Properties

Label 207.6.a.f.1.1
Level $207$
Weight $6$
Character 207.1
Self dual yes
Analytic conductor $33.199$
Analytic rank $1$
Dimension $5$
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: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \( x^{5} - 113x^{3} - 257x^{2} + 1404x + 2197 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 69)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.40352\) of defining polynomial
Character \(\chi\) \(=\) 207.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.34908 q^{2} +55.4053 q^{4} -70.5203 q^{5} -89.7132 q^{7} -218.818 q^{8} +O(q^{10})\) \(q-9.34908 q^{2} +55.4053 q^{4} -70.5203 q^{5} -89.7132 q^{7} -218.818 q^{8} +659.300 q^{10} +436.763 q^{11} -258.865 q^{13} +838.736 q^{14} +272.775 q^{16} -591.819 q^{17} +1663.69 q^{19} -3907.20 q^{20} -4083.33 q^{22} +529.000 q^{23} +1848.12 q^{25} +2420.15 q^{26} -4970.58 q^{28} +5121.48 q^{29} +1871.29 q^{31} +4451.97 q^{32} +5532.96 q^{34} +6326.60 q^{35} +884.534 q^{37} -15554.0 q^{38} +15431.1 q^{40} +18410.5 q^{41} +12334.9 q^{43} +24199.0 q^{44} -4945.66 q^{46} -23871.6 q^{47} -8758.55 q^{49} -17278.2 q^{50} -14342.5 q^{52} +14594.8 q^{53} -30800.7 q^{55} +19630.8 q^{56} -47881.1 q^{58} -47739.1 q^{59} -15351.5 q^{61} -17494.8 q^{62} -50350.6 q^{64} +18255.2 q^{65} -41174.4 q^{67} -32789.9 q^{68} -59147.9 q^{70} +45608.3 q^{71} -7898.24 q^{73} -8269.57 q^{74} +92177.1 q^{76} -39183.4 q^{77} +71435.2 q^{79} -19236.2 q^{80} -172121. q^{82} -112580. q^{83} +41735.3 q^{85} -115320. q^{86} -95571.5 q^{88} -137845. q^{89} +23223.6 q^{91} +29309.4 q^{92} +223177. q^{94} -117324. q^{95} +41679.8 q^{97} +81884.3 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 8 q^{2} + 118 q^{4} - 94 q^{5} + 272 q^{7} - 258 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 8 q^{2} + 118 q^{4} - 94 q^{5} + 272 q^{7} - 258 q^{8} - 172 q^{10} - 1100 q^{11} - 978 q^{13} + 344 q^{14} + 1218 q^{16} - 2522 q^{17} + 2060 q^{19} - 7720 q^{20} - 2572 q^{22} + 2645 q^{23} + 12035 q^{25} - 9280 q^{26} + 8072 q^{28} - 1526 q^{29} - 7392 q^{31} + 5086 q^{32} - 15608 q^{34} - 6056 q^{35} - 8210 q^{37} + 14276 q^{38} - 37472 q^{40} - 21250 q^{41} - 4548 q^{43} + 4260 q^{44} - 4232 q^{46} - 536 q^{47} - 27979 q^{49} + 81872 q^{50} - 76380 q^{52} + 11482 q^{53} - 77064 q^{55} + 28624 q^{56} - 79680 q^{58} - 74676 q^{59} - 44618 q^{61} - 64880 q^{62} - 137382 q^{64} + 24388 q^{65} - 1412 q^{67} - 80196 q^{68} - 222304 q^{70} - 37912 q^{71} + 46546 q^{73} - 111604 q^{74} - 79548 q^{76} - 157008 q^{77} + 50544 q^{79} - 69424 q^{80} - 233720 q^{82} - 89588 q^{83} + 147892 q^{85} - 77428 q^{86} + 54484 q^{88} - 280410 q^{89} - 27416 q^{91} + 62422 q^{92} + 113632 q^{94} - 203120 q^{95} + 90074 q^{97} - 32976 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.34908 −1.65270 −0.826350 0.563157i \(-0.809586\pi\)
−0.826350 + 0.563157i \(0.809586\pi\)
\(3\) 0 0
\(4\) 55.4053 1.73141
\(5\) −70.5203 −1.26151 −0.630753 0.775984i \(-0.717254\pi\)
−0.630753 + 0.775984i \(0.717254\pi\)
\(6\) 0 0
\(7\) −89.7132 −0.692008 −0.346004 0.938233i \(-0.612462\pi\)
−0.346004 + 0.938233i \(0.612462\pi\)
\(8\) −218.818 −1.20881
\(9\) 0 0
\(10\) 659.300 2.08489
\(11\) 436.763 1.08834 0.544170 0.838975i \(-0.316845\pi\)
0.544170 + 0.838975i \(0.316845\pi\)
\(12\) 0 0
\(13\) −258.865 −0.424830 −0.212415 0.977180i \(-0.568133\pi\)
−0.212415 + 0.977180i \(0.568133\pi\)
\(14\) 838.736 1.14368
\(15\) 0 0
\(16\) 272.775 0.266382
\(17\) −591.819 −0.496669 −0.248334 0.968674i \(-0.579883\pi\)
−0.248334 + 0.968674i \(0.579883\pi\)
\(18\) 0 0
\(19\) 1663.69 1.05727 0.528637 0.848848i \(-0.322703\pi\)
0.528637 + 0.848848i \(0.322703\pi\)
\(20\) −3907.20 −2.18419
\(21\) 0 0
\(22\) −4083.33 −1.79870
\(23\) 529.000 0.208514
\(24\) 0 0
\(25\) 1848.12 0.591398
\(26\) 2420.15 0.702116
\(27\) 0 0
\(28\) −4970.58 −1.19815
\(29\) 5121.48 1.13084 0.565419 0.824804i \(-0.308714\pi\)
0.565419 + 0.824804i \(0.308714\pi\)
\(30\) 0 0
\(31\) 1871.29 0.349733 0.174867 0.984592i \(-0.444051\pi\)
0.174867 + 0.984592i \(0.444051\pi\)
\(32\) 4451.97 0.768559
\(33\) 0 0
\(34\) 5532.96 0.820844
\(35\) 6326.60 0.872972
\(36\) 0 0
\(37\) 884.534 0.106221 0.0531105 0.998589i \(-0.483086\pi\)
0.0531105 + 0.998589i \(0.483086\pi\)
\(38\) −15554.0 −1.74736
\(39\) 0 0
\(40\) 15431.1 1.52492
\(41\) 18410.5 1.71043 0.855216 0.518271i \(-0.173424\pi\)
0.855216 + 0.518271i \(0.173424\pi\)
\(42\) 0 0
\(43\) 12334.9 1.01734 0.508669 0.860962i \(-0.330138\pi\)
0.508669 + 0.860962i \(0.330138\pi\)
\(44\) 24199.0 1.88437
\(45\) 0 0
\(46\) −4945.66 −0.344612
\(47\) −23871.6 −1.57629 −0.788146 0.615489i \(-0.788959\pi\)
−0.788146 + 0.615489i \(0.788959\pi\)
\(48\) 0 0
