Properties

Label 1859.2.a.s.1.5
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 1.5
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.14442 q^{2} -1.72478 q^{3} +2.59856 q^{4} +3.54668 q^{5} +3.69866 q^{6} +2.57025 q^{7} -1.28356 q^{8} -0.0251423 q^{9} +O(q^{10})\) \(q-2.14442 q^{2} -1.72478 q^{3} +2.59856 q^{4} +3.54668 q^{5} +3.69866 q^{6} +2.57025 q^{7} -1.28356 q^{8} -0.0251423 q^{9} -7.60558 q^{10} -1.00000 q^{11} -4.48193 q^{12} -5.51170 q^{14} -6.11723 q^{15} -2.44461 q^{16} +4.72512 q^{17} +0.0539157 q^{18} -4.99317 q^{19} +9.21624 q^{20} -4.43311 q^{21} +2.14442 q^{22} +4.05972 q^{23} +2.21386 q^{24} +7.57891 q^{25} +5.21770 q^{27} +6.67894 q^{28} +7.00199 q^{29} +13.1179 q^{30} +5.08275 q^{31} +7.80941 q^{32} +1.72478 q^{33} -10.1327 q^{34} +9.11584 q^{35} -0.0653336 q^{36} +5.18091 q^{37} +10.7075 q^{38} -4.55238 q^{40} -1.93123 q^{41} +9.50646 q^{42} -6.58494 q^{43} -2.59856 q^{44} -0.0891714 q^{45} -8.70576 q^{46} -12.6416 q^{47} +4.21641 q^{48} -0.393826 q^{49} -16.2524 q^{50} -8.14978 q^{51} -4.48415 q^{53} -11.1890 q^{54} -3.54668 q^{55} -3.29908 q^{56} +8.61211 q^{57} -15.0152 q^{58} -9.21857 q^{59} -15.8960 q^{60} +14.7423 q^{61} -10.8996 q^{62} -0.0646218 q^{63} -11.8575 q^{64} -3.69866 q^{66} +13.2163 q^{67} +12.2785 q^{68} -7.00211 q^{69} -19.5482 q^{70} +4.22483 q^{71} +0.0322717 q^{72} +0.634771 q^{73} -11.1101 q^{74} -13.0719 q^{75} -12.9750 q^{76} -2.57025 q^{77} +15.2751 q^{79} -8.67025 q^{80} -8.92394 q^{81} +4.14139 q^{82} -2.96049 q^{83} -11.5197 q^{84} +16.7585 q^{85} +14.1209 q^{86} -12.0769 q^{87} +1.28356 q^{88} +11.2939 q^{89} +0.191221 q^{90} +10.5494 q^{92} -8.76662 q^{93} +27.1089 q^{94} -17.7092 q^{95} -13.4695 q^{96} -1.28597 q^{97} +0.844529 q^{98} +0.0251423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14442 −1.51634 −0.758169 0.652058i \(-0.773906\pi\)
−0.758169 + 0.652058i \(0.773906\pi\)
\(3\) −1.72478 −0.995801 −0.497900 0.867234i \(-0.665895\pi\)
−0.497900 + 0.867234i \(0.665895\pi\)
\(4\) 2.59856 1.29928
\(5\) 3.54668 1.58612 0.793061 0.609142i \(-0.208486\pi\)
0.793061 + 0.609142i \(0.208486\pi\)
\(6\) 3.69866 1.50997
\(7\) 2.57025 0.971462 0.485731 0.874108i \(-0.338553\pi\)
0.485731 + 0.874108i \(0.338553\pi\)
\(8\) −1.28356 −0.453808
\(9\) −0.0251423 −0.00838075
\(10\) −7.60558 −2.40510
\(11\) −1.00000 −0.301511
\(12\) −4.48193 −1.29382
\(13\) 0 0
\(14\) −5.51170 −1.47306
\(15\) −6.11723 −1.57946
\(16\) −2.44461 −0.611153
\(17\) 4.72512 1.14601 0.573005 0.819552i \(-0.305778\pi\)
0.573005 + 0.819552i \(0.305778\pi\)
\(18\) 0.0539157 0.0127080
\(19\) −4.99317 −1.14551 −0.572756 0.819726i \(-0.694126\pi\)
−0.572756 + 0.819726i \(0.694126\pi\)
\(20\) 9.21624 2.06082
\(21\) −4.43311 −0.967383
\(22\) 2.14442 0.457193
\(23\) 4.05972 0.846510 0.423255 0.906011i \(-0.360887\pi\)
0.423255 + 0.906011i \(0.360887\pi\)
\(24\) 2.21386 0.451902
\(25\) 7.57891 1.51578
\(26\) 0 0
\(27\) 5.21770 1.00415
\(28\) 6.67894 1.26220
\(29\) 7.00199 1.30024 0.650118 0.759833i \(-0.274719\pi\)
0.650118 + 0.759833i \(0.274719\pi\)
\(30\) 13.1179 2.39500
\(31\) 5.08275 0.912889 0.456445 0.889752i \(-0.349123\pi\)
0.456445 + 0.889752i \(0.349123\pi\)
\(32\) 7.80941 1.38052
\(33\) 1.72478 0.300245
\(34\) −10.1327 −1.73774
\(35\) 9.11584 1.54086
\(36\) −0.0653336 −0.0108889
\(37\) 5.18091 0.851737 0.425868 0.904785i \(-0.359969\pi\)
0.425868 + 0.904785i \(0.359969\pi\)
\(38\) 10.7075 1.73698
\(39\) 0 0
\(40\) −4.55238 −0.719795
\(41\) −1.93123 −0.301608 −0.150804 0.988564i \(-0.548186\pi\)
−0.150804 + 0.988564i \(0.548186\pi\)
\(42\) 9.50646 1.46688
\(43\) −6.58494 −1.00419 −0.502097 0.864811i \(-0.667438\pi\)
−0.502097 + 0.864811i \(0.667438\pi\)
\(44\) −2.59856 −0.391747
\(45\) −0.0891714 −0.0132929
\(46\) −8.70576 −1.28359
\(47\) −12.6416 −1.84397 −0.921983 0.387231i \(-0.873432\pi\)
−0.921983 + 0.387231i \(0.873432\pi\)
\(48\) 4.21641 0.608587
\(49\) −0.393826 −0.0562608
\(50\) −16.2524 −2.29844
\(51\) −8.14978 −1.14120
\(52\) 0 0
\(53\) −4.48415 −0.615945 −0.307972 0.951395i \(-0.599650\pi\)
−0.307972 + 0.951395i \(0.599650\pi\)
\(54\) −11.1890 −1.52262
\(55\) −3.54668 −0.478234
\(56\) −3.29908 −0.440857
\(57\) 8.61211 1.14070
\(58\) −15.0152 −1.97160
\(59\) −9.21857 −1.20016 −0.600078 0.799941i \(-0.704864\pi\)
−0.600078 + 0.799941i \(0.704864\pi\)
\(60\) −15.8960 −2.05216
\(61\) 14.7423 1.88756 0.943778 0.330580i \(-0.107244\pi\)
0.943778 + 0.330580i \(0.107244\pi\)
\(62\) −10.8996 −1.38425
\(63\) −0.0646218 −0.00814159
\(64\) −11.8575 −1.48218
\(65\) 0 0
\(66\) −3.69866 −0.455273
\(67\) 13.2163 1.61463 0.807315 0.590121i \(-0.200920\pi\)
0.807315 + 0.590121i \(0.200920\pi\)
\(68\) 12.2785 1.48899
\(69\) −7.00211 −0.842955
\(70\) −19.5482 −2.33646
\(71\) 4.22483 0.501395 0.250697 0.968065i \(-0.419340\pi\)
0.250697 + 0.968065i \(0.419340\pi\)
\(72\) 0.0322717 0.00380325
\(73\) 0.634771 0.0742943 0.0371472 0.999310i \(-0.488173\pi\)
