Properties

Label 17.10.a.b.1.6
Level $17$
Weight $10$
Character 17.1
Self dual yes
Analytic conductor $8.756$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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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 1.6
Root \(-34.1532\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q+34.1532 q^{2} +169.801 q^{3} +654.438 q^{4} +195.287 q^{5} +5799.26 q^{6} -356.628 q^{7} +4864.71 q^{8} +9149.54 q^{9} +O(q^{10})\) \(q+34.1532 q^{2} +169.801 q^{3} +654.438 q^{4} +195.287 q^{5} +5799.26 q^{6} -356.628 q^{7} +4864.71 q^{8} +9149.54 q^{9} +6669.66 q^{10} -21467.8 q^{11} +111125. q^{12} -6206.76 q^{13} -12180.0 q^{14} +33160.0 q^{15} -168927. q^{16} +83521.0 q^{17} +312486. q^{18} +907187. q^{19} +127803. q^{20} -60556.0 q^{21} -733194. q^{22} -1.23486e6 q^{23} +826035. q^{24} -1.91499e6 q^{25} -211980. q^{26} -1.78860e6 q^{27} -233391. q^{28} -3.01596e6 q^{29} +1.13252e6 q^{30} -334277. q^{31} -8.26012e6 q^{32} -3.64527e6 q^{33} +2.85251e6 q^{34} -69644.7 q^{35} +5.98781e6 q^{36} +2.06102e7 q^{37} +3.09833e7 q^{38} -1.05392e6 q^{39} +950014. q^{40} +1.47571e7 q^{41} -2.06818e6 q^{42} -7.75953e6 q^{43} -1.40494e7 q^{44} +1.78679e6 q^{45} -4.21744e7 q^{46} +3.19993e7 q^{47} -2.86841e7 q^{48} -4.02264e7 q^{49} -6.54029e7 q^{50} +1.41820e7 q^{51} -4.06194e6 q^{52} +9.46750e7 q^{53} -6.10862e7 q^{54} -4.19238e6 q^{55} -1.73489e6 q^{56} +1.54042e8 q^{57} -1.03005e8 q^{58} +6.01771e7 q^{59} +2.17012e7 q^{60} +6.05254e7 q^{61} -1.14166e7 q^{62} -3.26298e6 q^{63} -1.95619e8 q^{64} -1.21210e6 q^{65} -1.24497e8 q^{66} -1.26316e8 q^{67} +5.46593e7 q^{68} -2.09681e8 q^{69} -2.37859e6 q^{70} +3.33917e7 q^{71} +4.45099e7 q^{72} +2.85706e8 q^{73} +7.03903e8 q^{74} -3.25168e8 q^{75} +5.93698e8 q^{76} +7.65603e6 q^{77} -3.59946e7 q^{78} -7.60575e7 q^{79} -3.29892e7 q^{80} -4.83797e8 q^{81} +5.04001e8 q^{82} -1.73620e7 q^{83} -3.96301e7 q^{84} +1.63105e7 q^{85} -2.65012e8 q^{86} -5.12115e8 q^{87} -1.04435e8 q^{88} +3.96876e8 q^{89} +6.10244e7 q^{90} +2.21350e6 q^{91} -8.08139e8 q^{92} -5.67608e7 q^{93} +1.09288e9 q^{94} +1.77162e8 q^{95} -1.40258e9 q^{96} +1.13120e9 q^{97} -1.37386e9 q^{98} -1.96421e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + O(q^{10}) \) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + 154226q^{10} + 135536q^{11} + 198160q^{12} + 166122q^{13} + 447252q^{14} + 159048q^{15} + 1463585q^{16} + 584647q^{17} + 149027q^{18} + 777172q^{19} - 917162q^{20} - 3412104q^{21} - 1222520q^{22} + 1357764q^{23} - 8487360q^{24} + 1065785q^{25} - 14379966q^{26} - 4519064q^{27} - 3328892q^{28} + 967002q^{29} - 12558992q^{30} + 3546740q^{31} + 4825461q^{32} + 11928016q^{33} - 83521q^{34} - 530736q^{35} + 4535009q^{36} + 18296498q^{37} - 49363020q^{38} + 86306872q^{39} + 127155062q^{40} + 10285686q^{41} + 14620416q^{42} + 21913204q^{43} + 96696624q^{44} + 108916410q^{45} - 151509484q^{46} + 56639800q^{47} - 201398496q^{48} + 27010351q^{49} - 261150303q^{50} + 7349848q^{51} - 156226378q^{52} + 121813562q^{53} - 93375344q^{54} + 40793128q^{55} - 196175436q^{56} + 153612960q^{57} - 236833910q^{58} + 29222388q^{59} - 628643488q^{60} - 49915846q^{61} - 73506556q^{62} - 2185356q^{63} + 317922057q^{64} - 122633668q^{65} - 624886144q^{66} + 301863420q^{67} + 199531669q^{68} + 379683432q^{69} + 966315960q^{70} + 652473940q^{71} + 655760385q^{72} + 306656342q^{73} + 249173874q^{74} + 919071912q^{75} + 128694700q^{76} - 102442536q^{77} + 323434416q^{78} + 959147884q^{79} - 692173602q^{80} - 374486977q^{81} + 1046441254q^{82} - 1512945268q^{83} - 481790592q^{84} + 113755602q^{85} - 164953236q^{86} - 1612550856q^{87} + 1132038848q^{88} - 1971327114q^{89} - 2284664662q^{90} - 1061062864q^{91} + 901186756q^{92} - 798598936q^{93} + 2534831232q^{94} - 3249631512q^{95} - 4442036640q^{96} + 2006526254q^{97} - 2170640009q^{98} - 2579159272q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 34.1532 1.50937 0.754685 0.656087i \(-0.227790\pi\)
0.754685 + 0.656087i \(0.227790\pi\)
\(3\) 169.801 1.21031 0.605154 0.796109i \(-0.293112\pi\)
0.605154 + 0.796109i \(0.293112\pi\)
\(4\) 654.438 1.27820
\(5\) 195.287 0.139736 0.0698679 0.997556i \(-0.477742\pi\)
0.0698679 + 0.997556i \(0.477742\pi\)
\(6\) 5799.26 1.82680
\(7\) −356.628 −0.0561402 −0.0280701 0.999606i \(-0.508936\pi\)
−0.0280701 + 0.999606i \(0.508936\pi\)
\(8\) 4864.71 0.419906
\(9\) 9149.54 0.464845
\(10\) 6669.66 0.210913
\(11\) −21467.8 −0.442101 −0.221050 0.975262i \(-0.570949\pi\)
−0.221050 + 0.975262i \(0.570949\pi\)
\(12\) 111125. 1.54701
\(13\) −6206.76 −0.0602726 −0.0301363 0.999546i \(-0.509594\pi\)
−0.0301363 + 0.999546i \(0.509594\pi\)
\(14\) −12180.0 −0.0847364
\(15\) 33160.0 0.169123
\(16\) −168927. −0.644406
\(17\) 83521.0 0.242536
\(18\) 312486. 0.701623
\(19\) 907187. 1.59700 0.798501 0.601993i \(-0.205627\pi\)
0.798501 + 0.601993i \(0.205627\pi\)
\(20\) 127803. 0.178610
\(21\) −60556.0 −0.0679470
\(22\) −733194. −0.667294
\(23\) −1.23486e6 −0.920115 −0.460058 0.887889i \(-0.652171\pi\)
−0.460058 + 0.887889i \(0.652171\pi\)
\(24\) 826035. 0.508216
\(25\) −1.91499e6 −0.980474
\(26\) −211980. −0.0909737
\(27\) −1.78860e6 −0.647702
\(28\) −233391. −0.0717584
\(29\) −3.01596e6 −0.791835 −0.395917 0.918286i \(-0.629573\pi\)
−0.395917 + 0.918286i \(0.629573\pi\)
\(30\) 1.13252e6 0.255270
\(31\) −334277. −0.0650099 −0.0325049 0.999472i \(-0.510348\pi\)
−0.0325049 + 0.999472i \(0.510348\pi\)
\(32\) −8.26012e6 −1.39255
\(33\) −3.64527e6 −0.535078
\(34\) 2.85251e6 0.366076
\(35\) −69644.7 −0.00784481
\(36\) 5.98781e6 0.594165
\(37\) 2.06102e7 1.80790 0.903949 0.427640i \(-0.140655\pi\)
0.903949 + 0.427640i \(0.140655\pi\)
\(38\) 3.09833e7 2.41047
