Properties

Label 2013.2.a.h.1.8
Level 2013
Weight 2
Character 2013.1
Self dual yes
Analytic conductor 16.074
Analytic rank 0
Dimension 14
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2013.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.0738859269\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} - 745 x^{5} - 802 x^{4} + 386 x^{3} + 74 x^{2} - 15 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.0561655\) of defining polynomial
Character \(\chi\) \(=\) 2013.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0561655 q^{2} -1.00000 q^{3} -1.99685 q^{4} -2.87016 q^{5} -0.0561655 q^{6} +3.53988 q^{7} -0.224485 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.0561655 q^{2} -1.00000 q^{3} -1.99685 q^{4} -2.87016 q^{5} -0.0561655 q^{6} +3.53988 q^{7} -0.224485 q^{8} +1.00000 q^{9} -0.161204 q^{10} -1.00000 q^{11} +1.99685 q^{12} +1.66374 q^{13} +0.198819 q^{14} +2.87016 q^{15} +3.98108 q^{16} -6.51228 q^{17} +0.0561655 q^{18} -4.27158 q^{19} +5.73126 q^{20} -3.53988 q^{21} -0.0561655 q^{22} -8.02418 q^{23} +0.224485 q^{24} +3.23780 q^{25} +0.0934449 q^{26} -1.00000 q^{27} -7.06858 q^{28} +3.26557 q^{29} +0.161204 q^{30} +6.97737 q^{31} +0.672570 q^{32} +1.00000 q^{33} -0.365766 q^{34} -10.1600 q^{35} -1.99685 q^{36} +0.826353 q^{37} -0.239916 q^{38} -1.66374 q^{39} +0.644307 q^{40} -11.9366 q^{41} -0.198819 q^{42} -2.21299 q^{43} +1.99685 q^{44} -2.87016 q^{45} -0.450683 q^{46} +10.4001 q^{47} -3.98108 q^{48} +5.53072 q^{49} +0.181853 q^{50} +6.51228 q^{51} -3.32224 q^{52} +8.11158 q^{53} -0.0561655 q^{54} +2.87016 q^{55} -0.794649 q^{56} +4.27158 q^{57} +0.183413 q^{58} +2.00484 q^{59} -5.73126 q^{60} +1.00000 q^{61} +0.391888 q^{62} +3.53988 q^{63} -7.92439 q^{64} -4.77520 q^{65} +0.0561655 q^{66} +10.0237 q^{67} +13.0040 q^{68} +8.02418 q^{69} -0.570642 q^{70} -2.13305 q^{71} -0.224485 q^{72} +2.54693 q^{73} +0.0464125 q^{74} -3.23780 q^{75} +8.52969 q^{76} -3.53988 q^{77} -0.0934449 q^{78} -6.81997 q^{79} -11.4263 q^{80} +1.00000 q^{81} -0.670428 q^{82} +0.562991 q^{83} +7.06858 q^{84} +18.6913 q^{85} -0.124294 q^{86} -3.26557 q^{87} +0.224485 q^{88} +7.23252 q^{89} -0.161204 q^{90} +5.88944 q^{91} +16.0231 q^{92} -6.97737 q^{93} +0.584128 q^{94} +12.2601 q^{95} -0.672570 q^{96} +11.1816 q^{97} +0.310636 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - q^{2} - 14q^{3} + 15q^{4} + q^{5} + q^{6} + 9q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - q^{2} - 14q^{3} + 15q^{4} + q^{5} + q^{6} + 9q^{7} + 14q^{9} + 6q^{10} - 14q^{11} - 15q^{12} + q^{13} - 7q^{14} - q^{15} + 17q^{16} - 9q^{17} - q^{18} + 22q^{19} + 23q^{20} - 9q^{21} + q^{22} + q^{23} + 25q^{25} + 4q^{26} - 14q^{27} + 37q^{28} - 6q^{29} - 6q^{30} + 9q^{31} + 4q^{32} + 14q^{33} + 8q^{34} + 18q^{35} + 15q^{36} + 18q^{37} + 8q^{38} - q^{39} + 16q^{40} - 25q^{41} + 7q^{42} + 25q^{43} - 15q^{44} + q^{45} + 20q^{46} + 36q^{47} - 17q^{48} + 25q^{49} + 2q^{50} + 9q^{51} - 13q^{52} + q^{54} - q^{55} - 40q^{56} - 22q^{57} + 33q^{58} + 17q^{59} - 23q^{60} + 14q^{61} - 13q^{62} + 9q^{63} - 6q^{64} - 61q^{65} - q^{66} + 22q^{67} + 66q^{68} - q^{69} + 44q^{70} - 13q^{71} + 20q^{73} - 12q^{74} - 25q^{75} + 49q^{76} - 9q^{77} - 4q^{78} + 31q^{79} + 88q^{80} + 14q^{81} + 2q^{82} + 32q^{83} - 37q^{84} + 2q^{85} - 14q^{86} + 6q^{87} - 21q^{89} + 6q^{90} + 45q^{91} - 14q^{92} - 9q^{93} - 31q^{94} + 23q^{95} - 4q^{96} + 37q^{97} - 38q^{98} - 14q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0561655 0.0397150 0.0198575 0.999803i \(-0.493679\pi\)
0.0198575 + 0.999803i \(0.493679\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99685 −0.998423
\(5\) −2.87016 −1.28357 −0.641786 0.766883i \(-0.721806\pi\)
−0.641786 + 0.766883i \(0.721806\pi\)
\(6\) −0.0561655 −0.0229295
\(7\) 3.53988 1.33795 0.668974 0.743286i \(-0.266734\pi\)
0.668974 + 0.743286i \(0.266734\pi\)
\(8\) −0.224485 −0.0793674
\(9\) 1.00000 0.333333
\(10\) −0.161204 −0.0509771
\(11\) −1.00000 −0.301511
\(12\) 1.99685 0.576440
\(13\) 1.66374 0.461439 0.230719 0.973020i \(-0.425892\pi\)
0.230719 + 0.973020i \(0.425892\pi\)
\(14\) 0.198819 0.0531366
\(15\) 2.87016 0.741071
\(16\) 3.98108 0.995271
\(17\) −6.51228 −1.57946 −0.789730 0.613455i \(-0.789779\pi\)
−0.789730 + 0.613455i \(0.789779\pi\)
\(18\) 0.0561655 0.0132383
\(19\) −4.27158 −0.979968 −0.489984 0.871731i \(-0.662997\pi\)
−0.489984 + 0.871731i \(0.662997\pi\)
\(20\) 5.73126 1.28155
\(21\) −3.53988 −0.772464
\(22\) −0.0561655 −0.0119745
\(23\) −8.02418 −1.67316 −0.836579 0.547846i \(-0.815448\pi\)
−0.836579 + 0.547846i \(0.815448\pi\)
\(24\) 0.224485 0.0458228
\(25\) 3.23780 0.647559
\(26\) 0.0934449 0.0183261
\(27\) −1.00000 −0.192450
\(28\) −7.06858 −1.33584
\(29\) 3.26557 0.606402 0.303201 0.952927i \(-0.401945\pi\)
0.303201 + 0.952927i \(0.401945\pi\)
\(30\) 0.161204 0.0294317
\(31\) 6.97737 1.25317 0.626587 0.779352i \(-0.284451\pi\)
0.626587 + 0.779352i \(0.284451\pi\)
\(32\) 0.672570 0.118895
\(33\) 1.00000 0.174078
\(34\) −0.365766 −0.0627283
\(35\) −10.1600 −1.71735
\(36\) −1.99685 −0.332808
\(37\) 0.826353 0.135852 0.0679258 0.997690i \(-0.478362\pi\)
0.0679258 + 0.997690i \(0.478362\pi\)
\(38\) −0.239916 −0.0389194
\(39\) −1.66374 −0.266412
\(40\) 0.644307 0.101874
\(41\) −11.9366 −1.86419 −0.932095 0.362214i \(-0.882021\pi\)
−0.932095 + 0.362214i \(0.882021\pi\)