\(49\) −8758.55 −0.521125
\(50\) −17278.2 −0.977403
\(51\) 0 0
\(52\) −14342.5 −0.735556
\(53\) 14594.8 0.713690 0.356845 0.934164i \(-0.383853\pi\)
0.356845 + 0.934164i \(0.383853\pi\)
\(54\) 0 0
\(55\) −30800.7 −1.37295
\(56\) 19630.8 0.836505
\(57\) 0 0
\(58\) −47881.1 −1.86894
\(59\) −47739.1 −1.78544 −0.892718 0.450616i \(-0.851205\pi\)
−0.892718 + 0.450616i \(0.851205\pi\)
\(60\) 0 0
\(61\) −15351.5 −0.528233 −0.264116 0.964491i \(-0.585080\pi\)
−0.264116 + 0.964491i \(0.585080\pi\)
\(62\) −17494.8 −0.578004
\(63\) 0 0
\(64\) −50350.6 −1.53658
\(65\) 18255.2 0.535925
\(66\) 0 0
\(67\) −41174.4 −1.12057 −0.560287 0.828299i \(-0.689309\pi\)
−0.560287 + 0.828299i \(0.689309\pi\)
\(68\) −32789.9 −0.859939
\(69\) 0 0
\(70\) −59147.9 −1.44276
\(71\) 45608.3 1.07374 0.536869 0.843666i \(-0.319607\pi\)
0.536869 + 0.843666i \(0.319607\pi\)
\(72\) 0 0
\(73\) −7898.24 −0.173470 −0.0867348 0.996231i \(-0.527643\pi\)
−0.0867348 + 0.996231i \(0.527643\pi\)
\(74\) −8269.57 −0.175551
\(75\) 0 0
\(76\) 92177.1 1.83058
\(77\) −39183.4 −0.753140
\(78\) 0 0
\(79\) 71435.2 1.28779 0.643894 0.765115i \(-0.277318\pi\)
0.643894 + 0.765115i \(0.277318\pi\)
\(80\) −19236.2 −0.336043
\(81\) 0 0
\(82\) −172121. −2.82683
\(83\) −112580. −1.79377 −0.896885 0.442264i \(-0.854175\pi\)
−0.896885 + 0.442264i \(0.854175\pi\)
\(84\) 0 0
\(85\) 41735.3 0.626551
\(86\) −115320. −1.68136
\(87\) 0 0
\(88\) −95571.5 −1.31559
\(89\) −137845. −1.84466 −0.922330 0.386404i \(-0.873717\pi\)
−0.922330 + 0.386404i \(0.873717\pi\)
\(90\) 0 0
\(91\) 23223.6 0.293985
\(92\) 29309.4 0.361025
\(93\) 0 0
\(94\) 223177. 2.60514
\(95\) −117324. −1.33376
\(96\) 0 0
\(97\) 41679.8 0.449776 0.224888 0.974385i \(-0.427798\pi\)
0.224888 + 0.974385i \(0.427798\pi\)
\(98\) 81884.3 0.861263
\(99\) 0 0
\(100\) 102395. 1.02395
\(101\) −37100.3 −0.361888 −0.180944 0.983493i \(-0.557915\pi\)
−0.180944 + 0.983493i \(0.557915\pi\)
\(102\) 0 0
\(103\) −123323. −1.14538 −0.572692 0.819771i \(-0.694101\pi\)
−0.572692 + 0.819771i \(0.694101\pi\)
\(104\) 56644.2 0.513538
\(105\) 0 0
\(106\) −136448. −1.17951
\(107\) −107455. −0.907338 −0.453669 0.891170i \(-0.649885\pi\)
−0.453669 + 0.891170i \(0.649885\pi\)
\(108\) 0 0
\(109\) 96652.7 0.779198 0.389599 0.920985i \(-0.372614\pi\)
0.389599 + 0.920985i \(0.372614\pi\)
\(110\) 287958. 2.26907
\(111\) 0 0
\(112\) −24471.5 −0.184338
\(113\) −55788.7 −0.411008 −0.205504 0.978656i \(-0.565883\pi\)
−0.205504 + 0.978656i \(0.565883\pi\)
\(114\) 0 0
\(115\) −37305.3 −0.263042
\(116\) 283757. 1.95795
\(117\) 0 0
\(118\) 446317. 2.95079
\(119\) 53094.0 0.343699
\(120\) 0 0
\(121\) 29711.1 0.184483
\(122\) 143522. 0.873010
\(123\) 0 0
\(124\) 103679. 0.605533
\(125\) 90046.2 0.515454
\(126\) 0 0
\(127\) 167839. 0.923388 0.461694 0.887039i \(-0.347242\pi\)
0.461694 + 0.887039i \(0.347242\pi\)
\(128\) 328269. 1.77094
\(129\) 0 0
\(130\) −170670. −0.885723
\(131\) −129729. −0.660476 −0.330238 0.943898i \(-0.607129\pi\)
−0.330238 + 0.943898i \(0.607129\pi\)
\(132\) 0 0
\(133\) −149255. −0.731643
\(134\) 384943. 1.85197
\(135\) 0 0
\(136\) 129501. 0.600377
\(137\) 226702. 1.03194 0.515970 0.856607i \(-0.327432\pi\)
0.515970 + 0.856607i \(0.327432\pi\)
\(138\) 0 0
\(139\) −419175. −1.84017 −0.920086 0.391716i \(-0.871882\pi\)
−0.920086 + 0.391716i \(0.871882\pi\)
\(140\) 350527. 1.51148
\(141\) 0 0
\(142\) −426396. −1.77457
\(143\) −113063. −0.462359
\(144\) 0 0
\(145\) −361169. −1.42656
\(146\) 73841.3 0.286693
\(147\) 0 0
\(148\) 49007.8 0.183912
\(149\) −503270. −1.85710 −0.928551 0.371206i \(-0.878945\pi\)
−0.928551 + 0.371206i \(0.878945\pi\)
\(150\) 0 0
\(151\) 517943. 1.84858 0.924292 0.381685i \(-0.124656\pi\)
0.924292 + 0.381685i \(0.124656\pi\)
\(152\) −364044. −1.27804
\(153\) 0 0
\(154\) 366329. 1.24471
\(155\) −131964. −0.441190
\(156\) 0 0
\(157\) −39747.9 −0.128696 −0.0643480 0.997928i \(-0.520497\pi\)
−0.0643480 + 0.997928i \(0.520497\pi\)
\(158\) −667853. −2.12833
\(159\) 0 0
\(160\) −313954. −0.969542
\(161\) −47458.3 −0.144294
\(162\) 0 0
\(163\) −157828. −0.465279 −0.232640 0.972563i \(-0.574736\pi\)
−0.232640 + 0.972563i \(0.574736\pi\)
\(164\) 1.02004e6 2.96147
\(165\) 0 0
\(166\) 1.05252e6 2.96456
\(167\) 101000. 0.280241 0.140120 0.990134i \(-0.455251\pi\)
0.140120 + 0.990134i \(0.455251\pi\)
\(168\) 0 0
\(169\) −304282. −0.819520
\(170\) −390187. −1.03550
\(171\) 0 0
\(172\) 683420. 1.76144
\(173\) −61568.5 −0.156402 −0.0782012 0.996938i \(-0.524918\pi\)
−0.0782012 + 0.996938i \(0.524918\pi\)
\(174\) 0 0
\(175\) −165801. −0.409252
\(176\) 119138. 0.289914
\(177\) 0 0
\(178\) 1.28872e6 3.04867
\(179\) 610536. 1.42423 0.712113 0.702065i \(-0.247738\pi\)
0.712113 + 0.702065i \(0.247738\pi\)
