Properties

Label 4527.2.a.k.1.9
Level $4527$
Weight $2$
Character 4527.1
Self dual yes
Analytic conductor $36.148$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4527 = 3^{2} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4527.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.1482769950\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - 9 x^{8} + 14 x^{7} + 27 x^{6} - 27 x^{5} - 34 x^{4} + 14 x^{3} + 17 x^{2} + x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 503)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.78533\) of defining polynomial
Character \(\chi\) \(=\) 4527.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.03947 q^{2} +2.15945 q^{4} +0.701114 q^{5} -2.02991 q^{7} +0.325186 q^{8} +O(q^{10})\) \(q+2.03947 q^{2} +2.15945 q^{4} +0.701114 q^{5} -2.02991 q^{7} +0.325186 q^{8} +1.42990 q^{10} +0.626970 q^{11} -2.93743 q^{13} -4.13995 q^{14} -3.65568 q^{16} +2.71003 q^{17} -1.11114 q^{19} +1.51402 q^{20} +1.27869 q^{22} +0.412395 q^{23} -4.50844 q^{25} -5.99081 q^{26} -4.38349 q^{28} -6.46349 q^{29} -4.14074 q^{31} -8.10604 q^{32} +5.52704 q^{34} -1.42320 q^{35} +2.98634 q^{37} -2.26613 q^{38} +0.227992 q^{40} +0.135430 q^{41} -0.861393 q^{43} +1.35391 q^{44} +0.841067 q^{46} -1.67307 q^{47} -2.87945 q^{49} -9.19483 q^{50} -6.34323 q^{52} +8.51721 q^{53} +0.439578 q^{55} -0.660099 q^{56} -13.1821 q^{58} +0.406685 q^{59} -8.53132 q^{61} -8.44492 q^{62} -9.22067 q^{64} -2.05948 q^{65} -13.0293 q^{67} +5.85217 q^{68} -2.90258 q^{70} -2.78095 q^{71} -2.11734 q^{73} +6.09055 q^{74} -2.39944 q^{76} -1.27270 q^{77} -0.317368 q^{79} -2.56305 q^{80} +0.276205 q^{82} +5.05120 q^{83} +1.90004 q^{85} -1.75679 q^{86} +0.203882 q^{88} -16.4699 q^{89} +5.96273 q^{91} +0.890544 q^{92} -3.41218 q^{94} -0.779033 q^{95} +7.68873 q^{97} -5.87256 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 4q^{2} + 4q^{4} + q^{5} - 5q^{7} + 3q^{8} + O(q^{10}) \) \( 10q + 4q^{2} + 4q^{4} + q^{5} - 5q^{7} + 3q^{8} - 4q^{10} + 3q^{11} - 18q^{13} - q^{14} - 4q^{16} + 11q^{17} + 3q^{20} - 18q^{22} + 2q^{23} - 27q^{25} - 11q^{26} - 22q^{28} + 9q^{29} - 22q^{31} + 10q^{32} - 10q^{34} + 6q^{35} - 35q^{37} - 2q^{38} - 19q^{40} + 4q^{41} - 20q^{43} - 9q^{44} - q^{46} - 7q^{47} - 27q^{49} - 16q^{50} - 7q^{52} + 24q^{53} - 11q^{55} - 12q^{56} + 2q^{58} - 17q^{59} - 4q^{61} - 8q^{62} + 3q^{64} + 16q^{65} - 6q^{67} - 28q^{68} + 26q^{70} + q^{71} - 31q^{73} - 11q^{74} + 20q^{76} - 3q^{77} - 10q^{79} - 24q^{80} - 9q^{82} - 22q^{83} - 6q^{85} - 38q^{86} - 3q^{88} - q^{89} + 10q^{91} - 27q^{92} + 33q^{94} - 39q^{95} - 57q^{97} - 40q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.03947 1.44212 0.721062 0.692870i \(-0.243654\pi\)
0.721062 + 0.692870i \(0.243654\pi\)
\(3\) 0 0
\(4\) 2.15945 1.07972
\(5\) 0.701114 0.313548 0.156774 0.987635i \(-0.449891\pi\)
0.156774 + 0.987635i \(0.449891\pi\)
\(6\) 0 0
\(7\) −2.02991 −0.767235 −0.383618 0.923492i \(-0.625322\pi\)
−0.383618 + 0.923492i \(0.625322\pi\)
\(8\) 0.325186 0.114971
\(9\) 0 0
\(10\) 1.42990 0.452175
\(11\) 0.626970 0.189039 0.0945194 0.995523i \(-0.469869\pi\)
0.0945194 + 0.995523i \(0.469869\pi\)
\(12\) 0 0
\(13\) −2.93743 −0.814697 −0.407349 0.913273i \(-0.633547\pi\)
−0.407349 + 0.913273i \(0.633547\pi\)
\(14\) −4.13995 −1.10645
\(15\) 0 0
\(16\) −3.65568 −0.913921
\(17\) 2.71003 0.657280 0.328640 0.944455i \(-0.393410\pi\)
0.328640 + 0.944455i \(0.393410\pi\)
\(18\) 0 0
\(19\) −1.11114 −0.254912 −0.127456 0.991844i \(-0.540681\pi\)
−0.127456 + 0.991844i \(0.540681\pi\)
\(20\) 1.51402 0.338545
\(21\) 0 0
\(22\) 1.27869 0.272617
\(23\) 0.412395 0.0859902 0.0429951 0.999075i \(-0.486310\pi\)
0.0429951 + 0.999075i \(0.486310\pi\)
\(24\) 0 0
\(25\) −4.50844 −0.901688
\(26\) −5.99081 −1.17489
\(27\) 0 0
\(28\) −4.38349 −0.828402
\(29\) −6.46349 −1.20024 −0.600120 0.799910i \(-0.704880\pi\)
−0.600120 + 0.799910i \(0.704880\pi\)
\(30\) 0 0
\(31\) −4.14074 −0.743698 −0.371849 0.928293i \(-0.621276\pi\)
−0.371849 + 0.928293i \(0.621276\pi\)
\(32\) −8.10604 −1.43296
\(33\) 0 0
\(34\) 5.52704 0.947879
\(35\) −1.42320 −0.240565
\(36\) 0 0
\(37\) 2.98634 0.490951 0.245475 0.969403i \(-0.421056\pi\)
0.245475 + 0.969403i \(0.421056\pi\)
\(38\) −2.26613 −0.367615
\(39\) 0 0
\(40\) 0.227992 0.0360488
\(41\) 0.135430 0.0211505 0.0105753 0.999944i \(-0.496634\pi\)
0.0105753 + 0.999944i \(0.496634\pi\)
\(42\) 0 0
\(43\) −0.861393 −0.131361 −0.0656806 0.997841i \(-0.520922\pi\)
−0.0656806 + 0.997841i \(0.520922\pi\)
\(44\) 1.35391 0.204109
\(45\) 0 0
\(46\) 0.841067 0.124009
\(47\) −1.67307 −0.244043 −0.122021 0.992527i \(-0.538938\pi\)