\(39\) −1.05392e6 −0.0729484
\(40\) 950014. 0.0586759
\(41\) 1.47571e7 0.815593 0.407796 0.913073i \(-0.366297\pi\)
0.407796 + 0.913073i \(0.366297\pi\)
\(42\) −2.06818e6 −0.102557
\(43\) −7.75953e6 −0.346120 −0.173060 0.984911i \(-0.555366\pi\)
−0.173060 + 0.984911i \(0.555366\pi\)
\(44\) −1.40494e7 −0.565093
\(45\) 1.78679e6 0.0649555
\(46\) −4.21744e7 −1.38880
\(47\) 3.19993e7 0.956534 0.478267 0.878214i \(-0.341265\pi\)
0.478267 + 0.878214i \(0.341265\pi\)
\(48\) −2.86841e7 −0.779929
\(49\) −4.02264e7 −0.996848
\(50\) −6.54029e7 −1.47990
\(51\) 1.41820e7 0.293543
\(52\) −4.06194e6 −0.0770404
\(53\) 9.46750e7 1.64814 0.824070 0.566488i \(-0.191698\pi\)
0.824070 + 0.566488i \(0.191698\pi\)
\(54\) −6.10862e7 −0.977623
\(55\) −4.19238e6 −0.0617773
\(56\) −1.73489e6 −0.0235736
\(57\) 1.54042e8 1.93286
\(58\) −1.03005e8 −1.19517
\(59\) 6.01771e7 0.646542 0.323271 0.946306i \(-0.395217\pi\)
0.323271 + 0.946306i \(0.395217\pi\)
\(60\) 2.17012e7 0.216173
\(61\) 6.05254e7 0.559698 0.279849 0.960044i \(-0.409716\pi\)
0.279849 + 0.960044i \(0.409716\pi\)
\(62\) −1.14166e7 −0.0981240
\(63\) −3.26298e6 −0.0260965
\(64\) −1.95619e8 −1.45747
\(65\) −1.21210e6 −0.00842224
\(66\) −1.24497e8 −0.807631
\(67\) −1.26316e8 −0.765813 −0.382907 0.923787i \(-0.625077\pi\)
−0.382907 + 0.923787i \(0.625077\pi\)
\(68\) 5.46593e7 0.310009
\(69\) −2.09681e8 −1.11362
\(70\) −2.37859e6 −0.0118407
\(71\) 3.33917e7 0.155947 0.0779734 0.996955i \(-0.475155\pi\)
0.0779734 + 0.996955i \(0.475155\pi\)
\(72\) 4.45099e7 0.195191
\(73\) 2.85706e8 1.17752 0.588758 0.808309i \(-0.299617\pi\)
0.588758 + 0.808309i \(0.299617\pi\)
\(74\) 7.03903e8 2.72879
\(75\) −3.25168e8 −1.18668
\(76\) 5.93698e8 2.04129
\(77\) 7.65603e6 0.0248196
\(78\) −3.59946e7 −0.110106
\(79\) −7.60575e7 −0.219695 −0.109848 0.993948i \(-0.535036\pi\)
−0.109848 + 0.993948i \(0.535036\pi\)
\(80\) −3.29892e7 −0.0900466
\(81\) −4.83797e8 −1.24876
\(82\) 5.04001e8 1.23103
\(83\) −1.73620e7 −0.0401558 −0.0200779 0.999798i \(-0.506391\pi\)
−0.0200779 + 0.999798i \(0.506391\pi\)
\(84\) −3.96301e7 −0.0868498
\(85\) 1.63105e7 0.0338909
\(86\) −2.65012e8 −0.522424
\(87\) −5.12115e8 −0.958364
\(88\) −1.04435e8 −0.185641
\(89\) 3.96876e8 0.670501 0.335251 0.942129i \(-0.391179\pi\)
0.335251 + 0.942129i \(0.391179\pi\)
\(90\) 6.10244e7 0.0980419
\(91\) 2.21350e6 0.00338372
\(92\) −8.08139e8 −1.17609
\(93\) −5.67608e7 −0.0786819
\(94\) 1.09288e9 1.44376
\(95\) 1.77162e8 0.223159
\(96\) −1.40258e9 −1.68542
\(97\) 1.13120e9 1.29737 0.648687 0.761055i \(-0.275318\pi\)
0.648687 + 0.761055i \(0.275318\pi\)
\(98\) −1.37386e9 −1.50461
\(99\) −1.96421e8 −0.205508
\(100\) −1.25324e9 −1.25324
\(101\) −1.58638e9 −1.51692 −0.758458 0.651722i \(-0.774047\pi\)
−0.758458 + 0.651722i \(0.774047\pi\)
\(102\) 4.84360e8 0.443065
\(103\) −9.77937e8 −0.856137 −0.428068 0.903746i \(-0.640806\pi\)
−0.428068 + 0.903746i \(0.640806\pi\)
\(104\) −3.01941e7 −0.0253088
\(105\) −1.18258e7 −0.00949463
\(106\) 3.23345e9 2.48765
\(107\) −1.71253e8 −0.126302 −0.0631511 0.998004i \(-0.520115\pi\)
−0.0631511 + 0.998004i \(0.520115\pi\)
\(108\) −1.17053e9 −0.827893
\(109\) 1.66962e9 1.13292 0.566461 0.824089i \(-0.308312\pi\)
0.566461 + 0.824089i \(0.308312\pi\)
\(110\) −1.43183e8 −0.0932449
\(111\) 3.49964e9 2.18811
\(112\) 6.02441e7 0.0361771
\(113\) −2.55660e9 −1.47506 −0.737531 0.675313i \(-0.764008\pi\)
−0.737531 + 0.675313i \(0.764008\pi\)
\(114\) 5.26101e9 2.91741
\(115\) −2.41152e8 −0.128573
\(116\) −1.97376e9 −1.01212
\(117\) −5.67890e7 −0.0280174
\(118\) 2.05524e9 0.975872
\(119\) −2.97859e7 −0.0136160
\(120\) 1.61314e8 0.0710159
\(121\) −1.89708e9 −0.804547
\(122\) 2.06713e9 0.844792
\(123\) 2.50578e9 0.987118
\(124\) −2.18764e8 −0.0830956
\(125\) −7.55391e8 −0.276743
\(126\) −1.11441e8 −0.0393893
\(127\) −1.57297e9 −0.536542 −0.268271 0.963344i \(-0.586452\pi\)
−0.268271 + 0.963344i \(0.586452\pi\)
\(128\) −2.45181e9 −0.807313
\(129\) −1.31758e9 −0.418912
\(130\) −4.13970e7 −0.0127123
\(131\) 1.54185e9 0.457426 0.228713 0.973494i \(-0.426548\pi\)
0.228713 + 0.973494i \(0.426548\pi\)
\(132\) −2.38560e9 −0.683936
\(133\) −3.23528e8 −0.0896561
\(134\) −4.31410e9 −1.15590
\(135\) −3.49289e8 −0.0905072
\(136\) 4.06306e8 0.101842
\(137\) −7.48495e9 −1.81529 −0.907646 0.419736i \(-0.862123\pi\)
−0.907646 + 0.419736i \(0.862123\pi\)
\(138\) −7.16127e9 −1.68087
\(139\) 4.97076e9 1.12942 0.564711 0.825289i \(-0.308988\pi\)
0.564711 + 0.825289i \(0.308988\pi\)
\(140\) −4.55782e7 −0.0100272
\(141\) 5.43353e9 1.15770
\(142\) 1.14043e9 0.235382
\(143\) 1.33246e8 0.0266465
\(144\) −1.54561e9 −0.299549
\(145\) −5.88977e8 −0.110648
\(146\) 9.75777e9 1.77731
\(147\) −6.83051e9 −1.20649
\(148\) 1.34881e10 2.31085
\(149\) −2.17167e9 −0.360957 −0.180479 0.983579i \(-0.557765\pi\)
−0.180479 + 0.983579i \(0.557765\pi\)
\(150\) −1.11055e10 −1.79113
\(151\) 5.05353e9 0.791040 0.395520 0.918457i \(-0.370564\pi\)
0.395520 + 0.918457i \(0.370564\pi\)
\(152\) 4.41320e9 0.670591
\(153\) 7.64179e8 0.112741
\(154\) 2.61478e8 0.0374620
\(155\) −6.52799e7 −0.00908421
\(156\) −6.89723e8 −0.0932426
\(157\) −1.14585e10 −1.50515 −0.752577 0.658504i \(-0.771190\pi\)
−0.752577 + 0.658504i \(0.771190\pi\)
\(158\) −2.59760e9 −0.331601
\(159\) 1.60760e10 1.99476
\(160\) −1.61309e9 −0.194590
\(161\) 4.40386e8 0.0516555
\(162\) −1.65232e10 −1.88485
\(163\) 1.58612e10 1.75992 0.879960 0.475048i \(-0.157569\pi\)
0.879960 + 0.475048i \(0.157569\pi\)
\(164\) 9.65760e9 1.04249
\(165\) −7.11873e8 −0.0747696
\(166\) −5.92966e8 −0.0606099
\(167\) −7.94993e9 −0.790932 −0.395466 0.918481i \(-0.629417\pi\)
−0.395466 + 0.918481i \(0.629417\pi\)
\(168\) −2.94587e8 −0.0285313
\(169\) −1.05660e10 −0.996367
\(170\) 5.57057e8 0.0511540
