Properties

Label 1045.4.a.d.1.2
Level $1045$
Weight $4$
Character 1045.1
Self dual yes
Analytic conductor $61.657$
Analytic rank $1$
Dimension $22$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1045,4,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(61.6569959560\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.84890 q^{2} -0.335233 q^{3} +15.5118 q^{4} +5.00000 q^{5} +1.62551 q^{6} -24.3429 q^{7} -36.4242 q^{8} -26.8876 q^{9} +O(q^{10})\) \(q-4.84890 q^{2} -0.335233 q^{3} +15.5118 q^{4} +5.00000 q^{5} +1.62551 q^{6} -24.3429 q^{7} -36.4242 q^{8} -26.8876 q^{9} -24.2445 q^{10} -11.0000 q^{11} -5.20008 q^{12} -65.8608 q^{13} +118.036 q^{14} -1.67616 q^{15} +52.5227 q^{16} +107.349 q^{17} +130.375 q^{18} -19.0000 q^{19} +77.5592 q^{20} +8.16054 q^{21} +53.3379 q^{22} +155.888 q^{23} +12.2106 q^{24} +25.0000 q^{25} +319.353 q^{26} +18.0649 q^{27} -377.604 q^{28} +261.779 q^{29} +8.12755 q^{30} +84.7954 q^{31} +36.7164 q^{32} +3.68756 q^{33} -520.525 q^{34} -121.715 q^{35} -417.077 q^{36} -289.499 q^{37} +92.1291 q^{38} +22.0787 q^{39} -182.121 q^{40} +393.259 q^{41} -39.5696 q^{42} +411.020 q^{43} -170.630 q^{44} -134.438 q^{45} -755.887 q^{46} -255.213 q^{47} -17.6073 q^{48} +249.578 q^{49} -121.223 q^{50} -35.9869 q^{51} -1021.62 q^{52} -725.773 q^{53} -87.5948 q^{54} -55.0000 q^{55} +886.672 q^{56} +6.36942 q^{57} -1269.34 q^{58} -23.2549 q^{59} -26.0004 q^{60} +605.310 q^{61} -411.164 q^{62} +654.523 q^{63} -598.216 q^{64} -329.304 q^{65} -17.8806 q^{66} -458.297 q^{67} +1665.18 q^{68} -52.2589 q^{69} +590.182 q^{70} +76.7635 q^{71} +979.361 q^{72} -226.631 q^{73} +1403.75 q^{74} -8.38081 q^{75} -294.725 q^{76} +267.772 q^{77} -107.057 q^{78} +1302.86 q^{79} +262.613 q^{80} +719.910 q^{81} -1906.87 q^{82} -810.866 q^{83} +126.585 q^{84} +536.745 q^{85} -1992.99 q^{86} -87.7569 q^{87} +400.666 q^{88} -619.255 q^{89} +651.877 q^{90} +1603.24 q^{91} +2418.12 q^{92} -28.4262 q^{93} +1237.50 q^{94} -95.0000 q^{95} -12.3085 q^{96} -741.234 q^{97} -1210.18 q^{98} +295.764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9} - 20 q^{10} - 242 q^{11} - 196 q^{12} - q^{13} - 63 q^{14} - 105 q^{15} + 6 q^{16} + 187 q^{17} - 361 q^{18} - 418 q^{19} + 370 q^{20} - 107 q^{21} + 44 q^{22} - 361 q^{23} + 208 q^{24} + 550 q^{25} - 365 q^{26} - 1467 q^{27} - 773 q^{28} - 319 q^{29} - 45 q^{30} - 402 q^{31} - 873 q^{32} + 231 q^{33} - 717 q^{34} - 205 q^{35} + 725 q^{36} - 838 q^{37} + 76 q^{38} - 607 q^{39} - 390 q^{40} - 392 q^{41} - 1350 q^{42} - 610 q^{43} - 814 q^{44} + 1045 q^{45} - 605 q^{46} - 1866 q^{47} - 1637 q^{48} + 379 q^{49} - 100 q^{50} - 2659 q^{51} - 638 q^{52} - 1303 q^{53} + 2338 q^{54} - 1210 q^{55} + 727 q^{56} + 399 q^{57} + 44 q^{58} - 2417 q^{59} - 980 q^{60} + 918 q^{61} - 1634 q^{62} - 374 q^{63} - 1716 q^{64} - 5 q^{65} + 99 q^{66} - 2339 q^{67} + 4940 q^{68} + 127 q^{69} - 315 q^{70} - 2370 q^{71} - 3306 q^{72} + 2207 q^{73} + 2051 q^{74} - 525 q^{75} - 1406 q^{76} + 451 q^{77} + 1380 q^{78} + 586 q^{79} + 30 q^{80} + 1950 q^{81} - 1566 q^{82} - 2870 q^{83} + 3076 q^{84} + 935 q^{85} - 1246 q^{86} - 1811 q^{87} + 858 q^{88} - 1768 q^{89} - 1805 q^{90} - 2195 q^{91} - 6728 q^{92} - 2916 q^{93} + 672 q^{94} - 2090 q^{95} + 6022 q^{96} - 4022 q^{97} + 1162 q^{98} - 2299 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.84890 −1.71435 −0.857173 0.515029i \(-0.827781\pi\)
−0.857173 + 0.515029i \(0.827781\pi\)
\(3\) −0.335233 −0.0645155 −0.0322578 0.999480i \(-0.510270\pi\)
−0.0322578 + 0.999480i \(0.510270\pi\)
\(4\) 15.5118 1.93898
\(5\) 5.00000 0.447214
\(6\) 1.62551 0.110602
\(7\) −24.3429 −1.31439 −0.657197 0.753719i \(-0.728258\pi\)
−0.657197 + 0.753719i \(0.728258\pi\)
\(8\) −36.4242 −1.60974
\(9\) −26.8876 −0.995838
\(10\) −24.2445 −0.766679
\(11\) −11.0000 −0.301511
\(12\) −5.20008 −0.125094
\(13\) −65.8608 −1.40512 −0.702558 0.711627i \(-0.747959\pi\)
−0.702558 + 0.711627i \(0.747959\pi\)
\(14\) 118.036 2.25333
\(15\) −1.67616 −0.0288522
\(16\) 52.5227 0.820667
\(17\) 107.349 1.53153 0.765763 0.643123i \(-0.222361\pi\)
0.765763 + 0.643123i \(0.222361\pi\)
\(18\) 130.375 1.70721
\(19\) −19.0000 −0.229416
\(20\) 77.5592 0.867139
\(21\) 8.16054 0.0847988
\(22\) 53.3379 0.516895
\(23\) 155.888 1.41326 0.706630 0.707583i \(-0.250215\pi\)
0.706630 + 0.707583i \(0.250215\pi\)
\(24\) 12.2106 0.103853
\(25\) 25.0000 0.200000
\(26\) 319.353 2.40885
\(27\) 18.0649 0.128763
\(28\) −377.604 −2.54859
\(29\) 261.779 1.67625 0.838124 0.545480i \(-0.183652\pi\)
0.838124 + 0.545480i \(0.183652\pi\)
\(30\) 8.12755 0.0494627
\(31\) 84.7954 0.491281 0.245640 0.969361i \(-0.421002\pi\)
0.245640 + 0.969361i \(0.421002\pi\)
\(32\) 36.7164 0.202831
\(33\) 3.68756 0.0194522
\(34\) −520.525 −2.62557
\(35\) −121.715 −0.587815
\(36\) −417.077 −1.93091
\(37\) −289.499 −1.28631 −0.643154 0.765737i \(-0.722374\pi\)
−0.643154 + 0.765737i \(0.722374\pi\)
\(38\) 92.1291 0.393298
\(39\) 22.0787 0.0906518
\(40\) −182.121 −0.719897
\(41\) 393.259 1.49797 0.748984 0.662588i \(-0.230542\pi\)
0.748984 + 0.662588i \(0.230542\pi\)
\(42\) −39.5696 −0.145374
\(43\) 411.020 1.45767 0.728836 0.684688i \(-0.240062\pi\)
0.728836 + 0.684688i \(0.240062\pi\)
\(44\) −170.630 −0.584625
\(45\) −134.438 −0.445352
