Properties

Label 4003.2.a.c.1.2
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 1.2
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.74344 q^{2} -0.797814 q^{3} +5.52649 q^{4} -1.01783 q^{5} +2.18876 q^{6} -0.805682 q^{7} -9.67473 q^{8} -2.36349 q^{9} +O(q^{10})\) \(q-2.74344 q^{2} -0.797814 q^{3} +5.52649 q^{4} -1.01783 q^{5} +2.18876 q^{6} -0.805682 q^{7} -9.67473 q^{8} -2.36349 q^{9} +2.79236 q^{10} -3.88772 q^{11} -4.40911 q^{12} -6.48475 q^{13} +2.21034 q^{14} +0.812040 q^{15} +15.4891 q^{16} +4.70499 q^{17} +6.48411 q^{18} +0.952589 q^{19} -5.62503 q^{20} +0.642784 q^{21} +10.6658 q^{22} +5.52793 q^{23} +7.71864 q^{24} -3.96402 q^{25} +17.7906 q^{26} +4.27907 q^{27} -4.45259 q^{28} +1.89102 q^{29} -2.22779 q^{30} -8.55568 q^{31} -23.1441 q^{32} +3.10168 q^{33} -12.9079 q^{34} +0.820048 q^{35} -13.0618 q^{36} -8.60810 q^{37} -2.61338 q^{38} +5.17363 q^{39} +9.84724 q^{40} -9.32339 q^{41} -1.76344 q^{42} -3.57557 q^{43} -21.4855 q^{44} +2.40564 q^{45} -15.1656 q^{46} +1.56027 q^{47} -12.3574 q^{48} -6.35088 q^{49} +10.8751 q^{50} -3.75371 q^{51} -35.8379 q^{52} +0.105651 q^{53} -11.7394 q^{54} +3.95705 q^{55} +7.79475 q^{56} -0.759989 q^{57} -5.18792 q^{58} -7.49240 q^{59} +4.48773 q^{60} -14.5640 q^{61} +23.4720 q^{62} +1.90422 q^{63} +32.5162 q^{64} +6.60038 q^{65} -8.50929 q^{66} +11.0343 q^{67} +26.0021 q^{68} -4.41026 q^{69} -2.24976 q^{70} +12.2178 q^{71} +22.8661 q^{72} -14.5805 q^{73} +23.6158 q^{74} +3.16255 q^{75} +5.26447 q^{76} +3.13227 q^{77} -14.1936 q^{78} -7.18098 q^{79} -15.7653 q^{80} +3.67657 q^{81} +25.5782 q^{82} -4.55351 q^{83} +3.55234 q^{84} -4.78888 q^{85} +9.80938 q^{86} -1.50869 q^{87} +37.6127 q^{88} -15.1320 q^{89} -6.59973 q^{90} +5.22465 q^{91} +30.5501 q^{92} +6.82584 q^{93} -4.28052 q^{94} -0.969575 q^{95} +18.4647 q^{96} -4.22485 q^{97} +17.4233 q^{98} +9.18861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74344 −1.93991 −0.969954 0.243288i \(-0.921774\pi\)
−0.969954 + 0.243288i \(0.921774\pi\)
\(3\) −0.797814 −0.460618 −0.230309 0.973118i \(-0.573974\pi\)
−0.230309 + 0.973118i \(0.573974\pi\)
\(4\) 5.52649 2.76324
\(5\) −1.01783 −0.455188 −0.227594 0.973756i \(-0.573086\pi\)
−0.227594 + 0.973756i \(0.573086\pi\)
\(6\) 2.18876 0.893557
\(7\) −0.805682 −0.304519 −0.152259 0.988341i \(-0.548655\pi\)
−0.152259 + 0.988341i \(0.548655\pi\)
\(8\) −9.67473 −3.42053
\(9\) −2.36349 −0.787831
\(10\) 2.79236 0.883023
\(11\) −3.88772 −1.17219 −0.586096 0.810241i \(-0.699336\pi\)
−0.586096 + 0.810241i \(0.699336\pi\)
\(12\) −4.40911 −1.27280
\(13\) −6.48475 −1.79855 −0.899273 0.437387i \(-0.855904\pi\)
−0.899273 + 0.437387i \(0.855904\pi\)
\(14\) 2.21034 0.590739
\(15\) 0.812040 0.209668
\(16\) 15.4891 3.87228
\(17\) 4.70499 1.14113 0.570564 0.821253i \(-0.306725\pi\)
0.570564 + 0.821253i \(0.306725\pi\)
\(18\) 6.48411 1.52832
\(19\) 0.952589 0.218539 0.109269 0.994012i \(-0.465149\pi\)
0.109269 + 0.994012i \(0.465149\pi\)
\(20\) −5.62503 −1.25780
\(21\) 0.642784 0.140267
\(22\) 10.6658 2.27395
\(23\) 5.52793 1.15265 0.576327 0.817219i \(-0.304486\pi\)
0.576327 + 0.817219i \(0.304486\pi\)
\(24\) 7.71864 1.57556
\(25\) −3.96402 −0.792804
\(26\) 17.7906 3.48902
\(27\) 4.27907 0.823508
\(28\) −4.45259 −0.841460
\(29\) 1.89102 0.351154 0.175577 0.984466i \(-0.443821\pi\)
0.175577 + 0.984466i \(0.443821\pi\)
\(30\) −2.22779 −0.406737
\(31\) −8.55568 −1.53665 −0.768323 0.640063i \(-0.778908\pi\)
−0.768323 + 0.640063i \(0.778908\pi\)
\(32\) −23.1441 −4.09133
\(33\) 3.10168 0.539934
\(34\) −12.9079 −2.21368
\(35\) 0.820048 0.138613
\(36\) −13.0618 −2.17697
\(37\) −8.60810 −1.41516 −0.707581 0.706632i \(-0.750214\pi\)
−0.707581 + 0.706632i \(0.750214\pi\)
\(38\) −2.61338 −0.423946
\(39\) 5.17363 0.828444
\(40\) 9.84724 1.55699
\(41\) −9.32339 −1.45607 −0.728034 0.685541i \(-0.759566\pi\)
−0.728034 + 0.685541i \(0.759566\pi\)
\(42\) −1.76344 −0.272105
\(43\) −3.57557 −0.545270 −0.272635 0.962118i \(-0.587895\pi\)
−0.272635 + 0.962118i \(0.587895\pi\)
\(44\) −21.4855 −3.23906
\(45\) 2.40564 0.358611
\(46\) −15.1656 −2.23604
\(47\) 1.56027 0.227589 0.113795 0.993504i \(-0.463699\pi\)
0.113795 + 0.993504i \(0.463699\pi\)
\(48\) −12.3574 −1.78364
\(49\) −6.35088 −0.907268
\(50\) 10.8751 1.53797
\(51\) −3.75371 −0.525624
\(52\) −35.8379 −4.96983
\(53\) 0.105651 0.0145122 0.00725611 0.999974i \(-0.497690\pi\)
0.00725611 + 0.999974i \(0.497690\pi\)
\(54\) −11.7394 −1.59753
\(55\) 3.95705 0.533568
\(56\) 7.79475 1.04162
\(57\) −0.759989 −0.100663
\(58\) −5.18792 −0.681207
\(59\) −7.49240 −0.975428 −0.487714 0.873004i \(-0.662169\pi\)
−0.487714 + 0.873004i \(0.662169\pi\)
\(60\) 4.48773 0.579364
\(61\) −14.5640 −1.86473 −0.932367 0.361514i \(-0.882260\pi\)
−0.932367 + 0.361514i \(0.882260\pi\)
\(62\) 23.4720 2.98095
\(63\) 1.90422 0.239909
\(64\) 32.5162 4.06453
\(65\) 6.60038 0.818677
\(66\) −8.50929 −1.04742
\(67\) 11.0343 1.34806 0.674029 0.738705i \(-0.264562\pi\)
0.674029 + 0.738705i \(0.264562\pi\)
\(68\) 26.0021 3.15321
\(69\) −4.41026 −0.530933
\(70\) −2.24976 −0.268897
