Properties

Label 4033.2.a.f.1.16
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.92648 q^{2} -3.23973 q^{3} +1.71134 q^{4} +1.34988 q^{5} +6.24129 q^{6} +3.96616 q^{7} +0.556094 q^{8} +7.49587 q^{9} +O(q^{10})\) \(q-1.92648 q^{2} -3.23973 q^{3} +1.71134 q^{4} +1.34988 q^{5} +6.24129 q^{6} +3.96616 q^{7} +0.556094 q^{8} +7.49587 q^{9} -2.60052 q^{10} -2.26646 q^{11} -5.54429 q^{12} -1.74141 q^{13} -7.64075 q^{14} -4.37325 q^{15} -4.49399 q^{16} +2.07799 q^{17} -14.4407 q^{18} -0.0556045 q^{19} +2.31011 q^{20} -12.8493 q^{21} +4.36630 q^{22} +2.13566 q^{23} -1.80160 q^{24} -3.17782 q^{25} +3.35480 q^{26} -14.5654 q^{27} +6.78746 q^{28} -1.24737 q^{29} +8.42500 q^{30} +6.48541 q^{31} +7.54542 q^{32} +7.34272 q^{33} -4.00321 q^{34} +5.35384 q^{35} +12.8280 q^{36} +1.00000 q^{37} +0.107121 q^{38} +5.64170 q^{39} +0.750660 q^{40} +9.82822 q^{41} +24.7540 q^{42} +5.56260 q^{43} -3.87869 q^{44} +10.1185 q^{45} -4.11431 q^{46} -4.31048 q^{47} +14.5593 q^{48} +8.73042 q^{49} +6.12203 q^{50} -6.73212 q^{51} -2.98015 q^{52} -3.11563 q^{53} +28.0600 q^{54} -3.05945 q^{55} +2.20556 q^{56} +0.180144 q^{57} +2.40305 q^{58} +4.26046 q^{59} -7.48413 q^{60} -5.43610 q^{61} -12.4941 q^{62} +29.7298 q^{63} -5.54815 q^{64} -2.35070 q^{65} -14.1456 q^{66} +0.851420 q^{67} +3.55615 q^{68} -6.91896 q^{69} -10.3141 q^{70} +13.0363 q^{71} +4.16841 q^{72} -1.26557 q^{73} -1.92648 q^{74} +10.2953 q^{75} -0.0951583 q^{76} -8.98914 q^{77} -10.8687 q^{78} -2.32278 q^{79} -6.06635 q^{80} +24.7004 q^{81} -18.9339 q^{82} -0.341132 q^{83} -21.9896 q^{84} +2.80503 q^{85} -10.7163 q^{86} +4.04116 q^{87} -1.26036 q^{88} -10.6367 q^{89} -19.4932 q^{90} -6.90671 q^{91} +3.65484 q^{92} -21.0110 q^{93} +8.30407 q^{94} -0.0750594 q^{95} -24.4451 q^{96} +0.0238378 q^{97} -16.8190 q^{98} -16.9891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92648 −1.36223 −0.681115 0.732176i \(-0.738505\pi\)
−0.681115 + 0.732176i \(0.738505\pi\)
\(3\) −3.23973 −1.87046 −0.935230 0.354040i \(-0.884808\pi\)
−0.935230 + 0.354040i \(0.884808\pi\)
\(4\) 1.71134 0.855671
\(5\) 1.34988 0.603685 0.301842 0.953358i \(-0.402398\pi\)
0.301842 + 0.953358i \(0.402398\pi\)
\(6\) 6.24129 2.54800
\(7\) 3.96616 1.49907 0.749534 0.661966i \(-0.230278\pi\)
0.749534 + 0.661966i \(0.230278\pi\)
\(8\) 0.556094 0.196609
\(9\) 7.49587 2.49862
\(10\) −2.60052 −0.822358
\(11\) −2.26646 −0.683363 −0.341682 0.939816i \(-0.610996\pi\)
−0.341682 + 0.939816i \(0.610996\pi\)
\(12\) −5.54429 −1.60050
\(13\) −1.74141 −0.482980 −0.241490 0.970403i \(-0.577636\pi\)
−0.241490 + 0.970403i \(0.577636\pi\)
\(14\) −7.64075 −2.04208
\(15\) −4.37325 −1.12917
\(16\) −4.49399 −1.12350
\(17\) 2.07799 0.503986 0.251993 0.967729i \(-0.418914\pi\)
0.251993 + 0.967729i \(0.418914\pi\)
\(18\) −14.4407 −3.40370
\(19\) −0.0556045 −0.0127565 −0.00637827 0.999980i \(-0.502030\pi\)
−0.00637827 + 0.999980i \(0.502030\pi\)
\(20\) 2.31011 0.516556
\(21\) −12.8493 −2.80395
\(22\) 4.36630 0.930898
\(23\) 2.13566 0.445316 0.222658 0.974897i \(-0.428527\pi\)
0.222658 + 0.974897i \(0.428527\pi\)
\(24\) −1.80160 −0.367749
\(25\) −3.17782 −0.635565
\(26\) 3.35480 0.657931
\(27\) −14.5654 −2.80311
\(28\) 6.78746 1.28271
\(29\) −1.24737 −0.231632 −0.115816 0.993271i \(-0.536948\pi\)
−0.115816 + 0.993271i \(0.536948\pi\)
\(30\) 8.42500 1.53819
\(31\) 6.48541 1.16481 0.582407 0.812897i \(-0.302111\pi\)
0.582407 + 0.812897i \(0.302111\pi\)
\(32\) 7.54542 1.33385
\(33\) 7.34272 1.27820
\(34\) −4.00321 −0.686545
\(35\) 5.35384 0.904964
\(36\) 12.8280 2.13800
\(37\) 1.00000 0.164399
\(38\) 0.107121 0.0173773
\(39\) 5.64170 0.903396
\(40\) 0.750660 0.118690
\(41\) 9.82822 1.53491 0.767455 0.641103i \(-0.221523\pi\)
0.767455 + 0.641103i \(0.221523\pi\)
\(42\) 24.7540 3.81962
\(43\) 5.56260 0.848288 0.424144 0.905595i \(-0.360575\pi\)
0.424144 + 0.905595i \(0.360575\pi\)
\(44\) −3.87869 −0.584734
\(45\) 10.1185 1.50838
\(46\) −4.11431 −0.606622
\(47\) −4.31048 −0.628748 −0.314374 0.949299i \(-0.601795\pi\)
−0.314374 + 0.949299i \(0.601795\pi\)
\(48\) 14.5593 2.10146
\(49\) 8.73042 1.24720
\(50\) 6.12203 0.865785
\(51\) −6.73212 −0.942685
\(52\) −2.98015 −0.413272
\(53\) −3.11563 −0.427964 −0.213982 0.976838i \(-0.568643\pi\)
−0.213982 + 0.976838i \(0.568643\pi\)
\(54\) 28.0600 3.81849
\(55\) −3.05945 −0.412536
\(56\) 2.20556 0.294730
\(57\) 0.180144 0.0238606
\(58\) 2.40305 0.315536
\(59\) 4.26046 0.554664 0.277332 0.960774i \(-0.410550\pi\)
0.277332 + 0.960774i \(0.410550\pi\)
\(60\) −7.48413 −0.966197
\(61\) −5.43610 −0.696022 −0.348011 0.937491i \(-0.613143\pi\)
−0.348011 + 0.937491i \(0.613143\pi\)
\(62\) −12.4941 −1.58675
\(63\) 29.7298 3.74560
\(64\) −5.54815 −0.693518
\(65\) −2.35070 −0.291568
\(66\) −14.1456 −1.74121
\(67\) 0.851420 0.104018 0.0520088 0.998647i \(-0.483438\pi\)
0.0520088 + 0.998647i \(0.483438\pi\)
\(68\) 3.55615 0.431246
\(69\) −6.91896 −0.832945
\(70\) −10.3141 −1.23277
\(71\) 13.0363 1.54712 0.773560 0.633723i \(-0.218474\pi\)
0.773560 + 0.633723i \(0.218474\pi\)
\(72\) 4.16841 0.491251
