Properties

Label 6017.2.a.c.1.16
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18387 q^{2} +1.05356 q^{3} +2.76930 q^{4} +1.41364 q^{5} -2.30083 q^{6} +4.87614 q^{7} -1.68005 q^{8} -1.89002 q^{9} +O(q^{10})\) \(q-2.18387 q^{2} +1.05356 q^{3} +2.76930 q^{4} +1.41364 q^{5} -2.30083 q^{6} +4.87614 q^{7} -1.68005 q^{8} -1.89002 q^{9} -3.08721 q^{10} +1.00000 q^{11} +2.91761 q^{12} +0.501016 q^{13} -10.6489 q^{14} +1.48935 q^{15} -1.86958 q^{16} -3.80935 q^{17} +4.12757 q^{18} -4.19367 q^{19} +3.91479 q^{20} +5.13728 q^{21} -2.18387 q^{22} -1.04856 q^{23} -1.77003 q^{24} -3.00163 q^{25} -1.09415 q^{26} -5.15191 q^{27} +13.5035 q^{28} +2.50838 q^{29} -3.25254 q^{30} -8.96340 q^{31} +7.44303 q^{32} +1.05356 q^{33} +8.31913 q^{34} +6.89309 q^{35} -5.23404 q^{36} +6.21728 q^{37} +9.15843 q^{38} +0.527848 q^{39} -2.37499 q^{40} +1.36683 q^{41} -11.2192 q^{42} -10.2419 q^{43} +2.76930 q^{44} -2.67181 q^{45} +2.28992 q^{46} -10.8797 q^{47} -1.96970 q^{48} +16.7767 q^{49} +6.55517 q^{50} -4.01336 q^{51} +1.38746 q^{52} +3.99296 q^{53} +11.2511 q^{54} +1.41364 q^{55} -8.19218 q^{56} -4.41826 q^{57} -5.47798 q^{58} -9.49024 q^{59} +4.12445 q^{60} -5.30877 q^{61} +19.5749 q^{62} -9.21600 q^{63} -12.5155 q^{64} +0.708255 q^{65} -2.30083 q^{66} -2.25286 q^{67} -10.5492 q^{68} -1.10471 q^{69} -15.0536 q^{70} -8.38292 q^{71} +3.17534 q^{72} +8.49245 q^{73} -13.5777 q^{74} -3.16238 q^{75} -11.6135 q^{76} +4.87614 q^{77} -1.15275 q^{78} -15.2896 q^{79} -2.64290 q^{80} +0.242242 q^{81} -2.98498 q^{82} -1.37370 q^{83} +14.2267 q^{84} -5.38503 q^{85} +22.3670 q^{86} +2.64272 q^{87} -1.68005 q^{88} +1.35696 q^{89} +5.83488 q^{90} +2.44302 q^{91} -2.90377 q^{92} -9.44344 q^{93} +23.7599 q^{94} -5.92832 q^{95} +7.84164 q^{96} -12.7861 q^{97} -36.6382 q^{98} -1.89002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 106q - 13q^{2} - 15q^{3} + 93q^{4} - 12q^{5} - 22q^{6} - 66q^{7} - 39q^{8} + 97q^{9} + O(q^{10}) \) \( 106q - 13q^{2} - 15q^{3} + 93q^{4} - 12q^{5} - 22q^{6} - 66q^{7} - 39q^{8} + 97q^{9} - 30q^{10} + 106q^{11} - 26q^{12} - 72q^{13} + 3q^{14} - 46q^{15} + 75q^{16} - 65q^{17} - 37q^{18} - 63q^{19} - 25q^{20} - 27q^{21} - 13q^{22} - 23q^{23} - 56q^{24} + 74q^{25} + 2q^{26} - 54q^{27} - 115q^{28} - 45q^{29} - 14q^{30} - 89q^{31} - 96q^{32} - 15q^{33} - 26q^{34} - 52q^{35} + 91q^{36} - 35q^{37} + 7q^{38} - 34q^{39} - 74q^{40} - 32q^{41} - 94q^{43} + 93q^{44} - 46q^{45} - 20q^{46} - 105q^{47} - 57q^{48} + 80q^{49} - 60q^{50} - 36q^{51} - 137q^{52} - 61q^{54} - 12q^{55} + 32q^{56} - 71q^{57} - 28q^{58} - 15q^{59} - 21q^{60} - 80q^{61} - 84q^{62} - 182q^{63} + 55q^{64} - 73q^{65} - 22q^{66} - 58q^{67} - 145q^{68} - 8q^{69} - 39q^{70} - 11q^{71} - 100q^{72} - 155q^{73} - 15q^{74} - 15q^{75} - 132q^{76} - 66q^{77} - 45q^{78} - 50q^{79} - 28q^{80} + 114q^{81} - 57q^{82} - 96q^{83} - 27q^{84} - 74q^{85} + 54q^{86} - 182q^{87} - 39q^{88} + 9q^{89} - 53q^{90} + 6q^{91} - 18q^{92} - 26q^{93} - 33q^{94} - 49q^{95} - 56q^{96} - 102q^{97} - 76q^{98} + 97q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18387 −1.54423 −0.772116 0.635482i \(-0.780801\pi\)
−0.772116 + 0.635482i \(0.780801\pi\)
\(3\) 1.05356 0.608271 0.304135 0.952629i \(-0.401633\pi\)
0.304135 + 0.952629i \(0.401633\pi\)
\(4\) 2.76930 1.38465
\(5\) 1.41364 0.632198 0.316099 0.948726i \(-0.397627\pi\)
0.316099 + 0.948726i \(0.397627\pi\)
\(6\) −2.30083 −0.939310
\(7\) 4.87614 1.84301 0.921504 0.388370i \(-0.126962\pi\)
0.921504 + 0.388370i \(0.126962\pi\)
\(8\) −1.68005 −0.593989
\(9\) −1.89002 −0.630007
\(10\) −3.08721 −0.976260
\(11\) 1.00000 0.301511
\(12\) 2.91761 0.842242
\(13\) 0.501016 0.138957 0.0694784 0.997583i \(-0.477867\pi\)
0.0694784 + 0.997583i \(0.477867\pi\)
\(14\) −10.6489 −2.84603
\(15\) 1.48935 0.384547
\(16\) −1.86958 −0.467394
\(17\) −3.80935 −0.923902 −0.461951 0.886905i \(-0.652850\pi\)
−0.461951 + 0.886905i \(0.652850\pi\)
\(18\) 4.12757 0.972876
\(19\) −4.19367 −0.962093 −0.481046 0.876695i \(-0.659743\pi\)
−0.481046 + 0.876695i \(0.659743\pi\)
\(20\) 3.91479 0.875373
\(21\) 5.13728 1.12105
\(22\) −2.18387 −0.465603
\(23\) −1.04856 −0.218639 −0.109320 0.994007i \(-0.534867\pi\)
−0.109320 + 0.994007i \(0.534867\pi\)
\(24\) −1.77003 −0.361306
\(25\) −3.00163 −0.600326
\(26\) −1.09415 −0.214581
\(27\) −5.15191 −0.991485
\(28\) 13.5035 2.55192
\(29\) 2.50838 0.465795 0.232897 0.972501i \(-0.425179\pi\)
0.232897 + 0.972501i \(0.425179\pi\)
\(30\) −3.25254 −0.593830
\(31\) −8.96340 −1.60987 −0.804937 0.593361i \(-0.797801\pi\)
−0.804937 + 0.593361i \(0.797801\pi\)
\(32\) 7.44303 1.31575
\(33\) 1.05356 0.183400
\(34\) 8.31913 1.42672
\(35\) 6.89309 1.16515
\(36\) −5.23404 −0.872339
\(37\) 6.21728 1.02211 0.511057 0.859547i \(-0.329254\pi\)
0.511057 + 0.859547i \(0.329254\pi\)
\(38\) 9.15843 1.48569
\(39\) 0.527848 0.0845233
\(40\) −2.37499 −0.375519
\(41\) 1.36683 0.213463 0.106731 0.994288i \(-0.465961\pi\)
0.106731 + 0.994288i \(0.465961\pi\)
\(42\) −11.2192 −1.73116
\(43\) −10.2419 −1.56188 −0.780938 0.624608i \(-0.785259\pi\)
−0.780938 + 0.624608i \(0.785259\pi\)
\(44\) 2.76930 0.417488
\(45\) −2.67181 −0.398289
\(46\) 2.28992 0.337630
\(47\) −10.8797 −1.58697 −0.793483 0.608592i \(-0.791735\pi\)
