Properties

Label 177.6.a.a.1.10
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3879361069\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + 13849341 x^{3} - 23890558 x^{2} - 74443300 x - 14846072\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(8.66878\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+7.66878 q^{2} +9.00000 q^{3} +26.8102 q^{4} -109.801 q^{5} +69.0190 q^{6} +156.301 q^{7} -39.7996 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+7.66878 q^{2} +9.00000 q^{3} +26.8102 q^{4} -109.801 q^{5} +69.0190 q^{6} +156.301 q^{7} -39.7996 q^{8} +81.0000 q^{9} -842.036 q^{10} -426.905 q^{11} +241.292 q^{12} -123.969 q^{13} +1198.64 q^{14} -988.205 q^{15} -1163.14 q^{16} -852.404 q^{17} +621.171 q^{18} +232.142 q^{19} -2943.77 q^{20} +1406.71 q^{21} -3273.84 q^{22} -3642.90 q^{23} -358.197 q^{24} +8931.16 q^{25} -950.692 q^{26} +729.000 q^{27} +4190.45 q^{28} -8173.34 q^{29} -7578.33 q^{30} -9358.70 q^{31} -7646.28 q^{32} -3842.15 q^{33} -6536.90 q^{34} -17161.9 q^{35} +2171.62 q^{36} +6317.09 q^{37} +1780.24 q^{38} -1115.72 q^{39} +4370.02 q^{40} +13017.8 q^{41} +10787.7 q^{42} +23355.0 q^{43} -11445.4 q^{44} -8893.84 q^{45} -27936.6 q^{46} -8861.12 q^{47} -10468.3 q^{48} +7622.89 q^{49} +68491.1 q^{50} -7671.64 q^{51} -3323.64 q^{52} +23012.3 q^{53} +5590.54 q^{54} +46874.4 q^{55} -6220.71 q^{56} +2089.28 q^{57} -62679.6 q^{58} +3481.00 q^{59} -26493.9 q^{60} +13699.8 q^{61} -71769.8 q^{62} +12660.4 q^{63} -21417.1 q^{64} +13611.9 q^{65} -29464.6 q^{66} -1424.88 q^{67} -22853.1 q^{68} -32786.1 q^{69} -131611. q^{70} +34543.2 q^{71} -3223.77 q^{72} -50120.2 q^{73} +48444.4 q^{74} +80380.4 q^{75} +6223.76 q^{76} -66725.5 q^{77} -8556.23 q^{78} -69723.6 q^{79} +127713. q^{80} +6561.00 q^{81} +99830.8 q^{82} +49883.0 q^{83} +37714.0 q^{84} +93594.5 q^{85} +179104. q^{86} -73560.1 q^{87} +16990.7 q^{88} -50735.3 q^{89} -68204.9 q^{90} -19376.5 q^{91} -97666.8 q^{92} -84228.3 q^{93} -67954.0 q^{94} -25489.3 q^{95} -68816.5 q^{96} +21922.7 q^{97} +58458.2 q^{98} -34579.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.66878 1.35566 0.677831 0.735218i \(-0.262920\pi\)
0.677831 + 0.735218i \(0.262920\pi\)
\(3\) 9.00000 0.577350
\(4\) 26.8102 0.837818
\(5\) −109.801 −1.96417 −0.982086 0.188434i \(-0.939659\pi\)
−0.982086 + 0.188434i \(0.939659\pi\)
\(6\) 69.0190 0.782692
\(7\) 156.301 1.20563 0.602817 0.797879i \(-0.294045\pi\)
0.602817 + 0.797879i \(0.294045\pi\)
\(8\) −39.7996 −0.219864
\(9\) 81.0000 0.333333
\(10\) −842.036 −2.66275
\(11\) −426.905 −1.06377 −0.531887 0.846815i \(-0.678517\pi\)
−0.531887 + 0.846815i \(0.678517\pi\)
\(12\) 241.292 0.483714
\(13\) −123.969 −0.203449 −0.101724 0.994813i \(-0.532436\pi\)
−0.101724 + 0.994813i \(0.532436\pi\)
\(14\) 1198.64 1.63443
\(15\) −988.205 −1.13402
\(16\) −1163.14 −1.13588
\(17\) −852.404 −0.715358 −0.357679 0.933845i \(-0.616432\pi\)
−0.357679 + 0.933845i \(0.616432\pi\)
\(18\) 621.171 0.451887
\(19\) 232.142 0.147526 0.0737631 0.997276i \(-0.476499\pi\)
0.0737631 + 0.997276i \(0.476499\pi\)
\(20\) −2943.77 −1.64562
\(21\) 1406.71 0.696073
\(22\) −3273.84 −1.44212
\(23\) −3642.90 −1.43591 −0.717956 0.696089i \(-0.754922\pi\)
−0.717956 + 0.696089i \(0.754922\pi\)
\(24\) −358.197 −0.126938
\(25\) 8931.16 2.85797
\(26\) −950.692 −0.275808
\(27\) 729.000 0.192450
\(28\) 4190.45 1.01010
\(29\) −8173.34 −1.80470 −0.902349 0.431005i \(-0.858159\pi\)
−0.902349 + 0.431005i \(0.858159\pi\)
\(30\) −7578.33 −1.53734
\(31\) −9358.70 −1.74909 −0.874544 0.484947i \(-0.838839\pi\)
−0.874544 + 0.484947i \(0.838839\pi\)
\(32\) −7646.28 −1.32000
\(33\) −3842.15 −0.614171
\(34\) −6536.90 −0.969783
\(35\) −17161.9 −2.36807
\(36\) 2171.62 0.279273
\(37\) 6317.09 0.758600 0.379300 0.925274i \(-0.376165\pi\)
0.379300 + 0.925274i \(0.376165\pi\)
\(38\) 1780.24 0.199996
\(39\) −1115.72 −0.117461
\(40\) 4370.02 0.431850
\(41\) 13017.8 1.20942 0.604712 0.796444i \(-0.293288\pi\)
0.604712 + 0.796444i \(0.293288\pi\)
\(42\) 10787.7 0.943640
\(43\) 23355.0 1.92623 0.963117 0.269084i \(-0.0867208\pi\)
0.963117 + 0.269084i \(0.0867208\pi\)
\(44\) −11445.4 −0.891250
\(45\) −8893.84 −0.654724
\(46\) −27936.6 −1.94661
\(47\) −8861.12 −0.585119 −0.292559 0.956247i \(-0.594507\pi\)
−0.292559 + 0.956247i \(0.594507\pi\)
\(48\) −10468.3 −0.655800
\(49\) 7622.89 0.453554
\(50\) 68491.1 3.87444
\(51\) −7671.64 −0.413012
\(52\) −3323.64 −0.170453
\(53\) 23012.3 1.12531 0.562653 0.826693i \(-0.309781\pi\)
0.562653 + 0.826693i \(0.309781\pi\)
\(54\) 5590.54 0.260897
\(55\) 46874.4 2.08944
\(56\) −6220.71 −0.265075
\(57\) 2089.28 0.0851743
\(58\) −62679.6 −2.44656
\(59\) 3481.00 0.130189
\(60\) −26493.9 −0.950098
\(61\) 13699.8 0.471399 0.235699 0.971826i \(-0.424262\pi\)
0.235699 + 0.971826i \(0.424262\pi\)
\(62\) −71769.8 −2.37117
\(63\) 12660.4 0.401878
\(64\) −21417.1 −0.653599
\(65\) 13611.9 0.399609
\(66\) −29464.6 −0.832607
\(67\) −1424.88 −0.0387785 −0.0193893 0.999812i \(-0.506172\pi\)
−0.0193893 + 0.999812i \(0.506172\pi\)
\(68\) −22853.1 −0.599340
\(69\) −32786.1 −0.829024
\(70\) −131611. −3.21031
\(71\) 34543.2 0.813235 0.406618 0.913598i \(-0.366708\pi\)
0.406618 + 0.913598i \(0.366708\pi\)
\(72\) −3223.77 −0.0732880
