Properties

Label 4003.2.a.c.1.18
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.34196 q^{2} -1.89472 q^{3} +3.48479 q^{4} -4.06412 q^{5} +4.43736 q^{6} +3.16270 q^{7} -3.47733 q^{8} +0.589962 q^{9} +O(q^{10})\) \(q-2.34196 q^{2} -1.89472 q^{3} +3.48479 q^{4} -4.06412 q^{5} +4.43736 q^{6} +3.16270 q^{7} -3.47733 q^{8} +0.589962 q^{9} +9.51803 q^{10} +5.59916 q^{11} -6.60270 q^{12} -4.59164 q^{13} -7.40692 q^{14} +7.70037 q^{15} +1.17419 q^{16} +4.80028 q^{17} -1.38167 q^{18} -5.33357 q^{19} -14.1626 q^{20} -5.99242 q^{21} -13.1130 q^{22} -4.15524 q^{23} +6.58856 q^{24} +11.5171 q^{25} +10.7535 q^{26} +4.56635 q^{27} +11.0213 q^{28} +9.77771 q^{29} -18.0340 q^{30} -0.132664 q^{31} +4.20474 q^{32} -10.6088 q^{33} -11.2421 q^{34} -12.8536 q^{35} +2.05589 q^{36} +1.55645 q^{37} +12.4910 q^{38} +8.69987 q^{39} +14.1323 q^{40} -3.68566 q^{41} +14.0340 q^{42} +9.30922 q^{43} +19.5119 q^{44} -2.39768 q^{45} +9.73143 q^{46} +7.95349 q^{47} -2.22477 q^{48} +3.00264 q^{49} -26.9726 q^{50} -9.09519 q^{51} -16.0009 q^{52} +10.7581 q^{53} -10.6942 q^{54} -22.7557 q^{55} -10.9977 q^{56} +10.1056 q^{57} -22.8990 q^{58} +12.0183 q^{59} +26.8342 q^{60} +2.39663 q^{61} +0.310695 q^{62} +1.86587 q^{63} -12.1957 q^{64} +18.6610 q^{65} +24.8455 q^{66} -2.16009 q^{67} +16.7280 q^{68} +7.87302 q^{69} +30.1026 q^{70} -2.27280 q^{71} -2.05149 q^{72} -13.9412 q^{73} -3.64515 q^{74} -21.8217 q^{75} -18.5864 q^{76} +17.7084 q^{77} -20.3748 q^{78} -17.2667 q^{79} -4.77207 q^{80} -10.4218 q^{81} +8.63168 q^{82} +7.58184 q^{83} -20.8823 q^{84} -19.5089 q^{85} -21.8019 q^{86} -18.5260 q^{87} -19.4701 q^{88} -6.84345 q^{89} +5.61527 q^{90} -14.5220 q^{91} -14.4802 q^{92} +0.251362 q^{93} -18.6268 q^{94} +21.6763 q^{95} -7.96680 q^{96} -15.7665 q^{97} -7.03208 q^{98} +3.30329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34196 −1.65602 −0.828009 0.560715i \(-0.810526\pi\)
−0.828009 + 0.560715i \(0.810526\pi\)
\(3\) −1.89472 −1.09392 −0.546958 0.837160i \(-0.684214\pi\)
−0.546958 + 0.837160i \(0.684214\pi\)
\(4\) 3.48479 1.74240
\(5\) −4.06412 −1.81753 −0.908765 0.417307i \(-0.862974\pi\)
−0.908765 + 0.417307i \(0.862974\pi\)
\(6\) 4.43736 1.81155
\(7\) 3.16270 1.19539 0.597693 0.801725i \(-0.296084\pi\)
0.597693 + 0.801725i \(0.296084\pi\)
\(8\) −3.47733 −1.22942
\(9\) 0.589962 0.196654
\(10\) 9.51803 3.00986
\(11\) 5.59916 1.68821 0.844105 0.536178i \(-0.180132\pi\)
0.844105 + 0.536178i \(0.180132\pi\)
\(12\) −6.60270 −1.90604
\(13\) −4.59164 −1.27349 −0.636746 0.771074i \(-0.719720\pi\)
−0.636746 + 0.771074i \(0.719720\pi\)
\(14\) −7.40692 −1.97958
\(15\) 7.70037 1.98823
\(16\) 1.17419 0.293548
\(17\) 4.80028 1.16424 0.582120 0.813103i \(-0.302224\pi\)
0.582120 + 0.813103i \(0.302224\pi\)
\(18\) −1.38167 −0.325662
\(19\) −5.33357 −1.22361 −0.611803 0.791010i \(-0.709555\pi\)
−0.611803 + 0.791010i \(0.709555\pi\)
\(20\) −14.1626 −3.16686
\(21\) −5.99242 −1.30765
\(22\) −13.1130 −2.79571
\(23\) −4.15524 −0.866428 −0.433214 0.901291i \(-0.642621\pi\)
−0.433214 + 0.901291i \(0.642621\pi\)
\(24\) 6.58856 1.34488
\(25\) 11.5171 2.30342
\(26\) 10.7535 2.10893
\(27\) 4.56635 0.878794
\(28\) 11.0213 2.08284
\(29\) 9.77771 1.81567 0.907837 0.419323i \(-0.137732\pi\)
0.907837 + 0.419323i \(0.137732\pi\)
\(30\) −18.0340 −3.29254
\(31\) −0.132664 −0.0238272 −0.0119136 0.999929i \(-0.503792\pi\)
−0.0119136 + 0.999929i \(0.503792\pi\)
\(32\) 4.20474 0.743300
\(33\) −10.6088 −1.84676
\(34\) −11.2421 −1.92800
\(35\) −12.8536 −2.17265
\(36\) 2.05589 0.342649
\(37\) 1.55645 0.255879 0.127939 0.991782i \(-0.459164\pi\)
0.127939 + 0.991782i \(0.459164\pi\)
\(38\) 12.4910 2.02631
\(39\) 8.69987 1.39309
\(40\) 14.1323 2.23451
\(41\) −3.68566 −0.575603 −0.287802 0.957690i \(-0.592924\pi\)
−0.287802 + 0.957690i \(0.592924\pi\)
\(42\) 14.0340 2.16550
\(43\) 9.30922 1.41964 0.709821 0.704382i \(-0.248776\pi\)
0.709821 + 0.704382i \(0.248776\pi\)
\(44\) 19.5119 2.94153
\(45\) −2.39768 −0.357425
\(46\) 9.73143 1.43482
\(47\) 7.95349 1.16014 0.580068 0.814568i \(-0.303026\pi\)
0.580068 + 0.814568i \(0.303026\pi\)
\(48\) −2.22477 −0.321117
\(49\) 3.00264 0.428949
\(50\) −26.9726 −3.81450
\(51\) −9.09519 −1.27358
\(52\) −16.0009 −2.21893
\(53\) 10.7581 1.47774 0.738868 0.673850i \(-0.235360\pi\)
0.738868 + 0.673850i \(0.235360\pi\)
\(54\) −10.6942 −1.45530
\(55\) −22.7557 −3.06837
\(56\) −10.9977 −1.46963
\(57\) 10.1056 1.33852
\(58\) −22.8990 −3.00679
\(59\) 12.0183 1.56464 0.782322 0.622874i \(-0.214035\pi\)
0.782322 + 0.622874i \(0.214035\pi\)
\(60\) 26.8342 3.46428
\(61\) 2.39663 0.306857 0.153428 0.988160i \(-0.450969\pi\)
0.153428 + 0.988160i \(0.450969\pi\)
\(62\) 0.310695 0.0394583
\(63\) 1.86587 0.235077
\(64\) −12.1957 −1.52447
\(65\) 18.6610 2.31461
\(66\) 24.8455 3.05827
\(67\) −2.16009 −0.263897 −0.131948 0.991257i \(-0.542123\pi\)
−0.131948 + 0.991257i \(0.542123\pi\)
\(68\) 16.7280 2.02857
\(69\) 7.87302 0.947800
\(70\) 30.1026 3.59795
\(71\) −2.27280 −0.269732 −0.134866 0.990864i \(-0.543060\pi\)
−0.134866 + 0.990864i \(0.543060\pi\)
