Properties

Label 4730.2.a.w.1.7
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 1
Dimension 8
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
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 1.7
Root \(2.57663\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.57663 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.57663 q^{6} +0.800428 q^{7} -1.00000 q^{8} -0.514223 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.57663 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.57663 q^{6} +0.800428 q^{7} -1.00000 q^{8} -0.514223 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.57663 q^{12} -1.02499 q^{13} -0.800428 q^{14} +1.57663 q^{15} +1.00000 q^{16} -5.32510 q^{17} +0.514223 q^{18} -2.64922 q^{19} +1.00000 q^{20} +1.26198 q^{21} -1.00000 q^{22} -3.02499 q^{23} -1.57663 q^{24} +1.00000 q^{25} +1.02499 q^{26} -5.54065 q^{27} +0.800428 q^{28} -0.208061 q^{29} -1.57663 q^{30} +1.97566 q^{31} -1.00000 q^{32} +1.57663 q^{33} +5.32510 q^{34} +0.800428 q^{35} -0.514223 q^{36} -6.73970 q^{37} +2.64922 q^{38} -1.61604 q^{39} -1.00000 q^{40} +10.4726 q^{41} -1.26198 q^{42} -1.00000 q^{43} +1.00000 q^{44} -0.514223 q^{45} +3.02499 q^{46} +3.55198 q^{47} +1.57663 q^{48} -6.35931 q^{49} -1.00000 q^{50} -8.39573 q^{51} -1.02499 q^{52} -9.61400 q^{53} +5.54065 q^{54} +1.00000 q^{55} -0.800428 q^{56} -4.17685 q^{57} +0.208061 q^{58} -11.8754 q^{59} +1.57663 q^{60} -2.97971 q^{61} -1.97566 q^{62} -0.411599 q^{63} +1.00000 q^{64} -1.02499 q^{65} -1.57663 q^{66} -10.5520 q^{67} -5.32510 q^{68} -4.76931 q^{69} -0.800428 q^{70} -6.73861 q^{71} +0.514223 q^{72} +1.32907 q^{73} +6.73970 q^{74} +1.57663 q^{75} -2.64922 q^{76} +0.800428 q^{77} +1.61604 q^{78} +8.33391 q^{79} +1.00000 q^{80} -7.19290 q^{81} -10.4726 q^{82} +10.2036 q^{83} +1.26198 q^{84} -5.32510 q^{85} +1.00000 q^{86} -0.328036 q^{87} -1.00000 q^{88} +9.34345 q^{89} +0.514223 q^{90} -0.820432 q^{91} -3.02499 q^{92} +3.11489 q^{93} -3.55198 q^{94} -2.64922 q^{95} -1.57663 q^{96} +0.294217 q^{97} +6.35931 q^{98} -0.514223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} + O(q^{10}) \) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} - 8q^{10} + 8q^{11} - 7q^{12} - 2q^{13} + 6q^{14} - 7q^{15} + 8q^{16} - 8q^{17} - 7q^{18} + 8q^{20} + 14q^{21} - 8q^{22} - 18q^{23} + 7q^{24} + 8q^{25} + 2q^{26} - 22q^{27} - 6q^{28} + 8q^{29} + 7q^{30} - 11q^{31} - 8q^{32} - 7q^{33} + 8q^{34} - 6q^{35} + 7q^{36} - 17q^{37} - 6q^{39} - 8q^{40} + 12q^{41} - 14q^{42} - 8q^{43} + 8q^{44} + 7q^{45} + 18q^{46} - 19q^{47} - 7q^{48} - 2q^{49} - 8q^{50} - q^{51} - 2q^{52} - 7q^{53} + 22q^{54} + 8q^{55} + 6q^{56} - 3q^{57} - 8q^{58} + q^{59} - 7q^{60} + 6q^{61} + 11q^{62} - 15q^{63} + 8q^{64} - 2q^{65} + 7q^{66} - 22q^{67} - 8q^{68} + 8q^{69} + 6q^{70} - 14q^{71} - 7q^{72} - 13q^{73} + 17q^{74} - 7q^{75} - 6q^{77} + 6q^{78} - 8q^{79} + 8q^{80} + 28q^{81} - 12q^{82} - 4q^{83} + 14q^{84} - 8q^{85} + 8q^{86} - 30q^{87} - 8q^{88} + 5q^{89} - 7q^{90} - 8q^{91} - 18q^{92} + q^{93} + 19q^{94} + 7q^{96} - 23q^{97} + 2q^{98} + 7q^{99} + O(q^{100}) \)

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
\(3\) 1.57663 0.910270 0.455135 0.890422i \(-0.349591\pi\)
0.455135 + 0.890422i \(0.349591\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.57663 −0.643658
\(7\) 0.800428 0.302533 0.151267 0.988493i \(-0.451665\pi\)
0.151267 + 0.988493i \(0.451665\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.514223 −0.171408
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 1.57663 0.455135
\(13\) −1.02499 −0.284281 −0.142141 0.989846i \(-0.545399\pi\)
−0.142141 + 0.989846i \(0.545399\pi\)
\(14\) −0.800428 −0.213923
\(15\) 1.57663 0.407085
\(16\) 1.00000 0.250000
\(17\) −5.32510 −1.29153 −0.645763 0.763538i \(-0.723461\pi\)
−0.645763 + 0.763538i \(0.723461\pi\)
\(18\) 0.514223 0.121204
\(19\) −2.64922 −0.607773 −0.303886 0.952708i \(-0.598284\pi\)
−0.303886 + 0.952708i \(0.598284\pi\)
\(20\) 1.00000 0.223607
\(21\) 1.26198 0.275387
\(22\) −1.00000 −0.213201
\(23\) −3.02499 −0.630754 −0.315377 0.948966i \(-0.602131\pi\)
−0.315377 + 0.948966i \(0.602131\pi\)
\(24\) −1.57663 −0.321829
\(25\) 1.00000 0.200000
\(26\) 1.02499 0.201017
\(27\) −5.54065 −1.06630
\(28\) 0.800428 0.151267
\(29\) −0.208061 −0.0386359 −0.0193180 0.999813i \(-0.506149\pi\)
−0.0193180 + 0.999813i \(0.506149\pi\)
\(30\) −1.57663 −0.287853
\(31\) 1.97566 0.354839 0.177419 0.984135i \(-0.443225\pi\)
0.177419 + 0.984135i \(0.443225\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.57663 0.274457
\(34\) 5.32510 0.913247
\(35\) 0.800428 0.135297
\(36\) −0.514223 −0.0857039
\(37\) −6.73970 −1.10800 −0.554000 0.832517i \(-0.686899\pi\)
−0.554000 + 0.832517i \(0.686899\pi\)
\(38\) 2.64922 0.429760
\(39\) −1.61604 −0.258773
\(40\) −1.00000 −0.158114
\(41\) 10.4726 1.63555 0.817774 0.575539i \(-0.195208\pi\)
0.817774 + 0.575539i \(0.195208\pi\)
\(42\) −1.26198 −0.194728
\(43\) −1.00000 −0.152499
\(44\) 1.00000 0.150756
\(45\) −0.514223 −0.0766559
\(46\) 3.02499 0.446011
\(47\) 3.55198 0.518110 0.259055 0.965863i \(-0.416589\pi\)
0.259055 + 0.965863i \(0.416589\pi\)
\(48\) 1.57663 0.227568
\(49\) −6.35931 −0.908474
\(50\) −1.00000 −0.141421
\(51\) −8.39573 −1.17564
\(52\) −1.02499 −0.142141
