Properties

Label 2013.2.a.h.1.14
Level $2013$
Weight $2$
Character 2013.1
Self dual yes
Analytic conductor $16.074$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

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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 1.14
Root \(-2.57087\) of defining polynomial
Character \(\chi\) \(=\) 2013.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.57087 q^{2} -1.00000 q^{3} +4.60938 q^{4} +4.00721 q^{5} -2.57087 q^{6} +2.04273 q^{7} +6.70837 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.57087 q^{2} -1.00000 q^{3} +4.60938 q^{4} +4.00721 q^{5} -2.57087 q^{6} +2.04273 q^{7} +6.70837 q^{8} +1.00000 q^{9} +10.3020 q^{10} -1.00000 q^{11} -4.60938 q^{12} -4.75237 q^{13} +5.25159 q^{14} -4.00721 q^{15} +8.02760 q^{16} -0.339679 q^{17} +2.57087 q^{18} +4.54116 q^{19} +18.4707 q^{20} -2.04273 q^{21} -2.57087 q^{22} -4.75749 q^{23} -6.70837 q^{24} +11.0577 q^{25} -12.2177 q^{26} -1.00000 q^{27} +9.41571 q^{28} -4.28494 q^{29} -10.3020 q^{30} +1.81765 q^{31} +7.22118 q^{32} +1.00000 q^{33} -0.873272 q^{34} +8.18565 q^{35} +4.60938 q^{36} -2.11204 q^{37} +11.6747 q^{38} +4.75237 q^{39} +26.8819 q^{40} -10.2585 q^{41} -5.25159 q^{42} -9.89546 q^{43} -4.60938 q^{44} +4.00721 q^{45} -12.2309 q^{46} -5.22451 q^{47} -8.02760 q^{48} -2.82726 q^{49} +28.4280 q^{50} +0.339679 q^{51} -21.9055 q^{52} +9.68455 q^{53} -2.57087 q^{54} -4.00721 q^{55} +13.7034 q^{56} -4.54116 q^{57} -11.0160 q^{58} -2.04679 q^{59} -18.4707 q^{60} +1.00000 q^{61} +4.67295 q^{62} +2.04273 q^{63} +2.50953 q^{64} -19.0437 q^{65} +2.57087 q^{66} +5.30981 q^{67} -1.56571 q^{68} +4.75749 q^{69} +21.0442 q^{70} +11.4906 q^{71} +6.70837 q^{72} -4.51365 q^{73} -5.42978 q^{74} -11.0577 q^{75} +20.9319 q^{76} -2.04273 q^{77} +12.2177 q^{78} +5.49270 q^{79} +32.1683 q^{80} +1.00000 q^{81} -26.3733 q^{82} +14.2207 q^{83} -9.41571 q^{84} -1.36117 q^{85} -25.4399 q^{86} +4.28494 q^{87} -6.70837 q^{88} -6.05470 q^{89} +10.3020 q^{90} -9.70780 q^{91} -21.9291 q^{92} -1.81765 q^{93} -13.4315 q^{94} +18.1974 q^{95} -7.22118 q^{96} +13.6004 q^{97} -7.26851 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - q^{2} - 14q^{3} + 15q^{4} + q^{5} + q^{6} + 9q^{7} + 14q^{9} + O(q^{10}) \) \( 14q - q^{2} - 14q^{3} + 15q^{4} + q^{5} + q^{6} + 9q^{7} + 14q^{9} + 6q^{10} - 14q^{11} - 15q^{12} + q^{13} - 7q^{14} - q^{15} + 17q^{16} - 9q^{17} - q^{18} + 22q^{19} + 23q^{20} - 9q^{21} + q^{22} + q^{23} + 25q^{25} + 4q^{26} - 14q^{27} + 37q^{28} - 6q^{29} - 6q^{30} + 9q^{31} + 4q^{32} + 14q^{33} + 8q^{34} + 18q^{35} + 15q^{36} + 18q^{37} + 8q^{38} - q^{39} + 16q^{40} - 25q^{41} + 7q^{42} + 25q^{43} - 15q^{44} + q^{45} + 20q^{46} + 36q^{47} - 17q^{48} + 25q^{49} + 2q^{50} + 9q^{51} - 13q^{52} + q^{54} - q^{55} - 40q^{56} - 22q^{57} + 33q^{58} + 17q^{59} - 23q^{60} + 14q^{61} - 13q^{62} + 9q^{63} - 6q^{64} - 61q^{65} - q^{66} + 22q^{67} + 66q^{68} - q^{69} + 44q^{70} - 13q^{71} + 20q^{73} - 12q^{74} - 25q^{75} + 49q^{76} - 9q^{77} - 4q^{78} + 31q^{79} + 88q^{80} + 14q^{81} + 2q^{82} + 32q^{83} - 37q^{84} + 2q^{85} - 14q^{86} + 6q^{87} - 21q^{89} + 6q^{90} + 45q^{91} - 14q^{92} - 9q^{93} - 31q^{94} + 23q^{95} - 4q^{96} + 37q^{97} - 38q^{98} - 14q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.57087 1.81788 0.908940 0.416927i \(-0.136893\pi\)
0.908940 + 0.416927i \(0.136893\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.60938 2.30469
\(5\) 4.00721 1.79208 0.896040 0.443974i \(-0.146432\pi\)
0.896040 + 0.443974i \(0.146432\pi\)
\(6\) −2.57087 −1.04955
\(7\) 2.04273 0.772079 0.386040 0.922482i \(-0.373843\pi\)
0.386040 + 0.922482i \(0.373843\pi\)
\(8\) 6.70837 2.37177
\(9\) 1.00000 0.333333
\(10\) 10.3020 3.25779
\(11\) −1.00000 −0.301511
\(12\) −4.60938 −1.33061
\(13\) −4.75237 −1.31807 −0.659035 0.752112i \(-0.729035\pi\)
−0.659035 + 0.752112i \(0.729035\pi\)
\(14\) 5.25159 1.40355
\(15\) −4.00721 −1.03466
\(16\) 8.02760 2.00690
\(17\) −0.339679 −0.0823844 −0.0411922 0.999151i \(-0.513116\pi\)
−0.0411922 + 0.999151i \(0.513116\pi\)
\(18\) 2.57087 0.605960
\(19\) 4.54116 1.04181 0.520907 0.853613i \(-0.325594\pi\)
0.520907 + 0.853613i \(0.325594\pi\)
\(20\) 18.4707 4.13018
\(21\) −2.04273 −0.445760
\(22\) −2.57087 −0.548112
\(23\) −4.75749 −0.992006 −0.496003 0.868321i \(-0.665200\pi\)
−0.496003 + 0.868321i \(0.665200\pi\)
\(24\) −6.70837 −1.36934
\(25\) 11.0577 2.21155
\(26\) −12.2177 −2.39609
\(27\) −1.00000 −0.192450
\(28\) 9.41571 1.77940
\(29\) −4.28494 −0.795693 −0.397846 0.917452i \(-0.630242\pi\)
−0.397846 + 0.917452i \(0.630242\pi\)
\(30\) −10.3020 −1.88088
\(31\) 1.81765 0.326460 0.163230 0.986588i \(-0.447809\pi\)
0.163230 + 0.986588i \(0.447809\pi\)
\(32\) 7.22118 1.27654
\(33\) 1.00000 0.174078
\(34\) −0.873272 −0.149765
\(35\) 8.18565 1.38363
\(36\) 4.60938 0.768229
\(37\) −2.11204 −0.347217 −0.173609 0.984815i \(-0.555543\pi\)
−0.173609 + 0.984815i \(0.555543\pi\)
\(38\) 11.6747 1.89389
\(39\) 4.75237 0.760988
\(40\) 26.8819 4.25039
\(41\) −10.2585 −1.60211 −0.801056 0.598589i \(-0.795728\pi\)
−0.801056 + 0.598589i \(0.795728\pi\)
\(42\) −5.25159 −0.810338
\(43\) −9.89546 −1.50904 −0.754522 0.656275i \(-0.772131\pi\)
−0.754522 + 0.656275i \(0.772131\pi\)
