Properties

Label 2151.4.a.g.1.57
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $1$
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: \(1\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.57
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.15423 q^{2} +18.5661 q^{4} -1.27174 q^{5} -23.0732 q^{7} +54.4599 q^{8} +O(q^{10})\) \(q+5.15423 q^{2} +18.5661 q^{4} -1.27174 q^{5} -23.0732 q^{7} +54.4599 q^{8} -6.55481 q^{10} +4.21412 q^{11} -16.3792 q^{13} -118.925 q^{14} +132.170 q^{16} +98.0605 q^{17} -60.2154 q^{19} -23.6111 q^{20} +21.7205 q^{22} -168.855 q^{23} -123.383 q^{25} -84.4224 q^{26} -428.378 q^{28} -72.3381 q^{29} -26.8941 q^{31} +245.556 q^{32} +505.426 q^{34} +29.3430 q^{35} -86.2049 q^{37} -310.364 q^{38} -69.2585 q^{40} +137.305 q^{41} -406.867 q^{43} +78.2396 q^{44} -870.316 q^{46} +382.766 q^{47} +189.373 q^{49} -635.942 q^{50} -304.098 q^{52} +173.620 q^{53} -5.35925 q^{55} -1256.56 q^{56} -372.847 q^{58} -425.847 q^{59} -508.759 q^{61} -138.618 q^{62} +208.290 q^{64} +20.8301 q^{65} -650.419 q^{67} +1820.60 q^{68} +151.241 q^{70} +132.426 q^{71} -291.054 q^{73} -444.320 q^{74} -1117.96 q^{76} -97.2333 q^{77} +948.306 q^{79} -168.085 q^{80} +707.699 q^{82} +585.449 q^{83} -124.707 q^{85} -2097.09 q^{86} +229.501 q^{88} +587.676 q^{89} +377.922 q^{91} -3134.97 q^{92} +1972.86 q^{94} +76.5781 q^{95} -479.173 q^{97} +976.069 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q - 8q^{2} + 238q^{4} - 80q^{5} - 10q^{7} - 96q^{8} + O(q^{10}) \) \( 59q - 8q^{2} + 238q^{4} - 80q^{5} - 10q^{7} - 96q^{8} - 36q^{10} - 132q^{11} + 104q^{13} - 280q^{14} + 822q^{16} - 408q^{17} + 20q^{19} - 800q^{20} - 2q^{22} - 276q^{23} + 1477q^{25} - 780q^{26} + 224q^{28} - 696q^{29} - 380q^{31} - 896q^{32} - 72q^{34} - 700q^{35} + 224q^{37} - 988q^{38} - 258q^{40} - 2706q^{41} - 156q^{43} - 1584q^{44} + 428q^{46} - 1316q^{47} + 2135q^{49} - 1400q^{50} + 1092q^{52} - 1484q^{53} - 992q^{55} - 3360q^{56} - 120q^{58} - 3186q^{59} - 254q^{61} - 1240q^{62} + 3054q^{64} - 5120q^{65} + 288q^{67} - 9420q^{68} + 1108q^{70} - 4468q^{71} - 1770q^{73} - 6214q^{74} + 720q^{76} - 6352q^{77} - 746q^{79} - 7040q^{80} + 276q^{82} - 5484q^{83} + 588q^{85} - 10152q^{86} + 1186q^{88} - 11570q^{89} + 1768q^{91} - 15366q^{92} - 2142q^{94} - 5736q^{95} + 2390q^{97} - 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.15423 1.82229 0.911147 0.412081i \(-0.135198\pi\)
0.911147 + 0.412081i \(0.135198\pi\)
\(3\) 0 0
\(4\) 18.5661 2.32076
\(5\) −1.27174 −0.113747 −0.0568737 0.998381i \(-0.518113\pi\)
−0.0568737 + 0.998381i \(0.518113\pi\)
\(6\) 0 0
\(7\) −23.0732 −1.24584 −0.622918 0.782287i \(-0.714053\pi\)
−0.622918 + 0.782287i \(0.714053\pi\)
\(8\) 54.4599 2.40681
\(9\) 0 0
\(10\) −6.55481 −0.207281
\(11\) 4.21412 0.115510 0.0577548 0.998331i \(-0.481606\pi\)
0.0577548 + 0.998331i \(0.481606\pi\)
\(12\) 0 0
\(13\) −16.3792 −0.349445 −0.174723 0.984618i \(-0.555903\pi\)
−0.174723 + 0.984618i \(0.555903\pi\)
\(14\) −118.925 −2.27028
\(15\) 0 0
\(16\) 132.170 2.06516
\(17\) 98.0605 1.39901 0.699505 0.714628i \(-0.253404\pi\)
0.699505 + 0.714628i \(0.253404\pi\)
\(18\) 0 0
\(19\) −60.2154 −0.727072 −0.363536 0.931580i \(-0.618431\pi\)
−0.363536 + 0.931580i \(0.618431\pi\)
\(20\) −23.6111 −0.263980
\(21\) 0 0
\(22\) 21.7205 0.210493
\(23\) −168.855 −1.53081 −0.765406 0.643548i \(-0.777462\pi\)
−0.765406 + 0.643548i \(0.777462\pi\)
\(24\) 0 0
\(25\) −123.383 −0.987062
\(26\) −84.4224 −0.636792
\(27\) 0 0
\(28\) −428.378 −2.89128
\(29\) −72.3381 −0.463202 −0.231601 0.972811i \(-0.574396\pi\)
−0.231601 + 0.972811i \(0.574396\pi\)
\(30\) 0 0
\(31\) −26.8941 −0.155817 −0.0779084 0.996961i \(-0.524824\pi\)
−0.0779084 + 0.996961i \(0.524824\pi\)
\(32\) 245.556 1.35652
\(33\) 0 0
\(34\) 505.426 2.54941
\(35\) 29.3430 0.141711
\(36\) 0 0
\(37\) −86.2049 −0.383027 −0.191514 0.981490i \(-0.561340\pi\)
−0.191514 + 0.981490i \(0.561340\pi\)
\(38\) −310.364 −1.32494
\(39\) 0 0
\(40\) −69.2585 −0.273768
\(41\) 137.305 0.523009 0.261505 0.965202i \(-0.415781\pi\)
0.261505 + 0.965202i \(0.415781\pi\)
\(42\) 0 0
\(43\) −406.867 −1.44295 −0.721473 0.692443i \(-0.756535\pi\)
−0.721473 + 0.692443i \(0.756535\pi\)
\(44\) 78.2396 0.268070
\(45\) 0 0
\(46\) −870.316 −2.78959
\(47\) 382.766 1.18792 0.593959 0.804495i \(-0.297564\pi\)
0.593959 + 0.804495i \(0.297564\pi\)
\(48\) 0 0
\(49\) 189.373 0.552107
\(50\) −635.942 −1.79872
\(51\) 0 0
\(52\) −304.098 −0.810977
\(53\) 173.620 0.449972 0.224986 0.974362i \(-0.427766\pi\)
