Properties

Label 17.10.a.b.1.7
Level $17$
Weight $10$
Character 17.1
Self dual yes
Analytic conductor $8.756$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 2986 x^{5} + 8252 x^{4} + 2252056 x^{3} - 10388768 x^{2} - 243559296 x - 675998208\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-43.1213\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q+43.1213 q^{2} -171.025 q^{3} +1347.45 q^{4} +1536.21 q^{5} -7374.84 q^{6} +3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +O(q^{10})\) \(q+43.1213 q^{2} -171.025 q^{3} +1347.45 q^{4} +1536.21 q^{5} -7374.84 q^{6} +3027.69 q^{7} +36025.5 q^{8} +9566.70 q^{9} +66243.5 q^{10} +51964.2 q^{11} -230448. q^{12} -166337. q^{13} +130558. q^{14} -262732. q^{15} +863574. q^{16} +83521.0 q^{17} +412529. q^{18} -1.03482e6 q^{19} +2.06997e6 q^{20} -517811. q^{21} +2.24076e6 q^{22} -647595. q^{23} -6.16128e6 q^{24} +406829. q^{25} -7.17269e6 q^{26} +1.73014e6 q^{27} +4.07964e6 q^{28} +101038. q^{29} -1.13293e7 q^{30} +1.03448e6 q^{31} +1.87934e7 q^{32} -8.88720e6 q^{33} +3.60153e6 q^{34} +4.65118e6 q^{35} +1.28906e7 q^{36} -5.58601e6 q^{37} -4.46226e7 q^{38} +2.84479e7 q^{39} +5.53429e7 q^{40} -4.18736e6 q^{41} -2.23287e7 q^{42} -9.60190e6 q^{43} +7.00190e7 q^{44} +1.46965e7 q^{45} -2.79251e7 q^{46} +3.98318e7 q^{47} -1.47693e8 q^{48} -3.11867e7 q^{49} +1.75430e7 q^{50} -1.42842e7 q^{51} -2.24131e8 q^{52} +6.22183e7 q^{53} +7.46060e7 q^{54} +7.98282e7 q^{55} +1.09074e8 q^{56} +1.76980e8 q^{57} +4.35690e6 q^{58} +9.60858e7 q^{59} -3.54017e8 q^{60} -1.86877e8 q^{61} +4.46079e7 q^{62} +2.89650e7 q^{63} +3.68245e8 q^{64} -2.55530e8 q^{65} -3.83228e8 q^{66} +3.73689e7 q^{67} +1.12540e8 q^{68} +1.10755e8 q^{69} +2.00565e8 q^{70} +2.04593e8 q^{71} +3.44645e8 q^{72} -1.95705e8 q^{73} -2.40876e8 q^{74} -6.95782e7 q^{75} -1.39436e9 q^{76} +1.57331e8 q^{77} +1.22671e9 q^{78} +2.72638e8 q^{79} +1.32663e9 q^{80} -4.84200e8 q^{81} -1.80564e8 q^{82} -1.96272e8 q^{83} -6.97723e8 q^{84} +1.28306e8 q^{85} -4.14046e8 q^{86} -1.72801e7 q^{87} +1.87204e9 q^{88} -3.93217e8 q^{89} +6.33732e8 q^{90} -5.03618e8 q^{91} -8.72600e8 q^{92} -1.76922e8 q^{93} +1.71760e9 q^{94} -1.58970e9 q^{95} -3.21414e9 q^{96} +8.75485e8 q^{97} -1.34481e9 q^{98} +4.97126e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + O(q^{10}) \) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + 154226q^{10} + 135536q^{11} + 198160q^{12} + 166122q^{13} + 447252q^{14} + 159048q^{15} + 1463585q^{16} + 584647q^{17} + 149027q^{18} + 777172q^{19} - 917162q^{20} - 3412104q^{21} - 1222520q^{22} + 1357764q^{23} - 8487360q^{24} + 1065785q^{25} - 14379966q^{26} - 4519064q^{27} - 3328892q^{28} + 967002q^{29} - 12558992q^{30} + 3546740q^{31} + 4825461q^{32} + 11928016q^{33} - 83521q^{34} - 530736q^{35} + 4535009q^{36} + 18296498q^{37} - 49363020q^{38} + 86306872q^{39} + 127155062q^{40} + 10285686q^{41} + 14620416q^{42} + 21913204q^{43} + 96696624q^{44} + 108916410q^{45} - 151509484q^{46} + 56639800q^{47} - 201398496q^{48} + 27010351q^{49} - 261150303q^{50} + 7349848q^{51} - 156226378q^{52} + 121813562q^{53} - 93375344q^{54} + 40793128q^{55} - 196175436q^{56} + 153612960q^{57} - 236833910q^{58} + 29222388q^{59} - 628643488q^{60} - 49915846q^{61} - 73506556q^{62} - 2185356q^{63} + 317922057q^{64} - 122633668q^{65} - 624886144q^{66} + 301863420q^{67} + 199531669q^{68} + 379683432q^{69} + 966315960q^{70} + 652473940q^{71} + 655760385q^{72} + 306656342q^{73} + 249173874q^{74} + 919071912q^{75} + 128694700q^{76} - 102442536q^{77} + 323434416q^{78} + 959147884q^{79} - 692173602q^{80} - 374486977q^{81} + 1046441254q^{82} - 1512945268q^{83} - 481790592q^{84} + 113755602q^{85} - 164953236q^{86} - 1612550856q^{87} + 1132038848q^{88} - 1971327114q^{89} - 2284664662q^{90} - 1061062864q^{91} + 901186756q^{92} - 798598936q^{93} + 2534831232q^{94} - 3249631512q^{95} - 4442036640q^{96} + 2006526254q^{97} - 2170640009q^{98} - 2579159272q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 43.1213 1.90571 0.952855 0.303426i \(-0.0981306\pi\)
0.952855 + 0.303426i \(0.0981306\pi\)
\(3\) −171.025 −1.21903 −0.609516 0.792774i \(-0.708636\pi\)
−0.609516 + 0.792774i \(0.708636\pi\)
\(4\) 1347.45 2.63173
\(5\) 1536.21 1.09923 0.549613 0.835420i \(-0.314775\pi\)
0.549613 + 0.835420i \(0.314775\pi\)
\(6\) −7374.84 −2.32312
\(7\) 3027.69 0.476617 0.238309 0.971189i \(-0.423407\pi\)
0.238309 + 0.971189i \(0.423407\pi\)
\(8\) 36025.5 3.10960
\(9\) 9566.70 0.486039
\(10\) 66243.5 2.09480
\(11\) 51964.2 1.07013 0.535066 0.844810i \(-0.320287\pi\)
0.535066 + 0.844810i \(0.320287\pi\)
\(12\) −230448. −3.20816
\(13\) −166337. −1.61527 −0.807635 0.589683i \(-0.799253\pi\)
−0.807635 + 0.589683i \(0.799253\pi\)
\(14\) 130558. 0.908294
\(15\) −262732. −1.33999
\(16\) 863574. 3.29427
\(17\) 83521.0 0.242536
\(18\) 412529. 0.926249
\(19\) −1.03482e6 −1.82168 −0.910840 0.412759i \(-0.864565\pi\)
−0.910840 + 0.412759i \(0.864565\pi\)
\(20\) 2.06997e6 2.89286
\(21\) −517811. −0.581012
\(22\) 2.24076e6 2.03936
\(23\) −647595. −0.482535 −0.241267 0.970459i \(-0.577563\pi\)
−0.241267 + 0.970459i \(0.577563\pi\)
\(24\) −6.16128e6 −3.79071
\(25\) 406829. 0.208297
\(26\) −7.17269e6 −3.07824
\(27\) 1.73014e6 0.626535
\(28\) 4.07964e6 1.25433
\(29\) 101038. 0.0265274 0.0132637 0.999912i \(-0.495778\pi\)
0.0132637 + 0.999912i \(0.495778\pi\)
\(30\) −1.13293e7 −2.55363
\(31\) 1.03448e6 0.201184 0.100592 0.994928i \(-0.467926\pi\)
0.100592 + 0.994928i \(0.467926\pi\)
\(32\) 1.87934e7 3.16833
\(33\) −8.88720e6 −1.30452
\(34\) 3.60153e6 0.462203
\(35\) 4.65118e6 0.523910
\(36\) 1.28906e7 1.27912
\(37\) −5.58601e6 −0.489998 −0.244999 0.969523i \(-0.578788\pi\)
