Properties

Label 4033.2.a.f.1.10
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 1.10
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.26706 q^{2} -2.69699 q^{3} +3.13957 q^{4} -3.90758 q^{5} +6.11425 q^{6} -4.79951 q^{7} -2.58348 q^{8} +4.27377 q^{9} +O(q^{10})\) \(q-2.26706 q^{2} -2.69699 q^{3} +3.13957 q^{4} -3.90758 q^{5} +6.11425 q^{6} -4.79951 q^{7} -2.58348 q^{8} +4.27377 q^{9} +8.85872 q^{10} -1.38285 q^{11} -8.46740 q^{12} +2.27493 q^{13} +10.8808 q^{14} +10.5387 q^{15} -0.422238 q^{16} +2.73391 q^{17} -9.68891 q^{18} -4.28446 q^{19} -12.2681 q^{20} +12.9442 q^{21} +3.13500 q^{22} +6.13686 q^{23} +6.96762 q^{24} +10.2692 q^{25} -5.15740 q^{26} -3.43536 q^{27} -15.0684 q^{28} -9.75536 q^{29} -23.8919 q^{30} +1.51721 q^{31} +6.12419 q^{32} +3.72953 q^{33} -6.19794 q^{34} +18.7545 q^{35} +13.4178 q^{36} +1.00000 q^{37} +9.71313 q^{38} -6.13547 q^{39} +10.0951 q^{40} -1.14774 q^{41} -29.3454 q^{42} -8.75122 q^{43} -4.34154 q^{44} -16.7001 q^{45} -13.9126 q^{46} +12.5748 q^{47} +1.13877 q^{48} +16.0353 q^{49} -23.2809 q^{50} -7.37334 q^{51} +7.14230 q^{52} -9.73727 q^{53} +7.78817 q^{54} +5.40358 q^{55} +12.3994 q^{56} +11.5551 q^{57} +22.1160 q^{58} -2.87631 q^{59} +33.0870 q^{60} -9.93731 q^{61} -3.43960 q^{62} -20.5120 q^{63} -13.0395 q^{64} -8.88946 q^{65} -8.45507 q^{66} +2.26696 q^{67} +8.58330 q^{68} -16.5511 q^{69} -42.5175 q^{70} -5.98115 q^{71} -11.0412 q^{72} -16.5196 q^{73} -2.26706 q^{74} -27.6959 q^{75} -13.4514 q^{76} +6.63698 q^{77} +13.9095 q^{78} -6.45107 q^{79} +1.64993 q^{80} -3.55618 q^{81} +2.60200 q^{82} +7.49907 q^{83} +40.6394 q^{84} -10.6830 q^{85} +19.8396 q^{86} +26.3101 q^{87} +3.57255 q^{88} +0.279679 q^{89} +37.8602 q^{90} -10.9185 q^{91} +19.2671 q^{92} -4.09190 q^{93} -28.5079 q^{94} +16.7418 q^{95} -16.5169 q^{96} -12.6937 q^{97} -36.3530 q^{98} -5.90997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26706 −1.60305 −0.801527 0.597958i \(-0.795979\pi\)
−0.801527 + 0.597958i \(0.795979\pi\)
\(3\) −2.69699 −1.55711 −0.778555 0.627576i \(-0.784047\pi\)
−0.778555 + 0.627576i \(0.784047\pi\)
\(4\) 3.13957 1.56979
\(5\) −3.90758 −1.74752 −0.873761 0.486355i \(-0.838326\pi\)
−0.873761 + 0.486355i \(0.838326\pi\)
\(6\) 6.11425 2.49613
\(7\) −4.79951 −1.81404 −0.907022 0.421083i \(-0.861650\pi\)
−0.907022 + 0.421083i \(0.861650\pi\)
\(8\) −2.58348 −0.913397
\(9\) 4.27377 1.42459
\(10\) 8.85872 2.80137
\(11\) −1.38285 −0.416944 −0.208472 0.978028i \(-0.566849\pi\)
−0.208472 + 0.978028i \(0.566849\pi\)
\(12\) −8.46740 −2.44433
\(13\) 2.27493 0.630952 0.315476 0.948934i \(-0.397836\pi\)
0.315476 + 0.948934i \(0.397836\pi\)
\(14\) 10.8808 2.90801
\(15\) 10.5387 2.72108
\(16\) −0.422238 −0.105559
\(17\) 2.73391 0.663071 0.331535 0.943443i \(-0.392433\pi\)
0.331535 + 0.943443i \(0.392433\pi\)
\(18\) −9.68891 −2.28370
\(19\) −4.28446 −0.982921 −0.491461 0.870900i \(-0.663537\pi\)
−0.491461 + 0.870900i \(0.663537\pi\)
\(20\) −12.2681 −2.74323
\(21\) 12.9442 2.82467
\(22\) 3.13500 0.668384
\(23\) 6.13686 1.27962 0.639812 0.768532i \(-0.279012\pi\)
0.639812 + 0.768532i \(0.279012\pi\)
\(24\) 6.96762 1.42226
\(25\) 10.2692 2.05383
\(26\) −5.15740 −1.01145
\(27\) −3.43536 −0.661135
\(28\) −15.0684 −2.84766
\(29\) −9.75536 −1.81152 −0.905762 0.423787i \(-0.860701\pi\)
−0.905762 + 0.423787i \(0.860701\pi\)
\(30\) −23.8919 −4.36205
\(31\) 1.51721 0.272498 0.136249 0.990675i \(-0.456495\pi\)
0.136249 + 0.990675i \(0.456495\pi\)
\(32\) 6.12419 1.08261
\(33\) 3.72953 0.649228
\(34\) −6.19794 −1.06294
\(35\) 18.7545 3.17008
\(36\) 13.4178 2.23630
\(37\) 1.00000 0.164399
\(38\) 9.71313 1.57568
\(39\) −6.13547 −0.982461
\(40\) 10.0951 1.59618
\(41\) −1.14774 −0.179247 −0.0896236 0.995976i \(-0.528566\pi\)
−0.0896236 + 0.995976i \(0.528566\pi\)
\(42\) −29.3454 −4.52809
\(43\) −8.75122 −1.33455 −0.667274 0.744812i \(-0.732539\pi\)
−0.667274 + 0.744812i \(0.732539\pi\)
\(44\) −4.34154 −0.654512
\(45\) −16.7001 −2.48951
\(46\) −13.9126 −2.05131
\(47\) 12.5748 1.83423 0.917113 0.398626i \(-0.130513\pi\)
0.917113 + 0.398626i \(0.130513\pi\)
\(48\) 1.13877 0.164368
\(49\) 16.0353 2.29076
\(50\) −23.2809 −3.29241
\(51\) −7.37334 −1.03247
\(52\) 7.14230 0.990459
\(53\) −9.73727 −1.33752 −0.668758 0.743480i \(-0.733174\pi\)
−0.668758 + 0.743480i \(0.733174\pi\)
\(54\) 7.78817 1.05984
\(55\) 5.40358 0.728619
\(56\) 12.3994 1.65694
\(57\) 11.5551 1.53052
\(58\) 22.1160 2.90397
\(59\) −2.87631 −0.374463 −0.187232 0.982316i \(-0.559951\pi\)
−0.187232 + 0.982316i \(0.559951\pi\)
\(60\) 33.0870 4.27152
\(61\) −9.93731 −1.27234 −0.636171 0.771548i \(-0.719483\pi\)
−0.636171 + 0.771548i \(0.719483\pi\)
\(62\) −3.43960 −0.436830
\(63\) −20.5120 −2.58427
\(64\) −13.0395 −1.62993
\(65\) −8.88946 −1.10260
\(66\) −8.45507 −1.04075
\(67\) 2.26696 0.276953 0.138476 0.990366i \(-0.455779\pi\)
0.138476 + 0.990366i \(0.455779\pi\)
\(68\) 8.58330 1.04088
\(69\) −16.5511 −1.99251
\(70\) −42.5175 −5.08182
\(71\) −5.98115 −0.709832 −0.354916 0.934898i \(-0.615490\pi\)