\(42\) −0.198819 −0.0306784
\(43\) −2.21299 −0.337477 −0.168739 0.985661i \(-0.553969\pi\)
−0.168739 + 0.985661i \(0.553969\pi\)
\(44\) 1.99685 0.301036
\(45\) −2.87016 −0.427858
\(46\) −0.450683 −0.0664495
\(47\) 10.4001 1.51701 0.758506 0.651666i \(-0.225930\pi\)
0.758506 + 0.651666i \(0.225930\pi\)
\(48\) −3.98108 −0.574620
\(49\) 5.53072 0.790103
\(50\) 0.181853 0.0257178
\(51\) 6.51228 0.911902
\(52\) −3.32224 −0.460711
\(53\) 8.11158 1.11421 0.557106 0.830442i \(-0.311912\pi\)
0.557106 + 0.830442i \(0.311912\pi\)
\(54\) −0.0561655 −0.00764316
\(55\) 2.87016 0.387012
\(56\) −0.794649 −0.106189
\(57\) 4.27158 0.565785
\(58\) 0.183413 0.0240833
\(59\) 2.00484 0.261007 0.130504 0.991448i \(-0.458341\pi\)
0.130504 + 0.991448i \(0.458341\pi\)
\(60\) −5.73126 −0.739902
\(61\) 1.00000 0.128037
\(62\) 0.391888 0.0497698
\(63\) 3.53988 0.445982
\(64\) −7.92439 −0.990549
\(65\) −4.77520 −0.592291
\(66\) 0.0561655 0.00691350
\(67\) 10.0237 1.22459 0.612293 0.790631i \(-0.290247\pi\)
0.612293 + 0.790631i \(0.290247\pi\)
\(68\) 13.0040 1.57697
\(69\) 8.02418 0.965998
\(70\) −0.570642 −0.0682047
\(71\) −2.13305 −0.253146 −0.126573 0.991957i \(-0.540398\pi\)
−0.126573 + 0.991957i \(0.540398\pi\)
\(72\) −0.224485 −0.0264558
\(73\) 2.54693 0.298096 0.149048 0.988830i \(-0.452379\pi\)
0.149048 + 0.988830i \(0.452379\pi\)
\(74\) 0.0464125 0.00539535
\(75\) −3.23780 −0.373868
\(76\) 8.52969 0.978422
\(77\) −3.53988 −0.403406
\(78\) −0.0934449 −0.0105806
\(79\) −6.81997 −0.767306 −0.383653 0.923477i \(-0.625334\pi\)
−0.383653 + 0.923477i \(0.625334\pi\)
\(80\) −11.4263 −1.27750
\(81\) 1.00000 0.111111
\(82\) −0.670428 −0.0740364
\(83\) 0.562991 0.0617963 0.0308982 0.999523i \(-0.490163\pi\)
0.0308982 + 0.999523i \(0.490163\pi\)
\(84\) 7.06858 0.771246
\(85\) 18.6913 2.02735
\(86\) −0.124294 −0.0134029
\(87\) −3.26557 −0.350106
\(88\) 0.224485 0.0239302
\(89\) 7.23252 0.766646 0.383323 0.923614i \(-0.374780\pi\)
0.383323 + 0.923614i \(0.374780\pi\)
\(90\) −0.161204 −0.0169924
\(91\) 5.88944 0.617381
\(92\) 16.0231 1.67052
\(93\) −6.97737 −0.723520
\(94\) 0.584128 0.0602482
\(95\) 12.2601 1.25786
\(96\) −0.672570 −0.0686438
\(97\) 11.1816 1.13532 0.567660 0.823263i \(-0.307849\pi\)
0.567660 + 0.823263i \(0.307849\pi\)
\(98\) 0.310636 0.0313789
\(99\) −1.00000 −0.100504
\(100\) −6.46538 −0.646538
\(101\) 10.8938 1.08398 0.541989 0.840386i \(-0.317671\pi\)
0.541989 + 0.840386i \(0.317671\pi\)
\(102\) 0.365766 0.0362162
\(103\) −1.11625 −0.109988 −0.0549938 0.998487i \(-0.517514\pi\)
−0.0549938 + 0.998487i \(0.517514\pi\)
\(104\) −0.373485 −0.0366232
\(105\) 10.1600 0.991514
\(106\) 0.455591 0.0442509
\(107\) −2.80022 −0.270707 −0.135354 0.990797i \(-0.543217\pi\)
−0.135354 + 0.990797i \(0.543217\pi\)
\(108\) 1.99685 0.192147
\(109\) 10.6923 1.02414 0.512069 0.858944i \(-0.328879\pi\)
0.512069 + 0.858944i \(0.328879\pi\)
\(110\) 0.161204 0.0153702
\(111\) −0.826353 −0.0784339
\(112\) 14.0925 1.33162
\(113\) 13.9443 1.31177 0.655885 0.754861i \(-0.272296\pi\)
0.655885 + 0.754861i \(0.272296\pi\)
\(114\) 0.239916 0.0224702
\(115\) 23.0307 2.14762
\(116\) −6.52085 −0.605446
\(117\) 1.66374 0.153813
\(118\) 0.112603 0.0103659
\(119\) −23.0527 −2.11323
\(120\) −0.644307 −0.0588169
\(121\) 1.00000 0.0909091
\(122\) 0.0561655 0.00508499
\(123\) 11.9366 1.07629
\(124\) −13.9327 −1.25120
\(125\) 5.05780 0.452383
\(126\) 0.198819 0.0177122
\(127\) −15.3492 −1.36202 −0.681012 0.732272i \(-0.738460\pi\)
−0.681012 + 0.732272i \(0.738460\pi\)
\(128\) −1.79022 −0.158234
\(129\) 2.21299 0.194843
\(130\) −0.268202 −0.0235228
\(131\) 17.1289 1.49656 0.748280 0.663383i \(-0.230880\pi\)
0.748280 + 0.663383i \(0.230880\pi\)
\(132\) −1.99685 −0.173803
\(133\) −15.1209 −1.31115
\(134\) 0.562985 0.0486345
\(135\) 2.87016 0.247024
\(136\) 1.46191 0.125358
\(137\) −1.15929 −0.0990451 −0.0495225 0.998773i \(-0.515770\pi\)
−0.0495225 + 0.998773i \(0.515770\pi\)
\(138\) 0.450683 0.0383646
\(139\) 7.66907 0.650482 0.325241 0.945631i \(-0.394555\pi\)
0.325241 + 0.945631i \(0.394555\pi\)
\(140\) 20.2879 1.71464
\(141\) −10.4001 −0.875847
\(142\) −0.119804 −0.0100537
\(143\) −1.66374 −0.139129
\(144\) 3.98108 0.331757
\(145\) −9.37271 −0.778361
\(146\) 0.143050 0.0118389
\(147\) −5.53072 −0.456166
\(148\) −1.65010 −0.135637
\(149\) −1.19140 −0.0976031 −0.0488015 0.998808i \(-0.515540\pi\)
−0.0488015 + 0.998808i \(0.515540\pi\)
\(150\) −0.181853 −0.0148482
\(151\) 11.2781 0.917798 0.458899 0.888488i \(-0.348244\pi\)
0.458899 + 0.888488i \(0.348244\pi\)
\(152\) 0.958906 0.0777775
\(153\) −6.51228 −0.526487
\(154\) −0.198819 −0.0160213
\(155\) −20.0262 −1.60854
\(156\) 3.32224 0.265992
\(157\) 17.0614 1.36165 0.680825 0.732446i \(-0.261621\pi\)
0.680825 + 0.732446i \(0.261621\pi\)
\(158\) −0.383047 −0.0304736
\(159\) −8.11158 −0.643290
\(160\) −1.93038 −0.152610
\(161\) −28.4046 −2.23860
\(162\) 0.0561655 0.00441278
\(163\) −18.8321 −1.47504 −0.737521 0.675325i \(-0.764004\pi\)
−0.737521 + 0.675325i \(0.764004\pi\)
\(164\) 23.8356 1.86125
\(165\) −2.87016 −0.223441
\(166\) 0.0316207 0.00245424
\(167\) 20.7776 1.60782 0.803911 0.594749i \(-0.202749\pi\)
0.803911 + 0.594749i \(0.202749\pi\)
\(168\) 0.794649 0.0613085
\(169\) −10.2320 −0.787074
\(170\) 1.04980 0.0805163
\(171\) −4.27158 −0.326656
\(172\) 4.41899 0.336945
