LMFDB - Embedded newform 289.10.a.d.1.3

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} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + \cdots + 245077910606835 $ x^12 - 5x^11 - 4542x^10 + 30079x^9 + 7481825x^8 - 58373994x^7 - 5553197164x^6 + 45662797046x^5 + 1825619566875x^4 - 13493392282513x^3 - 214257360688838x^2 + 1064197876989579*x + 245077910606835
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-31.5756$ 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)

$f(q)$	$=$	$q-30.5756 q^{2} -194.921 q^{3} +422.865 q^{4} +941.135 q^{5} +5959.81 q^{6} -4513.44 q^{7} +2725.35 q^{8} +18311.1 q^{9} +O(q^{10})$	\(q-30.5756 q^{2} -194.921 q^{3} +422.865 q^{4} +941.135 q^{5} +5959.81 q^{6} -4513.44 q^{7} +2725.35 q^{8} +18311.1 q^{9} -28775.7 q^{10} +41597.1 q^{11} -82425.2 q^{12} +101290. q^{13} +138001. q^{14} -183447. q^{15} -299836. q^{16} -559873. q^{18} +878675. q^{19} +397973. q^{20} +879763. q^{21} -1.27185e6 q^{22} -1.58058e6 q^{23} -531227. q^{24} -1.06739e6 q^{25} -3.09699e6 q^{26} +267410. q^{27} -1.90858e6 q^{28} +1.94618e6 q^{29} +5.60899e6 q^{30} -4.44805e6 q^{31} +7.77228e6 q^{32} -8.10814e6 q^{33} -4.24775e6 q^{35} +7.74313e6 q^{36} +9.92035e6 q^{37} -2.68660e7 q^{38} -1.97434e7 q^{39} +2.56492e6 q^{40} -3.03121e7 q^{41} -2.68993e7 q^{42} -4.15989e7 q^{43} +1.75900e7 q^{44} +1.72332e7 q^{45} +4.83272e7 q^{46} +2.96697e7 q^{47} +5.84443e7 q^{48} -1.99825e7 q^{49} +3.26361e7 q^{50} +4.28318e7 q^{52} -1.85086e7 q^{53} -8.17620e6 q^{54} +3.91485e7 q^{55} -1.23007e7 q^{56} -1.71272e8 q^{57} -5.95055e7 q^{58} +3.51354e7 q^{59} -7.75732e7 q^{60} -1.88656e8 q^{61} +1.36002e8 q^{62} -8.26461e7 q^{63} -8.41258e7 q^{64} +9.53271e7 q^{65} +2.47911e8 q^{66} +2.08556e8 q^{67} +3.08088e8 q^{69} +1.29878e8 q^{70} +4.89810e7 q^{71} +4.99041e7 q^{72} +1.30289e8 q^{73} -3.03320e8 q^{74} +2.08057e8 q^{75} +3.71561e8 q^{76} -1.87746e8 q^{77} +6.03667e8 q^{78} +2.59845e8 q^{79} -2.82186e8 q^{80} -4.12541e8 q^{81} +9.26809e8 q^{82} +4.12715e8 q^{83} +3.72021e8 q^{84} +1.27191e9 q^{86} -3.79351e8 q^{87} +1.13366e8 q^{88} +1.05219e9 q^{89} -5.26916e8 q^{90} -4.57164e8 q^{91} -6.68373e8 q^{92} +8.67017e8 q^{93} -9.07169e8 q^{94} +8.26952e8 q^{95} -1.51498e9 q^{96} +1.29676e9 q^{97} +6.10975e8 q^{98} +7.61689e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) $ 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9} + 2449 q^{10} - 152886 q^{11} - 41717 q^{12} + 23478 q^{13} - 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} + 2477218 q^{20} - 1395256 q^{21} - 2391095 q^{22} - 2012428 q^{23} - 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} - 3231638 q^{27} + 5978216 q^{28} - 12772842 q^{29} + 181633 q^{30} - 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} - 1352872 q^{37} + 3704404 q^{38} + 1380780 q^{39} - 44739331 q^{40} - 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} - 148233417 q^{44} + 79449336 q^{45} - 31855859 q^{46} + 133558002 q^{47} + 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} + 50215469 q^{54} - 91197532 q^{55} - 267350757 q^{56} - 49507694 q^{57} - 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} - 262041240 q^{61} + 314328847 q^{62} - 218532626 q^{63} + 595820098 q^{64} - 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} - 204290852 q^{71} - 208030791 q^{72} - 673538852 q^{73} - 1274510282 q^{74} - 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} - 165043245 q^{78} - 434002980 q^{79} - 599590757 q^{80} - 389011392 q^{81} + 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} + 262108460 q^{88} + 911678128 q^{89} + 2734590475 q^{90} + 560105446 q^{91} + 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} + 1116511966 q^{95} - 2204198979 q^{96} + 3589270998 q^{97} - 2677144485 q^{98} - 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9 + 2449 * q^10 - 152886 * q^11 - 41717 * q^12 + 23478 * q^13 - 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 + 2477218 * q^20 - 1395256 * q^21 - 2391095 * q^22 - 2012428 * q^23 - 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 - 3231638 * q^27 + 5978216 * q^28 - 12772842 * q^29 + 181633 * q^30 - 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 - 1352872 * q^37 + 3704404 * q^38 + 1380780 * q^39 - 44739331 * q^40 - 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 - 148233417 * q^44 + 79449336 * q^45 - 31855859 * q^46 + 133558002 * q^47 + 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 + 50215469 * q^54 - 91197532 * q^55 - 267350757 * q^56 - 49507694 * q^57 - 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 - 262041240 * q^61 + 314328847 * q^62 - 218532626 * q^63 + 595820098 * q^64 - 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 - 204290852 * q^71 - 208030791 * q^72 - 673538852 * q^73 - 1274510282 * q^74 - 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 - 165043245 * q^78 - 434002980 * q^79 - 599590757 * q^80 - 389011392 * q^81 + 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 + 262108460 * q^88 + 911678128 * q^89 + 2734590475 * q^90 + 560105446 * q^91 + 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 + 1116511966 * q^95 - 2204198979 * q^96 + 3589270998 * q^97 - 2677144485 * q^98 - 2056683494 * q^99

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 $

$2$	−30.5756	−1.35126	−0.675631	−	0.737240i	$-0.736129\pi$
$2$	−30.5756	−1.35126	−0.675631	+	0.737240i	$0.736129\pi$
$3$	−194.921	−1.38935	−0.694676	−	0.719322i	$-0.744452\pi$
$3$	−194.921	−1.38935	−0.694676	+	0.719322i	$0.744452\pi$
$4$	422.865	0.825909
$5$	941.135	0.673421	0.336711	−	0.941608i	$-0.390686\pi$
$5$	941.135	0.673421	0.336711	+	0.941608i	$0.390686\pi$
$6$	5959.81	1.87738
$7$	−4513.44	−0.710504	−0.355252	−	0.934771i	$-0.615605\pi$
$7$	−4513.44	−0.710504	−0.355252	+	0.934771i	$0.615605\pi$
$8$	2725.35	0.235243
$9$	18311.1	0.930301
$10$	−28775.7	−0.909968
$11$	41597.1	0.856635	0.428317	−	0.903628i	$-0.359106\pi$
$11$	41597.1	0.856635	0.428317	+	0.903628i	$0.359106\pi$
$12$	−82425.2	−1.14748
$13$	101290.	0.983602	0.491801	−	0.870708i	$-0.336339\pi$
$13$	101290.	0.983602	0.491801	+	0.870708i	$0.336339\pi$
$14$	138001.	0.960077
$15$	−183447.	−0.935620
$16$	−299836.	−1.14378
$17$	0	0
$17$	0	0
$18$	−559873.	−1.25708
$19$	878675.	1.54681	0.773405	−	0.633912i	$-0.218552\pi$
$19$	878675.	1.54681	0.773405	+	0.633912i	$0.218552\pi$
$20$	397973.	0.556184
$21$	879763.	0.987140
$22$	−1.27185e6	−1.15754
$23$	−1.58058e6	−1.17772	−0.588860	−	0.808235i	$-0.700423\pi$
$23$	−1.58058e6	−1.17772	−0.588860	+	0.808235i	$0.700423\pi$
$24$	−531227.	−0.326836
$25$	−1.06739e6	−0.546504
$26$	−3.09699e6	−1.32910