0.0371472 + 0.999310i \(0.488173\pi\)
\(74\) −11.1101 −1.29152
\(75\) −13.0719 −1.50942
\(76\) −12.9750 −1.48834
\(77\) −2.57025 −0.292907
\(78\) 0 0
\(79\) 15.2751 1.71859 0.859293 0.511484i \(-0.170904\pi\)
0.859293 + 0.511484i \(0.170904\pi\)
\(80\) −8.67025 −0.969363
\(81\) −8.92394 −0.991549
\(82\) 4.14139 0.457340
\(83\) −2.96049 −0.324956 −0.162478 0.986712i \(-0.551949\pi\)
−0.162478 + 0.986712i \(0.551949\pi\)
\(84\) −11.5197 −1.25690
\(85\) 16.7585 1.81771
\(86\) 14.1209 1.52270
\(87\) −12.0769 −1.29478
\(88\) 1.28356 0.136828
\(89\) 11.2939 1.19715 0.598576 0.801066i \(-0.295734\pi\)
0.598576 + 0.801066i \(0.295734\pi\)
\(90\) 0.191221 0.0201565
\(91\) 0 0
\(92\) 10.5494 1.09985
\(93\) −8.76662 −0.909056
\(94\) 27.1089 2.79607
\(95\) −17.7092 −1.81692
\(96\) −13.4695 −1.37473
\(97\) −1.28597 −0.130571 −0.0652854 0.997867i \(-0.520796\pi\)
−0.0652854 + 0.997867i \(0.520796\pi\)
\(98\) 0.844529 0.0853103
\(99\) 0.0251423 0.00252689
\(100\) 19.6942 1.96942
\(101\) −0.669816 −0.0666492 −0.0333246 0.999445i \(-0.510610\pi\)
−0.0333246 + 0.999445i \(0.510610\pi\)
\(102\) 17.4766 1.73044
\(103\) −8.63085 −0.850423 −0.425212 0.905094i \(-0.639800\pi\)
−0.425212 + 0.905094i \(0.639800\pi\)
\(104\) 0 0
\(105\) −15.7228 −1.53439
\(106\) 9.61592 0.933980
\(107\) −11.1760 −1.08043 −0.540214 0.841528i \(-0.681657\pi\)
−0.540214 + 0.841528i \(0.681657\pi\)
\(108\) 13.5585 1.30467
\(109\) −13.3313 −1.27690 −0.638452 0.769662i \(-0.720425\pi\)
−0.638452 + 0.769662i \(0.720425\pi\)
\(110\) 7.60558 0.725164
\(111\) −8.93592 −0.848160
\(112\) −6.28326 −0.593712
\(113\) −2.50302 −0.235464 −0.117732 0.993045i \(-0.537562\pi\)
−0.117732 + 0.993045i \(0.537562\pi\)
\(114\) −18.4680 −1.72969
\(115\) 14.3985 1.34267
\(116\) 18.1951 1.68937
\(117\) 0 0
\(118\) 19.7685 1.81984
\(119\) 12.1447 1.11330
\(120\) 7.85185 0.716772
\(121\) 1.00000 0.0909091
\(122\) −31.6137 −2.86217
\(123\) 3.33095 0.300342
\(124\) 13.2078 1.18610
\(125\) 9.14657 0.818094
\(126\) 0.138577 0.0123454
\(127\) 4.54101 0.402949 0.201475 0.979494i \(-0.435427\pi\)
0.201475 + 0.979494i \(0.435427\pi\)
\(128\) 9.80864 0.866969
\(129\) 11.3576 0.999978
\(130\) 0 0
\(131\) 14.7762 1.29100 0.645501 0.763759i \(-0.276649\pi\)
0.645501 + 0.763759i \(0.276649\pi\)
\(132\) 4.48193 0.390102
\(133\) −12.8337 −1.11282
\(134\) −28.3414 −2.44832
\(135\) 18.5055 1.59270
\(136\) −6.06499 −0.520068
\(137\) −21.8110 −1.86344 −0.931719 0.363181i \(-0.881691\pi\)
−0.931719 + 0.363181i \(0.881691\pi\)
\(138\) 15.0155 1.27820
\(139\) 9.65198 0.818671 0.409335 0.912384i \(-0.365761\pi\)
0.409335 + 0.912384i \(0.365761\pi\)
\(140\) 23.6880 2.00200
\(141\) 21.8039 1.83622
\(142\) −9.05983 −0.760284
\(143\) 0 0
\(144\) 0.0614631 0.00512192
\(145\) 24.8338 2.06233
\(146\) −1.36122 −0.112655
\(147\) 0.679262 0.0560245
\(148\) 13.4629 1.10664
\(149\) 0.517117 0.0423639 0.0211820 0.999776i \(-0.493257\pi\)
0.0211820 + 0.999776i \(0.493257\pi\)
\(150\) 28.0318 2.28879
\(151\) −7.42259 −0.604042 −0.302021 0.953301i \(-0.597661\pi\)
−0.302021 + 0.953301i \(0.597661\pi\)
\(152\) 6.40905 0.519843
\(153\) −0.118800 −0.00960442
\(154\) 5.51170 0.444146
\(155\) 18.0269 1.44795
\(156\) 0 0
\(157\) 19.9738 1.59409 0.797043 0.603923i \(-0.206396\pi\)
0.797043 + 0.603923i \(0.206396\pi\)
\(158\) −32.7564 −2.60596
\(159\) 7.73416 0.613359
\(160\) 27.6975 2.18968
\(161\) 10.4345 0.822353
\(162\) 19.1367 1.50352
\(163\) −11.3102 −0.885884 −0.442942 0.896550i \(-0.646065\pi\)
−0.442942 + 0.896550i \(0.646065\pi\)
\(164\) −5.01842 −0.391873
\(165\) 6.11723 0.476226
\(166\) 6.34854 0.492742
\(167\) −0.366013 −0.0283230 −0.0141615 0.999900i \(-0.504508\pi\)
−0.0141615 + 0.999900i \(0.504508\pi\)
\(168\) 5.69017 0.439006
\(169\) 0 0
\(170\) −35.9373 −2.75626
\(171\) 0.125540 0.00960025
\(172\) −17.1114 −1.30473
\(173\) 17.3822 1.32154 0.660771 0.750587i \(-0.270229\pi\)
0.660771 + 0.750587i \(0.270229\pi\)
\(174\) 25.8980 1.96332
\(175\) 19.4797 1.47253
\(176\) 2.44461 0.184270
\(177\) 15.9000 1.19512
\(178\) −24.2189 −1.81528
\(179\) −5.97206 −0.446373 −0.223187 0.974776i \(-0.571646\pi\)
−0.223187 + 0.974776i \(0.571646\pi\)
\(180\) −0.231717 −0.0172712
\(181\) 15.3470 1.14073 0.570366 0.821391i \(-0.306801\pi\)
0.570366 + 0.821391i \(0.306801\pi\)
\(182\) 0 0
\(183\) −25.4272 −1.87963
\(184\) −5.21091 −0.384153
\(185\) 18.3750 1.35096
\(186\) 18.7994 1.37844
\(187\) −4.72512 −0.345535
\(188\) −32.8499 −2.39583
\(189\) 13.4108 0.975490
\(190\) 37.9760 2.75507
\(191\) −7.43795 −0.538191 −0.269095 0.963114i \(-0.586725\pi\)
−0.269095 + 0.963114i \(0.586725\pi\)
\(192\) 20.4515 1.47596
\(193\) −10.1737 −0.732316 −0.366158 0.930553i \(-0.619327\pi\)
−0.366158 + 0.930553i \(0.619327\pi\)
\(194\) 2.75767 0.197989
\(195\) 0 0
\(196\) −1.02338 −0.0730985
\(197\) 8.87640 0.632417 0.316209 0.948690i \(-0.397590\pi\)
0.316209 + 0.948690i \(0.397590\pi\)
\(198\) −0.0539157 −0.00383162