\(173\) 8.58089 0.652393 0.326197 0.945302i \(-0.394233\pi\)
0.326197 + 0.945302i \(0.394233\pi\)
\(174\) −0.183413 −0.0139045
\(175\) 11.4614 0.866400
\(176\) −3.98108 −0.300085
\(177\) −2.00484 −0.150693
\(178\) 0.406218 0.0304474
\(179\) 1.62970 0.121810 0.0609049 0.998144i \(-0.480601\pi\)
0.0609049 + 0.998144i \(0.480601\pi\)
\(180\) 5.73126 0.427183
\(181\) −6.80075 −0.505496 −0.252748 0.967532i \(-0.581334\pi\)
−0.252748 + 0.967532i \(0.581334\pi\)
\(182\) 0.330783 0.0245193
\(183\) −1.00000 −0.0739221
\(184\) 1.80131 0.132794
\(185\) −2.37176 −0.174375
\(186\) −0.391888 −0.0287346
\(187\) 6.51228 0.476225
\(188\) −20.7674 −1.51462
\(189\) −3.53988 −0.257488
\(190\) 0.688595 0.0499559
\(191\) 21.1056 1.52714 0.763572 0.645723i \(-0.223444\pi\)
0.763572 + 0.645723i \(0.223444\pi\)
\(192\) 7.92439 0.571894
\(193\) −15.3449 −1.10455 −0.552276 0.833661i \(-0.686241\pi\)
−0.552276 + 0.833661i \(0.686241\pi\)
\(194\) 0.628021 0.0450893
\(195\) 4.77520 0.341959
\(196\) −11.0440 −0.788856
\(197\) 8.01939 0.571358 0.285679 0.958325i \(-0.407781\pi\)
0.285679 + 0.958325i \(0.407781\pi\)
\(198\) −0.0561655 −0.00399151
\(199\) 18.9435 1.34287 0.671435 0.741063i \(-0.265678\pi\)
0.671435 + 0.741063i \(0.265678\pi\)
\(200\) −0.726836 −0.0513951
\(201\) −10.0237 −0.707016
\(202\) 0.611859 0.0430502
\(203\) 11.5597 0.811334
\(204\) −13.0040 −0.910463
\(205\) 34.2600 2.39282
\(206\) −0.0626949 −0.00436816
\(207\) −8.02418 −0.557719
\(208\) 6.62349 0.459257
\(209\) 4.27158 0.295471
\(210\) 0.570642 0.0393780
\(211\) −14.2888 −0.983682 −0.491841 0.870685i \(-0.663676\pi\)
−0.491841 + 0.870685i \(0.663676\pi\)
\(212\) −16.1976 −1.11245
\(213\) 2.13305 0.146154
\(214\) −0.157276 −0.0107511
\(215\) 6.35162 0.433177
\(216\) 0.224485 0.0152743
\(217\) 24.6990 1.67668
\(218\) 0.600540 0.0406737
\(219\) −2.54693 −0.172106
\(220\) −5.73126 −0.386401
\(221\) −10.8348 −0.728824
\(222\) −0.0464125 −0.00311501
\(223\) −2.84596 −0.190580 −0.0952899 0.995450i \(-0.530378\pi\)
−0.0952899 + 0.995450i \(0.530378\pi\)
\(224\) 2.38081 0.159075
\(225\) 3.23780 0.215853
\(226\) 0.783189 0.0520970
\(227\) −19.4833 −1.29315 −0.646576 0.762849i \(-0.723800\pi\)
−0.646576 + 0.762849i \(0.723800\pi\)
\(228\) −8.52969 −0.564892
\(229\) −11.7161 −0.774219 −0.387109 0.922034i \(-0.626526\pi\)
−0.387109 + 0.922034i \(0.626526\pi\)
\(230\) 1.29353 0.0852928
\(231\) 3.53988 0.232907
\(232\) −0.733072 −0.0481286
\(233\) −27.8004 −1.82126 −0.910632 0.413219i \(-0.864404\pi\)
−0.910632 + 0.413219i \(0.864404\pi\)
\(234\) 0.0934449 0.00610869
\(235\) −29.8499 −1.94720
\(236\) −4.00335 −0.260596
\(237\) 6.81997 0.443004
\(238\) −1.29476 −0.0839271
\(239\) 1.27569 0.0825176 0.0412588 0.999148i \(-0.486863\pi\)
0.0412588 + 0.999148i \(0.486863\pi\)
\(240\) 11.4263 0.737566
\(241\) 14.9945 0.965878 0.482939 0.875654i \(-0.339569\pi\)
0.482939 + 0.875654i \(0.339569\pi\)
\(242\) 0.0561655 0.00361046
\(243\) −1.00000 −0.0641500
\(244\) −1.99685 −0.127835
\(245\) −15.8740 −1.01415
\(246\) 0.670428 0.0427449
\(247\) −7.10681 −0.452195
\(248\) −1.56632 −0.0994611
\(249\) −0.562991 −0.0356781
\(250\) 0.284074 0.0179664
\(251\) −25.6541 −1.61927 −0.809637 0.586931i \(-0.800336\pi\)
−0.809637 + 0.586931i \(0.800336\pi\)
\(252\) −7.06858 −0.445279
\(253\) 8.02418 0.504476
\(254\) −0.862098 −0.0540929
\(255\) −18.6913 −1.17049
\(256\) 15.7482 0.984264
\(257\) −23.5239 −1.46738 −0.733690 0.679485i \(-0.762203\pi\)
−0.733690 + 0.679485i \(0.762203\pi\)
\(258\) 0.124294 0.00773818
\(259\) 2.92519 0.181762
\(260\) 9.53533 0.591356
\(261\) 3.26557 0.202134
\(262\) 0.962055 0.0594360
\(263\) −7.55266 −0.465717 −0.232859 0.972511i \(-0.574808\pi\)
−0.232859 + 0.972511i \(0.574808\pi\)
\(264\) −0.224485 −0.0138161
\(265\) −23.2815 −1.43017
\(266\) −0.849271 −0.0520722
\(267\) −7.23252 −0.442623
\(268\) −20.0157 −1.22266
\(269\) 25.3390 1.54495 0.772474 0.635046i \(-0.219019\pi\)
0.772474 + 0.635046i \(0.219019\pi\)
\(270\) 0.161204 0.00981055
\(271\) −24.0494 −1.46090 −0.730449 0.682967i \(-0.760689\pi\)
−0.730449 + 0.682967i \(0.760689\pi\)
\(272\) −25.9259 −1.57199
\(273\) −5.88944 −0.356445
\(274\) −0.0651123 −0.00393358
\(275\) −3.23780 −0.195246
\(276\) −16.0231 −0.964475
\(277\) 25.9274 1.55782 0.778912 0.627133i \(-0.215772\pi\)
0.778912 + 0.627133i \(0.215772\pi\)
\(278\) 0.430738 0.0258339
\(279\) 6.97737 0.417724
\(280\) 2.28077 0.136302
\(281\) −16.8801 −1.00698 −0.503491 0.864000i \(-0.667951\pi\)
−0.503491 + 0.864000i \(0.667951\pi\)
\(282\) −0.584128 −0.0347843
\(283\) 14.2351 0.846191 0.423095 0.906085i \(-0.360944\pi\)
0.423095 + 0.906085i \(0.360944\pi\)
\(284\) 4.25937 0.252747
\(285\) −12.2601 −0.726226
\(286\) −0.0934449 −0.00552552
\(287\) −42.2542 −2.49419
\(288\) 0.672570 0.0396315
\(289\) 25.4098 1.49469
\(290\) −0.526423 −0.0309126
\(291\) −11.1816 −0.655477
\(292\) −5.08583 −0.297626
\(293\) 25.1762 1.47081 0.735406 0.677627i \(-0.236992\pi\)
0.735406 + 0.677627i \(0.236992\pi\)
\(294\) −0.310636 −0.0181166
\(295\) −5.75419 −0.335022
\(296\) −0.185504 −0.0107822
\(297\) 1.00000 0.0580259
\(298\) −0.0669155 −0.00387631
\(299\) −13.3502 −0.772060
\(300\) 6.46538 0.373279
\(301\) −7.83369 −0.451527
\(302\) 0.633440 0.0364504
\(303\) −10.8938 −0.625835
\(304\) −17.0055 −0.975333
\(305\) −2.87016 −0.164345
\(306\) −0.365766 −0.0209094
