Properties

Label 5577.2.a.y.1.3
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5577.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.5325692073\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 21 x^{4} + 13 x^{3} - 33 x^{2} - 7 x + 7\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 429)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.584778\) of defining polynomial
Character \(\chi\) \(=\) 5577.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.584778 q^{2} +1.00000 q^{3} -1.65803 q^{4} -1.95350 q^{5} -0.584778 q^{6} +1.51078 q^{7} +2.13914 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.584778 q^{2} +1.00000 q^{3} -1.65803 q^{4} -1.95350 q^{5} -0.584778 q^{6} +1.51078 q^{7} +2.13914 q^{8} +1.00000 q^{9} +1.14237 q^{10} +1.00000 q^{11} -1.65803 q^{12} -0.883474 q^{14} -1.95350 q^{15} +2.06515 q^{16} +3.44198 q^{17} -0.584778 q^{18} +5.09587 q^{19} +3.23897 q^{20} +1.51078 q^{21} -0.584778 q^{22} -0.701611 q^{23} +2.13914 q^{24} -1.18383 q^{25} +1.00000 q^{27} -2.50493 q^{28} +5.04937 q^{29} +1.14237 q^{30} +7.26957 q^{31} -5.48593 q^{32} +1.00000 q^{33} -2.01280 q^{34} -2.95132 q^{35} -1.65803 q^{36} -2.08160 q^{37} -2.97995 q^{38} -4.17882 q^{40} +1.03658 q^{41} -0.883474 q^{42} -5.48659 q^{43} -1.65803 q^{44} -1.95350 q^{45} +0.410287 q^{46} +3.75225 q^{47} +2.06515 q^{48} -4.71753 q^{49} +0.692276 q^{50} +3.44198 q^{51} -0.502747 q^{53} -0.584778 q^{54} -1.95350 q^{55} +3.23178 q^{56} +5.09587 q^{57} -2.95276 q^{58} -2.65023 q^{59} +3.23897 q^{60} -5.38195 q^{61} -4.25109 q^{62} +1.51078 q^{63} -0.922236 q^{64} -0.584778 q^{66} -8.47197 q^{67} -5.70692 q^{68} -0.701611 q^{69} +1.72587 q^{70} -2.31533 q^{71} +2.13914 q^{72} +2.21094 q^{73} +1.21727 q^{74} -1.18383 q^{75} -8.44913 q^{76} +1.51078 q^{77} -5.54589 q^{79} -4.03427 q^{80} +1.00000 q^{81} -0.606168 q^{82} +14.5137 q^{83} -2.50493 q^{84} -6.72392 q^{85} +3.20844 q^{86} +5.04937 q^{87} +2.13914 q^{88} -1.80966 q^{89} +1.14237 q^{90} +1.16330 q^{92} +7.26957 q^{93} -2.19424 q^{94} -9.95480 q^{95} -5.48593 q^{96} +14.5085 q^{97} +2.75871 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + 7q^{11} + 9q^{12} + 8q^{14} + 6q^{15} + 17q^{16} - 2q^{17} + 3q^{18} + 8q^{19} - 2q^{20} + 6q^{21} + 3q^{22} + 4q^{23} + 15q^{24} + 13q^{25} + 7q^{27} + 12q^{28} - 12q^{29} - 10q^{31} + 33q^{32} + 7q^{33} + 28q^{34} - 4q^{35} + 9q^{36} + 6q^{37} + 16q^{38} - 10q^{40} + 2q^{41} + 8q^{42} - 16q^{43} + 9q^{44} + 6q^{45} - 26q^{46} + 18q^{47} + 17q^{48} + 23q^{49} + 39q^{50} - 2q^{51} + 10q^{53} + 3q^{54} + 6q^{55} + 16q^{56} + 8q^{57} + 10q^{58} + 2q^{59} - 2q^{60} - 10q^{61} - 36q^{62} + 6q^{63} + 29q^{64} + 3q^{66} + 8q^{67} - 10q^{68} + 4q^{69} - 20q^{70} + 36q^{71} + 15q^{72} + 20q^{73} + 13q^{75} + 10q^{76} + 6q^{77} + 6q^{79} - 20q^{80} + 7q^{81} - 10q^{82} + 30q^{83} + 12q^{84} - 40q^{85} + 6q^{86} - 12q^{87} + 15q^{88} + 34q^{89} - 12q^{92} - 10q^{93} + 32q^{94} + 18q^{95} + 33q^{96} + 16q^{97} + q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.584778 −0.413501 −0.206750 0.978394i \(-0.566289\pi\)
−0.206750 + 0.978394i \(0.566289\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.65803 −0.829017
\(5\) −1.95350 −0.873633 −0.436817 0.899551i \(-0.643894\pi\)
−0.436817 + 0.899551i \(0.643894\pi\)
\(6\) −0.584778 −0.238735
\(7\) 1.51078 0.571023 0.285511 0.958375i \(-0.407837\pi\)
0.285511 + 0.958375i \(0.407837\pi\)
\(8\) 2.13914 0.756300
\(9\) 1.00000 0.333333
\(10\) 1.14237 0.361248
\(11\) 1.00000 0.301511
\(12\) −1.65803 −0.478633
\(13\) 0 0
\(14\) −0.883474 −0.236118
\(15\) −1.95350 −0.504392
\(16\) 2.06515 0.516286
\(17\) 3.44198 0.834803 0.417401 0.908722i \(-0.362941\pi\)
0.417401 + 0.908722i \(0.362941\pi\)
\(18\) −0.584778 −0.137834
\(19\) 5.09587 1.16907 0.584536 0.811368i \(-0.301276\pi\)
0.584536 + 0.811368i \(0.301276\pi\)
\(20\) 3.23897 0.724257
\(21\) 1.51078 0.329680
\(22\) −0.584778 −0.124675
\(23\) −0.701611 −0.146296 −0.0731480 0.997321i \(-0.523305\pi\)
−0.0731480 + 0.997321i \(0.523305\pi\)
\(24\) 2.13914 0.436650
\(25\) −1.18383 −0.236765
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −2.50493 −0.473388
\(29\) 5.04937 0.937645 0.468822 0.883292i \(-0.344678\pi\)
0.468822 + 0.883292i \(0.344678\pi\)
\(30\) 1.14237 0.208567
\(31\) 7.26957 1.30565 0.652827 0.757507i \(-0.273583\pi\)
0.652827 + 0.757507i \(0.273583\pi\)
\(32\) −5.48593 −0.969785
\(33\) 1.00000 0.174078
\(34\) −2.01280 −0.345192
\(35\) −2.95132 −0.498864
\(36\) −1.65803 −0.276339
\(37\) −2.08160 −0.342213 −0.171106 0.985253i \(-0.554734\pi\)
−0.171106 + 0.985253i \(0.554734\pi\)
\(38\) −2.97995 −0.483413
\(39\) 0 0
\(40\) −4.17882 −0.660729
\(41\) 1.03658 0.161886 0.0809430 0.996719i \(-0.474207\pi\)
0.0809430 + 0.996719i \(0.474207\pi\)
\(42\) −0.883474 −0.136323
\(43\) −5.48659 −0.836698 −0.418349 0.908286i \(-0.637391\pi\)
−0.418349 + 0.908286i \(0.637391\pi\)
\(44\) −1.65803 −0.249958
\(45\) −1.95350 −0.291211
\(46\) 0.410287 0.0604935
\(47\) 3.75225 0.547322 0.273661 0.961826i \(-0.411765\pi\)
0.273661 + 0.961826i \(0.411765\pi\)
\(48\) 2.06515 0.298078
\(49\) −4.71753 −0.673933
\(50\) 0.692276 0.0979026
