Properties

Label 289.10.a.f.1.18
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $24$
CM no
Inner twists $2$

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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 1.18
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)
 
\(f(q)\) \(=\) \(q+21.4252 q^{2} +32.0790 q^{3} -52.9591 q^{4} +1493.58 q^{5} +687.300 q^{6} +1220.42 q^{7} -12104.4 q^{8} -18653.9 q^{9} +O(q^{10})\) \(q+21.4252 q^{2} +32.0790 q^{3} -52.9591 q^{4} +1493.58 q^{5} +687.300 q^{6} +1220.42 q^{7} -12104.4 q^{8} -18653.9 q^{9} +32000.3 q^{10} -59934.7 q^{11} -1698.87 q^{12} +143048. q^{13} +26147.8 q^{14} +47912.5 q^{15} -232224. q^{16} -399665. q^{18} +897999. q^{19} -79098.5 q^{20} +39149.8 q^{21} -1.28412e6 q^{22} +1.66346e6 q^{23} -388297. q^{24} +277651. q^{25} +3.06483e6 q^{26} -1.22981e6 q^{27} -64632.3 q^{28} -4.05562e6 q^{29} +1.02654e6 q^{30} +488005. q^{31} +1.22198e6 q^{32} -1.92265e6 q^{33} +1.82279e6 q^{35} +987895. q^{36} -9.68561e6 q^{37} +1.92399e7 q^{38} +4.58883e6 q^{39} -1.80788e7 q^{40} -1.69156e7 q^{41} +838795. q^{42} +6.52450e6 q^{43} +3.17409e6 q^{44} -2.78611e7 q^{45} +3.56400e7 q^{46} -5.90622e7 q^{47} -7.44952e6 q^{48} -3.88642e7 q^{49} +5.94873e6 q^{50} -7.57568e6 q^{52} -1.27513e7 q^{53} -2.63490e7 q^{54} -8.95172e7 q^{55} -1.47724e7 q^{56} +2.88069e7 q^{57} -8.68927e7 q^{58} -4.63714e7 q^{59} -2.53740e6 q^{60} -4.21412e7 q^{61} +1.04556e7 q^{62} -2.27656e7 q^{63} +1.45080e8 q^{64} +2.13653e8 q^{65} -4.11931e7 q^{66} -2.39406e8 q^{67} +5.33622e7 q^{69} +3.90538e7 q^{70} +5.23949e7 q^{71} +2.25794e8 q^{72} +1.27072e8 q^{73} -2.07517e8 q^{74} +8.90675e6 q^{75} -4.75572e7 q^{76} -7.31455e7 q^{77} +9.83168e7 q^{78} +1.16128e8 q^{79} -3.46845e8 q^{80} +3.27714e8 q^{81} -3.62420e8 q^{82} +3.57245e8 q^{83} -2.07334e6 q^{84} +1.39789e8 q^{86} -1.30100e8 q^{87} +7.25473e8 q^{88} -4.24226e8 q^{89} -5.96931e8 q^{90} +1.74578e8 q^{91} -8.80954e7 q^{92} +1.56547e7 q^{93} -1.26542e9 q^{94} +1.34123e9 q^{95} +3.92000e7 q^{96} -8.27894e8 q^{97} -8.32674e8 q^{98} +1.11802e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 21.4252 0.946871 0.473435 0.880829i \(-0.343014\pi\)
0.473435 + 0.880829i \(0.343014\pi\)
\(3\) 32.0790 0.228652 0.114326 0.993443i \(-0.463529\pi\)
0.114326 + 0.993443i \(0.463529\pi\)
\(4\) −52.9591 −0.103436
\(5\) 1493.58 1.06872 0.534359 0.845258i \(-0.320553\pi\)
0.534359 + 0.845258i \(0.320553\pi\)
\(6\) 687.300 0.216504
\(7\) 1220.42 0.192118 0.0960590 0.995376i \(-0.469376\pi\)
0.0960590 + 0.995376i \(0.469376\pi\)
\(8\) −12104.4 −1.04481
\(9\) −18653.9 −0.947718
\(10\) 32000.3 1.01194
\(11\) −59934.7 −1.23427 −0.617137 0.786856i \(-0.711707\pi\)
−0.617137 + 0.786856i \(0.711707\pi\)
\(12\) −1698.87 −0.0236508
\(13\) 143048. 1.38911 0.694554 0.719440i \(-0.255602\pi\)
0.694554 + 0.719440i \(0.255602\pi\)
\(14\) 26147.8 0.181911
\(15\) 47912.5 0.244364
\(16\) −232224. −0.885865
\(17\) 0 0
\(18\) −399665. −0.897367
\(19\) 897999. 1.58083 0.790414 0.612573i \(-0.209865\pi\)
0.790414 + 0.612573i \(0.209865\pi\)
\(20\) −79098.5 −0.110544
\(21\) 39149.8 0.0439282
\(22\) −1.28412e6 −1.16870
\(23\) 1.66346e6 1.23947 0.619737 0.784810i \(-0.287239\pi\)
0.619737 + 0.784810i \(0.287239\pi\)
\(24\) −388297. −0.238898
\(25\) 277651. 0.142157
\(26\) 3.06483e6 1.31531
\(27\) −1.22981e6 −0.445350
\(28\) −64632.3 −0.0198719
\(29\) −4.05562e6 −1.06480 −0.532398 0.846494i \(-0.678709\pi\)
−0.532398 + 0.846494i \(0.678709\pi\)
\(30\) 1.02654e6 0.231382
\(31\) 488005. 0.0949066 0.0474533 0.998873i \(-0.484889\pi\)
0.0474533 + 0.998873i \(0.484889\pi\)
\(32\) 1.22198e6 0.206011
\(33\) −1.92265e6 −0.282219
\(34\) 0 0
\(35\) 1.82279e6 0.205320
\(36\) 987895. 0.0980279
\(37\) −9.68561e6 −0.849610 −0.424805 0.905285i \(-0.639657\pi\)
−0.424805 + 0.905285i \(0.639657\pi\)
\(38\) 1.92399e7 1.49684
\(39\) 4.58883e6 0.317623
\(40\) −1.80788e7 −1.11661
\(41\) −1.69156e7 −0.934888 −0.467444 0.884023i \(-0.654825\pi\)
−0.467444 + 0.884023i \(0.654825\pi\)
\(42\) 838795. 0.0415943
\(43\) 6.52450e6 0.291031 0.145516 0.989356i \(-0.453516\pi\)
0.145516 + 0.989356i \(0.453516\pi\)
\(44\) 3.17409e6 0.127668
\(45\) −2.78611e7 −1.01284
\(46\) 3.56400e7 1.17362
\(47\) −5.90622e7 −1.76551 −0.882753 0.469838i \(-0.844312\pi\)
−0.882753 + 0.469838i \(0.844312\pi\)
\(48\) −7.44952e6 −0.202555
\(49\) −3.88642e7 −0.963091
\(50\) 5.94873e6 0.134604
\(51\) 0 0
\(52\) −7.57568e6 −0.143683
\(53\) −1.27513e7 −0.221980 −0.110990 0.993822i \(-0.535402\pi\)
−0.110990 + 0.993822i \(0.535402\pi\)
\(54\) −2.63490e7 −0.421689
\(55\) −8.95172e7 −1.31909
\(56\) −1.47724e7 −0.200727
\(57\) 2.88069e7 0.361460
\(58\) −8.68927e7 −1.00822
\(59\) −4.63714e7 −0.498215 −0.249107 0.968476i \(-0.580137\pi\)
−0.249107 + 0.968476i \(0.580137\pi\)
\(60\) −2.53740e6 −0.0252760
\(61\) −4.21412e7 −0.389693 −0.194847 0.980834i \(-0.562421\pi\)
−0.194847 + 0.980834i \(0.562421\pi\)
\(62\) 1.04556e7 0.0898643
\(63\) −2.27656e7 −0.182074
\(64\) 1.45080e8 1.08093
\(65\) 2.13653e8 1.48456
\(66\) −4.11931e7 −0.267225
\(67\) −2.39406e8 −1.45144 −0.725719 0.687991i \(-0.758493\pi\)
−0.725719 + 0.687991i \(0.758493\pi\)
\(68\) 0 0
\(69\) 5.33622e7 0.283408
\(70\) 3.90538e7 0.194411
\(71\) 5.23949e7 0.244696 0.122348 0.992487i \(-0.460958\pi\)
0.122348 + 0.992487i \(0.460958\pi\)
\(72\) 2.25794e8 0.990186
