Properties

Label 6037.2.a.b.1.11
Level 6037
Weight 2
Character 6037.1
Self dual yes
Analytic conductor 48.206
Analytic rank 0
Dimension 259
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58398 q^{2} +0.626068 q^{3} +4.67694 q^{4} -1.39938 q^{5} -1.61774 q^{6} +0.699914 q^{7} -6.91715 q^{8} -2.60804 q^{9} +O(q^{10})\) \(q-2.58398 q^{2} +0.626068 q^{3} +4.67694 q^{4} -1.39938 q^{5} -1.61774 q^{6} +0.699914 q^{7} -6.91715 q^{8} -2.60804 q^{9} +3.61596 q^{10} -3.02715 q^{11} +2.92808 q^{12} -6.88837 q^{13} -1.80856 q^{14} -0.876105 q^{15} +8.51988 q^{16} -2.89267 q^{17} +6.73911 q^{18} -3.24077 q^{19} -6.54480 q^{20} +0.438193 q^{21} +7.82208 q^{22} +1.81731 q^{23} -4.33060 q^{24} -3.04174 q^{25} +17.7994 q^{26} -3.51101 q^{27} +3.27345 q^{28} -0.222845 q^{29} +2.26384 q^{30} -4.74383 q^{31} -8.18088 q^{32} -1.89520 q^{33} +7.47459 q^{34} -0.979444 q^{35} -12.1976 q^{36} -10.9936 q^{37} +8.37406 q^{38} -4.31258 q^{39} +9.67970 q^{40} +8.51933 q^{41} -1.13228 q^{42} -0.0231683 q^{43} -14.1578 q^{44} +3.64963 q^{45} -4.69590 q^{46} +4.68142 q^{47} +5.33402 q^{48} -6.51012 q^{49} +7.85979 q^{50} -1.81101 q^{51} -32.2165 q^{52} -10.0007 q^{53} +9.07238 q^{54} +4.23612 q^{55} -4.84141 q^{56} -2.02894 q^{57} +0.575825 q^{58} -1.06556 q^{59} -4.09749 q^{60} -1.03567 q^{61} +12.2579 q^{62} -1.82540 q^{63} +4.09945 q^{64} +9.63943 q^{65} +4.89715 q^{66} +7.21240 q^{67} -13.5288 q^{68} +1.13776 q^{69} +2.53086 q^{70} -15.5141 q^{71} +18.0402 q^{72} -13.5076 q^{73} +28.4072 q^{74} -1.90434 q^{75} -15.1569 q^{76} -2.11874 q^{77} +11.1436 q^{78} -14.0586 q^{79} -11.9225 q^{80} +5.62599 q^{81} -22.0138 q^{82} +3.32541 q^{83} +2.04940 q^{84} +4.04794 q^{85} +0.0598664 q^{86} -0.139516 q^{87} +20.9392 q^{88} -14.1653 q^{89} -9.43057 q^{90} -4.82126 q^{91} +8.49947 q^{92} -2.96996 q^{93} -12.0967 q^{94} +4.53505 q^{95} -5.12178 q^{96} +13.3047 q^{97} +16.8220 q^{98} +7.89491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58398 −1.82715 −0.913574 0.406673i \(-0.866689\pi\)
−0.913574 + 0.406673i \(0.866689\pi\)
\(3\) 0.626068 0.361460 0.180730 0.983533i \(-0.442154\pi\)
0.180730 + 0.983533i \(0.442154\pi\)
\(4\) 4.67694 2.33847
\(5\) −1.39938 −0.625821 −0.312910 0.949783i \(-0.601304\pi\)
−0.312910 + 0.949783i \(0.601304\pi\)
\(6\) −1.61774 −0.660441
\(7\) 0.699914 0.264543 0.132271 0.991214i \(-0.457773\pi\)
0.132271 + 0.991214i \(0.457773\pi\)
\(8\) −6.91715 −2.44558
\(9\) −2.60804 −0.869346
\(10\) 3.61596 1.14347
\(11\) −3.02715 −0.912719 −0.456359 0.889796i \(-0.650847\pi\)
−0.456359 + 0.889796i \(0.650847\pi\)
\(12\) 2.92808 0.845264
\(13\) −6.88837 −1.91049 −0.955245 0.295816i \(-0.904408\pi\)
−0.955245 + 0.295816i \(0.904408\pi\)
\(14\) −1.80856 −0.483358
\(15\) −0.876105 −0.226209
\(16\) 8.51988 2.12997
\(17\) −2.89267 −0.701575 −0.350788 0.936455i \(-0.614086\pi\)
−0.350788 + 0.936455i \(0.614086\pi\)
\(18\) 6.73911 1.58842
\(19\) −3.24077 −0.743483 −0.371741 0.928336i \(-0.621239\pi\)
−0.371741 + 0.928336i \(0.621239\pi\)
\(20\) −6.54480 −1.46346
\(21\) 0.438193 0.0956217
\(22\) 7.82208 1.66767
\(23\) 1.81731 0.378936 0.189468 0.981887i \(-0.439324\pi\)
0.189468 + 0.981887i \(0.439324\pi\)
\(24\) −4.33060 −0.883981
\(25\) −3.04174 −0.608348
\(26\) 17.7994 3.49075
\(27\) −3.51101 −0.675695
\(28\) 3.27345 0.618625
\(29\) −0.222845 −0.0413812 −0.0206906 0.999786i \(-0.506586\pi\)
−0.0206906 + 0.999786i \(0.506586\pi\)
\(30\) 2.26384 0.413318
\(31\) −4.74383 −0.852016 −0.426008 0.904719i \(-0.640081\pi\)
−0.426008 + 0.904719i \(0.640081\pi\)
\(32\) −8.18088 −1.44619
\(33\) −1.89520 −0.329912
\(34\) 7.47459 1.28188
\(35\) −0.979444 −0.165556
\(36\) −12.1976 −2.03294
\(37\) −10.9936 −1.80734 −0.903668 0.428233i \(-0.859136\pi\)
−0.903668 + 0.428233i \(0.859136\pi\)
\(38\) 8.37406 1.35845
\(39\) −4.31258 −0.690566
\(40\) 9.67970 1.53050
\(41\) 8.51933 1.33050 0.665248 0.746622i \(-0.268326\pi\)
0.665248 + 0.746622i \(0.268326\pi\)
\(42\) −1.13228 −0.174715
\(43\) −0.0231683 −0.00353314 −0.00176657 0.999998i \(-0.500562\pi\)
−0.00176657 + 0.999998i \(0.500562\pi\)
\(44\) −14.1578 −2.13436
\(45\) 3.64963 0.544055
\(46\) −4.69590 −0.692372
\(47\) 4.68142 0.682855 0.341428 0.939908i \(-0.389090\pi\)
0.341428 + 0.939908i \(0.389090\pi\)
\(48\) 5.33402 0.769900
\(49\) −6.51012 −0.930017
\(50\) 7.85979 1.11154
\(51\) −1.81101 −0.253592
\(52\) −32.2165 −4.46762
\(53\) −10.0007 −1.37370 −0.686851 0.726798i \(-0.741008\pi\)
−0.686851 + 0.726798i \(0.741008\pi\)
\(54\) 9.07238 1.23459
\(55\) 4.23612 0.571198
\(56\) −4.84141 −0.646961
\(57\) −2.02894 −0.268739
\(58\) 0.575825 0.0756096
\(59\) −1.06556 −0.138724 −0.0693622 0.997592i \(-0.522096\pi\)
−0.0693622 + 0.997592i \(0.522096\pi\)
\(60\) −4.09749 −0.528984
\(61\) −1.03567 −0.132604 −0.0663022 0.997800i \(-0.521120\pi\)
−0.0663022 + 0.997800i \(0.521120\pi\)
\(62\) 12.2579 1.55676
\(63\) −1.82540 −0.229979
\(64\) 4.09945 0.512431
\(65\) 9.63943 1.19562
\(66\) 4.89715 0.602797
\(67\) 7.21240 0.881135 0.440567 0.897720i \(-0.354777\pi\)
0.440567 + 0.897720i \(0.354777\pi\)
\(68\) −13.5288 −1.64061
