Properties

Label 1859.2.a.g.1.1
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.361.1
Defining polynomial: \( x^{3} - x^{2} - 6x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.28514\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.50702 q^{2} +2.28514 q^{3} +4.28514 q^{4} +1.22188 q^{5} -5.72889 q^{6} -0.778124 q^{7} -5.72889 q^{8} +2.22188 q^{9} +O(q^{10})\) \(q-2.50702 q^{2} +2.28514 q^{3} +4.28514 q^{4} +1.22188 q^{5} -5.72889 q^{6} -0.778124 q^{7} -5.72889 q^{8} +2.22188 q^{9} -3.06327 q^{10} -1.00000 q^{11} +9.79216 q^{12} +1.95077 q^{14} +2.79216 q^{15} +5.79216 q^{16} -4.28514 q^{17} -5.57028 q^{18} -8.29918 q^{19} +5.23591 q^{20} -1.77812 q^{21} +2.50702 q^{22} -2.72889 q^{23} -13.0913 q^{24} -3.50702 q^{25} -1.77812 q^{27} -3.33437 q^{28} +7.36245 q^{29} -7.00000 q^{30} +1.44375 q^{31} -3.06327 q^{32} -2.28514 q^{33} +10.7429 q^{34} -0.950771 q^{35} +9.52106 q^{36} +0.792161 q^{37} +20.8062 q^{38} -7.00000 q^{40} -9.74293 q^{41} +4.45779 q^{42} -9.67967 q^{43} -4.28514 q^{44} +2.71486 q^{45} +6.84139 q^{46} +3.38049 q^{47} +13.2359 q^{48} -6.39452 q^{49} +8.79216 q^{50} -9.79216 q^{51} +1.79216 q^{53} +4.45779 q^{54} -1.22188 q^{55} +4.45779 q^{56} -18.9648 q^{57} -18.4578 q^{58} -5.20784 q^{59} +11.9648 q^{60} -14.5211 q^{61} -3.61951 q^{62} -1.72889 q^{63} -3.90466 q^{64} +5.72889 q^{66} -6.06327 q^{67} -18.3624 q^{68} -6.23591 q^{69} +2.38360 q^{70} +6.50702 q^{71} -12.7289 q^{72} +2.00000 q^{73} -1.98596 q^{74} -8.01404 q^{75} -35.5632 q^{76} +0.778124 q^{77} +13.5843 q^{79} +7.07730 q^{80} -10.7289 q^{81} +24.4257 q^{82} +13.3624 q^{83} -7.61951 q^{84} -5.23591 q^{85} +24.2671 q^{86} +16.8242 q^{87} +5.72889 q^{88} +4.77812 q^{89} -6.80620 q^{90} -11.6937 q^{92} +3.29918 q^{93} -8.47494 q^{94} -10.1406 q^{95} -7.00000 q^{96} +4.14057 q^{97} +16.0312 q^{98} -2.22188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9} - 6 q^{10} - 3 q^{11} + 15 q^{12} - 8 q^{14} - 6 q^{15} + 3 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 4 q^{20} - 8 q^{21} - q^{22} + 3 q^{23} - 2 q^{24} - 2 q^{25} - 8 q^{27} - 18 q^{28} - 4 q^{29} - 21 q^{30} - q^{31} - 6 q^{32} - q^{33} + 4 q^{34} + 11 q^{35} + 3 q^{36} - 12 q^{37} + 31 q^{38} - 21 q^{40} - q^{41} - 9 q^{42} - 4 q^{43} - 7 q^{44} + 14 q^{45} + 20 q^{46} + 8 q^{47} + 20 q^{48} + 12 q^{50} - 15 q^{51} - 9 q^{53} - 9 q^{54} - q^{55} - 9 q^{56} - 26 q^{57} - 33 q^{58} - 30 q^{59} + 5 q^{60} - 18 q^{61} - 13 q^{62} + 6 q^{63} - 8 q^{64} + 6 q^{66} - 15 q^{67} - 29 q^{68} + q^{69} + 29 q^{70} + 11 q^{71} - 27 q^{72} + 6 q^{73} - 23 q^{74} - 7 q^{75} - 30 q^{76} + 5 q^{77} + 12 q^{79} + q^{80} - 21 q^{81} + 44 q^{82} + 14 q^{83} - 25 q^{84} + 4 q^{85} + 43 q^{86} + 43 q^{87} + 6 q^{88} + 17 q^{89} + 11 q^{90} + 7 q^{92} - 13 q^{93} - 10 q^{94} - 7 q^{95} - 21 q^{96} - 11 q^{97} + 38 q^{98} - 4 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50702 −1.77273 −0.886365 0.462987i \(-0.846778\pi\)
−0.886365 + 0.462987i \(0.846778\pi\)
\(3\) 2.28514 1.31933 0.659664 0.751561i \(-0.270699\pi\)
0.659664 + 0.751561i \(0.270699\pi\)
\(4\) 4.28514 2.14257
\(5\) 1.22188 0.546440 0.273220 0.961952i \(-0.411911\pi\)
0.273220 + 0.961952i \(0.411911\pi\)
\(6\) −5.72889 −2.33881
\(7\) −0.778124 −0.294103 −0.147052 0.989129i \(-0.546978\pi\)
−0.147052 + 0.989129i \(0.546978\pi\)
\(8\) −5.72889 −2.02547
\(9\) 2.22188 0.740625
\(10\) −3.06327 −0.968690
\(11\) −1.00000 −0.301511
\(12\) 9.79216 2.82675
\(13\) 0 0
\(14\) 1.95077 0.521365
\(15\) 2.79216 0.720933
\(16\) 5.79216 1.44804
\(17\) −4.28514 −1.03930 −0.519650 0.854379i \(-0.673938\pi\)
−0.519650 + 0.854379i \(0.673938\pi\)
\(18\) −5.57028 −1.31293
\(19\) −8.29918 −1.90396 −0.951981 0.306156i \(-0.900957\pi\)
−0.951981 + 0.306156i \(0.900957\pi\)
\(20\) 5.23591 1.17079
\(21\) −1.77812 −0.388018
\(22\) 2.50702 0.534498
\(23\) −2.72889 −0.569014 −0.284507 0.958674i \(-0.591830\pi\)
−0.284507 + 0.958674i \(0.591830\pi\)
\(24\) −13.0913 −2.67226
\(25\) −3.50702 −0.701404
\(26\) 0 0
\(27\) −1.77812 −0.342200
\(28\) −3.33437 −0.630137
\(29\) 7.36245 1.36717 0.683586 0.729870i \(-0.260419\pi\)
0.683586 + 0.729870i \(0.260419\pi\)
\(30\) −7.00000 −1.27802
\(31\) 1.44375 0.259306 0.129653 0.991559i \(-0.458614\pi\)
0.129653 + 0.991559i \(0.458614\pi\)
\(32\) −3.06327 −0.541514
\(33\) −2.28514 −0.397792
\(34\) 10.7429 1.84240
\(35\) −0.950771 −0.160710
\(36\) 9.52106 1.58684
\(37\) 0.792161 0.130230 0.0651152 0.997878i \(-0.479258\pi\)
0.0651152 + 0.997878i \(0.479258\pi\)
\(38\) 20.8062 3.37521
\(39\) 0 0
\(40\) −7.00000 −1.10680
\(41\) −9.74293 −1.52159 −0.760795 0.648992i \(-0.775191\pi\)
−0.760795 + 0.648992i \(0.775191\pi\)
\(42\) 4.45779 0.687852
\(43\) −9.67967 −1.47614 −0.738068 0.674727i \(-0.764261\pi\)
−0.738068 + 0.674727i \(0.764261\pi\)
\(44\) −4.28514 −0.646010
\(45\) 2.71486 0.404707
\(46\) 6.84139 1.00871
\(47\) 3.38049 0.493095 0.246547 0.969131i \(-0.420704\pi\)
0.246547 + 0.969131i \(0.420704\pi\)
\(48\) 13.2359 1.91044
\(49\) −6.39452 −0.913503
\(50\) 8.79216 1.24340
