Properties

Label 441.4.a.r.1.2
Level $441$
Weight $4$
Character 441.1
Self dual yes
Analytic conductor $26.020$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{57}) \)
Defining polynomial: \(x^{2} - x - 14\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(4.27492\) of defining polynomial
Character \(\chi\) \(=\) 441.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.27492 q^{2} +19.8248 q^{4} +10.5498 q^{5} +62.3746 q^{8} +O(q^{10})\) \(q+5.27492 q^{2} +19.8248 q^{4} +10.5498 q^{5} +62.3746 q^{8} +55.6495 q^{10} -34.7492 q^{11} +37.2990 q^{13} +170.423 q^{16} -10.5498 q^{17} +58.5980 q^{19} +209.148 q^{20} -183.299 q^{22} +125.347 q^{23} -13.7010 q^{25} +196.749 q^{26} +35.4020 q^{29} -291.794 q^{31} +399.969 q^{32} -55.6495 q^{34} -259.897 q^{37} +309.100 q^{38} +658.042 q^{40} -338.248 q^{41} +6.80397 q^{43} -688.894 q^{44} +661.196 q^{46} +250.694 q^{47} -72.2716 q^{50} +739.444 q^{52} +536.900 q^{53} -366.598 q^{55} +186.743 q^{58} -35.8904 q^{59} -57.7940 q^{61} -1539.19 q^{62} +746.423 q^{64} +393.498 q^{65} +481.691 q^{67} -209.148 q^{68} -363.752 q^{71} -581.299 q^{73} -1370.94 q^{74} +1161.69 q^{76} -693.691 q^{79} +1797.93 q^{80} -1784.23 q^{82} +1334.39 q^{83} -111.299 q^{85} +35.8904 q^{86} -2167.47 q^{88} -353.038 q^{89} +2484.98 q^{92} +1322.39 q^{94} +618.199 q^{95} -1445.88 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{2} + 17q^{4} + 6q^{5} + 87q^{8} + O(q^{10}) \) \( 2q + 3q^{2} + 17q^{4} + 6q^{5} + 87q^{8} + 66q^{10} + 6q^{11} - 16q^{13} + 137q^{16} - 6q^{17} - 64q^{19} + 222q^{20} - 276q^{22} - 6q^{23} - 118q^{25} + 318q^{26} + 252q^{29} - 40q^{31} + 279q^{32} - 66q^{34} - 248q^{37} + 588q^{38} + 546q^{40} - 450q^{41} + 376q^{43} - 804q^{44} + 960q^{46} - 12q^{47} + 165q^{50} + 890q^{52} + 1104q^{53} - 552q^{55} - 306q^{58} + 804q^{59} + 428q^{61} - 2112q^{62} + 1289q^{64} + 636q^{65} + 148q^{67} - 222q^{68} - 954q^{71} - 1072q^{73} - 1398q^{74} + 1508q^{76} - 572q^{79} + 1950q^{80} - 1530q^{82} + 1944q^{83} - 132q^{85} - 804q^{86} - 1164q^{88} + 366q^{89} + 2856q^{92} + 1920q^{94} + 1176q^{95} - 808q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.27492 1.86496 0.932482 0.361215i \(-0.117638\pi\)
0.932482 + 0.361215i \(0.117638\pi\)
\(3\) 0 0
\(4\) 19.8248 2.47809
\(5\) 10.5498 0.943606 0.471803 0.881704i \(-0.343603\pi\)
0.471803 + 0.881704i \(0.343603\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 62.3746 2.75659
\(9\) 0 0
\(10\) 55.6495 1.75979
\(11\) −34.7492 −0.952479 −0.476240 0.879316i \(-0.658000\pi\)
−0.476240 + 0.879316i \(0.658000\pi\)
\(12\) 0 0
\(13\) 37.2990 0.795760 0.397880 0.917437i \(-0.369746\pi\)
0.397880 + 0.917437i \(0.369746\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 170.423 2.66286
\(17\) −10.5498 −0.150512 −0.0752562 0.997164i \(-0.523977\pi\)
−0.0752562 + 0.997164i \(0.523977\pi\)
\(18\) 0 0
\(19\) 58.5980 0.707542 0.353771 0.935332i \(-0.384899\pi\)
0.353771 + 0.935332i \(0.384899\pi\)
\(20\) 209.148 2.33834
\(21\) 0 0
\(22\) −183.299 −1.77634
\(23\) 125.347 1.13638 0.568189 0.822898i \(-0.307644\pi\)
0.568189 + 0.822898i \(0.307644\pi\)
\(24\) 0 0
\(25\) −13.7010 −0.109608
\(26\) 196.749 1.48406
\(27\) 0 0
\(28\) 0 0
\(29\) 35.4020 0.226689 0.113345 0.993556i \(-0.463844\pi\)
0.113345 + 0.993556i \(0.463844\pi\)
\(30\) 0 0
\(31\) −291.794 −1.69057 −0.845286 0.534313i \(-0.820570\pi\)
−0.845286 + 0.534313i \(0.820570\pi\)
\(32\) 399.969 2.20954
\(33\) 0 0
\(34\) −55.6495 −0.280700
\(35\) 0 0
\(36\) 0 0
\(37\) −259.897 −1.15478 −0.577389 0.816469i \(-0.695928\pi\)
−0.577389 + 0.816469i \(0.695928\pi\)
\(38\) 309.100 1.31954
\(39\) 0 0
\(40\) 658.042 2.60114
\(41\) −338.248 −1.28842 −0.644212 0.764847i \(-0.722815\pi\)
−0.644212 + 0.764847i \(0.722815\pi\)
\(42\) 0 0
\(43\) 6.80397 0.0241301 0.0120651 0.999927i \(-0.496159\pi\)
0.0120651 + 0.999927i \(0.496159\pi\)
\(44\) −688.894 −2.36033
\(45\) 0 0
\(46\) 661.196 2.11931
\(47\) 250.694 0.778033 0.389016 0.921231i \(-0.372815\pi\)
0.389016 + 0.921231i \(0.372815\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −72.2716 −0.204415
\(51\) 0 0
\(52\) 739.444 1.97197
\(53\) 536.900 1.39149 0.695745 0.718289i \(-0.255075\pi\)
0.695745 + 0.718289i \(0.255075\pi\)
\(54\) 0 0
\(55\) −366.598 −0.898765
\(56\) 0 0
\(57\) 0 0
\(58\) 186.743 0.422767
\(59\) −35.8904 −0.0791955 −0.0395977 0.999216i \(-0.512608\pi\)
−0.0395977 + 0.999216i \(0.512608\pi\)
\(60\) 0 0
\(61\) −57.7940 −0.121308 −0.0606538 0.998159i \(-0.519319\pi\)
−0.0606538 + 0.998159i \(0.519319\pi\)