−0.354916 + 0.934898i \(0.615490\pi\)
\(72\) −11.0412 −1.30122
\(73\) −16.5196 −1.93347 −0.966736 0.255775i \(-0.917669\pi\)
−0.966736 + 0.255775i \(0.917669\pi\)
\(74\) −2.26706 −0.263541
\(75\) −27.6959 −3.19805
\(76\) −13.4514 −1.54298
\(77\) 6.63698 0.756355
\(78\) 13.9095 1.57494
\(79\) −6.45107 −0.725802 −0.362901 0.931828i \(-0.618214\pi\)
−0.362901 + 0.931828i \(0.618214\pi\)
\(80\) 1.64993 0.184468
\(81\) −3.55618 −0.395131
\(82\) 2.60200 0.287343
\(83\) 7.49907 0.823130 0.411565 0.911380i \(-0.364982\pi\)
0.411565 + 0.911380i \(0.364982\pi\)
\(84\) 40.6394 4.43412
\(85\) −10.6830 −1.15873
\(86\) 19.8396 2.13935
\(87\) 26.3101 2.82074
\(88\) 3.57255 0.380835
\(89\) 0.279679 0.0296460 0.0148230 0.999890i \(-0.495282\pi\)
0.0148230 + 0.999890i \(0.495282\pi\)
\(90\) 37.8602 3.99081
\(91\) −10.9185 −1.14457
\(92\) 19.2671 2.00873
\(93\) −4.09190 −0.424310
\(94\) −28.5079 −2.94037
\(95\) 16.7418 1.71768
\(96\) −16.5169 −1.68575
\(97\) −12.6937 −1.28885 −0.644426 0.764666i \(-0.722904\pi\)
−0.644426 + 0.764666i \(0.722904\pi\)
\(98\) −36.3530 −3.67221
\(99\) −5.90997 −0.593975
\(100\) 32.2408 3.22408
\(101\) −8.19444 −0.815377 −0.407689 0.913121i \(-0.633665\pi\)
−0.407689 + 0.913121i \(0.633665\pi\)
\(102\) 16.7158 1.65511
\(103\) 4.51496 0.444872 0.222436 0.974947i \(-0.428599\pi\)
0.222436 + 0.974947i \(0.428599\pi\)
\(104\) −5.87723 −0.576309
\(105\) −50.5807 −4.93617
\(106\) 22.0750 2.14411
\(107\) 14.8383 1.43447 0.717237 0.696830i \(-0.245407\pi\)
0.717237 + 0.696830i \(0.245407\pi\)
\(108\) −10.7856 −1.03784
\(109\) −1.00000 −0.0957826
\(110\) −12.2503 −1.16802
\(111\) −2.69699 −0.255987
\(112\) 2.02654 0.191490
\(113\) 11.4853 1.08045 0.540224 0.841521i \(-0.318339\pi\)
0.540224 + 0.841521i \(0.318339\pi\)
\(114\) −26.1962 −2.45350
\(115\) −23.9803 −2.23617
\(116\) −30.6276 −2.84370
\(117\) 9.72253 0.898848
\(118\) 6.52077 0.600285
\(119\) −13.1214 −1.20284
\(120\) −27.2265 −2.48543
\(121\) −9.08774 −0.826158
\(122\) 22.5285 2.03963
\(123\) 3.09545 0.279108
\(124\) 4.76338 0.427764
\(125\) −20.5897 −1.84160
\(126\) 46.5020 4.14273
\(127\) 2.27602 0.201964 0.100982 0.994888i \(-0.467802\pi\)
0.100982 + 0.994888i \(0.467802\pi\)
\(128\) 17.3129 1.53026
\(129\) 23.6020 2.07804
\(130\) 20.1530 1.76753
\(131\) −2.27581 −0.198838 −0.0994191 0.995046i \(-0.531698\pi\)
−0.0994191 + 0.995046i \(0.531698\pi\)
\(132\) 11.7091 1.01915
\(133\) 20.5633 1.78306
\(134\) −5.13933 −0.443971
\(135\) 13.4239 1.15535
\(136\) −7.06299 −0.605647
\(137\) −6.84896 −0.585146 −0.292573 0.956243i \(-0.594511\pi\)
−0.292573 + 0.956243i \(0.594511\pi\)
\(138\) 37.5223 3.19411
\(139\) −5.59110 −0.474231 −0.237115 0.971481i \(-0.576202\pi\)
−0.237115 + 0.971481i \(0.576202\pi\)
\(140\) 58.8810 4.97635
\(141\) −33.9142 −2.85609
\(142\) 13.5596 1.13790
\(143\) −3.14588 −0.263071
\(144\) −1.80455 −0.150379
\(145\) 38.1198 3.16568
\(146\) 37.4510 3.09946
\(147\) −43.2471 −3.56696
\(148\) 3.13957 0.258071
\(149\) −14.4316 −1.18228 −0.591141 0.806568i \(-0.701322\pi\)
−0.591141 + 0.806568i \(0.701322\pi\)
\(150\) 62.7883 5.12664
\(151\) 11.3800 0.926089 0.463044 0.886335i \(-0.346757\pi\)
0.463044 + 0.886335i \(0.346757\pi\)
\(152\) 11.0688 0.897798
\(153\) 11.6841 0.944605
\(154\) −15.0465 −1.21248
\(155\) −5.92860 −0.476197
\(156\) −19.2627 −1.54225
\(157\) −12.5949 −1.00518 −0.502592 0.864524i \(-0.667620\pi\)
−0.502592 + 0.864524i \(0.667620\pi\)
\(158\) 14.6250 1.16350
\(159\) 26.2614 2.08266
\(160\) −23.9308 −1.89189
\(161\) −29.4539 −2.32129
\(162\) 8.06208 0.633417
\(163\) −12.9150 −1.01158 −0.505791 0.862656i \(-0.668799\pi\)
−0.505791 + 0.862656i \(0.668799\pi\)
\(164\) −3.60342 −0.281380
\(165\) −14.5734 −1.13454
\(166\) −17.0009 −1.31952
\(167\) −12.9607 −1.00293 −0.501463 0.865179i \(-0.667205\pi\)
−0.501463 + 0.865179i \(0.667205\pi\)
\(168\) −33.4412 −2.58004
\(169\) −7.82470 −0.601900
\(170\) 24.2190 1.85751
\(171\) −18.3108 −1.40026
\(172\) −27.4751 −2.09495
\(173\) −2.25143 −0.171173 −0.0855866 0.996331i \(-0.527276\pi\)
−0.0855866 + 0.996331i \(0.527276\pi\)
\(174\) −59.6467 −4.52180
\(175\) −49.2870 −3.72575
\(176\) 0.583890 0.0440124
\(177\) 7.75738 0.583080
\(178\) −0.634051 −0.0475241
\(179\) −6.45763 −0.482666 −0.241333 0.970442i \(-0.577585\pi\)
−0.241333 + 0.970442i \(0.577585\pi\)
\(180\) −52.4312 −3.90799
\(181\) −22.4584 −1.66932 −0.834661 0.550763i \(-0.814337\pi\)
−0.834661 + 0.550763i \(0.814337\pi\)
\(182\) 24.7530 1.83482
\(183\) 26.8009 1.98118
\(184\) −15.8544 −1.16880
\(185\) −3.90758 −0.287291
\(186\) 9.27658 0.680192
\(187\) −3.78058 −0.276463
\(188\) 39.4796 2.87934
\(189\) 16.4880 1.19933
\(190\) −37.9548 −2.75353
\(191\) 16.7988 1.21552 0.607758 0.794122i \(-0.292069\pi\)
0.607758 + 0.794122i \(0.292069\pi\)
\(192\) 35.1673 2.53798
\(193\) −9.77320 −0.703490 −0.351745 0.936096i \(-0.614412\pi\)
−0.351745 + 0.936096i \(0.614412\pi\)
\(194\) 28.7775 2.06610
\(195\) 23.9748 1.71687
\(196\) 50.3439 3.59599
\(197\) −25.1556 −1.79226 −0.896132 0.443788i \(-0.853634\pi\)