−0.793483 + 0.608592i \(0.791735\pi\)
\(48\) −1.96970 −0.284302
\(49\) 16.7767 2.39668
\(50\) 6.55517 0.927042
\(51\) −4.01336 −0.561982
\(52\) 1.38746 0.192406
\(53\) 3.99296 0.548475 0.274238 0.961662i \(-0.411575\pi\)
0.274238 + 0.961662i \(0.411575\pi\)
\(54\) 11.2511 1.53108
\(55\) 1.41364 0.190615
\(56\) −8.19218 −1.09473
\(57\) −4.41826 −0.585213
\(58\) −5.47798 −0.719295
\(59\) −9.49024 −1.23552 −0.617762 0.786365i \(-0.711961\pi\)
−0.617762 + 0.786365i \(0.711961\pi\)
\(60\) 4.12445 0.532464
\(61\) −5.30877 −0.679718 −0.339859 0.940476i \(-0.610379\pi\)
−0.339859 + 0.940476i \(0.610379\pi\)
\(62\) 19.5749 2.48602
\(63\) −9.21600 −1.16111
\(64\) −12.5155 −1.56443
\(65\) 0.708255 0.0878482
\(66\) −2.30083 −0.283213
\(67\) −2.25286 −0.275230 −0.137615 0.990486i \(-0.543944\pi\)
−0.137615 + 0.990486i \(0.543944\pi\)
\(68\) −10.5492 −1.27928
\(69\) −1.10471 −0.132992
\(70\) −15.0536 −1.79925
\(71\) −8.38292 −0.994869 −0.497435 0.867502i \(-0.665725\pi\)
−0.497435 + 0.867502i \(0.665725\pi\)
\(72\) 3.17534 0.374217
\(73\) 8.49245 0.993966 0.496983 0.867760i \(-0.334441\pi\)
0.496983 + 0.867760i \(0.334441\pi\)
\(74\) −13.5777 −1.57838
\(75\) −3.16238 −0.365160
\(76\) −11.6135 −1.33216
\(77\) 4.87614 0.555688
\(78\) −1.15275 −0.130523
\(79\) −15.2896 −1.72022 −0.860109 0.510111i \(-0.829604\pi\)
−0.860109 + 0.510111i \(0.829604\pi\)
\(80\) −2.64290 −0.295486
\(81\) 0.242242 0.0269158
\(82\) −2.98498 −0.329636
\(83\) −1.37370 −0.150784 −0.0753918 0.997154i \(-0.524021\pi\)
−0.0753918 + 0.997154i \(0.524021\pi\)
\(84\) 14.2267 1.55226
\(85\) −5.38503 −0.584089
\(86\) 22.3670 2.41190
\(87\) 2.64272 0.283329
\(88\) −1.68005 −0.179094
\(89\) 1.35696 0.143838 0.0719189 0.997410i \(-0.477088\pi\)
0.0719189 + 0.997410i \(0.477088\pi\)
\(90\) 5.83488 0.615051
\(91\) 2.44302 0.256098
\(92\) −2.90377 −0.302739
\(93\) −9.44344 −0.979239
\(94\) 23.7599 2.45064
\(95\) −5.92832 −0.608233
\(96\) 7.84164 0.800334
\(97\) −12.7861 −1.29823 −0.649114 0.760691i \(-0.724860\pi\)
−0.649114 + 0.760691i \(0.724860\pi\)
\(98\) −36.6382 −3.70102
\(99\) −1.89002 −0.189954
\(100\) −8.31241 −0.831241
\(101\) −4.01323 −0.399332 −0.199666 0.979864i \(-0.563986\pi\)
−0.199666 + 0.979864i \(0.563986\pi\)
\(102\) 8.76466 0.867831
\(103\) 2.42773 0.239211 0.119606 0.992821i \(-0.461837\pi\)
0.119606 + 0.992821i \(0.461837\pi\)
\(104\) −0.841733 −0.0825387
\(105\) 7.26226 0.708724
\(106\) −8.72011 −0.846972
\(107\) 1.81293 0.175263 0.0876315 0.996153i \(-0.472070\pi\)
0.0876315 + 0.996153i \(0.472070\pi\)
\(108\) −14.2672 −1.37286
\(109\) −20.1301 −1.92812 −0.964059 0.265689i \(-0.914401\pi\)
−0.964059 + 0.265689i \(0.914401\pi\)
\(110\) −3.08721 −0.294353
\(111\) 6.55025 0.621722
\(112\) −9.11632 −0.861411
\(113\) 11.9530 1.12444 0.562222 0.826986i \(-0.309947\pi\)
0.562222 + 0.826986i \(0.309947\pi\)
\(114\) 9.64892 0.903704
\(115\) −1.48228 −0.138223
\(116\) 6.94646 0.644963
\(117\) −0.946930 −0.0875437
\(118\) 20.7255 1.90794
\(119\) −18.5749 −1.70276
\(120\) −2.50218 −0.228417
\(121\) 1.00000 0.0909091
\(122\) 11.5937 1.04964
\(123\) 1.44003 0.129843
\(124\) −24.8223 −2.22911
\(125\) −11.3114 −1.01172
\(126\) 20.1266 1.79302
\(127\) −10.5098 −0.932597 −0.466298 0.884627i \(-0.654413\pi\)
−0.466298 + 0.884627i \(0.654413\pi\)
\(128\) 12.4461 1.10009
\(129\) −10.7904 −0.950043
\(130\) −1.54674 −0.135658
\(131\) −2.43365 −0.212629 −0.106314 0.994333i \(-0.533905\pi\)
−0.106314 + 0.994333i \(0.533905\pi\)
\(132\) 2.91761 0.253945
\(133\) −20.4489 −1.77314
\(134\) 4.91995 0.425019
\(135\) −7.28293 −0.626815
\(136\) 6.39991 0.548787
\(137\) 18.7767 1.60420 0.802100 0.597190i \(-0.203716\pi\)
0.802100 + 0.597190i \(0.203716\pi\)
\(138\) 2.41256 0.205370
\(139\) −4.66596 −0.395761 −0.197881 0.980226i \(-0.563406\pi\)
−0.197881 + 0.980226i \(0.563406\pi\)
\(140\) 19.0890 1.61332
\(141\) −11.4624 −0.965305
\(142\) 18.3072 1.53631
\(143\) 0.501016 0.0418970
\(144\) 3.53354 0.294462
\(145\) 3.54594 0.294474
\(146\) −18.5464 −1.53491
\(147\) 17.6752 1.45783
\(148\) 17.2175 1.41527
\(149\) −5.42490 −0.444426 −0.222213 0.974998i \(-0.571328\pi\)
−0.222213 + 0.974998i \(0.571328\pi\)
\(150\) 6.90624 0.563892
\(151\) 3.47722 0.282972 0.141486 0.989940i \(-0.454812\pi\)
0.141486 + 0.989940i \(0.454812\pi\)
\(152\) 7.04558 0.571472
\(153\) 7.19974 0.582065
\(154\) −10.6489 −0.858110
\(155\) −12.6710 −1.01776
\(156\) 1.46177 0.117035
\(157\) 19.6087 1.56495 0.782474 0.622684i \(-0.213958\pi\)
0.782474 + 0.622684i \(0.213958\pi\)
\(158\) 33.3906 2.65641
\(159\) 4.20680 0.333621
\(160\) 10.5217 0.831817
\(161\) −5.11292 −0.402954
\(162\) −0.529025 −0.0415642
\(163\) −18.2826 −1.43200 −0.716002 0.698098i \(-0.754030\pi\)
−0.716002 + 0.698098i \(0.754030\pi\)
\(164\) 3.78516 0.295572
\(165\) 1.48935 0.115945
\(166\) 3.00000 0.232845
\(167\) 3.15255 0.243952 0.121976 0.992533i \(-0.461077\pi\)
0.121976 + 0.992533i \(0.461077\pi\)
\(168\) −8.63091 −0.665889
\(169\) −12.7490 −0.980691
\(170\) 11.7602 0.901969
\(171\) 7.92612 0.606125
\(172\) −28.3629 −2.16265
\(173\) −8.49595 −0.645935 −0.322968 0.946410i \(-0.604681\pi\)
−0.322968 + 0.946410i \(0.604681\pi\)
\(174\) −5.77136 −0.437526
