1.57580e12	−0.650552
$566$	−2.65723e11	−0.108832
$567$	1.06999e12	0.434765
$568$	−3.48275e12	−1.40396
$569$	−2.16083e12	−0.864202	−0.432101	−	0.901825i	$-0.642228\pi$
$569$	−2.16083e12	−0.864202	−0.432101	+	0.901825i	$0.642228\pi$
$570$	−1.38174e12	−0.548263
$571$	−2.50099e12	−0.984576	−0.492288	−	0.870432i	$-0.663839\pi$
$571$	−2.50099e12	−0.984576	−0.492288	+	0.870432i	$0.663839\pi$
$572$	8.56021e10	0.0334351
$573$	−1.86902e12	−0.724301
$574$	−4.47661e12	−1.72126
$575$	−3.19400e11	−0.121851
$576$	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	$0.230748\pi$
$578$	0	0
$579$	−4.27978e11	−0.158259
$580$	−2.69688e12	−0.989546
$581$	2.21944e12	0.808073
$582$	−4.34111e12	−1.56837
$583$	−6.32948e12	−2.26913
$584$	−2.51925e12	−0.896219
$585$	−9.45406e9	−0.00333747
$586$	3.45374e12	1.20990
$587$	−3.85772e11	−0.134110	−0.0670548	−	0.997749i	$-0.521360\pi$
$587$	−3.85772e11	−0.134110	−0.0670548	+	0.997749i	$0.521360\pi$
$588$	2.14399e12	0.739648
$589$	−1.12583e12	−0.385438
$590$	4.72145e12	1.60414
$591$	3.68913e12	1.24388
$592$	−3.77825e11	−0.126428
$593$	−3.33499e12	−1.10751	−0.553755	−	0.832679i	$-0.686806\pi$
$593$	−3.33499e12	−1.10751	−0.553755	+	0.832679i	$0.686806\pi$
$594$	6.04546e12	1.99246
$595$	0	0
$596$	−4.74397e12	−1.54004
$597$	1.78436e12	0.574907
$598$	2.01388e10	0.00643989
$599$	−3.02329e12	−0.959531	−0.479766	−	0.877397i	$-0.659278\pi$
$599$	−3.02329e12	−0.959531	−0.479766	+	0.877397i	$0.659278\pi$
$600$	1.31162e12	0.413169
$601$	1.33418e12	0.417137	0.208568	−	0.978008i	$-0.433120\pi$
$601$	1.33418e12	0.417137	0.208568	+	0.978008i	$0.433120\pi$
$602$	2.33070e12	0.723273
$603$	4.45915e11	0.137349
$604$	−5.94222e12	−1.81670
$605$	7.16254e11	0.217354
$606$	−6.60020e12	−1.98806
$607$	−8.24460e11	−0.246502	−0.123251	−	0.992376i	$-0.539332\pi$
$607$	−8.24460e11	−0.246502	−0.123251	+	0.992376i	$0.539332\pi$
$608$	−2.35511e12	−0.698947
$609$	−1.88357e12	−0.554886
$610$	9.16443e11	0.267992
$611$	−5.73131e10	−0.0166368
$612$	0	0
$613$	−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
$615$	−3.26118e12	−0.919256
$616$	−2.31122e12	−0.646737
$617$	3.34499e12	0.929206	0.464603	−	0.885519i	$-0.346197\pi$
$617$	3.34499e12	0.929206	0.464603	+	0.885519i	$0.346197\pi$
$618$	7.77104e11	0.214304
$619$	−3.20260e12	−0.876788	−0.438394	−	0.898783i	$-0.644453\pi$
$619$	−3.20260e12	−0.876788	−0.438394	+	0.898783i	$0.644453\pi$
$620$	−2.32556e12	−0.632069
$621$	8.60869e11	0.232287
$622$	4.82176e12	1.29166
$623$	2.65831e12	0.706983
$624$	1.11346e10	0.00293999
$625$	−4.07859e11	−0.106918