\(46\) −755.887 −2.42282
\(47\) −255.213 −0.792057 −0.396029 0.918238i \(-0.629612\pi\)
−0.396029 + 0.918238i \(0.629612\pi\)
\(48\) −17.6073 −0.0529458
\(49\) 249.578 0.727631
\(50\) −121.223 −0.342869
\(51\) −35.9869 −0.0988072
\(52\) −1021.62 −2.72449
\(53\) −725.773 −1.88099 −0.940496 0.339805i \(-0.889639\pi\)
−0.940496 + 0.339805i \(0.889639\pi\)
\(54\) −87.5948 −0.220743
\(55\) −55.0000 −0.134840
\(56\) 886.672 2.11583
\(57\) 6.36942 0.0148009
\(58\) −1269.34 −2.87367
\(59\) −23.2549 −0.0513140 −0.0256570 0.999671i \(-0.508168\pi\)
−0.0256570 + 0.999671i \(0.508168\pi\)
\(60\) −26.0004 −0.0559439
\(61\) 605.310 1.27052 0.635262 0.772297i \(-0.280892\pi\)
0.635262 + 0.772297i \(0.280892\pi\)
\(62\) −411.164 −0.842225
\(63\) 654.523 1.30892
\(64\) −598.216 −1.16839
\(65\) −329.304 −0.628387
\(66\) −17.8806 −0.0333477
\(67\) −458.297 −0.835670 −0.417835 0.908523i \(-0.637211\pi\)
−0.417835 + 0.908523i \(0.637211\pi\)
\(68\) 1665.18 2.96960
\(69\) −52.2589 −0.0911772
\(70\) 590.182 1.00772
\(71\) 76.7635 0.128312 0.0641560 0.997940i \(-0.479564\pi\)
0.0641560 + 0.997940i \(0.479564\pi\)
\(72\) 979.361 1.60304
\(73\) −226.631 −0.363358 −0.181679 0.983358i \(-0.558153\pi\)
−0.181679 + 0.983358i \(0.558153\pi\)
\(74\) 1403.75 2.20518
\(75\) −8.38081 −0.0129031
\(76\) −294.725 −0.444833
\(77\) 267.772 0.396305
\(78\) −107.057 −0.155409
\(79\) 1302.86 1.85548 0.927742 0.373221i \(-0.121747\pi\)
0.927742 + 0.373221i \(0.121747\pi\)
\(80\) 262.613 0.367013
\(81\) 719.910 0.987531
\(82\) −1906.87 −2.56804
\(83\) −810.866 −1.07234 −0.536170 0.844110i \(-0.680129\pi\)
−0.536170 + 0.844110i \(0.680129\pi\)
\(84\) 126.585 0.164423
\(85\) 536.745 0.684919
\(86\) −1992.99 −2.49895
\(87\) −87.7569 −0.108144
\(88\) 400.666 0.485354
\(89\) −619.255 −0.737538 −0.368769 0.929521i \(-0.620221\pi\)
−0.368769 + 0.929521i \(0.620221\pi\)
\(90\) 651.877 0.763488
\(91\) 1603.24 1.84688
\(92\) 2418.12 2.74028
\(93\) −28.4262 −0.0316952
\(94\) 1237.50 1.35786
\(95\) −95.0000 −0.102598
\(96\) −12.3085 −0.0130858
\(97\) −741.234 −0.775886 −0.387943 0.921683i \(-0.626814\pi\)
−0.387943 + 0.921683i \(0.626814\pi\)
\(98\) −1210.18 −1.24741
\(99\) 295.764 0.300256
\(100\) 387.796 0.387796
\(101\) −1589.90 −1.56635 −0.783173 0.621804i \(-0.786400\pi\)
−0.783173 + 0.621804i \(0.786400\pi\)
\(102\) 174.497 0.169390
\(103\) −1094.06 −1.04661 −0.523306 0.852145i \(-0.675302\pi\)
−0.523306 + 0.852145i \(0.675302\pi\)
\(104\) 2398.93 2.26187
\(105\) 40.8027 0.0379232
\(106\) 3519.20 3.22467
\(107\) −401.165 −0.362449 −0.181224 0.983442i \(-0.558006\pi\)
−0.181224 + 0.983442i \(0.558006\pi\)
\(108\) 280.220 0.249668
\(109\) 2079.44 1.82729 0.913643 0.406517i \(-0.133257\pi\)
0.913643 + 0.406517i \(0.133257\pi\)
\(110\) 266.690 0.231162
\(111\) 97.0496 0.0829868
\(112\) −1278.56 −1.07868
\(113\) 1934.66 1.61060 0.805298 0.592871i \(-0.202006\pi\)
0.805298 + 0.592871i \(0.202006\pi\)
\(114\) −30.8847 −0.0253738
\(115\) 779.442 0.632029
\(116\) 4060.68 3.25021
\(117\) 1770.84 1.39927
\(118\) 112.761 0.0879700
\(119\) −2613.19 −2.01303
\(120\) 61.0529 0.0464445
\(121\) 121.000 0.0909091
\(122\) −2935.09 −2.17812
\(123\) −131.833 −0.0966423
\(124\) 1315.33 0.952584
\(125\) 125.000 0.0894427
\(126\) −3173.72 −2.24395
\(127\) −1470.22 −1.02725 −0.513626 0.858014i \(-0.671698\pi\)
−0.513626 + 0.858014i \(0.671698\pi\)
\(128\) 2606.96 1.80019
\(129\) −137.787 −0.0940425
\(130\) 1596.76 1.07727
\(131\) −778.578 −0.519272 −0.259636 0.965706i \(-0.583603\pi\)
−0.259636 + 0.965706i \(0.583603\pi\)
\(132\) 57.2008 0.0377174
\(133\) 462.515 0.301543
\(134\) 2222.24 1.43263
\(135\) 90.3244 0.0575844
\(136\) −3910.10 −2.46536
\(137\) −355.728 −0.221839 −0.110919 0.993829i \(-0.535380\pi\)
−0.110919 + 0.993829i \(0.535380\pi\)
\(138\) 253.398 0.156309
\(139\) −840.905 −0.513127 −0.256564 0.966527i \(-0.582590\pi\)
−0.256564 + 0.966527i \(0.582590\pi\)
\(140\) −1888.02 −1.13976
\(141\) 85.5558 0.0511000
\(142\) −372.219 −0.219971
\(143\) 724.469 0.423658
\(144\) −1412.21 −0.817251
\(145\) 1308.90 0.749641
\(146\) 1098.91 0.622921
\(147\) −83.6665 −0.0469435
\(148\) −4490.67 −2.49413
\(149\) −915.972 −0.503620 −0.251810 0.967777i \(-0.581026\pi\)
−0.251810 + 0.967777i \(0.581026\pi\)
\(150\) 40.6377 0.0221204
\(151\) −623.915 −0.336248 −0.168124 0.985766i \(-0.553771\pi\)
−0.168124 + 0.985766i \(0.553771\pi\)
\(152\) 692.060 0.369299
\(153\) −2886.36 −1.52515
\(154\) −1298.40 −0.679403
\(155\) 423.977 0.219707
\(156\) 342.481 0.175772
\(157\) −547.634 −0.278382 −0.139191 0.990266i \(-0.544450\pi\)
−0.139191 + 0.990266i \(0.544450\pi\)
\(158\) −6317.44 −3.18094
\(159\) 243.303 0.121353
\(160\) 183.582 0.0907090
\(161\) −3794.78 −1.85758
\(162\) −3490.77 −1.69297
\(163\) −568.500 −0.273180 −0.136590 0.990628i \(-0.543614\pi\)
−0.136590 + 0.990628i \(0.543614\pi\)
\(164\) 6100.17 2.90453
\(165\) 18.4378 0.00869927
\(166\) 3931.81 1.83836
\(167\) 197.642 0.0915807 0.0457903 0.998951i \(-0.485419\pi\)
0.0457903 + 0.998951i \(0.485419\pi\)
\(168\) −297.241 −0.136504
\(169\) 2140.65 0.974351
\(170\) −2602.62 −1.17419
\(171\) 510.865 0.228461
\(172\) 6375.68 2.82640
\(173\) −2112.30 −0.928296 −0.464148 0.885758i \(-0.653639\pi\)
