Properties

Label 4010.2.a.i.1.9
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 1.9
Root \(-0.309245\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.30797 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.30797 q^{6} -5.12569 q^{7} -1.00000 q^{8} +2.32671 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.30797 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.30797 q^{6} -5.12569 q^{7} -1.00000 q^{8} +2.32671 q^{9} -1.00000 q^{10} -1.82595 q^{11} +2.30797 q^{12} +2.86793 q^{13} +5.12569 q^{14} +2.30797 q^{15} +1.00000 q^{16} +5.18022 q^{17} -2.32671 q^{18} -1.72311 q^{19} +1.00000 q^{20} -11.8299 q^{21} +1.82595 q^{22} -0.231977 q^{23} -2.30797 q^{24} +1.00000 q^{25} -2.86793 q^{26} -1.55393 q^{27} -5.12569 q^{28} +0.413275 q^{29} -2.30797 q^{30} -5.80270 q^{31} -1.00000 q^{32} -4.21423 q^{33} -5.18022 q^{34} -5.12569 q^{35} +2.32671 q^{36} -0.773298 q^{37} +1.72311 q^{38} +6.61910 q^{39} -1.00000 q^{40} -8.47555 q^{41} +11.8299 q^{42} -10.9517 q^{43} -1.82595 q^{44} +2.32671 q^{45} +0.231977 q^{46} -13.3750 q^{47} +2.30797 q^{48} +19.2727 q^{49} -1.00000 q^{50} +11.9558 q^{51} +2.86793 q^{52} +3.57653 q^{53} +1.55393 q^{54} -1.82595 q^{55} +5.12569 q^{56} -3.97687 q^{57} -0.413275 q^{58} -8.35966 q^{59} +2.30797 q^{60} +7.09267 q^{61} +5.80270 q^{62} -11.9260 q^{63} +1.00000 q^{64} +2.86793 q^{65} +4.21423 q^{66} +10.1853 q^{67} +5.18022 q^{68} -0.535395 q^{69} +5.12569 q^{70} -7.02748 q^{71} -2.32671 q^{72} -7.84968 q^{73} +0.773298 q^{74} +2.30797 q^{75} -1.72311 q^{76} +9.35925 q^{77} -6.61910 q^{78} +8.27089 q^{79} +1.00000 q^{80} -10.5665 q^{81} +8.47555 q^{82} +2.73735 q^{83} -11.8299 q^{84} +5.18022 q^{85} +10.9517 q^{86} +0.953824 q^{87} +1.82595 q^{88} +1.59254 q^{89} -2.32671 q^{90} -14.7001 q^{91} -0.231977 q^{92} -13.3924 q^{93} +13.3750 q^{94} -1.72311 q^{95} -2.30797 q^{96} -11.7123 q^{97} -19.2727 q^{98} -4.24846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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
\(3\) 2.30797 1.33251 0.666253 0.745726i \(-0.267897\pi\)
0.666253 + 0.745726i \(0.267897\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.30797 −0.942224
\(7\) −5.12569 −1.93733 −0.968664 0.248375i \(-0.920104\pi\)
−0.968664 + 0.248375i \(0.920104\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.32671 0.775571
\(10\) −1.00000 −0.316228
\(11\) −1.82595 −0.550545 −0.275272 0.961366i \(-0.588768\pi\)
−0.275272 + 0.961366i \(0.588768\pi\)
\(12\) 2.30797 0.666253
\(13\) 2.86793 0.795422 0.397711 0.917511i \(-0.369805\pi\)
0.397711 + 0.917511i \(0.369805\pi\)
\(14\) 5.12569 1.36990
\(15\) 2.30797 0.595915
\(16\) 1.00000 0.250000
\(17\) 5.18022 1.25639 0.628193 0.778057i \(-0.283795\pi\)
0.628193 + 0.778057i \(0.283795\pi\)
\(18\) −2.32671 −0.548411
\(19\) −1.72311 −0.395307 −0.197654 0.980272i \(-0.563332\pi\)
−0.197654 + 0.980272i \(0.563332\pi\)
\(20\) 1.00000 0.223607
\(21\) −11.8299 −2.58150
\(22\) 1.82595 0.389294
\(23\) −0.231977 −0.0483705 −0.0241853 0.999707i \(-0.507699\pi\)
−0.0241853 + 0.999707i \(0.507699\pi\)
\(24\) −2.30797 −0.471112
\(25\) 1.00000 0.200000
\(26\) −2.86793 −0.562448
\(27\) −1.55393 −0.299053
\(28\) −5.12569 −0.968664
\(29\) 0.413275 0.0767432 0.0383716 0.999264i \(-0.487783\pi\)
0.0383716 + 0.999264i \(0.487783\pi\)
\(30\) −2.30797 −0.421375
\(31\) −5.80270 −1.04219 −0.521097 0.853497i \(-0.674477\pi\)
−0.521097 + 0.853497i \(0.674477\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.21423 −0.733604
\(34\) −5.18022 −0.888400
\(35\) −5.12569 −0.866399
\(36\) 2.32671 0.387785
\(37\) −0.773298 −0.127129 −0.0635647 0.997978i \(-0.520247\pi\)
−0.0635647 + 0.997978i \(0.520247\pi\)
\(38\) 1.72311 0.279525
\(39\) 6.61910 1.05990
\(40\) −1.00000 −0.158114
\(41\) −8.47555 −1.32366 −0.661829 0.749655i \(-0.730220\pi\)
−0.661829 + 0.749655i \(0.730220\pi\)
\(42\) 11.8299 1.82540
\(43\) −10.9517 −1.67012 −0.835058 0.550161i \(-0.814566\pi\)
−0.835058 + 0.550161i \(0.814566\pi\)
\(44\) −1.82595 −0.275272
\(45\) 2.32671 0.346846
\(46\) 0.231977 0.0342031
\(47\) −13.3750 −1.95095 −0.975475 0.220111i \(-0.929358\pi\)
−0.975475 + 0.220111i \(0.929358\pi\)
\(48\) 2.30797 0.333126
\(49\) 19.2727 2.75324
\(50\) −1.00000 −0.141421
\(51\) 11.9558 1.67414
\(52\) 2.86793 0.397711
\(53\) 3.57653 0.491274 0.245637 0.969362i \(-0.421003\pi\)
0.245637 + 0.969362i \(0.421003\pi\)
\(54\) 1.55393 0.211463
\(55\) −1.82595 −0.246211
\(56\) 5.12569 0.684949
\(57\) −3.97687 −0.526749
\(58\) −0.413275 −0.0542656
\(59\) −8.35966 −1.08833 −0.544167 0.838977i \(-0.683154\pi\)
−0.544167 + 0.838977i \(0.683154\pi\)
\(60\) 2.30797 0.297957
\(61\) 7.09267 0.908123 0.454061 0.890970i \(-0.349975\pi\)
0.454061 + 0.890970i \(0.349975\pi\)
\(62\) 5.80270 0.736943
\(63\) −11.9260 −1.50253
\(64\) 1.00000 0.125000
\(65\) 2.86793 0.355723
\(66\) 4.21423 0.518736
\(67\) 10.1853 1.24433 0.622163 0.782888i \(-0.286254\pi\)
0.622163 + 0.782888i \(0.286254\pi\)
\(68\) 5.18022 0.628193
\(69\) −0.535395 −0.0644540
\(70\) 5.12569 0.612637
\(71\) −7.02748 −0.834008 −0.417004 0.908905i \(-0.636920\pi\)
