Properties

Label 2151.4.a.h.1.10
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.10283 q^{2} +8.83322 q^{4} -7.42154 q^{5} +5.67497 q^{7} -3.41855 q^{8} +O(q^{10})\) \(q-4.10283 q^{2} +8.83322 q^{4} -7.42154 q^{5} +5.67497 q^{7} -3.41855 q^{8} +30.4493 q^{10} +1.97818 q^{11} +0.731609 q^{13} -23.2834 q^{14} -56.6400 q^{16} +109.522 q^{17} +82.2039 q^{19} -65.5561 q^{20} -8.11612 q^{22} +189.006 q^{23} -69.9207 q^{25} -3.00167 q^{26} +50.1282 q^{28} +180.383 q^{29} -85.3258 q^{31} +259.733 q^{32} -449.352 q^{34} -42.1170 q^{35} +336.056 q^{37} -337.269 q^{38} +25.3709 q^{40} -337.799 q^{41} +46.0679 q^{43} +17.4737 q^{44} -775.460 q^{46} +411.751 q^{47} -310.795 q^{49} +286.873 q^{50} +6.46246 q^{52} +672.423 q^{53} -14.6811 q^{55} -19.4002 q^{56} -740.081 q^{58} +219.015 q^{59} +480.554 q^{61} +350.077 q^{62} -612.519 q^{64} -5.42967 q^{65} -575.008 q^{67} +967.434 q^{68} +172.799 q^{70} -483.841 q^{71} +165.298 q^{73} -1378.78 q^{74} +726.125 q^{76} +11.2261 q^{77} +539.826 q^{79} +420.356 q^{80} +1385.93 q^{82} +97.1930 q^{83} -812.825 q^{85} -189.009 q^{86} -6.76249 q^{88} +68.4685 q^{89} +4.15186 q^{91} +1669.53 q^{92} -1689.35 q^{94} -610.080 q^{95} -96.0144 q^{97} +1275.14 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.10283 −1.45057 −0.725285 0.688449i \(-0.758292\pi\)
−0.725285 + 0.688449i \(0.758292\pi\)
\(3\) 0 0
\(4\) 8.83322 1.10415
\(5\) −7.42154 −0.663803 −0.331902 0.943314i \(-0.607690\pi\)
−0.331902 + 0.943314i \(0.607690\pi\)
\(6\) 0 0
\(7\) 5.67497 0.306420 0.153210 0.988194i \(-0.451039\pi\)
0.153210 + 0.988194i \(0.451039\pi\)
\(8\) −3.41855 −0.151080
\(9\) 0 0
\(10\) 30.4493 0.962893
\(11\) 1.97818 0.0542221 0.0271110 0.999632i \(-0.491369\pi\)
0.0271110 + 0.999632i \(0.491369\pi\)
\(12\) 0 0
\(13\) 0.731609 0.0156086 0.00780430 0.999970i \(-0.497516\pi\)
0.00780430 + 0.999970i \(0.497516\pi\)
\(14\) −23.2834 −0.444483
\(15\) 0 0
\(16\) −56.6400 −0.885000
\(17\) 109.522 1.56253 0.781267 0.624197i \(-0.214574\pi\)
0.781267 + 0.624197i \(0.214574\pi\)
\(18\) 0 0
\(19\) 82.2039 0.992573 0.496286 0.868159i \(-0.334697\pi\)
0.496286 + 0.868159i \(0.334697\pi\)
\(20\) −65.5561 −0.732940
\(21\) 0 0
\(22\) −8.11612 −0.0786529
\(23\) 189.006 1.71350 0.856750 0.515732i \(-0.172480\pi\)
0.856750 + 0.515732i \(0.172480\pi\)
\(24\) 0 0
\(25\) −69.9207 −0.559365
\(26\) −3.00167 −0.0226414
\(27\) 0 0
\(28\) 50.1282 0.338334
\(29\) 180.383 1.15504 0.577522 0.816375i \(-0.304020\pi\)
0.577522 + 0.816375i \(0.304020\pi\)
\(30\) 0 0
\(31\) −85.3258 −0.494354 −0.247177 0.968970i \(-0.579503\pi\)
−0.247177 + 0.968970i \(0.579503\pi\)
\(32\) 259.733 1.43483
\(33\) 0 0
\(34\) −449.352 −2.26656
\(35\) −42.1170 −0.203402
\(36\) 0 0
\(37\) 336.056 1.49317 0.746584 0.665291i \(-0.231693\pi\)
0.746584 + 0.665291i \(0.231693\pi\)
\(38\) −337.269 −1.43980
\(39\) 0 0
\(40\) 25.3709 0.100287
\(41\) −337.799 −1.28672 −0.643358 0.765565i \(-0.722459\pi\)
−0.643358 + 0.765565i \(0.722459\pi\)
\(42\) 0 0
\(43\) 46.0679 0.163379 0.0816894 0.996658i \(-0.473968\pi\)
0.0816894 + 0.996658i \(0.473968\pi\)
\(44\) 17.4737 0.0598694
\(45\) 0 0
\(46\) −775.460 −2.48555
\(47\) 411.751 1.27787 0.638937 0.769259i \(-0.279374\pi\)
0.638937 + 0.769259i \(0.279374\pi\)
\(48\) 0 0
\(49\) −310.795 −0.906107
\(50\) 286.873 0.811399
\(51\) 0 0
\(52\) 6.46246 0.0172343
\(53\) 672.423 1.74272 0.871362 0.490641i \(-0.163237\pi\)
0.871362 + 0.490641i \(0.163237\pi\)
\(54\) 0 0
\(55\) −14.6811 −0.0359928
\(56\) −19.4002 −0.0462938
\(57\) 0 0
\(58\) −740.081 −1.67547
\(59\) 219.015 0.483277 0.241639 0.970366i \(-0.422315\pi\)
0.241639 + 0.970366i \(0.422315\pi\)
\(60\) 0 0
\(61\) 480.554 1.00867 0.504333 0.863509i \(-0.331739\pi\)
0.504333 + 0.863509i \(0.331739\pi\)
\(62\) 350.077 0.717094
\(63\) 0 0
\(64\) −612.519 −1.19633
\(65\) −5.42967 −0.0103610
\(66\) 0 0
\(67\) −575.008 −1.04848 −0.524241 0.851570i \(-0.675651\pi\)
−0.524241 + 0.851570i \(0.675651\pi\)
\(68\) 967.434 1.72527
\(69\) 0 0
\(70\) 172.799 0.295049
\(71\) −483.841 −0.808751 −0.404376 0.914593i \(-0.632511\pi\)
−0.404376 + 0.914593i \(0.632511\pi\)
\(72\) 0 0
\(73\) 165.298 0.265023 0.132511 0.991181i \(-0.457696\pi\)
0.132511 + 0.991181i \(0.457696\pi\)
\(74\) −1378.78 −2.16594
\(75\) 0 0
\(76\) 726.125 1.09595
\(77\) 11.2261 0.0166147
\(78\) 0 0
\(79\) 539.826 0.768799 0.384400 0.923167i \(-0.374408\pi\)
0.384400 + 0.923167i \(0.374408\pi\)