\(53\) −9.61400 −1.32058 −0.660292 0.751009i \(-0.729568\pi\)
−0.660292 + 0.751009i \(0.729568\pi\)
\(54\) 5.54065 0.753986
\(55\) 1.00000 0.134840
\(56\) −0.800428 −0.106962
\(57\) −4.17685 −0.553237
\(58\) 0.208061 0.0273197
\(59\) −11.8754 −1.54605 −0.773023 0.634378i \(-0.781256\pi\)
−0.773023 + 0.634378i \(0.781256\pi\)
\(60\) 1.57663 0.203543
\(61\) −2.97971 −0.381513 −0.190757 0.981637i \(-0.561094\pi\)
−0.190757 + 0.981637i \(0.561094\pi\)
\(62\) −1.97566 −0.250909
\(63\) −0.411599 −0.0518566
\(64\) 1.00000 0.125000
\(65\) −1.02499 −0.127135
\(66\) −1.57663 −0.194070
\(67\) −10.5520 −1.28913 −0.644567 0.764548i \(-0.722962\pi\)
−0.644567 + 0.764548i \(0.722962\pi\)
\(68\) −5.32510 −0.645763
\(69\) −4.76931 −0.574157
\(70\) −0.800428 −0.0956695
\(71\) −6.73861 −0.799726 −0.399863 0.916575i \(-0.630942\pi\)
−0.399863 + 0.916575i \(0.630942\pi\)
\(72\) 0.514223 0.0606018
\(73\) 1.32907 0.155556 0.0777780 0.996971i \(-0.475217\pi\)
0.0777780 + 0.996971i \(0.475217\pi\)
\(74\) 6.73970 0.783474
\(75\) 1.57663 0.182054
\(76\) −2.64922 −0.303886
\(77\) 0.800428 0.0912173
\(78\) 1.61604 0.182980
\(79\) 8.33391 0.937638 0.468819 0.883294i \(-0.344680\pi\)
0.468819 + 0.883294i \(0.344680\pi\)
\(80\) 1.00000 0.111803
\(81\) −7.19290 −0.799212
\(82\) −10.4726 −1.15651
\(83\) 10.2036 1.11999 0.559994 0.828496i \(-0.310803\pi\)
0.559994 + 0.828496i \(0.310803\pi\)
\(84\) 1.26198 0.137694
\(85\) −5.32510 −0.577588
\(86\) 1.00000 0.107833
\(87\) −0.328036 −0.0351691
\(88\) −1.00000 −0.106600
\(89\) 9.34345 0.990404 0.495202 0.868778i \(-0.335094\pi\)
0.495202 + 0.868778i \(0.335094\pi\)
\(90\) 0.514223 0.0542039
\(91\) −0.820432 −0.0860046
\(92\) −3.02499 −0.315377
\(93\) 3.11489 0.322999
\(94\) −3.55198 −0.366359
\(95\) −2.64922 −0.271804
\(96\) −1.57663 −0.160915
\(97\) 0.294217 0.0298732 0.0149366 0.999888i \(-0.495245\pi\)
0.0149366 + 0.999888i \(0.495245\pi\)
\(98\) 6.35931 0.642388
\(99\) −0.514223 −0.0516814
\(100\) 1.00000 0.100000
\(101\) 1.14270 0.113702 0.0568512 0.998383i \(-0.481894\pi\)
0.0568512 + 0.998383i \(0.481894\pi\)
\(102\) 8.39573 0.831302
\(103\) −9.50752 −0.936804 −0.468402 0.883516i \(-0.655170\pi\)
−0.468402 + 0.883516i \(0.655170\pi\)
\(104\) 1.02499 0.100509
\(105\) 1.26198 0.123157
\(106\) 9.61400 0.933794
\(107\) 4.79302 0.463359 0.231679 0.972792i \(-0.425578\pi\)
0.231679 + 0.972792i \(0.425578\pi\)
\(108\) −5.54065 −0.533149
\(109\) −17.2100 −1.64842 −0.824209 0.566286i \(-0.808380\pi\)
−0.824209 + 0.566286i \(0.808380\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −10.6260 −1.00858
\(112\) 0.800428 0.0756334
\(113\) −12.6986 −1.19458 −0.597292 0.802024i \(-0.703756\pi\)
−0.597292 + 0.802024i \(0.703756\pi\)
\(114\) 4.17685 0.391198
\(115\) −3.02499 −0.282082
\(116\) −0.208061 −0.0193180
\(117\) 0.527074 0.0487281
\(118\) 11.8754 1.09322
\(119\) −4.26236 −0.390730
\(120\) −1.57663 −0.143926
\(121\) 1.00000 0.0909091
\(122\) 2.97971 0.269771
\(123\) 16.5115 1.48879
\(124\) 1.97566 0.177419
\(125\) 1.00000 0.0894427
\(126\) 0.411599 0.0366682
\(127\) 19.3137 1.71381 0.856907 0.515471i \(-0.172383\pi\)
0.856907 + 0.515471i \(0.172383\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.57663 −0.138815
\(130\) 1.02499 0.0898977
\(131\) −2.23687 −0.195436 −0.0977180 0.995214i \(-0.531154\pi\)
−0.0977180 + 0.995214i \(0.531154\pi\)
\(132\) 1.57663 0.137228
\(133\) −2.12051 −0.183872
\(134\) 10.5520 0.911555
\(135\) −5.54065 −0.476863
\(136\) 5.32510 0.456623
\(137\) 15.3916 1.31499 0.657496 0.753458i \(-0.271616\pi\)
0.657496 + 0.753458i \(0.271616\pi\)
\(138\) 4.76931 0.405990
\(139\) −16.6321 −1.41072 −0.705358 0.708851i \(-0.749214\pi\)
−0.705358 + 0.708851i \(0.749214\pi\)
\(140\) 0.800428 0.0676485
\(141\) 5.60018 0.471620
\(142\) 6.73861 0.565492
\(143\) −1.02499 −0.0857141
\(144\) −0.514223 −0.0428520
\(145\) −0.208061 −0.0172785
\(146\) −1.32907 −0.109995
\(147\) −10.0263 −0.826957
\(148\) −6.73970 −0.554000
\(149\) −13.1363 −1.07617 −0.538083 0.842892i \(-0.680851\pi\)
−0.538083 + 0.842892i \(0.680851\pi\)
\(150\) −1.57663 −0.128732
\(151\) 5.38185 0.437969 0.218984 0.975728i \(-0.429726\pi\)
0.218984 + 0.975728i \(0.429726\pi\)
\(152\) 2.64922 0.214880
\(153\) 2.73829 0.221378
\(154\) −0.800428 −0.0645003
\(155\) 1.97566 0.158689
\(156\) −1.61604 −0.129386
\(157\) −15.7870 −1.25994 −0.629969 0.776620i \(-0.716932\pi\)
−0.629969 + 0.776620i \(0.716932\pi\)
\(158\) −8.33391 −0.663010
\(159\) −15.1578 −1.20209
\(160\) −1.00000 −0.0790569
\(161\) −2.42129 −0.190824
\(162\) 7.19290 0.565128
\(163\) −17.6800 −1.38481 −0.692403 0.721511i \(-0.743448\pi\)
−0.692403 + 0.721511i \(0.743448\pi\)
\(164\) 10.4726 0.817774
\(165\) 1.57663 0.122741
\(166\) −10.2036 −0.791952
\(167\) 4.11462 0.318399 0.159199 0.987246i \(-0.449109\pi\)
0.159199 + 0.987246i \(0.449109\pi\)
\(168\) −1.26198 −0.0973641
\(169\) −11.9494 −0.919184
\(170\) 5.32510 0.408416
\(171\) 1.36229 0.104177
\(172\) −1.00000 −0.0762493
\(173\) −17.3731 −1.32085 −0.660426 0.750891i \(-0.729624\pi\)
−0.660426 + 0.750891i \(0.729624\pi\)
\(174\) 0.328036 0.0248683
\(175\) 0.800428 0.0605067
\(176\) 1.00000 0.0753778
\(177\) −18.7232 −1.40732
\(178\) −9.34345 −0.700321
\(179\) 3.11052 0.232491 0.116246 0.993220i \(-0.462914\pi\)
