Properties

Label 363.6.a.b.1.1
Level $363$
Weight $6$
Character 363.1
Self dual yes
Analytic conductor $58.219$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 363.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.2193265921\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 363.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +9.00000 q^{3} -31.0000 q^{4} -92.0000 q^{5} -9.00000 q^{6} +26.0000 q^{7} +63.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +9.00000 q^{3} -31.0000 q^{4} -92.0000 q^{5} -9.00000 q^{6} +26.0000 q^{7} +63.0000 q^{8} +81.0000 q^{9} +92.0000 q^{10} -279.000 q^{12} +692.000 q^{13} -26.0000 q^{14} -828.000 q^{15} +929.000 q^{16} +1442.00 q^{17} -81.0000 q^{18} -2160.00 q^{19} +2852.00 q^{20} +234.000 q^{21} -1582.00 q^{23} +567.000 q^{24} +5339.00 q^{25} -692.000 q^{26} +729.000 q^{27} -806.000 q^{28} +5526.00 q^{29} +828.000 q^{30} +4792.00 q^{31} -2945.00 q^{32} -1442.00 q^{34} -2392.00 q^{35} -2511.00 q^{36} -10194.0 q^{37} +2160.00 q^{38} +6228.00 q^{39} -5796.00 q^{40} +10622.0 q^{41} -234.000 q^{42} -8580.00 q^{43} -7452.00 q^{45} +1582.00 q^{46} -2362.00 q^{47} +8361.00 q^{48} -16131.0 q^{49} -5339.00 q^{50} +12978.0 q^{51} -21452.0 q^{52} -30804.0 q^{53} -729.000 q^{54} +1638.00 q^{56} -19440.0 q^{57} -5526.00 q^{58} +6416.00 q^{59} +25668.0 q^{60} -42096.0 q^{61} -4792.00 q^{62} +2106.00 q^{63} -26783.0 q^{64} -63664.0 q^{65} -28444.0 q^{67} -44702.0 q^{68} -14238.0 q^{69} +2392.00 q^{70} +45690.0 q^{71} +5103.00 q^{72} +18374.0 q^{73} +10194.0 q^{74} +48051.0 q^{75} +66960.0 q^{76} -6228.00 q^{78} +105214. q^{79} -85468.0 q^{80} +6561.00 q^{81} -10622.0 q^{82} -62292.0 q^{83} -7254.00 q^{84} -132664. q^{85} +8580.00 q^{86} +49734.0 q^{87} -72246.0 q^{89} +7452.00 q^{90} +17992.0 q^{91} +49042.0 q^{92} +43128.0 q^{93} +2362.00 q^{94} +198720. q^{95} -26505.0 q^{96} +79262.0 q^{97} +16131.0 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.176777 −0.0883883 0.996086i \(-0.528172\pi\)
−0.0883883 + 0.996086i \(0.528172\pi\)
\(3\) 9.00000 0.577350
\(4\) −31.0000 −0.968750
\(5\) −92.0000 −1.64575 −0.822873 0.568225i \(-0.807630\pi\)
−0.822873 + 0.568225i \(0.807630\pi\)
\(6\) −9.00000 −0.102062
\(7\) 26.0000 0.200553 0.100276 0.994960i \(-0.468027\pi\)
0.100276 + 0.994960i \(0.468027\pi\)
\(8\) 63.0000 0.348029
\(9\) 81.0000 0.333333
\(10\) 92.0000 0.290930
\(11\) 0 0
\(12\) −279.000 −0.559308
\(13\) 692.000 1.13566 0.567829 0.823146i \(-0.307783\pi\)
0.567829 + 0.823146i \(0.307783\pi\)
\(14\) −26.0000 −0.0354530
\(15\) −828.000 −0.950172
\(16\) 929.000 0.907227
\(17\) 1442.00 1.21016 0.605080 0.796165i \(-0.293141\pi\)
0.605080 + 0.796165i \(0.293141\pi\)
\(18\) −81.0000 −0.0589256
\(19\) −2160.00 −1.37268 −0.686341 0.727280i \(-0.740784\pi\)
−0.686341 + 0.727280i \(0.740784\pi\)
\(20\) 2852.00 1.59432
\(21\) 234.000 0.115789
\(22\) 0 0
\(23\) −1582.00 −0.623572 −0.311786 0.950152i \(-0.600927\pi\)
−0.311786 + 0.950152i \(0.600927\pi\)
\(24\) 567.000 0.200935
\(25\) 5339.00 1.70848
\(26\) −692.000 −0.200758
\(27\) 729.000 0.192450
\(28\) −806.000 −0.194285
\(29\) 5526.00 1.22016 0.610079 0.792341i \(-0.291138\pi\)
0.610079 + 0.792341i \(0.291138\pi\)
\(30\) 828.000 0.167968
\(31\) 4792.00 0.895597 0.447798 0.894135i \(-0.352208\pi\)
0.447798 + 0.894135i \(0.352208\pi\)
\(32\) −2945.00 −0.508406
\(33\) 0 0
\(34\) −1442.00 −0.213928
\(35\) −2392.00 −0.330059
\(36\) −2511.00 −0.322917
\(37\) −10194.0 −1.22417 −0.612083 0.790794i \(-0.709668\pi\)
−0.612083 + 0.790794i \(0.709668\pi\)
\(38\) 2160.00 0.242658
\(39\) 6228.00 0.655673
\(40\) −5796.00 −0.572768
\(41\) 10622.0 0.986840 0.493420 0.869791i \(-0.335747\pi\)
0.493420 + 0.869791i \(0.335747\pi\)
\(42\) −234.000 −0.0204688
\(43\) −8580.00 −0.707646 −0.353823 0.935312i \(-0.615119\pi\)
−0.353823 + 0.935312i \(0.615119\pi\)
\(44\) 0 0
\(45\) −7452.00 −0.548582
\(46\) 1582.00 0.110233
\(47\) −2362.00 −0.155968 −0.0779840 0.996955i \(-0.524848\pi\)
−0.0779840 + 0.996955i \(0.524848\pi\)
\(48\) 8361.00 0.523788
\(49\) −16131.0 −0.959779
\(50\) −5339.00 −0.302019
\(51\) 12978.0 0.698686
\(52\) −21452.0 −1.10017
\(53\) −30804.0 −1.50632 −0.753160 0.657837i \(-0.771472\pi\)
−0.753160 + 0.657837i \(0.771472\pi\)
\(54\) −729.000 −0.0340207
\(55\) 0 0
\(56\) 1638.00 0.0697981
\(57\) −19440.0 −0.792518
\(58\) −5526.00 −0.215695
\(59\) 6416.00 0.239957 0.119979 0.992776i \(-0.461717\pi\)
0.119979 + 0.992776i \(0.461717\pi\)
\(60\) 25668.0 0.920479
\(61\) −42096.0 −1.44849 −0.724246 0.689541i \(-0.757812\pi\)
−0.724246 + 0.689541i \(0.757812\pi\)
\(62\) −4792.00 −0.158321
\(63\) 2106.00 0.0668509
\(64\) −26783.0 −0.817352
\(65\) −63664.0 −1.86901
\(66\) 0 0
\(67\) −28444.0 −0.774112 −0.387056 0.922056i \(-0.626508\pi\)
−0.387056 + 0.922056i \(0.626508\pi\)
\(68\) −44702.0 −1.17234
\(69\) −14238.0 −0.360020
\(70\) 2392.00 0.0583467
\(71\) 45690.0 1.07566 0.537830 0.843053i \(-0.319244\pi\)
0.537830 + 0.843053i \(0.319244\pi\)
\(72\) 5103.00 0.116010
\(73\) 18374.0 0.403549 0.201775 0.979432i \(-0.435329\pi\)
0.201775 + 0.979432i \(0.435329\pi\)