−0.122021 + 0.992527i \(0.538938\pi\)
\(48\) 0 0
\(49\) −2.87945 −0.411350
\(50\) −9.19483 −1.30035
\(51\) 0 0
\(52\) −6.34323 −0.879647
\(53\) 8.51721 1.16993 0.584964 0.811059i \(-0.301108\pi\)
0.584964 + 0.811059i \(0.301108\pi\)
\(54\) 0 0
\(55\) 0.439578 0.0592727
\(56\) −0.660099 −0.0882095
\(57\) 0 0
\(58\) −13.1821 −1.73089
\(59\) 0.406685 0.0529459 0.0264729 0.999650i \(-0.491572\pi\)
0.0264729 + 0.999650i \(0.491572\pi\)
\(60\) 0 0
\(61\) −8.53132 −1.09232 −0.546162 0.837680i \(-0.683912\pi\)
−0.546162 + 0.837680i \(0.683912\pi\)
\(62\) −8.44492 −1.07251
\(63\) 0 0
\(64\) −9.22067 −1.15258
\(65\) −2.05948 −0.255446
\(66\) 0 0
\(67\) −13.0293 −1.59178 −0.795889 0.605443i \(-0.792996\pi\)
−0.795889 + 0.605443i \(0.792996\pi\)
\(68\) 5.85217 0.709680
\(69\) 0 0
\(70\) −2.90258 −0.346925
\(71\) −2.78095 −0.330039 −0.165019 0.986290i \(-0.552769\pi\)
−0.165019 + 0.986290i \(0.552769\pi\)
\(72\) 0 0
\(73\) −2.11734 −0.247816 −0.123908 0.992294i \(-0.539543\pi\)
−0.123908 + 0.992294i \(0.539543\pi\)
\(74\) 6.09055 0.708012
\(75\) 0 0
\(76\) −2.39944 −0.275234
\(77\) −1.27270 −0.145037
\(78\) 0 0
\(79\) −0.317368 −0.0357067 −0.0178534 0.999841i \(-0.505683\pi\)
−0.0178534 + 0.999841i \(0.505683\pi\)
\(80\) −2.56305 −0.286558
\(81\) 0 0
\(82\) 0.276205 0.0305017
\(83\) 5.05120 0.554442 0.277221 0.960806i \(-0.410587\pi\)
0.277221 + 0.960806i \(0.410587\pi\)
\(84\) 0 0
\(85\) 1.90004 0.206089
\(86\) −1.75679 −0.189439
\(87\) 0 0
\(88\) 0.203882 0.0217339
\(89\) −16.4699 −1.74580 −0.872901 0.487897i \(-0.837764\pi\)
−0.872901 + 0.487897i \(0.837764\pi\)
\(90\) 0 0
\(91\) 5.96273 0.625064
\(92\) 0.890544 0.0928456
\(93\) 0 0
\(94\) −3.41218 −0.351940
\(95\) −0.779033 −0.0799271
\(96\) 0 0
\(97\) 7.68873 0.780673 0.390336 0.920672i \(-0.372359\pi\)
0.390336 + 0.920672i \(0.372359\pi\)
\(98\) −5.87256 −0.593218
\(99\) 0 0
\(100\) −9.73573 −0.973573
\(101\) 0.549020 0.0546296 0.0273148 0.999627i \(-0.491304\pi\)
0.0273148 + 0.999627i \(0.491304\pi\)
\(102\) 0 0
\(103\) 1.32758 0.130810 0.0654051 0.997859i \(-0.479166\pi\)
0.0654051 + 0.997859i \(0.479166\pi\)
\(104\) −0.955211 −0.0936662
\(105\) 0 0
\(106\) 17.3706 1.68718
\(107\) −2.57528 −0.248961 −0.124481 0.992222i \(-0.539726\pi\)
−0.124481 + 0.992222i \(0.539726\pi\)
\(108\) 0 0
\(109\) 8.89011 0.851518 0.425759 0.904837i \(-0.360007\pi\)
0.425759 + 0.904837i \(0.360007\pi\)
\(110\) 0.896507 0.0854786
\(111\) 0 0
\(112\) 7.42072 0.701192
\(113\) 1.91987 0.180606 0.0903032 0.995914i \(-0.471216\pi\)
0.0903032 + 0.995914i \(0.471216\pi\)
\(114\) 0 0
\(115\) 0.289136 0.0269621
\(116\) −13.9576 −1.29593
\(117\) 0 0
\(118\) 0.829423 0.0763546
\(119\) −5.50114 −0.504288
\(120\) 0 0
\(121\) −10.6069 −0.964264
\(122\) −17.3994 −1.57527
\(123\) 0 0
\(124\) −8.94170 −0.802988
\(125\) −6.66650 −0.596270
\(126\) 0 0
\(127\) 21.8010 1.93452 0.967261 0.253782i \(-0.0816746\pi\)
0.967261 + 0.253782i \(0.0816746\pi\)
\(128\) −2.59322 −0.229210
\(129\) 0 0
\(130\) −4.20024 −0.368386
\(131\) −8.78145 −0.767239 −0.383620 0.923491i \(-0.625323\pi\)
−0.383620 + 0.923491i \(0.625323\pi\)
\(132\) 0 0
\(133\) 2.25551 0.195577
\(134\) −26.5728 −2.29554
\(135\) 0 0
\(136\) 0.881265 0.0755678
\(137\) 4.26127 0.364065 0.182032 0.983293i \(-0.441732\pi\)
0.182032 + 0.983293i \(0.441732\pi\)
\(138\) 0 0
\(139\) 13.4951 1.14464 0.572321 0.820030i \(-0.306043\pi\)
0.572321 + 0.820030i \(0.306043\pi\)
\(140\) −3.07333 −0.259743
\(141\) 0 0
\(142\) −5.67168 −0.475957
\(143\) −1.84168 −0.154009
\(144\) 0 0
\(145\) −4.53164 −0.376332
\(146\) −4.31826 −0.357382
\(147\) 0 0
\(148\) 6.44884 0.530091
\(149\) −11.2453 −0.921253 −0.460626 0.887594i \(-0.652375\pi\)
−0.460626 + 0.887594i \(0.652375\pi\)
\(150\) 0 0
\(151\) −2.36107 −0.192141 −0.0960705 0.995375i \(-0.530627\pi\)
−0.0960705 + 0.995375i \(0.530627\pi\)
\(152\) −0.361325 −0.0293074
\(153\) 0 0
\(154\) −2.59563 −0.209162
\(155\) −2.90313 −0.233185
\(156\) 0 0
\(157\) −17.5242 −1.39859 −0.699293 0.714835i \(-0.746502\pi\)
−0.699293 + 0.714835i \(0.746502\pi\)
\(158\) −0.647264 −0.0514936
\(159\) 0 0
\(160\) −5.68326 −0.449301
\(161\) −0.837126 −0.0659747
\(162\) 0 0
\(163\) −7.12153 −0.557801 −0.278901 0.960320i \(-0.589970\pi\)
−0.278901 + 0.960320i \(0.589970\pi\)
\(164\) 0.292453 0.0228367
\(165\) 0 0
\(166\) 10.3018 0.799574
\(167\) −4.56080 −0.352925 −0.176463 0.984307i \(-0.556465\pi\)
−0.176463 + 0.984307i \(0.556465\pi\)
\(168\) 0 0
\(169\) −4.37149 −0.336269
\(170\) 3.87509 0.297206
\(171\) 0 0
\(172\) −1.86013 −0.141834
\(173\) −2.91357 −0.221514 −0.110757 0.993847i \(-0.535328\pi\)
−0.110757 + 0.993847i \(0.535328\pi\)
