Properties

Label 177.6.a.a.1.4
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.4
Root \(-5.62527\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.62527 q^{2} +9.00000 q^{3} +11.8942 q^{4} -85.2025 q^{5} -59.6275 q^{6} -103.010 q^{7} +133.206 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-6.62527 q^{2} +9.00000 q^{3} +11.8942 q^{4} -85.2025 q^{5} -59.6275 q^{6} -103.010 q^{7} +133.206 q^{8} +81.0000 q^{9} +564.490 q^{10} +579.703 q^{11} +107.048 q^{12} +435.487 q^{13} +682.469 q^{14} -766.822 q^{15} -1263.14 q^{16} +424.138 q^{17} -536.647 q^{18} +1540.54 q^{19} -1013.42 q^{20} -927.089 q^{21} -3840.69 q^{22} -4164.00 q^{23} +1198.86 q^{24} +4134.46 q^{25} -2885.22 q^{26} +729.000 q^{27} -1225.22 q^{28} -8418.14 q^{29} +5080.41 q^{30} +7073.40 q^{31} +4106.07 q^{32} +5217.32 q^{33} -2810.03 q^{34} +8776.70 q^{35} +963.434 q^{36} +12420.5 q^{37} -10206.5 q^{38} +3919.38 q^{39} -11349.5 q^{40} -2421.33 q^{41} +6142.22 q^{42} -11711.3 q^{43} +6895.12 q^{44} -6901.40 q^{45} +27587.6 q^{46} -9436.30 q^{47} -11368.3 q^{48} -6195.96 q^{49} -27391.9 q^{50} +3817.24 q^{51} +5179.79 q^{52} -23764.2 q^{53} -4829.82 q^{54} -49392.1 q^{55} -13721.5 q^{56} +13864.8 q^{57} +55772.5 q^{58} +3481.00 q^{59} -9120.77 q^{60} +5566.88 q^{61} -46863.2 q^{62} -8343.80 q^{63} +13216.7 q^{64} -37104.6 q^{65} -34566.2 q^{66} -57888.7 q^{67} +5044.80 q^{68} -37476.0 q^{69} -58148.0 q^{70} -11960.0 q^{71} +10789.7 q^{72} +25056.7 q^{73} -82289.1 q^{74} +37210.2 q^{75} +18323.5 q^{76} -59715.1 q^{77} -25967.0 q^{78} +17801.5 q^{79} +107623. q^{80} +6561.00 q^{81} +16042.0 q^{82} -2768.37 q^{83} -11027.0 q^{84} -36137.6 q^{85} +77590.7 q^{86} -75763.3 q^{87} +77219.9 q^{88} +17994.8 q^{89} +45723.7 q^{90} -44859.5 q^{91} -49527.6 q^{92} +63660.6 q^{93} +62518.1 q^{94} -131257. q^{95} +36954.6 q^{96} -166125. q^{97} +41049.9 q^{98} +46955.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.62527 −1.17119 −0.585597 0.810602i \(-0.699140\pi\)
−0.585597 + 0.810602i \(0.699140\pi\)
\(3\) 9.00000 0.577350
\(4\) 11.8942 0.371695
\(5\) −85.2025 −1.52415 −0.762074 0.647490i \(-0.775819\pi\)
−0.762074 + 0.647490i \(0.775819\pi\)
\(6\) −59.6275 −0.676189
\(7\) −103.010 −0.794573 −0.397287 0.917695i \(-0.630048\pi\)
−0.397287 + 0.917695i \(0.630048\pi\)
\(8\) 133.206 0.735867
\(9\) 81.0000 0.333333
\(10\) 564.490 1.78507
\(11\) 579.703 1.44452 0.722260 0.691622i \(-0.243103\pi\)
0.722260 + 0.691622i \(0.243103\pi\)
\(12\) 107.048 0.214598
\(13\) 435.487 0.714689 0.357344 0.933973i \(-0.383682\pi\)
0.357344 + 0.933973i \(0.383682\pi\)
\(14\) 682.469 0.930599
\(15\) −766.822 −0.879967
\(16\) −1263.14 −1.23354
\(17\) 424.138 0.355946 0.177973 0.984035i \(-0.443046\pi\)
0.177973 + 0.984035i \(0.443046\pi\)
\(18\) −536.647 −0.390398
\(19\) 1540.54 0.979012 0.489506 0.872000i \(-0.337177\pi\)
0.489506 + 0.872000i \(0.337177\pi\)
\(20\) −1013.42 −0.566518
\(21\) −927.089 −0.458747
\(22\) −3840.69 −1.69181
\(23\) −4164.00 −1.64131 −0.820656 0.571423i \(-0.806391\pi\)
−0.820656 + 0.571423i \(0.806391\pi\)
\(24\) 1198.86 0.424853
\(25\) 4134.46 1.32303
\(26\) −2885.22 −0.837039
\(27\) 729.000 0.192450
\(28\) −1225.22 −0.295339
\(29\) −8418.14 −1.85875 −0.929376 0.369135i \(-0.879654\pi\)
−0.929376 + 0.369135i \(0.879654\pi\)
\(30\) 5080.41 1.03061
\(31\) 7073.40 1.32198 0.660989 0.750396i \(-0.270137\pi\)
0.660989 + 0.750396i \(0.270137\pi\)
\(32\) 4106.07 0.708845
\(33\) 5217.32 0.833994
\(34\) −2810.03 −0.416882
\(35\) 8776.70 1.21105
\(36\) 963.434 0.123898
\(37\) 12420.5 1.49154 0.745769 0.666205i \(-0.232082\pi\)
0.745769 + 0.666205i \(0.232082\pi\)
\(38\) −10206.5 −1.14661
\(39\) 3919.38 0.412626
\(40\) −11349.5 −1.12157
\(41\) −2421.33 −0.224954 −0.112477 0.993654i \(-0.535878\pi\)
−0.112477 + 0.993654i \(0.535878\pi\)
\(42\) 6142.22 0.537282
\(43\) −11711.3 −0.965905 −0.482953 0.875646i \(-0.660436\pi\)
−0.482953 + 0.875646i \(0.660436\pi\)
\(44\) 6895.12 0.536921
\(45\) −6901.40 −0.508049
\(46\) 27587.6 1.92229
\(47\) −9436.30 −0.623099 −0.311550 0.950230i \(-0.600848\pi\)
−0.311550 + 0.950230i \(0.600848\pi\)
\(48\) −11368.3 −0.712183
\(49\) −6195.96 −0.368654
\(50\) −27391.9 −1.54952
\(51\) 3817.24 0.205506
\(52\) 5179.79 0.265646
\(53\) −23764.2 −1.16207 −0.581037 0.813877i \(-0.697353\pi\)
−0.581037 + 0.813877i \(0.697353\pi\)
\(54\) −4829.82 −0.225396
\(55\) −49392.1 −2.20166
\(56\) −13721.5 −0.584700
\(57\) 13864.8 0.565233
\(58\) 55772.5 2.17696
\(59\) 3481.00 0.130189
\(60\) −9120.77 −0.327080
\(61\) 5566.88 0.191552 0.0957761 0.995403i \(-0.469467\pi\)
0.0957761 + 0.995403i \(0.469467\pi\)
\(62\) −46863.2 −1.54829
\(63\) −8343.80 −0.264858
\(64\) 13216.7 0.403343
\(65\) −37104.6 −1.08929
\(66\) −34566.2 −0.976769
\(67\) −57888.7 −1.57546 −0.787729 0.616022i \(-0.788743\pi\)
−0.787729 + 0.616022i \(0.788743\pi\)
\(68\) 5044.80 0.132304
\(69\) −37476.0 −0.947611
\(70\) −58148.0 −1.41837
\(71\) −11960.0 −0.281569 −0.140784 0.990040i \(-0.544962\pi\)
−0.140784 + 0.990040i \(0.544962\pi\)
\(72\) 10789.7 0.245289
\(73\) 25056.7 0.550322 0.275161 0.961398i \(-0.411269\pi\)
0.275161 + 0.961398i \(0.411269\pi\)
\(74\) −82289.1 −1.74688
\(75\) 37210.2 0.763850
\(76\) 18323.5 0.363894
