Properties

Label 8027.2.a.f.1.9
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.62656 q^{2} +1.97110 q^{3} +4.89882 q^{4} -2.67061 q^{5} -5.17721 q^{6} +3.82377 q^{7} -7.61393 q^{8} +0.885230 q^{9} +O(q^{10})\) \(q-2.62656 q^{2} +1.97110 q^{3} +4.89882 q^{4} -2.67061 q^{5} -5.17721 q^{6} +3.82377 q^{7} -7.61393 q^{8} +0.885230 q^{9} +7.01453 q^{10} +5.21542 q^{11} +9.65606 q^{12} -1.19149 q^{13} -10.0434 q^{14} -5.26404 q^{15} +10.2008 q^{16} +3.34464 q^{17} -2.32511 q^{18} +0.211232 q^{19} -13.0829 q^{20} +7.53702 q^{21} -13.6986 q^{22} +1.00000 q^{23} -15.0078 q^{24} +2.13217 q^{25} +3.12952 q^{26} -4.16842 q^{27} +18.7319 q^{28} -0.308608 q^{29} +13.8263 q^{30} +7.17438 q^{31} -11.5652 q^{32} +10.2801 q^{33} -8.78490 q^{34} -10.2118 q^{35} +4.33658 q^{36} -5.24394 q^{37} -0.554814 q^{38} -2.34854 q^{39} +20.3339 q^{40} -5.30350 q^{41} -19.7964 q^{42} +3.18022 q^{43} +25.5494 q^{44} -2.36411 q^{45} -2.62656 q^{46} +0.360574 q^{47} +20.1068 q^{48} +7.62118 q^{49} -5.60028 q^{50} +6.59262 q^{51} -5.83689 q^{52} +1.71032 q^{53} +10.9486 q^{54} -13.9284 q^{55} -29.1139 q^{56} +0.416359 q^{57} +0.810577 q^{58} -1.58732 q^{59} -25.7876 q^{60} +9.22123 q^{61} -18.8440 q^{62} +3.38491 q^{63} +9.97503 q^{64} +3.18200 q^{65} -27.0013 q^{66} +9.27231 q^{67} +16.3848 q^{68} +1.97110 q^{69} +26.8219 q^{70} +0.623888 q^{71} -6.74008 q^{72} +5.13126 q^{73} +13.7735 q^{74} +4.20272 q^{75} +1.03479 q^{76} +19.9425 q^{77} +6.16858 q^{78} +8.42972 q^{79} -27.2424 q^{80} -10.8721 q^{81} +13.9300 q^{82} -14.6673 q^{83} +36.9225 q^{84} -8.93224 q^{85} -8.35305 q^{86} -0.608297 q^{87} -39.7098 q^{88} +1.12919 q^{89} +6.20947 q^{90} -4.55597 q^{91} +4.89882 q^{92} +14.1414 q^{93} -0.947070 q^{94} -0.564119 q^{95} -22.7961 q^{96} +6.84287 q^{97} -20.0175 q^{98} +4.61684 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62656 −1.85726 −0.928629 0.371009i \(-0.879012\pi\)
−0.928629 + 0.371009i \(0.879012\pi\)
\(3\) 1.97110 1.13801 0.569007 0.822333i \(-0.307328\pi\)
0.569007 + 0.822333i \(0.307328\pi\)
\(4\) 4.89882 2.44941
\(5\) −2.67061 −1.19433 −0.597167 0.802117i \(-0.703707\pi\)
−0.597167 + 0.802117i \(0.703707\pi\)
\(6\) −5.17721 −2.11359
\(7\) 3.82377 1.44525 0.722624 0.691242i \(-0.242936\pi\)
0.722624 + 0.691242i \(0.242936\pi\)
\(8\) −7.61393 −2.69193
\(9\) 0.885230 0.295077
\(10\) 7.01453 2.21819
\(11\) 5.21542 1.57251 0.786254 0.617904i \(-0.212018\pi\)
0.786254 + 0.617904i \(0.212018\pi\)
\(12\) 9.65606 2.78746
\(13\) −1.19149 −0.330459 −0.165230 0.986255i \(-0.552837\pi\)
−0.165230 + 0.986255i \(0.552837\pi\)
\(14\) −10.0434 −2.68420
\(15\) −5.26404 −1.35917
\(16\) 10.2008 2.55020
\(17\) 3.34464 0.811195 0.405597 0.914052i \(-0.367064\pi\)
0.405597 + 0.914052i \(0.367064\pi\)
\(18\) −2.32511 −0.548034
\(19\) 0.211232 0.0484600 0.0242300 0.999706i \(-0.492287\pi\)
0.0242300 + 0.999706i \(0.492287\pi\)
\(20\) −13.0829 −2.92541
\(21\) 7.53702 1.64471
\(22\) −13.6986 −2.92055
\(23\) 1.00000 0.208514
\(24\) −15.0078 −3.06346
\(25\) 2.13217 0.426434
\(26\) 3.12952 0.613748
\(27\) −4.16842 −0.802213
\(28\) 18.7319 3.54000
\(29\) −0.308608 −0.0573070 −0.0286535 0.999589i \(-0.509122\pi\)
−0.0286535 + 0.999589i \(0.509122\pi\)
\(30\) 13.8263 2.52433
\(31\) 7.17438 1.28856 0.644279 0.764791i \(-0.277158\pi\)
0.644279 + 0.764791i \(0.277158\pi\)
\(32\) −11.5652 −2.04445
\(33\) 10.2801 1.78954
\(34\) −8.78490 −1.50660
\(35\) −10.2118 −1.72611
\(36\) 4.33658 0.722764
\(37\) −5.24394 −0.862099 −0.431049 0.902328i \(-0.641857\pi\)
−0.431049 + 0.902328i \(0.641857\pi\)
\(38\) −0.554814 −0.0900027
\(39\) −2.34854 −0.376067
\(40\) 20.3339 3.21506
\(41\) −5.30350 −0.828267 −0.414134 0.910216i \(-0.635915\pi\)
−0.414134 + 0.910216i \(0.635915\pi\)
\(42\) −19.7964 −3.05466
\(43\) 3.18022 0.484980 0.242490 0.970154i \(-0.422036\pi\)
0.242490 + 0.970154i \(0.422036\pi\)
\(44\) 25.5494 3.85172
\(45\) −2.36411 −0.352420
\(46\) −2.62656 −0.387265
\(47\) 0.360574 0.0525952 0.0262976 0.999654i \(-0.491628\pi\)
0.0262976 + 0.999654i \(0.491628\pi\)
\(48\) 20.1068 2.90217
\(49\) 7.62118 1.08874
\(50\) −5.60028 −0.791999
\(51\) 6.59262 0.923151
\(52\) −5.83689 −0.809430
\(53\) 1.71032 0.234931 0.117466 0.993077i \(-0.462523\pi\)
0.117466 + 0.993077i \(0.462523\pi\)
\(54\) 10.9486 1.48992
\(55\) −13.9284 −1.87810
\(56\) −29.1139 −3.89051
\(57\) 0.416359 0.0551481
\(58\) 0.810577 0.106434
\(59\) −1.58732 −0.206652 −0.103326 0.994648i \(-0.532948\pi\)
−0.103326 + 0.994648i \(0.532948\pi\)
\(60\) −25.7876 −3.32916
\(61\) 9.22123 1.18066 0.590329 0.807163i \(-0.298998\pi\)
0.590329 + 0.807163i \(0.298998\pi\)
\(62\) −18.8440 −2.39318
\(63\) 3.38491 0.426459
\(64\) 9.97503 1.24688
\(65\) 3.18200 0.394679
\(66\) −27.0013 −3.32363
\(67\) 9.27231 1.13279 0.566397 0.824133i \(-0.308337\pi\)
0.566397 + 0.824133i \(0.308337\pi\)
\(68\) 16.3848 1.98695
\(69\) 1.97110 0.237292
\(70\) 26.8219 3.20583
\(71\) 0.623888 0.0740419 0.0370209 0.999314i \(-0.488213\pi\)
0.0370209 + 0.999314i \(0.488213\pi\)
\(72\) −6.74008 −0.794326