\(174\) 0 0
\(175\) 9.15174 0.691807
\(176\) −2.29201 −0.172766
\(177\) 0 0
\(178\) −33.5898 −2.51766
\(179\) 9.01141 0.673544 0.336772 0.941586i \(-0.390665\pi\)
0.336772 + 0.941586i \(0.390665\pi\)
\(180\) 0 0
\(181\) 14.4065 1.07082 0.535412 0.844591i \(-0.320156\pi\)
0.535412 + 0.844591i \(0.320156\pi\)
\(182\) 12.1608 0.901420
\(183\) 0 0
\(184\) 0.134105 0.00988635
\(185\) 2.09376 0.153937
\(186\) 0 0
\(187\) 1.69911 0.124251
\(188\) −3.61291 −0.263499
\(189\) 0 0
\(190\) −1.58882 −0.115265
\(191\) −4.40730 −0.318901 −0.159450 0.987206i \(-0.550972\pi\)
−0.159450 + 0.987206i \(0.550972\pi\)
\(192\) 0 0
\(193\) −2.90027 −0.208766 −0.104383 0.994537i \(-0.533287\pi\)
−0.104383 + 0.994537i \(0.533287\pi\)
\(194\) 15.6810 1.12583
\(195\) 0 0
\(196\) −6.21802 −0.444144
\(197\) −5.91510 −0.421433 −0.210717 0.977547i \(-0.567580\pi\)
−0.210717 + 0.977547i \(0.567580\pi\)
\(198\) 0 0
\(199\) −4.73473 −0.335636 −0.167818 0.985818i \(-0.553672\pi\)
−0.167818 + 0.985818i \(0.553672\pi\)
\(200\) −1.46608 −0.103668
\(201\) 0 0
\(202\) 1.11971 0.0787827
\(203\) 13.1203 0.920866
\(204\) 0 0
\(205\) 0.0949516 0.00663171
\(206\) 2.70756 0.188644
\(207\) 0 0
\(208\) 10.7383 0.744569
\(209\) −0.696649 −0.0481882
\(210\) 0 0
\(211\) −1.50671 −0.103726 −0.0518631 0.998654i \(-0.516516\pi\)
−0.0518631 + 0.998654i \(0.516516\pi\)
\(212\) 18.3925 1.26320
\(213\) 0 0
\(214\) −5.25220 −0.359033
\(215\) −0.603935 −0.0411880
\(216\) 0 0
\(217\) 8.40534 0.570591
\(218\) 18.1311 1.22799
\(219\) 0 0
\(220\) 0.949245 0.0639981
\(221\) −7.96054 −0.535484
\(222\) 0 0
\(223\) −9.79220 −0.655734 −0.327867 0.944724i \(-0.606330\pi\)
−0.327867 + 0.944724i \(0.606330\pi\)
\(224\) 16.4546 1.09942
\(225\) 0 0
\(226\) 3.91552 0.260457
\(227\) −6.88512 −0.456981 −0.228491 0.973546i \(-0.573379\pi\)
−0.228491 + 0.973546i \(0.573379\pi\)
\(228\) 0 0
\(229\) 12.1880 0.805405 0.402703 0.915331i \(-0.368071\pi\)
0.402703 + 0.915331i \(0.368071\pi\)
\(230\) 0.589684 0.0388826
\(231\) 0 0
\(232\) −2.10183 −0.137992
\(233\) 21.0547 1.37934 0.689669 0.724125i \(-0.257756\pi\)
0.689669 + 0.724125i \(0.257756\pi\)
\(234\) 0 0
\(235\) −1.17301 −0.0765190
\(236\) 0.878215 0.0571669
\(237\) 0 0
\(238\) −11.2194 −0.727247
\(239\) −9.11944 −0.589888 −0.294944 0.955515i \(-0.595301\pi\)
−0.294944 + 0.955515i \(0.595301\pi\)
\(240\) 0 0
\(241\) 22.7352 1.46450 0.732252 0.681034i \(-0.238469\pi\)
0.732252 + 0.681034i \(0.238469\pi\)
\(242\) −21.6325 −1.39059
\(243\) 0 0
\(244\) −18.4229 −1.17941
\(245\) −2.01882 −0.128978
\(246\) 0 0
\(247\) 3.26388 0.207676
\(248\) −1.34651 −0.0855034
\(249\) 0 0
\(250\) −13.5961 −0.859896
\(251\) 11.6824 0.737385 0.368692 0.929551i \(-0.379806\pi\)
0.368692 + 0.929551i \(0.379806\pi\)
\(252\) 0 0
\(253\) 0.258559 0.0162555
\(254\) 44.4625 2.78982
\(255\) 0 0
\(256\) 13.1525 0.822034
\(257\) 16.3010 1.01683 0.508415 0.861112i \(-0.330232\pi\)
0.508415 + 0.861112i \(0.330232\pi\)
\(258\) 0 0
\(259\) −6.06201 −0.376675
\(260\) −4.44733 −0.275811
\(261\) 0 0
\(262\) −17.9095 −1.10645
\(263\) 15.7955 0.973993 0.486996 0.873404i \(-0.338093\pi\)
0.486996 + 0.873404i \(0.338093\pi\)
\(264\) 0 0
\(265\) 5.97154 0.366829
\(266\) 4.60005 0.282047
\(267\) 0 0
\(268\) −28.1360 −1.71868
\(269\) −11.2401 −0.685323 −0.342662 0.939459i \(-0.611328\pi\)
−0.342662 + 0.939459i \(0.611328\pi\)
\(270\) 0 0
\(271\) 22.7114 1.37962 0.689809 0.723991i \(-0.257694\pi\)
0.689809 + 0.723991i \(0.257694\pi\)
\(272\) −9.90703 −0.600702
\(273\) 0 0
\(274\) 8.69074 0.525027
\(275\) −2.82666 −0.170454
\(276\) 0 0
\(277\) −3.42609 −0.205854 −0.102927 0.994689i \(-0.532821\pi\)
−0.102927 + 0.994689i \(0.532821\pi\)
\(278\) 27.5229 1.65072
\(279\) 0 0
\(280\) −0.462805 −0.0276579
\(281\) 6.41168 0.382488 0.191244 0.981542i \(-0.438748\pi\)
0.191244 + 0.981542i \(0.438748\pi\)
\(282\) 0 0
\(283\) −22.3462 −1.32834 −0.664172 0.747580i \(-0.731216\pi\)
−0.664172 + 0.747580i \(0.731216\pi\)
\(284\) −6.00532 −0.356350
\(285\) 0 0
\(286\) −3.75606 −0.222101
\(287\) −0.274910 −0.0162274
\(288\) 0 0
\(289\) −9.65571 −0.567983
\(290\) −9.24216 −0.542718
\(291\) 0 0
\(292\) −4.57228 −0.267573
\(293\) −4.95366 −0.289396 −0.144698 0.989476i \(-0.546221\pi\)
−0.144698 + 0.989476i \(0.546221\pi\)
\(294\) 0 0
\(295\) 0.285133 0.0166011
\(296\) 0.971115 0.0564449
\(297\) 0 0
\(298\) −22.9345 −1.32856
\(299\) −1.21138 −0.0700560
\(300\) 0 0
\(301\) 1.74855 0.100785
\(302\) −4.81533 −0.277091
\(303\) 0 0
\(304\) 4.06196 0.232969
\(305\) −5.98143 −0.342496
\(306\) 0 0
\(307\) −1.86937 −0.106690 −0.0533452 0.998576i \(-0.516988\pi\)
−0.0533452 + 0.998576i \(0.516988\pi\)