\(71\) 12.2178 1.44999 0.724996 0.688753i \(-0.241842\pi\)
0.724996 + 0.688753i \(0.241842\pi\)
\(72\) 22.8661 2.69480
\(73\) −14.5805 −1.70651 −0.853257 0.521491i \(-0.825376\pi\)
−0.853257 + 0.521491i \(0.825376\pi\)
\(74\) 23.6158 2.74529
\(75\) 3.16255 0.365180
\(76\) 5.26447 0.603877
\(77\) 3.13227 0.356955
\(78\) −14.1936 −1.60710
\(79\) −7.18098 −0.807924 −0.403962 0.914776i \(-0.632367\pi\)
−0.403962 + 0.914776i \(0.632367\pi\)
\(80\) −15.7653 −1.76261
\(81\) 3.67657 0.408508
\(82\) 25.5782 2.82464
\(83\) −4.55351 −0.499812 −0.249906 0.968270i \(-0.580400\pi\)
−0.249906 + 0.968270i \(0.580400\pi\)
\(84\) 3.55234 0.387592
\(85\) −4.78888 −0.519427
\(86\) 9.80938 1.05777
\(87\) −1.50869 −0.161748
\(88\) 37.6127 4.00953
\(89\) −15.1320 −1.60399 −0.801993 0.597334i \(-0.796227\pi\)
−0.801993 + 0.597334i \(0.796227\pi\)
\(90\) −6.59973 −0.695673
\(91\) 5.22465 0.547692
\(92\) 30.5501 3.18506
\(93\) 6.82584 0.707807
\(94\) −4.28052 −0.441502
\(95\) −0.969575 −0.0994763
\(96\) 18.4647 1.88454
\(97\) −4.22485 −0.428968 −0.214484 0.976727i \(-0.568807\pi\)
−0.214484 + 0.976727i \(0.568807\pi\)
\(98\) 17.4233 1.76002
\(99\) 9.18861 0.923490
\(100\) −21.9071 −2.19071
\(101\) −18.3759 −1.82847 −0.914237 0.405179i \(-0.867209\pi\)
−0.914237 + 0.405179i \(0.867209\pi\)
\(102\) 10.2981 1.01966
\(103\) −3.01970 −0.297540 −0.148770 0.988872i \(-0.547531\pi\)
−0.148770 + 0.988872i \(0.547531\pi\)
\(104\) 62.7382 6.15199
\(105\) −0.654246 −0.0638479
\(106\) −0.289846 −0.0281524
\(107\) 0.648338 0.0626772 0.0313386 0.999509i \(-0.490023\pi\)
0.0313386 + 0.999509i \(0.490023\pi\)
\(108\) 23.6482 2.27555
\(109\) 10.4532 1.00124 0.500618 0.865668i \(-0.333106\pi\)
0.500618 + 0.865668i \(0.333106\pi\)
\(110\) −10.8559 −1.03507
\(111\) 6.86767 0.651850
\(112\) −12.4793 −1.17918
\(113\) −2.58698 −0.243362 −0.121681 0.992569i \(-0.538829\pi\)
−0.121681 + 0.992569i \(0.538829\pi\)
\(114\) 2.08499 0.195277
\(115\) −5.62650 −0.524674
\(116\) 10.4507 0.970325
\(117\) 15.3267 1.41695
\(118\) 20.5550 1.89224
\(119\) −3.79072 −0.347495
\(120\) −7.85627 −0.717176
\(121\) 4.11440 0.374036
\(122\) 39.9556 3.61741
\(123\) 7.43834 0.670692
\(124\) −47.2829 −4.24613
\(125\) 9.12386 0.816063
\(126\) −5.22413 −0.465402
\(127\) −13.9480 −1.23768 −0.618841 0.785516i \(-0.712398\pi\)
−0.618841 + 0.785516i \(0.712398\pi\)
\(128\) −42.9183 −3.79348
\(129\) 2.85264 0.251161
\(130\) −18.1078 −1.58816
\(131\) −1.46981 −0.128418 −0.0642089 0.997936i \(-0.520452\pi\)
−0.0642089 + 0.997936i \(0.520452\pi\)
\(132\) 17.1414 1.49197
\(133\) −0.767484 −0.0665493
\(134\) −30.2721 −2.61511
\(135\) −4.35537 −0.374851
\(136\) −45.5195 −3.90326
\(137\) 4.58002 0.391297 0.195649 0.980674i \(-0.437319\pi\)
0.195649 + 0.980674i \(0.437319\pi\)
\(138\) 12.0993 1.02996
\(139\) 1.51770 0.128730 0.0643648 0.997926i \(-0.479498\pi\)
0.0643648 + 0.997926i \(0.479498\pi\)
\(140\) 4.53199 0.383023
\(141\) −1.24481 −0.104832
\(142\) −33.5190 −2.81285
\(143\) 25.2109 2.10824
\(144\) −36.6084 −3.05070
\(145\) −1.92474 −0.159841
\(146\) 40.0007 3.31048
\(147\) 5.06682 0.417904
\(148\) −47.5726 −3.91044
\(149\) 3.03447 0.248594 0.124297 0.992245i \(-0.460333\pi\)
0.124297 + 0.992245i \(0.460333\pi\)
\(150\) −8.67629 −0.708416
\(151\) −18.9250 −1.54010 −0.770049 0.637985i \(-0.779768\pi\)
−0.770049 + 0.637985i \(0.779768\pi\)
\(152\) −9.21604 −0.747520
\(153\) −11.1202 −0.899015
\(154\) −8.59320 −0.692460
\(155\) 8.70824 0.699462
\(156\) 28.5920 2.28919
\(157\) −0.0164040 −0.00130918 −0.000654590 1.00000i \(-0.500208\pi\)
−0.000654590 1.00000i \(0.500208\pi\)
\(158\) 19.7006 1.56730
\(159\) −0.0842895 −0.00668459
\(160\) 23.5567 1.86232
\(161\) −4.45375 −0.351005
\(162\) −10.0865 −0.792468
\(163\) −7.46977 −0.585078 −0.292539 0.956254i \(-0.594500\pi\)
−0.292539 + 0.956254i \(0.594500\pi\)
\(164\) −51.5256 −4.02347
\(165\) −3.15699 −0.245771
\(166\) 12.4923 0.969590
\(167\) −24.1373 −1.86780 −0.933900 0.357534i \(-0.883617\pi\)
−0.933900 + 0.357534i \(0.883617\pi\)
\(168\) −6.21876 −0.479788
\(169\) 29.0520 2.23477
\(170\) 13.1380 1.00764
\(171\) −2.25144 −0.172172
\(172\) −19.7604 −1.50671
\(173\) 10.7158 0.814707 0.407354 0.913271i \(-0.366452\pi\)
0.407354 + 0.913271i \(0.366452\pi\)
\(174\) 4.13900 0.313776
\(175\) 3.19374 0.241424
\(176\) −60.2174 −4.53906
\(177\) 5.97755 0.449300
\(178\) 41.5137 3.11159
\(179\) 7.54167 0.563691 0.281845 0.959460i \(-0.409053\pi\)
0.281845 + 0.959460i \(0.409053\pi\)
\(180\) 13.2947 0.990930
\(181\) 18.6305 1.38480 0.692398 0.721516i \(-0.256554\pi\)
0.692398 + 0.721516i \(0.256554\pi\)
\(182\) −14.3335 −1.06247
\(183\) 11.6194 0.858931
\(184\) −53.4812 −3.94269
\(185\) 8.76159 0.644165
\(186\) −18.7263 −1.37308
\(187\) −18.2917 −1.33762
\(188\) 8.62283 0.628885
\(189\) −3.44757 −0.250774
\(190\) 2.65998 0.192975
\(191\) −6.17183 −0.446578 −0.223289 0.974752i \(-0.571679\pi\)
−0.223289 + 0.974752i \(0.571679\pi\)
\(192\) −25.9419 −1.87220
\(193\) 20.8423 1.50026 0.750130 0.661290i \(-0.229991\pi\)
0.750130 + 0.661290i \(0.229991\pi\)
\(194\) 11.5906 0.832159