\(74\) 10194.0 0.216404
\(75\) 48051.0 0.986391
\(76\) 66960.0 1.32979
\(77\) 0 0
\(78\) −6228.00 −0.115908
\(79\) 105214. 1.89673 0.948366 0.317179i \(-0.102736\pi\)
0.948366 + 0.317179i \(0.102736\pi\)
\(80\) −85468.0 −1.49306
\(81\) 6561.00 0.111111
\(82\) −10622.0 −0.174450
\(83\) −62292.0 −0.992515 −0.496257 0.868175i \(-0.665293\pi\)
−0.496257 + 0.868175i \(0.665293\pi\)
\(84\) −7254.00 −0.112171
\(85\) −132664. −1.99162
\(86\) 8580.00 0.125095
\(87\) 49734.0 0.704458
\(88\) 0 0
\(89\) −72246.0 −0.966805 −0.483402 0.875398i \(-0.660599\pi\)
−0.483402 + 0.875398i \(0.660599\pi\)
\(90\) 7452.00 0.0969765
\(91\) 17992.0 0.227759
\(92\) 49042.0 0.604086
\(93\) 43128.0 0.517073
\(94\) 2362.00 0.0275715
\(95\) 198720. 2.25908
\(96\) −26505.0 −0.293528
\(97\) 79262.0 0.855334 0.427667 0.903936i \(-0.359336\pi\)
0.427667 + 0.903936i \(0.359336\pi\)
\(98\) 16131.0 0.169667
\(99\) 0 0
\(100\) −165509. −1.65509
\(101\) 24958.0 0.243448 0.121724 0.992564i \(-0.461158\pi\)
0.121724 + 0.992564i \(0.461158\pi\)
\(102\) −12978.0 −0.123511
\(103\) −56812.0 −0.527651 −0.263826 0.964570i \(-0.584984\pi\)
−0.263826 + 0.964570i \(0.584984\pi\)
\(104\) 43596.0 0.395242
\(105\) −21528.0 −0.190559
\(106\) 30804.0 0.266282
\(107\) 12492.0 0.105481 0.0527403 0.998608i \(-0.483204\pi\)
0.0527403 + 0.998608i \(0.483204\pi\)
\(108\) −22599.0 −0.186436
\(109\) −198748. −1.60227 −0.801137 0.598482i \(-0.795771\pi\)
−0.801137 + 0.598482i \(0.795771\pi\)
\(110\) 0 0
\(111\) −91746.0 −0.706773
\(112\) 24154.0 0.181947
\(113\) 166554. 1.22704 0.613520 0.789679i \(-0.289753\pi\)
0.613520 + 0.789679i \(0.289753\pi\)
\(114\) 19440.0 0.140099
\(115\) 145544. 1.02624
\(116\) −171306. −1.18203
\(117\) 56052.0 0.378553
\(118\) −6416.00 −0.0424189
\(119\) 37492.0 0.242701
\(120\) −52164.0 −0.330687
\(121\) 0 0
\(122\) 42096.0 0.256060
\(123\) 95598.0 0.569752
\(124\) −148552. −0.867609
\(125\) −203688. −1.16598
\(126\) −2106.00 −0.0118177
\(127\) −304226. −1.67374 −0.836868 0.547405i \(-0.815616\pi\)
−0.836868 + 0.547405i \(0.815616\pi\)
\(128\) 121023. 0.652894
\(129\) −77220.0 −0.408560
\(130\) 63664.0 0.330397
\(131\) −274428. −1.39717 −0.698586 0.715526i \(-0.746187\pi\)
−0.698586 + 0.715526i \(0.746187\pi\)
\(132\) 0 0
\(133\) −56160.0 −0.275295
\(134\) 28444.0 0.136845
\(135\) −67068.0 −0.316724
\(136\) 90846.0 0.421171
\(137\) −245458. −1.11732 −0.558658 0.829398i \(-0.688683\pi\)
−0.558658 + 0.829398i \(0.688683\pi\)
\(138\) 14238.0 0.0636431
\(139\) 59888.0 0.262907 0.131454 0.991322i \(-0.458036\pi\)
0.131454 + 0.991322i \(0.458036\pi\)
\(140\) 74152.0 0.319744
\(141\) −21258.0 −0.0900481
\(142\) −45690.0 −0.190152
\(143\) 0 0
\(144\) 75249.0 0.302409
\(145\) −508392. −2.00807
\(146\) −18374.0 −0.0713381
\(147\) −145179. −0.554128
\(148\) 316014. 1.18591
\(149\) −72038.0 −0.265825 −0.132913 0.991128i \(-0.542433\pi\)
−0.132913 + 0.991128i \(0.542433\pi\)
\(150\) −48051.0 −0.174371
\(151\) 323110. 1.15321 0.576605 0.817023i \(-0.304377\pi\)
0.576605 + 0.817023i \(0.304377\pi\)
\(152\) −136080. −0.477733
\(153\) 116802. 0.403387
\(154\) 0 0
\(155\) −440864. −1.47393
\(156\) −193068. −0.635183
\(157\) −318766. −1.03210 −0.516051 0.856558i \(-0.672599\pi\)
−0.516051 + 0.856558i \(0.672599\pi\)
\(158\) −105214. −0.335298
\(159\) −277236. −0.869675
\(160\) 270940. 0.836707
\(161\) −41132.0 −0.125059
\(162\) −6561.00 −0.0196419
\(163\) −431996. −1.27353 −0.636767 0.771056i \(-0.719729\pi\)
−0.636767 + 0.771056i \(0.719729\pi\)
\(164\) −329282. −0.956001
\(165\) 0 0
\(166\) 62292.0 0.175454
\(167\) 251580. 0.698047 0.349024 0.937114i \(-0.386513\pi\)
0.349024 + 0.937114i \(0.386513\pi\)
\(168\) 14742.0 0.0402980
\(169\) 107571. 0.289720
\(170\) 132664. 0.352071
\(171\) −174960. −0.457560
\(172\) 265980. 0.685532
\(173\) −476634. −1.21079 −0.605396 0.795924i \(-0.706985\pi\)
−0.605396 + 0.795924i \(0.706985\pi\)
\(174\) −49734.0 −0.124532
\(175\) 138814. 0.342640
\(176\) 0 0
\(177\) 57744.0 0.138540
\(178\) 72246.0 0.170909
\(179\) 90192.0 0.210395 0.105198 0.994451i \(-0.466453\pi\)
0.105198 + 0.994451i \(0.466453\pi\)
\(180\) 231012. 0.531439
\(181\) 248002. 0.562676 0.281338 0.959609i \(-0.409222\pi\)
0.281338 + 0.959609i \(0.409222\pi\)
\(182\) −17992.0 −0.0402625
\(183\) −378864. −0.836288
\(184\) −99666.0 −0.217021
\(185\) 937848. 2.01467
\(186\) −43128.0 −0.0914065
\(187\) 0 0
\(188\) 73222.0 0.151094
\(189\) 18954.0 0.0385964
\(190\) −198720. −0.399354
\(191\) −156802. −0.311006 −0.155503 0.987835i \(-0.549700\pi\)
−0.155503 + 0.987835i \(0.549700\pi\)
\(192\) −241047. −0.471899
\(193\) 431234. 0.833335 0.416668 0.909059i \(-0.363198\pi\)
0.416668 + 0.909059i \(0.363198\pi\)
\(194\) −79262.0 −0.151203
\(195\) −572976. −1.07907
\(196\) 500061. 0.929786
\(197\) 864974. 1.58795 0.793976 0.607949i \(-0.208007\pi\)
0.793976 + 0.607949i \(0.208007\pi\)
\(198\) 0 0
\(199\) −480060. −0.859336 −0.429668 0.902987i \(-0.641369\pi\)
−0.429668 + 0.902987i \(0.641369\pi\)
\(200\) 336357. 0.594601
\(201\) −255996. −0.446934
\(202\) −24958.0 −0.0430359
\(203\) 143676. 0.244706