\(180\) 0 0
\(181\) 121378. 0.275387 0.137694 0.990475i \(-0.456031\pi\)
0.137694 + 0.990475i \(0.456031\pi\)
\(182\) −217119. −0.485870
\(183\) 0 0
\(184\) −115755. −0.252054
\(185\) −62377.6 −0.133998
\(186\) 0 0
\(187\) −258485. −0.540544
\(188\) −1.32261e6 −2.72921
\(189\) 0 0
\(190\) 1.09687e6 2.20430
\(191\) 294581. 0.584280 0.292140 0.956376i \(-0.405633\pi\)
0.292140 + 0.956376i \(0.405633\pi\)
\(192\) 0 0
\(193\) −8895.53 −0.0171901 −0.00859505 0.999963i \(-0.502736\pi\)
−0.00859505 + 0.999963i \(0.502736\pi\)
\(194\) −389668. −0.743345
\(195\) 0 0
\(196\) −485270. −0.902283
\(197\) 698113. 1.28162 0.640811 0.767699i \(-0.278598\pi\)
0.640811 + 0.767699i \(0.278598\pi\)
\(198\) 0 0
\(199\) −533271. −0.954586 −0.477293 0.878744i \(-0.658382\pi\)
−0.477293 + 0.878744i \(0.658382\pi\)
\(200\) −404401. −0.714887
\(201\) 0 0
\(202\) 346854. 0.598092
\(203\) −459464. −0.782550
\(204\) 0 0
\(205\) −1.29831e6 −2.15772
\(206\) 1.15296e6 1.89298
\(207\) 0 0
\(208\) −70611.9 −0.113167
\(209\) 726638. 1.15067
\(210\) 0 0
\(211\) −658407. −1.01809 −0.509047 0.860739i \(-0.670002\pi\)
−0.509047 + 0.860739i \(0.670002\pi\)
\(212\) 808630. 1.23569
\(213\) 0 0
\(214\) 1.00461e6 1.49956
\(215\) −869864. −1.28338
\(216\) 0 0
\(217\) −167879. −0.242018
\(218\) −903614. −1.28778
\(219\) 0 0
\(220\) −1.70652e6 −2.37714
\(221\) 153201. 0.211000
\(222\) 0 0
\(223\) 79895.6 0.107587 0.0537936 0.998552i \(-0.482869\pi\)
0.0537936 + 0.998552i \(0.482869\pi\)
\(224\) −399400. −0.531849
\(225\) 0 0
\(226\) 521573. 0.679273
\(227\) −716111. −0.922393 −0.461196 0.887298i \(-0.652580\pi\)
−0.461196 + 0.887298i \(0.652580\pi\)
\(228\) 0 0
\(229\) −581299. −0.732506 −0.366253 0.930515i \(-0.619360\pi\)
−0.366253 + 0.930515i \(0.619360\pi\)
\(230\) 348770. 0.434730
\(231\) 0 0
\(232\) −1.12067e6 −1.36697
\(233\) −122734. −0.148107 −0.0740534 0.997254i \(-0.523594\pi\)
−0.0740534 + 0.997254i \(0.523594\pi\)
\(234\) 0 0
\(235\) 1.68343e6 1.98850
\(236\) −2.64500e6 −3.09133
\(237\) 0 0
\(238\) −496380. −0.568031
\(239\) −210076. −0.237893 −0.118946 0.992901i \(-0.537952\pi\)
−0.118946 + 0.992901i \(0.537952\pi\)
\(240\) 0 0
\(241\) 1.23224e6 1.36664 0.683319 0.730120i \(-0.260536\pi\)
0.683319 + 0.730120i \(0.260536\pi\)
\(242\) −277772. −0.304894
\(243\) 0 0
\(244\) −850553. −0.914590
\(245\) 617656. 0.657402
\(246\) 0 0
\(247\) −430670. −0.449162
\(248\) −409471. −0.422760
\(249\) 0 0
\(250\) −841849. −0.851891
\(251\) 545986. 0.547012 0.273506 0.961870i \(-0.411817\pi\)
0.273506 + 0.961870i \(0.411817\pi\)
\(252\) 0 0
\(253\) 231048. 0.226934
\(254\) −1.56914e6 −1.52608
\(255\) 0 0
\(256\) −1.45779e6 −1.39026
\(257\) −556705. −0.525765 −0.262883 0.964828i \(-0.584673\pi\)
−0.262883 + 0.964828i \(0.584673\pi\)
\(258\) 0 0
\(259\) −79354.3 −0.0735057
\(260\) 1.01144e6 0.927909
\(261\) 0 0
\(262\) 1.21284e6 1.09157
\(263\) −1.65392e6 −1.47443 −0.737217 0.675656i \(-0.763860\pi\)
−0.737217 + 0.675656i \(0.763860\pi\)
\(264\) 0 0
\(265\) −1.02923e6 −0.900324
\(266\) 1.39539e6 1.20919
\(267\) 0 0
\(268\) −2.28128e6 −1.94018
\(269\) 2.06545e6 1.74034 0.870168 0.492755i \(-0.164010\pi\)
0.870168 + 0.492755i \(0.164010\pi\)
\(270\) 0 0
\(271\) 708326. 0.585881 0.292941 0.956131i \(-0.405366\pi\)
0.292941 + 0.956131i \(0.405366\pi\)
\(272\) −161434. −0.132304
\(273\) 0 0
\(274\) −2.11946e6 −1.70549
\(275\) 807190. 0.643641
\(276\) 0 0
\(277\) −17729.4 −0.0138833 −0.00694167 0.999976i \(-0.502210\pi\)
−0.00694167 + 0.999976i \(0.502210\pi\)
\(278\) 3.91890e6 3.04125
\(279\) 0 0
\(280\) −1.38437e6 −1.05526
\(281\) −754660. −0.570145 −0.285073 0.958506i \(-0.592018\pi\)
−0.285073 + 0.958506i \(0.592018\pi\)
\(282\) 0 0
\(283\) −417633. −0.309976 −0.154988 0.987916i \(-0.549534\pi\)
−0.154988 + 0.987916i \(0.549534\pi\)
\(284\) 2.52694e6 1.85909
\(285\) 0 0
\(286\) 1.05703e6 0.764140
\(287\) −1.65166e6 −1.18363
\(288\) 0 0
\(289\) −1.06961e6 −0.753320
\(290\) 3.37659e6 2.35767
\(291\) 0 0
\(292\) −437604. −0.300348
\(293\) 2.68010e6 1.82382 0.911908 0.410394i \(-0.134609\pi\)
0.911908 + 0.410394i \(0.134609\pi\)
\(294\) 0 0
\(295\) 3.36658e6 2.25234
\(296\) −193552. −0.128401
\(297\) 0 0
\(298\) 4.70511e6 3.06923
\(299\) −136940. −0.0885831
\(300\) 0 0
\(301\) −1.10661e6 −0.704007
\(302\) −4.84229e6 −3.05515
\(303\) 0 0
\(304\) 453813. 0.281639
\(305\) 1.08259e6 0.666369
\(306\) 0 0
\(307\) −2.42927e6 −1.47106 −0.735528 0.677494i \(-0.763066\pi\)
−0.735528 + 0.677494i \(0.763066\pi\)
\(308\) −2.17097e6 −1.30400
\(309\) 0 0
\(310\) 1.23374e6 0.729155
\(311\) −1.71783e6 −1.00712 −0.503559 0.863961i \(-0.667976\pi\)
−0.503559 + 0.863961i \(0.667976\pi\)
\(312\) 0 0
