Properties

Label 8007.2.a.j.1.5
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.53596 q^{2}\) \(-1.00000 q^{3}\) \(+4.43108 q^{4}\) \(-0.923448 q^{5}\) \(+2.53596 q^{6}\) \(-0.313569 q^{7}\) \(-6.16510 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.53596 q^{2}\) \(-1.00000 q^{3}\) \(+4.43108 q^{4}\) \(-0.923448 q^{5}\) \(+2.53596 q^{6}\) \(-0.313569 q^{7}\) \(-6.16510 q^{8}\) \(+1.00000 q^{9}\) \(+2.34182 q^{10}\) \(+0.332092 q^{11}\) \(-4.43108 q^{12}\) \(-0.593045 q^{13}\) \(+0.795197 q^{14}\) \(+0.923448 q^{15}\) \(+6.77228 q^{16}\) \(+1.00000 q^{17}\) \(-2.53596 q^{18}\) \(-1.79756 q^{19}\) \(-4.09187 q^{20}\) \(+0.313569 q^{21}\) \(-0.842170 q^{22}\) \(-4.20574 q^{23}\) \(+6.16510 q^{24}\) \(-4.14724 q^{25}\) \(+1.50394 q^{26}\) \(-1.00000 q^{27}\) \(-1.38945 q^{28}\) \(-6.93910 q^{29}\) \(-2.34182 q^{30}\) \(+6.67131 q^{31}\) \(-4.84401 q^{32}\) \(-0.332092 q^{33}\) \(-2.53596 q^{34}\) \(+0.289564 q^{35}\) \(+4.43108 q^{36}\) \(-0.302087 q^{37}\) \(+4.55853 q^{38}\) \(+0.593045 q^{39}\) \(+5.69315 q^{40}\) \(-1.56912 q^{41}\) \(-0.795197 q^{42}\) \(-0.0472238 q^{43}\) \(+1.47152 q^{44}\) \(-0.923448 q^{45}\) \(+10.6656 q^{46}\) \(+0.813814 q^{47}\) \(-6.77228 q^{48}\) \(-6.90167 q^{49}\) \(+10.5172 q^{50}\) \(-1.00000 q^{51}\) \(-2.62783 q^{52}\) \(-10.6564 q^{53}\) \(+2.53596 q^{54}\) \(-0.306669 q^{55}\) \(+1.93318 q^{56}\) \(+1.79756 q^{57}\) \(+17.5972 q^{58}\) \(-8.10918 q^{59}\) \(+4.09187 q^{60}\) \(-5.49161 q^{61}\) \(-16.9181 q^{62}\) \(-0.313569 q^{63}\) \(-1.26037 q^{64}\) \(+0.547646 q^{65}\) \(+0.842170 q^{66}\) \(+9.35947 q^{67}\) \(+4.43108 q^{68}\) \(+4.20574 q^{69}\) \(-0.734323 q^{70}\) \(+1.59550 q^{71}\) \(-6.16510 q^{72}\) \(+14.0654 q^{73}\) \(+0.766079 q^{74}\) \(+4.14724 q^{75}\) \(-7.96511 q^{76}\) \(-0.104134 q^{77}\) \(-1.50394 q^{78}\) \(+2.58926 q^{79}\) \(-6.25385 q^{80}\) \(+1.00000 q^{81}\) \(+3.97922 q^{82}\) \(+7.39223 q^{83}\) \(+1.38945 q^{84}\) \(-0.923448 q^{85}\) \(+0.119757 q^{86}\) \(+6.93910 q^{87}\) \(-2.04738 q^{88}\) \(-9.87173 q^{89}\) \(+2.34182 q^{90}\) \(+0.185960 q^{91}\) \(-18.6360 q^{92}\) \(-6.67131 q^{93}\) \(-2.06380 q^{94}\) \(+1.65995 q^{95}\) \(+4.84401 q^{96}\) \(+11.2692 q^{97}\) \(+17.5023 q^{98}\) \(+0.332092 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53596 −1.79319 −0.896596 0.442849i \(-0.853968\pi\)
−0.896596 + 0.442849i \(0.853968\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.43108 2.21554
\(5\) −0.923448 −0.412978 −0.206489 0.978449i \(-0.566204\pi\)
−0.206489 + 0.978449i \(0.566204\pi\)
\(6\) 2.53596 1.03530
\(7\) −0.313569 −0.118518 −0.0592590 0.998243i \(-0.518874\pi\)
−0.0592590 + 0.998243i \(0.518874\pi\)
\(8\) −6.16510 −2.17969
\(9\) 1.00000 0.333333
\(10\) 2.34182 0.740550
\(11\) 0.332092 0.100129 0.0500647 0.998746i \(-0.484057\pi\)
0.0500647 + 0.998746i \(0.484057\pi\)
\(12\) −4.43108 −1.27914
\(13\) −0.593045 −0.164481 −0.0822405 0.996613i \(-0.526208\pi\)
−0.0822405 + 0.996613i \(0.526208\pi\)
\(14\) 0.795197 0.212525
\(15\) 0.923448 0.238433
\(16\) 6.77228 1.69307
\(17\) 1.00000 0.242536
\(18\) −2.53596 −0.597731
\(19\) −1.79756 −0.412388 −0.206194 0.978511i \(-0.566108\pi\)
−0.206194 + 0.978511i \(0.566108\pi\)
\(20\) −4.09187 −0.914969
\(21\) 0.313569 0.0684263
\(22\) −0.842170 −0.179551
\(23\) −4.20574 −0.876958 −0.438479 0.898741i \(-0.644483\pi\)
−0.438479 + 0.898741i \(0.644483\pi\)
\(24\) 6.16510 1.25845
\(25\) −4.14724 −0.829449
\(26\) 1.50394 0.294946
\(27\) −1.00000 −0.192450
\(28\) −1.38945 −0.262581
\(29\) −6.93910 −1.28856 −0.644279 0.764791i \(-0.722842\pi\)
−0.644279 + 0.764791i \(0.722842\pi\)
\(30\) −2.34182 −0.427556
\(31\) 6.67131 1.19820 0.599101 0.800673i \(-0.295525\pi\)
0.599101 + 0.800673i \(0.295525\pi\)
\(32\) −4.84401 −0.856307
\(33\) −0.332092 −0.0578097
\(34\) −2.53596 −0.434913
\(35\) 0.289564 0.0489453
\(36\) 4.43108 0.738513
\(37\) −0.302087 −0.0496628 −0.0248314 0.999692i \(-0.507905\pi\)
−0.0248314 + 0.999692i \(0.507905\pi\)
\(38\) 4.55853 0.739490
\(39\) 0.593045 0.0949632
\(40\) 5.69315 0.900166
\(41\) −1.56912 −0.245055 −0.122528 0.992465i \(-0.539100\pi\)
−0.122528 + 0.992465i \(0.539100\pi\)
\(42\) −0.795197 −0.122702
\(43\) −0.0472238 −0.00720156 −0.00360078 0.999994i \(-0.501146\pi\)
−0.00360078 + 0.999994i \(0.501146\pi\)
\(44\) 1.47152 0.221840
\(45\) −0.923448 −0.137659
\(46\) 10.6656 1.57255
\(47\) 0.813814 0.118707 0.0593535 0.998237i \(-0.481096\pi\)
0.0593535 + 0.998237i \(0.481096\pi\)
\(48\) −6.77228 −0.977495
\(49\) −6.90167 −0.985954
\(50\) 10.5172 1.48736
\(51\) −1.00000 −0.140028
\(52\) −2.62783 −0.364414
\(53\) −10.6564 −1.46377 −0.731887 0.681426i \(-0.761360\pi\)
−0.731887 + 0.681426i \(0.761360\pi\)
\(54\) 2.53596 0.345100
\(55\) −0.306669 −0.0413513
\(56\) 1.93318 0.258333
\(57\) 1.79756 0.238092
\(58\) 17.5972 2.31063
\(59\) −8.10918 −1.05573 −0.527863 0.849330i \(-0.677006\pi\)
−0.527863 + 0.849330i \(0.677006\pi\)
\(60\) 4.09187 0.528258
\(61\) −5.49161 −0.703129 −0.351565 0.936164i \(-0.614350\pi\)
−0.351565 + 0.936164i \(0.614350\pi\)
\(62\) −16.9181 −2.14861
\(63\) −0.313569 −0.0395060
\(64\) −1.26037 −0.157547
