Properties

Label 1859.2.a.t.1.16
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.13563 q^{2} -2.20961 q^{3} +2.56090 q^{4} -1.38469 q^{5} -4.71890 q^{6} +5.12151 q^{7} +1.19787 q^{8} +1.88237 q^{9} +O(q^{10})\) \(q+2.13563 q^{2} -2.20961 q^{3} +2.56090 q^{4} -1.38469 q^{5} -4.71890 q^{6} +5.12151 q^{7} +1.19787 q^{8} +1.88237 q^{9} -2.95718 q^{10} +1.00000 q^{11} -5.65858 q^{12} +10.9376 q^{14} +3.05962 q^{15} -2.56360 q^{16} -0.645800 q^{17} +4.02004 q^{18} +5.71986 q^{19} -3.54604 q^{20} -11.3165 q^{21} +2.13563 q^{22} -2.41000 q^{23} -2.64682 q^{24} -3.08264 q^{25} +2.46952 q^{27} +13.1157 q^{28} +2.88360 q^{29} +6.53420 q^{30} +3.43199 q^{31} -7.87062 q^{32} -2.20961 q^{33} -1.37919 q^{34} -7.09169 q^{35} +4.82056 q^{36} +10.2685 q^{37} +12.2155 q^{38} -1.65867 q^{40} -3.99879 q^{41} -24.1679 q^{42} +7.08446 q^{43} +2.56090 q^{44} -2.60650 q^{45} -5.14686 q^{46} +11.7099 q^{47} +5.66455 q^{48} +19.2298 q^{49} -6.58337 q^{50} +1.42697 q^{51} -12.7035 q^{53} +5.27398 q^{54} -1.38469 q^{55} +6.13489 q^{56} -12.6387 q^{57} +6.15828 q^{58} -0.0415150 q^{59} +7.83537 q^{60} -4.29284 q^{61} +7.32946 q^{62} +9.64058 q^{63} -11.6815 q^{64} -4.71890 q^{66} +14.4565 q^{67} -1.65383 q^{68} +5.32515 q^{69} -15.1452 q^{70} +4.10847 q^{71} +2.25483 q^{72} +4.85130 q^{73} +21.9297 q^{74} +6.81143 q^{75} +14.6480 q^{76} +5.12151 q^{77} +3.30530 q^{79} +3.54978 q^{80} -11.1038 q^{81} -8.53993 q^{82} +3.87295 q^{83} -28.9805 q^{84} +0.894231 q^{85} +15.1298 q^{86} -6.37162 q^{87} +1.19787 q^{88} +5.70850 q^{89} -5.56650 q^{90} -6.17176 q^{92} -7.58337 q^{93} +25.0080 q^{94} -7.92022 q^{95} +17.3910 q^{96} -0.622364 q^{97} +41.0677 q^{98} +1.88237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9} + 18 q^{10} + 21 q^{11} + 23 q^{12} + 20 q^{14} + 16 q^{15} + 50 q^{16} + 16 q^{17} + 3 q^{18} - 11 q^{19} + 24 q^{20} - 5 q^{21} - 9 q^{23} - 54 q^{24} + 36 q^{25} - 11 q^{28} + 28 q^{29} + 21 q^{30} + 15 q^{31} - 61 q^{32} + 6 q^{33} - 6 q^{34} - 3 q^{35} + 45 q^{36} - 12 q^{37} + q^{38} + 55 q^{40} - 4 q^{41} - 34 q^{42} + 17 q^{43} + 32 q^{44} + 9 q^{45} + 11 q^{46} + 36 q^{47} + 24 q^{48} + 72 q^{49} - 9 q^{50} + 2 q^{51} + 19 q^{53} + q^{54} + 7 q^{55} + 44 q^{56} - 4 q^{57} - 33 q^{58} + 54 q^{59} + 64 q^{60} + 98 q^{61} - 29 q^{62} - 81 q^{63} + 63 q^{64} - 19 q^{66} + 25 q^{67} + 4 q^{68} + 89 q^{69} + 65 q^{70} + 37 q^{71} + 55 q^{72} + 8 q^{73} - 11 q^{74} + 24 q^{75} + 13 q^{76} + q^{77} + 24 q^{79} + 26 q^{80} + 81 q^{81} + 26 q^{82} - 34 q^{83} - 103 q^{84} - 11 q^{85} + 30 q^{86} + 32 q^{87} - 3 q^{88} + 6 q^{89} + 47 q^{90} - 80 q^{92} + 41 q^{93} + 40 q^{94} + 20 q^{95} - 98 q^{96} - 5 q^{98} + 33 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.13563 1.51012 0.755058 0.655658i \(-0.227609\pi\)
0.755058 + 0.655658i \(0.227609\pi\)
\(3\) −2.20961 −1.27572 −0.637859 0.770153i \(-0.720180\pi\)
−0.637859 + 0.770153i \(0.720180\pi\)
\(4\) 2.56090 1.28045
\(5\) −1.38469 −0.619251 −0.309626 0.950859i \(-0.600204\pi\)
−0.309626 + 0.950859i \(0.600204\pi\)
\(6\) −4.71890 −1.92648
\(7\) 5.12151 1.93575 0.967874 0.251436i \(-0.0809030\pi\)
0.967874 + 0.251436i \(0.0809030\pi\)
\(8\) 1.19787 0.423510
\(9\) 1.88237 0.627457
\(10\) −2.95718 −0.935141
\(11\) 1.00000 0.301511
\(12\) −5.65858 −1.63349
\(13\) 0 0
\(14\) 10.9376 2.92320
\(15\) 3.05962 0.789990
\(16\) −2.56360 −0.640899
\(17\) −0.645800 −0.156629 −0.0783147 0.996929i \(-0.524954\pi\)
−0.0783147 + 0.996929i \(0.524954\pi\)
\(18\) 4.02004 0.947533
\(19\) 5.71986 1.31223 0.656113 0.754663i \(-0.272199\pi\)
0.656113 + 0.754663i \(0.272199\pi\)
\(20\) −3.54604 −0.792920
\(21\) −11.3165 −2.46947
\(22\) 2.13563 0.455317
\(23\) −2.41000 −0.502519 −0.251260 0.967920i \(-0.580845\pi\)
−0.251260 + 0.967920i \(0.580845\pi\)
\(24\) −2.64682 −0.540280
\(25\) −3.08264 −0.616528
\(26\) 0 0
\(27\) 2.46952 0.475260
\(28\) 13.1157 2.47863
\(29\) 2.88360 0.535471 0.267735 0.963493i \(-0.413725\pi\)
0.267735 + 0.963493i \(0.413725\pi\)
\(30\) 6.53420 1.19298
\(31\) 3.43199 0.616404 0.308202 0.951321i \(-0.400273\pi\)
0.308202 + 0.951321i \(0.400273\pi\)
\(32\) −7.87062 −1.39134
\(33\) −2.20961 −0.384644
\(34\) −1.37919 −0.236529
\(35\) −7.09169 −1.19871
\(36\) 4.82056 0.803427
\(37\) 10.2685 1.68813 0.844067 0.536238i \(-0.180155\pi\)
0.844067 + 0.536238i \(0.180155\pi\)
\(38\) 12.2155 1.98161
\(39\) 0 0
\(40\) −1.65867 −0.262259
\(41\) −3.99879 −0.624507 −0.312253 0.949999i \(-0.601084\pi\)
−0.312253 + 0.949999i \(0.601084\pi\)
\(42\) −24.1679 −3.72918
\(43\) 7.08446 1.08037 0.540185 0.841546i \(-0.318354\pi\)
0.540185 + 0.841546i \(0.318354\pi\)
\(44\) 2.56090 0.386070
\(45\) −2.60650 −0.388554
\(46\) −5.14686 −0.758862
\(47\) 11.7099 1.70807 0.854033 0.520219i \(-0.174150\pi\)
0.854033 + 0.520219i \(0.174150\pi\)
\(48\) 5.66455 0.817607
\(49\) 19.2298 2.74712
\(50\) −6.58337 −0.931028
\(51\) 1.42697 0.199815
\(52\) 0 0
\(53\) −12.7035 −1.74496 −0.872479 0.488651i \(-0.837489\pi\)
−0.872479 + 0.488651i \(0.837489\pi\)
\(54\) 5.27398 0.717697