\(73\) 5.13126 0.600569 0.300285 0.953850i \(-0.402918\pi\)
0.300285 + 0.953850i \(0.402918\pi\)
\(74\) 13.7735 1.60114
\(75\) 4.20272 0.485288
\(76\) 1.03479 0.118698
\(77\) 19.9425 2.27266
\(78\) 6.16858 0.698455
\(79\) 8.42972 0.948418 0.474209 0.880412i \(-0.342734\pi\)
0.474209 + 0.880412i \(0.342734\pi\)
\(80\) −27.2424 −3.04579
\(81\) −10.8721 −1.20801
\(82\) 13.9300 1.53831
\(83\) −14.6673 −1.60995 −0.804974 0.593311i \(-0.797821\pi\)
−0.804974 + 0.593311i \(0.797821\pi\)
\(84\) 36.9225 4.02858
\(85\) −8.93224 −0.968837
\(86\) −8.35305 −0.900733
\(87\) −0.608297 −0.0652162
\(88\) −39.7098 −4.23308
\(89\) 1.12919 0.119694 0.0598470 0.998208i \(-0.480939\pi\)
0.0598470 + 0.998208i \(0.480939\pi\)
\(90\) 6.20947 0.654535
\(91\) −4.55597 −0.477595
\(92\) 4.89882 0.510737
\(93\) 14.1414 1.46640
\(94\) −0.947070 −0.0976828
\(95\) −0.564119 −0.0578774
\(96\) −22.7961 −2.32662
\(97\) 6.84287 0.694789 0.347394 0.937719i \(-0.387067\pi\)
0.347394 + 0.937719i \(0.387067\pi\)
\(98\) −20.0175 −2.02207
\(99\) 4.61684 0.464010
\(100\) 10.4451 1.04451
\(101\) −11.3503 −1.12940 −0.564700 0.825296i \(-0.691008\pi\)
−0.564700 + 0.825296i \(0.691008\pi\)
\(102\) −17.3159 −1.71453
\(103\) 14.4180 1.42064 0.710322 0.703877i \(-0.248549\pi\)
0.710322 + 0.703877i \(0.248549\pi\)
\(104\) 9.07190 0.889573
\(105\) −20.1285 −1.96434
\(106\) −4.49227 −0.436328
\(107\) 13.3429 1.28991 0.644954 0.764221i \(-0.276876\pi\)
0.644954 + 0.764221i \(0.276876\pi\)
\(108\) −20.4203 −1.96495
\(109\) 12.8670 1.23243 0.616216 0.787577i \(-0.288665\pi\)
0.616216 + 0.787577i \(0.288665\pi\)
\(110\) 36.5837 3.48812
\(111\) −10.3363 −0.981081
\(112\) 39.0055 3.68567
\(113\) −2.09782 −0.197346 −0.0986732 0.995120i \(-0.531460\pi\)
−0.0986732 + 0.995120i \(0.531460\pi\)
\(114\) −1.09359 −0.102424
\(115\) −2.67061 −0.249036
\(116\) −1.51181 −0.140368
\(117\) −1.05474 −0.0975108
\(118\) 4.16920 0.383806
\(119\) 12.7891 1.17238
\(120\) 40.0800 3.65879
\(121\) 16.2006 1.47278
\(122\) −24.2201 −2.19279
\(123\) −10.4537 −0.942580
\(124\) 35.1460 3.15621
\(125\) 7.65886 0.685029
\(126\) −8.89068 −0.792044
\(127\) 11.2255 0.996102 0.498051 0.867148i \(-0.334049\pi\)
0.498051 + 0.867148i \(0.334049\pi\)
\(128\) −3.06966 −0.271322
\(129\) 6.26853 0.551914
\(130\) −8.35772 −0.733021
\(131\) −7.58164 −0.662411 −0.331206 0.943559i \(-0.607455\pi\)
−0.331206 + 0.943559i \(0.607455\pi\)
\(132\) 50.3604 4.38331
\(133\) 0.807702 0.0700367
\(134\) −24.3543 −2.10389
\(135\) 11.1322 0.958110
\(136\) −25.4659 −2.18368
\(137\) 8.62062 0.736509 0.368255 0.929725i \(-0.379955\pi\)
0.368255 + 0.929725i \(0.379955\pi\)
\(138\) −5.17721 −0.440713
\(139\) −10.5404 −0.894023 −0.447012 0.894528i \(-0.647512\pi\)
−0.447012 + 0.894528i \(0.647512\pi\)
\(140\) −50.0258 −4.22795
\(141\) 0.710727 0.0598540
\(142\) −1.63868 −0.137515
\(143\) −6.21411 −0.519650
\(144\) 9.03006 0.752505
\(145\) 0.824172 0.0684438
\(146\) −13.4776 −1.11541
\(147\) 15.0221 1.23900
\(148\) −25.6891 −2.11163
\(149\) 6.98670 0.572373 0.286186 0.958174i \(-0.407612\pi\)
0.286186 + 0.958174i \(0.407612\pi\)
\(150\) −11.0387 −0.901306
\(151\) −17.5260 −1.42625 −0.713123 0.701038i \(-0.752720\pi\)
−0.713123 + 0.701038i \(0.752720\pi\)
\(152\) −1.60831 −0.130451
\(153\) 2.96078 0.239365
\(154\) −52.3803 −4.22092
\(155\) −19.1600 −1.53897
\(156\) −11.5051 −0.921143
\(157\) 5.45553 0.435399 0.217700 0.976016i \(-0.430145\pi\)
0.217700 + 0.976016i \(0.430145\pi\)
\(158\) −22.1412 −1.76146
\(159\) 3.37122 0.267355
\(160\) 30.8861 2.44176
\(161\) 3.82377 0.301355
\(162\) 28.5561 2.24358
\(163\) 6.29409 0.492992 0.246496 0.969144i \(-0.420721\pi\)
0.246496 + 0.969144i \(0.420721\pi\)
\(164\) −25.9809 −2.02877
\(165\) −27.4542 −2.13730
\(166\) 38.5246 2.99009
\(167\) −24.3664 −1.88553 −0.942765 0.333457i \(-0.891785\pi\)
−0.942765 + 0.333457i \(0.891785\pi\)
\(168\) −57.3863 −4.42745
\(169\) −11.5804 −0.890797
\(170\) 23.4611 1.79938
\(171\) 0.186989 0.0142994
\(172\) 15.5793 1.18791
\(173\) −10.3300 −0.785374 −0.392687 0.919672i \(-0.628454\pi\)
−0.392687 + 0.919672i \(0.628454\pi\)
\(174\) 1.59773 0.121123
\(175\) 8.15292 0.616303
\(176\) 53.2015 4.01021
\(177\) −3.12877 −0.235173
\(178\) −2.96589 −0.222303
\(179\) 6.46514 0.483227 0.241614 0.970373i \(-0.422323\pi\)
0.241614 + 0.970373i \(0.422323\pi\)
\(180\) −11.5813 −0.863222
\(181\) −7.24732 −0.538689 −0.269345 0.963044i \(-0.586807\pi\)
−0.269345 + 0.963044i \(0.586807\pi\)
\(182\) 11.9665 0.887018
\(183\) 18.1760 1.34361
\(184\) −7.61393 −0.561306
\(185\) 14.0045 1.02963
\(186\) −37.1433 −2.72348
\(187\) 17.4437 1.27561
\(188\) 1.76639 0.128827
\(189\) −15.9391 −1.15940
\(190\) 1.48169 0.107493
\(191\) −25.4287 −1.83996 −0.919978 0.391969i \(-0.871794\pi\)
−0.919978 + 0.391969i \(0.871794\pi\)
\(192\) 19.6618 1.41897
\(193\) 8.72418 0.627980 0.313990 0.949426i \(-0.398334\pi\)
0.313990 + 0.949426i \(0.398334\pi\)
\(194\) −17.9732 −1.29040
\(195\) 6.27204 0.449150
\(196\) 37.3348 2.66677
