Properties

Label 165.4.a.c.1.1
Level $165$
Weight $4$
Character 165.1
Self dual yes
Analytic conductor $9.735$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 165.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.73531515095\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \( x^{2} - x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 165.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} -7.68466 q^{6} +6.24621 q^{7} +24.1771 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} -7.68466 q^{6} +6.24621 q^{7} +24.1771 q^{8} +9.00000 q^{9} +12.8078 q^{10} -11.0000 q^{11} -4.31534 q^{12} -49.1231 q^{13} -16.0000 q^{14} -15.0000 q^{15} -50.4233 q^{16} +82.7083 q^{17} -23.0540 q^{18} -130.354 q^{19} +7.19224 q^{20} +18.7386 q^{21} +28.1771 q^{22} -185.693 q^{23} +72.5312 q^{24} +25.0000 q^{25} +125.831 q^{26} +27.0000 q^{27} -8.98485 q^{28} -8.90720 q^{29} +38.4233 q^{30} +5.26137 q^{31} -64.2547 q^{32} -33.0000 q^{33} -211.862 q^{34} -31.2311 q^{35} -12.9460 q^{36} -416.894 q^{37} +333.909 q^{38} -147.369 q^{39} -120.885 q^{40} -298.479 q^{41} -48.0000 q^{42} -513.633 q^{43} +15.8229 q^{44} -45.0000 q^{45} +475.663 q^{46} +557.295 q^{47} -151.270 q^{48} -303.985 q^{49} -64.0388 q^{50} +248.125 q^{51} +70.6610 q^{52} -168.064 q^{53} -69.1619 q^{54} +55.0000 q^{55} +151.015 q^{56} -391.062 q^{57} +22.8163 q^{58} +618.773 q^{59} +21.5767 q^{60} +786.405 q^{61} -13.4773 q^{62} +56.2159 q^{63} +567.978 q^{64} +245.616 q^{65} +84.5312 q^{66} -339.015 q^{67} -118.972 q^{68} -557.080 q^{69} +80.0000 q^{70} +1120.71 q^{71} +217.594 q^{72} -123.430 q^{73} +1067.90 q^{74} +75.0000 q^{75} +187.508 q^{76} -68.7083 q^{77} +377.494 q^{78} -309.835 q^{79} +252.116 q^{80} +81.0000 q^{81} +764.570 q^{82} -1021.22 q^{83} -26.9545 q^{84} -413.542 q^{85} +1315.70 q^{86} -26.7216 q^{87} -265.948 q^{88} -141.879 q^{89} +115.270 q^{90} -306.833 q^{91} +267.110 q^{92} +15.7841 q^{93} -1427.54 q^{94} +651.771 q^{95} -192.764 q^{96} +798.345 q^{97} +778.673 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} - 3 q^{6} - 4 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} - 3 q^{6} - 4 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{10} - 22 q^{11} - 21 q^{12} - 90 q^{13} - 32 q^{14} - 30 q^{15} - 39 q^{16} - 16 q^{17} - 9 q^{18} - 170 q^{19} + 35 q^{20} - 12 q^{21} + 11 q^{22} - 124 q^{23} + 9 q^{24} + 50 q^{25} + 62 q^{26} + 54 q^{27} + 48 q^{28} - 158 q^{29} + 15 q^{30} + 60 q^{31} + 123 q^{32} - 66 q^{33} - 366 q^{34} + 20 q^{35} - 63 q^{36} - 372 q^{37} + 272 q^{38} - 270 q^{39} - 15 q^{40} + 38 q^{41} - 96 q^{42} - 516 q^{43} + 77 q^{44} - 90 q^{45} + 572 q^{46} + 224 q^{47} - 117 q^{48} - 542 q^{49} - 25 q^{50} - 48 q^{51} + 298 q^{52} + 472 q^{53} - 27 q^{54} + 110 q^{55} + 368 q^{56} - 510 q^{57} - 210 q^{58} + 248 q^{59} + 105 q^{60} + 72 q^{61} + 72 q^{62} - 36 q^{63} + 769 q^{64} + 450 q^{65} + 33 q^{66} - 744 q^{67} + 430 q^{68} - 372 q^{69} + 160 q^{70} + 2060 q^{71} + 27 q^{72} - 486 q^{73} + 1138 q^{74} + 150 q^{75} + 408 q^{76} + 44 q^{77} + 186 q^{78} + 642 q^{79} + 195 q^{80} + 162 q^{81} + 1290 q^{82} - 286 q^{83} + 144 q^{84} + 80 q^{85} + 1312 q^{86} - 474 q^{87} - 33 q^{88} + 244 q^{89} + 45 q^{90} + 112 q^{91} - 76 q^{92} + 180 q^{93} - 1948 q^{94} + 850 q^{95} + 369 q^{96} - 168 q^{97} + 407 q^{98} - 198 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56155 −0.905646 −0.452823 0.891601i \(-0.649583\pi\)
−0.452823 + 0.891601i \(0.649583\pi\)
\(3\) 3.00000 0.577350
\(4\) −1.43845 −0.179806
\(5\) −5.00000 −0.447214
\(6\) −7.68466 −0.522875
\(7\) 6.24621 0.337264 0.168632 0.985679i \(-0.446065\pi\)
0.168632 + 0.985679i \(0.446065\pi\)
\(8\) 24.1771 1.06849
\(9\) 9.00000 0.333333
\(10\) 12.8078 0.405017
\(11\) −11.0000 −0.301511
\(12\) −4.31534 −0.103811
\(13\) −49.1231 −1.04802 −0.524011 0.851711i \(-0.675565\pi\)
−0.524011 + 0.851711i \(0.675565\pi\)
\(14\) −16.0000 −0.305441
\(15\) −15.0000 −0.258199
\(16\) −50.4233 −0.787864
\(17\) 82.7083 1.17998 0.589992 0.807409i \(-0.299131\pi\)
0.589992 + 0.807409i \(0.299131\pi\)
\(18\) −23.0540 −0.301882
\(19\) −130.354 −1.57396 −0.786981 0.616977i \(-0.788357\pi\)
−0.786981 + 0.616977i \(0.788357\pi\)
\(20\) 7.19224 0.0804116
\(21\) 18.7386 0.194719
\(22\) 28.1771 0.273062
\(23\) −185.693 −1.68347 −0.841733 0.539895i \(-0.818464\pi\)
−0.841733 + 0.539895i \(0.818464\pi\)
\(24\) 72.5312 0.616891
\(25\) 25.0000 0.200000
\(26\) 125.831 0.949137
\(27\) 27.0000 0.192450
\(28\) −8.98485 −0.0606420
\(29\) −8.90720 −0.0570354 −0.0285177 0.999593i \(-0.509079\pi\)
−0.0285177 + 0.999593i \(0.509079\pi\)
\(30\) 38.4233 0.233837
\(31\) 5.26137 0.0304829 0.0152414 0.999884i \(-0.495148\pi\)
0.0152414 + 0.999884i \(0.495148\pi\)
\(32\) −64.2547 −0.354961
\(33\) −33.0000 −0.174078
\(34\) −211.862 −1.06865
\(35\) −31.2311 −0.150829
\(36\) −12.9460 −0.0599353
\(37\) −416.894 −1.85235 −0.926175 0.377094i \(-0.876923\pi\)
−0.926175 + 0.377094i \(0.876923\pi\)
\(38\) 333.909 1.42545
\(39\) −147.369 −0.605076
\(40\) −120.885 −0.477842
\(41\) −298.479 −1.13694 −0.568471 0.822703i \(-0.692465\pi\)
−0.568471 + 0.822703i \(0.692465\pi\)
\(42\) −48.0000 −0.176347
\(43\) −513.633 −1.82159 −0.910793 0.412863i \(-0.864529\pi\)
−0.910793 + 0.412863i \(0.864529\pi\)
\(44\) 15.8229 0.0542135
\(45\) −45.0000 −0.149071
