Properties

Label 207.6.a.c.1.3
Level $207$
Weight $6$
Character 207.1
Self dual yes
Analytic conductor $33.199$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 207.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.1994507013\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.5333.1
Defining polynomial: \(x^{3} - x^{2} - 11 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 69)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.714018\) of defining polynomial
Character \(\chi\) \(=\) 207.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.2042 q^{2} +72.1256 q^{4} +55.5168 q^{5} +2.50462 q^{7} +409.450 q^{8} +O(q^{10})\) \(q+10.2042 q^{2} +72.1256 q^{4} +55.5168 q^{5} +2.50462 q^{7} +409.450 q^{8} +566.504 q^{10} -228.550 q^{11} +658.703 q^{13} +25.5577 q^{14} +1870.09 q^{16} +1443.81 q^{17} -982.167 q^{19} +4004.18 q^{20} -2332.17 q^{22} -529.000 q^{23} -42.8875 q^{25} +6721.54 q^{26} +180.648 q^{28} +7157.56 q^{29} -9259.98 q^{31} +5980.33 q^{32} +14732.9 q^{34} +139.049 q^{35} +2422.50 q^{37} -10022.2 q^{38} +22731.3 q^{40} +4075.27 q^{41} -10417.3 q^{43} -16484.3 q^{44} -5398.02 q^{46} -9358.08 q^{47} -16800.7 q^{49} -437.632 q^{50} +47509.4 q^{52} +34280.3 q^{53} -12688.4 q^{55} +1025.52 q^{56} +73037.2 q^{58} +7268.79 q^{59} +26611.7 q^{61} -94490.6 q^{62} +1181.70 q^{64} +36569.1 q^{65} +53450.8 q^{67} +104136. q^{68} +1418.88 q^{70} -21673.7 q^{71} -82856.3 q^{73} +24719.7 q^{74} -70839.4 q^{76} -572.432 q^{77} -23960.0 q^{79} +103821. q^{80} +41584.9 q^{82} -81187.7 q^{83} +80155.6 q^{85} -106300. q^{86} -93579.7 q^{88} -100115. q^{89} +1649.80 q^{91} -38154.5 q^{92} -95491.7 q^{94} -54526.8 q^{95} +36122.1 q^{97} -171438. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 8 q^{2} + 22 q^{4} + 56 q^{5} - 114 q^{7} + 510 q^{8} + O(q^{10}) \) \( 3 q + 8 q^{2} + 22 q^{4} + 56 q^{5} - 114 q^{7} + 510 q^{8} + 282 q^{10} + 376 q^{11} - 858 q^{13} - 588 q^{14} + 2738 q^{16} + 2548 q^{17} - 2846 q^{19} + 4618 q^{20} - 5050 q^{22} - 1587 q^{23} + 753 q^{25} + 7788 q^{26} + 4736 q^{28} + 16370 q^{29} - 14756 q^{31} + 3878 q^{32} + 16520 q^{34} + 18520 q^{35} + 15874 q^{37} - 12438 q^{38} + 38270 q^{40} - 12606 q^{41} + 3154 q^{43} - 27114 q^{44} - 4232 q^{46} - 29928 q^{47} + 4471 q^{49} - 1452 q^{50} + 86856 q^{52} + 44084 q^{53} + 38360 q^{55} + 35704 q^{56} + 73316 q^{58} + 29300 q^{59} + 54010 q^{61} - 99908 q^{62} - 1582 q^{64} + 51216 q^{65} + 43390 q^{67} + 69840 q^{68} - 2476 q^{70} - 23424 q^{71} - 91402 q^{73} + 2294 q^{74} - 14274 q^{76} + 97208 q^{77} - 49398 q^{79} + 52626 q^{80} + 40152 q^{82} + 103936 q^{83} + 5888 q^{85} - 133634 q^{86} + 48898 q^{88} - 96112 q^{89} + 129228 q^{91} - 11638 q^{92} - 133688 q^{94} + 55928 q^{95} - 135318 q^{97} - 108440 q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.2042 1.80386 0.901932 0.431878i \(-0.142149\pi\)
0.901932 + 0.431878i \(0.142149\pi\)
\(3\) 0 0
\(4\) 72.1256 2.25393
\(5\) 55.5168 0.993114 0.496557 0.868004i \(-0.334597\pi\)
0.496557 + 0.868004i \(0.334597\pi\)
\(6\) 0 0
\(7\) 2.50462 0.0193196 0.00965978 0.999953i \(-0.496925\pi\)
0.00965978 + 0.999953i \(0.496925\pi\)
\(8\) 409.450 2.26191
\(9\) 0 0
\(10\) 566.504 1.79144
\(11\) −228.550 −0.569508 −0.284754 0.958601i \(-0.591912\pi\)
−0.284754 + 0.958601i \(0.591912\pi\)
\(12\) 0 0
\(13\) 658.703 1.08101 0.540507 0.841339i \(-0.318232\pi\)
0.540507 + 0.841339i \(0.318232\pi\)
\(14\) 25.5577 0.0348499
\(15\) 0 0
\(16\) 1870.09 1.82626
\(17\) 1443.81 1.21168 0.605839 0.795587i \(-0.292838\pi\)
0.605839 + 0.795587i \(0.292838\pi\)
\(18\) 0 0
\(19\) −982.167 −0.624168 −0.312084 0.950055i \(-0.601027\pi\)
−0.312084 + 0.950055i \(0.601027\pi\)
\(20\) 4004.18 2.23841
\(21\) 0 0
\(22\) −2332.17 −1.02731
\(23\) −529.000 −0.208514
\(24\) 0 0
\(25\) −42.8875 −0.0137240
\(26\) 6721.54 1.95000
\(27\) 0 0
\(28\) 180.648 0.0435449
\(29\) 7157.56 1.58041 0.790205 0.612842i \(-0.209974\pi\)
0.790205 + 0.612842i \(0.209974\pi\)
\(30\) 0 0
\(31\) −9259.98 −1.73064 −0.865318 0.501223i \(-0.832884\pi\)
−0.865318 + 0.501223i \(0.832884\pi\)
\(32\) 5980.33 1.03240
\(33\) 0 0
\(34\) 14732.9 2.18570
\(35\) 139.049 0.0191865
\(36\) 0 0
\(37\) 2422.50 0.290911 0.145455 0.989365i \(-0.453535\pi\)
0.145455 + 0.989365i \(0.453535\pi\)
\(38\) −10022.2 −1.12591
\(39\) 0 0
\(40\) 22731.3 2.24634
\(41\) 4075.27 0.378614 0.189307 0.981918i \(-0.439376\pi\)
0.189307 + 0.981918i \(0.439376\pi\)
\(42\) 0 0
\(43\) −10417.3 −0.859178 −0.429589 0.903024i \(-0.641342\pi\)
−0.429589 + 0.903024i \(0.641342\pi\)
\(44\) −16484.3 −1.28363
\(45\) 0 0
\(46\) −5398.02 −0.376132
\(47\) −9358.08 −0.617934 −0.308967 0.951073i \(-0.599983\pi\)
−0.308967 + 0.951073i \(0.599983\pi\)