−0.896132 + 0.443788i \(0.853634\pi\)
\(198\) 13.3983 0.952174
\(199\) 18.5202 1.31286 0.656431 0.754386i \(-0.272065\pi\)
0.656431 + 0.754386i \(0.272065\pi\)
\(200\) −26.5302 −1.87597
\(201\) −6.11397 −0.431246
\(202\) 18.5773 1.30709
\(203\) 46.8209 3.28618
\(204\) −23.1491 −1.62076
\(205\) 4.48489 0.313238
\(206\) −10.2357 −0.713154
\(207\) 26.2275 1.82294
\(208\) −0.960561 −0.0666029
\(209\) 5.92474 0.409823
\(210\) 114.669 7.91295
\(211\) 6.59359 0.453922 0.226961 0.973904i \(-0.427121\pi\)
0.226961 + 0.973904i \(0.427121\pi\)
\(212\) −30.5708 −2.09961
\(213\) 16.1311 1.10529
\(214\) −33.6394 −2.29954
\(215\) 34.1961 2.33215
\(216\) 8.87517 0.603879
\(217\) −7.28185 −0.494324
\(218\) 2.26706 0.153545
\(219\) 44.5532 3.01063
\(220\) 16.9649 1.14378
\(221\) 6.21945 0.418365
\(222\) 6.11425 0.410362
\(223\) −12.3053 −0.824024 −0.412012 0.911178i \(-0.635174\pi\)
−0.412012 + 0.911178i \(0.635174\pi\)
\(224\) −29.3931 −1.96391
\(225\) 43.8881 2.92587
\(226\) −26.0379 −1.73202
\(227\) −6.59178 −0.437512 −0.218756 0.975780i \(-0.570200\pi\)
−0.218756 + 0.975780i \(0.570200\pi\)
\(228\) 36.2782 2.40258
\(229\) 1.40131 0.0926015 0.0463007 0.998928i \(-0.485257\pi\)
0.0463007 + 0.998928i \(0.485257\pi\)
\(230\) 54.3647 3.58470
\(231\) −17.8999 −1.17773
\(232\) 25.2027 1.65464
\(233\) −9.92219 −0.650024 −0.325012 0.945710i \(-0.605368\pi\)
−0.325012 + 0.945710i \(0.605368\pi\)
\(234\) −22.0416 −1.44090
\(235\) −49.1371 −3.20535
\(236\) −9.03037 −0.587827
\(237\) 17.3985 1.13015
\(238\) 29.7471 1.92822
\(239\) −3.63292 −0.234994 −0.117497 0.993073i \(-0.537487\pi\)
−0.117497 + 0.993073i \(0.537487\pi\)
\(240\) −4.44985 −0.287236
\(241\) −8.95515 −0.576852 −0.288426 0.957502i \(-0.593132\pi\)
−0.288426 + 0.957502i \(0.593132\pi\)
\(242\) 20.6025 1.32438
\(243\) 19.8971 1.27640
\(244\) −31.1989 −1.99730
\(245\) −62.6592 −4.00315
\(246\) −7.01758 −0.447425
\(247\) −9.74683 −0.620176
\(248\) −3.91967 −0.248899
\(249\) −20.2250 −1.28170
\(250\) 46.6782 2.95219
\(251\) −6.07033 −0.383156 −0.191578 0.981477i \(-0.561360\pi\)
−0.191578 + 0.981477i \(0.561360\pi\)
\(252\) −64.3989 −4.05675
\(253\) −8.48633 −0.533531
\(254\) −5.15988 −0.323759
\(255\) 28.8119 1.80427
\(256\) −13.1704 −0.823151
\(257\) 23.5738 1.47049 0.735246 0.677800i \(-0.237067\pi\)
0.735246 + 0.677800i \(0.237067\pi\)
\(258\) −53.5071 −3.33121
\(259\) −4.79951 −0.298227
\(260\) −27.9091 −1.73085
\(261\) −41.6922 −2.58068
\(262\) 5.15940 0.318749
\(263\) 1.47912 0.0912067 0.0456034 0.998960i \(-0.485479\pi\)
0.0456034 + 0.998960i \(0.485479\pi\)
\(264\) −9.63515 −0.593003
\(265\) 38.0492 2.33734
\(266\) −46.6182 −2.85835
\(267\) −0.754294 −0.0461620
\(268\) 7.11727 0.434757
\(269\) 29.2441 1.78304 0.891522 0.452978i \(-0.149638\pi\)
0.891522 + 0.452978i \(0.149638\pi\)
\(270\) −30.4329 −1.85209
\(271\) −5.60187 −0.340289 −0.170145 0.985419i \(-0.554424\pi\)
−0.170145 + 0.985419i \(0.554424\pi\)
\(272\) −1.15436 −0.0699934
\(273\) 29.4472 1.78223
\(274\) 15.5270 0.938021
\(275\) −14.2007 −0.856334
\(276\) −51.9632 −3.12782
\(277\) −1.94784 −0.117034 −0.0585171 0.998286i \(-0.518637\pi\)
−0.0585171 + 0.998286i \(0.518637\pi\)
\(278\) 12.6754 0.760218
\(279\) 6.48420 0.388199
\(280\) −48.4517 −2.89554
\(281\) −26.9135 −1.60553 −0.802763 0.596298i \(-0.796638\pi\)
−0.802763 + 0.596298i \(0.796638\pi\)
\(282\) 76.8856 4.57847
\(283\) −5.39817 −0.320888 −0.160444 0.987045i \(-0.551293\pi\)
−0.160444 + 0.987045i \(0.551293\pi\)
\(284\) −18.7782 −1.11428
\(285\) −45.1527 −2.67461
\(286\) 7.13190 0.421718
\(287\) 5.50860 0.325162
\(288\) 26.1734 1.54228
\(289\) −9.52574 −0.560337
\(290\) −86.4200 −5.07476
\(291\) 34.2349 2.00689
\(292\) −51.8644 −3.03514
\(293\) −9.20631 −0.537838 −0.268919 0.963163i \(-0.586666\pi\)
−0.268919 + 0.963163i \(0.586666\pi\)
\(294\) 98.0438 5.71803
\(295\) 11.2394 0.654383
\(296\) −2.58348 −0.150162
\(297\) 4.75057 0.275656
\(298\) 32.7173 1.89526
\(299\) 13.9609 0.807381
\(300\) −86.9532 −5.02025
\(301\) 42.0015 2.42093
\(302\) −25.7991 −1.48457
\(303\) 22.1003 1.26963
\(304\) 1.80906 0.103757
\(305\) 38.8308 2.22345
\(306\) −26.4886 −1.51425
\(307\) −16.1861 −0.923791 −0.461896 0.886934i \(-0.652831\pi\)
−0.461896 + 0.886934i \(0.652831\pi\)
\(308\) 20.8373 1.18731
\(309\) −12.1768 −0.692715
\(310\) 13.4405 0.763370
\(311\) 29.3232 1.66277 0.831384 0.555698i \(-0.187549\pi\)
0.831384 + 0.555698i \(0.187549\pi\)
\(312\) 15.8508 0.897377
\(313\) 27.9445 1.57952 0.789758 0.613418i \(-0.210206\pi\)
0.789758 + 0.613418i \(0.210206\pi\)
\(314\) 28.5535 1.61137
\(315\) 80.1523 4.51607
\(316\) −20.2536 −1.13935
\(317\) 12.3817 0.695426 0.347713 0.937601i \(-0.386958\pi\)
0.347713 + 0.937601i \(0.386958\pi\)
\(318\) −59.5361 −3.33862
\(319\) 13.4902 0.755304
\(320\) 50.9527 2.84834
\(321\) −40.0188 −2.23363
\(322\) 66.7738 3.72116
\(323\) −11.7133 −0.651746
\(324\) −11.1649 −0.620271
\(325\) 23.3616 1.29587
\(326\) 29.2791 1.62162
\(327\) 2.69699 0.149144
\(328\) 2.96516 0.163724
\(329\) −60.3530 −3.32737