\(171\) 8.30035e9 0.742359
\(172\) −5.07813e9 −0.442411
\(173\) 4.82389e9 0.409440 0.204720 0.978821i \(-0.434372\pi\)
0.204720 + 0.978821i \(0.434372\pi\)
\(174\) −1.74903e10 −1.44653
\(175\) 6.82938e8 0.0550440
\(176\) 3.62650e9 0.284892
\(177\) 1.02182e10 0.782515
\(178\) 1.35546e10 1.01203
\(179\) −6.50866e9 −0.473863 −0.236932 0.971526i \(-0.576142\pi\)
−0.236932 + 0.971526i \(0.576142\pi\)
\(180\) 1.16934e9 0.0830261
\(181\) 9.87513e9 0.683895 0.341947 0.939719i \(-0.388914\pi\)
0.341947 + 0.939719i \(0.388914\pi\)
\(182\) 7.55982e7 0.00510728
\(183\) 1.02773e10 0.677407
\(184\) −6.00724e9 −0.386362
\(185\) 4.02490e9 0.252628
\(186\) −1.93856e9 −0.118760
\(187\) −1.79301e9 −0.107225
\(188\) 2.09416e10 1.22264
\(189\) 6.37864e8 0.0363622
\(190\) 6.05063e9 0.336829
\(191\) 1.73272e10 0.942060 0.471030 0.882117i \(-0.343882\pi\)
0.471030 + 0.882117i \(0.343882\pi\)
\(192\) −3.32163e10 −1.76399
\(193\) −5.92773e9 −0.307525 −0.153763 0.988108i \(-0.549139\pi\)
−0.153763 + 0.988108i \(0.549139\pi\)
\(194\) 3.86339e10 1.95822
\(195\) −2.05816e8 −0.0101935
\(196\) −2.63257e10 −1.27417
\(197\) −1.61285e10 −0.762948 −0.381474 0.924380i \(-0.624583\pi\)
−0.381474 + 0.924380i \(0.624583\pi\)
\(198\) −6.70839e9 −0.310188
\(199\) −4.38224e10 −1.98088 −0.990438 0.137958i \(-0.955946\pi\)
−0.990438 + 0.137958i \(0.955946\pi\)
\(200\) −9.31586e9 −0.411707
\(201\) −2.14487e10 −0.926870
\(202\) −5.41800e10 −2.28959
\(203\) 1.07558e9 0.0444538
\(204\) 9.28123e9 0.375206
\(205\) 2.88186e9 0.113968
\(206\) −3.33996e10 −1.29223
\(207\) −1.12984e10 −0.427711
\(208\) 1.04849e9 0.0388400
\(209\) −1.94753e10 −0.706036
\(210\) −4.03888e8 −0.0143309
\(211\) 4.85013e10 1.68454 0.842272 0.539053i \(-0.181218\pi\)
0.842272 + 0.539053i \(0.181218\pi\)
\(212\) 6.19589e10 2.10665
\(213\) 5.66997e9 0.188744
\(214\) −5.84883e9 −0.190637
\(215\) −1.51533e9 −0.0483654
\(216\) −8.70100e9 −0.271974
\(217\) 1.19213e8 0.00364967
\(218\) 5.70230e10 1.71000
\(219\) 4.85133e10 1.42516
\(220\) −2.74366e9 −0.0789637
\(221\) −5.18395e8 −0.0146182
\(222\) 1.19524e11 3.30267
\(223\) −1.32607e9 −0.0359082 −0.0179541 0.999839i \(-0.505715\pi\)
−0.0179541 + 0.999839i \(0.505715\pi\)
\(224\) 2.94579e9 0.0781783
\(225\) −1.75213e10 −0.455768
\(226\) −8.73161e10 −2.22642
\(227\) −6.30032e10 −1.57487 −0.787437 0.616395i \(-0.788593\pi\)
−0.787437 + 0.616395i \(0.788593\pi\)
\(228\) 1.00811e11 2.47059
\(229\) 3.36520e10 0.808632 0.404316 0.914619i \(-0.367510\pi\)
0.404316 + 0.914619i \(0.367510\pi\)
\(230\) −8.23610e9 −0.194064
\(231\) 1.30001e9 0.0300394
\(232\) −1.46718e10 −0.332496
\(233\) −3.25593e10 −0.723724 −0.361862 0.932232i \(-0.617859\pi\)
−0.361862 + 0.932232i \(0.617859\pi\)
\(234\) −1.93952e9 −0.0422887
\(235\) 6.24905e9 0.133662
\(236\) 3.93822e10 0.826410
\(237\) −1.29147e10 −0.265899
\(238\) −1.01728e9 −0.0205516
\(239\) 4.25086e10 0.842725 0.421363 0.906892i \(-0.361552\pi\)
0.421363 + 0.906892i \(0.361552\pi\)
\(240\) −5.60162e9 −0.108984
\(241\) −6.46314e10 −1.23415 −0.617074 0.786905i \(-0.711682\pi\)
−0.617074 + 0.786905i \(0.711682\pi\)
\(242\) −6.47913e10 −1.21436
\(243\) −4.69445e10 −0.863687
\(244\) 3.96102e10 0.715406
\(245\) −7.85569e9 −0.139295
\(246\) 8.55801e10 1.48993
\(247\) −5.63069e9 −0.0962555
\(248\) −1.62616e9 −0.0272980
\(249\) −2.94809e9 −0.0486008
\(250\) −2.57990e10 −0.417708
\(251\) −1.00795e11 −1.60290 −0.801452 0.598060i \(-0.795939\pi\)
−0.801452 + 0.598060i \(0.795939\pi\)
\(252\) −2.13542e9 −0.0333565
\(253\) 2.65098e10 0.406784
\(254\) −5.37219e10 −0.809840
\(255\) 2.76956e9 0.0410185
\(256\) 1.64197e10 0.238938
\(257\) −7.98430e10 −1.14166 −0.570831 0.821067i \(-0.693379\pi\)
−0.570831 + 0.821067i \(0.693379\pi\)
\(258\) −4.49995e10 −0.632294
\(259\) −7.35017e9 −0.101496
\(260\) −7.93243e8 −0.0107653
\(261\) −2.75947e10 −0.368080
\(262\) 5.26590e10 0.690425
\(263\) 9.26392e10 1.19397 0.596986 0.802252i \(-0.296365\pi\)
0.596986 + 0.802252i \(0.296365\pi\)
\(264\) −1.77332e10 −0.224682
\(265\) 1.84888e10 0.230304
\(266\) −1.10495e10 −0.135324
\(267\) 6.73901e10 0.811513
\(268\) −8.26662e10 −0.978862
\(269\) −6.38400e10 −0.743375 −0.371687 0.928358i \(-0.621221\pi\)
−0.371687 + 0.928358i \(0.621221\pi\)
\(270\) −1.19293e10 −0.136609
\(271\) 1.39281e11 1.56866 0.784331 0.620343i \(-0.213007\pi\)
0.784331 + 0.620343i \(0.213007\pi\)
\(272\) −1.41090e10 −0.156291
\(273\) 3.75856e8 0.00409534
\(274\) −2.55635e11 −2.73995
\(275\) 4.11106e10 0.433468
\(276\) −1.37223e11 −1.42343
\(277\) 1.33421e11 1.36165 0.680826 0.732445i \(-0.261621\pi\)
0.680826 + 0.732445i \(0.261621\pi\)
\(278\) 1.69767e11 1.70472
\(279\) −3.05848e9 −0.0302195
\(280\) −3.38802e8 −0.00329408
\(281\) −1.22205e11 −1.16926 −0.584629 0.811301i \(-0.698760\pi\)
−0.584629 + 0.811301i \(0.698760\pi\)
\(282\) 1.85572e11 1.74740
\(283\) 1.48138e11 1.37286 0.686430 0.727196i \(-0.259177\pi\)
0.686430 + 0.727196i \(0.259177\pi\)
\(284\) 2.18528e10 0.199331
\(285\) 3.00823e10 0.270090
\(286\) 4.55076e9 0.0402195
\(287\) −5.26279e9 −0.0457876
\(288\) −7.55764e10 −0.647321
\(289\) 6.97576e9 0.0588235
\(290\) −2.01154e10 −0.167008
\(291\) 1.92079e11 1.57022
\(292\) 1.86977e11 1.50510
\(293\) 1.17196e11 0.928986 0.464493 0.885577i \(-0.346237\pi\)
0.464493 + 0.885577i \(0.346237\pi\)
\(294\) −2.33283e11 −1.82105
\(295\) 1.17518e10 0.0903452
\(296\) 1.00263e11 0.759147
\(297\) 3.83973e10 0.286350
\(298\) −7.41694e10 −0.544818
\(299\) 7.66448e9 0.0554577
\(300\) −2.12802e11 −1.51681
\(301\) 2.76726e9 0.0194313
\(302\) 1.72594e11 1.19397
\(303\) −2.69370e11 −1.83594
\(304\) −1.53248e11 −1.02912
\(305\) 1.18198e10 0.0782099
\(306\) 2.60991e10 0.170169
\(307\) −4.33130e10 −0.278288 −0.139144 0.990272i \(-0.544435\pi\)