\(307\) 20.2369 1.15498 0.577490 0.816398i \(-0.304032\pi\)
0.577490 + 0.816398i \(0.304032\pi\)
\(308\) 7.06858 0.402770
\(309\) 1.11625 0.0635014
\(310\) −1.12478 −0.0638832
\(311\) 20.5089 1.16295 0.581477 0.813563i \(-0.302475\pi\)
0.581477 + 0.813563i \(0.302475\pi\)
\(312\) 0.373485 0.0211444
\(313\) −10.5734 −0.597644 −0.298822 0.954309i \(-0.596594\pi\)
−0.298822 + 0.954309i \(0.596594\pi\)
\(314\) 0.958264 0.0540780
\(315\) −10.1600 −0.572451
\(316\) 13.6184 0.766096
\(317\) 20.3836 1.14486 0.572429 0.819955i \(-0.306001\pi\)
0.572429 + 0.819955i \(0.306001\pi\)
\(318\) −0.455591 −0.0255483
\(319\) −3.26557 −0.182837
\(320\) 22.7442 1.27144
\(321\) 2.80022 0.156293
\(322\) −1.59536 −0.0889059
\(323\) 27.8177 1.54782
\(324\) −1.99685 −0.110936
\(325\) 5.38686 0.298809
\(326\) −1.05771 −0.0585813
\(327\) −10.6923 −0.591287
\(328\) 2.67960 0.147956
\(329\) 36.8151 2.02968
\(330\) −0.161204 −0.00887398
\(331\) 11.9595 0.657353 0.328676 0.944443i \(-0.393397\pi\)
0.328676 + 0.944443i \(0.393397\pi\)
\(332\) −1.12421 −0.0616989
\(333\) 0.826353 0.0452838
\(334\) 1.16699 0.0638547
\(335\) −28.7695 −1.57185
\(336\) −14.0925 −0.768811
\(337\) −17.6438 −0.961117 −0.480559 0.876963i \(-0.659566\pi\)
−0.480559 + 0.876963i \(0.659566\pi\)
\(338\) −0.574684 −0.0312587
\(339\) −13.9443 −0.757351
\(340\) −37.3236 −2.02415
\(341\) −6.97737 −0.377846
\(342\) −0.239916 −0.0129731
\(343\) −5.20108 −0.280832
\(344\) 0.496782 0.0267847
\(345\) −23.0307 −1.23993
\(346\) 0.481950 0.0259098
\(347\) 0.648489 0.0348127 0.0174063 0.999848i \(-0.494459\pi\)
0.0174063 + 0.999848i \(0.494459\pi\)
\(348\) 6.52085 0.349554
\(349\) −23.3381 −1.24926 −0.624631 0.780920i \(-0.714751\pi\)
−0.624631 + 0.780920i \(0.714751\pi\)
\(350\) 0.643735 0.0344091
\(351\) −1.66374 −0.0888040
\(352\) −0.672570 −0.0358481
\(353\) −35.7398 −1.90224 −0.951119 0.308825i \(-0.900064\pi\)
−0.951119 + 0.308825i \(0.900064\pi\)
\(354\) −0.112603 −0.00598476
\(355\) 6.12219 0.324932
\(356\) −14.4422 −0.765437
\(357\) 23.0527 1.22008
\(358\) 0.0915332 0.00483768
\(359\) 10.9472 0.577770 0.288885 0.957364i \(-0.406715\pi\)
0.288885 + 0.957364i \(0.406715\pi\)
\(360\) 0.644307 0.0339580
\(361\) −0.753598 −0.0396631
\(362\) −0.381968 −0.0200758
\(363\) −1.00000 −0.0524864
\(364\) −11.7603 −0.616407
\(365\) −7.31009 −0.382628
\(366\) −0.0561655 −0.00293582
\(367\) 17.0313 0.889025 0.444513 0.895773i \(-0.353377\pi\)
0.444513 + 0.895773i \(0.353377\pi\)
\(368\) −31.9449 −1.66525
\(369\) −11.9366 −0.621397
\(370\) −0.133211 −0.00692532
\(371\) 28.7140 1.49076
\(372\) 13.9327 0.722379
\(373\) 26.7579 1.38547 0.692735 0.721192i \(-0.256406\pi\)
0.692735 + 0.721192i \(0.256406\pi\)
\(374\) 0.365766 0.0189133
\(375\) −5.05780 −0.261184
\(376\) −2.33467 −0.120401
\(377\) 5.43307 0.279818
\(378\) −0.198819 −0.0102261
\(379\) 7.77600 0.399426 0.199713 0.979854i \(-0.435999\pi\)
0.199713 + 0.979854i \(0.435999\pi\)
\(380\) −24.4815 −1.25588
\(381\) 15.3492 0.786365
\(382\) 1.18540 0.0606506
\(383\) −28.3894 −1.45063 −0.725316 0.688416i \(-0.758306\pi\)
−0.725316 + 0.688416i \(0.758306\pi\)
\(384\) 1.79022 0.0913566
\(385\) 10.1600 0.517801
\(386\) −0.861857 −0.0438673
\(387\) −2.21299 −0.112492
\(388\) −22.3279 −1.13353
\(389\) 32.7737 1.66169 0.830846 0.556503i \(-0.187857\pi\)
0.830846 + 0.556503i \(0.187857\pi\)
\(390\) 0.268202 0.0135809
\(391\) 52.2557 2.64269
\(392\) −1.24156 −0.0627084
\(393\) −17.1289 −0.864040
\(394\) 0.450413 0.0226915
\(395\) 19.5744 0.984893
\(396\) 1.99685 0.100345
\(397\) 23.4981 1.17934 0.589668 0.807646i \(-0.299259\pi\)
0.589668 + 0.807646i \(0.299259\pi\)
\(398\) 1.06397 0.0533321
\(399\) 15.1209 0.756990
\(400\) 12.8899 0.644497
\(401\) −5.67692 −0.283492 −0.141746 0.989903i \(-0.545272\pi\)
−0.141746 + 0.989903i \(0.545272\pi\)
\(402\) −0.562985 −0.0280791
\(403\) 11.6086 0.578263
\(404\) −21.7533 −1.08227
\(405\) −2.87016 −0.142619
\(406\) 0.649258 0.0322221
\(407\) −0.826353 −0.0409608
\(408\) −1.46191 −0.0723753
\(409\) 15.8544 0.783950 0.391975 0.919976i \(-0.371792\pi\)
0.391975 + 0.919976i \(0.371792\pi\)
\(410\) 1.92423 0.0950311
\(411\) 1.15929 0.0571837
\(412\) 2.22898 0.109814
\(413\) 7.09687 0.349214
\(414\) −0.450683 −0.0221498
\(415\) −1.61587 −0.0793201
\(416\) 1.11898 0.0548626
\(417\) −7.66907 −0.375556
\(418\) 0.239916 0.0117347
\(419\) 9.40019 0.459229 0.229615 0.973282i \(-0.426253\pi\)
0.229615 + 0.973282i \(0.426253\pi\)
\(420\) −20.2879 −0.989950
\(421\) 19.3416 0.942650 0.471325 0.881960i \(-0.343776\pi\)
0.471325 + 0.881960i \(0.343776\pi\)
\(422\) −0.802538 −0.0390669
\(423\) 10.4001 0.505671
\(424\) −1.82093 −0.0884321
\(425\) −21.0854 −1.02279
\(426\) 0.119804 0.00580452
\(427\) 3.53988 0.171307
\(428\) 5.59160 0.270280
\(429\) 1.66374 0.0803262
\(430\) 0.356742 0.0172036
\(431\) 22.0619 1.06268 0.531342 0.847158i \(-0.321688\pi\)
0.531342 + 0.847158i \(0.321688\pi\)
\(432\) −3.98108 −0.191540
\(433\) 16.4389 0.790005 0.395002 0.918680i \(-0.370744\pi\)
0.395002 + 0.918680i \(0.370744\pi\)
\(434\) 1.38723 0.0665894
\(435\) 9.37271 0.449387
\(436\) −21.3509 −1.02252
\(437\) 34.2760 1.63964
\(438\) −0.143050 −0.00683518
\(439\) 29.1315 1.39037 0.695185 0.718831i \(-0.255322\pi\)
0.695185 + 0.718831i \(0.255322\pi\)
\(440\) −0.644307 −0.0307161
\(441\) 5.53072 0.263368
\(442\) −0.608540 −0.0289453