\(197\) −9.12983 −0.650474 −0.325237 0.945633i \(-0.605444\pi\)
−0.325237 + 0.945633i \(0.605444\pi\)
\(198\) −12.1264 −0.861787
\(199\) −0.00168745 −0.000119620 0 −5.98100e−5 1.00000i \(-0.500019\pi\)
−5.98100e−5 1.00000i \(0.500019\pi\)
\(200\) −16.2342 −1.14793
\(201\) 18.2766 1.28913
\(202\) 29.8124 2.09759
\(203\) −1.18004 −0.0828229
\(204\) 32.2961 2.26118
\(205\) 14.1636 0.989228
\(206\) −37.8697 −2.63850
\(207\) 0.885230 0.0615277
\(208\) −12.1541 −0.842738
\(209\) 1.10166 0.0762037
\(210\) 52.8686 3.64828
\(211\) 27.1276 1.86754 0.933769 0.357876i \(-0.116499\pi\)
0.933769 + 0.357876i \(0.116499\pi\)
\(212\) 8.37857 0.575443
\(213\) 1.22974 0.0842607
\(214\) −35.0460 −2.39569
\(215\) −8.49314 −0.579228
\(216\) 31.7381 2.15950
\(217\) 27.4332 1.86228
\(218\) −33.7959 −2.28895
\(219\) 10.1142 0.683456
\(220\) −68.2325 −4.60024
\(221\) −3.98510 −0.268067
\(222\) 27.1490 1.82212
\(223\) −26.3216 −1.76262 −0.881311 0.472537i \(-0.843338\pi\)
−0.881311 + 0.472537i \(0.843338\pi\)
\(224\) −44.2225 −2.95474
\(225\) 1.88746 0.125831
\(226\) 5.51006 0.366523
\(227\) 8.92730 0.592526 0.296263 0.955106i \(-0.404260\pi\)
0.296263 + 0.955106i \(0.404260\pi\)
\(228\) 2.03967 0.135080
\(229\) −5.71094 −0.377390 −0.188695 0.982036i \(-0.560426\pi\)
−0.188695 + 0.982036i \(0.560426\pi\)
\(230\) 7.01453 0.462524
\(231\) 39.3087 2.58632
\(232\) 2.34972 0.154267
\(233\) −15.4733 −1.01369 −0.506846 0.862037i \(-0.669189\pi\)
−0.506846 + 0.862037i \(0.669189\pi\)
\(234\) 2.77034 0.181103
\(235\) −0.962954 −0.0628162
\(236\) −7.77601 −0.506175
\(237\) 16.6158 1.07931
\(238\) −33.5914 −2.17741
\(239\) 12.9989 0.840828 0.420414 0.907332i \(-0.361885\pi\)
0.420414 + 0.907332i \(0.361885\pi\)
\(240\) −53.6975 −3.46616
\(241\) 8.74236 0.563145 0.281573 0.959540i \(-0.409144\pi\)
0.281573 + 0.959540i \(0.409144\pi\)
\(242\) −42.5518 −2.73533
\(243\) −8.92464 −0.572516
\(244\) 45.1732 2.89192
\(245\) −20.3532 −1.30032
\(246\) 27.4573 1.75061
\(247\) −0.251681 −0.0160140
\(248\) −54.6252 −3.46871
\(249\) −28.9107 −1.83214
\(250\) −20.1165 −1.27228
\(251\) −15.5939 −0.984279 −0.492140 0.870516i \(-0.663785\pi\)
−0.492140 + 0.870516i \(0.663785\pi\)
\(252\) 16.5821 1.04457
\(253\) 5.21542 0.327890
\(254\) −29.4845 −1.85002
\(255\) −17.6063 −1.10255
\(256\) −11.8874 −0.742963
\(257\) −9.27085 −0.578300 −0.289150 0.957284i \(-0.593373\pi\)
−0.289150 + 0.957284i \(0.593373\pi\)
\(258\) −16.4647 −1.02505
\(259\) −20.0516 −1.24595
\(260\) 15.5881 0.966730
\(261\) −0.273189 −0.0169100
\(262\) 19.9136 1.23027
\(263\) 28.4880 1.75665 0.878324 0.478066i \(-0.158662\pi\)
0.878324 + 0.478066i \(0.158662\pi\)
\(264\) −78.2720 −4.81731
\(265\) −4.56761 −0.280586
\(266\) −2.12148 −0.130076
\(267\) 2.22575 0.136214
\(268\) 45.4234 2.77468
\(269\) 24.0681 1.46746 0.733730 0.679441i \(-0.237778\pi\)
0.733730 + 0.679441i \(0.237778\pi\)
\(270\) −29.2395 −1.77946
\(271\) 20.6887 1.25675 0.628375 0.777910i \(-0.283720\pi\)
0.628375 + 0.777910i \(0.283720\pi\)
\(272\) 34.1180 2.06871
\(273\) −8.98027 −0.543510
\(274\) −22.6426 −1.36789
\(275\) 11.1202 0.670571
\(276\) 9.65606 0.581226
\(277\) 19.4390 1.16797 0.583987 0.811763i \(-0.301492\pi\)
0.583987 + 0.811763i \(0.301492\pi\)
\(278\) 27.6849 1.66043
\(279\) 6.35098 0.380223
\(280\) 77.7519 4.64656
\(281\) 8.23382 0.491188 0.245594 0.969373i \(-0.421017\pi\)
0.245594 + 0.969373i \(0.421017\pi\)
\(282\) −1.86677 −0.111164
\(283\) −12.7368 −0.757122 −0.378561 0.925576i \(-0.623581\pi\)
−0.378561 + 0.925576i \(0.623581\pi\)
\(284\) 3.05632 0.181359
\(285\) −1.11193 −0.0658653
\(286\) 16.3217 0.965124
\(287\) −20.2793 −1.19705
\(288\) −10.2378 −0.603271
\(289\) −5.81338 −0.341963
\(290\) −2.16474 −0.127118
\(291\) 13.4880 0.790679
\(292\) 25.1371 1.47104
\(293\) 16.9746 0.991670 0.495835 0.868417i \(-0.334862\pi\)
0.495835 + 0.868417i \(0.334862\pi\)
\(294\) −39.4565 −2.30115
\(295\) 4.23913 0.246811
\(296\) 39.9270 2.32071
\(297\) −21.7401 −1.26149
\(298\) −18.3510 −1.06304
\(299\) −1.19149 −0.0689055
\(300\) 20.5884 1.18867
\(301\) 12.1604 0.700915
\(302\) 46.0331 2.64891
\(303\) −22.3726 −1.28527
\(304\) 2.15474 0.123583
\(305\) −24.6263 −1.41010
\(306\) −7.77666 −0.444562
\(307\) 5.31764 0.303494 0.151747 0.988419i \(-0.451510\pi\)
0.151747 + 0.988419i \(0.451510\pi\)
\(308\) 97.6949 5.56668
\(309\) 28.4192 1.61671
\(310\) 50.3249 2.85826
\(311\) −13.0110 −0.737789 −0.368894 0.929471i \(-0.620264\pi\)
−0.368894 + 0.929471i \(0.620264\pi\)
\(312\) 17.8816 1.01235
\(313\) 19.6964 1.11331 0.556653 0.830745i \(-0.312085\pi\)
0.556653 + 0.830745i \(0.312085\pi\)
\(314\) −14.3293 −0.808649
\(315\) −9.03979 −0.509334
\(316\) 41.2957 2.32306
\(317\) 26.7688 1.50349 0.751744 0.659455i \(-0.229213\pi\)
0.751744 + 0.659455i \(0.229213\pi\)
\(318\) −8.85471 −0.496547
\(319\) −1.60952 −0.0901158
\(320\) −26.6394 −1.48919
\(321\) 26.3002 1.46793
\(322\) −10.0434 −0.559694
\(323\) 0.706496 0.0393105
\(324\) −53.2603 −2.95890
\(325\) −2.54046 −0.140919
\(326\) −16.5318 −0.915613
\(327\) 25.3621 1.40253
