Properties

Label 177.6.a.b.1.1
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $1$
Dimension $12$
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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + 3566264 x^{5} + 15496192 x^{4} - 53008480 x^{3} - 16576192 x^{2} + 120303168 x - 50564480\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(10.9029\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-10.9029 q^{2} -9.00000 q^{3} +86.8728 q^{4} +88.1143 q^{5} +98.1259 q^{6} +61.7114 q^{7} -598.272 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-10.9029 q^{2} -9.00000 q^{3} +86.8728 q^{4} +88.1143 q^{5} +98.1259 q^{6} +61.7114 q^{7} -598.272 q^{8} +81.0000 q^{9} -960.699 q^{10} +423.027 q^{11} -781.856 q^{12} -1047.72 q^{13} -672.832 q^{14} -793.028 q^{15} +3742.96 q^{16} -2034.81 q^{17} -883.133 q^{18} -1532.11 q^{19} +7654.74 q^{20} -555.403 q^{21} -4612.21 q^{22} +2986.67 q^{23} +5384.45 q^{24} +4639.12 q^{25} +11423.2 q^{26} -729.000 q^{27} +5361.05 q^{28} +115.477 q^{29} +8646.29 q^{30} -3626.28 q^{31} -21664.3 q^{32} -3807.24 q^{33} +22185.3 q^{34} +5437.66 q^{35} +7036.70 q^{36} -15040.3 q^{37} +16704.4 q^{38} +9429.51 q^{39} -52716.3 q^{40} -829.256 q^{41} +6055.49 q^{42} -12294.1 q^{43} +36749.5 q^{44} +7137.25 q^{45} -32563.3 q^{46} -16104.8 q^{47} -33686.6 q^{48} -12998.7 q^{49} -50579.8 q^{50} +18313.3 q^{51} -91018.7 q^{52} +34428.4 q^{53} +7948.20 q^{54} +37274.7 q^{55} -36920.2 q^{56} +13788.9 q^{57} -1259.04 q^{58} -3481.00 q^{59} -68892.6 q^{60} +16418.9 q^{61} +39536.9 q^{62} +4998.63 q^{63} +116429. q^{64} -92319.3 q^{65} +41509.9 q^{66} +9818.25 q^{67} -176770. q^{68} -26880.0 q^{69} -59286.1 q^{70} +3381.64 q^{71} -48460.0 q^{72} +27012.0 q^{73} +163982. q^{74} -41752.1 q^{75} -133098. q^{76} +26105.6 q^{77} -102809. q^{78} +20426.3 q^{79} +329808. q^{80} +6561.00 q^{81} +9041.29 q^{82} -54511.3 q^{83} -48249.4 q^{84} -179296. q^{85} +134041. q^{86} -1039.30 q^{87} -253085. q^{88} -69700.2 q^{89} -77816.6 q^{90} -64656.5 q^{91} +259460. q^{92} +32636.5 q^{93} +175589. q^{94} -135000. q^{95} +194979. q^{96} +48526.4 q^{97} +141723. q^{98} +34265.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - 108q^{3} + 198q^{4} + 36q^{5} + 36q^{6} - 411q^{7} - 69q^{8} + 972q^{9} - 863q^{10} + 492q^{11} - 1782q^{12} - 974q^{13} - 967q^{14} - 324q^{15} + 6370q^{16} - 1463q^{17} - 324q^{18} - 3189q^{19} - 835q^{20} + 3699q^{21} - 2726q^{22} - 2617q^{23} + 621q^{24} + 8642q^{25} + 2414q^{26} - 8748q^{27} - 20458q^{28} - 1963q^{29} + 7767q^{30} - 11929q^{31} - 14382q^{32} - 4428q^{33} - 20744q^{34} + 1829q^{35} + 16038q^{36} - 28105q^{37} - 23475q^{38} + 8766q^{39} - 100576q^{40} - 7585q^{41} + 8703q^{42} - 33146q^{43} + 26014q^{44} + 2916q^{45} - 142851q^{46} - 79215q^{47} - 57330q^{48} - 32569q^{49} - 136019q^{50} + 13167q^{51} - 248218q^{52} - 12220q^{53} + 2916q^{54} - 117770q^{55} - 186728q^{56} + 28701q^{57} - 188072q^{58} - 41772q^{59} + 7515q^{60} - 54195q^{61} + 36230q^{62} - 33291q^{63} + 45197q^{64} + 42368q^{65} + 24534q^{66} + 24224q^{67} - 209639q^{68} + 23553q^{69} - 35684q^{70} + 60254q^{71} - 5589q^{72} - 15385q^{73} + 214638q^{74} - 77778q^{75} - 167504q^{76} - 17169q^{77} - 21726q^{78} - 27054q^{79} + 216899q^{80} + 78732q^{81} + 37917q^{82} - 117595q^{83} + 184122q^{84} - 121585q^{85} + 306756q^{86} + 17667q^{87} - 105799q^{88} - 36033q^{89} - 69903q^{90} - 32217q^{91} - 30906q^{92} + 107361q^{93} + 128392q^{94} - 50721q^{95} + 129438q^{96} - 196914q^{97} + 574100q^{98} + 39852q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.9029 −1.92738 −0.963688 0.267032i \(-0.913957\pi\)
−0.963688 + 0.267032i \(0.913957\pi\)
\(3\) −9.00000 −0.577350
\(4\) 86.8728 2.71478
\(5\) 88.1143 1.57624 0.788118 0.615524i \(-0.211056\pi\)
0.788118 + 0.615524i \(0.211056\pi\)
\(6\) 98.1259 1.11277
\(7\) 61.7114 0.476015 0.238007 0.971263i \(-0.423506\pi\)
0.238007 + 0.971263i \(0.423506\pi\)
\(8\) −598.272 −3.30502
\(9\) 81.0000 0.333333
\(10\) −960.699 −3.03800
\(11\) 423.027 1.05411 0.527055 0.849831i \(-0.323296\pi\)
0.527055 + 0.849831i \(0.323296\pi\)
\(12\) −781.856 −1.56738
\(13\) −1047.72 −1.71944 −0.859722 0.510762i \(-0.829363\pi\)
−0.859722 + 0.510762i \(0.829363\pi\)
\(14\) −672.832 −0.917459
\(15\) −793.028 −0.910040
\(16\) 3742.96 3.65523
\(17\) −2034.81 −1.70766 −0.853831 0.520550i \(-0.825727\pi\)
−0.853831 + 0.520550i \(0.825727\pi\)
\(18\) −883.133 −0.642458
\(19\) −1532.11 −0.973654 −0.486827 0.873498i \(-0.661846\pi\)
−0.486827 + 0.873498i \(0.661846\pi\)
\(20\) 7654.74 4.27913
\(21\) −555.403 −0.274827
\(22\) −4612.21 −2.03167
\(23\) 2986.67 1.17725 0.588623 0.808408i \(-0.299670\pi\)
0.588623 + 0.808408i \(0.299670\pi\)
\(24\) 5384.45 1.90815
\(25\) 4639.12 1.48452
\(26\) 11423.2 3.31402
\(27\) −729.000 −0.192450
\(28\) 5361.05 1.29227
\(29\) 115.477 0.0254978 0.0127489 0.999919i \(-0.495942\pi\)
0.0127489 + 0.999919i \(0.495942\pi\)
\(30\) 8646.29 1.75399
\(31\) −3626.28 −0.677730 −0.338865 0.940835i \(-0.610043\pi\)
−0.338865 + 0.940835i \(0.610043\pi\)
\(32\) −21664.3 −3.73999
\(33\) −3807.24 −0.608591
\(34\) 22185.3 3.29131
\(35\) 5437.66 0.750312
\(36\) 7036.70 0.904925
\(37\) −15040.3 −1.80614 −0.903070 0.429493i \(-0.858692\pi\)
−0.903070 + 0.429493i \(0.858692\pi\)
\(38\) 16704.4 1.87660
\(39\) 9429.51 0.992722
\(40\) −52716.3 −5.20949
\(41\) −829.256 −0.0770423 −0.0385211 0.999258i \(-0.512265\pi\)
