Properties

Label 1045.4.a.g.1.12
Level $1045$
Weight $4$
Character 1045.1
Self dual yes
Analytic conductor $61.657$
Analytic rank $0$
Dimension $23$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(0\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
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)
 
\(f(q)\) \(=\) \(q+0.666010 q^{2} -10.2430 q^{3} -7.55643 q^{4} -5.00000 q^{5} -6.82192 q^{6} +4.34789 q^{7} -10.3607 q^{8} +77.9184 q^{9} +O(q^{10})\) \(q+0.666010 q^{2} -10.2430 q^{3} -7.55643 q^{4} -5.00000 q^{5} -6.82192 q^{6} +4.34789 q^{7} -10.3607 q^{8} +77.9184 q^{9} -3.33005 q^{10} -11.0000 q^{11} +77.4003 q^{12} +15.3859 q^{13} +2.89574 q^{14} +51.2148 q^{15} +53.5511 q^{16} -111.405 q^{17} +51.8944 q^{18} -19.0000 q^{19} +37.7822 q^{20} -44.5353 q^{21} -7.32611 q^{22} -182.322 q^{23} +106.125 q^{24} +25.0000 q^{25} +10.2472 q^{26} -521.555 q^{27} -32.8546 q^{28} +6.29537 q^{29} +34.1096 q^{30} +10.5762 q^{31} +118.551 q^{32} +112.673 q^{33} -74.1970 q^{34} -21.7395 q^{35} -588.785 q^{36} -310.552 q^{37} -12.6542 q^{38} -157.598 q^{39} +51.8037 q^{40} -291.283 q^{41} -29.6610 q^{42} +42.1352 q^{43} +83.1207 q^{44} -389.592 q^{45} -121.428 q^{46} -40.5254 q^{47} -548.522 q^{48} -324.096 q^{49} +16.6502 q^{50} +1141.12 q^{51} -116.263 q^{52} -337.809 q^{53} -347.361 q^{54} +55.0000 q^{55} -45.0474 q^{56} +194.616 q^{57} +4.19278 q^{58} +425.860 q^{59} -387.001 q^{60} -694.137 q^{61} +7.04385 q^{62} +338.781 q^{63} -349.452 q^{64} -76.9296 q^{65} +75.0411 q^{66} -899.527 q^{67} +841.826 q^{68} +1867.52 q^{69} -14.4787 q^{70} +745.640 q^{71} -807.292 q^{72} +103.964 q^{73} -206.831 q^{74} -256.074 q^{75} +143.572 q^{76} -47.8268 q^{77} -104.961 q^{78} -866.127 q^{79} -267.756 q^{80} +3238.48 q^{81} -193.997 q^{82} +1270.56 q^{83} +336.528 q^{84} +557.026 q^{85} +28.0625 q^{86} -64.4833 q^{87} +113.968 q^{88} -828.828 q^{89} -259.472 q^{90} +66.8964 q^{91} +1377.70 q^{92} -108.332 q^{93} -26.9903 q^{94} +95.0000 q^{95} -1214.32 q^{96} +655.359 q^{97} -215.851 q^{98} -857.102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9} - 30 q^{10} - 253 q^{11} + 44 q^{12} - 37 q^{13} + 61 q^{14} - 45 q^{15} + 588 q^{16} - 73 q^{17} + 391 q^{18} - 437 q^{19} - 460 q^{20} - 127 q^{21} - 66 q^{22} - 175 q^{23} + 16 q^{24} + 575 q^{25} + 719 q^{26} + 21 q^{27} + 253 q^{28} + 71 q^{29} + 125 q^{30} + 302 q^{31} + 1107 q^{32} - 99 q^{33} + 1267 q^{34} + 185 q^{35} + 703 q^{36} - 500 q^{37} - 114 q^{38} + 457 q^{39} - 210 q^{40} + 770 q^{41} + 2596 q^{42} - 902 q^{43} - 1012 q^{44} - 850 q^{45} - 1101 q^{46} + 356 q^{47} + 1221 q^{48} + 908 q^{49} + 150 q^{50} - 451 q^{51} - 358 q^{52} + 1327 q^{53} + 2534 q^{54} + 1265 q^{55} + 3135 