Properties

Label 177.6.a.a.1.5
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 1.5
Root \(-1.75662\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.75662 q^{2} +9.00000 q^{3} -24.4011 q^{4} +5.39522 q^{5} -24.8096 q^{6} -153.490 q^{7} +155.476 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-2.75662 q^{2} +9.00000 q^{3} -24.4011 q^{4} +5.39522 q^{5} -24.8096 q^{6} -153.490 q^{7} +155.476 q^{8} +81.0000 q^{9} -14.8726 q^{10} +761.180 q^{11} -219.609 q^{12} +217.951 q^{13} +423.115 q^{14} +48.5570 q^{15} +352.245 q^{16} -1059.30 q^{17} -223.286 q^{18} -2368.63 q^{19} -131.649 q^{20} -1381.41 q^{21} -2098.28 q^{22} +3572.52 q^{23} +1399.29 q^{24} -3095.89 q^{25} -600.809 q^{26} +729.000 q^{27} +3745.33 q^{28} +538.264 q^{29} -133.853 q^{30} -6089.90 q^{31} -5946.24 q^{32} +6850.62 q^{33} +2920.08 q^{34} -828.115 q^{35} -1976.49 q^{36} -12608.0 q^{37} +6529.41 q^{38} +1961.56 q^{39} +838.829 q^{40} -3786.34 q^{41} +3808.03 q^{42} +20706.6 q^{43} -18573.6 q^{44} +437.013 q^{45} -9848.09 q^{46} -19719.4 q^{47} +3170.20 q^{48} +6752.30 q^{49} +8534.19 q^{50} -9533.67 q^{51} -5318.24 q^{52} -18054.4 q^{53} -2009.58 q^{54} +4106.74 q^{55} -23864.1 q^{56} -21317.7 q^{57} -1483.79 q^{58} +3481.00 q^{59} -1184.84 q^{60} -8691.16 q^{61} +16787.5 q^{62} -12432.7 q^{63} +5119.69 q^{64} +1175.90 q^{65} -18884.6 q^{66} -26644.1 q^{67} +25847.9 q^{68} +32152.7 q^{69} +2282.80 q^{70} -16613.0 q^{71} +12593.6 q^{72} -57940.7 q^{73} +34755.4 q^{74} -27863.0 q^{75} +57797.1 q^{76} -116834. q^{77} -5407.28 q^{78} -34743.3 q^{79} +1900.44 q^{80} +6561.00 q^{81} +10437.5 q^{82} -58060.2 q^{83} +33707.9 q^{84} -5715.14 q^{85} -57080.3 q^{86} +4844.38 q^{87} +118345. q^{88} -27715.2 q^{89} -1204.68 q^{90} -33453.4 q^{91} -87173.4 q^{92} -54809.1 q^{93} +54358.8 q^{94} -12779.3 q^{95} -53516.2 q^{96} +64764.4 q^{97} -18613.5 q^{98} +61655.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75662 −0.487306 −0.243653 0.969862i \(-0.578346\pi\)
−0.243653 + 0.969862i \(0.578346\pi\)
\(3\) 9.00000 0.577350
\(4\) −24.4011 −0.762533
\(5\) 5.39522 0.0965127 0.0482563 0.998835i \(-0.484634\pi\)
0.0482563 + 0.998835i \(0.484634\pi\)
\(6\) −24.8096 −0.281346
\(7\) −153.490 −1.18396 −0.591979 0.805954i \(-0.701653\pi\)
−0.591979 + 0.805954i \(0.701653\pi\)
\(8\) 155.476 0.858893
\(9\) 81.0000 0.333333
\(10\) −14.8726 −0.0470312
\(11\) 761.180 1.89673 0.948366 0.317180i \(-0.102736\pi\)
0.948366 + 0.317180i \(0.102736\pi\)
\(12\) −219.609 −0.440249
\(13\) 217.951 0.357685 0.178843 0.983878i \(-0.442765\pi\)
0.178843 + 0.983878i \(0.442765\pi\)
\(14\) 423.115 0.576950
\(15\) 48.5570 0.0557216
\(16\) 352.245 0.343989
\(17\) −1059.30 −0.888987 −0.444493 0.895782i \(-0.646616\pi\)
−0.444493 + 0.895782i \(0.646616\pi\)
\(18\) −223.286 −0.162435
\(19\) −2368.63 −1.50527 −0.752633 0.658440i \(-0.771217\pi\)
−0.752633 + 0.658440i \(0.771217\pi\)
\(20\) −131.649 −0.0735941
\(21\) −1381.41 −0.683558
\(22\) −2098.28 −0.924288
\(23\) 3572.52 1.40817 0.704086 0.710115i \(-0.251357\pi\)
0.704086 + 0.710115i \(0.251357\pi\)
\(24\) 1399.29 0.495882
\(25\) −3095.89 −0.990685
\(26\) −600.809 −0.174302
\(27\) 729.000 0.192450
\(28\) 3745.33 0.902806
\(29\) 538.264 0.118850 0.0594251 0.998233i \(-0.481073\pi\)
0.0594251 + 0.998233i \(0.481073\pi\)
\(30\) −133.853 −0.0271535
\(31\) −6089.90 −1.13817 −0.569084 0.822279i \(-0.692702\pi\)
−0.569084 + 0.822279i \(0.692702\pi\)
\(32\) −5946.24 −1.02652
\(33\) 6850.62 1.09508
\(34\) 2920.08 0.433208
\(35\) −828.115 −0.114267
\(36\) −1976.49 −0.254178
\(37\) −12608.0 −1.51406 −0.757028 0.653383i \(-0.773349\pi\)
−0.757028 + 0.653383i \(0.773349\pi\)
\(38\) 6529.41 0.733526
\(39\) 1961.56 0.206510
\(40\) 838.829 0.0828940
\(41\) −3786.34 −0.351771 −0.175886 0.984411i \(-0.556279\pi\)
−0.175886 + 0.984411i \(0.556279\pi\)
\(42\) 3808.03 0.333102
\(43\) 20706.6 1.70780 0.853902 0.520434i \(-0.174230\pi\)
0.853902 + 0.520434i \(0.174230\pi\)
\(44\) −18573.6 −1.44632
\(45\) 437.013 0.0321709
\(46\) −9848.09 −0.686211
\(47\) −19719.4 −1.30211 −0.651056 0.759029i \(-0.725674\pi\)
−0.651056 + 0.759029i \(0.725674\pi\)
\(48\) 3170.20 0.198602
\(49\) 6752.30 0.401755
\(50\) 8534.19 0.482767
\(51\) −9533.67 −0.513257
\(52\) −5318.24 −0.272747
\(53\) −18054.4 −0.882865 −0.441433 0.897294i \(-0.645530\pi\)
−0.441433 + 0.897294i \(0.645530\pi\)
\(54\) −2009.58 −0.0937821
\(55\) 4106.74 0.183059
\(56\) −23864.1 −1.01689
\(57\) −21317.7 −0.869066
\(58\) −1483.79 −0.0579165
\(59\) 3481.00 0.130189
\(60\) −1184.84 −0.0424896
\(61\) −8691.16 −0.299056 −0.149528 0.988757i \(-0.547775\pi\)
−0.149528 + 0.988757i \(0.547775\pi\)
\(62\) 16787.5 0.554636
\(63\) −12432.7 −0.394652
\(64\) 5119.69 0.156241
\(65\) 1175.90 0.0345212
\(66\) −18884.6 −0.533638
\(67\) −26644.1 −0.725128 −0.362564 0.931959i \(-0.618099\pi\)
−0.362564 + 0.931959i \(0.618099\pi\)
\(68\) 25847.9 0.677881
\(69\) 32152.7 0.813008
\(70\) 2282.80 0.0556829
\(71\) −16613.0 −0.391114 −0.195557 0.980692i \(-0.562651\pi\)
−0.195557 + 0.980692i \(0.562651\pi\)
\(72\) 12593.6 0.286298
\(73\) −57940.7 −1.27255 −0.636277 0.771460i \(-0.719527\pi\)
−0.636277 + 0.771460i \(0.719527\pi\)
\(74\) 34755.4 0.737808
\(75\) −27863.0 −0.571972
