Properties

Label 4010.2.a.i.1.5
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 1.5
Root \(-0.557507\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.25862 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.25862 q^{6} +1.88678 q^{7} -1.00000 q^{8} -1.41588 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.25862 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.25862 q^{6} +1.88678 q^{7} -1.00000 q^{8} -1.41588 q^{9} -1.00000 q^{10} -3.48622 q^{11} -1.25862 q^{12} -6.95331 q^{13} -1.88678 q^{14} -1.25862 q^{15} +1.00000 q^{16} +2.07979 q^{17} +1.41588 q^{18} +3.03678 q^{19} +1.00000 q^{20} -2.37474 q^{21} +3.48622 q^{22} +6.09494 q^{23} +1.25862 q^{24} +1.00000 q^{25} +6.95331 q^{26} +5.55791 q^{27} +1.88678 q^{28} -1.90478 q^{29} +1.25862 q^{30} +8.71536 q^{31} -1.00000 q^{32} +4.38782 q^{33} -2.07979 q^{34} +1.88678 q^{35} -1.41588 q^{36} -7.53999 q^{37} -3.03678 q^{38} +8.75157 q^{39} -1.00000 q^{40} +2.87033 q^{41} +2.37474 q^{42} +8.26705 q^{43} -3.48622 q^{44} -1.41588 q^{45} -6.09494 q^{46} -0.387411 q^{47} -1.25862 q^{48} -3.44005 q^{49} -1.00000 q^{50} -2.61766 q^{51} -6.95331 q^{52} +10.1906 q^{53} -5.55791 q^{54} -3.48622 q^{55} -1.88678 q^{56} -3.82216 q^{57} +1.90478 q^{58} -11.5233 q^{59} -1.25862 q^{60} -6.34170 q^{61} -8.71536 q^{62} -2.67145 q^{63} +1.00000 q^{64} -6.95331 q^{65} -4.38782 q^{66} -14.2874 q^{67} +2.07979 q^{68} -7.67121 q^{69} -1.88678 q^{70} -8.46495 q^{71} +1.41588 q^{72} +7.64415 q^{73} +7.53999 q^{74} -1.25862 q^{75} +3.03678 q^{76} -6.57773 q^{77} -8.75157 q^{78} +7.07250 q^{79} +1.00000 q^{80} -2.74766 q^{81} -2.87033 q^{82} +4.66441 q^{83} -2.37474 q^{84} +2.07979 q^{85} -8.26705 q^{86} +2.39740 q^{87} +3.48622 q^{88} +1.33024 q^{89} +1.41588 q^{90} -13.1194 q^{91} +6.09494 q^{92} -10.9693 q^{93} +0.387411 q^{94} +3.03678 q^{95} +1.25862 q^{96} -3.66697 q^{97} +3.44005 q^{98} +4.93606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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
\(3\) −1.25862 −0.726664 −0.363332 0.931660i \(-0.618361\pi\)
−0.363332 + 0.931660i \(0.618361\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.25862 0.513829
\(7\) 1.88678 0.713137 0.356568 0.934269i \(-0.383947\pi\)
0.356568 + 0.934269i \(0.383947\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.41588 −0.471959
\(10\) −1.00000 −0.316228
\(11\) −3.48622 −1.05113 −0.525567 0.850752i \(-0.676147\pi\)
−0.525567 + 0.850752i \(0.676147\pi\)
\(12\) −1.25862 −0.363332
\(13\) −6.95331 −1.92850 −0.964250 0.264993i \(-0.914630\pi\)
−0.964250 + 0.264993i \(0.914630\pi\)
\(14\) −1.88678 −0.504264
\(15\) −1.25862 −0.324974
\(16\) 1.00000 0.250000
\(17\) 2.07979 0.504422 0.252211 0.967672i \(-0.418842\pi\)
0.252211 + 0.967672i \(0.418842\pi\)
\(18\) 1.41588 0.333725
\(19\) 3.03678 0.696686 0.348343 0.937367i \(-0.386744\pi\)
0.348343 + 0.937367i \(0.386744\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.37474 −0.518211
\(22\) 3.48622 0.743264
\(23\) 6.09494 1.27088 0.635441 0.772149i \(-0.280818\pi\)
0.635441 + 0.772149i \(0.280818\pi\)
\(24\) 1.25862 0.256915
\(25\) 1.00000 0.200000
\(26\) 6.95331 1.36366
\(27\) 5.55791 1.06962
\(28\) 1.88678 0.356568
\(29\) −1.90478 −0.353709 −0.176855 0.984237i \(-0.556592\pi\)
−0.176855 + 0.984237i \(0.556592\pi\)
\(30\) 1.25862 0.229791
\(31\) 8.71536 1.56533 0.782663 0.622446i \(-0.213861\pi\)
0.782663 + 0.622446i \(0.213861\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.38782 0.763822
\(34\) −2.07979 −0.356680
\(35\) 1.88678 0.318924
\(36\) −1.41588 −0.235980
\(37\) −7.53999 −1.23957 −0.619783 0.784773i \(-0.712779\pi\)
−0.619783 + 0.784773i \(0.712779\pi\)
\(38\) −3.03678 −0.492631
\(39\) 8.75157 1.40137
\(40\) −1.00000 −0.158114
\(41\) 2.87033 0.448271 0.224135 0.974558i \(-0.428044\pi\)
0.224135 + 0.974558i \(0.428044\pi\)
\(42\) 2.37474 0.366430
\(43\) 8.26705 1.26071 0.630357 0.776306i \(-0.282909\pi\)
0.630357 + 0.776306i \(0.282909\pi\)
\(44\) −3.48622 −0.525567
\(45\) −1.41588 −0.211067
\(46\) −6.09494 −0.898650
\(47\) −0.387411 −0.0565097 −0.0282548 0.999601i \(-0.508995\pi\)
−0.0282548 + 0.999601i \(0.508995\pi\)
\(48\) −1.25862 −0.181666
\(49\) −3.44005 −0.491436
\(50\) −1.00000 −0.141421
\(51\) −2.61766 −0.366546
\(52\) −6.95331 −0.964250
\(53\) 10.1906 1.39979 0.699893 0.714247i \(-0.253231\pi\)
0.699893 + 0.714247i \(0.253231\pi\)
\(54\) −5.55791 −0.756336
\(55\) −3.48622 −0.470081
\(56\) −1.88678 −0.252132
\(57\) −3.82216 −0.506257
\(58\) 1.90478 0.250110
\(59\) −11.5233 −1.50020 −0.750101 0.661323i \(-0.769995\pi\)
−0.750101 + 0.661323i \(0.769995\pi\)
\(60\) −1.25862 −0.162487
\(61\) −6.34170 −0.811971 −0.405986 0.913879i \(-0.633072\pi\)
−0.405986 + 0.913879i \(0.633072\pi\)
\(62\) −8.71536 −1.10685
\(63\) −2.67145 −0.336571
\(64\) 1.00000 0.125000
\(65\) −6.95331 −0.862452
\(66\) −4.38782 −0.540103
\(67\) −14.2874 −1.74549 −0.872743 0.488179i \(-0.837661\pi\)
−0.872743 + 0.488179i \(0.837661\pi\)
\(68\) 2.07979 0.252211
\(69\) −7.67121 −0.923505
\(70\) −1.88678 −0.225514
\(71\) −8.46495 −1.00461 −0.502303 0.864692i \(-0.667514\pi\)