\(65\) 0.547646 0.0679271
\(66\) 0.842170 0.103664
\(67\) 9.35947 1.14344 0.571721 0.820448i \(-0.306276\pi\)
0.571721 + 0.820448i \(0.306276\pi\)
\(68\) 4.43108 0.537347
\(69\) 4.20574 0.506312
\(70\) −0.734323 −0.0877684
\(71\) 1.59550 0.189351 0.0946756 0.995508i \(-0.469819\pi\)
0.0946756 + 0.995508i \(0.469819\pi\)
\(72\) −6.16510 −0.726564
\(73\) 14.0654 1.64623 0.823113 0.567878i \(-0.192235\pi\)
0.823113 + 0.567878i \(0.192235\pi\)
\(74\) 0.766079 0.0890549
\(75\) 4.14724 0.478883
\(76\) −7.96511 −0.913661
\(77\) −0.104134 −0.0118671
\(78\) −1.50394 −0.170287
\(79\) 2.58926 0.291314 0.145657 0.989335i \(-0.453470\pi\)
0.145657 + 0.989335i \(0.453470\pi\)
\(80\) −6.25385 −0.699201
\(81\) 1.00000 0.111111
\(82\) 3.97922 0.439432
\(83\) 7.39223 0.811402 0.405701 0.914006i \(-0.367027\pi\)
0.405701 + 0.914006i \(0.367027\pi\)
\(84\) 1.38945 0.151601
\(85\) −0.923448 −0.100162
\(86\) 0.119757 0.0129138
\(87\) 6.93910 0.743949
\(88\) −2.04738 −0.218251
\(89\) −9.87173 −1.04640 −0.523201 0.852210i \(-0.675262\pi\)
−0.523201 + 0.852210i \(0.675262\pi\)
\(90\) 2.34182 0.246850
\(91\) 0.185960 0.0194939
\(92\) −18.6360 −1.94293
\(93\) −6.67131 −0.691782
\(94\) −2.06380 −0.212865
\(95\) 1.65995 0.170307
\(96\) 4.84401 0.494389
\(97\) 11.2692 1.14421 0.572105 0.820181i \(-0.306127\pi\)
0.572105 + 0.820181i \(0.306127\pi\)
\(98\) 17.5023 1.76800
\(99\) 0.332092 0.0333765
\(100\) −18.3768 −1.83768
\(101\) −10.0976 −1.00475 −0.502374 0.864651i \(-0.667540\pi\)
−0.502374 + 0.864651i \(0.667540\pi\)
\(102\) 2.53596 0.251097
\(103\) −0.586459 −0.0577855 −0.0288928 0.999583i \(-0.509198\pi\)
−0.0288928 + 0.999583i \(0.509198\pi\)
\(104\) 3.65618 0.358518
\(105\) −0.289564 −0.0282586
\(106\) 27.0243 2.62483
\(107\) 8.33650 0.805920 0.402960 0.915218i \(-0.367981\pi\)
0.402960 + 0.915218i \(0.367981\pi\)
\(108\) −4.43108 −0.426380
\(109\) −2.22413 −0.213033 −0.106516 0.994311i \(-0.533970\pi\)
−0.106516 + 0.994311i \(0.533970\pi\)
\(110\) 0.777700 0.0741508
\(111\) 0.302087 0.0286728
\(112\) −2.12358 −0.200659
\(113\) −16.6199 −1.56347 −0.781734 0.623611i \(-0.785665\pi\)
−0.781734 + 0.623611i \(0.785665\pi\)
\(114\) −4.55853 −0.426945
\(115\) 3.88378 0.362165
\(116\) −30.7477 −2.85485
\(117\) −0.593045 −0.0548270
\(118\) 20.5645 1.89312
\(119\) −0.313569 −0.0287448
\(120\) −5.69315 −0.519711
\(121\) −10.8897 −0.989974
\(122\) 13.9265 1.26085
\(123\) 1.56912 0.141483
\(124\) 29.5611 2.65466
\(125\) 8.44700 0.755523
\(126\) 0.795197 0.0708418
\(127\) 15.3714 1.36399 0.681997 0.731355i \(-0.261112\pi\)
0.681997 + 0.731355i \(0.261112\pi\)
\(128\) 12.8843 1.13882
\(129\) 0.0472238 0.00415782
\(130\) −1.38881 −0.121806
\(131\) −8.97750 −0.784368 −0.392184 0.919887i \(-0.628280\pi\)
−0.392184 + 0.919887i \(0.628280\pi\)
\(132\) −1.47152 −0.128080
\(133\) 0.563658 0.0488753
\(134\) −23.7352 −2.05041
\(135\) 0.923448 0.0794777
\(136\) −6.16510 −0.528653
\(137\) 2.58144 0.220547 0.110274 0.993901i \(-0.464827\pi\)
0.110274 + 0.993901i \(0.464827\pi\)
\(138\) −10.6656 −0.907915
\(139\) 1.26738 0.107498 0.0537490 0.998554i \(-0.482883\pi\)
0.0537490 + 0.998554i \(0.482883\pi\)
\(140\) 1.28308 0.108440
\(141\) −0.813814 −0.0685355
\(142\) −4.04612 −0.339543
\(143\) −0.196945 −0.0164694
\(144\) 6.77228 0.564357
\(145\) 6.40789 0.532146
\(146\) −35.6691 −2.95200
\(147\) 6.90167 0.569241
\(148\) −1.33857 −0.110030
\(149\) −8.85684 −0.725580 −0.362790 0.931871i \(-0.618176\pi\)
−0.362790 + 0.931871i \(0.618176\pi\)
\(150\) −10.5172 −0.858728
\(151\) 18.6267 1.51582 0.757908 0.652361i \(-0.226221\pi\)
0.757908 + 0.652361i \(0.226221\pi\)
\(152\) 11.0821 0.898879
\(153\) 1.00000 0.0808452
\(154\) 0.264078 0.0212800
\(155\) −6.16060 −0.494832
\(156\) 2.62783 0.210394
\(157\) −1.00000 −0.0798087
\(158\) −6.56624 −0.522382
\(159\) 10.6564 0.845110
\(160\) 4.47319 0.353636
\(161\) 1.31879 0.103935
\(162\) −2.53596 −0.199244
\(163\) −21.9720 −1.72098 −0.860491 0.509465i \(-0.829843\pi\)
−0.860491 + 0.509465i \(0.829843\pi\)
\(164\) −6.95289 −0.542930
\(165\) 0.306669 0.0238742
\(166\) −18.7464 −1.45500
\(167\) −5.88828 −0.455649 −0.227824 0.973702i \(-0.573161\pi\)
−0.227824 + 0.973702i \(0.573161\pi\)
\(168\) −1.93318 −0.149148
\(169\) −12.6483 −0.972946
\(170\) 2.34182 0.179610
\(171\) −1.79756 −0.137463
\(172\) −0.209252 −0.0159553
\(173\) 4.36048 0.331521 0.165761 0.986166i \(-0.446992\pi\)
0.165761 + 0.986166i \(0.446992\pi\)
\(174\) −17.5972 −1.33404
\(175\) 1.30045 0.0983045
\(176\) 2.24902 0.169526
\(177\) 8.10918 0.609523
\(178\) 25.0343 1.87640
\(179\) −17.4253 −1.30243 −0.651216 0.758893i \(-0.725741\pi\)
−0.651216 + 0.758893i \(0.725741\pi\)
\(180\) −4.09187 −0.304990
\(181\) 2.09162 0.155469 0.0777346 0.996974i \(-0.475231\pi\)
0.0777346 + 0.996974i \(0.475231\pi\)
\(182\) −0.471587 −0.0349564
\(183\) 5.49161 0.405952
\(184\) 25.9288 1.91150
\(185\) 0.278961 0.0205096
\(186\) 16.9181 1.24050
\(187\) 0.332092 0.0242849
\(188\) 3.60607 0.263000
\(189\) 0.313569 0.0228088
\(190\) −4.20956 −0.305394
\(191\) 20.6202 1.49203 0.746014 0.665930i \(-0.231965\pi\)
0.746014 + 0.665930i \(0.231965\pi\)
\(192\) 1.26037 0.0909596