\(46\) 475.663 1.52462
\(47\) 557.295 1.72957 0.864786 0.502140i \(-0.167454\pi\)
0.864786 + 0.502140i \(0.167454\pi\)
\(48\) −151.270 −0.454873
\(49\) −303.985 −0.886253
\(50\) −64.0388 −0.181129
\(51\) 248.125 0.681264
\(52\) 70.6610 0.188441
\(53\) −168.064 −0.435574 −0.217787 0.975996i \(-0.569884\pi\)
−0.217787 + 0.975996i \(0.569884\pi\)
\(54\) −69.1619 −0.174292
\(55\) 55.0000 0.134840
\(56\) 151.015 0.360362
\(57\) −391.062 −0.908728
\(58\) 22.8163 0.0516539
\(59\) 618.773 1.36538 0.682689 0.730709i \(-0.260810\pi\)
0.682689 + 0.730709i \(0.260810\pi\)
\(60\) 21.5767 0.0464257
\(61\) 786.405 1.65064 0.825319 0.564667i \(-0.190996\pi\)
0.825319 + 0.564667i \(0.190996\pi\)
\(62\) −13.4773 −0.0276067
\(63\) 56.2159 0.112421
\(64\) 567.978 1.10933
\(65\) 245.616 0.468690
\(66\) 84.5312 0.157653
\(67\) −339.015 −0.618169 −0.309084 0.951035i \(-0.600023\pi\)
−0.309084 + 0.951035i \(0.600023\pi\)
\(68\) −118.972 −0.212168
\(69\) −557.080 −0.971949
\(70\) 80.0000 0.136598
\(71\) 1120.71 1.87329 0.936645 0.350280i \(-0.113913\pi\)
0.936645 + 0.350280i \(0.113913\pi\)
\(72\) 217.594 0.356162
\(73\) −123.430 −0.197896 −0.0989478 0.995093i \(-0.531548\pi\)
−0.0989478 + 0.995093i \(0.531548\pi\)
\(74\) 1067.90 1.67757
\(75\) 75.0000 0.115470
\(76\) 187.508 0.283008
\(77\) −68.7083 −0.101689
\(78\) 377.494 0.547985
\(79\) −309.835 −0.441255 −0.220628 0.975358i \(-0.570811\pi\)
−0.220628 + 0.975358i \(0.570811\pi\)
\(80\) 252.116 0.352343
\(81\) 81.0000 0.111111
\(82\) 764.570 1.02967
\(83\) −1021.22 −1.35053 −0.675263 0.737577i \(-0.735970\pi\)
−0.675263 + 0.737577i \(0.735970\pi\)
\(84\) −26.9545 −0.0350117
\(85\) −413.542 −0.527705
\(86\) 1315.70 1.64971
\(87\) −26.7216 −0.0329294
\(88\) −265.948 −0.322161
\(89\) −141.879 −0.168979 −0.0844894 0.996424i \(-0.526926\pi\)
−0.0844894 + 0.996424i \(0.526926\pi\)
\(90\) 115.270 0.135006
\(91\) −306.833 −0.353460
\(92\) 267.110 0.302697
\(93\) 15.7841 0.0175993
\(94\) −1427.54 −1.56638
\(95\) 651.771 0.703898
\(96\) −192.764 −0.204937
\(97\) 798.345 0.835666 0.417833 0.908524i \(-0.362790\pi\)
0.417833 + 0.908524i \(0.362790\pi\)
\(98\) 778.673 0.802631
\(99\) −99.0000 −0.100504
\(100\) −35.9612 −0.0359612
\(101\) 241.400 0.237823 0.118912 0.992905i \(-0.462059\pi\)
0.118912 + 0.992905i \(0.462059\pi\)
\(102\) −635.585 −0.616983
\(103\) 1168.38 1.11771 0.558853 0.829267i \(-0.311242\pi\)
0.558853 + 0.829267i \(0.311242\pi\)
\(104\) −1187.65 −1.11980
\(105\) −93.6932 −0.0870811
\(106\) 430.506 0.394476
\(107\) −2106.82 −1.90350 −0.951748 0.306882i \(-0.900714\pi\)
−0.951748 + 0.306882i \(0.900714\pi\)
\(108\) −38.8381 −0.0346037
\(109\) 493.792 0.433914 0.216957 0.976181i \(-0.430387\pi\)
0.216957 + 0.976181i \(0.430387\pi\)
\(110\) −140.885 −0.122117
\(111\) −1250.68 −1.06945
\(112\) −314.955 −0.265718
\(113\) 170.000 0.141524 0.0707622 0.997493i \(-0.477457\pi\)
0.0707622 + 0.997493i \(0.477457\pi\)
\(114\) 1001.73 0.822986
\(115\) 928.466 0.752869
\(116\) 12.8125 0.0102553
\(117\) −442.108 −0.349341
\(118\) −1585.02 −1.23655
\(119\) 516.614 0.397966
\(120\) −362.656 −0.275882
\(121\) 121.000 0.0909091
\(122\) −2014.42 −1.49489
\(123\) −895.437 −0.656414
\(124\) −7.56820 −0.00548100
\(125\) −125.000 −0.0894427
\(126\) −144.000 −0.101814
\(127\) −948.182 −0.662500 −0.331250 0.943543i \(-0.607470\pi\)
−0.331250 + 0.943543i \(0.607470\pi\)
\(128\) −940.868 −0.649702
\(129\) −1540.90 −1.05169
\(130\) −629.157 −0.424467
\(131\) −1484.84 −0.990312 −0.495156 0.868804i \(-0.664889\pi\)
−0.495156 + 0.868804i \(0.664889\pi\)
\(132\) 47.4688 0.0313002
\(133\) −814.220 −0.530841
\(134\) 868.405 0.559842
\(135\) −135.000 −0.0860663
\(136\) 1999.65 1.26080
\(137\) 684.928 0.427134 0.213567 0.976928i \(-0.431492\pi\)
0.213567 + 0.976928i \(0.431492\pi\)
\(138\) 1426.99 0.880242
\(139\) 830.483 0.506767 0.253384 0.967366i \(-0.418457\pi\)
0.253384 + 0.967366i \(0.418457\pi\)
\(140\) 44.9242 0.0271199
\(141\) 1671.89 0.998569
\(142\) −2870.75 −1.69654
\(143\) 540.354 0.315991
\(144\) −453.810 −0.262621
\(145\) 44.5360 0.0255070
\(146\) 316.172 0.179223
\(147\) −911.955 −0.511679
\(148\) 599.680 0.333063
\(149\) −1213.64 −0.667285 −0.333642 0.942700i \(-0.608278\pi\)
−0.333642 + 0.942700i \(0.608278\pi\)
\(150\) −192.116 −0.104575
\(151\) 30.8466 0.0166242 0.00831212 0.999965i \(-0.497354\pi\)
0.00831212 + 0.999965i \(0.497354\pi\)
\(152\) −3151.58 −1.68176
\(153\) 744.375 0.393328
\(154\) 176.000 0.0920941
\(155\) −26.3068 −0.0136324
\(156\) 211.983 0.108796
\(157\) 345.239 0.175497 0.0877485 0.996143i \(-0.472033\pi\)
0.0877485 + 0.996143i \(0.472033\pi\)
\(158\) 793.659 0.399621
\(159\) −504.193 −0.251479
\(160\) 321.274 0.158743
\(161\) −1159.88 −0.567772
\(162\) −207.486 −0.100627
\(163\) 1921.49 0.923331 0.461665 0.887054i \(-0.347252\pi\)
0.461665 + 0.887054i \(0.347252\pi\)
\(164\) 429.346 0.204429
\(165\) 165.000 0.0778499
\(166\) 2615.91 1.22310
\(167\) 172.297 0.0798369 0.0399185 0.999203i \(-0.487290\pi\)
0.0399185 + 0.999203i \(0.487290\pi\)
\(168\) 453.045 0.208055
\(169\) 216.080 0.0983521
\(170\) 1059.31 0.477913
\(171\) −1173.19 −0.524654
\(172\) 738.833 0.327532
\(173\) −1025.29 −0.450587 −0.225293 0.974291i \(-0.572334\pi\)
−0.225293 + 0.974291i \(0.572334\pi\)
\(174\) 68.4488 0.0298224
\(175\) 156.155 0.0674527
