LMFDB - Embedded newform 289.10.a.f.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:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-31.4159 q^{2} +60.4230 q^{3} +474.957 q^{4} -1582.21 q^{5} -1898.24 q^{6} +10488.5 q^{7} +1163.73 q^{8} -16032.1 q^{9} +O(q^{10})$	\(q-31.4159 q^{2} +60.4230 q^{3} +474.957 q^{4} -1582.21 q^{5} -1898.24 q^{6} +10488.5 q^{7} +1163.73 q^{8} -16032.1 q^{9} +49706.4 q^{10} +78187.1 q^{11} +28698.4 q^{12} +111709. q^{13} -329506. q^{14} -95601.8 q^{15} -279738. q^{16} +503661. q^{18} -202367. q^{19} -751481. q^{20} +633749. q^{21} -2.45632e6 q^{22} -759075. q^{23} +70316.3 q^{24} +550256. q^{25} -3.50943e6 q^{26} -2.15801e6 q^{27} +4.98160e6 q^{28} -7.48987e6 q^{29} +3.00341e6 q^{30} +1.06329e6 q^{31} +8.19237e6 q^{32} +4.72430e6 q^{33} -1.65950e7 q^{35} -7.61454e6 q^{36} +1.12518e7 q^{37} +6.35754e6 q^{38} +6.74979e6 q^{39} -1.84127e6 q^{40} +1.31299e6 q^{41} -1.99098e7 q^{42} +5.13056e6 q^{43} +3.71355e7 q^{44} +2.53660e7 q^{45} +2.38470e7 q^{46} -2.33308e7 q^{47} -1.69026e7 q^{48} +6.96556e7 q^{49} -1.72868e7 q^{50} +5.30569e7 q^{52} -4.46435e7 q^{53} +6.77959e7 q^{54} -1.23708e8 q^{55} +1.22058e7 q^{56} -1.22276e7 q^{57} +2.35301e8 q^{58} -1.89411e7 q^{59} -4.54068e7 q^{60} -1.34977e8 q^{61} -3.34042e7 q^{62} -1.68153e8 q^{63} -1.14145e8 q^{64} -1.76747e8 q^{65} -1.48418e8 q^{66} -3.24318e6 q^{67} -4.58657e7 q^{69} +5.21347e8 q^{70} -2.42466e8 q^{71} -1.86570e7 q^{72} -1.13987e8 q^{73} -3.53484e8 q^{74} +3.32481e7 q^{75} -9.61157e7 q^{76} +8.20068e8 q^{77} -2.12051e8 q^{78} -4.26199e7 q^{79} +4.42603e8 q^{80} +1.85165e8 q^{81} -4.12487e7 q^{82} +4.37207e8 q^{83} +3.01003e8 q^{84} -1.61181e8 q^{86} -4.52561e8 q^{87} +9.09890e7 q^{88} +5.60941e7 q^{89} -7.96896e8 q^{90} +1.17166e9 q^{91} -3.60528e8 q^{92} +6.42473e7 q^{93} +7.32958e8 q^{94} +3.20187e8 q^{95} +4.95008e8 q^{96} +1.52321e9 q^{97} -2.18829e9 q^{98} -1.25350e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) $ 24 * q + 5124 * q^4 + 108368 * q^9	$ 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) $ 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−31.4159	−1.38840	−0.694199	−	0.719783i	$-0.744241\pi$
$2$	−31.4159	−1.38840	−0.694199	+	0.719783i	$0.744241\pi$
$3$	60.4230	0.430682	0.215341	−	0.976539i	$-0.430914\pi$
$3$	60.4230	0.430682	0.215341	+	0.976539i	$0.430914\pi$
$4$	474.957	0.927651
$5$	−1582.21	−1.13214	−0.566068	−	0.824359i	$-0.691536\pi$
$5$	−1582.21	−1.13214	−0.566068	+	0.824359i	$0.691536\pi$
$6$	−1898.24	−0.597959
$7$	10488.5	1.65110	0.825550	−	0.564329i	$-0.190865\pi$
$7$	10488.5	1.65110	0.825550	+	0.564329i	$0.190865\pi$
$8$	1163.73	0.100450
$9$	−16032.1	−0.814513
$10$	49706.4	1.57186
$11$	78187.1	1.61016	0.805078	−	0.593169i	$-0.202123\pi$
$11$	78187.1	1.61016	0.805078	+	0.593169i	$0.202123\pi$
$12$	28698.4	0.399523
$13$	111709.	1.08478	0.542391	−	0.840126i	$-0.317519\pi$
$13$	111709.	1.08478	0.542391	+	0.840126i	$0.317519\pi$
$14$	−329506.	−2.29238
$15$	−95601.8	−0.487591
$16$	−279738.	−1.06711
$17$	0	0
$17$	0	0
$18$	503661.	1.13087
$19$	−202367.	−0.356245	−0.178123	−	0.984008i	$-0.557002\pi$
$19$	−202367.	−0.356245	−0.178123	+	0.984008i	$0.557002\pi$
$20$	−751481.	−1.05023
$21$	633749.	0.711099
$22$	−2.45632e6	−2.23554
$23$	−759075.	−0.565600	−0.282800	−	0.959179i	$-0.591263\pi$
$23$	−759075.	−0.565600	−0.282800	+	0.959179i	$0.591263\pi$
$24$	70316.3	0.0432619
$25$	550256.	0.281731
$26$	−3.50943e6	−1.50611
$27$	−2.15801e6	−0.781478
$28$	4.98160e6	1.53164
$29$	−7.48987e6	−1.96645	−0.983226	−	0.182389i	$-0.941617\pi$
$29$	−7.48987e6	−1.96645	−0.983226	+	0.182389i	$0.941617\pi$
$30$	3.00341e6	0.676970
$31$	1.06329e6	0.206788	0.103394	−	0.994640i	$-0.467030\pi$
$31$	1.06329e6	0.206788	0.103394	+	0.994640i	$0.467030\pi$
$32$	8.19237e6	1.38113
$33$	4.72430e6	0.693466
$34$	0	0
$35$	−1.65950e7	−1.86927
$36$	−7.61454e6	−0.755583
$37$	1.12518e7	0.986991	0.493496	−	0.869748i	$-0.335719\pi$
$37$	1.12518e7	0.986991	0.493496	+	0.869748i	$0.335719\pi$
$38$	6.35754e6	0.494610
$39$	6.74979e6	0.467196
$40$	−1.84127e6	−0.113723
$41$	1.31299e6	0.0725661	0.0362831	−	0.999342i	$-0.488448\pi$
$41$	1.31299e6	0.0725661	0.0362831	+	0.999342i	$0.488448\pi$
$42$	−1.99098e7	−0.987289
$43$	5.13056e6	0.228853	0.114427	−	0.993432i	$-0.463497\pi$
$43$	5.13056e6	0.228853	0.114427	+	0.993432i	$0.463497\pi$
$44$	3.71355e7	1.49366
$45$	2.53660e7	0.922139
$46$	2.38470e7	0.785279
$47$	−2.33308e7	−0.697412	−0.348706	−	0.937232i	$-0.613379\pi$
$47$	−2.33308e7	−0.697412	−0.348706	+	0.937232i	$0.613379\pi$
$48$	−1.69026e7	−0.459587
$49$	6.96556e7	1.72613
$50$	−1.72868e7	−0.391155
$51$	0	0
$52$	5.30569e7	1.00630
$53$	−4.46435e7	−0.777172	−0.388586	−	0.921413i	$-0.627036\pi$
$53$	−4.46435e7	−0.777172	−0.388586	+	0.921413i	$0.627036\pi$
$54$	6.77959e7	1.08500
$55$	−1.23708e8	−1.82292
$56$	1.22058e7	0.165852
$57$	−1.22276e7	−0.153428
$58$	2.35301e8	2.73022
$59$	−1.89411e7	−0.203503	−0.101751	−	0.994810i	$-0.532445\pi$
$59$	−1.89411e7	−0.203503	−0.101751	+	0.994810i	$0.532445\pi$
$60$	−4.54068e7	−0.452314
$61$	−1.34977e8	−1.24818	−0.624089	−	0.781353i	$-0.714530\pi$
$61$	−1.34977e8	−1.24818	−0.624089	+	0.781353i	$0.714530\pi$
$62$	−3.34042e7	−0.287104
$63$	−1.68153e8	−1.34484
$64$	−1.14145e8	−0.850446
$65$	−1.76747e8	−1.22812
$66$	−1.48418e8	−0.962807
$67$	−3.24318e6	−0.0196623	−0.00983115	−	0.999952i	$-0.503129\pi$
$67$	−3.24318e6	−0.0196623	−0.00983115	+	0.999952i	$0.503129\pi$
$68$	0	0
$69$	−4.58657e7	−0.243594
$70$	5.21347e8	2.59529
$71$	−2.42466e8	−1.13237	−0.566184	−	0.824279i	$-0.691581\pi$
$71$	−2.42466e8	−1.13237	−0.566184	+	0.824279i	$0.691581\pi$
$72$	−1.86570e7	−0.0818176
$73$	−1.13987e8	−0.469790	−0.234895	−	0.972021i	$-0.575475\pi$
$73$	−1.13987e8	−0.469790	−0.234895	+	0.972021i	$0.575475\pi$
$74$	−3.53484e8	−1.37034
$75$	3.32481e7	0.121336
$76$	−9.61157e7	−0.330471
$77$	8.20068e8	2.65853
$78$	−2.12051e8	−0.648655