−0.502303 + 0.864692i \(0.667514\pi\)
\(72\) 1.41588 0.166863
\(73\) 7.64415 0.894680 0.447340 0.894364i \(-0.352371\pi\)
0.447340 + 0.894364i \(0.352371\pi\)
\(74\) 7.53999 0.876506
\(75\) −1.25862 −0.145333
\(76\) 3.03678 0.348343
\(77\) −6.57773 −0.749602
\(78\) −8.75157 −0.990920
\(79\) 7.07250 0.795718 0.397859 0.917447i \(-0.369753\pi\)
0.397859 + 0.917447i \(0.369753\pi\)
\(80\) 1.00000 0.111803
\(81\) −2.74766 −0.305296
\(82\) −2.87033 −0.316975
\(83\) 4.66441 0.511985 0.255993 0.966679i \(-0.417598\pi\)
0.255993 + 0.966679i \(0.417598\pi\)
\(84\) −2.37474 −0.259105
\(85\) 2.07979 0.225584
\(86\) −8.26705 −0.891459
\(87\) 2.39740 0.257028
\(88\) 3.48622 0.371632
\(89\) 1.33024 0.141005 0.0705023 0.997512i \(-0.477540\pi\)
0.0705023 + 0.997512i \(0.477540\pi\)
\(90\) 1.41588 0.149247
\(91\) −13.1194 −1.37528
\(92\) 6.09494 0.635441
\(93\) −10.9693 −1.13747
\(94\) 0.387411 0.0399584
\(95\) 3.03678 0.311568
\(96\) 1.25862 0.128457
\(97\) −3.66697 −0.372325 −0.186162 0.982519i \(-0.559605\pi\)
−0.186162 + 0.982519i \(0.559605\pi\)
\(98\) 3.44005 0.347498
\(99\) 4.93606 0.496092
\(100\) 1.00000 0.100000
\(101\) −3.83152 −0.381251 −0.190625 0.981663i \(-0.561052\pi\)
−0.190625 + 0.981663i \(0.561052\pi\)
\(102\) 2.61766 0.259187
\(103\) −4.52834 −0.446191 −0.223095 0.974797i \(-0.571616\pi\)
−0.223095 + 0.974797i \(0.571616\pi\)
\(104\) 6.95331 0.681828
\(105\) −2.37474 −0.231751
\(106\) −10.1906 −0.989799
\(107\) −8.53972 −0.825566 −0.412783 0.910829i \(-0.635443\pi\)
−0.412783 + 0.910829i \(0.635443\pi\)
\(108\) 5.55791 0.534810
\(109\) −12.6859 −1.21509 −0.607544 0.794286i \(-0.707845\pi\)
−0.607544 + 0.794286i \(0.707845\pi\)
\(110\) 3.48622 0.332398
\(111\) 9.48997 0.900748
\(112\) 1.88678 0.178284
\(113\) 1.41079 0.132716 0.0663581 0.997796i \(-0.478862\pi\)
0.0663581 + 0.997796i \(0.478862\pi\)
\(114\) 3.82216 0.357978
\(115\) 6.09494 0.568356
\(116\) −1.90478 −0.176855
\(117\) 9.84503 0.910174
\(118\) 11.5233 1.06080
\(119\) 3.92410 0.359722
\(120\) 1.25862 0.114896
\(121\) 1.15371 0.104883
\(122\) 6.34170 0.574150
\(123\) −3.61266 −0.325742
\(124\) 8.71536 0.782663
\(125\) 1.00000 0.0894427
\(126\) 2.67145 0.237992
\(127\) −7.44437 −0.660581 −0.330290 0.943879i \(-0.607147\pi\)
−0.330290 + 0.943879i \(0.607147\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.4051 −0.916115
\(130\) 6.95331 0.609846
\(131\) −0.585301 −0.0511380 −0.0255690 0.999673i \(-0.508140\pi\)
−0.0255690 + 0.999673i \(0.508140\pi\)
\(132\) 4.38782 0.381911
\(133\) 5.72975 0.496832
\(134\) 14.2874 1.23425
\(135\) 5.55791 0.478349
\(136\) −2.07979 −0.178340
\(137\) −3.90577 −0.333692 −0.166846 0.985983i \(-0.553358\pi\)
−0.166846 + 0.985983i \(0.553358\pi\)
\(138\) 7.67121 0.653017
\(139\) −17.5948 −1.49237 −0.746185 0.665739i \(-0.768117\pi\)
−0.746185 + 0.665739i \(0.768117\pi\)
\(140\) 1.88678 0.159462
\(141\) 0.487603 0.0410636
\(142\) 8.46495 0.710363
\(143\) 24.2407 2.02711
\(144\) −1.41588 −0.117990
\(145\) −1.90478 −0.158184
\(146\) −7.64415 −0.632634
\(147\) 4.32972 0.357109
\(148\) −7.53999 −0.619783
\(149\) −9.54635 −0.782067 −0.391034 0.920376i \(-0.627882\pi\)
−0.391034 + 0.920376i \(0.627882\pi\)
\(150\) 1.25862 0.102766
\(151\) −13.8126 −1.12405 −0.562027 0.827119i \(-0.689978\pi\)
−0.562027 + 0.827119i \(0.689978\pi\)
\(152\) −3.03678 −0.246316
\(153\) −2.94472 −0.238067
\(154\) 6.57773 0.530049
\(155\) 8.71536 0.700035
\(156\) 8.75157 0.700686
\(157\) 3.53365 0.282016 0.141008 0.990008i \(-0.454966\pi\)
0.141008 + 0.990008i \(0.454966\pi\)
\(158\) −7.07250 −0.562658
\(159\) −12.8261 −1.01718
\(160\) −1.00000 −0.0790569
\(161\) 11.4998 0.906313
\(162\) 2.74766 0.215877
\(163\) 15.0237 1.17675 0.588373 0.808590i \(-0.299769\pi\)
0.588373 + 0.808590i \(0.299769\pi\)
\(164\) 2.87033 0.224135
\(165\) 4.38782 0.341591
\(166\) −4.66441 −0.362028
\(167\) −6.40103 −0.495327 −0.247663 0.968846i \(-0.579663\pi\)
−0.247663 + 0.968846i \(0.579663\pi\)
\(168\) 2.37474 0.183215
\(169\) 35.3485 2.71912
\(170\) −2.07979 −0.159512
\(171\) −4.29971 −0.328807
\(172\) 8.26705 0.630357
\(173\) −6.47210 −0.492065 −0.246032 0.969262i \(-0.579127\pi\)
−0.246032 + 0.969262i \(0.579127\pi\)
\(174\) −2.39740 −0.181746
\(175\) 1.88678 0.142627
\(176\) −3.48622 −0.262784
\(177\) 14.5034 1.09014
\(178\) −1.33024 −0.0997054
\(179\) −10.5935 −0.791798 −0.395899 0.918294i \(-0.629567\pi\)
−0.395899 + 0.918294i \(0.629567\pi\)
\(180\) −1.41588 −0.105533
\(181\) 0.882166 0.0655709 0.0327854 0.999462i \(-0.489562\pi\)
0.0327854 + 0.999462i \(0.489562\pi\)
\(182\) 13.1194 0.972473
\(183\) 7.98178 0.590030
\(184\) −6.09494 −0.449325
\(185\) −7.53999 −0.554351
\(186\) 10.9693 0.804310
\(187\) −7.25059 −0.530215
\(188\) −0.387411 −0.0282548
\(189\) 10.4866 0.762785
\(190\) −3.03678 −0.220312
\(191\) 22.7634 1.64710 0.823550 0.567243i \(-0.191990\pi\)
0.823550 + 0.567243i \(0.191990\pi\)
\(192\) −1.25862 −0.0908330
\(193\) −6.26949 −0.451288 −0.225644 0.974210i \(-0.572449\pi\)
−0.225644 + 0.974210i \(0.572449\pi\)
\(194\) 3.66697 0.263273
\(195\) 8.75157 0.626713