\(48\) 0 0
\(49\) −16800.7 −0.999627
\(50\) −437.632 −0.0247562
\(51\) 0 0
\(52\) 47509.4 2.43653
\(53\) 34280.3 1.67631 0.838157 0.545428i \(-0.183633\pi\)
0.838157 + 0.545428i \(0.183633\pi\)
\(54\) 0 0
\(55\) −12688.4 −0.565586
\(56\) 1025.52 0.0436991
\(57\) 0 0
\(58\) 73037.2 2.85085
\(59\) 7268.79 0.271852 0.135926 0.990719i \(-0.456599\pi\)
0.135926 + 0.990719i \(0.456599\pi\)
\(60\) 0 0
\(61\) 26611.7 0.915687 0.457844 0.889033i \(-0.348622\pi\)
0.457844 + 0.889033i \(0.348622\pi\)
\(62\) −94490.6 −3.12183
\(63\) 0 0
\(64\) 1181.70 0.0360625
\(65\) 36569.1 1.07357
\(66\) 0 0
\(67\) 53450.8 1.45468 0.727339 0.686278i \(-0.240757\pi\)
0.727339 + 0.686278i \(0.240757\pi\)
\(68\) 104136. 2.73103
\(69\) 0 0
\(70\) 1418.88 0.0346099
\(71\) −21673.7 −0.510255 −0.255128 0.966907i \(-0.582118\pi\)
−0.255128 + 0.966907i \(0.582118\pi\)
\(72\) 0 0
\(73\) −82856.3 −1.81978 −0.909889 0.414851i \(-0.863834\pi\)
−0.909889 + 0.414851i \(0.863834\pi\)
\(74\) 24719.7 0.524764
\(75\) 0 0
\(76\) −70839.4 −1.40683
\(77\) −572.432 −0.0110026
\(78\) 0 0
\(79\) −23960.0 −0.431936 −0.215968 0.976400i \(-0.569291\pi\)
−0.215968 + 0.976400i \(0.569291\pi\)
\(80\) 103821. 1.81368
\(81\) 0 0
\(82\) 41584.9 0.682968
\(83\) −81187.7 −1.29359 −0.646793 0.762666i \(-0.723890\pi\)
−0.646793 + 0.762666i \(0.723890\pi\)
\(84\) 0 0
\(85\) 80155.6 1.20334
\(86\) −106300. −1.54984
\(87\) 0 0
\(88\) −93579.7 −1.28818
\(89\) −100115. −1.33975 −0.669876 0.742473i \(-0.733653\pi\)
−0.669876 + 0.742473i \(0.733653\pi\)
\(90\) 0 0
\(91\) 1649.80 0.0208847
\(92\) −38154.5 −0.469976
\(93\) 0 0
\(94\) −95491.7 −1.11467
\(95\) −54526.8 −0.619870
\(96\) 0 0
\(97\) 36122.1 0.389802 0.194901 0.980823i \(-0.437562\pi\)
0.194901 + 0.980823i \(0.437562\pi\)
\(98\) −171438. −1.80319
\(99\) 0 0
\(100\) −3093.29 −0.0309329
\(101\) 41151.8 0.401408 0.200704 0.979652i \(-0.435677\pi\)
0.200704 + 0.979652i \(0.435677\pi\)
\(102\) 0 0
\(103\) −172534. −1.60244 −0.801221 0.598369i \(-0.795816\pi\)
−0.801221 + 0.598369i \(0.795816\pi\)
\(104\) 269706. 2.44516
\(105\) 0 0
\(106\) 349803. 3.02384
\(107\) −178228. −1.50493 −0.752464 0.658633i \(-0.771135\pi\)
−0.752464 + 0.658633i \(0.771135\pi\)
\(108\) 0 0
\(109\) −138352. −1.11537 −0.557686 0.830052i \(-0.688311\pi\)
−0.557686 + 0.830052i \(0.688311\pi\)
\(110\) −129475. −1.02024
\(111\) 0 0
\(112\) 4683.86 0.0352825
\(113\) 13523.5 0.0996307 0.0498153 0.998758i \(-0.484137\pi\)
0.0498153 + 0.998758i \(0.484137\pi\)
\(114\) 0 0
\(115\) −29368.4 −0.207079
\(116\) 516243. 3.56213
\(117\) 0 0
\(118\) 74172.1 0.490383
\(119\) 3616.20 0.0234091
\(120\) 0 0
\(121\) −108816. −0.675661
\(122\) 271551. 1.65178
\(123\) 0 0
\(124\) −667882. −3.90073
\(125\) −175871. −1.00674
\(126\) 0 0
\(127\) 158567. 0.872376 0.436188 0.899856i \(-0.356328\pi\)
0.436188 + 0.899856i \(0.356328\pi\)
\(128\) −179312. −0.967353
\(129\) 0 0
\(130\) 373158. 1.93658
\(131\) 383514. 1.95255 0.976277 0.216526i \(-0.0694727\pi\)
0.976277 + 0.216526i \(0.0694727\pi\)
\(132\) 0 0
\(133\) −2459.96 −0.0120587
\(134\) 545422. 2.62404
\(135\) 0 0
\(136\) 591167. 2.74071
\(137\) 33171.1 0.150994 0.0754968 0.997146i \(-0.475946\pi\)
0.0754968 + 0.997146i \(0.475946\pi\)
\(138\) 0 0
\(139\) −128488. −0.564060 −0.282030 0.959406i \(-0.591008\pi\)
−0.282030 + 0.959406i \(0.591008\pi\)
\(140\) 10029.0 0.0432450
\(141\) 0 0
\(142\) −221163. −0.920431
\(143\) −150547. −0.615646
\(144\) 0 0
\(145\) 397365. 1.56953
\(146\) −845482. −3.28263
\(147\) 0 0
\(148\) 174725. 0.655692
\(149\) 184228. 0.679814 0.339907 0.940459i \(-0.389604\pi\)
0.339907 + 0.940459i \(0.389604\pi\)
\(150\) 0 0
\(151\) −19798.1 −0.0706610 −0.0353305 0.999376i \(-0.511248\pi\)
−0.0353305 + 0.999376i \(0.511248\pi\)
\(152\) −402148. −1.41181
\(153\) 0 0
\(154\) −5841.21 −0.0198473
\(155\) −514084. −1.71872
\(156\) 0 0
\(157\) 193317. 0.625923 0.312962 0.949766i \(-0.398679\pi\)
0.312962 + 0.949766i \(0.398679\pi\)
\(158\) −244493. −0.779154
\(159\) 0 0
\(160\) 332008. 1.02530
\(161\) −1324.95 −0.00402841
\(162\) 0 0
\(163\) 106286. 0.313334 0.156667 0.987651i \(-0.449925\pi\)
0.156667 + 0.987651i \(0.449925\pi\)
\(164\) 293931. 0.853368
\(165\) 0 0
\(166\) −828456. −2.33345
\(167\) 77715.5 0.215634 0.107817 0.994171i \(-0.465614\pi\)
0.107817 + 0.994171i \(0.465614\pi\)
\(168\) 0 0
\(169\) 62597.3 0.168593
\(170\) 817923. 2.17065
\(171\) 0 0
\(172\) −751353. −1.93652
\(173\) −218524. −0.555115 −0.277558 0.960709i \(-0.589525\pi\)
−0.277558 + 0.960709i \(0.589525\pi\)
\(174\) 0 0
\(175\) −107.417 −0.000265142 0
\(176\) −427408. −1.04007
\(177\) 0 0
\(178\) −1.02159e6 −2.41673
\(179\) 545493. 1.27250 0.636248 0.771485i \(-0.280486\pi\)