$79$	−4.26199e7	−0.123109	−0.0615546	−	0.998104i	$-0.519606\pi$
$79$	−4.26199e7	−0.123109	−0.0615546	+	0.998104i	$0.519606\pi$
$80$	4.42603e8	1.20812
$81$	1.85165e8	0.477944
$82$	−4.12487e7	−0.100751
$83$	4.37207e8	1.01120	0.505598	−	0.862769i	$-0.331272\pi$
$83$	4.37207e8	1.01120	0.505598	+	0.862769i	$0.331272\pi$
$84$	3.01003e8	0.659652
$85$	0	0
$86$	−1.61181e8	−0.317739
$87$	−4.52561e8	−0.846916
$88$	9.09890e7	0.161740
$89$	5.60941e7	0.0947681	0.0473840	−	0.998877i	$-0.484912\pi$
$89$	5.60941e7	0.0947681	0.0473840	+	0.998877i	$0.484912\pi$
$90$	−7.96896e8	−1.28030
$91$	1.17166e9	1.79108
$92$	−3.60528e8	−0.524680
$93$	6.42473e7	0.0890598
$94$	7.32958e8	0.968286
$95$	3.20187e8	0.403318
$96$	4.95008e8	0.594829
$97$	1.52321e9	1.74698	0.873490	−	0.486842i	$-0.161851\pi$
$97$	1.52321e9	1.74698	0.873490	+	0.486842i	$0.161851\pi$
$98$	−2.18829e9	−2.39656
$99$	−1.25350e9	−1.31149
$100$	2.61348e8	0.261348
$101$	1.68043e9	1.60684	0.803422	−	0.595411i	$-0.203011\pi$
$101$	1.68043e9	1.60684	0.803422	+	0.595411i	$0.203011\pi$
$102$	0	0
$103$	−1.19381e9	−1.04513	−0.522563	−	0.852600i	$-0.675024\pi$
$103$	−1.19381e9	−1.04513	−0.522563	+	0.852600i	$0.675024\pi$
$104$	1.29999e8	0.108966
$105$	−1.00272e9	−0.805061
$106$	1.40251e9	1.07902
$107$	−1.74575e9	−1.28752	−0.643761	−	0.765227i	$-0.722627\pi$
$107$	−1.74575e9	−1.28752	−0.643761	+	0.765227i	$0.722627\pi$
$108$	−1.02496e9	−0.724939
$109$	−6.12631e8	−0.415700	−0.207850	−	0.978161i	$-0.566647\pi$
$109$	−6.12631e8	−0.415700	−0.207850	+	0.978161i	$0.566647\pi$
$110$	3.88640e9	2.53093
$111$	6.79866e8	0.425080
$112$	−2.93404e9	−1.76191
$113$	−8.81532e8	−0.508610	−0.254305	−	0.967124i	$-0.581847\pi$
$113$	−8.81532e8	−0.508610	−0.254305	+	0.967124i	$0.581847\pi$
$114$	3.84142e8	0.213020
$115$	1.20101e9	0.640336
$116$	−3.55737e9	−1.82418
$117$	−1.79092e9	−0.883569
$118$	5.95050e8	0.282543
$119$	0	0
$120$	−1.11255e8	−0.0489783
$121$	3.75528e9	1.59260
$122$	4.24043e9	1.73297
$123$	7.93348e7	0.0312529
$124$	5.05018e8	0.191827
$125$	2.21963e9	0.813178
$126$	5.28266e9	1.86718
$127$	−8.61290e8	−0.293787	−0.146894	−	0.989152i	$-0.546927\pi$
$127$	−8.61290e8	−0.293787	−0.146894	+	0.989152i	$0.546927\pi$
$128$	−6.08535e8	−0.200374
$129$	3.10004e8	0.0985629
$130$	5.55265e9	1.70512
$131$	7.81474e8	0.231843	0.115921	−	0.993258i	$-0.463018\pi$
$131$	7.81474e8	0.231843	0.115921	+	0.993258i	$0.463018\pi$
$132$	2.24384e9	0.643294
$133$	−2.12253e9	−0.588196
$134$	1.01887e8	0.0272991
$135$	3.41442e9	0.884740
$136$	0	0
$137$	6.19075e9	1.50141	0.750707	−	0.660635i	$-0.229713\pi$
$137$	6.19075e9	1.50141	0.750707	+	0.660635i	$0.229713\pi$
$138$	1.44091e9	0.338206
$139$	−2.41364e8	−0.0548410	−0.0274205	−	0.999624i	$-0.508729\pi$
$139$	−2.41364e8	−0.0548410	−0.0274205	+	0.999624i	$0.508729\pi$
$140$	−7.88193e9	−1.73403
$141$	−1.40972e9	−0.300363
$142$	7.61727e9	1.57218
$143$	8.73419e9	1.74667
$144$	4.48477e9	0.869179
$145$	1.18505e10	2.22629
$146$	3.58101e9	0.652256
$147$	4.20880e9	0.743414
$148$	5.34411e9	0.915583
$149$	−1.37424e9	−0.228415	−0.114208	−	0.993457i	$-0.536433\pi$
$149$	−1.37424e9	−0.228415	−0.114208	+	0.993457i	$0.536433\pi$
$150$	−1.04452e9	−0.168463
$151$	−4.38413e9	−0.686258	−0.343129	−	0.939288i	$-0.611487\pi$
$151$	−4.38413e9	−0.686258	−0.343129	+	0.939288i	$0.611487\pi$
$152$	−2.35501e8	−0.0357847
$153$	0	0
$154$	−2.57631e10	−3.69110
$155$	−1.68235e9	−0.234112
$156$	3.20586e9	0.433395
$157$	−8.04346e9	−1.05656	−0.528280	−	0.849070i	$-0.677163\pi$
$157$	−8.04346e9	−1.05656	−0.528280	+	0.849070i	$0.677163\pi$
$158$	1.33894e9	0.170925
$159$	−2.69750e9	−0.334714
$160$	−1.29620e10	−1.56363
$161$	−7.96158e9	−0.933863
$162$	−5.81713e9	−0.663577
$163$	5.04472e9	0.559749	0.279874	−	0.960037i	$-0.409707\pi$
$163$	5.04472e9	0.559749	0.279874	+	0.960037i	$0.409707\pi$
$164$	6.23614e8	0.0673160
$165$	−7.47483e9	−0.785097
$166$	−1.37352e10	−1.40394
$167$	−1.88827e10	−1.87862	−0.939311	−	0.343066i	$-0.888535\pi$
$167$	−1.88827e10	−1.87862	−0.939311	+	0.343066i	$0.888535\pi$
$168$	7.37515e8	0.0714297
$169$	1.87437e9	0.176752
$170$	0	0
$171$	3.24436e9	0.290166
$172$	2.43680e9	0.212296
$173$	−3.03545e9	−0.257642	−0.128821	−	0.991668i	$-0.541119\pi$
$173$	−3.03545e9	−0.257642	−0.128821	+	0.991668i	$0.541119\pi$
$174$	1.42176e10	1.17586
$175$	5.77137e9	0.465166
$176$	−2.18719e10	−1.71822
$177$	−1.14448e9	−0.0876451
$178$	−1.76225e9	−0.131576
$179$	−9.45985e9	−0.688724	−0.344362	−	0.938837i	$-0.611905\pi$
$179$	−9.45985e9	−0.688724	−0.344362	+	0.938837i	$0.611905\pi$
$180$	1.20478e10	0.855423
$181$	7.53245e9	0.521654	0.260827	−	0.965386i	$-0.416005\pi$
$181$	7.53245e9	0.521654	0.260827	+	0.965386i	$0.416005\pi$
$182$	−3.68088e10	−2.48674
$183$	−8.15574e9	−0.537568
$184$	−8.83362e8	−0.0568144
$185$	−1.78026e10	−1.11741
$186$	−2.01838e9	−0.123650
$187$	0	0
$188$	−1.10811e10	−0.646955
$189$	−2.26344e10	−1.29030
$190$	−1.00589e10	−0.559966
$191$	7.27813e9	0.395703	0.197852	−	0.980232i	$-0.436604\pi$
$191$	7.27813e9	0.395703	0.197852	+	0.980232i	$0.436604\pi$
$192$	−6.89698e9	−0.366272
$193$	7.60493e9	0.394537	0.197268	−	0.980350i	$-0.436793\pi$
$193$	7.60493e9	0.394537	0.197268	+	0.980350i	$0.436793\pi$
$194$	−4.78531e10	−2.42550
$195$	−1.06796e10	−0.528930
$196$	3.30834e10	1.60125
$197$	−2.18071e10	−1.03157	−0.515787	−	0.856717i	$-0.672500\pi$
$197$	−2.18071e10	−1.03157	−0.515787	+	0.856717i	$0.672500\pi$
$198$	3.93798e10	1.82088
$199$	1.40181e10	0.633652	0.316826	−	0.948484i	$-0.397383\pi$
$199$	1.40181e10	0.633652	0.316826	+	0.948484i	$0.397383\pi$
$200$	6.40351e8	0.0282998
$201$	−1.95963e8	−0.00846821
$202$	−5.27921e10	−2.23094
$203$	−7.85577e10	−3.24681
$204$	0	0
$205$	−2.07742e9	−0.0821547
$206$	3.75047e10	1.45105
$207$	1.21695e10	0.460689
$208$	−3.12492e10	−1.15759
$209$	−1.58225e10	−0.573610
$210$	3.15014e10	1.11775
$211$	−3.40494e10	−1.18260	−0.591301	−	0.806451i	$-0.701385\pi$