−0.417004 + 0.908905i \(0.636920\pi\)
\(72\) −2.32671 −0.274206
\(73\) −7.84968 −0.918735 −0.459368 0.888246i \(-0.651924\pi\)
−0.459368 + 0.888246i \(0.651924\pi\)
\(74\) 0.773298 0.0898940
\(75\) 2.30797 0.266501
\(76\) −1.72311 −0.197654
\(77\) 9.35925 1.06659
\(78\) −6.61910 −0.749465
\(79\) 8.27089 0.930548 0.465274 0.885167i \(-0.345956\pi\)
0.465274 + 0.885167i \(0.345956\pi\)
\(80\) 1.00000 0.111803
\(81\) −10.5665 −1.17406
\(82\) 8.47555 0.935968
\(83\) 2.73735 0.300464 0.150232 0.988651i \(-0.451998\pi\)
0.150232 + 0.988651i \(0.451998\pi\)
\(84\) −11.8299 −1.29075
\(85\) 5.18022 0.561873
\(86\) 10.9517 1.18095
\(87\) 0.953824 0.102261
\(88\) 1.82595 0.194647
\(89\) 1.59254 0.168809 0.0844043 0.996432i \(-0.473101\pi\)
0.0844043 + 0.996432i \(0.473101\pi\)
\(90\) −2.32671 −0.245257
\(91\) −14.7001 −1.54099
\(92\) −0.231977 −0.0241853
\(93\) −13.3924 −1.38873
\(94\) 13.3750 1.37953
\(95\) −1.72311 −0.176787
\(96\) −2.30797 −0.235556
\(97\) −11.7123 −1.18920 −0.594602 0.804021i \(-0.702690\pi\)
−0.594602 + 0.804021i \(0.702690\pi\)
\(98\) −19.2727 −1.94683
\(99\) −4.24846 −0.426986
\(100\) 1.00000 0.100000
\(101\) 6.71868 0.668533 0.334267 0.942479i \(-0.391511\pi\)
0.334267 + 0.942479i \(0.391511\pi\)
\(102\) −11.9558 −1.18380
\(103\) −4.23187 −0.416978 −0.208489 0.978025i \(-0.566855\pi\)
−0.208489 + 0.978025i \(0.566855\pi\)
\(104\) −2.86793 −0.281224
\(105\) −11.8299 −1.15448
\(106\) −3.57653 −0.347383
\(107\) 1.56139 0.150945 0.0754727 0.997148i \(-0.475953\pi\)
0.0754727 + 0.997148i \(0.475953\pi\)
\(108\) −1.55393 −0.149527
\(109\) 7.83377 0.750340 0.375170 0.926956i \(-0.377584\pi\)
0.375170 + 0.926956i \(0.377584\pi\)
\(110\) 1.82595 0.174098
\(111\) −1.78475 −0.169401
\(112\) −5.12569 −0.484332
\(113\) 1.88823 0.177630 0.0888150 0.996048i \(-0.471692\pi\)
0.0888150 + 0.996048i \(0.471692\pi\)
\(114\) 3.97687 0.372468
\(115\) −0.231977 −0.0216319
\(116\) 0.413275 0.0383716
\(117\) 6.67285 0.616906
\(118\) 8.35966 0.769569
\(119\) −26.5522 −2.43403
\(120\) −2.30797 −0.210688
\(121\) −7.66590 −0.696900
\(122\) −7.09267 −0.642140
\(123\) −19.5613 −1.76378
\(124\) −5.80270 −0.521097
\(125\) 1.00000 0.0894427
\(126\) 11.9260 1.06245
\(127\) 20.4205 1.81203 0.906014 0.423248i \(-0.139110\pi\)
0.906014 + 0.423248i \(0.139110\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −25.2761 −2.22544
\(130\) −2.86793 −0.251534
\(131\) −9.20972 −0.804657 −0.402329 0.915495i \(-0.631799\pi\)
−0.402329 + 0.915495i \(0.631799\pi\)
\(132\) −4.21423 −0.366802
\(133\) 8.83210 0.765840
\(134\) −10.1853 −0.879872
\(135\) −1.55393 −0.133741
\(136\) −5.18022 −0.444200
\(137\) −11.2959 −0.965073 −0.482537 0.875876i \(-0.660284\pi\)
−0.482537 + 0.875876i \(0.660284\pi\)
\(138\) 0.535395 0.0455758
\(139\) −9.18054 −0.778683 −0.389342 0.921093i \(-0.627297\pi\)
−0.389342 + 0.921093i \(0.627297\pi\)
\(140\) −5.12569 −0.433200
\(141\) −30.8691 −2.59965
\(142\) 7.02748 0.589733
\(143\) −5.23670 −0.437915
\(144\) 2.32671 0.193893
\(145\) 0.413275 0.0343206
\(146\) 7.84968 0.649644
\(147\) 44.4807 3.66871
\(148\) −0.773298 −0.0635647
\(149\) −12.1799 −0.997813 −0.498907 0.866656i \(-0.666265\pi\)
−0.498907 + 0.866656i \(0.666265\pi\)
\(150\) −2.30797 −0.188445
\(151\) −19.0556 −1.55072 −0.775360 0.631520i \(-0.782431\pi\)
−0.775360 + 0.631520i \(0.782431\pi\)
\(152\) 1.72311 0.139762
\(153\) 12.0529 0.974417
\(154\) −9.35925 −0.754190
\(155\) −5.80270 −0.466084
\(156\) 6.61910 0.529952
\(157\) −11.3912 −0.909118 −0.454559 0.890717i \(-0.650203\pi\)
−0.454559 + 0.890717i \(0.650203\pi\)
\(158\) −8.27089 −0.657997
\(159\) 8.25451 0.654625
\(160\) −1.00000 −0.0790569
\(161\) 1.18904 0.0937095
\(162\) 10.5665 0.830186
\(163\) −19.6319 −1.53769 −0.768845 0.639435i \(-0.779168\pi\)
−0.768845 + 0.639435i \(0.779168\pi\)
\(164\) −8.47555 −0.661829
\(165\) −4.21423 −0.328078
\(166\) −2.73735 −0.212460
\(167\) 19.5853 1.51556 0.757778 0.652513i \(-0.226285\pi\)
0.757778 + 0.652513i \(0.226285\pi\)
\(168\) 11.8299 0.912698
\(169\) −4.77496 −0.367304
\(170\) −5.18022 −0.397304
\(171\) −4.00917 −0.306589
\(172\) −10.9517 −0.835058
\(173\) −2.69712 −0.205058 −0.102529 0.994730i \(-0.532693\pi\)
−0.102529 + 0.994730i \(0.532693\pi\)
\(174\) −0.953824 −0.0723092
\(175\) −5.12569 −0.387466
\(176\) −1.82595 −0.137636
\(177\) −19.2938 −1.45021
\(178\) −1.59254 −0.119366
\(179\) −20.0859 −1.50129 −0.750644 0.660707i \(-0.770256\pi\)
−0.750644 + 0.660707i \(0.770256\pi\)
\(180\) 2.32671 0.173423
\(181\) 21.3607 1.58773 0.793866 0.608093i \(-0.208065\pi\)
0.793866 + 0.608093i \(0.208065\pi\)
\(182\) 14.7001 1.08965
\(183\) 16.3696 1.21008
\(184\) 0.231977 0.0171016
\(185\) −0.773298 −0.0568540
\(186\) 13.3924 0.981981
\(187\) −9.45882 −0.691697
\(188\) −13.3750 −0.975475
\(189\) 7.96495 0.579365
\(190\) 1.72311 0.125007
\(191\) −11.3414 −0.820633 −0.410316 0.911943i \(-0.634582\pi\)
−0.410316 + 0.911943i \(0.634582\pi\)
\(192\) 2.30797 0.166563
\(193\) 8.85428 0.637345 0.318672 0.947865i \(-0.396763\pi\)
0.318672 + 0.947865i \(0.396763\pi\)
\(194\) 11.7123 0.840894
\(195\) 6.61910 0.474003
