LMFDB - Embedded newform 289.10.a.e.1.6

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:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 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			1.6
Root			$-0.220633$ 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)

$f(q)$	$=$	$q+0.779367 q^{2} +32.1989 q^{3} -511.393 q^{4} -894.723 q^{5} +25.0947 q^{6} +2726.00 q^{7} -797.598 q^{8} -18646.2 q^{9} +O(q^{10})$	\(q+0.779367 q^{2} +32.1989 q^{3} -511.393 q^{4} -894.723 q^{5} +25.0947 q^{6} +2726.00 q^{7} -797.598 q^{8} -18646.2 q^{9} -697.318 q^{10} +18622.9 q^{11} -16466.3 q^{12} +50311.3 q^{13} +2124.55 q^{14} -28809.1 q^{15} +261211. q^{16} -14532.3 q^{18} -106811. q^{19} +457555. q^{20} +87774.1 q^{21} +14514.1 q^{22} -1.33151e6 q^{23} -25681.8 q^{24} -1.15260e6 q^{25} +39211.0 q^{26} -1.23416e6 q^{27} -1.39406e6 q^{28} -3.99697e6 q^{29} -22452.9 q^{30} -1.47297e6 q^{31} +611950. q^{32} +599637. q^{33} -2.43902e6 q^{35} +9.53554e6 q^{36} +7.90858e6 q^{37} -83245.1 q^{38} +1.61997e6 q^{39} +713630. q^{40} -2.29532e7 q^{41} +68408.3 q^{42} -1.21116e7 q^{43} -9.52362e6 q^{44} +1.66832e7 q^{45} -1.03773e6 q^{46} -3.35639e7 q^{47} +8.41072e6 q^{48} -3.29225e7 q^{49} -898295. q^{50} -2.57288e7 q^{52} +9.30903e7 q^{53} -961862. q^{54} -1.66624e7 q^{55} -2.17425e6 q^{56} -3.43920e6 q^{57} -3.11511e6 q^{58} +1.95305e7 q^{59} +1.47328e7 q^{60} -1.21384e8 q^{61} -1.14798e6 q^{62} -5.08296e7 q^{63} -1.33263e8 q^{64} -4.50147e7 q^{65} +467337. q^{66} +1.13597e8 q^{67} -4.28731e7 q^{69} -1.90089e6 q^{70} +1.11076e8 q^{71} +1.48722e7 q^{72} -2.77779e8 q^{73} +6.16369e6 q^{74} -3.71123e7 q^{75} +5.46224e7 q^{76} +5.07661e7 q^{77} +1.26255e6 q^{78} +1.52609e8 q^{79} -2.33712e8 q^{80} +3.27275e8 q^{81} -1.78890e7 q^{82} +4.69638e7 q^{83} -4.48870e7 q^{84} -9.43939e6 q^{86} -1.28698e8 q^{87} -1.48536e7 q^{88} +3.22965e8 q^{89} +1.30023e7 q^{90} +1.37149e8 q^{91} +6.80924e8 q^{92} -4.74280e7 q^{93} -2.61586e7 q^{94} +9.55664e7 q^{95} +1.97041e7 q^{96} +9.17256e8 q^{97} -2.56587e7 q^{98} -3.47247e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.779367	0.0344435	0.0172217	−	0.999852i	$-0.494518\pi$
$2$	0.779367	0.0344435	0.0172217	+	0.999852i	$0.494518\pi$
$3$	32.1989	0.229507	0.114753	−	0.993394i	$-0.463392\pi$
$3$	32.1989	0.229507	0.114753	+	0.993394i	$0.463392\pi$
$4$	−511.393	−0.998814
$5$	−894.723	−0.640212	−0.320106	−	0.947382i	$-0.603719\pi$
$5$	−894.723	−0.640212	−0.320106	+	0.947382i	$0.603719\pi$
$6$	25.0947	0.00790501
$7$	2726.00	0.429126	0.214563	−	0.976710i	$-0.431167\pi$
$7$	2726.00	0.429126	0.214563	+	0.976710i	$0.431167\pi$
$8$	−797.598	−0.0688461
$9$	−18646.2	−0.947327
$10$	−697.318	−0.0220511
$11$	18622.9	0.383513	0.191757	−	0.981442i	$-0.438582\pi$
$11$	18622.9	0.383513	0.191757	+	0.981442i	$0.438582\pi$
$12$	−16466.3	−0.229234
$13$	50311.3	0.488563	0.244281	−	0.969704i	$-0.421448\pi$
$13$	50311.3	0.488563	0.244281	+	0.969704i	$0.421448\pi$
$14$	2124.55	0.0147806
$15$	−28809.1	−0.146933
$16$	261211.	0.996442
$17$	0	0
$17$	0	0
$18$	−14532.3	−0.0326292
$19$	−106811.	−0.188029	−0.0940146	−	0.995571i	$-0.529970\pi$
$19$	−106811.	−0.188029	−0.0940146	+	0.995571i	$0.529970\pi$
$20$	457555.	0.639452
$21$	87774.1	0.0984872
$22$	14514.1	0.0132095
$23$	−1.33151e6	−0.992131	−0.496066	−	0.868285i	$-0.665222\pi$
$23$	−1.33151e6	−0.992131	−0.496066	+	0.868285i	$0.665222\pi$
$24$	−25681.8	−0.0158006
$25$	−1.15260e6	−0.590129
$26$	39211.0	0.0168278
$27$	−1.23416e6	−0.446924
$28$	−1.39406e6	−0.428617
$29$	−3.99697e6	−1.04940	−0.524699	−	0.851288i	$-0.675822\pi$
$29$	−3.99697e6	−1.04940	−0.524699	+	0.851288i	$0.675822\pi$
$30$	−22452.9	−0.00506088
$31$	−1.47297e6	−0.286461	−0.143231	−	0.989689i	$-0.545749\pi$
$31$	−1.47297e6	−0.286461	−0.143231	+	0.989689i	$0.545749\pi$
$32$	611950.	0.103167
$33$	599637.	0.0880189
$34$	0	0
$35$	−2.43902e6	−0.274731
$36$	9.53554e6	0.946203
$37$	7.90858e6	0.693730	0.346865	−	0.937915i	$-0.387246\pi$
$37$	7.90858e6	0.693730	0.346865	+	0.937915i	$0.387246\pi$
$38$	−83245.1	−0.00647638
$39$	1.61997e6	0.112128
$40$	713630.	0.0440761
$41$	−2.29532e7	−1.26857	−0.634287	−	0.773098i	$-0.718706\pi$
$41$	−2.29532e7	−1.26857	−0.634287	+	0.773098i	$0.718706\pi$
$42$	68408.3	0.00339224
$43$	−1.21116e7	−0.540249	−0.270124	−	0.962825i	$-0.587065\pi$
$43$	−1.21116e7	−0.540249	−0.270124	+	0.962825i	$0.587065\pi$
$44$	−9.52362e6	−0.383058
$45$	1.66832e7	0.606490
$46$	−1.03773e6	−0.0341725
$47$	−3.35639e7	−1.00330	−0.501651	−	0.865070i	$-0.667274\pi$
$47$	−3.35639e7	−1.00330	−0.501651	+	0.865070i	$0.667274\pi$
$48$	8.41072e6	0.228690
$49$	−3.29225e7	−0.815851
$50$	−898295.	−0.0203261
$51$	0	0
$52$	−2.57288e7	−0.487983
$53$	9.30903e7	1.62055	0.810276	−	0.586049i	$-0.199317\pi$
$53$	9.30903e7	1.62055	0.810276	+	0.586049i	$0.199317\pi$
$54$	−961862.	−0.0153936
$55$	−1.66624e7	−0.245530
$56$	−2.17425e6	−0.0295436
$57$	−3.43920e6	−0.0431540
$58$	−3.11511e6	−0.0361449
$59$	1.95305e7	0.209835	0.104918	−	0.994481i	$-0.466542\pi$
$59$	1.95305e7	0.209835	0.104918	+	0.994481i	$0.466542\pi$
$60$	1.47328e7	0.146759
$61$	−1.21384e8	−1.12248	−0.561239	−	0.827654i	$-0.689675\pi$
$61$	−1.21384e8	−1.12248	−0.561239	+	0.827654i	$0.689675\pi$
$62$	−1.14798e6	−0.00986673
$63$	−5.08296e7	−0.406522
$64$	−1.33263e8	−0.992889
$65$	−4.50147e7	−0.312784
$66$	467337.	0.00303168
$67$	1.13597e8	0.688700	0.344350	−	0.938841i	$-0.388099\pi$
$67$	1.13597e8	0.688700	0.344350	+	0.938841i	$0.388099\pi$
$68$	0	0
$69$	−4.28731e7	−0.227701
$70$	−1.90089e6	−0.00946270
$71$	1.11076e8	0.518749	0.259375	−	0.965777i	$-0.416484\pi$
$71$	1.11076e8	0.518749	0.259375	+	0.965777i	$0.416484\pi$
$72$	1.48722e7	0.0652197
$73$	−2.77779e8	−1.14485	−0.572423	−	0.819959i	$-0.693996\pi$
$73$	−2.77779e8	−1.14485	−0.572423	+	0.819959i	$0.693996\pi$
$74$	6.16369e6	0.0238945
$75$	−3.71123e7	−0.135438
$76$	5.46224e7	0.187806
$77$	5.07661e7	0.164576