−0.464148 + 0.885758i \(0.653639\pi\)
\(174\) 425.525 0.185396
\(175\) −608.573 −0.262879
\(176\) −577.750 −0.247440
\(177\) 7.79579 0.00331055
\(178\) 3002.71 1.26439
\(179\) −2032.30 −0.848612 −0.424306 0.905519i \(-0.639482\pi\)
−0.424306 + 0.905519i \(0.639482\pi\)
\(180\) −2085.38 −0.863530
\(181\) −2910.72 −1.19532 −0.597658 0.801752i \(-0.703902\pi\)
−0.597658 + 0.801752i \(0.703902\pi\)
\(182\) −7773.98 −3.16618
\(183\) −202.920 −0.0819686
\(184\) −5678.11 −2.27498
\(185\) −1447.50 −0.575254
\(186\) 137.836 0.0543366
\(187\) −1180.84 −0.461773
\(188\) −3958.83 −1.53578
\(189\) −439.752 −0.169245
\(190\) 460.646 0.175888
\(191\) 4350.25 1.64803 0.824013 0.566571i \(-0.191730\pi\)
0.824013 + 0.566571i \(0.191730\pi\)
\(192\) 200.541 0.0753793
\(193\) −151.944 −0.0566692 −0.0283346 0.999598i \(-0.509020\pi\)
−0.0283346 + 0.999598i \(0.509020\pi\)
\(194\) 3594.17 1.33014
\(195\) 110.393 0.0405407
\(196\) 3871.41 1.41086
\(197\) −1808.07 −0.653908 −0.326954 0.945040i \(-0.606022\pi\)
−0.326954 + 0.945040i \(0.606022\pi\)
\(198\) −1434.13 −0.514743
\(199\) 3670.56 1.30753 0.653767 0.756696i \(-0.273188\pi\)
0.653767 + 0.756696i \(0.273188\pi\)
\(200\) −910.606 −0.321948
\(201\) 153.636 0.0539137
\(202\) 7709.27 2.68526
\(203\) −6372.47 −2.20325
\(204\) −558.223 −0.191585
\(205\) 1966.29 0.669912
\(206\) 5305.00 1.79426
\(207\) −4191.47 −1.40738
\(208\) −3459.19 −1.15313
\(209\) 209.000 0.0691714
\(210\) −197.848 −0.0650135
\(211\) −5974.43 −1.94927 −0.974637 0.223790i \(-0.928157\pi\)
−0.974637 + 0.223790i \(0.928157\pi\)
\(212\) −11258.1 −3.64721
\(213\) −25.7336 −0.00827812
\(214\) 1945.21 0.621363
\(215\) 2055.10 0.651891
\(216\) −657.999 −0.207274
\(217\) −2064.17 −0.645736
\(218\) −10083.0 −3.13260
\(219\) 75.9740 0.0234422
\(220\) −853.152 −0.261452
\(221\) −7070.09 −2.15197
\(222\) −470.584 −0.142268
\(223\) 2505.37 0.752341 0.376171 0.926550i \(-0.377241\pi\)
0.376171 + 0.926550i \(0.377241\pi\)
\(224\) −893.785 −0.266600
\(225\) −672.190 −0.199168
\(226\) −9380.96 −2.76112
\(227\) −445.337 −0.130212 −0.0651058 0.997878i \(-0.520738\pi\)
−0.0651058 + 0.997878i \(0.520738\pi\)
\(228\) 98.8015 0.0286986
\(229\) −2308.16 −0.666060 −0.333030 0.942916i \(-0.608071\pi\)
−0.333030 + 0.942916i \(0.608071\pi\)
\(230\) −3779.44 −1.08352
\(231\) −89.7659 −0.0255678
\(232\) −9535.11 −2.69832
\(233\) 6871.96 1.93218 0.966088 0.258212i \(-0.0831334\pi\)
0.966088 + 0.258212i \(0.0831334\pi\)
\(234\) −8586.63 −2.39883
\(235\) −1276.07 −0.354219
\(236\) −360.726 −0.0994970
\(237\) −436.761 −0.119708
\(238\) 12671.1 3.45103
\(239\) −654.309 −0.177087 −0.0885434 0.996072i \(-0.528221\pi\)
−0.0885434 + 0.996072i \(0.528221\pi\)
\(240\) −88.0366 −0.0236781
\(241\) −2704.70 −0.722926 −0.361463 0.932387i \(-0.617723\pi\)
−0.361463 + 0.932387i \(0.617723\pi\)
\(242\) −586.717 −0.155850
\(243\) −729.089 −0.192474
\(244\) 9389.48 2.46352
\(245\) 1247.89 0.325407
\(246\) 639.246 0.165678
\(247\) 1251.36 0.322356
\(248\) −3088.61 −0.790833
\(249\) 271.829 0.0691825
\(250\) −606.113 −0.153336
\(251\) −5057.41 −1.27180 −0.635898 0.771773i \(-0.719370\pi\)
−0.635898 + 0.771773i \(0.719370\pi\)
\(252\) 10152.9 2.53798
\(253\) −1714.77 −0.426114
\(254\) 7128.96 1.76106
\(255\) −179.934 −0.0441879
\(256\) −7855.16 −1.91776
\(257\) 5035.43 1.22218 0.611092 0.791559i \(-0.290730\pi\)
0.611092 + 0.791559i \(0.290730\pi\)
\(258\) 668.117 0.161221
\(259\) 7047.26 1.69071
\(260\) −5108.12 −1.21843
\(261\) −7038.62 −1.66927
\(262\) 3775.25 0.890213
\(263\) 4428.01 1.03819 0.519093 0.854718i \(-0.326270\pi\)
0.519093 + 0.854718i \(0.326270\pi\)
\(264\) −134.316 −0.0313129
\(265\) −3628.86 −0.841205
\(266\) −2242.69 −0.516948
\(267\) 207.594 0.0475826
\(268\) −7109.04 −1.62035
\(269\) 6329.48 1.43463 0.717314 0.696750i \(-0.245371\pi\)
0.717314 + 0.696750i \(0.245371\pi\)
\(270\) −437.974 −0.0987195
\(271\) −1722.58 −0.386122 −0.193061 0.981187i \(-0.561842\pi\)
−0.193061 + 0.981187i \(0.561842\pi\)
\(272\) 5638.26 1.25687
\(273\) −537.460 −0.119152
\(274\) 1724.89 0.380309
\(275\) −275.000 −0.0603023
\(276\) −810.631 −0.176791
\(277\) 893.068 0.193716 0.0968578 0.995298i \(-0.469121\pi\)
0.0968578 + 0.995298i \(0.469121\pi\)
\(278\) 4077.47 0.879677
\(279\) −2279.95 −0.489236
\(280\) 4433.36 0.946228
\(281\) −6774.16 −1.43812 −0.719062 0.694946i \(-0.755428\pi\)
−0.719062 + 0.694946i \(0.755428\pi\)
\(282\) −414.852 −0.0876030
\(283\) −3876.99 −0.814356 −0.407178 0.913349i \(-0.633487\pi\)
−0.407178 + 0.913349i \(0.633487\pi\)
\(284\) 1190.74 0.248795
\(285\) 31.8471 0.00661915
\(286\) −3512.88 −0.726297
\(287\) −9573.07 −1.96892
\(288\) −987.217 −0.201987
\(289\) 6610.80 1.34557
\(290\) −6346.71 −1.28514
\(291\) 248.486 0.0500567
\(292\) −3515.46 −0.704544
\(293\) −2495.29 −0.497530 −0.248765 0.968564i \(-0.580025\pi\)
−0.248765 + 0.968564i \(0.580025\pi\)
\(294\) 405.691 0.0804774
\(295\) −116.274 −0.0229483
\(296\) 10544.8 2.07062
\(297\) −198.714 −0.0388234
\(298\) 4441.46 0.863378
\(299\) −10266.9 −1.98579
\(300\) −130.002 −0.0250189
\(301\) −10005.4 −1.91596
\(302\) 3025.30 0.576446
\(303\) 532.986 0.101054
\(304\) −997.931 −0.188274
\(305\) 3026.55 0.568196
\(306\) 13995.7 2.61464
\(307\) −9562.39 −1.77770 −0.888851 0.458196i \(-0.848496\pi\)
