Properties

Label 4034.2.a.d.1.3
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.09514 q^{3} +1.00000 q^{4} +3.37243 q^{5} -3.09514 q^{6} +1.17193 q^{7} +1.00000 q^{8} +6.57990 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.09514 q^{3} +1.00000 q^{4} +3.37243 q^{5} -3.09514 q^{6} +1.17193 q^{7} +1.00000 q^{8} +6.57990 q^{9} +3.37243 q^{10} -1.16179 q^{11} -3.09514 q^{12} +7.15502 q^{13} +1.17193 q^{14} -10.4381 q^{15} +1.00000 q^{16} +5.64765 q^{17} +6.57990 q^{18} +0.667721 q^{19} +3.37243 q^{20} -3.62727 q^{21} -1.16179 q^{22} +2.74436 q^{23} -3.09514 q^{24} +6.37325 q^{25} +7.15502 q^{26} -11.0803 q^{27} +1.17193 q^{28} -1.38111 q^{29} -10.4381 q^{30} -0.606427 q^{31} +1.00000 q^{32} +3.59590 q^{33} +5.64765 q^{34} +3.95223 q^{35} +6.57990 q^{36} +10.1198 q^{37} +0.667721 q^{38} -22.1458 q^{39} +3.37243 q^{40} -2.86718 q^{41} -3.62727 q^{42} +2.19997 q^{43} -1.16179 q^{44} +22.1902 q^{45} +2.74436 q^{46} -3.44861 q^{47} -3.09514 q^{48} -5.62659 q^{49} +6.37325 q^{50} -17.4803 q^{51} +7.15502 q^{52} -10.4093 q^{53} -11.0803 q^{54} -3.91805 q^{55} +1.17193 q^{56} -2.06669 q^{57} -1.38111 q^{58} +8.31170 q^{59} -10.4381 q^{60} -8.17995 q^{61} -0.606427 q^{62} +7.71115 q^{63} +1.00000 q^{64} +24.1298 q^{65} +3.59590 q^{66} -1.41052 q^{67} +5.64765 q^{68} -8.49417 q^{69} +3.95223 q^{70} +2.93219 q^{71} +6.57990 q^{72} +0.186200 q^{73} +10.1198 q^{74} -19.7261 q^{75} +0.667721 q^{76} -1.36153 q^{77} -22.1458 q^{78} -7.87285 q^{79} +3.37243 q^{80} +14.5553 q^{81} -2.86718 q^{82} -12.1226 q^{83} -3.62727 q^{84} +19.0463 q^{85} +2.19997 q^{86} +4.27472 q^{87} -1.16179 q^{88} -10.9044 q^{89} +22.1902 q^{90} +8.38515 q^{91} +2.74436 q^{92} +1.87698 q^{93} -3.44861 q^{94} +2.25184 q^{95} -3.09514 q^{96} +12.0786 q^{97} -5.62659 q^{98} -7.64445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.09514 −1.78698 −0.893490 0.449083i \(-0.851751\pi\)
−0.893490 + 0.449083i \(0.851751\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.37243 1.50819 0.754097 0.656763i \(-0.228075\pi\)
0.754097 + 0.656763i \(0.228075\pi\)
\(6\) −3.09514 −1.26359
\(7\) 1.17193 0.442946 0.221473 0.975166i \(-0.428913\pi\)
0.221473 + 0.975166i \(0.428913\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.57990 2.19330
\(10\) 3.37243 1.06645
\(11\) −1.16179 −0.350292 −0.175146 0.984542i \(-0.556040\pi\)
−0.175146 + 0.984542i \(0.556040\pi\)
\(12\) −3.09514 −0.893490
\(13\) 7.15502 1.98445 0.992223 0.124474i \(-0.0397243\pi\)
0.992223 + 0.124474i \(0.0397243\pi\)
\(14\) 1.17193 0.313210
\(15\) −10.4381 −2.69511
\(16\) 1.00000 0.250000
\(17\) 5.64765 1.36976 0.684878 0.728657i \(-0.259855\pi\)
0.684878 + 0.728657i \(0.259855\pi\)
\(18\) 6.57990 1.55090
\(19\) 0.667721 0.153186 0.0765929 0.997062i \(-0.475596\pi\)
0.0765929 + 0.997062i \(0.475596\pi\)
\(20\) 3.37243 0.754097
\(21\) −3.62727 −0.791536
\(22\) −1.16179 −0.247694
\(23\) 2.74436 0.572238 0.286119 0.958194i \(-0.407635\pi\)
0.286119 + 0.958194i \(0.407635\pi\)
\(24\) −3.09514 −0.631793
\(25\) 6.37325 1.27465
\(26\) 7.15502 1.40322
\(27\) −11.0803 −2.13240
\(28\) 1.17193 0.221473
\(29\) −1.38111 −0.256465 −0.128233 0.991744i \(-0.540930\pi\)
−0.128233 + 0.991744i \(0.540930\pi\)
\(30\) −10.4381 −1.90573
\(31\) −0.606427 −0.108917 −0.0544587 0.998516i \(-0.517343\pi\)
−0.0544587 + 0.998516i \(0.517343\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.59590 0.625966
\(34\) 5.64765 0.968564
\(35\) 3.95223 0.668049
\(36\) 6.57990 1.09665
\(37\) 10.1198 1.66369 0.831843 0.555011i \(-0.187286\pi\)
0.831843 + 0.555011i \(0.187286\pi\)
\(38\) 0.667721 0.108319
\(39\) −22.1458 −3.54617
\(40\) 3.37243 0.533227
\(41\) −2.86718 −0.447778 −0.223889 0.974615i \(-0.571875\pi\)
−0.223889 + 0.974615i \(0.571875\pi\)
\(42\) −3.62727 −0.559701
\(43\) 2.19997 0.335493 0.167746 0.985830i \(-0.446351\pi\)
0.167746 + 0.985830i \(0.446351\pi\)
\(44\) −1.16179 −0.175146
\(45\) 22.1902 3.30792
\(46\) 2.74436 0.404633
\(47\) −3.44861 −0.503032 −0.251516 0.967853i \(-0.580929\pi\)
−0.251516 + 0.967853i \(0.580929\pi\)
\(48\) −3.09514 −0.446745
\(49\) −5.62659 −0.803799
\(50\) 6.37325 0.901314
\(51\) −17.4803 −2.44773
\(52\) 7.15502 0.992223
\(53\) −10.4093 −1.42983 −0.714916 0.699210i \(-0.753535\pi\)
−0.714916 + 0.699210i \(0.753535\pi\)
\(54\) −11.0803 −1.50784
\(55\) −3.91805 −0.528309
\(56\) 1.17193 0.156605
\(57\) −2.06669 −0.273740
\(58\) −1.38111 −0.181348
\(59\) 8.31170 1.08209 0.541046 0.840993i \(-0.318029\pi\)
0.541046 + 0.840993i \(0.318029\pi\)
\(60\) −10.4381 −1.34756
\(61\) −8.17995 −1.04733 −0.523667 0.851923i \(-0.675437\pi\)
−0.523667 + 0.851923i \(0.675437\pi\)
\(62\) −0.606427 −0.0770163
\(63\) 7.71115 0.971513
\(64\) 1.00000 0.125000
\(65\) 24.1298 2.99293
\(66\) 3.59590 0.442625
\(67\) −1.41052 −0.172322 −0.0861611 0.996281i \(-0.527460\pi\)
−0.0861611 + 0.996281i \(0.527460\pi\)
\(68\) 5.64765 0.684878
\(69\) −8.49417 −1.02258
\(70\) 3.95223 0.472382
\(71\) 2.93219 0.347987 0.173994 0.984747i \(-0.444333\pi\)
0.173994 + 0.984747i \(0.444333\pi\)
\(72\) 6.57990 0.775448