q^{56} - 171 q^{57} + 1014 q^{58} + 3619 q^{59} - 220 q^{60} - 1432 q^{61} + 1826 q^{62} + 1658 q^{63} + 4006 q^{64} + 185 q^{65} + 275 q^{66} - 605 q^{67} + 5128 q^{68} + 3099 q^{69} - 305 q^{70} + 3230 q^{71} + 2152 q^{72} - 637 q^{73} + 5063 q^{74} + 225 q^{75} - 1748 q^{76} + 407 q^{77} + 7230 q^{78} + 2074 q^{79} - 2940 q^{80} + 2291 q^{81} + 530 q^{82} + 3882 q^{83} + 5096 q^{84} + 365 q^{85} + 2262 q^{86} - 27 q^{87} - 462 q^{88} - 210 q^{89} - 1955 q^{90} + 4133 q^{91} - 6064 q^{92} + 824 q^{93} - 392 q^{94} + 2185 q^{95} + 2462 q^{96} + 2032 q^{97} + 7896 q^{98} - 1870 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.666010 0.235470 0.117735 0.993045i \(-0.462437\pi\)
0.117735 + 0.993045i \(0.462437\pi\)
\(3\) −10.2430 −1.97126 −0.985630 0.168919i \(-0.945973\pi\)
−0.985630 + 0.168919i \(0.945973\pi\)
\(4\) −7.55643 −0.944554
\(5\) −5.00000 −0.447214
\(6\) −6.82192 −0.464173
\(7\) 4.34789 0.234764 0.117382 0.993087i \(-0.462550\pi\)
0.117382 + 0.993087i \(0.462550\pi\)
\(8\) −10.3607 −0.457884
\(9\) 77.9184 2.88587
\(10\) −3.33005 −0.105305
\(11\) −11.0000 −0.301511
\(12\) 77.4003 1.86196
\(13\) 15.3859 0.328253 0.164126 0.986439i \(-0.447519\pi\)
0.164126 + 0.986439i \(0.447519\pi\)
\(14\) 2.89574 0.0552799
\(15\) 51.2148 0.881574
\(16\) 53.5511 0.836736
\(17\) −111.405 −1.58940 −0.794698 0.607005i \(-0.792371\pi\)
−0.794698 + 0.607005i \(0.792371\pi\)
\(18\) 51.8944 0.679535
\(19\) −19.0000 −0.229416
\(20\) 37.7822 0.422417
\(21\) −44.5353 −0.462781
\(22\) −7.32611 −0.0709969
\(23\) −182.322 −1.65290 −0.826451 0.563009i \(-0.809644\pi\)
−0.826451 + 0.563009i \(0.809644\pi\)
\(24\) 106.125 0.902609
\(25\) 25.0000 0.200000
\(26\) 10.2472 0.0772937
\(27\) −521.555 −3.71753
\(28\) −32.8546 −0.221747
\(29\) 6.29537 0.0403111 0.0201555 0.999797i \(-0.493584\pi\)
0.0201555 + 0.999797i \(0.493584\pi\)
\(30\) 34.1096 0.207584
\(31\) 10.5762 0.0612756 0.0306378 0.999531i \(-0.490246\pi\)
0.0306378 + 0.999531i \(0.490246\pi\)
\(32\) 118.551 0.654910
\(33\) 112.673 0.594357
\(34\) −74.1970 −0.374255
\(35\) −21.7395 −0.104990
\(36\) −588.785 −2.72586
\(37\) −310.552 −1.37985 −0.689925 0.723881i \(-0.742356\pi\)
−0.689925 + 0.723881i \(0.742356\pi\)
\(38\) −12.6542 −0.0540205
\(39\) −157.598 −0.647072
\(40\) 51.8037 0.204772
\(41\) −291.283 −1.10953 −0.554765 0.832007i \(-0.687192\pi\)
−0.554765 + 0.832007i \(0.687192\pi\)
\(42\) −29.6610 −0.108971
\(43\) 42.1352 0.149432 0.0747158 0.997205i \(-0.476195\pi\)
0.0747158 + 0.997205i \(0.476195\pi\)
\(44\) 83.1207 0.284794
\(45\) −389.592 −1.29060
\(46\) −121.428 −0.389209
\(47\) −40.5254 −0.125771 −0.0628856 0.998021i \(-0.520030\pi\)
−0.0628856 + 0.998021i \(0.520030\pi\)
\(48\) −548.522 −1.64942
