Properties

Label 4033.2.a.f.1.13
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 1.13
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.03156 q^{2} +3.25300 q^{3} +2.12723 q^{4} +1.52354 q^{5} -6.60865 q^{6} -4.26037 q^{7} -0.258468 q^{8} +7.58200 q^{9} +O(q^{10})\) \(q-2.03156 q^{2} +3.25300 q^{3} +2.12723 q^{4} +1.52354 q^{5} -6.60865 q^{6} -4.26037 q^{7} -0.258468 q^{8} +7.58200 q^{9} -3.09515 q^{10} -0.546050 q^{11} +6.91986 q^{12} +0.570945 q^{13} +8.65518 q^{14} +4.95606 q^{15} -3.72936 q^{16} -1.08709 q^{17} -15.4033 q^{18} +2.45317 q^{19} +3.24091 q^{20} -13.8590 q^{21} +1.10933 q^{22} -8.77079 q^{23} -0.840796 q^{24} -2.67884 q^{25} -1.15991 q^{26} +14.9052 q^{27} -9.06277 q^{28} +4.87255 q^{29} -10.0685 q^{30} +4.77597 q^{31} +8.09335 q^{32} -1.77630 q^{33} +2.20849 q^{34} -6.49083 q^{35} +16.1286 q^{36} +1.00000 q^{37} -4.98375 q^{38} +1.85728 q^{39} -0.393786 q^{40} -4.73451 q^{41} +28.1553 q^{42} +5.48913 q^{43} -1.16157 q^{44} +11.5514 q^{45} +17.8184 q^{46} +8.15516 q^{47} -12.1316 q^{48} +11.1507 q^{49} +5.44221 q^{50} -3.53631 q^{51} +1.21453 q^{52} +13.8731 q^{53} -30.2808 q^{54} -0.831927 q^{55} +1.10117 q^{56} +7.98015 q^{57} -9.89887 q^{58} +14.4576 q^{59} +10.5427 q^{60} -1.32357 q^{61} -9.70265 q^{62} -32.3021 q^{63} -8.98338 q^{64} +0.869855 q^{65} +3.60865 q^{66} +2.92586 q^{67} -2.31249 q^{68} -28.5314 q^{69} +13.1865 q^{70} +8.48759 q^{71} -1.95970 q^{72} +7.16098 q^{73} -2.03156 q^{74} -8.71425 q^{75} +5.21844 q^{76} +2.32637 q^{77} -3.77318 q^{78} +17.5571 q^{79} -5.68182 q^{80} +25.7407 q^{81} +9.61844 q^{82} -15.5410 q^{83} -29.4812 q^{84} -1.65623 q^{85} -11.1515 q^{86} +15.8504 q^{87} +0.141136 q^{88} -15.4639 q^{89} -23.4674 q^{90} -2.43244 q^{91} -18.6575 q^{92} +15.5362 q^{93} -16.5677 q^{94} +3.73749 q^{95} +26.3276 q^{96} +4.97454 q^{97} -22.6534 q^{98} -4.14015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.03156 −1.43653 −0.718264 0.695771i \(-0.755063\pi\)
−0.718264 + 0.695771i \(0.755063\pi\)
\(3\) 3.25300 1.87812 0.939060 0.343754i \(-0.111699\pi\)
0.939060 + 0.343754i \(0.111699\pi\)
\(4\) 2.12723 1.06361
\(5\) 1.52354 0.681346 0.340673 0.940182i \(-0.389345\pi\)
0.340673 + 0.940182i \(0.389345\pi\)
\(6\) −6.60865 −2.69797
\(7\) −4.26037 −1.61027 −0.805134 0.593093i \(-0.797907\pi\)
−0.805134 + 0.593093i \(0.797907\pi\)
\(8\) −0.258468 −0.0913823
\(9\) 7.58200 2.52733
\(10\) −3.09515 −0.978773
\(11\) −0.546050 −0.164640 −0.0823201 0.996606i \(-0.526233\pi\)
−0.0823201 + 0.996606i \(0.526233\pi\)
\(12\) 6.91986 1.99759
\(13\) 0.570945 0.158352 0.0791758 0.996861i \(-0.474771\pi\)
0.0791758 + 0.996861i \(0.474771\pi\)
\(14\) 8.65518 2.31320
\(15\) 4.95606 1.27965
\(16\) −3.72936 −0.932340
\(17\) −1.08709 −0.263659 −0.131829 0.991272i \(-0.542085\pi\)
−0.131829 + 0.991272i \(0.542085\pi\)
\(18\) −15.4033 −3.63058
\(19\) 2.45317 0.562795 0.281398 0.959591i \(-0.409202\pi\)
0.281398 + 0.959591i \(0.409202\pi\)
\(20\) 3.24091 0.724689
\(21\) −13.8590 −3.02428
\(22\) 1.10933 0.236510
\(23\) −8.77079 −1.82884 −0.914418 0.404771i \(-0.867351\pi\)
−0.914418 + 0.404771i \(0.867351\pi\)
\(24\) −0.840796 −0.171627
\(25\) −2.67884 −0.535767
\(26\) −1.15991 −0.227477
\(27\) 14.9052 2.86851
\(28\) −9.06277 −1.71270
\(29\) 4.87255 0.904811 0.452405 0.891812i \(-0.350566\pi\)
0.452405 + 0.891812i \(0.350566\pi\)
\(30\) −10.0685 −1.83825
\(31\) 4.77597 0.857789 0.428895 0.903355i \(-0.358903\pi\)
0.428895 + 0.903355i \(0.358903\pi\)
\(32\) 8.09335 1.43072
\(33\) −1.77630 −0.309214
\(34\) 2.20849 0.378753
\(35\) −6.49083 −1.09715
\(36\) 16.1286 2.68810
\(37\) 1.00000 0.164399
\(38\) −4.98375 −0.808471
\(39\) 1.85728 0.297403
\(40\) −0.393786 −0.0622630
\(41\) −4.73451 −0.739407 −0.369703 0.929150i \(-0.620541\pi\)
−0.369703 + 0.929150i \(0.620541\pi\)
\(42\) 28.1553 4.34446
\(43\) 5.48913 0.837084 0.418542 0.908197i \(-0.362541\pi\)
0.418542 + 0.908197i \(0.362541\pi\)
\(44\) −1.16157 −0.175114
\(45\) 11.5514 1.72199
\(46\) 17.8184 2.62717
\(47\) 8.15516 1.18955 0.594776 0.803891i \(-0.297241\pi\)
0.594776 + 0.803891i \(0.297241\pi\)
\(48\) −12.1316 −1.75105
\(49\) 11.1507 1.59296
\(50\) 5.44221 0.769645
\(51\) −3.53631 −0.495183
\(52\) 1.21453 0.168425
\(53\) 13.8731 1.90561 0.952806 0.303581i \(-0.0981824\pi\)
0.952806 + 0.303581i \(0.0981824\pi\)
\(54\) −30.2808 −4.12070
\(55\) −0.831927 −0.112177
\(56\) 1.10117 0.147150
\(57\) 7.98015 1.05700
\(58\) −9.89887 −1.29979
\(59\) 14.4576 1.88222 0.941111 0.338097i \(-0.109783\pi\)
0.941111 + 0.338097i \(0.109783\pi\)
\(60\) 10.5427 1.36105
\(61\) −1.32357 −0.169466 −0.0847328 0.996404i \(-0.527004\pi\)
−0.0847328 + 0.996404i \(0.527004\pi\)
\(62\) −9.70265 −1.23224
\(63\) −32.3021 −4.06968
\(64\) −8.98338 −1.12292
\(65\) 0.869855 0.107892
\(66\) 3.60865 0.444195
\(67\) 2.92586 0.357451 0.178725 0.983899i \(-0.442803\pi\)
0.178725 + 0.983899i \(0.442803\pi\)
\(68\) −2.31249 −0.280431
\(69\) −28.5314 −3.43477
\(70\) 13.1865 1.57609
\(71\) 8.48759 1.00729 0.503646 0.863910i \(-0.331992\pi\)