$626$	3.12978e12	0.814571
$627$	−2.34306e12	−0.605452
$628$	2.82488e12	0.724738
$629$	0	0
$630$	7.33747e11	0.185573
$631$	−1.11507e12	−0.280007	−0.140004	−	0.990151i	$-0.544711\pi$
$631$	−1.11507e12	−0.280007	−0.140004	+	0.990151i	$0.544711\pi$
$632$	−3.34330e12	−0.833583
$633$	−4.16363e12	−1.03076
$634$	8.94129e12	2.19785
$635$	2.11551e12	0.516337
$636$	1.06395e13	2.57848
$637$	−4.43053e10	−0.0106618
$638$	−7.55548e12	−1.80538
$639$	1.87493e12	0.444868
$640$	−4.05790e12	−0.956074
$641$	4.56993e12	1.06917	0.534587	−	0.845113i	$-0.320467\pi$
$641$	4.56993e12	1.06917	0.534587	+	0.845113i	$0.320467\pi$
$642$	−1.02770e13	−2.38758
$643$	−2.30320e12	−0.531351	−0.265676	−	0.964062i	$-0.585595\pi$
$643$	−2.30320e12	−0.531351	−0.265676	+	0.964062i	$0.585595\pi$
$644$	−9.46062e11	−0.216737
$645$	1.69790e12	0.386272
$646$	0	0
$647$	−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
$649$	8.00633e12	1.77146
$650$	−7.79136e10	−0.0171200
$651$	−1.62422e12	−0.354431
$652$	1.93158e12	0.418598
$653$	−1.27396e12	−0.274186	−0.137093	−	0.990558i	$-0.543776\pi$
$653$	−1.27396e12	−0.274186	−0.137093	+	0.990558i	$0.543776\pi$
$654$	4.03187e11	0.0861800
$655$	−2.15574e12	−0.457625
$656$	−1.41377e12	−0.298066
$657$	1.35624e12	0.283982
$658$	4.44817e12	0.925050
$659$	−2.22728e12	−0.460035	−0.230017	−	0.973187i	$-0.573878\pi$
$659$	−2.22728e12	−0.460035	−0.230017	+	0.973187i	$0.573878\pi$
$660$	−4.83991e12	−0.992864
$661$	−5.98094e12	−1.21860	−0.609302	−	0.792938i	$-0.708550\pi$
$661$	−5.98094e12	−1.21860	−0.609302	+	0.792938i	$0.708550\pi$
$662$	1.04017e13	2.10497
$663$	0	0
$664$	−5.20602e12	−1.03932
$665$	−1.34136e12	−0.265979
$666$	−1.51073e12	−0.297545
$667$	−1.07589e12	−0.210476
$668$	−4.76128e12	−0.925186
$669$	−4.30679e12	−0.831259
$670$	−2.78193e12	−0.533346
$671$	1.55405e12	0.295946
$672$	−3.39769e12	−0.642720
$673$	6.43719e12	1.20956	0.604781	−	0.796392i	$-0.293261\pi$
$673$	6.43719e12	1.20956	0.604781	+	0.796392i	$0.293261\pi$
$674$	3.30425e12	0.616742
$675$	−3.33055e12	−0.617518
$676$	−8.32295e12	−1.53291
$677$	−7.34022e11	−0.134295	−0.0671476	−	0.997743i	$-0.521390\pi$
$677$	−7.34022e11	−0.134295	−0.0671476	+	0.997743i	$0.521390\pi$
$678$	7.42085e12	1.34871
$679$	−4.21425e12	−0.760863
$680$	0	0
$681$	6.73477e11	0.119994
$682$	−6.51519e12	−1.15318
$683$	4.45334e12	0.783057	0.391528	−	0.920166i	$-0.371947\pi$
$683$	4.45334e12	0.783057	0.391528	+	0.920166i	$0.371947\pi$
$684$	−1.44972e12	−0.253240
$685$	−2.16024e12	−0.374883
$686$	9.53363e12	1.64361
$687$	9.48460e12	1.62448
$688$	7.36067e11	0.125248