\(330\) 33.0389 1.81873
\(331\) −18.6325 −1.02414 −0.512068 0.858945i \(-0.671120\pi\)
−0.512068 + 0.858945i \(0.671120\pi\)
\(332\) 23.5439 1.29214
\(333\) 4.27377 0.234201
\(334\) 29.3826 1.60775
\(335\) −8.85831 −0.483981
\(336\) −5.46555 −0.298170
\(337\) −26.0497 −1.41902 −0.709510 0.704695i \(-0.751084\pi\)
−0.709510 + 0.704695i \(0.751084\pi\)
\(338\) 17.7391 0.964879
\(339\) −30.9758 −1.68238
\(340\) −33.5399 −1.81896
\(341\) −2.09806 −0.113617
\(342\) 41.5117 2.24470
\(343\) −43.3650 −2.34149
\(344\) 22.6086 1.21897
\(345\) 64.6746 3.48196
\(346\) 5.10414 0.274400
\(347\) −33.6303 −1.80537 −0.902686 0.430301i \(-0.858408\pi\)
−0.902686 + 0.430301i \(0.858408\pi\)
\(348\) 82.6025 4.42796
\(349\) 28.4304 1.52184 0.760921 0.648844i \(-0.224747\pi\)
0.760921 + 0.648844i \(0.224747\pi\)
\(350\) 111.737 5.97258
\(351\) −7.81520 −0.417144
\(352\) −8.46882 −0.451390
\(353\) −6.04422 −0.321701 −0.160851 0.986979i \(-0.551424\pi\)
−0.160851 + 0.986979i \(0.551424\pi\)
\(354\) −17.5865 −0.934710
\(355\) 23.3718 1.24045
\(356\) 0.878073 0.0465378
\(357\) 35.3884 1.87295
\(358\) 14.6399 0.773740
\(359\) −15.0125 −0.792328 −0.396164 0.918180i \(-0.629659\pi\)
−0.396164 + 0.918180i \(0.629659\pi\)
\(360\) 43.1443 2.27391
\(361\) −0.643441 −0.0338653
\(362\) 50.9147 2.67602
\(363\) 24.5096 1.28642
\(364\) −34.2795 −1.79674
\(365\) 64.5516 3.37879
\(366\) −60.7592 −3.17593
\(367\) −5.74743 −0.300013 −0.150007 0.988685i \(-0.547930\pi\)
−0.150007 + 0.988685i \(0.547930\pi\)
\(368\) −2.59121 −0.135076
\(369\) −4.90519 −0.255354
\(370\) 8.85872 0.460543
\(371\) 46.7341 2.42631
\(372\) −12.8468 −0.666075
\(373\) 5.73024 0.296700 0.148350 0.988935i \(-0.452604\pi\)
0.148350 + 0.988935i \(0.452604\pi\)
\(374\) 8.57081 0.443186
\(375\) 55.5303 2.86757
\(376\) −32.4868 −1.67538
\(377\) −22.1927 −1.14298
\(378\) −37.3794 −1.92259
\(379\) 2.33628 0.120007 0.0600034 0.998198i \(-0.480889\pi\)
0.0600034 + 0.998198i \(0.480889\pi\)
\(380\) 52.5622 2.69638
\(381\) −6.13841 −0.314480
\(382\) −38.0838 −1.94854
\(383\) 38.8560 1.98545 0.992724 0.120415i \(-0.0384226\pi\)
0.992724 + 0.120415i \(0.0384226\pi\)
\(384\) −46.6927 −2.38278
\(385\) −25.9345 −1.32175
\(386\) 22.1564 1.12773
\(387\) −37.4007 −1.90119
\(388\) −39.8528 −2.02322
\(389\) 25.0339 1.26927 0.634633 0.772813i \(-0.281151\pi\)
0.634633 + 0.772813i \(0.281151\pi\)
\(390\) −54.3524 −2.75224
\(391\) 16.7776 0.848481
\(392\) −41.4268 −2.09237
\(393\) 6.13784 0.309613
\(394\) 57.0293 2.87310
\(395\) 25.2081 1.26836
\(396\) −18.5548 −0.932413
\(397\) 0.770024 0.0386464 0.0193232 0.999813i \(-0.493849\pi\)
0.0193232 + 0.999813i \(0.493849\pi\)
\(398\) −41.9864 −2.10459
\(399\) −55.4590 −2.77642
\(400\) −4.33603 −0.216802
\(401\) −28.2063 −1.40856 −0.704279 0.709923i \(-0.748730\pi\)
−0.704279 + 0.709923i \(0.748730\pi\)
\(402\) 13.8607 0.691311
\(403\) 3.45154 0.171933
\(404\) −25.7270 −1.27997
\(405\) 13.8961 0.690501
\(406\) −106.146 −5.26793
\(407\) −1.38285 −0.0685452
\(408\) 19.0488 0.943059
\(409\) −39.6979 −1.96294 −0.981469 0.191623i \(-0.938625\pi\)
−0.981469 + 0.191623i \(0.938625\pi\)
\(410\) −10.1675 −0.502138
\(411\) 18.4716 0.911136
\(412\) 14.1750 0.698354
\(413\) 13.8049 0.679293
\(414\) −59.4595 −2.92227
\(415\) −29.3032 −1.43844
\(416\) 13.9321 0.683078
\(417\) 15.0792 0.738429
\(418\) −13.4318 −0.656969
\(419\) 13.0860 0.639293 0.319646 0.947537i \(-0.396436\pi\)
0.319646 + 0.947537i \(0.396436\pi\)
\(420\) −158.802 −7.74872
\(421\) 16.8470 0.821071 0.410536 0.911845i \(-0.365342\pi\)
0.410536 + 0.911845i \(0.365342\pi\)
\(422\) −14.9481 −0.727662
\(423\) 53.7420 2.61302
\(424\) 25.1560 1.22168
\(425\) 28.0750 1.36184
\(426\) −36.5702 −1.77183
\(427\) 47.6942 2.30808
\(428\) 46.5859 2.25181
\(429\) 8.48441 0.409631
\(430\) −77.5246 −3.73857
\(431\) −2.56848 −0.123719 −0.0618597 0.998085i \(-0.519703\pi\)
−0.0618597 + 0.998085i \(0.519703\pi\)
\(432\) 1.45054 0.0697891
\(433\) 9.02113 0.433528 0.216764 0.976224i \(-0.430450\pi\)
0.216764 + 0.976224i \(0.430450\pi\)
\(434\) 16.5084 0.792429
\(435\) −102.809 −4.92931
\(436\) −3.13957 −0.150358
\(437\) −26.2931 −1.25777
\(438\) −101.005 −4.82620
\(439\) −15.5195 −0.740704 −0.370352 0.928891i \(-0.620763\pi\)
−0.370352 + 0.928891i \(0.620763\pi\)
\(440\) −13.9600 −0.665518
\(441\) 68.5312 3.26339
\(442\) −14.0999 −0.670663
\(443\) −2.47284 −0.117488 −0.0587440 0.998273i \(-0.518710\pi\)
−0.0587440 + 0.998273i \(0.518710\pi\)
\(444\) −8.46740 −0.401845
\(445\) −1.09287 −0.0518070
\(446\) 27.8969 1.32096
\(447\) 38.9219 1.84094
\(448\) 62.5830 2.95677
\(449\) 0.118434 0.00558924 0.00279462 0.999996i \(-0.499110\pi\)
0.00279462 + 0.999996i \(0.499110\pi\)
\(450\) −99.4971 −4.69034
\(451\) 1.58715 0.0747360
\(452\) 36.0590 1.69607
\(453\) −30.6917 −1.44202
\(454\) 14.9440 0.701356
\(455\) 42.6651 2.00017
\(456\) −29.8525 −1.39797
\(457\) −36.8279 −1.72274 −0.861369 0.507979i \(-0.830393\pi\)
−0.861369 + 0.507979i \(0.830393\pi\)
\(458\) −3.17687 −0.148445
\(459\) −9.39196 −0.438379