\(69\) 1.13776 0.136970
\(70\) 2.53086 0.302496
\(71\) −15.5141 −1.84118 −0.920591 0.390528i \(-0.872293\pi\)
−0.920591 + 0.390528i \(0.872293\pi\)
\(72\) 18.0402 2.12606
\(73\) −13.5076 −1.58094 −0.790470 0.612501i \(-0.790164\pi\)
−0.790470 + 0.612501i \(0.790164\pi\)
\(74\) 28.4072 3.30227
\(75\) −1.90434 −0.219894
\(76\) −15.1569 −1.73861
\(77\) −2.11874 −0.241453
\(78\) 11.1436 1.26177
\(79\) −14.0586 −1.58172 −0.790858 0.612000i \(-0.790365\pi\)
−0.790858 + 0.612000i \(0.790365\pi\)
\(80\) −11.9225 −1.33298
\(81\) 5.62599 0.625110
\(82\) −22.0138 −2.43101
\(83\) 3.32541 0.365011 0.182505 0.983205i \(-0.441579\pi\)
0.182505 + 0.983205i \(0.441579\pi\)
\(84\) 2.04940 0.223608
\(85\) 4.04794 0.439060
\(86\) 0.0598664 0.00645556
\(87\) −0.139516 −0.0149577
\(88\) 20.9392 2.23213
\(89\) −14.1653 −1.50152 −0.750759 0.660576i \(-0.770312\pi\)
−0.750759 + 0.660576i \(0.770312\pi\)
\(90\) −9.43057 −0.994069
\(91\) −4.82126 −0.505406
\(92\) 8.49947 0.886131
\(93\) −2.96996 −0.307970
\(94\) −12.0967 −1.24768
\(95\) 4.53505 0.465287
\(96\) −5.12178 −0.522740
\(97\) 13.3047 1.35089 0.675446 0.737410i \(-0.263951\pi\)
0.675446 + 0.737410i \(0.263951\pi\)
\(98\) 16.8220 1.69928
\(99\) 7.89491 0.793469
\(100\) −14.2260 −1.42260
\(101\) 4.17271 0.415200 0.207600 0.978214i \(-0.433435\pi\)
0.207600 + 0.978214i \(0.433435\pi\)
\(102\) 4.67960 0.463349
\(103\) 1.42118 0.140033 0.0700167 0.997546i \(-0.477695\pi\)
0.0700167 + 0.997546i \(0.477695\pi\)
\(104\) 47.6479 4.67226
\(105\) −0.613198 −0.0598420
\(106\) 25.8416 2.50996
\(107\) 14.3717 1.38937 0.694683 0.719316i \(-0.255545\pi\)
0.694683 + 0.719316i \(0.255545\pi\)
\(108\) −16.4208 −1.58009
\(109\) 11.7517 1.12561 0.562804 0.826590i \(-0.309723\pi\)
0.562804 + 0.826590i \(0.309723\pi\)
\(110\) −10.9460 −1.04366
\(111\) −6.88274 −0.653280
\(112\) 5.96318 0.563468
\(113\) −2.95361 −0.277853 −0.138926 0.990303i \(-0.544365\pi\)
−0.138926 + 0.990303i \(0.544365\pi\)
\(114\) 5.24273 0.491027
\(115\) −2.54311 −0.237146
\(116\) −1.04223 −0.0967687
\(117\) 17.9651 1.66088
\(118\) 2.75339 0.253470
\(119\) −2.02462 −0.185597
\(120\) 6.06015 0.553213
\(121\) −1.83639 −0.166945
\(122\) 2.67616 0.242288
\(123\) 5.33368 0.480922
\(124\) −22.1866 −1.99241
\(125\) 11.2534 1.00654
\(126\) 4.71680 0.420206
\(127\) −12.7663 −1.13283 −0.566415 0.824120i \(-0.691670\pi\)
−0.566415 + 0.824120i \(0.691670\pi\)
\(128\) 5.76888 0.509902
\(129\) −0.0145049 −0.00127709
\(130\) −24.9081 −2.18458
\(131\) −14.9976 −1.31035 −0.655173 0.755479i \(-0.727404\pi\)
−0.655173 + 0.755479i \(0.727404\pi\)
\(132\) −8.86372 −0.771488
\(133\) −2.26826 −0.196683
\(134\) −18.6367 −1.60996
\(135\) 4.91323 0.422864
\(136\) 20.0090 1.71576
\(137\) 10.1074 0.863532 0.431766 0.901986i \(-0.357891\pi\)
0.431766 + 0.901986i \(0.357891\pi\)
\(138\) −2.93995 −0.250265
\(139\) −15.0089 −1.27303 −0.636517 0.771263i \(-0.719626\pi\)
−0.636517 + 0.771263i \(0.719626\pi\)
\(140\) −4.58080 −0.387148
\(141\) 2.93089 0.246825
\(142\) 40.0880 3.36411
\(143\) 20.8521 1.74374
\(144\) −22.2202 −1.85168
\(145\) 0.311844 0.0258972
\(146\) 34.9032 2.88861
\(147\) −4.07578 −0.336164
\(148\) −51.4164 −4.22640
\(149\) 2.53230 0.207454 0.103727 0.994606i \(-0.466923\pi\)
0.103727 + 0.994606i \(0.466923\pi\)
\(150\) 4.92076 0.401779
\(151\) −13.4690 −1.09609 −0.548047 0.836448i \(-0.684628\pi\)
−0.548047 + 0.836448i \(0.684628\pi\)
\(152\) 22.4169 1.81825
\(153\) 7.54419 0.609912
\(154\) 5.47478 0.441170
\(155\) 6.63840 0.533210
\(156\) −20.1697 −1.61487
\(157\) 2.23540 0.178405 0.0892023 0.996014i \(-0.471568\pi\)
0.0892023 + 0.996014i \(0.471568\pi\)
\(158\) 36.3271 2.89003
\(159\) −6.26112 −0.496539
\(160\) 11.4481 0.905055
\(161\) 1.27196 0.100245
\(162\) −14.5374 −1.14217
\(163\) −0.873560 −0.0684225 −0.0342112 0.999415i \(-0.510892\pi\)
−0.0342112 + 0.999415i \(0.510892\pi\)
\(164\) 39.8444 3.11133
\(165\) 2.65210 0.206465
\(166\) −8.59278 −0.666929
\(167\) −5.41365 −0.418921 −0.209461 0.977817i \(-0.567171\pi\)
−0.209461 + 0.977817i \(0.567171\pi\)
\(168\) −3.03105 −0.233851
\(169\) 34.4496 2.64997
\(170\) −10.4598 −0.802228
\(171\) 8.45204 0.646344
\(172\) −0.108357 −0.00826213
\(173\) −7.65989 −0.582371 −0.291185 0.956667i \(-0.594050\pi\)
−0.291185 + 0.956667i \(0.594050\pi\)
\(174\) 0.360506 0.0273299
\(175\) −2.12896 −0.160934
\(176\) −25.7909 −1.94406
\(177\) −0.667114 −0.0501434
\(178\) 36.6028 2.74349
\(179\) 4.87474 0.364355 0.182177 0.983266i \(-0.441685\pi\)
0.182177 + 0.983266i \(0.441685\pi\)
\(180\) 17.0691 1.27226
\(181\) 14.9660 1.11242 0.556209 0.831043i \(-0.312256\pi\)
0.556209 + 0.831043i \(0.312256\pi\)
\(182\) 12.4580 0.923451
\(183\) −0.648402 −0.0479313
\(184\) −12.5706 −0.926719
\(185\) 15.3842 1.13107
\(186\) 7.67430 0.562707
\(187\) 8.75653 0.640341
\(188\) 21.8947 1.59684
\(189\) −2.45741 −0.178750
\(190\) −11.7185 −0.850148
\(191\) 22.6861 1.64151 0.820753 0.571284i \(-0.193554\pi\)
0.820753 + 0.571284i \(0.193554\pi\)
\(192\) 2.56653 0.185223
\(193\) −20.2776 −1.45962 −0.729808 0.683653i \(-0.760390\pi\)
−0.729808 + 0.683653i \(0.760390\pi\)