$689$	−2.19864e11	−0.0371679
$690$	−1.13864e12	−0.191234
$691$	−1.18066e12	−0.197004	−0.0985019	−	0.995137i	$-0.531405\pi$
$691$	−1.18066e12	−0.197004	−0.0985019	+	0.995137i	$0.531405\pi$
$692$	−5.93685e12	−0.984189
$693$	1.24424e12	0.204930
$694$	1.74644e13	2.85782
$695$	−4.73213e12	−0.769352
$696$	4.41818e12	0.713678
$697$	0	0
$698$	2.31770e11	0.0369579
$699$	−8.17742e12	−1.29559
$700$	3.66015e12	0.576180
$701$	5.00732e11	0.0783202	0.0391601	−	0.999233i	$-0.487532\pi$
$701$	5.00732e11	0.0783202	0.0391601	+	0.999233i	$0.487532\pi$
$702$	2.09998e11	0.0326361
$703$	2.76175e12	0.426467
$704$	−1.22607e13	−1.88122
$705$	3.24046e12	0.494033
$706$	−6.61352e12	−1.00187
$707$	−6.40731e12	−0.964470
$708$	−1.34582e13	−2.01297
$709$	4.45528e12	0.662166	0.331083	−	0.943602i	$-0.392586\pi$
$709$	4.45528e12	0.662166	0.331083	+	0.943602i	$0.392586\pi$
$710$	−1.16971e13	−1.72749
$711$	1.79986e12	0.264135
$712$	−6.23545e12	−0.909301
$713$	−9.27757e11	−0.134441
$714$	0	0
$715$	1.00016e11	0.0143118
$716$	1.56216e12	0.222135
$717$	3.83773e12	0.542298
$718$	1.60288e13	2.25083
$719$	−2.07009e12	−0.288874	−0.144437	−	0.989514i	$-0.546137\pi$
$719$	−2.07009e12	−0.288874	−0.144437	+	0.989514i	$0.546137\pi$
$720$	2.31727e11	0.0321352
$721$	7.54394e11	0.103966
$722$	−7.24333e12	−0.992021
$723$	5.05105e11	0.0687479
$724$	−1.71080e13	−2.31407
$725$	4.16245e12	0.559536
$726$	−3.37303e12	−0.450615
$727$	−5.41864e12	−0.719425	−0.359713	−	0.933063i	$-0.617125\pi$
$727$	−5.41864e12	−0.719425	−0.359713	+	0.933063i	$0.617125\pi$
$728$	−8.02837e10	−0.0105934
$729$	8.42474e12	1.10480
$730$	−8.46114e12	−1.10275
$731$	0	0
$732$	−2.61226e12	−0.336292
$733$	−1.11750e13	−1.42982	−0.714909	−	0.699218i	$-0.753532\pi$
$733$	−1.11750e13	−1.42982	−0.714909	+	0.699218i	$0.753532\pi$
$734$	−1.46137e13	−1.85836
$735$	2.50501e12	0.316603
$736$	−1.94076e12	−0.243793
$737$	−4.71742e12	−0.588980
$738$	−5.65295e12	−0.701490
$739$	−5.17452e12	−0.638219	−0.319110	−	0.947718i	$-0.603384\pi$
$739$	−5.17452e12	−0.638219	−0.319110	+	0.947718i	$0.603384\pi$
$740$	5.70477e12	0.699351
$741$	−8.13898e10	−0.00991718
$742$	1.70640e13	2.06664
$743$	−6.63620e12	−0.798859	−0.399429	−	0.916764i	$-0.630792\pi$
$743$	−6.63620e12	−0.798859	−0.399429	+	0.916764i	$0.630792\pi$
$744$	3.80986e12	0.455859
$745$	−5.54278e12	−0.659211
$746$	1.46834e13	1.73581
$747$	2.80265e12	0.329326
$748$	0	0
$749$	−9.97665e12	−1.15829
$750$	1.21452e13	1.40161
$751$	−1.50960e13	−1.73173	−0.865866	−	0.500275i	$-0.833232\pi$
$751$	−1.50960e13	−1.73173	−0.865866	+	0.500275i	$0.833232\pi$