\(51\) 3.44198 0.481974
\(52\) 0 0
\(53\) −0.502747 −0.0690575 −0.0345288 0.999404i \(-0.510993\pi\)
−0.0345288 + 0.999404i \(0.510993\pi\)
\(54\) −0.584778 −0.0795783
\(55\) −1.95350 −0.263410
\(56\) 3.23178 0.431865
\(57\) 5.09587 0.674964
\(58\) −2.95276 −0.387717
\(59\) −2.65023 −0.345031 −0.172515 0.985007i \(-0.555189\pi\)
−0.172515 + 0.985007i \(0.555189\pi\)
\(60\) 3.23897 0.418150
\(61\) −5.38195 −0.689088 −0.344544 0.938770i \(-0.611967\pi\)
−0.344544 + 0.938770i \(0.611967\pi\)
\(62\) −4.25109 −0.539889
\(63\) 1.51078 0.190341
\(64\) −0.922236 −0.115279
\(65\) 0 0
\(66\) −0.584778 −0.0719813
\(67\) −8.47197 −1.03502 −0.517508 0.855679i \(-0.673140\pi\)
−0.517508 + 0.855679i \(0.673140\pi\)
\(68\) −5.70692 −0.692066
\(69\) −0.701611 −0.0844640
\(70\) 1.72587 0.206281
\(71\) −2.31533 −0.274779 −0.137390 0.990517i \(-0.543871\pi\)
−0.137390 + 0.990517i \(0.543871\pi\)
\(72\) 2.13914 0.252100
\(73\) 2.21094 0.258771 0.129385 0.991594i \(-0.458700\pi\)
0.129385 + 0.991594i \(0.458700\pi\)
\(74\) 1.21727 0.141505
\(75\) −1.18383 −0.136696
\(76\) −8.44913 −0.969181
\(77\) 1.51078 0.172170
\(78\) 0 0
\(79\) −5.54589 −0.623961 −0.311981 0.950088i \(-0.600992\pi\)
−0.311981 + 0.950088i \(0.600992\pi\)
\(80\) −4.03427 −0.451045
\(81\) 1.00000 0.111111
\(82\) −0.606168 −0.0669400
\(83\) 14.5137 1.59308 0.796541 0.604585i \(-0.206661\pi\)
0.796541 + 0.604585i \(0.206661\pi\)
\(84\) −2.50493 −0.273310
\(85\) −6.72392 −0.729311
\(86\) 3.20844 0.345975
\(87\) 5.04937 0.541350
\(88\) 2.13914 0.228033
\(89\) −1.80966 −0.191824 −0.0959119 0.995390i \(-0.530577\pi\)
−0.0959119 + 0.995390i \(0.530577\pi\)
\(90\) 1.14237 0.120416
\(91\) 0 0
\(92\) 1.16330 0.121282
\(93\) 7.26957 0.753819
\(94\) −2.19424 −0.226318
\(95\) −9.95480 −1.02134
\(96\) −5.48593 −0.559906
\(97\) 14.5085 1.47312 0.736560 0.676372i \(-0.236449\pi\)
0.736560 + 0.676372i \(0.236449\pi\)
\(98\) 2.75871 0.278672
\(99\) 1.00000 0.100504
\(100\) 1.96282 0.196282
\(101\) 8.63799 0.859512 0.429756 0.902945i \(-0.358600\pi\)
0.429756 + 0.902945i \(0.358600\pi\)
\(102\) −2.01280 −0.199296
\(103\) −2.90048 −0.285792 −0.142896 0.989738i \(-0.545642\pi\)
−0.142896 + 0.989738i \(0.545642\pi\)
\(104\) 0 0
\(105\) −2.95132 −0.288019
\(106\) 0.293995 0.0285554
\(107\) −2.29234 −0.221609 −0.110805 0.993842i \(-0.535343\pi\)
−0.110805 + 0.993842i \(0.535343\pi\)
\(108\) −1.65803 −0.159544
\(109\) 12.8818 1.23386 0.616929 0.787019i \(-0.288377\pi\)
0.616929 + 0.787019i \(0.288377\pi\)
\(110\) 1.14237 0.108920
\(111\) −2.08160 −0.197577
\(112\) 3.11999 0.294811
\(113\) −12.6273 −1.18788 −0.593940 0.804509i \(-0.702428\pi\)
−0.593940 + 0.804509i \(0.702428\pi\)
\(114\) −2.97995 −0.279098
\(115\) 1.37060 0.127809
\(116\) −8.37203 −0.777324
\(117\) 0 0
\(118\) 1.54980 0.142670
\(119\) 5.20009 0.476691
\(120\) −4.17882 −0.381472
\(121\) 1.00000 0.0909091
\(122\) 3.14725 0.284939
\(123\) 1.03658 0.0934649
\(124\) −12.0532 −1.08241
\(125\) 12.0801 1.08048
\(126\) −0.883474 −0.0787061
\(127\) 5.05085 0.448190 0.224095 0.974567i \(-0.428057\pi\)
0.224095 + 0.974567i \(0.428057\pi\)
\(128\) 11.5112 1.01745
\(129\) −5.48659 −0.483068
\(130\) 0 0
\(131\) 15.9772 1.39594 0.697968 0.716129i \(-0.254088\pi\)
0.697968 + 0.716129i \(0.254088\pi\)
\(132\) −1.65803 −0.144313
\(133\) 7.69876 0.667567
\(134\) 4.95422 0.427980
\(135\) −1.95350 −0.168131
\(136\) 7.36288 0.631361
\(137\) −17.2582 −1.47447 −0.737233 0.675639i \(-0.763868\pi\)
−0.737233 + 0.675639i \(0.763868\pi\)
\(138\) 0.410287 0.0349260
\(139\) −5.70544 −0.483929 −0.241965 0.970285i \(-0.577792\pi\)
−0.241965 + 0.970285i \(0.577792\pi\)
\(140\) 4.89339 0.413567
\(141\) 3.75225 0.315997
\(142\) 1.35395 0.113621
\(143\) 0 0
\(144\) 2.06515 0.172095
\(145\) −9.86396 −0.819158
\(146\) −1.29291 −0.107002
\(147\) −4.71753 −0.389095
\(148\) 3.45136 0.283700
\(149\) −0.161015 −0.0131908 −0.00659542 0.999978i \(-0.502099\pi\)
−0.00659542 + 0.999978i \(0.502099\pi\)
\(150\) 0.692276 0.0565241
\(151\) 16.3107 1.32734 0.663671 0.748025i \(-0.268997\pi\)
0.663671 + 0.748025i \(0.268997\pi\)
\(152\) 10.9008 0.884170
\(153\) 3.44198 0.278268
\(154\) −0.883474 −0.0711924
\(155\) −14.2011 −1.14066
\(156\) 0 0
\(157\) −14.2192 −1.13481 −0.567407 0.823437i \(-0.692053\pi\)
−0.567407 + 0.823437i \(0.692053\pi\)
\(158\) 3.24312 0.258008
\(159\) −0.502747 −0.0398704
\(160\) 10.7168 0.847236
\(161\) −1.05998 −0.0835384
\(162\) −0.584778 −0.0459445
\(163\) 13.0186 1.01970 0.509848 0.860264i \(-0.329702\pi\)
0.509848 + 0.860264i \(0.329702\pi\)
\(164\) −1.71868 −0.134206
\(165\) −1.95350 −0.152080
\(166\) −8.48728 −0.658740
\(167\) 14.0271 1.08545 0.542724 0.839911i \(-0.317393\pi\)
0.542724 + 0.839911i \(0.317393\pi\)
\(168\) 3.23178 0.249337
\(169\) 0 0
\(170\) 3.93200 0.301571
\(171\) 5.09587 0.389691
\(172\) 9.09696 0.693637
\(173\) 17.8674 1.35844 0.679218 0.733936i \(-0.262319\pi\)
0.679218 + 0.733936i \(0.262319\pi\)
\(174\) −2.95276 −0.223848
\(175\) −1.78851 −0.135198
\(176\) 2.06515 0.155666
\(177\) −2.65023 −0.199204
\(178\) 1.05825 0.0793193
\(179\) 17.2723 1.29099 0.645495 0.763764i \(-0.276651\pi\)