0.224986 + 0.974362i \(0.427766\pi\)
\(54\) 0 0
\(55\) −5.35925 −0.0131389
\(56\) −1256.56 −2.99849
\(57\) 0 0
\(58\) −372.847 −0.844090
\(59\) −425.847 −0.939670 −0.469835 0.882754i \(-0.655687\pi\)
−0.469835 + 0.882754i \(0.655687\pi\)
\(60\) 0 0
\(61\) −508.759 −1.06787 −0.533933 0.845527i \(-0.679287\pi\)
−0.533933 + 0.845527i \(0.679287\pi\)
\(62\) −138.618 −0.283944
\(63\) 0 0
\(64\) 208.290 0.406816
\(65\) 20.8301 0.0397485
\(66\) 0 0
\(67\) −650.419 −1.18599 −0.592995 0.805206i \(-0.702055\pi\)
−0.592995 + 0.805206i \(0.702055\pi\)
\(68\) 1820.60 3.24676
\(69\) 0 0
\(70\) 151.241 0.258239
\(71\) 132.426 0.221354 0.110677 0.993856i \(-0.464698\pi\)
0.110677 + 0.993856i \(0.464698\pi\)
\(72\) 0 0
\(73\) −291.054 −0.466648 −0.233324 0.972399i \(-0.574960\pi\)
−0.233324 + 0.972399i \(0.574960\pi\)
\(74\) −444.320 −0.697988
\(75\) 0 0
\(76\) −1117.96 −1.68736
\(77\) −97.2333 −0.143906
\(78\) 0 0
\(79\) 948.306 1.35054 0.675271 0.737570i \(-0.264027\pi\)
0.675271 + 0.737570i \(0.264027\pi\)
\(80\) −168.085 −0.234906
\(81\) 0 0
\(82\) 707.699 0.953077
\(83\) 585.449 0.774234 0.387117 0.922031i \(-0.373471\pi\)
0.387117 + 0.922031i \(0.373471\pi\)
\(84\) 0 0
\(85\) −124.707 −0.159134
\(86\) −2097.09 −2.62947
\(87\) 0 0
\(88\) 229.501 0.278010
\(89\) 587.676 0.699928 0.349964 0.936763i \(-0.386194\pi\)
0.349964 + 0.936763i \(0.386194\pi\)
\(90\) 0 0
\(91\) 377.922 0.435351
\(92\) −3134.97 −3.55264
\(93\) 0 0
\(94\) 1972.86 2.16474
\(95\) 76.5781 0.0827026
\(96\) 0 0
\(97\) −479.173 −0.501574 −0.250787 0.968042i \(-0.580689\pi\)
−0.250787 + 0.968042i \(0.580689\pi\)
\(98\) 976.069 1.00610
\(99\) 0 0
\(100\) −2290.73 −2.29073
\(101\) −1714.66 −1.68926 −0.844630 0.535350i \(-0.820180\pi\)
−0.844630 + 0.535350i \(0.820180\pi\)
\(102\) 0 0
\(103\) 41.4624 0.0396642 0.0198321 0.999803i \(-0.493687\pi\)
0.0198321 + 0.999803i \(0.493687\pi\)
\(104\) −892.012 −0.841048
\(105\) 0 0
\(106\) 894.876 0.819982
\(107\) 963.414 0.870437 0.435219 0.900325i \(-0.356671\pi\)
0.435219 + 0.900325i \(0.356671\pi\)
\(108\) 0 0
\(109\) 477.755 0.419822 0.209911 0.977720i \(-0.432683\pi\)
0.209911 + 0.977720i \(0.432683\pi\)
\(110\) −27.6228 −0.0239430
\(111\) 0 0
\(112\) −3049.59 −2.57285
\(113\) −785.408 −0.653850 −0.326925 0.945050i \(-0.606012\pi\)
−0.326925 + 0.945050i \(0.606012\pi\)
\(114\) 0 0
\(115\) 214.739 0.174126
\(116\) −1343.03 −1.07498
\(117\) 0 0
\(118\) −2194.91 −1.71236
\(119\) −2262.57 −1.74294
\(120\) 0 0
\(121\) −1313.24 −0.986658
\(122\) −2622.26 −1.94597
\(123\) 0 0
\(124\) −499.317 −0.361613
\(125\) 315.877 0.226023
\(126\) 0 0
\(127\) −847.836 −0.592388 −0.296194 0.955128i \(-0.595717\pi\)
−0.296194 + 0.955128i \(0.595717\pi\)
\(128\) −890.874 −0.615179
\(129\) 0 0
\(130\) 107.363 0.0724334
\(131\) 390.738 0.260602 0.130301 0.991474i \(-0.458406\pi\)
0.130301 + 0.991474i \(0.458406\pi\)
\(132\) 0 0
\(133\) 1389.36 0.905812
\(134\) −3352.41 −2.16122
\(135\) 0 0
\(136\) 5340.36 3.36715
\(137\) −2266.41 −1.41338 −0.706688 0.707525i \(-0.749812\pi\)
−0.706688 + 0.707525i \(0.749812\pi\)
\(138\) 0 0
\(139\) −1891.28 −1.15407 −0.577036 0.816719i \(-0.695791\pi\)
−0.577036 + 0.816719i \(0.695791\pi\)
\(140\) 544.784 0.328876
\(141\) 0 0
\(142\) 682.556 0.403372
\(143\) −69.0241 −0.0403643
\(144\) 0 0
\(145\) 91.9949 0.0526880
\(146\) −1500.16 −0.850369
\(147\) 0 0
\(148\) −1600.49 −0.888913
\(149\) −790.756 −0.434773 −0.217387 0.976086i \(-0.569753\pi\)
−0.217387 + 0.976086i \(0.569753\pi\)
\(150\) 0 0
\(151\) 2688.63 1.44899 0.724495 0.689280i \(-0.242073\pi\)
0.724495 + 0.689280i \(0.242073\pi\)
\(152\) −3279.33 −1.74992
\(153\) 0 0
\(154\) −501.162 −0.262239
\(155\) 34.2021 0.0177238
\(156\) 0 0
\(157\) −299.027 −0.152006 −0.0760031 0.997108i \(-0.524216\pi\)
−0.0760031 + 0.997108i \(0.524216\pi\)
\(158\) 4887.79 2.46108
\(159\) 0 0
\(160\) −312.282 −0.154300
\(161\) 3896.02 1.90714
\(162\) 0 0
\(163\) 148.627 0.0714195 0.0357098 0.999362i \(-0.488631\pi\)
0.0357098 + 0.999362i \(0.488631\pi\)
\(164\) 2549.21 1.21378
\(165\) 0 0
\(166\) 3017.54 1.41088
\(167\) −3277.62 −1.51874 −0.759372 0.650657i \(-0.774493\pi\)
−0.759372 + 0.650657i \(0.774493\pi\)
\(168\) 0 0
\(169\) −1928.72 −0.877888
\(170\) −642.768 −0.289989
\(171\) 0 0
\(172\) −7553.92 −3.34873
\(173\) 3263.65 1.43428 0.717141 0.696928i \(-0.245450\pi\)
0.717141 + 0.696928i \(0.245450\pi\)
\(174\) 0 0
\(175\) 2846.83 1.22972
\(176\) 556.981 0.238546
\(177\) 0 0
\(178\) 3029.02 1.27547
\(179\) 4519.98 1.88737 0.943684 0.330848i \(-0.107335\pi\)