\(44\) −4.60938 −0.694890
\(45\) 4.00721 0.597360
\(46\) −12.2309 −1.80335
\(47\) −5.22451 −0.762074 −0.381037 0.924560i \(-0.624433\pi\)
−0.381037 + 0.924560i \(0.624433\pi\)
\(48\) −8.02760 −1.15868
\(49\) −2.82726 −0.403894
\(50\) 28.4280 4.02033
\(51\) 0.339679 0.0475646
\(52\) −21.9055 −3.03774
\(53\) 9.68455 1.33028 0.665138 0.746721i \(-0.268373\pi\)
0.665138 + 0.746721i \(0.268373\pi\)
\(54\) −2.57087 −0.349851
\(55\) −4.00721 −0.540332
\(56\) 13.7034 1.83119
\(57\) −4.54116 −0.601492
\(58\) −11.0160 −1.44647
\(59\) −2.04679 −0.266469 −0.133235 0.991085i \(-0.542536\pi\)
−0.133235 + 0.991085i \(0.542536\pi\)
\(60\) −18.4707 −2.38456
\(61\) 1.00000 0.128037
\(62\) 4.67295 0.593465
\(63\) 2.04273 0.257360
\(64\) 2.50953 0.313691
\(65\) −19.0437 −2.36209
\(66\) 2.57087 0.316452
\(67\) 5.30981 0.648697 0.324348 0.945938i \(-0.394855\pi\)
0.324348 + 0.945938i \(0.394855\pi\)
\(68\) −1.56571 −0.189870
\(69\) 4.75749 0.572735
\(70\) 21.0442 2.51527
\(71\) 11.4906 1.36368 0.681841 0.731500i \(-0.261180\pi\)
0.681841 + 0.731500i \(0.261180\pi\)
\(72\) 6.70837 0.790589
\(73\) −4.51365 −0.528283 −0.264142 0.964484i \(-0.585089\pi\)
−0.264142 + 0.964484i \(0.585089\pi\)
\(74\) −5.42978 −0.631199
\(75\) −11.0577 −1.27684
\(76\) 20.9319 2.40106
\(77\) −2.04273 −0.232791
\(78\) 12.2177 1.38339
\(79\) 5.49270 0.617977 0.308989 0.951066i \(-0.400009\pi\)
0.308989 + 0.951066i \(0.400009\pi\)
\(80\) 32.1683 3.59652
\(81\) 1.00000 0.111111
\(82\) −26.3733 −2.91245
\(83\) 14.2207 1.56092 0.780460 0.625206i \(-0.214985\pi\)
0.780460 + 0.625206i \(0.214985\pi\)
\(84\) −9.41571 −1.02734
\(85\) −1.36117 −0.147639
\(86\) −25.4399 −2.74326
\(87\) 4.28494 0.459393
\(88\) −6.70837 −0.715115
\(89\) −6.05470 −0.641797 −0.320899 0.947114i \(-0.603985\pi\)
−0.320899 + 0.947114i \(0.603985\pi\)
\(90\) 10.3020 1.08593
\(91\) −9.70780 −1.01765
\(92\) −21.9291 −2.28626
\(93\) −1.81765 −0.188482
\(94\) −13.4315 −1.38536
\(95\) 18.1974 1.86701
\(96\) −7.22118 −0.737009
\(97\) 13.6004 1.38092 0.690458 0.723373i \(-0.257409\pi\)
0.690458 + 0.723373i \(0.257409\pi\)
\(98\) −7.26851 −0.734231
\(99\) −1.00000 −0.100504
\(100\) 50.9693 5.09693
\(101\) −10.2656 −1.02147 −0.510735 0.859738i \(-0.670627\pi\)
−0.510735 + 0.859738i \(0.670627\pi\)
\(102\) 0.873272 0.0864668
\(103\) 10.8307 1.06718 0.533590 0.845743i \(-0.320843\pi\)
0.533590 + 0.845743i \(0.320843\pi\)
\(104\) −31.8807 −3.12616
\(105\) −8.18565 −0.798837
\(106\) 24.8977 2.41828
\(107\) −10.3745 −1.00294 −0.501471 0.865174i \(-0.667208\pi\)
−0.501471 + 0.865174i \(0.667208\pi\)
\(108\) −4.60938 −0.443537
\(109\) −15.9251 −1.52534 −0.762672 0.646786i \(-0.776113\pi\)
−0.762672 + 0.646786i \(0.776113\pi\)
\(110\) −10.3020 −0.982259
\(111\) 2.11204 0.200466
\(112\) 16.3982 1.54949
\(113\) 4.50235 0.423546 0.211773 0.977319i \(-0.432076\pi\)
0.211773 + 0.977319i \(0.432076\pi\)
\(114\) −11.6747 −1.09344
\(115\) −19.0643 −1.77775
\(116\) −19.7509 −1.83382
\(117\) −4.75237 −0.439357
\(118\) −5.26203 −0.484409
\(119\) −0.693873 −0.0636072
\(120\) −26.8819 −2.45397
\(121\) 1.00000 0.0909091
\(122\) 2.57087 0.232756
\(123\) 10.2585 0.924980
\(124\) 8.37824 0.752388
\(125\) 24.2746 2.17119
\(126\) 5.25159 0.467849
\(127\) −12.2578 −1.08770 −0.543852 0.839181i \(-0.683035\pi\)
−0.543852 + 0.839181i \(0.683035\pi\)
\(128\) −7.99069 −0.706284
\(129\) 9.89546 0.871246
\(130\) −48.9590 −4.29399
\(131\) 14.1653 1.23763 0.618814 0.785538i \(-0.287614\pi\)
0.618814 + 0.785538i \(0.287614\pi\)
\(132\) 4.60938 0.401195
\(133\) 9.27637 0.804363
\(134\) 13.6508 1.17925
\(135\) −4.00721 −0.344886
\(136\) −2.27870 −0.195397
\(137\) 11.8311 1.01080 0.505401 0.862885i \(-0.331345\pi\)
0.505401 + 0.862885i \(0.331345\pi\)
\(138\) 12.2309 1.04116
\(139\) 21.4652 1.82066 0.910328 0.413887i \(-0.135829\pi\)
0.910328 + 0.413887i \(0.135829\pi\)
\(140\) 37.7307 3.18883
\(141\) 5.22451 0.439983
\(142\) 29.5408 2.47901
\(143\) 4.75237 0.397413
\(144\) 8.02760 0.668967
\(145\) −17.1706 −1.42594
\(146\) −11.6040 −0.960356
\(147\) 2.82726 0.233188
\(148\) −9.73519 −0.800227
\(149\) 5.71869 0.468493 0.234247 0.972177i \(-0.424738\pi\)
0.234247 + 0.972177i \(0.424738\pi\)
\(150\) −28.4280 −2.32114
\(151\) 4.53058 0.368694 0.184347 0.982861i \(-0.440983\pi\)
0.184347 + 0.982861i \(0.440983\pi\)
\(152\) 30.4638 2.47094
\(153\) −0.339679 −0.0274615
\(154\) −5.25159 −0.423185
\(155\) 7.28371 0.585042
\(156\) 21.9055 1.75384
\(157\) −10.4733 −0.835859 −0.417930 0.908479i \(-0.637244\pi\)
−0.417930 + 0.908479i \(0.637244\pi\)
\(158\) 14.1210 1.12341
\(159\) −9.68455 −0.768035
\(160\) 28.9368 2.28766
\(161\) −9.71827 −0.765907
\(162\) 2.57087 0.201987
\(163\) 12.0156 0.941136 0.470568 0.882364i \(-0.344049\pi\)
0.470568 + 0.882364i \(0.344049\pi\)
\(164\) −47.2854 −3.69237
\(165\) 4.00721 0.311961
\(166\) 36.5595 2.83756
\(167\) 7.72247 0.597582 0.298791 0.954318i \(-0.403417\pi\)
0.298791 + 0.954318i \(0.403417\pi\)
\(168\) −13.7034 −1.05724
\(169\) 9.58501 0.737308
\(170\) −3.49938 −0.268391
\(171\) 4.54116 0.347271
\(172\) −45.6119 −3.47787
\(173\) 14.5915 1.10937 0.554684 0.832061i \(-0.312839\pi\)
0.554684 + 0.832061i \(0.312839\pi\)
\(174\) 11.0160 0.835122
