Properties

Label 6037.2.a.b.1.18
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 1.18
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42952 q^{2} -2.16225 q^{3} +3.90258 q^{4} -1.13309 q^{5} +5.25323 q^{6} +1.20579 q^{7} -4.62237 q^{8} +1.67531 q^{9} +O(q^{10})\) \(q-2.42952 q^{2} -2.16225 q^{3} +3.90258 q^{4} -1.13309 q^{5} +5.25323 q^{6} +1.20579 q^{7} -4.62237 q^{8} +1.67531 q^{9} +2.75288 q^{10} -2.91069 q^{11} -8.43835 q^{12} -3.14120 q^{13} -2.92951 q^{14} +2.45003 q^{15} +3.42500 q^{16} +6.74170 q^{17} -4.07021 q^{18} +5.77323 q^{19} -4.42199 q^{20} -2.60723 q^{21} +7.07160 q^{22} +4.19239 q^{23} +9.99471 q^{24} -3.71610 q^{25} +7.63161 q^{26} +2.86430 q^{27} +4.70571 q^{28} +3.14378 q^{29} -5.95240 q^{30} +7.21485 q^{31} +0.923640 q^{32} +6.29364 q^{33} -16.3791 q^{34} -1.36628 q^{35} +6.53804 q^{36} +2.54895 q^{37} -14.0262 q^{38} +6.79204 q^{39} +5.23758 q^{40} -3.09135 q^{41} +6.33432 q^{42} -12.7605 q^{43} -11.3592 q^{44} -1.89828 q^{45} -10.1855 q^{46} -0.275255 q^{47} -7.40569 q^{48} -5.54606 q^{49} +9.02835 q^{50} -14.5772 q^{51} -12.2588 q^{52} +11.1705 q^{53} -6.95889 q^{54} +3.29809 q^{55} -5.57363 q^{56} -12.4832 q^{57} -7.63788 q^{58} +11.9945 q^{59} +9.56143 q^{60} +7.71644 q^{61} -17.5286 q^{62} +2.02008 q^{63} -9.09399 q^{64} +3.55927 q^{65} -15.2905 q^{66} -1.90029 q^{67} +26.3101 q^{68} -9.06499 q^{69} +3.31940 q^{70} -9.99754 q^{71} -7.74391 q^{72} +3.08586 q^{73} -6.19273 q^{74} +8.03513 q^{75} +22.5305 q^{76} -3.50970 q^{77} -16.5014 q^{78} +1.25545 q^{79} -3.88084 q^{80} -11.2193 q^{81} +7.51050 q^{82} +12.8657 q^{83} -10.1749 q^{84} -7.63897 q^{85} +31.0019 q^{86} -6.79762 q^{87} +13.4543 q^{88} +7.72452 q^{89} +4.61192 q^{90} -3.78764 q^{91} +16.3612 q^{92} -15.6003 q^{93} +0.668739 q^{94} -6.54161 q^{95} -1.99714 q^{96} +9.59124 q^{97} +13.4743 q^{98} -4.87632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42952 −1.71793 −0.858966 0.512032i \(-0.828893\pi\)
−0.858966 + 0.512032i \(0.828893\pi\)
\(3\) −2.16225 −1.24837 −0.624187 0.781275i \(-0.714570\pi\)
−0.624187 + 0.781275i \(0.714570\pi\)
\(4\) 3.90258 1.95129
\(5\) −1.13309 −0.506735 −0.253367 0.967370i \(-0.581538\pi\)
−0.253367 + 0.967370i \(0.581538\pi\)
\(6\) 5.25323 2.14462
\(7\) 1.20579 0.455747 0.227874 0.973691i \(-0.426823\pi\)
0.227874 + 0.973691i \(0.426823\pi\)
\(8\) −4.62237 −1.63426
\(9\) 1.67531 0.558437
\(10\) 2.75288 0.870536
\(11\) −2.91069 −0.877607 −0.438804 0.898583i \(-0.644598\pi\)
−0.438804 + 0.898583i \(0.644598\pi\)
\(12\) −8.43835 −2.43594
\(13\) −3.14120 −0.871211 −0.435606 0.900138i \(-0.643466\pi\)
−0.435606 + 0.900138i \(0.643466\pi\)
\(14\) −2.92951 −0.782943
\(15\) 2.45003 0.632594
\(16\) 3.42500 0.856249
\(17\) 6.74170 1.63510 0.817551 0.575856i \(-0.195331\pi\)
0.817551 + 0.575856i \(0.195331\pi\)
\(18\) −4.07021 −0.959357
\(19\) 5.77323 1.32447 0.662235 0.749296i \(-0.269608\pi\)
0.662235 + 0.749296i \(0.269608\pi\)
\(20\) −4.42199 −0.988787
\(21\) −2.60723 −0.568943
\(22\) 7.07160 1.50767
\(23\) 4.19239 0.874175 0.437087 0.899419i \(-0.356010\pi\)
0.437087 + 0.899419i \(0.356010\pi\)
\(24\) 9.99471 2.04016
\(25\) −3.71610 −0.743220
\(26\) 7.63161 1.49668
\(27\) 2.86430 0.551236
\(28\) 4.70571 0.889296
\(29\) 3.14378 0.583784 0.291892 0.956451i \(-0.405715\pi\)
0.291892 + 0.956451i \(0.405715\pi\)
\(30\) −5.95240 −1.08675
\(31\) 7.21485 1.29582 0.647912 0.761715i \(-0.275642\pi\)
0.647912 + 0.761715i \(0.275642\pi\)
\(32\) 0.923640 0.163278
\(33\) 6.29364 1.09558
\(34\) −16.3791 −2.80900
\(35\) −1.36628 −0.230943
\(36\) 6.53804 1.08967
\(37\) 2.54895 0.419044 0.209522 0.977804i \(-0.432809\pi\)
0.209522 + 0.977804i \(0.432809\pi\)
\(38\) −14.0262 −2.27535
\(39\) 6.79204 1.08760
\(40\) 5.23758 0.828134
\(41\) −3.09135 −0.482787 −0.241394 0.970427i \(-0.577605\pi\)
−0.241394 + 0.970427i \(0.577605\pi\)
\(42\) 6.33432 0.977406
\(43\) −12.7605 −1.94596 −0.972978 0.230899i \(-0.925833\pi\)
−0.972978 + 0.230899i \(0.925833\pi\)
\(44\) −11.3592 −1.71247
\(45\) −1.89828 −0.282979
\(46\) −10.1855 −1.50177
\(47\) −0.275255 −0.0401501 −0.0200750 0.999798i \(-0.506391\pi\)
−0.0200750 + 0.999798i \(0.506391\pi\)
\(48\) −7.40569 −1.06892
\(49\) −5.54606 −0.792294
\(50\) 9.02835 1.27680
\(51\) −14.5772 −2.04122
\(52\) −12.2588 −1.69999
\(53\) 11.1705 1.53438 0.767192 0.641417i \(-0.221653\pi\)
0.767192 + 0.641417i \(0.221653\pi\)
\(54\) −6.95889 −0.946985
\(55\) 3.29809 0.444714
\(56\) −5.57363 −0.744808
\(57\) −12.4832 −1.65343
\(58\) −7.63788 −1.00290
\(59\) 11.9945 1.56155 0.780774 0.624814i \(-0.214825\pi\)
0.780774 + 0.624814i \(0.214825\pi\)
\(60\) 9.56143 1.23438
\(61\) 7.71644 0.987989 0.493995 0.869465i \(-0.335536\pi\)
0.493995 + 0.869465i \(0.335536\pi\)
\(62\) −17.5286 −2.22614
\(63\) 2.02008 0.254506
\(64\) −9.09399 −1.13675
\(65\) 3.55927 0.441473
\(66\) −15.2905 −1.88214
\(67\) −1.90029 −0.232157 −0.116078 0.993240i \(-0.537032\pi\)
−0.116078 + 0.993240i \(0.537032\pi\)
\(68\) 26.3101 3.19056
\(69\) −9.06499 −1.09130
\(70\) 3.31940 0.396744