\(73\) −50120.2 −1.10079 −0.550397 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(74\) 48444.4 1.02840
\(75\) 80380.4 1.65005
\(76\) 6223.76 0.123600
\(77\) −66725.5 −1.28252
\(78\) −8556.23 −0.159238
\(79\) −69723.6 −1.25693 −0.628466 0.777837i \(-0.716317\pi\)
−0.628466 + 0.777837i \(0.716317\pi\)
\(80\) 127713. 2.23106
\(81\) 6561.00 0.111111
\(82\) 99830.8 1.63957
\(83\) 49883.0 0.794799 0.397399 0.917646i \(-0.369913\pi\)
0.397399 + 0.917646i \(0.369913\pi\)
\(84\) 37714.0 0.583183
\(85\) 93594.5 1.40509
\(86\) 179104. 2.61132
\(87\) −73560.1 −1.04194
\(88\) 16990.7 0.233886
\(89\) −50735.3 −0.678946 −0.339473 0.940616i \(-0.610249\pi\)
−0.339473 + 0.940616i \(0.610249\pi\)
\(90\) −68204.9 −0.887584
\(91\) −19376.5 −0.245285
\(92\) −97666.8 −1.20303
\(93\) −84228.3 −1.00984
\(94\) −67954.0 −0.793223
\(95\) −25489.3 −0.289767
\(96\) −68816.5 −0.762104
\(97\) 21922.7 0.236573 0.118286 0.992980i \(-0.462260\pi\)
0.118286 + 0.992980i \(0.462260\pi\)
\(98\) 58458.2 0.614866
\(99\) −34579.3 −0.354592
\(100\) 239446. 2.39446
\(101\) 136749. 1.33389 0.666944 0.745108i \(-0.267602\pi\)
0.666944 + 0.745108i \(0.267602\pi\)
\(102\) −58832.1 −0.559905
\(103\) −45802.7 −0.425400 −0.212700 0.977118i \(-0.568226\pi\)
−0.212700 + 0.977118i \(0.568226\pi\)
\(104\) 4933.93 0.0447311
\(105\) −154457. −1.36721
\(106\) 176476. 1.52553
\(107\) 42126.7 0.355711 0.177856 0.984057i \(-0.443084\pi\)
0.177856 + 0.984057i \(0.443084\pi\)
\(108\) 19544.6 0.161238
\(109\) −184019. −1.48353 −0.741765 0.670660i \(-0.766011\pi\)
−0.741765 + 0.670660i \(0.766011\pi\)
\(110\) 359470. 2.83257
\(111\) 56853.8 0.437978
\(112\) −181800. −1.36945
\(113\) −180222. −1.32773 −0.663867 0.747851i \(-0.731086\pi\)
−0.663867 + 0.747851i \(0.731086\pi\)
\(114\) 16022.2 0.115468
\(115\) 399992. 2.82038
\(116\) −219129. −1.51201
\(117\) −10041.5 −0.0678163
\(118\) 26695.0 0.176492
\(119\) −133231. −0.862460
\(120\) 39330.2 0.249329
\(121\) 21197.0 0.131616
\(122\) 105060. 0.639057
\(123\) 117160. 0.698261
\(124\) −250908. −1.46542
\(125\) −637519. −3.64937
\(126\) 97089.4 0.544811
\(127\) −25072.4 −0.137939 −0.0689694 0.997619i \(-0.521971\pi\)
−0.0689694 + 0.997619i \(0.521971\pi\)
\(128\) 80437.6 0.433945
\(129\) 210195. 1.11211
\(130\) 104387. 0.541734
\(131\) 28027.7 0.142695 0.0713475 0.997452i \(-0.477270\pi\)
0.0713475 + 0.997452i \(0.477270\pi\)
\(132\) −103009. −0.514563
\(133\) 36283.9 0.177863
\(134\) −10927.1 −0.0525705
\(135\) −80044.6 −0.378005
\(136\) 33925.4 0.157281
\(137\) 193823. 0.882277 0.441139 0.897439i \(-0.354575\pi\)
0.441139 + 0.897439i \(0.354575\pi\)
\(138\) −251429. −1.12388
\(139\) −385667. −1.69307 −0.846536 0.532331i \(-0.821316\pi\)
−0.846536 + 0.532331i \(0.821316\pi\)
\(140\) −460113. −1.98401
\(141\) −79750.1 −0.337818
\(142\) 264904. 1.10247
\(143\) 52923.1 0.216424
\(144\) −94214.3 −0.378626
\(145\) 897438. 3.54474
\(146\) −384361. −1.49230
\(147\) 68606.0 0.261860
\(148\) 169362. 0.635569
\(149\) −97076.0 −0.358217 −0.179109 0.983829i \(-0.557321\pi\)
−0.179109 + 0.983829i \(0.557321\pi\)
\(150\) 616420. 2.23691
\(151\) 28312.8 0.101051 0.0505255 0.998723i \(-0.483910\pi\)
0.0505255 + 0.998723i \(0.483910\pi\)
\(152\) −9239.15 −0.0324357
\(153\) −69044.8 −0.238453
\(154\) −511703. −1.73867
\(155\) 1.02759e6 3.43551
\(156\) −29912.7 −0.0984112
\(157\) −147457. −0.477439 −0.238719 0.971089i \(-0.576728\pi\)
−0.238719 + 0.971089i \(0.576728\pi\)
\(158\) −534695. −1.70398
\(159\) 207111. 0.649695
\(160\) 839565. 2.59271
\(161\) −569388. −1.73118
\(162\) 50314.9 0.150629
\(163\) −140469. −0.414105 −0.207053 0.978330i \(-0.566387\pi\)
−0.207053 + 0.978330i \(0.566387\pi\)
\(164\) 349010. 1.01328
\(165\) 421870. 1.20634
\(166\) 382542. 1.07748
\(167\) −33450.1 −0.0928125 −0.0464063 0.998923i \(-0.514777\pi\)
−0.0464063 + 0.998923i \(0.514777\pi\)
\(168\) −55986.3 −0.153041
\(169\) −355925. −0.958609
\(170\) 717755. 1.90482
\(171\) 18803.5 0.0491754
\(172\) 626152. 1.61383
\(173\) 359847. 0.914118 0.457059 0.889436i \(-0.348903\pi\)
0.457059 + 0.889436i \(0.348903\pi\)
\(174\) −564116. −1.41252
\(175\) 1.39595e6 3.44567
\(176\) 496550. 1.20832
\(177\) 31329.0 0.0751646
\(178\) −389078. −0.920422
\(179\) 51692.7 0.120586 0.0602930 0.998181i \(-0.480796\pi\)
0.0602930 + 0.998181i \(0.480796\pi\)
\(180\) −238446. −0.548540
\(181\) −649652. −1.47395 −0.736977 0.675918i \(-0.763748\pi\)
−0.736977 + 0.675918i \(0.763748\pi\)
\(182\) −148594. −0.332523
\(183\) 123298. 0.272162
\(184\) 144986. 0.315705
\(185\) −693620. −1.49002
\(186\) −645928. −1.36900
\(187\) 363896. 0.760980
\(188\) −237568. −0.490223
\(189\) 113943. 0.232024
\(190\) −195472. −0.392826
\(191\) 76790.3 0.152308 0.0761540 0.997096i \(-0.475736\pi\)
0.0761540 + 0.997096i \(0.475736\pi\)
\(192\) −192754. −0.377355
\(193\) 496266. 0.959006 0.479503 0.877540i \(-0.340817\pi\)
0.479503 + 0.877540i \(0.340817\pi\)
\(194\) 168120. 0.320712
\(195\) 122507. 0.230714
\(196\) 204371. 0.379996
\(197\) −442784. −0.812879 −0.406439 0.913678i \(-0.633230\pi\)
−0.406439 + 0.913678i \(0.633230\pi\)
\(198\) −265181. −0.480706
\(199\) 730332. 1.30734 0.653668 0.756781i \(-0.273229\pi\)
0.653668 + 0.756781i \(0.273229\pi\)
\(200\) −355457. −0.628365
\(201\) −12823.9 −0.0223888
