Properties

Label 6001.2.a.d.1.15
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24229 q^{2} +2.77352 q^{3} +3.02787 q^{4} +0.258648 q^{5} -6.21903 q^{6} +3.59133 q^{7} -2.30477 q^{8} +4.69240 q^{9} +O(q^{10})\) \(q-2.24229 q^{2} +2.77352 q^{3} +3.02787 q^{4} +0.258648 q^{5} -6.21903 q^{6} +3.59133 q^{7} -2.30477 q^{8} +4.69240 q^{9} -0.579964 q^{10} +1.04738 q^{11} +8.39784 q^{12} +1.78915 q^{13} -8.05280 q^{14} +0.717365 q^{15} -0.887758 q^{16} +1.00000 q^{17} -10.5217 q^{18} +2.63252 q^{19} +0.783152 q^{20} +9.96062 q^{21} -2.34854 q^{22} +8.20057 q^{23} -6.39233 q^{24} -4.93310 q^{25} -4.01179 q^{26} +4.69390 q^{27} +10.8741 q^{28} +9.95368 q^{29} -1.60854 q^{30} +0.457574 q^{31} +6.60016 q^{32} +2.90494 q^{33} -2.24229 q^{34} +0.928891 q^{35} +14.2080 q^{36} -0.988008 q^{37} -5.90288 q^{38} +4.96223 q^{39} -0.596126 q^{40} +2.03994 q^{41} -22.3346 q^{42} +4.37973 q^{43} +3.17134 q^{44} +1.21368 q^{45} -18.3881 q^{46} -7.94975 q^{47} -2.46221 q^{48} +5.89765 q^{49} +11.0614 q^{50} +2.77352 q^{51} +5.41730 q^{52} -12.8480 q^{53} -10.5251 q^{54} +0.270904 q^{55} -8.27721 q^{56} +7.30135 q^{57} -22.3191 q^{58} +4.08684 q^{59} +2.17209 q^{60} -6.93442 q^{61} -1.02601 q^{62} +16.8520 q^{63} -13.0240 q^{64} +0.462760 q^{65} -6.51371 q^{66} -0.0995187 q^{67} +3.02787 q^{68} +22.7444 q^{69} -2.08284 q^{70} -2.43494 q^{71} -10.8149 q^{72} +5.94332 q^{73} +2.21540 q^{74} -13.6820 q^{75} +7.97093 q^{76} +3.76150 q^{77} -11.1268 q^{78} +8.72057 q^{79} -0.229617 q^{80} -1.05859 q^{81} -4.57414 q^{82} -8.46331 q^{83} +30.1594 q^{84} +0.258648 q^{85} -9.82063 q^{86} +27.6067 q^{87} -2.41398 q^{88} -2.36482 q^{89} -2.72142 q^{90} +6.42542 q^{91} +24.8302 q^{92} +1.26909 q^{93} +17.8256 q^{94} +0.680897 q^{95} +18.3057 q^{96} -4.45176 q^{97} -13.2242 q^{98} +4.91474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24229 −1.58554 −0.792769 0.609522i \(-0.791362\pi\)
−0.792769 + 0.609522i \(0.791362\pi\)
\(3\) 2.77352 1.60129 0.800646 0.599138i \(-0.204490\pi\)
0.800646 + 0.599138i \(0.204490\pi\)
\(4\) 3.02787 1.51393
\(5\) 0.258648 0.115671 0.0578355 0.998326i \(-0.481580\pi\)
0.0578355 + 0.998326i \(0.481580\pi\)
\(6\) −6.21903 −2.53891
\(7\) 3.59133 1.35740 0.678698 0.734418i \(-0.262545\pi\)
0.678698 + 0.734418i \(0.262545\pi\)
\(8\) −2.30477 −0.814861
\(9\) 4.69240 1.56413
\(10\) −0.579964 −0.183401
\(11\) 1.04738 0.315798 0.157899 0.987455i \(-0.449528\pi\)
0.157899 + 0.987455i \(0.449528\pi\)
\(12\) 8.39784 2.42425
\(13\) 1.78915 0.496220 0.248110 0.968732i \(-0.420190\pi\)
0.248110 + 0.968732i \(0.420190\pi\)
\(14\) −8.05280 −2.15220
\(15\) 0.717365 0.185223
\(16\) −0.887758 −0.221940
\(17\) 1.00000 0.242536
\(18\) −10.5217 −2.47999
\(19\) 2.63252 0.603943 0.301971 0.953317i \(-0.402355\pi\)
0.301971 + 0.953317i \(0.402355\pi\)
\(20\) 0.783152 0.175118
\(21\) 9.96062 2.17358
\(22\) −2.34854 −0.500710
\(23\) 8.20057 1.70994 0.854969 0.518679i \(-0.173576\pi\)
0.854969 + 0.518679i \(0.173576\pi\)
\(24\) −6.39233 −1.30483
\(25\) −4.93310 −0.986620
\(26\) −4.01179 −0.786777
\(27\) 4.69390 0.903341
\(28\) 10.8741 2.05501
\(29\) 9.95368 1.84835 0.924176 0.381966i \(-0.124753\pi\)
0.924176 + 0.381966i \(0.124753\pi\)
\(30\) −1.60854 −0.293678
\(31\) 0.457574 0.0821827 0.0410914 0.999155i \(-0.486917\pi\)
0.0410914 + 0.999155i \(0.486917\pi\)
\(32\) 6.60016 1.16675
\(33\) 2.90494 0.505685
\(34\) −2.24229 −0.384550
\(35\) 0.928891 0.157011
\(36\) 14.2080 2.36799
\(37\) −0.988008 −0.162427 −0.0812137 0.996697i \(-0.525880\pi\)
−0.0812137 + 0.996697i \(0.525880\pi\)
\(38\) −5.90288 −0.957574
\(39\) 4.96223 0.794593
\(40\) −0.596126 −0.0942557
\(41\) 2.03994 0.318585 0.159292 0.987231i \(-0.449079\pi\)
0.159292 + 0.987231i \(0.449079\pi\)
\(42\) −22.3346 −3.44630
\(43\) 4.37973 0.667903 0.333951 0.942590i \(-0.391618\pi\)
0.333951 + 0.942590i \(0.391618\pi\)
\(44\) 3.17134 0.478097
\(45\) 1.21368 0.180925
\(46\) −18.3881 −2.71117
\(47\) −7.94975 −1.15959 −0.579795 0.814762i \(-0.696867\pi\)
−0.579795 + 0.814762i \(0.696867\pi\)
\(48\) −2.46221 −0.355390
\(49\) 5.89765 0.842522
\(50\) 11.0614 1.56432
\(51\) 2.77352 0.388370
\(52\) 5.41730 0.751245
\(53\) −12.8480 −1.76481 −0.882405 0.470491i \(-0.844077\pi\)
−0.882405 + 0.470491i \(0.844077\pi\)
\(54\) −10.5251 −1.43228
\(55\) 0.270904 0.0365287
\(56\) −8.27721 −1.10609
\(57\) 7.30135 0.967088
\(58\) −22.3191 −2.93064
\(59\) 4.08684 0.532061 0.266031 0.963965i \(-0.414288\pi\)
0.266031 + 0.963965i \(0.414288\pi\)
\(60\) 2.17209 0.280415
\(61\) −6.93442 −0.887862 −0.443931 0.896061i \(-0.646416\pi\)
−0.443931 + 0.896061i \(0.646416\pi\)
\(62\) −1.02601 −0.130304
\(63\) 16.8520 2.12315
\(64\) −13.0240 −1.62800
\(65\) 0.462760 0.0573983
\(66\) −6.51371 −0.801783
\(67\) −0.0995187 −0.0121581 −0.00607907 0.999982i \(-0.501935\pi\)
−0.00607907 + 0.999982i \(0.501935\pi\)
\(68\) 3.02787 0.367183
\(69\) 22.7444 2.73811
\(70\) −2.08284 −0.248947
\(71\) −2.43494 −0.288974 −0.144487 0.989507i \(-0.546153\pi\)
−0.144487 + 0.989507i \(0.546153\pi\)
\(72\) −10.8149 −1.27455