−0.244999 + 0.969523i \(0.578788\pi\)
\(38\) −4.46226e7 −3.47159
\(39\) 2.84479e7 1.96907
\(40\) 5.53429e7 3.41816
\(41\) −4.18736e6 −0.231426 −0.115713 0.993283i \(-0.536915\pi\)
−0.115713 + 0.993283i \(0.536915\pi\)
\(42\) −2.23287e7 −1.10724
\(43\) −9.60190e6 −0.428301 −0.214151 0.976801i \(-0.568698\pi\)
−0.214151 + 0.976801i \(0.568698\pi\)
\(44\) 7.00190e7 2.81630
\(45\) 1.46965e7 0.534266
\(46\) −2.79251e7 −0.919571
\(47\) 3.98318e7 1.19067 0.595333 0.803479i \(-0.297020\pi\)
0.595333 + 0.803479i \(0.297020\pi\)
\(48\) −1.47693e8 −4.01582
\(49\) −3.11867e7 −0.772836
\(50\) 1.75430e7 0.396953
\(51\) −1.42842e7 −0.295659
\(52\) −2.24131e8 −4.25095
\(53\) 6.22183e7 1.08312 0.541560 0.840662i \(-0.317834\pi\)
0.541560 + 0.840662i \(0.317834\pi\)
\(54\) 7.46060e7 1.19399
\(55\) 7.98282e7 1.17632
\(56\) 1.09074e8 1.48209
\(57\) 1.76980e8 2.22069
\(58\) 4.35690e6 0.0505536
\(59\) 9.60858e7 1.03235 0.516173 0.856484i \(-0.327356\pi\)
0.516173 + 0.856484i \(0.327356\pi\)
\(60\) −3.54017e8 −3.52649
\(61\) −1.86877e8 −1.72811 −0.864055 0.503398i \(-0.832083\pi\)
−0.864055 + 0.503398i \(0.832083\pi\)
\(62\) 4.46079e7 0.383398
\(63\) 2.89650e7 0.231655
\(64\) 3.68245e8 2.74364
\(65\) −2.55530e8 −1.77555
\(66\) −3.83228e8 −2.48605
\(67\) 3.73689e7 0.226555 0.113278 0.993563i \(-0.463865\pi\)
0.113278 + 0.993563i \(0.463865\pi\)
\(68\) 1.12540e8 0.638288
\(69\) 1.10755e8 0.588225
\(70\) 2.00565e8 0.998420
\(71\) 2.04593e8 0.955495 0.477748 0.878497i \(-0.341453\pi\)
0.477748 + 0.878497i \(0.341453\pi\)
\(72\) 3.44645e8 1.51139
\(73\) −1.95705e8 −0.806581 −0.403291 0.915072i \(-0.632134\pi\)
−0.403291 + 0.915072i \(0.632134\pi\)
\(74\) −2.40876e8 −0.933793
\(75\) −6.95782e7 −0.253920
\(76\) −1.39436e9 −4.79417
\(77\) 1.57331e8 0.510043
\(78\) 1.22671e9 3.75247
\(79\) 2.72638e8 0.787524 0.393762 0.919212i \(-0.371173\pi\)
0.393762 + 0.919212i \(0.371173\pi\)
\(80\) 1.32663e9 3.62115
\(81\) −4.84200e8 −1.24981
\(82\) −1.80564e8 −0.441032
\(83\) −1.96272e8 −0.453950 −0.226975 0.973901i \(-0.572884\pi\)
−0.226975 + 0.973901i \(0.572884\pi\)
\(84\) −6.97723e8 −1.52907
\(85\) 1.28306e8 0.266601
\(86\) −4.14046e8 −0.816218
\(87\) −1.72801e7 −0.0323378
\(88\) 1.87204e9 3.32769
\(89\) −3.93217e8 −0.664319 −0.332160 0.943223i \(-0.607777\pi\)
−0.332160 + 0.943223i \(0.607777\pi\)
\(90\) 6.33732e8 1.01816
\(91\) −5.03618e8 −0.769865
\(92\) −8.72600e8 −1.26990
\(93\) −1.76922e8 −0.245249
\(94\) 1.71760e9 2.26906
\(95\) −1.58970e9 −2.00244
\(96\) −3.21414e9 −3.86229
\(97\) 8.75485e8 1.00410 0.502049 0.864839i \(-0.332580\pi\)
0.502049 + 0.864839i \(0.332580\pi\)
\(98\) −1.34481e9 −1.47280
\(99\) 4.97126e8 0.520126
\(100\) 5.48180e8 0.548180
\(101\) 2.76987e8 0.264858 0.132429 0.991192i \(-0.457722\pi\)
0.132429 + 0.991192i \(0.457722\pi\)
\(102\) −6.15954e8 −0.563440
\(103\) −5.47928e7 −0.0479685 −0.0239842 0.999712i \(-0.507635\pi\)
−0.0239842 + 0.999712i \(0.507635\pi\)
\(104\) −5.99239e9 −5.02285
\(105\) −7.95469e8 −0.638663
\(106\) 2.68293e9 2.06411
\(107\) 1.33346e9 0.983449 0.491724 0.870751i \(-0.336367\pi\)
0.491724 + 0.870751i \(0.336367\pi\)
\(108\) 2.33128e9 1.64887
\(109\) −7.04251e8 −0.477868 −0.238934 0.971036i \(-0.576798\pi\)
−0.238934 + 0.971036i \(0.576798\pi\)
\(110\) 3.44229e9 2.24172
\(111\) 9.55350e8 0.597323
\(112\) 2.61463e9 1.57011
\(113\) 1.40406e9 0.810091 0.405045 0.914297i \(-0.367256\pi\)
0.405045 + 0.914297i \(0.367256\pi\)
\(114\) 7.63160e9 4.23198
\(115\) −9.94845e8 −0.530414
\(116\) 1.36144e8 0.0698130
\(117\) −1.59130e9 −0.785084
\(118\) 4.14335e9 1.96735
\(119\) 2.52875e8 0.115597
\(120\) −9.46504e9 −4.16684
\(121\) 3.42331e8 0.145182
\(122\) −8.05837e9 −3.29328
\(123\) 7.16145e8 0.282116
\(124\) 1.39390e9 0.529461
\(125\) −2.37544e9 −0.870261
\(126\) 1.24901e9 0.441466
\(127\) 4.64719e8 0.158516 0.0792581 0.996854i \(-0.474745\pi\)
0.0792581 + 0.996854i \(0.474745\pi\)
\(128\) 6.25697e9 2.06025
\(129\) 1.64217e9 0.522113
\(130\) −1.10188e10 −3.38367
\(131\) 4.70705e9 1.39646 0.698229 0.715874i \(-0.253972\pi\)
0.698229 + 0.715874i \(0.253972\pi\)
\(132\) −1.19750e10 −3.43316
\(133\) −3.13310e9 −0.868244
\(134\) 1.61140e9 0.431748
\(135\) 2.65787e9 0.688703
\(136\) 3.00889e9 0.754190
\(137\) 4.09197e9 0.992407 0.496203 0.868206i \(-0.334727\pi\)
0.496203 + 0.868206i \(0.334727\pi\)
\(138\) 4.77591e9 1.12099
\(139\) −4.61710e8 −0.104907 −0.0524533 0.998623i \(-0.516704\pi\)
−0.0524533 + 0.998623i \(0.516704\pi\)
\(140\) 6.26721e9 1.37879
\(141\) −6.81226e9 −1.45146
\(142\) 8.82232e9 1.82090
\(143\) −8.64359e9 −1.72855
\(144\) 8.26156e9 1.60115
\(145\) 1.55216e8 0.0291596
\(146\) −8.43904e9 −1.53711
\(147\) 5.33372e9 0.942112
\(148\) −7.52685e9 −1.28954
\(149\) 1.87018e9 0.310847 0.155423 0.987848i \(-0.450326\pi\)
0.155423 + 0.987848i \(0.450326\pi\)
\(150\) −3.00030e9 −0.483898
\(151\) −6.04895e9 −0.946856 −0.473428 0.880833i \(-0.656984\pi\)
−0.473428 + 0.880833i \(0.656984\pi\)
\(152\) −3.72798e10 −5.66470
\(153\) 7.99021e8 0.117882
\(154\) 6.78433e9 0.971994
\(155\) 1.58918e9 0.221146
\(156\) 3.83321e10 5.18205
\(157\) 5.87552e9 0.771788 0.385894 0.922543i \(-0.373893\pi\)
0.385894 + 0.922543i \(0.373893\pi\)
\(158\) 1.17565e10 1.50079
\(159\) −1.06409e10 −1.32036
\(160\) 2.88706e10 3.48270
\(161\) −1.96072e9 −0.229984
\(162\) −2.08793e10 −2.38177
\(163\) 1.19332e10 1.32408 0.662039 0.749470i \(-0.269691\pi\)
0.662039 + 0.749470i \(0.269691\pi\)
\(164\) −5.64224e9 −0.609052
\(165\) −1.36526e10 −1.43397
\(166\) −8.46352e9 −0.865096
\(167\) 2.11741e9 0.210659 0.105330 0.994437i \(-0.466410\pi\)
0.105330 + 0.994437i \(0.466410\pi\)
\(168\) −1.86544e10 −1.80672
\(169\) 1.70637e10 1.60910