\(195\) −5.26588 −0.377098
\(196\) −35.0981 −2.50700
\(197\) 26.6764 1.90062 0.950308 0.311311i \(-0.100768\pi\)
0.950308 + 0.311311i \(0.100768\pi\)
\(198\) −25.2084 −1.79149
\(199\) 20.3869 1.44519 0.722594 0.691272i \(-0.242949\pi\)
0.722594 + 0.691272i \(0.242949\pi\)
\(200\) 38.3508 2.71181
\(201\) −8.80334 −0.620940
\(202\) 50.4134 3.54707
\(203\) −1.52356 −0.106933
\(204\) −20.7448 −1.45243
\(205\) 9.48964 0.662785
\(206\) 8.28437 0.577199
\(207\) −13.0652 −0.908096
\(208\) −100.443 −6.96447
\(209\) −3.70340 −0.256170
\(210\) 1.79489 0.123859
\(211\) −2.19410 −0.151048 −0.0755239 0.997144i \(-0.524063\pi\)
−0.0755239 + 0.997144i \(0.524063\pi\)
\(212\) 0.583877 0.0401008
\(213\) −9.74757 −0.667893
\(214\) −1.77868 −0.121588
\(215\) 3.63933 0.248200
\(216\) −41.3989 −2.81684
\(217\) 6.89315 0.467938
\(218\) −28.6778 −1.94231
\(219\) 11.6325 0.786051
\(220\) 21.8686 1.47438
\(221\) −30.5107 −2.05237
\(222\) −18.8411 −1.26453
\(223\) −5.24656 −0.351336 −0.175668 0.984449i \(-0.556209\pi\)
−0.175668 + 0.984449i \(0.556209\pi\)
\(224\) 18.6467 1.24589
\(225\) 9.36893 0.624595
\(226\) 7.09723 0.472100
\(227\) 9.70655 0.644246 0.322123 0.946698i \(-0.395603\pi\)
0.322123 + 0.946698i \(0.395603\pi\)
\(228\) −4.20007 −0.278157
\(229\) 0.146497 0.00968082 0.00484041 0.999988i \(-0.498459\pi\)
0.00484041 + 0.999988i \(0.498459\pi\)
\(230\) 15.4360 1.01782
\(231\) −2.49897 −0.164420
\(232\) −18.2951 −1.20113
\(233\) 12.0852 0.791727 0.395863 0.918309i \(-0.370445\pi\)
0.395863 + 0.918309i \(0.370445\pi\)
\(234\) −42.0479 −2.74875
\(235\) −1.58809 −0.103596
\(236\) −41.4067 −2.69534
\(237\) 5.72909 0.372144
\(238\) 10.3996 0.674108
\(239\) −19.9018 −1.28734 −0.643669 0.765304i \(-0.722589\pi\)
−0.643669 + 0.765304i \(0.722589\pi\)
\(240\) 12.5778 0.811892
\(241\) −11.0969 −0.714817 −0.357408 0.933948i \(-0.616340\pi\)
−0.357408 + 0.933948i \(0.616340\pi\)
\(242\) −11.2876 −0.725596
\(243\) −15.7704 −1.01167
\(244\) −80.4880 −5.15272
\(245\) 6.46412 0.412978
\(246\) −20.4067 −1.30108
\(247\) −6.17731 −0.393053
\(248\) 82.7739 5.25615
\(249\) 3.63285 0.230223
\(250\) −25.0308 −1.58309
\(251\) −9.84628 −0.621492 −0.310746 0.950493i \(-0.600579\pi\)
−0.310746 + 0.950493i \(0.600579\pi\)
\(252\) 10.5237 0.662928
\(253\) −21.4911 −1.35113
\(254\) 38.2655 2.40099
\(255\) 3.82064 0.239258
\(256\) 52.7117 3.29448
\(257\) 9.73479 0.607239 0.303620 0.952793i \(-0.401805\pi\)
0.303620 + 0.952793i \(0.401805\pi\)
\(258\) −7.82607 −0.487230
\(259\) 6.93539 0.430944
\(260\) 36.4770 2.26220
\(261\) −4.46942 −0.276650
\(262\) 4.03234 0.249119
\(263\) 2.81849 0.173796 0.0868978 0.996217i \(-0.472305\pi\)
0.0868978 + 0.996217i \(0.472305\pi\)
\(264\) −30.0079 −1.84686
\(265\) −0.107534 −0.00660579
\(266\) 2.10555 0.129099
\(267\) 12.0725 0.738825
\(268\) 60.9811 3.72501
\(269\) −18.2497 −1.11271 −0.556353 0.830946i \(-0.687800\pi\)
−0.556353 + 0.830946i \(0.687800\pi\)
\(270\) 11.9487 0.727176
\(271\) −2.39730 −0.145626 −0.0728129 0.997346i \(-0.523198\pi\)
−0.0728129 + 0.997346i \(0.523198\pi\)
\(272\) 72.8761 4.41876
\(273\) −4.16830 −0.252277
\(274\) −12.5650 −0.759081
\(275\) 15.4110 0.929319
\(276\) −24.3733 −1.46710
\(277\) 17.0259 1.02299 0.511493 0.859287i \(-0.329093\pi\)
0.511493 + 0.859287i \(0.329093\pi\)
\(278\) −4.16373 −0.249724
\(279\) 20.2213 1.21062
\(280\) −7.93374 −0.474132
\(281\) 12.5202 0.746894 0.373447 0.927652i \(-0.378176\pi\)
0.373447 + 0.927652i \(0.378176\pi\)
\(282\) 3.41506 0.203364
\(283\) 20.6286 1.22625 0.613123 0.789988i \(-0.289913\pi\)
0.613123 + 0.789988i \(0.289913\pi\)
\(284\) 67.5218 4.00668
\(285\) 0.773541 0.0458206
\(286\) −69.1648 −4.08980
\(287\) 7.51168 0.443401
\(288\) 54.7008 3.22327
\(289\) 5.13690 0.302171
\(290\) 5.28043 0.310077
\(291\) 3.37064 0.197591
\(292\) −80.5787 −4.71551
\(293\) −30.6108 −1.78830 −0.894150 0.447768i \(-0.852219\pi\)
−0.894150 + 0.447768i \(0.852219\pi\)
\(294\) −13.9005 −0.810696
\(295\) 7.62600 0.444003
\(296\) 83.2810 4.84061
\(297\) −16.6358 −0.965310
\(298\) −8.32490 −0.482249
\(299\) −35.8473 −2.07310
\(300\) 17.4778 1.00908
\(301\) 2.88077 0.166045
\(302\) 51.9198 2.98765
\(303\) 14.6606 0.842229
\(304\) 14.7548 0.846243
\(305\) 14.8237 0.848804
\(306\) 30.5077 1.74401
\(307\) 19.6573 1.12190 0.560951 0.827849i \(-0.310436\pi\)
0.560951 + 0.827849i \(0.310436\pi\)
\(308\) 17.3104 0.986354
\(309\) 2.40916 0.137052
\(310\) −23.8906 −1.35689
\(311\) −14.8863 −0.844127 −0.422064 0.906566i \(-0.638694\pi\)
−0.422064 + 0.906566i \(0.638694\pi\)
\(312\) −50.0535 −2.83372
\(313\) −12.0163 −0.679202 −0.339601 0.940570i \(-0.610292\pi\)
−0.339601 + 0.940570i \(0.610292\pi\)
\(314\) 0.0450034 0.00253969
\(315\) −1.93818 −0.109204
\(316\) −39.6856 −2.23249
\(317\) 28.1671 1.58202 0.791011 0.611802i \(-0.209555\pi\)
0.791011 + 0.611802i \(0.209555\pi\)
\(318\) 0.231244 0.0129675
\(319\) −7.35178 −0.411620
\(320\) −33.0960 −1.85012
\(321\) −0.517254 −0.0288703
\(322\) 12.2186 0.680917
\(323\) 4.48192 0.249381
\(324\) 20.3185 1.12881
\(325\) 25.7057 1.42589
\(326\) 20.4929 1.13500