−0.0385211 + 0.999258i \(0.512265\pi\)
\(42\) 6055.49 0.529695
\(43\) −12294.1 −1.01397 −0.506985 0.861955i \(-0.669240\pi\)
−0.506985 + 0.861955i \(0.669240\pi\)
\(44\) 36749.5 2.86167
\(45\) 7137.25 0.525412
\(46\) −32563.3 −2.26900
\(47\) −16104.8 −1.06343 −0.531717 0.846922i \(-0.678453\pi\)
−0.531717 + 0.846922i \(0.678453\pi\)
\(48\) −33686.6 −2.11035
\(49\) −12998.7 −0.773410
\(50\) −50579.8 −2.86123
\(51\) 18313.3 0.985919
\(52\) −91018.7 −4.66791
\(53\) 34428.4 1.68356 0.841778 0.539824i \(-0.181509\pi\)
0.841778 + 0.539824i \(0.181509\pi\)
\(54\) 7948.20 0.370924
\(55\) 37274.7 1.66153
\(56\) −36920.2 −1.57324
\(57\) 13788.9 0.562139
\(58\) −1259.04 −0.0491438
\(59\) −3481.00 −0.130189
\(60\) −68892.6 −2.47056
\(61\) 16418.9 0.564961 0.282481 0.959273i \(-0.408843\pi\)
0.282481 + 0.959273i \(0.408843\pi\)
\(62\) 39536.9 1.30624
\(63\) 4998.63 0.158672
\(64\) 116429. 3.55313
\(65\) −92319.3 −2.71025
\(66\) 41509.9 1.17298
\(67\) 9818.25 0.267206 0.133603 0.991035i \(-0.457345\pi\)
0.133603 + 0.991035i \(0.457345\pi\)
\(68\) −176770. −4.63592
\(69\) −26880.0 −0.679683
\(70\) −59286.1 −1.44613
\(71\) 3381.64 0.0796125 0.0398062 0.999207i \(-0.487326\pi\)
0.0398062 + 0.999207i \(0.487326\pi\)
\(72\) −48460.0 −1.10167
\(73\) 27012.0 0.593267 0.296634 0.954991i \(-0.404136\pi\)
0.296634 + 0.954991i \(0.404136\pi\)
\(74\) 163982. 3.48111
\(75\) −41752.1 −0.857087
\(76\) −133098. −2.64325
\(77\) 26105.6 0.501772
\(78\) −102809. −1.91335
\(79\) 20426.3 0.368233 0.184117 0.982904i \(-0.441058\pi\)
0.184117 + 0.982904i \(0.441058\pi\)
\(80\) 329808. 5.76151
\(81\) 6561.00 0.111111
\(82\) 9041.29 0.148489
\(83\) −54511.3 −0.868543 −0.434272 0.900782i \(-0.642994\pi\)
−0.434272 + 0.900782i \(0.642994\pi\)
\(84\) −48249.4 −0.746095
\(85\) −179296. −2.69168
\(86\) 134041. 1.95430
\(87\) −1039.30 −0.0147211
\(88\) −253085. −3.48385
\(89\) −69700.2 −0.932736 −0.466368 0.884591i \(-0.654438\pi\)
−0.466368 + 0.884591i \(0.654438\pi\)
\(90\) −77816.6 −1.01267
\(91\) −64656.5 −0.818481
\(92\) 259460. 3.19596
\(93\) 32636.5 0.391287
\(94\) 175589. 2.04964
\(95\) −135000. −1.53471
\(96\) 194979. 2.15928
\(97\) 48526.4 0.523660 0.261830 0.965114i \(-0.415674\pi\)
0.261830 + 0.965114i \(0.415674\pi\)
\(98\) 141723. 1.49065
\(99\) 34265.1 0.351370
\(100\) 403014. 4.03014
\(101\) 107128. 1.04496 0.522478 0.852653i \(-0.325008\pi\)
0.522478 + 0.852653i \(0.325008\pi\)
\(102\) −199668. −1.90024
\(103\) −93523.6 −0.868617 −0.434308 0.900764i \(-0.643007\pi\)
−0.434308 + 0.900764i \(0.643007\pi\)
\(104\) 626823. 5.68279
\(105\) −48938.9 −0.433193
\(106\) −375369. −3.24484
\(107\) 51795.7 0.437356 0.218678 0.975797i \(-0.429826\pi\)
0.218678 + 0.975797i \(0.429826\pi\)
\(108\) −63330.3 −0.522459
\(109\) −147885. −1.19223 −0.596113 0.802901i \(-0.703289\pi\)
−0.596113 + 0.802901i \(0.703289\pi\)
\(110\) −406401. −3.20238
\(111\) 135363. 1.04278
\(112\) 230983. 1.73995
\(113\) −83662.7 −0.616362 −0.308181 0.951328i \(-0.599720\pi\)
−0.308181 + 0.951328i \(0.599720\pi\)
\(114\) −150339. −1.08345
\(115\) 263168. 1.85562
\(116\) 10031.9 0.0692208
\(117\) −84865.6 −0.573148
\(118\) 37952.9 0.250923
\(119\) −125571. −0.812873
\(120\) 474447. 3.00770
\(121\) 17900.5 0.111148
\(122\) −179013. −1.08889
\(123\) 7463.31 0.0444804
\(124\) −315025. −1.83988
\(125\) 133416. 0.763716
\(126\) −54499.4 −0.305820
\(127\) −155048. −0.853016 −0.426508 0.904484i \(-0.640256\pi\)
−0.426508 + 0.904484i \(0.640256\pi\)
\(128\) −576153. −3.10823
\(129\) 110647. 0.585416
\(130\) 1.00655e6 5.22367
\(131\) −370672. −1.88717 −0.943587 0.331124i \(-0.892572\pi\)
−0.943587 + 0.331124i \(0.892572\pi\)
\(132\) −330746. −1.65219
\(133\) −94548.4 −0.463474
\(134\) −107047. −0.515007
\(135\) −64235.3 −0.303347
\(136\) 1.21737e6 5.64385
\(137\) 194058. 0.883345 0.441673 0.897176i \(-0.354385\pi\)
0.441673 + 0.897176i \(0.354385\pi\)
\(138\) 293070. 1.31001
\(139\) −80499.1 −0.353390 −0.176695 0.984266i \(-0.556541\pi\)
−0.176695 + 0.984266i \(0.556541\pi\)
\(140\) 472385. 2.03693
\(141\) 144943. 0.613973
\(142\) −36869.6 −0.153443
\(143\) −443215. −1.81248
\(144\) 303180. 1.21841
\(145\) 10175.2 0.0401905
\(146\) −294509. −1.14345
\(147\) 116988. 0.446528
\(148\) −1.30659e6 −4.90327
\(149\) 229972. 0.848611 0.424305 0.905519i \(-0.360518\pi\)
0.424305 + 0.905519i \(0.360518\pi\)
\(150\) 455218. 1.65193
\(151\) −103481. −0.369333 −0.184667 0.982801i \(-0.559121\pi\)
−0.184667 + 0.982801i \(0.559121\pi\)
\(152\) 916616. 3.21794
\(153\) −164820. −0.569221
\(154\) −284626. −0.967103
\(155\) −319527. −1.06826
\(156\) 819168. 2.69502
\(157\) 222025. 0.718875 0.359438 0.933169i \(-0.382969\pi\)
0.359438 + 0.933169i \(0.382969\pi\)
\(158\) −222706. −0.709723
\(159\) −309856. −0.972001
\(160\) −1.90894e6 −5.89510
\(161\) 184312. 0.560387
\(162\) −71533.8 −0.214153
\(163\) −1674.56 −0.00493664 −0.00246832 0.999997i \(-0.500786\pi\)
−0.00246832 + 0.999997i \(0.500786\pi\)
\(164\) −72039.9 −0.209153
\(165\) −335472. −0.959282
\(166\) 594331. 1.67401
\(167\) −633831. −1.75866 −0.879330 0.476212i \(-0.842009\pi\)
−0.879330 + 0.476212i \(0.842009\pi\)
\(168\) 332282. 0.908309
\(169\) 726431. 1.95649
\(170\) 1.95484e6 5.18788
\(171\) −124101. −0.324551
\(172\) −1.06802e6 −2.75270
\(173\) 304757. 0.774175 0.387087 0.922043i \(-0.373481\pi\)
0.387087 + 0.922043i \(0.373481\pi\)
\(174\) 11331.3 0.0283732
\(175\) 286287. 0.706653