\(55\) −1.38469 −0.186711
\(56\) 6.13489 0.819809
\(57\) −12.6387 −1.67403
\(58\) 6.15828 0.808622
\(59\) −0.0415150 −0.00540480 −0.00270240 0.999996i \(-0.500860\pi\)
−0.00270240 + 0.999996i \(0.500860\pi\)
\(60\) 7.83537 1.01154
\(61\) −4.29284 −0.549641 −0.274821 0.961495i \(-0.588619\pi\)
−0.274821 + 0.961495i \(0.588619\pi\)
\(62\) 7.32946 0.930842
\(63\) 9.64058 1.21460
\(64\) −11.6815 −1.46019
\(65\) 0 0
\(66\) −4.71890 −0.580856
\(67\) 14.4565 1.76614 0.883071 0.469239i \(-0.155472\pi\)
0.883071 + 0.469239i \(0.155472\pi\)
\(68\) −1.65383 −0.200556
\(69\) 5.32515 0.641073
\(70\) −15.1452 −1.81020
\(71\) 4.10847 0.487586 0.243793 0.969827i \(-0.421608\pi\)
0.243793 + 0.969827i \(0.421608\pi\)
\(72\) 2.25483 0.265735
\(73\) 4.85130 0.567802 0.283901 0.958854i \(-0.408371\pi\)
0.283901 + 0.958854i \(0.408371\pi\)
\(74\) 21.9297 2.54928
\(75\) 6.81143 0.786516
\(76\) 14.6480 1.68024
\(77\) 5.12151 0.583650
\(78\) 0 0
\(79\) 3.30530 0.371875 0.185938 0.982562i \(-0.440468\pi\)
0.185938 + 0.982562i \(0.440468\pi\)
\(80\) 3.54978 0.396878
\(81\) −11.1038 −1.23375
\(82\) −8.53993 −0.943077
\(83\) 3.87295 0.425111 0.212556 0.977149i \(-0.431821\pi\)
0.212556 + 0.977149i \(0.431821\pi\)
\(84\) −28.9805 −3.16203
\(85\) 0.894231 0.0969930
\(86\) 15.1298 1.63148
\(87\) −6.37162 −0.683110
\(88\) 1.19787 0.127693
\(89\) 5.70850 0.605100 0.302550 0.953133i \(-0.402162\pi\)
0.302550 + 0.953133i \(0.402162\pi\)
\(90\) −5.56650 −0.586761
\(91\) 0 0
\(92\) −6.17176 −0.643450
\(93\) −7.58337 −0.786358
\(94\) 25.0080 2.57938
\(95\) −7.92022 −0.812598
\(96\) 17.3910 1.77496
\(97\) −0.622364 −0.0631915 −0.0315957 0.999501i \(-0.510059\pi\)
−0.0315957 + 0.999501i \(0.510059\pi\)
\(98\) 41.0677 4.14847
\(99\) 1.88237 0.189185
\(100\) −7.89433 −0.789433
\(101\) 17.8839 1.77951 0.889757 0.456435i \(-0.150874\pi\)
0.889757 + 0.456435i \(0.150874\pi\)
\(102\) 3.04746 0.301744
\(103\) −3.48136 −0.343029 −0.171515 0.985182i \(-0.554866\pi\)
−0.171515 + 0.985182i \(0.554866\pi\)
\(104\) 0 0
\(105\) 15.6699 1.52922
\(106\) −27.1299 −2.63509
\(107\) 0.270944 0.0261932 0.0130966 0.999914i \(-0.495831\pi\)
0.0130966 + 0.999914i \(0.495831\pi\)
\(108\) 6.32419 0.608546
\(109\) −11.2913 −1.08151 −0.540756 0.841179i \(-0.681862\pi\)
−0.540756 + 0.841179i \(0.681862\pi\)
\(110\) −2.95718 −0.281956
\(111\) −22.6894 −2.15358
\(112\) −13.1295 −1.24062
\(113\) −12.2758 −1.15481 −0.577407 0.816456i \(-0.695935\pi\)
−0.577407 + 0.816456i \(0.695935\pi\)
\(114\) −26.9914 −2.52798
\(115\) 3.33710 0.311186
\(116\) 7.38460 0.685643
\(117\) 0 0
\(118\) −0.0886606 −0.00816187
\(119\) −3.30747 −0.303195
\(120\) 3.66502 0.334569
\(121\) 1.00000 0.0909091
\(122\) −9.16789 −0.830022
\(123\) 8.83577 0.796694
\(124\) 8.78899 0.789274
\(125\) 11.1919 1.00104
\(126\) 20.5887 1.83418
\(127\) −2.37725 −0.210947 −0.105473 0.994422i \(-0.533636\pi\)
−0.105473 + 0.994422i \(0.533636\pi\)
\(128\) −9.20609 −0.813711
\(129\) −15.6539 −1.37825
\(130\) 0 0
\(131\) −19.2094 −1.67834 −0.839168 0.543872i \(-0.816958\pi\)
−0.839168 + 0.543872i \(0.816958\pi\)
\(132\) −5.65858 −0.492516
\(133\) 29.2943 2.54014
\(134\) 30.8737 2.66708
\(135\) −3.41952 −0.294305
\(136\) −0.773583 −0.0663342
\(137\) −18.7695 −1.60359 −0.801793 0.597602i \(-0.796120\pi\)
−0.801793 + 0.597602i \(0.796120\pi\)
\(138\) 11.3725 0.968095
\(139\) −0.0825625 −0.00700286 −0.00350143 0.999994i \(-0.501115\pi\)
−0.00350143 + 0.999994i \(0.501115\pi\)
\(140\) −18.1611 −1.53489
\(141\) −25.8743 −2.17901
\(142\) 8.77415 0.736311
\(143\) 0 0
\(144\) −4.82564 −0.402137
\(145\) −3.99288 −0.331591
\(146\) 10.3606 0.857446
\(147\) −42.4904 −3.50455
\(148\) 26.2966 2.16157
\(149\) 3.42408 0.280512 0.140256 0.990115i \(-0.455207\pi\)
0.140256 + 0.990115i \(0.455207\pi\)
\(150\) 14.5467 1.18773
\(151\) −14.8265 −1.20656 −0.603282 0.797528i \(-0.706141\pi\)
−0.603282 + 0.797528i \(0.706141\pi\)
\(152\) 6.85164 0.555741
\(153\) −1.21564 −0.0982783
\(154\) 10.9376 0.881379
\(155\) −4.75224 −0.381709
\(156\) 0 0
\(157\) 2.57432 0.205453 0.102727 0.994710i \(-0.467243\pi\)
0.102727 + 0.994710i \(0.467243\pi\)
\(158\) 7.05888 0.561575
\(159\) 28.0697 2.22608
\(160\) 10.8984 0.861591
\(161\) −12.3428 −0.972751
\(162\) −23.7135 −1.86311
\(163\) −12.5648 −0.984151 −0.492076 0.870552i \(-0.663762\pi\)
−0.492076 + 0.870552i \(0.663762\pi\)
\(164\) −10.2405 −0.799649
\(165\) 3.05962 0.238191
\(166\) 8.27116 0.641967
\(167\) −6.24946 −0.483598 −0.241799 0.970326i \(-0.577737\pi\)
−0.241799 + 0.970326i \(0.577737\pi\)
\(168\) −13.5557 −1.04585
\(169\) 0 0
\(170\) 1.90974 0.146471
\(171\) 10.7669 0.823366
\(172\) 18.1426 1.38336
\(173\) 7.40017 0.562624 0.281312 0.959616i \(-0.409230\pi\)
0.281312 + 0.959616i \(0.409230\pi\)
\(174\) −13.6074 −1.03157
\(175\) −15.7878 −1.19344
\(176\) −2.56360 −0.193238
\(177\) 0.0917320 0.00689500
\(178\) 12.1912 0.913771
\(179\) 13.5994 1.01647 0.508233 0.861220i \(-0.330299\pi\)
0.508233 + 0.861220i \(0.330299\pi\)
\(180\) −6.67497 −0.497523
\(181\) 5.41011 0.402130 0.201065 0.979578i \(-0.435560\pi\)