$211$	−3.40494e10	−1.18260	−0.591301	+	0.806451i	$0.701385\pi$
$212$	−2.12038e10	−0.720944
$213$	−1.46505e10	−0.487691
$214$	5.48442e10	1.78759
$215$	−8.11761e9	−0.259093
$216$	−2.51135e9	−0.0784993
$217$	1.11524e10	0.341427
$218$	1.92463e10	0.577157
$219$	−6.88746e9	−0.202330
$220$	−5.87561e10	−1.69103
$221$	0	0
$222$	−2.13586e10	−0.590180
$223$	−1.18689e10	−0.321396	−0.160698	−	0.987004i	$-0.551374\pi$
$223$	−1.18689e10	−0.321396	−0.160698	+	0.987004i	$0.551374\pi$
$224$	8.59259e10	2.28039
$225$	−8.82173e9	−0.229473
$226$	2.76941e10	0.706154
$227$	−4.22158e10	−1.05526	−0.527628	−	0.849475i	$-0.676919\pi$
$227$	−4.22158e10	−1.05526	−0.527628	+	0.849475i	$0.676919\pi$
$228$	−5.80760e9	−0.142328
$229$	3.83719e10	0.922047	0.461024	−	0.887388i	$-0.347482\pi$
$229$	3.83719e10	0.922047	0.461024	+	0.887388i	$0.347482\pi$
$230$	−3.77309e10	−0.889042
$231$	4.95510e10	1.14498
$232$	−8.71622e9	−0.197530
$233$	−1.60290e9	−0.0356290	−0.0178145	−	0.999841i	$-0.505671\pi$
$233$	−1.60290e9	−0.0356290	−0.0178145	+	0.999841i	$0.505671\pi$
$234$	5.62634e10	1.22675
$235$	3.69142e10	0.789565
$236$	−8.99620e9	−0.188780
$237$	−2.57522e9	−0.0530209
$238$	0	0
$239$	−5.18864e10	−1.02864	−0.514320	−	0.857598i	$-0.671956\pi$
$239$	−5.18864e10	−1.02864	−0.514320	+	0.857598i	$0.671956\pi$
$240$	2.67434e10	0.520315
$241$	4.27612e10	0.816532	0.408266	−	0.912863i	$-0.366134\pi$
$241$	4.27612e10	0.816532	0.408266	+	0.912863i	$0.366134\pi$
$242$	−1.17975e11	−2.21117
$243$	5.36644e10	0.987320
$244$	−6.41084e10	−1.15787
$245$	−1.10210e11	−1.95421
$246$	−2.49237e9	−0.0433915
$247$	−2.26062e10	−0.386448
$248$	1.23739e9	0.0207718
$249$	2.64174e10	0.435504
$250$	−6.97316e10	−1.12902
$251$	−3.86901e10	−0.615273	−0.307637	−	0.951504i	$-0.599538\pi$
$251$	−3.86901e10	−0.615273	−0.307637	+	0.951504i	$0.599538\pi$
$252$	−7.98653e10	−1.24754
$253$	−5.93499e10	−0.910705
$254$	2.70582e10	0.407894
$255$	0	0
$256$	7.75598e10	1.12864
$257$	−3.96876e10	−0.567487	−0.283743	−	0.958900i	$-0.591576\pi$
$257$	−3.96876e10	−0.567487	−0.283743	+	0.958900i	$0.591576\pi$
$258$	−9.73905e9	−0.136845
$259$	1.18015e11	1.62962
$260$	−8.39471e10	−1.13927
$261$	1.20078e11	1.60170
$262$	−2.45507e10	−0.321890
$263$	−4.03518e10	−0.520070	−0.260035	−	0.965599i	$-0.583734\pi$
$263$	−4.03518e10	−0.520070	−0.260035	+	0.965599i	$0.583734\pi$
$264$	5.49783e9	0.0696584
$265$	7.06353e10	0.879864
$266$	6.66812e10	0.816650
$267$	3.38938e9	0.0408149
$268$	−1.54037e9	−0.0182398
$269$	−2.49013e10	−0.289959	−0.144980	−	0.989435i	$-0.546312\pi$
$269$	−2.49013e10	−0.289959	−0.144980	+	0.989435i	$0.546312\pi$
$270$	−1.07267e11	−1.22837
$271$	−5.46121e10	−0.615074	−0.307537	−	0.951536i	$-0.599505\pi$
$271$	−5.46121e10	−0.615074	−0.307537	+	0.951536i	$0.599505\pi$
$272$	0	0
$273$	7.07954e10	0.771388
$274$	−1.94488e11	−2.08456
$275$	4.30229e10	0.453631
$276$	−2.17842e10	−0.225970
$277$	−5.60797e10	−0.572330	−0.286165	−	0.958180i	$-0.592381\pi$
$277$	−5.60797e10	−0.572330	−0.286165	+	0.958180i	$0.592381\pi$
$278$	7.58266e9	0.0761412
$279$	−1.70467e10	−0.168431
$280$	−1.93122e10	−0.187767
$281$	1.76224e10	0.168611	0.0843057	−	0.996440i	$-0.473133\pi$
$281$	1.76224e10	0.168611	0.0843057	+	0.996440i	$0.473133\pi$
$282$	4.42876e10	0.417024
$283$	1.40836e11	1.30520	0.652598	−	0.757705i	$-0.273679\pi$
$283$	1.40836e11	1.30520	0.652598	+	0.757705i	$0.273679\pi$
$284$	−1.15161e11	−1.05044
$285$	1.93467e10	0.173702
$286$	−2.74392e11	−2.42507
$287$	1.37713e10	0.119814
$288$	−1.31341e11	−1.12495
$289$	0	0
$290$	−3.72295e11	−3.09098
$291$	9.20372e10	0.752393
$292$	−5.41391e10	−0.435801
$293$	−8.38614e10	−0.664749	−0.332375	−	0.943147i	$-0.607850\pi$
$293$	−8.38614e10	−0.664749	−0.332375	+	0.943147i	$0.607850\pi$
$294$	−1.32223e11	−1.03215
$295$	2.99687e10	0.230393
$296$	1.30941e10	0.0991429
$297$	−1.68729e11	−1.25830
$298$	4.31730e10	0.317132
$299$	−8.47955e10	−0.613553
$300$	1.57914e10	0.112558
$301$	5.38120e10	0.377859
$302$	1.37731e11	0.952799
$303$	1.01537e11	0.692039
$304$	5.66097e10	0.380154
$305$	2.13562e11	1.41311
$306$	0	0
$307$	−1.75664e11	−1.12865	−0.564325	−	0.825553i	$-0.690863\pi$
$307$	−1.75664e11	−1.12865	−0.564325	+	0.825553i	$0.690863\pi$
$308$	3.89497e11	2.46619
$309$	−7.21338e10	−0.450118
$310$	5.28524e10	0.325040
$311$	2.63974e11	1.60007	0.800037	−	0.599951i	$-0.204813\pi$
$311$	2.63974e11	1.60007	0.800037	+	0.599951i	$0.204813\pi$
$312$	7.85496e9	0.0469297
$313$	2.54781e10	0.150044	0.0750220	−	0.997182i	$-0.476097\pi$
$313$	2.54781e10	0.150044	0.0750220	+	0.997182i	$0.476097\pi$
$314$	2.52692e11	1.46693
$315$	2.66052e11	1.52254
$316$	−2.02426e10	−0.114202
$317$	−2.50051e11	−1.39079	−0.695394	−	0.718628i	$-0.744770\pi$
$317$	−2.50051e11	−1.39079	−0.695394	+	0.718628i	$0.744770\pi$
$318$	8.47442e10	0.464716
$319$	−5.85612e11	−3.16630
$320$	1.80601e11	0.962820
$321$	−1.05483e11	−0.554512
$322$	2.50120e11	1.29657
$323$	0	0
$324$	8.79456e10	0.443365
$325$	6.14684e10	0.305617
$326$	−1.58484e11	−0.777154
$327$	−3.70170e10	−0.179034
$328$	1.52797e9	0.00728924
$329$	−2.44706e11	−1.15150
$330$	2.34828e11	1.09003
$331$	3.65757e11	1.67482	0.837408	−	0.546579i	$-0.184070\pi$
$331$	3.65757e11	1.67482	0.837408	+	0.546579i	$0.184070\pi$
$332$	2.07654e11	0.938037
$333$	−1.80389e11	−0.803917
$334$	5.93216e11	2.60828
$335$	5.13138e9	0.0222604
$336$	−1.77283e11	−0.758825
$337$	−4.56163e11	−1.92657	−0.963287	−	0.268474i	$-0.913481\pi$
$337$	−4.56163e11	−1.92657	−0.963287	+	0.268474i	$0.913481\pi$
$338$	−5.88850e10	−0.245403
$339$	−5.32649e10	−0.219049
$340$	0	0
$341$	8.31356e10	0.332960
$342$	−1.01924e11	−0.402866
$343$	3.07334e11	1.19891
$344$	5.97060e9	0.0229882
$345$	7.25690e10	0.275781
$346$	9.53615e10	0.357709
$347$	3.36335e11	1.24534	0.622671	−	0.782483i	$-0.286047\pi$
$347$	3.36335e11	1.24534	0.622671	+	0.782483i	$0.286047\pi$
$348$	−2.14947e11	−0.785643
$349$	−3.19659e8	−0.00115338	−0.000576690	−	1.00000i	$-0.500184\pi$