\(170\) 5.53273e9 0.508065
\(171\) −9.89978e9 −0.885407
\(172\) −1.29380e10 −1.12717
\(173\) 4.37524e9 0.371359 0.185680 0.982610i \(-0.440551\pi\)
0.185680 + 0.982610i \(0.440551\pi\)
\(174\) −7.45141e8 −0.0616264
\(175\) 1.23175e9 0.0992777
\(176\) 4.48749e10 3.52531
\(177\) −1.64331e10 −1.25846
\(178\) −1.69560e10 −1.26600
\(179\) 2.12791e9 0.154922 0.0774612 0.996995i \(-0.475319\pi\)
0.0774612 + 0.996995i \(0.475319\pi\)
\(180\) 1.98027e10 1.40604
\(181\) 1.80496e10 1.25001 0.625007 0.780619i \(-0.285096\pi\)
0.625007 + 0.780619i \(0.285096\pi\)
\(182\) −2.17166e10 −1.46714
\(183\) 3.19607e10 2.10662
\(184\) −2.33299e10 −1.50049
\(185\) −8.58131e9 −0.538618
\(186\) −7.62909e9 −0.467374
\(187\) 4.34010e9 0.259545
\(188\) 5.36713e10 3.13351
\(189\) 5.23833e9 0.298617
\(190\) −6.85499e10 −3.81606
\(191\) −6.31774e8 −0.0343488 −0.0171744 0.999853i \(-0.505467\pi\)
−0.0171744 + 0.999853i \(0.505467\pi\)
\(192\) −6.29792e10 −3.34458
\(193\) 1.51993e10 0.788524 0.394262 0.918998i \(-0.371000\pi\)
0.394262 + 0.918998i \(0.371000\pi\)
\(194\) 3.77520e10 1.91352
\(195\) 4.37021e10 2.16445
\(196\) −4.20224e10 −2.03390
\(197\) −2.63264e10 −1.24535 −0.622677 0.782479i \(-0.713955\pi\)
−0.622677 + 0.782479i \(0.713955\pi\)
\(198\) 2.14367e10 0.991209
\(199\) 3.40221e10 1.53788 0.768940 0.639321i \(-0.220784\pi\)
0.768940 + 0.639321i \(0.220784\pi\)
\(200\) 1.46562e10 0.647720
\(201\) −6.39104e9 −0.276178
\(202\) 1.19440e10 0.504743
\(203\) 3.05912e8 0.0126434
\(204\) −1.92472e10 −0.778094
\(205\) −6.43268e9 −0.254390
\(206\) −2.36273e9 −0.0914140
\(207\) −6.19535e9 −0.234531
\(208\) −1.43645e11 −5.32114
\(209\) −5.37734e10 −1.94944
\(210\) −3.43017e10 −1.21711
\(211\) −2.29918e10 −0.798550 −0.399275 0.916831i \(-0.630738\pi\)
−0.399275 + 0.916831i \(0.630738\pi\)
\(212\) 8.38358e10 2.85048
\(213\) −3.49906e10 −1.16478
\(214\) 5.75003e10 1.87417
\(215\) −1.47506e10 −0.470800
\(216\) 6.23293e10 1.94828
\(217\) 3.13207e9 0.0958876
\(218\) −3.03682e10 −0.910678
\(219\) 3.34705e10 0.983248
\(220\) 1.07564e11 3.09575
\(221\) −1.38927e10 −0.391760
\(222\) 4.11959e10 1.13832
\(223\) −5.81614e10 −1.57494 −0.787468 0.616355i \(-0.788609\pi\)
−0.787468 + 0.616355i \(0.788609\pi\)
\(224\) 5.69004e10 1.51008
\(225\) 3.89201e9 0.101240
\(226\) 6.05450e10 1.54380
\(227\) −6.36497e9 −0.159104 −0.0795518 0.996831i \(-0.525349\pi\)
−0.0795518 + 0.996831i \(0.525349\pi\)
\(228\) 2.38471e11 5.84425
\(229\) −7.25334e10 −1.74292 −0.871461 0.490464i \(-0.836827\pi\)
−0.871461 + 0.490464i \(0.836827\pi\)
\(230\) −4.28990e10 −1.01082
\(231\) −2.69077e10 −0.621759
\(232\) 3.63996e9 0.0824898
\(233\) −8.13370e10 −1.80795 −0.903975 0.427585i \(-0.859365\pi\)
−0.903975 + 0.427585i \(0.859365\pi\)
\(234\) −6.86190e10 −1.49614
\(235\) 6.11902e10 1.30881
\(236\) 1.29470e11 2.71686
\(237\) −4.66280e10 −0.960018
\(238\) 1.09043e10 0.220294
\(239\) 7.48651e10 1.48419 0.742094 0.670296i \(-0.233833\pi\)
0.742094 + 0.670296i \(0.233833\pi\)
\(240\) −2.26888e11 −4.41430
\(241\) −1.06255e10 −0.202896 −0.101448 0.994841i \(-0.532348\pi\)
−0.101448 + 0.994841i \(0.532348\pi\)
\(242\) 1.47618e10 0.276674
\(243\) 4.87561e10 0.897017
\(244\) −2.51806e11 −4.54792
\(245\) −4.79095e10 −0.849521
\(246\) 3.08811e10 0.537632
\(247\) 1.72129e11 2.94250
\(248\) 3.72675e10 0.625602
\(249\) 3.35676e10 0.553379
\(250\) −1.02432e11 −1.65846
\(251\) −9.55285e10 −1.51915 −0.759576 0.650418i \(-0.774594\pi\)
−0.759576 + 0.650418i \(0.774594\pi\)
\(252\) 3.90287e10 0.609652
\(253\) −3.36518e10 −0.516376
\(254\) 2.00393e10 0.302086
\(255\) −2.19436e10 −0.324996
\(256\) 8.12676e10 1.18260
\(257\) 6.50855e10 0.930647 0.465324 0.885141i \(-0.345938\pi\)
0.465324 + 0.885141i \(0.345938\pi\)
\(258\) 7.08125e10 0.994996
\(259\) −1.69127e10 −0.233541
\(260\) −3.44313e11 −4.67276
\(261\) 9.66604e8 0.0128934
\(262\) 2.02974e11 2.66124
\(263\) −6.33984e10 −0.817104 −0.408552 0.912735i \(-0.633966\pi\)
−0.408552 + 0.912735i \(0.633966\pi\)
\(264\) −3.20166e11 −4.05656
\(265\) 9.55806e10 1.19059
\(266\) −1.35103e11 −1.65462
\(267\) 6.72501e10 0.809826
\(268\) 5.03526e10 0.596232
\(269\) −7.50317e10 −0.873695 −0.436847 0.899536i \(-0.643905\pi\)
−0.436847 + 0.899536i \(0.643905\pi\)
\(270\) 1.14611e11 1.31247
\(271\) −9.55753e10 −1.07643 −0.538213 0.842809i \(-0.680900\pi\)
−0.538213 + 0.842809i \(0.680900\pi\)
\(272\) 7.21266e10 0.798979
\(273\) 8.61314e10 0.938490
\(274\) 1.76451e11 1.89124
\(275\) 2.11406e10 0.222905
\(276\) 1.49237e11 1.54805
\(277\) −1.40532e10 −0.143422 −0.0717110 0.997425i \(-0.522846\pi\)
−0.0717110 + 0.997425i \(0.522846\pi\)
\(278\) −1.99095e10 −0.199922
\(279\) 9.89653e9 0.0977831
\(280\) 1.67561e11 1.62915
\(281\) 1.00661e11 0.963124 0.481562 0.876412i \(-0.340070\pi\)
0.481562 + 0.876412i \(0.340070\pi\)
\(282\) −2.93753e11 −2.76606
\(283\) 7.78714e10 0.721670 0.360835 0.932630i \(-0.382492\pi\)
0.360835 + 0.932630i \(0.382492\pi\)
\(284\) 2.75678e11 2.51461
\(285\) 2.71879e11 2.44103
\(286\) −3.72723e11 −3.29412
\(287\) −1.26780e10 −0.110302
\(288\) 1.79791e11 1.53993
\(289\) 6.97576e9 0.0588235
\(290\) 6.69314e9 0.0555698
\(291\) −1.49730e11 −1.22403
\(292\) −2.63701e11 −2.12270
\(293\) −8.86150e10 −0.702429 −0.351215 0.936295i \(-0.614231\pi\)
−0.351215 + 0.936295i \(0.614231\pi\)
\(294\) 2.29997e11 1.79539
\(295\) 1.47608e11 1.13478
\(296\) −2.01239e11 −1.52370
\(297\) 8.99056e10 0.670475
\(298\) 8.06447e10 0.592383
\(299\) 1.07719e11 0.779423
\(300\) −9.37528e10 −0.668249
\(301\) −2.90716e10 −0.204136
\(302\) −2.60839e11 −1.80443
\(303\) −4.73718e10 −0.322871
\(304\) −8.93641e11 −6.00111
\(305\) −2.87083e11 −1.89958
\(306\) 3.44548e10 0.224648