\(73\) 1.27072e8 0.523719 0.261860 0.965106i \(-0.415664\pi\)
0.261860 + 0.965106i \(0.415664\pi\)
\(74\) −2.07517e8 −0.804470
\(75\) 8.90675e6 0.0325045
\(76\) −4.75572e7 −0.163514
\(77\) −7.31455e7 −0.237126
\(78\) 9.83168e7 0.300748
\(79\) 1.16128e8 0.335439 0.167720 0.985835i \(-0.446360\pi\)
0.167720 + 0.985835i \(0.446360\pi\)
\(80\) −3.46845e8 −0.946740
\(81\) 3.27714e8 0.845888
\(82\) −3.62420e8 −0.885218
\(83\) 3.57245e8 0.826257 0.413128 0.910673i \(-0.364436\pi\)
0.413128 + 0.910673i \(0.364436\pi\)
\(84\) −2.07334e6 −0.00454374
\(85\) 0 0
\(86\) 1.39789e8 0.275569
\(87\) −1.30100e8 −0.243468
\(88\) 7.25473e8 1.28958
\(89\) −4.24226e8 −0.716708 −0.358354 0.933586i \(-0.616662\pi\)
−0.358354 + 0.933586i \(0.616662\pi\)
\(90\) −5.96931e8 −0.959032
\(91\) 1.74578e8 0.266873
\(92\) −8.80954e7 −0.128206
\(93\) 1.56547e7 0.0217006
\(94\) −1.26542e9 −1.67171
\(95\) 1.34123e9 1.68946
\(96\) 3.92000e7 0.0471048
\(97\) −8.27894e8 −0.949515 −0.474757 0.880117i \(-0.657464\pi\)
−0.474757 + 0.880117i \(0.657464\pi\)
\(98\) −8.32674e8 −0.911922
\(99\) 1.11802e9 1.16974
\(100\) −1.47041e7 −0.0147041
\(101\) −1.39180e9 −1.33085 −0.665425 0.746465i \(-0.731750\pi\)
−0.665425 + 0.746465i \(0.731750\pi\)
\(102\) 0 0
\(103\) −1.58618e8 −0.138862 −0.0694310 0.997587i \(-0.522118\pi\)
−0.0694310 + 0.997587i \(0.522118\pi\)
\(104\) −1.73151e9 −1.45136
\(105\) 5.84733e7 0.0469468
\(106\) −2.73200e8 −0.210186
\(107\) 2.29686e9 1.69398 0.846988 0.531612i \(-0.178413\pi\)
0.846988 + 0.531612i \(0.178413\pi\)
\(108\) 6.51296e7 0.0460651
\(109\) −2.49735e9 −1.69457 −0.847286 0.531136i \(-0.821765\pi\)
−0.847286 + 0.531136i \(0.821765\pi\)
\(110\) −1.91793e9 −1.24901
\(111\) −3.10705e8 −0.194265
\(112\) −2.83411e8 −0.170191
\(113\) −1.12193e9 −0.647310 −0.323655 0.946175i \(-0.604912\pi\)
−0.323655 + 0.946175i \(0.604912\pi\)
\(114\) 6.17195e8 0.342256
\(115\) 2.48451e9 1.32465
\(116\) 2.14782e8 0.110138
\(117\) −2.66841e9 −1.31648
\(118\) −9.93519e8 −0.471745
\(119\) 0 0
\(120\) −5.79951e8 −0.255315
\(121\) 1.23422e9 0.523430
\(122\) −9.02886e8 −0.368989
\(123\) −5.42635e8 −0.213764
\(124\) −2.58443e7 −0.00981674
\(125\) −2.50245e9 −0.916792
\(126\) −4.87759e8 −0.172400
\(127\) −1.24547e9 −0.424830 −0.212415 0.977180i \(-0.568133\pi\)
−0.212415 + 0.977180i \(0.568133\pi\)
\(128\) 2.48272e9 0.817491
\(129\) 2.09300e8 0.0665449
\(130\) 4.57757e9 1.40569
\(131\) −4.12512e9 −1.22382 −0.611908 0.790929i \(-0.709598\pi\)
−0.611908 + 0.790929i \(0.709598\pi\)
\(132\) 1.01822e8 0.0291915
\(133\) 1.09594e9 0.303706
\(134\) −5.12934e9 −1.37433
\(135\) −1.83682e9 −0.475953
\(136\) 0 0
\(137\) −1.46624e9 −0.355600 −0.177800 0.984067i \(-0.556898\pi\)
−0.177800 + 0.984067i \(0.556898\pi\)
\(138\) 1.14330e9 0.268351
\(139\) −2.87070e8 −0.0652262 −0.0326131 0.999468i \(-0.510383\pi\)
−0.0326131 + 0.999468i \(0.510383\pi\)
\(140\) −9.65334e7 −0.0212374
\(141\) −1.89466e9 −0.403686
\(142\) 1.12257e9 0.231695
\(143\) −8.57353e9 −1.71454
\(144\) 4.33190e9 0.839551
\(145\) −6.05739e9 −1.13797
\(146\) 2.72256e9 0.495895
\(147\) −1.24672e9 −0.220213
\(148\) 5.12941e8 0.0878800
\(149\) −9.99209e9 −1.66080 −0.830401 0.557166i \(-0.811889\pi\)
−0.830401 + 0.557166i \(0.811889\pi\)
\(150\) 1.90829e8 0.0307776
\(151\) −1.36824e9 −0.214174 −0.107087 0.994250i \(-0.534152\pi\)
−0.107087 + 0.994250i \(0.534152\pi\)
\(152\) −1.08697e10 −1.65167
\(153\) 0 0
\(154\) −1.56716e9 −0.224528
\(155\) 7.28874e8 0.101428
\(156\) −2.43020e8 −0.0328535
\(157\) 1.80109e9 0.236585 0.118293 0.992979i \(-0.462258\pi\)
0.118293 + 0.992979i \(0.462258\pi\)
\(158\) 2.48806e9 0.317618
\(159\) −4.09050e8 −0.0507562
\(160\) 1.82513e9 0.220168
\(161\) 2.03012e9 0.238125
\(162\) 7.02136e9 0.800947
\(163\) 1.09895e10 1.21936 0.609681 0.792647i \(-0.291298\pi\)
0.609681 + 0.792647i \(0.291298\pi\)
\(164\) 8.95833e8 0.0967007
\(165\) −2.87162e9 −0.301612
\(166\) 7.65406e9 0.782358
\(167\) −1.13053e10 −1.12476 −0.562378 0.826880i \(-0.690113\pi\)
−0.562378 + 0.826880i \(0.690113\pi\)
\(168\) −4.73885e8 −0.0458966
\(169\) 9.85818e9 0.929623
\(170\) 0 0
\(171\) −1.67512e10 −1.49818
\(172\) −3.45532e8 −0.0301030
\(173\) 1.48170e10 1.25763 0.628817 0.777553i \(-0.283540\pi\)
0.628817 + 0.777553i \(0.283540\pi\)
\(174\) −2.78743e9 −0.230533
\(175\) 3.38850e8 0.0273109
\(176\) 1.39183e10 1.09340
\(177\) −1.48755e9 −0.113918
\(178\) −9.08914e9 −0.678630
\(179\) 7.88618e9 0.574154 0.287077 0.957908i \(-0.407316\pi\)
0.287077 + 0.957908i \(0.407316\pi\)
\(180\) 1.47550e9 0.104764
\(181\) 2.24536e10 1.55501 0.777505 0.628877i \(-0.216485\pi\)
0.777505 + 0.628877i \(0.216485\pi\)
\(182\) 3.74038e9 0.252694
\(183\) −1.35185e9 −0.0891042
\(184\) −2.01352e10 −1.29502
\(185\) −1.44662e10 −0.907993
\(186\) 3.35406e8 0.0205477
\(187\) 0 0
\(188\) 3.12788e9 0.182616
\(189\) −1.50088e9 −0.0855597
\(190\) 2.87362e10 1.59970
\(191\) −1.62873e10 −0.885519 −0.442759 0.896640i \(-0.646000\pi\)
−0.442759 + 0.896640i \(0.646000\pi\)
\(192\) 4.65402e9 0.247157
\(193\) −5.10953e9 −0.265078 −0.132539 0.991178i \(-0.542313\pi\)
−0.132539 + 0.991178i \(0.542313\pi\)
\(194\) −1.77378e10 −0.899068
\(195\) 6.85378e9 0.339449
\(196\) 2.05821e9 0.0996180
\(197\) −2.46354e10 −1.16536 −0.582681 0.812701i \(-0.697996\pi\)
−0.582681 + 0.812701i \(0.697996\pi\)
\(198\) 2.39538e10 1.10760
\(199\) −1.69660e10 −0.766901 −0.383451 0.923561i \(-0.625264\pi\)
