Properties

Label 4010.2.a.i.1.3
Level 4010
Weight 2
Character 4010.1
Self dual yes
Analytic conductor 32.020
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.54628\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.74362 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.74362 q^{6} +2.79885 q^{7} -1.00000 q^{8} +0.0402221 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.74362 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.74362 q^{6} +2.79885 q^{7} -1.00000 q^{8} +0.0402221 q^{9} -1.00000 q^{10} +2.90568 q^{11} -1.74362 q^{12} +3.29780 q^{13} -2.79885 q^{14} -1.74362 q^{15} +1.00000 q^{16} -4.26503 q^{17} -0.0402221 q^{18} -0.133159 q^{19} +1.00000 q^{20} -4.88013 q^{21} -2.90568 q^{22} -1.71130 q^{23} +1.74362 q^{24} +1.00000 q^{25} -3.29780 q^{26} +5.16074 q^{27} +2.79885 q^{28} -2.64609 q^{29} +1.74362 q^{30} -9.13104 q^{31} -1.00000 q^{32} -5.06642 q^{33} +4.26503 q^{34} +2.79885 q^{35} +0.0402221 q^{36} -11.8979 q^{37} +0.133159 q^{38} -5.75012 q^{39} -1.00000 q^{40} -5.26369 q^{41} +4.88013 q^{42} -4.56873 q^{43} +2.90568 q^{44} +0.0402221 q^{45} +1.71130 q^{46} +6.49550 q^{47} -1.74362 q^{48} +0.833534 q^{49} -1.00000 q^{50} +7.43660 q^{51} +3.29780 q^{52} +4.03808 q^{53} -5.16074 q^{54} +2.90568 q^{55} -2.79885 q^{56} +0.232179 q^{57} +2.64609 q^{58} -6.96517 q^{59} -1.74362 q^{60} -5.75525 q^{61} +9.13104 q^{62} +0.112575 q^{63} +1.00000 q^{64} +3.29780 q^{65} +5.06642 q^{66} -1.15003 q^{67} -4.26503 q^{68} +2.98386 q^{69} -2.79885 q^{70} -0.443856 q^{71} -0.0402221 q^{72} -0.955975 q^{73} +11.8979 q^{74} -1.74362 q^{75} -0.133159 q^{76} +8.13256 q^{77} +5.75012 q^{78} -14.5373 q^{79} +1.00000 q^{80} -9.11905 q^{81} +5.26369 q^{82} +16.8564 q^{83} -4.88013 q^{84} -4.26503 q^{85} +4.56873 q^{86} +4.61378 q^{87} -2.90568 q^{88} -13.2086 q^{89} -0.0402221 q^{90} +9.23003 q^{91} -1.71130 q^{92} +15.9211 q^{93} -6.49550 q^{94} -0.133159 q^{95} +1.74362 q^{96} -8.57086 q^{97} -0.833534 q^{98} +0.116873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.74362 −1.00668 −0.503341 0.864088i \(-0.667896\pi\)
−0.503341 + 0.864088i \(0.667896\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.74362 0.711831
\(7\) 2.79885 1.05786 0.528932 0.848664i \(-0.322593\pi\)
0.528932 + 0.848664i \(0.322593\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.0402221 0.0134074
\(10\) −1.00000 −0.316228
\(11\) 2.90568 0.876097 0.438048 0.898951i \(-0.355670\pi\)
0.438048 + 0.898951i \(0.355670\pi\)
\(12\) −1.74362 −0.503341
\(13\) 3.29780 0.914645 0.457322 0.889301i \(-0.348809\pi\)
0.457322 + 0.889301i \(0.348809\pi\)
\(14\) −2.79885 −0.748023
\(15\) −1.74362 −0.450202
\(16\) 1.00000 0.250000
\(17\) −4.26503 −1.03442 −0.517210 0.855858i \(-0.673030\pi\)
−0.517210 + 0.855858i \(0.673030\pi\)
\(18\) −0.0402221 −0.00948044
\(19\) −0.133159 −0.0305488 −0.0152744 0.999883i \(-0.504862\pi\)
−0.0152744 + 0.999883i \(0.504862\pi\)
\(20\) 1.00000 0.223607
\(21\) −4.88013 −1.06493
\(22\) −2.90568 −0.619494
\(23\) −1.71130 −0.356831 −0.178415 0.983955i \(-0.557097\pi\)
−0.178415 + 0.983955i \(0.557097\pi\)
\(24\) 1.74362 0.355916
\(25\) 1.00000 0.200000
\(26\) −3.29780 −0.646751
\(27\) 5.16074 0.993184
\(28\) 2.79885 0.528932
\(29\) −2.64609 −0.491366 −0.245683 0.969350i \(-0.579012\pi\)
−0.245683 + 0.969350i \(0.579012\pi\)
\(30\) 1.74362 0.318341
\(31\) −9.13104 −1.63998 −0.819992 0.572375i \(-0.806022\pi\)
−0.819992 + 0.572375i \(0.806022\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.06642 −0.881950
\(34\) 4.26503 0.731446
\(35\) 2.79885 0.473091
\(36\) 0.0402221 0.00670368
\(37\) −11.8979 −1.95600 −0.978001 0.208598i \(-0.933110\pi\)
−0.978001 + 0.208598i \(0.933110\pi\)
\(38\) 0.133159 0.0216012
\(39\) −5.75012 −0.920756
\(40\) −1.00000 −0.158114
\(41\) −5.26369 −0.822050 −0.411025 0.911624i \(-0.634829\pi\)
−0.411025 + 0.911624i \(0.634829\pi\)
\(42\) 4.88013 0.753021
\(43\) −4.56873 −0.696724 −0.348362 0.937360i \(-0.613262\pi\)
−0.348362 + 0.937360i \(0.613262\pi\)
\(44\) 2.90568 0.438048
\(45\) 0.0402221 0.00599596
\(46\) 1.71130 0.252317
\(47\) 6.49550 0.947466 0.473733 0.880668i \(-0.342906\pi\)
0.473733 + 0.880668i \(0.342906\pi\)
\(48\) −1.74362 −0.251670
\(49\) 0.833534 0.119076
\(50\) −1.00000 −0.141421
\(51\) 7.43660 1.04133
\(52\) 3.29780 0.457322
\(53\) 4.03808 0.554673 0.277336 0.960773i \(-0.410548\pi\)
0.277336 + 0.960773i \(0.410548\pi\)
\(54\) −5.16074 −0.702287
\(55\) 2.90568 0.391802
\(56\) −2.79885 −0.374011
\(57\) 0.232179 0.0307529
\(58\) 2.64609 0.347448
\(59\) −6.96517 −0.906788 −0.453394 0.891310i \(-0.649787\pi\)
−0.453394 + 0.891310i \(0.649787\pi\)
\(60\) −1.74362 −0.225101
\(61\) −5.75525 −0.736885 −0.368442 0.929651i \(-0.620109\pi\)
−0.368442 + 0.929651i \(0.620109\pi\)
\(62\) 9.13104 1.15964
\(63\) 0.112575 0.0141832
\(64\) 1.00000 0.125000
\(65\) 3.29780 0.409041
\(66\) 5.06642 0.623633
\(67\) −1.15003 −0.140499 −0.0702494 0.997529i \(-0.522380\pi\)
−0.0702494 + 0.997529i \(0.522380\pi\)
\(68\) −4.26503 −0.517210
\(69\) 2.98386 0.359215
\(70\) −2.79885 −0.334526
\(71\) −0.443856 −0.0526760 −0.0263380 0.999653i \(-0.508385\pi\)