\(202\) 1.04869e6 1.80830
\(203\) −1.27750e6 −2.17581
\(204\) −205678. −0.346029
\(205\) −1.42936e6 −2.37552
\(206\) −351251. −0.576699
\(207\) −295075. −0.478637
\(208\) 144194. 0.231093
\(209\) −99102.5 −0.156935
\(210\) −1.18450e6 −1.85347
\(211\) 960167. 1.48471 0.742353 0.670008i \(-0.233710\pi\)
0.742353 + 0.670008i \(0.233710\pi\)
\(212\) 616964. 0.942801
\(213\) 310889. 0.469522
\(214\) 323060. 0.482224
\(215\) −2.56439e6 −3.78345
\(216\) −29013.9 −0.0423128
\(217\) −1.46277e6 −2.10876
\(218\) −1.41120e6 −2.01117
\(219\) −451082. −0.635543
\(220\) 1.25671e6 1.75057
\(221\) 105672. 0.145539
\(222\) 435999. 0.593750
\(223\) −114848. −0.154655 −0.0773273 0.997006i \(-0.524639\pi\)
−0.0773273 + 0.997006i \(0.524639\pi\)
\(224\) −1.19512e6 −1.59144
\(225\) 723424. 0.952657
\(226\) −1.38208e6 −1.79996
\(227\) −316011. −0.407040 −0.203520 0.979071i \(-0.565238\pi\)
−0.203520 + 0.979071i \(0.565238\pi\)
\(228\) 56013.9 0.0713606
\(229\) −110133. −0.138781 −0.0693903 0.997590i \(-0.522105\pi\)
−0.0693903 + 0.997590i \(0.522105\pi\)
\(230\) 3.06745e6 3.82348
\(231\) −600530. −0.740465
\(232\) 325296. 0.396788
\(233\) 8645.45 0.0104327 0.00521636 0.999986i \(-0.498340\pi\)
0.00521636 + 0.999986i \(0.498340\pi\)
\(234\) −77006.1 −0.0919359
\(235\) 972956. 1.14927
\(236\) 93326.2 0.109075
\(237\) −627512. −0.725690
\(238\) −1.02172e6 −1.16920
\(239\) 623677. 0.706261 0.353131 0.935574i \(-0.385117\pi\)
0.353131 + 0.935574i \(0.385117\pi\)
\(240\) 1.14942e6 1.28810
\(241\) −1.73477e6 −1.92398 −0.961988 0.273092i \(-0.911954\pi\)
−0.961988 + 0.273092i \(0.911954\pi\)
\(242\) 162555. 0.178427
\(243\) 59049.0 0.0641500
\(244\) 367293. 0.394946
\(245\) −836997. −0.890859
\(246\) 898477. 0.946606
\(247\) −28778.4 −0.0300141
\(248\) 372473. 0.384561
\(249\) 448947. 0.458877
\(250\) −4.88900e6 −4.94732
\(251\) 1.44679e6 1.44951 0.724755 0.689006i \(-0.241953\pi\)
0.724755 + 0.689006i \(0.241953\pi\)
\(252\) 339426. 0.336701
\(253\) 1.55517e6 1.52749
\(254\) −192275. −0.186998
\(255\) 842350. 0.811227
\(256\) 1.30221e6 1.24188
\(257\) −177900. −0.168013 −0.0840064 0.996465i \(-0.526772\pi\)
−0.0840064 + 0.996465i \(0.526772\pi\)
\(258\) 1.61194e6 1.50765
\(259\) 987365. 0.914594
\(260\) 364937. 0.334799
\(261\) −662041. −0.601566
\(262\) 214938. 0.193446
\(263\) −662979. −0.591031 −0.295515 0.955338i \(-0.595491\pi\)
−0.295515 + 0.955338i \(0.595491\pi\)
\(264\) 152916. 0.135034
\(265\) −2.52676e6 −2.21029
\(266\) 278253. 0.241122
\(267\) −456618. −0.391990
\(268\) −38201.3 −0.0324893
\(269\) −1.10386e6 −0.930105 −0.465052 0.885283i \(-0.653965\pi\)
−0.465052 + 0.885283i \(0.653965\pi\)
\(270\) −613844. −0.512447
\(271\) −1.65544e6 −1.36927 −0.684635 0.728886i \(-0.740039\pi\)
−0.684635 + 0.728886i \(0.740039\pi\)
\(272\) 991466. 0.812560
\(273\) −174388. −0.141615
\(274\) 1.48639e6 1.19607
\(275\) −3.81276e6 −3.04024
\(276\) −879001. −0.694571
\(277\) −87836.5 −0.0687821 −0.0343911 0.999408i \(-0.510949\pi\)
−0.0343911 + 0.999408i \(0.510949\pi\)
\(278\) −2.95760e6 −2.29523
\(279\) −758055. −0.583029
\(280\) 683037. 0.520654
\(281\) −800455. −0.604743 −0.302372 0.953190i \(-0.597778\pi\)
−0.302372 + 0.953190i \(0.597778\pi\)
\(282\) −611586. −0.457967
\(283\) −2.09590e6 −1.55563 −0.777813 0.628495i \(-0.783671\pi\)
−0.777813 + 0.628495i \(0.783671\pi\)
\(284\) 926108. 0.681343
\(285\) −229404. −0.167297
\(286\) 405855. 0.293397
\(287\) 2.03469e6 1.45812
\(288\) −619348. −0.440001
\(289\) −693264. −0.488263
\(290\) 6.88225e6 4.80547
\(291\) 197304. 0.136585
\(292\) −1.34373e6 −0.922264
\(293\) 1.40390e6 0.955363 0.477681 0.878533i \(-0.341477\pi\)
0.477681 + 0.878533i \(0.341477\pi\)
\(294\) 526124. 0.354993
\(295\) −382216. −0.255713
\(296\) −251418. −0.166789
\(297\) −311214. −0.204724
\(298\) −744455. −0.485621
\(299\) 451607. 0.292135
\(300\) 2.15501e6 1.38244
\(301\) 3.65040e6 2.32233
\(302\) 217125. 0.136991
\(303\) 1.23074e6 0.770121
\(304\) −270013. −0.167572
\(305\) −1.50424e6 −0.925908
\(306\) −529489. −0.323261
\(307\) −1.33666e6 −0.809422 −0.404711 0.914445i \(-0.632628\pi\)
−0.404711 + 0.914445i \(0.632628\pi\)
\(308\) −1.78892e6 −1.07452
\(309\) −412224. −0.245605
\(310\) 7.88037e6 4.65739
\(311\) −2.02561e6 −1.18756 −0.593778 0.804629i \(-0.702364\pi\)
−0.593778 + 0.804629i \(0.702364\pi\)
\(312\) 44405.3 0.0258255
\(313\) 513441. 0.296231 0.148115 0.988970i \(-0.452679\pi\)
0.148115 + 0.988970i \(0.452679\pi\)
\(314\) −1.13082e6 −0.647245
\(315\) −1.39011e6 −0.789358
\(316\) −1.86930e6 −1.05308
\(317\) 4929.11 0.00275499 0.00137750 0.999999i \(-0.499562\pi\)
0.00137750 + 0.999999i \(0.499562\pi\)
\(318\) 1.58829e6 0.880767
\(319\) 3.48924e6 1.91979
\(320\) 2.35161e6 1.28378
\(321\) 379140. 0.205370
\(322\) −4.36651e6 −2.34690
\(323\) −197879. −0.105534
\(324\) 175902. 0.0930909
\(325\) −1.10719e6 −0.581451
\(326\) −1.07722e6 −0.561386
\(327\) −1.65617e6 −0.856517
\(328\) −518104. −0.265909
\(329\) −1.38500e6 −0.705439
\(330\) 3.23523e6 1.63538
\(331\) −1.97213e6 −0.989386 −0.494693 0.869068i \(-0.664719\pi\)
−0.494693 + 0.869068i \(0.664719\pi\)
\(332\) 1.33737e6 0.665897
\(333\) 511684. 0.252867
\(334\) −256522. −0.125822
\(335\) 156453. 0.0761676
\(336\) −1.63620e6 −0.790655