$27$	267410.	0.0968367
$28$	−1.90858e6	−0.586811
$29$	1.94618e6	0.510966	0.255483	−	0.966814i	$-0.417766\pi$
$29$	1.94618e6	0.510966	0.255483	+	0.966814i	$0.417766\pi$
$30$	5.60899e6	1.26427
$31$	−4.44805e6	−0.865051	−0.432525	−	0.901622i	$-0.642377\pi$
$31$	−4.44805e6	−0.865051	−0.432525	+	0.901622i	$0.642377\pi$
$32$	7.77228e6	1.31031
$33$	−8.10814e6	−1.19017
$34$	0	0
$35$	−4.24775e6	−0.478468
$36$	7.74313e6	0.768344
$37$	9.92035e6	0.870200	0.435100	−	0.900382i	$-0.356713\pi$
$37$	9.92035e6	0.870200	0.435100	+	0.900382i	$0.356713\pi$
$38$	−2.68660e7	−2.09015
$39$	−1.97434e7	−1.36657
$40$	2.56492e6	0.158418
$41$	−3.03121e7	−1.67528	−0.837642	−	0.546220i	$-0.816066\pi$
$41$	−3.03121e7	−1.67528	−0.837642	+	0.546220i	$0.816066\pi$
$42$	−2.68993e7	−1.33389
$43$	−4.15989e7	−1.85555	−0.927777	−	0.373135i	$-0.878283\pi$
$43$	−4.15989e7	−1.85555	−0.927777	+	0.373135i	$0.878283\pi$
$44$	1.75900e7	0.707502
$45$	1.72332e7	0.626484
$46$	4.83272e7	1.59141
$47$	2.96697e7	0.886897	0.443449	−	0.896300i	$-0.353755\pi$
$47$	2.96697e7	0.886897	0.443449	+	0.896300i	$0.353755\pi$
$48$	5.84443e7	1.58912
$49$	−1.99825e7	−0.495184
$50$	3.26361e7	0.738470
$51$	0	0
$52$	4.28318e7	0.812366
$53$	−1.85086e7	−0.322204	−0.161102	−	0.986938i	$-0.551505\pi$
$53$	−1.85086e7	−0.322204	−0.161102	+	0.986938i	$0.551505\pi$
$54$	−8.17620e6	−0.130852
$55$	3.91485e7	0.576876
$56$	−1.23007e7	−0.167141
$57$	−1.71272e8	−2.14907
$58$	−5.95055e7	−0.690448
$59$	3.51354e7	0.377495	0.188747	−	0.982026i	$-0.439557\pi$
$59$	3.51354e7	0.377495	0.188747	+	0.982026i	$0.439557\pi$
$60$	−7.75732e7	−0.772736
$61$	−1.88656e8	−1.74456	−0.872279	−	0.489009i	$-0.837359\pi$
$61$	−1.88656e8	−1.74456	−0.872279	+	0.489009i	$0.837359\pi$
$62$	1.36002e8	1.16891
$63$	−8.26461e7	−0.660982
$64$	−8.41258e7	−0.626786
$65$	9.53271e7	0.662379
$66$	2.47911e8	1.60823
$67$	2.08556e8	1.26440	0.632201	−	0.774804i	$-0.282152\pi$
$67$	2.08556e8	1.26440	0.632201	+	0.774804i	$0.282152\pi$
$68$	0	0
$69$	3.08088e8	1.63627
$70$	1.29878e8	0.646536
$71$	4.89810e7	0.228752	0.114376	−	0.993438i	$-0.463513\pi$
$71$	4.89810e7	0.228752	0.114376	+	0.993438i	$0.463513\pi$
$72$	4.99041e7	0.218847
$73$	1.30289e8	0.536978	0.268489	−	0.963283i	$-0.413476\pi$
$73$	1.30289e8	0.536978	0.268489	+	0.963283i	$0.413476\pi$
$74$	−3.03320e8	−1.17587
$75$	2.08057e8	0.759287
$76$	3.71561e8	1.27752
$77$	−1.87746e8	−0.608642
$78$	6.03667e8	1.84659
$79$	2.59845e8	0.750571	0.375286	−	0.926909i	$-0.377545\pi$
$79$	2.59845e8	0.750571	0.375286	+	0.926909i	$0.377545\pi$
$80$	−2.82186e8	−0.770248
$81$	−4.12541e8	−1.06484
$82$	9.26809e8	2.26375
$83$	4.12715e8	0.954550	0.477275	−	0.878754i	$-0.341625\pi$
$83$	4.12715e8	0.954550	0.477275	+	0.878754i	$0.341625\pi$
$84$	3.72021e8	0.815288
$85$	0	0
$86$	1.27191e9	2.50734
$87$	−3.79351e8	−0.709912
$88$	1.13366e8	0.201517
$89$	1.05219e9	1.77763	0.888815	−	0.458267i	$-0.151530\pi$
$89$	1.05219e9	1.77763	0.888815	+	0.458267i	$0.151530\pi$
$90$	−5.26916e8	−0.846544
$91$	−4.57164e8	−0.698853
$92$	−6.68373e8	−0.972689
$93$	8.67017e8	1.20186
$94$	−9.07169e8	−1.19843
$95$	8.26952e8	1.04166
$96$	−1.51498e9	−1.82048
$97$	1.29676e9	1.48726	0.743628	−	0.668594i	$-0.233104\pi$
$97$	1.29676e9	1.48726	0.743628	+	0.668594i	$0.233104\pi$
$98$	6.10975e8	0.669124
$99$	7.61689e8	0.796928
$100$	−4.51362e8	−0.451362
$101$	5.40379e8	0.516717	0.258358	−	0.966049i	$-0.416818\pi$
$101$	5.40379e8	0.516717	0.258358	+	0.966049i	$0.416818\pi$
$102$	0	0
$103$	−2.13430e9	−1.86848	−0.934238	−	0.356649i	$-0.883919\pi$
$103$	−2.13430e9	−1.86848	−0.934238	+	0.356649i	$0.883919\pi$
$104$	2.76049e8	0.231386
$105$	8.27976e8	0.664761
$106$	5.65910e8	0.435382
$107$	−5.12879e6	−0.00378258	−0.00189129	−	0.999998i	$-0.500602\pi$
$107$	−5.12879e6	−0.00378258	−0.00189129	+	0.999998i	$0.500602\pi$
$108$	1.13078e8	0.0799783
$109$	4.25009e8	0.288389	0.144195	−	0.989549i	$-0.453941\pi$
$109$	4.25009e8	0.288389	0.144195	+	0.989549i	$0.453941\pi$
$110$	−1.19699e9	−0.779511
$111$	−1.93368e9	−1.20902
$112$	1.35329e9	0.812663
$113$	7.28636e8	0.420395	0.210197	−	0.977659i	$-0.432589\pi$
$113$	7.28636e8	0.420395	0.210197	+	0.977659i	$0.432589\pi$
$114$	5.23674e9	2.90395
$115$	−1.48754e9	−0.793101
$116$	8.22971e8	0.422011
$117$	1.85472e9	0.915046
$118$	−1.07429e9	−0.510095
$119$	0	0
$120$	−4.99956e8	−0.220098
$121$	−6.27630e8	−0.266177
$122$	5.76825e9	2.35735
$123$	5.90845e9	2.32756
$124$	−1.88092e9	−0.714453
$125$	−2.84271e9	−1.04145
$126$	2.52695e9	0.893160
$127$	−2.52131e9	−0.860022	−0.430011	−	0.902824i	$-0.641490\pi$
$127$	−2.52131e9	−0.860022	−0.430011	+	0.902824i	$0.641490\pi$
$128$	−1.40721e9	−0.463356
$129$	8.10849e9	2.57802
$130$	−2.91468e9	−0.895047
$131$	−5.51873e9	−1.63726	−0.818631	−	0.574320i	$-0.805267\pi$
$131$	−5.51873e9	−1.63726	−0.818631	+	0.574320i	$0.805267\pi$
$132$	−3.42865e9	−0.982970
$133$	−3.96585e9	−1.09902
$134$	−6.37671e9	−1.70854
$135$	2.51668e8	0.0652119
$136$	0	0
$137$	9.40891e8	0.228190	0.114095	−	0.993470i	$-0.463603\pi$
$137$	9.40891e8	0.228190	0.114095	+	0.993470i	$0.463603\pi$
$138$	−9.41998e9	−2.21103
$139$	8.97314e8	0.203881	0.101941	−	0.994790i	$-0.467495\pi$
$139$	8.97314e8	0.203881	0.101941	+	0.994790i	$0.467495\pi$
$140$	−1.79623e9	−0.395171
$141$	−5.78325e9	−1.23221
$142$	−1.49762e9	−0.309104
$143$	4.21335e9	0.842588
$144$	−5.49033e9	−1.06406
$145$	1.83162e9	0.344095
$146$	−3.98367e9	−0.725598
$147$	3.89500e9	0.687986
$148$	4.19497e9	0.718706
$149$	−1.30561e9	−0.217009	−0.108504	−	0.994096i	$-0.534606\pi$
$149$	−1.30561e9	−0.217009	−0.108504	+	0.994096i	$0.534606\pi$
$150$	−6.36145e9	−1.02599
$151$	−6.19193e9	−0.969236	−0.484618	−	0.874726i	$-0.661041\pi$
$151$	−6.19193e9	−0.969236	−0.484618	+	0.874726i	$0.661041\pi$
$152$	2.39469e9	0.363876
$153$	0	0
$154$	5.74044e9	0.822435
$155$	−4.18621e9	−0.582544
$156$	−8.34881e9	−1.12866
$157$	1.28176e10	1.68367	0.841834	−	0.539736i	$-0.181476\pi$
$157$	1.28176e10	1.68367	0.841834	+	0.539736i	$0.181476\pi$
$158$	−7.94490e9	−1.01422
$159$	3.60770e9	0.447655
$160$	7.31476e9	0.882389
$161$	7.13386e9	0.836774
$162$	1.26137e10	1.43888
$163$	−9.23048e9	−1.02419	−0.512095	−	0.858929i	$-0.671130\pi$
$163$	−9.23048e9	−1.02419	−0.512095	+	0.858929i	$0.671130\pi$
$164$	−1.28179e10	−1.38363
$165$	−7.63085e9	−0.801485
$166$	−1.26190e10	−1.28985
$167$	2.26110e9	0.224955	0.112477	−	0.993654i	$-0.464121\pi$
$167$	2.26110e9	0.224955	0.112477	+	0.993654i	$0.464121\pi$
$168$	2.39766e9	0.232218
$169$	−3.44926e8	−0.0325264
$170$	0	0
$171$	1.60895e10	1.43900
$172$	−1.75907e10	−1.53252
$173$	−6.75290e8	−0.0573169	−0.0286585	−	0.999589i	$-0.509124\pi$
$173$	−6.75290e8	−0.0573169	−0.0286585	+	0.999589i	$0.509124\pi$