0.636248 + 0.771485i \(0.280486\pi\)
\(180\) 0 0
\(181\) 510878. 1.15910 0.579549 0.814937i \(-0.303229\pi\)
0.579549 + 0.814937i \(0.303229\pi\)
\(182\) 16834.9 0.0376732
\(183\) 0 0
\(184\) −216599. −0.471641
\(185\) 134490. 0.288908
\(186\) 0 0
\(187\) −329982. −0.690060
\(188\) −674957. −1.39278
\(189\) 0 0
\(190\) −556402. −1.11816
\(191\) 57685.2 0.114415 0.0572073 0.998362i \(-0.481780\pi\)
0.0572073 + 0.998362i \(0.481780\pi\)
\(192\) 0 0
\(193\) −822091. −1.58864 −0.794322 0.607497i \(-0.792174\pi\)
−0.794322 + 0.607497i \(0.792174\pi\)
\(194\) 368597. 0.703149
\(195\) 0 0
\(196\) −1.21176e6 −2.25308
\(197\) −971571. −1.78365 −0.891824 0.452383i \(-0.850574\pi\)
−0.891824 + 0.452383i \(0.850574\pi\)
\(198\) 0 0
\(199\) 806110. 1.44298 0.721492 0.692423i \(-0.243457\pi\)
0.721492 + 0.692423i \(0.243457\pi\)
\(200\) −17560.3 −0.0310425
\(201\) 0 0
\(202\) 419921. 0.724085
\(203\) 17927.0 0.0305329
\(204\) 0 0
\(205\) 226246. 0.376007
\(206\) −1.76057e6 −2.89059
\(207\) 0 0
\(208\) 1.23183e6 1.97421
\(209\) 224474. 0.355468
\(210\) 0 0
\(211\) −821913. −1.27092 −0.635462 0.772132i \(-0.719190\pi\)
−0.635462 + 0.772132i \(0.719190\pi\)
\(212\) 2.47249e6 3.77829
\(213\) 0 0
\(214\) −1.81867e6 −2.71469
\(215\) −578334. −0.853262
\(216\) 0 0
\(217\) −23192.8 −0.0334351
\(218\) −1.41177e6 −2.01198
\(219\) 0 0
\(220\) −915156. −1.27479
\(221\) 951042. 1.30984
\(222\) 0 0
\(223\) 511948. 0.689388 0.344694 0.938715i \(-0.387983\pi\)
0.344694 + 0.938715i \(0.387983\pi\)
\(224\) 14978.5 0.0199456
\(225\) 0 0
\(226\) 137996. 0.179720
\(227\) 1.45074e6 1.86864 0.934321 0.356433i \(-0.116007\pi\)
0.934321 + 0.356433i \(0.116007\pi\)
\(228\) 0 0
\(229\) 621169. 0.782747 0.391373 0.920232i \(-0.372000\pi\)
0.391373 + 0.920232i \(0.372000\pi\)
\(230\) −299681. −0.373542
\(231\) 0 0
\(232\) 2.93066e6 3.57475
\(233\) −490334. −0.591701 −0.295851 0.955234i \(-0.595603\pi\)
−0.295851 + 0.955234i \(0.595603\pi\)
\(234\) 0 0
\(235\) −519530. −0.613679
\(236\) 524266. 0.612733
\(237\) 0 0
\(238\) 36900.4 0.0422268
\(239\) −109503. −0.124003 −0.0620014 0.998076i \(-0.519748\pi\)
−0.0620014 + 0.998076i \(0.519748\pi\)
\(240\) 0 0
\(241\) 1.36171e6 1.51022 0.755111 0.655597i \(-0.227583\pi\)
0.755111 + 0.655597i \(0.227583\pi\)
\(242\) −1.11038e6 −1.21880
\(243\) 0 0
\(244\) 1.91938e6 2.06389
\(245\) −932722. −0.992744
\(246\) 0 0
\(247\) −646957. −0.674735
\(248\) −3.79150e6 −3.91455
\(249\) 0 0
\(250\) −1.79462e6 −1.81603
\(251\) −8042.27 −0.00805739 −0.00402869 0.999992i \(-0.501282\pi\)
−0.00402869 + 0.999992i \(0.501282\pi\)
\(252\) 0 0
\(253\) 120903. 0.118751
\(254\) 1.61805e6 1.57365
\(255\) 0 0
\(256\) −1.86755e6 −1.78104
\(257\) −1.16730e6 −1.10243 −0.551214 0.834364i \(-0.685835\pi\)
−0.551214 + 0.834364i \(0.685835\pi\)
\(258\) 0 0
\(259\) 6067.46 0.00562027
\(260\) 2.63757e6 2.41975
\(261\) 0 0
\(262\) 3.91345e6 3.52214
\(263\) 558051. 0.497490 0.248745 0.968569i \(-0.419982\pi\)
0.248745 + 0.968569i \(0.419982\pi\)
\(264\) 0 0
\(265\) 1.90313e6 1.66477
\(266\) −25101.9 −0.0217522
\(267\) 0 0
\(268\) 3.85517e6 3.27874
\(269\) 1.21947e6 1.02752 0.513759 0.857935i \(-0.328253\pi\)
0.513759 + 0.857935i \(0.328253\pi\)
\(270\) 0 0
\(271\) 1.40581e6 1.16280 0.581399 0.813618i \(-0.302505\pi\)
0.581399 + 0.813618i \(0.302505\pi\)
\(272\) 2.70005e6 2.21283
\(273\) 0 0
\(274\) 338484. 0.272372
\(275\) 9801.94 0.00781592
\(276\) 0 0
\(277\) 1.87799e6 1.47060 0.735300 0.677742i \(-0.237041\pi\)
0.735300 + 0.677742i \(0.237041\pi\)
\(278\) −1.31112e6 −1.01749
\(279\) 0 0
\(280\) 56933.4 0.0433982
\(281\) 2.11759e6 1.59984 0.799920 0.600106i \(-0.204875\pi\)
0.799920 + 0.600106i \(0.204875\pi\)
\(282\) 0 0
\(283\) 1.16042e6 0.861288 0.430644 0.902522i \(-0.358286\pi\)
0.430644 + 0.902522i \(0.358286\pi\)
\(284\) −1.56323e6 −1.15008
\(285\) 0 0
\(286\) −1.53621e6 −1.11054
\(287\) 10207.0 0.00731466
\(288\) 0 0
\(289\) 664726. 0.468164
\(290\) 4.05479e6 2.83122
\(291\) 0 0
\(292\) −5.97606e6 −4.10165
\(293\) 1.27325e6 0.866449 0.433225 0.901286i \(-0.357376\pi\)
0.433225 + 0.901286i \(0.357376\pi\)
\(294\) 0 0
\(295\) 403540. 0.269980
\(296\) 991893. 0.658015
\(297\) 0 0
\(298\) 1.87990e6 1.22629
\(299\) −348454. −0.225407
\(300\) 0 0
\(301\) −26091.4 −0.0165990
\(302\) −202023. −0.127463
\(303\) 0 0
\(304\) −1.83674e6 −1.13989
\(305\) 1.47739e6 0.909382
\(306\) 0 0
\(307\) −2.26175e6 −1.36961 −0.684807 0.728724i \(-0.740114\pi\)
−0.684807 + 0.728724i \(0.740114\pi\)
\(308\) −41287.0 −0.0247991
\(309\) 0 0
\(310\) −5.24582e6 −3.10034
\(311\) −1.20263e6 −0.705066 −0.352533 0.935799i \(-0.614680\pi\)
−0.352533 + 0.935799i \(0.614680\pi\)
\(312\) 0 0
