Properties

Label 4027.2.a.c.1.5
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.64301 q^{2} +3.39832 q^{3} +4.98550 q^{4} -0.538898 q^{5} -8.98178 q^{6} -0.766621 q^{7} -7.89070 q^{8} +8.54855 q^{9} +O(q^{10})\) \(q-2.64301 q^{2} +3.39832 q^{3} +4.98550 q^{4} -0.538898 q^{5} -8.98178 q^{6} -0.766621 q^{7} -7.89070 q^{8} +8.54855 q^{9} +1.42431 q^{10} +3.53118 q^{11} +16.9423 q^{12} +5.95840 q^{13} +2.02619 q^{14} -1.83135 q^{15} +10.8842 q^{16} +4.30030 q^{17} -22.5939 q^{18} -3.03480 q^{19} -2.68668 q^{20} -2.60522 q^{21} -9.33293 q^{22} -0.904445 q^{23} -26.8151 q^{24} -4.70959 q^{25} -15.7481 q^{26} +18.8557 q^{27} -3.82199 q^{28} +6.07098 q^{29} +4.84027 q^{30} -4.27899 q^{31} -12.9856 q^{32} +12.0001 q^{33} -11.3657 q^{34} +0.413131 q^{35} +42.6188 q^{36} +2.39736 q^{37} +8.02101 q^{38} +20.2485 q^{39} +4.25228 q^{40} -1.40672 q^{41} +6.88562 q^{42} +1.33175 q^{43} +17.6047 q^{44} -4.60680 q^{45} +2.39046 q^{46} -3.59450 q^{47} +36.9879 q^{48} -6.41229 q^{49} +12.4475 q^{50} +14.6138 q^{51} +29.7056 q^{52} +12.2518 q^{53} -49.8358 q^{54} -1.90295 q^{55} +6.04918 q^{56} -10.3132 q^{57} -16.0457 q^{58} +4.29260 q^{59} -9.13017 q^{60} +7.02427 q^{61} +11.3094 q^{62} -6.55350 q^{63} +12.5527 q^{64} -3.21097 q^{65} -31.7163 q^{66} -13.8068 q^{67} +21.4391 q^{68} -3.07359 q^{69} -1.09191 q^{70} +6.80216 q^{71} -67.4540 q^{72} +3.02047 q^{73} -6.33623 q^{74} -16.0047 q^{75} -15.1300 q^{76} -2.70707 q^{77} -53.5170 q^{78} -6.52080 q^{79} -5.86547 q^{80} +38.4320 q^{81} +3.71797 q^{82} -11.5643 q^{83} -12.9883 q^{84} -2.31742 q^{85} -3.51984 q^{86} +20.6311 q^{87} -27.8635 q^{88} -4.54173 q^{89} +12.1758 q^{90} -4.56783 q^{91} -4.50911 q^{92} -14.5414 q^{93} +9.50028 q^{94} +1.63545 q^{95} -44.1292 q^{96} -9.25650 q^{97} +16.9477 q^{98} +30.1864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64301 −1.86889 −0.934445 0.356108i \(-0.884104\pi\)
−0.934445 + 0.356108i \(0.884104\pi\)
\(3\) 3.39832 1.96202 0.981009 0.193961i \(-0.0621335\pi\)
0.981009 + 0.193961i \(0.0621335\pi\)
\(4\) 4.98550 2.49275
\(5\) −0.538898 −0.241003 −0.120501 0.992713i \(-0.538450\pi\)
−0.120501 + 0.992713i \(0.538450\pi\)
\(6\) −8.98178 −3.66680
\(7\) −0.766621 −0.289756 −0.144878 0.989450i \(-0.546279\pi\)
−0.144878 + 0.989450i \(0.546279\pi\)
\(8\) −7.89070 −2.78978
\(9\) 8.54855 2.84952
\(10\) 1.42431 0.450407
\(11\) 3.53118 1.06469 0.532345 0.846527i \(-0.321311\pi\)
0.532345 + 0.846527i \(0.321311\pi\)
\(12\) 16.9423 4.89082
\(13\) 5.95840 1.65256 0.826281 0.563258i \(-0.190452\pi\)
0.826281 + 0.563258i \(0.190452\pi\)
\(14\) 2.02619 0.541521
\(15\) −1.83135 −0.472852
\(16\) 10.8842 2.72105
\(17\) 4.30030 1.04298 0.521488 0.853259i \(-0.325377\pi\)
0.521488 + 0.853259i \(0.325377\pi\)
\(18\) −22.5939 −5.32543
\(19\) −3.03480 −0.696232 −0.348116 0.937452i \(-0.613178\pi\)
−0.348116 + 0.937452i \(0.613178\pi\)
\(20\) −2.68668 −0.600759
\(21\) −2.60522 −0.568506
\(22\) −9.33293 −1.98979
\(23\) −0.904445 −0.188590 −0.0942950 0.995544i \(-0.530060\pi\)
−0.0942950 + 0.995544i \(0.530060\pi\)
\(24\) −26.8151 −5.47361
\(25\) −4.70959 −0.941918
\(26\) −15.7481 −3.08846
\(27\) 18.8557 3.62879
\(28\) −3.82199 −0.722288
\(29\) 6.07098 1.12735 0.563676 0.825996i \(-0.309387\pi\)
0.563676 + 0.825996i \(0.309387\pi\)
\(30\) 4.84027 0.883707
\(31\) −4.27899 −0.768529 −0.384265 0.923223i \(-0.625545\pi\)
−0.384265 + 0.923223i \(0.625545\pi\)
\(32\) −12.9856 −2.29556
\(33\) 12.0001 2.08894
\(34\) −11.3657 −1.94921
\(35\) 0.413131 0.0698318
\(36\) 42.6188 7.10313
\(37\) 2.39736 0.394123 0.197061 0.980391i \(-0.436860\pi\)
0.197061 + 0.980391i \(0.436860\pi\)
\(38\) 8.02101 1.30118
\(39\) 20.2485 3.24236
\(40\) 4.25228 0.672345
\(41\) −1.40672 −0.219692 −0.109846 0.993949i \(-0.535036\pi\)
−0.109846 + 0.993949i \(0.535036\pi\)
\(42\) 6.88562 1.06247
\(43\) 1.33175 0.203091 0.101545 0.994831i \(-0.467621\pi\)
0.101545 + 0.994831i \(0.467621\pi\)
\(44\) 17.6047 2.65400
\(45\) −4.60680 −0.686741
\(46\) 2.39046 0.352454
\(47\) −3.59450 −0.524311 −0.262155 0.965026i \(-0.584433\pi\)
−0.262155 + 0.965026i \(0.584433\pi\)
\(48\) 36.9879 5.33875
\(49\) −6.41229 −0.916042
\(50\) 12.4475 1.76034
\(51\) 14.6138 2.04634
\(52\) 29.7056 4.11942
\(53\) 12.2518 1.68292 0.841458 0.540322i \(-0.181698\pi\)
0.841458 + 0.540322i \(0.181698\pi\)
\(54\) −49.8358 −6.78180
\(55\) −1.90295 −0.256593
\(56\) 6.04918 0.808355
\(57\) −10.3132 −1.36602
\(58\) −16.0457 −2.10690
\(59\) 4.29260 0.558849 0.279424 0.960168i \(-0.409856\pi\)
0.279424 + 0.960168i \(0.409856\pi\)
\(60\) −9.13017 −1.17870
\(61\) 7.02427 0.899366 0.449683 0.893188i \(-0.351537\pi\)
0.449683 + 0.893188i \(0.351537\pi\)
\(62\) 11.3094 1.43630
\(63\) −6.55350 −0.825663
\(64\) 12.5527 1.56909
\(65\) −3.21097 −0.398272
\(66\) −31.7163 −3.90400
\(67\) −13.8068 −1.68677 −0.843386 0.537308i \(-0.819441\pi\)
−0.843386 + 0.537308i \(0.819441\pi\)
\(68\) 21.4391 2.59988
\(69\) −3.07359 −0.370017
\(70\) −1.09191 −0.130508
\(71\) 6.80216 0.807268 0.403634 0.914921i \(-0.367747\pi\)