0.503646 + 0.863910i \(0.331992\pi\)
\(72\) −1.95970 −0.230953
\(73\) 7.16098 0.838129 0.419065 0.907956i \(-0.362358\pi\)
0.419065 + 0.907956i \(0.362358\pi\)
\(74\) −2.03156 −0.236164
\(75\) −8.71425 −1.00623
\(76\) 5.21844 0.598597
\(77\) 2.32637 0.265115
\(78\) −3.77318 −0.427228
\(79\) 17.5571 1.97533 0.987664 0.156590i \(-0.0500500\pi\)
0.987664 + 0.156590i \(0.0500500\pi\)
\(80\) −5.68182 −0.635246
\(81\) 25.7407 2.86007
\(82\) 9.61844 1.06218
\(83\) −15.5410 −1.70585 −0.852926 0.522032i \(-0.825174\pi\)
−0.852926 + 0.522032i \(0.825174\pi\)
\(84\) −29.4812 −3.21666
\(85\) −1.65623 −0.179643
\(86\) −11.1515 −1.20249
\(87\) 15.8504 1.69934
\(88\) 0.141136 0.0150452
\(89\) −15.4639 −1.63917 −0.819587 0.572954i \(-0.805797\pi\)
−0.819587 + 0.572954i \(0.805797\pi\)
\(90\) −23.4674 −2.47368
\(91\) −2.43244 −0.254989
\(92\) −18.6575 −1.94517
\(93\) 15.5362 1.61103
\(94\) −16.5677 −1.70883
\(95\) 3.73749 0.383459
\(96\) 26.3276 2.68705
\(97\) 4.97454 0.505088 0.252544 0.967585i \(-0.418733\pi\)
0.252544 + 0.967585i \(0.418733\pi\)
\(98\) −22.6534 −2.28834
\(99\) −4.14015 −0.416100
\(100\) −5.69849 −0.569849
\(101\) −9.88072 −0.983169 −0.491584 0.870830i \(-0.663582\pi\)
−0.491584 + 0.870830i \(0.663582\pi\)
\(102\) 7.18422 0.711344
\(103\) 12.1767 1.19981 0.599905 0.800071i \(-0.295205\pi\)
0.599905 + 0.800071i \(0.295205\pi\)
\(104\) −0.147571 −0.0144705
\(105\) −21.1146 −2.06058
\(106\) −28.1839 −2.73746
\(107\) −2.08068 −0.201147 −0.100573 0.994930i \(-0.532068\pi\)
−0.100573 + 0.994930i \(0.532068\pi\)
\(108\) 31.7068 3.05099
\(109\) −1.00000 −0.0957826
\(110\) 1.69011 0.161145
\(111\) 3.25300 0.308761
\(112\) 15.8884 1.50132
\(113\) 15.7320 1.47994 0.739971 0.672639i \(-0.234839\pi\)
0.739971 + 0.672639i \(0.234839\pi\)
\(114\) −16.2121 −1.51841
\(115\) −13.3626 −1.24607
\(116\) 10.3650 0.962369
\(117\) 4.32890 0.400207
\(118\) −29.3715 −2.70387
\(119\) 4.63142 0.424561
\(120\) −1.28098 −0.116937
\(121\) −10.7018 −0.972894
\(122\) 2.68891 0.243442
\(123\) −15.4014 −1.38869
\(124\) 10.1596 0.912356
\(125\) −11.6990 −1.04639
\(126\) 65.6236 5.84621
\(127\) 19.0714 1.69232 0.846158 0.532932i \(-0.178910\pi\)
0.846158 + 0.532932i \(0.178910\pi\)
\(128\) 2.06356 0.182395
\(129\) 17.8561 1.57214
\(130\) −1.76716 −0.154990
\(131\) −9.11248 −0.796161 −0.398081 0.917350i \(-0.630324\pi\)
−0.398081 + 0.917350i \(0.630324\pi\)
\(132\) −3.77859 −0.328884
\(133\) −10.4514 −0.906251
\(134\) −5.94406 −0.513488
\(135\) 22.7087 1.95445
\(136\) 0.280979 0.0240937
\(137\) 19.2948 1.64846 0.824232 0.566252i \(-0.191607\pi\)
0.824232 + 0.566252i \(0.191607\pi\)
\(138\) 57.9631 4.93415
\(139\) −2.46802 −0.209335 −0.104667 0.994507i \(-0.533378\pi\)
−0.104667 + 0.994507i \(0.533378\pi\)
\(140\) −13.8075 −1.16694
\(141\) 26.5287 2.23412
\(142\) −17.2430 −1.44700
\(143\) −0.311764 −0.0260710
\(144\) −28.2760 −2.35633
\(145\) 7.42352 0.616489
\(146\) −14.5479 −1.20400
\(147\) 36.2733 2.99177
\(148\) 2.12723 0.174857
\(149\) 12.6094 1.03300 0.516502 0.856286i \(-0.327234\pi\)
0.516502 + 0.856286i \(0.327234\pi\)
\(150\) 17.7035 1.44548
\(151\) 6.76150 0.550243 0.275121 0.961410i \(-0.411282\pi\)
0.275121 + 0.961410i \(0.411282\pi\)
\(152\) −0.634066 −0.0514295
\(153\) −8.24234 −0.666353
\(154\) −4.72616 −0.380845
\(155\) 7.27636 0.584451
\(156\) 3.95086 0.316322
\(157\) 14.6673 1.17058 0.585289 0.810825i \(-0.300981\pi\)
0.585289 + 0.810825i \(0.300981\pi\)
\(158\) −35.6683 −2.83761
\(159\) 45.1290 3.57896
\(160\) 12.3305 0.974812
\(161\) 37.3668 2.94492
\(162\) −52.2937 −4.10858
\(163\) −19.6288 −1.53744 −0.768722 0.639583i \(-0.779107\pi\)
−0.768722 + 0.639583i \(0.779107\pi\)
\(164\) −10.0714 −0.786443
\(165\) −2.70626 −0.210682
\(166\) 31.5725 2.45050
\(167\) 8.94289 0.692021 0.346011 0.938231i \(-0.387536\pi\)
0.346011 + 0.938231i \(0.387536\pi\)
\(168\) 3.58210 0.276365
\(169\) −12.6740 −0.974925
\(170\) 3.36472 0.258062
\(171\) 18.5999 1.42237
\(172\) 11.6766 0.890334
\(173\) 18.6601 1.41870 0.709350 0.704856i \(-0.248988\pi\)
0.709350 + 0.704856i \(0.248988\pi\)
\(174\) −32.2010 −2.44115
\(175\) 11.4128 0.862729
\(176\) 2.03642 0.153501
\(177\) 47.0306 3.53504
\(178\) 31.4159 2.35472
\(179\) −8.37869 −0.626252 −0.313126 0.949712i \(-0.601376\pi\)
−0.313126 + 0.949712i \(0.601376\pi\)
\(180\) 24.5725 1.83153
\(181\) 10.2413 0.761229 0.380615 0.924734i \(-0.375712\pi\)
0.380615 + 0.924734i \(0.375712\pi\)
\(182\) 4.94163 0.366298
\(183\) −4.30557 −0.318277
\(184\) 2.26697 0.167123
\(185\) 1.52354 0.112013
\(186\) −31.5627 −2.31429
\(187\) 0.593607 0.0434088
\(188\) 17.3479 1.26522
\(189\) −63.5017 −4.61907
\(190\) −7.59293 −0.550849
\(191\) −5.97566 −0.432384 −0.216192 0.976351i \(-0.569364\pi\)
−0.216192 + 0.976351i \(0.569364\pi\)
\(192\) −29.2229 −2.10898
\(193\) −3.50362 −0.252196 −0.126098 0.992018i \(-0.540245\pi\)
−0.126098 + 0.992018i \(0.540245\pi\)
\(194\) −10.1061 −0.725572
\(195\) 2.82964 0.202635
\(196\) 23.7201 1.69430
\(197\) −21.2101 −1.51116 −0.755578 0.655059i \(-0.772644\pi\)
−0.755578 + 0.655059i \(0.772644\pi\)