\(176\) 1.58337e6 3.85302
\(177\) 31329.0 0.0751646
\(178\) 759933. 1.79773
\(179\) 67132.3 0.156603 0.0783013 0.996930i \(-0.475050\pi\)
0.0783013 + 0.996930i \(0.475050\pi\)
\(180\) 620034. 1.42638
\(181\) 111781. 0.253613 0.126807 0.991927i \(-0.459527\pi\)
0.126807 + 0.991927i \(0.459527\pi\)
\(182\) 704942. 1.57752
\(183\) −147770. −0.326180
\(184\) −1.78684e6 −3.89082
\(185\) −1.32526e6 −2.84690
\(186\) −355832. −0.754158
\(187\) −860780. −1.80006
\(188\) −1.39907e6 −2.88698
\(189\) −44987.6 −0.0916091
\(190\) 1.47189e6 2.95796
\(191\) −731353. −1.45059 −0.725294 0.688440i \(-0.758296\pi\)
−0.725294 + 0.688440i \(0.758296\pi\)
\(192\) −1.04786e6 −2.05140
\(193\) 685155. 1.32402 0.662011 0.749494i \(-0.269703\pi\)
0.662011 + 0.749494i \(0.269703\pi\)
\(194\) −529078. −1.00929
\(195\) 830874. 1.56476
\(196\) −1.12923e6 −2.09963
\(197\) −723750. −1.32869 −0.664344 0.747427i \(-0.731289\pi\)
−0.664344 + 0.747427i \(0.731289\pi\)
\(198\) −373589. −0.677222
\(199\) −186876. −0.334519 −0.167260 0.985913i \(-0.553492\pi\)
−0.167260 + 0.985913i \(0.553492\pi\)
\(200\) −2.77546e6 −4.90636
\(201\) −88364.2 −0.154272
\(202\) −1.16800e6 −2.01402
\(203\) 7126.28 0.0121373
\(204\) 1.59093e6 2.67655
\(205\) −73069.3 −0.121437
\(206\) 1.01968e6 1.67415
\(207\) 241920. 0.392415
\(208\) −3.92158e6 −6.28497
\(209\) −648121. −1.02634
\(210\) 533575. 0.834925
\(211\) −143708. −0.222216 −0.111108 0.993808i \(-0.535440\pi\)
−0.111108 + 0.993808i \(0.535440\pi\)
\(212\) 2.99089e6 4.57048
\(213\) −30434.7 −0.0459643
\(214\) −564723. −0.842948
\(215\) −1.08329e6 −1.59826
\(216\) 436140. 0.636051
\(217\) −223783. −0.322609
\(218\) 1.61237e6 2.29787
\(219\) −243108. −0.342523
\(220\) 3.23816e6 4.51067
\(221\) 2.13192e6 2.93623
\(222\) −1.47584e6 −2.00982
\(223\) 299009. 0.402645 0.201322 0.979525i \(-0.435476\pi\)
0.201322 + 0.979525i \(0.435476\pi\)
\(224\) −1.33694e6 −1.78029
\(225\) 375769. 0.494840
\(226\) 912164. 1.18796
\(227\) 106091. 0.136651 0.0683255 0.997663i \(-0.478234\pi\)
0.0683255 + 0.997663i \(0.478234\pi\)
\(228\) 1.19789e6 1.52608
\(229\) −222769. −0.280715 −0.140358 0.990101i \(-0.544825\pi\)
−0.140358 + 0.990101i \(0.544825\pi\)
\(230\) −2.86929e6 −3.57647
\(231\) −234950. −0.289698
\(232\) −69086.9 −0.0842706
\(233\) −877575. −1.05900 −0.529498 0.848311i \(-0.677620\pi\)
−0.529498 + 0.848311i \(0.677620\pi\)
\(234\) 925279. 1.10467
\(235\) −1.41906e6 −1.67622
\(236\) −302404. −0.353434
\(237\) −183837. −0.212599
\(238\) 1.36909e6 1.56671
\(239\) 1.55403e6 1.75980 0.879902 0.475156i \(-0.157608\pi\)
0.879902 + 0.475156i \(0.157608\pi\)
\(240\) −2.96827e6 −3.32641
\(241\) −65896.5 −0.0730836 −0.0365418 0.999332i \(-0.511634\pi\)
−0.0365418 + 0.999332i \(0.511634\pi\)
\(242\) −195167. −0.214223
\(243\) −59049.0 −0.0641500
\(244\) 1.42635e6 1.53374
\(245\) −1.14537e6 −1.21908
\(246\) −81371.6 −0.0857304
\(247\) 1.60522e6 1.67414
\(248\) 2.16950e6 2.23991
\(249\) 490602. 0.501454
\(250\) −1.45462e6 −1.47197
\(251\) −24842.7 −0.0248894 −0.0124447 0.999923i \(-0.503961\pi\)
−0.0124447 + 0.999923i \(0.503961\pi\)
\(252\) 434245. 0.430758
\(253\) 1.26344e6 1.24095
\(254\) 1.69047e6 1.64408
\(255\) 1.61366e6 1.55404
\(256\) 2.55600e6 2.43759
\(257\) 501967. 0.474070 0.237035 0.971501i \(-0.423824\pi\)
0.237035 + 0.971501i \(0.423824\pi\)
\(258\) −1.20637e6 −1.12832
\(259\) −928157. −0.859750
\(260\) −8.02004e6 −7.35772
\(261\) 9353.68 0.00849926
\(262\) 4.04140e6 3.63729
\(263\) 1.26902e6 1.13130 0.565652 0.824644i \(-0.308624\pi\)
0.565652 + 0.824644i \(0.308624\pi\)
\(264\) 2.27776e6 2.01140
\(265\) 3.03363e6 2.65368
\(266\) 1.03085e6 0.893288
\(267\) 627302. 0.538516
\(268\) 852939. 0.725406
\(269\) −1.04097e6 −0.877121 −0.438560 0.898702i \(-0.644511\pi\)
−0.438560 + 0.898702i \(0.644511\pi\)
\(270\) 700350. 0.584663
\(271\) −2.07017e6 −1.71231 −0.856155 0.516718i \(-0.827153\pi\)
−0.856155 + 0.516718i \(0.827153\pi\)
\(272\) −7.61622e6 −6.24191
\(273\) 581908. 0.472550
\(274\) −2.11579e6 −1.70254
\(275\) 1.96247e6 1.56485
\(276\) −2.33514e6 −1.84519
\(277\) 1.93149e6 1.51249 0.756247 0.654287i \(-0.227031\pi\)
0.756247 + 0.654287i \(0.227031\pi\)
\(278\) 877672. 0.681115
\(279\) −293728. −0.225910
\(280\) −3.25320e6 −2.47979
\(281\) 859707. 0.649508 0.324754 0.945799i \(-0.394718\pi\)
0.324754 + 0.945799i \(0.394718\pi\)
\(282\) −1.58030e6 −1.18336
\(283\) −789427. −0.585930 −0.292965 0.956123i \(-0.594642\pi\)
−0.292965 + 0.956123i \(0.594642\pi\)
\(284\) 293772. 0.216130
\(285\) 1.21500e6 0.886064
\(286\) 4.83232e6 3.49334
\(287\) −51174.6 −0.0366733
\(288\) −1.75481e6 −1.24666
\(289\) 2.72060e6 1.91611
\(290\) −110939. −0.0774622
\(291\) −436738. −0.302335
\(292\) 2.34661e6 1.61059
\(293\) −1.83732e6 −1.25030 −0.625152 0.780503i \(-0.714963\pi\)
−0.625152 + 0.780503i \(0.714963\pi\)
\(294\) −1.27551e6 −0.860628
\(295\) −306726. −0.205208
\(296\) 8.99818e6 5.96933
\(297\) −308386. −0.202864
\(298\) −2.50735e6 −1.63559
\(299\) −3.12920e6 −2.02421
\(300\) −3.62712e6 −2.32680
\(301\) −758686. −0.482665
\(302\) 1.12824e6 0.711843
\(303\) −964148. −0.603305
\(304\) −5.73461e6 −3.55893
\(305\) 1.44674e6 0.890512
\(306\) 1.79701e6 1.09710
\(307\) −443750. −0.268715 −0.134358 0.990933i \(-0.542897\pi\)
−0.134358 + 0.990933i \(0.542897\pi\)
\(308\) 2.26787e6 1.36220
\(309\) 841713. 0.501496
\(310\) 3.48376e6 2.05894
\(311\) −651682. −0.382063 −0.191031 0.981584i \(-0.561183\pi\)