0.403634 + 0.914921i \(0.367747\pi\)
\(72\) −67.4540 −7.94953
\(73\) 3.02047 0.353519 0.176760 0.984254i \(-0.443438\pi\)
0.176760 + 0.984254i \(0.443438\pi\)
\(74\) −6.33623 −0.736572
\(75\) −16.0047 −1.84806
\(76\) −15.1300 −1.73553
\(77\) −2.70707 −0.308500
\(78\) −53.5170 −6.05961
\(79\) −6.52080 −0.733647 −0.366823 0.930291i \(-0.619555\pi\)
−0.366823 + 0.930291i \(0.619555\pi\)
\(80\) −5.86547 −0.655780
\(81\) 38.4320 4.27023
\(82\) 3.71797 0.410581
\(83\) −11.5643 −1.26935 −0.634673 0.772781i \(-0.718865\pi\)
−0.634673 + 0.772781i \(0.718865\pi\)
\(84\) −12.9883 −1.41714
\(85\) −2.31742 −0.251360
\(86\) −3.51984 −0.379554
\(87\) 20.6311 2.21189
\(88\) −27.8635 −2.97025
\(89\) −4.54173 −0.481423 −0.240711 0.970597i \(-0.577381\pi\)
−0.240711 + 0.970597i \(0.577381\pi\)
\(90\) 12.1758 1.28344
\(91\) −4.56783 −0.478839
\(92\) −4.50911 −0.470107
\(93\) −14.5414 −1.50787
\(94\) 9.50028 0.979879
\(95\) 1.63545 0.167794
\(96\) −44.1292 −4.50392
\(97\) −9.25650 −0.939855 −0.469928 0.882705i \(-0.655720\pi\)
−0.469928 + 0.882705i \(0.655720\pi\)
\(98\) 16.9477 1.71198
\(99\) 30.1864 3.03385
\(100\) −23.4796 −2.34796
\(101\) −7.99738 −0.795769 −0.397885 0.917435i \(-0.630256\pi\)
−0.397885 + 0.917435i \(0.630256\pi\)
\(102\) −38.6244 −3.82438
\(103\) −7.39298 −0.728452 −0.364226 0.931311i \(-0.618666\pi\)
−0.364226 + 0.931311i \(0.618666\pi\)
\(104\) −47.0159 −4.61029
\(105\) 1.40395 0.137011
\(106\) −32.3817 −3.14519
\(107\) 6.93047 0.669994 0.334997 0.942219i \(-0.391265\pi\)
0.334997 + 0.942219i \(0.391265\pi\)
\(108\) 94.0052 9.04565
\(109\) 3.35598 0.321444 0.160722 0.987000i \(-0.448618\pi\)
0.160722 + 0.987000i \(0.448618\pi\)
\(110\) 5.02950 0.479544
\(111\) 8.14697 0.773276
\(112\) −8.34405 −0.788439
\(113\) −0.482270 −0.0453682 −0.0226841 0.999743i \(-0.507221\pi\)
−0.0226841 + 0.999743i \(0.507221\pi\)
\(114\) 27.2579 2.55294
\(115\) 0.487404 0.0454507
\(116\) 30.2669 2.81021
\(117\) 50.9356 4.70900
\(118\) −11.3454 −1.04443
\(119\) −3.29670 −0.302208
\(120\) 14.4506 1.31915
\(121\) 1.46921 0.133565
\(122\) −18.5652 −1.68082
\(123\) −4.78047 −0.431040
\(124\) −21.3329 −1.91575
\(125\) 5.23248 0.468007
\(126\) 17.3210 1.54307
\(127\) 4.95900 0.440040 0.220020 0.975495i \(-0.429388\pi\)
0.220020 + 0.975495i \(0.429388\pi\)
\(128\) −7.20576 −0.636905
\(129\) 4.52572 0.398468
\(130\) 8.48662 0.744326
\(131\) 19.3864 1.69380 0.846900 0.531752i \(-0.178466\pi\)
0.846900 + 0.531752i \(0.178466\pi\)
\(132\) 59.8262 5.20721
\(133\) 2.32654 0.201737
\(134\) 36.4916 3.15239
\(135\) −10.1613 −0.874547
\(136\) −33.9324 −2.90968
\(137\) −19.8528 −1.69614 −0.848069 0.529887i \(-0.822234\pi\)
−0.848069 + 0.529887i \(0.822234\pi\)
\(138\) 8.12353 0.691521
\(139\) −19.8426 −1.68303 −0.841515 0.540233i \(-0.818336\pi\)
−0.841515 + 0.540233i \(0.818336\pi\)
\(140\) 2.05966 0.174073
\(141\) −12.2152 −1.02871
\(142\) −17.9782 −1.50869
\(143\) 21.0402 1.75947
\(144\) 93.0441 7.75367
\(145\) −3.27164 −0.271695
\(146\) −7.98313 −0.660688
\(147\) −21.7910 −1.79729
\(148\) 11.9520 0.982449
\(149\) 21.5847 1.76828 0.884142 0.467218i \(-0.154744\pi\)
0.884142 + 0.467218i \(0.154744\pi\)
\(150\) 42.3005 3.45382
\(151\) 9.37910 0.763261 0.381630 0.924315i \(-0.375363\pi\)
0.381630 + 0.924315i \(0.375363\pi\)
\(152\) 23.9467 1.94234
\(153\) 36.7613 2.97198
\(154\) 7.15482 0.576552
\(155\) 2.30594 0.185218
\(156\) 100.949 8.08238
\(157\) −20.7194 −1.65359 −0.826793 0.562506i \(-0.809837\pi\)
−0.826793 + 0.562506i \(0.809837\pi\)
\(158\) 17.2345 1.37110
\(159\) 41.6355 3.30191
\(160\) 6.99793 0.553235
\(161\) 0.693367 0.0546450
\(162\) −101.576 −7.98058
\(163\) 3.39625 0.266015 0.133007 0.991115i \(-0.457537\pi\)
0.133007 + 0.991115i \(0.457537\pi\)
\(164\) −7.01319 −0.547638
\(165\) −6.46681 −0.503440
\(166\) 30.5645 2.37227
\(167\) −23.9428 −1.85275 −0.926376 0.376601i \(-0.877093\pi\)
−0.926376 + 0.376601i \(0.877093\pi\)
\(168\) 20.5570 1.58601
\(169\) 22.5025 1.73096
\(170\) 6.12497 0.469764
\(171\) −25.9432 −1.98392
\(172\) 6.63946 0.506254
\(173\) 6.60965 0.502522 0.251261 0.967919i \(-0.419155\pi\)
0.251261 + 0.967919i \(0.419155\pi\)
\(174\) −54.5282 −4.13377
\(175\) 3.61047 0.272926
\(176\) 38.4340 2.89707
\(177\) 14.5876 1.09647
\(178\) 12.0038 0.899726
\(179\) −18.0160 −1.34658 −0.673291 0.739378i \(-0.735120\pi\)
−0.673291 + 0.739378i \(0.735120\pi\)
\(180\) −22.9672 −1.71187
\(181\) −5.48461 −0.407668 −0.203834 0.979005i \(-0.565340\pi\)
−0.203834 + 0.979005i \(0.565340\pi\)
\(182\) 12.0728 0.894897
\(183\) 23.8707 1.76457
\(184\) 7.13671 0.526125
\(185\) −1.29193 −0.0949846
\(186\) 38.4329 2.81804
\(187\) 15.1851 1.11045
\(188\) −17.9203 −1.30698
\(189\) −14.4552 −1.05146
\(190\) −4.32251 −0.313588
\(191\) −11.7679 −0.851497 −0.425749 0.904841i \(-0.639989\pi\)
−0.425749 + 0.904841i \(0.639989\pi\)
\(192\) 42.6582 3.07859
\(193\) 3.51518 0.253028 0.126514 0.991965i \(-0.459621\pi\)
0.126514 + 0.991965i \(0.459621\pi\)
\(194\) 24.4650 1.75649
\(195\) −10.9119 −0.781416
\(196\) −31.9685 −2.28346