$78$	1.26255e6	0.00386209
$79$	1.52609e8	0.440818	0.220409	−	0.975408i	$-0.429261\pi$
$79$	1.52609e8	0.440818	0.220409	+	0.975408i	$0.429261\pi$
$80$	−2.33712e8	−0.637934
$81$	3.27275e8	0.844755
$82$	−1.78890e7	−0.0436941
$83$	4.69638e7	0.108620	0.0543102	−	0.998524i	$-0.482704\pi$
$83$	4.69638e7	0.108620	0.0543102	+	0.998524i	$0.482704\pi$
$84$	−4.48870e7	−0.0983704
$85$	0	0
$86$	−9.43939e6	−0.0186080
$87$	−1.28698e8	−0.240844
$88$	−1.48536e7	−0.0264034
$89$	3.22965e8	0.545633	0.272816	−	0.962066i	$-0.412045\pi$
$89$	3.22965e8	0.545633	0.272816	+	0.962066i	$0.412045\pi$
$90$	1.30023e7	0.0208896
$91$	1.37149e8	0.209655
$92$	6.80924e8	0.990954
$93$	−4.74280e7	−0.0657448
$94$	−2.61586e7	−0.0345572
$95$	9.55664e7	0.120379
$96$	1.97041e7	0.0236775
$97$	9.17256e8	1.05201	0.526003	−	0.850483i	$-0.323690\pi$
$97$	9.17256e8	1.05201	0.526003	+	0.850483i	$0.323690\pi$
$98$	−2.56587e7	−0.0281007
$99$	−3.47247e8	−0.363313
$100$	5.89429e8	0.589429
$101$	−7.62747e8	−0.729347	−0.364673	−	0.931135i	$-0.618819\pi$
$101$	−7.62747e8	−0.729347	−0.364673	+	0.931135i	$0.618819\pi$
$102$	0	0
$103$	1.64466e9	1.43982	0.719912	−	0.694065i	$-0.244182\pi$
$103$	1.64466e9	1.43982	0.719912	+	0.694065i	$0.244182\pi$
$104$	−4.01282e7	−0.0336356
$105$	−7.85336e7	−0.0630527
$106$	7.25515e7	0.0558174
$107$	1.07132e9	0.790117	0.395059	−	0.918656i	$-0.370724\pi$
$107$	1.07132e9	0.790117	0.395059	+	0.918656i	$0.370724\pi$
$108$	6.31140e8	0.446394
$109$	4.13878e8	0.280836	0.140418	−	0.990092i	$-0.455155\pi$
$109$	4.13878e8	0.280836	0.140418	+	0.990092i	$0.455155\pi$
$110$	−1.29861e7	−0.00845690
$111$	2.54647e8	0.159216
$112$	7.12062e8	0.427599
$113$	−1.98843e8	−0.114725	−0.0573625	−	0.998353i	$-0.518269\pi$
$113$	−1.98843e8	−0.114725	−0.0573625	+	0.998353i	$0.518269\pi$
$114$	−2.68040e6	−0.00148637
$115$	1.19133e9	0.635174
$116$	2.04402e9	1.04815
$117$	−9.38116e8	−0.462829
$118$	1.52214e7	0.00722745
$119$	0	0
$120$	2.29781e7	0.0101158
$121$	−2.01113e9	−0.852917
$122$	−9.46027e7	−0.0386620
$123$	−7.39067e8	−0.291146
$124$	7.53266e8	0.286122
$125$	2.77876e9	1.01802
$126$	−3.96149e7	−0.0140020
$127$	−3.63691e9	−1.24056	−0.620278	−	0.784382i	$-0.712980\pi$
$127$	−3.63691e9	−1.24056	−0.620278	+	0.784382i	$0.712980\pi$
$128$	−4.17179e8	−0.137366
$129$	−3.89980e8	−0.123991
$130$	−3.50830e7	−0.0107734
$131$	−9.54875e8	−0.283287	−0.141643	−	0.989918i	$-0.545239\pi$
$131$	−9.54875e8	−0.283287	−0.141643	+	0.989918i	$0.545239\pi$
$132$	−3.06650e8	−0.0879145
$133$	−2.91167e8	−0.0806882
$134$	8.85337e7	0.0237212
$135$	1.10423e9	0.286126
$136$	0	0
$137$	1.40687e9	0.341203	0.170601	−	0.985340i	$-0.445429\pi$
$137$	1.40687e9	0.341203	0.170601	+	0.985340i	$0.445429\pi$
$138$	−3.34139e7	−0.00784280
$139$	4.50608e9	1.02384	0.511920	−	0.859033i	$-0.328934\pi$
$139$	4.50608e9	1.02384	0.511920	+	0.859033i	$0.328934\pi$
$140$	1.24729e9	0.274405
$141$	−1.08072e9	−0.230265
$142$	8.65690e7	0.0178675
$143$	9.36943e8	0.187370
$144$	−4.87061e9	−0.943956
$145$	3.57618e9	0.671837
$146$	−2.16492e8	−0.0394325
$147$	−1.06007e9	−0.187243
$148$	−4.04439e9	−0.692907
$149$	−6.12301e9	−1.01772	−0.508858	−	0.860851i	$-0.669932\pi$
$149$	−6.12301e9	−1.01772	−0.508858	+	0.860851i	$0.669932\pi$
$150$	−2.89241e7	−0.00466497
$151$	−7.02540e9	−1.09970	−0.549851	−	0.835263i	$-0.685315\pi$
$151$	−7.02540e9	−1.09970	−0.549851	+	0.835263i	$0.685315\pi$
$152$	8.51924e7	0.0129451
$153$	0	0
$154$	3.95654e7	0.00566855
$155$	1.31790e9	0.183396
$156$	−8.28440e8	−0.111995
$157$	8.92243e9	1.17202	0.586010	−	0.810304i	$-0.300698\pi$
$157$	8.92243e9	1.17202	0.586010	+	0.810304i	$0.300698\pi$
$158$	1.18939e8	0.0151833
$159$	2.99740e9	0.371927
$160$	−5.47526e8	−0.0660488
$161$	−3.62970e9	−0.425749
$162$	2.55067e8	0.0290963
$163$	−1.41974e10	−1.57530	−0.787651	−	0.616122i	$-0.788703\pi$
$163$	−1.41974e10	−1.57530	−0.787651	+	0.616122i	$0.788703\pi$
$164$	1.17381e10	1.26707
$165$	−5.36509e8	−0.0563507
$166$	3.66020e7	0.00374127
$167$	1.25753e10	1.25110	0.625552	−	0.780183i	$-0.284874\pi$
$167$	1.25753e10	1.25110	0.625552	+	0.780183i	$0.284874\pi$
$168$	−7.00085e7	−0.00678046
$169$	−8.07327e9	−0.761306
$170$	0	0
$171$	1.99163e9	0.178125
$172$	6.19379e9	0.539608
$173$	1.25403e10	1.06439	0.532194	−	0.846622i	$-0.321368\pi$
$173$	1.25403e10	1.06439	0.532194	+	0.846622i	$0.321368\pi$
$174$	−1.00303e8	−0.00829550
$175$	−3.14197e9	−0.253239
$176$	4.86452e9	0.382149
$177$	6.28859e8	0.0481586
$178$	2.51708e8	0.0187935
$179$	5.72919e9	0.417114	0.208557	−	0.978010i	$-0.433123\pi$
$179$	5.72919e9	0.417114	0.208557	+	0.978010i	$0.433123\pi$
$180$	−8.53167e9	−0.605770
$181$	2.19770e10	1.52200	0.760999	−	0.648753i	$-0.224709\pi$
$181$	2.19770e10	1.52200	0.760999	+	0.648753i	$0.224709\pi$
$182$	1.06889e8	0.00722124
$183$	−3.90843e9	−0.257616
$184$	1.06201e9	0.0683044
$185$	−7.07599e9	−0.444134
$186$	−3.69638e7	−0.00226448
$187$	0	0
$188$	1.71643e10	1.00211
$189$	−3.36432e9	−0.191787
$190$	7.44813e7	0.00414626
$191$	2.60888e10	1.41841	0.709207	−	0.705000i	$-0.249053\pi$
$191$	2.60888e10	1.41841	0.709207	+	0.705000i	$0.249053\pi$
$192$	−4.29093e9	−0.227875
$193$	2.79178e10	1.44835	0.724174	−	0.689617i	$-0.242221\pi$
$193$	2.79178e10	1.44835	0.724174	+	0.689617i	$0.242221\pi$
$194$	7.14879e8	0.0362347
$195$	−1.44942e9	−0.0717859
$196$	1.68363e10	0.814883
$197$	−2.21064e10	−1.04573	−0.522866	−	0.852415i	$-0.675137\pi$
$197$	−2.21064e10	−1.04573	−0.522866	+	0.852415i	$0.675137\pi$
$198$	−2.70633e8	−0.0125137
$199$	−1.50851e10	−0.681884	−0.340942	−	0.940084i	$-0.610746\pi$
$199$	−1.50851e10	−0.681884	−0.340942	+	0.940084i	$0.610746\pi$
$200$	9.19308e8	0.0406281
$201$	3.65769e9	0.158061
$202$	−5.94460e8	−0.0251212
$203$	−1.08957e10	−0.450324
$204$	0	0
$205$	2.05368e10	0.812156
$206$	1.28180e9	0.0495925
$207$	2.48276e10	0.939873
$208$	1.31419e10	0.486825
$209$	−1.98914e9	−0.0721118
$210$	−6.12065e7	−0.00217175