\(193\) 15.8887 1.14370 0.571848 0.820360i \(-0.306227\pi\)
0.571848 + 0.820360i \(0.306227\pi\)
\(194\) −28.5781 −2.05179
\(195\) −0.547646 −0.0392177
\(196\) −30.5818 −2.18442
\(197\) 25.7860 1.83718 0.918590 0.395212i \(-0.129329\pi\)
0.918590 + 0.395212i \(0.129329\pi\)
\(198\) −0.842170 −0.0598504
\(199\) −0.109309 −0.00774871 −0.00387436 0.999992i \(-0.501233\pi\)
−0.00387436 + 0.999992i \(0.501233\pi\)
\(200\) 25.5682 1.80794
\(201\) −9.35947 −0.660166
\(202\) 25.6070 1.80170
\(203\) 2.17588 0.152717
\(204\) −4.43108 −0.310237
\(205\) 1.44900 0.101203
\(206\) 1.48723 0.103621
\(207\) −4.20574 −0.292319
\(208\) −4.01627 −0.278478
\(209\) −0.596953 −0.0412921
\(210\) 0.734323 0.0506731
\(211\) −8.52744 −0.587053 −0.293526 0.955951i \(-0.594829\pi\)
−0.293526 + 0.955951i \(0.594829\pi\)
\(212\) −47.2195 −3.24305
\(213\) −1.59550 −0.109322
\(214\) −21.1410 −1.44517
\(215\) 0.0436087 0.00297409
\(216\) 6.16510 0.419482
\(217\) −2.09191 −0.142008
\(218\) 5.64030 0.382009
\(219\) −14.0654 −0.950449
\(220\) −1.35887 −0.0916153
\(221\) −0.593045 −0.0398925
\(222\) −0.766079 −0.0514159
\(223\) 8.31849 0.557048 0.278524 0.960429i \(-0.410155\pi\)
0.278524 + 0.960429i \(0.410155\pi\)
\(224\) 1.51893 0.101488
\(225\) −4.14724 −0.276483
\(226\) 42.1474 2.80360
\(227\) −9.17819 −0.609178 −0.304589 0.952484i \(-0.598519\pi\)
−0.304589 + 0.952484i \(0.598519\pi\)
\(228\) 7.96511 0.527502
\(229\) −5.27359 −0.348489 −0.174244 0.984702i \(-0.555748\pi\)
−0.174244 + 0.984702i \(0.555748\pi\)
\(230\) −9.84911 −0.649431
\(231\) 0.104134 0.00685149
\(232\) 42.7802 2.80866
\(233\) 17.6227 1.15450 0.577250 0.816567i \(-0.304126\pi\)
0.577250 + 0.816567i \(0.304126\pi\)
\(234\) 1.50394 0.0983153
\(235\) −0.751515 −0.0490234
\(236\) −35.9324 −2.33900
\(237\) −2.58926 −0.168190
\(238\) 0.795197 0.0515450
\(239\) −13.2303 −0.855794 −0.427897 0.903827i \(-0.640745\pi\)
−0.427897 + 0.903827i \(0.640745\pi\)
\(240\) 6.25385 0.403684
\(241\) 28.2183 1.81770 0.908850 0.417122i \(-0.136961\pi\)
0.908850 + 0.417122i \(0.136961\pi\)
\(242\) 27.6158 1.77521
\(243\) −1.00000 −0.0641500
\(244\) −24.3338 −1.55781
\(245\) 6.37334 0.407177
\(246\) −3.97922 −0.253706
\(247\) 1.06603 0.0678300
\(248\) −41.1293 −2.61171
\(249\) −7.39223 −0.468463
\(250\) −21.4212 −1.35480
\(251\) 8.95764 0.565401 0.282701 0.959208i \(-0.408770\pi\)
0.282701 + 0.959208i \(0.408770\pi\)
\(252\) −1.38945 −0.0875270
\(253\) −1.39669 −0.0878093
\(254\) −38.9813 −2.44590
\(255\) 0.923448 0.0578285
\(256\) −30.1532 −1.88457
\(257\) 24.0068 1.49750 0.748751 0.662852i \(-0.230654\pi\)
0.748751 + 0.662852i \(0.230654\pi\)
\(258\) −0.119757 −0.00745577
\(259\) 0.0947250 0.00588593
\(260\) 2.42666 0.150495
\(261\) −6.93910 −0.429519
\(262\) 22.7666 1.40652
\(263\) −15.3395 −0.945872 −0.472936 0.881097i \(-0.656806\pi\)
−0.472936 + 0.881097i \(0.656806\pi\)
\(264\) 2.04738 0.126007
\(265\) 9.84066 0.604507
\(266\) −1.42941 −0.0876429
\(267\) 9.87173 0.604140
\(268\) 41.4725 2.53334
\(269\) −15.7646 −0.961185 −0.480593 0.876944i \(-0.659578\pi\)
−0.480593 + 0.876944i \(0.659578\pi\)
\(270\) −2.34182 −0.142519
\(271\) −13.5474 −0.822945 −0.411473 0.911422i \(-0.634985\pi\)
−0.411473 + 0.911422i \(0.634985\pi\)
\(272\) 6.77228 0.410630
\(273\) −0.185960 −0.0112548
\(274\) −6.54642 −0.395484
\(275\) −1.37726 −0.0830522
\(276\) 18.6360 1.12175
\(277\) 29.4054 1.76680 0.883401 0.468619i \(-0.155248\pi\)
0.883401 + 0.468619i \(0.155248\pi\)
\(278\) −3.21403 −0.192765
\(279\) 6.67131 0.399401
\(280\) −1.78519 −0.106686
\(281\) 8.19382 0.488802 0.244401 0.969674i \(-0.421409\pi\)
0.244401 + 0.969674i \(0.421409\pi\)
\(282\) 2.06380 0.122897
\(283\) −16.3506 −0.971944 −0.485972 0.873974i \(-0.661534\pi\)
−0.485972 + 0.873974i \(0.661534\pi\)
\(284\) 7.06979 0.419515
\(285\) −1.65995 −0.0983269
\(286\) 0.499444 0.0295328
\(287\) 0.492027 0.0290435
\(288\) −4.84401 −0.285436
\(289\) 1.00000 0.0588235
\(290\) −16.2501 −0.954241
\(291\) −11.2692 −0.660610
\(292\) 62.3247 3.64727
\(293\) 2.33032 0.136139 0.0680693 0.997681i \(-0.478316\pi\)
0.0680693 + 0.997681i \(0.478316\pi\)
\(294\) −17.5023 −1.02076
\(295\) 7.48840 0.435992
\(296\) 1.86240 0.108250
\(297\) −0.332092 −0.0192699
\(298\) 22.4606 1.30111
\(299\) 2.49419 0.144243
\(300\) 18.3768 1.06098
\(301\) 0.0148079 0.000853514 0
\(302\) −47.2364 −2.71815
\(303\) 10.0976 0.580091
\(304\) −12.1736 −0.698201
\(305\) 5.07122 0.290377
\(306\) −2.53596 −0.144971
\(307\) −31.7382 −1.81139 −0.905696 0.423928i \(-0.860651\pi\)
−0.905696 + 0.423928i \(0.860651\pi\)
\(308\) −0.461424 −0.0262921
\(309\) 0.586459 0.0333625
\(310\) 15.6230 0.887328
\(311\) 15.1662 0.859997 0.429999 0.902830i \(-0.358514\pi\)
0.429999 + 0.902830i \(0.358514\pi\)
\(312\) −3.65618 −0.206991
\(313\) −11.2491 −0.635834 −0.317917 0.948118i \(-0.602983\pi\)
−0.317917 + 0.948118i \(0.602983\pi\)
\(314\) 2.53596 0.143112
\(315\) 0.289564 0.0163151
\(316\) 11.4732 0.645417
\(317\) −31.3618 −1.76146 −0.880728 0.473622i \(-0.842946\pi\)
−0.880728 + 0.473622i \(0.842946\pi\)
\(318\) −27.0243 −1.51545
\(319\) −2.30441 −0.129022
\(320\) 1.16389 0.0650634