0.943684 + 0.330848i \(0.107335\pi\)
\(180\) 0 0
\(181\) −3600.29 −1.47849 −0.739247 0.673435i \(-0.764818\pi\)
−0.739247 + 0.673435i \(0.764818\pi\)
\(182\) 1947.89 0.793338
\(183\) 0 0
\(184\) −9195.81 −3.68437
\(185\) 109.630 0.0435684
\(186\) 0 0
\(187\) 413.239 0.161599
\(188\) 7106.46 2.75687
\(189\) 0 0
\(190\) 394.701 0.150709
\(191\) 1601.68 0.606773 0.303387 0.952868i \(-0.401883\pi\)
0.303387 + 0.952868i \(0.401883\pi\)
\(192\) 0 0
\(193\) −3459.52 −1.29027 −0.645134 0.764069i \(-0.723198\pi\)
−0.645134 + 0.764069i \(0.723198\pi\)
\(194\) −2469.77 −0.914015
\(195\) 0 0
\(196\) 3515.90 1.28131
\(197\) −835.346 −0.302111 −0.151056 0.988525i \(-0.548267\pi\)
−0.151056 + 0.988525i \(0.548267\pi\)
\(198\) 0 0
\(199\) −1250.75 −0.445545 −0.222772 0.974871i \(-0.571511\pi\)
−0.222772 + 0.974871i \(0.571511\pi\)
\(200\) −6719.41 −2.37567
\(201\) 0 0
\(202\) −8837.76 −3.07833
\(203\) 1669.07 0.577073
\(204\) 0 0
\(205\) −174.615 −0.0594910
\(206\) 213.707 0.0722798
\(207\) 0 0
\(208\) −2164.85 −0.721659
\(209\) −253.755 −0.0839838
\(210\) 0 0
\(211\) 937.142 0.305761 0.152880 0.988245i \(-0.451145\pi\)
0.152880 + 0.988245i \(0.451145\pi\)
\(212\) 3223.44 1.04428
\(213\) 0 0
\(214\) 4965.66 1.58619
\(215\) 517.427 0.164131
\(216\) 0 0
\(217\) 620.532 0.194122
\(218\) 2462.46 0.765039
\(219\) 0 0
\(220\) −99.5001 −0.0304923
\(221\) −1606.16 −0.488877
\(222\) 0 0
\(223\) 2589.67 0.777655 0.388827 0.921311i \(-0.372880\pi\)
0.388827 + 0.921311i \(0.372880\pi\)
\(224\) −5665.76 −1.69000
\(225\) 0 0
\(226\) −4048.17 −1.19151
\(227\) 5121.76 1.49755 0.748773 0.662826i \(-0.230643\pi\)
0.748773 + 0.662826i \(0.230643\pi\)
\(228\) 0 0
\(229\) 3590.34 1.03605 0.518027 0.855364i \(-0.326666\pi\)
0.518027 + 0.855364i \(0.326666\pi\)
\(230\) 1106.81 0.317309
\(231\) 0 0
\(232\) −3939.52 −1.11484
\(233\) 883.730 0.248477 0.124238 0.992252i \(-0.460351\pi\)
0.124238 + 0.992252i \(0.460351\pi\)
\(234\) 0 0
\(235\) −486.777 −0.135123
\(236\) −7906.30 −2.18075
\(237\) 0 0
\(238\) −11661.8 −3.17614
\(239\) 239.000 0.0646846
\(240\) 0 0
\(241\) −1447.09 −0.386784 −0.193392 0.981122i \(-0.561949\pi\)
−0.193392 + 0.981122i \(0.561949\pi\)
\(242\) −6768.74 −1.79798
\(243\) 0 0
\(244\) −9445.64 −2.47826
\(245\) −240.832 −0.0628007
\(246\) 0 0
\(247\) 986.284 0.254072
\(248\) −1464.65 −0.375021
\(249\) 0 0
\(250\) 1628.10 0.411881
\(251\) −743.264 −0.186910 −0.0934550 0.995624i \(-0.529791\pi\)
−0.0934550 + 0.995624i \(0.529791\pi\)
\(252\) 0 0
\(253\) −711.575 −0.176823
\(254\) −4369.94 −1.07951
\(255\) 0 0
\(256\) −6258.09 −1.52785
\(257\) −2369.85 −0.575204 −0.287602 0.957750i \(-0.592858\pi\)
−0.287602 + 0.957750i \(0.592858\pi\)
\(258\) 0 0
\(259\) 1989.02 0.477189
\(260\) 386.732 0.0922466
\(261\) 0 0
\(262\) 2013.95 0.474894
\(263\) 6429.45 1.50744 0.753720 0.657196i \(-0.228258\pi\)
0.753720 + 0.657196i \(0.228258\pi\)
\(264\) 0 0
\(265\) −220.799 −0.0511832
\(266\) 7161.09 1.65066
\(267\) 0 0
\(268\) −12075.7 −2.75240
\(269\) −1740.36 −0.394468 −0.197234 0.980356i \(-0.563196\pi\)
−0.197234 + 0.980356i \(0.563196\pi\)
\(270\) 0 0
\(271\) 965.726 0.216471 0.108236 0.994125i \(-0.465480\pi\)
0.108236 + 0.994125i \(0.465480\pi\)
\(272\) 12960.7 2.88918
\(273\) 0 0
\(274\) −11681.6 −2.57559
\(275\) −519.950 −0.114015
\(276\) 0 0
\(277\) −1837.77 −0.398631 −0.199315 0.979935i \(-0.563872\pi\)
−0.199315 + 0.979935i \(0.563872\pi\)
\(278\) −9748.07 −2.10306
\(279\) 0 0
\(280\) 1598.02 0.341071
\(281\) 7292.56 1.54818 0.774088 0.633078i \(-0.218209\pi\)
0.774088 + 0.633078i \(0.218209\pi\)
\(282\) 0 0
\(283\) 4293.55 0.901855 0.450927 0.892561i \(-0.351093\pi\)
0.450927 + 0.892561i \(0.351093\pi\)
\(284\) 2458.64 0.513709
\(285\) 0 0
\(286\) −355.766 −0.0735556
\(287\) −3168.06 −0.651583
\(288\) 0 0
\(289\) 4702.86 0.957228
\(290\) 474.163 0.0960131
\(291\) 0 0
\(292\) −5403.72 −1.08298
\(293\) 3253.10 0.648629 0.324315 0.945949i \(-0.394866\pi\)
0.324315 + 0.945949i \(0.394866\pi\)
\(294\) 0 0
\(295\) 541.564 0.106885
\(296\) −4694.71 −0.921873
\(297\) 0 0
\(298\) −4075.74 −0.792285
\(299\) 2765.71 0.534934
\(300\) 0 0
\(301\) 9387.73 1.79767
\(302\) 13857.8 2.64049
\(303\) 0 0
\(304\) −7958.68 −1.50152
\(305\) 647.006 0.121467
\(306\) 0 0
\(307\) 3914.79 0.727781 0.363890 0.931442i \(-0.381448\pi\)
0.363890 + 0.931442i \(0.381448\pi\)
\(308\) −1805.24 −0.333971
\(309\) 0 0
\(310\) 176.286 0.0322979
\(311\) −3124.86 −0.569757 −0.284878 0.958564i \(-0.591953\pi\)
−0.284878 + 0.958564i \(0.591953\pi\)
\(312\) 0 0
