Properties

Label 177.6.a.a.1.9
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 1.9
Root \(7.91273\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+6.91273 q^{2} +9.00000 q^{3} +15.7858 q^{4} -11.1343 q^{5} +62.2145 q^{6} -193.283 q^{7} -112.084 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+6.91273 q^{2} +9.00000 q^{3} +15.7858 q^{4} -11.1343 q^{5} +62.2145 q^{6} -193.283 q^{7} -112.084 q^{8} +81.0000 q^{9} -76.9686 q^{10} -125.065 q^{11} +142.072 q^{12} +1116.22 q^{13} -1336.12 q^{14} -100.209 q^{15} -1279.95 q^{16} -1948.69 q^{17} +559.931 q^{18} -2116.73 q^{19} -175.764 q^{20} -1739.55 q^{21} -864.538 q^{22} -2537.35 q^{23} -1008.76 q^{24} -3001.03 q^{25} +7716.11 q^{26} +729.000 q^{27} -3051.13 q^{28} +4531.40 q^{29} -692.717 q^{30} -902.692 q^{31} -5261.27 q^{32} -1125.58 q^{33} -13470.8 q^{34} +2152.08 q^{35} +1278.65 q^{36} +15206.0 q^{37} -14632.4 q^{38} +10046.0 q^{39} +1247.98 q^{40} -8454.58 q^{41} -12025.0 q^{42} -9993.30 q^{43} -1974.25 q^{44} -901.881 q^{45} -17540.0 q^{46} +2702.02 q^{47} -11519.6 q^{48} +20551.5 q^{49} -20745.3 q^{50} -17538.2 q^{51} +17620.4 q^{52} +23313.3 q^{53} +5039.38 q^{54} +1392.51 q^{55} +21664.0 q^{56} -19050.6 q^{57} +31324.3 q^{58} +3481.00 q^{59} -1581.88 q^{60} -29163.2 q^{61} -6240.06 q^{62} -15656.0 q^{63} +4588.78 q^{64} -12428.3 q^{65} -7780.85 q^{66} -9692.20 q^{67} -30761.7 q^{68} -22836.2 q^{69} +14876.7 q^{70} -6707.84 q^{71} -9078.83 q^{72} +51879.5 q^{73} +105115. q^{74} -27009.2 q^{75} -33414.2 q^{76} +24172.9 q^{77} +69445.0 q^{78} -70812.0 q^{79} +14251.4 q^{80} +6561.00 q^{81} -58444.2 q^{82} +31987.2 q^{83} -27460.2 q^{84} +21697.4 q^{85} -69081.0 q^{86} +40782.6 q^{87} +14017.8 q^{88} +78629.4 q^{89} -6234.45 q^{90} -215746. q^{91} -40054.2 q^{92} -8124.23 q^{93} +18678.3 q^{94} +23568.3 q^{95} -47351.5 q^{96} +21462.8 q^{97} +142067. q^{98} -10130.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.91273 1.22201 0.611005 0.791627i \(-0.290766\pi\)
0.611005 + 0.791627i \(0.290766\pi\)
\(3\) 9.00000 0.577350
\(4\) 15.7858 0.493306
\(5\) −11.1343 −0.199177 −0.0995885 0.995029i \(-0.531753\pi\)
−0.0995885 + 0.995029i \(0.531753\pi\)
\(6\) 62.2145 0.705527
\(7\) −193.283 −1.49090 −0.745452 0.666560i \(-0.767766\pi\)
−0.745452 + 0.666560i \(0.767766\pi\)
\(8\) −112.084 −0.619185
\(9\) 81.0000 0.333333
\(10\) −76.9686 −0.243396
\(11\) −125.065 −0.311640 −0.155820 0.987785i \(-0.549802\pi\)
−0.155820 + 0.987785i \(0.549802\pi\)
\(12\) 142.072 0.284810
\(13\) 1116.22 1.83185 0.915927 0.401346i \(-0.131457\pi\)
0.915927 + 0.401346i \(0.131457\pi\)
\(14\) −1336.12 −1.82190
\(15\) −100.209 −0.114995
\(16\) −1279.95 −1.24996
\(17\) −1948.69 −1.63539 −0.817695 0.575652i \(-0.804748\pi\)
−0.817695 + 0.575652i \(0.804748\pi\)
\(18\) 559.931 0.407336
\(19\) −2116.73 −1.34518 −0.672591 0.740014i \(-0.734819\pi\)
−0.672591 + 0.740014i \(0.734819\pi\)
\(20\) −175.764 −0.0982552
\(21\) −1739.55 −0.860773
\(22\) −864.538 −0.380827
\(23\) −2537.35 −1.00014 −0.500071 0.865985i \(-0.666693\pi\)
−0.500071 + 0.865985i \(0.666693\pi\)
\(24\) −1008.76 −0.357486
\(25\) −3001.03 −0.960329
\(26\) 7716.11 2.23854
\(27\) 729.000 0.192450
\(28\) −3051.13 −0.735472
\(29\) 4531.40 1.00055 0.500273 0.865867i \(-0.333233\pi\)
0.500273 + 0.865867i \(0.333233\pi\)
\(30\) −692.717 −0.140525
\(31\) −902.692 −0.168708 −0.0843539 0.996436i \(-0.526883\pi\)
−0.0843539 + 0.996436i \(0.526883\pi\)
\(32\) −5261.27 −0.908272
\(33\) −1125.58 −0.179925
\(34\) −13470.8 −1.99846
\(35\) 2152.08 0.296953
\(36\) 1278.65 0.164435
\(37\) 15206.0 1.82604 0.913020 0.407916i \(-0.133744\pi\)
0.913020 + 0.407916i \(0.133744\pi\)
\(38\) −14632.4 −1.64382
\(39\) 10046.0 1.05762
\(40\) 1247.98 0.123327
\(41\) −8454.58 −0.785475 −0.392737 0.919651i \(-0.628472\pi\)
−0.392737 + 0.919651i \(0.628472\pi\)
\(42\) −12025.0 −1.05187
\(43\) −9993.30 −0.824210 −0.412105 0.911136i \(-0.635206\pi\)
−0.412105 + 0.911136i \(0.635206\pi\)
\(44\) −1974.25 −0.153734
\(45\) −901.881 −0.0663923
\(46\) −17540.0 −1.22218
\(47\) 2702.02 0.178420 0.0892100 0.996013i \(-0.471566\pi\)
0.0892100 + 0.996013i \(0.471566\pi\)
\(48\) −11519.6 −0.721662
\(49\) 20551.5 1.22279
\(50\) −20745.3 −1.17353
\(51\) −17538.2 −0.944193
\(52\) 17620.4 0.903664
\(53\) 23313.3 1.14003 0.570013 0.821636i \(-0.306938\pi\)
0.570013 + 0.821636i \(0.306938\pi\)
\(54\) 5039.38 0.235176
\(55\) 1392.51 0.0620715
\(56\) 21664.0 0.923144
\(57\) −19050.6 −0.776641
\(58\) 31324.3 1.22268
\(59\) 3481.00 0.130189
\(60\) −1581.88 −0.0567277
\(61\) −29163.2 −1.00348 −0.501742 0.865017i \(-0.667307\pi\)
−0.501742 + 0.865017i \(0.667307\pi\)
\(62\) −6240.06 −0.206162
\(63\) −15656.0 −0.496968
\(64\) 4588.78 0.140039
\(65\) −12428.3 −0.364863
\(66\) −7780.85 −0.219870
\(67\) −9692.20 −0.263776 −0.131888 0.991265i \(-0.542104\pi\)
−0.131888 + 0.991265i \(0.542104\pi\)
\(68\) −30761.7 −0.806748
\(69\) −22836.2 −0.577432
\(70\) 14876.7 0.362880
\(71\) −6707.84 −0.157920 −0.0789599 0.996878i \(-0.525160\pi\)
−0.0789599 + 0.996878i \(0.525160\pi\)
\(72\) −9078.83 −0.206395
\(73\) 51879.5 1.13943 0.569716 0.821841i \(-0.307053\pi\)
0.569716 + 0.821841i \(0.307053\pi\)
\(74\) 105115. 2.23144
\(75\) −27009.2 −0.554446