\(71\) −9.99754 −1.18649 −0.593245 0.805022i \(-0.702153\pi\)
−0.593245 + 0.805022i \(0.702153\pi\)
\(72\) −7.74391 −0.912629
\(73\) 3.08586 0.361172 0.180586 0.983559i \(-0.442201\pi\)
0.180586 + 0.983559i \(0.442201\pi\)
\(74\) −6.19273 −0.719890
\(75\) 8.03513 0.927817
\(76\) 22.5305 2.58443
\(77\) −3.50970 −0.399967
\(78\) −16.5014 −1.86842
\(79\) 1.25545 0.141249 0.0706245 0.997503i \(-0.477501\pi\)
0.0706245 + 0.997503i \(0.477501\pi\)
\(80\) −3.88084 −0.433891
\(81\) −11.2193 −1.24659
\(82\) 7.51050 0.829396
\(83\) 12.8657 1.41220 0.706099 0.708114i \(-0.250454\pi\)
0.706099 + 0.708114i \(0.250454\pi\)
\(84\) −10.1749 −1.11017
\(85\) −7.63897 −0.828563
\(86\) 31.0019 3.34302
\(87\) −6.79762 −0.728781
\(88\) 13.4543 1.43423
\(89\) 7.72452 0.818797 0.409399 0.912356i \(-0.365739\pi\)
0.409399 + 0.912356i \(0.365739\pi\)
\(90\) 4.61192 0.486139
\(91\) −3.78764 −0.397052
\(92\) 16.3612 1.70577
\(93\) −15.6003 −1.61767
\(94\) 0.668739 0.0689751
\(95\) −6.54161 −0.671155
\(96\) −1.99714 −0.203832
\(97\) 9.59124 0.973843 0.486921 0.873446i \(-0.338120\pi\)
0.486921 + 0.873446i \(0.338120\pi\)
\(98\) 13.4743 1.36111
\(99\) −4.87632 −0.490088
\(100\) −14.5024 −1.45024
\(101\) 7.32798 0.729161 0.364580 0.931172i \(-0.381212\pi\)
0.364580 + 0.931172i \(0.381212\pi\)
\(102\) 35.4157 3.50668
\(103\) −15.2574 −1.50336 −0.751678 0.659530i \(-0.770755\pi\)
−0.751678 + 0.659530i \(0.770755\pi\)
\(104\) 14.5198 1.42378
\(105\) 2.95423 0.288303
\(106\) −27.1390 −2.63597
\(107\) 12.2896 1.18808 0.594039 0.804436i \(-0.297532\pi\)
0.594039 + 0.804436i \(0.297532\pi\)
\(108\) 11.1782 1.07562
\(109\) 8.18098 0.783595 0.391798 0.920051i \(-0.371853\pi\)
0.391798 + 0.920051i \(0.371853\pi\)
\(110\) −8.01278 −0.763988
\(111\) −5.51145 −0.523124
\(112\) 4.12984 0.390233
\(113\) 11.7704 1.10727 0.553633 0.832761i \(-0.313241\pi\)
0.553633 + 0.832761i \(0.313241\pi\)
\(114\) 30.3281 2.84049
\(115\) −4.75037 −0.442974
\(116\) 12.2688 1.13913
\(117\) −5.26248 −0.486517
\(118\) −29.1409 −2.68263
\(119\) 8.12911 0.745194
\(120\) −11.3249 −1.03382
\(121\) −2.52786 −0.229806
\(122\) −18.7473 −1.69730
\(123\) 6.68426 0.602699
\(124\) 28.1565 2.52853
\(125\) 9.87615 0.883350
\(126\) −4.90783 −0.437225
\(127\) −9.88332 −0.877003 −0.438501 0.898731i \(-0.644491\pi\)
−0.438501 + 0.898731i \(0.644491\pi\)
\(128\) 20.2468 1.78958
\(129\) 27.5913 2.42928
\(130\) −8.64732 −0.758420
\(131\) 2.18432 0.190845 0.0954224 0.995437i \(-0.469580\pi\)
0.0954224 + 0.995437i \(0.469580\pi\)
\(132\) 24.5615 2.13780
\(133\) 6.96133 0.603624
\(134\) 4.61679 0.398830
\(135\) −3.24552 −0.279330
\(136\) −31.1627 −2.67218
\(137\) −20.2271 −1.72812 −0.864059 0.503391i \(-0.832086\pi\)
−0.864059 + 0.503391i \(0.832086\pi\)
\(138\) 22.0236 1.87477
\(139\) −14.8881 −1.26279 −0.631397 0.775460i \(-0.717518\pi\)
−0.631397 + 0.775460i \(0.717518\pi\)
\(140\) −5.33201 −0.450637
\(141\) 0.595170 0.0501223
\(142\) 24.2892 2.03831
\(143\) 9.14306 0.764581
\(144\) 5.73793 0.478161
\(145\) −3.56219 −0.295824
\(146\) −7.49716 −0.620469
\(147\) 11.9919 0.989079
\(148\) 9.94748 0.817678
\(149\) −16.9803 −1.39108 −0.695541 0.718486i \(-0.744835\pi\)
−0.695541 + 0.718486i \(0.744835\pi\)
\(150\) −19.5215 −1.59393
\(151\) −11.0082 −0.895838 −0.447919 0.894074i \(-0.647835\pi\)
−0.447919 + 0.894074i \(0.647835\pi\)
\(152\) −26.6860 −2.16452
\(153\) 11.2944 0.913102
\(154\) 8.52690 0.687117
\(155\) −8.17509 −0.656639
\(156\) 26.5065 2.12222
\(157\) 9.18206 0.732808 0.366404 0.930456i \(-0.380589\pi\)
0.366404 + 0.930456i \(0.380589\pi\)
\(158\) −3.05014 −0.242656
\(159\) −24.1534 −1.91549
\(160\) −1.04657 −0.0827386
\(161\) 5.05517 0.398403
\(162\) 27.2575 2.14155
\(163\) 16.7118 1.30897 0.654484 0.756076i \(-0.272886\pi\)
0.654484 + 0.756076i \(0.272886\pi\)
\(164\) −12.0642 −0.942059
\(165\) −7.13128 −0.555169
\(166\) −31.2576 −2.42606
\(167\) 8.47487 0.655805 0.327903 0.944711i \(-0.393658\pi\)
0.327903 + 0.944711i \(0.393658\pi\)
\(168\) 12.0516 0.929799
\(169\) −3.13288 −0.240991
\(170\) 18.5591 1.42342
\(171\) 9.67196 0.739634
\(172\) −49.7989 −3.79713
\(173\) 4.51158 0.343009 0.171504 0.985183i \(-0.445137\pi\)
0.171504 + 0.985183i \(0.445137\pi\)
\(174\) 16.5150 1.25200
\(175\) −4.48085 −0.338721
\(176\) −9.96911 −0.751450
\(177\) −25.9350 −1.94939
\(178\) −18.7669 −1.40664
\(179\) −23.7476 −1.77498 −0.887490 0.460827i \(-0.847553\pi\)
−0.887490 + 0.460827i \(0.847553\pi\)
\(180\) −7.40821 −0.552175
\(181\) 7.82315 0.581490 0.290745 0.956801i \(-0.406097\pi\)
0.290745 + 0.956801i \(0.406097\pi\)
\(182\) 9.20215 0.682109
\(183\) −16.6849 −1.23338
\(184\) −19.3788 −1.42862
\(185\) −2.88819 −0.212344
\(186\) 37.9012 2.77905
\(187\) −19.6230 −1.43498
\(188\) −1.07421 −0.0783445
\(189\) 3.45376 0.251224
\(190\) 15.8930 1.15300
\(191\) −12.2823 −0.888719 −0.444359 0.895849i \(-0.646569\pi\)
−0.444359 + 0.895849i \(0.646569\pi\)
\(192\) 19.6635 1.41909
\(193\) −13.4364 −0.967170 −0.483585 0.875297i \(-0.660666\pi\)
−0.483585 + 0.875297i \(0.660666\pi\)
\(194\) −23.3021 −1.67300