$349$	−3.19659e8	−0.00115338	−0.000576690		1.00000i	$0.500184\pi$
$350$	−1.81313e11	−0.645835
$351$	−2.41069e11	−0.847734
$352$	6.40538e11	2.22384
$353$	−5.74697e10	−0.196994	−0.0984970	−	0.995137i	$-0.531403\pi$
$353$	−5.74697e10	−0.196994	−0.0984970	+	0.995137i	$0.531403\pi$
$354$	3.59548e10	0.121686
$355$	3.83631e11	1.28199
$356$	2.66423e10	0.0879117
$357$	0	0
$358$	2.97189e11	0.956224
$359$	1.28501e10	0.0408302	0.0204151	−	0.999792i	$-0.493501\pi$
$359$	1.28501e10	0.0408302	0.0204151	+	0.999792i	$0.493501\pi$
$360$	2.95193e10	0.0926286
$361$	−2.81735e11	−0.873089
$362$	−2.36638e11	−0.724264
$363$	2.26905e11	0.685906
$364$	5.56489e11	1.66150
$365$	1.80352e11	0.531866
$366$	2.56220e11	0.746359
$367$	1.20128e11	0.345658	0.172829	−	0.984952i	$-0.444709\pi$
$367$	1.20128e11	0.345658	0.172829	+	0.984952i	$0.444709\pi$
$368$	2.12342e11	0.603561
$369$	−2.10499e10	−0.0591060
$370$	5.59285e11	1.55141
$371$	−4.68245e11	−1.28319
$372$	3.05147e10	0.0826163
$373$	2.29521e11	0.613949	0.306975	−	0.951718i	$-0.400683\pi$
$373$	2.29521e11	0.613949	0.306975	+	0.951718i	$0.400683\pi$
$374$	0	0
$375$	1.34117e11	0.350221
$376$	−2.71509e10	−0.0700549
$377$	−8.36685e11	−2.13317
$378$	7.11079e11	1.79145
$379$	1.85213e10	0.0461099	0.0230549	−	0.999734i	$-0.492661\pi$
$379$	1.85213e10	0.0461099	0.0230549	+	0.999734i	$0.492661\pi$
$380$	1.52075e11	0.374138
$381$	−5.20418e10	−0.126529
$382$	−2.28649e11	−0.549394
$383$	−7.04308e11	−1.67251	−0.836253	−	0.548343i	$-0.815259\pi$
$383$	−7.04308e11	−1.67251	−0.836253	+	0.548343i	$0.815259\pi$
$384$	−3.67695e10	−0.0862974
$385$	−1.29752e12	−3.00981
$386$	−2.38915e11	−0.547774
$387$	−8.22534e10	−0.186404
$388$	7.23461e11	1.62059
$389$	−8.72755e11	−1.93250	−0.966249	−	0.257611i	$-0.917065\pi$
$389$	−8.72755e11	−1.93250	−0.966249	+	0.257611i	$0.917065\pi$
$390$	3.35508e11	0.734365
$391$	0	0
$392$	8.10605e10	0.173389
$393$	4.72190e10	0.0998506
$394$	6.85090e11	1.43224
$395$	6.74335e10	0.139376
$396$	−5.95359e11	−1.21661
$397$	4.55747e11	0.920802	0.460401	−	0.887711i	$-0.347706\pi$
$397$	4.55747e11	0.920802	0.460401	+	0.887711i	$0.347706\pi$
$398$	−4.40392e11	−0.879762
$399$	−1.28250e11	−0.253326
$400$	−1.53927e11	−0.300639
$401$	−8.98679e11	−1.73562	−0.867810	−	0.496896i	$-0.834473\pi$
$401$	−8.98679e11	−1.73562	−0.867810	+	0.496896i	$0.834473\pi$
$402$	6.15634e9	0.0117572
$403$	1.18779e11	0.224320
$404$	7.98131e11	1.49059
$405$	−2.92970e11	−0.541097
$406$	2.46796e12	4.50787
$407$	8.79744e11	1.58921
$408$	0	0
$409$	−1.95210e11	−0.344943	−0.172472	−	0.985015i	$-0.555175\pi$
$409$	−1.95210e11	−0.344943	−0.172472	+	0.985015i	$0.555175\pi$
$410$	6.52640e10	0.114063
$411$	3.74064e11	0.646632
$412$	−5.67010e11	−0.969513
$413$	−1.98664e11	−0.336004
$414$	−3.82317e11	−0.639620
$415$	−6.91752e11	−1.14481
$416$	9.15161e11	1.49823
$417$	−1.45839e10	−0.0236191
$418$	4.97078e11	0.796400
$419$	1.38040e11	0.218796	0.109398	−	0.993998i	$-0.465108\pi$
$419$	1.38040e11	0.218796	0.109398	+	0.993998i	$0.465108\pi$
$420$	−4.76250e11	−0.746815
$421$	7.45047e11	1.15588	0.577942	−	0.816078i	$-0.303856\pi$
$421$	7.45047e11	1.15588	0.577942	+	0.816078i	$0.303856\pi$
$422$	1.06969e12	1.64192
$423$	3.74041e11	0.568051
$424$	−5.19531e10	−0.0780666
$425$	0	0
$426$	4.60259e11	0.677109
$427$	−1.41571e12	−2.06087
$428$	−8.29155e11	−1.19437
$429$	5.27747e11	0.752259
$430$	2.55022e11	0.359724
$431$	−1.02134e11	−0.142568	−0.0712841	−	0.997456i	$-0.522710\pi$
$431$	−1.02134e11	−0.142568	−0.0712841	+	0.997456i	$0.522710\pi$
$432$	6.03678e11	0.833927
$433$	−1.06370e12	−1.45420	−0.727102	−	0.686530i	$-0.759133\pi$
$433$	−1.06370e12	−1.45420	−0.727102	+	0.686530i	$0.759133\pi$
$434$	−3.50361e11	−0.474037
$435$	7.16045e11	0.958824
$436$	−2.90973e11	−0.385624
$437$	1.53612e11	0.201492
$438$	2.16376e11	0.280915
$439$	1.32178e12	1.69851	0.849254	−	0.527985i	$-0.177052\pi$
$439$	1.32178e12	1.69851	0.849254	+	0.527985i	$0.177052\pi$
$440$	−1.43963e11	−0.183111
$441$	−1.11672e12	−1.40595
$442$	0	0
$443$	1.29502e12	1.59757	0.798784	−	0.601618i	$-0.205477\pi$
$443$	1.29502e12	1.59757	0.798784	+	0.601618i	$0.205477\pi$
$444$	3.22907e11	0.394325
$445$	−8.87525e10	−0.107290
$446$	3.72873e11	0.446225
$447$	−8.30359e10	−0.0983744
$448$	−1.19721e12	−1.40417
$449$	4.24727e11	0.493176	0.246588	−	0.969120i	$-0.420691\pi$
$449$	4.24727e11	0.493176	0.246588	+	0.969120i	$0.420691\pi$
$450$	2.77142e11	0.318601
$451$	1.02659e11	0.116843
$452$	−4.18690e11	−0.471813
$453$	−2.64903e11	−0.295559
$454$	1.32624e12	1.46512
$455$	−1.85381e12	−2.02775
$456$	−1.42297e10	−0.0154118
$457$	−4.27181e11	−0.458131	−0.229065	−	0.973411i	$-0.573567\pi$
$457$	−4.27181e11	−0.458131	−0.229065	+	0.973411i	$0.573567\pi$
$458$	−1.20549e12	−1.28017
$459$	0	0
$460$	5.70431e11	0.594008
$461$	−1.13997e12	−1.17554	−0.587771	−	0.809027i	$-0.699994\pi$
$461$	−1.13997e12	−1.17554	−0.587771	+	0.809027i	$0.699994\pi$
$462$	−1.55669e12	−1.58969
$463$	1.72036e12	1.73982	0.869909	−	0.493213i	$-0.164178\pi$
$463$	1.72036e12	1.73982	0.869909	+	0.493213i	$0.164178\pi$
$464$	2.09520e12	2.09843
$465$	−1.01653e11	−0.100828
$466$	5.03564e10	0.0494673
$467$	−1.58108e12	−1.53825	−0.769125	−	0.639099i	$-0.779307\pi$
$467$	−1.58108e12	−1.53825	−0.769125	+	0.639099i	$0.779307\pi$
$468$	−8.50612e11	−0.819643
$469$	−3.40162e10	−0.0324644
$470$	−1.15969e12	−1.09623
$471$	−4.86010e11	−0.455042
$472$	−2.20424e10	−0.0204418
$473$	4.01144e11	0.368489
$474$	8.09029e10	0.0736142
$475$	−1.11354e11	−0.100365
$476$	0	0
$477$	7.15727e11	0.633016
$478$	1.63006e12	1.42816
$479$	1.08848e12	0.944737	0.472369	−	0.881401i	$-0.343399\pi$
$479$	1.08848e12	0.944737	0.472369	+	0.881401i	$0.343399\pi$
$480$	−7.83206e11	−0.673427
$481$	1.25692e12	1.07067
$482$	−1.34338e12	−1.13367
$483$	−4.81063e11	−0.402198
$484$	1.78360e12	1.47738
$485$	−2.41004e12	−1.97782
$486$	−1.68591e12	−1.37079