\(198\) 8.41095 0.597740
\(199\) −11.4000 −0.808126 −0.404063 0.914731i \(-0.632402\pi\)
−0.404063 + 0.914731i \(0.632402\pi\)
\(200\) 0.692394 0.0489596
\(201\) 9.51782 0.671336
\(202\) 20.0733 1.41235
\(203\) −20.7589 −1.45699
\(204\) −7.52254 −0.526683
\(205\) −7.21320 −0.503792
\(206\) −24.7378 −1.72356
\(207\) −66.5001 −4.62208
\(208\) −2.12926 −0.147638
\(209\) −1.33955 −0.0926587
\(210\) 42.8956 2.96008
\(211\) −19.7674 −1.36085 −0.680423 0.732819i \(-0.738204\pi\)
−0.680423 + 0.732819i \(0.738204\pi\)
\(212\) 29.5111 2.02683
\(213\) 27.6101 1.89181
\(214\) 4.22702 0.288953
\(215\) 8.36289 0.570344
\(216\) −3.85252 −0.262131
\(217\) −20.3474 −1.38127
\(218\) 2.03156 0.137594
\(219\) 23.2947 1.57411
\(220\) −1.76970 −0.119313
\(221\) −0.620670 −0.0417508
\(222\) −6.60865 −0.443544
\(223\) −0.578478 −0.0387378 −0.0193689 0.999812i \(-0.506166\pi\)
−0.0193689 + 0.999812i \(0.506166\pi\)
\(224\) −34.4806 −2.30383
\(225\) −20.3109 −1.35406
\(226\) −31.9605 −2.12598
\(227\) −15.2214 −1.01028 −0.505140 0.863037i \(-0.668559\pi\)
−0.505140 + 0.863037i \(0.668559\pi\)
\(228\) 16.9756 1.12424
\(229\) −21.4627 −1.41830 −0.709149 0.705059i \(-0.750921\pi\)
−0.709149 + 0.705059i \(0.750921\pi\)
\(230\) 27.1469 1.79002
\(231\) 7.56769 0.497917
\(232\) −1.25940 −0.0826837
\(233\) 3.46749 0.227163 0.113581 0.993529i \(-0.463768\pi\)
0.113581 + 0.993529i \(0.463768\pi\)
\(234\) −8.79441 −0.574909
\(235\) 12.4247 0.810497
\(236\) 30.7546 2.00196
\(237\) 57.1132 3.70990
\(238\) −9.40899 −0.609894
\(239\) 12.3627 0.799674 0.399837 0.916586i \(-0.369067\pi\)
0.399837 + 0.916586i \(0.369067\pi\)
\(240\) −18.4829 −1.19307
\(241\) −29.1046 −1.87479 −0.937395 0.348269i \(-0.886770\pi\)
−0.937395 + 0.348269i \(0.886770\pi\)
\(242\) 21.7414 1.39759
\(243\) 39.0187 2.50305
\(244\) −2.81553 −0.180246
\(245\) 16.9886 1.08536
\(246\) 31.2888 1.99490
\(247\) 1.40062 0.0891196
\(248\) −1.23444 −0.0783867
\(249\) −50.5550 −3.20379
\(250\) 23.7672 1.50317
\(251\) 5.58811 0.352718 0.176359 0.984326i \(-0.443568\pi\)
0.176359 + 0.984326i \(0.443568\pi\)
\(252\) −68.7139 −4.32857
\(253\) 4.78929 0.301100
\(254\) −38.7447 −2.43106
\(255\) −5.38770 −0.337391
\(256\) 13.7745 0.860907
\(257\) −0.999058 −0.0623195 −0.0311598 0.999514i \(-0.509920\pi\)
−0.0311598 + 0.999514i \(0.509920\pi\)
\(258\) −36.2757 −2.25843
\(259\) −4.26037 −0.264726
\(260\) 1.85038 0.114756
\(261\) 36.9437 2.28676
\(262\) 18.5125 1.14371
\(263\) −0.159863 −0.00985760 −0.00492880 0.999988i \(-0.501569\pi\)
−0.00492880 + 0.999988i \(0.501569\pi\)
\(264\) 0.459117 0.0282567
\(265\) 21.1361 1.29838
\(266\) 21.2326 1.30186
\(267\) −50.3042 −3.07857
\(268\) 6.22397 0.380190
\(269\) 3.46219 0.211093 0.105547 0.994414i \(-0.466341\pi\)
0.105547 + 0.994414i \(0.466341\pi\)
\(270\) −46.1339 −2.80762
\(271\) 1.09887 0.0667517 0.0333758 0.999443i \(-0.489374\pi\)
0.0333758 + 0.999443i \(0.489374\pi\)
\(272\) 4.05416 0.245820
\(273\) −7.91271 −0.478899
\(274\) −39.1985 −2.36807
\(275\) 1.46278 0.0882088
\(276\) −60.6927 −3.65327
\(277\) −14.8721 −0.893580 −0.446790 0.894639i \(-0.647433\pi\)
−0.446790 + 0.894639i \(0.647433\pi\)
\(278\) 5.01392 0.300715
\(279\) 36.2114 2.16792
\(280\) 1.67767 0.100260
\(281\) −22.5014 −1.34232 −0.671160 0.741313i \(-0.734204\pi\)
−0.671160 + 0.741313i \(0.734204\pi\)
\(282\) −53.8946 −3.20938
\(283\) 1.75989 0.104615 0.0523073 0.998631i \(-0.483342\pi\)
0.0523073 + 0.998631i \(0.483342\pi\)
\(284\) 18.0550 1.07137
\(285\) 12.1581 0.720181
\(286\) 0.633367 0.0374518
\(287\) 20.1708 1.19064
\(288\) 61.3637 3.61589
\(289\) −15.8182 −0.930484
\(290\) −15.0813 −0.885604
\(291\) 16.1822 0.948615
\(292\) 15.2330 0.891446
\(293\) 16.4577 0.961472 0.480736 0.876866i \(-0.340370\pi\)
0.480736 + 0.876866i \(0.340370\pi\)
\(294\) −73.6914 −4.29777
\(295\) 22.0267 1.28245
\(296\) −0.258468 −0.0150232
\(297\) −8.13899 −0.472272
\(298\) −25.6168 −1.48394
\(299\) −5.00764 −0.289599
\(300\) −18.5372 −1.07024
\(301\) −23.3857 −1.34793
\(302\) −13.7364 −0.790439
\(303\) −32.1420 −1.84651
\(304\) −9.14875 −0.524717
\(305\) −2.01651 −0.115465
\(306\) 16.7448 0.957235
\(307\) −17.5076 −0.999211 −0.499605 0.866253i \(-0.666522\pi\)
−0.499605 + 0.866253i \(0.666522\pi\)
\(308\) 4.94872 0.281980
\(309\) 39.6109 2.25339
\(310\) −14.7823 −0.839581
\(311\) 11.8326 0.670966 0.335483 0.942046i \(-0.391101\pi\)
0.335483 + 0.942046i \(0.391101\pi\)
\(312\) −0.480048 −0.0271774
\(313\) 24.9255 1.40887 0.704437 0.709766i \(-0.251199\pi\)
0.704437 + 0.709766i \(0.251199\pi\)
\(314\) −29.7974 −1.68157
\(315\) −49.2134 −2.77286
\(316\) 37.3479 2.10098
\(317\) 12.4199 0.697568 0.348784 0.937203i \(-0.386595\pi\)
0.348784 + 0.937203i \(0.386595\pi\)
\(318\) −91.6822 −5.14128
\(319\) −2.66066 −0.148968
\(320\) −13.6865 −0.765099
\(321\) −6.76844 −0.377778
\(322\) −75.9128 −4.23045
\(323\) −2.66682 −0.148386
\(324\) 54.7562 3.04201
\(325\) −1.52947 −0.0848396
\(326\) 39.8770 2.20858
\(327\) −3.25300 −0.179891
\(328\) 1.22372 0.0675687
\(329\) −34.7440 −1.91550