\(76\) −33414.2 −0.663586
\(77\) 24172.9 0.464625
\(78\) 69445.0 1.29242
\(79\) −70812.0 −1.27655 −0.638277 0.769807i \(-0.720352\pi\)
−0.638277 + 0.769807i \(0.720352\pi\)
\(80\) 14251.4 0.248962
\(81\) 6561.00 0.111111
\(82\) −58444.2 −0.959857
\(83\) 31987.2 0.509660 0.254830 0.966986i \(-0.417980\pi\)
0.254830 + 0.966986i \(0.417980\pi\)
\(84\) −27460.2 −0.424625
\(85\) 21697.4 0.325732
\(86\) −69081.0 −1.00719
\(87\) 40782.6 0.577666
\(88\) 14017.8 0.192963
\(89\) 78629.4 1.05223 0.526114 0.850414i \(-0.323649\pi\)
0.526114 + 0.850414i \(0.323649\pi\)
\(90\) −6234.45 −0.0811320
\(91\) −215746. −2.73112
\(92\) −40054.2 −0.493376
\(93\) −8124.23 −0.0974035
\(94\) 18678.3 0.218031
\(95\) 23568.3 0.267929
\(96\) −47351.5 −0.524391
\(97\) 21462.8 0.231610 0.115805 0.993272i \(-0.463055\pi\)
0.115805 + 0.993272i \(0.463055\pi\)
\(98\) 142067. 1.49426
\(99\) −10130.2 −0.103880
\(100\) −47373.6 −0.473736
\(101\) 4675.59 0.0456072 0.0228036 0.999740i \(-0.492741\pi\)
0.0228036 + 0.999740i \(0.492741\pi\)
\(102\) −121237. −1.15381
\(103\) 71375.2 0.662909 0.331455 0.943471i \(-0.392461\pi\)
0.331455 + 0.943471i \(0.392461\pi\)
\(104\) −125111. −1.13426
\(105\) 19368.7 0.171446
\(106\) 161159. 1.39312
\(107\) −227244. −1.91882 −0.959409 0.282019i \(-0.908996\pi\)
−0.959409 + 0.282019i \(0.908996\pi\)
\(108\) 11507.8 0.0949368
\(109\) 19845.6 0.159992 0.0799961 0.996795i \(-0.474509\pi\)
0.0799961 + 0.996795i \(0.474509\pi\)
\(110\) 9626.05 0.0758519
\(111\) 136854. 1.05426
\(112\) 247394. 1.86356
\(113\) 69900.0 0.514969 0.257484 0.966282i \(-0.417106\pi\)
0.257484 + 0.966282i \(0.417106\pi\)
\(114\) −131691. −0.949063
\(115\) 28251.7 0.199205
\(116\) 71531.8 0.493576
\(117\) 90413.7 0.610618
\(118\) 24063.2 0.159092
\(119\) 376650. 2.43821
\(120\) 11231.9 0.0712030
\(121\) −145410. −0.902881
\(122\) −201597. −1.22627
\(123\) −76091.2 −0.453494
\(124\) −14249.7 −0.0832246
\(125\) 68209.2 0.390452
\(126\) −108225. −0.607299
\(127\) 99756.3 0.548821 0.274411 0.961613i \(-0.411517\pi\)
0.274411 + 0.961613i \(0.411517\pi\)
\(128\) 200082. 1.07940
\(129\) −89939.7 −0.475858
\(130\) −85913.7 −0.445866
\(131\) −197499. −1.00551 −0.502756 0.864428i \(-0.667681\pi\)
−0.502756 + 0.864428i \(0.667681\pi\)
\(132\) −17768.2 −0.0887583
\(133\) 409128. 2.00554
\(134\) −66999.6 −0.322337
\(135\) −8116.92 −0.0383316
\(136\) 218418. 1.01261
\(137\) −244667. −1.11371 −0.556857 0.830608i \(-0.687993\pi\)
−0.556857 + 0.830608i \(0.687993\pi\)
\(138\) −157860. −0.705627
\(139\) −204234. −0.896584 −0.448292 0.893887i \(-0.647968\pi\)
−0.448292 + 0.893887i \(0.647968\pi\)
\(140\) 33972.3 0.146489
\(141\) 24318.2 0.103011
\(142\) −46369.4 −0.192979
\(143\) −139600. −0.570879
\(144\) −103676. −0.416652
\(145\) −50454.1 −0.199286
\(146\) 358629. 1.39240
\(147\) 184963. 0.705979
\(148\) 240038. 0.900796
\(149\) −410416. −1.51446 −0.757232 0.653146i \(-0.773449\pi\)
−0.757232 + 0.653146i \(0.773449\pi\)
\(150\) −186708. −0.677538
\(151\) −388786. −1.38761 −0.693807 0.720161i \(-0.744068\pi\)
−0.693807 + 0.720161i \(0.744068\pi\)
\(152\) 237252. 0.832916
\(153\) −157844. −0.545130
\(154\) 167101. 0.567776
\(155\) 10050.9 0.0336027
\(156\) 158584. 0.521731
\(157\) 336248. 1.08871 0.544353 0.838856i \(-0.316775\pi\)
0.544353 + 0.838856i \(0.316775\pi\)
\(158\) −489504. −1.55996
\(159\) 209820. 0.658194
\(160\) 58580.7 0.180907
\(161\) 490428. 1.49111
\(162\) 45354.4 0.135779
\(163\) 299758. 0.883694 0.441847 0.897091i \(-0.354323\pi\)
0.441847 + 0.897091i \(0.354323\pi\)
\(164\) −133462. −0.387479
\(165\) 12532.6 0.0358370
\(166\) 221119. 0.622810
\(167\) 263356. 0.730722 0.365361 0.930866i \(-0.380946\pi\)
0.365361 + 0.930866i \(0.380946\pi\)
\(168\) 194976. 0.532978
\(169\) 874650. 2.35569
\(170\) 149988. 0.398047
\(171\) −171455. −0.448394
\(172\) −157752. −0.406588
\(173\) −695281. −1.76622 −0.883111 0.469164i \(-0.844555\pi\)
−0.883111 + 0.469164i \(0.844555\pi\)
\(174\) 281919. 0.705913
\(175\) 580049. 1.43176
\(176\) 160077. 0.389536
\(177\) 31329.0 0.0751646
\(178\) 543543. 1.28583
\(179\) 450239. 1.05029 0.525147 0.851012i \(-0.324010\pi\)
0.525147 + 0.851012i \(0.324010\pi\)
\(180\) −14236.9 −0.0327517
\(181\) 289973. 0.657901 0.328951 0.944347i \(-0.393305\pi\)
0.328951 + 0.944347i \(0.393305\pi\)
\(182\) −1.49140e6 −3.33745
\(183\) −262469. −0.579362
\(184\) 284398. 0.619272
\(185\) −169308. −0.363705
\(186\) −56160.6 −0.119028
\(187\) 243713. 0.509653
\(188\) 42653.5 0.0880157
\(189\) −140904. −0.286924
\(190\) 162922. 0.327412
\(191\) −272091. −0.539673 −0.269836 0.962906i \(-0.586970\pi\)
−0.269836 + 0.962906i \(0.586970\pi\)
\(192\) 41299.1 0.0808513
\(193\) −800409. −1.54675 −0.773373 0.633951i \(-0.781432\pi\)
−0.773373 + 0.633951i \(0.781432\pi\)
\(194\) 148367. 0.283030
\(195\) −111855. −0.210654
\(196\) 324421. 0.603211
\(197\) −639502. −1.17402 −0.587012 0.809579i \(-0.699696\pi\)
−0.587012 + 0.809579i \(0.699696\pi\)
\(198\) −70027.6 −0.126942
\(199\) 812910. 1.45516 0.727579 0.686024i \(-0.240646\pi\)
0.727579 + 0.686024i \(0.240646\pi\)
\(200\) 336368. 0.594621
\(201\) −87229.8 −0.152291
\(202\) 32321.1 0.0557324
\(203\) −875845. −1.49172
\(204\) −276855. −0.465776
\(205\) 94136.0 0.156448