$752$	1.40479e12	0.160189
$753$	−1.52100e12	−0.172406
$754$	−2.62451e11	−0.0295718
$755$	−6.94280e12	−0.777630
$756$	−9.86511e12	−1.09838
$757$	−3.33377e12	−0.368981	−0.184491	−	0.982834i	$-0.559064\pi$
$757$	−3.33377e12	−0.368981	−0.184491	+	0.982834i	$0.559064\pi$
$758$	2.42379e13	2.66676
$759$	−1.93083e12	−0.211182
$760$	3.14635e12	0.342094
$761$	1.76503e13	1.90774	0.953872	−	0.300213i	$-0.0970579\pi$
$761$	1.76503e13	1.90774	0.953872	+	0.300213i	$0.0970579\pi$
$762$	−9.96249e12	−1.07046
$763$	3.91404e11	0.0418086
$764$	1.22340e13	1.29912
$765$	0	0
$766$	1.25908e13	1.32137
$767$	2.78112e11	0.0290162
$768$	5.66979e12	0.588087
$769$	1.65629e12	0.170793	0.0853963	−	0.996347i	$-0.472784\pi$
$769$	1.65629e12	0.170793	0.0853963	+	0.996347i	$0.472784\pi$
$770$	−7.76244e12	−0.795774
$771$	−9.73810e12	−0.992497
$772$	2.80139e12	0.283855
$773$	−9.98087e12	−1.00545	−0.502725	−	0.864446i	$-0.667669\pi$
$773$	−9.98087e12	−1.00545	−0.502725	+	0.864446i	$0.667669\pi$
$774$	2.94315e12	0.294767
$775$	3.58933e12	0.357401
$776$	9.88514e12	0.978600
$777$	3.98435e12	0.392160
$778$	−1.79150e13	−1.75311
$779$	1.03341e13	1.00544
$780$	−1.68122e11	−0.0162629
$781$	−1.98352e13	−1.90769
$782$	0	0
$783$	−1.12189e13	−1.06665
$784$	1.08596e12	0.102658
$785$	3.30054e12	0.310221
$786$	1.01519e13	0.948740
$787$	8.71656e12	0.809951	0.404975	−	0.914328i	$-0.367280\pi$
$787$	8.71656e12	0.809951	0.404975	+	0.914328i	$0.367280\pi$
$788$	−2.41478e13	−2.23105
$789$	5.24117e12	0.481484
$790$	−1.12288e13	−1.02568
$791$	7.20398e12	0.654302
$792$	−2.91855e12	−0.263575
$793$	5.39821e10	0.00484753
$794$	−5.69928e12	−0.508895
$795$	1.24310e13	1.10371
$796$	−1.16798e13	−1.03116
$797$	1.27804e13	1.12197	0.560987	−	0.827825i	$-0.310422\pi$
$797$	1.27804e13	1.12197	0.560987	+	0.827825i	$0.310422\pi$
$798$	6.31681e12	0.551423
$799$	0	0
$800$	7.50846e12	0.648106
$801$	3.35684e12	0.288127
$802$	3.27855e12	0.279832
$803$	−1.43479e13	−1.21778
$804$	7.92971e12	0.669276
$805$	−1.10536e12	−0.0927735
$806$	−2.26315e11	−0.0188888
$807$	−1.82816e13	−1.51734
$808$	1.50293e13	1.24047
$809$	−3.13377e12	−0.257216	−0.128608	−	0.991695i	$-0.541051\pi$
$809$	−3.13377e12	−0.257216	−0.128608	+	0.991695i	$0.541051\pi$
$810$	−8.42943e12	−0.688043
$811$	9.63303e12	0.781932	0.390966	−	0.920405i	$-0.372141\pi$
$811$	9.63303e12	0.781932	0.390966	+	0.920405i	$0.372141\pi$
$812$	1.23292e13	0.995250
$813$	−1.70114e12	−0.136563
$814$	1.59823e13	1.27593
$815$	2.25682e12	0.179180
$816$	0	0
$817$	−5.38036e12	−0.422485
$818$	1.52469e13	1.19067