\(176\) 554.656 0.237550
\(177\) 1856.32 0.788302
\(178\) 363.430 0.153035
\(179\) 1658.29 0.692437 0.346219 0.938154i \(-0.387466\pi\)
0.346219 + 0.938154i \(0.387466\pi\)
\(180\) 64.7301 0.0268039
\(181\) −2021.81 −0.830275 −0.415137 0.909759i \(-0.636266\pi\)
−0.415137 + 0.909759i \(0.636266\pi\)
\(182\) 785.970 0.320110
\(183\) 2359.22 0.952996
\(184\) −4489.52 −1.79876
\(185\) 2084.47 0.828396
\(186\) −40.4318 −0.0159387
\(187\) −909.792 −0.355778
\(188\) −801.640 −0.310987
\(189\) 168.648 0.0649064
\(190\) −1669.55 −0.637482
\(191\) 1440.22 0.545607 0.272803 0.962070i \(-0.412049\pi\)
0.272803 + 0.962070i \(0.412049\pi\)
\(192\) 1703.93 0.640473
\(193\) −2798.05 −1.04356 −0.521782 0.853079i \(-0.674733\pi\)
−0.521782 + 0.853079i \(0.674733\pi\)
\(194\) −2045.00 −0.756817
\(195\) 736.847 0.270598
\(196\) 437.266 0.159354
\(197\) 458.943 0.165982 0.0829908 0.996550i \(-0.473553\pi\)
0.0829908 + 0.996550i \(0.473553\pi\)
\(198\) 253.594 0.0910208
\(199\) −2371.04 −0.844615 −0.422308 0.906453i \(-0.638780\pi\)
−0.422308 + 0.906453i \(0.638780\pi\)
\(200\) 604.427 0.213697
\(201\) −1017.05 −0.356900
\(202\) −618.358 −0.215384
\(203\) −55.6363 −0.0192360
\(204\) −356.915 −0.122495
\(205\) 1492.40 0.508456
\(206\) −2992.86 −1.01225
\(207\) −1671.24 −0.561155
\(208\) 2476.95 0.825699
\(209\) 1433.90 0.474568
\(210\) 240.000 0.0788646
\(211\) 4319.87 1.40944 0.704721 0.709484i \(-0.251072\pi\)
0.704721 + 0.709484i \(0.251072\pi\)
\(212\) 241.752 0.0783187
\(213\) 3362.12 1.08154
\(214\) 5396.73 1.72389
\(215\) 2568.16 0.814638
\(216\) 652.781 0.205630
\(217\) 32.8636 0.0102808
\(218\) −1264.87 −0.392973
\(219\) −370.290 −0.114255
\(220\) −79.1146 −0.0242450
\(221\) −4062.89 −1.23665
\(222\) 3203.69 0.968547
\(223\) −3837.73 −1.15244 −0.576219 0.817295i \(-0.695473\pi\)
−0.576219 + 0.817295i \(0.695473\pi\)
\(224\) −401.349 −0.119715
\(225\) 225.000 0.0666667
\(226\) −435.464 −0.128171
\(227\) −5003.71 −1.46303 −0.731515 0.681825i \(-0.761187\pi\)
−0.731515 + 0.681825i \(0.761187\pi\)
\(228\) 562.523 0.163395
\(229\) −277.375 −0.0800412 −0.0400206 0.999199i \(-0.512742\pi\)
−0.0400206 + 0.999199i \(0.512742\pi\)
\(230\) −2378.31 −0.681832
\(231\) −206.125 −0.0587101
\(232\) −215.350 −0.0609415
\(233\) 2269.91 0.638225 0.319113 0.947717i \(-0.396615\pi\)
0.319113 + 0.947717i \(0.396615\pi\)
\(234\) 1132.48 0.316379
\(235\) −2786.48 −0.773488
\(236\) −890.072 −0.245503
\(237\) −929.505 −0.254759
\(238\) −1323.33 −0.360416
\(239\) −1617.11 −0.437665 −0.218832 0.975762i \(-0.570225\pi\)
−0.218832 + 0.975762i \(0.570225\pi\)
\(240\) 756.349 0.203426
\(241\) 5646.63 1.50926 0.754629 0.656151i \(-0.227817\pi\)
0.754629 + 0.656151i \(0.227817\pi\)
\(242\) −309.948 −0.0823314
\(243\) 243.000 0.0641500
\(244\) −1131.20 −0.296794
\(245\) 1519.92 0.396344
\(246\) 2293.71 0.594478
\(247\) 6403.40 1.64955
\(248\) 127.204 0.0325705
\(249\) −3063.66 −0.779726
\(250\) 320.194 0.0810034
\(251\) −6217.61 −1.56355 −0.781777 0.623558i \(-0.785687\pi\)
−0.781777 + 0.623558i \(0.785687\pi\)
\(252\) −80.8636 −0.0202140
\(253\) 2042.62 0.507584
\(254\) 2428.82 0.599991
\(255\) −1240.62 −0.304670
\(256\) −2133.74 −0.520933
\(257\) 7712.75 1.87202 0.936008 0.351980i \(-0.114491\pi\)
0.936008 + 0.351980i \(0.114491\pi\)
\(258\) 3947.09 0.952462
\(259\) −2604.01 −0.624730
\(260\) −353.305 −0.0842732
\(261\) −80.1648 −0.0190118
\(262\) 3803.49 0.896871
\(263\) 206.347 0.0483798 0.0241899 0.999707i \(-0.492299\pi\)
0.0241899 + 0.999707i \(0.492299\pi\)
\(264\) −797.844 −0.186000
\(265\) 840.322 0.194795
\(266\) 2085.67 0.480753
\(267\) −425.636 −0.0975600
\(268\) 487.655 0.111150
\(269\) 1712.47 0.388146 0.194073 0.980987i \(-0.437830\pi\)
0.194073 + 0.980987i \(0.437830\pi\)
\(270\) 345.810 0.0779456
\(271\) −477.081 −0.106940 −0.0534698 0.998569i \(-0.517028\pi\)
−0.0534698 + 0.998569i \(0.517028\pi\)
\(272\) −4170.43 −0.929666
\(273\) −920.500 −0.204070
\(274\) −1754.48 −0.386832
\(275\) −275.000 −0.0603023
\(276\) 801.329 0.174762
\(277\) 4283.48 0.929130 0.464565 0.885539i \(-0.346211\pi\)
0.464565 + 0.885539i \(0.346211\pi\)
\(278\) −2127.33 −0.458952
\(279\) 47.3523 0.0101610
\(280\) −755.076 −0.161159
\(281\) 3477.79 0.738319 0.369160 0.929366i \(-0.379646\pi\)
0.369160 + 0.929366i \(0.379646\pi\)
\(282\) −4282.62 −0.904350
\(283\) −6568.27 −1.37966 −0.689829 0.723973i \(-0.742314\pi\)
−0.689829 + 0.723973i \(0.742314\pi\)
\(284\) −1612.08 −0.336829
\(285\) 1955.31 0.406395
\(286\) −1384.15 −0.286176
\(287\) −1864.36 −0.383449
\(288\) −578.292 −0.118320
\(289\) 1927.67 0.392360
\(290\) −114.081 −0.0231003
\(291\) 2395.03 0.482472
\(292\) 177.547 0.0355828
\(293\) 8352.29 1.66534 0.832672 0.553766i \(-0.186810\pi\)
0.832672 + 0.553766i \(0.186810\pi\)
\(294\) 2336.02 0.463399
\(295\) −3093.86 −0.610616
\(296\) −10079.3 −1.97921
\(297\) −297.000 −0.0580259
\(298\) 3108.81 0.604324
\(299\) 9121.83 1.76431
\(300\) −107.884 −0.0207622
\(301\) −3208.26 −0.614355
\(302\) −79.0152 −0.0150557
\(303\) 724.199 0.137307
\(304\) 6572.89 1.24007
\(305\) −3932.03 −0.738187
\(306\) −1906.76 −0.356216
\(307\) 5383.89 1.00090 0.500448 0.865767i \(-0.333169\pi\)
0.500448 + 0.865767i \(0.333169\pi\)
\(308\) 98.8333 0.0182843
\(309\) 3505.14 0.645308
\(310\) 67.3863 0.0123461