\(206\) 493397. 0.810081
\(207\) −205526. −0.333381
\(208\) −1.42871e6 −2.28973
\(209\) 264728. 0.419212
\(210\) 133891. 0.209509
\(211\) 134678. 0.208253 0.104126 0.994564i \(-0.466795\pi\)
0.104126 + 0.994564i \(0.466795\pi\)
\(212\) 368019. 0.562382
\(213\) −60370.5 −0.0911751
\(214\) −1.57088e6 −2.34481
\(215\) 111269. 0.164164
\(216\) −81709.5 −0.119162
\(217\) 174475. 0.251527
\(218\) 137187. 0.195512
\(219\) 466916. 0.657852
\(220\) 21981.9 0.0306202
\(221\) −2.17517e6 −2.99579
\(222\) 946033. 1.28832
\(223\) −922919. −1.24280 −0.621401 0.783493i \(-0.713436\pi\)
−0.621401 + 0.783493i \(0.713436\pi\)
\(224\) 1.01692e6 1.35415
\(225\) −243083. −0.320110
\(226\) 483200. 0.629297
\(227\) −936298. −1.20601 −0.603003 0.797739i \(-0.706029\pi\)
−0.603003 + 0.797739i \(0.706029\pi\)
\(228\) −300728. −0.383122
\(229\) −1.13593e6 −1.43141 −0.715706 0.698402i \(-0.753895\pi\)
−0.715706 + 0.698402i \(0.753895\pi\)
\(230\) 195297. 0.243430
\(231\) 217556. 0.268251
\(232\) −507899. −0.619523
\(233\) −1.39667e6 −1.68540 −0.842700 0.538383i \(-0.819035\pi\)
−0.842700 + 0.538383i \(0.819035\pi\)
\(234\) 625005. 0.746180
\(235\) −30085.2 −0.0355372
\(236\) 54950.4 0.0642230
\(237\) −637308. −0.737019
\(238\) 2.60368e6 2.97951
\(239\) 833356. 0.943704 0.471852 0.881678i \(-0.343586\pi\)
0.471852 + 0.881678i \(0.343586\pi\)
\(240\) 128263. 0.143738
\(241\) 1.27013e6 1.40866 0.704331 0.709871i \(-0.251247\pi\)
0.704331 + 0.709871i \(0.251247\pi\)
\(242\) −1.00518e6 −1.10333
\(243\) 59049.0 0.0641500
\(244\) −460364. −0.495025
\(245\) −228827. −0.243552
\(246\) −525998. −0.554174
\(247\) −2.36273e6 −2.46418
\(248\) 101178. 0.104461
\(249\) 287885. 0.294253
\(250\) 471512. 0.477136
\(251\) −791023. −0.792510 −0.396255 0.918141i \(-0.629690\pi\)
−0.396255 + 0.918141i \(0.629690\pi\)
\(252\) −247142. −0.245157
\(253\) 317334. 0.311684
\(254\) 689588. 0.670665
\(255\) 195277. 0.188061
\(256\) 1.23627e6 1.17900
\(257\) −1.83299e6 −1.73112 −0.865559 0.500807i \(-0.833037\pi\)
−0.865559 + 0.500807i \(0.833037\pi\)
\(258\) −621729. −0.581502
\(259\) −2.93906e6 −2.72245
\(260\) −196191. −0.179989
\(261\) 367043. 0.333516
\(262\) −1.36526e6 −1.22874
\(263\) −12651.0 −0.0112781 −0.00563905 0.999984i \(-0.501795\pi\)
−0.00563905 + 0.999984i \(0.501795\pi\)
\(264\) 126160. 0.111407
\(265\) −259578. −0.227067
\(266\) 2.82819e6 2.45078
\(267\) 707664. 0.607504
\(268\) −152999. −0.130122
\(269\) −148582. −0.125195 −0.0625973 0.998039i \(-0.519938\pi\)
−0.0625973 + 0.998039i \(0.519938\pi\)
\(270\) −56110.1 −0.0468416
\(271\) 941611. 0.778840 0.389420 0.921060i \(-0.372675\pi\)
0.389420 + 0.921060i \(0.372675\pi\)
\(272\) 2.49424e6 2.04416
\(273\) −1.94172e6 −1.57681
\(274\) −1.69131e6 −1.36097
\(275\) 375323. 0.299277
\(276\) −360487. −0.284851
\(277\) 2.13299e6 1.67028 0.835140 0.550038i \(-0.185387\pi\)
0.835140 + 0.550038i \(0.185387\pi\)
\(278\) −1.41181e6 −1.09563
\(279\) −73118.0 −0.0562359
\(280\) −241215. −0.183869
\(281\) −890716. −0.672935 −0.336468 0.941695i \(-0.609232\pi\)
−0.336468 + 0.941695i \(0.609232\pi\)
\(282\) 168105. 0.125880
\(283\) 817581. 0.606826 0.303413 0.952859i \(-0.401874\pi\)
0.303413 + 0.952859i \(0.401874\pi\)
\(284\) −105889. −0.0779028
\(285\) 212115. 0.154689
\(286\) −965013. −0.697619
\(287\) 1.63413e6 1.17107
\(288\) −426163. −0.302757
\(289\) 2.37755e6 1.67450
\(290\) −348775. −0.243529
\(291\) 193165. 0.133720
\(292\) 818959. 0.562089
\(293\) 610411. 0.415388 0.207694 0.978194i \(-0.433404\pi\)
0.207694 + 0.978194i \(0.433404\pi\)
\(294\) 1.27860e6 0.862713
\(295\) −38758.6 −0.0259306
\(296\) −1.70435e6 −1.13066
\(297\) −91172.2 −0.0599751
\(298\) −2.83710e6 −1.85069
\(299\) −2.83224e6 −1.83211
\(300\) −426362. −0.273512
\(301\) 1.93154e6 1.22882
\(302\) −2.68757e6 −1.69568
\(303\) 42080.4 0.0263313
\(304\) 2.70931e6 1.68142
\(305\) 324713. 0.199871
\(306\) −1.09113e6 −0.666154
\(307\) −1.00422e6 −0.608112 −0.304056 0.952654i \(-0.598341\pi\)
−0.304056 + 0.952654i \(0.598341\pi\)
\(308\) 381589. 0.229202
\(309\) 642376. 0.382731
\(310\) 69478.9 0.0410628
\(311\) −35455.9 −0.0207868 −0.0103934 0.999946i \(-0.503308\pi\)
−0.0103934 + 0.999946i \(0.503308\pi\)
\(312\) −1.12600e6 −0.654863
\(313\) −1.63361e6 −0.942511 −0.471255 0.881997i \(-0.656199\pi\)
−0.471255 + 0.881997i \(0.656199\pi\)
\(314\) 2.32439e6 1.33041
\(315\) 174319. 0.0989845
\(316\) −1.11782e6 −0.629732
\(317\) −620992. −0.347086 −0.173543 0.984826i \(-0.555522\pi\)
−0.173543 + 0.984826i \(0.555522\pi\)
\(318\) 1.45043e6 0.804319
\(319\) −566718. −0.311810
\(320\) −51093.0 −0.0278925
\(321\) −2.04520e6 −1.10783
\(322\) 3.39020e6 1.82216
\(323\) 4.12485e6 2.19990
\(324\) 103571. 0.0548118
\(325\) −3.34980e6 −1.75918
\(326\) 2.07215e6 1.07988
\(327\) 178611. 0.0923715
\(328\) 947626. 0.486354
\(329\) −522255. −0.266007
\(330\) 86634.5 0.0437931
\(331\) 2.75397e6 1.38162 0.690812 0.723034i \(-0.257253\pi\)
0.690812 + 0.723034i \(0.257253\pi\)
\(332\) 504943. 0.251419
\(333\) 1.23168e6 0.608680
\(334\) 1.82051e6 0.892949
\(335\) 107916. 0.0525381
\(336\) 2.22654e6 1.07593
\(337\) 467039. 0.224016 0.112008 0.993707i \(-0.464272\pi\)
0.112008 + 0.993707i \(0.464272\pi\)
\(338\) 6.04622e6 2.87867
