Properties

Label 29.12.a.a.1.10
Level $29$
Weight $12$
Character 29.1
Self dual yes
Analytic conductor $22.282$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.2819522362\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + 1279291654973975 x^{2} - 65244901875230266 x - 758324542468966858\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(65.2743\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+62.2743 q^{2} -384.675 q^{3} +1830.09 q^{4} +1377.47 q^{5} -23955.4 q^{6} +33050.3 q^{7} -13570.0 q^{8} -29172.4 q^{9} +O(q^{10})\) \(q+62.2743 q^{2} -384.675 q^{3} +1830.09 q^{4} +1377.47 q^{5} -23955.4 q^{6} +33050.3 q^{7} -13570.0 q^{8} -29172.4 q^{9} +85780.8 q^{10} -800438. q^{11} -703990. q^{12} +1.48554e6 q^{13} +2.05818e6 q^{14} -529877. q^{15} -4.59309e6 q^{16} -1.13043e7 q^{17} -1.81669e6 q^{18} -9.78812e6 q^{19} +2.52089e6 q^{20} -1.27136e7 q^{21} -4.98468e7 q^{22} +546284. q^{23} +5.22005e6 q^{24} -4.69307e7 q^{25} +9.25112e7 q^{26} +7.93659e7 q^{27} +6.04851e7 q^{28} +2.05111e7 q^{29} -3.29977e7 q^{30} +4.17817e6 q^{31} -2.58240e8 q^{32} +3.07908e8 q^{33} -7.03969e8 q^{34} +4.55257e7 q^{35} -5.33882e7 q^{36} +3.50598e8 q^{37} -6.09549e8 q^{38} -5.71451e8 q^{39} -1.86923e7 q^{40} +7.34075e8 q^{41} -7.91731e8 q^{42} -1.74203e9 q^{43} -1.46488e9 q^{44} -4.01841e7 q^{45} +3.40195e7 q^{46} +1.70223e9 q^{47} +1.76685e9 q^{48} -8.85005e8 q^{49} -2.92258e9 q^{50} +4.34849e9 q^{51} +2.71868e9 q^{52} +2.30025e9 q^{53} +4.94246e9 q^{54} -1.10258e9 q^{55} -4.48494e8 q^{56} +3.76524e9 q^{57} +1.27732e9 q^{58} -2.84523e8 q^{59} -9.69723e8 q^{60} +5.13866e9 q^{61} +2.60193e8 q^{62} -9.64157e8 q^{63} -6.67509e9 q^{64} +2.04629e9 q^{65} +1.91748e10 q^{66} -3.85315e9 q^{67} -2.06880e10 q^{68} -2.10142e8 q^{69} +2.83508e9 q^{70} +2.82041e10 q^{71} +3.95871e8 q^{72} -1.81192e10 q^{73} +2.18333e10 q^{74} +1.80531e10 q^{75} -1.79132e10 q^{76} -2.64547e10 q^{77} -3.55867e10 q^{78} -3.94609e10 q^{79} -6.32684e9 q^{80} -2.53622e10 q^{81} +4.57140e10 q^{82} +1.27885e10 q^{83} -2.32671e10 q^{84} -1.55713e10 q^{85} -1.08484e11 q^{86} -7.89012e9 q^{87} +1.08620e10 q^{88} +4.46844e10 q^{89} -2.50244e9 q^{90} +4.90976e10 q^{91} +9.99751e8 q^{92} -1.60724e9 q^{93} +1.06005e11 q^{94} -1.34828e10 q^{95} +9.93386e10 q^{96} -7.40280e10 q^{97} -5.51131e10 q^{98} +2.33507e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} + O(q^{10}) \) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} - 685834q^{10} - 612246q^{11} + 2578538q^{12} + 1510364q^{13} + 3955400q^{14} - 2462818q^{15} + 3024818q^{16} - 3291098q^{17} - 27885614q^{18} - 44121388q^{19} - 49472662q^{20} - 46916800q^{21} - 43435618q^{22} - 88684076q^{23} - 224700678q^{24} - 44195521q^{25} - 324999762q^{26} - 236304286q^{27} - 391274848q^{28} + 225622639q^{29} - 494910382q^{30} - 292235934q^{31} - 632542514q^{32} - 1079766410q^{33} - 1113307936q^{34} - 1312820120q^{35} - 2236726492q^{36} - 1380429338q^{37} - 1222857284q^{38} - 1186931090q^{39} - 2713154106q^{40} - 1062067494q^{41} + 205598960q^{42} + 74588594q^{43} + 52891466q^{44} + 4527996830q^{45} - 87670324q^{46} - 1821239394q^{47} + 2666035542q^{48} + 4692522003q^{49} + 9494259926q^{50} + 8768158380q^{51} + 3266669866q^{52} + 7818635688q^{53} + 17402728558q^{54} - 191002682q^{55} + 11263587512q^{56} + 15495358340q^{57} - 656356768q^{58} + 1230002712q^{59} + 31834046430q^{60} - 18602654230q^{61} + 22075953162q^{62} - 9964531456q^{63} + 11813658086q^{64} + 32245789334q^{65} + 42677188354q^{66} + 27481284652q^{67} + 29588811820q^{68} - 20565315068q^{69} + 42862666712q^{70} - 20347168516q^{71} + 47061083616q^{72} - 57740010478q^{73} - 2640709564q^{74} - 23544691000q^{75} - 33350650772q^{76} + 871959792q^{77} - 15384525342q^{78} - 120245016462q^{79} - 84319695274q^{80} - 48880047865q^{81} - 111495532412q^{82} - 142463983824q^{83} - 134146226376q^{84} - 181628566552q^{85} + 47870165542q^{86} - 20141948318q^{87} - 180608014462q^{88} - 96700717270q^{89} - 25522461244q^{90} - 355162031176q^{91} - 22429477796q^{92} - 172582115142q^{93} + 172608565078q^{94} - 195922150708q^{95} + 226391047758q^{96} - 303190852014q^{97} - 123776497136q^{98} - 139125462440q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 62.2743 1.37608 0.688041 0.725672i \(-0.258471\pi\)
0.688041 + 0.725672i \(0.258471\pi\)
\(3\) −384.675 −0.913959 −0.456979 0.889477i \(-0.651069\pi\)
−0.456979 + 0.889477i \(0.651069\pi\)
\(4\) 1830.09 0.893600
\(5\) 1377.47 0.197127 0.0985635 0.995131i \(-0.468575\pi\)
0.0985635 + 0.995131i \(0.468575\pi\)
\(6\) −23955.4 −1.25768
\(7\) 33050.3 0.743252 0.371626 0.928383i \(-0.378800\pi\)
0.371626 + 0.928383i \(0.378800\pi\)
\(8\) −13570.0 −0.146415
\(9\) −29172.4 −0.164679
\(10\) 85780.8 0.271263
\(11\) −800438. −1.49854 −0.749270 0.662265i \(-0.769595\pi\)
−0.749270 + 0.662265i \(0.769595\pi\)
\(12\) −703990. −0.816714
\(13\) 1.48554e6 1.10968 0.554839 0.831958i \(-0.312780\pi\)
0.554839 + 0.831958i \(0.312780\pi\)
\(14\) 2.05818e6 1.02277
\(15\) −529877. −0.180166
\(16\) −4.59309e6 −1.09508
\(17\) −1.13043e7 −1.93097 −0.965485 0.260457i \(-0.916127\pi\)
−0.965485 + 0.260457i \(0.916127\pi\)
\(18\) −1.81669e6 −0.226612
\(19\) −9.78812e6 −0.906890 −0.453445 0.891284i \(-0.649805\pi\)
−0.453445 + 0.891284i \(0.649805\pi\)
\(20\) 2.52089e6 0.176153
\(21\) −1.27136e7 −0.679302
\(22\) −4.98468e7 −2.06211
\(23\) 546284. 0.0176977 0.00884883 0.999961i \(-0.497183\pi\)
0.00884883 + 0.999961i \(0.497183\pi\)
\(24\) 5.22005e6 0.133818
\(25\) −4.69307e7 −0.961141
\(26\) 9.25112e7 1.52701
\(27\) 7.93659e7 1.06447
\(28\) 6.04851e7 0.664170
\(29\) 2.05111e7 0.185695
\(30\) −3.29977e7 −0.247923
\(31\) 4.17817e6 0.0262118 0.0131059 0.999914i \(-0.495828\pi\)
0.0131059 + 0.999914i \(0.495828\pi\)