\(328\) 40.3805 2.22964
\(329\) 1.37875 0.0760130
\(330\) 72.1100 3.96953
\(331\) 8.73224 0.479967 0.239984 0.970777i \(-0.422858\pi\)
0.239984 + 0.970777i \(0.422858\pi\)
\(332\) −71.8526 −3.94342
\(333\) −4.64209 −0.254385
\(334\) 63.9999 3.50192
\(335\) −24.7628 −1.35293
\(336\) 76.8837 4.19435
\(337\) −6.98013 −0.380232 −0.190116 0.981762i \(-0.560886\pi\)
−0.190116 + 0.981762i \(0.560886\pi\)
\(338\) 30.4165 1.65444
\(339\) −4.13501 −0.224583
\(340\) −43.7574 −2.37308
\(341\) 37.4174 2.02627
\(342\) −0.491138 −0.0265577
\(343\) 2.37525 0.128251
\(344\) −24.2140 −1.30553
\(345\) −5.26404 −0.283406
\(346\) 27.1323 1.45864
\(347\) 23.6906 1.27178 0.635889 0.771780i \(-0.280634\pi\)
0.635889 + 0.771780i \(0.280634\pi\)
\(348\) −2.97994 −0.159741
\(349\) −1.00000 −0.0535288
\(350\) −21.4141 −1.14463
\(351\) 4.96662 0.265099
\(352\) −60.3172 −3.21492
\(353\) 5.25241 0.279557 0.139779 0.990183i \(-0.455361\pi\)
0.139779 + 0.990183i \(0.455361\pi\)
\(354\) 8.21791 0.436777
\(355\) −1.66616 −0.0884307
\(356\) 5.53171 0.293180
\(357\) 25.2086 1.33418
\(358\) −16.9811 −0.897478
\(359\) 23.8299 1.25769 0.628846 0.777530i \(-0.283528\pi\)
0.628846 + 0.777530i \(0.283528\pi\)
\(360\) 18.0001 0.948691
\(361\) −18.9554 −0.997652
\(362\) 19.0355 1.00049
\(363\) 31.9329 1.67604
\(364\) −22.3189 −1.16983
\(365\) −13.7036 −0.717280
\(366\) −47.7403 −2.49542
\(367\) 9.82660 0.512945 0.256472 0.966552i \(-0.417440\pi\)
0.256472 + 0.966552i \(0.417440\pi\)
\(368\) 10.2008 0.531754
\(369\) −4.69481 −0.244402
\(370\) −36.7838 −1.91230
\(371\) 6.53988 0.339534
\(372\) 69.2763 3.59181
\(373\) −12.3097 −0.637374 −0.318687 0.947860i \(-0.603242\pi\)
−0.318687 + 0.947860i \(0.603242\pi\)
\(374\) −45.8169 −2.36914
\(375\) 15.0964 0.779573
\(376\) −2.74539 −0.141583
\(377\) 0.367703 0.0189376
\(378\) 41.8649 2.15330
\(379\) 9.94465 0.510823 0.255411 0.966832i \(-0.417789\pi\)
0.255411 + 0.966832i \(0.417789\pi\)
\(380\) −2.76352 −0.141766
\(381\) 22.1266 1.13358
\(382\) 66.7900 3.41728
\(383\) −1.26617 −0.0646984 −0.0323492 0.999477i \(-0.510299\pi\)
−0.0323492 + 0.999477i \(0.510299\pi\)
\(384\) −6.05060 −0.308768
\(385\) −53.2588 −2.71432
\(386\) −22.9146 −1.16632
\(387\) 2.81523 0.143106
\(388\) 33.5220 1.70182
\(389\) 14.9957 0.760313 0.380157 0.924922i \(-0.375870\pi\)
0.380157 + 0.924922i \(0.375870\pi\)
\(390\) −16.4739 −0.834188
\(391\) 3.34464 0.169146
\(392\) −58.0271 −2.93081
\(393\) −14.9442 −0.753834
\(394\) 23.9801 1.20810
\(395\) −22.5125 −1.13273
\(396\) 22.6171 1.13655
\(397\) −32.2714 −1.61966 −0.809828 0.586668i \(-0.800439\pi\)
−0.809828 + 0.586668i \(0.800439\pi\)
\(398\) 0.00443218 0.000222165 0
\(399\) 1.59206 0.0797027
\(400\) 21.7499 1.08749
\(401\) 5.94362 0.296810 0.148405 0.988927i \(-0.452586\pi\)
0.148405 + 0.988927i \(0.452586\pi\)
\(402\) −48.0047 −2.39426
\(403\) −8.54819 −0.425816
\(404\) −55.6033 −2.76637
\(405\) 29.0351 1.44276
\(406\) 3.09946 0.153823
\(407\) −27.3493 −1.35566
\(408\) −50.1957 −2.48506
\(409\) −25.7643 −1.27396 −0.636981 0.770879i \(-0.719817\pi\)
−0.636981 + 0.770879i \(0.719817\pi\)
\(410\) −37.2015 −1.83725
\(411\) 16.9921 0.838158
\(412\) 70.6310 3.47974
\(413\) −6.06955 −0.298663
\(414\) −2.32511 −0.114273
\(415\) 39.1707 1.92282
\(416\) 13.7798 0.675609
\(417\) −20.7761 −1.01741
\(418\) −2.89359 −0.141530
\(419\) −28.8829 −1.41102 −0.705512 0.708698i \(-0.749283\pi\)
−0.705512 + 0.708698i \(0.749283\pi\)
\(420\) −98.6057 −4.81147
\(421\) −16.7846 −0.818033 −0.409017 0.912527i \(-0.634128\pi\)
−0.409017 + 0.912527i \(0.634128\pi\)
\(422\) −71.2522 −3.46850
\(423\) 0.319191 0.0155196
\(424\) −13.0223 −0.632418
\(425\) 7.13135 0.345921
\(426\) −3.23000 −0.156494
\(427\) 35.2598 1.70634
\(428\) 65.3646 3.15951
\(429\) −12.2486 −0.591369
\(430\) 22.3078 1.07578
\(431\) 30.7285 1.48014 0.740070 0.672529i \(-0.234792\pi\)
0.740070 + 0.672529i \(0.234792\pi\)
\(432\) −42.5212 −2.04580
\(433\) −16.7548 −0.805185 −0.402592 0.915379i \(-0.631891\pi\)
−0.402592 + 0.915379i \(0.631891\pi\)
\(434\) −72.0548 −3.45874
\(435\) 1.62452 0.0778900
\(436\) 63.0330 3.01873
\(437\) 0.211232 0.0101046
\(438\) −26.5656 −1.26936
\(439\) −4.81310 −0.229717 −0.114858 0.993382i \(-0.536641\pi\)
−0.114858 + 0.993382i \(0.536641\pi\)
\(440\) 106.050 5.05571
\(441\) 6.74650 0.321262
\(442\) 10.4671 0.497869
\(443\) 23.9624 1.13849 0.569245 0.822168i \(-0.307236\pi\)
0.569245 + 0.822168i \(0.307236\pi\)
\(444\) −50.6358 −2.40307
\(445\) −3.01563 −0.142955
\(446\) 69.1352 3.27364
\(447\) 13.7715 0.651368
\(448\) 38.1422 1.80205
\(449\) −3.52890 −0.166539 −0.0832695 0.996527i \(-0.526536\pi\)
−0.0832695 + 0.996527i \(0.526536\pi\)
\(450\) −4.95753 −0.233700
\(451\) −27.6600 −1.30246
\(452\) −10.2769 −0.483382
\(453\) −34.5455 −1.62309
\(454\) −23.4481 −1.10047
\(455\) 12.1672 0.570409
\(456\) −3.17013 −0.148455
\(457\) −8.14747 −0.381123 −0.190561 0.981675i \(-0.561031\pi\)
−0.190561 + 0.981675i \(0.561031\pi\)
\(458\) 15.0001 0.700911
\(459\) −13.9419 −0.650751
\(460\) −13.0829 −0.609991