\(194\) −34.3791 −2.46828
\(195\) 6.03493 0.432171
\(196\) −30.4474 −2.17482
\(197\) 7.76892 0.553513 0.276756 0.960940i \(-0.410741\pi\)
0.276756 + 0.960940i \(0.410741\pi\)
\(198\) −20.4003 −1.44978
\(199\) 5.73320 0.406416 0.203208 0.979136i \(-0.434863\pi\)
0.203208 + 0.979136i \(0.434863\pi\)
\(200\) 21.0402 1.48777
\(201\) 4.51545 0.318495
\(202\) −10.7822 −0.758632
\(203\) −0.155972 −0.0109471
\(204\) −8.46997 −0.593016
\(205\) −11.9218 −0.832652
\(206\) −3.67231 −0.255862
\(207\) −4.73963 −0.329427
\(208\) −58.6881 −4.06929
\(209\) 9.81027 0.678590
\(210\) 1.58449 0.109340
\(211\) −2.11447 −0.145566 −0.0727832 0.997348i \(-0.523188\pi\)
−0.0727832 + 0.997348i \(0.523188\pi\)
\(212\) −46.7727 −3.21236
\(213\) −9.71286 −0.665514
\(214\) −37.1362 −2.53858
\(215\) 0.0324212 0.00221111
\(216\) 24.2862 1.65247
\(217\) −3.32027 −0.225395
\(218\) −30.3661 −2.05665
\(219\) −8.45664 −0.571447
\(220\) 19.8121 1.33573
\(221\) 19.9258 1.34035
\(222\) 17.7848 1.19364
\(223\) −4.49102 −0.300741 −0.150370 0.988630i \(-0.548047\pi\)
−0.150370 + 0.988630i \(0.548047\pi\)
\(224\) −5.72591 −0.382579
\(225\) 7.93298 0.528866
\(226\) 7.63207 0.507678
\(227\) −19.0441 −1.26400 −0.632000 0.774968i \(-0.717766\pi\)
−0.632000 + 0.774968i \(0.717766\pi\)
\(228\) −9.48922 −0.628439
\(229\) 0.252318 0.0166737 0.00833683 0.999965i \(-0.497346\pi\)
0.00833683 + 0.999965i \(0.497346\pi\)
\(230\) 6.57133 0.433301
\(231\) −1.32648 −0.0872757
\(232\) 1.54145 0.101201
\(233\) 22.9092 1.50083 0.750416 0.660966i \(-0.229853\pi\)
0.750416 + 0.660966i \(0.229853\pi\)
\(234\) −46.4215 −3.03467
\(235\) −6.55108 −0.427345
\(236\) −4.98357 −0.324403
\(237\) −8.80163 −0.571727
\(238\) 5.23157 0.339112
\(239\) −9.32745 −0.603342 −0.301671 0.953412i \(-0.597544\pi\)
−0.301671 + 0.953412i \(0.597544\pi\)
\(240\) −7.46431 −0.481819
\(241\) −9.27151 −0.597230 −0.298615 0.954374i \(-0.596525\pi\)
−0.298615 + 0.954374i \(0.596525\pi\)
\(242\) 4.74519 0.305033
\(243\) 14.0553 0.901647
\(244\) −4.84378 −0.310091
\(245\) 9.11012 0.582024
\(246\) −13.7821 −0.878715
\(247\) 22.3236 1.42042
\(248\) 32.8138 2.08368
\(249\) 2.08193 0.131937
\(250\) −29.0786 −1.83909
\(251\) −7.39907 −0.467025 −0.233512 0.972354i \(-0.575022\pi\)
−0.233512 + 0.972354i \(0.575022\pi\)
\(252\) −8.53730 −0.537799
\(253\) −5.50127 −0.345862
\(254\) 32.9879 2.06985
\(255\) 2.53428 0.158703
\(256\) −23.1056 −1.44410
\(257\) 19.4871 1.21557 0.607787 0.794100i \(-0.292058\pi\)
0.607787 + 0.794100i \(0.292058\pi\)
\(258\) 0.0374804 0.00233343
\(259\) −7.69457 −0.478117
\(260\) 45.0830 2.79593
\(261\) 0.581187 0.0359746
\(262\) 38.7534 2.39419
\(263\) 4.02946 0.248467 0.124234 0.992253i \(-0.460353\pi\)
0.124234 + 0.992253i \(0.460353\pi\)
\(264\) 13.1094 0.806826
\(265\) 13.9948 0.859691
\(266\) 5.86112 0.359369
\(267\) −8.86843 −0.542739
\(268\) 33.7320 2.06051
\(269\) −24.2207 −1.47676 −0.738381 0.674384i \(-0.764409\pi\)
−0.738381 + 0.674384i \(0.764409\pi\)
\(270\) −12.6957 −0.772634
\(271\) 20.2125 1.22782 0.613910 0.789376i \(-0.289596\pi\)
0.613910 + 0.789376i \(0.289596\pi\)
\(272\) −24.6452 −1.49433
\(273\) −3.01844 −0.182684
\(274\) −26.1172 −1.57780
\(275\) 9.20780 0.555251
\(276\) 5.32124 0.320301
\(277\) 7.74837 0.465555 0.232777 0.972530i \(-0.425219\pi\)
0.232777 + 0.972530i \(0.425219\pi\)
\(278\) 38.7825 2.32602
\(279\) 12.3721 0.740697
\(280\) 6.77496 0.404881
\(281\) −6.73949 −0.402044 −0.201022 0.979587i \(-0.564426\pi\)
−0.201022 + 0.979587i \(0.564426\pi\)
\(282\) −7.57334 −0.450986
\(283\) 10.9423 0.650453 0.325227 0.945636i \(-0.394559\pi\)
0.325227 + 0.945636i \(0.394559\pi\)
\(284\) −72.5584 −4.30555
\(285\) 2.83925 0.168183
\(286\) −53.8813 −3.18607
\(287\) 5.96280 0.351973
\(288\) 21.3361 1.25724
\(289\) −8.63247 −0.507792
\(290\) −0.805797 −0.0473180
\(291\) 8.32967 0.488294
\(292\) −63.1740 −3.69698
\(293\) −21.1312 −1.23450 −0.617250 0.786767i \(-0.711753\pi\)
−0.617250 + 0.786767i \(0.711753\pi\)
\(294\) 10.5317 0.614222
\(295\) 1.49112 0.0868166
\(296\) 76.0444 4.41999
\(297\) 10.6283 0.616719
\(298\) −6.54341 −0.379050
\(299\) −12.5183 −0.723954
\(300\) −8.90647 −0.514215
\(301\) −0.0162158 −0.000934665 0
\(302\) 34.8037 2.00273
\(303\) 2.61240 0.150078
\(304\) −27.6109 −1.58360
\(305\) 1.44930 0.0829866
\(306\) −19.4940 −1.11440
\(307\) −7.10498 −0.405503 −0.202751 0.979230i \(-0.564988\pi\)
−0.202751 + 0.979230i \(0.564988\pi\)
\(308\) −9.90922 −0.564630
\(309\) 0.889757 0.0506165
\(310\) −17.1535 −0.974253
\(311\) −1.61329 −0.0914812 −0.0457406 0.998953i \(-0.514565\pi\)
−0.0457406 + 0.998953i \(0.514565\pi\)
\(312\) 29.8308 1.68884
\(313\) −19.2902 −1.09035 −0.545173 0.838323i \(-0.683536\pi\)
−0.545173 + 0.838323i \(0.683536\pi\)
\(314\) −5.77623 −0.325972
\(315\) 2.55443 0.143926
\(316\) −65.7512 −3.69879
\(317\) 2.49836 0.140322 0.0701608 0.997536i \(-0.477649\pi\)
0.0701608 + 0.997536i \(0.477649\pi\)
\(318\) 16.1786 0.907250
\(319\) 0.674583 0.0377694
\(320\) −5.73668 −0.320690
\(321\) 8.99766 0.502200
\(322\) −3.28672 −0.183162
\(323\) 9.37446 0.521609
\(324\) 26.3124 1.46180