\(311\) −1790.41 −0.326447 −0.163223 0.986589i \(-0.552189\pi\)
−0.163223 + 0.986589i \(0.552189\pi\)
\(312\) −3562.96 −0.646516
\(313\) −809.076 −0.146108 −0.0730538 0.997328i \(-0.523274\pi\)
−0.0730538 + 0.997328i \(0.523274\pi\)
\(314\) −884.347 −0.158938
\(315\) −281.080 −0.0502763
\(316\) 445.682 0.0793403
\(317\) 10744.5 1.90370 0.951849 0.306567i \(-0.0991804\pi\)
0.951849 + 0.306567i \(0.0991804\pi\)
\(318\) 1291.52 0.227751
\(319\) 97.9792 0.0171968
\(320\) −2839.89 −0.496109
\(321\) −6320.46 −1.09898
\(322\) 2971.09 0.514200
\(323\) −10781.4 −1.85725
\(324\) −116.514 −0.0199784
\(325\) −1228.08 −0.209605
\(326\) −4922.00 −0.836210
\(327\) 1481.37 0.250521
\(328\) −7216.35 −1.21481
\(329\) 3480.98 0.583322
\(330\) −422.656 −0.0705044
\(331\) 3399.12 0.564449 0.282224 0.959348i \(-0.408928\pi\)
0.282224 + 0.959348i \(0.408928\pi\)
\(332\) 1468.97 0.242832
\(333\) −3752.05 −0.617450
\(334\) −441.349 −0.0723039
\(335\) 1695.08 0.276453
\(336\) −944.864 −0.153412
\(337\) −11840.0 −1.91384 −0.956919 0.290356i \(-0.906226\pi\)
−0.956919 + 0.290356i \(0.906226\pi\)
\(338\) −553.499 −0.0890721
\(339\) 510.000 0.0817091
\(340\) 594.858 0.0948844
\(341\) −57.8750 −0.00919093
\(342\) 3005.18 0.475151
\(343\) −4041.20 −0.636165
\(344\) −12418.1 −1.94634
\(345\) 2785.40 0.434669
\(346\) 2626.34 0.408072
\(347\) −2076.67 −0.321272 −0.160636 0.987014i \(-0.551355\pi\)
−0.160636 + 0.987014i \(0.551355\pi\)
\(348\) 38.4376 0.00592090
\(349\) 5837.37 0.895322 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(350\) −400.000 −0.0610883
\(351\) −1326.32 −0.201692
\(352\) 706.802 0.107025
\(353\) −2423.64 −0.365431 −0.182715 0.983166i \(-0.558489\pi\)
−0.182715 + 0.983166i \(0.558489\pi\)
\(354\) −4755.06 −0.713922
\(355\) −5603.54 −0.837761
\(356\) 204.085 0.0303834
\(357\) 1549.84 0.229765
\(358\) −4247.79 −0.627103
\(359\) −3882.22 −0.570740 −0.285370 0.958417i \(-0.592116\pi\)
−0.285370 + 0.958417i \(0.592116\pi\)
\(360\) −1087.97 −0.159281
\(361\) 10133.2 1.47736
\(362\) 5178.96 0.751935
\(363\) 363.000 0.0524864
\(364\) 441.363 0.0635542
\(365\) 617.150 0.0885016
\(366\) −6043.26 −0.863077
\(367\) 5666.65 0.805986 0.402993 0.915203i \(-0.367970\pi\)
0.402993 + 0.915203i \(0.367970\pi\)
\(368\) 9363.26 1.32634
\(369\) −2686.31 −0.378981
\(370\) −5339.48 −0.750233
\(371\) −1049.77 −0.146903
\(372\) −22.7046 −0.00316446
\(373\) 174.771 0.0242608 0.0121304 0.999926i \(-0.496139\pi\)
0.0121304 + 0.999926i \(0.496139\pi\)
\(374\) 2330.48 0.322209
\(375\) −375.000 −0.0516398
\(376\) 13473.8 1.84802
\(377\) 437.550 0.0597744
\(378\) −432.000 −0.0587822
\(379\) 252.686 0.0342470 0.0171235 0.999853i \(-0.494549\pi\)
0.0171235 + 0.999853i \(0.494549\pi\)
\(380\) −937.538 −0.126565
\(381\) −2844.55 −0.382495
\(382\) −3689.21 −0.494126
\(383\) −11014.5 −1.46950 −0.734748 0.678340i \(-0.762700\pi\)
−0.734748 + 0.678340i \(0.762700\pi\)
\(384\) −2822.61 −0.375105
\(385\) 343.542 0.0454766
\(386\) 7167.35 0.945099
\(387\) −4622.69 −0.607196
\(388\) −1148.38 −0.150258
\(389\) 8099.40 1.05567 0.527835 0.849347i \(-0.323004\pi\)
0.527835 + 0.849347i \(0.323004\pi\)
\(390\) −1887.47 −0.245066
\(391\) −15358.4 −1.98646
\(392\) −7349.47 −0.946949
\(393\) −4454.51 −0.571757
\(394\) −1175.61 −0.150320
\(395\) 1549.18 0.197335
\(396\) 142.406 0.0180712
\(397\) −424.353 −0.0536465 −0.0268232 0.999640i \(-0.508539\pi\)
−0.0268232 + 0.999640i \(0.508539\pi\)
\(398\) 6073.54 0.764922
\(399\) −2442.66 −0.306481
\(400\) −1260.58 −0.157573
\(401\) −5904.18 −0.735263 −0.367632 0.929972i \(-0.619831\pi\)
−0.367632 + 0.929972i \(0.619831\pi\)
\(402\) 2605.22 0.323225
\(403\) −258.455 −0.0319468
\(404\) −347.241 −0.0427620
\(405\) −405.000 −0.0496904
\(406\) 142.515 0.0174210
\(407\) 4585.83 0.558504
\(408\) 5998.94 0.727921
\(409\) 1370.47 0.165686 0.0828430 0.996563i \(-0.473600\pi\)
0.0828430 + 0.996563i \(0.473600\pi\)
\(410\) −3822.85 −0.460481
\(411\) 2054.78 0.246606
\(412\) −1680.65 −0.200970
\(413\) 3864.98 0.460493
\(414\) 4280.97 0.508208
\(415\) 5106.11 0.603973
\(416\) 3156.39 0.372007
\(417\) 2491.45 0.292582
\(418\) −3673.00 −0.429790
\(419\) 1268.73 0.147927 0.0739635 0.997261i \(-0.476435\pi\)
0.0739635 + 0.997261i \(0.476435\pi\)
\(420\) 134.773 0.0156577
\(421\) −12241.9 −1.41719 −0.708594 0.705617i \(-0.750670\pi\)
−0.708594 + 0.705617i \(0.750670\pi\)
\(422\) −11065.6 −1.27646
\(423\) 5015.66 0.576524
\(424\) −4063.31 −0.465405
\(425\) 2067.71 0.235997
\(426\) −8612.26 −0.979496
\(427\) 4912.05 0.556700
\(428\) 3030.55 0.342260
\(429\) 1621.06 0.182437
\(430\) −6578.48 −0.737774
\(431\) 8050.11 0.899675 0.449838 0.893110i \(-0.351482\pi\)
0.449838 + 0.893110i \(0.351482\pi\)
\(432\) −1361.43 −0.151624
\(433\) −16565.7 −1.83856 −0.919282 0.393600i \(-0.871230\pi\)
−0.919282 + 0.393600i \(0.871230\pi\)
\(434\) −84.1819 −0.00931073
\(435\) 133.608 0.0147265
\(436\) −710.293 −0.0780203
\(437\) 24205.9 2.64971
\(438\) 948.517 0.103475
\(439\) 4705.80 0.511607 0.255804 0.966729i \(-0.417660\pi\)
0.255804 + 0.966729i \(0.417660\pi\)
\(440\) 1329.74 0.144075
\(441\) −2735.86 −0.295418
\(442\) 10407.3 1.11997
\(443\) 15094.0 1.61882 0.809408 0.587246i \(-0.199788\pi\)
0.809408 + 0.587246i \(0.199788\pi\)
\(444\) 1799.04 0.192294
\(445\) 709.394 0.0755696
\(446\) 9830.56 1.04370
\(447\) −3640.93 −0.385257