\(175\) −14.6364 −1.10640
\(176\) −1.86958 −0.140925
\(177\) −9.99850 −0.751533
\(178\) −2.96344 −0.222119
\(179\) 10.4457 0.780747 0.390374 0.920657i \(-0.372346\pi\)
0.390374 + 0.920657i \(0.372346\pi\)
\(180\) −7.39903 −0.551491
\(181\) 20.8548 1.55012 0.775061 0.631886i \(-0.217719\pi\)
0.775061 + 0.631886i \(0.217719\pi\)
\(182\) −5.33525 −0.395475
\(183\) −5.59308 −0.413452
\(184\) 1.76163 0.129869
\(185\) 8.78898 0.646179
\(186\) 20.6233 1.51217
\(187\) −3.80935 −0.278567
\(188\) −30.1291 −2.19739
\(189\) −25.1214 −1.82731
\(190\) 12.9467 0.939253
\(191\) −2.97957 −0.215594 −0.107797 0.994173i \(-0.534380\pi\)
−0.107797 + 0.994173i \(0.534380\pi\)
\(192\) −13.1857 −0.951599
\(193\) 15.2983 1.10120 0.550598 0.834771i \(-0.314400\pi\)
0.550598 + 0.834771i \(0.314400\pi\)
\(194\) 27.9231 2.00476
\(195\) 0.746186 0.0534355
\(196\) 46.4598 3.31856
\(197\) 13.9156 0.991444 0.495722 0.868481i \(-0.334904\pi\)
0.495722 + 0.868481i \(0.334904\pi\)
\(198\) 4.12757 0.293333
\(199\) −14.8673 −1.05391 −0.526956 0.849893i \(-0.676667\pi\)
−0.526956 + 0.849893i \(0.676667\pi\)
\(200\) 5.04290 0.356587
\(201\) −2.37351 −0.167414
\(202\) 8.76439 0.616660
\(203\) 12.2312 0.858463
\(204\) −11.1142 −0.778149
\(205\) 1.93220 0.134951
\(206\) −5.30186 −0.369398
\(207\) 1.98180 0.137744
\(208\) −0.936687 −0.0649476
\(209\) −4.19367 −0.290082
\(210\) −15.8598 −1.09443
\(211\) −17.0327 −1.17258 −0.586289 0.810102i \(-0.699412\pi\)
−0.586289 + 0.810102i \(0.699412\pi\)
\(212\) 11.0577 0.759446
\(213\) −8.83187 −0.605150
\(214\) −3.95922 −0.270647
\(215\) −14.4783 −0.987415
\(216\) 8.65548 0.588931
\(217\) −43.7068 −2.96701
\(218\) 43.9617 2.97746
\(219\) 8.94727 0.604600
\(220\) 3.91479 0.263935
\(221\) −1.90854 −0.128382
\(222\) −14.3049 −0.960082
\(223\) 6.88982 0.461376 0.230688 0.973028i \(-0.425902\pi\)
0.230688 + 0.973028i \(0.425902\pi\)
\(224\) 36.2932 2.42494
\(225\) 5.67314 0.378209
\(226\) −26.1038 −1.73640
\(227\) −13.8497 −0.919237 −0.459618 0.888117i \(-0.652014\pi\)
−0.459618 + 0.888117i \(0.652014\pi\)
\(228\) −12.2355 −0.810315
\(229\) 29.4098 1.94346 0.971729 0.236100i \(-0.0758694\pi\)
0.971729 + 0.236100i \(0.0758694\pi\)
\(230\) 3.23711 0.213449
\(231\) 5.13728 0.338008
\(232\) −4.21421 −0.276677
\(233\) 3.06208 0.200604 0.100302 0.994957i \(-0.468019\pi\)
0.100302 + 0.994957i \(0.468019\pi\)
\(234\) 2.06797 0.135188
\(235\) −15.3799 −1.00328
\(236\) −26.2813 −1.71077
\(237\) −16.1085 −1.04636
\(238\) 40.5652 2.62945
\(239\) 5.50666 0.356196 0.178098 0.984013i \(-0.443006\pi\)
0.178098 + 0.984013i \(0.443006\pi\)
\(240\) −2.78445 −0.179735
\(241\) −24.4791 −1.57684 −0.788418 0.615140i \(-0.789100\pi\)
−0.788418 + 0.615140i \(0.789100\pi\)
\(242\) −2.18387 −0.140385
\(243\) 15.7109 1.00786
\(244\) −14.7016 −0.941171
\(245\) 23.7162 1.51517
\(246\) −3.14484 −0.200508
\(247\) −2.10109 −0.133689
\(248\) 15.0590 0.956247
\(249\) −1.44727 −0.0917173
\(250\) 24.7027 1.56233
\(251\) −12.0602 −0.761231 −0.380615 0.924733i \(-0.624288\pi\)
−0.380615 + 0.924733i \(0.624288\pi\)
\(252\) −25.5219 −1.60773
\(253\) −1.04856 −0.0659223
\(254\) 22.9521 1.44015
\(255\) −5.67343 −0.355284
\(256\) −2.14984 −0.134365
\(257\) 1.12981 0.0704757 0.0352379 0.999379i \(-0.488781\pi\)
0.0352379 + 0.999379i \(0.488781\pi\)
\(258\) 23.5649 1.46709
\(259\) 30.3163 1.88376
\(260\) 1.96137 0.121639
\(261\) −4.74089 −0.293454
\(262\) 5.31478 0.328348
\(263\) 17.0413 1.05081 0.525407 0.850851i \(-0.323913\pi\)
0.525407 + 0.850851i \(0.323913\pi\)
\(264\) −1.77003 −0.108938
\(265\) 5.64460 0.346745
\(266\) 44.6578 2.73814
\(267\) 1.42964 0.0874923
\(268\) −6.23883 −0.381097
\(269\) 29.3449 1.78919 0.894595 0.446877i \(-0.147464\pi\)
0.894595 + 0.446877i \(0.147464\pi\)
\(270\) 15.9050 0.967947
\(271\) 3.19145 0.193867 0.0969334 0.995291i \(-0.469097\pi\)
0.0969334 + 0.995291i \(0.469097\pi\)
\(272\) 7.12186 0.431826
\(273\) 2.57386 0.155777
\(274\) −41.0059 −2.47726
\(275\) −3.00163 −0.181005
\(276\) −3.05929 −0.184147
\(277\) −14.0288 −0.842909 −0.421455 0.906850i \(-0.638480\pi\)
−0.421455 + 0.906850i \(0.638480\pi\)
\(278\) 10.1899 0.611147
\(279\) 16.9410 1.01423
\(280\) −11.5808 −0.692083
\(281\) 19.4628 1.16105 0.580527 0.814241i \(-0.302847\pi\)
0.580527 + 0.814241i \(0.302847\pi\)
\(282\) 25.0323 1.49065
\(283\) 22.0757 1.31227 0.656133 0.754645i \(-0.272191\pi\)
0.656133 + 0.754645i \(0.272191\pi\)
\(284\) −23.2148 −1.37755
\(285\) −6.24582 −0.369970
\(286\) −1.09415 −0.0646987
\(287\) 6.66485 0.393414
\(288\) −14.0675 −0.828934
\(289\) −2.48889 −0.146405
\(290\) −7.74389 −0.454737
\(291\) −13.4708 −0.789674
\(292\) 23.5181 1.37630
\(293\) 25.9076 1.51354 0.756769 0.653683i \(-0.226777\pi\)
0.756769 + 0.653683i \(0.226777\pi\)
\(294\) −38.6004 −2.25122
\(295\) −13.4158 −0.781096
\(296\) −10.4454 −0.607124
\(297\) −5.15191 −0.298944
\(298\) 11.8473 0.686296
\(299\) −0.525344 −0.0303814
\(300\) −8.75758 −0.505619
\(301\) −49.9410 −2.87855
\(302\) −7.59380 −0.436974
\(303\) −4.22816 −0.242902
\(304\) 7.84038 0.449677
\(305\) −7.50467 −0.429716
\(306\) −15.7233 −0.898842
\(307\) 24.4543 1.39568 0.697840 0.716254i \(-0.254145\pi\)
0.697840 + 0.716254i \(0.254145\pi\)