\(51\) −9.79216 −1.37118
\(52\) 0 0
\(53\) 1.79216 0.246172 0.123086 0.992396i \(-0.460721\pi\)
0.123086 + 0.992396i \(0.460721\pi\)
\(54\) 4.45779 0.606628
\(55\) −1.22188 −0.164758
\(56\) 4.45779 0.595697
\(57\) −18.9648 −2.51195
\(58\) −18.4578 −2.42363
\(59\) −5.20784 −0.678003 −0.339001 0.940786i \(-0.610089\pi\)
−0.339001 + 0.940786i \(0.610089\pi\)
\(60\) 11.9648 1.54465
\(61\) −14.5211 −1.85923 −0.929615 0.368531i \(-0.879861\pi\)
−0.929615 + 0.368531i \(0.879861\pi\)
\(62\) −3.61951 −0.459679
\(63\) −1.72889 −0.217820
\(64\) −3.90466 −0.488082
\(65\) 0 0
\(66\) 5.72889 0.705178
\(67\) −6.06327 −0.740746 −0.370373 0.928883i \(-0.620770\pi\)
−0.370373 + 0.928883i \(0.620770\pi\)
\(68\) −18.3624 −2.22677
\(69\) −6.23591 −0.750716
\(70\) 2.38360 0.284895
\(71\) 6.50702 0.772241 0.386121 0.922448i \(-0.373815\pi\)
0.386121 + 0.922448i \(0.373815\pi\)
\(72\) −12.7289 −1.50011
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −1.98596 −0.230863
\(75\) −8.01404 −0.925381
\(76\) −35.5632 −4.07938
\(77\) 0.778124 0.0886754
\(78\) 0 0
\(79\) 13.5843 1.52836 0.764178 0.645006i \(-0.223145\pi\)
0.764178 + 0.645006i \(0.223145\pi\)
\(80\) 7.07730 0.791267
\(81\) −10.7289 −1.19210
\(82\) 24.4257 2.69737
\(83\) 13.3624 1.46672 0.733360 0.679841i \(-0.237951\pi\)
0.733360 + 0.679841i \(0.237951\pi\)
\(84\) −7.61951 −0.831357
\(85\) −5.23591 −0.567915
\(86\) 24.2671 2.61679
\(87\) 16.8242 1.80375
\(88\) 5.72889 0.610702
\(89\) 4.77812 0.506480 0.253240 0.967403i \(-0.418504\pi\)
0.253240 + 0.967403i \(0.418504\pi\)
\(90\) −6.80620 −0.717436
\(91\) 0 0
\(92\) −11.6937 −1.21915
\(93\) 3.29918 0.342109
\(94\) −8.47494 −0.874123
\(95\) −10.1406 −1.04040
\(96\) −7.00000 −0.714435
\(97\) 4.14057 0.420411 0.210206 0.977657i \(-0.432587\pi\)
0.210206 + 0.977657i \(0.432587\pi\)
\(98\) 16.0312 1.61939
\(99\) −2.22188 −0.223307
\(100\) −15.0281 −1.50281
\(101\) 4.82424 0.480030 0.240015 0.970769i \(-0.422848\pi\)
0.240015 + 0.970769i \(0.422848\pi\)
\(102\) 24.5491 2.43073
\(103\) 9.76008 0.961690 0.480845 0.876806i \(-0.340330\pi\)
0.480845 + 0.876806i \(0.340330\pi\)
\(104\) 0 0
\(105\) −2.17265 −0.212029
\(106\) −4.49298 −0.436397
\(107\) 2.36245 0.228386 0.114193 0.993459i \(-0.463572\pi\)
0.114193 + 0.993459i \(0.463572\pi\)
\(108\) −7.61951 −0.733188
\(109\) 2.86946 0.274845 0.137422 0.990513i \(-0.456118\pi\)
0.137422 + 0.990513i \(0.456118\pi\)
\(110\) 3.06327 0.292071
\(111\) 1.81020 0.171817
\(112\) −4.50702 −0.425873
\(113\) −5.60236 −0.527026 −0.263513 0.964656i \(-0.584881\pi\)
−0.263513 + 0.964656i \(0.584881\pi\)
\(114\) 47.5451 4.45301
\(115\) −3.33437 −0.310932
\(116\) 31.5491 2.92926
\(117\) 0 0
\(118\) 13.0561 1.20192
\(119\) 3.33437 0.305661
\(120\) −15.9960 −1.46023
\(121\) 1.00000 0.0909091
\(122\) 36.4046 3.29591
\(123\) −22.2640 −2.00748
\(124\) 6.18668 0.555581
\(125\) −10.3945 −0.929714
\(126\) 4.33437 0.386137
\(127\) 7.23591 0.642083 0.321042 0.947065i \(-0.395967\pi\)
0.321042 + 0.947065i \(0.395967\pi\)
\(128\) 15.9156 1.40675
\(129\) −22.1194 −1.94751
\(130\) 0 0
\(131\) −10.3484 −0.904145 −0.452072 0.891981i \(-0.649315\pi\)
−0.452072 + 0.891981i \(0.649315\pi\)
\(132\) −9.79216 −0.852298
\(133\) 6.45779 0.559961
\(134\) 15.2007 1.31314
\(135\) −2.17265 −0.186992
\(136\) 24.5491 2.10507
\(137\) 4.93673 0.421774 0.210887 0.977510i \(-0.432365\pi\)
0.210887 + 0.977510i \(0.432365\pi\)
\(138\) 15.6336 1.33082
\(139\) 16.4718 1.39712 0.698561 0.715550i \(-0.253824\pi\)
0.698561 + 0.715550i \(0.253824\pi\)
\(140\) −4.07419 −0.344332
\(141\) 7.72489 0.650553
\(142\) −16.3132 −1.36897
\(143\) 0 0
\(144\) 12.8695 1.07246
\(145\) 8.99600 0.747077
\(146\) −5.01404 −0.414965
\(147\) −14.6124 −1.20521
\(148\) 3.39452 0.279028
\(149\) 1.90466 0.156036 0.0780178 0.996952i \(-0.475141\pi\)
0.0780178 + 0.996952i \(0.475141\pi\)
\(150\) 20.0913 1.64045
\(151\) −18.4086 −1.49807 −0.749034 0.662532i \(-0.769482\pi\)
−0.749034 + 0.662532i \(0.769482\pi\)
\(152\) 47.5451 3.85642
\(153\) −9.52106 −0.769732
\(154\) −1.95077 −0.157198
\(155\) 1.76409 0.141695
\(156\) 0 0
\(157\) −12.1054 −0.966114 −0.483057 0.875589i \(-0.660474\pi\)
−0.483057 + 0.875589i \(0.660474\pi\)
\(158\) −34.0561 −2.70936
\(159\) 4.09534 0.324782
\(160\) −3.74293 −0.295905
\(161\) 2.12342 0.167349
\(162\) 26.8975 2.11327
\(163\) −1.91869 −0.150284 −0.0751418 0.997173i \(-0.523941\pi\)
−0.0751418 + 0.997173i \(0.523941\pi\)
\(164\) −41.7499 −3.26012
\(165\) −2.79216 −0.217369
\(166\) −33.4999 −2.60010
\(167\) 7.06015 0.546331 0.273165 0.961967i \(-0.411929\pi\)
0.273165 + 0.961967i \(0.411929\pi\)
\(168\) 10.1867 0.785920
\(169\) 0 0
\(170\) 13.1265 1.00676
\(171\) −18.4397 −1.41012
\(172\) −41.4787 −3.16272
\(173\) 1.64759 0.125264 0.0626319 0.998037i \(-0.480051\pi\)
0.0626319 + 0.998037i \(0.480051\pi\)
\(174\) −42.1787 −3.19756
\(175\) 2.72889 0.206285
\(176\) −5.79216 −0.436601
\(177\) −11.9007 −0.894508
\(178\) −11.9788 −0.897852
\(179\) 7.33437 0.548197 0.274098 0.961702i \(-0.411621\pi\)
0.274098 + 0.961702i \(0.411621\pi\)