$174$	1.15989e10	0.959276
$175$	4.81760e9	0.388293
$176$	−1.24723e10	−0.979805
$177$	−6.84862e9	−0.524474
$178$	−3.21715e10	−2.40204
$179$	1.70190e10	1.23907	0.619533	−	0.784971i	$-0.287322\pi$
$179$	1.70190e10	1.23907	0.619533	+	0.784971i	$0.287322\pi$
$180$	7.28733e9	0.517419
$181$	9.47430e9	0.656136	0.328068	−	0.944654i	$-0.393603\pi$
$181$	9.47430e9	0.656136	0.328068	+	0.944654i	$0.393603\pi$
$182$	1.39781e10	0.944334
$183$	3.67729e10	2.42381
$184$	−4.30763e9	−0.277050
$185$	9.33639e9	0.586011
$186$	−2.65095e10	−1.62403
$187$	0	0
$188$	1.25463e10	0.732496
$189$	−1.20694e9	−0.0688028
$190$	−2.52845e10	−1.40755
$191$	−5.23707e8	−0.0284733	−0.0142367	−	0.999899i	$-0.504532\pi$
$191$	−5.23707e8	−0.0284733	−0.0142367	+	0.999899i	$0.504532\pi$
$192$	1.63979e10	0.870827
$193$	−1.35576e10	−0.703355	−0.351678	−	0.936121i	$-0.614389\pi$
$193$	−1.35576e10	−0.703355	−0.351678	+	0.936121i	$0.614389\pi$
$194$	−3.96491e10	−2.00967
$195$	−1.85812e10	−0.920278
$196$	−8.44989e9	−0.408977
$197$	2.22167e10	1.05095	0.525474	−	0.850810i	$-0.323888\pi$
$197$	2.22167e10	1.05095	0.525474	+	0.850810i	$0.323888\pi$
$198$	−2.32891e10	−1.07686
$199$	−1.58102e10	−0.714659	−0.357329	−	0.933978i	$-0.616313\pi$
$199$	−1.58102e10	−0.714659	−0.357329	+	0.933978i	$0.616313\pi$
$200$	−2.90901e9	−0.128561
$201$	−4.06518e10	−1.75670
$202$	−1.65224e10	−0.698220
$203$	−8.78396e9	−0.363043
$204$	0	0
$205$	−2.85278e10	−1.12817
$206$	6.52574e10	2.52480
$207$	−2.89422e10	−1.09563
$208$	−3.03703e10	−1.12503
$209$	3.65503e10	1.32505
$210$	−2.53158e10	−0.898267
$211$	−4.76983e10	−1.65666	−0.828328	−	0.560244i	$-0.810707\pi$
$211$	−4.76983e10	−1.65666	−0.828328	+	0.560244i	$0.810707\pi$
$212$	−7.82663e9	−0.266111
$213$	−9.54742e9	−0.317818
$214$	1.56816e8	0.00511125
$215$	−3.91502e10	−1.24957
$216$	7.28784e8	0.0227802
$217$	2.00760e10	0.614622
$218$	−1.29949e10	−0.389690
$219$	−2.53961e10	−0.746052
$220$	1.65545e10	0.476447
$221$	0	0
$222$	5.91234e10	1.63370
$223$	4.45882e10	1.20739	0.603696	−	0.797215i	$-0.293694\pi$
$223$	4.45882e10	1.20739	0.603696	+	0.797215i	$0.293694\pi$
$224$	−3.50797e10	−0.930979
$225$	−1.95451e10	−0.508413
$226$	−2.22784e10	−0.568064
$227$	−6.65541e10	−1.66364	−0.831818	−	0.555048i	$-0.812700\pi$
$227$	−6.65541e10	−1.66364	−0.831818	+	0.555048i	$0.812700\pi$
$228$	−7.24250e10	−1.77493
$229$	3.55296e10	0.853749	0.426875	−	0.904311i	$-0.359615\pi$
$229$	3.55296e10	0.853749	0.426875	+	0.904311i	$0.359615\pi$
$230$	4.54824e10	1.07169
$231$	3.65956e10	0.845619
$232$	5.30401e9	0.120201
$233$	4.02652e10	0.895010	0.447505	−	0.894281i	$-0.352313\pi$
$233$	4.02652e10	0.895010	0.447505	+	0.894281i	$0.352313\pi$
$234$	−5.67092e10	−1.23647
$235$	2.79232e10	0.597256
$236$	1.48575e10	0.311776
$237$	−5.06491e10	−1.04281
$238$	0	0
$239$	1.30898e10	0.259503	0.129752	−	0.991547i	$-0.458582\pi$
$239$	1.30898e10	0.259503	0.129752	+	0.991547i	$0.458582\pi$
$240$	5.50039e10	1.07015
$241$	−3.29841e10	−0.629836	−0.314918	−	0.949119i	$-0.601977\pi$
$241$	−3.29841e10	−0.629836	−0.314918	+	0.949119i	$0.601977\pi$
$242$	1.91902e10	0.359674
$243$	7.51494e10	1.38260
$244$	−7.97759e10	−1.44085
$245$	−1.88062e10	−0.333468
$246$	−1.80654e11	−3.14514
$247$	8.90006e10	1.52145
$248$	−1.21225e10	−0.203497
$249$	−8.04467e10	−1.32621
$250$	8.69175e10	1.40727
$251$	−5.32797e10	−0.847285	−0.423643	−	0.905829i	$-0.639249\pi$
$251$	−5.32797e10	−0.847285	−0.423643	+	0.905829i	$0.639249\pi$
$252$	−3.49482e10	−0.545911
$253$	−6.57476e10	−1.00888
$254$	7.70905e10	1.16212
$255$	0	0
$256$	8.60987e10	1.25290
$257$	3.34024e10	0.477615	0.238808	−	0.971067i	$-0.423243\pi$
$257$	3.34024e10	0.477615	0.238808	+	0.971067i	$0.423243\pi$
$258$	−2.47922e11	−3.48358
$259$	−4.47749e10	−0.618281
$260$	4.03105e10	0.547064
$261$	3.56367e10	0.475352
$262$	1.68738e11	2.21237
$263$	2.58102e10	0.332653	0.166326	−	0.986071i	$-0.446810\pi$
$263$	2.58102e10	0.332653	0.166326	+	0.986071i	$0.446810\pi$
$264$	−2.20975e10	−0.279979
$265$	−1.74190e10	−0.216979
$266$	1.21258e11	1.48506
$267$	−2.05095e11	−2.46975
$268$	8.81909e10	1.04428
$269$	3.02035e10	0.351700	0.175850	−	0.984417i	$-0.443733\pi$
$269$	3.02035e10	0.351700	0.175850	+	0.984417i	$0.443733\pi$
$270$	−7.69490e9	−0.0881183
$271$	−7.25899e10	−0.817550	−0.408775	−	0.912635i	$-0.634044\pi$
$271$	−7.25899e10	−0.817550	−0.408775	+	0.912635i	$0.634044\pi$
$272$	0	0
$273$	8.91108e10	0.970954
$274$	−2.87683e10	−0.308345
$275$	−4.44003e10	−0.468154
$276$	1.30280e11	1.35141
$277$	−8.69284e9	−0.0887161	−0.0443581	−	0.999016i	$-0.514124\pi$
$277$	−8.69284e9	−0.0887161	−0.0443581	+	0.999016i	$0.514124\pi$
$278$	−2.74359e10	−0.275497
$279$	−8.14487e10	−0.804758
$280$	−1.15766e10	−0.112556
$281$	1.30456e10	0.124820	0.0624100	−	0.998051i	$-0.480121\pi$
$281$	1.30456e10	0.124820	0.0624100	+	0.998051i	$0.480121\pi$
$282$	1.76826e11	1.66504
$283$	−1.25572e11	−1.16374	−0.581869	−	0.813282i	$-0.697679\pi$
$283$	−1.25572e11	−1.16374	−0.581869	+	0.813282i	$0.697679\pi$
$284$	2.07124e10	0.188929
$285$	−1.61190e11	−1.44723
$286$	−1.28826e11	−1.13856
$287$	1.36812e11	1.19030
$288$	1.42319e11	1.21898
$289$	0	0
$290$	−5.60027e10	−0.464963
$291$	−2.52765e11	−2.06632
$292$	5.50949e10	0.443495
$293$	2.09036e11	1.65698	0.828488	−	0.560006i	$-0.189201\pi$
$293$	2.09036e11	1.65698	0.828488	+	0.560006i	$0.189201\pi$
$294$	−1.19092e11	−0.929649
$295$	3.30672e10	0.254213
$296$	2.70364e10	0.204709
$297$	1.11235e10	0.0829537
$298$	3.99199e10	0.293235
$299$	−1.60096e11	−1.15841
$300$	8.79799e10	0.627101
$301$	1.87754e11	1.31838
$302$	1.89322e11	1.30969
$303$	−1.05331e11	−0.717902
$304$	−2.63458e11	−1.76922
$305$	−1.77550e11	−1.17482
$306$	0	0
$307$	1.44198e11	0.926484	0.463242	−	0.886232i	$-0.346686\pi$
$307$	1.44198e11	0.926484	0.463242	+	0.886232i	$0.346686\pi$
$308$	−7.93912e10	−0.502683
$309$	4.16019e11	2.59597
$310$	1.27996e11	0.787169
$311$	−3.05482e11	−1.85167	−0.925836	−	0.377925i	$-0.876638\pi$
$311$	−3.05482e11	−1.85167	−0.925836	+	0.377925i	$0.876638\pi$
$312$	−5.38077e10	−0.321476
$313$	−1.97546e11	−1.16337	−0.581685	−	0.813414i	$-0.697606\pi$
$313$	−1.97546e11	−1.16337	−0.581685	+	0.813414i	$0.697606\pi$
$314$	−3.91904e11	−2.27508
$315$	−7.77811e10	−0.445120
$316$	1.09879e11	0.619903
$317$	−2.53026e11	−1.40734	−0.703670	−	0.710527i	$-0.748457\pi$
$317$	−2.53026e11	−1.40734	−0.703670	+	0.710527i	$0.748457\pi$
$318$	−1.10308e11	−0.604899
$319$	8.09554e10	0.437711
$320$	−7.91737e10	−0.422091
$321$	9.99708e8	0.00525534
$322$	−2.18122e11	−1.13070
$323$	0	0
$324$	−1.74449e11	−0.879462
$325$	−1.08115e11	−0.537542
$326$	2.82227e11	1.38395
$327$	−8.28432e10	−0.400675