\(80\) 420.356 0.587466
\(81\) 0 0
\(82\) 1385.93 1.86647
\(83\) 97.1930 0.128534 0.0642670 0.997933i \(-0.479529\pi\)
0.0642670 + 0.997933i \(0.479529\pi\)
\(84\) 0 0
\(85\) −812.825 −1.03721
\(86\) −189.009 −0.236992
\(87\) 0 0
\(88\) −6.76249 −0.00819186
\(89\) 68.4685 0.0815465 0.0407733 0.999168i \(-0.487018\pi\)
0.0407733 + 0.999168i \(0.487018\pi\)
\(90\) 0 0
\(91\) 4.15186 0.00478278
\(92\) 1669.53 1.89196
\(93\) 0 0
\(94\) −1689.35 −1.85365
\(95\) −610.080 −0.658873
\(96\) 0 0
\(97\) −96.0144 −0.100503 −0.0502515 0.998737i \(-0.516002\pi\)
−0.0502515 + 0.998737i \(0.516002\pi\)
\(98\) 1275.14 1.31437
\(99\) 0 0
\(100\) −617.625 −0.617625
\(101\) −263.049 −0.259152 −0.129576 0.991570i \(-0.541362\pi\)
−0.129576 + 0.991570i \(0.541362\pi\)
\(102\) 0 0
\(103\) 658.943 0.630365 0.315183 0.949031i \(-0.397934\pi\)
0.315183 + 0.949031i \(0.397934\pi\)
\(104\) −2.50104 −0.00235815
\(105\) 0 0
\(106\) −2758.84 −2.52794
\(107\) 410.600 0.370973 0.185487 0.982647i \(-0.440614\pi\)
0.185487 + 0.982647i \(0.440614\pi\)
\(108\) 0 0
\(109\) 163.540 0.143709 0.0718547 0.997415i \(-0.477108\pi\)
0.0718547 + 0.997415i \(0.477108\pi\)
\(110\) 60.2342 0.0522100
\(111\) 0 0
\(112\) −321.430 −0.271181
\(113\) −329.469 −0.274282 −0.137141 0.990552i \(-0.543791\pi\)
−0.137141 + 0.990552i \(0.543791\pi\)
\(114\) 0 0
\(115\) −1402.72 −1.13743
\(116\) 1593.36 1.27534
\(117\) 0 0
\(118\) −898.582 −0.701027
\(119\) 621.536 0.478791
\(120\) 0 0
\(121\) −1327.09 −0.997060
\(122\) −1971.63 −1.46314
\(123\) 0 0
\(124\) −753.701 −0.545842
\(125\) 1446.61 1.03511
\(126\) 0 0
\(127\) −13.3598 −0.00933458 −0.00466729 0.999989i \(-0.501486\pi\)
−0.00466729 + 0.999989i \(0.501486\pi\)
\(128\) 435.201 0.300521
\(129\) 0 0
\(130\) 22.2770 0.0150294
\(131\) −2588.42 −1.72635 −0.863174 0.504906i \(-0.831527\pi\)
−0.863174 + 0.504906i \(0.831527\pi\)
\(132\) 0 0
\(133\) 466.505 0.304144
\(134\) 2359.16 1.52090
\(135\) 0 0
\(136\) −374.407 −0.236067
\(137\) −2002.40 −1.24873 −0.624367 0.781131i \(-0.714643\pi\)
−0.624367 + 0.781131i \(0.714643\pi\)
\(138\) 0 0
\(139\) −388.896 −0.237307 −0.118654 0.992936i \(-0.537858\pi\)
−0.118654 + 0.992936i \(0.537858\pi\)
\(140\) −372.029 −0.224587
\(141\) 0 0
\(142\) 1985.12 1.17315
\(143\) 1.44725 0.000846331 0
\(144\) 0 0
\(145\) −1338.72 −0.766722
\(146\) −678.190 −0.384434
\(147\) 0 0
\(148\) 2968.45 1.64868
\(149\) 2677.35 1.47206 0.736030 0.676949i \(-0.236698\pi\)
0.736030 + 0.676949i \(0.236698\pi\)
\(150\) 0 0
\(151\) −850.590 −0.458411 −0.229205 0.973378i \(-0.573613\pi\)
−0.229205 + 0.973378i \(0.573613\pi\)
\(152\) −281.018 −0.149958
\(153\) 0 0
\(154\) −46.0587 −0.0241008
\(155\) 633.249 0.328153
\(156\) 0 0
\(157\) 1988.14 1.01064 0.505320 0.862932i \(-0.331374\pi\)
0.505320 + 0.862932i \(0.331374\pi\)
\(158\) −2214.81 −1.11520
\(159\) 0 0
\(160\) −1927.62 −0.952447
\(161\) 1072.60 0.525050
\(162\) 0 0
\(163\) 1204.81 0.578946 0.289473 0.957186i \(-0.406520\pi\)
0.289473 + 0.957186i \(0.406520\pi\)
\(164\) −2983.85 −1.42073
\(165\) 0 0
\(166\) −398.766 −0.186447
\(167\) 3692.79 1.71112 0.855559 0.517706i \(-0.173214\pi\)
0.855559 + 0.517706i \(0.173214\pi\)
\(168\) 0 0
\(169\) −2196.46 −0.999756
\(170\) 3334.88 1.50455
\(171\) 0 0
\(172\) 406.928 0.180395
\(173\) −451.652 −0.198488 −0.0992442 0.995063i \(-0.531642\pi\)
−0.0992442 + 0.995063i \(0.531642\pi\)
\(174\) 0 0
\(175\) −396.798 −0.171400
\(176\) −112.044 −0.0479865
\(177\) 0 0
\(178\) −280.914 −0.118289
\(179\) 629.199 0.262729 0.131365 0.991334i \(-0.458064\pi\)
0.131365 + 0.991334i \(0.458064\pi\)
\(180\) 0 0
\(181\) −2513.18 −1.03206 −0.516032 0.856569i \(-0.672591\pi\)
−0.516032 + 0.856569i \(0.672591\pi\)
\(182\) −17.0344 −0.00693776
\(183\) 0 0
\(184\) −646.126 −0.258875
\(185\) −2494.05 −0.991169
\(186\) 0 0
\(187\) 216.654 0.0847238
\(188\) 3637.09 1.41097
\(189\) 0 0
\(190\) 2503.06 0.955741
\(191\) 228.649 0.0866201 0.0433100 0.999062i \(-0.486210\pi\)
0.0433100 + 0.999062i \(0.486210\pi\)
\(192\) 0 0
\(193\) −4350.14 −1.62243 −0.811217 0.584745i \(-0.801195\pi\)
−0.811217 + 0.584745i \(0.801195\pi\)
\(194\) 393.931 0.145787
\(195\) 0 0
\(196\) −2745.32 −1.00048
\(197\) 584.342 0.211333 0.105667 0.994402i \(-0.466302\pi\)
0.105667 + 0.994402i \(0.466302\pi\)
\(198\) 0 0
\(199\) −2528.13 −0.900576 −0.450288 0.892883i \(-0.648679\pi\)
−0.450288 + 0.892883i \(0.648679\pi\)
\(200\) 239.027 0.0845089
\(201\) 0 0