−0.0263380 + 0.999653i \(0.508385\pi\)
\(72\) −0.0402221 −0.00474022
\(73\) −0.955975 −0.111888 −0.0559442 0.998434i \(-0.517817\pi\)
−0.0559442 + 0.998434i \(0.517817\pi\)
\(74\) 11.8979 1.38310
\(75\) −1.74362 −0.201336
\(76\) −0.133159 −0.0152744
\(77\) 8.13256 0.926791
\(78\) 5.75012 0.651073
\(79\) −14.5373 −1.63557 −0.817785 0.575523i \(-0.804798\pi\)
−0.817785 + 0.575523i \(0.804798\pi\)
\(80\) 1.00000 0.111803
\(81\) −9.11905 −1.01323
\(82\) 5.26369 0.581277
\(83\) 16.8564 1.85023 0.925115 0.379688i \(-0.123969\pi\)
0.925115 + 0.379688i \(0.123969\pi\)
\(84\) −4.88013 −0.532466
\(85\) −4.26503 −0.462607
\(86\) 4.56873 0.492658
\(87\) 4.61378 0.494649
\(88\) −2.90568 −0.309747
\(89\) −13.2086 −1.40011 −0.700054 0.714090i \(-0.746841\pi\)
−0.700054 + 0.714090i \(0.746841\pi\)
\(90\) −0.0402221 −0.00423978
\(91\) 9.23003 0.967570
\(92\) −1.71130 −0.178415
\(93\) 15.9211 1.65094
\(94\) −6.49550 −0.669960
\(95\) −0.133159 −0.0136618
\(96\) 1.74362 0.177958
\(97\) −8.57086 −0.870239 −0.435120 0.900373i \(-0.643294\pi\)
−0.435120 + 0.900373i \(0.643294\pi\)
\(98\) −0.833534 −0.0841997
\(99\) 0.116873 0.0117462
\(100\) 1.00000 0.100000
\(101\) 13.3505 1.32842 0.664211 0.747545i \(-0.268768\pi\)
0.664211 + 0.747545i \(0.268768\pi\)
\(102\) −7.43660 −0.736333
\(103\) −16.0085 −1.57737 −0.788684 0.614799i \(-0.789237\pi\)
−0.788684 + 0.614799i \(0.789237\pi\)
\(104\) −3.29780 −0.323376
\(105\) −4.88013 −0.476252
\(106\) −4.03808 −0.392213
\(107\) −10.8925 −1.05302 −0.526511 0.850168i \(-0.676500\pi\)
−0.526511 + 0.850168i \(0.676500\pi\)
\(108\) 5.16074 0.496592
\(109\) 10.3384 0.990235 0.495117 0.868826i \(-0.335125\pi\)
0.495117 + 0.868826i \(0.335125\pi\)
\(110\) −2.90568 −0.277046
\(111\) 20.7455 1.96907
\(112\) 2.79885 0.264466
\(113\) 11.1906 1.05272 0.526360 0.850262i \(-0.323557\pi\)
0.526360 + 0.850262i \(0.323557\pi\)
\(114\) −0.232179 −0.0217456
\(115\) −1.71130 −0.159580
\(116\) −2.64609 −0.245683
\(117\) 0.132644 0.0122630
\(118\) 6.96517 0.641196
\(119\) −11.9371 −1.09428
\(120\) 1.74362 0.159170
\(121\) −2.55700 −0.232455
\(122\) 5.75525 0.521056
\(123\) 9.17789 0.827542
\(124\) −9.13104 −0.819992
\(125\) 1.00000 0.0894427
\(126\) −0.112575 −0.0100290
\(127\) −0.0819637 −0.00727310 −0.00363655 0.999993i \(-0.501158\pi\)
−0.00363655 + 0.999993i \(0.501158\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.96614 0.701379
\(130\) −3.29780 −0.289236
\(131\) 3.94983 0.345098 0.172549 0.985001i \(-0.444800\pi\)
0.172549 + 0.985001i \(0.444800\pi\)
\(132\) −5.06642 −0.440975
\(133\) −0.372691 −0.0323164
\(134\) 1.15003 0.0993477
\(135\) 5.16074 0.444166
\(136\) 4.26503 0.365723
\(137\) 17.4396 1.48996 0.744981 0.667085i \(-0.232458\pi\)
0.744981 + 0.667085i \(0.232458\pi\)
\(138\) −2.98386 −0.254003
\(139\) −6.57556 −0.557732 −0.278866 0.960330i \(-0.589958\pi\)
−0.278866 + 0.960330i \(0.589958\pi\)
\(140\) 2.79885 0.236546
\(141\) −11.3257 −0.953797
\(142\) 0.443856 0.0372476
\(143\) 9.58236 0.801317
\(144\) 0.0402221 0.00335184
\(145\) −2.64609 −0.219746
\(146\) 0.955975 0.0791170
\(147\) −1.45337 −0.119872
\(148\) −11.8979 −0.978001
\(149\) 6.75074 0.553042 0.276521 0.961008i \(-0.410818\pi\)
0.276521 + 0.961008i \(0.410818\pi\)
\(150\) 1.74362 0.142366
\(151\) 9.75498 0.793849 0.396925 0.917851i \(-0.370077\pi\)
0.396925 + 0.917851i \(0.370077\pi\)
\(152\) 0.133159 0.0108006
\(153\) −0.171548 −0.0138689
\(154\) −8.13256 −0.655340
\(155\) −9.13104 −0.733423
\(156\) −5.75012 −0.460378
\(157\) 16.8599 1.34557 0.672784 0.739839i \(-0.265098\pi\)
0.672784 + 0.739839i \(0.265098\pi\)
\(158\) 14.5373 1.15652
\(159\) −7.04089 −0.558379
\(160\) −1.00000 −0.0790569
\(161\) −4.78967 −0.377478
\(162\) 9.11905 0.716460
\(163\) 1.37041 0.107339 0.0536693 0.998559i \(-0.482908\pi\)
0.0536693 + 0.998559i \(0.482908\pi\)
\(164\) −5.26369 −0.411025
\(165\) −5.06642 −0.394420
\(166\) −16.8564 −1.30831
\(167\) −16.5346 −1.27949 −0.639743 0.768589i \(-0.720959\pi\)
−0.639743 + 0.768589i \(0.720959\pi\)
\(168\) 4.88013 0.376510
\(169\) −2.12453 −0.163425
\(170\) 4.26503 0.327113
\(171\) −0.00535593 −0.000409579 0
\(172\) −4.56873 −0.348362
\(173\) 16.2885 1.23840 0.619198 0.785235i \(-0.287458\pi\)
0.619198 + 0.785235i \(0.287458\pi\)
\(174\) −4.61378 −0.349770
\(175\) 2.79885 0.211573
\(176\) 2.90568 0.219024
\(177\) 12.1446 0.912846
\(178\) 13.2086 0.990026
\(179\) −4.16912 −0.311614 −0.155807 0.987787i \(-0.549798\pi\)
−0.155807 + 0.987787i \(0.549798\pi\)
\(180\) 0.0402221 0.00299798
\(181\) 0.834483 0.0620266 0.0310133 0.999519i \(-0.490127\pi\)
0.0310133 + 0.999519i \(0.490127\pi\)
\(182\) −9.23003 −0.684175
\(183\) 10.0350 0.741808
\(184\) 1.71130 0.126159
\(185\) −11.8979 −0.874751
\(186\) −15.9211 −1.16739
\(187\) −12.3928 −0.906253
\(188\) 6.49550 0.473733
\(189\) 14.4441 1.05065
\(190\) 0.133159 0.00966037
\(191\) 17.5122 1.26714 0.633569 0.773686i \(-0.281589\pi\)
0.633569 + 0.773686i \(0.281589\pi\)
\(192\) −1.74362 −0.125835
\(193\) −3.27577 −0.235795 −0.117897 0.993026i \(-0.537615\pi\)
−0.117897 + 0.993026i \(0.537615\pi\)
\(194\) 8.57086 0.615352
\(195\) −5.75012 −0.411774