$328$	−8.26109e10	−0.394099
$329$	−1.33913e11	−0.630144
$330$	2.33318e11	1.08302
$331$	4.14467e11	1.89786	0.948930	−	0.315486i	$-0.102167\pi$
$331$	4.14467e11	1.89786	0.948930	+	0.315486i	$0.102167\pi$
$332$	1.74523e11	0.788371
$333$	1.81653e11	0.809548
$334$	−6.91343e10	−0.303973
$335$	1.96279e11	0.851475
$336$	−2.63785e11	−1.12907
$337$	1.55413e11	0.656375	0.328187	−	0.944613i	$-0.393562\pi$
$337$	1.55413e11	0.656375	0.328187	+	0.944613i	$0.393562\pi$
$338$	1.05463e10	0.0439517
$339$	−1.42026e11	−0.584077
$340$	0	0
$341$	−1.85026e11	−0.741033
$342$	−4.91946e11	−1.94447
$343$	2.72323e11	1.06233
$344$	−1.13371e11	−0.436506
$345$	2.89953e11	1.10190
$346$	2.06474e10	0.0774501
$347$	1.69024e11	0.625844	0.312922	−	0.949779i	$-0.398692\pi$
$347$	1.69024e11	0.625844	0.312922	+	0.949779i	$0.398692\pi$
$348$	−1.60414e11	−0.586322
$349$	−2.15573e11	−0.777823	−0.388911	−	0.921275i	$-0.627149\pi$
$349$	−2.15573e11	−0.777823	−0.388911	+	0.921275i	$0.627149\pi$
$350$	−1.47301e11	−0.524686
$351$	2.70858e10	0.0952488
$352$	3.23304e11	1.12246
$353$	3.02994e11	1.03860	0.519299	−	0.854593i	$-0.326193\pi$
$353$	3.02994e11	1.03860	0.519299	+	0.854593i	$0.326193\pi$
$354$	2.09401e11	0.708701
$355$	4.60978e10	0.154047
$356$	4.44937e11	1.46816
$357$	0	0
$358$	−5.20364e11	−1.67430
$359$	−2.90075e11	−0.921692	−0.460846	−	0.887480i	$-0.652454\pi$
$359$	−2.90075e11	−0.921692	−0.460846	+	0.887480i	$0.652454\pi$
$360$	4.69665e10	0.147376
$361$	4.49383e11	1.39262
$362$	−2.89682e11	−0.886611
$363$	1.22338e11	0.369813
$364$	−1.93319e11	−0.577189
$365$	1.22620e11	0.361612
$366$	−1.12435e12	−3.27520
$367$	1.41373e11	0.406789	0.203394	−	0.979097i	$-0.434803\pi$
$367$	1.41373e11	0.406789	0.203394	+	0.979097i	$0.434803\pi$
$368$	4.73915e11	1.34706
$369$	−5.55048e11	−1.55852
$370$	−2.85465e11	−0.791855
$371$	8.35372e10	0.228927
$372$	3.66631e11	0.992627
$373$	1.79070e11	0.478998	0.239499	−	0.970897i	$-0.423017\pi$
$373$	1.79070e11	0.478998	0.239499	+	0.970897i	$0.423017\pi$
$374$	0	0
$375$	5.54104e11	1.44694
$376$	8.08603e10	0.208636
$377$	1.97128e11	0.502587
$378$	3.69028e10	0.0929707
$379$	−2.66182e11	−0.662677	−0.331338	−	0.943512i	$-0.607500\pi$
$379$	−2.66182e11	−0.662677	−0.331338	+	0.943512i	$0.607500\pi$
$380$	3.49689e11	0.860312
$381$	4.91456e11	1.19487
$382$	1.60126e10	0.0384749
$383$	6.18970e11	1.46986	0.734928	−	0.678145i	$-0.237216\pi$
$383$	6.18970e11	1.46986	0.734928	+	0.678145i	$0.237216\pi$
$384$	2.74295e11	0.643765
$385$	−1.76694e11	−0.409873
$386$	4.14531e11	0.950417
$387$	−7.61722e11	−1.72622
$388$	5.48353e11	1.22834
$389$	−1.72722e11	−0.382450	−0.191225	−	0.981546i	$-0.561246\pi$
$389$	−1.72722e11	−0.382450	−0.191225	+	0.981546i	$0.561246\pi$
$390$	5.68132e11	1.24354
$391$	0	0
$392$	−5.44592e10	−0.116489
$393$	1.07572e12	2.27473
$394$	−6.79288e11	−1.42011
$395$	2.44549e11	0.505451
$396$	3.22092e11	0.658190
$397$	5.98018e9	0.0120825	0.00604125	−	0.999982i	$-0.498077\pi$
$397$	5.98018e9	0.0120825	0.00604125	+	0.999982i	$0.498077\pi$
$398$	4.83406e11	0.965691
$399$	7.73026e11	1.52692
$400$	3.20042e11	0.625082
$401$	−2.91381e9	−0.00562745	−0.00281372	−	0.999996i	$-0.500896\pi$
$401$	−2.91381e9	−0.00562745	−0.00281372	+	0.999996i	$0.500896\pi$
$402$	1.24295e12	2.37376
$403$	−4.50541e11	−0.850866
$404$	2.28508e11	0.426761
$405$	−3.88257e11	−0.717087
$406$	2.68575e11	0.490566
$407$	4.12658e11	0.745444
$408$	0	0
$409$	4.39771e11	0.777091	0.388546	−	0.921430i	$-0.372978\pi$
$409$	4.39771e11	0.777091	0.388546	+	0.921430i	$0.372978\pi$
$410$	8.72252e11	1.52446
$411$	−1.83399e11	−0.317037
$412$	−9.02521e11	−1.54319
$413$	−1.58582e11	−0.268212
$414$	8.84925e11	1.48049
$415$	3.88420e11	0.642814
$416$	7.87251e11	1.28882
$417$	−1.74905e11	−0.283263
$418$	−1.11755e12	−1.79049
$419$	−8.88321e11	−1.40801	−0.704006	−	0.710194i	$-0.748607\pi$
$419$	−8.88321e11	−1.40801	−0.704006	+	0.710194i	$0.748607\pi$
$420$	3.50122e11	0.549032
$421$	3.91195e11	0.606910	0.303455	−	0.952846i	$-0.401860\pi$
$421$	3.91195e11	0.606910	0.303455	+	0.952846i	$0.401860\pi$
$422$	1.45840e12	2.23858
$423$	5.43286e11	0.825081
$424$	−5.04422e10	−0.0757963
$425$	0	0
$426$	2.91918e11	0.429455
$427$	8.51485e11	1.23951
$428$	−2.16879e9	−0.00312406
$429$	−8.21269e11	−1.17065
$430$	1.19704e12	1.68850
$431$	−7.81278e11	−1.09058	−0.545291	−	0.838247i	$-0.683581\pi$
$431$	−7.81278e11	−1.09058	−0.545291	+	0.838247i	$0.683581\pi$
$432$	−8.01790e10	−0.110760
$433$	9.03790e11	1.23558	0.617791	−	0.786342i	$-0.288028\pi$
$433$	9.03790e11	1.23558	0.617791	+	0.786342i	$0.288028\pi$
$434$	−6.13835e11	−0.830515
$435$	−3.57020e11	−0.478070
$436$	1.79722e11	0.238183
$437$	−1.38882e12	−1.82171
$438$	7.76501e11	1.00811
$439$	5.14908e11	0.661667	0.330834	−	0.943689i	$-0.392670\pi$
$439$	5.14908e11	0.661667	0.330834	+	0.943689i	$0.392670\pi$
$440$	1.06693e11	0.135706
$441$	−3.65901e11	−0.460670
$442$	0	0
$443$	−1.59851e12	−1.97196	−0.985981	−	0.166856i	$-0.946638\pi$
$443$	−1.59851e12	−1.97196	−0.985981	+	0.166856i	$0.946638\pi$
$444$	−8.17687e11	−0.998536
$445$	9.90257e11	1.19709
$446$	−1.36331e12	−1.63150
$447$	2.54491e11	0.301501
$448$	3.79697e11	0.445334
$449$	−8.81603e11	−1.02368	−0.511840	−	0.859081i	$-0.671036\pi$
$449$	−8.81603e11	−1.02368	−0.511840	+	0.859081i	$0.671036\pi$
$450$	5.97603e11	0.686999
$451$	−1.26089e12	−1.43511
$452$	3.08115e11	0.347208
$453$	1.20694e12	1.34661
$454$	2.03493e12	2.24801
$455$	−4.30253e11	−0.470623
$456$	−4.66776e11	−0.505553
$457$	−4.45550e11	−0.477830	−0.238915	−	0.971041i	$-0.576792\pi$
$457$	−4.45550e11	−0.477830	−0.238915	+	0.971041i	$0.576792\pi$
$458$	−1.08634e12	−1.15364
$459$	0	0
$460$	−6.29029e11	−0.655029
$461$	1.05555e12	1.08849	0.544247	−	0.838925i	$-0.316815\pi$
$461$	1.05555e12	1.08849	0.544247	+	0.838925i	$0.316815\pi$
$462$	−1.11893e12	−1.14265
$463$	−6.82069e11	−0.689785	−0.344892	−	0.938642i	$-0.612085\pi$
$463$	−6.82069e11	−0.689785	−0.344892	+	0.938642i	$0.612085\pi$
$464$	−5.83534e11	−0.584434
$465$	8.15980e11	0.809359
$466$	−1.23113e12	−1.20939
$467$	−1.14817e12	−1.11707	−0.558533	−	0.829482i	$-0.688636\pi$
$467$	−1.14817e12	−1.11707	−0.558533	+	0.829482i	$0.688636\pi$
$468$	7.84298e11	0.755745
$469$	−9.41303e11	−0.898363
$470$	−8.53768e11	−0.807049
$471$	−2.49841e12	−2.33921
$472$	9.57562e10	0.0888031
$473$	−1.73039e12	−1.58953
$474$	1.54863e12	1.40911
$475$	−9.37889e11	−0.845338
$476$	0	0
$477$	−3.38912e11	−0.299747
$478$	−4.00228e11	−0.350657
$479$	1.39726e11	0.121274	0.0606369	−	0.998160i	$-0.480687\pi$
$479$	1.39726e11	0.121274	0.0606369	+	0.998160i	$0.480687\pi$
$480$	−1.42580e12	−1.22595
$481$	1.00483e12	0.855931
$482$	1.00851e12	0.851074