−0.383451 + 0.923561i \(0.625264\pi\)
\(200\) −3.36079e9 −0.148527
\(201\) −7.67991e9 −0.331875
\(202\) −2.98196e10 −1.26014
\(203\) −4.94956e9 −0.204567
\(204\) 0 0
\(205\) −2.52647e10 −0.999131
\(206\) −3.39842e9 −0.131484
\(207\) −3.10301e10 −1.17467
\(208\) −3.32192e10 −1.23056
\(209\) −5.38213e10 −1.95117
\(210\) 1.25281e9 0.0444526
\(211\) 3.36381e10 1.16832 0.584158 0.811640i \(-0.301425\pi\)
0.584158 + 0.811640i \(0.301425\pi\)
\(212\) 6.75298e8 0.0229607
\(213\) 1.68078e9 0.0559502
\(214\) 4.92108e10 1.60398
\(215\) 9.74486e9 0.311030
\(216\) 1.48861e10 0.465306
\(217\) 5.95571e8 0.0182333
\(218\) −5.35063e10 −1.60454
\(219\) 4.07636e9 0.119750
\(220\) 4.74075e9 0.136441
\(221\) 0 0
\(222\) −6.65692e9 −0.183944
\(223\) 6.63366e10 1.79631 0.898155 0.439679i \(-0.144908\pi\)
0.898155 + 0.439679i \(0.144908\pi\)
\(224\) 1.49133e9 0.0395784
\(225\) −5.17928e9 −0.134725
\(226\) −2.40376e10 −0.612919
\(227\) −1.14996e10 −0.287453 −0.143727 0.989617i \(-0.545909\pi\)
−0.143727 + 0.989617i \(0.545909\pi\)
\(228\) −1.52559e9 −0.0373878
\(229\) 3.93654e10 0.945920 0.472960 0.881084i \(-0.343185\pi\)
0.472960 + 0.881084i \(0.343185\pi\)
\(230\) 5.32312e10 1.25427
\(231\) −2.34643e9 −0.0542194
\(232\) 4.90908e10 1.11251
\(233\) 4.79673e10 1.06621 0.533106 0.846049i \(-0.321025\pi\)
0.533106 + 0.846049i \(0.321025\pi\)
\(234\) −5.71712e10 −1.24654
\(235\) −8.82140e10 −1.88683
\(236\) 2.45579e9 0.0515332
\(237\) 3.72526e9 0.0766989
\(238\) 0 0
\(239\) −8.89651e10 −1.76372 −0.881859 0.471513i \(-0.843708\pi\)
−0.881859 + 0.471513i \(0.843708\pi\)
\(240\) −1.11264e10 −0.216474
\(241\) 7.98752e10 1.52523 0.762615 0.646852i \(-0.223915\pi\)
0.762615 + 0.646852i \(0.223915\pi\)
\(242\) 2.64435e10 0.495621
\(243\) 3.47191e10 0.638764
\(244\) 2.23176e9 0.0403082
\(245\) −5.80467e10 −1.02927
\(246\) −1.16261e10 −0.202407
\(247\) 1.28457e11 2.19594
\(248\) −5.90700e9 −0.0991595
\(249\) 1.14601e10 0.188925
\(250\) −5.36156e10 −0.868083
\(251\) −8.42255e10 −1.33941 −0.669703 0.742629i \(-0.733578\pi\)
−0.669703 + 0.742629i \(0.733578\pi\)
\(252\) 1.20565e9 0.0188329
\(253\) −9.96990e10 −1.52985
\(254\) −2.66844e10 −0.402259
\(255\) 0 0
\(256\) −2.10881e10 −0.306873
\(257\) 5.40709e10 0.773152 0.386576 0.922258i \(-0.373658\pi\)
0.386576 + 0.922258i \(0.373658\pi\)
\(258\) 4.48429e9 0.0630094
\(259\) −1.18205e10 −0.163225
\(260\) −1.13149e10 −0.153557
\(261\) 7.56534e10 1.00913
\(262\) −8.83818e10 −1.15880
\(263\) −1.90882e10 −0.246017 −0.123008 0.992406i \(-0.539254\pi\)
−0.123008 + 0.992406i \(0.539254\pi\)
\(264\) 2.32724e10 0.294866
\(265\) −1.90451e10 −0.237234
\(266\) 2.34807e10 0.287570
\(267\) −1.36087e10 −0.163877
\(268\) 1.26787e10 0.150131
\(269\) 3.26919e10 0.380676 0.190338 0.981719i \(-0.439042\pi\)
0.190338 + 0.981719i \(0.439042\pi\)
\(270\) −3.93543e10 −0.450666
\(271\) −4.55819e10 −0.513370 −0.256685 0.966495i \(-0.582630\pi\)
−0.256685 + 0.966495i \(0.582630\pi\)
\(272\) 0 0
\(273\) 5.60030e9 0.0610210
\(274\) −3.14145e10 −0.336707
\(275\) −1.66409e10 −0.175461
\(276\) −2.82601e9 −0.0293145
\(277\) −1.11315e10 −0.113604 −0.0568022 0.998385i \(-0.518090\pi\)
−0.0568022 + 0.998385i \(0.518090\pi\)
\(278\) −6.15055e9 −0.0617607
\(279\) −9.10321e9 −0.0899448
\(280\) −2.20638e10 −0.214520
\(281\) −3.07136e10 −0.293868 −0.146934 0.989146i \(-0.546940\pi\)
−0.146934 + 0.989146i \(0.546940\pi\)
\(282\) −4.05934e10 −0.382239
\(283\) 4.97422e10 0.460984 0.230492 0.973074i \(-0.425966\pi\)
0.230492 + 0.973074i \(0.425966\pi\)
\(284\) −2.77479e9 −0.0253103
\(285\) 4.30254e10 0.386298
\(286\) −1.83690e11 −1.62345
\(287\) −2.06441e10 −0.179609
\(288\) −2.27948e10 −0.195240
\(289\) 0 0
\(290\) −1.29781e11 −1.07751
\(291\) −2.65580e10 −0.217109
\(292\) −6.72964e9 −0.0541713
\(293\) −1.21705e11 −0.964728 −0.482364 0.875971i \(-0.660222\pi\)
−0.482364 + 0.875971i \(0.660222\pi\)
\(294\) −2.67114e10 −0.208513
\(295\) −6.92594e10 −0.532451
\(296\) 1.17238e11 0.887681
\(297\) 7.37083e10 0.549683
\(298\) −2.14083e11 −1.57257
\(299\) 2.37954e11 1.72176
\(300\) −4.71693e8 −0.00336213
\(301\) 7.96263e9 0.0559123
\(302\) −2.93150e10 −0.202795
\(303\) −4.46474e10 −0.304302
\(304\) −2.08537e11 −1.40040
\(305\) −6.29412e10 −0.416472
\(306\) 0 0
\(307\) 1.11287e11 0.715026 0.357513 0.933908i \(-0.383625\pi\)
0.357513 + 0.933908i \(0.383625\pi\)
\(308\) 3.87372e9 0.0245273
\(309\) −5.08829e9 −0.0317511
\(310\) 1.56163e10 0.0960396
\(311\) −7.63765e10 −0.462954 −0.231477 0.972840i \(-0.574356\pi\)
−0.231477 + 0.972840i \(0.574356\pi\)
\(312\) −5.55450e10 −0.331856
\(313\) −2.03210e11 −1.19673 −0.598364 0.801224i \(-0.704182\pi\)
−0.598364 + 0.801224i \(0.704182\pi\)
\(314\) 3.85889e10 0.224016
\(315\) −3.40022e10 −0.194585
\(316\) −6.15002e9 −0.0346964
\(317\) 3.45098e11 1.91945 0.959723 0.280949i \(-0.0906493\pi\)
0.959723 + 0.280949i \(0.0906493\pi\)
\(318\) −8.76399e9 −0.0480595
\(319\) 2.43073e11 1.31425
\(320\) 2.16688e11 1.15521
\(321\) 7.36809e10 0.387331
\(322\) 4.34958e10 0.225474
\(323\) 0 0
\(324\) −1.73555e10 −0.0874950
\(325\) 3.97173e10 0.197472
\(326\) 2.35452e11 1.15458
\(327\) −8.01125e10 −0.387468
\(328\) 2.04753e11 0.976781
\(329\) −7.20806e10 −0.339185
\(330\) −6.15252e10 −0.285588
\(331\) −2.73355e11 −1.25170 −0.625852 0.779942i \(-0.715249\pi\)
−0.625852 + 0.779942i \(0.715249\pi\)
\(332\) −1.89194e10 −0.0854644