0.645495 + 0.763764i \(0.276651\pi\)
\(180\) 3.23897 0.241419
\(181\) 3.70318 0.275255 0.137628 0.990484i \(-0.456052\pi\)
0.137628 + 0.990484i \(0.456052\pi\)
\(182\) 0 0
\(183\) −5.38195 −0.397845
\(184\) −1.50084 −0.110644
\(185\) 4.06641 0.298969
\(186\) −4.25109 −0.311705
\(187\) 3.44198 0.251703
\(188\) −6.22136 −0.453740
\(189\) 1.51078 0.109893
\(190\) 5.82135 0.422325
\(191\) −20.6259 −1.49243 −0.746217 0.665702i \(-0.768132\pi\)
−0.746217 + 0.665702i \(0.768132\pi\)
\(192\) −0.922236 −0.0665566
\(193\) 18.8475 1.35667 0.678335 0.734753i \(-0.262702\pi\)
0.678335 + 0.734753i \(0.262702\pi\)
\(194\) −8.48429 −0.609136
\(195\) 0 0
\(196\) 7.82183 0.558702
\(197\) −7.18370 −0.511818 −0.255909 0.966701i \(-0.582375\pi\)
−0.255909 + 0.966701i \(0.582375\pi\)
\(198\) −0.584778 −0.0415584
\(199\) −18.9591 −1.34398 −0.671989 0.740562i \(-0.734560\pi\)
−0.671989 + 0.740562i \(0.734560\pi\)
\(200\) −2.53237 −0.179066
\(201\) −8.47197 −0.597566
\(202\) −5.05131 −0.355409
\(203\) 7.62851 0.535417
\(204\) −5.70692 −0.399564
\(205\) −2.02496 −0.141429
\(206\) 1.69614 0.118175
\(207\) −0.701611 −0.0487653
\(208\) 0 0
\(209\) 5.09587 0.352489
\(210\) 1.72587 0.119096
\(211\) −19.9916 −1.37628 −0.688139 0.725578i \(-0.741572\pi\)
−0.688139 + 0.725578i \(0.741572\pi\)
\(212\) 0.833571 0.0572499
\(213\) −2.31533 −0.158644
\(214\) 1.34051 0.0916356
\(215\) 10.7181 0.730967
\(216\) 2.13914 0.145550
\(217\) 10.9828 0.745558
\(218\) −7.53303 −0.510201
\(219\) 2.21094 0.149401
\(220\) 3.23897 0.218372
\(221\) 0 0
\(222\) 1.21727 0.0816981
\(223\) −27.7784 −1.86018 −0.930091 0.367330i \(-0.880272\pi\)
−0.930091 + 0.367330i \(0.880272\pi\)
\(224\) −8.28806 −0.553769
\(225\) −1.18383 −0.0789218
\(226\) 7.38419 0.491189
\(227\) 28.6524 1.90173 0.950863 0.309612i \(-0.100199\pi\)
0.950863 + 0.309612i \(0.100199\pi\)
\(228\) −8.44913 −0.559557
\(229\) 4.83459 0.319479 0.159739 0.987159i \(-0.448935\pi\)
0.159739 + 0.987159i \(0.448935\pi\)
\(230\) −0.801497 −0.0528491
\(231\) 1.51078 0.0994023
\(232\) 10.8013 0.709141
\(233\) 13.6237 0.892518 0.446259 0.894904i \(-0.352756\pi\)
0.446259 + 0.894904i \(0.352756\pi\)
\(234\) 0 0
\(235\) −7.33004 −0.478159
\(236\) 4.39417 0.286036
\(237\) −5.54589 −0.360244
\(238\) −3.04090 −0.197112
\(239\) −5.99903 −0.388045 −0.194023 0.980997i \(-0.562154\pi\)
−0.194023 + 0.980997i \(0.562154\pi\)
\(240\) −4.03427 −0.260411
\(241\) −12.9290 −0.832831 −0.416416 0.909174i \(-0.636714\pi\)
−0.416416 + 0.909174i \(0.636714\pi\)
\(242\) −0.584778 −0.0375910
\(243\) 1.00000 0.0641500
\(244\) 8.92346 0.571266
\(245\) 9.21571 0.588770
\(246\) −0.606168 −0.0386478
\(247\) 0 0
\(248\) 15.5506 0.987466
\(249\) 14.5137 0.919766
\(250\) −7.06420 −0.446779
\(251\) −23.9724 −1.51313 −0.756563 0.653921i \(-0.773123\pi\)
−0.756563 + 0.653921i \(0.773123\pi\)
\(252\) −2.50493 −0.157796
\(253\) −0.701611 −0.0441099
\(254\) −2.95363 −0.185327
\(255\) −6.72392 −0.421068
\(256\) −4.88701 −0.305438
\(257\) 16.3441 1.01952 0.509758 0.860318i \(-0.329735\pi\)
0.509758 + 0.860318i \(0.329735\pi\)
\(258\) 3.20844 0.199749
\(259\) −3.14485 −0.195411
\(260\) 0 0
\(261\) 5.04937 0.312548
\(262\) −9.34313 −0.577220
\(263\) 10.1510 0.625936 0.312968 0.949764i \(-0.398677\pi\)
0.312968 + 0.949764i \(0.398677\pi\)
\(264\) 2.13914 0.131655
\(265\) 0.982117 0.0603310
\(266\) −4.50207 −0.276040
\(267\) −1.80966 −0.110750
\(268\) 14.0468 0.858045
\(269\) 16.5294 1.00781 0.503907 0.863758i \(-0.331895\pi\)
0.503907 + 0.863758i \(0.331895\pi\)
\(270\) 1.14237 0.0695222
\(271\) 20.8927 1.26914 0.634570 0.772865i \(-0.281177\pi\)
0.634570 + 0.772865i \(0.281177\pi\)
\(272\) 7.10819 0.430997
\(273\) 0 0
\(274\) 10.0922 0.609693
\(275\) −1.18383 −0.0713874
\(276\) 1.16330 0.0700221
\(277\) −17.3070 −1.03988 −0.519938 0.854204i \(-0.674045\pi\)
−0.519938 + 0.854204i \(0.674045\pi\)
\(278\) 3.33642 0.200105
\(279\) 7.26957 0.435218
\(280\) −6.31329 −0.377291
\(281\) −16.0666 −0.958450 −0.479225 0.877692i \(-0.659082\pi\)
−0.479225 + 0.877692i \(0.659082\pi\)
\(282\) −2.19424 −0.130665
\(283\) −17.2180 −1.02350 −0.511751 0.859134i \(-0.671003\pi\)
−0.511751 + 0.859134i \(0.671003\pi\)
\(284\) 3.83890 0.227797
\(285\) −9.95480 −0.589671
\(286\) 0 0
\(287\) 1.56604 0.0924406
\(288\) −5.48593 −0.323262
\(289\) −5.15277 −0.303104
\(290\) 5.76823 0.338722
\(291\) 14.5085 0.850506
\(292\) −3.66581 −0.214525
\(293\) 5.29670 0.309436 0.154718 0.987959i \(-0.450553\pi\)
0.154718 + 0.987959i \(0.450553\pi\)
\(294\) 2.75871 0.160891
\(295\) 5.17723 0.301430
\(296\) −4.45283 −0.258816
\(297\) 1.00000 0.0580259
\(298\) 0.0941580 0.00545443
\(299\) 0 0
\(300\) 1.96282 0.113324
\(301\) −8.28906 −0.477773
\(302\) −9.53812 −0.548857
\(303\) 8.63799 0.496240
\(304\) 10.5237 0.603576
\(305\) 10.5137 0.602010
\(306\) −2.01280 −0.115064
\(307\) 26.3020 1.50113 0.750567 0.660794i \(-0.229780\pi\)
0.750567 + 0.660794i \(0.229780\pi\)
\(308\) −2.50493 −0.142732
\(309\) −2.90048 −0.165002
\(310\) 8.30451 0.471665
\(311\) 32.8590 1.86326 0.931632 0.363403i \(-0.118385\pi\)
0.931632 + 0.363403i \(0.118385\pi\)
\(312\) 0 0