\(202\) 1079.24 0.375917
\(203\) 1023.67 0.353928
\(204\) 0 0
\(205\) 2506.99 0.854126
\(206\) −2703.53 −0.914389
\(207\) 0 0
\(208\) −41.4384 −0.0138136
\(209\) 162.614 0.0538193
\(210\) 0 0
\(211\) −5296.60 −1.72812 −0.864059 0.503390i \(-0.832086\pi\)
−0.864059 + 0.503390i \(0.832086\pi\)
\(212\) 5939.66 1.92423
\(213\) 0 0
\(214\) −1684.62 −0.538123
\(215\) −341.895 −0.108451
\(216\) 0 0
\(217\) −484.221 −0.151480
\(218\) −670.978 −0.208460
\(219\) 0 0
\(220\) −129.682 −0.0397415
\(221\) 80.1276 0.0243890
\(222\) 0 0
\(223\) 3139.10 0.942643 0.471321 0.881961i \(-0.343777\pi\)
0.471321 + 0.881961i \(0.343777\pi\)
\(224\) 1473.98 0.439661
\(225\) 0 0
\(226\) 1351.76 0.397865
\(227\) −11.5535 −0.00337812 −0.00168906 0.999999i \(-0.500538\pi\)
−0.00168906 + 0.999999i \(0.500538\pi\)
\(228\) 0 0
\(229\) −1148.68 −0.331470 −0.165735 0.986170i \(-0.553000\pi\)
−0.165735 + 0.986170i \(0.553000\pi\)
\(230\) 5755.11 1.64992
\(231\) 0 0
\(232\) −616.648 −0.174504
\(233\) −950.126 −0.267145 −0.133573 0.991039i \(-0.542645\pi\)
−0.133573 + 0.991039i \(0.542645\pi\)
\(234\) 0 0
\(235\) −3055.83 −0.848257
\(236\) 1934.61 0.533611
\(237\) 0 0
\(238\) −2550.06 −0.694519
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 1914.79 0.511794 0.255897 0.966704i \(-0.417629\pi\)
0.255897 + 0.966704i \(0.417629\pi\)
\(242\) 5444.81 1.44630
\(243\) 0 0
\(244\) 4244.83 1.11372
\(245\) 2306.58 0.601477
\(246\) 0 0
\(247\) 60.1412 0.0154927
\(248\) 291.690 0.0746869
\(249\) 0 0
\(250\) −5935.21 −1.50150
\(251\) −6780.29 −1.70505 −0.852526 0.522685i \(-0.824930\pi\)
−0.852526 + 0.522685i \(0.824930\pi\)
\(252\) 0 0
\(253\) 373.887 0.0929095
\(254\) 54.8131 0.0135405
\(255\) 0 0
\(256\) 3114.60 0.760400
\(257\) −2358.47 −0.572442 −0.286221 0.958164i \(-0.592399\pi\)
−0.286221 + 0.958164i \(0.592399\pi\)
\(258\) 0 0
\(259\) 1907.11 0.457536
\(260\) −47.9615 −0.0114402
\(261\) 0 0
\(262\) 10619.9 2.50419
\(263\) 3356.03 0.786849 0.393425 0.919357i \(-0.371290\pi\)
0.393425 + 0.919357i \(0.371290\pi\)
\(264\) 0 0
\(265\) −4990.42 −1.15683
\(266\) −1913.99 −0.441181
\(267\) 0 0
\(268\) −5079.17 −1.15768
\(269\) −7072.46 −1.60303 −0.801516 0.597973i \(-0.795973\pi\)
−0.801516 + 0.597973i \(0.795973\pi\)
\(270\) 0 0
\(271\) −2169.26 −0.486248 −0.243124 0.969995i \(-0.578172\pi\)
−0.243124 + 0.969995i \(0.578172\pi\)
\(272\) −6203.35 −1.38284
\(273\) 0 0
\(274\) 8215.51 1.81138
\(275\) −138.315 −0.0303299
\(276\) 0 0
\(277\) 3570.50 0.774479 0.387240 0.921979i \(-0.373429\pi\)
0.387240 + 0.921979i \(0.373429\pi\)
\(278\) 1595.57 0.344231
\(279\) 0 0
\(280\) 143.979 0.0307300
\(281\) 2408.14 0.511238 0.255619 0.966778i \(-0.417721\pi\)
0.255619 + 0.966778i \(0.417721\pi\)
\(282\) 0 0
\(283\) 4218.51 0.886093 0.443046 0.896499i \(-0.353898\pi\)
0.443046 + 0.896499i \(0.353898\pi\)
\(284\) −4273.87 −0.892984
\(285\) 0 0
\(286\) −5.93783 −0.00122766
\(287\) −1917.00 −0.394275
\(288\) 0 0
\(289\) 7082.14 1.44151
\(290\) 5492.54 1.11218
\(291\) 0 0
\(292\) 1460.11 0.292626
\(293\) −7019.97 −1.39970 −0.699848 0.714292i \(-0.746749\pi\)
−0.699848 + 0.714292i \(0.746749\pi\)
\(294\) 0 0
\(295\) −1625.43 −0.320801
\(296\) −1148.82 −0.225588
\(297\) 0 0
\(298\) −10984.7 −2.13533
\(299\) 138.279 0.0267453
\(300\) 0 0
\(301\) 261.434 0.0500624
\(302\) 3489.82 0.664956
\(303\) 0 0
\(304\) −4656.03 −0.878427
\(305\) −3566.45 −0.669555
\(306\) 0 0
\(307\) 3707.37 0.689221 0.344610 0.938746i \(-0.388011\pi\)
0.344610 + 0.938746i \(0.388011\pi\)
\(308\) 99.1625 0.0183452
\(309\) 0 0
\(310\) −2598.11 −0.476009
\(311\) 7560.97 1.37860 0.689298 0.724478i \(-0.257919\pi\)
0.689298 + 0.724478i \(0.257919\pi\)
\(312\) 0 0
\(313\) −629.159 −0.113617 −0.0568086 0.998385i \(-0.518092\pi\)
−0.0568086 + 0.998385i \(0.518092\pi\)
\(314\) −8156.99 −1.46600
\(315\) 0 0
\(316\) 4768.40 0.848871
\(317\) 10835.3 1.91979 0.959893 0.280366i \(-0.0904558\pi\)
0.959893 + 0.280366i \(0.0904558\pi\)
\(318\) 0 0
\(319\) 356.829 0.0626289
\(320\) 4545.84 0.794125
\(321\) 0 0
\(322\) −4400.71 −0.761621
\(323\) 9003.17 1.55093
\(324\) 0 0
\(325\) −51.1546 −0.00873092
\(326\) −4943.14 −0.839801
\(327\) 0 0
\(328\) 1154.78 0.194397
\(329\) 2336.68 0.391566
\(330\) 0 0
\(331\) −4714.96 −0.782953 −0.391476 0.920188i \(-0.628036\pi\)
−0.391476 + 0.920188i \(0.628036\pi\)
\(332\) 858.527 0.141921
\(333\) 0 0
\(334\) −15150.9 −2.48210
\(335\) 4267.44 0.695986
\(336\) 0 0