\(175\) 22.5880 1.70749
\(176\) −8.02760 −0.605103
\(177\) 2.04679 0.153846
\(178\) −15.5659 −1.16671
\(179\) −13.1655 −0.984037 −0.492019 0.870585i \(-0.663741\pi\)
−0.492019 + 0.870585i \(0.663741\pi\)
\(180\) 18.4707 1.37673
\(181\) −7.26104 −0.539709 −0.269854 0.962901i \(-0.586976\pi\)
−0.269854 + 0.962901i \(0.586976\pi\)
\(182\) −24.9575 −1.84997
\(183\) −1.00000 −0.0739221
\(184\) −31.9150 −2.35281
\(185\) −8.46339 −0.622241
\(186\) −4.67295 −0.342637
\(187\) 0.339679 0.0248398
\(188\) −24.0818 −1.75634
\(189\) −2.04273 −0.148587
\(190\) 46.7832 3.39401
\(191\) 3.04371 0.220235 0.110118 0.993919i \(-0.464877\pi\)
0.110118 + 0.993919i \(0.464877\pi\)
\(192\) −2.50953 −0.181110
\(193\) 6.85641 0.493535 0.246768 0.969075i \(-0.420632\pi\)
0.246768 + 0.969075i \(0.420632\pi\)
\(194\) 34.9650 2.51034
\(195\) 19.0437 1.36375
\(196\) −13.0319 −0.930850
\(197\) −12.1375 −0.864763 −0.432381 0.901691i \(-0.642327\pi\)
−0.432381 + 0.901691i \(0.642327\pi\)
\(198\) −2.57087 −0.182704
\(199\) −13.8050 −0.978613 −0.489306 0.872112i \(-0.662750\pi\)
−0.489306 + 0.872112i \(0.662750\pi\)
\(200\) 74.1794 5.24528
\(201\) −5.30981 −0.374525
\(202\) −26.3916 −1.85691
\(203\) −8.75297 −0.614338
\(204\) 1.56571 0.109622
\(205\) −41.1081 −2.87111
\(206\) 27.8443 1.94001
\(207\) −4.75749 −0.330669
\(208\) −38.1501 −2.64523
\(209\) −4.54116 −0.314119
\(210\) −21.0442 −1.45219
\(211\) 13.4936 0.928938 0.464469 0.885589i \(-0.346245\pi\)
0.464469 + 0.885589i \(0.346245\pi\)
\(212\) 44.6398 3.06587
\(213\) −11.4906 −0.787322
\(214\) −26.6715 −1.82323
\(215\) −39.6532 −2.70432
\(216\) −6.70837 −0.456447
\(217\) 3.71297 0.252053
\(218\) −40.9413 −2.77289
\(219\) 4.51365 0.305004
\(220\) −18.4707 −1.24530
\(221\) 1.61428 0.108588
\(222\) 5.42978 0.364423
\(223\) −3.65818 −0.244970 −0.122485 0.992470i \(-0.539086\pi\)
−0.122485 + 0.992470i \(0.539086\pi\)
\(224\) 14.7509 0.985588
\(225\) 11.0577 0.737183
\(226\) 11.5750 0.769956
\(227\) −6.72165 −0.446131 −0.223066 0.974803i \(-0.571606\pi\)
−0.223066 + 0.974803i \(0.571606\pi\)
\(228\) −20.9319 −1.38625
\(229\) −1.23766 −0.0817871 −0.0408935 0.999164i \(-0.513020\pi\)
−0.0408935 + 0.999164i \(0.513020\pi\)
\(230\) −49.0118 −3.23174
\(231\) 2.04273 0.134402
\(232\) −28.7449 −1.88720
\(233\) 12.9299 0.847065 0.423532 0.905881i \(-0.360790\pi\)
0.423532 + 0.905881i \(0.360790\pi\)
\(234\) −12.2177 −0.798698
\(235\) −20.9357 −1.36570
\(236\) −9.43442 −0.614128
\(237\) −5.49270 −0.356789
\(238\) −1.78386 −0.115630
\(239\) −18.5458 −1.19963 −0.599814 0.800140i \(-0.704759\pi\)
−0.599814 + 0.800140i \(0.704759\pi\)
\(240\) −32.1683 −2.07645
\(241\) −27.7936 −1.79034 −0.895171 0.445723i \(-0.852947\pi\)
−0.895171 + 0.445723i \(0.852947\pi\)
\(242\) 2.57087 0.165262
\(243\) −1.00000 −0.0641500
\(244\) 4.60938 0.295085
\(245\) −11.3294 −0.723810
\(246\) 26.3733 1.68150
\(247\) −21.5813 −1.37318
\(248\) 12.1935 0.774287
\(249\) −14.2207 −0.901197
\(250\) 62.4070 3.94696
\(251\) −4.56250 −0.287982 −0.143991 0.989579i \(-0.545994\pi\)
−0.143991 + 0.989579i \(0.545994\pi\)
\(252\) 9.41571 0.593134
\(253\) 4.75749 0.299101
\(254\) −31.5132 −1.97732
\(255\) 1.36117 0.0852396
\(256\) −25.5621 −1.59763
\(257\) −16.8127 −1.04874 −0.524372 0.851489i \(-0.675700\pi\)
−0.524372 + 0.851489i \(0.675700\pi\)
\(258\) 25.4399 1.58382
\(259\) −4.31433 −0.268079
\(260\) −87.7798 −5.44387
\(261\) −4.28494 −0.265231
\(262\) 36.4171 2.24986
\(263\) −8.19724 −0.505463 −0.252732 0.967536i \(-0.581329\pi\)
−0.252732 + 0.967536i \(0.581329\pi\)
\(264\) 6.70837 0.412872
\(265\) 38.8081 2.38396
\(266\) 23.8483 1.46224
\(267\) 6.05470 0.370542
\(268\) 24.4749 1.49504
\(269\) 12.7223 0.775690 0.387845 0.921725i \(-0.373220\pi\)
0.387845 + 0.921725i \(0.373220\pi\)
\(270\) −10.3020 −0.626961
\(271\) 28.9215 1.75686 0.878428 0.477875i \(-0.158593\pi\)
0.878428 + 0.477875i \(0.158593\pi\)
\(272\) −2.72681 −0.165337
\(273\) 9.70780 0.587543
\(274\) 30.4163 1.83752
\(275\) −11.0577 −0.666807
\(276\) 21.9291 1.31998
\(277\) 9.01259 0.541514 0.270757 0.962648i \(-0.412726\pi\)
0.270757 + 0.962648i \(0.412726\pi\)
\(278\) 55.1843 3.30974
\(279\) 1.81765 0.108820
\(280\) 54.9124 3.28164
\(281\) −20.0391 −1.19543 −0.597715 0.801708i \(-0.703925\pi\)
−0.597715 + 0.801708i \(0.703925\pi\)
\(282\) 13.4315 0.799837
\(283\) 29.2872 1.74094 0.870471 0.492221i \(-0.163815\pi\)
0.870471 + 0.492221i \(0.163815\pi\)
\(284\) 52.9645 3.14286
\(285\) −18.1974 −1.07792
\(286\) 12.2177 0.722449
\(287\) −20.9554 −1.23696
\(288\) 7.22118 0.425512
\(289\) −16.8846 −0.993213
\(290\) −44.1435 −2.59220
\(291\) −13.6004 −0.797272
\(292\) −20.8051 −1.21753
\(293\) 31.2913 1.82806 0.914029 0.405649i \(-0.132954\pi\)
0.914029 + 0.405649i \(0.132954\pi\)
\(294\) 7.26851 0.423908
\(295\) −8.20191 −0.477534
\(296\) −14.1683 −0.823518
\(297\) 1.00000 0.0580259
\(298\) 14.7020 0.851665
\(299\) 22.6094 1.30753
\(300\) −50.9693 −2.94271
\(301\) −20.2137 −1.16510
\(302\) 11.6475 0.670241
\(303\) 10.2656 0.589746
\(304\) 36.4547 2.09082
\(305\) 4.00721 0.229452
\(306\) −0.873272 −0.0499216
\(307\) 0.203717 0.0116268 0.00581338 0.999983i \(-0.498150\pi\)
0.00581338 + 0.999983i \(0.498150\pi\)
\(308\) −9.41571 −0.536510