\(460\) −75.2877 −3.51031
\(461\) 0.785039 0.0365629 0.0182815 0.999833i \(-0.494181\pi\)
0.0182815 + 0.999833i \(0.494181\pi\)
\(462\) 40.5802 1.88796
\(463\) 11.4484 0.532055 0.266027 0.963965i \(-0.414289\pi\)
0.266027 + 0.963965i \(0.414289\pi\)
\(464\) 4.11908 0.191224
\(465\) 15.9894 0.741491
\(466\) 22.4942 1.04202
\(467\) 37.9401 1.75566 0.877829 0.478974i \(-0.158991\pi\)
0.877829 + 0.478974i \(0.158991\pi\)
\(468\) 30.5246 1.41100
\(469\) −10.8803 −0.502405
\(470\) 111.397 5.13836
\(471\) 33.9684 1.56518
\(472\) 7.43087 0.342034
\(473\) 12.1016 0.556432
\(474\) −39.4435 −1.81170
\(475\) −43.9978 −2.01876
\(476\) −41.1956 −1.88820
\(477\) −41.6149 −1.90541
\(478\) 8.23605 0.376708
\(479\) −29.8738 −1.36497 −0.682484 0.730901i \(-0.739100\pi\)
−0.682484 + 0.730901i \(0.739100\pi\)
\(480\) 64.5411 2.94589
\(481\) 2.27493 0.103728
\(482\) 20.3019 0.924725
\(483\) 79.4370 3.61451
\(484\) −28.5316 −1.29689
\(485\) 49.6017 2.25230
\(486\) −45.1079 −2.04614
\(487\) −0.0302710 −0.00137171 −0.000685855 1.00000i \(-0.500218\pi\)
−0.000685855 1.00000i \(0.500218\pi\)
\(488\) 25.6728 1.16215
\(489\) 34.8317 1.57514
\(490\) 142.052 6.41726
\(491\) −25.4346 −1.14785 −0.573923 0.818909i \(-0.694579\pi\)
−0.573923 + 0.818909i \(0.694579\pi\)
\(492\) 9.71839 0.438139
\(493\) −26.6703 −1.20117
\(494\) 22.0967 0.994176
\(495\) 23.0937 1.03798
\(496\) −0.640622 −0.0287648
\(497\) 28.7066 1.28767
\(498\) 45.8512 2.05464
\(499\) 1.05251 0.0471169 0.0235584 0.999722i \(-0.492500\pi\)
0.0235584 + 0.999722i \(0.492500\pi\)
\(500\) −64.6429 −2.89092
\(501\) 34.9548 1.56167
\(502\) 13.7618 0.614219
\(503\) 13.6643 0.609259 0.304630 0.952471i \(-0.401467\pi\)
0.304630 + 0.952471i \(0.401467\pi\)
\(504\) 52.9923 2.36047
\(505\) 32.0204 1.42489
\(506\) 19.2390 0.855280
\(507\) 21.1032 0.937224
\(508\) 7.14572 0.317040
\(509\) −6.02784 −0.267179 −0.133590 0.991037i \(-0.542650\pi\)
−0.133590 + 0.991037i \(0.542650\pi\)
\(510\) −65.3184 −2.89235
\(511\) 79.2860 3.50740
\(512\) −4.76755 −0.210698
\(513\) 14.7186 0.649844
\(514\) −53.4432 −2.35728
\(515\) −17.6426 −0.777424
\(516\) 74.1001 3.26207
\(517\) −17.3891 −0.764770
\(518\) 10.8808 0.478074
\(519\) 6.07210 0.266535
\(520\) 22.9657 1.00711
\(521\) 4.47223 0.195932 0.0979661 0.995190i \(-0.468766\pi\)
0.0979661 + 0.995190i \(0.468766\pi\)
\(522\) 94.5188 4.13697
\(523\) −15.2839 −0.668316 −0.334158 0.942517i \(-0.608452\pi\)
−0.334158 + 0.942517i \(0.608452\pi\)
\(524\) −7.14506 −0.312133
\(525\) 132.927 5.80140
\(526\) −3.35327 −0.146209
\(527\) 4.14791 0.180686
\(528\) −1.57475 −0.0685321
\(529\) 14.6610 0.637436
\(530\) −86.2598 −3.74689
\(531\) −12.2927 −0.533457
\(532\) 64.5599 2.79903
\(533\) −2.61103 −0.113096
\(534\) 1.71003 0.0740003
\(535\) −57.9819 −2.50677
\(536\) −5.85663 −0.252968
\(537\) 17.4162 0.751564
\(538\) −66.2982 −2.85832
\(539\) −22.1743 −0.955117
\(540\) 42.1454 1.81365
\(541\) 15.9178 0.684362 0.342181 0.939634i \(-0.388834\pi\)
0.342181 + 0.939634i \(0.388834\pi\)
\(542\) 12.6998 0.545503
\(543\) 60.5703 2.59932
\(544\) 16.7430 0.717850
\(545\) 3.90758 0.167382
\(546\) −66.7587 −2.85701
\(547\) −43.0374 −1.84015 −0.920073 0.391747i \(-0.871871\pi\)
−0.920073 + 0.391747i \(0.871871\pi\)
\(548\) −21.5028 −0.918553
\(549\) −42.4698 −1.81257
\(550\) 32.1938 1.37275
\(551\) 41.7964 1.78059
\(552\) 42.7593 1.81996
\(553\) 30.9620 1.31664
\(554\) 4.41587 0.187612
\(555\) 10.5387 0.447344
\(556\) −17.5536 −0.744441
\(557\) 28.7849 1.21966 0.609829 0.792533i \(-0.291238\pi\)
0.609829 + 0.792533i \(0.291238\pi\)
\(558\) −14.7001 −0.622304
\(559\) −19.9084 −0.842035
\(560\) −7.91885 −0.334632
\(561\) 10.1962 0.430484
\(562\) 61.0146 2.57375
\(563\) −5.09060 −0.214543 −0.107272 0.994230i \(-0.534211\pi\)
−0.107272 + 0.994230i \(0.534211\pi\)
\(564\) −106.476 −4.48345
\(565\) −44.8798 −1.88811
\(566\) 12.2380 0.514401
\(567\) 17.0679 0.716785
\(568\) 15.4522 0.648358
\(569\) 44.7274 1.87507 0.937536 0.347889i \(-0.113101\pi\)
0.937536 + 0.347889i \(0.113101\pi\)
\(570\) 102.364 4.28755
\(571\) 36.7979 1.53994 0.769972 0.638077i \(-0.220270\pi\)
0.769972 + 0.638077i \(0.220270\pi\)
\(572\) −9.87670 −0.412966
\(573\) −45.3061 −1.89269
\(574\) −12.4883 −0.521253
\(575\) 63.0205 2.62814
\(576\) −55.7277 −2.32199
\(577\) −21.9204 −0.912556 −0.456278 0.889837i \(-0.650818\pi\)
−0.456278 + 0.889837i \(0.650818\pi\)
\(578\) 21.5954 0.898252
\(579\) 26.3583 1.09541
\(580\) 119.680 4.96944
\(581\) −35.9919 −1.49319
\(582\) −77.6126 −3.21715
\(583\) 13.4652 0.557670
\(584\) 42.6780 1.76603
\(585\) −37.9916 −1.57076
\(586\) 20.8713 0.862185
\(587\) −21.2708 −0.877938 −0.438969 0.898502i \(-0.644656\pi\)
−0.438969 + 0.898502i \(0.644656\pi\)
\(588\) −135.777 −5.59936
\(589\) −6.50040 −0.267844
\(590\) −25.4804 −1.04901
\(591\) 67.8445 2.79075
\(592\) −0.422238 −0.0173539
\(593\) 15.9520 0.655070 0.327535 0.944839i \(-0.393782\pi\)
0.327535 + 0.944839i \(0.393782\pi\)
\(594\) −10.7698 −0.441892
\(595\) 51.2730 2.10199
\(596\) −45.3090 −1.85593