\(73\) −1.26557 −0.148123 −0.0740616 0.997254i \(-0.523596\pi\)
−0.0740616 + 0.997254i \(0.523596\pi\)
\(74\) −1.92648 −0.223949
\(75\) 10.2953 1.18880
\(76\) −0.0951583 −0.0109154
\(77\) −8.98914 −1.02441
\(78\) −10.8687 −1.23063
\(79\) −2.32278 −0.261334 −0.130667 0.991426i \(-0.541712\pi\)
−0.130667 + 0.991426i \(0.541712\pi\)
\(80\) −6.06635 −0.678239
\(81\) 24.7004 2.74449
\(82\) −18.9339 −2.09090
\(83\) −0.341132 −0.0374441 −0.0187220 0.999825i \(-0.505960\pi\)
−0.0187220 + 0.999825i \(0.505960\pi\)
\(84\) −21.9896 −2.39926
\(85\) 2.80503 0.304249
\(86\) −10.7163 −1.15556
\(87\) 4.04116 0.433258
\(88\) −1.26036 −0.134355
\(89\) −10.6367 −1.12748 −0.563742 0.825951i \(-0.690639\pi\)
−0.563742 + 0.825951i \(0.690639\pi\)
\(90\) −19.4932 −2.05476
\(91\) −6.90671 −0.724020
\(92\) 3.65484 0.381044
\(93\) −21.0110 −2.17874
\(94\) 8.30407 0.856499
\(95\) −0.0750594 −0.00770093
\(96\) −24.4451 −2.49492
\(97\) 0.0238378 0.00242036 0.00121018 0.999999i \(-0.499615\pi\)
0.00121018 + 0.999999i \(0.499615\pi\)
\(98\) −16.8190 −1.69898
\(99\) −16.9891 −1.70747
\(100\) −5.43834 −0.543834
\(101\) −2.07023 −0.205995 −0.102998 0.994682i \(-0.532843\pi\)
−0.102998 + 0.994682i \(0.532843\pi\)
\(102\) 12.9693 1.28415
\(103\) 6.35658 0.626332 0.313166 0.949698i \(-0.398610\pi\)
0.313166 + 0.949698i \(0.398610\pi\)
\(104\) −0.968388 −0.0949582
\(105\) −17.3450 −1.69270
\(106\) 6.00220 0.582986
\(107\) 6.15416 0.594945 0.297473 0.954730i \(-0.403856\pi\)
0.297473 + 0.954730i \(0.403856\pi\)
\(108\) −24.9264 −2.39854
\(109\) −1.00000 −0.0957826
\(110\) 5.89398 0.561969
\(111\) −3.23973 −0.307502
\(112\) −17.8239 −1.68420
\(113\) 16.6497 1.56627 0.783134 0.621853i \(-0.213620\pi\)
0.783134 + 0.621853i \(0.213620\pi\)
\(114\) −0.347044 −0.0325036
\(115\) 2.88288 0.268830
\(116\) −2.13468 −0.198201
\(117\) −13.0534 −1.20679
\(118\) −8.20771 −0.755581
\(119\) 8.24163 0.755509
\(120\) −2.43194 −0.222005
\(121\) −5.86316 −0.533015
\(122\) 10.4726 0.948142
\(123\) −31.8408 −2.87099
\(124\) 11.0988 0.996699
\(125\) −11.0391 −0.987366
\(126\) −57.2740 −5.10237
\(127\) 5.64587 0.500990 0.250495 0.968118i \(-0.419407\pi\)
0.250495 + 0.968118i \(0.419407\pi\)
\(128\) −4.40242 −0.389122
\(129\) −18.0213 −1.58669
\(130\) 4.52858 0.397183
\(131\) 13.1502 1.14894 0.574469 0.818526i \(-0.305208\pi\)
0.574469 + 0.818526i \(0.305208\pi\)
\(132\) 12.5659 1.09372
\(133\) −0.220536 −0.0191229
\(134\) −1.64025 −0.141696
\(135\) −19.6616 −1.69220
\(136\) 1.15556 0.0990881
\(137\) −4.51177 −0.385467 −0.192733 0.981251i \(-0.561735\pi\)
−0.192733 + 0.981251i \(0.561735\pi\)
\(138\) 13.3293 1.13466
\(139\) −1.93497 −0.164122 −0.0820610 0.996627i \(-0.526150\pi\)
−0.0820610 + 0.996627i \(0.526150\pi\)
\(140\) 9.16226 0.774352
\(141\) 13.9648 1.17605
\(142\) −25.1142 −2.10753
\(143\) 3.94684 0.330051
\(144\) −33.6864 −2.80720
\(145\) −1.68381 −0.139832
\(146\) 2.43809 0.201778
\(147\) −28.2842 −2.33284
\(148\) 1.71134 0.140671
\(149\) 13.5228 1.10783 0.553917 0.832572i \(-0.313132\pi\)
0.553917 + 0.832572i \(0.313132\pi\)
\(150\) −19.8337 −1.61942
\(151\) −8.03719 −0.654058 −0.327029 0.945014i \(-0.606047\pi\)
−0.327029 + 0.945014i \(0.606047\pi\)
\(152\) −0.0309213 −0.00250805
\(153\) 15.5763 1.25927
\(154\) 17.3174 1.39548
\(155\) 8.75453 0.703181
\(156\) 9.65489 0.773010
\(157\) 5.49841 0.438821 0.219410 0.975633i \(-0.429587\pi\)
0.219410 + 0.975633i \(0.429587\pi\)
\(158\) 4.47481 0.355997
\(159\) 10.0938 0.800490
\(160\) 10.1854 0.805227
\(161\) 8.47036 0.667558
\(162\) −47.5850 −3.73863
\(163\) 3.77403 0.295605 0.147802 0.989017i \(-0.452780\pi\)
0.147802 + 0.989017i \(0.452780\pi\)
\(164\) 16.8194 1.31338
\(165\) 9.91180 0.771632
\(166\) 0.657185 0.0510075
\(167\) 22.0558 1.70673 0.853366 0.521313i \(-0.174558\pi\)
0.853366 + 0.521313i \(0.174558\pi\)
\(168\) −7.14542 −0.551281
\(169\) −9.96749 −0.766730
\(170\) −5.40385 −0.414457
\(171\) −0.416804 −0.0318738
\(172\) 9.51951 0.725856
\(173\) −18.6692 −1.41939 −0.709696 0.704508i \(-0.751168\pi\)
−0.709696 + 0.704508i \(0.751168\pi\)
\(174\) −7.78523 −0.590197
\(175\) −12.6038 −0.952754
\(176\) 10.1855 0.767757
\(177\) −13.8027 −1.03748
\(178\) 20.4914 1.53589
\(179\) −12.9707 −0.969474 −0.484737 0.874660i \(-0.661085\pi\)
−0.484737 + 0.874660i \(0.661085\pi\)
\(180\) 17.3163 1.29068
\(181\) −20.5983 −1.53106 −0.765531 0.643399i \(-0.777523\pi\)
−0.765531 + 0.643399i \(0.777523\pi\)
\(182\) 13.3057 0.986282
\(183\) 17.6115 1.30188
\(184\) 1.18763 0.0875530
\(185\) 1.34988 0.0992452
\(186\) 40.4774 2.96795
\(187\) −4.70967 −0.344405
\(188\) −7.37670 −0.538001
\(189\) −57.7687 −4.20206
\(190\) 0.144601 0.0104904
\(191\) 5.17869 0.374717 0.187358 0.982292i \(-0.440007\pi\)
0.187358 + 0.982292i \(0.440007\pi\)
\(192\) 17.9745 1.29720
\(193\) 14.4871 1.04280 0.521401 0.853312i \(-0.325410\pi\)
0.521401 + 0.853312i \(0.325410\pi\)
\(194\) −0.0459231 −0.00329709
\(195\) 7.61563 0.545366
\(196\) 14.9407 1.06720
\(197\) 0.161692 0.0115201 0.00576005 0.999983i \(-0.498167\pi\)
0.00576005 + 0.999983i \(0.498167\pi\)
\(198\) 32.7292 2.32596