\(77\) −59715.1 −1.14778
\(78\) −25967.0 −0.483265
\(79\) 17801.5 0.320914 0.160457 0.987043i \(-0.448703\pi\)
0.160457 + 0.987043i \(0.448703\pi\)
\(80\) 107623. 1.88009
\(81\) 6561.00 0.111111
\(82\) 16042.0 0.263465
\(83\) −2768.37 −0.0441092 −0.0220546 0.999757i \(-0.507021\pi\)
−0.0220546 + 0.999757i \(0.507021\pi\)
\(84\) −11027.0 −0.170514
\(85\) −36137.6 −0.542515
\(86\) 77590.7 1.13126
\(87\) −75763.3 −1.07315
\(88\) 77219.9 1.06297
\(89\) 17994.8 0.240809 0.120404 0.992725i \(-0.461581\pi\)
0.120404 + 0.992725i \(0.461581\pi\)
\(90\) 45723.7 0.595024
\(91\) −44859.5 −0.567872
\(92\) −49527.6 −0.610067
\(93\) 63660.6 0.763244
\(94\) 62518.1 0.729770
\(95\) −131257. −1.49216
\(96\) 36954.6 0.409252
\(97\) −166125. −1.79269 −0.896346 0.443355i \(-0.853788\pi\)
−0.896346 + 0.443355i \(0.853788\pi\)
\(98\) 41049.9 0.431765
\(99\) 46955.9 0.481507
\(100\) 49176.3 0.491763
\(101\) −38127.7 −0.371909 −0.185954 0.982558i \(-0.559538\pi\)
−0.185954 + 0.982558i \(0.559538\pi\)
\(102\) −25290.2 −0.240687
\(103\) 81615.4 0.758018 0.379009 0.925393i \(-0.376265\pi\)
0.379009 + 0.925393i \(0.376265\pi\)
\(104\) 58009.5 0.525916
\(105\) 78990.3 0.699198
\(106\) 157444. 1.36101
\(107\) 121265. 1.02395 0.511973 0.859002i \(-0.328915\pi\)
0.511973 + 0.859002i \(0.328915\pi\)
\(108\) 8670.90 0.0715328
\(109\) −153096. −1.23424 −0.617118 0.786870i \(-0.711700\pi\)
−0.617118 + 0.786870i \(0.711700\pi\)
\(110\) 327236. 2.57857
\(111\) 111784. 0.861140
\(112\) 130116. 0.980136
\(113\) −54428.5 −0.400987 −0.200494 0.979695i \(-0.564255\pi\)
−0.200494 + 0.979695i \(0.564255\pi\)
\(114\) −91858.3 −0.661997
\(115\) 354783. 2.50160
\(116\) −100127. −0.690889
\(117\) 35274.4 0.238230
\(118\) −23062.6 −0.152476
\(119\) −43690.4 −0.282825
\(120\) −102145. −0.647539
\(121\) 175004. 1.08664
\(122\) −36882.1 −0.224345
\(123\) −21791.9 −0.129877
\(124\) 84132.8 0.491373
\(125\) −86008.6 −0.492342
\(126\) 55280.0 0.310200
\(127\) −203111. −1.11744 −0.558721 0.829356i \(-0.688708\pi\)
−0.558721 + 0.829356i \(0.688708\pi\)
\(128\) −218959. −1.18124
\(129\) −105402. −0.557666
\(130\) 245828. 1.27577
\(131\) −282282. −1.43716 −0.718579 0.695445i \(-0.755207\pi\)
−0.718579 + 0.695445i \(0.755207\pi\)
\(132\) 62056.1 0.309992
\(133\) −158690. −0.777896
\(134\) 383529. 1.84517
\(135\) −62112.6 −0.293322
\(136\) 56497.7 0.261929
\(137\) −290437. −1.32206 −0.661029 0.750360i \(-0.729880\pi\)
−0.661029 + 0.750360i \(0.729880\pi\)
\(138\) 248289. 1.10984
\(139\) 429789. 1.88677 0.943383 0.331705i \(-0.107624\pi\)
0.943383 + 0.331705i \(0.107624\pi\)
\(140\) 104392. 0.450140
\(141\) −84926.7 −0.359746
\(142\) 79238.2 0.329772
\(143\) 252453. 1.03238
\(144\) −102315. −0.411179
\(145\) 717247. 2.83301
\(146\) −166008. −0.644534
\(147\) −55763.7 −0.212842
\(148\) 147732. 0.554397
\(149\) −383936. −1.41675 −0.708376 0.705835i \(-0.750572\pi\)
−0.708376 + 0.705835i \(0.750572\pi\)
\(150\) −246527. −0.894617
\(151\) −91551.4 −0.326755 −0.163378 0.986564i \(-0.552239\pi\)
−0.163378 + 0.986564i \(0.552239\pi\)
\(152\) 205209. 0.720422
\(153\) 34355.1 0.118649
\(154\) 395629. 1.34427
\(155\) −602671. −2.01489
\(156\) 46618.1 0.153371
\(157\) −18734.2 −0.0606578 −0.0303289 0.999540i \(-0.509655\pi\)
−0.0303289 + 0.999540i \(0.509655\pi\)
\(158\) −117940. −0.375852
\(159\) −213878. −0.670923
\(160\) −349847. −1.08039
\(161\) 428933. 1.30414
\(162\) −43468.4 −0.130133
\(163\) 85172.5 0.251091 0.125545 0.992088i \(-0.459932\pi\)
0.125545 + 0.992088i \(0.459932\pi\)
\(164\) −28799.9 −0.0836143
\(165\) −444529. −1.27113
\(166\) 18341.2 0.0516604
\(167\) 541622. 1.50281 0.751407 0.659839i \(-0.229375\pi\)
0.751407 + 0.659839i \(0.229375\pi\)
\(168\) −123494. −0.337577
\(169\) −181644. −0.489220
\(170\) 239421. 0.635390
\(171\) 124783. 0.326337
\(172\) −139297. −0.359022
\(173\) 238752. 0.606502 0.303251 0.952911i \(-0.401928\pi\)
0.303251 + 0.952911i \(0.401928\pi\)
\(174\) 501953. 1.25687
\(175\) −425890. −1.05124
\(176\) −732247. −1.78187
\(177\) 31329.0 0.0751646
\(178\) −119221. −0.282034
\(179\) 284533. 0.663744 0.331872 0.943324i \(-0.392320\pi\)
0.331872 + 0.943324i \(0.392320\pi\)
\(180\) −82086.9 −0.188839
\(181\) −402281. −0.912711 −0.456355 0.889798i \(-0.650845\pi\)
−0.456355 + 0.889798i \(0.650845\pi\)
\(182\) 297206. 0.665089
\(183\) 50101.9 0.110593
\(184\) −554670. −1.20779
\(185\) −1.05826e6 −2.27332
\(186\) −421769. −0.893907
\(187\) 245874. 0.514172
\(188\) −112238. −0.231603
\(189\) −75094.2 −0.152916
\(190\) 869617. 1.74761
\(191\) −624305. −1.23826 −0.619132 0.785287i \(-0.712515\pi\)
−0.619132 + 0.785287i \(0.712515\pi\)
\(192\) 118951. 0.232870
\(193\) 835697. 1.61494 0.807469 0.589910i \(-0.200837\pi\)
0.807469 + 0.589910i \(0.200837\pi\)
\(194\) 1.10062e6 2.09959
\(195\) −333941. −0.628903
\(196\) −73696.3 −0.137027
\(197\) −724552. −1.33016 −0.665080 0.746772i \(-0.731603\pi\)
−0.665080 + 0.746772i \(0.731603\pi\)
\(198\) −311096. −0.563938
\(199\) −691882. −1.23851 −0.619255 0.785190i \(-0.712565\pi\)
−0.619255 + 0.785190i \(0.712565\pi\)
\(200\) 550736. 0.973572
\(201\) −520999. −0.909591
\(202\) 252606. 0.435577
\(203\) 867152. 1.47691
\(204\) 45403.2 0.0763855
\(205\) 206303. 0.342863