\(199\) 3.08077 0.218390 0.109195 0.994020i \(-0.465173\pi\)
0.109195 + 0.994020i \(0.465173\pi\)
\(200\) −9.72801 −0.687874
\(201\) −22.7952 −1.60785
\(202\) 1.43637 0.101063
\(203\) 17.9969 1.26313
\(204\) −21.1777 −1.48273
\(205\) −6.84946 −0.478387
\(206\) 18.5082 1.28953
\(207\) −0.102071 −0.00709439
\(208\) 0 0
\(209\) 4.99317 0.345385
\(210\) 33.7163 2.32665
\(211\) 16.3487 1.12549 0.562744 0.826631i \(-0.309746\pi\)
0.562744 + 0.826631i \(0.309746\pi\)
\(212\) −11.6523 −0.800284
\(213\) −7.28689 −0.499289
\(214\) 23.9662 1.63829
\(215\) −23.3547 −1.59278
\(216\) −6.69724 −0.455690
\(217\) 13.0639 0.886838
\(218\) 28.5879 1.93622
\(219\) −1.09484 −0.0739823
\(220\) −9.21624 −0.621359
\(221\) 0 0
\(222\) 19.1624 1.28610
\(223\) −9.12661 −0.611163 −0.305581 0.952166i \(-0.598851\pi\)
−0.305581 + 0.952166i \(0.598851\pi\)
\(224\) 20.0721 1.34113
\(225\) −0.190551 −0.0127034
\(226\) 5.36754 0.357044
\(227\) 11.6168 0.771032 0.385516 0.922701i \(-0.374023\pi\)
0.385516 + 0.922701i \(0.374023\pi\)
\(228\) 22.3791 1.48209
\(229\) 1.87102 0.123640 0.0618202 0.998087i \(-0.480309\pi\)
0.0618202 + 0.998087i \(0.480309\pi\)
\(230\) −30.8765 −2.03594
\(231\) 4.43311 0.291677
\(232\) −8.98750 −0.590058
\(233\) −10.2911 −0.674189 −0.337095 0.941471i \(-0.609444\pi\)
−0.337095 + 0.941471i \(0.609444\pi\)
\(234\) 0 0
\(235\) −44.8356 −2.92475
\(236\) −23.9550 −1.55934
\(237\) −26.3462 −1.71137
\(238\) −26.0434 −1.68815
\(239\) 9.03038 0.584127 0.292063 0.956399i \(-0.405658\pi\)
0.292063 + 0.956399i \(0.405658\pi\)
\(240\) 14.9542 0.965292
\(241\) 17.6595 1.13755 0.568773 0.822494i \(-0.307418\pi\)
0.568773 + 0.822494i \(0.307418\pi\)
\(242\) −2.14442 −0.137849
\(243\) −0.261279 −0.0167611
\(244\) 38.3087 2.45246
\(245\) −1.39677 −0.0892365
\(246\) −7.14297 −0.455419
\(247\) 0 0
\(248\) −6.52403 −0.414277
\(249\) 5.10618 0.323591
\(250\) −19.6141 −1.24051
\(251\) −20.3256 −1.28294 −0.641471 0.767148i \(-0.721675\pi\)
−0.641471 + 0.767148i \(0.721675\pi\)
\(252\) −0.167924 −0.0105782
\(253\) −4.05972 −0.255232
\(254\) −9.73784 −0.611007
\(255\) −28.9046 −1.81008
\(256\) 2.68106 0.167566
\(257\) −25.0044 −1.55973 −0.779866 0.625947i \(-0.784713\pi\)
−0.779866 + 0.625947i \(0.784713\pi\)
\(258\) −24.3554 −1.51630
\(259\) 13.3162 0.827430
\(260\) 0 0
\(261\) −0.176046 −0.0108970
\(262\) −31.6864 −1.95760
\(263\) 16.8372 1.03822 0.519112 0.854706i \(-0.326263\pi\)
0.519112 + 0.854706i \(0.326263\pi\)
\(264\) −2.21386 −0.136254
\(265\) −15.9038 −0.976964
\(266\) 27.5209 1.68741
\(267\) −19.4795 −1.19212
\(268\) 34.3434 2.09785
\(269\) 26.1626 1.59516 0.797580 0.603213i \(-0.206113\pi\)
0.797580 + 0.603213i \(0.206113\pi\)
\(270\) −39.6836 −2.41507
\(271\) 5.03791 0.306031 0.153016 0.988224i \(-0.451102\pi\)
0.153016 + 0.988224i \(0.451102\pi\)
\(272\) −11.5511 −0.700387
\(273\) 0 0
\(274\) 46.7720 2.82560
\(275\) −7.57891 −0.457026
\(276\) −18.1954 −1.09523
\(277\) 26.2874 1.57946 0.789729 0.613456i \(-0.210221\pi\)
0.789729 + 0.613456i \(0.210221\pi\)
\(278\) −20.6980 −1.24138
\(279\) −0.127792 −0.00765070
\(280\) −11.7008 −0.699254
\(281\) 21.5484 1.28547 0.642734 0.766089i \(-0.277800\pi\)
0.642734 + 0.766089i \(0.277800\pi\)
\(282\) −46.7569 −2.78433
\(283\) 18.1673 1.07994 0.539968 0.841685i \(-0.318436\pi\)
0.539968 + 0.841685i \(0.318436\pi\)
\(284\) 10.9785 0.651452
\(285\) 30.5444 1.80929
\(286\) 0 0
\(287\) −4.96375 −0.293001
\(288\) −0.196346 −0.0115698
\(289\) 5.32673 0.313337
\(290\) −53.2542 −3.12719
\(291\) 2.21802 0.130022
\(292\) 1.64949 0.0965291
\(293\) 3.61441 0.211156 0.105578 0.994411i \(-0.466331\pi\)
0.105578 + 0.994411i \(0.466331\pi\)
\(294\) −1.45663 −0.0849521
\(295\) −32.6953 −1.90359
\(296\) −6.65003 −0.386525
\(297\) −5.21770 −0.302762
\(298\) −1.10892 −0.0642380
\(299\) 0 0
\(300\) −33.9682 −1.96115
\(301\) −16.9249 −0.975537
\(302\) 15.9172 0.915931
\(303\) 1.15528 0.0663693
\(304\) 12.2064 0.700083
\(305\) 52.2861 2.99389
\(306\) 0.254758 0.0145635
\(307\) 6.00757 0.342870 0.171435 0.985195i \(-0.445160\pi\)
0.171435 + 0.985195i \(0.445160\pi\)
\(308\) −6.67894 −0.380568
\(309\) 14.8863 0.846852
\(310\) −38.6573 −2.19559
\(311\) −9.64155 −0.546722 −0.273361 0.961911i \(-0.588135\pi\)
−0.273361 + 0.961911i \(0.588135\pi\)
\(312\) 0 0
\(313\) 1.62146 0.0916503 0.0458251 0.998949i \(-0.485408\pi\)
0.0458251 + 0.998949i \(0.485408\pi\)
\(314\) −42.8324 −2.41717
\(315\) −0.229193 −0.0129135
\(316\) 39.6933 2.23292
\(317\) 2.66354 0.149599 0.0747997 0.997199i \(-0.476168\pi\)
0.0747997 + 0.997199i \(0.476168\pi\)
\(318\) −16.5853 −0.930058
\(319\) −7.00199 −0.392036
\(320\) −42.0546 −2.35093
\(321\) 19.2762 1.07589
\(322\) −22.3760 −1.24696
\(323\) −23.5933 −1.31277
\(324\) −23.1894 −1.28830
\(325\) 0 0
\(326\) 24.2539 1.34330
\(327\) 22.9935 1.27154
\(328\) 2.47886 0.136872
\(329\) −32.4920 −1.79134
\(330\) −13.1179 −0.722119
\(331\) 5.98410 0.328916 0.164458 0.986384i \(-0.447413\pi\)