\(204\) −402318. −0.676853
\(205\) −977224. −1.62409
\(206\) 56812.0 0.0932765
\(207\) −128142. −0.207857
\(208\) 642868. 1.03030
\(209\) 0 0
\(210\) 21528.0 0.0336865
\(211\) −525900. −0.813199 −0.406600 0.913606i \(-0.633286\pi\)
−0.406600 + 0.913606i \(0.633286\pi\)
\(212\) 954924. 1.45925
\(213\) 411210. 0.621033
\(214\) −12492.0 −0.0186465
\(215\) 789360. 1.16461
\(216\) 45927.0 0.0669782
\(217\) 124592. 0.179614
\(218\) 198748. 0.283245
\(219\) 165366. 0.232989
\(220\) 0 0
\(221\) 997864. 1.37433
\(222\) 91746.0 0.124941
\(223\) −245264. −0.330272 −0.165136 0.986271i \(-0.552806\pi\)
−0.165136 + 0.986271i \(0.552806\pi\)
\(224\) −76570.0 −0.101962
\(225\) 432459. 0.569493
\(226\) −166554. −0.216912
\(227\) 799308. 1.02955 0.514777 0.857324i \(-0.327875\pi\)
0.514777 + 0.857324i \(0.327875\pi\)
\(228\) 602640. 0.767752
\(229\) −1.53989e6 −1.94045 −0.970224 0.242208i \(-0.922128\pi\)
−0.970224 + 0.242208i \(0.922128\pi\)
\(230\) −145544. −0.181416
\(231\) 0 0
\(232\) 348138. 0.424650
\(233\) 721830. 0.871054 0.435527 0.900176i \(-0.356562\pi\)
0.435527 + 0.900176i \(0.356562\pi\)
\(234\) −56052.0 −0.0669193
\(235\) 217304. 0.256684
\(236\) −198896. −0.232459
\(237\) 946926. 1.09508
\(238\) −37492.0 −0.0429038
\(239\) 638436. 0.722974 0.361487 0.932377i \(-0.382269\pi\)
0.361487 + 0.932377i \(0.382269\pi\)
\(240\) −769212. −0.862021
\(241\) −220990. −0.245092 −0.122546 0.992463i \(-0.539106\pi\)
−0.122546 + 0.992463i \(0.539106\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 1.30498e6 1.40323
\(245\) 1.48405e6 1.57955
\(246\) −95598.0 −0.100719
\(247\) −1.49472e6 −1.55890
\(248\) 301896. 0.311694
\(249\) −560628. −0.573029
\(250\) 203688. 0.206118
\(251\) 627304. 0.628483 0.314242 0.949343i \(-0.398250\pi\)
0.314242 + 0.949343i \(0.398250\pi\)
\(252\) −65286.0 −0.0647618
\(253\) 0 0
\(254\) 304226. 0.295878
\(255\) −1.19398e6 −1.14986
\(256\) 736033. 0.701936
\(257\) −468014. −0.442004 −0.221002 0.975273i \(-0.570933\pi\)
−0.221002 + 0.975273i \(0.570933\pi\)
\(258\) 77220.0 0.0722238
\(259\) −265044. −0.245510
\(260\) 1.97358e6 1.81060
\(261\) 447606. 0.406719
\(262\) 274428. 0.246988
\(263\) −1.54510e6 −1.37743 −0.688713 0.725034i \(-0.741824\pi\)
−0.688713 + 0.725034i \(0.741824\pi\)
\(264\) 0 0
\(265\) 2.83397e6 2.47902
\(266\) 56160.0 0.0486657
\(267\) −650214. −0.558185
\(268\) 881764. 0.749921
\(269\) −1.07457e6 −0.905430 −0.452715 0.891655i \(-0.649544\pi\)
−0.452715 + 0.891655i \(0.649544\pi\)
\(270\) 67068.0 0.0559894
\(271\) −1.58723e6 −1.31285 −0.656427 0.754389i \(-0.727933\pi\)
−0.656427 + 0.754389i \(0.727933\pi\)
\(272\) 1.33962e6 1.09789
\(273\) 161928. 0.131497
\(274\) 245458. 0.197515
\(275\) 0 0
\(276\) 441378. 0.348769
\(277\) −692704. −0.542436 −0.271218 0.962518i \(-0.587426\pi\)
−0.271218 + 0.962518i \(0.587426\pi\)
\(278\) −59888.0 −0.0464759
\(279\) 388152. 0.298532
\(280\) −150696. −0.114870
\(281\) 567018. 0.428382 0.214191 0.976792i \(-0.431289\pi\)
0.214191 + 0.976792i \(0.431289\pi\)
\(282\) 21258.0 0.0159184
\(283\) −714916. −0.530626 −0.265313 0.964162i \(-0.585475\pi\)
−0.265313 + 0.964162i \(0.585475\pi\)
\(284\) −1.41639e6 −1.04205
\(285\) 1.78848e6 1.30428
\(286\) 0 0
\(287\) 276172. 0.197913
\(288\) −238545. −0.169469
\(289\) 659507. 0.464488
\(290\) 508392. 0.354980
\(291\) 713358. 0.493827
\(292\) −569594. −0.390938
\(293\) −2.14409e6 −1.45907 −0.729533 0.683946i \(-0.760262\pi\)
−0.729533 + 0.683946i \(0.760262\pi\)
\(294\) 145179. 0.0979570
\(295\) −590272. −0.394909
\(296\) −642222. −0.426045
\(297\) 0 0
\(298\) 72038.0 0.0469917
\(299\) −1.09474e6 −0.708165
\(300\) −1.48958e6 −0.955567
\(301\) −223080. −0.141920
\(302\) −323110. −0.203860
\(303\) 224622. 0.140555
\(304\) −2.00664e6 −1.24533
\(305\) 3.87283e6 2.38385
\(306\) −116802. −0.0713094
\(307\) 588808. 0.356556 0.178278 0.983980i \(-0.442947\pi\)
0.178278 + 0.983980i \(0.442947\pi\)
\(308\) 0 0
\(309\) −511308. −0.304640
\(310\) 440864. 0.260556
\(311\) 2.51827e6 1.47639 0.738194 0.674588i \(-0.235679\pi\)
0.738194 + 0.674588i \(0.235679\pi\)
\(312\) 392364. 0.228193
\(313\) −2.23562e6 −1.28985 −0.644923 0.764248i \(-0.723110\pi\)
−0.644923 + 0.764248i \(0.723110\pi\)
\(314\) 318766. 0.182452
\(315\) −193752. −0.110020
\(316\) −3.26163e6 −1.83746
\(317\) 1.06079e6 0.592901 0.296450 0.955048i \(-0.404197\pi\)
0.296450 + 0.955048i \(0.404197\pi\)
\(318\) 277236. 0.153738
\(319\) 0 0
\(320\) 2.46404e6 1.34515
\(321\) 112428. 0.0608992
\(322\) 41132.0 0.0221075
\(323\) −3.11472e6 −1.66116
\(324\) −203391. −0.107639
\(325\) 3.69459e6 1.94025
\(326\) 431996. 0.225131
\(327\) −1.78873e6 −0.925073
\(328\) 669186. 0.343449
\(329\) −61412.0 −0.0312798
\(330\) 0 0
\(331\) −2.34566e6 −1.17678 −0.588390 0.808577i \(-0.700238\pi\)
−0.588390 + 0.808577i \(0.700238\pi\)
\(332\) 1.93105e6 0.961499
\(333\) −825714. −0.408055
\(334\) −251580. −0.123399
\(335\) 2.61685e6 1.27399
\(336\) 217386. 0.105047
\(337\) −839978. −0.402896 −0.201448 0.979499i \(-0.564565\pi\)
−0.201448 + 0.979499i \(0.564565\pi\)
\(338\) −107571. −0.0512157