\(313\) 33.2130 1.87731 0.938655 0.344858i \(-0.112073\pi\)
0.938655 + 0.344858i \(0.112073\pi\)
\(314\) 8.31507 0.469247
\(315\) −2.95132 −0.166288
\(316\) 9.19527 0.517274
\(317\) 30.8436 1.73235 0.866175 0.499740i \(-0.166571\pi\)
0.866175 + 0.499740i \(0.166571\pi\)
\(318\) 0.293995 0.0164864
\(319\) 5.04937 0.282711
\(320\) 1.80159 0.100712
\(321\) −2.29234 −0.127946
\(322\) 0.619855 0.0345432
\(323\) 17.5399 0.975945
\(324\) −1.65803 −0.0921130
\(325\) 0 0
\(326\) −7.61300 −0.421645
\(327\) 12.8818 0.712368
\(328\) 2.21738 0.122434
\(329\) 5.66884 0.312534
\(330\) 1.14237 0.0628852
\(331\) 5.75414 0.316276 0.158138 0.987417i \(-0.449451\pi\)
0.158138 + 0.987417i \(0.449451\pi\)
\(332\) −24.0641 −1.32069
\(333\) −2.08160 −0.114071
\(334\) −8.20273 −0.448833
\(335\) 16.5500 0.904224
\(336\) 3.11999 0.170209
\(337\) 10.9245 0.595094 0.297547 0.954707i \(-0.403831\pi\)
0.297547 + 0.954707i \(0.403831\pi\)
\(338\) 0 0
\(339\) −12.6273 −0.685823
\(340\) 11.1485 0.604612
\(341\) 7.26957 0.393669
\(342\) −2.97995 −0.161138
\(343\) −17.7027 −0.955854
\(344\) −11.7366 −0.632795
\(345\) 1.37060 0.0737906
\(346\) −10.4485 −0.561715
\(347\) 16.3474 0.877572 0.438786 0.898591i \(-0.355409\pi\)
0.438786 + 0.898591i \(0.355409\pi\)
\(348\) −8.37203 −0.448788
\(349\) 8.62758 0.461824 0.230912 0.972975i \(-0.425829\pi\)
0.230912 + 0.972975i \(0.425829\pi\)
\(350\) 1.04588 0.0559046
\(351\) 0 0
\(352\) −5.48593 −0.292401
\(353\) 16.5793 0.882425 0.441212 0.897403i \(-0.354549\pi\)
0.441212 + 0.897403i \(0.354549\pi\)
\(354\) 1.54980 0.0823708
\(355\) 4.52300 0.240056
\(356\) 3.00048 0.159025
\(357\) 5.20009 0.275218
\(358\) −10.1005 −0.533826
\(359\) −15.5233 −0.819289 −0.409645 0.912245i \(-0.634347\pi\)
−0.409645 + 0.912245i \(0.634347\pi\)
\(360\) −4.17882 −0.220243
\(361\) 6.96788 0.366731
\(362\) −2.16554 −0.113818
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) −4.31907 −0.226071
\(366\) 3.14725 0.164509
\(367\) 23.4682 1.22503 0.612514 0.790460i \(-0.290158\pi\)
0.612514 + 0.790460i \(0.290158\pi\)
\(368\) −1.44893 −0.0755306
\(369\) 1.03658 0.0539620
\(370\) −2.37795 −0.123624
\(371\) −0.759541 −0.0394334
\(372\) −12.0532 −0.624929
\(373\) 12.3222 0.638018 0.319009 0.947752i \(-0.396650\pi\)
0.319009 + 0.947752i \(0.396650\pi\)
\(374\) −2.01280 −0.104079
\(375\) 12.0801 0.623815
\(376\) 8.02659 0.413940
\(377\) 0 0
\(378\) −0.883474 −0.0454410
\(379\) −22.8695 −1.17473 −0.587365 0.809322i \(-0.699835\pi\)
−0.587365 + 0.809322i \(0.699835\pi\)
\(380\) 16.5054 0.846709
\(381\) 5.05085 0.258763
\(382\) 12.0616 0.617123
\(383\) −35.5259 −1.81529 −0.907646 0.419737i \(-0.862122\pi\)
−0.907646 + 0.419737i \(0.862122\pi\)
\(384\) 11.5112 0.587427
\(385\) −2.95132 −0.150413
\(386\) −11.0216 −0.560984
\(387\) −5.48659 −0.278899
\(388\) −24.0557 −1.22124
\(389\) −2.67074 −0.135412 −0.0677060 0.997705i \(-0.521568\pi\)
−0.0677060 + 0.997705i \(0.521568\pi\)
\(390\) 0 0
\(391\) −2.41493 −0.122128
\(392\) −10.0915 −0.509696
\(393\) 15.9772 0.805944
\(394\) 4.20087 0.211637
\(395\) 10.8339 0.545113
\(396\) −1.65803 −0.0833193
\(397\) −36.4406 −1.82890 −0.914451 0.404698i \(-0.867377\pi\)
−0.914451 + 0.404698i \(0.867377\pi\)
\(398\) 11.0869 0.555736
\(399\) 7.69876 0.385420
\(400\) −2.44477 −0.122239
\(401\) 13.6597 0.682132 0.341066 0.940039i \(-0.389212\pi\)
0.341066 + 0.940039i \(0.389212\pi\)
\(402\) 4.95422 0.247094
\(403\) 0 0
\(404\) −14.3221 −0.712550
\(405\) −1.95350 −0.0970703
\(406\) −4.46099 −0.221395
\(407\) −2.08160 −0.103181
\(408\) 7.36288 0.364517
\(409\) 25.8507 1.27823 0.639117 0.769110i \(-0.279300\pi\)
0.639117 + 0.769110i \(0.279300\pi\)
\(410\) 1.18415 0.0584810
\(411\) −17.2582 −0.851283
\(412\) 4.80909 0.236927
\(413\) −4.00393 −0.197020
\(414\) 0.410287 0.0201645
\(415\) −28.3525 −1.39177
\(416\) 0 0
\(417\) −5.70544 −0.279397
\(418\) −2.97995 −0.145754
\(419\) 22.6067 1.10441 0.552205 0.833708i \(-0.313787\pi\)
0.552205 + 0.833708i \(0.313787\pi\)
\(420\) 4.89339 0.238773
\(421\) 24.6918 1.20341 0.601703 0.798720i \(-0.294489\pi\)
0.601703 + 0.798720i \(0.294489\pi\)
\(422\) 11.6907 0.569092
\(423\) 3.75225 0.182441
\(424\) −1.07544 −0.0522282
\(425\) −4.07471 −0.197652
\(426\) 1.35395 0.0655993
\(427\) −8.13097 −0.393485
\(428\) 3.80079 0.183718
\(429\) 0 0
\(430\) −6.26770 −0.302255
\(431\) 30.1126 1.45047 0.725237 0.688499i \(-0.241730\pi\)
0.725237 + 0.688499i \(0.241730\pi\)
\(432\) 2.06515 0.0993594
\(433\) 30.9402 1.48689 0.743445 0.668797i \(-0.233191\pi\)
0.743445 + 0.668797i \(0.233191\pi\)
\(434\) −6.42248 −0.308289
\(435\) −9.86396 −0.472941
\(436\) −21.3585 −1.02289
\(437\) −3.57532 −0.171031
\(438\) −1.29291 −0.0617775
\(439\) −7.02158 −0.335122 −0.167561 0.985862i \(-0.553589\pi\)
−0.167561 + 0.985862i \(0.553589\pi\)
\(440\) −4.17882 −0.199217
\(441\) −4.71753 −0.224644
\(442\) 0 0
\(443\) −22.5411 −1.07096 −0.535480 0.844548i \(-0.679869\pi\)
−0.535480 + 0.844548i \(0.679869\pi\)
\(444\) 3.45136 0.163794
\(445\) 3.53518 0.167584
\(446\) 16.2442 0.769187
\(447\) −0.161015 −0.00761574
\(448\) −1.39330 −0.0658272
\(449\) −9.41670 −0.444401 −0.222201 0.975001i \(-0.571324\pi\)