\(196\) 0.833534 0.0595382
\(197\) −16.3680 −1.16617 −0.583087 0.812410i \(-0.698155\pi\)
−0.583087 + 0.812410i \(0.698155\pi\)
\(198\) −0.116873 −0.00830578
\(199\) 5.25004 0.372166 0.186083 0.982534i \(-0.440421\pi\)
0.186083 + 0.982534i \(0.440421\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 2.00522 0.141438
\(202\) −13.3505 −0.939336
\(203\) −7.40599 −0.519798
\(204\) 7.43660 0.520666
\(205\) −5.26369 −0.367632
\(206\) 16.0085 1.11537
\(207\) −0.0688321 −0.00478416
\(208\) 3.29780 0.228661
\(209\) −0.386918 −0.0267637
\(210\) 4.88013 0.336761
\(211\) −18.6119 −1.28130 −0.640648 0.767835i \(-0.721334\pi\)
−0.640648 + 0.767835i \(0.721334\pi\)
\(212\) 4.03808 0.277336
\(213\) 0.773917 0.0530280
\(214\) 10.8925 0.744599
\(215\) −4.56873 −0.311584
\(216\) −5.16074 −0.351144
\(217\) −25.5564 −1.73488
\(218\) −10.3384 −0.700202
\(219\) 1.66686 0.112636
\(220\) 2.90568 0.195901
\(221\) −14.0652 −0.946127
\(222\) −20.7455 −1.39234
\(223\) −5.61665 −0.376118 −0.188059 0.982158i \(-0.560220\pi\)
−0.188059 + 0.982158i \(0.560220\pi\)
\(224\) −2.79885 −0.187006
\(225\) 0.0402221 0.00268147
\(226\) −11.1906 −0.744385
\(227\) −19.0382 −1.26361 −0.631806 0.775127i \(-0.717686\pi\)
−0.631806 + 0.775127i \(0.717686\pi\)
\(228\) 0.232179 0.0153764
\(229\) −18.2529 −1.20618 −0.603092 0.797672i \(-0.706065\pi\)
−0.603092 + 0.797672i \(0.706065\pi\)
\(230\) 1.71130 0.112840
\(231\) −14.1801 −0.932983
\(232\) 2.64609 0.173724
\(233\) 17.9389 1.17522 0.587609 0.809145i \(-0.300069\pi\)
0.587609 + 0.809145i \(0.300069\pi\)
\(234\) −0.132644 −0.00867123
\(235\) 6.49550 0.423720
\(236\) −6.96517 −0.453394
\(237\) 25.3475 1.64650
\(238\) 11.9371 0.773770
\(239\) −27.5765 −1.78378 −0.891889 0.452254i \(-0.850620\pi\)
−0.891889 + 0.452254i \(0.850620\pi\)
\(240\) −1.74362 −0.112550
\(241\) 9.60993 0.619030 0.309515 0.950895i \(-0.399833\pi\)
0.309515 + 0.950895i \(0.399833\pi\)
\(242\) 2.55700 0.164370
\(243\) 0.417972 0.0268129
\(244\) −5.75525 −0.368442
\(245\) 0.833534 0.0532525
\(246\) −9.17789 −0.585161
\(247\) −0.439131 −0.0279413
\(248\) 9.13104 0.579822
\(249\) −29.3912 −1.86259
\(250\) −1.00000 −0.0632456
\(251\) −27.8466 −1.75766 −0.878832 0.477131i \(-0.841677\pi\)
−0.878832 + 0.477131i \(0.841677\pi\)
\(252\) 0.112575 0.00709159
\(253\) −4.97250 −0.312618
\(254\) 0.0819637 0.00514286
\(255\) 7.43660 0.465698
\(256\) 1.00000 0.0625000
\(257\) 1.46595 0.0914436 0.0457218 0.998954i \(-0.485441\pi\)
0.0457218 + 0.998954i \(0.485441\pi\)
\(258\) −7.96614 −0.495950
\(259\) −33.3004 −2.06919
\(260\) 3.29780 0.204521
\(261\) −0.106431 −0.00658792
\(262\) −3.94983 −0.244021
\(263\) 24.0201 1.48114 0.740570 0.671979i \(-0.234556\pi\)
0.740570 + 0.671979i \(0.234556\pi\)
\(264\) 5.06642 0.311816
\(265\) 4.03808 0.248057
\(266\) 0.372691 0.0228512
\(267\) 23.0308 1.40946
\(268\) −1.15003 −0.0702494
\(269\) 15.2572 0.930250 0.465125 0.885245i \(-0.346009\pi\)
0.465125 + 0.885245i \(0.346009\pi\)
\(270\) −5.16074 −0.314072
\(271\) −7.93860 −0.482235 −0.241118 0.970496i \(-0.577514\pi\)
−0.241118 + 0.970496i \(0.577514\pi\)
\(272\) −4.26503 −0.258605
\(273\) −16.0937 −0.974034
\(274\) −17.4396 −1.05356
\(275\) 2.90568 0.175219
\(276\) 2.98386 0.179607
\(277\) 4.90642 0.294798 0.147399 0.989077i \(-0.452910\pi\)
0.147399 + 0.989077i \(0.452910\pi\)
\(278\) 6.57556 0.394376
\(279\) −0.367270 −0.0219879
\(280\) −2.79885 −0.167263
\(281\) −29.6156 −1.76672 −0.883360 0.468695i \(-0.844724\pi\)
−0.883360 + 0.468695i \(0.844724\pi\)
\(282\) 11.3257 0.674436
\(283\) 2.32408 0.138152 0.0690762 0.997611i \(-0.477995\pi\)
0.0690762 + 0.997611i \(0.477995\pi\)
\(284\) −0.443856 −0.0263380
\(285\) 0.232179 0.0137531
\(286\) −9.58236 −0.566617
\(287\) −14.7322 −0.869617
\(288\) −0.0402221 −0.00237011
\(289\) 1.19045 0.0700267
\(290\) 2.64609 0.155384
\(291\) 14.9444 0.876054
\(292\) −0.955975 −0.0559442
\(293\) −24.9104 −1.45528 −0.727641 0.685958i \(-0.759384\pi\)
−0.727641 + 0.685958i \(0.759384\pi\)
\(294\) 1.45337 0.0847622
\(295\) −6.96517 −0.405528
\(296\) 11.8979 0.691551
\(297\) 14.9955 0.870126
\(298\) −6.75074 −0.391060
\(299\) −5.64352 −0.326373
\(300\) −1.74362 −0.100668
\(301\) −12.7872 −0.737039
\(302\) −9.75498 −0.561336
\(303\) −23.2782 −1.33730
\(304\) −0.133159 −0.00763719
\(305\) −5.75525 −0.329545
\(306\) 0.171548 0.00980677
\(307\) 21.2022 1.21008 0.605038 0.796197i \(-0.293158\pi\)
0.605038 + 0.796197i \(0.293158\pi\)
\(308\) 8.13256 0.463396
\(309\) 27.9128 1.58791
\(310\) 9.13104 0.518608
\(311\) 5.00671 0.283904 0.141952 0.989874i \(-0.454662\pi\)
0.141952 + 0.989874i \(0.454662\pi\)
\(312\) 5.75012 0.325536
\(313\) 23.1915 1.31086 0.655431 0.755255i \(-0.272487\pi\)
0.655431 + 0.755255i \(0.272487\pi\)
\(314\) −16.8599 −0.951460
\(315\) 0.112575 0.00634291
\(316\) −14.5373 −0.817785
\(317\) 16.0766 0.902952 0.451476 0.892283i \(-0.350898\pi\)
0.451476 + 0.892283i \(0.350898\pi\)
\(318\) 7.04089 0.394833
\(319\) −7.68869 −0.430484
\(320\) 1.00000 0.0559017
\(321\) 18.9925 1.06006
\(322\) 4.78967 0.266918
\(323\) 0.567927 0.0316003
\(324\) −9.11905 −0.506614
\(325\) 3.29780 0.182929
