Properties

Label 177.12.a.a.1.9
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $26$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-42.1259 q^{2} -243.000 q^{3} -273.404 q^{4} -6338.85 q^{5} +10236.6 q^{6} -22948.3 q^{7} +97791.4 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-42.1259 q^{2} -243.000 q^{3} -273.404 q^{4} -6338.85 q^{5} +10236.6 q^{6} -22948.3 q^{7} +97791.4 q^{8} +59049.0 q^{9} +267030. q^{10} -43451.8 q^{11} +66437.3 q^{12} -820123. q^{13} +966721. q^{14} +1.54034e6 q^{15} -3.55962e6 q^{16} -5.29095e6 q^{17} -2.48750e6 q^{18} -9.56089e6 q^{19} +1.73307e6 q^{20} +5.57645e6 q^{21} +1.83045e6 q^{22} -1.56497e7 q^{23} -2.37633e7 q^{24} -8.64713e6 q^{25} +3.45485e7 q^{26} -1.43489e7 q^{27} +6.27418e6 q^{28} -4.39579e7 q^{29} -6.48883e7 q^{30} +2.36187e8 q^{31} -5.03243e7 q^{32} +1.05588e7 q^{33} +2.22886e8 q^{34} +1.45466e8 q^{35} -1.61443e7 q^{36} +4.01725e8 q^{37} +4.02761e8 q^{38} +1.99290e8 q^{39} -6.19885e8 q^{40} -8.87829e8 q^{41} -2.34913e8 q^{42} +1.42442e9 q^{43} +1.18799e7 q^{44} -3.74303e8 q^{45} +6.59259e8 q^{46} +3.01297e9 q^{47} +8.64988e8 q^{48} -1.45070e9 q^{49} +3.64269e8 q^{50} +1.28570e9 q^{51} +2.24225e8 q^{52} -1.28336e8 q^{53} +6.04461e8 q^{54} +2.75434e8 q^{55} -2.24415e9 q^{56} +2.32330e9 q^{57} +1.85177e9 q^{58} +7.14924e8 q^{59} -4.21136e8 q^{60} -9.01975e8 q^{61} -9.94960e9 q^{62} -1.35508e9 q^{63} +9.41006e9 q^{64} +5.19864e9 q^{65} -4.44799e8 q^{66} -4.70084e9 q^{67} +1.44657e9 q^{68} +3.80288e9 q^{69} -6.12790e9 q^{70} +2.04793e10 q^{71} +5.77448e9 q^{72} -1.87288e10 q^{73} -1.69230e10 q^{74} +2.10125e9 q^{75} +2.61399e9 q^{76} +9.97146e8 q^{77} -8.39528e9 q^{78} +4.04588e10 q^{79} +2.25639e10 q^{80} +3.48678e9 q^{81} +3.74006e10 q^{82} +5.18160e10 q^{83} -1.52463e9 q^{84} +3.35385e10 q^{85} -6.00049e10 q^{86} +1.06818e10 q^{87} -4.24921e9 q^{88} -2.60402e10 q^{89} +1.57679e10 q^{90} +1.88205e10 q^{91} +4.27870e9 q^{92} -5.73935e10 q^{93} -1.26924e11 q^{94} +6.06050e10 q^{95} +1.22288e10 q^{96} -1.89722e10 q^{97} +6.11121e10 q^{98} -2.56578e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} + O(q^{10}) \) \( 26q - 78q^{2} - 6318q^{3} + 23070q^{4} + 3808q^{5} + 18954q^{6} - 98819q^{7} - 117645q^{8} + 1535274q^{9} - 859751q^{10} + 579094q^{11} - 5606010q^{12} - 2018538q^{13} + 4157413q^{14} - 925344q^{15} + 20190274q^{16} - 13084493q^{17} - 4605822q^{18} + 9917231q^{19} + 10165633q^{20} + 24013017q^{21} - 89820518q^{22} - 63513223q^{23} + 28587735q^{24} + 218986852q^{25} - 77999532q^{26} - 373071582q^{27} - 444601862q^{28} + 81530981q^{29} + 208919493q^{30} - 408861231q^{31} - 26253128q^{32} - 140719842q^{33} - 508910076q^{34} - 75731421q^{35} + 1362260430q^{36} - 802381301q^{37} + 732704675q^{38} + 490504734q^{39} - 646130800q^{40} - 1354472849q^{41} - 1010251359q^{42} + 282952194q^{43} + 1846047996q^{44} + 224858592q^{45} + 9629305849q^{46} - 1196794197q^{47} - 4906236582q^{48} + 10889725683q^{49} - 6236232091q^{50} + 3179531799q^{51} - 1968200812q^{52} - 8276044236q^{53} + 1119214746q^{54} - 6672895076q^{55} + 2579741342q^{56} - 2409887133q^{57} - 9401656060q^{58} + 18588031774q^{59} - 2470248819q^{60} - 21181559029q^{61} - 6117706514q^{62} - 5835163131q^{63} + 42975855037q^{64} + 25680681860q^{65} + 21826385874q^{66} + 26234163394q^{67} + 19707344091q^{68} + 15433713189q^{69} + 129203099090q^{70} + 52088830406q^{71} - 6946819605q^{72} + 20943384867q^{73} + 41969200146q^{74} - 53213805036q^{75} + 223987219368q^{76} + 94604773153q^{77} + 18953886276q^{78} + 68965662774q^{79} + 218947784293q^{80} + 90656394426q^{81} + 11938614923q^{82} + 17947446393q^{83} + 108038252466q^{84} - 52849386709q^{85} + 384986147852q^{86} - 19812028383q^{87} - 49061112607q^{88} + 38570593981q^{89} - 50767436799q^{90} - 226268806999q^{91} - 79559686310q^{92} + 99353279133q^{93} - 16709400108q^{94} - 252795831501q^{95} + 6379510104q^{96} - 186894587836q^{97} - 252443311612q^{98} + 34194921606q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −42.1259 −0.930861 −0.465430 0.885084i \(-0.654100\pi\)
−0.465430 + 0.885084i \(0.654100\pi\)
\(3\) −243.000 −0.577350
\(4\) −273.404 −0.133498
\(5\) −6338.85 −0.907142 −0.453571 0.891220i \(-0.649850\pi\)
−0.453571 + 0.891220i \(0.649850\pi\)
\(6\) 10236.6 0.537433
\(7\) −22948.3 −0.516074 −0.258037 0.966135i \(-0.583076\pi\)
−0.258037 + 0.966135i \(0.583076\pi\)
\(8\) 97791.4 1.05513
\(9\) 59049.0 0.333333
\(10\) 267030. 0.844423
\(11\) −43451.8 −0.0813481 −0.0406741 0.999172i \(-0.512951\pi\)
−0.0406741 + 0.999172i \(0.512951\pi\)
\(12\) 66437.3 0.0770752
\(13\) −820123. −0.612619 −0.306310 0.951932i \(-0.599094\pi\)
−0.306310 + 0.951932i \(0.599094\pi\)
\(14\) 966721. 0.480393
\(15\) 1.54034e6 0.523739
\(16\) −3.55962e6 −0.848680
\(17\) −5.29095e6 −0.903784 −0.451892 0.892073i \(-0.649251\pi\)
−0.451892 + 0.892073i \(0.649251\pi\)
\(18\) −2.48750e6 −0.310287
\(19\) −9.56089e6 −0.885836 −0.442918 0.896562i \(-0.646057\pi\)
−0.442918 + 0.896562i \(0.646057\pi\)
\(20\) 1.73307e6 0.121102
\(21\) 5.57645e6 0.297956
\(22\) 1.83045e6 0.0757238
\(23\) −1.56497e7 −0.506994 −0.253497 0.967336i \(-0.581581\pi\)
−0.253497 + 0.967336i \(0.581581\pi\)
\(24\) −2.37633e7 −0.609179
\(25\) −8.64713e6 −0.177093
\(26\) 3.45485e7 0.570263
\(27\) −1.43489e7 −0.192450
\(28\) 6.27418e6 0.0688950
\(29\) −4.39579e7 −0.397968 −0.198984 0.980003i \(-0.563764\pi\)
−0.198984 + 0.980003i \(0.563764\pi\)
\(30\) −6.48883e7 −0.487528
\(31\) 2.36187e8 1.48172 0.740861 0.671658i \(-0.234418\pi\)
0.740861 + 0.671658i \(0.234418\pi\)
\(32\) −5.03243e7 −0.265126
\(33\) 1.05588e7 0.0469664
\(34\) 2.22886e8 0.841297
\(35\) 1.45466e8 0.468153
\(36\) −1.61443e7 −0.0444994
\(37\) 4.01725e8 0.952399 0.476199 0.879337i \(-0.342014\pi\)