\(62\) −1539.19 −3.15286
\(63\) 0 0
\(64\) 746.423 1.45786
\(65\) 393.498 0.750884
\(66\) 0 0
\(67\) 481.691 0.878327 0.439164 0.898407i \(-0.355275\pi\)
0.439164 + 0.898407i \(0.355275\pi\)
\(68\) −209.148 −0.372984
\(69\) 0 0
\(70\) 0 0
\(71\) −363.752 −0.608021 −0.304010 0.952669i \(-0.598326\pi\)
−0.304010 + 0.952669i \(0.598326\pi\)
\(72\) 0 0
\(73\) −581.299 −0.931999 −0.465999 0.884785i \(-0.654305\pi\)
−0.465999 + 0.884785i \(0.654305\pi\)
\(74\) −1370.94 −2.15362
\(75\) 0 0
\(76\) 1161.69 1.75336
\(77\) 0 0
\(78\) 0 0
\(79\) −693.691 −0.987928 −0.493964 0.869482i \(-0.664453\pi\)
−0.493964 + 0.869482i \(0.664453\pi\)
\(80\) 1797.93 2.51269
\(81\) 0 0
\(82\) −1784.23 −2.40287
\(83\) 1334.39 1.76468 0.882341 0.470611i \(-0.155967\pi\)
0.882341 + 0.470611i \(0.155967\pi\)
\(84\) 0 0
\(85\) −111.299 −0.142024
\(86\) 35.8904 0.0450019
\(87\) 0 0
\(88\) −2167.47 −2.62560
\(89\) −353.038 −0.420472 −0.210236 0.977651i \(-0.567423\pi\)
−0.210236 + 0.977651i \(0.567423\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2484.98 2.81605
\(93\) 0 0
\(94\) 1322.39 1.45100
\(95\) 618.199 0.667641
\(96\) 0 0
\(97\) −1445.88 −1.51347 −0.756735 0.653722i \(-0.773207\pi\)
−0.756735 + 0.653722i \(0.773207\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −271.619 −0.271619
\(101\) 474.852 0.467817 0.233909 0.972259i \(-0.424848\pi\)
0.233909 + 0.972259i \(0.424848\pi\)
\(102\) 0 0
\(103\) 1999.59 1.91287 0.956433 0.291951i \(-0.0943044\pi\)
0.956433 + 0.291951i \(0.0943044\pi\)
\(104\) 2326.51 2.19359
\(105\) 0 0
\(106\) 2832.10 2.59508
\(107\) −1166.74 −1.05414 −0.527068 0.849823i \(-0.676709\pi\)
−0.527068 + 0.849823i \(0.676709\pi\)
\(108\) 0 0
\(109\) −1337.18 −1.17503 −0.587515 0.809213i \(-0.699894\pi\)
−0.587515 + 0.809213i \(0.699894\pi\)
\(110\) −1933.77 −1.67616
\(111\) 0 0
\(112\) 0 0
\(113\) −906.578 −0.754723 −0.377361 0.926066i \(-0.623169\pi\)
−0.377361 + 0.926066i \(0.623169\pi\)
\(114\) 0 0
\(115\) 1322.39 1.07229
\(116\) 701.836 0.561757
\(117\) 0 0
\(118\) −189.319 −0.147697
\(119\) 0 0
\(120\) 0 0
\(121\) −123.495 −0.0927836
\(122\) −304.859 −0.226235
\(123\) 0 0
\(124\) −5784.74 −4.18940
\(125\) −1463.27 −1.04703
\(126\) 0 0
\(127\) −1714.89 −1.19820 −0.599101 0.800674i \(-0.704475\pi\)
−0.599101 + 0.800674i \(0.704475\pi\)
\(128\) 737.564 0.509313
\(129\) 0 0
\(130\) 2075.67 1.40037
\(131\) 470.611 0.313874 0.156937 0.987609i \(-0.449838\pi\)
0.156937 + 0.987609i \(0.449838\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2540.88 1.63805
\(135\) 0 0
\(136\) −658.042 −0.414901
\(137\) 443.910 0.276831 0.138415 0.990374i \(-0.455799\pi\)
0.138415 + 0.990374i \(0.455799\pi\)
\(138\) 0 0
\(139\) −1669.98 −1.01904 −0.509518 0.860460i \(-0.670176\pi\)
−0.509518 + 0.860460i \(0.670176\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1918.76 −1.13394
\(143\) −1296.11 −0.757945
\(144\) 0 0
\(145\) 373.485 0.213905
\(146\) −3066.30 −1.73814
\(147\) 0 0
\(148\) −5152.39 −2.86165
\(149\) −743.871 −0.408995 −0.204497 0.978867i \(-0.565556\pi\)
−0.204497 + 0.978867i \(0.565556\pi\)
\(150\) 0 0
\(151\) 606.764 0.327005 0.163503 0.986543i \(-0.447721\pi\)
0.163503 + 0.986543i \(0.447721\pi\)
\(152\) 3655.03 1.95041
\(153\) 0 0
\(154\) 0 0
\(155\) −3078.38 −1.59523
\(156\) 0 0
\(157\) −3114.78 −1.58336 −0.791678 0.610939i \(-0.790792\pi\)
−0.791678 + 0.610939i \(0.790792\pi\)
\(158\) −3659.16 −1.84245
\(159\) 0 0
\(160\) 4219.61 2.08493
\(161\) 0 0
\(162\) 0 0
\(163\) 2413.07 1.15955 0.579774 0.814777i \(-0.303141\pi\)
0.579774 + 0.814777i \(0.303141\pi\)
\(164\) −6705.67 −3.19284
\(165\) 0 0
\(166\) 7038.81 3.29107
\(167\) −610.475 −0.282874 −0.141437 0.989947i \(-0.545172\pi\)
−0.141437 + 0.989947i \(0.545172\pi\)
\(168\) 0 0
\(169\) −805.784 −0.366766
\(170\) −587.093 −0.264870
\(171\) 0 0
\(172\) 134.887 0.0597968
\(173\) 3793.81 1.66727 0.833636 0.552315i \(-0.186255\pi\)
0.833636 + 0.552315i \(0.186255\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5922.05 −2.53631
\(177\) 0 0
\(178\) −1862.25 −0.784165
\(179\) 2804.68 1.17112 0.585562 0.810627i \(-0.300874\pi\)
0.585562 + 0.810627i \(0.300874\pi\)
\(180\) 0 0
\(181\) −3106.04 −1.27553 −0.637763 0.770232i \(-0.720140\pi\)
−0.637763 + 0.770232i \(0.720140\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 7818.48 3.13253
\(185\) −2741.87 −1.08966
\(186\) 0 0
\(187\) 366.598 0.143360
\(188\) 4969.95 1.92804
\(189\) 0 0
\(190\) 3260.95 1.24513
\(191\) −261.952 −0.0992365 −0.0496182 0.998768i \(-0.515800\pi\)
−0.0496182 + 0.998768i \(0.515800\pi\)