\(337\) 2.30193e6 1.10412 0.552062 0.833803i \(-0.313841\pi\)
0.552062 + 0.833803i \(0.313841\pi\)
\(338\) −2.72951e6 −1.29955
\(339\) −1.62200e6 −0.766567
\(340\) 2.50928e6 1.17721
\(341\) 3.99528e6 1.86063
\(342\) 144200. 0.0666652
\(343\) −1.43548e6 −0.658814
\(344\) −929521. −0.423509
\(345\) 3.59993e6 1.62835
\(346\) 2.75958e6 1.23923
\(347\) 947055. 0.422232 0.211116 0.977461i \(-0.432290\pi\)
0.211116 + 0.977461i \(0.432290\pi\)
\(348\) −1.97216e6 −0.872959
\(349\) 1.96092e6 0.861781 0.430891 0.902404i \(-0.358199\pi\)
0.430891 + 0.902404i \(0.358199\pi\)
\(350\) 1.07052e7 4.67116
\(351\) −90373.5 −0.0391538
\(352\) 3.26423e6 1.40419
\(353\) 2.49167e6 1.06427 0.532137 0.846658i \(-0.321389\pi\)
0.532137 + 0.846658i \(0.321389\pi\)
\(354\) 240255. 0.101898
\(355\) −3.79286e6 −1.59733
\(356\) −1.36022e6 −0.568834
\(357\) −1.19908e6 −0.497942
\(358\) 396420. 0.163474
\(359\) 282969. 0.115878 0.0579392 0.998320i \(-0.481547\pi\)
0.0579392 + 0.998320i \(0.481547\pi\)
\(360\) 353972. 0.143950
\(361\) −2.42221e6 −0.978236
\(362\) −4.98203e6 −1.99818
\(363\) 190773. 0.0759888
\(364\) −519486. −0.205504
\(365\) 5.50323e6 2.16215
\(366\) 945544. 0.368960
\(367\) 1.02276e6 0.396378 0.198189 0.980164i \(-0.436494\pi\)
0.198189 + 0.980164i \(0.436494\pi\)
\(368\) 4.23720e6 1.63102
\(369\) 1.05444e6 0.403141
\(370\) −5.31922e6 −2.01996
\(371\) 3.59684e6 1.35671
\(372\) −2.25818e6 −0.846059
\(373\) 3.02229e6 1.12477 0.562385 0.826876i \(-0.309884\pi\)
0.562385 + 0.826876i \(0.309884\pi\)
\(374\) 2.79064e6 1.03163
\(375\) −5.73768e6 −2.10697
\(376\) 352669. 0.128646
\(377\) 1.01324e6 0.367164
\(378\) 873805. 0.314547
\(379\) −529457. −0.189336 −0.0946679 0.995509i \(-0.530179\pi\)
−0.0946679 + 0.995509i \(0.530179\pi\)
\(380\) −683372. −0.242772
\(381\) −225652. −0.0796390
\(382\) 588887. 0.206478
\(383\) −2.95011e6 −1.02764 −0.513820 0.857898i \(-0.671770\pi\)
−0.513820 + 0.857898i \(0.671770\pi\)
\(384\) 723939. 0.250538
\(385\) 7.32650e6 2.51910
\(386\) 3.80575e6 1.30009
\(387\) 1.89176e6 0.642078
\(388\) 587751. 0.198205
\(389\) −2.96852e6 −0.994641 −0.497321 0.867567i \(-0.665683\pi\)
−0.497321 + 0.867567i \(0.665683\pi\)
\(390\) 939479. 0.312770
\(391\) 3.10522e6 1.02719
\(392\) −303388. −0.0997202
\(393\) 252249. 0.0823849
\(394\) −3.39561e6 −1.10199
\(395\) 7.65569e6 2.46883
\(396\) −927077. −0.297083
\(397\) 1.04019e6 0.331234 0.165617 0.986190i \(-0.447038\pi\)
0.165617 + 0.986190i \(0.447038\pi\)
\(398\) 5.60075e6 1.77231
\(399\) 326555. 0.102689
\(400\) −1.03882e7 −3.24631
\(401\) 3.31007e6 1.02796 0.513980 0.857802i \(-0.328171\pi\)
0.513980 + 0.857802i \(0.328171\pi\)
\(402\) −98343.8 −0.0303516
\(403\) 1.16019e6 0.355850
\(404\) 3.66625e6 1.11756
\(405\) −720401. −0.218241
\(406\) −9.79686e6 −2.94966
\(407\) −2.69680e6 −0.806979
\(408\) 305328. 0.0908065
\(409\) −5.21191e6 −1.54059 −0.770297 0.637685i \(-0.779892\pi\)
−0.770297 + 0.637685i \(0.779892\pi\)
\(410\) −1.09615e7 −3.22040
\(411\) 1.74441e6 0.509383
\(412\) −1.22798e6 −0.356408
\(413\) 544083. 0.156960
\(414\) −2.26286e6 −0.648870
\(415\) −5.47718e6 −1.56112
\(416\) 947903. 0.268553
\(417\) −3.47100e6 −0.977496
\(418\) −759995. −0.212750
\(419\) −3.41630e6 −0.950649 −0.475325 0.879810i \(-0.657669\pi\)
−0.475325 + 0.879810i \(0.657669\pi\)
\(420\) −4.14102e6 −1.14547
\(421\) 5.70486e6 1.56870 0.784350 0.620319i \(-0.212997\pi\)
0.784350 + 0.620319i \(0.212997\pi\)
\(422\) 7.36331e6 2.01276
\(423\) −717751. −0.195040
\(424\) −915881. −0.247414
\(425\) −7.61296e6 −2.04447
\(426\) 2.38414e6 0.636513
\(427\) 2.14128e6 0.568335
\(428\) 1.12942e6 0.298021
\(429\) 476308. 0.124952
\(430\) −1.96658e7 −5.12908
\(431\) −2.31113e6 −0.599281 −0.299640 0.954052i \(-0.596867\pi\)
−0.299640 + 0.954052i \(0.596867\pi\)
\(432\) −847929. −0.218600
\(433\) −55388.5 −0.0141971 −0.00709856 0.999975i \(-0.502260\pi\)
−0.00709856 + 0.999975i \(0.502260\pi\)
\(434\) −1.12177e7 −2.85876
\(435\) 8.07694e6 2.04656
\(436\) −4.93358e6 −1.24293
\(437\) −845669. −0.211835
\(438\) −3.45925e6 −0.861582
\(439\) −5.60645e6 −1.38844 −0.694219 0.719764i \(-0.744250\pi\)
−0.694219 + 0.719764i \(0.744250\pi\)
\(440\) −1.86558e6 −0.459392
\(441\) 617454. 0.151185
\(442\) 810374. 0.197301
\(443\) 5.33809e6 1.29234 0.646170 0.763194i \(-0.276370\pi\)
0.646170 + 0.763194i \(0.276370\pi\)
\(444\) 1.52426e6 0.366946
\(445\) 5.57077e6 1.33357
\(446\) −880747. −0.209659
\(447\) −873684. −0.206817
\(448\) −3.34751e6 −0.788001
\(449\) −3.68121e6 −0.861737 −0.430869 0.902415i \(-0.641793\pi\)
−0.430869 + 0.902415i \(0.641793\pi\)
\(450\) 5.54778e6 1.29148
\(451\) −5.55737e6 −1.28655
\(452\) −4.83177e6 −1.11240
\(453\) 254815. 0.0583418
\(454\) −2.42342e6 −0.551809
\(455\) 2.12755e6 0.481782
\(456\) −83152.4 −0.0187268
\(457\) 3.14852e6 0.705205 0.352603 0.935773i \(-0.385297\pi\)
0.352603 + 0.935773i \(0.385297\pi\)
\(458\) −844585. −0.188139
\(459\) −621403. −0.137671
\(460\) 1.07239e7 2.36296
\(461\) −3.05916e6 −0.670425 −0.335213 0.942143i \(-0.608808\pi\)
−0.335213 + 0.942143i \(0.608808\pi\)
\(462\) −4.60533e6 −1.00382
\(463\) 8.35625e6 1.81159 0.905793 0.423721i \(-0.139276\pi\)
0.905793 + 0.423721i \(0.139276\pi\)
\(464\) 9.50674e6 2.04992
\(465\) 9.24832e6 1.98349
\(466\) 66300.1 0.0141432