$211$	5.27406e10	1.83178	0.915891	−	0.401428i	$-0.131486\pi$
$211$	5.27406e10	1.83178	0.915891	+	0.401428i	$0.131486\pi$
$212$	−4.76057e10	−1.61863
$213$	3.57652e9	0.119056
$214$	8.34950e8	0.0272144
$215$	1.08365e10	0.345874
$216$	9.84363e8	0.0307690
$217$	−4.01531e9	−0.122928
$218$	3.22563e8	0.00967297
$219$	−8.94418e9	−0.262750
$220$	8.52101e9	0.245239
$221$	0	0
$222$	1.98464e8	0.00548394
$223$	−4.66541e10	−1.26333	−0.631666	−	0.775240i	$-0.717629\pi$
$223$	−4.66541e10	−1.26333	−0.631666	+	0.775240i	$0.717629\pi$
$224$	1.66817e9	0.0442716
$225$	2.14916e10	0.559045
$226$	−1.54972e8	−0.00395153
$227$	7.06458e10	1.76592	0.882958	−	0.469451i	$-0.155548\pi$
$227$	7.06458e10	1.76592	0.882958	+	0.469451i	$0.155548\pi$
$228$	1.75878e9	0.0431028
$229$	−6.05407e10	−1.45475	−0.727374	−	0.686241i	$-0.759259\pi$
$229$	−6.05407e10	−1.45475	−0.727374	+	0.686241i	$0.759259\pi$
$230$	9.28485e8	0.0218776
$231$	1.63461e9	0.0377712
$232$	3.18798e9	0.0722469
$233$	−1.65324e10	−0.367480	−0.183740	−	0.982975i	$-0.558820\pi$
$233$	−1.65324e10	−0.367480	−0.183740	+	0.982975i	$0.558820\pi$
$234$	−7.31137e8	−0.0159414
$235$	3.00304e10	0.642326
$236$	−9.98773e9	−0.209586
$237$	4.91385e9	0.101171
$238$	0	0
$239$	8.94845e10	1.77401	0.887007	−	0.461755i	$-0.152780\pi$
$239$	8.94845e10	1.77401	0.887007	+	0.461755i	$0.152780\pi$
$240$	−7.52526e9	−0.146410
$241$	5.87295e10	1.12145	0.560725	−	0.828002i	$-0.310523\pi$
$241$	5.87295e10	1.12145	0.560725	+	0.828002i	$0.310523\pi$
$242$	−1.56741e9	−0.0293774
$243$	3.48298e10	0.640801
$244$	6.20749e10	1.12115
$245$	2.94566e10	0.522318
$246$	−5.76005e8	−0.0100281
$247$	−5.37381e9	−0.0918641
$248$	1.17484e9	0.0197217
$249$	1.51218e9	0.0249291
$250$	2.16567e9	0.0350641
$251$	2.89840e10	0.460920	0.230460	−	0.973082i	$-0.425977\pi$
$251$	2.89840e10	0.460920	0.230460	+	0.973082i	$0.425977\pi$
$252$	2.59939e10	0.406040
$253$	−2.47966e10	−0.380496
$254$	−2.83449e9	−0.0427290
$255$	0	0
$256$	6.79057e10	0.988158
$257$	2.53245e10	0.362111	0.181055	−	0.983473i	$-0.442049\pi$
$257$	2.53245e10	0.362111	0.181055	+	0.983473i	$0.442049\pi$
$258$	−3.03938e8	−0.00427067
$259$	2.15588e10	0.297698
$260$	2.30202e10	0.312413
$261$	7.45285e10	0.994123
$262$	−7.44198e8	−0.00975737
$263$	−1.12966e11	−1.45596	−0.727978	−	0.685601i	$-0.759540\pi$
$263$	−1.12966e11	−1.45596	−0.727978	+	0.685601i	$0.759540\pi$
$264$	−4.78270e8	−0.00605976
$265$	−8.32900e10	−1.03750
$266$	−2.26926e8	−0.00277918
$267$	1.03991e10	0.125226
$268$	−5.80926e10	−0.687883
$269$	4.60210e10	0.535884	0.267942	−	0.963435i	$-0.413656\pi$
$269$	4.60210e10	0.535884	0.267942	+	0.963435i	$0.413656\pi$
$270$	8.60601e8	0.00985518
$271$	−9.91151e10	−1.11629	−0.558146	−	0.829743i	$-0.688487\pi$
$271$	−9.91151e10	−1.11629	−0.558146	+	0.829743i	$0.688487\pi$
$272$	0	0
$273$	4.41603e9	0.0481172
$274$	1.09647e9	0.0117522
$275$	−2.14647e10	−0.226322
$276$	2.19250e10	0.227431
$277$	5.58341e10	0.569824	0.284912	−	0.958554i	$-0.408036\pi$
$277$	5.58341e10	0.569824	0.284912	+	0.958554i	$0.408036\pi$
$278$	3.51189e9	0.0352646
$279$	2.74653e10	0.271373
$280$	1.94535e9	0.0189142
$281$	8.69561e10	0.831997	0.415998	−	0.909365i	$-0.363432\pi$
$281$	8.69561e10	0.831997	0.415998	+	0.909365i	$0.363432\pi$
$282$	−8.42277e8	−0.00793111
$283$	1.23295e11	1.14263	0.571314	−	0.820732i	$-0.306434\pi$
$283$	1.23295e11	1.14263	0.571314	+	0.820732i	$0.306434\pi$
$284$	−5.68034e10	−0.518134
$285$	3.07713e9	0.0276277
$286$	7.30222e8	0.00645369
$287$	−6.25704e10	−0.544378
$288$	−1.14106e10	−0.0977329
$289$	0	0
$290$	2.78716e9	0.0231404
$291$	2.95346e10	0.241442
$292$	1.42054e11	1.14349
$293$	1.61705e11	1.28179	0.640896	−	0.767627i	$-0.278563\pi$
$293$	1.61705e11	1.28179	0.640896	+	0.767627i	$0.278563\pi$
$294$	−8.26183e8	−0.00644931
$295$	−1.74744e10	−0.134339
$296$	−6.30787e9	−0.0477606
$297$	−2.29836e10	−0.171402
$298$	−4.77207e9	−0.0350537
$299$	−6.69900e10	−0.484718
$300$	1.89789e10	0.135278
$301$	−3.30162e10	−0.231835
$302$	−5.47536e9	−0.0378775
$303$	−2.45596e10	−0.167390
$304$	−2.79003e10	−0.187360
$305$	1.08605e11	0.718623
$306$	0	0
$307$	1.09712e9	0.00704906	0.00352453	−	0.999994i	$-0.498878\pi$
$307$	1.09712e9	0.00704906	0.00352453	+	0.999994i	$0.498878\pi$
$308$	−2.59614e10	−0.164380
$309$	5.29563e10	0.330449
$310$	1.02713e9	0.00631680
$311$	−3.14000e11	−1.90330	−0.951650	−	0.307184i	$-0.900613\pi$
$311$	−3.14000e11	−1.90330	−0.951650	+	0.307184i	$0.900613\pi$
$312$	−1.29208e9	−0.00771960
$313$	−1.94805e10	−0.114723	−0.0573615	−	0.998353i	$-0.518269\pi$
$313$	−1.94805e10	−0.114723	−0.0573615	+	0.998353i	$0.518269\pi$
$314$	6.95385e9	0.0403684
$315$	4.54784e10	0.260260
$316$	−7.80432e10	−0.440295
$317$	1.38120e11	0.768227	0.384113	−	0.923286i	$-0.374507\pi$
$317$	1.38120e11	0.768227	0.384113	+	0.923286i	$0.374507\pi$
$318$	2.33608e9	0.0128105
$319$	−7.44353e10	−0.402458
$320$	1.19234e11	0.635659
$321$	3.44953e10	0.181337
$322$	−2.82886e9	−0.0146643
$323$	0	0
$324$	−1.67366e11	−0.843752
$325$	−5.79886e10	−0.288315
$326$	−1.10650e10	−0.0542589
$327$	1.33264e10	0.0644537
$328$	1.83074e10	0.0873364
$329$	−9.14951e10	−0.430543
$330$	−4.18138e8	−0.00194092
$331$	2.60047e10	0.119076	0.0595382	−	0.998226i	$-0.481037\pi$
$331$	2.60047e10	0.119076	0.0595382	+	0.998226i	$0.481037\pi$
$332$	−2.40169e10	−0.108492
$333$	−1.47465e11	−0.657189
$334$	9.80075e9	0.0430924
$335$	−1.01638e11	−0.440914
$336$	2.29276e10	0.0981368
$337$	−1.17662e11	−0.496939	−0.248470	−	0.968640i	$-0.579928\pi$
$337$	−1.17662e11	−0.496939	−0.248470	+	0.968640i	$0.579928\pi$
$338$	−6.29204e9	−0.0262220
$339$	−6.40254e9	−0.0263302
$340$	0	0
$341$	−2.74310e10	−0.109862
$342$	1.55221e9	0.00613525
$343$	−1.99751e11	−0.779228
$344$	9.66020e9	0.0371940
$345$	3.83596e10	0.145777
$346$	9.77349e9	0.0366612
$347$	4.51270e9	0.0167091	0.00835457	−	0.999965i	$-0.497341\pi$
$347$	4.51270e9	0.0167091	0.00835457	+	0.999965i	$0.497341\pi$