\(32\) −2.58240e8 −1.36050
\(33\) 3.07908e8 1.36960
\(34\) −7.03969e8 −2.65717
\(35\) 4.55257e7 0.146515
\(36\) −5.33882e7 −0.147157
\(37\) 3.50598e8 0.831190 0.415595 0.909550i \(-0.363573\pi\)
0.415595 + 0.909550i \(0.363573\pi\)
\(38\) −6.09549e8 −1.24795
\(39\) −5.71451e8 −1.01420
\(40\) −1.86923e7 −0.0288624
\(41\) 7.34075e8 0.989531 0.494765 0.869027i \(-0.335254\pi\)
0.494765 + 0.869027i \(0.335254\pi\)
\(42\) −7.91731e8 −0.934774
\(43\) −1.74203e9 −1.80709 −0.903545 0.428494i \(-0.859044\pi\)
−0.903545 + 0.428494i \(0.859044\pi\)
\(44\) −1.46488e9 −1.33909
\(45\) −4.01841e7 −0.0324627
\(46\) 3.40195e7 0.0243534
\(47\) 1.70223e9 1.08263 0.541315 0.840820i \(-0.317927\pi\)
0.541315 + 0.840820i \(0.317927\pi\)
\(48\) 1.76685e9 1.00086
\(49\) −8.85005e8 −0.447577
\(50\) −2.92258e9 −1.32261
\(51\) 4.34849e9 1.76483
\(52\) 2.71868e9 0.991608
\(53\) 2.30025e9 0.755539 0.377770 0.925900i \(-0.376691\pi\)
0.377770 + 0.925900i \(0.376691\pi\)
\(54\) 4.94246e9 1.46480
\(55\) −1.10258e9 −0.295403
\(56\) −4.48494e8 −0.108823
\(57\) 3.76524e9 0.828860
\(58\) 1.27732e9 0.255532
\(59\) −2.84523e8 −0.0518121 −0.0259060 0.999664i \(-0.508247\pi\)
−0.0259060 + 0.999664i \(0.508247\pi\)
\(60\) −9.69723e8 −0.160996
\(61\) 5.13866e9 0.778997 0.389499 0.921027i \(-0.372648\pi\)
0.389499 + 0.921027i \(0.372648\pi\)
\(62\) 2.60193e8 0.0360696
\(63\) −9.64157e8 −0.122398
\(64\) −6.67509e9 −0.777083
\(65\) 2.04629e9 0.218747
\(66\) 1.91748e10 1.88469
\(67\) −3.85315e9 −0.348662 −0.174331 0.984687i \(-0.555776\pi\)
−0.174331 + 0.984687i \(0.555776\pi\)
\(68\) −2.06880e10 −1.72552
\(69\) −2.10142e8 −0.0161749
\(70\) 2.83508e9 0.201617
\(71\) 2.82041e10 1.85520 0.927602 0.373570i \(-0.121867\pi\)
0.927602 + 0.373570i \(0.121867\pi\)
\(72\) 3.95871e8 0.0241115
\(73\) −1.81192e10 −1.02297 −0.511484 0.859293i \(-0.670904\pi\)
−0.511484 + 0.859293i \(0.670904\pi\)
\(74\) 2.18333e10 1.14378
\(75\) 1.80531e10 0.878443
\(76\) −1.79132e10 −0.810396
\(77\) −2.64547e10 −1.11379
\(78\) −3.55867e10 −1.39562
\(79\) −3.94609e10 −1.44284 −0.721419 0.692499i \(-0.756510\pi\)
−0.721419 + 0.692499i \(0.756510\pi\)
\(80\) −6.32684e9 −0.215870
\(81\) −2.53622e10 −0.808202
\(82\) 4.57140e10 1.36168
\(83\) 1.27885e10 0.356362 0.178181 0.983998i \(-0.442979\pi\)
0.178181 + 0.983998i \(0.442979\pi\)
\(84\) −2.32671e10 −0.607024
\(85\) −1.55713e10 −0.380646
\(86\) −1.08484e11 −2.48670
\(87\) −7.89012e9 −0.169718
\(88\) 1.08620e10 0.219409
\(89\) 4.46844e10 0.848225 0.424112 0.905610i \(-0.360586\pi\)
0.424112 + 0.905610i \(0.360586\pi\)
\(90\) −2.50244e9 −0.0446714
\(91\) 4.90976e10 0.824770
\(92\) 9.99751e8 0.0158146
\(93\) −1.60724e9 −0.0239565
\(94\) 1.06005e11 1.48979
\(95\) −1.34828e10 −0.178772
\(96\) 9.93386e10 1.24344
\(97\) −7.40280e10 −0.875289 −0.437644 0.899148i \(-0.644187\pi\)
−0.437644 + 0.899148i \(0.644187\pi\)
\(98\) −5.51131e10 −0.615902
\(99\) 2.33507e10 0.246778
\(100\) −8.58875e10 −0.858875
\(101\) −8.70065e10 −0.823728 −0.411864 0.911245i \(-0.635122\pi\)
−0.411864 + 0.911245i \(0.635122\pi\)
\(102\) 2.70799e11 2.42855
\(103\) −2.00277e11 −1.70227 −0.851133 0.524951i \(-0.824084\pi\)
−0.851133 + 0.524951i \(0.824084\pi\)
\(104\) −2.01589e10 −0.162474
\(105\) −1.75126e10 −0.133909
\(106\) 1.43246e11 1.03968
\(107\) −6.27684e10 −0.432644 −0.216322 0.976322i \(-0.569406\pi\)
−0.216322 + 0.976322i \(0.569406\pi\)
\(108\) 1.45247e11 0.951209
\(109\) 1.65628e11 1.03107 0.515535 0.856868i \(-0.327593\pi\)
0.515535 + 0.856868i \(0.327593\pi\)
\(110\) −6.86623e10 −0.406498
\(111\) −1.34866e11 −0.759673
\(112\) −1.51803e11 −0.813920
\(113\) 1.11390e11 0.568741 0.284370 0.958714i \(-0.408215\pi\)
0.284370 + 0.958714i \(0.408215\pi\)
\(114\) 2.34478e11 1.14058
\(115\) 7.52489e8 0.00348869
\(116\) 3.75373e10 0.165937
\(117\) −4.33369e10 −0.182741
\(118\) −1.77185e10 −0.0712977
\(119\) −3.73611e11 −1.43520
\(120\) 7.19045e9 0.0263790
\(121\) 3.55390e11 1.24562
\(122\) 3.20007e11 1.07196
\(123\) −2.82380e11 −0.904391
\(124\) 7.64644e9 0.0234229
\(125\) −1.31905e11 −0.386594
\(126\) −6.00422e10 −0.168430
\(127\) −4.11525e11 −1.10529 −0.552644 0.833417i \(-0.686381\pi\)
−0.552644 + 0.833417i \(0.686381\pi\)
\(128\) 1.13189e11 0.291173
\(129\) 6.70115e11 1.65161
\(130\) 1.27431e11 0.301014
\(131\) −9.62047e10 −0.217873 −0.108937 0.994049i \(-0.534745\pi\)
−0.108937 + 0.994049i \(0.534745\pi\)
\(132\) 5.63501e11 1.22388
\(133\) −3.23500e11 −0.674047
\(134\) −2.39952e11 −0.479787
\(135\) 1.09324e11 0.209836
\(136\) 1.53400e11 0.282724
\(137\) −3.08367e11 −0.545890 −0.272945 0.962030i \(-0.587998\pi\)
−0.272945 + 0.962030i \(0.587998\pi\)
\(138\) −1.30864e10 −0.0222580
\(139\) 6.03606e11 0.986671 0.493336 0.869839i \(-0.335777\pi\)
0.493336 + 0.869839i \(0.335777\pi\)
\(140\) 8.33162e10 0.130926
\(141\) −6.54804e11 −0.989479
\(142\) 1.75639e12 2.55291
\(143\) −1.18909e12 −1.66290
\(144\) 1.33992e11 0.180337
\(145\) 2.82534e10 0.0366056
\(146\) −1.12836e12 −1.40769
\(147\) 3.40439e11 0.409067
\(148\) 6.41627e11 0.742751
\(149\) −1.18808e12 −1.32532 −0.662660 0.748920i \(-0.730573\pi\)
−0.662660 + 0.748920i \(0.730573\pi\)
\(150\) 1.12424e12 1.20881
\(151\) 4.61543e11 0.478453 0.239226 0.970964i \(-0.423106\pi\)
0.239226 + 0.970964i \(0.423106\pi\)
\(152\) 1.32825e11 0.132782
\(153\) 3.29775e11 0.317991
\(154\) −1.64745e12 −1.53267
\(155\) 5.75529e9 0.00516706
\(156\) −1.04581e12 −0.906289
\(157\) 4.49681e11 0.376232 0.188116 0.982147i \(-0.439762\pi\)
0.188116 + 0.982147i \(0.439762\pi\)
\(158\) −2.45740e12 −1.98546
\(159\) −8.84846e11 −0.690532
\(160\) −3.55718e11 −0.268192
\(161\) 1.80549e10 0.0131538
\(162\) −1.57942e12 −1.11215
\(163\) −1.77931e12 −1.21121 −0.605604 0.795766i \(-0.707068\pi\)
−0.605604 + 0.795766i \(0.707068\pi\)