\(206\) −540725. −0.887786
\(207\) −337284. −0.547104
\(208\) −550082. −0.881595
\(209\) 893053. 1.41420
\(210\) −523332. −0.818897
\(211\) 249343. 0.385559 0.192779 0.981242i \(-0.438250\pi\)
0.192779 + 0.981242i \(0.438250\pi\)
\(212\) −282657. −0.431937
\(213\) −107640. −0.162564
\(214\) −803416. −1.19924
\(215\) 997833. 1.47218
\(216\) 97107.3 0.141618
\(217\) −728630. −1.05041
\(218\) 1.01430e6 1.44553
\(219\) 225510. 0.317729
\(220\) −587482. −0.818347
\(221\) 184706. 0.254391
\(222\) −740602. −1.00856
\(223\) −542135. −0.730038 −0.365019 0.931000i \(-0.618938\pi\)
−0.365019 + 0.931000i \(0.618938\pi\)
\(224\) −422966. −0.563229
\(225\) 334891. 0.441009
\(226\) 360604. 0.469634
\(227\) −480667. −0.619127 −0.309563 0.950879i \(-0.600183\pi\)
−0.309563 + 0.950879i \(0.600183\pi\)
\(228\) 164912. 0.210094
\(229\) −623840. −0.786112 −0.393056 0.919514i \(-0.628582\pi\)
−0.393056 + 0.919514i \(0.628582\pi\)
\(230\) −2.35053e6 −2.92986
\(231\) −537436. −0.662669
\(232\) −1.12135e6 −1.36779
\(233\) 645676. 0.779157 0.389579 0.920993i \(-0.372621\pi\)
0.389579 + 0.920993i \(0.372621\pi\)
\(234\) −233703. −0.279013
\(235\) 803996. 0.949695
\(236\) 41403.9 0.0483906
\(237\) 160213. 0.185280
\(238\) 289461. 0.331243
\(239\) 1.10502e6 1.25134 0.625669 0.780089i \(-0.284826\pi\)
0.625669 + 0.780089i \(0.284826\pi\)
\(240\) 968606. 1.08547
\(241\) 1.44502e6 1.60262 0.801309 0.598250i \(-0.204137\pi\)
0.801309 + 0.598250i \(0.204137\pi\)
\(242\) −1.15945e6 −1.27266
\(243\) 59049.0 0.0641500
\(244\) 66213.8 0.0711990
\(245\) 527911. 0.561883
\(246\) 144378. 0.152112
\(247\) 670883. 0.699688
\(248\) 942220. 0.972799
\(249\) −24915.3 −0.0254664
\(250\) 569830. 0.576628
\(251\) 528809. 0.529803 0.264902 0.964275i \(-0.414660\pi\)
0.264902 + 0.964275i \(0.414660\pi\)
\(252\) −99243.2 −0.0984463
\(253\) −2.41388e6 −2.37091
\(254\) 1.34567e6 1.30874
\(255\) −325238. −0.313221
\(256\) 1.02773e6 0.980116
\(257\) −1.15172e6 −1.08771 −0.543856 0.839179i \(-0.683036\pi\)
−0.543856 + 0.839179i \(0.683036\pi\)
\(258\) 698316. 0.653135
\(259\) −1.27943e6 −1.18514
\(260\) −441331. −0.404884
\(261\) −681870. −0.619584
\(262\) 1.87019e6 1.68319
\(263\) 452277. 0.403195 0.201598 0.979468i \(-0.435387\pi\)
0.201598 + 0.979468i \(0.435387\pi\)
\(264\) 694979. 0.613709
\(265\) 2.02477e6 1.77117
\(266\) 1.05137e6 0.911067
\(267\) 161953. 0.139031
\(268\) −688543. −0.585590
\(269\) −1.71384e6 −1.44407 −0.722036 0.691856i \(-0.756793\pi\)
−0.722036 + 0.691856i \(0.756793\pi\)
\(270\) 411513. 0.343537
\(271\) 1.32879e6 1.09909 0.549546 0.835463i \(-0.314801\pi\)
0.549546 + 0.835463i \(0.314801\pi\)
\(272\) −535746. −0.439073
\(273\) −403735. −0.327861
\(274\) 1.92422e6 1.54839
\(275\) 2.39676e6 1.91114
\(276\) −445748. −0.352223
\(277\) −1.54297e6 −1.20825 −0.604126 0.796889i \(-0.706478\pi\)
−0.604126 + 0.796889i \(0.706478\pi\)
\(278\) −2.84747e6 −2.20977
\(279\) 572946. 0.440659
\(280\) 1.16911e6 0.891169
\(281\) −5515.62 −0.00416705 −0.00208352 0.999998i \(-0.500663\pi\)
−0.00208352 + 0.999998i \(0.500663\pi\)
\(282\) 562663. 0.421333
\(283\) −944988. −0.701391 −0.350696 0.936489i \(-0.614055\pi\)
−0.350696 + 0.936489i \(0.614055\pi\)
\(284\) −142255. −0.104658
\(285\) −1.18132e6 −0.861498
\(286\) −1.67257e6 −1.20912
\(287\) 249421. 0.178742
\(288\) 332592. 0.236282
\(289\) −1.23996e6 −0.873302
\(290\) −4.75196e6 −3.31801
\(291\) −1.49513e6 −1.03501
\(292\) 298031. 0.204552
\(293\) −1.52734e6 −1.03936 −0.519681 0.854361i \(-0.673949\pi\)
−0.519681 + 0.854361i \(0.673949\pi\)
\(294\) 369449. 0.249280
\(295\) −296590. −0.198427
\(296\) 1.65448e6 1.09757
\(297\) 422603. 0.277998
\(298\) 2.54368e6 1.65929
\(299\) −1.81337e6 −1.17303
\(300\) 442587. 0.283919
\(301\) 1.20638e6 0.767482
\(302\) 606553. 0.382694
\(303\) −343149. −0.214722
\(304\) −1.94592e6 −1.20765
\(305\) −474312. −0.291954
\(306\) −227612. −0.138961
\(307\) −2.82858e6 −1.71286 −0.856431 0.516261i \(-0.827323\pi\)
−0.856431 + 0.516261i \(0.827323\pi\)
\(308\) −710266. −0.426623
\(309\) 734539. 0.437642
\(310\) 3.99286e6 2.35983
\(311\) 490910. 0.287806 0.143903 0.989592i \(-0.454035\pi\)
0.143903 + 0.989592i \(0.454035\pi\)
\(312\) 522086. 0.303638
\(313\) 3.05776e6 1.76418 0.882089 0.471083i \(-0.156137\pi\)
0.882089 + 0.471083i \(0.156137\pi\)
\(314\) 124119. 0.0710420
\(315\) 710912. 0.403682
\(316\) 211735. 0.119282
\(317\) −3.44305e6 −1.92440 −0.962199 0.272348i \(-0.912200\pi\)
−0.962199 + 0.272348i \(0.912200\pi\)
\(318\) 1.41700e6 0.785781
\(319\) −4.88002e6 −2.68500
\(320\) −1.12610e6 −0.614754
\(321\) 1.09139e6 0.591176
\(322\) −2.84180e6 −1.52740
\(323\) 653399. 0.348476
\(324\) 78038.1 0.0412995
\(325\) 1.80050e6 0.945553
\(326\) −564291. −0.294076
\(327\) −1.37787e6 −0.712587
\(328\) −322536. −0.165536
\(329\) 972032. 0.495098
\(330\) 2.94513e6 1.48874
\(331\) −2.53352e6 −1.27102 −0.635512 0.772091i \(-0.719211\pi\)
−0.635512 + 0.772091i \(0.719211\pi\)
\(332\) −32927.7 −0.0163952
\(333\) 1.00606e6 0.497179
\(334\) −3.58840e6 −1.76009
\(335\) 4.93226e6 2.40123
\(336\) 1.17105e6 0.565882
\(337\) −2.44618e6 −1.17331 −0.586657 0.809835i \(-0.699556\pi\)
−0.586657 + 0.809835i \(0.699556\pi\)
\(338\) 1.20344e6 0.572972
\(339\) −489857. −0.231510