0.116246 + 0.993220i \(0.462914\pi\)
\(180\) −0.514223 −0.0383280
\(181\) 19.5553 1.45353 0.726766 0.686885i \(-0.241023\pi\)
0.726766 + 0.686885i \(0.241023\pi\)
\(182\) 0.820432 0.0608145
\(183\) −4.69792 −0.347280
\(184\) 3.02499 0.223005
\(185\) −6.73970 −0.495513
\(186\) −3.11489 −0.228395
\(187\) −5.32510 −0.389410
\(188\) 3.55198 0.259055
\(189\) −4.43489 −0.322591
\(190\) 2.64922 0.192195
\(191\) 11.5515 0.835840 0.417920 0.908484i \(-0.362759\pi\)
0.417920 + 0.908484i \(0.362759\pi\)
\(192\) 1.57663 0.113784
\(193\) 15.7250 1.13191 0.565955 0.824436i \(-0.308508\pi\)
0.565955 + 0.824436i \(0.308508\pi\)
\(194\) −0.294217 −0.0211235
\(195\) −1.61604 −0.115727
\(196\) −6.35931 −0.454237
\(197\) −12.6214 −0.899236 −0.449618 0.893221i \(-0.648440\pi\)
−0.449618 + 0.893221i \(0.648440\pi\)
\(198\) 0.514223 0.0365443
\(199\) 8.27011 0.586253 0.293126 0.956074i \(-0.405304\pi\)
0.293126 + 0.956074i \(0.405304\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −16.6367 −1.17346
\(202\) −1.14270 −0.0803998
\(203\) −0.166538 −0.0116887
\(204\) −8.39573 −0.587819
\(205\) 10.4726 0.731440
\(206\) 9.50752 0.662420
\(207\) 1.55552 0.108116
\(208\) −1.02499 −0.0710703
\(209\) −2.64922 −0.183250
\(210\) −1.26198 −0.0870851
\(211\) −4.00515 −0.275726 −0.137863 0.990451i \(-0.544023\pi\)
−0.137863 + 0.990451i \(0.544023\pi\)
\(212\) −9.61400 −0.660292
\(213\) −10.6243 −0.727967
\(214\) −4.79302 −0.327644
\(215\) −1.00000 −0.0681994
\(216\) 5.54065 0.376993
\(217\) 1.58137 0.107351
\(218\) 17.2100 1.16561
\(219\) 2.09546 0.141598
\(220\) 1.00000 0.0674200
\(221\) 5.45818 0.367157
\(222\) 10.6260 0.713173
\(223\) −9.48329 −0.635048 −0.317524 0.948250i \(-0.602851\pi\)
−0.317524 + 0.948250i \(0.602851\pi\)
\(224\) −0.800428 −0.0534809
\(225\) −0.514223 −0.0342816
\(226\) 12.6986 0.844698
\(227\) 12.2245 0.811372 0.405686 0.914013i \(-0.367033\pi\)
0.405686 + 0.914013i \(0.367033\pi\)
\(228\) −4.17685 −0.276619
\(229\) 16.0960 1.06365 0.531826 0.846854i \(-0.321506\pi\)
0.531826 + 0.846854i \(0.321506\pi\)
\(230\) 3.02499 0.199462
\(231\) 1.26198 0.0830324
\(232\) 0.208061 0.0136599
\(233\) 23.9182 1.56693 0.783466 0.621435i \(-0.213450\pi\)
0.783466 + 0.621435i \(0.213450\pi\)
\(234\) −0.527074 −0.0344559
\(235\) 3.55198 0.231706
\(236\) −11.8754 −0.773023
\(237\) 13.1395 0.853504
\(238\) 4.26236 0.276288
\(239\) 20.7070 1.33942 0.669711 0.742622i \(-0.266418\pi\)
0.669711 + 0.742622i \(0.266418\pi\)
\(240\) 1.57663 0.101771
\(241\) −13.8160 −0.889968 −0.444984 0.895539i \(-0.646791\pi\)
−0.444984 + 0.895539i \(0.646791\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 5.28136 0.338799
\(244\) −2.97971 −0.190757
\(245\) −6.35931 −0.406282
\(246\) −16.5115 −1.05273
\(247\) 2.71543 0.172778
\(248\) −1.97566 −0.125454
\(249\) 16.0873 1.01949
\(250\) −1.00000 −0.0632456
\(251\) −5.08380 −0.320887 −0.160443 0.987045i \(-0.551292\pi\)
−0.160443 + 0.987045i \(0.551292\pi\)
\(252\) −0.411599 −0.0259283
\(253\) −3.02499 −0.190180
\(254\) −19.3137 −1.21185
\(255\) −8.39573 −0.525761
\(256\) 1.00000 0.0625000
\(257\) −16.8556 −1.05142 −0.525712 0.850663i \(-0.676201\pi\)
−0.525712 + 0.850663i \(0.676201\pi\)
\(258\) 1.57663 0.0981570
\(259\) −5.39465 −0.335207
\(260\) −1.02499 −0.0635673
\(261\) 0.106990 0.00662250
\(262\) 2.23687 0.138194
\(263\) 11.0417 0.680861 0.340431 0.940270i \(-0.389427\pi\)
0.340431 + 0.940270i \(0.389427\pi\)
\(264\) −1.57663 −0.0970351
\(265\) −9.61400 −0.590583
\(266\) 2.12051 0.130017
\(267\) 14.7312 0.901536
\(268\) −10.5520 −0.644567
\(269\) 5.90487 0.360026 0.180013 0.983664i \(-0.442386\pi\)
0.180013 + 0.983664i \(0.442386\pi\)
\(270\) 5.54065 0.337193
\(271\) −0.109692 −0.00666330 −0.00333165 0.999994i \(-0.501060\pi\)
−0.00333165 + 0.999994i \(0.501060\pi\)
\(272\) −5.32510 −0.322882
\(273\) −1.29352 −0.0782875
\(274\) −15.3916 −0.929840
\(275\) 1.00000 0.0603023
\(276\) −4.76931 −0.287078
\(277\) −10.1828 −0.611825 −0.305913 0.952060i \(-0.598962\pi\)
−0.305913 + 0.952060i \(0.598962\pi\)
\(278\) 16.6321 0.997527
\(279\) −1.01593 −0.0608221
\(280\) −0.800428 −0.0478347
\(281\) 12.0954 0.721549 0.360774 0.932653i \(-0.382512\pi\)
0.360774 + 0.932653i \(0.382512\pi\)
\(282\) −5.60018 −0.333486
\(283\) 3.46228 0.205811 0.102906 0.994691i \(-0.467186\pi\)
0.102906 + 0.994691i \(0.467186\pi\)
\(284\) −6.73861 −0.399863
\(285\) −4.17685 −0.247415
\(286\) 1.02499 0.0606090
\(287\) 8.38258 0.494808
\(288\) 0.514223 0.0303009
\(289\) 11.3567 0.668040
\(290\) 0.208061 0.0122177
\(291\) 0.463873 0.0271927
\(292\) 1.32907 0.0777780
\(293\) −32.8264 −1.91774 −0.958869 0.283848i \(-0.908389\pi\)
−0.958869 + 0.283848i \(0.908389\pi\)
\(294\) 10.0263 0.584747
\(295\) −11.8754 −0.691413
\(296\) 6.73970 0.391737
\(297\) −5.54065 −0.321501
\(298\) 13.1363 0.760964
\(299\) 3.10059 0.179312
\(300\) 1.57663 0.0910270
\(301\) −0.800428 −0.0461359
\(302\) −5.38185 −0.309691
\(303\) 1.80161 0.103500
\(304\) −2.64922 −0.151943
\(305\) −2.97971 −0.170618
\(306\) −2.73829 −0.156538
\(307\) 15.8101 0.902327 0.451164 0.892441i \(-0.351009\pi\)
0.451164 + 0.892441i \(0.351009\pi\)
\(308\) 0.800428 0.0456086
\(309\) −14.9899 −0.852745
\(310\) −1.97566 −0.112210
\(311\) −7.41195 −0.420293 −0.210147 0.977670i \(-0.567394\pi\)