\(195\) −7.69601 −0.551123
\(196\) −21.6440 −1.54600
\(197\) −13.0669 −0.930979 −0.465490 0.885053i \(-0.654122\pi\)
−0.465490 + 0.885053i \(0.654122\pi\)
\(198\) 11.8471 0.841939
\(199\) −6.91379 −0.490105 −0.245053 0.969510i \(-0.578805\pi\)
−0.245053 + 0.969510i \(0.578805\pi\)
\(200\) 17.1772 1.21461
\(201\) 4.10889 0.289819
\(202\) −17.8035 −1.25265
\(203\) 3.79075 0.266058
\(204\) −56.8888 −3.98302
\(205\) 3.50278 0.244645
\(206\) 37.0682 2.58266
\(207\) 7.02357 0.488172
\(208\) −10.7586 −0.745974
\(209\) −16.8041 −1.16237
\(210\) −7.17737 −0.495285
\(211\) 15.5687 1.07179 0.535897 0.844284i \(-0.319974\pi\)
0.535897 + 0.844284i \(0.319974\pi\)
\(212\) 43.5938 2.99403
\(213\) 21.6171 1.48118
\(214\) −29.8578 −2.04104
\(215\) 14.4588 0.986083
\(216\) −13.2399 −0.900860
\(217\) 8.69962 0.590569
\(218\) −19.8759 −1.34616
\(219\) −6.67238 −0.450878
\(220\) 12.8711 0.867767
\(221\) −21.1770 −1.42452
\(222\) 13.3902 0.898691
\(223\) 7.91555 0.530065 0.265032 0.964240i \(-0.414617\pi\)
0.265032 + 0.964240i \(0.414617\pi\)
\(224\) 1.11372 0.0744135
\(225\) −6.22563 −0.415042
\(226\) −28.5964 −1.90221
\(227\) −24.1472 −1.60271 −0.801355 0.598190i \(-0.795887\pi\)
−0.801355 + 0.598190i \(0.795887\pi\)
\(228\) −48.7166 −3.22633
\(229\) −21.9075 −1.44769 −0.723845 0.689962i \(-0.757627\pi\)
−0.723845 + 0.689962i \(0.757627\pi\)
\(230\) 11.5411 0.761000
\(231\) 7.58883 0.499309
\(232\) −14.5317 −0.954053
\(233\) 23.0093 1.50739 0.753694 0.657225i \(-0.228270\pi\)
0.753694 + 0.657225i \(0.228270\pi\)
\(234\) 12.7853 0.835803
\(235\) 0.311890 0.0203454
\(236\) 46.8094 3.04703
\(237\) −2.71459 −0.176332
\(238\) −19.7499 −1.28019
\(239\) −6.51574 −0.421468 −0.210734 0.977543i \(-0.567585\pi\)
−0.210734 + 0.977543i \(0.567585\pi\)
\(240\) 8.39133 0.541658
\(241\) −19.2571 −1.24046 −0.620228 0.784422i \(-0.712960\pi\)
−0.620228 + 0.784422i \(0.712960\pi\)
\(242\) 6.14150 0.394790
\(243\) 15.6659 1.00497
\(244\) 30.1141 1.92786
\(245\) 6.28420 0.401483
\(246\) −16.2396 −1.03540
\(247\) −18.1349 −1.15389
\(248\) −33.3497 −2.11771
\(249\) −27.8189 −1.76295
\(250\) −23.9943 −1.51754
\(251\) −9.02631 −0.569735 −0.284868 0.958567i \(-0.591950\pi\)
−0.284868 + 0.958567i \(0.591950\pi\)
\(252\) 7.88354 0.496616
\(253\) −12.2028 −0.767182
\(254\) 24.0118 1.50663
\(255\) 16.5173 1.03436
\(256\) −31.0021 −1.93763
\(257\) 14.7742 0.921592 0.460796 0.887506i \(-0.347564\pi\)
0.460796 + 0.887506i \(0.347564\pi\)
\(258\) −67.0337 −4.17334
\(259\) 3.07351 0.190978
\(260\) 13.8903 0.861442
\(261\) 5.26680 0.326007
\(262\) −5.30685 −0.327859
\(263\) 6.66917 0.411239 0.205619 0.978632i \(-0.434079\pi\)
0.205619 + 0.978632i \(0.434079\pi\)
\(264\) −29.0915 −1.79046
\(265\) −12.6572 −0.777526
\(266\) −16.9127 −1.03699
\(267\) −16.7023 −1.02217
\(268\) −7.41603 −0.453006
\(269\) −19.8172 −1.20827 −0.604137 0.796880i \(-0.706482\pi\)
−0.604137 + 0.796880i \(0.706482\pi\)
\(270\) 7.88507 0.479870
\(271\) 19.8253 1.20430 0.602151 0.798383i \(-0.294311\pi\)
0.602151 + 0.798383i \(0.294311\pi\)
\(272\) 23.0903 1.40005
\(273\) 8.18981 0.495670
\(274\) 49.1422 2.96879
\(275\) 10.8164 0.652255
\(276\) −35.3769 −2.12944
\(277\) 17.8817 1.07441 0.537203 0.843453i \(-0.319481\pi\)
0.537203 + 0.843453i \(0.319481\pi\)
\(278\) 36.1710 2.16939
\(279\) 12.0871 0.723637
\(280\) 6.31544 0.377420
\(281\) −3.24679 −0.193687 −0.0968437 0.995300i \(-0.530875\pi\)
−0.0968437 + 0.995300i \(0.530875\pi\)
\(282\) −1.44598 −0.0861068
\(283\) 18.3239 1.08924 0.544620 0.838683i \(-0.316674\pi\)
0.544620 + 0.838683i \(0.316674\pi\)
\(284\) −39.0162 −2.31519
\(285\) 14.1446 0.837852
\(286\) −22.2133 −1.31350
\(287\) −3.72753 −0.220029
\(288\) 1.54738 0.0911805
\(289\) 28.4505 1.67356
\(290\) 8.65442 0.508205
\(291\) −20.7386 −1.21572
\(292\) 12.0428 0.704752
\(293\) 31.9594 1.86709 0.933545 0.358460i \(-0.116698\pi\)
0.933545 + 0.358460i \(0.116698\pi\)
\(294\) −29.1347 −1.69917
\(295\) −13.5908 −0.791290
\(296\) −11.7822 −0.684825
\(297\) −8.33711 −0.483768
\(298\) 41.2541 2.38979
\(299\) −13.1691 −0.761591
\(300\) 31.3578 1.81044
\(301\) −15.3865 −0.886864
\(302\) 26.7448 1.53899
\(303\) −15.8449 −0.910265
\(304\) 19.7733 1.13408
\(305\) −8.74345 −0.500648
\(306\) −27.4401 −1.56865
\(307\) −16.9910 −0.969725 −0.484862 0.874590i \(-0.661130\pi\)
−0.484862 + 0.874590i \(0.661130\pi\)
\(308\) −13.6969 −0.780453
\(309\) 32.9903 1.87675
\(310\) 19.8616 1.12806
\(311\) 31.2893 1.77425 0.887126 0.461527i \(-0.152698\pi\)
0.887126 + 0.461527i \(0.152698\pi\)
\(312\) −31.3954 −1.77741
\(313\) 4.73998 0.267920 0.133960 0.990987i \(-0.457231\pi\)
0.133960 + 0.990987i \(0.457231\pi\)
\(314\) −22.3080 −1.25892
\(315\) −2.28894 −0.128967
\(316\) 4.89949 0.275618
\(317\) −1.57015 −0.0881884 −0.0440942 0.999027i \(-0.514040\pi\)
−0.0440942 + 0.999027i \(0.514040\pi\)
\(318\) 58.6811 3.29067
\(319\) −9.15057 −0.512333
\(320\) 10.3043 0.576030
\(321\) −26.5731 −1.48317
\(322\) −12.2816 −0.684429
\(323\) 38.9214 2.16565
\(324\) −43.7841 −2.43245
\(325\) 11.6730 0.647502
\(326\) −40.6017 −2.24872