\(313\) 7914.98 1.42933 0.714667 0.699465i \(-0.246578\pi\)
0.714667 + 0.699465i \(0.246578\pi\)
\(314\) −1541.25 −0.277000
\(315\) 0 0
\(316\) 17606.3 3.13428
\(317\) 3512.36 0.622314 0.311157 0.950358i \(-0.399283\pi\)
0.311157 + 0.950358i \(0.399283\pi\)
\(318\) 0 0
\(319\) −304.842 −0.0535042
\(320\) −264.889 −0.0462743
\(321\) 0 0
\(322\) 20081.0 3.47537
\(323\) −5904.76 −1.01718
\(324\) 0 0
\(325\) 2020.92 0.344924
\(326\) 766.058 0.130147
\(327\) 0 0
\(328\) 7477.59 1.25878
\(329\) −8831.64 −1.47995
\(330\) 0 0
\(331\) 8333.51 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(332\) 10869.5 1.79681
\(333\) 0 0
\(334\) −16893.6 −2.76760
\(335\) 827.161 0.134903
\(336\) 0 0
\(337\) 4668.20 0.754578 0.377289 0.926096i \(-0.376856\pi\)
0.377289 + 0.926096i \(0.376856\pi\)
\(338\) −9941.06 −1.59977
\(339\) 0 0
\(340\) −2315.32 −0.369311
\(341\) −113.335 −0.0179983
\(342\) 0 0
\(343\) 3544.68 0.558002
\(344\) −22157.9 −3.47290
\(345\) 0 0
\(346\) 16821.6 2.61369
\(347\) 4398.94 0.680541 0.340270 0.940328i \(-0.389481\pi\)
0.340270 + 0.940328i \(0.389481\pi\)
\(348\) 0 0
\(349\) 5610.61 0.860541 0.430271 0.902700i \(-0.358418\pi\)
0.430271 + 0.902700i \(0.358418\pi\)
\(350\) 14673.2 2.24091
\(351\) 0 0
\(352\) 1034.80 0.156691
\(353\) −97.4593 −0.0146947 −0.00734736 0.999973i \(-0.502339\pi\)
−0.00734736 + 0.999973i \(0.502339\pi\)
\(354\) 0 0
\(355\) −168.411 −0.0251785
\(356\) 10910.8 1.62436
\(357\) 0 0
\(358\) 23297.0 3.43934
\(359\) −8080.31 −1.18792 −0.593958 0.804496i \(-0.702436\pi\)
−0.593958 + 0.804496i \(0.702436\pi\)
\(360\) 0 0
\(361\) −3233.10 −0.471366
\(362\) −18556.7 −2.69425
\(363\) 0 0
\(364\) 7016.52 1.01034
\(365\) 370.143 0.0530800
\(366\) 0 0
\(367\) 4871.70 0.692918 0.346459 0.938065i \(-0.387384\pi\)
0.346459 + 0.938065i \(0.387384\pi\)
\(368\) −22317.6 −3.16137
\(369\) 0 0
\(370\) 565.057 0.0793944
\(371\) −4005.97 −0.560591
\(372\) 0 0
\(373\) −7045.04 −0.977957 −0.488979 0.872296i \(-0.662630\pi\)
−0.488979 + 0.872296i \(0.662630\pi\)
\(374\) 2129.93 0.294481
\(375\) 0 0
\(376\) 20845.4 2.85909
\(377\) 1184.84 0.161864
\(378\) 0 0
\(379\) 5969.39 0.809043 0.404521 0.914529i \(-0.367438\pi\)
0.404521 + 0.914529i \(0.367438\pi\)
\(380\) 1421.75 0.191933
\(381\) 0 0
\(382\) 8255.44 1.10572
\(383\) −3617.38 −0.482610 −0.241305 0.970449i \(-0.577575\pi\)
−0.241305 + 0.970449i \(0.577575\pi\)
\(384\) 0 0
\(385\) 123.655 0.0163689
\(386\) −17831.2 −2.35125
\(387\) 0 0
\(388\) −8896.36 −1.16403
\(389\) −3143.72 −0.409750 −0.204875 0.978788i \(-0.565679\pi\)
−0.204875 + 0.978788i \(0.565679\pi\)
\(390\) 0 0
\(391\) −16558.0 −2.14162
\(392\) 10313.2 1.32882
\(393\) 0 0
\(394\) −4305.57 −0.550536
\(395\) −1205.99 −0.153621
\(396\) 0 0
\(397\) 3961.64 0.500828 0.250414 0.968139i \(-0.419433\pi\)
0.250414 + 0.968139i \(0.419433\pi\)
\(398\) −6446.65 −0.811913
\(399\) 0 0
\(400\) −16307.5 −2.03844
\(401\) −5164.39 −0.643135 −0.321568 0.946887i \(-0.604210\pi\)
−0.321568 + 0.946887i \(0.604210\pi\)
\(402\) 0 0
\(403\) 440.505 0.0544494
\(404\) −31834.5 −3.92036
\(405\) 0 0
\(406\) 8602.77 1.05160
\(407\) −363.278 −0.0442433
\(408\) 0 0
\(409\) −15261.8 −1.84510 −0.922550 0.385879i \(-0.873898\pi\)
−0.922550 + 0.385879i \(0.873898\pi\)
\(410\) −900.006 −0.108410
\(411\) 0 0
\(412\) 769.793 0.0920510
\(413\) 9825.65 1.17067
\(414\) 0 0
\(415\) −744.537 −0.0880671
\(416\) −4022.02 −0.474028
\(417\) 0 0
\(418\) −1307.91 −0.153043
\(419\) −8757.77 −1.02111 −0.510555 0.859845i \(-0.670560\pi\)
−0.510555 + 0.859845i \(0.670560\pi\)
\(420\) 0 0
\(421\) −2925.07 −0.338620 −0.169310 0.985563i \(-0.554154\pi\)
−0.169310 + 0.985563i \(0.554154\pi\)
\(422\) 4830.24 0.557186
\(423\) 0 0
\(424\) 9455.32 1.08300
\(425\) −12099.0 −1.38091
\(426\) 0 0
\(427\) 11738.7 1.33039
\(428\) 17886.8 2.02007
\(429\) 0 0
\(430\) 2666.94 0.299096
\(431\) 5246.34 0.586327 0.293164 0.956062i \(-0.405292\pi\)
0.293164 + 0.956062i \(0.405292\pi\)
\(432\) 0 0
\(433\) −2901.54 −0.322030 −0.161015 0.986952i \(-0.551477\pi\)
−0.161015 + 0.986952i \(0.551477\pi\)
\(434\) 3198.36 0.353748
\(435\) 0 0
\(436\) 8870.02 0.974305
\(437\) 10167.7 1.11301
\(438\) 0 0
\(439\) 4567.53 0.496575 0.248287 0.968686i \(-0.420132\pi\)
0.248287 + 0.968686i \(0.420132\pi\)
\(440\) −291.864 −0.0316229
\(441\) 0 0
\(442\) −8278.50 −0.890878
\(443\) 2082.15 0.223309 0.111654 0.993747i \(-0.464385\pi\)
0.111654 + 0.993747i \(0.464385\pi\)
\(444\) 0 0
\(445\) −747.369 −0.0796150
\(446\) 13347.7 1.41712
\(447\) 0 0
\(448\) −4805.91 −0.506826