\(325\) 20.9526 1.16224
\(326\) 2.25726 0.125018
\(327\) 7.35736 0.406863
\(328\) −58.9295 −3.25384
\(329\) 3.27659 0.180644
\(330\) −6.85296 −0.377243
\(331\) 25.1031 1.37979 0.689896 0.723909i \(-0.257656\pi\)
0.689896 + 0.723909i \(0.257656\pi\)
\(332\) 15.5527 0.853567
\(333\) 28.6717 1.57120
\(334\) 13.9888 0.765431
\(335\) −10.0929 −0.551432
\(336\) 3.73336 0.203671
\(337\) −13.4755 −0.734058 −0.367029 0.930210i \(-0.619625\pi\)
−0.367029 + 0.930210i \(0.619625\pi\)
\(338\) −89.0170 −4.84189
\(339\) −1.84916 −0.100433
\(340\) 18.9320 1.02673
\(341\) 14.3603 0.777651
\(342\) −21.8399 −1.18097
\(343\) −9.45592 −0.510572
\(344\) 0.160259 0.00864057
\(345\) −1.59216 −0.0857189
\(346\) 19.7930 1.06408
\(347\) 2.67885 0.143808 0.0719041 0.997412i \(-0.477092\pi\)
0.0719041 + 0.997412i \(0.477092\pi\)
\(348\) −0.652507 −0.0349780
\(349\) −9.76413 −0.522662 −0.261331 0.965249i \(-0.584161\pi\)
−0.261331 + 0.965249i \(0.584161\pi\)
\(350\) 5.50118 0.294050
\(351\) 24.1851 1.29091
\(352\) 24.7647 1.31996
\(353\) 16.4302 0.874491 0.437245 0.899342i \(-0.355954\pi\)
0.437245 + 0.899342i \(0.355954\pi\)
\(354\) 1.72381 0.0916194
\(355\) 21.7101 1.15225
\(356\) −66.2502 −3.51125
\(357\) −1.26755 −0.0670858
\(358\) −12.5962 −0.665730
\(359\) 4.51482 0.238283 0.119142 0.992877i \(-0.461986\pi\)
0.119142 + 0.992877i \(0.461986\pi\)
\(360\) −25.2451 −1.33053
\(361\) −8.49744 −0.447234
\(362\) −38.6719 −2.03255
\(363\) −1.14971 −0.0603439
\(364\) −22.5488 −1.18188
\(365\) 18.9022 0.989385
\(366\) 1.67546 0.0875775
\(367\) −28.4491 −1.48503 −0.742516 0.669829i \(-0.766368\pi\)
−0.742516 + 0.669829i \(0.766368\pi\)
\(368\) 15.4833 0.807123
\(369\) −22.2188 −1.15666
\(370\) −39.7524 −2.06663
\(371\) −6.99963 −0.363403
\(372\) −13.8903 −0.720179
\(373\) 10.4080 0.538907 0.269454 0.963013i \(-0.413157\pi\)
0.269454 + 0.963013i \(0.413157\pi\)
\(374\) −22.6267 −1.17000
\(375\) 7.04541 0.363823
\(376\) −32.3821 −1.66998
\(377\) 1.53504 0.0790583
\(378\) 6.34988 0.326603
\(379\) −11.8996 −0.611242 −0.305621 0.952153i \(-0.598864\pi\)
−0.305621 + 0.952153i \(0.598864\pi\)
\(380\) 21.2102 1.08806
\(381\) −7.99259 −0.409473
\(382\) −58.6203 −2.99927
\(383\) 6.77230 0.346048 0.173024 0.984918i \(-0.444646\pi\)
0.173024 + 0.984918i \(0.444646\pi\)
\(384\) 3.61171 0.184309
\(385\) 2.96492 0.151106
\(386\) 52.3969 2.66693
\(387\) 0.0604239 0.00307152
\(388\) 62.2255 3.15902
\(389\) −18.7466 −0.950489 −0.475244 0.879854i \(-0.657640\pi\)
−0.475244 + 0.879854i \(0.657640\pi\)
\(390\) −15.5941 −0.789640
\(391\) −5.25689 −0.265852
\(392\) 45.0315 2.27443
\(393\) −9.38951 −0.473638
\(394\) −20.0747 −1.01135
\(395\) 19.6733 0.989870
\(396\) 36.9240 1.85550
\(397\) −15.1719 −0.761457 −0.380729 0.924687i \(-0.624327\pi\)
−0.380729 + 0.924687i \(0.624327\pi\)
\(398\) −14.8145 −0.742582
\(399\) −1.42008 −0.0710930
\(400\) −25.9153 −1.29576
\(401\) −0.777098 −0.0388064 −0.0194032 0.999812i \(-0.506177\pi\)
−0.0194032 + 0.999812i \(0.506177\pi\)
\(402\) −11.6678 −0.581938
\(403\) 32.6772 1.62777
\(404\) 19.5155 0.970933
\(405\) −7.87288 −0.391207
\(406\) 0.403028 0.0200020
\(407\) 33.2792 1.64959
\(408\) 12.5270 0.620179
\(409\) 26.4764 1.30917 0.654587 0.755987i \(-0.272843\pi\)
0.654587 + 0.755987i \(0.272843\pi\)
\(410\) 30.8056 1.52138
\(411\) 6.32791 0.312133
\(412\) 6.64679 0.327464
\(413\) −0.745802 −0.0366985
\(414\) 12.2471 0.601911
\(415\) −4.65350 −0.228431
\(416\) 56.3529 2.76293
\(417\) −9.39656 −0.460151
\(418\) −25.3495 −1.23989
\(419\) −24.3403 −1.18910 −0.594551 0.804058i \(-0.702670\pi\)
−0.594551 + 0.804058i \(0.702670\pi\)
\(420\) −2.86789 −0.139939
\(421\) −8.67616 −0.422850 −0.211425 0.977394i \(-0.567810\pi\)
−0.211425 + 0.977394i \(0.567810\pi\)
\(422\) 5.46375 0.265971
\(423\) −12.2093 −0.593638
\(424\) 69.1764 3.35950
\(425\) 8.79875 0.426802
\(426\) 25.0978 1.21599
\(427\) −0.724883 −0.0350795
\(428\) 67.2156 3.24899
\(429\) 13.0548 0.630293
\(430\) −0.0837757 −0.00404002
\(431\) −24.8809 −1.19847 −0.599236 0.800573i \(-0.704529\pi\)
−0.599236 + 0.800573i \(0.704529\pi\)
\(432\) −29.9134 −1.43921
\(433\) −22.8532 −1.09826 −0.549128 0.835738i \(-0.685040\pi\)
−0.549128 + 0.835738i \(0.685040\pi\)
\(434\) 8.57950 0.411829
\(435\) 0.195235 0.00936081
\(436\) 54.9620 2.63220
\(437\) −5.88949 −0.281732
\(438\) 21.8518 1.04412
\(439\) −25.2549 −1.20535 −0.602675 0.797987i \(-0.705899\pi\)
−0.602675 + 0.797987i \(0.705899\pi\)
\(440\) −29.3019 −1.39691
\(441\) 16.9787 0.808507
\(442\) −51.4877 −2.44902
\(443\) −22.2833 −1.05871 −0.529355 0.848400i \(-0.677566\pi\)
−0.529355 + 0.848400i \(0.677566\pi\)
\(444\) −32.1901 −1.52768
\(445\) 19.8226 0.939681
\(446\) 11.6047 0.549498
\(447\) 1.58539 0.0749865
\(448\) 2.86926 0.135560
\(449\) −8.75715 −0.413276 −0.206638 0.978418i \(-0.566252\pi\)
−0.206638 + 0.978418i \(0.566252\pi\)
\(450\) −20.4987 −0.966316
\(451\) −25.7893 −1.21437
\(452\) −13.8139 −0.649750
\(453\) −8.43252 −0.396194
\(454\) 49.2095 2.30952
\(455\) 6.74677 0.316293
\(456\) 14.0345 0.657224
\(457\) 10.7524 0.502975 0.251487 0.967861i \(-0.419080\pi\)