−0.888851 + 0.458196i \(0.848496\pi\)
\(308\) 4153.64 0.768427
\(309\) 366.765 0.0675228
\(310\) −2055.82 −0.376654
\(311\) 6307.27 1.15001 0.575004 0.818151i \(-0.305001\pi\)
0.575004 + 0.818151i \(0.305001\pi\)
\(312\) −804.199 −0.145926
\(313\) 9562.65 1.72688 0.863439 0.504453i \(-0.168306\pi\)
0.863439 + 0.504453i \(0.168306\pi\)
\(314\) 2655.42 0.477242
\(315\) 3272.62 0.585368
\(316\) 20209.8 3.59775
\(317\) 1604.15 0.284221 0.142111 0.989851i \(-0.454611\pi\)
0.142111 + 0.989851i \(0.454611\pi\)
\(318\) −1179.75 −0.208041
\(319\) −2879.57 −0.505408
\(320\) −2991.08 −0.522520
\(321\) 134.483 0.0233836
\(322\) 18400.5 3.18453
\(323\) −2039.63 −0.351356
\(324\) 11167.1 1.91480
\(325\) −1646.52 −0.281023
\(326\) 2756.60 0.468325
\(327\) −697.096 −0.117888
\(328\) −14324.1 −2.41134
\(329\) 6212.64 1.04108
\(330\) −89.4030 −0.0149136
\(331\) −7490.74 −1.24389 −0.621946 0.783060i \(-0.713658\pi\)
−0.621946 + 0.783060i \(0.713658\pi\)
\(332\) −12578.0 −2.07925
\(333\) 7783.94 1.28095
\(334\) −958.345 −0.157001
\(335\) −2291.49 −0.373723
\(336\) 428.613 0.0695916
\(337\) 4632.55 0.748816 0.374408 0.927264i \(-0.377846\pi\)
0.374408 + 0.927264i \(0.377846\pi\)
\(338\) −10379.8 −1.67037
\(339\) −648.560 −0.103908
\(340\) 8325.90 1.32805
\(341\) −932.749 −0.148127
\(342\) −2477.13 −0.391661
\(343\) 2274.17 0.358000
\(344\) −14971.1 −2.34647
\(345\) −261.294 −0.0407757
\(346\) 10242.3 1.59142
\(347\) 6820.26 1.05513 0.527566 0.849514i \(-0.323105\pi\)
0.527566 + 0.849514i \(0.323105\pi\)
\(348\) −1361.27 −0.209689
\(349\) 5115.95 0.784672 0.392336 0.919822i \(-0.371667\pi\)
0.392336 + 0.919822i \(0.371667\pi\)
\(350\) 2950.91 0.450665
\(351\) −1189.77 −0.180926
\(352\) −403.881 −0.0611560
\(353\) −4576.34 −0.690012 −0.345006 0.938600i \(-0.612123\pi\)
−0.345006 + 0.938600i \(0.612123\pi\)
\(354\) −37.8010 −0.00567543
\(355\) 383.818 0.0573829
\(356\) −9605.79 −1.43007
\(357\) 876.025 0.129872
\(358\) 9854.44 1.45481
\(359\) 10848.8 1.59492 0.797462 0.603369i \(-0.206175\pi\)
0.797462 + 0.603369i \(0.206175\pi\)
\(360\) 4896.80 0.716901
\(361\) 361.000 0.0526316
\(362\) 14113.8 2.04918
\(363\) −40.5631 −0.00586505
\(364\) 24869.3 3.58106
\(365\) −1133.15 −0.162499
\(366\) 983.937 0.140522
\(367\) −5381.75 −0.765463 −0.382732 0.923860i \(-0.625017\pi\)
−0.382732 + 0.923860i \(0.625017\pi\)
\(368\) 8187.68 1.15982
\(369\) −10573.8 −1.49173
\(370\) 7018.77 0.986185
\(371\) 17667.4 2.47236
\(372\) −440.942 −0.0614565
\(373\) −7350.19 −1.02032 −0.510158 0.860080i \(-0.670413\pi\)
−0.510158 + 0.860080i \(0.670413\pi\)
\(374\) 5725.77 0.791638
\(375\) −41.9041 −0.00577044
\(376\) 9295.95 1.27500
\(377\) −17241.0 −2.35532
\(378\) 2132.31 0.290144
\(379\) 2990.66 0.405330 0.202665 0.979248i \(-0.435040\pi\)
0.202665 + 0.979248i \(0.435040\pi\)
\(380\) −1473.63 −0.198935
\(381\) 492.866 0.0662737
\(382\) −21093.9 −2.82529
\(383\) −8139.77 −1.08596 −0.542980 0.839746i \(-0.682704\pi\)
−0.542980 + 0.839746i \(0.682704\pi\)
\(384\) −873.937 −0.116140
\(385\) 1338.86 0.177233
\(386\) 736.760 0.0971505
\(387\) −11051.3 −1.45161
\(388\) −11497.9 −1.50443
\(389\) −617.999 −0.0805495 −0.0402748 0.999189i \(-0.512823\pi\)
−0.0402748 + 0.999189i \(0.512823\pi\)
\(390\) −535.287 −0.0695008
\(391\) 16734.5 2.16444
\(392\) −9090.67 −1.17130
\(393\) 261.005 0.0335011
\(394\) 8767.17 1.12102
\(395\) 6514.30 0.829798
\(396\) 4587.84 0.582191
\(397\) −2715.22 −0.343257 −0.171629 0.985162i \(-0.554903\pi\)
−0.171629 + 0.985162i \(0.554903\pi\)
\(398\) −17798.2 −2.24156
\(399\) −155.050 −0.0194542
\(400\) 1313.07 0.164133
\(401\) −935.792 −0.116537 −0.0582683 0.998301i \(-0.518558\pi\)
−0.0582683 + 0.998301i \(0.518558\pi\)
\(402\) −744.967 −0.0924267
\(403\) −5584.69 −0.690306
\(404\) −24662.3 −3.03712
\(405\) 3599.55 0.441637
\(406\) 30899.5 3.77713
\(407\) 3184.49 0.387836
\(408\) 1310.79 0.159054
\(409\) −352.684 −0.0426384 −0.0213192 0.999773i \(-0.506787\pi\)
−0.0213192 + 0.999773i \(0.506787\pi\)
\(410\) −9534.37 −1.14846
\(411\) 119.252 0.0143121
\(412\) −16970.9 −2.02936
\(413\) 566.092 0.0674469
\(414\) 20324.0 2.41273
\(415\) −4054.33 −0.479565
\(416\) −2418.17 −0.285002
\(417\) 281.899 0.0331047
\(418\) −1013.42 −0.118584
\(419\) −1231.37 −0.143571 −0.0717857 0.997420i \(-0.522870\pi\)
−0.0717857 + 0.997420i \(0.522870\pi\)
\(420\) 632.925 0.0735323
\(421\) −6171.04 −0.714390 −0.357195 0.934030i \(-0.616267\pi\)
−0.357195 + 0.934030i \(0.616267\pi\)
\(422\) 28969.4 3.34173
\(423\) 6862.08 0.788760
\(424\) 26435.7 3.02790
\(425\) 2683.72 0.306305
\(426\) 124.780 0.0141916
\(427\) −14735.0 −1.66997
\(428\) −6222.80 −0.702782
\(429\) −242.866 −0.0273325
\(430\) −9964.97 −1.11757
\(431\) −12984.0 −1.45108 −0.725541 0.688179i \(-0.758410\pi\)
−0.725541 + 0.688179i \(0.758410\pi\)
\(432\) 948.816 0.105671
\(433\) −4284.52 −0.475522 −0.237761 0.971324i \(-0.576413\pi\)
−0.237761 + 0.971324i \(0.576413\pi\)
\(434\) 10008.9 1.10702
\(435\) −438.785 −0.0483635
\(436\) 32256.0 3.54307
\(437\) −2961.88 −0.324224
\(438\) −368.391 −0.0401881
\(439\) −740.867 −0.0805459 −0.0402729 0.999189i \(-0.512823\pi\)
−0.0402729 + 0.999189i \(0.512823\pi\)
\(440\) 2003.33 0.217057
\(441\) −6710.55 −0.724603
\(442\) 34282.2 3.68922