−0.222201 + 0.975001i \(0.571324\pi\)
\(450\) 0.692276 0.0326342
\(451\) 1.03658 0.0488105
\(452\) 20.9365 0.984772
\(453\) 16.3107 0.766341
\(454\) −16.7553 −0.786365
\(455\) 0 0
\(456\) 10.9008 0.510476
\(457\) −3.48691 −0.163111 −0.0815554 0.996669i \(-0.525989\pi\)
−0.0815554 + 0.996669i \(0.525989\pi\)
\(458\) −2.82717 −0.132105
\(459\) 3.44198 0.160658
\(460\) −2.27250 −0.105956
\(461\) 15.1983 0.707855 0.353928 0.935273i \(-0.384846\pi\)
0.353928 + 0.935273i \(0.384846\pi\)
\(462\) −0.883474 −0.0411029
\(463\) 15.9882 0.743035 0.371518 0.928426i \(-0.378838\pi\)
0.371518 + 0.928426i \(0.378838\pi\)
\(464\) 10.4277 0.484093
\(465\) −14.2011 −0.658562
\(466\) −7.96684 −0.369057
\(467\) 32.9225 1.52347 0.761736 0.647888i \(-0.224348\pi\)
0.761736 + 0.647888i \(0.224348\pi\)
\(468\) 0 0
\(469\) −12.7993 −0.591017
\(470\) 4.28645 0.197719
\(471\) −14.2192 −0.655185
\(472\) −5.66921 −0.260947
\(473\) −5.48659 −0.252274
\(474\) 3.24312 0.148961
\(475\) −6.03262 −0.276796
\(476\) −8.62193 −0.395185
\(477\) −0.502747 −0.0230192
\(478\) 3.50811 0.160457
\(479\) 33.6023 1.53533 0.767664 0.640853i \(-0.221419\pi\)
0.767664 + 0.640853i \(0.221419\pi\)
\(480\) 10.7168 0.489152
\(481\) 0 0
\(482\) 7.56061 0.344376
\(483\) −1.05998 −0.0482309
\(484\) −1.65803 −0.0753652
\(485\) −28.3425 −1.28697
\(486\) −0.584778 −0.0265261
\(487\) 3.70001 0.167663 0.0838316 0.996480i \(-0.473284\pi\)
0.0838316 + 0.996480i \(0.473284\pi\)
\(488\) −11.5127 −0.521158
\(489\) 13.0186 0.588722
\(490\) −5.38915 −0.243457
\(491\) −10.1397 −0.457599 −0.228799 0.973474i \(-0.573480\pi\)
−0.228799 + 0.973474i \(0.573480\pi\)
\(492\) −1.71868 −0.0774840
\(493\) 17.3798 0.782749
\(494\) 0 0
\(495\) −1.95350 −0.0878034
\(496\) 15.0127 0.674091
\(497\) −3.49796 −0.156905
\(498\) −8.48728 −0.380324
\(499\) −15.1124 −0.676525 −0.338263 0.941052i \(-0.609839\pi\)
−0.338263 + 0.941052i \(0.609839\pi\)
\(500\) −20.0293 −0.895736
\(501\) 14.0271 0.626683
\(502\) 14.0185 0.625678
\(503\) 11.9190 0.531441 0.265721 0.964050i \(-0.414390\pi\)
0.265721 + 0.964050i \(0.414390\pi\)
\(504\) 3.23178 0.143955
\(505\) −16.8743 −0.750898
\(506\) 0.410287 0.0182395
\(507\) 0 0
\(508\) −8.37448 −0.371558
\(509\) −35.2059 −1.56047 −0.780236 0.625485i \(-0.784901\pi\)
−0.780236 + 0.625485i \(0.784901\pi\)
\(510\) 3.93200 0.174112
\(511\) 3.34025 0.147764
\(512\) −20.1645 −0.891154
\(513\) 5.09587 0.224988
\(514\) −9.55767 −0.421571
\(515\) 5.66609 0.249678
\(516\) 9.09696 0.400471
\(517\) 3.75225 0.165024
\(518\) 1.83904 0.0808028
\(519\) 17.8674 0.784294
\(520\) 0 0
\(521\) −2.84143 −0.124485 −0.0622426 0.998061i \(-0.519825\pi\)
−0.0622426 + 0.998061i \(0.519825\pi\)
\(522\) −2.95276 −0.129239
\(523\) −17.8564 −0.780804 −0.390402 0.920644i \(-0.627664\pi\)
−0.390402 + 0.920644i \(0.627664\pi\)
\(524\) −26.4908 −1.15725
\(525\) −1.78851 −0.0780568
\(526\) −5.93607 −0.258825
\(527\) 25.0217 1.08996
\(528\) 2.06515 0.0898739
\(529\) −22.5077 −0.978597
\(530\) −0.574321 −0.0249469
\(531\) −2.65023 −0.115010
\(532\) −12.7648 −0.553424
\(533\) 0 0
\(534\) 1.05825 0.0457950
\(535\) 4.47810 0.193605
\(536\) −18.1227 −0.782782
\(537\) 17.2723 0.745354
\(538\) −9.66602 −0.416732
\(539\) −4.71753 −0.203198
\(540\) 3.23897 0.139383
\(541\) −3.56883 −0.153436 −0.0767179 0.997053i \(-0.524444\pi\)
−0.0767179 + 0.997053i \(0.524444\pi\)
\(542\) −12.2176 −0.524791
\(543\) 3.70318 0.158919
\(544\) −18.8825 −0.809579
\(545\) −25.1647 −1.07794
\(546\) 0 0
\(547\) 3.50639 0.149923 0.0749613 0.997186i \(-0.476117\pi\)
0.0749613 + 0.997186i \(0.476117\pi\)
\(548\) 28.6146 1.22236
\(549\) −5.38195 −0.229696
\(550\) 0.692276 0.0295188
\(551\) 25.7309 1.09617
\(552\) −1.50084 −0.0638802
\(553\) −8.37864 −0.356296
\(554\) 10.1207 0.429989
\(555\) 4.06641 0.172610
\(556\) 9.45982 0.401186
\(557\) 7.38164 0.312770 0.156385 0.987696i \(-0.450016\pi\)
0.156385 + 0.987696i \(0.450016\pi\)
\(558\) −4.25109 −0.179963
\(559\) 0 0
\(560\) −6.09491 −0.257557
\(561\) 3.44198 0.145321
\(562\) 9.39537 0.396320
\(563\) −35.5383 −1.49776 −0.748879 0.662706i \(-0.769408\pi\)
−0.748879 + 0.662706i \(0.769408\pi\)
\(564\) −6.22136 −0.261967
\(565\) 24.6675 1.03777
\(566\) 10.0687 0.423219
\(567\) 1.51078 0.0634470
\(568\) −4.95281 −0.207815
\(569\) −19.6546 −0.823966 −0.411983 0.911192i \(-0.635164\pi\)
−0.411983 + 0.911192i \(0.635164\pi\)
\(570\) 5.82135 0.243830
\(571\) −18.6081 −0.778726 −0.389363 0.921084i \(-0.627305\pi\)
−0.389363 + 0.921084i \(0.627305\pi\)
\(572\) 0 0
\(573\) −20.6259 −0.861658
\(574\) −0.915788 −0.0382243
\(575\) 0.830586 0.0346378
\(576\) −0.922236 −0.0384265
\(577\) 25.5485 1.06360 0.531799 0.846871i \(-0.321516\pi\)
0.531799 + 0.846871i \(0.321516\pi\)
\(578\) 3.01323 0.125334
\(579\) 18.8475 0.783274
\(580\) 16.3548 0.679096
\(581\) 21.9270 0.909686
\(582\) −8.48429 −0.351685
\(583\) −0.502747 −0.0208216
\(584\) 4.72950 0.195708
\(585\) 0 0
\(586\) −3.09739 −0.127952
\(587\) 2.35936 0.0973813 0.0486907 0.998814i \(-0.484495\pi\)
0.0486907 + 0.998814i \(0.484495\pi\)
\(588\) 7.82183 0.322567
\(589\) 37.0448 1.52640
\(590\) −3.02753 −0.124642
\(591\) −7.18370 −0.295498