0.251487 + 0.967861i \(0.419080\pi\)
\(458\) −0.651985 −0.0304652
\(459\) 10.1562 0.474051
\(460\) −11.8940 −0.554559
\(461\) −19.4465 −0.905715 −0.452858 0.891583i \(-0.649595\pi\)
−0.452858 + 0.891583i \(0.649595\pi\)
\(462\) 3.42758 0.159466
\(463\) −28.0390 −1.30308 −0.651542 0.758613i \(-0.725877\pi\)
−0.651542 + 0.758613i \(0.725877\pi\)
\(464\) −1.89861 −0.0881407
\(465\) 4.15609 0.192734
\(466\) −59.1968 −2.74224
\(467\) −6.04116 −0.279552 −0.139776 0.990183i \(-0.544638\pi\)
−0.139776 + 0.990183i \(0.544638\pi\)
\(468\) 84.0218 3.88391
\(469\) 5.04806 0.233098
\(470\) 16.9278 0.780823
\(471\) 1.39951 0.0644862
\(472\) 7.37066 0.339262
\(473\) 0.0701339 0.00322476
\(474\) 22.7432 1.04463
\(475\) 9.85757 0.452297
\(476\) −9.46902 −0.434012
\(477\) 26.0822 1.19422
\(478\) 24.1019 1.10240
\(479\) 11.3273 0.517557 0.258779 0.965937i \(-0.416680\pi\)
0.258779 + 0.965937i \(0.416680\pi\)
\(480\) 7.16731 0.327141
\(481\) 75.7280 3.45290
\(482\) 23.9574 1.09123
\(483\) 0.796335 0.0362345
\(484\) −8.58869 −0.390395
\(485\) −18.6184 −0.845416
\(486\) −36.3185 −1.64744
\(487\) −30.1218 −1.36495 −0.682475 0.730909i \(-0.739096\pi\)
−0.682475 + 0.730909i \(0.739096\pi\)
\(488\) 7.16391 0.324295
\(489\) −0.546908 −0.0247320
\(490\) −23.5403 −1.06344
\(491\) −13.8237 −0.623857 −0.311928 0.950106i \(-0.600975\pi\)
−0.311928 + 0.950106i \(0.600975\pi\)
\(492\) 24.9453 1.12462
\(493\) 0.644616 0.0290320
\(494\) −57.6836 −2.59531
\(495\) −11.0480 −0.496569
\(496\) −40.4168 −1.81477
\(497\) −10.8585 −0.487071
\(498\) −5.37966 −0.241068
\(499\) 16.9795 0.760106 0.380053 0.924965i \(-0.375906\pi\)
0.380053 + 0.924965i \(0.375906\pi\)
\(500\) 52.6316 2.35376
\(501\) −3.38931 −0.151423
\(502\) 19.1190 0.853324
\(503\) −19.9737 −0.890584 −0.445292 0.895385i \(-0.646900\pi\)
−0.445292 + 0.895385i \(0.646900\pi\)
\(504\) 12.6266 0.562433
\(505\) −5.83920 −0.259841
\(506\) 14.2152 0.631941
\(507\) 21.5678 0.957859
\(508\) −59.7074 −2.64909
\(509\) 16.2070 0.718364 0.359182 0.933268i \(-0.383056\pi\)
0.359182 + 0.933268i \(0.383056\pi\)
\(510\) −6.54853 −0.289974
\(511\) −9.45412 −0.418226
\(512\) 48.1665 2.12868
\(513\) 11.3784 0.502367
\(514\) −50.3543 −2.22103
\(515\) −1.98877 −0.0876358
\(516\) −0.0678387 −0.00298643
\(517\) −14.1713 −0.623255
\(518\) 19.8826 0.873591
\(519\) −4.79561 −0.210504
\(520\) −66.6774 −2.92400
\(521\) −1.24066 −0.0543543 −0.0271772 0.999631i \(-0.508652\pi\)
−0.0271772 + 0.999631i \(0.508652\pi\)
\(522\) −1.50178 −0.0657309
\(523\) 35.9724 1.57296 0.786481 0.617615i \(-0.211901\pi\)
0.786481 + 0.617615i \(0.211901\pi\)
\(524\) −70.1428 −3.06420
\(525\) −1.33287 −0.0581713
\(526\) −10.4120 −0.453986
\(527\) 13.7223 0.597754
\(528\) −16.1469 −0.702702
\(529\) −19.6974 −0.856407
\(530\) −36.1621 −1.57078
\(531\) 2.77903 0.120600
\(532\) −10.6085 −0.459937
\(533\) −58.6843 −2.54190
\(534\) 22.9158 0.991665
\(535\) −20.1114 −0.869493
\(536\) −49.8892 −2.15489
\(537\) 3.05191 0.131700
\(538\) 62.5857 2.69826
\(539\) 19.7071 0.848844
\(540\) 22.9789 0.988854
\(541\) 9.11925 0.392067 0.196034 0.980597i \(-0.437194\pi\)
0.196034 + 0.980597i \(0.437194\pi\)
\(542\) −52.2286 −2.24341
\(543\) 9.36976 0.402095
\(544\) 23.6646 1.01461
\(545\) −16.4451 −0.704429
\(546\) 7.79958 0.333791
\(547\) 7.95075 0.339950 0.169975 0.985448i \(-0.445631\pi\)
0.169975 + 0.985448i \(0.445631\pi\)
\(548\) 47.2716 2.01934
\(549\) 2.70108 0.115279
\(550\) −23.7927 −1.01453
\(551\) 0.722187 0.0307662
\(552\) −7.87007 −0.334972
\(553\) −9.83981 −0.418431
\(554\) −20.0216 −0.850637
\(555\) 9.63155 0.408836
\(556\) −70.1955 −2.97695
\(557\) 24.5538 1.04038 0.520189 0.854051i \(-0.325861\pi\)
0.520189 + 0.854051i \(0.325861\pi\)
\(558\) −31.9692 −1.35336
\(559\) 0.159592 0.00675002
\(560\) −8.34475 −0.352630
\(561\) 5.48218 0.231458
\(562\) 17.4147 0.734594
\(563\) 27.0620 1.14053 0.570264 0.821462i \(-0.306841\pi\)
0.570264 + 0.821462i \(0.306841\pi\)
\(564\) 13.7076 0.577193
\(565\) 4.13322 0.173886
\(566\) −28.2747 −1.18847
\(567\) 3.93771 0.165368
\(568\) 107.313 4.50276
\(569\) 17.0815 0.716094 0.358047 0.933704i \(-0.383443\pi\)
0.358047 + 0.933704i \(0.383443\pi\)
\(570\) −7.33656 −0.307295
\(571\) −22.3587 −0.935684 −0.467842 0.883812i \(-0.654968\pi\)
−0.467842 + 0.883812i \(0.654968\pi\)
\(572\) 97.5240 4.07768
\(573\) 14.2030 0.593339
\(574\) −15.4077 −0.643107
\(575\) −5.52780 −0.230525
\(576\) −10.6915 −0.445480
\(577\) 17.2800 0.719376 0.359688 0.933073i \(-0.382883\pi\)
0.359688 + 0.933073i \(0.382883\pi\)
\(578\) 22.3061 0.927811
\(579\) −12.6952 −0.527593
\(580\) 1.45847 0.0605598
\(581\) 2.32750 0.0965609
\(582\) −21.5237 −0.892185
\(583\) 30.2736 1.25380
\(584\) 93.4338 3.86632
\(585\) −25.1400 −1.03941
\(586\) 54.6026 2.25561
\(587\) −17.3807 −0.717380 −0.358690 0.933457i \(-0.616776\pi\)
−0.358690 + 0.933457i \(0.616776\pi\)
\(588\) −19.0622 −0.786110
\(589\) 15.3736 0.633459
\(590\) −3.85303 −0.158627
\(591\) 4.86387 0.200073
\(592\) −93.6642 −3.84957
\(593\) 27.9992 1.14979 0.574896 0.818227i \(-0.305043\pi\)
0.574896 + 0.818227i \(0.305043\pi\)