\(196\) 19.2727 1.37662
\(197\) 17.6270 1.25587 0.627937 0.778264i \(-0.283899\pi\)
0.627937 + 0.778264i \(0.283899\pi\)
\(198\) 4.24846 0.301925
\(199\) −12.1913 −0.864220 −0.432110 0.901821i \(-0.642231\pi\)
−0.432110 + 0.901821i \(0.642231\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 23.5072 1.65807
\(202\) −6.71868 −0.472725
\(203\) −2.11832 −0.148677
\(204\) 11.9558 0.837071
\(205\) −8.47555 −0.591958
\(206\) 4.23187 0.294848
\(207\) −0.539743 −0.0375147
\(208\) 2.86793 0.198855
\(209\) 3.14630 0.217634
\(210\) 11.8299 0.816342
\(211\) −14.3087 −0.985052 −0.492526 0.870298i \(-0.663926\pi\)
−0.492526 + 0.870298i \(0.663926\pi\)
\(212\) 3.57653 0.245637
\(213\) −16.2192 −1.11132
\(214\) −1.56139 −0.106735
\(215\) −10.9517 −0.746899
\(216\) 1.55393 0.105731
\(217\) 29.7428 2.01907
\(218\) −7.83377 −0.530570
\(219\) −18.1168 −1.22422
\(220\) −1.82595 −0.123106
\(221\) 14.8565 0.999357
\(222\) 1.78475 0.119784
\(223\) −5.89664 −0.394868 −0.197434 0.980316i \(-0.563261\pi\)
−0.197434 + 0.980316i \(0.563261\pi\)
\(224\) 5.12569 0.342474
\(225\) 2.32671 0.155114
\(226\) −1.88823 −0.125603
\(227\) −1.03025 −0.0683801 −0.0341900 0.999415i \(-0.510885\pi\)
−0.0341900 + 0.999415i \(0.510885\pi\)
\(228\) −3.97687 −0.263375
\(229\) −24.4978 −1.61886 −0.809431 0.587215i \(-0.800224\pi\)
−0.809431 + 0.587215i \(0.800224\pi\)
\(230\) 0.231977 0.0152961
\(231\) 21.6008 1.42123
\(232\) −0.413275 −0.0271328
\(233\) −0.0260579 −0.00170711 −0.000853556 1.00000i \(-0.500272\pi\)
−0.000853556 1.00000i \(0.500272\pi\)
\(234\) −6.67285 −0.436218
\(235\) −13.3750 −0.872491
\(236\) −8.35966 −0.544167
\(237\) 19.0889 1.23996
\(238\) 26.5522 1.72112
\(239\) 23.2032 1.50089 0.750446 0.660931i \(-0.229839\pi\)
0.750446 + 0.660931i \(0.229839\pi\)
\(240\) 2.30797 0.148979
\(241\) 10.5016 0.676465 0.338232 0.941063i \(-0.390171\pi\)
0.338232 + 0.941063i \(0.390171\pi\)
\(242\) 7.66590 0.492783
\(243\) −19.7255 −1.26539
\(244\) 7.09267 0.454061
\(245\) 19.2727 1.23129
\(246\) 19.5613 1.24718
\(247\) −4.94175 −0.314436
\(248\) 5.80270 0.368472
\(249\) 6.31772 0.400369
\(250\) −1.00000 −0.0632456
\(251\) −14.3549 −0.906074 −0.453037 0.891492i \(-0.649659\pi\)
−0.453037 + 0.891492i \(0.649659\pi\)
\(252\) −11.9260 −0.751267
\(253\) 0.423578 0.0266301
\(254\) −20.4205 −1.28130
\(255\) 11.9558 0.748699
\(256\) 1.00000 0.0625000
\(257\) 24.1714 1.50777 0.753885 0.657007i \(-0.228178\pi\)
0.753885 + 0.657007i \(0.228178\pi\)
\(258\) 25.2761 1.57362
\(259\) 3.96368 0.246291
\(260\) 2.86793 0.177862
\(261\) 0.961571 0.0595197
\(262\) 9.20972 0.568979
\(263\) −1.26365 −0.0779200 −0.0389600 0.999241i \(-0.512404\pi\)
−0.0389600 + 0.999241i \(0.512404\pi\)
\(264\) 4.21423 0.259368
\(265\) 3.57653 0.219704
\(266\) −8.83210 −0.541531
\(267\) 3.67552 0.224938
\(268\) 10.1853 0.622163
\(269\) −19.8337 −1.20928 −0.604640 0.796499i \(-0.706683\pi\)
−0.604640 + 0.796499i \(0.706683\pi\)
\(270\) 1.55393 0.0945690
\(271\) 11.2534 0.683594 0.341797 0.939774i \(-0.388965\pi\)
0.341797 + 0.939774i \(0.388965\pi\)
\(272\) 5.18022 0.314097
\(273\) −33.9274 −2.05338
\(274\) 11.2959 0.682410
\(275\) −1.82595 −0.110109
\(276\) −0.535395 −0.0322270
\(277\) −13.8413 −0.831643 −0.415822 0.909446i \(-0.636506\pi\)
−0.415822 + 0.909446i \(0.636506\pi\)
\(278\) 9.18054 0.550612
\(279\) −13.5012 −0.808296
\(280\) 5.12569 0.306318
\(281\) −29.1862 −1.74110 −0.870552 0.492076i \(-0.836238\pi\)
−0.870552 + 0.492076i \(0.836238\pi\)
\(282\) 30.8691 1.83823
\(283\) 5.31391 0.315879 0.157940 0.987449i \(-0.449515\pi\)
0.157940 + 0.987449i \(0.449515\pi\)
\(284\) −7.02748 −0.417004
\(285\) −3.97687 −0.235569
\(286\) 5.23670 0.309653
\(287\) 43.4430 2.56436
\(288\) −2.32671 −0.137103
\(289\) 9.83464 0.578508
\(290\) −0.413275 −0.0242683
\(291\) −27.0316 −1.58462
\(292\) −7.84968 −0.459368
\(293\) 24.4177 1.42650 0.713248 0.700911i \(-0.247223\pi\)
0.713248 + 0.700911i \(0.247223\pi\)
\(294\) −44.4807 −2.59417
\(295\) −8.35966 −0.486718
\(296\) 0.773298 0.0449470
\(297\) 2.83739 0.164642
\(298\) 12.1799 0.705561
\(299\) −0.665294 −0.0384749
\(300\) 2.30797 0.133251
\(301\) 56.1349 3.23556
\(302\) 19.0556 1.09652
\(303\) 15.5065 0.890824
\(304\) −1.72311 −0.0988269
\(305\) 7.09267 0.406125
\(306\) −12.0529 −0.689017
\(307\) 29.2291 1.66819 0.834096 0.551619i \(-0.185990\pi\)
0.834096 + 0.551619i \(0.185990\pi\)
\(308\) 9.35925 0.533293
\(309\) −9.76702 −0.555626
\(310\) 5.80270 0.329571
\(311\) −8.05463 −0.456736 −0.228368 0.973575i \(-0.573339\pi\)
−0.228368 + 0.973575i \(0.573339\pi\)
\(312\) −6.61910 −0.374732
\(313\) 15.8471 0.895728 0.447864 0.894102i \(-0.352185\pi\)
0.447864 + 0.894102i \(0.352185\pi\)
\(314\) 11.3912 0.642844
\(315\) −11.9260 −0.671954
\(316\) 8.27089 0.465274
\(317\) 2.72043 0.152795 0.0763973 0.997077i \(-0.475658\pi\)
0.0763973 + 0.997077i \(0.475658\pi\)
\(318\) −8.25451 −0.462890
\(319\) −0.754619 −0.0422506
\(320\) 1.00000 0.0559017
\(321\) 3.60364 0.201136
\(322\) −1.18904 −0.0662627
\(323\) −8.92606 −0.496659
\(324\) −10.5665 −0.587030
\(325\) 2.86793 0.159084