$819$	4.32206e10	0.00335670
$820$	2.13465e13	1.64879
$821$	2.49670e13	1.91788	0.958942	−	0.283602i	$-0.0915294\pi$
$821$	2.49670e13	1.91788	0.958942	+	0.283602i	$0.0915294\pi$
$822$	1.01732e13	0.777200
$823$	4.54640e12	0.345437	0.172718	−	0.984971i	$-0.444745\pi$
$823$	4.54640e12	0.345437	0.172718	+	0.984971i	$0.444745\pi$
$824$	−1.76954e12	−0.133718
$825$	7.47006e12	0.561412
$826$	−2.15848e13	−1.61338
$827$	−2.42269e13	−1.80104	−0.900518	−	0.434819i	$-0.856812\pi$
$827$	−2.42269e13	−1.80104	−0.900518	+	0.434819i	$0.856812\pi$
$828$	−1.19466e12	−0.0883302
$829$	1.77633e13	1.30626	0.653130	−	0.757246i	$-0.273456\pi$
$829$	1.77633e13	1.30626	0.653130	+	0.757246i	$0.273456\pi$
$830$	−1.74849e13	−1.27883
$831$	9.43052e12	0.686011
$832$	−4.25895e11	−0.0308140
$833$	0	0
$834$	2.22849e13	1.59501
$835$	−5.56300e12	−0.396023
$836$	1.53369e13	1.08595
$837$	−9.67423e12	−0.681321
$838$	−2.24171e13	−1.57029
$839$	1.27875e13	0.890955	0.445477	−	0.895293i	$-0.353034\pi$
$839$	1.27875e13	0.890955	0.445477	+	0.895293i	$0.353034\pi$
$840$	4.53921e12	0.314574
$841$	−4.85991e11	−0.0335001
$842$	1.68299e13	1.15393
$843$	−4.46364e12	−0.304414
$844$	2.72537e13	1.84878
$845$	−9.72440e12	−0.656157
$846$	5.61704e12	0.377000
$847$	−3.27446e12	−0.218607
$848$	5.38906e12	0.357875
$849$	8.84966e11	0.0584577
$850$	0	0
$851$	2.27586e12	0.148752
$852$	3.33419e13	2.16777
$853$	−1.39538e13	−0.902450	−0.451225	−	0.892410i	$-0.649013\pi$
$853$	−1.39538e13	−0.902450	−0.451225	+	0.892410i	$0.649013\pi$
$854$	−4.18965e12	−0.269536
$855$	−1.69383e12	−0.108398
$856$	2.34017e13	1.48976
$857$	1.46381e13	0.926984	0.463492	−	0.886101i	$-0.346596\pi$
$857$	1.46381e13	0.926984	0.463492	+	0.886101i	$0.346596\pi$
$858$	−4.71003e11	−0.0296709
$859$	−1.39610e13	−0.874876	−0.437438	−	0.899249i	$-0.644114\pi$
$859$	−1.39610e13	−0.874876	−0.437438	+	0.899249i	$0.644114\pi$
$860$	−1.11138e13	−0.692822
$861$	1.49089e13	0.924554
$862$	9.29093e12	0.573161
$863$	3.05848e13	1.87697	0.938485	−	0.345321i	$-0.112230\pi$
$863$	3.05848e13	1.87697	0.938485	+	0.345321i	$0.112230\pi$
$864$	−2.02373e13	−1.23550
$865$	−6.93652e12	−0.421278
$866$	9.87480e12	0.596620
$867$	0	0
$868$	1.06316e13	0.635712
$869$	−1.90411e13	−1.13267
$870$	1.48389e13	0.878141
$871$	−1.63867e11	−0.00964737
$872$	−9.18096e11	−0.0537730
$873$	−5.32165e12	−0.310086
$874$	3.60816e12	0.209163
$875$	1.17902e13	0.679965
$876$	2.41179e13	1.38380
$877$	1.08401e13	0.618781	0.309391	−	0.950935i	$-0.399875\pi$
$877$	1.08401e13	0.618781	0.309391	+	0.950935i	$0.399875\pi$