\(73\) 0.186200 0.0217931 0.0108965 0.999941i \(-0.496531\pi\)
0.0108965 + 0.999941i \(0.496531\pi\)
\(74\) 10.1198 1.17640
\(75\) −19.7261 −2.27778
\(76\) 0.667721 0.0765929
\(77\) −1.36153 −0.155161
\(78\) −22.1458 −2.50752
\(79\) −7.87285 −0.885765 −0.442883 0.896580i \(-0.646044\pi\)
−0.442883 + 0.896580i \(0.646044\pi\)
\(80\) 3.37243 0.377049
\(81\) 14.5553 1.61726
\(82\) −2.86718 −0.316627
\(83\) −12.1226 −1.33063 −0.665314 0.746563i \(-0.731702\pi\)
−0.665314 + 0.746563i \(0.731702\pi\)
\(84\) −3.62727 −0.395768
\(85\) 19.0463 2.06586
\(86\) 2.19997 0.237229
\(87\) 4.27472 0.458298
\(88\) −1.16179 −0.123847
\(89\) −10.9044 −1.15587 −0.577934 0.816084i \(-0.696141\pi\)
−0.577934 + 0.816084i \(0.696141\pi\)
\(90\) 22.1902 2.33905
\(91\) 8.38515 0.879003
\(92\) 2.74436 0.286119
\(93\) 1.87698 0.194633
\(94\) −3.44861 −0.355697
\(95\) 2.25184 0.231034
\(96\) −3.09514 −0.315896
\(97\) 12.0786 1.22640 0.613200 0.789928i \(-0.289882\pi\)
0.613200 + 0.789928i \(0.289882\pi\)
\(98\) −5.62659 −0.568371
\(99\) −7.64445 −0.768296
\(100\) 6.37325 0.637325
\(101\) −2.77146 −0.275771 −0.137885 0.990448i \(-0.544031\pi\)
−0.137885 + 0.990448i \(0.544031\pi\)
\(102\) −17.4803 −1.73081
\(103\) −12.0754 −1.18983 −0.594913 0.803790i \(-0.702814\pi\)
−0.594913 + 0.803790i \(0.702814\pi\)
\(104\) 7.15502 0.701608
\(105\) −12.2327 −1.19379
\(106\) −10.4093 −1.01104
\(107\) −1.25914 −0.121726 −0.0608628 0.998146i \(-0.519385\pi\)
−0.0608628 + 0.998146i \(0.519385\pi\)
\(108\) −11.0803 −1.06620
\(109\) −7.66963 −0.734617 −0.367309 0.930099i \(-0.619721\pi\)
−0.367309 + 0.930099i \(0.619721\pi\)
\(110\) −3.91805 −0.373571
\(111\) −31.3222 −2.97297
\(112\) 1.17193 0.110737
\(113\) 6.88774 0.647944 0.323972 0.946067i \(-0.394982\pi\)
0.323972 + 0.946067i \(0.394982\pi\)
\(114\) −2.06669 −0.193563
\(115\) 9.25514 0.863046
\(116\) −1.38111 −0.128233
\(117\) 47.0793 4.35248
\(118\) 8.31170 0.765154
\(119\) 6.61863 0.606729
\(120\) −10.4381 −0.952867
\(121\) −9.65025 −0.877295
\(122\) −8.17995 −0.740577
\(123\) 8.87433 0.800171
\(124\) −0.606427 −0.0544587
\(125\) 4.63119 0.414227
\(126\) 7.71115 0.686964
\(127\) 19.8666 1.76288 0.881438 0.472300i \(-0.156576\pi\)
0.881438 + 0.472300i \(0.156576\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.80923 −0.599519
\(130\) 24.1298 2.11632
\(131\) −10.9687 −0.958344 −0.479172 0.877721i \(-0.659063\pi\)
−0.479172 + 0.877721i \(0.659063\pi\)
\(132\) 3.59590 0.312983
\(133\) 0.782520 0.0678531
\(134\) −1.41052 −0.121850
\(135\) −37.3674 −3.21608
\(136\) 5.64765 0.484282
\(137\) −1.02417 −0.0875009 −0.0437504 0.999042i \(-0.513931\pi\)
−0.0437504 + 0.999042i \(0.513931\pi\)
\(138\) −8.49417 −0.723072
\(139\) 6.63619 0.562875 0.281437 0.959580i \(-0.409189\pi\)
0.281437 + 0.959580i \(0.409189\pi\)
\(140\) 3.95223 0.334025
\(141\) 10.6739 0.898909
\(142\) 2.93219 0.246064
\(143\) −8.31262 −0.695136
\(144\) 6.57990 0.548325
\(145\) −4.65768 −0.386800
\(146\) 0.186200 0.0154100
\(147\) 17.4151 1.43637
\(148\) 10.1198 0.831843
\(149\) −18.2122 −1.49200 −0.746001 0.665945i \(-0.768029\pi\)
−0.746001 + 0.665945i \(0.768029\pi\)
\(150\) −19.7261 −1.61063
\(151\) −4.39046 −0.357291 −0.178645 0.983914i \(-0.557171\pi\)
−0.178645 + 0.983914i \(0.557171\pi\)
\(152\) 0.667721 0.0541593
\(153\) 37.1610 3.00429
\(154\) −1.36153 −0.109715
\(155\) −2.04513 −0.164269
\(156\) −22.1458 −1.77308
\(157\) −10.6060 −0.846448 −0.423224 0.906025i \(-0.639102\pi\)
−0.423224 + 0.906025i \(0.639102\pi\)
\(158\) −7.87285 −0.626331
\(159\) 32.2184 2.55508
\(160\) 3.37243 0.266614
\(161\) 3.21618 0.253471
\(162\) 14.5553 1.14358
\(163\) 9.28058 0.726911 0.363456 0.931611i \(-0.381597\pi\)
0.363456 + 0.931611i \(0.381597\pi\)
\(164\) −2.86718 −0.223889
\(165\) 12.1269 0.944078
\(166\) −12.1226 −0.940897
\(167\) −25.5066 −1.97376 −0.986880 0.161456i \(-0.948381\pi\)
−0.986880 + 0.161456i \(0.948381\pi\)
\(168\) −3.62727 −0.279850
\(169\) 38.1943 2.93802
\(170\) 19.0463 1.46078
\(171\) 4.39354 0.335982
\(172\) 2.19997 0.167746
\(173\) 9.08870 0.691001 0.345500 0.938419i \(-0.387709\pi\)
0.345500 + 0.938419i \(0.387709\pi\)
\(174\) 4.27472 0.324066
\(175\) 7.46898 0.564602
\(176\) −1.16179 −0.0875731
\(177\) −25.7259 −1.93368
\(178\) −10.9044 −0.817321
\(179\) 12.9207 0.965737 0.482868 0.875693i \(-0.339595\pi\)
0.482868 + 0.875693i \(0.339595\pi\)
\(180\) 22.1902 1.65396
\(181\) 4.46300 0.331732 0.165866 0.986148i \(-0.446958\pi\)
0.165866 + 0.986148i \(0.446958\pi\)
\(182\) 8.38515 0.621549
\(183\) 25.3181 1.87157
\(184\) 2.74436 0.202317
\(185\) 34.1283 2.50916
\(186\) 1.87698 0.137627
\(187\) −6.56138 −0.479815
\(188\) −3.44861 −0.251516
\(189\) −12.9853 −0.944539
\(190\) 2.25184 0.163366
\(191\) 7.39196 0.534863 0.267432 0.963577i \(-0.413825\pi\)
0.267432 + 0.963577i \(0.413825\pi\)
\(192\) −3.09514 −0.223373
\(193\) −1.96179 −0.141212 −0.0706062 0.997504i \(-0.522493\pi\)
−0.0706062 + 0.997504i \(0.522493\pi\)
\(194\) 12.0786 0.867196
\(195\) −74.6850 −5.34831
\(196\) −5.62659 −0.401899
\(197\) −16.3156 −1.16244 −0.581219 0.813747i \(-0.697424\pi\)