\(73\) 5.94332 0.695613 0.347807 0.937566i \(-0.386927\pi\)
0.347807 + 0.937566i \(0.386927\pi\)
\(74\) 2.21540 0.257535
\(75\) −13.6820 −1.57987
\(76\) 7.97093 0.914329
\(77\) 3.76150 0.428663
\(78\) −11.1268 −1.25986
\(79\) 8.72057 0.981140 0.490570 0.871402i \(-0.336789\pi\)
0.490570 + 0.871402i \(0.336789\pi\)
\(80\) −0.229617 −0.0256720
\(81\) −1.05859 −0.117621
\(82\) −4.57414 −0.505129
\(83\) −8.46331 −0.928969 −0.464485 0.885581i \(-0.653760\pi\)
−0.464485 + 0.885581i \(0.653760\pi\)
\(84\) 30.1594 3.29066
\(85\) 0.258648 0.0280543
\(86\) −9.82063 −1.05899
\(87\) 27.6067 2.95975
\(88\) −2.41398 −0.257332
\(89\) −2.36482 −0.250671 −0.125335 0.992114i \(-0.540001\pi\)
−0.125335 + 0.992114i \(0.540001\pi\)
\(90\) −2.72142 −0.286863
\(91\) 6.42542 0.673567
\(92\) 24.8302 2.58873
\(93\) 1.26909 0.131598
\(94\) 17.8256 1.83858
\(95\) 0.680897 0.0698586
\(96\) 18.3057 1.86831
\(97\) −4.45176 −0.452008 −0.226004 0.974126i \(-0.572566\pi\)
−0.226004 + 0.974126i \(0.572566\pi\)
\(98\) −13.2242 −1.33585
\(99\) 4.91474 0.493950
\(100\) −14.9368 −1.49368
\(101\) 10.4437 1.03918 0.519591 0.854415i \(-0.326084\pi\)
0.519591 + 0.854415i \(0.326084\pi\)
\(102\) −6.21903 −0.615776
\(103\) −8.43017 −0.830649 −0.415324 0.909673i \(-0.636332\pi\)
−0.415324 + 0.909673i \(0.636332\pi\)
\(104\) −4.12358 −0.404351
\(105\) 2.57629 0.251421
\(106\) 28.8090 2.79817
\(107\) −3.69819 −0.357518 −0.178759 0.983893i \(-0.557208\pi\)
−0.178759 + 0.983893i \(0.557208\pi\)
\(108\) 14.2125 1.36760
\(109\) 2.01455 0.192959 0.0964796 0.995335i \(-0.469242\pi\)
0.0964796 + 0.995335i \(0.469242\pi\)
\(110\) −0.607445 −0.0579176
\(111\) −2.74026 −0.260094
\(112\) −3.18823 −0.301260
\(113\) −3.71376 −0.349361 −0.174681 0.984625i \(-0.555889\pi\)
−0.174681 + 0.984625i \(0.555889\pi\)
\(114\) −16.3718 −1.53336
\(115\) 2.12106 0.197790
\(116\) 30.1384 2.79828
\(117\) 8.39540 0.776155
\(118\) −9.16388 −0.843603
\(119\) 3.59133 0.329217
\(120\) −1.65336 −0.150931
\(121\) −9.90299 −0.900272
\(122\) 15.5490 1.40774
\(123\) 5.65781 0.510147
\(124\) 1.38547 0.124419
\(125\) −2.56918 −0.229794
\(126\) −37.7870 −3.36633
\(127\) −11.6349 −1.03243 −0.516216 0.856458i \(-0.672660\pi\)
−0.516216 + 0.856458i \(0.672660\pi\)
\(128\) 16.0032 1.41449
\(129\) 12.1473 1.06951
\(130\) −1.03764 −0.0910072
\(131\) 6.07247 0.530554 0.265277 0.964172i \(-0.414537\pi\)
0.265277 + 0.964172i \(0.414537\pi\)
\(132\) 8.79576 0.765573
\(133\) 9.45426 0.819789
\(134\) 0.223150 0.0192772
\(135\) 1.21407 0.104490
\(136\) −2.30477 −0.197633
\(137\) 4.49058 0.383656 0.191828 0.981429i \(-0.438558\pi\)
0.191828 + 0.981429i \(0.438558\pi\)
\(138\) −50.9996 −4.34138
\(139\) −5.38986 −0.457162 −0.228581 0.973525i \(-0.573409\pi\)
−0.228581 + 0.973525i \(0.573409\pi\)
\(140\) 2.81256 0.237704
\(141\) −22.0488 −1.85684
\(142\) 5.45985 0.458180
\(143\) 1.87393 0.156706
\(144\) −4.16572 −0.347143
\(145\) 2.57450 0.213801
\(146\) −13.3267 −1.10292
\(147\) 16.3572 1.34912
\(148\) −2.99156 −0.245904
\(149\) −6.37695 −0.522420 −0.261210 0.965282i \(-0.584121\pi\)
−0.261210 + 0.965282i \(0.584121\pi\)
\(150\) 30.6791 2.50494
\(151\) −18.9515 −1.54225 −0.771127 0.636681i \(-0.780307\pi\)
−0.771127 + 0.636681i \(0.780307\pi\)
\(152\) −6.06738 −0.492129
\(153\) 4.69240 0.379358
\(154\) −8.43438 −0.679662
\(155\) 0.118351 0.00950616
\(156\) 15.0250 1.20296
\(157\) −5.15979 −0.411796 −0.205898 0.978573i \(-0.566012\pi\)
−0.205898 + 0.978573i \(0.566012\pi\)
\(158\) −19.5540 −1.55564
\(159\) −35.6342 −2.82597
\(160\) 1.70712 0.134960
\(161\) 29.4510 2.32106
\(162\) 2.37366 0.186492
\(163\) 20.8270 1.63130 0.815649 0.578547i \(-0.196380\pi\)
0.815649 + 0.578547i \(0.196380\pi\)
\(164\) 6.17666 0.482316
\(165\) 0.751357 0.0584930
\(166\) 18.9772 1.47292
\(167\) −13.6357 −1.05516 −0.527581 0.849504i \(-0.676901\pi\)
−0.527581 + 0.849504i \(0.676901\pi\)
\(168\) −22.9570 −1.77117
\(169\) −9.79895 −0.753765
\(170\) −0.579964 −0.0444812
\(171\) 12.3529 0.944647
\(172\) 13.2612 1.01116
\(173\) 20.4789 1.55698 0.778490 0.627657i \(-0.215986\pi\)
0.778490 + 0.627657i \(0.215986\pi\)
\(174\) −61.9023 −4.69280
\(175\) −17.7164 −1.33923
\(176\) −0.929824 −0.0700881
\(177\) 11.3349 0.851985
\(178\) 5.30262 0.397448
\(179\) 21.1761 1.58277 0.791387 0.611315i \(-0.209359\pi\)
0.791387 + 0.611315i \(0.209359\pi\)
\(180\) 3.67486 0.273908
\(181\) −5.44323 −0.404592 −0.202296 0.979324i \(-0.564840\pi\)
−0.202296 + 0.979324i \(0.564840\pi\)
\(182\) −14.4077 −1.06797
\(183\) −19.2327 −1.42172
\(184\) −18.9005 −1.39336
\(185\) −0.255546 −0.0187881
\(186\) −2.84567 −0.208655
\(187\) 1.04738 0.0765923
\(188\) −24.0708 −1.75554
\(189\) 16.8573 1.22619
\(190\) −1.52677 −0.110764
\(191\) −12.7225 −0.920569 −0.460284 0.887771i \(-0.652253\pi\)
−0.460284 + 0.887771i \(0.652253\pi\)
\(192\) −36.1222 −2.60689
\(193\) −4.08332 −0.293924 −0.146962 0.989142i \(-0.546949\pi\)
−0.146962 + 0.989142i \(0.546949\pi\)
\(194\) 9.98214 0.716676
\(195\) 1.28347 0.0919114
\(196\) 17.8573 1.27552
\(197\) 13.0564 0.930231 0.465116 0.885250i \(-0.346013\pi\)