\(196\) −3.44005 −0.245718
\(197\) 16.9202 1.20551 0.602756 0.797925i \(-0.294069\pi\)
0.602756 + 0.797925i \(0.294069\pi\)
\(198\) −4.93606 −0.350790
\(199\) −23.9409 −1.69713 −0.848563 0.529095i \(-0.822532\pi\)
−0.848563 + 0.529095i \(0.822532\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 17.9824 1.26838
\(202\) 3.83152 0.269585
\(203\) −3.59391 −0.252243
\(204\) −2.61766 −0.183273
\(205\) 2.87033 0.200473
\(206\) 4.52834 0.315504
\(207\) −8.62968 −0.599805
\(208\) −6.95331 −0.482125
\(209\) −10.5869 −0.732311
\(210\) 2.37474 0.163873
\(211\) 4.80818 0.331009 0.165505 0.986209i \(-0.447075\pi\)
0.165505 + 0.986209i \(0.447075\pi\)
\(212\) 10.1906 0.699893
\(213\) 10.6542 0.730011
\(214\) 8.53972 0.583763
\(215\) 8.26705 0.563808
\(216\) −5.55791 −0.378168
\(217\) 16.4440 1.11629
\(218\) 12.6859 0.859197
\(219\) −9.62107 −0.650132
\(220\) −3.48622 −0.235041
\(221\) −14.4614 −0.972778
\(222\) −9.48997 −0.636925
\(223\) −21.4209 −1.43445 −0.717226 0.696841i \(-0.754588\pi\)
−0.717226 + 0.696841i \(0.754588\pi\)
\(224\) −1.88678 −0.126066
\(225\) −1.41588 −0.0943918
\(226\) −1.41079 −0.0938446
\(227\) −17.0216 −1.12976 −0.564880 0.825173i \(-0.691078\pi\)
−0.564880 + 0.825173i \(0.691078\pi\)
\(228\) −3.82216 −0.253128
\(229\) −16.2986 −1.07704 −0.538520 0.842613i \(-0.681016\pi\)
−0.538520 + 0.842613i \(0.681016\pi\)
\(230\) −6.09494 −0.401888
\(231\) 8.27886 0.544709
\(232\) 1.90478 0.125055
\(233\) 3.22300 0.211146 0.105573 0.994412i \(-0.466332\pi\)
0.105573 + 0.994412i \(0.466332\pi\)
\(234\) −9.84503 −0.643590
\(235\) −0.387411 −0.0252719
\(236\) −11.5233 −0.750101
\(237\) −8.90158 −0.578220
\(238\) −3.92410 −0.254362
\(239\) −4.21601 −0.272711 −0.136355 0.990660i \(-0.543539\pi\)
−0.136355 + 0.990660i \(0.543539\pi\)
\(240\) −1.25862 −0.0812435
\(241\) 13.6898 0.881837 0.440919 0.897547i \(-0.354653\pi\)
0.440919 + 0.897547i \(0.354653\pi\)
\(242\) −1.15371 −0.0741635
\(243\) −13.2155 −0.847773
\(244\) −6.34170 −0.405986
\(245\) −3.44005 −0.219777
\(246\) 3.61266 0.230335
\(247\) −21.1157 −1.34356
\(248\) −8.71536 −0.553426
\(249\) −5.87072 −0.372042
\(250\) −1.00000 −0.0632456
\(251\) −25.3286 −1.59872 −0.799362 0.600849i \(-0.794829\pi\)
−0.799362 + 0.600849i \(0.794829\pi\)
\(252\) −2.67145 −0.168286
\(253\) −21.2483 −1.33587
\(254\) 7.44437 0.467101
\(255\) −2.61766 −0.163924
\(256\) 1.00000 0.0625000
\(257\) 15.7819 0.984447 0.492223 0.870469i \(-0.336184\pi\)
0.492223 + 0.870469i \(0.336184\pi\)
\(258\) 10.4051 0.647791
\(259\) −14.2263 −0.883980
\(260\) −6.95331 −0.431226
\(261\) 2.69694 0.166936
\(262\) 0.585301 0.0361600
\(263\) 9.08680 0.560316 0.280158 0.959954i \(-0.409613\pi\)
0.280158 + 0.959954i \(0.409613\pi\)
\(264\) −4.38782 −0.270052
\(265\) 10.1906 0.626004
\(266\) −5.72975 −0.351314
\(267\) −1.67426 −0.102463
\(268\) −14.2874 −0.872743
\(269\) −12.6123 −0.768988 −0.384494 0.923127i \(-0.625624\pi\)
−0.384494 + 0.923127i \(0.625624\pi\)
\(270\) −5.55791 −0.338244
\(271\) −22.6668 −1.37691 −0.688454 0.725280i \(-0.741710\pi\)
−0.688454 + 0.725280i \(0.741710\pi\)
\(272\) 2.07979 0.126106
\(273\) 16.5123 0.999370
\(274\) 3.90577 0.235956
\(275\) −3.48622 −0.210227
\(276\) −7.67121 −0.461752
\(277\) −3.47620 −0.208865 −0.104432 0.994532i \(-0.533303\pi\)
−0.104432 + 0.994532i \(0.533303\pi\)
\(278\) 17.5948 1.05526
\(279\) −12.3399 −0.738770
\(280\) −1.88678 −0.112757
\(281\) −16.1204 −0.961661 −0.480830 0.876814i \(-0.659665\pi\)
−0.480830 + 0.876814i \(0.659665\pi\)
\(282\) −0.487603 −0.0290363
\(283\) −11.4837 −0.682636 −0.341318 0.939948i \(-0.610873\pi\)
−0.341318 + 0.939948i \(0.610873\pi\)
\(284\) −8.46495 −0.502303
\(285\) −3.82216 −0.226405
\(286\) −24.2407 −1.43339
\(287\) 5.41569 0.319678
\(288\) 1.41588 0.0834314
\(289\) −12.6745 −0.745558
\(290\) 1.90478 0.111853
\(291\) 4.61532 0.270555
\(292\) 7.64415 0.447340
\(293\) 32.6546 1.90770 0.953852 0.300276i \(-0.0970789\pi\)
0.953852 + 0.300276i \(0.0970789\pi\)
\(294\) −4.32972 −0.252514
\(295\) −11.5233 −0.670911
\(296\) 7.53999 0.438253
\(297\) −19.3761 −1.12431
\(298\) 9.54635 0.553005
\(299\) −42.3800 −2.45090
\(300\) −1.25862 −0.0726664
\(301\) 15.5981 0.899061
\(302\) 13.8126 0.794827
\(303\) 4.82243 0.277041
\(304\) 3.03678 0.174172
\(305\) −6.34170 −0.363125
\(306\) 2.94472 0.168339
\(307\) −33.4934 −1.91157 −0.955783 0.294072i \(-0.904990\pi\)
−0.955783 + 0.294072i \(0.904990\pi\)
\(308\) −6.57773 −0.374801
\(309\) 5.69946 0.324231
\(310\) −8.71536 −0.494999
\(311\) 23.5276 1.33413 0.667064 0.745000i \(-0.267551\pi\)
0.667064 + 0.745000i \(0.267551\pi\)
\(312\) −8.75157 −0.495460
\(313\) 0.110421 0.00624134 0.00312067 0.999995i \(-0.499007\pi\)
0.00312067 + 0.999995i \(0.499007\pi\)
\(314\) −3.53365 −0.199415
\(315\) −2.67145 −0.150519
\(316\) 7.07250 0.397859
\(317\) 27.3570 1.53652 0.768260 0.640137i \(-0.221123\pi\)
0.768260 + 0.640137i \(0.221123\pi\)
\(318\) 12.8261 0.719251
\(319\) 6.64049 0.371796
\(320\) 1.00000 0.0559017
\(321\) 10.7483 0.599909
\(322\) −11.4998 −0.640860
\(323\) 6.31586 0.351424
\(324\) −2.74766 −0.152648
\(325\) −6.95331 −0.385700