\(76\) 57797.1 1.14782
\(77\) −116834. −2.24565
\(78\) −5407.28 −0.100633
\(79\) −34743.3 −0.626331 −0.313165 0.949699i \(-0.601389\pi\)
−0.313165 + 0.949699i \(0.601389\pi\)
\(80\) 1900.44 0.0331993
\(81\) 6561.00 0.111111
\(82\) 10437.5 0.171420
\(83\) −58060.2 −0.925088 −0.462544 0.886596i \(-0.653063\pi\)
−0.462544 + 0.886596i \(0.653063\pi\)
\(84\) 33707.9 0.521236
\(85\) −5715.14 −0.0857985
\(86\) −57080.3 −0.832223
\(87\) 4844.38 0.0686182
\(88\) 118345. 1.62909
\(89\) −27715.2 −0.370888 −0.185444 0.982655i \(-0.559372\pi\)
−0.185444 + 0.982655i \(0.559372\pi\)
\(90\) −1204.68 −0.0156771
\(91\) −33453.4 −0.423484
\(92\) −87173.4 −1.07378
\(93\) −54809.1 −0.657121
\(94\) 54358.8 0.634527
\(95\) −12779.3 −0.145277
\(96\) −53516.2 −0.592662
\(97\) 64764.4 0.698887 0.349444 0.936957i \(-0.386371\pi\)
0.349444 + 0.936957i \(0.386371\pi\)
\(98\) −18613.5 −0.195778
\(99\) 61655.6 0.632244
\(100\) 75543.0 0.755430
\(101\) 74064.2 0.722445 0.361222 0.932480i \(-0.382360\pi\)
0.361222 + 0.932480i \(0.382360\pi\)
\(102\) 26280.7 0.250113
\(103\) −92839.9 −0.862266 −0.431133 0.902288i \(-0.641886\pi\)
−0.431133 + 0.902288i \(0.641886\pi\)
\(104\) 33886.2 0.307213
\(105\) −7453.03 −0.0659720
\(106\) 49769.2 0.430225
\(107\) 140418. 1.18567 0.592834 0.805324i \(-0.298009\pi\)
0.592834 + 0.805324i \(0.298009\pi\)
\(108\) −17788.4 −0.146750
\(109\) 87790.6 0.707753 0.353876 0.935292i \(-0.384863\pi\)
0.353876 + 0.935292i \(0.384863\pi\)
\(110\) −11320.7 −0.0892055
\(111\) −113472. −0.874140
\(112\) −54066.2 −0.407269
\(113\) −48010.0 −0.353700 −0.176850 0.984238i \(-0.556591\pi\)
−0.176850 + 0.984238i \(0.556591\pi\)
\(114\) 58764.7 0.423501
\(115\) 19274.6 0.135906
\(116\) −13134.2 −0.0906273
\(117\) 17654.1 0.119228
\(118\) −9595.79 −0.0634418
\(119\) 162592. 1.05252
\(120\) 7549.46 0.0478589
\(121\) 418344. 2.59759
\(122\) 23958.2 0.145732
\(123\) −34077.1 −0.203095
\(124\) 148600. 0.867890
\(125\) −33563.1 −0.192126
\(126\) 34272.3 0.192317
\(127\) 198782. 1.09362 0.546812 0.837255i \(-0.315841\pi\)
0.546812 + 0.837255i \(0.315841\pi\)
\(128\) 176167. 0.950384
\(129\) 186360. 0.986001
\(130\) −3241.50 −0.0168224
\(131\) −28009.5 −0.142603 −0.0713013 0.997455i \(-0.522715\pi\)
−0.0713013 + 0.997455i \(0.522715\pi\)
\(132\) −167162. −0.835033
\(133\) 363562. 1.78217
\(134\) 73447.8 0.353359
\(135\) 3933.12 0.0185739
\(136\) −164695. −0.763544
\(137\) −169288. −0.770593 −0.385296 0.922793i \(-0.625901\pi\)
−0.385296 + 0.922793i \(0.625901\pi\)
\(138\) −88632.8 −0.396184
\(139\) −20974.7 −0.0920786 −0.0460393 0.998940i \(-0.514660\pi\)
−0.0460393 + 0.998940i \(0.514660\pi\)
\(140\) 20206.9 0.0871322
\(141\) −177474. −0.751775
\(142\) 45795.8 0.190592
\(143\) 165900. 0.678433
\(144\) 28531.8 0.114663
\(145\) 2904.05 0.0114706
\(146\) 159720. 0.620124
\(147\) 60770.7 0.231953
\(148\) 307648. 1.15452
\(149\) 1132.13 0.00417762 0.00208881 0.999998i \(-0.499335\pi\)
0.00208881 + 0.999998i \(0.499335\pi\)
\(150\) 76807.7 0.278726
\(151\) −338574. −1.20840 −0.604200 0.796833i \(-0.706507\pi\)
−0.604200 + 0.796833i \(0.706507\pi\)
\(152\) −368266. −1.29286
\(153\) −85803.0 −0.296329
\(154\) 322066. 1.09432
\(155\) −32856.4 −0.109848
\(156\) −47864.2 −0.157470
\(157\) 124948. 0.404558 0.202279 0.979328i \(-0.435165\pi\)
0.202279 + 0.979328i \(0.435165\pi\)
\(158\) 95774.1 0.305215
\(159\) −162490. −0.509722
\(160\) −32081.3 −0.0990723
\(161\) −548348. −1.66722
\(162\) −18086.2 −0.0541451
\(163\) −280389. −0.826595 −0.413297 0.910596i \(-0.635623\pi\)
−0.413297 + 0.910596i \(0.635623\pi\)
\(164\) 92390.7 0.268237
\(165\) 36960.6 0.105689
\(166\) 160050. 0.450801
\(167\) −613337. −1.70180 −0.850900 0.525328i \(-0.823942\pi\)
−0.850900 + 0.525328i \(0.823942\pi\)
\(168\) −214777. −0.587103
\(169\) −323790. −0.872061
\(170\) 15754.5 0.0418101
\(171\) −191859. −0.501756
\(172\) −505263. −1.30226
\(173\) −490483. −1.24597 −0.622986 0.782233i \(-0.714081\pi\)
−0.622986 + 0.782233i \(0.714081\pi\)
\(174\) −13354.1 −0.0334381
\(175\) 475190. 1.17293
\(176\) 268122. 0.652455
\(177\) 31329.0 0.0751646
\(178\) 76400.2 0.180736
\(179\) 480903. 1.12183 0.560913 0.827875i \(-0.310450\pi\)
0.560913 + 0.827875i \(0.310450\pi\)
\(180\) −10663.6 −0.0245314
\(181\) 230617. 0.523234 0.261617 0.965172i \(-0.415744\pi\)
0.261617 + 0.965172i \(0.415744\pi\)
\(182\) 92218.4 0.206366
\(183\) −78220.4 −0.172660
\(184\) 555443. 1.20947
\(185\) −68022.9 −0.146125
\(186\) 151088. 0.320219
\(187\) −806315. −1.68617
\(188\) 481174. 0.992904
\(189\) −111894. −0.227853
\(190\) 35227.6 0.0707945
\(191\) 788835. 1.56460 0.782299 0.622903i \(-0.214047\pi\)
0.782299 + 0.622903i \(0.214047\pi\)
\(192\) 46077.2 0.0902055
\(193\) 693991. 1.34110 0.670549 0.741865i \(-0.266059\pi\)
0.670549 + 0.741865i \(0.266059\pi\)
\(194\) −178531. −0.340572
\(195\) 10583.1 0.0199308
\(196\) −164763. −0.306352
\(197\) 514963. 0.945388 0.472694 0.881227i \(-0.343282\pi\)
0.472694 + 0.881227i \(0.343282\pi\)
\(198\) −169961. −0.308096
\(199\) −402836. −0.721100 −0.360550 0.932740i \(-0.617411\pi\)
−0.360550 + 0.932740i \(0.617411\pi\)
\(200\) −481337. −0.850893
\(201\) −239797. −0.418653
\(202\) −204167. −0.352052
\(203\) −82618.3 −0.140714
\(204\) 232632. 0.391375