\(594\) −27.4634 −1.12684
\(595\) 2.83321 0.116150
\(596\) 11.8434 0.485126
\(597\) 3.58937 0.146903
\(598\) 32.3471 1.32277
\(599\) −25.4871 −1.04138 −0.520688 0.853747i \(-0.674324\pi\)
−0.520688 + 0.853747i \(0.674324\pi\)
\(600\) 13.1726 0.537768
\(601\) 9.03306 0.368466 0.184233 0.982883i \(-0.441020\pi\)
0.184233 + 0.982883i \(0.441020\pi\)
\(602\) 0.0419013 0.00170777
\(603\) −18.8102 −0.766011
\(604\) −62.9938 −2.56318
\(605\) 2.56980 0.104477
\(606\) −6.75038 −0.274215
\(607\) 11.8368 0.480442 0.240221 0.970718i \(-0.422780\pi\)
0.240221 + 0.970718i \(0.422780\pi\)
\(608\) 26.5123 1.07522
\(609\) −0.0976490 −0.00395694
\(610\) −3.74496 −0.151629
\(611\) −32.2474 −1.30459
\(612\) 35.2837 1.42626
\(613\) 11.9870 0.484152 0.242076 0.970257i \(-0.422172\pi\)
0.242076 + 0.970257i \(0.422172\pi\)
\(614\) 18.3591 0.740913
\(615\) −7.46383 −0.300971
\(616\) 14.6557 0.590493
\(617\) −22.5867 −0.909308 −0.454654 0.890668i \(-0.650237\pi\)
−0.454654 + 0.890668i \(0.650237\pi\)
\(618\) −2.29911 −0.0924839
\(619\) 21.9122 0.880727 0.440364 0.897820i \(-0.354850\pi\)
0.440364 + 0.897820i \(0.354850\pi\)
\(620\) 31.0474 1.24689
\(621\) −6.38061 −0.256045
\(622\) 4.16870 0.167150
\(623\) −9.91448 −0.397215
\(624\) −36.7427 −1.47089
\(625\) −0.539091 −0.0215636
\(626\) 49.8455 1.99222
\(627\) 6.14189 0.245284
\(628\) 10.4549 0.417194
\(629\) 31.8008 1.26798
\(630\) −6.60058 −0.262974
\(631\) 25.6828 1.02242 0.511208 0.859457i \(-0.329198\pi\)
0.511208 + 0.859457i \(0.329198\pi\)
\(632\) 97.2454 3.86822
\(633\) −1.32380 −0.0526165
\(634\) −6.45570 −0.256388
\(635\) 17.8649 0.708948
\(636\) −29.2829 −1.16114
\(637\) 44.8441 1.77679
\(638\) −1.74311 −0.0690103
\(639\) 40.4613 1.60063
\(640\) −8.07284 −0.319107
\(641\) −10.7846 −0.425967 −0.212983 0.977056i \(-0.568318\pi\)
−0.212983 + 0.977056i \(0.568318\pi\)
\(642\) −23.2497 −0.917594
\(643\) 30.2443 1.19272 0.596360 0.802717i \(-0.296613\pi\)
0.596360 + 0.802717i \(0.296613\pi\)
\(644\) 5.94889 0.234419
\(645\) 0.0202979 0.000799228 0
\(646\) −24.2234 −0.953057
\(647\) −8.28070 −0.325548 −0.162774 0.986663i \(-0.552044\pi\)
−0.162774 + 0.986663i \(0.552044\pi\)
\(648\) −38.9158 −1.52876
\(649\) 3.22561 0.126616
\(650\) −54.1412 −2.12359
\(651\) −2.07871 −0.0814712
\(652\) −4.08559 −0.160004
\(653\) 29.3822 1.14981 0.574906 0.818219i \(-0.305038\pi\)
0.574906 + 0.818219i \(0.305038\pi\)
\(654\) −19.0112 −0.743398
\(655\) 20.9873 0.820041
\(656\) 72.5837 2.83392
\(657\) 35.2282 1.37438
\(658\) −8.46664 −0.330064
\(659\) 20.9313 0.815368 0.407684 0.913123i \(-0.366337\pi\)
0.407684 + 0.913123i \(0.366337\pi\)
\(660\) 12.4037 0.482813
\(661\) 16.7971 0.653331 0.326665 0.945140i \(-0.394075\pi\)
0.326665 + 0.945140i \(0.394075\pi\)
\(662\) −64.8659 −2.52108
\(663\) 12.4749 0.484484
\(664\) −23.0023 −0.892664
\(665\) 3.17415 0.123088
\(666\) −74.0871 −2.87082
\(667\) −0.404979 −0.0156808
\(668\) −25.3193 −0.979634
\(669\) −2.81168 −0.108706
\(670\) 26.0797 1.00755
\(671\) 3.13514 0.121031
\(672\) −3.58481 −0.138287
\(673\) −32.0943 −1.23715 −0.618573 0.785727i \(-0.712289\pi\)
−0.618573 + 0.785727i \(0.712289\pi\)
\(674\) 34.8204 1.34123
\(675\) 10.6796 0.411058
\(676\) 161.119 6.19688
\(677\) 13.0335 0.500918 0.250459 0.968127i \(-0.419418\pi\)
0.250459 + 0.968127i \(0.419418\pi\)
\(678\) 4.77819 0.183505
\(679\) 9.31217 0.357368
\(680\) −28.0002 −1.07376
\(681\) −11.9229 −0.456886
\(682\) −37.1066 −1.42088
\(683\) −11.0359 −0.422277 −0.211139 0.977456i \(-0.567717\pi\)
−0.211139 + 0.977456i \(0.567717\pi\)
\(684\) 39.5297 1.51146
\(685\) −14.1440 −0.540416
\(686\) 24.4339 0.932890
\(687\) 0.157968 0.00602687
\(688\) −0.197391 −0.00752548
\(689\) 68.8885 2.62444
\(690\) 4.11410 0.156621
\(691\) 20.1701 0.767308 0.383654 0.923477i \(-0.374666\pi\)
0.383654 + 0.923477i \(0.374666\pi\)
\(692\) −35.8248 −1.36186
\(693\) 5.52576 0.209906
\(694\) −6.92209 −0.262759
\(695\) 21.0031 0.796691
\(696\) 0.965052 0.0365802
\(697\) −24.6436 −0.933444
\(698\) 25.2303 0.954981
\(699\) 14.3427 0.542491
\(700\) −9.95701 −0.376339
\(701\) 19.2959 0.728796 0.364398 0.931243i \(-0.381275\pi\)
0.364398 + 0.931243i \(0.381275\pi\)
\(702\) −62.4939 −2.35868
\(703\) 35.6277 1.34372
\(704\) −12.4096 −0.467705
\(705\) −4.10142 −0.154468
\(706\) −42.4552 −1.59782
\(707\) 2.92054 0.109838
\(708\) −3.12005 −0.117259
\(709\) 29.9703 1.12556 0.562779 0.826607i \(-0.309732\pi\)
0.562779 + 0.826607i \(0.309732\pi\)
\(710\) −56.0983 −2.10533
\(711\) 36.6654 1.37506
\(712\) 97.9834 3.67208
\(713\) −8.62102 −0.322860
\(714\) 3.27532 0.122576
\(715\) −29.1799 −1.09127
\(716\) 22.7988 0.852033
\(717\) −5.83961 −0.218084
\(718\) −11.6662 −0.435379
\(719\) −52.1807 −1.94601 −0.973005 0.230782i \(-0.925871\pi\)
−0.973005 + 0.230782i \(0.925871\pi\)
\(720\) 31.0944 1.15882
\(721\) 0.994706 0.0370448
\(722\) 21.9572 0.817162
\(723\) −5.80459 −0.215875
\(724\) 69.9953 2.60135
\(725\) 0.677836 0.0251742
\(726\) 2.97081 0.110257
\(727\) 33.8166 1.25419 0.627095 0.778943i \(-0.284244\pi\)
0.627095 + 0.778943i \(0.284244\pi\)
\(728\) 33.3494 1.23601