\(180\) 11.6336 0.867114
\(181\) 11.7750 0.875230 0.437615 0.899163i \(-0.355823\pi\)
0.437615 + 0.899163i \(0.355823\pi\)
\(182\) 0 0
\(183\) −33.1827 −2.45293
\(184\) 15.6336 1.15252
\(185\) 0.967923 0.0711631
\(186\) −8.27111 −0.606467
\(187\) 4.28514 0.313361
\(188\) 14.4859 1.05649
\(189\) 1.38360 0.100642
\(190\) 25.4226 1.84435
\(191\) 14.7429 1.06676 0.533381 0.845875i \(-0.320921\pi\)
0.533381 + 0.845875i \(0.320921\pi\)
\(192\) −8.92270 −0.643940
\(193\) 8.90154 0.640747 0.320374 0.947291i \(-0.396192\pi\)
0.320374 + 0.947291i \(0.396192\pi\)
\(194\) −10.3805 −0.745275
\(195\) 0 0
\(196\) −27.4014 −1.95725
\(197\) 6.11250 0.435497 0.217749 0.976005i \(-0.430129\pi\)
0.217749 + 0.976005i \(0.430129\pi\)
\(198\) 5.57028 0.395863
\(199\) 9.34529 0.662470 0.331235 0.943548i \(-0.392535\pi\)
0.331235 + 0.943548i \(0.392535\pi\)
\(200\) 20.0913 1.42067
\(201\) −13.8554 −0.977287
\(202\) −12.0945 −0.850963
\(203\) −5.72889 −0.402090
\(204\) −41.9608 −2.93784
\(205\) −11.9047 −0.831457
\(206\) −24.4687 −1.70482
\(207\) −6.06327 −0.421426
\(208\) 0 0
\(209\) 8.29918 0.574066
\(210\) 5.44687 0.375870
\(211\) −5.18668 −0.357066 −0.178533 0.983934i \(-0.557135\pi\)
−0.178533 + 0.983934i \(0.557135\pi\)
\(212\) 7.67967 0.527442
\(213\) 14.8695 1.01884
\(214\) −5.92270 −0.404867
\(215\) −11.8274 −0.806619
\(216\) 10.1867 0.693116
\(217\) −1.12342 −0.0762626
\(218\) −7.19380 −0.487226
\(219\) 4.57028 0.308831
\(220\) −5.23591 −0.353005
\(221\) 0 0
\(222\) −4.53821 −0.304585
\(223\) −16.8343 −1.12731 −0.563653 0.826012i \(-0.690605\pi\)
−0.563653 + 0.826012i \(0.690605\pi\)
\(224\) 2.38360 0.159261
\(225\) −7.79216 −0.519477
\(226\) 14.0452 0.934275
\(227\) 17.6164 1.16924 0.584621 0.811307i \(-0.301243\pi\)
0.584621 + 0.811307i \(0.301243\pi\)
\(228\) −81.2669 −5.38203
\(229\) −26.8554 −1.77466 −0.887328 0.461138i \(-0.847441\pi\)
−0.887328 + 0.461138i \(0.847441\pi\)
\(230\) 8.35933 0.551198
\(231\) 1.77812 0.116992
\(232\) −42.1787 −2.76917
\(233\) −27.1406 −1.77804 −0.889019 0.457870i \(-0.848612\pi\)
−0.889019 + 0.457870i \(0.848612\pi\)
\(234\) 0 0
\(235\) 4.13054 0.269446
\(236\) −22.3163 −1.45267
\(237\) 31.0421 2.01640
\(238\) −8.35933 −0.541855
\(239\) −0.746047 −0.0482577 −0.0241289 0.999709i \(-0.507681\pi\)
−0.0241289 + 0.999709i \(0.507681\pi\)
\(240\) 16.1726 1.04394
\(241\) −16.1726 −1.04177 −0.520886 0.853626i \(-0.674398\pi\)
−0.520886 + 0.853626i \(0.674398\pi\)
\(242\) −2.50702 −0.161157
\(243\) −19.1827 −1.23057
\(244\) −62.2248 −3.98353
\(245\) −7.81332 −0.499174
\(246\) 55.8162 3.55871
\(247\) 0 0
\(248\) −8.27111 −0.525216
\(249\) 30.5351 1.93508
\(250\) 26.0593 1.64813
\(251\) −11.0281 −0.696086 −0.348043 0.937479i \(-0.613154\pi\)
−0.348043 + 0.937479i \(0.613154\pi\)
\(252\) −7.40856 −0.466695
\(253\) 2.72889 0.171564
\(254\) −18.1406 −1.13824
\(255\) −11.9648 −0.749265
\(256\) −32.0913 −2.00571
\(257\) 18.8523 1.17597 0.587987 0.808870i \(-0.299920\pi\)
0.587987 + 0.808870i \(0.299920\pi\)
\(258\) 55.4538 3.45240
\(259\) −0.616399 −0.0383012
\(260\) 0 0
\(261\) 16.3584 1.01256
\(262\) 25.9437 1.60280
\(263\) −15.5522 −0.958993 −0.479496 0.877544i \(-0.659181\pi\)
−0.479496 + 0.877544i \(0.659181\pi\)
\(264\) 13.0913 0.805716
\(265\) 2.18980 0.134518
\(266\) −16.1898 −0.992660
\(267\) 10.9187 0.668213
\(268\) −25.9820 −1.58710
\(269\) −5.22188 −0.318383 −0.159192 0.987248i \(-0.550889\pi\)
−0.159192 + 0.987248i \(0.550889\pi\)
\(270\) 5.44687 0.331486
\(271\) −25.9367 −1.57554 −0.787772 0.615967i \(-0.788766\pi\)
−0.787772 + 0.615967i \(0.788766\pi\)
\(272\) −24.8202 −1.50495
\(273\) 0 0
\(274\) −12.3765 −0.747691
\(275\) 3.50702 0.211481
\(276\) −26.7218 −1.60846
\(277\) −17.7741 −1.06794 −0.533972 0.845502i \(-0.679301\pi\)
−0.533972 + 0.845502i \(0.679301\pi\)
\(278\) −41.2952 −2.47672
\(279\) 3.20784 0.192048
\(280\) 5.44687 0.325513
\(281\) −7.41168 −0.442143 −0.221072 0.975258i \(-0.570955\pi\)
−0.221072 + 0.975258i \(0.570955\pi\)
\(282\) −19.3664 −1.15326
\(283\) 9.31722 0.553851 0.276926 0.960891i \(-0.410684\pi\)
0.276926 + 0.960891i \(0.410684\pi\)
\(284\) 27.8835 1.65458
\(285\) −23.1726 −1.37263
\(286\) 0 0
\(287\) 7.58121 0.447505
\(288\) −6.80620 −0.401059
\(289\) 1.36245 0.0801439
\(290\) −22.5531 −1.32437
\(291\) 9.46179 0.554660
\(292\) 8.57028 0.501538
\(293\) 28.7530 1.67977 0.839883 0.542767i \(-0.182623\pi\)
0.839883 + 0.542767i \(0.182623\pi\)
\(294\) 36.6336 2.13651
\(295\) −6.36333 −0.370488
\(296\) −4.53821 −0.263778
\(297\) 1.77812 0.103177
\(298\) −4.77501 −0.276609
\(299\) 0 0
\(300\) −34.3413 −1.98270
\(301\) 7.53198 0.434136
\(302\) 46.1506 2.65567
\(303\) 11.0241 0.633316
\(304\) −48.0702 −2.75701
\(305\) −17.7429 −1.01596
\(306\) 23.8695 1.36453
\(307\) 0.792161 0.0452110 0.0226055 0.999744i \(-0.492804\pi\)
0.0226055 + 0.999744i \(0.492804\pi\)
\(308\) 3.33437 0.189993
\(309\) 22.3032 1.26878
\(310\) −4.42260 −0.251187
\(311\) 25.8022 1.46311 0.731554 0.681783i \(-0.238795\pi\)
0.731554 + 0.681783i \(0.238795\pi\)
\(312\) 0 0