\(308\) −2.74832 −0.156600
\(309\) 0 0
\(310\) −5.92085 −0.336282
\(311\) 4.29662 0.243639 0.121819 0.992552i \(-0.461127\pi\)
0.121819 + 0.992552i \(0.461127\pi\)
\(312\) 0 0
\(313\) −24.2378 −1.37000 −0.684999 0.728544i \(-0.740198\pi\)
−0.684999 + 0.728544i \(0.740198\pi\)
\(314\) −35.7402 −2.01693
\(315\) 0 0
\(316\) −0.685340 −0.0385534
\(317\) 28.1902 1.58332 0.791661 0.610961i \(-0.209217\pi\)
0.791661 + 0.610961i \(0.209217\pi\)
\(318\) 0 0
\(319\) −4.05242 −0.226892
\(320\) −6.46474 −0.361390
\(321\) 0 0
\(322\) −1.70729 −0.0951438
\(323\) −3.01121 −0.167548
\(324\) 0 0
\(325\) 13.2432 0.734602
\(326\) −14.5242 −0.804419
\(327\) 0 0
\(328\) 0.0440398 0.00243169
\(329\) 3.39619 0.187238
\(330\) 0 0
\(331\) 13.5185 0.743046 0.371523 0.928424i \(-0.378836\pi\)
0.371523 + 0.928424i \(0.378836\pi\)
\(332\) 10.9078 0.598644
\(333\) 0 0
\(334\) −9.30162 −0.508962
\(335\) −9.13500 −0.499098
\(336\) 0 0
\(337\) −1.73199 −0.0943475 −0.0471738 0.998887i \(-0.515021\pi\)
−0.0471738 + 0.998887i \(0.515021\pi\)
\(338\) −8.91554 −0.484941
\(339\) 0 0
\(340\) 4.10304 0.222519
\(341\) −2.59612 −0.140588
\(342\) 0 0
\(343\) 20.0544 1.08284
\(344\) −0.280113 −0.0151027
\(345\) 0 0
\(346\) −5.94214 −0.319451
\(347\) 27.7262 1.48842 0.744210 0.667946i \(-0.232826\pi\)
0.744210 + 0.667946i \(0.232826\pi\)
\(348\) 0 0
\(349\) −16.0612 −0.859737 −0.429869 0.902891i \(-0.641440\pi\)
−0.429869 + 0.902891i \(0.641440\pi\)
\(350\) 18.6647 0.997671
\(351\) 0 0
\(352\) −5.08225 −0.270885
\(353\) 16.0011 0.851652 0.425826 0.904805i \(-0.359984\pi\)
0.425826 + 0.904805i \(0.359984\pi\)
\(354\) 0 0
\(355\) −1.94977 −0.103483
\(356\) −35.5658 −1.88498
\(357\) 0 0
\(358\) 18.3785 0.971335
\(359\) −29.2698 −1.54480 −0.772400 0.635136i \(-0.780944\pi\)
−0.772400 + 0.635136i \(0.780944\pi\)
\(360\) 0 0
\(361\) −17.7654 −0.935020
\(362\) 29.3816 1.54426
\(363\) 0 0
\(364\) 12.8762 0.674896
\(365\) −1.48450 −0.0777022
\(366\) 0 0
\(367\) 19.5331 1.01962 0.509810 0.860287i \(-0.329716\pi\)
0.509810 + 0.860287i \(0.329716\pi\)
\(368\) −1.50759 −0.0785883
\(369\) 0 0
\(370\) 4.27017 0.221996
\(371\) −17.2892 −0.897611
\(372\) 0 0
\(373\) −22.0592 −1.14218 −0.571091 0.820887i \(-0.693480\pi\)
−0.571091 + 0.820887i \(0.693480\pi\)
\(374\) 3.46529 0.179186
\(375\) 0 0
\(376\) −0.544059 −0.0280577
\(377\) 18.9861 0.977832
\(378\) 0 0
\(379\) 10.7429 0.551828 0.275914 0.961182i \(-0.411020\pi\)
0.275914 + 0.961182i \(0.411020\pi\)
\(380\) −1.68228 −0.0862991
\(381\) 0 0
\(382\) −8.98856 −0.459895
\(383\) −7.81876 −0.399520 −0.199760 0.979845i \(-0.564016\pi\)
−0.199760 + 0.979845i \(0.564016\pi\)
\(384\) 0 0
\(385\) −0.892305 −0.0454761
\(386\) −5.91502 −0.301067
\(387\) 0 0
\(388\) 16.6034 0.842910
\(389\) 35.0312 1.77615 0.888075 0.459698i \(-0.152043\pi\)
0.888075 + 0.459698i \(0.152043\pi\)
\(390\) 0 0
\(391\) 1.11760 0.0565197
\(392\) −0.936357 −0.0472932
\(393\) 0 0
\(394\) −12.0637 −0.607759
\(395\) −0.222512 −0.0111958
\(396\) 0 0
\(397\) −0.245438 −0.0123182 −0.00615909 0.999981i \(-0.501961\pi\)
−0.00615909 + 0.999981i \(0.501961\pi\)
\(398\) −9.65635 −0.484029
\(399\) 0 0
\(400\) 16.4814 0.824072
\(401\) 16.3434 0.816151 0.408075 0.912948i \(-0.366200\pi\)
0.408075 + 0.912948i \(0.366200\pi\)
\(402\) 0 0
\(403\) 12.1631 0.605889
\(404\) 1.18558 0.0589848
\(405\) 0 0
\(406\) 26.7585 1.32800
\(407\) 1.87235 0.0928087
\(408\) 0 0
\(409\) 4.60893 0.227897 0.113948 0.993487i \(-0.463650\pi\)
0.113948 + 0.993487i \(0.463650\pi\)
\(410\) 0.193651 0.00956375
\(411\) 0 0
\(412\) 2.86683 0.141239
\(413\) −0.825536 −0.0406220
\(414\) 0 0
\(415\) 3.54147 0.173844
\(416\) 23.8109 1.16743
\(417\) 0 0
\(418\) −1.42080 −0.0694934
\(419\) −11.4509 −0.559414 −0.279707 0.960085i \(-0.590237\pi\)
−0.279707 + 0.960085i \(0.590237\pi\)
\(420\) 0 0
\(421\) −22.2626 −1.08501 −0.542505 0.840052i \(-0.682524\pi\)
−0.542505 + 0.840052i \(0.682524\pi\)
\(422\) −3.07289 −0.149586
\(423\) 0 0
\(424\) 2.76968 0.134507
\(425\) −12.2180 −0.592661
\(426\) 0 0
\(427\) 17.3178 0.838069
\(428\) −5.56117 −0.268809
\(429\) 0 0
\(430\) −1.23171 −0.0593982
\(431\) 1.13299 0.0545741 0.0272871 0.999628i \(-0.491313\pi\)
0.0272871 + 0.999628i \(0.491313\pi\)
\(432\) 0 0
\(433\) −2.65692 −0.127683 −0.0638417 0.997960i \(-0.520335\pi\)
−0.0638417 + 0.997960i \(0.520335\pi\)
\(434\) 17.1425 0.822864
\(435\) 0 0
\(436\) 19.1977 0.919403
\(437\) −0.458226 −0.0219199
\(438\) 0 0
\(439\) 6.57228 0.313678 0.156839 0.987624i \(-0.449870\pi\)
0.156839 + 0.987624i \(0.449870\pi\)
\(440\) 0.142945 0.00681461
\(441\) 0 0
\(442\) −16.2353 −0.772235