\(327\) −8.33973 −0.461188
\(328\) 90.2013 4.98053
\(329\) −1.25708 −0.0693052
\(330\) 8.66103 0.476774
\(331\) −28.4684 −1.56476 −0.782381 0.622799i \(-0.785995\pi\)
−0.782381 + 0.622799i \(0.785995\pi\)
\(332\) −25.1649 −1.38110
\(333\) 20.3452 1.11491
\(334\) 66.2193 3.62336
\(335\) −11.2311 −0.613619
\(336\) 9.95615 0.543153
\(337\) 26.5305 1.44521 0.722604 0.691263i \(-0.242945\pi\)
0.722604 + 0.691263i \(0.242945\pi\)
\(338\) −79.7026 −4.33525
\(339\) 2.06393 0.112097
\(340\) −26.4657 −1.43530
\(341\) 33.2621 1.80124
\(342\) 6.17669 0.333997
\(343\) 10.7566 0.580799
\(344\) 34.5927 1.86511
\(345\) 4.48890 0.241675
\(346\) −29.3982 −1.58046
\(347\) 15.1453 0.813041 0.406520 0.913642i \(-0.366742\pi\)
0.406520 + 0.913642i \(0.366742\pi\)
\(348\) −8.33774 −0.446950
\(349\) −14.4188 −0.771821 −0.385911 0.922536i \(-0.626113\pi\)
−0.385911 + 0.922536i \(0.626113\pi\)
\(350\) −8.76184 −0.468340
\(351\) −27.7487 −1.48112
\(352\) 89.9777 4.79583
\(353\) −16.2620 −0.865539 −0.432769 0.901505i \(-0.642464\pi\)
−0.432769 + 0.901505i \(0.642464\pi\)
\(354\) −16.3991 −0.871600
\(355\) −12.4357 −0.660019
\(356\) −83.6267 −4.43220
\(357\) 3.02429 0.160062
\(358\) −20.6902 −1.09351
\(359\) 11.1924 0.590714 0.295357 0.955387i \(-0.404561\pi\)
0.295357 + 0.955387i \(0.404561\pi\)
\(360\) −23.2739 −1.22664
\(361\) −18.0926 −0.952241
\(362\) −51.1118 −2.68638
\(363\) −3.28253 −0.172288
\(364\) 28.8739 1.51341
\(365\) 14.8404 0.776784
\(366\) −31.8772 −1.66625
\(367\) 29.6788 1.54922 0.774609 0.632440i \(-0.217947\pi\)
0.774609 + 0.632440i \(0.217947\pi\)
\(368\) 85.6227 4.46339
\(369\) 22.0358 1.14714
\(370\) −24.0369 −1.24962
\(371\) −0.0851207 −0.00441925
\(372\) 37.7229 1.95584
\(373\) −27.7563 −1.43717 −0.718583 0.695442i \(-0.755209\pi\)
−0.718583 + 0.695442i \(0.755209\pi\)
\(374\) 50.1822 2.59486
\(375\) −7.27915 −0.375894
\(376\) −15.0952 −0.778476
\(377\) −12.2628 −0.631567
\(378\) 9.45821 0.486478
\(379\) −13.0067 −0.668111 −0.334056 0.942553i \(-0.608417\pi\)
−0.334056 + 0.942553i \(0.608417\pi\)
\(380\) −5.35835 −0.274877
\(381\) 11.1279 0.570099
\(382\) 16.9321 0.866321
\(383\) −12.3805 −0.632614 −0.316307 0.948657i \(-0.602443\pi\)
−0.316307 + 0.948657i \(0.602443\pi\)
\(384\) 34.2409 1.74735
\(385\) −3.18812 −0.162482
\(386\) −57.1796 −2.91037
\(387\) 8.45084 0.429580
\(388\) −23.3486 −1.18534
\(389\) −5.71573 −0.289799 −0.144899 0.989446i \(-0.546286\pi\)
−0.144899 + 0.989446i \(0.546286\pi\)
\(390\) 14.4467 0.731535
\(391\) 26.0089 1.31532
\(392\) 61.4430 3.10334
\(393\) 1.17263 0.0591516
\(394\) −73.1853 −3.68702
\(395\) 7.30903 0.367757
\(396\) 50.7807 2.55183
\(397\) 16.2062 0.813367 0.406683 0.913569i \(-0.366685\pi\)
0.406683 + 0.913569i \(0.366685\pi\)
\(398\) −55.9303 −2.80353
\(399\) 0.612309 0.0306538
\(400\) −61.3991 −3.06996
\(401\) −34.6508 −1.73038 −0.865189 0.501446i \(-0.832802\pi\)
−0.865189 + 0.501446i \(0.832802\pi\)
\(402\) 24.1515 1.20457
\(403\) 55.4815 2.76373
\(404\) −101.554 −5.05252
\(405\) −3.74213 −0.185948
\(406\) 4.17981 0.207440
\(407\) 33.4659 1.65884
\(408\) 36.3161 1.79791
\(409\) 6.50847 0.321823 0.160912 0.986969i \(-0.448557\pi\)
0.160912 + 0.986969i \(0.448557\pi\)
\(410\) −26.0343 −1.28574
\(411\) −3.65400 −0.180239
\(412\) −16.6883 −0.822174
\(413\) 6.03649 0.297036
\(414\) 35.8437 1.76162
\(415\) 4.63470 0.227509
\(416\) 150.083 7.35845
\(417\) −1.21084 −0.0592952
\(418\) 10.1601 0.496946
\(419\) −3.93852 −0.192409 −0.0962047 0.995362i \(-0.530670\pi\)
−0.0962047 + 0.995362i \(0.530670\pi\)
\(420\) −3.61568 −0.176427
\(421\) 18.9035 0.921302 0.460651 0.887581i \(-0.347616\pi\)
0.460651 + 0.887581i \(0.347616\pi\)
\(422\) 6.01938 0.293019
\(423\) −3.68769 −0.179302
\(424\) −1.02214 −0.0496395
\(425\) −18.6507 −0.904690
\(426\) 26.7419 1.29565
\(427\) 11.7340 0.567847
\(428\) 3.58304 0.173193
\(429\) −20.1136 −0.971096
\(430\) −9.98430 −0.481486
\(431\) 4.12628 0.198756 0.0993779 0.995050i \(-0.468315\pi\)
0.0993779 + 0.995050i \(0.468315\pi\)
\(432\) 66.2790 3.18885
\(433\) −27.0909 −1.30190 −0.650952 0.759119i \(-0.725630\pi\)
−0.650952 + 0.759119i \(0.725630\pi\)
\(434\) −18.9110 −0.907756
\(435\) 1.53559 0.0736258
\(436\) 57.7696 2.76666
\(437\) 5.26585 0.251900
\(438\) −31.9131 −1.52487
\(439\) 27.4441 1.30983 0.654917 0.755701i \(-0.272704\pi\)
0.654917 + 0.755701i \(0.272704\pi\)
\(440\) −38.2834 −1.82509
\(441\) 15.0102 0.714774
\(442\) 83.7044 3.98141
\(443\) 17.7325 0.842497 0.421249 0.906945i \(-0.361592\pi\)
0.421249 + 0.906945i \(0.361592\pi\)
\(444\) 37.9541 1.80122
\(445\) 15.4018 0.730115
\(446\) 14.3937 0.681559
\(447\) −2.42094 −0.114507
\(448\) −26.1977 −1.23773
\(449\) −5.95846 −0.281197 −0.140599 0.990067i \(-0.544903\pi\)
−0.140599 + 0.990067i \(0.544903\pi\)
\(450\) −25.7031 −1.21166
\(451\) 36.2468 1.70679
\(452\) −14.2969 −0.672469
\(453\) 15.0987 0.709397
\(454\) −26.6294 −1.24978
\(455\) −5.31781 −0.249303
\(456\) 7.35269 0.344321
\(457\) −9.70648 −0.454050 −0.227025 0.973889i \(-0.572900\pi\)
−0.227025 + 0.973889i \(0.572900\pi\)