\(327\) −17.6893 −0.978220
\(328\) 14.2894 0.788998
\(329\) −0.331901 −0.0182983
\(330\) 17.3256 0.953743
\(331\) 8.75076 0.480986 0.240493 0.970651i \(-0.422691\pi\)
0.240493 + 0.970651i \(0.422691\pi\)
\(332\) 50.2096 2.75561
\(333\) 4.27028 0.234010
\(334\) −20.5899 −1.12663
\(335\) 2.15320 0.117642
\(336\) −8.92973 −0.487157
\(337\) −28.8013 −1.56890 −0.784452 0.620189i \(-0.787056\pi\)
−0.784452 + 0.620189i \(0.787056\pi\)
\(338\) 7.61141 0.414006
\(339\) −25.4505 −1.38228
\(340\) −29.8117 −1.61677
\(341\) −21.0002 −1.13723
\(342\) −23.4983 −1.27064
\(343\) −15.1280 −0.816834
\(344\) 58.9837 3.18019
\(345\) 10.2715 0.552998
\(346\) −10.9610 −0.589266
\(347\) −3.55521 −0.190854 −0.0954270 0.995436i \(-0.530422\pi\)
−0.0954270 + 0.995436i \(0.530422\pi\)
\(348\) −26.5283 −1.42207
\(349\) 0.377854 0.0202261 0.0101130 0.999949i \(-0.496781\pi\)
0.0101130 + 0.999949i \(0.496781\pi\)
\(350\) 10.8863 0.581899
\(351\) −8.99734 −0.480243
\(352\) −2.68843 −0.143294
\(353\) −12.9341 −0.688412 −0.344206 0.938894i \(-0.611852\pi\)
−0.344206 + 0.938894i \(0.611852\pi\)
\(354\) 63.0097 3.34893
\(355\) 11.3281 0.601235
\(356\) 30.1456 1.59771
\(357\) −17.5771 −0.930281
\(358\) 57.6954 3.04930
\(359\) −4.71116 −0.248646 −0.124323 0.992242i \(-0.539676\pi\)
−0.124323 + 0.992242i \(0.539676\pi\)
\(360\) 8.77457 0.462461
\(361\) 14.3302 0.754223
\(362\) −19.0065 −0.998961
\(363\) 5.46586 0.286883
\(364\) −14.7816 −0.774765
\(365\) −3.49656 −0.183018
\(366\) 40.5362 2.11886
\(367\) 25.8897 1.35143 0.675715 0.737163i \(-0.263835\pi\)
0.675715 + 0.737163i \(0.263835\pi\)
\(368\) 14.3589 0.748511
\(369\) −5.17897 −0.269606
\(370\) 7.01693 0.364793
\(371\) 13.4693 0.699292
\(372\) −60.8814 −3.15655
\(373\) −1.31790 −0.0682383 −0.0341192 0.999418i \(-0.510863\pi\)
−0.0341192 + 0.999418i \(0.510863\pi\)
\(374\) 47.6746 2.46520
\(375\) −21.3547 −1.10275
\(376\) 1.27233 0.0656155
\(377\) −9.87522 −0.508600
\(378\) −8.39100 −0.431586
\(379\) 31.3631 1.61101 0.805506 0.592587i \(-0.201894\pi\)
0.805506 + 0.592587i \(0.201894\pi\)
\(380\) −25.5292 −1.30962
\(381\) 21.3702 1.09483
\(382\) 29.8402 1.52676
\(383\) −25.0157 −1.27824 −0.639122 0.769105i \(-0.720702\pi\)
−0.639122 + 0.769105i \(0.720702\pi\)
\(384\) −43.7786 −2.23407
\(385\) 3.97681 0.202677
\(386\) 32.6439 1.66153
\(387\) −21.3778 −1.08669
\(388\) 37.4306 1.90025
\(389\) −4.73108 −0.239875 −0.119938 0.992781i \(-0.538269\pi\)
−0.119938 + 0.992781i \(0.538269\pi\)
\(390\) 18.6976 0.946792
\(391\) 28.2639 1.42937
\(392\) 25.6360 1.29481
\(393\) −4.72304 −0.238246
\(394\) 31.7464 1.59936
\(395\) −1.42254 −0.0715757
\(396\) −19.0302 −0.956306
\(397\) −32.4447 −1.62835 −0.814177 0.580617i \(-0.802811\pi\)
−0.814177 + 0.580617i \(0.802811\pi\)
\(398\) 16.7972 0.841968
\(399\) −15.0521 −0.753549
\(400\) −12.7276 −0.636381
\(401\) −5.80611 −0.289943 −0.144972 0.989436i \(-0.546309\pi\)
−0.144972 + 0.989436i \(0.546309\pi\)
\(402\) −9.98264 −0.497889
\(403\) −22.6633 −1.12894
\(404\) 28.5980 1.42281
\(405\) 12.7125 0.631688
\(406\) −9.20971 −0.457070
\(407\) −7.41920 −0.367756
\(408\) 67.3814 3.33587
\(409\) −11.3016 −0.558828 −0.279414 0.960171i \(-0.590140\pi\)
−0.279414 + 0.960171i \(0.590140\pi\)
\(410\) −8.51010 −0.420284
\(411\) 43.7360 2.15734
\(412\) −59.5433 −2.93349
\(413\) 14.4629 0.711671
\(414\) −17.0639 −0.838646
\(415\) −14.5781 −0.715609
\(416\) −2.90133 −0.142250
\(417\) 32.1918 1.57644
\(418\) 40.8260 1.99686
\(419\) 12.7378 0.622283 0.311142 0.950364i \(-0.399289\pi\)
0.311142 + 0.950364i \(0.399289\pi\)
\(420\) 11.5291 0.562564
\(421\) −25.2598 −1.23109 −0.615543 0.788103i \(-0.711063\pi\)
−0.615543 + 0.788103i \(0.711063\pi\)
\(422\) −37.8245 −1.84127
\(423\) −0.461138 −0.0224213
\(424\) −51.6342 −2.50758
\(425\) −25.0528 −1.21524
\(426\) −52.5193 −2.54457
\(427\) 9.30444 0.450274
\(428\) 47.9611 2.31829
\(429\) −19.7696 −0.954483
\(430\) −35.1280 −1.69402
\(431\) 24.4161 1.17608 0.588041 0.808831i \(-0.299899\pi\)
0.588041 + 0.808831i \(0.299899\pi\)
\(432\) 9.81023 0.471995
\(433\) 28.2304 1.35667 0.678333 0.734754i \(-0.262703\pi\)
0.678333 + 0.734754i \(0.262703\pi\)
\(434\) −21.1359 −1.01456
\(435\) 7.70233 0.369299
\(436\) 31.9270 1.52902
\(437\) 24.2037 1.15782
\(438\) 16.2107 0.774578
\(439\) 30.6244 1.46162 0.730810 0.682580i \(-0.239142\pi\)
0.730810 + 0.682580i \(0.239142\pi\)
\(440\) −15.2450 −0.726776
\(441\) −9.29138 −0.442447
\(442\) 51.4500 2.44723
\(443\) 9.40752 0.446965 0.223482 0.974708i \(-0.428257\pi\)
0.223482 + 0.974708i \(0.428257\pi\)
\(444\) −21.5089 −1.02077
\(445\) −8.75260 −0.414913
\(446\) −19.2310 −0.910615
\(447\) 36.7157 1.73659
\(448\) −10.9655 −0.518071
\(449\) −26.1614 −1.23463 −0.617316 0.786715i \(-0.711780\pi\)
−0.617316 + 0.786715i \(0.711780\pi\)
\(450\) 15.1253 0.713014
\(451\) 8.99797 0.423698
\(452\) 45.9349 2.16060
\(453\) 23.8025 1.11834
\(454\) 58.6663 2.75335
\(455\) 4.29175 0.201200
\(456\) 57.7018 2.70213
\(457\) −37.9355 −1.77455 −0.887274 0.461244i \(-0.847403\pi\)
−0.887274 + 0.461244i \(0.847403\pi\)