\(164\) 1.34343e12 0.884245
\(165\) 4.24134e11 0.269986
\(166\) 7.96398e11 0.490383
\(167\) 5.68373e11 0.338604 0.169302 0.985564i \(-0.445849\pi\)
0.169302 + 0.985564i \(0.445849\pi\)
\(168\) 1.72524e11 0.0994601
\(169\) 4.14679e11 0.231385
\(170\) −9.69695e11 −0.523801
\(171\) 2.85543e11 0.149346
\(172\) −3.18808e12 −1.61481
\(173\) −3.46675e11 −0.170086 −0.0850430 0.996377i \(-0.527103\pi\)
−0.0850430 + 0.996377i \(0.527103\pi\)
\(174\) −4.91352e11 −0.233546
\(175\) −1.55107e12 −0.714370
\(176\) 3.67649e12 1.64102
\(177\) 1.09449e11 0.0473541
\(178\) 2.78269e12 1.16723
\(179\) −1.84659e12 −0.751068 −0.375534 0.926809i \(-0.622541\pi\)
−0.375534 + 0.926809i \(0.622541\pi\)
\(180\) −7.35405e10 −0.0290087
\(181\) 1.69842e12 0.649849 0.324925 0.945740i \(-0.394661\pi\)
0.324925 + 0.945740i \(0.394661\pi\)
\(182\) 3.05752e12 1.13495
\(183\) −1.97671e12 −0.711971
\(184\) −7.41310e9 −0.00259121
\(185\) 4.82938e11 0.163850
\(186\) −1.00090e11 −0.0329661
\(187\) 9.04842e12 2.89364
\(188\) 3.11524e12 0.967437
\(189\) 2.62306e12 0.791168
\(190\) −8.39633e11 −0.246005
\(191\) 6.53577e12 1.86043 0.930215 0.367016i \(-0.119621\pi\)
0.930215 + 0.367016i \(0.119621\pi\)
\(192\) 2.56774e12 0.710222
\(193\) 2.24825e12 0.604338 0.302169 0.953254i \(-0.402289\pi\)
0.302169 + 0.953254i \(0.402289\pi\)
\(194\) −4.61004e12 −1.20447
\(195\) −7.87155e11 −0.199926
\(196\) −1.61964e12 −0.399955
\(197\) 4.50505e12 1.08177 0.540885 0.841097i \(-0.318089\pi\)
0.540885 + 0.841097i \(0.318089\pi\)
\(198\) 1.45415e12 0.339587
\(199\) −4.83401e12 −1.09803 −0.549017 0.835811i \(-0.684998\pi\)
−0.549017 + 0.835811i \(0.684998\pi\)
\(200\) 6.36852e11 0.140726
\(201\) 1.48221e12 0.318662
\(202\) −5.41827e12 −1.13352
\(203\) 6.77899e11 0.138018
\(204\) 7.95814e12 1.57705
\(205\) 1.01116e12 0.195063
\(206\) −1.24721e13 −2.34246
\(207\) −1.59364e10 −0.00291444
\(208\) −6.82324e12 −1.21519
\(209\) 7.83479e12 1.35901
\(210\) −1.09058e12 −0.184269
\(211\) −1.10099e13 −1.81229 −0.906146 0.422964i \(-0.860990\pi\)
−0.906146 + 0.422964i \(0.860990\pi\)
\(212\) 4.20966e12 0.675150
\(213\) −1.08494e13 −1.69558
\(214\) −3.90886e12 −0.595353
\(215\) −2.39959e12 −0.356226
\(216\) −1.07700e12 −0.155854
\(217\) 1.38090e11 0.0194820
\(218\) 1.03144e13 1.41884
\(219\) 6.96998e12 0.934951
\(220\) −2.01782e12 −0.263972
\(221\) −1.67931e13 −2.14276
\(222\) −8.39871e12 −1.04537
\(223\) −5.53451e12 −0.672051 −0.336026 0.941853i \(-0.609083\pi\)
−0.336026 + 0.941853i \(0.609083\pi\)
\(224\) −8.53492e12 −1.01120
\(225\) 1.36908e12 0.158280
\(226\) 6.93673e12 0.782634
\(227\) −4.70942e12 −0.518592 −0.259296 0.965798i \(-0.583490\pi\)
−0.259296 + 0.965798i \(0.583490\pi\)
\(228\) 6.89074e12 0.740669
\(229\) −4.06336e12 −0.426374 −0.213187 0.977011i \(-0.568384\pi\)
−0.213187 + 0.977011i \(0.568384\pi\)
\(230\) 4.68607e10 0.00480072
\(231\) 1.01765e13 1.01796
\(232\) −2.78337e11 −0.0271886
\(233\) 1.96315e13 1.87282 0.936411 0.350906i \(-0.114126\pi\)
0.936411 + 0.350906i \(0.114126\pi\)
\(234\) −2.69878e12 −0.251466
\(235\) 2.34476e12 0.213415
\(236\) −5.20703e11 −0.0462993
\(237\) 1.51796e13 1.31869
\(238\) −2.32664e13 −1.97495
\(239\) 1.39900e13 1.16046 0.580231 0.814452i \(-0.302962\pi\)
0.580231 + 0.814452i \(0.302962\pi\)
\(240\) 2.43377e12 0.197296
\(241\) −1.44074e13 −1.14154 −0.570772 0.821109i \(-0.693356\pi\)
−0.570772 + 0.821109i \(0.693356\pi\)
\(242\) 2.21317e13 1.71408
\(243\) −4.30322e12 −0.325806
\(244\) 9.40423e12 0.696112
\(245\) −1.21907e12 −0.0882295
\(246\) −1.75850e13 −1.24451
\(247\) −1.45407e13 −1.00636
\(248\) −5.66980e10 −0.00383781
\(249\) −4.91943e12 −0.325700
\(250\) −8.21427e12 −0.531985
\(251\) −2.15745e13 −1.36689 −0.683446 0.730001i \(-0.739520\pi\)
−0.683446 + 0.730001i \(0.739520\pi\)
\(252\) −1.76450e12 −0.109375
\(253\) −4.37267e11 −0.0265206
\(254\) −2.56274e13 −1.52097
\(255\) 5.98990e12 0.347895
\(256\) 2.07194e13 1.17776
\(257\) 2.02393e13 1.12607 0.563034 0.826434i \(-0.309634\pi\)
0.563034 + 0.826434i \(0.309634\pi\)
\(258\) 4.17310e13 2.27274
\(259\) 1.15874e13 0.617783
\(260\) 3.74489e12 0.195473
\(261\) −5.98360e11 −0.0305802
\(262\) −5.99108e12 −0.299811
\(263\) 1.12028e13 0.548997 0.274499 0.961587i \(-0.411488\pi\)
0.274499 + 0.961587i \(0.411488\pi\)
\(264\) −4.17833e12 −0.200531
\(265\) 3.16851e12 0.148937
\(266\) −2.01458e13 −0.927544
\(267\) −1.71890e13 −0.775242
\(268\) −7.05162e12 −0.311564
\(269\) −1.31186e13 −0.567871 −0.283935 0.958843i \(-0.591640\pi\)
−0.283935 + 0.958843i \(0.591640\pi\)
\(270\) 6.80807e12 0.288751
\(271\) −1.61271e13 −0.670232 −0.335116 0.942177i \(-0.608775\pi\)
−0.335116 + 0.942177i \(0.608775\pi\)
\(272\) 5.19219e13 2.11457
\(273\) −1.88866e13 −0.753806
\(274\) −1.92034e13 −0.751189
\(275\) 3.75651e13 1.44031
\(276\) −3.84579e11 −0.0144539
\(277\) 3.78738e13 1.39540 0.697702 0.716388i \(-0.254206\pi\)
0.697702 + 0.716388i \(0.254206\pi\)
\(278\) 3.75892e13 1.35774
\(279\) −1.21887e11 −0.00431654
\(280\) −6.17785e11 −0.0214520
\(281\) −5.07029e12 −0.172643 −0.0863214 0.996267i \(-0.527511\pi\)
−0.0863214 + 0.996267i \(0.527511\pi\)
\(282\) −4.07775e13 −1.36160
\(283\) −5.45868e13 −1.78757 −0.893783 0.448500i \(-0.851958\pi\)
−0.893783 + 0.448500i \(0.851958\pi\)
\(284\) 5.16161e13 1.65781
\(285\) 5.18649e12 0.163391
\(286\) −7.40495e13 −2.28828
\(287\) 2.42614e13 0.735471
\(288\) 7.53350e12 0.224047
\(289\) 9.35159e13 2.72865
\(290\) 1.75946e12 0.0503722
\(291\) 2.84767e13 0.799978
\(292\) −3.31597e13 −0.914125
\(293\) −3.12899e13 −0.846511 −0.423256 0.906010i \(-0.639113\pi\)
−0.423256 + 0.906010i \(0.639113\pi\)
\(294\) 2.12006e13 0.562909
\(295\) −3.91921e11 −0.0102136
\(296\) −4.75763e12 −0.121699
\(297\) −6.35275e13 −1.59515