\(449\) 64.4340 0.00677245 0.00338622 0.999994i \(-0.498922\pi\)
0.00338622 + 0.999994i \(0.498922\pi\)
\(450\) 0 0
\(451\) 578.618 0.0604126
\(452\) −14581.9 −1.51743
\(453\) 0 0
\(454\) 26398.7 2.72897
\(455\) −480.616 −0.0495201
\(456\) 0 0
\(457\) −8606.13 −0.880915 −0.440457 0.897774i \(-0.645184\pi\)
−0.440457 + 0.897774i \(0.645184\pi\)
\(458\) 18505.4 1.88800
\(459\) 0 0
\(460\) 3986.85 0.404104
\(461\) −15415.3 −1.55740 −0.778698 0.627398i \(-0.784120\pi\)
−0.778698 + 0.627398i \(0.784120\pi\)
\(462\) 0 0
\(463\) 10632.2 1.06722 0.533609 0.845732i \(-0.320836\pi\)
0.533609 + 0.845732i \(0.320836\pi\)
\(464\) −9560.94 −0.956585
\(465\) 0 0
\(466\) 4554.95 0.452798
\(467\) 2712.98 0.268826 0.134413 0.990925i \(-0.457085\pi\)
0.134413 + 0.990925i \(0.457085\pi\)
\(468\) 0 0
\(469\) 15007.2 1.47755
\(470\) −2508.96 −0.246233
\(471\) 0 0
\(472\) −23191.6 −2.26161
\(473\) −1714.59 −0.166674
\(474\) 0 0
\(475\) 7429.54 0.717665
\(476\) −42007.0 −4.04493
\(477\) 0 0
\(478\) 1231.86 0.117874
\(479\) −9677.65 −0.923138 −0.461569 0.887104i \(-0.652713\pi\)
−0.461569 + 0.887104i \(0.652713\pi\)
\(480\) 0 0
\(481\) 1411.97 0.133847
\(482\) −7458.61 −0.704835
\(483\) 0 0
\(484\) −24381.7 −2.28979
\(485\) 609.381 0.0570527
\(486\) 0 0
\(487\) −1458.67 −0.135726 −0.0678630 0.997695i \(-0.521618\pi\)
−0.0678630 + 0.997695i \(0.521618\pi\)
\(488\) −27706.9 −2.57015
\(489\) 0 0
\(490\) −1241.30 −0.114441
\(491\) 10497.8 0.964884 0.482442 0.875928i \(-0.339750\pi\)
0.482442 + 0.875928i \(0.339750\pi\)
\(492\) 0 0
\(493\) −7093.51 −0.648024
\(494\) 5083.53 0.462994
\(495\) 0 0
\(496\) −3554.59 −0.321786
\(497\) −3055.50 −0.275771
\(498\) 0 0
\(499\) 18915.4 1.69694 0.848468 0.529247i \(-0.177525\pi\)
0.848468 + 0.529247i \(0.177525\pi\)
\(500\) 5864.59 0.524545
\(501\) 0 0
\(502\) −3830.95 −0.340605
\(503\) 910.675 0.0807257 0.0403628 0.999185i \(-0.487149\pi\)
0.0403628 + 0.999185i \(0.487149\pi\)
\(504\) 0 0
\(505\) 2180.60 0.192149
\(506\) −3667.62 −0.322224
\(507\) 0 0
\(508\) −15741.0 −1.37479
\(509\) −2067.73 −0.180060 −0.0900301 0.995939i \(-0.528696\pi\)
−0.0900301 + 0.995939i \(0.528696\pi\)
\(510\) 0 0
\(511\) 6715.54 0.581366
\(512\) −25128.6 −2.16902
\(513\) 0 0
\(514\) −12214.8 −1.04819
\(515\) −52.7292 −0.00451170
\(516\) 0 0
\(517\) 1613.02 0.137216
\(518\) 10251.9 0.869579
\(519\) 0 0
\(520\) 1134.40 0.0956670
\(521\) −9551.18 −0.803157 −0.401579 0.915825i \(-0.631538\pi\)
−0.401579 + 0.915825i \(0.631538\pi\)
\(522\) 0 0
\(523\) −22594.0 −1.88904 −0.944520 0.328455i \(-0.893472\pi\)
−0.944520 + 0.328455i \(0.893472\pi\)
\(524\) 7254.46 0.604795
\(525\) 0 0
\(526\) 33138.8 2.74700
\(527\) −2637.25 −0.217989
\(528\) 0 0
\(529\) 16345.0 1.34338
\(530\) −1138.05 −0.0932709
\(531\) 0 0
\(532\) 25795.0 2.10217
\(533\) −2248.95 −0.182763
\(534\) 0 0
\(535\) −1225.21 −0.0990100
\(536\) −35421.7 −2.85445
\(537\) 0 0
\(538\) −8970.23 −0.718837
\(539\) 798.039 0.0637736
\(540\) 0 0
\(541\) 10689.3 0.849479 0.424740 0.905316i \(-0.360366\pi\)
0.424740 + 0.905316i \(0.360366\pi\)
\(542\) 4977.57 0.394474
\(543\) 0 0
\(544\) 24079.3 1.89778
\(545\) −607.577 −0.0477537
\(546\) 0 0
\(547\) −18533.4 −1.44869 −0.724344 0.689439i \(-0.757857\pi\)
−0.724344 + 0.689439i \(0.757857\pi\)
\(548\) −42078.3 −3.28010
\(549\) 0 0
\(550\) −2679.94 −0.207769
\(551\) 4355.87 0.336781
\(552\) 0 0
\(553\) −21880.5 −1.68255
\(554\) −9472.27 −0.726423
\(555\) 0 0
\(556\) −35113.5 −2.67832
\(557\) −18530.5 −1.40963 −0.704814 0.709393i \(-0.748969\pi\)
−0.704814 + 0.709393i \(0.748969\pi\)
\(558\) 0 0
\(559\) 6664.18 0.504230
\(560\) 3878.27 0.292655
\(561\) 0 0
\(562\) 37587.5 2.82123
\(563\) 12789.8 0.957417 0.478709 0.877974i \(-0.341105\pi\)
0.478709 + 0.877974i \(0.341105\pi\)
\(564\) 0 0
\(565\) 998.832 0.0743737
\(566\) 22129.9 1.64345
\(567\) 0 0
\(568\) 7211.93 0.532757
\(569\) −10151.1 −0.747904 −0.373952 0.927448i \(-0.621998\pi\)
−0.373952 + 0.927448i \(0.621998\pi\)
\(570\) 0 0
\(571\) −3426.70 −0.251144 −0.125572 0.992085i \(-0.540077\pi\)
−0.125572 + 0.992085i \(0.540077\pi\)
\(572\) −1281.51 −0.0936756
\(573\) 0 0
\(574\) −16328.9 −1.18738
\(575\) 20833.8 1.51101
\(576\) 0 0
\(577\) 7548.20 0.544603 0.272301 0.962212i \(-0.412215\pi\)
0.272301 + 0.962212i \(0.412215\pi\)
\(578\) 24239.6 1.74435
\(579\) 0 0
\(580\) 1707.98 0.122276
\(581\) −13508.2 −0.964568
\(582\) 0 0
\(583\) 731.655 0.0519761
\(584\) −15850.8 −1.12313
\(585\) 0 0
\(586\) 16767.2 1.18199
\(587\) 12736.8 0.895577 0.447789 0.894139i \(-0.352212\pi\)
0.447789 + 0.894139i \(0.352212\pi\)