−0.191031 + 0.981584i \(0.561183\pi\)
\(312\) −5.64141e6 −3.28096
\(313\) −1.28063e6 −0.738859 −0.369430 0.929259i \(-0.620447\pi\)
−0.369430 + 0.929259i \(0.620447\pi\)
\(314\) −2.42072e6 −1.38554
\(315\) 440450. 0.250104
\(316\) 1.77449e6 0.999670
\(317\) 1.85275e6 1.03554 0.517772 0.855518i \(-0.326761\pi\)
0.517772 + 0.855518i \(0.326761\pi\)
\(318\) 3.37832e6 1.87341
\(319\) 48850.0 0.0268775
\(320\) 1.02591e7 5.60057
\(321\) −466162. −0.252507
\(322\) −2.00953e6 −1.08008
\(323\) 3.11755e6 1.66267
\(324\) 569973. 0.301642
\(325\) −4.86052e6 −2.55255
\(326\) 18257.5 0.00951475
\(327\) 1.33097e6 0.688332
\(328\) 496121. 0.254626
\(329\) −993849. −0.506210
\(330\) 3.65761e6 1.84890
\(331\) −646915. −0.324547 −0.162273 0.986746i \(-0.551883\pi\)
−0.162273 + 0.986746i \(0.551883\pi\)
\(332\) −4.73555e6 −2.35790
\(333\) −1.21826e6 −0.602047
\(334\) 6.91058e6 3.38960
\(335\) 865128. 0.421180
\(336\) −2.07885e6 −1.00456
\(337\) −1.93315e6 −0.927235 −0.463618 0.886035i \(-0.653449\pi\)
−0.463618 + 0.886035i \(0.653449\pi\)
\(338\) −7.92019e6 −3.77089
\(339\) 752964. 0.355857
\(340\) −1.55759e7 −7.30731
\(341\) −1.53401e6 −0.714402
\(342\) 1.35305e6 0.625532
\(343\) −1.83935e6 −0.844169
\(344\) 7.35521e6 3.35119
\(345\) −2.36851e6 −1.07134
\(346\) −3.32273e6 −1.49213
\(347\) −2.55520e6 −1.13920 −0.569601 0.821921i \(-0.692902\pi\)
−0.569601 + 0.821921i \(0.692902\pi\)
\(348\) −90286.7 −0.0399646
\(349\) −106267. −0.0467019 −0.0233509 0.999727i \(-0.507434\pi\)
−0.0233509 + 0.999727i \(0.507434\pi\)
\(350\) −3.12135e6 −1.36199
\(351\) 763790. 0.330907
\(352\) −9.16459e6 −3.94236
\(353\) 421809. 0.180169 0.0900844 0.995934i \(-0.471286\pi\)
0.0900844 + 0.995934i \(0.471286\pi\)
\(354\) −341576. −0.144870
\(355\) 297970. 0.125488
\(356\) −6.05505e6 −2.53217
\(357\) 1.13014e6 0.469312
\(358\) −731936. −0.301832
\(359\) 2.33843e6 0.957607 0.478804 0.877922i \(-0.341071\pi\)
0.478804 + 0.877922i \(0.341071\pi\)
\(360\) −4.27002e6 −1.73650
\(361\) −128752. −0.0519980
\(362\) −1.21874e6 −0.488808
\(363\) −161104. −0.0641712
\(364\) −5.61689e6 −2.22199
\(365\) 2.38015e6 0.935129
\(366\) 1.61112e6 0.628672
\(367\) 1.76169e6 0.682755 0.341377 0.939926i \(-0.389107\pi\)
0.341377 + 0.939926i \(0.389107\pi\)
\(368\) 1.11790e7 4.30311
\(369\) −67169.8 −0.0256808
\(370\) 1.44492e7 5.48705
\(371\) 2.12463e6 0.801397
\(372\) 2.83522e6 1.06226
\(373\) 555814. 0.206851 0.103425 0.994637i \(-0.467020\pi\)
0.103425 + 0.994637i \(0.467020\pi\)
\(374\) 9.38498e6 3.46940
\(375\) −1.20074e6 −0.440932
\(376\) 9.63504e6 3.51467
\(377\) −120988. −0.0438420
\(378\) 490495. 0.176565
\(379\) 1.23190e6 0.440532 0.220266 0.975440i \(-0.429307\pi\)
0.220266 + 0.975440i \(0.429307\pi\)
\(380\) −1.17279e7 −4.16639
\(381\) 1.39543e6 0.492489
\(382\) 7.97386e6 2.79583
\(383\) 2.07159e6 0.721617 0.360808 0.932640i \(-0.382501\pi\)
0.360808 + 0.932640i \(0.382501\pi\)
\(384\) 5.18538e6 1.79454
\(385\) 2.30027e6 0.790911
\(386\) −7.47016e6 −2.55189
\(387\) −995822. −0.337990
\(388\) 4.21563e6 1.42162
\(389\) −4.06653e6 −1.36254 −0.681271 0.732031i \(-0.738573\pi\)
−0.681271 + 0.732031i \(0.738573\pi\)
\(390\) −9.05892e6 −3.01589
\(391\) −6.07731e6 −2.01034
\(392\) 7.77676e6 2.55613
\(393\) 3.33605e6 1.08956
\(394\) 7.89096e6 2.56088
\(395\) 1.79985e6 0.580422
\(396\) 2.97671e6 0.953891
\(397\) −4.63853e6 −1.47708 −0.738541 0.674209i \(-0.764485\pi\)
−0.738541 + 0.674209i \(0.764485\pi\)
\(398\) 2.03749e6 0.644744
\(399\) 850936. 0.267587
\(400\) 1.73640e7 5.42626
\(401\) 2.63194e6 0.817363 0.408681 0.912677i \(-0.365989\pi\)
0.408681 + 0.912677i \(0.365989\pi\)
\(402\) 963425. 0.297340
\(403\) 3.79933e6 1.16532
\(404\) 9.30647e6 2.83682
\(405\) 578118. 0.175137
\(406\) −77697.0 −0.0233932
\(407\) −6.36244e6 −1.90387
\(408\) −1.09563e7 −3.25848
\(409\) 3.04976e6 0.901482 0.450741 0.892655i \(-0.351160\pi\)
0.450741 + 0.892655i \(0.351160\pi\)
\(410\) 796666. 0.234054
\(411\) −1.74652e6 −0.510000
\(412\) −8.12466e6 −2.35810
\(413\) −214817. −0.0619719
\(414\) −2.63763e6 −0.756332
\(415\) −4.80322e6 −1.36903
\(416\) 2.26982e7 6.43070
\(417\) 724492. 0.204030
\(418\) 7.06639e6 1.97814
\(419\) 1.34161e6 0.373329 0.186664 0.982424i \(-0.440232\pi\)
0.186664 + 0.982424i \(0.440232\pi\)
\(420\) −4.25146e6 −1.17602
\(421\) 2.54019e6 0.698492 0.349246 0.937031i \(-0.386438\pi\)
0.349246 + 0.937031i \(0.386438\pi\)
\(422\) 1.56683e6 0.428293
\(423\) −1.30449e6 −0.354478
\(424\) −2.05976e7 −5.56418
\(425\) −9.43974e6 −2.53506
\(426\) 331826. 0.0885904
\(427\) 1.01323e6 0.268930
\(428\) 4.49964e6 1.18732
\(429\) 3.98893e6 1.04644
\(430\) 1.18109e7 3.08044
\(431\) 4.17832e6 1.08345 0.541725 0.840556i \(-0.317772\pi\)
0.541725 + 0.840556i \(0.317772\pi\)
\(432\) −2.72862e6 −0.703450
\(433\) −74580.5 −0.0191164 −0.00955819 0.999954i \(-0.503043\pi\)
−0.00955819 + 0.999954i \(0.503043\pi\)
\(434\) 2.43988e6 0.621790
\(435\) −91576.9 −0.0232040
\(436\) −1.28472e7 −3.23663
\(437\) −4.57589e6 −1.14623
\(438\) 2.65058e6 0.660170
\(439\) 7.12201e6 1.76377 0.881884 0.471466i \(-0.156275\pi\)
0.881884 + 0.471466i \(0.156275\pi\)
\(440\) −2.23004e7 −5.49137
\(441\) −1.05289e6 −0.257803
\(442\) −2.32441e7 −5.65922
\(443\) −7.36242e6 −1.78243 −0.891213 0.453585i \(-0.850145\pi\)
−0.891213 + 0.453585i \(0.850145\pi\)
\(444\) 1.17593e7 2.83090
\(445\) −6.14158e6 −1.47021
\(446\) −3.26006e6 −0.776047
\(447\) −2.06974e6 −0.489946