\(458\) −0.401908 −0.0187799
\(459\) 20.1330 0.939727
\(460\) −31.0948 −1.44980
\(461\) −4.88230 −0.227391 −0.113696 0.993516i \(-0.536269\pi\)
−0.113696 + 0.993516i \(0.536269\pi\)
\(462\) 6.85578 0.318960
\(463\) 12.1435 0.564356 0.282178 0.959362i \(-0.408943\pi\)
0.282178 + 0.959362i \(0.408943\pi\)
\(464\) 29.2903 1.35977
\(465\) −6.94756 −0.322185
\(466\) −33.1550 −1.53588
\(467\) 35.6792 1.65104 0.825519 0.564375i \(-0.190883\pi\)
0.825519 + 0.564375i \(0.190883\pi\)
\(468\) 84.7026 3.91538
\(469\) −8.89015 −0.410509
\(470\) 4.35685 0.200966
\(471\) 0.0130873 0.000603032 0
\(472\) 72.4870 3.33648
\(473\) 13.9008 0.639161
\(474\) −15.7174 −0.721926
\(475\) −3.77608 −0.173259
\(476\) −20.9494 −0.960213
\(477\) −0.249704 −0.0114332
\(478\) 54.5994 2.49732
\(479\) −6.26099 −0.286072 −0.143036 0.989717i \(-0.545686\pi\)
−0.143036 + 0.989717i \(0.545686\pi\)
\(480\) −18.7939 −0.857821
\(481\) 55.8214 2.54524
\(482\) 30.4438 1.38668
\(483\) 3.55327 0.161679
\(484\) 22.7382 1.03355
\(485\) 4.30018 0.195261
\(486\) 43.2653 1.96255
\(487\) −31.5411 −1.42926 −0.714631 0.699502i \(-0.753405\pi\)
−0.714631 + 0.699502i \(0.753405\pi\)
\(488\) 140.903 6.37838
\(489\) 5.95949 0.269497
\(490\) −17.7340 −0.801139
\(491\) −6.02337 −0.271831 −0.135916 0.990720i \(-0.543398\pi\)
−0.135916 + 0.990720i \(0.543398\pi\)
\(492\) 41.1079 1.85329
\(493\) 8.89724 0.400712
\(494\) 16.9471 0.762486
\(495\) −9.35245 −0.420361
\(496\) −132.520 −5.95032
\(497\) −9.84369 −0.441550
\(498\) −9.96653 −0.446611
\(499\) 15.1184 0.676794 0.338397 0.941003i \(-0.390115\pi\)
0.338397 + 0.941003i \(0.390115\pi\)
\(500\) 50.4229 2.25498
\(501\) 19.2571 0.860343
\(502\) 27.0127 1.20564
\(503\) −43.1616 −1.92448 −0.962241 0.272199i \(-0.912249\pi\)
−0.962241 + 0.272199i \(0.912249\pi\)
\(504\) −18.4228 −0.820618
\(505\) 18.7036 0.832300
\(506\) 58.9596 2.62107
\(507\) −23.1781 −1.02938
\(508\) −77.0833 −3.42002
\(509\) −15.4551 −0.685036 −0.342518 0.939511i \(-0.611280\pi\)
−0.342518 + 0.939511i \(0.611280\pi\)
\(510\) −10.4817 −0.464138
\(511\) 11.7472 0.519666
\(512\) −58.7749 −2.59751
\(513\) 4.07620 0.179969
\(514\) −26.7069 −1.17799
\(515\) 3.07354 0.135436
\(516\) 15.7651 0.694020
\(517\) −6.06591 −0.266778
\(518\) −19.0269 −0.835992
\(519\) −8.54922 −0.375269
\(520\) −63.8569 −2.80031
\(521\) −2.81455 −0.123308 −0.0616538 0.998098i \(-0.519637\pi\)
−0.0616538 + 0.998098i \(0.519637\pi\)
\(522\) 12.2616 0.536676
\(523\) −7.98193 −0.349025 −0.174513 0.984655i \(-0.555835\pi\)
−0.174513 + 0.984655i \(0.555835\pi\)
\(524\) −8.12288 −0.354850
\(525\) −2.54801 −0.111204
\(526\) −7.73238 −0.337148
\(527\) −40.2544 −1.75351
\(528\) 48.0423 2.09077
\(529\) 7.55803 0.328610
\(530\) 0.295015 0.0128146
\(531\) 17.7082 0.768472
\(532\) −4.24149 −0.183892
\(533\) 60.4599 2.61881
\(534\) −33.1202 −1.43325
\(535\) −0.659899 −0.0285299
\(536\) −106.754 −4.61107
\(537\) −6.01685 −0.259646
\(538\) 50.0672 2.15855
\(539\) 24.6905 1.06349
\(540\) −24.0699 −1.03580
\(541\) 23.0203 0.989718 0.494859 0.868973i \(-0.335220\pi\)
0.494859 + 0.868973i \(0.335220\pi\)
\(542\) 6.57687 0.282501
\(543\) −14.8637 −0.637863
\(544\) −108.892 −4.66873
\(545\) −10.6396 −0.455751
\(546\) 11.4355 0.489394
\(547\) −16.1124 −0.688915 −0.344458 0.938802i \(-0.611937\pi\)
−0.344458 + 0.938802i \(0.611937\pi\)
\(548\) 25.3114 1.08125
\(549\) 34.4220 1.46909
\(550\) −42.2793 −1.80279
\(551\) 1.80137 0.0767409
\(552\) 42.6681 1.81608
\(553\) 5.78558 0.246028
\(554\) −46.7096 −1.98450
\(555\) −6.99013 −0.296714
\(556\) 8.38756 0.355712
\(557\) 26.4079 1.11894 0.559469 0.828851i \(-0.311005\pi\)
0.559469 + 0.828851i \(0.311005\pi\)
\(558\) −55.4760 −2.34848
\(559\) 23.1867 0.980693
\(560\) 12.7018 0.536749
\(561\) 14.5934 0.616133
\(562\) −34.3485 −1.44891
\(563\) 39.7996 1.67735 0.838677 0.544629i \(-0.183330\pi\)
0.838677 + 0.544629i \(0.183330\pi\)
\(564\) −6.87942 −0.289676
\(565\) 2.63310 0.110776
\(566\) −56.5936 −2.37880
\(567\) −2.96215 −0.124398
\(568\) −118.204 −4.95974
\(569\) 10.4109 0.436447 0.218223 0.975899i \(-0.429974\pi\)
0.218223 + 0.975899i \(0.429974\pi\)
\(570\) −2.12217 −0.0888878
\(571\) 11.5107 0.481707 0.240854 0.970561i \(-0.422573\pi\)
0.240854 + 0.970561i \(0.422573\pi\)
\(572\) 139.328 5.82559
\(573\) 4.92398 0.205702
\(574\) −20.6079 −0.860157
\(575\) −21.9128 −0.913828
\(576\) −76.8518 −3.20216
\(577\) −35.3312 −1.47086 −0.735429 0.677602i \(-0.763019\pi\)
−0.735429 + 0.677602i \(0.763019\pi\)
\(578\) −14.0928 −0.586184
\(579\) −16.6283 −0.691047
\(580\) −10.6371 −0.441680
\(581\) 3.66868 0.152202
\(582\) −9.24718 −0.383308
\(583\) −0.410740 −0.0170111
\(584\) 141.062 5.83719
\(585\) −15.6000 −0.644979
\(586\) 83.9789 3.46914
\(587\) 0.728241 0.0300577 0.0150289 0.999887i \(-0.495216\pi\)
0.0150289 + 0.999887i \(0.495216\pi\)
\(588\) 28.0017 1.15477
\(589\) −8.15005 −0.335817
\(590\) −20.9215 −0.861325
\(591\) −21.2828 −0.875459
\(592\) −133.332 −5.47990
\(593\) −30.6506 −1.25867 −0.629334 0.777135i \(-0.716672\pi\)
−0.629334 + 0.777135i \(0.716672\pi\)
\(594\) 45.6395 1.87261