\(326\) −1.37041 −0.0758999
\(327\) −18.0262 −0.996851
\(328\) 5.26369 0.290639
\(329\) 18.1799 1.00229
\(330\) 5.06642 0.278897
\(331\) 3.88676 0.213636 0.106818 0.994279i \(-0.465934\pi\)
0.106818 + 0.994279i \(0.465934\pi\)
\(332\) 16.8564 0.925115
\(333\) −0.478559 −0.0262249
\(334\) 16.5346 0.904733
\(335\) −1.15003 −0.0628330
\(336\) −4.88013 −0.266233
\(337\) 9.32872 0.508168 0.254084 0.967182i \(-0.418226\pi\)
0.254084 + 0.967182i \(0.418226\pi\)
\(338\) 2.12453 0.115559
\(339\) −19.5121 −1.05975
\(340\) −4.26503 −0.231304
\(341\) −26.5319 −1.43678
\(342\) 0.00535593 0.000289616 0
\(343\) −17.2590 −0.931897
\(344\) 4.56873 0.246329
\(345\) 2.98386 0.160646
\(346\) −16.2885 −0.875678
\(347\) −34.2218 −1.83712 −0.918560 0.395282i \(-0.870647\pi\)
−0.918560 + 0.395282i \(0.870647\pi\)
\(348\) 4.61378 0.247324
\(349\) −33.0131 −1.76715 −0.883576 0.468288i \(-0.844871\pi\)
−0.883576 + 0.468288i \(0.844871\pi\)
\(350\) −2.79885 −0.149605
\(351\) 17.0191 0.908411
\(352\) −2.90568 −0.154873
\(353\) 11.6475 0.619934 0.309967 0.950747i \(-0.399682\pi\)
0.309967 + 0.950747i \(0.399682\pi\)
\(354\) −12.1446 −0.645480
\(355\) −0.443856 −0.0235574
\(356\) −13.2086 −0.700054
\(357\) 20.8139 1.10159
\(358\) 4.16912 0.220345
\(359\) −11.8552 −0.625695 −0.312848 0.949803i \(-0.601283\pi\)
−0.312848 + 0.949803i \(0.601283\pi\)
\(360\) −0.0402221 −0.00211989
\(361\) −18.9823 −0.999067
\(362\) −0.834483 −0.0438594
\(363\) 4.45845 0.234008
\(364\) 9.23003 0.483785
\(365\) −0.955975 −0.0500380
\(366\) −10.0350 −0.524538
\(367\) −21.3941 −1.11676 −0.558382 0.829584i \(-0.688578\pi\)
−0.558382 + 0.829584i \(0.688578\pi\)
\(368\) −1.71130 −0.0892077
\(369\) −0.211717 −0.0110215
\(370\) 11.8979 0.618542
\(371\) 11.3020 0.586768
\(372\) 15.9211 0.825471
\(373\) −22.1828 −1.14858 −0.574291 0.818651i \(-0.694722\pi\)
−0.574291 + 0.818651i \(0.694722\pi\)
\(374\) 12.3928 0.640817
\(375\) −1.74362 −0.0900403
\(376\) −6.49550 −0.334980
\(377\) −8.72626 −0.449425
\(378\) −14.4441 −0.742925
\(379\) 21.7483 1.11714 0.558569 0.829458i \(-0.311351\pi\)
0.558569 + 0.829458i \(0.311351\pi\)
\(380\) −0.133159 −0.00683091
\(381\) 0.142914 0.00732169
\(382\) −17.5122 −0.896002
\(383\) 15.3907 0.786429 0.393214 0.919447i \(-0.371363\pi\)
0.393214 + 0.919447i \(0.371363\pi\)
\(384\) 1.74362 0.0889789
\(385\) 8.13256 0.414474
\(386\) 3.27577 0.166732
\(387\) −0.183764 −0.00934124
\(388\) −8.57086 −0.435120
\(389\) 21.0759 1.06859 0.534296 0.845297i \(-0.320577\pi\)
0.534296 + 0.845297i \(0.320577\pi\)
\(390\) 5.75012 0.291168
\(391\) 7.29874 0.369113
\(392\) −0.833534 −0.0420998
\(393\) −6.88701 −0.347404
\(394\) 16.3680 0.824610
\(395\) −14.5373 −0.731450
\(396\) 0.116873 0.00587308
\(397\) −35.7748 −1.79549 −0.897744 0.440518i \(-0.854795\pi\)
−0.897744 + 0.440518i \(0.854795\pi\)
\(398\) −5.25004 −0.263161
\(399\) 0.649833 0.0325324
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −2.00522 −0.100011
\(403\) −30.1123 −1.50000
\(404\) 13.3505 0.664211
\(405\) −9.11905 −0.453129
\(406\) 7.40599 0.367553
\(407\) −34.5715 −1.71365
\(408\) −7.43660 −0.368167
\(409\) −33.6239 −1.66259 −0.831297 0.555828i \(-0.812401\pi\)
−0.831297 + 0.555828i \(0.812401\pi\)
\(410\) 5.26369 0.259955
\(411\) −30.4080 −1.49992
\(412\) −16.0085 −0.788684
\(413\) −19.4944 −0.959258
\(414\) 0.0688321 0.00338291
\(415\) 16.8564 0.827448
\(416\) −3.29780 −0.161688
\(417\) 11.4653 0.561458
\(418\) 0.386918 0.0189248
\(419\) −5.91594 −0.289012 −0.144506 0.989504i \(-0.546159\pi\)
−0.144506 + 0.989504i \(0.546159\pi\)
\(420\) −4.88013 −0.238126
\(421\) −15.9075 −0.775284 −0.387642 0.921810i \(-0.626710\pi\)
−0.387642 + 0.921810i \(0.626710\pi\)
\(422\) 18.6119 0.906013
\(423\) 0.261263 0.0127030
\(424\) −4.03808 −0.196106
\(425\) −4.26503 −0.206884
\(426\) −0.773917 −0.0374964
\(427\) −16.1081 −0.779524
\(428\) −10.8925 −0.526511
\(429\) −16.7080 −0.806671
\(430\) 4.56873 0.220324
\(431\) 21.9256 1.05612 0.528059 0.849208i \(-0.322920\pi\)
0.528059 + 0.849208i \(0.322920\pi\)
\(432\) 5.16074 0.248296
\(433\) 31.5732 1.51731 0.758656 0.651491i \(-0.225856\pi\)
0.758656 + 0.651491i \(0.225856\pi\)
\(434\) 25.5564 1.22675
\(435\) 4.61378 0.221214
\(436\) 10.3384 0.495117
\(437\) 0.227875 0.0109007
\(438\) −1.66686 −0.0796456
\(439\) 5.12336 0.244525 0.122262 0.992498i \(-0.460985\pi\)
0.122262 + 0.992498i \(0.460985\pi\)
\(440\) −2.90568 −0.138523
\(441\) 0.0335265 0.00159650
\(442\) 14.0652 0.669013
\(443\) −35.2770 −1.67606 −0.838030 0.545625i \(-0.816292\pi\)
−0.838030 + 0.545625i \(0.816292\pi\)
\(444\) 20.7455 0.984536
\(445\) −13.2086 −0.626148
\(446\) 5.61665 0.265956
\(447\) −11.7708 −0.556737
\(448\) 2.79885 0.132233
\(449\) −13.7311 −0.648009 −0.324005 0.946056i \(-0.605029\pi\)
−0.324005 + 0.946056i \(0.605029\pi\)
\(450\) −0.0402221 −0.00189609
\(451\) −15.2946 −0.720195
\(452\) 11.1906 0.526360
\(453\) −17.0090 −0.799153
\(454\) 19.0382 0.893508
\(455\) 9.23003 0.432710
\(456\) −0.232179 −0.0108728
\(457\) 32.3369 1.51265 0.756327 0.654194i \(-0.226992\pi\)
0.756327 + 0.654194i \(0.226992\pi\)
\(458\) 18.2529 0.852900
\(459\) −22.0107 −1.02737