\(333\) 1.80675e11 0.805190
\(334\) −2.42219e11 −1.06500
\(335\) −3.57572e11 −1.55118
\(336\) −9.09154e9 −0.0389144
\(337\) 3.40769e11 1.43921 0.719606 0.694382i \(-0.244322\pi\)
0.719606 + 0.694382i \(0.244322\pi\)
\(338\) 2.11214e11 0.880233
\(339\) −3.59903e10 −0.148009
\(340\) 0 0
\(341\) −2.92484e10 −0.117141
\(342\) −3.58899e11 −1.41858
\(343\) −9.66789e10 −0.377145
\(344\) −7.89751e10 −0.304073
\(345\) 7.97005e10 0.302883
\(346\) 3.17459e11 1.19082
\(347\) 6.65505e10 0.246416 0.123208 0.992381i \(-0.460682\pi\)
0.123208 + 0.992381i \(0.460682\pi\)
\(348\) 6.88999e9 0.0251833
\(349\) −4.92387e10 −0.177661 −0.0888304 0.996047i \(-0.528313\pi\)
−0.0888304 + 0.996047i \(0.528313\pi\)
\(350\) 7.25995e9 0.0258599
\(351\) −1.75922e11 −0.618639
\(352\) −7.32392e10 −0.254274
\(353\) 2.30862e11 0.791346 0.395673 0.918391i \(-0.370511\pi\)
0.395673 + 0.918391i \(0.370511\pi\)
\(354\) −3.18711e10 −0.107865
\(355\) 7.82559e10 0.261511
\(356\) 2.24666e10 0.0741332
\(357\) 0 0
\(358\) 1.68963e11 0.543649
\(359\) −2.04329e11 −0.649241 −0.324620 0.945844i \(-0.605237\pi\)
−0.324620 + 0.945844i \(0.605237\pi\)
\(360\) 3.37242e11 1.05823
\(361\) 4.83715e11 1.49902
\(362\) 4.81075e11 1.47239
\(363\) 3.95926e10 0.119683
\(364\) −9.24551e9 −0.0276042
\(365\) 1.89793e11 0.559708
\(366\) −2.89637e10 −0.0843701
\(367\) −2.97395e11 −0.855729 −0.427865 0.903843i \(-0.640734\pi\)
−0.427865 + 0.903843i \(0.640734\pi\)
\(368\) −3.86296e11 −1.09801
\(369\) 3.15542e11 0.886010
\(370\) −3.09942e11 −0.859752
\(371\) −1.55620e10 −0.0426463
\(372\) −8.29059e8 −0.00224462
\(373\) −6.65444e11 −1.78001 −0.890004 0.455952i \(-0.849299\pi\)
−0.890004 + 0.455952i \(0.849299\pi\)
\(374\) 0 0
\(375\) −8.02761e10 −0.209626
\(376\) 7.14911e11 1.84462
\(377\) −5.80148e11 −1.47912
\(378\) −3.21568e10 −0.0810140
\(379\) −4.69183e11 −1.16806 −0.584031 0.811731i \(-0.698525\pi\)
−0.584031 + 0.811731i \(0.698525\pi\)
\(380\) −7.10304e10 −0.174750
\(381\) −3.99533e10 −0.0971382
\(382\) −3.48958e11 −0.838472
\(383\) −2.89004e11 −0.686293 −0.343146 0.939282i \(-0.611493\pi\)
−0.343146 + 0.939282i \(0.611493\pi\)
\(384\) 7.96432e10 0.186921
\(385\) −1.09248e11 −0.253421
\(386\) −1.09473e11 −0.250994
\(387\) −1.21708e11 −0.275815
\(388\) 4.38445e10 0.0982137
\(389\) −2.39881e11 −0.531156 −0.265578 0.964089i \(-0.585563\pi\)
−0.265578 + 0.964089i \(0.585563\pi\)
\(390\) 1.46844e11 0.321414
\(391\) 0 0
\(392\) 4.70427e11 1.00625
\(393\) −1.32330e11 −0.279828
\(394\) −5.27819e11 −1.10345
\(395\) 1.73446e11 0.358490
\(396\) −5.92092e10 −0.120993
\(397\) −4.67123e11 −0.943787 −0.471894 0.881655i \(-0.656429\pi\)
−0.471894 + 0.881655i \(0.656429\pi\)
\(398\) −3.63500e11 −0.726156
\(399\) 3.51565e10 0.0694429
\(400\) −6.44772e10 −0.125932
\(401\) 9.49217e10 0.183323 0.0916613 0.995790i \(-0.470782\pi\)
0.0916613 + 0.995790i \(0.470782\pi\)
\(402\) −1.64544e11 −0.314242
\(403\) 6.98081e10 0.131836
\(404\) 7.37082e10 0.137657
\(405\) 4.89467e11 0.904015
\(406\) −1.06046e11 −0.193698
\(407\) 5.80504e11 1.04865
\(408\) 0 0
\(409\) 6.05913e11 1.07067 0.535334 0.844640i \(-0.320186\pi\)
0.535334 + 0.844640i \(0.320186\pi\)
\(410\) −5.41303e11 −0.946048
\(411\) −4.70354e10 −0.0813086
\(412\) 8.40024e9 0.0143633
\(413\) −5.65926e10 −0.0957160
\(414\) −6.64827e11 −1.11226
\(415\) 5.33574e11 0.883035
\(416\) 1.74802e11 0.286172
\(417\) −9.20893e9 −0.0149141
\(418\) −1.15313e12 −1.84751
\(419\) −2.42811e11 −0.384862 −0.192431 0.981311i \(-0.561637\pi\)
−0.192431 + 0.981311i \(0.561637\pi\)
\(420\) −3.09669e9 −0.00485598
\(421\) 8.70105e10 0.134990 0.0674951 0.997720i \(-0.478499\pi\)
0.0674951 + 0.997720i \(0.478499\pi\)
\(422\) 7.20704e11 1.10624
\(423\) 1.10174e12 1.67320
\(424\) 1.54347e11 0.231927
\(425\) 0 0
\(426\) 3.60110e10 0.0529776
\(427\) −5.14300e10 −0.0748671
\(428\) −1.21640e11 −0.175218
\(429\) −2.75030e11 −0.392033
\(430\) 2.08786e11 0.294505
\(431\) 3.68348e11 0.514175 0.257087 0.966388i \(-0.417237\pi\)
0.257087 + 0.966388i \(0.417237\pi\)
\(432\) 2.85592e11 0.394520
\(433\) 7.44038e10 0.101718 0.0508592 0.998706i \(-0.483804\pi\)
0.0508592 + 0.998706i \(0.483804\pi\)
\(434\) 1.27602e10 0.0172645
\(435\) −1.94315e11 −0.260198
\(436\) 1.32257e11 0.175279
\(437\) 1.49379e12 1.95940
\(438\) 8.73369e10 0.113387
\(439\) 5.10991e11 0.656634 0.328317 0.944568i \(-0.393519\pi\)
0.328317 + 0.944568i \(0.393519\pi\)
\(440\) 1.08355e12 1.37820
\(441\) 7.24970e11 0.912739
\(442\) 0 0
\(443\) −1.03324e11 −0.127462 −0.0637312 0.997967i \(-0.520300\pi\)
−0.0637312 + 0.997967i \(0.520300\pi\)
\(444\) 1.64546e10 0.0200939
\(445\) −6.33615e11 −0.765958
\(446\) 1.42128e12 1.70087
\(447\) −3.20536e11 −0.379746
\(448\) 1.77059e11 0.207666
\(449\) 1.40092e12 1.62669 0.813346 0.581780i \(-0.197643\pi\)
0.813346 + 0.581780i \(0.197643\pi\)
\(450\) −1.10967e11 −0.127567
\(451\) 1.01383e12 1.15391
\(452\) 5.94163e10 0.0669549
\(453\) −4.38919e10 −0.0489714
\(454\) −2.46382e11 −0.272181
\(455\) 2.60746e11 0.285212
\(456\) −3.48690e11 −0.377657
\(457\) 8.90825e11 0.955366 0.477683 0.878532i \(-0.341477\pi\)
0.477683 + 0.878532i \(0.341477\pi\)
\(458\) 8.43412e11 0.895664
\(459\) 0 0
\(460\) −1.31577e11 −0.137016
\(461\) 1.36094e12 1.40341 0.701707 0.712466i \(-0.252422\pi\)
0.701707 + 0.712466i \(0.252422\pi\)
\(462\) −5.02729e10 −0.0513387
\(463\) −1.00418e12 −1.01554 −0.507770 0.861493i \(-0.669530\pi\)