−0.581219 + 0.813747i \(0.697424\pi\)
\(198\) −7.64445 −0.543267
\(199\) −1.67899 −0.119021 −0.0595103 0.998228i \(-0.518954\pi\)
−0.0595103 + 0.998228i \(0.518954\pi\)
\(200\) 6.37325 0.450657
\(201\) 4.36575 0.307937
\(202\) −2.77146 −0.194999
\(203\) −1.61856 −0.113600
\(204\) −17.4803 −1.22386
\(205\) −9.66935 −0.675337
\(206\) −12.0754 −0.841334
\(207\) 18.0576 1.25509
\(208\) 7.15502 0.496111
\(209\) −0.775751 −0.0536598
\(210\) −12.2327 −0.844137
\(211\) 8.78900 0.605060 0.302530 0.953140i \(-0.402169\pi\)
0.302530 + 0.953140i \(0.402169\pi\)
\(212\) −10.4093 −0.714916
\(213\) −9.07555 −0.621847
\(214\) −1.25914 −0.0860730
\(215\) 7.41925 0.505988
\(216\) −11.0803 −0.753918
\(217\) −0.710687 −0.0482446
\(218\) −7.66963 −0.519453
\(219\) −0.576315 −0.0389438
\(220\) −3.91805 −0.264155
\(221\) 40.4091 2.71821
\(222\) −31.3222 −2.10221
\(223\) 0.320562 0.0214664 0.0107332 0.999942i \(-0.496583\pi\)
0.0107332 + 0.999942i \(0.496583\pi\)
\(224\) 1.17193 0.0783026
\(225\) 41.9353 2.79569
\(226\) 6.88774 0.458165
\(227\) −1.84108 −0.122197 −0.0610984 0.998132i \(-0.519460\pi\)
−0.0610984 + 0.998132i \(0.519460\pi\)
\(228\) −2.06669 −0.136870
\(229\) 13.7556 0.908994 0.454497 0.890748i \(-0.349819\pi\)
0.454497 + 0.890748i \(0.349819\pi\)
\(230\) 9.25514 0.610266
\(231\) 4.21413 0.277269
\(232\) −1.38111 −0.0906742
\(233\) 16.9457 1.11015 0.555076 0.831800i \(-0.312689\pi\)
0.555076 + 0.831800i \(0.312689\pi\)
\(234\) 47.0793 3.07767
\(235\) −11.6302 −0.758670
\(236\) 8.31170 0.541046
\(237\) 24.3676 1.58285
\(238\) 6.61863 0.429022
\(239\) 22.2326 1.43810 0.719052 0.694956i \(-0.244576\pi\)
0.719052 + 0.694956i \(0.244576\pi\)
\(240\) −10.4381 −0.673778
\(241\) −27.1467 −1.74867 −0.874336 0.485322i \(-0.838702\pi\)
−0.874336 + 0.485322i \(0.838702\pi\)
\(242\) −9.65025 −0.620341
\(243\) −11.8100 −0.757611
\(244\) −8.17995 −0.523667
\(245\) −18.9753 −1.21228
\(246\) 8.87433 0.565806
\(247\) 4.77756 0.303989
\(248\) −0.606427 −0.0385081
\(249\) 37.5212 2.37781
\(250\) 4.63119 0.292902
\(251\) 17.8201 1.12480 0.562398 0.826866i \(-0.309879\pi\)
0.562398 + 0.826866i \(0.309879\pi\)
\(252\) 7.71115 0.485757
\(253\) −3.18836 −0.200451
\(254\) 19.8666 1.24654
\(255\) −58.9509 −3.69165
\(256\) 1.00000 0.0625000
\(257\) 3.92176 0.244632 0.122316 0.992491i \(-0.460968\pi\)
0.122316 + 0.992491i \(0.460968\pi\)
\(258\) −6.80923 −0.423924
\(259\) 11.8597 0.736924
\(260\) 24.1298 1.49647
\(261\) −9.08755 −0.562505
\(262\) −10.9687 −0.677652
\(263\) 3.73202 0.230126 0.115063 0.993358i \(-0.463293\pi\)
0.115063 + 0.993358i \(0.463293\pi\)
\(264\) 3.59590 0.221312
\(265\) −35.1047 −2.15647
\(266\) 0.782520 0.0479794
\(267\) 33.7507 2.06551
\(268\) −1.41052 −0.0861611
\(269\) 21.3147 1.29958 0.649789 0.760115i \(-0.274857\pi\)
0.649789 + 0.760115i \(0.274857\pi\)
\(270\) −37.3674 −2.27411
\(271\) −9.22422 −0.560332 −0.280166 0.959952i \(-0.590389\pi\)
−0.280166 + 0.959952i \(0.590389\pi\)
\(272\) 5.64765 0.342439
\(273\) −25.9532 −1.57076
\(274\) −1.02417 −0.0618724
\(275\) −7.40437 −0.446500
\(276\) −8.49417 −0.511289
\(277\) 12.6430 0.759645 0.379823 0.925059i \(-0.375985\pi\)
0.379823 + 0.925059i \(0.375985\pi\)
\(278\) 6.63619 0.398012
\(279\) −3.99023 −0.238889
\(280\) 3.95223 0.236191
\(281\) 9.42829 0.562444 0.281222 0.959643i \(-0.409260\pi\)
0.281222 + 0.959643i \(0.409260\pi\)
\(282\) 10.6739 0.635624
\(283\) 29.5589 1.75709 0.878547 0.477656i \(-0.158514\pi\)
0.878547 + 0.477656i \(0.158514\pi\)
\(284\) 2.93219 0.173994
\(285\) −6.96976 −0.412853
\(286\) −8.31262 −0.491536
\(287\) −3.36012 −0.198342
\(288\) 6.57990 0.387724
\(289\) 14.8960 0.876233
\(290\) −4.65768 −0.273509
\(291\) −37.3851 −2.19155
\(292\) 0.186200 0.0108965
\(293\) −15.8714 −0.927216 −0.463608 0.886040i \(-0.653445\pi\)
−0.463608 + 0.886040i \(0.653445\pi\)
\(294\) 17.4151 1.01567
\(295\) 28.0306 1.63200
\(296\) 10.1198 0.588202
\(297\) 12.8729 0.746964
\(298\) −18.2122 −1.05501
\(299\) 19.6359 1.13558
\(300\) −19.7261 −1.13889
\(301\) 2.57821 0.148605
\(302\) −4.39046 −0.252643
\(303\) 8.57807 0.492797
\(304\) 0.667721 0.0382964
\(305\) −27.5863 −1.57958
\(306\) 37.1610 2.12435
\(307\) 30.9033 1.76375 0.881873 0.471488i \(-0.156283\pi\)
0.881873 + 0.471488i \(0.156283\pi\)
\(308\) −1.36153 −0.0775804
\(309\) 37.3751 2.12620
\(310\) −2.04513 −0.116156
\(311\) 12.3858 0.702337 0.351168 0.936312i \(-0.385784\pi\)
0.351168 + 0.936312i \(0.385784\pi\)
\(312\) −22.1458 −1.25376
\(313\) 1.52608 0.0862594 0.0431297 0.999069i \(-0.486267\pi\)
0.0431297 + 0.999069i \(0.486267\pi\)
\(314\) −10.6060 −0.598529
\(315\) 26.0053 1.46523
\(316\) −7.87285 −0.442883
\(317\) −3.61250 −0.202898 −0.101449 0.994841i \(-0.532348\pi\)
−0.101449 + 0.994841i \(0.532348\pi\)
\(318\) 32.2184 1.80672
\(319\) 1.60456 0.0898378
\(320\) 3.37243 0.188524
\(321\) 3.89722 0.217521
\(322\) 3.21618 0.179231
\(323\) 3.77106 0.209827
\(324\) 14.5553 0.808630
\(325\) 45.6008 2.52948
\(326\) 9.28058 0.514004
\(327\) 23.7386 1.31275
\(328\) −2.86718 −0.158314
\(329\) −4.04152 −0.222816
\(330\) 12.1269 0.667564