\(199\) −3.85590 −0.273337 −0.136669 0.990617i \(-0.543640\pi\)
−0.136669 + 0.990617i \(0.543640\pi\)
\(200\) −1.76717 −0.124958
\(201\) −2.75837 −0.194561
\(202\) 3.98826 0.280613
\(203\) −4.94729 −0.347231
\(204\) −11.5210 −0.806629
\(205\) 13.2669 0.926602
\(206\) −12.2458 −0.853209
\(207\) 16.0086 1.11268
\(208\) 7.82588 0.542627
\(209\) 0.126025 0.00871735
\(210\) 33.4149 2.30585
\(211\) −4.80857 −0.331036 −0.165518 0.986207i \(-0.552930\pi\)
−0.165518 + 0.986207i \(0.552930\pi\)
\(212\) −5.33190 −0.366197
\(213\) −42.2340 −2.89383
\(214\) −11.8559 −0.810453
\(215\) 7.50884 0.512099
\(216\) −8.09974 −0.551117
\(217\) 25.7222 1.74614
\(218\) 1.92648 0.130478
\(219\) 4.10009 0.277059
\(220\) −5.23577 −0.352995
\(221\) −3.61863 −0.243415
\(222\) 6.24129 0.418888
\(223\) 12.8924 0.863337 0.431669 0.902032i \(-0.357925\pi\)
0.431669 + 0.902032i \(0.357925\pi\)
\(224\) 29.9263 1.99954
\(225\) −23.8205 −1.58804
\(226\) −32.0753 −2.13362
\(227\) 25.3867 1.68497 0.842487 0.538717i \(-0.181091\pi\)
0.842487 + 0.538717i \(0.181091\pi\)
\(228\) 0.308288 0.0204168
\(229\) −11.8144 −0.780720 −0.390360 0.920662i \(-0.627650\pi\)
−0.390360 + 0.920662i \(0.627650\pi\)
\(230\) −5.55383 −0.366209
\(231\) 29.1224 1.91611
\(232\) −0.693657 −0.0455408
\(233\) −28.9936 −1.89943 −0.949716 0.313112i \(-0.898628\pi\)
−0.949716 + 0.313112i \(0.898628\pi\)
\(234\) 25.1471 1.64392
\(235\) −5.81863 −0.379565
\(236\) 7.29110 0.474610
\(237\) 7.52520 0.488814
\(238\) −15.8774 −1.02918
\(239\) −1.92586 −0.124573 −0.0622867 0.998058i \(-0.519839\pi\)
−0.0622867 + 0.998058i \(0.519839\pi\)
\(240\) 19.6534 1.26862
\(241\) 2.04690 0.131852 0.0659261 0.997825i \(-0.479000\pi\)
0.0659261 + 0.997825i \(0.479000\pi\)
\(242\) 11.2953 0.726089
\(243\) −36.3266 −2.33035
\(244\) −9.30303 −0.595566
\(245\) 11.7850 0.752918
\(246\) 61.3408 3.91095
\(247\) 0.0968302 0.00616116
\(248\) 3.60650 0.229013
\(249\) 1.10518 0.0700377
\(250\) 21.2666 1.34502
\(251\) 8.84677 0.558403 0.279202 0.960232i \(-0.409930\pi\)
0.279202 + 0.960232i \(0.409930\pi\)
\(252\) 50.8779 3.20501
\(253\) −4.84038 −0.304312
\(254\) −10.8767 −0.682464
\(255\) −9.08756 −0.569085
\(256\) 19.5775 1.22359
\(257\) 25.9731 1.62016 0.810079 0.586321i \(-0.199424\pi\)
0.810079 + 0.586321i \(0.199424\pi\)
\(258\) 34.7178 2.16144
\(259\) 3.96616 0.246445
\(260\) −4.02285 −0.249486
\(261\) −9.35015 −0.578760
\(262\) −25.3337 −1.56512
\(263\) 0.803203 0.0495276 0.0247638 0.999693i \(-0.492117\pi\)
0.0247638 + 0.999693i \(0.492117\pi\)
\(264\) 4.08324 0.251306
\(265\) −4.20572 −0.258355
\(266\) 0.424860 0.0260498
\(267\) 34.4599 2.10891
\(268\) 1.45707 0.0890048
\(269\) 22.4963 1.37162 0.685812 0.727779i \(-0.259447\pi\)
0.685812 + 0.727779i \(0.259447\pi\)
\(270\) 37.8777 2.30516
\(271\) −23.2444 −1.41200 −0.706000 0.708212i \(-0.749502\pi\)
−0.706000 + 0.708212i \(0.749502\pi\)
\(272\) −9.33845 −0.566227
\(273\) 22.3759 1.35425
\(274\) 8.69186 0.525094
\(275\) 7.20241 0.434322
\(276\) −11.8407 −0.712727
\(277\) −23.4400 −1.40838 −0.704188 0.710014i \(-0.748689\pi\)
−0.704188 + 0.710014i \(0.748689\pi\)
\(278\) 3.72769 0.223572
\(279\) 48.6138 2.91043
\(280\) 2.97724 0.177924
\(281\) −0.318088 −0.0189755 −0.00948777 0.999955i \(-0.503020\pi\)
−0.00948777 + 0.999955i \(0.503020\pi\)
\(282\) −26.9030 −1.60205
\(283\) −23.9981 −1.42654 −0.713270 0.700889i \(-0.752787\pi\)
−0.713270 + 0.700889i \(0.752787\pi\)
\(284\) 22.3095 1.32383
\(285\) 0.243172 0.0144043
\(286\) −7.60352 −0.449606
\(287\) 38.9803 2.30093
\(288\) 56.5595 3.33280
\(289\) −12.6820 −0.745998
\(290\) 3.24383 0.190484
\(291\) −0.0772280 −0.00452718
\(292\) −2.16582 −0.126745
\(293\) 11.7660 0.687376 0.343688 0.939084i \(-0.388324\pi\)
0.343688 + 0.939084i \(0.388324\pi\)
\(294\) 54.4891 3.17787
\(295\) 5.75111 0.334842
\(296\) 0.556094 0.0323223
\(297\) 33.0119 1.91555
\(298\) −26.0515 −1.50913
\(299\) −3.71906 −0.215079
\(300\) 17.6188 1.01722
\(301\) 22.0621 1.27164
\(302\) 15.4835 0.890977
\(303\) 6.70699 0.385306
\(304\) 0.249886 0.0143319
\(305\) −7.33809 −0.420178
\(306\) −30.0075 −1.71542
\(307\) 33.1856 1.89400 0.947002 0.321227i \(-0.104095\pi\)
0.947002 + 0.321227i \(0.104095\pi\)
\(308\) −15.3835 −0.876556
\(309\) −20.5936 −1.17153
\(310\) −16.8655 −0.957894
\(311\) −19.9194 −1.12952 −0.564761 0.825254i \(-0.691032\pi\)
−0.564761 + 0.825254i \(0.691032\pi\)
\(312\) 3.13732 0.177616
\(313\) 12.6244 0.713573 0.356786 0.934186i \(-0.383872\pi\)
0.356786 + 0.934186i \(0.383872\pi\)
\(314\) −10.5926 −0.597775
\(315\) 40.1317 2.26116
\(316\) −3.97508 −0.223616
\(317\) 31.4879 1.76854 0.884268 0.466979i \(-0.154658\pi\)
0.884268 + 0.466979i \(0.154658\pi\)
\(318\) −19.4455 −1.09045
\(319\) 2.82712 0.158289
\(320\) −7.48933 −0.418666
\(321\) −19.9378 −1.11282
\(322\) −16.3180 −0.909368
\(323\) −0.115545 −0.00642912
\(324\) 42.2709 2.34838
\(325\) 5.53390 0.306965
\(326\) −7.27061 −0.402682
\(327\) 3.23973 0.179158
\(328\) 5.46541 0.301777
\(329\) −17.0960 −0.942535
\(330\) −19.0949 −1.05114
\(331\) −19.0817 −1.04882 −0.524412 0.851465i \(-0.675715\pi\)