0.201065 + 0.979578i \(0.435560\pi\)
\(182\) 0 0
\(183\) 9.48549 0.701188
\(184\) −2.88686 −0.212822
\(185\) −14.2187 −1.04538
\(186\) −16.1952 −1.18749
\(187\) −0.645800 −0.0472256
\(188\) 29.9879 2.18709
\(189\) 12.6477 0.919983
\(190\) −16.9146 −1.22712
\(191\) 3.73932 0.270568 0.135284 0.990807i \(-0.456805\pi\)
0.135284 + 0.990807i \(0.456805\pi\)
\(192\) 25.8116 1.86279
\(193\) −8.49207 −0.611273 −0.305636 0.952148i \(-0.598869\pi\)
−0.305636 + 0.952148i \(0.598869\pi\)
\(194\) −1.32914 −0.0954265
\(195\) 0 0
\(196\) 49.2456 3.51755
\(197\) −17.5966 −1.25371 −0.626855 0.779136i \(-0.715658\pi\)
−0.626855 + 0.779136i \(0.715658\pi\)
\(198\) 4.02004 0.285692
\(199\) 15.1611 1.07474 0.537372 0.843346i \(-0.319417\pi\)
0.537372 + 0.843346i \(0.319417\pi\)
\(200\) −3.69260 −0.261106
\(201\) −31.9432 −2.25310
\(202\) 38.1933 2.68727
\(203\) 14.7684 1.03654
\(204\) 3.65431 0.255853
\(205\) 5.53708 0.386726
\(206\) −7.43489 −0.518014
\(207\) −4.53651 −0.315309
\(208\) 0 0
\(209\) 5.71986 0.395651
\(210\) 33.4650 2.30930
\(211\) −11.0003 −0.757295 −0.378648 0.925541i \(-0.623611\pi\)
−0.378648 + 0.925541i \(0.623611\pi\)
\(212\) −32.5323 −2.23433
\(213\) −9.07811 −0.622022
\(214\) 0.578636 0.0395547
\(215\) −9.80977 −0.669021
\(216\) 2.95816 0.201277
\(217\) 17.5770 1.19320
\(218\) −24.1140 −1.63321
\(219\) −10.7195 −0.724355
\(220\) −3.54604 −0.239074
\(221\) 0 0
\(222\) −48.4561 −3.25216
\(223\) −16.6700 −1.11631 −0.558153 0.829738i \(-0.688490\pi\)
−0.558153 + 0.829738i \(0.688490\pi\)
\(224\) −40.3094 −2.69329
\(225\) −5.80267 −0.386845
\(226\) −26.2166 −1.74390
\(227\) 18.4415 1.22401 0.612003 0.790856i \(-0.290364\pi\)
0.612003 + 0.790856i \(0.290364\pi\)
\(228\) −32.3663 −2.14351
\(229\) −26.5377 −1.75366 −0.876829 0.480803i \(-0.840345\pi\)
−0.876829 + 0.480803i \(0.840345\pi\)
\(230\) 7.12679 0.469926
\(231\) −11.3165 −0.744573
\(232\) 3.45417 0.226777
\(233\) 2.00904 0.131617 0.0658084 0.997832i \(-0.479037\pi\)
0.0658084 + 0.997832i \(0.479037\pi\)
\(234\) 0 0
\(235\) −16.2146 −1.05772
\(236\) −0.106316 −0.00692056
\(237\) −7.30342 −0.474408
\(238\) −7.06352 −0.457860
\(239\) −24.3230 −1.57333 −0.786663 0.617383i \(-0.788193\pi\)
−0.786663 + 0.617383i \(0.788193\pi\)
\(240\) −7.84363 −0.506304
\(241\) −14.0789 −0.906905 −0.453452 0.891280i \(-0.649808\pi\)
−0.453452 + 0.891280i \(0.649808\pi\)
\(242\) 2.13563 0.137283
\(243\) 17.1265 1.09866
\(244\) −10.9935 −0.703788
\(245\) −26.6273 −1.70116
\(246\) 18.8699 1.20310
\(247\) 0 0
\(248\) 4.11108 0.261054
\(249\) −8.55770 −0.542322
\(250\) 23.9018 1.51168
\(251\) −10.8501 −0.684853 −0.342427 0.939545i \(-0.611249\pi\)
−0.342427 + 0.939545i \(0.611249\pi\)
\(252\) 24.6885 1.55523
\(253\) −2.41000 −0.151515
\(254\) −5.07692 −0.318554
\(255\) −1.97590 −0.123736
\(256\) 3.70226 0.231391
\(257\) −11.5040 −0.717600 −0.358800 0.933415i \(-0.616814\pi\)
−0.358800 + 0.933415i \(0.616814\pi\)
\(258\) −33.4309 −2.08131
\(259\) 52.5903 3.26780
\(260\) 0 0
\(261\) 5.42800 0.335985
\(262\) −41.0242 −2.53448
\(263\) −16.7453 −1.03256 −0.516281 0.856419i \(-0.672684\pi\)
−0.516281 + 0.856419i \(0.672684\pi\)
\(264\) −2.64682 −0.162901
\(265\) 17.5904 1.08057
\(266\) 62.5617 3.83590
\(267\) −12.6136 −0.771937
\(268\) 37.0216 2.26146
\(269\) −4.08991 −0.249366 −0.124683 0.992197i \(-0.539791\pi\)
−0.124683 + 0.992197i \(0.539791\pi\)
\(270\) −7.30281 −0.444435
\(271\) 10.5903 0.643316 0.321658 0.946856i \(-0.395760\pi\)
0.321658 + 0.946856i \(0.395760\pi\)
\(272\) 1.65557 0.100384
\(273\) 0 0
\(274\) −40.0846 −2.42160
\(275\) −3.08264 −0.185890
\(276\) 13.6372 0.820862
\(277\) 11.8675 0.713047 0.356524 0.934286i \(-0.383962\pi\)
0.356524 + 0.934286i \(0.383962\pi\)
\(278\) −0.176323 −0.0105751
\(279\) 6.46029 0.386767
\(280\) −8.49491 −0.507668
\(281\) 11.6973 0.697803 0.348901 0.937159i \(-0.386555\pi\)
0.348901 + 0.937159i \(0.386555\pi\)
\(282\) −55.2579 −3.29056
\(283\) −9.31846 −0.553925 −0.276963 0.960881i \(-0.589328\pi\)
−0.276963 + 0.960881i \(0.589328\pi\)
\(284\) 10.5214 0.624328
\(285\) 17.5006 1.03665
\(286\) 0 0
\(287\) −20.4798 −1.20889
\(288\) −14.8154 −0.873008
\(289\) −16.5829 −0.975467
\(290\) −8.52730 −0.500740
\(291\) 1.37518 0.0806145
\(292\) 12.4237 0.727041
\(293\) 14.4492 0.844130 0.422065 0.906566i \(-0.361305\pi\)
0.422065 + 0.906566i \(0.361305\pi\)
\(294\) −90.7436 −5.29227
\(295\) 0.0574853 0.00334693
\(296\) 12.3003 0.714942
\(297\) 2.46952 0.143296
\(298\) 7.31256 0.423605
\(299\) 0 0
\(300\) 17.4434 1.00709
\(301\) 36.2831 2.09132
\(302\) −31.6639 −1.82205
\(303\) −39.5164 −2.27016
\(304\) −14.6634 −0.841005
\(305\) 5.94424 0.340366
\(306\) −2.59614 −0.148412
\(307\) 8.18391 0.467081 0.233540 0.972347i \(-0.424969\pi\)
0.233540 + 0.972347i \(0.424969\pi\)
\(308\) 13.1157 0.747334
\(309\) 7.69245 0.437608
\(310\) −10.1490 −0.576425
\(311\) −0.0504367 −0.00286000 −0.00143000 0.999999i \(-0.500455\pi\)
−0.00143000 + 0.999999i \(0.500455\pi\)
\(312\) 0 0
\(313\) 15.6601 0.885162 0.442581 0.896729i \(-0.354063\pi\)