−0.210147 + 0.977670i \(0.567394\pi\)
\(312\) 1.61604 0.0914900
\(313\) 14.8333 0.838426 0.419213 0.907888i \(-0.362306\pi\)
0.419213 + 0.907888i \(0.362306\pi\)
\(314\) 15.7870 0.890911
\(315\) −0.411599 −0.0231910
\(316\) 8.33391 0.468819
\(317\) 18.5511 1.04193 0.520967 0.853577i \(-0.325571\pi\)
0.520967 + 0.853577i \(0.325571\pi\)
\(318\) 15.1578 0.850005
\(319\) −0.208061 −0.0116492
\(320\) 1.00000 0.0559017
\(321\) 7.55684 0.421782
\(322\) 2.42129 0.134933
\(323\) 14.1074 0.784954
\(324\) −7.19290 −0.399606
\(325\) −1.02499 −0.0568563
\(326\) 17.6800 0.979206
\(327\) −27.1338 −1.50051
\(328\) −10.4726 −0.578254
\(329\) 2.84311 0.156745
\(330\) −1.57663 −0.0867909
\(331\) 11.7965 0.648393 0.324196 0.945990i \(-0.394906\pi\)
0.324196 + 0.945990i \(0.394906\pi\)
\(332\) 10.2036 0.559994
\(333\) 3.46571 0.189920
\(334\) −4.11462 −0.225142
\(335\) −10.5520 −0.576518
\(336\) 1.26198 0.0688468
\(337\) 10.8501 0.591043 0.295521 0.955336i \(-0.404507\pi\)
0.295521 + 0.955336i \(0.404507\pi\)
\(338\) 11.9494 0.649961
\(339\) −20.0210 −1.08739
\(340\) −5.32510 −0.288794
\(341\) 1.97566 0.106988
\(342\) −1.36229 −0.0736642
\(343\) −10.6932 −0.577377
\(344\) 1.00000 0.0539164
\(345\) −4.76931 −0.256771
\(346\) 17.3731 0.933984
\(347\) −21.8988 −1.17559 −0.587794 0.809011i \(-0.700003\pi\)
−0.587794 + 0.809011i \(0.700003\pi\)
\(348\) −0.328036 −0.0175846
\(349\) 4.86814 0.260585 0.130293 0.991476i \(-0.458408\pi\)
0.130293 + 0.991476i \(0.458408\pi\)
\(350\) −0.800428 −0.0427847
\(351\) 5.67911 0.303129
\(352\) −1.00000 −0.0533002
\(353\) −3.25663 −0.173333 −0.0866664 0.996237i \(-0.527621\pi\)
−0.0866664 + 0.996237i \(0.527621\pi\)
\(354\) 18.7232 0.995126
\(355\) −6.73861 −0.357648
\(356\) 9.34345 0.495202
\(357\) −6.72018 −0.355670
\(358\) −3.11052 −0.164396
\(359\) 9.66427 0.510061 0.255030 0.966933i \(-0.417915\pi\)
0.255030 + 0.966933i \(0.417915\pi\)
\(360\) 0.514223 0.0271020
\(361\) −11.9816 −0.630613
\(362\) −19.5553 −1.02780
\(363\) 1.57663 0.0827519
\(364\) −0.820432 −0.0430023
\(365\) 1.32907 0.0695668
\(366\) 4.69792 0.245564
\(367\) −27.2816 −1.42409 −0.712043 0.702136i \(-0.752230\pi\)
−0.712043 + 0.702136i \(0.752230\pi\)
\(368\) −3.02499 −0.157689
\(369\) −5.38527 −0.280346
\(370\) 6.73970 0.350380
\(371\) −7.69532 −0.399521
\(372\) 3.11489 0.161500
\(373\) −26.5850 −1.37652 −0.688259 0.725465i \(-0.741625\pi\)
−0.688259 + 0.725465i \(0.741625\pi\)
\(374\) 5.32510 0.275354
\(375\) 1.57663 0.0814171
\(376\) −3.55198 −0.183179
\(377\) 0.213260 0.0109835
\(378\) 4.43489 0.228106
\(379\) −17.8037 −0.914514 −0.457257 0.889335i \(-0.651168\pi\)
−0.457257 + 0.889335i \(0.651168\pi\)
\(380\) −2.64922 −0.135902
\(381\) 30.4506 1.56003
\(382\) −11.5515 −0.591028
\(383\) 17.7357 0.906253 0.453126 0.891446i \(-0.350309\pi\)
0.453126 + 0.891446i \(0.350309\pi\)
\(384\) −1.57663 −0.0804573
\(385\) 0.800428 0.0407936
\(386\) −15.7250 −0.800381
\(387\) 0.514223 0.0261394
\(388\) 0.294217 0.0149366
\(389\) −29.6312 −1.50236 −0.751180 0.660098i \(-0.770515\pi\)
−0.751180 + 0.660098i \(0.770515\pi\)
\(390\) 1.61604 0.0818312
\(391\) 16.1084 0.814636
\(392\) 6.35931 0.321194
\(393\) −3.52672 −0.177900
\(394\) 12.6214 0.635856
\(395\) 8.33391 0.419324
\(396\) −0.514223 −0.0258407
\(397\) −0.874875 −0.0439087 −0.0219543 0.999759i \(-0.506989\pi\)
−0.0219543 + 0.999759i \(0.506989\pi\)
\(398\) −8.27011 −0.414543
\(399\) −3.34327 −0.167373
\(400\) 1.00000 0.0500000
\(401\) 16.7273 0.835322 0.417661 0.908603i \(-0.362850\pi\)
0.417661 + 0.908603i \(0.362850\pi\)
\(402\) 16.6367 0.829761
\(403\) −2.02503 −0.100874
\(404\) 1.14270 0.0568512
\(405\) −7.19290 −0.357418
\(406\) 0.166538 0.00826513
\(407\) −6.73970 −0.334075
\(408\) 8.39573 0.415651
\(409\) 11.4333 0.565341 0.282670 0.959217i \(-0.408780\pi\)
0.282670 + 0.959217i \(0.408780\pi\)
\(410\) −10.4726 −0.517206
\(411\) 24.2669 1.19700
\(412\) −9.50752 −0.468402
\(413\) −9.50541 −0.467731
\(414\) −1.55552 −0.0764497
\(415\) 10.2036 0.500874
\(416\) 1.02499 0.0502543
\(417\) −26.2227 −1.28413
\(418\) 2.64922 0.129578
\(419\) −0.915714 −0.0447356 −0.0223678 0.999750i \(-0.507120\pi\)
−0.0223678 + 0.999750i \(0.507120\pi\)
\(420\) 1.26198 0.0615785
\(421\) 23.5860 1.14951 0.574757 0.818324i \(-0.305097\pi\)
0.574757 + 0.818324i \(0.305097\pi\)
\(422\) 4.00515 0.194968
\(423\) −1.82651 −0.0888080
\(424\) 9.61400 0.466897
\(425\) −5.32510 −0.258305
\(426\) 10.6243 0.514750
\(427\) −2.38505 −0.115420
\(428\) 4.79302 0.231679
\(429\) −1.61604 −0.0780230
\(430\) 1.00000 0.0482243
\(431\) 26.1671 1.26043 0.630213 0.776423i \(-0.282968\pi\)
0.630213 + 0.776423i \(0.282968\pi\)
\(432\) −5.54065 −0.266574
\(433\) −15.9409 −0.766072 −0.383036 0.923733i \(-0.625121\pi\)
−0.383036 + 0.923733i \(0.625121\pi\)
\(434\) −1.58137 −0.0759083
\(435\) −0.328036 −0.0157281
\(436\) −17.2100 −0.824209
\(437\) 8.01386 0.383355
\(438\) −2.09546 −0.100125
\(439\) −30.0150 −1.43254 −0.716268 0.697825i \(-0.754151\pi\)
−0.716268 + 0.697825i \(0.754151\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 3.27011 0.155719
\(442\) −5.45818 −0.259619
\(443\) 24.5171 1.16484 0.582421 0.812887i \(-0.302105\pi\)
0.582421 + 0.812887i \(0.302105\pi\)
\(444\) −10.6260 −0.504290
\(445\) 9.34345 0.442922