\(443\) −39.8835 −1.89492 −0.947461 0.319871i \(-0.896360\pi\)
−0.947461 + 0.319871i \(0.896360\pi\)
\(444\) 1.65010 0.0783102
\(445\) −20.7585 −0.984046
\(446\) −0.159845 −0.00756888
\(447\) 1.19140 0.0563512
\(448\) −28.0514 −1.32530
\(449\) −6.39145 −0.301631 −0.150816 0.988562i \(-0.548190\pi\)
−0.150816 + 0.988562i \(0.548190\pi\)
\(450\) 0.181853 0.00857261
\(451\) 11.9366 0.562074
\(452\) −27.8446 −1.30970
\(453\) −11.2781 −0.529891
\(454\) −1.09429 −0.0513576
\(455\) −16.9036 −0.792453
\(456\) −0.958906 −0.0449049
\(457\) −6.55699 −0.306723 −0.153362 0.988170i \(-0.549010\pi\)
−0.153362 + 0.988170i \(0.549010\pi\)
\(458\) −0.658038 −0.0307481
\(459\) 6.51228 0.303967
\(460\) −45.9887 −2.14423
\(461\) −7.90935 −0.368375 −0.184188 0.982891i \(-0.558965\pi\)
−0.184188 + 0.982891i \(0.558965\pi\)
\(462\) 0.198819 0.00924990
\(463\) 29.9602 1.39237 0.696184 0.717864i \(-0.254880\pi\)
0.696184 + 0.717864i \(0.254880\pi\)
\(464\) 13.0005 0.603534
\(465\) 20.0262 0.928691
\(466\) −1.56142 −0.0723315
\(467\) 11.4395 0.529355 0.264678 0.964337i \(-0.414734\pi\)
0.264678 + 0.964337i \(0.414734\pi\)
\(468\) −3.32224 −0.153570
\(469\) 35.4826 1.63843
\(470\) −1.67654 −0.0773329
\(471\) −17.0614 −0.786149
\(472\) −0.450055 −0.0207155
\(473\) 2.21299 0.101753
\(474\) 0.383047 0.0175939
\(475\) −13.8305 −0.634587
\(476\) 46.0326 2.10990
\(477\) 8.11158 0.371404
\(478\) 0.0716499 0.00327719
\(479\) 6.05533 0.276675 0.138338 0.990385i \(-0.455824\pi\)
0.138338 + 0.990385i \(0.455824\pi\)
\(480\) 1.93038 0.0881094
\(481\) 1.37484 0.0626872
\(482\) 0.842172 0.0383599
\(483\) 28.4046 1.29245
\(484\) −1.99685 −0.0907657
\(485\) −32.0930 −1.45727
\(486\) −0.0561655 −0.00254772
\(487\) 5.74022 0.260114 0.130057 0.991507i \(-0.458484\pi\)
0.130057 + 0.991507i \(0.458484\pi\)
\(488\) −0.224485 −0.0101620
\(489\) 18.8321 0.851616
\(490\) −0.891573 −0.0402772
\(491\) 5.78303 0.260984 0.130492 0.991449i \(-0.458344\pi\)
0.130492 + 0.991449i \(0.458344\pi\)
\(492\) −23.8356 −1.07459
\(493\) −21.2663 −0.957788
\(494\) −0.399158 −0.0179590
\(495\) 2.87016 0.129004
\(496\) 27.7775 1.24725
\(497\) −7.55073 −0.338697
\(498\) −0.0316207 −0.00141696
\(499\) −9.90735 −0.443514 −0.221757 0.975102i \(-0.571179\pi\)
−0.221757 + 0.975102i \(0.571179\pi\)
\(500\) −10.0996 −0.451670
\(501\) −20.7776 −0.928277
\(502\) −1.44088 −0.0643095
\(503\) 33.8356 1.50865 0.754327 0.656499i \(-0.227963\pi\)
0.754327 + 0.656499i \(0.227963\pi\)
\(504\) −0.794649 −0.0353965
\(505\) −31.2670 −1.39136
\(506\) 0.450683 0.0200353
\(507\) 10.2320 0.454417
\(508\) 30.6501 1.35988
\(509\) −18.3516 −0.813422 −0.406711 0.913557i \(-0.633324\pi\)
−0.406711 + 0.913557i \(0.633324\pi\)
\(510\) −1.04980 −0.0464861
\(511\) 9.01582 0.398836
\(512\) 4.46494 0.197324
\(513\) 4.27158 0.188595
\(514\) −1.32123 −0.0582770
\(515\) 3.20382 0.141177
\(516\) −4.41899 −0.194535
\(517\) −10.4001 −0.457396
\(518\) 0.164295 0.00721869
\(519\) −8.58089 −0.376659
\(520\) 1.07196 0.0470086
\(521\) 14.9139 0.653389 0.326694 0.945130i \(-0.394065\pi\)
0.326694 + 0.945130i \(0.394065\pi\)
\(522\) 0.183413 0.00802776
\(523\) 12.6492 0.553112 0.276556 0.960998i \(-0.410807\pi\)
0.276556 + 0.960998i \(0.410807\pi\)
\(524\) −34.2038 −1.49420
\(525\) −11.4614 −0.500216
\(526\) −0.424199 −0.0184960
\(527\) −45.4386 −1.97934
\(528\) 3.98108 0.173254
\(529\) 41.3875 1.79946
\(530\) −1.30762 −0.0567993
\(531\) 2.00484 0.0870024
\(532\) 30.1940 1.30908
\(533\) −19.8595 −0.860210
\(534\) −0.406218 −0.0175788
\(535\) 8.03706 0.347472
\(536\) −2.25016 −0.0971923
\(537\) −1.62970 −0.0703269
\(538\) 1.42318 0.0613577
\(539\) −5.53072 −0.238225
\(540\) −5.73126 −0.246634
\(541\) 16.0561 0.690305 0.345153 0.938547i \(-0.387827\pi\)
0.345153 + 0.938547i \(0.387827\pi\)
\(542\) −1.35075 −0.0580196
\(543\) 6.80075 0.291848
\(544\) −4.37996 −0.187789
\(545\) −30.6886 −1.31456
\(546\) −0.330783 −0.0141562
\(547\) 7.91664 0.338491 0.169246 0.985574i \(-0.445867\pi\)
0.169246 + 0.985574i \(0.445867\pi\)
\(548\) 2.31493 0.0988889
\(549\) 1.00000 0.0426790
\(550\) −0.181853 −0.00775422
\(551\) −13.9492 −0.594254
\(552\) −1.80131 −0.0766688
\(553\) −24.1418 −1.02662
\(554\) 1.45622 0.0618691
\(555\) 2.37176 0.100676
\(556\) −15.3140 −0.649456
\(557\) −30.0118 −1.27164 −0.635821 0.771837i \(-0.719338\pi\)
−0.635821 + 0.771837i \(0.719338\pi\)
\(558\) 0.391888 0.0165899
\(559\) −3.68184 −0.155725
\(560\) −40.4478 −1.70923
\(561\) −6.51228 −0.274949
\(562\) −0.948080 −0.0399923
\(563\) −0.239936 −0.0101121 −0.00505604 0.999987i \(-0.501609\pi\)
−0.00505604 + 0.999987i \(0.501609\pi\)
\(564\) 20.7674 0.874466
\(565\) −40.0223 −1.68375
\(566\) 0.799524 0.0336065
\(567\) 3.53988 0.148661
\(568\) 0.478838 0.0200916
\(569\) −7.76917 −0.325701 −0.162850 0.986651i \(-0.552069\pi\)
−0.162850 + 0.986651i \(0.552069\pi\)
\(570\) −0.688595 −0.0288421
\(571\) −46.4165 −1.94247 −0.971235 0.238124i \(-0.923468\pi\)
−0.971235 + 0.238124i \(0.923468\pi\)
\(572\) 3.32224 0.138910
\(573\) −21.1056 −0.881697
\(574\) −2.37323 −0.0990567
\(575\) −25.9807 −1.08347
\(576\) −7.92439 −0.330183
\(577\) 41.0776 1.71008 0.855042 0.518559i \(-0.173531\pi\)
0.855042 + 0.518559i \(0.173531\pi\)
\(578\) 1.42715 0.0593618
\(579\) 15.3449 0.637714
\(580\) 18.7159 0.777133
\(581\) 1.99292 0.0826802
\(582\) −0.628021 −0.0260323