0.164458 + 0.986384i \(0.447413\pi\)
\(332\) −7.69300 −0.422208
\(333\) −0.130260 −0.00713819
\(334\) 0.784888 0.0429472
\(335\) 46.8740 2.56100
\(336\) 10.8372 0.591219
\(337\) 21.3322 1.16204 0.581018 0.813890i \(-0.302654\pi\)
0.581018 + 0.813890i \(0.302654\pi\)
\(338\) 0 0
\(339\) 4.31716 0.234476
\(340\) 43.5478 2.36171
\(341\) −5.08275 −0.275247
\(342\) −0.269210 −0.0145572
\(343\) −19.0040 −1.02612
\(344\) 8.45219 0.455712
\(345\) −24.8342 −1.33703
\(346\) −37.2748 −2.00390
\(347\) 2.65792 0.142685 0.0713423 0.997452i \(-0.477272\pi\)
0.0713423 + 0.997452i \(0.477272\pi\)
\(348\) −31.3825 −1.68228
\(349\) −27.0398 −1.44741 −0.723703 0.690111i \(-0.757562\pi\)
−0.723703 + 0.690111i \(0.757562\pi\)
\(350\) −41.7727 −2.23285
\(351\) 0 0
\(352\) −7.80941 −0.416243
\(353\) 21.3343 1.13551 0.567754 0.823198i \(-0.307813\pi\)
0.567754 + 0.823198i \(0.307813\pi\)
\(354\) −34.0963 −1.81220
\(355\) 14.9841 0.795273
\(356\) 29.3479 1.55543
\(357\) −20.9469 −1.10863
\(358\) 12.8066 0.676852
\(359\) 4.54231 0.239734 0.119867 0.992790i \(-0.461753\pi\)
0.119867 + 0.992790i \(0.461753\pi\)
\(360\) 0.114457 0.00603242
\(361\) 5.93175 0.312197
\(362\) −32.9104 −1.72973
\(363\) −1.72478 −0.0905273
\(364\) 0 0
\(365\) 2.25133 0.117840
\(366\) 54.5266 2.85015
\(367\) −1.89674 −0.0990091 −0.0495045 0.998774i \(-0.515764\pi\)
−0.0495045 + 0.998774i \(0.515764\pi\)
\(368\) −9.92444 −0.517347
\(369\) 0.0485556 0.00252770
\(370\) −39.4039 −2.04851
\(371\) −11.5254 −0.598367
\(372\) −22.7806 −1.18112
\(373\) 13.4499 0.696409 0.348204 0.937419i \(-0.386792\pi\)
0.348204 + 0.937419i \(0.386792\pi\)
\(374\) 10.1327 0.523947
\(375\) −15.7758 −0.814659
\(376\) 16.2263 0.836806
\(377\) 0 0
\(378\) −28.7584 −1.47917
\(379\) 12.3262 0.633155 0.316578 0.948567i \(-0.397466\pi\)
0.316578 + 0.948567i \(0.397466\pi\)
\(380\) −46.0183 −2.36069
\(381\) −7.83222 −0.401257
\(382\) 15.9501 0.816079
\(383\) −20.1380 −1.02900 −0.514501 0.857490i \(-0.672023\pi\)
−0.514501 + 0.857490i \(0.672023\pi\)
\(384\) −16.9177 −0.863329
\(385\) −9.11584 −0.464586
\(386\) 21.8166 1.11044
\(387\) 0.165560 0.00841591
\(388\) −3.34167 −0.169648
\(389\) −3.79806 −0.192569 −0.0962846 0.995354i \(-0.530696\pi\)
−0.0962846 + 0.995354i \(0.530696\pi\)
\(390\) 0 0
\(391\) 19.1827 0.970108
\(392\) 0.505500 0.0255316
\(393\) −25.4857 −1.28558
\(394\) −19.0348 −0.958958
\(395\) 54.1759 2.72589
\(396\) 0.0653336 0.00328314
\(397\) 6.34245 0.318319 0.159159 0.987253i \(-0.449122\pi\)
0.159159 + 0.987253i \(0.449122\pi\)
\(398\) −6.60648 −0.331153
\(399\) 22.1353 1.10815
\(400\) −18.5275 −0.926375
\(401\) −23.4516 −1.17112 −0.585558 0.810630i \(-0.699125\pi\)
−0.585558 + 0.810630i \(0.699125\pi\)
\(402\) 48.8826 2.43804
\(403\) 0 0
\(404\) −1.74056 −0.0865959
\(405\) −31.6503 −1.57272
\(406\) −38.5929 −1.91533
\(407\) −5.18091 −0.256808
\(408\) 10.4608 0.517884
\(409\) −23.9114 −1.18234 −0.591171 0.806546i \(-0.701334\pi\)
−0.591171 + 0.806546i \(0.701334\pi\)
\(410\) 14.6882 0.725396
\(411\) 37.6191 1.85561
\(412\) −22.4278 −1.10494
\(413\) −23.6940 −1.16591
\(414\) 0.218883 0.0107575
\(415\) −10.4999 −0.515419
\(416\) 0 0
\(417\) −16.6475 −0.815233
\(418\) −10.7075 −0.523720
\(419\) −25.7815 −1.25951 −0.629755 0.776794i \(-0.716845\pi\)
−0.629755 + 0.776794i \(0.716845\pi\)
\(420\) −40.8566 −1.99360
\(421\) 35.1936 1.71523 0.857616 0.514290i \(-0.171945\pi\)
0.857616 + 0.514290i \(0.171945\pi\)
\(422\) −35.0585 −1.70662
\(423\) 0.317838 0.0154538
\(424\) 5.75569 0.279521
\(425\) 35.8113 1.73710
\(426\) 15.6262 0.757091
\(427\) 37.8913 1.83369
\(428\) −29.0416 −1.40378
\(429\) 0 0
\(430\) 50.0823 2.41518
\(431\) 1.23727 0.0595973 0.0297987 0.999556i \(-0.490513\pi\)
0.0297987 + 0.999556i \(0.490513\pi\)
\(432\) −12.7552 −0.613687
\(433\) 28.2869 1.35938 0.679691 0.733499i \(-0.262114\pi\)
0.679691 + 0.733499i \(0.262114\pi\)
\(434\) −28.0146 −1.34475
\(435\) −42.8328 −2.05367
\(436\) −34.6421 −1.65905
\(437\) −20.2709 −0.969687
\(438\) 2.34780 0.112182
\(439\) −4.72129 −0.225335 −0.112668 0.993633i \(-0.535940\pi\)
−0.112668 + 0.993633i \(0.535940\pi\)
\(440\) 4.55238 0.217026
\(441\) 0.00990166 0.000471508 0
\(442\) 0 0
\(443\) −30.7146 −1.45930 −0.729648 0.683823i \(-0.760316\pi\)
−0.729648 + 0.683823i \(0.760316\pi\)
\(444\) −23.2205 −1.10200
\(445\) 40.0558 1.89883
\(446\) 19.5713 0.926729
\(447\) −0.891912 −0.0421860
\(448\) −30.4767 −1.43989
\(449\) 27.6456 1.30468 0.652338 0.757928i \(-0.273788\pi\)
0.652338 + 0.757928i \(0.273788\pi\)
\(450\) 0.408622 0.0192626
\(451\) 1.93123 0.0909383
\(452\) −6.50425 −0.305934
\(453\) 12.8023 0.601505
\(454\) −24.9113 −1.16915
\(455\) 0 0
\(456\) −11.0542 −0.517660
\(457\) 3.15166 0.147428 0.0737142 0.997279i \(-0.476515\pi\)
0.0737142 + 0.997279i \(0.476515\pi\)
\(458\) −4.01226 −0.187481
\(459\) 24.6542 1.15076
\(460\) 37.4154 1.74450
\(461\) 5.36574 0.249908 0.124954 0.992163i \(-0.460122\pi\)