\(309\) −10.8307 −0.616137
\(310\) 18.7255 1.06354
\(311\) −15.4938 −0.878573 −0.439287 0.898347i \(-0.644769\pi\)
−0.439287 + 0.898347i \(0.644769\pi\)
\(312\) 31.8807 1.80489
\(313\) −27.2007 −1.53747 −0.768737 0.639565i \(-0.779114\pi\)
−0.768737 + 0.639565i \(0.779114\pi\)
\(314\) −26.9255 −1.51949
\(315\) 8.18565 0.461209
\(316\) 25.3179 1.42425
\(317\) −11.9050 −0.668653 −0.334327 0.942457i \(-0.608509\pi\)
−0.334327 + 0.942457i \(0.608509\pi\)
\(318\) −24.8977 −1.39620
\(319\) 4.28494 0.239910
\(320\) 10.0562 0.562159
\(321\) 10.3745 0.579049
\(322\) −24.9844 −1.39233
\(323\) −1.54254 −0.0858292
\(324\) 4.60938 0.256076
\(325\) −52.5505 −2.91497
\(326\) 30.8906 1.71087
\(327\) 15.9251 0.880657
\(328\) −68.8180 −3.79984
\(329\) −10.6723 −0.588381
\(330\) 10.3020 0.567108
\(331\) −5.44265 −0.299155 −0.149577 0.988750i \(-0.547791\pi\)
−0.149577 + 0.988750i \(0.547791\pi\)
\(332\) 65.5483 3.59743
\(333\) −2.11204 −0.115739
\(334\) 19.8535 1.08633
\(335\) 21.2775 1.16252
\(336\) −16.3982 −0.894596
\(337\) 11.5595 0.629687 0.314843 0.949144i \(-0.398048\pi\)
0.314843 + 0.949144i \(0.398048\pi\)
\(338\) 24.6418 1.34034
\(339\) −4.50235 −0.244534
\(340\) −6.27413 −0.340263
\(341\) −1.81765 −0.0984314
\(342\) 11.6747 0.631298
\(343\) −20.0744 −1.08392
\(344\) −66.3824 −3.57910
\(345\) 19.0643 1.02639
\(346\) 37.5128 2.01670
\(347\) −34.9338 −1.87535 −0.937673 0.347519i \(-0.887024\pi\)
−0.937673 + 0.347519i \(0.887024\pi\)
\(348\) 19.7509 1.05876
\(349\) −16.4637 −0.881281 −0.440641 0.897684i \(-0.645249\pi\)
−0.440641 + 0.897684i \(0.645249\pi\)
\(350\) 58.0708 3.10401
\(351\) 4.75237 0.253663
\(352\) −7.22118 −0.384890
\(353\) 36.1064 1.92175 0.960876 0.276980i \(-0.0893335\pi\)
0.960876 + 0.276980i \(0.0893335\pi\)
\(354\) 5.26203 0.279674
\(355\) 46.0452 2.44383
\(356\) −27.9084 −1.47914
\(357\) 0.693873 0.0367237
\(358\) −33.8469 −1.78886
\(359\) −16.1146 −0.850498 −0.425249 0.905076i \(-0.639813\pi\)
−0.425249 + 0.905076i \(0.639813\pi\)
\(360\) 26.8819 1.41680
\(361\) 1.62217 0.0853773
\(362\) −18.6672 −0.981126
\(363\) −1.00000 −0.0524864
\(364\) −44.7469 −2.34538
\(365\) −18.0872 −0.946725
\(366\) −2.57087 −0.134382
\(367\) 35.8180 1.86969 0.934843 0.355061i \(-0.115540\pi\)
0.934843 + 0.355061i \(0.115540\pi\)
\(368\) −38.1913 −1.99086
\(369\) −10.2585 −0.534038
\(370\) −21.7583 −1.13116
\(371\) 19.7829 1.02708
\(372\) −8.37824 −0.434392
\(373\) −18.3914 −0.952273 −0.476137 0.879371i \(-0.657963\pi\)
−0.476137 + 0.879371i \(0.657963\pi\)
\(374\) 0.873272 0.0451558
\(375\) −24.2746 −1.25354
\(376\) −35.0480 −1.80746
\(377\) 20.3636 1.04878
\(378\) −5.25159 −0.270113
\(379\) −5.27053 −0.270729 −0.135364 0.990796i \(-0.543221\pi\)
−0.135364 + 0.990796i \(0.543221\pi\)
\(380\) 83.8787 4.30289
\(381\) 12.2578 0.627986
\(382\) 7.82499 0.400361
\(383\) 32.5167 1.66153 0.830763 0.556626i \(-0.187904\pi\)
0.830763 + 0.556626i \(0.187904\pi\)
\(384\) 7.99069 0.407773
\(385\) −8.18565 −0.417179
\(386\) 17.6269 0.897188
\(387\) −9.89546 −0.503014
\(388\) 62.6895 3.18258
\(389\) −24.3758 −1.23590 −0.617950 0.786217i \(-0.712037\pi\)
−0.617950 + 0.786217i \(0.712037\pi\)
\(390\) 48.9590 2.47914
\(391\) 1.61602 0.0817258
\(392\) −18.9663 −0.957942
\(393\) −14.1653 −0.714544
\(394\) −31.2040 −1.57203
\(395\) 22.0104 1.10746
\(396\) −4.60938 −0.231630
\(397\) −18.0276 −0.904779 −0.452390 0.891820i \(-0.649428\pi\)
−0.452390 + 0.891820i \(0.649428\pi\)
\(398\) −35.4909 −1.77900
\(399\) −9.27637 −0.464399
\(400\) 88.7671 4.43836
\(401\) −29.1981 −1.45808 −0.729042 0.684469i \(-0.760034\pi\)
−0.729042 + 0.684469i \(0.760034\pi\)
\(402\) −13.6508 −0.680842
\(403\) −8.63815 −0.430297
\(404\) −47.3182 −2.35417
\(405\) 4.00721 0.199120
\(406\) −22.5027 −1.11679
\(407\) 2.11204 0.104690
\(408\) 2.27870 0.112812
\(409\) 2.63476 0.130280 0.0651401 0.997876i \(-0.479251\pi\)
0.0651401 + 0.997876i \(0.479251\pi\)
\(410\) −105.684 −5.21934
\(411\) −11.8311 −0.583587
\(412\) 49.9227 2.45952
\(413\) −4.18103 −0.205735
\(414\) −12.2309 −0.601116
\(415\) 56.9852 2.79729
\(416\) −34.3177 −1.68257
\(417\) −21.4652 −1.05116
\(418\) −11.6747 −0.571030
\(419\) 32.0724 1.56684 0.783420 0.621492i \(-0.213473\pi\)
0.783420 + 0.621492i \(0.213473\pi\)
\(420\) −37.7307 −1.84107
\(421\) 6.02368 0.293576 0.146788 0.989168i \(-0.453106\pi\)
0.146788 + 0.989168i \(0.453106\pi\)
\(422\) 34.6903 1.68870
\(423\) −5.22451 −0.254025
\(424\) 64.9676 3.15510
\(425\) −3.75609 −0.182197
\(426\) −29.5408 −1.43126
\(427\) 2.04273 0.0988546
\(428\) −47.8200 −2.31147
\(429\) −4.75237 −0.229447
\(430\) −101.943 −4.91614
\(431\) −19.6288 −0.945487 −0.472744 0.881200i \(-0.656736\pi\)
−0.472744 + 0.881200i \(0.656736\pi\)
\(432\) −8.02760 −0.386228
\(433\) 27.8579 1.33876 0.669382 0.742919i \(-0.266559\pi\)
0.669382 + 0.742919i \(0.266559\pi\)
\(434\) 9.54557 0.458202
\(435\) 17.1706 0.823269
\(436\) −73.4046 −3.51544
\(437\) −21.6046 −1.03349
\(438\) 11.6040 0.554462
\(439\) −25.4823 −1.21620 −0.608102 0.793859i \(-0.708069\pi\)
−0.608102 + 0.793859i \(0.708069\pi\)
\(440\) −26.8819 −1.28154
\(441\) −2.82726 −0.134631
\(442\) 4.15011 0.197401
\(443\) 29.0256 1.37905 0.689524 0.724263i \(-0.257820\pi\)