\(448\) 3547.71 0.374138
\(449\) 973.478 0.102319 0.0511595 0.998690i \(-0.483708\pi\)
0.0511595 + 0.998690i \(0.483708\pi\)
\(450\) −576.349 −0.0603764
\(451\) 3283.27 0.342801
\(452\) −244.536 −0.0254469
\(453\) 92.5398 0.00959801
\(454\) 12817.3 1.32499
\(455\) 1534.17 0.158072
\(456\) −9454.75 −0.970963
\(457\) 62.6577 0.00641358 0.00320679 0.999995i \(-0.498979\pi\)
0.00320679 + 0.999995i \(0.498979\pi\)
\(458\) 710.510 0.0724890
\(459\) 2233.12 0.227088
\(460\) −1335.55 −0.135370
\(461\) −11866.2 −1.19884 −0.599419 0.800436i \(-0.704602\pi\)
−0.599419 + 0.800436i \(0.704602\pi\)
\(462\) 528.000 0.0531705
\(463\) −13144.8 −1.31942 −0.659711 0.751519i \(-0.729321\pi\)
−0.659711 + 0.751519i \(0.729321\pi\)
\(464\) 449.131 0.0449361
\(465\) −78.9205 −0.00787065
\(466\) −5814.48 −0.578006
\(467\) −10176.8 −1.00840 −0.504201 0.863586i \(-0.668213\pi\)
−0.504201 + 0.863586i \(0.668213\pi\)
\(468\) 635.949 0.0628136
\(469\) −2117.56 −0.208486
\(470\) 7137.71 0.700506
\(471\) 1035.72 0.101323
\(472\) 14960.1 1.45889
\(473\) 5649.96 0.549229
\(474\) 2380.98 0.230721
\(475\) −3258.85 −0.314793
\(476\) −743.121 −0.0715565
\(477\) −1512.58 −0.145191
\(478\) 4142.30 0.396369
\(479\) 3431.25 0.327302 0.163651 0.986518i \(-0.447673\pi\)
0.163651 + 0.986518i \(0.447673\pi\)
\(480\) 963.821 0.0916504
\(481\) 20479.1 1.94130
\(482\) −14464.1 −1.36685
\(483\) −3479.64 −0.327803
\(484\) −174.052 −0.0163460
\(485\) −3991.72 −0.373721
\(486\) −622.457 −0.0580972
\(487\) −2833.20 −0.263624 −0.131812 0.991275i \(-0.542079\pi\)
−0.131812 + 0.991275i \(0.542079\pi\)
\(488\) 19013.0 1.76368
\(489\) 5764.48 0.533085
\(490\) −3893.37 −0.358948
\(491\) −2667.29 −0.245159 −0.122580 0.992459i \(-0.539117\pi\)
−0.122580 + 0.992459i \(0.539117\pi\)
\(492\) 1288.04 0.118027
\(493\) −736.700 −0.0673008
\(494\) −16402.7 −1.49391
\(495\) 495.000 0.0449467
\(496\) −265.295 −0.0240164
\(497\) 7000.18 0.631793
\(498\) 7847.74 0.706156
\(499\) −11137.0 −0.999120 −0.499560 0.866279i \(-0.666505\pi\)
−0.499560 + 0.866279i \(0.666505\pi\)
\(500\) 179.806 0.0160823
\(501\) 516.892 0.0460939
\(502\) 15926.7 1.41603
\(503\) 8780.30 0.778319 0.389159 0.921170i \(-0.372766\pi\)
0.389159 + 0.921170i \(0.372766\pi\)
\(504\) 1359.14 0.120121
\(505\) −1207.00 −0.106358
\(506\) −5232.29 −0.459691
\(507\) 648.239 0.0567836
\(508\) 1363.91 0.119121
\(509\) 13597.4 1.18408 0.592039 0.805910i \(-0.298323\pi\)
0.592039 + 0.805910i \(0.298323\pi\)
\(510\) 3177.93 0.275923
\(511\) −770.969 −0.0667430
\(512\) 12992.6 1.12148
\(513\) −3519.56 −0.302909
\(514\) −19756.6 −1.69538
\(515\) −5841.89 −0.499854
\(516\) 2216.50 0.189101
\(517\) −6130.25 −0.521486
\(518\) 6670.30 0.565784
\(519\) −3075.88 −0.260146
\(520\) 5938.27 0.500789
\(521\) 14001.3 1.17736 0.588682 0.808364i \(-0.299647\pi\)
0.588682 + 0.808364i \(0.299647\pi\)
\(522\) 205.346 0.0172180
\(523\) −14749.8 −1.23320 −0.616602 0.787275i \(-0.711491\pi\)
−0.616602 + 0.787275i \(0.711491\pi\)
\(524\) 2135.86 0.178064
\(525\) 468.466 0.0389439
\(526\) −528.568 −0.0438149
\(527\) 435.159 0.0359693
\(528\) 1663.97 0.137150
\(529\) 22315.0 1.83406
\(530\) −2152.53 −0.176415
\(531\) 5568.95 0.455126
\(532\) 1171.21 0.0954483
\(533\) 14662.2 1.19154
\(534\) 1090.29 0.0883548
\(535\) 10534.1 0.851269
\(536\) −8196.40 −0.660505
\(537\) 4974.86 0.399779
\(538\) −4386.59 −0.351523
\(539\) 3343.83 0.267215
\(540\) 194.190 0.0154752
\(541\) 1484.06 0.117939 0.0589694 0.998260i \(-0.481219\pi\)
0.0589694 + 0.998260i \(0.481219\pi\)
\(542\) 1222.07 0.0968493
\(543\) −6065.42 −0.479359
\(544\) −5314.40 −0.418847
\(545\) −2468.96 −0.194052
\(546\) 2357.91 0.184815
\(547\) −16562.2 −1.29460 −0.647302 0.762234i \(-0.724103\pi\)
−0.647302 + 0.762234i \(0.724103\pi\)
\(548\) −985.233 −0.0768012
\(549\) 7077.65 0.550212
\(550\) 704.427 0.0546125
\(551\) 1161.09 0.0897716
\(552\) −13468.6 −1.03851
\(553\) −1935.30 −0.148819
\(554\) −10972.3 −0.841463
\(555\) 6253.41 0.478275
\(556\) −1194.61 −0.0911197
\(557\) −8821.52 −0.671059 −0.335529 0.942030i \(-0.608915\pi\)
−0.335529 + 0.942030i \(0.608915\pi\)
\(558\) −121.295 −0.00920223
\(559\) 25231.2 1.90906
\(560\) 1574.77 0.118833
\(561\) −2729.37 −0.205409
\(562\) −8908.55 −0.668656
\(563\) −5985.53 −0.448064 −0.224032 0.974582i \(-0.571922\pi\)
−0.224032 + 0.974582i \(0.571922\pi\)
\(564\) −2404.92 −0.179549
\(565\) −850.000 −0.0632916
\(566\) 16825.0 1.24948
\(567\) 505.943 0.0374737
\(568\) 27095.5 2.00158
\(569\) −3453.08 −0.254413 −0.127206 0.991876i \(-0.540601\pi\)
−0.127206 + 0.991876i \(0.540601\pi\)
\(570\) −5008.64 −0.368050
\(571\) −21484.5 −1.57460 −0.787302 0.616568i \(-0.788523\pi\)
−0.787302 + 0.616568i \(0.788523\pi\)
\(572\) −777.271 −0.0568170
\(573\) 4320.67 0.315006
\(574\) 4775.67 0.347269
\(575\) −4642.33 −0.336693
\(576\) 5111.80 0.369777
\(577\) −13294.4 −0.959189 −0.479594 0.877490i \(-0.659216\pi\)
−0.479594 + 0.877490i \(0.659216\pi\)
\(578\) −4937.82 −0.355340
\(579\) −8394.14 −0.602502
\(580\) −64.0627 −0.00458631
\(581\) −6378.77 −0.455483
\(582\) −6135.01 −0.436949
\(583\) 1848.71 0.131330
\(584\) −2984.18 −0.211449
\(585\) 2210.54 0.156230
\(586\) −21394.8 −1.50821
\(587\) 6695.73 0.470805 0.235402 0.971898i \(-0.424359\pi\)
0.235402 + 0.971898i \(0.424359\pi\)
\(588\) 1311.80 0.0920028
\(589\) −685.841 −0.0479789