\(72\) −2.05149 −0.241771
\(73\) −13.9412 −1.63169 −0.815847 0.578267i \(-0.803729\pi\)
−0.815847 + 0.578267i \(0.803729\pi\)
\(74\) −3.64515 −0.423740
\(75\) −21.8217 −2.51975
\(76\) −18.5864 −2.13201
\(77\) 17.7084 2.01806
\(78\) −20.3748 −2.30699
\(79\) −17.2667 −1.94266 −0.971328 0.237744i \(-0.923592\pi\)
−0.971328 + 0.237744i \(0.923592\pi\)
\(80\) −4.77207 −0.533533
\(81\) −10.4218 −1.15798
\(82\) 8.63168 0.953209
\(83\) 7.58184 0.832215 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(84\) −20.8823 −2.27845
\(85\) −19.5089 −2.11604
\(86\) −21.8019 −2.35095
\(87\) −18.5260 −1.98620
\(88\) −19.4701 −2.07552
\(89\) −6.84345 −0.725404 −0.362702 0.931905i \(-0.618146\pi\)
−0.362702 + 0.931905i \(0.618146\pi\)
\(90\) 5.61527 0.591901
\(91\) −14.5220 −1.52232
\(92\) −14.4802 −1.50966
\(93\) 0.251362 0.0260650
\(94\) −18.6268 −1.92120
\(95\) 21.6763 2.22394
\(96\) −7.96680 −0.813109
\(97\) −15.7665 −1.60084 −0.800420 0.599439i \(-0.795390\pi\)
−0.800420 + 0.599439i \(0.795390\pi\)
\(98\) −7.03208 −0.710348
\(99\) 3.30329 0.331993
\(100\) 40.1347 4.01347
\(101\) −15.8106 −1.57321 −0.786605 0.617457i \(-0.788163\pi\)
−0.786605 + 0.617457i \(0.788163\pi\)
\(102\) 21.3006 2.10907
\(103\) 14.1609 1.39532 0.697659 0.716430i \(-0.254225\pi\)
0.697659 + 0.716430i \(0.254225\pi\)
\(104\) 15.9666 1.56566
\(105\) 24.3539 2.37670
\(106\) −25.1950 −2.44716
\(107\) −2.67185 −0.258297 −0.129149 0.991625i \(-0.541224\pi\)
−0.129149 + 0.991625i \(0.541224\pi\)
\(108\) 15.9128 1.53121
\(109\) −4.31831 −0.413619 −0.206809 0.978381i \(-0.566308\pi\)
−0.206809 + 0.978381i \(0.566308\pi\)
\(110\) 53.2930 5.08128
\(111\) −2.94903 −0.279910
\(112\) 3.71362 0.350904
\(113\) −4.99336 −0.469736 −0.234868 0.972027i \(-0.575466\pi\)
−0.234868 + 0.972027i \(0.575466\pi\)
\(114\) −23.6670 −2.21662
\(115\) 16.8874 1.57476
\(116\) 34.0733 3.16362
\(117\) −2.70889 −0.250437
\(118\) −28.1463 −2.59108
\(119\) 15.1818 1.39172
\(120\) −26.7767 −2.44437
\(121\) 20.3506 1.85005
\(122\) −5.61281 −0.508160
\(123\) 6.98329 0.629662
\(124\) −0.462308 −0.0415165
\(125\) −26.4863 −2.36900
\(126\) −4.36980 −0.389292
\(127\) 12.0313 1.06760 0.533801 0.845610i \(-0.320763\pi\)
0.533801 + 0.845610i \(0.320763\pi\)
\(128\) 20.1525 1.78124
\(129\) −17.6384 −1.55297
\(130\) −43.7034 −3.83304
\(131\) −8.20236 −0.716643 −0.358322 0.933598i \(-0.616651\pi\)
−0.358322 + 0.933598i \(0.616651\pi\)
\(132\) −36.9696 −3.21779
\(133\) −16.8685 −1.46268
\(134\) 5.05885 0.437018
\(135\) −18.5582 −1.59723
\(136\) −16.6922 −1.43134
\(137\) −5.94864 −0.508226 −0.254113 0.967174i \(-0.581784\pi\)
−0.254113 + 0.967174i \(0.581784\pi\)
\(138\) −18.4383 −1.56957
\(139\) −2.87726 −0.244046 −0.122023 0.992527i \(-0.538938\pi\)
−0.122023 + 0.992527i \(0.538938\pi\)
\(140\) −44.7921 −3.78562
\(141\) −15.0696 −1.26909
\(142\) 5.32281 0.446680
\(143\) −25.7093 −2.14992
\(144\) 0.692729 0.0577274
\(145\) −39.7378 −3.30004
\(146\) 32.6498 2.70212
\(147\) −5.68917 −0.469235
\(148\) 5.42390 0.445842
\(149\) 1.16436 0.0953878 0.0476939 0.998862i \(-0.484813\pi\)
0.0476939 + 0.998862i \(0.484813\pi\)
\(150\) 51.1055 4.17275
\(151\) 7.96515 0.648194 0.324097 0.946024i \(-0.394940\pi\)
0.324097 + 0.946024i \(0.394940\pi\)
\(152\) 18.5466 1.50433
\(153\) 2.83198 0.228952
\(154\) −41.4725 −3.34195
\(155\) 0.539165 0.0433067
\(156\) 30.3172 2.42732
\(157\) 15.0675 1.20251 0.601257 0.799056i \(-0.294667\pi\)
0.601257 + 0.799056i \(0.294667\pi\)
\(158\) 40.4380 3.21707
\(159\) −20.3836 −1.61652
\(160\) −17.0886 −1.35097
\(161\) −13.1418 −1.03572
\(162\) 24.4075 1.91764
\(163\) 12.5273 0.981214 0.490607 0.871381i \(-0.336775\pi\)
0.490607 + 0.871381i \(0.336775\pi\)
\(164\) −12.8438 −1.00293
\(165\) 43.1156 3.35655
\(166\) −17.7564 −1.37816
\(167\) −16.0652 −1.24316 −0.621580 0.783350i \(-0.713509\pi\)
−0.621580 + 0.783350i \(0.713509\pi\)
\(168\) 20.8376 1.60766
\(169\) 8.08317 0.621782
\(170\) 45.6892 3.50420
\(171\) −3.14660 −0.240627
\(172\) 32.4407 2.47358
\(173\) 1.17632 0.0894338 0.0447169 0.999000i \(-0.485761\pi\)
0.0447169 + 0.999000i \(0.485761\pi\)
\(174\) 43.3872 3.28918
\(175\) 36.4251 2.75348
\(176\) 6.57450 0.495571
\(177\) −22.7712 −1.71159
\(178\) 16.0271 1.20128
\(179\) 16.1286 1.20551 0.602753 0.797928i \(-0.294071\pi\)
0.602753 + 0.797928i \(0.294071\pi\)
\(180\) −8.35540 −0.622775
\(181\) −9.88410 −0.734680 −0.367340 0.930087i \(-0.619731\pi\)
−0.367340 + 0.930087i \(0.619731\pi\)
\(182\) 34.0099 2.52098
\(183\) −4.54094 −0.335676
\(184\) 14.4491 1.06521
\(185\) −6.32560 −0.465067
\(186\) −0.588680 −0.0431641
\(187\) 26.8775 1.96548
\(188\) 27.7162 2.02142
\(189\) 14.4420 1.05050
\(190\) −50.7651 −3.68289
\(191\) 8.08293 0.584860 0.292430 0.956287i \(-0.405536\pi\)
0.292430 + 0.956287i \(0.405536\pi\)
\(192\) 23.1075 1.66764
\(193\) 13.1816 0.948836 0.474418 0.880300i \(-0.342659\pi\)
0.474418 + 0.880300i \(0.342659\pi\)
\(194\) 36.9245 2.65102
\(195\) −35.3573 −2.53199
\(196\) 10.4636 0.747399
\(197\) 7.21903 0.514334 0.257167 0.966367i \(-0.417211\pi\)