\(205\) −20428.2 −0.0339504
\(206\) 255924. 0.420188
\(207\) 289375. 0.469391
\(208\) 76772.2 0.123040
\(209\) −1.80296e6 −2.85509
\(210\) 20545.2 0.0321486
\(211\) −621140. −0.960469 −0.480235 0.877140i \(-0.659449\pi\)
−0.480235 + 0.877140i \(0.659449\pi\)
\(212\) 440547. 0.673214
\(213\) −149517. −0.225810
\(214\) −387079. −0.577783
\(215\) 111717. 0.164825
\(216\) 113342. 0.165294
\(217\) 934742. 1.34754
\(218\) −242005. −0.344892
\(219\) −521466. −0.734710
\(220\) −100209. −0.139588
\(221\) −230875. −0.317977
\(222\) 312799. 0.425974
\(223\) 507140. 0.682913 0.341457 0.939898i \(-0.389080\pi\)
0.341457 + 0.939898i \(0.389080\pi\)
\(224\) 912691. 1.21536
\(225\) −250767. −0.330228
\(226\) 132345. 0.172360
\(227\) −1.48547e6 −1.91337 −0.956686 0.291121i \(-0.905972\pi\)
−0.956686 + 0.291121i \(0.905972\pi\)
\(228\) 520174. 0.662692
\(229\) −460323. −0.580062 −0.290031 0.957017i \(-0.593666\pi\)
−0.290031 + 0.957017i \(0.593666\pi\)
\(230\) −53132.6 −0.0662280
\(231\) −1.05150e6 −1.29653
\(232\) 83687.2 0.102080
\(233\) 1.45102e6 1.75099 0.875496 0.483225i \(-0.160535\pi\)
0.875496 + 0.483225i \(0.160535\pi\)
\(234\) −48665.5 −0.0581007
\(235\) −106390. −0.125670
\(236\) −84940.1 −0.0992733
\(237\) −312690. −0.361612
\(238\) −448204. −0.512900
\(239\) 536002. 0.606976 0.303488 0.952835i \(-0.401849\pi\)
0.303488 + 0.952835i \(0.401849\pi\)
\(240\) 17104.0 0.0191676
\(241\) −1.55236e6 −1.72166 −0.860832 0.508889i \(-0.830056\pi\)
−0.860832 + 0.508889i \(0.830056\pi\)
\(242\) −1.15322e6 −1.26582
\(243\) 59049.0 0.0641500
\(244\) 212073. 0.228040
\(245\) 36430.2 0.0387745
\(246\) 93937.5 0.0989695
\(247\) −516246. −0.538412
\(248\) −946835. −0.977564
\(249\) −522542. −0.534100
\(250\) 92520.6 0.0936243
\(251\) 1.35415e6 1.35669 0.678347 0.734742i \(-0.262697\pi\)
0.678347 + 0.734742i \(0.262697\pi\)
\(252\) 303371. 0.300935
\(253\) 2.71934e6 2.67092
\(254\) −547967. −0.532930
\(255\) −51436.2 −0.0495358
\(256\) −649455. −0.619368
\(257\) 1.62655e6 1.53615 0.768075 0.640360i \(-0.221215\pi\)
0.768075 + 0.640360i \(0.221215\pi\)
\(258\) −513722. −0.480484
\(259\) 1.93521e6 1.79258
\(260\) −28693.1 −0.0263235
\(261\) 43599.4 0.0396168
\(262\) 77211.6 0.0694911
\(263\) −210060. −0.187264 −0.0936319 0.995607i \(-0.529848\pi\)
−0.0936319 + 0.995607i \(0.529848\pi\)
\(264\) 1.06511e6 0.940555
\(265\) −97407.7 −0.0852076
\(266\) −1.00220e6 −0.868463
\(267\) −249437. −0.214132
\(268\) 650145. 0.552934
\(269\) −1.70569e6 −1.43721 −0.718606 0.695418i \(-0.755219\pi\)
−0.718606 + 0.695418i \(0.755219\pi\)
\(270\) −10842.1 −0.00905116
\(271\) 496417. 0.410604 0.205302 0.978699i \(-0.434182\pi\)
0.205302 + 0.978699i \(0.434182\pi\)
\(272\) −373132. −0.305802
\(273\) −301081. −0.244499
\(274\) 466663. 0.375515
\(275\) −2.35653e6 −1.87906
\(276\) −784560. −0.619946
\(277\) −964655. −0.755392 −0.377696 0.925930i \(-0.623284\pi\)
−0.377696 + 0.925930i \(0.623284\pi\)
\(278\) 57819.2 0.0448704
\(279\) −493282. −0.379389
\(280\) −128752. −0.0981430
\(281\) −304671. −0.230179 −0.115089 0.993355i \(-0.536715\pi\)
−0.115089 + 0.993355i \(0.536715\pi\)
\(282\) 489229. 0.366344
\(283\) −1.20302e6 −0.892908 −0.446454 0.894807i \(-0.647313\pi\)
−0.446454 + 0.894807i \(0.647313\pi\)
\(284\) 405375. 0.298237
\(285\) −115014. −0.0838759
\(286\) −457324. −0.330604
\(287\) 581167. 0.416482
\(288\) −481646. −0.342174
\(289\) −297748. −0.209703
\(290\) −8005.37 −0.00558967
\(291\) 582880. 0.403503
\(292\) 1.41381e6 0.970365
\(293\) −1.44326e6 −0.982146 −0.491073 0.871118i \(-0.663395\pi\)
−0.491073 + 0.871118i \(0.663395\pi\)
\(294\) −167522. −0.113032
\(295\) 18780.8 0.0125649
\(296\) −1.96024e6 −1.30041
\(297\) 554900. 0.365026
\(298\) −3120.84 −0.00203578
\(299\) 778636. 0.503682
\(300\) 679887. 0.436148
\(301\) −3.17827e6 −2.02197
\(302\) 933318. 0.588861
\(303\) 666577. 0.417104
\(304\) −834339. −0.517796
\(305\) −46890.7 −0.0288627
\(306\) 236526. 0.144403
\(307\) −591937. −0.358451 −0.179226 0.983808i \(-0.557359\pi\)
−0.179226 + 0.983808i \(0.557359\pi\)
\(308\) 2.85087e6 1.71238
\(309\) −835559. −0.497830
\(310\) 90572.5 0.0535294
\(311\) 1.22564e6 0.718560 0.359280 0.933230i \(-0.383022\pi\)
0.359280 + 0.933230i \(0.383022\pi\)
\(312\) 304976. 0.177370
\(313\) 2.29772e6 1.32567 0.662835 0.748766i \(-0.269353\pi\)
0.662835 + 0.748766i \(0.269353\pi\)
\(314\) −344435. −0.197144
\(315\) −67077.3 −0.0380890
\(316\) 847774. 0.477598
\(317\) −2.05515e6 −1.14867 −0.574335 0.818620i \(-0.694739\pi\)
−0.574335 + 0.818620i \(0.694739\pi\)
\(318\) 447923. 0.248391
\(319\) 409716. 0.225427
\(320\) 27621.9 0.0150792
\(321\) 1.26376e6 0.684546
\(322\) 1.51159e6 0.812444
\(323\) 2.50908e6 1.33816
\(324\) −160095. −0.0847259
\(325\) −674754. −0.354354
\(326\) 772927. 0.402805
\(327\) 790115. 0.408621
\(328\) −588686. −0.302134
\(329\) 3.02673e6 1.54165
\(330\) −101886. −0.0515028
\(331\) 1.63165e6 0.818570 0.409285 0.912407i \(-0.365778\pi\)
0.409285 + 0.912407i \(0.365778\pi\)
\(332\) 1.41673e6 0.705410
\(333\) −1.02125e6 −0.504685
\(334\) 1.69074e6 0.829297
\(335\) −143751. −0.0699841
\(336\) −486596. −0.235137
\(337\) −1.28987e6 −0.618689 −0.309344 0.950950i \(-0.600110\pi\)
−0.309344 + 0.950950i \(0.600110\pi\)