\(583\) −8.11158 −0.335947
\(584\) −0.571748 −0.0236591
\(585\) −4.77520 −0.197430
\(586\) 1.41404 0.0584133
\(587\) 32.5698 1.34430 0.672150 0.740415i \(-0.265371\pi\)
0.672150 + 0.740415i \(0.265371\pi\)
\(588\) 11.0440 0.455446
\(589\) −29.8044 −1.22807
\(590\) −0.323187 −0.0133054
\(591\) −8.01939 −0.329874
\(592\) 3.28978 0.135209
\(593\) −37.9151 −1.55699 −0.778493 0.627653i \(-0.784016\pi\)
−0.778493 + 0.627653i \(0.784016\pi\)
\(594\) 0.0561655 0.00230450
\(595\) 66.1647 2.71249
\(596\) 2.37904 0.0974491
\(597\) −18.9435 −0.775307
\(598\) −0.749820 −0.0306624
\(599\) −6.61867 −0.270432 −0.135216 0.990816i \(-0.543173\pi\)
−0.135216 + 0.990816i \(0.543173\pi\)
\(600\) 0.726836 0.0296730
\(601\) 28.1603 1.14868 0.574341 0.818616i \(-0.305258\pi\)
0.574341 + 0.818616i \(0.305258\pi\)
\(602\) −0.439984 −0.0179324
\(603\) 10.0237 0.408196
\(604\) −22.5206 −0.916351
\(605\) −2.87016 −0.116688
\(606\) −0.611859 −0.0248551
\(607\) −43.2487 −1.75541 −0.877705 0.479201i \(-0.840927\pi\)
−0.877705 + 0.479201i \(0.840927\pi\)
\(608\) −2.87293 −0.116513
\(609\) −11.5597 −0.468424
\(610\) −0.161204 −0.00652695
\(611\) 17.3031 0.700009
\(612\) 13.0040 0.525656
\(613\) −28.6880 −1.15870 −0.579349 0.815079i \(-0.696693\pi\)
−0.579349 + 0.815079i \(0.696693\pi\)
\(614\) 1.13661 0.0458700
\(615\) −34.2600 −1.38150
\(616\) 0.794649 0.0320173
\(617\) −0.710736 −0.0286132 −0.0143066 0.999898i \(-0.504554\pi\)
−0.0143066 + 0.999898i \(0.504554\pi\)
\(618\) 0.0626949 0.00252196
\(619\) −47.7932 −1.92097 −0.960486 0.278329i \(-0.910220\pi\)
−0.960486 + 0.278329i \(0.910220\pi\)
\(620\) 39.9891 1.60600
\(621\) 8.02418 0.321999
\(622\) 1.15189 0.0461867
\(623\) 25.6022 1.02573
\(624\) −6.62349 −0.265152
\(625\) −30.7057 −1.22823
\(626\) −0.593861 −0.0237355
\(627\) −4.27158 −0.170591
\(628\) −34.0690 −1.35950
\(629\) −5.38144 −0.214572
\(630\) −0.570642 −0.0227349
\(631\) −20.5702 −0.818889 −0.409444 0.912335i \(-0.634277\pi\)
−0.409444 + 0.912335i \(0.634277\pi\)
\(632\) 1.53098 0.0608991
\(633\) 14.2888 0.567929
\(634\) 1.14486 0.0454680
\(635\) 44.0547 1.74826
\(636\) 16.1976 0.642276
\(637\) 9.20169 0.364584
\(638\) −0.183413 −0.00726138
\(639\) −2.13305 −0.0843822
\(640\) 5.13820 0.203105
\(641\) −13.0911 −0.517069 −0.258535 0.966002i \(-0.583240\pi\)
−0.258535 + 0.966002i \(0.583240\pi\)
\(642\) 0.157276 0.00620717
\(643\) 23.2585 0.917226 0.458613 0.888636i \(-0.348346\pi\)
0.458613 + 0.888636i \(0.348346\pi\)
\(644\) 56.7196 2.23507
\(645\) −6.35162 −0.250095
\(646\) 1.56240 0.0614717
\(647\) 30.4427 1.19683 0.598413 0.801188i \(-0.295798\pi\)
0.598413 + 0.801188i \(0.295798\pi\)
\(648\) −0.224485 −0.00881860
\(649\) −2.00484 −0.0786967
\(650\) 0.302556 0.0118672
\(651\) −24.6990 −0.968032
\(652\) 37.6047 1.47271
\(653\) −28.5204 −1.11609 −0.558045 0.829811i \(-0.688448\pi\)
−0.558045 + 0.829811i \(0.688448\pi\)
\(654\) −0.600540 −0.0234830
\(655\) −49.1627 −1.92094
\(656\) −47.5207 −1.85537
\(657\) 2.54693 0.0993653
\(658\) 2.06774 0.0806089
\(659\) 9.78396 0.381129 0.190564 0.981675i \(-0.438968\pi\)
0.190564 + 0.981675i \(0.438968\pi\)
\(660\) 5.73126 0.223089
\(661\) −26.0822 −1.01448 −0.507239 0.861805i \(-0.669334\pi\)
−0.507239 + 0.861805i \(0.669334\pi\)
\(662\) 0.671711 0.0261068
\(663\) 10.8348 0.420787
\(664\) −0.126383 −0.00490462
\(665\) 43.3992 1.68295
\(666\) 0.0464125 0.00179845
\(667\) −26.2036 −1.01461
\(668\) −41.4897 −1.60529
\(669\) 2.84596 0.110031
\(670\) −1.61586 −0.0624259
\(671\) −1.00000 −0.0386046
\(672\) −2.38081 −0.0918418
\(673\) −6.37530 −0.245750 −0.122875 0.992422i \(-0.539211\pi\)
−0.122875 + 0.992422i \(0.539211\pi\)
\(674\) −0.990972 −0.0381708
\(675\) −3.23780 −0.124623
\(676\) 20.4316 0.785833
\(677\) −22.2919 −0.856747 −0.428374 0.903602i \(-0.640913\pi\)
−0.428374 + 0.903602i \(0.640913\pi\)
\(678\) −0.783189 −0.0300782
\(679\) 39.5815 1.51900
\(680\) −4.19591 −0.160906
\(681\) 19.4833 0.746602
\(682\) −0.391888 −0.0150062
\(683\) 24.9233 0.953662 0.476831 0.878995i \(-0.341785\pi\)
0.476831 + 0.878995i \(0.341785\pi\)
\(684\) 8.52969 0.326141
\(685\) 3.32735 0.127132
\(686\) −0.292121 −0.0111532
\(687\) 11.7161 0.446995
\(688\) −8.81008 −0.335881
\(689\) 13.4956 0.514141
\(690\) −1.29353 −0.0492438
\(691\) −0.490891 −0.0186744 −0.00933718 0.999956i \(-0.502972\pi\)
−0.00933718 + 0.999956i \(0.502972\pi\)
\(692\) −17.1347 −0.651364
\(693\) −3.53988 −0.134469
\(694\) 0.0364227 0.00138259
\(695\) −22.0114 −0.834941
\(696\) 0.733072 0.0277870
\(697\) 77.7347 2.94441
\(698\) −1.31080 −0.0496145
\(699\) 27.8004 1.05151
\(700\) −22.8866 −0.865033
\(701\) −12.9149 −0.487791 −0.243895 0.969802i \(-0.578425\pi\)
−0.243895 + 0.969802i \(0.578425\pi\)
\(702\) −0.0934449 −0.00352685
\(703\) −3.52983 −0.133130
\(704\) 7.92439 0.298662
\(705\) 29.8499 1.12421
\(706\) −2.00735 −0.0755474
\(707\) 38.5628 1.45031
\(708\) 4.00335 0.150455
\(709\) −21.6649 −0.813642 −0.406821 0.913508i \(-0.633363\pi\)
−0.406821 + 0.913508i \(0.633363\pi\)
\(710\) 0.343856 0.0129047
\(711\) −6.81997 −0.255769
\(712\) −1.62359 −0.0608467
\(713\) −55.9877 −2.09676
\(714\) 1.29476 0.0484554
\(715\) 4.77520 0.178582
\(716\) −3.25427 −0.121618
\(717\) −1.27569 −0.0476416
\(718\) 0.614854 0.0229462
\(719\) 3.05414 0.113900 0.0569502 0.998377i \(-0.481862\pi\)
0.0569502 + 0.998377i \(0.481862\pi\)