\(313\) −484311. −0.279424 −0.139712 0.990192i \(-0.544618\pi\)
−0.139712 + 0.990192i \(0.544618\pi\)
\(314\) 1.97265e6 1.12908
\(315\) 0 0
\(316\) −1.72813e6 −0.973551
\(317\) −796624. −0.445251 −0.222626 0.974904i \(-0.571463\pi\)
−0.222626 + 0.974904i \(0.571463\pi\)
\(318\) 0 0
\(319\) −1.63586e6 −0.900056
\(320\) 65603.9 0.0358142
\(321\) 0 0
\(322\) −13520.0 −0.00726670
\(323\) −1.41806e6 −0.756291
\(324\) 0 0
\(325\) −28250.1 −0.0148358
\(326\) 1.08456e6 0.565212
\(327\) 0 0
\(328\) 1.66862e6 0.856391
\(329\) −23438.5 −0.0119382
\(330\) 0 0
\(331\) −262856. −0.131871 −0.0659353 0.997824i \(-0.521003\pi\)
−0.0659353 + 0.997824i \(0.521003\pi\)
\(332\) −5.85572e6 −2.91565
\(333\) 0 0
\(334\) 793024. 0.388974
\(335\) 2.96741e6 1.44466
\(336\) 0 0
\(337\) 1.23123e6 0.590558 0.295279 0.955411i \(-0.404587\pi\)
0.295279 + 0.955411i \(0.404587\pi\)
\(338\) 638755. 0.304118
\(339\) 0 0
\(340\) 5.78127e6 2.71223
\(341\) 2.11637e6 0.985611
\(342\) 0 0
\(343\) −84174.7 −0.0386319
\(344\) −4.26535e6 −1.94339
\(345\) 0 0
\(346\) −2.22986e6 −1.00135
\(347\) 3.70344e6 1.65113 0.825567 0.564305i \(-0.190856\pi\)
0.825567 + 0.564305i \(0.190856\pi\)
\(348\) 0 0
\(349\) 1.62884e6 0.715837 0.357918 0.933753i \(-0.383487\pi\)
0.357918 + 0.933753i \(0.383487\pi\)
\(350\) −1096.10 −0.000478279 0
\(351\) 0 0
\(352\) −1.36680e6 −0.587962
\(353\) −2.56589e6 −1.09598 −0.547989 0.836486i \(-0.684606\pi\)
−0.547989 + 0.836486i \(0.684606\pi\)
\(354\) 0 0
\(355\) −1.20326e6 −0.506742
\(356\) −7.22086e6 −3.01970
\(357\) 0 0
\(358\) 5.56631e6 2.29541
\(359\) 3.46895e6 1.42057 0.710284 0.703916i \(-0.248567\pi\)
0.710284 + 0.703916i \(0.248567\pi\)
\(360\) 0 0
\(361\) −1.51145e6 −0.610414
\(362\) 5.21310e6 2.09086
\(363\) 0 0
\(364\) 118993. 0.0470726
\(365\) −4.59992e6 −1.80725
\(366\) 0 0
\(367\) 1.64135e6 0.636115 0.318058 0.948071i \(-0.396969\pi\)
0.318058 + 0.948071i \(0.396969\pi\)
\(368\) −989275. −0.380801
\(369\) 0 0
\(370\) 1.37236e6 0.521151
\(371\) 85859.4 0.0323857
\(372\) 0 0
\(373\) 1.58607e6 0.590268 0.295134 0.955456i \(-0.404636\pi\)
0.295134 + 0.955456i \(0.404636\pi\)
\(374\) −3.36721e6 −1.24477
\(375\) 0 0
\(376\) −3.83166e6 −1.39771
\(377\) 4.71471e6 1.70845
\(378\) 0 0
\(379\) −966030. −0.345456 −0.172728 0.984970i \(-0.555258\pi\)
−0.172728 + 0.984970i \(0.555258\pi\)
\(380\) −3.93278e6 −1.39714
\(381\) 0 0
\(382\) 588631. 0.206388
\(383\) 3.10322e6 1.08097 0.540487 0.841352i \(-0.318240\pi\)
0.540487 + 0.841352i \(0.318240\pi\)
\(384\) 0 0
\(385\) −31779.6 −0.0109269
\(386\) −8.38878e6 −2.86570
\(387\) 0 0
\(388\) 2.60533e6 0.878584
\(389\) −624568. −0.209269 −0.104635 0.994511i \(-0.533367\pi\)
−0.104635 + 0.994511i \(0.533367\pi\)
\(390\) 0 0
\(391\) −763775. −0.252652
\(392\) −6.87905e6 −2.26107
\(393\) 0 0
\(394\) −9.91410e6 −3.21746
\(395\) −1.33018e6 −0.428962
\(396\) 0 0
\(397\) 2.80814e6 0.894216 0.447108 0.894480i \(-0.352454\pi\)
0.447108 + 0.894480i \(0.352454\pi\)
\(398\) 8.22570e6 2.60295
\(399\) 0 0
\(400\) −80203.3 −0.0250635
\(401\) −3.81287e6 −1.18411 −0.592053 0.805899i \(-0.701682\pi\)
−0.592053 + 0.805899i \(0.701682\pi\)
\(402\) 0 0
\(403\) −6.09958e6 −1.87084
\(404\) 2.96810e6 0.904743
\(405\) 0 0
\(406\) 182931. 0.0550771
\(407\) −553663. −0.165676
\(408\) 0 0
\(409\) −3.86268e6 −1.14178 −0.570888 0.821028i \(-0.693401\pi\)
−0.570888 + 0.821028i \(0.693401\pi\)
\(410\) 2.30866e6 0.678266
\(411\) 0 0
\(412\) −1.24441e7 −3.61178
\(413\) 18205.6 0.00525206
\(414\) 0 0
\(415\) −4.50728e6 −1.28468
\(416\) 3.93926e6 1.11604
\(417\) 0 0
\(418\) 2.29058e6 0.641217
\(419\) 4.00521e6 1.11453 0.557263 0.830336i \(-0.311851\pi\)
0.557263 + 0.830336i \(0.311851\pi\)
\(420\) 0 0
\(421\) 4.89697e6 1.34655 0.673275 0.739392i \(-0.264887\pi\)
0.673275 + 0.739392i \(0.264887\pi\)
\(422\) −8.38696e6 −2.29257
\(423\) 0 0
\(424\) 1.40361e7 3.79168
\(425\) −61921.3 −0.0166291
\(426\) 0 0
\(427\) 66652.2 0.0176907
\(428\) −1.28548e7 −3.39200
\(429\) 0 0
\(430\) −5.90143e6 −1.53917
\(431\) −1.81874e6 −0.471605 −0.235803 0.971801i \(-0.575772\pi\)
−0.235803 + 0.971801i \(0.575772\pi\)
\(432\) 0 0
\(433\) 545672. 0.139866 0.0699330 0.997552i \(-0.477721\pi\)
0.0699330 + 0.997552i \(0.477721\pi\)
\(434\) −236663. −0.0603124
\(435\) 0 0
\(436\) −9.97874e6 −2.51397
\(437\) 519566. 0.130148
\(438\) 0 0
\(439\) 2.81114e6 0.696179 0.348090 0.937461i \(-0.386830\pi\)
0.348090 + 0.937461i \(0.386830\pi\)
\(440\) −5.19525e6 −1.27931
\(441\) 0 0
\(442\) 9.70462e6 2.36278
\(443\) 2.81428e6 0.681332 0.340666 0.940184i \(-0.389348\pi\)
0.340666 + 0.940184i \(0.389348\pi\)
\(444\) 0 0
\(445\) −5.55807e6 −1.33053
\(446\) 5.22402e6 1.24356
\(447\) 0 0
\(448\) 2959.70 0.000696712 0