\(592\) −4.29881 −0.176680
\(593\) 11.6707 0.479257 0.239628 0.970865i \(-0.422974\pi\)
0.239628 + 0.970865i \(0.422974\pi\)
\(594\) −0.584778 −0.0239938
\(595\) −10.1584 −0.416453
\(596\) 0.266968 0.0109354
\(597\) −18.9591 −0.775946
\(598\) 0 0
\(599\) 9.12181 0.372707 0.186354 0.982483i \(-0.440333\pi\)
0.186354 + 0.982483i \(0.440333\pi\)
\(600\) −2.53237 −0.103384
\(601\) 6.90316 0.281586 0.140793 0.990039i \(-0.455035\pi\)
0.140793 + 0.990039i \(0.455035\pi\)
\(602\) 4.84726 0.197560
\(603\) −8.47197 −0.345005
\(604\) −27.0436 −1.10039
\(605\) −1.95350 −0.0794212
\(606\) −5.05131 −0.205196
\(607\) 11.5559 0.469038 0.234519 0.972112i \(-0.424648\pi\)
0.234519 + 0.972112i \(0.424648\pi\)
\(608\) −27.9556 −1.13375
\(609\) 7.62851 0.309123
\(610\) −6.14816 −0.248932
\(611\) 0 0
\(612\) −5.70692 −0.230689
\(613\) −37.7362 −1.52415 −0.762075 0.647488i \(-0.775819\pi\)
−0.762075 + 0.647488i \(0.775819\pi\)
\(614\) −15.3808 −0.620720
\(615\) −2.02496 −0.0816541
\(616\) 3.23178 0.130212
\(617\) −28.2159 −1.13593 −0.567964 0.823053i \(-0.692269\pi\)
−0.567964 + 0.823053i \(0.692269\pi\)
\(618\) 1.69614 0.0682286
\(619\) −38.4407 −1.54506 −0.772530 0.634978i \(-0.781009\pi\)
−0.772530 + 0.634978i \(0.781009\pi\)
\(620\) 23.5460 0.945628
\(621\) −0.701611 −0.0281547
\(622\) −19.2152 −0.770461
\(623\) −2.73401 −0.109536
\(624\) 0 0
\(625\) −17.6794 −0.707177
\(626\) −19.4222 −0.776269
\(627\) 5.09587 0.203509
\(628\) 23.5759 0.940781
\(629\) −7.16483 −0.285680
\(630\) 1.72587 0.0687603
\(631\) 16.9688 0.675519 0.337759 0.941232i \(-0.390331\pi\)
0.337759 + 0.941232i \(0.390331\pi\)
\(632\) −11.8634 −0.471902
\(633\) −19.9916 −0.794595
\(634\) −18.0367 −0.716328
\(635\) −9.86685 −0.391554
\(636\) 0.833571 0.0330532
\(637\) 0 0
\(638\) −2.95276 −0.116901
\(639\) −2.31533 −0.0915930
\(640\) −22.4871 −0.888881
\(641\) 6.00876 0.237332 0.118666 0.992934i \(-0.462138\pi\)
0.118666 + 0.992934i \(0.462138\pi\)
\(642\) 1.34051 0.0529059
\(643\) −9.64269 −0.380270 −0.190135 0.981758i \(-0.560893\pi\)
−0.190135 + 0.981758i \(0.560893\pi\)
\(644\) 1.75749 0.0692547
\(645\) 10.7181 0.422024
\(646\) −10.2569 −0.403554
\(647\) −34.1912 −1.34420 −0.672098 0.740463i \(-0.734606\pi\)
−0.672098 + 0.740463i \(0.734606\pi\)
\(648\) 2.13914 0.0840333
\(649\) −2.65023 −0.104031
\(650\) 0 0
\(651\) 10.9828 0.430448
\(652\) −21.5853 −0.845345
\(653\) −2.32307 −0.0909086 −0.0454543 0.998966i \(-0.514474\pi\)
−0.0454543 + 0.998966i \(0.514474\pi\)
\(654\) −7.53303 −0.294565
\(655\) −31.2115 −1.21954
\(656\) 2.14068 0.0835796
\(657\) 2.21094 0.0862568
\(658\) −3.31502 −0.129233
\(659\) 4.07928 0.158906 0.0794532 0.996839i \(-0.474683\pi\)
0.0794532 + 0.996839i \(0.474683\pi\)
\(660\) 3.23897 0.126077
\(661\) −42.2740 −1.64427 −0.822135 0.569293i \(-0.807217\pi\)
−0.822135 + 0.569293i \(0.807217\pi\)
\(662\) −3.36489 −0.130780
\(663\) 0 0
\(664\) 31.0467 1.20485
\(665\) −15.0395 −0.583209
\(666\) 1.21727 0.0471684
\(667\) −3.54270 −0.137174
\(668\) −23.2574 −0.899854
\(669\) −27.7784 −1.07398
\(670\) −9.67809 −0.373897
\(671\) −5.38195 −0.207768
\(672\) −8.28806 −0.319719
\(673\) −10.6688 −0.411252 −0.205626 0.978631i \(-0.565923\pi\)
−0.205626 + 0.978631i \(0.565923\pi\)
\(674\) −6.38840 −0.246072
\(675\) −1.18383 −0.0455655
\(676\) 0 0
\(677\) 24.2174 0.930752 0.465376 0.885113i \(-0.345919\pi\)
0.465376 + 0.885113i \(0.345919\pi\)
\(678\) 7.38419 0.283588
\(679\) 21.9193 0.841185
\(680\) −14.3834 −0.551578
\(681\) 28.6524 1.09796
\(682\) −4.25109 −0.162783
\(683\) 37.1698 1.42226 0.711132 0.703059i \(-0.248183\pi\)
0.711132 + 0.703059i \(0.248183\pi\)
\(684\) −8.44913 −0.323060
\(685\) 33.7139 1.28814
\(686\) 10.3521 0.395246
\(687\) 4.83459 0.184451
\(688\) −11.3306 −0.431976
\(689\) 0 0
\(690\) −0.801497 −0.0305125
\(691\) −15.9632 −0.607268 −0.303634 0.952789i \(-0.598200\pi\)
−0.303634 + 0.952789i \(0.598200\pi\)
\(692\) −29.6248 −1.12617
\(693\) 1.51078 0.0573899
\(694\) −9.55959 −0.362877
\(695\) 11.1456 0.422777
\(696\) 10.8013 0.409423
\(697\) 3.56788 0.135143
\(698\) −5.04522 −0.190965
\(699\) 13.6237 0.515295
\(700\) 2.96540 0.112082
\(701\) −2.01736 −0.0761947 −0.0380974 0.999274i \(-0.512130\pi\)
−0.0380974 + 0.999274i \(0.512130\pi\)
\(702\) 0 0
\(703\) −10.6076 −0.400072
\(704\) −0.922236 −0.0347581
\(705\) −7.33004 −0.276065
\(706\) −9.69519 −0.364883
\(707\) 13.0501 0.490801
\(708\) 4.39417 0.165143
\(709\) −29.6428 −1.11326 −0.556629 0.830761i \(-0.687905\pi\)
−0.556629 + 0.830761i \(0.687905\pi\)
\(710\) −2.64495 −0.0992634
\(711\) −5.54589 −0.207987
\(712\) −3.87112 −0.145076
\(713\) −5.10041 −0.191012
\(714\) −3.04090 −0.113803
\(715\) 0 0
\(716\) −28.6380 −1.07025
\(717\) −5.99903 −0.224038
\(718\) 9.07770 0.338777
\(719\) 32.3389 1.20604 0.603018 0.797728i \(-0.293965\pi\)
0.603018 + 0.797728i \(0.293965\pi\)
\(720\) −4.03427 −0.150348
\(721\) −4.38199 −0.163194
\(722\) −4.07467 −0.151643
\(723\) −12.9290 −0.480835
\(724\) −6.13999 −0.228191
\(725\) −5.97758 −0.222002
\(726\) −0.584778 −0.0217032
\(727\) 37.9325 1.40684 0.703419 0.710775i \(-0.251656\pi\)
