Properties

Label 17.10.a.b.1.3
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 1.3
Root \(16.8116\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.8116 q^{2} -116.887 q^{3} -229.369 q^{4} -1103.40 q^{5} +1965.06 q^{6} -5164.29 q^{7} +12463.6 q^{8} -6020.47 q^{9} +O(q^{10})\) \(q-16.8116 q^{2} -116.887 q^{3} -229.369 q^{4} -1103.40 q^{5} +1965.06 q^{6} -5164.29 q^{7} +12463.6 q^{8} -6020.47 q^{9} +18549.9 q^{10} +44537.1 q^{11} +26810.2 q^{12} +69656.8 q^{13} +86820.2 q^{14} +128973. q^{15} -92097.3 q^{16} +83521.0 q^{17} +101214. q^{18} -170217. q^{19} +253085. q^{20} +603638. q^{21} -748741. q^{22} -2.00737e6 q^{23} -1.45683e6 q^{24} -735637. q^{25} -1.17105e6 q^{26} +3.00440e6 q^{27} +1.18453e6 q^{28} +155688. q^{29} -2.16824e6 q^{30} +4.27490e6 q^{31} -4.83307e6 q^{32} -5.20580e6 q^{33} -1.40413e6 q^{34} +5.69827e6 q^{35} +1.38091e6 q^{36} +1.51022e7 q^{37} +2.86163e6 q^{38} -8.14197e6 q^{39} -1.37523e7 q^{40} +1.59320e7 q^{41} -1.01481e7 q^{42} +1.49261e7 q^{43} -1.02154e7 q^{44} +6.64298e6 q^{45} +3.37471e7 q^{46} +3.36137e7 q^{47} +1.07650e7 q^{48} -1.36837e7 q^{49} +1.23673e7 q^{50} -9.76250e6 q^{51} -1.59771e7 q^{52} -5.50379e7 q^{53} -5.05089e7 q^{54} -4.91421e7 q^{55} -6.43658e7 q^{56} +1.98961e7 q^{57} -2.61737e6 q^{58} -7.94611e7 q^{59} -2.95823e7 q^{60} +1.27852e7 q^{61} -7.18682e7 q^{62} +3.10915e7 q^{63} +1.28406e8 q^{64} -7.68593e7 q^{65} +8.75180e7 q^{66} +2.73169e8 q^{67} -1.91571e7 q^{68} +2.34635e8 q^{69} -9.57973e7 q^{70} +3.88392e6 q^{71} -7.50369e7 q^{72} +2.32369e8 q^{73} -2.53892e8 q^{74} +8.59862e7 q^{75} +3.90425e7 q^{76} -2.30002e8 q^{77} +1.36880e8 q^{78} +3.38948e8 q^{79} +1.01620e8 q^{80} -2.32673e8 q^{81} -2.67843e8 q^{82} +5.74624e8 q^{83} -1.38456e8 q^{84} -9.21569e7 q^{85} -2.50932e8 q^{86} -1.81978e7 q^{87} +5.55093e8 q^{88} -9.82429e8 q^{89} -1.11679e8 q^{90} -3.59728e8 q^{91} +4.60427e8 q^{92} -4.99680e8 q^{93} -5.65102e8 q^{94} +1.87817e8 q^{95} +5.64922e8 q^{96} -1.03147e9 q^{97} +2.30046e8 q^{98} -2.68134e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + O(q^{10}) \) \( 7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + 16821q^{8} + 81419q^{9} + 154226q^{10} + 135536q^{11} + 198160q^{12} + 166122q^{13} + 447252q^{14} + 159048q^{15} + 1463585q^{16} + 584647q^{17} + 149027q^{18} + 777172q^{19} - 917162q^{20} - 3412104q^{21} - 1222520q^{22} + 1357764q^{23} - 8487360q^{24} + 1065785q^{25} - 14379966q^{26} - 4519064q^{27} - 3328892q^{28} + 967002q^{29} - 12558992q^{30} + 3546740q^{31} + 4825461q^{32} + 11928016q^{33} - 83521q^{34} - 530736q^{35} + 4535009q^{36} + 18296498q^{37} - 49363020q^{38} + 86306872q^{39} + 127155062q^{40} + 10285686q^{41} + 14620416q^{42} + 21913204q^{43} + 96696624q^{44} + 108916410q^{45} - 151509484q^{46} + 56639800q^{47} - 201398496q^{48} + 27010351q^{49} - 261150303q^{50} + 7349848q^{51} - 156226378q^{52} + 121813562q^{53} - 93375344q^{54} + 40793128q^{55} - 196175436q^{56} + 153612960q^{57} - 236833910q^{58} + 29222388q^{59} - 628643488q^{60} - 49915846q^{61} - 73506556q^{62} - 2185356q^{63} + 317922057q^{64} - 122633668q^{65} - 624886144q^{66} + 301863420q^{67} + 199531669q^{68} + 379683432q^{69} + 966315960q^{70} + 652473940q^{71} + 655760385q^{72} + 306656342q^{73} + 249173874q^{74} + 919071912q^{75} + 128694700q^{76} - 102442536q^{77} + 323434416q^{78} + 959147884q^{79} - 692173602q^{80} - 374486977q^{81} + 1046441254q^{82} - 1512945268q^{83} - 481790592q^{84} + 113755602q^{85} - 164953236q^{86} - 1612550856q^{87} + 1132038848q^{88} - 1971327114q^{89} - 2284664662q^{90} - 1061062864q^{91} + 901186756q^{92} - 798598936q^{93} + 2534831232q^{94} - 3249631512q^{95} - 4442036640q^{96} + 2006526254q^{97} - 2170640009q^{98} - 2579159272q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.8116 −0.742977 −0.371488 0.928438i \(-0.621152\pi\)
−0.371488 + 0.928438i \(0.621152\pi\)
\(3\) −116.887 −0.833144 −0.416572 0.909103i \(-0.636769\pi\)
−0.416572 + 0.909103i \(0.636769\pi\)
\(4\) −229.369 −0.447986
\(5\) −1103.40 −0.789528 −0.394764 0.918783i \(-0.629174\pi\)
−0.394764 + 0.918783i \(0.629174\pi\)
\(6\) 1965.06 0.619006
\(7\) −5164.29 −0.812961 −0.406480 0.913660i \(-0.633244\pi\)
−0.406480 + 0.913660i \(0.633244\pi\)
\(8\) 12463.6 1.07582
\(9\) −6020.47 −0.305872
\(10\) 18549.9 0.586601
\(11\) 44537.1 0.917180 0.458590 0.888648i \(-0.348355\pi\)
0.458590 + 0.888648i \(0.348355\pi\)
\(12\) 26810.2 0.373236
\(13\) 69656.8 0.676424 0.338212 0.941070i \(-0.390178\pi\)
0.338212 + 0.941070i \(0.390178\pi\)
\(14\) 86820.2 0.604011
\(15\) 128973. 0.657790
\(16\) −92097.3 −0.351323
\(17\) 83521.0 0.242536
\(18\) 101214. 0.227255
\(19\) −170217. −0.299648 −0.149824 0.988713i \(-0.547871\pi\)
−0.149824 + 0.988713i \(0.547871\pi\)
\(20\) 253085. 0.353697
\(21\) 603638. 0.677313
\(22\) −748741. −0.681443
\(23\) −2.00737e6 −1.49572 −0.747861 0.663855i \(-0.768919\pi\)
−0.747861 + 0.663855i \(0.768919\pi\)
\(24\) −1.45683e6 −0.896312
\(25\) −735637. −0.376646
\(26\) −1.17105e6 −0.502567
\(27\) 3.00440e6 1.08798
\(28\) 1.18453e6 0.364195
\(29\) 155688. 0.0408755 0.0204378 0.999791i \(-0.493494\pi\)
0.0204378 + 0.999791i \(0.493494\pi\)
\(30\) −2.16824e6 −0.488723
\(31\) 4.27490e6 0.831379 0.415689 0.909507i \(-0.363540\pi\)
0.415689 + 0.909507i \(0.363540\pi\)
\(32\) −4.83307e6 −0.814795
\(33\) −5.20580e6 −0.764143
\(34\) −1.40413e6 −0.180198
\(35\) 5.69827e6 0.641855
\(36\) 1.38091e6 0.137026
\(37\) 1.51022e7 1.32474 0.662371 0.749176i \(-0.269550\pi\)
0.662371 + 0.749176i \(0.269550\pi\)
\(38\) 2.86163e6 0.222632
\(39\) −8.14197e6 −0.563558
\(40\) −1.37523e7 −0.849389
\(41\) 1.59320e7 0.880526 0.440263 0.897869i \(-0.354885\pi\)