\(449\) −4.00644e6 −0.937871 −0.468936 0.883232i \(-0.655362\pi\)
−0.468936 + 0.883232i \(0.655362\pi\)
\(450\) 0 0
\(451\) −931403. −0.215624
\(452\) 975391. 0.224560
\(453\) 0 0
\(454\) 1.48037e7 3.37078
\(455\) 91591.8 0.0207409
\(456\) 0 0
\(457\) −5.43801e6 −1.21801 −0.609003 0.793168i \(-0.708430\pi\)
−0.609003 + 0.793168i \(0.708430\pi\)
\(458\) 6.33853e6 1.41197
\(459\) 0 0
\(460\) −2.11821e6 −0.466740
\(461\) −2.50966e6 −0.550001 −0.275000 0.961444i \(-0.588678\pi\)
−0.275000 + 0.961444i \(0.588678\pi\)
\(462\) 0 0
\(463\) 108662. 0.0235573 0.0117787 0.999931i \(-0.496251\pi\)
0.0117787 + 0.999931i \(0.496251\pi\)
\(464\) 1.33852e7 2.88623
\(465\) 0 0
\(466\) −5.00347e6 −1.06735
\(467\) −3.09125e6 −0.655906 −0.327953 0.944694i \(-0.606359\pi\)
−0.327953 + 0.944694i \(0.606359\pi\)
\(468\) 0 0
\(469\) 133874. 0.0281037
\(470\) −5.30139e6 −1.10699
\(471\) 0 0
\(472\) 2.97620e6 0.614904
\(473\) 2.38087e6 0.489309
\(474\) 0 0
\(475\) 42122.7 0.00856608
\(476\) 260820. 0.0527624
\(477\) 0 0
\(478\) −1.11739e6 −0.223684
\(479\) 7.74743e6 1.54283 0.771417 0.636330i \(-0.219548\pi\)
0.771417 + 0.636330i \(0.219548\pi\)
\(480\) 0 0
\(481\) 1.59571e6 0.314479
\(482\) 1.38951e7 2.72424
\(483\) 0 0
\(484\) −7.84841e6 −1.52289
\(485\) 2.00538e6 0.387118
\(486\) 0 0
\(487\) 6.60929e6 1.26279 0.631397 0.775460i \(-0.282482\pi\)
0.631397 + 0.775460i \(0.282482\pi\)
\(488\) 1.08961e7 2.07120
\(489\) 0 0
\(490\) −9.51768e6 −1.79077
\(491\) −1.68453e6 −0.315337 −0.157669 0.987492i \(-0.550398\pi\)
−0.157669 + 0.987492i \(0.550398\pi\)
\(492\) 0 0
\(493\) 1.03341e7 1.91495
\(494\) −6.60168e6 −1.21713
\(495\) 0 0
\(496\) −1.73170e7 −3.16058
\(497\) −54284.5 −0.00985791
\(498\) 0 0
\(499\) 6.29003e6 1.13084 0.565420 0.824803i \(-0.308714\pi\)
0.565420 + 0.824803i \(0.308714\pi\)
\(500\) −1.26848e7 −2.26913
\(501\) 0 0
\(502\) −82064.9 −0.0145344
\(503\) −3.68350e6 −0.649143 −0.324572 0.945861i \(-0.605220\pi\)
−0.324572 + 0.945861i \(0.605220\pi\)
\(504\) 0 0
\(505\) 2.28462e6 0.398644
\(506\) 1.23372e6 0.214210
\(507\) 0 0
\(508\) 1.14367e7 1.96627
\(509\) −3.33612e6 −0.570752 −0.285376 0.958416i \(-0.592118\pi\)
−0.285376 + 0.958416i \(0.592118\pi\)
\(510\) 0 0
\(511\) −207524. −0.0351573
\(512\) −1.33189e7 −2.24539
\(513\) 0 0
\(514\) −1.19114e7 −1.98863
\(515\) −9.57854e6 −1.59141
\(516\) 0 0
\(517\) 2.13879e6 0.351918
\(518\) 61913.5 0.0101382
\(519\) 0 0
\(520\) 1.49732e7 2.42832
\(521\) 987399. 0.159367 0.0796835 0.996820i \(-0.474609\pi\)
0.0796835 + 0.996820i \(0.474609\pi\)
\(522\) 0 0
\(523\) 6.57834e6 1.05163 0.525814 0.850600i \(-0.323761\pi\)
0.525814 + 0.850600i \(0.323761\pi\)
\(524\) 2.76612e7 4.40091
\(525\) 0 0
\(526\) 5.69446e6 0.897404
\(527\) −1.33696e7 −2.09697
\(528\) 0 0
\(529\) 279841. 0.0434783
\(530\) 1.94200e7 3.00302
\(531\) 0 0
\(532\) −177426. −0.0271793
\(533\) 2.68439e6 0.409287
\(534\) 0 0
\(535\) −9.89463e6 −1.49457
\(536\) 2.18854e7 3.29035
\(537\) 0 0
\(538\) 1.24437e7 1.85350
\(539\) 3.83981e6 0.569295
\(540\) 0 0
\(541\) −6.47470e6 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(542\) 1.43452e7 2.09753
\(543\) 0 0
\(544\) 8.63445e6 1.25094
\(545\) −7.68087e6 −1.10769
\(546\) 0 0
\(547\) −495799. −0.0708496 −0.0354248 0.999372i \(-0.511278\pi\)
−0.0354248 + 0.999372i \(0.511278\pi\)
\(548\) 2.39249e6 0.340328
\(549\) 0 0
\(550\) 100021. 0.0140989
\(551\) −7.02992e6 −0.986442
\(552\) 0 0
\(553\) −60010.8 −0.00834481
\(554\) 1.91634e7 2.65276
\(555\) 0 0
\(556\) −9.26727e6 −1.27135
\(557\) −3.94887e6 −0.539306 −0.269653 0.962958i \(-0.586909\pi\)
−0.269653 + 0.962958i \(0.586909\pi\)
\(558\) 0 0
\(559\) −6.86190e6 −0.928784
\(560\) 260033. 0.0350395
\(561\) 0 0
\(562\) 2.16083e7 2.88590
\(563\) 2.70237e6 0.359314 0.179657 0.983729i \(-0.442501\pi\)
0.179657 + 0.983729i \(0.442501\pi\)
\(564\) 0 0
\(565\) 750781. 0.0989447
\(566\) 1.18411e7 1.55365
\(567\) 0 0
\(568\) −8.87430e6 −1.15415
\(569\) −1.33108e7 −1.72355 −0.861773 0.507294i \(-0.830646\pi\)
−0.861773 + 0.507294i \(0.830646\pi\)
\(570\) 0 0
\(571\) −1.10053e7 −1.41257 −0.706286 0.707926i \(-0.749631\pi\)
−0.706286 + 0.707926i \(0.749631\pi\)
\(572\) −1.08583e7 −1.38762
\(573\) 0 0
\(574\) 104154. 0.0131947
\(575\) 22687.5 0.00286165
\(576\) 0 0
\(577\) −480544. −0.0600888 −0.0300444 0.999549i \(-0.509565\pi\)
−0.0300444 + 0.999549i \(0.509565\pi\)
\(578\) 6.78300e6 0.844505
\(579\) 0 0
\(580\) 2.86602e7 3.53760
\(581\) −203345. −0.0249915
\(582\) 0 0
\(583\) −7.83477e6 −0.954674
\(584\) −3.39255e7 −4.11618
\(585\) 0 0
\(586\) 1.29924e7 1.56296
\(587\) −9.12805e6 −1.09341 −0.546705 0.837325i \(-0.684118\pi\)
−0.546705 + 0.837325i \(0.684118\pi\)
\(588\) 0 0
\(589\) 9.09485e6 1.08021