$348$	6.58152e10	0.240558
$349$	2.36847e11	0.854582	0.427291	−	0.904114i	$-0.359468\pi$
$349$	2.36847e11	0.854582	0.427291	+	0.904114i	$0.359468\pi$
$350$	−2.44875e9	−0.00872245
$351$	−6.20921e10	−0.218351
$352$	1.13963e10	0.0395659
$353$	−7.38411e10	−0.253112	−0.126556	−	0.991959i	$-0.540392\pi$
$353$	−7.38411e10	−0.253112	−0.126556	+	0.991959i	$0.540392\pi$
$354$	4.90112e8	0.00165875
$355$	−9.93823e10	−0.332110
$356$	−1.65162e11	−0.544985
$357$	0	0
$358$	4.46514e9	0.0143669
$359$	1.36609e11	0.434064	0.217032	−	0.976165i	$-0.430362\pi$
$359$	1.36609e11	0.434064	0.217032	+	0.976165i	$0.430362\pi$
$360$	−1.33065e10	−0.0417544
$361$	−3.11279e11	−0.964645
$362$	1.71281e10	0.0524229
$363$	−6.47563e10	−0.195750
$364$	−7.01368e10	−0.209406
$365$	2.48536e11	0.732944
$366$	−3.04610e9	−0.00887319
$367$	4.84798e11	1.39497	0.697483	−	0.716601i	$-0.254303\pi$
$367$	4.84798e11	1.39497	0.697483	+	0.716601i	$0.254303\pi$
$368$	−3.47806e11	−0.988602
$369$	4.27991e11	1.20175
$370$	−5.51479e9	−0.0152975
$371$	2.53764e11	0.695421
$372$	2.42543e10	0.0656668
$373$	1.66467e11	0.445285	0.222643	−	0.974900i	$-0.428532\pi$
$373$	1.66467e11	0.445285	0.222643	+	0.974900i	$0.428532\pi$
$374$	0	0
$375$	8.94730e10	0.233642
$376$	2.67705e10	0.0690735
$377$	−2.01093e11	−0.512697
$378$	−2.62204e9	−0.00660580
$379$	3.25337e11	0.809949	0.404974	−	0.914328i	$-0.367280\pi$
$379$	3.25337e11	0.809949	0.404974	+	0.914328i	$0.367280\pi$
$380$	−4.88720e10	−0.120236
$381$	−1.17105e11	−0.284716
$382$	2.03327e10	0.0488551
$383$	−6.99081e11	−1.66009	−0.830047	−	0.557693i	$-0.811687\pi$
$383$	−6.99081e11	−1.66009	−0.830047	+	0.557693i	$0.811687\pi$
$384$	−1.34327e10	−0.0315263
$385$	−4.54216e10	−0.105363
$386$	2.17582e10	0.0498861
$387$	2.25836e11	0.511792
$388$	−4.69078e11	−1.05076
$389$	3.82012e11	0.845871	0.422936	−	0.906160i	$-0.361000\pi$
$389$	3.82012e11	0.845871	0.422936	+	0.906160i	$0.361000\pi$
$390$	−1.12963e9	−0.00247256
$391$	0	0
$392$	2.62590e10	0.0561682
$393$	−3.07459e10	−0.0650161
$394$	−1.72290e10	−0.0360187
$395$	−1.36543e11	−0.282217
$396$	1.77580e11	0.362882
$397$	−1.90754e11	−0.385405	−0.192702	−	0.981257i	$-0.561725\pi$
$397$	−1.90754e11	−0.385405	−0.192702	+	0.981257i	$0.561725\pi$
$398$	−1.17569e10	−0.0234864
$399$	−9.37526e9	−0.0185185
$400$	−3.01071e11	−0.588029
$401$	9.14970e11	1.76708	0.883542	−	0.468352i	$-0.155152\pi$
$401$	9.14970e11	1.76708	0.883542	+	0.468352i	$0.155152\pi$
$402$	2.85069e9	0.00544418
$403$	−7.41070e10	−0.139954
$404$	3.90063e11	0.728482
$405$	−2.92821e11	−0.540822
$406$	−8.49178e9	−0.0155107
$407$	1.47281e11	0.266055
$408$	0	0
$409$	−6.06321e11	−1.07139	−0.535695	−	0.844412i	$-0.679950\pi$
$409$	−6.06321e11	−1.07139	−0.535695	+	0.844412i	$0.679950\pi$
$410$	1.60057e10	0.0279735
$411$	4.52997e10	0.0783083
$412$	−8.41068e11	−1.43812
$413$	5.32400e10	0.0900457
$414$	1.93498e10	0.0323725
$415$	−4.20196e10	−0.0695401
$416$	3.07880e10	0.0504036
$417$	1.45091e11	0.234978
$418$	−1.55027e9	−0.00248378
$419$	−1.12482e12	−1.78287	−0.891436	−	0.453146i	$-0.850302\pi$
$419$	−1.12482e12	−1.78287	−0.891436	+	0.453146i	$0.850302\pi$
$420$	4.01615e10	0.0629779
$421$	1.60780e11	0.249439	0.124719	−	0.992192i	$-0.460197\pi$
$421$	1.60780e11	0.249439	0.124719	+	0.992192i	$0.460197\pi$
$422$	4.11042e10	0.0630929
$423$	6.25840e11	0.950455
$424$	−7.42486e10	−0.111569
$425$	0	0
$426$	2.78742e9	0.00410072
$427$	−3.30893e11	−0.481684
$428$	−5.47864e11	−0.789180
$429$	3.01685e10	0.0430028
$430$	8.44564e9	0.0119131
$431$	−1.32759e12	−1.85317	−0.926584	−	0.376088i	$-0.877269\pi$
$431$	−1.32759e12	−1.85317	−0.926584	+	0.376088i	$0.877269\pi$
$432$	−3.22376e11	−0.445334
$433$	6.87578e11	0.939998	0.469999	−	0.882667i	$-0.344254\pi$
$433$	6.87578e11	0.939998	0.469999	+	0.882667i	$0.344254\pi$
$434$	−3.12940e9	−0.00423407
$435$	1.15149e11	0.154191
$436$	−2.11654e11	−0.280503
$437$	1.42220e11	0.186550
$438$	−6.97080e9	−0.00905001
$439$	−7.48155e11	−0.961394	−0.480697	−	0.876887i	$-0.659616\pi$
$439$	−7.48155e11	−0.961394	−0.480697	+	0.876887i	$0.659616\pi$
$440$	1.32899e10	0.0169038
$441$	6.13881e11	0.772878
$442$	0	0
$443$	9.01469e9	0.0111207	0.00556037	−	0.999985i	$-0.498230\pi$
$443$	9.01469e9	0.0111207	0.00556037	+	0.999985i	$0.498230\pi$
$444$	−1.30225e11	−0.159027
$445$	−2.88964e11	−0.349320
$446$	−3.63606e10	−0.0435136
$447$	−1.97154e11	−0.233573
$448$	−3.63276e11	−0.426074
$449$	−4.09134e10	−0.0475069	−0.0237535	−	0.999718i	$-0.507562\pi$
$449$	−4.09134e10	−0.0475069	−0.0237535	+	0.999718i	$0.507562\pi$
$450$	1.67498e10	0.0192554
$451$	−4.27455e11	−0.486515
$452$	1.01687e11	0.114589
$453$	−2.26210e11	−0.252389
$454$	5.50590e10	0.0608243
$455$	−1.22710e11	−0.134224
$456$	2.74310e9	0.00297098
$457$	4.94033e11	0.529826	0.264913	−	0.964272i	$-0.414657\pi$
$457$	4.94033e11	0.529826	0.264913	+	0.964272i	$0.414657\pi$
$458$	−4.71834e10	−0.0501066
$459$	0	0
$460$	−6.09239e11	−0.634421
$461$	1.00197e12	1.03324	0.516621	−	0.856214i	$-0.327190\pi$
$461$	1.00197e12	1.03324	0.516621	+	0.856214i	$0.327190\pi$
$462$	1.27396e9	0.00130097
$463$	−9.11192e11	−0.921500	−0.460750	−	0.887530i	$-0.652420\pi$
$463$	−9.11192e11	−0.921500	−0.460750	+	0.887530i	$0.652420\pi$
$464$	−1.04405e12	−1.04566
$465$	4.24349e10	0.0420906
$466$	−1.28848e10	−0.0126573
$467$	2.03431e12	1.97921	0.989603	−	0.143826i	$-0.0459404\pi$
$467$	2.03431e12	1.97921	0.989603	+	0.143826i	$0.0459404\pi$
$468$	4.79746e11	0.462280
$469$	3.09665e11	0.295539
$470$	2.34047e10	0.0221239
$471$	2.87292e11	0.268986
$472$	−1.55775e10	−0.0144463
$473$	−2.25554e11	−0.207193
$474$	3.82969e9	0.00348467
$475$	1.23110e11	0.110961
$476$	0	0
$477$	−1.73578e12	−1.53519
$478$	6.97412e10	0.0611032
$479$	−1.30117e12	−1.12934	−0.564670	−	0.825316i	$-0.690997\pi$
$479$	−1.30117e12	−1.12934	−0.564670	+	0.825316i	$0.690997\pi$
$480$	−1.76297e10	−0.0151586
$481$	3.97891e11	0.338931