\(313\) −26.2780 −1.48532 −0.742661 0.669668i \(-0.766437\pi\)
−0.742661 + 0.669668i \(0.766437\pi\)
\(314\) 30.3484 1.71266
\(315\) −2.11250 −0.119026
\(316\) 58.2108 3.27461
\(317\) −10.9788 −0.616633 −0.308317 0.951284i \(-0.599766\pi\)
−0.308317 + 0.951284i \(0.599766\pi\)
\(318\) −10.2671 −0.575751
\(319\) −7.36245 −0.412218
\(320\) −4.77101 −0.266707
\(321\) 5.39853 0.301316
\(322\) −5.32345 −0.296664
\(323\) 35.5632 1.97879
\(324\) −45.9748 −2.55416
\(325\) 0 0
\(326\) 4.81020 0.266412
\(327\) 6.55714 0.362610
\(328\) 55.8162 3.08194
\(329\) −2.63044 −0.145021
\(330\) 7.00000 0.385337
\(331\) −10.0561 −0.552736 −0.276368 0.961052i \(-0.589131\pi\)
−0.276368 + 0.961052i \(0.589131\pi\)
\(332\) 57.2600 3.14255
\(333\) 1.76008 0.0964520
\(334\) −17.6999 −0.968497
\(335\) −7.40856 −0.404773
\(336\) −10.2992 −0.561866
\(337\) 19.7398 1.07530 0.537648 0.843169i \(-0.319313\pi\)
0.537648 + 0.843169i \(0.319313\pi\)
\(338\) 0 0
\(339\) −12.8022 −0.695320
\(340\) −22.4366 −1.21680
\(341\) −1.44375 −0.0781836
\(342\) 46.2288 2.49977
\(343\) 10.4226 0.562767
\(344\) 55.4538 2.98987
\(345\) −7.61951 −0.410221
\(346\) −4.13054 −0.222059
\(347\) 18.3132 0.983105 0.491553 0.870848i \(-0.336430\pi\)
0.491553 + 0.870848i \(0.336430\pi\)
\(348\) 72.0943 3.86466
\(349\) −17.3765 −0.930142 −0.465071 0.885273i \(-0.653971\pi\)
−0.465071 + 0.885273i \(0.653971\pi\)
\(350\) −6.84139 −0.365688
\(351\) 0 0
\(352\) 3.06327 0.163273
\(353\) −33.7670 −1.79724 −0.898618 0.438732i \(-0.855428\pi\)
−0.898618 + 0.438732i \(0.855428\pi\)
\(354\) 29.8352 1.58572
\(355\) 7.95077 0.421983
\(356\) 20.4749 1.08517
\(357\) 7.61951 0.403267
\(358\) −18.3874 −0.971805
\(359\) 4.72889 0.249582 0.124791 0.992183i \(-0.460174\pi\)
0.124791 + 0.992183i \(0.460174\pi\)
\(360\) −15.5531 −0.819722
\(361\) 49.8764 2.62507
\(362\) −29.5202 −1.55155
\(363\) 2.28514 0.119939
\(364\) 0 0
\(365\) 2.44375 0.127912
\(366\) 83.1896 4.34839
\(367\) 6.42660 0.335466 0.167733 0.985832i \(-0.446355\pi\)
0.167733 + 0.985832i \(0.446355\pi\)
\(368\) −15.8062 −0.823955
\(369\) −21.6476 −1.12693
\(370\) −2.42660 −0.126153
\(371\) −1.39452 −0.0724000
\(372\) 14.1375 0.732993
\(373\) −4.41168 −0.228428 −0.114214 0.993456i \(-0.536435\pi\)
−0.114214 + 0.993456i \(0.536435\pi\)
\(374\) −10.7429 −0.555504
\(375\) −23.7530 −1.22660
\(376\) −19.3664 −0.998748
\(377\) 0 0
\(378\) −3.46871 −0.178411
\(379\) −19.5070 −1.00201 −0.501004 0.865445i \(-0.667036\pi\)
−0.501004 + 0.865445i \(0.667036\pi\)
\(380\) −43.4538 −2.22913
\(381\) 16.5351 0.847118
\(382\) −36.9608 −1.89108
\(383\) −27.6304 −1.41185 −0.705925 0.708287i \(-0.749468\pi\)
−0.705925 + 0.708287i \(0.749468\pi\)
\(384\) 36.3694 1.85597
\(385\) 0.950771 0.0484558
\(386\) −22.3163 −1.13587
\(387\) −21.5070 −1.09326
\(388\) 17.7429 0.900761
\(389\) −28.9960 −1.47016 −0.735078 0.677983i \(-0.762854\pi\)
−0.735078 + 0.677983i \(0.762854\pi\)
\(390\) 0 0
\(391\) 11.6937 0.591376
\(392\) 36.6336 1.85027
\(393\) −23.6476 −1.19286
\(394\) −15.3241 −0.772019
\(395\) 16.5984 0.835154
\(396\) −9.52106 −0.478451
\(397\) −34.6585 −1.73946 −0.869730 0.493527i \(-0.835707\pi\)
−0.869730 + 0.493527i \(0.835707\pi\)
\(398\) −23.4288 −1.17438
\(399\) 14.7570 0.738773
\(400\) −20.3132 −1.01566
\(401\) 14.5874 0.728462 0.364231 0.931309i \(-0.381332\pi\)
0.364231 + 0.931309i \(0.381332\pi\)
\(402\) 34.7358 1.73246
\(403\) 0 0
\(404\) 20.6725 1.02850
\(405\) −13.1094 −0.651410
\(406\) 14.3624 0.712796
\(407\) −0.792161 −0.0392660
\(408\) 56.0983 2.77728
\(409\) −16.6015 −0.820890 −0.410445 0.911885i \(-0.634627\pi\)
−0.410445 + 0.911885i \(0.634627\pi\)
\(410\) 29.8452 1.47395
\(411\) 11.2811 0.556458
\(412\) 41.8234 2.06049
\(413\) 4.05234 0.199403
\(414\) 15.2007 0.747075
\(415\) 16.3273 0.801473
\(416\) 0 0
\(417\) 37.6405 1.84326
\(418\) −20.8062 −1.01766
\(419\) −22.2952 −1.08919 −0.544595 0.838699i \(-0.683317\pi\)
−0.544595 + 0.838699i \(0.683317\pi\)
\(420\) −9.31010 −0.454286
\(421\) 3.45779 0.168522 0.0842612 0.996444i \(-0.473147\pi\)
0.0842612 + 0.996444i \(0.473147\pi\)
\(422\) 13.0031 0.632982
\(423\) 7.51102 0.365198
\(424\) −10.2671 −0.498615
\(425\) 15.0281 0.728969
\(426\) −37.2780 −1.80613
\(427\) 11.2992 0.546806
\(428\) 10.1234 0.489334
\(429\) 0 0
\(430\) 29.6514 1.42992
\(431\) −25.8804 −1.24661 −0.623307 0.781977i \(-0.714211\pi\)
−0.623307 + 0.781977i \(0.714211\pi\)
\(432\) −10.2992 −0.495520
\(433\) 14.3805 0.691082 0.345541 0.938404i \(-0.387695\pi\)
0.345541 + 0.938404i \(0.387695\pi\)
\(434\) 2.81643 0.135193
\(435\) 20.5571 0.985639
\(436\) 12.2961 0.588875
\(437\) 22.6476 1.08338
\(438\) −11.4578 −0.547474
\(439\) 4.56628 0.217937 0.108968 0.994045i \(-0.465245\pi\)
0.108968 + 0.994045i \(0.465245\pi\)
\(440\) 7.00000 0.333712
\(441\) −14.2078 −0.676564
\(442\) 0 0
\(443\) 18.1718 0.863366 0.431683 0.902025i \(-0.357920\pi\)
0.431683 + 0.902025i \(0.357920\pi\)
\(444\) 7.75697 0.368129
\(445\) 5.83828 0.276761
\(446\) 42.2038 1.99841
\(447\) 4.35241 0.205862
\(448\) 3.03831 0.143546
\(449\) 12.6295 0.596025 0.298013 0.954562i \(-0.403676\pi\)