\(197\) −6.32965 −0.450969 −0.225485 0.974247i \(-0.572397\pi\)
−0.225485 + 0.974247i \(0.572397\pi\)
\(198\) −79.7830 −5.66993
\(199\) −4.18571 −0.296717 −0.148358 0.988934i \(-0.547399\pi\)
−0.148358 + 0.988934i \(0.547399\pi\)
\(200\) 37.1619 2.62775
\(201\) −46.9199 −3.30948
\(202\) 21.1372 1.48721
\(203\) −4.65414 −0.326657
\(204\) 72.8570 5.10101
\(205\) 0.758077 0.0529464
\(206\) 19.5397 1.36140
\(207\) −7.73170 −0.537390
\(208\) 64.8523 4.49670
\(209\) −10.7164 −0.741271
\(210\) −3.71065 −0.256059
\(211\) 13.0183 0.896215 0.448108 0.893980i \(-0.352098\pi\)
0.448108 + 0.893980i \(0.352098\pi\)
\(212\) 61.0814 4.19509
\(213\) 23.1159 1.58387
\(214\) −18.3173 −1.25214
\(215\) −0.717680 −0.0489454
\(216\) −148.785 −10.1235
\(217\) 3.28036 0.222686
\(218\) −8.86988 −0.600744
\(219\) 10.2645 0.693611
\(220\) −9.48713 −0.639622
\(221\) 25.6229 1.72358
\(222\) −21.5325 −1.44517
\(223\) 10.5932 0.709375 0.354688 0.934985i \(-0.384587\pi\)
0.354688 + 0.934985i \(0.384587\pi\)
\(224\) 9.95505 0.665150
\(225\) −40.2602 −2.68401
\(226\) 1.27465 0.0847881
\(227\) −14.4668 −0.960194 −0.480097 0.877215i \(-0.659399\pi\)
−0.480097 + 0.877215i \(0.659399\pi\)
\(228\) −51.4165 −3.40514
\(229\) 6.17814 0.408263 0.204131 0.978943i \(-0.434563\pi\)
0.204131 + 0.978943i \(0.434563\pi\)
\(230\) −1.28821 −0.0849423
\(231\) −9.19950 −0.605282
\(232\) −47.9043 −3.14507
\(233\) 6.81936 0.446751 0.223376 0.974732i \(-0.428292\pi\)
0.223376 + 0.974732i \(0.428292\pi\)
\(234\) −134.623 −8.80060
\(235\) 1.93707 0.126360
\(236\) 21.4007 1.39307
\(237\) −22.1597 −1.43943
\(238\) 8.71321 0.564794
\(239\) −24.1310 −1.56091 −0.780453 0.625214i \(-0.785012\pi\)
−0.780453 + 0.625214i \(0.785012\pi\)
\(240\) −19.9327 −1.28665
\(241\) 24.5130 1.57902 0.789510 0.613737i \(-0.210335\pi\)
0.789510 + 0.613737i \(0.210335\pi\)
\(242\) −3.88315 −0.249618
\(243\) 74.0371 4.74948
\(244\) 35.0195 2.24189
\(245\) 3.45557 0.220768
\(246\) 12.6348 0.805567
\(247\) −18.0826 −1.15057
\(248\) 33.7642 2.14403
\(249\) −39.2991 −2.49048
\(250\) −13.8295 −0.874654
\(251\) 4.13873 0.261234 0.130617 0.991433i \(-0.458304\pi\)
0.130617 + 0.991433i \(0.458304\pi\)
\(252\) −32.6724 −2.05817
\(253\) −3.19376 −0.200790
\(254\) −13.1067 −0.822386
\(255\) −7.87534 −0.493173
\(256\) −6.06059 −0.378787
\(257\) 7.37653 0.460135 0.230068 0.973175i \(-0.426105\pi\)
0.230068 + 0.973175i \(0.426105\pi\)
\(258\) −11.9615 −0.744692
\(259\) −1.83786 −0.114199
\(260\) −16.0083 −0.992791
\(261\) 51.8981 3.21241
\(262\) −51.2385 −3.16553
\(263\) 20.5740 1.26865 0.634324 0.773067i \(-0.281278\pi\)
0.634324 + 0.773067i \(0.281278\pi\)
\(264\) −94.6888 −5.82769
\(265\) −6.60248 −0.405587
\(266\) −6.14908 −0.377024
\(267\) −15.4342 −0.944560
\(268\) −68.8339 −4.20470
\(269\) −2.28741 −0.139466 −0.0697328 0.997566i \(-0.522215\pi\)
−0.0697328 + 0.997566i \(0.522215\pi\)
\(270\) 26.8564 1.63443
\(271\) −25.3112 −1.53754 −0.768772 0.639522i \(-0.779132\pi\)
−0.768772 + 0.639522i \(0.779132\pi\)
\(272\) 46.8053 2.83799
\(273\) −15.5229 −0.939491
\(274\) 52.4711 3.16989
\(275\) −16.6304 −1.00285
\(276\) −15.3234 −0.922359
\(277\) −13.7706 −0.827394 −0.413697 0.910415i \(-0.635763\pi\)
−0.413697 + 0.910415i \(0.635763\pi\)
\(278\) 52.4443 3.14540
\(279\) −36.5792 −2.18994
\(280\) −3.25989 −0.194816
\(281\) 26.5276 1.58251 0.791253 0.611489i \(-0.209429\pi\)
0.791253 + 0.611489i \(0.209429\pi\)
\(282\) 32.2850 1.92254
\(283\) 11.2254 0.667279 0.333639 0.942701i \(-0.391723\pi\)
0.333639 + 0.942701i \(0.391723\pi\)
\(284\) 33.9121 2.01232
\(285\) 5.55778 0.329214
\(286\) −55.6093 −3.28825
\(287\) 1.07842 0.0636571
\(288\) −111.008 −6.54122
\(289\) 1.49259 0.0877992
\(290\) 8.64698 0.507768
\(291\) −31.4565 −1.84401
\(292\) 15.0585 0.881234
\(293\) 21.7378 1.26994 0.634969 0.772538i \(-0.281013\pi\)
0.634969 + 0.772538i \(0.281013\pi\)
\(294\) 57.5938 3.35894
\(295\) −2.31327 −0.134684
\(296\) −18.9168 −1.09952
\(297\) 66.5829 3.86353
\(298\) −57.0485 −3.30473
\(299\) −5.38904 −0.311656
\(300\) −79.7912 −4.60675
\(301\) −1.02095 −0.0588466
\(302\) −24.7891 −1.42645
\(303\) −27.1776 −1.56131
\(304\) −33.0314 −1.89448
\(305\) −3.78537 −0.216750
\(306\) −97.1605 −5.55430
\(307\) −5.75768 −0.328608 −0.164304 0.986410i \(-0.552538\pi\)
−0.164304 + 0.986410i \(0.552538\pi\)
\(308\) −13.4961 −0.769013
\(309\) −25.1237 −1.42924
\(310\) −6.09462 −0.346151
\(311\) −27.8689 −1.58030 −0.790149 0.612914i \(-0.789997\pi\)
−0.790149 + 0.612914i \(0.789997\pi\)
\(312\) −159.775 −9.04547
\(313\) 24.4026 1.37932 0.689658 0.724135i \(-0.257761\pi\)
0.689658 + 0.724135i \(0.257761\pi\)
\(314\) 54.7615 3.09037
\(315\) 3.53167 0.198987
\(316\) −32.5094 −1.82880
\(317\) 32.9600 1.85122 0.925608 0.378484i \(-0.123554\pi\)
0.925608 + 0.378484i \(0.123554\pi\)
\(318\) −110.043 −6.17091
\(319\) 21.4377 1.20028
\(320\) −6.76465 −0.378155
\(321\) 23.5519 1.31454
\(322\) −1.83258 −0.102125
\(323\) −13.0506 −0.726153
\(324\) 191.603 10.6446
\(325\) −28.0616 −1.55658
\(326\) −8.97632 −0.497153
\(327\) 11.4047 0.630680