0.442581 + 0.896729i \(0.354063\pi\)
\(314\) 5.49779 0.310258
\(315\) −13.3492 −0.752142
\(316\) 8.46454 0.476167
\(317\) 5.10412 0.286676 0.143338 0.989674i \(-0.454216\pi\)
0.143338 + 0.989674i \(0.454216\pi\)
\(318\) 59.9465 3.36163
\(319\) 2.88360 0.161450
\(320\) 16.1752 0.904223
\(321\) −0.598681 −0.0334151
\(322\) −26.3597 −1.46897
\(323\) −3.69389 −0.205533
\(324\) −28.4357 −1.57976
\(325\) 0 0
\(326\) −26.8337 −1.48618
\(327\) 24.9494 1.37970
\(328\) −4.79003 −0.264485
\(329\) 59.9724 3.30638
\(330\) 6.53420 0.359696
\(331\) 27.0938 1.48921 0.744604 0.667507i \(-0.232638\pi\)
0.744604 + 0.667507i \(0.232638\pi\)
\(332\) 9.91822 0.544333
\(333\) 19.3292 1.05923
\(334\) −13.3465 −0.730289
\(335\) −20.0177 −1.09369
\(336\) 29.0110 1.58268
\(337\) −14.5894 −0.794735 −0.397368 0.917660i \(-0.630076\pi\)
−0.397368 + 0.917660i \(0.630076\pi\)
\(338\) 0 0
\(339\) 27.1248 1.47322
\(340\) 2.29003 0.124195
\(341\) 3.43199 0.185853
\(342\) 22.9941 1.24338
\(343\) 62.6352 3.38198
\(344\) 8.48625 0.457548
\(345\) −7.37368 −0.396985
\(346\) 15.8040 0.849628
\(347\) 0.368012 0.0197559 0.00987796 0.999951i \(-0.496856\pi\)
0.00987796 + 0.999951i \(0.496856\pi\)
\(348\) −16.3171 −0.874687
\(349\) 36.4344 1.95029 0.975145 0.221566i \(-0.0711168\pi\)
0.975145 + 0.221566i \(0.0711168\pi\)
\(350\) −33.7168 −1.80224
\(351\) 0 0
\(352\) −7.87062 −0.419506
\(353\) −21.6896 −1.15442 −0.577210 0.816596i \(-0.695859\pi\)
−0.577210 + 0.816596i \(0.695859\pi\)
\(354\) 0.195905 0.0104122
\(355\) −5.68895 −0.301938
\(356\) 14.6189 0.774800
\(357\) 7.30821 0.386792
\(358\) 29.0432 1.53498
\(359\) −15.7429 −0.830881 −0.415440 0.909620i \(-0.636373\pi\)
−0.415440 + 0.909620i \(0.636373\pi\)
\(360\) −3.12224 −0.164556
\(361\) 13.7168 0.721937
\(362\) 11.5540 0.607263
\(363\) −2.20961 −0.115974
\(364\) 0 0
\(365\) −6.71754 −0.351612
\(366\) 20.2575 1.05887
\(367\) 8.24346 0.430305 0.215153 0.976580i \(-0.430975\pi\)
0.215153 + 0.976580i \(0.430975\pi\)
\(368\) 6.17827 0.322064
\(369\) −7.52721 −0.391851
\(370\) −30.3658 −1.57864
\(371\) −65.0610 −3.37780
\(372\) −19.4202 −1.00689
\(373\) 2.74984 0.142382 0.0711908 0.997463i \(-0.477320\pi\)
0.0711908 + 0.997463i \(0.477320\pi\)
\(374\) −1.37919 −0.0713161
\(375\) −24.7298 −1.27704
\(376\) 14.0269 0.723384
\(377\) 0 0
\(378\) 27.0107 1.38928
\(379\) −21.1587 −1.08685 −0.543424 0.839458i \(-0.682872\pi\)
−0.543424 + 0.839458i \(0.682872\pi\)
\(380\) −20.2829 −1.04049
\(381\) 5.25280 0.269109
\(382\) 7.98580 0.408589
\(383\) −27.9252 −1.42691 −0.713457 0.700699i \(-0.752872\pi\)
−0.713457 + 0.700699i \(0.752872\pi\)
\(384\) 20.3419 1.03807
\(385\) −7.09169 −0.361426
\(386\) −18.1359 −0.923093
\(387\) 13.3356 0.677886
\(388\) −1.59381 −0.0809135
\(389\) −20.4825 −1.03850 −0.519251 0.854622i \(-0.673789\pi\)
−0.519251 + 0.854622i \(0.673789\pi\)
\(390\) 0 0
\(391\) 1.55638 0.0787094
\(392\) 23.0348 1.16343
\(393\) 42.4454 2.14108
\(394\) −37.5799 −1.89325
\(395\) −4.57681 −0.230284
\(396\) 4.82056 0.242242
\(397\) 3.57380 0.179364 0.0896821 0.995970i \(-0.471415\pi\)
0.0896821 + 0.995970i \(0.471415\pi\)
\(398\) 32.3785 1.62299
\(399\) −64.7290 −3.24050
\(400\) 7.90265 0.395132
\(401\) 14.8809 0.743119 0.371559 0.928409i \(-0.378823\pi\)
0.371559 + 0.928409i \(0.378823\pi\)
\(402\) −68.2188 −3.40244
\(403\) 0 0
\(404\) 45.7988 2.27858
\(405\) 15.3753 0.764004
\(406\) 31.5397 1.56529
\(407\) 10.2685 0.508991
\(408\) 1.70932 0.0846238
\(409\) −21.5122 −1.06371 −0.531854 0.846836i \(-0.678504\pi\)
−0.531854 + 0.846836i \(0.678504\pi\)
\(410\) 11.8251 0.584002
\(411\) 41.4732 2.04572
\(412\) −8.91542 −0.439231
\(413\) −0.212619 −0.0104623
\(414\) −9.68829 −0.476154
\(415\) −5.36282 −0.263251
\(416\) 0 0
\(417\) 0.182431 0.00893368
\(418\) 12.2155 0.597479
\(419\) 3.78497 0.184908 0.0924539 0.995717i \(-0.470529\pi\)
0.0924539 + 0.995717i \(0.470529\pi\)
\(420\) 40.1289 1.95809
\(421\) −37.4751 −1.82643 −0.913213 0.407483i \(-0.866407\pi\)
−0.913213 + 0.407483i \(0.866407\pi\)
\(422\) −23.4926 −1.14360
\(423\) 22.0424 1.07174
\(424\) −15.2171 −0.739008
\(425\) 1.99077 0.0965665
\(426\) −19.3874 −0.939325
\(427\) −21.9858 −1.06397
\(428\) 0.693861 0.0335390
\(429\) 0 0
\(430\) −20.9500 −1.01030
\(431\) 13.9068 0.669867 0.334934 0.942242i \(-0.391286\pi\)
0.334934 + 0.942242i \(0.391286\pi\)
\(432\) −6.33086 −0.304594
\(433\) −8.39781 −0.403573 −0.201787 0.979430i \(-0.564675\pi\)
−0.201787 + 0.979430i \(0.564675\pi\)
\(434\) 37.5379 1.80188
\(435\) 8.82271 0.423016
\(436\) −28.9159 −1.38482
\(437\) −13.7849 −0.659419
\(438\) −22.8928 −1.09386
\(439\) −3.77193 −0.180024 −0.0900122 0.995941i \(-0.528691\pi\)
−0.0900122 + 0.995941i \(0.528691\pi\)
\(440\) −1.65867 −0.0790741
\(441\) 36.1977 1.72370
\(442\) 0 0
\(443\) −5.55546 −0.263948 −0.131974 0.991253i \(-0.542132\pi\)
−0.131974 + 0.991253i \(0.542132\pi\)
\(444\) −58.1053 −2.75755
\(445\) −7.90450 −0.374709
\(446\) −35.6009 −1.68575
\(447\) −7.56588 −0.357854
\(448\) −59.8269 −2.82656
\(449\) 25.3384 1.19579 0.597896 0.801574i \(-0.296004\pi\)