\(729\) −8.07840 −0.299200
\(730\) −48.8428 −1.80775
\(731\) 0.0670183 0.00247876
\(732\) −3.03254 −0.112086
\(733\) 33.3532 1.23193 0.615965 0.787774i \(-0.288766\pi\)
0.615965 + 0.787774i \(0.288766\pi\)
\(734\) 73.5118 2.71337
\(735\) 5.70355 0.210379
\(736\) −14.8672 −0.548013
\(737\) −21.8330 −0.804228
\(738\) 57.4128 2.11339
\(739\) −31.0837 −1.14343 −0.571716 0.820452i \(-0.693722\pi\)
−0.571716 + 0.820452i \(0.693722\pi\)
\(740\) 71.9509 2.64497
\(741\) 13.9761 0.513424
\(742\) 18.0869 0.663991
\(743\) −19.6728 −0.721723 −0.360862 0.932619i \(-0.617517\pi\)
−0.360862 + 0.932619i \(0.617517\pi\)
\(744\) 20.5436 0.753166
\(745\) −3.54365 −0.129829
\(746\) −26.8941 −0.984663
\(747\) −8.67279 −0.317321
\(748\) 40.9538 1.49742
\(749\) 10.0590 0.367546
\(750\) −18.2052 −0.664759
\(751\) −47.4211 −1.73042 −0.865210 0.501410i \(-0.832815\pi\)
−0.865210 + 0.501410i \(0.832815\pi\)
\(752\) 39.8852 1.45446
\(753\) −4.63232 −0.168811
\(754\) −3.96650 −0.144451
\(755\) 18.8483 0.685958
\(756\) −11.4931 −0.418001
\(757\) 32.4881 1.18080 0.590400 0.807111i \(-0.298970\pi\)
0.590400 + 0.807111i \(0.298970\pi\)
\(758\) 30.7483 1.11683
\(759\) −3.44417 −0.125015
\(760\) −31.3697 −1.13790
\(761\) −25.4961 −0.924231 −0.462116 0.886820i \(-0.652910\pi\)
−0.462116 + 0.886820i \(0.652910\pi\)
\(762\) 20.6527 0.748167
\(763\) 8.22518 0.297771
\(764\) 106.101 3.83861
\(765\) −10.5572 −0.381696
\(766\) −17.4995 −0.632282
\(767\) 7.33999 0.265032
\(768\) −14.4656 −0.521984
\(769\) 30.8680 1.11313 0.556564 0.830805i \(-0.312119\pi\)
0.556564 + 0.830805i \(0.312119\pi\)
\(770\) −7.66128 −0.276093
\(771\) 12.2003 0.439381
\(772\) −94.8372 −3.41327
\(773\) 24.3108 0.874400 0.437200 0.899364i \(-0.355970\pi\)
0.437200 + 0.899364i \(0.355970\pi\)
\(774\) −0.156134 −0.00561212
\(775\) 14.4295 0.518323
\(776\) −92.0309 −3.30372
\(777\) −4.81732 −0.172820
\(778\) 48.4407 1.73668
\(779\) −27.6092 −0.989201
\(780\) 28.2250 1.01062
\(781\) 46.9634 1.68048
\(782\) 13.5837 0.485751
\(783\) 0.782410 0.0279611
\(784\) −55.4655 −1.98091
\(785\) −3.12817 −0.111649
\(786\) 24.2623 0.865406
\(787\) −13.4463 −0.479310 −0.239655 0.970858i \(-0.577034\pi\)
−0.239655 + 0.970858i \(0.577034\pi\)
\(788\) 36.3348 1.29437
\(789\) 2.52271 0.0898110
\(790\) −50.8353 −1.80864
\(791\) −2.06727 −0.0735038
\(792\) −54.6103 −1.94049
\(793\) 7.13410 0.253339
\(794\) 39.2039 1.39129
\(795\) 8.76167 0.310744
\(796\) 26.8138 0.950391
\(797\) −22.8816 −0.810507 −0.405253 0.914204i \(-0.632817\pi\)
−0.405253 + 0.914204i \(0.632817\pi\)
\(798\) 3.66946 0.129897
\(799\) −13.5418 −0.479075
\(800\) 24.8841 0.879787
\(801\) 36.9436 1.30534
\(802\) 2.00800 0.0709050
\(803\) 40.8893 1.44295
\(804\) 21.1185 0.744792
\(805\) −1.77996 −0.0627352
\(806\) −84.4372 −2.97417
\(807\) −15.1638 −0.533791
\(808\) −28.8633 −1.01541
\(809\) 12.0450 0.423478 0.211739 0.977326i \(-0.432087\pi\)
0.211739 + 0.977326i \(0.432087\pi\)
\(810\) 20.3433 0.714792
\(811\) 33.3915 1.17253 0.586266 0.810118i \(-0.300597\pi\)
0.586266 + 0.810118i \(0.300597\pi\)
\(812\) −0.729472 −0.0255994
\(813\) 12.6544 0.443808
\(814\) −85.9927 −3.01404
\(815\) 1.22244 0.0428202
\(816\) −15.4296 −0.540143
\(817\) 0.0750831 0.00262683
\(818\) −68.4144 −2.39205
\(819\) 12.5740 0.439373
\(820\) −55.7574 −1.94713
\(821\) −1.19373 −0.0416616 −0.0208308 0.999783i \(-0.506631\pi\)
−0.0208308 + 0.999783i \(0.506631\pi\)
\(822\) −16.3512 −0.570312
\(823\) −43.6389 −1.52116 −0.760578 0.649247i \(-0.775084\pi\)
−0.760578 + 0.649247i \(0.775084\pi\)
\(824\) −9.83054 −0.342463
\(825\) 5.76470 0.200701
\(826\) 1.92714 0.0670536
\(827\) 4.59153 0.159663 0.0798315 0.996808i \(-0.474562\pi\)
0.0798315 + 0.996808i \(0.474562\pi\)
\(828\) −22.1669 −0.770354
\(829\) −6.31638 −0.219377 −0.109688 0.993966i \(-0.534985\pi\)
−0.109688 + 0.993966i \(0.534985\pi\)
\(830\) 12.0245 0.417378
\(831\) 4.85100 0.168279
\(832\) −28.2385 −0.978994
\(833\) 18.8316 0.652477
\(834\) 24.2805 0.840765
\(835\) 7.57575 0.262170
\(836\) 45.8820 1.58686
\(837\) 16.6556 0.575703
\(838\) 62.8948 2.17266
\(839\) 17.1067 0.590588 0.295294 0.955406i \(-0.404582\pi\)
0.295294 + 0.955406i \(0.404582\pi\)
\(840\) 4.24158 0.146349
\(841\) −28.9503 −0.998288
\(842\) 22.4190 0.772610
\(843\) −4.21938 −0.145323
\(844\) −9.88926 −0.340403
\(845\) −48.2080 −1.65841
\(846\) 31.5486 1.08466
\(847\) −1.28532 −0.0441640
\(848\) −85.2048 −2.92594
\(849\) 6.85063 0.235113
\(850\) −22.7358 −0.779831
\(851\) −19.9788 −0.684865
\(852\) −45.4265 −1.55629
\(853\) −30.2106 −1.03439 −0.517196 0.855867i \(-0.673024\pi\)
−0.517196 + 0.855867i \(0.673024\pi\)
\(854\) 1.87308 0.0640955
\(855\) −11.8276 −0.404495
\(856\) −99.4112 −3.39781
\(857\) 34.7559 1.18724 0.593620 0.804746i \(-0.297698\pi\)
0.593620 + 0.804746i \(0.297698\pi\)
\(858\) −33.7334 −1.15164
\(859\) 48.3871 1.65095 0.825473 0.564441i \(-0.190908\pi\)
0.825473 + 0.564441i \(0.190908\pi\)
\(860\) 0.151632 0.00517061
\(861\) 3.73312 0.127224
\(862\) 64.2917 2.18978
\(863\) 38.3726 1.30622 0.653109 0.757264i \(-0.273464\pi\)
0.653109 + 0.757264i \(0.273464\pi\)