−0.139144 + 0.990272i \(0.544435\pi\)
\(308\) 5.01040e9 0.0317244
\(309\) −1.66055e11 −1.03619
\(310\) −2.22952e9 −0.0137114
\(311\) 1.79166e11 1.08601 0.543006 0.839729i \(-0.317286\pi\)
0.543006 + 0.839729i \(0.317286\pi\)
\(312\) −5.12700e9 −0.0306315
\(313\) −6.30182e10 −0.371122 −0.185561 0.982633i \(-0.559410\pi\)
−0.185561 + 0.982633i \(0.559410\pi\)
\(314\) −3.91346e11 −2.27184
\(315\) −6.37218e8 −0.00364662
\(316\) −4.97749e10 −0.280814
\(317\) 4.25331e10 0.236570 0.118285 0.992980i \(-0.462260\pi\)
0.118285 + 0.992980i \(0.462260\pi\)
\(318\) 5.49045e11 3.01083
\(319\) 6.47461e10 0.350071
\(320\) −3.82017e10 −0.203661
\(321\) −2.90790e10 −0.152865
\(322\) 1.50406e10 0.0779673
\(323\) 7.57692e10 0.387330
\(324\) −3.16615e11 −1.59617
\(325\) 1.18859e10 0.0590957
\(326\) 5.41711e11 2.65637
\(327\) 2.83505e11 1.37118
\(328\) 7.17890e10 0.342472
\(329\) −1.14119e10 −0.0537001
\(330\) −2.43127e10 −0.112855
\(331\) −1.36038e11 −0.622921 −0.311461 0.950259i \(-0.600818\pi\)
−0.311461 + 0.950259i \(0.600818\pi\)
\(332\) −1.13623e10 −0.0513271
\(333\) 1.88574e11 0.840393
\(334\) −2.71515e11 −1.19381
\(335\) −2.46679e10 −0.107012
\(336\) 1.02295e10 0.0437854
\(337\) −4.52614e11 −1.91158 −0.955792 0.294042i \(-0.904999\pi\)
−0.955792 + 0.294042i \(0.904999\pi\)
\(338\) −3.60861e11 −1.50389
\(339\) −4.34115e11 −1.78528
\(340\) 1.06742e10 0.0433194
\(341\) 7.17621e9 0.0287409
\(342\) 2.83483e11 1.12049
\(343\) 2.87371e10 0.112104
\(344\) −3.77479e10 −0.145338
\(345\) −4.09479e10 −0.155613
\(346\) 1.64751e11 0.617996
\(347\) −2.00653e11 −0.742955 −0.371478 0.928442i \(-0.621149\pi\)
−0.371478 + 0.928442i \(0.621149\pi\)
\(348\) −3.35147e11 −1.22498
\(349\) 1.48945e11 0.537416 0.268708 0.963222i \(-0.413403\pi\)
0.268708 + 0.963222i \(0.413403\pi\)
\(350\) 2.33245e10 0.0830819
\(351\) 1.11014e10 0.0390387
\(352\) 1.77327e11 0.615649
\(353\) −3.46998e11 −1.18944 −0.594718 0.803934i \(-0.702736\pi\)
−0.594718 + 0.803934i \(0.702736\pi\)
\(354\) 3.48982e11 1.18111
\(355\) 6.52097e9 0.0217914
\(356\) 2.59731e11 0.857034
\(357\) −5.05769e9 −0.0164796
\(358\) −2.22291e11 −0.715235
\(359\) −5.87619e11 −1.86711 −0.933556 0.358431i \(-0.883312\pi\)
−0.933556 + 0.358431i \(0.883312\pi\)
\(360\) 8.69219e9 0.0272752
\(361\) 5.00300e11 1.55042
\(362\) 3.37267e11 1.03225
\(363\) −3.22127e11 −0.973750
\(364\) 1.44860e9 0.00432507
\(365\) 5.57947e10 0.164541
\(366\) 3.51003e11 1.02246
\(367\) −8.17833e10 −0.235325 −0.117662 0.993054i \(-0.537540\pi\)
−0.117662 + 0.993054i \(0.537540\pi\)
\(368\) 2.08601e11 0.592928
\(369\) 1.35021e11 0.379124
\(370\) 1.37463e11 0.381310
\(371\) −3.37638e10 −0.0925269
\(372\) −3.71464e10 −0.100571
\(373\) 3.70187e11 0.990218 0.495109 0.868831i \(-0.335128\pi\)
0.495109 + 0.868831i \(0.335128\pi\)
\(374\) −6.12371e10 −0.161842
\(375\) −1.28267e11 −0.334945
\(376\) 1.55668e11 0.401655
\(377\) 1.87193e10 0.0477259
\(378\) 2.17851e10 0.0548840
\(379\) 5.17440e11 1.28820 0.644100 0.764941i \(-0.277232\pi\)
0.644100 + 0.764941i \(0.277232\pi\)
\(380\) 1.15941e11 0.285241
\(381\) −2.67092e11 −0.649380
\(382\) 5.91779e11 1.42192
\(383\) 2.03437e11 0.483099 0.241549 0.970389i \(-0.422344\pi\)
0.241549 + 0.970389i \(0.422344\pi\)
\(384\) −4.16321e11 −0.977098
\(385\) 1.49512e9 0.00346819
\(386\) −2.02451e11 −0.464170
\(387\) −7.09961e10 −0.160892
\(388\) 7.40298e11 1.65830
\(389\) 7.76405e11 1.71916 0.859578 0.511005i \(-0.170727\pi\)
0.859578 + 0.511005i \(0.170727\pi\)
\(390\) −7.02927e9 −0.0153858
\(391\) −1.03137e11 −0.223161
\(392\) −1.95690e11 −0.418583
\(393\) 2.61808e11 0.553626
\(394\) −5.50838e11 −1.15157
\(395\) −1.48530e10 −0.0306993
\(396\) −1.28545e11 −0.262681
\(397\) 4.33956e11 0.876776 0.438388 0.898786i \(-0.355550\pi\)
0.438388 + 0.898786i \(0.355550\pi\)
\(398\) −1.49667e12 −2.98988
\(399\) −5.49356e10 −0.108511
\(400\) 3.23493e11 0.631823
\(401\) 3.07899e11 0.594645 0.297323 0.954777i \(-0.403906\pi\)
0.297323 + 0.954777i \(0.403906\pi\)
\(402\) −7.32541e11 −1.39899
\(403\) 2.07478e9 0.00391831
\(404\) −1.03819e12 −1.93892
\(405\) −9.44791e10 −0.174497
\(406\) 3.67343e10 0.0670973
\(407\) −4.42456e11 −0.799273
\(408\) 6.89913e10 0.123260
\(409\) −5.32344e11 −0.940671 −0.470335 0.882488i \(-0.655867\pi\)
−0.470335 + 0.882488i \(0.655867\pi\)
\(410\) 9.84248e10 0.172019
\(411\) −1.27096e12 −2.19706
\(412\) −6.39999e11 −1.09431
\(413\) −2.14608e10 −0.0362970
\(414\) −3.85876e11 −0.645574
\(415\) −3.39057e9 −0.00561120
\(416\) 5.12686e10 0.0839328
\(417\) 8.44042e11 1.36695
\(418\) −6.65144e11 −1.06567
\(419\) −1.78965e11 −0.283665 −0.141833 0.989891i \(-0.545299\pi\)
−0.141833 + 0.989891i \(0.545299\pi\)
\(420\) −7.73924e9 −0.0121360
\(421\) 1.88185e11 0.291954 0.145977 0.989288i \(-0.453367\pi\)
0.145977 + 0.989288i \(0.453367\pi\)
\(422\) 1.65647e12 2.54260
\(423\) 2.92779e11 0.444640
\(424\) 4.60567e11 0.692064
\(425\) −1.59942e11 −0.237800
\(426\) 1.93647e11 0.284884
\(427\) −2.15851e10 −0.0314216
\(428\) −1.12074e11 −0.161439
\(429\) 2.26253e10 0.0322505
\(430\) −5.17534e10 −0.0730014
\(431\) −6.39015e11 −0.891997 −0.445998 0.895034i \(-0.647151\pi\)
−0.445998 + 0.895034i \(0.647151\pi\)
\(432\) 3.02142e11 0.417383
\(433\) 3.97400e11 0.543291 0.271645 0.962397i \(-0.412432\pi\)
0.271645 + 0.962397i \(0.412432\pi\)
\(434\) 4.07149e9 0.00550870
\(435\) −1.00009e11 −0.133918
\(436\) 1.09267e12 1.44810
\(437\) −1.12025e12 −1.46943
\(438\) 1.65688e12 2.15109
\(439\) −1.41931e11 −0.182384 −0.0911918 0.995833i \(-0.529068\pi\)
−0.0911918 + 0.995833i \(0.529068\pi\)
\(440\) −2.03947e10 −0.0259407
\(441\) −3.68053e11 −0.463380
\(442\) −1.77048e10 −0.0220644
\(443\) 1.16614e12 1.43858 0.719289 0.694711i \(-0.244468\pi\)