\(307\) −1.69929e11 −1.09180 −0.545902 0.837849i \(-0.683813\pi\)
−0.545902 + 0.837849i \(0.683813\pi\)
\(308\) 2.11995e11 1.34230
\(309\) 9.37096e9 0.0584751
\(310\) 6.85274e10 0.421441
\(311\) 1.18662e11 0.719265 0.359633 0.933094i \(-0.382902\pi\)
0.359633 + 0.933094i \(0.382902\pi\)
\(312\) 1.02485e12 6.12301
\(313\) 2.52103e11 1.48467 0.742333 0.670032i \(-0.233719\pi\)
0.742333 + 0.670032i \(0.233719\pi\)
\(314\) 2.53360e11 1.47080
\(315\) 4.44964e10 0.254641
\(316\) 3.67365e11 2.07255
\(317\) 7.54487e10 0.419648 0.209824 0.977739i \(-0.432711\pi\)
0.209824 + 0.977739i \(0.432711\pi\)
\(318\) −4.58850e11 −2.51622
\(319\) 5.25038e9 0.0283878
\(320\) 5.65702e11 3.01587
\(321\) −2.28055e11 −1.19886
\(322\) −8.45486e10 −0.438283
\(323\) −8.64289e10 −0.441822
\(324\) −6.52433e11 −3.28915
\(325\) −6.76709e10 −0.336455
\(326\) 5.14576e11 2.52331
\(327\) 1.20445e11 0.582537
\(328\) −1.50852e11 −0.719645
\(329\) 1.20598e11 0.567492
\(330\) −5.88720e11 −2.73272
\(331\) −2.39508e11 −1.09672 −0.548358 0.836244i \(-0.684747\pi\)
−0.548358 + 0.836244i \(0.684747\pi\)
\(332\) −2.64466e11 −1.19467
\(333\) −5.34397e10 −0.238158
\(334\) 9.13054e10 0.401455
\(335\) 5.74067e10 0.249035
\(336\) −4.47169e11 −1.91401
\(337\) 8.05715e10 0.340288 0.170144 0.985419i \(-0.445577\pi\)
0.170144 + 0.985419i \(0.445577\pi\)
\(338\) 7.35807e11 3.06647
\(339\) −2.40131e11 −0.987526
\(340\) 1.72886e11 0.701623
\(341\) 5.37557e10 0.215293
\(342\) −4.26891e11 −1.68733
\(343\) −2.16602e11 −0.844964
\(344\) −3.45913e11 −1.33185
\(345\) 1.70144e11 0.646592
\(346\) 1.88666e11 0.707703
\(347\) −3.81897e11 −1.41405 −0.707024 0.707190i \(-0.749963\pi\)
−0.707024 + 0.707190i \(0.749963\pi\)
\(348\) −2.32840e10 −0.0851043
\(349\) −2.86306e11 −1.03304 −0.516518 0.856276i \(-0.672772\pi\)
−0.516518 + 0.856276i \(0.672772\pi\)
\(350\) 5.31147e10 0.189195
\(351\) −2.87788e11 −1.01202
\(352\) 9.76583e11 3.39053
\(353\) 3.83234e10 0.131364 0.0656822 0.997841i \(-0.479078\pi\)
0.0656822 + 0.997841i \(0.479078\pi\)
\(354\) −7.08618e11 −2.39827
\(355\) 3.14299e11 1.05030
\(356\) −5.29838e11 −1.74831
\(357\) −4.32481e10 −0.140916
\(358\) 9.17581e10 0.295237
\(359\) −8.46163e10 −0.268862 −0.134431 0.990923i \(-0.542921\pi\)
−0.134431 + 0.990923i \(0.542921\pi\)
\(360\) 5.29449e11 1.66136
\(361\) 7.48157e11 2.31852
\(362\) 7.78323e11 2.38216
\(363\) −5.85473e10 −0.176981
\(364\) −6.78598e11 −2.02608
\(365\) −3.00644e11 −0.886615
\(366\) 1.37819e12 4.01461
\(367\) 6.52825e11 1.87845 0.939225 0.343301i \(-0.111545\pi\)
0.939225 + 0.343301i \(0.111545\pi\)
\(368\) −5.59246e11 −1.58960
\(369\) −4.00592e10 −0.112482
\(370\) −3.70037e11 −1.02645
\(371\) 1.88377e11 0.516234
\(372\) −2.38392e11 −0.645430
\(373\) −9.69405e10 −0.259308 −0.129654 0.991559i \(-0.541387\pi\)
−0.129654 + 0.991559i \(0.541387\pi\)
\(374\) 1.87151e11 0.494618
\(375\) 4.06261e11 1.06088
\(376\) 1.43496e12 3.70250
\(377\) −1.68065e10 −0.0428489
\(378\) 2.25884e11 0.569078
\(379\) −6.80659e11 −1.69454 −0.847272 0.531159i \(-0.821757\pi\)
−0.847272 + 0.531159i \(0.821757\pi\)
\(380\) −2.14203e12 −5.26987
\(381\) −7.94788e10 −0.193236
\(382\) −2.72429e10 −0.0654589
\(383\) 1.56533e11 0.371717 0.185858 0.982577i \(-0.440493\pi\)
0.185858 + 0.982577i \(0.440493\pi\)
\(384\) −1.07010e12 −2.51151
\(385\) 2.41695e11 0.560652
\(386\) 6.55412e11 1.50270
\(387\) −9.18586e10 −0.208171
\(388\) 1.17967e12 2.64251
\(389\) −5.55777e11 −1.23063 −0.615315 0.788282i \(-0.710971\pi\)
−0.615315 + 0.788282i \(0.710971\pi\)
\(390\) 1.88449e12 4.12481
\(391\) −5.40878e10 −0.117032
\(392\) −1.12352e12 −2.40321
\(393\) −8.05025e11 −1.70233
\(394\) −1.13523e12 −2.37328
\(395\) 4.18830e11 0.865667
\(396\) 6.69851e11 1.36883
\(397\) −2.61410e11 −0.528159 −0.264079 0.964501i \(-0.585068\pi\)
−0.264079 + 0.964501i \(0.585068\pi\)
\(398\) 1.46708e12 2.93075
\(399\) 5.35840e11 1.05842
\(400\) 3.51327e11 0.686186
\(401\) 8.04746e10 0.155421 0.0777104 0.996976i \(-0.475239\pi\)
0.0777104 + 0.996976i \(0.475239\pi\)
\(402\) −2.75590e11 −0.526315
\(403\) −1.72072e11 −0.324966
\(404\) 3.73225e11 0.697035
\(405\) −7.43835e11 −1.37382
\(406\) 1.31913e10 0.0240947
\(407\) −2.90273e11 −0.524362
\(408\) −5.14596e11 −0.919382
\(409\) 4.96676e11 0.877643 0.438822 0.898574i \(-0.355396\pi\)
0.438822 + 0.898574i \(0.355396\pi\)
\(410\) −2.77386e11 −0.484793
\(411\) −6.99831e11 −1.20978
\(412\) −7.38303e10 −0.126240
\(413\) 2.90918e11 0.492034
\(414\) −2.67152e11 −0.446947
\(415\) −3.01516e11 −0.498993
\(416\) −3.12604e12 −5.11770
\(417\) 7.89642e10 0.127885
\(418\) −2.31878e12 −3.71506
\(419\) 5.00093e11 0.792661 0.396331 0.918108i \(-0.370283\pi\)
0.396331 + 0.918108i \(0.370283\pi\)
\(420\) −1.07185e12 −1.68079
\(421\) 9.47398e11 1.46982 0.734908 0.678167i \(-0.237225\pi\)
0.734908 + 0.678167i \(0.237225\pi\)
\(422\) −9.91436e11 −1.52180
\(423\) 3.81059e11 0.578710
\(424\) 2.24145e12 3.36808
\(425\) 3.39788e10 0.0505193
\(426\) −1.50884e12 −2.21973
\(427\) −5.65805e11 −0.823647
\(428\) 1.79676e12 2.58817
\(429\) 1.47827e12 2.10716
\(430\) −6.36064e11 −0.897207
\(431\) −5.09374e11 −0.711032 −0.355516 0.934670i \(-0.615695\pi\)
−0.355516 + 0.934670i \(0.615695\pi\)
\(432\) 1.49411e12 2.06398
\(433\) 1.25104e12 1.71032 0.855160 0.518365i \(-0.173459\pi\)
0.855160 + 0.518365i \(0.173459\pi\)
\(434\) 1.35059e11 0.182734
\(435\) −2.65460e10 −0.0355465
\(436\) −9.48940e11 −1.25762
\(437\) 6.70142e11 0.879024
\(438\) 1.44329e12 1.87379
\(439\) −1.15261e12 −1.48112 −0.740561 0.671989i \(-0.765440\pi\)
−0.740561 + 0.671989i \(0.765440\pi\)
\(440\) 2.87585e12 3.65788
\(441\) −2.98354e11 −0.375628
\(442\) −5.99070e11 −0.746582