\(49\) −324.096 −0.944886
\(50\) 16.6502 0.0470940
\(51\) 1141.12 3.13311
\(52\) −116.263 −0.310053
\(53\) −337.809 −0.875501 −0.437751 0.899096i \(-0.644225\pi\)
−0.437751 + 0.899096i \(0.644225\pi\)
\(54\) −347.361 −0.875367
\(55\) 55.0000 0.134840
\(56\) −45.0474 −0.107495
\(57\) 194.616 0.452238
\(58\) 4.19278 0.00949204
\(59\) 425.860 0.939699 0.469850 0.882746i \(-0.344308\pi\)
0.469850 + 0.882746i \(0.344308\pi\)
\(60\) −387.001 −0.832694
\(61\) −694.137 −1.45697 −0.728485 0.685062i \(-0.759775\pi\)
−0.728485 + 0.685062i \(0.759775\pi\)
\(62\) 7.04385 0.0144286
\(63\) 338.781 0.677498
\(64\) −349.452 −0.682524
\(65\) −76.9296 −0.146799
\(66\) 75.0411 0.139953
\(67\) −899.527 −1.64022 −0.820110 0.572206i \(-0.806088\pi\)
−0.820110 + 0.572206i \(0.806088\pi\)
\(68\) 841.826 1.50127
\(69\) 1867.52 3.25830
\(70\) −14.4787 −0.0247219
\(71\) 745.640 1.24636 0.623178 0.782080i \(-0.285841\pi\)
0.623178 + 0.782080i \(0.285841\pi\)
\(72\) −807.292 −1.32139
\(73\) 103.964 0.166686 0.0833429 0.996521i \(-0.473440\pi\)
0.0833429 + 0.996521i \(0.473440\pi\)
\(74\) −206.831 −0.324913
\(75\) −256.074 −0.394252
\(76\) 143.572 0.216696
\(77\) −47.8268 −0.0707841
\(78\) −104.961 −0.152366
\(79\) −866.127 −1.23350 −0.616752 0.787157i \(-0.711552\pi\)
−0.616752 + 0.787157i \(0.711552\pi\)
\(80\) −267.756 −0.374200
\(81\) 3238.48 4.44236
\(82\) −193.997 −0.261261
\(83\) 1270.56 1.68026 0.840132 0.542381i \(-0.182477\pi\)
0.840132 + 0.542381i \(0.182477\pi\)
\(84\) 336.528 0.437122
\(85\) 557.026 0.710800
\(86\) 28.0625 0.0351867
\(87\) −64.4833 −0.0794636
\(88\) 113.968 0.138057
\(89\) −828.828 −0.987142 −0.493571 0.869706i \(-0.664309\pi\)
−0.493571 + 0.869706i \(0.664309\pi\)
\(90\) −259.472 −0.303897
\(91\) 66.8964 0.0770620
\(92\) 1377.70 1.56126
\(93\) −108.332 −0.120790
\(94\) −26.9903 −0.0296153
\(95\) 95.0000 0.102598
\(96\) −1214.32 −1.29100
\(97\) 655.359 0.685996 0.342998 0.939336i \(-0.388558\pi\)
0.342998 + 0.939336i \(0.388558\pi\)
\(98\) −215.851 −0.222492
\(99\) −857.102 −0.870121
\(100\) −188.911 −0.188911
\(101\) −994.650 −0.979915 −0.489957 0.871746i \(-0.662988\pi\)
−0.489957 + 0.871746i \(0.662988\pi\)
\(102\) 759.997 0.737754
\(103\) 36.2047 0.0346345 0.0173173 0.999850i \(-0.494487\pi\)
0.0173173 + 0.999850i \(0.494487\pi\)
\(104\) −159.409 −0.150302
\(105\) 222.677 0.206962
\(106\) −224.984 −0.206154
\(107\) −411.866 −0.372117 −0.186059 0.982539i \(-0.559571\pi\)
−0.186059 + 0.982539i \(0.559571\pi\)
\(108\) 3941.10 3.51141
\(109\) −487.137 −0.428067 −0.214033 0.976826i \(-0.568660\pi\)
−0.214033 + 0.976826i \(0.568660\pi\)
\(110\) 36.6305 0.0317508
\(111\) 3180.97 2.72004
\(112\) 232.834 0.196436