\(588\) 0 0
\(589\) 1619.44 0.113290
\(590\) 2791.35 0.194776
\(591\) 0 0
\(592\) −11393.7 −0.791012
\(593\) −15108.1 −1.04623 −0.523117 0.852261i \(-0.675231\pi\)
−0.523117 + 0.852261i \(0.675231\pi\)
\(594\) 0 0
\(595\) 2877.39 0.198255
\(596\) −14681.2 −1.00900
\(597\) 0 0
\(598\) 14255.1 0.974808
\(599\) −4294.17 −0.292913 −0.146457 0.989217i \(-0.546787\pi\)
−0.146457 + 0.989217i \(0.546787\pi\)
\(600\) 0 0
\(601\) −10426.3 −0.707648 −0.353824 0.935312i \(-0.615119\pi\)
−0.353824 + 0.935312i \(0.615119\pi\)
\(602\) 48386.5 3.27589
\(603\) 0 0
\(604\) 49917.3 3.36276
\(605\) 1670.10 0.112230
\(606\) 0 0
\(607\) −28473.2 −1.90394 −0.951971 0.306188i \(-0.900946\pi\)
−0.951971 + 0.306188i \(0.900946\pi\)
\(608\) −14786.3 −0.986286
\(609\) 0 0
\(610\) 3334.82 0.221349
\(611\) −6269.42 −0.415112
\(612\) 0 0
\(613\) 14942.9 0.984561 0.492281 0.870437i \(-0.336163\pi\)
0.492281 + 0.870437i \(0.336163\pi\)
\(614\) 20177.7 1.32623
\(615\) 0 0
\(616\) −5295.31 −0.346354
\(617\) −11955.4 −0.780072 −0.390036 0.920800i \(-0.627537\pi\)
−0.390036 + 0.920800i \(0.627537\pi\)
\(618\) 0 0
\(619\) 13024.9 0.845746 0.422873 0.906189i \(-0.361022\pi\)
0.422873 + 0.906189i \(0.361022\pi\)
\(620\) 634.999 0.0411325
\(621\) 0 0
\(622\) −16106.2 −1.03826
\(623\) −13559.6 −0.871995
\(624\) 0 0
\(625\) 15021.1 0.961352
\(626\) 40795.6 2.60467
\(627\) 0 0
\(628\) −5551.76 −0.352769
\(629\) −8453.30 −0.535859
\(630\) 0 0
\(631\) −9384.17 −0.592041 −0.296021 0.955182i \(-0.595660\pi\)
−0.296021 + 0.955182i \(0.595660\pi\)
\(632\) 51644.6 3.25050
\(633\) 0 0
\(634\) 18103.5 1.13404
\(635\) 1078.22 0.0673826
\(636\) 0 0
\(637\) −3101.78 −0.192931
\(638\) −1571.22 −0.0975005
\(639\) 0 0
\(640\) 1132.96 0.0699751
\(641\) 520.895 0.0320969 0.0160484 0.999871i \(-0.494891\pi\)
0.0160484 + 0.999871i \(0.494891\pi\)
\(642\) 0 0
\(643\) −24141.1 −1.48061 −0.740306 0.672270i \(-0.765320\pi\)
−0.740306 + 0.672270i \(0.765320\pi\)
\(644\) 72333.8 4.42601
\(645\) 0 0
\(646\) −30434.5 −1.85360
\(647\) −8801.57 −0.534815 −0.267408 0.963583i \(-0.586167\pi\)
−0.267408 + 0.963583i \(0.586167\pi\)
\(648\) 0 0
\(649\) −1794.57 −0.108541
\(650\) 10416.3 0.628553
\(651\) 0 0
\(652\) 2759.42 0.165747
\(653\) 12705.6 0.761422 0.380711 0.924694i \(-0.375679\pi\)
0.380711 + 0.924694i \(0.375679\pi\)
\(654\) 0 0
\(655\) −496.915 −0.0296429
\(656\) 18147.6 1.08010
\(657\) 0 0
\(658\) −45520.3 −2.69691
\(659\) 15876.5 0.938483 0.469241 0.883070i \(-0.344527\pi\)
0.469241 + 0.883070i \(0.344527\pi\)
\(660\) 0 0
\(661\) 18295.7 1.07658 0.538291 0.842759i \(-0.319070\pi\)
0.538291 + 0.842759i \(0.319070\pi\)
\(662\) 42952.8 2.52176
\(663\) 0 0
\(664\) 31883.5 1.86343
\(665\) −1766.90 −0.103034
\(666\) 0 0
\(667\) 12214.6 0.709075
\(668\) −60852.6 −3.52463
\(669\) 0 0
\(670\) 4263.38 0.245834
\(671\) −2143.97 −0.123349
\(672\) 0 0
\(673\) 20647.4 1.18261 0.591307 0.806446i \(-0.298612\pi\)
0.591307 + 0.806446i \(0.298612\pi\)
\(674\) 24060.9 1.37506
\(675\) 0 0
\(676\) −35808.7 −2.03737
\(677\) −32567.1 −1.84883 −0.924413 0.381393i \(-0.875444\pi\)
−0.924413 + 0.381393i \(0.875444\pi\)
\(678\) 0 0
\(679\) 11056.1 0.624879
\(680\) −6791.53 −0.383005
\(681\) 0 0
\(682\) −584.154 −0.0327983
\(683\) −5557.74 −0.311363 −0.155682 0.987807i \(-0.549757\pi\)
−0.155682 + 0.987807i \(0.549757\pi\)
\(684\) 0 0
\(685\) 2882.28 0.160768
\(686\) 18270.1 1.01684
\(687\) 0 0
\(688\) −53775.7 −2.97991
\(689\) −2843.76 −0.157241
\(690\) 0 0
\(691\) 28353.5 1.56095 0.780477 0.625185i \(-0.214976\pi\)
0.780477 + 0.625185i \(0.214976\pi\)
\(692\) 60593.2 3.32862
\(693\) 0 0
\(694\) 22673.1 1.24015
\(695\) 2405.20 0.131273
\(696\) 0 0
\(697\) 13464.2 0.731695
\(698\) 28918.3 1.56816
\(699\) 0 0
\(700\) 52854.5 2.85387
\(701\) −4271.73 −0.230159 −0.115079 0.993356i \(-0.536712\pi\)
−0.115079 + 0.993356i \(0.536712\pi\)
\(702\) 0 0
\(703\) 5190.87 0.278488
\(704\) 877.758 0.0469911
\(705\) 0 0
\(706\) −502.327 −0.0267781
\(707\) 39562.8 2.10454
\(708\) 0 0
\(709\) 9667.95 0.512112 0.256056 0.966662i \(-0.417577\pi\)
0.256056 + 0.966662i \(0.417577\pi\)
\(710\) −868.031 −0.0458826
\(711\) 0 0
\(712\) 32004.8 1.68459
\(713\) 4541.19 0.238526
\(714\) 0 0
\(715\) 87.7804 0.00459133
\(716\) 83918.1 4.38012
\(717\) 0 0
\(718\) −41647.7 −2.16473
\(719\) −25456.1 −1.32038 −0.660188 0.751100i \(-0.729524\pi\)
−0.660188 + 0.751100i \(0.729524\pi\)
\(720\) 0 0
\(721\) −956.670 −0.0494151
\(722\) −16664.1 −0.858968
\(723\) 0 0
\(724\) −66843.2 −3.43122
\(725\) 8925.27 0.457209