$487$	−2.07370e12	−1.67057	−0.835287	−	0.549815i	$-0.814698\pi$
$487$	−2.07370e12	−1.67057	−0.835287	+	0.549815i	$0.814698\pi$
$488$	−1.57078e11	−0.125379
$489$	3.04818e11	0.241074
$490$	3.46233e12	2.71323
$491$	−1.27855e11	−0.0992772	−0.0496386	−	0.998767i	$-0.515807\pi$
$491$	−1.27855e11	−0.0992772	−0.0496386	+	0.998767i	$0.515807\pi$
$492$	3.76806e10	0.0289918
$493$	0	0
$494$	7.10194e11	0.536544
$495$	1.98330e12	1.48479
$496$	−2.97443e11	−0.220666
$497$	−2.54311e12	−1.86965
$498$	−8.29924e11	−0.604653
$499$	1.57050e12	1.13393	0.566964	−	0.823743i	$-0.308118\pi$
$499$	1.57050e12	1.13393	0.566964	+	0.823743i	$0.308118\pi$
$500$	1.05423e12	0.754345
$501$	−1.14095e12	−0.809090
$502$	1.21548e12	0.854245
$503$	1.11074e12	0.773670	0.386835	−	0.922149i	$-0.373568\pi$
$503$	1.11074e12	0.773670	0.386835	+	0.922149i	$0.373568\pi$
$504$	−1.95685e11	−0.135089
$505$	−2.65878e12	−1.81916
$506$	1.86453e12	1.26442
$507$	1.13255e11	0.0761241
$508$	−4.09076e11	−0.272532
$509$	−2.12203e12	−1.40127	−0.700636	−	0.713519i	$-0.747100\pi$
$509$	−2.12203e12	−1.40127	−0.700636	+	0.713519i	$0.747100\pi$
$510$	0	0
$511$	−1.19556e12	−0.775670
$512$	−2.12504e12	−1.36663
$513$	4.36711e11	0.278398
$514$	1.24682e12	0.787898
$515$	1.88886e12	1.18323
$516$	1.47239e11	0.0914320
$517$	−1.82417e12	−1.12294
$518$	−3.70753e12	−2.26256
$519$	−1.83411e11	−0.110962
$520$	−2.05686e11	−0.123364
$521$	1.64335e12	0.977150	0.488575	−	0.872522i	$-0.337517\pi$
$521$	1.64335e12	0.977150	0.488575	+	0.872522i	$0.337517\pi$
$522$	−3.77236e12	−2.22380
$523$	−1.94542e12	−1.13699	−0.568493	−	0.822688i	$-0.692473\pi$
$523$	−1.94542e12	−1.13699	−0.568493	+	0.822688i	$0.692473\pi$
$524$	3.71167e11	0.215069
$525$	3.48724e11	0.200339
$526$	1.26769e12	0.722065
$527$	0	0
$528$	−1.32157e12	−0.740008
$529$	−1.22496e12	−0.680096
$530$	−2.21907e12	−1.22160
$531$	3.03664e11	0.165756
$532$	−1.00811e12	−0.545640
$533$	1.46673e11	0.0787184
$534$	−1.06480e11	−0.0566674
$535$	2.76213e12	1.45765
$536$	−3.77420e9	−0.00197507
$537$	−5.71593e11	−0.296621
$538$	7.82297e11	0.402579
$539$	5.44617e12	2.77934
$540$	1.62170e12	0.820729
$541$	−2.58123e12	−1.29551	−0.647753	−	0.761850i	$-0.724291\pi$
$541$	−2.58123e12	−1.29551	−0.647753	+	0.761850i	$0.724291\pi$
$542$	1.71569e12	0.853967
$543$	4.55133e11	0.224667
$544$	0	0
$545$	9.69309e11	0.470628
$546$	−2.22410e12	−1.07099
$547$	−8.12819e11	−0.388196	−0.194098	−	0.980982i	$-0.562178\pi$
$547$	−8.12819e11	−0.388196	−0.194098	+	0.980982i	$0.562178\pi$
$548$	2.94034e12	1.39279
$549$	2.16396e12	1.01666
$550$	−1.35160e12	−0.629820
$551$	1.51570e12	0.700539
$552$	−5.33754e10	−0.0244689
$553$	−4.47020e11	−0.203266
$554$	1.76179e12	0.794622
$555$	−1.07569e12	−0.481248
$556$	−1.14637e11	−0.0508733
$557$	2.77064e12	1.21964	0.609819	−	0.792540i	$-0.291242\pi$
$557$	2.77064e12	1.21964	0.609819	+	0.792540i	$0.291242\pi$
$558$	5.35538e11	0.233850
$559$	5.73129e11	0.248256
$560$	4.64226e12	1.99472
$561$	0	0
$562$	−5.53623e11	−0.234100
$563$	−3.89099e12	−1.63220	−0.816098	−	0.577914i	$-0.803867\pi$
$563$	−3.89099e12	−1.63220	−0.816098	+	0.577914i	$0.803867\pi$
$564$	−6.69556e11	−0.278632
$565$	1.39477e12	0.575816
$566$	−4.42449e12	−1.81213
$567$	1.94211e12	0.789133
$568$	−2.82165e11	−0.113746
$569$	1.29595e12	0.518304	0.259152	−	0.965837i	$-0.416557\pi$
$569$	1.29595e12	0.518304	0.259152	+	0.965837i	$0.416557\pi$
$570$	−6.07792e11	−0.241167
$571$	3.67635e12	1.44728	0.723642	−	0.690175i	$-0.242467\pi$
$571$	3.67635e12	1.44728	0.723642	+	0.690175i	$0.242467\pi$
$572$	4.14837e12	1.62030
$573$	4.39767e11	0.170422
$574$	−4.32638e11	−0.166349
$575$	−4.17686e11	−0.159347
$576$	1.82998e12	0.692699
$577$	−7.12314e11	−0.267535	−0.133767	−	0.991013i	$-0.542707\pi$
$577$	−7.12314e11	−0.267535	−0.133767	+	0.991013i	$0.542707\pi$
$578$	0	0
$579$	4.59513e11	0.169920
$580$	5.62850e12	2.06522
$581$	4.58565e12	1.66959
$582$	−2.89143e12	−1.04462
$583$	−3.49055e12	−1.25137
$584$	−1.32651e11	−0.0471903
$585$	2.83361e12	1.00032
$586$	2.63458e12	0.922937
$587$	2.45642e11	0.0853948	0.0426974	−	0.999088i	$-0.486405\pi$
$587$	2.45642e11	0.0853948	0.0426974	+	0.999088i	$0.486405\pi$
$588$	1.99900e12	0.689628
$589$	−2.15175e11	−0.0736670
$590$	−9.41493e11	−0.319877
$591$	−1.31765e12	−0.444280
$592$	−3.14755e12	−1.05323
$593$	−7.70573e11	−0.255899	−0.127949	−	0.991781i	$-0.540839\pi$
$593$	−7.70573e11	−0.255899	−0.127949	+	0.991781i	$0.540839\pi$
$594$	5.30076e12	1.74703
$595$	0	0
$596$	−6.52706e11	−0.211890
$597$	8.47018e11	0.272903
$598$	2.66392e12	0.851856
$599$	−4.21472e12	−1.33767	−0.668834	−	0.743412i	$-0.733206\pi$
$599$	−4.21472e12	−1.33767	−0.668834	+	0.743412i	$0.733206\pi$
$600$	3.86920e10	0.0121882
$601$	1.24558e12	0.389437	0.194719	−	0.980859i	$-0.437621\pi$
$601$	1.24558e12	0.389437	0.194719	+	0.980859i	$0.437621\pi$
$602$	−1.69055e12	−0.524619
$603$	5.19948e10	0.0160152
$604$	−2.08227e12	−0.636608
$605$	−5.94163e12	−1.80304
$606$	−3.18986e12	−0.960826
$607$	3.32695e12	0.994711	0.497355	−	0.867547i	$-0.334305\pi$
$607$	3.32695e12	0.994711	0.497355	+	0.867547i	$0.334305\pi$
$608$	−1.65787e12	−0.492021
$609$	−4.74670e12	−1.39834
$610$	−6.70924e12	−1.96195
$611$	−2.60626e12	−0.756541
$612$	0	0
$613$	2.74693e12	0.785733	0.392867	−	0.919595i	$-0.371483\pi$
$613$	2.74693e12	0.785733	0.392867	+	0.919595i	$0.371483\pi$
$614$	5.51863e12	1.56702
$615$	−1.25524e11	−0.0353826
$616$	9.54340e11	0.267048
$617$	−2.28297e12	−0.634187	−0.317094	−	0.948394i	$-0.602707\pi$
$617$	−2.28297e12	−0.634187	−0.317094	+	0.948394i	$0.602707\pi$
$618$	2.26615e12	0.624943
$619$	−1.30761e10	−0.00357989	−0.00178995	−	0.999998i	$-0.500570\pi$
$619$	−1.30761e10	−0.00357989	−0.00178995	+	0.999998i	$0.500570\pi$
$620$	−7.99043e11	−0.217174
$621$	1.63809e12	0.442005
$622$	−8.29299e12	−2.22154
$623$	5.88344e11	0.156472
$624$	−1.88817e12	−0.498552
$625$	−4.58663e12	−1.20236
$626$	−8.00418e11	−0.208321
$627$	−9.56044e11	−0.247044