$482$	4.57718e10	0.0386266
$483$	−1.16872e11	−0.0977122
$484$	1.02848e12	0.851906
$485$	−8.20691e11	−0.673506
$486$	2.71452e10	0.0220714
$487$	1.49690e12	1.20591	0.602953	−	0.797777i	$-0.293991\pi$
$487$	1.49690e12	1.20591	0.602953	+	0.797777i	$0.293991\pi$
$488$	9.68157e10	0.0772782
$489$	−4.57140e11	−0.361542
$490$	2.29575e10	0.0179904
$491$	−1.75875e12	−1.36564	−0.682822	−	0.730585i	$-0.739248\pi$
$491$	−1.75875e12	−1.36564	−0.682822	+	0.730585i	$0.739248\pi$
$492$	3.77954e11	0.290801
$493$	0	0
$494$	−4.18817e9	−0.00316412
$495$	3.10690e11	0.232597
$496$	−3.84756e11	−0.285442
$497$	3.02793e11	0.222609
$498$	1.17854e9	0.000858645 0
$499$	−2.16969e12	−1.56655	−0.783276	−	0.621674i	$-0.786453\pi$
$499$	−2.16969e12	−1.56655	−0.783276	+	0.621674i	$0.786453\pi$
$500$	−1.42104e12	−1.01681
$501$	4.04910e11	0.287137
$502$	2.25891e10	0.0158757
$503$	−4.58784e11	−0.319560	−0.159780	−	0.987153i	$-0.551078\pi$
$503$	−4.58784e11	−0.319560	−0.159780	+	0.987153i	$0.551078\pi$
$504$	4.05416e10	0.0279875
$505$	6.82447e11	0.466937
$506$	−1.93256e10	−0.0131056
$507$	−2.59950e11	−0.174725
$508$	1.85989e12	1.23908
$509$	−9.32948e11	−0.616066	−0.308033	−	0.951376i	$-0.599671\pi$
$509$	−9.32948e11	−0.616066	−0.308033	+	0.951376i	$0.599671\pi$
$510$	0	0
$511$	−7.57226e11	−0.491283
$512$	2.66519e11	0.171401
$513$	1.31822e11	0.0840349
$514$	1.97371e10	0.0124723
$515$	−1.47152e12	−0.921792
$516$	1.99433e11	0.123844
$517$	−6.25058e11	−0.384780
$518$	1.68022e10	0.0102537
$519$	4.03783e11	0.244284
$520$	3.59036e10	0.0215339
$521$	−1.73581e12	−1.03213	−0.516064	−	0.856550i	$-0.672603\pi$
$521$	−1.73581e12	−1.03213	−0.516064	+	0.856550i	$0.672603\pi$
$522$	5.80850e10	0.0342410
$523$	−8.84542e11	−0.516965	−0.258482	−	0.966016i	$-0.583222\pi$
$523$	−8.84542e11	−0.516965	−0.258482	+	0.966016i	$0.583222\pi$
$524$	4.88316e11	0.282950
$525$	−1.01168e11	−0.0581201
$526$	−8.80422e10	−0.0501482
$527$	0	0
$528$	1.56632e11	0.0877057
$529$	−2.82337e10	−0.0156754
$530$	−6.49135e10	−0.0357350
$531$	−3.64169e11	−0.198783
$532$	1.48901e11	0.0805925
$533$	−1.15481e12	−0.619778
$534$	8.10472e9	0.00431323
$535$	−9.58533e11	−0.505842
$536$	−9.06047e10	−0.0474143
$537$	1.84474e11	0.0957304
$538$	3.58673e10	0.0184577
$539$	−6.13114e11	−0.312890
$540$	−5.64695e11	−0.285787
$541$	−1.32655e12	−0.665787	−0.332893	−	0.942964i	$-0.608025\pi$
$541$	−1.32655e12	−0.665787	−0.332893	+	0.942964i	$0.608025\pi$
$542$	−7.72470e10	−0.0384490
$543$	7.07634e11	0.349309
$544$	0	0
$545$	−3.70306e11	−0.179795
$546$	3.44171e9	0.00165732
$547$	9.98506e11	0.476879	0.238439	−	0.971157i	$-0.423364\pi$
$547$	9.98506e11	0.476879	0.238439	+	0.971157i	$0.423364\pi$
$548$	−7.19464e11	−0.340798
$549$	2.26336e12	1.06335
$550$	−1.67289e10	−0.00779533
$551$	4.26921e11	0.197317
$552$	3.41955e10	0.0156763
$553$	4.16013e11	0.189166
$554$	4.35153e10	0.0196267
$555$	−2.27839e11	−0.101932
$556$	−2.30438e12	−1.02263
$557$	3.43127e12	1.51045	0.755226	−	0.655465i	$-0.227527\pi$
$557$	3.43127e12	1.51045	0.755226	+	0.655465i	$0.227527\pi$
$558$	2.14056e10	0.00934701
$559$	−6.09351e11	−0.263945
$560$	−6.37099e11	−0.273754
$561$	0	0
$562$	6.77707e10	0.0286569
$563$	−5.19511e11	−0.217925	−0.108962	−	0.994046i	$-0.534753\pi$
$563$	−5.19511e11	−0.217925	−0.108962	+	0.994046i	$0.534753\pi$
$564$	5.52672e11	0.229991
$565$	1.77910e11	0.0734484
$566$	9.60917e10	0.0393561
$567$	8.92152e11	0.362506
$568$	−8.85940e10	−0.0357139
$569$	−2.71055e12	−1.08406	−0.542029	−	0.840360i	$-0.682344\pi$
$569$	−2.71055e12	−1.08406	−0.542029	+	0.840360i	$0.682344\pi$
$570$	2.39822e9	0.000951593 0
$571$	5.10172e11	0.200842	0.100421	−	0.994945i	$-0.467981\pi$
$571$	5.10172e11	0.200842	0.100421	+	0.994945i	$0.467981\pi$
$572$	−4.79146e11	−0.187148
$573$	8.40029e11	0.325536
$574$	−4.87653e10	−0.0187503
$575$	1.53469e12	0.585485
$576$	2.48486e12	0.940590
$577$	2.12813e12	0.799296	0.399648	−	0.916669i	$-0.369132\pi$
$577$	2.12813e12	0.799296	0.399648	+	0.916669i	$0.369132\pi$
$578$	0	0
$579$	8.98921e11	0.332405
$580$	−1.82883e12	−0.671040
$581$	1.28023e11	0.0466118
$582$	2.30183e10	0.00831611
$583$	1.73361e12	0.621503
$584$	2.21556e11	0.0788181
$585$	8.39354e11	0.296308
$586$	1.26027e11	0.0441494
$587$	−3.72613e12	−1.29535	−0.647675	−	0.761917i	$-0.724258\pi$
$587$	−3.72613e12	−1.29535	−0.647675	+	0.761917i	$0.724258\pi$
$588$	5.42111e11	0.187021
$589$	1.57330e11	0.0538631
$590$	−1.36189e10	−0.00462710
$591$	−7.11802e11	−0.240002
$592$	2.06581e12	0.691262
$593$	−4.17129e12	−1.38524	−0.692619	−	0.721304i	$-0.743543\pi$
$593$	−4.17129e12	−1.38524	−0.692619	+	0.721304i	$0.743543\pi$
$594$	−1.79127e10	−0.00590366
$595$	0	0
$596$	3.13126e12	1.01651
$597$	−4.85724e11	−0.156497
$598$	−5.22098e10	−0.0166954
$599$	1.45781e12	0.462680	0.231340	−	0.972873i	$-0.425689\pi$
$599$	1.45781e12	0.462680	0.231340	+	0.972873i	$0.425689\pi$
$600$	2.96007e10	0.00932441
$601$	4.68500e12	1.46479	0.732393	−	0.680882i	$-0.238404\pi$
$601$	4.68500e12	1.46479	0.732393	+	0.680882i	$0.238404\pi$
$602$	−2.57318e10	−0.00798519
$603$	−2.11815e12	−0.652424
$604$	3.59274e12	1.09840
$605$	1.79941e12	0.546048
$606$	−1.91409e10	−0.00576549
$607$	3.47157e12	1.03795	0.518976	−	0.854789i	$-0.326314\pi$
$607$	3.47157e12	1.03795	0.518976	+	0.854789i	$0.326314\pi$
$608$	−6.53631e10	−0.0193984
$609$	−3.50831e11	−0.103352
$610$	8.46433e10	0.0247519
$611$	−1.68864e12	−0.490176
$612$	0	0
$613$	2.30507e12	0.659344	0.329672	−	0.944095i	$-0.393062\pi$
$613$	2.30507e12	0.659344	0.329672	+	0.944095i	$0.393062\pi$
$614$	8.55059e8	0.000242794 0
$615$	6.61261e11	0.186395
$616$	−4.04909e10	−0.0113304
$617$	−8.72828e9	−0.00242463	−0.00121231	−	0.999999i	$-0.500386\pi$
$617$	−8.72828e9	−0.00242463	−0.00121231	+	0.999999i	$0.500386\pi$
$618$	4.12724e10	0.0113818
$619$	4.02662e12	1.10238	0.551192	−	0.834378i	$-0.314173\pi$
$619$	4.02662e12	1.10238	0.551192	+	0.834378i	$0.314173\pi$