\(338\) 892566. 0.424961
\(339\) −432090. −0.204209
\(340\) 139455. 0.0654241
\(341\) −4.63551e6 −2.15880
\(342\) 528883. 0.244509
\(343\) 1.54330e6 0.708296
\(344\) 3.21939e6 1.46682
\(345\) 173471. 0.0784656
\(346\) 1.35207e6 0.607170
\(347\) 3.13549e6 1.39792 0.698959 0.715161i \(-0.253647\pi\)
0.698959 + 0.715161i \(0.253647\pi\)
\(348\) −118208. −0.0523237
\(349\) −4.47945e6 −1.96862 −0.984308 0.176458i \(-0.943536\pi\)
−0.984308 + 0.176458i \(0.943536\pi\)
\(350\) −1.30992e6 −0.571575
\(351\) 158886. 0.0688366
\(352\) −4.52616e6 −1.94703
\(353\) −749388. −0.320088 −0.160044 0.987110i \(-0.551164\pi\)
−0.160044 + 0.987110i \(0.551164\pi\)
\(354\) −86362.1 −0.0366282
\(355\) −89631.0 −0.0377474
\(356\) 676279. 0.282814
\(357\) 1.46333e6 0.607674
\(358\) −1.32567e6 −0.546672
\(359\) −320342. −0.131183 −0.0655916 0.997847i \(-0.520893\pi\)
−0.0655916 + 0.997847i \(0.520893\pi\)
\(360\) 67945.1 0.0276313
\(361\) 3.13432e6 1.26583
\(362\) −635724. −0.254975
\(363\) 3.76510e6 1.49972
\(364\) 816299. 0.322921
\(365\) −312603. −0.122818
\(366\) 215624. 0.0841384
\(367\) 2.58137e6 1.00043 0.500214 0.865902i \(-0.333255\pi\)
0.500214 + 0.865902i \(0.333255\pi\)
\(368\) 1.25840e6 0.484396
\(369\) −306694. −0.117257
\(370\) 187513. 0.0712078
\(371\) 2.77118e6 1.04527
\(372\) 1.33740e6 0.501077
\(373\) −5.10128e6 −1.89849 −0.949243 0.314543i \(-0.898149\pi\)
−0.949243 + 0.314543i \(0.898149\pi\)
\(374\) 2.22270e6 0.821680
\(375\) −302068. −0.110924
\(376\) −3.06589e6 −1.11838
\(377\) 117315. 0.0425110
\(378\) 308450. 0.111034
\(379\) −3.63450e6 −1.29971 −0.649855 0.760058i \(-0.725170\pi\)
−0.649855 + 0.760058i \(0.725170\pi\)
\(380\) 311828. 0.110779
\(381\) 1.78904e6 0.631404
\(382\) −2.17452e6 −0.762438
\(383\) −492940. −0.171710 −0.0858552 0.996308i \(-0.527362\pi\)
−0.0858552 + 0.996308i \(0.527362\pi\)
\(384\) 1.58550e6 0.548704
\(385\) −630344. −0.216734
\(386\) −1.91307e6 −0.653525
\(387\) 1.67724e6 0.569268
\(388\) −1.58032e6 −0.532924
\(389\) 2.72335e6 0.912494 0.456247 0.889853i \(-0.349193\pi\)
0.456247 + 0.889853i \(0.349193\pi\)
\(390\) −29173.5 −0.00971240
\(391\) −3.78436e6 −1.25185
\(392\) 1.04982e6 0.345065
\(393\) −252086. −0.0823317
\(394\) −1.41956e6 −0.460693
\(395\) −187448. −0.0604489
\(396\) −1.50446e6 −0.482107
\(397\) 4.08799e6 1.30177 0.650885 0.759177i \(-0.274398\pi\)
0.650885 + 0.759177i \(0.274398\pi\)
\(398\) 1.11047e6 0.351397
\(399\) 3.27206e6 1.02894
\(400\) −1.09051e6 −0.340785
\(401\) 4.53424e6 1.40813 0.704067 0.710134i \(-0.251366\pi\)
0.704067 + 0.710134i \(0.251366\pi\)
\(402\) 661030. 0.204012
\(403\) −1.32730e6 −0.407106
\(404\) −1.80724e6 −0.550888
\(405\) 35398.0 0.0107236
\(406\) 227747. 0.0685706
\(407\) −9.59696e6 −2.87176
\(408\) −1.48226e6 −0.440832
\(409\) 4.51979e6 1.33601 0.668005 0.744156i \(-0.267148\pi\)
0.668005 + 0.744156i \(0.267148\pi\)
\(410\) 56312.6 0.0165442
\(411\) −1.52359e6 −0.444902
\(412\) 2.26539e6 0.657506
\(413\) −534300. −0.154138
\(414\) −797695. −0.228737
\(415\) −313248. −0.0892827
\(416\) −1.29599e6 −0.367171
\(417\) −188772. −0.0531616
\(418\) 4.97006e6 1.39130
\(419\) 1.11078e6 0.309095 0.154548 0.987985i \(-0.450608\pi\)
0.154548 + 0.987985i \(0.450608\pi\)
\(420\) 181862. 0.0503058
\(421\) 6.16251e6 1.69454 0.847270 0.531162i \(-0.178244\pi\)
0.847270 + 0.531162i \(0.178244\pi\)
\(422\) 1.71225e6 0.468042
\(423\) −1.59727e6 −0.434038
\(424\) −2.80704e6 −0.758286
\(425\) 3.27947e6 0.880706
\(426\) 412162. 0.110038
\(427\) 1.33401e6 0.354070
\(428\) −3.42635e6 −0.904111
\(429\) 1.49310e6 0.391693
\(430\) −307961. −0.0803201
\(431\) 3.15040e6 0.816907 0.408453 0.912779i \(-0.366068\pi\)
0.408453 + 0.912779i \(0.366068\pi\)
\(432\) 256787. 0.0662008
\(433\) 1.13247e6 0.290273 0.145136 0.989412i \(-0.453638\pi\)
0.145136 + 0.989412i \(0.453638\pi\)
\(434\) −2.57673e6 −0.656665
\(435\) 26136.5 0.00662253
\(436\) −2.14218e6 −0.539685
\(437\) −8.46199e6 −2.11967
\(438\) 1.43748e6 0.358028
\(439\) −5.79846e6 −1.43599 −0.717995 0.696048i \(-0.754940\pi\)
−0.717995 + 0.696048i \(0.754940\pi\)
\(440\) 638500. 0.157228
\(441\) 546936. 0.133918
\(442\) 636434. 0.154952
\(443\) −6.79918e6 −1.64607 −0.823033 0.567994i \(-0.807720\pi\)
−0.823033 + 0.567994i \(0.807720\pi\)
\(444\) 2.76883e6 0.666561
\(445\) −149530. −0.0357954
\(446\) −1.39799e6 −0.332788
\(447\) 10189.1 0.00241195
\(448\) −785823. −0.184982
\(449\) 3.96539e6 0.928261 0.464131 0.885767i \(-0.346367\pi\)
0.464131 + 0.885767i \(0.346367\pi\)
\(450\) 691270. 0.160922
\(451\) −2.88209e6 −0.667215
\(452\) 1.17149e6 0.269708
\(453\) −3.04716e6 −0.697670
\(454\) 4.09488e6 0.932398
\(455\) −180489. −0.0408716
\(456\) −3.31439e6 −0.746435
\(457\) 4.45488e6 0.997804 0.498902 0.866659i \(-0.333737\pi\)
0.498902 + 0.866659i \(0.333737\pi\)
\(458\) 1.26894e6 0.282667
\(459\) −772227. −0.171086
\(460\) −470320. −0.103633
\(461\) 302131. 0.0662129 0.0331065 0.999452i \(-0.489460\pi\)
0.0331065 + 0.999452i \(0.489460\pi\)
\(462\) 2.89860e6 0.631805
\(463\) −6.99444e6 −1.51635 −0.758177 0.652049i \(-0.773910\pi\)
−0.758177 + 0.652049i \(0.773910\pi\)
\(464\) 189601. 0.0408832
\(465\) −295707. −0.0634205
\(466\) −3.99992e6 −0.853269
\(467\) 737365. 0.156455 0.0782276 0.996936i \(-0.475074\pi\)