0.476199 + 0.879337i \(0.342014\pi\)
\(38\) 4.02761e8 0.824590
\(39\) 1.99290e8 0.353696
\(40\) −6.19885e8 −0.957152
\(41\) −8.87829e8 −1.19679 −0.598395 0.801201i \(-0.704195\pi\)
−0.598395 + 0.801201i \(0.704195\pi\)
\(42\) −2.34913e8 −0.277355
\(43\) 1.42442e9 1.47761 0.738806 0.673918i \(-0.235390\pi\)
0.738806 + 0.673918i \(0.235390\pi\)
\(44\) 1.18799e7 0.0108598
\(45\) −3.74303e8 −0.302381
\(46\) 6.59259e8 0.471941
\(47\) 3.01297e9 1.91627 0.958133 0.286322i \(-0.0924329\pi\)
0.958133 + 0.286322i \(0.0924329\pi\)
\(48\) 8.64988e8 0.489986
\(49\) −1.45070e9 −0.733667
\(50\) 3.64269e8 0.164849
\(51\) 1.28570e9 0.521800
\(52\) 2.24225e8 0.0817836
\(53\) −1.28336e8 −0.0421534 −0.0210767 0.999778i \(-0.506709\pi\)
−0.0210767 + 0.999778i \(0.506709\pi\)
\(54\) 6.04461e8 0.179144
\(55\) 2.75434e8 0.0737943
\(56\) −2.24415e9 −0.544525
\(57\) 2.32330e9 0.511438
\(58\) 1.85177e9 0.370453
\(59\) 7.14924e8 0.130189
\(60\) −4.21136e8 −0.0699182
\(61\) −9.01975e8 −0.136735 −0.0683676 0.997660i \(-0.521779\pi\)
−0.0683676 + 0.997660i \(0.521779\pi\)
\(62\) −9.94960e9 −1.37928
\(63\) −1.35508e9 −0.172025
\(64\) 9.41006e9 1.09548
\(65\) 5.19864e9 0.555733
\(66\) −4.44799e8 −0.0437191
\(67\) −4.70084e9 −0.425367 −0.212684 0.977121i \(-0.568220\pi\)
−0.212684 + 0.977121i \(0.568220\pi\)
\(68\) 1.44657e9 0.120654
\(69\) 3.80288e9 0.292713
\(70\) −6.12790e9 −0.435785
\(71\) 2.04793e10 1.34708 0.673541 0.739150i \(-0.264773\pi\)
0.673541 + 0.739150i \(0.264773\pi\)
\(72\) 5.77448e9 0.351710
\(73\) −1.87288e10 −1.05739 −0.528695 0.848812i \(-0.677318\pi\)
−0.528695 + 0.848812i \(0.677318\pi\)
\(74\) −1.69230e10 −0.886551
\(75\) 2.10125e9 0.102245
\(76\) 2.61399e9 0.118258
\(77\) 9.97146e8 0.0419817
\(78\) −8.39528e9 −0.329242
\(79\) 4.04588e10 1.47933 0.739664 0.672977i \(-0.234985\pi\)
0.739664 + 0.672977i \(0.234985\pi\)
\(80\) 2.25639e10 0.769873
\(81\) 3.48678e9 0.111111
\(82\) 3.74006e10 1.11405
\(83\) 5.18160e10 1.44389 0.721945 0.691950i \(-0.243248\pi\)
0.721945 + 0.691950i \(0.243248\pi\)
\(84\) −1.52463e9 −0.0397765
\(85\) 3.35385e10 0.819860
\(86\) −6.00049e10 −1.37545
\(87\) 1.06818e10 0.229767
\(88\) −4.24921e9 −0.0858328
\(89\) −2.60402e10 −0.494309 −0.247155 0.968976i \(-0.579496\pi\)
−0.247155 + 0.968976i \(0.579496\pi\)
\(90\) 1.57679e10 0.281474
\(91\) 1.88205e10 0.316157
\(92\) 4.27870e9 0.0676828
\(93\) −5.73935e10 −0.855473
\(94\) −1.26924e11 −1.78378
\(95\) 6.06050e10 0.803579
\(96\) 1.22288e10 0.153071
\(97\) −1.89722e10 −0.224323 −0.112161 0.993690i \(-0.535777\pi\)
−0.112161 + 0.993690i \(0.535777\pi\)
\(98\) 6.11121e10 0.682942
\(99\) −2.56578e9 −0.0271160
\(100\) 2.36416e9 0.0236416
\(101\) 5.38175e10 0.509514 0.254757 0.967005i \(-0.418004\pi\)
0.254757 + 0.967005i \(0.418004\pi\)
\(102\) −5.41614e10 −0.485723
\(103\) 8.25502e10 0.701638 0.350819 0.936443i \(-0.385903\pi\)
0.350819 + 0.936443i \(0.385903\pi\)
\(104\) −8.02010e10 −0.646393
\(105\) −3.53483e10 −0.270288
\(106\) 5.40630e9 0.0392390
\(107\) −5.51260e10 −0.379967 −0.189983 0.981787i \(-0.560843\pi\)
−0.189983 + 0.981787i \(0.560843\pi\)
\(108\) 3.92305e9 0.0256917
\(109\) 3.01295e11 1.87563 0.937813 0.347140i \(-0.112847\pi\)
0.937813 + 0.347140i \(0.112847\pi\)
\(110\) −1.16029e10 −0.0686922
\(111\) −9.76191e10 −0.549868
\(112\) 8.16874e10 0.437982
\(113\) 1.06462e11 0.543578 0.271789 0.962357i \(-0.412385\pi\)
0.271789 + 0.962357i \(0.412385\pi\)
\(114\) −9.78710e10 −0.476077
\(115\) 9.92011e10 0.459916
\(116\) 1.20183e10 0.0531280
\(117\) −4.84275e10 −0.204206
\(118\) −3.01169e10 −0.121188
\(119\) 1.21419e11 0.466420
\(120\) 1.50632e11 0.552612
\(121\) −2.83424e11 −0.993382
\(122\) 3.79965e10 0.127281
\(123\) 2.15742e11 0.690967
\(124\) −6.45746e10 −0.197807
\(125\) 3.64327e11 1.06779
\(126\) 5.70839e10 0.160131
\(127\) −8.13135e10 −0.218395 −0.109197 0.994020i \(-0.534828\pi\)
−0.109197 + 0.994020i \(0.534828\pi\)
\(128\) −2.93344e11 −0.754609
\(129\) −3.46133e11 −0.853100
\(130\) −2.18998e11 −0.517310
\(131\) −6.71116e11 −1.51987 −0.759934 0.650001i \(-0.774769\pi\)
−0.759934 + 0.650001i \(0.774769\pi\)
\(132\) −2.88682e9 −0.00626993
\(133\) 2.19407e11 0.457157
\(134\) 1.98027e11 0.395958
\(135\) 9.09555e10 0.174580
\(136\) −5.17409e11 −0.953609
\(137\) 9.04544e11 1.60128 0.800639 0.599147i \(-0.204493\pi\)
0.800639 + 0.599147i \(0.204493\pi\)
\(138\) −1.60200e11 −0.272475
\(139\) −1.05942e12 −1.73176 −0.865881 0.500250i \(-0.833241\pi\)
−0.865881 + 0.500250i \(0.833241\pi\)
\(140\) −3.97711e10 −0.0624975
\(141\) −7.32151e11 −1.10636
\(142\) −8.62709e11 −1.25395
\(143\) 3.56358e10 0.0498354
\(144\) −2.10192e11 −0.282893
\(145\) 2.78643e11 0.361014
\(146\) 7.88970e11 0.984282
\(147\) 3.52520e11 0.423583
\(148\) −1.09833e11 −0.127144
\(149\) 1.19574e12 1.33386 0.666932 0.745118i \(-0.267607\pi\)
0.666932 + 0.745118i \(0.267607\pi\)
\(150\) −8.85173e10 −0.0951757
\(151\) 1.93531e11 0.200621 0.100310 0.994956i \(-0.468016\pi\)
0.100310 + 0.994956i \(0.468016\pi\)
\(152\) −9.34972e11 −0.934672
\(153\) −3.12425e11 −0.301261
\(154\) −4.20057e10 −0.0390791
\(155\) −1.49715e12 −1.34413
\(156\) −5.44867e10 −0.0472178
\(157\) −5.92815e11 −0.495988 −0.247994 0.968762i \(-0.579771\pi\)
−0.247994 + 0.968762i \(0.579771\pi\)
\(158\) −1.70437e12 −1.37705
\(159\) 3.11858e10 0.0243373
\(160\) 3.18998e11 0.240507
\(161\) 3.59135e11 0.261647
\(162\) −1.46884e11 −0.103429
\(163\) −1.24681e12 −0.848731 −0.424366 0.905491i \(-0.639503\pi\)
−0.424366 + 0.905491i \(0.639503\pi\)
\(164\) 2.42736e11 0.159769
\(165\) −6.69305e10 −0.0426052
\(166\) −2.18280e12 −1.34406
\(167\) 1.26546e12 0.753891 0.376946 0.926235i \(-0.376974\pi\)
0.376946 + 0.926235i \(0.376974\pi\)