\(298\) −7.39869e13 −1.82375
\(299\) 8.11529e11 0.0196387
\(300\) 3.30388e13 0.784977
\(301\) −5.75746e13 −1.34312
\(302\) 2.87423e13 0.658390
\(303\) 3.34692e13 0.752854
\(304\) 4.49578e13 0.993116
\(305\) 7.07834e12 0.153561
\(306\) 2.05365e13 0.437581
\(307\) −2.08032e12 −0.0435381 −0.0217691 0.999763i \(-0.506930\pi\)
−0.0217691 + 0.999763i \(0.506930\pi\)
\(308\) −4.84146e13 −0.995285
\(309\) 7.70416e13 1.55580
\(310\) 3.58407e11 0.00711029
\(311\) 3.53426e13 0.688837 0.344418 0.938816i \(-0.388076\pi\)
0.344418 + 0.938816i \(0.388076\pi\)
\(312\) 7.75461e12 0.148494
\(313\) 2.98830e13 0.562252 0.281126 0.959671i \(-0.409292\pi\)
0.281126 + 0.959671i \(0.409292\pi\)
\(314\) 2.80036e13 0.517726
\(315\) −1.32809e12 −0.0241280
\(316\) −7.22170e13 −1.28932
\(317\) −4.25262e13 −0.746157 −0.373079 0.927800i \(-0.621698\pi\)
−0.373079 + 0.927800i \(0.621698\pi\)
\(318\) −5.51032e13 −0.950228
\(319\) −1.64179e13 −0.278272
\(320\) −9.19472e12 −0.153184
\(321\) 2.41454e13 0.395418
\(322\) 1.12435e12 0.0181007
\(323\) 1.10648e14 1.75118
\(324\) −4.64152e13 −0.722209
\(325\) −6.97176e13 −1.06656
\(326\) −1.10805e14 −1.66672
\(327\) −6.37129e13 −0.942356
\(328\) −9.96143e12 −0.144882
\(329\) 5.62592e13 0.804666
\(330\) 2.64126e13 0.371522
\(331\) 3.15763e12 0.0436825 0.0218412 0.999761i \(-0.493047\pi\)
0.0218412 + 0.999761i \(0.493047\pi\)
\(332\) 2.34042e13 0.318445
\(333\) −1.02278e13 −0.136880
\(334\) 3.53950e13 0.465947
\(335\) −5.30758e12 −0.0687307
\(336\) 5.83948e13 0.743889
\(337\) −6.97371e13 −0.873976 −0.436988 0.899467i \(-0.643955\pi\)
−0.436988 + 0.899467i \(0.643955\pi\)
\(338\) 2.58239e13 0.318405
\(339\) −4.28489e13 −0.519806
\(340\) −2.84970e13 −0.340146
\(341\) −3.34437e12 −0.0392794
\(342\) 1.77820e13 0.205512
\(343\) −9.46009e13 −1.07591
\(344\) 2.36394e13 0.264585
\(345\) −2.89463e11 −0.00318852
\(346\) −2.15889e13 −0.234052
\(347\) −1.18515e14 −1.26462 −0.632309 0.774716i \(-0.717893\pi\)
−0.632309 + 0.774716i \(0.717893\pi\)
\(348\) −1.44396e13 −0.151660
\(349\) −3.54876e13 −0.366890 −0.183445 0.983030i \(-0.558725\pi\)
−0.183445 + 0.983030i \(0.558725\pi\)
\(350\) −9.65921e13 −0.983031
\(351\) 1.17901e14 1.18122
\(352\) 2.06706e14 2.03877
\(353\) −1.48557e14 −1.44256 −0.721278 0.692645i \(-0.756445\pi\)
−0.721278 + 0.692645i \(0.756445\pi\)
\(354\) 6.81585e12 0.0651631
\(355\) 3.88502e13 0.365711
\(356\) 8.17766e13 0.757973
\(357\) 1.43719e14 1.31171
\(358\) −1.14995e14 −1.03353
\(359\) −1.39595e14 −1.23552 −0.617760 0.786367i \(-0.711960\pi\)
−0.617760 + 0.786367i \(0.711960\pi\)
\(360\) 5.45299e11 0.00475304
\(361\) −2.06830e13 −0.177551
\(362\) 1.05768e14 0.894246
\(363\) −1.36710e14 −1.13845
\(364\) 8.98532e13 0.737014
\(365\) −2.49585e13 −0.201655
\(366\) −1.23098e14 −0.979731
\(367\) −2.38895e14 −1.87303 −0.936514 0.350631i \(-0.885967\pi\)
−0.936514 + 0.350631i \(0.885967\pi\)
\(368\) −2.50914e12 −0.0193803
\(369\) −2.14148e13 −0.162955
\(370\) 3.00746e13 0.225471
\(371\) 7.60238e13 0.561556
\(372\) −2.94139e12 −0.0214075
\(373\) −3.21648e13 −0.230665 −0.115333 0.993327i \(-0.536793\pi\)
−0.115333 + 0.993327i \(0.536793\pi\)
\(374\) 5.63484e14 3.98188
\(375\) 5.07404e13 0.353331
\(376\) −2.30993e13 −0.158513
\(377\) 3.04702e13 0.206062
\(378\) 1.63350e14 1.08871
\(379\) 1.37788e14 0.905099 0.452550 0.891739i \(-0.350515\pi\)
0.452550 + 0.891739i \(0.350515\pi\)
\(380\) −2.46748e13 −0.159751
\(381\) 1.58303e14 1.01019
\(382\) 4.07011e14 2.56010
\(383\) −1.73711e14 −1.07704 −0.538522 0.842611i \(-0.681017\pi\)
−0.538522 + 0.842611i \(0.681017\pi\)
\(384\) −4.35411e13 −0.266120
\(385\) −3.64405e13 −0.219559
\(386\) 1.40008e14 0.831618
\(387\) 5.08193e13 0.297590
\(388\) −1.35478e14 −0.782158
\(389\) 2.34150e14 1.33282 0.666411 0.745585i \(-0.267830\pi\)
0.666411 + 0.745585i \(0.267830\pi\)
\(390\) −4.90195e13 −0.275115
\(391\) −6.17538e12 −0.0341737
\(392\) 1.20096e13 0.0655321
\(393\) 3.70075e13 0.199127
\(394\) 2.80549e14 1.48860
\(395\) −5.43560e13 −0.284422
\(396\) 4.27340e13 0.220521
\(397\) −1.79333e14 −0.912669 −0.456334 0.889808i \(-0.650838\pi\)
−0.456334 + 0.889808i \(0.650838\pi\)
\(398\) −3.01035e14 −1.51098
\(399\) 1.24442e14 0.616051
\(400\) 2.15557e14 1.05253
\(401\) −3.03065e14 −1.45963 −0.729813 0.683646i \(-0.760393\pi\)
−0.729813 + 0.683646i \(0.760393\pi\)
\(402\) 9.23035e13 0.438506
\(403\) 6.20686e12 0.0290867
\(404\) −1.59230e14 −0.736083
\(405\) −3.49356e13 −0.159318
\(406\) 4.22157e13 0.189925
\(407\) −2.80632e14 −1.24557
\(408\) −5.90092e13 −0.258398
\(409\) 1.52684e14 0.659651 0.329825 0.944042i \(-0.393010\pi\)
0.329825 + 0.944042i \(0.393010\pi\)
\(410\) 6.29696e13 0.268423
\(411\) 1.18621e14 0.498921
\(412\) −3.66526e14 −1.52114
\(413\) −9.40356e12 −0.0385094
\(414\) −9.92432e11 −0.00401050
\(415\) 1.76158e13 0.0702486
\(416\) −3.83627e14 −1.50972
\(417\) −2.32192e14 −0.901777
\(418\) 4.87906e14 1.87011
\(419\) −2.74751e14 −1.03935 −0.519676 0.854363i \(-0.673947\pi\)
−0.519676 + 0.854363i \(0.673947\pi\)
\(420\) −3.20496e13 −0.119661
\(421\) −9.97837e13 −0.367712 −0.183856 0.982953i \(-0.558858\pi\)
−0.183856 + 0.982953i \(0.558858\pi\)
\(422\) −6.85632e14 −2.49386
\(423\) −4.96582e13 −0.178287
\(424\) −3.12144e13 −0.110622
\(425\) 5.30520e14 1.85593
\(426\) −6.75640e14 −2.33326
\(427\) 1.69834e14 0.578991
\(428\) −1.14872e14 −0.386610
\(429\) 4.57411e14 1.51982
\(430\) −1.49433e14 −0.490196
\(431\) −9.82326e13 −0.318149 −0.159075 0.987267i \(-0.550851\pi\)
−0.159075 + 0.987267i \(0.550851\pi\)
\(432\) −3.64535e14 −1.16568
\(433\) 1.34165e14 0.423601 0.211800 0.977313i \(-0.432067\pi\)
0.211800 + 0.977313i \(0.432067\pi\)
\(434\) 8.59945e12 0.0268088
\(435\) −1.08684e13 −0.0334560
\(436\) 3.03115e14 0.921364
\(437\) −5.34710e12 −0.0160498