\(460\) −1.71130 −0.0797898
\(461\) 0.219374 0.0102173 0.00510864 0.999987i \(-0.498374\pi\)
0.00510864 + 0.999987i \(0.498374\pi\)
\(462\) 14.1801 0.659719
\(463\) −7.36374 −0.342222 −0.171111 0.985252i \(-0.554736\pi\)
−0.171111 + 0.985252i \(0.554736\pi\)
\(464\) −2.64609 −0.122841
\(465\) 15.9211 0.738323
\(466\) −17.9389 −0.831005
\(467\) −13.1656 −0.609232 −0.304616 0.952475i \(-0.598528\pi\)
−0.304616 + 0.952475i \(0.598528\pi\)
\(468\) 0.132644 0.00613149
\(469\) −3.21876 −0.148629
\(470\) −6.49550 −0.299615
\(471\) −29.3974 −1.35456
\(472\) 6.96517 0.320598
\(473\) −13.2753 −0.610398
\(474\) −25.3475 −1.16425
\(475\) −0.133159 −0.00610975
\(476\) −11.9371 −0.547138
\(477\) 0.162420 0.00743670
\(478\) 27.5765 1.26132
\(479\) −28.8129 −1.31650 −0.658249 0.752801i \(-0.728702\pi\)
−0.658249 + 0.752801i \(0.728702\pi\)
\(480\) 1.74362 0.0795851
\(481\) −39.2369 −1.78905
\(482\) −9.60993 −0.437720
\(483\) 8.35137 0.380001
\(484\) −2.55700 −0.116227
\(485\) −8.57086 −0.389183
\(486\) −0.417972 −0.0189596
\(487\) −2.51157 −0.113810 −0.0569051 0.998380i \(-0.518123\pi\)
−0.0569051 + 0.998380i \(0.518123\pi\)
\(488\) 5.75525 0.260528
\(489\) −2.38947 −0.108056
\(490\) −0.833534 −0.0376552
\(491\) −11.0188 −0.497272 −0.248636 0.968597i \(-0.579982\pi\)
−0.248636 + 0.968597i \(0.579982\pi\)
\(492\) 9.17789 0.413771
\(493\) 11.2856 0.508279
\(494\) 0.439131 0.0197575
\(495\) 0.116873 0.00525304
\(496\) −9.13104 −0.409996
\(497\) −1.24228 −0.0557241
\(498\) 29.3912 1.31705
\(499\) 18.0283 0.807058 0.403529 0.914967i \(-0.367783\pi\)
0.403529 + 0.914967i \(0.367783\pi\)
\(500\) 1.00000 0.0447214
\(501\) 28.8301 1.28803
\(502\) 27.8466 1.24286
\(503\) 30.9924 1.38188 0.690941 0.722911i \(-0.257196\pi\)
0.690941 + 0.722911i \(0.257196\pi\)
\(504\) −0.112575 −0.00501451
\(505\) 13.3505 0.594088
\(506\) 4.97250 0.221055
\(507\) 3.70438 0.164517
\(508\) −0.0819637 −0.00363655
\(509\) 10.7138 0.474880 0.237440 0.971402i \(-0.423692\pi\)
0.237440 + 0.971402i \(0.423692\pi\)
\(510\) −7.43660 −0.329298
\(511\) −2.67562 −0.118363
\(512\) −1.00000 −0.0441942
\(513\) −0.687198 −0.0303406
\(514\) −1.46595 −0.0646604
\(515\) −16.0085 −0.705420
\(516\) 7.96614 0.350690
\(517\) 18.8739 0.830072
\(518\) 33.3004 1.46313
\(519\) −28.4011 −1.24667
\(520\) −3.29780 −0.144618
\(521\) 37.4207 1.63943 0.819715 0.572772i \(-0.194132\pi\)
0.819715 + 0.572772i \(0.194132\pi\)
\(522\) 0.106431 0.00465837
\(523\) 18.2035 0.795982 0.397991 0.917389i \(-0.369708\pi\)
0.397991 + 0.917389i \(0.369708\pi\)
\(524\) 3.94983 0.172549
\(525\) −4.88013 −0.212986
\(526\) −24.0201 −1.04732
\(527\) 38.9441 1.69643
\(528\) −5.06642 −0.220488
\(529\) −20.0715 −0.872672
\(530\) −4.03808 −0.175403
\(531\) −0.280154 −0.0121576
\(532\) −0.372691 −0.0161582
\(533\) −17.3586 −0.751883
\(534\) −23.0308 −0.996641
\(535\) −10.8925 −0.470926
\(536\) 1.15003 0.0496738
\(537\) 7.26937 0.313696
\(538\) −15.2572 −0.657786
\(539\) 2.42199 0.104322
\(540\) 5.16074 0.222083
\(541\) 12.4127 0.533662 0.266831 0.963743i \(-0.414023\pi\)
0.266831 + 0.963743i \(0.414023\pi\)
\(542\) 7.93860 0.340992
\(543\) −1.45502 −0.0624410
\(544\) 4.26503 0.182862
\(545\) 10.3384 0.442846
\(546\) 16.0937 0.688746
\(547\) 36.2153 1.54845 0.774227 0.632908i \(-0.218139\pi\)
0.774227 + 0.632908i \(0.218139\pi\)
\(548\) 17.4396 0.744981
\(549\) −0.231488 −0.00987969
\(550\) −2.90568 −0.123899
\(551\) 0.352350 0.0150106
\(552\) −2.98386 −0.127002
\(553\) −40.6876 −1.73021
\(554\) −4.90642 −0.208454
\(555\) 20.7455 0.880596
\(556\) −6.57556 −0.278866
\(557\) 10.1921 0.431854 0.215927 0.976410i \(-0.430723\pi\)
0.215927 + 0.976410i \(0.430723\pi\)
\(558\) 0.367270 0.0155478
\(559\) −15.0667 −0.637255
\(560\) 2.79885 0.118273
\(561\) 21.6084 0.912308
\(562\) 29.6156 1.24926
\(563\) 0.952127 0.0401274 0.0200637 0.999799i \(-0.493613\pi\)
0.0200637 + 0.999799i \(0.493613\pi\)
\(564\) −11.3257 −0.476898
\(565\) 11.1906 0.470790
\(566\) −2.32408 −0.0976885
\(567\) −25.5228 −1.07186
\(568\) 0.443856 0.0186238
\(569\) −1.70621 −0.0715282 −0.0357641 0.999360i \(-0.511386\pi\)
−0.0357641 + 0.999360i \(0.511386\pi\)
\(570\) −0.232179 −0.00972491
\(571\) 1.32147 0.0553017 0.0276508 0.999618i \(-0.491197\pi\)
0.0276508 + 0.999618i \(0.491197\pi\)
\(572\) 9.58236 0.400659
\(573\) −30.5347 −1.27560
\(574\) 14.7322 0.614912
\(575\) −1.71130 −0.0713662
\(576\) 0.0402221 0.00167592
\(577\) −23.1428 −0.963448 −0.481724 0.876323i \(-0.659989\pi\)
−0.481724 + 0.876323i \(0.659989\pi\)
\(578\) −1.19045 −0.0495164
\(579\) 5.71170 0.237370
\(580\) −2.64609 −0.109873
\(581\) 47.1784 1.95729
\(582\) −14.9444 −0.619464
\(583\) 11.7334 0.485947
\(584\) 0.955975 0.0395585
\(585\) 0.132644 0.00548417
\(586\) 24.9104 1.02904
\(587\) 37.1775 1.53448 0.767240 0.641360i \(-0.221629\pi\)
0.767240 + 0.641360i \(0.221629\pi\)
\(588\) −1.45337 −0.0599360
\(589\) 1.21588 0.0500995
\(590\) 6.96517 0.286751
\(591\) 28.5397 1.17397
\(592\) −11.8979 −0.489001
\(593\) 20.3523 0.835769 0.417885 0.908500i \(-0.362772\pi\)
0.417885 + 0.908500i \(0.362772\pi\)
\(594\) −14.9955 −0.615272
\(595\) −11.9371 −0.489375
