Properties

Label 1815.4.a.n.1.2
Level $1815$
Weight $4$
Character 1815.1
Self dual yes
Analytic conductor $107.088$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(107.088466660\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 1815.1

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56155 0.905646 0.452823 0.891601i \(-0.350417\pi\)
0.452823 + 0.891601i \(0.350417\pi\)
\(3\) 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 \(-0.553935\pi\)
−0.168632 + 0.985679i \(0.553935\pi\)
\(8\) −24.1771 −1.06849
\(9\) 9.00000 0.333333
\(10\) −12.8078 −0.405017
\(11\) 0 0
\(12\) −4.31534 −0.103811
\(13\) 49.1231 1.04802 0.524011 0.851711i \(-0.324435\pi\)
0.524011 + 0.851711i \(0.324435\pi\)
\(14\) −16.0000 −0.305441
\(15\) −15.0000 −0.258199
\(16\) −50.4233 −0.787864
\(17\) −82.7083 −1.17998 −0.589992 0.807409i \(-0.700869\pi\)
−0.589992 + 0.807409i \(0.700869\pi\)
\(18\) 23.0540 0.301882
\(19\) 130.354 1.57396 0.786981 0.616977i \(-0.211643\pi\)
0.786981 + 0.616977i \(0.211643\pi\)
\(20\) 7.19224 0.0804116
\(21\) −18.7386 −0.194719
\(22\) 0 0
\(23\) −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 \(-0.490921\pi\)
0.0285177 + 0.999593i \(0.490921\pi\)
\(30\) −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
\(33\) 0 0
\(34\) −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 \(-0.307535\pi\)
0.568471 + 0.822703i \(0.307535\pi\)
\(42\) −48.0000 −0.176347
\(43\) 513.633 1.82159 0.910793 0.412863i \(-0.135471\pi\)
0.910793 + 0.412863i \(0.135471\pi\)
\(44\) 0 0
\(45\) −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
\(55\) 0 0
\(56\) 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 \(-0.809004\pi\)
−0.825319 + 0.564667i \(0.809004\pi\)
\(62\) 13.4773 0.0276067
\(63\) −56.2159 −0.112421
\(64\) 567.978 1.10933
\(65\) −245.616 −0.468690
\(66\) 0 0
\(67\) −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 \(-0.468452\pi\)
0.0989478 + 0.995093i \(0.468452\pi\)
\(74\) −1067.90 −1.67757
\(75\) 75.0000 0.115470
\(76\) −187.508 −0.283008
\(77\) 0 0
\(78\) 377.494 0.547985
\(79\) 309.835 0.441255 0.220628 0.975358i \(-0.429189\pi\)
0.220628 + 0.975358i \(0.429189\pi\)
\(80\) 252.116 0.352343
\(81\) 81.0000 0.111111
\(82\) 764.570 1.02967
\(83\) 1021.22 1.35053 0.675263 0.737577i \(-0.264030\pi\)
0.675263 + 0.737577i \(0.264030\pi\)
\(84\) 26.9545 0.0350117
\(85\) 413.542 0.527705
\(86\) 1315.70 1.64971
\(87\) 26.7216 0.0329294
\(88\) 0 0
\(89\) −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
\(99\) 0 0
\(100\) −35.9612 −0.0359612
\(101\) −241.400 −0.237823 −0.118912 0.992905i \(-0.537941\pi\)
−0.118912 + 0.992905i \(0.537941\pi\)
\(102\) −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 \(-0.0992857\pi\)
0.951748 + 0.306882i \(0.0992857\pi\)
\(108\) −38.8381 −0.0346037
\(109\) −493.792 −0.433914 −0.216957 0.976181i \(-0.569613\pi\)
−0.216957 + 0.976181i \(0.569613\pi\)
\(110\) 0 0
\(111\) −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
\(121\) 0 0
\(122\) −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 \(-0.392530\pi\)
0.331250 + 0.943543i \(0.392530\pi\)
\(128\) 940.868 0.649702
\(129\) 1540.90 1.05169
\(130\) −629.157 −0.424467
\(131\) 1484.84 0.990312 0.495156 0.868804i \(-0.335111\pi\)
0.495156 + 0.868804i \(0.335111\pi\)
\(132\) 0 0
\(133\) −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 \(-0.581543\pi\)
−0.253384 + 0.967366i \(0.581543\pi\)
\(140\) −44.9242 −0.0271199
\(141\) 1671.89 0.998569
\(142\) 2870.75 1.69654
\(143\) 0 0
\(144\) −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 \(-0.391722\pi\)