\(337\) −2761.14 −0.446318 −0.223159 0.974782i \(-0.571637\pi\)
−0.223159 + 0.974782i \(0.571637\pi\)
\(338\) 9011.72 1.45022
\(339\) 0 0
\(340\) −7179.86 −1.14524
\(341\) −168.789 −0.0268049
\(342\) 0 0
\(343\) −3710.26 −0.584068
\(344\) −157.485 −0.0246832
\(345\) 0 0
\(346\) 1853.05 0.287921
\(347\) 2930.86 0.453420 0.226710 0.973962i \(-0.427203\pi\)
0.226710 + 0.973962i \(0.427203\pi\)
\(348\) 0 0
\(349\) 11425.2 1.75236 0.876181 0.481982i \(-0.160083\pi\)
0.876181 + 0.481982i \(0.160083\pi\)
\(350\) 1627.99 0.248628
\(351\) 0 0
\(352\) 513.797 0.0777997
\(353\) −3672.52 −0.553735 −0.276868 0.960908i \(-0.589296\pi\)
−0.276868 + 0.960908i \(0.589296\pi\)
\(354\) 0 0
\(355\) 3590.85 0.536852
\(356\) 604.797 0.0900398
\(357\) 0 0
\(358\) −2581.50 −0.381107
\(359\) −194.274 −0.0285609 −0.0142805 0.999898i \(-0.504546\pi\)
−0.0142805 + 0.999898i \(0.504546\pi\)
\(360\) 0 0
\(361\) −101.511 −0.0147997
\(362\) 10311.2 1.49708
\(363\) 0 0
\(364\) 36.6743 0.00528092
\(365\) −1226.77 −0.175923
\(366\) 0 0
\(367\) −8736.56 −1.24263 −0.621315 0.783561i \(-0.713401\pi\)
−0.621315 + 0.783561i \(0.713401\pi\)
\(368\) −10705.3 −1.51645
\(369\) 0 0
\(370\) 10232.7 1.43776
\(371\) 3815.98 0.534005
\(372\) 0 0
\(373\) 8401.37 1.16624 0.583118 0.812387i \(-0.301832\pi\)
0.583118 + 0.812387i \(0.301832\pi\)
\(374\) −888.897 −0.122898
\(375\) 0 0
\(376\) −1407.59 −0.193061
\(377\) 131.970 0.0180286
\(378\) 0 0
\(379\) 8294.84 1.12421 0.562107 0.827064i \(-0.309991\pi\)
0.562107 + 0.827064i \(0.309991\pi\)
\(380\) −5388.97 −0.727496
\(381\) 0 0
\(382\) −938.106 −0.125648
\(383\) −13231.8 −1.76531 −0.882656 0.470020i \(-0.844247\pi\)
−0.882656 + 0.470020i \(0.844247\pi\)
\(384\) 0 0
\(385\) −83.3149 −0.0110289
\(386\) 17847.9 2.35345
\(387\) 0 0
\(388\) −848.116 −0.110971
\(389\) 1343.03 0.175050 0.0875250 0.996162i \(-0.472104\pi\)
0.0875250 + 0.996162i \(0.472104\pi\)
\(390\) 0 0
\(391\) 20700.4 2.67740
\(392\) 1062.47 0.136895
\(393\) 0 0
\(394\) −2397.46 −0.306553
\(395\) −4006.34 −0.510331
\(396\) 0 0
\(397\) −5223.00 −0.660290 −0.330145 0.943930i \(-0.607098\pi\)
−0.330145 + 0.943930i \(0.607098\pi\)
\(398\) 10372.5 1.30635
\(399\) 0 0
\(400\) 3960.31 0.495039
\(401\) −2065.04 −0.257165 −0.128582 0.991699i \(-0.541043\pi\)
−0.128582 + 0.991699i \(0.541043\pi\)
\(402\) 0 0
\(403\) −62.4251 −0.00771617
\(404\) −2323.57 −0.286143
\(405\) 0 0
\(406\) −4199.94 −0.513397
\(407\) 664.777 0.0809626
\(408\) 0 0
\(409\) 6781.26 0.819833 0.409917 0.912123i \(-0.365558\pi\)
0.409917 + 0.912123i \(0.365558\pi\)
\(410\) −10285.8 −1.23897
\(411\) 0 0
\(412\) 5820.59 0.696019
\(413\) 1242.90 0.148086
\(414\) 0 0
\(415\) −721.322 −0.0853213
\(416\) 190.023 0.0223958
\(417\) 0 0
\(418\) −667.177 −0.0780687
\(419\) 12444.2 1.45092 0.725462 0.688262i \(-0.241626\pi\)
0.725462 + 0.688262i \(0.241626\pi\)
\(420\) 0 0
\(421\) 1394.38 0.161420 0.0807099 0.996738i \(-0.474281\pi\)
0.0807099 + 0.996738i \(0.474281\pi\)
\(422\) 21731.1 2.50676
\(423\) 0 0
\(424\) −2298.71 −0.263291
\(425\) −7657.88 −0.874027
\(426\) 0 0
\(427\) 2727.13 0.309075
\(428\) 3626.91 0.409611
\(429\) 0 0
\(430\) 1402.74 0.157316
\(431\) 10732.9 1.19950 0.599750 0.800187i \(-0.295266\pi\)
0.599750 + 0.800187i \(0.295266\pi\)
\(432\) 0 0
\(433\) 4781.67 0.530698 0.265349 0.964152i \(-0.414513\pi\)
0.265349 + 0.964152i \(0.414513\pi\)
\(434\) 1986.68 0.219732
\(435\) 0 0
\(436\) 1444.59 0.158677
\(437\) 15537.0 1.70077
\(438\) 0 0
\(439\) 7803.24 0.848356 0.424178 0.905579i \(-0.360563\pi\)
0.424178 + 0.905579i \(0.360563\pi\)
\(440\) 50.1881 0.00543778
\(441\) 0 0
\(442\) −328.750 −0.0353779
\(443\) 5285.63 0.566880 0.283440 0.958990i \(-0.408524\pi\)
0.283440 + 0.958990i \(0.408524\pi\)
\(444\) 0 0
\(445\) −508.142 −0.0541308
\(446\) −12879.2 −1.36737
\(447\) 0 0
\(448\) −3476.03 −0.366578
\(449\) 12053.2 1.26687 0.633436 0.773795i \(-0.281644\pi\)
0.633436 + 0.773795i \(0.281644\pi\)
\(450\) 0 0
\(451\) −668.227 −0.0697684
\(452\) −2910.27 −0.302849
\(453\) 0 0
\(454\) 47.4021 0.00490020
\(455\) −30.8132 −0.00317483
\(456\) 0 0
\(457\) 3222.88 0.329891 0.164945 0.986303i \(-0.447255\pi\)
0.164945 + 0.986303i \(0.447255\pi\)
\(458\) 4712.83 0.480821
\(459\) 0 0
\(460\) −12390.5 −1.25589
\(461\) 11082.0 1.11961 0.559805 0.828624i \(-0.310876\pi\)
0.559805 + 0.828624i \(0.310876\pi\)
\(462\) 0 0
\(463\) 9696.33 0.973276 0.486638 0.873604i \(-0.338223\pi\)