0.440263 + 0.897869i \(0.354885\pi\)
\(42\) −1.01481e7 −0.503228
\(43\) 1.49261e7 0.665790 0.332895 0.942964i \(-0.391975\pi\)
0.332895 + 0.942964i \(0.391975\pi\)
\(44\) −1.02154e7 −0.410883
\(45\) 6.64298e6 0.241494
\(46\) 3.37471e7 1.11129
\(47\) 3.36137e7 1.00479 0.502396 0.864638i \(-0.332452\pi\)
0.502396 + 0.864638i \(0.332452\pi\)
\(48\) 1.07650e7 0.292703
\(49\) −1.36837e7 −0.339095
\(50\) 1.23673e7 0.279839
\(51\) −9.76250e6 −0.202067
\(52\) −1.59771e7 −0.303028
\(53\) −5.50379e7 −0.958121 −0.479060 0.877782i \(-0.659023\pi\)
−0.479060 + 0.877782i \(0.659023\pi\)
\(54\) −5.05089e7 −0.808343
\(55\) −4.91421e7 −0.724139
\(56\) −6.43658e7 −0.874599
\(57\) 1.98961e7 0.249650
\(58\) −2.61737e6 −0.0303696
\(59\) −7.94611e7 −0.853730 −0.426865 0.904315i \(-0.640382\pi\)
−0.426865 + 0.904315i \(0.640382\pi\)
\(60\) −2.95823e7 −0.294680
\(61\) 1.27852e7 0.118229 0.0591146 0.998251i \(-0.481172\pi\)
0.0591146 + 0.998251i \(0.481172\pi\)
\(62\) −7.18682e7 −0.617695
\(63\) 3.10915e7 0.248662
\(64\) 1.28406e8 0.956697
\(65\) −7.68593e7 −0.534055
\(66\) 8.75180e7 0.567740
\(67\) 2.73169e8 1.65613 0.828066 0.560631i \(-0.189441\pi\)
0.828066 + 0.560631i \(0.189441\pi\)
\(68\) −1.91571e7 −0.108652
\(69\) 2.34635e8 1.24615
\(70\) −9.57973e7 −0.476883
\(71\) 3.88392e6 0.0181388 0.00906938 0.999959i \(-0.497113\pi\)
0.00906938 + 0.999959i \(0.497113\pi\)
\(72\) −7.50369e7 −0.329063
\(73\) 2.32369e8 0.957690 0.478845 0.877900i \(-0.341056\pi\)
0.478845 + 0.877900i \(0.341056\pi\)
\(74\) −2.53892e8 −0.984253
\(75\) 8.59862e7 0.313800
\(76\) 3.90425e7 0.134238
\(77\) −2.30002e8 −0.745631
\(78\) 1.36880e8 0.418710
\(79\) 3.38948e8 0.979064 0.489532 0.871985i \(-0.337168\pi\)
0.489532 + 0.871985i \(0.337168\pi\)
\(80\) 1.01620e8 0.277379
\(81\) −2.32673e8 −0.600571
\(82\) −2.67843e8 −0.654210
\(83\) 5.74624e8 1.32902 0.664511 0.747278i \(-0.268640\pi\)
0.664511 + 0.747278i \(0.268640\pi\)
\(84\) −1.38456e8 −0.303427
\(85\) −9.21569e7 −0.191489
\(86\) −2.50932e8 −0.494666
\(87\) −1.81978e7 −0.0340552
\(88\) 5.55093e8 0.986720
\(89\) −9.82429e8 −1.65976 −0.829882 0.557940i \(-0.811592\pi\)
−0.829882 + 0.557940i \(0.811592\pi\)
\(90\) −1.11679e8 −0.179424
\(91\) −3.59728e8 −0.549906
\(92\) 4.60427e8 0.670062
\(93\) −4.99680e8 −0.692658
\(94\) −5.65102e8 −0.746537
\(95\) 1.87817e8 0.236581
\(96\) 5.64922e8 0.678841
\(97\) −1.03147e9 −1.18300 −0.591500 0.806305i \(-0.701464\pi\)
−0.591500 + 0.806305i \(0.701464\pi\)
\(98\) 2.30046e8 0.251940
\(99\) −2.68134e8 −0.280539
\(100\) 1.68732e8 0.168732
\(101\) −5.23482e7 −0.0500559 −0.0250280 0.999687i \(-0.507967\pi\)
−0.0250280 + 0.999687i \(0.507967\pi\)
\(102\) 1.64124e8 0.150131
\(103\) 4.65791e8 0.407778 0.203889 0.978994i \(-0.434642\pi\)
0.203889 + 0.978994i \(0.434642\pi\)
\(104\) 8.68177e8 0.727710
\(105\) −6.66053e8 −0.534757
\(106\) 9.25277e8 0.711861
\(107\) −1.44228e9 −1.06371 −0.531854 0.846836i \(-0.678504\pi\)
−0.531854 + 0.846836i \(0.678504\pi\)
\(108\) −6.89114e8 −0.487399
\(109\) 2.37882e9 1.61414 0.807072 0.590453i \(-0.201051\pi\)
0.807072 + 0.590453i \(0.201051\pi\)
\(110\) 8.26160e8 0.538018
\(111\) −1.76524e9 −1.10370
\(112\) 4.75617e8 0.285612
\(113\) −5.54552e8 −0.319955 −0.159978 0.987121i \(-0.551142\pi\)
−0.159978 + 0.987121i \(0.551142\pi\)
\(114\) −3.34487e8 −0.185484
\(115\) 2.21492e9 1.18091
\(116\) −3.57099e7 −0.0183117
\(117\) −4.19367e8 −0.206899
\(118\) 1.33587e9 0.634302
\(119\) −4.31327e8 −0.197172
\(120\) 1.60747e9 0.707663
\(121\) −3.74397e8 −0.158781
\(122\) −2.14941e8 −0.0878415
\(123\) −1.86224e9 −0.733605
\(124\) −9.80529e8 −0.372446
\(125\) 2.96678e9 1.08690
\(126\) −5.22699e8 −0.184750
\(127\) 3.25473e9 1.11019 0.555097 0.831786i \(-0.312681\pi\)
0.555097 + 0.831786i \(0.312681\pi\)
\(128\) 3.15822e8 0.103991
\(129\) −1.74466e9 −0.554699
\(130\) 1.29213e9 0.396791
\(131\) −2.29117e9 −0.679731 −0.339865 0.940474i \(-0.610382\pi\)
−0.339865 + 0.940474i \(0.610382\pi\)
\(132\) 1.19405e9 0.342325
\(133\) 8.79051e8 0.243602
\(134\) −4.59242e9 −1.23047
\(135\) −3.31505e9 −0.858989
\(136\) 1.04097e9 0.260925
\(137\) 7.07071e9 1.71483 0.857413 0.514628i \(-0.172070\pi\)
0.857413 + 0.514628i \(0.172070\pi\)
\(138\) −3.94459e9 −0.925862
\(139\) −2.13323e9 −0.484697 −0.242349 0.970189i \(-0.577918\pi\)
−0.242349 + 0.970189i \(0.577918\pi\)
\(140\) −1.30700e9 −0.287542
\(141\) −3.92900e9 −0.837136
\(142\) −6.52951e7 −0.0134767
\(143\) 3.10231e9 0.620402
\(144\) 5.54469e8 0.107460
\(145\) −1.71786e8 −0.0322724
\(146\) −3.90650e9 −0.711541
\(147\) 1.59944e9 0.282515
\(148\) −3.46396e9 −0.593465
\(149\) −8.98904e9 −1.49408 −0.747042 0.664777i \(-0.768527\pi\)
−0.747042 + 0.664777i \(0.768527\pi\)
\(150\) −1.44557e9 −0.233146
\(151\) 4.53054e9 0.709175 0.354588 0.935023i \(-0.384621\pi\)
0.354588 + 0.935023i \(0.384621\pi\)
\(152\) −2.12152e9 −0.322368
\(153\) −5.02836e8 −0.0741848
\(154\) 3.86672e9 0.553987
\(155\) −4.71692e9 −0.656396
\(156\) 1.86751e9 0.252466
\(157\) −3.69961e9 −0.485967 −0.242984 0.970030i \(-0.578126\pi\)
−0.242984 + 0.970030i \(0.578126\pi\)
\(158\) −5.69827e9 −0.727422
\(159\) 6.43320e9 0.798252
\(160\) 5.33280e9 0.643303
\(161\) 1.03666e10 1.21596
\(162\) 3.91162e9 0.446210
\(163\) 1.71522e10 1.90317 0.951583 0.307393i \(-0.0994565\pi\)
0.951583 + 0.307393i \(0.0994565\pi\)
\(164\) −3.65430e9 −0.394463
\(165\) 5.74407e9 0.603312
\(166\) −9.66037e9 −0.987433
\(167\) 1.39036e10 1.38326 0.691628 0.722254i \(-0.256894\pi\)
0.691628 + 0.722254i \(0.256894\pi\)
\(168\) 7.52351e9 0.728667
\(169\) −5.75242e9 −0.542451
\(170\) 1.54931e9 0.142272
\(171\) 1.02479e9 0.0916540
\(172\) −3.42357e9 −0.298264
\(173\) 1.51288e9 0.128409 0.0642047 0.997937i \(-0.479549\pi\)