\(331\) −1.39092 −0.0764521 −0.0382260 0.999269i \(-0.512171\pi\)
−0.0382260 + 0.999269i \(0.512171\pi\)
\(332\) −12.1226 −0.665314
\(333\) 66.5873 3.64896
\(334\) −25.5066 −1.39566
\(335\) −4.75687 −0.259896
\(336\) −3.62727 −0.197884
\(337\) −10.5385 −0.574068 −0.287034 0.957920i \(-0.592669\pi\)
−0.287034 + 0.957920i \(0.592669\pi\)
\(338\) 38.1943 2.07750
\(339\) −21.3185 −1.15786
\(340\) 19.0463 1.03293
\(341\) 0.704540 0.0381530
\(342\) 4.39354 0.237575
\(343\) −14.7974 −0.798986
\(344\) 2.19997 0.118615
\(345\) −28.6460 −1.54225
\(346\) 9.08870 0.488611
\(347\) −24.8164 −1.33221 −0.666107 0.745856i \(-0.732040\pi\)
−0.666107 + 0.745856i \(0.732040\pi\)
\(348\) 4.27472 0.229149
\(349\) 2.03598 0.108983 0.0544917 0.998514i \(-0.482646\pi\)
0.0544917 + 0.998514i \(0.482646\pi\)
\(350\) 7.46898 0.399234
\(351\) −79.2797 −4.23163
\(352\) −1.16179 −0.0619235
\(353\) 3.04380 0.162005 0.0810027 0.996714i \(-0.474188\pi\)
0.0810027 + 0.996714i \(0.474188\pi\)
\(354\) −25.7259 −1.36732
\(355\) 9.88861 0.524833
\(356\) −10.9044 −0.577934
\(357\) −20.4856 −1.08421
\(358\) 12.9207 0.682879
\(359\) −28.6668 −1.51297 −0.756487 0.654008i \(-0.773086\pi\)
−0.756487 + 0.654008i \(0.773086\pi\)
\(360\) 22.1902 1.16953
\(361\) −18.5541 −0.976534
\(362\) 4.46300 0.234570
\(363\) 29.8689 1.56771
\(364\) 8.38515 0.439501
\(365\) 0.627946 0.0328682
\(366\) 25.3181 1.32340
\(367\) −24.9528 −1.30253 −0.651263 0.758852i \(-0.725760\pi\)
−0.651263 + 0.758852i \(0.725760\pi\)
\(368\) 2.74436 0.143060
\(369\) −18.8658 −0.982112
\(370\) 34.1283 1.77425
\(371\) −12.1990 −0.633339
\(372\) 1.87698 0.0973167
\(373\) −37.7095 −1.95252 −0.976262 0.216594i \(-0.930505\pi\)
−0.976262 + 0.216594i \(0.930505\pi\)
\(374\) −6.56138 −0.339281
\(375\) −14.3342 −0.740215
\(376\) −3.44861 −0.177849
\(377\) −9.88185 −0.508941
\(378\) −12.9853 −0.667890
\(379\) 16.6962 0.857624 0.428812 0.903394i \(-0.358932\pi\)
0.428812 + 0.903394i \(0.358932\pi\)
\(380\) 2.25184 0.115517
\(381\) −61.4899 −3.15022
\(382\) 7.39196 0.378205
\(383\) −21.8061 −1.11424 −0.557119 0.830433i \(-0.688093\pi\)
−0.557119 + 0.830433i \(0.688093\pi\)
\(384\) −3.09514 −0.157948
\(385\) −4.59166 −0.234013
\(386\) −1.96179 −0.0998523
\(387\) 14.4756 0.735836
\(388\) 12.0786 0.613200
\(389\) −3.95997 −0.200778 −0.100389 0.994948i \(-0.532009\pi\)
−0.100389 + 0.994948i \(0.532009\pi\)
\(390\) −74.6850 −3.78182
\(391\) 15.4992 0.783827
\(392\) −5.62659 −0.284186
\(393\) 33.9498 1.71254
\(394\) −16.3156 −0.821968
\(395\) −26.5506 −1.33591
\(396\) −7.64445 −0.384148
\(397\) −27.5576 −1.38308 −0.691538 0.722340i \(-0.743066\pi\)
−0.691538 + 0.722340i \(0.743066\pi\)
\(398\) −1.67899 −0.0841602
\(399\) −2.42201 −0.121252
\(400\) 6.37325 0.318663
\(401\) −23.8418 −1.19060 −0.595301 0.803503i \(-0.702967\pi\)
−0.595301 + 0.803503i \(0.702967\pi\)
\(402\) 4.36575 0.217744
\(403\) −4.33900 −0.216141
\(404\) −2.77146 −0.137885
\(405\) 49.0868 2.43914
\(406\) −1.61856 −0.0803276
\(407\) −11.7571 −0.582777
\(408\) −17.4803 −0.865403
\(409\) 33.6154 1.66217 0.831087 0.556142i \(-0.187719\pi\)
0.831087 + 0.556142i \(0.187719\pi\)
\(410\) −9.66935 −0.477535
\(411\) 3.16995 0.156362
\(412\) −12.0754 −0.594913
\(413\) 9.74070 0.479308
\(414\) 18.0576 0.887482
\(415\) −40.8826 −2.00685
\(416\) 7.15502 0.350804
\(417\) −20.5400 −1.00585
\(418\) −0.775751 −0.0379432
\(419\) 30.4159 1.48591 0.742956 0.669340i \(-0.233423\pi\)
0.742956 + 0.669340i \(0.233423\pi\)
\(420\) −12.2327 −0.596895
\(421\) −6.73706 −0.328344 −0.164172 0.986432i \(-0.552495\pi\)
−0.164172 + 0.986432i \(0.552495\pi\)
\(422\) 8.78900 0.427842
\(423\) −22.6915 −1.10330
\(424\) −10.4093 −0.505522
\(425\) 35.9939 1.74596
\(426\) −9.07555 −0.439712
\(427\) −9.58629 −0.463913
\(428\) −1.25914 −0.0608628
\(429\) 25.7287 1.24219
\(430\) 7.41925 0.357788
\(431\) −30.7365 −1.48052 −0.740262 0.672319i \(-0.765298\pi\)
−0.740262 + 0.672319i \(0.765298\pi\)
\(432\) −11.0803 −0.533100
\(433\) 30.2304 1.45278 0.726390 0.687283i \(-0.241197\pi\)
0.726390 + 0.687283i \(0.241197\pi\)
\(434\) −0.710687 −0.0341141
\(435\) 14.4162 0.691203
\(436\) −7.66963 −0.367309
\(437\) 1.83247 0.0876587
\(438\) −0.576315 −0.0275374
\(439\) −30.0192 −1.43274 −0.716370 0.697720i \(-0.754198\pi\)
−0.716370 + 0.697720i \(0.754198\pi\)
\(440\) −3.91805 −0.186785
\(441\) −37.0224 −1.76297
\(442\) 40.4091 1.92206
\(443\) −23.7170 −1.12683 −0.563415 0.826174i \(-0.690513\pi\)
−0.563415 + 0.826174i \(0.690513\pi\)
\(444\) −31.3222 −1.48649
\(445\) −36.7744 −1.74327
\(446\) 0.320562 0.0151790
\(447\) 56.3694 2.66618
\(448\) 1.17193 0.0553683
\(449\) −0.516878 −0.0243930 −0.0121965 0.999926i \(-0.503882\pi\)
−0.0121965 + 0.999926i \(0.503882\pi\)
\(450\) 41.9353 1.97685
\(451\) 3.33106 0.156853
\(452\) 6.88774 0.323972
\(453\) 13.5891 0.638471
\(454\) −1.84108 −0.0864062
\(455\) 28.2783 1.32571
\(456\) −2.06669 −0.0967817
\(457\) −25.0503 −1.17180 −0.585902 0.810382i \(-0.699260\pi\)
−0.585902 + 0.810382i \(0.699260\pi\)
\(458\) 13.7556 0.642756
\(459\) −62.5776 −2.92087