\(330\) 5.49792 0.302650
\(331\) −4.59258 −0.252431 −0.126215 0.992003i \(-0.540283\pi\)
−0.126215 + 0.992003i \(0.540283\pi\)
\(332\) −33.0593 −1.81437
\(333\) 7.58200 0.415491
\(334\) −18.1680 −0.994108
\(335\) 4.45766 0.243548
\(336\) 51.6851 2.81965
\(337\) −5.21831 −0.284259 −0.142130 0.989848i \(-0.545395\pi\)
−0.142130 + 0.989848i \(0.545395\pi\)
\(338\) 25.7480 1.40051
\(339\) 51.1762 2.77951
\(340\) −3.52317 −0.191071
\(341\) −2.60792 −0.141227
\(342\) −37.7868 −2.04328
\(343\) −17.6837 −0.954829
\(344\) −1.41876 −0.0764946
\(345\) −43.4686 −2.34027
\(346\) −37.9091 −2.03800
\(347\) 23.1616 1.24338 0.621690 0.783264i \(-0.286446\pi\)
0.621690 + 0.783264i \(0.286446\pi\)
\(348\) 33.7174 1.80744
\(349\) −13.4990 −0.722587 −0.361294 0.932452i \(-0.617665\pi\)
−0.361294 + 0.932452i \(0.617665\pi\)
\(350\) −23.1858 −1.23933
\(351\) 8.51006 0.454233
\(352\) −4.41937 −0.235553
\(353\) 4.26309 0.226902 0.113451 0.993544i \(-0.463810\pi\)
0.113451 + 0.993544i \(0.463810\pi\)
\(354\) −95.5454 −5.07818
\(355\) 12.9312 0.686314
\(356\) −32.8953 −1.74345
\(357\) 15.0660 0.797377
\(358\) 17.0218 0.899629
\(359\) −5.33744 −0.281699 −0.140850 0.990031i \(-0.544983\pi\)
−0.140850 + 0.990031i \(0.544983\pi\)
\(360\) −2.98568 −0.157359
\(361\) −12.9820 −0.683261
\(362\) −20.8058 −1.09353
\(363\) −34.8130 −1.82721
\(364\) −5.17434 −0.271209
\(365\) 10.9100 0.571056
\(366\) 8.74701 0.457214
\(367\) 17.0429 0.889631 0.444816 0.895622i \(-0.353269\pi\)
0.444816 + 0.895622i \(0.353269\pi\)
\(368\) 32.7094 1.70510
\(369\) −35.8971 −1.86873
\(370\) −3.09515 −0.160909
\(371\) −59.1043 −3.06854
\(372\) 33.0490 1.71351
\(373\) −30.5449 −1.58156 −0.790778 0.612102i \(-0.790324\pi\)
−0.790778 + 0.612102i \(0.790324\pi\)
\(374\) −1.20595 −0.0623580
\(375\) −38.0568 −1.96524
\(376\) −2.10785 −0.108704
\(377\) 2.78196 0.143278
\(378\) 129.007 6.63543
\(379\) 17.2349 0.885299 0.442650 0.896695i \(-0.354039\pi\)
0.442650 + 0.896695i \(0.354039\pi\)
\(380\) 7.95049 0.407852
\(381\) 62.0393 3.17837
\(382\) 12.1399 0.621132
\(383\) −20.2777 −1.03614 −0.518072 0.855337i \(-0.673350\pi\)
−0.518072 + 0.855337i \(0.673350\pi\)
\(384\) 6.71276 0.342559
\(385\) 3.54431 0.180635
\(386\) 7.11780 0.362286
\(387\) 41.6185 2.11559
\(388\) 10.5820 0.537218
\(389\) −14.5265 −0.736522 −0.368261 0.929722i \(-0.620047\pi\)
−0.368261 + 0.929722i \(0.620047\pi\)
\(390\) −5.74857 −0.291090
\(391\) 9.53467 0.482189
\(392\) −2.88211 −0.145569
\(393\) −29.6429 −1.49529
\(394\) 43.0895 2.17082
\(395\) 26.7489 1.34588
\(396\) −8.80703 −0.442570
\(397\) 7.68874 0.385887 0.192943 0.981210i \(-0.438197\pi\)
0.192943 + 0.981210i \(0.438197\pi\)
\(398\) 23.1598 1.16090
\(399\) −33.9984 −1.70205
\(400\) 9.99034 0.499517
\(401\) 28.1492 1.40571 0.702853 0.711336i \(-0.251909\pi\)
0.702853 + 0.711336i \(0.251909\pi\)
\(402\) −19.3360 −0.964392
\(403\) 2.72681 0.135832
\(404\) −21.0185 −1.04571
\(405\) 39.2169 1.94870
\(406\) 42.1729 2.09300
\(407\) −0.546050 −0.0270667
\(408\) 0.914024 0.0452509
\(409\) −30.3569 −1.50105 −0.750527 0.660840i \(-0.770200\pi\)
−0.750527 + 0.660840i \(0.770200\pi\)
\(410\) 14.6540 0.723711
\(411\) 62.7659 3.09601
\(412\) 25.9027 1.27613
\(413\) −61.5948 −3.03088
\(414\) 135.099 6.63974
\(415\) −23.6774 −1.16228
\(416\) 4.62085 0.226556
\(417\) −8.02846 −0.393155
\(418\) 2.72138 0.133107
\(419\) 24.4611 1.19500 0.597501 0.801868i \(-0.296160\pi\)
0.597501 + 0.801868i \(0.296160\pi\)
\(420\) −44.9156 −2.19166
\(421\) 4.33624 0.211335 0.105668 0.994401i \(-0.466302\pi\)
0.105668 + 0.994401i \(0.466302\pi\)
\(422\) 40.1587 1.95489
\(423\) 61.8324 3.00639
\(424\) −3.58574 −0.174139
\(425\) 2.91214 0.141260
\(426\) −56.0915 −2.71764
\(427\) 5.63889 0.272885
\(428\) −4.42607 −0.213942
\(429\) −1.01417 −0.0489645
\(430\) −16.9897 −0.819315
\(431\) −16.8228 −0.810328 −0.405164 0.914244i \(-0.632786\pi\)
−0.405164 + 0.914244i \(0.632786\pi\)
\(432\) −55.5869 −2.67443
\(433\) 37.5028 1.80227 0.901136 0.433537i \(-0.142735\pi\)
0.901136 + 0.433537i \(0.142735\pi\)
\(434\) 41.3369 1.98423
\(435\) 24.1487 1.15784
\(436\) −2.12723 −0.101876
\(437\) −21.5162 −1.02926
\(438\) −47.3244 −2.26125
\(439\) −32.3433 −1.54366 −0.771830 0.635829i \(-0.780658\pi\)
−0.771830 + 0.635829i \(0.780658\pi\)
\(440\) 0.215027 0.0102510
\(441\) 84.5449 4.02595
\(442\) 1.26093 0.0599762
\(443\) 6.14982 0.292187 0.146093 0.989271i \(-0.453330\pi\)
0.146093 + 0.989271i \(0.453330\pi\)
\(444\) 6.91986 0.328402
\(445\) −23.5599 −1.11685
\(446\) 1.17521 0.0556479
\(447\) 41.0184 1.94011
\(448\) 38.2725 1.80821
\(449\) −37.5136 −1.77038 −0.885189 0.465231i \(-0.845971\pi\)
−0.885189 + 0.465231i \(0.845971\pi\)
\(450\) 41.2628 1.94515
\(451\) 2.58528 0.121736
\(452\) 33.4655 1.57409
\(453\) 21.9951 1.03342
\(454\) 30.9232 1.45130
\(455\) −3.70590 −0.173735
\(456\) −2.06261 −0.0965908
\(457\) −22.8020 −1.06663 −0.533315 0.845917i \(-0.679054\pi\)
−0.533315 + 0.845917i \(0.679054\pi\)
\(458\) 43.6028 2.03742
\(459\) −16.2034 −0.756308
\(460\) −28.4253 −1.32534