\(458\) 53.2249 2.48703
\(459\) 19.3103 0.901327
\(460\) −18.5387 −0.864373
\(461\) 19.6902 0.917066 0.458533 0.888677i \(-0.348375\pi\)
0.458533 + 0.888677i \(0.348375\pi\)
\(462\) −18.4373 −0.857779
\(463\) 7.02564 0.326509 0.163255 0.986584i \(-0.447801\pi\)
0.163255 + 0.986584i \(0.447801\pi\)
\(464\) 10.7674 0.499865
\(465\) 17.6766 0.819731
\(466\) −55.9016 −2.58959
\(467\) 40.9087 1.89303 0.946514 0.322662i \(-0.104578\pi\)
0.946514 + 0.322662i \(0.104578\pi\)
\(468\) −20.5373 −0.949336
\(469\) −2.29135 −0.105805
\(470\) −0.757743 −0.0349521
\(471\) −19.8539 −0.914819
\(472\) −55.4429 −2.55197
\(473\) 37.1419 1.70778
\(474\) 6.59516 0.302926
\(475\) −21.4539 −0.984373
\(476\) 31.7245 1.45409
\(477\) 18.7140 0.856857
\(478\) 15.8301 0.724054
\(479\) −12.7318 −0.581729 −0.290865 0.956764i \(-0.593943\pi\)
−0.290865 + 0.956764i \(0.593943\pi\)
\(480\) 2.26294 0.103289
\(481\) −8.00674 −0.365076
\(482\) 46.7855 2.13102
\(483\) −10.9305 −0.497356
\(484\) −9.86519 −0.448418
\(485\) −10.8678 −0.493480
\(486\) −38.0607 −1.72647
\(487\) −16.1689 −0.732682 −0.366341 0.930481i \(-0.619390\pi\)
−0.366341 + 0.930481i \(0.619390\pi\)
\(488\) −35.6683 −1.61463
\(489\) −36.1350 −1.63408
\(490\) −15.2676 −0.689720
\(491\) 7.25375 0.327357 0.163679 0.986514i \(-0.447664\pi\)
0.163679 + 0.986514i \(0.447664\pi\)
\(492\) 26.0859 1.17604
\(493\) 21.1944 0.954548
\(494\) 44.0591 1.98231
\(495\) 5.52532 0.248345
\(496\) 24.7108 1.10955
\(497\) −12.0550 −0.540739
\(498\) 67.5866 3.02863
\(499\) −1.99545 −0.0893285 −0.0446642 0.999002i \(-0.514222\pi\)
−0.0446642 + 0.999002i \(0.514222\pi\)
\(500\) 38.5425 1.72367
\(501\) −18.3248 −0.818690
\(502\) 21.9296 0.978767
\(503\) −6.02386 −0.268590 −0.134295 0.990941i \(-0.542877\pi\)
−0.134295 + 0.990941i \(0.542877\pi\)
\(504\) −9.33757 −0.415928
\(505\) −8.30328 −0.369491
\(506\) 29.6469 1.31797
\(507\) 6.77407 0.300847
\(508\) −38.5705 −1.71129
\(509\) 5.84429 0.259044 0.129522 0.991577i \(-0.458656\pi\)
0.129522 + 0.991577i \(0.458656\pi\)
\(510\) −40.1293 −1.77695
\(511\) 3.72091 0.164603
\(512\) 34.8267 1.53914
\(513\) 16.5363 0.730095
\(514\) −35.8944 −1.58323
\(515\) 17.2880 0.761802
\(516\) 107.677 4.74023
\(517\) 0.801183 0.0352360
\(518\) −7.46715 −0.328088
\(519\) −9.75515 −0.428203
\(520\) −16.4523 −0.721479
\(521\) 29.9497 1.31212 0.656060 0.754708i \(-0.272222\pi\)
0.656060 + 0.754708i \(0.272222\pi\)
\(522\) −12.7958 −0.560058
\(523\) −24.5879 −1.07516 −0.537578 0.843214i \(-0.680661\pi\)
−0.537578 + 0.843214i \(0.680661\pi\)
\(524\) 8.52449 0.372394
\(525\) 9.68871 0.422850
\(526\) −16.2029 −0.706480
\(527\) 48.6403 2.11881
\(528\) 21.5557 0.938091
\(529\) −5.42383 −0.235819
\(530\) 30.7510 1.33574
\(531\) 20.0945 0.872026
\(532\) 27.1672 1.17785
\(533\) 9.71053 0.420610
\(534\) 40.5787 1.75601
\(535\) −13.9252 −0.602040
\(536\) 8.78383 0.379404
\(537\) 51.3482 2.21584
\(538\) 48.1463 2.07573
\(539\) 16.1429 0.695323
\(540\) −12.6659 −0.545055
\(541\) −25.6420 −1.10244 −0.551219 0.834361i \(-0.685837\pi\)
−0.551219 + 0.834361i \(0.685837\pi\)
\(542\) −48.1660 −2.06891
\(543\) −16.9156 −0.725917
\(544\) 6.22690 0.266976
\(545\) −9.26981 −0.397075
\(546\) −19.8973 −0.851527
\(547\) 0.383314 0.0163893 0.00819466 0.999966i \(-0.497392\pi\)
0.00819466 + 0.999966i \(0.497392\pi\)
\(548\) −78.9379 −3.37206
\(549\) 12.9274 0.551730
\(550\) −26.2788 −1.12053
\(551\) 18.1498 0.773205
\(552\) 41.9018 1.78346
\(553\) 1.51381 0.0643739
\(554\) −43.4440 −1.84576
\(555\) 6.24499 0.265085
\(556\) −58.1021 −2.46408
\(557\) 10.2543 0.434489 0.217244 0.976117i \(-0.430293\pi\)
0.217244 + 0.976117i \(0.430293\pi\)
\(558\) −29.3659 −1.24316
\(559\) 40.0832 1.69534
\(560\) −4.67949 −0.197745
\(561\) 42.4298 1.79139
\(562\) 7.88816 0.332742
\(563\) −7.14626 −0.301179 −0.150589 0.988596i \(-0.548117\pi\)
−0.150589 + 0.988596i \(0.548117\pi\)
\(564\) 2.32270 0.0978033
\(565\) −13.3369 −0.561089
\(566\) −44.5182 −1.87124
\(567\) −13.5281 −0.568128
\(568\) 46.2123 1.93903
\(569\) −38.5234 −1.61499 −0.807493 0.589878i \(-0.799176\pi\)
−0.807493 + 0.589878i \(0.799176\pi\)
\(570\) −34.3646 −1.43937
\(571\) 32.1528 1.34555 0.672776 0.739847i \(-0.265102\pi\)
0.672776 + 0.739847i \(0.265102\pi\)
\(572\) 35.6816 1.49192
\(573\) 26.5575 1.10945
\(574\) 9.05612 0.377995
\(575\) −15.5794 −0.649704
\(576\) −15.2353 −0.634803
\(577\) 18.6254 0.775384 0.387692 0.921789i \(-0.373272\pi\)
0.387692 + 0.921789i \(0.373272\pi\)
\(578\) −69.1212 −2.87506
\(579\) 29.0527 1.20739
\(580\) −13.9017 −0.577239
\(581\) 15.5134 0.643605
\(582\) 50.3850 2.08852
\(583\) −32.5139 −1.34659
\(584\) −14.2640 −0.590248
\(585\) 5.96288 0.246535
\(586\) −77.6462 −3.20754
\(587\) 11.7808 0.486245 0.243123 0.969996i \(-0.421828\pi\)
0.243123 + 0.969996i \(0.421828\pi\)
\(588\) 46.7996 1.92998
\(589\) 41.6530 1.71628
\(590\) 33.0193 1.35938
\(591\) 28.2539 1.16221
\(592\) 8.73013 0.358806
\(593\) 16.8458 0.691774 0.345887 0.938276i \(-0.387578\pi\)
0.345887 + 0.938276i \(0.387578\pi\)
\(594\) 20.2552 0.831081