0.0642047 + 0.997937i \(0.479549\pi\)
\(174\) 3.05936e8 0.0253022
\(175\) 3.79904e9 0.306198
\(176\) −4.10174e9 −0.322227
\(177\) 9.28796e9 0.711280
\(178\) 1.65162e10 1.23317
\(179\) −2.09830e10 −1.52767 −0.763835 0.645411i \(-0.776686\pi\)
−0.763835 + 0.645411i \(0.776686\pi\)
\(180\) −1.52369e9 −0.108186
\(181\) −1.75141e10 −1.21293 −0.606464 0.795111i \(-0.707413\pi\)
−0.606464 + 0.795111i \(0.707413\pi\)
\(182\) 6.04762e9 0.408567
\(183\) −1.49443e9 −0.0985018
\(184\) −2.50190e10 −1.60913
\(185\) −1.66637e10 −1.04592
\(186\) 8.40044e9 0.514629
\(187\) 3.71978e9 0.222449
\(188\) −7.70993e9 −0.450132
\(189\) −1.55156e10 −0.884484
\(190\) −3.15752e9 −0.175774
\(191\) 1.64385e10 0.893741 0.446871 0.894599i \(-0.352538\pi\)
0.446871 + 0.894599i \(0.352538\pi\)
\(192\) −1.50089e10 −0.797066
\(193\) −9.12709e9 −0.473505 −0.236753 0.971570i \(-0.576083\pi\)
−0.236753 + 0.971570i \(0.576083\pi\)
\(194\) 1.73407e10 0.878942
\(195\) 8.98383e9 0.444945
\(196\) 3.13861e9 0.151910
\(197\) 1.53151e9 0.0724472 0.0362236 0.999344i \(-0.488467\pi\)
0.0362236 + 0.999344i \(0.488467\pi\)
\(198\) 4.50778e9 0.208434
\(199\) 1.77679e10 0.803152 0.401576 0.915826i \(-0.368463\pi\)
0.401576 + 0.915826i \(0.368463\pi\)
\(200\) −9.16870e9 −0.405203
\(201\) −3.19299e10 −1.37980
\(202\) 8.80059e8 0.0371904
\(203\) −8.04017e8 −0.0332302
\(204\) 2.23921e9 0.0905231
\(205\) −1.75793e10 −0.695200
\(206\) −7.83072e9 −0.302970
\(207\) 1.20853e10 0.457499
\(208\) −6.41521e9 −0.237643
\(209\) −7.58097e9 −0.274832
\(210\) 1.11974e10 0.397312
\(211\) 5.19005e10 1.80260 0.901302 0.433192i \(-0.142613\pi\)
0.901302 + 0.433192i \(0.142613\pi\)
\(212\) 1.26240e10 0.429224
\(213\) −4.53979e8 −0.0151122
\(214\) 2.42471e10 0.790310
\(215\) −1.64694e10 −0.525660
\(216\) 3.74457e10 1.17047
\(217\) −2.20769e10 −0.675878
\(218\) −3.99919e10 −1.19927
\(219\) −2.71608e10 −0.797893
\(220\) 1.12717e10 0.324404
\(221\) 5.81781e9 0.164057
\(222\) 2.96766e10 0.820024
\(223\) −6.09533e10 −1.65054 −0.825269 0.564740i \(-0.808976\pi\)
−0.825269 + 0.564740i \(0.808976\pi\)
\(224\) 2.49594e10 0.662396
\(225\) 4.42888e9 0.115205
\(226\) 9.32293e9 0.237719
\(227\) 6.35858e10 1.58944 0.794720 0.606977i \(-0.207618\pi\)
0.794720 + 0.606977i \(0.207618\pi\)
\(228\) −4.56355e9 −0.111840
\(229\) −6.22903e10 −1.49679 −0.748395 0.663254i \(-0.769175\pi\)
−0.748395 + 0.663254i \(0.769175\pi\)
\(230\) −3.72365e10 −0.877392
\(231\) 2.68842e10 0.621218
\(232\) 1.94043e9 0.0439747
\(233\) 8.69026e10 1.93166 0.965831 0.259172i \(-0.0834496\pi\)
0.965831 + 0.259172i \(0.0834496\pi\)
\(234\) 7.05025e9 0.153721
\(235\) −3.70893e10 −0.793311
\(236\) 1.82259e10 0.382459
\(237\) −3.96186e10 −0.815701
\(238\) 7.25131e9 0.146494
\(239\) 7.04686e10 1.39703 0.698514 0.715597i \(-0.253845\pi\)
0.698514 + 0.715597i \(0.253845\pi\)
\(240\) −1.18780e10 −0.231097
\(241\) 6.25058e10 1.19356 0.596779 0.802405i \(-0.296447\pi\)
0.596779 + 0.802405i \(0.296447\pi\)
\(242\) 6.29423e9 0.117971
\(243\) −3.19391e10 −0.587617
\(244\) −2.93253e9 −0.0529649
\(245\) 1.50986e10 0.267725
\(246\) 3.13073e10 0.545051
\(247\) −1.18568e10 −0.202689
\(248\) 5.32808e10 0.894413
\(249\) −6.71660e10 −1.10727
\(250\) −4.98764e10 −0.807541
\(251\) −7.26518e9 −0.115535 −0.0577676 0.998330i \(-0.518398\pi\)
−0.0577676 + 0.998330i \(0.518398\pi\)
\(252\) −7.13141e9 −0.111397
\(253\) −8.94022e10 −1.37185
\(254\) −5.47174e10 −0.824848
\(255\) 1.07719e10 0.159538
\(256\) −7.10532e10 −1.03396
\(257\) −8.23779e10 −1.17791 −0.588955 0.808166i \(-0.700460\pi\)
−0.588955 + 0.808166i \(0.700460\pi\)
\(258\) 2.93306e10 0.412128
\(259\) −7.79920e10 −1.07696
\(260\) 1.76291e10 0.239249
\(261\) −9.37314e8 −0.0125027
\(262\) 3.85184e10 0.505024
\(263\) 8.05229e10 1.03781 0.518906 0.854831i \(-0.326340\pi\)
0.518906 + 0.854831i \(0.326340\pi\)
\(264\) −6.48831e10 −0.822080
\(265\) 6.07287e10 0.756463
\(266\) −1.47783e10 −0.180991
\(267\) 1.14833e11 1.38282
\(268\) −6.26564e10 −0.741923
\(269\) 3.37804e10 0.393350 0.196675 0.980469i \(-0.436986\pi\)
0.196675 + 0.980469i \(0.436986\pi\)
\(270\) 5.57314e10 0.638209
\(271\) 5.31396e10 0.598489 0.299245 0.954176i \(-0.403265\pi\)
0.299245 + 0.954176i \(0.403265\pi\)
\(272\) −7.69206e9 −0.0852084
\(273\) 4.20475e10 0.458150
\(274\) −1.18870e11 −1.27408
\(275\) −3.27631e10 −0.345452
\(276\) −5.38178e10 −0.558258
\(277\) −1.33887e11 −1.36640 −0.683201 0.730231i \(-0.739413\pi\)
−0.683201 + 0.730231i \(0.739413\pi\)
\(278\) 3.58631e10 0.360119
\(279\) −2.57369e10 −0.254295
\(280\) 7.10211e10 0.690520
\(281\) −6.71427e10 −0.642422 −0.321211 0.947008i \(-0.604090\pi\)
−0.321211 + 0.947008i \(0.604090\pi\)
\(282\) 6.60530e10 0.621973
\(283\) 1.11880e11 1.03684 0.518420 0.855126i \(-0.326520\pi\)
0.518420 + 0.855126i \(0.326520\pi\)
\(284\) −8.90850e8 −0.00812591
\(285\) −2.19534e10 −0.197106
\(286\) −5.21550e10 −0.460944
\(287\) −8.22774e10 −0.715833
\(288\) 2.90974e10 0.249223
\(289\) 6.97576e9 0.0588235
\(290\) 2.88800e9 0.0239776
\(291\) 1.20566e11 0.985609
\(292\) −5.32981e10 −0.429031
\(293\) 1.51192e11 1.19846 0.599230 0.800577i \(-0.295474\pi\)
0.599230 + 0.800577i \(0.295474\pi\)
\(294\) −2.68893e10 −0.209902
\(295\) 8.76773e10 0.674044
\(296\) 1.88228e11 1.42518
\(297\) 1.33807e11 0.997872
\(298\) 1.51121e11 1.11007
\(299\) −1.39827e11 −1.01174
\(300\) −1.97225e10 −0.140578
\(301\) −7.70825e10 −0.541261
\(302\) −7.61658e10 −0.526901
\(303\) 6.11881e9 0.0417038
\(304\) 1.56765e10 0.105273
\(305\) −1.41072e10 −0.0933452
\(306\) 8.45350e9 0.0551175
\(307\) 6.62355e10 0.425567 0.212784 0.977099i \(-0.431747\pi\)
0.212784 + 0.977099i \(0.431747\pi\)
\(308\) 5.27553e10 0.334032