0.486638 + 0.873604i \(0.338223\pi\)
\(464\) −10216.9 −1.02221
\(465\) 0 0
\(466\) 3898.21 0.387513
\(467\) 13395.3 1.32732 0.663662 0.748033i \(-0.269001\pi\)
0.663662 + 0.748033i \(0.269001\pi\)
\(468\) 0 0
\(469\) −3263.15 −0.321276
\(470\) 12537.6 1.23046
\(471\) 0 0
\(472\) −748.714 −0.0730135
\(473\) 91.1304 0.00885873
\(474\) 0 0
\(475\) −5747.76 −0.555211
\(476\) 5490.16 0.528658
\(477\) 0 0
\(478\) 980.576 0.0938295
\(479\) 12902.1 1.23071 0.615356 0.788249i \(-0.289012\pi\)
0.615356 + 0.788249i \(0.289012\pi\)
\(480\) 0 0
\(481\) 245.861 0.0233063
\(482\) −7856.05 −0.742392
\(483\) 0 0
\(484\) −11722.4 −1.10091
\(485\) 712.575 0.0667142
\(486\) 0 0
\(487\) 15869.1 1.47658 0.738292 0.674481i \(-0.235633\pi\)
0.738292 + 0.674481i \(0.235633\pi\)
\(488\) −1642.80 −0.152389
\(489\) 0 0
\(490\) −9463.49 −0.872484
\(491\) 15691.2 1.44223 0.721114 0.692816i \(-0.243630\pi\)
0.721114 + 0.692816i \(0.243630\pi\)
\(492\) 0 0
\(493\) 19756.0 1.80480
\(494\) −246.749 −0.0224732
\(495\) 0 0
\(496\) 4832.85 0.437503
\(497\) −2745.78 −0.247817
\(498\) 0 0
\(499\) −15943.3 −1.43030 −0.715149 0.698972i \(-0.753641\pi\)
−0.715149 + 0.698972i \(0.753641\pi\)
\(500\) 12778.2 1.14292
\(501\) 0 0
\(502\) 27818.4 2.47330
\(503\) −1777.64 −0.157576 −0.0787882 0.996891i \(-0.525105\pi\)
−0.0787882 + 0.996891i \(0.525105\pi\)
\(504\) 0 0
\(505\) 1952.23 0.172026
\(506\) −1534.00 −0.134772
\(507\) 0 0
\(508\) −118.010 −0.0103068
\(509\) 9604.37 0.836358 0.418179 0.908365i \(-0.362669\pi\)
0.418179 + 0.908365i \(0.362669\pi\)
\(510\) 0 0
\(511\) 938.061 0.0812082
\(512\) −16260.3 −1.40353
\(513\) 0 0
\(514\) 9676.42 0.830367
\(515\) −4890.38 −0.418438
\(516\) 0 0
\(517\) 814.517 0.0692890
\(518\) −7824.53 −0.663688
\(519\) 0 0
\(520\) 18.5616 0.00156535
\(521\) 3976.84 0.334412 0.167206 0.985922i \(-0.446526\pi\)
0.167206 + 0.985922i \(0.446526\pi\)
\(522\) 0 0
\(523\) 5611.16 0.469137 0.234569 0.972100i \(-0.424632\pi\)
0.234569 + 0.972100i \(0.424632\pi\)
\(524\) −22864.1 −1.90615
\(525\) 0 0
\(526\) −13769.2 −1.14138
\(527\) −9345.08 −0.772444
\(528\) 0 0
\(529\) 23556.3 1.93608
\(530\) 20474.8 1.67806
\(531\) 0 0
\(532\) 4120.74 0.335821
\(533\) −247.137 −0.0200839
\(534\) 0 0
\(535\) −3047.28 −0.246253
\(536\) 1965.69 0.158405
\(537\) 0 0
\(538\) 29017.1 2.32531
\(539\) −614.807 −0.0491310
\(540\) 0 0
\(541\) −8065.22 −0.640944 −0.320472 0.947258i \(-0.603842\pi\)
−0.320472 + 0.947258i \(0.603842\pi\)
\(542\) 8900.12 0.705337
\(543\) 0 0
\(544\) 28446.5 2.24198
\(545\) −1213.72 −0.0953947
\(546\) 0 0
\(547\) −7739.19 −0.604943 −0.302472 0.953158i \(-0.597812\pi\)
−0.302472 + 0.953158i \(0.597812\pi\)
\(548\) −17687.6 −1.37879
\(549\) 0 0
\(550\) 567.485 0.0439957
\(551\) 14828.2 1.14647
\(552\) 0 0
\(553\) 3063.49 0.235575
\(554\) −14649.2 −1.12344
\(555\) 0 0
\(556\) −3435.20 −0.262024
\(557\) −12486.6 −0.949865 −0.474933 0.880022i \(-0.657528\pi\)
−0.474933 + 0.880022i \(0.657528\pi\)
\(558\) 0 0
\(559\) 33.7037 0.00255012
\(560\) 2385.51 0.180011
\(561\) 0 0
\(562\) −9880.20 −0.741586
\(563\) −11511.2 −0.861703 −0.430852 0.902423i \(-0.641787\pi\)
−0.430852 + 0.902423i \(0.641787\pi\)
\(564\) 0 0
\(565\) 2445.17 0.182069
\(566\) −17307.8 −1.28534
\(567\) 0 0
\(568\) 1654.03 0.122186
\(569\) 15667.4 1.15432 0.577162 0.816629i \(-0.304160\pi\)
0.577162 + 0.816629i \(0.304160\pi\)
\(570\) 0 0
\(571\) −3951.30 −0.289591 −0.144796 0.989462i \(-0.546252\pi\)
−0.144796 + 0.989462i \(0.546252\pi\)
\(572\) 12.7839 0.000934478 0
\(573\) 0 0
\(574\) 7865.13 0.571923
\(575\) −13215.4 −0.958473
\(576\) 0 0
\(577\) 1864.58 0.134530 0.0672648 0.997735i \(-0.478573\pi\)
0.0672648 + 0.997735i \(0.478573\pi\)
\(578\) −29056.8 −2.09101
\(579\) 0 0
\(580\) −11825.2 −0.846578
\(581\) 551.567 0.0393853
\(582\) 0 0
\(583\) 1330.17 0.0944941
\(584\) −565.079 −0.0400396
\(585\) 0 0
\(586\) 28801.7 2.03036
\(587\) −22511.7 −1.58289 −0.791447 0.611238i \(-0.790672\pi\)
−0.791447 + 0.611238i \(0.790672\pi\)
\(588\) 0 0
\(589\) −7014.12 −0.490682
\(590\) 6668.87 0.465344
\(591\) 0 0
\(592\) −19034.2 −1.32145
\(593\) 6682.50 0.462761 0.231380 0.972863i \(-0.425676\pi\)
0.231380 + 0.972863i \(0.425676\pi\)
\(594\) 0 0
\(595\) −4612.76 −0.317823
\(596\) 23649.6 1.62538
\(597\) 0 0
\(598\) −567.334 −0.0387960
\(599\) −14057.5 −0.958890 −0.479445 0.877572i \(-0.659162\pi\)
−0.479445 + 0.877572i \(0.659162\pi\)
\(600\) 0 0