0.333642 + 0.942700i \(0.391722\pi\)
\(150\) 192.116 0.104575
\(151\) −30.8466 −0.0166242 −0.00831212 0.999965i \(-0.502646\pi\)
−0.00831212 + 0.999965i \(0.502646\pi\)
\(152\) −3151.58 −1.68176
\(153\) −744.375 −0.393328
\(154\) 0 0
\(155\) −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
\(165\) 0 0
\(166\) 2615.91 1.22310
\(167\) −172.297 −0.0798369 −0.0399185 0.999203i \(-0.512710\pi\)
−0.0399185 + 0.999203i \(0.512710\pi\)
\(168\) 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 \(-0.427666\pi\)
0.225293 + 0.974291i \(0.427666\pi\)
\(174\) 68.4488 0.0298224
\(175\) −156.155 −0.0674527
\(176\) 0 0
\(177\) 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
\(187\) 0 0
\(188\) −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 \(-0.325267\pi\)
0.521782 + 0.853079i \(0.325267\pi\)
\(194\) 2045.00 0.756817
\(195\) −736.847 −0.270598
\(196\) 437.266 0.159354
\(197\) −458.943 −0.165982 −0.0829908 0.996550i \(-0.526447\pi\)
−0.0829908 + 0.996550i \(0.526447\pi\)
\(198\) 0 0
\(199\) −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
\(209\) 0 0
\(210\) 240.000 0.0788646
\(211\) −4319.87 −1.40944 −0.704721 0.709484i \(-0.748928\pi\)
−0.704721 + 0.709484i \(0.748928\pi\)
\(212\) 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
\(220\) 0 0
\(221\) −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 \(-0.238813\pi\)
0.731515 + 0.681825i \(0.238813\pi\)
\(228\) −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
\(231\) 0 0
\(232\) −215.350 −0.0609415
\(233\) −2269.91 −0.638225 −0.319113 0.947717i \(-0.603385\pi\)
−0.319113 + 0.947717i \(0.603385\pi\)
\(234\) 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 \(-0.429775\pi\)
0.218832 + 0.975762i \(0.429775\pi\)
\(240\) 756.349 0.203426
\(241\) −5646.63 −1.50926 −0.754629 0.656151i \(-0.772183\pi\)
−0.754629 + 0.656151i \(0.772183\pi\)
\(242\) 0 0
\(243\) 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
\(253\) 0 0
\(254\) 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 \(-0.507701\pi\)
−0.0241899 + 0.999707i \(0.507701\pi\)
\(264\) 0 0
\(265\) 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 \(-0.482972\pi\)
0.0534698 + 0.998569i \(0.482972\pi\)
\(272\) 4170.43 0.929666
\(273\) −920.500 −0.204070
\(274\) 1754.48 0.386832
\(275\) 0 0
\(276\) 801.329 0.174762
\(277\) −4283.48 −0.929130 −0.464565 0.885539i \(-0.653789\pi\)
−0.464565 + 0.885539i \(0.653789\pi\)
\(278\) −2127.33 −0.458952
\(279\) 47.3523 0.0101610
\(280\) −755.076 −0.161159
\(281\) −3477.79 −0.738319 −0.369160 0.929366i \(-0.620354\pi\)
−0.369160 + 0.929366i \(0.620354\pi\)
\(282\) 4282.62 0.904350
\(283\) 6568.27 1.37966 0.689829 0.723973i \(-0.257686\pi\)
0.689829 + 0.723973i \(0.257686\pi\)
\(284\) −1612.08 −0.336829
\(285\) −1955.31 −0.406395
\(286\) 0 0
\(287\) −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 \(-0.813190\pi\)
−0.832672 + 0.553766i \(0.813190\pi\)
\(294\) −2336.02 −0.463399
\(295\) −3093.86 −0.610616
\(296\) 10079.3 1.97921
\(297\) 0 0
\(298\) 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 \(-0.666831\pi\)
−0.500448 + 0.865767i \(0.666831\pi\)
\(308\) 0 0
\(309\) 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
\(319\) 0 0
\(320\) −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
\(330\) 0 0
\(331\) 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 \(-0.0937736\pi\)
0.956919 + 0.290356i \(0.0937736\pi\)
\(338\) 553.499 0.0890721
\(339\) 510.000 0.0817091
\(340\) −594.858 −0.0948844
\(341\) 0 0
\(342\) 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 \(-0.448645\pi\)