0.0782276 + 0.996936i \(0.475074\pi\)
\(468\) −430778. −0.0909156
\(469\) 4.08962e6 0.858521
\(470\) 293278. 0.0612399
\(471\) 1.12453e6 0.233572
\(472\) 541213. 0.111818
\(473\) 1.57615e7 3.23925
\(474\) 861967. 0.176216
\(475\) 7.33303e6 1.49125
\(476\) −3.96741e6 −0.802583
\(477\) −1.46241e6 −0.294288
\(478\) −1.47755e6 −0.295783
\(479\) −1.30251e6 −0.259383 −0.129692 0.991554i \(-0.541399\pi\)
−0.129692 + 0.991554i \(0.541399\pi\)
\(480\) −288732. −0.0571994
\(481\) −2.74793e6 −0.541555
\(482\) 4.27925e6 0.838977
\(483\) −4.93513e6 −0.962567
\(484\) −1.02080e7 −1.98075
\(485\) 349418. 0.0674515
\(486\) −162776. −0.0312607
\(487\) −3.74819e6 −0.716142 −0.358071 0.933694i \(-0.616565\pi\)
−0.358071 + 0.933694i \(0.616565\pi\)
\(488\) −1.35127e6 −0.256857
\(489\) −2.52351e6 −0.477235
\(490\) −100424. −0.0188950
\(491\) 1.58539e6 0.296779 0.148389 0.988929i \(-0.452591\pi\)
0.148389 + 0.988929i \(0.452591\pi\)
\(492\) 831517. 0.154867
\(493\) −570181. −0.105656
\(494\) 1.42309e6 0.262371
\(495\) 332646. 0.0610195
\(496\) −2.14514e6 −0.391517
\(497\) 2.54994e6 0.463062
\(498\) 1.44045e6 0.260270
\(499\) −600537. −0.107966 −0.0539831 0.998542i \(-0.517192\pi\)
−0.0539831 + 0.998542i \(0.517192\pi\)
\(500\) 818975. 0.146503
\(501\) −5.52004e6 −0.982534
\(502\) −3.73287e6 −0.661125
\(503\) 2.49025e6 0.438858 0.219429 0.975628i \(-0.429581\pi\)
0.219429 + 0.975628i \(0.429581\pi\)
\(504\) −1.93299e6 −0.338964
\(505\) 399593. 0.0697251
\(506\) −7.49617e6 −1.30156
\(507\) −2.91411e6 −0.503485
\(508\) −4.85049e6 −0.833925
\(509\) 945025. 0.161677 0.0808386 0.996727i \(-0.474240\pi\)
0.0808386 + 0.996727i \(0.474240\pi\)
\(510\) 141790. 0.0241391
\(511\) 8.89334e6 1.50665
\(512\) −3.84704e6 −0.648562
\(513\) −1.72673e6 −0.289689
\(514\) −4.48377e6 −0.748575
\(515\) −500892. −0.0832196
\(516\) −4.54737e6 −0.751858
\(517\) −1.50100e7 −2.46976
\(518\) −5.33463e6 −0.873533
\(519\) −4.41434e6 −0.719363
\(520\) 182824. 0.0296500
\(521\) −7.80138e6 −1.25915 −0.629575 0.776940i \(-0.716771\pi\)
−0.629575 + 0.776940i \(0.716771\pi\)
\(522\) −120187. −0.0193055
\(523\) −5.57082e6 −0.890564 −0.445282 0.895390i \(-0.646897\pi\)
−0.445282 + 0.895390i \(0.646897\pi\)
\(524\) 683462. 0.108739
\(525\) 4.27671e6 0.677191
\(526\) 579055. 0.0912547
\(527\) 6.45101e6 1.01182
\(528\) 2.41310e6 0.376695
\(529\) 6.32659e6 0.982948
\(530\) 268516. 0.0415222
\(531\) 281961. 0.0433963
\(532\) −8.87130e6 −1.35896
\(533\) −825238. −0.125823
\(534\) 687602. 0.104348
\(535\) 757586. 0.114432
\(536\) −4.14253e6 −0.622807
\(537\) 4.32813e6 0.647686
\(538\) 4.70195e6 0.700362
\(539\) 5.13972e6 0.762022
\(540\) −95972.2 −0.0141632
\(541\) −4.82906e6 −0.709365 −0.354683 0.934987i \(-0.615411\pi\)
−0.354683 + 0.934987i \(0.615411\pi\)
\(542\) −1.36843e6 −0.200090
\(543\) 2.07556e6 0.302089
\(544\) 6.29883e6 0.912563
\(545\) 473650. 0.0683071
\(546\) 829965. 0.119146
\(547\) 1.44580e6 0.206605 0.103302 0.994650i \(-0.467059\pi\)
0.103302 + 0.994650i \(0.467059\pi\)
\(548\) 4.13081e6 0.587602
\(549\) −703984. −0.0996855
\(550\) 6.49606e6 0.915679
\(551\) −1.27495e6 −0.178901
\(552\) 4.99898e6 0.698287
\(553\) 5.33277e6 0.741549
\(554\) 2.65919e6 0.368107
\(555\) −612206. −0.0843656
\(556\) 511805. 0.0702129
\(557\) 5.82905e6 0.796085 0.398043 0.917367i \(-0.369690\pi\)
0.398043 + 0.917367i \(0.369690\pi\)
\(558\) 1.35979e6 0.184879
\(559\) 4.51304e6 0.610856
\(560\) −291699. −0.0393066
\(561\) −7.25684e6 −0.973510
\(562\) 839862. 0.112168
\(563\) −1.31388e7 −1.74696 −0.873482 0.486856i \(-0.838144\pi\)
−0.873482 + 0.486856i \(0.838144\pi\)
\(564\) 4.33056e6 0.573253
\(565\) −259025. −0.0341366
\(566\) 3.31627e6 0.435119
\(567\) −1.00705e6 −0.131551
\(568\) −2.58293e6 −0.335925
\(569\) −1.52848e6 −0.197915 −0.0989576 0.995092i \(-0.531551\pi\)
−0.0989576 + 0.995092i \(0.531551\pi\)
\(570\) 317049. 0.0408732
\(571\) 1.28959e6 0.165524 0.0827621 0.996569i \(-0.473626\pi\)
0.0827621 + 0.996569i \(0.473626\pi\)
\(572\) −4.04814e6 −0.517327
\(573\) 7.09952e6 0.903321
\(574\) −1.60206e6 −0.202954
\(575\) −1.10601e7 −1.39506
\(576\) 414695. 0.0520802
\(577\) 1.20588e7 1.50787 0.753937 0.656947i \(-0.228152\pi\)
0.753937 + 0.656947i \(0.228152\pi\)
\(578\) 820778. 0.102190
\(579\) 6.24592e6 0.774283
\(580\) −70861.9 −0.00874668
\(581\) 8.91168e6 1.09527
\(582\) −1.60678e6 −0.196629
\(583\) −1.37427e7 −1.67456
\(584\) −9.00840e6 −1.09299
\(585\) 95247.5 0.0115071
\(586\) 3.97852e6 0.478606
\(587\) −8.94749e6 −1.07178 −0.535890 0.844288i \(-0.680024\pi\)
−0.535890 + 0.844288i \(0.680024\pi\)
\(588\) −1.48287e6 −0.176872
\(589\) 1.44247e7 1.71325
\(590\) −51771.4 −0.00612294
\(591\) 4.63466e6 0.545820
\(592\) −4.44110e6 −0.520819
\(593\) −5.05616e6 −0.590451 −0.295225 0.955428i \(-0.595395\pi\)
−0.295225 + 0.955428i \(0.595395\pi\)
\(594\) −1.52965e6 −0.177879
\(595\) 877219. 0.101582
\(596\) −27625.1 −0.00318557
\(597\) −3.62552e6 −0.416327
\(598\) −2.14640e6 −0.245447
\(599\) −873873. −0.0995133 −0.0497567 0.998761i \(-0.515845\pi\)
−0.0497567 + 0.998761i \(0.515845\pi\)
\(600\) −4.33204e6 −0.491263
\(601\) 1.08755e7 1.22818 0.614091 0.789235i \(-0.289523\pi\)
0.614091 + 0.789235i \(0.289523\pi\)