−0.507770 + 0.861493i \(0.669530\pi\)
\(464\) 9.41814e11 0.943266
\(465\) 2.33815e10 0.0231918
\(466\) 1.02771e12 1.00956
\(467\) 6.55686e11 0.637926 0.318963 0.947767i \(-0.396665\pi\)
0.318963 + 0.947767i \(0.396665\pi\)
\(468\) 1.41316e11 0.136171
\(469\) −2.92176e11 −0.278847
\(470\) −1.89001e12 −1.78658
\(471\) 5.77773e10 0.0540957
\(472\) 5.61298e11 0.520540
\(473\) −3.91044e11 −0.359212
\(474\) 7.98146e10 0.0726240
\(475\) 2.49330e11 0.224726
\(476\) 0 0
\(477\) 2.37862e11 0.210374
\(478\) −1.90610e12 −1.67001
\(479\) 1.52667e12 1.32506 0.662531 0.749034i \(-0.269482\pi\)
0.662531 + 0.749034i \(0.269482\pi\)
\(480\) 5.85483e10 0.0503418
\(481\) −1.38551e12 −1.18020
\(482\) 1.71135e12 1.44420
\(483\) 6.51242e10 0.0544478
\(484\) −6.53632e10 −0.0541414
\(485\) −1.23652e12 −1.01476
\(486\) 7.43865e11 0.604827
\(487\) −7.50120e11 −0.604297 −0.302149 0.953261i \(-0.597704\pi\)
−0.302149 + 0.953261i \(0.597704\pi\)
\(488\) 5.10094e11 0.407156
\(489\) 3.52531e11 0.278810
\(490\) −1.24366e12 −0.974587
\(491\) 9.77091e11 0.758697 0.379348 0.925254i \(-0.376148\pi\)
0.379348 + 0.925254i \(0.376148\pi\)
\(492\) 2.87374e10 0.0221108
\(493\) 0 0
\(494\) 2.75222e12 2.07927
\(495\) 1.66985e12 1.25012
\(496\) −1.13327e11 −0.0840745
\(497\) 6.39438e10 0.0470105
\(498\) 2.45535e11 0.178888
\(499\) 3.34485e11 0.241504 0.120752 0.992683i \(-0.461469\pi\)
0.120752 + 0.992683i \(0.461469\pi\)
\(500\) 1.32528e11 0.0948290
\(501\) −3.62663e11 −0.257178
\(502\) −1.80455e12 −1.26824
\(503\) −8.94503e11 −0.623054 −0.311527 0.950237i \(-0.600840\pi\)
−0.311527 + 0.950237i \(0.600840\pi\)
\(504\) 2.75564e11 0.190233
\(505\) −2.07876e12 −1.42230
\(506\) −2.13608e12 −1.44857
\(507\) 3.16241e11 0.212560
\(508\) 6.59587e10 0.0439426
\(509\) 2.06105e12 1.36100 0.680500 0.732748i \(-0.261763\pi\)
0.680500 + 0.732748i \(0.261763\pi\)
\(510\) 0 0
\(511\) 1.55082e11 0.100616
\(512\) −1.72297e12 −1.10806
\(513\) −1.10437e12 −0.704022
\(514\) 1.15848e12 0.732075
\(515\) −2.36908e11 −0.148404
\(516\) −1.10843e10 −0.00688311
\(517\) 3.53987e12 2.17912
\(518\) −2.53257e11 −0.154553
\(519\) 4.75316e11 0.287561
\(520\) −2.58614e12 −1.55109
\(521\) 8.82079e11 0.524491 0.262245 0.965001i \(-0.415537\pi\)
0.262245 + 0.965001i \(0.415537\pi\)
\(522\) 1.62089e12 0.955513
\(523\) 1.84775e12 1.07990 0.539952 0.841696i \(-0.318442\pi\)
0.539952 + 0.841696i \(0.318442\pi\)
\(524\) 2.18463e11 0.126586
\(525\) 1.08700e10 0.00624470
\(526\) −4.08970e11 −0.232946
\(527\) 0 0
\(528\) 4.46485e11 0.250008
\(529\) 9.65949e11 0.536295
\(530\) −4.08046e11 −0.224630
\(531\) 8.65010e11 0.472167
\(532\) −5.80398e10 −0.0314140
\(533\) −2.41974e12 −1.29866
\(534\) −2.91571e11 −0.155170
\(535\) 3.43054e12 1.81038
\(536\) 2.89786e12 1.51648
\(537\) 2.52981e11 0.131281
\(538\) 7.00432e11 0.360451
\(539\) 2.32931e12 1.18872
\(540\) 9.72762e10 0.0492305
\(541\) 1.98969e12 0.998616 0.499308 0.866424i \(-0.333588\pi\)
0.499308 + 0.866424i \(0.333588\pi\)
\(542\) −9.76604e11 −0.486095
\(543\) 7.20290e11 0.355556
\(544\) 0 0
\(545\) −3.72999e12 −1.81102
\(546\) 1.19988e11 0.0577790
\(547\) −2.90319e12 −1.38654 −0.693270 0.720678i \(-0.743831\pi\)
−0.693270 + 0.720678i \(0.743831\pi\)
\(548\) 7.76505e10 0.0367817
\(549\) 7.86100e11 0.369319
\(550\) −3.56535e11 −0.166139
\(551\) −3.64195e12 −1.68326
\(552\) −6.45916e11 −0.296108
\(553\) 1.41725e11 0.0644439
\(554\) −2.38495e11 −0.107569
\(555\) −4.64062e11 −0.207614
\(556\) 1.52030e10 0.00674671
\(557\) −7.01764e11 −0.308918 −0.154459 0.987999i \(-0.549363\pi\)
−0.154459 + 0.987999i \(0.549363\pi\)
\(558\) −1.95039e11 −0.0851661
\(559\) 9.33316e11 0.404274
\(560\) −4.23297e11 −0.181886
\(561\) 0 0
\(562\) −6.58045e11 −0.278255
\(563\) 1.39790e10 0.00586393 0.00293196 0.999996i \(-0.499067\pi\)
0.00293196 + 0.999996i \(0.499067\pi\)
\(564\) 1.00339e11 0.0417556
\(565\) −1.67569e12 −0.691791
\(566\) 1.06574e12 0.436493
\(567\) 3.99949e11 0.162510
\(568\) −6.34208e11 −0.255661
\(569\) −2.78982e12 −1.11576 −0.557880 0.829922i \(-0.688385\pi\)
−0.557880 + 0.829922i \(0.688385\pi\)
\(570\) 9.21829e11 0.365775
\(571\) 3.89052e12 1.53160 0.765800 0.643079i \(-0.222343\pi\)
0.765800 + 0.643079i \(0.222343\pi\)
\(572\) 4.54046e11 0.177345
\(573\) −5.22479e11 −0.202476
\(574\) −4.42305e11 −0.170066
\(575\) 4.61861e11 0.176200
\(576\) −2.70632e12 −1.02442
\(577\) −2.43855e12 −0.915883 −0.457942 0.888982i \(-0.651413\pi\)
−0.457942 + 0.888982i \(0.651413\pi\)
\(578\) 0 0
\(579\) −1.63909e11 −0.0606106
\(580\) 3.20794e11 0.117706
\(581\) 4.35989e11 0.158739
\(582\) −5.69012e11 −0.205574
\(583\) 7.64247e11 0.273984
\(584\) −1.53813e12 −0.547188
\(585\) −3.98547e12 −1.40695
\(586\) −2.60756e12 −0.913473
\(587\) −3.11396e12 −1.08254 −0.541268 0.840850i \(-0.682056\pi\)
−0.541268 + 0.840850i \(0.682056\pi\)
\(588\) 6.60254e10 0.0227779
\(589\) 4.38228e11 0.150031
\(590\) −1.48390e12 −0.504162
\(591\) −7.90278e11 −0.266463
\(592\) 2.24923e12 0.752640
\(593\) −7.59897e11 −0.252353 −0.126177 0.992008i \(-0.540271\pi\)
−0.126177 + 0.992008i \(0.540271\pi\)
\(594\) 1.57922e12 0.520479
\(595\) 0 0
\(596\) 5.29172e11 0.171786
\(597\) −5.44251e11 −0.175354
\(598\) 5.09823e12 1.63029
\(599\) −8.96263e11 −0.284456 −0.142228 0.989834i \(-0.545427\pi\)
−0.142228 + 0.989834i \(0.545427\pi\)
\(600\) −1.07811e11 −0.0339611