\(443\) 1.57617e12 1.94440 0.972199 0.234155i \(-0.0752322\pi\)
0.972199 + 0.234155i \(0.0752322\pi\)
\(444\) 1.28728e12 1.57199
\(445\) −6.04065e11 −0.730237
\(446\) −2.50800e12 −3.00137
\(447\) −3.19849e11 −0.378932
\(448\) 1.11493e12 1.30766
\(449\) −1.39885e12 −1.62428 −0.812141 0.583461i \(-0.801698\pi\)
−0.812141 + 0.583461i \(0.801698\pi\)
\(450\) 1.67829e11 0.192935
\(451\) −2.17593e11 −0.247657
\(452\) 1.89190e12 2.13194
\(453\) 1.03452e12 1.15425
\(454\) −2.74466e11 −0.303205
\(455\) −7.73665e11 −0.846255
\(456\) 6.37579e12 6.90546
\(457\) 3.76472e11 0.403747 0.201874 0.979412i \(-0.435297\pi\)
0.201874 + 0.979412i \(0.435297\pi\)
\(458\) −3.12773e12 −3.32151
\(459\) 1.44503e11 0.151957
\(460\) −1.34050e12 −1.39591
\(461\) 2.03996e11 0.210362 0.105181 0.994453i \(-0.466458\pi\)
0.105181 + 0.994453i \(0.466458\pi\)
\(462\) −1.16029e12 −1.18489
\(463\) −1.19166e12 −1.20514 −0.602571 0.798065i \(-0.705857\pi\)
−0.602571 + 0.798065i \(0.705857\pi\)
\(464\) 8.72541e10 0.0873886
\(465\) −2.71790e11 −0.269584
\(466\) −3.50736e12 −3.44543
\(467\) −1.20046e12 −1.16795 −0.583973 0.811773i \(-0.698503\pi\)
−0.583973 + 0.811773i \(0.698503\pi\)
\(468\) −2.14419e12 −2.06613
\(469\) 1.13141e11 0.107980
\(470\) 2.63860e12 2.49421
\(471\) −1.00486e12 −0.940834
\(472\) 3.46154e12 3.21019
\(473\) −4.98955e11 −0.458339
\(474\) −2.01066e12 −1.82951
\(475\) −4.20994e11 −0.379450
\(476\) 3.40736e11 0.304219
\(477\) 5.95224e11 0.526439
\(478\) 3.22828e12 2.82843
\(479\) −3.78765e10 −0.0328746 −0.0164373 0.999865i \(-0.505232\pi\)
−0.0164373 + 0.999865i \(0.505232\pi\)
\(480\) −4.93761e12 −4.24553
\(481\) 9.29163e11 0.791478
\(482\) −4.58187e11 −0.386662
\(483\) 3.35332e11 0.280358
\(484\) 4.61273e11 0.382079
\(485\) 1.34493e12 1.10373
\(486\) 2.10243e12 1.70945
\(487\) 1.88071e12 1.51510 0.757550 0.652778i \(-0.226396\pi\)
0.757550 + 0.652778i \(0.226396\pi\)
\(488\) −6.73233e12 −5.37374
\(489\) −2.04088e12 −1.61409
\(490\) −2.06592e12 −1.61894
\(491\) −2.42874e11 −0.188588 −0.0942942 0.995544i \(-0.530059\pi\)
−0.0942942 + 0.995544i \(0.530059\pi\)
\(492\) 9.64967e11 0.742454
\(493\) 8.43882e9 0.00643384
\(494\) 7.42241e12 5.60756
\(495\) 7.63692e11 0.571735
\(496\) 8.93347e11 0.662754
\(497\) 6.19444e11 0.455405
\(498\) 1.44748e12 1.05458
\(499\) 7.88648e11 0.569417 0.284709 0.958614i \(-0.408103\pi\)
0.284709 + 0.958614i \(0.408103\pi\)
\(500\) −3.20078e12 −2.29029
\(501\) −3.62131e11 −0.256800
\(502\) −4.11931e12 −2.89506
\(503\) 1.92372e12 1.33994 0.669972 0.742386i \(-0.266306\pi\)
0.669972 + 0.742386i \(0.266306\pi\)
\(504\) 1.04348e12 0.720354
\(505\) 4.25512e11 0.291139
\(506\) −1.45111e12 −0.984062
\(507\) −2.91832e12 −1.96154
\(508\) 6.26184e11 0.417172
\(509\) 2.87805e12 1.90050 0.950250 0.311487i \(-0.100827\pi\)
0.950250 + 0.311487i \(0.100827\pi\)
\(510\) −9.46237e11 −0.619347
\(511\) −5.92532e11 −0.384431
\(512\) 3.00794e11 0.193443
\(513\) −1.79038e12 −1.14135
\(514\) 2.80657e12 1.77354
\(515\) −8.41734e10 −0.0527281
\(516\) 2.21273e12 1.37406
\(517\) 2.06983e12 1.27417
\(518\) −7.29297e11 −0.445062
\(519\) −7.48277e11 −0.452699
\(520\) −9.20560e12 −5.52124
\(521\) 2.41942e12 1.43861 0.719303 0.694697i \(-0.244461\pi\)
0.719303 + 0.694697i \(0.244461\pi\)
\(522\) 4.16812e10 0.0245710
\(523\) 2.25636e12 1.31872 0.659358 0.751829i \(-0.270828\pi\)
0.659358 + 0.751829i \(0.270828\pi\)
\(524\) 6.34249e12 3.67510
\(525\) −2.10661e11 −0.121023
\(526\) −2.73382e12 −1.55716
\(527\) 8.64005e10 0.0487942
\(528\) −7.67476e12 −4.29746
\(529\) −1.38177e12 −0.767160
\(530\) 4.12156e12 2.26893
\(531\) 9.19225e11 0.501760
\(532\) −4.22168e12 −2.28498
\(533\) 6.96515e11 0.373816
\(534\) 2.89991e12 1.54329
\(535\) 2.04847e12 1.08103
\(536\) 1.34623e12 0.704497
\(537\) −3.63926e11 −0.188855
\(538\) −3.23547e12 −1.66501
\(539\) −1.62059e12 −0.827036
\(540\) 3.58134e12 1.81248
\(541\) −2.18649e12 −1.09739 −0.548694 0.836023i \(-0.684875\pi\)
−0.548694 + 0.836023i \(0.684875\pi\)
\(542\) −4.12133e12 −2.05135
\(543\) −3.08695e12 −1.52381
\(544\) 1.56964e12 0.768432
\(545\) −1.08188e12 −0.525285
\(546\) 3.71410e12 1.78849
\(547\) −7.53862e11 −0.360039 −0.180019 0.983663i \(-0.557616\pi\)
−0.180019 + 0.983663i \(0.557616\pi\)
\(548\) 5.51371e12 2.61175
\(549\) −1.78780e12 −0.839929
\(550\) 9.11608e11 0.424792
\(551\) −1.04556e11 −0.0483245
\(552\) 3.99001e12 1.82915
\(553\) 8.25462e11 0.375348
\(554\) −6.05991e11 −0.273321
\(555\) 1.46762e12 0.656592
\(556\) −6.22130e11 −0.276086
\(557\) −2.08949e12 −0.919797 −0.459898 0.887972i \(-0.652114\pi\)
−0.459898 + 0.887972i \(0.652114\pi\)
\(558\) 4.26751e11 0.186346
\(559\) 1.59716e12 0.691822
\(560\) 4.01663e12 1.72590
\(561\) −7.42268e11 −0.316394
\(562\) 4.34063e12 1.83544
\(563\) −6.61278e11 −0.277393 −0.138697 0.990335i \(-0.544291\pi\)
−0.138697 + 0.990335i \(0.544291\pi\)
\(564\) −9.17915e12 −3.81985
\(565\) 2.15694e12 0.890472
\(566\) 3.35791e12 1.37529
\(567\) −1.46601e12 −0.595679
\(568\) 7.37057e12 2.97121
\(569\) −1.47797e12 −0.591100 −0.295550 0.955327i \(-0.595503\pi\)
−0.295550 + 0.955327i \(0.595503\pi\)
\(570\) 1.17238e13 4.65190
\(571\) −2.27003e12 −0.893652 −0.446826 0.894621i \(-0.647446\pi\)
−0.446826 + 0.894621i \(0.647446\pi\)
\(572\) −1.16468e13 −4.54908
\(573\) 1.08049e11 0.0418723
\(574\) −5.46692e11 −0.210203
\(575\) −2.63461e11 −0.100510
\(576\) 3.52289e12 1.33351
\(577\) −1.93038e12 −0.725021 −0.362511 0.931980i \(-0.618080\pi\)
−0.362511 + 0.931980i \(0.618080\pi\)
\(578\) 3.00804e11 0.112101
\(579\) −2.59946e12 −0.961235
\(580\) 2.09146e11 0.0767402
\(581\) −5.94251e11 −0.216360
\(582\) −6.45656e12 −2.33264
\(583\) 3.23312e12 1.15908
\(584\) −7.05036e12 −2.50815