\(601\) −17801.8 −1.20824 −0.604118 0.796895i \(-0.706474\pi\)
−0.604118 + 0.796895i \(0.706474\pi\)
\(602\) −1072.62 −0.0726191
\(603\) 0 0
\(604\) −7513.44 −0.506155
\(605\) 9849.03 0.661851
\(606\) 0 0
\(607\) 19937.3 1.33316 0.666581 0.745433i \(-0.267757\pi\)
0.666581 + 0.745433i \(0.267757\pi\)
\(608\) 21351.1 1.42418
\(609\) 0 0
\(610\) 14632.5 0.971237
\(611\) 301.241 0.0199458
\(612\) 0 0
\(613\) 27224.1 1.79375 0.896877 0.442281i \(-0.145831\pi\)
0.896877 + 0.442281i \(0.145831\pi\)
\(614\) −15210.7 −0.999762
\(615\) 0 0
\(616\) −38.3769 −0.00251015
\(617\) −15111.7 −0.986018 −0.493009 0.870024i \(-0.664103\pi\)
−0.493009 + 0.870024i \(0.664103\pi\)
\(618\) 0 0
\(619\) 12209.5 0.792796 0.396398 0.918079i \(-0.370260\pi\)
0.396398 + 0.918079i \(0.370260\pi\)
\(620\) 5593.63 0.362331
\(621\) 0 0
\(622\) −31021.4 −1.99975
\(623\) 388.556 0.0249874
\(624\) 0 0
\(625\) −1996.01 −0.127745
\(626\) 2581.33 0.164810
\(627\) 0 0
\(628\) 17561.6 1.11590
\(629\) 36805.6 2.33312
\(630\) 0 0
\(631\) 3761.08 0.237284 0.118642 0.992937i \(-0.462146\pi\)
0.118642 + 0.992937i \(0.462146\pi\)
\(632\) −1845.42 −0.116150
\(633\) 0 0
\(634\) −44455.5 −2.78478
\(635\) 99.1505 0.00619633
\(636\) 0 0
\(637\) −227.380 −0.0141431
\(638\) −1464.01 −0.0908476
\(639\) 0 0
\(640\) −3229.86 −0.199487
\(641\) −29899.9 −1.84239 −0.921197 0.389097i \(-0.872787\pi\)
−0.921197 + 0.389097i \(0.872787\pi\)
\(642\) 0 0
\(643\) 21028.7 1.28972 0.644860 0.764300i \(-0.276915\pi\)
0.644860 + 0.764300i \(0.276915\pi\)
\(644\) 9474.54 0.579735
\(645\) 0 0
\(646\) −36938.5 −2.24973
\(647\) −6910.94 −0.419934 −0.209967 0.977709i \(-0.567336\pi\)
−0.209967 + 0.977709i \(0.567336\pi\)
\(648\) 0 0
\(649\) 433.251 0.0262043
\(650\) 209.879 0.0126648
\(651\) 0 0
\(652\) 10642.4 0.639244
\(653\) −24024.8 −1.43976 −0.719879 0.694099i \(-0.755803\pi\)
−0.719879 + 0.694099i \(0.755803\pi\)
\(654\) 0 0
\(655\) 19210.1 1.14596
\(656\) 19133.0 1.13874
\(657\) 0 0
\(658\) −9586.98 −0.567993
\(659\) 7052.74 0.416898 0.208449 0.978033i \(-0.433159\pi\)
0.208449 + 0.978033i \(0.433159\pi\)
\(660\) 0 0
\(661\) 4552.03 0.267857 0.133929 0.990991i \(-0.457241\pi\)
0.133929 + 0.990991i \(0.457241\pi\)
\(662\) 19344.7 1.13573
\(663\) 0 0
\(664\) −332.259 −0.0194189
\(665\) −3462.19 −0.201891
\(666\) 0 0
\(667\) 34093.5 1.97917
\(668\) 32619.2 1.88933
\(669\) 0 0
\(670\) −17508.6 −1.00958
\(671\) 950.620 0.0546919
\(672\) 0 0
\(673\) −7578.33 −0.434061 −0.217031 0.976165i \(-0.569637\pi\)
−0.217031 + 0.976165i \(0.569637\pi\)
\(674\) 11328.5 0.647415
\(675\) 0 0
\(676\) −19401.8 −1.10388
\(677\) 14482.8 0.822187 0.411093 0.911593i \(-0.365147\pi\)
0.411093 + 0.911593i \(0.365147\pi\)
\(678\) 0 0
\(679\) −544.879 −0.0307961
\(680\) 2778.68 0.156702
\(681\) 0 0
\(682\) 692.514 0.0388823
\(683\) 12786.8 0.716357 0.358179 0.933653i \(-0.383398\pi\)
0.358179 + 0.933653i \(0.383398\pi\)
\(684\) 0 0
\(685\) 14860.9 0.828914
\(686\) 15222.6 0.847232
\(687\) 0 0
\(688\) −2609.29 −0.144590
\(689\) 491.951 0.0272015
\(690\) 0 0
\(691\) −20525.4 −1.12999 −0.564994 0.825095i \(-0.691122\pi\)
−0.564994 + 0.825095i \(0.691122\pi\)
\(692\) −3989.54 −0.219161
\(693\) 0 0
\(694\) −12024.8 −0.657718
\(695\) 2886.21 0.157525
\(696\) 0 0
\(697\) −36996.6 −2.01054
\(698\) −46875.5 −2.54192
\(699\) 0 0
\(700\) −3505.00 −0.189252
\(701\) −26106.0 −1.40658 −0.703288 0.710905i \(-0.748286\pi\)
−0.703288 + 0.710905i \(0.748286\pi\)
\(702\) 0 0
\(703\) 27625.1 1.48208
\(704\) −1211.67 −0.0648673
\(705\) 0 0
\(706\) 15067.7 0.803231
\(707\) −1492.79 −0.0794091
\(708\) 0 0
\(709\) 11015.3 0.583480 0.291740 0.956498i \(-0.405766\pi\)
0.291740 + 0.956498i \(0.405766\pi\)
\(710\) −14732.6 −0.778741
\(711\) 0 0
\(712\) −234.063 −0.0123200
\(713\) −16127.1 −0.847075
\(714\) 0 0
\(715\) −10.7408 −0.000561797 0
\(716\) 5557.85 0.290093
\(717\) 0 0
\(718\) 797.072 0.0414296
\(719\) −22222.9 −1.15267 −0.576337 0.817212i \(-0.695518\pi\)
−0.576337 + 0.817212i \(0.695518\pi\)
\(720\) 0 0
\(721\) 3739.48 0.193156
\(722\) 416.483 0.0214680
\(723\) 0 0
\(724\) −22199.5 −1.13956
\(725\) −12612.5 −0.646092
\(726\) 0 0
\(727\) −1110.63 −0.0566591 −0.0283295 0.999599i \(-0.509019\pi\)
−0.0283295 + 0.999599i \(0.509019\pi\)
\(728\) −14.1933 −0.000722582 0
\(729\) 0 0
\(730\) 5033.21 0.255189
\(731\) 5045.46 0.255285
\(732\) 0 0
\(733\) −12745.1 −0.642225 −0.321113 0.947041i \(-0.604057\pi\)
−0.321113 + 0.947041i \(0.604057\pi\)