\(595\) 3.85831 0.158175
\(596\) 16.7700 0.686925
\(597\) −16.2650 −0.665681
\(598\) 98.3450 4.02163
\(599\) 24.8892 1.01695 0.508473 0.861078i \(-0.330210\pi\)
0.508473 + 0.861078i \(0.330210\pi\)
\(600\) −30.5968 −1.24911
\(601\) 43.2468 1.76407 0.882037 0.471179i \(-0.156171\pi\)
0.882037 + 0.471179i \(0.156171\pi\)
\(602\) −7.90324 −0.322112
\(603\) −26.0795 −1.06204
\(604\) −104.589 −4.25567
\(605\) −4.18776 −0.170257
\(606\) −40.2205 −1.63385
\(607\) −41.7585 −1.69492 −0.847462 0.530856i \(-0.821871\pi\)
−0.847462 + 0.530856i \(0.821871\pi\)
\(608\) −22.0468 −0.894115
\(609\) 1.21552 0.0492554
\(610\) −40.6681 −1.64660
\(611\) −10.1180 −0.409330
\(612\) −61.4557 −2.48420
\(613\) 38.7321 1.56437 0.782187 0.623044i \(-0.214104\pi\)
0.782187 + 0.623044i \(0.214104\pi\)
\(614\) −53.9287 −2.17639
\(615\) −7.57097 −0.305291
\(616\) −30.3038 −1.22098
\(617\) −23.8056 −0.958376 −0.479188 0.877712i \(-0.659069\pi\)
−0.479188 + 0.877712i \(0.659069\pi\)
\(618\) −6.60939 −0.265869
\(619\) 23.1020 0.928548 0.464274 0.885692i \(-0.346315\pi\)
0.464274 + 0.885692i \(0.346315\pi\)
\(620\) 48.1260 1.93279
\(621\) 23.6544 0.949219
\(622\) 40.8399 1.63753
\(623\) 12.1915 0.488444
\(624\) 80.1349 3.20796
\(625\) 10.5335 0.421342
\(626\) 32.9661 1.31759
\(627\) 2.95463 0.117997
\(628\) −0.0906564 −0.00361758
\(629\) −40.5010 −1.61488
\(630\) 5.31728 0.211846
\(631\) 7.46573 0.297206 0.148603 0.988897i \(-0.452522\pi\)
0.148603 + 0.988897i \(0.452522\pi\)
\(632\) 69.4741 2.76353
\(633\) 1.75048 0.0695754
\(634\) −77.2749 −3.06898
\(635\) 14.1967 0.563378
\(636\) −0.465825 −0.0184712
\(637\) 41.1839 1.63176
\(638\) 20.1692 0.798506
\(639\) −28.8768 −1.14235
\(640\) 43.6836 1.72675
\(641\) 14.0511 0.554985 0.277493 0.960728i \(-0.410497\pi\)
0.277493 + 0.960728i \(0.410497\pi\)
\(642\) 1.41906 0.0560057
\(643\) −17.2338 −0.679636 −0.339818 0.940491i \(-0.610365\pi\)
−0.339818 + 0.940491i \(0.610365\pi\)
\(644\) −24.6136 −0.969912
\(645\) −2.90351 −0.114326
\(646\) −12.2959 −0.483776
\(647\) 43.2827 1.70162 0.850809 0.525475i \(-0.176112\pi\)
0.850809 + 0.525475i \(0.176112\pi\)
\(648\) −35.5698 −1.39732
\(649\) 29.1284 1.14339
\(650\) −70.5221 −2.76611
\(651\) −5.49946 −0.215541
\(652\) −41.2816 −1.61671
\(653\) 6.07160 0.237600 0.118800 0.992918i \(-0.462095\pi\)
0.118800 + 0.992918i \(0.462095\pi\)
\(654\) 22.8796 0.894662
\(655\) 1.49602 0.0584542
\(656\) −144.411 −5.63830
\(657\) 34.4608 1.34444
\(658\) 3.44874 0.134446
\(659\) 1.38048 0.0537759 0.0268879 0.999638i \(-0.491440\pi\)
0.0268879 + 0.999638i \(0.491440\pi\)
\(660\) −17.4471 −0.679126
\(661\) 5.64104 0.219411 0.109706 0.993964i \(-0.465009\pi\)
0.109706 + 0.993964i \(0.465009\pi\)
\(662\) 78.1014 3.03550
\(663\) 24.3419 0.945359
\(664\) 44.0539 1.70962
\(665\) 0.781169 0.0302924
\(666\) −55.8159 −2.16282
\(667\) 10.4534 0.404759
\(668\) −133.395 −5.16119
\(669\) 4.18578 0.161832
\(670\) 30.8119 1.19037
\(671\) 56.6210 2.18583
\(672\) −14.8766 −0.573879
\(673\) −40.0651 −1.54440 −0.772198 0.635382i \(-0.780843\pi\)
−0.772198 + 0.635382i \(0.780843\pi\)
\(674\) −72.7849 −2.80357
\(675\) −16.9623 −0.652880
\(676\) 160.556 6.17522
\(677\) 13.5849 0.522112 0.261056 0.965324i \(-0.415929\pi\)
0.261056 + 0.965324i \(0.415929\pi\)
\(678\) −5.66227 −0.217458
\(679\) 3.40388 0.130629
\(680\) 46.3311 1.77672
\(681\) −7.74403 −0.296752
\(682\) −91.2528 −3.49425
\(683\) −30.6600 −1.17317 −0.586585 0.809888i \(-0.699528\pi\)
−0.586585 + 0.809888i \(0.699528\pi\)
\(684\) −12.4425 −0.475753
\(685\) −4.66168 −0.178114
\(686\) −29.5100 −1.12670
\(687\) −0.116878 −0.00445916
\(688\) −55.3824 −2.11143
\(689\) −0.685118 −0.0261009
\(690\) −12.3151 −0.468826
\(691\) −3.12360 −0.118828 −0.0594138 0.998233i \(-0.518923\pi\)
−0.0594138 + 0.998233i \(0.518923\pi\)
\(692\) 59.2208 2.25124
\(693\) −7.40309 −0.281220
\(694\) −41.5502 −1.57722
\(695\) −1.54476 −0.0585962
\(696\) 14.5961 0.553265
\(697\) −43.8664 −1.66156
\(698\) 39.5572 1.49726
\(699\) −9.64173 −0.364684
\(700\) 17.6502 0.667113
\(701\) −9.69683 −0.366244 −0.183122 0.983090i \(-0.558620\pi\)
−0.183122 + 0.983090i \(0.558620\pi\)
\(702\) 76.1271 2.87323
\(703\) −8.19998 −0.309268
\(704\) −126.414 −4.76441
\(705\) 1.26700 0.0477182
\(706\) 44.6139 1.67907
\(707\) 14.8052 0.556805
\(708\) 33.0348 1.24153
\(709\) 26.1289 0.981291 0.490646 0.871359i \(-0.336761\pi\)
0.490646 + 0.871359i \(0.336761\pi\)
\(710\) 34.1167 1.28038
\(711\) 16.9722 0.636507
\(712\) 146.398 5.48649
\(713\) −47.2952 −1.77122
\(714\) −8.29698 −0.310507
\(715\) −25.6605 −0.959647
\(716\) 41.6790 1.55762
\(717\) 15.8779 0.592972
\(718\) −30.7058 −1.14593
\(719\) 29.9678 1.11761 0.558806 0.829298i \(-0.311260\pi\)
0.558806 + 0.829298i \(0.311260\pi\)
\(720\) 37.2612 1.38864
\(721\) 2.43291 0.0906064
\(722\) 49.6360 1.84726
\(723\) 8.85330 0.329258
\(724\) 102.961 3.82653
\(725\) −7.49605 −0.278396
\(726\) 9.00543 0.334223
\(727\) −47.9143 −1.77704 −0.888522 0.458833i \(-0.848268\pi\)
−0.888522 + 0.458833i \(0.848268\pi\)
\(728\) −50.5470 −1.87340
\(729\) 1.55216 0.0574876