0.689524 + 0.724263i \(0.257820\pi\)
\(444\) 9.73519 0.462012
\(445\) −24.2625 −1.15015
\(446\) −9.40471 −0.445326
\(447\) −5.71869 −0.270485
\(448\) 5.12629 0.242194
\(449\) 23.3018 1.09968 0.549840 0.835270i \(-0.314689\pi\)
0.549840 + 0.835270i \(0.314689\pi\)
\(450\) 28.4280 1.34011
\(451\) 10.2585 0.483055
\(452\) 20.7530 0.976141
\(453\) −4.53058 −0.212865
\(454\) −17.2805 −0.811013
\(455\) −38.9012 −1.82372
\(456\) −30.4638 −1.42660
\(457\) 38.8508 1.81737 0.908683 0.417487i \(-0.137089\pi\)
0.908683 + 0.417487i \(0.137089\pi\)
\(458\) −3.18187 −0.148679
\(459\) 0.339679 0.0158549
\(460\) −87.8745 −4.09717
\(461\) 2.42547 0.112965 0.0564827 0.998404i \(-0.482011\pi\)
0.0564827 + 0.998404i \(0.482011\pi\)
\(462\) 5.25159 0.244326
\(463\) 37.3362 1.73516 0.867581 0.497295i \(-0.165673\pi\)
0.867581 + 0.497295i \(0.165673\pi\)
\(464\) −34.3978 −1.59688
\(465\) −7.28371 −0.337774
\(466\) 33.2411 1.53986
\(467\) −7.55898 −0.349788 −0.174894 0.984587i \(-0.555958\pi\)
−0.174894 + 0.984587i \(0.555958\pi\)
\(468\) −21.9055 −1.01258
\(469\) 10.8465 0.500845
\(470\) −53.8231 −2.48267
\(471\) 10.4733 0.482583
\(472\) −13.7306 −0.632003
\(473\) 9.89546 0.454994
\(474\) −14.1210 −0.648600
\(475\) 50.2150 2.30402
\(476\) −3.19832 −0.146595
\(477\) 9.68455 0.443425
\(478\) −47.6788 −2.18078
\(479\) −35.7614 −1.63398 −0.816990 0.576651i \(-0.804359\pi\)
−0.816990 + 0.576651i \(0.804359\pi\)
\(480\) −28.9368 −1.32078
\(481\) 10.0372 0.457657
\(482\) −71.4537 −3.25463
\(483\) 9.71827 0.442197
\(484\) 4.60938 0.209517
\(485\) 54.4998 2.47471
\(486\) −2.57087 −0.116617
\(487\) −6.39232 −0.289664 −0.144832 0.989456i \(-0.546264\pi\)
−0.144832 + 0.989456i \(0.546264\pi\)
\(488\) 6.70837 0.303674
\(489\) −12.0156 −0.543365
\(490\) −29.1265 −1.31580
\(491\) 16.7893 0.757691 0.378846 0.925460i \(-0.376321\pi\)
0.378846 + 0.925460i \(0.376321\pi\)
\(492\) 47.2854 2.13179
\(493\) 1.45550 0.0655526
\(494\) −55.4827 −2.49628
\(495\) −4.00721 −0.180111
\(496\) 14.5914 0.655172
\(497\) 23.4722 1.05287
\(498\) −36.5595 −1.63827
\(499\) 2.39493 0.107212 0.0536060 0.998562i \(-0.482929\pi\)
0.0536060 + 0.998562i \(0.482929\pi\)
\(500\) 111.891 5.00392
\(501\) −7.72247 −0.345014
\(502\) −11.7296 −0.523517
\(503\) 2.97796 0.132781 0.0663903 0.997794i \(-0.478852\pi\)
0.0663903 + 0.997794i \(0.478852\pi\)
\(504\) 13.7034 0.610397
\(505\) −41.1366 −1.83055
\(506\) 12.2309 0.543730
\(507\) −9.58501 −0.425685
\(508\) −56.5008 −2.50682
\(509\) −13.6035 −0.602964 −0.301482 0.953472i \(-0.597481\pi\)
−0.301482 + 0.953472i \(0.597481\pi\)
\(510\) 3.49938 0.154955
\(511\) −9.22017 −0.407876
\(512\) −49.7355 −2.19802
\(513\) −4.54116 −0.200497
\(514\) −43.2232 −1.90649
\(515\) 43.4009 1.91247
\(516\) 45.6119 2.00795
\(517\) 5.22451 0.229774
\(518\) −11.0916 −0.487336
\(519\) −14.5915 −0.640494
\(520\) −127.752 −5.60232
\(521\) 4.86305 0.213054 0.106527 0.994310i \(-0.466027\pi\)
0.106527 + 0.994310i \(0.466027\pi\)
\(522\) −11.0160 −0.482158
\(523\) 4.06198 0.177618 0.0888091 0.996049i \(-0.471694\pi\)
0.0888091 + 0.996049i \(0.471694\pi\)
\(524\) 65.2932 2.85234
\(525\) −22.5880 −0.985820
\(526\) −21.0740 −0.918872
\(527\) −0.617419 −0.0268952
\(528\) 8.02760 0.349357
\(529\) −0.366250 −0.0159239
\(530\) 99.7705 4.33375
\(531\) −2.04679 −0.0888230
\(532\) 42.7583 1.85381
\(533\) 48.7523 2.11170
\(534\) 15.5659 0.673601
\(535\) −41.5729 −1.79735
\(536\) 35.6202 1.53856
\(537\) 13.1655 0.568134
\(538\) 32.7073 1.41011
\(539\) 2.82726 0.121779
\(540\) −18.4707 −0.794854
\(541\) 43.0563 1.85113 0.925566 0.378585i \(-0.123589\pi\)
0.925566 + 0.378585i \(0.123589\pi\)
\(542\) 74.3534 3.19375
\(543\) 7.26104 0.311601
\(544\) −2.45289 −0.105167
\(545\) −63.8150 −2.73354
\(546\) 24.9575 1.06808
\(547\) 8.25809 0.353090 0.176545 0.984293i \(-0.443508\pi\)
0.176545 + 0.984293i \(0.443508\pi\)
\(548\) 54.5341 2.32958
\(549\) 1.00000 0.0426790
\(550\) −28.4280 −1.21217
\(551\) −19.4586 −0.828964
\(552\) 31.9150 1.35839
\(553\) 11.2201 0.477127
\(554\) 23.1702 0.984408
\(555\) 8.46339 0.359251
\(556\) 98.9413 4.19605
\(557\) −12.2925 −0.520852 −0.260426 0.965494i \(-0.583863\pi\)
−0.260426 + 0.965494i \(0.583863\pi\)
\(558\) 4.67295 0.197822
\(559\) 47.0269 1.98902
\(560\) 65.7111 2.77680
\(561\) −0.339679 −0.0143413
\(562\) −51.5179 −2.17315
\(563\) −20.3279 −0.856719 −0.428359 0.903609i \(-0.640908\pi\)
−0.428359 + 0.903609i \(0.640908\pi\)
\(564\) 24.0818 1.01402
\(565\) 18.0419 0.759028
\(566\) 75.2935 3.16482
\(567\) 2.04273 0.0857866
\(568\) 77.0831 3.23434
\(569\) −6.99933 −0.293427 −0.146714 0.989179i \(-0.546870\pi\)
−0.146714 + 0.989179i \(0.546870\pi\)
\(570\) −46.7832 −1.95953
\(571\) −28.0828 −1.17523 −0.587615 0.809141i \(-0.699933\pi\)
−0.587615 + 0.809141i \(0.699933\pi\)
\(572\) 21.9055 0.915913
\(573\) −3.04371 −0.127153
\(574\) −53.8736 −2.24864
\(575\) −52.6071 −2.19387
\(576\) 2.50953 0.104564
\(577\) −20.0459 −0.834523 −0.417262 0.908786i \(-0.637010\pi\)
−0.417262 + 0.908786i \(0.637010\pi\)
\(578\) −43.4082 −1.80554
\(579\) −6.85641 −0.284943
\(580\) −79.1460 −3.28636
\(581\) 29.0489 1.20515
\(582\) −34.9650 −1.44934
\(583\) −9.68455 −0.401093
\(584\) −30.2793 −1.25296