\(734\) 35844.6 1.80252
\(735\) 0 0
\(736\) 49091.1 2.45859
\(737\) −1137.47 −0.0568509
\(738\) 0 0
\(739\) −33895.1 −1.68721 −0.843607 0.536961i \(-0.819572\pi\)
−0.843607 + 0.536961i \(0.819572\pi\)
\(740\) −22030.5 −1.09440
\(741\) 0 0
\(742\) −15656.3 −0.774611
\(743\) −22181.2 −1.09522 −0.547611 0.836733i \(-0.684463\pi\)
−0.547611 + 0.836733i \(0.684463\pi\)
\(744\) 0 0
\(745\) −19870.1 −0.977158
\(746\) −34469.4 −1.69171
\(747\) 0 0
\(748\) 1913.76 0.0935479
\(749\) 2330.14 0.113673
\(750\) 0 0
\(751\) −11657.1 −0.566410 −0.283205 0.959059i \(-0.591398\pi\)
−0.283205 + 0.959059i \(0.591398\pi\)
\(752\) −23321.6 −1.13092
\(753\) 0 0
\(754\) −541.450 −0.0261518
\(755\) 6312.69 0.304294
\(756\) 0 0
\(757\) −15371.4 −0.738021 −0.369010 0.929425i \(-0.620303\pi\)
−0.369010 + 0.929425i \(0.620303\pi\)
\(758\) −34032.3 −1.63075
\(759\) 0 0
\(760\) 2085.59 0.0995424
\(761\) −6164.19 −0.293629 −0.146815 0.989164i \(-0.546902\pi\)
−0.146815 + 0.989164i \(0.546902\pi\)
\(762\) 0 0
\(763\) 928.086 0.0440354
\(764\) 2019.70 0.0956417
\(765\) 0 0
\(766\) 54287.9 2.56071
\(767\) 160.234 0.00754328
\(768\) 0 0
\(769\) 15507.5 0.727197 0.363599 0.931556i \(-0.381548\pi\)
0.363599 + 0.931556i \(0.381548\pi\)
\(770\) 341.827 0.0159982
\(771\) 0 0
\(772\) −38425.7 −1.79141
\(773\) 31731.2 1.47644 0.738222 0.674558i \(-0.235666\pi\)
0.738222 + 0.674558i \(0.235666\pi\)
\(774\) 0 0
\(775\) 5966.04 0.276524
\(776\) 328.230 0.0151840
\(777\) 0 0
\(778\) −5510.23 −0.253922
\(779\) −27768.4 −1.27716
\(780\) 0 0
\(781\) −957.122 −0.0438522
\(782\) −84930.2 −3.88376
\(783\) 0 0
\(784\) 17603.4 0.801905
\(785\) −14755.0 −0.670867
\(786\) 0 0
\(787\) 42805.3 1.93881 0.969405 0.245467i \(-0.0789414\pi\)
0.969405 + 0.245467i \(0.0789414\pi\)
\(788\) 5161.62 0.233344
\(789\) 0 0
\(790\) 16437.3 0.740271
\(791\) −1869.73 −0.0840453
\(792\) 0 0
\(793\) 351.578 0.0157439
\(794\) 21429.1 0.957796
\(795\) 0 0
\(796\) −22331.6 −0.994373
\(797\) −644.298 −0.0286351 −0.0143176 0.999897i \(-0.504558\pi\)
−0.0143176 + 0.999897i \(0.504558\pi\)
\(798\) 0 0
\(799\) 45096.0 1.99672
\(800\) −18160.7 −0.802597
\(801\) 0 0
\(802\) 8472.50 0.373036
\(803\) 326.989 0.0143701
\(804\) 0 0
\(805\) −7960.38 −0.348530
\(806\) 256.120 0.0111928
\(807\) 0 0
\(808\) 899.244 0.0391526
\(809\) −23877.9 −1.03771 −0.518853 0.854864i \(-0.673641\pi\)
−0.518853 + 0.854864i \(0.673641\pi\)
\(810\) 0 0
\(811\) −5572.29 −0.241270 −0.120635 0.992697i \(-0.538493\pi\)
−0.120635 + 0.992697i \(0.538493\pi\)
\(812\) 9042.28 0.390791
\(813\) 0 0
\(814\) −2727.47 −0.117442
\(815\) −8941.57 −0.384306
\(816\) 0 0
\(817\) 3786.96 0.162165
\(818\) −27822.4 −1.18923
\(819\) 0 0
\(820\) 22144.8 0.943086
\(821\) 33978.6 1.44441 0.722206 0.691678i \(-0.243128\pi\)
0.722206 + 0.691678i \(0.243128\pi\)
\(822\) 0 0
\(823\) 35936.7 1.52208 0.761042 0.648702i \(-0.224688\pi\)
0.761042 + 0.648702i \(0.224688\pi\)
\(824\) −2252.63 −0.0952355
\(825\) 0 0
\(826\) −5099.43 −0.214808
\(827\) 42648.5 1.79327 0.896634 0.442773i \(-0.146005\pi\)
0.896634 + 0.442773i \(0.146005\pi\)
\(828\) 0 0
\(829\) 4856.64 0.203472 0.101736 0.994811i \(-0.467560\pi\)
0.101736 + 0.994811i \(0.467560\pi\)
\(830\) 2959.46 0.123764
\(831\) 0 0
\(832\) −448.125 −0.0186730
\(833\) −34039.0 −1.41582
\(834\) 0 0
\(835\) −27406.2 −1.13585
\(836\) 1436.40 0.0594247
\(837\) 0 0
\(838\) −51056.3 −2.10467
\(839\) 2091.03 0.0860435 0.0430217 0.999074i \(-0.486302\pi\)
0.0430217 + 0.999074i \(0.486302\pi\)
\(840\) 0 0
\(841\) 8149.04 0.334128
\(842\) −5720.89 −0.234151
\(843\) 0 0
\(844\) −46786.0 −1.90811
\(845\) 16301.2 0.663641
\(846\) 0 0
\(847\) −7531.18 −0.305519
\(848\) −38086.0 −1.54231
\(849\) 0 0
\(850\) 31419.0 1.26784
\(851\) 63516.6 2.55854
\(852\) 0 0
\(853\) −23427.5 −0.940377 −0.470188 0.882566i \(-0.655814\pi\)
−0.470188 + 0.882566i \(0.655814\pi\)
\(854\) −11188.9 −0.448334
\(855\) 0 0
\(856\) −1403.65 −0.0560466
\(857\) −13818.2 −0.550781 −0.275390 0.961332i \(-0.588807\pi\)
−0.275390 + 0.961332i \(0.588807\pi\)
\(858\) 0 0
\(859\) 4369.03 0.173538 0.0867692 0.996228i \(-0.472346\pi\)
0.0867692 + 0.996228i \(0.472346\pi\)
\(860\) −3020.03 −0.119747
\(861\) 0 0
\(862\) −44035.2 −1.73996
\(863\) −47079.7 −1.85702 −0.928511 0.371304i \(-0.878911\pi\)
−0.928511 + 0.371304i \(0.878911\pi\)
\(864\) 0 0
\(865\) 3351.96 0.131757
\(866\) −19618.4 −0.769815
\(867\) 0 0
\(868\) −4277.23 −0.167257