0.597896 + 0.801574i \(0.296004\pi\)
\(450\) −12.3923 −0.584180
\(451\) −3.99879 −0.188296
\(452\) −31.4372 −1.47868
\(453\) 32.7608 1.53924
\(454\) 39.3841 1.84839
\(455\) 0 0
\(456\) −15.1394 −0.708969
\(457\) 30.4784 1.42572 0.712859 0.701308i \(-0.247400\pi\)
0.712859 + 0.701308i \(0.247400\pi\)
\(458\) −56.6745 −2.64823
\(459\) −1.59482 −0.0744397
\(460\) 8.54596 0.398457
\(461\) 33.7216 1.57057 0.785285 0.619134i \(-0.212516\pi\)
0.785285 + 0.619134i \(0.212516\pi\)
\(462\) −24.1679 −1.12439
\(463\) −24.1398 −1.12187 −0.560935 0.827860i \(-0.689558\pi\)
−0.560935 + 0.827860i \(0.689558\pi\)
\(464\) −7.39238 −0.343183
\(465\) 10.5006 0.486953
\(466\) 4.29057 0.198757
\(467\) 22.4626 1.03945 0.519723 0.854335i \(-0.326035\pi\)
0.519723 + 0.854335i \(0.326035\pi\)
\(468\) 0 0
\(469\) 74.0391 3.41881
\(470\) −34.6283 −1.59728
\(471\) −5.68824 −0.262100
\(472\) −0.0497295 −0.00228899
\(473\) 7.08446 0.325744
\(474\) −15.5974 −0.716411
\(475\) −17.6323 −0.809024
\(476\) −8.47009 −0.388226
\(477\) −23.9127 −1.09489
\(478\) −51.9449 −2.37590
\(479\) −9.61420 −0.439284 −0.219642 0.975581i \(-0.570489\pi\)
−0.219642 + 0.975581i \(0.570489\pi\)
\(480\) −24.0811 −1.09915
\(481\) 0 0
\(482\) −30.0674 −1.36953
\(483\) 27.2728 1.24096
\(484\) 2.56090 0.116404
\(485\) 0.861780 0.0391314
\(486\) 36.5757 1.65911
\(487\) −18.7202 −0.848295 −0.424147 0.905593i \(-0.639426\pi\)
−0.424147 + 0.905593i \(0.639426\pi\)
\(488\) −5.14225 −0.232779
\(489\) 27.7633 1.25550
\(490\) −56.8660 −2.56894
\(491\) 18.5850 0.838728 0.419364 0.907818i \(-0.362253\pi\)
0.419364 + 0.907818i \(0.362253\pi\)
\(492\) 22.6275 1.02013
\(493\) −1.86223 −0.0838705
\(494\) 0 0
\(495\) −2.60650 −0.117153
\(496\) −8.79825 −0.395053
\(497\) 21.0416 0.943843
\(498\) −18.2760 −0.818969
\(499\) 16.2463 0.727285 0.363642 0.931539i \(-0.381533\pi\)
0.363642 + 0.931539i \(0.381533\pi\)
\(500\) 28.6614 1.28178
\(501\) 13.8089 0.616935
\(502\) −23.1718 −1.03421
\(503\) −14.9137 −0.664971 −0.332485 0.943108i \(-0.607887\pi\)
−0.332485 + 0.943108i \(0.607887\pi\)
\(504\) 11.5481 0.514395
\(505\) −24.7636 −1.10197
\(506\) −5.14686 −0.228806
\(507\) 0 0
\(508\) −6.08790 −0.270107
\(509\) −1.60613 −0.0711904 −0.0355952 0.999366i \(-0.511333\pi\)
−0.0355952 + 0.999366i \(0.511333\pi\)
\(510\) −4.21979 −0.186855
\(511\) 24.8460 1.09912
\(512\) 26.3188 1.16314
\(513\) 14.1253 0.623648
\(514\) −24.5682 −1.08366
\(515\) 4.82060 0.212421
\(516\) −40.0880 −1.76478
\(517\) 11.7099 0.515001
\(518\) 112.313 4.93476
\(519\) −16.3515 −0.717750
\(520\) 0 0
\(521\) 15.5845 0.682769 0.341385 0.939924i \(-0.389104\pi\)
0.341385 + 0.939924i \(0.389104\pi\)
\(522\) 11.5922 0.507376
\(523\) 30.1082 1.31654 0.658269 0.752783i \(-0.271289\pi\)
0.658269 + 0.752783i \(0.271289\pi\)
\(524\) −49.1934 −2.14902
\(525\) 34.8848 1.52250
\(526\) −35.7618 −1.55929
\(527\) −2.21638 −0.0965471
\(528\) 5.66455 0.246518
\(529\) −17.1919 −0.747474
\(530\) 37.5664 1.63178
\(531\) −0.0781467 −0.00339128
\(532\) 75.0197 3.25252
\(533\) 0 0
\(534\) −26.9378 −1.16571
\(535\) −0.375173 −0.0162202
\(536\) 17.3170 0.747980
\(537\) −30.0493 −1.29672
\(538\) −8.73452 −0.376572
\(539\) 19.2298 0.828287
\(540\) −8.75703 −0.376843
\(541\) −7.07231 −0.304062 −0.152031 0.988376i \(-0.548581\pi\)
−0.152031 + 0.988376i \(0.548581\pi\)
\(542\) 22.6170 0.971482
\(543\) −11.9542 −0.513005
\(544\) 5.08285 0.217925
\(545\) 15.6350 0.669728
\(546\) 0 0
\(547\) 3.83951 0.164166 0.0820828 0.996626i \(-0.473843\pi\)
0.0820828 + 0.996626i \(0.473843\pi\)
\(548\) −48.0668 −2.05331
\(549\) −8.08071 −0.344876
\(550\) −6.58337 −0.280716
\(551\) 16.4938 0.702658
\(552\) 6.37883 0.271501
\(553\) 16.9281 0.719857
\(554\) 25.3445 1.07678
\(555\) 31.4177 1.33361
\(556\) −0.211434 −0.00896680
\(557\) −9.17155 −0.388611 −0.194305 0.980941i \(-0.562245\pi\)
−0.194305 + 0.980941i \(0.562245\pi\)
\(558\) 13.7968 0.584063
\(559\) 0 0
\(560\) 18.1802 0.768255
\(561\) 1.42697 0.0602465
\(562\) 24.9811 1.05376
\(563\) −17.3419 −0.730872 −0.365436 0.930836i \(-0.619080\pi\)
−0.365436 + 0.930836i \(0.619080\pi\)
\(564\) −66.2615 −2.79011
\(565\) 16.9982 0.715120
\(566\) −19.9008 −0.836491
\(567\) −56.8681 −2.38824
\(568\) 4.92140 0.206498
\(569\) 26.9476 1.12970 0.564851 0.825193i \(-0.308934\pi\)
0.564851 + 0.825193i \(0.308934\pi\)
\(570\) 37.3747 1.56545
\(571\) −29.1884 −1.22149 −0.610747 0.791825i \(-0.709131\pi\)
−0.610747 + 0.791825i \(0.709131\pi\)
\(572\) 0 0
\(573\) −8.26244 −0.345169
\(574\) −43.7373 −1.82556
\(575\) 7.42916 0.309817
\(576\) −21.9889 −0.916206
\(577\) −16.7437 −0.697049 −0.348524 0.937300i \(-0.613317\pi\)
−0.348524 + 0.937300i \(0.613317\pi\)
\(578\) −35.4150 −1.47307
\(579\) 18.7642 0.779812
\(580\) −10.2254 −0.424585
\(581\) 19.8353 0.822908
\(582\) 2.93687 0.121737
\(583\) −12.7035 −0.526125
\(584\) 5.81122 0.240470
\(585\) 0 0
\(586\) 30.8580 1.27473
\(587\) −2.05072 −0.0846423 −0.0423212 0.999104i \(-0.513475\pi\)
−0.0423212 + 0.999104i \(0.513475\pi\)
\(588\) −108.814 −4.48740