\(443\) −1.34406 −0.0638583 −0.0319291 0.999490i \(-0.510165\pi\)
−0.0319291 + 0.999490i \(0.510165\pi\)
\(444\) 0 0
\(445\) −11.5473 −0.547393
\(446\) −19.9709 −0.945650
\(447\) 0 0
\(448\) 18.7172 0.884303
\(449\) −26.3410 −1.24311 −0.621555 0.783371i \(-0.713499\pi\)
−0.621555 + 0.783371i \(0.713499\pi\)
\(450\) 0 0
\(451\) 0.0849103 0.00399827
\(452\) 4.14586 0.195005
\(453\) 0 0
\(454\) −14.0420 −0.659024
\(455\) 4.18056 0.195988
\(456\) 0 0
\(457\) −30.0693 −1.40658 −0.703290 0.710903i \(-0.748287\pi\)
−0.703290 + 0.710903i \(0.748287\pi\)
\(458\) 24.8571 1.16149
\(459\) 0 0
\(460\) 0.624373 0.0291115
\(461\) 7.72477 0.359778 0.179889 0.983687i \(-0.442426\pi\)
0.179889 + 0.983687i \(0.442426\pi\)
\(462\) 0 0
\(463\) 7.82961 0.363873 0.181936 0.983310i \(-0.441764\pi\)
0.181936 + 0.983310i \(0.441764\pi\)
\(464\) 23.6285 1.09692
\(465\) 0 0
\(466\) 42.9404 1.98918
\(467\) 7.19623 0.333002 0.166501 0.986041i \(-0.446753\pi\)
0.166501 + 0.986041i \(0.446753\pi\)
\(468\) 0 0
\(469\) 26.4483 1.22127
\(470\) −2.39233 −0.110350
\(471\) 0 0
\(472\) 0.132248 0.00608722
\(473\) −0.540068 −0.0248323
\(474\) 0 0
\(475\) 5.00948 0.229851
\(476\) −11.8794 −0.544492
\(477\) 0 0
\(478\) −18.5988 −0.850691
\(479\) 12.1955 0.557229 0.278614 0.960403i \(-0.410125\pi\)
0.278614 + 0.960403i \(0.410125\pi\)
\(480\) 0 0
\(481\) −8.77217 −0.399976
\(482\) 46.3678 2.11200
\(483\) 0 0
\(484\) −22.9050 −1.04114
\(485\) 5.39068 0.244778
\(486\) 0 0
\(487\) 35.9684 1.62988 0.814942 0.579543i \(-0.196769\pi\)
0.814942 + 0.579543i \(0.196769\pi\)
\(488\) −2.77426 −0.125585
\(489\) 0 0
\(490\) −4.11734 −0.186002
\(491\) 17.3618 0.783527 0.391763 0.920066i \(-0.371865\pi\)
0.391763 + 0.920066i \(0.371865\pi\)
\(492\) 0 0
\(493\) −17.5163 −0.788893
\(494\) 6.65660 0.299495
\(495\) 0 0
\(496\) 15.1372 0.679682
\(497\) 5.64510 0.253217
\(498\) 0 0
\(499\) −30.0817 −1.34664 −0.673320 0.739351i \(-0.735133\pi\)
−0.673320 + 0.739351i \(0.735133\pi\)
\(500\) −14.3960 −0.643806
\(501\) 0 0
\(502\) 23.8259 1.06340
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) 0.384926 0.0171290
\(506\) 0.527324 0.0234424
\(507\) 0 0
\(508\) 47.0780 2.08875
\(509\) 32.5495 1.44273 0.721366 0.692554i \(-0.243515\pi\)
0.721366 + 0.692554i \(0.243515\pi\)
\(510\) 0 0
\(511\) 4.29802 0.190133
\(512\) 32.0107 1.41469
\(513\) 0 0
\(514\) 33.2455 1.46639
\(515\) 0.930784 0.0410152
\(516\) 0 0
\(517\) −1.04897 −0.0461335
\(518\) −12.3633 −0.543212
\(519\) 0 0
\(520\) −0.669712 −0.0293688
\(521\) 12.6474 0.554094 0.277047 0.960856i \(-0.410644\pi\)
0.277047 + 0.960856i \(0.410644\pi\)
\(522\) 0 0
\(523\) 14.7294 0.644073 0.322036 0.946727i \(-0.395633\pi\)
0.322036 + 0.946727i \(0.395633\pi\)
\(524\) −18.9631 −0.828406
\(525\) 0 0
\(526\) 32.2145 1.40462
\(527\) −11.2215 −0.488818
\(528\) 0 0
\(529\) −22.8299 −0.992606
\(530\) 12.1788 0.529013
\(531\) 0 0
\(532\) 4.87065 0.211169
\(533\) −0.397815 −0.0172313
\(534\) 0 0
\(535\) −1.80556 −0.0780613
\(536\) −4.23693 −0.183008
\(537\) 0 0
\(538\) −22.9239 −0.988321
\(539\) −1.80533 −0.0777611
\(540\) 0 0
\(541\) −27.4172 −1.17876 −0.589379 0.807857i \(-0.700627\pi\)
−0.589379 + 0.807857i \(0.700627\pi\)
\(542\) 46.3192 1.98958
\(543\) 0 0
\(544\) −21.9676 −0.941855
\(545\) 6.23298 0.266992
\(546\) 0 0
\(547\) −16.1884 −0.692164 −0.346082 0.938204i \(-0.612488\pi\)
−0.346082 + 0.938204i \(0.612488\pi\)
\(548\) 9.20198 0.393089
\(549\) 0 0
\(550\) −5.76489 −0.245816
\(551\) 7.18181 0.305955
\(552\) 0 0
\(553\) 0.644231 0.0273955
\(554\) −6.98742 −0.296867
\(555\) 0 0
\(556\) 29.1420 1.23590
\(557\) 13.3858 0.567176 0.283588 0.958946i \(-0.408475\pi\)
0.283588 + 0.958946i \(0.408475\pi\)
\(558\) 0 0
\(559\) 2.53028 0.107020
\(560\) 5.20277 0.219857
\(561\) 0 0
\(562\) 13.0764 0.551596
\(563\) −23.3845 −0.985538 −0.492769 0.870160i \(-0.664015\pi\)
−0.492769 + 0.870160i \(0.664015\pi\)
\(564\) 0 0
\(565\) 1.34605 0.0566287
\(566\) −45.5745 −1.91564
\(567\) 0 0
\(568\) −0.904327 −0.0379447
\(569\) −43.0171 −1.80337 −0.901685 0.432393i \(-0.857669\pi\)
−0.901685 + 0.432393i \(0.857669\pi\)
\(570\) 0 0
\(571\) −1.24920 −0.0522772 −0.0261386 0.999658i \(-0.508321\pi\)
−0.0261386 + 0.999658i \(0.508321\pi\)
\(572\) −3.97702 −0.166287
\(573\) 0 0
\(574\) −0.560672 −0.0234020
\(575\) −1.85926 −0.0775364
\(576\) 0 0
\(577\) −38.6392 −1.60857 −0.804284 0.594244i \(-0.797451\pi\)
−0.804284 + 0.594244i \(0.797451\pi\)
\(578\) −19.6926 −0.819102
\(579\) 0 0
\(580\) −9.78584 −0.406335
\(581\) −10.2535 −0.425387
\(582\) 0 0
\(583\) 5.34004 0.221162
\(584\) −0.688529 −0.0284915
\(585\) 0 0
\(586\) −10.1029 −0.417345