0.719289 + 0.694711i \(0.244468\pi\)
\(444\) 2.29030e12 2.79685
\(445\) 7.75046e10 0.0936931
\(446\) −4.52893e10 −0.0541987
\(447\) −3.68753e11 −0.436870
\(448\) 6.97631e10 0.0818229
\(449\) 9.04654e11 1.05045 0.525223 0.850964i \(-0.323982\pi\)
0.525223 + 0.850964i \(0.323982\pi\)
\(450\) −5.98407e11 −0.687923
\(451\) −3.16803e11 −0.360574
\(452\) −1.67314e12 −1.88542
\(453\) 8.58097e11 0.957402
\(454\) −2.15176e12 −2.37707
\(455\) 4.32268e8 0.000472827 0
\(456\) 7.49368e11 0.811621
\(457\) −2.89019e10 −0.0309959 −0.0154979 0.999880i \(-0.504933\pi\)
−0.0154979 + 0.999880i \(0.504933\pi\)
\(458\) 1.14932e12 1.22052
\(459\) −1.49385e11 −0.157091
\(460\) −1.57819e11 −0.164342
\(461\) −3.33362e11 −0.343765 −0.171883 0.985117i \(-0.554985\pi\)
−0.171883 + 0.985117i \(0.554985\pi\)
\(462\) 4.43993e10 0.0453406
\(463\) 9.65145e11 0.976064 0.488032 0.872826i \(-0.337715\pi\)
0.488032 + 0.872826i \(0.337715\pi\)
\(464\) 5.09477e11 0.510263
\(465\) −1.10846e10 −0.0109947
\(466\) −1.11200e12 −1.09237
\(467\) −7.21341e11 −0.701802 −0.350901 0.936413i \(-0.614125\pi\)
−0.350901 + 0.936413i \(0.614125\pi\)
\(468\) −3.71649e10 −0.0358118
\(469\) 4.50479e10 0.0429929
\(470\) 2.13425e11 0.201746
\(471\) −1.94568e12 −1.82170
\(472\) 2.92744e11 0.271487
\(473\) 1.66580e11 0.153020
\(474\) −4.41077e11 −0.401340
\(475\) −1.73725e12 −1.56582
\(476\) −1.94930e10 −0.0174040
\(477\) 8.66233e11 0.766129
\(478\) 1.45180e12 1.27198
\(479\) 1.57016e12 1.36281 0.681403 0.731909i \(-0.261370\pi\)
0.681403 + 0.731909i \(0.261370\pi\)
\(480\) −2.73906e11 −0.235513
\(481\) −1.27922e11 −0.108967
\(482\) −2.20737e12 −1.86279
\(483\) 7.47781e10 0.0625191
\(484\) −1.24152e12 −1.02837
\(485\) 2.20908e11 0.181290
\(486\) −1.60330e12 −1.30362
\(487\) 1.48730e12 1.19817 0.599084 0.800686i \(-0.295532\pi\)
0.599084 + 0.800686i \(0.295532\pi\)
\(488\) 2.94439e11 0.235021
\(489\) 2.69326e12 2.13004
\(490\) −2.68297e11 −0.210248
\(491\) 9.71236e11 0.754150 0.377075 0.926183i \(-0.376930\pi\)
0.377075 + 0.926183i \(0.376930\pi\)
\(492\) 1.63987e12 1.26173
\(493\) −2.51896e11 −0.192048
\(494\) −1.92306e11 −0.145285
\(495\) −3.83584e10 −0.0287169
\(496\) 5.64685e10 0.0418927
\(497\) −1.19084e10 −0.00875489
\(498\) −1.00687e11 −0.0733567
\(499\) 1.21621e12 0.878127 0.439064 0.898456i \(-0.355310\pi\)
0.439064 + 0.898456i \(0.355310\pi\)
\(500\) −4.94357e11 −0.353733
\(501\) −1.34991e12 −0.957272
\(502\) −3.44247e12 −2.41938
\(503\) 2.43415e12 1.69548 0.847739 0.530414i \(-0.177964\pi\)
0.847739 + 0.530414i \(0.177964\pi\)
\(504\) −1.58735e10 −0.0109581
\(505\) −3.09799e11 −0.211968
\(506\) 9.05392e11 0.613987
\(507\) −1.79412e12 −1.20591
\(508\) −1.02941e12 −0.685807
\(509\) −2.50151e12 −1.65186 −0.825930 0.563773i \(-0.809349\pi\)
−0.825930 + 0.563773i \(0.809349\pi\)
\(510\) 9.45891e10 0.0619120
\(511\) −1.01891e11 −0.0661060
\(512\) 1.81611e12 1.16796
\(513\) −1.62259e12 −1.03438
\(514\) −2.72689e12 −1.72319
\(515\) −1.90978e11 −0.119633
\(516\) −8.62274e11 −0.535453
\(517\) −6.86956e11 −0.422884
\(518\) −2.51031e11 −0.153195
\(519\) 8.19103e11 0.495548
\(520\) −5.89651e9 −0.00353655
\(521\) 2.28180e12 1.35678 0.678388 0.734704i \(-0.262679\pi\)
0.678388 + 0.734704i \(0.262679\pi\)
\(522\) −9.42445e11 −0.555570
\(523\) 1.67259e12 0.977537 0.488768 0.872414i \(-0.337446\pi\)
0.488768 + 0.872414i \(0.337446\pi\)
\(524\) 1.00904e12 0.584682
\(525\) 1.15964e11 0.0666202
\(526\) 3.16392e12 1.80215
\(527\) −2.79192e10 −0.0157672
\(528\) 6.15785e11 0.344807
\(529\) −2.76274e11 −0.153388
\(530\) 6.31450e11 0.347614
\(531\) 5.50593e11 0.300542
\(532\) −2.11729e11 −0.114598
\(533\) −9.15937e10 −0.0491579
\(534\) 2.30158e12 1.22487
\(535\) −3.34434e10 −0.0176489
\(536\) −6.14492e11 −0.321570
\(537\) −1.10518e12 −0.573520
\(538\) −2.18034e12 −1.12203
\(539\) 8.63574e11 0.440707
\(540\) −2.28588e11 −0.115686
\(541\) −8.84734e11 −0.444043 −0.222021 0.975042i \(-0.571265\pi\)
−0.222021 + 0.975042i \(0.571265\pi\)
\(542\) 4.75688e12 2.36769
\(543\) 1.67681e12 0.827723
\(544\) −6.89894e11 −0.337744
\(545\) 3.26056e11 0.158310
\(546\) 1.28367e10 0.00618138
\(547\) −2.72146e12 −1.29975 −0.649874 0.760042i \(-0.725178\pi\)
−0.649874 + 0.760042i \(0.725178\pi\)
\(548\) −4.89844e12 −2.32031
\(549\) 5.53780e11 0.260173
\(550\) 1.40406e12 0.654264
\(551\) −2.73604e12 −1.26456
\(552\) −1.02004e12 −0.467617
\(553\) 2.71242e10 0.0123337
\(554\) 4.55676e12 2.05524
\(555\) 6.83433e11 0.305758
\(556\) 3.25305e12 1.44363
\(557\) −2.68557e12 −1.18219 −0.591096 0.806601i \(-0.701305\pi\)
−0.591096 + 0.806601i \(0.701305\pi\)
\(558\) −1.04457e11 −0.0456124
\(559\) 4.81615e10 0.0208616
\(560\) 1.17649e10 0.00505524
\(561\) −3.04457e11 −0.129775
\(562\) −4.17369e12 −1.76484
\(563\) −2.81923e12 −1.18261 −0.591307 0.806446i \(-0.701388\pi\)
−0.591307 + 0.806446i \(0.701388\pi\)
\(564\) 3.55591e12 1.47977
\(565\) −4.99271e11 −0.206119
\(566\) 5.05936e12 2.07215
\(567\) 1.72535e11 0.0701059
\(568\) 1.62441e11 0.0654830
\(569\) 3.57453e11 0.142960 0.0714799 0.997442i \(-0.477228\pi\)
0.0714799 + 0.997442i \(0.477228\pi\)
\(570\) 1.02741e12 0.407667
\(571\) −3.25953e11 −0.128319 −0.0641596 0.997940i \(-0.520437\pi\)
−0.0641596 + 0.997940i \(0.520437\pi\)
\(572\) 8.72010e10 0.0340596
\(573\) 2.94219e12 1.14018
\(574\) −1.79741e11 −0.0691104
\(575\) 2.36474e12 0.902149
\(576\) −1.78982e12 −0.677499
\(577\) −2.50107e11 −0.0939365 −0.0469683 0.998896i \(-0.514956\pi\)
−0.0469683 + 0.998896i \(0.514956\pi\)
\(578\) 2.38244e11 0.0887865
\(579\) −1.00654e12 −0.372200
\(580\) −3.85449e11 −0.141430
\(581\) 6.19177e9 0.00225435
\(582\) 6.56010e12 2.37005
\(583\) −2.03247e12 −0.728643
\(584\) 1.38988e12 0.494446
\(585\) −1.10901e10 −0.00391504