0.124954 + 0.992163i \(0.460122\pi\)
\(462\) −9.50646 −0.442281
\(463\) 16.3015 0.757594 0.378797 0.925480i \(-0.376338\pi\)
0.378797 + 0.925480i \(0.376338\pi\)
\(464\) −17.1171 −0.794644
\(465\) −31.0924 −1.44187
\(466\) 22.0684 1.02230
\(467\) −38.1313 −1.76450 −0.882252 0.470777i \(-0.843973\pi\)
−0.882252 + 0.470777i \(0.843973\pi\)
\(468\) 0 0
\(469\) 33.9692 1.56855
\(470\) 96.1466 4.43491
\(471\) −34.4504 −1.58739
\(472\) 11.8326 0.544641
\(473\) 6.58494 0.302776
\(474\) 56.4974 2.59501
\(475\) −37.8428 −1.73635
\(476\) 31.5588 1.44649
\(477\) 0.112742 0.00516208
\(478\) −19.3650 −0.885733
\(479\) −7.24692 −0.331120 −0.165560 0.986200i \(-0.552943\pi\)
−0.165560 + 0.986200i \(0.552943\pi\)
\(480\) −47.7720 −2.18048
\(481\) 0 0
\(482\) −37.8694 −1.72490
\(483\) −17.9972 −0.818899
\(484\) 2.59856 0.118116
\(485\) −4.56093 −0.207101
\(486\) 0.560293 0.0254154
\(487\) 19.5823 0.887361 0.443680 0.896185i \(-0.353673\pi\)
0.443680 + 0.896185i \(0.353673\pi\)
\(488\) −18.9227 −0.856588
\(489\) 19.5076 0.882164
\(490\) 2.99527 0.135313
\(491\) −0.556479 −0.0251136 −0.0125568 0.999921i \(-0.503997\pi\)
−0.0125568 + 0.999921i \(0.503997\pi\)
\(492\) 8.65567 0.390228
\(493\) 33.0852 1.49008
\(494\) 0 0
\(495\) 0.0891714 0.00400796
\(496\) −12.4254 −0.557915
\(497\) 10.8589 0.487086
\(498\) −10.9498 −0.490673
\(499\) 22.5020 1.00733 0.503664 0.863900i \(-0.331985\pi\)
0.503664 + 0.863900i \(0.331985\pi\)
\(500\) 23.7679 1.06293
\(501\) 0.631292 0.0282040
\(502\) 43.5867 1.94537
\(503\) 9.61297 0.428621 0.214310 0.976766i \(-0.431250\pi\)
0.214310 + 0.976766i \(0.431250\pi\)
\(504\) 0.0829462 0.00369472
\(505\) −2.37562 −0.105714
\(506\) 8.70576 0.387018
\(507\) 0 0
\(508\) 11.8001 0.523543
\(509\) −15.0569 −0.667384 −0.333692 0.942682i \(-0.608295\pi\)
−0.333692 + 0.942682i \(0.608295\pi\)
\(510\) 61.9838 2.74469
\(511\) 1.63152 0.0721741
\(512\) −25.3666 −1.12106
\(513\) −26.0529 −1.15026
\(514\) 53.6200 2.36508
\(515\) −30.6108 −1.34888
\(516\) 29.5133 1.29925
\(517\) 12.6416 0.555976
\(518\) −28.5557 −1.25466
\(519\) −29.9804 −1.31599
\(520\) 0 0
\(521\) −11.3300 −0.496375 −0.248188 0.968712i \(-0.579835\pi\)
−0.248188 + 0.968712i \(0.579835\pi\)
\(522\) 0.377517 0.0165235
\(523\) −11.1265 −0.486527 −0.243264 0.969960i \(-0.578218\pi\)
−0.243264 + 0.969960i \(0.578218\pi\)
\(524\) 38.3968 1.67737
\(525\) −33.5981 −1.46634
\(526\) −36.1060 −1.57430
\(527\) 24.0166 1.04618
\(528\) −4.21641 −0.183496
\(529\) −6.51868 −0.283421
\(530\) 34.1045 1.48141
\(531\) 0.231776 0.0100582
\(532\) −33.3491 −1.44587
\(533\) 0 0
\(534\) 41.7723 1.80766
\(535\) −39.6378 −1.71369
\(536\) −16.9640 −0.732732
\(537\) 10.3005 0.444499
\(538\) −56.1037 −2.41880
\(539\) 0.393826 0.0169633
\(540\) 48.0876 2.06936
\(541\) −45.0049 −1.93491 −0.967455 0.253044i \(-0.918568\pi\)
−0.967455 + 0.253044i \(0.918568\pi\)
\(542\) −10.8034 −0.464047
\(543\) −26.4701 −1.13594
\(544\) 36.9004 1.58209
\(545\) −47.2817 −2.02533
\(546\) 0 0
\(547\) −3.30701 −0.141397 −0.0706987 0.997498i \(-0.522523\pi\)
−0.0706987 + 0.997498i \(0.522523\pi\)
\(548\) −56.6771 −2.42113
\(549\) −0.370654 −0.0158191
\(550\) 16.2524 0.693005
\(551\) −34.9621 −1.48944
\(552\) 8.98765 0.382540
\(553\) 39.2609 1.66954
\(554\) −56.3714 −2.39499
\(555\) −31.6928 −1.34529
\(556\) 25.0812 1.06368
\(557\) 7.28456 0.308657 0.154328 0.988020i \(-0.450679\pi\)
0.154328 + 0.988020i \(0.450679\pi\)
\(558\) 0.274040 0.0116010
\(559\) 0 0
\(560\) −22.2847 −0.941700
\(561\) 8.14978 0.344084
\(562\) −46.2089 −1.94920
\(563\) 21.4623 0.904527 0.452263 0.891884i \(-0.350617\pi\)
0.452263 + 0.891884i \(0.350617\pi\)
\(564\) 56.6588 2.38576
\(565\) −8.87741 −0.373475
\(566\) −38.9585 −1.63755
\(567\) −22.9367 −0.963253
\(568\) −5.42283 −0.227537
\(569\) 29.8261 1.25037 0.625187 0.780475i \(-0.285023\pi\)
0.625187 + 0.780475i \(0.285023\pi\)
\(570\) −65.5001 −2.74350
\(571\) 23.2173 0.971615 0.485807 0.874066i \(-0.338526\pi\)
0.485807 + 0.874066i \(0.338526\pi\)
\(572\) 0 0
\(573\) 12.8288 0.535931
\(574\) 10.6444 0.444288
\(575\) 30.7683 1.28313
\(576\) 0.298124 0.0124218
\(577\) −11.5542 −0.481007 −0.240503 0.970648i \(-0.577313\pi\)
−0.240503 + 0.970648i \(0.577313\pi\)
\(578\) −11.4228 −0.475125
\(579\) 17.5473 0.729241
\(580\) 64.5321 2.67955
\(581\) −7.60919 −0.315682
\(582\) −4.75637 −0.197158
\(583\) 4.48415 0.185714
\(584\) −0.814769 −0.0337154
\(585\) 0 0
\(586\) −7.75082 −0.320183
\(587\) 29.3693 1.21220 0.606101 0.795388i \(-0.292733\pi\)
0.606101 + 0.795388i \(0.292733\pi\)
\(588\) 1.76510 0.0727915
\(589\) −25.3791 −1.04573
\(590\) 70.1126 2.88649
\(591\) −15.3098 −0.629761
\(592\) −12.6653 −0.520541
\(593\) −27.8117 −1.14209 −0.571045 0.820919i \(-0.693462\pi\)
−0.571045 + 0.820919i \(0.693462\pi\)
\(594\) 11.1890 0.459089
\(595\) 43.0734 1.76584
\(596\) 1.34376 0.0550425
\(597\) −5.31364 −0.217473
\(598\) 0 0