0.257167 + 0.966367i \(0.417211\pi\)
\(198\) −7.73618 −0.549787
\(199\) 3.24740 0.230202 0.115101 0.993354i \(-0.463281\pi\)
0.115101 + 0.993354i \(0.463281\pi\)
\(200\) −40.0487 −2.83187
\(201\) 4.09276 0.288681
\(202\) 37.0277 2.60526
\(203\) 30.9239 2.17043
\(204\) −31.6948 −2.21908
\(205\) 14.9790 1.04618
\(206\) −33.1644 −2.31067
\(207\) −2.45143 −0.170386
\(208\) −5.39147 −0.373832
\(209\) −29.8635 −2.06570
\(210\) −57.0360 −3.93586
\(211\) −5.03731 −0.346783 −0.173391 0.984853i \(-0.555473\pi\)
−0.173391 + 0.984853i \(0.555473\pi\)
\(212\) 37.4897 2.57480
\(213\) 4.30632 0.295064
\(214\) 6.25737 0.427745
\(215\) −37.8338 −2.58024
\(216\) −15.8787 −1.08041
\(217\) −0.419577 −0.0284828
\(218\) 10.1133 0.684960
\(219\) 26.4147 1.78494
\(220\) −79.2988 −5.34632
\(221\) −22.0412 −1.48265
\(222\) 6.90653 0.463536
\(223\) 15.0556 1.00819 0.504097 0.863647i \(-0.331825\pi\)
0.504097 + 0.863647i \(0.331825\pi\)
\(224\) 13.2983 0.888531
\(225\) 6.79464 0.452976
\(226\) 11.6943 0.777892
\(227\) −2.00794 −0.133272 −0.0666359 0.997777i \(-0.521227\pi\)
−0.0666359 + 0.997777i \(0.521227\pi\)
\(228\) 35.2160 2.33224
\(229\) −7.06117 −0.466615 −0.233308 0.972403i \(-0.574955\pi\)
−0.233308 + 0.972403i \(0.574955\pi\)
\(230\) −39.5497 −2.60783
\(231\) −33.5525 −2.20759
\(232\) −34.0003 −2.23223
\(233\) −21.3694 −1.39995 −0.699977 0.714165i \(-0.746806\pi\)
−0.699977 + 0.714165i \(0.746806\pi\)
\(234\) 6.34413 0.414729
\(235\) −32.3239 −2.10858
\(236\) 41.8812 2.72623
\(237\) 32.7156 2.12510
\(238\) −35.5553 −2.30471
\(239\) 5.28312 0.341737 0.170868 0.985294i \(-0.445343\pi\)
0.170868 + 0.985294i \(0.445343\pi\)
\(240\) 9.04173 0.583641
\(241\) −18.2101 −1.17302 −0.586509 0.809943i \(-0.699498\pi\)
−0.586509 + 0.809943i \(0.699498\pi\)
\(242\) −47.6603 −3.06372
\(243\) 6.04740 0.387941
\(244\) 8.35175 0.534666
\(245\) −12.2031 −0.779628
\(246\) −16.3546 −1.04273
\(247\) 24.4899 1.55825
\(248\) 0.461318 0.0292937
\(249\) −14.3655 −0.910374
\(250\) 62.0299 3.92311
\(251\) 19.9923 1.26190 0.630951 0.775823i \(-0.282665\pi\)
0.630951 + 0.775823i \(0.282665\pi\)
\(252\) 6.50217 0.409598
\(253\) −23.2659 −1.46271
\(254\) −28.1768 −1.76797
\(255\) 36.9640 2.31477
\(256\) −22.8049 −1.42531
\(257\) 9.53494 0.594773 0.297387 0.954757i \(-0.403885\pi\)
0.297387 + 0.954757i \(0.403885\pi\)
\(258\) 41.3084 2.57175
\(259\) 4.92257 0.305874
\(260\) 65.0297 4.03297
\(261\) 5.76847 0.357059
\(262\) 19.2096 1.18677
\(263\) 17.8563 1.10107 0.550535 0.834812i \(-0.314424\pi\)
0.550535 + 0.834812i \(0.314424\pi\)
\(264\) 36.8904 2.27045
\(265\) −43.7222 −2.68583
\(266\) 39.5053 2.42223
\(267\) 12.9664 0.793532
\(268\) −7.52746 −0.459813
\(269\) 14.9685 0.912648 0.456324 0.889814i \(-0.349166\pi\)
0.456324 + 0.889814i \(0.349166\pi\)
\(270\) 43.4626 2.64505
\(271\) 0.641322 0.0389575 0.0194788 0.999810i \(-0.493799\pi\)
0.0194788 + 0.999810i \(0.493799\pi\)
\(272\) 5.63646 0.341761
\(273\) 27.5150 1.66529
\(274\) 13.9315 0.841632
\(275\) 64.4861 3.88866
\(276\) 27.4358 1.65144
\(277\) −16.7074 −1.00385 −0.501926 0.864911i \(-0.667375\pi\)
−0.501926 + 0.864911i \(0.667375\pi\)
\(278\) 6.73843 0.404144
\(279\) −0.0782669 −0.00468572
\(280\) 44.6961 2.67111
\(281\) −29.8919 −1.78320 −0.891601 0.452822i \(-0.850417\pi\)
−0.891601 + 0.452822i \(0.850417\pi\)
\(282\) 35.2925 2.10164
\(283\) −24.4290 −1.45215 −0.726076 0.687614i \(-0.758658\pi\)
−0.726076 + 0.687614i \(0.758658\pi\)
\(284\) −7.92023 −0.469979
\(285\) −41.0705 −2.43281
\(286\) 60.2103 3.56031
\(287\) −11.6566 −0.688068
\(288\) 2.48064 0.146173
\(289\) 6.04271 0.355453
\(290\) 93.0645 5.46493
\(291\) 29.8730 1.75119
\(292\) −48.5822 −2.84306
\(293\) −19.5340 −1.14119 −0.570593 0.821233i \(-0.693287\pi\)
−0.570593 + 0.821233i \(0.693287\pi\)
\(294\) 13.3238 0.777061
\(295\) −48.8437 −2.84379
\(296\) −5.41228 −0.314583
\(297\) 25.5677 1.48359
\(298\) −2.72688 −0.157964
\(299\) 19.0794 1.10339
\(300\) −76.0440 −4.39040
\(301\) 29.4422 1.69702
\(302\) −18.6541 −1.07342
\(303\) 29.9566 1.72096
\(304\) −6.26265 −0.359187
\(305\) −9.74019 −0.557721
\(306\) −6.63240 −0.379149
\(307\) 0.261102 0.0149019 0.00745093 0.999972i \(-0.497628\pi\)
0.00745093 + 0.999972i \(0.497628\pi\)
\(308\) 61.7102 3.51627
\(309\) −26.8310 −1.52636
\(310\) −1.26270 −0.0717168
\(311\) 2.78486 0.157915 0.0789576 0.996878i \(-0.474841\pi\)
0.0789576 + 0.996878i \(0.474841\pi\)
\(312\) −30.2523 −1.71270
\(313\) 4.24954 0.240198 0.120099 0.992762i \(-0.461679\pi\)
0.120099 + 0.992762i \(0.461679\pi\)
\(314\) −35.2874 −1.99138
\(315\) −7.58312 −0.427260
\(316\) −60.1709 −3.38488
\(317\) −7.24390 −0.406858 −0.203429 0.979090i \(-0.565209\pi\)
−0.203429 + 0.979090i \(0.565209\pi\)
\(318\) 47.7375 2.67699
\(319\) 54.7469 3.06524
\(320\) 49.5650 2.77077
\(321\) 5.06240 0.282556
\(322\) 30.7775 1.71517
\(323\) −25.6027 −1.42457
\(324\) −36.3179 −2.01766
\(325\) −52.8824 −2.93339
\(326\) −29.3385 −1.62491
\(327\) 8.18198 0.452464
\(328\) 12.8162 0.707659
\(329\) 25.1545 1.38681