\(467\) 1.16583e6 0.247367 0.123683 0.992322i \(-0.460529\pi\)
0.123683 + 0.992322i \(0.460529\pi\)
\(468\) −269214. −0.0568177
\(469\) −222710. −0.0467527
\(470\) 7.46138e6 1.55803
\(471\) −1.32712e6 −0.275649
\(472\) −138542. −0.0286238
\(473\) −9.97037e6 −2.04908
\(474\) −4.81225e6 −0.983791
\(475\) 2.07330e6 0.421626
\(476\) −3.57196e6 −0.722585
\(477\) 1.86400e6 0.375102
\(478\) 4.78284e6 0.957451
\(479\) −1.23399e6 −0.245737 −0.122869 0.992423i \(-0.539209\pi\)
−0.122869 + 0.992423i \(0.539209\pi\)
\(480\) 7.55609e6 1.49690
\(481\) −783124. −0.154336
\(482\) −1.33036e7 −2.60826
\(483\) −5.12449e6 −0.999500
\(484\) 568294. 0.110271
\(485\) −2.40712e6 −0.464669
\(486\) 452834. 0.0869657
\(487\) 1.60158e6 0.306004 0.153002 0.988226i \(-0.451106\pi\)
0.153002 + 0.988226i \(0.451106\pi\)
\(488\) −545245. −0.103644
\(489\) −1.26422e6 −0.239084
\(490\) −6.41875e6 −1.20770
\(491\) 1.78594e6 0.334321 0.167161 0.985930i \(-0.446540\pi\)
0.167161 + 0.985930i \(0.446540\pi\)
\(492\) 3.14109e6 0.585016
\(493\) 6.96699e6 1.29101
\(494\) −220695. −0.0406889
\(495\) 3.79683e6 0.696479
\(496\) 1.08855e7 1.98675
\(497\) 5.39912e6 0.980465
\(498\) 3.44287e6 0.622082
\(499\) 7.98618e6 1.43578 0.717889 0.696157i \(-0.245108\pi\)
0.717889 + 0.696157i \(0.245108\pi\)
\(500\) −1.70920e7 −3.05751
\(501\) −301051. −0.0535853
\(502\) 1.10951e7 1.96505
\(503\) −3.77866e6 −0.665914 −0.332957 0.942942i \(-0.608046\pi\)
−0.332957 + 0.942942i \(0.608046\pi\)
\(504\) −503877. −0.0883585
\(505\) −1.50151e7 −2.61999
\(506\) 1.19263e7 2.07075
\(507\) −3.20332e6 −0.553453
\(508\) −672196. −0.115568
\(509\) −5.46200e6 −0.934452 −0.467226 0.884138i \(-0.654747\pi\)
−0.467226 + 0.884138i \(0.654747\pi\)
\(510\) 6.45980e6 1.09975
\(511\) −7.83382e6 −1.32715
\(512\) 7.41233e6 1.24963
\(513\) 169231. 0.0283914
\(514\) −1.36427e6 −0.227768
\(515\) 5.02916e6 0.835559
\(516\) 5.63537e6 0.931747
\(517\) 3.78286e6 0.622434
\(518\) 7.57189e6 1.23988
\(519\) 3.23862e6 0.527766
\(520\) −541748. −0.0878595
\(521\) −3.79145e6 −0.611944 −0.305972 0.952041i \(-0.598981\pi\)
−0.305972 + 0.952041i \(0.598981\pi\)
\(522\) −5.07705e6 −0.815520
\(523\) 2.52314e6 0.403355 0.201678 0.979452i \(-0.435361\pi\)
0.201678 + 0.979452i \(0.435361\pi\)
\(524\) 751426. 0.119552
\(525\) 1.25635e7 1.98936
\(526\) −5.08424e6 −0.801238
\(527\) 7.97740e6 1.25122
\(528\) 4.46895e6 0.697623
\(529\) 6.83438e6 1.06184
\(530\) −1.93772e7 −2.99641
\(531\) 281961. 0.0433963
\(532\) 972778. 0.149017
\(533\) −1.61381e6 −0.246056
\(534\) −3.50170e6 −0.531406
\(535\) −4.62553e6 −0.698678
\(536\) 56709.6 0.00852599
\(537\) 465235. 0.0696204
\(538\) −8.46523e6 −1.26091
\(539\) −3.25425e6 −0.482480
\(540\) −2.14601e6 −0.316699
\(541\) 3.18382e6 0.467687 0.233844 0.972274i \(-0.424870\pi\)
0.233844 + 0.972274i \(0.424870\pi\)
\(542\) −1.26952e7 −1.85627
\(543\) −5.84686e6 −0.850988
\(544\) 6.51772e6 0.944275
\(545\) 2.02054e7 2.91391
\(546\) −1.33734e6 −0.191982
\(547\) 1.08153e7 1.54550 0.772749 0.634712i \(-0.218881\pi\)
0.772749 + 0.634712i \(0.218881\pi\)
\(548\) 5.19644e6 0.739188
\(549\) 1.10968e6 0.157133
\(550\) −2.92392e7 −4.12153
\(551\) −1.89737e6 −0.266240
\(552\) 1.30487e6 0.182272
\(553\) −1.08978e7 −1.51540
\(554\) −673599. −0.0932453
\(555\) −6.24258e6 −0.860264
\(556\) −1.03398e7 −1.41849
\(557\) −300600. −0.0410536 −0.0205268 0.999789i \(-0.506534\pi\)
−0.0205268 + 0.999789i \(0.506534\pi\)
\(558\) −5.81336e6 −0.790390
\(559\) −2.89530e6 −0.391890
\(560\) 1.99617e7 2.68984
\(561\) 3.27506e6 0.439352
\(562\) −6.13851e6 −0.819827
\(563\) −9.21092e6 −1.22471 −0.612353 0.790584i \(-0.709777\pi\)
−0.612353 + 0.790584i \(0.709777\pi\)
\(564\) −2.13811e6 −0.283030
\(565\) 1.97884e7 2.60790
\(566\) −1.60730e7 −2.10890
\(567\) 1.02549e6 0.133959
\(568\) −1.37480e6 −0.178801
\(569\) −1.44126e6 −0.186621 −0.0933106 0.995637i \(-0.529745\pi\)
−0.0933106 + 0.995637i \(0.529745\pi\)
\(570\) −1.75925e6 −0.226798
\(571\) 4.03264e6 0.517606 0.258803 0.965930i \(-0.416672\pi\)
0.258803 + 0.965930i \(0.416672\pi\)
\(572\) 1.41888e6 0.181324
\(573\) 691112. 0.0879351
\(574\) 1.56036e7 1.97672
\(575\) −3.25353e7 −4.10379
\(576\) −1.73479e6 −0.217866
\(577\) 2.52617e6 0.315880 0.157940 0.987449i \(-0.449515\pi\)
0.157940 + 0.987449i \(0.449515\pi\)
\(578\) −5.31649e6 −0.661919
\(579\) 4.46639e6 0.553682
\(580\) 2.40605e7 2.96985
\(581\) 7.79674e6 0.958237
\(582\) 1.51308e6 0.185163
\(583\) −9.82407e6 −1.19707
\(584\) 1.99477e6 0.242025
\(585\) 1.10256e6 0.133203
\(586\) 1.07662e7 1.29515
\(587\) 5.01886e6 0.601188 0.300594 0.953752i \(-0.402815\pi\)
0.300594 + 0.953752i \(0.402815\pi\)
\(588\) 1.83934e6 0.219391
\(589\) −2.17255e6 −0.258036
\(590\) −2.93113e6 −0.346661
\(591\) −3.98505e6 −0.469316
\(592\) −7.34766e6 −0.861678
\(593\) −1.51902e7 −1.77390 −0.886948 0.461870i \(-0.847179\pi\)
−0.886948 + 0.461870i \(0.847179\pi\)
\(594\) −2.38663e6 −0.277536
\(595\) 1.46289e7 1.69402
\(596\) −2.60263e6 −0.300121
\(597\) 6.57299e6 0.754791
\(598\) 3.46328e6 0.396036
\(599\) 7.13948e6 0.813017 0.406509 0.913647i \(-0.366746\pi\)
0.406509 + 0.913647i \(0.366746\pi\)
\(600\) −3.19911e6 −0.362786
\(601\) 8.80337e6 0.994175 0.497088 0.867700i \(-0.334403\pi\)
0.497088 + 0.867700i \(0.334403\pi\)