\(113\) 1397.53 1.16344 0.581718 0.813391i \(-0.302381\pi\)
0.581718 + 0.813391i \(0.302381\pi\)
\(114\) 129.616 0.106488
\(115\) 911.610 0.739200
\(116\) −47.5705 −0.0380760
\(117\) 1198.85 0.947294
\(118\) 283.627 0.221271
\(119\) −484.378 −0.373133
\(120\) −530.623 −0.403659
\(121\) 121.000 0.0909091
\(122\) −462.302 −0.343073
\(123\) 2983.60 2.18717
\(124\) −79.9184 −0.0578781
\(125\) −125.000 −0.0894427
\(126\) 225.631 0.159530
\(127\) −2699.83 −1.88638 −0.943192 0.332248i \(-0.892193\pi\)
−0.943192 + 0.332248i \(0.892193\pi\)
\(128\) −1181.15 −0.815624
\(129\) −431.590 −0.294569
\(130\) −51.2359 −0.0345668
\(131\) 2784.16 1.85689 0.928447 0.371465i \(-0.121144\pi\)
0.928447 + 0.371465i \(0.121144\pi\)
\(132\) −851.403 −0.561402
\(133\) −82.6100 −0.0538586
\(134\) −599.094 −0.386223
\(135\) 2607.78 1.66253
\(136\) 1154.24 0.727759
\(137\) −2071.50 −1.29183 −0.645913 0.763411i \(-0.723523\pi\)
−0.645913 + 0.763411i \(0.723523\pi\)
\(138\) 1243.78 0.767232
\(139\) 491.030 0.299630 0.149815 0.988714i \(-0.452132\pi\)
0.149815 + 0.988714i \(0.452132\pi\)
\(140\) 164.273 0.0991685
\(141\) 415.101 0.247928
\(142\) 496.604 0.293479
\(143\) −169.245 −0.0989720
\(144\) 4172.62 2.41471
\(145\) −31.4768 −0.0180277
\(146\) 69.2410 0.0392495
\(147\) 3319.70 1.86262
\(148\) 2346.66 1.30334
\(149\) 243.919 0.134112 0.0670558 0.997749i \(-0.478639\pi\)
0.0670558 + 0.997749i \(0.478639\pi\)
\(150\) −170.548 −0.0928345
\(151\) −2683.31 −1.44612 −0.723061 0.690785i \(-0.757265\pi\)
−0.723061 + 0.690785i \(0.757265\pi\)
\(152\) 196.854 0.105046
\(153\) −8680.52 −4.58679
\(154\) −31.8531 −0.0166675
\(155\) −52.8810 −0.0274033
\(156\) 1190.87 0.611194
\(157\) −1489.89 −0.757366 −0.378683 0.925526i \(-0.623623\pi\)
−0.378683 + 0.925526i \(0.623623\pi\)
\(158\) −576.849 −0.290453
\(159\) 3460.16 1.72584
\(160\) −592.757 −0.292885
\(161\) −792.716 −0.388042
\(162\) 2156.86 1.04604
\(163\) 239.149 0.114918 0.0574590 0.998348i \(-0.481700\pi\)
0.0574590 + 0.998348i \(0.481700\pi\)
\(164\) 2201.06 1.04801
\(165\) −563.363 −0.265805
\(166\) 846.205 0.395652
\(167\) 394.272 0.182693 0.0913463 0.995819i \(-0.470883\pi\)
0.0913463 + 0.995819i \(0.470883\pi\)
\(168\) 461.419 0.211900
\(169\) −1960.27 −0.892250
\(170\) 370.985 0.167372
\(171\) −1480.45 −0.662063
\(172\) −318.392 −0.141146
\(173\) −3760.11 −1.65246 −0.826230 0.563333i \(-0.809519\pi\)
−0.826230 + 0.563333i \(0.809519\pi\)
\(174\) −42.9465 −0.0187113
\(175\) 108.697 0.0469528
\(176\) −589.062 −0.252285
\(177\) −4362.07 −1.85239
\(178\) −552.008 −0.232442
\(179\) 1572.58 0.656649 0.328325 0.944565i \(-0.393516\pi\)
0.328325 + 0.944565i \(0.393516\pi\)
\(180\) 2943.92 1.21904
\(181\) 1578.45 0.648206 0.324103 0.946022i \(-0.394938\pi\)