\(596\) 6.75074 0.276521
\(597\) −9.15410 −0.374652
\(598\) 5.64352 0.230781
\(599\) −41.5364 −1.69713 −0.848566 0.529089i \(-0.822534\pi\)
−0.848566 + 0.529089i \(0.822534\pi\)
\(600\) 1.74362 0.0711831
\(601\) 26.1358 1.06610 0.533050 0.846084i \(-0.321046\pi\)
0.533050 + 0.846084i \(0.321046\pi\)
\(602\) 12.7872 0.521166
\(603\) −0.0462567 −0.00188372
\(604\) 9.75498 0.396925
\(605\) −2.55700 −0.103957
\(606\) 23.2782 0.945612
\(607\) −6.25162 −0.253745 −0.126873 0.991919i \(-0.540494\pi\)
−0.126873 + 0.991919i \(0.540494\pi\)
\(608\) 0.133159 0.00540031
\(609\) 12.9133 0.523271
\(610\) 5.75525 0.233023
\(611\) 21.4209 0.866595
\(612\) −0.171548 −0.00693443
\(613\) 4.38076 0.176937 0.0884685 0.996079i \(-0.471803\pi\)
0.0884685 + 0.996079i \(0.471803\pi\)
\(614\) −21.2022 −0.855653
\(615\) 9.17789 0.370088
\(616\) −8.13256 −0.327670
\(617\) −35.3261 −1.42217 −0.711087 0.703104i \(-0.751797\pi\)
−0.711087 + 0.703104i \(0.751797\pi\)
\(618\) −27.9128 −1.12282
\(619\) −13.5824 −0.545922 −0.272961 0.962025i \(-0.588003\pi\)
−0.272961 + 0.962025i \(0.588003\pi\)
\(620\) −9.13104 −0.366712
\(621\) −8.83157 −0.354399
\(622\) −5.00671 −0.200751
\(623\) −36.9688 −1.48112
\(624\) −5.75012 −0.230189
\(625\) 1.00000 0.0400000
\(626\) −23.1915 −0.926920
\(627\) 0.674639 0.0269425
\(628\) 16.8599 0.672784
\(629\) 50.7449 2.02333
\(630\) −0.112575 −0.00448511
\(631\) 8.62253 0.343257 0.171629 0.985162i \(-0.445097\pi\)
0.171629 + 0.985162i \(0.445097\pi\)
\(632\) 14.5373 0.578262
\(633\) 32.4521 1.28986
\(634\) −16.0766 −0.638483
\(635\) −0.0819637 −0.00325263
\(636\) −7.04089 −0.279189
\(637\) 2.74883 0.108913
\(638\) 7.68869 0.304398
\(639\) −0.0178528 −0.000706247 0
\(640\) −1.00000 −0.0395285
\(641\) 4.17080 0.164737 0.0823683 0.996602i \(-0.473752\pi\)
0.0823683 + 0.996602i \(0.473752\pi\)
\(642\) −18.9925 −0.749574
\(643\) 31.3917 1.23797 0.618984 0.785403i \(-0.287544\pi\)
0.618984 + 0.785403i \(0.287544\pi\)
\(644\) −4.78967 −0.188739
\(645\) 7.96614 0.313666
\(646\) −0.567927 −0.0223448
\(647\) 16.0835 0.632309 0.316154 0.948708i \(-0.397608\pi\)
0.316154 + 0.948708i \(0.397608\pi\)
\(648\) 9.11905 0.358230
\(649\) −20.2386 −0.794434
\(650\) −3.29780 −0.129350
\(651\) 44.5607 1.74647
\(652\) 1.37041 0.0536693
\(653\) −14.8296 −0.580328 −0.290164 0.956977i \(-0.593710\pi\)
−0.290164 + 0.956977i \(0.593710\pi\)
\(654\) 18.0262 0.704880
\(655\) 3.94983 0.154332
\(656\) −5.26369 −0.205512
\(657\) −0.0384513 −0.00150013
\(658\) −18.1799 −0.708726
\(659\) −45.1202 −1.75763 −0.878817 0.477159i \(-0.841667\pi\)
−0.878817 + 0.477159i \(0.841667\pi\)
\(660\) −5.06642 −0.197210
\(661\) 22.9207 0.891513 0.445757 0.895154i \(-0.352935\pi\)
0.445757 + 0.895154i \(0.352935\pi\)
\(662\) −3.88676 −0.151063
\(663\) 24.5244 0.952449
\(664\) −16.8564 −0.654155
\(665\) −0.372691 −0.0144523
\(666\) 0.478559 0.0185438
\(667\) 4.52825 0.175335
\(668\) −16.5346 −0.639743
\(669\) 9.79331 0.378631
\(670\) 1.15003 0.0444296
\(671\) −16.7229 −0.645582
\(672\) 4.88013 0.188255
\(673\) 22.9161 0.883352 0.441676 0.897175i \(-0.354384\pi\)
0.441676 + 0.897175i \(0.354384\pi\)
\(674\) −9.32872 −0.359329
\(675\) 5.16074 0.198637
\(676\) −2.12453 −0.0817127
\(677\) −22.9572 −0.882317 −0.441158 0.897429i \(-0.645432\pi\)
−0.441158 + 0.897429i \(0.645432\pi\)
\(678\) 19.5121 0.749358
\(679\) −23.9885 −0.920595
\(680\) 4.26503 0.163556
\(681\) 33.1955 1.27205
\(682\) 26.5319 1.01596
\(683\) 3.83965 0.146920 0.0734600 0.997298i \(-0.476596\pi\)
0.0734600 + 0.997298i \(0.476596\pi\)
\(684\) −0.00535593 −0.000204789 0
\(685\) 17.4396 0.666331
\(686\) 17.2590 0.658951
\(687\) 31.8261 1.21424
\(688\) −4.56873 −0.174181
\(689\) 13.3168 0.507328
\(690\) −2.98386 −0.113594
\(691\) −22.2790 −0.847533 −0.423767 0.905771i \(-0.639292\pi\)
−0.423767 + 0.905771i \(0.639292\pi\)
\(692\) 16.2885 0.619198
\(693\) 0.327109 0.0124258
\(694\) 34.2218 1.29904
\(695\) −6.57556 −0.249425
\(696\) −4.61378 −0.174885
\(697\) 22.4498 0.850346
\(698\) 33.0131 1.24956
\(699\) −31.2787 −1.18307
\(700\) 2.79885 0.105786
\(701\) 45.8891 1.73321 0.866603 0.498997i \(-0.166298\pi\)
0.866603 + 0.498997i \(0.166298\pi\)
\(702\) −17.0191 −0.642343
\(703\) 1.58431 0.0597535
\(704\) 2.90568 0.109512
\(705\) −11.3257 −0.426551
\(706\) −11.6475 −0.438359
\(707\) 37.3659 1.40529
\(708\) 12.1446 0.456423
\(709\) 24.5503 0.922006 0.461003 0.887398i \(-0.347490\pi\)
0.461003 + 0.887398i \(0.347490\pi\)
\(710\) 0.443856 0.0166576
\(711\) −0.584720 −0.0219287
\(712\) 13.2086 0.495013
\(713\) 15.6260 0.585197
\(714\) −20.8139 −0.778940
\(715\) 9.58236 0.358360
\(716\) −4.16912 −0.155807
\(717\) 48.0831 1.79570
\(718\) 11.8552 0.442433
\(719\) −19.2846 −0.719193 −0.359597 0.933108i \(-0.617086\pi\)
−0.359597 + 0.933108i \(0.617086\pi\)
\(720\) 0.0402221 0.00149899
\(721\) −44.8054 −1.66864
\(722\) 18.9823 0.706447
\(723\) −16.7561 −0.623166
\(724\) 0.834483 0.0310133
\(725\) −2.64609 −0.0982732
\(726\) −4.45845 −0.165468
\(727\) 6.33098 0.234803 0.117402 0.993085i \(-0.462544\pi\)
0.117402 + 0.993085i \(0.462544\pi\)
\(728\) −9.23003 −0.342088
\(729\) 26.6284 0.986236