\(326\) 19.6319 1.08731
\(327\) 18.0801 0.999831
\(328\) 8.47555 0.467984
\(329\) 68.5563 3.77963
\(330\) 4.21423 0.231986
\(331\) 15.5224 0.853187 0.426593 0.904444i \(-0.359714\pi\)
0.426593 + 0.904444i \(0.359714\pi\)
\(332\) 2.73735 0.150232
\(333\) −1.79924 −0.0985978
\(334\) −19.5853 −1.07166
\(335\) 10.1853 0.556480
\(336\) −11.8299 −0.645375
\(337\) −34.2266 −1.86444 −0.932222 0.361886i \(-0.882133\pi\)
−0.932222 + 0.361886i \(0.882133\pi\)
\(338\) 4.77496 0.259724
\(339\) 4.35798 0.236693
\(340\) 5.18022 0.280937
\(341\) 10.5954 0.573775
\(342\) 4.00917 0.216791
\(343\) −62.9059 −3.39660
\(344\) 10.9517 0.590475
\(345\) −0.535395 −0.0288247
\(346\) 2.69712 0.144998
\(347\) −3.94198 −0.211616 −0.105808 0.994387i \(-0.533743\pi\)
−0.105808 + 0.994387i \(0.533743\pi\)
\(348\) 0.953824 0.0511303
\(349\) −24.9824 −1.33728 −0.668640 0.743587i \(-0.733123\pi\)
−0.668640 + 0.743587i \(0.733123\pi\)
\(350\) 5.12569 0.273980
\(351\) −4.45656 −0.237874
\(352\) 1.82595 0.0973235
\(353\) −21.7570 −1.15801 −0.579003 0.815325i \(-0.696558\pi\)
−0.579003 + 0.815325i \(0.696558\pi\)
\(354\) 19.2938 1.02545
\(355\) −7.02748 −0.372980
\(356\) 1.59254 0.0844043
\(357\) −61.2815 −3.24336
\(358\) 20.0859 1.06157
\(359\) 25.8043 1.36190 0.680949 0.732331i \(-0.261568\pi\)
0.680949 + 0.732331i \(0.261568\pi\)
\(360\) −2.32671 −0.122628
\(361\) −16.0309 −0.843732
\(362\) −21.3607 −1.12270
\(363\) −17.6927 −0.928624
\(364\) −14.7001 −0.770496
\(365\) −7.84968 −0.410871
\(366\) −16.3696 −0.855655
\(367\) 8.98516 0.469022 0.234511 0.972114i \(-0.424651\pi\)
0.234511 + 0.972114i \(0.424651\pi\)
\(368\) −0.231977 −0.0120926
\(369\) −19.7202 −1.02659
\(370\) 0.773298 0.0402018
\(371\) −18.3322 −0.951758
\(372\) −13.3924 −0.694365
\(373\) −18.0327 −0.933700 −0.466850 0.884336i \(-0.654611\pi\)
−0.466850 + 0.884336i \(0.654611\pi\)
\(374\) 9.45882 0.489104
\(375\) 2.30797 0.119183
\(376\) 13.3750 0.689765
\(377\) 1.18524 0.0610432
\(378\) −7.96495 −0.409673
\(379\) −12.1860 −0.625955 −0.312977 0.949761i \(-0.601326\pi\)
−0.312977 + 0.949761i \(0.601326\pi\)
\(380\) −1.72311 −0.0883934
\(381\) 47.1299 2.41454
\(382\) 11.3414 0.580275
\(383\) 28.3229 1.44723 0.723616 0.690202i \(-0.242479\pi\)
0.723616 + 0.690202i \(0.242479\pi\)
\(384\) −2.30797 −0.117778
\(385\) 9.35925 0.476992
\(386\) −8.85428 −0.450671
\(387\) −25.4814 −1.29529
\(388\) −11.7123 −0.594602
\(389\) 14.5586 0.738152 0.369076 0.929399i \(-0.379674\pi\)
0.369076 + 0.929399i \(0.379674\pi\)
\(390\) −6.61910 −0.335171
\(391\) −1.20169 −0.0607721
\(392\) −19.2727 −0.973417
\(393\) −21.2557 −1.07221
\(394\) −17.6270 −0.888037
\(395\) 8.27089 0.416154
\(396\) −4.24846 −0.213493
\(397\) 33.7418 1.69345 0.846727 0.532027i \(-0.178570\pi\)
0.846727 + 0.532027i \(0.178570\pi\)
\(398\) 12.1913 0.611096
\(399\) 20.3842 1.02049
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −23.5072 −1.17243
\(403\) −16.6417 −0.828984
\(404\) 6.71868 0.334267
\(405\) −10.5665 −0.525056
\(406\) 2.11832 0.105130
\(407\) 1.41200 0.0699904
\(408\) −11.9558 −0.591899
\(409\) 8.73493 0.431915 0.215957 0.976403i \(-0.430713\pi\)
0.215957 + 0.976403i \(0.430713\pi\)
\(410\) 8.47555 0.418578
\(411\) −26.0705 −1.28597
\(412\) −4.23187 −0.208489
\(413\) 42.8490 2.10846
\(414\) 0.539743 0.0265269
\(415\) 2.73735 0.134371
\(416\) −2.86793 −0.140612
\(417\) −21.1884 −1.03760
\(418\) −3.14630 −0.153891
\(419\) −4.49937 −0.219808 −0.109904 0.993942i \(-0.535054\pi\)
−0.109904 + 0.993942i \(0.535054\pi\)
\(420\) −11.8299 −0.577241
\(421\) −12.0532 −0.587439 −0.293720 0.955892i \(-0.594893\pi\)
−0.293720 + 0.955892i \(0.594893\pi\)
\(422\) 14.3087 0.696537
\(423\) −31.1199 −1.51310
\(424\) −3.57653 −0.173692
\(425\) 5.18022 0.251277
\(426\) 16.2192 0.785822
\(427\) −36.3548 −1.75933
\(428\) 1.56139 0.0754727
\(429\) −12.0861 −0.583524
\(430\) 10.9517 0.528137
\(431\) 16.8432 0.811309 0.405655 0.914026i \(-0.367044\pi\)
0.405655 + 0.914026i \(0.367044\pi\)
\(432\) −1.55393 −0.0747634
\(433\) 7.54922 0.362792 0.181396 0.983410i \(-0.441938\pi\)
0.181396 + 0.983410i \(0.441938\pi\)
\(434\) −29.7428 −1.42770
\(435\) 0.953824 0.0457324
\(436\) 7.83377 0.375170
\(437\) 0.399720 0.0191212
\(438\) 18.1168 0.865654
\(439\) 23.5893 1.12586 0.562928 0.826506i \(-0.309675\pi\)
0.562928 + 0.826506i \(0.309675\pi\)
\(440\) 1.82595 0.0870488
\(441\) 44.8420 2.13533
\(442\) −14.8565 −0.706652
\(443\) 6.87149 0.326474 0.163237 0.986587i \(-0.447806\pi\)
0.163237 + 0.986587i \(0.447806\pi\)
\(444\) −1.78475 −0.0847003
\(445\) 1.59254 0.0754935
\(446\) 5.89664 0.279214
\(447\) −28.1107 −1.32959
\(448\) −5.12569 −0.242166
\(449\) 7.37577 0.348084 0.174042 0.984738i \(-0.444317\pi\)
0.174042 + 0.984738i \(0.444317\pi\)
\(450\) −2.32671 −0.109682
\(451\) 15.4759 0.728733
\(452\) 1.88823 0.0888150
\(453\) −43.9796 −2.06634
\(454\) 1.03025 0.0483520
\(455\) −14.7001 −0.689153
\(456\) 3.97687 0.186234
\(457\) −37.2443 −1.74221 −0.871107 0.491093i \(-0.836598\pi\)
−0.871107 + 0.491093i \(0.836598\pi\)
\(458\) 24.4978 1.14471
\(459\) −8.04968 −0.375727
\(460\) −0.231977 −0.0108160