\(330\) −100.975 −5.55850
\(331\) −21.3414 −1.17303 −0.586516 0.809938i \(-0.699501\pi\)
−0.586516 + 0.809938i \(0.699501\pi\)
\(332\) 26.4211 1.45005
\(333\) 0.918245 0.0503195
\(334\) 37.6241 2.05870
\(335\) 8.77887 0.479641
\(336\) −7.03626 −0.383859
\(337\) 35.2178 1.91844 0.959218 0.282667i \(-0.0912190\pi\)
0.959218 + 0.282667i \(0.0912190\pi\)
\(338\) −18.9305 −1.02968
\(339\) 9.46103 0.513852
\(340\) −67.9846 −3.68698
\(341\) −0.742810 −0.0402254
\(342\) 7.36923 0.398482
\(343\) −12.6424 −0.682626
\(344\) −32.3712 −1.74534
\(345\) −31.9969 −1.72266
\(346\) −2.75489 −0.148104
\(347\) −8.85399 −0.475307 −0.237653 0.971350i \(-0.576378\pi\)
−0.237653 + 0.971350i \(0.576378\pi\)
\(348\) −64.5593 −3.46074
\(349\) 28.1363 1.50610 0.753050 0.657964i \(-0.228582\pi\)
0.753050 + 0.657964i \(0.228582\pi\)
\(350\) −85.3062 −4.55981
\(351\) −20.9670 −1.11914
\(352\) 23.5430 1.25485
\(353\) −6.28531 −0.334533 −0.167267 0.985912i \(-0.553494\pi\)
−0.167267 + 0.985912i \(0.553494\pi\)
\(354\) 53.3294 2.83443
\(355\) 9.23693 0.490246
\(356\) −23.8480 −1.26394
\(357\) −28.7653 −1.52242
\(358\) −37.7725 −1.99634
\(359\) −30.4246 −1.60575 −0.802876 0.596147i \(-0.796698\pi\)
−0.802876 + 0.596147i \(0.796698\pi\)
\(360\) 8.33751 0.439425
\(361\) 9.44702 0.497211
\(362\) 23.1482 1.21664
\(363\) −38.5587 −2.02380
\(364\) −50.6060 −2.65248
\(365\) 56.6588 2.96566
\(366\) 10.6347 0.555885
\(367\) 20.0395 1.04605 0.523026 0.852317i \(-0.324803\pi\)
0.523026 + 0.852317i \(0.324803\pi\)
\(368\) −4.87906 −0.254338
\(369\) −2.17440 −0.113195
\(370\) 14.8143 0.770160
\(371\) 34.0246 1.76647
\(372\) 0.875944 0.0454156
\(373\) 18.7242 0.969502 0.484751 0.874652i \(-0.338910\pi\)
0.484751 + 0.874652i \(0.338910\pi\)
\(374\) −62.9462 −3.25487
\(375\) 50.1841 2.59149
\(376\) −27.6569 −1.42630
\(377\) −44.8957 −2.31225
\(378\) −33.8226 −1.73964
\(379\) 13.8010 0.708909 0.354454 0.935073i \(-0.384667\pi\)
0.354454 + 0.935073i \(0.384667\pi\)
\(380\) 75.5374 3.87499
\(381\) −22.7959 −1.16787
\(382\) −18.9299 −0.968539
\(383\) −0.632437 −0.0323160 −0.0161580 0.999869i \(-0.505143\pi\)
−0.0161580 + 0.999869i \(0.505143\pi\)
\(384\) −38.1833 −1.94853
\(385\) −71.9693 −3.66789
\(386\) −30.8709 −1.57129
\(387\) 5.49208 0.279178
\(388\) −54.9428 −2.78930
\(389\) 32.6105 1.65342 0.826710 0.562629i \(-0.190210\pi\)
0.826710 + 0.562629i \(0.190210\pi\)
\(390\) 82.8056 4.19303
\(391\) −19.9463 −1.00873
\(392\) −10.4412 −0.527359
\(393\) 15.5412 0.783948
\(394\) −16.9067 −0.851747
\(395\) 70.1740 3.53084
\(396\) 11.5113 0.578463
\(397\) 9.52323 0.477957 0.238979 0.971025i \(-0.423187\pi\)
0.238979 + 0.971025i \(0.423187\pi\)
\(398\) −7.60530 −0.381219
\(399\) 31.9610 1.60005
\(400\) 13.5233 0.676165
\(401\) −1.93808 −0.0967832 −0.0483916 0.998828i \(-0.515410\pi\)
−0.0483916 + 0.998828i \(0.515410\pi\)
\(402\) −9.58510 −0.478061
\(403\) 0.609148 0.0303438
\(404\) −55.0965 −2.74115
\(405\) 42.3556 2.10467
\(406\) −72.4227 −3.59428
\(407\) 8.71480 0.431977
\(408\) 31.6270 1.56577
\(409\) 33.4374 1.65337 0.826687 0.562663i \(-0.190223\pi\)
0.826687 + 0.562663i \(0.190223\pi\)
\(410\) −35.0802 −1.73249
\(411\) 11.2710 0.555957
\(412\) 49.3479 2.43120
\(413\) 38.0101 1.87036
\(414\) 5.74117 0.282163
\(415\) −30.8135 −1.51258
\(416\) −19.3067 −0.946587
\(417\) 5.45159 0.266966
\(418\) 69.9393 3.42084
\(419\) 20.3242 0.992902 0.496451 0.868065i \(-0.334636\pi\)
0.496451 + 0.868065i \(0.334636\pi\)
\(420\) 84.8684 4.14115
\(421\) −9.61186 −0.468454 −0.234227 0.972182i \(-0.575256\pi\)
−0.234227 + 0.972182i \(0.575256\pi\)
\(422\) 11.7972 0.574279
\(423\) 4.69225 0.228145
\(424\) −37.4094 −1.81676
\(425\) 55.2853 2.68173
\(426\) −10.0852 −0.488631
\(427\) 7.57980 0.366812
\(428\) −9.31084 −0.450056
\(429\) 48.7120 2.35184
\(430\) 88.6054 4.27293
\(431\) −22.6012 −1.08866 −0.544331 0.838870i \(-0.683216\pi\)
−0.544331 + 0.838870i \(0.683216\pi\)
\(432\) 5.36177 0.257968
\(433\) −17.4977 −0.840884 −0.420442 0.907319i \(-0.638125\pi\)
−0.420442 + 0.907319i \(0.638125\pi\)
\(434\) 0.982635 0.0471680
\(435\) 75.2920 3.60997
\(436\) −15.0484 −0.720688
\(437\) 22.1623 1.06017
\(438\) −61.8622 −2.95589
\(439\) −19.5837 −0.934681 −0.467340 0.884078i \(-0.654788\pi\)
−0.467340 + 0.884078i \(0.654788\pi\)
\(440\) 79.1290 3.77233
\(441\) 1.77144 0.0843545
\(442\) 51.6196 2.45529
\(443\) 27.5231 1.30766 0.653831 0.756640i \(-0.273161\pi\)
0.653831 + 0.756640i \(0.273161\pi\)
\(444\) −10.2768 −0.487714
\(445\) 27.8126 1.31844
\(446\) −35.2596 −1.66959
\(447\) −2.20613 −0.104346
\(448\) −38.5714 −1.82233
\(449\) 6.87377 0.324393 0.162197 0.986758i \(-0.448142\pi\)
0.162197 + 0.986758i \(0.448142\pi\)
\(450\) −15.9128 −0.750137
\(451\) −20.6366 −0.971739
\(452\) −17.4008 −0.818467
\(453\) −15.0917 −0.709071
\(454\) 4.70253 0.220701
\(455\) 59.0190 2.76686
\(456\) −35.1406 −1.64561
\(457\) 11.2935 0.528285 0.264143 0.964484i \(-0.414911\pi\)
0.264143 + 0.964484i \(0.414911\pi\)
\(458\) 16.5370 0.772723
\(459\) 21.9198 1.02313