\(590\) 7925.09 0.553002
\(591\) 1376.83 0.0958295
\(592\) 21021.2 1.45940
\(593\) −10239.6 −0.709088 −0.354544 0.935039i \(-0.615364\pi\)
−0.354544 + 0.935039i \(0.615364\pi\)
\(594\) 760.781 0.0525509
\(595\) −2583.07 −0.177976
\(596\) 1745.76 0.119982
\(597\) −7113.11 −0.487639
\(598\) −23366.0 −1.59784
\(599\) −23890.8 −1.62963 −0.814817 0.579719i \(-0.803162\pi\)
−0.814817 + 0.579719i \(0.803162\pi\)
\(600\) 1813.28 0.123378
\(601\) −11343.8 −0.769920 −0.384960 0.922933i \(-0.625785\pi\)
−0.384960 + 0.922933i \(0.625785\pi\)
\(602\) 8218.12 0.556388
\(603\) −3051.14 −0.206056
\(604\) −44.3712 −0.00298914
\(605\) −605.000 −0.0406558
\(606\) −1855.07 −0.124352
\(607\) −26032.5 −1.74074 −0.870369 0.492399i \(-0.836120\pi\)
−0.870369 + 0.492399i \(0.836120\pi\)
\(608\) 8375.87 0.558695
\(609\) −166.909 −0.0111059
\(610\) 10072.1 0.668536
\(611\) −27376.1 −1.81263
\(612\) −1070.74 −0.0707226
\(613\) −4568.13 −0.300987 −0.150493 0.988611i \(-0.548086\pi\)
−0.150493 + 0.988611i \(0.548086\pi\)
\(614\) −13791.1 −0.906457
\(615\) 4477.19 0.293557
\(616\) −1661.17 −0.108653
\(617\) −12755.9 −0.832308 −0.416154 0.909294i \(-0.636622\pi\)
−0.416154 + 0.909294i \(0.636622\pi\)
\(618\) −8978.59 −0.584421
\(619\) −1138.94 −0.0739545 −0.0369772 0.999316i \(-0.511773\pi\)
−0.0369772 + 0.999316i \(0.511773\pi\)
\(620\) 37.8410 0.00245118
\(621\) −5013.72 −0.323983
\(622\) 4586.24 0.295645
\(623\) −886.205 −0.0569904
\(624\) 7430.85 0.476718
\(625\) 625.000 0.0400000
\(626\) 2072.49 0.132322
\(627\) 4301.69 0.273992
\(628\) −496.607 −0.0315554
\(629\) −34480.6 −2.18574
\(630\) 720.000 0.0455325
\(631\) 7997.36 0.504548 0.252274 0.967656i \(-0.418822\pi\)
0.252274 + 0.967656i \(0.418822\pi\)
\(632\) −7490.91 −0.471475
\(633\) 12959.6 0.813742
\(634\) −27522.7 −1.72408
\(635\) 4740.91 0.296279
\(636\) 725.255 0.0452173
\(637\) 14932.7 0.928814
\(638\) −250.979 −0.0155742
\(639\) 10086.4 0.624430
\(640\) 4704.34 0.290555
\(641\) −573.115 −0.0353146 −0.0176573 0.999844i \(-0.505621\pi\)
−0.0176573 + 0.999844i \(0.505621\pi\)
\(642\) 16190.2 0.995290
\(643\) −16027.8 −0.983009 −0.491504 0.870875i \(-0.663553\pi\)
−0.491504 + 0.870875i \(0.663553\pi\)
\(644\) 1668.42 0.102089
\(645\) 7704.49 0.470332
\(646\) 27617.1 1.68201
\(647\) −2622.74 −0.159367 −0.0796837 0.996820i \(-0.525391\pi\)
−0.0796837 + 0.996820i \(0.525391\pi\)
\(648\) 1958.34 0.118721
\(649\) −6806.50 −0.411677
\(650\) 3145.79 0.189827
\(651\) 98.5908 0.00593560
\(652\) −2763.97 −0.166020
\(653\) 3102.00 0.185897 0.0929484 0.995671i \(-0.470371\pi\)
0.0929484 + 0.995671i \(0.470371\pi\)
\(654\) −3794.62 −0.226883
\(655\) 7424.19 0.442881
\(656\) 15050.3 0.895755
\(657\) −1110.87 −0.0659652
\(658\) −8916.73 −0.528283
\(659\) −20840.2 −1.23190 −0.615948 0.787787i \(-0.711227\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(660\) −237.344 −0.0139979
\(661\) 18242.9 1.07348 0.536738 0.843749i \(-0.319657\pi\)
0.536738 + 0.843749i \(0.319657\pi\)
\(662\) −8707.03 −0.511191
\(663\) −12188.7 −0.713980
\(664\) −24690.2 −1.44302
\(665\) 4071.10 0.237399
\(666\) 9611.06 0.559191
\(667\) 1654.01 0.0960171
\(668\) −247.841 −0.0143551
\(669\) −11513.2 −0.665361
\(670\) −4342.03 −0.250369
\(671\) −8650.46 −0.497686
\(672\) −1204.05 −0.0691177
\(673\) −12746.6 −0.730084 −0.365042 0.930991i \(-0.618945\pi\)
−0.365042 + 0.930991i \(0.618945\pi\)
\(674\) 30328.7 1.73326
\(675\) 675.000 0.0384900
\(676\) −310.819 −0.0176843
\(677\) −7683.11 −0.436168 −0.218084 0.975930i \(-0.569981\pi\)
−0.218084 + 0.975930i \(0.569981\pi\)
\(678\) −1306.39 −0.0739995
\(679\) 4986.63 0.281840
\(680\) −9998.23 −0.563845
\(681\) −15011.1 −0.844681
\(682\) 148.250 0.00832373
\(683\) −21397.1 −1.19874 −0.599368 0.800473i \(-0.704582\pi\)
−0.599368 + 0.800473i \(0.704582\pi\)
\(684\) 1687.57 0.0943359
\(685\) −3424.64 −0.191020
\(686\) 10351.8 0.576140
\(687\) −832.124 −0.0462118
\(688\) 25899.0 1.43516
\(689\) 8255.84 0.456491
\(690\) −7134.94 −0.393656
\(691\) 26137.5 1.43895 0.719477 0.694516i \(-0.244381\pi\)
0.719477 + 0.694516i \(0.244381\pi\)
\(692\) 1474.83 0.0810181
\(693\) −618.375 −0.0338963
\(694\) 5319.50 0.290959
\(695\) −4152.41 −0.226633
\(696\) −646.051 −0.0351846
\(697\) −24686.7 −1.34157
\(698\) −14952.7 −0.810845
\(699\) 6809.72 0.368479
\(700\) −224.621 −0.0121284
\(701\) 13382.4 0.721036 0.360518 0.932752i \(-0.382600\pi\)
0.360518 + 0.932752i \(0.382600\pi\)
\(702\) 3397.45 0.182662
\(703\) 54343.9 2.91553
\(704\) −6247.76 −0.334476
\(705\) −8359.43 −0.446574
\(706\) 6208.27 0.330951
\(707\) 1507.83 0.0802092
\(708\) −2670.22 −0.141741
\(709\) 18164.6 0.962179 0.481090 0.876671i \(-0.340241\pi\)
0.481090 + 0.876671i \(0.340241\pi\)
\(710\) 14353.8 0.758715
\(711\) −2788.52 −0.147085
\(712\) −3430.21 −0.180552
\(713\) −977.000 −0.0513169
\(714\) −3970.00 −0.208086
\(715\) −2701.77 −0.141315
\(716\) −2385.36 −0.124504
\(717\) −4851.32 −0.252686
\(718\) 9944.50 0.516888
\(719\) 9665.62 0.501344 0.250672 0.968072i \(-0.419348\pi\)
0.250672 + 0.968072i \(0.419348\pi\)
\(720\) 2269.05 0.117448
\(721\) 7297.94 0.376962
\(722\) −25956.7 −1.33796
\(723\) 16939.9 0.871371
\(724\) 2908.26 0.149288
\(725\) −222.680 −0.0114071
\(726\) −929.844 −0.0475341
\(727\) −29779.6 −1.51921 −0.759605 0.650385i \(-0.774608\pi\)