\(461\) −17.2287 −0.802420 −0.401210 0.915986i \(-0.631410\pi\)
−0.401210 + 0.915986i \(0.631410\pi\)
\(462\) −21.6008 −1.00496
\(463\) −9.75535 −0.453370 −0.226685 0.973968i \(-0.572789\pi\)
−0.226685 + 0.973968i \(0.572789\pi\)
\(464\) 0.413275 0.0191858
\(465\) −13.3924 −0.621059
\(466\) 0.0260579 0.00120711
\(467\) −2.98148 −0.137966 −0.0689831 0.997618i \(-0.521975\pi\)
−0.0689831 + 0.997618i \(0.521975\pi\)
\(468\) 6.67285 0.308453
\(469\) −52.2064 −2.41067
\(470\) 13.3750 0.616945
\(471\) −26.2906 −1.21140
\(472\) 8.35966 0.384784
\(473\) 19.9972 0.919474
\(474\) −19.0889 −0.876784
\(475\) −1.72311 −0.0790615
\(476\) −26.5522 −1.21702
\(477\) 8.32155 0.381017
\(478\) −23.2032 −1.06129
\(479\) 0.647726 0.0295954 0.0147977 0.999891i \(-0.495290\pi\)
0.0147977 + 0.999891i \(0.495290\pi\)
\(480\) −2.30797 −0.105344
\(481\) −2.21777 −0.101121
\(482\) −10.5016 −0.478333
\(483\) 2.74427 0.124868
\(484\) −7.66590 −0.348450
\(485\) −11.7123 −0.531828
\(486\) 19.7255 0.894765
\(487\) −5.61871 −0.254608 −0.127304 0.991864i \(-0.540632\pi\)
−0.127304 + 0.991864i \(0.540632\pi\)
\(488\) −7.09267 −0.321070
\(489\) −45.3098 −2.04898
\(490\) −19.2727 −0.870651
\(491\) 31.2742 1.41138 0.705692 0.708519i \(-0.250636\pi\)
0.705692 + 0.708519i \(0.250636\pi\)
\(492\) −19.5613 −0.881891
\(493\) 2.14085 0.0964191
\(494\) 4.94175 0.222340
\(495\) −4.24846 −0.190954
\(496\) −5.80270 −0.260549
\(497\) 36.0207 1.61575
\(498\) −6.31772 −0.283104
\(499\) 12.9780 0.580976 0.290488 0.956879i \(-0.406182\pi\)
0.290488 + 0.956879i \(0.406182\pi\)
\(500\) 1.00000 0.0447214
\(501\) 45.2022 2.01949
\(502\) 14.3549 0.640691
\(503\) −34.2674 −1.52791 −0.763954 0.645270i \(-0.776745\pi\)
−0.763954 + 0.645270i \(0.776745\pi\)
\(504\) 11.9260 0.531226
\(505\) 6.71868 0.298977
\(506\) −0.423578 −0.0188303
\(507\) −11.0204 −0.489435
\(508\) 20.4205 0.906014
\(509\) 35.4963 1.57334 0.786672 0.617371i \(-0.211802\pi\)
0.786672 + 0.617371i \(0.211802\pi\)
\(510\) −11.9558 −0.529410
\(511\) 40.2350 1.77989
\(512\) −1.00000 −0.0441942
\(513\) 2.67758 0.118218
\(514\) −24.1714 −1.06615
\(515\) −4.23187 −0.186478
\(516\) −25.2761 −1.11272
\(517\) 24.4222 1.07409
\(518\) −3.96368 −0.174154
\(519\) −6.22486 −0.273241
\(520\) −2.86793 −0.125767
\(521\) 10.3684 0.454250 0.227125 0.973866i \(-0.427067\pi\)
0.227125 + 0.973866i \(0.427067\pi\)
\(522\) −0.961571 −0.0420868
\(523\) 18.8843 0.825754 0.412877 0.910787i \(-0.364524\pi\)
0.412877 + 0.910787i \(0.364524\pi\)
\(524\) −9.20972 −0.402329
\(525\) −11.8299 −0.516300
\(526\) 1.26365 0.0550977
\(527\) −30.0592 −1.30940
\(528\) −4.21423 −0.183401
\(529\) −22.9462 −0.997660
\(530\) −3.57653 −0.155354
\(531\) −19.4505 −0.844080
\(532\) 8.83210 0.382920
\(533\) −24.3073 −1.05287
\(534\) −3.67552 −0.159055
\(535\) 1.56139 0.0675048
\(536\) −10.1853 −0.439936
\(537\) −46.3575 −2.00047
\(538\) 19.8337 0.855090
\(539\) −35.1910 −1.51578
\(540\) −1.55393 −0.0668704
\(541\) −2.77574 −0.119339 −0.0596693 0.998218i \(-0.519005\pi\)
−0.0596693 + 0.998218i \(0.519005\pi\)
\(542\) −11.2534 −0.483374
\(543\) 49.2999 2.11566
\(544\) −5.18022 −0.222100
\(545\) 7.83377 0.335562
\(546\) 33.9274 1.45196
\(547\) 38.9675 1.66613 0.833064 0.553176i \(-0.186584\pi\)
0.833064 + 0.553176i \(0.186584\pi\)
\(548\) −11.2959 −0.482537
\(549\) 16.5026 0.704313
\(550\) 1.82595 0.0778588
\(551\) −0.712116 −0.0303371
\(552\) 0.535395 0.0227879
\(553\) −42.3940 −1.80278
\(554\) 13.8413 0.588061
\(555\) −1.78475 −0.0757582
\(556\) −9.18054 −0.389342
\(557\) −5.49865 −0.232985 −0.116493 0.993192i \(-0.537165\pi\)
−0.116493 + 0.993192i \(0.537165\pi\)
\(558\) 13.5012 0.571551
\(559\) −31.4087 −1.32845
\(560\) −5.12569 −0.216600
\(561\) −21.8306 −0.921690
\(562\) 29.1862 1.23115
\(563\) 36.2516 1.52782 0.763912 0.645320i \(-0.223276\pi\)
0.763912 + 0.645320i \(0.223276\pi\)
\(564\) −30.8691 −1.29983
\(565\) 1.88823 0.0794386
\(566\) −5.31391 −0.223360
\(567\) 54.1608 2.27454
\(568\) 7.02748 0.294866
\(569\) 9.19206 0.385351 0.192676 0.981262i \(-0.438283\pi\)
0.192676 + 0.981262i \(0.438283\pi\)
\(570\) 3.97687 0.166573
\(571\) 19.6825 0.823688 0.411844 0.911254i \(-0.364885\pi\)
0.411844 + 0.911254i \(0.364885\pi\)
\(572\) −5.23670 −0.218958
\(573\) −26.1755 −1.09350
\(574\) −43.4430 −1.81328
\(575\) −0.231977 −0.00967410
\(576\) 2.32671 0.0969463
\(577\) −3.53813 −0.147294 −0.0736471 0.997284i \(-0.523464\pi\)
−0.0736471 + 0.997284i \(0.523464\pi\)
\(578\) −9.83464 −0.409067
\(579\) 20.4354 0.849265
\(580\) 0.413275 0.0171603
\(581\) −14.0308 −0.582097
\(582\) 27.0316 1.12050
\(583\) −6.53056 −0.270468
\(584\) 7.84968 0.324822
\(585\) 6.67285 0.275889
\(586\) −24.4177 −1.00869
\(587\) 47.1302 1.94527 0.972636 0.232336i \(-0.0746370\pi\)
0.972636 + 0.232336i \(0.0746370\pi\)
\(588\) 44.4807 1.83435
\(589\) 9.99865 0.411987
\(590\) 8.35966 0.344162
\(591\) 40.6826 1.67346
\(592\) −0.773298 −0.0317823
\(593\) −3.98467 −0.163631 −0.0818154 0.996647i \(-0.526072\pi\)
−0.0818154 + 0.996647i \(0.526072\pi\)
\(594\) −2.83739 −0.116420
\(595\) −26.5522 −1.08853