$878$	−2.84676e13	−1.61668
$879$	−1.15024e13	−0.649886
$880$	−2.45148e12	−0.137802
$881$	2.25641e13	1.26190	0.630952	−	0.775822i	$-0.282665\pi$
$881$	2.25641e13	1.26190	0.630952	+	0.775822i	$0.282665\pi$
$882$	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	$0.767400\pi$
$884$	0	0
$885$	−1.57243e13	−0.861644
$886$	−2.37301e12	−0.129374
$887$	−1.58992e12	−0.0862422	−0.0431211	−	0.999070i	$-0.513730\pi$
$887$	−1.58992e12	−0.0862422	−0.0431211	+	0.999070i	$0.513730\pi$
$888$	−9.34587e12	−0.504384
$889$	−9.67135e12	−0.519313
$890$	−2.09423e13	−1.11884
$891$	−1.42941e13	−0.759813
$892$	2.81908e13	1.49096
$893$	−1.02685e13	−0.540349
$894$	2.61024e13	1.36666
$895$	1.82520e12	0.0950839
$896$	1.85513e13	0.961585
$897$	−6.70704e10	−0.00345911
$898$	3.12088e13	1.60153
$899$	1.20906e13	0.617348
$900$	4.62195e12	0.234819
$901$	0	0
$902$	5.98036e13	3.00814
$903$	−7.76218e12	−0.388498
$904$	−1.68980e13	−0.841545
$905$	−1.99887e13	−0.990527
$906$	3.26955e13	1.61217
$907$	1.69740e13	0.832821	0.416411	−	0.909177i	$-0.363288\pi$
$907$	1.69740e13	0.832821	0.416411	+	0.909177i	$0.363288\pi$
$908$	−4.40834e12	−0.215223
$909$	−8.09099e12	−0.393065
$910$	−2.69640e11	−0.0130346
$911$	−7.56497e12	−0.363894	−0.181947	−	0.983308i	$-0.558240\pi$
$911$	−7.56497e12	−0.363894	−0.181947	+	0.983308i	$0.558240\pi$
$912$	1.99493e12	0.0954886
$913$	−2.96497e13	−1.41222
$914$	−2.25226e13	−1.06748
$915$	−3.05213e12	−0.143949
$916$	−6.20829e13	−2.91368
$917$	9.85525e12	0.460263
$918$	0	0
$919$	−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
$921$	−1.63502e13	−0.748782
$922$	5.25360e13	2.39424
$923$	−6.89007e11	−0.0312476
$924$	2.21263e13	0.998586
$925$	−8.80491e12	−0.395446
$926$	5.60068e13	2.50318
$927$	9.52630e11	0.0423707
$928$	2.52922e13	1.11949
$929$	3.31874e13	1.46185	0.730925	−	0.682457i	$-0.239089\pi$
$929$	3.31874e13	1.46185	0.730925	+	0.682457i	$0.239089\pi$
$930$	1.27958e13	0.560909
$931$	−7.93795e12	−0.346286
$932$	5.35265e13	2.32379
$933$	−1.60584e13	−0.693803
$934$	−6.98306e13	−3.00251
$935$	0	0
$936$	−1.01380e11	−0.00431730
$937$	−1.99592e13	−0.845891	−0.422945	−	0.906155i	$-0.639004\pi$
$937$	−1.99592e13	−0.845891	−0.422945	+	0.906155i	$0.639004\pi$
$938$	1.27180e13	0.536421
$939$	−1.04234e13	−0.437538
$940$	−2.12109e13	−0.886103
$941$	9.88180e12	0.410849	0.205425	−	0.978673i	$-0.434142\pi$
$941$	9.88180e12	0.410849	0.205425	+	0.978673i	$0.434142\pi$
$942$	−1.55431e13	−0.643146
$943$	8.51598e12	0.350697
$944$	−6.81677e12	−0.279386
$945$	−1.15262e13	−0.470159
$946$	−3.11361e13	−1.26402