$483$	−1.39054e12	−1.16257
$484$	−2.65403e11	−0.219837
$485$	1.22042e12	1.00155
$486$	−2.29774e12	−1.86826
$487$	6.54778e11	0.527489	0.263745	−	0.964593i	$-0.415042\pi$
$487$	6.54778e11	0.527489	0.263745	+	0.964593i	$0.415042\pi$
$488$	−5.14152e11	−0.410395
$489$	1.79921e12	1.42296
$490$	5.75010e11	0.450602
$491$	−1.33697e11	−0.103814	−0.0519069	−	0.998652i	$-0.516530\pi$
$491$	−1.33697e11	−0.103814	−0.0519069	+	0.998652i	$0.516530\pi$
$492$	2.49848e12	1.92235
$493$	0	0
$494$	−2.72124e12	−2.05587
$495$	7.16852e11	0.536668
$496$	1.33368e12	0.989431
$497$	−2.21073e11	−0.162529
$498$	2.45970e12	1.79205
$499$	7.51123e11	0.542323	0.271162	−	0.962534i	$-0.412592\pi$
$499$	7.51123e11	0.542323	0.271162	+	0.962534i	$0.412592\pi$
$500$	−1.20208e12	−0.860141
$501$	−4.40735e11	−0.312541
$502$	1.62906e12	1.14490
$503$	−3.90993e10	−0.0272341	−0.0136170	−	0.999907i	$-0.504335\pi$
$503$	−3.90993e10	−0.0272341	−0.0136170	+	0.999907i	$0.504335\pi$
$504$	−2.25239e11	−0.155491
$505$	5.08570e11	0.347968
$506$	2.01027e12	1.36326
$507$	6.72332e10	0.0451906
$508$	−1.06617e12	−0.710300
$509$	−1.04082e12	−0.687296	−0.343648	−	0.939098i	$-0.611663\pi$
$509$	−1.04082e12	−0.687296	−0.343648	+	0.939098i	$0.611663\pi$
$510$	0	0
$511$	−5.88054e11	−0.381525
$512$	−1.91202e12	−1.22964
$513$	2.34966e11	0.149788
$514$	−1.02130e12	−0.645383
$515$	−2.00866e12	−1.25827
$516$	3.42880e12	2.12921
$517$	1.23417e12	0.759747
$518$	1.36902e12	0.835459
$519$	1.31628e11	0.0796334
$520$	2.59799e11	0.155820
$521$	2.49791e12	1.48528	0.742638	−	0.669693i	$-0.233574\pi$
$521$	2.49791e12	1.48528	0.742638	+	0.669693i	$0.233574\pi$
$522$	−1.08961e12	−0.642325
$523$	2.04811e11	0.119700	0.0598501	−	0.998207i	$-0.480938\pi$
$523$	2.04811e11	0.119700	0.0598501	+	0.998207i	$0.480938\pi$
$524$	−2.33368e12	−1.35223
$525$	−9.39050e11	−0.539476
$526$	−7.89162e11	−0.449501
$527$	0	0
$528$	2.43111e12	1.36129
$529$	6.97088e11	0.387023
$530$	5.32597e11	0.293196
$531$	6.43369e11	0.351184
$532$	−1.67702e12	−0.907686
$533$	−3.07030e12	−1.64781
$534$	6.27088e12	3.33728
$535$	−4.82688e9	−0.00254727
$536$	5.68386e11	0.297442
$537$	−3.31735e12	−1.72150
$538$	−9.23489e11	−0.475238
$539$	−8.31213e11	−0.424192
$540$	1.06422e11	0.0538591
$541$	−2.24094e12	−1.12471	−0.562357	−	0.826894i	$-0.690105\pi$
$541$	−2.24094e12	−1.12471	−0.562357	+	0.826894i	$0.690105\pi$
$542$	2.21948e12	1.10472
$543$	−1.84674e12	−0.911604
$544$	0	0
$545$	3.99991e11	0.194208
$546$	−2.72461e12	−1.31201
$547$	−1.94999e12	−0.931300	−0.465650	−	0.884969i	$-0.654179\pi$
$547$	−1.94999e12	−0.931300	−0.465650	+	0.884969i	$0.654179\pi$
$548$	3.97870e11	0.188464
$549$	−3.45449e12	−1.62296
$550$	1.35756e12	0.632599
$551$	1.71006e12	0.790367
$552$	8.39647e11	0.384921
$553$	−1.17279e12	−0.533284
$554$	2.65788e11	0.119879
$555$	−1.81986e12	−0.814177
$556$	3.79443e11	0.168387
$557$	−3.69055e12	−1.62459	−0.812293	−	0.583250i	$-0.801781\pi$
$557$	−3.69055e12	−1.62459	−0.812293	+	0.583250i	$0.801781\pi$
$558$	2.49034e12	1.08744
$559$	−4.21353e12	−1.82513
$560$	1.27363e12	0.547264
$561$	0	0
$562$	−3.98876e11	−0.168665
$563$	−7.69327e11	−0.322718	−0.161359	−	0.986896i	$-0.551588\pi$
$563$	−7.69327e11	−0.322718	−0.161359	+	0.986896i	$0.551588\pi$
$564$	−2.44553e12	−1.01770
$565$	6.85744e11	0.283103
$566$	3.83945e12	1.57252
$567$	1.86198e12	0.756574
$568$	1.33490e11	0.0538124
$569$	4.75620e11	0.190219	0.0951097	−	0.995467i	$-0.469680\pi$
$569$	4.75620e11	0.190219	0.0951097	+	0.995467i	$0.469680\pi$
$570$	4.92848e12	1.95558
$571$	3.53469e12	1.39152	0.695759	−	0.718276i	$-0.255068\pi$
$571$	3.53469e12	1.39152	0.695759	+	0.718276i	$0.255068\pi$
$572$	1.78168e12	0.695901
$573$	1.02081e11	0.0395595
$574$	−4.18310e12	−1.60840
$575$	1.68710e12	0.643628
$576$	−1.54044e12	−0.583099
$577$	−6.21322e11	−0.233360	−0.116680	−	0.993170i	$-0.537225\pi$
$577$	−6.21322e11	−0.233360	−0.116680	+	0.993170i	$0.537225\pi$
$578$	0	0
$579$	2.64266e12	0.977209
$580$	7.74527e11	0.284191
$581$	−1.86276e12	−0.678211
$582$	7.72842e12	2.79214
$583$	−7.69902e11	−0.276011
$584$	3.55084e11	0.126320
$585$	1.74555e12	0.616212
$586$	−6.39139e12	−2.23901
$587$	−5.46826e12	−1.90098	−0.950490	−	0.310756i	$-0.899418\pi$
$587$	−5.46826e12	−1.90098	−0.950490	+	0.310756i	$0.899418\pi$
$588$	1.64706e12	0.568213
$589$	−3.90839e12	−1.33807
$590$	−1.01105e12	−0.343509
$591$	−4.33049e12	−1.46014
$592$	−2.97448e12	−0.995321
$593$	1.92966e12	0.640819	0.320410	−	0.947279i	$-0.396179\pi$
$593$	1.92966e12	0.640819	0.320410	+	0.947279i	$0.396179\pi$
$594$	−3.40106e11	−0.112092
$595$	0	0
$596$	−5.52099e11	−0.179229
$597$	3.08174e12	0.992913
$598$	4.89504e12	1.56531
$599$	−4.29083e12	−1.36182	−0.680911	−	0.732366i	$-0.738416\pi$
$599$	−4.29083e12	−1.36182	−0.680911	+	0.732366i	$0.738416\pi$
$600$	5.67026e11	0.178617
$601$	1.72436e12	0.539128	0.269564	−	0.962982i	$-0.413120\pi$
$601$	1.72436e12	0.539128	0.269564	+	0.962982i	$0.413120\pi$
$602$	−5.74069e12	−1.78147
$603$	3.81888e12	1.17627
$604$	−2.61835e12	−0.800500
$605$	−5.90685e11	−0.179249
$606$	3.22056e12	0.970073
$607$	3.54265e12	1.05920	0.529602	−	0.848246i	$-0.322341\pi$
$607$	3.54265e12	1.05920	0.529602	+	0.848246i	$0.322341\pi$
$608$	6.82931e12	2.02680
$609$	1.71218e12	0.504395
$610$	5.42870e12	1.58749
$611$	3.00523e12	0.872354
$612$	0	0
$613$	−2.75371e12	−0.787674	−0.393837	−	0.919180i	$-0.628853\pi$
$613$	−2.75371e12	−0.787674	−0.393837	+	0.919180i	$0.628853\pi$
$614$	−4.40895e12	−1.25192
$615$	5.56065e12	1.56743
$616$	−5.11673e11	−0.143179
$617$	−6.84976e12	−1.90280	−0.951398	−	0.307963i	$-0.900353\pi$
$617$	−6.84976e12	−1.90280	−0.951398	+	0.307963i	$0.900353\pi$
$618$	−1.27200e13	−3.50784
$619$	6.91984e11	0.189447	0.0947235	−	0.995504i	$-0.469803\pi$
$619$	6.91984e11	0.189447	0.0947235	+	0.995504i	$0.469803\pi$
$620$	−1.77020e12	−0.481128
$621$	−4.22663e11	−0.114046
$622$	9.34029e12	2.50209
$623$	−4.74902e12	−1.26301
$624$	5.91979e12	1.56306
$625$	−5.90629e11	−0.154830
$626$	6.04007e12	1.57202
$627$	−7.12442e12	−1.84097
$628$	5.42010e12	1.39056
$629$	0	0
$630$	2.37820e12	0.601473
$631$	2.99016e12	0.750866	0.375433	−	0.926850i	$-0.377494\pi$
$631$	2.99016e12	0.750866	0.375433	+	0.926850i	$0.377494\pi$
$632$	7.08167e11	0.176567
$633$	9.29740e12	2.30168
$634$	7.73643e12	1.90169
$635$	−2.37289e12	−0.579157
$636$	1.52557e12	0.369722
$637$	−2.02402e12	−0.487065
$638$	−2.47526e12	−0.591462
$639$	8.96897e11	0.212808
$640$	−1.32438e12	−0.312034
$641$	3.46519e12	0.810711	0.405356	−	0.914159i	$-0.367148\pi$
$641$	3.46519e12	0.810711	0.405356	+	0.914159i	$0.367148\pi$
$642$	−3.05666e10	−0.00710133
$643$	−3.07922e10	−0.00710381	−0.00355190	−	0.999994i	$-0.501131\pi$