\(443\) −8848.31 −0.948975 −0.474488 0.880262i \(-0.657367\pi\)
−0.474488 + 0.880262i \(0.657367\pi\)
\(444\) 1505.42 0.160910
\(445\) −3096.27 −0.329837
\(446\) −12148.3 −1.28977
\(447\) 307.063 0.0324913
\(448\) 14562.3 1.53573
\(449\) −13874.1 −1.45826 −0.729129 0.684376i \(-0.760075\pi\)
−0.729129 + 0.684376i \(0.760075\pi\)
\(450\) 3259.39 0.341442
\(451\) −4325.85 −0.451655
\(452\) 30010.1 3.12291
\(453\) 209.157 0.0216932
\(454\) 2159.39 0.223228
\(455\) 8016.22 0.825948
\(456\) −232.001 −0.0238255
\(457\) 17608.0 1.80234 0.901169 0.433468i \(-0.142710\pi\)
0.901169 + 0.433468i \(0.142710\pi\)
\(458\) 11192.1 1.14186
\(459\) 1939.25 0.197203
\(460\) 12090.6 1.22549
\(461\) 2130.74 0.215268 0.107634 0.994191i \(-0.465673\pi\)
0.107634 + 0.994191i \(0.465673\pi\)
\(462\) 435.266 0.0438321
\(463\) −7211.05 −0.723814 −0.361907 0.932214i \(-0.617874\pi\)
−0.361907 + 0.932214i \(0.617874\pi\)
\(464\) 13749.4 1.37564
\(465\) −142.131 −0.0141745
\(466\) −33321.5 −3.31242
\(467\) −2606.92 −0.258316 −0.129158 0.991624i \(-0.541228\pi\)
−0.129158 + 0.991624i \(0.541228\pi\)
\(468\) 27469.0 2.71315
\(469\) 11156.3 1.09840
\(470\) 6187.52 0.607253
\(471\) 183.585 0.0179599
\(472\) 847.041 0.0826022
\(473\) −4521.22 −0.439505
\(474\) 2117.81 0.205220
\(475\) −475.000 −0.0458831
\(476\) −40535.4 −3.90323
\(477\) 19514.3 1.87316
\(478\) 3172.68 0.303588
\(479\) −11439.9 −1.09124 −0.545620 0.838032i \(-0.683706\pi\)
−0.545620 + 0.838032i \(0.683706\pi\)
\(480\) −61.5427 −0.00585214
\(481\) 19066.7 1.80741
\(482\) 13114.8 1.23934
\(483\) 1272.13 0.119843
\(484\) 1876.93 0.176271
\(485\) −3706.17 −0.346987
\(486\) 3535.28 0.329966
\(487\) −13680.4 −1.27293 −0.636465 0.771306i \(-0.719604\pi\)
−0.636465 + 0.771306i \(0.719604\pi\)
\(488\) −22047.9 −2.04521
\(489\) 190.580 0.0176244
\(490\) −6050.89 −0.557860
\(491\) 11627.4 1.06872 0.534358 0.845258i \(-0.320554\pi\)
0.534358 + 0.845258i \(0.320554\pi\)
\(492\) −2044.98 −0.187388
\(493\) 28101.7 2.56722
\(494\) −6067.70 −0.552629
\(495\) 1478.82 0.134279
\(496\) 4453.68 0.403178
\(497\) −1868.65 −0.168653
\(498\) −1318.07 −0.118603
\(499\) 1048.34 0.0940488 0.0470244 0.998894i \(-0.485026\pi\)
0.0470244 + 0.998894i \(0.485026\pi\)
\(500\) 1938.98 0.173428
\(501\) −66.2559 −0.00590838
\(502\) 24522.9 2.18030
\(503\) −9203.22 −0.815808 −0.407904 0.913025i \(-0.633740\pi\)
−0.407904 + 0.913025i \(0.633740\pi\)
\(504\) −23840.5 −2.10702
\(505\) −7949.50 −0.700491
\(506\) 8314.76 0.730506
\(507\) −717.615 −0.0628608
\(508\) −22805.8 −1.99182
\(509\) 20683.0 1.80109 0.900546 0.434760i \(-0.143167\pi\)
0.900546 + 0.434760i \(0.143167\pi\)
\(510\) 872.484 0.0757534
\(511\) 5516.86 0.477596
\(512\) 17233.2 1.48752
\(513\) −343.233 −0.0295402
\(514\) −24416.3 −2.09525
\(515\) −5470.31 −0.468060
\(516\) −2137.33 −0.182347
\(517\) 2807.35 0.238814
\(518\) −34171.5 −2.89847
\(519\) 708.112 0.0598895
\(520\) 11994.6 1.01154
\(521\) −9527.24 −0.801144 −0.400572 0.916265i \(-0.631189\pi\)
−0.400572 + 0.916265i \(0.631189\pi\)
\(522\) 34129.6 2.86171
\(523\) 6570.02 0.549306 0.274653 0.961543i \(-0.411437\pi\)
0.274653 + 0.961543i \(0.411437\pi\)
\(524\) −12077.2 −1.00686
\(525\) 204.013 0.0169598
\(526\) −21471.0 −1.77981
\(527\) 9102.69 0.752409
\(528\) 193.680 0.0159637
\(529\) 12134.2 0.997303
\(530\) 17596.0 1.44212
\(531\) 625.269 0.0511005
\(532\) 7174.47 0.584686
\(533\) −25900.4 −2.10482
\(534\) −1006.60 −0.0815731
\(535\) −2005.82 −0.162092
\(536\) 16693.1 1.34521
\(537\) 681.294 0.0547486
\(538\) −30691.0 −2.45945
\(539\) −2745.35 −0.219389
\(540\) 1401.10 0.111655
\(541\) −1924.13 −0.152911 −0.0764553 0.997073i \(-0.524360\pi\)
−0.0764553 + 0.997073i \(0.524360\pi\)
\(542\) 8352.61 0.661947
\(543\) 975.768 0.0771164
\(544\) 3941.47 0.310642
\(545\) 10397.2 0.817187
\(546\) 2606.09 0.204268
\(547\) −355.641 −0.0277991 −0.0138995 0.999903i \(-0.504425\pi\)
−0.0138995 + 0.999903i \(0.504425\pi\)
\(548\) −5518.01 −0.430142
\(549\) −16275.3 −1.26524
\(550\) 1333.45 0.103379
\(551\) −4973.81 −0.384558
\(552\) 1903.49 0.146771
\(553\) −31715.4 −2.43884
\(554\) −4330.40 −0.332096
\(555\) 485.248 0.0371128
\(556\) −13044.0 −0.994944
\(557\) 11937.6 0.908103 0.454051 0.890976i \(-0.349978\pi\)
0.454051 + 0.890976i \(0.349978\pi\)
\(558\) 11055.2 0.838719
\(559\) −27070.1 −2.04820
\(560\) −6392.78 −0.482400
\(561\) 395.855 0.0297915
\(562\) 32847.3 2.46544
\(563\) −9234.85 −0.691301 −0.345650 0.938363i \(-0.612342\pi\)
−0.345650 + 0.938363i \(0.612342\pi\)
\(564\) 1327.13 0.0990819
\(565\) 9673.29 0.720280
\(566\) 18799.1 1.39609
\(567\) −17524.7 −1.29800
\(568\) −2796.05 −0.206549
\(569\) −17518.2 −1.29069 −0.645344 0.763892i \(-0.723286\pi\)
−0.645344 + 0.763892i \(0.723286\pi\)
\(570\) −154.423 −0.0113475
\(571\) −10137.6 −0.742987 −0.371493 0.928436i \(-0.621154\pi\)
−0.371493 + 0.928436i \(0.621154\pi\)
\(572\) 11237.9 0.821466
\(573\) −1458.34 −0.106323
\(574\) 46418.9 3.37541
\(575\) 3897.21 0.282652
\(576\) 16084.6 1.16353
\(577\) 21440.8 1.54696 0.773478 0.633824i \(-0.218516\pi\)
0.773478 + 0.633824i \(0.218516\pi\)
\(578\) −32055.1 −2.30678
\(579\) 50.9365 0.00365604
\(580\) 20303.4 1.45354
\(581\) 19738.9 1.40948
\(582\) −1204.88 −0.0858145