\(313\) 1.56583e6 0.903406 0.451703 0.892168i \(-0.350817\pi\)
0.451703 + 0.892168i \(0.350817\pi\)
\(314\) 371606. 0.212696
\(315\) 0 0
\(316\) 3.95789e6 2.22970
\(317\) −673750. −0.376574 −0.188287 0.982114i \(-0.560294\pi\)
−0.188287 + 0.982114i \(0.560294\pi\)
\(318\) 0 0
\(319\) 2.23688e6 1.23074
\(320\) 3.55074e6 1.93840
\(321\) 0 0
\(322\) 443691. 0.238474
\(323\) −984603. −0.525115
\(324\) 0 0
\(325\) −478413. −0.251243
\(326\) 1.47554e6 0.768967
\(327\) 0 0
\(328\) −4.02854e6 −2.06759
\(329\) 2.14159e6 1.09081
\(330\) 0 0
\(331\) 1.69768e6 0.851699 0.425850 0.904794i \(-0.359975\pi\)
0.425850 + 0.904794i \(0.359975\pi\)
\(332\) −6.23754e6 −3.10576
\(333\) 0 0
\(334\) −944259. −0.463153
\(335\) 2.90363e6 1.41361
\(336\) 0 0
\(337\) −2.37281e6 −1.13812 −0.569061 0.822295i \(-0.692693\pi\)
−0.569061 + 0.822295i \(0.692693\pi\)
\(338\) 2.84476e6 1.35442
\(339\) 0 0
\(340\) 2.31236e6 1.08482
\(341\) 817310. 0.380628
\(342\) 0 0
\(343\) 2.29357e6 1.05263
\(344\) −2.69910e6 −1.22977
\(345\) 0 0
\(346\) 575609. 0.258486
\(347\) −3.98316e6 −1.77584 −0.887921 0.459996i \(-0.847851\pi\)
−0.887921 + 0.459996i \(0.847851\pi\)
\(348\) 0 0
\(349\) −2.10463e6 −0.924935 −0.462468 0.886636i \(-0.653036\pi\)
−0.462468 + 0.886636i \(0.653036\pi\)
\(350\) 1.55008e6 0.676370
\(351\) 0 0
\(352\) 1.94446e6 0.836453
\(353\) −3.41107e6 −1.45698 −0.728490 0.685056i \(-0.759778\pi\)
−0.728490 + 0.685056i \(0.759778\pi\)
\(354\) 0 0
\(355\) −3.21631e6 −1.35453
\(356\) −7.63734e6 −3.19387
\(357\) 0 0
\(358\) −5.70795e6 −2.35382
\(359\) 1.86760e6 0.764800 0.382400 0.923997i \(-0.375098\pi\)
0.382400 + 0.923997i \(0.375098\pi\)
\(360\) 0 0
\(361\) 291759. 0.117830
\(362\) −1.13477e6 −0.455132
\(363\) 0 0
\(364\) 1.28671e6 0.509011
\(365\) 556987. 0.218833
\(366\) 0 0
\(367\) −437210. −0.169444 −0.0847218 0.996405i \(-0.527000\pi\)
−0.0847218 + 0.996405i \(0.527000\pi\)
\(368\) 144298. 0.0555445
\(369\) 0 0
\(370\) 583173. 0.221459
\(371\) −1.30935e6 −0.493879
\(372\) 0 0
\(373\) −921734. −0.343031 −0.171516 0.985181i \(-0.554866\pi\)
−0.171516 + 0.985181i \(0.554866\pi\)
\(374\) 2.41660e6 0.893357
\(375\) 0 0
\(376\) 5.22352e6 1.90543
\(377\) −1.32577e6 −0.480414
\(378\) 0 0
\(379\) −3.80141e6 −1.35940 −0.679699 0.733491i \(-0.737889\pi\)
−0.679699 + 0.733491i \(0.737889\pi\)
\(380\) −6.50036e6 −2.30929
\(381\) 0 0
\(382\) −2.75406e6 −0.965639
\(383\) 4.52311e6 1.57558 0.787790 0.615944i \(-0.211225\pi\)
0.787790 + 0.615944i \(0.211225\pi\)
\(384\) 0 0
\(385\) 2.76323e6 0.950090
\(386\) 83165.0 0.0284101
\(387\) 0 0
\(388\) 2.30928e6 0.778749
\(389\) −4.48168e6 −1.50164 −0.750822 0.660505i \(-0.770342\pi\)
−0.750822 + 0.660505i \(0.770342\pi\)
\(390\) 0 0
\(391\) −313072. −0.103563
\(392\) 1.91652e6 0.629940
\(393\) 0 0
\(394\) −6.52671e6 −2.11814
\(395\) −5.03763e6 −1.62455
\(396\) 0 0
\(397\) 1.76656e6 0.562539 0.281269 0.959629i \(-0.409245\pi\)
0.281269 + 0.959629i \(0.409245\pi\)
\(398\) 4.98559e6 1.57764
\(399\) 0 0
\(400\) 504121. 0.157538
\(401\) 522373. 0.162226 0.0811128 0.996705i \(-0.474153\pi\)
0.0811128 + 0.996705i \(0.474153\pi\)
\(402\) 0 0
\(403\) −484411. −0.148577
\(404\) −2.05555e6 −0.626579
\(405\) 0 0
\(406\) 4.29557e6 1.29332
\(407\) 386332. 0.115604
\(408\) 0 0
\(409\) −1.60642e6 −0.474845 −0.237422 0.971407i \(-0.576303\pi\)
−0.237422 + 0.971407i \(0.576303\pi\)
\(410\) 1.21380e7 3.56606
\(411\) 0 0
\(412\) −6.83275e6 −1.98314
\(413\) 4.28283e6 1.23554
\(414\) 0 0
\(415\) 7.93919e6 2.26285
\(416\) −1.15246e6 −0.326507
\(417\) 0 0
\(418\) −6.79339e6 −1.90172
\(419\) 5.30658e6 1.47666 0.738329 0.674441i \(-0.235615\pi\)
0.738329 + 0.674441i \(0.235615\pi\)
\(420\) 0 0
\(421\) −2.30575e6 −0.634025 −0.317012 0.948421i \(-0.602680\pi\)
−0.317012 + 0.948421i \(0.602680\pi\)
\(422\) 6.15549e6 1.68260
\(423\) 0 0
\(424\) −3.19361e6 −0.862714
\(425\) −1.09375e6 −0.293729
\(426\) 0 0
\(427\) 1.37723e6 0.365541
\(428\) −5.95360e6 −1.57098
\(429\) 0 0
\(430\) 8.13242e6 2.12104
\(431\) 1.27091e6 0.329549 0.164775 0.986331i \(-0.447310\pi\)
0.164775 + 0.986331i \(0.447310\pi\)
\(432\) 0 0
\(433\) −3.71880e6 −0.953199 −0.476599 0.879121i \(-0.658131\pi\)
−0.476599 + 0.879121i \(0.658131\pi\)
\(434\) 1.56952e6 0.399983
\(435\) 0 0
\(436\) 5.35507e6 1.34911
\(437\) 880091. 0.220457
\(438\) 0 0
\(439\) −3.51069e6 −0.869423 −0.434711 0.900570i \(-0.643150\pi\)
−0.434711 + 0.900570i \(0.643150\pi\)
\(440\) 6.73974e6 1.65963
\(441\) 0 0
\(442\) −1.43229e6 −0.348719
\(443\) −2.67040e6 −0.646497 −0.323248 0.946314i \(-0.604775\pi\)
−0.323248 + 0.946314i \(0.604775\pi\)
\(444\) 0 0
\(445\) 9.72088e6 2.32705
\(446\) −746950. −0.177809
\(447\) 0 0
\(448\) 4.51711e6 1.06332
\(449\) −808771. −0.189326 −0.0946628 0.995509i \(-0.530177\pi\)