\(597\) −49.9489 −2.04427
\(598\) −31.6503 −1.29428
\(599\) −30.0794 −1.22901 −0.614506 0.788912i \(-0.710645\pi\)
−0.614506 + 0.788912i \(0.710645\pi\)
\(600\) 71.5517 2.92109
\(601\) −20.3443 −0.829861 −0.414930 0.909853i \(-0.636194\pi\)
−0.414930 + 0.909853i \(0.636194\pi\)
\(602\) −95.2201 −3.88088
\(603\) 9.68846 0.394545
\(604\) 35.7282 1.45376
\(605\) 35.5110 1.44373
\(606\) −50.1029 −2.03529
\(607\) −20.3111 −0.824402 −0.412201 0.911093i \(-0.635240\pi\)
−0.412201 + 0.911093i \(0.635240\pi\)
\(608\) −26.2388 −1.06413
\(609\) −126.276 −5.11695
\(610\) −88.0319 −3.56431
\(611\) 28.6068 1.15731
\(612\) 36.6831 1.48283
\(613\) 36.1412 1.45973 0.729864 0.683592i \(-0.239583\pi\)
0.729864 + 0.683592i \(0.239583\pi\)
\(614\) 36.6950 1.48089
\(615\) −12.0957 −0.487747
\(616\) −17.1465 −0.690852
\(617\) −13.2986 −0.535383 −0.267691 0.963505i \(-0.586261\pi\)
−0.267691 + 0.963505i \(0.586261\pi\)
\(618\) 27.6056 1.11046
\(619\) −7.63434 −0.306850 −0.153425 0.988160i \(-0.549030\pi\)
−0.153425 + 0.988160i \(0.549030\pi\)
\(620\) −18.6133 −0.747527
\(621\) −21.0823 −0.846004
\(622\) −66.4776 −2.66551
\(623\) −1.34232 −0.0537791
\(624\) 2.59063 0.103708
\(625\) 29.1101 1.16440
\(626\) −63.3519 −2.53205
\(627\) −15.9790 −0.638140
\(628\) −39.5427 −1.57792
\(629\) 2.73391 0.109008
\(630\) −181.710 −7.23951
\(631\) −35.6061 −1.41746 −0.708729 0.705481i \(-0.750731\pi\)
−0.708729 + 0.705481i \(0.750731\pi\)
\(632\) 16.6662 0.662945
\(633\) −17.7829 −0.706806
\(634\) −28.0701 −1.11481
\(635\) −8.89373 −0.352937
\(636\) 82.4494 3.26933
\(637\) 36.4791 1.44536
\(638\) −30.5830 −1.21079
\(639\) −25.5621 −1.01122
\(640\) −67.6514 −2.67416
\(641\) −17.9187 −0.707745 −0.353873 0.935294i \(-0.615135\pi\)
−0.353873 + 0.935294i \(0.615135\pi\)
\(642\) 90.7251 3.58064
\(643\) 7.99908 0.315453 0.157726 0.987483i \(-0.449584\pi\)
0.157726 + 0.987483i \(0.449584\pi\)
\(644\) −92.4726 −3.64393
\(645\) −92.2266 −3.63142
\(646\) 26.5548 1.04479
\(647\) −18.6325 −0.732521 −0.366260 0.930512i \(-0.619362\pi\)
−0.366260 + 0.930512i \(0.619362\pi\)
\(648\) 9.18731 0.360912
\(649\) 3.97749 0.156130
\(650\) −52.9623 −2.07735
\(651\) 19.6391 0.769717
\(652\) −40.5476 −1.58797
\(653\) −1.83131 −0.0716648 −0.0358324 0.999358i \(-0.511408\pi\)
−0.0358324 + 0.999358i \(0.511408\pi\)
\(654\) −6.11425 −0.239086
\(655\) 8.89290 0.347474
\(656\) 0.484620 0.0189212
\(657\) −70.6010 −2.75441
\(658\) 136.824 5.33395
\(659\) −6.29243 −0.245118 −0.122559 0.992461i \(-0.539110\pi\)
−0.122559 + 0.992461i \(0.539110\pi\)
\(660\) −45.7543 −1.78098
\(661\) 21.7758 0.846979 0.423489 0.905901i \(-0.360805\pi\)
0.423489 + 0.905901i \(0.360805\pi\)
\(662\) 42.2411 1.64175
\(663\) −16.7738 −0.651441
\(664\) −19.3737 −0.751845
\(665\) −80.3527 −3.11594
\(666\) −9.68891 −0.375438
\(667\) −59.8672 −2.31807
\(668\) −40.6909 −1.57438
\(669\) 33.1873 1.28310
\(670\) 20.0823 0.775849
\(671\) 13.7418 0.530495
\(672\) 79.2731 3.05802
\(673\) 3.07068 0.118366 0.0591831 0.998247i \(-0.481150\pi\)
0.0591831 + 0.998247i \(0.481150\pi\)
\(674\) 59.0564 2.27477
\(675\) −35.2783 −1.35786
\(676\) −24.5662 −0.944854
\(677\) −3.24960 −0.124892 −0.0624462 0.998048i \(-0.519890\pi\)
−0.0624462 + 0.998048i \(0.519890\pi\)
\(678\) 70.2242 2.69694
\(679\) 60.9237 2.33804
\(680\) 27.5992 1.05838
\(681\) 17.7780 0.681254
\(682\) 4.75644 0.182134
\(683\) −40.0227 −1.53143 −0.765714 0.643182i \(-0.777614\pi\)
−0.765714 + 0.643182i \(0.777614\pi\)
\(684\) −57.4880 −2.19811
\(685\) 26.7628 1.02256
\(686\) 98.3110 3.75353
\(687\) −3.77934 −0.144191
\(688\) 3.69510 0.140874
\(689\) −22.1516 −0.843909
\(690\) −146.621 −5.58178
\(691\) 4.10442 0.156139 0.0780697 0.996948i \(-0.475124\pi\)
0.0780697 + 0.996948i \(0.475124\pi\)
\(692\) −7.06853 −0.268705
\(693\) 28.3650 1.07750
\(694\) 76.2421 2.89411
\(695\) 21.8477 0.828729
\(696\) −67.9716 −2.57646
\(697\) −3.13782 −0.118854
\(698\) −64.4534 −2.43960
\(699\) 26.7601 1.01216
\(700\) −154.740 −5.84862
\(701\) −41.9022 −1.58262 −0.791312 0.611413i \(-0.790602\pi\)
−0.791312 + 0.611413i \(0.790602\pi\)
\(702\) 17.7175 0.668705
\(703\) −4.28446 −0.161591
\(704\) 18.0316 0.679590
\(705\) 132.522 4.99109
\(706\) 13.7026 0.515705
\(707\) 39.3293 1.47913
\(708\) 24.3548 0.915311
\(709\) −11.0237 −0.414004 −0.207002 0.978340i \(-0.566371\pi\)
−0.207002 + 0.978340i \(0.566371\pi\)
\(710\) −52.9853 −1.98850
\(711\) −27.5704 −1.03397
\(712\) −0.722545 −0.0270785
\(713\) 9.31088 0.348695
\(714\) −80.2277 −3.00245
\(715\) 12.2928 0.459723
\(716\) −20.2742 −0.757682
\(717\) 9.79796 0.365911
\(718\) 34.0342 1.27015
\(719\) −28.1282 −1.04900 −0.524502 0.851409i \(-0.675749\pi\)
−0.524502 + 0.851409i \(0.675749\pi\)
\(720\) 7.05142 0.262791
\(721\) −21.6696 −0.807018
\(722\) 1.45872 0.0542880
\(723\) 24.1520 0.898222
\(724\) −70.5099 −2.62048
\(725\) −100.179 −3.72057
\(726\) −55.5647 −2.06220
\(727\) −12.6327 −0.468522 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(728\) 28.2078 1.04545
\(729\) −42.9937 −1.59236
\(730\) −146.343 −5.41638