\(340\) −429829. −0.201650
\(341\) 4.10047e6 1.90962
\(342\) −826724. −0.382204
\(343\) 2.36953e6 1.08750
\(344\) −1.56002e6 −0.710778
\(345\) 3.19305e6 1.44430
\(346\) −1.58180e6 −0.710332
\(347\) 92368.8 0.0411815 0.0205907 0.999788i \(-0.493445\pi\)
0.0205907 + 0.999788i \(0.493445\pi\)
\(348\) −901147. −0.398885
\(349\) 519444. 0.228284 0.114142 0.993464i \(-0.463588\pi\)
0.114142 + 0.993464i \(0.463588\pi\)
\(350\) 2.82164e6 1.23121
\(351\) 317470. 0.137542
\(352\) 2.38030e6 1.02394
\(353\) −1.65548e6 −0.707109 −0.353555 0.935414i \(-0.615027\pi\)
−0.353555 + 0.935414i \(0.615027\pi\)
\(354\) −207563. −0.0880323
\(355\) 1.01902e6 0.429153
\(356\) 214035. 0.0895074
\(357\) −393213. −0.163289
\(358\) −1.88511e6 −0.777373
\(359\) 2.51488e6 1.02987 0.514934 0.857230i \(-0.327816\pi\)
0.514934 + 0.857230i \(0.327816\pi\)
\(360\) −919309. −0.373857
\(361\) −102848. −0.0415361
\(362\) 2.66522e6 1.06896
\(363\) 1.57504e6 0.627371
\(364\) −533570. −0.211075
\(365\) −2.13489e6 −0.838773
\(366\) −331939. −0.129525
\(367\) −792348. −0.307080 −0.153540 0.988142i \(-0.549067\pi\)
−0.153540 + 0.988142i \(0.549067\pi\)
\(368\) 5.25972e6 2.02462
\(369\) −196128. −0.0749847
\(370\) 7.01124e6 2.66250
\(371\) 2.44795e6 0.923352
\(372\) 757195. 0.283694
\(373\) 846687. 0.315102 0.157551 0.987511i \(-0.449640\pi\)
0.157551 + 0.987511i \(0.449640\pi\)
\(374\) −1.62898e6 −0.602195
\(375\) −774077. −0.284254
\(376\) −1.25697e6 −0.458518
\(377\) −3.66599e6 −1.32843
\(378\) 497520. 0.179094
\(379\) 1.63333e6 0.584085 0.292043 0.956405i \(-0.405665\pi\)
0.292043 + 0.956405i \(0.405665\pi\)
\(380\) −1.56121e6 −0.554628
\(381\) −1.82800e6 −0.645155
\(382\) 4.13619e6 1.45025
\(383\) −4.23461e6 −1.47508 −0.737541 0.675302i \(-0.764013\pi\)
−0.737541 + 0.675302i \(0.764013\pi\)
\(384\) −1.97063e6 −0.681988
\(385\) 5.08787e6 1.74938
\(386\) −5.53672e6 −1.89141
\(387\) −948617. −0.321968
\(388\) −1.97593e6 −0.666335
\(389\) 4.32595e6 1.44946 0.724732 0.689031i \(-0.241963\pi\)
0.724732 + 0.689031i \(0.241963\pi\)
\(390\) 2.21245e6 0.736567
\(391\) −1.76611e6 −0.584219
\(392\) −825340. −0.271280
\(393\) −2.54054e6 −0.829744
\(394\) 4.80035e6 1.55787
\(395\) −1.51673e6 −0.489120
\(396\) 558505. 0.178974
\(397\) 3.34065e6 1.06379 0.531894 0.846811i \(-0.321480\pi\)
0.531894 + 0.846811i \(0.321480\pi\)
\(398\) 4.58391e6 1.45054
\(399\) −1.42821e6 −0.449119
\(400\) −5.22241e6 −1.63200
\(401\) −600538. −0.186500 −0.0932502 0.995643i \(-0.529726\pi\)
−0.0932502 + 0.995643i \(0.529726\pi\)
\(402\) 3.45176e6 1.06531
\(403\) 3.08037e6 0.944802
\(404\) −453500. −0.138237
\(405\) −559013. −0.169350
\(406\) −5.74512e6 −1.72975
\(407\) 7.20019e6 2.15456
\(408\) 508480. 0.151225
\(409\) −1.87846e6 −0.555256 −0.277628 0.960689i \(-0.589548\pi\)
−0.277628 + 0.960689i \(0.589548\pi\)
\(410\) −1.36681e6 −0.401559
\(411\) −2.61393e6 −0.763291
\(412\) 970754. 0.281751
\(413\) −358577. −0.103445
\(414\) 2.23460e6 0.640765
\(415\) 235872. 0.0672289
\(416\) 1.78814e6 0.506604
\(417\) 3.86810e6 1.08932
\(418\) −5.91672e6 −1.65630
\(419\) −4.65041e6 −1.29407 −0.647033 0.762462i \(-0.723990\pi\)
−0.647033 + 0.762462i \(0.723990\pi\)
\(420\) 939530. 0.259889
\(421\) −1.24723e6 −0.342959 −0.171479 0.985188i \(-0.554855\pi\)
−0.171479 + 0.985188i \(0.554855\pi\)
\(422\) −1.65196e6 −0.451564
\(423\) −764340. −0.207700
\(424\) −3.16554e6 −0.855131
\(425\) 1.75358e6 0.470927
\(426\) 713144. 0.190394
\(427\) −573443. −0.152202
\(428\) 1.44236e6 0.380596
\(429\) 2.27208e6 0.596046
\(430\) −6.61092e6 −1.72421
\(431\) 975574. 0.252969 0.126484 0.991969i \(-0.459631\pi\)
0.126484 + 0.991969i \(0.459631\pi\)
\(432\) −920831. −0.237394
\(433\) 2.56758e6 0.658119 0.329060 0.944309i \(-0.393268\pi\)
0.329060 + 0.944309i \(0.393268\pi\)
\(434\) 4.82737e6 1.23023
\(435\) 6.45522e6 1.63564
\(436\) −1.82096e6 −0.458760
\(437\) −6.41479e6 −1.60686
\(438\) −1.49407e6 −0.372122
\(439\) 875156. 0.216733 0.108366 0.994111i \(-0.465438\pi\)
0.108366 + 0.994111i \(0.465438\pi\)
\(440\) −6.57933e6 −1.62013
\(441\) −501873. −0.122885
\(442\) −1.22373e6 −0.297941
\(443\) 4.39426e6 1.06384 0.531920 0.846795i \(-0.321471\pi\)
0.531920 + 0.846795i \(0.321471\pi\)
\(444\) 1.32959e6 0.320081
\(445\) −1.53320e6 −0.367028
\(446\) 3.59180e6 0.855016
\(447\) −3.45543e6 −0.817962
\(448\) −1.36145e6 −0.320485
\(449\) 2.22268e6 0.520308 0.260154 0.965567i \(-0.416227\pi\)
0.260154 + 0.965567i \(0.416227\pi\)
\(450\) −2.21875e6 −0.516507
\(451\) −1.40365e6 −0.324951
\(452\) −647386. −0.149045
\(453\) −823962. −0.188652
\(454\) 3.18455e6 0.725118
\(455\) 3.82214e6 0.865521
\(456\) 1.84688e6 0.415936
\(457\) −3.49053e6 −0.781810 −0.390905 0.920431i \(-0.627838\pi\)
−0.390905 + 0.920431i \(0.627838\pi\)
\(458\) 4.13311e6 0.920690
\(459\) 309196. 0.0685019
\(460\) 4.21987e6 0.929833
\(461\) 341191. 0.0747732 0.0373866 0.999301i \(-0.488097\pi\)
0.0373866 + 0.999301i \(0.488097\pi\)
\(462\) 3.56066e6 0.776114
\(463\) −6.72986e6 −1.45899 −0.729497 0.683984i \(-0.760246\pi\)
−0.729497 + 0.683984i \(0.760246\pi\)
\(464\) 1.06333e7 2.29284
\(465\) −5.42404e6 −1.16330
\(466\) −4.27778e6 −0.912544
\(467\) −2.11594e6 −0.448964 −0.224482 0.974478i \(-0.572069\pi\)