\(730\) 0.955975 0.0353822
\(731\) 19.4857 0.720706
\(732\) 10.0350 0.370904
\(733\) 39.5562 1.46104 0.730521 0.682890i \(-0.239277\pi\)
0.730521 + 0.682890i \(0.239277\pi\)
\(734\) 21.3941 0.789671
\(735\) −1.45337 −0.0536083
\(736\) 1.71130 0.0630794
\(737\) −3.34163 −0.123091
\(738\) 0.211717 0.00779340
\(739\) −2.00932 −0.0739141 −0.0369571 0.999317i \(-0.511766\pi\)
−0.0369571 + 0.999317i \(0.511766\pi\)
\(740\) −11.8979 −0.437376
\(741\) 0.765680 0.0281279
\(742\) −11.3020 −0.414908
\(743\) −39.4729 −1.44812 −0.724060 0.689737i \(-0.757726\pi\)
−0.724060 + 0.689737i \(0.757726\pi\)
\(744\) −15.9211 −0.583696
\(745\) 6.75074 0.247328
\(746\) 22.1828 0.812170
\(747\) 0.678000 0.0248067
\(748\) −12.3928 −0.453126
\(749\) −30.4865 −1.11395
\(750\) 1.74362 0.0636681
\(751\) 0.749562 0.0273519 0.0136760 0.999906i \(-0.495647\pi\)
0.0136760 + 0.999906i \(0.495647\pi\)
\(752\) 6.49550 0.236867
\(753\) 48.5541 1.76941
\(754\) 8.72626 0.317792
\(755\) 9.75498 0.355020
\(756\) 14.4441 0.525327
\(757\) 13.3021 0.483472 0.241736 0.970342i \(-0.422283\pi\)
0.241736 + 0.970342i \(0.422283\pi\)
\(758\) −21.7483 −0.789935
\(759\) 8.67016 0.314707
\(760\) 0.133159 0.00483018
\(761\) −30.1643 −1.09345 −0.546727 0.837311i \(-0.684126\pi\)
−0.546727 + 0.837311i \(0.684126\pi\)
\(762\) −0.142914 −0.00517722
\(763\) 28.9355 1.04753
\(764\) 17.5122 0.633569
\(765\) −0.171548 −0.00620234
\(766\) −15.3907 −0.556089
\(767\) −22.9697 −0.829388
\(768\) −1.74362 −0.0629176
\(769\) −31.2458 −1.12675 −0.563377 0.826200i \(-0.690498\pi\)
−0.563377 + 0.826200i \(0.690498\pi\)
\(770\) −8.13256 −0.293077
\(771\) −2.55607 −0.0920546
\(772\) −3.27577 −0.117897
\(773\) 5.49037 0.197475 0.0987375 0.995114i \(-0.468520\pi\)
0.0987375 + 0.995114i \(0.468520\pi\)
\(774\) 0.183764 0.00660525
\(775\) −9.13104 −0.327997
\(776\) 8.57086 0.307676
\(777\) 58.0633 2.08301
\(778\) −21.0759 −0.755609
\(779\) 0.700907 0.0251126
\(780\) −5.75012 −0.205887
\(781\) −1.28971 −0.0461493
\(782\) −7.29874 −0.261003
\(783\) −13.6558 −0.488017
\(784\) 0.833534 0.0297691
\(785\) 16.8599 0.601756
\(786\) 6.88701 0.245651
\(787\) −19.4370 −0.692854 −0.346427 0.938077i \(-0.612605\pi\)
−0.346427 + 0.938077i \(0.612605\pi\)
\(788\) −16.3680 −0.583087
\(789\) −41.8819 −1.49104
\(790\) 14.5373 0.517213
\(791\) 31.3206 1.11363
\(792\) −0.116873 −0.00415289
\(793\) −18.9797 −0.673988
\(794\) 35.7748 1.26960
\(795\) −7.04089 −0.249715
\(796\) 5.25004 0.186083
\(797\) −8.35740 −0.296034 −0.148017 0.988985i \(-0.547289\pi\)
−0.148017 + 0.988985i \(0.547289\pi\)
\(798\) −0.649833 −0.0230038
\(799\) −27.7035 −0.980079
\(800\) −1.00000 −0.0353553
\(801\) −0.531278 −0.0187718
\(802\) −1.00000 −0.0353112
\(803\) −2.77776 −0.0980250
\(804\) 2.00522 0.0707188
\(805\) −4.78967 −0.168814
\(806\) 30.1123 1.06066
\(807\) −26.6029 −0.936465
\(808\) −13.3505 −0.469668
\(809\) 46.6245 1.63923 0.819615 0.572914i \(-0.194187\pi\)
0.819615 + 0.572914i \(0.194187\pi\)
\(810\) 9.11905 0.320411
\(811\) 25.6122 0.899368 0.449684 0.893188i \(-0.351537\pi\)
0.449684 + 0.893188i \(0.351537\pi\)
\(812\) −7.40599 −0.259899
\(813\) 13.8419 0.485457
\(814\) 34.5715 1.21173
\(815\) 1.37041 0.0480033
\(816\) 7.43660 0.260333
\(817\) 0.608367 0.0212841
\(818\) 33.6239 1.17563
\(819\) 0.371251 0.0129726
\(820\) −5.26369 −0.183816
\(821\) 27.8303 0.971285 0.485643 0.874157i \(-0.338586\pi\)
0.485643 + 0.874157i \(0.338586\pi\)
\(822\) 30.4080 1.06060
\(823\) −3.07396 −0.107151 −0.0535757 0.998564i \(-0.517062\pi\)
−0.0535757 + 0.998564i \(0.517062\pi\)
\(824\) 16.0085 0.557684
\(825\) −5.06642 −0.176390
\(826\) 19.4944 0.678298
\(827\) 39.3794 1.36935 0.684677 0.728846i \(-0.259943\pi\)
0.684677 + 0.728846i \(0.259943\pi\)
\(828\) −0.0688321 −0.00239208
\(829\) −35.6968 −1.23980 −0.619900 0.784680i \(-0.712827\pi\)
−0.619900 + 0.784680i \(0.712827\pi\)
\(830\) −16.8564 −0.585094
\(831\) −8.55495 −0.296768
\(832\) 3.29780 0.114331
\(833\) −3.55505 −0.123175
\(834\) −11.4653 −0.397011
\(835\) −16.5346 −0.572203
\(836\) −0.386918 −0.0133818
\(837\) −47.1229 −1.62881
\(838\) 5.91594 0.204363
\(839\) −40.1386 −1.38574 −0.692869 0.721063i \(-0.743654\pi\)
−0.692869 + 0.721063i \(0.743654\pi\)
\(840\) 4.88013 0.168381
\(841\) −21.9982 −0.758560
\(842\) 15.9075 0.548209
\(843\) 51.6385 1.77852
\(844\) −18.6119 −0.640648
\(845\) −2.12453 −0.0730860
\(846\) −0.261263 −0.00898240
\(847\) −7.15665 −0.245905
\(848\) 4.03808 0.138668
\(849\) −4.05232 −0.139075
\(850\) 4.26503 0.146289
\(851\) 20.3609 0.697962
\(852\) 0.773917 0.0265140
\(853\) −29.0724 −0.995421 −0.497711 0.867343i \(-0.665826\pi\)
−0.497711 + 0.867343i \(0.665826\pi\)
\(854\) 16.1081 0.551207
\(855\) −0.00535593 −0.000183169 0
\(856\) 10.8925 0.372299
\(857\) 51.8740 1.77198 0.885990 0.463704i \(-0.153480\pi\)
0.885990 + 0.463704i \(0.153480\pi\)
\(858\) 16.7080 0.570403
\(859\) 27.4459 0.936443 0.468222 0.883611i \(-0.344895\pi\)
0.468222 + 0.883611i \(0.344895\pi\)
\(860\) −4.56873 −0.155792
\(861\) 25.6875 0.875427
\(862\) −21.9256 −0.746788
\(863\) −44.1100 −1.50152 −0.750761 0.660574i \(-0.770313\pi\)
−0.750761 + 0.660574i \(0.770313\pi\)