\(448\) 7.18500e6 1.69134
\(449\) −5.60487e6 −1.31205 −0.656023 0.754741i \(-0.727763\pi\)
−0.656023 + 0.754741i \(0.727763\pi\)
\(450\) −4.09696e6 −0.953742
\(451\) −350798. −0.0812111
\(452\) −7.26801e6 −1.67328
\(453\) 931329. 0.213235
\(454\) −1.15669e6 −0.263378
\(455\) −5.69716e6 −1.29012
\(456\) −8.24954e6 −1.85788
\(457\) −2.27985e6 −0.510641 −0.255320 0.966856i \(-0.582181\pi\)
−0.255320 + 0.966856i \(0.582181\pi\)
\(458\) 2.42883e6 0.541044
\(459\) 1.48338e6 0.328640
\(460\) 2.28621e7 5.03759
\(461\) 5.70375e6 1.24999 0.624997 0.780627i \(-0.285100\pi\)
0.624997 + 0.780627i \(0.285100\pi\)
\(462\) 2.56163e6 0.558357
\(463\) 3.15681e6 0.684378 0.342189 0.939631i \(-0.388832\pi\)
0.342189 + 0.939631i \(0.388832\pi\)
\(464\) 432227. 0.0932003
\(465\) 2.87574e6 0.616761
\(466\) 9.56810e6 2.04108
\(467\) 4.10668e6 0.871362 0.435681 0.900101i \(-0.356508\pi\)
0.435681 + 0.900101i \(0.356508\pi\)
\(468\) −7.37251e6 −1.55597
\(469\) 605898. 0.127194
\(470\) 1.54719e7 3.23071
\(471\) −1.99823e6 −0.415043
\(472\) 2.08259e6 0.430277
\(473\) −5.20073e6 −1.06884
\(474\) 2.00435e6 0.409759
\(475\) −7.10762e6 −1.44541
\(476\) −1.09087e7 −2.20677
\(477\) 2.78870e6 0.561185
\(478\) −1.69434e7 −3.39180
\(479\) −3.96139e6 −0.788876 −0.394438 0.918923i \(-0.629061\pi\)
−0.394438 + 0.918923i \(0.629061\pi\)
\(480\) 1.71804e7 3.40354
\(481\) 1.57580e7 3.10556
\(482\) 718462. 0.140860
\(483\) −1.65880e6 −0.323539
\(484\) 1.55506e6 0.301741
\(485\) 4.27587e6 0.825411
\(486\) 643804. 0.123641
\(487\) −9.18635e6 −1.75517 −0.877587 0.479417i \(-0.840848\pi\)
−0.877587 + 0.479417i \(0.840848\pi\)
\(488\) −9.82295e6 −1.86721
\(489\) 15071.0 0.00285017
\(490\) 1.24878e7 2.34962
\(491\) 3.85969e6 0.722518 0.361259 0.932465i \(-0.382347\pi\)
0.361259 + 0.932465i \(0.382347\pi\)
\(492\) 648359. 0.120754
\(493\) −234975. −0.0435416
\(494\) −1.75015e7 −3.22670
\(495\) 3.01925e6 0.553842
\(496\) −1.35730e7 −2.47726
\(497\) 208686. 0.0378967
\(498\) −5.34897e6 −0.966490
\(499\) −3.44774e6 −0.619845 −0.309922 0.950762i \(-0.600303\pi\)
−0.309922 + 0.950762i \(0.600303\pi\)
\(500\) 1.15902e7 2.07332
\(501\) 5.70448e6 1.01536
\(502\) 270857. 0.0479712
\(503\) 5.17527e6 0.912038 0.456019 0.889970i \(-0.349275\pi\)
0.456019 + 0.889970i \(0.349275\pi\)
\(504\) −2.99054e6 −0.524412
\(505\) 9.43946e6 1.64710
\(506\) −1.37751e7 −2.39177
\(507\) −6.53788e6 −1.12958
\(508\) −1.34695e7 −2.31575
\(509\) −86953.7 −0.0148763 −0.00743813 0.999972i \(-0.502368\pi\)
−0.00743813 + 0.999972i \(0.502368\pi\)
\(510\) −1.75936e7 −2.99522
\(511\) 1.66695e6 0.282404
\(512\) −9.43086e6 −1.58992
\(513\) 1.11690e6 0.187380
\(514\) −5.47289e6 −0.913710
\(515\) −8.24077e6 −1.36915
\(516\) 9.61221e6 1.58927
\(517\) −6.81275e6 −1.12098
\(518\) 1.01196e7 1.65706
\(519\) −2.74282e6 −0.446970
\(520\) 5.52321e7 8.95742
\(521\) −6.15153e6 −0.992861 −0.496431 0.868076i \(-0.665356\pi\)
−0.496431 + 0.868076i \(0.665356\pi\)
\(522\) −101982. −0.0163813
\(523\) 1.72407e6 0.275613 0.137807 0.990459i \(-0.455995\pi\)
0.137807 + 0.990459i \(0.455995\pi\)
\(524\) −3.22014e7 −5.12326
\(525\) −2.57658e6 −0.407986
\(526\) −1.38360e7 −2.18045
\(527\) 7.37879e6 1.15733
\(528\) −1.42503e7 −2.22454
\(529\) 2.48384e6 0.385909
\(530\) −3.30754e7 −5.11464
\(531\) −281961. −0.0433963
\(532\) −8.21369e6 −1.25823
\(533\) 868831. 0.132470
\(534\) −6.83940e6 −1.03792
\(535\) 4.56394e6 0.689375
\(536\) −5.87398e6 −0.883122
\(537\) −604191. −0.0904146
\(538\) 1.13496e7 1.69054
\(539\) −5.49879e6 −0.815259
\(540\) −5.58030e6 −0.823518
\(541\) −8.39290e6 −1.23287 −0.616437 0.787404i \(-0.711425\pi\)
−0.616437 + 0.787404i \(0.711425\pi\)
\(542\) 2.25708e7 3.30027
\(543\) −1.00603e6 −0.146424
\(544\) 4.40829e7 6.38664
\(545\) −1.30308e7 −1.87923
\(546\) −6.34448e6 −0.910782
\(547\) −1.01323e7 −1.44790 −0.723952 0.689850i \(-0.757676\pi\)
−0.723952 + 0.689850i \(0.757676\pi\)
\(548\) 1.68584e7 2.39808
\(549\) 1.32993e6 0.188320
\(550\) −2.13966e7 −3.01605
\(551\) −176924. −0.0248260
\(552\) 1.60816e7 2.24637
\(553\) 1.26054e6 0.175284
\(554\) −2.10588e7 −2.91514
\(555\) 1.19274e7 1.64366
\(556\) −6.99318e6 −0.959374
\(557\) 9.82722e6 1.34212 0.671062 0.741401i \(-0.265838\pi\)
0.671062 + 0.741401i \(0.265838\pi\)
\(558\) 3.20249e6 0.435413
\(559\) 1.28808e7 1.74347
\(560\) 2.03529e7 2.74256
\(561\) 7.74702e6 1.03927
\(562\) −9.37328e6 −1.25185
\(563\) 9.96382e6 1.32481 0.662407 0.749144i \(-0.269535\pi\)
0.662407 + 0.749144i \(0.269535\pi\)
\(564\) 1.25916e7 1.66680
\(565\) −7.37187e6 −0.971531
\(566\) 8.60703e6 1.12931
\(567\) 404889. 0.0528905
\(568\) −2.02314e6 −0.263121
\(569\) 1.30624e7 1.69138 0.845692 0.533672i \(-0.179188\pi\)
0.845692 + 0.533672i \(0.179188\pi\)
\(570\) −1.32470e7 −1.70778
\(571\) 1.30362e7 1.67325 0.836625 0.547776i \(-0.184525\pi\)
0.836625 + 0.547776i \(0.184525\pi\)
\(572\) −3.85033e7 −4.92049
\(573\) 6.58218e6 0.837497
\(574\) 557951. 0.0706832
\(575\) 1.38555e7 1.74764
\(576\) 9.43075e6 1.18438
\(577\) −1.37814e7 −1.72327 −0.861637 0.507524i \(-0.830561\pi\)
−0.861637 + 0.507524i \(0.830561\pi\)
\(578\) −2.96624e7 −3.69307
\(579\) −6.16639e6 −0.764425
\(580\) 883949. 0.109108
\(581\) −3.36397e6 −0.413440
\(582\) 4.76170e6 0.582713
\(583\) 1.45641e7 1.77465
\(584\) −1.61606e7 −1.96076
\(585\) −7.47787e6 −0.903417
\(586\) 2.00321e7 2.40981
\(587\) −4.70405e6 −0.563478 −0.281739 0.959491i \(-0.590911\pi\)