\(321\) −8.33650 −0.465298
\(322\) −3.34439 −0.186376
\(323\) −1.79756 −0.100019
\(324\) 4.43108 0.246171
\(325\) 2.45950 0.136429
\(326\) 55.7201 3.08605
\(327\) 2.22413 0.122995
\(328\) 9.67379 0.534146
\(329\) −0.255187 −0.0140689
\(330\) −0.777700 −0.0428110
\(331\) 24.2806 1.33458 0.667292 0.744796i \(-0.267453\pi\)
0.667292 + 0.744796i \(0.267453\pi\)
\(332\) 32.7555 1.79769
\(333\) −0.302087 −0.0165543
\(334\) 14.9324 0.817066
\(335\) −8.64298 −0.472217
\(336\) 2.12358 0.115851
\(337\) −21.3301 −1.16192 −0.580962 0.813931i \(-0.697324\pi\)
−0.580962 + 0.813931i \(0.697324\pi\)
\(338\) 32.0755 1.74468
\(339\) 16.6199 0.902669
\(340\) −4.09187 −0.221913
\(341\) 2.21548 0.119975
\(342\) 4.55853 0.246497
\(343\) 4.35913 0.235371
\(344\) 0.291139 0.0156972
\(345\) −3.88378 −0.209096
\(346\) −11.0580 −0.594481
\(347\) −11.9899 −0.643652 −0.321826 0.946799i \(-0.604297\pi\)
−0.321826 + 0.946799i \(0.604297\pi\)
\(348\) 30.7477 1.64825
\(349\) 19.2235 1.02901 0.514504 0.857488i \(-0.327976\pi\)
0.514504 + 0.857488i \(0.327976\pi\)
\(350\) −3.29788 −0.176279
\(351\) 0.593045 0.0316544
\(352\) −1.60865 −0.0857415
\(353\) 16.8133 0.894880 0.447440 0.894314i \(-0.352336\pi\)
0.447440 + 0.894314i \(0.352336\pi\)
\(354\) −20.5645 −1.09299
\(355\) −1.47336 −0.0781980
\(356\) −43.7424 −2.31834
\(357\) 0.313569 0.0165958
\(358\) 44.1899 2.33551
\(359\) −17.5793 −0.927801 −0.463901 0.885887i \(-0.653551\pi\)
−0.463901 + 0.885887i \(0.653551\pi\)
\(360\) 5.69315 0.300055
\(361\) −15.7688 −0.829936
\(362\) −5.30427 −0.278786
\(363\) 10.8897 0.571562
\(364\) 0.824005 0.0431896
\(365\) −12.9886 −0.679855
\(366\) −13.9265 −0.727950
\(367\) −6.31057 −0.329409 −0.164705 0.986343i \(-0.552667\pi\)
−0.164705 + 0.986343i \(0.552667\pi\)
\(368\) −28.4825 −1.48475
\(369\) −1.56912 −0.0816852
\(370\) −0.707434 −0.0367777
\(371\) 3.34153 0.173483
\(372\) −29.5611 −1.53267
\(373\) −1.26394 −0.0654443 −0.0327221 0.999464i \(-0.510418\pi\)
−0.0327221 + 0.999464i \(0.510418\pi\)
\(374\) −0.842170 −0.0435476
\(375\) −8.44700 −0.436201
\(376\) −5.01725 −0.258745
\(377\) 4.11519 0.211943
\(378\) −0.795197 −0.0409005
\(379\) −36.8623 −1.89349 −0.946744 0.321986i \(-0.895649\pi\)
−0.946744 + 0.321986i \(0.895649\pi\)
\(380\) 7.35536 0.377322
\(381\) −15.3714 −0.787503
\(382\) −52.2920 −2.67549
\(383\) −17.0762 −0.872553 −0.436277 0.899813i \(-0.643703\pi\)
−0.436277 + 0.899813i \(0.643703\pi\)
\(384\) −12.8843 −0.657497
\(385\) 0.0961619 0.00490087
\(386\) −40.2931 −2.05087
\(387\) −0.0472238 −0.00240052
\(388\) 49.9345 2.53504
\(389\) 5.23543 0.265447 0.132723 0.991153i \(-0.457628\pi\)
0.132723 + 0.991153i \(0.457628\pi\)
\(390\) 1.38881 0.0703249
\(391\) −4.20574 −0.212694
\(392\) 42.5495 2.14908
\(393\) 8.97750 0.452855
\(394\) −65.3923 −3.29442
\(395\) −2.39104 −0.120306
\(396\) 1.47152 0.0739468
\(397\) 9.37319 0.470427 0.235214 0.971944i \(-0.424421\pi\)
0.235214 + 0.971944i \(0.424421\pi\)
\(398\) 0.277203 0.0138949
\(399\) −0.563658 −0.0282182
\(400\) −28.0863 −1.40432
\(401\) 11.9830 0.598404 0.299202 0.954190i \(-0.403280\pi\)
0.299202 + 0.954190i \(0.403280\pi\)
\(402\) 23.7352 1.18380
\(403\) −3.95638 −0.197081
\(404\) −44.7432 −2.22606
\(405\) −0.923448 −0.0458865
\(406\) −5.51795 −0.273851
\(407\) −0.100320 −0.00497270
\(408\) 6.16510 0.305218
\(409\) 25.9635 1.28381 0.641907 0.766783i \(-0.278144\pi\)
0.641907 + 0.766783i \(0.278144\pi\)
\(410\) −3.67460 −0.181476
\(411\) −2.58144 −0.127333
\(412\) −2.59864 −0.128026
\(413\) 2.54279 0.125122
\(414\) 10.6656 0.524185
\(415\) −6.82633 −0.335092
\(416\) 2.87271 0.140846
\(417\) −1.26738 −0.0620640
\(418\) 1.51385 0.0740447
\(419\) −10.0075 −0.488899 −0.244450 0.969662i \(-0.578607\pi\)
−0.244450 + 0.969662i \(0.578607\pi\)
\(420\) −1.28308 −0.0626080
\(421\) 6.16395 0.300412 0.150206 0.988655i \(-0.452006\pi\)
0.150206 + 0.988655i \(0.452006\pi\)
\(422\) 21.6252 1.05270
\(423\) 0.813814 0.0395690
\(424\) 65.6980 3.19058
\(425\) −4.14724 −0.201171
\(426\) 4.04612 0.196035
\(427\) 1.72200 0.0833334
\(428\) 36.9397 1.78555
\(429\) 0.196945 0.00950860
\(430\) −0.110590 −0.00533311
\(431\) −28.0146 −1.34942 −0.674709 0.738084i \(-0.735731\pi\)
−0.674709 + 0.738084i \(0.735731\pi\)
\(432\) −6.77228 −0.325832
\(433\) −21.2919 −1.02323 −0.511613 0.859216i \(-0.670952\pi\)
−0.511613 + 0.859216i \(0.670952\pi\)
\(434\) 5.30500 0.254648
\(435\) −6.40789 −0.307235
\(436\) −9.85529 −0.471983
\(437\) 7.56006 0.361647
\(438\) 35.6691 1.70434
\(439\) −26.2587 −1.25326 −0.626630 0.779317i \(-0.715566\pi\)
−0.626630 + 0.779317i \(0.715566\pi\)
\(440\) 1.89065 0.0901331
\(441\) −6.90167 −0.328651
\(442\) 1.50394 0.0715349
\(443\) 25.5260 1.21278 0.606388 0.795169i \(-0.292618\pi\)
0.606388 + 0.795169i \(0.292618\pi\)
\(444\) 1.33857 0.0635257
\(445\) 9.11603 0.432141
\(446\) −21.0953 −0.998893
\(447\) 8.85684 0.418914
\(448\) 0.395214 0.0186721
\(449\) −18.6871 −0.881899 −0.440950 0.897532i \(-0.645358\pi\)
−0.440950 + 0.897532i \(0.645358\pi\)
\(450\) 10.5172 0.495787
\(451\) −0.521092 −0.0245372
\(452\) −73.6441 −3.46392
\(453\) −18.6267 −0.875157
\(454\) 23.2755 1.09237