\(602\) 2.79941e7 3.14830
\(603\) −115415. −0.0129262
\(604\) 759072. 0.0846624
\(605\) −2.32744e6 −0.258517
\(606\) 9.43825e6 1.04402
\(607\) −9.90444e6 −1.09108 −0.545542 0.838084i \(-0.683676\pi\)
−0.545542 + 0.838084i \(0.683676\pi\)
\(608\) −1.77502e6 −0.194735
\(609\) −1.14975e7 −1.25620
\(610\) −1.15357e7 −1.25522
\(611\) 1.09851e6 0.119042
\(612\) −1.85110e6 −0.199780
\(613\) 7.13725e6 0.767149 0.383574 0.923510i \(-0.374693\pi\)
0.383574 + 0.923510i \(0.374693\pi\)
\(614\) −1.02506e7 −1.09730
\(615\) −1.28643e7 −1.37151
\(616\) 2.65565e6 0.281981
\(617\) −6.15006e6 −0.650379 −0.325189 0.945649i \(-0.605428\pi\)
−0.325189 + 0.945649i \(0.605428\pi\)
\(618\) −3.16125e6 −0.332957
\(619\) −749330. −0.0786043 −0.0393022 0.999227i \(-0.512513\pi\)
−0.0393022 + 0.999227i \(0.512513\pi\)
\(620\) 2.75499e7 2.87833
\(621\) −2.65567e6 −0.276341
\(622\) −1.55339e7 −1.60992
\(623\) −7.92997e6 −0.818561
\(624\) 1.29774e6 0.133422
\(625\) 4.20901e7 4.31003
\(626\) 3.93747e6 0.401588
\(627\) −891923. −0.0906063
\(628\) −3.95336e6 −0.400007
\(629\) −5.38472e6 −0.542670
\(630\) −1.06605e7 −1.07010
\(631\) −2.06221e6 −0.206186 −0.103093 0.994672i \(-0.532874\pi\)
−0.103093 + 0.994672i \(0.532874\pi\)
\(632\) 2.77497e6 0.276354
\(633\) 8.64150e6 0.857196
\(634\) 37800.2 0.00373483
\(635\) 2.75296e6 0.270936
\(636\) 5.55267e6 0.544326
\(637\) −945003. −0.0922751
\(638\) 2.67582e7 2.60259
\(639\) 2.79800e6 0.271078
\(640\) −8.83210e6 −0.852342
\(641\) −3.59859e6 −0.345929 −0.172964 0.984928i \(-0.555335\pi\)
−0.172964 + 0.984928i \(0.555335\pi\)
\(642\) 2.90754e6 0.278412
\(643\) 1.37456e7 1.31110 0.655549 0.755153i \(-0.272437\pi\)
0.655549 + 0.755153i \(0.272437\pi\)
\(644\) −1.52654e7 −1.45042
\(645\) −2.30795e7 −2.18438
\(646\) −1.51749e6 −0.143068
\(647\) 5.03818e6 0.473165 0.236583 0.971611i \(-0.423973\pi\)
0.236583 + 0.971611i \(0.423973\pi\)
\(648\) −261125. −0.0244293
\(649\) −1.48606e6 −0.138492
\(650\) −8.49078e6 −0.788251
\(651\) −1.31649e7 −1.21749
\(652\) −3.76599e6 −0.346945
\(653\) 1.53399e7 1.40780 0.703898 0.710301i \(-0.251441\pi\)
0.703898 + 0.710301i \(0.251441\pi\)
\(654\) −1.27008e7 −1.16115
\(655\) −3.07745e6 −0.280277
\(656\) −1.51415e7 −1.37376
\(657\) −4.05974e6 −0.366931
\(658\) −1.06212e7 −0.956337
\(659\) −3.56478e6 −0.319756 −0.159878 0.987137i \(-0.551110\pi\)
−0.159878 + 0.987137i \(0.551110\pi\)
\(660\) 1.13104e7 1.01069
\(661\) −1.62245e7 −1.44434 −0.722168 0.691718i \(-0.756854\pi\)
−0.722168 + 0.691718i \(0.756854\pi\)
\(662\) −1.51238e7 −1.34127
\(663\) 951047. 0.0840269
\(664\) −1.98532e6 −0.174748
\(665\) −3.98399e6 −0.349353
\(666\) 3.92399e6 0.342802
\(667\) 2.97747e7 2.59139
\(668\) −896804. −0.0777600
\(669\) −1.03364e6 −0.0892899
\(670\) 1.19980e6 0.103258
\(671\) −5.84850e6 −0.501462
\(672\) −1.07561e7 −0.918819
\(673\) 3.40408e6 0.289709 0.144854 0.989453i \(-0.453729\pi\)
0.144854 + 0.989453i \(0.453729\pi\)
\(674\) 1.76530e7 1.49682
\(675\) 6.51082e6 0.550017
\(676\) −9.54240e6 −0.803139
\(677\) 1.17767e7 0.987531 0.493766 0.869595i \(-0.335620\pi\)
0.493766 + 0.869595i \(0.335620\pi\)
\(678\) −1.24387e7 −1.03921
\(679\) 3.42653e6 0.285220
\(680\) −3.72502e6 −0.308928
\(681\) −2.84410e6 −0.235005
\(682\) 3.06389e7 2.52239
\(683\) 1.47519e7 1.21003 0.605015 0.796214i \(-0.293167\pi\)
0.605015 + 0.796214i \(0.293167\pi\)
\(684\) 504125. 0.0412000
\(685\) −2.12819e7 −1.73294
\(686\) −1.10084e7 −0.893128
\(687\) −991196. −0.0801250
\(688\) −2.71652e7 −2.18797
\(689\) −2.85282e6 −0.228942
\(690\) 2.76071e7 2.20749
\(691\) −1.18621e6 −0.0945079 −0.0472539 0.998883i \(-0.515047\pi\)
−0.0472539 + 0.998883i \(0.515047\pi\)
\(692\) 9.64755e6 0.765864
\(693\) −5.40477e6 −0.427508
\(694\) 7.26275e6 0.572404
\(695\) 4.23465e7 3.32549
\(696\) 2.92766e6 0.229086
\(697\) −1.10964e7 −0.865171
\(698\) 1.50379e7 1.16828
\(699\) 77809.1 0.00602334
\(700\) 3.74256e7 2.88684
\(701\) −1.36391e7 −1.04831 −0.524155 0.851623i \(-0.675619\pi\)
−0.524155 + 0.851623i \(0.675619\pi\)
\(702\) −693055. −0.0530792
\(703\) 1.46646e6 0.111913
\(704\) 9.14308e6 0.695282
\(705\) 8.75660e6 0.663534
\(706\) 1.91081e7 1.44280
\(707\) 2.13739e7 1.60818
\(708\) 839936. 0.0629743
\(709\) −1.43919e7 −1.07524 −0.537618 0.843189i \(-0.680676\pi\)
−0.537618 + 0.843189i \(0.680676\pi\)
\(710\) −2.90866e7 −2.16544
\(711\) −5.64761e6 −0.418978
\(712\) 2.01925e6 0.149276
\(713\) 3.40928e7 2.51153
\(714\) −9.19550e6 −0.675040
\(715\) −5.81098e6 −0.425093
\(716\) 1.38589e6 0.101029
\(717\) 5.61310e6 0.407760
\(718\) 2.17003e6 0.157092
\(719\) 1.64117e7 1.18395 0.591974 0.805957i \(-0.298349\pi\)
0.591974 + 0.805957i \(0.298349\pi\)
\(720\) 1.03448e7 0.743687
\(721\) −7.15899e6 −0.512877
\(722\) −1.85754e7 −1.32616
\(723\) −1.56129e7 −1.11081
\(724\) −1.74173e7 −1.23491
\(725\) −7.29974e7 −5.15778
\(726\) 1.46299e6 0.103015
\(727\) −1.31438e7 −0.922328 −0.461164 0.887315i \(-0.652568\pi\)
−0.461164 + 0.887315i \(0.652568\pi\)
\(728\) 771176. 0.0539293
\(729\) 531441. 0.0370370
\(730\) 4.22030e7 2.93114
\(731\) −1.99079e7 −1.37795
\(732\) 3.30564e6 0.228022
\(733\) 2.02772e6 0.139395 0.0696977 0.997568i \(-0.477797\pi\)
0.0696977 + 0.997568i \(0.477797\pi\)
\(734\) 7.84333e6 0.537354