\(461\) −9.54569 −0.444587 −0.222293 0.974980i \(-0.571354\pi\)
−0.222293 + 0.974980i \(0.571354\pi\)
\(462\) −103.247 −4.80347
\(463\) −20.1439 −0.936167 −0.468084 0.883684i \(-0.655055\pi\)
−0.468084 + 0.883684i \(0.655055\pi\)
\(464\) −3.14805 −0.146145
\(465\) −37.7662 −1.75137
\(466\) 40.6417 1.88269
\(467\) −21.8444 −1.01084 −0.505419 0.862874i \(-0.668662\pi\)
−0.505419 + 0.862874i \(0.668662\pi\)
\(468\) −5.16699 −0.238844
\(469\) 35.4551 1.63717
\(470\) 2.52926 0.116666
\(471\) 10.7534 0.495490
\(472\) 12.0858 0.556293
\(473\) 16.5862 0.762634
\(474\) −43.6424 −2.00456
\(475\) 0.450383 0.0206650
\(476\) 62.6516 2.87163
\(477\) 1.51403 0.0693227
\(478\) −34.1424 −1.56164
\(479\) 11.2558 0.514291 0.257146 0.966373i \(-0.417218\pi\)
0.257146 + 0.966373i \(0.417218\pi\)
\(480\) 60.8796 2.77876
\(481\) 6.24809 0.284889
\(482\) −22.9623 −1.04591
\(483\) 7.53702 0.342946
\(484\) 79.3637 3.60744
\(485\) −18.2747 −0.829810
\(486\) 23.4411 1.06331
\(487\) −3.66963 −0.166287 −0.0831435 0.996538i \(-0.526496\pi\)
−0.0831435 + 0.996538i \(0.526496\pi\)
\(488\) −70.2098 −3.17825
\(489\) 12.4063 0.561031
\(490\) 53.4590 2.41503
\(491\) 2.64609 0.119416 0.0597081 0.998216i \(-0.480983\pi\)
0.0597081 + 0.998216i \(0.480983\pi\)
\(492\) −51.2109 −2.30877
\(493\) −1.03218 −0.0464872
\(494\) 0.661054 0.0297422
\(495\) −12.3298 −0.554183
\(496\) 73.1845 3.28608
\(497\) 2.38560 0.107009
\(498\) 75.9358 3.40276
\(499\) −15.3025 −0.685036 −0.342518 0.939511i \(-0.611280\pi\)
−0.342518 + 0.939511i \(0.611280\pi\)
\(500\) 37.5194 1.67792
\(501\) −48.0286 −2.14576
\(502\) 40.9584 1.82806
\(503\) −17.3798 −0.774927 −0.387463 0.921885i \(-0.626649\pi\)
−0.387463 + 0.921885i \(0.626649\pi\)
\(504\) −25.7725 −1.14800
\(505\) 30.3124 1.34888
\(506\) −13.6986 −0.608977
\(507\) −22.8260 −1.01374
\(508\) 54.9917 2.43986
\(509\) −7.92802 −0.351403 −0.175702 0.984443i \(-0.556219\pi\)
−0.175702 + 0.984443i \(0.556219\pi\)
\(510\) 46.2441 2.04772
\(511\) 19.6208 0.867971
\(512\) 37.3623 1.65120
\(513\) −0.880504 −0.0388752
\(514\) 24.3505 1.07405
\(515\) −38.5048 −1.69672
\(516\) 30.7084 1.35186
\(517\) 1.88055 0.0827063
\(518\) 52.6668 2.31404
\(519\) −20.3614 −0.893767
\(520\) −24.2275 −1.06245
\(521\) −1.62464 −0.0711766 −0.0355883 0.999367i \(-0.511330\pi\)
−0.0355883 + 0.999367i \(0.511330\pi\)
\(522\) 0.717547 0.0314062
\(523\) 34.5033 1.50873 0.754363 0.656458i \(-0.227946\pi\)
0.754363 + 0.656458i \(0.227946\pi\)
\(524\) −37.1411 −1.62252
\(525\) 16.0702 0.701362
\(526\) −74.8256 −3.26255
\(527\) 23.9957 1.04527
\(528\) 104.865 4.56368
\(529\) 1.00000 0.0434783
\(530\) 11.9971 0.521121
\(531\) −1.40515 −0.0609782
\(532\) 3.95679 0.171549
\(533\) 6.31905 0.273709
\(534\) −5.84606 −0.252984
\(535\) −35.6338 −1.54058
\(536\) −70.5987 −3.04940
\(537\) 12.7434 0.549920
\(538\) −63.2164 −2.72545
\(539\) 39.7476 1.71205
\(540\) 54.5348 2.34681
\(541\) −5.15632 −0.221688 −0.110844 0.993838i \(-0.535355\pi\)
−0.110844 + 0.993838i \(0.535355\pi\)
\(542\) −54.3402 −2.33411
\(543\) −14.2852 −0.613036
\(544\) −38.6814 −1.65845
\(545\) −34.3627 −1.47194
\(546\) 23.5872 1.00944
\(547\) −15.2794 −0.653300 −0.326650 0.945145i \(-0.605920\pi\)
−0.326650 + 0.945145i \(0.605920\pi\)
\(548\) 42.2309 1.80401
\(549\) 8.16291 0.348385
\(550\) −29.2078 −1.24542
\(551\) −0.0651879 −0.00277710
\(552\) −15.0078 −0.638775
\(553\) 32.2333 1.37070
\(554\) −51.0576 −2.16923
\(555\) 27.6043 1.17174
\(556\) −51.6354 −2.18983
\(557\) 3.50118 0.148350 0.0741748 0.997245i \(-0.476368\pi\)
0.0741748 + 0.997245i \(0.476368\pi\)
\(558\) −16.6812 −0.706173
\(559\) −3.78920 −0.160266
\(560\) −104.169 −4.40192
\(561\) 34.3832 1.45166
\(562\) −21.6266 −0.912264
\(563\) 7.87967 0.332088 0.166044 0.986118i \(-0.446901\pi\)
0.166044 + 0.986118i \(0.446901\pi\)
\(564\) 3.48173 0.146607
\(565\) 5.60247 0.235698
\(566\) 33.4539 1.40617
\(567\) −41.5722 −1.74587
\(568\) −4.75024 −0.199316
\(569\) −22.8374 −0.957392 −0.478696 0.877981i \(-0.658890\pi\)
−0.478696 + 0.877981i \(0.658890\pi\)
\(570\) 2.92056 0.122329
\(571\) 3.72806 0.156015 0.0780073 0.996953i \(-0.475144\pi\)
0.0780073 + 0.996953i \(0.475144\pi\)
\(572\) −30.4418 −1.27284
\(573\) −50.1225 −2.09390
\(574\) 53.2649 2.22323
\(575\) 2.13217 0.0889177
\(576\) 8.83019 0.367925
\(577\) 15.1812 0.632003 0.316001 0.948759i \(-0.397660\pi\)
0.316001 + 0.948759i \(0.397660\pi\)
\(578\) 15.2692 0.635114
\(579\) 17.1962 0.714651
\(580\) 4.03747 0.167647
\(581\) −56.0844 −2.32677
\(582\) −35.4270 −1.46850
\(583\) 8.92005 0.369431
\(584\) −39.0691 −1.61669
\(585\) 2.81680 0.116461
\(586\) −44.5849 −1.84179
\(587\) 18.1931 0.750910 0.375455 0.926841i \(-0.377486\pi\)
0.375455 + 0.926841i \(0.377486\pi\)
\(588\) 73.5906 3.03482
\(589\) 1.51546 0.0624434
\(590\) −11.1343 −0.458393
\(591\) −17.9958 −0.740248
\(592\) −53.4924 −2.19853
\(593\) −10.7388 −0.440991 −0.220495 0.975388i \(-0.570767\pi\)
−0.220495 + 0.975388i \(0.570767\pi\)
\(594\) 57.1016 2.34291
\(595\) −34.1548 −1.40021