\(585\) −19.0437 −0.787362
\(586\) 80.4459 3.32319
\(587\) −16.2870 −0.672235 −0.336118 0.941820i \(-0.609114\pi\)
−0.336118 + 0.941820i \(0.609114\pi\)
\(588\) 13.0319 0.537426
\(589\) 8.25425 0.340111
\(590\) −21.0861 −0.868099
\(591\) 12.1375 0.499271
\(592\) −16.9546 −0.696830
\(593\) −36.0721 −1.48130 −0.740652 0.671889i \(-0.765483\pi\)
−0.740652 + 0.671889i \(0.765483\pi\)
\(594\) 2.57087 0.105484
\(595\) −2.78050 −0.113989
\(596\) 26.3596 1.07973
\(597\) 13.8050 0.565002
\(598\) 58.1258 2.37694
\(599\) −12.5585 −0.513125 −0.256563 0.966528i \(-0.582590\pi\)
−0.256563 + 0.966528i \(0.582590\pi\)
\(600\) −74.1794 −3.02836
\(601\) 35.2090 1.43621 0.718103 0.695936i \(-0.245010\pi\)
0.718103 + 0.695936i \(0.245010\pi\)
\(602\) −51.9669 −2.11801
\(603\) 5.30981 0.216232
\(604\) 20.8832 0.849724
\(605\) 4.00721 0.162916
\(606\) 26.3916 1.07209
\(607\) 1.60580 0.0651773 0.0325886 0.999469i \(-0.489625\pi\)
0.0325886 + 0.999469i \(0.489625\pi\)
\(608\) 32.7926 1.32991
\(609\) 8.75297 0.354688
\(610\) 10.3020 0.417117
\(611\) 24.8288 1.00447
\(612\) −1.56571 −0.0632901
\(613\) −2.16291 −0.0873591 −0.0436796 0.999046i \(-0.513908\pi\)
−0.0436796 + 0.999046i \(0.513908\pi\)
\(614\) 0.523731 0.0211361
\(615\) 41.1081 1.65764
\(616\) −13.7034 −0.552125
\(617\) −14.6864 −0.591253 −0.295627 0.955304i \(-0.595528\pi\)
−0.295627 + 0.955304i \(0.595528\pi\)
\(618\) −27.8443 −1.12006
\(619\) 47.1847 1.89651 0.948257 0.317505i \(-0.102845\pi\)
0.948257 + 0.317505i \(0.102845\pi\)
\(620\) 33.5734 1.34834
\(621\) 4.75749 0.190912
\(622\) −39.8326 −1.59714
\(623\) −12.3681 −0.495518
\(624\) 38.1501 1.52723
\(625\) 41.9849 1.67940
\(626\) −69.9294 −2.79494
\(627\) 4.54116 0.181357
\(628\) −48.2753 −1.92639
\(629\) 0.717416 0.0286053
\(630\) 21.0442 0.838423
\(631\) 44.0652 1.75421 0.877104 0.480300i \(-0.159472\pi\)
0.877104 + 0.480300i \(0.159472\pi\)
\(632\) 36.8471 1.46570
\(633\) −13.4936 −0.536323
\(634\) −30.6063 −1.21553
\(635\) −49.1196 −1.94925
\(636\) −44.6398 −1.77008
\(637\) 13.4362 0.532360
\(638\) 11.0160 0.436128
\(639\) 11.4906 0.454561
\(640\) −32.0204 −1.26572
\(641\) −32.9295 −1.30064 −0.650319 0.759661i \(-0.725365\pi\)
−0.650319 + 0.759661i \(0.725365\pi\)
\(642\) 26.6715 1.05264
\(643\) 34.3960 1.35645 0.678223 0.734856i \(-0.262750\pi\)
0.678223 + 0.734856i \(0.262750\pi\)
\(644\) −44.7952 −1.76518
\(645\) 39.6532 1.56134
\(646\) −3.96567 −0.156027
\(647\) 40.6293 1.59730 0.798652 0.601793i \(-0.205547\pi\)
0.798652 + 0.601793i \(0.205547\pi\)
\(648\) 6.70837 0.263530
\(649\) 2.04679 0.0803435
\(650\) −135.100 −5.29908
\(651\) −3.71297 −0.145523
\(652\) 55.3845 2.16903
\(653\) −0.882411 −0.0345314 −0.0172657 0.999851i \(-0.505496\pi\)
−0.0172657 + 0.999851i \(0.505496\pi\)
\(654\) 40.9413 1.60093
\(655\) 56.7633 2.21793
\(656\) −82.3514 −3.21528
\(657\) −4.51365 −0.176094
\(658\) −27.4370 −1.06961
\(659\) 24.8985 0.969906 0.484953 0.874540i \(-0.338837\pi\)
0.484953 + 0.874540i \(0.338837\pi\)
\(660\) 18.4707 0.718973
\(661\) 40.3972 1.57127 0.785635 0.618690i \(-0.212336\pi\)
0.785635 + 0.618690i \(0.212336\pi\)
\(662\) −13.9923 −0.543828
\(663\) −1.61428 −0.0626935
\(664\) 95.3974 3.70214
\(665\) 37.1724 1.44148
\(666\) −5.42978 −0.210400
\(667\) 20.3856 0.789332
\(668\) 35.5958 1.37724
\(669\) 3.65818 0.141433
\(670\) 54.7018 2.11331
\(671\) −1.00000 −0.0386046
\(672\) −14.7509 −0.569029
\(673\) −4.08661 −0.157527 −0.0787636 0.996893i \(-0.525097\pi\)
−0.0787636 + 0.996893i \(0.525097\pi\)
\(674\) 29.7180 1.14469
\(675\) −11.0577 −0.425613
\(676\) 44.1809 1.69927
\(677\) −3.16188 −0.121521 −0.0607604 0.998152i \(-0.519353\pi\)
−0.0607604 + 0.998152i \(0.519353\pi\)
\(678\) −11.5750 −0.444534
\(679\) 27.7820 1.06618
\(680\) −9.13121 −0.350166
\(681\) 6.72165 0.257574
\(682\) −4.67295 −0.178936
\(683\) −2.84581 −0.108892 −0.0544459 0.998517i \(-0.517339\pi\)
−0.0544459 + 0.998517i \(0.517339\pi\)
\(684\) 20.9319 0.800353
\(685\) 47.4098 1.81144
\(686\) −51.6088 −1.97043
\(687\) 1.23766 0.0472198
\(688\) −79.4368 −3.02850
\(689\) −46.0246 −1.75340
\(690\) 49.0118 1.86585
\(691\) 24.9625 0.949620 0.474810 0.880088i \(-0.342517\pi\)
0.474810 + 0.880088i \(0.342517\pi\)
\(692\) 67.2576 2.55675
\(693\) −2.04273 −0.0775969
\(694\) −89.8104 −3.40915
\(695\) 86.0157 3.26276
\(696\) 28.7449 1.08957
\(697\) 3.48461 0.131989
\(698\) −42.3260 −1.60206
\(699\) −12.9299 −0.489053
\(700\) 104.116 3.93523
\(701\) 3.42189 0.129243 0.0646216 0.997910i \(-0.479416\pi\)
0.0646216 + 0.997910i \(0.479416\pi\)
\(702\) 12.2177 0.461128
\(703\) −9.59112 −0.361736
\(704\) −2.50953 −0.0945815
\(705\) 20.9357 0.788485
\(706\) 92.8250 3.49351
\(707\) −20.9699 −0.788655
\(708\) 9.43442 0.354567
\(709\) −52.0319 −1.95410 −0.977050 0.213008i \(-0.931674\pi\)
−0.977050 + 0.213008i \(0.931674\pi\)
\(710\) 118.376 4.44258
\(711\) 5.49270 0.205992
\(712\) −40.6172 −1.52219
\(713\) −8.64747 −0.323850
\(714\) 1.78386 0.0667592
\(715\) 19.0437 0.712196
\(716\) −60.6849 −2.26790
\(717\) 18.5458 0.692605
\(718\) −41.4287 −1.54610
\(719\) −10.9759 −0.409332 −0.204666 0.978832i \(-0.565611\pi\)
−0.204666 + 0.978832i \(0.565611\pi\)
\(720\) 32.1683 1.19884
\(721\) 22.1242 0.823947
\(722\) 4.17038 0.155206