0.324103 + 0.946022i \(0.394938\pi\)
\(182\) 44.5536 0.0181458
\(183\) 7110.02 2.87207
\(184\) 1888.99 0.756837
\(185\) 1552.76 0.617087
\(186\) −72.1500 −0.0284424
\(187\) 1225.46 0.479221
\(188\) 306.228 0.118798
\(189\) −2267.67 −0.872743
\(190\) 63.2709 0.0241587
\(191\) 2227.16 0.843728 0.421864 0.906659i \(-0.361376\pi\)
0.421864 + 0.906659i \(0.361376\pi\)
\(192\) 3579.43 1.34543
\(193\) −57.8787 −0.0215865 −0.0107933 0.999942i \(-0.503436\pi\)
−0.0107933 + 0.999942i \(0.503436\pi\)
\(194\) 436.476 0.161532
\(195\) 787.988 0.289379
\(196\) 2449.01 0.892496
\(197\) 2473.85 0.894694 0.447347 0.894360i \(-0.352369\pi\)
0.447347 + 0.894360i \(0.352369\pi\)
\(198\) −570.838 −0.204887
\(199\) −3694.38 −1.31602 −0.658010 0.753009i \(-0.728601\pi\)
−0.658010 + 0.753009i \(0.728601\pi\)
\(200\) −259.018 −0.0915768
\(201\) 9213.83 3.23330
\(202\) −662.447 −0.230740
\(203\) 27.3716 0.00946359
\(204\) −8622.80 −2.95940
\(205\) 1456.42 0.496197
\(206\) 24.1127 0.00815540
\(207\) −14206.2 −4.77005
\(208\) 823.933 0.274661
\(209\) 209.000 0.0691714
\(210\) 148.305 0.0487333
\(211\) 2678.20 0.873814 0.436907 0.899507i \(-0.356074\pi\)
0.436907 + 0.899507i \(0.356074\pi\)
\(212\) 2552.63 0.826958
\(213\) −7637.57 −2.45689
\(214\) −274.307 −0.0876225
\(215\) −210.676 −0.0668279
\(216\) 5403.70 1.70220
\(217\) 45.9842 0.0143853
\(218\) −324.438 −0.100797
\(219\) −1064.90 −0.328581
\(220\) −415.604 −0.127364
\(221\) −1714.07 −0.521724
\(222\) 2118.56 0.640488
\(223\) 2932.58 0.880629 0.440315 0.897844i \(-0.354867\pi\)
0.440315 + 0.897844i \(0.354867\pi\)
\(224\) 515.449 0.153749
\(225\) 1947.96 0.577173
\(226\) 930.766 0.273954
\(227\) 6488.53 1.89718 0.948588 0.316513i \(-0.102512\pi\)
0.948588 + 0.316513i \(0.102512\pi\)
\(228\) −1470.61 −0.427163
\(229\) −2031.56 −0.586242 −0.293121 0.956075i \(-0.594694\pi\)
−0.293121 + 0.956075i \(0.594694\pi\)
\(230\) 607.141 0.174059
\(231\) 489.889 0.139534
\(232\) −65.2246 −0.0184578
\(233\) −6992.00 −1.96593 −0.982963 0.183803i \(-0.941159\pi\)
−0.982963 + 0.183803i \(0.941159\pi\)
\(234\) 798.443 0.223059
\(235\) 202.627 0.0562466
\(236\) −3217.98 −0.887597
\(237\) 8871.71 2.43156
\(238\) −322.601 −0.0878617
\(239\) −924.735 −0.250277 −0.125138 0.992139i \(-0.539937\pi\)
−0.125138 + 0.992139i \(0.539937\pi\)
\(240\) 2742.61 0.737645
\(241\) 1737.40 0.464380 0.232190 0.972670i \(-0.425411\pi\)
0.232190 + 0.972670i \(0.425411\pi\)
\(242\) 80.5872 0.0214064
\(243\) −19089.6 −5.03951
\(244\) 5245.20 1.37619
\(245\) 1620.48 0.422566
\(246\) 1987.11 0.515014
\(247\) −292.333 −0.0753064
\(248\) −109.577 −0.0280571
\(249\) −13014.3 −3.31224
\(250\) −83.2512 −0.0210611