\(460\) 58.8491 2.74386
\(461\) −9.70031 −0.451788 −0.225894 0.974152i \(-0.572530\pi\)
−0.225894 + 0.974152i \(0.572530\pi\)
\(462\) 78.5788 3.65582
\(463\) 31.9880 1.48661 0.743305 0.668953i \(-0.233257\pi\)
0.743305 + 0.668953i \(0.233257\pi\)
\(464\) 11.4809 0.532988
\(465\) −1.02157 −0.0473740
\(466\) 50.0463 2.31835
\(467\) 7.00803 0.324293 0.162147 0.986767i \(-0.448158\pi\)
0.162147 + 0.986767i \(0.448158\pi\)
\(468\) −9.43993 −0.436361
\(469\) −6.83170 −0.315459
\(470\) 75.7015 3.49185
\(471\) −28.5486 −1.31545
\(472\) −41.7915 −1.92361
\(473\) 52.1238 2.39666
\(474\) −76.6186 −3.51921
\(475\) −61.4273 −2.81848
\(476\) 52.9055 2.42492
\(477\) 6.34686 0.290603
\(478\) −12.3729 −0.565922
\(479\) 24.1558 1.10371 0.551854 0.833941i \(-0.313921\pi\)
0.551854 + 0.833941i \(0.313921\pi\)
\(480\) 32.3781 1.47785
\(481\) −7.14665 −0.325859
\(482\) 42.6474 1.94254
\(483\) 24.9000 1.13299
\(484\) 70.9176 3.22353
\(485\) 64.0768 2.90958
\(486\) −14.1628 −0.642438
\(487\) 10.1678 0.460748 0.230374 0.973102i \(-0.426005\pi\)
0.230374 + 0.973102i \(0.426005\pi\)
\(488\) −8.33386 −0.377256
\(489\) −23.7357 −1.07337
\(490\) 28.5792 1.29108
\(491\) 17.8240 0.804386 0.402193 0.915555i \(-0.368248\pi\)
0.402193 + 0.915555i \(0.368248\pi\)
\(492\) 24.3353 1.09712
\(493\) 46.9357 2.11388
\(494\) −57.3544 −2.58049
\(495\) −13.4250 −0.603408
\(496\) −0.155774 −0.00699445
\(497\) −7.18817 −0.322434
\(498\) 33.6434 1.50760
\(499\) −26.9964 −1.20852 −0.604262 0.796786i \(-0.706532\pi\)
−0.604262 + 0.796786i \(0.706532\pi\)
\(500\) −92.2992 −4.12774
\(501\) 30.4390 1.35991
\(502\) −46.8212 −2.08973
\(503\) 12.3233 0.549467 0.274734 0.961520i \(-0.411410\pi\)
0.274734 + 0.961520i \(0.411410\pi\)
\(504\) −6.48824 −0.289009
\(505\) 64.2560 2.85936
\(506\) 54.4878 2.42228
\(507\) −15.3153 −0.680178
\(508\) 41.9265 1.86019
\(509\) −0.613117 −0.0271759 −0.0135880 0.999908i \(-0.504325\pi\)
−0.0135880 + 0.999908i \(0.504325\pi\)
\(510\) −86.5682 −3.83331
\(511\) −44.0918 −1.95051
\(512\) 13.1033 0.579089
\(513\) −24.3549 −1.07530
\(514\) −22.3305 −0.984955
\(515\) −57.5518 −2.53604
\(516\) −61.4660 −2.70589
\(517\) 44.5328 1.95855
\(518\) −11.5285 −0.506533
\(519\) −2.22879 −0.0978332
\(520\) −64.8904 −2.84563
\(521\) −13.3204 −0.583578 −0.291789 0.956483i \(-0.594250\pi\)
−0.291789 + 0.956483i \(0.594250\pi\)
\(522\) −13.5095 −0.591297
\(523\) 7.12252 0.311446 0.155723 0.987801i \(-0.450229\pi\)
0.155723 + 0.987801i \(0.450229\pi\)
\(524\) −28.5835 −1.24868
\(525\) −69.0153 −3.01207
\(526\) −41.8189 −1.82339
\(527\) −0.636827 −0.0277406
\(528\) −12.4568 −0.542114
\(529\) −5.73396 −0.249303
\(530\) 102.396 4.44779
\(531\) 7.09031 0.307693
\(532\) −58.7831 −2.54857
\(533\) 16.9232 0.733026
\(534\) −30.3669 −1.31410
\(535\) 10.8587 0.469463
\(536\) 7.51134 0.324441
\(537\) −30.5591 −1.31872
\(538\) −35.0558 −1.51136
\(539\) 16.8123 0.724156
\(540\) −64.6714 −2.78302
\(541\) 8.77727 0.377364 0.188682 0.982038i \(-0.439578\pi\)
0.188682 + 0.982038i \(0.439578\pi\)
\(542\) −1.50195 −0.0645144
\(543\) 18.7276 0.803678
\(544\) 20.1839 0.865379
\(545\) 17.5501 0.751765
\(546\) −64.4392 −2.75774
\(547\) −26.3213 −1.12542 −0.562709 0.826655i \(-0.690241\pi\)
−0.562709 + 0.826655i \(0.690241\pi\)
\(548\) −20.7298 −0.885532
\(549\) 1.41392 0.0603446
\(550\) −151.024 −6.43968
\(551\) −52.1501 −2.22167
\(552\) −27.3771 −1.16525
\(553\) −54.6093 −2.32222
\(554\) 39.1282 1.66240
\(555\) 11.9852 0.508745
\(556\) −10.0266 −0.425224
\(557\) 38.4138 1.62765 0.813823 0.581113i \(-0.197382\pi\)
0.813823 + 0.581113i \(0.197382\pi\)
\(558\) 0.183298 0.00775964
\(559\) −42.7446 −1.80790
\(560\) −15.0926 −0.637778
\(561\) −50.9254 −2.15007
\(562\) 70.0058 2.95301
\(563\) −16.0296 −0.675569 −0.337784 0.941223i \(-0.609677\pi\)
−0.337784 + 0.941223i \(0.609677\pi\)
\(564\) −52.5145 −2.21126
\(565\) 20.2936 0.853760
\(566\) 57.2118 2.40479
\(567\) −32.9611 −1.38424
\(568\) 7.90327 0.331614
\(569\) 34.9494 1.46516 0.732578 0.680683i \(-0.238317\pi\)
0.732578 + 0.680683i \(0.238317\pi\)
\(570\) 96.1856 4.02877
\(571\) −7.88836 −0.330118 −0.165059 0.986284i \(-0.552781\pi\)
−0.165059 + 0.986284i \(0.552781\pi\)
\(572\) −89.5917 −3.74602
\(573\) −15.3149 −0.639788
\(574\) 27.2994 1.13945
\(575\) −47.8563 −1.99575
\(576\) −7.19502 −0.299792
\(577\) 20.7664 0.864515 0.432258 0.901750i \(-0.357717\pi\)
0.432258 + 0.901750i \(0.357717\pi\)
\(578\) −14.1518 −0.588637
\(579\) −24.9755 −1.03795
\(580\) −138.478 −5.74999
\(581\) 23.9790 0.994818
\(582\) −69.9615 −2.90000
\(583\) 60.2363 2.49473
\(584\) 48.4782 2.00604
\(585\) 11.0093 0.455177
\(586\) 45.7478 1.88982
\(587\) 39.7603 1.64108 0.820542 0.571586i \(-0.193672\pi\)
0.820542 + 0.571586i \(0.193672\pi\)
\(588\) −19.8256 −0.817593
\(589\) 0.707576 0.0291552
\(590\) 114.390 4.70937
\(591\) −13.6780 −0.562639
\(592\) 1.82757 0.0751127
\(593\) −15.3053 −0.628513 −0.314257 0.949338i \(-0.601755\pi\)
−0.314257 + 0.949338i \(0.601755\pi\)
\(594\) −59.8786 −2.45685
\(595\) −61.7008 −2.52949
\(596\) 4.05754 0.166203