\(723\) 27.7936 1.03365
\(724\) −33.4689 −1.24386
\(725\) −47.3817 −1.75971
\(726\) −2.57087 −0.0954140
\(727\) 32.1350 1.19182 0.595911 0.803051i \(-0.296791\pi\)
0.595911 + 0.803051i \(0.296791\pi\)
\(728\) −65.1235 −2.41364
\(729\) 1.00000 0.0370370
\(730\) −46.4998 −1.72103
\(731\) 3.36128 0.124322
\(732\) −4.60938 −0.170367
\(733\) 17.1024 0.631693 0.315846 0.948810i \(-0.397712\pi\)
0.315846 + 0.948810i \(0.397712\pi\)
\(734\) 92.0835 3.39887
\(735\) 11.3294 0.417892
\(736\) −34.3547 −1.26633
\(737\) −5.30981 −0.195589
\(738\) −26.3733 −0.970816
\(739\) 43.8812 1.61420 0.807098 0.590417i \(-0.201037\pi\)
0.807098 + 0.590417i \(0.201037\pi\)
\(740\) −39.0109 −1.43407
\(741\) 21.5813 0.792808
\(742\) 50.8593 1.86711
\(743\) −34.0979 −1.25093 −0.625465 0.780252i \(-0.715091\pi\)
−0.625465 + 0.780252i \(0.715091\pi\)
\(744\) −12.1935 −0.447035
\(745\) 22.9160 0.839577
\(746\) −47.2820 −1.73112
\(747\) 14.2207 0.520306
\(748\) 1.56571 0.0572480
\(749\) −21.1923 −0.774351
\(750\) −62.4070 −2.27878
\(751\) −0.462726 −0.0168851 −0.00844255 0.999964i \(-0.502687\pi\)
−0.00844255 + 0.999964i \(0.502687\pi\)
\(752\) −41.9403 −1.52941
\(753\) 4.56250 0.166267
\(754\) 52.3522 1.90655
\(755\) 18.1550 0.660728
\(756\) −9.41571 −0.342446
\(757\) −15.0488 −0.546957 −0.273479 0.961878i \(-0.588174\pi\)
−0.273479 + 0.961878i \(0.588174\pi\)
\(758\) −13.5498 −0.492153
\(759\) −4.75749 −0.172686
\(760\) 122.075 4.42812
\(761\) −3.40565 −0.123455 −0.0617274 0.998093i \(-0.519661\pi\)
−0.0617274 + 0.998093i \(0.519661\pi\)
\(762\) 31.5132 1.14160
\(763\) −32.5306 −1.17769
\(764\) 14.0296 0.507574
\(765\) −1.36117 −0.0492131
\(766\) 83.5963 3.02046
\(767\) 9.72709 0.351225
\(768\) 25.5621 0.922393
\(769\) 16.3158 0.588363 0.294182 0.955750i \(-0.404953\pi\)
0.294182 + 0.955750i \(0.404953\pi\)
\(770\) −21.0442 −0.758382
\(771\) 16.8127 0.605493
\(772\) 31.6038 1.13744
\(773\) 33.0741 1.18959 0.594797 0.803876i \(-0.297232\pi\)
0.594797 + 0.803876i \(0.297232\pi\)
\(774\) −25.4399 −0.914420
\(775\) 20.0991 0.721982
\(776\) 91.2368 3.27521
\(777\) 4.31433 0.154776
\(778\) −62.6669 −2.24672
\(779\) −46.5857 −1.66910
\(780\) 87.7798 3.14302
\(781\) −11.4906 −0.411166
\(782\) 4.15459 0.148568
\(783\) 4.28494 0.153131
\(784\) −22.6961 −0.810575
\(785\) −41.9687 −1.49793
\(786\) −36.4171 −1.29896
\(787\) 13.5591 0.483328 0.241664 0.970360i \(-0.422307\pi\)
0.241664 + 0.970360i \(0.422307\pi\)
\(788\) −55.9464 −1.99301
\(789\) 8.19724 0.291829
\(790\) 56.5860 2.01324
\(791\) 9.19709 0.327011
\(792\) −6.70837 −0.238372
\(793\) −4.75237 −0.168762
\(794\) −46.3466 −1.64478
\(795\) −38.8081 −1.37638
\(796\) −63.6326 −2.25540
\(797\) 18.0188 0.638257 0.319129 0.947711i \(-0.396610\pi\)
0.319129 + 0.947711i \(0.396610\pi\)
\(798\) −23.8483 −0.844222
\(799\) 1.77466 0.0627829
\(800\) 79.8500 2.82312
\(801\) −6.05470 −0.213932
\(802\) −75.0646 −2.65062
\(803\) 4.51365 0.159283
\(804\) −24.4749 −0.863164
\(805\) −38.9432 −1.37257
\(806\) −22.2076 −0.782228
\(807\) −12.7223 −0.447845
\(808\) −68.8657 −2.42269
\(809\) 11.1179 0.390883 0.195441 0.980715i \(-0.437386\pi\)
0.195441 + 0.980715i \(0.437386\pi\)
\(810\) 10.3020 0.361976
\(811\) 9.75699 0.342614 0.171307 0.985218i \(-0.445201\pi\)
0.171307 + 0.985218i \(0.445201\pi\)
\(812\) −40.3457 −1.41586
\(813\) −28.9215 −1.01432
\(814\) 5.42978 0.190314
\(815\) 48.1491 1.68659
\(816\) 2.72681 0.0954575
\(817\) −44.9369 −1.57214
\(818\) 6.77362 0.236834
\(819\) −9.70780 −0.339218
\(820\) −189.483 −6.61702
\(821\) 17.6656 0.616535 0.308268 0.951300i \(-0.400251\pi\)
0.308268 + 0.951300i \(0.400251\pi\)
\(822\) −30.4163 −1.06089
\(823\) 45.2415 1.57702 0.788510 0.615022i \(-0.210853\pi\)
0.788510 + 0.615022i \(0.210853\pi\)
\(824\) 72.6563 2.53110
\(825\) 11.0577 0.384981
\(826\) −10.7489 −0.374002
\(827\) −26.0944 −0.907392 −0.453696 0.891157i \(-0.649895\pi\)
−0.453696 + 0.891157i \(0.649895\pi\)
\(828\) −21.9291 −0.762088
\(829\) −36.7769 −1.27732 −0.638658 0.769491i \(-0.720510\pi\)
−0.638658 + 0.769491i \(0.720510\pi\)
\(830\) 146.501 5.08514
\(831\) −9.01259 −0.312643
\(832\) −11.9262 −0.413467
\(833\) 0.960361 0.0332745
\(834\) −55.1843 −1.91088
\(835\) 30.9456 1.07092
\(836\) −20.9319 −0.723946
\(837\) −1.81765 −0.0628272
\(838\) 82.4541 2.84833
\(839\) −5.35112 −0.184741 −0.0923706 0.995725i \(-0.529444\pi\)
−0.0923706 + 0.995725i \(0.529444\pi\)
\(840\) −54.9124 −1.89466
\(841\) −10.6393 −0.366873
\(842\) 15.4861 0.533686
\(843\) 20.0391 0.690182
\(844\) 62.1971 2.14091
\(845\) 38.4092 1.32131
\(846\) −13.4315 −0.461786
\(847\) 2.04273 0.0701890
\(848\) 77.7437 2.66973
\(849\) −29.2872 −1.00513
\(850\) −9.65641 −0.331212
\(851\) 10.0480 0.344442
\(852\) −52.9645 −1.81453
\(853\) 44.6105 1.52744 0.763718 0.645550i \(-0.223372\pi\)
0.763718 + 0.645550i \(0.223372\pi\)
\(854\) 5.25159 0.179706
\(855\) 18.1974 0.622338
\(856\) −69.5961 −2.37875
\(857\) −7.03968 −0.240471 −0.120235 0.992745i \(-0.538365\pi\)
−0.120235 + 0.992745i \(0.538365\pi\)
\(858\) −12.2177 −0.417106
\(859\) 55.9231 1.90807 0.954036 0.299693i \(-0.0968841\pi\)
0.954036 + 0.299693i \(0.0968841\pi\)
\(860\) −182.776 −6.23263
\(861\) 20.9554 0.714158
\(862\) −50.4632 −1.71878