\(595\) −9.21103 −0.377615
\(596\) −66.2672 −2.71441
\(597\) 14.9493 0.611835
\(598\) 31.9947 1.30836
\(599\) −27.8880 −1.13947 −0.569736 0.821828i \(-0.692955\pi\)
−0.569736 + 0.821828i \(0.692955\pi\)
\(600\) −37.1414 −1.51629
\(601\) −21.4935 −0.876739 −0.438369 0.898795i \(-0.644444\pi\)
−0.438369 + 0.898795i \(0.644444\pi\)
\(602\) 37.3819 1.52357
\(603\) −3.18357 −0.129645
\(604\) −42.9606 −1.74804
\(605\) 2.86430 0.116450
\(606\) 38.4955 1.56377
\(607\) 33.1472 1.34540 0.672702 0.739913i \(-0.265133\pi\)
0.672702 + 0.739913i \(0.265133\pi\)
\(608\) 5.33239 0.216257
\(609\) −8.19653 −0.332140
\(610\) 21.2424 0.860080
\(611\) 0.864630 0.0349792
\(612\) 44.0775 1.78173
\(613\) 37.0620 1.49692 0.748460 0.663180i \(-0.230794\pi\)
0.748460 + 0.663180i \(0.230794\pi\)
\(614\) 41.2799 1.66592
\(615\) −7.57388 −0.305408
\(616\) 16.2231 0.653649
\(617\) 9.54452 0.384248 0.192124 0.981371i \(-0.438462\pi\)
0.192124 + 0.981371i \(0.438462\pi\)
\(618\) −80.1506 −3.22413
\(619\) 5.13604 0.206435 0.103217 0.994659i \(-0.467086\pi\)
0.103217 + 0.994659i \(0.467086\pi\)
\(620\) −31.9040 −1.28129
\(621\) 12.0083 0.481876
\(622\) −76.0180 −3.04805
\(623\) 9.31418 0.373165
\(624\) 23.2627 0.931254
\(625\) 7.38991 0.295596
\(626\) −11.5159 −0.460268
\(627\) 36.3346 1.45107
\(628\) 35.8338 1.42992
\(629\) 17.1842 0.685180
\(630\) 5.56103 0.221557
\(631\) 21.0297 0.837179 0.418589 0.908176i \(-0.362525\pi\)
0.418589 + 0.908176i \(0.362525\pi\)
\(632\) −5.80315 −0.230837
\(633\) −33.6634 −1.33800
\(634\) 3.81471 0.151502
\(635\) 11.1987 0.444408
\(636\) −94.2605 −3.73767
\(637\) 17.4213 0.690256
\(638\) 22.2315 0.880154
\(639\) −16.7490 −0.662580
\(640\) −22.9415 −0.906842
\(641\) −18.5599 −0.733074 −0.366537 0.930404i \(-0.619457\pi\)
−0.366537 + 0.930404i \(0.619457\pi\)
\(642\) 64.5600 2.54798
\(643\) −11.9071 −0.469571 −0.234786 0.972047i \(-0.575439\pi\)
−0.234786 + 0.972047i \(0.575439\pi\)
\(644\) 19.7282 0.777400
\(645\) −31.2635 −1.23100
\(646\) −94.5605 −3.72043
\(647\) 29.3573 1.15416 0.577078 0.816689i \(-0.304193\pi\)
0.577078 + 0.816689i \(0.304193\pi\)
\(648\) 51.8596 2.03724
\(649\) −34.9122 −1.37043
\(650\) −28.3598 −1.11236
\(651\) −18.8107 −0.737251
\(652\) 65.2192 2.55418
\(653\) −2.30916 −0.0903645 −0.0451822 0.998979i \(-0.514387\pi\)
−0.0451822 + 0.998979i \(0.514387\pi\)
\(654\) 42.9765 1.68052
\(655\) −2.47504 −0.0967077
\(656\) −10.5879 −0.413386
\(657\) 5.16977 0.201692
\(658\) 0.806362 0.0314352
\(659\) −24.8218 −0.966922 −0.483461 0.875366i \(-0.660620\pi\)
−0.483461 + 0.875366i \(0.660620\pi\)
\(660\) −27.8304 −1.08330
\(661\) −5.06761 −0.197107 −0.0985536 0.995132i \(-0.531422\pi\)
−0.0985536 + 0.995132i \(0.531422\pi\)
\(662\) −21.2602 −0.826301
\(663\) 45.7899 1.77833
\(664\) −59.4702 −2.30789
\(665\) −7.88784 −0.305877
\(666\) −10.3747 −0.402013
\(667\) 13.1799 0.510330
\(668\) 33.0739 1.27967
\(669\) −17.1154 −0.661719
\(670\) −5.23125 −0.202101
\(671\) −22.4602 −0.867067
\(672\) −2.40814 −0.0928959
\(673\) −29.6257 −1.14199 −0.570994 0.820954i \(-0.693442\pi\)
−0.570994 + 0.820954i \(0.693442\pi\)
\(674\) 69.9733 2.69527
\(675\) −10.6440 −0.409689
\(676\) −12.2263 −0.470244
\(677\) 28.3482 1.08951 0.544755 0.838595i \(-0.316623\pi\)
0.544755 + 0.838595i \(0.316623\pi\)
\(678\) 61.8326 2.37466
\(679\) 11.5651 0.443826
\(680\) 35.3102 1.35408
\(681\) 52.2123 2.00078
\(682\) 51.0205 1.95368
\(683\) −5.83526 −0.223280 −0.111640 0.993749i \(-0.535610\pi\)
−0.111640 + 0.993749i \(0.535610\pi\)
\(684\) 37.7457 1.44324
\(685\) 22.9192 0.875697
\(686\) 36.7538 1.40326
\(687\) 47.3695 1.80726
\(688\) −43.7046 −1.66622
\(689\) −35.0887 −1.33677
\(690\) −24.9548 −0.950013
\(691\) −38.2946 −1.45680 −0.728398 0.685154i \(-0.759735\pi\)
−0.728398 + 0.685154i \(0.759735\pi\)
\(692\) 17.6068 0.669311
\(693\) −5.87984 −0.223357
\(694\) 8.63748 0.327874
\(695\) 16.8696 0.639901
\(696\) 31.4211 1.19101
\(697\) −20.8409 −0.789407
\(698\) −0.918006 −0.0347471
\(699\) −49.7517 −1.88178
\(700\) −17.4869 −0.660943
\(701\) 39.3678 1.48690 0.743451 0.668790i \(-0.233188\pi\)
0.743451 + 0.668790i \(0.233188\pi\)
\(702\) 21.8593 0.825024
\(703\) 14.7157 0.555012
\(704\) 26.4698 0.997619
\(705\) −0.674382 −0.0253987
\(706\) 31.4237 1.18265
\(707\) 8.83603 0.332313
\(708\) −101.214 −3.80384
\(709\) 16.9692 0.637291 0.318646 0.947874i \(-0.396772\pi\)
0.318646 + 0.947874i \(0.396772\pi\)
\(710\) −27.5220 −1.03288
\(711\) 2.10327 0.0788787
\(712\) −35.7056 −1.33812
\(713\) 30.2475 1.13278
\(714\) 42.7041 1.59816
\(715\) −10.3599 −0.387440
\(716\) −92.6771 −3.46350
\(717\) 14.0886 0.526150
\(718\) 11.4459 0.427156
\(719\) 13.4575 0.501880 0.250940 0.968003i \(-0.419260\pi\)
0.250940 + 0.968003i \(0.419260\pi\)
\(720\) −6.50161 −0.242301
\(721\) −18.3973 −0.685151
\(722\) −34.8156 −1.29570
\(723\) 41.6385 1.54855
\(724\) 30.5305 1.13466
\(725\) −11.6826 −0.433880
\(726\) −13.2794 −0.492846
\(727\) −20.7508 −0.769604 −0.384802 0.922999i \(-0.625730\pi\)
−0.384802 + 0.922999i \(0.625730\pi\)