\(455\) −0.171725 −0.00805058
\(456\) −11.0821 −0.518968
\(457\) −38.9868 −1.82373 −0.911863 0.410495i \(-0.865356\pi\)
−0.911863 + 0.410495i \(0.865356\pi\)
\(458\) 13.3736 0.624908
\(459\) −1.00000 −0.0466760
\(460\) 17.2093 0.802390
\(461\) −33.4769 −1.55918 −0.779588 0.626293i \(-0.784571\pi\)
−0.779588 + 0.626293i \(0.784571\pi\)
\(462\) −0.264078 −0.0122860
\(463\) −9.04105 −0.420173 −0.210087 0.977683i \(-0.567375\pi\)
−0.210087 + 0.977683i \(0.567375\pi\)
\(464\) −46.9935 −2.18162
\(465\) 6.16060 0.285691
\(466\) −44.6904 −2.07024
\(467\) 16.9066 0.782346 0.391173 0.920317i \(-0.372069\pi\)
0.391173 + 0.920317i \(0.372069\pi\)
\(468\) −2.62783 −0.121471
\(469\) −2.93484 −0.135518
\(470\) 1.90581 0.0879084
\(471\) 1.00000 0.0460776
\(472\) 49.9939 2.30116
\(473\) −0.0156826 −0.000721088 0
\(474\) 6.56624 0.301597
\(475\) 7.45491 0.342055
\(476\) −1.38945 −0.0636852
\(477\) −10.6564 −0.487925
\(478\) 33.5514 1.53460
\(479\) 7.14652 0.326533 0.163266 0.986582i \(-0.447797\pi\)
0.163266 + 0.986582i \(0.447797\pi\)
\(480\) −4.47319 −0.204172
\(481\) 0.179151 0.00816858
\(482\) −71.5604 −3.25949
\(483\) −1.31879 −0.0600070
\(484\) −48.2532 −2.19333
\(485\) −10.4065 −0.472534
\(486\) 2.53596 0.115033
\(487\) −9.59834 −0.434942 −0.217471 0.976067i \(-0.569781\pi\)
−0.217471 + 0.976067i \(0.569781\pi\)
\(488\) 33.8564 1.53261
\(489\) 21.9720 0.993610
\(490\) −16.1625 −0.730147
\(491\) −24.3039 −1.09682 −0.548410 0.836210i \(-0.684766\pi\)
−0.548410 + 0.836210i \(0.684766\pi\)
\(492\) 6.95289 0.313461
\(493\) −6.93910 −0.312521
\(494\) −2.70341 −0.121632
\(495\) −0.306669 −0.0137838
\(496\) 45.1800 2.02864
\(497\) −0.500300 −0.0224415
\(498\) 18.7464 0.840045
\(499\) 9.78357 0.437973 0.218986 0.975728i \(-0.429725\pi\)
0.218986 + 0.975728i \(0.429725\pi\)
\(500\) 37.4293 1.67389
\(501\) 5.88828 0.263069
\(502\) −22.7162 −1.01387
\(503\) −38.0479 −1.69647 −0.848237 0.529617i \(-0.822336\pi\)
−0.848237 + 0.529617i \(0.822336\pi\)
\(504\) 1.93318 0.0861109
\(505\) 9.32459 0.414939
\(506\) 3.54195 0.157459
\(507\) 12.6483 0.561731
\(508\) 68.1120 3.02198
\(509\) 34.8691 1.54554 0.772772 0.634683i \(-0.218869\pi\)
0.772772 + 0.634683i \(0.218869\pi\)
\(510\) −2.34182 −0.103698
\(511\) −4.41046 −0.195107
\(512\) 50.6986 2.24058
\(513\) 1.79756 0.0793641
\(514\) −60.8801 −2.68531
\(515\) 0.541564 0.0238642
\(516\) 0.209252 0.00921181
\(517\) 0.270261 0.0118861
\(518\) −0.240219 −0.0105546
\(519\) −4.36048 −0.191404
\(520\) −3.37629 −0.148060
\(521\) 33.2457 1.45652 0.728260 0.685301i \(-0.240329\pi\)
0.728260 + 0.685301i \(0.240329\pi\)
\(522\) 17.5972 0.770210
\(523\) 21.3107 0.931852 0.465926 0.884824i \(-0.345721\pi\)
0.465926 + 0.884824i \(0.345721\pi\)
\(524\) −39.7800 −1.73780
\(525\) −1.30045 −0.0567562
\(526\) 38.9002 1.69613
\(527\) 6.67131 0.290607
\(528\) −2.24902 −0.0978759
\(529\) −5.31172 −0.230944
\(530\) −24.9555 −1.08400
\(531\) −8.10918 −0.351908
\(532\) 2.49761 0.108285
\(533\) 0.930559 0.0403070
\(534\) −25.0343 −1.08334
\(535\) −7.69832 −0.332827
\(536\) −57.7021 −2.49235
\(537\) 17.4253 0.751959
\(538\) 39.9784 1.72359
\(539\) −2.29199 −0.0987229
\(540\) 4.09187 0.176086
\(541\) −11.7978 −0.507228 −0.253614 0.967305i \(-0.581619\pi\)
−0.253614 + 0.967305i \(0.581619\pi\)
\(542\) 34.3556 1.47570
\(543\) −2.09162 −0.0897602
\(544\) −4.84401 −0.207685
\(545\) 2.05387 0.0879780
\(546\) 0.471587 0.0201821
\(547\) 18.7172 0.800289 0.400144 0.916452i \(-0.368960\pi\)
0.400144 + 0.916452i \(0.368960\pi\)
\(548\) 11.4386 0.488631
\(549\) −5.49161 −0.234376
\(550\) 3.49268 0.148929
\(551\) 12.4734 0.531385
\(552\) −25.9288 −1.10360
\(553\) −0.811910 −0.0345259
\(554\) −74.5709 −3.16821
\(555\) −0.278961 −0.0118413
\(556\) 5.61587 0.238166
\(557\) −10.5176 −0.445646 −0.222823 0.974859i \(-0.571527\pi\)
−0.222823 + 0.974859i \(0.571527\pi\)
\(558\) −16.9181 −0.716202
\(559\) 0.0280058 0.00118452
\(560\) 1.96101 0.0828679
\(561\) −0.332092 −0.0140209
\(562\) −20.7792 −0.876516
\(563\) 12.9143 0.544275 0.272137 0.962258i \(-0.412269\pi\)
0.272137 + 0.962258i \(0.412269\pi\)
\(564\) −3.60607 −0.151843
\(565\) 15.3476 0.645679
\(566\) 41.4645 1.74288
\(567\) −0.313569 −0.0131687
\(568\) −9.83644 −0.412728
\(569\) 10.0914 0.423053 0.211526 0.977372i \(-0.432157\pi\)
0.211526 + 0.977372i \(0.432157\pi\)
\(570\) 4.20956 0.176319
\(571\) 45.8348 1.91813 0.959063 0.283194i \(-0.0913942\pi\)
0.959063 + 0.283194i \(0.0913942\pi\)
\(572\) −0.872679 −0.0364885
\(573\) −20.6202 −0.861423
\(574\) −1.24776 −0.0520805
\(575\) 17.4422 0.727392
\(576\) −1.26037 −0.0525156
\(577\) 14.5344 0.605076 0.302538 0.953137i \(-0.402166\pi\)
0.302538 + 0.953137i \(0.402166\pi\)
\(578\) −2.53596 −0.105482
\(579\) −15.8887 −0.660313
\(580\) 28.3939 1.17899
\(581\) −2.31797 −0.0961657
\(582\) 28.5781 1.18460
\(583\) −3.53891 −0.146567
\(584\) −86.7144 −3.58827
\(585\) 0.547646 0.0226424
\(586\) −5.90958 −0.244123
\(587\) 36.9283 1.52420 0.762098 0.647462i \(-0.224169\pi\)
0.762098 + 0.647462i \(0.224169\pi\)
\(588\) 30.5818 1.26117
\(589\) −11.9921 −0.494124
\(590\) −18.9903 −0.781817
\(591\) −25.7860 −1.06070