−0.0946628 + 0.995509i \(0.530177\pi\)
\(450\) 0 0
\(451\) 8.04103e6 1.86153
\(452\) −3.09099e6 −0.711625
\(453\) 0 0
\(454\) 6.69498e6 1.52444
\(455\) −1.63774e6 −0.370864
\(456\) 0 0
\(457\) −6.03865e6 −1.35254 −0.676269 0.736655i \(-0.736404\pi\)
−0.676269 + 0.736655i \(0.736404\pi\)
\(458\) 5.43461e6 1.21061
\(459\) 0 0
\(460\) −2.06691e6 −0.455435
\(461\) 6.06334e6 1.32880 0.664399 0.747378i \(-0.268687\pi\)
0.664399 + 0.747378i \(0.268687\pi\)
\(462\) 0 0
\(463\) −987185. −0.214016 −0.107008 0.994258i \(-0.534127\pi\)
−0.107008 + 0.994258i \(0.534127\pi\)
\(464\) 1.39701e6 0.301235
\(465\) 0 0
\(466\) 1.14745e6 0.244776
\(467\) 2.75869e6 0.585344 0.292672 0.956213i \(-0.405456\pi\)
0.292672 + 0.956213i \(0.405456\pi\)
\(468\) 0 0
\(469\) 3.69389e6 0.775446
\(470\) −1.57385e7 −3.28639
\(471\) 0 0
\(472\) 1.04462e7 2.15825
\(473\) 5.38745e6 1.10721
\(474\) 0 0
\(475\) 3.07469e6 0.625270
\(476\) 2.94169e6 0.595085
\(477\) 0 0
\(478\) 1.96402e6 0.393165
\(479\) 1.43871e6 0.286507 0.143254 0.989686i \(-0.454244\pi\)
0.143254 + 0.989686i \(0.454244\pi\)
\(480\) 0 0
\(481\) −228975. −0.0451258
\(482\) −1.15203e7 −2.25864
\(483\) 0 0
\(484\) 1.64615e6 0.319416
\(485\) −2.93927e6 −0.567395
\(486\) 0 0
\(487\) −9.54793e6 −1.82426 −0.912130 0.409901i \(-0.865563\pi\)
−0.912130 + 0.409901i \(0.865563\pi\)
\(488\) 3.35917e6 0.638532
\(489\) 0 0
\(490\) −5.77451e6 −1.08649
\(491\) −8.94131e6 −1.67378 −0.836889 0.547373i \(-0.815628\pi\)
−0.836889 + 0.547373i \(0.815628\pi\)
\(492\) 0 0
\(493\) −3.03099e6 −0.561652
\(494\) 4.02637e6 0.742329
\(495\) 0 0
\(496\) 510441. 0.0931626
\(497\) −4.09167e6 −0.743035
\(498\) 0 0
\(499\) 2.34135e6 0.420934 0.210467 0.977601i \(-0.432501\pi\)
0.210467 + 0.977601i \(0.432501\pi\)
\(500\) 4.98903e6 0.892465
\(501\) 0 0
\(502\) −5.10446e6 −0.904046
\(503\) −41307.7 −0.00727966 −0.00363983 0.999993i \(-0.501159\pi\)
−0.00363983 + 0.999993i \(0.501159\pi\)
\(504\) 0 0
\(505\) 2.61633e6 0.456524
\(506\) −2.16008e6 −0.375054
\(507\) 0 0
\(508\) 9.29918e6 1.59877
\(509\) −3.09166e6 −0.528929 −0.264464 0.964395i \(-0.585195\pi\)
−0.264464 + 0.964395i \(0.585195\pi\)
\(510\) 0 0
\(511\) 708576. 0.120042
\(512\) 3.12440e6 0.526735
\(513\) 0 0
\(514\) 5.20467e6 0.868932
\(515\) 8.69678e6 1.44491
\(516\) 0 0
\(517\) −1.04262e7 −1.71554
\(518\) 741890. 0.121483
\(519\) 0 0
\(520\) −3.99457e6 −0.647831
\(521\) −6.02002e6 −0.971635 −0.485818 0.874060i \(-0.661478\pi\)
−0.485818 + 0.874060i \(0.661478\pi\)
\(522\) 0 0
\(523\) −6.39458e6 −1.02225 −0.511125 0.859506i \(-0.670771\pi\)
−0.511125 + 0.859506i \(0.670771\pi\)
\(524\) −7.18764e6 −1.14356
\(525\) 0 0
\(526\) 1.54626e7 2.43679
\(527\) −1.10746e6 −0.173701
\(528\) 0 0
\(529\) 279841. 0.0434783
\(530\) 9.62237e6 1.48796
\(531\) 0 0
\(532\) −8.26950e6 −1.26678
\(533\) −4.76583e6 −0.726642
\(534\) 0 0
\(535\) 7.57779e6 1.14461
\(536\) 9.00969e6 1.35456
\(537\) 0 0
\(538\) −1.93100e7 −2.87625
\(539\) −3.82541e6 −0.567161
\(540\) 0 0
\(541\) −3.24248e6 −0.476304 −0.238152 0.971228i \(-0.576542\pi\)
−0.238152 + 0.971228i \(0.576542\pi\)
\(542\) −6.62219e6 −0.968286
\(543\) 0 0
\(544\) −2.63476e6 −0.381719
\(545\) −6.81598e6 −0.982963
\(546\) 0 0
\(547\) 9.39508e6 1.34255 0.671277 0.741206i \(-0.265746\pi\)
0.671277 + 0.741206i \(0.265746\pi\)
\(548\) 1.25605e7 1.78671
\(549\) 0 0
\(550\) −7.54648e6 −1.06375
\(551\) 8.52055e6 1.19561
\(552\) 0 0
\(553\) −6.40868e6 −0.891160
\(554\) 165753. 0.0229450
\(555\) 0 0
\(556\) −2.32245e7 −3.18610
\(557\) −2.95696e6 −0.403839 −0.201919 0.979402i \(-0.564718\pi\)
−0.201919 + 0.979402i \(0.564718\pi\)
\(558\) 0 0
\(559\) −3.19308e6 −0.432196
\(560\) 1.72574e6 0.232544
\(561\) 0 0
\(562\) 7.05538e6 0.942279
\(563\) 1.35314e7 1.79917 0.899584 0.436747i \(-0.143870\pi\)
0.899584 + 0.436747i \(0.143870\pi\)
\(564\) 0 0
\(565\) 3.93424e6 0.518489
\(566\) 3.90448e6 0.512297
\(567\) 0 0
\(568\) −9.97991e6 −1.29794
\(569\) −1.32776e7 −1.71924 −0.859622 0.510931i \(-0.829301\pi\)
−0.859622 + 0.510931i \(0.829301\pi\)
\(570\) 0 0
\(571\) 7.74960e6 0.994693 0.497346 0.867552i \(-0.334308\pi\)
0.497346 + 0.867552i \(0.334308\pi\)
\(572\) −6.26427e6 −0.800535
\(573\) 0 0
\(574\) 1.54415e7 1.95619
\(575\) 977654. 0.123315
\(576\) 0 0
\(577\) −4.83479e6 −0.604558 −0.302279 0.953220i \(-0.597747\pi\)
−0.302279 + 0.953220i \(0.597747\pi\)
\(578\) 9.99984e6 1.24501
\(579\) 0 0
\(580\) −2.00106e7 −2.46997
\(581\) 1.00999e7 1.24130
\(582\) 0 0
\(583\) 6.37448e6 0.776736
\(584\) 1.72827e6 0.209691
\(585\) 0 0
\(586\) −2.50564e7 −3.01422
\(587\) −5.13380e6 −0.614955 −0.307478 0.951555i \(-0.599485\pi\)
−0.307478 + 0.951555i \(0.599485\pi\)
\(588\) 0 0