0.298013 + 0.954562i \(0.403676\pi\)
\(450\) 19.5351 0.920893
\(451\) 9.74293 0.458777
\(452\) −24.0069 −1.12919
\(453\) −42.0662 −1.97644
\(454\) −44.1646 −2.07275
\(455\) 0 0
\(456\) 108.647 5.08788
\(457\) 25.7882 1.20632 0.603160 0.797621i \(-0.293908\pi\)
0.603160 + 0.797621i \(0.293908\pi\)
\(458\) 67.3271 3.14599
\(459\) 7.61951 0.355648
\(460\) −14.2883 −0.666193
\(461\) 12.6336 0.588403 0.294202 0.955743i \(-0.404946\pi\)
0.294202 + 0.955743i \(0.404946\pi\)
\(462\) −4.45779 −0.207395
\(463\) 3.47494 0.161494 0.0807471 0.996735i \(-0.474269\pi\)
0.0807471 + 0.996735i \(0.474269\pi\)
\(464\) 42.6445 1.97972
\(465\) 4.03119 0.186942
\(466\) 68.0419 3.15198
\(467\) −18.7258 −0.866526 −0.433263 0.901268i \(-0.642638\pi\)
−0.433263 + 0.901268i \(0.642638\pi\)
\(468\) 0 0
\(469\) 4.71797 0.217856
\(470\) −10.3553 −0.477656
\(471\) −27.6625 −1.27462
\(472\) 29.8352 1.37327
\(473\) 9.67967 0.445072
\(474\) −77.8232 −3.57454
\(475\) 29.1054 1.33545
\(476\) 14.2883 0.654901
\(477\) 3.98196 0.182321
\(478\) 1.87035 0.0855479
\(479\) −9.28514 −0.424249 −0.212124 0.977243i \(-0.568038\pi\)
−0.212124 + 0.977243i \(0.568038\pi\)
\(480\) −8.55313 −0.390395
\(481\) 0 0
\(482\) 40.5451 1.84678
\(483\) 4.85231 0.220788
\(484\) 4.28514 0.194779
\(485\) 5.05926 0.229729
\(486\) 48.0913 2.18147
\(487\) 39.9296 1.80938 0.904692 0.426067i \(-0.140101\pi\)
0.904692 + 0.426067i \(0.140101\pi\)
\(488\) 83.1896 3.76582
\(489\) −4.38449 −0.198273
\(490\) 19.5881 0.884901
\(491\) −41.1827 −1.85855 −0.929274 0.369391i \(-0.879566\pi\)
−0.929274 + 0.369391i \(0.879566\pi\)
\(492\) −95.4044 −4.30116
\(493\) −31.5491 −1.42090
\(494\) 0 0
\(495\) −2.71486 −0.122024
\(496\) 8.36245 0.375485
\(497\) −5.06327 −0.227119
\(498\) −76.5520 −3.43038
\(499\) −19.3132 −0.864578 −0.432289 0.901735i \(-0.642294\pi\)
−0.432289 + 0.901735i \(0.642294\pi\)
\(500\) −44.5420 −1.99198
\(501\) 16.1335 0.720790
\(502\) 27.6476 1.23397
\(503\) 19.6897 0.877920 0.438960 0.898507i \(-0.355347\pi\)
0.438960 + 0.898507i \(0.355347\pi\)
\(504\) 9.90466 0.441188
\(505\) 5.89462 0.262307
\(506\) −6.84139 −0.304137
\(507\) 0 0
\(508\) 31.0069 1.37571
\(509\) −13.4749 −0.597266 −0.298633 0.954368i \(-0.596531\pi\)
−0.298633 + 0.954368i \(0.596531\pi\)
\(510\) 29.9960 1.32825
\(511\) −1.55625 −0.0688443
\(512\) 48.6224 2.14883
\(513\) 14.7570 0.651536
\(514\) −47.2631 −2.08469
\(515\) 11.9256 0.525505
\(516\) −94.7848 −4.17267
\(517\) −3.38049 −0.148674
\(518\) 1.54532 0.0678977
\(519\) 3.76497 0.165264
\(520\) 0 0
\(521\) 19.4266 0.851095 0.425547 0.904936i \(-0.360082\pi\)
0.425547 + 0.904936i \(0.360082\pi\)
\(522\) −41.0109 −1.79500
\(523\) 10.9227 0.477616 0.238808 0.971067i \(-0.423243\pi\)
0.238808 + 0.971067i \(0.423243\pi\)
\(524\) −44.3444 −1.93719
\(525\) 6.23591 0.272158
\(526\) 38.9898 1.70003
\(527\) −6.18668 −0.269496
\(528\) −13.2359 −0.576019
\(529\) −15.5531 −0.676223
\(530\) −5.48987 −0.238465
\(531\) −11.5712 −0.502146
\(532\) 27.6725 1.19976
\(533\) 0 0
\(534\) −27.3734 −1.18456
\(535\) 2.88662 0.124799
\(536\) 34.7358 1.50036
\(537\) 16.7601 0.723251
\(538\) 13.0913 0.564408
\(539\) 6.39452 0.275432
\(540\) −9.31010 −0.400643
\(541\) 16.9820 0.730111 0.365056 0.930986i \(-0.381050\pi\)
0.365056 + 0.930986i \(0.381050\pi\)
\(542\) 65.0239 2.79301
\(543\) 26.9076 1.15471
\(544\) 13.1265 0.562795
\(545\) 3.50613 0.150186
\(546\) 0 0
\(547\) 1.13345 0.0484629 0.0242315 0.999706i \(-0.492286\pi\)
0.0242315 + 0.999706i \(0.492286\pi\)
\(548\) 21.1546 0.903680
\(549\) −32.2640 −1.37699
\(550\) −8.79216 −0.374899
\(551\) −61.1023 −2.60304
\(552\) 35.7249 1.52055
\(553\) −10.5703 −0.449494
\(554\) 44.5601 1.89318
\(555\) 2.21184 0.0938874
\(556\) 70.5841 2.99343
\(557\) 20.2671 0.858745 0.429372 0.903128i \(-0.358735\pi\)
0.429372 + 0.903128i \(0.358735\pi\)
\(558\) −8.04211 −0.340450
\(559\) 0 0
\(560\) −5.50702 −0.232714
\(561\) 9.79216 0.413425
\(562\) 18.5812 0.783801
\(563\) 0.313217 0.0132005 0.00660026 0.999978i \(-0.497899\pi\)
0.00660026 + 0.999978i \(0.497899\pi\)
\(564\) 33.1023 1.39386
\(565\) −6.84539 −0.287988
\(566\) −23.3584 −0.981829
\(567\) 8.34841 0.350600
\(568\) −37.2780 −1.56415
\(569\) −11.0842 −0.464675 −0.232337 0.972635i \(-0.574637\pi\)
−0.232337 + 0.972635i \(0.574637\pi\)
\(570\) 58.0943 2.43330
\(571\) 41.7037 1.74525 0.872624 0.488393i \(-0.162417\pi\)
0.872624 + 0.488393i \(0.162417\pi\)
\(572\) 0 0
\(573\) 33.6897 1.40741
\(574\) −19.0062 −0.793305
\(575\) 9.57028 0.399108
\(576\) −8.67566 −0.361486
\(577\) −19.1867 −0.798752 −0.399376 0.916787i \(-0.630773\pi\)
−0.399376 + 0.916787i \(0.630773\pi\)
\(578\) −3.41568 −0.142073
\(579\) 20.3413 0.845355
\(580\) 38.5491 1.60067
\(581\) −10.3976 −0.431367
\(582\) −23.7209 −0.983263
\(583\) −1.79216 −0.0742237
\(584\) −11.4578 −0.474127
\(585\) 0 0
\(586\) −72.0842 −2.97777
\(587\) 12.5843 0.519411 0.259705 0.965688i \(-0.416375\pi\)
0.259705 + 0.965688i \(0.416375\pi\)
\(588\) −62.6162 −2.58225
\(589\) −11.9820 −0.493708
\(590\) 15.9530 0.656775