−0.281739 + 0.959491i \(0.590911\pi\)
\(588\) 1.01631e7 1.21222
\(589\) 5.55584e6 0.659874
\(590\) 3.34419e6 0.395514
\(591\) 6.51375e6 0.767118
\(592\) −5.62951e7 −6.60187
\(593\) 4.77416e6 0.557519 0.278760 0.960361i \(-0.410077\pi\)
0.278760 + 0.960361i \(0.410077\pi\)
\(594\) 3.36230e6 0.390994
\(595\) −1.10646e7 −1.28128
\(596\) 1.99783e7 2.30379
\(597\) 1.68188e6 0.193135
\(598\) 3.41173e7 3.90141
\(599\) −1.34470e6 −0.153129 −0.0765645 0.997065i \(-0.524395\pi\)
−0.0765645 + 0.997065i \(0.524395\pi\)
\(600\) 2.49791e7 2.83269
\(601\) −1.25261e7 −1.41458 −0.707292 0.706921i \(-0.750084\pi\)
−0.707292 + 0.706921i \(0.750084\pi\)
\(602\) 8.27187e6 0.930277
\(603\) 795278. 0.0890688
\(604\) −8.98969e6 −1.00266
\(605\) 1.57728e6 0.175195
\(606\) 1.05120e7 1.16280
\(607\) −1.01433e7 −1.11740 −0.558698 0.829371i \(-0.688699\pi\)
−0.558698 + 0.829371i \(0.688699\pi\)
\(608\) 3.31920e7 3.64146
\(609\) −64136.5 −0.00700749
\(610\) −1.57736e7 −1.71635
\(611\) 1.68734e7 1.82851
\(612\) −1.43184e7 −1.54531
\(613\) 5.39122e6 0.579476 0.289738 0.957106i \(-0.406432\pi\)
0.289738 + 0.957106i \(0.406432\pi\)
\(614\) 4.83815e6 0.517915
\(615\) 657624. 0.0701116
\(616\) −1.56182e7 −1.65837
\(617\) 1.83062e6 0.193591 0.0967957 0.995304i \(-0.469141\pi\)
0.0967957 + 0.995304i \(0.469141\pi\)
\(618\) −9.17709e6 −0.966572
\(619\) 1.04088e7 1.09188 0.545939 0.837825i \(-0.316173\pi\)
0.545939 + 0.837825i \(0.316173\pi\)
\(620\) −2.77582e7 −2.90009
\(621\) −2.17728e6 −0.226561
\(622\) 7.10521e6 0.736378
\(623\) −4.30130e6 −0.443996
\(624\) 3.52943e7 3.62863
\(625\) −2.74143e6 −0.280722
\(626\) 1.39625e7 1.42406
\(627\) 5.83309e6 0.592557
\(628\) 1.92880e7 1.95159
\(629\) 3.06041e7 3.08428
\(630\) −4.80218e6 −0.482044
\(631\) 4.99395e6 0.499310 0.249655 0.968335i \(-0.419683\pi\)
0.249655 + 0.968335i \(0.419683\pi\)
\(632\) −1.22205e7 −1.21702
\(633\) 1.29337e6 0.128296
\(634\) −2.02003e7 −1.99588
\(635\) −1.36620e7 −1.34455
\(636\) −2.69181e7 −2.63877
\(637\) 1.36190e7 1.32984
\(638\) −532606. −0.0518030
\(639\) 273913. 0.0265375
\(640\) −5.07673e7 −4.89930
\(641\) 6.06889e6 0.583397 0.291699 0.956510i \(-0.405780\pi\)
0.291699 + 0.956510i \(0.405780\pi\)
\(642\) 5.08251e6 0.486676
\(643\) −1.56458e7 −1.49235 −0.746176 0.665748i \(-0.768112\pi\)
−0.746176 + 0.665748i \(0.768112\pi\)
\(644\) 1.60117e7 1.52132
\(645\) 9.74957e6 0.922754
\(646\) −3.39902e7 −3.20459
\(647\) 1.46905e7 1.37967 0.689837 0.723964i \(-0.257682\pi\)
0.689837 + 0.723964i \(0.257682\pi\)
\(648\) −3.92526e6 −0.367224
\(649\) −1.47256e6 −0.137233
\(650\) 5.29936e7 4.91972
\(651\) 2.01404e6 0.186259
\(652\) −145474. −0.0134019
\(653\) 1.07967e7 0.990852 0.495426 0.868650i \(-0.335012\pi\)
0.495426 + 0.868650i \(0.335012\pi\)
\(654\) −1.45114e7 −1.32667
\(655\) −3.26615e7 −2.97463
\(656\) −3.10387e6 −0.281608
\(657\) 2.18798e6 0.197756
\(658\) 1.08358e7 0.975657
\(659\) −1.33499e7 −1.19747 −0.598734 0.800948i \(-0.704329\pi\)
−0.598734 + 0.800948i \(0.704329\pi\)
\(660\) −2.91434e7 −2.60424
\(661\) −1.52627e7 −1.35871 −0.679354 0.733810i \(-0.737740\pi\)
−0.679354 + 0.733810i \(0.737740\pi\)
\(662\) 7.05324e6 0.625524
\(663\) −1.91873e7 −1.69523
\(664\) 3.26126e7 2.87055
\(665\) −8.33106e6 −0.730544
\(666\) 1.32826e7 1.16037
\(667\) 344893. 0.0300172
\(668\) −5.50627e7 −4.77437
\(669\) −2.69108e6 −0.232467
\(670\) −9.43238e6 −0.811773
\(671\) 6.94562e6 0.595531
\(672\) 1.20324e7 1.02785
\(673\) 700630. 0.0596281 0.0298141 0.999555i \(-0.490508\pi\)
0.0298141 + 0.999555i \(0.490508\pi\)
\(674\) 2.10769e7 1.78713
\(675\) −3.38192e6 −0.285696
\(676\) 6.31071e7 5.31143
\(677\) 1.76900e7 1.48339 0.741697 0.670735i \(-0.234021\pi\)
0.741697 + 0.670735i \(0.234021\pi\)
\(678\) −8.20948e6 −0.685869
\(679\) 2.99464e6 0.249270
\(680\) 1.07268e8 8.89605
\(681\) −954816. −0.0788954
\(682\) 1.67251e7 1.37692
\(683\) −1.72148e7 −1.41205 −0.706024 0.708187i \(-0.749513\pi\)
−0.706024 + 0.708187i \(0.749513\pi\)
\(684\) −1.07810e7 −0.881084
\(685\) 1.70993e7 1.39236
\(686\) 2.00542e7 1.62703
\(687\) 2.00492e6 0.162071
\(688\) −4.60163e7 −3.70630
\(689\) −3.60715e7 −2.89478
\(690\) 2.58236e7 2.06488
\(691\) −1.54571e7 −1.23149 −0.615746 0.787944i \(-0.711145\pi\)
−0.615746 + 0.787944i \(0.711145\pi\)
\(692\) 2.64751e7 2.10171
\(693\) 2.11455e6 0.167257
\(694\) 2.78590e7 2.19567
\(695\) −7.09312e6 −0.557025
\(696\) 621783. 0.0486536
\(697\) 1.68738e6 0.131562
\(698\) 1.15862e6 0.0900120
\(699\) 7.89818e6 0.611412
\(700\) 2.48706e7 1.91841
\(701\) 90599.9 0.00696358 0.00348179 0.999994i \(-0.498892\pi\)
0.00348179 + 0.999994i \(0.498892\pi\)
\(702\) −8.32751e6 −0.637783
\(703\) 2.30433e7 1.75856
\(704\) 4.92526e7 3.74539
\(705\) 1.27715e7 0.967767
\(706\) −4.59894e6 −0.347253
\(707\) 6.61099e6 0.497414
\(708\) 2.72164e6 0.204055
\(709\) 7.81917e6 0.584178 0.292089 0.956391i \(-0.405650\pi\)
0.292089 + 0.956391i \(0.405650\pi\)
\(710\) −3.24874e6 −0.241863
\(711\) 1.65453e6 0.122744
\(712\) 4.16997e7 3.08271
\(713\) −1.08305e7 −0.797855
\(714\) −1.23218e7 −0.904541
\(715\) −3.90535e7 −2.85690
\(716\) 5.83197e6 0.425141
\(717\) −1.39863e7 −1.01602
\(718\) −2.54956e7 −1.84567
\(719\) 2.06917e7 1.49270 0.746352 0.665552i \(-0.231804\pi\)
0.746352 + 0.665552i \(0.231804\pi\)
\(720\) 2.67145e7 1.92050
\(721\) −5.77148e6 −0.413475
\(722\) 1.40377e6 0.100220
\(723\) 593069. 0.0421948
\(724\) 9.71073e6 0.688503
\(725\) 535714. 0.0378519
\(726\) 1.75650e6 0.123682