$628$	−3.82030e12	−0.980119
$629$	0	0
$630$	−8.35827e12	−2.11390
$631$	1.82848e12	0.459154	0.229577	−	0.973291i	$-0.426266\pi$
$631$	1.82848e12	0.459154	0.229577	+	0.973291i	$0.426266\pi$
$632$	−4.95982e10	−0.0123663
$633$	−2.05737e12	−0.509325
$634$	7.85556e12	1.93097
$635$	1.36274e12	0.332607
$636$	−1.28120e12	−0.310498
$637$	7.78114e12	1.87248
$638$	1.83975e13	4.39608
$639$	3.88722e12	0.922328
$640$	9.62828e11	0.226850
$641$	4.34210e12	1.01587	0.507936	−	0.861395i	$-0.330409\pi$
$641$	4.34210e12	1.01587	0.507936	+	0.861395i	$0.330409\pi$
$642$	3.31385e12	0.769884
$643$	−7.89392e11	−0.182114	−0.0910570	−	0.995846i	$-0.529025\pi$
$643$	−7.89392e11	−0.182114	−0.0910570	+	0.995846i	$0.529025\pi$
$644$	−3.78141e12	−0.866298
$645$	−4.90491e11	−0.111587
$646$	0	0
$647$	2.49662e11	0.0560122	0.0280061	−	0.999608i	$-0.491084\pi$
$647$	2.49662e11	0.0560122	0.0280061	+	0.999608i	$0.491084\pi$
$648$	2.15483e11	0.0480093
$649$	−1.48095e12	−0.327672
$650$	−1.93108e12	−0.424318
$651$	6.73859e11	0.147047
$652$	2.39603e12	0.519251
$653$	2.48710e12	0.535284	0.267642	−	0.963518i	$-0.413755\pi$
$653$	2.48710e12	0.535284	0.267642	+	0.963518i	$0.413755\pi$
$654$	1.16292e12	0.248571
$655$	−1.23645e12	−0.262477
$656$	−3.67293e11	−0.0774364
$657$	1.82745e12	0.382650
$658$	7.68765e12	1.59874
$659$	−1.78184e12	−0.368031	−0.184015	−	0.982923i	$-0.558910\pi$
$659$	−1.78184e12	−0.368031	−0.184015	+	0.982923i	$0.558910\pi$
$660$	−3.55022e12	−0.728296
$661$	−3.14479e11	−0.0640744	−0.0320372	−	0.999487i	$-0.510200\pi$
$661$	−3.14479e11	−0.0640744	−0.0320372	+	0.999487i	$0.510200\pi$
$662$	−1.14906e13	−2.32531
$663$	0	0
$664$	5.08792e11	0.101574
$665$	3.35829e12	0.665918
$666$	5.66708e12	1.11616
$667$	5.68538e12	1.11223
$668$	−8.96847e12	−1.74271
$669$	−7.17157e11	−0.138419
$670$	−1.61207e11	−0.0309063
$671$	−1.05535e13	−2.00976
$672$	5.19191e12	0.982121
$673$	−6.58350e11	−0.123706	−0.0618528	−	0.998085i	$-0.519701\pi$
$673$	−6.58350e11	−0.123706	−0.0618528	+	0.998085i	$0.519701\pi$
$674$	1.43308e13	2.67485
$675$	−1.18746e12	−0.220167
$676$	8.90246e11	0.163965
$677$	−3.47369e12	−0.635540	−0.317770	−	0.948168i	$-0.602934\pi$
$677$	−3.47369e12	−0.635540	−0.317770	+	0.948168i	$0.602934\pi$
$678$	1.67336e12	0.304128
$679$	1.59763e13	2.88444
$680$	0	0
$681$	−2.55080e12	−0.454480
$682$	−2.61178e12	−0.462282
$683$	−3.82712e12	−0.672944	−0.336472	−	0.941693i	$-0.609234\pi$
$683$	−3.82712e12	−0.672944	−0.336472	+	0.941693i	$0.609234\pi$
$684$	1.54093e12	0.269173
$685$	−9.79504e12	−1.69980
$686$	−9.65518e12	−1.66457
$687$	2.31854e12	0.397109
$688$	−1.43521e12	−0.244212
$689$	−4.98708e12	−0.843062
$690$	−2.27982e12	−0.382895
$691$	−6.65485e11	−0.111042	−0.0555210	−	0.998458i	$-0.517682\pi$
$691$	−6.65485e11	−0.111042	−0.0555210	+	0.998458i	$0.517682\pi$
$692$	−1.44171e12	−0.239002
$693$	−1.31474e13	−2.16541
$694$	−1.05662e13	−1.72903
$695$	3.81888e11	0.0620875
$696$	−5.26660e11	−0.0850725
$697$	0	0
$698$	1.00424e10	0.00160135
$699$	−9.68519e10	−0.0153448
$700$	2.74115e12	0.431511
$701$	−8.18142e12	−1.27967	−0.639835	−	0.768513i	$-0.720997\pi$
$701$	−8.18142e12	−1.27967	−0.639835	+	0.768513i	$0.720997\pi$
$702$	7.57340e12	1.17699
$703$	−2.27699e12	−0.351611
$704$	−8.92466e12	−1.36935
$705$	2.23047e12	0.340052
$706$	1.80546e12	0.273506
$707$	1.76252e13	2.65306
$708$	−5.43578e11	−0.0813040
$709$	−1.25644e13	−1.86739	−0.933695	−	0.358069i	$-0.883435\pi$
$709$	−1.25644e13	−1.86739	−0.933695	+	0.358069i	$0.883435\pi$
$710$	−1.20521e13	−1.77992
$711$	6.83285e11	0.100274
$712$	6.52786e10	0.00951943
$713$	−8.07118e11	−0.116959
$714$	0	0
$715$	−1.38193e13	−1.97747
$716$	−4.49302e12	−0.638896
$717$	−3.13514e12	−0.443017
$718$	−4.03698e11	−0.0566887
$719$	−2.91184e12	−0.406337	−0.203169	−	0.979144i	$-0.565124\pi$
$719$	−2.91184e12	−0.406337	−0.203169	+	0.979144i	$0.565124\pi$
$720$	−7.09584e12	−0.984028
$721$	−1.25213e13	−1.72561
$722$	8.85096e12	1.21220
$723$	2.58376e12	0.351666
$724$	3.57759e12	0.483913
$725$	−4.12134e12	−0.554010
$726$	−7.12843e12	−0.952311
$727$	6.75451e12	0.896786	0.448393	−	0.893836i	$-0.351996\pi$
$727$	6.75451e12	0.896786	0.448393	+	0.893836i	$0.351996\pi$
$728$	1.36350e12	0.179914
$729$	−4.02040e11	−0.0527225
$730$	−5.66590e12	−0.738442
$731$	0	0
$732$	−3.87363e12	−0.498675
$733$	7.06417e12	0.903843	0.451922	−	0.892058i	$-0.350739\pi$
$733$	7.06417e12	0.903843	0.451922	+	0.892058i	$0.350739\pi$
$734$	−3.77392e12	−0.479911
$735$	−6.65920e12	−0.841645
$736$	−6.21863e12	−0.781168
$737$	−2.53575e11	−0.0316594
$738$	6.61302e11	0.0820627
$739$	−1.12061e13	−1.38215	−0.691075	−	0.722783i	$-0.742862\pi$
$739$	−1.12061e13	−1.38215	−0.691075	+	0.722783i	$0.742862\pi$
$740$	−8.45549e12	−1.03656
$741$	−1.36594e12	−0.166436
$742$	1.47103e13	1.78158
$743$	−8.45595e12	−1.01792	−0.508959	−	0.860791i	$-0.669970\pi$
$743$	−8.45595e12	−1.01792	−0.508959	+	0.860791i	$0.669970\pi$
$744$	7.47667e10	0.00894602
$745$	2.17434e12	0.258597
$746$	−7.21060e12	−0.852406
$747$	−7.00932e12	−0.823632
$748$	0	0
$749$	−1.83103e13	−2.12583
$750$	−4.21340e12	−0.486247
$751$	1.41553e12	0.162382	0.0811911	−	0.996699i	$-0.474128\pi$
$751$	1.41553e12	0.162382	0.0811911	+	0.996699i	$0.474128\pi$
$752$	6.52651e12	0.744219
$753$	−2.33777e12	−0.264987
$754$	2.62852e13	2.96169
$755$	6.93661e12	0.776937
$756$	−1.07504e13	−1.19695
$757$	−9.02103e12	−0.998446	−0.499223	−	0.866473i	$-0.666381\pi$
$757$	−9.02103e12	−0.998446	−0.499223	+	0.866473i	$0.666381\pi$
$758$	−5.81861e11	−0.0640189
$759$	−3.58610e12	−0.392225
$760$	3.72612e11	0.0405131
$761$	1.71746e13	1.85633	0.928165	−	0.372169i	$-0.121386\pi$
$761$	1.71746e13	1.85633	0.928165	+	0.372169i	$0.121386\pi$
$762$	1.63494e12	0.175673
$763$	−6.42559e12	−0.686361
$764$	3.45680e12	0.367075
$765$	0	0
$766$	2.21264e13	2.32211
$767$	−2.11589e12	−0.220756
$768$	4.68640e12	0.486087
$769$	−4.58214e12	−0.472498	−0.236249	−	0.971693i	$-0.575918\pi$