\(192\) 0 0
\(193\) 4051.07 1.51089 0.755447 0.655210i \(-0.227420\pi\)
0.755447 + 0.655210i \(0.227420\pi\)
\(194\) −7626.88 −2.82257
\(195\) 0 0
\(196\) 0 0
\(197\) 2874.83 1.03971 0.519855 0.854254i \(-0.325986\pi\)
0.519855 + 0.854254i \(0.325986\pi\)
\(198\) 0 0
\(199\) 3066.97 1.09252 0.546261 0.837615i \(-0.316051\pi\)
0.546261 + 0.837615i \(0.316051\pi\)
\(200\) −854.594 −0.302145
\(201\) 0 0
\(202\) 2504.81 0.872463
\(203\) 0 0
\(204\) 0 0
\(205\) −3568.46 −1.21576
\(206\) 10547.7 3.56743
\(207\) 0 0
\(208\) 6356.60 2.11899
\(209\) −2036.23 −0.673919
\(210\) 0 0
\(211\) 595.422 0.194268 0.0971340 0.995271i \(-0.469032\pi\)
0.0971340 + 0.995271i \(0.469032\pi\)
\(212\) 10643.9 3.44824
\(213\) 0 0
\(214\) −6154.44 −1.96593
\(215\) 71.7808 0.0227693
\(216\) 0 0
\(217\) 0 0
\(218\) −7053.49 −2.19139
\(219\) 0 0
\(220\) −7267.71 −2.22722
\(221\) −393.498 −0.119772
\(222\) 0 0
\(223\) 3779.79 1.13504 0.567520 0.823360i \(-0.307903\pi\)
0.567520 + 0.823360i \(0.307903\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4782.12 −1.40753
\(227\) 1827.62 0.534376 0.267188 0.963644i \(-0.413906\pi\)
0.267188 + 0.963644i \(0.413906\pi\)
\(228\) 0 0
\(229\) 850.249 0.245354 0.122677 0.992447i \(-0.460852\pi\)
0.122677 + 0.992447i \(0.460852\pi\)
\(230\) 6975.51 1.99979
\(231\) 0 0
\(232\) 2208.18 0.624890
\(233\) 6591.10 1.85321 0.926604 0.376039i \(-0.122714\pi\)
0.926604 + 0.376039i \(0.122714\pi\)
\(234\) 0 0
\(235\) 2644.78 0.734156
\(236\) −711.518 −0.196254
\(237\) 0 0
\(238\) 0 0
\(239\) 182.556 0.0494083 0.0247042 0.999695i \(-0.492136\pi\)
0.0247042 + 0.999695i \(0.492136\pi\)
\(240\) 0 0
\(241\) −1523.90 −0.407315 −0.203657 0.979042i \(-0.565283\pi\)
−0.203657 + 0.979042i \(0.565283\pi\)
\(242\) −651.426 −0.173038
\(243\) 0 0
\(244\) −1145.75 −0.300612
\(245\) 0 0
\(246\) 0 0
\(247\) 2185.65 0.563034
\(248\) −18200.5 −4.66022
\(249\) 0 0
\(250\) −7718.64 −1.95268
\(251\) 2357.73 0.592903 0.296451 0.955048i \(-0.404197\pi\)
0.296451 + 0.955048i \(0.404197\pi\)
\(252\) 0 0
\(253\) −4355.71 −1.08238
\(254\) −9045.89 −2.23460
\(255\) 0 0
\(256\) −2080.79 −0.508006
\(257\) 2782.55 0.675372 0.337686 0.941259i \(-0.390356\pi\)
0.337686 + 0.941259i \(0.390356\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7801.01 1.86076
\(261\) 0 0
\(262\) 2482.44 0.585364
\(263\) −2043.78 −0.479183 −0.239591 0.970874i \(-0.577013\pi\)
−0.239591 + 0.970874i \(0.577013\pi\)
\(264\) 0 0
\(265\) 5664.21 1.31302
\(266\) 0 0
\(267\) 0 0
\(268\) 9549.41 2.17658
\(269\) 3452.84 0.782614 0.391307 0.920260i \(-0.372023\pi\)
0.391307 + 0.920260i \(0.372023\pi\)
\(270\) 0 0
\(271\) −2644.29 −0.592728 −0.296364 0.955075i \(-0.595774\pi\)
−0.296364 + 0.955075i \(0.595774\pi\)
\(272\) −1797.93 −0.400793
\(273\) 0 0
\(274\) 2341.59 0.516280
\(275\) 476.098 0.104399
\(276\) 0 0
\(277\) 2679.49 0.581208 0.290604 0.956843i \(-0.406144\pi\)
0.290604 + 0.956843i \(0.406144\pi\)
\(278\) −8809.01 −1.90046
\(279\) 0 0
\(280\) 0 0
\(281\) 1019.69 0.216476 0.108238 0.994125i \(-0.465479\pi\)
0.108238 + 0.994125i \(0.465479\pi\)
\(282\) 0 0
\(283\) −432.206 −0.0907844 −0.0453922 0.998969i \(-0.514454\pi\)
−0.0453922 + 0.998969i \(0.514454\pi\)
\(284\) −7211.30 −1.50673
\(285\) 0 0
\(286\) −6836.87 −1.41354
\(287\) 0 0
\(288\) 0 0
\(289\) −4801.70 −0.977346
\(290\) 1970.10 0.398926
\(291\) 0 0
\(292\) −11524.1 −2.30958
\(293\) −2245.92 −0.447809 −0.223904 0.974611i \(-0.571880\pi\)
−0.223904 + 0.974611i \(0.571880\pi\)
\(294\) 0 0
\(295\) −378.638 −0.0747293
\(296\) −16211.0 −3.18325
\(297\) 0 0
\(298\) −3923.86 −0.762761
\(299\) 4675.33 0.904284
\(300\) 0 0
\(301\) 0 0
\(302\) 3200.63 0.609853
\(303\) 0 0
\(304\) 9986.44 1.88408
\(305\) −609.718 −0.114467
\(306\) 0 0
\(307\) 3197.08 0.594354 0.297177 0.954822i \(-0.403955\pi\)
0.297177 + 0.954822i \(0.403955\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −16238.2 −2.97506
\(311\) −3355.60 −0.611829 −0.305915 0.952059i \(-0.598962\pi\)
−0.305915 + 0.952059i \(0.598962\pi\)
\(312\) 0 0
\(313\) 2256.39 0.407472 0.203736 0.979026i \(-0.434692\pi\)
0.203736 + 0.979026i \(0.434692\pi\)
\(314\) −16430.2 −2.95290
\(315\) 0 0
\(316\) −13752.3 −2.44818
\(317\) 6139.19 1.08773 0.543866 0.839172i \(-0.316960\pi\)
0.543866 + 0.839172i \(0.316960\pi\)
\(318\) 0 0
\(319\) −1230.19 −0.215917
\(320\) 7874.64 1.37564
\(321\) 0 0
\(322\) 0 0
\(323\) −618.199 −0.106494
\(324\) 0 0
\(325\) −511.033 −0.0872216
\(326\) 12728.8 2.16252
\(327\) 0 0
\(328\) −21098.0 −3.55166
\(329\) 0 0
\(330\) 0 0