\(328\) 11.1000 0.612894
\(329\) 2.75562 0.151922
\(330\) 17.0918 0.940875
\(331\) −18.7262 −1.02929 −0.514643 0.857404i \(-0.672076\pi\)
−0.514643 + 0.857404i \(0.672076\pi\)
\(332\) −57.6538 −3.16416
\(333\) 20.4939 1.12306
\(334\) 63.2811 3.46259
\(335\) 7.44047 0.406516
\(336\) −28.3557 −1.54693
\(337\) 1.42709 0.0777383 0.0388691 0.999244i \(-0.487624\pi\)
0.0388691 + 0.999244i \(0.487624\pi\)
\(338\) −59.4742 −3.23497
\(339\) −1.63891 −0.0890132
\(340\) −11.5535 −0.626577
\(341\) −15.1099 −0.818245
\(342\) 68.5680 3.70773
\(343\) 10.2821 0.555184
\(344\) −10.5085 −0.566579
\(345\) 1.65635 0.0891750
\(346\) −17.4694 −0.939159
\(347\) −3.87199 −0.207859 −0.103930 0.994585i \(-0.533142\pi\)
−0.103930 + 0.994585i \(0.533142\pi\)
\(348\) 102.856 5.51368
\(349\) 11.7362 0.628224 0.314112 0.949386i \(-0.398293\pi\)
0.314112 + 0.949386i \(0.398293\pi\)
\(350\) −9.54251 −0.510068
\(351\) 112.350 5.99679
\(352\) −45.8545 −2.44406
\(353\) 16.8316 0.895855 0.447928 0.894070i \(-0.352162\pi\)
0.447928 + 0.894070i \(0.352162\pi\)
\(354\) −38.5552 −2.04918
\(355\) −3.66567 −0.194554
\(356\) −22.6428 −1.20007
\(357\) −11.2032 −0.592938
\(358\) 47.6165 2.51661
\(359\) 8.79034 0.463937 0.231968 0.972723i \(-0.425483\pi\)
0.231968 + 0.972723i \(0.425483\pi\)
\(360\) 36.3509 1.91586
\(361\) −9.78997 −0.515261
\(362\) 14.4959 0.761887
\(363\) 4.99285 0.262057
\(364\) −22.7729 −1.19362
\(365\) −1.62773 −0.0851990
\(366\) −63.0905 −3.29779
\(367\) 35.0997 1.83219 0.916095 0.400962i \(-0.131324\pi\)
0.916095 + 0.400962i \(0.131324\pi\)
\(368\) −9.84416 −0.513162
\(369\) −12.0254 −0.626017
\(370\) 3.41458 0.177516
\(371\) −9.39250 −0.487634
\(372\) −72.4959 −3.75874
\(373\) −34.4225 −1.78233 −0.891166 0.453678i \(-0.850112\pi\)
−0.891166 + 0.453678i \(0.850112\pi\)
\(374\) −40.1344 −2.07530
\(375\) 17.7816 0.918239
\(376\) 28.3631 1.46271
\(377\) 36.1733 1.86302
\(378\) 38.2052 1.96506
\(379\) −34.7481 −1.78489 −0.892444 0.451158i \(-0.851011\pi\)
−0.892444 + 0.451158i \(0.851011\pi\)
\(380\) 8.15353 0.418267
\(381\) 16.8522 0.863366
\(382\) 31.1027 1.59135
\(383\) 14.7302 0.752676 0.376338 0.926482i \(-0.377183\pi\)
0.376338 + 0.926482i \(0.377183\pi\)
\(384\) −24.4874 −1.24962
\(385\) 1.45884 0.0743493
\(386\) −9.29064 −0.472881
\(387\) 11.3846 0.578710
\(388\) −46.1483 −2.34282
\(389\) −5.57475 −0.282651 −0.141326 0.989963i \(-0.545136\pi\)
−0.141326 + 0.989963i \(0.545136\pi\)
\(390\) 28.8402 1.46038
\(391\) −3.88939 −0.196695
\(392\) 50.5975 2.55556
\(393\) 65.8812 3.32327
\(394\) 16.7293 0.842812
\(395\) 3.51405 0.176811
\(396\) 150.494 7.56263
\(397\) 5.01910 0.251902 0.125951 0.992036i \(-0.459802\pi\)
0.125951 + 0.992036i \(0.459802\pi\)
\(398\) 11.0629 0.554531
\(399\) 7.90633 0.395812
\(400\) −51.2601 −2.56300
\(401\) 28.4081 1.41863 0.709317 0.704890i \(-0.249003\pi\)
0.709317 + 0.704890i \(0.249003\pi\)
\(402\) 124.010 6.18505
\(403\) −25.4959 −1.27004
\(404\) −39.8709 −1.98365
\(405\) −20.7110 −1.02914
\(406\) 12.3009 0.610485
\(407\) 8.46549 0.419619
\(408\) −115.313 −5.70884
\(409\) 1.66558 0.0823578 0.0411789 0.999152i \(-0.486889\pi\)
0.0411789 + 0.999152i \(0.486889\pi\)
\(410\) −2.00361 −0.0989510
\(411\) −67.4660 −3.32785
\(412\) −36.8577 −1.81585
\(413\) −3.29080 −0.161930
\(414\) 20.4349 1.00432
\(415\) 6.23198 0.305916
\(416\) −77.3735 −3.79355
\(417\) −67.4315 −3.30214
\(418\) 28.3236 1.38535
\(419\) −25.1116 −1.22678 −0.613390 0.789780i \(-0.710195\pi\)
−0.613390 + 0.789780i \(0.710195\pi\)
\(420\) 6.99938 0.341535
\(421\) 8.09141 0.394351 0.197176 0.980368i \(-0.436823\pi\)
0.197176 + 0.980368i \(0.436823\pi\)
\(422\) −34.4074 −1.67493
\(423\) −30.7277 −1.49403
\(424\) −96.6754 −4.69497
\(425\) −20.2526 −0.982398
\(426\) −61.0955 −2.96009
\(427\) −5.38496 −0.260596
\(428\) 34.5518 1.67013
\(429\) 71.5011 3.45210
\(430\) 1.89684 0.0914735
\(431\) −12.9219 −0.622428 −0.311214 0.950340i \(-0.600736\pi\)
−0.311214 + 0.950340i \(0.600736\pi\)
\(432\) 205.229 9.87410
\(433\) −6.57882 −0.316158 −0.158079 0.987426i \(-0.550530\pi\)
−0.158079 + 0.987426i \(0.550530\pi\)
\(434\) −8.67003 −0.416175
\(435\) −11.1181 −0.533071
\(436\) 16.7312 0.801280
\(437\) 2.74481 0.131302
\(438\) −27.1292 −1.29628
\(439\) 20.9929 1.00194 0.500969 0.865465i \(-0.332977\pi\)
0.500969 + 0.865465i \(0.332977\pi\)
\(440\) 15.0156 0.715839
\(441\) −54.8158 −2.61028
\(442\) −67.7215 −3.22119
\(443\) 5.70417 0.271013 0.135507 0.990776i \(-0.456734\pi\)
0.135507 + 0.990776i \(0.456734\pi\)
\(444\) 40.6167 1.92758
\(445\) 2.44753 0.116024
\(446\) −27.9980 −1.32574
\(447\) 73.3515 3.46941
\(448\) −9.62319 −0.454653
\(449\) −32.9101 −1.55312 −0.776562 0.630041i \(-0.783038\pi\)
−0.776562 + 0.630041i \(0.783038\pi\)
\(450\) 106.408 5.01612
\(451\) −4.96737 −0.233904
\(452\) −2.40436 −0.113091
\(453\) 31.8732 1.49753
\(454\) 38.2359 1.79450
\(455\) 2.46160 0.115401
\(456\) 81.3785 3.81090
\(457\) 37.6707 1.76216 0.881081 0.472966i \(-0.156817\pi\)
0.881081 + 0.472966i \(0.156817\pi\)
\(458\) −16.3289 −0.762998