\(592\) −2.04582 −0.0840826
\(593\) −21.7314 −0.892401 −0.446200 0.894933i \(-0.647223\pi\)
−0.446200 + 0.894933i \(0.647223\pi\)
\(594\) 0.842170 0.0345546
\(595\) 0.289564 0.0118710
\(596\) −39.2453 −1.60755
\(597\) 0.109309 0.00447372
\(598\) −6.32517 −0.258655
\(599\) 46.0633 1.88209 0.941047 0.338276i \(-0.109844\pi\)
0.941047 + 0.338276i \(0.109844\pi\)
\(600\) −25.5682 −1.04382
\(601\) 21.7684 0.887953 0.443977 0.896038i \(-0.353567\pi\)
0.443977 + 0.896038i \(0.353567\pi\)
\(602\) −0.0375522 −0.00153051
\(603\) 9.35947 0.381147
\(604\) 82.5362 3.35835
\(605\) 10.0561 0.408838
\(606\) −25.6070 −1.04021
\(607\) −23.8993 −0.970043 −0.485022 0.874502i \(-0.661188\pi\)
−0.485022 + 0.874502i \(0.661188\pi\)
\(608\) 8.70737 0.353131
\(609\) −2.17588 −0.0881713
\(610\) −12.8604 −0.520702
\(611\) −0.482628 −0.0195251
\(612\) 4.43108 0.179116
\(613\) 8.52372 0.344270 0.172135 0.985073i \(-0.444934\pi\)
0.172135 + 0.985073i \(0.444934\pi\)
\(614\) 80.4866 3.24817
\(615\) −1.44900 −0.0584294
\(616\) 0.641994 0.0258667
\(617\) 39.1477 1.57603 0.788014 0.615657i \(-0.211109\pi\)
0.788014 + 0.615657i \(0.211109\pi\)
\(618\) −1.48723 −0.0598254
\(619\) 47.1167 1.89378 0.946890 0.321558i \(-0.104206\pi\)
0.946890 + 0.321558i \(0.104206\pi\)
\(620\) −27.2981 −1.09632
\(621\) 4.20574 0.168771
\(622\) −38.4609 −1.54214
\(623\) 3.09547 0.124017
\(624\) 4.01627 0.160779
\(625\) 12.9359 0.517434
\(626\) 28.5271 1.14017
\(627\) 0.596953 0.0238400
\(628\) −4.43108 −0.176819
\(629\) −0.302087 −0.0120450
\(630\) −0.734323 −0.0292561
\(631\) 9.73238 0.387440 0.193720 0.981057i \(-0.437945\pi\)
0.193720 + 0.981057i \(0.437945\pi\)
\(632\) −15.9630 −0.634975
\(633\) 8.52744 0.338935
\(634\) 79.5322 3.15863
\(635\) −14.1947 −0.563300
\(636\) 47.2195 1.87237
\(637\) 4.09300 0.162171
\(638\) 5.84390 0.231362
\(639\) 1.59550 0.0631171
\(640\) −11.8979 −0.470308
\(641\) 34.7684 1.37327 0.686634 0.727003i \(-0.259087\pi\)
0.686634 + 0.727003i \(0.259087\pi\)
\(642\) 21.1410 0.834369
\(643\) 23.8071 0.938859 0.469430 0.882970i \(-0.344460\pi\)
0.469430 + 0.882970i \(0.344460\pi\)
\(644\) 5.84366 0.230272
\(645\) −0.0436087 −0.00171709
\(646\) 4.55853 0.179353
\(647\) 30.8358 1.21228 0.606141 0.795357i \(-0.292717\pi\)
0.606141 + 0.795357i \(0.292717\pi\)
\(648\) −6.16510 −0.242188
\(649\) −2.69299 −0.105709
\(650\) −6.23719 −0.244643
\(651\) 2.09191 0.0819886
\(652\) −97.3597 −3.81290
\(653\) 31.1426 1.21870 0.609352 0.792900i \(-0.291430\pi\)
0.609352 + 0.792900i \(0.291430\pi\)
\(654\) −5.64030 −0.220553
\(655\) 8.29025 0.323927
\(656\) −10.6265 −0.414896
\(657\) 14.0654 0.548742
\(658\) 0.647143 0.0252283
\(659\) 11.1909 0.435935 0.217968 0.975956i \(-0.430057\pi\)
0.217968 + 0.975956i \(0.430057\pi\)
\(660\) 1.35887 0.0528941
\(661\) 28.3192 1.10149 0.550744 0.834674i \(-0.314344\pi\)
0.550744 + 0.834674i \(0.314344\pi\)
\(662\) −61.5746 −2.39317
\(663\) 0.593045 0.0230319
\(664\) −45.5738 −1.76861
\(665\) −0.520509 −0.0201845
\(666\) 0.766079 0.0296850
\(667\) 29.1841 1.13001
\(668\) −26.0914 −1.00951
\(669\) −8.31849 −0.321612
\(670\) 21.9182 0.846775
\(671\) −1.82372 −0.0704039
\(672\) −1.51893 −0.0585940
\(673\) −27.3602 −1.05466 −0.527328 0.849662i \(-0.676806\pi\)
−0.527328 + 0.849662i \(0.676806\pi\)
\(674\) 54.0922 2.08355
\(675\) 4.14724 0.159628
\(676\) −56.0456 −2.15560
\(677\) −31.3378 −1.20441 −0.602204 0.798342i \(-0.705711\pi\)
−0.602204 + 0.798342i \(0.705711\pi\)
\(678\) −42.1474 −1.61866
\(679\) −3.53366 −0.135609
\(680\) 5.69315 0.218322
\(681\) 9.17819 0.351709
\(682\) −5.61837 −0.215139
\(683\) 47.1546 1.80432 0.902159 0.431403i \(-0.141981\pi\)
0.902159 + 0.431403i \(0.141981\pi\)
\(684\) −7.96511 −0.304554
\(685\) −2.38382 −0.0910812
\(686\) −11.0546 −0.422065
\(687\) 5.27359 0.201200
\(688\) −0.319813 −0.0121927
\(689\) 6.31974 0.240763
\(690\) 9.84911 0.374949
\(691\) −0.589097 −0.0224103 −0.0112052 0.999937i \(-0.503567\pi\)
−0.0112052 + 0.999937i \(0.503567\pi\)
\(692\) 19.3216 0.734498
\(693\) −0.104134 −0.00395571
\(694\) 30.4059 1.15419
\(695\) −1.17036 −0.0443944
\(696\) −42.7802 −1.62158
\(697\) −1.56912 −0.0594347
\(698\) −48.7499 −1.84521
\(699\) −17.6227 −0.666551
\(700\) 5.76238 0.217797
\(701\) 22.9695 0.867547 0.433773 0.901022i \(-0.357182\pi\)
0.433773 + 0.901022i \(0.357182\pi\)
\(702\) −1.50394 −0.0567624
\(703\) 0.543018 0.0204803
\(704\) −0.418559 −0.0157751
\(705\) 0.751515 0.0283037
\(706\) −42.6377 −1.60469
\(707\) 3.16629 0.119081
\(708\) 35.9324 1.35042
\(709\) −36.0984 −1.35570 −0.677852 0.735199i \(-0.737089\pi\)
−0.677852 + 0.735199i \(0.737089\pi\)
\(710\) 3.73638 0.140224
\(711\) 2.58926 0.0971047
\(712\) 60.8602 2.28083
\(713\) −28.0578 −1.05077
\(714\) −0.795197 −0.0297595
\(715\) 0.181869 0.00680150
\(716\) −77.2130 −2.88559
\(717\) 13.2303 0.494093
\(718\) 44.5804 1.66373
\(719\) −1.28684 −0.0479910 −0.0239955 0.999712i \(-0.507639\pi\)
−0.0239955 + 0.999712i \(0.507639\pi\)
\(720\) −6.25385 −0.233067
\(721\) 0.183895 0.00684862
\(722\) 39.9890 1.48824
\(723\) −28.2183 −1.04945
\(724\) 9.26814 0.344448
\(725\) 28.7781 1.06879
\(726\) −27.6158 −1.02492