\(589\) 3.11324e6 0.369764
\(590\) −3.14744e7 −3.72244
\(591\) 0 0
\(592\) 241279. 0.0282953
\(593\) −1.29134e7 −1.50801 −0.754003 0.656871i \(-0.771879\pi\)
−0.754003 + 0.656871i \(0.771879\pi\)
\(594\) 0 0
\(595\) −3.74421e6 −0.433578
\(596\) −2.78838e7 −3.21541
\(597\) 0 0
\(598\) 1.28026e6 0.146401
\(599\) 5.79980e6 0.660460 0.330230 0.943901i \(-0.392874\pi\)
0.330230 + 0.943901i \(0.392874\pi\)
\(600\) 0 0
\(601\) 1.06993e7 1.20829 0.604144 0.796875i \(-0.293515\pi\)
0.604144 + 0.796875i \(0.293515\pi\)
\(602\) 1.03457e7 1.16351
\(603\) 0 0
\(604\) 2.86968e7 3.20067
\(605\) −2.09524e6 −0.232726
\(606\) 0 0
\(607\) −1.48509e7 −1.63600 −0.817998 0.575221i \(-0.804916\pi\)
−0.817998 + 0.575221i \(0.804916\pi\)
\(608\) 7.40669e6 0.812578
\(609\) 0 0
\(610\) −1.01212e7 −1.10131
\(611\) 6.17951e6 0.669655
\(612\) 0 0
\(613\) −7.64415e6 −0.821633 −0.410816 0.911718i \(-0.634756\pi\)
−0.410816 + 0.911718i \(0.634756\pi\)
\(614\) 2.27114e7 2.43121
\(615\) 0 0
\(616\) 8.57402e6 0.910401
\(617\) 8.02025e6 0.848155 0.424077 0.905626i \(-0.360598\pi\)
0.424077 + 0.905626i \(0.360598\pi\)
\(618\) 0 0
\(619\) 9.46459e6 0.992831 0.496416 0.868085i \(-0.334649\pi\)
0.496416 + 0.868085i \(0.334649\pi\)
\(620\) −7.31150e6 −0.763883
\(621\) 0 0
\(622\) 1.60602e7 1.66446
\(623\) 1.23665e7 1.27652
\(624\) 0 0
\(625\) −1.21255e7 −1.24165
\(626\) −1.46390e7 −1.49306
\(627\) 0 0
\(628\) −2.20224e6 −0.222826
\(629\) −523484. −0.0527566
\(630\) 0 0
\(631\) 8.76525e6 0.876377 0.438189 0.898883i \(-0.355620\pi\)
0.438189 + 0.898883i \(0.355620\pi\)
\(632\) −1.56313e7 −1.55669
\(633\) 0 0
\(634\) 6.29894e6 0.622364
\(635\) −1.18361e7 −1.16486
\(636\) 0 0
\(637\) 2.26728e6 0.221389
\(638\) −2.09127e7 −2.03404
\(639\) 0 0
\(640\) −2.31496e7 −2.23406
\(641\) 8.04677e6 0.773529 0.386764 0.922179i \(-0.373593\pi\)
0.386764 + 0.922179i \(0.373593\pi\)
\(642\) 0 0
\(643\) 1.81157e7 1.72794 0.863970 0.503543i \(-0.167970\pi\)
0.863970 + 0.503543i \(0.167970\pi\)
\(644\) −2.62944e6 −0.249832
\(645\) 0 0
\(646\) 9.20513e6 0.867858
\(647\) −6.09047e6 −0.571992 −0.285996 0.958231i \(-0.592324\pi\)
−0.285996 + 0.958231i \(0.592324\pi\)
\(648\) 0 0
\(649\) −2.08507e7 −1.94316
\(650\) 4.47272e6 0.415230
\(651\) 0 0
\(652\) −8.74448e6 −0.805591
\(653\) −1.73408e7 −1.59142 −0.795712 0.605675i \(-0.792903\pi\)
−0.795712 + 0.605675i \(0.792903\pi\)
\(654\) 0 0
\(655\) 9.14850e6 0.833195
\(656\) 5.02193e6 0.455629
\(657\) 0 0
\(658\) −2.00219e7 −1.80277
\(659\) −1.27618e7 −1.14471 −0.572357 0.820004i \(-0.693971\pi\)
−0.572357 + 0.820004i \(0.693971\pi\)
\(660\) 0 0
\(661\) −6.44195e6 −0.573474 −0.286737 0.958009i \(-0.592571\pi\)
−0.286737 + 0.958009i \(0.592571\pi\)
\(662\) −1.58718e7 −1.40760
\(663\) 0 0
\(664\) 2.46345e7 2.16832
\(665\) 1.05255e7 0.922972
\(666\) 0 0
\(667\) 2.70926e6 0.235796
\(668\) 5.59594e6 0.485213
\(669\) 0 0
\(670\) −2.71463e7 −2.33627
\(671\) −6.70496e6 −0.574897
\(672\) 0 0
\(673\) 8.64864e6 0.736055 0.368028 0.929815i \(-0.380033\pi\)
0.368028 + 0.929815i \(0.380033\pi\)
\(674\) 2.21836e7 1.88097
\(675\) 0 0
\(676\) −1.68588e7 −1.41893
\(677\) 1.22020e7 1.02320 0.511600 0.859223i \(-0.329053\pi\)
0.511600 + 0.859223i \(0.329053\pi\)
\(678\) 0 0
\(679\) −3.73923e6 −0.311249
\(680\) −9.13242e6 −0.757380
\(681\) 0 0
\(682\) −7.64110e6 −0.629064
\(683\) 1.10784e7 0.908708 0.454354 0.890821i \(-0.349870\pi\)
0.454354 + 0.890821i \(0.349870\pi\)
\(684\) 0 0
\(685\) −1.59871e7 −1.30180
\(686\) −2.14427e7 −1.73968
\(687\) 0 0
\(688\) 3.36466e6 0.271001
\(689\) −3.77809e6 −0.303196
\(690\) 0 0
\(691\) −1.24814e7 −0.994415 −0.497207 0.867632i \(-0.665641\pi\)
−0.497207 + 0.867632i \(0.665641\pi\)
\(692\) −3.41122e6 −0.270797
\(693\) 0 0
\(694\) 3.72389e7 2.93493
\(695\) 2.95604e7 2.32139
\(696\) 0 0
\(697\) −1.08957e7 −0.849518
\(698\) 1.96763e7 1.52864
\(699\) 0 0
\(700\) −9.18622e6 −0.708585
\(701\) 4.71570e6 0.362452 0.181226 0.983441i \(-0.441993\pi\)
0.181226 + 0.983441i \(0.441993\pi\)
\(702\) 0 0
\(703\) 1.47159e6 0.112305
\(704\) −2.19913e7 −1.67232
\(705\) 0 0
\(706\) 3.18903e7 2.40795
\(707\) 3.32839e6 0.250430
\(708\) 0 0
\(709\) 1.05958e7 0.791620 0.395810 0.918332i \(-0.370464\pi\)
0.395810 + 0.918332i \(0.370464\pi\)
\(710\) 3.00696e7 2.23863
\(711\) 0 0
\(712\) 3.01629e7 2.22984
\(713\) 989912. 0.0729244
\(714\) 0 0
\(715\) 7.97322e6 0.583268
\(716\) 3.38269e7 2.46593
\(717\) 0 0
\(718\) −1.74603e7 −1.26398
\(719\) −2.95783e6 −0.213379 −0.106689 0.994292i \(-0.534025\pi\)
−0.106689 + 0.994292i \(0.534025\pi\)
\(720\) 0 0
\(721\) 1.10637e7 0.792615
\(722\) −2.72768e6 −0.194738
\(723\) 0 0
\(724\) 6.72499e6 0.476810
\(725\) 9.46510e6 0.668776
\(726\) 0 0