\(339\) 629100. 0.297317
\(340\) 342511. 0.160686
\(341\) 112895. 0.0525761
\(342\) −1.18522e6 −0.547942
\(343\) −723744. −0.332162
\(344\) 1.12009e6 0.510338
\(345\) 254266. 0.115011
\(346\) −4.80629e6 −2.15834
\(347\) 3.27711e6 1.46106 0.730530 0.682881i \(-0.239273\pi\)
0.730530 + 0.682881i \(0.239273\pi\)
\(348\) 643786. 0.284966
\(349\) −3.92940e6 −1.72688 −0.863441 0.504450i \(-0.831695\pi\)
−0.863441 + 0.504450i \(0.831695\pi\)
\(350\) 4.00972e6 1.74962
\(351\) 813723. 0.352540
\(352\) 658000. 0.283054
\(353\) 3.34115e6 1.42712 0.713558 0.700597i \(-0.247083\pi\)
0.713558 + 0.700597i \(0.247083\pi\)
\(354\) 216569. 0.0918518
\(355\) 74687.3 0.0314540
\(356\) 1.24123e6 0.519070
\(357\) 3.38985e6 1.40770
\(358\) 3.11238e6 1.28347
\(359\) −772755. −0.316450 −0.158225 0.987403i \(-0.550577\pi\)
−0.158225 + 0.987403i \(0.550577\pi\)
\(360\) 101087. 0.0411091
\(361\) 2.00444e6 0.809514
\(362\) 2.00450e6 0.803961
\(363\) −1.30869e6 −0.521278
\(364\) −3.40573e6 −1.34728
\(365\) −577643. −0.226949
\(366\) −1.81437e6 −0.707985
\(367\) −640958. −0.248407 −0.124204 0.992257i \(-0.539638\pi\)
−0.124204 + 0.992257i \(0.539638\pi\)
\(368\) 3.24770e6 1.25013
\(369\) −684821. −0.261825
\(370\) −1.17038e6 −0.444451
\(371\) −4.50608e6 −1.69967
\(372\) −128247. −0.0480497
\(373\) −2.37093e6 −0.882360 −0.441180 0.897419i \(-0.645440\pi\)
−0.441180 + 0.897419i \(0.645440\pi\)
\(374\) 1.68472e6 0.622800
\(375\) 613883. 0.225428
\(376\) −302854. −0.110475
\(377\) 5.05803e6 1.83286
\(378\) −974028. −0.350624
\(379\) −2.59822e6 −0.929134 −0.464567 0.885538i \(-0.653790\pi\)
−0.464567 + 0.885538i \(0.653790\pi\)
\(380\) 372045. 0.132171
\(381\) 897807. 0.316862
\(382\) −1.88089e6 −0.659485
\(383\) −2.73909e6 −0.954135 −0.477067 0.878867i \(-0.658300\pi\)
−0.477067 + 0.878867i \(0.658300\pi\)
\(384\) 1.80074e6 0.623192
\(385\) −269149. −0.0925426
\(386\) −5.53301e6 −1.89014
\(387\) −809457. −0.274737
\(388\) 338808. 0.114255
\(389\) 1.26060e6 0.422381 0.211190 0.977445i \(-0.432266\pi\)
0.211190 + 0.977445i \(0.432266\pi\)
\(390\) −773223. −0.257421
\(391\) 4.94453e6 1.63562
\(392\) −2.30350e6 −0.757134
\(393\) −1.77749e6 −0.580533
\(394\) −4.42071e6 −1.43467
\(395\) 788444. 0.254260
\(396\) −159914. −0.0512446
\(397\) 146031. 0.0465017 0.0232508 0.999730i \(-0.492598\pi\)
0.0232508 + 0.999730i \(0.492598\pi\)
\(398\) 5.61943e6 1.77822
\(399\) 3.68216e6 1.15790
\(400\) 3.84118e6 1.20037
\(401\) −2.94941e6 −0.915956 −0.457978 0.888964i \(-0.651426\pi\)
−0.457978 + 0.888964i \(0.651426\pi\)
\(402\) −602996. −0.186101
\(403\) −1.00760e6 −0.309048
\(404\) 73808.0 0.0224983
\(405\) −73052.3 −0.0221308
\(406\) −6.05447e6 −1.82289
\(407\) −1.90173e6 −0.569067
\(408\) 1.96576e6 0.584630
\(409\) 3.43709e6 1.01597 0.507987 0.861365i \(-0.330390\pi\)
0.507987 + 0.861365i \(0.330390\pi\)
\(410\) 650737. 0.191181
\(411\) −2.20200e6 −0.643003
\(412\) 1.12671e6 0.327017
\(413\) −672819. −0.194099
\(414\) −1.42074e6 −0.407394
\(415\) −356156. −0.101513
\(416\) −5.87273e6 −1.66382
\(417\) −1.83811e6 −0.517643
\(418\) 1.82999e6 0.512281
\(419\) −6.48770e6 −1.80533 −0.902664 0.430347i \(-0.858391\pi\)
−0.902664 + 0.430347i \(0.858391\pi\)
\(420\) 305751. 0.0845754
\(421\) −3.88945e6 −1.06951 −0.534753 0.845008i \(-0.679595\pi\)
−0.534753 + 0.845008i \(0.679595\pi\)
\(422\) 930992. 0.254487
\(423\) 218863. 0.0594733
\(424\) −2.61306e6 −0.705886
\(425\) 5.84808e6 1.57051
\(426\) −417325. −0.111417
\(427\) 5.63676e6 1.49610
\(428\) −3.58723e6 −0.946565
\(429\) −1.25640e6 −0.329597
\(430\) 769170. 0.200609
\(431\) 268690. 0.0696721 0.0348361 0.999393i \(-0.488909\pi\)
0.0348361 + 0.999393i \(0.488909\pi\)
\(432\) −933087. −0.240554
\(433\) −1.71353e6 −0.439210 −0.219605 0.975589i \(-0.570477\pi\)
−0.219605 + 0.975589i \(0.570477\pi\)
\(434\) 1.20610e6 0.307368
\(435\) −454087. −0.115058
\(436\) 313279. 0.0789251
\(437\) 5.37089e6 1.34537
\(438\) 3.22766e6 0.803901
\(439\) 663061. 0.164207 0.0821035 0.996624i \(-0.473836\pi\)
0.0821035 + 0.996624i \(0.473836\pi\)
\(440\) −156079. −0.0384337
\(441\) 1.66467e6 0.407597
\(442\) −1.50363e7 −3.66089
\(443\) −1.92044e6 −0.464934 −0.232467 0.972604i \(-0.574680\pi\)
−0.232467 + 0.972604i \(0.574680\pi\)
\(444\) 2.16035e6 0.520075
\(445\) −875485. −0.209579
\(446\) −6.37989e6 −1.51871
\(447\) −3.69375e6 −0.874376
\(448\) −886936. −0.208784
\(449\) −641166. −0.150091 −0.0750454 0.997180i \(-0.523910\pi\)
−0.0750454 + 0.997180i \(0.523910\pi\)
\(450\) −1.68037e6 −0.391177
\(451\) 1.05737e6 0.244785
\(452\) 1.10343e6 0.254037
\(453\) −3.49908e6 −0.801139
\(454\) −6.47237e6 −1.47375
\(455\) 2.40219e6 0.543975
\(456\) 2.13527e6 0.480884
\(457\) 2.82002e6 0.631629 0.315814 0.948821i \(-0.397722\pi\)
0.315814 + 0.948821i \(0.397722\pi\)
\(458\) −7.85241e6 −1.74920
\(459\) −1.42060e6 −0.314731
\(460\) 445976. 0.0982691
\(461\) −4.36961e6 −0.957613 −0.478806 0.877920i \(-0.658930\pi\)
−0.478806 + 0.877920i \(0.658930\pi\)
\(462\) 1.50391e6 0.327806
\(463\) 712732. 0.154516 0.0772580 0.997011i \(-0.475383\pi\)
0.0772580 + 0.997011i \(0.475383\pi\)
\(464\) −5.79999e6 −1.25064
\(465\) 90457.8 0.0194005
\(466\) −9.65478e6 −2.05957
\(467\) 2.02176e6 0.428981 0.214491 0.976726i \(-0.431191\pi\)