\(309\) −5.44449e10 −0.339738
\(310\) 7.92992e10 0.487687
\(311\) −9.27102e10 −0.561960 −0.280980 0.959714i \(-0.590660\pi\)
−0.280980 + 0.959714i \(0.590660\pi\)
\(312\) −1.01478e11 −0.606287
\(313\) 2.58675e11 1.52337 0.761684 0.647949i \(-0.224373\pi\)
0.761684 + 0.647949i \(0.224373\pi\)
\(314\) 6.21965e10 0.361062
\(315\) −3.43063e10 −0.196325
\(316\) −7.77440e10 −0.438607
\(317\) −4.47169e10 −0.248717 −0.124358 0.992237i \(-0.539687\pi\)
−0.124358 + 0.992237i \(0.539687\pi\)
\(318\) −1.08153e11 −0.593083
\(319\) 6.93388e9 0.0374902
\(320\) −1.41683e11 −0.755338
\(321\) 1.68583e11 0.886221
\(322\) −1.74280e11 −0.903433
\(323\) −1.42167e10 −0.0726754
\(324\) 5.33680e10 0.269047
\(325\) −5.12421e10 −0.254772
\(326\) −2.88357e11 −1.41401
\(327\) −2.78053e11 −1.34481
\(328\) 1.98570e11 0.947287
\(329\) −1.73591e11 −0.816856
\(330\) −9.65672e10 −0.448247
\(331\) 4.78159e10 0.218951 0.109475 0.993990i \(-0.465083\pi\)
0.109475 + 0.993990i \(0.465083\pi\)
\(332\) −1.31801e11 −0.595383
\(333\) −9.09221e10 −0.405201
\(334\) −2.33742e11 −1.02773
\(335\) −3.01414e11 −1.30756
\(336\) −5.55934e10 −0.237956
\(337\) 3.76342e11 1.58945 0.794727 0.606968i \(-0.207614\pi\)
0.794727 + 0.606968i \(0.207614\pi\)
\(338\) 9.67077e10 0.403029
\(339\) 6.48198e10 0.266569
\(340\) 2.11379e10 0.0857841
\(341\) 1.90392e11 0.762524
\(342\) −1.72284e10 −0.0680968
\(343\) 2.79064e11 1.08863
\(344\) 1.86033e11 0.716270
\(345\) −2.58895e11 −0.983872
\(346\) −2.54340e10 −0.0954052
\(347\) −1.77078e11 −0.655665 −0.327833 0.944736i \(-0.606318\pi\)
−0.327833 + 0.944736i \(0.606318\pi\)
\(348\) 4.17402e9 0.0152562
\(349\) 2.43883e11 0.879967 0.439984 0.898006i \(-0.354984\pi\)
0.439984 + 0.898006i \(0.354984\pi\)
\(350\) −6.38681e10 −0.227498
\(351\) 2.09277e11 0.735934
\(352\) −2.15251e11 −0.747313
\(353\) 1.91758e11 0.657304 0.328652 0.944451i \(-0.393406\pi\)
0.328652 + 0.944451i \(0.393406\pi\)
\(354\) −1.56146e11 −0.528465
\(355\) −4.28551e9 −0.0143211
\(356\) 2.25338e11 0.743550
\(357\) 5.04164e10 0.164273
\(358\) 3.52759e11 1.13502
\(359\) −6.43139e10 −0.204352 −0.102176 0.994766i \(-0.532581\pi\)
−0.102176 + 0.994766i \(0.532581\pi\)
\(360\) 8.27956e10 0.259804
\(361\) −2.93714e11 −0.910211
\(362\) 2.94441e11 0.901177
\(363\) 4.37621e10 0.132287
\(364\) 8.25104e10 0.246350
\(365\) −2.56395e11 −0.756123
\(366\) 2.51237e10 0.0731846
\(367\) 7.24947e10 0.208597 0.104299 0.994546i \(-0.466740\pi\)
0.104299 + 0.994546i \(0.466740\pi\)
\(368\) 1.84873e11 0.525482
\(369\) −9.59180e10 −0.269328
\(370\) 2.80144e11 0.777095
\(371\) 2.84232e11 0.778914
\(372\) 1.14611e11 0.310301
\(373\) −5.44526e10 −0.145656 −0.0728281 0.997345i \(-0.523202\pi\)
−0.0728281 + 0.997345i \(0.523202\pi\)
\(374\) −6.25356e10 −0.165274
\(375\) −3.46777e11 −0.905544
\(376\) 4.18949e11 1.08097
\(377\) 1.08447e10 0.0276492
\(378\) 2.60842e11 0.657151
\(379\) −2.15005e11 −0.535270 −0.267635 0.963520i \(-0.586242\pi\)
−0.267635 + 0.963520i \(0.586242\pi\)
\(380\) −4.30794e10 −0.105985
\(381\) −3.80435e11 −0.924951
\(382\) −2.76358e11 −0.664029
\(383\) −4.29189e11 −1.01919 −0.509594 0.860415i \(-0.670204\pi\)
−0.509594 + 0.860415i \(0.670204\pi\)
\(384\) −3.69154e10 −0.0866397
\(385\) 2.53784e11 0.588696
\(386\) 1.53441e11 0.351803
\(387\) −8.98619e10 −0.203646
\(388\) 2.36587e11 0.529967
\(389\) −2.02217e11 −0.447760 −0.223880 0.974617i \(-0.571872\pi\)
−0.223880 + 0.974617i \(0.571872\pi\)
\(390\) −1.51033e11 −0.330584
\(391\) −1.67657e11 −0.362766
\(392\) −1.70549e11 −0.364805
\(393\) 2.67808e11 0.566313
\(394\) −2.57472e10 −0.0538266
\(395\) −3.73995e11 −0.772998
\(396\) 6.15016e10 0.125678
\(397\) 1.81106e11 0.365911 0.182955 0.983121i \(-0.441434\pi\)
0.182955 + 0.983121i \(0.441434\pi\)
\(398\) −2.98708e11 −0.596723
\(399\) −1.02749e11 −0.202956
\(400\) 6.77501e10 0.132324
\(401\) −1.40602e11 −0.271545 −0.135772 0.990740i \(-0.543352\pi\)
−0.135772 + 0.990740i \(0.543352\pi\)
\(402\) 5.36793e11 1.02516
\(403\) 2.97776e11 0.562364
\(404\) 1.20070e10 0.0224243
\(405\) 2.56732e11 0.474167
\(406\) 1.35168e10 0.0246893
\(407\) 6.72606e11 1.21503
\(408\) −1.21676e11 −0.217388
\(409\) −6.11843e11 −1.08115 −0.540574 0.841297i \(-0.681793\pi\)
−0.540574 + 0.841297i \(0.681793\pi\)
\(410\) 2.95537e11 0.516517
\(411\) −8.26472e11 −1.42870
\(412\) −1.06838e11 −0.182679
\(413\) 4.10360e11 0.694049
\(414\) −2.03173e11 −0.339911
\(415\) −6.34039e11 −1.04930
\(416\) −3.36656e11 −0.551146
\(417\) 2.49346e11 0.403822
\(418\) 1.27449e11 0.204193
\(419\) 2.89071e10 0.0458186 0.0229093 0.999738i \(-0.492707\pi\)
0.0229093 + 0.999738i \(0.492707\pi\)
\(420\) 1.52772e11 0.239564
\(421\) 1.06260e12 1.64854 0.824272 0.566193i \(-0.191584\pi\)
0.824272 + 0.566193i \(0.191584\pi\)
\(422\) −8.72532e11 −1.33929
\(423\) −2.02370e11 −0.307337
\(424\) −6.85971e11 −1.03077
\(425\) −6.14411e10 −0.0913501
\(426\) 7.63214e9 0.0112280
\(427\) −6.60267e10 −0.0961156
\(428\) 3.30814e11 0.476526
\(429\) −3.62619e11 −0.516884
\(430\) 2.76878e11 0.390553
\(431\) −5.09485e10 −0.0711187 −0.0355594 0.999368i \(-0.511321\pi\)
−0.0355594 + 0.999368i \(0.511321\pi\)
\(432\) −2.76697e11 −0.382232
\(433\) −1.02428e12 −1.40030 −0.700152 0.713994i \(-0.746885\pi\)
−0.700152 + 0.713994i \(0.746885\pi\)
\(434\) 3.71148e11 0.502162
\(435\) 2.00795e10 0.0268875
\(436\) −5.45627e11 −0.723113
\(437\) 3.41688e11 0.448191
\(438\) 4.56618e11 0.592816
\(439\) 3.70271e11 0.475805 0.237903 0.971289i \(-0.423540\pi\)
0.237903 + 0.971289i \(0.423540\pi\)
\(440\) −6.12489e11 −0.779043
\(441\) 8.23824e10 0.103720
\(442\) −9.78069e10 −0.121890
\(443\) −1.17113e12 −1.44473 −0.722366 0.691511i \(-0.756946\pi\)
−0.722366 + 0.691511i \(0.756946\pi\)