\(446\) 9.48329 0.449047
\(447\) −20.7111 −0.979602
\(448\) 0.800428 0.0378167
\(449\) 26.7819 1.26391 0.631957 0.775003i \(-0.282252\pi\)
0.631957 + 0.775003i \(0.282252\pi\)
\(450\) 0.514223 0.0242407
\(451\) 10.4726 0.493136
\(452\) −12.6986 −0.597292
\(453\) 8.48521 0.398670
\(454\) −12.2245 −0.573726
\(455\) −0.820432 −0.0384624
\(456\) 4.17685 0.195599
\(457\) −6.46219 −0.302289 −0.151144 0.988512i \(-0.548296\pi\)
−0.151144 + 0.988512i \(0.548296\pi\)
\(458\) −16.0960 −0.752116
\(459\) 29.5045 1.37715
\(460\) −3.02499 −0.141041
\(461\) 26.6725 1.24226 0.621132 0.783706i \(-0.286673\pi\)
0.621132 + 0.783706i \(0.286673\pi\)
\(462\) −1.26198 −0.0587128
\(463\) −16.9910 −0.789638 −0.394819 0.918759i \(-0.629193\pi\)
−0.394819 + 0.918759i \(0.629193\pi\)
\(464\) −0.208061 −0.00965898
\(465\) 3.11489 0.144450
\(466\) −23.9182 −1.10799
\(467\) −24.6468 −1.14052 −0.570258 0.821465i \(-0.693157\pi\)
−0.570258 + 0.821465i \(0.693157\pi\)
\(468\) 0.527074 0.0243640
\(469\) −8.44613 −0.390006
\(470\) −3.55198 −0.163841
\(471\) −24.8903 −1.14688
\(472\) 11.8754 0.546610
\(473\) −1.00000 −0.0459800
\(474\) −13.1395 −0.603519
\(475\) −2.64922 −0.121555
\(476\) −4.26236 −0.195365
\(477\) 4.94374 0.226358
\(478\) −20.7070 −0.947114
\(479\) −31.3134 −1.43074 −0.715372 0.698744i \(-0.753743\pi\)
−0.715372 + 0.698744i \(0.753743\pi\)
\(480\) −1.57663 −0.0719632
\(481\) 6.90813 0.314984
\(482\) 13.8160 0.629302
\(483\) −3.81749 −0.173702
\(484\) 1.00000 0.0454545
\(485\) 0.294217 0.0133597
\(486\) −5.28136 −0.239567
\(487\) 3.47565 0.157497 0.0787484 0.996895i \(-0.474908\pi\)
0.0787484 + 0.996895i \(0.474908\pi\)
\(488\) 2.97971 0.134885
\(489\) −27.8749 −1.26055
\(490\) 6.35931 0.287285
\(491\) −2.76700 −0.124873 −0.0624365 0.998049i \(-0.519887\pi\)
−0.0624365 + 0.998049i \(0.519887\pi\)
\(492\) 16.5115 0.744396
\(493\) 1.10794 0.0498993
\(494\) −2.71543 −0.122173
\(495\) −0.514223 −0.0231126
\(496\) 1.97566 0.0887097
\(497\) −5.39378 −0.241944
\(498\) −16.0873 −0.720890
\(499\) 29.7798 1.33313 0.666564 0.745448i \(-0.267764\pi\)
0.666564 + 0.745448i \(0.267764\pi\)
\(500\) 1.00000 0.0447214
\(501\) 6.48724 0.289829
\(502\) 5.08380 0.226901
\(503\) 27.3250 1.21836 0.609181 0.793031i \(-0.291498\pi\)
0.609181 + 0.793031i \(0.291498\pi\)
\(504\) 0.411599 0.0183341
\(505\) 1.14270 0.0508493
\(506\) 3.02499 0.134477
\(507\) −18.8398 −0.836706
\(508\) 19.3137 0.856907
\(509\) −32.3336 −1.43316 −0.716581 0.697503i \(-0.754294\pi\)
−0.716581 + 0.697503i \(0.754294\pi\)
\(510\) 8.39573 0.371769
\(511\) 1.06383 0.0470609
\(512\) −1.00000 −0.0441942
\(513\) 14.6784 0.648067
\(514\) 16.8556 0.743469
\(515\) −9.50752 −0.418951
\(516\) −1.57663 −0.0694075
\(517\) 3.55198 0.156216
\(518\) 5.39465 0.237027
\(519\) −27.3910 −1.20233
\(520\) 1.02499 0.0449488
\(521\) 2.19231 0.0960470 0.0480235 0.998846i \(-0.484708\pi\)
0.0480235 + 0.998846i \(0.484708\pi\)
\(522\) −0.106990 −0.00468281
\(523\) −22.2363 −0.972326 −0.486163 0.873868i \(-0.661604\pi\)
−0.486163 + 0.873868i \(0.661604\pi\)
\(524\) −2.23687 −0.0977180
\(525\) 1.26198 0.0550774
\(526\) −11.0417 −0.481442
\(527\) −10.5206 −0.458284
\(528\) 1.57663 0.0686142
\(529\) −13.8494 −0.602149
\(530\) 9.61400 0.417605
\(531\) 6.10661 0.265004
\(532\) −2.12051 −0.0919358
\(533\) −10.7343 −0.464956
\(534\) −14.7312 −0.637482
\(535\) 4.79302 0.207220
\(536\) 10.5520 0.455777
\(537\) 4.90416 0.211630
\(538\) −5.90487 −0.254577
\(539\) −6.35931 −0.273915
\(540\) −5.54065 −0.238431
\(541\) −4.52948 −0.194737 −0.0973687 0.995248i \(-0.531043\pi\)
−0.0973687 + 0.995248i \(0.531043\pi\)
\(542\) 0.109692 0.00471167
\(543\) 30.8315 1.32311
\(544\) 5.32510 0.228312
\(545\) −17.2100 −0.737195
\(546\) 1.29352 0.0553576
\(547\) −25.8318 −1.10449 −0.552243 0.833683i \(-0.686228\pi\)
−0.552243 + 0.833683i \(0.686228\pi\)
\(548\) 15.3916 0.657496
\(549\) 1.53224 0.0653943
\(550\) −1.00000 −0.0426401
\(551\) 0.551199 0.0234818
\(552\) 4.76931 0.202995
\(553\) 6.67070 0.283667
\(554\) 10.1828 0.432626
\(555\) −10.6260 −0.451050
\(556\) −16.6321 −0.705358
\(557\) −14.6117 −0.619118 −0.309559 0.950880i \(-0.600181\pi\)
−0.309559 + 0.950880i \(0.600181\pi\)
\(558\) 1.01593 0.0430078
\(559\) 1.02499 0.0433525
\(560\) 0.800428 0.0338243
\(561\) −8.39573 −0.354468
\(562\) −12.0954 −0.510212
\(563\) −29.5053 −1.24350 −0.621750 0.783216i \(-0.713578\pi\)
−0.621750 + 0.783216i \(0.713578\pi\)
\(564\) 5.60018 0.235810
\(565\) −12.6986 −0.534234
\(566\) −3.46228 −0.145531
\(567\) −5.75740 −0.241788
\(568\) 6.73861 0.282746
\(569\) 20.9018 0.876251 0.438125 0.898914i \(-0.355643\pi\)
0.438125 + 0.898914i \(0.355643\pi\)
\(570\) 4.17685 0.174949
\(571\) −4.47120 −0.187114 −0.0935569 0.995614i \(-0.529824\pi\)
−0.0935569 + 0.995614i \(0.529824\pi\)
\(572\) −1.02499 −0.0428570
\(573\) 18.2126 0.760840
\(574\) −8.38258 −0.349882
\(575\) −3.02499 −0.126151
\(576\) −0.514223 −0.0214260
\(577\) −38.6359 −1.60843 −0.804217 0.594335i \(-0.797415\pi\)
−0.804217 + 0.594335i \(0.797415\pi\)
\(578\) −11.3567 −0.472375
\(579\) 24.7926 1.03034
\(580\) −0.208061 −0.00863925
\(581\) 8.16724 0.338834
\(582\) −0.463873 −0.0192281
\(583\) −9.61400 −0.398171
\(584\) −1.32907 −0.0549974
\(585\) 0.527074 0.0217918
\(586\) 32.8264 1.35605