\(596\) 34.2266 1.40198
\(597\) −0.00332612 −0.000136129 0
\(598\) 3.12952 0.127975
\(599\) −36.0450 −1.47276 −0.736379 0.676569i \(-0.763466\pi\)
−0.736379 + 0.676569i \(0.763466\pi\)
\(600\) −31.9992 −1.30636
\(601\) 9.47037 0.386305 0.193152 0.981169i \(-0.438129\pi\)
0.193152 + 0.981169i \(0.438129\pi\)
\(602\) −31.9401 −1.30178
\(603\) 8.20813 0.334261
\(604\) −85.8568 −3.49346
\(605\) −43.2655 −1.75899
\(606\) 58.7631 2.38709
\(607\) −35.7278 −1.45015 −0.725074 0.688671i \(-0.758194\pi\)
−0.725074 + 0.688671i \(0.758194\pi\)
\(608\) −2.44294 −0.0990742
\(609\) −2.32598 −0.0942536
\(610\) 64.6826 2.61892
\(611\) −0.429620 −0.0173806
\(612\) 14.5043 0.586302
\(613\) 44.2471 1.78713 0.893563 0.448938i \(-0.148198\pi\)
0.893563 + 0.448938i \(0.148198\pi\)
\(614\) −13.9671 −0.563667
\(615\) 27.9178 1.12576
\(616\) −151.841 −6.11785
\(617\) −28.1225 −1.13217 −0.566084 0.824348i \(-0.691542\pi\)
−0.566084 + 0.824348i \(0.691542\pi\)
\(618\) −74.6448 −3.00266
\(619\) 38.0722 1.53025 0.765126 0.643881i \(-0.222677\pi\)
0.765126 + 0.643881i \(0.222677\pi\)
\(620\) −93.8614 −3.76956
\(621\) −4.16842 −0.167273
\(622\) 34.1743 1.37026
\(623\) 4.31776 0.172988
\(624\) −23.9570 −0.959048
\(625\) −31.1147 −1.24459
\(626\) −51.7338 −2.06770
\(627\) 2.17149 0.0867209
\(628\) 26.7257 1.06647
\(629\) −17.5391 −0.699330
\(630\) 23.7436 0.945966
\(631\) 37.1951 1.48071 0.740356 0.672215i \(-0.234657\pi\)
0.740356 + 0.672215i \(0.234657\pi\)
\(632\) −64.1833 −2.55308
\(633\) 53.4711 2.12529
\(634\) −70.3100 −2.79236
\(635\) −29.9790 −1.18968
\(636\) 16.5150 0.654862
\(637\) −9.08054 −0.359784
\(638\) 4.22750 0.167368
\(639\) 0.552284 0.0218480
\(640\) 8.19787 0.324049
\(641\) 25.8934 1.02273 0.511363 0.859365i \(-0.329141\pi\)
0.511363 + 0.859365i \(0.329141\pi\)
\(642\) −69.0791 −2.72633
\(643\) −18.7412 −0.739080 −0.369540 0.929215i \(-0.620485\pi\)
−0.369540 + 0.929215i \(0.620485\pi\)
\(644\) 18.7319 0.738142
\(645\) −16.7408 −0.659169
\(646\) −1.85565 −0.0730097
\(647\) 17.8529 0.701871 0.350936 0.936400i \(-0.385864\pi\)
0.350936 + 0.936400i \(0.385864\pi\)
\(648\) 82.7791 3.25187
\(649\) −8.27856 −0.324962
\(650\) 6.67266 0.261723
\(651\) 54.0735 2.11931
\(652\) 30.8336 1.20754
\(653\) −1.36185 −0.0532935 −0.0266467 0.999645i \(-0.508483\pi\)
−0.0266467 + 0.999645i \(0.508483\pi\)
\(654\) −66.6151 −2.60485
\(655\) 20.2476 0.791141
\(656\) −54.0999 −2.11225
\(657\) 4.54235 0.177214
\(658\) −3.62137 −0.141176
\(659\) 18.6674 0.727180 0.363590 0.931559i \(-0.381551\pi\)
0.363590 + 0.931559i \(0.381551\pi\)
\(660\) −134.493 −5.23514
\(661\) 3.60224 0.140111 0.0700555 0.997543i \(-0.477682\pi\)
0.0700555 + 0.997543i \(0.477682\pi\)
\(662\) −22.9358 −0.891423
\(663\) −7.85502 −0.305064
\(664\) 111.676 4.33387
\(665\) −2.15706 −0.0836472
\(666\) 12.1927 0.472459
\(667\) −0.308608 −0.0119493
\(668\) −119.367 −4.61844
\(669\) −51.8824 −2.00589
\(670\) 65.0409 2.51275
\(671\) 48.0926 1.85659
\(672\) −87.1669 −3.36254
\(673\) −29.0556 −1.12001 −0.560006 0.828488i \(-0.689201\pi\)
−0.560006 + 0.828488i \(0.689201\pi\)
\(674\) 18.3337 0.706189
\(675\) −8.88779 −0.342091
\(676\) −56.7301 −2.18193
\(677\) 19.6160 0.753903 0.376951 0.926233i \(-0.376972\pi\)
0.376951 + 0.926233i \(0.376972\pi\)
\(678\) 10.8609 0.417109
\(679\) 26.1655 1.00414
\(680\) 68.0094 2.60804
\(681\) 17.5966 0.674303
\(682\) −98.2791 −3.76330
\(683\) 13.3497 0.510811 0.255406 0.966834i \(-0.417791\pi\)
0.255406 + 0.966834i \(0.417791\pi\)
\(684\) 0.916026 0.0350251
\(685\) −23.0223 −0.879638
\(686\) −6.23874 −0.238196
\(687\) −11.2568 −0.429475
\(688\) 32.4408 1.23680
\(689\) −2.03783 −0.0776352
\(690\) 13.8263 0.526359
\(691\) −4.16491 −0.158441 −0.0792204 0.996857i \(-0.525243\pi\)
−0.0792204 + 0.996857i \(0.525243\pi\)
\(692\) −50.6047 −1.92370
\(693\) 17.6537 0.670610
\(694\) −62.2248 −2.36202
\(695\) 28.1493 1.06776
\(696\) 4.63153 0.175558
\(697\) −17.7383 −0.671886
\(698\) 2.62656 0.0994168
\(699\) −30.4995 −1.15360
\(700\) 39.9397 1.50958
\(701\) −5.26640 −0.198909 −0.0994546 0.995042i \(-0.531710\pi\)
−0.0994546 + 0.995042i \(0.531710\pi\)
\(702\) −13.0451 −0.492357
\(703\) −1.10769 −0.0417773
\(704\) 52.0239 1.96073
\(705\) −1.89808 −0.0714857
\(706\) −13.7958 −0.519210
\(707\) −43.4010 −1.63226
\(708\) −15.3273 −0.576035
\(709\) 41.7214 1.56688 0.783439 0.621469i \(-0.213464\pi\)
0.783439 + 0.621469i \(0.213464\pi\)
\(710\) 4.37628 0.164239
\(711\) 7.46224 0.279856
\(712\) −8.59758 −0.322208
\(713\) 7.17438 0.268683
\(714\) −66.2120 −2.47792
\(715\) 16.5955 0.620635
\(716\) 31.6716 1.18362
\(717\) 25.6221 0.956875
\(718\) −62.5906 −2.33586
\(719\) −27.8433 −1.03838 −0.519190 0.854659i \(-0.673766\pi\)
−0.519190 + 0.854659i \(0.673766\pi\)
\(720\) −24.1158 −0.898742
\(721\) 55.1309 2.05318
\(722\) 49.7875 1.85290
\(723\) 17.2321 0.640867
\(724\) −35.5033 −1.31947
\(725\) −0.658005 −0.0244377
\(726\) −83.8738 −3.11285
\(727\) 31.8230 1.18025 0.590125 0.807312i \(-0.299079\pi\)
0.590125 + 0.807312i \(0.299079\pi\)