\(728\) 17.5079 0.648885
\(729\) −0.215769 −0.00799144
\(730\) 8.49498 0.314413
\(731\) −86.0274 −3.18184
\(732\) −65.1140 −2.40668
\(733\) 16.8567 0.622616 0.311308 0.950309i \(-0.399233\pi\)
0.311308 + 0.950309i \(0.399233\pi\)
\(734\) −62.8995 −2.32166
\(735\) −13.5880 −0.501201
\(736\) 3.87226 0.142733
\(737\) 5.53115 0.203743
\(738\) 12.5824 0.463166
\(739\) 33.3778 1.22782 0.613912 0.789375i \(-0.289595\pi\)
0.613912 + 0.789375i \(0.289595\pi\)
\(740\) −11.2714 −0.414345
\(741\) 39.2121 1.44049
\(742\) −32.7240 −1.20134
\(743\) 46.2811 1.69789 0.848944 0.528483i \(-0.177239\pi\)
0.848944 + 0.528483i \(0.177239\pi\)
\(744\) 72.1103 2.64369
\(745\) 19.2403 0.704910
\(746\) 3.20187 0.117229
\(747\) 21.5541 0.788623
\(748\) −76.5805 −2.80006
\(749\) 14.8187 0.541464
\(750\) 51.8817 1.89445
\(751\) −42.1144 −1.53677 −0.768387 0.639985i \(-0.778941\pi\)
−0.768387 + 0.639985i \(0.778941\pi\)
\(752\) −0.942747 −0.0343785
\(753\) 19.5171 0.711243
\(754\) 23.9921 0.873740
\(755\) 12.4734 0.453952
\(756\) 13.4786 0.490212
\(757\) 24.2739 0.882250 0.441125 0.897446i \(-0.354579\pi\)
0.441125 + 0.897446i \(0.354579\pi\)
\(758\) −76.1973 −2.76761
\(759\) 26.3854 0.957730
\(760\) 30.2378 1.09684
\(761\) −37.9078 −1.37416 −0.687078 0.726583i \(-0.741107\pi\)
−0.687078 + 0.726583i \(0.741107\pi\)
\(762\) −51.9193 −1.88084
\(763\) 9.86458 0.357122
\(764\) −47.9329 −1.73415
\(765\) −12.7977 −0.462700
\(766\) 60.7763 2.19594
\(767\) −37.6770 −1.36044
\(768\) 67.0341 2.41889
\(769\) 50.0151 1.80359 0.901795 0.432164i \(-0.142250\pi\)
0.901795 + 0.432164i \(0.142250\pi\)
\(770\) −9.66176 −0.348186
\(771\) −31.9456 −1.15049
\(772\) −52.4365 −1.88723
\(773\) −12.1258 −0.436136 −0.218068 0.975934i \(-0.569976\pi\)
−0.218068 + 0.975934i \(0.569976\pi\)
\(774\) 51.9378 1.86687
\(775\) −26.8111 −0.963083
\(776\) −44.3343 −1.59151
\(777\) −6.64568 −0.238412
\(778\) 11.4943 0.412090
\(779\) −17.8471 −0.639438
\(780\) −30.0343 −1.07540
\(781\) 29.0998 1.04127
\(782\) −68.6677 −2.45555
\(783\) 9.00473 0.321803
\(784\) −18.9952 −0.678401
\(785\) −10.4041 −0.371339
\(786\) 11.4747 0.409290
\(787\) 41.5952 1.48271 0.741354 0.671114i \(-0.234184\pi\)
0.741354 + 0.671114i \(0.234184\pi\)
\(788\) −50.9947 −1.81661
\(789\) −14.4204 −0.513380
\(790\) 3.45609 0.122962
\(791\) 14.1927 0.504633
\(792\) 22.5402 0.800930
\(793\) −24.2389 −0.860747
\(794\) 78.8252 2.79740
\(795\) 27.3680 0.970643
\(796\) −26.9816 −0.956339
\(797\) 30.0828 1.06559 0.532795 0.846245i \(-0.321142\pi\)
0.532795 + 0.846245i \(0.321142\pi\)
\(798\) 36.5695 1.29455
\(799\) −1.85569 −0.0656495
\(800\) −3.43234 −0.121351
\(801\) 12.9410 0.457247
\(802\) 14.1061 0.498103
\(803\) −8.98198 −0.316967
\(804\) 16.0353 0.565521
\(805\) −5.72797 −0.201885
\(806\) 55.0609 1.93944
\(807\) 42.8496 1.50838
\(808\) −33.8726 −1.19164
\(809\) 5.10173 0.179367 0.0896836 0.995970i \(-0.471414\pi\)
0.0896836 + 0.995970i \(0.471414\pi\)
\(810\) −30.8852 −1.08520
\(811\) 48.5151 1.70360 0.851798 0.523870i \(-0.175512\pi\)
0.851798 + 0.523870i \(0.175512\pi\)
\(812\) 14.7937 0.519157
\(813\) −42.8672 −1.50342
\(814\) 18.0251 0.631780
\(815\) −18.9360 −0.663299
\(816\) −49.9269 −1.74779
\(817\) −73.6692 −2.57736
\(818\) 27.4575 0.960029
\(819\) −6.34547 −0.221729
\(820\) 13.6699 0.477374
\(821\) 29.7966 1.03991 0.519954 0.854194i \(-0.325949\pi\)
0.519954 + 0.854194i \(0.325949\pi\)
\(822\) −106.258 −3.70616
\(823\) 54.2447 1.89085 0.945425 0.325840i \(-0.105647\pi\)
0.945425 + 0.325840i \(0.105647\pi\)
\(824\) 70.5254 2.45687
\(825\) −23.3878 −0.814259
\(826\) −35.1379 −1.22260
\(827\) −23.0355 −0.801024 −0.400512 0.916292i \(-0.631168\pi\)
−0.400512 + 0.916292i \(0.631168\pi\)
\(828\) 27.4101 0.952565
\(829\) −23.6140 −0.820149 −0.410074 0.912052i \(-0.634497\pi\)
−0.410074 + 0.912052i \(0.634497\pi\)
\(830\) 35.4177 1.22937
\(831\) −38.6646 −1.34126
\(832\) 28.5660 0.990349
\(833\) −37.3899 −1.29548
\(834\) −78.2107 −2.70822
\(835\) −9.60282 −0.332319
\(836\) −65.5795 −2.26811
\(837\) 20.6655 0.714305
\(838\) −30.9468 −1.06904
\(839\) 31.4672 1.08637 0.543184 0.839614i \(-0.317219\pi\)
0.543184 + 0.839614i \(0.317219\pi\)
\(840\) −13.6555 −0.471161
\(841\) −19.1167 −0.659196
\(842\) 61.3692 2.11492
\(843\) 7.02037 0.241794
\(844\) 60.7581 2.09138
\(845\) 3.54985 0.122118
\(846\) 1.12035 0.0385183
\(847\) −3.04808 −0.104733
\(848\) 38.2589 1.31382
\(849\) −39.6207 −1.35978
\(850\) 60.8665 2.08770
\(851\) 10.6862 0.366318
\(852\) 84.3627 2.89022
\(853\) 38.0626 1.30324 0.651619 0.758546i \(-0.274090\pi\)
0.651619 + 0.758546i \(0.274090\pi\)
\(854\) −22.6054 −0.773540
\(855\) −10.9592 −0.374798
\(856\) −56.8070 −1.94162
\(857\) −56.3698 −1.92555 −0.962777 0.270296i \(-0.912879\pi\)
−0.962777 + 0.270296i \(0.912879\pi\)
\(858\) 48.0306 1.63974
\(859\) 50.7563 1.73178 0.865892 0.500232i \(-0.166752\pi\)
0.865892 + 0.500232i \(0.166752\pi\)
\(860\) 56.4267 1.92414
\(861\) 8.05984 0.274679
\(862\) −59.3195 −2.02043
\(863\) −5.43595 −0.185042 −0.0925210 0.995711i \(-0.529493\pi\)