−0.224482 + 0.974478i \(0.572069\pi\)
\(468\) 419563. 0.0885488
\(469\) 5.96311e6 1.25182
\(470\) −5.32669e6 −1.11228
\(471\) −168608. −0.0350208
\(472\) 463691. 0.0958017
\(473\) −6.78908e6 −1.39527
\(474\) −1.06146e6 −0.216998
\(475\) 6.36929e6 1.29526
\(476\) −519664. −0.105125
\(477\) −1.92490e6 −0.387358
\(478\) −7.32105e6 −1.46556
\(479\) −8.71672e6 −1.73586 −0.867929 0.496688i \(-0.834549\pi\)
−0.867929 + 0.496688i \(0.834549\pi\)
\(480\) −3.14863e6 −0.623761
\(481\) 5.40896e6 1.06599
\(482\) −9.57363e6 −1.87698
\(483\) 3.86040e6 0.752946
\(484\) 2.08154e6 0.403898
\(485\) 1.41543e7 2.73233
\(486\) −391216. −0.0751321
\(487\) −8.19716e6 −1.56618 −0.783089 0.621910i \(-0.786357\pi\)
−0.783089 + 0.621910i \(0.786357\pi\)
\(488\) 741542. 0.140957
\(489\) 766553. 0.144967
\(490\) −3.49756e6 −0.658074
\(491\) −6.65738e6 −1.24623 −0.623117 0.782128i \(-0.714134\pi\)
−0.623117 + 0.782128i \(0.714134\pi\)
\(492\) −259199. −0.0482748
\(493\) −3.57045e6 −0.661616
\(494\) −4.44479e6 −0.819471
\(495\) −4.00076e6 −0.733887
\(496\) −8.93472e6 −1.63071
\(497\) 1.23200e6 0.223727
\(498\) 165071. 0.0298261
\(499\) −2.16723e6 −0.389630 −0.194815 0.980840i \(-0.562411\pi\)
−0.194815 + 0.980840i \(0.562411\pi\)
\(500\) −1.02301e6 −0.183001
\(501\) 4.87460e6 0.867650
\(502\) −3.50351e6 −0.620503
\(503\) −3.01053e6 −0.530547 −0.265273 0.964173i \(-0.585462\pi\)
−0.265273 + 0.964173i \(0.585462\pi\)
\(504\) −1.11145e6 −0.194900
\(505\) 3.24857e6 0.566844
\(506\) 1.59926e7 2.77679
\(507\) −1.63480e6 −0.282451
\(508\) −2.41586e6 −0.415348
\(509\) 8.34439e6 1.42758 0.713790 0.700360i \(-0.246977\pi\)
0.713790 + 0.700360i \(0.246977\pi\)
\(510\) 2.15479e6 0.366843
\(511\) −2.58109e6 −0.437271
\(512\) 197715. 0.0333322
\(513\) 1.12305e6 0.188411
\(514\) 7.63045e6 1.27392
\(515\) −6.95384e6 −1.15533
\(516\) −1.25368e6 −0.207282
\(517\) −5.47025e6 −0.900079
\(518\) 8.47659e6 1.38802
\(519\) 2.14877e6 0.350164
\(520\) −4.94256e6 −0.801573
\(521\) 7.03207e6 1.13498 0.567491 0.823380i \(-0.307914\pi\)
0.567491 + 0.823380i \(0.307914\pi\)
\(522\) 4.51757e6 0.725653
\(523\) 4.76023e6 0.760982 0.380491 0.924785i \(-0.375755\pi\)
0.380491 + 0.924785i \(0.375755\pi\)
\(524\) −3.35753e6 −0.534185
\(525\) −3.83301e6 −0.606935
\(526\) −2.99646e6 −0.472220
\(527\) 3.00010e6 0.470553
\(528\) −6.59022e6 −1.02876
\(529\) 1.09025e7 1.69390
\(530\) −1.34146e7 −2.07439
\(531\) 281961. 0.0433963
\(532\) −1.88750e6 −0.289140
\(533\) −1.05446e6 −0.160772
\(534\) −1.07298e6 −0.162832
\(535\) −1.03321e7 −1.56065
\(536\) −7.71113e6 −1.15933
\(537\) 2.56080e6 0.383213
\(538\) 1.13546e7 1.69129
\(539\) −3.59182e6 −0.532528
\(540\) −738782. −0.109027
\(541\) 1.92671e6 0.283024 0.141512 0.989937i \(-0.454804\pi\)
0.141512 + 0.989937i \(0.454804\pi\)
\(542\) −8.80362e6 −1.28725
\(543\) −3.62053e6 −0.526954
\(544\) 1.74154e6 0.252311
\(545\) 1.30442e7 1.88116
\(546\) 2.67486e6 0.383989
\(547\) 2.45466e6 0.350771 0.175385 0.984500i \(-0.443883\pi\)
0.175385 + 0.984500i \(0.443883\pi\)
\(548\) −3.45453e6 −0.491403
\(549\) 450917. 0.0638507
\(550\) −1.58792e7 −2.23832
\(551\) −1.29685e7 −1.81974
\(552\) −4.99203e6 −0.697316
\(553\) −1.83373e6 −0.254989
\(554\) 1.02226e7 1.41510
\(555\) −9.52431e6 −1.31250
\(556\) 5.11201e6 0.701302
\(557\) 7.38777e6 1.00896 0.504482 0.863422i \(-0.331684\pi\)
0.504482 + 0.863422i \(0.331684\pi\)
\(558\) −3.79592e6 −0.516097
\(559\) −5.10013e6 −0.690322
\(560\) −1.10862e7 −1.49387
\(561\) 2.21286e6 0.296857
\(562\) 36542.5 0.00488042
\(563\) 2.38312e6 0.316866 0.158433 0.987370i \(-0.449356\pi\)
0.158433 + 0.987370i \(0.449356\pi\)
\(564\) −1.01014e6 −0.133716
\(565\) 4.63745e6 0.611164
\(566\) 6.26081e6 0.821465
\(567\) −675848. −0.0882859
\(568\) −1.59314e6 −0.207197
\(569\) −7.30870e6 −0.946367 −0.473184 0.880964i \(-0.656895\pi\)
−0.473184 + 0.880964i \(0.656895\pi\)
\(570\) 7.82655e6 1.00898
\(571\) 2.52181e6 0.323684 0.161842 0.986817i \(-0.448256\pi\)
0.161842 + 0.986817i \(0.448256\pi\)
\(572\) 3.00274e6 0.383731
\(573\) −5.61874e6 −0.714912
\(574\) −1.65248e6 −0.209342
\(575\) −1.72159e7 −2.17150
\(576\) 1.07056e6 0.134448
\(577\) −758503. −0.0948457 −0.0474229 0.998875i \(-0.515101\pi\)
−0.0474229 + 0.998875i \(0.515101\pi\)
\(578\) 8.21510e6 1.02281
\(579\) 7.52128e6 0.932385
\(580\) 8.53111e6 1.05302
\(581\) 285169. 0.0350480
\(582\) 9.90561e6 1.21220
\(583\) −1.37762e7 −1.67864
\(584\) 3.33771e6 0.404964
\(585\) −3.00547e6 −0.363097
\(586\) 1.01190e7 1.21729
\(587\) 4.83844e6 0.579576 0.289788 0.957091i \(-0.406415\pi\)
0.289788 + 0.957091i \(0.406415\pi\)
\(588\) −663267. −0.0791124
\(589\) 1.08968e7 1.29423
\(590\) 1.96499e6 0.232397
\(591\) −6.52096e6 −0.767968
\(592\) −1.56888e7 −1.83987
\(593\) −3.38920e6 −0.395785 −0.197893 0.980224i \(-0.563410\pi\)
−0.197893 + 0.980224i \(0.563410\pi\)
\(594\) −2.79986e6 −0.325590
\(595\) 3.72253e6 0.431068
\(596\) −4.56663e6 −0.526600
\(597\) −6.22694e6 −0.715054
\(598\) 1.20141e7 1.37384
\(599\) 7.50330e6 0.854447 0.427224 0.904146i \(-0.359492\pi\)
0.427224 + 0.904146i \(0.359492\pi\)
\(600\) 4.95662e6 0.562092
\(601\) 1.43644e7 1.62219 0.811095 0.584915i \(-0.198872\pi\)
0.811095 + 0.584915i \(0.198872\pi\)
\(602\) −7.99261e6 −0.898871