\(730\) −40.7139 −1.50689
\(731\) −16.8230 −0.622222
\(732\) 64.2145 2.37344
\(733\) −14.4450 −0.533537 −0.266769 0.963761i \(-0.585956\pi\)
−0.266769 + 0.963761i \(0.585956\pi\)
\(734\) −81.4220 −3.00534
\(735\) −5.15717 −0.190225
\(736\) −127.939 −4.71588
\(737\) −42.8984 −1.58018
\(738\) −60.4539 −2.22534
\(739\) −38.5129 −1.41672 −0.708360 0.705851i \(-0.750565\pi\)
−0.708360 + 0.705851i \(0.750565\pi\)
\(740\) 48.4209 1.77999
\(741\) 4.92834 0.181047
\(742\) 0.233524 0.00857293
\(743\) 31.8480 1.16839 0.584196 0.811613i \(-0.301410\pi\)
0.584196 + 0.811613i \(0.301410\pi\)
\(744\) −66.0382 −2.42108
\(745\) −3.08858 −0.113157
\(746\) 76.1478 2.78797
\(747\) 10.7622 0.393768
\(748\) −101.089 −3.69617
\(749\) −0.522354 −0.0190864
\(750\) 19.9699 0.729199
\(751\) −21.3377 −0.778622 −0.389311 0.921106i \(-0.627287\pi\)
−0.389311 + 0.921106i \(0.627287\pi\)
\(752\) 24.1672 0.881288
\(753\) 7.85550 0.286270
\(754\) 33.6424 1.22518
\(755\) 19.2625 0.701034
\(756\) −19.0530 −0.692949
\(757\) 30.0001 1.09037 0.545187 0.838315i \(-0.316459\pi\)
0.545187 + 0.838315i \(0.316459\pi\)
\(758\) 35.6833 1.29607
\(759\) 17.1459 0.622356
\(760\) 9.38038 0.340262
\(761\) 27.0162 0.979338 0.489669 0.871908i \(-0.337118\pi\)
0.489669 + 0.871908i \(0.337118\pi\)
\(762\) −30.5288 −1.10594
\(763\) −8.42196 −0.304896
\(764\) −34.1086 −1.23400
\(765\) 11.3185 0.409221
\(766\) 33.9652 1.22721
\(767\) 48.5864 1.75435
\(768\) −42.0541 −1.51750
\(769\) −19.1013 −0.688809 −0.344404 0.938821i \(-0.611919\pi\)
−0.344404 + 0.938821i \(0.611919\pi\)
\(770\) 8.74643 0.315199
\(771\) −7.76655 −0.279706
\(772\) 115.185 4.14559
\(773\) −42.3484 −1.52317 −0.761583 0.648067i \(-0.775578\pi\)
−0.761583 + 0.648067i \(0.775578\pi\)
\(774\) −23.1844 −0.833346
\(775\) 33.9149 1.21826
\(776\) 40.8743 1.46730
\(777\) −5.53315 −0.198501
\(778\) 15.6808 0.562183
\(779\) −8.88136 −0.318208
\(780\) −29.1018 −1.04201
\(781\) −47.4996 −1.69967
\(782\) −71.3538 −2.55161
\(783\) 8.09182 0.289178
\(784\) −98.3694 −3.51319
\(785\) 0.0166965 0.000595923 0
\(786\) −3.21706 −0.114749
\(787\) −13.2466 −0.472190 −0.236095 0.971730i \(-0.575868\pi\)
−0.236095 + 0.971730i \(0.575868\pi\)
\(788\) 147.427 5.25187
\(789\) −2.24863 −0.0800535
\(790\) −20.0519 −0.713415
\(791\) 2.08428 0.0741084
\(792\) −88.8973 −3.15883
\(793\) 94.4442 3.35381
\(794\) −44.4609 −1.57786
\(795\) 0.0857925 0.00304275
\(796\) 112.668 3.99341
\(797\) 40.6437 1.43967 0.719836 0.694144i \(-0.244217\pi\)
0.719836 + 0.694144i \(0.244217\pi\)
\(798\) −1.67984 −0.0594656
\(799\) 7.34106 0.259708
\(800\) 91.7435 3.24362
\(801\) 35.7643 1.26367
\(802\) 95.0625 3.35678
\(803\) 56.6848 2.00036
\(804\) −48.6516 −1.71581
\(805\) 4.53317 0.159773
\(806\) −152.210 −5.36138
\(807\) 14.5599 0.512533
\(808\) 177.782 6.25436
\(809\) −7.82407 −0.275080 −0.137540 0.990496i \(-0.543920\pi\)
−0.137540 + 0.990496i \(0.543920\pi\)
\(810\) 10.2663 0.360722
\(811\) 17.7878 0.624612 0.312306 0.949981i \(-0.398899\pi\)
0.312306 + 0.949981i \(0.398899\pi\)
\(812\) −8.41995 −0.295482
\(813\) 1.91260 0.0670779
\(814\) −91.8119 −3.21801
\(815\) 7.60297 0.266320
\(816\) −58.1416 −2.03536
\(817\) −3.40605 −0.119163
\(818\) −17.8556 −0.624308
\(819\) −12.3484 −0.431488
\(820\) 52.4444 1.83144
\(821\) 2.07091 0.0722754 0.0361377 0.999347i \(-0.488495\pi\)
0.0361377 + 0.999347i \(0.488495\pi\)
\(822\) 10.0246 0.349646
\(823\) −12.2346 −0.426470 −0.213235 0.977001i \(-0.568400\pi\)
−0.213235 + 0.977001i \(0.568400\pi\)
\(824\) 29.2147 1.01774
\(825\) −12.2951 −0.428061
\(826\) −16.5608 −0.576223
\(827\) −31.4470 −1.09352 −0.546759 0.837290i \(-0.684139\pi\)
−0.546759 + 0.837290i \(0.684139\pi\)
\(828\) −72.2048 −2.50929
\(829\) 24.4672 0.849782 0.424891 0.905245i \(-0.360312\pi\)
0.424891 + 0.905245i \(0.360312\pi\)
\(830\) −12.7150 −0.441346
\(831\) −13.5835 −0.471206
\(832\) −210.860 −7.31024
\(833\) −29.8808 −1.03531
\(834\) 3.32188 0.115027
\(835\) 24.5677 0.850200
\(836\) −20.4668 −0.707860
\(837\) −36.6104 −1.26544
\(838\) 10.8051 0.373257
\(839\) −3.29409 −0.113724 −0.0568622 0.998382i \(-0.518110\pi\)
−0.0568622 + 0.998382i \(0.518110\pi\)
\(840\) 6.32965 0.218394
\(841\) −25.4240 −0.876691
\(842\) −51.8608 −1.78724
\(843\) −9.98881 −0.344033
\(844\) −12.1257 −0.417382
\(845\) −29.5701 −1.01724
\(846\) 10.1170 0.347829
\(847\) −3.31490 −0.113901
\(848\) 1.63643 0.0561953
\(849\) −16.4578 −0.564831
\(850\) 51.1671 1.75502
\(851\) −47.5850 −1.63119
\(852\) −53.8699 −1.84555
\(853\) 26.1441 0.895156 0.447578 0.894245i \(-0.352287\pi\)
0.447578 + 0.894245i \(0.352287\pi\)
\(854\) −32.1915 −1.10157
\(855\) 2.29158 0.0783705
\(856\) −6.27250 −0.214390
\(857\) −46.8536 −1.60049 −0.800245 0.599673i \(-0.795297\pi\)
−0.800245 + 0.599673i \(0.795297\pi\)
\(858\) 55.1807 1.88384
\(859\) −31.6175 −1.07877 −0.539387 0.842058i \(-0.681344\pi\)
−0.539387 + 0.842058i \(0.681344\pi\)
\(860\) 20.1127 0.685838
\(861\) −5.99293 −0.204238
\(862\) −11.3202 −0.385568
\(863\) 18.3228 0.623714 0.311857 0.950129i \(-0.399049\pi\)