\(727\) −1.54163e7 −1.08179 −0.540896 0.841089i \(-0.681915\pi\)
−0.540896 + 0.841089i \(0.681915\pi\)
\(728\) 3.86822e7 2.70509
\(729\) 531441. 0.0370370
\(730\) −2.59505e7 −1.80234
\(731\) 2.50162e7 1.73152
\(732\) −1.28372e7 −0.885507
\(733\) 1.32653e7 0.911924 0.455962 0.889999i \(-0.349295\pi\)
0.455962 + 0.889999i \(0.349295\pi\)
\(734\) −1.92075e7 −1.31592
\(735\) 1.03083e7 0.703834
\(736\) −6.47042e7 −4.40289
\(737\) 4.15338e6 0.281665
\(738\) 732344. 0.0494965
\(739\) 1.43430e7 0.966114 0.483057 0.875589i \(-0.339526\pi\)
0.483057 + 0.875589i \(0.339526\pi\)
\(740\) −1.15129e8 −7.72871
\(741\) −1.44470e7 −0.966567
\(742\) −2.31646e7 −1.54459
\(743\) 6.61514e6 0.439609 0.219805 0.975544i \(-0.429458\pi\)
0.219805 + 0.975544i \(0.429458\pi\)
\(744\) −1.95255e7 −1.29321
\(745\) 2.02638e7 1.33761
\(746\) −6.05998e6 −0.398679
\(747\) −4.41542e6 −0.289514
\(748\) −7.47784e7 −4.88677
\(749\) 3.19639e6 0.208188
\(750\) 1.30915e7 0.849841
\(751\) 5.45848e6 0.353160 0.176580 0.984286i \(-0.443497\pi\)
0.176580 + 0.984286i \(0.443497\pi\)
\(752\) −6.02795e7 −3.88710
\(753\) 223584. 0.0143699
\(754\) 1.31912e6 0.0845000
\(755\) −9.11815e6 −0.582156
\(756\) −3.90820e6 −0.248698
\(757\) 1.40547e7 0.891416 0.445708 0.895178i \(-0.352952\pi\)
0.445708 + 0.895178i \(0.352952\pi\)
\(758\) −1.34313e7 −0.849070
\(759\) −1.13710e7 −0.716461
\(760\) 8.07669e7 5.07224
\(761\) −7.51836e6 −0.470610 −0.235305 0.971922i \(-0.575609\pi\)
−0.235305 + 0.971922i \(0.575609\pi\)
\(762\) −1.52142e7 −0.949212
\(763\) −9.12621e6 −0.567517
\(764\) −6.35347e7 −3.93802
\(765\) −1.45230e7 −0.897226
\(766\) −2.25863e7 −1.39083
\(767\) 3.64712e6 0.223853
\(768\) −2.30040e7 −1.40734
\(769\) 1.72875e7 1.05418 0.527091 0.849809i \(-0.323283\pi\)
0.527091 + 0.849809i \(0.323283\pi\)
\(770\) −2.50796e7 −1.52438
\(771\) −4.51770e6 −0.273704
\(772\) 5.95213e7 3.59442
\(773\) 7.13686e6 0.429594 0.214797 0.976659i \(-0.431091\pi\)
0.214797 + 0.976659i \(0.431091\pi\)
\(774\) 1.08573e7 0.651434
\(775\) −1.68227e7 −1.00610
\(776\) −2.90320e7 −1.73070
\(777\) 8.35342e6 0.496377
\(778\) 4.43369e7 2.62613
\(779\) 1.27051e6 0.0750125
\(780\) 7.21804e7 4.24798
\(781\) 1.43052e6 0.0839203
\(782\) 6.62602e7 3.87468
\(783\) −84183.1 −0.00490705
\(784\) −4.86536e7 −2.82699
\(785\) 1.95636e7 1.13312
\(786\) −3.63726e7 −2.09999
\(787\) −5.86391e6 −0.337482 −0.168741 0.985660i \(-0.553970\pi\)
−0.168741 + 0.985660i \(0.553970\pi\)
\(788\) −6.28742e7 −3.60709
\(789\) −1.14212e7 −0.653159
\(790\) −1.96236e7 −1.11869
\(791\) −5.16294e6 −0.293397
\(792\) −2.04999e7 −1.16128
\(793\) −1.72024e7 −0.971419
\(794\) 5.05734e7 2.84689
\(795\) −2.73027e7 −1.53210
\(796\) −1.62344e7 −0.908144
\(797\) 1.96169e7 1.09392 0.546958 0.837160i \(-0.315786\pi\)
0.546958 + 0.837160i \(0.315786\pi\)
\(798\) −9.27765e6 −0.515740
\(799\) 3.27702e7 1.81599
\(800\) −1.00503e8 −5.55209
\(801\) −5.64571e6 −0.310912
\(802\) −2.86957e7 −1.57536
\(803\) 1.14268e7 0.625369
\(804\) −7.67645e6 −0.418813
\(805\) 1.62405e7 0.883302
\(806\) −4.14237e7 −2.24601
\(807\) 9.36877e6 0.506406
\(808\) −6.40914e7 −3.45360
\(809\) −2.49811e7 −1.34196 −0.670982 0.741474i \(-0.734127\pi\)
−0.670982 + 0.741474i \(0.734127\pi\)
\(810\) −6.30315e6 −0.337555
\(811\) −1.44411e7 −0.770987 −0.385493 0.922711i \(-0.625969\pi\)
−0.385493 + 0.922711i \(0.625969\pi\)
\(812\) 619080. 0.0329501
\(813\) 1.86315e7 0.988603
\(814\) 6.93689e7 3.66947
\(815\) −147552. −0.00778130
\(816\) 6.85460e7 3.60377
\(817\) 1.88359e7 0.987257
\(818\) −3.32512e7 −1.73749
\(819\) −5.23718e6 −0.272827
\(820\) −6.34774e6 −0.329674
\(821\) −625911. −0.0324082 −0.0162041 0.999869i \(-0.505158\pi\)
−0.0162041 + 0.999869i \(0.505158\pi\)
\(822\) 1.90421e7 0.982961
\(823\) 2.15073e7 1.10684 0.553422 0.832901i \(-0.313322\pi\)
0.553422 + 0.832901i \(0.313322\pi\)
\(824\) 5.59526e7 2.87079
\(825\) −1.76622e7 −0.903464
\(826\) 2.34213e6 0.119443
\(827\) 2.06626e7 1.05056 0.525280 0.850929i \(-0.323960\pi\)
0.525280 + 0.850929i \(0.323960\pi\)
\(828\) 2.10163e7 1.06532
\(829\) −5.93386e6 −0.299882 −0.149941 0.988695i \(-0.547908\pi\)
−0.149941 + 0.988695i \(0.547908\pi\)
\(830\) 5.23690e7 2.63863
\(831\) −1.73834e7 −0.873238
\(832\) −1.21985e8 −6.10941
\(833\) 2.64499e7 1.32072
\(834\) −7.89905e6 −0.393242
\(835\) −5.58495e7 −2.77206
\(836\) −5.63041e7 −2.78628
\(837\) 2.64355e6 0.130429
\(838\) −1.46274e7 −0.719544
\(839\) −925271. −0.0453800 −0.0226900 0.999743i \(-0.507223\pi\)
−0.0226900 + 0.999743i \(0.507223\pi\)
\(840\) 2.92788e7 1.43171
\(841\) −2.04978e7 −0.999350
\(842\) −2.76954e7 −1.34626
\(843\) −7.73736e6 −0.374994
\(844\) −1.24843e7 −0.603265
\(845\) 6.40089e7 3.08389
\(846\) 1.42227e7 0.683212
\(847\) 1.10466e6 0.0529080
\(848\) 1.28864e8 6.15379
\(849\) 7.10485e6 0.338287
\(850\) 1.02920e8 4.88601
\(851\) −4.49203e7 −2.12627
\(852\) −2.64395e6 −0.124783
\(853\) 1.48698e7 0.699732 0.349866 0.936800i \(-0.386227\pi\)
0.349866 + 0.936800i \(0.386227\pi\)
\(854\) −1.10471e7 −0.518329
\(855\) −1.09350e7 −0.511569
\(856\) −3.09879e7 −1.44547
\(857\) −4.11203e7 −1.91251 −0.956256 0.292531i \(-0.905503\pi\)
−0.956256 + 0.292531i \(0.905503\pi\)
\(858\) −4.34909e7 −2.01688
\(859\) 1.38706e7 0.641378 0.320689 0.947185i \(-0.396086\pi\)
0.320689 + 0.947185i \(0.396086\pi\)
\(860\) −9.41081e7 −4.33891
\(861\) 460571. 0.0211733
\(862\) −4.55557e7 −2.08821