0.160636 + 0.987014i \(0.448645\pi\)
\(348\) −38.4376 −0.00592090
\(349\) −5837.37 −0.895322 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(350\) −400.000 −0.0610883
\(351\) 1326.32 0.201692
\(352\) 0 0
\(353\) −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 \(-0.407884\pi\)
0.285370 + 0.958417i \(0.407884\pi\)
\(360\) 1087.97 0.159281
\(361\) 10133.2 1.47736
\(362\) −5178.96 −0.751935
\(363\) 0 0
\(364\) 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 \(-0.503861\pi\)
−0.0121304 + 0.999926i \(0.503861\pi\)
\(374\) 0 0
\(375\) −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
\(385\) 0 0
\(386\) 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
\(396\) 0 0
\(397\) −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
\(407\) 0 0
\(408\) 5998.94 0.727921
\(409\) −1370.47 −0.165686 −0.0828430 0.996563i \(-0.526400\pi\)
−0.0828430 + 0.996563i \(0.526400\pi\)
\(410\) −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
\(418\) 0 0
\(419\) 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
\(429\) 0 0
\(430\) −6578.48 −0.737774
\(431\) −8050.11 −0.899675 −0.449838 0.893110i \(-0.648518\pi\)
−0.449838 + 0.893110i \(0.648518\pi\)
\(432\) −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 \(-0.582340\pi\)
−0.255804 + 0.966729i \(0.582340\pi\)
\(440\) 0 0
\(441\) −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
\(451\) 0 0
\(452\) −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 \(-0.501021\pi\)
−0.00320679 + 0.999995i \(0.501021\pi\)
\(458\) −710.510 −0.0724890
\(459\) −2233.12 −0.227088
\(460\) −1335.55 −0.135370
\(461\) 11866.2 1.19884 0.599419 0.800436i \(-0.295398\pi\)
0.599419 + 0.800436i \(0.295398\pi\)
\(462\) 0 0
\(463\) −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
\(473\) 0 0
\(474\) 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 \(-0.552327\pi\)
−0.163651 + 0.986518i \(0.552327\pi\)
\(480\) −963.821 −0.0916504
\(481\) −20479.1 −1.94130
\(482\) −14464.1 −1.36685
\(483\) 3479.64 0.327803
\(484\) 0 0
\(485\) −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 \(-0.460883\pi\)
0.122580 + 0.992459i \(0.460883\pi\)
\(492\) −1288.04 −0.118027
\(493\) −736.700 −0.0673008
\(494\) 16402.7 1.49391
\(495\) 0 0
\(496\) −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 \(-0.627234\pi\)
−0.389159 + 0.921170i \(0.627234\pi\)
\(504\) 1359.14 0.120121
\(505\) 1207.00 0.106358
\(506\) 0 0
\(507\) 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
\(517\) 0 0
\(518\) 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 \(-0.288509\pi\)
0.616602 + 0.787275i \(0.288509\pi\)
\(524\) −2135.86 −0.178064
\(525\) −468.466 −0.0389439
\(526\) −528.568 −0.0438149
\(527\) −435.159 −0.0359693
\(528\) 0 0
\(529\) 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
\(539\) 0 0
\(540\) 194.190 0.0154752
\(541\) −1484.06 −0.117939 −0.0589694 0.998260i \(-0.518781\pi\)
−0.0589694 + 0.998260i \(0.518781\pi\)
\(542\) 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 \(-0.275897\pi\)
0.647302 + 0.762234i \(0.275897\pi\)
\(548\) −985.233 −0.0768012
\(549\) −7077.65 −0.550212
\(550\) 0 0
\(551\) 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 \(-0.391085\pi\)
0.335529 + 0.942030i \(0.391085\pi\)
\(558\) 121.295 0.00920223
\(559\) 25231.2 1.90906
\(560\) −1574.77 −0.118833
\(561\) 0 0
\(562\) −8908.55 −0.668656
\(563\) 5985.53 0.448064 0.224032 0.974582i \(-0.428078\pi\)
0.224032 + 0.974582i \(0.428078\pi\)
\(564\) −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 \(-0.459399\pi\)