\(585\) −2.44458e12 −0.862984
\(586\) −3.82119e12 −1.33863
\(587\) 2.62778e12 0.913518 0.456759 0.889590i \(-0.349010\pi\)
0.456759 + 0.889590i \(0.349010\pi\)
\(588\) 7.18690e12 2.47938
\(589\) −1.07049e12 −0.366492
\(590\) 6.36507e12 2.16256
\(591\) 4.50248e12 1.51813
\(592\) −4.82393e12 −1.61419
\(593\) 5.85157e12 1.94324 0.971620 0.236548i \(-0.0760162\pi\)
0.971620 + 0.236548i \(0.0760162\pi\)
\(594\) 3.87684e12 1.27773
\(595\) 3.88471e11 0.127067
\(596\) 2.51997e12 0.818064
\(597\) −5.81865e12 −1.87472
\(598\) 4.64500e12 1.48535
\(599\) 4.56968e11 0.145033 0.0725163 0.997367i \(-0.476897\pi\)
0.0725163 + 0.997367i \(0.476897\pi\)
\(600\) −2.50659e12 −0.789591
\(601\) −4.72333e12 −1.47677 −0.738385 0.674379i \(-0.764411\pi\)
−0.738385 + 0.674379i \(0.764411\pi\)
\(602\) −1.25360e12 −0.389023
\(603\) 3.57497e11 0.110115
\(604\) −8.15063e12 −2.49187
\(605\) 5.25894e11 0.159588
\(606\) −2.04274e12 −0.615298
\(607\) 1.89920e12 0.567836 0.283918 0.958849i \(-0.408366\pi\)
0.283918 + 0.958849i \(0.408366\pi\)
\(608\) −1.94477e13 −5.77168
\(609\) −5.23188e10 −0.0154127
\(610\) −1.23794e13 −3.62005
\(611\) −6.62553e12 −1.92325
\(612\) 1.07664e12 0.310233
\(613\) −5.38704e12 −1.54091 −0.770456 0.637493i \(-0.779971\pi\)
−0.770456 + 0.637493i \(0.779971\pi\)
\(614\) −7.32756e12 −2.08066
\(615\) 1.10015e12 0.310109
\(616\) 5.66794e12 1.58603
\(617\) −5.80011e11 −0.161121 −0.0805607 0.996750i \(-0.525671\pi\)
−0.0805607 + 0.996750i \(0.525671\pi\)
\(618\) 4.04088e11 0.111437
\(619\) −1.58371e12 −0.433579 −0.216790 0.976218i \(-0.569559\pi\)
−0.216790 + 0.976218i \(0.569559\pi\)
\(620\) 2.14133e12 0.581997
\(621\) −1.12043e12 −0.302325
\(622\) 5.11685e12 1.37071
\(623\) −1.19054e12 −0.316626
\(624\) 2.45669e13 6.48664
\(625\) −4.44378e12 −1.16491
\(626\) 1.08710e13 2.82934
\(627\) 9.19662e12 2.37643
\(628\) 7.91695e12 2.03114
\(629\) −4.66549e11 −0.118842
\(630\) 1.91874e12 0.485271
\(631\) 3.36740e12 0.845595 0.422797 0.906224i \(-0.361048\pi\)
0.422797 + 0.906224i \(0.361048\pi\)
\(632\) 9.82191e12 2.44889
\(633\) 3.93218e12 0.973458
\(634\) 3.25344e12 0.799727
\(635\) 7.13908e11 0.174245
\(636\) −1.43381e13 −3.47483
\(637\) 5.18752e12 1.24834
\(638\) 2.26403e11 0.0540990
\(639\) 1.95728e12 0.464408
\(640\) 9.61205e12 2.26468
\(641\) −7.80868e12 −1.82691 −0.913454 0.406943i \(-0.866595\pi\)
−0.913454 + 0.406943i \(0.866595\pi\)
\(642\) −9.83402e12 −2.28467
\(643\) −2.11639e12 −0.488255 −0.244128 0.969743i \(-0.578502\pi\)
−0.244128 + 0.969743i \(0.578502\pi\)
\(644\) −2.64196e12 −0.605257
\(645\) 2.52272e12 0.573920
\(646\) −3.72693e12 −0.841985
\(647\) 3.18454e12 0.714460 0.357230 0.934016i \(-0.383721\pi\)
0.357230 + 0.934016i \(0.383721\pi\)
\(648\) −1.74436e13 −3.88640
\(649\) 4.99302e12 1.10475
\(650\) −2.91806e12 −0.641186
\(651\) −5.35664e11 −0.116890
\(652\) 1.60794e13 3.48462
\(653\) 1.82854e12 0.393545 0.196772 0.980449i \(-0.436954\pi\)
0.196772 + 0.980449i \(0.436954\pi\)
\(654\) 5.19374e12 1.11015
\(655\) 7.23104e12 1.53502
\(656\) −3.61609e12 −0.762382
\(657\) −1.87225e12 −0.392030
\(658\) 5.20036e12 1.08148
\(659\) 7.92252e11 0.163636 0.0818181 0.996647i \(-0.473927\pi\)
0.0818181 + 0.996647i \(0.473927\pi\)
\(660\) −1.83962e13 −3.77381
\(661\) −7.49133e11 −0.152634 −0.0763172 0.997084i \(-0.524316\pi\)
−0.0763172 + 0.997084i \(0.524316\pi\)
\(662\) −1.03279e13 −2.09002
\(663\) 2.37600e12 0.477568
\(664\) −7.07081e12 −1.41160
\(665\) −4.81311e12 −0.954396
\(666\) −2.30439e12 −0.453860
\(667\) −6.54319e10 −0.0128004
\(668\) 2.85309e12 0.554398
\(669\) 9.94708e12 1.91990
\(670\) 2.47545e12 0.474589
\(671\) −9.71091e12 −1.84931
\(672\) −9.73142e12 −1.84083
\(673\) 7.01486e12 1.31811 0.659055 0.752095i \(-0.270957\pi\)
0.659055 + 0.752095i \(0.270957\pi\)
\(674\) 3.47435e12 0.648490
\(675\) 7.03873e11 0.130505
\(676\) 2.29923e13 4.23471
\(677\) 7.71992e12 1.41242 0.706210 0.708002i \(-0.250403\pi\)
0.706210 + 0.708002i \(0.250403\pi\)
\(678\) −1.03547e13 −1.88194
\(679\) 2.65069e12 0.478570
\(680\) 4.62229e12 0.829025
\(681\) 1.08857e12 0.193952
\(682\) 2.31802e12 0.410286
\(683\) −4.25216e12 −0.747680 −0.373840 0.927493i \(-0.621959\pi\)
−0.373840 + 0.927493i \(0.621959\pi\)
\(684\) −1.33394e13 −2.33015
\(685\) 6.28614e12 1.09088
\(686\) −9.34014e12 −1.61026
\(687\) 1.24051e13 2.12468
\(688\) −8.29195e12 −1.41094
\(689\) −1.03492e13 −1.74953
\(690\) 7.33682e12 1.23222
\(691\) −2.49111e12 −0.415664 −0.207832 0.978165i \(-0.566641\pi\)
−0.207832 + 0.978165i \(0.566641\pi\)
\(692\) 5.89539e12 0.977317
\(693\) 1.50514e12 0.247901
\(694\) −1.64679e13 −2.69476
\(695\) −7.09286e11 −0.115316
\(696\) −6.22525e11 −0.100558
\(697\) −3.49732e11 −0.0561291
\(698\) −1.23459e13 −1.96867
\(699\) 1.39107e13 2.20395
\(700\) 1.65972e12 0.261272
\(701\) −3.08136e11 −0.0481961 −0.0240980 0.999710i \(-0.507671\pi\)
−0.0240980 + 0.999710i \(0.507671\pi\)
\(702\) −1.24098e13 −1.92862
\(703\) 5.78049e12 0.892619
\(704\) 1.91355e13 2.93605
\(705\) −1.04651e13 −1.59548
\(706\) 1.65255e12 0.250342
\(707\) 8.38630e11 0.126236
\(708\) −2.21427e13 −3.31194
\(709\) −6.98388e12 −1.03798 −0.518990 0.854780i \(-0.673692\pi\)
−0.518990 + 0.854780i \(0.673692\pi\)
\(710\) 1.35530e13 2.00158
\(711\) 2.60824e12 0.382768
\(712\) −1.41658e13 −2.06577
\(713\) −6.69922e11 −0.0970781
\(714\) −1.86492e12 −0.268545
\(715\) −1.32784e13 −1.90007
\(716\) 2.86724e12 0.407714
\(717\) −1.28038e13 −1.80927
\(718\) −3.64876e12 −0.512373
\(719\) −1.30686e13 −1.82368 −0.911842 0.410540i \(-0.865340\pi\)
−0.911842 + 0.410540i \(0.865340\pi\)
\(720\) 1.26915e13 1.76002
\(721\) −1.65895e11 −0.0228626
\(722\) 3.22615e13 4.41842
\(723\) 1.81724e12 0.247337