\(583\) 7983.50 0.567140
\(584\) 8254.85 0.584911
\(585\) 8854.20 0.625771
\(586\) 12099.4 0.852939
\(587\) −18112.4 −1.27356 −0.636780 0.771046i \(-0.719734\pi\)
−0.636780 + 0.771046i \(0.719734\pi\)
\(588\) −1297.82 −0.0910226
\(589\) −1611.11 −0.112707
\(590\) 563.803 0.0393414
\(591\) 606.125 0.0421872
\(592\) −15205.3 −1.05563
\(593\) −1229.57 −0.0851472 −0.0425736 0.999093i \(-0.513556\pi\)
−0.0425736 + 0.999093i \(0.513556\pi\)
\(594\) 963.543 0.0665567
\(595\) −13065.9 −0.900254
\(596\) −14208.4 −0.976509
\(597\) −1230.49 −0.0843562
\(598\) 49783.4 3.40434
\(599\) 6194.89 0.422565 0.211283 0.977425i \(-0.432236\pi\)
0.211283 + 0.977425i \(0.432236\pi\)
\(600\) 305.265 0.0207706
\(601\) −1463.50 −0.0993298 −0.0496649 0.998766i \(-0.515815\pi\)
−0.0496649 + 0.998766i \(0.515815\pi\)
\(602\) 48515.3 3.28461
\(603\) 12322.5 0.832192
\(604\) −9678.08 −0.651979
\(605\) 605.000 0.0406558
\(606\) −2584.40 −0.173241
\(607\) −15347.4 −1.02625 −0.513124 0.858315i \(-0.671512\pi\)
−0.513124 + 0.858315i \(0.671512\pi\)
\(608\) −697.612 −0.0465327
\(609\) 2136.26 0.142144
\(610\) −14675.4 −0.974084
\(611\) 16808.6 1.11293
\(612\) −44772.8 −2.95724
\(613\) −774.556 −0.0510343 −0.0255171 0.999674i \(-0.508123\pi\)
−0.0255171 + 0.999674i \(0.508123\pi\)
\(614\) 46367.1 3.04760
\(615\) −659.166 −0.0432197
\(616\) −9753.39 −0.637947
\(617\) 11653.2 0.760358 0.380179 0.924913i \(-0.375862\pi\)
0.380179 + 0.924913i \(0.375862\pi\)
\(618\) −1778.41 −0.115757
\(619\) −3190.69 −0.207181 −0.103590 0.994620i \(-0.533033\pi\)
−0.103590 + 0.994620i \(0.533033\pi\)
\(620\) 6576.67 0.426008
\(621\) 2816.11 0.181975
\(622\) −30583.3 −1.97151
\(623\) 15074.5 0.969415
\(624\) 1159.63 0.0743949
\(625\) 625.000 0.0400000
\(626\) −46368.4 −2.96047
\(627\) −70.0636 −0.00446263
\(628\) −8494.81 −0.539777
\(629\) −31077.4 −1.97001
\(630\) −15868.6 −1.00352
\(631\) 10683.6 0.674021 0.337011 0.941501i \(-0.390584\pi\)
0.337011 + 0.941501i \(0.390584\pi\)
\(632\) −47455.7 −2.98685
\(633\) 2002.82 0.125759
\(634\) −7778.37 −0.487253
\(635\) −7351.10 −0.459401
\(636\) 3774.07 0.235302
\(637\) −16437.4 −1.02241
\(638\) 13962.8 0.866444
\(639\) −2063.99 −0.127778
\(640\) 13034.8 0.805071
\(641\) −20559.0 −1.26682 −0.633411 0.773815i \(-0.718346\pi\)
−0.633411 + 0.773815i \(0.718346\pi\)
\(642\) −652.097 −0.0400876
\(643\) −27658.7 −1.69635 −0.848176 0.529715i \(-0.822299\pi\)
−0.848176 + 0.529715i \(0.822299\pi\)
\(644\) −58864.0 −3.60181
\(645\) −688.936 −0.0420571
\(646\) 9889.97 0.602346
\(647\) 6760.73 0.410806 0.205403 0.978677i \(-0.434149\pi\)
0.205403 + 0.978677i \(0.434149\pi\)
\(648\) −26222.2 −1.58967
\(649\) 255.804 0.0154718
\(650\) 7983.82 0.481771
\(651\) 691.976 0.0416600
\(652\) −8818.49 −0.529691
\(653\) −11580.2 −0.693978 −0.346989 0.937869i \(-0.612796\pi\)
−0.346989 + 0.937869i \(0.612796\pi\)
\(654\) 3380.15 0.202101
\(655\) −3892.89 −0.232226
\(656\) 20655.0 1.22933
\(657\) 6093.56 0.361846
\(658\) −30124.5 −1.78476
\(659\) −14320.8 −0.846523 −0.423261 0.906008i \(-0.639115\pi\)
−0.423261 + 0.906008i \(0.639115\pi\)
\(660\) 286.004 0.0168677
\(661\) 16932.9 0.996391 0.498196 0.867065i \(-0.333996\pi\)
0.498196 + 0.867065i \(0.333996\pi\)
\(662\) 36321.9 2.13246
\(663\) 2370.12 0.138836
\(664\) 29535.2 1.72619
\(665\) 2312.58 0.134854
\(666\) −37743.6 −2.19600
\(667\) 40808.4 2.36897
\(668\) 3065.79 0.177573
\(669\) −839.882 −0.0485377
\(670\) 11111.2 0.640691
\(671\) −6658.41 −0.383078
\(672\) 299.626 0.0171999
\(673\) −13147.3 −0.753032 −0.376516 0.926410i \(-0.622878\pi\)
−0.376516 + 0.926410i \(0.622878\pi\)
\(674\) −22462.8 −1.28373
\(675\) 451.622 0.0257525
\(676\) 33205.4 1.88925
\(677\) −20941.0 −1.18882 −0.594409 0.804163i \(-0.702614\pi\)
−0.594409 + 0.804163i \(0.702614\pi\)
\(678\) 3144.80 0.178135
\(679\) 18043.8 1.01982
\(680\) −19550.5 −1.10254
\(681\) 149.291 0.00840067
\(682\) 4522.81 0.253940
\(683\) 12724.4 0.712865 0.356432 0.934321i \(-0.383993\pi\)
0.356432 + 0.934321i \(0.383993\pi\)
\(684\) 7924.46 0.442981
\(685\) −1778.64 −0.0992094
\(686\) −11027.2 −0.613735
\(687\) 773.771 0.0429712
\(688\) 21587.9 1.19626
\(689\) 47800.0 2.64301
\(690\) 1266.99 0.0699036
\(691\) −12348.4 −0.679818 −0.339909 0.940458i \(-0.610396\pi\)
−0.339909 + 0.940458i \(0.610396\pi\)
\(692\) −32765.7 −1.79995
\(693\) −7199.75 −0.394655
\(694\) −33070.8 −1.80886
\(695\) −4204.53 −0.229477
\(696\) 3196.48 0.174084
\(697\) 42215.9 2.29418
\(698\) −24806.7 −1.34520
\(699\) −2303.70 −0.124655
\(700\) −9440.09 −0.509717
\(701\) 9524.59 0.513180 0.256590 0.966520i \(-0.417401\pi\)
0.256590 + 0.966520i \(0.417401\pi\)
\(702\) 5769.07 0.310170
\(703\) 5500.49 0.295099
\(704\) 6580.37 0.352283
\(705\) 427.779 0.0228526
\(706\) 22190.2 1.18292
\(707\) 38702.8 2.05880
\(708\) 120.927 0.00641910
\(709\) −4351.98 −0.230525 −0.115262 0.993335i \(-0.536771\pi\)
−0.115262 + 0.993335i \(0.536771\pi\)
\(710\) −1861.09 −0.0983741
\(711\) −35030.8 −1.84776
\(712\) 22555.9 1.18724
\(713\) 13218.6 0.694307
\(714\) −4247.76 −0.222645
\(715\) 3622.35 0.189466
\(716\) −31524.8 −1.64544
\(717\) 219.346 0.0114248
\(718\) −52604.8 −2.73425
\(719\) −36989.8 −1.91862 −0.959309 0.282360i \(-0.908883\pi\)
−0.959309 + 0.282360i \(0.908883\pi\)