\(599\) 26.9070 1.09939 0.549695 0.835366i \(-0.314744\pi\)
0.549695 + 0.835366i \(0.314744\pi\)
\(600\) 16.7787 0.684986
\(601\) 24.9122 1.01619 0.508095 0.861301i \(-0.330350\pi\)
0.508095 + 0.861301i \(0.330350\pi\)
\(602\) 36.2943 1.47924
\(603\) −0.332288 −0.0135318
\(604\) −19.2880 −0.784819
\(605\) 3.54668 0.144193
\(606\) −2.47742 −0.100638
\(607\) −29.8024 −1.20964 −0.604821 0.796361i \(-0.706755\pi\)
−0.604821 + 0.796361i \(0.706755\pi\)
\(608\) −38.9937 −1.58140
\(609\) −31.0406 −1.25783
\(610\) −112.124 −4.53975
\(611\) 0 0
\(612\) −0.308709 −0.0124788
\(613\) −12.7050 −0.513151 −0.256575 0.966524i \(-0.582594\pi\)
−0.256575 + 0.966524i \(0.582594\pi\)
\(614\) −12.8828 −0.519907
\(615\) 11.8138 0.476378
\(616\) 3.29908 0.132924
\(617\) 14.3958 0.579552 0.289776 0.957095i \(-0.406419\pi\)
0.289776 + 0.957095i \(0.406419\pi\)
\(618\) −31.9226 −1.28411
\(619\) −11.0835 −0.445485 −0.222742 0.974877i \(-0.571501\pi\)
−0.222742 + 0.974877i \(0.571501\pi\)
\(620\) 46.8439 1.88130
\(621\) 21.1824 0.850020
\(622\) 20.6756 0.829015
\(623\) 29.0281 1.16299
\(624\) 0 0
\(625\) −5.45464 −0.218186
\(626\) −3.47710 −0.138973
\(627\) −8.61211 −0.343934
\(628\) 51.9032 2.07116
\(629\) 24.4804 0.976098
\(630\) 0.491487 0.0195813
\(631\) −31.1311 −1.23931 −0.619655 0.784874i \(-0.712727\pi\)
−0.619655 + 0.784874i \(0.712727\pi\)
\(632\) −19.6066 −0.779908
\(633\) −28.1978 −1.12076
\(634\) −5.71176 −0.226843
\(635\) 16.1055 0.639126
\(636\) 20.0977 0.796924
\(637\) 0 0
\(638\) 15.0152 0.594459
\(639\) −0.106222 −0.00420207
\(640\) 34.7881 1.37512
\(641\) 32.0469 1.26578 0.632889 0.774243i \(-0.281869\pi\)
0.632889 + 0.774243i \(0.281869\pi\)
\(642\) −41.3363 −1.63141
\(643\) 6.56917 0.259063 0.129531 0.991575i \(-0.458653\pi\)
0.129531 + 0.991575i \(0.458653\pi\)
\(644\) 27.1146 1.06847
\(645\) 40.2816 1.58609
\(646\) 50.5941 1.99060
\(647\) −11.1001 −0.436391 −0.218195 0.975905i \(-0.570017\pi\)
−0.218195 + 0.975905i \(0.570017\pi\)
\(648\) 11.4544 0.449973
\(649\) 9.21857 0.361861
\(650\) 0 0
\(651\) −22.5324 −0.883114
\(652\) −29.3902 −1.15101
\(653\) −22.5719 −0.883307 −0.441653 0.897186i \(-0.645608\pi\)
−0.441653 + 0.897186i \(0.645608\pi\)
\(654\) −49.3078 −1.92809
\(655\) 52.4064 2.04769
\(656\) 4.72112 0.184329
\(657\) −0.0159596 −0.000622642 0
\(658\) 69.6767 2.71628
\(659\) −1.18788 −0.0462734 −0.0231367 0.999732i \(-0.507365\pi\)
−0.0231367 + 0.999732i \(0.507365\pi\)
\(660\) 15.8960 0.618750
\(661\) 8.66908 0.337188 0.168594 0.985686i \(-0.446077\pi\)
0.168594 + 0.985686i \(0.446077\pi\)
\(662\) −12.8325 −0.498748
\(663\) 0 0
\(664\) 3.79997 0.147468
\(665\) −45.5169 −1.76507
\(666\) 0.279332 0.0108239
\(667\) 28.4261 1.10066
\(668\) −0.951107 −0.0367994
\(669\) 15.7414 0.608597
\(670\) −100.518 −3.88334
\(671\) −14.7423 −0.569120
\(672\) −34.6200 −1.33549
\(673\) −12.2403 −0.471828 −0.235914 0.971774i \(-0.575808\pi\)
−0.235914 + 0.971774i \(0.575808\pi\)
\(674\) −45.7452 −1.76204
\(675\) 39.5445 1.52207
\(676\) 0 0
\(677\) 7.83784 0.301233 0.150616 0.988592i \(-0.451874\pi\)
0.150616 + 0.988592i \(0.451874\pi\)
\(678\) −9.25782 −0.355544
\(679\) −3.30527 −0.126845
\(680\) −21.5105 −0.824892
\(681\) −20.0364 −0.767795
\(682\) 10.8996 0.417367
\(683\) −38.2481 −1.46352 −0.731761 0.681561i \(-0.761301\pi\)
−0.731761 + 0.681561i \(0.761301\pi\)
\(684\) 0.326222 0.0124734
\(685\) −77.3565 −2.95564
\(686\) 40.7526 1.55594
\(687\) −3.22709 −0.123121
\(688\) 16.0976 0.613717
\(689\) 0 0
\(690\) 53.2551 2.02739
\(691\) 15.0173 0.571284 0.285642 0.958336i \(-0.407793\pi\)
0.285642 + 0.958336i \(0.407793\pi\)
\(692\) 45.1686 1.71705
\(693\) 0.0646218 0.00245478
\(694\) −5.69971 −0.216358
\(695\) 34.2325 1.29851
\(696\) 15.5014 0.587580
\(697\) −9.12531 −0.345646
\(698\) 57.9848 2.19476
\(699\) 17.7498 0.671358
\(700\) 50.6191 1.91322
\(701\) 45.1498 1.70528 0.852641 0.522497i \(-0.174999\pi\)
0.852641 + 0.522497i \(0.174999\pi\)
\(702\) 0 0
\(703\) −25.8692 −0.975675
\(704\) 11.8575 0.446895
\(705\) 77.3315 2.91247
\(706\) −45.7497 −1.72181
\(707\) −1.72159 −0.0647472
\(708\) 41.3170 1.55279
\(709\) 4.75440 0.178555 0.0892777 0.996007i \(-0.471544\pi\)
0.0892777 + 0.996007i \(0.471544\pi\)
\(710\) −32.1323 −1.20590
\(711\) −0.384051 −0.0144030
\(712\) −14.4964 −0.543277
\(713\) 20.6346 0.772770
\(714\) 44.9192 1.68106
\(715\) 0 0
\(716\) −15.5188 −0.579963
\(717\) −15.5754 −0.581674
\(718\) −9.74065 −0.363518
\(719\) −48.1031 −1.79394 −0.896971 0.442090i \(-0.854237\pi\)
−0.896971 + 0.442090i \(0.854237\pi\)
\(720\) 0.217990 0.00812399
\(721\) −22.1834 −0.826154
\(722\) −12.7202 −0.473397
\(723\) −30.4587 −1.13277
\(724\) 39.8800 1.48213
\(725\) 53.0675 1.97088
\(726\) 3.69866 0.137270
\(727\) −29.3876 −1.08993 −0.544963 0.838460i \(-0.683456\pi\)
−0.544963 + 0.838460i \(0.683456\pi\)
\(728\) 0 0
\(729\) 27.2225 1.00824
\(730\) −4.82780 −0.178685
\(731\) −31.1146 −1.15082
\(732\) −66.0740 −2.44216