0.465116 + 0.885250i \(0.346013\pi\)
\(198\) −11.0203 −0.783178
\(199\) 17.2319 1.22154 0.610768 0.791809i \(-0.290861\pi\)
0.610768 + 0.791809i \(0.290861\pi\)
\(200\) 11.3697 0.803958
\(201\) −0.276017 −0.0194687
\(202\) −23.4177 −1.64766
\(203\) 35.7470 2.50895
\(204\) 8.39784 0.587966
\(205\) 0.527626 0.0368510
\(206\) 18.9029 1.31703
\(207\) 38.4804 2.67457
\(208\) −1.58833 −0.110131
\(209\) 2.75726 0.190724
\(210\) −5.77680 −0.398637
\(211\) −21.7765 −1.49916 −0.749579 0.661915i \(-0.769744\pi\)
−0.749579 + 0.661915i \(0.769744\pi\)
\(212\) −38.9021 −2.67180
\(213\) −6.75335 −0.462732
\(214\) 8.29242 0.566858
\(215\) 1.13281 0.0772570
\(216\) −10.8184 −0.736098
\(217\) 1.64330 0.111554
\(218\) −4.51722 −0.305944
\(219\) 16.4839 1.11388
\(220\) 0.820261 0.0553020
\(221\) 1.78915 0.120351
\(222\) 6.14445 0.412389
\(223\) 7.02715 0.470573 0.235286 0.971926i \(-0.424397\pi\)
0.235286 + 0.971926i \(0.424397\pi\)
\(224\) 23.7034 1.58375
\(225\) −23.1481 −1.54321
\(226\) 8.32733 0.553926
\(227\) −9.11686 −0.605107 −0.302554 0.953132i \(-0.597839\pi\)
−0.302554 + 0.953132i \(0.597839\pi\)
\(228\) 22.1075 1.46411
\(229\) −23.6000 −1.55953 −0.779764 0.626073i \(-0.784661\pi\)
−0.779764 + 0.626073i \(0.784661\pi\)
\(230\) −4.75604 −0.313604
\(231\) 10.4326 0.686414
\(232\) −22.9410 −1.50615
\(233\) 0.931390 0.0610174 0.0305087 0.999535i \(-0.490287\pi\)
0.0305087 + 0.999535i \(0.490287\pi\)
\(234\) −18.8249 −1.23062
\(235\) −2.05619 −0.134131
\(236\) 12.3744 0.805505
\(237\) 24.1866 1.57109
\(238\) −8.05280 −0.521986
\(239\) 20.3762 1.31802 0.659012 0.752133i \(-0.270975\pi\)
0.659012 + 0.752133i \(0.270975\pi\)
\(240\) −0.636847 −0.0411083
\(241\) −11.0296 −0.710477 −0.355238 0.934776i \(-0.615600\pi\)
−0.355238 + 0.934776i \(0.615600\pi\)
\(242\) 22.2054 1.42742
\(243\) −17.0177 −1.09169
\(244\) −20.9965 −1.34416
\(245\) 1.52542 0.0974553
\(246\) −12.6864 −0.808858
\(247\) 4.70998 0.299689
\(248\) −1.05461 −0.0669675
\(249\) −23.4731 −1.48755
\(250\) 5.76084 0.364348
\(251\) −1.68230 −0.106186 −0.0530929 0.998590i \(-0.516908\pi\)
−0.0530929 + 0.998590i \(0.516908\pi\)
\(252\) 51.0255 3.21430
\(253\) 8.58915 0.539995
\(254\) 26.0889 1.63696
\(255\) 0.717365 0.0449231
\(256\) −9.83586 −0.614741
\(257\) 13.0149 0.811850 0.405925 0.913906i \(-0.366949\pi\)
0.405925 + 0.913906i \(0.366949\pi\)
\(258\) −27.2377 −1.69574
\(259\) −3.54826 −0.220478
\(260\) 1.40117 0.0868972
\(261\) 46.7067 2.89107
\(262\) −13.6162 −0.841214
\(263\) 6.09649 0.375926 0.187963 0.982176i \(-0.439812\pi\)
0.187963 + 0.982176i \(0.439812\pi\)
\(264\) −6.69523 −0.412063
\(265\) −3.32311 −0.204137
\(266\) −21.1992 −1.29981
\(267\) −6.55888 −0.401397
\(268\) −0.301329 −0.0184066
\(269\) −13.4226 −0.818391 −0.409196 0.912447i \(-0.634191\pi\)
−0.409196 + 0.912447i \(0.634191\pi\)
\(270\) −2.72229 −0.165673
\(271\) −25.8215 −1.56854 −0.784272 0.620417i \(-0.786963\pi\)
−0.784272 + 0.620417i \(0.786963\pi\)
\(272\) −0.887758 −0.0538283
\(273\) 17.8210 1.07858
\(274\) −10.0692 −0.608301
\(275\) −5.16685 −0.311573
\(276\) 68.8671 4.14531
\(277\) −26.6230 −1.59962 −0.799810 0.600253i \(-0.795067\pi\)
−0.799810 + 0.600253i \(0.795067\pi\)
\(278\) 12.0856 0.724848
\(279\) 2.14712 0.128545
\(280\) −2.14088 −0.127942
\(281\) 23.3833 1.39493 0.697466 0.716618i \(-0.254311\pi\)
0.697466 + 0.716618i \(0.254311\pi\)
\(282\) 49.4397 2.94409
\(283\) 3.58458 0.213081 0.106541 0.994308i \(-0.466023\pi\)
0.106541 + 0.994308i \(0.466023\pi\)
\(284\) −7.37268 −0.437488
\(285\) 1.88848 0.111864
\(286\) −4.20188 −0.248463
\(287\) 7.32609 0.432446
\(288\) 30.9706 1.82496
\(289\) 1.00000 0.0588235
\(290\) −5.77278 −0.338989
\(291\) −12.3470 −0.723796
\(292\) 17.9956 1.05311
\(293\) 10.0477 0.586992 0.293496 0.955960i \(-0.405181\pi\)
0.293496 + 0.955960i \(0.405181\pi\)
\(294\) −36.6777 −2.13909
\(295\) 1.05705 0.0615440
\(296\) 2.27714 0.132356
\(297\) 4.91632 0.285274
\(298\) 14.2990 0.828317
\(299\) 14.6720 0.848506
\(300\) −41.4274 −2.39181
\(301\) 15.7291 0.906608
\(302\) 42.4949 2.44530
\(303\) 28.9657 1.66403
\(304\) −2.33705 −0.134039
\(305\) −1.79357 −0.102700
\(306\) −10.5217 −0.601487
\(307\) 5.64621 0.322246 0.161123 0.986934i \(-0.448488\pi\)
0.161123 + 0.986934i \(0.448488\pi\)
\(308\) 11.3893 0.648967
\(309\) −23.3812 −1.33011
\(310\) −0.265377 −0.0150724
\(311\) −26.2048 −1.48594 −0.742968 0.669327i \(-0.766583\pi\)
−0.742968 + 0.669327i \(0.766583\pi\)
\(312\) −11.4368 −0.647483
\(313\) 19.7246 1.11490 0.557450 0.830210i \(-0.311780\pi\)
0.557450 + 0.830210i \(0.311780\pi\)
\(314\) 11.5697 0.652919
\(315\) 4.35873 0.245586
\(316\) 26.4047 1.48538
\(317\) 11.3334 0.636550 0.318275 0.947998i \(-0.396896\pi\)
0.318275 + 0.947998i \(0.396896\pi\)
\(318\) 79.9022 4.48069
\(319\) 10.4253 0.583706
\(320\) −3.36862 −0.188312
\(321\) −10.2570 −0.572490
\(322\) −66.0376 −3.68013
\(323\) 2.63252 0.146478
\(324\) −3.20526 −0.178070
\(325\) −8.82605 −0.489581
\(326\) −46.7002 −2.58649
\(327\) 5.58740 0.308984
\(328\) −4.70160 −0.259602
\(329\) −28.5502 −1.57402