\(590\) 4.11780e6 0.487007
\(591\) 0 0
\(592\) 4.53029e6 0.531278
\(593\) 2.66114e6 0.310765 0.155382 0.987854i \(-0.450339\pi\)
0.155382 + 0.987854i \(0.450339\pi\)
\(594\) 0 0
\(595\) 200760. 0.0232479
\(596\) 1.32876e7 1.53225
\(597\) 0 0
\(598\) −3.55569e6 −0.406604
\(599\) −6.44915e6 −0.734405 −0.367202 0.930141i \(-0.619684\pi\)
−0.367202 + 0.930141i \(0.619684\pi\)
\(600\) 0 0
\(601\) −1.48491e6 −0.167693 −0.0838463 0.996479i \(-0.526720\pi\)
−0.0838463 + 0.996479i \(0.526720\pi\)
\(602\) −266241. −0.0299423
\(603\) 0 0
\(604\) −1.42795e6 −0.159265
\(605\) −6.04111e6 −0.671009
\(606\) 0 0
\(607\) −6.56656e6 −0.723379 −0.361690 0.932299i \(-0.617800\pi\)
−0.361690 + 0.932299i \(0.617800\pi\)
\(608\) −5.87368e6 −0.644394
\(609\) 0 0
\(610\) 1.50756e7 1.64040
\(611\) −6.16420e6 −0.667996
\(612\) 0 0
\(613\) −9.33817e6 −1.00372 −0.501858 0.864950i \(-0.667350\pi\)
−0.501858 + 0.864950i \(0.667350\pi\)
\(614\) −2.30793e7 −2.47060
\(615\) 0 0
\(616\) −234382. −0.0248870
\(617\) −7.56128e6 −0.799617 −0.399809 0.916599i \(-0.630923\pi\)
−0.399809 + 0.916599i \(0.630923\pi\)
\(618\) 0 0
\(619\) 1.16180e7 1.21872 0.609359 0.792895i \(-0.291427\pi\)
0.609359 + 0.792895i \(0.291427\pi\)
\(620\) −3.70786e7 −3.87387
\(621\) 0 0
\(622\) −1.22718e7 −1.27184
\(623\) −250751. −0.0258834
\(624\) 0 0
\(625\) −9.62976e6 −0.986088
\(626\) −4.94201e6 −0.504043
\(627\) 0 0
\(628\) 1.39431e7 1.41078
\(629\) 3.49763e6 0.352491
\(630\) 0 0
\(631\) −8.43872e6 −0.843730 −0.421865 0.906659i \(-0.638624\pi\)
−0.421865 + 0.906659i \(0.638624\pi\)
\(632\) −9.81042e6 −0.977001
\(633\) 0 0
\(634\) −8.12891e6 −0.803173
\(635\) 8.80313e6 0.866369
\(636\) 0 0
\(637\) −1.10667e7 −1.08061
\(638\) −1.66926e7 −1.62358
\(639\) 0 0
\(640\) −9.95483e6 −0.960692
\(641\) −1.32010e7 −1.26900 −0.634500 0.772923i \(-0.718794\pi\)
−0.634500 + 0.772923i \(0.718794\pi\)
\(642\) 0 0
\(643\) −1.57321e7 −1.50058 −0.750290 0.661109i \(-0.770086\pi\)
−0.750290 + 0.661109i \(0.770086\pi\)
\(644\) −95562.5 −0.00907973
\(645\) 0 0
\(646\) −1.44702e7 −1.36425
\(647\) 6.22066e6 0.584219 0.292109 0.956385i \(-0.405643\pi\)
0.292109 + 0.956385i \(0.405643\pi\)
\(648\) 0 0
\(649\) −1.66128e6 −0.154822
\(650\) −288270. −0.0267618
\(651\) 0 0
\(652\) 7.66595e6 0.706231
\(653\) 1.57628e7 1.44660 0.723302 0.690532i \(-0.242624\pi\)
0.723302 + 0.690532i \(0.242624\pi\)
\(654\) 0 0
\(655\) 2.12915e7 1.93911
\(656\) 7.62110e6 0.691446
\(657\) 0 0
\(658\) −239171. −0.0215349
\(659\) 5.77008e6 0.517569 0.258784 0.965935i \(-0.416678\pi\)
0.258784 + 0.965935i \(0.416678\pi\)
\(660\) 0 0
\(661\) −1.48192e7 −1.31924 −0.659618 0.751601i \(-0.729282\pi\)
−0.659618 + 0.751601i \(0.729282\pi\)
\(662\) −2.68223e6 −0.237877
\(663\) 0 0
\(664\) −3.32423e7 −2.92598
\(665\) −136569. −0.0119756
\(666\) 0 0
\(667\) −3.78635e6 −0.329538
\(668\) 5.60528e6 0.486022
\(669\) 0 0
\(670\) 3.02801e7 2.60597
\(671\) −6.08209e6 −0.521491
\(672\) 0 0
\(673\) −1.74615e7 −1.48609 −0.743045 0.669242i \(-0.766619\pi\)
−0.743045 + 0.669242i \(0.766619\pi\)
\(674\) 1.25637e7 1.06529
\(675\) 0 0
\(676\) 4.51487e6 0.379995
\(677\) 2.10975e7 1.76913 0.884564 0.466418i \(-0.154456\pi\)
0.884564 + 0.466418i \(0.154456\pi\)
\(678\) 0 0
\(679\) 90472.2 0.00753080
\(680\) 3.28197e7 2.72184
\(681\) 0 0
\(682\) 2.15958e7 1.77791
\(683\) 1.43654e7 1.17833 0.589163 0.808014i \(-0.299458\pi\)
0.589163 + 0.808014i \(0.299458\pi\)
\(684\) 0 0
\(685\) 1.84155e6 0.149954
\(686\) −858935. −0.0696867
\(687\) 0 0
\(688\) −1.94812e7 −1.56908
\(689\) 2.25806e7 1.81212
\(690\) 0 0
\(691\) 1.64154e7 1.30785 0.653923 0.756561i \(-0.273122\pi\)
0.653923 + 0.756561i \(0.273122\pi\)
\(692\) −1.57612e7 −1.25119
\(693\) 0 0
\(694\) 3.77907e7 2.97842
\(695\) −7.13324e6 −0.560176
\(696\) 0 0
\(697\) 5.88391e6 0.458758
\(698\) 1.66210e7 1.29127
\(699\) 0 0
\(700\) −7747.52 −0.000597609 0
\(701\) 1.07940e7 0.829635 0.414818 0.909905i \(-0.363845\pi\)
0.414818 + 0.909905i \(0.363845\pi\)
\(702\) 0 0
\(703\) −2.37930e6 −0.181577
\(704\) −270077. −0.0205379
\(705\) 0 0
\(706\) −2.61829e7 −1.97700
\(707\) 103070. 0.00775502
\(708\) 0 0
\(709\) 2.44390e7 1.82586 0.912930 0.408115i \(-0.133814\pi\)
0.912930 + 0.408115i \(0.133814\pi\)
\(710\) −1.22783e7 −0.914093
\(711\) 0 0
\(712\) −4.09921e7 −3.03040
\(713\) 4.89853e6 0.360863
\(714\) 0 0
\(715\) −8.35787e6 −0.611407
\(716\) 3.93440e7 2.86811
\(717\) 0 0
\(718\) 3.53978e7 2.56251
\(719\) 6.41280e6 0.462621 0.231310 0.972880i \(-0.425699\pi\)
0.231310 + 0.972880i \(0.425699\pi\)
\(720\) 0 0
\(721\) −432133. −0.0309585
\(722\) −1.54231e7 −1.10110
\(723\) 0 0
\(724\) 3.68474e7 2.61252
\(725\) −306970. −0.0216896
\(726\) 0 0