\(733\) −30.8866 −1.14082 −0.570411 0.821360i \(-0.693216\pi\)
−0.570411 + 0.821360i \(0.693216\pi\)
\(734\) 4.06742 0.150131
\(735\) 2.40912 0.0888618
\(736\) 31.7040 1.16863
\(737\) −13.2163 −0.486829
\(738\) −0.104124 −0.00383285
\(739\) −1.22732 −0.0451475 −0.0225738 0.999745i \(-0.507186\pi\)
−0.0225738 + 0.999745i \(0.507186\pi\)
\(740\) 47.7486 1.75527
\(741\) 0 0
\(742\) 24.7153 0.907327
\(743\) 28.2751 1.03731 0.518656 0.854983i \(-0.326433\pi\)
0.518656 + 0.854983i \(0.326433\pi\)
\(744\) 11.2525 0.412537
\(745\) 1.83405 0.0671943
\(746\) −28.8423 −1.05599
\(747\) 0.0744333 0.00272337
\(748\) −12.2785 −0.448946
\(749\) −28.7252 −1.04960
\(750\) 33.8300 1.23530
\(751\) −17.1244 −0.624879 −0.312439 0.949938i \(-0.601146\pi\)
−0.312439 + 0.949938i \(0.601146\pi\)
\(752\) 30.9038 1.12694
\(753\) 35.0572 1.27755
\(754\) 0 0
\(755\) −26.3255 −0.958084
\(756\) 34.8487 1.26743
\(757\) 30.5788 1.11141 0.555703 0.831381i \(-0.312449\pi\)
0.555703 + 0.831381i \(0.312449\pi\)
\(758\) −26.4327 −0.960077
\(759\) 7.00211 0.254161
\(760\) 22.7308 0.824534
\(761\) −35.0432 −1.27031 −0.635157 0.772383i \(-0.719065\pi\)
−0.635157 + 0.772383i \(0.719065\pi\)
\(762\) 16.7956 0.608441
\(763\) −34.2647 −1.24046
\(764\) −19.3279 −0.699260
\(765\) −0.421346 −0.0152338
\(766\) 43.1843 1.56031
\(767\) 0 0
\(768\) −4.62423 −0.166862
\(769\) 21.7812 0.785451 0.392725 0.919656i \(-0.371532\pi\)
0.392725 + 0.919656i \(0.371532\pi\)
\(770\) 19.5482 0.704469
\(771\) 43.1270 1.55318
\(772\) −26.4368 −0.951483
\(773\) −43.4039 −1.56113 −0.780565 0.625075i \(-0.785068\pi\)
−0.780565 + 0.625075i \(0.785068\pi\)
\(774\) −0.355032 −0.0127614
\(775\) 38.5217 1.38374
\(776\) 1.65063 0.0592540
\(777\) −22.9675 −0.823956
\(778\) 8.14465 0.292000
\(779\) 9.64298 0.345496
\(780\) 0 0
\(781\) −4.22483 −0.151176
\(782\) −41.1358 −1.47101
\(783\) 36.5343 1.30563
\(784\) 0.962751 0.0343840
\(785\) 70.8407 2.52841
\(786\) 54.6521 1.94937
\(787\) 18.9269 0.674670 0.337335 0.941385i \(-0.390475\pi\)
0.337335 + 0.941385i \(0.390475\pi\)
\(788\) 23.0658 0.821686
\(789\) −29.0404 −1.03386
\(790\) −116.176 −4.13336
\(791\) −6.43339 −0.228745
\(792\) −0.0322717 −0.00114672
\(793\) 0 0
\(794\) −13.6009 −0.482678
\(795\) 27.4306 0.972861
\(796\) 8.00556 0.283749
\(797\) 1.81101 0.0641492 0.0320746 0.999485i \(-0.489789\pi\)
0.0320746 + 0.999485i \(0.489789\pi\)
\(798\) −47.4674 −1.68033
\(799\) −59.7330 −2.11320
\(800\) 59.1869 2.09257
\(801\) −0.283954 −0.0100330
\(802\) 50.2902 1.77581
\(803\) −0.634771 −0.0224006
\(804\) −59.2346 −2.08904
\(805\) 37.0077 1.30435
\(806\) 0 0
\(807\) −45.1246 −1.58846
\(808\) 0.859751 0.0302459
\(809\) 38.2291 1.34407 0.672033 0.740522i \(-0.265421\pi\)
0.672033 + 0.740522i \(0.265421\pi\)
\(810\) 67.8718 2.38477
\(811\) −22.0319 −0.773644 −0.386822 0.922154i \(-0.626427\pi\)
−0.386822 + 0.922154i \(0.626427\pi\)
\(812\) 46.7659 1.64116
\(813\) −8.68927 −0.304746
\(814\) 11.1101 0.389408
\(815\) −40.1136 −1.40512
\(816\) 19.9230 0.697446
\(817\) 32.8798 1.15032
\(818\) 51.2762 1.79283
\(819\) 0 0
\(820\) −17.7987 −0.621559
\(821\) −24.0571 −0.839599 −0.419800 0.907617i \(-0.637900\pi\)
−0.419800 + 0.907617i \(0.637900\pi\)
\(822\) −80.6713 −2.81373
\(823\) −31.3858 −1.09404 −0.547019 0.837120i \(-0.684238\pi\)
−0.547019 + 0.837120i \(0.684238\pi\)
\(824\) 11.0782 0.385929
\(825\) 13.0719 0.455107
\(826\) 50.8100 1.76791
\(827\) −1.22049 −0.0424407 −0.0212203 0.999775i \(-0.506755\pi\)
−0.0212203 + 0.999775i \(0.506755\pi\)
\(828\) −0.265236 −0.00921759
\(829\) 53.2052 1.84789 0.923947 0.382520i \(-0.124944\pi\)
0.923947 + 0.382520i \(0.124944\pi\)
\(830\) 22.5162 0.781550
\(831\) −45.3399 −1.57283
\(832\) 0 0
\(833\) −1.86087 −0.0644754
\(834\) 35.6994 1.23617
\(835\) −1.29813 −0.0449237
\(836\) 12.9750 0.448751
\(837\) 26.5203 0.916675
\(838\) 55.2865 1.90984
\(839\) 8.59689 0.296798 0.148399 0.988928i \(-0.452588\pi\)
0.148399 + 0.988928i \(0.452588\pi\)
\(840\) 20.1812 0.696317
\(841\) 20.0279 0.690616
\(842\) −75.4701 −2.60087
\(843\) −37.1662 −1.28007
\(844\) 42.4830 1.46232
\(845\) 0 0
\(846\) −0.681580 −0.0234332
\(847\) 2.57025 0.0883148
\(848\) 10.9620 0.376437
\(849\) −31.3346 −1.07540
\(850\) −76.7945 −2.63403
\(851\) 21.0331 0.721004
\(852\) −18.9354 −0.648716
\(853\) 34.7749 1.19067 0.595335 0.803477i \(-0.297019\pi\)
0.595335 + 0.803477i \(0.297019\pi\)
\(854\) −81.2551 −2.78049
\(855\) 0.445248 0.0152272
\(856\) 14.3452 0.490307
\(857\) −25.7161 −0.878446 −0.439223 0.898378i \(-0.644746\pi\)
−0.439223 + 0.898378i \(0.644746\pi\)
\(858\) 0 0
\(859\) 37.7344 1.28748 0.643740 0.765244i \(-0.277382\pi\)
0.643740 + 0.765244i \(0.277382\pi\)
\(860\) −60.6885 −2.06946
\(861\) 8.56137 0.291771
\(862\) −2.65324 −0.0903696
\(863\) −43.3135 −1.47441 −0.737204 0.675671i \(-0.763854\pi\)
−0.737204 + 0.675671i \(0.763854\pi\)
\(864\) 40.7472 1.38625
\(865\) 61.6490 2.09613
\(866\) −60.6591 −2.06128