\(438\) 4.34051e14 1.28657
\(439\) 1.46616e14 0.429168 0.214584 0.976705i \(-0.431160\pi\)
0.214584 + 0.976705i \(0.431160\pi\)
\(440\) 1.49620e13 0.0432514
\(441\) 2.58178e13 0.0737066
\(442\) −1.04578e15 −2.94861
\(443\) −1.21156e13 −0.0337385 −0.0168693 0.999858i \(-0.505370\pi\)
−0.0168693 + 0.999858i \(0.505370\pi\)
\(444\) −2.46818e14 −0.678844
\(445\) 6.15513e13 0.167208
\(446\) −3.44658e14 −0.924797
\(447\) 4.57024e14 1.21129
\(448\) −2.20614e14 −0.577569
\(449\) 4.14075e14 1.07084 0.535419 0.844586i \(-0.320154\pi\)
0.535419 + 0.844586i \(0.320154\pi\)
\(450\) 8.52587e13 0.217806
\(451\) −5.87582e14 −1.48285
\(452\) 2.03854e14 0.508227
\(453\) −1.77544e14 −0.437286
\(454\) −2.93276e14 −0.713624
\(455\) 6.76304e13 0.162584
\(456\) −5.10945e13 −0.121358
\(457\) 6.86418e14 1.61083 0.805415 0.592711i \(-0.201942\pi\)
0.805415 + 0.592711i \(0.201942\pi\)
\(458\) −2.53043e14 −0.586725
\(459\) −8.97178e14 −2.05546
\(460\) 1.37712e12 0.00311749
\(461\) 8.82601e14 1.97428 0.987142 0.159848i \(-0.0511003\pi\)
0.987142 + 0.159848i \(0.0511003\pi\)
\(462\) 6.33732e14 1.40080
\(463\) −3.93909e14 −0.860399 −0.430200 0.902734i \(-0.641557\pi\)
−0.430200 + 0.902734i \(0.641557\pi\)
\(464\) −9.42097e13 −0.203351
\(465\) −2.21392e12 −0.00472248
\(466\) 1.22254e15 2.57715
\(467\) −4.51731e13 −0.0941102 −0.0470551 0.998892i \(-0.514984\pi\)
−0.0470551 + 0.998892i \(0.514984\pi\)
\(468\) −7.93106e13 −0.163297
\(469\) −1.27348e14 −0.259143
\(470\) 1.46019e14 0.293677
\(471\) −1.72981e14 −0.343861
\(472\) 3.86099e12 0.00758608
\(473\) 1.39439e15 2.70799
\(474\) 9.45299e14 1.81463
\(475\) 4.59363e14 0.871649
\(476\) −6.83743e14 −1.28249
\(477\) −6.71038e13 −0.124422
\(478\) 8.71221e14 1.59689
\(479\) −4.93799e14 −0.894756 −0.447378 0.894345i \(-0.647642\pi\)
−0.447378 + 0.894345i \(0.647642\pi\)
\(480\) 1.36836e14 0.245116
\(481\) 5.20829e14 0.922353
\(482\) −8.97213e14 −1.57086
\(483\) −6.94525e12 −0.0120220
\(484\) 6.50397e14 1.11309
\(485\) −1.01971e14 −0.172543
\(486\) −2.67980e14 −0.448336
\(487\) 5.62413e14 0.930350 0.465175 0.885219i \(-0.345991\pi\)
0.465175 + 0.885219i \(0.345991\pi\)
\(488\) −6.97319e13 −0.114057
\(489\) 6.84454e14 1.10699
\(490\) −7.59165e13 −0.121411
\(491\) −6.06349e14 −0.958902 −0.479451 0.877569i \(-0.659164\pi\)
−0.479451 + 0.877569i \(0.659164\pi\)
\(492\) −5.16782e14 −0.808163
\(493\) −2.31865e14 −0.358572
\(494\) −9.05511e14 −1.38483
\(495\) 3.21649e13 0.0486467
\(496\) −1.91907e13 −0.0287040
\(497\) 9.32154e14 1.37888
\(498\) −3.06354e14 −0.448190
\(499\) −9.66448e14 −1.39838 −0.699191 0.714935i \(-0.746456\pi\)
−0.699191 + 0.714935i \(0.746456\pi\)
\(500\) −2.41398e14 −0.345460
\(501\) −2.18639e14 −0.309470
\(502\) −1.34353e15 −1.88095
\(503\) 5.10073e14 0.706331 0.353166 0.935561i \(-0.385105\pi\)
0.353166 + 0.935561i \(0.385105\pi\)
\(504\) 1.30837e13 0.0179210
\(505\) −1.19849e14 −0.162379
\(506\) −2.72305e13 −0.0364946
\(507\) −1.59517e14 −0.211476
\(508\) −7.53128e14 −0.987685
\(509\) −5.21410e12 −0.00676443 −0.00338222 0.999994i \(-0.501077\pi\)
−0.00338222 + 0.999994i \(0.501077\pi\)
\(510\) 3.73017e14 0.478732
\(511\) −5.98843e14 −0.760323
\(512\) 1.05847e15 1.32952
\(513\) −7.76842e14 −0.965356
\(514\) 1.26039e15 1.54956
\(515\) −2.75876e14 −0.335562
\(516\) 1.22637e15 1.47587
\(517\) −1.36253e15 −1.62236
\(518\) 7.21596e14 0.850120
\(519\) 1.33357e14 0.155452
\(520\) −2.77682e13 −0.0320280
\(521\) 4.21554e14 0.481112 0.240556 0.970635i \(-0.422670\pi\)
0.240556 + 0.970635i \(0.422670\pi\)
\(522\) −3.72625e13 −0.0420808
\(523\) 8.60935e14 0.962080 0.481040 0.876699i \(-0.340259\pi\)
0.481040 + 0.876699i \(0.340259\pi\)
\(524\) −1.76064e14 −0.194692
\(525\) 5.96659e14 0.652905
\(526\) 6.97648e14 0.755465
\(527\) −4.72314e13 −0.0506142
\(528\) −1.41425e15 −1.49982
\(529\) −9.52511e14 −0.999687
\(530\) 1.97317e14 0.204950
\(531\) 8.30022e12 0.00853238
\(532\) −5.92035e14 −0.602329
\(533\) 1.09050e15 1.09806
\(534\) −1.07043e15 −1.06680
\(535\) −8.64614e13 −0.0852858
\(536\) 5.22874e13 0.0510494
\(537\) 7.10337e14 0.686446
\(538\) −8.16951e14 −0.781436
\(539\) 7.08392e14 0.670711
\(540\) 2.00073e14 0.187509
\(541\) −2.89790e14 −0.268842 −0.134421 0.990924i \(-0.542918\pi\)
−0.134421 + 0.990924i \(0.542918\pi\)
\(542\) −1.00430e15 −0.922293
\(543\) −6.53339e14 −0.593936
\(544\) 2.91923e15 2.62709
\(545\) 2.28147e14 0.203252
\(546\) −1.17615e15 −1.03730
\(547\) 2.01239e15 1.75704 0.878520 0.477705i \(-0.158531\pi\)
0.878520 + 0.477705i \(0.158531\pi\)
\(548\) −5.64340e14 −0.487807
\(549\) −1.49907e14 −0.128285
\(550\) 2.33934e15 1.98198
\(551\) −2.00766e14 −0.168405
\(552\) 2.85163e12 0.00236826
\(553\) −1.30419e15 −1.07239
\(554\) 2.35857e15 1.92019
\(555\) −1.85774e14 −0.149752
\(556\) 1.10466e15 0.881689
\(557\) 1.45243e15 1.14787 0.573933 0.818902i \(-0.305417\pi\)
0.573933 + 0.818902i \(0.305417\pi\)
\(558\) −7.59046e12 −0.00593991
\(559\) −2.58786e15 −2.00529
\(560\) −2.09104e14 −0.160446
\(561\) −3.48070e15 −2.64466
\(562\) −3.15749e14 −0.237571
\(563\) −1.90166e15 −1.41689 −0.708447 0.705764i \(-0.750604\pi\)
−0.708447 + 0.705764i \(0.750604\pi\)
\(564\) −1.19835e15 −0.884198
\(565\) 1.53436e14 0.112114
\(566\) −3.39935e15 −2.45984
\(567\) −8.38229e14 −0.600697
\(568\) −3.82731e14 −0.271630
\(569\) 1.27765e15 0.898041 0.449020 0.893522i \(-0.351773\pi\)
0.449020 + 0.893522i \(0.351773\pi\)
\(570\) 3.22985e14 0.224839
\(571\) 8.73926e14 0.602527 0.301263 0.953541i \(-0.402592\pi\)
0.301263 + 0.953541i \(0.402592\pi\)
\(572\) −2.17614e15 −1.48596
\(573\) −2.51414e15 −1.70036
\(574\) 1.51086e15 1.01207
\(575\) −2.56375e13 −0.0170099
\(576\) 1.94729e14 0.127969
\(577\) 1.90100e15 1.23741 0.618706 0.785623i \(-0.287657\pi\)