0.214491 + 0.976726i \(0.431191\pi\)
\(468\) 1.42725e6 0.301221
\(469\) 1.87334e6 0.393265
\(470\) −207970. −0.0434267
\(471\) 3.02623e6 0.628564
\(472\) −390166. −0.0806110
\(473\) 1.24981e6 0.256857
\(474\) −4.40554e6 −0.900643
\(475\) 6.35236e6 1.29182
\(476\) 5.94572e6 1.20278
\(477\) 1.88838e6 0.380009
\(478\) 5.76076e6 1.15322
\(479\) 5.57705e6 1.11062 0.555310 0.831643i \(-0.312600\pi\)
0.555310 + 0.831643i \(0.312600\pi\)
\(480\) 527227. 0.104447
\(481\) 1.69732e7 3.34504
\(482\) 8.78009e6 1.72140
\(483\) 4.41386e6 0.860895
\(484\) −2.29541e6 −0.445396
\(485\) −238974. −0.0461314
\(486\) 408190. 0.0783919
\(487\) −1.31991e6 −0.252186 −0.126093 0.992018i \(-0.540244\pi\)
−0.126093 + 0.992018i \(0.540244\pi\)
\(488\) 3.26874e6 0.621342
\(489\) 2.69782e6 0.510201
\(490\) −1.58182e6 −0.297623
\(491\) 5.36809e6 1.00488 0.502442 0.864611i \(-0.332435\pi\)
0.502442 + 0.864611i \(0.332435\pi\)
\(492\) −1.20116e6 −0.223711
\(493\) −8.83031e6 −1.63628
\(494\) −1.63329e7 −3.01125
\(495\) 112793. 0.0206905
\(496\) 1.15540e6 0.210877
\(497\) 1.29651e6 0.235443
\(498\) 1.99007e6 0.359579
\(499\) −1.33480e6 −0.239974 −0.119987 0.992775i \(-0.538285\pi\)
−0.119987 + 0.992775i \(0.538285\pi\)
\(500\) 1.07674e6 0.192612
\(501\) 2.37021e6 0.421883
\(502\) −5.46812e6 −0.968454
\(503\) −7.34574e6 −1.29454 −0.647270 0.762260i \(-0.724090\pi\)
−0.647270 + 0.762260i \(0.724090\pi\)
\(504\) 1.75479e6 0.307715
\(505\) −52059.6 −0.00908390
\(506\) 2.19364e6 0.380881
\(507\) 7.87185e6 1.36006
\(508\) 1.57473e6 0.270737
\(509\) 1.37057e6 0.234480 0.117240 0.993104i \(-0.462595\pi\)
0.117240 + 0.993104i \(0.462595\pi\)
\(510\) 1.34989e6 0.229813
\(511\) −1.00274e7 −1.69878
\(512\) 2.14338e6 0.361346
\(513\) −1.54309e6 −0.258880
\(514\) −1.26709e7 −2.11544
\(515\) −794714. −0.132036
\(516\) −1.41977e6 −0.234744
\(517\) −337927. −0.0556028
\(518\) −2.03169e7 −3.32686
\(519\) −6.25753e6 −1.01973
\(520\) 1.39302e6 0.225917
\(521\) −1.52552e6 −0.246220 −0.123110 0.992393i \(-0.539287\pi\)
−0.123110 + 0.992393i \(0.539287\pi\)
\(522\) 2.53727e6 0.407559
\(523\) 4.78382e6 0.764751 0.382376 0.924007i \(-0.375106\pi\)
0.382376 + 0.924007i \(0.375106\pi\)
\(524\) −3.11768e6 −0.496025
\(525\) 5.22044e6 0.826625
\(526\) −87452.9 −0.0137819
\(527\) 1.75907e6 0.275903
\(528\) 1.44069e6 0.224899
\(529\) 1823.55 0.000283320 0
\(530\) −1.79439e6 −0.277478
\(531\) 281961. 0.0433963
\(532\) 6.45842e6 0.989343
\(533\) −9.43715e6 −1.43887
\(534\) 4.89189e6 0.742375
\(535\) 2.53021e6 0.382184
\(536\) 1.08634e6 0.163326
\(537\) 4.05215e6 0.606387
\(538\) −1.02711e6 −0.152989
\(539\) −2.57026e6 −0.381071
\(540\) −128132. −0.0189092
\(541\) 1.22324e7 1.79688 0.898440 0.439096i \(-0.144701\pi\)
0.898440 + 0.439096i \(0.144701\pi\)
\(542\) 6.50910e6 0.951749
\(543\) 2.60975e6 0.379839
\(544\) 1.02526e7 1.48538
\(545\) −220968. −0.0318667
\(546\) −1.34226e7 −1.92688
\(547\) 1.06742e7 1.52534 0.762669 0.646789i \(-0.223889\pi\)
0.762669 + 0.646789i \(0.223889\pi\)
\(548\) −3.86226e6 −0.549402
\(549\) −2.36222e6 −0.334495
\(550\) 2.59450e6 0.365719
\(551\) −9.59174e6 −1.34592
\(552\) 2.55958e6 0.357537
\(553\) 1.36868e7 1.90322
\(554\) 1.47448e7 2.04110
\(555\) −1.52378e6 −0.209985
\(556\) −3.22400e6 −0.442291
\(557\) 5.16477e6 0.705363 0.352682 0.935743i \(-0.385270\pi\)
0.352682 + 0.935743i \(0.385270\pi\)
\(558\) −505445. −0.0687208
\(559\) −1.11547e7 −1.50983
\(560\) −2.75456e6 −0.371179
\(561\) 2.19342e6 0.294248
\(562\) −6.15727e6 −0.822333
\(563\) −4.48550e6 −0.596403 −0.298201 0.954503i \(-0.596387\pi\)
−0.298201 + 0.954503i \(0.596387\pi\)
\(564\) 383882. 0.0508159
\(565\) −778289. −0.102570
\(566\) 5.65171e6 0.741547
\(567\) −1.26813e6 −0.165656
\(568\) 751844. 0.0977815
\(569\) 1.02493e7 1.32713 0.663566 0.748118i \(-0.269042\pi\)
0.663566 + 0.748118i \(0.269042\pi\)
\(570\) 1.46629e6 0.189031
\(571\) −7.69920e6 −0.988224 −0.494112 0.869398i \(-0.664507\pi\)
−0.494112 + 0.869398i \(0.664507\pi\)
\(572\) −2.20369e6 −0.281618
\(573\) −2.44882e6 −0.311580
\(574\) 1.12963e7 1.43105
\(575\) 7.61467e6 0.960465
\(576\) 371692. 0.0466795
\(577\) 1.53456e7 1.91887 0.959435 0.281929i \(-0.0909743\pi\)
0.959435 + 0.281929i \(0.0909743\pi\)
\(578\) 1.64354e7 2.04625
\(579\) −7.20369e6 −0.893014
\(580\) −796458. −0.0983089
\(581\) −6.18259e6 −0.759854
\(582\) 1.33530e6 0.163407
\(583\) −2.91568e6 −0.355278
\(584\) −5.81488e6 −0.705519
\(585\) −1.00670e6 −0.121621
\(586\) 4.21961e6 0.507607
\(587\) −1.11377e7 −1.33413 −0.667066 0.744999i \(-0.732450\pi\)
−0.667066 + 0.744999i \(0.732450\pi\)
\(588\) 2.91979e6 0.348264
\(589\) 1.91075e6 0.226943
\(590\) −267928. −0.0316875
\(591\) −5.75552e6 −0.677823
\(592\) −1.94630e7 −2.28247
\(593\) 2.86489e6 0.334558 0.167279 0.985910i \(-0.446502\pi\)
0.167279 + 0.985910i \(0.446502\pi\)
\(594\) −630248. −0.0732902
\(595\) −4.19375e6 −0.485635
\(596\) −6.47875e6 −0.747094
\(597\) 7.31619e6 0.840135
\(598\) −1.95785e7 −2.23886
\(599\) 5.10093e6 0.580874 0.290437 0.956894i \(-0.406199\pi\)
0.290437 + 0.956894i \(0.406199\pi\)
\(600\) 3.02731e6 0.343304
\(601\) 6.57438e6 0.742452 0.371226 0.928543i \(-0.378937\pi\)
0.371226 + 0.928543i \(0.378937\pi\)
\(602\) 1.33522e7 1.50163