−0.759605 + 0.650385i \(0.774608\pi\)
\(728\) −7418.33 −0.377667
\(729\) 729.000 0.0370370
\(730\) −1580.86 −0.0801511
\(731\) −42481.7 −2.14944
\(732\) −3393.61 −0.171354
\(733\) 35029.5 1.76513 0.882567 0.470187i \(-0.155814\pi\)
0.882567 + 0.470187i \(0.155814\pi\)
\(734\) −14515.4 −0.729937
\(735\) 4559.77 0.228830
\(736\) 11931.7 0.597564
\(737\) 3729.17 0.186385
\(738\) 6881.13 0.343222
\(739\) 23297.3 1.15968 0.579842 0.814729i \(-0.303114\pi\)
0.579842 + 0.814729i \(0.303114\pi\)
\(740\) −2998.40 −0.148950
\(741\) 19210.2 0.952368
\(742\) 2689.03 0.133042
\(743\) 21570.4 1.06506 0.532530 0.846411i \(-0.321241\pi\)
0.532530 + 0.846411i \(0.321241\pi\)
\(744\) 381.613 0.0188046
\(745\) 6068.21 0.298419
\(746\) −447.684 −0.0219717
\(747\) −9190.99 −0.450175
\(748\) 1308.69 0.0639710
\(749\) −13159.6 −0.641980
\(750\) 960.582 0.0467673
\(751\) 28554.8 1.38746 0.693729 0.720236i \(-0.255966\pi\)
0.693729 + 0.720236i \(0.255966\pi\)
\(752\) −28100.7 −1.36267
\(753\) −18652.8 −0.902719
\(754\) −1120.81 −0.0541344
\(755\) −154.233 −0.00743458
\(756\) −242.591 −0.0116706
\(757\) 7812.81 0.375114 0.187557 0.982254i \(-0.439943\pi\)
0.187557 + 0.982254i \(0.439943\pi\)
\(758\) −647.268 −0.0310156
\(759\) 6127.87 0.293054
\(760\) 15757.9 0.752105
\(761\) 2875.13 0.136956 0.0684778 0.997653i \(-0.478186\pi\)
0.0684778 + 0.997653i \(0.478186\pi\)
\(762\) 7286.45 0.346405
\(763\) 3084.33 0.146344
\(764\) −2071.69 −0.0981033
\(765\) −3721.87 −0.175902
\(766\) 28214.3 1.33084
\(767\) −30396.0 −1.43095
\(768\) −6401.22 −0.300761
\(769\) −27657.7 −1.29696 −0.648479 0.761233i \(-0.724594\pi\)
−0.648479 + 0.761233i \(0.724594\pi\)
\(770\) −880.000 −0.0411857
\(771\) 23138.2 1.08081
\(772\) 4024.84 0.187639
\(773\) −3929.35 −0.182832 −0.0914160 0.995813i \(-0.529139\pi\)
−0.0914160 + 0.995813i \(0.529139\pi\)
\(774\) 11841.3 0.549904
\(775\) 131.534 0.00609658
\(776\) 19301.6 0.892898
\(777\) −7812.02 −0.360688
\(778\) −20747.0 −0.956064
\(779\) 38908.0 1.78950
\(780\) −1059.91 −0.0486552
\(781\) −12327.8 −0.564818
\(782\) 39341.3 1.79903
\(783\) −240.495 −0.0109765
\(784\) 15327.9 0.698247
\(785\) −1726.19 −0.0784847
\(786\) 11410.5 0.517809
\(787\) −21125.7 −0.956860 −0.478430 0.878126i \(-0.658794\pi\)
−0.478430 + 0.878126i \(0.658794\pi\)
\(788\) −660.166 −0.0298445
\(789\) 619.040 0.0279321
\(790\) −3968.30 −0.178716
\(791\) 1061.86 0.0477310
\(792\) −2393.53 −0.107387
\(793\) −38630.7 −1.72991
\(794\) 1087.00 0.0485847
\(795\) 2520.97 0.112465
\(796\) 3410.61 0.151867
\(797\) 11696.3 0.519828 0.259914 0.965632i \(-0.416306\pi\)
0.259914 + 0.965632i \(0.416306\pi\)
\(798\) 6257.00 0.277563
\(799\) 46093.0 2.04087
\(800\) −1606.37 −0.0709921
\(801\) −1276.91 −0.0563263
\(802\) 15123.9 0.665888
\(803\) 1357.73 0.0596678
\(804\) 1462.97 0.0641727
\(805\) 5799.39 0.253915
\(806\) 662.045 0.0289324
\(807\) 5137.42 0.224096
\(808\) 5836.34 0.254111
\(809\) 14310.2 0.621902 0.310951 0.950426i \(-0.399352\pi\)
0.310951 + 0.950426i \(0.399352\pi\)
\(810\) 1037.43 0.0450019
\(811\) 21697.9 0.939477 0.469739 0.882806i \(-0.344348\pi\)
0.469739 + 0.882806i \(0.344348\pi\)
\(812\) 80.0299 0.00345874
\(813\) −1431.24 −0.0617416
\(814\) −11746.9 −0.505807
\(815\) −9607.46 −0.412926
\(816\) −12511.3 −0.536743
\(817\) 66954.1 2.86711
\(818\) −3510.54 −0.150053
\(819\) −2761.50 −0.117820
\(820\) −2146.73 −0.0914233
\(821\) 3613.00 0.153587 0.0767934 0.997047i \(-0.475532\pi\)
0.0767934 + 0.997047i \(0.475532\pi\)
\(822\) −5263.44 −0.223338
\(823\) −4763.98 −0.201776 −0.100888 0.994898i \(-0.532168\pi\)
−0.100888 + 0.994898i \(0.532168\pi\)
\(824\) 28248.0 1.19425
\(825\) −825.000 −0.0348155
\(826\) −9900.36 −0.417043
\(827\) −33571.7 −1.41161 −0.705806 0.708405i \(-0.749415\pi\)
−0.705806 + 0.708405i \(0.749415\pi\)
\(828\) 2403.99 0.100899
\(829\) 17980.5 0.753303 0.376652 0.926355i \(-0.377075\pi\)
0.376652 + 0.926355i \(0.377075\pi\)
\(830\) −13079.6 −0.546986
\(831\) 12850.4 0.536434
\(832\) −27900.9 −1.16261
\(833\) −25142.1 −1.04576
\(834\) −6381.98 −0.264976
\(835\) −861.486 −0.0357041
\(836\) −2062.58 −0.0853301
\(837\) 142.057 0.00586643
\(838\) −3249.91 −0.133969
\(839\) −40139.5 −1.65169 −0.825847 0.563895i \(-0.809302\pi\)
−0.825847 + 0.563895i \(0.809302\pi\)
\(840\) −2265.23 −0.0930450
\(841\) −24309.7 −0.996747
\(842\) 31358.4 1.28347
\(843\) 10433.4 0.426269
\(844\) −6213.91 −0.253426
\(845\) −1080.40 −0.0439844
\(846\) −12847.9 −0.522127
\(847\) 755.792 0.0306603
\(848\) 8474.36 0.343173
\(849\) −19704.8 −0.796546
\(850\) −5296.54 −0.213729
\(851\) 77414.4 3.11837
\(852\) −4836.24 −0.194468
\(853\) −15369.2 −0.616919 −0.308459 0.951237i \(-0.599813\pi\)
−0.308459 + 0.951237i \(0.599813\pi\)
\(854\) −12582.5 −0.504173
\(855\) 5865.94 0.234633
\(856\) −50936.8 −2.03386
\(857\) 10324.9 0.411541 0.205770 0.978600i \(-0.434030\pi\)
0.205770 + 0.978600i \(0.434030\pi\)
\(858\) −4152.44 −0.165224
\(859\) −27112.5 −1.07691 −0.538455 0.842655i \(-0.680992\pi\)
−0.538455 + 0.842655i \(0.680992\pi\)
\(860\) −3694.17 −0.146477
\(861\) −5593.09 −0.221384
\(862\) −20620.8 −0.814787
\(863\) 30463.6 1.20161 0.600807 0.799394i \(-0.294846\pi\)
0.600807 + 0.799394i \(0.294846\pi\)
\(864\) −1734.88 −0.0683122
\(865\) 5126.46 0.201508
\(866\) 42434.0 1.66509
\(867\) 5783.00 0.226529
\(868\) −47.2726 −0.00184854