\(331\) 7029.81 1.16735 0.583676 0.811987i \(-0.301614\pi\)
0.583676 + 0.811987i \(0.301614\pi\)
\(332\) 26454.0 4.37305
\(333\) 0 0
\(334\) −3220.21 −0.527550
\(335\) 5081.76 0.828795
\(336\) 0 0
\(337\) 10328.4 1.66951 0.834757 0.550619i \(-0.185608\pi\)
0.834757 + 0.550619i \(0.185608\pi\)
\(338\) −4250.44 −0.684005
\(339\) 0 0
\(340\) −2206.48 −0.351950
\(341\) 10139.6 1.61024
\(342\) 0 0
\(343\) 0 0
\(344\) 424.395 0.0665170
\(345\) 0 0
\(346\) 20012.0 3.10940
\(347\) −1967.54 −0.304389 −0.152194 0.988351i \(-0.548634\pi\)
−0.152194 + 0.988351i \(0.548634\pi\)
\(348\) 0 0
\(349\) 4365.46 0.669564 0.334782 0.942296i \(-0.391337\pi\)
0.334782 + 0.942296i \(0.391337\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −13898.6 −2.10454
\(353\) −6071.59 −0.915462 −0.457731 0.889091i \(-0.651338\pi\)
−0.457731 + 0.889091i \(0.651338\pi\)
\(354\) 0 0
\(355\) −3837.53 −0.573732
\(356\) −6998.90 −1.04197
\(357\) 0 0
\(358\) 14794.4 2.18411
\(359\) −9638.04 −1.41693 −0.708463 0.705748i \(-0.750611\pi\)
−0.708463 + 0.705748i \(0.750611\pi\)
\(360\) 0 0
\(361\) −3425.27 −0.499384
\(362\) −16384.1 −2.37881
\(363\) 0 0
\(364\) 0 0
\(365\) −6132.61 −0.879439
\(366\) 0 0
\(367\) −522.725 −0.0743488 −0.0371744 0.999309i \(-0.511836\pi\)
−0.0371744 + 0.999309i \(0.511836\pi\)
\(368\) 21362.0 3.02601
\(369\) 0 0
\(370\) −14463.1 −2.03217
\(371\) 0 0
\(372\) 0 0
\(373\) 3229.84 0.448351 0.224175 0.974549i \(-0.428031\pi\)
0.224175 + 0.974549i \(0.428031\pi\)
\(374\) 1933.77 0.267361
\(375\) 0 0
\(376\) 15637.0 2.14472
\(377\) 1320.46 0.180390
\(378\) 0 0
\(379\) 6639.71 0.899892 0.449946 0.893056i \(-0.351443\pi\)
0.449946 + 0.893056i \(0.351443\pi\)
\(380\) 12255.6 1.65448
\(381\) 0 0
\(382\) −1381.77 −0.185073
\(383\) −14224.4 −1.89774 −0.948871 0.315664i \(-0.897773\pi\)
−0.948871 + 0.315664i \(0.897773\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21369.1 2.81777
\(387\) 0 0
\(388\) −28664.2 −3.75052
\(389\) −2921.82 −0.380828 −0.190414 0.981704i \(-0.560983\pi\)
−0.190414 + 0.981704i \(0.560983\pi\)
\(390\) 0 0
\(391\) −1322.39 −0.171039
\(392\) 0 0
\(393\) 0 0
\(394\) 15164.5 1.93902
\(395\) −7318.33 −0.932215
\(396\) 0 0
\(397\) −811.940 −0.102645 −0.0513226 0.998682i \(-0.516344\pi\)
−0.0513226 + 0.998682i \(0.516344\pi\)
\(398\) 16178.0 2.03751
\(399\) 0 0
\(400\) −2334.96 −0.291870
\(401\) −2338.63 −0.291237 −0.145618 0.989341i \(-0.546517\pi\)
−0.145618 + 0.989341i \(0.546517\pi\)
\(402\) 0 0
\(403\) −10883.6 −1.34529
\(404\) 9413.83 1.15930
\(405\) 0 0
\(406\) 0 0
\(407\) 9031.21 1.09990
\(408\) 0 0
\(409\) 2727.57 0.329755 0.164877 0.986314i \(-0.447277\pi\)
0.164877 + 0.986314i \(0.447277\pi\)
\(410\) −18823.3 −2.26736
\(411\) 0 0
\(412\) 39641.3 4.74026
\(413\) 0 0
\(414\) 0 0
\(415\) 14077.6 1.66516
\(416\) 14918.5 1.75826
\(417\) 0 0
\(418\) −10741.0 −1.25684
\(419\) 13306.3 1.55144 0.775721 0.631076i \(-0.217386\pi\)
0.775721 + 0.631076i \(0.217386\pi\)
\(420\) 0 0
\(421\) −11007.5 −1.27428 −0.637138 0.770750i \(-0.719882\pi\)
−0.637138 + 0.770750i \(0.719882\pi\)
\(422\) 3140.80 0.362303
\(423\) 0 0
\(424\) 33488.9 3.83577
\(425\) 144.543 0.0164974
\(426\) 0 0
\(427\) 0 0
\(428\) −23130.2 −2.61225
\(429\) 0 0
\(430\) 378.638 0.0424640
\(431\) 6525.62 0.729300 0.364650 0.931145i \(-0.381189\pi\)
0.364650 + 0.931145i \(0.381189\pi\)
\(432\) 0 0
\(433\) 11716.3 1.30034 0.650171 0.759788i \(-0.274697\pi\)
0.650171 + 0.759788i \(0.274697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −26509.2 −2.91183
\(437\) 7345.10 0.804036
\(438\) 0 0
\(439\) 14611.4 1.58853 0.794264 0.607573i \(-0.207857\pi\)
0.794264 + 0.607573i \(0.207857\pi\)
\(440\) −22866.4 −2.47753
\(441\) 0 0
\(442\) −2075.67 −0.223370
\(443\) 15239.8 1.63446 0.817228 0.576314i \(-0.195510\pi\)
0.817228 + 0.576314i \(0.195510\pi\)
\(444\) 0 0
\(445\) −3724.50 −0.396760
\(446\) 19938.1 2.11681
\(447\) 0 0
\(448\) 0 0
\(449\) −10678.8 −1.12241 −0.561206 0.827676i \(-0.689662\pi\)
−0.561206 + 0.827676i \(0.689662\pi\)
\(450\) 0 0
\(451\) 11753.8 1.22720
\(452\) −17972.7 −1.87027
\(453\) 0 0
\(454\) 9640.53 0.996592
\(455\) 0 0
\(456\) 0 0
\(457\) 4228.23 0.432797 0.216399 0.976305i \(-0.430569\pi\)
0.216399 + 0.976305i \(0.430569\pi\)
\(458\) 4484.99 0.457577
\(459\) 0 0
\(460\) 26216.1 2.65724
\(461\) 910.121 0.0919492 0.0459746 0.998943i \(-0.485361\pi\)
0.0459746 + 0.998943i \(0.485361\pi\)
\(462\) 0 0
\(463\) 4456.16 0.447290 0.223645 0.974671i \(-0.428204\pi\)
0.223645 + 0.974671i \(0.428204\pi\)
\(464\) 6033.30 0.603640
\(465\) 0 0