\(168\) 5.45328e11 0.314382
\(169\) −1.11956e12 −0.624697
\(170\) −1.41284e12 −0.763176
\(171\) −5.64561e11 −0.295279
\(172\) −3.89442e11 −0.197259
\(173\) −3.14569e12 −1.54334 −0.771672 0.636020i \(-0.780579\pi\)
−0.771672 + 0.636020i \(0.780579\pi\)
\(174\) −4.49980e11 −0.213881
\(175\) 1.98437e11 0.0913932
\(176\) 1.54672e11 0.0690385
\(177\) −1.73727e11 −0.0751646
\(178\) 1.09697e12 0.460133
\(179\) 4.17961e12 1.69998 0.849991 0.526797i \(-0.176607\pi\)
0.849991 + 0.526797i \(0.176607\pi\)
\(180\) 1.02336e11 0.0403673
\(181\) −1.62172e12 −0.620504 −0.310252 0.950654i \(-0.600413\pi\)
−0.310252 + 0.950654i \(0.600413\pi\)
\(182\) −7.92830e11 −0.294298
\(183\) 2.19180e11 0.0789441
\(184\) −1.53041e12 −0.534944
\(185\) −2.54647e12 −0.863961
\(186\) 2.41775e12 0.796326
\(187\) 2.29901e11 0.0735211
\(188\) −8.23758e11 −0.255818
\(189\) 3.29284e11 0.0993185
\(190\) −2.55304e12 −0.748020
\(191\) −1.51844e12 −0.432229 −0.216115 0.976368i \(-0.569338\pi\)
−0.216115 + 0.976368i \(0.569338\pi\)
\(192\) −2.28665e12 −0.632473
\(193\) −2.43837e12 −0.655441 −0.327720 0.944775i \(-0.606280\pi\)
−0.327720 + 0.944775i \(0.606280\pi\)
\(194\) 7.99223e11 0.208813
\(195\) −1.26327e12 −0.320853
\(196\) 3.96628e11 0.0979433
\(197\) −3.16608e12 −0.760252 −0.380126 0.924935i \(-0.624119\pi\)
−0.380126 + 0.924935i \(0.624119\pi\)
\(198\) 1.08086e11 0.0252413
\(199\) −7.69861e11 −0.174872 −0.0874360 0.996170i \(-0.527867\pi\)
−0.0874360 + 0.996170i \(0.527867\pi\)
\(200\) −8.45615e11 −0.186856
\(201\) 1.14230e12 0.245586
\(202\) −2.26711e12 −0.474287
\(203\) 1.00876e12 0.205381
\(204\) −3.51516e11 −0.0696594
\(205\) 5.62781e12 1.08566
\(206\) −3.47750e12 −0.653127
\(207\) −9.24099e11 −0.168998
\(208\) 2.91933e12 0.519918
\(209\) 4.15437e11 0.0720611
\(210\) 1.48908e12 0.251601
\(211\) 1.12202e13 1.84692 0.923459 0.383696i \(-0.125349\pi\)
0.923459 + 0.383696i \(0.125349\pi\)
\(212\) 3.50878e10 0.00562741
\(213\) −4.97647e12 −0.777738
\(214\) 2.32224e12 0.353696
\(215\) −9.02916e12 −1.34040
\(216\) −1.40320e12 −0.203060
\(217\) −5.42010e12 −0.764679
\(218\) −1.26923e13 −1.74595
\(219\) 4.55111e12 0.610484
\(220\) −7.53049e10 −0.00985141
\(221\) 4.33923e12 0.553676
\(222\) 4.11230e12 0.511850
\(223\) −6.37305e12 −0.773874 −0.386937 0.922106i \(-0.626467\pi\)
−0.386937 + 0.922106i \(0.626467\pi\)
\(224\) 1.15486e12 0.136825
\(225\) −5.10604e11 −0.0590311
\(226\) −4.48480e12 −0.505995
\(227\) −1.20818e13 −1.33043 −0.665213 0.746654i \(-0.731659\pi\)
−0.665213 + 0.746654i \(0.731659\pi\)
\(228\) −6.35199e11 −0.0682760
\(229\) 1.24786e13 1.30939 0.654696 0.755893i \(-0.272797\pi\)
0.654696 + 0.755893i \(0.272797\pi\)
\(230\) −4.17894e12 −0.428118
\(231\) −2.42306e11 −0.0242381
\(232\) −4.29871e12 −0.419908
\(233\) −1.29692e13 −1.23724 −0.618622 0.785688i \(-0.712309\pi\)
−0.618622 + 0.785688i \(0.712309\pi\)
\(234\) 2.04005e12 0.190088
\(235\) −1.90987e13 −1.73833
\(236\) −1.95463e11 −0.0173800
\(237\) −9.83150e12 −0.854090
\(238\) −5.11487e12 −0.434172
\(239\) 7.24829e12 0.601239 0.300619 0.953744i \(-0.402807\pi\)
0.300619 + 0.953744i \(0.402807\pi\)
\(240\) −5.48303e12 −0.444487
\(241\) −2.18446e13 −1.73082 −0.865408 0.501069i \(-0.832940\pi\)
−0.865408 + 0.501069i \(0.832940\pi\)
\(242\) 1.19395e13 0.924701
\(243\) −8.47289e11 −0.0641500
\(244\) 2.46604e11 0.0182539
\(245\) 9.19577e12 0.665541
\(246\) −9.08836e12 −0.643194
\(247\) 7.84111e12 0.542680
\(248\) 2.30971e13 1.56341
\(249\) −1.25913e13 −0.833630
\(250\) −1.53476e13 −0.993965
\(251\) −8.06503e12 −0.510976 −0.255488 0.966812i \(-0.582236\pi\)
−0.255488 + 0.966812i \(0.582236\pi\)
\(252\) 3.70484e11 0.0229650
\(253\) 6.80007e11 0.0412430
\(254\) 3.42541e12 0.203295
\(255\) −8.14986e12 −0.473347
\(256\) −6.91442e12 −0.393040
\(257\) 2.01417e13 1.12064 0.560318 0.828278i \(-0.310679\pi\)
0.560318 + 0.828278i \(0.310679\pi\)
\(258\) 1.45812e13 0.794117
\(259\) −9.21891e12 −0.491508
\(260\) −1.42133e12 −0.0741893
\(261\) −2.59567e12 −0.132656
\(262\) 2.82714e13 1.41478
\(263\) 1.65928e13 0.813135 0.406568 0.913621i \(-0.366726\pi\)
0.406568 + 0.913621i \(0.366726\pi\)
\(264\) 1.03256e12 0.0495556
\(265\) 8.13505e11 0.0382391
\(266\) −9.24271e12 −0.425550
\(267\) 6.32776e12 0.285390
\(268\) 1.28523e12 0.0567858
\(269\) −6.97094e12 −0.301754 −0.150877 0.988553i \(-0.548210\pi\)
−0.150877 + 0.988553i \(0.548210\pi\)
\(270\) −3.83159e12 −0.162509
\(271\) 1.91165e13 0.794471 0.397236 0.917717i \(-0.369970\pi\)
0.397236 + 0.917717i \(0.369970\pi\)
\(272\) 1.88338e13 0.767023
\(273\) −4.57337e12 −0.182533
\(274\) −3.81048e13 −1.49057
\(275\) 3.75733e11 0.0144062
\(276\) −1.03972e12 −0.0390767
\(277\) −1.82569e13 −0.672647 −0.336324 0.941746i \(-0.609184\pi\)
−0.336324 + 0.941746i \(0.609184\pi\)
\(278\) 4.46292e13 1.61203
\(279\) 1.39466e13 0.493907
\(280\) 1.42253e13 0.493961
\(281\) 5.49608e13 1.87141 0.935704 0.352786i \(-0.114766\pi\)
0.935704 + 0.352786i \(0.114766\pi\)
\(282\) 3.08425e13 1.02986
\(283\) −3.20931e12 −0.105096 −0.0525479 0.998618i \(-0.516734\pi\)
−0.0525479 + 0.998618i \(0.516734\pi\)
\(284\) −5.59913e12 −0.179833
\(285\) −1.47270e13 −0.463947
\(286\) −1.50119e12 −0.0463899
\(287\) 2.03742e13 0.617633
\(288\) −2.97160e12 −0.0883754
\(289\) −6.27774e12 −0.183175
\(290\) −1.17381e13 −0.336053
\(291\) 4.61025e12 0.129513
\(292\) 5.12054e12 0.141160
\(293\) 4.15063e13 1.12290 0.561451 0.827510i \(-0.310243\pi\)
0.561451 + 0.827510i \(0.310243\pi\)
\(294\) −1.48502e13 −0.394297
\(295\) −4.53180e12 −0.118100
\(296\) 3.92852e13 1.00490
\(297\) 6.23485e11 0.0156555
\(298\) −5.03716e13 −1.24164
\(299\) 1.28347e13 0.310595
\(300\) −5.74492e11 −0.0136495
\(301\) −3.26880e13 −0.762557
\(302\) −8.15266e12 −0.186750