\(587\) 13.5179 0.557943 0.278972 0.960299i \(-0.410006\pi\)
0.278972 + 0.960299i \(0.410006\pi\)
\(588\) 0 0
\(589\) 4.60092 0.189578
\(590\) 0.581520 0.0239408
\(591\) 0 0
\(592\) −10.9171 −0.448690
\(593\) 6.72274 0.276070 0.138035 0.990427i \(-0.455921\pi\)
0.138035 + 0.990427i \(0.455921\pi\)
\(594\) 0 0
\(595\) −3.85692 −0.158118
\(596\) −24.2837 −0.994698
\(597\) 0 0
\(598\) −2.47058 −0.101029
\(599\) −4.15139 −0.169621 −0.0848106 0.996397i \(-0.527029\pi\)
−0.0848106 + 0.996397i \(0.527029\pi\)
\(600\) 0 0
\(601\) −39.8754 −1.62655 −0.813276 0.581878i \(-0.802318\pi\)
−0.813276 + 0.581878i \(0.802318\pi\)
\(602\) 3.56612 0.145344
\(603\) 0 0
\(604\) −5.09860 −0.207459
\(605\) −7.43665 −0.302343
\(606\) 0 0
\(607\) −27.9713 −1.13532 −0.567660 0.823263i \(-0.692151\pi\)
−0.567660 + 0.823263i \(0.692151\pi\)
\(608\) 9.00690 0.365278
\(609\) 0 0
\(610\) −12.1990 −0.493921
\(611\) 4.91454 0.198821
\(612\) 0 0
\(613\) −30.7521 −1.24207 −0.621033 0.783785i \(-0.713287\pi\)
−0.621033 + 0.783785i \(0.713287\pi\)
\(614\) −3.81252 −0.153861
\(615\) 0 0
\(616\) −0.413863 −0.0166750
\(617\) 24.4669 0.984999 0.492500 0.870313i \(-0.336083\pi\)
0.492500 + 0.870313i \(0.336083\pi\)
\(618\) 0 0
\(619\) 37.1492 1.49315 0.746575 0.665301i \(-0.231697\pi\)
0.746575 + 0.665301i \(0.231697\pi\)
\(620\) −6.26915 −0.251775
\(621\) 0 0
\(622\) 8.76284 0.351358
\(623\) 33.4324 1.33944
\(624\) 0 0
\(625\) 17.8682 0.714729
\(626\) −49.4322 −1.97571
\(627\) 0 0
\(628\) −37.8426 −1.51009
\(629\) 8.09308 0.322692
\(630\) 0 0
\(631\) −15.7642 −0.627563 −0.313781 0.949495i \(-0.601596\pi\)
−0.313781 + 0.949495i \(0.601596\pi\)
\(632\) −0.103204 −0.00410522
\(633\) 0 0
\(634\) 57.4932 2.28335
\(635\) 15.2850 0.606565
\(636\) 0 0
\(637\) 8.45819 0.335126
\(638\) −8.26479 −0.327206
\(639\) 0 0
\(640\) −1.81814 −0.0718684
\(641\) −48.3528 −1.90982 −0.954911 0.296892i \(-0.904050\pi\)
−0.954911 + 0.296892i \(0.904050\pi\)
\(642\) 0 0
\(643\) 3.30378 0.130288 0.0651441 0.997876i \(-0.479249\pi\)
0.0651441 + 0.997876i \(0.479249\pi\)
\(644\) −1.80773 −0.0712344
\(645\) 0 0
\(646\) −6.14129 −0.241626
\(647\) −34.3017 −1.34854 −0.674269 0.738486i \(-0.735541\pi\)
−0.674269 + 0.738486i \(0.735541\pi\)
\(648\) 0 0
\(649\) 0.254980 0.0100088
\(650\) 27.0092 1.05939
\(651\) 0 0
\(652\) −15.3786 −0.602271
\(653\) 13.5211 0.529120 0.264560 0.964369i \(-0.414773\pi\)
0.264560 + 0.964369i \(0.414773\pi\)
\(654\) 0 0
\(655\) −6.15680 −0.240566
\(656\) −0.495088 −0.0193299
\(657\) 0 0
\(658\) 6.92644 0.270021
\(659\) −29.2605 −1.13983 −0.569914 0.821704i \(-0.693023\pi\)
−0.569914 + 0.821704i \(0.693023\pi\)
\(660\) 0 0
\(661\) 36.0006 1.40026 0.700131 0.714015i \(-0.253125\pi\)
0.700131 + 0.714015i \(0.253125\pi\)
\(662\) 27.5707 1.07157
\(663\) 0 0
\(664\) 1.64258 0.0637445
\(665\) 1.58137 0.0613229
\(666\) 0 0
\(667\) −2.66551 −0.103209
\(668\) −9.84880 −0.381061
\(669\) 0 0
\(670\) −18.6306 −0.719762
\(671\) −5.34889 −0.206491
\(672\) 0 0
\(673\) 14.3874 0.554595 0.277298 0.960784i \(-0.410561\pi\)
0.277298 + 0.960784i \(0.410561\pi\)
\(674\) −3.53235 −0.136061
\(675\) 0 0
\(676\) −9.44000 −0.363077
\(677\) −25.3712 −0.975094 −0.487547 0.873097i \(-0.662108\pi\)
−0.487547 + 0.873097i \(0.662108\pi\)
\(678\) 0 0
\(679\) −15.6075 −0.598960
\(680\) 0.617867 0.0236941
\(681\) 0 0
\(682\) −5.29471 −0.202745
\(683\) −31.2549 −1.19594 −0.597968 0.801520i \(-0.704025\pi\)
−0.597968 + 0.801520i \(0.704025\pi\)
\(684\) 0 0
\(685\) 2.98764 0.114152
\(686\) 40.9005 1.56159
\(687\) 0 0
\(688\) 3.14898 0.120054
\(689\) −25.0187 −0.953138
\(690\) 0 0
\(691\) −1.92143 −0.0730946 −0.0365473 0.999332i \(-0.511636\pi\)
−0.0365473 + 0.999332i \(0.511636\pi\)
\(692\) −6.29169 −0.239174
\(693\) 0 0
\(694\) 56.5468 2.14649
\(695\) 9.46162 0.358900
\(696\) 0 0
\(697\) 0.367019 0.0139018
\(698\) −32.7564 −1.23985
\(699\) 0 0
\(700\) 19.7627 0.746960
\(701\) −5.22129 −0.197205 −0.0986027 0.995127i \(-0.531437\pi\)
−0.0986027 + 0.995127i \(0.531437\pi\)
\(702\) 0 0
\(703\) −3.31823 −0.125149
\(704\) −5.78109 −0.217883
\(705\) 0 0
\(706\) 32.6338 1.22819
\(707\) −1.11446 −0.0419137
\(708\) 0 0
\(709\) 1.68414 0.0632493 0.0316247 0.999500i \(-0.489932\pi\)
0.0316247 + 0.999500i \(0.489932\pi\)
\(710\) −3.97649 −0.149235
\(711\) 0 0
\(712\) −5.35577 −0.200716
\(713\) −1.70762 −0.0639508
\(714\) 0 0
\(715\) −1.29123 −0.0482893
\(716\) 19.4596 0.727241
\(717\) 0 0
\(718\) −59.6949 −2.22779
\(719\) 38.7868 1.44651 0.723253 0.690583i \(-0.242646\pi\)
0.723253 + 0.690583i \(0.242646\pi\)
\(720\) 0 0
\(721\) −2.69487 −0.100362
\(722\) −36.2320 −1.34842
\(723\) 0 0