$769$	−4.58214e12	−0.472498	−0.236249	+	0.971693i	$0.575918\pi$
$770$	4.07626e13	4.17882
$771$	−2.39805e12	−0.244407
$772$	3.61202e12	0.365992
$773$	1.36741e12	0.137750	0.0688750	−	0.997625i	$-0.478059\pi$
$773$	1.36741e12	0.137750	0.0688750	+	0.997625i	$0.478059\pi$
$774$	2.58406e12	0.258803
$775$	5.85082e11	0.0582584
$776$	1.77261e12	0.175484
$777$	7.13080e12	0.701849
$778$	2.74183e13	2.68308
$779$	−2.65706e11	−0.0258513
$780$	−5.07234e12	−0.490662
$781$	−1.89577e13	−1.82329
$782$	0	0
$783$	1.61632e13	1.53674
$784$	−1.94853e13	−1.84198
$785$	1.27264e13	1.19617
$786$	−1.48343e12	−0.138632
$787$	−1.11886e13	−1.03966	−0.519830	−	0.854270i	$-0.674005\pi$
$787$	−1.11886e13	−1.03966	−0.519830	+	0.854270i	$0.674005\pi$
$788$	−1.03574e13	−0.956940
$789$	−2.43818e12	−0.223985
$790$	−2.11848e12	−0.193510
$791$	−9.24597e12	−0.839766
$792$	−1.45874e12	−0.131739
$793$	−1.50782e13	−1.35400
$794$	−1.43177e13	−1.27844
$795$	4.26800e12	0.378942
$796$	6.65801e12	0.587808
$797$	1.02469e13	0.899561	0.449781	−	0.893139i	$-0.351502\pi$
$797$	1.02469e13	0.899561	0.449781	+	0.893139i	$0.351502\pi$
$798$	4.02908e12	0.351717
$799$	0	0
$800$	4.50790e12	0.389107
$801$	−8.99304e11	−0.0771898
$802$	2.82328e13	2.40973
$803$	−8.91234e12	−0.756436
$804$	−9.30739e10	−0.00785554
$805$	1.25969e13	1.05726
$806$	−3.73155e12	−0.311445
$807$	−1.50461e12	−0.124880
$808$	1.95557e12	0.161407
$809$	8.43291e12	0.692165	0.346082	−	0.938204i	$-0.387512\pi$
$809$	8.43291e12	0.692165	0.346082	+	0.938204i	$0.387512\pi$
$810$	9.20390e12	0.751259
$811$	1.23986e13	1.00642	0.503210	−	0.864164i	$-0.332152\pi$
$811$	1.23986e13	1.00642	0.503210	+	0.864164i	$0.332152\pi$
$812$	−3.73116e13	−3.01190
$813$	−3.29983e12	−0.264901
$814$	−2.76379e13	−2.20646
$815$	−7.98180e12	−0.633712
$816$	0	0
$817$	−1.03826e12	−0.0815278
$818$	6.13270e12	0.478918
$819$	−1.87841e13	−1.45886
$820$	−9.86686e11	−0.0762108
$821$	1.11578e13	0.857109	0.428554	−	0.903516i	$-0.359023\pi$
$821$	1.11578e13	0.857109	0.428554	+	0.903516i	$0.359023\pi$
$822$	−1.17515e13	−0.897783
$823$	−2.14178e13	−1.62733	−0.813665	−	0.581335i	$-0.802531\pi$
$823$	−2.14178e13	−1.62733	−0.813665	+	0.581335i	$0.802531\pi$
$824$	−1.38928e12	−0.104983
$825$	2.59957e12	0.195371
$826$	6.24120e12	0.466507
$827$	7.63979e12	0.567946	0.283973	−	0.958832i	$-0.408347\pi$
$827$	7.63979e12	0.567946	0.283973	+	0.958832i	$0.408347\pi$
$828$	5.78001e12	0.427358
$829$	2.44316e13	1.79662	0.898309	−	0.439365i	$-0.144796\pi$
$829$	2.44316e13	1.79662	0.898309	+	0.439365i	$0.144796\pi$
$830$	2.17320e13	1.58945
$831$	−3.38850e12	−0.246492
$832$	−1.27510e13	−0.922548
$833$	0	0
$834$	4.58167e11	0.0327927
$835$	2.98763e13	2.12686
$836$	−7.51501e12	−0.532110
$837$	−2.29460e12	−0.161600
$838$	−4.33663e12	−0.303777
$839$	2.37461e12	0.165449	0.0827244	−	0.996572i	$-0.473638\pi$
$839$	2.37461e12	0.165449	0.0827244	+	0.996572i	$0.473638\pi$
$840$	−1.16690e12	−0.0808681
$841$	4.15911e13	2.86694
$842$	−2.34063e13	−1.60483
$843$	1.06480e12	0.0726179
$844$	−1.61720e13	−1.09704
$845$	−2.96564e12	−0.200108
$846$	−1.17508e13	−0.788682
$847$	3.93873e13	2.62955
$848$	1.24885e13	0.829331
$849$	8.50976e12	0.562125
$850$	0	0
$851$	−8.54095e12	−0.558243
$852$	−6.95836e12	−0.452407
$853$	−7.13731e12	−0.461598	−0.230799	−	0.973001i	$-0.574134\pi$
$853$	−7.13731e12	−0.461598	−0.230799	+	0.973001i	$0.574134\pi$
$854$	4.44758e13	2.86130
$855$	−5.13325e12	−0.328507
$856$	−2.03158e12	−0.129331
$857$	1.20992e12	0.0766203	0.0383102	−	0.999266i	$-0.487803\pi$
$857$	1.20992e12	0.0766203	0.0383102	+	0.999266i	$0.487803\pi$
$858$	−1.65796e13	−1.04444
$859$	−2.16132e13	−1.35441	−0.677203	−	0.735796i	$-0.736808\pi$
$859$	−2.16132e13	−1.35441	−0.677203	+	0.735796i	$0.736808\pi$
$860$	−3.85552e12	−0.240347
$861$	8.32105e11	0.0516017
$862$	3.20863e12	0.197941
$863$	−2.21387e13	−1.35864	−0.679319	−	0.733843i	$-0.737725\pi$
$863$	−2.21387e13	−1.35864	−0.679319	+	0.733843i	$0.737725\pi$
$864$	−1.76792e13	−1.07932
$865$	4.80272e12	0.291685
$866$	3.34172e13	2.01901
$867$	0	0
$868$	5.29689e12	0.316725
$869$	−3.33233e12	−0.198225
$870$	−2.24952e13	−1.33123
$871$	−3.62292e11	−0.0213293
$872$	−7.12939e11	−0.0417569
$873$	−2.44202e13	−1.42294
$874$	−4.82585e12	−0.279752
$875$	2.32807e13	1.34264
$876$	−3.27125e12	−0.187692
$877$	−7.22814e11	−0.0412599	−0.0206300	−	0.999787i	$-0.506567\pi$
$877$	−7.22814e11	−0.0412599	−0.0206300	+	0.999787i	$0.506567\pi$
$878$	−4.15247e13	−2.35820
$879$	−5.06716e12	−0.286296
$880$	3.46059e13	1.94526
$881$	3.21071e12	0.179560	0.0897801	−	0.995962i	$-0.471384\pi$
$881$	3.21071e12	0.179560	0.0897801	+	0.995962i	$0.471384\pi$
$882$	3.50828e13	1.95203
$883$	−2.33032e13	−1.29001	−0.645004	−	0.764179i	$-0.723144\pi$
$883$	−2.33032e13	−1.29001	−0.645004	+	0.764179i	$0.723144\pi$
$884$	0	0
$885$	1.81080e12	0.0992261
$886$	−4.06841e13	−2.21806
$887$	−7.98735e12	−0.433258	−0.216629	−	0.976254i	$-0.569506\pi$
$887$	−7.98735e12	−0.433258	−0.216629	+	0.976254i	$0.569506\pi$
$888$	7.91183e11	0.0426991
$889$	−9.03366e12	−0.485072
$890$	2.78824e12	0.148962
$891$	1.44775e13	0.769564
$892$	−5.63724e12	−0.298143
$893$	4.72139e12	0.248450
$894$	2.60865e12	0.136583
$895$	1.49674e13	0.779729
$896$	−6.38263e12	−0.330837
$897$	−5.12360e12	−0.264247
$898$	−1.33432e13	−0.684725
$899$	−7.96392e12	−0.406638
$900$	−4.18994e12	−0.212871
$901$	0	0
$902$	−3.22512e12	−0.162224
$903$	3.25149e12	0.162737
$904$	−1.02587e12	−0.0510898
$905$	−1.19179e13	−0.590583
$906$	8.32215e12	0.410354
$907$	1.23526e13	0.606072	0.303036	−	0.952979i	$-0.402000\pi$
$907$	1.23526e13	0.606072	0.303036	+	0.952979i	$0.402000\pi$
$908$	−2.00507e13	−0.978910
$909$	−2.69407e13	−1.30879
$910$	5.82391e13	2.81532
$911$	−1.91339e13	−0.920388	−0.460194	−	0.887818i	$-0.652220\pi$
$911$	−1.91339e13	−0.920388	−0.460194	+	0.887818i	$0.652220\pi$
$912$	3.42053e12	0.163726
$913$	3.41839e13	1.62818