\(603\) −785068. −0.0879254
\(604\) −6.13730e6 −0.684518
\(605\) 1.61904e6 0.179833
\(606\) 290890. 0.0321771
\(607\) −2.53033e6 −0.278744 −0.139372 0.990240i \(-0.544508\pi\)
−0.139372 + 0.990240i \(0.544508\pi\)
\(608\) 1.11367e7 1.22179
\(609\) −7.88260e6 −0.861244
\(610\) 2.24465e6 0.244244
\(611\) 3.01604e6 0.326839
\(612\) −2.49170e6 −0.268916
\(613\) −6.47911e6 −0.696409 −0.348204 0.937419i \(-0.613208\pi\)
−0.348204 + 0.937419i \(0.613208\pi\)
\(614\) −6.94191e6 −0.743118
\(615\) 847224. 0.0903255
\(616\) −2.70941e6 −0.287689
\(617\) 499984. 0.0528741 0.0264371 0.999650i \(-0.491584\pi\)
0.0264371 + 0.999650i \(0.491584\pi\)
\(618\) 4.44057e6 0.467700
\(619\) −2.37362e6 −0.248991 −0.124496 0.992220i \(-0.539731\pi\)
−0.124496 + 0.992220i \(0.539731\pi\)
\(620\) 158661. 0.0165764
\(621\) −1.84973e6 −0.192477
\(622\) −245097. −0.0254016
\(623\) −1.51977e7 −1.56877
\(624\) −1.28584e7 −1.32198
\(625\) 8.61875e6 0.882560
\(626\) −1.12927e7 −1.15176
\(627\) 2.38255e6 0.242032
\(628\) 5.30794e6 0.537065
\(629\) −2.96318e7 −2.98629
\(630\) 1.20502e6 0.120960
\(631\) 968968. 0.0968804 0.0484402 0.998826i \(-0.484575\pi\)
0.0484402 + 0.998826i \(0.484575\pi\)
\(632\) 7.93692e6 0.790422
\(633\) 1.21210e6 0.120235
\(634\) −4.29275e6 −0.424143
\(635\) −1.11072e6 −0.109313
\(636\) 3.31217e6 0.324691
\(637\) 2.29399e7 2.23998
\(638\) −3.91757e6 −0.381035
\(639\) −543335. −0.0526399
\(640\) −2.22778e6 −0.214992
\(641\) −1.30259e7 −1.25216 −0.626082 0.779757i \(-0.715343\pi\)
−0.626082 + 0.779757i \(0.715343\pi\)
\(642\) −1.41379e7 −1.35378
\(643\) 8.48030e6 0.808879 0.404440 0.914565i \(-0.367467\pi\)
0.404440 + 0.914565i \(0.367467\pi\)
\(644\) 7.74180e6 0.735576
\(645\) 1.00142e6 0.0947799
\(646\) 2.85140e7 2.68829
\(647\) −1.14711e7 −1.07732 −0.538660 0.842523i \(-0.681069\pi\)
−0.538660 + 0.842523i \(0.681069\pi\)
\(648\) −735386. −0.0687983
\(649\) −435350. −0.0405721
\(650\) −2.31563e7 −2.14974
\(651\) 1.57028e6 0.145219
\(652\) 4.73192e6 0.435931
\(653\) 1.41233e7 1.29614 0.648072 0.761579i \(-0.275575\pi\)
0.648072 + 0.761579i \(0.275575\pi\)
\(654\) 1.23469e6 0.112879
\(655\) 2.19902e6 0.200275
\(656\) 1.08215e7 0.981808
\(657\) 4.20224e6 0.379811
\(658\) −3.61021e6 −0.325063
\(659\) 4.29463e6 0.385223 0.192611 0.981275i \(-0.438304\pi\)
0.192611 + 0.981275i \(0.438304\pi\)
\(660\) 197837. 0.0176786
\(661\) 1.57272e7 1.40006 0.700032 0.714111i \(-0.253169\pi\)
0.700032 + 0.714111i \(0.253169\pi\)
\(662\) 1.90375e7 1.68836
\(663\) −1.95765e7 −1.72962
\(664\) −3.58526e6 −0.315574
\(665\) −4.55537e6 −0.399456
\(666\) 8.51430e6 0.743812
\(667\) −1.14978e7 −1.00069
\(668\) 4.15729e6 0.360470
\(669\) −8.30627e6 −0.717532
\(670\) 745995. 0.0642020
\(671\) 3.64729e6 0.312726
\(672\) 9.15225e6 0.781816
\(673\) −2.25572e6 −0.191976 −0.0959881 0.995382i \(-0.530601\pi\)
−0.0959881 + 0.995382i \(0.530601\pi\)
\(674\) 3.22851e6 0.273749
\(675\) −2.18775e6 −0.184815
\(676\) 1.38070e7 1.16207
\(677\) −1.19113e7 −0.998818 −0.499409 0.866366i \(-0.666449\pi\)
−0.499409 + 0.866366i \(0.666449\pi\)
\(678\) 4.34880e6 0.363325
\(679\) −4.14841e6 −0.345308
\(680\) −2.43194e6 −0.201688
\(681\) −8.42668e6 −0.696288
\(682\) 780412. 0.0642485
\(683\) 2.37444e7 1.94765 0.973823 0.227309i \(-0.0729926\pi\)
0.973823 + 0.227309i \(0.0729926\pi\)
\(684\) −2.70655e6 −0.221195
\(685\) 2.72420e6 0.221826
\(686\) −5.00304e6 −0.405905
\(687\) −1.02234e7 −0.826426
\(688\) 1.27910e7 1.03023
\(689\) 2.60228e7 2.08836
\(690\) 1.75767e6 0.140545
\(691\) −671726. −0.0535176 −0.0267588 0.999642i \(-0.508519\pi\)
−0.0267588 + 0.999642i \(0.508519\pi\)
\(692\) −1.09756e7 −0.871288
\(693\) 1.95801e6 0.154875
\(694\) 2.26538e7 1.78543
\(695\) 2.27401e6 0.178579
\(696\) −4.57109e6 −0.357682
\(697\) 1.64754e7 1.28456
\(698\) −2.71629e7 −2.11027
\(699\) −1.25700e7 −0.973067
\(700\) 9.15653e6 0.706294
\(701\) 7.09210e6 0.545105 0.272552 0.962141i \(-0.412132\pi\)
0.272552 + 0.962141i \(0.412132\pi\)
\(702\) 5.62505e6 0.430807
\(703\) −3.21869e7 −2.45635
\(704\) −573895. −0.0436416
\(705\) −270766. −0.0205174
\(706\) 2.30964e7 1.74395
\(707\) −903715. −0.0679959
\(708\) 494553. 0.0370792
\(709\) 1.22100e7 0.912222 0.456111 0.889923i \(-0.349242\pi\)
0.456111 + 0.889923i \(0.349242\pi\)
\(710\) 516293. 0.0384371
\(711\) −5.73577e6 −0.425518
\(712\) −8.81312e6 −0.651523
\(713\) 2.29045e6 0.168732
\(714\) 2.34331e7 1.72022
\(715\) 1.55435e6 0.113706
\(716\) 7.10738e6 0.518116
\(717\) 7.50021e6 0.544848
\(718\) −5.34184e6 −0.386705
\(719\) −1.62202e7 −1.17013 −0.585066 0.810986i \(-0.698931\pi\)
−0.585066 + 0.810986i \(0.698931\pi\)
\(720\) 1.15437e6 0.0829874
\(721\) −1.37956e7 −0.988333
\(722\) 1.38561e7 0.989234
\(723\) 1.14312e7 0.813292
\(724\) 4.57745e6 0.324547
\(725\) −1.35989e7 −0.960854
\(726\) −9.04661e6 −0.637007
\(727\) 2.20651e7 1.54835 0.774175 0.632972i \(-0.218165\pi\)
0.774175 + 0.632972i \(0.218165\pi\)
\(728\) 2.41818e7 1.69106
\(729\) 531441. 0.0370370
\(730\) −3.99309e6 −0.277333
\(731\) 1.94739e7 1.34790
\(732\) −4.14328e6 −0.285803
\(733\) −1.13061e7 −0.777233 −0.388617 0.921400i \(-0.627047\pi\)
−0.388617 + 0.921400i \(0.627047\pi\)
\(734\) −4.43077e6 −0.303556
\(735\) −2.05944e6 −0.140615