\(724\) 31.1100 1.15619
\(725\) 29.1402 1.08224
\(726\) 0 0
\(727\) −18.0472 −0.669333 −0.334666 0.942337i \(-0.608624\pi\)
−0.334666 + 0.942337i \(0.608624\pi\)
\(728\) 1.93900 0.0718640
\(729\) 0 0
\(730\) −3.02759 −0.112056
\(731\) −2.33440 −0.0863410
\(732\) 0 0
\(733\) 2.36945 0.0875175 0.0437587 0.999042i \(-0.486067\pi\)
0.0437587 + 0.999042i \(0.486067\pi\)
\(734\) 39.8373 1.47042
\(735\) 0 0
\(736\) −3.34289 −0.123220
\(737\) −8.16896 −0.300907
\(738\) 0 0
\(739\) 23.0868 0.849260 0.424630 0.905367i \(-0.360404\pi\)
0.424630 + 0.905367i \(0.360404\pi\)
\(740\) 4.52137 0.166209
\(741\) 0 0
\(742\) −35.2608 −1.29447
\(743\) −2.24456 −0.0823449 −0.0411725 0.999152i \(-0.513109\pi\)
−0.0411725 + 0.999152i \(0.513109\pi\)
\(744\) 0 0
\(745\) −7.88426 −0.288857
\(746\) −44.9891 −1.64717
\(747\) 0 0
\(748\) 3.66914 0.134157
\(749\) 5.22759 0.191012
\(750\) 0 0
\(751\) 54.7798 1.99894 0.999472 0.0324826i \(-0.0103413\pi\)
0.999472 + 0.0324826i \(0.0103413\pi\)
\(752\) 6.11622 0.223036
\(753\) 0 0
\(754\) 38.7215 1.41015
\(755\) −1.65538 −0.0602454
\(756\) 0 0
\(757\) −5.96003 −0.216621 −0.108311 0.994117i \(-0.534544\pi\)
−0.108311 + 0.994117i \(0.534544\pi\)
\(758\) 21.9099 0.795804
\(759\) 0 0
\(760\) −0.253330 −0.00918926
\(761\) 33.5210 1.21513 0.607567 0.794268i \(-0.292146\pi\)
0.607567 + 0.794268i \(0.292146\pi\)
\(762\) 0 0
\(763\) −18.0461 −0.653314
\(764\) −9.51732 −0.344325
\(765\) 0 0
\(766\) −15.9461 −0.576158
\(767\) −1.19461 −0.0431349
\(768\) 0 0
\(769\) −41.9889 −1.51416 −0.757080 0.653322i \(-0.773375\pi\)
−0.757080 + 0.653322i \(0.773375\pi\)
\(770\) −1.81983 −0.0655822
\(771\) 0 0
\(772\) −6.26298 −0.225409
\(773\) −11.9695 −0.430512 −0.215256 0.976558i \(-0.569059\pi\)
−0.215256 + 0.976558i \(0.569059\pi\)
\(774\) 0 0
\(775\) 18.6683 0.670584
\(776\) 2.50027 0.0897544
\(777\) 0 0
\(778\) 71.4451 2.56143
\(779\) −0.150481 −0.00539153
\(780\) 0 0
\(781\) −1.74358 −0.0623901
\(782\) 2.27932 0.0815084
\(783\) 0 0
\(784\) 10.5264 0.375942
\(785\) −12.2865 −0.438523
\(786\) 0 0
\(787\) −14.5883 −0.520017 −0.260008 0.965606i \(-0.583725\pi\)
−0.260008 + 0.965606i \(0.583725\pi\)
\(788\) −12.7733 −0.455031
\(789\) 0 0
\(790\) −0.453806 −0.0161457
\(791\) −3.89717 −0.138568
\(792\) 0 0
\(793\) 25.0602 0.889913
\(794\) −0.500564 −0.0177643
\(795\) 0 0
\(796\) −10.2244 −0.362394
\(797\) −13.0225 −0.461281 −0.230641 0.973039i \(-0.574082\pi\)
−0.230641 + 0.973039i \(0.574082\pi\)
\(798\) 0 0
\(799\) −4.53408 −0.160404
\(800\) 36.5456 1.29208
\(801\) 0 0
\(802\) 33.3319 1.17699
\(803\) −1.32751 −0.0468468
\(804\) 0 0
\(805\) −0.586921 −0.0206862
\(806\) 24.8064 0.873767
\(807\) 0 0
\(808\) 0.178534 0.00628079
\(809\) −23.5857 −0.829230 −0.414615 0.909997i \(-0.636084\pi\)
−0.414615 + 0.909997i \(0.636084\pi\)
\(810\) 0 0
\(811\) 44.3230 1.55639 0.778195 0.628023i \(-0.216136\pi\)
0.778195 + 0.628023i \(0.216136\pi\)
\(812\) 28.3326 0.994280
\(813\) 0 0
\(814\) 3.81860 0.133842
\(815\) −4.99300 −0.174897
\(816\) 0 0
\(817\) 0.957124 0.0334855
\(818\) 9.39977 0.328655
\(819\) 0 0
\(820\) 0.205043 0.00716041
\(821\) 11.0481 0.385581 0.192791 0.981240i \(-0.438246\pi\)
0.192791 + 0.981240i \(0.438246\pi\)
\(822\) 0 0
\(823\) 8.97374 0.312805 0.156403 0.987693i \(-0.450010\pi\)
0.156403 + 0.987693i \(0.450010\pi\)
\(824\) 0.431710 0.0150393
\(825\) 0 0
\(826\) −1.68366 −0.0585819
\(827\) −36.0996 −1.25531 −0.627654 0.778493i \(-0.715985\pi\)
−0.627654 + 0.778493i \(0.715985\pi\)
\(828\) 0 0
\(829\) −5.63971 −0.195875 −0.0979375 0.995193i \(-0.531225\pi\)
−0.0979375 + 0.995193i \(0.531225\pi\)
\(830\) 7.22273 0.250705
\(831\) 0 0
\(832\) 27.0851 0.939007
\(833\) −7.80341 −0.270372
\(834\) 0 0
\(835\) −3.19764 −0.110659
\(836\) −1.50438 −0.0520299
\(837\) 0 0
\(838\) −23.3538 −0.806745
\(839\) 19.2580 0.664859 0.332429 0.943128i \(-0.392132\pi\)
0.332429 + 0.943128i \(0.392132\pi\)
\(840\) 0 0
\(841\) 12.7767 0.440575
\(842\) −45.4039 −1.56472
\(843\) 0 0
\(844\) −3.25366 −0.111996
\(845\) −3.06492 −0.105436
\(846\) 0 0
\(847\) 21.5311 0.739818
\(848\) −31.1362 −1.06922
\(849\) 0 0
\(850\) −24.9183 −0.854691
\(851\) 1.23155 0.0422170
\(852\) 0 0
\(853\) 29.1126 0.996796 0.498398 0.866948i \(-0.333922\pi\)
0.498398 + 0.866948i \(0.333922\pi\)
\(854\) 35.3193 1.20860
\(855\) 0 0
\(856\) −0.837443 −0.0286232
\(857\) 18.6286 0.636342 0.318171 0.948033i \(-0.396931\pi\)
0.318171 + 0.948033i \(0.396931\pi\)
\(858\) 0 0
\(859\) 18.5140 0.631690 0.315845 0.948811i \(-0.397712\pi\)
0.315845 + 0.948811i \(0.397712\pi\)
\(860\) −1.30416 −0.0444716
\(861\) 0 0
\(862\) 2.31070 0.0787027