\(597\) −6.15292 −0.251822
\(598\) −44.6832 −1.82723
\(599\) 23.0462 0.941644 0.470822 0.882228i \(-0.343957\pi\)
0.470822 + 0.882228i \(0.343957\pi\)
\(600\) 75.8811 3.09783
\(601\) −12.6853 −0.517445 −0.258723 0.965952i \(-0.583302\pi\)
−0.258723 + 0.965952i \(0.583302\pi\)
\(602\) −68.9526 −2.81030
\(603\) −1.27437 −0.0518963
\(604\) 27.7569 1.12941
\(605\) −82.7073 −3.36253
\(606\) −70.1572 −2.84994
\(607\) 12.2482 0.497138 0.248569 0.968614i \(-0.420040\pi\)
0.248569 + 0.968614i \(0.420040\pi\)
\(608\) −22.4263 −0.909507
\(609\) −58.5921 −2.37427
\(610\) 22.8112 0.923597
\(611\) −36.5196 −1.47742
\(612\) 9.86887 0.398925
\(613\) −46.5406 −1.87976 −0.939878 0.341510i \(-0.889062\pi\)
−0.939878 + 0.341510i \(0.889062\pi\)
\(614\) −0.611490 −0.0246777
\(615\) −28.3809 −1.14443
\(616\) −61.5781 −2.48105
\(617\) 26.5930 1.07059 0.535296 0.844664i \(-0.320200\pi\)
0.535296 + 0.844664i \(0.320200\pi\)
\(618\) 62.8372 2.52768
\(619\) 34.4712 1.38552 0.692758 0.721170i \(-0.256396\pi\)
0.692758 + 0.721170i \(0.256396\pi\)
\(620\) 1.87888 0.0754575
\(621\) −18.9743 −0.761411
\(622\) −6.52205 −0.261510
\(623\) −21.6438 −0.867139
\(624\) 10.2153 0.408941
\(625\) 50.0580 2.00232
\(626\) −9.95228 −0.397773
\(627\) 56.5830 2.25971
\(628\) 52.5069 2.09526
\(629\) 7.47139 0.297904
\(630\) 17.7594 0.707551
\(631\) 23.1379 0.921106 0.460553 0.887632i \(-0.347651\pi\)
0.460553 + 0.887632i \(0.347651\pi\)
\(632\) 60.0420 2.38834
\(633\) 9.54430 0.379352
\(634\) 16.9650 0.673764
\(635\) −48.8966 −1.94040
\(636\) −71.0325 −2.81662
\(637\) −13.7871 −0.546263
\(638\) −128.215 −5.07609
\(639\) −1.34086 −0.0530438
\(640\) −81.9022 −3.23747
\(641\) −28.5719 −1.12852 −0.564262 0.825596i \(-0.690839\pi\)
−0.564262 + 0.825596i \(0.690839\pi\)
\(642\) −11.8560 −0.467918
\(643\) 28.5210 1.12476 0.562379 0.826880i \(-0.309886\pi\)
0.562379 + 0.826880i \(0.309886\pi\)
\(644\) −45.7963 −1.80463
\(645\) 71.6845 2.82257
\(646\) 59.9605 2.35911
\(647\) 4.25473 0.167271 0.0836354 0.996496i \(-0.473347\pi\)
0.0836354 + 0.996496i \(0.473347\pi\)
\(648\) 36.2401 1.42365
\(649\) 67.2922 2.64145
\(650\) 123.849 4.85774
\(651\) 0.794981 0.0311578
\(652\) 43.6550 1.70966
\(653\) −9.52702 −0.372821 −0.186411 0.982472i \(-0.559685\pi\)
−0.186411 + 0.982472i \(0.559685\pi\)
\(654\) −19.1619 −0.749289
\(655\) 33.3354 1.30252
\(656\) −4.32768 −0.168967
\(657\) −8.22478 −0.320879
\(658\) −58.9108 −2.29658
\(659\) 19.6043 0.763675 0.381837 0.924229i \(-0.375291\pi\)
0.381837 + 0.924229i \(0.375291\pi\)
\(660\) 150.249 5.84843
\(661\) −30.2185 −1.17536 −0.587681 0.809092i \(-0.699959\pi\)
−0.587681 + 0.809092i \(0.699959\pi\)
\(662\) 49.9809 1.94256
\(663\) 41.7618 1.62190
\(664\) −26.3645 −1.02314
\(665\) 68.5555 2.65847
\(666\) −2.15050 −0.0833300
\(667\) −40.6287 −1.57315
\(668\) −55.9838 −2.16608
\(669\) −28.5260 −1.10288
\(670\) −20.5598 −0.794294
\(671\) 13.4191 0.518039
\(672\) −25.1966 −0.971979
\(673\) 9.13421 0.352098 0.176049 0.984381i \(-0.443668\pi\)
0.176049 + 0.984381i \(0.443668\pi\)
\(674\) −82.4788 −3.17697
\(675\) 52.5910 2.02423
\(676\) 28.1682 1.08339
\(677\) 3.48343 0.133879 0.0669395 0.997757i \(-0.478677\pi\)
0.0669395 + 0.997757i \(0.478677\pi\)
\(678\) −22.1574 −0.850949
\(679\) −49.8645 −1.91362
\(680\) 67.8390 2.60151
\(681\) 3.80449 0.145788
\(682\) 1.73963 0.0666140
\(683\) −25.8033 −0.987335 −0.493668 0.869651i \(-0.664344\pi\)
−0.493668 + 0.869651i \(0.664344\pi\)
\(684\) −10.9653 −0.419267
\(685\) 24.1760 0.923717
\(686\) 29.6081 1.13044
\(687\) 13.3789 0.510438
\(688\) 10.9308 0.416734
\(689\) −49.3973 −1.88189
\(690\) 74.9356 2.85275
\(691\) 11.4009 0.433711 0.216856 0.976204i \(-0.430420\pi\)
0.216856 + 0.976204i \(0.430420\pi\)
\(692\) 4.09923 0.155829
\(693\) 10.4473 0.396860
\(694\) 20.7357 0.787117
\(695\) 11.6935 0.443560
\(696\) 64.4210 2.44187
\(697\) −17.6922 −0.670140
\(698\) −65.8941 −2.49413
\(699\) 40.4890 1.53143
\(700\) 126.934 4.79765
\(701\) 37.9243 1.43238 0.716190 0.697905i \(-0.245884\pi\)
0.716190 + 0.697905i \(0.245884\pi\)
\(702\) 49.1040 1.85331
\(703\) −8.30143 −0.313094
\(704\) −68.2859 −2.57362
\(705\) 61.2448 2.30661
\(706\) 14.7200 0.553993
\(707\) −50.0040 −1.88059
\(708\) −79.3530 −2.98227
\(709\) −33.3004 −1.25062 −0.625312 0.780375i \(-0.715028\pi\)
−0.625312 + 0.780375i \(0.715028\pi\)
\(710\) −21.6326 −0.811856
\(711\) −10.1867 −0.382031
\(712\) 23.7969 0.891828
\(713\) 0.551253 0.0206446
\(714\) 67.3673 2.52116
\(715\) 104.486 3.90755
\(716\) 56.2047 2.10047
\(717\) −10.0100 −0.373831
\(718\) 71.2534 2.65915
\(719\) 4.61966 0.172284 0.0861421 0.996283i \(-0.472546\pi\)
0.0861421 + 0.996283i \(0.472546\pi\)
\(720\) −2.81534 −0.104921
\(721\) 44.7867 1.66795
\(722\) −22.1246 −0.823391
\(723\) 34.5031 1.28318
\(724\) −34.4440 −1.28010
\(725\) 112.611 4.18226
\(726\) 90.3030 3.35146
\(727\) 21.4774 0.796553 0.398276 0.917265i \(-0.369608\pi\)
0.398276 + 0.917265i \(0.369608\pi\)
\(728\) 50.4977 1.87157
\(729\) 19.8074 0.733606
\(730\) −132.693 −4.91118