\(444\) 4.04892e11 0.494442
\(445\) 1.08401e12 1.31043
\(446\) 1.02473e12 1.22631
\(447\) 1.05070e12 1.24479
\(448\) −6.63124e11 −0.777757
\(449\) 6.79800e10 0.0789355 0.0394678 0.999221i \(-0.487434\pi\)
0.0394678 + 0.999221i \(0.487434\pi\)
\(450\) −7.44567e10 −0.0855949
\(451\) 7.09563e11 0.807601
\(452\) 1.27197e11 0.143335
\(453\) −5.29560e11 −0.590845
\(454\) −1.06898e12 −1.18092
\(455\) 3.96924e11 0.434166
\(456\) 2.47978e11 0.268579
\(457\) 1.72167e12 1.84640 0.923202 0.384315i \(-0.125562\pi\)
0.923202 + 0.384315i \(0.125562\pi\)
\(458\) 1.04720e12 1.11208
\(459\) 2.50930e11 0.263874
\(460\) −5.08034e11 −0.529033
\(461\) 1.42332e12 1.46774 0.733868 0.679292i \(-0.237713\pi\)
0.733868 + 0.679292i \(0.237713\pi\)
\(462\) −4.51968e11 −0.461550
\(463\) 1.62089e12 1.63922 0.819611 0.572920i \(-0.194189\pi\)
0.819611 + 0.572920i \(0.194189\pi\)
\(464\) −1.43384e10 −0.0143605
\(465\) 5.51346e11 0.546873
\(466\) −1.46098e12 −1.43518
\(467\) −1.13569e12 −1.10493 −0.552465 0.833536i \(-0.686313\pi\)
−0.552465 + 0.833536i \(0.686313\pi\)
\(468\) 9.61896e10 0.0926877
\(469\) −1.41072e12 −1.34637
\(470\) 6.23533e11 0.589412
\(471\) 4.32435e11 0.404881
\(472\) −9.90374e11 −0.918460
\(473\) 6.64763e11 0.610649
\(474\) 6.66053e11 0.606047
\(475\) 1.25218e11 0.112861
\(476\) 9.89328e10 0.0883302
\(477\) 3.31354e11 0.293062
\(478\) −1.18469e12 −1.03796
\(479\) 1.54480e11 0.134080 0.0670398 0.997750i \(-0.478645\pi\)
0.0670398 + 0.997750i \(0.478645\pi\)
\(480\) −6.23334e11 −0.535964
\(481\) 1.05197e12 0.896087
\(482\) −1.05083e12 −0.886786
\(483\) −1.21172e12 −1.01307
\(484\) 8.58750e10 0.0711316
\(485\) 1.13813e12 0.934011
\(486\) 5.36948e11 0.436586
\(487\) −9.40063e11 −0.757315 −0.378657 0.925537i \(-0.623614\pi\)
−0.378657 + 0.925537i \(0.623614\pi\)
\(488\) 1.59350e11 0.127193
\(489\) −2.00487e12 −1.58561
\(490\) −2.53832e11 −0.198913
\(491\) −5.38393e11 −0.418055 −0.209027 0.977910i \(-0.567030\pi\)
−0.209027 + 0.977910i \(0.567030\pi\)
\(492\) 4.27139e11 0.328644
\(493\) 1.30032e10 0.00991377
\(494\) 1.99332e11 0.150593
\(495\) 2.95859e11 0.221494
\(496\) −3.93707e11 −0.292083
\(497\) −2.00577e10 −0.0147461
\(498\) 1.12917e12 0.822673
\(499\) −6.12934e11 −0.442549 −0.221274 0.975212i \(-0.571022\pi\)
−0.221274 + 0.975212i \(0.571022\pi\)
\(500\) −6.80485e11 −0.486916
\(501\) −1.62514e12 −1.15245
\(502\) 1.22140e11 0.0858400
\(503\) −2.31510e12 −1.61255 −0.806277 0.591538i \(-0.798521\pi\)
−0.806277 + 0.591538i \(0.798521\pi\)
\(504\) 3.87512e11 0.267515
\(505\) 5.77609e10 0.0395205
\(506\) 1.50300e12 1.01925
\(507\) 6.72382e11 0.451940
\(508\) −7.46534e11 −0.497351
\(509\) −1.48597e12 −0.981249 −0.490625 0.871371i \(-0.663231\pi\)
−0.490625 + 0.871371i \(0.663231\pi\)
\(510\) −1.81094e11 −0.118533
\(511\) −1.20002e12 −0.778564
\(512\) 1.03282e12 0.664217
\(513\) −5.11400e11 −0.326011
\(514\) 1.38491e12 0.875159
\(515\) −5.13954e11 −0.321952
\(516\) 4.00170e11 0.248497
\(517\) 1.49706e12 0.921575
\(518\) 1.31117e12 0.800159
\(519\) −1.76836e11 −0.106984
\(520\) −9.57945e11 −0.574547
\(521\) −2.26648e11 −0.134766 −0.0673832 0.997727i \(-0.521465\pi\)
−0.0673832 + 0.997727i \(0.521465\pi\)
\(522\) 1.57578e10 0.00928919
\(523\) −1.52624e12 −0.891998 −0.445999 0.895033i \(-0.647152\pi\)
−0.445999 + 0.895033i \(0.647152\pi\)
\(524\) 5.25523e11 0.304510
\(525\) −4.44058e11 −0.255107
\(526\) −1.35372e12 −0.771070
\(527\) 3.57044e11 0.201639
\(528\) 4.79440e11 0.268461
\(529\) 2.22836e12 1.23719
\(530\) −1.02095e12 −0.562034
\(531\) 4.78393e11 0.261132
\(532\) −2.01627e11 −0.109130
\(533\) 1.10977e12 0.595609
\(534\) −1.93053e12 −1.02740
\(535\) 1.59141e12 0.839827
\(536\) 3.40468e12 1.78170
\(537\) 2.45264e12 1.27277
\(538\) −5.67903e11 −0.292250
\(539\) −6.09432e11 −0.311011
\(540\) 7.60368e11 0.384815
\(541\) 8.24488e11 0.413806 0.206903 0.978361i \(-0.433662\pi\)
0.206903 + 0.978361i \(0.433662\pi\)
\(542\) −8.93364e11 −0.444663
\(543\) 2.04717e12 1.01054
\(544\) −4.03663e11 −0.197617
\(545\) −2.62479e12 −1.27441
\(546\) −7.06887e11 −0.340395
\(547\) −3.27510e11 −0.156416 −0.0782082 0.996937i \(-0.524920\pi\)
−0.0782082 + 0.996937i \(0.524920\pi\)
\(548\) −1.62180e12 −0.768218
\(549\) −7.69731e10 −0.0361629
\(550\) 5.50802e11 0.256663
\(551\) −2.65007e10 −0.0122483
\(552\) 2.92440e12 1.34063
\(553\) −1.75043e12 −0.795941
\(554\) 2.25085e12 1.01520
\(555\) 1.94777e12 0.871402
\(556\) 4.89296e11 0.217137
\(557\) 6.54333e11 0.288038 0.144019 0.989575i \(-0.453997\pi\)
0.144019 + 0.989575i \(0.453997\pi\)
\(558\) 4.32680e11 0.188935
\(559\) 1.03970e12 0.450356
\(560\) −5.24795e11 −0.225499
\(561\) −4.34793e11 −0.185332
\(562\) 1.12878e12 0.477304
\(563\) −2.05130e12 −0.860483 −0.430242 0.902714i \(-0.641572\pi\)
−0.430242 + 0.902714i \(0.641572\pi\)
\(564\) 9.01190e11 0.375025
\(565\) 6.11892e11 0.252614
\(566\) −1.88088e12 −0.770348
\(567\) 1.20159e12 0.488241
\(568\) 4.84077e10 0.0195140
\(569\) 9.21470e11 0.368533 0.184266 0.982876i \(-0.441009\pi\)
0.184266 + 0.982876i \(0.441009\pi\)
\(570\) 3.69072e11 0.146445
\(571\) −1.70877e12 −0.672701 −0.336351 0.941737i \(-0.609193\pi\)
−0.336351 + 0.941737i \(0.609193\pi\)
\(572\) −7.11573e11 −0.277931
\(573\) −1.92144e12 −0.744615
\(574\) 1.38322e12 0.531847
\(575\) 1.47669e12 0.563358
\(576\) −7.73062e11 −0.292626
\(577\) −1.50384e12 −0.564820 −0.282410 0.959294i \(-0.591134\pi\)
−0.282410 + 0.959294i \(0.591134\pi\)
\(578\) −1.17274e11 −0.0437045
\(579\) 1.06684e12 0.394498
\(580\) 3.94022e10 0.0144576
\(581\) −2.96753e12 −1.08044
\(582\) −2.02690e12 −0.732285
\(583\) −2.45123e12 −0.878769
\(584\) 2.89616e12 1.03030
\(585\) 4.62729e11 0.163352
\(586\) −2.54178e12 −0.890428