0.127206 + 0.991876i \(0.459399\pi\)
\(570\) −5008.64 −0.368050
\(571\) 21484.5 1.57460 0.787302 0.616568i \(-0.211477\pi\)
0.787302 + 0.616568i \(0.211477\pi\)
\(572\) 0 0
\(573\) 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
\(583\) 0 0
\(584\) −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 \(-0.384636\pi\)
0.354544 + 0.935039i \(0.384636\pi\)
\(594\) 0 0
\(595\) −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 \(-0.374215\pi\)
0.384960 + 0.922933i \(0.374215\pi\)
\(602\) −8218.12 −0.556388
\(603\) −3051.14 −0.206056
\(604\) 44.3712 0.00298914
\(605\) 0 0
\(606\) −1855.07 −0.124352
\(607\) 26032.5 1.74074 0.870369 0.492399i \(-0.163880\pi\)
0.870369 + 0.492399i \(0.163880\pi\)
\(608\) 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 \(-0.451914\pi\)
0.150493 + 0.988611i \(0.451914\pi\)
\(614\) −13791.1 −0.906457
\(615\) −4477.19 −0.293557
\(616\) 0 0
\(617\) −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
\(627\) 0 0
\(628\) −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
\(638\) 0 0
\(639\) 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
\(649\) 0 0
\(650\) 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 \(-0.288773\pi\)
0.615948 + 0.787787i \(0.288773\pi\)
\(660\) 0 0
\(661\) 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
\(671\) 0 0
\(672\) −1204.05 −0.0691177
\(673\) 12746.6 0.730084 0.365042 0.930991i \(-0.381055\pi\)
0.365042 + 0.930991i \(0.381055\pi\)
\(674\) 30328.7 1.73326
\(675\) 675.000 0.0384900
\(676\) −310.819 −0.0176843
\(677\) 7683.11 0.436168 0.218084 0.975930i \(-0.430019\pi\)
0.218084 + 0.975930i \(0.430019\pi\)
\(678\) 1306.39 0.0739995
\(679\) −4986.63 −0.281840
\(680\) −9998.23 −0.563845
\(681\) 15011.1 0.844681
\(682\) 0 0
\(683\) −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
\(693\) 0 0
\(694\) 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 \(-0.617400\pi\)
−0.360518 + 0.932752i \(0.617400\pi\)
\(702\) 3397.45 0.182662
\(703\) −54343.9 −2.91553
\(704\) 0 0
\(705\) −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
\(715\) 0 0
\(716\) −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
\(726\) 0 0
\(727\) −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 \(-0.844186\pi\)
−0.882567 + 0.470187i \(0.844186\pi\)
\(734\) 14515.4 0.729937
\(735\) 4559.77 0.228830
\(736\) −11931.7 −0.597564
\(737\) 0 0
\(738\) 6881.13 0.343222
\(739\) −23297.3 −1.15968 −0.579842 0.814729i \(-0.696886\pi\)
−0.579842 + 0.814729i \(0.696886\pi\)
\(740\) −2998.40 −0.148950
\(741\) 19210.2 0.952368
\(742\) 2689.03 0.133042
\(743\) −21570.4 −1.06506 −0.532530 0.846411i \(-0.678759\pi\)
−0.532530 + 0.846411i \(0.678759\pi\)
\(744\) −381.613 −0.0188046
\(745\) −6068.21 −0.298419
\(746\) −447.684 −0.0219717
\(747\) 9190.99 0.450175
\(748\) 0 0
\(749\) −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
\(759\) 0 0
\(760\) 15757.9 0.752105
\(761\) −2875.13 −0.136956 −0.0684778 0.997653i \(-0.521814\pi\)
−0.0684778 + 0.997653i \(0.521814\pi\)
\(762\) 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 \(-0.275406\pi\)
0.648479 + 0.761233i \(0.275406\pi\)
\(770\) 0 0
\(771\) 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
\(781\) 0 0
\(782\) 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 \(-0.341206\pi\)
0.478430 + 0.878126i \(0.341206\pi\)
\(788\) 660.166 0.0298445
\(789\) −619.040 −0.0279321
\(790\) −3968.30 −0.178716
\(791\) −1061.86 −0.0477310
\(792\) 0 0
\(793\) −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
\(803\) 0 0