\(330\) −1.68476 −0.0927430
\(331\) 4.01321 0.220586 0.110293 0.993899i \(-0.464821\pi\)
0.110293 + 0.993899i \(0.464821\pi\)
\(332\) −25.6258 −1.40640
\(333\) −4.63613 −0.254058
\(334\) 30.5752 1.67300
\(335\) −0.0257403 −0.00140634
\(336\) −8.84262 −0.482405
\(337\) −19.1692 −1.04421 −0.522106 0.852881i \(-0.674853\pi\)
−0.522106 + 0.852881i \(0.674853\pi\)
\(338\) 21.9721 1.19512
\(339\) −10.3002 −0.559429
\(340\) 0.783152 0.0424724
\(341\) 0.479256 0.0259532
\(342\) −27.6987 −1.49777
\(343\) −3.95890 −0.213760
\(344\) −10.0943 −0.544248
\(345\) 5.88280 0.316720
\(346\) −45.9196 −2.46865
\(347\) 3.06838 0.164719 0.0823597 0.996603i \(-0.473754\pi\)
0.0823597 + 0.996603i \(0.473754\pi\)
\(348\) 83.5895 4.48087
\(349\) 16.3185 0.873508 0.436754 0.899581i \(-0.356128\pi\)
0.436754 + 0.899581i \(0.356128\pi\)
\(350\) 39.7253 2.12341
\(351\) 8.39808 0.448256
\(352\) 6.91290 0.368459
\(353\) −1.00000 −0.0532246
\(354\) −25.4162 −1.35085
\(355\) −0.629793 −0.0334259
\(356\) −7.16037 −0.379499
\(357\) 9.96062 0.527172
\(358\) −47.4829 −2.50955
\(359\) 27.6205 1.45775 0.728877 0.684645i \(-0.240043\pi\)
0.728877 + 0.684645i \(0.240043\pi\)
\(360\) −2.79726 −0.147428
\(361\) −12.0698 −0.635253
\(362\) 12.2053 0.641497
\(363\) −27.4661 −1.44160
\(364\) 19.4553 1.01974
\(365\) 1.53723 0.0804622
\(366\) 43.1254 2.25420
\(367\) 5.40277 0.282022 0.141011 0.990008i \(-0.454965\pi\)
0.141011 + 0.990008i \(0.454965\pi\)
\(368\) −7.28013 −0.379503
\(369\) 9.57221 0.498309
\(370\) 0.573009 0.0297893
\(371\) −46.1414 −2.39554
\(372\) 3.84263 0.199231
\(373\) −16.7246 −0.865966 −0.432983 0.901402i \(-0.642539\pi\)
−0.432983 + 0.901402i \(0.642539\pi\)
\(374\) −2.34854 −0.121440
\(375\) −7.12566 −0.367967
\(376\) 18.3224 0.944905
\(377\) 17.8086 0.917190
\(378\) −37.7991 −1.94417
\(379\) −25.1388 −1.29129 −0.645647 0.763636i \(-0.723412\pi\)
−0.645647 + 0.763636i \(0.723412\pi\)
\(380\) 2.06167 0.105761
\(381\) −32.2697 −1.65322
\(382\) 28.5276 1.45960
\(383\) 12.4483 0.636076 0.318038 0.948078i \(-0.396976\pi\)
0.318038 + 0.948078i \(0.396976\pi\)
\(384\) 44.3851 2.26502
\(385\) 0.972905 0.0495838
\(386\) 9.15598 0.466027
\(387\) 20.5515 1.04469
\(388\) −13.4793 −0.684309
\(389\) 10.4541 0.530043 0.265022 0.964242i \(-0.414621\pi\)
0.265022 + 0.964242i \(0.414621\pi\)
\(390\) −2.87792 −0.145729
\(391\) 8.20057 0.414721
\(392\) −13.5928 −0.686538
\(393\) 16.8421 0.849571
\(394\) −29.2763 −1.47492
\(395\) 2.25556 0.113489
\(396\) 14.8812 0.747808
\(397\) −8.80292 −0.441806 −0.220903 0.975296i \(-0.570900\pi\)
−0.220903 + 0.975296i \(0.570900\pi\)
\(398\) −38.6389 −1.93679
\(399\) 26.2216 1.31272
\(400\) 4.37940 0.218970
\(401\) −25.1831 −1.25758 −0.628791 0.777574i \(-0.716450\pi\)
−0.628791 + 0.777574i \(0.716450\pi\)
\(402\) 0.618910 0.0308684
\(403\) 0.818668 0.0407808
\(404\) 31.6220 1.57325
\(405\) −0.273801 −0.0136053
\(406\) −80.1551 −3.97803
\(407\) −1.03482 −0.0512943
\(408\) −6.39233 −0.316468
\(409\) −23.2562 −1.14994 −0.574972 0.818173i \(-0.694987\pi\)
−0.574972 + 0.818173i \(0.694987\pi\)
\(410\) −1.18309 −0.0584287
\(411\) 12.4547 0.614344
\(412\) −25.5254 −1.25755
\(413\) 14.6772 0.722217
\(414\) −86.2842 −4.24064
\(415\) −2.18902 −0.107455
\(416\) 11.8087 0.578968
\(417\) −14.9489 −0.732049
\(418\) −6.18259 −0.302400
\(419\) 3.34458 0.163393 0.0816967 0.996657i \(-0.473966\pi\)
0.0816967 + 0.996657i \(0.473966\pi\)
\(420\) 7.80067 0.380634
\(421\) −5.73812 −0.279659 −0.139829 0.990176i \(-0.544655\pi\)
−0.139829 + 0.990176i \(0.544655\pi\)
\(422\) 48.8293 2.37697
\(423\) −37.3034 −1.81375
\(424\) 29.6118 1.43807
\(425\) −4.93310 −0.239291
\(426\) 15.1430 0.733680
\(427\) −24.9038 −1.20518
\(428\) −11.1976 −0.541258
\(429\) 5.19736 0.250931
\(430\) −2.54009 −0.122494
\(431\) 20.0619 0.966349 0.483174 0.875524i \(-0.339484\pi\)
0.483174 + 0.875524i \(0.339484\pi\)
\(432\) −4.16705 −0.200487
\(433\) 25.0529 1.20396 0.601982 0.798510i \(-0.294378\pi\)
0.601982 + 0.798510i \(0.294378\pi\)
\(434\) −3.68476 −0.176874
\(435\) 7.14042 0.342357
\(436\) 6.09980 0.292127
\(437\) 21.5882 1.03270
\(438\) −36.9617 −1.76610
\(439\) 2.44243 0.116571 0.0582853 0.998300i \(-0.481437\pi\)
0.0582853 + 0.998300i \(0.481437\pi\)
\(440\) −0.624372 −0.0297658
\(441\) 27.6741 1.31782
\(442\) −4.01179 −0.190821
\(443\) −20.5611 −0.976887 −0.488444 0.872595i \(-0.662435\pi\)
−0.488444 + 0.872595i \(0.662435\pi\)
\(444\) −8.29713 −0.393764
\(445\) −0.611657 −0.0289953
\(446\) −15.7569 −0.746111
\(447\) −17.6866 −0.836546
\(448\) −46.7733 −2.20983
\(449\) 13.9589 0.658759 0.329380 0.944198i \(-0.393160\pi\)
0.329380 + 0.944198i \(0.393160\pi\)
\(450\) 51.9047 2.44681
\(451\) 2.13660 0.100609
\(452\) −11.2448 −0.528910
\(453\) −52.5624 −2.46960
\(454\) 20.4427 0.959421
\(455\) 1.66192 0.0779122
\(456\) −16.8280 −0.788042
\(457\) −3.07697 −0.143934 −0.0719672 0.997407i \(-0.522928\pi\)
−0.0719672 + 0.997407i \(0.522928\pi\)
\(458\) 52.9179 2.47269
\(459\) 4.69390 0.219092
\(460\) 6.42229 0.299441
\(461\) −16.1174 −0.750660 −0.375330 0.926891i \(-0.622471\pi\)