\(461\) −13.6269 −0.634669 −0.317335 0.948314i \(-0.602788\pi\)
−0.317335 + 0.948314i \(0.602788\pi\)
\(462\) −15.3742 −0.715272
\(463\) 13.1806 0.612556 0.306278 0.951942i \(-0.400916\pi\)
0.306278 + 0.951942i \(0.400916\pi\)
\(464\) −18.1715 −0.843591
\(465\) 23.6700 1.09767
\(466\) −7.04440 −0.326326
\(467\) −16.2683 −0.752806 −0.376403 0.926456i \(-0.622839\pi\)
−0.376403 + 0.926456i \(0.622839\pi\)
\(468\) 9.20855 0.425666
\(469\) −12.4653 −0.575592
\(470\) −25.2415 −1.16430
\(471\) 47.7127 2.19848
\(472\) −3.73684 −0.172002
\(473\) −2.99734 −0.137818
\(474\) −116.029 −5.32938
\(475\) −6.57163 −0.301527
\(476\) 9.85208 0.451569
\(477\) 105.185 4.81611
\(478\) −25.1155 −1.14875
\(479\) 25.5435 1.16711 0.583557 0.812072i \(-0.301661\pi\)
0.583557 + 0.812072i \(0.301661\pi\)
\(480\) 40.1111 1.83081
\(481\) 0.570945 0.0260328
\(482\) 59.1276 2.69319
\(483\) 121.554 5.53090
\(484\) −22.7652 −1.03478
\(485\) 7.57889 0.344140
\(486\) −79.2687 −3.59570
\(487\) 17.2990 0.783891 0.391945 0.919988i \(-0.371802\pi\)
0.391945 + 0.919988i \(0.371802\pi\)
\(488\) 0.342100 0.0154862
\(489\) −63.8523 −2.88750
\(490\) −34.5132 −1.55915
\(491\) 11.9903 0.541113 0.270557 0.962704i \(-0.412792\pi\)
0.270557 + 0.962704i \(0.412792\pi\)
\(492\) −32.7622 −1.47703
\(493\) −5.29692 −0.238561
\(494\) −2.84545 −0.128023
\(495\) −6.30767 −0.283508
\(496\) −17.8113 −0.799751
\(497\) −36.1603 −1.62201
\(498\) 102.705 4.60234
\(499\) −30.7510 −1.37660 −0.688302 0.725424i \(-0.741644\pi\)
−0.688302 + 0.725424i \(0.741644\pi\)
\(500\) −24.8864 −1.11295
\(501\) 29.0912 1.29970
\(502\) −11.3526 −0.506690
\(503\) 44.2161 1.97150 0.985750 0.168219i \(-0.0538015\pi\)
0.985750 + 0.168219i \(0.0538015\pi\)
\(504\) 8.34906 0.371897
\(505\) −15.0536 −0.669878
\(506\) −9.72971 −0.432539
\(507\) −41.2286 −1.83102
\(508\) 40.5693 1.79997
\(509\) 14.1213 0.625917 0.312958 0.949767i \(-0.398680\pi\)
0.312958 + 0.949767i \(0.398680\pi\)
\(510\) 10.9454 0.484672
\(511\) −30.5084 −1.34961
\(512\) −32.1108 −1.41911
\(513\) 36.5650 1.61438
\(514\) 2.02964 0.0895237
\(515\) 18.5517 0.817486
\(516\) 37.9840 1.67215
\(517\) −4.45312 −0.195848
\(518\) 8.65518 0.380287
\(519\) 60.7012 2.66449
\(520\) −0.224830 −0.00985944
\(521\) 17.8809 0.783376 0.391688 0.920098i \(-0.371891\pi\)
0.391688 + 0.920098i \(0.371891\pi\)
\(522\) −75.0532 −3.28499
\(523\) 7.52606 0.329092 0.164546 0.986369i \(-0.447384\pi\)
0.164546 + 0.986369i \(0.447384\pi\)
\(524\) −19.3843 −0.846808
\(525\) 37.1259 1.62031
\(526\) 0.324772 0.0141607
\(527\) −5.19192 −0.226164
\(528\) 6.62446 0.288293
\(529\) 53.9267 2.34464
\(530\) −42.9392 −1.86516
\(531\) 109.618 4.75700
\(532\) −22.2325 −0.963901
\(533\) −2.70315 −0.117086
\(534\) 102.196 4.42245
\(535\) −3.16999 −0.137051
\(536\) −0.756242 −0.0326647
\(537\) −27.2558 −1.17618
\(538\) −7.03364 −0.303242
\(539\) −6.08886 −0.262266
\(540\) 48.3064 2.07878
\(541\) −12.2104 −0.524968 −0.262484 0.964936i \(-0.584542\pi\)
−0.262484 + 0.964936i \(0.584542\pi\)
\(542\) −2.23242 −0.0958907
\(543\) 33.3149 1.42968
\(544\) −8.79822 −0.377221
\(545\) −1.52354 −0.0652611
\(546\) 16.0751 0.687952
\(547\) 7.19022 0.307432 0.153716 0.988115i \(-0.450876\pi\)
0.153716 + 0.988115i \(0.450876\pi\)
\(548\) 41.0444 1.75333
\(549\) −10.0353 −0.428296
\(550\) −2.97172 −0.126714
\(551\) 11.9532 0.509223
\(552\) 7.37445 0.313877
\(553\) −74.7997 −3.18081
\(554\) 30.2136 1.28365
\(555\) 4.95606 0.210373
\(556\) −5.25004 −0.222651
\(557\) −7.47673 −0.316799 −0.158400 0.987375i \(-0.550633\pi\)
−0.158400 + 0.987375i \(0.550633\pi\)
\(558\) −73.5655 −3.11427
\(559\) 3.13399 0.132554
\(560\) 24.2066 1.02292
\(561\) 1.93100 0.0815270
\(562\) 45.7128 1.92828
\(563\) 12.7736 0.538343 0.269171 0.963092i \(-0.413250\pi\)
0.269171 + 0.963092i \(0.413250\pi\)
\(564\) 56.4326 2.37624
\(565\) 23.9683 1.00835
\(566\) −3.57532 −0.150282
\(567\) −109.665 −4.60549
\(568\) −2.19377 −0.0920486
\(569\) −12.6510 −0.530359 −0.265180 0.964199i \(-0.585431\pi\)
−0.265180 + 0.964199i \(0.585431\pi\)
\(570\) −24.6998 −1.03456
\(571\) −7.32976 −0.306741 −0.153371 0.988169i \(-0.549013\pi\)
−0.153371 + 0.988169i \(0.549013\pi\)
\(572\) −0.663193 −0.0277295
\(573\) −19.4388 −0.812068
\(574\) −40.9781 −1.71039
\(575\) 23.4955 0.979830
\(576\) −68.1119 −2.83800
\(577\) −24.1092 −1.00368 −0.501839 0.864961i \(-0.667343\pi\)
−0.501839 + 0.864961i \(0.667343\pi\)
\(578\) 32.1356 1.33667
\(579\) −11.3973 −0.473654
\(580\) 15.7915 0.655706
\(581\) 66.2106 2.74688
\(582\) −32.8750 −1.36271
\(583\) −7.57538 −0.313740
\(584\) −1.85089 −0.0765902
\(585\) 6.59524 0.272680
\(586\) −33.4349 −1.38118
\(587\) −9.43115 −0.389265 −0.194633 0.980876i \(-0.562351\pi\)
−0.194633 + 0.980876i \(0.562351\pi\)
\(588\) 77.1616 3.18209
\(589\) 11.7163 0.482760
\(590\) −44.7486 −1.84227
\(591\) −68.9963 −2.83813
\(592\) −3.72936 −0.153276
\(593\) 8.68112 0.356491 0.178245 0.983986i \(-0.442958\pi\)
0.178245 + 0.983986i \(0.442958\pi\)
\(594\) 16.5348 0.678432
\(595\) 7.05614 0.289273
\(596\) 26.8231 1.09872