\(724\) 2.43209e13 3.28970
\(725\) 4.11053e10 0.00552557
\(726\) −2.52464e12 −0.337275
\(727\) −1.13650e12 −0.150891 −0.0754456 0.997150i \(-0.524038\pi\)
−0.0754456 + 0.997150i \(0.524038\pi\)
\(728\) −1.81431e13 −2.39398
\(729\) 1.19197e12 0.156312
\(730\) −1.29642e13 −1.68963
\(731\) −8.01960e11 −0.103878
\(732\) 4.30653e13 5.54406
\(733\) 5.78287e12 0.739904 0.369952 0.929051i \(-0.379374\pi\)
0.369952 + 0.929051i \(0.379374\pi\)
\(734\) 2.81507e13 3.57978
\(735\) 8.19374e12 1.03559
\(736\) −1.21705e13 −1.52883
\(737\) 1.94185e12 0.242444
\(738\) −1.72741e12 −0.214359
\(739\) −1.05562e13 −1.30199 −0.650996 0.759081i \(-0.725649\pi\)
−0.650996 + 0.759081i \(0.725649\pi\)
\(740\) −1.15628e13 −1.41750
\(741\) −2.94384e13 −3.58701
\(742\) 8.12308e12 0.983792
\(743\) 1.33049e13 1.60163 0.800815 0.598912i \(-0.204400\pi\)
0.800815 + 0.598912i \(0.204400\pi\)
\(744\) −6.37370e12 −0.762629
\(745\) 2.87300e12 0.341690
\(746\) −4.18020e12 −0.494165
\(747\) −1.87768e12 −0.220637
\(748\) 5.84805e12 0.683053
\(749\) 4.03729e12 0.468729
\(750\) 1.75185e13 2.02172
\(751\) −2.33606e12 −0.267982 −0.133991 0.990983i \(-0.542779\pi\)
−0.133991 + 0.990983i \(0.542779\pi\)
\(752\) 3.43977e13 3.92238
\(753\) 1.63378e13 1.85190
\(754\) −7.24716e11 −0.0816576
\(755\) −9.29248e12 −1.04081
\(756\) 7.05837e12 0.785880
\(757\) −1.17644e13 −1.30208 −0.651039 0.759045i \(-0.725666\pi\)
−0.651039 + 0.759045i \(0.725666\pi\)
\(758\) −2.93509e13 −3.22931
\(759\) 5.75531e12 0.629478
\(760\) −5.72697e13 −6.22679
\(761\) 3.21795e12 0.347815 0.173907 0.984762i \(-0.444361\pi\)
0.173907 + 0.984762i \(0.444361\pi\)
\(762\) −3.42723e12 −0.368252
\(763\) −2.13225e12 −0.227760
\(764\) −8.51281e11 −0.0903968
\(765\) 1.22747e12 0.129579
\(766\) 6.74991e12 0.708384
\(767\) −1.59827e13 −1.66752
\(768\) −1.38988e13 −1.44163
\(769\) −9.65995e12 −0.996108 −0.498054 0.867146i \(-0.665952\pi\)
−0.498054 + 0.867146i \(0.665952\pi\)
\(770\) 1.04222e13 1.06844
\(771\) −1.11313e13 −1.13449
\(772\) 2.04802e13 2.07518
\(773\) −3.02219e12 −0.304449 −0.152224 0.988346i \(-0.548644\pi\)
−0.152224 + 0.988346i \(0.548644\pi\)
\(774\) −3.96106e12 −0.396714
\(775\) 4.20855e11 0.0419059
\(776\) 3.15398e13 3.12235
\(777\) 2.89250e12 0.284694
\(778\) −2.39658e13 −2.34522
\(779\) 4.33315e12 0.421585
\(780\) 5.88863e13 5.69624
\(781\) 1.06315e13 1.02251
\(782\) −2.33234e12 −0.223029
\(783\) 1.74811e11 0.0166204
\(784\) −2.69320e13 −2.54593
\(785\) 9.02606e12 0.848369
\(786\) −3.47137e13 −3.24414
\(787\) −1.47037e13 −1.36628 −0.683141 0.730286i \(-0.739387\pi\)
−0.683141 + 0.730286i \(0.739387\pi\)
\(788\) −3.54734e13 −3.27744
\(789\) 1.08427e13 0.996076
\(790\) 1.80605e13 1.64971
\(791\) 4.25106e12 0.386103
\(792\) 1.79092e13 1.61739
\(793\) 3.10846e13 2.79136
\(794\) −1.12723e13 −1.00652
\(795\) −1.63467e13 −1.45137
\(796\) 4.58430e13 4.04729
\(797\) −1.44405e13 −1.26771 −0.633856 0.773451i \(-0.718529\pi\)
−0.633856 + 0.773451i \(0.718529\pi\)
\(798\) 2.31061e13 2.01704
\(799\) 3.32680e12 0.288779
\(800\) 7.64569e12 0.659951
\(801\) −3.76179e12 −0.322885
\(802\) 3.47017e12 0.296187
\(803\) −1.01696e13 −0.863148
\(804\) −8.61158e12 −0.726826
\(805\) −3.01208e12 −0.252805
\(806\) −7.41997e12 −0.619291
\(807\) 1.28323e13 1.06506
\(808\) 9.97860e12 0.823604
\(809\) 1.10265e13 0.905041 0.452521 0.891754i \(-0.350525\pi\)
0.452521 + 0.891754i \(0.350525\pi\)
\(810\) −3.20751e13 −2.61810
\(811\) 1.97221e12 0.160088 0.0800440 0.996791i \(-0.474494\pi\)
0.0800440 + 0.996791i \(0.474494\pi\)
\(812\) 4.12200e11 0.0332741
\(813\) 1.63458e13 1.31220
\(814\) −1.25169e13 −0.999282
\(815\) 1.83320e13 1.45546
\(816\) −1.23355e13 −0.973981
\(817\) 9.93621e12 0.780228
\(818\) 2.14173e13 1.67253
\(819\) −4.81796e12 −0.374184
\(820\) −8.66769e12 −0.669485
\(821\) −1.24725e13 −0.958093 −0.479047 0.877789i \(-0.659018\pi\)
−0.479047 + 0.877789i \(0.659018\pi\)
\(822\) −3.01776e13 −2.30548
\(823\) 5.63904e12 0.428455 0.214228 0.976784i \(-0.431277\pi\)
0.214228 + 0.976784i \(0.431277\pi\)
\(824\) −1.97394e12 −0.149163
\(825\) −3.61557e12 −0.271728
\(826\) 1.25448e13 0.937674
\(827\) −6.43118e12 −0.478097 −0.239048 0.971008i \(-0.576835\pi\)
−0.239048 + 0.971008i \(0.576835\pi\)
\(828\) −8.34790e12 −0.617221
\(829\) −4.51844e12 −0.332272 −0.166136 0.986103i \(-0.553129\pi\)
−0.166136 + 0.986103i \(0.553129\pi\)
\(830\) −1.30018e13 −0.950936
\(831\) 2.40345e12 0.174836
\(832\) −6.12529e13 −4.43171
\(833\) −2.60475e12 −0.187440
\(834\) 3.40504e12 0.243711
\(835\) 3.25279e12 0.231562
\(836\) −7.24568e13 −5.13039
\(837\) 1.78979e12 0.126049
\(838\) 2.15647e13 1.51058
\(839\) 1.73764e13 1.21068 0.605342 0.795965i \(-0.293036\pi\)
0.605342 + 0.795965i \(0.293036\pi\)
\(840\) −2.86572e13 −1.98599
\(841\) −1.44969e13 −0.999296
\(842\) 4.08530e13 2.80104
\(843\) −1.72156e13 −1.17408
\(844\) −3.09802e13 −2.10157
\(845\) 2.62134e13 1.76876
\(846\) 1.64318e13 1.10285
\(847\) 1.03647e12 0.0691962
\(848\) 5.37301e13 3.56809
\(849\) −1.33180e13 −0.879739
\(850\) 1.46521e12 0.0962752
\(851\) 3.61747e12 0.236441
\(852\) −4.71480e13 −3.06538
\(853\) −3.23489e12 −0.209213 −0.104607 0.994514i \(-0.533358\pi\)
−0.104607 + 0.994514i \(0.533358\pi\)
\(854\) −2.43982e13 −1.56963
\(855\) −1.52082e13 −0.973262
\(856\) 4.80384e13 3.05814
\(857\) 6.56773e12 0.415912 0.207956 0.978138i \(-0.433319\pi\)
0.207956 + 0.978138i \(0.433319\pi\)
\(858\) 6.37451e13 4.01563
\(859\) −1.06597e13 −0.668001 −0.334000 0.942573i \(-0.608399\pi\)
−0.334000 + 0.942573i \(0.608399\pi\)
\(860\) −1.98756e13 −1.23902
\(861\) 2.16826e12 0.134461
\(862\) −2.19649e13 −1.35502
\(863\) −2.96333e12 −0.181857 −0.0909287 0.995857i \(-0.528984\pi\)