\(460\) 9.25514 0.431523
\(461\) 15.4363 0.718939 0.359469 0.933157i \(-0.382958\pi\)
0.359469 + 0.933157i \(0.382958\pi\)
\(462\) 4.21413 0.196059
\(463\) −7.55311 −0.351023 −0.175511 0.984477i \(-0.556158\pi\)
−0.175511 + 0.984477i \(0.556158\pi\)
\(464\) −1.38111 −0.0641163
\(465\) 6.32996 0.293545
\(466\) 16.9457 0.784996
\(467\) 6.52998 0.302172 0.151086 0.988521i \(-0.451723\pi\)
0.151086 + 0.988521i \(0.451723\pi\)
\(468\) 47.0793 2.17624
\(469\) −1.65302 −0.0763295
\(470\) −11.6302 −0.536461
\(471\) 32.8270 1.51259
\(472\) 8.31170 0.382577
\(473\) −2.55590 −0.117521
\(474\) 24.3676 1.11924
\(475\) 4.25556 0.195258
\(476\) 6.61863 0.303364
\(477\) −68.4924 −3.13605
\(478\) 22.2326 1.01689
\(479\) 32.4328 1.48189 0.740946 0.671565i \(-0.234377\pi\)
0.740946 + 0.671565i \(0.234377\pi\)
\(480\) −10.4381 −0.476433
\(481\) 72.4074 3.30150
\(482\) −27.1467 −1.23650
\(483\) −9.95454 −0.452947
\(484\) −9.65025 −0.438648
\(485\) 40.7343 1.84965
\(486\) −11.8100 −0.535712
\(487\) 8.89083 0.402882 0.201441 0.979501i \(-0.435438\pi\)
0.201441 + 0.979501i \(0.435438\pi\)
\(488\) −8.17995 −0.370289
\(489\) −28.7247 −1.29898
\(490\) −18.9753 −0.857215
\(491\) −22.8834 −1.03271 −0.516357 0.856374i \(-0.672712\pi\)
−0.516357 + 0.856374i \(0.672712\pi\)
\(492\) 8.87433 0.400086
\(493\) −7.80002 −0.351295
\(494\) 4.77756 0.214953
\(495\) −25.7803 −1.15874
\(496\) −0.606427 −0.0272294
\(497\) 3.43631 0.154140
\(498\) 37.5212 1.68136
\(499\) −31.6203 −1.41552 −0.707760 0.706453i \(-0.750294\pi\)
−0.707760 + 0.706453i \(0.750294\pi\)
\(500\) 4.63119 0.207113
\(501\) 78.9465 3.52707
\(502\) 17.8201 0.795351
\(503\) 2.41795 0.107811 0.0539055 0.998546i \(-0.482833\pi\)
0.0539055 + 0.998546i \(0.482833\pi\)
\(504\) 7.71115 0.343482
\(505\) −9.34655 −0.415916
\(506\) −3.18836 −0.141740
\(507\) −118.217 −5.25019
\(508\) 19.8666 0.881438
\(509\) −24.9486 −1.10583 −0.552914 0.833238i \(-0.686484\pi\)
−0.552914 + 0.833238i \(0.686484\pi\)
\(510\) −58.9509 −2.61039
\(511\) 0.218213 0.00965316
\(512\) 1.00000 0.0441942
\(513\) −7.39854 −0.326654
\(514\) 3.92176 0.172981
\(515\) −40.7234 −1.79449
\(516\) −6.80923 −0.299760
\(517\) 4.00656 0.176208
\(518\) 11.8597 0.521084
\(519\) −28.1308 −1.23480
\(520\) 24.1298 1.05816
\(521\) −7.88696 −0.345534 −0.172767 0.984963i \(-0.555271\pi\)
−0.172767 + 0.984963i \(0.555271\pi\)
\(522\) −9.08755 −0.397751
\(523\) 12.9709 0.567178 0.283589 0.958946i \(-0.408475\pi\)
0.283589 + 0.958946i \(0.408475\pi\)
\(524\) −10.9687 −0.479172
\(525\) −23.1175 −1.00893
\(526\) 3.73202 0.162724
\(527\) −3.42489 −0.149190
\(528\) 3.59590 0.156491
\(529\) −15.4685 −0.672544
\(530\) −35.1047 −1.52485
\(531\) 54.6901 2.37335
\(532\) 0.782520 0.0339265
\(533\) −20.5147 −0.888592
\(534\) 33.7507 1.46054
\(535\) −4.24636 −0.183586
\(536\) −1.41052 −0.0609251
\(537\) −39.9913 −1.72575
\(538\) 21.3147 0.918940
\(539\) 6.53691 0.281565
\(540\) −37.3674 −1.60804
\(541\) −20.8661 −0.897103 −0.448551 0.893757i \(-0.648060\pi\)
−0.448551 + 0.893757i \(0.648060\pi\)
\(542\) −9.22422 −0.396214
\(543\) −13.8136 −0.592799
\(544\) 5.64765 0.242141
\(545\) −25.8653 −1.10795
\(546\) −25.9532 −1.11070
\(547\) 16.8095 0.718723 0.359362 0.933198i \(-0.382994\pi\)
0.359362 + 0.933198i \(0.382994\pi\)
\(548\) −1.02417 −0.0437504
\(549\) −53.8232 −2.29712
\(550\) −7.40437 −0.315723
\(551\) −0.922195 −0.0392868
\(552\) −8.49417 −0.361536
\(553\) −9.22640 −0.392346
\(554\) 12.6430 0.537150
\(555\) −105.632 −4.48382
\(556\) 6.63619 0.281437
\(557\) −36.0122 −1.52588 −0.762942 0.646467i \(-0.776246\pi\)
−0.762942 + 0.646467i \(0.776246\pi\)
\(558\) −3.99023 −0.168920
\(559\) 15.7409 0.665767
\(560\) 3.95223 0.167012
\(561\) 20.3084 0.857421
\(562\) 9.42829 0.397708
\(563\) 37.2911 1.57163 0.785817 0.618459i \(-0.212243\pi\)
0.785817 + 0.618459i \(0.212243\pi\)
\(564\) 10.6739 0.449454
\(565\) 23.2284 0.977225
\(566\) 29.5589 1.24245
\(567\) 17.0578 0.716360
\(568\) 2.93219 0.123032
\(569\) 34.1456 1.43146 0.715730 0.698377i \(-0.246094\pi\)
0.715730 + 0.698377i \(0.246094\pi\)
\(570\) −6.96976 −0.291931
\(571\) 16.5738 0.693592 0.346796 0.937941i \(-0.387270\pi\)
0.346796 + 0.937941i \(0.387270\pi\)
\(572\) −8.31262 −0.347568
\(573\) −22.8791 −0.955790
\(574\) −3.36012 −0.140249
\(575\) 17.4905 0.729404
\(576\) 6.57990 0.274162
\(577\) −33.8131 −1.40766 −0.703830 0.710369i \(-0.748528\pi\)
−0.703830 + 0.710369i \(0.748528\pi\)
\(578\) 14.8960 0.619590
\(579\) 6.07200 0.252344
\(580\) −4.65768 −0.193400
\(581\) −14.2068 −0.589397
\(582\) −37.3851 −1.54966
\(583\) 12.0935 0.500860
\(584\) 0.186200 0.00770501
\(585\) 158.771 6.56439
\(586\) −15.8714 −0.655641
\(587\) 23.6026 0.974182 0.487091 0.873351i \(-0.338058\pi\)
0.487091 + 0.873351i \(0.338058\pi\)
\(588\) 17.4151 0.718186
\(589\) −0.404924 −0.0166846
\(590\) 28.0306 1.15400
\(591\) 50.4990 2.07725
\(592\) 10.1198 0.415922
\(593\) −0.551759 −0.0226580 −0.0113290 0.999936i \(-0.503606\pi\)
−0.0113290 + 0.999936i \(0.503606\pi\)
\(594\) 12.8729 0.528183
\(595\) 22.3208 0.915065
\(596\) −18.2122 −0.746001