\(603\) −4.68899e6 −0.525153
\(604\) −1.08893e6 −0.121453
\(605\) −1.49108e7 −1.65620
\(606\) 2.27345e6 0.251481
\(607\) −7.75401e6 −0.854191 −0.427095 0.904207i \(-0.640463\pi\)
−0.427095 + 0.904207i \(0.640463\pi\)
\(608\) 6.32555e6 0.693968
\(609\) 7.80437e6 0.852697
\(610\) 3.14244e6 0.341935
\(611\) −4.10939e6 −0.445322
\(612\) 408628. 0.0441012
\(613\) 2.52805e6 0.271728 0.135864 0.990727i \(-0.456619\pi\)
0.135864 + 0.990727i \(0.456619\pi\)
\(614\) 1.87401e7 2.00609
\(615\) 1.85673e6 0.197952
\(616\) −7.95442e6 −0.844611
\(617\) 8.69599e6 0.919615 0.459808 0.888018i \(-0.347918\pi\)
0.459808 + 0.888018i \(0.347918\pi\)
\(618\) −4.86652e6 −0.512563
\(619\) −1.01187e6 −0.106145 −0.0530723 0.998591i \(-0.516901\pi\)
−0.0530723 + 0.998591i \(0.516901\pi\)
\(620\) −7.16832e6 −0.748925
\(621\) −3.03555e6 −0.315870
\(622\) −3.25241e6 −0.337077
\(623\) −1.85364e6 −0.191340
\(624\) −4.95074e6 −0.508989
\(625\) −5.59205e6 −0.572626
\(626\) −2.02585e7 −2.06619
\(627\) 8.03748e6 0.816490
\(628\) −222829. −0.0225462
\(629\) 5.26800e6 0.530907
\(630\) −4.70999e6 −0.472790
\(631\) 1.14790e7 1.14771 0.573854 0.818958i \(-0.305448\pi\)
0.573854 + 0.818958i \(0.305448\pi\)
\(632\) 2.37126e6 0.236150
\(633\) 2.24408e6 0.222602
\(634\) 2.28111e7 2.25384
\(635\) 1.73056e7 1.70315
\(636\) −2.54391e6 −0.249379
\(637\) −2.69826e6 −0.263473
\(638\) 3.23315e7 3.14466
\(639\) −968759. −0.0938563
\(640\) 1.86558e7 1.80038
\(641\) 1.67427e7 1.60946 0.804728 0.593643i \(-0.202311\pi\)
0.804728 + 0.593643i \(0.202311\pi\)
\(642\) −7.23074e6 −0.692381
\(643\) −8.05866e6 −0.768662 −0.384331 0.923195i \(-0.625568\pi\)
−0.384331 + 0.923195i \(0.625568\pi\)
\(644\) 5.10183e6 0.484743
\(645\) 8.98050e6 0.849965
\(646\) −4.32895e6 −0.408132
\(647\) 3.80079e6 0.356955 0.178477 0.983944i \(-0.442883\pi\)
0.178477 + 0.983944i \(0.442883\pi\)
\(648\) 873965. 0.0817630
\(649\) 2.01794e6 0.188060
\(650\) −1.19288e7 −1.10743
\(651\) −6.55767e6 −0.606453
\(652\) 1.01306e6 0.0933291
\(653\) −7.58623e6 −0.696215 −0.348107 0.937455i \(-0.613176\pi\)
−0.348107 + 0.937455i \(0.613176\pi\)
\(654\) 9.12874e6 0.834577
\(655\) 2.40511e7 2.19044
\(656\) 3.05848e6 0.277489
\(657\) 2.02959e6 0.183441
\(658\) −6.43998e6 −0.579856
\(659\) 1.09734e7 0.984299 0.492149 0.870511i \(-0.336211\pi\)
0.492149 + 0.870511i \(0.336211\pi\)
\(660\) −5.28734e6 −0.472473
\(661\) −5.85236e6 −0.520988 −0.260494 0.965476i \(-0.583885\pi\)
−0.260494 + 0.965476i \(0.583885\pi\)
\(662\) 1.67852e7 1.48862
\(663\) 1.66236e6 0.146873
\(664\) −368764. −0.0324585
\(665\) 1.35208e7 1.18563
\(666\) −6.66542e6 −0.582293
\(667\) 3.50531e7 3.05079
\(668\) 6.44219e6 0.558589
\(669\) −4.87922e6 −0.421488
\(670\) −3.26776e7 −2.81231
\(671\) 3.22713e6 0.276701
\(672\) −3.80669e6 −0.325181
\(673\) 6.43218e6 0.547420 0.273710 0.961812i \(-0.411749\pi\)
0.273710 + 0.961812i \(0.411749\pi\)
\(674\) 1.62066e7 1.37418
\(675\) 3.01402e6 0.254617
\(676\) −2.16052e6 −0.181841
\(677\) −2.35723e7 −1.97665 −0.988325 0.152363i \(-0.951312\pi\)
−0.988325 + 0.152363i \(0.951312\pi\)
\(678\) 3.24544e6 0.271143
\(679\) 1.71125e7 1.42442
\(680\) −4.81375e6 −0.399219
\(681\) −4.32600e6 −0.357453
\(682\) −2.71667e7 −2.23654
\(683\) 2.00530e7 1.64486 0.822428 0.568870i \(-0.192619\pi\)
0.822428 + 0.568870i \(0.192619\pi\)
\(684\) 1.48420e6 0.121298
\(685\) 2.47460e7 2.01501
\(686\) −1.56988e7 −1.27367
\(687\) −5.61456e6 −0.453862
\(688\) 1.47931e7 1.19148
\(689\) −1.03490e7 −0.830520
\(690\) −2.11548e7 −1.69156
\(691\) 2.03136e7 1.61842 0.809211 0.587518i \(-0.199895\pi\)
0.809211 + 0.587518i \(0.199895\pi\)
\(692\) 2.83978e6 0.225434
\(693\) −4.83692e6 −0.382592
\(694\) −611969. −0.0482315
\(695\) −3.66191e7 −2.87571
\(696\) −1.00921e7 −0.789696
\(697\) −1.02698e6 −0.0800716
\(698\) −3.44146e6 −0.267365
\(699\) 5.81109e6 0.449847
\(700\) −5.06564e6 −0.390742
\(701\) 1.59318e7 1.22453 0.612265 0.790653i \(-0.290259\pi\)
0.612265 + 0.790653i \(0.290259\pi\)
\(702\) −2.10333e6 −0.161088
\(703\) 1.91342e7 1.46023
\(704\) 7.66178e6 0.582637
\(705\) 7.23597e6 0.548307
\(706\) 1.09680e7 0.828162
\(707\) 3.92753e6 0.295509
\(708\) 372635. 0.0279383
\(709\) 2.13021e7 1.59150 0.795749 0.605626i \(-0.207077\pi\)
0.795749 + 0.605626i \(0.207077\pi\)
\(710\) −6.75129e6 −0.502621
\(711\) 1.44192e6 0.106971
\(712\) 2.39702e6 0.177203
\(713\) −2.94536e7 −2.16978
\(714\) 2.60515e6 0.191243
\(715\) −2.15096e7 −1.57350
\(716\) 3.38431e6 0.246710
\(717\) 9.94517e6 0.722461
\(718\) −1.66618e7 −1.20618
\(719\) −1.46154e7 −1.05436 −0.527180 0.849753i \(-0.676751\pi\)
−0.527180 + 0.849753i \(0.676751\pi\)
\(720\) 8.71745e6 0.626698
\(721\) −8.40720e6 −0.602300
\(722\) 681393. 0.0486469
\(723\) 1.30051e7 0.925272
\(724\) −4.78483e6 −0.339250
\(725\) −3.48045e7 −2.45918
\(726\) −1.04351e7 −0.734773
\(727\) −6.13626e6 −0.430594 −0.215297 0.976549i \(-0.569072\pi\)
−0.215297 + 0.976549i \(0.569072\pi\)
\(728\) −5.97556e6 −0.417878
\(729\) 531441. 0.0370370
\(730\) 1.41443e7 0.982365
\(731\) −4.96721e6 −0.343810
\(732\) 595924. 0.0411068
\(733\) 1.06072e7 0.729190 0.364595 0.931166i \(-0.381207\pi\)
0.364595 + 0.931166i \(0.381207\pi\)
\(734\) 5.24953e6 0.359650
\(735\) 4.75120e6 0.324403