\(326\) −15.0237 −0.832085
\(327\) 15.9667 0.882961
\(328\) −2.87033 −0.158488
\(329\) −0.730960 −0.0402991
\(330\) −4.38782 −0.241542
\(331\) −18.3665 −1.00952 −0.504758 0.863261i \(-0.668418\pi\)
−0.504758 + 0.863261i \(0.668418\pi\)
\(332\) 4.66441 0.255993
\(333\) 10.6757 0.585025
\(334\) 6.40103 0.350249
\(335\) −14.2874 −0.780605
\(336\) −2.37474 −0.129553
\(337\) −14.8058 −0.806521 −0.403260 0.915085i \(-0.632123\pi\)
−0.403260 + 0.915085i \(0.632123\pi\)
\(338\) −35.3485 −1.92271
\(339\) −1.77565 −0.0964402
\(340\) 2.07979 0.112792
\(341\) −30.3837 −1.64537
\(342\) 4.29971 0.232502
\(343\) −19.6981 −1.06360
\(344\) −8.26705 −0.445729
\(345\) −7.67121 −0.413004
\(346\) 6.47210 0.347942
\(347\) 18.7785 1.00808 0.504042 0.863679i \(-0.331846\pi\)
0.504042 + 0.863679i \(0.331846\pi\)
\(348\) 2.39740 0.128514
\(349\) 6.81508 0.364803 0.182401 0.983224i \(-0.441613\pi\)
0.182401 + 0.983224i \(0.441613\pi\)
\(350\) −1.88678 −0.100853
\(351\) −38.6459 −2.06276
\(352\) 3.48622 0.185816
\(353\) −24.6282 −1.31083 −0.655413 0.755271i \(-0.727505\pi\)
−0.655413 + 0.755271i \(0.727505\pi\)
\(354\) −14.5034 −0.770847
\(355\) −8.46495 −0.449273
\(356\) 1.33024 0.0705023
\(357\) −4.93895 −0.261397
\(358\) 10.5935 0.559885
\(359\) 1.95793 0.103335 0.0516677 0.998664i \(-0.483546\pi\)
0.0516677 + 0.998664i \(0.483546\pi\)
\(360\) 1.41588 0.0746233
\(361\) −9.77794 −0.514628
\(362\) −0.882166 −0.0463656
\(363\) −1.45209 −0.0762147
\(364\) −13.1194 −0.687642
\(365\) 7.64415 0.400113
\(366\) −7.98178 −0.417215
\(367\) 23.1187 1.20679 0.603393 0.797444i \(-0.293815\pi\)
0.603393 + 0.797444i \(0.293815\pi\)
\(368\) 6.09494 0.317721
\(369\) −4.06404 −0.211565
\(370\) 7.53999 0.391985
\(371\) 19.2274 0.998239
\(372\) −10.9693 −0.568733
\(373\) 36.1412 1.87132 0.935659 0.352905i \(-0.114806\pi\)
0.935659 + 0.352905i \(0.114806\pi\)
\(374\) 7.25059 0.374919
\(375\) −1.25862 −0.0649948
\(376\) 0.387411 0.0199792
\(377\) 13.2445 0.682129
\(378\) −10.4866 −0.539371
\(379\) 3.64173 0.187063 0.0935316 0.995616i \(-0.470184\pi\)
0.0935316 + 0.995616i \(0.470184\pi\)
\(380\) 3.03678 0.155784
\(381\) 9.36963 0.480020
\(382\) −22.7634 −1.16468
\(383\) 7.17961 0.366861 0.183430 0.983033i \(-0.441280\pi\)
0.183430 + 0.983033i \(0.441280\pi\)
\(384\) 1.25862 0.0642287
\(385\) −6.57773 −0.335232
\(386\) 6.26949 0.319109
\(387\) −11.7051 −0.595005
\(388\) −3.66697 −0.186162
\(389\) −16.5162 −0.837404 −0.418702 0.908124i \(-0.637515\pi\)
−0.418702 + 0.908124i \(0.637515\pi\)
\(390\) −8.75157 −0.443153
\(391\) 12.6762 0.641061
\(392\) 3.44005 0.173749
\(393\) 0.736671 0.0371602
\(394\) −16.9202 −0.852426
\(395\) 7.07250 0.355856
\(396\) 4.93606 0.248046
\(397\) −10.1468 −0.509253 −0.254627 0.967039i \(-0.581953\pi\)
−0.254627 + 0.967039i \(0.581953\pi\)
\(398\) 23.9409 1.20005
\(399\) −7.21158 −0.361030
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −17.9824 −0.896882
\(403\) −60.6006 −3.01873
\(404\) −3.83152 −0.190625
\(405\) −2.74766 −0.136532
\(406\) 3.59391 0.178363
\(407\) 26.2860 1.30295
\(408\) 2.61766 0.129593
\(409\) −6.66002 −0.329317 −0.164658 0.986351i \(-0.552652\pi\)
−0.164658 + 0.986351i \(0.552652\pi\)
\(410\) −2.87033 −0.141756
\(411\) 4.91587 0.242482
\(412\) −4.52834 −0.223095
\(413\) −21.7419 −1.06985
\(414\) 8.62968 0.424126
\(415\) 4.66441 0.228967
\(416\) 6.95331 0.340914
\(417\) 22.1451 1.08445
\(418\) 10.5869 0.517822
\(419\) −2.49145 −0.121715 −0.0608577 0.998146i \(-0.519384\pi\)
−0.0608577 + 0.998146i \(0.519384\pi\)
\(420\) −2.37474 −0.115875
\(421\) −6.59406 −0.321375 −0.160687 0.987005i \(-0.551371\pi\)
−0.160687 + 0.987005i \(0.551371\pi\)
\(422\) −4.80818 −0.234059
\(423\) 0.548526 0.0266703
\(424\) −10.1906 −0.494899
\(425\) 2.07979 0.100884
\(426\) −10.6542 −0.516195
\(427\) −11.9654 −0.579047
\(428\) −8.53972 −0.412783
\(429\) −30.5099 −1.47303
\(430\) −8.26705 −0.398673
\(431\) −18.1593 −0.874702 −0.437351 0.899291i \(-0.644083\pi\)
−0.437351 + 0.899291i \(0.644083\pi\)
\(432\) 5.55791 0.267405
\(433\) 19.1718 0.921338 0.460669 0.887572i \(-0.347610\pi\)
0.460669 + 0.887572i \(0.347610\pi\)
\(434\) −16.4440 −0.789337
\(435\) 2.39740 0.114946
\(436\) −12.6859 −0.607544
\(437\) 18.5090 0.885406
\(438\) 9.62107 0.459713
\(439\) 29.0910 1.38844 0.694218 0.719765i \(-0.255750\pi\)
0.694218 + 0.719765i \(0.255750\pi\)
\(440\) 3.48622 0.166199
\(441\) 4.87069 0.231938
\(442\) 14.4614 0.687858
\(443\) −8.67590 −0.412205 −0.206102 0.978530i \(-0.566078\pi\)
−0.206102 + 0.978530i \(0.566078\pi\)
\(444\) 9.48997 0.450374
\(445\) 1.33024 0.0630592
\(446\) 21.4209 1.01431
\(447\) 12.0152 0.568300
\(448\) 1.88678 0.0891421
\(449\) −33.8132 −1.59574 −0.797872 0.602826i \(-0.794041\pi\)
−0.797872 + 0.602826i \(0.794041\pi\)
\(450\) 1.41588 0.0667451
\(451\) −10.0066 −0.471193
\(452\) 1.41079 0.0663581
\(453\) 17.3848 0.816811
\(454\) 17.0216 0.798861
\(455\) −13.1194 −0.615046
\(456\) 3.82216 0.178989
\(457\) 13.2145 0.618146 0.309073 0.951038i \(-0.399981\pi\)
0.309073 + 0.951038i \(0.399981\pi\)
\(458\) 16.2986 0.761582
\(459\) 11.5593 0.539540