\(727\) −1.58788e7 −1.11424 −0.557122 0.830431i \(-0.688095\pi\)
−0.557122 + 0.830431i \(0.688095\pi\)
\(728\) 675512. 0.0472394
\(729\) 0 0
\(730\) −4.69385e7 −3.26003
\(731\) −1.50406e7 −1.04105
\(732\) 0 0
\(733\) 2.52517e7 1.73592 0.867962 0.496631i \(-0.165430\pi\)
0.867962 + 0.496631i \(0.165430\pi\)
\(734\) 1.67487e7 1.14747
\(735\) 0 0
\(736\) −3.16359e6 −0.215271
\(737\) −1.22162e7 −0.828450
\(738\) 0 0
\(739\) −1.56260e7 −1.05253 −0.526267 0.850319i \(-0.676409\pi\)
−0.526267 + 0.850319i \(0.676409\pi\)
\(740\) 9.70015e6 0.651177
\(741\) 0 0
\(742\) 876126. 0.0584193
\(743\) −1.42696e7 −0.948284 −0.474142 0.880448i \(-0.657242\pi\)
−0.474142 + 0.880448i \(0.657242\pi\)
\(744\) 0 0
\(745\) 1.02278e7 0.675133
\(746\) 1.61845e7 1.06476
\(747\) 0 0
\(748\) −2.38002e7 −1.55534
\(749\) −446393. −0.0290746
\(750\) 0 0
\(751\) 2.22359e7 1.43865 0.719323 0.694676i \(-0.244452\pi\)
0.719323 + 0.694676i \(0.244452\pi\)
\(752\) −1.75004e7 −1.12851
\(753\) 0 0
\(754\) 4.81098e7 3.08181
\(755\) −1.09912e6 −0.0701745
\(756\) 0 0
\(757\) −1.09113e7 −0.692048 −0.346024 0.938226i \(-0.612468\pi\)
−0.346024 + 0.938226i \(0.612468\pi\)
\(758\) −9.85756e6 −0.623155
\(759\) 0 0
\(760\) −2.23260e7 −1.40209
\(761\) −2.42444e6 −0.151758 −0.0758788 0.997117i \(-0.524176\pi\)
−0.0758788 + 0.997117i \(0.524176\pi\)
\(762\) 0 0
\(763\) −346520. −0.0215485
\(764\) 4.16058e6 0.257882
\(765\) 0 0
\(766\) 3.16659e7 1.94993
\(767\) 4.78798e6 0.293876
\(768\) 0 0
\(769\) 2.00363e6 0.122181 0.0610903 0.998132i \(-0.480542\pi\)
0.0610903 + 0.998132i \(0.480542\pi\)
\(770\) −324285. −0.0197106
\(771\) 0 0
\(772\) −5.92938e7 −3.58069
\(773\) −3.91181e6 −0.235466 −0.117733 0.993045i \(-0.537563\pi\)
−0.117733 + 0.993045i \(0.537563\pi\)
\(774\) 0 0
\(775\) 397137. 0.0237512
\(776\) 1.47902e7 0.881697
\(777\) 0 0
\(778\) −6.37322e6 −0.377494
\(779\) −4.00260e6 −0.236319
\(780\) 0 0
\(781\) 4.95353e6 0.290594
\(782\) −7.79371e6 −0.455751
\(783\) 0 0
\(784\) −3.14188e7 −1.82557
\(785\) 1.07323e7 0.621614
\(786\) 0 0
\(787\) −2.37516e7 −1.36696 −0.683479 0.729970i \(-0.739534\pi\)
−0.683479 + 0.729970i \(0.739534\pi\)
\(788\) −7.00752e7 −4.02021
\(789\) 0 0
\(790\) −1.35734e7 −0.773789
\(791\) 33871.3 0.00192482
\(792\) 0 0
\(793\) 1.75292e7 0.989872
\(794\) 2.86548e7 1.61304
\(795\) 0 0
\(796\) 5.81412e7 3.25238
\(797\) 2.50486e7 1.39681 0.698405 0.715703i \(-0.253894\pi\)
0.698405 + 0.715703i \(0.253894\pi\)
\(798\) 0 0
\(799\) −1.35113e7 −0.748737
\(800\) −256481. −0.0141687
\(801\) 0 0
\(802\) −3.89072e7 −2.13597
\(803\) 1.89368e7 1.03638
\(804\) 0 0
\(805\) −73556.7 −0.00400067
\(806\) −6.22413e7 −3.37475
\(807\) 0 0
\(808\) 1.68496e7 0.907949
\(809\) 2.26709e7 1.21786 0.608931 0.793223i \(-0.291598\pi\)
0.608931 + 0.793223i \(0.291598\pi\)
\(810\) 0 0
\(811\) −1.66885e7 −0.890974 −0.445487 0.895288i \(-0.646969\pi\)
−0.445487 + 0.895288i \(0.646969\pi\)
\(812\) 1.29300e6 0.0688188
\(813\) 0 0
\(814\) −5.64969e6 −0.298857
\(815\) 5.90066e6 0.311176
\(816\) 0 0
\(817\) 1.02315e7 0.536272
\(818\) −3.94156e7 −2.05961
\(819\) 0 0
\(820\) 1.63181e7 0.847492
\(821\) 2.41094e7 1.24833 0.624164 0.781293i \(-0.285440\pi\)
0.624164 + 0.781293i \(0.285440\pi\)
\(822\) 0 0
\(823\) −9.03070e6 −0.464753 −0.232376 0.972626i \(-0.574650\pi\)
−0.232376 + 0.972626i \(0.574650\pi\)
\(824\) −7.06441e7 −3.62458
\(825\) 0 0
\(826\) 185773. 0.00947399
\(827\) −1.22307e7 −0.621852 −0.310926 0.950434i \(-0.600639\pi\)
−0.310926 + 0.950434i \(0.600639\pi\)
\(828\) 0 0
\(829\) 2.01683e7 1.01925 0.509627 0.860395i \(-0.329783\pi\)
0.509627 + 0.860395i \(0.329783\pi\)
\(830\) −4.59932e7 −2.31739
\(831\) 0 0
\(832\) 778387. 0.0389841
\(833\) −2.42570e7 −1.21123
\(834\) 0 0
\(835\) 4.31452e6 0.214149
\(836\) 1.61904e7 0.801199
\(837\) 0 0
\(838\) 4.08700e7 2.01045
\(839\) −1.80995e7 −0.887690 −0.443845 0.896103i \(-0.646386\pi\)
−0.443845 + 0.896103i \(0.646386\pi\)
\(840\) 0 0
\(841\) 3.07195e7 1.49770
\(842\) 4.99697e7 2.42899
\(843\) 0 0
\(844\) −5.92810e7 −2.86457
\(845\) 3.47520e6 0.167432
\(846\) 0 0
\(847\) −272543. −0.0130535
\(848\) 6.41072e7 3.06138
\(849\) 0 0
\(850\) −631857. −0.0299966
\(851\) −1.28150e6 −0.0606591
\(852\) 0 0
\(853\) −1.82781e7 −0.860121 −0.430060 0.902800i \(-0.641508\pi\)
−0.430060 + 0.902800i \(0.641508\pi\)
\(854\) 680132. 0.0319116
\(855\) 0 0
\(856\) −7.29753e7 −3.40402
\(857\) 1.47267e7 0.684940 0.342470 0.939529i \(-0.388736\pi\)
0.342470 + 0.939529i \(0.388736\pi\)
\(858\) 0 0
\(859\) −1.82990e7 −0.846142 −0.423071 0.906096i \(-0.639048\pi\)
−0.423071 + 0.906096i \(0.639048\pi\)
\(860\) −4.17127e7 −1.92319
\(861\) 0 0
\(862\) −1.85588e7 −0.850712
\(863\) 3.92569e6 0.179427 0.0897137 0.995968i \(-0.471405\pi\)