\(736\) −1.70977e7 −1.16344
\(737\) −3.35582e7 −2.27578
\(738\) 1.29940e6 0.0878216
\(739\) −75441.2 −0.00508156 −0.00254078 0.999997i \(-0.500809\pi\)
−0.00254078 + 0.999997i \(0.500809\pi\)
\(740\) −1.25872e7 −0.844984
\(741\) 6.03795e6 0.403965
\(742\) −1.62183e7 −1.08142
\(743\) −3.43706e6 −0.228410 −0.114205 0.993457i \(-0.536432\pi\)
−0.114205 + 0.993457i \(0.536432\pi\)
\(744\) 8.47998e6 0.561646
\(745\) 3.27123e7 2.15934
\(746\) −5.60953e6 −0.369045
\(747\) −224238. −0.0147031
\(748\) 2.92448e6 0.191115
\(749\) −1.24915e7 −0.813600
\(750\) 5.12847e6 0.332916
\(751\) 8.47000e6 0.548004 0.274002 0.961729i \(-0.411653\pi\)
0.274002 + 0.961729i \(0.411653\pi\)
\(752\) 1.19194e7 0.768616
\(753\) 4.75928e6 0.305882
\(754\) 2.42882e7 1.55585
\(755\) 7.80040e6 0.498023
\(756\) −893189. −0.0568380
\(757\) −9.70756e6 −0.615702 −0.307851 0.951435i \(-0.599610\pi\)
−0.307851 + 0.951435i \(0.599610\pi\)
\(758\) −1.08213e7 −0.684077
\(759\) −2.17249e7 −1.36884
\(760\) −1.74843e7 −1.09803
\(761\) −4.60781e6 −0.288425 −0.144212 0.989547i \(-0.546065\pi\)
−0.144212 + 0.989547i \(0.546065\pi\)
\(762\) 1.21110e7 0.755602
\(763\) 1.57704e7 0.980691
\(764\) −7.42564e6 −0.460257
\(765\) −2.92714e6 −0.180838
\(766\) 2.80554e7 1.72761
\(767\) 1.51593e6 0.0930445
\(768\) 9.24953e6 0.565870
\(769\) −1.09236e7 −0.666114 −0.333057 0.942907i \(-0.608080\pi\)
−0.333057 + 0.942907i \(0.608080\pi\)
\(770\) −3.37086e7 −2.04887
\(771\) −1.03655e7 −0.627990
\(772\) 9.93999e6 0.600265
\(773\) 6.36770e6 0.383295 0.191648 0.981464i \(-0.438617\pi\)
0.191648 + 0.981464i \(0.438617\pi\)
\(774\) 6.28484e6 0.377088
\(775\) 2.92447e7 1.74901
\(776\) −2.21289e7 −1.31918
\(777\) −1.15149e7 −0.684238
\(778\) −2.86606e7 −1.69760
\(779\) −3.73014e6 −0.220233
\(780\) −3.97198e6 −0.233760
\(781\) −6.93323e6 −0.406732
\(782\) 1.17009e7 0.684233
\(783\) −6.13683e6 −0.357717
\(784\) 7.82638e6 0.454748
\(785\) 1.59620e6 0.0924514
\(786\) 1.68317e7 0.971791
\(787\) −2.17413e7 −1.25126 −0.625631 0.780119i \(-0.715159\pi\)
−0.625631 + 0.780119i \(0.715159\pi\)
\(788\) −8.61799e6 −0.494414
\(789\) 4.07050e6 0.232785
\(790\) 1.00487e7 0.572854
\(791\) 5.60668e6 0.318614
\(792\) 6.25482e6 0.354325
\(793\) 2.42430e6 0.136900
\(794\) −2.21328e7 −1.24590
\(795\) 1.82229e7 1.02259
\(796\) −8.22942e6 −0.460348
\(797\) −1.29730e7 −0.723424 −0.361712 0.932290i \(-0.617808\pi\)
−0.361712 + 0.932290i \(0.617808\pi\)
\(798\) 9.46231e6 0.526005
\(799\) −4.00229e6 −0.221790
\(800\) 1.69764e7 0.937822
\(801\) 1.45758e6 0.0802696
\(802\) 3.97873e6 0.218428
\(803\) 1.45254e7 0.794951
\(804\) −6.19688e6 −0.338091
\(805\) −3.65461e7 −1.98770
\(806\) −2.04083e7 −1.10655
\(807\) −1.54245e7 −0.833735
\(808\) −5.07884e6 −0.273675
\(809\) −1.50725e7 −0.809682 −0.404841 0.914387i \(-0.632673\pi\)
−0.404841 + 0.914387i \(0.632673\pi\)
\(810\) 3.70362e6 0.198341
\(811\) −9.99366e6 −0.533547 −0.266773 0.963759i \(-0.585958\pi\)
−0.266773 + 0.963759i \(0.585958\pi\)
\(812\) 1.03141e7 0.548962
\(813\) 1.19591e7 0.634561
\(814\) −4.77032e7 −2.52340
\(815\) −7.25691e6 −0.382699
\(816\) −4.82172e6 −0.253499
\(817\) −1.80417e7 −0.945633
\(818\) 1.24453e7 0.650312
\(819\) −3.63362e6 −0.189291
\(820\) 2.45382e6 0.127441
\(821\) 2.35975e7 1.22182 0.610912 0.791698i \(-0.290803\pi\)
0.610912 + 0.791698i \(0.290803\pi\)
\(822\) 1.73180e7 0.893962
\(823\) −7.42657e6 −0.382198 −0.191099 0.981571i \(-0.561205\pi\)
−0.191099 + 0.981571i \(0.561205\pi\)
\(824\) 1.08717e7 0.557800
\(825\) 2.15708e7 1.10340
\(826\) 2.37567e6 0.121154
\(827\) −2.03546e7 −1.03490 −0.517451 0.855713i \(-0.673119\pi\)
−0.517451 + 0.855713i \(0.673119\pi\)
\(828\) −4.01174e6 −0.203356
\(829\) 1.84957e7 0.934725 0.467362 0.884066i \(-0.345204\pi\)
0.467362 + 0.884066i \(0.345204\pi\)
\(830\) −1.56272e6 −0.0787381
\(831\) −1.38867e7 −0.697584
\(832\) 5.75572e6 0.288264
\(833\) −2.62794e6 −0.131221
\(834\) −2.56272e7 −1.27581
\(835\) −4.61476e7 −2.29051
\(836\) 1.06222e7 0.525652
\(837\) 5.15651e6 0.254415
\(838\) 3.08103e7 1.51560
\(839\) 4.89142e6 0.239900 0.119950 0.992780i \(-0.461727\pi\)
0.119950 + 0.992780i \(0.461727\pi\)
\(840\) 1.05220e7 0.514517
\(841\) 5.03540e7 2.45496
\(842\) 8.26325e6 0.401671
\(843\) −49640.6 −0.00240585
\(844\) 2.96574e6 0.143310
\(845\) 1.54765e7 0.745644
\(846\) 5.06396e6 0.243257
\(847\) −1.80272e7 −0.863413
\(848\) 3.00176e7 1.43346
\(849\) −8.50490e6 −0.404948
\(850\) −1.16179e7 −0.551547
\(851\) −5.17189e7 −2.44808
\(852\) −1.28029e6 −0.0604242
\(853\) −2.49648e7 −1.17478 −0.587389 0.809305i \(-0.699844\pi\)
−0.587389 + 0.809305i \(0.699844\pi\)
\(854\) 3.79922e6 0.178258
\(855\) −1.06319e7 −0.497386
\(856\) 1.61533e7 0.753488
\(857\) −4.44419e6 −0.206700 −0.103350 0.994645i \(-0.532956\pi\)
−0.103350 + 0.994645i \(0.532956\pi\)
\(858\) −1.50531e7 −0.698085
\(859\) −2.83513e7 −1.31096 −0.655480 0.755212i \(-0.727534\pi\)
−0.655480 + 0.755212i \(0.727534\pi\)
\(860\) 1.18685e7 0.547203
\(861\) 2.24479e6 0.103197
\(862\) −6.46345e6 −0.296276
\(863\) 1.98739e7 0.908358 0.454179 0.890911i \(-0.349933\pi\)
0.454179 + 0.890911i \(0.349933\pi\)
\(864\) 2.99332e6 0.136417
\(865\) −2.03423e7 −0.924400
\(866\) −1.70109e7 −0.770785
\(867\) −1.11597e7 −0.504201