$643$	−3.07922e10	−0.00710381	−0.00355190	+	0.999994i	$0.501131\pi$
$644$	3.01666e12	0.691099
$645$	7.63118e12	1.73609
$646$	0	0
$647$	−8.58031e11	−0.192501	−0.0962506	−	0.995357i	$-0.530685\pi$
$647$	−8.58031e11	−0.192501	−0.0962506	+	0.995357i	$0.530685\pi$
$648$	−1.12432e12	−0.250496
$649$	1.46153e12	0.323375
$650$	3.30569e12	0.726361
$651$	−3.91323e12	−0.853927
$652$	−3.90325e12	−0.845887
$653$	−7.56711e12	−1.62862	−0.814312	−	0.580428i	$-0.802885\pi$
$653$	−7.56711e12	−1.62862	−0.814312	+	0.580428i	$0.802885\pi$
$654$	2.53298e12	0.541416
$655$	−5.19387e12	−1.10257
$656$	9.08865e12	1.91616
$657$	2.38575e12	0.499551
$658$	4.09445e12	0.851489
$659$	1.21600e12	0.251159	0.125580	−	0.992084i	$-0.459921\pi$
$659$	1.21600e12	0.251159	0.125580	+	0.992084i	$0.459921\pi$
$660$	−3.22682e12	−0.661953
$661$	−6.17442e11	−0.125803	−0.0629013	−	0.998020i	$-0.520035\pi$
$661$	−6.17442e11	−0.125803	−0.0629013	+	0.998020i	$0.520035\pi$
$662$	−1.26726e13	−2.56451
$663$	0	0
$664$	1.12479e12	0.224551
$665$	−3.73240e12	−0.740100
$666$	−5.55413e12	−1.09391
$667$	−3.07610e12	−0.601774
$668$	9.56139e11	0.185792
$669$	−8.69117e12	−1.67749
$670$	−6.00134e12	−1.15057
$671$	−7.84752e12	−1.49445
$672$	6.83776e12	1.29346
$673$	4.43202e12	0.832786	0.416393	−	0.909185i	$-0.363294\pi$
$673$	4.43202e12	0.832786	0.416393	+	0.909185i	$0.363294\pi$
$674$	−4.75183e12	−0.886934
$675$	−2.85430e11	−0.0529216
$676$	−1.45857e11	−0.0268638
$677$	7.03236e12	1.28663	0.643313	−	0.765603i	$-0.277559\pi$
$677$	7.03236e12	1.28663	0.643313	+	0.765603i	$0.277559\pi$
$678$	4.34253e12	0.789241
$679$	−5.85283e12	−1.05670
$680$	0	0
$681$	1.29728e13	2.31138
$682$	5.65727e12	1.00133
$683$	−3.12019e12	−0.548640	−0.274320	−	0.961638i	$-0.588453\pi$
$683$	−3.12019e12	−0.548640	−0.274320	+	0.961638i	$0.588453\pi$
$684$	6.80370e12	1.18848
$685$	8.85505e11	0.153668
$686$	−8.32644e12	−1.43549
$687$	−6.92545e12	−1.18616
$688$	1.24728e13	2.12235
$689$	−1.87472e12	−0.316921
$690$	−8.86547e12	−1.48895
$691$	7.61866e10	0.0127124	0.00635620	−	0.999980i	$-0.497977\pi$
$691$	7.61866e10	0.0127124	0.00635620	+	0.999980i	$0.497977\pi$
$692$	−2.85557e11	−0.0473385
$693$	−3.43784e12	−0.566221
$694$	−5.16801e12	−0.845679
$695$	8.44493e11	0.137298
$696$	−1.03386e12	−0.167002
$697$	0	0
$698$	6.59128e12	1.05104
$699$	−7.84852e12	−1.24348
$700$	2.03720e12	0.320695
$701$	−4.55938e12	−0.713139	−0.356570	−	0.934269i	$-0.616054\pi$
$701$	−4.55938e12	−0.713139	−0.356570	+	0.934269i	$0.616054\pi$
$702$	−8.28163e11	−0.128706
$703$	8.71677e12	1.34604
$704$	−3.49939e12	−0.536927
$705$	−5.44282e12	−0.829799
$706$	−9.26420e12	−1.40342
$707$	−2.43897e12	−0.367129
$708$	−2.89605e12	−0.433167
$709$	−9.54492e12	−1.41861	−0.709307	−	0.704899i	$-0.750992\pi$
$709$	−9.54492e12	−1.41861	−0.709307	+	0.704899i	$0.750992\pi$
$710$	−1.40947e12	−0.208157
$711$	4.75804e12	0.698257
$712$	2.86760e12	0.418175
$713$	7.03050e12	1.01879
$714$	0	0
$715$	3.96533e12	0.567417
$716$	7.19673e12	1.02336
$717$	−2.55148e12	−0.360541
$718$	8.86922e12	1.24545
$719$	−1.65457e12	−0.230890	−0.115445	−	0.993314i	$-0.536829\pi$
$719$	−1.65457e12	−0.230890	−0.115445	+	0.993314i	$0.536829\pi$
$720$	−5.16714e12	−0.716563
$721$	9.63303e12	1.32756
$722$	−1.37401e13	−1.88180
$723$	6.42928e12	0.875065
$724$	4.00635e12	0.541908
$725$	−2.07733e12	−0.279245
$726$	−3.74056e12	−0.499714
$727$	−2.21622e12	−0.294244	−0.147122	−	0.989118i	$-0.547001\pi$
$727$	−2.21622e12	−0.294244	−0.147122	+	0.989118i	$0.547001\pi$
$728$	−1.24593e12	−0.164400
$729$	−6.52814e12	−0.856082
$730$	−3.74918e12	−0.488633
$731$	0	0
$732$	1.55500e13	2.00184
$733$	2.96185e11	0.0378961	0.0189481	−	0.999820i	$-0.493968\pi$
$733$	2.96185e11	0.0378961	0.0189481	+	0.999820i	$0.493968\pi$
$734$	−4.32255e12	−0.549678
$735$	3.66572e12	0.463304
$736$	−1.22847e13	−1.54318
$737$	8.67530e12	1.08313
$738$	1.69709e13	2.10597
$739$	−4.82363e12	−0.594941	−0.297470	−	0.954731i	$-0.596143\pi$
$739$	−4.82363e12	−0.594941	−0.297470	+	0.954731i	$0.596143\pi$
$740$	3.94803e12	0.483992
$741$	−1.73481e13	−2.11383
$742$	−2.55420e12	−0.309341
$743$	−4.52977e12	−0.545288	−0.272644	−	0.962115i	$-0.587898\pi$
$743$	−4.52977e12	−0.545288	−0.272644	+	0.962115i	$0.587898\pi$
$744$	2.36292e12	0.282729
$745$	−1.22876e12	−0.146138
$746$	−5.47518e12	−0.647252
$747$	7.55726e12	0.888018
$748$	0	0
$749$	2.31485e10	0.00268754
$750$	−1.69420e13	−1.95519
$751$	−1.65211e13	−1.89522	−0.947610	−	0.319430i	$-0.896509\pi$
$751$	−1.65211e13	−1.89522	−0.947610	+	0.319430i	$0.896509\pi$
$752$	−8.89606e12	−1.01442
$753$	1.03853e13	1.17718
$754$	−6.02729e12	−0.679127
$755$	−5.82744e12	−0.652704
$756$	−5.10372e11	−0.0568249
$757$	1.53269e13	1.69638	0.848192	−	0.529690i	$-0.177692\pi$
$757$	1.53269e13	1.69638	0.848192	+	0.529690i	$0.177692\pi$
$758$	8.13865e12	0.895450
$759$	1.28156e13	1.40168
$760$	2.25373e12	0.245042
$761$	2.48205e12	0.268274	0.134137	−	0.990963i	$-0.457174\pi$
$761$	2.48205e12	0.268274	0.134137	+	0.990963i	$0.457174\pi$
$762$	−1.50265e13	−1.61459
$763$	−1.91825e12	−0.204902
$764$	−2.21457e11	−0.0235164
$765$	0	0
$766$	−1.89254e13	−1.98616
$767$	3.55885e12	0.371305
$768$	−1.67824e13	−1.74072
$769$	1.57447e13	1.62356	0.811778	−	0.583967i	$-0.198500\pi$
$769$	1.57447e13	1.62356	0.811778	+	0.583967i	$0.198500\pi$
$770$	5.40253e12	0.553845
$771$	−6.51082e12	−0.663576
$772$	−5.73304e12	−0.580907
$773$	−1.47271e11	−0.0148357	−0.00741786	−	0.999972i	$-0.502361\pi$
$773$	−1.47271e11	−0.0148357	−0.00741786	+	0.999972i	$0.502361\pi$
$774$	2.32901e13	2.33258
$775$	4.74780e12	0.472754
$776$	3.53411e12	0.349866
$777$	8.72756e12	0.859010
$778$	5.28108e12	0.516790
$779$	−2.66345e13	−2.59135
$780$	−7.85736e12	−0.760065
$781$	2.03747e12	0.195957
$782$	0	0
$783$	5.20427e11	0.0494802
$784$	5.99147e12	0.566384
$785$	1.20630e13	1.13382
$786$	−3.28906e13	−3.07376
$787$	1.64023e13	1.52412	0.762059	−	0.647508i	$-0.224189\pi$
$787$	1.64023e13	1.52412	0.762059	+	0.647508i	$0.224189\pi$
$788$	9.39466e12	0.867987
$789$	−5.03095e12	−0.462172
$790$	−7.47722e12	−0.682996
$791$	−3.28865e12	−0.298692
$792$	2.07587e12	0.187472
$793$	−1.91088e13	−1.71595
$794$	−1.82847e11	−0.0163266
$795$	3.39533e12	0.301461
$796$	−6.68559e12	−0.590243
$797$	−3.29266e12	−0.289058	−0.144529	−	0.989501i	$-0.546167\pi$
$797$	−3.29266e12	−0.289058	−0.144529	+	0.989501i	$0.546167\pi$
$798$	−2.36357e13	−2.06327
$799$	0	0
$800$	−8.29605e12	−0.716088
$801$	1.92669e13	1.65373
$802$	8.90914e10	0.00760416
$803$	5.41966e12	0.459994
$804$	−1.71902e13	−1.45087
$805$	6.71393e12	0.563501
$806$	1.37755e13	1.14974
$807$	−5.88729e12	−0.488635
$808$	1.47272e12	0.121554