\(726\) 0 0
\(727\) 6884.94 0.351235 0.175618 0.984458i \(-0.443808\pi\)
0.175618 + 0.984458i \(0.443808\pi\)
\(728\) 20581.6 1.04781
\(729\) 0 0
\(730\) 1907.80 0.0967274
\(731\) −39897.6 −2.01870
\(732\) 0 0
\(733\) 96.5247 0.00486387 0.00243194 0.999997i \(-0.499226\pi\)
0.00243194 + 0.999997i \(0.499226\pi\)
\(734\) 25109.9 1.26270
\(735\) 0 0
\(736\) −41463.3 −2.07657
\(737\) −2740.95 −0.136993
\(738\) 0 0
\(739\) −18330.0 −0.912423 −0.456212 0.889871i \(-0.650794\pi\)
−0.456212 + 0.889871i \(0.650794\pi\)
\(740\) 2035.39 0.101112
\(741\) 0 0
\(742\) −20647.7 −1.02156
\(743\) 17703.9 0.874152 0.437076 0.899425i \(-0.356014\pi\)
0.437076 + 0.899425i \(0.356014\pi\)
\(744\) 0 0
\(745\) 1005.63 0.0494544
\(746\) −36311.7 −1.78213
\(747\) 0 0
\(748\) 7672.22 0.375032
\(749\) −22229.1 −1.08442
\(750\) 0 0
\(751\) 20342.4 0.988421 0.494210 0.869342i \(-0.335457\pi\)
0.494210 + 0.869342i \(0.335457\pi\)
\(752\) 50590.2 2.45324
\(753\) 0 0
\(754\) 6106.95 0.294963
\(755\) −3419.23 −0.164819
\(756\) 0 0
\(757\) 26846.7 1.28898 0.644490 0.764612i \(-0.277070\pi\)
0.644490 + 0.764612i \(0.277070\pi\)
\(758\) 30767.6 1.47431
\(759\) 0 0
\(760\) 4170.43 0.199049
\(761\) −1474.28 −0.0702269 −0.0351134 0.999383i \(-0.511179\pi\)
−0.0351134 + 0.999383i \(0.511179\pi\)
\(762\) 0 0
\(763\) −11023.3 −0.523029
\(764\) 29736.9 1.40817
\(765\) 0 0
\(766\) −18644.8 −0.879458
\(767\) 6975.05 0.328363
\(768\) 0 0
\(769\) 24129.6 1.13152 0.565758 0.824571i \(-0.308584\pi\)
0.565758 + 0.824571i \(0.308584\pi\)
\(770\) 637.346 0.0298290
\(771\) 0 0
\(772\) −64229.7 −2.99440
\(773\) 30272.0 1.40855 0.704273 0.709929i \(-0.251273\pi\)
0.704273 + 0.709929i \(0.251273\pi\)
\(774\) 0 0
\(775\) 3318.26 0.153801
\(776\) −26095.7 −1.20719
\(777\) 0 0
\(778\) −16203.4 −0.746686
\(779\) −8267.86 −0.380265
\(780\) 0 0
\(781\) 558.061 0.0255685
\(782\) −85343.7 −3.90266
\(783\) 0 0
\(784\) 25029.4 1.14019
\(785\) 380.283 0.0172903
\(786\) 0 0
\(787\) −30974.7 −1.40296 −0.701480 0.712690i \(-0.747477\pi\)
−0.701480 + 0.712690i \(0.747477\pi\)
\(788\) −15509.1 −0.701128
\(789\) 0 0
\(790\) −6215.97 −0.279942
\(791\) 18121.9 0.814589
\(792\) 0 0
\(793\) 8333.08 0.373161
\(794\) 20419.2 0.912657
\(795\) 0 0
\(796\) −23221.5 −1.03400
\(797\) −9007.64 −0.400335 −0.200168 0.979762i \(-0.564149\pi\)
−0.200168 + 0.979762i \(0.564149\pi\)
\(798\) 0 0
\(799\) 37534.2 1.66191
\(800\) −30297.3 −1.33897
\(801\) 0 0
\(802\) −26618.4 −1.17198
\(803\) −1226.54 −0.0539023
\(804\) 0 0
\(805\) −4954.71 −0.216932
\(806\) 2270.46 0.0992228
\(807\) 0 0
\(808\) −93380.3 −4.06573
\(809\) 12327.4 0.535732 0.267866 0.963456i \(-0.413682\pi\)
0.267866 + 0.963456i \(0.413682\pi\)
\(810\) 0 0
\(811\) −19319.9 −0.836514 −0.418257 0.908329i \(-0.637359\pi\)
−0.418257 + 0.908329i \(0.637359\pi\)
\(812\) 30988.1 1.33925
\(813\) 0 0
\(814\) −1872.42 −0.0806243
\(815\) −189.014 −0.00812379
\(816\) 0 0
\(817\) 24499.7 1.04913
\(818\) −78662.6 −3.36231
\(819\) 0 0
\(820\) −3241.91 −0.138064
\(821\) 811.897 0.0345133 0.0172566 0.999851i \(-0.494507\pi\)
0.0172566 + 0.999851i \(0.494507\pi\)
\(822\) 0 0
\(823\) 21030.5 0.890737 0.445369 0.895347i \(-0.353073\pi\)
0.445369 + 0.895347i \(0.353073\pi\)
\(824\) 2258.04 0.0954642
\(825\) 0 0
\(826\) 50643.6 2.13331
\(827\) −33934.2 −1.42686 −0.713428 0.700729i \(-0.752858\pi\)
−0.713428 + 0.700729i \(0.752858\pi\)
\(828\) 0 0
\(829\) 21393.4 0.896289 0.448144 0.893961i \(-0.352085\pi\)
0.448144 + 0.893961i \(0.352085\pi\)
\(830\) −3837.51 −0.160484
\(831\) 0 0
\(832\) −3411.63 −0.142160
\(833\) 18570.0 0.772402
\(834\) 0 0
\(835\) 4168.27 0.172753
\(836\) −4711.24 −0.194906
\(837\) 0 0
\(838\) −45139.6 −1.86076
\(839\) −7747.11 −0.318784 −0.159392 0.987215i \(-0.550953\pi\)
−0.159392 + 0.987215i \(0.550953\pi\)
\(840\) 0 0
\(841\) −19156.2 −0.785444
\(842\) −15076.5 −0.617066
\(843\) 0 0
\(844\) 17399.0 0.709597
\(845\) 2452.82 0.0998575
\(846\) 0 0
\(847\) 30300.7 1.22921
\(848\) 22947.4 0.929264
\(849\) 0 0
\(850\) −62360.8 −2.51642
\(851\) 14556.1 0.586342
\(852\) 0 0
\(853\) −16935.0 −0.679769 −0.339884 0.940467i \(-0.610388\pi\)
−0.339884 + 0.940467i \(0.610388\pi\)
\(854\) 60503.9 2.42436
\(855\) 0 0
\(856\) 52467.4 2.09498
\(857\) −3777.17 −0.150555 −0.0752776 0.997163i \(-0.523984\pi\)
−0.0752776 + 0.997163i \(0.523984\pi\)
\(858\) 0 0
\(859\) −21017.0 −0.834798 −0.417399 0.908723i \(-0.637058\pi\)
−0.417399 + 0.908723i \(0.637058\pi\)
\(860\) 9606.59 0.380909
\(861\) 0 0
\(862\) 27040.8 1.06846