\(591\) 13.9679 0.574564
\(592\) 4.58832 0.188579
\(593\) 13.7117 0.563074 0.281537 0.959550i \(-0.409156\pi\)
0.281537 + 0.959550i \(0.409156\pi\)
\(594\) −4.45779 −0.182905
\(595\) 4.07419 0.167025
\(596\) 8.16172 0.334317
\(597\) 21.3553 0.874015
\(598\) 0 0
\(599\) −15.3905 −0.628840 −0.314420 0.949284i \(-0.601810\pi\)
−0.314420 + 0.949284i \(0.601810\pi\)
\(600\) 45.9116 1.87433
\(601\) −16.2148 −0.661414 −0.330707 0.943734i \(-0.607287\pi\)
−0.330707 + 0.943734i \(0.607287\pi\)
\(602\) −18.8828 −0.769606
\(603\) −13.4718 −0.548615
\(604\) −78.8833 −3.20972
\(605\) 1.22188 0.0496763
\(606\) −27.6376 −1.12270
\(607\) 2.68278 0.108891 0.0544453 0.998517i \(-0.482661\pi\)
0.0544453 + 0.998517i \(0.482661\pi\)
\(608\) 25.4226 1.03102
\(609\) −13.0913 −0.530488
\(610\) 44.4819 1.80102
\(611\) 0 0
\(612\) −40.7991 −1.64921
\(613\) 36.0913 1.45772 0.728858 0.684665i \(-0.240052\pi\)
0.728858 + 0.684665i \(0.240052\pi\)
\(614\) −1.98596 −0.0801469
\(615\) −27.2038 −1.09696
\(616\) −4.45779 −0.179609
\(617\) 19.1718 0.771826 0.385913 0.922535i \(-0.373886\pi\)
0.385913 + 0.922535i \(0.373886\pi\)
\(618\) −55.9145 −2.24921
\(619\) −6.38049 −0.256453 −0.128227 0.991745i \(-0.540929\pi\)
−0.128227 + 0.991745i \(0.540929\pi\)
\(620\) 7.55936 0.303591
\(621\) 4.85231 0.194717
\(622\) −64.6866 −2.59370
\(623\) −3.71797 −0.148957
\(624\) 0 0
\(625\) 4.83427 0.193371
\(626\) 65.8795 2.63307
\(627\) 18.9648 0.757381
\(628\) −51.8733 −2.06997
\(629\) −3.39452 −0.135349
\(630\) 5.29607 0.211000
\(631\) 20.9007 0.832042 0.416021 0.909355i \(-0.363424\pi\)
0.416021 + 0.909355i \(0.363424\pi\)
\(632\) −77.8232 −3.09564
\(633\) −11.8523 −0.471087
\(634\) 27.5242 1.09312
\(635\) 8.84139 0.350860
\(636\) 17.5491 0.695868
\(637\) 0 0
\(638\) 18.4578 0.730751
\(639\) 14.4578 0.571941
\(640\) 19.4469 0.768705
\(641\) 19.1085 0.754740 0.377370 0.926063i \(-0.376828\pi\)
0.377370 + 0.926063i \(0.376828\pi\)
\(642\) −13.5342 −0.534152
\(643\) 3.50702 0.138303 0.0691517 0.997606i \(-0.477971\pi\)
0.0691517 + 0.997606i \(0.477971\pi\)
\(644\) 9.09915 0.358557
\(645\) −27.0272 −1.06419
\(646\) −89.1575 −3.50786
\(647\) 20.8343 0.819080 0.409540 0.912292i \(-0.365689\pi\)
0.409540 + 0.912292i \(0.365689\pi\)
\(648\) 61.4647 2.41456
\(649\) 5.20784 0.204426
\(650\) 0 0
\(651\) −2.56717 −0.100615
\(652\) −8.22188 −0.321994
\(653\) −12.6757 −0.496037 −0.248019 0.968755i \(-0.579779\pi\)
−0.248019 + 0.968755i \(0.579779\pi\)
\(654\) −16.4389 −0.642810
\(655\) −12.6445 −0.494060
\(656\) −56.4326 −2.20332
\(657\) 4.44375 0.173367
\(658\) 6.59455 0.257082
\(659\) 4.37960 0.170605 0.0853025 0.996355i \(-0.472814\pi\)
0.0853025 + 0.996355i \(0.472814\pi\)
\(660\) −11.9648 −0.465730
\(661\) 1.12253 0.0436614 0.0218307 0.999762i \(-0.493051\pi\)
0.0218307 + 0.999762i \(0.493051\pi\)
\(662\) 25.2110 0.979852
\(663\) 0 0
\(664\) −76.5520 −2.97080
\(665\) 7.89062 0.305985
\(666\) −4.41256 −0.170983
\(667\) −20.0913 −0.777940
\(668\) 30.2538 1.17055
\(669\) −38.4687 −1.48729
\(670\) 18.5734 0.717553
\(671\) 14.5211 0.560579
\(672\) 5.44687 0.210117
\(673\) 18.0492 0.695747 0.347873 0.937542i \(-0.386904\pi\)
0.347873 + 0.937542i \(0.386904\pi\)
\(674\) −49.4881 −1.90621
\(675\) 6.23591 0.240020
\(676\) 0 0
\(677\) −26.7037 −1.02631 −0.513154 0.858297i \(-0.671523\pi\)
−0.513154 + 0.858297i \(0.671523\pi\)
\(678\) 32.0953 1.23261
\(679\) −3.22188 −0.123644
\(680\) 29.9960 1.15029
\(681\) 40.2560 1.54261
\(682\) 3.61951 0.138598
\(683\) −30.9788 −1.18537 −0.592686 0.805433i \(-0.701933\pi\)
−0.592686 + 0.805433i \(0.701933\pi\)
\(684\) −79.0170 −3.02129
\(685\) 6.03208 0.230474
\(686\) −26.1296 −0.997635
\(687\) −61.3685 −2.34135
\(688\) −56.0662 −2.13750
\(689\) 0 0
\(690\) 19.1023 0.727211
\(691\) 2.33126 0.0886852 0.0443426 0.999016i \(-0.485881\pi\)
0.0443426 + 0.999016i \(0.485881\pi\)
\(692\) 7.06015 0.268387
\(693\) 1.72889 0.0656753
\(694\) −45.9116 −1.74278
\(695\) 20.1265 0.763443
\(696\) −96.3843 −3.65344
\(697\) 41.7499 1.58139
\(698\) 43.5632 1.64889
\(699\) −62.0201 −2.34581
\(700\) 11.6937 0.441980
\(701\) −22.5834 −0.852965 −0.426482 0.904496i \(-0.640247\pi\)
−0.426482 + 0.904496i \(0.640247\pi\)
\(702\) 0 0
\(703\) −6.57429 −0.247954
\(704\) 3.90466 0.147162
\(705\) 9.43886 0.355488
\(706\) 84.6545 3.18601
\(707\) −3.75385 −0.141178
\(708\) −50.9960 −1.91655
\(709\) 15.7218 0.590444 0.295222 0.955429i \(-0.404606\pi\)
0.295222 + 0.955429i \(0.404606\pi\)
\(710\) −19.9327 −0.748062
\(711\) 30.1827 1.13194
\(712\) −27.3734 −1.02586
\(713\) −3.93985 −0.147548
\(714\) −19.1023 −0.714884
\(715\) 0 0
\(716\) 31.4288 1.17455
\(717\) −1.70482 −0.0636678
\(718\) −11.8554 −0.442441
\(719\) −29.8303 −1.11248 −0.556241 0.831021i \(-0.687757\pi\)
−0.556241 + 0.831021i \(0.687757\pi\)
\(720\) 15.7249 0.586032
\(721\) −7.59455 −0.282836
\(722\) −125.041 −4.65355
\(723\) −36.9568 −1.37444
\(724\) 50.4576 1.87524
\(725\) −25.8202 −0.958939
\(726\) −5.72889 −0.212619
\(727\) −36.6053 −1.35761 −0.678807 0.734316i \(-0.737503\pi\)