\(459\) 81.0853 3.78474
\(460\) 2.42995 0.113297
\(461\) 21.9097 1.02044 0.510218 0.860045i \(-0.329565\pi\)
0.510218 + 0.860045i \(0.329565\pi\)
\(462\) 24.3144 1.13121
\(463\) 37.9279 1.76266 0.881329 0.472502i \(-0.156649\pi\)
0.881329 + 0.472502i \(0.156649\pi\)
\(464\) 66.0777 3.06758
\(465\) 7.83631 0.363400
\(466\) −18.0236 −0.834929
\(467\) −4.06536 −0.188122 −0.0940612 0.995566i \(-0.529985\pi\)
−0.0940612 + 0.995566i \(0.529985\pi\)
\(468\) 253.939 11.7384
\(469\) 10.5846 0.488751
\(470\) −5.11969 −0.236154
\(471\) −70.4110 −3.24437
\(472\) −33.8716 −1.55907
\(473\) 4.70266 0.216229
\(474\) 58.5683 2.69013
\(475\) 14.2927 0.655793
\(476\) −16.4357 −0.753329
\(477\) 104.735 4.79550
\(478\) 63.7785 2.91716
\(479\) 23.7766 1.08638 0.543190 0.839610i \(-0.317216\pi\)
0.543190 + 0.839610i \(0.317216\pi\)
\(480\) 23.7812 1.08546
\(481\) 14.2844 0.651312
\(482\) −64.7881 −2.95102
\(483\) 2.35628 0.107214
\(484\) 7.32476 0.332944
\(485\) 4.98831 0.226508
\(486\) −195.681 −8.87625
\(487\) −29.0815 −1.31781 −0.658905 0.752226i \(-0.728980\pi\)
−0.658905 + 0.752226i \(0.728980\pi\)
\(488\) −55.4264 −2.50904
\(489\) 11.5415 0.521926
\(490\) −9.13311 −0.412592
\(491\) −29.3129 −1.32287 −0.661437 0.750001i \(-0.730053\pi\)
−0.661437 + 0.750001i \(0.730053\pi\)
\(492\) −23.8330 −1.07448
\(493\) 26.1070 1.17580
\(494\) 47.7924 2.15028
\(495\) −16.2674 −0.731166
\(496\) −46.5733 −2.09120
\(497\) −5.21468 −0.233910
\(498\) 103.868 4.65444
\(499\) −5.00868 −0.224219 −0.112110 0.993696i \(-0.535761\pi\)
−0.112110 + 0.993696i \(0.535761\pi\)
\(500\) 26.0865 1.16662
\(501\) −81.3653 −3.63513
\(502\) −10.9387 −0.488218
\(503\) 28.9435 1.29053 0.645264 0.763959i \(-0.276747\pi\)
0.645264 + 0.763959i \(0.276747\pi\)
\(504\) 51.7117 2.30342
\(505\) 4.30978 0.191783
\(506\) 8.44113 0.375254
\(507\) 76.4705 3.39617
\(508\) 24.7231 1.09691
\(509\) 19.1032 0.846733 0.423367 0.905958i \(-0.360848\pi\)
0.423367 + 0.905958i \(0.360848\pi\)
\(510\) 20.8146 0.921686
\(511\) −2.31556 −0.102434
\(512\) 30.4297 1.34482
\(513\) −57.2234 −2.52648
\(514\) −19.4962 −0.859942
\(515\) 3.98406 0.175559
\(516\) 22.5630 0.993280
\(517\) −12.6928 −0.558229
\(518\) 4.85749 0.213426
\(519\) 22.4617 0.985958
\(520\) 25.3368 1.11109
\(521\) −30.4577 −1.33438 −0.667188 0.744889i \(-0.732502\pi\)
−0.667188 + 0.744889i \(0.732502\pi\)
\(522\) −137.167 −6.00364
\(523\) 12.2475 0.535546 0.267773 0.963482i \(-0.413712\pi\)
0.267773 + 0.963482i \(0.413712\pi\)
\(524\) 96.6510 4.22222
\(525\) 12.2695 0.535486
\(526\) −54.3773 −2.37096
\(527\) −18.4009 −0.801558
\(528\) 130.611 5.68411
\(529\) −22.1820 −0.964434
\(530\) 17.4504 0.757998
\(531\) 36.6955 1.59245
\(532\) 11.5990 0.502880
\(533\) −8.38178 −0.363055
\(534\) 40.7928 1.76528
\(535\) −3.73482 −0.161470
\(536\) 108.945 4.70573
\(537\) −61.2242 −2.64202
\(538\) 6.04564 0.260646
\(539\) −22.6429 −0.975301
\(540\) −50.6592 −2.18003
\(541\) −18.1901 −0.782053 −0.391026 0.920380i \(-0.627880\pi\)
−0.391026 + 0.920380i \(0.627880\pi\)
\(542\) 66.8977 2.87350
\(543\) −18.6385 −0.799853
\(544\) −55.8421 −2.39421
\(545\) −1.80853 −0.0774689
\(546\) 41.0273 1.75580
\(547\) −15.2069 −0.650202 −0.325101 0.945679i \(-0.605398\pi\)
−0.325101 + 0.945679i \(0.605398\pi\)
\(548\) −98.9760 −4.22804
\(549\) 60.0474 2.56276
\(550\) 43.9543 1.87422
\(551\) −18.4242 −0.784899
\(552\) 24.2528 1.03227
\(553\) 4.99898 0.212578
\(554\) 36.3958 1.54631
\(555\) −4.39039 −0.186362
\(556\) −98.9254 −4.19537
\(557\) −27.2107 −1.15296 −0.576478 0.817113i \(-0.695573\pi\)
−0.576478 + 0.817113i \(0.695573\pi\)
\(558\) 96.6790 4.09275
\(559\) 7.93512 0.335620
\(560\) 4.49659 0.190016
\(561\) 51.6038 2.17872
\(562\) −70.1128 −2.95753
\(563\) −8.92123 −0.375985 −0.187993 0.982170i \(-0.560198\pi\)
−0.187993 + 0.982170i \(0.560198\pi\)
\(564\) −60.8990 −2.56431
\(565\) 0.259895 0.0109339
\(566\) −29.6688 −1.24707
\(567\) −29.4628 −1.23732
\(568\) −53.6738 −2.25210
\(569\) 8.53413 0.357769 0.178885 0.983870i \(-0.442751\pi\)
0.178885 + 0.983870i \(0.442751\pi\)
\(570\) −14.6893 −0.615265
\(571\) −42.9954 −1.79930 −0.899651 0.436609i \(-0.856179\pi\)
−0.899651 + 0.436609i \(0.856179\pi\)
\(572\) 104.896 4.38591
\(573\) −39.9911 −1.67065
\(574\) −2.85027 −0.118968
\(575\) 4.25957 0.177636
\(576\) 107.308 4.47115
\(577\) −21.7602 −0.905890 −0.452945 0.891539i \(-0.649627\pi\)
−0.452945 + 0.891539i \(0.649627\pi\)
\(578\) −3.94492 −0.164087
\(579\) 11.9457 0.496445
\(580\) −16.3108 −0.677267
\(581\) 8.86544 0.367800
\(582\) 83.1398 3.44626
\(583\) 43.2633 1.79178
\(584\) −23.8336 −0.986242
\(585\) −27.4491 −1.13488
\(586\) −57.4533 −2.37337
\(587\) 3.16774 0.130746 0.0653732 0.997861i \(-0.479176\pi\)
0.0653732 + 0.997861i \(0.479176\pi\)
\(588\) −108.639 −4.48019
\(589\) 12.9859 0.535074
\(590\) 6.11400 0.251710
\(591\) −21.5102 −0.884810
\(592\) 26.0933 1.07243
\(593\) −30.9260 −1.26998 −0.634989 0.772521i \(-0.718995\pi\)
−0.634989 + 0.772521i \(0.718995\pi\)
\(594\) −175.979 −7.22051
\(595\) 1.77659 0.0728329