\(466\) 34767.5 3.45617
\(467\) −4429.42 −0.438907 −0.219453 0.975623i \(-0.570427\pi\)
−0.219453 + 0.975623i \(0.570427\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 13951.0 1.36918
\(471\) 0 0
\(472\) −2238.65 −0.218310
\(473\) −236.432 −0.0229835
\(474\) 0 0
\(475\) −802.851 −0.0775523
\(476\) 0 0
\(477\) 0 0
\(478\) 962.970 0.0921448
\(479\) 2752.85 0.262591 0.131296 0.991343i \(-0.458086\pi\)
0.131296 + 0.991343i \(0.458086\pi\)
\(480\) 0 0
\(481\) −9693.90 −0.918927
\(482\) −8038.43 −0.759628
\(483\) 0 0
\(484\) −2448.26 −0.229927
\(485\) −15253.8 −1.42812
\(486\) 0 0
\(487\) −670.598 −0.0623977 −0.0311989 0.999513i \(-0.509933\pi\)
−0.0311989 + 0.999513i \(0.509933\pi\)
\(488\) −3604.88 −0.334396
\(489\) 0 0
\(490\) 0 0
\(491\) 8244.70 0.757797 0.378898 0.925438i \(-0.376303\pi\)
0.378898 + 0.925438i \(0.376303\pi\)
\(492\) 0 0
\(493\) −373.485 −0.0341195
\(494\) 11529.1 1.05004
\(495\) 0 0
\(496\) −49728.3 −4.50175
\(497\) 0 0
\(498\) 0 0
\(499\) 8164.91 0.732488 0.366244 0.930519i \(-0.380644\pi\)
0.366244 + 0.930519i \(0.380644\pi\)
\(500\) −29009.0 −2.59465
\(501\) 0 0
\(502\) 12436.8 1.10574
\(503\) 8175.59 0.724715 0.362357 0.932039i \(-0.381972\pi\)
0.362357 + 0.932039i \(0.381972\pi\)
\(504\) 0 0
\(505\) 5009.61 0.441435
\(506\) −22976.0 −2.01859
\(507\) 0 0
\(508\) −33997.2 −2.96926
\(509\) −878.448 −0.0764961 −0.0382480 0.999268i \(-0.512178\pi\)
−0.0382480 + 0.999268i \(0.512178\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16876.5 −1.45673
\(513\) 0 0
\(514\) 14677.7 1.25955
\(515\) 21095.3 1.80499
\(516\) 0 0
\(517\) −8711.42 −0.741060
\(518\) 0 0
\(519\) 0 0
\(520\) 24544.3 2.06988
\(521\) 11712.6 0.984910 0.492455 0.870338i \(-0.336100\pi\)
0.492455 + 0.870338i \(0.336100\pi\)
\(522\) 0 0
\(523\) 7341.82 0.613834 0.306917 0.951736i \(-0.400703\pi\)
0.306917 + 0.951736i \(0.400703\pi\)
\(524\) 9329.75 0.777809
\(525\) 0 0
\(526\) −10780.8 −0.893659
\(527\) 3078.38 0.254452
\(528\) 0 0
\(529\) 3544.92 0.291355
\(530\) 29878.2 2.44873
\(531\) 0 0
\(532\) 0 0
\(533\) −12616.3 −1.02528
\(534\) 0 0
\(535\) −12308.9 −0.994690
\(536\) 30045.3 2.42119
\(537\) 0 0
\(538\) 18213.4 1.45955
\(539\) 0 0
\(540\) 0 0
\(541\) −15868.7 −1.26109 −0.630545 0.776153i \(-0.717169\pi\)
−0.630545 + 0.776153i \(0.717169\pi\)
\(542\) −13948.4 −1.10542
\(543\) 0 0
\(544\) −4219.61 −0.332563
\(545\) −14107.0 −1.10877
\(546\) 0 0
\(547\) 2315.26 0.180975 0.0904875 0.995898i \(-0.471157\pi\)
0.0904875 + 0.995898i \(0.471157\pi\)
\(548\) 8800.41 0.686013
\(549\) 0 0
\(550\) 2511.38 0.194701
\(551\) 2074.49 0.160392
\(552\) 0 0
\(553\) 0 0
\(554\) 14134.1 1.08393
\(555\) 0 0
\(556\) −33106.9 −2.52526
\(557\) 4819.05 0.366588 0.183294 0.983058i \(-0.441324\pi\)
0.183294 + 0.983058i \(0.441324\pi\)
\(558\) 0 0
\(559\) 253.781 0.0192018
\(560\) 0 0
\(561\) 0 0
\(562\) 5378.79 0.403720
\(563\) 2540.86 0.190203 0.0951017 0.995468i \(-0.469682\pi\)
0.0951017 + 0.995468i \(0.469682\pi\)
\(564\) 0 0
\(565\) −9564.25 −0.712161
\(566\) −2279.85 −0.169310
\(567\) 0 0
\(568\) −22688.9 −1.67607
\(569\) 24220.0 1.78445 0.892227 0.451587i \(-0.149142\pi\)
0.892227 + 0.451587i \(0.149142\pi\)
\(570\) 0 0
\(571\) −11772.1 −0.862778 −0.431389 0.902166i \(-0.641976\pi\)
−0.431389 + 0.902166i \(0.641976\pi\)
\(572\) −25695.1 −1.87826
\(573\) 0 0
\(574\) 0 0
\(575\) −1717.38 −0.124556
\(576\) 0 0
\(577\) −10584.3 −0.763655 −0.381827 0.924234i \(-0.624705\pi\)
−0.381827 + 0.924234i \(0.624705\pi\)
\(578\) −25328.6 −1.82272
\(579\) 0 0
\(580\) 7404.25 0.530077
\(581\) 0 0
\(582\) 0 0
\(583\) −18656.8 −1.32536
\(584\) −36258.3 −2.56914
\(585\) 0 0
\(586\) −11847.0 −0.835148
\(587\) −8712.63 −0.612621 −0.306311 0.951932i \(-0.599095\pi\)
−0.306311 + 0.951932i \(0.599095\pi\)
\(588\) 0 0
\(589\) −17098.6 −1.19615
\(590\) −1997.28 −0.139368
\(591\) 0 0
\(592\) −44292.4 −3.07501
\(593\) −15362.9 −1.06387 −0.531937 0.846784i \(-0.678536\pi\)
−0.531937 + 0.846784i \(0.678536\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −14747.0 −1.01353
\(597\) 0 0
\(598\) 24662.0 1.68646
\(599\) −26003.8 −1.77377 −0.886883 0.461994i \(-0.847134\pi\)
−0.886883 + 0.461994i \(0.847134\pi\)
\(600\) 0 0
\(601\) −20567.7 −1.39596 −0.697982 0.716115i \(-0.745918\pi\)
−0.697982 + 0.716115i \(0.745918\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 12029.0 0.810349
\(605\) −1302.85 −0.0875512
\(606\) 0 0
\(607\) −19642.1 −1.31342 −0.656711 0.754142i \(-0.728053\pi\)
−0.656711 + 0.754142i \(0.728053\pi\)
\(608\) 23437.4 1.56334
\(609\) 0 0