\(731\) −23.9250 −0.884900
\(732\) 84.1432 3.11002
\(733\) 29.0669 1.07361 0.536805 0.843707i \(-0.319631\pi\)
0.536805 + 0.843707i \(0.319631\pi\)
\(734\) 13.0298 0.480938
\(735\) 168.991 6.23334
\(736\) 37.5833 1.38534
\(737\) −3.13485 −0.115474
\(738\) 11.1204 0.409346
\(739\) 23.0222 0.846887 0.423444 0.905922i \(-0.360821\pi\)
0.423444 + 0.905922i \(0.360821\pi\)
\(740\) −12.2681 −0.450985
\(741\) 26.2871 0.965682
\(742\) −105.949 −3.88952
\(743\) −37.0672 −1.35986 −0.679931 0.733276i \(-0.737990\pi\)
−0.679931 + 0.733276i \(0.737990\pi\)
\(744\) 10.5713 0.387563
\(745\) 56.3926 2.06607
\(746\) −12.9908 −0.475627
\(747\) 32.0493 1.17262
\(748\) −11.8694 −0.433988
\(749\) −71.2166 −2.60220
\(750\) −125.891 −4.59688
\(751\) −1.41819 −0.0517505 −0.0258753 0.999665i \(-0.508237\pi\)
−0.0258753 + 0.999665i \(0.508237\pi\)
\(752\) −5.30957 −0.193620
\(753\) 16.3716 0.596615
\(754\) 50.3123 1.83227
\(755\) −44.4681 −1.61836
\(756\) 51.7654 1.88269
\(757\) −0.0199105 −0.000723659 0 −0.000361830 1.00000i \(-0.500115\pi\)
−0.000361830 1.00000i \(0.500115\pi\)
\(758\) −5.29650 −0.192378
\(759\) 22.8876 0.830767
\(760\) −43.2522 −1.56892
\(761\) 21.1444 0.766484 0.383242 0.923648i \(-0.374808\pi\)
0.383242 + 0.923648i \(0.374808\pi\)
\(762\) 13.9162 0.504129
\(763\) 4.79951 0.173754
\(764\) 52.7409 1.90810
\(765\) −45.6566 −1.65072
\(766\) −88.0889 −3.18278
\(767\) −6.54339 −0.236268
\(768\) 35.5205 1.28174
\(769\) −7.28020 −0.262531 −0.131265 0.991347i \(-0.541904\pi\)
−0.131265 + 0.991347i \(0.541904\pi\)
\(770\) 58.7952 2.11883
\(771\) −63.5783 −2.28972
\(772\) −30.6836 −1.10433
\(773\) −18.8747 −0.678877 −0.339438 0.940628i \(-0.610237\pi\)
−0.339438 + 0.940628i \(0.610237\pi\)
\(774\) 84.7897 3.04770
\(775\) 15.5805 0.559667
\(776\) 32.7939 1.17723
\(777\) 12.9442 0.464372
\(778\) −56.7533 −2.03470
\(779\) 4.91745 0.176186
\(780\) 75.2706 2.69512
\(781\) 8.27101 0.295960
\(782\) −38.0359 −1.36016
\(783\) 33.5131 1.19766
\(784\) −6.77071 −0.241811
\(785\) 49.2157 1.75658
\(786\) −13.9149 −0.496327
\(787\) −34.8376 −1.24183 −0.620914 0.783879i \(-0.713238\pi\)
−0.620914 + 0.783879i \(0.713238\pi\)
\(788\) −78.9778 −2.81347
\(789\) −3.98919 −0.142019
\(790\) −57.1482 −2.03324
\(791\) −55.1239 −1.95998
\(792\) 15.2683 0.542535
\(793\) −22.6067 −0.802786
\(794\) −1.74569 −0.0619523
\(795\) −102.618 −3.63950
\(796\) 58.1455 2.06091
\(797\) 15.4218 0.546270 0.273135 0.961976i \(-0.411939\pi\)
0.273135 + 0.961976i \(0.411939\pi\)
\(798\) 125.729 4.45076
\(799\) 34.3784 1.21622
\(800\) 62.8904 2.22351
\(801\) 1.19529 0.0422334
\(802\) 63.9455 2.25800
\(803\) 22.8441 0.806150
\(804\) −19.1952 −0.676964
\(805\) 115.093 4.05651
\(806\) −7.82485 −0.275618
\(807\) −78.8711 −2.77639
\(808\) 21.1701 0.744763
\(809\) −25.0283 −0.879947 −0.439973 0.898011i \(-0.645012\pi\)
−0.439973 + 0.898011i \(0.645012\pi\)
\(810\) −31.5032 −1.10691
\(811\) −46.7655 −1.64216 −0.821080 0.570813i \(-0.806628\pi\)
−0.821080 + 0.570813i \(0.806628\pi\)
\(812\) 146.998 5.15860
\(813\) 15.1082 0.529868
\(814\) 3.13500 0.109882
\(815\) 50.4664 1.76776
\(816\) 3.11330 0.108987
\(817\) 37.4942 1.31176
\(818\) 89.9977 3.14670
\(819\) −46.6634 −1.63055
\(820\) 14.0806 0.491717
\(821\) −4.93802 −0.172338 −0.0861690 0.996281i \(-0.527463\pi\)
−0.0861690 + 0.996281i \(0.527463\pi\)
\(822\) −41.8762 −1.46060
\(823\) −10.0634 −0.350788 −0.175394 0.984498i \(-0.556120\pi\)
−0.175394 + 0.984498i \(0.556120\pi\)
\(824\) −11.6643 −0.406345
\(825\) 38.2992 1.33341
\(826\) −31.2965 −1.08894
\(827\) −8.66040 −0.301152 −0.150576 0.988598i \(-0.548113\pi\)
−0.150576 + 0.988598i \(0.548113\pi\)
\(828\) 82.3432 2.86162
\(829\) −34.4007 −1.19478 −0.597392 0.801949i \(-0.703797\pi\)
−0.597392 + 0.801949i \(0.703797\pi\)
\(830\) 66.4322 2.30590
\(831\) 5.25331 0.182235
\(832\) −29.6638 −1.02841
\(833\) 43.8390 1.51893
\(834\) −34.1854 −1.18374
\(835\) 50.6448 1.75264
\(836\) 18.6012 0.643334
\(837\) −5.21215 −0.180158
\(838\) −29.6668 −1.02482
\(839\) 15.1294 0.522324 0.261162 0.965295i \(-0.415894\pi\)
0.261162 + 0.965295i \(0.415894\pi\)
\(840\) 130.674 4.50868
\(841\) 66.1670 2.28162
\(842\) −38.1931 −1.31622
\(843\) 72.5856 2.49998
\(844\) 20.7011 0.712560
\(845\) 30.5756 1.05183
\(846\) −121.836 −4.18882
\(847\) 43.6167 1.49869
\(848\) 4.11145 0.141188
\(849\) 14.5588 0.499658
\(850\) −63.6478 −2.18310
\(851\) 6.13686 0.210369
\(852\) 50.6448 1.73506
\(853\) 2.12121 0.0726288 0.0363144 0.999340i \(-0.488438\pi\)
0.0363144 + 0.999340i \(0.488438\pi\)
\(854\) −108.126 −3.69999
\(855\) 71.5509 2.44699
\(856\) −38.3344 −1.31024
\(857\) −25.4613 −0.869742 −0.434871 0.900493i \(-0.643206\pi\)
−0.434871 + 0.900493i \(0.643206\pi\)
\(858\) −19.2347 −0.656661
\(859\) −15.7319 −0.536765 −0.268383 0.963312i \(-0.586489\pi\)
−0.268383 + 0.963312i \(0.586489\pi\)
\(860\) 107.361 3.66098
\(861\) −14.8567 −0.506313
\(862\) 5.82290 0.198329
\(863\) −3.88810 −0.132353 −0.0661763 0.997808i \(-0.521080\pi\)
−0.0661763 + 0.997808i \(0.521080\pi\)