−0.375330 + 0.926891i \(0.622471\pi\)
\(462\) −23.3929 −1.08834
\(463\) −17.7718 −0.825923 −0.412962 0.910748i \(-0.635506\pi\)
−0.412962 + 0.910748i \(0.635506\pi\)
\(464\) −8.83647 −0.410223
\(465\) 0.328248 0.0152221
\(466\) −2.08845 −0.0967454
\(467\) −23.8307 −1.10275 −0.551377 0.834256i \(-0.685898\pi\)
−0.551377 + 0.834256i \(0.685898\pi\)
\(468\) 25.4201 1.17505
\(469\) −0.357405 −0.0165034
\(470\) 4.61057 0.212670
\(471\) −14.3108 −0.659405
\(472\) −9.41924 −0.433556
\(473\) 4.58726 0.210923
\(474\) −54.2335 −2.49103
\(475\) −12.9865 −0.595862
\(476\) 10.8741 0.498412
\(477\) −60.2880 −2.76040
\(478\) −45.6893 −2.08978
\(479\) −40.6516 −1.85742 −0.928709 0.370810i \(-0.879080\pi\)
−0.928709 + 0.370810i \(0.879080\pi\)
\(480\) 4.73472 0.216110
\(481\) −1.76769 −0.0805998
\(482\) 24.7315 1.12649
\(483\) 81.6828 3.71669
\(484\) −29.9849 −1.36295
\(485\) −1.15144 −0.0522841
\(486\) 38.1586 1.73091
\(487\) 15.9016 0.720569 0.360285 0.932842i \(-0.382680\pi\)
0.360285 + 0.932842i \(0.382680\pi\)
\(488\) 15.9823 0.723484
\(489\) 57.7641 2.61218
\(490\) −3.42043 −0.154519
\(491\) 34.3728 1.55122 0.775611 0.631212i \(-0.217442\pi\)
0.775611 + 0.631212i \(0.217442\pi\)
\(492\) 17.1311 0.772329
\(493\) 9.95368 0.448291
\(494\) −10.5611 −0.475168
\(495\) 1.27119 0.0571357
\(496\) −0.406215 −0.0182396
\(497\) −8.74468 −0.392252
\(498\) 52.6336 2.35857
\(499\) −2.29217 −0.102611 −0.0513057 0.998683i \(-0.516338\pi\)
−0.0513057 + 0.998683i \(0.516338\pi\)
\(500\) −7.77913 −0.347893
\(501\) −37.8189 −1.68962
\(502\) 3.77220 0.168362
\(503\) −1.96361 −0.0875532 −0.0437766 0.999041i \(-0.513939\pi\)
−0.0437766 + 0.999041i \(0.513939\pi\)
\(504\) −38.8400 −1.73007
\(505\) 2.70123 0.120203
\(506\) −19.2594 −0.856183
\(507\) −27.1776 −1.20700
\(508\) −35.2290 −1.56303
\(509\) 13.5156 0.599070 0.299535 0.954085i \(-0.403168\pi\)
0.299535 + 0.954085i \(0.403168\pi\)
\(510\) −1.60854 −0.0712274
\(511\) 21.3444 0.944222
\(512\) −9.95151 −0.439799
\(513\) 12.3568 0.545566
\(514\) −29.1833 −1.28722
\(515\) −2.18045 −0.0960819
\(516\) 36.7803 1.61916
\(517\) −8.32644 −0.366196
\(518\) 7.95623 0.349577
\(519\) 56.7985 2.49318
\(520\) −1.06656 −0.0467716
\(521\) 0.274929 0.0120448 0.00602242 0.999982i \(-0.498083\pi\)
0.00602242 + 0.999982i \(0.498083\pi\)
\(522\) −104.730 −4.58390
\(523\) −4.64897 −0.203285 −0.101643 0.994821i \(-0.532410\pi\)
−0.101643 + 0.994821i \(0.532410\pi\)
\(524\) 18.3866 0.803223
\(525\) −49.1367 −2.14450
\(526\) −13.6701 −0.596045
\(527\) 0.457574 0.0199322
\(528\) −2.57888 −0.112231
\(529\) 44.2494 1.92389
\(530\) 7.45138 0.323667
\(531\) 19.1771 0.832214
\(532\) 28.6262 1.24111
\(533\) 3.64975 0.158088
\(534\) 14.7069 0.636431
\(535\) −0.956530 −0.0413544
\(536\) 0.229368 0.00990720
\(537\) 58.7322 2.53448
\(538\) 30.0974 1.29759
\(539\) 6.17711 0.266067
\(540\) 3.67604 0.158191
\(541\) 6.77060 0.291091 0.145545 0.989352i \(-0.453506\pi\)
0.145545 + 0.989352i \(0.453506\pi\)
\(542\) 57.8993 2.48699
\(543\) −15.0969 −0.647870
\(544\) 6.60016 0.282980
\(545\) 0.521061 0.0223198
\(546\) −39.9599 −1.71013
\(547\) 18.1744 0.777080 0.388540 0.921432i \(-0.372980\pi\)
0.388540 + 0.921432i \(0.372980\pi\)
\(548\) 13.5969 0.580829
\(549\) −32.5391 −1.38873
\(550\) 11.5856 0.494011
\(551\) 26.2033 1.11630
\(552\) −52.4208 −2.23118
\(553\) 31.3184 1.33180
\(554\) 59.6965 2.53626
\(555\) −0.708762 −0.0300853
\(556\) −16.3198 −0.692113
\(557\) −1.95955 −0.0830288 −0.0415144 0.999138i \(-0.513218\pi\)
−0.0415144 + 0.999138i \(0.513218\pi\)
\(558\) −4.81447 −0.203813
\(559\) 7.83599 0.331427
\(560\) −0.824630 −0.0348470
\(561\) 2.90494 0.122647
\(562\) −52.4322 −2.21172
\(563\) −24.8639 −1.04789 −0.523943 0.851753i \(-0.675540\pi\)
−0.523943 + 0.851753i \(0.675540\pi\)
\(564\) −66.7607 −2.81113
\(565\) −0.960558 −0.0404110
\(566\) −8.03767 −0.337848
\(567\) −3.80173 −0.159658
\(568\) 5.61199 0.235474
\(569\) 25.2778 1.05970 0.529850 0.848091i \(-0.322248\pi\)
0.529850 + 0.848091i \(0.322248\pi\)
\(570\) −4.23452 −0.177365
\(571\) −17.4454 −0.730068 −0.365034 0.930994i \(-0.618943\pi\)
−0.365034 + 0.930994i \(0.618943\pi\)
\(572\) 5.67400 0.237242
\(573\) −35.2861 −1.47410
\(574\) −16.4272 −0.685659
\(575\) −40.4543 −1.68706
\(576\) −61.1136 −2.54640
\(577\) 0.686171 0.0285657 0.0142828 0.999898i \(-0.495453\pi\)
0.0142828 + 0.999898i \(0.495453\pi\)
\(578\) −2.24229 −0.0932670
\(579\) −11.3251 −0.470657
\(580\) 7.79525 0.323680
\(581\) −30.3946 −1.26098
\(582\) 27.6856 1.14761
\(583\) −13.4568 −0.557324
\(584\) −13.6980 −0.566828
\(585\) 2.17145 0.0897786
\(586\) −22.5298 −0.930699
\(587\) −16.6202 −0.685990 −0.342995 0.939337i \(-0.611441\pi\)
−0.342995 + 0.939337i \(0.611441\pi\)
\(588\) 49.5275 2.04248
\(589\) 1.20458 0.0496337
\(590\) −2.37022 −0.0975804
\(591\) 36.2122 1.48957
\(592\) 0.877112 0.0360491
\(593\) 12.4402 0.510859 0.255430 0.966828i \(-0.417783\pi\)
0.255430 + 0.966828i \(0.417783\pi\)
\(594\) −11.0238 −0.452312
\(595\) 0.928891 0.0380808
\(596\) −19.3085 −0.790909