\(597\) −37.0843 −1.51776
\(598\) 10.1733 0.416017
\(599\) 33.4414 1.36638 0.683189 0.730242i \(-0.260592\pi\)
0.683189 + 0.730242i \(0.260592\pi\)
\(600\) 2.25236 0.0919520
\(601\) −47.5882 −1.94116 −0.970581 0.240774i \(-0.922599\pi\)
−0.970581 + 0.240774i \(0.922599\pi\)
\(602\) 47.5094 1.93634
\(603\) 22.1839 0.903397
\(604\) 14.3832 0.585245
\(605\) −16.3046 −0.662877
\(606\) 65.2983 2.65256
\(607\) 2.42123 0.0982746 0.0491373 0.998792i \(-0.484353\pi\)
0.0491373 + 0.998792i \(0.484353\pi\)
\(608\) 19.8543 0.805200
\(609\) −67.5286 −2.73640
\(610\) 4.09665 0.165868
\(611\) 4.65615 0.188368
\(612\) −17.5333 −0.708742
\(613\) −15.6552 −0.632307 −0.316153 0.948708i \(-0.602391\pi\)
−0.316153 + 0.948708i \(0.602391\pi\)
\(614\) 35.5677 1.43539
\(615\) −23.4645 −0.946181
\(616\) −0.601293 −0.0242268
\(617\) 6.59231 0.265397 0.132698 0.991156i \(-0.457636\pi\)
0.132698 + 0.991156i \(0.457636\pi\)
\(618\) −80.4719 −3.23705
\(619\) 2.34081 0.0940852 0.0470426 0.998893i \(-0.485020\pi\)
0.0470426 + 0.998893i \(0.485020\pi\)
\(620\) 15.4785 0.621630
\(621\) −130.731 −5.24604
\(622\) −24.0386 −0.963861
\(623\) 65.8821 2.63951
\(624\) −6.92648 −0.277281
\(625\) −4.42966 −0.177186
\(626\) −50.6377 −2.02389
\(627\) −4.35756 −0.174024
\(628\) 31.2007 1.24504
\(629\) −1.08709 −0.0433452
\(630\) 99.9799 3.98330
\(631\) 1.00802 0.0401286 0.0200643 0.999799i \(-0.493613\pi\)
0.0200643 + 0.999799i \(0.493613\pi\)
\(632\) −4.53795 −0.180510
\(633\) −64.3034 −2.55583
\(634\) −25.2316 −1.00208
\(635\) 29.0560 1.15305
\(636\) 95.9997 3.80663
\(637\) 6.36646 0.252248
\(638\) 5.40528 0.213997
\(639\) 64.3529 2.54576
\(640\) 3.14391 0.124274
\(641\) 3.56920 0.140975 0.0704874 0.997513i \(-0.477545\pi\)
0.0704874 + 0.997513i \(0.477545\pi\)
\(642\) 13.7505 0.542688
\(643\) −7.60317 −0.299840 −0.149920 0.988698i \(-0.547902\pi\)
−0.149920 + 0.988698i \(0.547902\pi\)
\(644\) 79.4876 3.13225
\(645\) 27.2044 1.07117
\(646\) 5.41780 0.213161
\(647\) 5.53566 0.217629 0.108815 0.994062i \(-0.465294\pi\)
0.108815 + 0.994062i \(0.465294\pi\)
\(648\) −6.65314 −0.261360
\(649\) −7.89458 −0.309890
\(650\) 3.10720 0.121874
\(651\) −66.1900 −2.59419
\(652\) −41.7548 −1.63525
\(653\) 39.9341 1.56274 0.781371 0.624067i \(-0.214521\pi\)
0.781371 + 0.624067i \(0.214521\pi\)
\(654\) 6.60865 0.258419
\(655\) −13.8832 −0.542462
\(656\) 17.6567 0.689378
\(657\) 54.2945 2.11823
\(658\) 70.5844 2.75167
\(659\) 22.2365 0.866210 0.433105 0.901343i \(-0.357418\pi\)
0.433105 + 0.901343i \(0.357418\pi\)
\(660\) −5.75682 −0.224084
\(661\) 3.76253 0.146346 0.0731728 0.997319i \(-0.476688\pi\)
0.0731728 + 0.997319i \(0.476688\pi\)
\(662\) 9.33008 0.362624
\(663\) −2.01904 −0.0784130
\(664\) 4.01687 0.155885
\(665\) −15.9231 −0.617471
\(666\) −15.4033 −0.596864
\(667\) −42.7361 −1.65475
\(668\) 19.0235 0.736043
\(669\) −1.88179 −0.0727541
\(670\) −9.05599 −0.349863
\(671\) 0.722735 0.0279009
\(672\) −112.165 −4.32688
\(673\) −17.8885 −0.689551 −0.344776 0.938685i \(-0.612045\pi\)
−0.344776 + 0.938685i \(0.612045\pi\)
\(674\) 10.6013 0.408347
\(675\) −39.9286 −1.53685
\(676\) −26.9605 −1.03694
\(677\) −24.2267 −0.931108 −0.465554 0.885019i \(-0.654145\pi\)
−0.465554 + 0.885019i \(0.654145\pi\)
\(678\) −103.967 −3.99284
\(679\) −21.1934 −0.813326
\(680\) 0.428082 0.0164162
\(681\) −49.5152 −1.89743
\(682\) 5.29813 0.202876
\(683\) −24.8015 −0.949002 −0.474501 0.880255i \(-0.657372\pi\)
−0.474501 + 0.880255i \(0.657372\pi\)
\(684\) 39.5662 1.51285
\(685\) 29.3963 1.12318
\(686\) 35.9254 1.37164
\(687\) −69.8182 −2.66373
\(688\) −20.4709 −0.780447
\(689\) 7.92075 0.301757
\(690\) 88.3089 3.36186
\(691\) 28.4367 1.08178 0.540892 0.841092i \(-0.318087\pi\)
0.540892 + 0.841092i \(0.318087\pi\)
\(692\) 39.6942 1.50895
\(693\) 17.6386 0.670033
\(694\) −47.0541 −1.78615
\(695\) −3.76012 −0.142629
\(696\) −4.09683 −0.155290
\(697\) 5.14686 0.194951
\(698\) 27.4241 1.03802
\(699\) 11.2797 0.426639
\(700\) 24.2777 0.917610
\(701\) 15.4812 0.584717 0.292358 0.956309i \(-0.405560\pi\)
0.292358 + 0.956309i \(0.405560\pi\)
\(702\) −17.2887 −0.652519
\(703\) 2.45317 0.0925230
\(704\) 4.90537 0.184878
\(705\) 40.4175 1.52221
\(706\) −8.66072 −0.325951
\(707\) 42.0955 1.58316
\(708\) 100.045 3.75991
\(709\) −25.5895 −0.961033 −0.480516 0.876986i \(-0.659551\pi\)
−0.480516 + 0.876986i \(0.659551\pi\)
\(710\) −26.2704 −0.985910
\(711\) 133.118 4.99231
\(712\) 3.99694 0.149791
\(713\) −41.8890 −1.56876
\(714\) −30.6074 −1.14545
\(715\) −0.474984 −0.0177634
\(716\) −17.8234 −0.666090
\(717\) 40.2157 1.50188
\(718\) 10.8433 0.404669
\(719\) 19.7569 0.736809 0.368405 0.929666i \(-0.379904\pi\)
0.368405 + 0.929666i \(0.379904\pi\)
\(720\) −43.0795 −1.60548
\(721\) −51.8774 −1.93202
\(722\) 26.3736 0.981524
\(723\) −94.6771 −3.52108
\(724\) 21.7856 0.809654
\(725\) −13.0528 −0.484768
\(726\) 70.7247 2.62484
\(727\) 3.69059 0.136876 0.0684382 0.997655i \(-0.478198\pi\)
0.0684382 + 0.997655i \(0.478198\pi\)
\(728\) 0.628707 0.0233014
\(729\) 49.7057 1.84095