\(251\) 6716.81 1.68909 0.844545 0.535485i \(-0.179871\pi\)
0.844545 + 0.535485i \(0.179871\pi\)
\(252\) −2559.97 −0.639933
\(253\) 2005.54 0.498369
\(254\) −1798.11 −0.444187
\(255\) −5705.60 −1.40117
\(256\) 2008.96 0.490469
\(257\) −385.405 −0.0935445 −0.0467722 0.998906i \(-0.514894\pi\)
−0.0467722 + 0.998906i \(0.514894\pi\)
\(258\) −287.443 −0.0693621
\(259\) −1350.25 −0.323939
\(260\) 581.313 0.138660
\(261\) 490.525 0.116332
\(262\) 1854.28 0.437243
\(263\) −6938.45 −1.62678 −0.813390 0.581718i \(-0.802381\pi\)
−0.813390 + 0.581718i \(0.802381\pi\)
\(264\) −1167.37 −0.272147
\(265\) 1689.04 0.391536
\(266\) −55.0190 −0.0126821
\(267\) 8489.66 1.94591
\(268\) 6797.22 1.54928
\(269\) 5764.26 1.30652 0.653259 0.757135i \(-0.273401\pi\)
0.653259 + 0.757135i \(0.273401\pi\)
\(270\) 1736.80 0.391476
\(271\) −2934.60 −0.657801 −0.328901 0.944365i \(-0.606678\pi\)
−0.328901 + 0.944365i \(0.606678\pi\)
\(272\) −5965.87 −1.32991
\(273\) −685.217 −0.151909
\(274\) −1379.64 −0.304186
\(275\) −275.000 −0.0603023
\(276\) −14111.8 −3.07764
\(277\) 746.505 0.161925 0.0809624 0.996717i \(-0.474201\pi\)
0.0809624 + 0.996717i \(0.474201\pi\)
\(278\) 327.031 0.0705539
\(279\) 824.081 0.176833
\(280\) 225.237 0.0480731
\(281\) 5041.44 1.07027 0.535137 0.844765i \(-0.320260\pi\)
0.535137 + 0.844765i \(0.320260\pi\)
\(282\) 276.461 0.0583795
\(283\) −2324.25 −0.488207 −0.244104 0.969749i \(-0.578494\pi\)
−0.244104 + 0.969749i \(0.578494\pi\)
\(284\) −5634.38 −1.17725
\(285\) −973.082 −0.202247
\(286\) −112.719 −0.0233049
\(287\) −1266.47 −0.260478
\(288\) 9237.33 1.88998
\(289\) 7498.13 1.52618
\(290\) −20.9639 −0.00424497
\(291\) −6712.82 −1.35228
\(292\) −785.597 −0.157444
\(293\) 299.264 0.0596697 0.0298348 0.999555i \(-0.490502\pi\)
0.0298348 + 0.999555i \(0.490502\pi\)
\(294\) 2210.95 0.438590
\(295\) −2129.30 −0.420246
\(296\) 3217.55 0.631811
\(297\) 5737.11 1.12088
\(298\) 162.452 0.0315793
\(299\) −2805.19 −0.542570
\(300\) 1935.01 0.372392
\(301\) 183.199 0.0350812
\(302\) −1787.11 −0.340518
\(303\) 10188.2 1.93167
\(304\) −1017.47 −0.191960
\(305\) 3470.69 0.651577
\(306\) −5781.31 −1.08005
\(307\) 7261.64 1.34998 0.674990 0.737827i \(-0.264148\pi\)
0.674990 + 0.737827i \(0.264148\pi\)
\(308\) 361.400 0.0668594
\(309\) −370.844 −0.0682737
\(310\) −35.2193 −0.00645265
\(311\) −6208.70 −1.13204 −0.566018 0.824393i \(-0.691517\pi\)
−0.566018 + 0.824393i \(0.691517\pi\)
\(312\) 1632.83 0.296284
\(313\) −1127.40 −0.203592 −0.101796 0.994805i \(-0.532459\pi\)
−0.101796 + 0.994805i \(0.532459\pi\)
\(314\) −992.284 −0.178337
\(315\) −1693.90 −0.302986
\(316\) 6544.83 1.16511
\(317\) −7253.45 −1.28516 −0.642578 0.766220i \(-0.722135\pi\)
−0.642578 + 0.766220i \(0.722135\pi\)