\(735\) −7.53298e6 −0.514338
\(736\) 2.78546e7 1.89541
\(737\) 608288. 0.0412516
\(738\) 8.08629e6 0.546523
\(739\) −1.39245e7 −0.937929 −0.468964 0.883217i \(-0.655373\pi\)
−0.468964 + 0.883217i \(0.655373\pi\)
\(740\) −1.85961e7 −1.24837
\(741\) −259006. −0.0173286
\(742\) 2.75834e7 1.83924
\(743\) −1.13430e6 −0.0753800 −0.0376900 0.999289i \(-0.512000\pi\)
−0.0376900 + 0.999289i \(0.512000\pi\)
\(744\) 3.35226e6 0.222026
\(745\) 1.06590e7 0.703600
\(746\) 2.31772e7 1.52481
\(747\) 4.04052e6 0.264933
\(748\) 9.75611e6 0.637562
\(749\) 6.58442e6 0.428858
\(750\) −4.40010e7 −2.85633
\(751\) −2.62894e7 −1.70091 −0.850456 0.526047i \(-0.823674\pi\)
−0.850456 + 0.526047i \(0.823674\pi\)
\(752\) 1.03067e7 0.664624
\(753\) 1.30211e7 0.836875
\(754\) 7.77033e6 0.497750
\(755\) −3.10876e6 −0.198482
\(756\) 3.05484e6 0.194394
\(757\) 2.04231e7 1.29534 0.647668 0.761923i \(-0.275744\pi\)
0.647668 + 0.761923i \(0.275744\pi\)
\(758\) −4.06029e6 −0.256675
\(759\) 1.39966e7 0.881895
\(760\) 1.01446e6 0.0637093
\(761\) 671201. 0.0420137 0.0210068 0.999779i \(-0.493313\pi\)
0.0210068 + 0.999779i \(0.493313\pi\)
\(762\) −1.73047e6 −0.107964
\(763\) −2.87623e7 −1.78860
\(764\) 2.05876e6 0.127606
\(765\) 7.58115e6 0.468362
\(766\) −2.26237e7 −1.39313
\(767\) −431537. −0.0264868
\(768\) 1.17199e7 0.717000
\(769\) 5.15936e6 0.314616 0.157308 0.987550i \(-0.449719\pi\)
0.157308 + 0.987550i \(0.449719\pi\)
\(770\) 5.61853e7 3.41504
\(771\) −1.60110e6 −0.0970022
\(772\) 1.33050e7 0.803472
\(773\) 1.30533e7 0.785727 0.392863 0.919597i \(-0.371485\pi\)
0.392863 + 0.919597i \(0.371485\pi\)
\(774\) 1.45075e7 0.870440
\(775\) −8.35841e7 −4.99884
\(776\) −872515. −0.0520138
\(777\) 8.88629e6 0.528041
\(778\) −2.27650e7 −1.34840
\(779\) 3.02198e6 0.178422
\(780\) 3.28443e6 0.193296
\(781\) −1.47467e7 −0.865099
\(782\) 2.38133e7 1.39252
\(783\) −5.95837e6 −0.347314
\(784\) −8.86649e6 −0.515183
\(785\) 1.61909e7 0.937772
\(786\) 1.93444e6 0.111686
\(787\) −1.77189e7 −1.01977 −0.509883 0.860244i \(-0.670311\pi\)
−0.509883 + 0.860244i \(0.670311\pi\)
\(788\) −1.18711e7 −0.681045
\(789\) −5.96681e6 −0.341232
\(790\) 5.87098e7 3.34690
\(791\) −2.81688e7 −1.60076
\(792\) 1.37624e6 0.0779619
\(793\) −1.69835e6 −0.0959056
\(794\) 7.97695e6 0.449041
\(795\) −2.27409e7 −1.27611
\(796\) 1.95803e7 1.09531
\(797\) 1.81052e7 1.00962 0.504809 0.863231i \(-0.331563\pi\)
0.504809 + 0.863231i \(0.331563\pi\)
\(798\) 2.50428e6 0.139212
\(799\) 7.55326e6 0.418569
\(800\) −6.82901e7 −3.77253
\(801\) −4.10956e6 −0.226315
\(802\) 2.53842e7 1.39357
\(803\) 2.13966e7 1.17100
\(804\) −343811. −0.0187577
\(805\) 6.25191e7 3.40034
\(806\) 8.89725e6 0.482412
\(807\) −9.93471e6 −0.536996
\(808\) −5.44254e6 −0.293274
\(809\) −1.50822e7 −0.810204 −0.405102 0.914272i \(-0.632764\pi\)
−0.405102 + 0.914272i \(0.632764\pi\)
\(810\) −5.52460e6 −0.295861
\(811\) 3.23070e7 1.72482 0.862411 0.506209i \(-0.168954\pi\)
0.862411 + 0.506209i \(0.168954\pi\)
\(812\) −3.42500e7 −1.82293
\(813\) −1.48989e7 −0.790549
\(814\) −2.06811e7 −1.09399
\(815\) 1.54235e7 0.813374
\(816\) 8.92319e6 0.469132
\(817\) 5.42167e6 0.284170
\(818\) −3.99690e7 −2.08852
\(819\) −1.56949e6 −0.0817617
\(820\) −3.83215e7 −1.99025
\(821\) −3.33802e7 −1.72835 −0.864175 0.503191i \(-0.832159\pi\)
−0.864175 + 0.503191i \(0.832159\pi\)
\(822\) 1.33775e7 0.690551
\(823\) 3.38256e7 1.74079 0.870393 0.492357i \(-0.163865\pi\)
0.870393 + 0.492357i \(0.163865\pi\)
\(824\) 1.82293e6 0.0935301
\(825\) −3.43148e7 −1.75528
\(826\) 4.17245e6 0.212785
\(827\) 3.25009e7 1.65246 0.826231 0.563332i \(-0.190481\pi\)
0.826231 + 0.563332i \(0.190481\pi\)
\(828\) −7.91101e6 −0.401011
\(829\) −508321. −0.0256893 −0.0128446 0.999918i \(-0.504089\pi\)
−0.0128446 + 0.999918i \(0.504089\pi\)
\(830\) −4.20033e7 −2.11635
\(831\) −790529. −0.0397114
\(832\) 2.65506e6 0.132974
\(833\) −6.49778e6 −0.324454
\(834\) −2.66184e7 −1.32515
\(835\) 3.67284e6 0.182300
\(836\) −2.65696e6 −0.131483
\(837\) −6.82249e6 −0.336612
\(838\) −2.61988e7 −1.28876
\(839\) −583710. −0.0286281 −0.0143140 0.999898i \(-0.504556\pi\)
−0.0143140 + 0.999898i \(0.504556\pi\)
\(840\) 6.14733e6 0.300600
\(841\) 4.62924e7 2.25694
\(842\) 4.37493e7 2.12663
\(843\) −7.20409e6 −0.349149
\(844\) 2.57423e7 1.24391
\(845\) 3.90807e7 1.88287
\(846\) −5.50427e6 −0.264408
\(847\) 3.31310e6 0.158681
\(848\) −2.67665e7 −1.27821
\(849\) −1.88631e7 −0.898141
\(850\) −5.83821e7 −2.77161
\(851\) −2.30125e7 −1.08928
\(852\) 8.33498e6 0.393374
\(853\) 9.83319e6 0.462724 0.231362 0.972868i \(-0.425682\pi\)
0.231362 + 0.972868i \(0.425682\pi\)
\(854\) 1.64210e7 0.770469
\(855\) −2.06463e6 −0.0965890
\(856\) −1.67662e6 −0.0782081
\(857\) 1.07762e7 0.501201 0.250601 0.968091i \(-0.419372\pi\)
0.250601 + 0.968091i \(0.419372\pi\)
\(858\) 3.65270e6 0.169393
\(859\) −3.47029e7 −1.60466 −0.802329 0.596883i \(-0.796406\pi\)
−0.802329 + 0.596883i \(0.796406\pi\)
\(860\) −6.87518e7 −3.16985
\(861\) 1.83122e7 0.841848
\(862\) −1.77235e7 −0.812422
\(863\) −2.34351e7 −1.07112 −0.535561 0.844496i \(-0.679900\pi\)
−0.535561 + 0.844496i \(0.679900\pi\)
\(864\) −5.57414e6 −0.254035
\(865\) −3.95114e7 −1.79548
\(866\) −424762. −0.0192465
\(867\) −6.23937e6 −0.281899
\(868\) −3.92172e7 −1.76676