\(728\) 34.6888 1.28565
\(729\) 15.0248 0.556475
\(730\) 35.9934 1.33218
\(731\) 10.6367 0.393413
\(732\) 89.0408 3.29104
\(733\) 17.3711 0.641618 0.320809 0.947144i \(-0.396045\pi\)
0.320809 + 0.947144i \(0.396045\pi\)
\(734\) −25.8102 −0.952671
\(735\) −40.1182 −1.47978
\(736\) −11.5652 −0.426298
\(737\) 48.3590 1.78133
\(738\) 12.3312 0.453918
\(739\) −28.3829 −1.04408 −0.522040 0.852921i \(-0.674829\pi\)
−0.522040 + 0.852921i \(0.674829\pi\)
\(740\) 68.6057 2.52200
\(741\) −0.496087 −0.0182242
\(742\) −17.1774 −0.630602
\(743\) 38.5200 1.41316 0.706580 0.707633i \(-0.250237\pi\)
0.706580 + 0.707633i \(0.250237\pi\)
\(744\) −107.672 −3.94744
\(745\) −18.6588 −0.683604
\(746\) 32.3323 1.18377
\(747\) −12.9839 −0.475058
\(748\) 85.4536 3.12449
\(749\) 51.0202 1.86424
\(750\) −39.6515 −1.44787
\(751\) −4.04389 −0.147564 −0.0737819 0.997274i \(-0.523507\pi\)
−0.0737819 + 0.997274i \(0.523507\pi\)
\(752\) 3.67815 0.134128
\(753\) −30.7371 −1.12012
\(754\) −0.965793 −0.0351721
\(755\) 46.8052 1.70342
\(756\) −78.0826 −2.83984
\(757\) 27.9758 1.01680 0.508398 0.861122i \(-0.330238\pi\)
0.508398 + 0.861122i \(0.330238\pi\)
\(758\) −26.1202 −0.948730
\(759\) 10.2801 0.373144
\(760\) 4.29516 0.155802
\(761\) 2.95489 0.107115 0.0535573 0.998565i \(-0.482944\pi\)
0.0535573 + 0.998565i \(0.482944\pi\)
\(762\) −58.1168 −2.10535
\(763\) 49.2003 1.78117
\(764\) −124.571 −4.50681
\(765\) −7.90709 −0.285881
\(766\) 3.32568 0.120162
\(767\) 1.89128 0.0682901
\(768\) −23.4313 −0.845503
\(769\) −17.0170 −0.613648 −0.306824 0.951766i \(-0.599266\pi\)
−0.306824 + 0.951766i \(0.599266\pi\)
\(770\) 139.887 5.04119
\(771\) −18.2738 −0.658113
\(772\) 42.7382 1.53818
\(773\) −21.0966 −0.758794 −0.379397 0.925234i \(-0.623868\pi\)
−0.379397 + 0.925234i \(0.623868\pi\)
\(774\) −7.39437 −0.265785
\(775\) 15.2970 0.549485
\(776\) −52.1012 −1.87032
\(777\) −39.5237 −1.41790
\(778\) −39.3872 −1.41210
\(779\) −1.12027 −0.0401378
\(780\) 30.7256 1.10015
\(781\) 3.25384 0.116431
\(782\) −8.78490 −0.314147
\(783\) 1.28641 0.0459724
\(784\) 77.7422 2.77651
\(785\) −14.5696 −0.520012
\(786\) 39.2518 1.40006
\(787\) 8.57364 0.305617 0.152809 0.988256i \(-0.451168\pi\)
0.152809 + 0.988256i \(0.451168\pi\)
\(788\) −44.7254 −1.59328
\(789\) 56.1527 1.99909
\(790\) 59.1305 2.10377
\(791\) −8.02158 −0.285214
\(792\) −35.1523 −1.24908
\(793\) −10.9870 −0.390159
\(794\) 84.7628 3.00812
\(795\) −9.00322 −0.319311
\(796\) −0.00826650 −0.000292998 0
\(797\) −6.31745 −0.223775 −0.111888 0.993721i \(-0.535690\pi\)
−0.111888 + 0.993721i \(0.535690\pi\)
\(798\) −4.18164 −0.148029
\(799\) 1.20599 0.0426649
\(800\) −24.6589 −0.871825
\(801\) 0.999594 0.0353189
\(802\) −15.6113 −0.551254
\(803\) 26.7617 0.944399
\(804\) 89.5340 3.15762
\(805\) −10.2118 −0.359918
\(806\) 22.4523 0.790850
\(807\) 47.4407 1.66999
\(808\) 86.4207 3.04027
\(809\) 19.4280 0.683051 0.341526 0.939872i \(-0.389056\pi\)
0.341526 + 0.939872i \(0.389056\pi\)
\(810\) −76.2623 −2.67959
\(811\) 43.0651 1.51222 0.756111 0.654444i \(-0.227097\pi\)
0.756111 + 0.654444i \(0.227097\pi\)
\(812\) −5.78082 −0.202867
\(813\) 40.7795 1.43020
\(814\) 71.8347 2.51781
\(815\) −16.8091 −0.588797
\(816\) 67.2500 2.35422
\(817\) 0.671765 0.0235021
\(818\) 67.6715 2.36608
\(819\) −4.03308 −0.140927
\(820\) 69.3849 2.42302
\(821\) 7.40859 0.258562 0.129281 0.991608i \(-0.458733\pi\)
0.129281 + 0.991608i \(0.458733\pi\)
\(822\) −44.6308 −1.55668
\(823\) 1.25403 0.0437129 0.0218564 0.999761i \(-0.493042\pi\)
0.0218564 + 0.999761i \(0.493042\pi\)
\(824\) −109.777 −3.82428
\(825\) 21.9189 0.763119
\(826\) 15.9420 0.554695
\(827\) 34.7288 1.20764 0.603819 0.797121i \(-0.293645\pi\)
0.603819 + 0.797121i \(0.293645\pi\)
\(828\) 4.33658 0.150707
\(829\) 41.2183 1.43157 0.715786 0.698320i \(-0.246069\pi\)
0.715786 + 0.698320i \(0.246069\pi\)
\(830\) −102.884 −3.57117
\(831\) 38.3161 1.32917
\(832\) −11.8851 −0.412042
\(833\) 25.4901 0.883180
\(834\) 54.5698 1.88960
\(835\) 65.0733 2.25195
\(836\) 5.39685 0.186654
\(837\) −29.9058 −1.03370
\(838\) 75.8628 2.62064
\(839\) 35.5481 1.22726 0.613628 0.789596i \(-0.289710\pi\)
0.613628 + 0.789596i \(0.289710\pi\)
\(840\) 153.257 5.28786
\(841\) −28.9048 −0.996716
\(842\) 44.0859 1.51930
\(843\) 16.2297 0.558979
\(844\) 132.893 4.57437
\(845\) 30.9266 1.06391
\(846\) −0.838375 −0.0288239
\(847\) 61.9472 2.12853
\(848\) 17.4467 0.599122
\(849\) −25.1054 −0.861615
\(850\) −18.7309 −0.642465
\(851\) −5.24394 −0.179760
\(852\) 6.02430 0.206389
\(853\) −28.5245 −0.976659 −0.488329 0.872659i \(-0.662394\pi\)
−0.488329 + 0.872659i \(0.662394\pi\)
\(854\) −92.6121 −3.16912
\(855\) −0.499375 −0.0170783
\(856\) −101.592 −3.47234
\(857\) 34.6553 1.18380 0.591900 0.806011i \(-0.298378\pi\)
0.591900 + 0.806011i \(0.298378\pi\)
\(858\) 32.1717 1.09832
\(859\) 24.9302 0.850607 0.425304 0.905051i \(-0.360167\pi\)
0.425304 + 0.905051i \(0.360167\pi\)
\(860\) −41.6064 −1.41877
\(861\) −39.9726 −1.36226
\(862\) −80.7103 −2.74900
\(863\) −26.2800 −0.894580 −0.447290 0.894389i \(-0.647611\pi\)