\(863\) 43.5150 1.48127 0.740635 0.671908i \(-0.234525\pi\)
0.740635 + 0.671908i \(0.234525\pi\)
\(864\) 0 0
\(865\) −2.04274 −0.0694553
\(866\) −5.41872 −0.184135
\(867\) 0 0
\(868\) 18.1509 0.616081
\(869\) −0.198981 −0.00674996
\(870\) 0 0
\(871\) 38.2726 1.29682
\(872\) 2.89094 0.0978995
\(873\) 0 0
\(874\) −0.934540 −0.0316113
\(875\) 13.5324 0.457479
\(876\) 0 0
\(877\) 11.9837 0.404662 0.202331 0.979317i \(-0.435148\pi\)
0.202331 + 0.979317i \(0.435148\pi\)
\(878\) 13.4040 0.452363
\(879\) 0 0
\(880\) −1.60696 −0.0541705
\(881\) 8.33770 0.280904 0.140452 0.990087i \(-0.455144\pi\)
0.140452 + 0.990087i \(0.455144\pi\)
\(882\) 0 0
\(883\) 14.7773 0.497296 0.248648 0.968594i \(-0.420014\pi\)
0.248648 + 0.968594i \(0.420014\pi\)
\(884\) −17.1904 −0.578174
\(885\) 0 0
\(886\) −2.74118 −0.0920916
\(887\) 26.6636 0.895278 0.447639 0.894214i \(-0.352265\pi\)
0.447639 + 0.894214i \(0.352265\pi\)
\(888\) 0 0
\(889\) −44.2541 −1.48423
\(890\) −23.5503 −0.789408
\(891\) 0 0
\(892\) −21.1457 −0.708011
\(893\) 1.85901 0.0622094
\(894\) 0 0
\(895\) 6.31803 0.211188
\(896\) 5.26401 0.175858
\(897\) 0 0
\(898\) −53.7218 −1.79272
\(899\) 26.7636 0.892616
\(900\) 0 0
\(901\) 23.0819 0.768971
\(902\) 0.173172 0.00576601
\(903\) 0 0
\(904\) 0.624315 0.0207644
\(905\) 10.1006 0.335754
\(906\) 0 0
\(907\) −41.3358 −1.37253 −0.686266 0.727351i \(-0.740751\pi\)
−0.686266 + 0.727351i \(0.740751\pi\)
\(908\) −14.8680 −0.493413
\(909\) 0 0
\(910\) 8.52613 0.282638
\(911\) 32.2613 1.06887 0.534433 0.845211i \(-0.320525\pi\)
0.534433 + 0.845211i \(0.320525\pi\)
\(912\) 0 0
\(913\) 3.16696 0.104811
\(914\) −61.3254 −2.02846
\(915\) 0 0
\(916\) 26.3193 0.869615
\(917\) 17.8256 0.588653
\(918\) 0 0
\(919\) −48.5538 −1.60164 −0.800821 0.598903i \(-0.795603\pi\)
−0.800821 + 0.598903i \(0.795603\pi\)
\(920\) 0.0940229 0.00309984
\(921\) 0 0
\(922\) 15.7545 0.518845
\(923\) 8.16886 0.268881
\(924\) 0 0
\(925\) −13.4637 −0.442684
\(926\) 15.9683 0.524750
\(927\) 0 0
\(928\) 52.3933 1.71989
\(929\) −28.1849 −0.924717 −0.462358 0.886693i \(-0.652997\pi\)
−0.462358 + 0.886693i \(0.652997\pi\)
\(930\) 0 0
\(931\) 3.19946 0.104858
\(932\) 45.4664 1.48930
\(933\) 0 0
\(934\) 14.6765 0.480230
\(935\) 1.19127 0.0389587
\(936\) 0 0
\(937\) −59.4487 −1.94211 −0.971053 0.238865i \(-0.923225\pi\)
−0.971053 + 0.238865i \(0.923225\pi\)
\(938\) 53.9405 1.76122
\(939\) 0 0
\(940\) −2.53306 −0.0826194
\(941\) −24.0890 −0.785277 −0.392639 0.919693i \(-0.628438\pi\)
−0.392639 + 0.919693i \(0.628438\pi\)
\(942\) 0 0
\(943\) 0.0558504 0.00181874
\(944\) −1.48671 −0.0483884
\(945\) 0 0
\(946\) −1.10145 −0.0358113
\(947\) −40.0415 −1.30117 −0.650586 0.759432i \(-0.725477\pi\)
−0.650586 + 0.759432i \(0.725477\pi\)
\(948\) 0 0
\(949\) 6.21955 0.201895
\(950\) 10.2167 0.331474
\(951\) 0 0
\(952\) −1.78889 −0.0579783
\(953\) 24.4039 0.790521 0.395261 0.918569i \(-0.370654\pi\)
0.395261 + 0.918569i \(0.370654\pi\)
\(954\) 0 0
\(955\) −3.09002 −0.0999907
\(956\) −19.6929 −0.636915
\(957\) 0 0
\(958\) 24.8725 0.803593
\(959\) −8.65001 −0.279323
\(960\) 0 0
\(961\) −13.8543 −0.446913
\(962\) −17.8906 −0.576816
\(963\) 0 0
\(964\) 49.0955 1.58126
\(965\) −2.03342 −0.0654581
\(966\) 0 0
\(967\) −16.2701 −0.523212 −0.261606 0.965175i \(-0.584252\pi\)
−0.261606 + 0.965175i \(0.584252\pi\)
\(968\) −3.44922 −0.110862
\(969\) 0 0
\(970\) 10.9941 0.353001
\(971\) 53.0256 1.70167 0.850837 0.525430i \(-0.176096\pi\)
0.850837 + 0.525430i \(0.176096\pi\)
\(972\) 0 0
\(973\) −27.3939 −0.878209
\(974\) 73.3565 2.35050
\(975\) 0 0
\(976\) 31.1878 0.998298
\(977\) 47.0435 1.50505 0.752527 0.658561i \(-0.228835\pi\)
0.752527 + 0.658561i \(0.228835\pi\)
\(978\) 0 0
\(979\) −10.3261 −0.330024
\(980\) −4.35954 −0.139260
\(981\) 0 0
\(982\) 35.4089 1.12994
\(983\) 10.9007 0.347678 0.173839 0.984774i \(-0.444383\pi\)
0.173839 + 0.984774i \(0.444383\pi\)
\(984\) 0 0
\(985\) −4.14716 −0.132139
\(986\) −35.7239 −1.13768
\(987\) 0 0
\(988\) 7.04818 0.224233
\(989\) −0.355234 −0.0112958
\(990\) 0 0
\(991\) −48.5839 −1.54332 −0.771659 0.636036i \(-0.780573\pi\)
−0.771659 + 0.636036i \(0.780573\pi\)
\(992\) 33.5650 1.06569
\(993\) 0 0
\(994\) 11.5130 0.365171
\(995\) −3.31959 −0.105238
\(996\) 0 0
\(997\) 20.3630 0.644902 0.322451 0.946586i \(-0.395493\pi\)
0.322451 + 0.946586i \(0.395493\pi\)
\(998\) −61.3507 −1.94202
\(999\) 0 0
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 4527.2.a.k.1.9 10
3.2 odd 2 503.2.a.e.1.2 10
12.11 even 2 8048.2.a.p.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
503.2.a.e.1.2 10 3.2 odd 2
4527.2.a.k.1.9 10 1.1 even 1 trivial
8048.2.a.p.1.1 10 12.11 even 2