\(736\) 1.33497e7 0.908401
\(737\) 1.21215e6 0.0822032
\(738\) −4.73398e6 −0.319952
\(739\) 9.23997e6 0.622386 0.311193 0.950347i \(-0.399272\pi\)
0.311193 + 0.950347i \(0.399272\pi\)
\(740\) −2.67267e6 −0.179418
\(741\) −2.12646e7 −1.42269
\(742\) −3.11493e7 −2.07701
\(743\) 1.10636e7 0.735233 0.367617 0.929977i \(-0.380174\pi\)
0.367617 + 0.929977i \(0.380174\pi\)
\(744\) 910599. 0.0603107
\(745\) 4.56971e6 0.301646
\(746\) −1.63896e7 −1.07825
\(747\) 2.59096e6 0.169887
\(748\) 3.84720e6 0.251415
\(749\) 4.39226e7 2.86077
\(750\) 4.24360e6 0.275475
\(751\) −1.63941e6 −0.106069 −0.0530343 0.998593i \(-0.516889\pi\)
−0.0530343 + 0.998593i \(0.516889\pi\)
\(752\) −3.45846e6 −0.223017
\(753\) −7.11920e6 −0.457556
\(754\) 3.49648e7 2.23977
\(755\) 4.32887e6 0.276381
\(756\) −2.22428e6 −0.141542
\(757\) −3.02306e7 −1.91738 −0.958688 0.284461i \(-0.908185\pi\)
−0.958688 + 0.284461i \(0.908185\pi\)
\(758\) −1.79608e7 −1.13541
\(759\) 2.85600e6 0.179951
\(760\) −2.64164e6 −0.165898
\(761\) 2.90933e7 1.82109 0.910546 0.413408i \(-0.135662\pi\)
0.910546 + 0.413408i \(0.135662\pi\)
\(762\) 6.20629e6 0.387208
\(763\) −3.83583e6 −0.238533
\(764\) −4.29517e6 −0.266224
\(765\) 1.75749e6 0.108577
\(766\) −1.89346e7 −1.16596
\(767\) 3.88556e6 0.238487
\(768\) 1.11264e7 0.680695
\(769\) −6.83882e6 −0.417028 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(770\) −1.86056e6 −0.113088
\(771\) −1.64969e7 −0.999461
\(772\) −1.26351e7 −0.763019
\(773\) −2.33000e7 −1.40252 −0.701258 0.712907i \(-0.747378\pi\)
−0.701258 + 0.712907i \(0.747378\pi\)
\(774\) −5.59556e6 −0.335731
\(775\) 2.70900e6 0.162015
\(776\) −2.40565e6 −0.143409
\(777\) −2.64516e7 −1.57181
\(778\) 8.71420e6 0.516153
\(779\) 1.78960e7 1.05661
\(780\) −1.76572e6 −0.103917
\(781\) 838914. 0.0492141
\(782\) 3.41802e7 1.99874
\(783\) 3.30339e6 0.192555
\(784\) −2.63049e7 −1.52844
\(785\) −3.74389e6 −0.216845
\(786\) −1.22873e7 −0.709416
\(787\) −2.73298e7 −1.57290 −0.786448 0.617657i \(-0.788082\pi\)
−0.786448 + 0.617657i \(0.788082\pi\)
\(788\) −1.00951e7 −0.579153
\(789\) −113859. −0.00651141
\(790\) 5.45030e6 0.310708
\(791\) −1.35105e7 −0.767769
\(792\) 1.13544e6 0.0643209
\(793\) −3.25525e7 −1.83824
\(794\) 1.00947e6 0.0568255
\(795\) −2.33620e6 −0.131097
\(796\) 1.28324e7 0.717838
\(797\) 2.61123e7 1.45613 0.728064 0.685509i \(-0.240420\pi\)
0.728064 + 0.685509i \(0.240420\pi\)
\(798\) 2.54537e7 1.41496
\(799\) −5.26541e6 −0.291786
\(800\) 1.57892e7 0.872240
\(801\) 6.36898e6 0.350743
\(802\) −2.03885e7 −1.11931
\(803\) −6.48830e6 −0.355093
\(804\) −1.37699e6 −0.0751262
\(805\) −5.46059e6 −0.296996
\(806\) −6.96527e6 −0.377659
\(807\) −1.33724e6 −0.0722812
\(808\) −524061. −0.0282393
\(809\) 1.70399e7 0.915369 0.457684 0.889115i \(-0.348679\pi\)
0.457684 + 0.889115i \(0.348679\pi\)
\(810\) −504991. −0.0270440
\(811\) −1.19527e7 −0.638136 −0.319068 0.947732i \(-0.603370\pi\)
−0.319068 + 0.947732i \(0.603370\pi\)
\(812\) −1.38259e7 −0.735874
\(813\) 8.47450e6 0.449663
\(814\) −1.31462e7 −0.695405
\(815\) −3.33760e6 −0.176011
\(816\) 2.24481e7 1.18020
\(817\) 2.11531e7 1.10871
\(818\) 2.37597e7 1.24153
\(819\) −1.74755e7 −0.910372
\(820\) 1.48601e6 0.0771770
\(821\) −2.76018e7 −1.42915 −0.714577 0.699556i \(-0.753381\pi\)
−0.714577 + 0.699556i \(0.753381\pi\)
\(822\) −1.52218e7 −0.785755
\(823\) 1.60010e7 0.823472 0.411736 0.911303i \(-0.364923\pi\)
0.411736 + 0.911303i \(0.364923\pi\)
\(824\) −8.00004e6 −0.410463
\(825\) 3.37790e6 0.172788
\(826\) −4.65102e6 −0.237191
\(827\) 2.61565e7 1.32989 0.664945 0.746892i \(-0.268455\pi\)
0.664945 + 0.746892i \(0.268455\pi\)
\(828\) −3.24439e6 −0.164459
\(829\) 1.29226e7 0.653076 0.326538 0.945184i \(-0.394118\pi\)
0.326538 + 0.945184i \(0.394118\pi\)
\(830\) −2.46201e6 −0.124049
\(831\) 1.91969e7 0.964336
\(832\) 5.12209e6 0.256530
\(833\) −4.00485e7 −1.99974
\(834\) −1.27063e7 −0.632565
\(835\) −2.93229e6 −0.145543
\(836\) 4.17894e6 0.206800
\(837\) −658062. −0.0324678
\(838\) −4.48477e7 −2.20613
\(839\) −2.17442e7 −1.06644 −0.533222 0.845975i \(-0.679019\pi\)
−0.533222 + 0.845975i \(0.679019\pi\)
\(840\) −2.17093e6 −0.106157
\(841\) 22444.5 0.00109426
\(842\) −2.68867e7 −1.30695
\(843\) −8.01644e6 −0.388519
\(844\) 2.12600e6 0.102732
\(845\) −9.73864e6 −0.469198
\(846\) 1.51294e6 0.0726770
\(847\) 2.81053e7 1.34611
\(848\) −2.98400e7 −1.42498
\(849\) 7.35823e6 0.350351
\(850\) 4.04262e7 1.91918
\(851\) −3.85830e7 −1.82630
\(852\) −952997. −0.0449772
\(853\) −2.35835e7 −1.10978 −0.554888 0.831925i \(-0.687239\pi\)
−0.554888 + 0.831925i \(0.687239\pi\)
\(854\) 3.89654e7 1.82824
\(855\) 1.90904e6 0.0893097
\(856\) 2.54705e7 1.18810
\(857\) −1.24991e7 −0.581337 −0.290668 0.956824i \(-0.593878\pi\)
−0.290668 + 0.956824i \(0.593878\pi\)
\(858\) −8.68512e6 −0.402770
\(859\) 3.62400e7 1.67573 0.837867 0.545875i \(-0.183803\pi\)
0.837867 + 0.545875i \(0.183803\pi\)
\(860\) 1.75646e6 0.0809829
\(861\) 1.47072e7 0.676116
\(862\) 1.85738e6 0.0851400
\(863\) −1.92175e7 −0.878353 −0.439177 0.898401i \(-0.644730\pi\)
−0.439177 + 0.898401i \(0.644730\pi\)
\(864\) −3.83547e6 −0.174797
\(865\) 7.74149e6 0.351791
\(866\) −1.18452e7 −0.536719
\(867\) 2.13979e7 0.966773
\(868\) 2.75423e6 0.124080