−0.678807 + 0.734316i \(0.737503\pi\)
\(728\) 0 0
\(729\) −11.6485 −0.431425
\(730\) −6.12653 −0.226753
\(731\) 41.4787 1.53415
\(732\) −142.193 −5.25559
\(733\) −29.8695 −1.10325 −0.551627 0.834091i \(-0.685993\pi\)
−0.551627 + 0.834091i \(0.685993\pi\)
\(734\) −16.1116 −0.594690
\(735\) −17.8545 −0.658575
\(736\) 8.35933 0.308129
\(737\) 6.06327 0.223343
\(738\) 54.2709 1.99774
\(739\) −30.2569 −1.11302 −0.556508 0.830842i \(-0.687859\pi\)
−0.556508 + 0.830842i \(0.687859\pi\)
\(740\) 4.14769 0.152472
\(741\) 0 0
\(742\) 3.49610 0.128346
\(743\) −39.2419 −1.43965 −0.719824 0.694157i \(-0.755777\pi\)
−0.719824 + 0.694157i \(0.755777\pi\)
\(744\) −18.9007 −0.692932
\(745\) 2.32725 0.0852640
\(746\) 11.0602 0.404941
\(747\) 29.6897 1.08629
\(748\) 18.3624 0.671398
\(749\) −1.83828 −0.0671691
\(750\) 59.5491 2.17443
\(751\) 6.82335 0.248988 0.124494 0.992220i \(-0.460269\pi\)
0.124494 + 0.992220i \(0.460269\pi\)
\(752\) 19.5803 0.714021
\(753\) −25.2007 −0.918365
\(754\) 0 0
\(755\) −22.4930 −0.818603
\(756\) 5.92893 0.215633
\(757\) −0.752967 −0.0273670 −0.0136835 0.999906i \(-0.504356\pi\)
−0.0136835 + 0.999906i \(0.504356\pi\)
\(758\) 48.9045 1.77629
\(759\) 6.23591 0.226349
\(760\) 58.0943 2.10730
\(761\) −34.9748 −1.26784 −0.633919 0.773400i \(-0.718555\pi\)
−0.633919 + 0.773400i \(0.718555\pi\)
\(762\) −41.4538 −1.50171
\(763\) −2.23280 −0.0808327
\(764\) 63.1756 2.28561
\(765\) −11.6336 −0.420612
\(766\) 69.2700 2.50283
\(767\) 0 0
\(768\) −73.3333 −2.64619
\(769\) −15.4649 −0.557679 −0.278839 0.960338i \(-0.589950\pi\)
−0.278839 + 0.960338i \(0.589950\pi\)
\(770\) −2.38360 −0.0858990
\(771\) 43.0802 1.55150
\(772\) 38.1444 1.37285
\(773\) 36.1366 1.29974 0.649871 0.760045i \(-0.274823\pi\)
0.649871 + 0.760045i \(0.274823\pi\)
\(774\) 53.9185 1.93806
\(775\) −5.06327 −0.181878
\(776\) −23.7209 −0.851530
\(777\) −1.40856 −0.0505318
\(778\) 72.6935 2.60619
\(779\) 80.8583 2.89705
\(780\) 0 0
\(781\) −6.50702 −0.232839
\(782\) −29.3163 −1.04835
\(783\) −13.0913 −0.467846
\(784\) −37.0381 −1.32279
\(785\) −14.7913 −0.527923
\(786\) 59.2849 2.11462
\(787\) 22.9499 0.818075 0.409037 0.912518i \(-0.365865\pi\)
0.409037 + 0.912518i \(0.365865\pi\)
\(788\) 26.1929 0.933084
\(789\) −35.5391 −1.26523
\(790\) −41.6124 −1.48050
\(791\) 4.35933 0.155000
\(792\) 12.7289 0.452302
\(793\) 0 0
\(794\) 86.8895 3.08359
\(795\) 5.00400 0.177474
\(796\) 40.0459 1.41939
\(797\) 43.4498 1.53907 0.769535 0.638604i \(-0.220488\pi\)
0.769535 + 0.638604i \(0.220488\pi\)
\(798\) −36.9960 −1.30964
\(799\) −14.4859 −0.512473
\(800\) 10.7429 0.379820
\(801\) 10.6164 0.375112
\(802\) −36.5710 −1.29137
\(803\) −2.00000 −0.0705785
\(804\) −59.3725 −2.09391
\(805\) 2.59455 0.0914460
\(806\) 0 0
\(807\) −11.9327 −0.420052
\(808\) −27.6376 −0.972286
\(809\) −43.1094 −1.51565 −0.757823 0.652461i \(-0.773737\pi\)
−0.757823 + 0.652461i \(0.773737\pi\)
\(810\) 32.8655 1.15477
\(811\) 17.9428 0.630056 0.315028 0.949082i \(-0.397986\pi\)
0.315028 + 0.949082i \(0.397986\pi\)
\(812\) −24.5491 −0.861506
\(813\) −59.2691 −2.07866
\(814\) 1.98596 0.0696080
\(815\) −2.34441 −0.0821210
\(816\) −56.7178 −1.98552
\(817\) 80.3333 2.81051
\(818\) 41.6202 1.45522
\(819\) 0 0
\(820\) −51.0131 −1.78146
\(821\) −15.6647 −0.546703 −0.273352 0.961914i \(-0.588132\pi\)
−0.273352 + 0.961914i \(0.588132\pi\)
\(822\) −28.2820 −0.986449
\(823\) 3.69771 0.128894 0.0644470 0.997921i \(-0.479472\pi\)
0.0644470 + 0.997921i \(0.479472\pi\)
\(824\) −55.9145 −1.94787
\(825\) 8.01404 0.279013
\(826\) −10.1593 −0.353487
\(827\) 42.3201 1.47162 0.735808 0.677191i \(-0.236803\pi\)
0.735808 + 0.677191i \(0.236803\pi\)
\(828\) −25.9820 −0.902936
\(829\) 7.15461 0.248490 0.124245 0.992252i \(-0.460349\pi\)
0.124245 + 0.992252i \(0.460349\pi\)
\(830\) −40.9327 −1.42080
\(831\) −40.6164 −1.40897
\(832\) 0 0
\(833\) 27.4014 0.949404
\(834\) −94.3654 −3.26761
\(835\) 8.62663 0.298537
\(836\) 35.5632 1.22998
\(837\) −2.56717 −0.0887344
\(838\) 55.8944 1.93084
\(839\) −2.76008 −0.0952887 −0.0476443 0.998864i \(-0.515171\pi\)
−0.0476443 + 0.998864i \(0.515171\pi\)
\(840\) 12.4469 0.429458
\(841\) 25.2056 0.869159
\(842\) −8.66874 −0.298745
\(843\) −16.9367 −0.583332
\(844\) −22.2257 −0.765040
\(845\) 0 0
\(846\) −18.8303 −0.647398
\(847\) −0.778124 −0.0267367
\(848\) 10.3805 0.356467
\(849\) 21.2912 0.730711
\(850\) −37.6757 −1.29226
\(851\) −2.16172 −0.0741030
\(852\) 63.7178 2.18294
\(853\) −46.1615 −1.58054 −0.790270 0.612758i \(-0.790060\pi\)
−0.790270 + 0.612758i \(0.790060\pi\)
\(854\) −28.3273 −0.969339
\(855\) −22.5311 −0.770547
\(856\) −13.5342 −0.462590
\(857\) 26.2680 0.897297 0.448649 0.893708i \(-0.351905\pi\)
0.448649 + 0.893708i \(0.351905\pi\)
\(858\) 0 0
\(859\) −32.0381 −1.09313 −0.546563 0.837418i \(-0.684064\pi\)
−0.546563 + 0.837418i \(0.684064\pi\)
\(860\) −50.6819 −1.72824
\(861\) 17.3241 0.590405
\(862\) 64.8826 2.20991
\(863\) 24.2078 0.824044 0.412022 0.911174i \(-0.364823\pi\)
0.412022 + 0.911174i \(0.364823\pi\)
\(864\) 5.44687 0.185306
\(865\) 2.01315 0.0684491