\(589\) 19.6305 0.808862
\(590\) 0.122767 0.00505425
\(591\) 38.8817 1.59938
\(592\) −26.3243 −1.08192
\(593\) 21.3813 0.878023 0.439012 0.898481i \(-0.355329\pi\)
0.439012 + 0.898481i \(0.355329\pi\)
\(594\) 5.27398 0.216394
\(595\) 4.57981 0.187754
\(596\) 8.76873 0.359181
\(597\) −33.5001 −1.37107
\(598\) 0 0
\(599\) −18.8361 −0.769624 −0.384812 0.922995i \(-0.625734\pi\)
−0.384812 + 0.922995i \(0.625734\pi\)
\(600\) 8.15919 0.333098
\(601\) −8.56448 −0.349352 −0.174676 0.984626i \(-0.555888\pi\)
−0.174676 + 0.984626i \(0.555888\pi\)
\(602\) 77.4872 3.15814
\(603\) 27.2125 1.10818
\(604\) −37.9692 −1.54494
\(605\) −1.38469 −0.0562956
\(606\) −84.3923 −3.42820
\(607\) 35.0755 1.42367 0.711836 0.702345i \(-0.247864\pi\)
0.711836 + 0.702345i \(0.247864\pi\)
\(608\) −45.0189 −1.82576
\(609\) −32.6323 −1.32233
\(610\) 12.6947 0.513992
\(611\) 0 0
\(612\) −3.11312 −0.125840
\(613\) 13.5499 0.547276 0.273638 0.961833i \(-0.411773\pi\)
0.273638 + 0.961833i \(0.411773\pi\)
\(614\) 17.4778 0.705346
\(615\) −12.2348 −0.493354
\(616\) 6.13489 0.247182
\(617\) −21.5419 −0.867243 −0.433621 0.901095i \(-0.642764\pi\)
−0.433621 + 0.901095i \(0.642764\pi\)
\(618\) 16.4282 0.660839
\(619\) −33.1911 −1.33406 −0.667031 0.745030i \(-0.732435\pi\)
−0.667031 + 0.745030i \(0.732435\pi\)
\(620\) −12.1700 −0.488759
\(621\) −5.95154 −0.238827
\(622\) −0.107714 −0.00431893
\(623\) 29.2361 1.17132
\(624\) 0 0
\(625\) −0.0841326 −0.00336530
\(626\) 33.4441 1.33670
\(627\) −12.6387 −0.504739
\(628\) 6.59257 0.263072
\(629\) −6.63141 −0.264412
\(630\) −28.5089 −1.13582
\(631\) 40.7567 1.62250 0.811250 0.584700i \(-0.198788\pi\)
0.811250 + 0.584700i \(0.198788\pi\)
\(632\) 3.95931 0.157493
\(633\) 24.3065 0.966095
\(634\) 10.9005 0.432914
\(635\) 3.29175 0.130629
\(636\) 71.8838 2.85038
\(637\) 0 0
\(638\) 6.15828 0.243809
\(639\) 7.73366 0.305939
\(640\) 12.7476 0.503891
\(641\) 21.9440 0.866737 0.433368 0.901217i \(-0.357325\pi\)
0.433368 + 0.901217i \(0.357325\pi\)
\(642\) −1.27856 −0.0504607
\(643\) −3.60153 −0.142031 −0.0710153 0.997475i \(-0.522624\pi\)
−0.0710153 + 0.997475i \(0.522624\pi\)
\(644\) −31.6087 −1.24556
\(645\) 21.6758 0.853482
\(646\) −7.88876 −0.310379
\(647\) 32.3457 1.27164 0.635821 0.771837i \(-0.280662\pi\)
0.635821 + 0.771837i \(0.280662\pi\)
\(648\) −13.3009 −0.522508
\(649\) −0.0415150 −0.00162961
\(650\) 0 0
\(651\) −38.8383 −1.52219
\(652\) −32.1772 −1.26016
\(653\) −18.5689 −0.726659 −0.363330 0.931661i \(-0.618360\pi\)
−0.363330 + 0.931661i \(0.618360\pi\)
\(654\) 53.2826 2.08351
\(655\) 26.5991 1.03931
\(656\) 10.2513 0.400246
\(657\) 9.13195 0.356271
\(658\) 128.079 4.99302
\(659\) −25.7325 −1.00240 −0.501198 0.865332i \(-0.667107\pi\)
−0.501198 + 0.865332i \(0.667107\pi\)
\(660\) 7.83537 0.304991
\(661\) 18.7214 0.728179 0.364090 0.931364i \(-0.381380\pi\)
0.364090 + 0.931364i \(0.381380\pi\)
\(662\) 57.8621 2.24888
\(663\) 0 0
\(664\) 4.63928 0.180039
\(665\) −40.5635 −1.57298
\(666\) 41.2799 1.59956
\(667\) −6.94946 −0.269084
\(668\) −16.0042 −0.619222
\(669\) 36.8342 1.42409
\(670\) −42.7504 −1.65159
\(671\) −4.29284 −0.165723
\(672\) 89.0681 3.43588
\(673\) 23.4403 0.903558 0.451779 0.892130i \(-0.350790\pi\)
0.451779 + 0.892130i \(0.350790\pi\)
\(674\) −31.1575 −1.20014
\(675\) −7.61265 −0.293011
\(676\) 0 0
\(677\) 13.1583 0.505714 0.252857 0.967504i \(-0.418630\pi\)
0.252857 + 0.967504i \(0.418630\pi\)
\(678\) 57.9285 2.22473
\(679\) −3.18744 −0.122323
\(680\) 1.07117 0.0410775
\(681\) −40.7485 −1.56149
\(682\) 7.32946 0.280659
\(683\) 19.3245 0.739432 0.369716 0.929145i \(-0.379455\pi\)
0.369716 + 0.929145i \(0.379455\pi\)
\(684\) 27.5729 1.05428
\(685\) 25.9899 0.993022
\(686\) 133.765 5.10718
\(687\) 58.6378 2.23717
\(688\) −18.1617 −0.692409
\(689\) 0 0
\(690\) −15.7474 −0.599494
\(691\) −28.1049 −1.06916 −0.534581 0.845117i \(-0.679530\pi\)
−0.534581 + 0.845117i \(0.679530\pi\)
\(692\) 18.9511 0.720412
\(693\) 9.64058 0.366215
\(694\) 0.785936 0.0298337
\(695\) 0.114323 0.00433653
\(696\) −7.63236 −0.289304
\(697\) 2.58242 0.0978161
\(698\) 77.8103 2.94516
\(699\) −4.43920 −0.167906
\(700\) −40.4308 −1.52814
\(701\) 8.63821 0.326261 0.163130 0.986605i \(-0.447841\pi\)
0.163130 + 0.986605i \(0.447841\pi\)
\(702\) 0 0
\(703\) 58.7345 2.21521
\(704\) −11.6815 −0.440263
\(705\) 35.8279 1.34936
\(706\) −46.3208 −1.74331
\(707\) 91.5925 3.44469
\(708\) 0.234916 0.00882869
\(709\) 22.7877 0.855811 0.427905 0.903823i \(-0.359252\pi\)
0.427905 + 0.903823i \(0.359252\pi\)
\(710\) −12.1495 −0.455961
\(711\) 6.22180 0.233336
\(712\) 6.83804 0.256266
\(713\) −8.27110 −0.309755
\(714\) 15.6076 0.584100
\(715\) 0 0
\(716\) 34.8266 1.30153
\(717\) 53.7444 2.00712
\(718\) −33.6210 −1.25473
\(719\) −23.4448 −0.874343 −0.437171 0.899378i \(-0.644020\pi\)
−0.437171 + 0.899378i \(0.644020\pi\)
\(720\) 6.68201 0.249024
\(721\) −17.8298 −0.664018
\(722\) 29.2940 1.09021
\(723\) 31.1090 1.15696
\(724\) 13.8547 0.514908
\(725\) −8.88909 −0.330133
\(726\) −4.71890 −0.175135