\(303\) −1.30777e13 −0.294168
\(304\) 3.40331e13 0.751791
\(305\) 5.71748e12 0.124038
\(306\) 1.31612e13 0.280432
\(307\) 4.41029e13 0.923009 0.461505 0.887138i \(-0.347310\pi\)
0.461505 + 0.887138i \(0.347310\pi\)
\(308\) −2.72624e11 −0.00560448
\(309\) −2.00597e13 −0.405091
\(310\) 6.30690e13 1.25120
\(311\) 6.84662e13 1.33442 0.667212 0.744868i \(-0.267488\pi\)
0.667212 + 0.744868i \(0.267488\pi\)
\(312\) 1.94888e13 0.373195
\(313\) 6.28941e13 1.18336 0.591679 0.806173i \(-0.298465\pi\)
0.591679 + 0.806173i \(0.298465\pi\)
\(314\) 2.49729e13 0.461696
\(315\) 8.58963e12 0.156051
\(316\) −1.10616e13 −0.197488
\(317\) −5.13678e13 −0.901290 −0.450645 0.892703i \(-0.648806\pi\)
−0.450645 + 0.892703i \(0.648806\pi\)
\(318\) −1.31373e12 −0.0226546
\(319\) 1.91005e12 0.0323740
\(320\) −5.96490e13 −0.993752
\(321\) 1.33956e13 0.219374
\(322\) −1.51289e13 −0.243557
\(323\) 5.05862e13 0.800605
\(324\) −9.53302e11 −0.0148331
\(325\) 7.09171e12 0.108491
\(326\) 5.25233e13 0.790050
\(327\) −7.32147e13 −1.08289
\(328\) −8.68220e13 −1.26277
\(329\) −6.91426e13 −0.988936
\(330\) 2.81951e12 0.0396595
\(331\) −1.07656e14 −1.48930 −0.744652 0.667453i \(-0.767384\pi\)
−0.744652 + 0.667453i \(0.767384\pi\)
\(332\) −1.41667e13 −0.192757
\(333\) 2.37214e13 0.317466
\(334\) −5.33088e13 −0.701768
\(335\) 2.97979e13 0.385868
\(336\) −1.98500e13 −0.252869
\(337\) −8.93066e13 −1.11923 −0.559615 0.828753i \(-0.689051\pi\)
−0.559615 + 0.828753i \(0.689051\pi\)
\(338\) 4.71624e13 0.581506
\(339\) −2.58702e13 −0.313835
\(340\) −9.16958e12 −0.109450
\(341\) −1.02627e13 −0.120535
\(342\) 2.37827e13 0.274863
\(343\) 7.86675e13 0.894701
\(344\) 1.39296e14 1.55907
\(345\) −2.41059e13 −0.265533
\(346\) 1.32515e14 1.43664
\(347\) −1.03776e14 −1.10735 −0.553677 0.832732i \(-0.686776\pi\)
−0.553677 + 0.832732i \(0.686776\pi\)
\(348\) −2.92044e12 −0.0306735
\(349\) 7.86088e12 0.0812701 0.0406351 0.999174i \(-0.487062\pi\)
0.0406351 + 0.999174i \(0.487062\pi\)
\(350\) −8.35936e12 −0.0850744
\(351\) 1.17679e13 0.117899
\(352\) 2.18668e12 0.0215675
\(353\) 3.58529e13 0.348148 0.174074 0.984733i \(-0.444307\pi\)
0.174074 + 0.984733i \(0.444307\pi\)
\(354\) 7.31840e12 0.0699678
\(355\) −1.29815e14 −1.22199
\(356\) 7.11950e12 0.0659894
\(357\) −2.95047e13 −0.269287
\(358\) −1.76070e14 −1.58245
\(359\) −5.98494e13 −0.529713 −0.264856 0.964288i \(-0.585325\pi\)
−0.264856 + 0.964288i \(0.585325\pi\)
\(360\) −3.66036e13 −0.319051
\(361\) −2.50797e13 −0.215294
\(362\) 6.83166e13 0.577602
\(363\) 6.88719e13 0.573530
\(364\) −5.14560e12 −0.0422064
\(365\) 1.18719e14 0.959202
\(366\) −9.23316e12 −0.0734860
\(367\) −1.42760e14 −1.11929 −0.559646 0.828732i \(-0.689063\pi\)
−0.559646 + 0.828732i \(0.689063\pi\)
\(368\) 5.57070e13 0.430276
\(369\) −5.24254e13 −0.398930
\(370\) 1.07273e14 0.804228
\(371\) 2.94511e12 0.0217543
\(372\) 1.56916e13 0.114204
\(373\) 1.71705e14 1.23136 0.615680 0.787996i \(-0.288881\pi\)
0.615680 + 0.787996i \(0.288881\pi\)
\(374\) −9.68480e12 −0.0684379
\(375\) −8.85314e13 −0.616489
\(376\) 2.94642e14 2.02191
\(377\) 3.60509e13 0.243803
\(378\) −1.38714e13 −0.0924517
\(379\) −5.75920e13 −0.378309 −0.189155 0.981947i \(-0.560575\pi\)
−0.189155 + 0.981947i \(0.560575\pi\)
\(380\) −1.65697e13 −0.107276
\(381\) 1.97592e13 0.126090
\(382\) 6.39657e13 0.402345
\(383\) 1.08461e14 0.672481 0.336241 0.941776i \(-0.390844\pi\)
0.336241 + 0.941776i \(0.390844\pi\)
\(384\) 7.12825e13 0.435674
\(385\) −6.32076e12 −0.0380833
\(386\) 1.02718e14 0.610124
\(387\) 8.41104e13 0.492537
\(388\) 5.18709e12 0.0299467
\(389\) 2.10424e14 1.19777 0.598883 0.800837i \(-0.295612\pi\)
0.598883 + 0.800837i \(0.295612\pi\)
\(390\) 5.32164e13 0.298669
\(391\) 8.28018e13 0.458213
\(392\) −1.41866e14 −0.774114
\(393\) 1.63081e14 0.877496
\(394\) 1.33374e14 0.707688
\(395\) −2.56462e14 −1.34196
\(396\) 7.01496e11 0.00361994
\(397\) 2.01577e14 1.02587 0.512936 0.858427i \(-0.328558\pi\)
0.512936 + 0.858427i \(0.328558\pi\)
\(398\) 3.24311e13 0.162781
\(399\) −5.33158e13 −0.263940
\(400\) 3.07805e13 0.150295
\(401\) 1.92815e14 0.928639 0.464319 0.885668i \(-0.346299\pi\)
0.464319 + 0.885668i \(0.346299\pi\)
\(402\) −4.81206e13 −0.228606
\(403\) −1.93703e14 −0.907732
\(404\) −1.47139e13 −0.0680192
\(405\) −2.21022e13 −0.100794
\(406\) −4.24950e13 −0.191181
\(407\) −1.74556e13 −0.0774759
\(408\) 1.25730e14 0.550566
\(409\) −2.88002e14 −1.24428 −0.622140 0.782906i \(-0.713736\pi\)
−0.622140 + 0.782906i \(0.713736\pi\)
\(410\) −2.37077e14 −1.01060
\(411\) −2.19804e14 −0.924498
\(412\) −2.25696e13 −0.0936674
\(413\) −1.64063e13 −0.0671871
\(414\) 3.89286e13 0.157314
\(415\) −3.28454e14 −1.30981
\(416\) 4.12721e13 0.162421
\(417\) 2.57440e14 0.999833
\(418\) −1.75007e13 −0.0670789
\(419\) 4.16674e12 0.0157623 0.00788114 0.999969i \(-0.497491\pi\)
0.00788114 + 0.999969i \(0.497491\pi\)
\(420\) 9.66437e12 0.0360830
\(421\) −1.19932e14 −0.441960 −0.220980 0.975278i \(-0.570926\pi\)
−0.220980 + 0.975278i \(0.570926\pi\)
\(422\) −4.72662e14 −1.71922
\(423\) 1.77913e14 0.638756
\(424\) −1.25502e13 −0.0444773
\(425\) 4.57515e13 0.160054
\(426\) 2.09638e14 0.723966
\(427\) 2.06988e13 0.0705655
\(428\) 1.50717e13 0.0507249
\(429\) −8.65950e12 −0.0287725
\(430\) 3.80362e14 1.24773
\(431\) 3.51165e14 1.13733 0.568665 0.822569i \(-0.307460\pi\)
0.568665 + 0.822569i \(0.307460\pi\)
\(432\) 5.10767e13 0.163329
\(433\) −2.56097e14 −0.808577 −0.404289 0.914631i \(-0.632481\pi\)
−0.404289 + 0.914631i \(0.632481\pi\)
\(434\) 2.28327e14 0.711809
\(435\) −6.77102e13 −0.208431
\(436\) −8.23754e13 −0.250393
\(437\) 1.49625e14 0.449114
\(438\) −1.91720e14 −0.568276
\(439\) −4.65884e14 −1.36371 −0.681856 0.731486i \(-0.738827\pi\)