\(869\) 2.97654e7 1.33709
\(870\) 6.19403e7 2.77444
\(871\) 176641. 0.00788944
\(872\) 7.32389e6 0.326175
\(873\) 1.77574e6 0.0788575
\(874\) −6.48525e6 −0.287176
\(875\) −9.96447e7 −4.39981
\(876\) −1.20936e7 −0.532470
\(877\) 5.93447e6 0.260545 0.130273 0.991478i \(-0.458415\pi\)
0.130273 + 0.991478i \(0.458415\pi\)
\(878\) −4.29946e7 −1.88225
\(879\) 1.26351e7 0.551579
\(880\) −5.45215e7 −2.37335
\(881\) −7.45973e6 −0.323805 −0.161902 0.986807i \(-0.551763\pi\)
−0.161902 + 0.986807i \(0.551763\pi\)
\(882\) 4.73512e6 0.204955
\(883\) −2.46902e7 −1.06567 −0.532835 0.846219i \(-0.678873\pi\)
−0.532835 + 0.846219i \(0.678873\pi\)
\(884\) 2.83308e6 0.121935
\(885\) −3.43994e6 −0.147636
\(886\) 4.09366e7 1.75198
\(887\) 2.56140e7 1.09312 0.546562 0.837419i \(-0.315936\pi\)
0.546562 + 0.837419i \(0.315936\pi\)
\(888\) −2.26276e6 −0.0962955
\(889\) −3.91883e6 −0.166304
\(890\) 4.27210e7 1.80787
\(891\) −2.80092e6 −0.118197
\(892\) −3.07911e6 −0.129572
\(893\) −2.05704e6 −0.0863204
\(894\) −6.70009e6 −0.280374
\(895\) −5.67589e6 −0.236852
\(896\) 1.25725e7 0.523179
\(897\) 4.06447e6 0.168664
\(898\) −2.82304e7 −1.16822
\(899\) 7.64919e7 3.15658
\(900\) 1.93951e7 0.798153
\(901\) −1.96158e7 −0.804996
\(902\) −4.26183e7 −1.74413
\(903\) 3.28536e7 1.34080
\(904\) 7.17275e6 0.291921
\(905\) 7.13321e7 2.89510
\(906\) 1.95412e6 0.0790918
\(907\) −1.05309e7 −0.425055 −0.212528 0.977155i \(-0.568170\pi\)
−0.212528 + 0.977155i \(0.568170\pi\)
\(908\) −8.47231e6 −0.341026
\(909\) 1.10766e7 0.444629
\(910\) 1.63157e7 0.653133
\(911\) 8.73649e6 0.348772 0.174386 0.984677i \(-0.444206\pi\)
0.174386 + 0.984677i \(0.444206\pi\)
\(912\) −2.43012e6 −0.0967477
\(913\) −2.12953e7 −0.845487
\(914\) 2.41453e7 0.956019
\(915\) −1.35382e7 −0.534573
\(916\) −2.95268e6 −0.116273
\(917\) 4.38074e6 0.172038
\(918\) −4.76540e6 −0.186635
\(919\) −1.11596e7 −0.435874 −0.217937 0.975963i \(-0.569933\pi\)
−0.217937 + 0.975963i \(0.569933\pi\)
\(920\) −1.59195e7 −0.620099
\(921\) −1.20299e7 −0.467320
\(922\) −2.34600e7 −0.908870
\(923\) −4.28229e6 −0.165452
\(924\) −1.61003e7 −0.620375
\(925\) 5.64189e7 2.16806
\(926\) 6.40822e7 2.45590
\(927\) −3.71002e6 −0.141800
\(928\) 6.24957e7 2.38221
\(929\) 334818. 0.0127283 0.00636415 0.999980i \(-0.497974\pi\)
0.00636415 + 0.999980i \(0.497974\pi\)
\(930\) 7.09233e7 2.68894
\(931\) 1.76959e6 0.0669112
\(932\) 231786. 0.00874073
\(933\) −1.82305e7 −0.685636
\(934\) 8.94046e6 0.335345
\(935\) −3.99560e7 −1.49469
\(936\) 399648. 0.0149104
\(937\) −4.10034e6 −0.152571 −0.0762853 0.997086i \(-0.524306\pi\)
−0.0762853 + 0.997086i \(0.524306\pi\)
\(938\) −1.70791e6 −0.0633808
\(939\) 4.62097e6 0.171029
\(940\) 2.60851e7 0.962882
\(941\) −760066. −0.0279819 −0.0139910 0.999902i \(-0.504454\pi\)
−0.0139910 + 0.999902i \(0.504454\pi\)
\(942\) −1.01774e7 −0.373687
\(943\) −4.74226e7 −1.73663
\(944\) −4.04889e6 −0.147879
\(945\) −1.25110e7 −0.455736
\(946\) −7.64606e7 −2.77786
\(947\) 2.02978e7 0.735486 0.367743 0.929927i \(-0.380131\pi\)
0.367743 + 0.929927i \(0.380131\pi\)
\(948\) −1.68237e7 −0.607997
\(949\) 6.21336e6 0.223955
\(950\) 1.58996e7 0.571582
\(951\) 44362.0 0.00159059
\(952\) 5.30256e6 0.189624
\(953\) −7.64595e6 −0.272709 −0.136354 0.990660i \(-0.543539\pi\)
−0.136354 + 0.990660i \(0.543539\pi\)
\(954\) 1.42946e7 0.508511
\(955\) −8.43161e6 −0.299159
\(956\) 1.67209e7 0.591718
\(957\) 3.14032e7 1.10839
\(958\) −9.46316e6 −0.333137
\(959\) 3.02947e7 1.06370
\(960\) 2.11645e7 0.741191
\(961\) 5.89562e7 2.05931
\(962\) −6.00561e6 −0.209228
\(963\) 3.41226e6 0.118570
\(964\) −4.65095e7 −1.61194
\(965\) −5.44903e7 −1.88365
\(966\) −3.92986e7 −1.35498
\(967\) −362592. −0.0124696 −0.00623479 0.999981i \(-0.501985\pi\)
−0.00623479 + 0.999981i \(0.501985\pi\)
\(968\) −843631. −0.0289377
\(969\) −1.78091e6 −0.0609301
\(970\) −1.84597e7 −0.629934
\(971\) −4.16836e7 −1.41879 −0.709393 0.704813i \(-0.751031\pi\)
−0.709393 + 0.704813i \(0.751031\pi\)
\(972\) 1.58311e6 0.0537460
\(973\) −6.02800e7 −2.04123
\(974\) 1.22822e7 0.414838
\(975\) −9.96470e6 −0.335701
\(976\) −1.59347e7 −0.535452
\(977\) −2.63657e7 −0.883695 −0.441847 0.897090i \(-0.645677\pi\)
−0.441847 + 0.897090i \(0.645677\pi\)
\(978\) −9.69501e6 −0.324117
\(979\) 2.16592e7 0.722246
\(980\) −2.24400e7 −0.746377
\(981\) −1.49055e7 −0.494510
\(982\) 1.36960e7 0.453227
\(983\) 3.95927e6 0.130687 0.0653433 0.997863i \(-0.479186\pi\)
0.0653433 + 0.997863i \(0.479186\pi\)
\(984\) −4.66294e6 −0.153522
\(985\) 4.86179e7 1.59663
\(986\) 5.34283e7 1.75017
\(987\) −1.24650e7 −0.407286
\(988\) −771555. −0.0251463
\(989\) −8.50800e7 −2.76590
\(990\) 2.91170e7 0.944189
\(991\) −3.87210e7 −1.25246 −0.626228 0.779640i \(-0.715402\pi\)
−0.626228 + 0.779640i \(0.715402\pi\)
\(992\) 7.15592e7 2.30880
\(993\) −1.77492e7 −0.571222
\(994\) 4.14047e7 1.32918
\(995\) −8.01908e7 −2.56783
\(996\) 1.20363e7 0.384456
\(997\) 3.15392e7 1.00488 0.502438 0.864613i \(-0.332436\pi\)
0.502438 + 0.864613i \(0.332436\pi\)
\(998\) 6.12442e7 1.94643
\(999\) 4.60516e6 0.145993
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 177.6.a.a.1.10 11
3.2 odd 2 531.6.a.b.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.10 11 1.1 even 1 trivial
531.6.a.b.1.2 11 3.2 odd 2