\(587\) −3.06312e12 −1.06486 −0.532430 0.846474i \(-0.678721\pi\)
−0.532430 + 0.846474i \(0.678721\pi\)
\(588\) −3.66863e11 −0.126563
\(589\) −7.27662e11 −0.249121
\(590\) −1.47400e12 −0.500799
\(591\) −1.79013e11 −0.0603589
\(592\) −1.39087e12 −0.465413
\(593\) −7.03492e11 −0.233622 −0.116811 0.993154i \(-0.537267\pi\)
−0.116811 + 0.993154i \(0.537267\pi\)
\(594\) −2.24952e12 −0.741396
\(595\) 4.75925e11 0.155673
\(596\) 2.06180e12 0.669328
\(597\) −2.07683e12 −0.669141
\(598\) 2.35072e12 0.751701
\(599\) 2.22780e12 0.707060 0.353530 0.935423i \(-0.384981\pi\)
0.353530 + 0.935423i \(0.384981\pi\)
\(600\) 1.07170e12 0.337592
\(601\) −3.12659e12 −0.977541 −0.488771 0.872412i \(-0.662555\pi\)
−0.488771 + 0.872412i \(0.662555\pi\)
\(602\) 1.29588e12 0.402144
\(603\) −1.64461e12 −0.506564
\(604\) −1.03916e12 −0.317700
\(605\) 4.13109e11 0.125362
\(606\) −1.02867e11 −0.0309849
\(607\) 8.02028e11 0.239795 0.119898 0.992786i \(-0.461743\pi\)
0.119898 + 0.992786i \(0.461743\pi\)
\(608\) 8.22671e11 0.244152
\(609\) 9.39790e10 0.0276855
\(610\) 2.37165e11 0.0693533
\(611\) 2.34143e12 0.679665
\(612\) 1.15335e11 0.0332337
\(613\) 4.27823e12 1.22375 0.611874 0.790955i \(-0.290416\pi\)
0.611874 + 0.790955i \(0.290416\pi\)
\(614\) −1.11353e12 −0.316186
\(615\) 2.05479e12 0.579201
\(616\) −2.86666e12 −0.802165
\(617\) −2.33959e12 −0.649914 −0.324957 0.945729i \(-0.605350\pi\)
−0.324957 + 0.945729i \(0.605350\pi\)
\(618\) 9.15308e11 0.252417
\(619\) 7.17485e12 1.96429 0.982144 0.188131i \(-0.0602429\pi\)
0.982144 + 0.188131i \(0.0602429\pi\)
\(620\) 1.08191e12 0.294056
\(621\) −6.03092e12 −1.62731
\(622\) 1.55861e12 0.417523
\(623\) 5.07355e12 1.34932
\(624\) 7.49853e11 0.197991
\(625\) −1.83675e12 −0.481492
\(626\) −4.34875e12 −1.13183
\(627\) 8.86116e11 0.228974
\(628\) 8.48574e11 0.217706
\(629\) 1.26135e12 0.321297
\(630\) 5.76745e11 0.145865
\(631\) 2.21641e12 0.556567 0.278283 0.960499i \(-0.410235\pi\)
0.278283 + 0.960499i \(0.410235\pi\)
\(632\) 4.22452e12 1.05330
\(633\) −6.06648e12 −1.50183
\(634\) 7.51764e11 0.184791
\(635\) −3.59127e12 −0.876528
\(636\) −1.47557e12 −0.357606
\(637\) −9.53164e11 −0.229372
\(638\) −1.16570e11 −0.0278544
\(639\) −2.33830e10 −0.00554813
\(640\) −3.48477e11 −0.0821040
\(641\) 5.69709e10 0.0133288 0.00666442 0.999978i \(-0.497879\pi\)
0.00666442 + 0.999978i \(0.497879\pi\)
\(642\) −2.83416e12 −0.658442
\(643\) −3.26271e12 −0.752713 −0.376356 0.926475i \(-0.622823\pi\)
−0.376356 + 0.926475i \(0.622823\pi\)
\(644\) −2.37778e12 −0.544734
\(645\) 1.92506e12 0.437950
\(646\) 2.39006e11 0.0539962
\(647\) 4.42290e12 0.992289 0.496144 0.868240i \(-0.334749\pi\)
0.496144 + 0.868240i \(0.334749\pi\)
\(648\) −2.89996e12 −0.646106
\(649\) −3.53897e12 −0.783024
\(650\) 8.61464e11 0.189290
\(651\) 2.58049e12 0.563104
\(652\) −3.93419e12 −0.852591
\(653\) 4.99365e12 1.07475 0.537376 0.843343i \(-0.319416\pi\)
0.537376 + 0.843343i \(0.319416\pi\)
\(654\) 4.67452e12 0.999165
\(655\) 2.52808e12 0.536666
\(656\) −1.46729e12 −0.309349
\(657\) −1.39897e12 −0.292930
\(658\) 2.91835e12 0.606905
\(659\) 1.68196e12 0.347401 0.173701 0.984799i \(-0.444428\pi\)
0.173701 + 0.984799i \(0.444428\pi\)
\(660\) −1.31751e12 −0.270275
\(661\) 8.83788e12 1.80070 0.900351 0.435165i \(-0.143310\pi\)
0.900351 + 0.435165i \(0.143310\pi\)
\(662\) −8.03864e11 −0.162675
\(663\) −6.80025e11 −0.136683
\(664\) 7.16190e12 1.42979
\(665\) −9.69943e11 −0.192331
\(666\) 1.52855e12 0.301055
\(667\) −3.12522e11 −0.0611385
\(668\) −3.18904e12 −0.619678
\(669\) 7.12464e12 1.37514
\(670\) 5.06727e12 0.971488
\(671\) 5.69417e11 0.108437
\(672\) −2.91742e12 −0.551871
\(673\) 4.41749e12 0.830057 0.415029 0.909808i \(-0.363772\pi\)
0.415029 + 0.909808i \(0.363772\pi\)
\(674\) −6.32692e12 −1.18093
\(675\) −2.21014e12 −0.409783
\(676\) 1.31943e12 0.243010
\(677\) −8.50941e12 −1.55686 −0.778431 0.627730i \(-0.783984\pi\)
−0.778431 + 0.627730i \(0.783984\pi\)
\(678\) −1.08973e12 −0.198054
\(679\) 5.32682e12 0.961733
\(680\) −1.14861e12 −0.206007
\(681\) −7.43235e12 −1.32423
\(682\) −3.20080e12 −0.566537
\(683\) 3.49030e12 0.613719 0.306859 0.951755i \(-0.400722\pi\)
0.306859 + 0.951755i \(0.400722\pi\)
\(684\) −2.35054e11 −0.0410597
\(685\) −7.80181e12 −1.35390
\(686\) −4.69153e12 −0.808828
\(687\) 7.28092e12 1.24704
\(688\) −1.37465e12 −0.233907
\(689\) −3.83376e12 −0.648095
\(690\) 4.35246e12 0.730994
\(691\) 3.30831e12 0.552019 0.276010 0.961155i \(-0.410988\pi\)
0.276010 + 0.961155i \(0.410988\pi\)
\(692\) −3.47007e11 −0.0575256
\(693\) 1.38472e12 0.228067
\(694\) 2.97697e12 0.487144
\(695\) 2.35380e12 0.382682
\(696\) −2.26811e11 −0.0366372
\(697\) 1.33065e12 0.213559
\(698\) −4.10007e12 −0.653795
\(699\) −1.01578e13 −1.60935
\(700\) −8.71381e11 −0.137172
\(701\) 1.72300e12 0.269497 0.134749 0.990880i \(-0.456977\pi\)
0.134749 + 0.990880i \(0.456977\pi\)
\(702\) −3.51829e12 −0.546782
\(703\) −2.57065e12 −0.396957
\(704\) 5.71881e12 0.877463
\(705\) 4.33525e12 0.660942
\(706\) −3.22376e12 −0.488362
\(707\) 2.70341e11 0.0406935
\(708\) −2.13037e12 −0.318643
\(709\) 8.11666e12 1.20634 0.603169 0.797613i \(-0.293904\pi\)
0.603169 + 0.797613i \(0.293904\pi\)
\(710\) 7.20465e10 0.0106402
\(711\) −2.04063e12 −0.299468
\(712\) −1.22446e13 −1.78561
\(713\) −8.58130e12 −1.24351
\(714\) −8.47583e11 −0.122051
\(715\) −3.42309e12 −0.489825
\(716\) 4.81285e12 0.684374
\(717\) −8.23685e12 −1.16392
\(718\) 1.08122e12 0.151829
\(719\) −3.41170e12 −0.476092 −0.238046 0.971254i \(-0.576507\pi\)
−0.238046 + 0.971254i \(0.576507\pi\)
\(720\) −6.11800e11 −0.0848425
\(721\) −2.40548e12 −0.331508
\(722\) 4.93781e12 0.676265
\(723\) −7.30611e12 −0.994406
\(724\) 4.01719e12 0.543374