\(597\) 47.7930 1.95604
\(598\) −32.8990 −1.34534
\(599\) 10.6327 0.434438 0.217219 0.976123i \(-0.430301\pi\)
0.217219 + 0.976123i \(0.430301\pi\)
\(600\) 31.5340 1.28737
\(601\) 28.8198 1.17558 0.587792 0.809012i \(-0.299997\pi\)
0.587792 + 0.809012i \(0.299997\pi\)
\(602\) −35.2691 −1.43746
\(603\) −0.466982 −0.0190170
\(604\) −57.3827 −2.33487
\(605\) −2.56139 −0.104135
\(606\) −64.9495 −2.63839
\(607\) −19.0495 −0.773194 −0.386597 0.922249i \(-0.626350\pi\)
−0.386597 + 0.922249i \(0.626350\pi\)
\(608\) 17.3751 0.704653
\(609\) 99.1448 4.01755
\(610\) 4.02171 0.162834
\(611\) −14.2233 −0.575412
\(612\) 14.2080 0.574323
\(613\) −12.5793 −0.508073 −0.254037 0.967195i \(-0.581758\pi\)
−0.254037 + 0.967195i \(0.581758\pi\)
\(614\) −12.6604 −0.510934
\(615\) 1.46338 0.0590092
\(616\) −8.66941 −0.349301
\(617\) 1.80701 0.0727475 0.0363737 0.999338i \(-0.488419\pi\)
0.0363737 + 0.999338i \(0.488419\pi\)
\(618\) 52.4275 2.10894
\(619\) 33.0958 1.33023 0.665115 0.746741i \(-0.268382\pi\)
0.665115 + 0.746741i \(0.268382\pi\)
\(620\) 0.358350 0.0143917
\(621\) 38.4927 1.54466
\(622\) 58.7587 2.35601
\(623\) −8.49287 −0.340259
\(624\) −4.40526 −0.176352
\(625\) 24.0010 0.960040
\(626\) −44.2283 −1.76772
\(627\) 7.64732 0.305405
\(628\) −15.6232 −0.623432
\(629\) −0.988008 −0.0393945
\(630\) −9.77353 −0.389387
\(631\) −26.9155 −1.07149 −0.535744 0.844380i \(-0.679969\pi\)
−0.535744 + 0.844380i \(0.679969\pi\)
\(632\) −20.0989 −0.799493
\(633\) −60.3976 −2.40059
\(634\) −25.4129 −1.00927
\(635\) −3.00935 −0.119422
\(636\) −107.896 −4.27834
\(637\) 10.5518 0.418076
\(638\) −23.3766 −0.925489
\(639\) −11.4257 −0.451994
\(640\) 4.13919 0.163616
\(641\) −24.0217 −0.948801 −0.474401 0.880309i \(-0.657335\pi\)
−0.474401 + 0.880309i \(0.657335\pi\)
\(642\) 22.9992 0.907705
\(643\) 15.1679 0.598165 0.299083 0.954227i \(-0.403319\pi\)
0.299083 + 0.954227i \(0.403319\pi\)
\(644\) 89.1736 3.51393
\(645\) 3.14187 0.123711
\(646\) −5.90288 −0.232246
\(647\) 1.41870 0.0557747 0.0278874 0.999611i \(-0.491122\pi\)
0.0278874 + 0.999611i \(0.491122\pi\)
\(648\) 2.43980 0.0958445
\(649\) 4.28049 0.168024
\(650\) 19.7906 0.776250
\(651\) 4.55772 0.178631
\(652\) 63.0614 2.46968
\(653\) 46.7022 1.82760 0.913799 0.406166i \(-0.133134\pi\)
0.913799 + 0.406166i \(0.133134\pi\)
\(654\) −12.5286 −0.489906
\(655\) 1.57063 0.0613697
\(656\) −1.81097 −0.0707066
\(657\) 27.8884 1.08803
\(658\) 64.0178 2.49567
\(659\) −4.78889 −0.186549 −0.0932743 0.995640i \(-0.529733\pi\)
−0.0932743 + 0.995640i \(0.529733\pi\)
\(660\) 2.27501 0.0885545
\(661\) 27.2045 1.05813 0.529065 0.848581i \(-0.322543\pi\)
0.529065 + 0.848581i \(0.322543\pi\)
\(662\) −8.99878 −0.349748
\(663\) 4.96223 0.192717
\(664\) 19.5060 0.756981
\(665\) 2.44533 0.0948257
\(666\) 10.3955 0.402819
\(667\) 81.6259 3.16057
\(668\) −41.2871 −1.59745
\(669\) 19.4899 0.753524
\(670\) 0.0577173 0.00222981
\(671\) −7.26300 −0.280385
\(672\) 65.7417 2.53604
\(673\) −32.5710 −1.25552 −0.627760 0.778407i \(-0.716028\pi\)
−0.627760 + 0.778407i \(0.716028\pi\)
\(674\) 42.9829 1.65564
\(675\) −23.1555 −0.891255
\(676\) −29.6699 −1.14115
\(677\) 1.44429 0.0555086 0.0277543 0.999615i \(-0.491164\pi\)
0.0277543 + 0.999615i \(0.491164\pi\)
\(678\) 23.0960 0.886997
\(679\) −15.9877 −0.613553
\(680\) −0.596126 −0.0228604
\(681\) −25.2858 −0.968953
\(682\) −1.07463 −0.0411497
\(683\) 9.08456 0.347611 0.173806 0.984780i \(-0.444394\pi\)
0.173806 + 0.984780i \(0.444394\pi\)
\(684\) 37.4028 1.43013
\(685\) 1.16148 0.0443778
\(686\) 8.87700 0.338925
\(687\) −65.4549 −2.49726
\(688\) −3.88814 −0.148234
\(689\) −22.9870 −0.875735
\(690\) −13.1910 −0.502171
\(691\) 48.1281 1.83088 0.915439 0.402457i \(-0.131844\pi\)
0.915439 + 0.402457i \(0.131844\pi\)
\(692\) 62.0073 2.35716
\(693\) 17.6505 0.670486
\(694\) −6.88021 −0.261169
\(695\) −1.39408 −0.0528803
\(696\) −63.6273 −2.41179
\(697\) 2.03994 0.0772682
\(698\) −36.5908 −1.38498
\(699\) 2.58323 0.0977066
\(700\) −53.6429 −2.02751
\(701\) 11.4232 0.431449 0.215724 0.976454i \(-0.430789\pi\)
0.215724 + 0.976454i \(0.430789\pi\)
\(702\) −18.8309 −0.710728
\(703\) −2.60095 −0.0980969
\(704\) −13.6411 −0.514118
\(705\) −5.70287 −0.214783
\(706\) 2.24229 0.0843897
\(707\) 37.5066 1.41058
\(708\) 34.3206 1.28985
\(709\) 4.66813 0.175315 0.0876577 0.996151i \(-0.472062\pi\)
0.0876577 + 0.996151i \(0.472062\pi\)
\(710\) 1.41218 0.0529981
\(711\) 40.9204 1.53463
\(712\) 5.45039 0.204262
\(713\) 3.75237 0.140527
\(714\) −22.3346 −0.835851
\(715\) 0.484687 0.0181263
\(716\) 64.1183 2.39621
\(717\) 56.5136 2.11054
\(718\) −61.9332 −2.31133
\(719\) −15.7575 −0.587656 −0.293828 0.955858i \(-0.594929\pi\)
−0.293828 + 0.955858i \(0.594929\pi\)
\(720\) −1.07745 −0.0401544
\(721\) −30.2755 −1.12752
\(722\) 27.0640 1.00722
\(723\) −30.5907 −1.13768
\(724\) −16.4814 −0.612526
\(725\) −49.1025 −1.82362
\(726\) 61.5870 2.28571
\(727\) −17.6293 −0.653836 −0.326918 0.945053i \(-0.606010\pi\)
−0.326918 + 0.945053i \(0.606010\pi\)
\(728\) −14.8091 −0.548864
\(729\) −44.0231 −1.63049