\(727\) −29.4337 −1.09164 −0.545818 0.837904i \(-0.683781\pi\)
−0.545818 + 0.837904i \(0.683781\pi\)
\(728\) 0 0
\(729\) −4.53143 −0.167831
\(730\) −14.3461 −0.530975
\(731\) −4.57515 −0.169218
\(732\) 24.2914 0.897835
\(733\) −23.7507 −0.877253 −0.438627 0.898669i \(-0.644535\pi\)
−0.438627 + 0.898669i \(0.644535\pi\)
\(734\) 17.6049 0.649810
\(735\) 58.8359 2.17020
\(736\) 18.9682 0.699177
\(737\) 14.4565 0.532512
\(738\) −16.0753 −0.591740
\(739\) −34.0665 −1.25316 −0.626578 0.779359i \(-0.715545\pi\)
−0.626578 + 0.779359i \(0.715545\pi\)
\(740\) −36.4126 −1.33855
\(741\) 0 0
\(742\) −138.946 −5.10087
\(743\) −11.5487 −0.423681 −0.211840 0.977304i \(-0.567946\pi\)
−0.211840 + 0.977304i \(0.567946\pi\)
\(744\) −9.08387 −0.333031
\(745\) −4.74129 −0.173707
\(746\) 5.87264 0.215013
\(747\) 7.29032 0.266739
\(748\) −1.65383 −0.0604699
\(749\) 1.38764 0.0507034
\(750\) −52.8136 −1.92848
\(751\) −5.63835 −0.205746 −0.102873 0.994694i \(-0.532804\pi\)
−0.102873 + 0.994694i \(0.532804\pi\)
\(752\) −30.0195 −1.09470
\(753\) 23.9745 0.873680
\(754\) 0 0
\(755\) 20.5301 0.747166
\(756\) 32.3894 1.17799
\(757\) −22.7592 −0.827197 −0.413599 0.910459i \(-0.635728\pi\)
−0.413599 + 0.910459i \(0.635728\pi\)
\(758\) −45.1870 −1.64127
\(759\) 5.32515 0.193291
\(760\) −9.48738 −0.344143
\(761\) −3.78582 −0.137236 −0.0686180 0.997643i \(-0.521859\pi\)
−0.0686180 + 0.997643i \(0.521859\pi\)
\(762\) 11.2180 0.406385
\(763\) −57.8286 −2.09353
\(764\) 9.57603 0.346449
\(765\) 1.68328 0.0608589
\(766\) −59.6379 −2.15480
\(767\) 0 0
\(768\) −8.18054 −0.295190
\(769\) −13.7937 −0.497412 −0.248706 0.968579i \(-0.580005\pi\)
−0.248706 + 0.968579i \(0.580005\pi\)
\(770\) −15.1452 −0.545795
\(771\) 25.4193 0.915455
\(772\) −21.7473 −0.782704
\(773\) 1.79049 0.0643995 0.0321998 0.999481i \(-0.489749\pi\)
0.0321998 + 0.999481i \(0.489749\pi\)
\(774\) 28.4798 1.02369
\(775\) −10.5796 −0.380031
\(776\) −0.745510 −0.0267623
\(777\) −116.204 −4.16879
\(778\) −43.7429 −1.56826
\(779\) −22.8725 −0.819494
\(780\) 0 0
\(781\) 4.10847 0.147013
\(782\) 3.32384 0.118860
\(783\) 7.12111 0.254488
\(784\) −49.2976 −1.76063
\(785\) −3.56463 −0.127227
\(786\) 90.6474 3.23329
\(787\) 35.3418 1.25980 0.629899 0.776677i \(-0.283096\pi\)
0.629899 + 0.776677i \(0.283096\pi\)
\(788\) −45.0632 −1.60531
\(789\) 37.0007 1.31726
\(790\) −9.77435 −0.347756
\(791\) −62.8708 −2.23543
\(792\) 2.25483 0.0801220
\(793\) 0 0
\(794\) 7.63231 0.270861
\(795\) −38.8678 −1.37850
\(796\) 38.8261 1.37615
\(797\) −28.5171 −1.01013 −0.505063 0.863082i \(-0.668531\pi\)
−0.505063 + 0.863082i \(0.668531\pi\)
\(798\) −138.237 −4.89353
\(799\) −7.56226 −0.267533
\(800\) 24.2623 0.857802
\(801\) 10.7455 0.379674
\(802\) 31.7801 1.12220
\(803\) 4.85130 0.171199
\(804\) −81.8033 −2.88498
\(805\) 17.0910 0.602377
\(806\) 0 0
\(807\) 9.03711 0.318121
\(808\) 21.4225 0.753643
\(809\) −30.2037 −1.06190 −0.530952 0.847402i \(-0.678166\pi\)
−0.530952 + 0.847402i \(0.678166\pi\)
\(810\) 32.8359 1.15373
\(811\) 34.1934 1.20069 0.600347 0.799740i \(-0.295029\pi\)
0.600347 + 0.799740i \(0.295029\pi\)
\(812\) 37.8203 1.32723
\(813\) −23.4005 −0.820690
\(814\) 21.9297 0.768636
\(815\) 17.3983 0.609437
\(816\) −3.65816 −0.128061
\(817\) 40.5221 1.41769
\(818\) −45.9419 −1.60632
\(819\) 0 0
\(820\) 14.1799 0.495183
\(821\) 45.9333 1.60308 0.801541 0.597939i \(-0.204014\pi\)
0.801541 + 0.597939i \(0.204014\pi\)
\(822\) 88.5713 3.08928
\(823\) −30.1187 −1.04987 −0.524936 0.851142i \(-0.675911\pi\)
−0.524936 + 0.851142i \(0.675911\pi\)
\(824\) −4.17022 −0.145276
\(825\) 6.81143 0.237143
\(826\) −0.454076 −0.0157993
\(827\) −27.8723 −0.969214 −0.484607 0.874732i \(-0.661037\pi\)
−0.484607 + 0.874732i \(0.661037\pi\)
\(828\) −11.6175 −0.403738
\(829\) −7.33079 −0.254609 −0.127304 0.991864i \(-0.540633\pi\)
−0.127304 + 0.991864i \(0.540633\pi\)
\(830\) −11.4530 −0.397539
\(831\) −26.2225 −0.909647
\(832\) 0 0
\(833\) −12.4186 −0.430280
\(834\) 0.389604 0.0134909
\(835\) 8.65355 0.299469
\(836\) 14.6480 0.506611
\(837\) 8.47539 0.292952
\(838\) 8.08328 0.279232
\(839\) 40.2027 1.38795 0.693975 0.719999i \(-0.255858\pi\)
0.693975 + 0.719999i \(0.255858\pi\)
\(840\) 18.7704 0.647641
\(841\) −20.6849 −0.713271
\(842\) −80.0328 −2.75811
\(843\) −25.8465 −0.890200
\(844\) −28.1708 −0.969678
\(845\) 0 0
\(846\) 47.0743 1.61845
\(847\) 5.12151 0.175977
\(848\) 32.5666 1.11834
\(849\) 20.5902 0.706653
\(850\) 4.25154 0.145826
\(851\) −24.7471 −0.848320
\(852\) −23.2481 −0.796467
\(853\) −8.07861 −0.276606 −0.138303 0.990390i \(-0.544165\pi\)
−0.138303 + 0.990390i \(0.544165\pi\)
\(854\) −46.9534 −1.60671
\(855\) −14.9088 −0.509870
\(856\) 0.324556 0.0110931
\(857\) −46.1547 −1.57661 −0.788307 0.615282i \(-0.789042\pi\)
−0.788307 + 0.615282i \(0.789042\pi\)
\(858\) 0 0
\(859\) −30.1760 −1.02959 −0.514796 0.857313i \(-0.672132\pi\)
−0.514796 + 0.857313i \(0.672132\pi\)
\(860\) −25.1218 −0.856647
\(861\) 45.2524 1.54220
\(862\) 29.6997 1.01158
\(863\) −24.3157 −0.827715 −0.413858 0.910342i \(-0.635819\pi\)