\(597\) 5.19671 0.212687
\(598\) 19.6359 0.802973
\(599\) 8.91389 0.364212 0.182106 0.983279i \(-0.441709\pi\)
0.182106 + 0.983279i \(0.441709\pi\)
\(600\) −19.7261 −0.805315
\(601\) 7.12005 0.290433 0.145217 0.989400i \(-0.453612\pi\)
0.145217 + 0.989400i \(0.453612\pi\)
\(602\) 2.57821 0.105080
\(603\) −9.28107 −0.377954
\(604\) −4.39046 −0.178645
\(605\) −32.5447 −1.32313
\(606\) 8.57807 0.348460
\(607\) −17.0202 −0.690830 −0.345415 0.938450i \(-0.612262\pi\)
−0.345415 + 0.938450i \(0.612262\pi\)
\(608\) 0.667721 0.0270797
\(609\) 5.00966 0.203002
\(610\) −27.5863 −1.11693
\(611\) −24.6749 −0.998240
\(612\) 37.1610 1.50214
\(613\) −28.4716 −1.14996 −0.574978 0.818169i \(-0.694990\pi\)
−0.574978 + 0.818169i \(0.694990\pi\)
\(614\) 30.9033 1.24716
\(615\) 29.9280 1.20681
\(616\) −1.36153 −0.0548576
\(617\) −6.04550 −0.243383 −0.121691 0.992568i \(-0.538832\pi\)
−0.121691 + 0.992568i \(0.538832\pi\)
\(618\) 37.3751 1.50345
\(619\) 30.5467 1.22777 0.613887 0.789394i \(-0.289605\pi\)
0.613887 + 0.789394i \(0.289605\pi\)
\(620\) −2.04513 −0.0821344
\(621\) −30.4083 −1.22024
\(622\) 12.3858 0.496627
\(623\) −12.7792 −0.511987
\(624\) −22.1458 −0.886541
\(625\) −16.2479 −0.649916
\(626\) 1.52608 0.0609946
\(627\) 2.40106 0.0958890
\(628\) −10.6060 −0.423224
\(629\) 57.1532 2.27885
\(630\) 26.0053 1.03607
\(631\) −36.0509 −1.43516 −0.717581 0.696475i \(-0.754751\pi\)
−0.717581 + 0.696475i \(0.754751\pi\)
\(632\) −7.87285 −0.313165
\(633\) −27.2032 −1.08123
\(634\) −3.61250 −0.143471
\(635\) 66.9986 2.65876
\(636\) 32.2184 1.27754
\(637\) −40.2584 −1.59509
\(638\) 1.60456 0.0635249
\(639\) 19.2935 0.763240
\(640\) 3.37243 0.133307
\(641\) 33.7479 1.33296 0.666482 0.745521i \(-0.267799\pi\)
0.666482 + 0.745521i \(0.267799\pi\)
\(642\) 3.89722 0.153811
\(643\) 42.4192 1.67285 0.836424 0.548083i \(-0.184642\pi\)
0.836424 + 0.548083i \(0.184642\pi\)
\(644\) 3.21618 0.126735
\(645\) −22.9636 −0.904191
\(646\) 3.77106 0.148370
\(647\) 14.2000 0.558260 0.279130 0.960253i \(-0.409954\pi\)
0.279130 + 0.960253i \(0.409954\pi\)
\(648\) 14.5553 0.571788
\(649\) −9.65644 −0.379048
\(650\) 45.6008 1.78861
\(651\) 2.19968 0.0862121
\(652\) 9.28058 0.363456
\(653\) −0.454310 −0.0177785 −0.00888927 0.999960i \(-0.502830\pi\)
−0.00888927 + 0.999960i \(0.502830\pi\)
\(654\) 23.7386 0.928252
\(655\) −36.9913 −1.44537
\(656\) −2.86718 −0.111945
\(657\) 1.22518 0.0477987
\(658\) −4.04152 −0.157555
\(659\) −47.9828 −1.86915 −0.934573 0.355771i \(-0.884218\pi\)
−0.934573 + 0.355771i \(0.884218\pi\)
\(660\) 12.1269 0.472039
\(661\) 41.5059 1.61439 0.807196 0.590283i \(-0.200984\pi\)
0.807196 + 0.590283i \(0.200984\pi\)
\(662\) −1.39092 −0.0540598
\(663\) −125.072 −4.85738
\(664\) −12.1226 −0.470448
\(665\) 2.63899 0.102336
\(666\) 66.5873 2.58021
\(667\) −3.79025 −0.146759
\(668\) −25.5066 −0.986880
\(669\) −0.992184 −0.0383600
\(670\) −4.75687 −0.183774
\(671\) 9.50337 0.366873
\(672\) −3.62727 −0.139925
\(673\) −5.87453 −0.226447 −0.113223 0.993570i \(-0.536118\pi\)
−0.113223 + 0.993570i \(0.536118\pi\)
\(674\) −10.5385 −0.405927
\(675\) −70.6174 −2.71807
\(676\) 38.1943 1.46901
\(677\) −20.5059 −0.788107 −0.394053 0.919088i \(-0.628927\pi\)
−0.394053 + 0.919088i \(0.628927\pi\)
\(678\) −21.3185 −0.818732
\(679\) 14.1553 0.543230
\(680\) 19.0463 0.730392
\(681\) 5.69840 0.218363
\(682\) 0.704540 0.0269782
\(683\) −23.4471 −0.897177 −0.448588 0.893738i \(-0.648073\pi\)
−0.448588 + 0.893738i \(0.648073\pi\)
\(684\) 4.39354 0.167991
\(685\) −3.45394 −0.131968
\(686\) −14.7974 −0.564968
\(687\) −42.5754 −1.62435
\(688\) 2.19997 0.0838732
\(689\) −74.4790 −2.83743
\(690\) −28.6460 −1.09053
\(691\) 7.75353 0.294958 0.147479 0.989065i \(-0.452884\pi\)
0.147479 + 0.989065i \(0.452884\pi\)
\(692\) 9.08870 0.345500
\(693\) −8.95872 −0.340314
\(694\) −24.8164 −0.942017
\(695\) 22.3801 0.848924
\(696\) 4.27472 0.162033
\(697\) −16.1928 −0.613347
\(698\) 2.03598 0.0770629
\(699\) −52.4494 −1.98382
\(700\) 7.46898 0.282301
\(701\) 35.7356 1.34972 0.674858 0.737948i \(-0.264205\pi\)
0.674858 + 0.737948i \(0.264205\pi\)
\(702\) −79.2797 −2.99222
\(703\) 6.75721 0.254853
\(704\) −1.16179 −0.0437866
\(705\) 35.9971 1.35573
\(706\) 3.04380 0.114555
\(707\) −3.24795 −0.122152
\(708\) −25.7259 −0.966838
\(709\) 34.4470 1.29368 0.646842 0.762624i \(-0.276089\pi\)
0.646842 + 0.762624i \(0.276089\pi\)
\(710\) 9.88861 0.371113
\(711\) −51.8026 −1.94275
\(712\) −10.9044 −0.408661
\(713\) −1.66425 −0.0623267
\(714\) −20.4856 −0.766654
\(715\) −28.0337 −1.04840
\(716\) 12.9207 0.482868
\(717\) −68.8129 −2.56986
\(718\) −28.6668 −1.06983
\(719\) −15.9311 −0.594129 −0.297064 0.954857i \(-0.596008\pi\)
−0.297064 + 0.954857i \(0.596008\pi\)
\(720\) 22.1902 0.826980
\(721\) −14.1515 −0.527029
\(722\) −18.5541 −0.690514
\(723\) 84.0228 3.12484
\(724\) 4.46300 0.165866
\(725\) −8.80215 −0.326904
\(726\) 29.8689 1.10854
\(727\) 16.6532 0.617633 0.308816 0.951122i \(-0.400067\pi\)
0.308816 + 0.951122i \(0.400067\pi\)
\(728\) 8.38515 0.310774
\(729\) −7.11244 −0.263424
\(730\) 0.627946 0.0232413