\(863\) 1.87918e7 0.858898 0.429449 0.903091i \(-0.358708\pi\)
0.429449 + 0.903091i \(0.358708\pi\)
\(864\) 1.57933e7 0.719761
\(865\) 2.68535e7 1.22028
\(866\) 813143. 0.0368445
\(867\) −2.44854e7 −1.10627
\(868\) −1.94406e7 −0.875812
\(869\) 8.64088e6 0.388158
\(870\) 998452. 0.0447228
\(871\) −1.02868e7 −0.459447
\(872\) 8.84756e7 3.94033
\(873\) 3.93064e6 0.174553
\(874\) 4.98904e7 2.20922
\(875\) 8.23327e6 0.363540
\(876\) −2.11195e7 −0.929873
\(877\) 4.12113e7 1.80933 0.904665 0.426124i \(-0.140121\pi\)
0.904665 + 0.426124i \(0.140121\pi\)
\(878\) −7.76505e7 −3.39944
\(879\) 1.65359e7 0.721863
\(880\) 1.39518e8 6.07326
\(881\) 3.73000e7 1.61908 0.809542 0.587062i \(-0.199716\pi\)
0.809542 + 0.587062i \(0.199716\pi\)
\(882\) 1.14796e7 0.496884
\(883\) −3.73701e7 −1.61295 −0.806477 0.591265i \(-0.798629\pi\)
−0.806477 + 0.591265i \(0.798629\pi\)
\(884\) 1.85206e8 7.97121
\(885\) 2.76053e6 0.118477
\(886\) 8.02716e7 3.43540
\(887\) −2.39606e6 −0.102256 −0.0511280 0.998692i \(-0.516282\pi\)
−0.0511280 + 0.998692i \(0.516282\pi\)
\(888\) −8.09836e7 −3.44639
\(889\) −9.56824e6 −0.406048
\(890\) 6.69609e7 2.83365
\(891\) 2.77548e6 0.117123
\(892\) 2.59758e7 1.09309
\(893\) 2.46742e7 1.03542
\(894\) 2.25662e7 0.944309
\(895\) 5.91531e6 0.246843
\(896\) −3.55552e7 −1.47956
\(897\) 2.81628e7 1.16868
\(898\) 6.11092e7 2.52881
\(899\) −418753. −0.0172806
\(900\) 3.26441e7 1.34338
\(901\) −7.00554e7 −2.87494
\(902\) 3.82470e6 0.156524
\(903\) 6.82818e6 0.278667
\(904\) 5.00530e7 2.03709
\(905\) 9.84950e6 0.399754
\(906\) −1.01542e7 −0.410983
\(907\) −6.32877e6 −0.255447 −0.127724 0.991810i \(-0.540767\pi\)
−0.127724 + 0.991810i \(0.540767\pi\)
\(908\) 9.21640e6 0.370977
\(909\) 8.67733e6 0.348318
\(910\) 6.21155e7 2.48654
\(911\) −1.22155e6 −0.0487659 −0.0243830 0.999703i \(-0.507762\pi\)
−0.0243830 + 0.999703i \(0.507762\pi\)
\(912\) 5.16115e7 2.05475
\(913\) −2.30597e7 −0.915540
\(914\) 2.48569e7 0.984197
\(915\) −1.30206e7 −0.514137
\(916\) −1.93526e7 −0.762080
\(917\) −2.28747e7 −0.898323
\(918\) −1.61731e7 −0.633412
\(919\) −2.44744e7 −0.955924 −0.477962 0.878381i \(-0.658624\pi\)
−0.477962 + 0.878381i \(0.658624\pi\)
\(920\) −1.57446e8 −6.13285
\(921\) 3.99375e6 0.155143
\(922\) −6.21873e7 −2.40921
\(923\) −3.54302e6 −0.136889
\(924\) −2.04108e7 −0.786466
\(925\) −6.97737e7 −2.68125
\(926\) −3.44184e7 −1.31905
\(927\) −7.57541e6 −0.289539
\(928\) −2.50174e6 −0.0953614
\(929\) 471008. 0.0179056 0.00895280 0.999960i \(-0.497150\pi\)
0.00895280 + 0.999960i \(0.497150\pi\)
\(930\) −3.13538e7 −1.18873
\(931\) 1.99154e7 0.753034
\(932\) −7.62374e7 −2.87494
\(933\) 5.86513e6 0.220584
\(934\) −4.47746e7 −1.67944
\(935\) −7.58470e7 −2.83733
\(936\) 5.07727e7 1.89426
\(937\) 9.92896e6 0.369449 0.184725 0.982790i \(-0.440861\pi\)
0.184725 + 0.982790i \(0.440861\pi\)
\(938\) −6.60604e6 −0.245151
\(939\) 1.15256e7 0.426581
\(940\) −1.23278e8 −4.55057
\(941\) −2.51107e7 −0.924452 −0.462226 0.886762i \(-0.652949\pi\)
−0.462226 + 0.886762i \(0.652949\pi\)
\(942\) 2.17865e7 0.799943
\(943\) −2.47671e6 −0.0906978
\(944\) −1.30292e7 −0.475871
\(945\) −3.96405e6 −0.144398
\(946\) 5.67029e7 2.06005
\(947\) 1.98803e7 0.720356 0.360178 0.932884i \(-0.382716\pi\)
0.360178 + 0.932884i \(0.382716\pi\)
\(948\) −1.59704e7 −0.577160
\(949\) −2.83011e7 −1.02009
\(950\) 7.74936e7 2.78584
\(951\) −1.66748e7 −0.597872
\(952\) 7.51257e7 2.68656
\(953\) 3.07521e7 1.09684 0.548418 0.836204i \(-0.315230\pi\)
0.548418 + 0.836204i \(0.315230\pi\)
\(954\) −3.04049e7 −1.08161
\(955\) −6.44427e7 −2.28647
\(956\) 1.35003e8 4.77747
\(957\) −439650. −0.0155177
\(958\) 4.31905e7 1.52046
\(959\) 1.19756e7 0.420486
\(960\) −9.23315e7 −3.23349
\(961\) −1.54793e7 −0.540682
\(962\) −1.71808e8 −5.98558
\(963\) 4.19546e6 0.145785
\(964\) −5.72462e6 −0.198406
\(965\) 6.03719e7 2.08697
\(966\) 1.80857e7 0.623582
\(967\) 3.47128e7 1.19378 0.596888 0.802324i \(-0.296404\pi\)
0.596888 + 0.802324i \(0.296404\pi\)
\(968\) −1.07093e7 −0.367345
\(969\) −2.80579e7 −0.959944
\(970\) −4.66193e7 −1.59088
\(971\) 6.63760e6 0.225924 0.112962 0.993599i \(-0.463966\pi\)
0.112962 + 0.993599i \(0.463966\pi\)
\(972\) −5.12975e6 −0.174153
\(973\) −4.96771e6 −0.168219
\(974\) 1.00158e8 3.38288
\(975\) 4.37446e7 1.47371
\(976\) 6.14551e7 2.06506
\(977\) 2.24812e7 0.753500 0.376750 0.926315i \(-0.377042\pi\)
0.376750 + 0.926315i \(0.377042\pi\)
\(978\) −164318. −0.00549334
\(979\) −2.94850e7 −0.983207
\(980\) −9.95016e7 −3.30952
\(981\) −1.19787e7 −0.397409
\(982\) −4.20818e7 −1.39256
\(983\) −4.47702e7 −1.47776 −0.738882 0.673835i \(-0.764646\pi\)
−0.738882 + 0.673835i \(0.764646\pi\)
\(984\) −4.46509e6 −0.147008
\(985\) −6.37727e7 −2.09432
\(986\) 2.56190e6 0.0839210
\(987\) 8.94464e6 0.292260
\(988\) 1.39450e8 4.54493
\(989\) −3.67184e7 −1.19369
\(990\) −3.29185e7 −1.06746
\(991\) −173229. −0.00560320 −0.00280160 0.999996i \(-0.500892\pi\)
−0.00280160 + 0.999996i \(0.500892\pi\)
\(992\) 7.85608e7 2.53470
\(993\) 5.82224e6 0.187377
\(994\) −2.27528e6 −0.0730412
\(995\) −1.64664e7 −0.527281
\(996\) 4.26200e7 1.36133
\(997\) 1.72883e7 0.550825 0.275413 0.961326i \(-0.411186\pi\)
0.275413 + 0.961326i \(0.411186\pi\)
\(998\) 3.75903e7 1.19467
\(999\) 1.09644e7 0.347592
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.b.1.1 12
3.2 odd 2 531.6.a.d.1.12 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.b.1.1 12 1.1 even 1 trivial
531.6.a.d.1.12 12 3.2 odd 2