\(601\) 3.76154e12 1.17606 0.588032 0.808838i \(-0.299903\pi\)
0.588032 + 0.808838i \(0.299903\pi\)
\(602\) 1.70601e11 0.0529417
\(603\) 4.46587e12 1.37556
\(604\) 7.24609e10 0.0221533
\(605\) 1.84340e12 0.559399
\(606\) −9.56581e11 −0.288134
\(607\) −1.60985e12 −0.481323 −0.240662 0.970609i \(-0.577364\pi\)
−0.240662 + 0.970609i \(0.577364\pi\)
\(608\) 1.09734e12 0.325668
\(609\) −1.58777e11 −0.0467746
\(610\) −1.34853e12 −0.394345
\(611\) −8.44872e12 −2.45248
\(612\) 0 0
\(613\) 9.46562e11 0.270755 0.135378 0.990794i \(-0.456775\pi\)
0.135378 + 0.990794i \(0.456775\pi\)
\(614\) 2.38435e12 0.677037
\(615\) −8.10467e11 −0.228453
\(616\) 8.85381e11 0.247752
\(617\) −6.21655e12 −1.72690 −0.863448 0.504438i \(-0.831700\pi\)
−0.863448 + 0.504438i \(0.831700\pi\)
\(618\) −1.09018e11 −0.0300642
\(619\) −6.25622e11 −0.171279 −0.0856395 0.996326i \(-0.527293\pi\)
−0.0856395 + 0.996326i \(0.527293\pi\)
\(620\) −3.86005e10 −0.0104913
\(621\) −2.04574e12 −0.551999
\(622\) −1.63639e12 −0.438358
\(623\) −5.17734e11 −0.137692
\(624\) −1.06564e12 −0.281371
\(625\) −4.27989e12 −1.12195
\(626\) −4.35382e12 −1.13315
\(627\) −1.72653e12 −0.446140
\(628\) −9.53842e10 −0.0244714
\(629\) 0 0
\(630\) −7.28506e11 −0.184247
\(631\) −2.47719e12 −0.622053 −0.311026 0.950401i \(-0.600673\pi\)
−0.311026 + 0.950401i \(0.600673\pi\)
\(632\) −1.40565e12 −0.350471
\(633\) 1.07908e12 0.267138
\(634\) 7.39381e12 1.81747
\(635\) −1.86020e12 −0.454023
\(636\) 2.16629e10 0.00525000
\(637\) −5.55944e12 −1.33784
\(638\) 5.20789e12 1.24442
\(639\) −9.77372e11 −0.231903
\(640\) 3.70814e12 0.873667
\(641\) −6.99847e12 −1.63735 −0.818675 0.574257i \(-0.805291\pi\)
−0.818675 + 0.574257i \(0.805291\pi\)
\(642\) 1.57863e12 0.366753
\(643\) −7.69131e12 −1.77440 −0.887199 0.461387i \(-0.847352\pi\)
−0.887199 + 0.461387i \(0.847352\pi\)
\(644\) −1.07513e11 −0.0246306
\(645\) 3.12605e11 0.0711177
\(646\) 0 0
\(647\) 2.23210e11 0.0500777 0.0250389 0.999686i \(-0.492029\pi\)
0.0250389 + 0.999686i \(0.492029\pi\)
\(648\) −3.96678e12 −0.883793
\(649\) 2.77926e12 0.614933
\(650\) 8.50953e11 0.186980
\(651\) 1.91053e10 0.00416907
\(652\) −5.81992e11 −0.126126
\(653\) −3.47267e11 −0.0747402 −0.0373701 0.999301i \(-0.511898\pi\)
−0.0373701 + 0.999301i \(0.511898\pi\)
\(654\) −1.71643e12 −0.366882
\(655\) −6.16120e12 −1.30791
\(656\) 3.92821e12 0.828184
\(657\) −2.37040e12 −0.496338
\(658\) −1.54434e12 −0.321165
\(659\) 6.95963e12 1.43748 0.718740 0.695279i \(-0.244719\pi\)
0.718740 + 0.695279i \(0.244719\pi\)
\(660\) 1.52078e11 0.0311975
\(661\) −5.93268e12 −1.20877 −0.604386 0.796692i \(-0.706581\pi\)
−0.604386 + 0.796692i \(0.706581\pi\)
\(662\) −5.85671e12 −1.18520
\(663\) 0 0
\(664\) −4.32423e12 −0.863282
\(665\) 1.63687e12 0.324575
\(666\) 3.87100e12 0.762411
\(667\) −6.74637e12 −1.31979
\(668\) 5.98719e11 0.116340
\(669\) 2.12801e12 0.410730
\(670\) −7.66106e12 −1.46877
\(671\) 2.52572e12 0.480988
\(672\) 4.78404e10 0.00904969
\(673\) 9.27751e12 1.74327 0.871633 0.490158i \(-0.163061\pi\)
0.871633 + 0.490158i \(0.163061\pi\)
\(674\) 7.30105e12 1.36275
\(675\) −3.41458e11 −0.0633096
\(676\) −5.22080e11 −0.0961562
\(677\) 6.80134e12 1.24436 0.622179 0.782875i \(-0.286248\pi\)
0.622179 + 0.782875i \(0.286248\pi\)
\(678\) −7.71102e11 −0.140145
\(679\) −1.01038e12 −0.182419
\(680\) 0 0
\(681\) −3.68897e11 −0.0657268
\(682\) −6.26655e11 −0.110917
\(683\) 8.67042e12 1.52457 0.762284 0.647242i \(-0.224078\pi\)
0.762284 + 0.647242i \(0.224078\pi\)
\(684\) 8.87129e11 0.154965
\(685\) −2.18994e12 −0.380036
\(686\) −2.07137e12 −0.357108
\(687\) 1.26280e12 0.216287
\(688\) −1.51515e12 −0.257814
\(689\) −1.82405e12 −0.308354
\(690\) 1.70760e12 0.286791
\(691\) 1.03357e13 1.72461 0.862304 0.506390i \(-0.169020\pi\)
0.862304 + 0.506390i \(0.169020\pi\)
\(692\) −7.84697e11 −0.130084
\(693\) 1.36445e12 0.224729
\(694\) 1.42586e12 0.233324
\(695\) −4.28762e11 −0.0697083
\(696\) 1.57478e12 0.254378
\(697\) 0 0
\(698\) −1.05495e12 −0.168222
\(699\) 1.53874e12 0.243791
\(700\) −1.79452e10 −0.00282492
\(701\) −1.00027e13 −1.56453 −0.782267 0.622944i \(-0.785937\pi\)
−0.782267 + 0.622944i \(0.785937\pi\)
\(702\) −3.76917e12 −0.585771
\(703\) −8.69767e12 −1.34309
\(704\) −8.69533e12 −1.33416
\(705\) −2.82982e12 −0.431427
\(706\) 4.94628e12 0.749302
\(707\) −1.69857e12 −0.255680
\(708\) 7.87793e10 0.0117832
\(709\) 7.69309e12 1.14339 0.571693 0.820467i \(-0.306287\pi\)
0.571693 + 0.820467i \(0.306287\pi\)
\(710\) 1.67665e12 0.247617
\(711\) −2.16624e12 −0.317902
\(712\) 5.13499e12 0.748824
\(713\) 8.11777e11 0.117634
\(714\) 0 0
\(715\) −1.28052e13 −1.83236
\(716\) −4.17645e11 −0.0593880
\(717\) −2.85391e12 −0.403278
\(718\) −4.37781e12 −0.614747
\(719\) −3.98924e12 −0.556686 −0.278343 0.960482i \(-0.589785\pi\)
−0.278343 + 0.960482i \(0.589785\pi\)
\(720\) 6.47003e12 0.897243
\(721\) −1.93580e11 −0.0266779
\(722\) 1.03637e13 1.41938
\(723\) 2.56232e12 0.348747
\(724\) −1.18912e12 −0.160844
\(725\) −1.12605e12 −0.151368
\(726\) 8.48280e11 0.113325
\(727\) −1.39684e13 −1.85456 −0.927279 0.374370i \(-0.877859\pi\)
−0.927279 + 0.374370i \(0.877859\pi\)
\(728\) −2.11316e12 −0.278832
\(729\) −5.33665e12 −0.699833
\(730\) 4.06635e12 0.529971
\(731\) 0 0
\(732\) 7.15926e10 0.00921655
\(733\) 8.88183e12 1.13641 0.568204 0.822887i \(-0.307638\pi\)
0.568204 + 0.822887i \(0.307638\pi\)
\(734\) −6.37176e12 −0.810265