0.703419 + 0.710775i \(0.251656\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 2.52570 0.0934803
\(731\) −18.8847 −0.698478
\(732\) 8.92346 0.329821
\(733\) −16.7917 −0.620217 −0.310109 0.950701i \(-0.600365\pi\)
−0.310109 + 0.950701i \(0.600365\pi\)
\(734\) −13.7237 −0.506550
\(735\) 9.21571 0.339927
\(736\) 3.84899 0.141876
\(737\) −8.47197 −0.312069
\(738\) −0.606168 −0.0223133
\(739\) −25.4629 −0.936668 −0.468334 0.883551i \(-0.655146\pi\)
−0.468334 + 0.883551i \(0.655146\pi\)
\(740\) −6.74225 −0.247850
\(741\) 0 0
\(742\) 0.444164 0.0163058
\(743\) −4.81269 −0.176560 −0.0882802 0.996096i \(-0.528137\pi\)
−0.0882802 + 0.996096i \(0.528137\pi\)
\(744\) 15.5506 0.570114
\(745\) 0.314543 0.0115240
\(746\) −7.20574 −0.263821
\(747\) 14.5137 0.531027
\(748\) −5.70692 −0.208666
\(749\) −3.46324 −0.126544
\(750\) −7.06420 −0.257948
\(751\) −24.9537 −0.910574 −0.455287 0.890345i \(-0.650463\pi\)
−0.455287 + 0.890345i \(0.650463\pi\)
\(752\) 7.74895 0.282575
\(753\) −23.9724 −0.873603
\(754\) 0 0
\(755\) −31.8629 −1.15961
\(756\) −2.50493 −0.0911035
\(757\) −33.8373 −1.22984 −0.614919 0.788591i \(-0.710811\pi\)
−0.614919 + 0.788591i \(0.710811\pi\)
\(758\) 13.3736 0.485752
\(759\) −0.701611 −0.0254669
\(760\) −21.2947 −0.772440
\(761\) 50.5981 1.83418 0.917091 0.398679i \(-0.130531\pi\)
0.917091 + 0.398679i \(0.130531\pi\)
\(762\) −2.95363 −0.106999
\(763\) 19.4617 0.704561
\(764\) 34.1984 1.23725
\(765\) −6.72392 −0.243104
\(766\) 20.7748 0.750624
\(767\) 0 0
\(768\) −4.88701 −0.176345
\(769\) −26.1333 −0.942389 −0.471195 0.882029i \(-0.656177\pi\)
−0.471195 + 0.882029i \(0.656177\pi\)
\(770\) 1.72587 0.0621960
\(771\) 16.3441 0.588618
\(772\) −31.2497 −1.12470
\(773\) 0.778578 0.0280035 0.0140018 0.999902i \(-0.495543\pi\)
0.0140018 + 0.999902i \(0.495543\pi\)
\(774\) 3.20844 0.115325
\(775\) −8.60591 −0.309133
\(776\) 31.0358 1.11412
\(777\) −3.14485 −0.112821
\(778\) 1.56179 0.0559930
\(779\) 5.28226 0.189257
\(780\) 0 0
\(781\) −2.31533 −0.0828490
\(782\) 1.41220 0.0505002
\(783\) 5.04937 0.180450
\(784\) −9.74239 −0.347942
\(785\) 27.7772 0.991411
\(786\) −9.34313 −0.333258
\(787\) −33.9128 −1.20886 −0.604431 0.796658i \(-0.706599\pi\)
−0.604431 + 0.796658i \(0.706599\pi\)
\(788\) 11.9108 0.424305
\(789\) 10.1510 0.361384
\(790\) −6.33544 −0.225405
\(791\) −19.0772 −0.678306
\(792\) 2.13914 0.0760110
\(793\) 0 0
\(794\) 21.3097 0.756252
\(795\) 0.982117 0.0348321
\(796\) 31.4349 1.11418
\(797\) 26.9305 0.953928 0.476964 0.878923i \(-0.341737\pi\)
0.476964 + 0.878923i \(0.341737\pi\)
\(798\) −4.50207 −0.159372
\(799\) 12.9152 0.456906
\(800\) 6.49439 0.229611
\(801\) −1.80966 −0.0639413
\(802\) −7.98789 −0.282062
\(803\) 2.21094 0.0780223
\(804\) 14.0468 0.495393
\(805\) 2.07068 0.0729819
\(806\) 0 0
\(807\) 16.5294 0.581862
\(808\) 18.4779 0.650049
\(809\) 52.4814 1.84515 0.922575 0.385819i \(-0.126081\pi\)
0.922575 + 0.385819i \(0.126081\pi\)
\(810\) 1.14237 0.0401387
\(811\) 19.2236 0.675033 0.337516 0.941320i \(-0.390413\pi\)
0.337516 + 0.941320i \(0.390413\pi\)
\(812\) −12.6483 −0.443869
\(813\) 20.8927 0.732739
\(814\) 1.21727 0.0426655
\(815\) −25.4319 −0.890840
\(816\) 7.10819 0.248836
\(817\) −27.9590 −0.978160
\(818\) −15.1169 −0.528551
\(819\) 0 0
\(820\) 3.35744 0.117247
\(821\) 30.4099 1.06131 0.530657 0.847587i \(-0.321945\pi\)
0.530657 + 0.847587i \(0.321945\pi\)
\(822\) 10.0922 0.352006
\(823\) 16.1575 0.563216 0.281608 0.959530i \(-0.409132\pi\)
0.281608 + 0.959530i \(0.409132\pi\)
\(824\) −6.20452 −0.216145
\(825\) −1.18383 −0.0412155
\(826\) 2.34141 0.0814681
\(827\) −47.5066 −1.65197 −0.825983 0.563695i \(-0.809379\pi\)
−0.825983 + 0.563695i \(0.809379\pi\)
\(828\) 1.16330 0.0404273
\(829\) 56.6932 1.96904 0.984519 0.175278i \(-0.0560825\pi\)
0.984519 + 0.175278i \(0.0560825\pi\)
\(830\) 16.5799 0.575497
\(831\) −17.3070 −0.600372
\(832\) 0 0
\(833\) −16.2376 −0.562601
\(834\) 3.33642 0.115531
\(835\) −27.4019 −0.948283
\(836\) −8.44913 −0.292219
\(837\) 7.26957 0.251273
\(838\) −13.2199 −0.456674
\(839\) 35.2293 1.21625 0.608125 0.793841i \(-0.291922\pi\)
0.608125 + 0.793841i \(0.291922\pi\)
\(840\) −6.31329 −0.217829
\(841\) −3.50384 −0.120822
\(842\) −14.4393 −0.497610
\(843\) −16.0666 −0.553361
\(844\) 33.1468 1.14096
\(845\) 0 0
\(846\) −2.19424 −0.0754394
\(847\) 1.51078 0.0519112
\(848\) −1.03824 −0.0356535
\(849\) −17.2180 −0.590919
\(850\) 2.38280 0.0817294
\(851\) 1.46047 0.0500644
\(852\) 3.83890 0.131518
\(853\) 18.7185 0.640909 0.320454 0.947264i \(-0.396164\pi\)
0.320454 + 0.947264i \(0.396164\pi\)
\(854\) 4.75482 0.162706
\(855\) −9.95480 −0.340447
\(856\) −4.90365 −0.167603
\(857\) 47.3032 1.61585 0.807924 0.589287i \(-0.200591\pi\)
0.807924 + 0.589287i \(0.200591\pi\)
\(858\) 0 0
\(859\) −40.6908 −1.38835 −0.694176 0.719805i \(-0.744231\pi\)
−0.694176 + 0.719805i \(0.744231\pi\)
\(860\) −17.7709 −0.605984
\(861\) 1.56604 0.0533706
\(862\) −17.6092 −0.599772
\(863\) −1.42374 −0.0484647 −0.0242324 0.999706i \(-0.507714\pi\)
−0.0242324 + 0.999706i \(0.507714\pi\)
\(864\) −5.48593 −0.186635
\(865\) −34.9041 −1.18678
\(866\) −18.0931 −0.614830
\(867\) −5.15277 −0.174997