−0.681856 + 0.731486i \(0.738827\pi\)
\(440\) 2.69351e13 0.0778625
\(441\) −8.56624e13 −0.244556
\(442\) −1.82794e14 −0.515395
\(443\) 2.81744e14 0.784574 0.392287 0.919843i \(-0.371684\pi\)
0.392287 + 0.919843i \(0.371684\pi\)
\(444\) 2.66895e13 0.0734064
\(445\) 1.65065e14 0.448409
\(446\) 2.68471e14 0.720369
\(447\) −2.90564e14 −0.770107
\(448\) −2.15945e14 −0.565347
\(449\) −5.79944e13 −0.149979 −0.0749897 0.997184i \(-0.523892\pi\)
−0.0749897 + 0.997184i \(0.523892\pi\)
\(450\) 2.15097e13 0.0549497
\(451\) 3.85777e13 0.0973567
\(452\) −2.91071e13 −0.0725667
\(453\) −4.70279e13 −0.115829
\(454\) 5.08959e14 1.23844
\(455\) −1.19300e14 −0.286799
\(456\) 2.27198e14 0.539633
\(457\) −5.19449e14 −1.21900 −0.609500 0.792786i \(-0.708630\pi\)
−0.609500 + 0.792786i \(0.708630\pi\)
\(458\) −5.25671e14 −1.21886
\(459\) 7.59194e13 0.173933
\(460\) −2.71220e13 −0.0613979
\(461\) −8.64623e14 −1.93407 −0.967033 0.254650i \(-0.918040\pi\)
−0.967033 + 0.254650i \(0.918040\pi\)
\(462\) 1.02074e13 0.0225623
\(463\) 3.06029e14 0.668448 0.334224 0.942494i \(-0.391526\pi\)
0.334224 + 0.942494i \(0.391526\pi\)
\(464\) 1.56474e14 0.337748
\(465\) 3.63808e14 0.776035
\(466\) 5.46340e14 1.15170
\(467\) 3.41995e14 0.712487 0.356243 0.934393i \(-0.384057\pi\)
0.356243 + 0.934393i \(0.384057\pi\)
\(468\) 1.32403e13 0.0272612
\(469\) 1.07876e14 0.219521
\(470\) 8.04552e14 1.61814
\(471\) 1.44054e14 0.286359
\(472\) 6.99134e13 0.137366
\(473\) −6.18934e13 −0.120201
\(474\) 4.14161e14 0.795039
\(475\) 8.26743e13 0.156876
\(476\) −3.31964e13 −0.0622662
\(477\) −7.57814e12 −0.0140511
\(478\) −3.05341e14 −0.559670
\(479\) 3.83828e14 0.695490 0.347745 0.937589i \(-0.386948\pi\)
0.347745 + 0.937589i \(0.386948\pi\)
\(480\) −7.75165e13 −0.138857
\(481\) −3.29464e14 −0.583458
\(482\) 9.20225e14 1.61115
\(483\) −8.72698e13 −0.151062
\(484\) 7.74892e13 0.132615
\(485\) 1.20262e14 0.203493
\(486\) 3.56928e13 0.0597147
\(487\) 3.12675e14 0.517230 0.258615 0.965981i \(-0.416734\pi\)
0.258615 + 0.965981i \(0.416734\pi\)
\(488\) −8.82054e13 −0.144273
\(489\) 3.02976e14 0.490015
\(490\) −3.87380e14 −0.619526
\(491\) −5.31503e14 −0.840538 −0.420269 0.907399i \(-0.638064\pi\)
−0.420269 + 0.907399i \(0.638064\pi\)
\(492\) −5.89849e13 −0.0922429
\(493\) 2.32579e14 0.359677
\(494\) −3.30314e14 −0.505160
\(495\) 1.62641e13 0.0245981
\(496\) −8.40737e14 −1.25751
\(497\) −4.69966e14 −0.695194
\(498\) 5.30420e14 0.775994
\(499\) −2.07233e14 −0.299852 −0.149926 0.988697i \(-0.547904\pi\)
−0.149926 + 0.988697i \(0.547904\pi\)
\(500\) −9.96086e13 −0.142548
\(501\) −3.07507e14 −0.435259
\(502\) 3.39747e14 0.475647
\(503\) −1.27957e15 −1.77190 −0.885952 0.463776i \(-0.846494\pi\)
−0.885952 + 0.463776i \(0.846494\pi\)
\(504\) −1.32515e14 −0.181508
\(505\) −3.41141e14 −0.462202
\(506\) −2.86460e13 −0.0383915
\(507\) 2.72053e14 0.360669
\(508\) 2.22315e13 0.0291553
\(509\) 4.87736e14 0.632757 0.316379 0.948633i \(-0.397533\pi\)
0.316379 + 0.948633i \(0.397533\pi\)
\(510\) 3.43321e14 0.440620
\(511\) 4.29796e14 0.545691
\(512\) 8.92045e14 1.12047
\(513\) 1.37188e14 0.170479
\(514\) −8.48489e14 −1.04316
\(515\) −5.23273e14 −0.636485
\(516\) 9.46343e13 0.113887
\(517\) −1.30919e14 −0.155885
\(518\) 3.88355e14 0.457526
\(519\) 7.64404e14 0.891050
\(520\) 5.08382e14 0.586370
\(521\) −6.24714e14 −0.712974 −0.356487 0.934300i \(-0.616026\pi\)
−0.356487 + 0.934300i \(0.616026\pi\)
\(522\) 1.09345e14 0.123484
\(523\) −6.72168e14 −0.751136 −0.375568 0.926795i \(-0.622552\pi\)
−0.375568 + 0.926795i \(0.622552\pi\)
\(524\) 1.83486e14 0.202900
\(525\) −4.82203e13 −0.0527659
\(526\) −6.98987e14 −0.756916
\(527\) −1.24965e15 −1.33916
\(528\) −3.75853e13 −0.0398594
\(529\) −7.07896e14 −0.742957
\(530\) −3.42697e13 −0.0355953
\(531\) 4.22156e13 0.0433963
\(532\) −5.99867e13 −0.0610297
\(533\) 7.28129e14 0.733177
\(534\) −2.66563e14 −0.265658
\(535\) 3.49435e14 0.344684
\(536\) −4.59701e14 −0.448817
\(537\) −1.01565e15 −0.981485
\(538\) 2.93657e14 0.280891
\(539\) 6.30355e13 0.0596825
\(540\) −2.48676e13 −0.0233061
\(541\) −1.89209e15 −1.75532 −0.877660 0.479284i \(-0.840896\pi\)
−0.877660 + 0.479284i \(0.840896\pi\)
\(542\) −8.05302e14 −0.739542
\(543\) 3.94078e14 0.358248
\(544\) 2.66263e14 0.239617
\(545\) −1.90986e15 −1.70146
\(546\) 1.92658e14 0.169913
\(547\) 4.47659e14 0.390856 0.195428 0.980718i \(-0.437390\pi\)
0.195428 + 0.980718i \(0.437390\pi\)
\(548\) −2.47306e14 −0.213768
\(549\) −5.32607e13 −0.0455784
\(550\) −1.58281e13 −0.0134102
\(551\) 4.20277e14 0.352535
\(552\) 3.71889e14 0.308850
\(553\) −9.28463e14 −0.763443
\(554\) 7.69088e14 0.626141
\(555\) 6.18792e14 0.498808
\(556\) 2.89651e14 0.231187
\(557\) −1.13843e15 −0.899708 −0.449854 0.893102i \(-0.648524\pi\)
−0.449854 + 0.893102i \(0.648524\pi\)
\(558\) −5.87514e14 −0.459759
\(559\) −1.16820e15 −0.905214
\(560\) −5.17804e14 −0.397312
\(561\) −5.58660e13 −0.0424474
\(562\) −2.31528e15 −1.74202
\(563\) −7.36979e14 −0.549110 −0.274555 0.961571i \(-0.588530\pi\)
−0.274555 + 0.961571i \(0.588530\pi\)
\(564\) 2.00173e14 0.147697
\(565\) −6.74844e14 −0.493102
\(566\) 1.35195e14 0.0978296
\(567\) −8.00159e13 −0.0573416
\(568\) 2.00270e15 1.42135
\(569\) 5.76359e14 0.405112 0.202556 0.979271i \(-0.435075\pi\)
0.202556 + 0.979271i \(0.435075\pi\)
\(570\) 6.20390e14 0.431870
\(571\) −3.57344e14 −0.246370 −0.123185 0.992384i \(-0.539311\pi\)
−0.123185 + 0.992384i \(0.539311\pi\)
\(572\) −9.74298e12 −0.00665294
\(573\) 3.68981e14 0.249548
\(574\) −8.58283e14 −0.574930
\(575\) 1.35325e14 0.0897853
\(576\) 5.55655e14 0.365158
\(577\) −2.37673e15 −1.54708 −0.773542 0.633746i \(-0.781517\pi\)
−0.773542 + 0.633746i \(0.781517\pi\)
\(578\) 2.64456e14 0.170510
\(579\) 5.92523e14 0.378419