−0.524412 + 0.851465i \(0.675715\pi\)
\(332\) −0.583794 −0.0320398
\(333\) 7.49587 0.410771
\(334\) −42.4902 −2.32496
\(335\) 1.14932 0.0627938
\(336\) 57.7446 3.15023
\(337\) 29.6681 1.61612 0.808062 0.589097i \(-0.200517\pi\)
0.808062 + 0.589097i \(0.200517\pi\)
\(338\) 19.2022 1.04446
\(339\) −53.9404 −2.92964
\(340\) 4.80037 0.260337
\(341\) −14.6989 −0.795992
\(342\) 0.802966 0.0434194
\(343\) 6.86313 0.370574
\(344\) 3.09333 0.166781
\(345\) −9.33977 −0.502836
\(346\) 35.9659 1.93354
\(347\) −9.89584 −0.531237 −0.265618 0.964078i \(-0.585576\pi\)
−0.265618 + 0.964078i \(0.585576\pi\)
\(348\) 6.91581 0.370726
\(349\) 3.30139 0.176719 0.0883597 0.996089i \(-0.471837\pi\)
0.0883597 + 0.996089i \(0.471837\pi\)
\(350\) 24.2809 1.29787
\(351\) 25.3644 1.35385
\(352\) −17.1014 −0.911507
\(353\) 11.0858 0.590036 0.295018 0.955492i \(-0.404674\pi\)
0.295018 + 0.955492i \(0.404674\pi\)
\(354\) 26.5908 1.41328
\(355\) 17.5974 0.933973
\(356\) −18.2030 −0.964755
\(357\) −26.7007 −1.41315
\(358\) 24.9878 1.32065
\(359\) 6.34740 0.335003 0.167502 0.985872i \(-0.446430\pi\)
0.167502 + 0.985872i \(0.446430\pi\)
\(360\) 5.62685 0.296561
\(361\) −18.9969 −0.999837
\(362\) 39.6824 2.08566
\(363\) 18.9951 0.996983
\(364\) −11.8198 −0.619523
\(365\) −1.70836 −0.0894197
\(366\) −33.9283 −1.77346
\(367\) 32.5563 1.69942 0.849712 0.527247i \(-0.176776\pi\)
0.849712 + 0.527247i \(0.176776\pi\)
\(368\) −9.59763 −0.500311
\(369\) 73.6710 3.83516
\(370\) −2.60052 −0.135195
\(371\) −12.3571 −0.641547
\(372\) −35.9570 −1.86429
\(373\) 3.47387 0.179870 0.0899350 0.995948i \(-0.471334\pi\)
0.0899350 + 0.995948i \(0.471334\pi\)
\(374\) 9.07311 0.469159
\(375\) 35.7637 1.84683
\(376\) −2.39703 −0.123617
\(377\) 2.17219 0.111874
\(378\) 111.291 5.72417
\(379\) −9.28610 −0.476995 −0.238497 0.971143i \(-0.576655\pi\)
−0.238497 + 0.971143i \(0.576655\pi\)
\(380\) −0.128452 −0.00658947
\(381\) −18.2911 −0.937083
\(382\) −9.97667 −0.510451
\(383\) −28.2878 −1.44544 −0.722720 0.691141i \(-0.757108\pi\)
−0.722720 + 0.691141i \(0.757108\pi\)
\(384\) 14.2627 0.727838
\(385\) −12.1343 −0.618419
\(386\) −27.9091 −1.42054
\(387\) 41.6965 2.11955
\(388\) 0.0407946 0.00207103
\(389\) −1.02205 −0.0518202 −0.0259101 0.999664i \(-0.508248\pi\)
−0.0259101 + 0.999664i \(0.508248\pi\)
\(390\) −14.6714 −0.742914
\(391\) 4.43787 0.224433
\(392\) 4.85493 0.245211
\(393\) −42.6032 −2.14904
\(394\) −0.311498 −0.0156930
\(395\) −3.13548 −0.157763
\(396\) −29.0741 −1.46103
\(397\) −8.22353 −0.412727 −0.206364 0.978475i \(-0.566163\pi\)
−0.206364 + 0.978475i \(0.566163\pi\)
\(398\) 7.42833 0.372348
\(399\) 0.714478 0.0357687
\(400\) 14.2811 0.714056
\(401\) −11.1475 −0.556681 −0.278341 0.960482i \(-0.589784\pi\)
−0.278341 + 0.960482i \(0.589784\pi\)
\(402\) 5.31397 0.265037
\(403\) −11.2938 −0.562583
\(404\) −3.54287 −0.176264
\(405\) 33.3426 1.65681
\(406\) 9.53087 0.473009
\(407\) −2.26646 −0.112344
\(408\) −3.74369 −0.185340
\(409\) −22.8940 −1.13204 −0.566018 0.824393i \(-0.691517\pi\)
−0.566018 + 0.824393i \(0.691517\pi\)
\(410\) −25.5585 −1.26224
\(411\) 14.6169 0.721000
\(412\) 10.8783 0.535934
\(413\) 16.8977 0.831479
\(414\) −30.8403 −1.51572
\(415\) −0.460487 −0.0226044
\(416\) −13.1397 −0.644225
\(417\) 6.26878 0.306984
\(418\) −0.242786 −0.0118750
\(419\) −0.628840 −0.0307208 −0.0153604 0.999882i \(-0.504890\pi\)
−0.0153604 + 0.999882i \(0.504890\pi\)
\(420\) −29.6833 −1.44839
\(421\) 9.90182 0.482585 0.241293 0.970452i \(-0.422429\pi\)
0.241293 + 0.970452i \(0.422429\pi\)
\(422\) 9.26364 0.450947
\(423\) −32.3108 −1.57100
\(424\) −1.73258 −0.0841415
\(425\) −6.60347 −0.320316
\(426\) 81.3632 3.94206
\(427\) −21.5604 −1.04338
\(428\) 10.5319 0.509078
\(429\) −12.7867 −0.617347
\(430\) −14.4657 −0.697596
\(431\) 13.9722 0.673015 0.336507 0.941681i \(-0.390754\pi\)
0.336507 + 0.941681i \(0.390754\pi\)
\(432\) 65.4568 3.14929
\(433\) −8.97314 −0.431222 −0.215611 0.976479i \(-0.569174\pi\)
−0.215611 + 0.976479i \(0.569174\pi\)
\(434\) −49.5534 −2.37864
\(435\) 5.45508 0.261551
\(436\) −1.71134 −0.0819584
\(437\) −0.118752 −0.00568069
\(438\) −7.89877 −0.377418
\(439\) −35.1841 −1.67925 −0.839623 0.543169i \(-0.817224\pi\)
−0.839623 + 0.543169i \(0.817224\pi\)
\(440\) −1.70134 −0.0811083
\(441\) 65.4421 3.11629
\(442\) 6.97123 0.331588
\(443\) −1.42393 −0.0676531 −0.0338266 0.999428i \(-0.510769\pi\)
−0.0338266 + 0.999428i \(0.510769\pi\)
\(444\) −5.54429 −0.263120
\(445\) −14.3582 −0.680645
\(446\) −24.8370 −1.17606
\(447\) −43.8104 −2.07216
\(448\) −22.0048 −1.03963
\(449\) −17.0025 −0.802398 −0.401199 0.915991i \(-0.631406\pi\)
−0.401199 + 0.915991i \(0.631406\pi\)
\(450\) 45.8899 2.16327
\(451\) −22.2753 −1.04890
\(452\) 28.4933 1.34021
\(453\) 26.0384 1.22339
\(454\) −48.9071 −2.29532
\(455\) −9.32323 −0.437080
\(456\) 0.100177 0.00469121
\(457\) 3.03418 0.141933 0.0709665 0.997479i \(-0.477392\pi\)
0.0709665 + 0.997479i \(0.477392\pi\)
\(458\) 22.7603 1.06352
\(459\) −30.2667 −1.41273
\(460\) 4.93360 0.230030