\(720\) −11.4263 −0.425834
\(721\) −3.95140 −0.147158
\(722\) −0.0423262 −0.00157522
\(723\) −14.9945 −0.557650
\(724\) 13.5800 0.504698
\(725\) 10.5733 0.392681
\(726\) −0.0561655 −0.00208450
\(727\) −11.0808 −0.410964 −0.205482 0.978661i \(-0.565876\pi\)
−0.205482 + 0.978661i \(0.565876\pi\)
\(728\) −1.32209 −0.0489999
\(729\) 1.00000 0.0370370
\(730\) −0.410575 −0.0151961
\(731\) 14.4116 0.533032
\(732\) 1.99685 0.0738055
\(733\) −10.7441 −0.396843 −0.198421 0.980117i \(-0.563581\pi\)
−0.198421 + 0.980117i \(0.563581\pi\)
\(734\) 0.956571 0.0353077
\(735\) 15.8740 0.585522
\(736\) −5.39682 −0.198929
\(737\) −10.0237 −0.369227
\(738\) −0.670428 −0.0246788
\(739\) −25.1340 −0.924569 −0.462284 0.886732i \(-0.652970\pi\)
−0.462284 + 0.886732i \(0.652970\pi\)
\(740\) 4.73604 0.174100
\(741\) 7.10681 0.261075
\(742\) 1.61274 0.0592054
\(743\) −25.0852 −0.920285 −0.460143 0.887845i \(-0.652202\pi\)
−0.460143 + 0.887845i \(0.652202\pi\)
\(744\) 1.56632 0.0574239
\(745\) 3.41950 0.125281
\(746\) 1.50287 0.0550240
\(747\) 0.562991 0.0205988
\(748\) −13.0040 −0.475474
\(749\) −9.91242 −0.362192
\(750\) −0.284074 −0.0103729
\(751\) 40.8602 1.49101 0.745505 0.666500i \(-0.232209\pi\)
0.745505 + 0.666500i \(0.232209\pi\)
\(752\) 41.4037 1.50984
\(753\) 25.6541 0.934888
\(754\) 0.305151 0.0111130
\(755\) −32.3699 −1.17806
\(756\) 7.06858 0.257082
\(757\) −23.1061 −0.839807 −0.419903 0.907569i \(-0.637936\pi\)
−0.419903 + 0.907569i \(0.637936\pi\)
\(758\) 0.436743 0.0158632
\(759\) −8.02418 −0.291259
\(760\) −2.75221 −0.0998331
\(761\) −24.9673 −0.905066 −0.452533 0.891748i \(-0.649479\pi\)
−0.452533 + 0.891748i \(0.649479\pi\)
\(762\) 0.862098 0.0312305
\(763\) 37.8495 1.37024
\(764\) −42.1445 −1.52474
\(765\) 18.6913 0.675784
\(766\) −1.59451 −0.0576119
\(767\) 3.33553 0.120439
\(768\) −15.7482 −0.568265
\(769\) −39.7456 −1.43326 −0.716632 0.697452i \(-0.754317\pi\)
−0.716632 + 0.697452i \(0.754317\pi\)
\(770\) 0.570642 0.0205645
\(771\) 23.5239 0.847192
\(772\) 30.6415 1.10281
\(773\) 47.6555 1.71405 0.857025 0.515276i \(-0.172310\pi\)
0.857025 + 0.515276i \(0.172310\pi\)
\(774\) −0.124294 −0.00446764
\(775\) 22.5913 0.811504
\(776\) −2.51010 −0.0901074
\(777\) −2.92519 −0.104940
\(778\) 1.84075 0.0659941
\(779\) 50.9883 1.82685
\(780\) −9.53533 −0.341420
\(781\) 2.13305 0.0763265
\(782\) 2.93497 0.104954
\(783\) −3.26557 −0.116702
\(784\) 22.0182 0.786366
\(785\) −48.9690 −1.74778
\(786\) −0.962055 −0.0343154
\(787\) 25.6637 0.914811 0.457405 0.889258i \(-0.348779\pi\)
0.457405 + 0.889258i \(0.348779\pi\)
\(788\) −16.0135 −0.570457
\(789\) 7.55266 0.268882
\(790\) 1.09940 0.0391151
\(791\) 49.3611 1.75508
\(792\) 0.224485 0.00797673
\(793\) 1.66374 0.0590812
\(794\) 1.31978 0.0468374
\(795\) 23.2815 0.825710
\(796\) −37.8273 −1.34075
\(797\) 8.44244 0.299047 0.149523 0.988758i \(-0.452226\pi\)
0.149523 + 0.988758i \(0.452226\pi\)
\(798\) 0.849271 0.0300639
\(799\) −67.7284 −2.39606
\(800\) 2.17764 0.0769913
\(801\) 7.23252 0.255549
\(802\) −0.318848 −0.0112589
\(803\) −2.54693 −0.0898793
\(804\) 20.0157 0.705900
\(805\) 81.5257 2.87340
\(806\) 0.652000 0.0229657
\(807\) −25.3390 −0.891976
\(808\) −2.44550 −0.0860325
\(809\) 14.1868 0.498780 0.249390 0.968403i \(-0.419770\pi\)
0.249390 + 0.968403i \(0.419770\pi\)
\(810\) −0.161204 −0.00566413
\(811\) −2.52616 −0.0887054 −0.0443527 0.999016i \(-0.514123\pi\)
−0.0443527 + 0.999016i \(0.514123\pi\)
\(812\) −23.0830 −0.810054
\(813\) 24.0494 0.843450
\(814\) −0.0464125 −0.00162676
\(815\) 54.0510 1.89332
\(816\) 25.9259 0.907589
\(817\) 9.45295 0.330717
\(818\) 0.890471 0.0311346
\(819\) 5.88944 0.205794
\(820\) −68.4120 −2.38905
\(821\) 14.9783 0.522746 0.261373 0.965238i \(-0.415825\pi\)
0.261373 + 0.965238i \(0.415825\pi\)
\(822\) 0.0651123 0.00227105
\(823\) 1.14435 0.0398894 0.0199447 0.999801i \(-0.493651\pi\)
0.0199447 + 0.999801i \(0.493651\pi\)
\(824\) 0.250582 0.00872944
\(825\) 3.23780 0.112726
\(826\) 0.398599 0.0138690
\(827\) 40.5209 1.40905 0.704525 0.709679i \(-0.251160\pi\)
0.704525 + 0.709679i \(0.251160\pi\)
\(828\) 16.0231 0.556840
\(829\) −41.9288 −1.45625 −0.728124 0.685446i \(-0.759607\pi\)
−0.728124 + 0.685446i \(0.759607\pi\)
\(830\) −0.0907564 −0.00315020
\(831\) −25.9274 −0.899411
\(832\) −13.1841 −0.457078
\(833\) −36.0176 −1.24794
\(834\) −0.430738 −0.0149152
\(835\) −59.6351 −2.06376
\(836\) −8.52969 −0.295005
\(837\) −6.97737 −0.241173
\(838\) 0.527967 0.0182383
\(839\) −17.9705 −0.620412 −0.310206 0.950669i \(-0.600398\pi\)
−0.310206 + 0.950669i \(0.600398\pi\)
\(840\) −2.28077 −0.0786939
\(841\) −18.3360 −0.632277
\(842\) 1.08633 0.0374374
\(843\) 16.8801 0.581382
\(844\) 28.5325 0.982130
\(845\) 29.3673 1.01027
\(846\) 0.584128 0.0200827
\(847\) 3.53988 0.121632
\(848\) 32.2929 1.10894
\(849\) −14.2351 −0.488548
\(850\) −1.18427 −0.0406203
\(851\) −6.63081 −0.227301
\(852\) −4.25937 −0.145924
\(853\) −29.2979 −1.00314 −0.501571 0.865117i \(-0.667244\pi\)
−0.501571 + 0.865117i \(0.667244\pi\)
\(854\) 0.198819 0.00680345
\(855\) 12.2601 0.419287
\(856\) 0.628606 0.0214853
\(857\) 13.4529 0.459543 0.229772 0.973245i \(-0.426202\pi\)
0.229772 + 0.973245i \(0.426202\pi\)
\(858\) 0.0934449 0.00319016
\(859\) 11.4298 0.389981 0.194990 0.980805i \(-0.437532\pi\)
0.194990 + 0.980805i \(0.437532\pi\)
\(860\) −12.6832 −0.432493