\(339\) 1.49899e6 0.708432
\(340\) 4.11258e6 1.92938
\(341\) 0 0
\(342\) 174960. 0.0808860
\(343\) −856388. −0.393039
\(344\) −540540. −0.246281
\(345\) 1.30990e6 0.592501
\(346\) 476634. 0.214040
\(347\) 2.02560e6 0.903086 0.451543 0.892249i \(-0.350874\pi\)
0.451543 + 0.892249i \(0.350874\pi\)
\(348\) −1.54175e6 −0.682444
\(349\) 378924. 0.166528 0.0832642 0.996528i \(-0.473465\pi\)
0.0832642 + 0.996528i \(0.473465\pi\)
\(350\) −138814. −0.0605708
\(351\) 504468. 0.218558
\(352\) 0 0
\(353\) −1.98730e6 −0.848842 −0.424421 0.905465i \(-0.639522\pi\)
−0.424421 + 0.905465i \(0.639522\pi\)
\(354\) −57744.0 −0.0244906
\(355\) −4.20348e6 −1.77026
\(356\) 2.23963e6 0.936592
\(357\) 337428. 0.140123
\(358\) −90192.0 −0.0371929
\(359\) 3.43975e6 1.40861 0.704305 0.709898i \(-0.251259\pi\)
0.704305 + 0.709898i \(0.251259\pi\)
\(360\) −469476. −0.190923
\(361\) 2.18950e6 0.884254
\(362\) −248002. −0.0994681
\(363\) 0 0
\(364\) −557752. −0.220642
\(365\) −1.69041e6 −0.664140
\(366\) 378864. 0.147836
\(367\) −1.79679e6 −0.696358 −0.348179 0.937428i \(-0.613200\pi\)
−0.348179 + 0.937428i \(0.613200\pi\)
\(368\) −1.46968e6 −0.565721
\(369\) 860382. 0.328947
\(370\) −937848. −0.356146
\(371\) −800904. −0.302096
\(372\) −1.33697e6 −0.500915
\(373\) 1.43541e6 0.534201 0.267100 0.963669i \(-0.413934\pi\)
0.267100 + 0.963669i \(0.413934\pi\)
\(374\) 0 0
\(375\) −1.83319e6 −0.673178
\(376\) −148806. −0.0542814
\(377\) 3.82399e6 1.38568
\(378\) −18954.0 −0.00682294
\(379\) 2.66235e6 0.952065 0.476033 0.879428i \(-0.342074\pi\)
0.476033 + 0.879428i \(0.342074\pi\)
\(380\) −6.16032e6 −2.18849
\(381\) −2.73803e6 −0.966332
\(382\) 156802. 0.0549785
\(383\) 2.04091e6 0.710932 0.355466 0.934689i \(-0.384322\pi\)
0.355466 + 0.934689i \(0.384322\pi\)
\(384\) 1.08921e6 0.376949
\(385\) 0 0
\(386\) −431234. −0.147314
\(387\) −694980. −0.235882
\(388\) −2.45712e6 −0.828605
\(389\) −4.29947e6 −1.44059 −0.720296 0.693667i \(-0.755994\pi\)
−0.720296 + 0.693667i \(0.755994\pi\)
\(390\) 572976. 0.190755
\(391\) −2.28124e6 −0.754623
\(392\) −1.01625e6 −0.334031
\(393\) −2.46985e6 −0.806658
\(394\) −864974. −0.280713
\(395\) −9.67969e6 −3.12154
\(396\) 0 0
\(397\) 728818. 0.232083 0.116041 0.993244i \(-0.462979\pi\)
0.116041 + 0.993244i \(0.462979\pi\)
\(398\) 480060. 0.151911
\(399\) −505440. −0.158942
\(400\) 4.95993e6 1.54998
\(401\) −5.92515e6 −1.84009 −0.920044 0.391814i \(-0.871848\pi\)
−0.920044 + 0.391814i \(0.871848\pi\)
\(402\) 255996. 0.0790075
\(403\) 3.31606e6 1.01709
\(404\) −773698. −0.235840
\(405\) −603612. −0.182861
\(406\) −143676. −0.0432583
\(407\) 0 0
\(408\) 817614. 0.243163
\(409\) −1.38212e6 −0.408542 −0.204271 0.978914i \(-0.565482\pi\)
−0.204271 + 0.978914i \(0.565482\pi\)
\(410\) 977224. 0.287101
\(411\) −2.20912e6 −0.645082
\(412\) 1.76117e6 0.511162
\(413\) 166816. 0.0481241
\(414\) 128142. 0.0367444
\(415\) 5.73086e6 1.63343
\(416\) −2.03794e6 −0.577375
\(417\) 538992. 0.151790
\(418\) 0 0
\(419\) 5.47794e6 1.52434 0.762170 0.647377i \(-0.224134\pi\)
0.762170 + 0.647377i \(0.224134\pi\)
\(420\) 667368. 0.184604
\(421\) 1.02873e6 0.282877 0.141439 0.989947i \(-0.454827\pi\)
0.141439 + 0.989947i \(0.454827\pi\)
\(422\) 525900. 0.143755
\(423\) −191322. −0.0519893
\(424\) −1.94065e6 −0.524243
\(425\) 7.69884e6 2.06753
\(426\) −411210. −0.109784
\(427\) −1.09450e6 −0.290499
\(428\) −387252. −0.102184
\(429\) 0 0
\(430\) −789360. −0.205875
\(431\) 5.14310e6 1.33362 0.666810 0.745228i \(-0.267659\pi\)
0.666810 + 0.745228i \(0.267659\pi\)
\(432\) 677241. 0.174596
\(433\) 412954. 0.105848 0.0529239 0.998599i \(-0.483146\pi\)
0.0529239 + 0.998599i \(0.483146\pi\)
\(434\) −124592. −0.0317516
\(435\) −4.57553e6 −1.15936
\(436\) 6.16119e6 1.55220
\(437\) 3.41712e6 0.855966
\(438\) −165366. −0.0411871
\(439\) −5.96365e6 −1.47690 −0.738450 0.674309i \(-0.764442\pi\)
−0.738450 + 0.674309i \(0.764442\pi\)
\(440\) 0 0
\(441\) −1.30661e6 −0.319926
\(442\) −997864. −0.242949
\(443\) 2.18433e6 0.528821 0.264410 0.964410i \(-0.414823\pi\)
0.264410 + 0.964410i \(0.414823\pi\)
\(444\) 2.84413e6 0.684686
\(445\) 6.64663e6 1.59112
\(446\) 245264. 0.0583844
\(447\) −648342. −0.153474
\(448\) −696358. −0.163922
\(449\) −7858.00 −0.00183948 −0.000919742 1.00000i \(-0.500293\pi\)
−0.000919742 1.00000i \(0.500293\pi\)
\(450\) −432459. −0.100673
\(451\) 0 0
\(452\) −5.16317e6 −1.18870
\(453\) 2.90799e6 0.665806
\(454\) −799308. −0.182001
\(455\) −1.65526e6 −0.374834
\(456\) −1.22472e6 −0.275819
\(457\) 899922. 0.201565 0.100782 0.994908i \(-0.467865\pi\)
0.100782 + 0.994908i \(0.467865\pi\)
\(458\) 1.53989e6 0.343026
\(459\) 1.05122e6 0.232895
\(460\) −4.51186e6 −0.994172
\(461\) −1.13619e6 −0.249000 −0.124500 0.992220i \(-0.539733\pi\)
−0.124500 + 0.992220i \(0.539733\pi\)
\(462\) 0 0
\(463\) −7.38964e6 −1.60203 −0.801016 0.598643i \(-0.795707\pi\)
−0.801016 + 0.598643i \(0.795707\pi\)
\(464\) 5.13365e6 1.10696
\(465\) −3.96778e6 −0.850971
\(466\) −721830. −0.153982
\(467\) 4.20851e6 0.892968 0.446484 0.894792i \(-0.352676\pi\)
0.446484 + 0.894792i \(0.352676\pi\)
\(468\) −1.73761e6 −0.366723