\(596\) 107.610 4.40789
\(597\) −14.2243 −0.582164
\(598\) 14.2433 0.582451
\(599\) −12.3337 −0.503943 −0.251972 0.967735i \(-0.581079\pi\)
−0.251972 + 0.967735i \(0.581079\pi\)
\(600\) 126.288 5.15569
\(601\) 25.9101 1.05689 0.528447 0.848966i \(-0.322774\pi\)
0.528447 + 0.848966i \(0.322774\pi\)
\(602\) 2.69838 0.109978
\(603\) −118.028 −4.80648
\(604\) 46.7595 1.90262
\(605\) −0.791757 −0.0321895
\(606\) 71.8307 2.91792
\(607\) 37.6259 1.52719 0.763595 0.645696i \(-0.223433\pi\)
0.763595 + 0.645696i \(0.223433\pi\)
\(608\) 39.4088 1.59824
\(609\) −15.8162 −0.640907
\(610\) 10.0048 0.405081
\(611\) −21.4174 −0.866456
\(612\) 183.274 7.40839
\(613\) 20.9962 0.848029 0.424015 0.905655i \(-0.360620\pi\)
0.424015 + 0.905655i \(0.360620\pi\)
\(614\) 15.2176 0.614133
\(615\) 2.57619 0.103882
\(616\) 21.3607 0.860648
\(617\) 15.0335 0.605224 0.302612 0.953114i \(-0.402141\pi\)
0.302612 + 0.953114i \(0.402141\pi\)
\(618\) 66.4021 2.67108
\(619\) 19.7248 0.792806 0.396403 0.918077i \(-0.370258\pi\)
0.396403 + 0.918077i \(0.370258\pi\)
\(620\) 11.4963 0.461701
\(621\) −17.0540 −0.684352
\(622\) 73.6577 2.95340
\(623\) 3.48179 0.139495
\(624\) 220.389 8.82261
\(625\) 20.7282 0.829127
\(626\) −64.4963 −2.57779
\(627\) −36.4178 −1.45439
\(628\) −103.296 −4.12198
\(629\) 10.3093 0.411061
\(630\) −9.33423 −0.371885
\(631\) 3.32990 0.132561 0.0662807 0.997801i \(-0.478887\pi\)
0.0662807 + 0.997801i \(0.478887\pi\)
\(632\) 51.4536 2.04672
\(633\) 44.2402 1.75839
\(634\) −87.1135 −3.45972
\(635\) −2.67239 −0.106051
\(636\) 207.574 8.23084
\(637\) −38.2070 −1.51382
\(638\) −56.6601 −2.24319
\(639\) 58.1486 2.30032
\(640\) 3.88317 0.153496
\(641\) −0.774237 −0.0305805 −0.0152903 0.999883i \(-0.504867\pi\)
−0.0152903 + 0.999883i \(0.504867\pi\)
\(642\) −62.2479 −2.45673
\(643\) 36.2381 1.42909 0.714546 0.699589i \(-0.246633\pi\)
0.714546 + 0.699589i \(0.246633\pi\)
\(644\) 3.45678 0.136216
\(645\) −2.43890 −0.0960317
\(646\) 34.4928 1.35710
\(647\) −30.1243 −1.18431 −0.592153 0.805825i \(-0.701722\pi\)
−0.592153 + 0.805825i \(0.701722\pi\)
\(648\) −303.256 −11.9130
\(649\) 15.1579 0.595001
\(650\) 74.1670 2.90907
\(651\) 11.1477 0.436913
\(652\) 16.9320 0.663108
\(653\) 16.2875 0.637379 0.318689 0.947859i \(-0.396757\pi\)
0.318689 + 0.947859i \(0.396757\pi\)
\(654\) −30.1426 −1.17867
\(655\) −10.4473 −0.408210
\(656\) −15.3110 −0.597793
\(657\) 25.8206 1.00736
\(658\) −7.28312 −0.283925
\(659\) −48.5799 −1.89241 −0.946203 0.323574i \(-0.895116\pi\)
−0.946203 + 0.323574i \(0.895116\pi\)
\(660\) −32.2403 −1.25495
\(661\) 12.9403 0.503318 0.251659 0.967816i \(-0.419024\pi\)
0.251659 + 0.967816i \(0.419024\pi\)
\(662\) 49.4936 1.92362
\(663\) 87.0747 3.38170
\(664\) 91.2504 3.54120
\(665\) −1.25377 −0.0486191
\(666\) −54.1656 −2.09887
\(667\) −5.49087 −0.212607
\(668\) −119.367 −4.61844
\(669\) 35.9991 1.39181
\(670\) −19.6652 −0.759734
\(671\) 24.8040 0.957546
\(672\) 33.8304 1.30504
\(673\) −39.6373 −1.52791 −0.763953 0.645272i \(-0.776744\pi\)
−0.763953 + 0.645272i \(0.776744\pi\)
\(674\) −3.77180 −0.145284
\(675\) −88.8027 −3.41802
\(676\) 112.186 4.31485
\(677\) 1.73122 0.0665361 0.0332680 0.999446i \(-0.489408\pi\)
0.0332680 + 0.999446i \(0.489408\pi\)
\(678\) 4.33165 0.166356
\(679\) 7.09623 0.272328
\(680\) 18.2861 0.701240
\(681\) −49.1627 −1.88392
\(682\) 39.9355 1.52921
\(683\) −15.6405 −0.598467 −0.299233 0.954180i \(-0.596731\pi\)
−0.299233 + 0.954180i \(0.596731\pi\)
\(684\) −129.340 −4.94542
\(685\) 10.6986 0.408773
\(686\) −27.1758 −1.03758
\(687\) 20.9953 0.801019
\(688\) 14.4951 0.552619
\(689\) 73.0012 2.78112
\(690\) −4.37776 −0.166658
\(691\) −14.9599 −0.569102 −0.284551 0.958661i \(-0.591845\pi\)
−0.284551 + 0.958661i \(0.591845\pi\)
\(692\) 32.9524 1.25266
\(693\) −23.1416 −0.879075
\(694\) 10.2337 0.388466
\(695\) 10.6932 0.405615
\(696\) −162.794 −6.17068
\(697\) −6.04931 −0.229134
\(698\) −31.0188 −1.17408
\(699\) 23.1744 0.876535
\(700\) 18.0000 0.680336
\(701\) 24.9631 0.942842 0.471421 0.881908i \(-0.343741\pi\)
0.471421 + 0.881908i \(0.343741\pi\)
\(702\) −296.942 −11.2073
\(703\) −7.27550 −0.274401
\(704\) 44.3259 1.67060
\(705\) 6.58277 0.247921
\(706\) −44.4860 −1.67425
\(707\) 6.13096 0.230579
\(708\) 72.7265 2.73323
\(709\) −48.8325 −1.83394 −0.916971 0.398955i \(-0.869373\pi\)
−0.916971 + 0.398955i \(0.869373\pi\)
\(710\) 9.68840 0.363599
\(711\) −55.7433 −2.09054
\(712\) 35.8374 1.34306
\(713\) 3.87011 0.144937
\(714\) 29.6102 1.10814
\(715\) −11.3385 −0.424036
\(716\) −89.8189 −3.35669
\(717\) −82.0049 −3.06253
\(718\) −23.2330 −0.867046
\(719\) 37.6124 1.40270 0.701352 0.712815i \(-0.252580\pi\)
0.701352 + 0.712815i \(0.252580\pi\)
\(720\) −50.1413 −1.86865
\(721\) 5.66761 0.211073
\(722\) 25.8750 0.962967
\(723\) 83.3029 3.09807
\(724\) −27.3435 −1.01621
\(725\) −28.5918 −1.06187
\(726\) −13.1962 −0.489755
\(727\) 43.6749 1.61981 0.809906 0.586560i \(-0.199518\pi\)
0.809906 + 0.586560i \(0.199518\pi\)
\(728\) 36.0434 1.33586
\(729\) 136.305 5.04834
\(730\) 4.30209 0.159228