\(730\) −22.1643 −0.820339
\(731\) −5.96719 −0.220705
\(732\) −9.15892 −0.338523
\(733\) −40.1289 −1.48219 −0.741097 0.671398i \(-0.765694\pi\)
−0.741097 + 0.671398i \(0.765694\pi\)
\(734\) −34.6236 −1.27798
\(735\) 55.2637 2.03843
\(736\) −70.9850 −2.61654
\(737\) −1.59767 −0.0588508
\(738\) 72.9269 2.68448
\(739\) 19.4003 0.713650 0.356825 0.934171i \(-0.383859\pi\)
0.356825 + 0.934171i \(0.383859\pi\)
\(740\) 3.24091 0.119138
\(741\) 4.55623 0.167377
\(742\) 120.074 4.40805
\(743\) 46.6873 1.71279 0.856395 0.516321i \(-0.172699\pi\)
0.856395 + 0.516321i \(0.172699\pi\)
\(744\) −4.01562 −0.147220
\(745\) 19.2109 0.703834
\(746\) 62.0538 2.27195
\(747\) −117.832 −4.31125
\(748\) 1.26274 0.0461702
\(749\) 8.86445 0.323900
\(750\) 77.3146 2.82313
\(751\) −36.3853 −1.32772 −0.663859 0.747858i \(-0.731082\pi\)
−0.663859 + 0.747858i \(0.731082\pi\)
\(752\) −30.4135 −1.10907
\(753\) 18.1781 0.662447
\(754\) −5.65171 −0.205823
\(755\) 10.3014 0.374906
\(756\) −135.083 −4.91291
\(757\) −17.9072 −0.650849 −0.325424 0.945568i \(-0.605507\pi\)
−0.325424 + 0.945568i \(0.605507\pi\)
\(758\) −35.0138 −1.27176
\(759\) 15.5795 0.565502
\(760\) −0.966022 −0.0350413
\(761\) 29.3886 1.06534 0.532668 0.846324i \(-0.321189\pi\)
0.532668 + 0.846324i \(0.321189\pi\)
\(762\) −126.036 −4.56582
\(763\) 4.26037 0.154236
\(764\) −12.7116 −0.459889
\(765\) −12.5575 −0.454017
\(766\) 41.1954 1.48845
\(767\) 8.25451 0.298053
\(768\) 44.8085 1.61689
\(769\) 38.7058 1.39577 0.697883 0.716212i \(-0.254125\pi\)
0.697883 + 0.716212i \(0.254125\pi\)
\(770\) −7.20048 −0.259487
\(771\) −3.24993 −0.117043
\(772\) −7.45298 −0.268239
\(773\) −4.78935 −0.172261 −0.0861304 0.996284i \(-0.527450\pi\)
−0.0861304 + 0.996284i \(0.527450\pi\)
\(774\) −84.5504 −3.03910
\(775\) −12.7940 −0.459575
\(776\) −1.28576 −0.0461561
\(777\) −13.8590 −0.497188
\(778\) 29.5114 1.05804
\(779\) −11.6146 −0.416135
\(780\) 6.01928 0.215525
\(781\) −4.63465 −0.165841
\(782\) −19.3702 −0.692678
\(783\) 72.6265 2.59546
\(784\) −41.5851 −1.48518
\(785\) 22.3462 0.797569
\(786\) 60.2212 2.14802
\(787\) 45.8941 1.63595 0.817974 0.575255i \(-0.195097\pi\)
0.817974 + 0.575255i \(0.195097\pi\)
\(788\) −45.1186 −1.60729
\(789\) −0.520036 −0.0185138
\(790\) −54.3419 −1.93340
\(791\) −67.0241 −2.38310
\(792\) 1.07010 0.0380242
\(793\) −0.755685 −0.0268352
\(794\) −15.6201 −0.554337
\(795\) 68.7557 2.43851
\(796\) −24.2504 −0.859534
\(797\) −36.8119 −1.30394 −0.651972 0.758243i \(-0.726058\pi\)
−0.651972 + 0.758243i \(0.726058\pi\)
\(798\) 69.0697 2.44504
\(799\) −8.86542 −0.313636
\(800\) −21.6807 −0.766530
\(801\) −117.248 −4.14274
\(802\) −57.1868 −2.01934
\(803\) −3.91025 −0.137990
\(804\) 20.2466 0.714041
\(805\) 56.9297 2.00651
\(806\) −5.53968 −0.195127
\(807\) 11.2625 0.396459
\(808\) 2.55385 0.0898442
\(809\) −23.1517 −0.813970 −0.406985 0.913435i \(-0.633420\pi\)
−0.406985 + 0.913435i \(0.633420\pi\)
\(810\) −79.6713 −2.79936
\(811\) −15.7483 −0.552999 −0.276500 0.961014i \(-0.589174\pi\)
−0.276500 + 0.961014i \(0.589174\pi\)
\(812\) −44.1588 −1.54967
\(813\) 3.57463 0.125368
\(814\) 1.10933 0.0388821
\(815\) −29.9051 −1.04753
\(816\) 13.1882 0.461679
\(817\) 13.4657 0.471107
\(818\) 61.6718 2.15631
\(819\) −18.4427 −0.644441
\(820\) −15.3441 −0.535840
\(821\) 11.3572 0.396370 0.198185 0.980165i \(-0.436495\pi\)
0.198185 + 0.980165i \(0.436495\pi\)
\(822\) −127.513 −4.44751
\(823\) 3.01683 0.105160 0.0525800 0.998617i \(-0.483256\pi\)
0.0525800 + 0.998617i \(0.483256\pi\)
\(824\) −3.14730 −0.109641
\(825\) 4.75841 0.165667
\(826\) 125.133 4.35395
\(827\) 7.88004 0.274016 0.137008 0.990570i \(-0.456251\pi\)
0.137008 + 0.990570i \(0.456251\pi\)
\(828\) −141.461 −4.91610
\(829\) 1.54781 0.0537575 0.0268788 0.999639i \(-0.491443\pi\)
0.0268788 + 0.999639i \(0.491443\pi\)
\(830\) 48.1019 1.66964
\(831\) −48.3790 −1.67825
\(832\) −5.12901 −0.177817
\(833\) −12.1219 −0.419999
\(834\) 16.3103 0.564779
\(835\) 13.6248 0.471506
\(836\) −2.84953 −0.0985531
\(837\) 71.1869 2.46058
\(838\) −49.6941 −1.71665
\(839\) 19.8629 0.685744 0.342872 0.939382i \(-0.388600\pi\)
0.342872 + 0.939382i \(0.388600\pi\)
\(840\) 5.45746 0.188300
\(841\) −5.25821 −0.181318
\(842\) −8.80932 −0.303589
\(843\) −73.1969 −2.52104
\(844\) −42.0498 −1.44741
\(845\) −19.3093 −0.664261
\(846\) −125.616 −4.31877
\(847\) 45.5937 1.56662
\(848\) −51.7376 −1.77668
\(849\) 5.72492 0.196479
\(850\) −5.91619 −0.202924
\(851\) −8.77079 −0.300659
\(852\) 58.7330 2.01216
\(853\) −24.2198 −0.829271 −0.414636 0.909988i \(-0.636091\pi\)
−0.414636 + 0.909988i \(0.636091\pi\)
\(854\) −11.4557 −0.392007
\(855\) 28.3376 0.969127
\(856\) 0.537789 0.0183812
\(857\) 9.26327 0.316427 0.158214 0.987405i \(-0.449427\pi\)
0.158214 + 0.987405i \(0.449427\pi\)
\(858\) 2.06034 0.0703389
\(859\) 36.8697 1.25798 0.628989 0.777414i \(-0.283469\pi\)
0.628989 + 0.777414i \(0.283469\pi\)
\(860\) 17.7898 0.606626
\(861\) 65.6155 2.23617
\(862\) 34.1766 1.16406
\(863\) −44.8377 −1.52629 −0.763147 0.646225i \(-0.776347\pi\)