\(731\) 12.4247 0.459544
\(732\) 25.3181 0.935783
\(733\) 47.0999 1.73967 0.869837 0.493339i \(-0.164224\pi\)
0.869837 + 0.493339i \(0.164224\pi\)
\(734\) −24.9528 −0.921025
\(735\) 58.7311 2.16633
\(736\) 2.74436 0.101158
\(737\) 1.63872 0.0603632
\(738\) −18.8658 −0.694458
\(739\) 15.5047 0.570350 0.285175 0.958475i \(-0.407948\pi\)
0.285175 + 0.958475i \(0.407948\pi\)
\(740\) 34.1283 1.25458
\(741\) −14.7872 −0.543222
\(742\) −12.1990 −0.447838
\(743\) −5.29716 −0.194334 −0.0971669 0.995268i \(-0.530978\pi\)
−0.0971669 + 0.995268i \(0.530978\pi\)
\(744\) 1.87698 0.0688133
\(745\) −61.4193 −2.25023
\(746\) −37.7095 −1.38064
\(747\) −79.7655 −2.91847
\(748\) −6.56138 −0.239908
\(749\) −1.47562 −0.0539179
\(750\) −14.3342 −0.523411
\(751\) 44.1613 1.61147 0.805735 0.592277i \(-0.201771\pi\)
0.805735 + 0.592277i \(0.201771\pi\)
\(752\) −3.44861 −0.125758
\(753\) −55.1558 −2.00999
\(754\) −9.88185 −0.359876
\(755\) −14.8065 −0.538864
\(756\) −12.9853 −0.472270
\(757\) −5.45753 −0.198357 −0.0991787 0.995070i \(-0.531622\pi\)
−0.0991787 + 0.995070i \(0.531622\pi\)
\(758\) 16.6962 0.606432
\(759\) 9.86843 0.358201
\(760\) 2.25184 0.0816828
\(761\) −15.5976 −0.565412 −0.282706 0.959207i \(-0.591232\pi\)
−0.282706 + 0.959207i \(0.591232\pi\)
\(762\) −61.4899 −2.22754
\(763\) −8.98824 −0.325396
\(764\) 7.39196 0.267432
\(765\) 125.323 4.53105
\(766\) −21.8061 −0.787886
\(767\) 59.4704 2.14735
\(768\) −3.09514 −0.111686
\(769\) −41.1744 −1.48479 −0.742393 0.669965i \(-0.766309\pi\)
−0.742393 + 0.669965i \(0.766309\pi\)
\(770\) −4.59166 −0.165472
\(771\) −12.1384 −0.437153
\(772\) −1.96179 −0.0706062
\(773\) −37.5374 −1.35013 −0.675063 0.737760i \(-0.735883\pi\)
−0.675063 + 0.737760i \(0.735883\pi\)
\(774\) 14.4756 0.520315
\(775\) −3.86491 −0.138832
\(776\) 12.0786 0.433598
\(777\) −36.7073 −1.31687
\(778\) −3.95997 −0.141972
\(779\) −1.91448 −0.0685933
\(780\) −74.6850 −2.67415
\(781\) −3.40659 −0.121897
\(782\) 15.4992 0.554249
\(783\) 15.3031 0.546887
\(784\) −5.62659 −0.200950
\(785\) −35.7678 −1.27661
\(786\) 33.9498 1.21095
\(787\) 13.8501 0.493702 0.246851 0.969053i \(-0.420604\pi\)
0.246851 + 0.969053i \(0.420604\pi\)
\(788\) −16.3156 −0.581219
\(789\) −11.5511 −0.411230
\(790\) −26.5506 −0.944628
\(791\) 8.07191 0.287004
\(792\) −7.64445 −0.271634
\(793\) −58.5277 −2.07838
\(794\) −27.5576 −0.977982
\(795\) 108.654 3.85356
\(796\) −1.67899 −0.0595103
\(797\) 52.4957 1.85949 0.929746 0.368201i \(-0.120026\pi\)
0.929746 + 0.368201i \(0.120026\pi\)
\(798\) −2.42201 −0.0857382
\(799\) −19.4766 −0.689032
\(800\) 6.37325 0.225329
\(801\) −71.7500 −2.53516
\(802\) −23.8418 −0.841882
\(803\) −0.216325 −0.00763395
\(804\) 4.36575 0.153968
\(805\) 10.8463 0.382283
\(806\) −4.33900 −0.152835
\(807\) −65.9719 −2.32232
\(808\) −2.77146 −0.0974997
\(809\) 29.0869 1.02264 0.511320 0.859390i \(-0.329157\pi\)
0.511320 + 0.859390i \(0.329157\pi\)
\(810\) 49.0868 1.72473
\(811\) −46.5542 −1.63474 −0.817370 0.576113i \(-0.804569\pi\)
−0.817370 + 0.576113i \(0.804569\pi\)
\(812\) −1.61856 −0.0568002
\(813\) 28.5503 1.00130
\(814\) −11.7571 −0.412085
\(815\) 31.2981 1.09632
\(816\) −17.4803 −0.611932
\(817\) 1.46897 0.0513927
\(818\) 33.6154 1.17533
\(819\) 55.1734 1.92792
\(820\) −9.66935 −0.337668
\(821\) −27.7167 −0.967318 −0.483659 0.875256i \(-0.660693\pi\)
−0.483659 + 0.875256i \(0.660693\pi\)
\(822\) 3.16995 0.110565
\(823\) −21.1696 −0.737925 −0.368963 0.929444i \(-0.620287\pi\)
−0.368963 + 0.929444i \(0.620287\pi\)
\(824\) −12.0754 −0.420667
\(825\) 22.9176 0.797888
\(826\) 9.74070 0.338922
\(827\) 41.8849 1.45648 0.728240 0.685322i \(-0.240339\pi\)
0.728240 + 0.685322i \(0.240339\pi\)
\(828\) 18.0576 0.627544
\(829\) 40.3873 1.40271 0.701354 0.712813i \(-0.252579\pi\)
0.701354 + 0.712813i \(0.252579\pi\)
\(830\) −40.8826 −1.41905
\(831\) −39.1319 −1.35747
\(832\) 7.15502 0.248056
\(833\) −31.7770 −1.10101
\(834\) −20.5400 −0.711240
\(835\) −86.0191 −2.97681
\(836\) −0.775751 −0.0268299
\(837\) 6.71938 0.232256
\(838\) 30.4159 1.05070
\(839\) 18.2820 0.631163 0.315582 0.948898i \(-0.397800\pi\)
0.315582 + 0.948898i \(0.397800\pi\)
\(840\) −12.2327 −0.422069
\(841\) −27.0925 −0.934226
\(842\) −6.73706 −0.232174
\(843\) −29.1819 −1.00508
\(844\) 8.78900 0.302530
\(845\) 128.808 4.43111
\(846\) −22.6915 −0.780151
\(847\) −11.3094 −0.388595
\(848\) −10.4093 −0.357458
\(849\) −91.4889 −3.13989
\(850\) 35.9939 1.23458
\(851\) 27.7724 0.952025
\(852\) −9.07555 −0.310923
\(853\) −12.6294 −0.432421 −0.216211 0.976347i \(-0.569370\pi\)
−0.216211 + 0.976347i \(0.569370\pi\)
\(854\) −9.58629 −0.328036
\(855\) 14.8169 0.506726
\(856\) −1.25914 −0.0430365
\(857\) −6.89281 −0.235454 −0.117727 0.993046i \(-0.537561\pi\)
−0.117727 + 0.993046i \(0.537561\pi\)
\(858\) 25.7287 0.878364
\(859\) −4.77038 −0.162763 −0.0813817 0.996683i \(-0.525933\pi\)
−0.0813817 + 0.996683i \(0.525933\pi\)
\(860\) 7.41925 0.252994
\(861\) 10.4001 0.354433
\(862\) −30.7365 −1.04689
\(863\) −22.4496 −0.764194 −0.382097 0.924122i \(-0.624798\pi\)
−0.382097 + 0.924122i \(0.624798\pi\)