\(864\) 28.7232 0.977182
\(865\) 10.7191 0.364460
\(866\) 59.0522 2.00668
\(867\) −5.40451 −0.183547
\(868\) −15.5287 −0.527079
\(869\) 42.5574 1.44366
\(870\) −0.504483 −0.0171036
\(871\) −49.6817 −1.68340
\(872\) −81.2882 −2.75277
\(873\) −34.6993 −1.17439
\(874\) 15.2183 0.514767
\(875\) 7.87643 0.266272
\(876\) −39.5512 −1.33631
\(877\) 39.1132 1.32076 0.660380 0.750932i \(-0.270395\pi\)
0.660380 + 0.750932i \(0.270395\pi\)
\(878\) 65.2581 2.20235
\(879\) −13.2296 −0.446223
\(880\) 36.0912 1.21664
\(881\) −41.1181 −1.38530 −0.692652 0.721272i \(-0.743558\pi\)
−0.692652 + 0.721272i \(0.743558\pi\)
\(882\) −43.8724 −1.47726
\(883\) −14.4750 −0.487123 −0.243561 0.969886i \(-0.578316\pi\)
−0.243561 + 0.969886i \(0.578316\pi\)
\(884\) 93.1916 3.13437
\(885\) 0.933545 0.0313808
\(886\) 57.5795 1.93442
\(887\) −6.82479 −0.229154 −0.114577 0.993414i \(-0.536551\pi\)
−0.114577 + 0.993414i \(0.536551\pi\)
\(888\) 47.6089 1.59765
\(889\) −8.93534 −0.299682
\(890\) −51.2211 −1.71694
\(891\) −17.0307 −0.570549
\(892\) −21.0042 −0.703273
\(893\) −15.1714 −0.507691
\(894\) −4.09662 −0.137011
\(895\) −6.82160 −0.228021
\(896\) 4.03772 0.134891
\(897\) −7.83732 −0.261680
\(898\) 22.6283 0.755116
\(899\) 1.05714 0.0352575
\(900\) 37.1021 1.23674
\(901\) 28.9287 0.963756
\(902\) 66.6389 2.21883
\(903\) −0.0101522 −0.000337844 0
\(904\) 20.4306 0.679511
\(905\) −20.9431 −0.696174
\(906\) 21.7894 0.723906
\(907\) 7.58795 0.251954 0.125977 0.992033i \(-0.459793\pi\)
0.125977 + 0.992033i \(0.459793\pi\)
\(908\) −89.0680 −2.95583
\(909\) −10.8826 −0.360953
\(910\) −17.4335 −0.577915
\(911\) −53.7662 −1.78135 −0.890676 0.454638i \(-0.849769\pi\)
−0.890676 + 0.454638i \(0.849769\pi\)
\(912\) −17.2863 −0.572407
\(913\) −10.0665 −0.333152
\(914\) −27.7839 −0.919010
\(915\) 0.907359 0.0299964
\(916\) 1.18008 0.0389908
\(917\) −10.4970 −0.346642
\(918\) −26.2434 −0.866161
\(919\) 23.2464 0.766828 0.383414 0.923577i \(-0.374748\pi\)
0.383414 + 0.923577i \(0.374748\pi\)
\(920\) 17.5911 0.579960
\(921\) −4.44820 −0.146573
\(922\) 50.2494 1.65488
\(923\) 106.867 3.51756
\(924\) −6.20384 −0.204091
\(925\) 33.4397 1.09949
\(926\) 72.4522 2.38093
\(927\) −3.70650 −0.121738
\(928\) 1.82306 0.0598450
\(929\) −56.9903 −1.86979 −0.934896 0.354921i \(-0.884508\pi\)
−0.934896 + 0.354921i \(0.884508\pi\)
\(930\) −10.7392 −0.352154
\(931\) 21.0978 0.691452
\(932\) 107.145 3.50965
\(933\) −1.01003 −0.0330668
\(934\) 15.6102 0.510782
\(935\) −12.2537 −0.400739
\(936\) −124.268 −4.06181
\(937\) −23.6415 −0.772333 −0.386167 0.922429i \(-0.626201\pi\)
−0.386167 + 0.922429i \(0.626201\pi\)
\(938\) −13.0441 −0.425904
\(939\) −12.0770 −0.394117
\(940\) −30.6390 −0.999333
\(941\) 22.0207 0.717855 0.358927 0.933365i \(-0.383143\pi\)
0.358927 + 0.933365i \(0.383143\pi\)
\(942\) −3.61631 −0.117826
\(943\) 15.4823 0.504173
\(944\) −9.07847 −0.295479
\(945\) 3.43884 0.111865
\(946\) −0.181224 −0.00589211
\(947\) −9.91359 −0.322149 −0.161074 0.986942i \(-0.551496\pi\)
−0.161074 + 0.986942i \(0.551496\pi\)
\(948\) −41.1647 −1.33697
\(949\) 93.0450 3.02037
\(950\) −25.4717 −0.826413
\(951\) 1.56414 0.0507207
\(952\) 14.0046 0.453892
\(953\) 0.188075 0.00609233 0.00304617 0.999995i \(-0.499030\pi\)
0.00304617 + 0.999995i \(0.499030\pi\)
\(954\) −67.3959 −2.18202
\(955\) −31.7464 −1.02729
\(956\) −43.6239 −1.41090
\(957\) 0.422335 0.0136521
\(958\) −29.2695 −0.945654
\(959\) 7.07430 0.228441
\(960\) −3.59155 −0.115917
\(961\) −8.49611 −0.274068
\(962\) −195.679 −6.30895
\(963\) −37.4820 −1.20784
\(964\) −43.3623 −1.39660
\(965\) 28.3760 0.913457
\(966\) −2.05771 −0.0662058
\(967\) 0.0656192 0.00211017 0.00105509 0.999999i \(-0.499664\pi\)
0.00105509 + 0.999999i \(0.499664\pi\)
\(968\) 12.7026 0.408277
\(969\) 5.86905 0.188541
\(970\) 48.1094 1.54470
\(971\) −15.4909 −0.497127 −0.248563 0.968616i \(-0.579958\pi\)
−0.248563 + 0.968616i \(0.579958\pi\)
\(972\) 65.7357 2.10847
\(973\) −10.5049 −0.336772
\(974\) 77.8341 2.49397
\(975\) 13.1178 0.420105
\(976\) −8.82382 −0.282444
\(977\) 11.2387 0.359558 0.179779 0.983707i \(-0.442462\pi\)
0.179779 + 0.983707i \(0.442462\pi\)
\(978\) 1.41320 0.0451891
\(979\) 42.8804 1.37046
\(980\) 42.6075 1.36105
\(981\) −30.6489 −0.978544
\(982\) 35.7202 1.13988
\(983\) −56.5750 −1.80446 −0.902231 0.431254i \(-0.858071\pi\)
−0.902231 + 0.431254i \(0.858071\pi\)
\(984\) −36.8939 −1.17613
\(985\) −10.8717 −0.346400
\(986\) −1.66567 −0.0530458
\(987\) 2.05137 0.0652958
\(988\) 104.406 3.32160
\(989\) −0.0421041 −0.00133883
\(990\) 28.5477 0.907305
\(991\) −36.6590 −1.16451 −0.582255 0.813006i \(-0.697830\pi\)
−0.582255 + 0.813006i \(0.697830\pi\)
\(992\) 38.8087 1.23218
\(993\) 15.7162 0.498740
\(994\) 28.0582 0.889951
\(995\) −8.02291 −0.254343
\(996\) 9.73706 0.308531
\(997\) 7.83835 0.248243 0.124122 0.992267i \(-0.460389\pi\)
0.124122 + 0.992267i \(0.460389\pi\)
\(998\) −43.8746 −1.38883
\(999\) 38.5987 1.22121
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 6037.2.a.b.1.11 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.11 259 1.1 even 1 trivial