\(318\) 2304.50 0.406384
\(319\) −69.2491 −0.0121542
\(320\) 1747.26 0.305234
\(321\) 4218.73 0.733540
\(322\) −527.957 −0.0913723
\(323\) 2116.70 0.364633
\(324\) −24471.3 −4.19605
\(325\) 384.648 0.0656506
\(326\) 159.276 0.0270597
\(327\) 4989.73 0.843831
\(328\) 3017.91 0.508036
\(329\) −176.200 −0.0295266
\(330\) −375.205 −0.0625890
\(331\) −5641.53 −0.936817 −0.468409 0.883512i \(-0.655172\pi\)
−0.468409 + 0.883512i \(0.655172\pi\)
\(332\) −9600.89 −1.58710
\(333\) −24197.7 −3.98206
\(334\) 262.589 0.0430186
\(335\) 4497.64 0.733529
\(336\) −2384.92 −0.387226
\(337\) −1961.00 −0.316980 −0.158490 0.987361i \(-0.550663\pi\)
−0.158490 + 0.987361i \(0.550663\pi\)
\(338\) −1305.56 −0.210098
\(339\) −14314.8 −2.29343
\(340\) −4209.13 −0.671389
\(341\) −116.338 −0.0184753
\(342\) −985.994 −0.155896
\(343\) −2900.46 −0.456589
\(344\) −436.552 −0.0684224
\(345\) −9337.59 −1.45716
\(346\) −2504.27 −0.389105
\(347\) −2007.00 −0.310494 −0.155247 0.987876i \(-0.549617\pi\)
−0.155247 + 0.987876i \(0.549617\pi\)
\(348\) 487.263 0.0750576
\(349\) 3057.04 0.468881 0.234441 0.972130i \(-0.424674\pi\)
0.234441 + 0.972130i \(0.424674\pi\)
\(350\) 72.3935 0.0110560
\(351\) −8024.61 −1.22029
\(352\) −1304.07 −0.197463
\(353\) 9203.36 1.38766 0.693832 0.720137i \(-0.255921\pi\)
0.693832 + 0.720137i \(0.255921\pi\)
\(354\) −2905.18 −0.436183
\(355\) −3728.20 −0.557387
\(356\) 6262.98 0.932409
\(357\) 4961.47 0.735543
\(358\) 1047.35 0.154621
\(359\) 10561.6 1.55270 0.776352 0.630300i \(-0.217068\pi\)
0.776352 + 0.630300i \(0.217068\pi\)
\(360\) 4036.46 0.590944
\(361\) 361.000 0.0526316
\(362\) 1051.26 0.152633
\(363\) −1239.40 −0.179205
\(364\) −505.498 −0.0727892
\(365\) −519.820 −0.0745441
\(366\) 4735.34 0.676285
\(367\) −6210.01 −0.883269 −0.441634 0.897195i \(-0.645601\pi\)
−0.441634 + 0.897195i \(0.645601\pi\)
\(368\) −9763.54 −1.38304
\(369\) −22696.3 −3.20196
\(370\) 1034.15 0.145306
\(371\) −1468.76 −0.205536
\(372\) 818.601 0.114093
\(373\) 83.0043 0.0115223 0.00576113 0.999983i \(-0.498166\pi\)
0.00576113 + 0.999983i \(0.498166\pi\)
\(374\) 816.167 0.112842
\(375\) 1280.37 0.176315
\(376\) 419.873 0.0575886
\(377\) 96.8601 0.0132322
\(378\) −1510.29 −0.205505
\(379\) −4246.30 −0.575509 −0.287754 0.957704i \(-0.592909\pi\)
−0.287754 + 0.957704i \(0.592909\pi\)
\(380\) −717.861 −0.0969092
\(381\) 27654.2 3.71855
\(382\) 1483.31 0.198672
\(383\) 4862.08 0.648670 0.324335 0.945942i \(-0.394860\pi\)
0.324335 + 0.945942i \(0.394860\pi\)
\(384\) 12098.5 1.60781
\(385\) 239.134 0.0316556
\(386\) −38.5478 −0.00508298
\(387\) 3283.11 0.431240
\(388\) −4952.18 −0.647960
\(389\) 7325.70 0.954827 0.477413 0.878679i \(-0.341574\pi\)
0.477413 + 0.878679i \(0.341574\pi\)