\(727\) −1.30768e7 −0.917625 −0.458813 0.888533i \(-0.651725\pi\)
−0.458813 + 0.888533i \(0.651725\pi\)
\(728\) −5.08173e6 −0.355372
\(729\) 0 0
\(730\) −5.20731e6 −0.361665
\(731\) −7.30005e6 −0.505280
\(732\) 0 0
\(733\) 5.06819e6 0.348412 0.174206 0.984709i \(-0.444264\pi\)
0.174206 + 0.984709i \(0.444264\pi\)
\(734\) 4.08751e6 0.280039
\(735\) 0 0
\(736\) 2.35509e6 0.160256
\(737\) −1.79835e7 −1.21956
\(738\) 0 0
\(739\) 5.39832e6 0.363620 0.181810 0.983334i \(-0.441804\pi\)
0.181810 + 0.983334i \(0.441804\pi\)
\(740\) −3.45605e6 −0.232007
\(741\) 0 0
\(742\) 1.22412e7 0.816233
\(743\) −3.71690e6 −0.247007 −0.123503 0.992344i \(-0.539413\pi\)
−0.123503 + 0.992344i \(0.539413\pi\)
\(744\) 0 0
\(745\) 3.54908e7 2.34274
\(746\) 8.61736e6 0.566927
\(747\) 0 0
\(748\) −1.43214e7 −0.935906
\(749\) 9.64017e6 0.627885
\(750\) 0 0
\(751\) 1.00711e7 0.651594 0.325797 0.945440i \(-0.394367\pi\)
0.325797 + 0.945440i \(0.394367\pi\)
\(752\) −6.51157e6 −0.419896
\(753\) 0 0
\(754\) 1.23947e7 0.793979
\(755\) −3.65255e7 −2.33200
\(756\) 0 0
\(757\) −8.49996e6 −0.539110 −0.269555 0.962985i \(-0.586877\pi\)
−0.269555 + 0.962985i \(0.586877\pi\)
\(758\) 3.55397e7 2.24667
\(759\) 0 0
\(760\) 2.56725e7 1.61226
\(761\) −2.62780e7 −1.64487 −0.822434 0.568861i \(-0.807384\pi\)
−0.822434 + 0.568861i \(0.807384\pi\)
\(762\) 0 0
\(763\) −8.67102e6 −0.539211
\(764\) 1.63213e7 1.01163
\(765\) 0 0
\(766\) −4.22869e7 −2.60396
\(767\) 1.23580e7 0.758506
\(768\) 0 0
\(769\) 899889. 0.0548748 0.0274374 0.999624i \(-0.491265\pi\)
0.0274374 + 0.999624i \(0.491265\pi\)
\(770\) −2.58336e7 −1.57021
\(771\) 0 0
\(772\) −492859. −0.0297632
\(773\) 1.33758e7 0.805140 0.402570 0.915389i \(-0.368117\pi\)
0.402570 + 0.915389i \(0.368117\pi\)
\(774\) 0 0
\(775\) 3.45836e6 0.206831
\(776\) −9.12028e6 −0.543693
\(777\) 0 0
\(778\) 4.18996e7 2.48177
\(779\) 3.06293e7 1.80840
\(780\) 0 0
\(781\) 1.99200e7 1.16859
\(782\) 2.92694e6 0.171158
\(783\) 0 0
\(784\) −2.38911e6 −0.138818
\(785\) 2.80304e6 0.162351
\(786\) 0 0
\(787\) 1.67690e7 0.965098 0.482549 0.875869i \(-0.339711\pi\)
0.482549 + 0.875869i \(0.339711\pi\)
\(788\) 3.86791e7 2.21902
\(789\) 0 0
\(790\) 4.70972e7 2.68490
\(791\) 5.00498e6 0.284421
\(792\) 0 0
\(793\) 3.97396e6 0.224409
\(794\) −1.65157e7 −0.929707
\(795\) 0 0
\(796\) −2.95460e7 −1.65278
\(797\) −2.78280e7 −1.55180 −0.775902 0.630854i \(-0.782705\pi\)
−0.775902 + 0.630854i \(0.782705\pi\)
\(798\) 0 0
\(799\) 1.41277e7 0.782894
\(800\) 8.22776e6 0.454524
\(801\) 0 0
\(802\) −4.88370e6 −0.268110
\(803\) −3.44966e6 −0.188794
\(804\) 0 0
\(805\) 3.34677e6 0.182027
\(806\) 4.52880e6 0.245553
\(807\) 0 0
\(808\) 8.11821e6 0.437454
\(809\) 1.98606e7 1.06689 0.533447 0.845834i \(-0.320897\pi\)
0.533447 + 0.845834i \(0.320897\pi\)
\(810\) 0 0
\(811\) 1.95245e7 1.04238 0.521192 0.853439i \(-0.325488\pi\)
0.521192 + 0.853439i \(0.325488\pi\)
\(812\) −2.54568e7 −1.35492
\(813\) 0 0
\(814\) −3.61185e6 −0.191059
\(815\) 1.11301e7 0.586953
\(816\) 0 0
\(817\) 2.05215e7 1.07561
\(818\) 1.50186e7 0.784775
\(819\) 0 0
\(820\) −7.19335e7 −3.73591
\(821\) 2.39444e7 1.23978 0.619891 0.784688i \(-0.287177\pi\)
0.619891 + 0.784688i \(0.287177\pi\)
\(822\) 0 0
\(823\) −2.78310e7 −1.43229 −0.716143 0.697953i \(-0.754094\pi\)
−0.716143 + 0.697953i \(0.754094\pi\)
\(824\) 2.69853e7 1.38455
\(825\) 0 0
\(826\) −4.00405e7 −2.04197
\(827\) 1.94204e7 0.987405 0.493703 0.869631i \(-0.335643\pi\)
0.493703 + 0.869631i \(0.335643\pi\)
\(828\) 0 0
\(829\) 2.66039e7 1.34449 0.672247 0.740327i \(-0.265329\pi\)
0.672247 + 0.740327i \(0.265329\pi\)
\(830\) −7.42241e7 −3.73981
\(831\) 0 0
\(832\) 1.30340e7 0.652784
\(833\) 5.18348e6 0.258826
\(834\) 0 0
\(835\) −7.12257e6 −0.353525
\(836\) 4.02596e7 1.99229
\(837\) 0 0
\(838\) −4.96117e7 −2.44047
\(839\) 1.41085e7 0.691954 0.345977 0.938243i \(-0.387547\pi\)
0.345977 + 0.938243i \(0.387547\pi\)
\(840\) 0 0
\(841\) 5.71843e6 0.278796
\(842\) 2.15566e7 1.04785
\(843\) 0 0
\(844\) −3.64792e7 −1.76274
\(845\) 2.14581e7 1.03383
\(846\) 0 0
\(847\) −2.66548e6 −0.127664
\(848\) 3.98111e6 0.190114
\(849\) 0 0
\(850\) 1.02256e7 0.485445
\(851\) 467918. 0.0221486
\(852\) 0 0
\(853\) −1.87882e7 −0.884122 −0.442061 0.896985i \(-0.645752\pi\)
−0.442061 + 0.896985i \(0.645752\pi\)
\(854\) −1.28758e7 −0.604130
\(855\) 0 0
\(856\) 2.35131e7 1.09680
\(857\) −3.67369e7 −1.70864 −0.854320 0.519748i \(-0.826026\pi\)
−0.854320 + 0.519748i \(0.826026\pi\)
\(858\) 0 0
\(859\) 2.03228e6 0.0939723 0.0469861 0.998896i \(-0.485038\pi\)
0.0469861 + 0.998896i \(0.485038\pi\)
\(860\) −4.81950e7 −2.22206
\(861\) 0 0
\(862\) −1.18818e7 −0.544646
\(863\) 1.21735e7 0.556400 0.278200 0.960523i \(-0.410262\pi\)
0.278200 + 0.960523i \(0.410262\pi\)