\(587\) 5.43021 0.224129 0.112064 0.993701i \(-0.464254\pi\)
0.112064 + 0.993701i \(0.464254\pi\)
\(588\) −10.0263 −0.413478
\(589\) −5.23395 −0.215661
\(590\) 11.8754 0.488903
\(591\) −19.8993 −0.818548
\(592\) −6.73970 −0.277000
\(593\) 14.8798 0.611039 0.305520 0.952186i \(-0.401170\pi\)
0.305520 + 0.952186i \(0.401170\pi\)
\(594\) 5.54065 0.227335
\(595\) −4.26236 −0.174740
\(596\) −13.1363 −0.538083
\(597\) 13.0389 0.533649
\(598\) −3.10059 −0.126793
\(599\) 1.29419 0.0528791 0.0264396 0.999650i \(-0.491583\pi\)
0.0264396 + 0.999650i \(0.491583\pi\)
\(600\) −1.57663 −0.0643658
\(601\) 12.1106 0.494002 0.247001 0.969015i \(-0.420555\pi\)
0.247001 + 0.969015i \(0.420555\pi\)
\(602\) 0.800428 0.0326230
\(603\) 5.42609 0.220968
\(604\) 5.38185 0.218984
\(605\) 1.00000 0.0406558
\(606\) −1.80161 −0.0731855
\(607\) −25.9256 −1.05229 −0.526143 0.850396i \(-0.676362\pi\)
−0.526143 + 0.850396i \(0.676362\pi\)
\(608\) 2.64922 0.107440
\(609\) −0.262569 −0.0106398
\(610\) 2.97971 0.120645
\(611\) −3.64075 −0.147289
\(612\) 2.73829 0.110689
\(613\) 10.8232 0.437143 0.218571 0.975821i \(-0.429860\pi\)
0.218571 + 0.975821i \(0.429860\pi\)
\(614\) −15.8101 −0.638042
\(615\) 16.5115 0.665808
\(616\) −0.800428 −0.0322502
\(617\) −2.94986 −0.118757 −0.0593785 0.998236i \(-0.518912\pi\)
−0.0593785 + 0.998236i \(0.518912\pi\)
\(618\) 14.9899 0.602982
\(619\) 10.5819 0.425323 0.212662 0.977126i \(-0.431787\pi\)
0.212662 + 0.977126i \(0.431787\pi\)
\(620\) 1.97566 0.0793444
\(621\) 16.7604 0.672572
\(622\) 7.41195 0.297192
\(623\) 7.47876 0.299630
\(624\) −1.61604 −0.0646932
\(625\) 1.00000 0.0400000
\(626\) −14.8333 −0.592856
\(627\) −4.17685 −0.166807
\(628\) −15.7870 −0.629969
\(629\) 35.8896 1.43101
\(630\) 0.411599 0.0163985
\(631\) −21.4951 −0.855706 −0.427853 0.903848i \(-0.640730\pi\)
−0.427853 + 0.903848i \(0.640730\pi\)
\(632\) −8.33391 −0.331505
\(633\) −6.31466 −0.250985
\(634\) −18.5511 −0.736759
\(635\) 19.3137 0.766441
\(636\) −15.1578 −0.601044
\(637\) 6.51824 0.258262
\(638\) 0.208061 0.00823721
\(639\) 3.46515 0.137079
\(640\) −1.00000 −0.0395285
\(641\) −9.38771 −0.370792 −0.185396 0.982664i \(-0.559357\pi\)
−0.185396 + 0.982664i \(0.559357\pi\)
\(642\) −7.55684 −0.298245
\(643\) 10.4007 0.410164 0.205082 0.978745i \(-0.434254\pi\)
0.205082 + 0.978745i \(0.434254\pi\)
\(644\) −2.42129 −0.0954121
\(645\) −1.57663 −0.0620799
\(646\) −14.1074 −0.555046
\(647\) −43.1859 −1.69781 −0.848907 0.528542i \(-0.822739\pi\)
−0.848907 + 0.528542i \(0.822739\pi\)
\(648\) 7.19290 0.282564
\(649\) −11.8754 −0.466151
\(650\) 1.02499 0.0402035
\(651\) 2.49325 0.0977181
\(652\) −17.6800 −0.692403
\(653\) 3.31176 0.129599 0.0647996 0.997898i \(-0.479359\pi\)
0.0647996 + 0.997898i \(0.479359\pi\)
\(654\) 27.1338 1.06102
\(655\) −2.23687 −0.0874016
\(656\) 10.4726 0.408887
\(657\) −0.683440 −0.0266635
\(658\) −2.84311 −0.110836
\(659\) −32.0509 −1.24853 −0.624264 0.781214i \(-0.714601\pi\)
−0.624264 + 0.781214i \(0.714601\pi\)
\(660\) 1.57663 0.0613704
\(661\) −17.2999 −0.672887 −0.336444 0.941704i \(-0.609224\pi\)
−0.336444 + 0.941704i \(0.609224\pi\)
\(662\) −11.7965 −0.458483
\(663\) 8.60555 0.334212
\(664\) −10.2036 −0.395976
\(665\) −2.12051 −0.0822298
\(666\) −3.46571 −0.134294
\(667\) 0.629382 0.0243698
\(668\) 4.11462 0.159199
\(669\) −14.9517 −0.578066
\(670\) 10.5520 0.407660
\(671\) −2.97971 −0.115031
\(672\) −1.26198 −0.0486820
\(673\) −27.9517 −1.07746 −0.538729 0.842479i \(-0.681095\pi\)
−0.538729 + 0.842479i \(0.681095\pi\)
\(674\) −10.8501 −0.417930
\(675\) −5.54065 −0.213260
\(676\) −11.9494 −0.459592
\(677\) −13.5715 −0.521594 −0.260797 0.965394i \(-0.583985\pi\)
−0.260797 + 0.965394i \(0.583985\pi\)
\(678\) 20.0210 0.768903
\(679\) 0.235500 0.00903764
\(680\) 5.32510 0.204208
\(681\) 19.2736 0.738568
\(682\) −1.97566 −0.0756519
\(683\) −9.40214 −0.359763 −0.179881 0.983688i \(-0.557571\pi\)
−0.179881 + 0.983688i \(0.557571\pi\)
\(684\) 1.36229 0.0520885
\(685\) 15.3916 0.588082
\(686\) 10.6932 0.408267
\(687\) 25.3775 0.968211
\(688\) −1.00000 −0.0381246
\(689\) 9.85426 0.375418
\(690\) 4.76931 0.181564
\(691\) 15.2503 0.580150 0.290075 0.957004i \(-0.406320\pi\)
0.290075 + 0.957004i \(0.406320\pi\)
\(692\) −17.3731 −0.660426
\(693\) −0.411599 −0.0156354
\(694\) 21.8988 0.831266
\(695\) −16.6321 −0.630891
\(696\) 0.328036 0.0124342
\(697\) −55.7677 −2.11235
\(698\) −4.86814 −0.184262
\(699\) 37.7102 1.42633
\(700\) 0.800428 0.0302533
\(701\) −37.1132 −1.40174 −0.700872 0.713287i \(-0.747206\pi\)
−0.700872 + 0.713287i \(0.747206\pi\)
\(702\) −5.67911 −0.214344
\(703\) 17.8549 0.673412
\(704\) 1.00000 0.0376889
\(705\) 5.60018 0.210915
\(706\) 3.25663 0.122565
\(707\) 0.914646 0.0343988
\(708\) −18.7232 −0.703660
\(709\) 36.6980 1.37822 0.689110 0.724657i \(-0.258002\pi\)
0.689110 + 0.724657i \(0.258002\pi\)
\(710\) 6.73861 0.252896
\(711\) −4.28549 −0.160718
\(712\) −9.34345 −0.350161
\(713\) −5.97635 −0.223816
\(714\) 6.72018 0.251497
\(715\) −1.02499 −0.0383325
\(716\) 3.11052 0.116246
\(717\) 32.6473 1.21924
\(718\) −9.66427 −0.360667
\(719\) −30.0585 −1.12099 −0.560497 0.828156i \(-0.689390\pi\)
−0.560497 + 0.828156i \(0.689390\pi\)
\(720\) −0.514223 −0.0191640
\(721\) −7.61009 −0.283414
\(722\) 11.9816 0.445910