\(308\) 13.5035 0.769433
\(309\) 2.55775 0.145505
\(310\) 27.6718 1.57166
\(311\) −16.5940 −0.940962 −0.470481 0.882410i \(-0.655920\pi\)
−0.470481 + 0.882410i \(0.655920\pi\)
\(312\) −0.886813 −0.0502059
\(313\) −14.3918 −0.813475 −0.406737 0.913545i \(-0.633334\pi\)
−0.406737 + 0.913545i \(0.633334\pi\)
\(314\) −42.8230 −2.41664
\(315\) −13.0281 −0.734050
\(316\) −42.3416 −2.38190
\(317\) −7.74596 −0.435056 −0.217528 0.976054i \(-0.569799\pi\)
−0.217528 + 0.976054i \(0.569799\pi\)
\(318\) −9.18712 −0.515188
\(319\) 2.50838 0.140442
\(320\) −17.6923 −0.989032
\(321\) 1.91003 0.106607
\(322\) 11.1660 0.622254
\(323\) 15.9751 0.888880
\(324\) 0.670840 0.0372689
\(325\) −1.50386 −0.0834193
\(326\) 39.9269 2.21134
\(327\) −21.2082 −1.17282
\(328\) −2.29635 −0.126795
\(329\) −53.0509 −2.92479
\(330\) −3.25254 −0.179047
\(331\) 14.2007 0.780538 0.390269 0.920701i \(-0.372382\pi\)
0.390269 + 0.920701i \(0.372382\pi\)
\(332\) −3.80420 −0.208783
\(333\) −11.7508 −0.643939
\(334\) −6.88477 −0.376718
\(335\) −3.18472 −0.174000
\(336\) −9.60454 −0.523971
\(337\) −2.25049 −0.122592 −0.0612959 0.998120i \(-0.519523\pi\)
−0.0612959 + 0.998120i \(0.519523\pi\)
\(338\) 27.8422 1.51441
\(339\) 12.5932 0.683966
\(340\) −14.9128 −0.808759
\(341\) −8.96340 −0.485395
\(342\) −17.3096 −0.935998
\(343\) 47.6727 2.57408
\(344\) 17.2070 0.927737
\(345\) −1.56167 −0.0840773
\(346\) 18.5541 0.997474
\(347\) −18.4841 −0.992281 −0.496140 0.868242i \(-0.665250\pi\)
−0.496140 + 0.868242i \(0.665250\pi\)
\(348\) 7.31848 0.392312
\(349\) 2.30388 0.123324 0.0616620 0.998097i \(-0.480360\pi\)
0.0616620 + 0.998097i \(0.480360\pi\)
\(350\) 31.9639 1.70854
\(351\) −2.58119 −0.137774
\(352\) 7.44303 0.396715
\(353\) 24.8937 1.32496 0.662478 0.749082i \(-0.269505\pi\)
0.662478 + 0.749082i \(0.269505\pi\)
\(354\) 21.8354 1.16054
\(355\) −11.8504 −0.628954
\(356\) 3.75784 0.199165
\(357\) −19.5697 −1.03574
\(358\) −22.8120 −1.20565
\(359\) 33.5314 1.76972 0.884860 0.465857i \(-0.154254\pi\)
0.884860 + 0.465857i \(0.154254\pi\)
\(360\) 4.48878 0.236579
\(361\) −1.41317 −0.0743772
\(362\) −45.5442 −2.39375
\(363\) 1.05356 0.0552973
\(364\) 6.76546 0.354606
\(365\) 12.0052 0.628383
\(366\) 12.2146 0.638466
\(367\) 18.7097 0.976637 0.488319 0.872665i \(-0.337610\pi\)
0.488319 + 0.872665i \(0.337610\pi\)
\(368\) 1.96036 0.102191
\(369\) −2.58334 −0.134483
\(370\) −19.1940 −0.997849
\(371\) 19.4702 1.01084
\(372\) −26.1517 −1.35590
\(373\) −23.0470 −1.19333 −0.596664 0.802491i \(-0.703508\pi\)
−0.596664 + 0.802491i \(0.703508\pi\)
\(374\) 8.31913 0.430172
\(375\) −11.9172 −0.615401
\(376\) 18.2785 0.942640
\(377\) 1.25674 0.0647253
\(378\) 54.8620 2.82180
\(379\) −15.0729 −0.774241 −0.387120 0.922029i \(-0.626530\pi\)
−0.387120 + 0.922029i \(0.626530\pi\)
\(380\) −16.4173 −0.842190
\(381\) −11.0727 −0.567271
\(382\) 6.50701 0.332928
\(383\) 16.1386 0.824643 0.412321 0.911038i \(-0.364718\pi\)
0.412321 + 0.911038i \(0.364718\pi\)
\(384\) 13.1127 0.669154
\(385\) 6.89309 0.351305
\(386\) −33.4095 −1.70050
\(387\) 19.3574 0.983993
\(388\) −35.4085 −1.79759
\(389\) 6.25842 0.317315 0.158657 0.987334i \(-0.449284\pi\)
0.158657 + 0.987334i \(0.449284\pi\)
\(390\) −1.62957 −0.0825167
\(391\) 3.99432 0.202001
\(392\) −28.1858 −1.42360
\(393\) −2.56398 −0.129336
\(394\) −30.3899 −1.53102
\(395\) −21.6140 −1.08752
\(396\) −5.23404 −0.263020
\(397\) 24.2095 1.21504 0.607520 0.794305i \(-0.292165\pi\)
0.607520 + 0.794305i \(0.292165\pi\)
\(398\) 32.4682 1.62748
\(399\) −21.5440 −1.07855
\(400\) 5.61177 0.280589
\(401\) 15.0934 0.753728 0.376864 0.926269i \(-0.377002\pi\)
0.376864 + 0.926269i \(0.377002\pi\)
\(402\) 5.18344 0.258526
\(403\) −4.49080 −0.223703
\(404\) −11.1138 −0.552935
\(405\) 0.342442 0.0170161
\(406\) −26.7114 −1.32567
\(407\) 6.21728 0.308179
\(408\) 6.74265 0.333811
\(409\) −34.9246 −1.72691 −0.863455 0.504426i \(-0.831704\pi\)
−0.863455 + 0.504426i \(0.831704\pi\)
\(410\) −4.21968 −0.208395
\(411\) 19.7823 0.975788
\(412\) 6.72312 0.331224
\(413\) −46.2757 −2.27708
\(414\) −4.32799 −0.212709
\(415\) −1.94192 −0.0953252
\(416\) 3.72907 0.182833
\(417\) −4.91585 −0.240730
\(418\) 9.15843 0.447954
\(419\) 18.2862 0.893340 0.446670 0.894699i \(-0.352610\pi\)
0.446670 + 0.894699i \(0.352610\pi\)
\(420\) 20.1114 0.981334
\(421\) 7.54789 0.367862 0.183931 0.982939i \(-0.441118\pi\)
0.183931 + 0.982939i \(0.441118\pi\)
\(422\) 37.1972 1.81073
\(423\) 20.5628 0.999800
\(424\) −6.70839 −0.325788
\(425\) 11.4342 0.554642
\(426\) 19.2877 0.934491
\(427\) −25.8863 −1.25272
\(428\) 5.02056 0.242678
\(429\) 0.527848 0.0254847
\(430\) 31.6189 1.52480
\(431\) 8.81633 0.424668 0.212334 0.977197i \(-0.431894\pi\)
0.212334 + 0.977197i \(0.431894\pi\)
\(432\) 9.63189 0.463414
\(433\) 14.0610 0.675728 0.337864 0.941195i \(-0.390296\pi\)
0.337864 + 0.941195i \(0.390296\pi\)
\(434\) 95.4500 4.58175
\(435\) 3.73585 0.179120
\(436\) −55.7464 −2.66977
\(437\) 4.39730 0.210352
\(438\) −19.5397 −0.933643
\(439\) −30.5036 −1.45586 −0.727929 0.685652i \(-0.759517\pi\)
−0.727929 + 0.685652i \(0.759517\pi\)
\(440\) −2.37499 −0.113223
\(441\) −31.7084 −1.50992
\(442\) 4.16801 0.198252
\(443\) 19.5621 0.929422 0.464711 0.885462i \(-0.346158\pi\)