0.0897137 + 0.995968i \(0.471405\pi\)
\(864\) 0 0
\(865\) −1.21317e7 −0.551293
\(866\) 5.56814e6 0.252299
\(867\) 0 0
\(868\) −1.67279e6 −0.0753603
\(869\) 5.47606e6 0.245991
\(870\) 0 0
\(871\) 3.52082e7 1.57253
\(872\) −5.66483e7 −2.52287
\(873\) 0 0
\(874\) 5.30176e6 0.234769
\(875\) −440490. −0.0194499
\(876\) 0 0
\(877\) −3.49463e7 −1.53427 −0.767135 0.641486i \(-0.778318\pi\)
−0.767135 + 0.641486i \(0.778318\pi\)
\(878\) 2.86854e7 1.25581
\(879\) 0 0
\(880\) −2.37283e7 −1.03290
\(881\) 3.45541e7 1.49989 0.749945 0.661501i \(-0.230080\pi\)
0.749945 + 0.661501i \(0.230080\pi\)
\(882\) 0 0
\(883\) 2.29538e6 0.0990722 0.0495361 0.998772i \(-0.484226\pi\)
0.0495361 + 0.998772i \(0.484226\pi\)
\(884\) 6.85945e7 2.95229
\(885\) 0 0
\(886\) 2.87175e7 1.22903
\(887\) −2.48902e7 −1.06223 −0.531116 0.847299i \(-0.678227\pi\)
−0.531116 + 0.847299i \(0.678227\pi\)
\(888\) 0 0
\(889\) 397151. 0.0168539
\(890\) −5.67156e7 −2.40009
\(891\) 0 0
\(892\) 3.69246e7 1.55383
\(893\) 9.19120e6 0.385695
\(894\) 0 0
\(895\) 3.02840e7 1.26373
\(896\) −449109. −0.0186888
\(897\) 0 0
\(898\) −4.08826e7 −1.69179
\(899\) −6.62789e7 −2.73512
\(900\) 0 0
\(901\) 4.94943e7 2.03115
\(902\) −9.50422e6 −0.388956
\(903\) 0 0
\(904\) 5.53719e6 0.225356
\(905\) 2.83623e7 1.15112
\(906\) 0 0
\(907\) −1.12581e7 −0.454411 −0.227205 0.973847i \(-0.572959\pi\)
−0.227205 + 0.973847i \(0.572959\pi\)
\(908\) 1.04636e8 4.21178
\(909\) 0 0
\(910\) 934621. 0.0374138
\(911\) 2.07869e7 0.829837 0.414919 0.909859i \(-0.363810\pi\)
0.414919 + 0.909859i \(0.363810\pi\)
\(912\) 0 0
\(913\) 1.85555e7 0.736707
\(914\) −5.54905e7 −2.19712
\(915\) 0 0
\(916\) 4.48022e7 1.76425
\(917\) 960558. 0.0377225
\(918\) 0 0
\(919\) −1.17836e7 −0.460244 −0.230122 0.973162i \(-0.573913\pi\)
−0.230122 + 0.973162i \(0.573913\pi\)
\(920\) −1.20249e7 −0.468394
\(921\) 0 0
\(922\) −2.56091e7 −0.992126
\(923\) −1.42766e7 −0.551594
\(924\) 0 0
\(925\) −103895. −0.00399246
\(926\) 1.10881e6 0.0424942
\(927\) 0 0
\(928\) 4.28045e7 1.63162
\(929\) 2.82219e7 1.07287 0.536435 0.843942i \(-0.319771\pi\)
0.536435 + 0.843942i \(0.319771\pi\)
\(930\) 0 0
\(931\) 1.65011e7 0.623935
\(932\) −3.53657e7 −1.33365
\(933\) 0 0
\(934\) −3.15437e7 −1.18316
\(935\) −1.83196e7 −0.685308
\(936\) 0 0
\(937\) 1.34325e7 0.499814 0.249907 0.968270i \(-0.419600\pi\)
0.249907 + 0.968270i \(0.419600\pi\)
\(938\) 1.36608e6 0.0506953
\(939\) 0 0
\(940\) −3.74715e7 −1.38319
\(941\) −4.06264e7 −1.49566 −0.747832 0.663888i \(-0.768905\pi\)
−0.747832 + 0.663888i \(0.768905\pi\)
\(942\) 0 0
\(943\) −2.15582e6 −0.0789465
\(944\) 1.35933e7 0.496470
\(945\) 0 0
\(946\) 2.42949e7 0.882646
\(947\) 3.34341e7 1.21148 0.605738 0.795664i \(-0.292878\pi\)
0.605738 + 0.795664i \(0.292878\pi\)
\(948\) 0 0
\(949\) −5.45778e7 −1.96721
\(950\) 429828. 0.0154520
\(951\) 0 0
\(952\) 1.48065e6 0.0529493
\(953\) 8.95158e6 0.319277 0.159638 0.987176i \(-0.448967\pi\)
0.159638 + 0.987176i \(0.448967\pi\)
\(954\) 0 0
\(955\) 3.20250e6 0.113627
\(956\) −7.89797e6 −0.279493
\(957\) 0 0
\(958\) 7.90563e7 2.78306
\(959\) 83081.1 0.00291713
\(960\) 0 0
\(961\) 5.71181e7 1.99510
\(962\) 1.62830e7 0.567277
\(963\) 0 0
\(964\) 9.82140e7 3.40393
\(965\) −4.56399e7 −1.57771
\(966\) 0 0
\(967\) −2.94663e7 −1.01335 −0.506675 0.862137i \(-0.669126\pi\)
−0.506675 + 0.862137i \(0.669126\pi\)
\(968\) −4.45546e7 −1.52829
\(969\) 0 0
\(970\) 2.04633e7 0.698307
\(971\) 3.03617e7 1.03342 0.516712 0.856159i \(-0.327156\pi\)
0.516712 + 0.856159i \(0.327156\pi\)
\(972\) 0 0
\(973\) −321814. −0.0108974
\(974\) 6.74425e7 2.27791
\(975\) 0 0
\(976\) 4.97661e7 1.67228
\(977\) −3.77587e6 −0.126555 −0.0632777 0.997996i \(-0.520155\pi\)
−0.0632777 + 0.997996i \(0.520155\pi\)
\(978\) 0 0
\(979\) 2.28813e7 0.762999
\(980\) −6.72732e7 −2.23757
\(981\) 0 0
\(982\) −1.71893e7 −0.568826
\(983\) −1.74788e7 −0.576938 −0.288469 0.957489i \(-0.593146\pi\)
−0.288469 + 0.957489i \(0.593146\pi\)
\(984\) 0 0
\(985\) −5.39385e7 −1.77137
\(986\) 1.05452e8 3.45431
\(987\) 0 0
\(988\) −4.66622e7 −1.52080
\(989\) 5.51074e6 0.179151
\(990\) 0 0
\(991\) 4.83380e7 1.56352 0.781762 0.623576i \(-0.214321\pi\)
0.781762 + 0.623576i \(0.214321\pi\)
\(992\) −5.53777e7 −1.78672
\(993\) 0 0
\(994\) −553930. −0.0177823
\(995\) 4.47526e7 1.43305
\(996\) 0 0
\(997\) −1.74335e7 −0.555452 −0.277726 0.960660i \(-0.589581\pi\)
−0.277726 + 0.960660i \(0.589581\pi\)
\(998\) 6.41847e7 2.03988
\(999\) 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 207.6.a.c.1.3 3
3.2 odd 2 69.6.a.b.1.1 3
12.11 even 2 1104.6.a.i.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.a.b.1.1 3 3.2 odd 2
207.6.a.c.1.3 3 1.1 even 1 trivial
1104.6.a.i.1.2 3 12.11 even 2