\(580\) −7.61821e13 −0.0481947
\(581\) −1.18909e15 −0.745154
\(582\) −1.94211e14 −0.120558
\(583\) 5.57645e12 0.00342910
\(584\) −1.83152e15 −1.11568
\(585\) 3.06974e14 0.185244
\(586\) −1.74849e15 −1.04527
\(587\) 2.70630e15 1.60275 0.801376 0.598161i \(-0.204102\pi\)
0.801376 + 0.598161i \(0.204102\pi\)
\(588\) −9.63805e13 −0.0565476
\(589\) −2.25816e15 −1.31256
\(590\) 1.90906e14 0.109935
\(591\) 7.69357e14 0.438931
\(592\) −1.42999e15 −0.808282
\(593\) 1.40696e15 0.787919 0.393959 0.919128i \(-0.371105\pi\)
0.393959 + 0.919128i \(0.371105\pi\)
\(594\) −2.62649e13 −0.0145730
\(595\) −7.69654e14 −0.423109
\(596\) −3.26920e14 −0.178069
\(597\) 1.87076e14 0.100962
\(598\) −5.40673e14 −0.289120
\(599\) −1.52686e15 −0.809005 −0.404503 0.914537i \(-0.632555\pi\)
−0.404503 + 0.914537i \(0.632555\pi\)
\(600\) 2.05484e14 0.107881
\(601\) 2.89353e15 1.50529 0.752643 0.658429i \(-0.228779\pi\)
0.752643 + 0.658429i \(0.228779\pi\)
\(602\) 1.37701e15 0.709835
\(603\) −2.77580e14 −0.141789
\(604\) −5.29121e13 −0.0267825
\(605\) 1.79658e15 0.901139
\(606\) 5.50909e14 0.273830
\(607\) −3.95001e15 −1.94563 −0.972815 0.231583i \(-0.925610\pi\)
−0.972815 + 0.231583i \(0.925610\pi\)
\(608\) 4.81145e14 0.234858
\(609\) −2.45129e14 −0.118577
\(610\) −2.40854e14 −0.115462
\(611\) −2.47100e15 −1.17394
\(612\) 8.54184e13 0.0402178
\(613\) 2.65826e15 1.24041 0.620204 0.784441i \(-0.287050\pi\)
0.620204 + 0.784441i \(0.287050\pi\)
\(614\) −1.85788e15 −0.859193
\(615\) −1.36756e15 −0.626805
\(616\) 9.75123e13 0.0442961
\(617\) 1.38264e15 0.622502 0.311251 0.950328i \(-0.399252\pi\)
0.311251 + 0.950328i \(0.399252\pi\)
\(618\) 8.45033e14 0.377083
\(619\) −4.95786e14 −0.219278 −0.109639 0.993971i \(-0.534969\pi\)
−0.109639 + 0.993971i \(0.534969\pi\)
\(620\) 4.09328e14 0.179439
\(621\) 2.24556e14 0.0975711
\(622\) −2.88420e15 −1.24216
\(623\) 5.97579e14 0.255100
\(624\) −7.09397e14 −0.300175
\(625\) −1.88719e15 −0.791545
\(626\) −2.64948e15 −1.10154
\(627\) −1.00951e14 −0.0416045
\(628\) 1.62078e14 0.0662135
\(629\) −2.12550e15 −0.860763
\(630\) −3.61846e14 −0.145262
\(631\) −4.17470e13 −0.0166136 −0.00830681 0.999965i \(-0.502644\pi\)
−0.00830681 + 0.999965i \(0.502644\pi\)
\(632\) 3.95652e15 1.56088
\(633\) −2.72651e15 −1.06632
\(634\) 2.16392e15 0.838976
\(635\) 5.15434e14 0.198115
\(636\) −8.52632e12 −0.00324898
\(637\) 1.18975e15 0.449459
\(638\) −8.04627e13 −0.0301357
\(639\) 1.20928e15 0.449027
\(640\) 1.85946e15 0.684538
\(641\) 1.00484e15 0.366758 0.183379 0.983042i \(-0.441296\pi\)
0.183379 + 0.983042i \(0.441296\pi\)
\(642\) −5.64303e14 −0.204207
\(643\) 2.31335e15 0.830004 0.415002 0.909820i \(-0.363781\pi\)
0.415002 + 0.909820i \(0.363781\pi\)
\(644\) −9.81890e13 −0.0349294
\(645\) 2.19409e15 0.773883
\(646\) −2.13099e15 −0.745251
\(647\) −1.17420e15 −0.407162 −0.203581 0.979058i \(-0.565258\pi\)
−0.203581 + 0.979058i \(0.565258\pi\)
\(648\) 3.40977e14 0.117237
\(649\) −3.10647e13 −0.0105906
\(650\) −2.98745e14 −0.100990
\(651\) 1.31708e15 0.441487
\(652\) 3.40885e14 0.113304
\(653\) 2.20085e15 0.725383 0.362692 0.931909i \(-0.381858\pi\)
0.362692 + 0.931909i \(0.381858\pi\)
\(654\) 3.08424e15 1.00802
\(655\) 4.25410e15 1.37874
\(656\) 3.16034e15 1.01569
\(657\) −1.10592e15 −0.352463
\(658\) 2.91270e15 0.920561
\(659\) 7.28603e14 0.228361 0.114180 0.993460i \(-0.463576\pi\)
0.114180 + 0.993460i \(0.463576\pi\)
\(660\) 1.82991e13 0.00568771
\(661\) −3.22679e15 −0.994634 −0.497317 0.867569i \(-0.665681\pi\)
−0.497317 + 0.867569i \(0.665681\pi\)
\(662\) 4.53510e15 1.38633
\(663\) −1.05443e15 −0.319665
\(664\) 5.06715e15 1.52349
\(665\) −1.39078e15 −0.414707
\(666\) −9.99288e14 −0.295517
\(667\) 6.87929e14 0.201768
\(668\) −3.45983e14 −0.100643
\(669\) 1.54865e15 0.446796
\(670\) −1.25526e15 −0.359190
\(671\) 3.91924e13 0.0111232
\(672\) −2.80631e14 −0.0789958
\(673\) −3.32154e15 −0.927376 −0.463688 0.885998i \(-0.653474\pi\)
−0.463688 + 0.885998i \(0.653474\pi\)
\(674\) 3.76213e15 1.04185
\(675\) 1.24077e14 0.0340816
\(676\) 3.06092e14 0.0833960
\(677\) 9.35823e14 0.252904 0.126452 0.991973i \(-0.459641\pi\)
0.126452 + 0.991973i \(0.459641\pi\)
\(678\) 1.08981e15 0.292137
\(679\) 4.35381e14 0.115767
\(680\) 3.27978e15 0.865059
\(681\) 2.93589e15 0.768122
\(682\) 4.32328e14 0.112202
\(683\) −5.74313e14 −0.147854 −0.0739272 0.997264i \(-0.523553\pi\)
−0.0739272 + 0.997264i \(0.523553\pi\)
\(684\) 1.54353e14 0.0394192
\(685\) −5.73377e15 −1.45259
\(686\) −3.31394e15 −0.832842
\(687\) −3.03229e15 −0.755978
\(688\) −5.07038e15 −1.25402
\(689\) 1.05252e14 0.0258240
\(690\) 1.01548e15 0.247174
\(691\) 4.32175e15 1.04359 0.521796 0.853070i \(-0.325262\pi\)
0.521796 + 0.853070i \(0.325262\pi\)
\(692\) 8.60046e14 0.206034
\(693\) 5.88805e13 0.0139939
\(694\) 4.37168e15 1.03079
\(695\) 6.71552e15 1.57095
\(696\) 1.04459e15 0.242434
\(697\) 4.69746e15 1.08164
\(698\) −3.31147e14 −0.0756512
\(699\) 3.15152e15 0.714324
\(700\) −5.42536e13 −0.0122008
\(701\) 5.20866e14 0.116219 0.0581094 0.998310i \(-0.481493\pi\)
0.0581094 + 0.998310i \(0.481493\pi\)
\(702\) −4.95733e14 −0.109747
\(703\) −3.84084e15 −0.843669
\(704\) −4.08884e14 −0.0891149
\(705\) 4.64099e15 1.00362
\(706\) −1.51034e15 −0.324077
\(707\) −1.23502e15 −0.262947
\(708\) 4.74976e13 0.0100343
\(709\) 7.72575e15 1.61952 0.809760 0.586762i \(-0.199597\pi\)
0.809760 + 0.586762i \(0.199597\pi\)
\(710\) 5.46858e15 1.13751
\(711\) 2.38905e15 0.493109
\(712\) −2.54650e15 −0.521560
\(713\) −3.69626e15 −0.751225
\(714\) 1.24291e15 0.250669
\(715\) −2.25890e14 −0.0452078
\(716\) −1.14272e15 −0.226945
\(717\) −1.76133e15 −0.347125
\(718\) 2.52121e15 0.493089
\(719\) 5.14644e15 0.998844 0.499422 0.866359i \(-0.333546\pi\)