\(602\) 8.76127e6 0.985317
\(603\) −2.15818e6 −0.241709
\(604\) 8.26155e6 0.921445
\(605\) 2.25706e6 0.250700
\(606\) −1.83750e6 −0.203257
\(607\) −5.06183e6 −0.557617 −0.278809 0.960347i \(-0.589940\pi\)
−0.278809 + 0.960347i \(0.589940\pi\)
\(608\) 1.40845e7 1.54519
\(609\) −743565. −0.0812411
\(610\) 129260. 0.0140650
\(611\) −4.29786e6 −0.465747
\(612\) 2.09368e6 0.225960
\(613\) −5.66357e6 −0.608750 −0.304375 0.952552i \(-0.598448\pi\)
−0.304375 + 0.952552i \(0.598448\pi\)
\(614\) 1.63175e6 0.174675
\(615\) −183853. −0.0196013
\(616\) −1.81649e7 −1.92877
\(617\) −3.87368e6 −0.409648 −0.204824 0.978799i \(-0.565662\pi\)
−0.204824 + 0.978799i \(0.565662\pi\)
\(618\) 2.30332e6 0.242595
\(619\) 3.10004e6 0.325193 0.162596 0.986693i \(-0.448013\pi\)
0.162596 + 0.986693i \(0.448013\pi\)
\(620\) 801730. 0.0837624
\(621\) 2.60437e6 0.271003
\(622\) −3.37863e6 −0.350158
\(623\) 4.25401e6 0.439115
\(624\) 690950. 0.0710371
\(625\) 9.49358e6 0.972143
\(626\) −6.33393e6 −0.646007
\(627\) −1.62266e7 −1.64838
\(628\) −3.04887e6 −0.308489
\(629\) 1.33556e7 1.34597
\(630\) 184907. 0.0185610
\(631\) 6.13084e6 0.612981 0.306490 0.951874i \(-0.400845\pi\)
0.306490 + 0.951874i \(0.400845\pi\)
\(632\) −5.40176e6 −0.537951
\(633\) −5.59026e6 −0.554527
\(634\) 5.66527e6 0.559754
\(635\) 1.07247e6 0.105549
\(636\) 3.96493e6 0.388680
\(637\) 1.47167e6 0.143702
\(638\) −1.12943e6 −0.109852
\(639\) −1.34566e6 −0.130371
\(640\) 950459. 0.0917241
\(641\) 7.71788e6 0.741913 0.370956 0.928650i \(-0.379030\pi\)
0.370956 + 0.928650i \(0.379030\pi\)
\(642\) −3.48371e6 −0.333583
\(643\) 1.95943e7 1.86897 0.934483 0.356007i \(-0.115862\pi\)
0.934483 + 0.356007i \(0.115862\pi\)
\(644\) 1.33803e7 1.27131
\(645\) 1.00545e6 0.0951616
\(646\) −6.91659e6 −0.652094
\(647\) −3.83076e6 −0.359769 −0.179885 0.983688i \(-0.557572\pi\)
−0.179885 + 0.983688i \(0.557572\pi\)
\(648\) 1.02008e6 0.0954325
\(649\) 2.64967e6 0.246933
\(650\) 1.86004e6 0.172679
\(651\) 8.41268e6 0.778004
\(652\) 6.84180e6 0.630306
\(653\) 5.17420e6 0.474854 0.237427 0.971405i \(-0.423696\pi\)
0.237427 + 0.971405i \(0.423696\pi\)
\(654\) −2.17805e6 −0.199124
\(655\) −151118. −0.0137630
\(656\) −1.33372e6 −0.121005
\(657\) −4.69320e6 −0.424185
\(658\) −8.34355e6 −0.751253
\(659\) −237453. −0.0212992 −0.0106496 0.999943i \(-0.503390\pi\)
−0.0106496 + 0.999943i \(0.503390\pi\)
\(660\) −901878. −0.0805913
\(661\) 1.38935e7 1.23683 0.618414 0.785852i \(-0.287775\pi\)
0.618414 + 0.785852i \(0.287775\pi\)
\(662\) −4.49782e6 −0.398894
\(663\) −2.07788e6 −0.183584
\(664\) −9.02698e6 −0.794552
\(665\) 1.96150e6 0.172002
\(666\) 2.81519e6 0.245936
\(667\) 1.92296e6 0.167362
\(668\) 1.49661e7 1.29768
\(669\) 4.56426e6 0.394280
\(670\) 396267. 0.0341036
\(671\) −6.61554e6 −0.567230
\(672\) 8.21422e6 0.701687
\(673\) 6.38741e6 0.543609 0.271805 0.962352i \(-0.412380\pi\)
0.271805 + 0.962352i \(0.412380\pi\)
\(674\) 3.55569e6 0.301491
\(675\) −2.25690e6 −0.190657
\(676\) 7.90082e6 0.664975
\(677\) 2.23699e7 1.87583 0.937914 0.346867i \(-0.112754\pi\)
0.937914 + 0.346867i \(0.112754\pi\)
\(678\) 1.19111e6 0.0995123
\(679\) −9.94071e6 −0.827453
\(680\) −888568. −0.0736917
\(681\) −1.33692e7 −1.10469
\(682\) 1.27783e7 1.05200
\(683\) −1.38765e6 −0.113823 −0.0569114 0.998379i \(-0.518125\pi\)
−0.0569114 + 0.998379i \(0.518125\pi\)
\(684\) 4.68157e6 0.382605
\(685\) −913347. −0.0743720
\(686\) −4.25429e6 −0.345157
\(687\) −4.14291e6 −0.334899
\(688\) 7.29380e6 0.587466
\(689\) −3.93499e6 −0.315788
\(690\) −478194. −0.0382368
\(691\) 2.42471e7 1.93181 0.965905 0.258898i \(-0.0833594\pi\)
0.965905 + 0.258898i \(0.0833594\pi\)
\(692\) 1.19683e7 0.950095
\(693\) −9.46354e6 −0.748550
\(694\) −8.64336e6 −0.681214
\(695\) −113163. −0.00888675
\(696\) 753185. 0.0589357
\(697\) 4.01086e6 0.312720
\(698\) 1.23481e7 0.959318
\(699\) 1.30592e7 1.01094
\(700\) −1.15951e7 −0.894397
\(701\) −1.41759e7 −1.08957 −0.544784 0.838577i \(-0.683388\pi\)
−0.544784 + 0.838577i \(0.683388\pi\)
\(702\) −437990. −0.0335445
\(703\) 2.98637e7 2.27906
\(704\) 3.89701e6 0.296346
\(705\) −957514. −0.0725558
\(706\) 2.06578e6 0.155981
\(707\) −1.13681e7 −0.855344
\(708\) −764461. −0.0573155
\(709\) 2.10353e7 1.57157 0.785783 0.618502i \(-0.212260\pi\)
0.785783 + 0.618502i \(0.212260\pi\)
\(710\) 247078. 0.0183945
\(711\) −2.81421e6 −0.208777
\(712\) −4.30905e6 −0.318553
\(713\) −2.17563e7 −1.60274
\(714\) −4.03383e6 −0.296123
\(715\) 895068. 0.0654774
\(716\) −1.17346e7 −0.855429
\(717\) 4.82401e6 0.350438
\(718\) 883062. 0.0639263
\(719\) 549187. 0.0396185 0.0198092 0.999804i \(-0.493694\pi\)
0.0198092 + 0.999804i \(0.493694\pi\)
\(720\) 153936. 0.0110664
\(721\) 1.42500e7 1.02089
\(722\) −8.64012e6 −0.616846
\(723\) −1.39712e7 −0.994003
\(724\) −5.62731e6 −0.398983
\(725\) −1.66641e6 −0.117743
\(726\) −1.03789e7 −0.730822
\(727\) −7.73782e6 −0.542979 −0.271489 0.962441i \(-0.587516\pi\)
−0.271489 + 0.962441i \(0.587516\pi\)
\(728\) −5.20121e6 −0.363728
\(729\) 531441. 0.0370370
\(730\) 861727. 0.0598498
\(731\) −2.19344e7 −1.51822
\(732\) 1.90866e6 0.131659
\(733\) 6.46053e6 0.444128 0.222064 0.975032i \(-0.428721\pi\)
0.222064 + 0.975032i \(0.428721\pi\)
\(734\) −7.11586e6 −0.487514
\(735\) 327871. 0.0223864