\(460\) 6.09494 0.284178
\(461\) −2.10624 −0.0980975 −0.0490488 0.998796i \(-0.515619\pi\)
−0.0490488 + 0.998796i \(0.515619\pi\)
\(462\) −8.27886 −0.385168
\(463\) −1.56942 −0.0729374 −0.0364687 0.999335i \(-0.511611\pi\)
−0.0364687 + 0.999335i \(0.511611\pi\)
\(464\) −1.90478 −0.0884274
\(465\) −10.9693 −0.508690
\(466\) −3.22300 −0.149302
\(467\) 38.9296 1.80145 0.900725 0.434391i \(-0.143036\pi\)
0.900725 + 0.434391i \(0.143036\pi\)
\(468\) 9.84503 0.455087
\(469\) −26.9573 −1.24477
\(470\) 0.387411 0.0178699
\(471\) −4.44752 −0.204931
\(472\) 11.5233 0.530401
\(473\) −28.8207 −1.32518
\(474\) 8.90158 0.408863
\(475\) 3.03678 0.139337
\(476\) 3.92410 0.179861
\(477\) −14.4286 −0.660642
\(478\) 4.21601 0.192836
\(479\) 10.4833 0.478994 0.239497 0.970897i \(-0.423017\pi\)
0.239497 + 0.970897i \(0.423017\pi\)
\(480\) 1.25862 0.0574479
\(481\) 52.4279 2.39050
\(482\) −13.6898 −0.623553
\(483\) −14.4739 −0.658585
\(484\) 1.15371 0.0524415
\(485\) −3.66697 −0.166509
\(486\) 13.2155 0.599466
\(487\) −24.6487 −1.11694 −0.558471 0.829524i \(-0.688612\pi\)
−0.558471 + 0.829524i \(0.688612\pi\)
\(488\) 6.34170 0.287075
\(489\) −18.9091 −0.855099
\(490\) 3.44005 0.155406
\(491\) 14.8353 0.669509 0.334754 0.942305i \(-0.391347\pi\)
0.334754 + 0.942305i \(0.391347\pi\)
\(492\) −3.61266 −0.162871
\(493\) −3.96154 −0.178419
\(494\) 21.1157 0.950040
\(495\) 4.93606 0.221859
\(496\) 8.71536 0.391331
\(497\) −15.9715 −0.716421
\(498\) 5.87072 0.263073
\(499\) −5.40224 −0.241837 −0.120919 0.992662i \(-0.538584\pi\)
−0.120919 + 0.992662i \(0.538584\pi\)
\(500\) 1.00000 0.0447214
\(501\) 8.05647 0.359936
\(502\) 25.3286 1.13047
\(503\) −16.4494 −0.733440 −0.366720 0.930331i \(-0.619519\pi\)
−0.366720 + 0.930331i \(0.619519\pi\)
\(504\) 2.67145 0.118996
\(505\) −3.83152 −0.170500
\(506\) 21.2483 0.944601
\(507\) −44.4903 −1.97588
\(508\) −7.44437 −0.330290
\(509\) −32.7990 −1.45379 −0.726894 0.686749i \(-0.759037\pi\)
−0.726894 + 0.686749i \(0.759037\pi\)
\(510\) 2.61766 0.115912
\(511\) 14.4228 0.638029
\(512\) −1.00000 −0.0441942
\(513\) 16.8782 0.745189
\(514\) −15.7819 −0.696109
\(515\) −4.52834 −0.199543
\(516\) −10.4051 −0.458058
\(517\) 1.35060 0.0593992
\(518\) 14.2263 0.625068
\(519\) 8.14591 0.357566
\(520\) 6.95331 0.304923
\(521\) 37.5053 1.64314 0.821568 0.570111i \(-0.193100\pi\)
0.821568 + 0.570111i \(0.193100\pi\)
\(522\) −2.69694 −0.118042
\(523\) 26.1649 1.14411 0.572055 0.820215i \(-0.306146\pi\)
0.572055 + 0.820215i \(0.306146\pi\)
\(524\) −0.585301 −0.0255690
\(525\) −2.37474 −0.103642
\(526\) −9.08680 −0.396203
\(527\) 18.1261 0.789585
\(528\) 4.38782 0.190955
\(529\) 14.1483 0.615142
\(530\) −10.1906 −0.442651
\(531\) 16.3155 0.708034
\(532\) 5.72975 0.248416
\(533\) −19.9583 −0.864491
\(534\) 1.67426 0.0724523
\(535\) −8.53972 −0.369204
\(536\) 14.2874 0.617123
\(537\) 13.3332 0.575371
\(538\) 12.6123 0.543757
\(539\) 11.9928 0.516565
\(540\) 5.55791 0.239174
\(541\) −38.6718 −1.66263 −0.831315 0.555802i \(-0.812411\pi\)
−0.831315 + 0.555802i \(0.812411\pi\)
\(542\) 22.6668 0.973621
\(543\) −1.11031 −0.0476480
\(544\) −2.07979 −0.0891701
\(545\) −12.6859 −0.543404
\(546\) −16.5123 −0.706661
\(547\) −7.45495 −0.318751 −0.159375 0.987218i \(-0.550948\pi\)
−0.159375 + 0.987218i \(0.550948\pi\)
\(548\) −3.90577 −0.166846
\(549\) 8.97907 0.383217
\(550\) 3.48622 0.148653
\(551\) −5.78442 −0.246424
\(552\) 7.67121 0.326508
\(553\) 13.3443 0.567456
\(554\) 3.47620 0.147690
\(555\) 9.48997 0.402827
\(556\) −17.5948 −0.746185
\(557\) 22.7958 0.965889 0.482944 0.875651i \(-0.339567\pi\)
0.482944 + 0.875651i \(0.339567\pi\)
\(558\) 12.3399 0.522389
\(559\) −57.4833 −2.43129
\(560\) 1.88678 0.0797311
\(561\) 9.12573 0.385288
\(562\) 16.1204 0.679997
\(563\) −10.1923 −0.429552 −0.214776 0.976663i \(-0.568902\pi\)
−0.214776 + 0.976663i \(0.568902\pi\)
\(564\) 0.487603 0.0205318
\(565\) 1.41079 0.0593525
\(566\) 11.4837 0.482696
\(567\) −5.18424 −0.217717
\(568\) 8.46495 0.355182
\(569\) 23.4550 0.983286 0.491643 0.870797i \(-0.336396\pi\)
0.491643 + 0.870797i \(0.336396\pi\)
\(570\) 3.82216 0.160092
\(571\) 14.7947 0.619138 0.309569 0.950877i \(-0.399815\pi\)
0.309569 + 0.950877i \(0.399815\pi\)
\(572\) 24.2407 1.01356
\(573\) −28.6504 −1.19689
\(574\) −5.41569 −0.226047
\(575\) 6.09494 0.254176
\(576\) −1.41588 −0.0589949
\(577\) −4.14266 −0.172461 −0.0862305 0.996275i \(-0.527482\pi\)
−0.0862305 + 0.996275i \(0.527482\pi\)
\(578\) 12.6745 0.527189
\(579\) 7.89091 0.327935
\(580\) −1.90478 −0.0790918
\(581\) 8.80073 0.365116
\(582\) −4.61532 −0.191311
\(583\) −35.5267 −1.47136
\(584\) −7.64415 −0.316317
\(585\) 9.84503 0.407042
\(586\) −32.6546 −1.34895
\(587\) 9.09515 0.375397 0.187698 0.982227i \(-0.439897\pi\)
0.187698 + 0.982227i \(0.439897\pi\)
\(588\) 4.32972 0.178555
\(589\) 26.4667 1.09054
\(590\) 11.5233 0.474405
\(591\) −21.2961 −0.876003
\(592\) −7.53999 −0.309892
\(593\) 1.36584 0.0560883 0.0280442 0.999607i \(-0.491072\pi\)
0.0280442 + 0.999607i \(0.491072\pi\)
\(594\) 19.3761 0.795010
\(595\) 3.92410 0.160873
\(596\) −9.54635 −0.391034