\(596\) −12.1799 −0.498907
\(597\) −28.1372 −1.15158
\(598\) 0.665294 0.0272059
\(599\) 33.0504 1.35040 0.675201 0.737633i \(-0.264057\pi\)
0.675201 + 0.737633i \(0.264057\pi\)
\(600\) −2.30797 −0.0942224
\(601\) −36.8508 −1.50318 −0.751588 0.659633i \(-0.770712\pi\)
−0.751588 + 0.659633i \(0.770712\pi\)
\(602\) −56.1349 −2.28789
\(603\) 23.6981 0.965063
\(604\) −19.0556 −0.775360
\(605\) −7.66590 −0.311663
\(606\) −15.5065 −0.629908
\(607\) 27.5452 1.11802 0.559012 0.829160i \(-0.311181\pi\)
0.559012 + 0.829160i \(0.311181\pi\)
\(608\) 1.72311 0.0698811
\(609\) −4.88901 −0.198113
\(610\) −7.09267 −0.287174
\(611\) −38.3587 −1.55183
\(612\) 12.0529 0.487208
\(613\) 26.4420 1.06798 0.533992 0.845490i \(-0.320691\pi\)
0.533992 + 0.845490i \(0.320691\pi\)
\(614\) −29.2291 −1.17959
\(615\) −19.5613 −0.788787
\(616\) −9.35925 −0.377095
\(617\) 4.83808 0.194774 0.0973868 0.995247i \(-0.468952\pi\)
0.0973868 + 0.995247i \(0.468952\pi\)
\(618\) 9.76702 0.392887
\(619\) 14.2988 0.574717 0.287358 0.957823i \(-0.407223\pi\)
0.287358 + 0.957823i \(0.407223\pi\)
\(620\) −5.80270 −0.233042
\(621\) 0.360475 0.0144654
\(622\) 8.05463 0.322961
\(623\) −8.16285 −0.327038
\(624\) 6.61910 0.264976
\(625\) 1.00000 0.0400000
\(626\) −15.8471 −0.633376
\(627\) 7.26157 0.289999
\(628\) −11.3912 −0.454559
\(629\) −4.00585 −0.159724
\(630\) 11.9260 0.475143
\(631\) 17.0071 0.677043 0.338522 0.940959i \(-0.390073\pi\)
0.338522 + 0.940959i \(0.390073\pi\)
\(632\) −8.27089 −0.328998
\(633\) −33.0240 −1.31259
\(634\) −2.72043 −0.108042
\(635\) 20.4205 0.810364
\(636\) 8.25451 0.327312
\(637\) 55.2728 2.18999
\(638\) 0.754619 0.0298757
\(639\) −16.3509 −0.646832
\(640\) −1.00000 −0.0395285
\(641\) 5.83510 0.230472 0.115236 0.993338i \(-0.463237\pi\)
0.115236 + 0.993338i \(0.463237\pi\)
\(642\) −3.60364 −0.142224
\(643\) 34.7747 1.37138 0.685690 0.727894i \(-0.259501\pi\)
0.685690 + 0.727894i \(0.259501\pi\)
\(644\) 1.18904 0.0468548
\(645\) −25.2761 −0.995247
\(646\) 8.92606 0.351191
\(647\) 8.47425 0.333157 0.166579 0.986028i \(-0.446728\pi\)
0.166579 + 0.986028i \(0.446728\pi\)
\(648\) 10.5665 0.415093
\(649\) 15.2643 0.599177
\(650\) −2.86793 −0.112490
\(651\) 68.6454 2.69043
\(652\) −19.6319 −0.768845
\(653\) 0.0423644 0.00165785 0.000828923 1.00000i \(-0.499736\pi\)
0.000828923 1.00000i \(0.499736\pi\)
\(654\) −18.0801 −0.706988
\(655\) −9.20972 −0.359854
\(656\) −8.47555 −0.330915
\(657\) −18.2639 −0.712544
\(658\) −68.5563 −2.67260
\(659\) 26.3834 1.02775 0.513876 0.857864i \(-0.328209\pi\)
0.513876 + 0.857864i \(0.328209\pi\)
\(660\) −4.21423 −0.164039
\(661\) −49.0691 −1.90857 −0.954283 0.298906i \(-0.903378\pi\)
−0.954283 + 0.298906i \(0.903378\pi\)
\(662\) −15.5224 −0.603294
\(663\) 34.2883 1.33165
\(664\) −2.73735 −0.106230
\(665\) 8.83210 0.342494
\(666\) 1.79924 0.0697192
\(667\) −0.0958701 −0.00371211
\(668\) 19.5853 0.757778
\(669\) −13.6093 −0.526164
\(670\) −10.1853 −0.393491
\(671\) −12.9509 −0.499962
\(672\) 11.8299 0.456349
\(673\) 48.2721 1.86075 0.930377 0.366605i \(-0.119480\pi\)
0.930377 + 0.366605i \(0.119480\pi\)
\(674\) 34.2266 1.31836
\(675\) −1.55393 −0.0598107
\(676\) −4.77496 −0.183652
\(677\) 26.8038 1.03016 0.515078 0.857143i \(-0.327763\pi\)
0.515078 + 0.857143i \(0.327763\pi\)
\(678\) −4.35798 −0.167367
\(679\) 60.0336 2.30388
\(680\) −5.18022 −0.198652
\(681\) −2.37778 −0.0911168
\(682\) −10.5954 −0.405720
\(683\) −2.71524 −0.103896 −0.0519478 0.998650i \(-0.516543\pi\)
−0.0519478 + 0.998650i \(0.516543\pi\)
\(684\) −4.00917 −0.153294
\(685\) −11.2959 −0.431594
\(686\) 62.9059 2.40176
\(687\) −56.5402 −2.15714
\(688\) −10.9517 −0.417529
\(689\) 10.2572 0.390770
\(690\) 0.535395 0.0203821
\(691\) −20.7474 −0.789268 −0.394634 0.918838i \(-0.629129\pi\)
−0.394634 + 0.918838i \(0.629129\pi\)
\(692\) −2.69712 −0.102529
\(693\) 21.7763 0.827213
\(694\) 3.94198 0.149635
\(695\) −9.18054 −0.348238
\(696\) −0.953824 −0.0361546
\(697\) −43.9052 −1.66303
\(698\) 24.9824 0.945599
\(699\) −0.0601408 −0.00227474
\(700\) −5.12569 −0.193733
\(701\) 0.0465657 0.00175876 0.000879382 1.00000i \(-0.499720\pi\)
0.000879382 1.00000i \(0.499720\pi\)
\(702\) 4.45656 0.168202
\(703\) 1.33247 0.0502552
\(704\) −1.82595 −0.0688181
\(705\) −30.8691 −1.16260
\(706\) 21.7570 0.818834
\(707\) −34.4379 −1.29517
\(708\) −19.2938 −0.725106
\(709\) −12.0686 −0.453248 −0.226624 0.973982i \(-0.572769\pi\)
−0.226624 + 0.973982i \(0.572769\pi\)
\(710\) 7.02748 0.263737
\(711\) 19.2440 0.721706
\(712\) −1.59254 −0.0596829
\(713\) 1.34609 0.0504115
\(714\) 61.2815 2.29340
\(715\) −5.23670 −0.195842
\(716\) −20.0859 −0.750644
\(717\) 53.5523 1.99995
\(718\) −25.8043 −0.963007
\(719\) −24.4646 −0.912377 −0.456188 0.889883i \(-0.650786\pi\)
−0.456188 + 0.889883i \(0.650786\pi\)
\(720\) 2.32671 0.0867114
\(721\) 21.6912 0.807824
\(722\) 16.0309 0.596609
\(723\) 24.2373 0.901393
\(724\) 21.3607 0.793866
\(725\) 0.413275 0.0153486
\(726\) 17.6927 0.656636
\(727\) −32.2257 −1.19519 −0.597593 0.801799i \(-0.703876\pi\)
−0.597593 + 0.801799i \(0.703876\pi\)
\(728\) 14.7001 0.544823