\(735\) −1.86208e12 −0.235345
\(736\) 2.03272e12 0.255345
\(737\) 1.43487e13 1.79147
\(738\) 6.76056e12 0.838937
\(739\) −4.12811e12 −0.509156 −0.254578 0.967052i \(-0.581937\pi\)
−0.254578 + 0.967052i \(0.581937\pi\)
\(740\) 7.66118e11 0.0939188
\(741\) 4.12077e12 0.502107
\(742\) −3.33419e11 −0.0403806
\(743\) 1.16810e13 1.40615 0.703073 0.711118i \(-0.251811\pi\)
0.703073 + 0.711118i \(0.251811\pi\)
\(744\) −1.89491e11 −0.0226730
\(745\) −1.49240e13 −1.77493
\(746\) −1.42573e13 −1.68544
\(747\) −6.66403e12 −0.783059
\(748\) 0 0
\(749\) 2.80313e12 0.325443
\(750\) −1.71994e12 −0.198489
\(751\) 8.87631e11 0.101825 0.0509123 0.998703i \(-0.483787\pi\)
0.0509123 + 0.998703i \(0.483787\pi\)
\(752\) 1.37157e13 1.56400
\(753\) −2.70187e12 −0.306258
\(754\) −1.24298e13 −1.40053
\(755\) −2.04358e12 −0.228892
\(756\) 7.94855e10 0.00884993
\(757\) 1.30648e13 1.44602 0.723008 0.690840i \(-0.242759\pi\)
0.723008 + 0.690840i \(0.242759\pi\)
\(758\) −1.00524e13 −1.10600
\(759\) −3.19824e12 −0.349803
\(760\) −1.62348e13 −1.76517
\(761\) −1.23220e12 −0.133183 −0.0665915 0.997780i \(-0.521212\pi\)
−0.0665915 + 0.997780i \(0.521212\pi\)
\(762\) −8.56009e11 −0.0919773
\(763\) −3.04781e12 −0.325558
\(764\) 8.62558e11 0.0915943
\(765\) 0 0
\(766\) −6.19198e12 −0.649831
\(767\) −6.63333e12 −0.692074
\(768\) −6.76486e11 −0.0701671
\(769\) 1.35515e13 1.39739 0.698697 0.715417i \(-0.253763\pi\)
0.698697 + 0.715417i \(0.253763\pi\)
\(770\) −2.34067e12 −0.239957
\(771\) 1.73454e12 0.176783
\(772\) 2.70596e11 0.0274185
\(773\) 4.78823e12 0.482355 0.241178 0.970481i \(-0.422466\pi\)
0.241178 + 0.970481i \(0.422466\pi\)
\(774\) −2.60762e12 −0.261162
\(775\) 1.35495e11 0.0134917
\(776\) 1.00211e13 0.992064
\(777\) −3.79190e11 −0.0373218
\(778\) −5.13950e12 −0.502936
\(779\) −1.51902e13 −1.47790
\(780\) −3.62970e11 −0.0351111
\(781\) −3.14027e12 −0.302022
\(782\) 0 0
\(783\) 4.98765e12 0.474207
\(784\) 9.02521e12 0.853169
\(785\) 2.69007e12 0.252843
\(786\) −2.83520e12 −0.264961
\(787\) 1.01965e13 0.947470 0.473735 0.880668i \(-0.342906\pi\)
0.473735 + 0.880668i \(0.342906\pi\)
\(788\) 1.30467e12 0.120540
\(789\) −6.12331e11 −0.0562522
\(790\) 3.71612e12 0.339444
\(791\) −1.36922e12 −0.124360
\(792\) −1.35329e13 −1.22216
\(793\) −6.02821e12 −0.541326
\(794\) −1.00082e13 −0.893645
\(795\) −6.10947e11 −0.0542440
\(796\) 8.98501e11 0.0793250
\(797\) −2.90050e11 −0.0254631 −0.0127315 0.999919i \(-0.504053\pi\)
−0.0127315 + 0.999919i \(0.504053\pi\)
\(798\) 7.53237e11 0.0657535
\(799\) 0 0
\(800\) 3.39284e11 0.0292859
\(801\) 7.91348e12 0.679237
\(802\) 2.03372e12 0.173583
\(803\) −7.61605e12 −0.646413
\(804\) 4.06721e11 0.0343277
\(805\) 3.03214e12 0.254488
\(806\) 1.49565e12 0.124831
\(807\) 1.04872e12 0.0870422
\(808\) 1.68468e13 1.39049
\(809\) 8.66799e12 0.711459 0.355730 0.934589i \(-0.384232\pi\)
0.355730 + 0.934589i \(0.384232\pi\)
\(810\) 1.04869e13 0.855986
\(811\) 1.70242e13 1.38189 0.690943 0.722909i \(-0.257196\pi\)
0.690943 + 0.722909i \(0.257196\pi\)
\(812\) 2.62124e11 0.0211595
\(813\) −1.46222e12 −0.117383
\(814\) 1.24374e13 0.992936
\(815\) 1.64136e13 1.30315
\(816\) 0 0
\(817\) 5.85900e12 0.460070
\(818\) 1.29818e13 1.01379
\(819\) −3.25657e12 −0.252920
\(820\) 1.33800e12 0.103346
\(821\) −4.27376e12 −0.328296 −0.164148 0.986436i \(-0.552488\pi\)
−0.164148 + 0.986436i \(0.552488\pi\)
\(822\) −1.00774e12 −0.0769887
\(823\) 1.34081e13 1.01875 0.509376 0.860544i \(-0.329876\pi\)
0.509376 + 0.860544i \(0.329876\pi\)
\(824\) 1.91997e12 0.145085
\(825\) −5.33823e11 −0.0401194
\(826\) −1.21251e12 −0.0906307
\(827\) −1.90577e13 −1.41676 −0.708378 0.705833i \(-0.750573\pi\)
−0.708378 + 0.705833i \(0.750573\pi\)
\(828\) 1.64333e12 0.121503
\(829\) −2.19283e13 −1.61253 −0.806267 0.591551i \(-0.798516\pi\)
−0.806267 + 0.591551i \(0.798516\pi\)
\(830\) 1.14319e13 0.836120
\(831\) −3.57088e11 −0.0259759
\(832\) 2.07534e13 1.50153
\(833\) 0 0
\(834\) −1.97304e11 −0.0141217
\(835\) −1.68854e13 −1.20205
\(836\) 2.85033e12 0.201821
\(837\) −6.00154e11 −0.0422667
\(838\) −5.20228e12 −0.364414
\(839\) 2.60613e13 1.81580 0.907898 0.419192i \(-0.137687\pi\)
0.907898 + 0.419192i \(0.137687\pi\)
\(840\) −7.07784e11 −0.0490505
\(841\) 1.94094e12 0.133792
\(842\) 1.86422e12 0.127818
\(843\) −9.85260e11 −0.0671934
\(844\) −1.78144e12 −0.120846
\(845\) 1.47240e13 0.993504
\(846\) 2.36051e13 1.58431
\(847\) 1.50627e12 0.100560
\(848\) 2.96117e12 0.196644
\(849\) 1.59568e12 0.105405
\(850\) 0 0
\(851\) −1.61116e13 −1.05307
\(852\) −8.90124e10 −0.00578725
\(853\) −1.12348e13 −0.726598 −0.363299 0.931673i \(-0.618350\pi\)
−0.363299 + 0.931673i \(0.618350\pi\)
\(854\) −1.10190e12 −0.0708894
\(855\) −2.50193e13 −1.60113
\(856\) −2.78021e13 −1.76989
\(857\) 1.22547e13 0.776046 0.388023 0.921650i \(-0.373158\pi\)
0.388023 + 0.921650i \(0.373158\pi\)
\(858\) −5.89259e12 −0.371205
\(859\) −4.30100e12 −0.269526 −0.134763 0.990878i \(-0.543027\pi\)
−0.134763 + 0.990878i \(0.543027\pi\)
\(860\) −5.16079e11 −0.0321716
\(861\) −6.62242e11 −0.0410679
\(862\) 7.89195e12 0.486857
\(863\) 2.80501e12 0.172141 0.0860707 0.996289i \(-0.472569\pi\)
0.0860707 + 0.996289i \(0.472569\pi\)
\(864\) −1.50281e12 −0.0917470
\(865\) 2.21304e13 1.34406
\(866\) 1.59412e12 0.0963142
\(867\) 0 0
\(868\) −3.15409e10 −0.00188597
\(869\) −6.96008e12 −0.414024
\(870\) −4.16325e12 −0.246374