\(597\) 30.1325 1.23324
\(598\) 42.3800 1.73305
\(599\) 31.3707 1.28177 0.640886 0.767636i \(-0.278567\pi\)
0.640886 + 0.767636i \(0.278567\pi\)
\(600\) 1.25862 0.0513829
\(601\) −20.6139 −0.840860 −0.420430 0.907325i \(-0.638121\pi\)
−0.420430 + 0.907325i \(0.638121\pi\)
\(602\) −15.5981 −0.635732
\(603\) 20.2292 0.823798
\(604\) −13.8126 −0.562027
\(605\) 1.15371 0.0469051
\(606\) −4.82243 −0.195898
\(607\) −12.9985 −0.527594 −0.263797 0.964578i \(-0.584975\pi\)
−0.263797 + 0.964578i \(0.584975\pi\)
\(608\) −3.03678 −0.123158
\(609\) 4.52337 0.183296
\(610\) 6.34170 0.256768
\(611\) 2.69379 0.108979
\(612\) −2.94472 −0.119033
\(613\) −2.88549 −0.116544 −0.0582720 0.998301i \(-0.518559\pi\)
−0.0582720 + 0.998301i \(0.518559\pi\)
\(614\) 33.4934 1.35168
\(615\) −3.61266 −0.145676
\(616\) 6.57773 0.265024
\(617\) −1.94625 −0.0783532 −0.0391766 0.999232i \(-0.512473\pi\)
−0.0391766 + 0.999232i \(0.512473\pi\)
\(618\) −5.69946 −0.229266
\(619\) 32.9784 1.32551 0.662757 0.748834i \(-0.269386\pi\)
0.662757 + 0.748834i \(0.269386\pi\)
\(620\) 8.71536 0.350017
\(621\) 33.8751 1.35936
\(622\) −23.5276 −0.943371
\(623\) 2.50986 0.100556
\(624\) 8.75157 0.350343
\(625\) 1.00000 0.0400000
\(626\) −0.110421 −0.00441329
\(627\) 13.3249 0.532144
\(628\) 3.53365 0.141008
\(629\) −15.6816 −0.625265
\(630\) 2.67145 0.106433
\(631\) 10.4077 0.414324 0.207162 0.978307i \(-0.433577\pi\)
0.207162 + 0.978307i \(0.433577\pi\)
\(632\) −7.07250 −0.281329
\(633\) −6.05167 −0.240532
\(634\) −27.3570 −1.08648
\(635\) −7.44437 −0.295421
\(636\) −12.8261 −0.508588
\(637\) 23.9197 0.947735
\(638\) −6.64049 −0.262900
\(639\) 11.9853 0.474133
\(640\) −1.00000 −0.0395285
\(641\) −23.2972 −0.920184 −0.460092 0.887871i \(-0.652183\pi\)
−0.460092 + 0.887871i \(0.652183\pi\)
\(642\) −10.7483 −0.424200
\(643\) 12.0025 0.473333 0.236667 0.971591i \(-0.423945\pi\)
0.236667 + 0.971591i \(0.423945\pi\)
\(644\) 11.4998 0.453156
\(645\) −10.4051 −0.409699
\(646\) −6.31586 −0.248494
\(647\) −36.7478 −1.44470 −0.722352 0.691526i \(-0.756939\pi\)
−0.722352 + 0.691526i \(0.756939\pi\)
\(648\) 2.74766 0.107938
\(649\) 40.1726 1.57691
\(650\) 6.95331 0.272731
\(651\) −20.6967 −0.811169
\(652\) 15.0237 0.588373
\(653\) 22.6251 0.885389 0.442695 0.896672i \(-0.354023\pi\)
0.442695 + 0.896672i \(0.354023\pi\)
\(654\) −15.9667 −0.624348
\(655\) −0.585301 −0.0228696
\(656\) 2.87033 0.112068
\(657\) −10.8232 −0.422252
\(658\) 0.730960 0.0284958
\(659\) −23.5581 −0.917692 −0.458846 0.888516i \(-0.651737\pi\)
−0.458846 + 0.888516i \(0.651737\pi\)
\(660\) 4.38782 0.170796
\(661\) −22.5040 −0.875304 −0.437652 0.899144i \(-0.644190\pi\)
−0.437652 + 0.899144i \(0.644190\pi\)
\(662\) 18.3665 0.713835
\(663\) 18.2014 0.706883
\(664\) −4.66441 −0.181014
\(665\) 5.72975 0.222190
\(666\) −10.6757 −0.413675
\(667\) −11.6095 −0.449523
\(668\) −6.40103 −0.247663
\(669\) 26.9608 1.04236
\(670\) 14.2874 0.551971
\(671\) 22.1085 0.853491
\(672\) 2.37474 0.0916076
\(673\) −44.0253 −1.69705 −0.848524 0.529156i \(-0.822509\pi\)
−0.848524 + 0.529156i \(0.822509\pi\)
\(674\) 14.8058 0.570296
\(675\) 5.55791 0.213924
\(676\) 35.3485 1.35956
\(677\) 0.560216 0.0215308 0.0107654 0.999942i \(-0.496573\pi\)
0.0107654 + 0.999942i \(0.496573\pi\)
\(678\) 1.77565 0.0681935
\(679\) −6.91878 −0.265518
\(680\) −2.07979 −0.0797561
\(681\) 21.4237 0.820956
\(682\) 30.3837 1.16345
\(683\) −3.23259 −0.123692 −0.0618458 0.998086i \(-0.519699\pi\)
−0.0618458 + 0.998086i \(0.519699\pi\)
\(684\) −4.29971 −0.164404
\(685\) −3.90577 −0.149232
\(686\) 19.6981 0.752077
\(687\) 20.5137 0.782646
\(688\) 8.26705 0.315178
\(689\) −70.8584 −2.69949
\(690\) 7.67121 0.292038
\(691\) −13.2122 −0.502615 −0.251307 0.967907i \(-0.580860\pi\)
−0.251307 + 0.967907i \(0.580860\pi\)
\(692\) −6.47210 −0.246032
\(693\) 9.31326 0.353782
\(694\) −18.7785 −0.712822
\(695\) −17.5948 −0.667408
\(696\) −2.39740 −0.0908731
\(697\) 5.96968 0.226118
\(698\) −6.81508 −0.257955
\(699\) −4.05653 −0.153432
\(700\) 1.88678 0.0713137
\(701\) −11.2730 −0.425777 −0.212888 0.977077i \(-0.568287\pi\)
−0.212888 + 0.977077i \(0.568287\pi\)
\(702\) 38.6459 1.45859
\(703\) −22.8973 −0.863589
\(704\) −3.48622 −0.131392
\(705\) 0.487603 0.0183642
\(706\) 24.6282 0.926894
\(707\) −7.22925 −0.271884
\(708\) 14.5034 0.545071
\(709\) −33.0445 −1.24101 −0.620505 0.784202i \(-0.713073\pi\)
−0.620505 + 0.784202i \(0.713073\pi\)
\(710\) 8.46495 0.317684
\(711\) −10.0138 −0.375546
\(712\) −1.33024 −0.0498527
\(713\) 53.1196 1.98935
\(714\) 4.93895 0.184836
\(715\) 24.2407 0.906553
\(716\) −10.5935 −0.395899
\(717\) 5.30635 0.198169
\(718\) −1.95793 −0.0730691
\(719\) −1.88027 −0.0701222 −0.0350611 0.999385i \(-0.511163\pi\)
−0.0350611 + 0.999385i \(0.511163\pi\)
\(720\) −1.41588 −0.0527666
\(721\) −8.54399 −0.318195
\(722\) 9.77794 0.363897
\(723\) −17.2302 −0.640800
\(724\) 0.882166 0.0327854
\(725\) −1.90478 −0.0707419
\(726\) 1.45209 0.0538919
\(727\) −49.2235 −1.82560 −0.912799 0.408409i \(-0.866084\pi\)
−0.912799 + 0.408409i \(0.866084\pi\)
\(728\) 13.1194 0.486237
\(729\) 24.8762 0.921342