\(720\) −7061.05 −0.365486
\(721\) 26632.7 1.37566
\(722\) −1750.45 −0.0902287
\(723\) 906.704 0.0466399
\(724\) −45150.6 −2.31769
\(725\) 6544.48 0.335250
\(726\) 196.687 0.0100547
\(727\) 5679.08 0.289719 0.144859 0.989452i \(-0.453727\pi\)
0.144859 + 0.989452i \(0.453727\pi\)
\(728\) −58396.9 −2.97299
\(729\) −19193.1 −0.975113
\(730\) 5494.55 0.278579
\(731\) 44122.5 2.23246
\(732\) −3147.66 −0.158935
\(733\) −22573.4 −1.13747 −0.568737 0.822519i \(-0.692568\pi\)
−0.568737 + 0.822519i \(0.692568\pi\)
\(734\) 26095.6 1.31227
\(735\) −418.333 −0.0209938
\(736\) 5723.66 0.286654
\(737\) 5041.27 0.251964
\(738\) 51271.3 2.55735
\(739\) −11632.7 −0.579047 −0.289524 0.957171i \(-0.593497\pi\)
−0.289524 + 0.957171i \(0.593497\pi\)
\(740\) −22453.3 −1.11541
\(741\) −419.495 −0.0207969
\(742\) −85667.6 −4.23849
\(743\) 17304.0 0.854404 0.427202 0.904156i \(-0.359499\pi\)
0.427202 + 0.904156i \(0.359499\pi\)
\(744\) 1035.40 0.0510210
\(745\) −4579.86 −0.225226
\(746\) 35640.3 1.74918
\(747\) 21802.3 1.06788
\(748\) −18317.0 −0.895368
\(749\) 9765.51 0.476401
\(750\) 203.189 0.00989254
\(751\) 27655.4 1.34375 0.671877 0.740663i \(-0.265488\pi\)
0.671877 + 0.740663i \(0.265488\pi\)
\(752\) −13404.5 −0.650015
\(753\) 1695.41 0.0820506
\(754\) 83599.9 4.03784
\(755\) −3119.58 −0.150375
\(756\) −6821.37 −0.328162
\(757\) 3795.48 0.182231 0.0911157 0.995840i \(-0.470957\pi\)
0.0911157 + 0.995840i \(0.470957\pi\)
\(758\) −14501.4 −0.694876
\(759\) 574.847 0.0274910
\(760\) 3460.30 0.165156
\(761\) 2254.23 0.107379 0.0536897 0.998558i \(-0.482902\pi\)
0.0536897 + 0.998558i \(0.482902\pi\)
\(762\) −2389.86 −0.113616
\(763\) −50619.6 −2.40177
\(764\) 67480.4 3.19549
\(765\) −14431.8 −0.682069
\(766\) 39468.9 1.86171
\(767\) 1531.59 0.0721022
\(768\) 2633.31 0.123726
\(769\) −24643.9 −1.15563 −0.577817 0.816166i \(-0.696095\pi\)
−0.577817 + 0.816166i \(0.696095\pi\)
\(770\) −6492.00 −0.303838
\(771\) −1688.04 −0.0788499
\(772\) −2356.93 −0.109880
\(773\) 13801.6 0.642183 0.321092 0.947048i \(-0.395950\pi\)
0.321092 + 0.947048i \(0.395950\pi\)
\(774\) 53586.9 2.48855
\(775\) 2119.88 0.0982561
\(776\) 26998.9 1.24897
\(777\) −2362.47 −0.109077
\(778\) 2996.61 0.138090
\(779\) −7471.92 −0.343658
\(780\) 1712.41 0.0786077
\(781\) −844.399 −0.0386875
\(782\) −81143.7 −3.71061
\(783\) 4729.01 0.215838
\(784\) 13108.5 0.597143
\(785\) −2738.17 −0.124496
\(786\) −1265.59 −0.0574325
\(787\) 5698.19 0.258092 0.129046 0.991639i \(-0.458808\pi\)
0.129046 + 0.991639i \(0.458808\pi\)
\(788\) −28046.6 −1.26792
\(789\) −1484.41 −0.0669792
\(790\) −31587.2 −1.42256
\(791\) −47095.2 −2.11696
\(792\) −10773.0 −0.483334
\(793\) −39866.2 −1.78523
\(794\) 13165.8 0.588462
\(795\) 1216.51 0.0542708
\(796\) 56937.2 2.53528
\(797\) −30047.5 −1.33543 −0.667716 0.744416i \(-0.732728\pi\)
−0.667716 + 0.744416i \(0.732728\pi\)
\(798\) 751.823 0.0333512
\(799\) −27396.9 −1.21306
\(800\) 917.911 0.0405663
\(801\) 16650.3 0.734468
\(802\) 4537.56 0.199784
\(803\) 2492.94 0.109557
\(804\) 2383.18 0.104538
\(805\) −18973.9 −0.830735
\(806\) 27079.6 1.18342
\(807\) −2121.85 −0.0925558
\(808\) 57910.9 2.52141
\(809\) 7931.99 0.344714 0.172357 0.985035i \(-0.444862\pi\)
0.172357 + 0.985035i \(0.444862\pi\)
\(810\) −17453.9 −0.757119
\(811\) −27810.0 −1.20412 −0.602061 0.798450i \(-0.705653\pi\)
−0.602061 + 0.798450i \(0.705653\pi\)
\(812\) −98848.8 −4.27206
\(813\) 577.464 0.0249109
\(814\) −15441.3 −0.664886
\(815\) −2842.50 −0.122170
\(816\) −1890.13 −0.0810878
\(817\) −7809.38 −0.334413
\(818\) 1710.13 0.0730970
\(819\) −43107.4 −1.83919
\(820\) 30500.9 1.29895
\(821\) 25236.1 1.07277 0.536385 0.843973i \(-0.319789\pi\)
0.536385 + 0.843973i \(0.319789\pi\)
\(822\) −578.240 −0.0245358
\(823\) −7664.59 −0.324630 −0.162315 0.986739i \(-0.551896\pi\)
−0.162315 + 0.986739i \(0.551896\pi\)
\(824\) 39850.4 1.68477
\(825\) 92.1889 0.00389043
\(826\) −2744.92 −0.115627
\(827\) 8971.46 0.377229 0.188614 0.982051i \(-0.439600\pi\)
0.188614 + 0.982051i \(0.439600\pi\)
\(828\) −65017.4 −2.72888
\(829\) 37004.1 1.55031 0.775155 0.631771i \(-0.217672\pi\)
0.775155 + 0.631771i \(0.217672\pi\)
\(830\) 19659.1 0.822139
\(831\) −299.385 −0.0124977
\(832\) 39399.0 1.64172
\(833\) 26791.9 1.11439
\(834\) −1366.90 −0.0567528
\(835\) 988.209 0.0409561
\(836\) 3241.98 0.134122
\(837\) 1531.82 0.0632585
\(838\) 5970.80 0.246131
\(839\) −35393.7 −1.45641 −0.728204 0.685360i \(-0.759645\pi\)
−0.728204 + 0.685360i \(0.759645\pi\)
\(840\) −1486.21 −0.0610464
\(841\) 44139.4 1.80981
\(842\) 29922.8 1.22471
\(843\) 2270.92 0.0927813
\(844\) −92674.5 −3.77961
\(845\) 10703.2 0.435743
\(846\) −33273.5 −1.35221
\(847\) −2945.49 −0.119490
\(848\) −38119.5 −1.54367
\(849\) 1299.69 0.0525386
\(850\) −13013.1 −0.525113
\(851\) −45129.6 −1.81789
\(852\) −399.176 −0.0160511
\(853\) 13773.6 0.552872 0.276436 0.961032i \(-0.410847\pi\)
0.276436 + 0.961032i \(0.410847\pi\)
\(854\) 71448.6 2.86291
\(855\) 2554.32 0.102171
\(856\) 14612.1 0.583448
\(857\) −44540.6 −1.77535 −0.887677 0.460467i \(-0.847682\pi\)
−0.887677 + 0.460467i \(0.847682\pi\)
\(858\) 1177.63 0.0468574
\(859\) 1113.60 0.0442325 0.0221162 0.999755i \(-0.492960\pi\)
0.0221162 + 0.999755i \(0.492960\pi\)
\(860\) 31878.4 1.26400