$809$	−1.55916e13	−1.27974	−0.639870	−	0.768483i	$-0.721012\pi$
$809$	−1.55916e13	−1.27974	−0.639870	+	0.768483i	$0.721012\pi$
$810$	1.18712e13	0.968972
$811$	1.51604e11	0.0123060	0.00615301	−	0.999981i	$-0.498041\pi$
$811$	1.51604e11	0.0123060	0.00615301	+	0.999981i	$0.498041\pi$
$812$	−3.71443e12	−0.299840
$813$	1.41493e13	1.13587
$814$	−1.26172e13	−1.00729
$815$	−8.68713e12	−0.689711
$816$	0	0
$817$	−3.65519e13	−2.87019
$818$	−1.34463e13	−1.05005
$819$	−8.37119e12	−0.650144
$820$	−1.20634e13	−0.931767
$821$	−1.44623e13	−1.11095	−0.555475	−	0.831533i	$-0.687464\pi$
$821$	−1.44623e13	−1.11095	−0.555475	+	0.831533i	$0.687464\pi$
$822$	5.60754e12	0.428399
$823$	−2.42578e13	−1.84311	−0.921557	−	0.388243i	$-0.873082\pi$
$823$	−2.42578e13	−1.84311	−0.921557	+	0.388243i	$0.873082\pi$
$824$	−5.81670e12	−0.439546
$825$	8.65455e12	0.650431
$826$	4.84872e12	0.362424
$827$	6.48867e12	0.482371	0.241185	−	0.970479i	$-0.422464\pi$
$827$	6.48867e12	0.482371	0.241185	+	0.970479i	$0.422464\pi$
$828$	−1.22387e13	−0.904893
$829$	−1.83303e12	−0.134795	−0.0673977	−	0.997726i	$-0.521470\pi$
$829$	−1.83303e12	−0.134795	−0.0673977	+	0.997726i	$0.521470\pi$
$830$	−1.18762e13	−0.868610
$831$	1.69441e12	0.123258
$832$	−8.52106e12	−0.616508
$833$	0	0
$834$	5.34782e12	0.382763
$835$	2.12800e12	0.151489
$836$	1.54559e13	1.09437
$837$	−1.18945e12	−0.0837687
$838$	2.71609e13	1.90259
$839$	2.21690e13	1.54461	0.772303	−	0.635254i	$-0.219105\pi$
$839$	2.21690e13	1.54461	0.772303	+	0.635254i	$0.219105\pi$
$840$	2.25652e12	0.156380
$841$	−1.07195e13	−0.738914
$842$	−1.19610e13	−0.820094
$843$	−2.54285e12	−0.173419
$844$	−2.01700e13	−1.36825
$845$	−3.24622e11	−0.0219040
$846$	−1.66113e13	−1.11490
$847$	2.83277e12	0.189119
$848$	5.54953e12	0.368532
$849$	2.44767e13	1.61684
$850$	0	0
$851$	−1.56799e13	−1.02485
$852$	−4.03727e12	−0.262488
$853$	1.03748e13	0.670979	0.335489	−	0.942044i	$-0.391098\pi$
$853$	1.03748e13	0.670979	0.335489	+	0.942044i	$0.391098\pi$
$854$	−2.60346e13	−1.67491
$855$	1.51424e13	0.969053
$856$	−1.39777e10	−0.000889825 0
$857$	−6.86176e12	−0.434532	−0.217266	−	0.976112i	$-0.569714\pi$
$857$	−6.86176e12	−0.434532	−0.217266	+	0.976112i	$0.569714\pi$
$858$	2.51108e13	1.58186
$859$	−1.74774e13	−1.09524	−0.547619	−	0.836728i	$-0.684466\pi$
$859$	−1.74774e13	−1.09524	−0.547619	+	0.836728i	$0.684466\pi$
$860$	−1.65552e13	−1.03203
$861$	−2.66674e13	−1.65374
$862$	2.38880e13	1.47366
$863$	2.44274e13	1.49910	0.749548	−	0.661950i	$-0.230271\pi$
$863$	2.44274e13	1.49910	0.749548	+	0.661950i	$0.230271\pi$
$864$	2.07838e12	0.126886
$865$	−6.35539e11	−0.0385984
$866$	−2.76339e13	−1.66960
$867$	0	0
$868$	8.48944e12	0.507622
$869$	1.08088e13	0.642965
$870$	1.09161e13	0.645997
$871$	2.11245e13	1.24367
$872$	1.15830e12	0.0678416
$873$	2.37450e13	1.38359
$874$	4.24639e13	2.46161
$875$	1.28304e13	0.739953
$876$	−1.07391e13	−0.616171
$877$	2.67317e13	1.52591	0.762953	−	0.646454i	$-0.223749\pi$
$877$	2.67317e13	1.52591	0.762953	+	0.646454i	$0.223749\pi$
$878$	−1.57436e13	−0.894086
$879$	−4.07454e13	−2.30212
$880$	−1.17381e13	−0.659822
$881$	−1.44360e13	−0.807338	−0.403669	−	0.914905i	$-0.632265\pi$
$881$	−1.44360e13	−0.807338	−0.403669	+	0.914905i	$0.632265\pi$
$882$	1.11876e13	0.622486
$883$	4.32149e12	0.239227	0.119613	−	0.992821i	$-0.461834\pi$
$883$	4.32149e12	0.239227	0.119613	+	0.992821i	$0.461834\pi$
$884$	0	0
$885$	−6.44548e12	−0.353192
$886$	4.88754e13	2.66464
$887$	−1.12787e13	−0.611792	−0.305896	−	0.952065i	$-0.598956\pi$
$887$	−1.12787e13	−0.611792	−0.305896	+	0.952065i	$0.598956\pi$
$888$	−5.26995e12	−0.284412
$889$	1.13798e13	0.611049
$890$	−3.02777e13	−1.61759
$891$	−1.71605e13	−0.912180
$892$	1.88548e13	0.997195
$893$	2.60701e13	1.37186
$894$	−7.78122e12	−0.407407
$895$	1.60171e13	0.834413
$896$	6.35137e12	0.329216
$897$	3.12061e13	1.60944
$898$	2.69555e13	1.38326
$899$	−8.65669e12	−0.442011
$900$	−8.26494e12	−0.419903
$901$	0	0
$902$	3.85526e13	1.93920
$903$	−3.65972e13	−1.83169
$904$	1.98578e12	0.0988950
$905$	8.91659e12	0.441856
$906$	−3.69027e13	−1.81962
$907$	5.70352e12	0.279840	0.139920	−	0.990163i	$-0.455315\pi$
$907$	5.70352e12	0.279840	0.139920	+	0.990163i	$0.455315\pi$
$908$	−2.81434e13	−1.37401
$909$	9.89495e12	0.480702
$910$	1.31552e13	0.635934
$911$	−3.37049e13	−1.62129	−0.810643	−	0.585540i	$-0.800882\pi$
$911$	−3.37049e13	−1.62129	−0.810643	+	0.585540i	$0.800882\pi$
$912$	5.13535e13	2.45807
$913$	1.71677e13	0.817701
$914$	1.36229e13	0.645673
$915$	3.46082e13	1.63224
$916$	1.50242e13	0.705119
$917$	2.49084e13	1.16328
$918$	0	0
$919$	−2.15276e13	−0.995577	−0.497789	−	0.867298i	$-0.665854\pi$
$919$	−2.15276e13	−0.995577	−0.497789	+	0.867298i	$0.665854\pi$
$920$	−4.05406e12	−0.186572
$921$	−2.81073e13	−1.28721
$922$	−3.22742e13	−1.47084
$923$	4.96127e12	0.225001
$924$	1.54750e13	0.698404
$925$	−1.05889e13	−0.475568
$926$	2.08546e13	0.932080
$927$	−3.90814e13	−1.73825
$928$	1.51262e13	0.669522
$929$	3.52619e13	1.55323	0.776613	−	0.629978i	$-0.216936\pi$
$929$	3.52619e13	1.55323	0.776613	+	0.629978i	$0.216936\pi$
$930$	−2.49490e13	−1.09366
$931$	−1.75581e13	−0.765957
$932$	1.70267e13	0.739196
$933$	5.95448e13	2.57263
$934$	3.51059e13	1.50945
$935$	0	0
$936$	5.05477e12	0.215258
$937$	−6.89322e12	−0.292142	−0.146071	−	0.989274i	$-0.546663\pi$
$937$	−6.89322e12	−0.292142	−0.146071	+	0.989274i	$0.546663\pi$
$938$	2.87809e13	1.21392
$939$	3.85058e13	1.61633
$940$	1.18078e13	0.493279
$941$	−5.81040e12	−0.241575	−0.120788	−	0.992678i	$-0.538542\pi$
$941$	−5.81040e12	−0.241575	−0.120788	+	0.992678i	$0.538542\pi$
$942$	7.63902e13	3.16088
$943$	4.79107e13	1.97301
$944$	−1.05349e13	−0.431773
$945$	−1.13589e12	−0.0463333
$946$	5.29077e13	2.14788
$947$	2.09948e13	0.848277	0.424139	−	0.905597i	$-0.360577\pi$
$947$	2.09948e13	0.848277	0.424139	+	0.905597i	$0.360577\pi$
$948$	−2.14178e13	−0.861264
$949$	1.31970e13	0.528173
$950$	2.86765e13	1.14227
$951$	4.93201e13	1.95529
$952$	0	0
$953$	4.60372e13	1.80797	0.903984	−	0.427567i	$-0.140629\pi$
$953$	4.60372e13	1.80797	0.903984	+	0.427567i	$0.140629\pi$
$954$	1.03624e13	0.405036
$955$	−4.92879e11	−0.0191745
$956$	5.53522e12	0.214326
$957$	−1.57799e13	−0.608135
$958$	−4.27220e12	−0.163873
$959$	−4.24666e12	−0.162130
$960$	1.54326e13	0.586433
$961$	−6.65451e12	−0.251687
$962$	−3.07232e13	−1.15659
$963$	−9.39138e10	−0.00351894
$964$	−1.39478e13	−0.520187
$965$	−1.27595e13	−0.473655
$966$	4.25165e13	1.57094
$967$	−3.36646e13	−1.23809	−0.619047	−	0.785354i	$-0.712481\pi$
$967$	−3.36646e13	−1.23809	−0.619047	+	0.785354i	$0.712481\pi$
$968$	−1.71051e12	−0.0626162
$969$	0	0
$970$	−3.73151e13	−1.35336