\(469\) −739544. −0.155250
\(470\) −217304. −0.0453757
\(471\) −2.86889e6 −0.595885
\(472\) 404208. 0.0835122
\(473\) 0 0
\(474\) −946926. −0.193584
\(475\) −1.15322e7 −2.34520
\(476\) −1.16225e6 −0.235116
\(477\) −2.49512e6 −0.502107
\(478\) −638436. −0.127805
\(479\) −7.39441e6 −1.47253 −0.736266 0.676692i \(-0.763413\pi\)
−0.736266 + 0.676692i \(0.763413\pi\)
\(480\) 2.43846e6 0.483073
\(481\) −7.05425e6 −1.39023
\(482\) 220990. 0.0433266
\(483\) −370188. −0.0722029
\(484\) 0 0
\(485\) −7.29210e6 −1.40766
\(486\) −59049.0 −0.0113402
\(487\) −3.81644e6 −0.729181 −0.364591 0.931168i \(-0.618791\pi\)
−0.364591 + 0.931168i \(0.618791\pi\)
\(488\) −2.65205e6 −0.504118
\(489\) −3.88796e6 −0.735275
\(490\) −1.48405e6 −0.279228
\(491\) −1.69716e6 −0.317702 −0.158851 0.987303i \(-0.550779\pi\)
−0.158851 + 0.987303i \(0.550779\pi\)
\(492\) −2.96354e6 −0.551947
\(493\) 7.96849e6 1.47659
\(494\) 1.49472e6 0.275577
\(495\) 0 0
\(496\) 4.45177e6 0.812509
\(497\) 1.18794e6 0.215727
\(498\) 560628. 0.101298
\(499\) 6.95160e6 1.24978 0.624889 0.780713i \(-0.285144\pi\)
0.624889 + 0.780713i \(0.285144\pi\)
\(500\) 6.31433e6 1.12954
\(501\) 2.26422e6 0.403018
\(502\) −627304. −0.111101
\(503\) −6.01023e6 −1.05918 −0.529591 0.848253i \(-0.677655\pi\)
−0.529591 + 0.848253i \(0.677655\pi\)
\(504\) 132678. 0.0232660
\(505\) −2.29614e6 −0.400654
\(506\) 0 0
\(507\) 968139. 0.167270
\(508\) 9.43101e6 1.62143
\(509\) 624660. 0.106868 0.0534342 0.998571i \(-0.482983\pi\)
0.0534342 + 0.998571i \(0.482983\pi\)
\(510\) 1.19398e6 0.203269
\(511\) 477724. 0.0809328
\(512\) −4.60877e6 −0.776980
\(513\) −1.57464e6 −0.264173
\(514\) 468014. 0.0781360
\(515\) 5.22670e6 0.868380
\(516\) 2.39382e6 0.395792
\(517\) 0 0
\(518\) 265044. 0.0434004
\(519\) −4.28971e6 −0.699051
\(520\) −4.01083e6 −0.650468
\(521\) −647490. −0.104505 −0.0522527 0.998634i \(-0.516640\pi\)
−0.0522527 + 0.998634i \(0.516640\pi\)
\(522\) −447606. −0.0718985
\(523\) 114676. 0.0183324 0.00916618 0.999958i \(-0.497082\pi\)
0.00916618 + 0.999958i \(0.497082\pi\)
\(524\) 8.50727e6 1.35351
\(525\) 1.24933e6 0.197823
\(526\) 1.54510e6 0.243497
\(527\) 6.91006e6 1.08382
\(528\) 0 0
\(529\) −3.93362e6 −0.611157
\(530\) −2.83397e6 −0.438233
\(531\) 519696. 0.0799858
\(532\) 1.74096e6 0.266692
\(533\) 7.35042e6 1.12071
\(534\) 650214. 0.0986741
\(535\) −1.14926e6 −0.173594
\(536\) −1.79197e6 −0.269413
\(537\) 811728. 0.121472
\(538\) 1.07457e6 0.160059
\(539\) 0 0
\(540\) 2.07911e6 0.306826
\(541\) 2.12404e6 0.312011 0.156006 0.987756i \(-0.450138\pi\)
0.156006 + 0.987756i \(0.450138\pi\)
\(542\) 1.58723e6 0.232082
\(543\) 2.23202e6 0.324861
\(544\) −4.24669e6 −0.615252
\(545\) 1.82848e7 2.63693
\(546\) −161928. −0.0232456
\(547\) −1.22672e7 −1.75299 −0.876494 0.481413i \(-0.840124\pi\)
−0.876494 + 0.481413i \(0.840124\pi\)
\(548\) 7.60920e6 1.08240
\(549\) −3.40978e6 −0.482831
\(550\) 0 0
\(551\) −1.19362e7 −1.67489
\(552\) −896994. −0.125297
\(553\) 2.73556e6 0.380394
\(554\) 692704. 0.0958900
\(555\) 8.44063e6 1.16317
\(556\) −1.85653e6 −0.254692
\(557\) −1.10980e7 −1.51568 −0.757839 0.652442i \(-0.773745\pi\)
−0.757839 + 0.652442i \(0.773745\pi\)
\(558\) −388152. −0.0527736
\(559\) −5.93736e6 −0.803644
\(560\) −2.22217e6 −0.299438
\(561\) 0 0
\(562\) −567018. −0.0757279
\(563\) −4.61984e6 −0.614265 −0.307132 0.951667i \(-0.599369\pi\)
−0.307132 + 0.951667i \(0.599369\pi\)
\(564\) 658998. 0.0872341
\(565\) −1.53230e7 −2.01940
\(566\) 714916. 0.0938024
\(567\) 170586. 0.0222836
\(568\) 2.87847e6 0.374361
\(569\) −1.01716e7 −1.31707 −0.658537 0.752548i \(-0.728824\pi\)
−0.658537 + 0.752548i \(0.728824\pi\)
\(570\) −1.78848e6 −0.230567
\(571\) 9.36866e6 1.20251 0.601253 0.799059i \(-0.294669\pi\)
0.601253 + 0.799059i \(0.294669\pi\)
\(572\) 0 0
\(573\) −1.41122e6 −0.179559
\(574\) −276172. −0.0349865
\(575\) −8.44630e6 −1.06536
\(576\) −2.16942e6 −0.272451
\(577\) −6.14973e6 −0.768983 −0.384491 0.923129i \(-0.625623\pi\)
−0.384491 + 0.923129i \(0.625623\pi\)
\(578\) −659507. −0.0821107
\(579\) 3.88111e6 0.481126
\(580\) 1.57602e7 1.94532
\(581\) −1.61959e6 −0.199051
\(582\) −713358. −0.0872972
\(583\) 0 0
\(584\) 1.15756e6 0.140447
\(585\) −5.15678e6 −0.623002
\(586\) 2.14409e6 0.257929
\(587\) 1.04649e6 0.125354 0.0626771 0.998034i \(-0.480036\pi\)
0.0626771 + 0.998034i \(0.480036\pi\)
\(588\) 4.50055e6 0.536812
\(589\) −1.03507e7 −1.22937
\(590\) 590272. 0.0698107
\(591\) 7.78477e6 0.916805
\(592\) −9.47023e6 −1.11060
\(593\) 3.31784e6 0.387453 0.193726 0.981056i \(-0.437943\pi\)
0.193726 + 0.981056i \(0.437943\pi\)
\(594\) 0 0
\(595\) −3.44926e6 −0.399424
\(596\) 2.23318e6 0.257518
\(597\) −4.32054e6 −0.496138
\(598\) 1.09474e6 0.125187
\(599\) −1.73991e7 −1.98134 −0.990670 0.136280i \(-0.956485\pi\)
−0.990670 + 0.136280i \(0.956485\pi\)
\(600\) 3.02721e6 0.343293
\(601\) −7.13163e6 −0.805383 −0.402691 0.915336i \(-0.631925\pi\)
−0.402691 + 0.915336i \(0.631925\pi\)
\(602\) 223080. 0.0250882
\(603\) −2.30396e6 −0.258037
\(604\) −1.00164e7 −1.11717
\(605\) 0 0
\(606\) −224622. −0.0248468