0.618706 + 0.785623i \(0.287657\pi\)
\(578\) 5.82364e15 3.75484
\(579\) −8.64846e14 −0.552340
\(580\) 5.17064e13 0.0327107
\(581\) 4.22665e14 0.264867
\(582\) 1.77337e15 1.10083
\(583\) −1.84121e15 −1.13221
\(584\) 2.45878e14 0.149778
\(585\) −5.96952e13 −0.0360232
\(586\) −1.94856e15 −1.16487
\(587\) −5.70371e14 −0.337791 −0.168895 0.985634i \(-0.554020\pi\)
−0.168895 + 0.985634i \(0.554020\pi\)
\(588\) 6.23035e14 0.365542
\(589\) −4.08964e13 −0.0237712
\(590\) −2.44066e13 −0.0140547
\(591\) −1.73298e15 −0.988693
\(592\) −1.61033e15 −0.910219
\(593\) 6.76252e14 0.378711 0.189355 0.981909i \(-0.439360\pi\)
0.189355 + 0.981909i \(0.439360\pi\)
\(594\) −3.95613e15 −2.19505
\(595\) −5.14637e14 −0.282916
\(596\) −2.17430e15 −1.18431
\(597\) 1.85952e15 1.00356
\(598\) 5.05375e13 0.0270244
\(599\) −5.41473e14 −0.286899 −0.143449 0.989658i \(-0.545819\pi\)
−0.143449 + 0.989658i \(0.545819\pi\)
\(600\) −2.44981e14 −0.128617
\(601\) 2.86332e15 1.48957 0.744785 0.667305i \(-0.232552\pi\)
0.744785 + 0.667305i \(0.232552\pi\)
\(602\) −3.58542e15 −1.84825
\(603\) 1.12406e14 0.0574174
\(604\) 8.44666e14 0.427545
\(605\) 4.89538e14 0.245545
\(606\) 2.08427e15 1.03599
\(607\) 2.24665e15 1.10662 0.553310 0.832976i \(-0.313365\pi\)
0.553310 + 0.832976i \(0.313365\pi\)
\(608\) 2.52769e15 1.23383
\(609\) −2.60771e14 −0.126143
\(610\) 4.40799e14 0.211313
\(611\) 2.52874e15 1.20137
\(612\) 6.03518e14 0.284157
\(613\) −1.37966e15 −0.643783 −0.321891 0.946777i \(-0.604319\pi\)
−0.321891 + 0.946777i \(0.604319\pi\)
\(614\) −1.29551e14 −0.0599120
\(615\) −3.88969e14 −0.178280
\(616\) 3.58992e14 0.163076
\(617\) −1.77458e15 −0.798966 −0.399483 0.916741i \(-0.630810\pi\)
−0.399483 + 0.916741i \(0.630810\pi\)
\(618\) 4.79772e15 2.14091
\(619\) −6.71770e14 −0.297113 −0.148557 0.988904i \(-0.547463\pi\)
−0.148557 + 0.988904i \(0.547463\pi\)
\(620\) 1.05327e13 0.00461728
\(621\) 4.33563e13 0.0188386
\(622\) 2.20094e15 0.947895
\(623\) 1.47683e15 0.630445
\(624\) 2.62473e15 1.11063
\(625\) 2.10984e15 0.884933
\(626\) 1.86095e15 0.773705
\(627\) −3.01384e15 −1.24208
\(628\) 8.22957e14 0.336201
\(629\) −3.96328e15 −1.60500
\(630\) −8.27062e13 −0.0332021
\(631\) 3.94122e15 1.56845 0.784223 0.620479i \(-0.213062\pi\)
0.784223 + 0.620479i \(0.213062\pi\)
\(632\) 5.35486e14 0.211253
\(633\) 4.23521e15 1.65636
\(634\) −2.64829e15 −1.02677
\(635\) −5.66862e14 −0.217882
\(636\) −1.61935e15 −0.617059
\(637\) −1.31471e15 −0.496666
\(638\) −1.02241e15 −0.382925
\(639\) −8.22783e14 −0.305514
\(640\) 1.55915e14 0.0573980
\(641\) −2.71163e15 −0.989716 −0.494858 0.868974i \(-0.664780\pi\)
−0.494858 + 0.868974i \(0.664780\pi\)
\(642\) 1.50364e15 0.544128
\(643\) 1.11976e15 0.401757 0.200879 0.979616i \(-0.435620\pi\)
0.200879 + 0.979616i \(0.435620\pi\)
\(644\) 3.30421e13 0.0117542
\(645\) 9.23062e14 0.325576
\(646\) 6.89054e15 2.40976
\(647\) −5.20369e14 −0.180442 −0.0902210 0.995922i \(-0.528757\pi\)
−0.0902210 + 0.995922i \(0.528757\pi\)
\(648\) 3.44166e14 0.118333
\(649\) 2.27743e14 0.0776425
\(650\) −4.34162e15 −1.46767
\(651\) −5.31196e13 −0.0178057
\(652\) −3.25629e15 −1.08234
\(653\) 6.45444e14 0.212734 0.106367 0.994327i \(-0.466078\pi\)
0.106367 + 0.994327i \(0.466078\pi\)
\(654\) −3.96768e15 −1.29676
\(655\) −1.32519e14 −0.0429487
\(656\) −3.37168e15 −1.08361
\(657\) 5.28580e14 0.168462
\(658\) 3.50350e15 1.10729
\(659\) −4.90862e14 −0.153847 −0.0769236 0.997037i \(-0.524510\pi\)
−0.0769236 + 0.997037i \(0.524510\pi\)
\(660\) 7.76204e14 0.241259
\(661\) −1.13195e15 −0.348915 −0.174458 0.984665i \(-0.555817\pi\)
−0.174458 + 0.984665i \(0.555817\pi\)
\(662\) 1.96639e14 0.0601106
\(663\) 6.45987e15 1.95839
\(664\) −1.73541e14 −0.0521768
\(665\) −4.45611e14 −0.132873
\(666\) −6.36930e14 −0.188358
\(667\) 1.12049e13 0.00328637
\(668\) 1.04017e15 0.302577
\(669\) 2.12899e15 0.614227
\(670\) −3.30526e14 −0.0945790
\(671\) −4.11318e15 −1.16736
\(672\) 3.28317e15 0.924192
\(673\) −1.66789e15 −0.465676 −0.232838 0.972516i \(-0.574801\pi\)
−0.232838 + 0.972516i \(0.574801\pi\)
\(674\) −4.34283e15 −1.20266
\(675\) −3.72470e15 −1.02310
\(676\) 7.58901e14 0.206766
\(677\) 3.40687e15 0.920699 0.460349 0.887738i \(-0.347724\pi\)
0.460349 + 0.887738i \(0.347724\pi\)
\(678\) −2.66839e15 −0.715295
\(679\) −2.44665e15 −0.650560
\(680\) 2.11304e14 0.0557324
\(681\) 1.81160e15 0.473971
\(682\) −2.08268e14 −0.0540517
\(683\) 1.01334e15 0.260882 0.130441 0.991456i \(-0.458361\pi\)
0.130441 + 0.991456i \(0.458361\pi\)
\(684\) 5.22570e14 0.133455
\(685\) −4.24765e14 −0.107610
\(686\) −5.89121e15 −1.48055
\(687\) 1.56307e15 0.389688
\(688\) 8.00132e15 1.97891
\(689\) 3.41712e15 0.838405
\(690\) −1.80261e13 −0.00438766
\(691\) −3.43978e15 −0.830618 −0.415309 0.909680i \(-0.636327\pi\)
−0.415309 + 0.909680i \(0.636327\pi\)
\(692\) −6.34447e14 −0.151989
\(693\) 7.71748e14 0.183418
\(694\) −7.38041e15 −1.74022
\(695\) 8.31448e14 0.194500
\(696\) 1.07069e14 0.0248493
\(697\) −8.29823e15 −1.91076
\(698\) −2.20996e15 −0.504871
\(699\) −7.55175e15 −1.71168
\(700\) −2.83861e15 −0.638361
\(701\) −1.06049e15 −0.236622 −0.118311 0.992977i \(-0.537748\pi\)
−0.118311 + 0.992977i \(0.537748\pi\)
\(702\) 7.34223e15 1.62545
\(703\) −3.43170e15 −0.753797
\(704\) 5.34300e15 1.16449
\(705\) −9.01971e14 −0.195053
\(706\) −9.25130e15 −1.98507
\(707\) −2.87559e15 −0.612237
\(708\) 2.00301e14 0.0423156
\(709\) 2.55303e15 0.535181 0.267591 0.963533i \(-0.413773\pi\)
0.267591 + 0.963533i \(0.413773\pi\)
\(710\) 2.41937e15 0.503248
\(711\) 1.15117e15 0.237605
\(712\) −6.06369e14 −0.124193
\(713\) 2.28247e12 0.000463888 0
\(714\) 8.94999e15 1.80502
\(715\) −1.63793e15 −0.327802
\(716\) −3.37944e15 −0.671155
\(717\) −5.38161e15 −1.06061
\(718\) −8.69317e15 −1.70018