−0.447290 + 0.894389i \(0.647611\pi\)
\(864\) 48.2085 1.64009
\(865\) 27.5874 0.937999
\(866\) 44.0075 1.49544
\(867\) −11.4587 −0.389159
\(868\) 134.390 4.56150
\(869\) 43.9645 1.49139
\(870\) −4.26691 −0.144662
\(871\) −11.0478 −0.374342
\(872\) −97.9683 −3.31762
\(873\) 6.05752 0.205016
\(874\) −0.554814 −0.0187669
\(875\) 29.2857 0.990037
\(876\) 49.5478 1.67406
\(877\) −22.7884 −0.769508 −0.384754 0.923019i \(-0.625714\pi\)
−0.384754 + 0.923019i \(0.625714\pi\)
\(878\) 12.6419 0.426644
\(879\) 33.4587 1.12853
\(880\) −142.080 −4.78953
\(881\) −35.3506 −1.19099 −0.595497 0.803358i \(-0.703045\pi\)
−0.595497 + 0.803358i \(0.703045\pi\)
\(882\) −17.7201 −0.596666
\(883\) −25.3421 −0.852829 −0.426414 0.904528i \(-0.640223\pi\)
−0.426414 + 0.904528i \(0.640223\pi\)
\(884\) −19.5223 −0.656606
\(885\) 8.35574 0.280875
\(886\) −62.9388 −2.11447
\(887\) −7.49068 −0.251512 −0.125756 0.992061i \(-0.540136\pi\)
−0.125756 + 0.992061i \(0.540136\pi\)
\(888\) 78.7001 2.64100
\(889\) 42.9237 1.43961
\(890\) 7.92074 0.265504
\(891\) −56.7023 −1.89960
\(892\) −128.945 −4.31738
\(893\) 0.0761649 0.00254876
\(894\) −36.1716 −1.20976
\(895\) −17.2659 −0.577135
\(896\) −11.7377 −0.392127
\(897\) −2.34854 −0.0784155
\(898\) 9.26887 0.309306
\(899\) −2.21407 −0.0738434
\(900\) 9.24634 0.308211
\(901\) 5.72042 0.190575
\(902\) 72.6505 2.41900
\(903\) 23.9694 0.797652
\(904\) 15.9727 0.531243
\(905\) 19.3548 0.643375
\(906\) 90.7359 3.01450
\(907\) 51.0827 1.69617 0.848087 0.529856i \(-0.177754\pi\)
0.848087 + 0.529856i \(0.177754\pi\)
\(908\) 43.7333 1.45134
\(909\) −10.0477 −0.333260
\(910\) −31.9580 −1.05940
\(911\) 26.5780 0.880568 0.440284 0.897859i \(-0.354878\pi\)
0.440284 + 0.897859i \(0.354878\pi\)
\(912\) 4.24720 0.140639
\(913\) −76.4962 −2.53165
\(914\) 21.3998 0.707843
\(915\) −48.5409 −1.60471
\(916\) −27.9769 −0.924383
\(917\) −28.9904 −0.957348
\(918\) 36.6192 1.20861
\(919\) 22.1758 0.731512 0.365756 0.930711i \(-0.380810\pi\)
0.365756 + 0.930711i \(0.380810\pi\)
\(920\) 20.3339 0.670387
\(921\) 10.4816 0.345380
\(922\) 25.0723 0.825713
\(923\) −0.743355 −0.0244678
\(924\) 192.566 6.33497
\(925\) −11.1810 −0.367628
\(926\) 52.9092 1.73871
\(927\) 12.7632 0.419199
\(928\) 3.56910 0.117162
\(929\) −2.16222 −0.0709401 −0.0354701 0.999371i \(-0.511293\pi\)
−0.0354701 + 0.999371i \(0.511293\pi\)
\(930\) 99.1953 3.25274
\(931\) 1.60984 0.0527603
\(932\) −75.8011 −2.48295
\(933\) −25.6461 −0.839614
\(934\) 57.3756 1.87739
\(935\) −46.5854 −1.52350
\(936\) 8.03072 0.262492
\(937\) 16.4794 0.538360 0.269180 0.963090i \(-0.413247\pi\)
0.269180 + 0.963090i \(0.413247\pi\)
\(938\) −93.1251 −3.04064
\(939\) 38.8235 1.26696
\(940\) −4.71734 −0.153863
\(941\) −31.5114 −1.02724 −0.513620 0.858018i \(-0.671696\pi\)
−0.513620 + 0.858018i \(0.671696\pi\)
\(942\) −28.2444 −0.920254
\(943\) −5.30350 −0.172706
\(944\) −16.1920 −0.527004
\(945\) 42.5671 1.38471
\(946\) −43.5646 −1.41641
\(947\) 49.0380 1.59352 0.796760 0.604296i \(-0.206545\pi\)
0.796760 + 0.604296i \(0.206545\pi\)
\(948\) 81.3979 2.64368
\(949\) −6.11384 −0.198464
\(950\) −1.18296 −0.0383802
\(951\) 52.7640 1.71099
\(952\) −97.3755 −3.15596
\(953\) −58.0513 −1.88047 −0.940234 0.340530i \(-0.889394\pi\)
−0.940234 + 0.340530i \(0.889394\pi\)
\(954\) −3.97669 −0.128750
\(955\) 67.9102 2.19752
\(956\) 63.6792 2.05953
\(957\) −3.17252 −0.102553
\(958\) −29.5641 −0.955172
\(959\) 32.9632 1.06444
\(960\) −52.5089 −1.69472
\(961\) 20.4718 0.660380
\(962\) −16.4110 −0.529112
\(963\) 11.8115 0.380622
\(964\) 42.8273 1.37937
\(965\) −23.2989 −0.750018
\(966\) −19.7964 −0.636940
\(967\) 41.9562 1.34922 0.674610 0.738174i \(-0.264312\pi\)
0.674610 + 0.738174i \(0.264312\pi\)
\(968\) −123.350 −3.96462
\(969\) 1.39257 0.0447359
\(970\) 47.9995 1.54117
\(971\) −57.2201 −1.83628 −0.918141 0.396254i \(-0.870310\pi\)
−0.918141 + 0.396254i \(0.870310\pi\)
\(972\) −43.7202 −1.40233
\(973\) −40.3039 −1.29208
\(974\) 9.63852 0.308838
\(975\) −5.00749 −0.160368
\(976\) 94.0640 3.01091
\(977\) 14.4731 0.463034 0.231517 0.972831i \(-0.425631\pi\)
0.231517 + 0.972831i \(0.425631\pi\)
\(978\) −32.5859 −1.04198
\(979\) 5.88920 0.188220
\(980\) −99.7068 −3.18502
\(981\) 11.3902 0.363662
\(982\) −6.95011 −0.221787
\(983\) 61.0151 1.94608 0.973039 0.230639i \(-0.0740818\pi\)
0.973039 + 0.230639i \(0.0740818\pi\)
\(984\) 79.5939 2.53736
\(985\) 24.3822 0.776883
\(986\) 2.71109 0.0863387
\(987\) 2.71765 0.0865039
\(988\) −1.23294 −0.0392250
\(989\) 3.18022 0.101125
\(990\) 32.3850 1.02926
\(991\) −15.7813 −0.501308 −0.250654 0.968077i \(-0.580646\pi\)
−0.250654 + 0.968077i \(0.580646\pi\)
\(992\) −82.9730 −2.63440
\(993\) 17.2121 0.546210
\(994\) −6.26593 −0.198743
\(995\) 0.00450652 0.000142866 0
\(996\) −141.628 −4.48767
\(997\) 0.171832 0.00544199 0.00272099 0.999996i \(-0.499134\pi\)
0.00272099 + 0.999996i \(0.499134\pi\)
\(998\) 40.1931 1.27229
\(999\) 21.8590 0.691587
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 \(a_p\))