\(864\) −11.0803 −0.376959
\(865\) 30.6510 1.04216
\(866\) 30.2304 1.02727
\(867\) −46.1051 −1.56581
\(868\) −0.710687 −0.0241223
\(869\) 9.14659 0.310277
\(870\) 14.4162 0.488754
\(871\) −10.0923 −0.341964
\(872\) −7.66963 −0.259726
\(873\) 79.4762 2.68986
\(874\) 1.83247 0.0619841
\(875\) 5.42741 0.183480
\(876\) −0.576315 −0.0194719
\(877\) 23.0906 0.779713 0.389856 0.920876i \(-0.372525\pi\)
0.389856 + 0.920876i \(0.372525\pi\)
\(878\) −30.0192 −1.01310
\(879\) 49.1241 1.65692
\(880\) −3.91805 −0.132077
\(881\) −17.3678 −0.585136 −0.292568 0.956245i \(-0.594510\pi\)
−0.292568 + 0.956245i \(0.594510\pi\)
\(882\) −37.0224 −1.24661
\(883\) 13.1839 0.443672 0.221836 0.975084i \(-0.428795\pi\)
0.221836 + 0.975084i \(0.428795\pi\)
\(884\) 40.4091 1.35910
\(885\) −86.7586 −2.91636
\(886\) −23.7170 −0.796789
\(887\) −36.6399 −1.23025 −0.615124 0.788430i \(-0.710894\pi\)
−0.615124 + 0.788430i \(0.710894\pi\)
\(888\) −31.3222 −1.05111
\(889\) 23.2822 0.780859
\(890\) −36.7744 −1.23268
\(891\) −16.9102 −0.566514
\(892\) 0.320562 0.0107332
\(893\) −2.30271 −0.0770574
\(894\) 56.3694 1.88527
\(895\) 43.5740 1.45652
\(896\) 1.17193 0.0391513
\(897\) −60.7760 −2.02925
\(898\) −0.516878 −0.0172485
\(899\) 0.837541 0.0279336
\(900\) 41.9353 1.39784
\(901\) −58.7883 −1.95852
\(902\) 3.33106 0.110912
\(903\) −7.97991 −0.265555
\(904\) 6.88774 0.229083
\(905\) 15.0511 0.500317
\(906\) 13.5891 0.451467
\(907\) −23.7389 −0.788238 −0.394119 0.919059i \(-0.628950\pi\)
−0.394119 + 0.919059i \(0.628950\pi\)
\(908\) −1.84108 −0.0610984
\(909\) −18.2359 −0.604848
\(910\) 28.2783 0.937417
\(911\) 53.1573 1.76118 0.880591 0.473878i \(-0.157146\pi\)
0.880591 + 0.473878i \(0.157146\pi\)
\(912\) −2.06669 −0.0684350
\(913\) 14.0839 0.466109
\(914\) −25.0503 −0.828590
\(915\) 85.3833 2.82269
\(916\) 13.7556 0.454497
\(917\) −12.8546 −0.424495
\(918\) −62.5776 −2.06537
\(919\) −47.5739 −1.56932 −0.784659 0.619928i \(-0.787162\pi\)
−0.784659 + 0.619928i \(0.787162\pi\)
\(920\) 9.25514 0.305133
\(921\) −95.6501 −3.15178
\(922\) 15.4363 0.508367
\(923\) 20.9799 0.690562
\(924\) 4.21413 0.138635
\(925\) 64.4961 2.12062
\(926\) −7.55311 −0.248211
\(927\) −79.4550 −2.60964
\(928\) −1.38111 −0.0453371
\(929\) −2.58507 −0.0848133 −0.0424067 0.999100i \(-0.513503\pi\)
−0.0424067 + 0.999100i \(0.513503\pi\)
\(930\) 6.32996 0.207568
\(931\) −3.75699 −0.123131
\(932\) 16.9457 0.555076
\(933\) −38.3359 −1.25506
\(934\) 6.52998 0.213668
\(935\) −22.1278 −0.723655
\(936\) 47.0793 1.53883
\(937\) 33.6028 1.09775 0.548877 0.835903i \(-0.315055\pi\)
0.548877 + 0.835903i \(0.315055\pi\)
\(938\) −1.65302 −0.0539731
\(939\) −4.72345 −0.154144
\(940\) −11.6302 −0.379335
\(941\) 13.2256 0.431141 0.215571 0.976488i \(-0.430839\pi\)
0.215571 + 0.976488i \(0.430839\pi\)
\(942\) 32.8270 1.06956
\(943\) −7.86857 −0.256236
\(944\) 8.31170 0.270523
\(945\) −43.7918 −1.42455
\(946\) −2.55590 −0.0830996
\(947\) 15.2233 0.494692 0.247346 0.968927i \(-0.420442\pi\)
0.247346 + 0.968927i \(0.420442\pi\)
\(948\) 24.3676 0.791423
\(949\) 1.33227 0.0432472
\(950\) 4.25556 0.138068
\(951\) 11.1812 0.362575
\(952\) 6.61863 0.214511
\(953\) 33.4859 1.08471 0.542357 0.840148i \(-0.317532\pi\)
0.542357 + 0.840148i \(0.317532\pi\)
\(954\) −68.4924 −2.21752
\(955\) 24.9288 0.806678
\(956\) 22.2326 0.719052
\(957\) −4.96632 −0.160538
\(958\) 32.4328 1.04786
\(959\) −1.20025 −0.0387582
\(960\) −10.4381 −0.336889
\(961\) −30.6322 −0.988137
\(962\) 72.4074 2.33451
\(963\) −8.28501 −0.266981
\(964\) −27.1467 −0.874336
\(965\) −6.61598 −0.212976
\(966\) −9.95454 −0.320282
\(967\) −25.4020 −0.816872 −0.408436 0.912787i \(-0.633926\pi\)
−0.408436 + 0.912787i \(0.633926\pi\)
\(968\) −9.65025 −0.310171
\(969\) −11.6720 −0.374957
\(970\) 40.7343 1.30790
\(971\) −38.8539 −1.24688 −0.623441 0.781871i \(-0.714266\pi\)
−0.623441 + 0.781871i \(0.714266\pi\)
\(972\) −11.8100 −0.378806
\(973\) 7.77713 0.249323
\(974\) 8.89083 0.284880
\(975\) −141.141 −4.52012
\(976\) −8.17995 −0.261834
\(977\) 47.1513 1.50850 0.754251 0.656586i \(-0.228000\pi\)
0.754251 + 0.656586i \(0.228000\pi\)
\(978\) −28.7247 −0.918515
\(979\) 12.6686 0.404891
\(980\) −18.9753 −0.606142
\(981\) −50.4654 −1.61124
\(982\) −22.8834 −0.730239
\(983\) −9.88423 −0.315258 −0.157629 0.987498i \(-0.550385\pi\)
−0.157629 + 0.987498i \(0.550385\pi\)
\(984\) 8.87433 0.282903
\(985\) −55.0231 −1.75318
\(986\) −7.80002 −0.248403
\(987\) 12.5091 0.398168
\(988\) 4.77756 0.151994
\(989\) 6.03751 0.191982
\(990\) −25.7803 −0.819353
\(991\) −24.5650 −0.780333 −0.390166 0.920744i \(-0.627583\pi\)
−0.390166 + 0.920744i \(0.627583\pi\)
\(992\) −0.606427 −0.0192541
\(993\) 4.30511 0.136618
\(994\) 3.43631 0.108993
\(995\) −5.66227 −0.179506
\(996\) 37.5212 1.18890
\(997\) −42.6533 −1.35084 −0.675422 0.737432i \(-0.736038\pi\)
−0.675422 + 0.737432i \(0.736038\pi\)
\(998\) −31.6203 −1.00092
\(999\) −112.130 −3.54765
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 4034.2.a.d.1.3 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.3 52 1.1 even 1 trivial