\(586\) 4.00262e12 1.40218
\(587\) 9.14514e10 0.0317921 0.0158960 0.999874i \(-0.494940\pi\)
0.0158960 + 0.999874i \(0.494940\pi\)
\(588\) −4.47014e12 −1.54214
\(589\) −3.03252e11 −0.103821
\(590\) 4.01361e11 0.136364
\(591\) −2.73864e12 −0.923402
\(592\) −3.48162e12 −1.16502
\(593\) −2.60815e12 −0.866138 −0.433069 0.901361i \(-0.642569\pi\)
−0.433069 + 0.901361i \(0.642569\pi\)
\(594\) 1.31139e12 0.432208
\(595\) −5.81680e9 −0.00190264
\(596\) −1.42122e12 −0.461376
\(597\) −7.44111e12 −2.39747
\(598\) 2.61766e11 0.0837063
\(599\) 1.25671e12 0.398853 0.199427 0.979913i \(-0.436092\pi\)
0.199427 + 0.979913i \(0.436092\pi\)
\(600\) −1.58185e12 −0.498292
\(601\) −9.01991e11 −0.282012 −0.141006 0.990009i \(-0.545034\pi\)
−0.141006 + 0.990009i \(0.545034\pi\)
\(602\) 9.45108e10 0.0293290
\(603\) −1.15574e12 −0.355984
\(604\) 3.30722e12 1.01111
\(605\) −3.70475e11 −0.112424
\(606\) −9.19984e12 −2.77111
\(607\) 4.29234e12 1.28335 0.641675 0.766977i \(-0.278240\pi\)
0.641675 + 0.766977i \(0.278240\pi\)
\(608\) −7.49348e12 −2.22391
\(609\) 1.82634e11 0.0538028
\(610\) 4.03684e11 0.118048
\(611\) −1.98612e11 −0.0576528
\(612\) 5.00108e11 0.144106
\(613\) 3.09808e12 0.886178 0.443089 0.896478i \(-0.353883\pi\)
0.443089 + 0.896478i \(0.353883\pi\)
\(614\) −1.47927e12 −0.420040
\(615\) 4.89345e11 0.137936
\(616\) 3.72444e10 0.0104219
\(617\) −2.97483e12 −0.826378 −0.413189 0.910645i \(-0.635585\pi\)
−0.413189 + 0.910645i \(0.635585\pi\)
\(618\) −5.67131e12 −1.56399
\(619\) −3.10484e10 −0.00850025 −0.00425012 0.999991i \(-0.501353\pi\)
−0.00425012 + 0.999991i \(0.501353\pi\)
\(620\) −4.27217e10 −0.0116114
\(621\) 2.20867e12 0.595961
\(622\) 6.11910e12 1.63920
\(623\) −1.41537e11 −0.0376421
\(624\) 1.78035e11 0.0470083
\(625\) 3.59269e12 0.941803
\(626\) −2.15227e12 −0.560160
\(627\) −3.30694e12 −0.854521
\(628\) −7.49891e12 −1.92389
\(629\) 1.72138e12 0.438480
\(630\) −2.17630e10 −0.00550410
\(631\) 5.20764e12 1.30770 0.653851 0.756623i \(-0.273152\pi\)
0.653851 + 0.756623i \(0.273152\pi\)
\(632\) −3.69998e11 −0.0922513
\(633\) 8.23559e12 2.03882
\(634\) 1.45264e12 0.357072
\(635\) −3.07180e11 −0.0749741
\(636\) 1.05207e13 2.54970
\(637\) 2.49676e11 0.0600826
\(638\) 2.21128e12 0.528386
\(639\) 3.05519e11 0.0724911
\(640\) −4.78806e11 −0.112811
\(641\) 2.80533e12 0.656330 0.328165 0.944620i \(-0.393570\pi\)
0.328165 + 0.944620i \(0.393570\pi\)
\(642\) −9.93139e11 −0.230729
\(643\) 2.80520e12 0.647164 0.323582 0.946200i \(-0.395113\pi\)
0.323582 + 0.946200i \(0.395113\pi\)
\(644\) 2.88205e11 0.0660260
\(645\) −2.57306e11 −0.0585371
\(646\) 2.58776e12 0.584624
\(647\) 4.72530e12 1.06013 0.530066 0.847956i \(-0.322167\pi\)
0.530066 + 0.847956i \(0.322167\pi\)
\(648\) −2.35353e12 −0.524364
\(649\) −1.29187e12 −0.285837
\(650\) 4.05940e11 0.0891973
\(651\) 2.02425e10 0.00441722
\(652\) 1.03802e13 2.24953
\(653\) −7.04467e12 −1.51618 −0.758091 0.652149i \(-0.773868\pi\)
−0.758091 + 0.652149i \(0.773868\pi\)
\(654\) 9.68258e12 2.06962
\(655\) 3.01103e11 0.0639188
\(656\) −2.49287e12 −0.525572
\(657\) 2.61408e12 0.547362
\(658\) −3.89751e11 −0.0810533
\(659\) −2.93823e12 −0.606879 −0.303439 0.952851i \(-0.598135\pi\)
−0.303439 + 0.952851i \(0.598135\pi\)
\(660\) −4.65877e11 −0.0955704
\(661\) −7.72453e11 −0.157386 −0.0786929 0.996899i \(-0.525075\pi\)
−0.0786929 + 0.996899i \(0.525075\pi\)
\(662\) −4.64611e12 −0.940219
\(663\) −8.80242e10 −0.0176926
\(664\) −8.44610e10 −0.0168616
\(665\) −6.31808e10 −0.0125282
\(666\) 6.44039e12 1.26846
\(667\) 3.72429e12 0.728580
\(668\) −5.20274e12 −1.01097
\(669\) −2.25168e11 −0.0434599
\(670\) −8.42487e11 −0.161520
\(671\) −1.29935e12 −0.247443
\(672\) 5.00200e11 0.0946198
\(673\) 2.83634e12 0.532954 0.266477 0.963841i \(-0.414140\pi\)
0.266477 + 0.963841i \(0.414140\pi\)
\(674\) −1.54582e13 −2.88529
\(675\) 3.42514e12 0.635055
\(676\) −6.91478e12 −1.27356
\(677\) −2.65986e12 −0.486642 −0.243321 0.969946i \(-0.578237\pi\)
−0.243321 + 0.969946i \(0.578237\pi\)
\(678\) −1.48264e13 −2.69465
\(679\) −4.03416e11 −0.0728349
\(680\) 7.93461e10 0.0142310
\(681\) −1.06980e13 −1.90608
\(682\) 2.45090e11 0.0433807
\(683\) −2.44022e12 −0.429078 −0.214539 0.976715i \(-0.568825\pi\)
−0.214539 + 0.976715i \(0.568825\pi\)
\(684\) 5.43206e12 0.948882
\(685\) −1.46171e12 −0.253661
\(686\) 9.81463e11 0.169206
\(687\) 5.71415e12 0.978693
\(688\) 1.31079e12 0.223042
\(689\) −5.87625e11 −0.0993376
\(690\) −1.39850e12 −0.234878
\(691\) 5.13446e12 0.856730 0.428365 0.903606i \(-0.359090\pi\)
0.428365 + 0.903606i \(0.359090\pi\)
\(692\) 3.15694e12 0.523345
\(693\) 7.00492e10 0.0115373
\(694\) −6.85293e12 −1.12139
\(695\) 9.70724e11 0.157821
\(696\) −2.49129e12 −0.402423
\(697\) 1.23253e12 0.197810
\(698\) 5.08693e12 0.811159
\(699\) −5.52861e12 −0.875929
\(700\) 4.46941e11 0.0703573
\(701\) −4.00510e12 −0.626444 −0.313222 0.949680i \(-0.601408\pi\)
−0.313222 + 0.949680i \(0.601408\pi\)
\(702\) 3.79147e11 0.0589238
\(703\) 1.86973e13 2.88722
\(704\) 4.19951e12 0.644350
\(705\) 1.06110e12 0.161772
\(706\) −1.18511e13 −1.79530
\(707\) 5.65748e11 0.0851600
\(708\) 6.68715e12 1.00021
\(709\) −7.18171e12 −1.06738 −0.533691 0.845680i \(-0.679195\pi\)
−0.533691 + 0.845680i \(0.679195\pi\)
\(710\) 2.22712e11 0.0328912
\(711\) −6.95892e11 −0.102124
\(712\) 1.93069e12 0.281548
\(713\) 4.12785e11 0.0598166
\(714\) −1.72736e11 −0.0248738
\(715\) 2.60211e10 0.00372348
\(716\) −4.25951e12 −0.605691
\(717\) 7.21802e12 1.01996
\(718\) −2.00690e13 −2.81816
\(719\) 2.19372e10 0.00306127 0.00153063 0.999999i \(-0.499513\pi\)
0.00153063 + 0.999999i \(0.499513\pi\)
\(720\) −3.01836e11 −0.0418577
\(721\) 3.48760e11 0.0480637
\(722\) 1.70868e13 2.34015
\(723\) −1.09745e13 −1.49370