\(610\) −3216.21 −0.213476
\(611\) 9350.65 0.619127
\(612\) 0 0
\(613\) 8454.59 0.557060 0.278530 0.960428i \(-0.410153\pi\)
0.278530 + 0.960428i \(0.410153\pi\)
\(614\) 16864.3 1.10845
\(615\) 0 0
\(616\) 0 0
\(617\) 24168.4 1.57696 0.788479 0.615061i \(-0.210869\pi\)
0.788479 + 0.615061i \(0.210869\pi\)
\(618\) 0 0
\(619\) 2037.56 0.132305 0.0661523 0.997810i \(-0.478928\pi\)
0.0661523 + 0.997810i \(0.478928\pi\)
\(620\) −61028.1 −3.95314
\(621\) 0 0
\(622\) −17700.5 −1.14104
\(623\) 0 0
\(624\) 0 0
\(625\) −13724.7 −0.878378
\(626\) 11902.3 0.759921
\(627\) 0 0
\(628\) −61749.8 −3.92370
\(629\) 2741.87 0.173808
\(630\) 0 0
\(631\) 12339.5 0.778489 0.389244 0.921135i \(-0.372736\pi\)
0.389244 + 0.921135i \(0.372736\pi\)
\(632\) −43268.7 −2.72332
\(633\) 0 0
\(634\) 32383.7 2.02858
\(635\) −18091.8 −1.13063
\(636\) 0 0
\(637\) 0 0
\(638\) −6489.15 −0.402677
\(639\) 0 0
\(640\) 7781.18 0.480591
\(641\) 10222.6 0.629906 0.314953 0.949107i \(-0.398011\pi\)
0.314953 + 0.949107i \(0.398011\pi\)
\(642\) 0 0
\(643\) 1211.75 0.0743187 0.0371594 0.999309i \(-0.488169\pi\)
0.0371594 + 0.999309i \(0.488169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3260.95 −0.198607
\(647\) −2817.22 −0.171184 −0.0855922 0.996330i \(-0.527278\pi\)
−0.0855922 + 0.996330i \(0.527278\pi\)
\(648\) 0 0
\(649\) 1247.16 0.0754320
\(650\) −2695.66 −0.162665
\(651\) 0 0
\(652\) 47838.6 2.87347
\(653\) −20986.2 −1.25766 −0.628831 0.777542i \(-0.716466\pi\)
−0.628831 + 0.777542i \(0.716466\pi\)
\(654\) 0 0
\(655\) 4964.87 0.296173
\(656\) −57645.1 −3.43089
\(657\) 0 0
\(658\) 0 0
\(659\) 2384.09 0.140927 0.0704635 0.997514i \(-0.477552\pi\)
0.0704635 + 0.997514i \(0.477552\pi\)
\(660\) 0 0
\(661\) 7577.10 0.445862 0.222931 0.974834i \(-0.428438\pi\)
0.222931 + 0.974834i \(0.428438\pi\)
\(662\) 37081.7 2.17707
\(663\) 0 0
\(664\) 83232.2 4.86451
\(665\) 0 0
\(666\) 0 0
\(667\) 4437.54 0.257605
\(668\) −12102.5 −0.700989
\(669\) 0 0
\(670\) 26805.9 1.54567
\(671\) 2008.30 0.115543
\(672\) 0 0
\(673\) 11724.6 0.671547 0.335774 0.941943i \(-0.391002\pi\)
0.335774 + 0.941943i \(0.391002\pi\)
\(674\) 54481.7 3.11358
\(675\) 0 0
\(676\) −15974.5 −0.908880
\(677\) 32304.3 1.83390 0.916952 0.398997i \(-0.130642\pi\)
0.916952 + 0.398997i \(0.130642\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6942.23 −0.391503
\(681\) 0 0
\(682\) 53485.6 3.00303
\(683\) −33367.1 −1.86934 −0.934669 0.355519i \(-0.884304\pi\)
−0.934669 + 0.355519i \(0.884304\pi\)
\(684\) 0 0
\(685\) 4683.18 0.261219
\(686\) 0 0
\(687\) 0 0
\(688\) 1159.55 0.0642551
\(689\) 20025.8 1.10729
\(690\) 0 0
\(691\) 1043.67 0.0574577 0.0287288 0.999587i \(-0.490854\pi\)
0.0287288 + 0.999587i \(0.490854\pi\)
\(692\) 75211.3 4.13166
\(693\) 0 0
\(694\) −10378.6 −0.567674
\(695\) −17618.0 −0.961567
\(696\) 0 0
\(697\) 3568.46 0.193924
\(698\) 23027.4 1.24871
\(699\) 0 0
\(700\) 0 0
\(701\) 11305.7 0.609143 0.304572 0.952489i \(-0.401487\pi\)
0.304572 + 0.952489i \(0.401487\pi\)
\(702\) 0 0
\(703\) −15229.4 −0.817055
\(704\) −25937.6 −1.38858
\(705\) 0 0
\(706\) −32027.1 −1.70730
\(707\) 0 0
\(708\) 0 0
\(709\) −13306.8 −0.704860 −0.352430 0.935838i \(-0.614645\pi\)
−0.352430 + 0.935838i \(0.614645\pi\)
\(710\) −20242.6 −1.06999
\(711\) 0 0
\(712\) −22020.6 −1.15907
\(713\) −36575.6 −1.92113
\(714\) 0 0
\(715\) −13673.7 −0.715201
\(716\) 55602.0 2.90216
\(717\) 0 0
\(718\) −50839.9 −2.64252
\(719\) 10701.2 0.555062 0.277531 0.960717i \(-0.410484\pi\)
0.277531 + 0.960717i \(0.410484\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −18068.0 −0.931333
\(723\) 0 0
\(724\) −61576.5 −3.16088
\(725\) −485.042 −0.0248469
\(726\) 0 0
\(727\) 2121.14 0.108210 0.0541051 0.998535i \(-0.482769\pi\)
0.0541051 + 0.998535i \(0.482769\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −32349.0 −1.64012
\(731\) −71.7808 −0.00363189
\(732\) 0 0
\(733\) 21584.0 1.08762 0.543809 0.839209i \(-0.316981\pi\)
0.543809 + 0.839209i \(0.316981\pi\)
\(734\) −2757.33 −0.138658
\(735\) 0 0
\(736\) 50135.0 2.51087
\(737\) −16738.4 −0.836588
\(738\) 0 0
\(739\) −9945.21 −0.495048 −0.247524 0.968882i \(-0.579617\pi\)
−0.247524 + 0.968882i \(0.579617\pi\)
\(740\) −54356.9 −2.70027
\(741\) 0 0
\(742\) 0 0
\(743\) −2867.01 −0.141562 −0.0707808 0.997492i \(-0.522549\pi\)
−0.0707808 + 0.997492i \(0.522549\pi\)
\(744\) 0 0
\(745\) −7847.71 −0.385930
\(746\) 17037.1 0.836158
\(747\) 0 0
\(748\) 7267.71 0.355259
\(749\) 0 0
\(750\) 0 0
\(751\) −10824.1 −0.525934 −0.262967 0.964805i \(-0.584701\pi\)