\(864\) 0 0
\(865\) 4.34183e6 0.197303
\(866\) 3.47674e7 1.57535
\(867\) 0 0
\(868\) −9.30140e6 −0.419034
\(869\) 3.12003e7 1.40155
\(870\) 0 0
\(871\) 1.06586e7 0.476053
\(872\) −2.11493e7 −0.941901
\(873\) 0 0
\(874\) −8.22804e6 −0.364349
\(875\) −8.07833e6 −0.356698
\(876\) 0 0
\(877\) 4.13453e7 1.81521 0.907605 0.419825i \(-0.137909\pi\)
0.907605 + 0.419825i \(0.137909\pi\)
\(878\) 3.28217e7 1.43689
\(879\) 0 0
\(880\) −8.40166e6 −0.365728
\(881\) −1.92417e7 −0.835227 −0.417613 0.908625i \(-0.637133\pi\)
−0.417613 + 0.908625i \(0.637133\pi\)
\(882\) 0 0
\(883\) 4.59010e6 0.198117 0.0990583 0.995082i \(-0.468417\pi\)
0.0990583 + 0.995082i \(0.468417\pi\)
\(884\) 8.48815e6 0.365328
\(885\) 0 0
\(886\) 2.49657e7 1.06846
\(887\) 1.34822e7 0.575374 0.287687 0.957724i \(-0.407114\pi\)
0.287687 + 0.957724i \(0.407114\pi\)
\(888\) 0 0
\(889\) −1.50574e7 −0.638992
\(890\) −9.08813e7 −3.84591
\(891\) 0 0
\(892\) 4.42663e6 0.186278
\(893\) −3.97149e7 −1.66657
\(894\) 0 0
\(895\) −4.30552e7 −1.79667
\(896\) −2.94500e7 −1.22551
\(897\) 0 0
\(898\) 7.56126e6 0.312898
\(899\) 9.58377e6 0.395492
\(900\) 0 0
\(901\) −8.63750e6 −0.354467
\(902\) −7.51762e7 −3.07655
\(903\) 0 0
\(904\) 1.22076e7 0.496830
\(905\) −8.55962e6 −0.347403
\(906\) 0 0
\(907\) 5.13039e6 0.207077 0.103539 0.994625i \(-0.466983\pi\)
0.103539 + 0.994625i \(0.466983\pi\)
\(908\) −3.96763e7 −1.59704
\(909\) 0 0
\(910\) 1.53113e7 0.612927
\(911\) −3.88471e7 −1.55082 −0.775411 0.631456i \(-0.782457\pi\)
−0.775411 + 0.631456i \(0.782457\pi\)
\(912\) 0 0
\(913\) −4.91709e7 −1.95223
\(914\) 5.64558e7 2.23534
\(915\) 0 0
\(916\) −3.22071e7 −1.26827
\(917\) 1.16384e7 0.457055
\(918\) 0 0
\(919\) 2.43482e7 0.950993 0.475496 0.879718i \(-0.342268\pi\)
0.475496 + 0.879718i \(0.342268\pi\)
\(920\) 8.16305e6 0.317968
\(921\) 0 0
\(922\) −5.66866e7 −2.19610
\(923\) −1.18064e7 −0.456156
\(924\) 0 0
\(925\) 1.63472e6 0.0628188
\(926\) 9.22927e6 0.353704
\(927\) 0 0
\(928\) 2.28007e7 0.869116
\(929\) −2.17027e7 −0.825040 −0.412520 0.910948i \(-0.635351\pi\)
−0.412520 + 0.910948i \(0.635351\pi\)
\(930\) 0 0
\(931\) −1.45715e7 −0.550972
\(932\) −6.80010e6 −0.256434
\(933\) 0 0
\(934\) −2.57912e7 −0.967397
\(935\) 1.82284e7 0.681900
\(936\) 0 0
\(937\) −2.01218e6 −0.0748718 −0.0374359 0.999299i \(-0.511919\pi\)
−0.0374359 + 0.999299i \(0.511919\pi\)
\(938\) −3.45344e7 −1.28158
\(939\) 0 0
\(940\) 9.32710e7 3.44292
\(941\) 1.17136e7 0.431237 0.215618 0.976478i \(-0.430823\pi\)
0.215618 + 0.976478i \(0.430823\pi\)
\(942\) 0 0
\(943\) 9.73916e6 0.356650
\(944\) −1.30220e7 −0.475608
\(945\) 0 0
\(946\) −5.03676e7 −1.82989
\(947\) −571455. −0.0207065 −0.0103533 0.999946i \(-0.503296\pi\)
−0.0103533 + 0.999946i \(0.503296\pi\)
\(948\) 0 0
\(949\) 2.04458e6 0.0736950
\(950\) −2.87455e7 −1.03338
\(951\) 0 0
\(952\) −1.16179e7 −0.415466
\(953\) −2.03678e7 −0.726461 −0.363231 0.931699i \(-0.618326\pi\)
−0.363231 + 0.931699i \(0.618326\pi\)
\(954\) 0 0
\(955\) −2.07739e7 −0.737073
\(956\) −1.16393e7 −0.411891
\(957\) 0 0
\(958\) −1.34506e7 −0.473510
\(959\) −2.03382e7 −0.714110
\(960\) 0 0
\(961\) −2.51274e7 −0.877687
\(962\) 2.14070e6 0.0745794
\(963\) 0 0
\(964\) 6.82727e7 2.36622
\(965\) 627316. 0.0216854
\(966\) 0 0
\(967\) −3.93183e7 −1.35216 −0.676081 0.736827i \(-0.736323\pi\)
−0.676081 + 0.736827i \(0.736323\pi\)
\(968\) −6.50132e6 −0.223004
\(969\) 0 0
\(970\) 2.74795e7 0.937734
\(971\) −4.86930e7 −1.65736 −0.828682 0.559719i \(-0.810909\pi\)
−0.828682 + 0.559719i \(0.810909\pi\)
\(972\) 0 0
\(973\) 3.76055e7 1.27341
\(974\) 8.92643e7 3.01495
\(975\) 0 0
\(976\) −4.18750e6 −0.140712
\(977\) 1.11758e7 0.374577 0.187288 0.982305i \(-0.440030\pi\)
0.187288 + 0.982305i \(0.440030\pi\)
\(978\) 0 0
\(979\) −6.02056e7 −2.00762
\(980\) 3.42214e7 1.13824
\(981\) 0 0
\(982\) 8.35930e7 2.76625
\(983\) −2.09439e7 −0.691310 −0.345655 0.938362i \(-0.612343\pi\)
−0.345655 + 0.938362i \(0.612343\pi\)
\(984\) 0 0
\(985\) −4.92311e7 −1.61677
\(986\) 2.83370e7 0.928242
\(987\) 0 0
\(988\) −2.38614e7 −0.777685
\(989\) 6.52518e6 0.212130
\(990\) 0 0
\(991\) −1.95125e7 −0.631144 −0.315572 0.948902i \(-0.602196\pi\)
−0.315572 + 0.948902i \(0.602196\pi\)
\(992\) 8.33092e6 0.268790
\(993\) 0 0
\(994\) 3.82533e7 1.22801
\(995\) 3.76064e7 1.20422
\(996\) 0 0
\(997\) 1.32696e7 0.422786 0.211393 0.977401i \(-0.432200\pi\)
0.211393 + 0.977401i \(0.432200\pi\)
\(998\) −2.18894e7 −0.695678
\(999\) 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.f.1.1 5
3.2 odd 2 69.6.a.e.1.5 5
12.11 even 2 1104.6.a.r.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.a.e.1.5 5 3.2 odd 2
207.6.a.f.1.1 5 1.1 even 1 trivial
1104.6.a.r.1.4 5 12.11 even 2