\(868\) −18.2098 −0.618080
\(869\) −5.54589 −0.188131
\(870\) 5.76823 0.195561
\(871\) 0 0
\(872\) 27.5561 0.933166
\(873\) 14.5085 0.491040
\(874\) 2.09077 0.0707213
\(875\) 18.2505 0.616978
\(876\) −3.66581 −0.123856
\(877\) 56.1060 1.89457 0.947283 0.320397i \(-0.103816\pi\)
0.947283 + 0.320397i \(0.103816\pi\)
\(878\) 4.10607 0.138573
\(879\) 5.29670 0.178653
\(880\) −4.03427 −0.135995
\(881\) 16.2234 0.546581 0.273290 0.961932i \(-0.411888\pi\)
0.273290 + 0.961932i \(0.411888\pi\)
\(882\) 2.75871 0.0928906
\(883\) −33.0296 −1.11153 −0.555767 0.831338i \(-0.687575\pi\)
−0.555767 + 0.831338i \(0.687575\pi\)
\(884\) 0 0
\(885\) 5.17723 0.174031
\(886\) 13.1815 0.442843
\(887\) −54.6149 −1.83379 −0.916894 0.399130i \(-0.869312\pi\)
−0.916894 + 0.399130i \(0.869312\pi\)
\(888\) −4.45283 −0.149427
\(889\) 7.63074 0.255927
\(890\) −2.06730 −0.0692960
\(891\) 1.00000 0.0335013
\(892\) 46.0576 1.54212
\(893\) 19.1210 0.639860
\(894\) 0.0941580 0.00314911
\(895\) −33.7414 −1.12785
\(896\) 17.3909 0.580989
\(897\) 0 0
\(898\) 5.50668 0.183760
\(899\) 36.7068 1.22424
\(900\) 1.96282 0.0654275
\(901\) −1.73044 −0.0576494
\(902\) −0.606168 −0.0201832
\(903\) −8.28906 −0.275843
\(904\) −27.0116 −0.898393
\(905\) −7.23417 −0.240472
\(906\) −9.53812 −0.316883
\(907\) 31.1937 1.03577 0.517884 0.855451i \(-0.326720\pi\)
0.517884 + 0.855451i \(0.326720\pi\)
\(908\) −47.5066 −1.57656
\(909\) 8.63799 0.286504
\(910\) 0 0
\(911\) 53.7300 1.78015 0.890077 0.455810i \(-0.150650\pi\)
0.890077 + 0.455810i \(0.150650\pi\)
\(912\) 10.5237 0.348475
\(913\) 14.5137 0.480332
\(914\) 2.03907 0.0674464
\(915\) 10.5137 0.347571
\(916\) −8.01592 −0.264853
\(917\) 24.1381 0.797111
\(918\) −2.01280 −0.0664322
\(919\) 16.3202 0.538353 0.269177 0.963091i \(-0.413248\pi\)
0.269177 + 0.963091i \(0.413248\pi\)
\(920\) 2.93190 0.0966620
\(921\) 26.3020 0.866680
\(922\) −8.88764 −0.292699
\(923\) 0 0
\(924\) −2.50493 −0.0824062
\(925\) 2.46425 0.0810241
\(926\) −9.34956 −0.307246
\(927\) −2.90048 −0.0952641
\(928\) −27.7005 −0.909314
\(929\) 56.4975 1.85362 0.926811 0.375527i \(-0.122538\pi\)
0.926811 + 0.375527i \(0.122538\pi\)
\(930\) 8.30451 0.272316
\(931\) −24.0399 −0.787877
\(932\) −22.5885 −0.739912
\(933\) 32.8590 1.07576
\(934\) −19.2524 −0.629957
\(935\) −6.72392 −0.219896
\(936\) 0 0
\(937\) 52.5328 1.71617 0.858086 0.513506i \(-0.171654\pi\)
0.858086 + 0.513506i \(0.171654\pi\)
\(938\) 7.48476 0.244386
\(939\) 33.2130 1.08387
\(940\) 12.1535 0.396402
\(941\) 24.3963 0.795296 0.397648 0.917538i \(-0.369826\pi\)
0.397648 + 0.917538i \(0.369826\pi\)
\(942\) 8.31507 0.270920
\(943\) −0.727273 −0.0236833
\(944\) −5.47311 −0.178135
\(945\) −2.95132 −0.0960065
\(946\) 3.20844 0.104315
\(947\) −38.9960 −1.26720 −0.633600 0.773661i \(-0.718423\pi\)
−0.633600 + 0.773661i \(0.718423\pi\)
\(948\) 9.19527 0.298648
\(949\) 0 0
\(950\) 3.52775 0.114455
\(951\) 30.8436 1.00017
\(952\) 11.1237 0.360522
\(953\) −30.9120 −1.00134 −0.500670 0.865638i \(-0.666913\pi\)
−0.500670 + 0.865638i \(0.666913\pi\)
\(954\) 0.293995 0.00951845
\(955\) 40.2927 1.30384
\(956\) 9.94660 0.321696
\(957\) 5.04937 0.163223
\(958\) −19.6499 −0.634859
\(959\) −26.0734 −0.841953
\(960\) 1.80159 0.0581461
\(961\) 21.8467 0.704731
\(962\) 0 0
\(963\) −2.29234 −0.0738698
\(964\) 21.4367 0.690431
\(965\) −36.8186 −1.18523
\(966\) 0.619855 0.0199435
\(967\) −31.5859 −1.01573 −0.507867 0.861435i \(-0.669566\pi\)
−0.507867 + 0.861435i \(0.669566\pi\)
\(968\) 2.13914 0.0687546
\(969\) 17.5399 0.563462
\(970\) 16.5741 0.532162
\(971\) −32.5555 −1.04476 −0.522378 0.852714i \(-0.674955\pi\)
−0.522378 + 0.852714i \(0.674955\pi\)
\(972\) −1.65803 −0.0531815
\(973\) −8.61969 −0.276335
\(974\) −2.16368 −0.0693289
\(975\) 0 0
\(976\) −11.1145 −0.355767
\(977\) −3.54984 −0.113569 −0.0567847 0.998386i \(-0.518085\pi\)
−0.0567847 + 0.998386i \(0.518085\pi\)
\(978\) −7.61300 −0.243437
\(979\) −1.80966 −0.0578371
\(980\) −15.2800 −0.488101
\(981\) 12.8818 0.411286
\(982\) 5.92949 0.189218
\(983\) −16.6279 −0.530349 −0.265174 0.964200i \(-0.585430\pi\)
−0.265174 + 0.964200i \(0.585430\pi\)
\(984\) 2.21738 0.0706875
\(985\) 14.0334 0.447141
\(986\) −10.1634 −0.323667
\(987\) 5.66884 0.180441
\(988\) 0 0
\(989\) 3.84946 0.122406
\(990\) 1.14237 0.0363068
\(991\) 36.4447 1.15770 0.578852 0.815433i \(-0.303501\pi\)
0.578852 + 0.815433i \(0.303501\pi\)
\(992\) −39.8804 −1.26620
\(993\) 5.75414 0.182602
\(994\) 2.04553 0.0648804
\(995\) 37.0367 1.17414
\(996\) −24.0641 −0.762502
\(997\) −2.23772 −0.0708692 −0.0354346 0.999372i \(-0.511282\pi\)
−0.0354346 + 0.999372i \(0.511282\pi\)
\(998\) 8.83742 0.279744
\(999\) −2.08160 −0.0658589
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 5577.2.a.y.1.3 7
13.5 odd 4 429.2.b.b.298.9 yes 14
13.8 odd 4 429.2.b.b.298.6 14
13.12 even 2 5577.2.a.x.1.5 7
39.5 even 4 1287.2.b.c.298.6 14
39.8 even 4 1287.2.b.c.298.9 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.6 14 13.8 odd 4
429.2.b.b.298.9 yes 14 13.5 odd 4
1287.2.b.c.298.6 14 39.5 even 4
1287.2.b.c.298.9 14 39.8 even 4
5577.2.a.x.1.5 7 13.12 even 2
5577.2.a.y.1.3 7 1.1 even 1 trivial