$620$	−6.73964e11	−0.183178
$621$	1.64329e12	0.443408
$622$	−2.44721e11	−0.0655563
$623$	8.80402e11	0.234145
$624$	4.23154e11	0.111729
$625$	−2.35059e11	−0.0616193
$626$	−1.51825e10	−0.00395146
$627$	−6.40479e10	−0.0165501
$628$	−4.56286e12	−1.17063
$629$	0	0
$630$	3.54444e10	0.00896427
$631$	2.15928e10	0.00542222	0.00271111	−	0.999996i	$-0.499137\pi$
$631$	2.15928e10	0.00542222	0.00271111	+	0.999996i	$0.499137\pi$
$632$	−1.21721e11	−0.0303486
$633$	1.69819e12	0.420406
$634$	1.07646e11	0.0264604
$635$	3.25403e12	0.794218
$636$	−1.53285e12	−0.371486
$637$	−1.65638e12	−0.398595
$638$	−5.80124e10	−0.0138621
$639$	−2.07115e12	−0.491425
$640$	3.73260e11	0.0879431
$641$	−3.19798e12	−0.748195	−0.374098	−	0.927389i	$-0.622047\pi$
$641$	−3.19798e12	−0.748195	−0.374098	+	0.927389i	$0.622047\pi$
$642$	2.68845e10	0.00624588
$643$	−3.65477e11	−0.0843162	−0.0421581	−	0.999111i	$-0.513423\pi$
$643$	−3.65477e11	−0.0843162	−0.0421581	+	0.999111i	$0.513423\pi$
$644$	1.85620e12	0.425244
$645$	3.48925e11	0.0793803
$646$	0	0
$647$	3.96485e12	0.889524	0.444762	−	0.895649i	$-0.353288\pi$
$647$	3.96485e12	0.889524	0.444762	+	0.895649i	$0.353288\pi$
$648$	−2.61034e11	−0.0581580
$649$	3.63714e11	0.0804746
$650$	−4.51944e10	−0.00993057
$651$	−1.29289e11	−0.0282128
$652$	7.26043e12	1.57343
$653$	6.94635e12	1.49502	0.747511	−	0.664249i	$-0.231249\pi$
$653$	6.94635e12	1.49502	0.747511	+	0.664249i	$0.231249\pi$
$654$	1.03862e10	0.00222001
$655$	8.54349e11	0.181363
$656$	−5.99564e12	−1.26406
$657$	5.17954e12	1.08454
$658$	−7.13083e10	−0.0148294
$659$	−4.54637e12	−0.939032	−0.469516	−	0.882924i	$-0.655572\pi$
$659$	−4.54637e12	−0.939032	−0.469516	+	0.882924i	$0.655572\pi$
$660$	2.74367e11	0.0562839
$661$	−1.43628e12	−0.292640	−0.146320	−	0.989237i	$-0.546743\pi$
$661$	−1.43628e12	−0.292640	−0.146320	+	0.989237i	$0.546743\pi$
$662$	2.02672e10	0.00410140
$663$	0	0
$664$	−3.74582e10	−0.00747809
$665$	2.60514e11	0.0516575
$666$	−1.14930e11	−0.0226359
$667$	5.32201e12	1.04114
$668$	−6.43090e12	−1.24962
$669$	−1.50221e12	−0.289943
$670$	−7.92131e10	−0.0151866
$671$	−2.26053e12	−0.430485
$672$	5.37134e10	0.0101606
$673$	−3.31284e12	−0.622490	−0.311245	−	0.950330i	$-0.600746\pi$
$673$	−3.31284e12	−0.622490	−0.311245	+	0.950330i	$0.600746\pi$
$674$	−9.17022e10	−0.0171163
$675$	1.42249e12	0.263743
$676$	4.12861e12	0.760403
$677$	5.77140e12	1.05592	0.527961	−	0.849269i	$-0.322957\pi$
$677$	5.77140e12	1.05592	0.527961	+	0.849269i	$0.322957\pi$
$678$	−4.98993e9	−0.000906902 0
$679$	2.50044e12	0.451443
$680$	0	0
$681$	2.27472e12	0.405290
$682$	−2.13788e10	−0.00378402
$683$	1.04373e13	1.83524	0.917620	−	0.397458i	$-0.130107\pi$
$683$	1.04373e13	1.83524	0.917620	+	0.397458i	$0.130107\pi$
$684$	−1.01850e12	−0.177914
$685$	−1.25876e12	−0.218442
$686$	−1.55679e11	−0.0268393
$687$	−1.94934e12	−0.333874
$688$	−3.16369e12	−0.538327
$689$	4.68349e12	0.791741
$690$	2.98962e10	0.00502106
$691$	7.77913e12	1.29801	0.649007	−	0.760782i	$-0.275184\pi$
$691$	7.77913e12	1.29801	0.649007	+	0.760782i	$0.275184\pi$
$692$	−6.41301e12	−1.06313
$693$	−9.46596e11	−0.155907
$694$	3.51705e9	0.000575521 0
$695$	−4.03170e12	−0.655475
$696$	1.02649e11	0.0165811
$697$	0	0
$698$	1.84591e11	0.0294348
$699$	−5.32324e11	−0.0843391
$700$	1.60678e12	0.252939
$701$	1.12758e13	1.76367	0.881836	−	0.471557i	$-0.156308\pi$
$701$	1.12758e13	1.76367	0.881836	+	0.471557i	$0.156308\pi$
$702$	−4.83925e10	−0.00752075
$703$	−8.44725e11	−0.130442
$704$	−2.48175e12	−0.380786
$705$	9.66945e11	0.147418
$706$	−5.75493e10	−0.00871804
$707$	−2.07925e12	−0.312982
$708$	−3.21594e11	−0.0481014
$709$	−5.80955e12	−0.863445	−0.431722	−	0.902006i	$-0.642094\pi$
$709$	−5.80955e12	−0.863445	−0.431722	+	0.902006i	$0.642094\pi$
$710$	−7.74553e10	−0.0114390
$711$	−2.84559e12	−0.417598
$712$	−2.57596e11	−0.0375647
$713$	1.96127e12	0.284207
$714$	0	0
$715$	−8.38305e11	−0.119957
$716$	−2.92987e12	−0.416619
$717$	2.88130e12	0.407148
$718$	1.06468e11	0.0149507
$719$	3.73999e12	0.521904	0.260952	−	0.965352i	$-0.415964\pi$
$719$	3.73999e12	0.521904	0.260952	+	0.965352i	$0.415964\pi$
$720$	4.35785e12	0.604332
$721$	4.48335e12	0.617866
$722$	−2.42601e11	−0.0332257
$723$	1.89102e12	0.257380
$724$	−1.12389e13	−1.52019
$725$	4.60689e12	0.619280
$726$	−5.04689e10	−0.00674232
$727$	−4.47054e12	−0.593547	−0.296774	−	0.954948i	$-0.595911\pi$
$727$	−4.47054e12	−0.593547	−0.296774	+	0.954948i	$0.595911\pi$
$728$	−1.09389e11	−0.0144339
$729$	−5.32028e12	−0.697686
$730$	1.93700e11	0.0252451
$731$	0	0
$732$	1.99874e12	0.257310
$733$	1.27179e13	1.62722	0.813611	−	0.581410i	$-0.197499\pi$
$733$	1.27179e13	1.62722	0.813611	+	0.581410i	$0.197499\pi$
$734$	3.77836e11	0.0480475
$735$	9.48468e11	0.119875
$736$	−8.14817e11	−0.102355
$737$	2.11551e12	0.264126
$738$	3.33562e11	0.0413926
$739$	−1.34347e13	−1.65702	−0.828509	−	0.559976i	$-0.810810\pi$
$739$	−1.34347e13	−1.65702	−0.828509	+	0.559976i	$0.810810\pi$
$740$	3.61861e12	0.443608
$741$	−1.73031e11	−0.0210834
$742$	1.97775e11	0.0239527
$743$	1.78979e12	0.215453	0.107727	−	0.994181i	$-0.465643\pi$
$743$	1.78979e12	0.215453	0.107727	+	0.994181i	$0.465643\pi$
$744$	3.78285e10	0.00452627
$745$	5.47840e12	0.651554
$746$	1.29739e11	0.0153372
$747$	−8.75698e11	−0.102899
$748$	0	0
$749$	2.92041e12	0.339060
$750$	6.97323e10	0.00804745
$751$	1.33750e12	0.153431	0.0767156	−	0.997053i	$-0.475557\pi$
$751$	1.33750e12	0.153431	0.0767156	+	0.997053i	$0.475557\pi$
$752$	−8.76727e12	−0.999733
$753$	9.33251e11	0.105784
$754$	−1.56725e11	−0.0176591
$755$	6.28579e12	0.704042
$756$	1.72049e12	0.191559
$757$	−6.15593e12	−0.681338	−0.340669	−	0.940183i	$-0.610654\pi$
$757$	−6.15593e12	−0.681338	−0.340669	+	0.940183i	$0.610654\pi$
$758$	2.53557e11	0.0278974
$759$	−7.98423e11	−0.0873263
$760$	−7.62236e10	−0.00828759
$761$	−6.40055e12	−0.691810	−0.345905	−	0.938270i	$-0.612428\pi$
$761$	−6.40055e12	−0.691810	−0.345905	+	0.938270i	$0.612428\pi$