\(461\) 33.7244 1.57070 0.785350 0.619051i \(-0.212483\pi\)
0.785350 + 0.619051i \(0.212483\pi\)
\(462\) −56.1039 −2.61019
\(463\) 17.8786 0.830891 0.415446 0.909618i \(-0.363626\pi\)
0.415446 + 0.909618i \(0.363626\pi\)
\(464\) 5.60569 0.260238
\(465\) −28.3623 −1.31527
\(466\) 55.8557 2.58746
\(467\) −17.1965 −0.795758 −0.397879 0.917438i \(-0.630254\pi\)
−0.397879 + 0.917438i \(0.630254\pi\)
\(468\) −22.3388 −1.03261
\(469\) 3.37687 0.155929
\(470\) 11.2095 0.517055
\(471\) −17.8134 −0.820797
\(472\) 2.36921 0.109052
\(473\) −12.6074 −0.579689
\(474\) −14.4972 −0.665878
\(475\) 0.176701 0.00810761
\(476\) 14.1042 0.646467
\(477\) −23.3543 −1.06932
\(478\) 3.71013 0.169698
\(479\) 4.32679 0.197696 0.0988480 0.995103i \(-0.468484\pi\)
0.0988480 + 0.995103i \(0.468484\pi\)
\(480\) −32.9980 −1.50615
\(481\) −1.74141 −0.0794015
\(482\) −3.94331 −0.179613
\(483\) −27.4417 −1.24864
\(484\) −10.0339 −0.456085
\(485\) 0.0321781 0.00146113
\(486\) 69.9826 3.17447
\(487\) 8.43485 0.382220 0.191110 0.981569i \(-0.438791\pi\)
0.191110 + 0.981569i \(0.438791\pi\)
\(488\) −3.02298 −0.136844
\(489\) −12.2268 −0.552917
\(490\) −22.7037 −1.02565
\(491\) −15.3908 −0.694577 −0.347288 0.937758i \(-0.612898\pi\)
−0.347288 + 0.937758i \(0.612898\pi\)
\(492\) −54.4905 −2.45662
\(493\) −2.59203 −0.116739
\(494\) −0.186542 −0.00839292
\(495\) −22.9332 −1.03077
\(496\) −29.1454 −1.30867
\(497\) 51.7039 2.31924
\(498\) −2.12911 −0.0954075
\(499\) 34.6105 1.54938 0.774688 0.632343i \(-0.217907\pi\)
0.774688 + 0.632343i \(0.217907\pi\)
\(500\) −18.8917 −0.844860
\(501\) −71.4550 −3.19237
\(502\) −17.0432 −0.760674
\(503\) 33.0545 1.47383 0.736913 0.675988i \(-0.236283\pi\)
0.736913 + 0.675988i \(0.236283\pi\)
\(504\) 16.5326 0.736419
\(505\) −2.79456 −0.124356
\(506\) 9.32493 0.414543
\(507\) 32.2920 1.43414
\(508\) 9.66203 0.428683
\(509\) −17.6100 −0.780550 −0.390275 0.920698i \(-0.627620\pi\)
−0.390275 + 0.920698i \(0.627620\pi\)
\(510\) 17.5070 0.775225
\(511\) −5.01943 −0.222047
\(512\) −28.9109 −1.27769
\(513\) 0.809902 0.0357580
\(514\) −50.0368 −2.20703
\(515\) 8.58062 0.378107
\(516\) −30.8407 −1.35768
\(517\) 9.76952 0.429663
\(518\) −7.64075 −0.335715
\(519\) 60.4832 2.65492
\(520\) −1.30721 −0.0573248
\(521\) 19.9261 0.872978 0.436489 0.899710i \(-0.356222\pi\)
0.436489 + 0.899710i \(0.356222\pi\)
\(522\) 18.0129 0.788404
\(523\) 14.0995 0.616530 0.308265 0.951301i \(-0.400252\pi\)
0.308265 + 0.951301i \(0.400252\pi\)
\(524\) 22.5045 0.983114
\(525\) 40.8328 1.78209
\(526\) −1.54736 −0.0674680
\(527\) 13.4766 0.587050
\(528\) −32.9981 −1.43606
\(529\) −18.4390 −0.801694
\(530\) 8.10226 0.351940
\(531\) 31.9358 1.38590
\(532\) −0.377413 −0.0163629
\(533\) −17.1150 −0.741331
\(534\) −66.3865 −2.87283
\(535\) 8.30738 0.359159
\(536\) 0.473470 0.0204508
\(537\) 42.0215 1.81336
\(538\) −43.3388 −1.86847
\(539\) −19.7872 −0.852293
\(540\) −33.6477 −1.44796
\(541\) 0.421224 0.0181098 0.00905491 0.999959i \(-0.497118\pi\)
0.00905491 + 0.999959i \(0.497118\pi\)
\(542\) 44.7801 1.92347
\(543\) 66.7331 2.86379
\(544\) 15.6793 0.672243
\(545\) −1.34988 −0.0578225
\(546\) −43.1068 −1.84480
\(547\) 3.06417 0.131014 0.0655072 0.997852i \(-0.479133\pi\)
0.0655072 + 0.997852i \(0.479133\pi\)
\(548\) −7.72118 −0.329833
\(549\) −40.7483 −1.73910
\(550\) −13.8753 −0.591646
\(551\) 0.0693596 0.00295482
\(552\) −3.84759 −0.163764
\(553\) −9.21253 −0.391757
\(554\) 45.1569 1.91853
\(555\) −4.37325 −0.185634
\(556\) −3.31140 −0.140434
\(557\) 36.6361 1.55232 0.776161 0.630534i \(-0.217164\pi\)
0.776161 + 0.630534i \(0.217164\pi\)
\(558\) −93.6537 −3.96468
\(559\) −9.68676 −0.409706
\(560\) −24.0601 −1.01673
\(561\) 15.2581 0.644197
\(562\) 0.612792 0.0258491
\(563\) −40.4196 −1.70348 −0.851741 0.523964i \(-0.824453\pi\)
−0.851741 + 0.523964i \(0.824453\pi\)
\(564\) 23.8985 1.00631
\(565\) 22.4750 0.945532
\(566\) 46.2320 1.94328
\(567\) 97.9658 4.11418
\(568\) 7.24939 0.304178
\(569\) 36.6620 1.53695 0.768475 0.639879i \(-0.221016\pi\)
0.768475 + 0.639879i \(0.221016\pi\)
\(570\) −0.468468 −0.0196220
\(571\) −6.54264 −0.273801 −0.136900 0.990585i \(-0.543714\pi\)
−0.136900 + 0.990585i \(0.543714\pi\)
\(572\) 6.75439 0.282415
\(573\) −16.7776 −0.700893
\(574\) −75.0949 −3.13440
\(575\) −6.78675 −0.283027
\(576\) −41.5882 −1.73284
\(577\) −9.21807 −0.383753 −0.191877 0.981419i \(-0.561457\pi\)
−0.191877 + 0.981419i \(0.561457\pi\)
\(578\) 24.4316 1.01622
\(579\) −46.9342 −1.95052
\(580\) −2.88157 −0.119651
\(581\) −1.35298 −0.0561312
\(582\) 0.148779 0.00616707
\(583\) 7.06144 0.292455
\(584\) −0.703773 −0.0291223
\(585\) −17.6205 −0.728518
\(586\) −22.6670 −0.936364
\(587\) 19.6619 0.811535 0.405767 0.913976i \(-0.367004\pi\)
0.405767 + 0.913976i \(0.367004\pi\)
\(588\) −48.4040 −1.99615
\(589\) −0.360618 −0.0148590
\(590\) −11.0794 −0.456132
\(591\) −0.523840 −0.0215479
\(592\) −4.49399 −0.184702
\(593\) 3.16157 0.129830 0.0649151 0.997891i \(-0.479322\pi\)
0.0649151 + 0.997891i \(0.479322\pi\)
\(594\) −63.5969 −2.60941
\(595\) 11.1252 0.456089
\(596\) 23.1422 0.947942
\(597\) 12.4921 0.511267