\(724\) 6.46266e12 0.874154
\(725\) 5.77553e12 0.776373
\(726\) −1.10017e13 −1.46975
\(727\) 3.47360e11 0.0461185 0.0230593 0.999734i \(-0.492659\pi\)
0.0230593 + 0.999734i \(0.492659\pi\)
\(728\) 1.07681e10 0.00142084
\(729\) 1.55133e12 0.203437
\(730\) 1.90556e12 0.248354
\(731\) −6.48083e11 −0.0839465
\(732\) 6.72586e12 0.865861
\(733\) 3.58285e11 0.0458417 0.0229208 0.999737i \(-0.492703\pi\)
0.0229208 + 0.999737i \(0.492703\pi\)
\(734\) −2.79316e12 −0.355192
\(735\) −1.33391e12 −0.168590
\(736\) 1.02001e13 1.28131
\(737\) 2.71174e12 0.338566
\(738\) 4.61138e12 0.572239
\(739\) −2.16274e12 −0.266750 −0.133375 0.991066i \(-0.542581\pi\)
−0.133375 + 0.991066i \(0.542581\pi\)
\(740\) 2.63405e12 0.322909
\(741\) −9.56100e11 −0.116499
\(742\) −1.15314e12 −0.139657
\(743\) 6.42105e12 0.772959 0.386479 0.922298i \(-0.373691\pi\)
0.386479 + 0.922298i \(0.373691\pi\)
\(744\) −2.76125e11 −0.0330390
\(745\) −4.24099e11 −0.0504387
\(746\) 1.26430e13 1.49461
\(747\) −1.58854e11 −0.0186662
\(748\) −1.17342e12 −0.137055
\(749\) 6.10736e10 0.00709064
\(750\) −4.38071e12 −0.505555
\(751\) −1.15069e13 −1.32002 −0.660010 0.751257i \(-0.729448\pi\)
−0.660010 + 0.751257i \(0.729448\pi\)
\(752\) −5.40555e12 −0.616396
\(753\) −1.71151e13 −1.94001
\(754\) 6.39325e11 0.0720361
\(755\) 9.86888e11 0.110537
\(756\) 4.17442e11 0.0464781
\(757\) −7.80850e12 −0.864243 −0.432122 0.901815i \(-0.642235\pi\)
−0.432122 + 0.901815i \(0.642235\pi\)
\(758\) 1.76722e13 1.94437
\(759\) 4.50140e12 0.492333
\(760\) 8.61840e11 0.0937056
\(761\) −6.58284e12 −0.711512 −0.355756 0.934579i \(-0.615777\pi\)
−0.355756 + 0.934579i \(0.615777\pi\)
\(762\) −9.12205e12 −0.980156
\(763\) −5.95435e11 −0.0636025
\(764\) 1.13396e13 1.20414
\(765\) 1.49234e11 0.0157540
\(766\) 6.94803e12 0.729175
\(767\) −3.73505e11 −0.0389688
\(768\) 2.78808e12 0.289188
\(769\) −1.27459e13 −1.31433 −0.657163 0.753748i \(-0.728244\pi\)
−0.657163 + 0.753748i \(0.728244\pi\)
\(770\) 5.10631e10 0.00523479
\(771\) −1.35575e13 −1.38176
\(772\) −3.87933e12 −0.393079
\(773\) −1.07389e13 −1.08181 −0.540907 0.841083i \(-0.681919\pi\)
−0.540907 + 0.841083i \(0.681919\pi\)
\(774\) −2.42474e12 −0.242846
\(775\) 6.40137e11 0.0637405
\(776\) 5.50294e12 0.544775
\(777\) −1.24807e12 −0.122841
\(778\) 2.65167e13 2.59484
\(779\) 1.33874e13 1.30250
\(780\) −1.34694e11 −0.0130293
\(781\) −7.16848e11 −0.0689442
\(782\) −3.52244e12 −0.336832
\(783\) 5.39434e12 0.512873
\(784\) 6.79533e12 0.642375
\(785\) −2.23770e12 −0.210324
\(786\) 8.94158e12 0.835627
\(787\) 3.76105e12 0.349481 0.174740 0.984615i \(-0.444091\pi\)
0.174740 + 0.984615i \(0.444091\pi\)
\(788\) −1.05551e13 −0.975200
\(789\) 1.57303e13 1.44507
\(790\) −5.07278e11 −0.0463366
\(791\) 9.11756e11 0.0828103
\(792\) −9.55531e11 −0.0862942
\(793\) −3.75667e11 −0.0337344
\(794\) 1.48210e13 1.32338
\(795\) 3.13942e12 0.278739
\(796\) −2.86790e13 −2.53195
\(797\) 2.18200e13 1.91555 0.957773 0.287524i \(-0.0928322\pi\)
0.957773 + 0.287524i \(0.0928322\pi\)
\(798\) −1.87622e12 −0.163784
\(799\) 2.67262e12 0.231994
\(800\) 1.58180e13 1.36536
\(801\) 3.63123e12 0.311679
\(802\) 1.05157e13 0.897540
\(803\) −6.13349e12 −0.520581
\(804\) −1.40368e13 −1.18472
\(805\) 8.60015e10 0.00721813
\(806\) 7.08602e10 0.00591418
\(807\) −1.08401e13 −0.899712
\(808\) −7.71729e12 −0.636962
\(809\) −1.90714e13 −1.56536 −0.782681 0.622423i \(-0.786148\pi\)
−0.782681 + 0.622423i \(0.786148\pi\)
\(810\) −3.22676e12 −0.263381
\(811\) −1.86624e13 −1.51486 −0.757430 0.652916i \(-0.773546\pi\)
−0.757430 + 0.652916i \(0.773546\pi\)
\(812\) 7.03898e11 0.0568208
\(813\) 2.36501e13 1.89856
\(814\) −1.51113e13 −1.20640
\(815\) 3.09749e12 0.245924
\(816\) −2.39572e12 −0.189161
\(817\) −7.03934e12 −0.552755
\(818\) −1.81812e13 −1.41982
\(819\) 2.02526e10 0.00157290
\(820\) 1.88600e12 0.145673
\(821\) −4.79906e12 −0.368648 −0.184324 0.982866i \(-0.559010\pi\)
−0.184324 + 0.982866i \(0.559010\pi\)
\(822\) −4.34072e13 −3.31618
\(823\) 2.14502e13 1.62979 0.814895 0.579609i \(-0.196795\pi\)
0.814895 + 0.579609i \(0.196795\pi\)
\(824\) −4.75738e12 −0.359497
\(825\) 6.98065e12 0.524630
\(826\) −7.32955e11 −0.0547857
\(827\) −1.32157e13 −0.982463 −0.491231 0.871029i \(-0.663453\pi\)
−0.491231 + 0.871029i \(0.663453\pi\)
\(828\) −7.39411e12 −0.546700
\(829\) −7.78893e12 −0.572773 −0.286386 0.958114i \(-0.592454\pi\)
−0.286386 + 0.958114i \(0.592454\pi\)
\(830\) −1.15799e11 −0.00846938
\(831\) 2.26551e13 1.64802
\(832\) 1.21416e12 0.0878456
\(833\) −3.35975e12 −0.241771
\(834\) 2.88267e13 2.06323
\(835\) −1.55252e12 −0.110522
\(836\) −1.27454e13 −0.902454
\(837\) 5.97887e11 0.0421070
\(838\) −6.11223e12 −0.428156
\(839\) −9.65976e12 −0.673035 −0.336517 0.941677i \(-0.609249\pi\)
−0.336517 + 0.941677i \(0.609249\pi\)
\(840\) −5.75290e10 −0.00398685
\(841\) −5.41113e12 −0.372997
\(842\) 6.42710e12 0.440667
\(843\) −2.07506e13 −1.41516
\(844\) 3.17411e13 2.15318
\(845\) −2.06340e12 −0.139228
\(846\) 9.99934e12 0.671127
\(847\) 6.76552e11 0.0451675
\(848\) −1.59932e13 −1.06207
\(849\) 2.51540e13 1.66158
\(850\) −5.46251e12 −0.358928
\(851\) −2.54507e13 −1.66348
\(852\) 3.71064e12 0.241252
\(853\) 2.43508e13 1.57486 0.787430 0.616404i \(-0.211411\pi\)
0.787430 + 0.616404i \(0.211411\pi\)
\(854\) −7.37198e11 −0.0474268
\(855\) 1.62095e12 0.103734
\(856\) −8.33096e11 −0.0530351
\(857\) 2.45424e13 1.55419 0.777095 0.629383i \(-0.216692\pi\)
0.777095 + 0.629383i \(0.216692\pi\)
\(858\) 7.72726e11 0.0486780
\(859\) −2.12084e13 −1.32904 −0.664521 0.747270i \(-0.731364\pi\)
−0.664521 + 0.747270i \(0.731364\pi\)
\(860\) −9.91692e11 −0.0618207
\(861\) −8.93630e11 −0.0554170
\(862\) −2.18244e13 −1.34635