\(866\) −36.0521 −1.22510
\(867\) 3.11338 0.105736
\(868\) −4.81401 −0.163398
\(869\) −13.5843 −0.460817
\(870\) −51.5371 −1.74727
\(871\) 0 0
\(872\) −16.4389 −0.556690
\(873\) 9.19983 0.311367
\(874\) −56.7779 −1.92054
\(875\) 8.08823 0.273432
\(876\) 19.5843 0.661693
\(877\) −1.05635 −0.0356703 −0.0178351 0.999841i \(-0.505677\pi\)
−0.0178351 + 0.999841i \(0.505677\pi\)
\(878\) −11.4478 −0.386343
\(879\) 65.7046 2.21616
\(880\) −7.07730 −0.238576
\(881\) −24.1655 −0.814157 −0.407079 0.913393i \(-0.633453\pi\)
−0.407079 + 0.913393i \(0.633453\pi\)
\(882\) 35.6193 1.19936
\(883\) 5.84831 0.196811 0.0984057 0.995146i \(-0.468626\pi\)
0.0984057 + 0.995146i \(0.468626\pi\)
\(884\) 0 0
\(885\) −14.5411 −0.488795
\(886\) −45.5569 −1.53052
\(887\) −8.67566 −0.291300 −0.145650 0.989336i \(-0.546527\pi\)
−0.145650 + 0.989336i \(0.546527\pi\)
\(888\) −10.3705 −0.348010
\(889\) −5.63044 −0.188839
\(890\) −14.6367 −0.490622
\(891\) 10.7289 0.359431
\(892\) −72.1373 −2.41533
\(893\) −28.0553 −0.938834
\(894\) −10.9116 −0.364938
\(895\) 8.96169 0.299556
\(896\) −12.3843 −0.413730
\(897\) 0 0
\(898\) −31.6625 −1.05659
\(899\) 10.6295 0.354515
\(900\) −33.3905 −1.11302
\(901\) −7.67967 −0.255847
\(902\) −24.4257 −0.813287
\(903\) 17.2116 0.572768
\(904\) 32.0953 1.06748
\(905\) 14.3876 0.478260
\(906\) 105.461 3.50370
\(907\) −15.5952 −0.517832 −0.258916 0.965900i \(-0.583365\pi\)
−0.258916 + 0.965900i \(0.583365\pi\)
\(908\) 75.4888 2.50518
\(909\) 10.7189 0.355522
\(910\) 0 0
\(911\) 24.5672 0.813947 0.406973 0.913440i \(-0.366584\pi\)
0.406973 + 0.913440i \(0.366584\pi\)
\(912\) −109.847 −3.63741
\(913\) −13.3624 −0.442232
\(914\) −64.6514 −2.13848
\(915\) −40.5451 −1.34038
\(916\) −115.079 −3.80233
\(917\) 8.05234 0.265912
\(918\) −19.1023 −0.630469
\(919\) 17.2811 0.570052 0.285026 0.958520i \(-0.407998\pi\)
0.285026 + 0.958520i \(0.407998\pi\)
\(920\) 19.1023 0.629783
\(921\) 1.81020 0.0596482
\(922\) −31.6725 −1.04308
\(923\) 0 0
\(924\) 7.61951 0.250664
\(925\) −2.77812 −0.0913441
\(926\) −8.71174 −0.286286
\(927\) 21.6857 0.712252
\(928\) −22.5531 −0.740343
\(929\) 48.2569 1.58326 0.791628 0.611003i \(-0.209234\pi\)
0.791628 + 0.611003i \(0.209234\pi\)
\(930\) −10.1063 −0.331398
\(931\) 53.0693 1.73928
\(932\) −116.301 −3.80957
\(933\) 58.9617 1.93032
\(934\) 46.9459 1.53612
\(935\) 5.23591 0.171233
\(936\) 0 0
\(937\) −17.7209 −0.578916 −0.289458 0.957191i \(-0.593475\pi\)
−0.289458 + 0.957191i \(0.593475\pi\)
\(938\) −11.8280 −0.386199
\(939\) −60.0490 −1.95963
\(940\) 17.6999 0.577308
\(941\) −7.96392 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(942\) 69.3504 2.25956
\(943\) 26.5874 0.865806
\(944\) −30.1646 −0.981775
\(945\) 1.69059 0.0549948
\(946\) −24.2671 −0.788992
\(947\) −15.5632 −0.505735 −0.252867 0.967501i \(-0.581374\pi\)
−0.252867 + 0.967501i \(0.581374\pi\)
\(948\) 133.020 4.32028
\(949\) 0 0
\(950\) −72.9677 −2.36739
\(951\) −25.0882 −0.813541
\(952\) −19.1023 −0.619108
\(953\) −31.8483 −1.03167 −0.515834 0.856689i \(-0.672518\pi\)
−0.515834 + 0.856689i \(0.672518\pi\)
\(954\) −9.98285 −0.323207
\(955\) 18.0140 0.582921
\(956\) −3.19692 −0.103396
\(957\) −16.8242 −0.543850
\(958\) 23.2780 0.752079
\(959\) −3.84139 −0.124045
\(960\) −10.9024 −0.351874
\(961\) −28.9156 −0.932761
\(962\) 0 0
\(963\) 5.24906 0.169149
\(964\) −69.3021 −2.23207
\(965\) 10.8766 0.350130
\(966\) −12.1648 −0.391397
\(967\) 46.1023 1.48255 0.741274 0.671202i \(-0.234222\pi\)
0.741274 + 0.671202i \(0.234222\pi\)
\(968\) −5.72889 −0.184134
\(969\) 81.2669 2.61067
\(970\) −12.6837 −0.407248
\(971\) −14.7882 −0.474575 −0.237287 0.971440i \(-0.576258\pi\)
−0.237287 + 0.971440i \(0.576258\pi\)
\(972\) −82.2005 −2.63658
\(973\) −12.8171 −0.410898
\(974\) −100.104 −3.20755
\(975\) 0 0
\(976\) −84.1083 −2.69224
\(977\) −1.35933 −0.0434889 −0.0217444 0.999764i \(-0.506922\pi\)
−0.0217444 + 0.999764i \(0.506922\pi\)
\(978\) 10.9920 0.351485
\(979\) −4.77812 −0.152710
\(980\) −33.4812 −1.06952
\(981\) 6.37560 0.203557
\(982\) 103.246 3.29470
\(983\) −27.4709 −0.876187 −0.438093 0.898929i \(-0.644346\pi\)
−0.438093 + 0.898929i \(0.644346\pi\)
\(984\) 127.548 4.06608
\(985\) 7.46871 0.237973
\(986\) 79.0943 2.51887
\(987\) −6.01092 −0.191330
\(988\) 0 0
\(989\) 26.4148 0.839941
\(990\) 6.80620 0.216315
\(991\) 0.173535 0.00551253 0.00275626 0.999996i \(-0.499123\pi\)
0.00275626 + 0.999996i \(0.499123\pi\)
\(992\) −4.42260 −0.140418
\(993\) −22.9797 −0.729240
\(994\) 12.6937 0.402620
\(995\) 11.4188 0.362000
\(996\) 130.847 4.14605
\(997\) 44.1896 1.39950 0.699749 0.714388i \(-0.253295\pi\)
0.699749 + 0.714388i \(0.253295\pi\)
\(998\) 48.4186 1.53266
\(999\) −1.40856 −0.0445649
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 1859.2.a.g.1.1 3
13.4 even 6 143.2.e.b.133.1 yes 6
13.10 even 6 143.2.e.b.100.1 6
13.12 even 2 1859.2.a.f.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.e.b.100.1 6 13.10 even 6
143.2.e.b.133.1 yes 6 13.4 even 6
1859.2.a.f.1.3 3 13.12 even 2
1859.2.a.g.1.1 3 1.1 even 1 trivial