\(723\) −21.7828 −0.810112
\(724\) 19.5553 0.726766
\(725\) −0.208061 −0.00772718
\(726\) −1.57663 −0.0585144
\(727\) −2.91194 −0.107998 −0.0539989 0.998541i \(-0.517197\pi\)
−0.0539989 + 0.998541i \(0.517197\pi\)
\(728\) 0.820432 0.0304072
\(729\) 29.9055 1.10761
\(730\) −1.32907 −0.0491912
\(731\) 5.32510 0.196956
\(732\) −4.69792 −0.173640
\(733\) 31.7751 1.17364 0.586821 0.809717i \(-0.300379\pi\)
0.586821 + 0.809717i \(0.300379\pi\)
\(734\) 27.2816 1.00698
\(735\) −10.0263 −0.369826
\(736\) 3.02499 0.111503
\(737\) −10.5520 −0.388688
\(738\) 5.38527 0.198234
\(739\) 3.10556 0.114240 0.0571200 0.998367i \(-0.481808\pi\)
0.0571200 + 0.998367i \(0.481808\pi\)
\(740\) −6.73970 −0.247756
\(741\) 4.28123 0.157275
\(742\) 7.69532 0.282504
\(743\) 16.5595 0.607508 0.303754 0.952750i \(-0.401760\pi\)
0.303754 + 0.952750i \(0.401760\pi\)
\(744\) −3.11489 −0.114197
\(745\) −13.1363 −0.481276
\(746\) 26.5850 0.973345
\(747\) −5.24692 −0.191975
\(748\) −5.32510 −0.194705
\(749\) 3.83647 0.140182
\(750\) −1.57663 −0.0575706
\(751\) 49.7609 1.81580 0.907900 0.419186i \(-0.137684\pi\)
0.907900 + 0.419186i \(0.137684\pi\)
\(752\) 3.55198 0.129527
\(753\) −8.01530 −0.292094
\(754\) −0.213260 −0.00776649
\(755\) 5.38185 0.195866
\(756\) −4.43489 −0.161295
\(757\) 33.0266 1.20037 0.600186 0.799861i \(-0.295093\pi\)
0.600186 + 0.799861i \(0.295093\pi\)
\(758\) 17.8037 0.646659
\(759\) −4.76931 −0.173115
\(760\) 2.64922 0.0960973
\(761\) 35.4359 1.28455 0.642276 0.766474i \(-0.277991\pi\)
0.642276 + 0.766474i \(0.277991\pi\)
\(762\) −30.4506 −1.10311
\(763\) −13.7754 −0.498701
\(764\) 11.5515 0.417920
\(765\) 2.73829 0.0990031
\(766\) −17.7357 −0.640817
\(767\) 12.1722 0.439512
\(768\) 1.57663 0.0568919
\(769\) −13.3462 −0.481277 −0.240639 0.970615i \(-0.577357\pi\)
−0.240639 + 0.970615i \(0.577357\pi\)
\(770\) −0.800428 −0.0288454
\(771\) −26.5751 −0.957080
\(772\) 15.7250 0.565955
\(773\) 39.3147 1.41405 0.707026 0.707188i \(-0.250036\pi\)
0.707026 + 0.707188i \(0.250036\pi\)
\(774\) −0.514223 −0.0184834
\(775\) 1.97566 0.0709678
\(776\) −0.294217 −0.0105618
\(777\) −8.50539 −0.305129
\(778\) 29.6312 1.06233
\(779\) −27.7443 −0.994041
\(780\) −1.61604 −0.0578634
\(781\) −6.73861 −0.241127
\(782\) −16.1084 −0.576034
\(783\) 1.15279 0.0411974
\(784\) −6.35931 −0.227118
\(785\) −15.7870 −0.563461
\(786\) 3.52672 0.125794
\(787\) −37.5439 −1.33830 −0.669148 0.743129i \(-0.733341\pi\)
−0.669148 + 0.743129i \(0.733341\pi\)
\(788\) −12.6214 −0.449618
\(789\) 17.4088 0.619768
\(790\) −8.33391 −0.296507
\(791\) −10.1643 −0.361401
\(792\) 0.514223 0.0182721
\(793\) 3.05418 0.108457
\(794\) 0.874875 0.0310481
\(795\) −15.1578 −0.537590
\(796\) 8.27011 0.293126
\(797\) −23.2800 −0.824620 −0.412310 0.911044i \(-0.635278\pi\)
−0.412310 + 0.911044i \(0.635278\pi\)
\(798\) 3.34327 0.118350
\(799\) −18.9146 −0.669152
\(800\) −1.00000 −0.0353553
\(801\) −4.80462 −0.169763
\(802\) −16.7273 −0.590662
\(803\) 1.32907 0.0469019
\(804\) −16.6367 −0.586730
\(805\) −2.42129 −0.0853392
\(806\) 2.02503 0.0713287
\(807\) 9.30982 0.327721
\(808\) −1.14270 −0.0401999
\(809\) 3.65160 0.128383 0.0641917 0.997938i \(-0.479553\pi\)
0.0641917 + 0.997938i \(0.479553\pi\)
\(810\) 7.19290 0.252733
\(811\) −11.2086 −0.393589 −0.196794 0.980445i \(-0.563053\pi\)
−0.196794 + 0.980445i \(0.563053\pi\)
\(812\) −0.166538 −0.00584433
\(813\) −0.172944 −0.00606541
\(814\) 6.73970 0.236226
\(815\) −17.6800 −0.619304
\(816\) −8.39573 −0.293909
\(817\) 2.64922 0.0926844
\(818\) −11.4333 −0.399756
\(819\) 0.421885 0.0147419
\(820\) 10.4726 0.365720
\(821\) 41.0787 1.43366 0.716828 0.697250i \(-0.245593\pi\)
0.716828 + 0.697250i \(0.245593\pi\)
\(822\) −24.2669 −0.846406
\(823\) −0.499858 −0.0174240 −0.00871198 0.999962i \(-0.502773\pi\)
−0.00871198 + 0.999962i \(0.502773\pi\)
\(824\) 9.50752 0.331210
\(825\) 1.57663 0.0548914
\(826\) 9.50541 0.330736
\(827\) 13.0330 0.453203 0.226602 0.973988i \(-0.427238\pi\)
0.226602 + 0.973988i \(0.427238\pi\)
\(828\) 1.55552 0.0540581
\(829\) 37.6377 1.30721 0.653606 0.756835i \(-0.273255\pi\)
0.653606 + 0.756835i \(0.273255\pi\)
\(830\) −10.2036 −0.354172
\(831\) −16.0546 −0.556927
\(832\) −1.02499 −0.0355352
\(833\) 33.8640 1.17332
\(834\) 26.2227 0.908019
\(835\) 4.11462 0.142392
\(836\) −2.64922 −0.0916252
\(837\) −10.9464 −0.378364
\(838\) 0.915714 0.0316328
\(839\) −10.6040 −0.366089 −0.183045 0.983105i \(-0.558595\pi\)
−0.183045 + 0.983105i \(0.558595\pi\)
\(840\) −1.26198 −0.0435425
\(841\) −28.9567 −0.998507
\(842\) −23.5860 −0.812829
\(843\) 19.0700 0.656805
\(844\) −4.00515 −0.137863
\(845\) −11.9494 −0.411072
\(846\) 1.82651 0.0627968
\(847\) 0.800428 0.0275030
\(848\) −9.61400 −0.330146
\(849\) 5.45875 0.187344
\(850\) 5.32510 0.182649
\(851\) 20.3875 0.698876
\(852\) −10.6243 −0.363984
\(853\) 44.7626 1.53264 0.766322 0.642457i \(-0.222085\pi\)
0.766322 + 0.642457i \(0.222085\pi\)
\(854\) 2.38505 0.0816146
\(855\) 1.36229 0.0465894
\(856\) −4.79302 −0.163822
\(857\) 40.9407 1.39851 0.699254 0.714873i \(-0.253516\pi\)
0.699254 + 0.714873i \(0.253516\pi\)
\(858\) 1.61604 0.0551706
\(859\) −11.5373 −0.393647 −0.196824 0.980439i \(-0.563063\pi\)
−0.196824 + 0.980439i \(0.563063\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 13.2163 0.450409