\(607\) 9.64617e6 1.06263 0.531317 0.847173i \(-0.321697\pi\)
0.531317 + 0.847173i \(0.321697\pi\)
\(608\) 6.36120e6 0.697879
\(609\) 1.29308e6 0.141281
\(610\) −3.87283e6 −0.421409
\(611\) −1.63450e6 −0.177126
\(612\) −3.62086e6 −0.390781
\(613\) −3.68170e6 −0.395729 −0.197864 0.980229i \(-0.563401\pi\)
−0.197864 + 0.980229i \(0.563401\pi\)
\(614\) −588808. −0.0630308
\(615\) −8.79502e6 −0.937667
\(616\) 0 0
\(617\) 1.83190e7 1.93727 0.968635 0.248489i \(-0.0799340\pi\)
0.968635 + 0.248489i \(0.0799340\pi\)
\(618\) 511308. 0.0538532
\(619\) 1.09660e6 0.115033 0.0575166 0.998345i \(-0.481682\pi\)
0.0575166 + 0.998345i \(0.481682\pi\)
\(620\) 1.36668e7 1.42786
\(621\) −1.15328e6 −0.120007
\(622\) −2.51827e6 −0.260991
\(623\) −1.87840e6 −0.193895
\(624\) 5.78581e6 0.594844
\(625\) 2.05492e6 0.210424
\(626\) 2.23562e6 0.228015
\(627\) 0 0
\(628\) 9.88175e6 0.999849
\(629\) −1.46997e7 −1.48144
\(630\) 193752. 0.0194489
\(631\) −9.58030e6 −0.957869 −0.478934 0.877851i \(-0.658977\pi\)
−0.478934 + 0.877851i \(0.658977\pi\)
\(632\) 6.62848e6 0.660118
\(633\) −4.73310e6 −0.469501
\(634\) −1.06079e6 −0.104811
\(635\) 2.79888e7 2.75454
\(636\) 8.59432e6 0.842497
\(637\) −1.11627e7 −1.08998
\(638\) 0 0
\(639\) 3.70089e6 0.358554
\(640\) −1.11341e7 −1.07450
\(641\) −1.18062e7 −1.13492 −0.567462 0.823400i \(-0.692075\pi\)
−0.567462 + 0.823400i \(0.692075\pi\)
\(642\) −112428. −0.0107656
\(643\) −5.88298e6 −0.561138 −0.280569 0.959834i \(-0.590523\pi\)
−0.280569 + 0.959834i \(0.590523\pi\)
\(644\) 1.27509e6 0.121151
\(645\) 7.10424e6 0.672385
\(646\) 3.11472e6 0.293655
\(647\) −3.62822e6 −0.340748 −0.170374 0.985379i \(-0.554498\pi\)
−0.170374 + 0.985379i \(0.554498\pi\)
\(648\) 413343. 0.0386699
\(649\) 0 0
\(650\) −3.69459e6 −0.342991
\(651\) 1.12133e6 0.103700
\(652\) 1.33919e7 1.23374
\(653\) −5.70795e6 −0.523838 −0.261919 0.965090i \(-0.584355\pi\)
−0.261919 + 0.965090i \(0.584355\pi\)
\(654\) 1.78873e6 0.163531
\(655\) 2.52474e7 2.29939
\(656\) 9.86784e6 0.895287
\(657\) 1.48829e6 0.134516
\(658\) 61412.0 0.00552953
\(659\) −1.08205e7 −0.970588 −0.485294 0.874351i \(-0.661287\pi\)
−0.485294 + 0.874351i \(0.661287\pi\)
\(660\) 0 0
\(661\) 1.14311e7 1.01762 0.508809 0.860879i \(-0.330086\pi\)
0.508809 + 0.860879i \(0.330086\pi\)
\(662\) 2.34566e6 0.208027
\(663\) 8.98078e6 0.793469
\(664\) −3.92440e6 −0.345424
\(665\) 5.16672e6 0.453065
\(666\) 825714. 0.0721347
\(667\) −8.74213e6 −0.760857
\(668\) −7.79898e6 −0.676233
\(669\) −2.20738e6 −0.190683
\(670\) −2.61685e6 −0.225212
\(671\) 0 0
\(672\) −689130. −0.0588678
\(673\) 2.03858e7 1.73496 0.867482 0.497468i \(-0.165737\pi\)
0.867482 + 0.497468i \(0.165737\pi\)
\(674\) 839978. 0.0712227
\(675\) 3.89213e6 0.328797
\(676\) −3.33470e6 −0.280666
\(677\) −6.09278e6 −0.510909 −0.255455 0.966821i \(-0.582225\pi\)
−0.255455 + 0.966821i \(0.582225\pi\)
\(678\) −1.49899e6 −0.125234
\(679\) 2.06081e6 0.171539
\(680\) −8.35783e6 −0.693141
\(681\) 7.19377e6 0.594414
\(682\) 0 0
\(683\) 1.44978e7 1.18918 0.594592 0.804027i \(-0.297314\pi\)
0.594592 + 0.804027i \(0.297314\pi\)
\(684\) 5.42376e6 0.443262
\(685\) 2.25821e7 1.83882
\(686\) 856388. 0.0694801
\(687\) −1.38590e7 −1.12032
\(688\) −7.97082e6 −0.641995
\(689\) −2.13164e7 −1.71067
\(690\) −1.30990e6 −0.104740
\(691\) 9.87069e6 0.786416 0.393208 0.919449i \(-0.371365\pi\)
0.393208 + 0.919449i \(0.371365\pi\)
\(692\) 1.47757e7 1.17296
\(693\) 0 0
\(694\) −2.02560e6 −0.159645
\(695\) −5.50970e6 −0.432679
\(696\) 3.13324e6 0.245172
\(697\) 1.53169e7 1.19423
\(698\) −378924. −0.0294384
\(699\) 6.49647e6 0.502903
\(700\) −4.30323e6 −0.331933
\(701\) −6.35411e6 −0.488382 −0.244191 0.969727i \(-0.578522\pi\)
−0.244191 + 0.969727i \(0.578522\pi\)
\(702\) −504468. −0.0386359
\(703\) 2.20190e7 1.68039
\(704\) 0 0
\(705\) 1.95574e6 0.148196
\(706\) 1.98730e6 0.150056
\(707\) 648908. 0.0488241
\(708\) −1.79006e6 −0.134210
\(709\) −411382. −0.0307348 −0.0153674 0.999882i \(-0.504892\pi\)
−0.0153674 + 0.999882i \(0.504892\pi\)
\(710\) 4.20348e6 0.312941
\(711\) 8.52233e6 0.632244
\(712\) −4.55150e6 −0.336476
\(713\) −7.58094e6 −0.558470
\(714\) −337428. −0.0247705
\(715\) 0 0
\(716\) −2.79595e6 −0.203820
\(717\) 5.74592e6 0.417409
\(718\) −3.43975e6 −0.249009
\(719\) 6.29795e6 0.454336 0.227168 0.973856i \(-0.427053\pi\)
0.227168 + 0.973856i \(0.427053\pi\)
\(720\) −6.92291e6 −0.497688
\(721\) −1.47711e6 −0.105822
\(722\) −2.18950e6 −0.156316
\(723\) −1.98891e6 −0.141504
\(724\) −7.68806e6 −0.545093
\(725\) 2.95033e7 2.08461
\(726\) 0 0
\(727\) 1.14699e7 0.804866 0.402433 0.915449i \(-0.368165\pi\)
0.402433 + 0.915449i \(0.368165\pi\)
\(728\) 1.13350e6 0.0792668
\(729\) 531441. 0.0370370
\(730\) 1.69041e6 0.117404
\(731\) −1.23724e7 −0.856365
\(732\) 1.17448e7 0.810154
\(733\) 1.87547e7 1.28929 0.644646 0.764481i \(-0.277005\pi\)
0.644646 + 0.764481i \(0.277005\pi\)
\(734\) 1.79679e6 0.123100
\(735\) 1.33565e7 0.911955
\(736\) 4.65899e6 0.317028
\(737\) 0 0
\(738\) −860382. −0.0581501
\(739\) −2.79727e6 −0.188418 −0.0942091 0.995552i \(-0.530032\pi\)