\(598\) 7.16471 0.292987
\(599\) 19.3669 0.791308 0.395654 0.918400i \(-0.370518\pi\)
0.395654 + 0.918400i \(0.370518\pi\)
\(600\) 5.72515 0.233728
\(601\) 32.6005 1.32980 0.664901 0.746932i \(-0.268474\pi\)
0.664901 + 0.746932i \(0.268474\pi\)
\(602\) −42.5024 −1.73227
\(603\) 6.38214 0.259901
\(604\) −13.7544 −0.559658
\(605\) −7.91456 −0.321773
\(606\) −12.9209 −0.524876
\(607\) 37.3475 1.51589 0.757945 0.652319i \(-0.226204\pi\)
0.757945 + 0.652319i \(0.226204\pi\)
\(608\) −0.419559 −0.0170154
\(609\) 16.0279 0.649483
\(610\) 14.1367 0.572379
\(611\) 7.50631 0.303673
\(612\) 26.6564 1.07752
\(613\) 19.4375 0.785072 0.392536 0.919737i \(-0.371598\pi\)
0.392536 + 0.919737i \(0.371598\pi\)
\(614\) −63.9316 −2.58007
\(615\) −42.9813 −1.73317
\(616\) −4.99881 −0.201408
\(617\) −10.5770 −0.425813 −0.212906 0.977073i \(-0.568293\pi\)
−0.212906 + 0.977073i \(0.568293\pi\)
\(618\) 39.6733 1.59589
\(619\) −32.7979 −1.31826 −0.659129 0.752030i \(-0.729075\pi\)
−0.659129 + 0.752030i \(0.729075\pi\)
\(620\) 14.9820 0.601692
\(621\) −31.1067 −1.24827
\(622\) 38.3743 1.53867
\(623\) −42.1867 −1.69017
\(624\) −25.3538 −1.01496
\(625\) 0.987677 0.0395071
\(626\) −24.3207 −0.972050
\(627\) −0.408288 −0.0163055
\(628\) 9.40966 0.375486
\(629\) 2.07799 0.0828547
\(630\) −77.3131 −3.08023
\(631\) −18.5308 −0.737699 −0.368850 0.929489i \(-0.620248\pi\)
−0.368850 + 0.929489i \(0.620248\pi\)
\(632\) −1.29169 −0.0513805
\(633\) 15.5785 0.619189
\(634\) −60.6609 −2.40915
\(635\) 7.62125 0.302440
\(636\) 17.2739 0.684956
\(637\) −15.2033 −0.602375
\(638\) −5.44641 −0.215625
\(639\) 97.7181 3.86567
\(640\) −5.94273 −0.234907
\(641\) 13.2777 0.524437 0.262218 0.965009i \(-0.415546\pi\)
0.262218 + 0.965009i \(0.415546\pi\)
\(642\) 38.4099 1.51592
\(643\) 31.1781 1.22954 0.614772 0.788705i \(-0.289248\pi\)
0.614772 + 0.788705i \(0.289248\pi\)
\(644\) 14.4957 0.571210
\(645\) −24.3266 −0.957860
\(646\) 0.222596 0.00875794
\(647\) 9.16297 0.360234 0.180117 0.983645i \(-0.442352\pi\)
0.180117 + 0.983645i \(0.442352\pi\)
\(648\) 13.7358 0.539592
\(649\) −9.65615 −0.379037
\(650\) −10.6610 −0.418157
\(651\) −83.3330 −3.26608
\(652\) 6.45866 0.252940
\(653\) 12.6327 0.494354 0.247177 0.968970i \(-0.420497\pi\)
0.247177 + 0.968970i \(0.420497\pi\)
\(654\) −6.24129 −0.244054
\(655\) 17.7512 0.693597
\(656\) −44.1679 −1.72447
\(657\) −9.48651 −0.370104
\(658\) 32.9353 1.28395
\(659\) 50.5499 1.96914 0.984572 0.174983i \(-0.0559869\pi\)
0.984572 + 0.174983i \(0.0559869\pi\)
\(660\) 16.9625 0.660264
\(661\) −15.2491 −0.593121 −0.296561 0.955014i \(-0.595840\pi\)
−0.296561 + 0.955014i \(0.595840\pi\)
\(662\) 36.7605 1.42874
\(663\) 11.7234 0.455299
\(664\) −0.189701 −0.00736184
\(665\) −0.297698 −0.0115442
\(666\) −14.4407 −0.559565
\(667\) −2.66397 −0.103149
\(668\) 37.7451 1.46040
\(669\) −41.7679 −1.61484
\(670\) −2.21414 −0.0855396
\(671\) 12.3207 0.475636
\(672\) −96.9533 −3.74006
\(673\) −43.3797 −1.67217 −0.836083 0.548603i \(-0.815160\pi\)
−0.836083 + 0.548603i \(0.815160\pi\)
\(674\) −57.1551 −2.20153
\(675\) 46.2863 1.78156
\(676\) −17.0578 −0.656069
\(677\) −33.5075 −1.28780 −0.643898 0.765111i \(-0.722684\pi\)
−0.643898 + 0.765111i \(0.722684\pi\)
\(678\) 103.915 3.99085
\(679\) 0.0945444 0.00362828
\(680\) 1.55986 0.0598180
\(681\) −82.2461 −3.15168
\(682\) 28.3173 1.08432
\(683\) 28.2494 1.08093 0.540467 0.841365i \(-0.318248\pi\)
0.540467 + 0.841365i \(0.318248\pi\)
\(684\) −0.713294 −0.0272735
\(685\) −6.09035 −0.232700
\(686\) −13.2217 −0.504808
\(687\) 38.2756 1.46031
\(688\) −24.9983 −0.953050
\(689\) 5.42558 0.206698
\(690\) 17.9929 0.684979
\(691\) 25.7424 0.979288 0.489644 0.871922i \(-0.337127\pi\)
0.489644 + 0.871922i \(0.337127\pi\)
\(692\) −31.9494 −1.21453
\(693\) −67.3814 −2.55961
\(694\) 19.0642 0.723666
\(695\) −2.61198 −0.0990779
\(696\) 2.24726 0.0851823
\(697\) 20.4229 0.773573
\(698\) −6.36008 −0.240733
\(699\) 93.9314 3.55281
\(700\) −21.5693 −0.815245
\(701\) 12.6667 0.478416 0.239208 0.970968i \(-0.423112\pi\)
0.239208 + 0.970968i \(0.423112\pi\)
\(702\) −48.8640 −1.84425
\(703\) −0.0556045 −0.00209716
\(704\) 12.5747 0.473925
\(705\) 18.8508 0.709962
\(706\) −21.3566 −0.803765
\(707\) −8.21086 −0.308801
\(708\) −23.6212 −0.887740
\(709\) 24.1517 0.907035 0.453518 0.891247i \(-0.350169\pi\)
0.453518 + 0.891247i \(0.350169\pi\)
\(710\) −33.9011 −1.27229
\(711\) −17.4113 −0.652974
\(712\) −5.91498 −0.221673
\(713\) 13.8506 0.518710
\(714\) 51.4384 1.92503
\(715\) 5.32776 0.199247
\(716\) −22.1973 −0.829551
\(717\) 6.23926 0.233010
\(718\) −12.2282 −0.456351
\(719\) 21.0475 0.784941 0.392471 0.919765i \(-0.371620\pi\)
0.392471 + 0.919765i \(0.371620\pi\)
\(720\) −45.4726 −1.69466
\(721\) 25.2112 0.938914
\(722\) 36.5972 1.36201
\(723\) −6.63140 −0.246624
\(724\) −35.2508 −1.31009
\(725\) 3.96394 0.147217
\(726\) −36.5937 −1.35812
\(727\) 47.2143 1.75108 0.875541 0.483144i \(-0.160505\pi\)
0.875541 + 0.483144i \(0.160505\pi\)
\(728\) −3.84078 −0.142349
\(729\) 43.5871 1.61434
\(730\) 3.29113 0.121810