$971$	−4.32838e13	−1.56257	−0.781284	−	0.624175i	$-0.785435\pi$
$971$	−4.32838e13	−1.56257	−0.781284	+	0.624175i	$0.785435\pi$
$972$	3.17781e13	1.14190
$973$	−4.04997e12	−0.144859
$974$	−2.00202e13	−0.712776
$975$	2.10740e13	0.746836
$976$	5.65657e13	1.99540
$977$	−2.72015e13	−0.955141	−0.477570	−	0.878593i	$-0.658482\pi$
$977$	−2.72015e13	−0.955141	−0.477570	+	0.878593i	$0.658482\pi$
$978$	−5.50120e13	−1.92279
$979$	4.37682e13	1.52278
$980$	−7.95249e12	−0.275414
$981$	7.78240e12	0.268289
$982$	4.08787e12	0.140280
$983$	3.51517e13	1.20076	0.600379	−	0.799716i	$-0.295016\pi$
$983$	3.51517e13	1.20076	0.600379	+	0.799716i	$0.295016\pi$
$984$	1.61026e13	0.547542
$985$	2.09089e13	0.707731
$986$	0	0
$987$	2.61023e13	0.875492
$988$	3.76353e13	1.25658
$989$	6.57505e13	2.18532
$990$	−2.19182e13	−0.725180
$991$	−2.19268e13	−0.722177	−0.361088	−	0.932532i	$-0.617595\pi$
$991$	−2.19268e13	−0.722177	−0.361088	+	0.932532i	$0.617595\pi$
$992$	−3.45715e13	−1.13348
$993$	−8.07883e13	−2.63680
$994$	6.75943e12	0.219620
$995$	−1.48795e13	−0.481266
$996$	−3.40181e13	−1.09532
$997$	−5.52175e13	−1.76990	−0.884949	−	0.465688i	$-0.845807\pi$
$997$	−5.52175e13	−1.76990	−0.884949	+	0.465688i	$0.845807\pi$
$998$	−2.29660e13	−0.732821
$999$	2.65280e12	0.0842673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.d.1.3	✓	12
17.16	even	2		289.10.a.e.1.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.3	✓	12	1.1	even	1	trivial
289.10.a.e.1.3	yes	12	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-30.5756 q^{2} -194.921 q^{3} +422.865 q^{4} +941.135 q^{5} +5959.81 q^{6} -4513.44 q^{7} +2725.35 q^{8} +18311.1 q^{9} +O(q^{10})\)	\(q-30.5756 q^{2} -194.921 q^{3} +422.865 q^{4} +941.135 q^{5} +5959.81 q^{6} -4513.44 q^{7} +2725.35 q^{8} +18311.1 q^{9} -28775.7 q^{10} +41597.1 q^{11} -82425.2 q^{12} +101290. q^{13} +138001. q^{14} -183447. q^{15} -299836. q^{16} -559873. q^{18} +878675. q^{19} +397973. q^{20} +879763. q^{21} -1.27185e6 q^{22} -1.58058e6 q^{23} -531227. q^{24} -1.06739e6 q^{25} -3.09699e6 q^{26} +267410. q^{27} -1.90858e6 q^{28} +1.94618e6 q^{29} +5.60899e6 q^{30} -4.44805e6 q^{31} +7.77228e6 q^{32} -8.10814e6 q^{33} -4.24775e6 q^{35} +7.74313e6 q^{36} +9.92035e6 q^{37} -2.68660e7 q^{38} -1.97434e7 q^{39} +2.56492e6 q^{40} -3.03121e7 q^{41} -2.68993e7 q^{42} -4.15989e7 q^{43} +1.75900e7 q^{44} +1.72332e7 q^{45} +4.83272e7 q^{46} +2.96697e7 q^{47} +5.84443e7 q^{48} -1.99825e7 q^{49} +3.26361e7 q^{50} +4.28318e7 q^{52} -1.85086e7 q^{53} -8.17620e6 q^{54} +3.91485e7 q^{55} -1.23007e7 q^{56} -1.71272e8 q^{57} -5.95055e7 q^{58} +3.51354e7 q^{59} -7.75732e7 q^{60} -1.88656e8 q^{61} +1.36002e8 q^{62} -8.26461e7 q^{63} -8.41258e7 q^{64} +9.53271e7 q^{65} +2.47911e8 q^{66} +2.08556e8 q^{67} +3.08088e8 q^{69} +1.29878e8 q^{70} +4.89810e7 q^{71} +4.99041e7 q^{72} +1.30289e8 q^{73} -3.03320e8 q^{74} +2.08057e8 q^{75} +3.71561e8 q^{76} -1.87746e8 q^{77} +6.03667e8 q^{78} +2.59845e8 q^{79} -2.82186e8 q^{80} -4.12541e8 q^{81} +9.26809e8 q^{82} +4.12715e8 q^{83} +3.72021e8 q^{84} +1.27191e9 q^{86} -3.79351e8 q^{87} +1.13366e8 q^{88} +1.05219e9 q^{89} -5.26916e8 q^{90} -4.57164e8 q^{91} -6.68373e8 q^{92} +8.67017e8 q^{93} -9.07169e8 q^{94} +8.26952e8 q^{95} -1.51498e9 q^{96} +1.29676e9 q^{97} +6.10975e8 q^{98} +7.61689e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9	\( 12 q + 17 q^{2} - 74 q^{3} + 2987 q^{4} - 454 q^{5} - 2674 q^{6} + 5524 q^{7} - 12036 q^{8} + 71898 q^{9} + 2449 q^{10} - 152886 q^{11} - 41717 q^{12} + 23478 q^{13} - 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} + 2477218 q^{20} - 1395256 q^{21} - 2391095 q^{22} - 2012428 q^{23} - 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} - 3231638 q^{27} + 5978216 q^{28} - 12772842 q^{29} + 181633 q^{30} - 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} - 1352872 q^{37} + 3704404 q^{38} + 1380780 q^{39} - 44739331 q^{40} - 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} - 148233417 q^{44} + 79449336 q^{45} - 31855859 q^{46} + 133558002 q^{47} + 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} + 50215469 q^{54} - 91197532 q^{55} - 267350757 q^{56} - 49507694 q^{57} - 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} - 262041240 q^{61} + 314328847 q^{62} - 218532626 q^{63} + 595820098 q^{64} - 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} - 204290852 q^{71} - 208030791 q^{72} - 673538852 q^{73} - 1274510282 q^{74} - 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} - 165043245 q^{78} - 434002980 q^{79} - 599590757 q^{80} - 389011392 q^{81} + 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} + 262108460 q^{88} + 911678128 q^{89} + 2734590475 q^{90} + 560105446 q^{91} + 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} + 1116511966 q^{95} - 2204198979 q^{96} + 3589270998 q^{97} - 2677144485 q^{98} - 2056683494 q^{99}+O(q^{100}) \) 12 * q + 17 * q^2 - 74 * q^3 + 2987 * q^4 - 454 * q^5 - 2674 * q^6 + 5524 * q^7 - 12036 * q^8 + 71898 * q^9 + 2449 * q^10 - 152886 * q^11 - 41717 * q^12 + 23478 * q^13 - 492839 * q^14 - 149346 * q^15 + 272743 * q^16 + 1610378 * q^18 + 1053982 * q^19 + 2477218 * q^20 - 1395256 * q^21 - 2391095 * q^22 - 2012428 * q^23 - 708393 * q^24 + 6123166 * q^25 - 733144 * q^26 - 3231638 * q^27 + 5978216 * q^28 - 12772842 * q^29 + 181633 * q^30 - 5535814 * q^31 - 5277485 * q^32 - 16526054 * q^33 + 23712622 * q^35 - 37692723 * q^36 - 1352872 * q^37 + 3704404 * q^38 + 1380780 * q^39 - 44739331 * q^40 - 40941240 * q^41 - 73649073 * q^42 - 14142490 * q^43 - 148233417 * q^44 + 79449336 * q^45 - 31855859 * q^46 + 133558002 * q^47 + 80444894 * q^48 + 184488050 * q^49 + 103322437 * q^50 + 179597031 * q^52 - 299319258 * q^53 + 50215469 * q^54 - 91197532 * q^55 - 267350757 * q^56 - 49507694 * q^57 - 367048088 * q^58 - 106431852 * q^59 + 103650215 * q^60 - 262041240 * q^61 + 314328847 * q^62 - 218532626 * q^63 + 595820098 * q^64 - 330279796 * q^65 - 117450322 * q^66 - 489635100 * q^67 + 661586712 * q^69 - 226277420 * q^70 - 204290852 * q^71 - 208030791 * q^72 - 673538852 * q^73 - 1274510282 * q^74 - 588895258 * q^75 - 403517977 * q^76 - 705301770 * q^77 - 165043245 * q^78 - 434002980 * q^79 - 599590757 * q^80 - 389011392 * q^81 + 180073450 * q^82 + 411781442 * q^83 - 475971445 * q^84 + 492988379 * q^86 + 1513399800 * q^87 + 262108460 * q^88 + 911678128 * q^89 + 2734590475 * q^90 + 560105446 * q^91 + 847049266 * q^92 - 1228562570 * q^93 + 2009871759 * q^94 + 1116511966 * q^95 - 2204198979 * q^96 + 3589270998 * q^97 - 2677144485 * q^98 - 2056683494 * q^99

Introduction

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