\(864\) −5.16074 −0.175572
\(865\) 16.2885 0.553827
\(866\) −31.5732 −1.07290
\(867\) −2.07570 −0.0704946
\(868\) −25.5564 −0.867440
\(869\) −42.2407 −1.43292
\(870\) −4.61378 −0.156422
\(871\) −3.79257 −0.128506
\(872\) −10.3384 −0.350101
\(873\) −0.344738 −0.0116676
\(874\) −0.227875 −0.00770799
\(875\) 2.79885 0.0946182
\(876\) 1.66686 0.0563180
\(877\) 13.0104 0.439331 0.219666 0.975575i \(-0.429503\pi\)
0.219666 + 0.975575i \(0.429503\pi\)
\(878\) −5.12336 −0.172905
\(879\) 43.4344 1.46501
\(880\) 2.90568 0.0979506
\(881\) 47.0400 1.58482 0.792408 0.609991i \(-0.208827\pi\)
0.792408 + 0.609991i \(0.208827\pi\)
\(882\) −0.0335265 −0.00112890
\(883\) −52.3454 −1.76156 −0.880782 0.473522i \(-0.842982\pi\)
−0.880782 + 0.473522i \(0.842982\pi\)
\(884\) −14.0652 −0.473064
\(885\) 12.1446 0.408237
\(886\) 35.2770 1.18515
\(887\) 29.3491 0.985447 0.492723 0.870186i \(-0.336001\pi\)
0.492723 + 0.870186i \(0.336001\pi\)
\(888\) −20.7455 −0.696172
\(889\) −0.229404 −0.00769395
\(890\) 13.2086 0.442753
\(891\) −26.4971 −0.887685
\(892\) −5.61665 −0.188059
\(893\) −0.864934 −0.0289439
\(894\) 11.7708 0.393673
\(895\) −4.16912 −0.139358
\(896\) −2.79885 −0.0935029
\(897\) 9.84018 0.328554
\(898\) 13.7311 0.458212
\(899\) 24.1615 0.805832
\(900\) 0.0402221 0.00134074
\(901\) −17.2225 −0.573765
\(902\) 15.2946 0.509255
\(903\) 22.2960 0.741964
\(904\) −11.1906 −0.372192
\(905\) 0.834483 0.0277392
\(906\) 17.0090 0.565087
\(907\) −10.7838 −0.358069 −0.179034 0.983843i \(-0.557297\pi\)
−0.179034 + 0.983843i \(0.557297\pi\)
\(908\) −19.0382 −0.631806
\(909\) 0.536984 0.0178106
\(910\) −9.23003 −0.305972
\(911\) 24.3801 0.807747 0.403874 0.914815i \(-0.367664\pi\)
0.403874 + 0.914815i \(0.367664\pi\)
\(912\) 0.232179 0.00768822
\(913\) 48.9793 1.62098
\(914\) −32.3369 −1.06961
\(915\) 10.0350 0.331747
\(916\) −18.2529 −0.603092
\(917\) 11.0550 0.365067
\(918\) 22.0107 0.726461
\(919\) −37.3006 −1.23043 −0.615216 0.788358i \(-0.710931\pi\)
−0.615216 + 0.788358i \(0.710931\pi\)
\(920\) 1.71130 0.0564199
\(921\) −36.9687 −1.21816
\(922\) −0.219374 −0.00722470
\(923\) −1.46375 −0.0481798
\(924\) −14.1801 −0.466492
\(925\) −11.8979 −0.391201
\(926\) 7.36374 0.241988
\(927\) −0.643897 −0.0211483
\(928\) 2.64609 0.0868620
\(929\) 42.9751 1.40997 0.704984 0.709223i \(-0.250954\pi\)
0.704984 + 0.709223i \(0.250954\pi\)
\(930\) −15.9211 −0.522073
\(931\) −0.110993 −0.00363763
\(932\) 17.9389 0.587609
\(933\) −8.72981 −0.285801
\(934\) 13.1656 0.430792
\(935\) −12.3928 −0.405289
\(936\) −0.132644 −0.00433562
\(937\) 11.9642 0.390853 0.195426 0.980718i \(-0.437391\pi\)
0.195426 + 0.980718i \(0.437391\pi\)
\(938\) 3.21876 0.105096
\(939\) −40.4373 −1.31962
\(940\) 6.49550 0.211860
\(941\) −6.91846 −0.225535 −0.112768 0.993621i \(-0.535972\pi\)
−0.112768 + 0.993621i \(0.535972\pi\)
\(942\) 29.3974 0.957817
\(943\) 9.00775 0.293333
\(944\) −6.96517 −0.226697
\(945\) 14.4441 0.469867
\(946\) 13.2753 0.431616
\(947\) −9.80580 −0.318646 −0.159323 0.987227i \(-0.550931\pi\)
−0.159323 + 0.987227i \(0.550931\pi\)
\(948\) 25.3475 0.823249
\(949\) −3.15261 −0.102338
\(950\) 0.133159 0.00432025
\(951\) −28.0315 −0.908985
\(952\) 11.9371 0.386885
\(953\) 22.4361 0.726776 0.363388 0.931638i \(-0.381620\pi\)
0.363388 + 0.931638i \(0.381620\pi\)
\(954\) −0.162420 −0.00525854
\(955\) 17.5122 0.566681
\(956\) −27.5765 −0.891889
\(957\) 13.4062 0.433360
\(958\) 28.8129 0.930904
\(959\) 48.8106 1.57618
\(960\) −1.74362 −0.0562752
\(961\) 52.3759 1.68955
\(962\) 39.2369 1.26505
\(963\) −0.438121 −0.0141182
\(964\) 9.60993 0.309515
\(965\) −3.27577 −0.105451
\(966\) −8.35137 −0.268701
\(967\) −52.4073 −1.68531 −0.842653 0.538457i \(-0.819008\pi\)
−0.842653 + 0.538457i \(0.819008\pi\)
\(968\) 2.55700 0.0821851
\(969\) −0.990250 −0.0318114
\(970\) 8.57086 0.275194
\(971\) −13.7733 −0.442005 −0.221002 0.975273i \(-0.570933\pi\)
−0.221002 + 0.975273i \(0.570933\pi\)
\(972\) 0.417972 0.0134065
\(973\) −18.4040 −0.590004
\(974\) 2.51157 0.0804760
\(975\) −5.75012 −0.184151
\(976\) −5.75525 −0.184221
\(977\) 2.88069 0.0921616 0.0460808 0.998938i \(-0.485327\pi\)
0.0460808 + 0.998938i \(0.485327\pi\)
\(978\) 2.38947 0.0764070
\(979\) −38.3800 −1.22663
\(980\) 0.833534 0.0266263
\(981\) 0.415830 0.0132764
\(982\) 11.0188 0.351624
\(983\) 16.0515 0.511963 0.255981 0.966682i \(-0.417601\pi\)
0.255981 + 0.966682i \(0.417601\pi\)
\(984\) −9.17789 −0.292580
\(985\) −16.3680 −0.521529
\(986\) −11.2856 −0.359408
\(987\) −31.6989 −1.00899
\(988\) −0.439131 −0.0139706
\(989\) 7.81846 0.248613
\(990\) −0.116873 −0.00371446
\(991\) 28.2981 0.898920 0.449460 0.893301i \(-0.351616\pi\)
0.449460 + 0.893301i \(0.351616\pi\)
\(992\) 9.13104 0.289911
\(993\) −6.77705 −0.215063
\(994\) 1.24228 0.0394029
\(995\) 5.25004 0.166438
\(996\) −29.3912 −0.931296
\(997\) −39.4637 −1.24983 −0.624913 0.780694i \(-0.714866\pi\)
−0.624913 + 0.780694i \(0.714866\pi\)
\(998\) −18.0283 −0.570676
\(999\) −61.4019 −1.94267
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4010.2.a.i.1.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.3 10 1.1 even 1 trivial