−0.0942091 + 0.995552i \(0.530032\pi\)
\(740\) −2.90733e7 −1.95171
\(741\) −1.34525e7 −0.900030
\(742\) 800904. 0.0534036
\(743\) 2.25651e7 1.49956 0.749781 0.661686i \(-0.230159\pi\)
0.749781 + 0.661686i \(0.230159\pi\)
\(744\) 2.71706e6 0.179956
\(745\) 6.62750e6 0.437481
\(746\) −1.43541e6 −0.0944342
\(747\) −5.04565e6 −0.330838
\(748\) 0 0
\(749\) 324792. 0.0211544
\(750\) 1.83319e6 0.119002
\(751\) −7.49233e6 −0.484749 −0.242375 0.970183i \(-0.577926\pi\)
−0.242375 + 0.970183i \(0.577926\pi\)
\(752\) −2.19430e6 −0.141498
\(753\) 5.64574e6 0.362855
\(754\) −3.82399e6 −0.244956
\(755\) −2.97261e7 −1.89789
\(756\) −587574. −0.0373902
\(757\) 2.88492e7 1.82976 0.914880 0.403727i \(-0.132285\pi\)
0.914880 + 0.403727i \(0.132285\pi\)
\(758\) −2.66235e6 −0.168303
\(759\) 0 0
\(760\) 1.25194e7 0.786227
\(761\) 9.56279e6 0.598581 0.299291 0.954162i \(-0.403250\pi\)
0.299291 + 0.954162i \(0.403250\pi\)
\(762\) 2.73803e6 0.170825
\(763\) −5.16745e6 −0.321340
\(764\) 4.86086e6 0.301287
\(765\) −1.07458e7 −0.663872
\(766\) −2.04091e6 −0.125676
\(767\) 4.43987e6 0.272510
\(768\) 6.62430e6 0.405263
\(769\) 744898. 0.0454235 0.0227118 0.999742i \(-0.492770\pi\)
0.0227118 + 0.999742i \(0.492770\pi\)
\(770\) 0 0
\(771\) −4.21213e6 −0.255191
\(772\) −1.33683e7 −0.807293
\(773\) 6.07336e6 0.365578 0.182789 0.983152i \(-0.441487\pi\)
0.182789 + 0.983152i \(0.441487\pi\)
\(774\) 694980. 0.0416984
\(775\) 2.55845e7 1.53011
\(776\) 4.99351e6 0.297681
\(777\) −2.38540e6 −0.141745
\(778\) 4.29947e6 0.254663
\(779\) −2.29435e7 −1.35462
\(780\) 1.77623e7 1.04535
\(781\) 0 0
\(782\) 2.28124e6 0.133400
\(783\) 4.02845e6 0.234819
\(784\) −1.49857e7 −0.870737
\(785\) 2.93265e7 1.69858
\(786\) 2.46985e6 0.142598
\(787\) 1.47512e7 0.848966 0.424483 0.905436i \(-0.360456\pi\)
0.424483 + 0.905436i \(0.360456\pi\)
\(788\) −2.68142e7 −1.53833
\(789\) −1.39059e7 −0.795257
\(790\) 9.67969e6 0.551815
\(791\) 4.33040e6 0.246086
\(792\) 0 0
\(793\) −2.91304e7 −1.64499
\(794\) −728818. −0.0410268
\(795\) 2.55057e7 1.43126
\(796\) 1.48819e7 0.832481
\(797\) −2.78359e7 −1.55224 −0.776121 0.630584i \(-0.782815\pi\)
−0.776121 + 0.630584i \(0.782815\pi\)
\(798\) 505440. 0.0280972
\(799\) −3.40600e6 −0.188746
\(800\) −1.57234e7 −0.868601
\(801\) −5.85193e6 −0.322268
\(802\) 5.92515e6 0.325285
\(803\) 0 0
\(804\) 7.93588e6 0.432967
\(805\) 3.78414e6 0.205815
\(806\) −3.31606e6 −0.179798
\(807\) −9.67115e6 −0.522750
\(808\) 1.57235e6 0.0847270
\(809\) −2.54767e7 −1.36859 −0.684293 0.729207i \(-0.739889\pi\)
−0.684293 + 0.729207i \(0.739889\pi\)
\(810\) 603612. 0.0323255
\(811\) 1.91915e7 1.02460 0.512302 0.858805i \(-0.328793\pi\)
0.512302 + 0.858805i \(0.328793\pi\)
\(812\) −4.45396e6 −0.237059
\(813\) −1.42851e7 −0.757977
\(814\) 0 0
\(815\) 3.97436e7 2.09591
\(816\) 1.20566e7 0.633867
\(817\) 1.85328e7 0.971373
\(818\) 1.38212e6 0.0722207
\(819\) 1.45735e6 0.0759197
\(820\) 3.02939e7 1.57333
\(821\) −3.27107e6 −0.169368 −0.0846840 0.996408i \(-0.526988\pi\)
−0.0846840 + 0.996408i \(0.526988\pi\)
\(822\) 2.20912e6 0.114036
\(823\) −3.19195e7 −1.64269 −0.821347 0.570430i \(-0.806777\pi\)
−0.821347 + 0.570430i \(0.806777\pi\)
\(824\) −3.57916e6 −0.183638
\(825\) 0 0
\(826\) −166816. −0.00850722
\(827\) −2.45556e7 −1.24850 −0.624248 0.781226i \(-0.714595\pi\)
−0.624248 + 0.781226i \(0.714595\pi\)
\(828\) 3.97240e6 0.201362
\(829\) −1.40969e7 −0.712421 −0.356211 0.934406i \(-0.615931\pi\)
−0.356211 + 0.934406i \(0.615931\pi\)
\(830\) −5.73086e6 −0.288752
\(831\) −6.23434e6 −0.313175
\(832\) −1.85338e7 −0.928233
\(833\) −2.32609e7 −1.16149
\(834\) −538992. −0.0268329
\(835\) −2.31454e7 −1.14881
\(836\) 0 0
\(837\) 3.49337e6 0.172358
\(838\) −5.47794e6 −0.269468
\(839\) −3.01443e6 −0.147843 −0.0739213 0.997264i \(-0.523551\pi\)
−0.0739213 + 0.997264i \(0.523551\pi\)
\(840\) −1.35626e6 −0.0663202
\(841\) 1.00255e7 0.488784
\(842\) −1.02873e6 −0.0500061
\(843\) 5.10316e6 0.247326
\(844\) 1.63029e7 0.787787
\(845\) −9.89653e6 −0.476806
\(846\) 191322. 0.00919050
\(847\) 0 0
\(848\) −2.86169e7 −1.36657
\(849\) −6.43424e6 −0.306357
\(850\) −7.69884e6 −0.365492
\(851\) 1.61269e7 0.763356
\(852\) −1.27475e7 −0.601626
\(853\) 1.67201e7 0.786806 0.393403 0.919366i \(-0.371298\pi\)
0.393403 + 0.919366i \(0.371298\pi\)
\(854\) 1.09450e6 0.0513534
\(855\) 1.60963e7 0.753028
\(856\) 786996. 0.0367103
\(857\) 9.15871e6 0.425973 0.212987 0.977055i \(-0.431681\pi\)
0.212987 + 0.977055i \(0.431681\pi\)
\(858\) 0 0
\(859\) 1.51068e7 0.698536 0.349268 0.937023i \(-0.386430\pi\)
0.349268 + 0.937023i \(0.386430\pi\)
\(860\) −2.44702e7 −1.12821
\(861\) 2.48555e6 0.114265
\(862\) −5.14310e6 −0.235753
\(863\) 5.11568e6 0.233817 0.116909 0.993143i \(-0.462702\pi\)
0.116909 + 0.993143i \(0.462702\pi\)
\(864\) −2.14690e6 −0.0978427
\(865\) 4.38503e7 1.99266
\(866\) −412954. −0.0187114
\(867\) 5.93556e6 0.268172
\(868\) −3.86235e6 −0.174001
\(869\) 0 0
\(870\) 4.57553e6 0.204948
\(871\) −1.96832e7 −0.879127
\(872\) −1.25211e7 −0.557638
\(873\) 6.42022e6 0.285111
\(874\) −3.41712e6 −0.151315
\(875\) −5.29589e6 −0.233840