−0.262967 + 0.964805i \(0.584701\pi\)
\(752\) 42724.0 2.07179
\(753\) 0 0
\(754\) 6965.31 0.336421
\(755\) 6401.26 0.308564
\(756\) 0 0
\(757\) −14512.0 −0.696761 −0.348381 0.937353i \(-0.613268\pi\)
−0.348381 + 0.937353i \(0.613268\pi\)
\(758\) 35023.9 1.67827
\(759\) 0 0
\(760\) 38559.9 1.84042
\(761\) −33075.8 −1.57556 −0.787778 0.615959i \(-0.788769\pi\)
−0.787778 + 0.615959i \(0.788769\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −5193.13 −0.245917
\(765\) 0 0
\(766\) −75032.8 −3.53922
\(767\) −1338.68 −0.0630206
\(768\) 0 0
\(769\) −6728.44 −0.315518 −0.157759 0.987478i \(-0.550427\pi\)
−0.157759 + 0.987478i \(0.550427\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 80311.5 3.74414
\(773\) −24233.3 −1.12757 −0.563784 0.825922i \(-0.690655\pi\)
−0.563784 + 0.825922i \(0.690655\pi\)
\(774\) 0 0
\(775\) 3997.87 0.185300
\(776\) −90186.0 −4.17202
\(777\) 0 0
\(778\) −15412.4 −0.710231
\(779\) −19820.6 −0.911615
\(780\) 0 0
\(781\) 12640.1 0.579127
\(782\) −6975.51 −0.318982
\(783\) 0 0
\(784\) 0 0
\(785\) −32860.5 −1.49406
\(786\) 0 0
\(787\) 17200.4 0.779069 0.389535 0.921012i \(-0.372636\pi\)
0.389535 + 0.921012i \(0.372636\pi\)
\(788\) 56992.7 2.57650
\(789\) 0 0
\(790\) −38603.6 −1.73855
\(791\) 0 0
\(792\) 0 0
\(793\) −2155.66 −0.0965318
\(794\) −4282.92 −0.191430
\(795\) 0 0
\(796\) 60801.9 2.70737
\(797\) −4208.87 −0.187059 −0.0935295 0.995617i \(-0.529815\pi\)
−0.0935295 + 0.995617i \(0.529815\pi\)
\(798\) 0 0
\(799\) −2644.78 −0.117104
\(800\) −5479.98 −0.242183
\(801\) 0 0
\(802\) −12336.1 −0.543146
\(803\) 20199.7 0.887709
\(804\) 0 0
\(805\) 0 0
\(806\) −57410.2 −2.50892
\(807\) 0 0
\(808\) 29618.7 1.28958
\(809\) 23632.1 1.02702 0.513511 0.858083i \(-0.328344\pi\)
0.513511 + 0.858083i \(0.328344\pi\)
\(810\) 0 0
\(811\) −28425.1 −1.23075 −0.615377 0.788233i \(-0.710996\pi\)
−0.615377 + 0.788233i \(0.710996\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 47638.9 2.05128
\(815\) 25457.5 1.09416
\(816\) 0 0
\(817\) 398.699 0.0170731
\(818\) 14387.7 0.614981
\(819\) 0 0
\(820\) −70743.7 −3.01278
\(821\) −39409.6 −1.67528 −0.837640 0.546223i \(-0.816065\pi\)
−0.837640 + 0.546223i \(0.816065\pi\)
\(822\) 0 0
\(823\) 16346.6 0.692352 0.346176 0.938170i \(-0.387480\pi\)
0.346176 + 0.938170i \(0.387480\pi\)
\(824\) 124723. 5.27300
\(825\) 0 0
\(826\) 0 0
\(827\) 3738.87 0.157211 0.0786054 0.996906i \(-0.474953\pi\)
0.0786054 + 0.996906i \(0.474953\pi\)
\(828\) 0 0
\(829\) 45196.2 1.89352 0.946761 0.321937i \(-0.104334\pi\)
0.946761 + 0.321937i \(0.104334\pi\)
\(830\) 74258.3 3.10547
\(831\) 0 0
\(832\) 27840.8 1.16010
\(833\) 0 0
\(834\) 0 0
\(835\) −6440.41 −0.266922
\(836\) −40367.8 −1.67004
\(837\) 0 0
\(838\) 70189.5 2.89338
\(839\) 15899.7 0.654254 0.327127 0.944980i \(-0.393920\pi\)
0.327127 + 0.944980i \(0.393920\pi\)
\(840\) 0 0
\(841\) −23135.7 −0.948612
\(842\) −58063.4 −2.37648
\(843\) 0 0
\(844\) 11804.1 0.481414
\(845\) −8500.89 −0.346082
\(846\) 0 0
\(847\) 0 0
\(848\) 91500.0 3.70534
\(849\) 0 0
\(850\) 762.453 0.0307670
\(851\) −32577.4 −1.31227
\(852\) 0 0
\(853\) −33926.7 −1.36182 −0.680908 0.732369i \(-0.738415\pi\)
−0.680908 + 0.732369i \(0.738415\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −72774.7 −2.90583
\(857\) −35432.4 −1.41231 −0.706154 0.708058i \(-0.749572\pi\)
−0.706154 + 0.708058i \(0.749572\pi\)
\(858\) 0 0
\(859\) 6780.17 0.269309 0.134655 0.990893i \(-0.457008\pi\)
0.134655 + 0.990893i \(0.457008\pi\)
\(860\) 1423.04 0.0564246
\(861\) 0 0
\(862\) 34422.1 1.36012
\(863\) 30675.1 1.20995 0.604977 0.796243i \(-0.293182\pi\)
0.604977 + 0.796243i \(0.293182\pi\)
\(864\) 0 0
\(865\) 40024.1 1.57325
\(866\) 61802.4 2.42509
\(867\) 0 0
\(868\) 0 0
\(869\) 24105.2 0.940981
\(870\) 0 0
\(871\) 17966.6 0.698938
\(872\) −83405.8 −3.23908
\(873\) 0 0
\(874\) 38744.8 1.49950
\(875\) 0 0
\(876\) 0 0
\(877\) 40861.3 1.57330 0.786652 0.617397i \(-0.211813\pi\)
0.786652 + 0.617397i \(0.211813\pi\)
\(878\) 77073.9 2.96255
\(879\) 0 0
\(880\) −62476.6 −2.39328
\(881\) −43839.0 −1.67647 −0.838236 0.545308i \(-0.816413\pi\)
−0.838236 + 0.545308i \(0.816413\pi\)
\(882\) 0 0
\(883\) 44625.1 1.70074 0.850371 0.526183i \(-0.176377\pi\)
0.850371 + 0.526183i \(0.176377\pi\)
\(884\) −7801.01 −0.296806
\(885\) 0 0
\(886\) 80388.6 3.04820
\(887\) −43967.5 −1.66436 −0.832178 0.554509i \(-0.812906\pi\)
−0.832178 + 0.554509i \(0.812906\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −19646.4 −0.739943
\(891\) 0 0
\(892\) 74933.5 2.81273
\(893\) 14690.2 0.550491
\(894\) 0 0