\(719\) 2.96226e15 0.574929 0.287464 0.957791i \(-0.407188\pi\)
0.287464 + 0.957791i \(0.407188\pi\)
\(720\) 1.84569e14 0.0355493
\(721\) −6.61923e15 −1.26521
\(722\) −1.28802e15 −0.244325
\(723\) 5.54217e15 1.04332
\(724\) 3.10826e15 0.580705
\(725\) −9.62603e14 −0.178479
\(726\) −8.51350e15 −1.56659
\(727\) 1.27741e15 0.233287 0.116643 0.993174i \(-0.462787\pi\)
0.116643 + 0.993174i \(0.462787\pi\)
\(728\) −6.66257e14 −0.120759
\(729\) 6.14818e15 1.10597
\(730\) −1.55428e15 −0.277493
\(731\) 1.96925e16 3.48944
\(732\) −3.61757e15 −0.636218
\(733\) 7.57379e15 1.32203 0.661015 0.750372i \(-0.270126\pi\)
0.661015 + 0.750372i \(0.270126\pi\)
\(734\) −1.48770e16 −2.57744
\(735\) 4.68944e14 0.0806381
\(736\) −1.41073e14 −0.0240777
\(737\) 3.08421e15 0.522483
\(738\) −1.33359e15 −0.224240
\(739\) −3.67278e15 −0.612986 −0.306493 0.951873i \(-0.599156\pi\)
−0.306493 + 0.951873i \(0.599156\pi\)
\(740\) 8.83820e14 0.146416
\(741\) 5.59343e15 0.919767
\(742\) 4.73433e15 0.772747
\(743\) 7.23474e15 1.17215 0.586077 0.810256i \(-0.300672\pi\)
0.586077 + 0.810256i \(0.300672\pi\)
\(744\) 2.18103e13 0.00350760
\(745\) −1.63654e15 −0.261257
\(746\) −2.00304e15 −0.317414
\(747\) −3.73073e14 −0.0586854
\(748\) 1.65594e16 2.58575
\(749\) −2.07451e15 −0.321563
\(750\) 3.15982e15 0.486212
\(751\) −2.47237e15 −0.377654 −0.188827 0.982010i \(-0.560469\pi\)
−0.188827 + 0.982010i \(0.560469\pi\)
\(752\) −7.81850e15 −1.18556
\(753\) 8.29914e15 1.24928
\(754\) 1.89751e15 0.283558
\(755\) 6.35760e14 0.0943159
\(756\) 4.80045e15 0.706988
\(757\) 1.07908e15 0.157771 0.0788854 0.996884i \(-0.474864\pi\)
0.0788854 + 0.996884i \(0.474864\pi\)
\(758\) 8.58066e15 1.24549
\(759\) 1.68206e14 0.0242388
\(760\) 1.82962e14 0.0261750
\(761\) 8.35973e15 1.18734 0.593672 0.804707i \(-0.297678\pi\)
0.593672 + 0.804707i \(0.297678\pi\)
\(762\) 9.85822e15 1.39010
\(763\) 5.47406e15 0.766345
\(764\) 1.19611e16 1.66248
\(765\) 4.54254e14 0.0626846
\(766\) −1.08177e16 −1.48210
\(767\) −4.22671e14 −0.0574947
\(768\) −7.97022e15 −1.07643
\(769\) 8.47458e15 1.13638 0.568190 0.822898i \(-0.307644\pi\)
0.568190 + 0.822898i \(0.307644\pi\)
\(770\) −2.26931e15 −0.302130
\(771\) −7.78556e15 −1.02918
\(772\) 4.11451e15 0.540036
\(773\) −1.35997e16 −1.77232 −0.886159 0.463381i \(-0.846636\pi\)
−0.886159 + 0.463381i \(0.846636\pi\)
\(774\) 3.16474e15 0.409508
\(775\) −1.96085e14 −0.0251932
\(776\) 1.00456e15 0.128156
\(777\) −4.45737e15 −0.564629
\(778\) 1.45816e16 1.83407
\(779\) −7.18522e15 −0.897395
\(780\) −1.44057e15 −0.178654
\(781\) −2.25757e16 −2.78010
\(782\) −3.84568e14 −0.0470257
\(783\) 1.62788e15 0.197667
\(784\) 4.06491e15 0.490132
\(785\) 6.19420e14 0.0741655
\(786\) 2.30462e15 0.274015
\(787\) 6.33252e15 0.747680 0.373840 0.927493i \(-0.378041\pi\)
0.373840 + 0.927493i \(0.378041\pi\)
\(788\) 8.24465e15 0.966670
\(789\) −4.30944e15 −0.501761
\(790\) −3.38499e15 −0.391388
\(791\) 3.68147e15 0.422718
\(792\) −3.16870e14 −0.0361321
\(793\) 7.63370e15 0.864436
\(794\) −1.11679e16 −1.25591
\(795\) −1.21885e15 −0.136122
\(796\) −8.84669e15 −0.981203
\(797\) −1.53574e16 −1.69159 −0.845796 0.533507i \(-0.820874\pi\)
−0.845796 + 0.533507i \(0.820874\pi\)
\(798\) 7.74956e15 0.847737
\(799\) −1.92426e16 −2.09053
\(800\) 1.21194e16 1.30763
\(801\) −1.30355e15 −0.139685
\(802\) −1.88732e16 −2.00857
\(803\) 1.45033e16 1.53296
\(804\) 2.71258e15 0.284757
\(805\) 2.48700e13 0.00259297
\(806\) 3.86528e14 0.0400256
\(807\) 5.04639e15 0.519010
\(808\) 1.18068e15 0.120606
\(809\) −8.68168e15 −0.880819 −0.440410 0.897797i \(-0.645167\pi\)
−0.440410 + 0.897797i \(0.645167\pi\)
\(810\) −2.17559e15 −0.219235
\(811\) −1.24520e16 −1.24630 −0.623151 0.782102i \(-0.714148\pi\)
−0.623151 + 0.782102i \(0.714148\pi\)
\(812\) 1.24062e15 0.123333
\(813\) 6.20368e15 0.612564
\(814\) −1.74762e16 −1.71401
\(815\) −2.45093e15 −0.238762
\(816\) −1.99730e16 −1.93263
\(817\) 1.70512e16 1.63883
\(818\) 9.50827e15 0.907733
\(819\) −1.43230e15 −0.135823
\(820\) 1.85052e15 0.174309
\(821\) 1.60834e16 1.50484 0.752420 0.658684i \(-0.228887\pi\)
0.752420 + 0.658684i \(0.228887\pi\)
\(822\) 7.38704e15 0.686555
\(823\) 9.49861e15 0.876922 0.438461 0.898750i \(-0.355524\pi\)
0.438461 + 0.898750i \(0.355524\pi\)
\(824\) 2.71777e15 0.249238
\(825\) −1.44504e16 −1.31638
\(826\) −5.85601e14 −0.0529921
\(827\) 2.12819e15 0.191306 0.0956532 0.995415i \(-0.469506\pi\)
0.0956532 + 0.995415i \(0.469506\pi\)
\(828\) −2.91652e13 −0.00260434
\(829\) −1.90510e15 −0.168993 −0.0844965 0.996424i \(-0.526928\pi\)
−0.0844965 + 0.996424i \(0.526928\pi\)
\(830\) 1.09701e15 0.0966678
\(831\) −1.45691e16 −1.27534
\(832\) −9.91614e15 −0.862312
\(833\) 1.00044e16 0.864258
\(834\) −1.44596e16 −1.24092
\(835\) 7.82914e14 0.0667481
\(836\) 1.43384e16 1.21441
\(837\) 3.31604e14 0.0279017
\(838\) −1.71100e16 −1.43023
\(839\) 2.03621e15 0.169095 0.0845477 0.996419i \(-0.473055\pi\)
0.0845477 + 0.996419i \(0.473055\pi\)
\(840\) 2.37646e14 0.0196063
\(841\) 4.20707e14 0.0344828
\(842\) −6.21396e15 −0.506002
\(843\) 1.95041e15 0.157788
\(844\) −2.01491e16 −1.61946
\(845\) 5.71207e14 0.0456122
\(846\) −3.09243e15 −0.245337
\(847\) 1.17457e16 0.925810
\(848\) −1.05652e16 −0.827375
\(849\) 2.09981e16 1.63376
\(850\) 3.30378e16 2.55392
\(851\) 1.91526e14 0.0147101
\(852\) −1.98554e16 −1.51517
\(853\) −1.08461e16 −0.822343 −0.411172 0.911558i \(-0.634880\pi\)
−0.411172 + 0.911558i \(0.634880\pi\)
\(854\) 1.05763e16 0.796739
\(855\) 3.93326e14 0.0294401
\(856\) 8.51770e14 0.0633456
\(857\) 2.23715e16 1.65311 0.826553 0.562859i \(-0.190299\pi\)
0.826553 + 0.562859i \(0.190299\pi\)
\(858\) 2.84850e16 2.09139
\(859\) 1.15245e16 0.840738 0.420369 0.907353i \(-0.361901\pi\)
0.420369 + 0.907353i \(0.361901\pi\)