\(730\) −3.44691 −0.127576
\(731\) 4.37973 0.161990
\(732\) −58.2342 −2.15240
\(733\) 14.1992 0.524460 0.262230 0.965005i \(-0.415542\pi\)
0.262230 + 0.965005i \(0.415542\pi\)
\(734\) −12.1146 −0.447157
\(735\) 4.23077 0.156054
\(736\) 54.1251 1.99508
\(737\) −0.104234 −0.00383952
\(738\) −21.4637 −0.790089
\(739\) 12.9712 0.477153 0.238576 0.971124i \(-0.423319\pi\)
0.238576 + 0.971124i \(0.423319\pi\)
\(740\) −0.773760 −0.0284440
\(741\) 13.0632 0.479889
\(742\) 103.463 3.79823
\(743\) −29.8536 −1.09522 −0.547611 0.836733i \(-0.684463\pi\)
−0.547611 + 0.836733i \(0.684463\pi\)
\(744\) −2.92497 −0.107234
\(745\) −1.64938 −0.0604288
\(746\) 37.5014 1.37302
\(747\) −39.7132 −1.45303
\(748\) 3.17134 0.115956
\(749\) −13.2814 −0.485293
\(750\) 15.9778 0.583427
\(751\) −5.59982 −0.204340 −0.102170 0.994767i \(-0.532579\pi\)
−0.102170 + 0.994767i \(0.532579\pi\)
\(752\) 7.05746 0.257359
\(753\) −4.66589 −0.170034
\(754\) −39.9321 −1.45424
\(755\) −4.90178 −0.178394
\(756\) 51.0418 1.85637
\(757\) 12.0124 0.436596 0.218298 0.975882i \(-0.429949\pi\)
0.218298 + 0.975882i \(0.429949\pi\)
\(758\) 56.3685 2.04740
\(759\) 23.8222 0.864690
\(760\) −1.56932 −0.0569250
\(761\) −7.81185 −0.283180 −0.141590 0.989925i \(-0.545221\pi\)
−0.141590 + 0.989925i \(0.545221\pi\)
\(762\) 72.3580 2.62125
\(763\) 7.23493 0.261922
\(764\) −38.5221 −1.39368
\(765\) 1.21368 0.0438807
\(766\) −27.9126 −1.00852
\(767\) 7.31196 0.264020
\(768\) −27.2799 −0.984379
\(769\) −11.1644 −0.402598 −0.201299 0.979530i \(-0.564516\pi\)
−0.201299 + 0.979530i \(0.564516\pi\)
\(770\) −2.18154 −0.0786171
\(771\) 36.0972 1.30001
\(772\) −12.3637 −0.444981
\(773\) 43.1464 1.55187 0.775934 0.630814i \(-0.217279\pi\)
0.775934 + 0.630814i \(0.217279\pi\)
\(774\) −46.0823 −1.65640
\(775\) −2.25726 −0.0810832
\(776\) 10.2603 0.368323
\(777\) −9.84117 −0.353050
\(778\) −23.4411 −0.840404
\(779\) 5.37019 0.192407
\(780\) 3.88618 0.139148
\(781\) −2.55032 −0.0912576
\(782\) −18.3881 −0.657556
\(783\) 46.7216 1.66969
\(784\) −5.23569 −0.186989
\(785\) −1.33457 −0.0476328
\(786\) −37.7649 −1.34703
\(787\) −7.56238 −0.269570 −0.134785 0.990875i \(-0.543034\pi\)
−0.134785 + 0.990875i \(0.543034\pi\)
\(788\) 39.5331 1.40831
\(789\) 16.9087 0.601966
\(790\) −5.05762 −0.179942
\(791\) −13.3373 −0.474221
\(792\) −11.3274 −0.402501
\(793\) −12.4067 −0.440575
\(794\) 19.7387 0.700500
\(795\) −9.21671 −0.326883
\(796\) 52.1759 1.84932
\(797\) 42.9869 1.52268 0.761338 0.648355i \(-0.224543\pi\)
0.761338 + 0.648355i \(0.224543\pi\)
\(798\) −58.7964 −2.08137
\(799\) −7.94975 −0.281242
\(800\) −32.5593 −1.15114
\(801\) −11.0967 −0.392083
\(802\) 56.4677 1.99394
\(803\) 6.22494 0.219673
\(804\) −0.835742 −0.0294744
\(805\) 7.61744 0.268479
\(806\) −1.83569 −0.0646595
\(807\) −37.2279 −1.31048
\(808\) −24.0703 −0.846790
\(809\) 1.06032 0.0372789 0.0186394 0.999826i \(-0.494067\pi\)
0.0186394 + 0.999826i \(0.494067\pi\)
\(810\) 0.613942 0.0215717
\(811\) 47.3065 1.66116 0.830578 0.556902i \(-0.188010\pi\)
0.830578 + 0.556902i \(0.188010\pi\)
\(812\) 108.237 3.79838
\(813\) −71.6164 −2.51170
\(814\) 2.32038 0.0813291
\(815\) 5.38687 0.188694
\(816\) −2.46221 −0.0861947
\(817\) 11.5298 0.403375
\(818\) 52.1471 1.82328
\(819\) 30.1506 1.05355
\(820\) 1.59758 0.0557900
\(821\) −36.5810 −1.27668 −0.638342 0.769753i \(-0.720379\pi\)
−0.638342 + 0.769753i \(0.720379\pi\)
\(822\) −27.9270 −0.974067
\(823\) 54.1160 1.88637 0.943183 0.332274i \(-0.107816\pi\)
0.943183 + 0.332274i \(0.107816\pi\)
\(824\) 19.4296 0.676863
\(825\) −14.3304 −0.498919
\(826\) −32.9105 −1.14510
\(827\) 46.6636 1.62265 0.811327 0.584593i \(-0.198746\pi\)
0.811327 + 0.584593i \(0.198746\pi\)
\(828\) 116.513 4.04912
\(829\) 35.5682 1.23533 0.617667 0.786440i \(-0.288078\pi\)
0.617667 + 0.786440i \(0.288078\pi\)
\(830\) 4.90842 0.170374
\(831\) −73.8393 −2.56146
\(832\) −23.3018 −0.807845
\(833\) 5.89765 0.204342
\(834\) 33.5197 1.16069
\(835\) −3.52685 −0.122052
\(836\) 8.34863 0.288743
\(837\) 2.14781 0.0742391
\(838\) −7.49952 −0.259067
\(839\) −7.20767 −0.248836 −0.124418 0.992230i \(-0.539706\pi\)
−0.124418 + 0.992230i \(0.539706\pi\)
\(840\) −5.93778 −0.204873
\(841\) 70.0758 2.41641
\(842\) 12.8665 0.443410
\(843\) 64.8541 2.23369
\(844\) −65.9364 −2.26962
\(845\) −2.53448 −0.0871887
\(846\) 83.6451 2.87578
\(847\) −35.5649 −1.22202
\(848\) 11.4059 0.391681
\(849\) 9.94189 0.341205
\(850\) 11.0614 0.379404
\(851\) −8.10223 −0.277741
\(852\) −20.4482 −0.700545
\(853\) 35.8698 1.22816 0.614079 0.789245i \(-0.289528\pi\)
0.614079 + 0.789245i \(0.289528\pi\)
\(854\) 55.8415 1.91086
\(855\) 3.19504 0.109268
\(856\) 8.52350 0.291327
\(857\) 29.0155 0.991152 0.495576 0.868565i \(-0.334957\pi\)
0.495576 + 0.868565i \(0.334957\pi\)
\(858\) −11.6540 −0.397861
\(859\) 20.4675 0.698343 0.349172 0.937059i \(-0.386463\pi\)
0.349172 + 0.937059i \(0.386463\pi\)
\(860\) 3.43000 0.116962
\(861\) 20.3190 0.692471
\(862\) −44.9847 −1.53218
\(863\) 17.7562 0.604429 0.302214 0.953240i \(-0.402274\pi\)
0.302214 + 0.953240i \(0.402274\pi\)