\(731\) 11.5590 0.427525
\(732\) 30.1393 1.11398
\(733\) −18.8782 −0.697282 −0.348641 0.937256i \(-0.613357\pi\)
−0.348641 + 0.937256i \(0.613357\pi\)
\(734\) −62.7192 −2.31501
\(735\) −38.1803 −1.40830
\(736\) 16.1144 0.593986
\(737\) −1.92971 −0.0710818
\(738\) −141.926 −5.22437
\(739\) 27.2012 1.00061 0.500306 0.865849i \(-0.333221\pi\)
0.500306 + 0.865849i \(0.333221\pi\)
\(740\) 2.31011 0.0849212
\(741\) −0.313704 −0.0115242
\(742\) 23.8057 0.873935
\(743\) 39.7775 1.45929 0.729647 0.683824i \(-0.239684\pi\)
0.729647 + 0.683824i \(0.239684\pi\)
\(744\) −11.6841 −0.428360
\(745\) 18.2542 0.668783
\(746\) −6.69235 −0.245024
\(747\) −2.55708 −0.0935587
\(748\) −8.05986 −0.294698
\(749\) 24.4084 0.891863
\(750\) −68.8982 −2.51581
\(751\) 43.7727 1.59729 0.798644 0.601804i \(-0.205551\pi\)
0.798644 + 0.601804i \(0.205551\pi\)
\(752\) 19.3712 0.706397
\(753\) −28.6612 −1.04447
\(754\) −4.18469 −0.152397
\(755\) −10.8492 −0.394845
\(756\) −98.8621 −3.59558
\(757\) −28.3539 −1.03054 −0.515270 0.857028i \(-0.672308\pi\)
−0.515270 + 0.857028i \(0.672308\pi\)
\(758\) 17.8895 0.649777
\(759\) 15.6816 0.569204
\(760\) −0.0417401 −0.00151407
\(761\) −21.0154 −0.761809 −0.380904 0.924614i \(-0.624387\pi\)
−0.380904 + 0.924614i \(0.624387\pi\)
\(762\) 35.2376 1.27652
\(763\) −3.96616 −0.143585
\(764\) 8.86251 0.320634
\(765\) 21.0262 0.760202
\(766\) 54.4960 1.96902
\(767\) −7.41921 −0.267892
\(768\) −63.4258 −2.28868
\(769\) −35.5062 −1.28039 −0.640193 0.768214i \(-0.721146\pi\)
−0.640193 + 0.768214i \(0.721146\pi\)
\(770\) 23.3765 0.842430
\(771\) −84.1459 −3.03044
\(772\) 24.7923 0.892295
\(773\) −8.93550 −0.321387 −0.160694 0.987004i \(-0.551373\pi\)
−0.160694 + 0.987004i \(0.551373\pi\)
\(774\) −80.3276 −2.88732
\(775\) −20.6095 −0.740315
\(776\) 0.0132560 0.000475864 0
\(777\) −12.8493 −0.460966
\(778\) 1.96897 0.0705910
\(779\) −0.546493 −0.0195801
\(780\) 13.0329 0.466654
\(781\) −29.5462 −1.05725
\(782\) −8.54949 −0.305729
\(783\) 18.1685 0.649290
\(784\) −39.2344 −1.40123
\(785\) 7.42219 0.264909
\(786\) 82.0743 2.92749
\(787\) −4.74107 −0.169001 −0.0845005 0.996423i \(-0.526929\pi\)
−0.0845005 + 0.996423i \(0.526929\pi\)
\(788\) 0.276711 0.00985743
\(789\) −2.60216 −0.0926395
\(790\) 6.04045 0.214910
\(791\) 66.0352 2.34794
\(792\) −9.44752 −0.335703
\(793\) 9.46649 0.336165
\(794\) 15.8425 0.562229
\(795\) 13.6254 0.483244
\(796\) −6.59876 −0.233887
\(797\) −13.3979 −0.474579 −0.237290 0.971439i \(-0.576259\pi\)
−0.237290 + 0.971439i \(0.576259\pi\)
\(798\) −1.37643 −0.0487252
\(799\) −8.95711 −0.316880
\(800\) −23.9780 −0.847750
\(801\) −79.7310 −2.81716
\(802\) 21.4755 0.758328
\(803\) 2.86835 0.101222
\(804\) −4.72052 −0.166480
\(805\) 11.4340 0.402995
\(806\) 21.7573 0.766367
\(807\) −72.8820 −2.56557
\(808\) −1.15124 −0.0405005
\(809\) 44.5045 1.56469 0.782347 0.622843i \(-0.214022\pi\)
0.782347 + 0.622843i \(0.214022\pi\)
\(810\) −64.2340 −2.25695
\(811\) 52.7827 1.85345 0.926726 0.375738i \(-0.122611\pi\)
0.926726 + 0.375738i \(0.122611\pi\)
\(812\) −8.46650 −0.297116
\(813\) 75.3058 2.64109
\(814\) 4.36630 0.153039
\(815\) 5.09449 0.178452
\(816\) 30.2541 1.05911
\(817\) −0.309305 −0.0108212
\(818\) 44.1050 1.54209
\(819\) −51.7718 −1.80905
\(820\) 22.7042 0.792867
\(821\) 1.83938 0.0641949 0.0320974 0.999485i \(-0.489781\pi\)
0.0320974 + 0.999485i \(0.489781\pi\)
\(822\) −28.1593 −0.982168
\(823\) 22.1676 0.772714 0.386357 0.922349i \(-0.373733\pi\)
0.386357 + 0.922349i \(0.373733\pi\)
\(824\) 3.53485 0.123142
\(825\) −23.3339 −0.812381
\(826\) −32.5531 −1.13267
\(827\) −1.42069 −0.0494021 −0.0247010 0.999695i \(-0.507863\pi\)
−0.0247010 + 0.999695i \(0.507863\pi\)
\(828\) 27.3962 0.952085
\(829\) −24.1328 −0.838168 −0.419084 0.907948i \(-0.637649\pi\)
−0.419084 + 0.907948i \(0.637649\pi\)
\(830\) 0.887122 0.0307924
\(831\) 75.9395 2.63431
\(832\) 9.66160 0.334956
\(833\) 18.1417 0.628573
\(834\) −12.0767 −0.418182
\(835\) 29.7727 1.03033
\(836\) 0.215672 0.00745919
\(837\) −94.4627 −3.26511
\(838\) 1.21145 0.0418488
\(839\) 5.86000 0.202310 0.101155 0.994871i \(-0.467746\pi\)
0.101155 + 0.994871i \(0.467746\pi\)
\(840\) −9.64546 −0.332800
\(841\) −27.4441 −0.946347
\(842\) −19.0757 −0.657392
\(843\) 1.03052 0.0354930
\(844\) −8.22911 −0.283258
\(845\) −13.4549 −0.462863
\(846\) 62.2462 2.14007
\(847\) −23.2542 −0.799025
\(848\) 14.0016 0.480817
\(849\) 77.7475 2.66829
\(850\) 12.7215 0.436343
\(851\) 2.13566 0.0732094
\(852\) −72.2769 −2.47617
\(853\) 32.6845 1.11909 0.559547 0.828798i \(-0.310975\pi\)
0.559547 + 0.828798i \(0.310975\pi\)
\(854\) 41.5359 1.42133
\(855\) −0.562635 −0.0192417
\(856\) 3.42229 0.116972
\(857\) −31.8881 −1.08928 −0.544639 0.838671i \(-0.683333\pi\)
−0.544639 + 0.838671i \(0.683333\pi\)
\(858\) 24.6334 0.840969
\(859\) −21.7249 −0.741244 −0.370622 0.928784i \(-0.620855\pi\)
−0.370622 + 0.928784i \(0.620855\pi\)
\(860\) 12.8502 0.438188
\(861\) −126.286 −4.30381
\(862\) −26.9171 −0.916801
\(863\) −39.5074 −1.34485 −0.672424 0.740166i \(-0.734747\pi\)
−0.672424 + 0.740166i \(0.734747\pi\)