\(869\) 8.85608e6 0.397825
\(870\) −3.13898e6 −0.140602
\(871\) −1.08186e7 −0.483199
\(872\) −2.22438e6 −0.0990646
\(873\) 1.73849e6 0.0772034
\(874\) 3.71275e7 1.64406
\(875\) −1.31837e7 −0.582126
\(876\) 7.37063e6 0.324522
\(877\) 2.97880e7 1.30780 0.653901 0.756580i \(-0.273131\pi\)
0.653901 + 0.756580i \(0.273131\pi\)
\(878\) 4.58356e6 0.200663
\(879\) 5.49370e6 0.239824
\(880\) −1.78235e6 −0.0775866
\(881\) 1.64782e7 0.715272 0.357636 0.933861i \(-0.383583\pi\)
0.357636 + 0.933861i \(0.383583\pi\)
\(882\) 1.15074e7 0.498088
\(883\) −1.95035e7 −0.841802 −0.420901 0.907106i \(-0.638286\pi\)
−0.420901 + 0.907106i \(0.638286\pi\)
\(884\) −3.43367e7 −1.47784
\(885\) −348827. −0.0149711
\(886\) −1.32755e7 −0.568153
\(887\) 2.38782e7 1.01904 0.509522 0.860457i \(-0.329822\pi\)
0.509522 + 0.860457i \(0.329822\pi\)
\(888\) −1.53392e7 −0.652784
\(889\) −1.92812e7 −0.818240
\(890\) −6.05199e6 −0.256108
\(891\) −820550. −0.0346267
\(892\) −1.45690e7 −0.613081
\(893\) −5.71944e6 −0.240007
\(894\) −2.55339e7 −1.06850
\(895\) −5.01311e6 −0.209194
\(896\) −3.86725e7 −1.60928
\(897\) −2.54902e7 −1.05777
\(898\) −4.43220e6 −0.183412
\(899\) −4.09046e6 −0.168800
\(900\) −3.83726e6 −0.157912
\(901\) −4.54305e7 −1.86439
\(902\) 7.30931e6 0.299130
\(903\) 1.73839e7 0.709458
\(904\) −7.83470e6 −0.318861
\(905\) −3.22865e6 −0.131039
\(906\) −2.41882e7 −0.978999
\(907\) 3.15297e7 1.27263 0.636315 0.771429i \(-0.280458\pi\)
0.636315 + 0.771429i \(0.280458\pi\)
\(908\) −1.47802e7 −0.594930
\(909\) 378723. 0.0152024
\(910\) 1.66057e7 0.664743
\(911\) −1.40130e7 −0.559418 −0.279709 0.960085i \(-0.590238\pi\)
−0.279709 + 0.960085i \(0.590238\pi\)
\(912\) 2.43838e7 0.970767
\(913\) −4.00047e6 −0.158831
\(914\) 1.94940e7 0.771856
\(915\) 2.92241e6 0.115395
\(916\) −1.79316e7 −0.706124
\(917\) 3.81733e7 1.49912
\(918\) −9.82020e6 −0.384604
\(919\) −3.77111e7 −1.47293 −0.736463 0.676478i \(-0.763505\pi\)
−0.736463 + 0.676478i \(0.763505\pi\)
\(920\) −3.16658e6 −0.123345
\(921\) −9.03799e6 −0.351094
\(922\) −3.02059e7 −1.17021
\(923\) −7.48741e6 −0.289286
\(924\) 3.43430e6 0.132330
\(925\) −4.56336e7 −1.75360
\(926\) 4.92692e6 0.188820
\(927\) 5.78139e6 0.220970
\(928\) −2.38409e7 −0.908769
\(929\) −2.22014e7 −0.843997 −0.421998 0.906597i \(-0.638671\pi\)
−0.421998 + 0.906597i \(0.638671\pi\)
\(930\) 625310. 0.0237076
\(931\) −4.35019e7 −1.64488
\(932\) −2.20475e7 −0.831418
\(933\) −319103. −0.0120012
\(934\) 1.39759e7 0.524219
\(935\) −2.71358e6 −0.101511
\(936\) −1.01340e7 −0.378085
\(937\) 3.15581e7 1.17425 0.587127 0.809495i \(-0.300259\pi\)
0.587127 + 0.809495i \(0.300259\pi\)
\(938\) 1.29499e7 0.480573
\(939\) −1.47025e7 −0.544159
\(940\) −474918. −0.0175307
\(941\) −1.61367e7 −0.594075 −0.297037 0.954866i \(-0.595999\pi\)
−0.297037 + 0.954866i \(0.595999\pi\)
\(942\) 2.09195e7 0.768111
\(943\) 2.14523e7 0.785586
\(944\) −4.45552e6 −0.162730
\(945\) 1.56887e6 0.0571487
\(946\) 8.63959e6 0.313881
\(947\) −5.18477e7 −1.87869 −0.939343 0.342978i \(-0.888564\pi\)
−0.939343 + 0.342978i \(0.888564\pi\)
\(948\) −1.00604e7 −0.363576
\(949\) 5.79088e7 2.08727
\(950\) 4.39121e7 1.57861
\(951\) −5.58893e6 −0.200390
\(952\) −4.22166e7 −1.50970
\(953\) 3.02972e7 1.08061 0.540307 0.841468i \(-0.318308\pi\)
0.540307 + 0.841468i \(0.318308\pi\)
\(954\) 1.30539e7 0.464374
\(955\) 3.02955e6 0.107490
\(956\) 1.31552e7 0.465535
\(957\) −5.10047e6 −0.180024
\(958\) 3.85526e7 1.35719
\(959\) 4.72900e7 1.66044
\(960\) −459837. −0.0161037
\(961\) −2.78143e7 −0.971538
\(962\) 1.17331e8 4.08766
\(963\) −1.84068e7 −0.639606
\(964\) 2.00501e7 0.694902
\(965\) 8.91202e6 0.308076
\(966\) 3.05118e7 1.05202
\(967\) 1.15030e7 0.395591 0.197795 0.980243i \(-0.436622\pi\)
0.197795 + 0.980243i \(0.436622\pi\)
\(968\) 1.62982e7 0.559050
\(969\) 3.71237e7 1.27011
\(970\) −1.65196e6 −0.0563730
\(971\) −1.92341e7 −0.654673 −0.327336 0.944908i \(-0.606151\pi\)
−0.327336 + 0.944908i \(0.606151\pi\)
\(972\) 932135. 0.0316456
\(973\) 3.94751e7 1.33672
\(974\) −9.12417e6 −0.308174
\(975\) −3.01482e7 −1.01566
\(976\) 3.73275e7 1.25431
\(977\) −7.41320e6 −0.248467 −0.124234 0.992253i \(-0.539647\pi\)
−0.124234 + 0.992253i \(0.539647\pi\)
\(978\) 1.86493e7 0.623470
\(979\) −9.83376e6 −0.327916
\(980\) −3.61221e6 −0.120146
\(981\) 1.60750e6 0.0533307
\(982\) 3.71081e7 1.22798
\(983\) −4.98279e7 −1.64471 −0.822354 0.568976i \(-0.807340\pi\)
−0.822354 + 0.568976i \(0.807340\pi\)
\(984\) 8.52863e6 0.280797
\(985\) 7.12043e6 0.233838
\(986\) −6.10415e7 −1.99955
\(987\) −4.70030e6 −0.153579
\(988\) −3.72976e7 −1.21559
\(989\) 2.53565e7 0.824327
\(990\) 779710. 0.0252840
\(991\) 3.87158e7 1.25229 0.626144 0.779708i \(-0.284632\pi\)
0.626144 + 0.779708i \(0.284632\pi\)
\(992\) 4.74931e6 0.153233
\(993\) 2.47858e7 0.797681
\(994\) 8.96244e6 0.287714
\(995\) −9.05121e6 −0.289834
\(996\) 4.54449e6 0.145157
\(997\) 1.92043e7 0.611873 0.305937 0.952052i \(-0.401030\pi\)
0.305937 + 0.952052i \(0.401030\pi\)
\(998\) −9.22708e6 −0.293250
\(999\) 1.10852e7 0.351421
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.1.9 11
3.2 odd 2 531.6.a.b.1.3 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.9 11 1.1 even 1 trivial
531.6.a.b.1.3 11 3.2 odd 2