\(861\) 42.2542 1.44002
\(862\) 1.23912 0.0422045
\(863\) 22.5690 0.768259 0.384129 0.923279i \(-0.374502\pi\)
0.384129 + 0.923279i \(0.374502\pi\)
\(864\) −0.672570 −0.0228813
\(865\) −24.6285 −0.837394
\(866\) 0.923301 0.0313751
\(867\) −25.4098 −0.862962
\(868\) −49.3202 −1.67404
\(869\) 6.81997 0.231352
\(870\) 0.526423 0.0178474
\(871\) 16.6768 0.565072
\(872\) −2.40027 −0.0812833
\(873\) 11.1816 0.378440
\(874\) 1.92513 0.0651184
\(875\) 17.9040 0.605265
\(876\) 5.08583 0.171834
\(877\) 42.1546 1.42346 0.711729 0.702454i \(-0.247912\pi\)
0.711729 + 0.702454i \(0.247912\pi\)
\(878\) 1.63619 0.0552186
\(879\) −25.1762 −0.849173
\(880\) 11.4263 0.385181
\(881\) 4.79100 0.161413 0.0807065 0.996738i \(-0.474282\pi\)
0.0807065 + 0.996738i \(0.474282\pi\)
\(882\) 0.310636 0.0104596
\(883\) 35.8055 1.20495 0.602476 0.798137i \(-0.294181\pi\)
0.602476 + 0.798137i \(0.294181\pi\)
\(884\) 21.6353 0.727675
\(885\) 5.75419 0.193425
\(886\) −2.24008 −0.0752569
\(887\) 17.9056 0.601210 0.300605 0.953749i \(-0.402811\pi\)
0.300605 + 0.953749i \(0.402811\pi\)
\(888\) 0.185504 0.00622510
\(889\) −54.3344 −1.82232
\(890\) −1.16591 −0.0390814
\(891\) −1.00000 −0.0335013
\(892\) 5.68295 0.190279
\(893\) −44.4249 −1.48662
\(894\) 0.0669155 0.00223799
\(895\) −4.67751 −0.156352
\(896\) −6.33714 −0.211709
\(897\) 13.3502 0.445749
\(898\) −0.358979 −0.0119793
\(899\) 22.7851 0.759927
\(900\) −6.46538 −0.215513
\(901\) −52.8249 −1.75985
\(902\) 0.670428 0.0223228
\(903\) 7.83369 0.260689
\(904\) −3.13029 −0.104112
\(905\) 19.5192 0.648841
\(906\) −0.633440 −0.0210446
\(907\) 16.6708 0.553544 0.276772 0.960936i \(-0.410735\pi\)
0.276772 + 0.960936i \(0.410735\pi\)
\(908\) 38.9052 1.29111
\(909\) 10.8938 0.361326
\(910\) −0.949400 −0.0314723
\(911\) −36.4248 −1.20681 −0.603403 0.797436i \(-0.706189\pi\)
−0.603403 + 0.797436i \(0.706189\pi\)
\(912\) 17.0055 0.563109
\(913\) −0.562991 −0.0186323
\(914\) −0.368277 −0.0121815
\(915\) 2.87016 0.0948844
\(916\) 23.3952 0.772998
\(917\) 60.6342 2.00232
\(918\) 0.365766 0.0120721
\(919\) 4.21597 0.139072 0.0695359 0.997579i \(-0.477848\pi\)
0.0695359 + 0.997579i \(0.477848\pi\)
\(920\) −5.17004 −0.170451
\(921\) −20.2369 −0.666827
\(922\) −0.444233 −0.0146300
\(923\) −3.54884 −0.116812
\(924\) −7.06858 −0.232539
\(925\) 2.67556 0.0879719
\(926\) 1.68273 0.0552979
\(927\) −1.11625 −0.0366626
\(928\) 2.19633 0.0720979
\(929\) 28.4286 0.932713 0.466356 0.884597i \(-0.345566\pi\)
0.466356 + 0.884597i \(0.345566\pi\)
\(930\) 1.12478 0.0368830
\(931\) −23.6249 −0.774275
\(932\) 55.5131 1.81839
\(933\) −20.5089 −0.671431
\(934\) 0.642503 0.0210234
\(935\) −18.6913 −0.611270
\(936\) −0.373485 −0.0122077
\(937\) −20.5654 −0.671843 −0.335921 0.941890i \(-0.609048\pi\)
−0.335921 + 0.941890i \(0.609048\pi\)
\(938\) 1.99290 0.0650704
\(939\) 10.5734 0.345050
\(940\) 59.6057 1.94412
\(941\) −7.87253 −0.256637 −0.128318 0.991733i \(-0.540958\pi\)
−0.128318 + 0.991733i \(0.540958\pi\)
\(942\) −0.958264 −0.0312219
\(943\) 95.7818 3.11908
\(944\) 7.98142 0.259773
\(945\) 10.1600 0.330505
\(946\) 0.124294 0.00404113
\(947\) 51.6536 1.67852 0.839258 0.543734i \(-0.182990\pi\)
0.839258 + 0.543734i \(0.182990\pi\)
\(948\) −13.6184 −0.442306
\(949\) 4.23744 0.137553
\(950\) −0.776798 −0.0252026
\(951\) −20.3836 −0.660984
\(952\) 5.17498 0.167722
\(953\) −50.9942 −1.65186 −0.825932 0.563769i \(-0.809351\pi\)
−0.825932 + 0.563769i \(0.809351\pi\)
\(954\) 0.455591 0.0147503
\(955\) −60.5762 −1.96020
\(956\) −2.54736 −0.0823875
\(957\) 3.26557 0.105561
\(958\) 0.340101 0.0109882
\(959\) −4.10375 −0.132517
\(960\) −22.7442 −0.734067
\(961\) 17.6838 0.570444
\(962\) 0.0772185 0.00248962
\(963\) −2.80022 −0.0902357
\(964\) −29.9416 −0.964355
\(965\) 44.0424 1.41777
\(966\) 1.59536 0.0513299
\(967\) 31.7512 1.02105 0.510524 0.859863i \(-0.329451\pi\)
0.510524 + 0.859863i \(0.329451\pi\)
\(968\) −0.224485 −0.00721522
\(969\) −27.8177 −0.893634
\(970\) −1.80252 −0.0578754
\(971\) 27.2104 0.873222 0.436611 0.899650i \(-0.356179\pi\)
0.436611 + 0.899650i \(0.356179\pi\)
\(972\) 1.99685 0.0640488
\(973\) 27.1476 0.870311
\(974\) 0.322402 0.0103304
\(975\) −5.38686 −0.172517
\(976\) 3.98108 0.127431
\(977\) 49.0474 1.56916 0.784582 0.620025i \(-0.212877\pi\)
0.784582 + 0.620025i \(0.212877\pi\)
\(978\) 1.05771 0.0338219
\(979\) −7.23252 −0.231152
\(980\) 31.6980 1.01255
\(981\) 10.6923 0.341380
\(982\) 0.324807 0.0103650
\(983\) 29.9573 0.955490 0.477745 0.878499i \(-0.341454\pi\)
0.477745 + 0.878499i \(0.341454\pi\)
\(984\) −2.67960 −0.0854224
\(985\) −23.0169 −0.733380
\(986\) −1.19444 −0.0380386
\(987\) −36.8151 −1.17184
\(988\) 14.1912 0.451482
\(989\) 17.7574 0.564653
\(990\) 0.161204 0.00512339
\(991\) −45.8678 −1.45704 −0.728519 0.685026i \(-0.759791\pi\)
−0.728519 + 0.685026i \(0.759791\pi\)
\(992\) 4.69277 0.148996
\(993\) −11.9595 −0.379523
\(994\) −0.424091 −0.0134513
\(995\) −54.3709 −1.72367
\(996\) 1.12421 0.0356219
\(997\) −17.7103 −0.560892 −0.280446 0.959870i \(-0.590482\pi\)
−0.280446 + 0.959870i \(0.590482\pi\)
\(998\) −0.556452 −0.0176142
\(999\) −0.826353 −0.0261446
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 2013.2.a.h.1.8 14
3.2 odd 2 6039.2.a.j.1.7 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.2.a.h.1.8 14 1.1 even 1 trivial
6039.2.a.j.1.7 14 3.2 odd 2