\(864\) −109.902 −3.73895
\(865\) −25.2012 −0.856865
\(866\) 17.2866 0.587423
\(867\) 41.0862 1.39536
\(868\) 44.0195 1.49412
\(869\) 5.26450 0.178586
\(870\) −10.5091 −0.356293
\(871\) −1.48267 −0.0502384
\(872\) −0.556094 −0.0188317
\(873\) 0.178685 0.00604756
\(874\) 0.228774 0.00773840
\(875\) −43.7828 −1.48013
\(876\) 7.01666 0.237071
\(877\) −7.82967 −0.264389 −0.132195 0.991224i \(-0.542202\pi\)
−0.132195 + 0.991224i \(0.542202\pi\)
\(878\) 67.7817 2.28752
\(879\) −38.1186 −1.28571
\(880\) 13.7491 0.463483
\(881\) 4.05232 0.136526 0.0682631 0.997667i \(-0.478254\pi\)
0.0682631 + 0.997667i \(0.478254\pi\)
\(882\) −126.073 −4.24510
\(883\) −30.9967 −1.04312 −0.521562 0.853214i \(-0.674650\pi\)
−0.521562 + 0.853214i \(0.674650\pi\)
\(884\) −6.19271 −0.208283
\(885\) −18.6321 −0.626310
\(886\) 2.74319 0.0921592
\(887\) −16.4517 −0.552395 −0.276197 0.961101i \(-0.589074\pi\)
−0.276197 + 0.961101i \(0.589074\pi\)
\(888\) −1.80160 −0.0604576
\(889\) 22.3924 0.751018
\(890\) 27.6609 0.927195
\(891\) −55.9825 −1.87549
\(892\) 22.0633 0.738733
\(893\) 0.239682 0.00802065
\(894\) 84.4000 2.82276
\(895\) −17.5089 −0.585257
\(896\) −17.4607 −0.583321
\(897\) 12.0488 0.402296
\(898\) 32.7551 1.09305
\(899\) −8.08974 −0.269808
\(900\) −40.7651 −1.35884
\(901\) −6.47423 −0.215688
\(902\) 42.9129 1.42884
\(903\) −71.4754 −2.37855
\(904\) 9.25877 0.307942
\(905\) −27.8053 −0.924279
\(906\) −50.1625 −1.66654
\(907\) 21.4650 0.712733 0.356366 0.934346i \(-0.384015\pi\)
0.356366 + 0.934346i \(0.384015\pi\)
\(908\) 43.4453 1.44178
\(909\) −15.5182 −0.514705
\(910\) 17.9611 0.595404
\(911\) −33.0791 −1.09596 −0.547979 0.836492i \(-0.684603\pi\)
−0.547979 + 0.836492i \(0.684603\pi\)
\(912\) −0.809564 −0.0268073
\(913\) 0.773162 0.0255879
\(914\) −5.84530 −0.193345
\(915\) 23.7734 0.785926
\(916\) −20.2186 −0.668040
\(917\) 52.1558 1.72234
\(918\) 58.3084 1.92446
\(919\) 18.7178 0.617442 0.308721 0.951153i \(-0.400099\pi\)
0.308721 + 0.951153i \(0.400099\pi\)
\(920\) 1.60315 0.0528544
\(921\) −107.513 −3.54266
\(922\) −64.9695 −2.13966
\(923\) −22.7015 −0.747229
\(924\) 49.8384 1.63956
\(925\) −3.17782 −0.104486
\(926\) −34.4429 −1.13186
\(927\) 47.6481 1.56497
\(928\) −9.41196 −0.308963
\(929\) 50.7241 1.66420 0.832102 0.554623i \(-0.187137\pi\)
0.832102 + 0.554623i \(0.187137\pi\)
\(930\) 54.6396 1.79170
\(931\) −0.485451 −0.0159100
\(932\) −49.6179 −1.62529
\(933\) 64.5334 2.11273
\(934\) 33.1288 1.08401
\(935\) −6.35749 −0.207912
\(936\) −7.25891 −0.237265
\(937\) −22.8934 −0.747894 −0.373947 0.927450i \(-0.621996\pi\)
−0.373947 + 0.927450i \(0.621996\pi\)
\(938\) −6.50549 −0.212412
\(939\) −40.8996 −1.33471
\(940\) −9.95766 −0.324783
\(941\) 35.0799 1.14357 0.571786 0.820403i \(-0.306251\pi\)
0.571786 + 0.820403i \(0.306251\pi\)
\(942\) 34.3172 1.11811
\(943\) 20.9897 0.683519
\(944\) −19.1465 −0.623164
\(945\) −77.9809 −2.53672
\(946\) 24.2880 0.789670
\(947\) 22.6453 0.735872 0.367936 0.929851i \(-0.380065\pi\)
0.367936 + 0.929851i \(0.380065\pi\)
\(948\) 12.8782 0.418264
\(949\) 2.20387 0.0715406
\(950\) −0.340412 −0.0110444
\(951\) −102.012 −3.30798
\(952\) 4.58312 0.148540
\(953\) 3.92428 0.127120 0.0635599 0.997978i \(-0.479755\pi\)
0.0635599 + 0.997978i \(0.479755\pi\)
\(954\) 44.9917 1.45666
\(955\) 6.99061 0.226211
\(956\) −3.29580 −0.106594
\(957\) −9.15912 −0.296072
\(958\) −8.33549 −0.269307
\(959\) −17.8944 −0.577840
\(960\) 24.2634 0.783099
\(961\) 11.0606 0.356793
\(962\) 3.35480 0.108163
\(963\) 46.1308 1.48654
\(964\) 3.50294 0.112822
\(965\) 19.5558 0.629523
\(966\) 52.8660 1.70094
\(967\) −15.2485 −0.490358 −0.245179 0.969478i \(-0.578847\pi\)
−0.245179 + 0.969478i \(0.578847\pi\)
\(968\) −3.26047 −0.104795
\(969\) 0.374336 0.0120254
\(970\) −0.0619907 −0.00199040
\(971\) 40.7839 1.30882 0.654409 0.756141i \(-0.272917\pi\)
0.654409 + 0.756141i \(0.272917\pi\)
\(972\) −62.1672 −1.99401
\(973\) −7.67440 −0.246030
\(974\) −16.2496 −0.520671
\(975\) −17.9283 −0.574166
\(976\) 24.4298 0.781979
\(977\) −16.0448 −0.513318 −0.256659 0.966502i \(-0.582622\pi\)
−0.256659 + 0.966502i \(0.582622\pi\)
\(978\) 23.5548 0.753200
\(979\) 24.1076 0.770481
\(980\) 20.1682 0.644250
\(981\) −7.49587 −0.239325
\(982\) 29.6501 0.946174
\(983\) 26.5463 0.846694 0.423347 0.905968i \(-0.360855\pi\)
0.423347 + 0.905968i \(0.360855\pi\)
\(984\) −17.7065 −0.564462
\(985\) 0.218265 0.00695452
\(986\) 4.99350 0.159025
\(987\) 55.3866 1.76297
\(988\) 0.165710 0.00527193
\(989\) 11.8798 0.377756
\(990\) 44.1805 1.40415
\(991\) −7.26308 −0.230719 −0.115360 0.993324i \(-0.536802\pi\)
−0.115360 + 0.993324i \(0.536802\pi\)
\(992\) 48.9352 1.55369
\(993\) 61.8195 1.96178
\(994\) −99.6068 −3.15934
\(995\) −5.20500 −0.165010
\(996\) 1.89134 0.0599293
\(997\) 2.34142 0.0741536 0.0370768 0.999312i \(-0.488195\pi\)
0.0370768 + 0.999312i \(0.488195\pi\)
\(998\) −66.6765 −2.11061
\(999\) −14.5654 −0.460829
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 4033.2.a.f.1.16 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.16 85 1.1 even 1 trivial