$762$	−9.12674e10	−0.00980660
$763$	1.12823e12	0.120514
$764$	−1.33416e13	−1.41673
$765$	0	0
$766$	−5.44840e11	−0.0571794
$767$	9.82603e11	0.102518
$768$	2.18649e12	0.226789
$769$	1.07113e13	1.10452	0.552259	−	0.833673i	$-0.313766\pi$
$769$	1.07113e13	1.10452	0.552259	+	0.833673i	$0.313766\pi$
$770$	−3.54001e10	−0.00362907
$771$	8.15420e11	0.0831068
$772$	−1.42769e13	−1.44663
$773$	−2.88044e12	−0.290169	−0.145084	−	0.989419i	$-0.546345\pi$
$773$	−2.88044e12	−0.290169	−0.145084	+	0.989419i	$0.546345\pi$
$774$	1.76009e11	0.0176279
$775$	1.69774e12	0.169049
$776$	−7.31602e11	−0.0724265
$777$	6.94169e11	0.0683236
$778$	2.97728e11	0.0291347
$779$	2.45166e12	0.238529
$780$	7.41224e11	0.0717008
$781$	2.06856e12	0.198947
$782$	0	0
$783$	4.93290e12	0.469001
$784$	−8.59974e12	−0.812949
$785$	−7.98311e12	−0.750341
$786$	−2.39624e10	−0.00223938
$787$	7.97631e12	0.741166	0.370583	−	0.928799i	$-0.379158\pi$
$787$	7.97631e12	0.741166	0.370583	+	0.928799i	$0.379158\pi$
$788$	1.13051e13	1.04449
$789$	−3.63739e12	−0.334151
$790$	−1.06417e11	−0.00972052
$791$	−5.42047e11	−0.0492315
$792$	2.76964e11	0.0250126
$793$	−6.10699e12	−0.548401
$794$	−1.48668e11	−0.0132747
$795$	−2.68185e12	−0.238112
$796$	7.71442e12	0.681075
$797$	−8.35103e12	−0.733124	−0.366562	−	0.930394i	$-0.619465\pi$
$797$	−8.35103e12	−0.733124	−0.366562	+	0.930394i	$0.619465\pi$
$798$	−7.30677e9	−0.000637841 0
$799$	0	0
$800$	−7.05330e11	−0.0608818
$801$	−6.02208e12	−0.516892
$802$	7.13097e11	0.0608645
$803$	−5.17306e12	−0.439064
$804$	−1.87052e12	−0.157874
$805$	3.24757e12	0.272570
$806$	−5.77565e10	−0.00482052
$807$	1.48183e12	0.122989
$808$	6.08365e11	0.0502127
$809$	1.72474e13	1.41565	0.707823	−	0.706390i	$-0.249678\pi$
$809$	1.72474e13	1.41565	0.707823	+	0.706390i	$0.249678\pi$
$810$	−2.28215e11	−0.0186278
$811$	1.43590e13	1.16555	0.582776	−	0.812633i	$-0.301966\pi$
$811$	1.43590e13	1.16555	0.582776	+	0.812633i	$0.301966\pi$
$812$	5.57200e12	0.449789
$813$	−3.19139e12	−0.256196
$814$	1.14786e11	0.00916386
$815$	1.27027e13	1.00853
$816$	0	0
$817$	1.29366e12	0.101583
$818$	−4.72546e11	−0.0369024
$819$	−2.55730e12	−0.198612
$820$	−1.05023e13	−0.811193
$821$	5.55258e12	0.426531	0.213265	−	0.976994i	$-0.431590\pi$
$821$	5.55258e12	0.426531	0.213265	+	0.976994i	$0.431590\pi$
$822$	3.53051e10	0.00269721
$823$	1.42535e13	1.08298	0.541491	−	0.840706i	$-0.317860\pi$
$823$	1.42535e13	1.08298	0.541491	+	0.840706i	$0.317860\pi$
$824$	−1.31178e12	−0.0991263
$825$	−6.91139e11	−0.0519425
$826$	4.14935e10	0.00310149
$827$	1.26379e13	0.939505	0.469752	−	0.882798i	$-0.344343\pi$
$827$	1.26379e13	0.939505	0.469752	+	0.882798i	$0.344343\pi$
$828$	−1.26967e13	−0.938758
$829$	1.04860e13	0.771104	0.385552	−	0.922686i	$-0.374011\pi$
$829$	1.04860e13	0.771104	0.385552	+	0.922686i	$0.374011\pi$
$830$	−3.27487e10	−0.00239520
$831$	1.79780e12	0.130778
$832$	−6.70465e12	−0.485089
$833$	0	0
$834$	1.13079e11	0.00809347
$835$	−1.12514e13	−0.800972
$836$	1.01723e12	0.0720262
$837$	1.81788e12	0.128027
$838$	−8.76648e11	−0.0614083
$839$	−1.64507e13	−1.14618	−0.573092	−	0.819491i	$-0.694256\pi$
$839$	−1.64507e13	−1.14618	−0.573092	+	0.819491i	$0.694256\pi$
$840$	6.26382e10	0.00434093
$841$	1.46864e12	0.101236
$842$	1.25307e11	0.00859153
$843$	2.79989e12	0.190949
$844$	−2.69711e13	−1.82961
$845$	7.22335e12	0.487397
$846$	4.87759e11	0.0327370
$847$	−5.48235e12	−0.366009
$848$	2.43162e13	1.61479
$849$	3.96995e12	0.262241
$850$	0	0
$851$	−1.05304e13	−0.688272
$852$	−1.82901e12	−0.118915
$853$	−1.11182e13	−0.719057	−0.359528	−	0.933134i	$-0.617062\pi$
$853$	−1.11182e13	−0.719057	−0.359528	+	0.933134i	$0.617062\pi$
$854$	−2.57887e11	−0.0165909
$855$	−1.78195e12	−0.114038
$856$	−8.54482e11	−0.0543965
$857$	7.82649e12	0.495625	0.247813	−	0.968808i	$-0.420288\pi$
$857$	7.82649e12	0.495625	0.247813	+	0.968808i	$0.420288\pi$
$858$	2.35123e10	0.00148116
$859$	−3.68708e12	−0.231054	−0.115527	−	0.993304i	$-0.536856\pi$
$859$	−3.68708e12	−0.231054	−0.115527	+	0.993304i	$0.536856\pi$
$860$	−5.54173e12	−0.345463
$861$	−2.01470e12	−0.124938
$862$	−1.03468e12	−0.0638295
$863$	1.56166e13	0.958380	0.479190	−	0.877711i	$-0.340931\pi$
$863$	1.56166e13	0.958380	0.479190	+	0.877711i	$0.340931\pi$
$864$	−7.55243e11	−0.0461079
$865$	−1.12201e13	−0.681434
$866$	5.35876e11	0.0323768
$867$	0	0
$868$	2.05340e12	0.122782
$869$	2.84203e12	0.169059
$870$	8.97434e10	0.00531087
$871$	5.71521e12	0.336473
$872$	−3.30108e11	−0.0193345
$873$	−1.71034e13	−0.996593
$874$	1.10842e11	0.00642542
$875$	7.57490e12	0.436858
$876$	4.57399e12	0.262438
$877$	1.84491e13	1.05312	0.526559	−	0.850139i	$-0.323482\pi$
$877$	1.84491e13	1.05312	0.526559	+	0.850139i	$0.323482\pi$
$878$	−5.83087e11	−0.0331137
$879$	5.20671e12	0.294180
$880$	−4.35240e12	−0.244656
$881$	−2.55028e13	−1.42625	−0.713125	−	0.701037i	$-0.752721\pi$
$881$	−2.55028e13	−1.42625	−0.713125	+	0.701037i	$0.752721\pi$
$882$	4.78439e11	0.0266206
$883$	9.14795e12	0.506408	0.253204	−	0.967413i	$-0.418516\pi$
$883$	9.14795e12	0.506408	0.253204	+	0.967413i	$0.418516\pi$
$884$	0	0
$885$	−5.62655e11	−0.0308317
$886$	7.02575e9	0.000383037 0
$887$	−8.88742e12	−0.482081	−0.241040	−	0.970515i	$-0.577489\pi$
$887$	−8.88742e12	−0.482081	−0.241040	+	0.970515i	$0.577489\pi$
$888$	−2.03106e11	−0.0109614
$889$	−9.91422e12	−0.532354
$890$	−2.25209e11	−0.0120318
$891$	6.09482e12	0.323975
$892$	2.38585e13	1.26183
$893$	3.58500e12	0.188650
$894$	−1.53655e11	−0.00804505
$895$	−5.12604e12	−0.267041
$896$	−1.13723e12	−0.0589471
$897$	−2.15700e12	−0.111246
$898$	−3.18865e10	−0.00163630
$899$	5.88742e12	0.300612
$900$	−1.09906e13	−0.558382
$901$	0	0
$902$	−3.33145e11	−0.0167573
$903$	−1.06309e12	−0.0532076
$904$	1.58597e11	0.00789837
$905$	−1.96633e13	−0.974401
$906$	−1.76301e11	−0.00869315
$907$	−1.73486e13	−0.851202	−0.425601	−	0.904911i	$-0.639937\pi$