−0.0909287 + 0.995857i \(0.528984\pi\)
\(864\) 3.25152e13 1.98507
\(865\) 6.72130e12 0.408207
\(866\) 5.39466e13 3.25937
\(867\) −1.19303e12 −0.0717078
\(868\) 4.22029e12 0.252350
\(869\) 1.41674e13 0.842755
\(870\) −1.14470e12 −0.0677413
\(871\) −6.21585e12 −0.365948
\(872\) −2.53710e13 −1.48598
\(873\) 8.37551e12 0.488030
\(874\) 2.88974e13 1.67516
\(875\) −7.19209e12 −0.414781
\(876\) 4.50996e13 2.58764
\(877\) −1.22652e13 −0.700128 −0.350064 0.936726i \(-0.613840\pi\)
−0.350064 + 0.936726i \(0.613840\pi\)
\(878\) −4.97019e13 −2.82259
\(879\) 1.51554e13 0.856284
\(880\) 6.89375e13 3.87511
\(881\) 2.36185e13 1.32087 0.660435 0.750883i \(-0.270372\pi\)
0.660435 + 0.750883i \(0.270372\pi\)
\(882\) −1.28654e13 −0.715839
\(883\) 2.46792e13 1.36618 0.683089 0.730335i \(-0.260636\pi\)
0.683089 + 0.730335i \(0.260636\pi\)
\(884\) −1.87196e13 −1.03101
\(885\) −2.52448e13 −1.38333
\(886\) 6.79663e13 3.70546
\(887\) −8.49974e12 −0.461051 −0.230526 0.973066i \(-0.574045\pi\)
−0.230526 + 0.973066i \(0.574045\pi\)
\(888\) 3.44170e13 1.85744
\(889\) 1.40702e12 0.0755516
\(890\) −2.60481e13 −1.39162
\(891\) −2.51611e13 −1.33746
\(892\) −7.83694e13 −4.14481
\(893\) −4.12186e13 −2.16901
\(894\) −1.37923e13 −0.722134
\(895\) 3.26892e12 0.170295
\(896\) 1.89442e13 0.981950
\(897\) −1.84228e13 −0.950142
\(898\) −6.03201e13 −3.09541
\(899\) 1.04522e11 0.00533689
\(900\) 5.24428e12 0.266437
\(901\) 5.19653e12 0.262695
\(902\) −9.38288e12 −0.471962
\(903\) 4.97197e12 0.248848
\(904\) 5.05821e13 2.51906
\(905\) 2.77281e13 1.37405
\(906\) 4.46100e13 2.19966
\(907\) −1.51717e13 −0.744390 −0.372195 0.928155i \(-0.621395\pi\)
−0.372195 + 0.928155i \(0.621395\pi\)
\(908\) −8.57645e12 −0.418718
\(909\) 2.64985e12 0.128731
\(910\) −3.33614e13 −1.61272
\(911\) −2.65044e12 −0.127493 −0.0637464 0.997966i \(-0.520305\pi\)
−0.0637464 + 0.997966i \(0.520305\pi\)
\(912\) 1.52835e14 7.31555
\(913\) −1.01991e13 −0.485786
\(914\) 1.62340e13 0.769425
\(915\) 4.90985e13 2.31565
\(916\) −9.77348e13 −4.58690
\(917\) 1.42515e13 0.665576
\(918\) 6.23117e12 0.289586
\(919\) −1.10783e13 −0.512336 −0.256168 0.966632i \(-0.582460\pi\)
−0.256168 + 0.966632i \(0.582460\pi\)
\(920\) −3.58398e13 −1.64938
\(921\) 2.90622e13 1.33094
\(922\) 8.79656e12 0.400889
\(923\) −3.40315e13 −1.54338
\(924\) −3.62566e13 −1.63630
\(925\) −2.27255e12 −0.102065
\(926\) −5.13860e13 −2.29665
\(927\) −5.24186e11 −0.0233145
\(928\) 1.89885e12 0.0840475
\(929\) −1.10570e13 −0.487044 −0.243522 0.969895i \(-0.578303\pi\)
−0.243522 + 0.969895i \(0.578303\pi\)
\(930\) −1.17199e13 −0.513750
\(931\) 3.22725e13 1.40786
\(932\) −1.09597e14 −4.75804
\(933\) −2.02942e13 −0.876808
\(934\) −5.17655e13 −2.22577
\(935\) 6.66733e12 0.285299
\(936\) −5.73274e13 −2.44130
\(937\) −3.12152e13 −1.32293 −0.661466 0.749975i \(-0.730065\pi\)
−0.661466 + 0.749975i \(0.730065\pi\)
\(938\) 4.87880e12 0.205779
\(939\) −4.31160e13 −1.80985
\(940\) 8.24505e13 3.44444
\(941\) 3.48495e13 1.44891 0.724457 0.689320i \(-0.242090\pi\)
0.724457 + 0.689320i \(0.242090\pi\)
\(942\) −4.33310e13 −1.79296
\(943\) 2.71171e12 0.111671
\(944\) 8.29772e13 3.40083
\(945\) 8.04720e12 0.328248
\(946\) −2.15156e13 −0.873460
\(947\) 2.89060e13 1.16792 0.583960 0.811783i \(-0.301503\pi\)
0.583960 + 0.811783i \(0.301503\pi\)
\(948\) −6.28287e13 −2.52651
\(949\) 3.25530e13 1.30285
\(950\) −1.81538e13 −0.723121
\(951\) −1.29036e13 −0.511564
\(952\) 9.10996e12 0.359460
\(953\) 1.17377e13 0.460963 0.230482 0.973077i \(-0.425970\pi\)
0.230482 + 0.973077i \(0.425970\pi\)
\(954\) 2.56668e13 1.00324
\(955\) −9.70540e11 −0.0377571
\(956\) 1.00877e14 3.90598
\(957\) −8.97948e11 −0.0346057
\(958\) −1.63328e12 −0.0626494
\(959\) 1.23892e13 0.472998
\(960\) −9.67495e13 −3.67645
\(961\) −2.53695e13 −0.959525
\(962\) 4.00667e13 1.50833
\(963\) 1.27568e13 0.477994
\(964\) −1.43173e13 −0.533969
\(965\) 2.33493e13 0.866765
\(966\) 1.44600e13 0.534281
\(967\) 4.64159e13 1.70705 0.853527 0.521048i \(-0.174459\pi\)
0.853527 + 0.521048i \(0.174459\pi\)
\(968\) 1.23327e13 0.451458
\(969\) 1.47815e13 0.538596
\(970\) 5.79952e13 2.10339
\(971\) −3.56315e12 −0.128632 −0.0643158 0.997930i \(-0.520486\pi\)
−0.0643158 + 0.997930i \(0.520486\pi\)
\(972\) 6.56962e13 2.36071
\(973\) −1.39791e12 −0.0500003
\(974\) 8.10986e13 2.88734
\(975\) 1.15735e13 0.410150
\(976\) −1.61382e14 −5.69287
\(977\) −1.39593e13 −0.490160 −0.245080 0.969503i \(-0.578814\pi\)
−0.245080 + 0.969503i \(0.578814\pi\)
\(978\) −8.80056e13 −3.07599
\(979\) −2.04332e13 −0.710909
\(980\) −6.45554e13 −2.23571
\(981\) −6.73736e12 −0.232263
\(982\) −1.04731e13 −0.359395
\(983\) −6.28271e12 −0.214613 −0.107306 0.994226i \(-0.534223\pi\)
−0.107306 + 0.994226i \(0.534223\pi\)
\(984\) 2.57995e13 0.877270
\(985\) −4.04429e13 −1.36893
\(986\) 3.63893e11 0.0122610
\(987\) −2.06254e13 −0.691791
\(988\) 2.31934e14 7.74388
\(989\) 6.21815e12 0.206670
\(990\) 3.29314e13 1.08956
\(991\) −4.49640e13 −1.48093 −0.740463 0.672097i \(-0.765394\pi\)
−0.740463 + 0.672097i \(0.765394\pi\)
\(992\) 1.94413e13 0.637416
\(993\) 4.09619e13 1.33693
\(994\) 2.67112e13 0.867871
\(995\) 5.22653e13 1.69048
\(996\) 4.52305e13 1.45634
\(997\) −1.21770e13 −0.390311 −0.195156 0.980772i \(-0.562521\pi\)
−0.195156 + 0.980772i \(0.562521\pi\)
\(998\) 3.40075e13 1.08514
\(999\) −9.66460e12 −0.307001
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 17.10.a.b.1.7 7
3.2 odd 2 153.10.a.f.1.1 7
4.3 odd 2 272.10.a.g.1.6 7
17.16 even 2 289.10.a.b.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.b.1.7 7 1.1 even 1 trivial
153.10.a.f.1.1 7 3.2 odd 2
272.10.a.g.1.6 7 4.3 odd 2
289.10.a.b.1.7 7 17.16 even 2