\(876\) −5.12635e6 −0.225708
\(877\) 1.26998e7 0.557568 0.278784 0.960354i \(-0.410069\pi\)
0.278784 + 0.960354i \(0.410069\pi\)
\(878\) 5.96365e6 0.261081
\(879\) −1.92968e7 −0.842392
\(880\) 0 0
\(881\) −8.38173e6 −0.363826 −0.181913 0.983315i \(-0.558229\pi\)
−0.181913 + 0.983315i \(0.558229\pi\)
\(882\) 1.30661e6 0.0565555
\(883\) −1.69529e7 −0.731715 −0.365858 0.930671i \(-0.619224\pi\)
−0.365858 + 0.930671i \(0.619224\pi\)
\(884\) −3.09338e7 −1.33138
\(885\) −5.31245e6 −0.228001
\(886\) −2.18433e6 −0.0934832
\(887\) 1.05143e7 0.448717 0.224359 0.974507i \(-0.427971\pi\)
0.224359 + 0.974507i \(0.427971\pi\)
\(888\) −5.78000e6 −0.245977
\(889\) −7.90988e6 −0.335672
\(890\) −6.64663e6 −0.281272
\(891\) 0 0
\(892\) 7.60318e6 0.319951
\(893\) 5.10192e6 0.214094
\(894\) 648342. 0.0271307
\(895\) −8.29766e6 −0.346257
\(896\) 3.14660e6 0.130940
\(897\) −9.85270e6 −0.408859
\(898\) 7858.00 0.000325178 0
\(899\) 2.64806e7 1.09277
\(900\) −1.34062e7 −0.551697
\(901\) −4.44194e7 −1.82289
\(902\) 0 0
\(903\) −2.00772e6 −0.0819377
\(904\) 1.04929e7 0.427046
\(905\) −2.28162e7 −0.926023
\(906\) −2.90799e6 −0.117699
\(907\) −1.53747e7 −0.620569 −0.310284 0.950644i \(-0.600424\pi\)
−0.310284 + 0.950644i \(0.600424\pi\)
\(908\) −2.47785e7 −0.997381
\(909\) 2.02160e6 0.0811494
\(910\) 1.65526e6 0.0662619
\(911\) 1.25424e7 0.500708 0.250354 0.968154i \(-0.419453\pi\)
0.250354 + 0.968154i \(0.419453\pi\)
\(912\) −1.80598e7 −0.718993
\(913\) 0 0
\(914\) −899922. −0.0356319
\(915\) 3.48555e7 1.37632
\(916\) 4.77367e7 1.87981
\(917\) −7.13513e6 −0.280207
\(918\) −1.05122e6 −0.0411705
\(919\) −3.31432e7 −1.29451 −0.647256 0.762273i \(-0.724084\pi\)
−0.647256 + 0.762273i \(0.724084\pi\)
\(920\) 9.16927e6 0.357162
\(921\) 5.29927e6 0.205858
\(922\) 1.13619e6 0.0440173
\(923\) 3.16175e7 1.22158
\(924\) 0 0
\(925\) −5.44258e7 −2.09146
\(926\) 7.38964e6 0.283202
\(927\) −4.60177e6 −0.175884
\(928\) −1.62741e7 −0.620335
\(929\) 3.10442e7 1.18016 0.590080 0.807345i \(-0.299096\pi\)
0.590080 + 0.807345i \(0.299096\pi\)
\(930\) 3.96778e6 0.150432
\(931\) 3.48430e7 1.31747
\(932\) −2.23767e7 −0.843834
\(933\) 2.26644e7 0.852393
\(934\) −4.20851e6 −0.157856
\(935\) 0 0
\(936\) 3.53128e6 0.131747
\(937\) 3.10737e7 1.15623 0.578115 0.815955i \(-0.303788\pi\)
0.578115 + 0.815955i \(0.303788\pi\)
\(938\) 739544. 0.0274446
\(939\) −2.01206e7 −0.744692
\(940\) −6.73642e6 −0.248662
\(941\) 2.50349e7 0.921664 0.460832 0.887488i \(-0.347551\pi\)
0.460832 + 0.887488i \(0.347551\pi\)
\(942\) 2.86889e6 0.105339
\(943\) −1.68040e7 −0.615366
\(944\) 5.96046e6 0.217696
\(945\) −1.74377e6 −0.0635198
\(946\) 0 0
\(947\) −5.37383e6 −0.194719 −0.0973596 0.995249i \(-0.531040\pi\)
−0.0973596 + 0.995249i \(0.531040\pi\)
\(948\) −2.93547e7 −1.06086
\(949\) 1.27148e7 0.458294
\(950\) 1.15322e7 0.414576
\(951\) 9.54713e6 0.342311
\(952\) 2.36200e6 0.0844669
\(953\) −7.26908e6 −0.259267 −0.129634 0.991562i \(-0.541380\pi\)
−0.129634 + 0.991562i \(0.541380\pi\)
\(954\) 2.49512e6 0.0887608
\(955\) 1.44258e7 0.511836
\(956\) −1.97915e7 −0.700381
\(957\) 0 0
\(958\) 7.39441e6 0.260309
\(959\) −6.38191e6 −0.224080
\(960\) 2.21763e7 0.776625
\(961\) −5.66589e6 −0.197906
\(962\) 7.05425e6 0.245761
\(963\) 1.01185e6 0.0351602
\(964\) 6.85069e6 0.237433
\(965\) −3.96735e7 −1.37146
\(966\) 370188. 0.0127638
\(967\) 2.54428e7 0.874983 0.437491 0.899223i \(-0.355867\pi\)
0.437491 + 0.899223i \(0.355867\pi\)
\(968\) 0 0
\(969\) −2.80325e7 −0.959074
\(970\) 7.29210e6 0.248842
\(971\) 9.88213e6 0.336358 0.168179 0.985756i \(-0.446211\pi\)
0.168179 + 0.985756i \(0.446211\pi\)
\(972\) −1.83052e6 −0.0621453
\(973\) 1.55709e6 0.0527268
\(974\) 3.81644e6 0.128902
\(975\) 3.32513e7 1.12020
\(976\) −3.91072e7 −1.31411
\(977\) 2.22197e6 0.0744736 0.0372368 0.999306i \(-0.488144\pi\)
0.0372368 + 0.999306i \(0.488144\pi\)
\(978\) 3.88796e6 0.129980
\(979\) 0 0
\(980\) −4.60056e7 −1.53019
\(981\) −1.60986e7 −0.534091
\(982\) 1.69716e6 0.0561623
\(983\) 2.53706e7 0.837428 0.418714 0.908118i \(-0.362481\pi\)
0.418714 + 0.908118i \(0.362481\pi\)
\(984\) 6.02267e6 0.198290
\(985\) −7.95776e7 −2.61337
\(986\) −7.96849e6 −0.261026
\(987\) −552708. −0.0180594
\(988\) 4.63363e7 1.51018
\(989\) 1.35736e7 0.441269
\(990\) 0 0
\(991\) 3.24132e7 1.04843 0.524214 0.851587i \(-0.324359\pi\)
0.524214 + 0.851587i \(0.324359\pi\)
\(992\) −1.41124e7 −0.455327
\(993\) −2.11109e7 −0.679414
\(994\) −1.18794e6 −0.0381354
\(995\) 4.41655e7 1.41425
\(996\) 1.73795e7 0.555122
\(997\) 1.55048e6 0.0494000 0.0247000 0.999695i \(-0.492137\pi\)
0.0247000 + 0.999695i \(0.492137\pi\)
\(998\) −6.95160e6 −0.220932
\(999\) −7.43143e6 −0.235591
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 363.6.a.b.1.1 1
3.2 odd 2 1089.6.a.h.1.1 1
11.10 odd 2 33.6.a.b.1.1 1
33.32 even 2 99.6.a.a.1.1 1
44.43 even 2 528.6.a.a.1.1 1
55.54 odd 2 825.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.6.a.b.1.1 1 11.10 odd 2
99.6.a.a.1.1 1 33.32 even 2
363.6.a.b.1.1 1 1.1 even 1 trivial
528.6.a.a.1.1 1 44.43 even 2
825.6.a.a.1.1 1 55.54 odd 2
1089.6.a.h.1.1 1 3.2 odd 2