\(729\) −13.8261 −0.512077
\(730\) 7.84968 0.290530
\(731\) −56.7321 −2.09831
\(732\) 16.3696 0.605039
\(733\) 35.2482 1.30192 0.650960 0.759112i \(-0.274366\pi\)
0.650960 + 0.759112i \(0.274366\pi\)
\(734\) −8.98516 −0.331648
\(735\) 44.4807 1.64070
\(736\) 0.231977 0.00855078
\(737\) −18.5978 −0.685057
\(738\) 19.7202 0.725909
\(739\) 41.8010 1.53768 0.768838 0.639444i \(-0.220835\pi\)
0.768838 + 0.639444i \(0.220835\pi\)
\(740\) −0.773298 −0.0284270
\(741\) −11.4054 −0.418988
\(742\) 18.3322 0.672995
\(743\) 1.82320 0.0668865 0.0334433 0.999441i \(-0.489353\pi\)
0.0334433 + 0.999441i \(0.489353\pi\)
\(744\) 13.3924 0.490990
\(745\) −12.1799 −0.446236
\(746\) 18.0327 0.660226
\(747\) 6.36903 0.233031
\(748\) −9.45882 −0.345849
\(749\) −8.00321 −0.292431
\(750\) −2.30797 −0.0842750
\(751\) 18.9084 0.689977 0.344989 0.938607i \(-0.387883\pi\)
0.344989 + 0.938607i \(0.387883\pi\)
\(752\) −13.3750 −0.487737
\(753\) −33.1307 −1.20735
\(754\) −1.18524 −0.0431640
\(755\) −19.0556 −0.693503
\(756\) 7.96495 0.289682
\(757\) −25.6931 −0.933830 −0.466915 0.884302i \(-0.654635\pi\)
−0.466915 + 0.884302i \(0.654635\pi\)
\(758\) 12.1860 0.442617
\(759\) 0.977604 0.0354848
\(760\) 1.72311 0.0625036
\(761\) −12.6870 −0.459905 −0.229952 0.973202i \(-0.573857\pi\)
−0.229952 + 0.973202i \(0.573857\pi\)
\(762\) −47.1299 −1.70734
\(763\) −40.1535 −1.45365
\(764\) −11.3414 −0.410316
\(765\) 12.0529 0.435772
\(766\) −28.3229 −1.02335
\(767\) −23.9749 −0.865685
\(768\) 2.30797 0.0832816
\(769\) −29.7039 −1.07115 −0.535575 0.844488i \(-0.679905\pi\)
−0.535575 + 0.844488i \(0.679905\pi\)
\(770\) −9.35925 −0.337284
\(771\) 55.7868 2.00911
\(772\) 8.85428 0.318672
\(773\) −18.8053 −0.676380 −0.338190 0.941078i \(-0.609815\pi\)
−0.338190 + 0.941078i \(0.609815\pi\)
\(774\) 25.4814 0.915911
\(775\) −5.80270 −0.208439
\(776\) 11.7123 0.420447
\(777\) 9.14805 0.328184
\(778\) −14.5586 −0.521952
\(779\) 14.6043 0.523252
\(780\) 6.61910 0.237002
\(781\) 12.8318 0.459159
\(782\) 1.20169 0.0429723
\(783\) −0.642199 −0.0229503
\(784\) 19.2727 0.688310
\(785\) −11.3912 −0.406570
\(786\) 21.2557 0.758167
\(787\) 1.57307 0.0560741 0.0280370 0.999607i \(-0.491074\pi\)
0.0280370 + 0.999607i \(0.491074\pi\)
\(788\) 17.6270 0.627937
\(789\) −2.91646 −0.103829
\(790\) −8.27089 −0.294265
\(791\) −9.67849 −0.344128
\(792\) 4.24846 0.150962
\(793\) 20.3413 0.722341
\(794\) −33.7418 −1.19745
\(795\) 8.25451 0.292757
\(796\) −12.1913 −0.432110
\(797\) 8.26168 0.292644 0.146322 0.989237i \(-0.453256\pi\)
0.146322 + 0.989237i \(0.453256\pi\)
\(798\) −20.3842 −0.721593
\(799\) −69.2856 −2.45115
\(800\) −1.00000 −0.0353553
\(801\) 3.70537 0.130923
\(802\) −1.00000 −0.0353112
\(803\) 14.3331 0.505805
\(804\) 23.5072 0.829036
\(805\) 1.18904 0.0419082
\(806\) 16.6417 0.586180
\(807\) −45.7754 −1.61137
\(808\) −6.71868 −0.236362
\(809\) −10.7860 −0.379217 −0.189609 0.981860i \(-0.560722\pi\)
−0.189609 + 0.981860i \(0.560722\pi\)
\(810\) 10.5665 0.371271
\(811\) −14.1210 −0.495854 −0.247927 0.968779i \(-0.579749\pi\)
−0.247927 + 0.968779i \(0.579749\pi\)
\(812\) −2.11832 −0.0743384
\(813\) 25.9724 0.910892
\(814\) −1.41200 −0.0494907
\(815\) −19.6319 −0.687676
\(816\) 11.9558 0.418536
\(817\) 18.8709 0.660210
\(818\) −8.73493 −0.305410
\(819\) −34.2030 −1.19515
\(820\) −8.47555 −0.295979
\(821\) −34.9677 −1.22038 −0.610190 0.792255i \(-0.708907\pi\)
−0.610190 + 0.792255i \(0.708907\pi\)
\(822\) 26.0705 0.909315
\(823\) −28.7138 −1.00090 −0.500451 0.865765i \(-0.666832\pi\)
−0.500451 + 0.865765i \(0.666832\pi\)
\(824\) 4.23187 0.147424
\(825\) −4.21423 −0.146721
\(826\) −42.8490 −1.49091
\(827\) 15.4099 0.535855 0.267928 0.963439i \(-0.413661\pi\)
0.267928 + 0.963439i \(0.413661\pi\)
\(828\) −0.539743 −0.0187574
\(829\) −43.5715 −1.51330 −0.756651 0.653819i \(-0.773166\pi\)
−0.756651 + 0.653819i \(0.773166\pi\)
\(830\) −2.73735 −0.0950150
\(831\) −31.9453 −1.10817
\(832\) 2.86793 0.0994277
\(833\) 99.8367 3.45913
\(834\) 21.1884 0.733694
\(835\) 19.5853 0.677777
\(836\) 3.14630 0.108817
\(837\) 9.01697 0.311672
\(838\) 4.49937 0.155428
\(839\) −40.4824 −1.39761 −0.698803 0.715314i \(-0.746284\pi\)
−0.698803 + 0.715314i \(0.746284\pi\)
\(840\) 11.8299 0.408171
\(841\) −28.8292 −0.994110
\(842\) 12.0532 0.415382
\(843\) −67.3609 −2.32003
\(844\) −14.3087 −0.492526
\(845\) −4.77496 −0.164264
\(846\) 31.1199 1.06992
\(847\) 39.2930 1.35012
\(848\) 3.57653 0.122818
\(849\) 12.2643 0.420910
\(850\) −5.18022 −0.177680
\(851\) 0.179387 0.00614931
\(852\) −16.2192 −0.555660
\(853\) 54.6849 1.87237 0.936187 0.351501i \(-0.114329\pi\)
0.936187 + 0.351501i \(0.114329\pi\)
\(854\) 36.3548 1.24404
\(855\) −4.00917 −0.137111
\(856\) −1.56139 −0.0533673
\(857\) −7.45735 −0.254738 −0.127369 0.991855i \(-0.540653\pi\)
−0.127369 + 0.991855i \(0.540653\pi\)
\(858\) 12.0861 0.412614
\(859\) −27.1284 −0.925610 −0.462805 0.886460i \(-0.653157\pi\)
−0.462805 + 0.886460i \(0.653157\pi\)
\(860\) −10.9517 −0.373449
\(861\) 100.265 3.41702
\(862\) −16.8432 −0.573682
\(863\) 38.9673 1.32646 0.663232 0.748414i \(-0.269184\pi\)