−0.413858 + 0.910342i \(0.635819\pi\)
\(864\) −19.4367 −0.661249
\(865\) −10.2469 −0.348406
\(866\) −17.9346 −0.609442
\(867\) 36.6418 1.24442
\(868\) 45.0129 1.52784
\(869\) 3.30530 0.112125
\(870\) 18.8420 0.638804
\(871\) 0 0
\(872\) −13.5255 −0.458032
\(873\) −1.17152 −0.0396500
\(874\) −29.4393 −0.995799
\(875\) 57.3196 1.93775
\(876\) −27.4515 −0.927500
\(877\) −15.6622 −0.528876 −0.264438 0.964403i \(-0.585186\pi\)
−0.264438 + 0.964403i \(0.585186\pi\)
\(878\) −8.05543 −0.271858
\(879\) −31.9270 −1.07687
\(880\) 3.54978 0.119663
\(881\) −39.6536 −1.33596 −0.667981 0.744178i \(-0.732841\pi\)
−0.667981 + 0.744178i \(0.732841\pi\)
\(882\) 77.3047 2.60299
\(883\) −1.49267 −0.0502323 −0.0251161 0.999685i \(-0.507996\pi\)
−0.0251161 + 0.999685i \(0.507996\pi\)
\(884\) 0 0
\(885\) −0.127020 −0.00426973
\(886\) −11.8644 −0.398592
\(887\) 26.5235 0.890573 0.445287 0.895388i \(-0.353102\pi\)
0.445287 + 0.895388i \(0.353102\pi\)
\(888\) −27.1789 −0.912065
\(889\) −12.1751 −0.408340
\(890\) −16.8810 −0.565854
\(891\) −11.1038 −0.371991
\(892\) −42.6902 −1.42937
\(893\) 66.9791 2.24137
\(894\) −16.1579 −0.540401
\(895\) −18.8309 −0.629448
\(896\) −47.1490 −1.57514
\(897\) 0 0
\(898\) 54.1133 1.80578
\(899\) 9.89649 0.330066
\(900\) −14.8601 −0.495335
\(901\) 8.20391 0.273312
\(902\) −8.53993 −0.284348
\(903\) −80.1715 −2.66794
\(904\) −14.7048 −0.489076
\(905\) −7.49132 −0.249020
\(906\) 69.9648 2.32442
\(907\) 48.7847 1.61987 0.809935 0.586519i \(-0.199502\pi\)
0.809935 + 0.586519i \(0.199502\pi\)
\(908\) 47.2268 1.56728
\(909\) 33.6641 1.11657
\(910\) 0 0
\(911\) −36.7550 −1.21775 −0.608874 0.793267i \(-0.708379\pi\)
−0.608874 + 0.793267i \(0.708379\pi\)
\(912\) 32.4004 1.07289
\(913\) 3.87295 0.128176
\(914\) 65.0904 2.15300
\(915\) −13.1344 −0.434211
\(916\) −67.9602 −2.24547
\(917\) −98.3813 −3.24884
\(918\) −3.40593 −0.112413
\(919\) −31.1775 −1.02845 −0.514225 0.857655i \(-0.671920\pi\)
−0.514225 + 0.857655i \(0.671920\pi\)
\(920\) 3.99740 0.131790
\(921\) −18.0832 −0.595863
\(922\) 72.0167 2.37174
\(923\) 0 0
\(924\) −28.9805 −0.953387
\(925\) −31.6541 −1.04078
\(926\) −51.5535 −1.69415
\(927\) −6.55322 −0.215236
\(928\) −22.6957 −0.745023
\(929\) 22.0105 0.722141 0.361071 0.932538i \(-0.382411\pi\)
0.361071 + 0.932538i \(0.382411\pi\)
\(930\) 22.4253 0.735356
\(931\) 109.992 3.60484
\(932\) 5.14495 0.168529
\(933\) 0.111445 0.00364856
\(934\) 47.9717 1.56968
\(935\) 0.894231 0.0292445
\(936\) 0 0
\(937\) −9.10082 −0.297311 −0.148655 0.988889i \(-0.547495\pi\)
−0.148655 + 0.988889i \(0.547495\pi\)
\(938\) 158.120 5.16279
\(939\) −34.6027 −1.12922
\(940\) −41.5239 −1.35436
\(941\) −10.7409 −0.350142 −0.175071 0.984556i \(-0.556015\pi\)
−0.175071 + 0.984556i \(0.556015\pi\)
\(942\) −12.1480 −0.395802
\(943\) 9.63708 0.313827
\(944\) 0.106428 0.00346393
\(945\) −17.5131 −0.569701
\(946\) 15.1298 0.491911
\(947\) −22.9686 −0.746379 −0.373190 0.927755i \(-0.621736\pi\)
−0.373190 + 0.927755i \(0.621736\pi\)
\(948\) −18.7033 −0.607455
\(949\) 0 0
\(950\) −37.6559 −1.22172
\(951\) −11.2781 −0.365718
\(952\) −3.96191 −0.128406
\(953\) 11.3117 0.366421 0.183211 0.983074i \(-0.441351\pi\)
0.183211 + 0.983074i \(0.441351\pi\)
\(954\) −51.0686 −1.65341
\(955\) −5.17780 −0.167550
\(956\) −62.2888 −2.01456
\(957\) −6.37162 −0.205965
\(958\) −20.5323 −0.663370
\(959\) −96.1281 −3.10414
\(960\) −35.7410 −1.15353
\(961\) −19.2214 −0.620046
\(962\) 0 0
\(963\) 0.510018 0.0164351
\(964\) −36.0547 −1.16125
\(965\) 11.7589 0.378531
\(966\) 58.2445 1.87399
\(967\) −28.6154 −0.920211 −0.460105 0.887864i \(-0.652188\pi\)
−0.460105 + 0.887864i \(0.652188\pi\)
\(968\) 1.19787 0.0385009
\(969\) 8.16204 0.262203
\(970\) 1.84044 0.0590929
\(971\) 14.1652 0.454583 0.227292 0.973827i \(-0.427013\pi\)
0.227292 + 0.973827i \(0.427013\pi\)
\(972\) 43.8591 1.40678
\(973\) −0.422844 −0.0135558
\(974\) −39.9794 −1.28102
\(975\) 0 0
\(976\) 11.0051 0.352265
\(977\) 33.7336 1.07923 0.539617 0.841910i \(-0.318569\pi\)
0.539617 + 0.841910i \(0.318569\pi\)
\(978\) 59.2920 1.89595
\(979\) 5.70850 0.182445
\(980\) −68.1898 −2.17824
\(981\) −21.2545 −0.678603
\(982\) 39.6906 1.26658
\(983\) −39.6732 −1.26538 −0.632689 0.774406i \(-0.718049\pi\)
−0.632689 + 0.774406i \(0.718049\pi\)
\(984\) 10.5841 0.337408
\(985\) 24.3659 0.776361
\(986\) −3.97702 −0.126654
\(987\) −132.516 −4.21802
\(988\) 0 0
\(989\) −17.0735 −0.542907
\(990\) −5.56650 −0.176915
\(991\) −21.8300 −0.693453 −0.346726 0.937966i \(-0.612707\pi\)
−0.346726 + 0.937966i \(0.612707\pi\)
\(992\) −27.0119 −0.857630
\(993\) −59.8666 −1.89981
\(994\) 44.9369 1.42531
\(995\) −20.9934 −0.665536
\(996\) −21.9154 −0.694416
\(997\) 40.9743 1.29767 0.648834 0.760930i \(-0.275257\pi\)
0.648834 + 0.760930i \(0.275257\pi\)
\(998\) 34.6960 1.09828
\(999\) 25.3583 0.802302
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 1859.2.a.t.1.16 yes 21
13.12 even 2 1859.2.a.s.1.6 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.6 21 13.12 even 2
1859.2.a.t.1.16 yes 21 1.1 even 1 trivial