\(862\) −26.1671 −0.891255
\(863\) −11.7277 −0.399215 −0.199608 0.979876i \(-0.563967\pi\)
−0.199608 + 0.979876i \(0.563967\pi\)
\(864\) 5.54065 0.188497
\(865\) −17.3731 −0.590703
\(866\) 15.9409 0.541695
\(867\) 17.9053 0.608097
\(868\) 1.58137 0.0536753
\(869\) 8.33391 0.282709
\(870\) 0.328036 0.0111215
\(871\) 10.8157 0.366477
\(872\) 17.2100 0.582803
\(873\) −0.151293 −0.00512050
\(874\) −8.01386 −0.271073
\(875\) 0.800428 0.0270594
\(876\) 2.09546 0.0707990
\(877\) −2.53727 −0.0856775 −0.0428388 0.999082i \(-0.513640\pi\)
−0.0428388 + 0.999082i \(0.513640\pi\)
\(878\) 30.0150 1.01296
\(879\) −51.7552 −1.74566
\(880\) 1.00000 0.0337100
\(881\) 8.32215 0.280380 0.140190 0.990125i \(-0.455229\pi\)
0.140190 + 0.990125i \(0.455229\pi\)
\(882\) −3.27011 −0.110110
\(883\) −11.3446 −0.381777 −0.190888 0.981612i \(-0.561137\pi\)
−0.190888 + 0.981612i \(0.561137\pi\)
\(884\) 5.45818 0.183578
\(885\) −18.7232 −0.629373
\(886\) −24.5171 −0.823668
\(887\) 32.8951 1.10451 0.552254 0.833676i \(-0.313768\pi\)
0.552254 + 0.833676i \(0.313768\pi\)
\(888\) 10.6260 0.356587
\(889\) 15.4592 0.518486
\(890\) −9.34345 −0.313193
\(891\) −7.19290 −0.240971
\(892\) −9.48329 −0.317524
\(893\) −9.40998 −0.314893
\(894\) 20.7111 0.692683
\(895\) 3.11052 0.103973
\(896\) −0.800428 −0.0267404
\(897\) 4.88850 0.163222
\(898\) −26.7819 −0.893723
\(899\) −0.411057 −0.0137095
\(900\) −0.514223 −0.0171408
\(901\) 51.1955 1.70557
\(902\) −10.4726 −0.348700
\(903\) −1.26198 −0.0419962
\(904\) 12.6986 0.422349
\(905\) 19.5553 0.650039
\(906\) −8.48521 −0.281902
\(907\) −14.7363 −0.489312 −0.244656 0.969610i \(-0.578675\pi\)
−0.244656 + 0.969610i \(0.578675\pi\)
\(908\) 12.2245 0.405686
\(909\) −0.587601 −0.0194895
\(910\) 0.820432 0.0271971
\(911\) 23.9691 0.794131 0.397065 0.917790i \(-0.370029\pi\)
0.397065 + 0.917790i \(0.370029\pi\)
\(912\) −4.17685 −0.138309
\(913\) 10.2036 0.337689
\(914\) 6.46219 0.213750
\(915\) −4.69792 −0.155308
\(916\) 16.0960 0.531826
\(917\) −1.79045 −0.0591259
\(918\) −29.5045 −0.973793
\(919\) 31.9385 1.05355 0.526777 0.850004i \(-0.323400\pi\)
0.526777 + 0.850004i \(0.323400\pi\)
\(920\) 3.02499 0.0997310
\(921\) 24.9267 0.821362
\(922\) −26.6725 −0.878413
\(923\) 6.90702 0.227347
\(924\) 1.26198 0.0415162
\(925\) −6.73970 −0.221600
\(926\) 16.9910 0.558359
\(927\) 4.88899 0.160575
\(928\) 0.208061 0.00682993
\(929\) −25.9985 −0.852984 −0.426492 0.904491i \(-0.640251\pi\)
−0.426492 + 0.904491i \(0.640251\pi\)
\(930\) −3.11489 −0.102141
\(931\) 16.8472 0.552145
\(932\) 23.9182 0.783466
\(933\) −11.6859 −0.382581
\(934\) 24.6468 0.806467
\(935\) −5.32510 −0.174149
\(936\) −0.527074 −0.0172280
\(937\) −42.1033 −1.37545 −0.687727 0.725969i \(-0.741391\pi\)
−0.687727 + 0.725969i \(0.741391\pi\)
\(938\) 8.44613 0.275776
\(939\) 23.3866 0.763194
\(940\) 3.55198 0.115853
\(941\) 45.0237 1.46773 0.733865 0.679296i \(-0.237715\pi\)
0.733865 + 0.679296i \(0.237715\pi\)
\(942\) 24.8903 0.810969
\(943\) −31.6796 −1.03163
\(944\) −11.8754 −0.386512
\(945\) −4.43489 −0.144267
\(946\) 1.00000 0.0325128
\(947\) 32.0104 1.04020 0.520100 0.854106i \(-0.325895\pi\)
0.520100 + 0.854106i \(0.325895\pi\)
\(948\) 13.1395 0.426752
\(949\) −1.36229 −0.0442217
\(950\) 2.64922 0.0859520
\(951\) 29.2483 0.948442
\(952\) 4.26236 0.138144
\(953\) 52.4310 1.69841 0.849203 0.528066i \(-0.177083\pi\)
0.849203 + 0.528066i \(0.177083\pi\)
\(954\) −4.94374 −0.160060
\(955\) 11.5515 0.373799
\(956\) 20.7070 0.669711
\(957\) −0.328036 −0.0106039
\(958\) 31.3134 1.01169
\(959\) 12.3199 0.397829
\(960\) 1.57663 0.0508857
\(961\) −27.0968 −0.874089
\(962\) −6.90813 −0.222727
\(963\) −2.46468 −0.0794233
\(964\) −13.8160 −0.444984
\(965\) 15.7250 0.506205
\(966\) 3.81749 0.122826
\(967\) −26.7669 −0.860764 −0.430382 0.902647i \(-0.641621\pi\)
−0.430382 + 0.902647i \(0.641621\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 22.2421 0.714520
\(970\) −0.294217 −0.00944674
\(971\) 42.0144 1.34831 0.674153 0.738592i \(-0.264509\pi\)
0.674153 + 0.738592i \(0.264509\pi\)
\(972\) 5.28136 0.169400
\(973\) −13.3128 −0.426789
\(974\) −3.47565 −0.111367
\(975\) −1.61604 −0.0517546
\(976\) −2.97971 −0.0953783
\(977\) −15.6696 −0.501316 −0.250658 0.968076i \(-0.580647\pi\)
−0.250658 + 0.968076i \(0.580647\pi\)
\(978\) 27.8749 0.891342
\(979\) 9.34345 0.298618
\(980\) −6.35931 −0.203141
\(981\) 8.84978 0.282552
\(982\) 2.76700 0.0882985
\(983\) −15.7881 −0.503562 −0.251781 0.967784i \(-0.581016\pi\)
−0.251781 + 0.967784i \(0.581016\pi\)
\(984\) −16.5115 −0.526367
\(985\) −12.6214 −0.402151
\(986\) −1.10794 −0.0352841
\(987\) 4.48254 0.142681
\(988\) 2.71543 0.0863892
\(989\) 3.02499 0.0961891
\(990\) 0.514223 0.0163431
\(991\) −7.31945 −0.232510 −0.116255 0.993219i \(-0.537089\pi\)
−0.116255 + 0.993219i \(0.537089\pi\)
\(992\) −1.97566 −0.0627272
\(993\) 18.5987 0.590213
\(994\) 5.39378 0.171080
\(995\) 8.27011 0.262180
\(996\) 16.0873 0.509746
\(997\) −26.1994 −0.829744 −0.414872 0.909880i \(-0.636174\pi\)
−0.414872 + 0.909880i \(0.636174\pi\)
\(998\) −29.7798 −0.942663
\(999\) 37.3423 1.18146
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 4730.2.a.w.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.w.1.7 8 1.1 even 1 trivial