\(895\) 29588.9 1.10508
\(896\) 0 0
\(897\) 0 0
\(898\) −56329.7 −2.09326
\(899\) −10330.1 −0.383234
\(900\) 0 0
\(901\) −5664.21 −0.209436
\(902\) 62000.4 2.28868
\(903\) 0 0
\(904\) −56547.4 −2.08046
\(905\) −32768.2 −1.20359
\(906\) 0 0
\(907\) −13584.3 −0.497309 −0.248654 0.968592i \(-0.579988\pi\)
−0.248654 + 0.968592i \(0.579988\pi\)
\(908\) 36232.1 1.32423
\(909\) 0 0
\(910\) 0 0
\(911\) 16421.6 0.597226 0.298613 0.954374i \(-0.403476\pi\)
0.298613 + 0.954374i \(0.403476\pi\)
\(912\) 0 0
\(913\) −46369.0 −1.68082
\(914\) 22303.6 0.807152
\(915\) 0 0
\(916\) 16856.0 0.608010
\(917\) 0 0
\(918\) 0 0
\(919\) −29487.3 −1.05843 −0.529214 0.848488i \(-0.677513\pi\)
−0.529214 + 0.848488i \(0.677513\pi\)
\(920\) 82483.7 2.95588
\(921\) 0 0
\(922\) 4800.81 0.171482
\(923\) −13567.6 −0.483839
\(924\) 0 0
\(925\) 3560.85 0.126573
\(926\) 23505.9 0.834181
\(927\) 0 0
\(928\) 14159.7 0.500878
\(929\) 3441.85 0.121554 0.0607769 0.998151i \(-0.480642\pi\)
0.0607769 + 0.998151i \(0.480642\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 130667. 4.59242
\(933\) 0 0
\(934\) −23364.8 −0.818545
\(935\) 3867.55 0.135275
\(936\) 0 0
\(937\) −5646.60 −0.196869 −0.0984346 0.995144i \(-0.531384\pi\)
−0.0984346 + 0.995144i \(0.531384\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 52432.2 1.81931
\(941\) −44680.1 −1.54785 −0.773927 0.633275i \(-0.781710\pi\)
−0.773927 + 0.633275i \(0.781710\pi\)
\(942\) 0 0
\(943\) −42398.4 −1.46414
\(944\) −6116.54 −0.210886
\(945\) 0 0
\(946\) −1247.16 −0.0428633
\(947\) 48924.6 1.67881 0.839406 0.543505i \(-0.182903\pi\)
0.839406 + 0.543505i \(0.182903\pi\)
\(948\) 0 0
\(949\) −21681.9 −0.741647
\(950\) −4234.97 −0.144632
\(951\) 0 0
\(952\) 0 0
\(953\) −52014.3 −1.76801 −0.884003 0.467482i \(-0.845161\pi\)
−0.884003 + 0.467482i \(0.845161\pi\)
\(954\) 0 0
\(955\) −2763.55 −0.0936401
\(956\) 3619.14 0.122439
\(957\) 0 0
\(958\) 14521.1 0.489723
\(959\) 0 0
\(960\) 0 0
\(961\) 55352.8 1.85804
\(962\) −51134.5 −1.71377
\(963\) 0 0
\(964\) −30210.9 −1.00936
\(965\) 42738.2 1.42569
\(966\) 0 0
\(967\) −47117.7 −1.56691 −0.783456 0.621448i \(-0.786545\pi\)
−0.783456 + 0.621448i \(0.786545\pi\)
\(968\) −7702.95 −0.255767
\(969\) 0 0
\(970\) −80462.3 −2.66339
\(971\) −8195.04 −0.270846 −0.135423 0.990788i \(-0.543239\pi\)
−0.135423 + 0.990788i \(0.543239\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −3537.35 −0.116370
\(975\) 0 0
\(976\) −9849.42 −0.323025
\(977\) −4643.51 −0.152056 −0.0760282 0.997106i \(-0.524224\pi\)
−0.0760282 + 0.997106i \(0.524224\pi\)
\(978\) 0 0
\(979\) 12267.8 0.400490
\(980\) 0 0
\(981\) 0 0
\(982\) 43490.1 1.41326
\(983\) 43986.5 1.42721 0.713607 0.700546i \(-0.247060\pi\)
0.713607 + 0.700546i \(0.247060\pi\)
\(984\) 0 0
\(985\) 30329.0 0.981077
\(986\) −1970.10 −0.0636317
\(987\) 0 0
\(988\) 43329.9 1.39525
\(989\) 852.859 0.0274210
\(990\) 0 0
\(991\) 1595.21 0.0511337 0.0255668 0.999673i \(-0.491861\pi\)
0.0255668 + 0.999673i \(0.491861\pi\)
\(992\) −116709. −3.73539
\(993\) 0 0
\(994\) 0 0
\(995\) 32356.0 1.03091
\(996\) 0 0
\(997\) −21501.2 −0.682998 −0.341499 0.939882i \(-0.610935\pi\)
−0.341499 + 0.939882i \(0.610935\pi\)
\(998\) 43069.2 1.36606
\(999\) 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 441.4.a.r.1.2 2
3.2 odd 2 147.4.a.i.1.1 2
7.2 even 3 441.4.e.p.361.1 4
7.3 odd 6 441.4.e.q.226.1 4
7.4 even 3 441.4.e.p.226.1 4
7.5 odd 6 441.4.e.q.361.1 4
7.6 odd 2 63.4.a.e.1.2 2
12.11 even 2 2352.4.a.bz.1.1 2
21.2 odd 6 147.4.e.m.67.2 4
21.5 even 6 147.4.e.l.67.2 4
21.11 odd 6 147.4.e.m.79.2 4
21.17 even 6 147.4.e.l.79.2 4
21.20 even 2 21.4.a.c.1.1 2
28.27 even 2 1008.4.a.ba.1.1 2
35.34 odd 2 1575.4.a.p.1.1 2
84.83 odd 2 336.4.a.m.1.2 2
105.62 odd 4 525.4.d.g.274.1 4
105.83 odd 4 525.4.d.g.274.4 4
105.104 even 2 525.4.a.n.1.2 2
168.83 odd 2 1344.4.a.bo.1.1 2
168.125 even 2 1344.4.a.bg.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.a.c.1.1 2 21.20 even 2
63.4.a.e.1.2 2 7.6 odd 2
147.4.a.i.1.1 2 3.2 odd 2
147.4.e.l.67.2 4 21.5 even 6
147.4.e.l.79.2 4 21.17 even 6
147.4.e.m.67.2 4 21.2 odd 6
147.4.e.m.79.2 4 21.11 odd 6
336.4.a.m.1.2 2 84.83 odd 2
441.4.a.r.1.2 2 1.1 even 1 trivial
441.4.e.p.226.1 4 7.4 even 3
441.4.e.p.361.1 4 7.2 even 3
441.4.e.q.226.1 4 7.3 odd 6
441.4.e.q.361.1 4 7.5 odd 6
525.4.a.n.1.2 2 105.104 even 2
525.4.d.g.274.1 4 105.62 odd 4
525.4.d.g.274.4 4 105.83 odd 4
1008.4.a.ba.1.1 2 28.27 even 2
1344.4.a.bg.1.1 2 168.125 even 2
1344.4.a.bo.1.1 2 168.83 odd 2
1575.4.a.p.1.1 2 35.34 odd 2
2352.4.a.bz.1.1 2 12.11 even 2