\(731\) 5.72695 0.211819
\(732\) 119.007 4.39864
\(733\) −25.4278 −0.939198 −0.469599 0.882880i \(-0.655602\pi\)
−0.469599 + 0.882880i \(0.655602\pi\)
\(734\) −92.7688 −3.42416
\(735\) 11.7431 0.433152
\(736\) 11.7448 0.432919
\(737\) −48.7543 −1.79589
\(738\) 31.7832 1.16996
\(739\) 16.4385 0.604701 0.302351 0.953197i \(-0.402229\pi\)
0.302351 + 0.953197i \(0.402229\pi\)
\(740\) −6.44092 −0.236773
\(741\) −61.4502 −2.25743
\(742\) 24.8245 0.911335
\(743\) −13.1615 −0.482848 −0.241424 0.970420i \(-0.577615\pi\)
−0.241424 + 0.970420i \(0.577615\pi\)
\(744\) 114.741 4.20663
\(745\) −11.6319 −0.426161
\(746\) 90.9791 3.33098
\(747\) −98.8580 −3.61702
\(748\) 75.7054 2.76806
\(749\) −5.31304 −0.194134
\(750\) −46.9970 −1.71609
\(751\) −2.19127 −0.0799605 −0.0399802 0.999200i \(-0.512729\pi\)
−0.0399802 + 0.999200i \(0.512729\pi\)
\(752\) −39.1232 −1.42668
\(753\) 14.0647 0.512546
\(754\) −95.6064 −3.48178
\(755\) −5.05438 −0.183948
\(756\) −72.0663 −2.62103
\(757\) −9.12413 −0.331622 −0.165811 0.986158i \(-0.553024\pi\)
−0.165811 + 0.986158i \(0.553024\pi\)
\(758\) 91.8395 3.33576
\(759\) −10.8534 −0.393953
\(760\) −12.9048 −0.468108
\(761\) −22.3110 −0.808773 −0.404387 0.914588i \(-0.632515\pi\)
−0.404387 + 0.914588i \(0.632515\pi\)
\(762\) −44.5406 −1.61354
\(763\) −2.57276 −0.0931403
\(764\) −58.6690 −2.12257
\(765\) −19.8106 −0.716254
\(766\) −38.9320 −1.40667
\(767\) 25.5770 0.923532
\(768\) −20.5958 −0.743187
\(769\) −21.9569 −0.791786 −0.395893 0.918297i \(-0.629565\pi\)
−0.395893 + 0.918297i \(0.629565\pi\)
\(770\) −3.85572 −0.138951
\(771\) 25.0678 0.902794
\(772\) 17.5249 0.630735
\(773\) 37.9323 1.36433 0.682165 0.731198i \(-0.261039\pi\)
0.682165 + 0.731198i \(0.261039\pi\)
\(774\) −30.0895 −1.08155
\(775\) 20.1523 0.723891
\(776\) 73.0402 2.62199
\(777\) −6.24564 −0.224061
\(778\) 14.7341 0.528244
\(779\) 4.26911 0.152957
\(780\) −54.4012 −1.94787
\(781\) 24.0196 0.859490
\(782\) 10.2797 0.367601
\(783\) 114.473 4.09092
\(784\) −69.7926 −2.49259
\(785\) 11.1656 0.398519
\(786\) −174.125 −6.21082
\(787\) 2.92294 0.104191 0.0520957 0.998642i \(-0.483410\pi\)
0.0520957 + 0.998642i \(0.483410\pi\)
\(788\) −31.5565 −1.12415
\(789\) 69.9170 2.48911
\(790\) −9.28765 −0.330440
\(791\) 0.369719 0.0131457
\(792\) −238.192 −8.46379
\(793\) 41.8534 1.48626
\(794\) −13.2655 −0.470776
\(795\) −22.4373 −0.795770
\(796\) −20.8678 −0.739640
\(797\) 18.6167 0.659438 0.329719 0.944079i \(-0.393046\pi\)
0.329719 + 0.944079i \(0.393046\pi\)
\(798\) −20.8965 −0.739728
\(799\) −15.4574 −0.546844
\(800\) 61.1569 2.16222
\(801\) −38.8252 −1.37182
\(802\) −75.0829 −2.65127
\(803\) 10.6658 0.376388
\(804\) −233.919 −8.24970
\(805\) −0.373654 −0.0131696
\(806\) 67.3859 2.37357
\(807\) −7.77333 −0.273634
\(808\) 63.1049 2.22002
\(809\) −29.7620 −1.04638 −0.523189 0.852217i \(-0.675258\pi\)
−0.523189 + 0.852217i \(0.675258\pi\)
\(810\) 54.7393 1.92334
\(811\) −37.3455 −1.31138 −0.655690 0.755030i \(-0.727622\pi\)
−0.655690 + 0.755030i \(0.727622\pi\)
\(812\) −23.2032 −0.814273
\(813\) −86.0154 −3.01669
\(814\) −22.3744 −0.784221
\(815\) −1.83023 −0.0641103
\(816\) 159.059 5.56819
\(817\) −4.04161 −0.141398
\(818\) −4.40215 −0.153918
\(819\) −39.0483 −1.36446
\(820\) 3.77939 0.131982
\(821\) 5.14191 0.179454 0.0897269 0.995966i \(-0.471401\pi\)
0.0897269 + 0.995966i \(0.471401\pi\)
\(822\) 178.313 6.21939
\(823\) 19.3509 0.674528 0.337264 0.941410i \(-0.390498\pi\)
0.337264 + 0.941410i \(0.390498\pi\)
\(824\) 58.3358 2.03222
\(825\) −56.5153 −1.96761
\(826\) 8.69761 0.302628
\(827\) 28.5534 0.992900 0.496450 0.868065i \(-0.334637\pi\)
0.496450 + 0.868065i \(0.334637\pi\)
\(828\) −38.5464 −1.33958
\(829\) −34.2301 −1.18886 −0.594431 0.804147i \(-0.702623\pi\)
−0.594431 + 0.804147i \(0.702623\pi\)
\(830\) −16.4712 −0.571723
\(831\) −46.7968 −1.62336
\(832\) 74.7942 2.59302
\(833\) −27.5748 −0.955410
\(834\) 178.222 6.17133
\(835\) 12.9027 0.446518
\(836\) −53.4267 −1.84780
\(837\) −80.6834 −2.78883
\(838\) 66.3701 2.29272
\(839\) −5.87969 −0.202989 −0.101495 0.994836i \(-0.532362\pi\)
−0.101495 + 0.994836i \(0.532362\pi\)
\(840\) −11.0781 −0.382232
\(841\) 7.85681 0.270924
\(842\) −21.3857 −0.736999
\(843\) 90.1493 3.10491
\(844\) 64.9026 2.23404
\(845\) −12.1265 −0.417166
\(846\) 81.2136 2.79218
\(847\) −1.12633 −0.0387012
\(848\) 133.351 4.57930
\(849\) 38.1473 1.30921
\(850\) 53.5279 1.83599
\(851\) −2.16828 −0.0743276
\(852\) 115.244 3.94820
\(853\) 20.0162 0.685343 0.342671 0.939455i \(-0.388668\pi\)
0.342671 + 0.939455i \(0.388668\pi\)
\(854\) 14.2325 0.487026
\(855\) 13.9807 0.478131
\(856\) −54.6862 −1.86914
\(857\) 17.1083 0.584408 0.292204 0.956356i \(-0.405611\pi\)
0.292204 + 0.956356i \(0.405611\pi\)
\(858\) −188.978 −6.45160
\(859\) −47.4499 −1.61897 −0.809485 0.587141i \(-0.800253\pi\)
−0.809485 + 0.587141i \(0.800253\pi\)
\(860\) −3.57799 −0.122009
\(861\) 3.66481 0.124896
\(862\) 34.1528 1.16325
\(863\) 24.6280 0.838348 0.419174 0.907906i \(-0.362320\pi\)
0.419174 + 0.907906i \(0.362320\pi\)