\(864\) −21.0388 −0.715755
\(865\) 8.79765 0.299129
\(866\) −20.4515 −0.694969
\(867\) 25.6908 0.872507
\(868\) −22.8619 −0.775982
\(869\) 8.92084 0.302619
\(870\) 233.074 7.90196
\(871\) 5.15717 0.174744
\(872\) 2.58348 0.0874876
\(873\) −54.2501 −1.83609
\(874\) 59.6081 2.01627
\(875\) 98.8205 3.34074
\(876\) 139.878 4.72604
\(877\) 9.84333 0.332386 0.166193 0.986093i \(-0.446853\pi\)
0.166193 + 0.986093i \(0.446853\pi\)
\(878\) 35.1836 1.18739
\(879\) 24.8294 0.837473
\(880\) −2.28160 −0.0769126
\(881\) −27.6161 −0.930410 −0.465205 0.885203i \(-0.654019\pi\)
−0.465205 + 0.885203i \(0.654019\pi\)
\(882\) −155.364 −5.23139
\(883\) 18.4095 0.619529 0.309765 0.950813i \(-0.399750\pi\)
0.309765 + 0.950813i \(0.399750\pi\)
\(884\) 19.5264 0.656744
\(885\) −30.3126 −1.01895
\(886\) 5.60607 0.188340
\(887\) −23.9276 −0.803412 −0.401706 0.915769i \(-0.631583\pi\)
−0.401706 + 0.915769i \(0.631583\pi\)
\(888\) 6.96762 0.233818
\(889\) −10.9238 −0.366372
\(890\) 2.47760 0.0830494
\(891\) 4.91765 0.164748
\(892\) −38.6334 −1.29354
\(893\) −53.8763 −1.80290
\(894\) −88.2384 −2.95113
\(895\) 25.2337 0.843470
\(896\) −83.0932 −2.77595
\(897\) −37.6525 −1.25718
\(898\) −0.268497 −0.00895985
\(899\) −14.8009 −0.493637
\(900\) 137.790 4.59300
\(901\) −26.6208 −0.886868
\(902\) −3.59817 −0.119806
\(903\) −113.278 −3.76965
\(904\) −29.6721 −0.986878
\(905\) 87.7581 2.91718
\(906\) 69.5800 2.31164
\(907\) 33.0950 1.09890 0.549451 0.835526i \(-0.314837\pi\)
0.549451 + 0.835526i \(0.314837\pi\)
\(908\) −20.6954 −0.686800
\(909\) −35.0212 −1.16158
\(910\) −96.7243 −3.20638
\(911\) −44.7060 −1.48118 −0.740588 0.671959i \(-0.765453\pi\)
−0.740588 + 0.671959i \(0.765453\pi\)
\(912\) −4.87902 −0.161561
\(913\) −10.3701 −0.343199
\(914\) 83.4912 2.76164
\(915\) −104.726 −3.46215
\(916\) 4.39953 0.145364
\(917\) 10.9228 0.360701
\(918\) 21.2922 0.702746
\(919\) −18.3157 −0.604179 −0.302090 0.953280i \(-0.597684\pi\)
−0.302090 + 0.953280i \(0.597684\pi\)
\(920\) 61.9525 2.04251
\(921\) 43.6539 1.43844
\(922\) −1.77973 −0.0586124
\(923\) −13.6067 −0.447869
\(924\) −56.1980 −1.84878
\(925\) 10.2692 0.337648
\(926\) −25.9543 −0.852913
\(927\) 19.2959 0.633761
\(928\) −59.7437 −1.96118
\(929\) 8.47775 0.278146 0.139073 0.990282i \(-0.455588\pi\)
0.139073 + 0.990282i \(0.455588\pi\)
\(930\) −36.2490 −1.18865
\(931\) −68.7025 −2.25163
\(932\) −31.1514 −1.02040
\(933\) −79.0846 −2.58911
\(934\) −86.0126 −2.81442
\(935\) 14.7729 0.483126
\(936\) −25.1179 −0.821005
\(937\) −48.0495 −1.56971 −0.784855 0.619680i \(-0.787263\pi\)
−0.784855 + 0.619680i \(0.787263\pi\)
\(938\) 24.6663 0.805382
\(939\) −75.3661 −2.45948
\(940\) −154.269 −5.03172
\(941\) 36.3086 1.18363 0.591813 0.806076i \(-0.298413\pi\)
0.591813 + 0.806076i \(0.298413\pi\)
\(942\) −77.0085 −2.50907
\(943\) −7.04353 −0.229369
\(944\) 1.21449 0.0395281
\(945\) −64.4283 −2.09585
\(946\) −27.4351 −0.891991
\(947\) 4.69074 0.152429 0.0762144 0.997091i \(-0.475717\pi\)
0.0762144 + 0.997091i \(0.475717\pi\)
\(948\) 54.6238 1.77410
\(949\) −37.5809 −1.21993
\(950\) 99.7458 3.23618
\(951\) −33.3934 −1.08285
\(952\) 33.8989 1.09867
\(953\) 58.8275 1.90561 0.952805 0.303582i \(-0.0981828\pi\)
0.952805 + 0.303582i \(0.0981828\pi\)
\(954\) 94.3435 3.05448
\(955\) −65.6425 −2.12414
\(956\) −11.4058 −0.368890
\(957\) −36.3829 −1.17609
\(958\) 67.7257 2.18812
\(959\) 32.8716 1.06148
\(960\) −137.419 −4.43518
\(961\) −28.6981 −0.925745
\(962\) −5.15740 −0.166281
\(963\) 63.4156 2.04354
\(964\) −28.1153 −0.905533
\(965\) 38.1895 1.22937
\(966\) −180.089 −5.79426
\(967\) −28.7247 −0.923725 −0.461862 0.886952i \(-0.652819\pi\)
−0.461862 + 0.886952i \(0.652819\pi\)
\(968\) 23.4780 0.754610
\(969\) 31.5907 1.01484
\(970\) −112.450 −3.61056
\(971\) 41.6689 1.33722 0.668609 0.743614i \(-0.266890\pi\)
0.668609 + 0.743614i \(0.266890\pi\)
\(972\) 62.4683 2.00367
\(973\) 26.8345 0.860276
\(974\) 0.0686262 0.00219893
\(975\) −63.0062 −2.01781
\(976\) 4.19591 0.134308
\(977\) −53.4803 −1.71099 −0.855493 0.517814i \(-0.826746\pi\)
−0.855493 + 0.517814i \(0.826746\pi\)
\(978\) −78.9656 −2.52504
\(979\) −0.386754 −0.0123607
\(980\) −196.723 −6.28408
\(981\) −4.27377 −0.136451
\(982\) 57.6617 1.84006
\(983\) −6.75920 −0.215585 −0.107793 0.994173i \(-0.534378\pi\)
−0.107793 + 0.994173i \(0.534378\pi\)
\(984\) −7.99703 −0.254936
\(985\) 98.2976 3.13202
\(986\) 60.4632 1.92554
\(987\) 162.772 5.18108
\(988\) −30.6009 −0.973543
\(989\) −53.7050 −1.70772
\(990\) −52.3548 −1.66395
\(991\) −58.2238 −1.84954 −0.924770 0.380525i \(-0.875743\pi\)
−0.924770 + 0.380525i \(0.875743\pi\)
\(992\) 9.29167 0.295011
\(993\) 50.2518 1.59469
\(994\) −65.0796 −2.06420
\(995\) −72.3691 −2.29426
\(996\) −63.4977 −2.01200
\(997\) 39.0144 1.23560 0.617800 0.786336i \(-0.288024\pi\)
0.617800 + 0.786336i \(0.288024\pi\)
\(998\) −2.38611 −0.0755310
\(999\) −3.43536 −0.108690
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.1.10 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.10 85 1.1 even 1 trivial