\(727\) 39.7396 1.47386 0.736930 0.675969i \(-0.236275\pi\)
0.736930 + 0.675969i \(0.236275\pi\)
\(728\) −1.14646 −0.0424908
\(729\) 1.00000 0.0370370
\(730\) 32.9386 1.21911
\(731\) −0.0472238 −0.00174663
\(732\) 24.3338 0.899402
\(733\) −15.5985 −0.576145 −0.288072 0.957609i \(-0.593014\pi\)
−0.288072 + 0.957609i \(0.593014\pi\)
\(734\) 16.0033 0.590694
\(735\) −6.37334 −0.235084
\(736\) 20.3726 0.750946
\(737\) 3.10820 0.114492
\(738\) 3.97922 0.146477
\(739\) −5.42021 −0.199386 −0.0996928 0.995018i \(-0.531786\pi\)
−0.0996928 + 0.995018i \(0.531786\pi\)
\(740\) 1.23610 0.0454399
\(741\) −1.06603 −0.0391616
\(742\) −8.47397 −0.311089
\(743\) −19.5038 −0.715523 −0.357762 0.933813i \(-0.616460\pi\)
−0.357762 + 0.933813i \(0.616460\pi\)
\(744\) 41.1293 1.50787
\(745\) 8.17883 0.299649
\(746\) 3.20529 0.117354
\(747\) 7.39223 0.270467
\(748\) 1.47152 0.0538042
\(749\) −2.61407 −0.0955159
\(750\) 21.4212 0.782193
\(751\) −30.3153 −1.10622 −0.553111 0.833107i \(-0.686560\pi\)
−0.553111 + 0.833107i \(0.686560\pi\)
\(752\) 5.51138 0.200979
\(753\) −8.95764 −0.326434
\(754\) −10.4360 −0.380055
\(755\) −17.2008 −0.625999
\(756\) 1.38945 0.0505337
\(757\) 34.4270 1.25127 0.625634 0.780116i \(-0.284840\pi\)
0.625634 + 0.780116i \(0.284840\pi\)
\(758\) 93.4812 3.39539
\(759\) 1.39669 0.0506967
\(760\) −10.2338 −0.371217
\(761\) 10.4328 0.378188 0.189094 0.981959i \(-0.439445\pi\)
0.189094 + 0.981959i \(0.439445\pi\)
\(762\) 38.9813 1.41214
\(763\) 0.697418 0.0252482
\(764\) 91.3699 3.30565
\(765\) −0.923448 −0.0333873
\(766\) 43.3045 1.56466
\(767\) 4.80911 0.173647
\(768\) 30.1532 1.08806
\(769\) 49.5981 1.78855 0.894276 0.447516i \(-0.147691\pi\)
0.894276 + 0.447516i \(0.147691\pi\)
\(770\) −0.243862 −0.00878819
\(771\) −24.0068 −0.864583
\(772\) 70.4041 2.53390
\(773\) −44.8291 −1.61239 −0.806195 0.591649i \(-0.798477\pi\)
−0.806195 + 0.591649i \(0.798477\pi\)
\(774\) 0.119757 0.00430459
\(775\) −27.6675 −0.993847
\(776\) −69.4755 −2.49403
\(777\) −0.0947250 −0.00339824
\(778\) −13.2768 −0.475997
\(779\) 2.82058 0.101058
\(780\) −2.42666 −0.0868884
\(781\) 0.529853 0.0189596
\(782\) 10.6656 0.381400
\(783\) 6.93910 0.247983
\(784\) −46.7401 −1.66929
\(785\) 0.923448 0.0329593
\(786\) −22.7666 −0.812056
\(787\) −34.6405 −1.23480 −0.617400 0.786649i \(-0.711814\pi\)
−0.617400 + 0.786649i \(0.711814\pi\)
\(788\) 114.260 4.07034
\(789\) 15.3395 0.546100
\(790\) 6.06358 0.215733
\(791\) 5.21148 0.185299
\(792\) −2.04738 −0.0727504
\(793\) 3.25677 0.115651
\(794\) −23.7700 −0.843566
\(795\) −9.84066 −0.349012
\(796\) −0.484357 −0.0171676
\(797\) 45.9079 1.62614 0.813070 0.582166i \(-0.197795\pi\)
0.813070 + 0.582166i \(0.197795\pi\)
\(798\) 1.42941 0.0506006
\(799\) 0.813814 0.0287907
\(800\) 20.0893 0.710263
\(801\) −9.87173 −0.348800
\(802\) −30.3885 −1.07305
\(803\) 4.67099 0.164836
\(804\) −41.4725 −1.46262
\(805\) −1.21783 −0.0429230
\(806\) 10.0332 0.353405
\(807\) 15.7646 0.554941
\(808\) 62.2526 2.19004
\(809\) 30.1172 1.05887 0.529433 0.848352i \(-0.322405\pi\)
0.529433 + 0.848352i \(0.322405\pi\)
\(810\) 2.34182 0.0822833
\(811\) −51.6411 −1.81336 −0.906682 0.421814i \(-0.861393\pi\)
−0.906682 + 0.421814i \(0.861393\pi\)
\(812\) 9.64151 0.338351
\(813\) 13.5474 0.475128
\(814\) 0.254408 0.00891701
\(815\) 20.2900 0.710728
\(816\) −6.77228 −0.237077
\(817\) 0.0848874 0.00296984
\(818\) −65.8423 −2.30212
\(819\) 0.185960 0.00649798
\(820\) 6.42063 0.224218
\(821\) 53.1082 1.85349 0.926744 0.375693i \(-0.122595\pi\)
0.926744 + 0.375693i \(0.122595\pi\)
\(822\) 6.54642 0.228333
\(823\) −5.03817 −0.175619 −0.0878097 0.996137i \(-0.527987\pi\)
−0.0878097 + 0.996137i \(0.527987\pi\)
\(824\) 3.61558 0.125955
\(825\) 1.37726 0.0479502
\(826\) −6.44840 −0.224368
\(827\) −26.6843 −0.927902 −0.463951 0.885861i \(-0.653569\pi\)
−0.463951 + 0.885861i \(0.653569\pi\)
\(828\) −18.6360 −0.647645
\(829\) 34.6830 1.20459 0.602296 0.798273i \(-0.294253\pi\)
0.602296 + 0.798273i \(0.294253\pi\)
\(830\) 17.3113 0.600884
\(831\) −29.4054 −1.02006
\(832\) 0.747458 0.0259134
\(833\) −6.90167 −0.239129
\(834\) 3.21403 0.111293
\(835\) 5.43752 0.188173
\(836\) −2.64515 −0.0914843
\(837\) −6.67131 −0.230594
\(838\) 25.3786 0.876690
\(839\) 7.94707 0.274363 0.137182 0.990546i \(-0.456196\pi\)
0.137182 + 0.990546i \(0.456196\pi\)
\(840\) 1.78519 0.0615951
\(841\) 19.1510 0.660381
\(842\) −15.6315 −0.538697
\(843\) −8.19382 −0.282210
\(844\) −37.7857 −1.30064
\(845\) 11.6800 0.401806
\(846\) −2.06380 −0.0709548
\(847\) 3.41468 0.117330
\(848\) −72.1684 −2.47827
\(849\) 16.3506 0.561152
\(850\) 10.5172 0.360738
\(851\) 1.27050 0.0435522
\(852\) −7.06979 −0.242207
\(853\) 40.3597 1.38189 0.690945 0.722907i \(-0.257195\pi\)
0.690945 + 0.722907i \(0.257195\pi\)
\(854\) −4.36692 −0.149433
\(855\) 1.65995 0.0567691
\(856\) −51.3954 −1.75666
\(857\) 25.9641 0.886916 0.443458 0.896295i \(-0.353751\pi\)
0.443458 + 0.896295i \(0.353751\pi\)
\(858\) −0.499444 −0.0170507
\(859\) −26.0911 −0.890217 −0.445109 0.895477i \(-0.646835\pi\)
−0.445109 + 0.895477i \(0.646835\pi\)
\(860\) 0.193233 0.00658921
\(861\) −0.492027 −0.0167682