0.464711 + 0.885462i \(0.346158\pi\)
\(444\) 18.1396 0.860867
\(445\) 1.91825 0.0909340
\(446\) −15.0465 −0.712471
\(447\) −5.71544 −0.270331
\(448\) −61.0272 −2.88326
\(449\) −0.535403 −0.0252672 −0.0126336 0.999920i \(-0.504022\pi\)
−0.0126336 + 0.999920i \(0.504022\pi\)
\(450\) −12.3894 −0.584043
\(451\) 1.36683 0.0643615
\(452\) 33.1015 1.55696
\(453\) 3.66344 0.172123
\(454\) 30.2460 1.41951
\(455\) 3.45355 0.161905
\(456\) 7.42291 0.347610
\(457\) 0.633495 0.0296337 0.0148168 0.999890i \(-0.495283\pi\)
0.0148168 + 0.999890i \(0.495283\pi\)
\(458\) −64.2274 −3.00115
\(459\) 19.6254 0.916035
\(460\) −4.10488 −0.191391
\(461\) 2.53078 0.117870 0.0589351 0.998262i \(-0.481229\pi\)
0.0589351 + 0.998262i \(0.481229\pi\)
\(462\) −11.2192 −0.521963
\(463\) −6.02308 −0.279916 −0.139958 0.990157i \(-0.544697\pi\)
−0.139958 + 0.990157i \(0.544697\pi\)
\(464\) −4.68961 −0.217710
\(465\) −13.3496 −0.619073
\(466\) −6.68720 −0.309779
\(467\) −10.2117 −0.472542 −0.236271 0.971687i \(-0.575925\pi\)
−0.236271 + 0.971687i \(0.575925\pi\)
\(468\) −2.62233 −0.121217
\(469\) −10.9852 −0.507251
\(470\) 33.5878 1.54929
\(471\) 20.6589 0.951911
\(472\) 15.9441 0.733888
\(473\) −10.2419 −0.470923
\(474\) 35.1788 1.61582
\(475\) 12.5878 0.577569
\(476\) −51.4395 −2.35772
\(477\) −7.54678 −0.345543
\(478\) −12.0258 −0.550049
\(479\) 12.6053 0.575949 0.287975 0.957638i \(-0.407018\pi\)
0.287975 + 0.957638i \(0.407018\pi\)
\(480\) 11.0852 0.505970
\(481\) 3.11495 0.142030
\(482\) 53.4592 2.43500
\(483\) −5.38674 −0.245105
\(484\) 2.76930 0.125877
\(485\) −18.0749 −0.820737
\(486\) −34.3107 −1.55636
\(487\) 38.0829 1.72570 0.862849 0.505461i \(-0.168678\pi\)
0.862849 + 0.505461i \(0.168678\pi\)
\(488\) 8.91901 0.403745
\(489\) −19.2617 −0.871046
\(490\) −51.7932 −2.33978
\(491\) −38.0827 −1.71865 −0.859323 0.511433i \(-0.829115\pi\)
−0.859323 + 0.511433i \(0.829115\pi\)
\(492\) 3.98788 0.179787
\(493\) −9.55529 −0.430349
\(494\) 4.58852 0.206447
\(495\) −2.67181 −0.120089
\(496\) 16.7578 0.752446
\(497\) −40.8763 −1.83355
\(498\) 3.16066 0.141633
\(499\) 0.934781 0.0418465 0.0209233 0.999781i \(-0.493339\pi\)
0.0209233 + 0.999781i \(0.493339\pi\)
\(500\) −31.3247 −1.40088
\(501\) 3.32139 0.148389
\(502\) 26.3379 1.17552
\(503\) 1.90503 0.0849410 0.0424705 0.999098i \(-0.486477\pi\)
0.0424705 + 0.999098i \(0.486477\pi\)
\(504\) 15.4834 0.689685
\(505\) −5.67326 −0.252457
\(506\) 2.28992 0.101799
\(507\) −13.4318 −0.596525
\(508\) −29.1049 −1.29132
\(509\) −10.5278 −0.466638 −0.233319 0.972400i \(-0.574959\pi\)
−0.233319 + 0.972400i \(0.574959\pi\)
\(510\) 12.3901 0.548641
\(511\) 41.4104 1.83189
\(512\) −20.1973 −0.892602
\(513\) 21.6054 0.953901
\(514\) −2.46737 −0.108831
\(515\) 3.43193 0.151229
\(516\) −29.8819 −1.31548
\(517\) −10.8797 −0.478488
\(518\) −66.2070 −2.90897
\(519\) −8.95096 −0.392904
\(520\) −1.18991 −0.0521808
\(521\) 7.98725 0.349928 0.174964 0.984575i \(-0.444019\pi\)
0.174964 + 0.984575i \(0.444019\pi\)
\(522\) 10.3535 0.453161
\(523\) −41.3774 −1.80931 −0.904654 0.426147i \(-0.859871\pi\)
−0.904654 + 0.426147i \(0.859871\pi\)
\(524\) −6.73950 −0.294417
\(525\) −15.4202 −0.672993
\(526\) −37.2161 −1.62270
\(527\) 34.1447 1.48737
\(528\) −1.96970 −0.0857203
\(529\) −21.9005 −0.952197
\(530\) −12.3271 −0.535454
\(531\) 17.9368 0.778389
\(532\) −56.6291 −2.45518
\(533\) 0.684803 0.0296621
\(534\) −3.12214 −0.135108
\(535\) 2.56283 0.110801
\(536\) 3.78492 0.163484
\(537\) 11.0051 0.474905
\(538\) −64.0856 −2.76292
\(539\) 16.7767 0.722625
\(540\) −20.1686 −0.867919
\(541\) 17.9121 0.770103 0.385052 0.922895i \(-0.374184\pi\)
0.385052 + 0.922895i \(0.374184\pi\)
\(542\) −6.96972 −0.299375
\(543\) 21.9717 0.942894
\(544\) −28.3531 −1.21563
\(545\) −28.4567 −1.21895
\(546\) −5.62098 −0.240556
\(547\) 1.00000 0.0427569
\(548\) 51.9983 2.22126
\(549\) 10.0337 0.428227
\(550\) 6.55517 0.279514
\(551\) −10.5193 −0.448138
\(552\) 1.85598 0.0789957
\(553\) −74.5543 −3.17037
\(554\) 30.6371 1.30165
\(555\) 9.25968 0.393051
\(556\) −12.9214 −0.547991
\(557\) −15.8000 −0.669467 −0.334733 0.942313i \(-0.608646\pi\)
−0.334733 + 0.942313i \(0.608646\pi\)
\(558\) −36.9970 −1.56621
\(559\) −5.13136 −0.217033
\(560\) −12.8872 −0.544582
\(561\) −4.01336 −0.169444
\(562\) −42.5043 −1.79294
\(563\) −1.06041 −0.0446911 −0.0223455 0.999750i \(-0.507113\pi\)
−0.0223455 + 0.999750i \(0.507113\pi\)
\(564\) −31.7427 −1.33661
\(565\) 16.8972 0.710871
\(566\) −48.2106 −2.02644
\(567\) 1.18120 0.0496059
\(568\) 14.0838 0.590941
\(569\) −21.3551 −0.895252 −0.447626 0.894221i \(-0.647730\pi\)
−0.447626 + 0.894221i \(0.647730\pi\)
\(570\) 13.6401 0.571320
\(571\) −30.3426 −1.26980 −0.634899 0.772595i \(-0.718958\pi\)
−0.634899 + 0.772595i \(0.718958\pi\)
\(572\) 1.38746 0.0580127
\(573\) −3.13915 −0.131140
\(574\) −14.5552 −0.607522
\(575\) 3.14738 0.131255
\(576\) 23.6545 0.985604
\(577\) 29.0193 1.20809 0.604044 0.796951i \(-0.293555\pi\)
0.604044 + 0.796951i \(0.293555\pi\)
\(578\) 5.43541 0.226083
\(579\) 16.1176 0.669825
\(580\) 9.81978 0.407744
\(581\) −6.69838 −0.277895
\(582\) 29.4186 1.21944
\(583\) 3.99296 0.165371
\(584\) −14.2678 −0.590405
\(585\) −1.33862 −0.0553450