\(730\) −7.64415 −0.282923
\(731\) 17.1937 0.635932
\(732\) 7.98178 0.295015
\(733\) −36.7645 −1.35793 −0.678964 0.734172i \(-0.737571\pi\)
−0.678964 + 0.734172i \(0.737571\pi\)
\(734\) −23.1187 −0.853327
\(735\) 4.32972 0.159704
\(736\) −6.09494 −0.224662
\(737\) 49.8091 1.83474
\(738\) 4.06404 0.149599
\(739\) −38.4371 −1.41393 −0.706966 0.707248i \(-0.749936\pi\)
−0.706966 + 0.707248i \(0.749936\pi\)
\(740\) −7.53999 −0.277175
\(741\) 26.5766 0.976317
\(742\) −19.2274 −0.705862
\(743\) 12.3760 0.454031 0.227016 0.973891i \(-0.427103\pi\)
0.227016 + 0.973891i \(0.427103\pi\)
\(744\) 10.9693 0.402155
\(745\) −9.54635 −0.349751
\(746\) −36.1412 −1.32322
\(747\) −6.60423 −0.241636
\(748\) −7.25059 −0.265108
\(749\) −16.1126 −0.588741
\(750\) 1.25862 0.0459583
\(751\) −42.3955 −1.54703 −0.773517 0.633775i \(-0.781504\pi\)
−0.773517 + 0.633775i \(0.781504\pi\)
\(752\) −0.387411 −0.0141274
\(753\) 31.8790 1.16174
\(754\) −13.2445 −0.482338
\(755\) −13.8126 −0.502693
\(756\) 10.4866 0.381393
\(757\) −44.3231 −1.61095 −0.805476 0.592629i \(-0.798090\pi\)
−0.805476 + 0.592629i \(0.798090\pi\)
\(758\) −3.64173 −0.132274
\(759\) 26.7435 0.970727
\(760\) −3.03678 −0.110156
\(761\) 2.39114 0.0866788 0.0433394 0.999060i \(-0.486200\pi\)
0.0433394 + 0.999060i \(0.486200\pi\)
\(762\) −9.36963 −0.339426
\(763\) −23.9355 −0.866524
\(764\) 22.7634 0.823550
\(765\) −2.94472 −0.106467
\(766\) −7.17961 −0.259410
\(767\) 80.1248 2.89314
\(768\) −1.25862 −0.0454165
\(769\) 15.5486 0.560698 0.280349 0.959898i \(-0.409550\pi\)
0.280349 + 0.959898i \(0.409550\pi\)
\(770\) 6.57773 0.237045
\(771\) −19.8634 −0.715362
\(772\) −6.26949 −0.225644
\(773\) −9.15143 −0.329154 −0.164577 0.986364i \(-0.552626\pi\)
−0.164577 + 0.986364i \(0.552626\pi\)
\(774\) 11.7051 0.420732
\(775\) 8.71536 0.313065
\(776\) 3.66697 0.131637
\(777\) 17.9055 0.642357
\(778\) 16.5162 0.592134
\(779\) 8.71658 0.312304
\(780\) 8.75157 0.313356
\(781\) 29.5107 1.05597
\(782\) −12.6762 −0.453299
\(783\) −10.5866 −0.378335
\(784\) −3.44005 −0.122859
\(785\) 3.53365 0.126121
\(786\) −0.736671 −0.0262762
\(787\) −47.1340 −1.68014 −0.840072 0.542475i \(-0.817487\pi\)
−0.840072 + 0.542475i \(0.817487\pi\)
\(788\) 16.9202 0.602756
\(789\) −11.4368 −0.407162
\(790\) −7.07250 −0.251628
\(791\) 2.66186 0.0946448
\(792\) −4.93606 −0.175395
\(793\) 44.0958 1.56589
\(794\) 10.1468 0.360096
\(795\) −12.8261 −0.454894
\(796\) −23.9409 −0.848563
\(797\) −14.3376 −0.507864 −0.253932 0.967222i \(-0.581724\pi\)
−0.253932 + 0.967222i \(0.581724\pi\)
\(798\) 7.21158 0.255287
\(799\) −0.805731 −0.0285047
\(800\) −1.00000 −0.0353553
\(801\) −1.88345 −0.0665484
\(802\) −1.00000 −0.0353112
\(803\) −26.6492 −0.940428
\(804\) 17.9824 0.634191
\(805\) 11.4998 0.405315
\(806\) 60.6006 2.13457
\(807\) 15.8741 0.558796
\(808\) 3.83152 0.134792
\(809\) 17.9724 0.631876 0.315938 0.948780i \(-0.397681\pi\)
0.315938 + 0.948780i \(0.397681\pi\)
\(810\) 2.74766 0.0965429
\(811\) −23.5508 −0.826980 −0.413490 0.910509i \(-0.635690\pi\)
−0.413490 + 0.910509i \(0.635690\pi\)
\(812\) −3.59391 −0.126122
\(813\) 28.5288 1.00055
\(814\) −26.2860 −0.921325
\(815\) 15.0237 0.526257
\(816\) −2.61766 −0.0916364
\(817\) 25.1052 0.878321
\(818\) 6.66002 0.232862
\(819\) 18.5754 0.649078
\(820\) 2.87033 0.100236
\(821\) −35.9550 −1.25484 −0.627419 0.778682i \(-0.715888\pi\)
−0.627419 + 0.778682i \(0.715888\pi\)
\(822\) −4.91587 −0.171461
\(823\) 34.0074 1.18542 0.592712 0.805414i \(-0.298057\pi\)
0.592712 + 0.805414i \(0.298057\pi\)
\(824\) 4.52834 0.157752
\(825\) 4.38782 0.152764
\(826\) 21.7419 0.756497
\(827\) −3.97871 −0.138353 −0.0691766 0.997604i \(-0.522037\pi\)
−0.0691766 + 0.997604i \(0.522037\pi\)
\(828\) −8.62968 −0.299902
\(829\) 21.7250 0.754540 0.377270 0.926103i \(-0.376863\pi\)
0.377270 + 0.926103i \(0.376863\pi\)
\(830\) −4.66441 −0.161904
\(831\) 4.37521 0.151775
\(832\) −6.95331 −0.241063
\(833\) −7.15457 −0.247891
\(834\) −22.1451 −0.766823
\(835\) −6.40103 −0.221517
\(836\) −10.5869 −0.366155
\(837\) 48.4392 1.67430
\(838\) 2.49145 0.0860658
\(839\) −22.9960 −0.793912 −0.396956 0.917838i \(-0.629933\pi\)
−0.396956 + 0.917838i \(0.629933\pi\)
\(840\) 2.37474 0.0819363
\(841\) −25.3718 −0.874890
\(842\) 6.59406 0.227246
\(843\) 20.2894 0.698804
\(844\) 4.80818 0.165505
\(845\) 35.3485 1.21603
\(846\) −0.548526 −0.0188587
\(847\) 2.17680 0.0747959
\(848\) 10.1906 0.349947
\(849\) 14.4536 0.496047
\(850\) −2.07979 −0.0713361
\(851\) −45.9558 −1.57534
\(852\) 10.6542 0.365005
\(853\) 43.9999 1.50653 0.753263 0.657719i \(-0.228479\pi\)
0.753263 + 0.657719i \(0.228479\pi\)
\(854\) 11.9654 0.409448
\(855\) −4.29971 −0.147047
\(856\) 8.53972 0.291882
\(857\) 46.2326 1.57927 0.789637 0.613574i \(-0.210269\pi\)
0.789637 + 0.613574i \(0.210269\pi\)
\(858\) 30.5099 1.04159
\(859\) 19.4465 0.663506 0.331753 0.943366i \(-0.392360\pi\)
0.331753 + 0.943366i \(0.392360\pi\)
\(860\) 8.26705 0.281904
\(861\) −6.81630 −0.232299
\(862\) 18.1593 0.618508
\(863\) 31.9882 1.08889 0.544446 0.838796i \(-0.316740\pi\)
0.544446 + 0.838796i \(0.316740\pi\)