\(864\) 30.9805 1.05398
\(865\) 5.29682 0.180097
\(866\) −56.1758 −1.90893
\(867\) 2.77352 0.0941936
\(868\) 4.97569 0.168886
\(869\) 9.13378 0.309842
\(870\) −16.0109 −0.542821
\(871\) −0.178054 −0.00603312
\(872\) −4.64309 −0.157235
\(873\) −20.8894 −0.707000
\(874\) −48.4070 −1.63739
\(875\) −9.22676 −0.311922
\(876\) 49.9111 1.68634
\(877\) −15.3350 −0.517827 −0.258913 0.965901i \(-0.583364\pi\)
−0.258913 + 0.965901i \(0.583364\pi\)
\(878\) −5.47663 −0.184827
\(879\) 27.8674 0.939945
\(880\) −0.240497 −0.00810716
\(881\) 32.5068 1.09518 0.547592 0.836746i \(-0.315545\pi\)
0.547592 + 0.836746i \(0.315545\pi\)
\(882\) −62.0535 −2.08945
\(883\) −55.6882 −1.87406 −0.937028 0.349254i \(-0.886435\pi\)
−0.937028 + 0.349254i \(0.886435\pi\)
\(884\) 5.41730 0.182204
\(885\) 2.93175 0.0985499
\(886\) 46.1040 1.54889
\(887\) 35.8222 1.20279 0.601395 0.798952i \(-0.294612\pi\)
0.601395 + 0.798952i \(0.294612\pi\)
\(888\) 6.31567 0.211940
\(889\) −41.7849 −1.40142
\(890\) 1.37151 0.0459732
\(891\) −1.10875 −0.0371444
\(892\) 21.2773 0.712416
\(893\) −20.9279 −0.700326
\(894\) 39.6584 1.32638
\(895\) 5.47715 0.183081
\(896\) 57.4727 1.92003
\(897\) 40.6932 1.35871
\(898\) −31.2998 −1.04449
\(899\) 4.55455 0.151903
\(900\) −70.0893 −2.33631
\(901\) −12.8480 −0.428029
\(902\) −4.79088 −0.159519
\(903\) 43.6248 1.45174
\(904\) 8.55939 0.284681
\(905\) −1.40788 −0.0467996
\(906\) 117.860 3.91564
\(907\) −13.7643 −0.457034 −0.228517 0.973540i \(-0.573388\pi\)
−0.228517 + 0.973540i \(0.573388\pi\)
\(908\) −27.6046 −0.916092
\(909\) 49.0058 1.62542
\(910\) −3.72651 −0.123533
\(911\) 29.5818 0.980087 0.490044 0.871698i \(-0.336981\pi\)
0.490044 + 0.871698i \(0.336981\pi\)
\(912\) −6.48184 −0.214635
\(913\) −8.86434 −0.293367
\(914\) 6.89946 0.228214
\(915\) −4.97451 −0.164452
\(916\) −71.4575 −2.36102
\(917\) 21.8082 0.720171
\(918\) −10.5251 −0.347380
\(919\) −26.9933 −0.890426 −0.445213 0.895425i \(-0.646872\pi\)
−0.445213 + 0.895425i \(0.646872\pi\)
\(920\) −4.88857 −0.161171
\(921\) 15.6599 0.516010
\(922\) 36.1398 1.19020
\(923\) −4.35647 −0.143395
\(924\) 31.5885 1.03919
\(925\) 4.87394 0.160254
\(926\) 39.8494 1.30953
\(927\) −39.5577 −1.29925
\(928\) 65.6959 2.15657
\(929\) −48.5772 −1.59377 −0.796883 0.604134i \(-0.793519\pi\)
−0.796883 + 0.604134i \(0.793519\pi\)
\(930\) −0.736027 −0.0241353
\(931\) 15.5257 0.508835
\(932\) 2.82012 0.0923762
\(933\) −72.6794 −2.37942
\(934\) 53.4354 1.74846
\(935\) 0.270904 0.00885950
\(936\) −19.3495 −0.632458
\(937\) 57.9308 1.89252 0.946259 0.323409i \(-0.104829\pi\)
0.946259 + 0.323409i \(0.104829\pi\)
\(938\) 0.801405 0.0261668
\(939\) 54.7065 1.78528
\(940\) −6.22586 −0.203065
\(941\) 45.9864 1.49911 0.749557 0.661940i \(-0.230267\pi\)
0.749557 + 0.661940i \(0.230267\pi\)
\(942\) 32.0889 1.04551
\(943\) 16.7287 0.544760
\(944\) −3.62812 −0.118085
\(945\) 4.36012 0.141835
\(946\) −10.2860 −0.334426
\(947\) 41.1110 1.33593 0.667964 0.744194i \(-0.267166\pi\)
0.667964 + 0.744194i \(0.267166\pi\)
\(948\) 73.2339 2.37853
\(949\) 10.6335 0.345177
\(950\) 29.1195 0.944762
\(951\) 31.4335 1.01930
\(952\) −8.27721 −0.268266
\(953\) −12.8160 −0.415149 −0.207575 0.978219i \(-0.566557\pi\)
−0.207575 + 0.978219i \(0.566557\pi\)
\(954\) 135.183 4.37672
\(955\) −3.29065 −0.106483
\(956\) 61.6963 1.99540
\(957\) 28.9148 0.934684
\(958\) 91.1526 2.94501
\(959\) 16.1271 0.520772
\(960\) −9.34293 −0.301542
\(961\) −30.7906 −0.993246
\(962\) 3.96368 0.127794
\(963\) −17.3534 −0.559205
\(964\) −33.3961 −1.07561
\(965\) −1.05614 −0.0339984
\(966\) −183.156 −5.89296
\(967\) 13.5822 0.436773 0.218386 0.975862i \(-0.429921\pi\)
0.218386 + 0.975862i \(0.429921\pi\)
\(968\) 22.8242 0.733596
\(969\) 7.30135 0.234553
\(970\) 2.58186 0.0828985
\(971\) −38.8817 −1.24777 −0.623886 0.781515i \(-0.714447\pi\)
−0.623886 + 0.781515i \(0.714447\pi\)
\(972\) −51.5273 −1.65274
\(973\) −19.3568 −0.620549
\(974\) −35.6559 −1.14249
\(975\) −24.4792 −0.783962
\(976\) 6.15609 0.197052
\(977\) 62.3859 1.99590 0.997951 0.0639817i \(-0.0203799\pi\)
0.997951 + 0.0639817i \(0.0203799\pi\)
\(978\) −129.524 −4.14172
\(979\) −2.47688 −0.0791614
\(980\) 4.61876 0.147541
\(981\) 9.45309 0.301814
\(982\) −77.0737 −2.45952
\(983\) −0.0798366 −0.00254639 −0.00127320 0.999999i \(-0.500405\pi\)
−0.00127320 + 0.999999i \(0.500405\pi\)
\(984\) −13.0400 −0.415699
\(985\) 3.37702 0.107601
\(986\) −22.3191 −0.710783
\(987\) −79.1844 −2.52047
\(988\) 14.2612 0.453709
\(989\) 35.9163 1.14207
\(990\) −2.85038 −0.0905909
\(991\) 30.0863 0.955722 0.477861 0.878435i \(-0.341412\pi\)
0.477861 + 0.878435i \(0.341412\pi\)
\(992\) 3.02006 0.0958871
\(993\) 11.1307 0.353222
\(994\) 19.6081 0.621931
\(995\) 4.45700 0.141296
\(996\) −71.0735 −2.25205
\(997\) −32.4348 −1.02722 −0.513610 0.858024i \(-0.671692\pi\)
−0.513610 + 0.858024i \(0.671692\pi\)
\(998\) 5.13970 0.162694
\(999\) −4.63761 −0.146727
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 6001.2.a.d.1.15 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.15 121 1.1 even 1 trivial