\(731\) 44.6869 1.65280
\(732\) −15.8242 −0.584880
\(733\) 19.3447 0.714514 0.357257 0.934006i \(-0.383712\pi\)
0.357257 + 0.934006i \(0.383712\pi\)
\(734\) −46.9317 −1.73228
\(735\) 23.1215 0.852849
\(736\) −17.4717 −0.644016
\(737\) −12.0947 −0.445513
\(738\) 5.09236 0.187452
\(739\) −5.60363 −0.206133 −0.103067 0.994674i \(-0.532865\pi\)
−0.103067 + 0.994674i \(0.532865\pi\)
\(740\) −22.0434 −0.810331
\(741\) −46.4014 −1.70460
\(742\) −79.6843 −2.92530
\(743\) 19.7233 0.723578 0.361789 0.932260i \(-0.382166\pi\)
0.361789 + 0.932260i \(0.382166\pi\)
\(744\) −0.874068 −0.0320449
\(745\) −4.73209 −0.173370
\(746\) −43.8514 −1.60551
\(747\) 4.47299 0.163658
\(748\) 93.6627 3.42465
\(749\) −8.45024 −0.308765
\(750\) −117.529 −4.29156
\(751\) −32.3025 −1.17874 −0.589368 0.807865i \(-0.700623\pi\)
−0.589368 + 0.807865i \(0.700623\pi\)
\(752\) 9.33893 0.340556
\(753\) −37.8798 −1.38042
\(754\) 105.144 3.82912
\(755\) −32.3713 −1.17811
\(756\) 50.3272 1.83038
\(757\) −30.9493 −1.12487 −0.562436 0.826841i \(-0.690136\pi\)
−0.562436 + 0.826841i \(0.690136\pi\)
\(758\) −32.3214 −1.17397
\(759\) 44.0823 1.60009
\(760\) −75.3756 −2.73416
\(761\) −17.3883 −0.630325 −0.315163 0.949038i \(-0.602059\pi\)
−0.315163 + 0.949038i \(0.602059\pi\)
\(762\) 53.3871 1.93401
\(763\) −13.6575 −0.494434
\(764\) 28.1673 1.01906
\(765\) −11.5095 −0.416128
\(766\) 1.48114 0.0535159
\(767\) −55.1836 −1.99256
\(768\) 43.2089 1.55917
\(769\) −44.5928 −1.60806 −0.804028 0.594591i \(-0.797314\pi\)
−0.804028 + 0.594591i \(0.797314\pi\)
\(770\) 168.549 6.07410
\(771\) −18.0660 −0.650632
\(772\) 45.9353 1.65325
\(773\) 43.2678 1.55623 0.778117 0.628120i \(-0.216175\pi\)
0.778117 + 0.628120i \(0.216175\pi\)
\(774\) −12.8623 −0.462324
\(775\) −1.52791 −0.0548841
\(776\) 54.8252 1.96811
\(777\) −9.32689 −0.334600
\(778\) −76.3726 −2.73809
\(779\) 19.6577 0.704311
\(780\) −123.213 −4.41173
\(781\) −12.7258 −0.455364
\(782\) 46.7136 1.67047
\(783\) 44.6484 1.59560
\(784\) 3.52569 0.125917
\(785\) −61.2360 −2.18561
\(786\) −36.3968 −1.29823
\(787\) −17.9471 −0.639747 −0.319873 0.947460i \(-0.603640\pi\)
−0.319873 + 0.947460i \(0.603640\pi\)
\(788\) 25.1568 0.896174
\(789\) −33.8328 −1.20448
\(790\) −164.345 −5.84713
\(791\) −15.7925 −0.561516
\(792\) −11.4866 −0.408159
\(793\) −11.0045 −0.390780
\(794\) −22.3031 −0.791506
\(795\) 82.8413 2.93808
\(796\) 11.3165 0.401104
\(797\) −6.99950 −0.247935 −0.123967 0.992286i \(-0.539562\pi\)
−0.123967 + 0.992286i \(0.539562\pi\)
\(798\) −74.8515 −2.64972
\(799\) 38.1790 1.35067
\(800\) 48.4264 1.71213
\(801\) −4.03737 −0.142654
\(802\) 4.53892 0.160275
\(803\) −78.0590 −2.75464
\(804\) 14.2624 0.502997
\(805\) 53.4098 1.88245
\(806\) −1.42660 −0.0502499
\(807\) −28.3612 −0.998361
\(808\) 54.9785 1.93414
\(809\) −30.3896 −1.06844 −0.534221 0.845345i \(-0.679395\pi\)
−0.534221 + 0.845345i \(0.679395\pi\)
\(810\) −99.1953 −3.48537
\(811\) 33.8095 1.18721 0.593606 0.804756i \(-0.297704\pi\)
0.593606 + 0.804756i \(0.297704\pi\)
\(812\) 107.763 3.78175
\(813\) −1.21512 −0.0426163
\(814\) −20.4098 −0.715361
\(815\) −50.9125 −1.78339
\(816\) −10.6795 −0.373858
\(817\) −49.6514 −1.73708
\(818\) −78.3092 −2.73802
\(819\) −8.56740 −0.299369
\(820\) 52.1986 1.82285
\(821\) 34.2786 1.19633 0.598165 0.801373i \(-0.295897\pi\)
0.598165 + 0.801373i \(0.295897\pi\)
\(822\) −26.3963 −0.920676
\(823\) −3.37653 −0.117699 −0.0588493 0.998267i \(-0.518743\pi\)
−0.0588493 + 0.998267i \(0.518743\pi\)
\(824\) −49.2423 −1.71544
\(825\) −122.183 −4.25387
\(826\) −89.0183 −3.09734
\(827\) 11.3084 0.393232 0.196616 0.980481i \(-0.437005\pi\)
0.196616 + 0.980481i \(0.437005\pi\)
\(828\) −8.54274 −0.296881
\(829\) −30.7774 −1.06894 −0.534472 0.845186i \(-0.679489\pi\)
−0.534472 + 0.845186i \(0.679489\pi\)
\(830\) 72.1641 2.50485
\(831\) 31.6559 1.09813
\(832\) 55.9984 1.94140
\(833\) 14.4135 0.499400
\(834\) −12.7674 −0.442100
\(835\) 65.2909 2.25948
\(836\) −104.068 −3.59927
\(837\) −0.605792 −0.0209392
\(838\) −47.5985 −1.64426
\(839\) 19.1455 0.660977 0.330489 0.943810i \(-0.392786\pi\)
0.330489 + 0.943810i \(0.392786\pi\)
\(840\) −84.6867 −2.92197
\(841\) 66.6036 2.29667
\(842\) 22.5106 0.775768
\(843\) 56.6368 1.95067
\(844\) −17.5540 −0.604233
\(845\) −32.8510 −1.13011
\(846\) −10.9891 −0.377812
\(847\) 64.3627 2.21153
\(848\) 12.6321 0.433787
\(849\) 46.2861 1.58853
\(850\) −129.476 −4.44100
\(851\) −6.46742 −0.221700
\(852\) 15.0066 0.514118
\(853\) 43.5067 1.48964 0.744820 0.667265i \(-0.232535\pi\)
0.744820 + 0.667265i \(0.232535\pi\)
\(854\) −17.7516 −0.607448
\(855\) 12.7882 0.437347
\(856\) 9.29090 0.317556
\(857\) 10.4837 0.358117 0.179059 0.983838i \(-0.442695\pi\)
0.179059 + 0.983838i \(0.442695\pi\)
\(858\) −114.082 −3.89468
\(859\) 48.1138 1.64162 0.820810 0.571201i \(-0.193522\pi\)
0.820810 + 0.571201i \(0.193522\pi\)
\(860\) −131.843 −4.49581
\(861\) 22.0860 0.752689
\(862\) 52.9312 1.80284
\(863\) −13.8070 −0.469996 −0.234998 0.971996i \(-0.575508\pi\)
−0.234998 + 0.971996i \(0.575508\pi\)