\(862\) 71.0439 2.41976
\(863\) 22.7478 0.774344 0.387172 0.922007i \(-0.373452\pi\)
0.387172 + 0.922007i \(0.373452\pi\)
\(864\) 4.84401 0.164796
\(865\) −4.02668 −0.136911
\(866\) 53.9954 1.83484
\(867\) −1.00000 −0.0339618
\(868\) −9.26943 −0.314625
\(869\) 0.859870 0.0291691
\(870\) 16.2501 0.550931
\(871\) −5.55059 −0.188074
\(872\) 13.7120 0.464347
\(873\) 11.2692 0.381403
\(874\) −19.1720 −0.648502
\(875\) −2.64872 −0.0895430
\(876\) −62.3247 −2.10576
\(877\) −27.3883 −0.924838 −0.462419 0.886661i \(-0.653018\pi\)
−0.462419 + 0.886661i \(0.653018\pi\)
\(878\) 66.5910 2.24734
\(879\) −2.33032 −0.0785997
\(880\) −2.07685 −0.0700106
\(881\) −48.2041 −1.62404 −0.812018 0.583632i \(-0.801631\pi\)
−0.812018 + 0.583632i \(0.801631\pi\)
\(882\) 17.5023 0.589335
\(883\) 48.7104 1.63923 0.819617 0.572912i \(-0.194186\pi\)
0.819617 + 0.572912i \(0.194186\pi\)
\(884\) −2.62783 −0.0883834
\(885\) −7.48840 −0.251720
\(886\) −64.7328 −2.17474
\(887\) 36.4043 1.22234 0.611169 0.791500i \(-0.290699\pi\)
0.611169 + 0.791500i \(0.290699\pi\)
\(888\) −1.86240 −0.0624979
\(889\) −4.82001 −0.161658
\(890\) −23.1178 −0.774912
\(891\) 0.332092 0.0111255
\(892\) 36.8599 1.23416
\(893\) −1.46288 −0.0489533
\(894\) −22.4606 −0.751193
\(895\) 16.0914 0.537876
\(896\) −4.04010 −0.134970
\(897\) −2.49419 −0.0832787
\(898\) 47.3897 1.58142
\(899\) −46.2928 −1.54395
\(900\) −18.3768 −0.612558
\(901\) −10.6564 −0.355017
\(902\) 1.32147 0.0440000
\(903\) −0.0148079 −0.000492776 0
\(904\) 102.463 3.40788
\(905\) −1.93151 −0.0642054
\(906\) 47.2364 1.56932
\(907\) −6.05898 −0.201185 −0.100592 0.994928i \(-0.532074\pi\)
−0.100592 + 0.994928i \(0.532074\pi\)
\(908\) −40.6692 −1.34966
\(909\) −10.0976 −0.334916
\(910\) 0.435486 0.0144362
\(911\) 13.0017 0.430765 0.215382 0.976530i \(-0.430900\pi\)
0.215382 + 0.976530i \(0.430900\pi\)
\(912\) 12.1736 0.403107
\(913\) 2.45490 0.0812452
\(914\) 98.8689 3.27029
\(915\) −5.07122 −0.167649
\(916\) −23.3677 −0.772090
\(917\) 2.81506 0.0929616
\(918\) 2.53596 0.0836990
\(919\) −36.1559 −1.19267 −0.596337 0.802734i \(-0.703378\pi\)
−0.596337 + 0.802734i \(0.703378\pi\)
\(920\) −23.9439 −0.789408
\(921\) 31.7382 1.04581
\(922\) 84.8960 2.79590
\(923\) −0.946204 −0.0311447
\(924\) 0.461424 0.0151797
\(925\) 1.25283 0.0411927
\(926\) 22.9277 0.753452
\(927\) −0.586459 −0.0192618
\(928\) 33.6130 1.10340
\(929\) 35.2188 1.15549 0.577746 0.816217i \(-0.303932\pi\)
0.577746 + 0.816217i \(0.303932\pi\)
\(930\) −15.6230 −0.512299
\(931\) 12.4061 0.406595
\(932\) 78.0875 2.55784
\(933\) −15.1662 −0.496520
\(934\) −42.8745 −1.40290
\(935\) −0.306669 −0.0100292
\(936\) 3.65618 0.119506
\(937\) 29.2136 0.954367 0.477184 0.878804i \(-0.341658\pi\)
0.477184 + 0.878804i \(0.341658\pi\)
\(938\) 7.44263 0.243010
\(939\) 11.2491 0.367099
\(940\) −3.33002 −0.108613
\(941\) 31.4811 1.02625 0.513127 0.858313i \(-0.328487\pi\)
0.513127 + 0.858313i \(0.328487\pi\)
\(942\) −2.53596 −0.0826259
\(943\) 6.59932 0.214903
\(944\) −54.9176 −1.78742
\(945\) −0.289564 −0.00941953
\(946\) 0.0397704 0.00129305
\(947\) −25.0363 −0.813569 −0.406785 0.913524i \(-0.633350\pi\)
−0.406785 + 0.913524i \(0.633350\pi\)
\(948\) −11.4732 −0.372632
\(949\) −8.34138 −0.270773
\(950\) −18.9053 −0.613370
\(951\) 31.3618 1.01698
\(952\) 1.93318 0.0626549
\(953\) 19.6534 0.636635 0.318317 0.947984i \(-0.396882\pi\)
0.318317 + 0.947984i \(0.396882\pi\)
\(954\) 27.0243 0.874943
\(955\) −19.0417 −0.616176
\(956\) −58.6243 −1.89604
\(957\) 2.30441 0.0744912
\(958\) −18.1233 −0.585536
\(959\) −0.809459 −0.0261388
\(960\) −1.16389 −0.0375644
\(961\) 13.5063 0.435688
\(962\) −0.454319 −0.0146478
\(963\) 8.33650 0.268640
\(964\) 125.037 4.02719
\(965\) −14.6724 −0.472321
\(966\) 3.34439 0.107604
\(967\) 30.2418 0.972511 0.486256 0.873817i \(-0.338362\pi\)
0.486256 + 0.873817i \(0.338362\pi\)
\(968\) 67.1362 2.15784
\(969\) 1.79756 0.0577458
\(970\) 26.3904 0.847344
\(971\) 43.6795 1.40174 0.700871 0.713288i \(-0.252795\pi\)
0.700871 + 0.713288i \(0.252795\pi\)
\(972\) −4.43108 −0.142127
\(973\) −0.397412 −0.0127404
\(974\) 24.3410 0.779935
\(975\) −2.45950 −0.0787671
\(976\) −37.1908 −1.19045
\(977\) −35.1447 −1.12438 −0.562189 0.827009i \(-0.690041\pi\)
−0.562189 + 0.827009i \(0.690041\pi\)
\(978\) −55.7201 −1.78173
\(979\) −3.27832 −0.104776
\(980\) 28.2407 0.902117
\(981\) −2.22413 −0.0710110
\(982\) 61.6336 1.96681
\(983\) −17.9334 −0.571986 −0.285993 0.958232i \(-0.592323\pi\)
−0.285993 + 0.958232i \(0.592323\pi\)
\(984\) −9.67379 −0.308389
\(985\) −23.8121 −0.758715
\(986\) 17.5972 0.560410
\(987\) 0.255187 0.00812269
\(988\) 4.72367 0.150280
\(989\) 0.198611 0.00631547
\(990\) 0.777700 0.0247169
\(991\) −29.8720 −0.948916 −0.474458 0.880278i \(-0.657356\pi\)
−0.474458 + 0.880278i \(0.657356\pi\)
\(992\) −32.3159 −1.02603
\(993\) −24.2806 −0.770522
\(994\) 1.26874 0.0402419
\(995\) 0.100941 0.00320005
\(996\) −32.7555 −1.03790
\(997\) −13.0881 −0.414505 −0.207253 0.978287i \(-0.566452\pi\)
−0.207253 + 0.978287i \(0.566452\pi\)
\(998\) −24.8107 −0.785370
\(999\) 0.302087 0.00955760
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 \(a_p\))