\(863\) 1.64190e13 1.00762 0.503811 0.863814i \(-0.331931\pi\)
0.503811 + 0.863814i \(0.331931\pi\)
\(864\) 1.47740e13 0.901960
\(865\) 9.42042e11 0.0572134
\(866\) 1.35725e13 0.820027
\(867\) 1.18449e12 0.0711946
\(868\) 7.80173e10 0.00466500
\(869\) 1.63279e12 0.0971273
\(870\) −3.41563e12 −0.202132
\(871\) 7.84015e11 0.0461575
\(872\) 8.12224e12 0.475720
\(873\) 1.03499e13 0.603078
\(874\) −3.82600e13 −2.21791
\(875\) 2.69394e11 0.0155364
\(876\) 3.17490e13 1.82163
\(877\) 7.74986e12 0.442380 0.221190 0.975231i \(-0.429006\pi\)
0.221190 + 0.975231i \(0.429006\pi\)
\(878\) −4.84738e12 −0.275285
\(879\) 1.99001e13 1.12436
\(880\) 7.08207e11 0.0398096
\(881\) 1.47006e12 0.0822135 0.0411068 0.999155i \(-0.486912\pi\)
0.0411068 + 0.999155i \(0.486912\pi\)
\(882\) −1.25702e13 −0.699412
\(883\) −2.27229e13 −1.25788 −0.628941 0.777453i \(-0.716511\pi\)
−0.628941 + 0.777453i \(0.716511\pi\)
\(884\) −3.39257e11 −0.0186850
\(885\) 1.99547e12 0.109345
\(886\) 3.98273e13 2.17135
\(887\) −2.54193e13 −1.37882 −0.689411 0.724371i \(-0.742130\pi\)
−0.689411 + 0.724371i \(0.742130\pi\)
\(888\) 1.70247e13 0.918802
\(889\) 5.60965e11 0.0301216
\(890\) 2.64703e12 0.141418
\(891\) 1.03861e13 0.552079
\(892\) −8.67828e11 −0.0458978
\(893\) 2.90294e13 1.52759
\(894\) −1.25941e13 −0.659398
\(895\) −1.27106e12 −0.0662157
\(896\) 8.74385e11 0.0453228
\(897\) 1.30144e12 0.0671209
\(898\) 3.08968e13 1.58551
\(899\) 1.00817e12 0.0514771
\(900\) −1.14666e13 −0.582563
\(901\) 7.90735e12 0.399733
\(902\) −1.08198e13 −0.544240
\(903\) 4.69886e11 0.0235178
\(904\) −1.24371e13 −0.619387
\(905\) 1.92848e12 0.0955646
\(906\) 2.93067e13 1.44508
\(907\) 2.33059e13 1.14349 0.571745 0.820431i \(-0.306267\pi\)
0.571745 + 0.820431i \(0.306267\pi\)
\(908\) −4.12317e13 −2.01300
\(909\) −1.45147e13 −0.705131
\(910\) 1.47633e10 0.000713671 0
\(911\) −6.19635e12 −0.298060 −0.149030 0.988833i \(-0.547615\pi\)
−0.149030 + 0.988833i \(0.547615\pi\)
\(912\) −2.60218e13 −1.24555
\(913\) 3.72724e11 0.0177529
\(914\) −9.87092e11 −0.0467842
\(915\) 2.00702e12 0.0946580
\(916\) 2.20231e13 1.03359
\(917\) −5.49866e11 −0.0256800
\(918\) −5.10198e12 −0.237108
\(919\) −2.57602e13 −1.19132 −0.595661 0.803236i \(-0.703110\pi\)
−0.595661 + 0.803236i \(0.703110\pi\)
\(920\) −1.17313e12 −0.0539886
\(921\) −7.35460e12 −0.336815
\(922\) −1.13854e13 −0.518869
\(923\) −2.07255e11 −0.00939932
\(924\) 8.50773e11 0.0383963
\(925\) −3.94682e13 −1.77260
\(926\) 3.29628e13 1.47324
\(927\) −8.94768e12 −0.397971
\(928\) 2.49122e13 1.10267
\(929\) 1.87578e13 0.826251 0.413126 0.910674i \(-0.364437\pi\)
0.413126 + 0.910674i \(0.364437\pi\)
\(930\) −3.78575e11 −0.0165951
\(931\) −3.64929e13 −1.59197
\(932\) −2.13080e13 −0.925064
\(933\) 3.04227e13 1.31441
\(934\) −2.46361e13 −1.05928
\(935\) −3.50152e11 −0.0149832
\(936\) −2.76262e11 −0.0117647
\(937\) 5.64054e12 0.239052 0.119526 0.992831i \(-0.461863\pi\)
0.119526 + 0.992831i \(0.461863\pi\)
\(938\) 1.53853e12 0.0648923
\(939\) −1.07006e13 −0.449172
\(940\) 4.08962e12 0.170847
\(941\) 2.26889e13 0.943321 0.471660 0.881780i \(-0.343655\pi\)
0.471660 + 0.881780i \(0.343655\pi\)
\(942\) −6.64511e13 −2.74962
\(943\) −1.82229e13 −0.750439
\(944\) −1.01655e13 −0.416636
\(945\) 1.24566e11 0.00508110
\(946\) 5.68924e12 0.230964
\(947\) −1.49881e13 −0.605582 −0.302791 0.953057i \(-0.597918\pi\)
−0.302791 + 0.953057i \(0.597918\pi\)
\(948\) −8.45186e12 −0.339871
\(949\) −1.77331e12 −0.0709719
\(950\) −5.93326e13 −2.36340
\(951\) 7.22218e12 0.286323
\(952\) −1.44900e11 −0.00571744
\(953\) −4.04272e13 −1.58765 −0.793827 0.608143i \(-0.791915\pi\)
−0.793827 + 0.608143i \(0.791915\pi\)
\(954\) 2.95846e13 1.15637
\(955\) 3.38377e12 0.131640
\(956\) 2.78192e13 1.07717
\(957\) 1.09940e13 0.423693
\(958\) 5.36259e13 2.05698
\(959\) 2.66934e12 0.101911
\(960\) −6.48671e12 −0.246493
\(961\) −2.63279e13 −0.995774
\(962\) −4.36895e12 −0.164471
\(963\) −1.56689e12 −0.0587109
\(964\) −4.22973e13 −1.57749
\(965\) −1.15761e12 −0.0429723
\(966\) 2.55391e12 0.0943644
\(967\) −7.15269e12 −0.263057 −0.131529 0.991312i \(-0.541989\pi\)
−0.131529 + 0.991312i \(0.541989\pi\)
\(968\) −9.22875e12 −0.337834
\(969\) 1.28657e13 0.468788
\(970\) 7.54470e12 0.273633
\(971\) 2.34500e13 0.846556 0.423278 0.906000i \(-0.360879\pi\)
0.423278 + 0.906000i \(0.360879\pi\)
\(972\) −3.07223e13 −1.10396
\(973\) −1.77271e12 −0.0634060
\(974\) 5.07959e13 1.80848
\(975\) 2.01824e12 0.0715240
\(976\) −1.02244e13 −0.360673
\(977\) 3.75171e13 1.31736 0.658678 0.752425i \(-0.271116\pi\)
0.658678 + 0.752425i \(0.271116\pi\)
\(978\) 9.19834e13 3.21503
\(979\) −8.52006e12 −0.296429
\(980\) −5.14106e12 −0.178047
\(981\) 1.52763e13 0.526633
\(982\) 3.31708e13 1.13829
\(983\) 5.31777e13 1.81651 0.908256 0.418414i \(-0.137414\pi\)
0.908256 + 0.418414i \(0.137414\pi\)
\(984\) 1.21899e13 0.414497
\(985\) −3.14968e12 −0.106611
\(986\) −8.60304e12 −0.289872
\(987\) −1.93775e12 −0.0649936
\(988\) −3.68494e12 −0.123034
\(989\) 9.58193e12 0.318471
\(990\) −1.31006e12 −0.0433444
\(991\) 3.41823e13 1.12582 0.562912 0.826517i \(-0.309681\pi\)
0.562912 + 0.826517i \(0.309681\pi\)
\(992\) 2.76117e12 0.0905297
\(993\) −2.30994e13 −0.753926
\(994\) −4.06711e11 −0.0132144
\(995\) −8.55794e12 −0.276799
\(996\) −1.92934e12 −0.0621216
\(997\) 4.83269e13 1.54903 0.774517 0.632553i \(-0.217993\pi\)
0.774517 + 0.632553i \(0.217993\pi\)
\(998\) 4.15375e13 1.32542
\(999\) −3.68633e13 −1.17098
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.1.6 7
3.2 odd 2 153.10.a.f.1.2 7
4.3 odd 2 272.10.a.g.1.2 7
17.16 even 2 289.10.a.b.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.b.1.6 7 1.1 even 1 trivial
153.10.a.f.1.2 7 3.2 odd 2
272.10.a.g.1.2 7 4.3 odd 2
289.10.a.b.1.6 7 17.16 even 2