0.663232 + 0.748414i \(0.269184\pi\)
\(864\) 1.55393 0.0528657
\(865\) −2.69712 −0.0917048
\(866\) −7.54922 −0.256533
\(867\) 22.6980 0.770865
\(868\) 29.7428 1.00954
\(869\) −15.1022 −0.512308
\(870\) −0.953824 −0.0323377
\(871\) 29.2106 0.989764
\(872\) −7.83377 −0.265285
\(873\) −27.2511 −0.922311
\(874\) −0.399720 −0.0135207
\(875\) −5.12569 −0.173280
\(876\) −18.1168 −0.612110
\(877\) 43.9381 1.48368 0.741842 0.670574i \(-0.233952\pi\)
0.741842 + 0.670574i \(0.233952\pi\)
\(878\) −23.5893 −0.796100
\(879\) 56.3552 1.90081
\(880\) −1.82595 −0.0615528
\(881\) −2.74025 −0.0923215 −0.0461608 0.998934i \(-0.514699\pi\)
−0.0461608 + 0.998934i \(0.514699\pi\)
\(882\) −44.8420 −1.50991
\(883\) 18.4545 0.621045 0.310523 0.950566i \(-0.399496\pi\)
0.310523 + 0.950566i \(0.399496\pi\)
\(884\) 14.8565 0.499679
\(885\) −19.2938 −0.648554
\(886\) −6.87149 −0.230852
\(887\) 4.12679 0.138564 0.0692820 0.997597i \(-0.477929\pi\)
0.0692820 + 0.997597i \(0.477929\pi\)
\(888\) 1.78475 0.0598921
\(889\) −104.669 −3.51049
\(890\) −1.59254 −0.0533820
\(891\) 19.2940 0.646373
\(892\) −5.89664 −0.197434
\(893\) 23.0466 0.771225
\(894\) 28.1107 0.940163
\(895\) −20.0859 −0.671396
\(896\) 5.12569 0.171237
\(897\) −1.53548 −0.0512681
\(898\) −7.37577 −0.246133
\(899\) −2.39811 −0.0799813
\(900\) 2.32671 0.0775571
\(901\) 18.5272 0.617230
\(902\) −15.4759 −0.515292
\(903\) 129.558 4.31141
\(904\) −1.88823 −0.0628017
\(905\) 21.3607 0.710055
\(906\) 43.9796 1.46112
\(907\) −1.81472 −0.0602568 −0.0301284 0.999546i \(-0.509592\pi\)
−0.0301284 + 0.999546i \(0.509592\pi\)
\(908\) −1.03025 −0.0341900
\(909\) 15.6324 0.518495
\(910\) 14.7001 0.487305
\(911\) 47.8218 1.58441 0.792204 0.610256i \(-0.208934\pi\)
0.792204 + 0.610256i \(0.208934\pi\)
\(912\) −3.97687 −0.131687
\(913\) −4.99827 −0.165419
\(914\) 37.2443 1.23193
\(915\) 16.3696 0.541164
\(916\) −24.4978 −0.809431
\(917\) 47.2062 1.55889
\(918\) 8.04968 0.265679
\(919\) −10.0624 −0.331928 −0.165964 0.986132i \(-0.553074\pi\)
−0.165964 + 0.986132i \(0.553074\pi\)
\(920\) 0.231977 0.00764805
\(921\) 67.4598 2.22288
\(922\) 17.2287 0.567397
\(923\) −20.1543 −0.663388
\(924\) 21.6008 0.710616
\(925\) −0.773298 −0.0254259
\(926\) 9.75535 0.320581
\(927\) −9.84634 −0.323396
\(928\) −0.413275 −0.0135664
\(929\) 38.7262 1.27056 0.635282 0.772280i \(-0.280884\pi\)
0.635282 + 0.772280i \(0.280884\pi\)
\(930\) 13.3924 0.439155
\(931\) −33.2089 −1.08838
\(932\) −0.0260579 −0.000853556 0
\(933\) −18.5898 −0.608603
\(934\) 2.98148 0.0975568
\(935\) −9.45882 −0.309336
\(936\) −6.67285 −0.218109
\(937\) −28.7252 −0.938410 −0.469205 0.883089i \(-0.655459\pi\)
−0.469205 + 0.883089i \(0.655459\pi\)
\(938\) 52.2064 1.70460
\(939\) 36.5745 1.19356
\(940\) −13.3750 −0.436246
\(941\) 3.52295 0.114845 0.0574225 0.998350i \(-0.481712\pi\)
0.0574225 + 0.998350i \(0.481712\pi\)
\(942\) 26.2906 0.856593
\(943\) 1.96613 0.0640260
\(944\) −8.35966 −0.272084
\(945\) 7.96495 0.259100
\(946\) −19.9972 −0.650166
\(947\) 52.5309 1.70702 0.853512 0.521073i \(-0.174468\pi\)
0.853512 + 0.521073i \(0.174468\pi\)
\(948\) 19.0889 0.619980
\(949\) −22.5123 −0.730782
\(950\) 1.72311 0.0559049
\(951\) 6.27867 0.203600
\(952\) 26.5522 0.860561
\(953\) 21.0748 0.682680 0.341340 0.939940i \(-0.389119\pi\)
0.341340 + 0.939940i \(0.389119\pi\)
\(954\) −8.32155 −0.269420
\(955\) −11.3414 −0.366998
\(956\) 23.2032 0.750446
\(957\) −1.74164 −0.0562991
\(958\) −0.647726 −0.0209271
\(959\) 57.8992 1.86966
\(960\) 2.30797 0.0744893
\(961\) 2.67127 0.0861700
\(962\) 2.21777 0.0715037
\(963\) 3.63291 0.117069
\(964\) 10.5016 0.338232
\(965\) 8.85428 0.285029
\(966\) −2.74427 −0.0882953
\(967\) 16.9212 0.544150 0.272075 0.962276i \(-0.412290\pi\)
0.272075 + 0.962276i \(0.412290\pi\)
\(968\) 7.66590 0.246392
\(969\) −20.6010 −0.661801
\(970\) 11.7123 0.376059
\(971\) 8.87437 0.284792 0.142396 0.989810i \(-0.454519\pi\)
0.142396 + 0.989810i \(0.454519\pi\)
\(972\) −19.7255 −0.632694
\(973\) 47.0566 1.50857
\(974\) 5.61871 0.180035
\(975\) 6.61910 0.211981
\(976\) 7.09267 0.227031
\(977\) −26.8400 −0.858689 −0.429345 0.903141i \(-0.641255\pi\)
−0.429345 + 0.903141i \(0.641255\pi\)
\(978\) 45.3098 1.44885
\(979\) −2.90789 −0.0929367
\(980\) 19.2727 0.615643
\(981\) 18.2269 0.581941
\(982\) −31.2742 −0.997999
\(983\) 17.7900 0.567412 0.283706 0.958911i \(-0.408436\pi\)
0.283706 + 0.958911i \(0.408436\pi\)
\(984\) 19.5613 0.623591
\(985\) 17.6270 0.561644
\(986\) −2.14085 −0.0681786
\(987\) 158.226 5.03638
\(988\) −4.94175 −0.157218
\(989\) 2.54054 0.0807844
\(990\) 4.24846 0.135025
\(991\) 13.5584 0.430698 0.215349 0.976537i \(-0.430911\pi\)
0.215349 + 0.976537i \(0.430911\pi\)
\(992\) 5.80270 0.184236
\(993\) 35.8251 1.13688
\(994\) −36.0207 −1.14251
\(995\) −12.1913 −0.386491
\(996\) 6.31772 0.200185
\(997\) −7.95242 −0.251856 −0.125928 0.992039i \(-0.540191\pi\)
−0.125928 + 0.992039i \(0.540191\pi\)
\(998\) −12.9780 −0.410812
\(999\) 1.20165 0.0380185
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.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.9 10 1.1 even 1 trivial