\(586\) −56.5789 −2.33725
\(587\) 19.0132 0.784757 0.392378 0.919804i \(-0.371652\pi\)
0.392378 + 0.919804i \(0.371652\pi\)
\(588\) 48.9480 2.01858
\(589\) 37.5895 1.54885
\(590\) 29.2983 1.20619
\(591\) 14.6608 0.603066
\(592\) −11.6237 −0.477730
\(593\) 16.6967 0.685653 0.342826 0.939399i \(-0.388616\pi\)
0.342826 + 0.939399i \(0.388616\pi\)
\(594\) 11.2511 0.461639
\(595\) −26.2582 −1.07648
\(596\) −15.0232 −0.615374
\(597\) −15.6635 −0.641064
\(598\) 1.14728 0.0469160
\(599\) −19.1336 −0.781779 −0.390889 0.920438i \(-0.627833\pi\)
−0.390889 + 0.920438i \(0.627833\pi\)
\(600\) 5.31297 0.216901
\(601\) −14.2037 −0.579381 −0.289690 0.957120i \(-0.593552\pi\)
−0.289690 + 0.957120i \(0.593552\pi\)
\(602\) 109.065 4.44515
\(603\) 4.25794 0.173397
\(604\) 9.62946 0.391817
\(605\) 1.41364 0.0574726
\(606\) 9.23377 0.375096
\(607\) 12.6932 0.515201 0.257600 0.966252i \(-0.417068\pi\)
0.257600 + 0.966252i \(0.417068\pi\)
\(608\) −31.2136 −1.26588
\(609\) 12.8863 0.522178
\(610\) 16.3892 0.663581
\(611\) −5.45090 −0.220520
\(612\) 19.9382 0.805956
\(613\) 21.4708 0.867199 0.433599 0.901106i \(-0.357243\pi\)
0.433599 + 0.901106i \(0.357243\pi\)
\(614\) −53.4050 −2.15525
\(615\) 2.03568 0.0820866
\(616\) −8.19218 −0.330072
\(617\) 18.1322 0.729975 0.364988 0.931012i \(-0.381073\pi\)
0.364988 + 0.931012i \(0.381073\pi\)
\(618\) −5.58580 −0.224694
\(619\) −5.34304 −0.214755 −0.107378 0.994218i \(-0.534245\pi\)
−0.107378 + 0.994218i \(0.534245\pi\)
\(620\) −35.0898 −1.40924
\(621\) 5.40208 0.216778
\(622\) 36.2393 1.45306
\(623\) 6.61674 0.265094
\(624\) −0.986852 −0.0395057
\(625\) −0.982089 −0.0392836
\(626\) 31.4299 1.25619
\(627\) −4.41826 −0.176448
\(628\) 54.3025 2.16690
\(629\) −23.6838 −0.944333
\(630\) 28.4517 1.13354
\(631\) −7.44612 −0.296425 −0.148213 0.988956i \(-0.547352\pi\)
−0.148213 + 0.988956i \(0.547352\pi\)
\(632\) 25.6874 1.02179
\(633\) −17.9449 −0.713245
\(634\) 16.9162 0.671828
\(635\) −14.8571 −0.589586
\(636\) 11.6499 0.461949
\(637\) 8.40540 0.333034
\(638\) −5.47798 −0.216875
\(639\) 15.8439 0.626774
\(640\) 17.5943 0.695477
\(641\) −3.40029 −0.134303 −0.0671517 0.997743i \(-0.521391\pi\)
−0.0671517 + 0.997743i \(0.521391\pi\)
\(642\) −4.17126 −0.164626
\(643\) −16.3080 −0.643124 −0.321562 0.946889i \(-0.604208\pi\)
−0.321562 + 0.946889i \(0.604208\pi\)
\(644\) −14.1592 −0.557951
\(645\) −15.2537 −0.600615
\(646\) −34.8876 −1.37264
\(647\) 24.9406 0.980516 0.490258 0.871577i \(-0.336903\pi\)
0.490258 + 0.871577i \(0.336903\pi\)
\(648\) −0.406979 −0.0159877
\(649\) −9.49024 −0.372525
\(650\) 3.28424 0.128819
\(651\) −46.0475 −1.80474
\(652\) −50.6300 −1.98282
\(653\) 17.1886 0.672641 0.336321 0.941748i \(-0.390817\pi\)
0.336321 + 0.941748i \(0.390817\pi\)
\(654\) 46.3160 1.81110
\(655\) −3.44030 −0.134424
\(656\) −2.55539 −0.0997713
\(657\) −16.0509 −0.626206
\(658\) 115.856 4.51655
\(659\) 25.4227 0.990327 0.495164 0.868800i \(-0.335108\pi\)
0.495164 + 0.868800i \(0.335108\pi\)
\(660\) 4.12445 0.160544
\(661\) 14.1580 0.550684 0.275342 0.961346i \(-0.411209\pi\)
0.275342 + 0.961346i \(0.411209\pi\)
\(662\) −31.0124 −1.20533
\(663\) −2.01075 −0.0780912
\(664\) 2.30790 0.0895638
\(665\) −28.9073 −1.12098
\(666\) 25.6622 0.994391
\(667\) −2.63018 −0.101841
\(668\) 8.73036 0.337788
\(669\) 7.25880 0.280642
\(670\) 6.95503 0.268696
\(671\) −5.30877 −0.204943
\(672\) 38.2369 1.47502
\(673\) 41.6177 1.60425 0.802123 0.597160i \(-0.203704\pi\)
0.802123 + 0.597160i \(0.203704\pi\)
\(674\) 4.91477 0.189310
\(675\) 15.4641 0.595214
\(676\) −35.3058 −1.35791
\(677\) −1.95263 −0.0750455 −0.0375227 0.999296i \(-0.511947\pi\)
−0.0375227 + 0.999296i \(0.511947\pi\)
\(678\) −27.5018 −1.05620
\(679\) −62.3466 −2.39264
\(680\) 9.04715 0.346942
\(681\) −14.5914 −0.559145
\(682\) 19.5749 0.749562
\(683\) −5.53863 −0.211930 −0.105965 0.994370i \(-0.533793\pi\)
−0.105965 + 0.994370i \(0.533793\pi\)
\(684\) 21.9498 0.839271
\(685\) 26.5434 1.01417
\(686\) −104.111 −3.97498
\(687\) 30.9849 1.18215
\(688\) 19.1480 0.730012
\(689\) 2.00053 0.0762143
\(690\) 3.41048 0.129835
\(691\) −14.4895 −0.551208 −0.275604 0.961271i \(-0.588878\pi\)
−0.275604 + 0.961271i \(0.588878\pi\)
\(692\) −23.5278 −0.894395
\(693\) −9.21600 −0.350087
\(694\) 40.3670 1.53231
\(695\) −6.59598 −0.250200
\(696\) −4.43991 −0.168294
\(697\) −5.20673 −0.197219
\(698\) −5.03138 −0.190441
\(699\) 3.22607 0.122021
\(700\) −40.5325 −1.53198
\(701\) −36.6739 −1.38515 −0.692577 0.721344i \(-0.743525\pi\)
−0.692577 + 0.721344i \(0.743525\pi\)
\(702\) 5.63698 0.212754
\(703\) −26.0732 −0.983369
\(704\) −12.5155 −0.471694
\(705\) −16.2036 −0.610264
\(706\) −54.3646 −2.04604
\(707\) −19.5691 −0.735971
\(708\) −27.6888 −1.04061
\(709\) 18.8704 0.708691 0.354345 0.935115i \(-0.384704\pi\)
0.354345 + 0.935115i \(0.384704\pi\)
\(710\) 25.8798 0.971251
\(711\) 28.8977 1.08375
\(712\) −2.27977 −0.0854381
\(713\) 9.39864 0.351982
\(714\) 42.7377 1.59942
\(715\) 0.708255 0.0264872
\(716\) 28.9272 1.08106
\(717\) 5.80157 0.216664
\(718\) −73.2283 −2.73286
\(719\) −6.81124 −0.254016 −0.127008 0.991902i \(-0.540537\pi\)
−0.127008 + 0.991902i \(0.540537\pi\)
\(720\) 4.99514 0.186158
\(721\) 11.8380 0.440869