\(736\) −2.12431e7 −1.44552
\(737\) −2.02810e7 −1.37537
\(738\) 845438. 0.0571401
\(739\) −6.27646e6 −0.422770 −0.211385 0.977403i \(-0.567797\pi\)
−0.211385 + 0.977403i \(0.567797\pi\)
\(740\) 1.65983e6 0.111425
\(741\) −4.64622e6 −0.310852
\(742\) −7.63910e6 −0.509369
\(743\) 775801. 0.0515559 0.0257780 0.999668i \(-0.491794\pi\)
0.0257780 + 0.999668i \(0.491794\pi\)
\(744\) −8.52152e6 −0.564397
\(745\) 6108.07 0.000403193 0
\(746\) 1.40623e7 0.925144
\(747\) −4.70288e6 −0.308363
\(748\) 1.96749e7 1.28576
\(749\) −2.15528e7 −1.40378
\(750\) 832686. 0.0540540
\(751\) −2.78444e7 −1.80151 −0.900756 0.434325i \(-0.856987\pi\)
−0.900756 + 0.434325i \(0.856987\pi\)
\(752\) −6.94605e6 −0.447913
\(753\) 1.21873e7 0.783288
\(754\) −323394. −0.0207159
\(755\) −1.82668e6 −0.116626
\(756\) 2.73034e6 0.173745
\(757\) 2.30184e7 1.45994 0.729970 0.683479i \(-0.239534\pi\)
0.729970 + 0.683479i \(0.239534\pi\)
\(758\) 1.00189e7 0.633356
\(759\) 2.44740e7 1.54206
\(760\) −1.98688e6 −0.124778
\(761\) 2.41431e7 1.51123 0.755616 0.655015i \(-0.227338\pi\)
0.755616 + 0.655015i \(0.227338\pi\)
\(762\) −4.93170e6 −0.307687
\(763\) −1.34750e7 −0.837949
\(764\) −1.92484e7 −1.19306
\(765\) −462926. −0.0285995
\(766\) 1.35885e6 0.0836755
\(767\) 758688. 0.0465667
\(768\) −5.84509e6 −0.357592
\(769\) 1.52125e7 0.927651 0.463825 0.885927i \(-0.346476\pi\)
0.463825 + 0.885927i \(0.346476\pi\)
\(770\) 1.73762e6 0.105616
\(771\) 1.46389e7 0.886897
\(772\) −1.69341e7 −1.02263
\(773\) −1.47219e7 −0.886168 −0.443084 0.896480i \(-0.646116\pi\)
−0.443084 + 0.896480i \(0.646116\pi\)
\(774\) −4.62350e6 −0.277408
\(775\) 1.88537e7 1.12757
\(776\) 1.00693e7 0.600269
\(777\) 1.74169e7 1.03494
\(778\) −7.50725e6 −0.444664
\(779\) 8.96845e6 0.529509
\(780\) −258238. −0.0151979
\(781\) −1.26455e7 −0.741837
\(782\) 1.04320e7 0.610032
\(783\) 392394. 0.0228727
\(784\) 2.37846e6 0.138199
\(785\) 674123. 0.0390450
\(786\) 694905. 0.0401207
\(787\) −8.62728e6 −0.496520 −0.248260 0.968693i \(-0.579859\pi\)
−0.248260 + 0.968693i \(0.579859\pi\)
\(788\) −1.25656e7 −0.720889
\(789\) −1.89054e6 −0.108117
\(790\) 516723. 0.0294571
\(791\) 7.36907e6 0.418766
\(792\) 9.58598e6 0.543030
\(793\) −1.89425e6 −0.106968
\(794\) −1.12690e7 −0.634360
\(795\) −876669. −0.0491947
\(796\) 9.82962e6 0.549863
\(797\) −3.78019e6 −0.210798 −0.105399 0.994430i \(-0.533612\pi\)
−0.105399 + 0.994430i \(0.533612\pi\)
\(798\) −9.01982e6 −0.501407
\(799\) 2.08887e7 1.15756
\(800\) 1.84089e7 1.01696
\(801\) −2.24493e6 −0.123629
\(802\) −1.24992e7 −0.686192
\(803\) −4.41033e7 −2.41369
\(804\) 5.85131e6 0.319237
\(805\) −2.95846e6 −0.160907
\(806\) 3.65887e6 0.198385
\(807\) −1.53513e7 −0.829774
\(808\) 1.15152e7 0.620503
\(809\) 4.91572e6 0.264068 0.132034 0.991245i \(-0.457849\pi\)
0.132034 + 0.991245i \(0.457849\pi\)
\(810\) −97578.9 −0.00522569
\(811\) 1.59029e7 0.849032 0.424516 0.905421i \(-0.360444\pi\)
0.424516 + 0.905421i \(0.360444\pi\)
\(812\) 2.01597e6 0.107299
\(813\) 4.46775e6 0.237062
\(814\) 2.64551e7 1.39942
\(815\) −1.51276e6 −0.0797769
\(816\) −3.35819e6 −0.176555
\(817\) −4.90464e7 −2.57070
\(818\) −1.24593e7 −0.651046
\(819\) −2.70973e6 −0.141161
\(820\) 498468. 0.0258883
\(821\) −4.00292e6 −0.207262 −0.103631 0.994616i \(-0.533046\pi\)
−0.103631 + 0.994616i \(0.533046\pi\)
\(822\) 4.19996e6 0.216803
\(823\) −223649. −0.0115098 −0.00575489 0.999983i \(-0.501832\pi\)
−0.00575489 + 0.999983i \(0.501832\pi\)
\(824\) −1.44344e7 −0.740594
\(825\) −2.12088e7 −1.08488
\(826\) 1.47286e6 0.0751124
\(827\) 1.68423e7 0.856325 0.428163 0.903702i \(-0.359161\pi\)
0.428163 + 0.903702i \(0.359161\pi\)
\(828\) −7.06104e6 −0.357926
\(829\) 2.09362e6 0.105806 0.0529032 0.998600i \(-0.483153\pi\)
0.0529032 + 0.998600i \(0.483153\pi\)
\(830\) 863504. 0.0435080
\(831\) −8.68189e6 −0.436126
\(832\) 1.11584e6 0.0558849
\(833\) −7.15269e6 −0.357155
\(834\) 520373. 0.0259060
\(835\) −3.30909e6 −0.164245
\(836\) 4.39940e7 2.17710
\(837\) −4.43954e6 −0.219040
\(838\) −3.06199e6 −0.150624
\(839\) −1.59903e7 −0.784244 −0.392122 0.919913i \(-0.628259\pi\)
−0.392122 + 0.919913i \(0.628259\pi\)
\(840\) −1.15877e6 −0.0566629
\(841\) −2.02214e7 −0.985875
\(842\) −1.69877e7 −0.825760
\(843\) −2.74204e6 −0.132894
\(844\) 1.51565e7 0.732389
\(845\) −1.74692e6 −0.0841649
\(846\) 4.40306e6 0.211509
\(847\) −6.42118e7 −3.07543
\(848\) −6.35959e6 −0.303696
\(849\) −1.08272e7 −0.515521
\(850\) −9.04024e6 −0.429173
\(851\) −4.50424e7 −2.13205
\(852\) 3.64838e6 0.172187
\(853\) 3.34429e7 1.57373 0.786867 0.617122i \(-0.211702\pi\)
0.786867 + 0.617122i \(0.211702\pi\)
\(854\) −3.67736e6 −0.172540
\(855\) −1.03512e6 −0.0484258
\(856\) 2.18317e7 1.01836
\(857\) −2.16267e7 −1.00586 −0.502932 0.864326i \(-0.667745\pi\)
−0.502932 + 0.864326i \(0.667745\pi\)
\(858\) −4.11591e6 −0.190875
\(859\) 8.97034e6 0.414788 0.207394 0.978258i \(-0.433502\pi\)
0.207394 + 0.978258i \(0.433502\pi\)
\(860\) −2.72601e6 −0.125684
\(861\) 5.23050e6 0.240456
\(862\) −8.68445e6 −0.398084
\(863\) 2.02065e7 0.923557 0.461778 0.886995i \(-0.347212\pi\)
0.461778 + 0.886995i \(0.347212\pi\)
\(864\) −4.33481e6 −0.197554
\(865\) −2.64626e6 −0.120252
\(866\) −3.12178e6 −0.141452
\(867\) −2.67973e6 −0.121072