0.311857 + 0.950129i \(0.399049\pi\)
\(864\) −99.0350 −3.36924
\(865\) −10.9069 −0.370845
\(866\) 74.3223 2.52557
\(867\) −4.09830 −0.139185
\(868\) 38.0949 1.29303
\(869\) 27.9177 0.947042
\(870\) −4.21280 −0.142827
\(871\) −71.5549 −2.42454
\(872\) −101.132 −3.42476
\(873\) 9.98539 0.337954
\(874\) −14.4466 −0.488662
\(875\) −7.35092 −0.248507
\(876\) 64.2869 2.17205
\(877\) −27.3909 −0.924926 −0.462463 0.886639i \(-0.653034\pi\)
−0.462463 + 0.886639i \(0.653034\pi\)
\(878\) −75.2913 −2.54096
\(879\) 24.4217 0.823724
\(880\) 61.2911 2.06612
\(881\) 34.2769 1.15482 0.577409 0.816455i \(-0.304064\pi\)
0.577409 + 0.816455i \(0.304064\pi\)
\(882\) −41.1798 −1.38660
\(883\) 26.5819 0.894553 0.447276 0.894396i \(-0.352394\pi\)
0.447276 + 0.894396i \(0.352394\pi\)
\(884\) −168.617 −5.67120
\(885\) −6.08413 −0.204516
\(886\) −48.6482 −1.63437
\(887\) −33.2913 −1.11781 −0.558907 0.829231i \(-0.688779\pi\)
−0.558907 + 0.829231i \(0.688779\pi\)
\(888\) −66.4428 −2.22967
\(889\) 11.2376 0.376898
\(890\) −42.2540 −1.41636
\(891\) −14.2935 −0.478850
\(892\) −28.9951 −0.970827
\(893\) 1.48630 0.0497371
\(894\) 6.64173 0.222133
\(895\) −7.67615 −0.256585
\(896\) 34.5785 1.15519
\(897\) 28.5995 0.954909
\(898\) 16.3467 0.545497
\(899\) −16.1790 −0.539599
\(900\) 51.7773 1.72591
\(901\) 0.497084 0.0165603
\(902\) −99.4410 −3.31102
\(903\) −2.29832 −0.0764833
\(904\) 25.0283 0.832429
\(905\) −18.9627 −0.630343
\(906\) −41.4224 −1.37617
\(907\) −21.7900 −0.723524 −0.361762 0.932271i \(-0.617825\pi\)
−0.361762 + 0.932271i \(0.617825\pi\)
\(908\) 53.6432 1.78021
\(909\) 43.4314 1.44053
\(910\) 14.5891 0.483624
\(911\) −27.7332 −0.918842 −0.459421 0.888219i \(-0.651943\pi\)
−0.459421 + 0.888219i \(0.651943\pi\)
\(912\) −11.7716 −0.389795
\(913\) 17.7028 0.585876
\(914\) 26.6292 0.880815
\(915\) −11.8266 −0.390975
\(916\) 0.809616 0.0267505
\(917\) 1.18420 0.0391056
\(918\) −55.2337 −1.82298
\(919\) −28.3629 −0.935605 −0.467803 0.883833i \(-0.654954\pi\)
−0.467803 + 0.883833i \(0.654954\pi\)
\(920\) 54.4349 1.79467
\(921\) −15.6829 −0.516768
\(922\) 13.3943 0.441119
\(923\) −79.2297 −2.60788
\(924\) −13.8105 −0.454333
\(925\) 34.1227 1.12195
\(926\) −33.3150 −1.09480
\(927\) 7.13703 0.234411
\(928\) −43.7659 −1.43669
\(929\) 50.4294 1.65454 0.827268 0.561807i \(-0.189894\pi\)
0.827268 + 0.561807i \(0.189894\pi\)
\(930\) 19.0602 0.625010
\(931\) −6.04978 −0.198273
\(932\) 66.7886 2.18773
\(933\) 11.8765 0.388820
\(934\) −97.8840 −3.20286
\(935\) 18.6179 0.608869
\(936\) −148.281 −4.84673
\(937\) −6.22652 −0.203411 −0.101706 0.994815i \(-0.532430\pi\)
−0.101706 + 0.994815i \(0.532430\pi\)
\(938\) 24.3896 0.796350
\(939\) 9.58679 0.312853
\(940\) −8.77659 −0.286261
\(941\) −38.6183 −1.25892 −0.629460 0.777033i \(-0.716724\pi\)
−0.629460 + 0.777033i \(0.716724\pi\)
\(942\) −0.0359043 −0.00116983
\(943\) −51.5391 −1.67834
\(944\) −116.051 −3.77713
\(945\) 3.50904 0.114149
\(946\) −38.1362 −1.23991
\(947\) 36.7639 1.19467 0.597334 0.801993i \(-0.296227\pi\)
0.597334 + 0.801993i \(0.296227\pi\)
\(948\) 31.6618 1.02833
\(949\) 94.5507 3.06924
\(950\) 10.3595 0.336106
\(951\) −22.4721 −0.728708
\(952\) 36.6742 1.18862
\(953\) −2.18751 −0.0708605 −0.0354302 0.999372i \(-0.511280\pi\)
−0.0354302 + 0.999372i \(0.511280\pi\)
\(954\) 0.685050 0.0221793
\(955\) 6.28189 0.203277
\(956\) −109.987 −3.55723
\(957\) 5.86535 0.189600
\(958\) 17.1767 0.554953
\(959\) −3.69003 −0.119157
\(960\) 26.4045 0.852201
\(961\) 42.1996 1.36128
\(962\) −153.143 −4.93753
\(963\) −1.53234 −0.0493791
\(964\) −61.3271 −1.97521
\(965\) −21.2139 −0.682900
\(966\) −9.74819 −0.313643
\(967\) −43.3573 −1.39428 −0.697138 0.716937i \(-0.745543\pi\)
−0.697138 + 0.716937i \(0.745543\pi\)
\(968\) −39.8057 −1.27940
\(969\) −3.57574 −0.114869
\(970\) −11.7973 −0.378789
\(971\) 8.17945 0.262491 0.131246 0.991350i \(-0.458102\pi\)
0.131246 + 0.991350i \(0.458102\pi\)
\(972\) −87.1551 −2.79550
\(973\) −1.22278 −0.0392006
\(974\) 86.5312 2.77264
\(975\) −20.5084 −0.656793
\(976\) −225.584 −7.22076
\(977\) 9.87257 0.315851 0.157926 0.987451i \(-0.449519\pi\)
0.157926 + 0.987451i \(0.449519\pi\)
\(978\) −16.3495 −0.522800
\(979\) 58.8289 1.88018
\(980\) 35.7239 1.14116
\(981\) −24.7061 −0.788805
\(982\) 16.5248 0.527327
\(983\) −24.0265 −0.766325 −0.383162 0.923681i \(-0.625165\pi\)
−0.383162 + 0.923681i \(0.625165\pi\)
\(984\) −71.9639 −2.29412
\(985\) −27.1521 −0.865138
\(986\) −24.4091 −0.777344
\(987\) 1.00292 0.0319233
\(988\) −34.1388 −1.08610
\(989\) −19.7655 −0.628507
\(990\) 25.6579 0.815463
\(991\) 1.09816 0.0348841 0.0174421 0.999848i \(-0.494448\pi\)
0.0174421 + 0.999848i \(0.494448\pi\)
\(992\) 198.013 6.28692
\(993\) 22.7125 0.720759
\(994\) 27.0056 0.856567
\(995\) −20.7504 −0.657833
\(996\) 20.0769 0.636162
\(997\) −6.39804 −0.202628 −0.101314 0.994855i \(-0.532305\pi\)
−0.101314 + 0.994855i \(0.532305\pi\)
\(998\) −41.4766 −1.31292
\(999\) −36.8347 −1.16540
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.1.2 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.2 179 1.1 even 1 trivial