\(722\) 3.08618 0.114856
\(723\) −25.7901 −0.959143
\(724\) 57.7531 2.14638
\(725\) −7.52923 −0.279628
\(726\) −2.30083 −0.0853918
\(727\) −42.6320 −1.58113 −0.790567 0.612375i \(-0.790214\pi\)
−0.790567 + 0.612375i \(0.790214\pi\)
\(728\) −4.10441 −0.152119
\(729\) 15.8256 0.586134
\(730\) −26.2179 −0.970369
\(731\) 39.0150 1.44302
\(732\) −15.4889 −0.572487
\(733\) −5.43901 −0.200895 −0.100447 0.994942i \(-0.532027\pi\)
−0.100447 + 0.994942i \(0.532027\pi\)
\(734\) −40.8596 −1.50815
\(735\) 24.9864 0.921635
\(736\) −7.80445 −0.287676
\(737\) −2.25286 −0.0829850
\(738\) 5.64168 0.207673
\(739\) −3.73867 −0.137529 −0.0687647 0.997633i \(-0.521906\pi\)
−0.0687647 + 0.997633i \(0.521906\pi\)
\(740\) 24.3393 0.894731
\(741\) −2.21362 −0.0813193
\(742\) −42.5205 −1.56098
\(743\) −30.8466 −1.13165 −0.565826 0.824524i \(-0.691443\pi\)
−0.565826 + 0.824524i \(0.691443\pi\)
\(744\) 15.8655 0.581657
\(745\) −7.66885 −0.280965
\(746\) 50.3317 1.84278
\(747\) 2.59633 0.0949948
\(748\) −10.5492 −0.385718
\(749\) 8.84012 0.323011
\(750\) 26.0256 0.950322
\(751\) −5.99027 −0.218588 −0.109294 0.994009i \(-0.534859\pi\)
−0.109294 + 0.994009i \(0.534859\pi\)
\(752\) 20.3404 0.741739
\(753\) −12.7061 −0.463034
\(754\) −2.74456 −0.0999508
\(755\) 4.91552 0.178894
\(756\) −69.5688 −2.53019
\(757\) −4.20580 −0.152863 −0.0764313 0.997075i \(-0.524353\pi\)
−0.0764313 + 0.997075i \(0.524353\pi\)
\(758\) 32.9172 1.19561
\(759\) −1.10471 −0.0400986
\(760\) 9.95990 0.361284
\(761\) −14.1484 −0.512878 −0.256439 0.966560i \(-0.582549\pi\)
−0.256439 + 0.966560i \(0.582549\pi\)
\(762\) 24.1814 0.875998
\(763\) −98.1574 −3.55353
\(764\) −8.25133 −0.298523
\(765\) 10.1778 0.367980
\(766\) −35.2446 −1.27344
\(767\) −4.75476 −0.171684
\(768\) −2.26498 −0.0817304
\(769\) −14.4585 −0.521386 −0.260693 0.965422i \(-0.583951\pi\)
−0.260693 + 0.965422i \(0.583951\pi\)
\(770\) −15.0536 −0.542496
\(771\) 1.19032 0.0428683
\(772\) 42.3656 1.52477
\(773\) −12.1996 −0.438789 −0.219394 0.975636i \(-0.570408\pi\)
−0.219394 + 0.975636i \(0.570408\pi\)
\(774\) −42.2741 −1.51951
\(775\) 26.9048 0.966448
\(776\) 21.4813 0.771133
\(777\) 31.9399 1.14584
\(778\) −13.6676 −0.490007
\(779\) −5.73203 −0.205371
\(780\) 2.06641 0.0739894
\(781\) −8.38292 −0.299964
\(782\) −8.72309 −0.311937
\(783\) −12.9229 −0.461828
\(784\) −31.3654 −1.12019
\(785\) 27.7196 0.989357
\(786\) 5.59941 0.199724
\(787\) −9.57506 −0.341314 −0.170657 0.985331i \(-0.554589\pi\)
−0.170657 + 0.985331i \(0.554589\pi\)
\(788\) 38.5364 1.37280
\(789\) 17.9540 0.639179
\(790\) 47.2022 1.67938
\(791\) 58.2845 2.07236
\(792\) 3.17534 0.112831
\(793\) −2.65977 −0.0944514
\(794\) −52.8704 −1.87630
\(795\) 5.94690 0.210915
\(796\) −41.1719 −1.45930
\(797\) −35.9353 −1.27289 −0.636446 0.771321i \(-0.719596\pi\)
−0.636446 + 0.771321i \(0.719596\pi\)
\(798\) 47.0495 1.66553
\(799\) 41.4445 1.46620
\(800\) −22.3412 −0.789880
\(801\) −2.56469 −0.0906188
\(802\) −32.9620 −1.16393
\(803\) 8.49245 0.299692
\(804\) −6.57296 −0.231810
\(805\) −7.22781 −0.254747
\(806\) 9.80734 0.345449
\(807\) 30.9165 1.08831
\(808\) 6.74245 0.237198
\(809\) −0.492652 −0.0173207 −0.00866037 0.999962i \(-0.502757\pi\)
−0.00866037 + 0.999962i \(0.502757\pi\)
\(810\) −0.747850 −0.0262768
\(811\) 2.60114 0.0913383 0.0456691 0.998957i \(-0.485458\pi\)
0.0456691 + 0.998957i \(0.485458\pi\)
\(812\) 33.8719 1.18867
\(813\) 3.36237 0.117924
\(814\) −13.5777 −0.475900
\(815\) −25.8450 −0.905310
\(816\) 7.50328 0.262667
\(817\) 42.9511 1.50267
\(818\) 76.2709 2.66675
\(819\) −4.61736 −0.161344
\(820\) 5.35085 0.186860
\(821\) −31.7214 −1.10708 −0.553542 0.832821i \(-0.686724\pi\)
−0.553542 + 0.832821i \(0.686724\pi\)
\(822\) −43.2020 −1.50684
\(823\) −1.98973 −0.0693575 −0.0346788 0.999399i \(-0.511041\pi\)
−0.0346788 + 0.999399i \(0.511041\pi\)
\(824\) −4.07872 −0.142089
\(825\) −3.16238 −0.110100
\(826\) 101.060 3.51634
\(827\) −36.9343 −1.28433 −0.642166 0.766566i \(-0.721964\pi\)
−0.642166 + 0.766566i \(0.721964\pi\)
\(828\) 5.48819 0.190728
\(829\) −15.5922 −0.541541 −0.270770 0.962644i \(-0.587278\pi\)
−0.270770 + 0.962644i \(0.587278\pi\)
\(830\) 4.24091 0.147204
\(831\) −14.7801 −0.512717
\(832\) −6.27044 −0.217389
\(833\) −63.9084 −2.21429
\(834\) 10.7356 0.371743
\(835\) 4.45656 0.154226
\(836\) −11.6135 −0.401662
\(837\) 46.1786 1.59617
\(838\) −39.9347 −1.37952
\(839\) −46.3569 −1.60042 −0.800209 0.599722i \(-0.795278\pi\)
−0.800209 + 0.599722i \(0.795278\pi\)
\(840\) −12.2010 −0.420974
\(841\) −22.7080 −0.783035
\(842\) −16.4836 −0.568064
\(843\) 20.5052 0.706235
\(844\) −47.1686 −1.62361
\(845\) −18.0224 −0.619991
\(846\) −44.9066 −1.54392
\(847\) 4.87614 0.167546
\(848\) −7.46514 −0.256354
\(849\) 23.2580 0.798213
\(850\) −24.9709 −0.856495
\(851\) −6.51918 −0.223475
\(852\) −24.4581 −0.837920
\(853\) −18.5279 −0.634382 −0.317191 0.948362i \(-0.602740\pi\)
−0.317191 + 0.948362i \(0.602740\pi\)
\(854\) 56.5323 1.93450
\(855\) 11.2047 0.383191
\(856\) −3.04583 −0.104104
\(857\) 39.3928 1.34563 0.672816 0.739810i \(-0.265085\pi\)
0.672816 + 0.739810i \(0.265085\pi\)
\(858\) −1.15275 −0.0393543
\(859\) −42.3995 −1.44665 −0.723325 0.690507i \(-0.757387\pi\)