\(869\) 3408.19 0.133044
\(870\) −342.244 −0.0133370
\(871\) 16653.5 0.647855
\(872\) 11938.4 0.463631
\(873\) 7185.10 0.278555
\(874\) −62004.6 −2.39970
\(875\) −780.776 −0.0301658
\(876\) 532.642 0.0205437
\(877\) −5086.12 −0.195833 −0.0979167 0.995195i \(-0.531218\pi\)
−0.0979167 + 0.995195i \(0.531218\pi\)
\(878\) −12054.2 −0.463335
\(879\) 25056.9 0.961487
\(880\) −2773.28 −0.106236
\(881\) −10625.5 −0.406338 −0.203169 0.979144i \(-0.565124\pi\)
−0.203169 + 0.979144i \(0.565124\pi\)
\(882\) 7008.06 0.267544
\(883\) 13112.2 0.499728 0.249864 0.968281i \(-0.419614\pi\)
0.249864 + 0.968281i \(0.419614\pi\)
\(884\) 5844.25 0.222357
\(885\) −9281.59 −0.352539
\(886\) −38664.0 −1.46607
\(887\) −14442.8 −0.546719 −0.273360 0.961912i \(-0.588135\pi\)
−0.273360 + 0.961912i \(0.588135\pi\)
\(888\) −30237.8 −1.14270
\(889\) −5922.54 −0.223437
\(890\) −1817.15 −0.0684393
\(891\) −891.000 −0.0335013
\(892\) 5520.38 0.207215
\(893\) −72645.8 −2.72228
\(894\) 9326.43 0.348906
\(895\) −8291.44 −0.309667
\(896\) −5876.86 −0.219121
\(897\) 27365.5 1.01863
\(898\) −2493.61 −0.0926648
\(899\) −46.8641 −0.00173860
\(900\) −323.651 −0.0119871
\(901\) −13900.3 −0.513970
\(902\) −8410.27 −0.310456
\(903\) −9624.77 −0.354698
\(904\) 4110.10 0.151217
\(905\) 10109.0 0.371310
\(906\) −237.045 −0.00869239
\(907\) −44981.9 −1.64675 −0.823374 0.567499i \(-0.807911\pi\)
−0.823374 + 0.567499i \(0.807911\pi\)
\(908\) 7197.57 0.263062
\(909\) 2172.60 0.0792745
\(910\) −3929.85 −0.143157
\(911\) 6841.96 0.248830 0.124415 0.992230i \(-0.460295\pi\)
0.124415 + 0.992230i \(0.460295\pi\)
\(912\) 19718.7 0.715954
\(913\) 11233.4 0.407199
\(914\) −160.501 −0.00580843
\(915\) −11796.1 −0.426193
\(916\) 398.989 0.0143919
\(917\) −9274.61 −0.333996
\(918\) −5720.27 −0.205661
\(919\) −4753.54 −0.170625 −0.0853127 0.996354i \(-0.527189\pi\)
−0.0853127 + 0.996354i \(0.527189\pi\)
\(920\) 22447.6 0.804430
\(921\) 16151.7 0.577868
\(922\) 30395.9 1.08572
\(923\) −55052.7 −1.96325
\(924\) 296.500 0.0105564
\(925\) −10422.3 −0.370470
\(926\) 33671.2 1.19493
\(927\) 10515.4 0.372569
\(928\) 572.330 0.0202453
\(929\) −7507.93 −0.265153 −0.132576 0.991173i \(-0.542325\pi\)
−0.132576 + 0.991173i \(0.542325\pi\)
\(930\) 202.159 0.00712802
\(931\) 39625.7 1.39493
\(932\) −3265.14 −0.114757
\(933\) −5371.24 −0.188474
\(934\) 26068.3 0.913256
\(935\) 4548.96 0.159109
\(936\) −10688.9 −0.373266
\(937\) 8540.47 0.297764 0.148882 0.988855i \(-0.452433\pi\)
0.148882 + 0.988855i \(0.452433\pi\)
\(938\) 5424.24 0.188814
\(939\) −2427.23 −0.0843552
\(940\) 4008.20 0.139078
\(941\) 9101.13 0.315290 0.157645 0.987496i \(-0.449610\pi\)
0.157645 + 0.987496i \(0.449610\pi\)
\(942\) −2653.04 −0.0917630
\(943\) 55425.5 1.91400
\(944\) −31200.6 −1.07573
\(945\) −843.239 −0.0290270
\(946\) −14472.7 −0.497407
\(947\) 47540.0 1.63130 0.815650 0.578546i \(-0.196380\pi\)
0.815650 + 0.578546i \(0.196380\pi\)
\(948\) 1337.04 0.0458072
\(949\) 6063.26 0.207399
\(950\) 8347.73 0.285091
\(951\) 32233.6 1.09910
\(952\) 12490.2 0.425221
\(953\) 47370.7 1.61016 0.805082 0.593164i \(-0.202121\pi\)
0.805082 + 0.593164i \(0.202121\pi\)
\(954\) 3874.55 0.131492
\(955\) −7201.12 −0.244003
\(956\) 2326.12 0.0786947
\(957\) 293.938 0.00992859
\(958\) −8789.33 −0.296420
\(959\) 4278.20 0.144057
\(960\) −8519.67 −0.286428
\(961\) −29763.3 −0.999071
\(962\) −52458.4 −1.75813
\(963\) −18961.4 −0.634498
\(964\) −8122.38 −0.271374
\(965\) 13990.2 0.466696
\(966\) 8913.27 0.296874
\(967\) −36171.6 −1.20290 −0.601448 0.798912i \(-0.705409\pi\)
−0.601448 + 0.798912i \(0.705409\pi\)
\(968\) 2925.43 0.0971351
\(969\) −32344.1 −1.07228
\(970\) 10225.0 0.338459
\(971\) −31713.2 −1.04812 −0.524060 0.851681i \(-0.675583\pi\)
−0.524060 + 0.851681i \(0.675583\pi\)
\(972\) −349.543 −0.0115346
\(973\) 5187.37 0.170914
\(974\) 7257.40 0.238750
\(975\) −3684.23 −0.121015
\(976\) −39653.1 −1.30048
\(977\) 22800.5 0.746626 0.373313 0.927706i \(-0.378222\pi\)
0.373313 + 0.927706i \(0.378222\pi\)
\(978\) −14766.0 −0.482786
\(979\) 1560.67 0.0509490
\(980\) −2186.33 −0.0712651
\(981\) 4444.12 0.144638
\(982\) 6832.41 0.222027
\(983\) −44597.4 −1.44704 −0.723518 0.690305i \(-0.757476\pi\)
−0.723518 + 0.690305i \(0.757476\pi\)
\(984\) −21649.1 −0.701369
\(985\) −2294.72 −0.0742292
\(986\) 1887.10 0.0609507
\(987\) 10443.0 0.336781
\(988\) −9210.95 −0.296599
\(989\) 95378.1 3.06658
\(990\) −1267.97 −0.0407057
\(991\) −34788.1 −1.11512 −0.557558 0.830138i \(-0.688261\pi\)
−0.557558 + 0.830138i \(0.688261\pi\)
\(992\) −338.068 −0.0108202
\(993\) 10197.4 0.325885
\(994\) −17931.3 −0.572180
\(995\) 11855.2 0.377723
\(996\) 4406.92 0.140199
\(997\) −20360.5 −0.646765 −0.323383 0.946268i \(-0.604820\pi\)
−0.323383 + 0.946268i \(0.604820\pi\)
\(998\) 28528.0 0.904849
\(999\) −11256.1 −0.356485
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 165.4.a.c.1.1 2
3.2 odd 2 495.4.a.d.1.2 2
5.2 odd 4 825.4.c.j.199.1 4
5.3 odd 4 825.4.c.j.199.4 4
5.4 even 2 825.4.a.m.1.2 2
11.10 odd 2 1815.4.a.n.1.2 2
15.14 odd 2 2475.4.a.n.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.4.a.c.1.1 2 1.1 even 1 trivial
495.4.a.d.1.2 2 3.2 odd 2
825.4.a.m.1.2 2 5.4 even 2
825.4.c.j.199.1 4 5.2 odd 4
825.4.c.j.199.4 4 5.3 odd 4
1815.4.a.n.1.2 2 11.10 odd 2
2475.4.a.n.1.1 2 15.14 odd 2