−0.0925210 + 0.995711i \(0.529493\pi\)
\(864\) 2.64558 0.0900046
\(865\) −5.11204 −0.173814
\(866\) −68.5864 −2.33066
\(867\) −61.5171 −2.08923
\(868\) 33.9510 1.15237
\(869\) −3.65423 −0.123961
\(870\) −18.7130 −0.634430
\(871\) 5.96917 0.202258
\(872\) −37.8155 −1.28060
\(873\) 16.0683 0.543830
\(874\) −58.8034 −1.98905
\(875\) 11.9086 0.402584
\(876\) −26.0395 −0.879794
\(877\) −35.5748 −1.20128 −0.600639 0.799521i \(-0.705087\pi\)
−0.600639 + 0.799521i \(0.705087\pi\)
\(878\) −74.4026 −2.51097
\(879\) −69.1042 −2.33083
\(880\) 11.2959 0.380786
\(881\) −14.3705 −0.484155 −0.242077 0.970257i \(-0.577829\pi\)
−0.242077 + 0.970257i \(0.577829\pi\)
\(882\) 22.5736 0.760093
\(883\) 55.2397 1.85896 0.929482 0.368869i \(-0.120255\pi\)
0.929482 + 0.368869i \(0.120255\pi\)
\(884\) −82.6451 −2.77965
\(885\) 29.3868 0.987826
\(886\) −22.8558 −0.767855
\(887\) −2.67705 −0.0898865 −0.0449432 0.998990i \(-0.514311\pi\)
−0.0449432 + 0.998990i \(0.514311\pi\)
\(888\) 25.4760 0.854918
\(889\) −11.9173 −0.399692
\(890\) 21.2646 0.712792
\(891\) 32.6558 1.09401
\(892\) 30.8911 1.03431
\(893\) −1.58911 −0.0531776
\(894\) −89.2016 −2.98335
\(895\) 26.9083 0.899444
\(896\) 24.4135 0.815597
\(897\) 28.4749 0.950750
\(898\) 63.5597 2.12101
\(899\) 22.6819 0.756482
\(900\) −24.2960 −0.809868
\(901\) 75.3081 2.50888
\(902\) −21.8608 −0.727884
\(903\) 33.2695 1.10714
\(904\) −54.4071 −1.80955
\(905\) −8.86435 −0.294661
\(906\) −57.8288 −1.92123
\(907\) 26.0065 0.863531 0.431765 0.901986i \(-0.357891\pi\)
0.431765 + 0.901986i \(0.357891\pi\)
\(908\) −94.2367 −3.12735
\(909\) 12.2766 0.407190
\(910\) −10.4269 −0.345648
\(911\) 2.07456 0.0687333 0.0343666 0.999409i \(-0.489059\pi\)
0.0343666 + 0.999409i \(0.489059\pi\)
\(912\) −42.7548 −1.41575
\(913\) −37.4482 −1.23935
\(914\) 92.1651 3.04855
\(915\) 18.9055 0.624996
\(916\) −85.4960 −2.82487
\(917\) 2.63384 0.0869771
\(918\) −46.9148 −1.54842
\(919\) −52.2370 −1.72314 −0.861570 0.507638i \(-0.830519\pi\)
−0.861570 + 0.507638i \(0.830519\pi\)
\(920\) 21.9580 0.723934
\(921\) 36.7386 1.21058
\(922\) −47.8379 −1.57546
\(923\) 31.4042 1.03368
\(924\) 29.6161 0.974297
\(925\) −9.47214 −0.311442
\(926\) −17.0690 −0.560921
\(927\) −25.5609 −0.839530
\(928\) 2.90372 0.0953192
\(929\) 10.1992 0.334625 0.167312 0.985904i \(-0.446491\pi\)
0.167312 + 0.985904i \(0.446491\pi\)
\(930\) −42.9456 −1.40824
\(931\) −32.0187 −1.04937
\(932\) 89.7957 2.94135
\(933\) −67.6551 −2.21493
\(934\) −99.3886 −3.25210
\(935\) 22.2347 0.727153
\(936\) 24.3252 0.795093
\(937\) −30.2886 −0.989484 −0.494742 0.869040i \(-0.664737\pi\)
−0.494742 + 0.869040i \(0.664737\pi\)
\(938\) 5.56690 0.181766
\(939\) −10.2490 −0.334464
\(940\) 1.21718 0.0396999
\(941\) −39.0125 −1.27177 −0.635885 0.771784i \(-0.719365\pi\)
−0.635885 + 0.771784i \(0.719365\pi\)
\(942\) 48.2355 1.57160
\(943\) −12.9602 −0.422041
\(944\) 41.0810 1.33707
\(945\) −3.91343 −0.127304
\(946\) −90.2370 −2.93386
\(947\) 57.0512 1.85392 0.926958 0.375166i \(-0.122414\pi\)
0.926958 + 0.375166i \(0.122414\pi\)
\(948\) −10.5939 −0.344074
\(949\) −9.69328 −0.314657
\(950\) 52.1228 1.69109
\(951\) 3.39505 0.110092
\(952\) −37.5758 −1.21784
\(953\) −10.9520 −0.354770 −0.177385 0.984142i \(-0.556764\pi\)
−0.177385 + 0.984142i \(0.556764\pi\)
\(954\) −45.4662 −1.47202
\(955\) 13.9170 0.450345
\(956\) −25.4282 −0.822408
\(957\) 19.7858 0.639584
\(958\) 30.9321 0.999371
\(959\) −24.3897 −0.787585
\(960\) −22.2805 −0.719101
\(961\) 21.0540 0.679162
\(962\) 19.4526 0.627176
\(963\) 20.5889 0.663467
\(964\) −75.1523 −2.42049
\(965\) 15.2246 0.490098
\(966\) 26.5559 0.854424
\(967\) 40.9674 1.31742 0.658711 0.752396i \(-0.271102\pi\)
0.658711 + 0.752396i \(0.271102\pi\)
\(968\) 11.6847 0.375561
\(969\) −84.1577 −2.70354
\(970\) 26.4035 0.847765
\(971\) −0.341254 −0.0109514 −0.00547568 0.999985i \(-0.501743\pi\)
−0.00547568 + 0.999985i \(0.501743\pi\)
\(972\) 61.1375 1.96099
\(973\) −17.9520 −0.575515
\(974\) 39.2827 1.25870
\(975\) −25.2399 −0.808324
\(976\) 26.4288 0.845965
\(977\) −7.30258 −0.233630 −0.116815 0.993154i \(-0.537268\pi\)
−0.116815 + 0.993154i \(0.537268\pi\)
\(978\) 87.7909 2.80724
\(979\) −22.4837 −0.718582
\(980\) 24.5246 0.783410
\(981\) 13.7057 0.437589
\(982\) −17.6231 −0.562377
\(983\) 38.1253 1.21601 0.608004 0.793934i \(-0.291970\pi\)
0.608004 + 0.793934i \(0.291970\pi\)
\(984\) −30.8971 −0.984965
\(985\) 14.8060 0.471759
\(986\) −51.4923 −1.63985
\(987\) 0.717652 0.0228431
\(988\) −70.7728 −2.25158
\(989\) −53.4970 −1.70110
\(990\) −13.4239 −0.426639
\(991\) 36.2273 1.15080 0.575400 0.817872i \(-0.304846\pi\)
0.575400 + 0.817872i \(0.304846\pi\)
\(992\) 6.66392 0.211580
\(993\) −18.9213 −0.600450
\(994\) 29.2878 0.928954
\(995\) 7.83396 0.248353
\(996\) −108.566 −3.44003
\(997\) 48.9334 1.54974 0.774868 0.632124i \(-0.217817\pi\)
0.774868 + 0.632124i \(0.217817\pi\)
\(998\) 4.84799 0.153460
\(999\) 7.30096 0.230992
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.1.18 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.18 259 1.1 even 1 trivial