−0.723325 + 0.690507i \(0.757387\pi\)
\(860\) −40.0949 −1.36722
\(861\) 7.02179 0.239302
\(862\) −19.2537 −0.655785
\(863\) 32.7692 1.11548 0.557738 0.830017i \(-0.311669\pi\)
0.557738 + 0.830017i \(0.311669\pi\)
\(864\) −38.3458 −1.30455
\(865\) −12.0102 −0.408359
\(866\) −30.7074 −1.04348
\(867\) −2.62218 −0.0890540
\(868\) −121.037 −4.10827
\(869\) −15.2896 −0.518665
\(870\) −8.15861 −0.276603
\(871\) −1.12872 −0.0382451
\(872\) 33.8197 1.14528
\(873\) 24.1659 0.817893
\(874\) −9.60315 −0.324831
\(875\) −55.1560 −1.86461
\(876\) 24.7777 0.837160
\(877\) 18.4330 0.622438 0.311219 0.950338i \(-0.399263\pi\)
0.311219 + 0.950338i \(0.399263\pi\)
\(878\) 66.6160 2.24818
\(879\) 27.2951 0.920640
\(880\) −2.64290 −0.0890923
\(881\) −35.8216 −1.20686 −0.603430 0.797416i \(-0.706200\pi\)
−0.603430 + 0.797416i \(0.706200\pi\)
\(882\) 69.2470 2.33167
\(883\) −43.2725 −1.45623 −0.728117 0.685453i \(-0.759604\pi\)
−0.728117 + 0.685453i \(0.759604\pi\)
\(884\) −5.28532 −0.177765
\(885\) −14.1343 −0.475118
\(886\) −42.7211 −1.43524
\(887\) −9.88011 −0.331742 −0.165871 0.986147i \(-0.553043\pi\)
−0.165871 + 0.986147i \(0.553043\pi\)
\(888\) −11.0048 −0.369296
\(889\) −51.2474 −1.71878
\(890\) −4.18922 −0.140423
\(891\) 0.242242 0.00811541
\(892\) 19.0800 0.638845
\(893\) 45.6258 1.52681
\(894\) 12.4818 0.417453
\(895\) 14.7664 0.493587
\(896\) 60.6891 2.02748
\(897\) −0.553479 −0.0184801
\(898\) 1.16925 0.0390184
\(899\) −22.4836 −0.749870
\(900\) 15.7106 0.523688
\(901\) −15.2106 −0.506737
\(902\) −2.98498 −0.0993890
\(903\) −52.6156 −1.75094
\(904\) −20.0817 −0.667907
\(905\) 29.4811 0.979985
\(906\) −8.00049 −0.265798
\(907\) 0.859225 0.0285301 0.0142650 0.999898i \(-0.495459\pi\)
0.0142650 + 0.999898i \(0.495459\pi\)
\(908\) −38.3540 −1.27282
\(909\) 7.58509 0.251582
\(910\) −7.54211 −0.250018
\(911\) 29.7435 0.985448 0.492724 0.870186i \(-0.336001\pi\)
0.492724 + 0.870186i \(0.336001\pi\)
\(912\) 8.26028 0.273525
\(913\) −1.37370 −0.0454630
\(914\) −1.38347 −0.0457612
\(915\) −7.90659 −0.261384
\(916\) 81.4447 2.69101
\(917\) −11.8668 −0.391876
\(918\) −42.8594 −1.41457
\(919\) 45.5013 1.50095 0.750475 0.660899i \(-0.229825\pi\)
0.750475 + 0.660899i \(0.229825\pi\)
\(920\) 2.49031 0.0821032
\(921\) 25.7639 0.848951
\(922\) −5.52691 −0.182019
\(923\) −4.19997 −0.138244
\(924\) 14.2267 0.468023
\(925\) −18.6620 −0.613601
\(926\) 13.1536 0.432255
\(927\) −4.58846 −0.150705
\(928\) 18.6699 0.612871
\(929\) −50.1197 −1.64437 −0.822186 0.569218i \(-0.807246\pi\)
−0.822186 + 0.569218i \(0.807246\pi\)
\(930\) 29.1538 0.955992
\(931\) −70.3560 −2.30582
\(932\) 8.47983 0.277766
\(933\) −17.4827 −0.572359
\(934\) 22.3011 0.729714
\(935\) −5.38503 −0.176109
\(936\) 1.59089 0.0520000
\(937\) −18.7886 −0.613798 −0.306899 0.951742i \(-0.599291\pi\)
−0.306899 + 0.951742i \(0.599291\pi\)
\(938\) 23.9904 0.783313
\(939\) −15.1626 −0.494813
\(940\) −42.5917 −1.38919
\(941\) −27.6298 −0.900705 −0.450353 0.892851i \(-0.648702\pi\)
−0.450353 + 0.892851i \(0.648702\pi\)
\(942\) −45.1164 −1.46997
\(943\) −1.43320 −0.0466714
\(944\) 17.7427 0.577477
\(945\) −35.5126 −1.15522
\(946\) 22.3670 0.727215
\(947\) −21.5652 −0.700776 −0.350388 0.936605i \(-0.613950\pi\)
−0.350388 + 0.936605i \(0.613950\pi\)
\(948\) −44.6092 −1.44884
\(949\) 4.25485 0.138118
\(950\) −27.4902 −0.891900
\(951\) −8.16080 −0.264632
\(952\) 31.2068 1.01142
\(953\) −37.8932 −1.22748 −0.613741 0.789508i \(-0.710336\pi\)
−0.613741 + 0.789508i \(0.710336\pi\)
\(954\) 16.4812 0.533598
\(955\) −4.21204 −0.136298
\(956\) 15.2496 0.493207
\(957\) 2.64272 0.0854269
\(958\) −27.5283 −0.889399
\(959\) 91.5577 2.95655
\(960\) −18.6399 −0.601599
\(961\) 49.3425 1.59169
\(962\) −6.80266 −0.219327
\(963\) −3.42648 −0.110417
\(964\) −67.7899 −2.18337
\(965\) 21.6262 0.696174
\(966\) 11.7640 0.378499
\(967\) 4.75853 0.153024 0.0765120 0.997069i \(-0.475622\pi\)
0.0765120 + 0.997069i \(0.475622\pi\)
\(968\) −1.68005 −0.0539990
\(969\) 16.8307 0.540679
\(970\) 39.4732 1.26741
\(971\) 22.1858 0.711978 0.355989 0.934490i \(-0.384144\pi\)
0.355989 + 0.934490i \(0.384144\pi\)
\(972\) 43.5083 1.39553
\(973\) −22.7519 −0.729391
\(974\) −83.1681 −2.66488
\(975\) −1.58440 −0.0507415
\(976\) 9.92514 0.317696
\(977\) −36.5605 −1.16967 −0.584837 0.811151i \(-0.698841\pi\)
−0.584837 + 0.811151i \(0.698841\pi\)
\(978\) 42.0652 1.34510
\(979\) 1.35696 0.0433687
\(980\) 65.6773 2.09799
\(981\) 38.0464 1.21473
\(982\) 83.1677 2.65399
\(983\) 30.6509 0.977613 0.488807 0.872392i \(-0.337432\pi\)
0.488807 + 0.872392i \(0.337432\pi\)
\(984\) −2.41933 −0.0771254
\(985\) 19.6716 0.626789
\(986\) 20.8675 0.664558
\(987\) −55.8921 −1.77906
\(988\) −5.81855 −0.185113
\(989\) 10.7392 0.341488
\(990\) 5.83488 0.185445
\(991\) 5.31786 0.168927 0.0844637 0.996427i \(-0.473082\pi\)
0.0844637 + 0.996427i \(0.473082\pi\)
\(992\) −66.7148 −2.11820
\(993\) 14.9612 0.474779
\(994\) 89.2686 2.83143
\(995\) −21.0169 −0.666281
\(996\) −4.00794 −0.126996
\(997\) −43.3390 −1.37256 −0.686280 0.727338i \(-0.740757\pi\)
−0.686280 + 0.727338i \(0.740757\pi\)
\(998\) −2.04144 −0.0646207
\(999\) −32.0308 −1.01341
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 \(a_p\))