\(725\) −1.14530e11 −0.0153956
\(726\) −7.35713e11 −0.0982864
\(727\) −6.77588e12 −0.899624 −0.449812 0.893123i \(-0.648509\pi\)
−0.449812 + 0.893123i \(0.648509\pi\)
\(728\) −4.48352e12 −0.591599
\(729\) 8.31297e12 1.09014
\(730\) 4.31043e12 0.561781
\(731\) 1.24664e12 0.161478
\(732\) 3.42774e11 0.0441274
\(733\) −1.34191e13 −1.71694 −0.858469 0.512866i \(-0.828584\pi\)
−0.858469 + 0.512866i \(0.828584\pi\)
\(734\) −1.21875e12 −0.154983
\(735\) −1.76483e12 −0.223053
\(736\) 9.70174e12 1.21871
\(737\) 1.21661e13 1.51897
\(738\) 1.61254e12 0.200104
\(739\) 9.85851e12 1.21594 0.607969 0.793961i \(-0.291984\pi\)
0.607969 + 0.793961i \(0.291984\pi\)
\(740\) 3.82213e12 0.468557
\(741\) 1.38590e12 0.168869
\(742\) −4.77840e12 −0.578715
\(743\) 6.66107e12 0.801853 0.400926 0.916110i \(-0.368688\pi\)
0.400926 + 0.916110i \(0.368688\pi\)
\(744\) −6.22782e12 −0.745175
\(745\) 9.91849e12 1.17962
\(746\) 9.15437e11 0.108219
\(747\) −3.45951e12 −0.406510
\(748\) −8.53201e11 −0.0996539
\(749\) 7.44835e12 0.864752
\(750\) 5.82989e12 0.672798
\(751\) 2.09306e12 0.240106 0.120053 0.992767i \(-0.461694\pi\)
0.120053 + 0.992767i \(0.461694\pi\)
\(752\) −3.09573e12 −0.353007
\(753\) 8.49203e11 0.0962575
\(754\) −1.82318e11 −0.0205427
\(755\) −4.99899e12 −0.559913
\(756\) 3.55879e12 0.396236
\(757\) 1.26189e13 1.39666 0.698330 0.715776i \(-0.253927\pi\)
0.698330 + 0.715776i \(0.253927\pi\)
\(758\) 3.61459e12 0.397693
\(759\) 1.04499e13 1.14295
\(760\) 2.34088e12 0.254518
\(761\) −6.62893e12 −0.716494 −0.358247 0.933627i \(-0.616625\pi\)
−0.358247 + 0.933627i \(0.616625\pi\)
\(762\) 6.39574e12 0.687217
\(763\) −1.22849e13 −1.31224
\(764\) −3.77047e12 −0.400383
\(765\) 5.54828e11 0.0585709
\(766\) 7.21538e12 0.757233
\(767\) −5.53501e12 −0.577483
\(768\) 8.30518e12 0.861437
\(769\) 3.47382e12 0.358210 0.179105 0.983830i \(-0.442680\pi\)
0.179105 + 0.983830i \(0.442680\pi\)
\(770\) −4.26653e12 −0.437388
\(771\) 9.62889e12 0.981368
\(772\) 2.09347e12 0.212123
\(773\) −1.16131e13 −1.16988 −0.584941 0.811076i \(-0.698882\pi\)
−0.584941 + 0.811076i \(0.698882\pi\)
\(774\) 1.51073e12 0.151304
\(775\) −3.14478e12 −0.313135
\(776\) −1.28559e13 −1.27269
\(777\) 9.11623e12 0.897265
\(778\) 3.39961e12 0.332675
\(779\) −2.71190e12 −0.263848
\(780\) −2.06061e12 −0.199329
\(781\) 1.72978e11 0.0166365
\(782\) 2.81859e12 0.269527
\(783\) 4.67748e11 0.0444717
\(784\) 1.26023e12 0.119132
\(785\) 4.08214e12 0.383685
\(786\) −4.50229e12 −0.420758
\(787\) −1.50665e13 −1.39999 −0.699997 0.714146i \(-0.746815\pi\)
−0.699997 + 0.714146i \(0.746815\pi\)
\(788\) −3.51280e11 −0.0324553
\(789\) −9.41207e12 −0.864646
\(790\) 6.28747e12 0.574320
\(791\) 2.86387e12 0.260111
\(792\) −3.34192e12 −0.301810
\(793\) 8.90579e11 0.0799730
\(794\) −3.04469e12 −0.271863
\(795\) −7.09839e12 −0.630242
\(796\) −4.07540e12 −0.359800
\(797\) −7.67142e12 −0.673463 −0.336731 0.941601i \(-0.609321\pi\)
−0.336731 + 0.941601i \(0.609321\pi\)
\(798\) 1.72739e12 0.150791
\(799\) 2.80745e12 0.243698
\(800\) 3.55538e12 0.306889
\(801\) 5.91468e12 0.507674
\(802\) 2.36375e12 0.201751
\(803\) 1.03490e13 0.878374
\(804\) 7.32371e12 0.618129
\(805\) −1.14385e13 −0.960037
\(806\) −5.00611e12 −0.417823
\(807\) −3.94848e12 −0.327717
\(808\) −6.52448e11 −0.0538512
\(809\) −6.00907e12 −0.493218 −0.246609 0.969115i \(-0.579316\pi\)
−0.246609 + 0.969115i \(0.579316\pi\)
\(810\) −4.31608e12 −0.352295
\(811\) −1.51786e13 −1.23208 −0.616038 0.787717i \(-0.711263\pi\)
−0.616038 + 0.787717i \(0.711263\pi\)
\(812\) 1.84416e11 0.0148867
\(813\) −6.21132e12 −0.498627
\(814\) −1.13076e13 −0.902737
\(815\) −1.89258e13 −1.50260
\(816\) 8.99100e11 0.0709908
\(817\) −2.54067e12 −0.199503
\(818\) 1.02861e13 0.803267
\(819\) 2.16573e12 0.168201
\(820\) 4.03214e12 0.311440
\(821\) 1.51618e13 1.16468 0.582339 0.812946i \(-0.302138\pi\)
0.582339 + 0.812946i \(0.302138\pi\)
\(822\) 1.38944e13 1.06149
\(823\) −8.88314e12 −0.674943 −0.337472 0.941336i \(-0.609572\pi\)
−0.337472 + 0.941336i \(0.609572\pi\)
\(824\) 5.80545e12 0.438696
\(825\) 3.82958e12 0.287811
\(826\) −6.89883e12 −0.515662
\(827\) 9.71703e9 0.000722368 0 0.000361184 1.00000i \(-0.499885\pi\)
0.000361184 1.00000i \(0.499885\pi\)
\(828\) −2.77199e12 −0.204953
\(829\) −6.15249e12 −0.452434 −0.226217 0.974077i \(-0.572636\pi\)
−0.226217 + 0.974077i \(0.572636\pi\)
\(830\) 1.06592e13 0.779606
\(831\) 1.56496e13 1.13841
\(832\) 8.94433e12 0.647132
\(833\) −1.14288e12 −0.0822426
\(834\) −4.19192e12 −0.300031
\(835\) −1.53412e13 −1.09212
\(836\) 1.73884e12 0.123121
\(837\) 1.28435e13 0.904522
\(838\) −4.85976e11 −0.0340421
\(839\) 2.01899e13 1.40671 0.703355 0.710839i \(-0.251684\pi\)
0.703355 + 0.710839i \(0.251684\pi\)
\(840\) −8.30143e12 −0.575302
\(841\) −1.44829e13 −0.998329
\(842\) −1.78641e13 −1.22483
\(843\) 7.84810e12 0.535230
\(844\) −1.19043e13 −0.807540
\(845\) 6.34722e12 0.428280
\(846\) 3.40218e12 0.228344
\(847\) 1.93350e12 0.129083
\(848\) 5.06884e12 0.336610
\(849\) −1.30773e13 −0.863837
\(850\) 1.03293e12 0.0678710
\(851\) −3.03156e13 −1.98145
\(852\) 1.04129e11 0.00677005
\(853\) −2.71140e13 −1.75357 −0.876784 0.480885i \(-0.840315\pi\)
−0.876784 + 0.480885i \(0.840315\pi\)
\(854\) 1.11002e12 0.0714117
\(855\) −1.13075e12 −0.0723633
\(856\) −1.79760e13 −1.14436
\(857\) 2.66987e13 1.69074 0.845371 0.534180i \(-0.179380\pi\)
0.845371 + 0.534180i \(0.179380\pi\)
\(858\) 6.09623e12 0.384033
\(859\) 2.62702e13 1.64624 0.823122 0.567864i \(-0.192230\pi\)
0.823122 + 0.567864i \(0.192230\pi\)
\(860\) 3.77756e12 0.235488
\(861\) 9.61714e12 0.596392
\(862\) 8.56529e11 0.0528396
\(863\) 2.34256e13 1.43761 0.718806 0.695211i \(-0.244689\pi\)