\(804\) 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 \(-0.600648\pi\)
−0.310951 + 0.950426i \(0.600648\pi\)
\(810\) −1037.43 −0.0450019
\(811\) −21697.9 −0.939477 −0.469739 0.882806i \(-0.655652\pi\)
−0.469739 + 0.882806i \(0.655652\pi\)
\(812\) 80.0299 0.00345874
\(813\) 1431.24 0.0617416
\(814\) 0 0
\(815\) −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 \(-0.524468\pi\)
−0.0767934 + 0.997047i \(0.524468\pi\)
\(822\) 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
\(825\) 0 0
\(826\) −9900.36 −0.417043
\(827\) 33571.7 1.41161 0.705806 0.708405i \(-0.250585\pi\)
0.705806 + 0.708405i \(0.250585\pi\)
\(828\) 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
\(836\) 0 0
\(837\) 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
\(847\) 0 0
\(848\) 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 \(-0.400187\pi\)
0.308459 + 0.951237i \(0.400187\pi\)
\(854\) 12582.5 0.504173
\(855\) −5865.94 −0.234633
\(856\) −50936.8 −2.03386
\(857\) −10324.9 −0.411541 −0.205770 0.978600i \(-0.565970\pi\)
−0.205770 + 0.978600i \(0.565970\pi\)
\(858\) 0 0
\(859\) −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
\(869\) 0 0
\(870\) −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 \(-0.468782\pi\)
0.0979167 + 0.995195i \(0.468782\pi\)
\(878\) −12054.2 −0.463335
\(879\) −25056.9 −0.961487
\(880\) 0 0
\(881\) −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 \(-0.411865\pi\)
0.273360 + 0.961912i \(0.411865\pi\)
\(888\) 30237.8 1.14270
\(889\) −5922.54 −0.223437
\(890\) 1817.15 0.0684393
\(891\) 0 0
\(892\) 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
\(902\) 0 0
\(903\) −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
\(913\) 0 0
\(914\) −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 \(-0.472811\pi\)
0.0853127 + 0.996354i \(0.472811\pi\)
\(920\) −22447.6 −0.804430
\(921\) −16151.7 −0.577868
\(922\) 30395.9 1.08572
\(923\) 55052.7 1.96325
\(924\) 0 0
\(925\) −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
\(935\) 0 0
\(936\) −10688.9 −0.373266
\(937\) −8540.47 −0.297764 −0.148882 0.988855i \(-0.547567\pi\)
−0.148882 + 0.988855i \(0.547567\pi\)
\(938\) 5424.24 0.188814
\(939\) −2427.23 −0.0843552
\(940\) 4008.20 0.139078
\(941\) −9101.13 −0.315290 −0.157645 0.987496i \(-0.550390\pi\)
−0.157645 + 0.987496i \(0.550390\pi\)
\(942\) 2653.04 0.0917630
\(943\) −55425.5 −1.91400
\(944\) −31200.6 −1.07573
\(945\) 843.239 0.0290270
\(946\) 0 0
\(947\) 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 \(-0.797879\pi\)
−0.805082 + 0.593164i \(0.797879\pi\)
\(954\) −3874.55 −0.131492
\(955\) −7201.12 −0.244003
\(956\) −2326.12 −0.0786947
\(957\) 0 0
\(958\) −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 \(-0.294591\pi\)
0.601448 + 0.798912i \(0.294591\pi\)
\(968\) 0 0
\(969\) −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
\(979\) 0 0
\(980\) −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
\(990\) 0 0
\(991\) −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 \(-0.395180\pi\)
0.323383 + 0.946268i \(0.395180\pi\)
\(998\) −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 1815.4.a.n.1.2 2
11.10 odd 2 165.4.a.c.1.1 2
33.32 even 2 495.4.a.d.1.2 2
55.32 even 4 825.4.c.j.199.1 4
55.43 even 4 825.4.c.j.199.4 4
55.54 odd 2 825.4.a.m.1.2 2
165.164 even 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 11.10 odd 2
495.4.a.d.1.2 2 33.32 even 2
825.4.a.m.1.2 2 55.54 odd 2
825.4.c.j.199.1 4 55.32 even 4
825.4.c.j.199.4 4 55.43 even 4
1815.4.a.n.1.2 2 1.1 even 1 trivial
2475.4.a.n.1.1 2 165.164 even 2