\(864\) −244.853 −8.33008
\(865\) −3.56193 −0.121109
\(866\) 17.3879 0.590864
\(867\) 5.07228 0.172264
\(868\) 16.3542 0.555099
\(869\) −23.0261 −0.781106
\(870\) 29.3852 0.996250
\(871\) −82.2665 −2.78749
\(872\) −26.4810 −0.896760
\(873\) −79.1296 −2.67813
\(874\) −7.25457 −0.245389
\(875\) −4.01133 −0.135608
\(876\) 51.1737 1.72900
\(877\) 36.1108 1.21938 0.609688 0.792641i \(-0.291295\pi\)
0.609688 + 0.792641i \(0.291295\pi\)
\(878\) −55.4845 −1.87251
\(879\) 73.8720 2.49164
\(880\) −20.7120 −0.698202
\(881\) −54.6533 −1.84132 −0.920659 0.390369i \(-0.872348\pi\)
−0.920659 + 0.390369i \(0.872348\pi\)
\(882\) 144.879 4.87832
\(883\) 4.44337 0.149531 0.0747657 0.997201i \(-0.476179\pi\)
0.0747657 + 0.997201i \(0.476179\pi\)
\(884\) 127.743 4.29646
\(885\) −7.86123 −0.264252
\(886\) −15.0762 −0.506494
\(887\) −2.56509 −0.0861274 −0.0430637 0.999072i \(-0.513712\pi\)
−0.0430637 + 0.999072i \(0.513712\pi\)
\(888\) −64.2853 −2.15727
\(889\) −3.80167 −0.127504
\(890\) −6.46885 −0.216836
\(891\) 135.710 4.54647
\(892\) 52.8125 1.76829
\(893\) 10.9086 0.365042
\(894\) −193.869 −6.48394
\(895\) 9.70881 0.324530
\(896\) 5.52409 0.184547
\(897\) −18.3137 −0.611476
\(898\) 86.9817 2.90262
\(899\) −25.9777 −0.866404
\(900\) −200.717 −6.69056
\(901\) 52.6865 1.75524
\(902\) 13.1288 0.437141
\(903\) −3.46951 −0.115458
\(904\) 3.80545 0.126567
\(905\) 2.95565 0.0982491
\(906\) −84.2410 −2.79872
\(907\) 28.7252 0.953803 0.476902 0.878957i \(-0.341760\pi\)
0.476902 + 0.878957i \(0.341760\pi\)
\(908\) −72.1241 −2.39352
\(909\) −68.3660 −2.26756
\(910\) −6.50602 −0.215673
\(911\) 40.6836 1.34791 0.673953 0.738774i \(-0.264595\pi\)
0.673953 + 0.738774i \(0.264595\pi\)
\(912\) −112.251 −3.71700
\(913\) −40.8356 −1.35146
\(914\) −99.5640 −3.29329
\(915\) −12.8639 −0.425267
\(916\) 30.8011 1.01770
\(917\) −14.8621 −0.490788
\(918\) −214.309 −7.07326
\(919\) −0.463363 −0.0152849 −0.00764247 0.999971i \(-0.502433\pi\)
−0.00764247 + 0.999971i \(0.502433\pi\)
\(920\) −3.84596 −0.126797
\(921\) −19.5664 −0.644736
\(922\) −57.9075 −1.90708
\(923\) 40.5299 1.33406
\(924\) −45.8641 −1.50882
\(925\) −11.2906 −0.371231
\(926\) −100.244 −3.29422
\(927\) −63.1992 −2.07574
\(928\) −78.8355 −2.58790
\(929\) −18.7449 −0.615001 −0.307500 0.951548i \(-0.599493\pi\)
−0.307500 + 0.951548i \(0.599493\pi\)
\(930\) −20.7114 −0.679155
\(931\) 19.4600 0.637777
\(932\) 33.9979 1.11364
\(933\) −94.7072 −3.10057
\(934\) 10.7448 0.351580
\(935\) −8.18324 −0.267620
\(936\) −401.918 −13.1371
\(937\) −30.8652 −1.00832 −0.504161 0.863609i \(-0.668198\pi\)
−0.504161 + 0.863609i \(0.668198\pi\)
\(938\) −27.9752 −0.913422
\(939\) 82.9277 2.70624
\(940\) 9.65724 0.314985
\(941\) 9.02895 0.294335 0.147168 0.989112i \(-0.452984\pi\)
0.147168 + 0.989112i \(0.452984\pi\)
\(942\) 186.097 6.06336
\(943\) 1.27230 0.0414318
\(944\) 46.7215 1.52065
\(945\) 7.78988 0.253405
\(946\) −12.4292 −0.404107
\(947\) 34.9491 1.13569 0.567846 0.823135i \(-0.307777\pi\)
0.567846 + 0.823135i \(0.307777\pi\)
\(948\) −110.477 −3.58813
\(949\) 17.9971 0.584212
\(950\) −37.7757 −1.22560
\(951\) 112.008 3.63212
\(952\) 26.0133 0.843095
\(953\) −4.88111 −0.158115 −0.0790574 0.996870i \(-0.525191\pi\)
−0.0790574 + 0.996870i \(0.525191\pi\)
\(954\) −276.816 −8.96226
\(955\) 6.34172 0.205213
\(956\) −120.305 −3.89095
\(957\) 72.8521 2.35497
\(958\) −62.8417 −2.03032
\(959\) 15.2196 0.491465
\(960\) −22.9884 −0.741948
\(961\) −12.6903 −0.409363
\(962\) −37.7538 −1.21723
\(963\) 59.2454 1.90916
\(964\) 122.209 3.93610
\(965\) −1.89432 −0.0609804
\(966\) −6.22767 −0.200372
\(967\) −7.59910 −0.244370 −0.122185 0.992507i \(-0.538990\pi\)
−0.122185 + 0.992507i \(0.538990\pi\)
\(968\) −11.5931 −0.372617
\(969\) −44.3500 −1.42473
\(970\) −13.1842 −0.423318
\(971\) 28.6258 0.918647 0.459323 0.888269i \(-0.348092\pi\)
0.459323 + 0.888269i \(0.348092\pi\)
\(972\) 369.112 11.8393
\(973\) 15.2118 0.487667
\(974\) 76.8628 2.46284
\(975\) −95.3621 −3.05403
\(976\) 76.4535 2.44722
\(977\) 48.9492 1.56602 0.783012 0.622007i \(-0.213682\pi\)
0.783012 + 0.622007i \(0.213682\pi\)
\(978\) −30.5044 −0.975423
\(979\) −16.0377 −0.512566
\(980\) 17.2278 0.550320
\(981\) 28.6887 0.915961
\(982\) 77.4743 2.47231
\(983\) −45.0087 −1.43555 −0.717777 0.696273i \(-0.754840\pi\)
−0.717777 + 0.696273i \(0.754840\pi\)
\(984\) 37.7212 1.20251
\(985\) 3.41104 0.108685
\(986\) −69.0012 −2.19744
\(987\) 9.36445 0.298074
\(988\) −90.1506 −2.86807
\(989\) −1.20450 −0.0383009
\(990\) 42.9949 1.36647
\(991\) 56.2460 1.78671 0.893356 0.449350i \(-0.148344\pi\)
0.893356 + 0.449350i \(0.148344\pi\)
\(992\) 55.5653 1.76420
\(993\) −63.6376 −2.01948
\(994\) 13.7824 0.437152
\(995\) 2.25567 0.0715095
\(996\) −195.926 −6.20815
\(997\) −1.58315 −0.0501389 −0.0250694 0.999686i \(-0.507981\pi\)
−0.0250694 + 0.999686i \(0.507981\pi\)
\(998\) 13.2380 0.419041
\(999\) 45.2039 1.43019
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 4027.2.a.c.1.5 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.5 174 1.1 even 1 trivial