0.499422 + 0.866359i \(0.333546\pi\)
\(720\) 1.33238e15 0.256624
\(721\) −1.89439e15 −0.362097
\(722\) 1.05651e15 0.200409
\(723\) 5.30824e15 0.999287
\(724\) 4.43386e14 0.0828361
\(725\) 3.80110e14 0.0704775
\(726\) −2.90130e15 −0.533876
\(727\) 8.84127e15 1.61464 0.807320 0.590115i \(-0.200917\pi\)
0.807320 + 0.590115i \(0.200917\pi\)
\(728\) 1.84048e15 0.333586
\(729\) 2.05891e14 0.0370370
\(730\) −5.00116e15 −0.892884
\(731\) −7.53652e15 −1.33544
\(732\) −5.99247e13 −0.0105389
\(733\) −4.36942e15 −0.762698 −0.381349 0.924431i \(-0.624540\pi\)
−0.381349 + 0.924431i \(0.624540\pi\)
\(734\) 6.01390e15 1.04190
\(735\) −2.23457e15 −0.384250
\(736\) 7.87560e14 0.134417
\(737\) 2.04260e14 0.0346028
\(738\) 2.20847e15 0.371348
\(739\) −4.46605e15 −0.745383 −0.372691 0.927955i \(-0.621565\pi\)
−0.372691 + 0.927955i \(0.621565\pi\)
\(740\) 6.96216e14 0.115337
\(741\) −1.90539e15 −0.313317
\(742\) −1.24066e14 −0.0202502
\(743\) 1.09534e16 1.77464 0.887319 0.461157i \(-0.152565\pi\)
0.887319 + 0.461157i \(0.152565\pi\)
\(744\) −5.61258e15 −0.902634
\(745\) −7.57960e15 −1.21000
\(746\) −7.23325e15 −1.14622
\(747\) 3.05968e15 0.481297
\(748\) −6.28560e13 −0.00981494
\(749\) 1.26505e15 0.196091
\(750\) 3.72947e15 0.573866
\(751\) 6.98221e15 1.06653 0.533265 0.845948i \(-0.320965\pi\)
0.533265 + 0.845948i \(0.320965\pi\)
\(752\) −1.07250e16 −1.62630
\(753\) 1.95980e15 0.295012
\(754\) −1.51868e15 −0.226947
\(755\) −1.22676e15 −0.181992
\(756\) −9.00276e13 −0.0132588
\(757\) 8.12477e14 0.118791 0.0593955 0.998235i \(-0.481083\pi\)
0.0593955 + 0.998235i \(0.481083\pi\)
\(758\) 2.42612e15 0.352153
\(759\) −1.65242e14 −0.0238117
\(760\) 5.92665e15 0.847880
\(761\) 9.50296e15 1.34972 0.674859 0.737946i \(-0.264204\pi\)
0.674859 + 0.737946i \(0.264204\pi\)
\(762\) −8.32374e14 −0.117372
\(763\) −6.91422e15 −0.967962
\(764\) 4.15148e14 0.0577018
\(765\) 1.98042e15 0.273287
\(766\) −4.56902e15 −0.625986
\(767\) −5.86326e14 −0.0797563
\(768\) 1.68021e15 0.226921
\(769\) 6.18404e15 0.829235 0.414617 0.909996i \(-0.363915\pi\)
0.414617 + 0.909996i \(0.363915\pi\)
\(770\) 2.66268e14 0.0354503
\(771\) −4.89444e15 −0.646999
\(772\) 6.66660e14 0.0875002
\(773\) 1.21781e16 1.58705 0.793526 0.608537i \(-0.208243\pi\)
0.793526 + 0.608537i \(0.208243\pi\)
\(774\) −3.54323e15 −0.458484
\(775\) −2.04234e15 −0.262403
\(776\) −1.85532e15 −0.236690
\(777\) 2.24020e15 0.283773
\(778\) −8.86430e15 −1.11495
\(779\) 8.48843e15 1.06016
\(780\) 3.45383e14 0.0428332
\(781\) −8.89861e14 −0.109583
\(782\) −3.48810e15 −0.426533
\(783\) 6.30748e14 0.0765890
\(784\) 5.16394e15 0.622649
\(785\) 3.75777e15 0.449932
\(786\) −6.86995e15 −0.816826
\(787\) −9.68489e15 −1.14349 −0.571747 0.820430i \(-0.693734\pi\)
−0.571747 + 0.820430i \(0.693734\pi\)
\(788\) 8.65619e14 0.101492
\(789\) −4.03205e15 −0.469464
\(790\) 1.08037e16 1.24918
\(791\) −2.44312e15 −0.280526
\(792\) −2.50911e14 −0.0286109
\(793\) 7.39731e14 0.0837666
\(794\) −8.49162e15 −0.954944
\(795\) −1.97682e14 −0.0220774
\(796\) 2.10483e14 0.0233451
\(797\) −9.19553e15 −1.01288 −0.506438 0.862277i \(-0.669038\pi\)
−0.506438 + 0.862277i \(0.669038\pi\)
\(798\) 2.24598e15 0.245691
\(799\) −1.59415e16 −1.73189
\(800\) 4.35160e14 0.0469520
\(801\) −1.53765e15 −0.164770
\(802\) −8.12251e15 −0.864433
\(803\) 8.13801e14 0.0860166
\(804\) −3.12311e14 −0.0327853
\(805\) −2.27650e15 −0.237351
\(806\) 8.15990e15 0.844972
\(807\) 1.69394e15 0.174218
\(808\) 5.26289e15 0.537603
\(809\) −1.38493e16 −1.40511 −0.702557 0.711628i \(-0.747958\pi\)
−0.702557 + 0.711628i \(0.747958\pi\)
\(810\) 9.31076e14 0.0938248
\(811\) 1.47735e16 1.47866 0.739332 0.673341i \(-0.235141\pi\)
0.739332 + 0.673341i \(0.235141\pi\)
\(812\) −2.75800e14 −0.0274180
\(813\) −4.64532e15 −0.458688
\(814\) 7.35335e14 0.0721193
\(815\) 7.90337e15 0.769920
\(816\) −4.57661e15 −0.442841
\(817\) −1.36187e16 −1.30892
\(818\) 1.21324e16 1.15825
\(819\) 1.11133e15 0.105386
\(820\) −1.53867e15 −0.144934
\(821\) −6.05257e15 −0.566307 −0.283154 0.959075i \(-0.591381\pi\)
−0.283154 + 0.959075i \(0.591381\pi\)
\(822\) 9.25946e15 0.860579
\(823\) −1.42072e16 −1.31163 −0.655814 0.754923i \(-0.727674\pi\)
−0.655814 + 0.754923i \(0.727674\pi\)
\(824\) 8.07269e15 0.740319
\(825\) −9.13031e13 −0.00831743
\(826\) 6.91132e14 0.0625419
\(827\) −1.76034e16 −1.58240 −0.791200 0.611558i \(-0.790543\pi\)
−0.791200 + 0.611558i \(0.790543\pi\)
\(828\) 2.52653e14 0.0225609
\(829\) 1.80575e16 1.60180 0.800900 0.598798i \(-0.204355\pi\)
0.800900 + 0.598798i \(0.204355\pi\)
\(830\) 1.38364e16 1.21925
\(831\) 4.43642e15 0.388353
\(832\) −7.71741e15 −0.671110
\(833\) 7.67558e15 0.663077
\(834\) −1.08449e16 −0.930706
\(835\) −8.02158e15 −0.683887
\(836\) −1.13582e14 −0.00962003
\(837\) −3.38903e15 −0.285158
\(838\) −1.75528e14 −0.0146725
\(839\) 1.10398e16 0.916793 0.458396 0.888748i \(-0.348424\pi\)
0.458396 + 0.888748i \(0.348424\pi\)
\(840\) −3.45675e15 −0.285189
\(841\) −1.02682e16 −0.841621
\(842\) 5.05224e15 0.411403
\(843\) −1.33555e16 −1.08046
\(844\) −3.06766e15 −0.246560
\(845\) 7.09671e15 0.566689
\(846\) −7.49474e15 −0.594592
\(847\) 6.50410e15 0.512659
\(848\) 4.56829e14 0.0357748
\(849\) 7.79861e14 0.0606771
\(850\) −1.92733e15 −0.148988
\(851\) −6.28687e15 −0.482861
\(852\) 1.36059e15 0.103827
\(853\) 2.18701e16 1.65818 0.829089 0.559117i \(-0.188860\pi\)
0.829089 + 0.559117i \(0.188860\pi\)
\(854\) −8.71958e14 −0.0656867
\(855\) 3.57867e15 0.267860
\(856\) −5.39085e15 −0.400914
\(857\) −1.48496e16 −1.09729 −0.548645 0.836055i \(-0.684856\pi\)
−0.548645 + 0.836055i \(0.684856\pi\)
\(858\) 3.64790e14 0.0267832
\(859\) 8.24023e15 0.601142 0.300571 0.953760i \(-0.402823\pi\)
0.300571 + 0.953760i \(0.402823\pi\)