\(864\) 19.2003 0.653208
\(865\) −4.78070 −0.162549
\(866\) 40.9789 1.39252
\(867\) −11.4492 −0.388836
\(868\) −1.46214 −0.0496283
\(869\) −96.6790 −3.27961
\(870\) −176.331 −5.97818
\(871\) 9.91835 0.336071
\(872\) 15.0162 0.508512
\(873\) −9.30160 −0.314812
\(874\) −51.9033 −1.75565
\(875\) −83.7680 −2.83188
\(876\) 92.0496 3.11007
\(877\) 28.5026 0.962464 0.481232 0.876593i \(-0.340189\pi\)
0.481232 + 0.876593i \(0.340189\pi\)
\(878\) 45.8644 1.54785
\(879\) 37.0114 1.24836
\(880\) −26.7196 −0.900716
\(881\) −23.4700 −0.790724 −0.395362 0.918525i \(-0.629381\pi\)
−0.395362 + 0.918525i \(0.629381\pi\)
\(882\) −4.14866 −0.139693
\(883\) −6.64052 −0.223471 −0.111736 0.993738i \(-0.535641\pi\)
−0.111736 + 0.993738i \(0.535641\pi\)
\(884\) −76.8089 −2.58336
\(885\) 92.5451 3.11087
\(886\) −64.4581 −2.16551
\(887\) −26.8120 −0.900259 −0.450130 0.892963i \(-0.648622\pi\)
−0.450130 + 0.892963i \(0.648622\pi\)
\(888\) 10.2548 0.344127
\(889\) 38.0512 1.27620
\(890\) −65.1361 −2.18337
\(891\) −58.3535 −1.95492
\(892\) 52.4655 1.75667
\(893\) −42.4205 −1.41955
\(894\) 5.16667 0.172799
\(895\) −65.5484 −2.19104
\(896\) 63.7362 2.12928
\(897\) −36.1501 −1.20702
\(898\) −16.0981 −0.537201
\(899\) −1.29715 −0.0432625
\(900\) 23.6779 0.789264
\(901\) 51.6419 1.72044
\(902\) 48.3301 1.60922
\(903\) −55.7848 −1.85640
\(904\) 17.3636 0.577504
\(905\) 40.1702 1.33530
\(906\) 35.3442 1.17423
\(907\) −13.7447 −0.456385 −0.228192 0.973616i \(-0.573281\pi\)
−0.228192 + 0.973616i \(0.573281\pi\)
\(908\) −6.99726 −0.232212
\(909\) −9.32762 −0.309378
\(910\) −138.220 −4.58196
\(911\) −8.26440 −0.273812 −0.136906 0.990584i \(-0.543716\pi\)
−0.136906 + 0.990584i \(0.543716\pi\)
\(912\) 11.8660 0.392921
\(913\) 42.4519 1.40495
\(914\) −26.4488 −0.874850
\(915\) 18.4549 0.610101
\(916\) −24.6067 −0.813029
\(917\) −25.9416 −0.856666
\(918\) −51.3353 −1.69432
\(919\) −7.54936 −0.249030 −0.124515 0.992218i \(-0.539738\pi\)
−0.124515 + 0.992218i \(0.539738\pi\)
\(920\) −58.7231 −1.93604
\(921\) −0.494714 −0.0163014
\(922\) 22.7178 0.748170
\(923\) 10.4359 0.343501
\(924\) −116.924 −3.84650
\(925\) 17.9258 0.589395
\(926\) −74.9148 −2.46185
\(927\) 8.35441 0.274395
\(928\) 41.1127 1.34959
\(929\) 35.4602 1.16341 0.581706 0.813399i \(-0.302385\pi\)
0.581706 + 0.813399i \(0.302385\pi\)
\(930\) 2.39247 0.0784522
\(931\) −16.0148 −0.524865
\(932\) −74.4678 −2.43927
\(933\) −5.27654 −0.172746
\(934\) −16.4126 −0.537035
\(935\) −109.234 −3.57232
\(936\) 9.41971 0.307893
\(937\) −3.99175 −0.130405 −0.0652024 0.997872i \(-0.520769\pi\)
−0.0652024 + 0.997872i \(0.520769\pi\)
\(938\) 15.9996 0.522406
\(939\) −8.05169 −0.262757
\(940\) −112.642 −3.67398
\(941\) 25.7831 0.840504 0.420252 0.907408i \(-0.361942\pi\)
0.420252 + 0.907408i \(0.361942\pi\)
\(942\) 66.8598 2.17841
\(943\) 15.3148 0.498719
\(944\) 14.1118 0.459299
\(945\) −58.6939 −1.90931
\(946\) −122.072 −3.96891
\(947\) −41.7089 −1.35536 −0.677678 0.735359i \(-0.737014\pi\)
−0.677678 + 0.735359i \(0.737014\pi\)
\(948\) 114.007 3.70277
\(949\) 64.0130 2.07795
\(950\) 143.860 4.66745
\(951\) 13.7252 0.445069
\(952\) −52.7922 −1.71101
\(953\) 35.4747 1.14914 0.574569 0.818456i \(-0.305170\pi\)
0.574569 + 0.818456i \(0.305170\pi\)
\(954\) −14.8641 −0.481243
\(955\) −32.8500 −1.06300
\(956\) 18.4106 0.595441
\(957\) −103.730 −3.35312
\(958\) −56.5720 −1.82776
\(959\) −18.8137 −0.607527
\(960\) −93.9117 −3.03099
\(961\) −30.9824 −0.999432
\(962\) 16.7372 0.539629
\(963\) −1.57629 −0.0507952
\(964\) −63.4585 −2.04386
\(965\) −53.5718 −1.72454
\(966\) −58.3148 −1.87625
\(967\) 17.0130 0.547100 0.273550 0.961858i \(-0.411802\pi\)
0.273550 + 0.961858i \(0.411802\pi\)
\(968\) −70.7657 −2.27450
\(969\) 48.5099 1.55836
\(970\) −150.066 −4.81831
\(971\) −10.2644 −0.329400 −0.164700 0.986344i \(-0.552666\pi\)
−0.164700 + 0.986344i \(0.552666\pi\)
\(972\) 21.0739 0.675947
\(973\) −9.09988 −0.291729
\(974\) −23.8127 −0.763008
\(975\) 100.197 3.20888
\(976\) 2.81410 0.0900773
\(977\) 45.5027 1.45576 0.727881 0.685704i \(-0.240505\pi\)
0.727881 + 0.685704i \(0.240505\pi\)
\(978\) 55.5882 1.77751
\(979\) −38.3176 −1.22463
\(980\) −42.5253 −1.35842
\(981\) −2.54763 −0.0813397
\(982\) −41.7432 −1.33208
\(983\) 23.0587 0.735459 0.367730 0.929933i \(-0.380135\pi\)
0.367730 + 0.929933i \(0.380135\pi\)
\(984\) −24.2832 −0.774120
\(985\) −29.3390 −0.934819
\(986\) −109.922 −3.50062
\(987\) −47.6606 −1.51705
\(988\) 85.3421 2.71509
\(989\) −38.6821 −1.23002
\(990\) 31.4408 0.999254
\(991\) 23.6496 0.751256 0.375628 0.926771i \(-0.377427\pi\)
0.375628 + 0.926771i \(0.377427\pi\)
\(992\) −0.557820 −0.0177108
\(993\) 40.4360 1.28320
\(994\) 16.8344 0.533956
\(995\) −13.1978 −0.418400
\(996\) −50.0606 −1.58623
\(997\) 35.6067 1.12768 0.563838 0.825886i \(-0.309324\pi\)
0.563838 + 0.825886i \(0.309324\pi\)
\(998\) 63.2246 2.00134
\(999\) 7.10728 0.224864
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 4003.2.a.c.1.18 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.18 179 1.1 even 1 trivial