\(864\) −5.55791 −0.189084
\(865\) −6.47210 −0.220058
\(866\) −19.1718 −0.651484
\(867\) 15.9524 0.541771
\(868\) 16.4440 0.558146
\(869\) −24.6563 −0.836407
\(870\) −2.39740 −0.0812794
\(871\) 99.3449 3.36617
\(872\) 12.6859 0.429599
\(873\) 5.19198 0.175722
\(874\) −18.5090 −0.626077
\(875\) 1.88678 0.0637849
\(876\) −9.62107 −0.325066
\(877\) 53.2785 1.79909 0.899544 0.436830i \(-0.143899\pi\)
0.899544 + 0.436830i \(0.143899\pi\)
\(878\) −29.0910 −0.981772
\(879\) −41.0998 −1.38626
\(880\) −3.48622 −0.117520
\(881\) 51.1456 1.72314 0.861569 0.507640i \(-0.169482\pi\)
0.861569 + 0.507640i \(0.169482\pi\)
\(882\) −4.87069 −0.164005
\(883\) 36.1378 1.21613 0.608066 0.793886i \(-0.291945\pi\)
0.608066 + 0.793886i \(0.291945\pi\)
\(884\) −14.4614 −0.486389
\(885\) 14.5034 0.487527
\(886\) 8.67590 0.291473
\(887\) −13.8667 −0.465599 −0.232800 0.972525i \(-0.574789\pi\)
−0.232800 + 0.972525i \(0.574789\pi\)
\(888\) −9.48997 −0.318463
\(889\) −14.0459 −0.471084
\(890\) −1.33024 −0.0445896
\(891\) 9.57894 0.320907
\(892\) −21.4209 −0.717226
\(893\) −1.17648 −0.0393695
\(894\) −12.0152 −0.401849
\(895\) −10.5935 −0.354103
\(896\) −1.88678 −0.0630330
\(897\) 53.3403 1.78098
\(898\) 33.8132 1.12836
\(899\) −16.6009 −0.553671
\(900\) −1.41588 −0.0471959
\(901\) 21.1943 0.706083
\(902\) 10.0066 0.333184
\(903\) −19.6321 −0.653315
\(904\) −1.41079 −0.0469223
\(905\) 0.882166 0.0293242
\(906\) −17.3848 −0.577572
\(907\) 19.6834 0.653577 0.326788 0.945098i \(-0.394034\pi\)
0.326788 + 0.945098i \(0.394034\pi\)
\(908\) −17.0216 −0.564880
\(909\) 5.42496 0.179935
\(910\) 13.1194 0.434903
\(911\) −4.58554 −0.151926 −0.0759628 0.997111i \(-0.524203\pi\)
−0.0759628 + 0.997111i \(0.524203\pi\)
\(912\) −3.82216 −0.126564
\(913\) −16.2611 −0.538165
\(914\) −13.2145 −0.437095
\(915\) 7.98178 0.263870
\(916\) −16.2986 −0.538520
\(917\) −1.10434 −0.0364684
\(918\) −11.5593 −0.381512
\(919\) −13.3272 −0.439623 −0.219812 0.975542i \(-0.570544\pi\)
−0.219812 + 0.975542i \(0.570544\pi\)
\(920\) −6.09494 −0.200944
\(921\) 42.1554 1.38907
\(922\) 2.10624 0.0693654
\(923\) 58.8594 1.93738
\(924\) 8.27886 0.272355
\(925\) −7.53999 −0.247913
\(926\) 1.56942 0.0515745
\(927\) 6.41158 0.210584
\(928\) 1.90478 0.0625276
\(929\) −22.5902 −0.741160 −0.370580 0.928801i \(-0.620841\pi\)
−0.370580 + 0.928801i \(0.620841\pi\)
\(930\) 10.9693 0.359698
\(931\) −10.4467 −0.342377
\(932\) 3.22300 0.105573
\(933\) −29.6123 −0.969463
\(934\) −38.9296 −1.27382
\(935\) −7.25059 −0.237119
\(936\) −9.84503 −0.321795
\(937\) −40.3554 −1.31835 −0.659177 0.751988i \(-0.729095\pi\)
−0.659177 + 0.751988i \(0.729095\pi\)
\(938\) 26.9573 0.880186
\(939\) −0.138977 −0.00453536
\(940\) −0.387411 −0.0126359
\(941\) 20.8444 0.679509 0.339755 0.940514i \(-0.389656\pi\)
0.339755 + 0.940514i \(0.389656\pi\)
\(942\) 4.44752 0.144908
\(943\) 17.4945 0.569699
\(944\) −11.5233 −0.375050
\(945\) 10.4866 0.341128
\(946\) 28.8207 0.937043
\(947\) −29.5450 −0.960082 −0.480041 0.877246i \(-0.659378\pi\)
−0.480041 + 0.877246i \(0.659378\pi\)
\(948\) −8.90158 −0.289110
\(949\) −53.1521 −1.72539
\(950\) −3.03678 −0.0985263
\(951\) −34.4320 −1.11653
\(952\) −3.92410 −0.127181
\(953\) −27.8195 −0.901162 −0.450581 0.892735i \(-0.648783\pi\)
−0.450581 + 0.892735i \(0.648783\pi\)
\(954\) 14.4286 0.467145
\(955\) 22.7634 0.736606
\(956\) −4.21601 −0.136355
\(957\) −8.35785 −0.270171
\(958\) −10.4833 −0.338700
\(959\) −7.36933 −0.237968
\(960\) −1.25862 −0.0406218
\(961\) 44.9576 1.45024
\(962\) −52.4279 −1.69034
\(963\) 12.0912 0.389633
\(964\) 13.6898 0.440919
\(965\) −6.26949 −0.201822
\(966\) 14.4739 0.465690
\(967\) 17.5961 0.565853 0.282926 0.959142i \(-0.408695\pi\)
0.282926 + 0.959142i \(0.408695\pi\)
\(968\) −1.15371 −0.0370817
\(969\) −7.94926 −0.255367
\(970\) 3.66697 0.117739
\(971\) 43.5488 1.39755 0.698774 0.715343i \(-0.253729\pi\)
0.698774 + 0.715343i \(0.253729\pi\)
\(972\) −13.2155 −0.423886
\(973\) −33.1975 −1.06426
\(974\) 24.6487 0.789797
\(975\) 8.75157 0.280275
\(976\) −6.34170 −0.202993
\(977\) 10.0435 0.321321 0.160661 0.987010i \(-0.448638\pi\)
0.160661 + 0.987010i \(0.448638\pi\)
\(978\) 18.9091 0.604646
\(979\) −4.63749 −0.148215
\(980\) −3.44005 −0.109888
\(981\) 17.9617 0.573472
\(982\) −14.8353 −0.473414
\(983\) −41.6833 −1.32949 −0.664745 0.747070i \(-0.731460\pi\)
−0.664745 + 0.747070i \(0.731460\pi\)
\(984\) 3.61266 0.115167
\(985\) 16.9202 0.539122
\(986\) 3.96154 0.126161
\(987\) 0.920000 0.0292839
\(988\) −21.1157 −0.671780
\(989\) 50.3872 1.60222
\(990\) −4.93606 −0.156878
\(991\) −50.7125 −1.61094 −0.805468 0.592640i \(-0.798086\pi\)
−0.805468 + 0.592640i \(0.798086\pi\)
\(992\) −8.71536 −0.276713
\(993\) 23.1165 0.733579
\(994\) 15.9715 0.506586
\(995\) −23.9409 −0.758978
\(996\) −5.87072 −0.186021
\(997\) 17.9887 0.569707 0.284853 0.958571i \(-0.408055\pi\)
0.284853 + 0.958571i \(0.408055\pi\)
\(998\) 5.40224 0.171005
\(999\) −41.9066 −1.32586
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.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.5 10 1.1 even 1 trivial