\(860\) 2.46861e15 0.178942
\(861\) −4.95093e15 −0.356590
\(862\) −1.47932e16 −1.05870
\(863\) −4.56565e15 −0.324671 −0.162336 0.986736i \(-0.551903\pi\)
−0.162336 + 0.986736i \(0.551903\pi\)
\(864\) 7.22098e14 0.0510235
\(865\) 1.99401e16 1.40003
\(866\) 1.07883e16 0.752673
\(867\) 1.52549e15 0.105756
\(868\) 1.48188e15 0.102083
\(869\) −1.75801e15 −0.120341
\(870\) 2.85235e15 0.194021
\(871\) 3.85527e15 0.260588
\(872\) 2.94641e16 1.97903
\(873\) −1.12029e15 −0.0747743
\(874\) −6.30310e15 −0.418063
\(875\) −8.36070e15 −0.551059
\(876\) −1.24429e15 −0.0814985
\(877\) −1.90914e16 −1.24263 −0.621314 0.783562i \(-0.713401\pi\)
−0.621314 + 0.783562i \(0.713401\pi\)
\(878\) 1.96258e16 1.26943
\(879\) −1.00860e16 −0.648308
\(880\) −9.80441e14 −0.0626278
\(881\) −4.49894e15 −0.285590 −0.142795 0.989752i \(-0.545609\pi\)
−0.142795 + 0.989752i \(0.545609\pi\)
\(882\) 3.60861e15 0.227647
\(883\) −2.15548e16 −1.35133 −0.675663 0.737211i \(-0.736143\pi\)
−0.675663 + 0.737211i \(0.736143\pi\)
\(884\) −1.18636e15 −0.0739147
\(885\) 1.10123e15 0.0681850
\(886\) −1.18687e16 −0.730330
\(887\) −2.49524e16 −1.52592 −0.762962 0.646443i \(-0.776256\pi\)
−0.762962 + 0.646443i \(0.776256\pi\)
\(888\) −9.54630e15 −0.580181
\(889\) 1.86601e15 0.112708
\(890\) −6.95351e15 −0.417406
\(891\) −1.51507e14 −0.00903868
\(892\) 1.74242e15 0.103311
\(893\) −2.88066e16 −1.69750
\(894\) 1.22403e16 0.716862
\(895\) −2.64939e16 −1.54213
\(896\) 6.73175e15 0.389434
\(897\) −3.11883e15 −0.179322
\(898\) 2.44307e15 0.139610
\(899\) −1.03823e16 −0.589678
\(900\) 1.39601e14 0.00788054
\(901\) 6.79022e14 0.0380976
\(902\) −1.62512e15 −0.0906255
\(903\) 7.94318e15 0.440263
\(904\) 1.04110e16 0.573545
\(905\) 1.02798e16 0.562885
\(906\) 1.98110e15 0.107820
\(907\) 1.55921e16 0.843462 0.421731 0.906721i \(-0.361423\pi\)
0.421731 + 0.906721i \(0.361423\pi\)
\(908\) 3.30323e15 0.177609
\(909\) 3.17787e15 0.169838
\(910\) 5.02563e15 0.266970
\(911\) 8.10417e15 0.427915 0.213957 0.976843i \(-0.431365\pi\)
0.213957 + 0.976843i \(0.431365\pi\)
\(912\) −8.27005e15 −0.434047
\(913\) −2.25150e15 −0.117458
\(914\) 2.18823e16 1.13472
\(915\) −1.38935e15 −0.0716135
\(916\) −3.41169e15 −0.174801
\(917\) 1.54010e16 0.784364
\(918\) −3.19817e15 −0.161908
\(919\) −3.49537e16 −1.75897 −0.879484 0.475928i \(-0.842112\pi\)
−0.879484 + 0.475928i \(0.842112\pi\)
\(920\) 9.70101e15 0.485271
\(921\) −1.07170e16 −0.532900
\(922\) 3.64230e16 1.80035
\(923\) −1.67955e16 −0.825248
\(924\) 6.62476e13 0.00323575
\(925\) −3.47376e15 −0.168663
\(926\) −1.28918e16 −0.622232
\(927\) 4.87450e15 0.233879
\(928\) 2.21215e15 0.105512
\(929\) −2.60620e16 −1.23572 −0.617861 0.786287i \(-0.712001\pi\)
−0.617861 + 0.786287i \(0.712001\pi\)
\(930\) −1.53258e16 −0.722381
\(931\) 1.38700e16 0.649909
\(932\) 3.54584e15 0.165170
\(933\) −1.66373e16 −0.770430
\(934\) −1.44069e16 −0.663226
\(935\) −1.45731e15 −0.0666941
\(936\) −4.73579e15 −0.215464
\(937\) −4.21844e16 −1.90802 −0.954012 0.299770i \(-0.903090\pi\)
−0.954012 + 0.299770i \(0.903090\pi\)
\(938\) −4.54440e15 −0.204343
\(939\) −1.52833e16 −0.683212
\(940\) 5.22168e15 0.232063
\(941\) −1.68830e16 −0.745944 −0.372972 0.927842i \(-0.621661\pi\)
−0.372972 + 0.927842i \(0.621661\pi\)
\(942\) −6.06842e15 −0.266560
\(943\) 1.38943e16 0.606766
\(944\) −2.54486e15 −0.110489
\(945\) −2.08728e15 −0.0900960
\(946\) 2.60732e15 0.111890
\(947\) 1.02757e16 0.438416 0.219208 0.975678i \(-0.429653\pi\)
0.219208 + 0.975678i \(0.429653\pi\)
\(948\) 2.68797e15 0.114020
\(949\) 1.53600e16 0.647777
\(950\) −3.48273e15 −0.146029
\(951\) 1.24824e16 0.520360
\(952\) 1.18737e16 0.492133
\(953\) −3.75513e16 −1.54744 −0.773719 0.633528i \(-0.781606\pi\)
−0.773719 + 0.633528i \(0.781606\pi\)
\(954\) 3.19236e14 0.0130797
\(955\) 9.62516e15 0.392093
\(956\) −1.98171e15 −0.0802643
\(957\) −4.64142e14 −0.0186911
\(958\) −1.61691e16 −0.647404
\(959\) −2.07578e16 −0.826378
\(960\) 1.44947e16 0.573743
\(961\) 3.03758e16 1.19550
\(962\) 1.38790e16 0.543118
\(963\) −3.25514e15 −0.126656
\(964\) 5.97241e15 0.231061
\(965\) 1.54564e16 0.594578
\(966\) 3.67632e15 0.140617
\(967\) −7.88651e13 −0.00299943 −0.00149972 0.999999i \(-0.500477\pi\)
−0.00149972 + 0.999999i \(0.500477\pi\)
\(968\) −2.77164e16 −1.04815
\(969\) −1.22924e16 −0.462229
\(970\) −5.06615e15 −0.189423
\(971\) −2.34143e16 −0.870515 −0.435257 0.900306i \(-0.643343\pi\)
−0.435257 + 0.900306i \(0.643343\pi\)
\(972\) 2.31652e14 0.00856391
\(973\) 2.43120e16 0.893718
\(974\) −1.31717e16 −0.481469
\(975\) −1.72329e15 −0.0626372
\(976\) 3.21069e15 0.116044
\(977\) −1.70904e16 −0.614233 −0.307117 0.951672i \(-0.599364\pi\)
−0.307117 + 0.951672i \(0.599364\pi\)
\(978\) −1.27632e16 −0.456136
\(979\) 1.13149e15 0.0402112
\(980\) −2.51416e15 −0.0888485
\(981\) 1.77912e16 0.625209
\(982\) 2.23901e16 0.782424
\(983\) −3.92844e16 −1.36514 −0.682568 0.730822i \(-0.739137\pi\)
−0.682568 + 0.730822i \(0.739137\pi\)
\(984\) 2.10977e16 0.729060
\(985\) 2.00693e16 0.689656
\(986\) −9.79762e15 −0.334809
\(987\) 1.68016e16 0.570962
\(988\) −2.14379e15 −0.0724469
\(989\) −2.22917e16 −0.749141
\(990\) −6.85141e14 −0.0228974
\(991\) −2.16313e16 −0.718914 −0.359457 0.933162i \(-0.617038\pi\)
−0.359457 + 0.933162i \(0.617038\pi\)
\(992\) −1.18859e16 −0.392843
\(993\) 2.61603e16 0.859850
\(994\) 1.97978e16 0.647129
\(995\) 4.88003e15 0.158634
\(996\) 3.44251e15 0.111288
\(997\) −1.41029e16 −0.453403 −0.226702 0.973964i \(-0.572794\pi\)
−0.226702 + 0.973964i \(0.572794\pi\)
\(998\) 8.72991e15 0.279120
\(999\) −5.76431e15 −0.183289
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 177.12.a.a.1.9 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.a.1.9 26 1.1 even 1 trivial