\(861\) 3209.20 0.127026
\(862\) 62958.0 2.48766
\(863\) 2425.98 0.0956908 0.0478454 0.998855i \(-0.484765\pi\)
0.0478454 + 0.998855i \(0.484765\pi\)
\(864\) 663.278 0.0261171
\(865\) −10561.5 −0.415146
\(866\) 20775.2 0.815208
\(867\) −2216.15 −0.0868103
\(868\) −32019.0 −1.25207
\(869\) −14331.5 −0.559450
\(870\) 2127.62 0.0829117
\(871\) 30183.8 1.17421
\(872\) −75742.0 −2.94145
\(873\) 19930.0 0.772657
\(874\) 14361.9 0.555832
\(875\) −3042.86 −0.117563
\(876\) 1178.50 0.0454541
\(877\) −19956.6 −0.768399 −0.384200 0.923250i \(-0.625523\pi\)
−0.384200 + 0.923250i \(0.625523\pi\)
\(878\) 3592.39 0.138083
\(879\) 836.503 0.0320984
\(880\) −2888.75 −0.110659
\(881\) −32187.7 −1.23091 −0.615455 0.788172i \(-0.711028\pi\)
−0.615455 + 0.788172i \(0.711028\pi\)
\(882\) 32538.8 1.24222
\(883\) −146.393 −0.00557930 −0.00278965 0.999996i \(-0.500888\pi\)
−0.00278965 + 0.999996i \(0.500888\pi\)
\(884\) −109670. −4.17263
\(885\) 38.9790 0.00148052
\(886\) 42904.6 1.62687
\(887\) −17105.5 −0.647517 −0.323758 0.946140i \(-0.604947\pi\)
−0.323758 + 0.946140i \(0.604947\pi\)
\(888\) −3534.95 −0.133587
\(889\) 35789.5 1.35021
\(890\) 15013.5 0.565454
\(891\) −7919.01 −0.297752
\(892\) 38863.0 1.45878
\(893\) 4849.05 0.181710
\(894\) −1488.92 −0.0557013
\(895\) −10161.5 −0.379511
\(896\) −63461.0 −2.36616
\(897\) 3441.81 0.128115
\(898\) 67274.0 2.49996
\(899\) 22197.7 0.823508
\(900\) −10426.9 −0.386182
\(901\) −77911.0 −2.88079
\(902\) 20975.6 0.774292
\(903\) 3354.14 0.123609
\(904\) −70468.4 −2.59264
\(905\) −14553.6 −0.534561
\(906\) −1014.18 −0.0371897
\(907\) −12393.8 −0.453724 −0.226862 0.973927i \(-0.572847\pi\)
−0.226862 + 0.973927i \(0.572847\pi\)
\(908\) −6908.00 −0.252478
\(909\) 42748.6 1.55983
\(910\) −38869.9 −1.41596
\(911\) −33492.0 −1.21804 −0.609022 0.793153i \(-0.708438\pi\)
−0.609022 + 0.793153i \(0.708438\pi\)
\(912\) 334.539 0.0121466
\(913\) 8919.53 0.323322
\(914\) −85379.6 −3.08983
\(915\) −1014.60 −0.0366575
\(916\) −35803.9 −1.29148
\(917\) 18952.9 0.682529
\(918\) −9403.22 −0.338074
\(919\) 21900.4 0.786101 0.393051 0.919517i \(-0.371420\pi\)
0.393051 + 0.919517i \(0.371420\pi\)
\(920\) −28390.6 −1.01740
\(921\) 3205.63 0.114689
\(922\) −10331.8 −0.369044
\(923\) −5055.71 −0.180293
\(924\) −1392.44 −0.0495755
\(925\) −7237.48 −0.257262
\(926\) 34965.7 1.24087
\(927\) 29416.7 1.04226
\(928\) 9611.60 0.339996
\(929\) 51558.4 1.82086 0.910429 0.413666i \(-0.135752\pi\)
0.910429 + 0.413666i \(0.135752\pi\)
\(930\) 689.178 0.0243001
\(931\) −4741.97 −0.166930
\(932\) 106597. 3.74645
\(933\) −2114.40 −0.0741934
\(934\) 12640.7 0.442844
\(935\) −5904.19 −0.206511
\(936\) −64501.5 −2.25245
\(937\) 16866.3 0.588046 0.294023 0.955798i \(-0.405006\pi\)
0.294023 + 0.955798i \(0.405006\pi\)
\(938\) −54095.8 −1.88304
\(939\) −3205.71 −0.111411
\(940\) −19794.2 −0.686823
\(941\) −27743.0 −0.961102 −0.480551 0.876967i \(-0.659563\pi\)
−0.480551 + 0.876967i \(0.659563\pi\)
\(942\) −890.184 −0.0307895
\(943\) 61304.5 2.11702
\(944\) −1221.41 −0.0421117
\(945\) −2198.76 −0.0756885
\(946\) 21922.9 0.753463
\(947\) 11329.1 0.388751 0.194376 0.980927i \(-0.437732\pi\)
0.194376 + 0.980927i \(0.437732\pi\)
\(948\) −6774.98 −0.232111
\(949\) 14926.1 0.510560
\(950\) 2303.23 0.0786596
\(951\) −537.763 −0.0183367
\(952\) 95183.3 3.24045
\(953\) −3552.96 −0.120768 −0.0603840 0.998175i \(-0.519233\pi\)
−0.0603840 + 0.998175i \(0.519233\pi\)
\(954\) −94622.9 −3.21125
\(955\) 21751.2 0.737019
\(956\) −10149.5 −0.343368
\(957\) 965.326 0.0326067
\(958\) 55471.2 1.87076
\(959\) 8659.47 0.291584
\(960\) 1002.71 0.0337107
\(961\) −22600.7 −0.758643
\(962\) −92452.4 −3.09853
\(963\) 10786.4 0.360940
\(964\) −41954.9 −1.40174
\(965\) −759.718 −0.0253432
\(966\) −6168.45 −0.205452
\(967\) 15513.9 0.515918 0.257959 0.966156i \(-0.416950\pi\)
0.257959 + 0.966156i \(0.416950\pi\)
\(968\) −4407.33 −0.146340
\(969\) 683.750 0.0226679
\(970\) 17970.9 0.594855
\(971\) 13083.5 0.432410 0.216205 0.976348i \(-0.430632\pi\)
0.216205 + 0.976348i \(0.430632\pi\)
\(972\) −11309.5 −0.373203
\(973\) 20470.1 0.674451
\(974\) 66334.8 2.18224
\(975\) 551.967 0.0181304
\(976\) 31792.5 1.04268
\(977\) −31709.2 −1.03835 −0.519174 0.854668i \(-0.673761\pi\)
−0.519174 + 0.854668i \(0.673761\pi\)
\(978\) −924.103 −0.0302143
\(979\) 6811.80 0.222376
\(980\) 19357.1 0.630957
\(981\) −55911.2 −1.81968
\(982\) −56380.3 −1.83215
\(983\) 22307.9 0.723816 0.361908 0.932214i \(-0.382125\pi\)
0.361908 + 0.932214i \(0.382125\pi\)
\(984\) 4801.92 0.155569
\(985\) −9040.36 −0.292436
\(986\) −136263. −4.40110
\(987\) −2082.68 −0.0671655
\(988\) 19410.8 0.625042
\(989\) 64073.2 2.06007
\(990\) −7170.65 −0.230200
\(991\) −43858.1 −1.40585 −0.702926 0.711263i \(-0.748124\pi\)
−0.702926 + 0.711263i \(0.748124\pi\)
\(992\) 3113.38 0.0996472
\(993\) 2511.14 0.0802504
\(994\) 9060.89 0.289129
\(995\) 18352.8 0.584747
\(996\) 4216.57 0.134144
\(997\) −8757.89 −0.278200 −0.139100 0.990278i \(-0.544421\pi\)
−0.139100 + 0.990278i \(0.544421\pi\)
\(998\) −5083.32 −0.161232
\(999\) −5229.77 −0.165628
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 1045.4.a.d.1.2 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.4.a.d.1.2 22 1.1 even 1 trivial