\(860\) −4.39147e15 −0.318324
\(861\) −9.33274e15 −0.672190
\(862\) −6.11737e15 −0.437799
\(863\) −6.38998e15 −0.454402 −0.227201 0.973848i \(-0.572957\pi\)
−0.227201 + 0.973848i \(0.572957\pi\)
\(864\) −2.04955e16 −1.44821
\(865\) −4.77533e14 −0.0335286
\(866\) 8.35505e15 0.582909
\(867\) −3.59732e16 −2.49387
\(868\) 2.52717e14 0.0174091
\(869\) 3.15860e16 2.16215
\(870\) −6.76821e14 −0.0460382
\(871\) −5.72402e15 −0.386902
\(872\) −2.24758e15 −0.150964
\(873\) 2.15958e15 0.144142
\(874\) −3.32987e14 −0.0220859
\(875\) −4.35949e15 −0.287337
\(876\) 1.27557e16 0.835472
\(877\) −1.02607e16 −0.667849 −0.333924 0.942600i \(-0.608373\pi\)
−0.333924 + 0.942600i \(0.608373\pi\)
\(878\) 9.13044e15 0.590571
\(879\) 1.20364e16 0.773676
\(880\) 5.06424e15 0.323489
\(881\) −7.21654e15 −0.458101 −0.229051 0.973415i \(-0.573562\pi\)
−0.229051 + 0.973415i \(0.573562\pi\)
\(882\) 1.60778e15 0.101426
\(883\) 8.51122e15 0.533591 0.266795 0.963753i \(-0.414035\pi\)
0.266795 + 0.963753i \(0.414035\pi\)
\(884\) −3.07329e16 −1.91477
\(885\) 1.50762e14 0.00933478
\(886\) −7.54494e14 −0.0464269
\(887\) −1.37601e16 −0.841477 −0.420739 0.907182i \(-0.638229\pi\)
−0.420739 + 0.907182i \(0.638229\pi\)
\(888\) 1.83014e15 0.111228
\(889\) −1.36010e16 −0.821507
\(890\) 3.83307e15 0.230092
\(891\) 2.03009e16 1.21112
\(892\) −1.01287e16 −0.600545
\(893\) −1.66616e16 −0.981825
\(894\) 2.84609e16 1.66683
\(895\) −2.54362e15 −0.148056
\(896\) 3.74094e15 0.216415
\(897\) −3.12175e14 −0.0179490
\(898\) 2.57862e16 1.47356
\(899\) 8.56991e13 0.00486741
\(900\) 2.50555e15 0.141439
\(901\) −2.60027e16 −1.45892
\(902\) −3.65913e16 −2.04052
\(903\) 2.21475e16 1.22756
\(904\) −1.51157e15 −0.0832723
\(905\) 2.33952e15 0.128103
\(906\) −1.10564e16 −0.601741
\(907\) −1.86017e15 −0.100626 −0.0503132 0.998733i \(-0.516022\pi\)
−0.0503132 + 0.998733i \(0.516022\pi\)
\(908\) −8.61868e15 −0.463413
\(909\) 2.53819e15 0.135651
\(910\) 4.21164e15 0.223729
\(911\) 1.78581e15 0.0942939 0.0471469 0.998888i \(-0.484987\pi\)
0.0471469 + 0.998888i \(0.484987\pi\)
\(912\) −1.72941e16 −0.907667
\(913\) −1.02364e16 −0.534023
\(914\) 4.27462e16 2.21663
\(915\) −2.72286e15 −0.140349
\(916\) −7.43633e15 −0.381008
\(917\) −3.17959e15 −0.161935
\(918\) −5.58711e16 −2.82848
\(919\) −1.41640e15 −0.0712770 −0.0356385 0.999365i \(-0.511346\pi\)
−0.0356385 + 0.999365i \(0.511346\pi\)
\(920\) −1.02113e13 −0.000510797 0
\(921\) 8.00247e14 0.0397920
\(922\) 5.49634e16 2.71677
\(923\) 4.18984e16 2.05868
\(924\) 1.86239e16 0.909649
\(925\) −1.64538e16 −0.798891
\(926\) −2.45304e16 −1.18398
\(927\) 5.84258e15 0.280328
\(928\) −5.29681e15 −0.252639
\(929\) −3.39995e16 −1.61208 −0.806039 0.591862i \(-0.798393\pi\)
−0.806039 + 0.591862i \(0.798393\pi\)
\(930\) −1.37870e14 −0.00649851
\(931\) 8.66254e15 0.405903
\(932\) 3.59275e16 1.67355
\(933\) −1.35954e16 −0.629568
\(934\) −2.81312e15 −0.129503
\(935\) 1.24639e16 0.570414
\(936\) 5.88084e14 0.0267561
\(937\) −7.34935e14 −0.0332415 −0.0166208 0.999862i \(-0.505291\pi\)
−0.0166208 + 0.999862i \(0.505291\pi\)
\(938\) −7.93049e15 −0.356603
\(939\) −1.14953e16 −0.513875
\(940\) 4.29114e15 0.190708
\(941\) −3.19965e16 −1.41371 −0.706854 0.707360i \(-0.749886\pi\)
−0.706854 + 0.707360i \(0.749886\pi\)
\(942\) −1.07723e16 −0.473180
\(943\) 4.01014e14 0.0175124
\(944\) 1.30684e15 0.0567383
\(945\) 3.61318e15 0.155961
\(946\) 8.68347e16 3.72642
\(947\) 3.54537e16 1.51264 0.756321 0.654201i \(-0.226995\pi\)
0.756321 + 0.654201i \(0.226995\pi\)
\(948\) 2.77801e16 1.17839
\(949\) −2.69168e16 −1.13517
\(950\) 2.86065e16 1.19946
\(951\) 1.63587e16 0.681957
\(952\) 5.06992e15 0.210135
\(953\) 1.61742e16 0.666519 0.333260 0.942835i \(-0.391851\pi\)
0.333260 + 0.942835i \(0.391851\pi\)
\(954\) −4.17884e15 −0.171214
\(955\) 9.00281e15 0.366741
\(956\) 2.56031e16 1.03699
\(957\) 6.31555e15 0.254329
\(958\) −3.07510e16 −1.23126
\(959\) −1.01916e16 −0.405733
\(960\) 3.53698e15 0.140004
\(961\) −2.53910e16 −0.999313
\(962\) 3.24343e16 1.26923
\(963\) 1.83111e15 0.0712474
\(964\) −2.63669e16 −1.02008
\(965\) 3.09689e15 0.119131
\(966\) −4.32511e14 −0.0165433
\(967\) 2.66442e16 1.01335 0.506673 0.862138i \(-0.330875\pi\)
0.506673 + 0.862138i \(0.330875\pi\)
\(968\) −4.82266e15 −0.182378
\(969\) −4.25635e16 −1.60050
\(970\) −6.35018e15 −0.237433
\(971\) −3.55781e16 −1.32275 −0.661374 0.750056i \(-0.730026\pi\)
−0.661374 + 0.750056i \(0.730026\pi\)
\(972\) −7.87529e15 −0.291140
\(973\) 1.99494e16 0.733345
\(974\) 3.50239e16 1.28024
\(975\) 2.68186e16 0.974789
\(976\) −2.36024e16 −0.853064
\(977\) 8.11999e15 0.291834 0.145917 0.989297i \(-0.453387\pi\)
0.145917 + 0.989297i \(0.453387\pi\)
\(978\) 4.26239e16 1.52331
\(979\) −3.57671e16 −1.27110
\(980\) −2.23100e15 −0.0788418
\(981\) −4.83177e15 −0.169796
\(982\) −3.77600e16 −1.31953
\(983\) 1.07762e15 0.0374472 0.0187236 0.999825i \(-0.494040\pi\)
0.0187236 + 0.999825i \(0.494040\pi\)
\(984\) 3.83191e15 0.132417
\(985\) 6.20555e15 0.213246
\(986\) −1.44392e16 −0.493425
\(987\) −2.16415e16 −0.735432
\(988\) −2.66108e16 −0.899279
\(989\) −9.51645e14 −0.0319812
\(990\) 2.00305e15 0.0669418
\(991\) 1.71972e16 0.571547 0.285773 0.958297i \(-0.407750\pi\)
0.285773 + 0.958297i \(0.407750\pi\)
\(992\) −1.07897e15 −0.0356612
\(993\) −1.21466e15 −0.0399240
\(994\) 5.80493e16 1.89746
\(995\) −6.65869e15 −0.216452
\(996\) −9.00301e15 −0.291046
\(997\) 3.20573e16 1.03063 0.515316 0.857000i \(-0.327674\pi\)
0.515316 + 0.857000i \(0.327674\pi\)
\(998\) −6.01849e16 −1.92429
\(999\) 2.78255e16 0.884776
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 29.12.a.a.1.10 11
3.2 odd 2 261.12.a.a.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.12.a.a.1.10 11 1.1 even 1 trivial
261.12.a.a.1.2 11 3.2 odd 2