$914$	1.34203e13	0.636068
$915$	1.29041e13	0.608600
$916$	1.82250e13	0.855338
$917$	8.19651e12	0.382796
$918$	0	0
$919$	2.87258e13	1.32847	0.664236	−	0.747523i	$-0.268757\pi$
$919$	2.87258e13	1.32847	0.664236	+	0.747523i	$0.268757\pi$
$920$	1.39766e12	0.0643216
$921$	−1.06141e13	−0.486089
$922$	3.58131e13	1.63212
$923$	−2.70856e13	−1.22837
$924$	2.35346e13	1.06214
$925$	6.19135e12	0.278066
$926$	−5.40465e13	−2.41556
$927$	1.91393e13	0.851269
$928$	−6.13599e13	−2.71593
$929$	−1.08767e13	−0.479101	−0.239550	−	0.970884i	$-0.577000\pi$
$929$	−1.08767e13	−0.479101	−0.239550	+	0.970884i	$0.577000\pi$
$930$	3.19350e12	0.139989
$931$	−1.40960e13	−0.614925
$932$	−7.61307e11	−0.0330513
$933$	1.59501e13	0.689124
$934$	4.96709e13	2.13570
$935$	0	0
$936$	−2.08416e12	−0.0887542
$937$	2.93915e13	1.24564	0.622822	−	0.782363i	$-0.285986\pi$
$937$	2.93915e13	1.24564	0.622822	+	0.782363i	$0.285986\pi$
$938$	1.06865e12	0.0450736
$939$	1.53947e12	0.0646213
$940$	1.75327e13	0.732441
$941$	−1.74873e10	−0.000727058 0	−0.000363529	−	1.00000i	$-0.500116\pi$
$941$	−1.74873e10	−0.000727058 0	−0.000363529		1.00000i	$0.500116\pi$
$942$	1.52684e13	0.631779
$943$	−9.96658e11	−0.0410434
$944$	5.29853e12	0.217161
$945$	3.58123e13	1.46079
$946$	−1.26023e13	−0.511610
$947$	−3.36845e13	−1.36099	−0.680494	−	0.732753i	$-0.738235\pi$
$947$	−3.36845e13	−1.36099	−0.680494	+	0.732753i	$0.738235\pi$
$948$	−1.22312e12	−0.0491849
$949$	−1.27334e13	−0.509620
$950$	3.49827e12	0.139347
$951$	−1.51088e13	−0.598988
$952$	0	0
$953$	−1.95197e13	−0.766577	−0.383288	−	0.923629i	$-0.625208\pi$
$953$	−1.95197e13	−0.766577	−0.383288	+	0.923629i	$0.625208\pi$
$954$	−2.24852e13	−0.878879
$955$	−1.15155e13	−0.447990
$956$	−2.46438e13	−0.954218
$957$	−3.53844e13	−1.36367
$958$	−3.41956e13	−1.31167
$959$	6.49318e13	2.47898
$960$	1.09125e13	0.414669
$961$	−2.53090e13	−0.957239
$962$	−3.94873e13	−1.48652
$963$	2.79879e13	1.04870
$964$	2.03097e13	0.757457
$965$	−1.20326e13	−0.446669
$966$	1.51130e13	0.558411
$967$	−5.04513e12	−0.185547	−0.0927733	−	0.995687i	$-0.529573\pi$
$967$	−5.04513e12	−0.185547	−0.0927733	+	0.995687i	$0.529573\pi$
$968$	4.37014e12	0.159977
$969$	0	0
$970$	7.57135e13	2.74600
$971$	2.97871e13	1.07533	0.537665	−	0.843158i	$-0.319306\pi$
$971$	2.97871e13	1.07533	0.537665	+	0.843158i	$0.319306\pi$
$972$	2.54883e13	0.915888
$973$	−2.53155e12	−0.0905480
$974$	6.51471e13	2.31942
$975$	3.71411e12	0.131624
$976$	3.77582e13	1.33195
$977$	1.68301e13	0.590965	0.295483	−	0.955348i	$-0.404520\pi$
$977$	1.68301e13	0.590965	0.295483	+	0.955348i	$0.404520\pi$
$978$	−9.57611e12	−0.334707
$979$	4.38584e12	0.152591
$980$	−5.23448e13	−1.81283
$981$	9.82173e12	0.338593
$982$	4.01666e12	0.137836
$983$	−4.53002e13	−1.54742	−0.773711	−	0.633538i	$-0.781602\pi$
$983$	−4.53002e13	−1.54742	−0.773711	+	0.633538i	$0.781602\pi$
$984$	9.23246e10	0.00313935
$985$	3.45034e13	1.16788
$986$	0	0
$987$	−1.47859e13	−0.495929
$988$	−1.07370e13	−0.358489
$989$	−3.89448e12	−0.129439
$990$	−6.23070e13	−2.06148
$991$	−5.13942e13	−1.69271	−0.846356	−	0.532618i	$-0.821208\pi$
$991$	−5.13942e13	−1.69271	−0.846356	+	0.532618i	$0.821208\pi$
$992$	8.71088e12	0.285601
$993$	2.21002e13	0.721313
$994$	7.98939e13	2.59582
$995$	−2.21796e13	−0.717380
$996$	1.25471e13	0.403996
$997$	−3.28523e13	−1.05302	−0.526512	−	0.850168i	$-0.676500\pi$
$997$	−3.28523e13	−1.05302	−0.526512	+	0.850168i	$0.676500\pi$
$998$	−4.93386e13	−1.57434
$999$	−2.42815e13	−0.771312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.6		24
17.2	even	8		17.10.c.a.4.3	✓	24
17.9	even	8		17.10.c.a.13.10	yes	24
17.16	even	2	inner	289.10.a.f.1.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.3	✓	24	17.2	even	8
17.10.c.a.13.10	yes	24	17.9	even	8
289.10.a.f.1.5		24	17.16	even	2	inner
289.10.a.f.1.6		24	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)

\(f(q)\)	\(=\)	\(q-31.4159 q^{2} +60.4230 q^{3} +474.957 q^{4} -1582.21 q^{5} -1898.24 q^{6} +10488.5 q^{7} +1163.73 q^{8} -16032.1 q^{9} +O(q^{10})\)	\(q-31.4159 q^{2} +60.4230 q^{3} +474.957 q^{4} -1582.21 q^{5} -1898.24 q^{6} +10488.5 q^{7} +1163.73 q^{8} -16032.1 q^{9} +49706.4 q^{10} +78187.1 q^{11} +28698.4 q^{12} +111709. q^{13} -329506. q^{14} -95601.8 q^{15} -279738. q^{16} +503661. q^{18} -202367. q^{19} -751481. q^{20} +633749. q^{21} -2.45632e6 q^{22} -759075. q^{23} +70316.3 q^{24} +550256. q^{25} -3.50943e6 q^{26} -2.15801e6 q^{27} +4.98160e6 q^{28} -7.48987e6 q^{29} +3.00341e6 q^{30} +1.06329e6 q^{31} +8.19237e6 q^{32} +4.72430e6 q^{33} -1.65950e7 q^{35} -7.61454e6 q^{36} +1.12518e7 q^{37} +6.35754e6 q^{38} +6.74979e6 q^{39} -1.84127e6 q^{40} +1.31299e6 q^{41} -1.99098e7 q^{42} +5.13056e6 q^{43} +3.71355e7 q^{44} +2.53660e7 q^{45} +2.38470e7 q^{46} -2.33308e7 q^{47} -1.69026e7 q^{48} +6.96556e7 q^{49} -1.72868e7 q^{50} +5.30569e7 q^{52} -4.46435e7 q^{53} +6.77959e7 q^{54} -1.23708e8 q^{55} +1.22058e7 q^{56} -1.22276e7 q^{57} +2.35301e8 q^{58} -1.89411e7 q^{59} -4.54068e7 q^{60} -1.34977e8 q^{61} -3.34042e7 q^{62} -1.68153e8 q^{63} -1.14145e8 q^{64} -1.76747e8 q^{65} -1.48418e8 q^{66} -3.24318e6 q^{67} -4.58657e7 q^{69} +5.21347e8 q^{70} -2.42466e8 q^{71} -1.86570e7 q^{72} -1.13987e8 q^{73} -3.53484e8 q^{74} +3.32481e7 q^{75} -9.61157e7 q^{76} +8.20068e8 q^{77} -2.12051e8 q^{78} -4.26199e7 q^{79} +4.42603e8 q^{80} +1.85165e8 q^{81} -4.12487e7 q^{82} +4.37207e8 q^{83} +3.01003e8 q^{84} -1.61181e8 q^{86} -4.52561e8 q^{87} +9.09890e7 q^{88} +5.60941e7 q^{89} -7.96896e8 q^{90} +1.17166e9 q^{91} -3.60528e8 q^{92} +6.42473e7 q^{93} +7.32958e8 q^{94} +3.20187e8 q^{95} +4.95008e8 q^{96} +1.52321e9 q^{97} -2.18829e9 q^{98} -1.25350e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) 24 * q + 5124 * q^4 + 108368 * q^9	\( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) \) 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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