\(868\) −8.66651e6 −0.390431
\(869\) 1.03196e7 0.463566
\(870\) −4.27676e7 −1.91565
\(871\) −2.52098e7 −1.12596
\(872\) −2.03934e7 −0.908234
\(873\) −1.34561e7 −0.597564
\(874\) 4.24997e7 1.88195
\(875\) 8.85973e6 0.391202
\(876\) 2.68228e6 0.118098
\(877\) 2.39535e7 1.05165 0.525823 0.850594i \(-0.323757\pi\)
0.525823 + 0.850594i \(0.323757\pi\)
\(878\) −5.79815e6 −0.253836
\(879\) −1.37461e7 −0.600076
\(880\) 6.23893e7 2.71583
\(881\) 1.44336e7 0.626522 0.313261 0.949667i \(-0.398579\pi\)
0.313261 + 0.949667i \(0.398579\pi\)
\(882\) 3.32505e6 0.143922
\(883\) −1.96597e7 −0.848547 −0.424274 0.905534i \(-0.639471\pi\)
−0.424274 + 0.905534i \(0.639471\pi\)
\(884\) 2.19694e6 0.0945558
\(885\) −2.66931e6 −0.114562
\(886\) −2.91131e7 −1.24596
\(887\) 430936. 0.0183909 0.00919547 0.999958i \(-0.497073\pi\)
0.00919547 + 0.999958i \(0.497073\pi\)
\(888\) 1.48904e7 0.633684
\(889\) 2.09225e7 0.887889
\(890\) 1.01579e7 0.429861
\(891\) 3.80343e6 0.160502
\(892\) −6.44829e6 −0.271352
\(893\) −1.45370e7 −0.610021
\(894\) 2.28932e7 0.957992
\(895\) −2.42430e7 −1.01164
\(896\) 2.25549e7 0.938580
\(897\) −1.63203e7 −0.677247
\(898\) −1.47258e7 −0.609381
\(899\) −5.95449e7 −2.45723
\(900\) 3.98328e6 0.163921
\(901\) −1.00793e7 −0.413636
\(902\) 9.29956e6 0.380580
\(903\) 1.08574e7 0.443106
\(904\) −7.25021e6 −0.295073
\(905\) 3.42753e7 1.39111
\(906\) 5.45898e6 0.220948
\(907\) −1.15056e7 −0.464398 −0.232199 0.972668i \(-0.574592\pi\)
−0.232199 + 0.972668i \(0.574592\pi\)
\(908\) −5.71717e6 −0.230126
\(909\) −3.08834e6 −0.123970
\(910\) −2.53227e7 −1.01369
\(911\) 3.19861e7 1.27693 0.638463 0.769653i \(-0.279571\pi\)
0.638463 + 0.769653i \(0.279571\pi\)
\(912\) −1.75133e7 −0.697236
\(913\) −1.60483e6 −0.0637166
\(914\) 2.31257e7 0.915652
\(915\) −4.26881e6 −0.168560
\(916\) −7.42011e6 −0.292194
\(917\) 2.90778e7 1.14193
\(918\) −2.04851e6 −0.0802290
\(919\) 3.83417e7 1.49756 0.748778 0.662821i \(-0.230641\pi\)
0.748778 + 0.662821i \(0.230641\pi\)
\(920\) 4.72593e7 1.84085
\(921\) −2.54572e7 −0.988922
\(922\) −2.26049e6 −0.0875739
\(923\) −5.20842e6 −0.201234
\(924\) −6.39239e6 −0.246311
\(925\) 5.13520e7 1.97335
\(926\) 4.45872e7 1.70877
\(927\) 6.61085e6 0.252673
\(928\) −3.45655e7 −1.31757
\(929\) 3.81222e7 1.44923 0.724617 0.689151i \(-0.242016\pi\)
0.724617 + 0.689151i \(0.242016\pi\)
\(930\) 3.59358e7 1.36245
\(931\) −9.54510e6 −0.360916
\(932\) 7.67983e6 0.289609
\(933\) 4.41819e6 0.166165
\(934\) 1.40187e7 0.525824
\(935\) −2.09490e7 −0.783674
\(936\) 4.69877e6 0.175305
\(937\) −1.63559e7 −0.608591 −0.304295 0.952578i \(-0.598421\pi\)
−0.304295 + 0.952578i \(0.598421\pi\)
\(938\) −3.95072e7 −1.46612
\(939\) 2.75198e7 1.01855
\(940\) 9.56293e6 0.352997
\(941\) 1.57758e7 0.580789 0.290395 0.956907i \(-0.406213\pi\)
0.290395 + 0.956907i \(0.406213\pi\)
\(942\) 1.11707e6 0.0410161
\(943\) 1.00824e7 0.369220
\(944\) −4.39700e6 −0.160593
\(945\) 6.39821e6 0.233066
\(946\) 4.49795e7 1.63413
\(947\) −2.76570e7 −1.00214 −0.501072 0.865405i \(-0.667061\pi\)
−0.501072 + 0.865405i \(0.667061\pi\)
\(948\) 1.90562e6 0.0688675
\(949\) 1.09119e7 0.393309
\(950\) −4.21983e7 −1.51700
\(951\) −3.09874e7 −1.11105
\(952\) −5.81982e6 −0.208122
\(953\) 1.15464e6 0.0411825 0.0205912 0.999788i \(-0.493445\pi\)
0.0205912 + 0.999788i \(0.493445\pi\)
\(954\) 1.27530e7 0.453671
\(955\) 5.31923e7 1.88730
\(956\) 1.31434e7 0.465116
\(957\) −4.39202e7 −1.55019
\(958\) 5.77507e7 2.03303
\(959\) 2.99179e7 1.05047
\(960\) −1.01349e7 −0.354928
\(961\) 2.14039e7 0.747625
\(962\) −3.58358e7 −1.24848
\(963\) 9.82249e6 0.341315
\(964\) 1.71874e7 0.595686
\(965\) −7.12035e7 −2.46140
\(966\) −2.55762e7 −0.881846
\(967\) −4.77090e7 −1.64072 −0.820360 0.571848i \(-0.806227\pi\)
−0.820360 + 0.571848i \(0.806227\pi\)
\(968\) 2.33116e7 0.799621
\(969\) 5.88059e6 0.201192
\(970\) −9.37759e7 −3.20009
\(971\) 3.61364e7 1.22998 0.614988 0.788537i \(-0.289161\pi\)
0.614988 + 0.788537i \(0.289161\pi\)
\(972\) 702343. 0.0238443
\(973\) −4.42725e7 −1.49917
\(974\) 5.43084e7 1.83430
\(975\) 1.62045e7 0.545915
\(976\) −7.03176e6 −0.236287
\(977\) 2.58953e7 0.867930 0.433965 0.900930i \(-0.357114\pi\)
0.433965 + 0.900930i \(0.357114\pi\)
\(978\) −5.07862e6 −0.169785
\(979\) 1.04316e7 0.347853
\(980\) 6.27911e6 0.208849
\(981\) −1.24008e7 −0.411412
\(982\) 4.41070e7 1.45958
\(983\) −3.78204e7 −1.24837 −0.624183 0.781278i \(-0.714568\pi\)
−0.624183 + 0.781278i \(0.714568\pi\)
\(984\) −2.90282e6 −0.0955724
\(985\) 6.17336e7 2.02736
\(986\) 2.36552e7 0.774880
\(987\) 8.74829e6 0.285845
\(988\) 7.97965e6 0.260071
\(989\) 4.87659e7 1.58535
\(990\) 2.65061e7 0.859525
\(991\) −3.64574e7 −1.17924 −0.589619 0.807681i \(-0.700722\pi\)
−0.589619 + 0.807681i \(0.700722\pi\)
\(992\) 2.90439e7 0.937077
\(993\) −2.28017e7 −0.733826
\(994\) −8.16232e6 −0.262028
\(995\) 5.89501e7 1.88767
\(996\) −296349. −0.00946575
\(997\) 1.17735e6 0.0375119 0.0187559 0.999824i \(-0.494029\pi\)
0.0187559 + 0.999824i \(0.494029\pi\)
\(998\) 1.43585e7 0.456333
\(999\) 9.05453e6 0.287047
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.1.4 11
3.2 odd 2 531.6.a.b.1.8 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.4 11 1.1 even 1 trivial
531.6.a.b.1.8 11 3.2 odd 2