\(867\) −9.18743 −0.312022
\(868\) 33.9474 1.15225
\(869\) −15.2751 −0.518173
\(870\) 91.8517 3.11406
\(871\) 0 0
\(872\) 17.1115 0.579469
\(873\) 0.0323322 0.00109428
\(874\) 43.4694 1.47037
\(875\) 23.5090 0.794748
\(876\) −2.84500 −0.0961237
\(877\) −29.9138 −1.01012 −0.505058 0.863085i \(-0.668529\pi\)
−0.505058 + 0.863085i \(0.668529\pi\)
\(878\) 10.1245 0.341684
\(879\) −6.23404 −0.210269
\(880\) 8.67025 0.292274
\(881\) −6.35670 −0.214163 −0.107081 0.994250i \(-0.534151\pi\)
−0.107081 + 0.994250i \(0.534151\pi\)
\(882\) −0.0212334 −0.000714965 0
\(883\) −7.65280 −0.257537 −0.128769 0.991675i \(-0.541102\pi\)
−0.128769 + 0.991675i \(0.541102\pi\)
\(884\) 0 0
\(885\) 56.3921 1.89560
\(886\) 65.8652 2.21279
\(887\) −8.90168 −0.298889 −0.149445 0.988770i \(-0.547749\pi\)
−0.149445 + 0.988770i \(0.547749\pi\)
\(888\) 11.4698 0.384902
\(889\) 11.6715 0.391450
\(890\) −85.8967 −2.87926
\(891\) 8.92394 0.298963
\(892\) −23.7160 −0.794071
\(893\) 63.1216 2.11228
\(894\) 1.91264 0.0639682
\(895\) −21.1810 −0.708002
\(896\) 25.2106 0.842228
\(897\) 0 0
\(898\) −59.2839 −1.97833
\(899\) 35.5894 1.18697
\(900\) −0.495158 −0.0165053
\(901\) −21.1881 −0.705879
\(902\) −4.14139 −0.137893
\(903\) 29.1918 0.971441
\(904\) 3.21279 0.106856
\(905\) 54.4308 1.80934
\(906\) −27.4536 −0.912085
\(907\) −34.8690 −1.15781 −0.578903 0.815396i \(-0.696519\pi\)
−0.578903 + 0.815396i \(0.696519\pi\)
\(908\) 30.1869 1.00179
\(909\) 0.0168407 0.000558570 0
\(910\) 0 0
\(911\) −13.8230 −0.457976 −0.228988 0.973429i \(-0.573542\pi\)
−0.228988 + 0.973429i \(0.573542\pi\)
\(912\) −21.0533 −0.697143
\(913\) 2.96049 0.0979778
\(914\) −6.75849 −0.223551
\(915\) −90.1819 −2.98132
\(916\) 4.86195 0.160644
\(917\) 37.9785 1.25416
\(918\) −52.8692 −1.74494
\(919\) −18.7389 −0.618139 −0.309070 0.951039i \(-0.600018\pi\)
−0.309070 + 0.951039i \(0.600018\pi\)
\(920\) −18.4814 −0.609314
\(921\) −10.3617 −0.341430
\(922\) −11.5064 −0.378944
\(923\) 0 0
\(924\) 11.5197 0.378970
\(925\) 39.2657 1.29105
\(926\) −34.9573 −1.14877
\(927\) 0.216999 0.00712719
\(928\) 54.6814 1.79501
\(929\) 10.8192 0.354966 0.177483 0.984124i \(-0.443205\pi\)
0.177483 + 0.984124i \(0.443205\pi\)
\(930\) 66.6752 2.18637
\(931\) 1.96644 0.0644474
\(932\) −26.7419 −0.875960
\(933\) 16.6295 0.544426
\(934\) 81.7696 2.67558
\(935\) −16.7585 −0.548060
\(936\) 0 0
\(937\) −50.1230 −1.63745 −0.818724 0.574187i \(-0.805318\pi\)
−0.818724 + 0.574187i \(0.805318\pi\)
\(938\) −72.8444 −2.37845
\(939\) −2.79666 −0.0912654
\(940\) −116.508 −3.80007
\(941\) −54.8886 −1.78932 −0.894659 0.446749i \(-0.852582\pi\)
−0.894659 + 0.446749i \(0.852582\pi\)
\(942\) 73.8764 2.40702
\(943\) −7.84027 −0.255314
\(944\) 22.5358 0.733479
\(945\) 47.5637 1.54725
\(946\) −14.1209 −0.459111
\(947\) 0.903664 0.0293651 0.0146826 0.999892i \(-0.495326\pi\)
0.0146826 + 0.999892i \(0.495326\pi\)
\(948\) −68.4621 −2.22355
\(949\) 0 0
\(950\) 81.1511 2.63289
\(951\) −4.59402 −0.148971
\(952\) −15.5885 −0.505227
\(953\) −33.0470 −1.07050 −0.535248 0.844695i \(-0.679782\pi\)
−0.535248 + 0.844695i \(0.679782\pi\)
\(954\) −0.241766 −0.00782746
\(955\) −26.3800 −0.853636
\(956\) 23.4660 0.758944
\(957\) 12.0769 0.390390
\(958\) 15.5405 0.502090
\(959\) −56.0596 −1.81026
\(960\) 72.5349 2.34105
\(961\) −5.16562 −0.166633
\(962\) 0 0
\(963\) 0.280991 0.00905480
\(964\) 45.8892 1.47799
\(965\) −36.0827 −1.16154
\(966\) 38.5936 1.24173
\(967\) −12.7841 −0.411108 −0.205554 0.978646i \(-0.565900\pi\)
−0.205554 + 0.978646i \(0.565900\pi\)
\(968\) −1.28356 −0.0412553
\(969\) 40.6932 1.30725
\(970\) 9.78057 0.314035
\(971\) 8.74157 0.280530 0.140265 0.990114i \(-0.455204\pi\)
0.140265 + 0.990114i \(0.455204\pi\)
\(972\) −0.678949 −0.0217773
\(973\) 24.8080 0.795308
\(974\) −41.9929 −1.34554
\(975\) 0 0
\(976\) −36.0392 −1.15359
\(977\) 28.2808 0.904784 0.452392 0.891819i \(-0.350571\pi\)
0.452392 + 0.891819i \(0.350571\pi\)
\(978\) −41.8326 −1.33766
\(979\) −11.2939 −0.360955
\(980\) −3.62959 −0.115943
\(981\) 0.335178 0.0107014
\(982\) 1.19333 0.0380806
\(983\) −37.8496 −1.20722 −0.603608 0.797281i \(-0.706271\pi\)
−0.603608 + 0.797281i \(0.706271\pi\)
\(984\) −4.27548 −0.136297
\(985\) 31.4817 1.00309
\(986\) −70.9488 −2.25947
\(987\) 56.0415 1.78382
\(988\) 0 0
\(989\) −26.7330 −0.850061
\(990\) −0.191221 −0.00607742
\(991\) 0.282659 0.00897896 0.00448948 0.999990i \(-0.498571\pi\)
0.00448948 + 0.999990i \(0.498571\pi\)
\(992\) 39.6933 1.26026
\(993\) −10.3212 −0.327535
\(994\) −23.2860 −0.738587
\(995\) 10.9265 0.346393
\(996\) 13.2687 0.420435
\(997\) 9.47402 0.300045 0.150023 0.988683i \(-0.452065\pi\)
0.150023 + 0.988683i \(0.452065\pi\)
\(998\) −48.2539 −1.52745
\(999\) 27.0324 0.855268
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.s.1.5 21
13.12 even 2 1859.2.a.t.1.17 yes 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.5 21 1.1 even 1 trivial
1859.2.a.t.1.17 yes 21 13.12 even 2