$947$	4.35997e13	1.76161	0.880803	−	0.473482i	$-0.157003\pi$
$947$	4.35997e13	1.76161	0.880803	+	0.473482i	$0.157003\pi$
$948$	3.20069e13	1.28708
$949$	−4.98395e11	−0.0199469
$950$	−1.39594e13	−0.556044
$951$	−2.97781e13	−1.18055
$952$	0	0
$953$	−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
$955$	1.42940e13	0.556082
$956$	−2.51204e13	−0.972672
$957$	2.51628e13	0.969740
$958$	−6.45670e13	−2.47666
$959$	9.87587e12	0.377043
$960$	2.40799e13	0.915029
$961$	−1.60137e13	−0.605671
$962$	5.55168e11	0.0208995
$963$	−1.25983e13	−0.472055
$964$	−3.30624e12	−0.123307
$965$	3.27310e12	0.121503
$966$	5.20545e12	0.192336
$967$	−5.16213e13	−1.89850	−0.949249	−	0.314525i	$-0.898155\pi$
$967$	−5.16213e13	−1.89850	−0.949249	+	0.314525i	$0.898155\pi$
$968$	7.68072e12	0.281166
$969$	0	0
$970$	3.32001e13	1.20411
$971$	−2.90086e13	−1.04722	−0.523612	−	0.851957i	$-0.675416\pi$
$971$	−2.90086e13	−1.04722	−0.523612	+	0.851957i	$0.675416\pi$
$972$	−2.22737e13	−0.800377
$973$	2.16336e13	0.773787
$974$	−6.77651e13	−2.41263
$975$	2.59484e11	0.00919581
$976$	−1.32315e12	−0.0466750
$977$	3.35721e13	1.17883	0.589417	−	0.807829i	$-0.299358\pi$
$977$	3.35721e13	1.17883	0.589417	+	0.807829i	$0.299358\pi$
$978$	−1.06280e13	−0.371472
$979$	−3.55126e13	−1.23555
$980$	−1.63969e13	−0.567864
$981$	4.94256e11	0.0170389
$982$	−7.36895e13	−2.52874
$983$	−3.00685e13	−1.02712	−0.513559	−	0.858054i	$-0.671673\pi$
$983$	−3.00685e13	−1.02712	−0.513559	+	0.858054i	$0.671673\pi$
$984$	−3.49711e13	−1.18914
$985$	−2.82139e13	−0.954991
$986$	0	0
$987$	−1.48142e13	−0.496880
$988$	5.32749e11	0.0177876
$989$	−4.43376e12	−0.147363
$990$	−9.80221e12	−0.324314
$991$	−2.45476e13	−0.808494	−0.404247	−	0.914650i	$-0.632466\pi$
$991$	−2.45476e13	−0.808494	−0.404247	+	0.914650i	$0.632466\pi$
$992$	2.18098e13	0.715069
$993$	−3.46420e13	−1.13066
$994$	5.34751e13	1.73745
$995$	−1.36465e13	−0.441384
$996$	4.98395e13	1.60475
$997$	−4.26106e13	−1.36581	−0.682904	−	0.730509i	$-0.739283\pi$
$997$	−4.26106e13	−1.36581	−0.682904	+	0.730509i	$0.739283\pi$
$998$	−9.00156e13	−2.87230
$999$	2.37316e13	0.753846

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.1	✓	12	17.13	even	4
17.10.b.a.16.2	yes	12	17.4	even	4
153.10.d.b.118.11		12	51.47	odd	4
153.10.d.b.118.12		12	51.38	odd	4
272.10.b.c.33.3		12	68.55	odd	4
272.10.b.c.33.10		12	68.47	odd	4
289.10.a.c.1.11		12	1.1	even	1	trivial
289.10.a.c.1.12		12	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

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

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