\(871\) −3.42465e13 −2.01621
\(872\) 3.02289e13 1.77051
\(873\) 1.54435e13 0.899873
\(874\) 3.20047e13 1.85529
\(875\) −3.05404e12 −0.176132
\(876\) −2.15880e11 −0.0123864
\(877\) 1.65539e13 0.944937 0.472468 0.881348i \(-0.343363\pi\)
0.472468 + 0.881348i \(0.343363\pi\)
\(878\) 1.09481e13 0.621747
\(879\) −3.90418e12 −0.220587
\(880\) 2.07881e13 1.16854
\(881\) 5.47621e12 0.306259 0.153129 0.988206i \(-0.451065\pi\)
0.153129 + 0.988206i \(0.451065\pi\)
\(882\) 1.55327e13 0.864246
\(883\) −1.05997e13 −0.586775 −0.293387 0.955994i \(-0.594783\pi\)
−0.293387 + 0.955994i \(0.594783\pi\)
\(884\) 0 0
\(885\) −2.22177e12 −0.121746
\(886\) −2.21373e12 −0.120691
\(887\) −4.63428e12 −0.251377 −0.125689 0.992070i \(-0.540114\pi\)
−0.125689 + 0.992070i \(0.540114\pi\)
\(888\) 3.76089e12 0.202970
\(889\) −1.51999e12 −0.0816174
\(890\) −1.35753e13 −0.725263
\(891\) −1.96415e13 −1.04406
\(892\) −3.51313e12 −0.185803
\(893\) −5.30378e13 −2.79096
\(894\) −6.86757e12 −0.359570
\(895\) 1.17786e13 0.613608
\(896\) 3.02996e12 0.157055
\(897\) 7.63334e12 0.393685
\(898\) 3.00151e13 1.54027
\(899\) −1.97916e12 −0.101056
\(900\) 2.74290e11 0.0139354
\(901\) 0 0
\(902\) 2.17215e13 1.09260
\(903\) 2.55433e11 0.0127845
\(904\) 1.35803e13 0.676316
\(905\) 3.35363e13 1.66187
\(906\) −9.40394e11 −0.0463696
\(907\) −2.01528e13 −0.988789 −0.494395 0.869238i \(-0.664610\pi\)
−0.494395 + 0.869238i \(0.664610\pi\)
\(908\) 6.09010e11 0.0297330
\(909\) 2.59625e13 1.26127
\(910\) 5.58655e12 0.270058
\(911\) −2.42307e13 −1.16556 −0.582778 0.812632i \(-0.698034\pi\)
−0.582778 + 0.812632i \(0.698034\pi\)
\(912\) −6.68967e12 −0.320205
\(913\) −2.14114e13 −1.01983
\(914\) 1.90861e13 0.904608
\(915\) −2.01909e12 −0.0952272
\(916\) −2.08475e12 −0.0978419
\(917\) −5.03438e12 −0.235117
\(918\) 0 0
\(919\) 3.39352e13 1.56939 0.784695 0.619881i \(-0.212819\pi\)
0.784695 + 0.619881i \(0.212819\pi\)
\(920\) −3.00734e13 −1.38401
\(921\) 3.56998e12 0.163492
\(922\) 2.91585e13 1.32885
\(923\) 7.49498e12 0.339909
\(924\) 1.24265e11 0.00560822
\(925\) −2.68922e12 −0.120778
\(926\) −2.15148e13 −0.961585
\(927\) 2.95884e12 0.131602
\(928\) −4.95590e12 −0.219360
\(929\) −4.44344e13 −1.95726 −0.978629 0.205632i \(-0.934075\pi\)
−0.978629 + 0.205632i \(0.934075\pi\)
\(930\) 5.00955e11 0.0219596
\(931\) −3.49000e13 −1.52248
\(932\) −2.54030e12 −0.110284
\(933\) −2.45008e12 −0.105855
\(934\) 1.40482e13 0.604033
\(935\) 0 0
\(936\) 3.22994e13 1.37548
\(937\) 1.07753e13 0.456669 0.228335 0.973583i \(-0.426672\pi\)
0.228335 + 0.973583i \(0.426672\pi\)
\(938\) −6.25994e12 −0.264033
\(939\) −6.51877e12 −0.273634
\(940\) 4.67173e12 0.195165
\(941\) −7.03292e12 −0.292403 −0.146202 0.989255i \(-0.546705\pi\)
−0.146202 + 0.989255i \(0.546705\pi\)
\(942\) 1.23789e12 0.0512217
\(943\) −2.81384e13 −1.15877
\(944\) 1.07686e13 0.441351
\(945\) −2.24169e12 −0.0914391
\(946\) −8.37821e12 −0.340127
\(947\) −2.60497e13 −1.05251 −0.526257 0.850325i \(-0.676405\pi\)
−0.526257 + 0.850325i \(0.676405\pi\)
\(948\) −1.97286e11 −0.00793341
\(949\) 1.81774e13 0.727503
\(950\) 5.34196e12 0.212787
\(951\) 1.10704e13 0.438885
\(952\) 0 0
\(953\) 2.63568e13 1.03508 0.517541 0.855658i \(-0.326847\pi\)
0.517541 + 0.855658i \(0.326847\pi\)
\(954\) 5.09626e12 0.199197
\(955\) −2.43263e13 −0.946370
\(956\) 4.71151e12 0.182431
\(957\) 7.79752e12 0.300506
\(958\) 3.27093e13 1.25466
\(959\) −1.78942e12 −0.0683171
\(960\) 6.95115e12 0.264141
\(961\) −2.62015e13 −0.990993
\(962\) −2.96848e13 −1.11750
\(963\) −4.28455e13 −1.60541
\(964\) −4.23012e12 −0.157763
\(965\) −7.63149e12 −0.283293
\(966\) 1.39530e12 0.0515550
\(967\) 3.86295e13 1.42069 0.710347 0.703852i \(-0.248538\pi\)
0.710347 + 0.703852i \(0.248538\pi\)
\(968\) −1.49395e13 −0.546885
\(969\) 0 0
\(970\) −2.64928e13 −0.960850
\(971\) 5.64860e12 0.203917 0.101959 0.994789i \(-0.467489\pi\)
0.101959 + 0.994789i \(0.467489\pi\)
\(972\) −1.83869e12 −0.0660710
\(973\) −3.50346e11 −0.0125311
\(974\) −1.60715e13 −0.572191
\(975\) 1.27409e12 0.0451523
\(976\) 9.78622e12 0.345216
\(977\) 1.04338e13 0.366368 0.183184 0.983079i \(-0.441360\pi\)
0.183184 + 0.983079i \(0.441360\pi\)
\(978\) 7.55306e12 0.263997
\(979\) 2.54259e13 0.884613
\(980\) 3.07410e12 0.106463
\(981\) 4.65854e13 1.60598
\(982\) 2.09344e13 0.718388
\(983\) 3.49221e13 1.19292 0.596458 0.802644i \(-0.296574\pi\)
0.596458 + 0.802644i \(0.296574\pi\)
\(984\) 6.56826e12 0.223343
\(985\) −3.67949e13 −1.24544
\(986\) 0 0
\(987\) −2.31227e12 −0.0775554
\(988\) −6.80296e12 −0.227139
\(989\) 1.08533e13 0.360725
\(990\) 3.57769e13 1.18371
\(991\) 2.80238e13 0.922986 0.461493 0.887144i \(-0.347314\pi\)
0.461493 + 0.887144i \(0.347314\pi\)
\(992\) 5.96334e11 0.0195518
\(993\) −8.76897e12 −0.286205
\(994\) 1.37001e12 0.0445128
\(995\) −2.53400e13 −0.819601
\(996\) −6.06915e11 −0.0195416
\(997\) −1.82363e13 −0.584532 −0.292266 0.956337i \(-0.594409\pi\)
−0.292266 + 0.956337i \(0.594409\pi\)
\(998\) 7.16643e12 0.228673
\(999\) 1.19115e13 0.378373
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 289.10.a.f.1.18 24
17.2 even 8 17.10.c.a.4.9 24
17.9 even 8 17.10.c.a.13.4 yes 24
17.16 even 2 inner 289.10.a.f.1.17 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.c.a.4.9 24 17.2 even 8
17.10.c.a.13.4 yes 24 17.9 even 8
289.10.a.f.1.17 24 17.16 even 2 inner
289.10.a.f.1.18 24 1.1 even 1 trivial