−0.763147 + 0.646225i \(0.776347\pi\)
\(864\) 120.633 4.10402
\(865\) 28.4293 0.966626
\(866\) −76.1892 −2.58901
\(867\) −51.4567 −1.74756
\(868\) −43.2835 −1.46914
\(869\) −9.58705 −0.325218
\(870\) −49.0594 −1.66327
\(871\) 1.67051 0.0566029
\(872\) 0.258468 0.00875284
\(873\) 37.7169 1.27652
\(874\) 43.7114 1.47856
\(875\) 49.8420 1.68497
\(876\) 49.5530 1.67424
\(877\) 46.2569 1.56199 0.780993 0.624540i \(-0.214713\pi\)
0.780993 + 0.624540i \(0.214713\pi\)
\(878\) 65.7072 2.21751
\(879\) 53.5370 1.80576
\(880\) 3.10256 0.104587
\(881\) 3.17860 0.107090 0.0535449 0.998565i \(-0.482948\pi\)
0.0535449 + 0.998565i \(0.482948\pi\)
\(882\) −171.758 −5.78338
\(883\) −42.9231 −1.44448 −0.722238 0.691645i \(-0.756886\pi\)
−0.722238 + 0.691645i \(0.756886\pi\)
\(884\) −1.32031 −0.0444067
\(885\) 71.6529 2.40859
\(886\) −12.4937 −0.419734
\(887\) −3.07092 −0.103111 −0.0515556 0.998670i \(-0.516418\pi\)
−0.0515556 + 0.998670i \(0.516418\pi\)
\(888\) −0.840796 −0.0282153
\(889\) −81.2513 −2.72508
\(890\) 47.8633 1.60438
\(891\) −14.0557 −0.470883
\(892\) −1.23055 −0.0412020
\(893\) 20.0060 0.669475
\(894\) −83.3313 −2.78702
\(895\) −12.7652 −0.426695
\(896\) −8.79153 −0.293704
\(897\) −16.2898 −0.543902
\(898\) 76.2111 2.54320
\(899\) 23.2712 0.776137
\(900\) −43.2059 −1.44020
\(901\) −15.0813 −0.502431
\(902\) −5.25214 −0.174877
\(903\) −76.0736 −2.53157
\(904\) −4.06622 −0.135240
\(905\) 15.6030 0.518661
\(906\) −44.6844 −1.48454
\(907\) 34.8612 1.15755 0.578773 0.815489i \(-0.303532\pi\)
0.578773 + 0.815489i \(0.303532\pi\)
\(908\) −32.3794 −1.07455
\(909\) −74.9156 −2.48479
\(910\) 7.52876 0.249576
\(911\) 11.6735 0.386759 0.193379 0.981124i \(-0.438055\pi\)
0.193379 + 0.981124i \(0.438055\pi\)
\(912\) −29.7609 −0.985480
\(913\) 8.48619 0.280852
\(914\) 46.3235 1.53224
\(915\) −6.55969 −0.216857
\(916\) −45.6561 −1.50852
\(917\) 38.8225 1.28203
\(918\) 32.9181 1.08646
\(919\) −21.3173 −0.703193 −0.351596 0.936152i \(-0.614361\pi\)
−0.351596 + 0.936152i \(0.614361\pi\)
\(920\) 3.45381 0.113869
\(921\) −56.9521 −1.87664
\(922\) 27.6839 0.911721
\(923\) 4.84595 0.159506
\(924\) 16.0982 0.529591
\(925\) −2.67884 −0.0880796
\(926\) −26.7772 −0.879954
\(927\) 92.3240 3.03232
\(928\) 39.4353 1.29453
\(929\) 19.1324 0.627715 0.313858 0.949470i \(-0.398379\pi\)
0.313858 + 0.949470i \(0.398379\pi\)
\(930\) −48.0870 −1.57683
\(931\) 27.3546 0.896512
\(932\) 7.37613 0.241613
\(933\) 38.4915 1.26015
\(934\) 33.0499 1.08143
\(935\) 0.904382 0.0295765
\(936\) −1.11888 −0.0365718
\(937\) −2.54020 −0.0829847 −0.0414924 0.999139i \(-0.513211\pi\)
−0.0414924 + 0.999139i \(0.513211\pi\)
\(938\) 25.3239 0.826854
\(939\) 81.0827 2.64603
\(940\) 26.4301 0.862056
\(941\) −32.3291 −1.05390 −0.526950 0.849897i \(-0.676664\pi\)
−0.526950 + 0.849897i \(0.676664\pi\)
\(942\) −96.9310 −3.15818
\(943\) 41.5254 1.35225
\(944\) −53.9177 −1.75487
\(945\) −96.7472 −3.14719
\(946\) 6.08926 0.197979
\(947\) −50.2228 −1.63202 −0.816011 0.578037i \(-0.803819\pi\)
−0.816011 + 0.578037i \(0.803819\pi\)
\(948\) 121.493 3.94590
\(949\) 4.08853 0.132719
\(950\) 13.3507 0.433152
\(951\) 40.4017 1.31012
\(952\) −1.19707 −0.0387974
\(953\) 45.9492 1.48844 0.744221 0.667934i \(-0.232821\pi\)
0.744221 + 0.667934i \(0.232821\pi\)
\(954\) −213.690 −6.91848
\(955\) −9.10414 −0.294603
\(956\) 26.2982 0.850544
\(957\) −8.65511 −0.279780
\(958\) −51.8931 −1.67659
\(959\) −82.2029 −2.65447
\(960\) −44.5222 −1.43695
\(961\) −8.19013 −0.264198
\(962\) −1.15991 −0.0373969
\(963\) −15.7757 −0.508364
\(964\) −61.9120 −1.99405
\(965\) −5.33789 −0.171833
\(966\) −246.944 −7.94530
\(967\) −26.8671 −0.863988 −0.431994 0.901877i \(-0.642190\pi\)
−0.431994 + 0.901877i \(0.642190\pi\)
\(968\) 2.76608 0.0889052
\(969\) −8.67517 −0.278687
\(970\) −15.3969 −0.494366
\(971\) 9.99159 0.320645 0.160323 0.987065i \(-0.448747\pi\)
0.160323 + 0.987065i \(0.448747\pi\)
\(972\) 83.0016 2.66228
\(973\) 10.5147 0.337085
\(974\) −35.1438 −1.12608
\(975\) −4.97536 −0.159339
\(976\) 4.93607 0.158000
\(977\) 17.5745 0.562258 0.281129 0.959670i \(-0.409291\pi\)
0.281129 + 0.959670i \(0.409291\pi\)
\(978\) 129.720 4.14798
\(979\) 8.44408 0.269874
\(980\) 36.1385 1.15440
\(981\) −7.58200 −0.242074
\(982\) −24.3589 −0.777325
\(983\) 35.4648 1.13115 0.565576 0.824696i \(-0.308654\pi\)
0.565576 + 0.824696i \(0.308654\pi\)
\(984\) 3.98076 0.126902
\(985\) −32.3143 −1.02962
\(986\) 10.7610 0.342700
\(987\) −113.022 −3.59753
\(988\) 2.97944 0.0947887
\(989\) −48.1440 −1.53089
\(990\) 12.8144 0.407268
\(991\) 4.33294 0.137640 0.0688202 0.997629i \(-0.478077\pi\)
0.0688202 + 0.997629i \(0.478077\pi\)
\(992\) 38.6536 1.22725
\(993\) −14.9396 −0.474095
\(994\) 73.4617 2.33006
\(995\) −17.3684 −0.550614
\(996\) −107.542 −3.40760
\(997\) 4.82838 0.152916 0.0764581 0.997073i \(-0.475639\pi\)
0.0764581 + 0.997073i \(0.475639\pi\)
\(998\) 62.4725 1.97753
\(999\) 14.9052 0.471580
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.1.13 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.13 85 1.1 even 1 trivial