\(863\) −47.1465 −1.60489 −0.802443 0.596729i \(-0.796467\pi\)
−0.802443 + 0.596729i \(0.796467\pi\)
\(864\) −7.22118 −0.245670
\(865\) 58.4711 1.98808
\(866\) 71.6190 2.43371
\(867\) 16.8846 0.573432
\(868\) 17.1145 0.580903
\(869\) −5.49270 −0.186327
\(870\) 44.1435 1.49661
\(871\) −25.2342 −0.855028
\(872\) −106.831 −3.61776
\(873\) 13.6004 0.460305
\(874\) −55.5425 −1.87875
\(875\) 49.5865 1.67633
\(876\) 20.8051 0.702940
\(877\) −15.8127 −0.533957 −0.266979 0.963702i \(-0.586025\pi\)
−0.266979 + 0.963702i \(0.586025\pi\)
\(878\) −65.5117 −2.21091
\(879\) −31.2913 −1.05543
\(880\) −32.1683 −1.08439
\(881\) 13.2185 0.445343 0.222672 0.974894i \(-0.428522\pi\)
0.222672 + 0.974894i \(0.428522\pi\)
\(882\) −7.26851 −0.244744
\(883\) −31.4226 −1.05746 −0.528728 0.848791i \(-0.677331\pi\)
−0.528728 + 0.848791i \(0.677331\pi\)
\(884\) 7.44083 0.250262
\(885\) 8.20191 0.275704
\(886\) 74.6211 2.50694
\(887\) −26.4566 −0.888326 −0.444163 0.895946i \(-0.646499\pi\)
−0.444163 + 0.895946i \(0.646499\pi\)
\(888\) 14.1683 0.475459
\(889\) −25.0394 −0.839793
\(890\) −62.3757 −2.09084
\(891\) −1.00000 −0.0335013
\(892\) −16.8619 −0.564579
\(893\) −23.7254 −0.793939
\(894\) −14.7020 −0.491709
\(895\) −52.7570 −1.76347
\(896\) −16.3228 −0.545307
\(897\) −22.6094 −0.754905
\(898\) 59.9059 1.99909
\(899\) −7.78852 −0.259762
\(900\) 50.9693 1.69898
\(901\) −3.28964 −0.109594
\(902\) 26.3733 0.878136
\(903\) 20.2137 0.672671
\(904\) 30.2035 1.00455
\(905\) −29.0965 −0.967201
\(906\) −11.6475 −0.386964
\(907\) −34.1071 −1.13251 −0.566254 0.824231i \(-0.691608\pi\)
−0.566254 + 0.824231i \(0.691608\pi\)
\(908\) −30.9826 −1.02819
\(909\) −10.2656 −0.340490
\(910\) −100.010 −3.31530
\(911\) 9.45811 0.313361 0.156681 0.987649i \(-0.449921\pi\)
0.156681 + 0.987649i \(0.449921\pi\)
\(912\) −36.4547 −1.20713
\(913\) −14.2207 −0.470635
\(914\) 99.8805 3.30375
\(915\) −4.00721 −0.132474
\(916\) −5.70485 −0.188494
\(917\) 28.9359 0.955546
\(918\) 0.873272 0.0288223
\(919\) 21.9708 0.724750 0.362375 0.932032i \(-0.381966\pi\)
0.362375 + 0.932032i \(0.381966\pi\)
\(920\) −127.890 −4.21642
\(921\) −0.203717 −0.00671272
\(922\) 6.23557 0.205357
\(923\) −54.6075 −1.79743
\(924\) 9.41571 0.309754
\(925\) −23.3544 −0.767887
\(926\) 95.9867 3.15432
\(927\) 10.8307 0.355727
\(928\) −30.9423 −1.01573
\(929\) −0.381863 −0.0125285 −0.00626425 0.999980i \(-0.501994\pi\)
−0.00626425 + 0.999980i \(0.501994\pi\)
\(930\) −18.7255 −0.614033
\(931\) −12.8390 −0.420782
\(932\) 59.5987 1.95222
\(933\) 15.4938 0.507245
\(934\) −19.4332 −0.635873
\(935\) 1.36117 0.0445149
\(936\) −31.8807 −1.04205
\(937\) −45.5441 −1.48786 −0.743931 0.668256i \(-0.767041\pi\)
−0.743931 + 0.668256i \(0.767041\pi\)
\(938\) 27.8850 0.910477
\(939\) 27.2007 0.887661
\(940\) −96.5007 −3.14750
\(941\) −24.7833 −0.807911 −0.403956 0.914779i \(-0.632365\pi\)
−0.403956 + 0.914779i \(0.632365\pi\)
\(942\) 26.9255 0.877279
\(943\) 48.8049 1.58931
\(944\) −16.4308 −0.534777
\(945\) −8.18565 −0.266279
\(946\) 25.4399 0.827124
\(947\) 3.66692 0.119159 0.0595794 0.998224i \(-0.481024\pi\)
0.0595794 + 0.998224i \(0.481024\pi\)
\(948\) −25.3179 −0.822288
\(949\) 21.4505 0.696314
\(950\) 129.096 4.18844
\(951\) 11.9050 0.386047
\(952\) −4.65476 −0.150862
\(953\) −55.9404 −1.81209 −0.906044 0.423184i \(-0.860912\pi\)
−0.906044 + 0.423184i \(0.860912\pi\)
\(954\) 24.8977 0.806094
\(955\) 12.1968 0.394679
\(956\) −85.4845 −2.76477
\(957\) −4.28494 −0.138512
\(958\) −91.9380 −2.97038
\(959\) 24.1678 0.780419
\(960\) −10.0562 −0.324563
\(961\) −27.6961 −0.893424
\(962\) 25.8043 0.831965
\(963\) −10.3745 −0.334314
\(964\) −128.111 −4.12618
\(965\) 27.4751 0.884454
\(966\) 24.9844 0.803861
\(967\) 40.3407 1.29727 0.648634 0.761100i \(-0.275341\pi\)
0.648634 + 0.761100i \(0.275341\pi\)
\(968\) 6.70837 0.215615
\(969\) 1.54254 0.0495535
\(970\) 140.112 4.49873
\(971\) 23.6883 0.760193 0.380096 0.924947i \(-0.375891\pi\)
0.380096 + 0.924947i \(0.375891\pi\)
\(972\) −4.60938 −0.147846
\(973\) 43.8476 1.40569
\(974\) −16.4338 −0.526574
\(975\) 52.5505 1.68296
\(976\) 8.02760 0.256957
\(977\) 10.2404 0.327620 0.163810 0.986492i \(-0.447622\pi\)
0.163810 + 0.986492i \(0.447622\pi\)
\(978\) −30.8906 −0.987773
\(979\) 6.05470 0.193509
\(980\) −52.2215 −1.66816
\(981\) −15.9251 −0.508448
\(982\) 43.1632 1.37739
\(983\) −26.3822 −0.841461 −0.420730 0.907186i \(-0.638226\pi\)
−0.420730 + 0.907186i \(0.638226\pi\)
\(984\) 68.8180 2.19384
\(985\) −48.6376 −1.54972
\(986\) 3.74191 0.119167
\(987\) 10.6723 0.339702
\(988\) −99.4763 −3.16476
\(989\) 47.0776 1.49698
\(990\) −10.3020 −0.327420
\(991\) 35.8606 1.13915 0.569575 0.821939i \(-0.307108\pi\)
0.569575 + 0.821939i \(0.307108\pi\)
\(992\) 13.1256 0.416738
\(993\) 5.44265 0.172717
\(994\) 60.3439 1.91399
\(995\) −55.3197 −1.75375
\(996\) −65.5483 −2.07698
\(997\) 7.80670 0.247241 0.123620 0.992330i \(-0.460550\pi\)
0.123620 + 0.992330i \(0.460550\pi\)
\(998\) 6.15707 0.194899
\(999\) 2.11204 0.0668220
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.1.14 14
3.2 odd 2 6039.2.a.j.1.1 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.2.a.h.1.14 14 1.1 even 1 trivial
6039.2.a.j.1.1 14 3.2 odd 2