$907$	−1.73486e13	−0.851202	−0.425601	+	0.904911i	$0.639937\pi$
$908$	−3.61278e13	−1.76382
$909$	1.42224e13	0.690930
$910$	−9.56361e10	−0.00462313
$911$	1.37894e12	0.0663302	0.0331651	−	0.999450i	$-0.489441\pi$
$911$	1.37894e12	0.0663302	0.0331651	+	0.999450i	$0.489441\pi$
$912$	−8.98358e11	−0.0430004
$913$	8.74603e11	0.0416574
$914$	3.85033e11	0.0182490
$915$	3.49697e12	0.164929
$916$	3.09601e13	1.45302
$917$	−2.60299e12	−0.121566
$918$	0	0
$919$	−2.85500e13	−1.32034	−0.660170	−	0.751116i	$-0.729516\pi$
$919$	−2.85500e13	−1.32034	−0.660170	+	0.751116i	$0.729516\pi$
$920$	−9.50205e11	−0.0437293
$921$	3.53260e10	0.00161781
$922$	7.80905e11	0.0355884
$923$	5.58838e12	0.253442
$924$	−8.35928e11	−0.0377264
$925$	−9.11539e12	−0.409390
$926$	−7.10153e11	−0.0317397
$927$	−3.06668e13	−1.36398
$928$	−2.44595e12	−0.108263
$929$	1.97136e13	0.868351	0.434175	−	0.900828i	$-0.357040\pi$
$929$	1.97136e13	0.868351	0.434175	+	0.900828i	$0.357040\pi$
$930$	3.30724e10	0.00144975
$931$	3.51649e12	0.153404
$932$	8.45454e12	0.367044
$933$	−1.01104e13	−0.436820
$934$	1.58547e12	0.0681707
$935$	0	0
$936$	7.48240e11	0.0318639
$937$	3.51151e13	1.48822	0.744108	−	0.668060i	$-0.232875\pi$
$937$	3.51151e13	1.48822	0.744108	+	0.668060i	$0.232875\pi$
$938$	2.41343e11	0.0101794
$939$	−6.27250e11	−0.0263297
$940$	−1.53573e13	−0.641564
$941$	−2.11548e13	−0.879540	−0.439770	−	0.898110i	$-0.644940\pi$
$941$	−2.11548e13	−0.879540	−0.439770	+	0.898110i	$0.644940\pi$
$942$	2.23906e11	0.00926482
$943$	3.05624e13	1.25859
$944$	5.10158e12	0.209089
$945$	3.01013e12	0.122784
$946$	−1.75789e11	−0.00713644
$947$	3.76128e13	1.51971	0.759854	−	0.650093i	$-0.225270\pi$
$947$	3.76128e13	1.51971	0.759854	+	0.650093i	$0.225270\pi$
$948$	−2.51291e12	−0.101051
$949$	−1.39754e13	−0.559329
$950$	9.59479e10	0.00382190
$951$	4.44730e12	0.176313
$952$	0	0
$953$	−3.31338e13	−1.30123	−0.650613	−	0.759410i	$-0.725488\pi$
$953$	−3.31338e13	−1.30123	−0.650613	+	0.759410i	$0.725488\pi$
$954$	−1.35281e12	−0.0528773
$955$	−2.33422e13	−0.908086
$956$	−4.57617e13	−1.77191
$957$	−2.39673e12	−0.0923668
$958$	−1.01409e12	−0.0388984
$959$	3.83514e12	0.146419
$960$	3.83919e12	0.145888
$961$	−2.42700e13	−0.917940
$962$	3.10103e11	0.0116740
$963$	−1.99760e13	−0.748499
$964$	−3.00338e13	−1.12012
$965$	−2.49787e13	−0.927250
$966$	−9.10863e10	−0.00336555
$967$	−1.59894e13	−0.588047	−0.294023	−	0.955798i	$-0.594994\pi$
$967$	−1.59894e13	−0.588047	−0.294023	+	0.955798i	$0.594994\pi$
$968$	1.60408e12	0.0587200
$969$	0	0
$970$	−6.39619e11	−0.0231979
$971$	4.36090e13	1.57431	0.787154	−	0.616756i	$-0.211554\pi$
$971$	4.36090e13	1.57431	0.787154	+	0.616756i	$0.211554\pi$
$972$	−1.78117e13	−0.640041
$973$	1.22836e13	0.439356
$974$	1.16664e12	0.0415356
$975$	−1.86717e12	−0.0661702
$976$	−3.17069e13	−1.11848
$977$	2.51816e13	0.884213	0.442107	−	0.896962i	$-0.354231\pi$
$977$	2.51816e13	0.884213	0.442107	+	0.896962i	$0.354231\pi$
$978$	−3.56279e11	−0.0124528
$979$	6.01455e12	0.209257
$980$	−1.50639e13	−0.521698
$981$	−7.71726e12	−0.266044
$982$	−1.37071e12	−0.0470375
$983$	−3.06207e13	−1.04598	−0.522992	−	0.852338i	$-0.675184\pi$
$983$	−3.06207e13	−1.04598	−0.522992	+	0.852338i	$0.675184\pi$
$984$	5.89479e11	0.0200443
$985$	1.97791e13	0.669490
$986$	0	0
$987$	−2.94604e12	−0.0988125
$988$	2.74813e12	0.0917551
$989$	1.61267e13	0.535998
$990$	2.42142e11	0.00801145
$991$	3.59113e12	0.118277	0.0591385	−	0.998250i	$-0.481165\pi$
$991$	3.59113e12	0.118277	0.0591385	+	0.998250i	$0.481165\pi$
$992$	−9.01383e11	−0.0295534
$993$	8.37322e11	0.0273288
$994$	2.35987e11	0.00766742
$995$	1.34970e13	0.436550
$996$	−7.73318e11	−0.0248995
$997$	−1.79571e13	−0.575582	−0.287791	−	0.957693i	$-0.592921\pi$
$997$	−1.79571e13	−0.575582	−0.287791	+	0.957693i	$0.592921\pi$
$998$	−1.69098e12	−0.0539575
$999$	−9.76044e12	−0.310045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.e.1.6	yes	12
17.16	even	2		289.10.a.d.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.d.1.6	✓	12	17.16	even	2
289.10.a.e.1.6	yes	12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+0.779367 q^{2} +32.1989 q^{3} -511.393 q^{4} -894.723 q^{5} +25.0947 q^{6} +2726.00 q^{7} -797.598 q^{8} -18646.2 q^{9} +O(q^{10})\)	\(q+0.779367 q^{2} +32.1989 q^{3} -511.393 q^{4} -894.723 q^{5} +25.0947 q^{6} +2726.00 q^{7} -797.598 q^{8} -18646.2 q^{9} -697.318 q^{10} +18622.9 q^{11} -16466.3 q^{12} +50311.3 q^{13} +2124.55 q^{14} -28809.1 q^{15} +261211. q^{16} -14532.3 q^{18} -106811. q^{19} +457555. q^{20} +87774.1 q^{21} +14514.1 q^{22} -1.33151e6 q^{23} -25681.8 q^{24} -1.15260e6 q^{25} +39211.0 q^{26} -1.23416e6 q^{27} -1.39406e6 q^{28} -3.99697e6 q^{29} -22452.9 q^{30} -1.47297e6 q^{31} +611950. q^{32} +599637. q^{33} -2.43902e6 q^{35} +9.53554e6 q^{36} +7.90858e6 q^{37} -83245.1 q^{38} +1.61997e6 q^{39} +713630. q^{40} -2.29532e7 q^{41} +68408.3 q^{42} -1.21116e7 q^{43} -9.52362e6 q^{44} +1.66832e7 q^{45} -1.03773e6 q^{46} -3.35639e7 q^{47} +8.41072e6 q^{48} -3.29225e7 q^{49} -898295. q^{50} -2.57288e7 q^{52} +9.30903e7 q^{53} -961862. q^{54} -1.66624e7 q^{55} -2.17425e6 q^{56} -3.43920e6 q^{57} -3.11511e6 q^{58} +1.95305e7 q^{59} +1.47328e7 q^{60} -1.21384e8 q^{61} -1.14798e6 q^{62} -5.08296e7 q^{63} -1.33263e8 q^{64} -4.50147e7 q^{65} +467337. q^{66} +1.13597e8 q^{67} -4.28731e7 q^{69} -1.90089e6 q^{70} +1.11076e8 q^{71} +1.48722e7 q^{72} -2.77779e8 q^{73} +6.16369e6 q^{74} -3.71123e7 q^{75} +5.46224e7 q^{76} +5.07661e7 q^{77} +1.26255e6 q^{78} +1.52609e8 q^{79} -2.33712e8 q^{80} +3.27275e8 q^{81} -1.78890e7 q^{82} +4.69638e7 q^{83} -4.48870e7 q^{84} -9.43939e6 q^{86} -1.28698e8 q^{87} -1.48536e7 q^{88} +3.22965e8 q^{89} +1.30023e7 q^{90} +1.37149e8 q^{91} +6.80924e8 q^{92} -4.74280e7 q^{93} -2.61586e7 q^{94} +9.55664e7 q^{95} +1.97041e7 q^{96} +9.17256e8 q^{97} -2.56587e7 q^{98} -3.47247e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more