\(863\) 9505.46 0.374936 0.187468 0.982271i \(-0.439972\pi\)
0.187468 + 0.982271i \(0.439972\pi\)
\(864\) 0 0
\(865\) −4150.50 −0.163146
\(866\) −14955.2 −0.586834
\(867\) 0 0
\(868\) 11520.8 0.450510
\(869\) 3996.28 0.156001
\(870\) 0 0
\(871\) 10653.4 0.414438
\(872\) 26018.5 1.01043
\(873\) 0 0
\(874\) 52406.5 2.02823
\(875\) −7288.29 −0.281588
\(876\) 0 0
\(877\) 27293.6 1.05090 0.525450 0.850824i \(-0.323897\pi\)
0.525450 + 0.850824i \(0.323897\pi\)
\(878\) 23542.1 0.904906
\(879\) 0 0
\(880\) −708.332 −0.0271340
\(881\) −28578.9 −1.09290 −0.546451 0.837491i \(-0.684022\pi\)
−0.546451 + 0.837491i \(0.684022\pi\)
\(882\) 0 0
\(883\) −5713.16 −0.217738 −0.108869 0.994056i \(-0.534723\pi\)
−0.108869 + 0.994056i \(0.534723\pi\)
\(884\) −29820.0 −1.13457
\(885\) 0 0
\(886\) 10731.9 0.406934
\(887\) 43896.4 1.66166 0.830832 0.556523i \(-0.187865\pi\)
0.830832 + 0.556523i \(0.187865\pi\)
\(888\) 0 0
\(889\) 19562.3 0.738018
\(890\) −3852.11 −0.145082
\(891\) 0 0
\(892\) 48079.9 1.80475
\(893\) −23048.4 −0.863703
\(894\) 0 0
\(895\) −5748.21 −0.214683
\(896\) 20555.3 0.766412
\(897\) 0 0
\(898\) 332.108 0.0123414
\(899\) 1945.47 0.0721746
\(900\) 0 0
\(901\) 17025.3 0.629515
\(902\) 2982.33 0.110089
\(903\) 0 0
\(904\) −42773.2 −1.57369
\(905\) 4578.61 0.168175
\(906\) 0 0
\(907\) 23392.1 0.856362 0.428181 0.903693i \(-0.359155\pi\)
0.428181 + 0.903693i \(0.359155\pi\)
\(908\) 95090.9 3.47544
\(909\) 0 0
\(910\) −2477.21 −0.0902402
\(911\) 1315.19 0.0478310 0.0239155 0.999714i \(-0.492387\pi\)
0.0239155 + 0.999714i \(0.492387\pi\)
\(912\) 0 0
\(913\) 2467.15 0.0894314
\(914\) −44358.0 −1.60529
\(915\) 0 0
\(916\) 66658.5 2.40443
\(917\) −9015.57 −0.324668
\(918\) 0 0
\(919\) −47277.7 −1.69701 −0.848503 0.529191i \(-0.822496\pi\)
−0.848503 + 0.529191i \(0.822496\pi\)
\(920\) 11694.6 0.419088
\(921\) 0 0
\(922\) −79453.7 −2.83804
\(923\) −2169.05 −0.0773510
\(924\) 0 0
\(925\) 10636.2 0.378071
\(926\) 54800.9 1.94478
\(927\) 0 0
\(928\) −17763.0 −0.628341
\(929\) 36239.8 1.27986 0.639930 0.768433i \(-0.278963\pi\)
0.639930 + 0.768433i \(0.278963\pi\)
\(930\) 0 0
\(931\) −11403.2 −0.401421
\(932\) 16407.4 0.576654
\(933\) 0 0
\(934\) 13983.3 0.489879
\(935\) −525.531 −0.0183815
\(936\) 0 0
\(937\) 12678.9 0.442051 0.221026 0.975268i \(-0.429060\pi\)
0.221026 + 0.975268i \(0.429060\pi\)
\(938\) 77350.8 2.69253
\(939\) 0 0
\(940\) −9037.53 −0.313587
\(941\) −50353.2 −1.74438 −0.872192 0.489163i \(-0.837302\pi\)
−0.872192 + 0.489163i \(0.837302\pi\)
\(942\) 0 0
\(943\) −23184.5 −0.800628
\(944\) −56284.2 −1.94057
\(945\) 0 0
\(946\) −8837.38 −0.303729
\(947\) 33033.7 1.13353 0.566763 0.823881i \(-0.308195\pi\)
0.566763 + 0.823881i \(0.308195\pi\)
\(948\) 0 0
\(949\) 4767.24 0.163068
\(950\) 38293.6 1.30780
\(951\) 0 0
\(952\) −123219. −4.19492
\(953\) 12625.3 0.429142 0.214571 0.976708i \(-0.431165\pi\)
0.214571 + 0.976708i \(0.431165\pi\)
\(954\) 0 0
\(955\) −2036.92 −0.0690189
\(956\) 4437.29 0.150117
\(957\) 0 0
\(958\) −49880.8 −1.68223
\(959\) 52293.4 1.76083
\(960\) 0 0
\(961\) −29067.7 −0.975721
\(962\) 7277.62 0.243909
\(963\) 0 0
\(964\) −26866.7 −0.897633
\(965\) 4399.59 0.146765
\(966\) 0 0
\(967\) −20457.9 −0.680333 −0.340167 0.940365i \(-0.610484\pi\)
−0.340167 + 0.940365i \(0.610484\pi\)
\(968\) −71519.0 −2.37470
\(969\) 0 0
\(970\) 3140.89 0.103967
\(971\) −41805.4 −1.38167 −0.690834 0.723014i \(-0.742756\pi\)
−0.690834 + 0.723014i \(0.742756\pi\)
\(972\) 0 0
\(973\) 43637.8 1.43778
\(974\) −7518.31 −0.247333
\(975\) 0 0
\(976\) −67242.7 −2.20531
\(977\) −47505.6 −1.55562 −0.777808 0.628502i \(-0.783669\pi\)
−0.777808 + 0.628502i \(0.783669\pi\)
\(978\) 0 0
\(979\) 2476.54 0.0808484
\(980\) −4471.30 −0.145745
\(981\) 0 0
\(982\) 54108.0 1.75830
\(983\) −58004.1 −1.88204 −0.941020 0.338352i \(-0.890131\pi\)
−0.941020 + 0.338352i \(0.890131\pi\)
\(984\) 0 0
\(985\) 1062.34 0.0343644
\(986\) −36561.6 −1.18089
\(987\) 0 0
\(988\) 18311.4 0.589639
\(989\) 68701.5 2.20888
\(990\) 0 0
\(991\) 46228.7 1.48184 0.740920 0.671593i \(-0.234390\pi\)
0.740920 + 0.671593i \(0.234390\pi\)
\(992\) −6604.00 −0.211368
\(993\) 0 0
\(994\) −15748.8 −0.502535
\(995\) 1590.62 0.0506796
\(996\) 0 0
\(997\) −35226.8 −1.11900 −0.559501 0.828830i \(-0.689007\pi\)
−0.559501 + 0.828830i \(0.689007\pi\)
\(998\) 97494.4 3.09232
\(999\) 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.g.1.57 59
3.2 odd 2 2151.4.a.h.1.3 yes 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.57 59 1.1 even 1 trivial
2151.4.a.h.1.3 yes 59 3.2 odd 2