\(868\) −2.28087e7 −1.02755
\(869\) −2.64459e7 −1.18798
\(870\) −72048.3 −0.00322720
\(871\) −5.80713e6 −0.259368
\(872\) 1.36493e7 0.607884
\(873\) 5.24592e6 0.232962
\(874\) 2.33265e7 1.03293
\(875\) 5.15161e6 0.227469
\(876\) 1.27243e7 0.560240
\(877\) −3.46086e7 −1.51945 −0.759724 0.650246i \(-0.774666\pi\)
−0.759724 + 0.650246i \(0.774666\pi\)
\(878\) 1.59842e7 0.699767
\(879\) −1.29894e7 −0.567042
\(880\) 1.44658e6 0.0629702
\(881\) 3.00593e7 1.30479 0.652393 0.757881i \(-0.273765\pi\)
0.652393 + 0.757881i \(0.273765\pi\)
\(882\) −1.50770e6 −0.0652592
\(883\) 3.54978e7 1.53214 0.766072 0.642755i \(-0.222208\pi\)
0.766072 + 0.642755i \(0.222208\pi\)
\(884\) 5.63359e6 0.242468
\(885\) 169027. 0.00725434
\(886\) 1.87427e7 0.802137
\(887\) 2.49795e6 0.106604 0.0533021 0.998578i \(-0.483025\pi\)
0.0533021 + 0.998578i \(0.483025\pi\)
\(888\) −1.76422e7 −0.750793
\(889\) −3.05112e7 −1.29480
\(890\) 412196. 0.0174433
\(891\) 4.99410e6 0.210748
\(892\) −1.23747e7 −0.520744
\(893\) 4.67079e7 1.96003
\(894\) −28087.6 −0.00117536
\(895\) 2.59458e6 0.108270
\(896\) −2.70399e7 −1.12521
\(897\) 7.00773e6 0.290801
\(898\) −1.09311e7 −0.452347
\(899\) −3.27798e6 −0.135272
\(900\) 6.11898e6 0.251810
\(901\) 1.91250e7 0.784855
\(902\) 7.94482e6 0.325138
\(903\) −2.86044e7 −1.16738
\(904\) −7.46441e6 −0.303791
\(905\) 1.24423e6 0.0504987
\(906\) 8.39987e6 0.339979
\(907\) −1.00612e7 −0.406101 −0.203050 0.979168i \(-0.565085\pi\)
−0.203050 + 0.979168i \(0.565085\pi\)
\(908\) 3.62471e7 1.45901
\(909\) 5.99920e6 0.240815
\(910\) 497538. 0.0199170
\(911\) 2.02381e7 0.807932 0.403966 0.914774i \(-0.367631\pi\)
0.403966 + 0.914774i \(0.367631\pi\)
\(912\) −7.50905e6 −0.298949
\(913\) −4.41943e7 −1.75464
\(914\) −1.22804e7 −0.486236
\(915\) −422017. −0.0166639
\(916\) 1.12324e7 0.442316
\(917\) 4.29919e6 0.168836
\(918\) 2.12874e6 0.0833710
\(919\) −1.76993e7 −0.691301 −0.345650 0.938363i \(-0.612342\pi\)
−0.345650 + 0.938363i \(0.612342\pi\)
\(920\) 2.99674e6 0.116729
\(921\) −5.32744e6 −0.206952
\(922\) −832860. −0.0322660
\(923\) −3.62083e6 −0.139896
\(924\) 2.56578e7 0.988644
\(925\) 3.90330e7 1.49995
\(926\) 1.92810e7 0.738928
\(927\) −7.52003e6 −0.287422
\(928\) −3.20065e6 −0.122002
\(929\) 4.09764e7 1.55774 0.778868 0.627187i \(-0.215794\pi\)
0.778868 + 0.627187i \(0.215794\pi\)
\(930\) 815153. 0.0309052
\(931\) −1.59937e7 −0.604749
\(932\) −3.54065e7 −1.33519
\(933\) 1.10308e7 0.414861
\(934\) −2.03263e6 −0.0762416
\(935\) −4.35025e6 −0.162737
\(936\) 2.74479e6 0.102404
\(937\) 3.39931e7 1.26486 0.632429 0.774618i \(-0.282058\pi\)
0.632429 + 0.774618i \(0.282058\pi\)
\(938\) −1.12735e7 −0.418362
\(939\) 2.06794e7 0.765376
\(940\) 2.59604e6 0.0958278
\(941\) 1.43970e7 0.530027 0.265013 0.964245i \(-0.414624\pi\)
0.265013 + 0.964245i \(0.414624\pi\)
\(942\) −3.09991e6 −0.113821
\(943\) −1.35268e7 −0.495354
\(944\) 1.22616e6 0.0447836
\(945\) −603696. −0.0219907
\(946\) −4.34484e7 −1.57850
\(947\) −4.96509e7 −1.79909 −0.899544 0.436831i \(-0.856101\pi\)
−0.899544 + 0.436831i \(0.856101\pi\)
\(948\) 7.62997e6 0.275741
\(949\) −1.26282e7 −0.455174
\(950\) −2.02144e7 −0.726693
\(951\) −1.84964e7 −0.663185
\(952\) 2.52792e7 0.904004
\(953\) −4.52874e7 −1.61527 −0.807635 0.589683i \(-0.799253\pi\)
−0.807635 + 0.589683i \(0.799253\pi\)
\(954\) 4.03131e6 0.143408
\(955\) 4.25594e6 0.151004
\(956\) −1.30790e7 −0.462839
\(957\) 3.68744e6 0.130150
\(958\) 3.59052e6 0.126399
\(959\) 2.59841e7 0.912349
\(960\) 248597. 0.00870597
\(961\) 8.45779e6 0.295426
\(962\) 7.57499e6 0.263903
\(963\) 1.13739e7 0.395223
\(964\) 3.78791e7 1.31283
\(965\) 3.74423e6 0.129433
\(966\) 1.36043e7 0.469065
\(967\) −2.67183e7 −0.918846 −0.459423 0.888218i \(-0.651944\pi\)
−0.459423 + 0.888218i \(0.651944\pi\)
\(968\) 6.50426e7 2.23105
\(969\) 2.25817e7 0.772588
\(970\) −963213. −0.0328695
\(971\) 1.78197e7 0.606529 0.303265 0.952906i \(-0.401923\pi\)
0.303265 + 0.952906i \(0.401923\pi\)
\(972\) −1.44086e6 −0.0489165
\(973\) 3.21941e6 0.109017
\(974\) 1.03323e7 0.348980
\(975\) −6.07278e6 −0.204586
\(976\) −3.06142e6 −0.102872
\(977\) 5.43351e7 1.82114 0.910572 0.413351i \(-0.135642\pi\)
0.910572 + 0.413351i \(0.135642\pi\)
\(978\) 6.95634e6 0.232559
\(979\) −2.10962e7 −0.703475
\(980\) −888934. −0.0295668
\(981\) 7.11104e6 0.235918
\(982\) −4.37032e6 −0.144622
\(983\) −5.43884e7 −1.79524 −0.897620 0.440769i \(-0.854706\pi\)
−0.897620 + 0.440769i \(0.854706\pi\)
\(984\) −5.29818e6 −0.174437
\(985\) 2.77834e6 0.0912419
\(986\) 1.57177e6 0.0514870
\(987\) 2.72406e7 0.890070
\(988\) 1.25970e7 0.410557
\(989\) 7.39749e7 2.40488
\(990\) −916977. −0.0297352
\(991\) 3.77447e7 1.22088 0.610439 0.792064i \(-0.290993\pi\)
0.610439 + 0.792064i \(0.290993\pi\)
\(992\) 3.62121e7 1.16835
\(993\) 1.46848e7 0.472602
\(994\) −7.02921e6 −0.225653
\(995\) −2.17339e6 −0.0695953
\(996\) 1.27506e7 0.407269
\(997\) −3.51167e7 −1.11886 −0.559431 0.828877i \(-0.688980\pi\)
−0.559431 + 0.828877i \(0.688980\pi\)
\(998\) 1.65545e6 0.0526126
\(999\) −9.19123e6 −0.291380
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.1.5 11
3.2 odd 2 531.6.a.b.1.7 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.5 11 1.1 even 1 trivial
531.6.a.b.1.7 11 3.2 odd 2