\(869\) 1067.87 0.0416859
\(870\) 0 0
\(871\) −420.681 −0.0163654
\(872\) −559.070 −0.0217116
\(873\) 0 0
\(874\) −63745.9 −2.46709
\(875\) 8209.48 0.317178
\(876\) 0 0
\(877\) −47259.9 −1.81967 −0.909837 0.414966i \(-0.863794\pi\)
−0.909837 + 0.414966i \(0.863794\pi\)
\(878\) −32015.3 −1.23060
\(879\) 0 0
\(880\) 831.539 0.0318536
\(881\) 46130.0 1.76409 0.882043 0.471169i \(-0.156168\pi\)
0.882043 + 0.471169i \(0.156168\pi\)
\(882\) 0 0
\(883\) −45009.5 −1.71539 −0.857695 0.514158i \(-0.828104\pi\)
−0.857695 + 0.514158i \(0.828104\pi\)
\(884\) 707.784 0.0269291
\(885\) 0 0
\(886\) −21686.0 −0.822299
\(887\) 4655.29 0.176223 0.0881113 0.996111i \(-0.471917\pi\)
0.0881113 + 0.996111i \(0.471917\pi\)
\(888\) 0 0
\(889\) −75.8166 −0.00286030
\(890\) 2084.82 0.0785205
\(891\) 0 0
\(892\) 27728.3 1.04082
\(893\) 33847.6 1.26838
\(894\) 0 0
\(895\) −4669.63 −0.174400
\(896\) 2469.75 0.0920855
\(897\) 0 0
\(898\) −49452.3 −1.83769
\(899\) −15391.3 −0.571000
\(900\) 0 0
\(901\) 73645.3 2.72306
\(902\) 2741.62 0.101204
\(903\) 0 0
\(904\) 1126.31 0.0414384
\(905\) 18651.7 0.685087
\(906\) 0 0
\(907\) −11431.6 −0.418500 −0.209250 0.977862i \(-0.567102\pi\)
−0.209250 + 0.977862i \(0.567102\pi\)
\(908\) −102.055 −0.00372996
\(909\) 0 0
\(910\) 126.421 0.00460531
\(911\) −37817.7 −1.37536 −0.687682 0.726012i \(-0.741372\pi\)
−0.687682 + 0.726012i \(0.741372\pi\)
\(912\) 0 0
\(913\) 192.265 0.00696938
\(914\) −13222.9 −0.478529
\(915\) 0 0
\(916\) −10146.5 −0.365994
\(917\) −14689.2 −0.528987
\(918\) 0 0
\(919\) 23292.2 0.836058 0.418029 0.908434i \(-0.362721\pi\)
0.418029 + 0.908434i \(0.362721\pi\)
\(920\) 4795.25 0.171842
\(921\) 0 0
\(922\) −45467.6 −1.62407
\(923\) −353.982 −0.0126235
\(924\) 0 0
\(925\) −23497.2 −0.835227
\(926\) −39782.4 −1.41180
\(927\) 0 0
\(928\) 46851.4 1.65730
\(929\) 19457.9 0.687183 0.343591 0.939119i \(-0.388356\pi\)
0.343591 + 0.939119i \(0.388356\pi\)
\(930\) 0 0
\(931\) −25548.6 −0.899377
\(932\) −8392.67 −0.294969
\(933\) 0 0
\(934\) −54958.6 −1.92538
\(935\) −1607.91 −0.0562399
\(936\) 0 0
\(937\) 10504.7 0.366247 0.183124 0.983090i \(-0.441379\pi\)
0.183124 + 0.983090i \(0.441379\pi\)
\(938\) 13388.2 0.466033
\(939\) 0 0
\(940\) −26992.8 −0.936605
\(941\) −14020.6 −0.485717 −0.242858 0.970062i \(-0.578085\pi\)
−0.242858 + 0.970062i \(0.578085\pi\)
\(942\) 0 0
\(943\) −63846.1 −2.20479
\(944\) −12405.0 −0.427700
\(945\) 0 0
\(946\) −373.893 −0.0128502
\(947\) −4803.37 −0.164824 −0.0824121 0.996598i \(-0.526262\pi\)
−0.0824121 + 0.996598i \(0.526262\pi\)
\(948\) 0 0
\(949\) 120.934 0.00413664
\(950\) 23582.1 0.805372
\(951\) 0 0
\(952\) −2124.75 −0.0723356
\(953\) 28669.0 0.974482 0.487241 0.873268i \(-0.338003\pi\)
0.487241 + 0.873268i \(0.338003\pi\)
\(954\) 0 0
\(955\) −1696.93 −0.0574987
\(956\) −2111.14 −0.0714217
\(957\) 0 0
\(958\) −52935.0 −1.78523
\(959\) −11363.6 −0.382636
\(960\) 0 0
\(961\) −22510.5 −0.755615
\(962\) −1008.73 −0.0338074
\(963\) 0 0
\(964\) 16913.7 0.565098
\(965\) 32284.7 1.07698
\(966\) 0 0
\(967\) 37377.7 1.24300 0.621502 0.783413i \(-0.286523\pi\)
0.621502 + 0.783413i \(0.286523\pi\)
\(968\) 4536.71 0.150636
\(969\) 0 0
\(970\) −2923.58 −0.0967736
\(971\) −15760.4 −0.520880 −0.260440 0.965490i \(-0.583868\pi\)
−0.260440 + 0.965490i \(0.583868\pi\)
\(972\) 0 0
\(973\) −2206.97 −0.0727156
\(974\) −65108.1 −2.14189
\(975\) 0 0
\(976\) −27218.6 −0.892669
\(977\) −6093.82 −0.199548 −0.0997741 0.995010i \(-0.531812\pi\)
−0.0997741 + 0.995010i \(0.531812\pi\)
\(978\) 0 0
\(979\) 135.443 0.00442162
\(980\) 20374.5 0.664122
\(981\) 0 0
\(982\) −64378.3 −2.09205
\(983\) −23957.8 −0.777351 −0.388676 0.921375i \(-0.627067\pi\)
−0.388676 + 0.921375i \(0.627067\pi\)
\(984\) 0 0
\(985\) −4336.72 −0.140284
\(986\) −81055.4 −2.61798
\(987\) 0 0
\(988\) 531.240 0.0171063
\(989\) 8707.11 0.279949
\(990\) 0 0
\(991\) 15949.9 0.511267 0.255633 0.966774i \(-0.417716\pi\)
0.255633 + 0.966774i \(0.417716\pi\)
\(992\) −22161.9 −0.709316
\(993\) 0 0
\(994\) 11265.5 0.359476
\(995\) 18762.7 0.597805
\(996\) 0 0
\(997\) −2544.36 −0.0808232 −0.0404116 0.999183i \(-0.512867\pi\)
−0.0404116 + 0.999183i \(0.512867\pi\)
\(998\) 65412.6 2.07475
\(999\) 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 2151.4.a.h.1.10 yes 59
3.2 odd 2 2151.4.a.g.1.50 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.50 59 3.2 odd 2
2151.4.a.h.1.10 yes 59 1.1 even 1 trivial