0.718806 + 0.695211i \(0.244689\pi\)
\(864\) −1.45205e13 −0.886479
\(865\) −1.66931e12 −0.101383
\(866\) 1.72198e13 1.04039
\(867\) −8.15374e11 −0.0490085
\(868\) 5.06374e12 0.302784
\(869\) 1.50958e13 0.897978
\(870\) −3.37569e11 −0.0199768
\(871\) 1.90281e13 1.12025
\(872\) 2.96487e13 1.73653
\(873\) 6.20995e12 0.361846
\(874\) −5.74434e12 −0.332996
\(875\) −1.53213e13 −0.883607
\(876\) 6.22985e12 0.357445
\(877\) −4.84217e12 −0.276402 −0.138201 0.990404i \(-0.544132\pi\)
−0.138201 + 0.990404i \(0.544132\pi\)
\(878\) −6.22486e12 −0.353512
\(879\) −1.76723e13 −0.998489
\(880\) 4.52586e12 0.254407
\(881\) 1.59269e13 0.890718 0.445359 0.895352i \(-0.353076\pi\)
0.445359 + 0.895352i \(0.353076\pi\)
\(882\) −1.38498e12 −0.0770612
\(883\) 4.71830e12 0.261194 0.130597 0.991436i \(-0.458311\pi\)
0.130597 + 0.991436i \(0.458311\pi\)
\(884\) −1.33442e12 −0.0734951
\(885\) −1.02483e13 −0.561575
\(886\) 1.96886e13 1.07340
\(887\) 1.26007e13 0.683502 0.341751 0.939790i \(-0.388980\pi\)
0.341751 + 0.939790i \(0.388980\pi\)
\(888\) −2.20013e13 −1.18738
\(889\) −1.68084e13 −0.902544
\(890\) −1.82240e13 −0.973618
\(891\) −1.03626e13 −0.550832
\(892\) 1.39808e13 0.739417
\(893\) −5.72163e12 −0.301084
\(894\) −1.76640e13 −0.924848
\(895\) 2.31527e13 1.20614
\(896\) −1.63100e12 −0.0845408
\(897\) 1.63439e13 0.842927
\(898\) −1.14286e12 −0.0586473
\(899\) 6.65550e11 0.0339830
\(900\) −1.01585e12 −0.0516103
\(901\) −4.59682e12 −0.232378
\(902\) −1.19289e13 −0.600029
\(903\) 9.00993e12 0.450948
\(904\) −6.91173e12 −0.344214
\(905\) 1.93251e13 0.957640
\(906\) 8.90278e12 0.438984
\(907\) −2.04459e13 −1.00317 −0.501584 0.865109i \(-0.667249\pi\)
−0.501584 + 0.865109i \(0.667249\pi\)
\(908\) −1.45846e13 −0.712046
\(909\) 3.15161e11 0.0153107
\(910\) −6.67294e12 −0.322575
\(911\) 6.21126e12 0.298777 0.149388 0.988779i \(-0.452270\pi\)
0.149388 + 0.988779i \(0.452270\pi\)
\(912\) −1.83238e12 −0.0877079
\(913\) 2.55921e13 1.21895
\(914\) −2.89441e13 −1.37183
\(915\) 1.64895e12 0.0777699
\(916\) 1.42874e13 0.670540
\(917\) 1.18323e13 0.552594
\(918\) −4.21855e12 −0.196052
\(919\) −9.32576e12 −0.431285 −0.215642 0.976472i \(-0.569185\pi\)
−0.215642 + 0.976472i \(0.569185\pi\)
\(920\) 2.76060e13 1.27045
\(921\) −7.74206e12 −0.354559
\(922\) −2.39283e13 −1.09049
\(923\) 2.70542e11 0.0122695
\(924\) −6.16640e12 −0.278297
\(925\) −1.11097e13 −0.498959
\(926\) −2.72498e13 −1.21790
\(927\) −2.80428e12 −0.124728
\(928\) −7.52450e11 −0.0333052
\(929\) 2.57119e13 1.13256 0.566282 0.824211i \(-0.308381\pi\)
0.566282 + 0.824211i \(0.308381\pi\)
\(930\) −9.26904e12 −0.406314
\(931\) 2.32920e12 0.101609
\(932\) −1.99327e13 −0.865357
\(933\) 1.08366e13 0.468194
\(934\) 1.90928e13 0.820937
\(935\) −4.10440e12 −0.175629
\(936\) −5.22683e12 −0.222586
\(937\) 7.29891e12 0.309336 0.154668 0.987967i \(-0.450569\pi\)
0.154668 + 0.987967i \(0.450569\pi\)
\(938\) 2.37166e13 1.00032
\(939\) −3.02357e13 −1.26918
\(940\) 8.50713e12 0.355392
\(941\) −1.10493e13 −0.459389 −0.229695 0.973263i \(-0.573773\pi\)
−0.229695 + 0.973263i \(0.573773\pi\)
\(942\) −7.26995e12 −0.300817
\(943\) −3.19813e13 −1.31702
\(944\) 7.31815e12 0.299935
\(945\) 1.71199e13 0.698324
\(946\) −1.11758e13 −0.453698
\(947\) −9.10292e12 −0.367795 −0.183898 0.982945i \(-0.558871\pi\)
−0.183898 + 0.982945i \(0.558871\pi\)
\(948\) 9.08725e12 0.365422
\(949\) 1.61861e13 0.647804
\(950\) −2.10512e12 −0.0838534
\(951\) 5.22681e12 0.207217
\(952\) −5.37589e12 −0.212121
\(953\) 4.09267e13 1.60727 0.803635 0.595123i \(-0.202896\pi\)
0.803635 + 0.595123i \(0.202896\pi\)
\(954\) −5.57060e12 −0.217738
\(955\) −1.81382e13 −0.705633
\(956\) −1.61633e13 −0.625848
\(957\) −8.10479e11 −0.0312347
\(958\) −2.59707e12 −0.0996181
\(959\) −3.65152e13 −1.39409
\(960\) 1.65608e13 0.629305
\(961\) −8.16481e12 −0.308810
\(962\) −1.76853e13 −0.665772
\(963\) 8.68320e12 0.325358
\(964\) −1.43369e13 −0.534697
\(965\) 1.00708e13 0.373845
\(966\) 2.03710e13 0.752689
\(967\) 5.16443e13 1.89934 0.949671 0.313248i \(-0.101417\pi\)
0.949671 + 0.313248i \(0.101417\pi\)
\(968\) −4.66635e12 −0.170820
\(969\) 1.66175e12 0.0605491
\(970\) −1.91338e13 −0.693949
\(971\) −4.69234e13 −1.69396 −0.846979 0.531627i \(-0.821581\pi\)
−0.846979 + 0.531627i \(0.821581\pi\)
\(972\) 7.32582e12 0.263244
\(973\) 1.10166e13 0.394040
\(974\) 1.58040e13 0.562667
\(975\) 5.98953e12 0.212262
\(976\) −1.17749e12 −0.0415366
\(977\) −4.71530e13 −1.65571 −0.827854 0.560944i \(-0.810438\pi\)
−0.827854 + 0.560944i \(0.810438\pi\)
\(978\) 3.37052e13 1.17807
\(979\) −4.37545e13 −1.52230
\(980\) −3.46314e12 −0.119937
\(981\) −1.43216e13 −0.493721
\(982\) 9.05128e12 0.310605
\(983\) 4.10494e13 1.40222 0.701110 0.713053i \(-0.252688\pi\)
0.701110 + 0.713053i \(0.252688\pi\)
\(984\) −2.32102e13 −0.789226
\(985\) −1.68986e12 −0.0571990
\(986\) −2.18605e11 −0.00736570
\(987\) 2.02905e13 0.680559
\(988\) 2.71958e12 0.0908019
\(989\) −2.99621e13 −0.995837
\(990\) −4.97387e12 −0.164565
\(991\) 8.40949e12 0.276973 0.138487 0.990364i \(-0.455776\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(992\) −2.06609e13 −0.677403
\(993\) −5.58905e12 −0.182417
\(994\) 3.37203e11 0.0109560
\(995\) −1.96051e13 −0.634110
\(996\) 1.54058e13 0.496040
\(997\) 2.54531e13 0.815854 0.407927 0.913015i \(-0.366252\pi\)
0.407927 + 0.913015i \(0.366252\pi\)
\(998\) 1.03044e13 0.328803
\(999\) 4.53729e13 1.44129
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.1.3 7
3.2 odd 2 153.10.a.f.1.5 7
4.3 odd 2 272.10.a.g.1.5 7
17.16 even 2 289.10.a.b.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.b.1.3 7 1.1 even 1 trivial
153.10.a.f.1.5 7 3.2 odd 2
272.10.a.g.1.5 7 4.3 odd 2
289.10.a.b.1.3 7 17.16 even 2