\(390\) 524.807 0.0681401
\(391\) 20311.6 2.62712
\(392\) 3357.87 0.432648
\(393\) −28518.0 −3.66042
\(394\) 1647.61 0.210674
\(395\) 4330.63 0.551640
\(396\) 6476.63 0.821877
\(397\) −617.885 −0.0781128 −0.0390564 0.999237i \(-0.512435\pi\)
−0.0390564 + 0.999237i \(0.512435\pi\)
\(398\) −2460.50 −0.309883
\(399\) 846.171 0.106169
\(400\) 1338.78 0.167347
\(401\) 7135.88 0.888651 0.444325 0.895865i \(-0.353443\pi\)
0.444325 + 0.895865i \(0.353443\pi\)
\(402\) 6136.50 0.761345
\(403\) 162.725 0.0201139
\(404\) 7516.00 0.925582
\(405\) −16192.4 −1.98668
\(406\) 18.2297 0.00222839
\(407\) 3416.07 0.416040
\(408\) −11822.8 −1.43460
\(409\) 8740.86 1.05674 0.528371 0.849013i \(-0.322803\pi\)
0.528371 + 0.849013i \(0.322803\pi\)
\(410\) 969.986 0.116840
\(411\) 21218.3 2.54652
\(412\) −273.579 −0.0327142
\(413\) 1851.59 0.220608
\(414\) −9461.49 −1.12320
\(415\) −6352.80 −0.751437
\(416\) 1824.02 0.214976
\(417\) −5029.60 −0.590649
\(418\) 139.196 0.0162878
\(419\) −8004.55 −0.933288 −0.466644 0.884445i \(-0.654537\pi\)
−0.466644 + 0.884445i \(0.654537\pi\)
\(420\) −1682.64 −0.195487
\(421\) −83.8784 −0.00971017 −0.00485509 0.999988i \(-0.501545\pi\)
−0.00485509 + 0.999988i \(0.501545\pi\)
\(422\) 1783.71 0.205757
\(423\) −3157.68 −0.362959
\(424\) 3499.94 0.400878
\(425\) −2785.13 −0.317879
\(426\) −5086.69 −0.578524
\(427\) −3018.03 −0.342044
\(428\) 3112.24 0.351485
\(429\) 1733.57 0.195099
\(430\) −140.312 −0.0157360
\(431\) 13730.5 1.53451 0.767255 0.641342i \(-0.221622\pi\)
0.767255 + 0.641342i \(0.221622\pi\)
\(432\) −27929.9 −3.11059
\(433\) 737.909 0.0818975 0.0409488 0.999161i \(-0.486962\pi\)
0.0409488 + 0.999161i \(0.486962\pi\)
\(434\) 30.6259 0.00338731
\(435\) 322.416 0.0355372
\(436\) 3681.02 0.404332
\(437\) 3464.12 0.379202
\(438\) −709.233 −0.0773710
\(439\) 8355.23 0.908367 0.454184 0.890908i \(-0.349931\pi\)
0.454184 + 0.890908i \(0.349931\pi\)
\(440\) −569.840 −0.0617411
\(441\) −25253.0 −2.72681
\(442\) −1141.59 −0.122850
\(443\) 11798.0 1.26533 0.632665 0.774426i \(-0.281961\pi\)
0.632665 + 0.774426i \(0.281961\pi\)
\(444\) −24036.8 −2.56923
\(445\) 4144.14 0.441463
\(446\) 1953.13 0.207362
\(447\) −2498.45 −0.264369
\(448\) −1519.38 −0.160232
\(449\) 1784.73 0.187587 0.0937933 0.995592i \(-0.470101\pi\)
0.0937933 + 0.995592i \(0.470101\pi\)
\(450\) 1297.36 0.135907
\(451\) 3204.11 0.334536
\(452\) −10560.3 −1.09893
\(453\) 27485.0 2.85068
\(454\) 4321.42 0.446728
\(455\) −334.482 −0.0344632
\(456\) −2016.37 −0.207073
\(457\) −15327.1 −1.56887 −0.784434 0.620213i \(-0.787046\pi\)
−0.784434 + 0.620213i \(0.787046\pi\)
\(458\) −1353.04 −0.138042
\(459\) 58104.0 5.90863
\(460\) −6888.52 −0.698215
\(461\) 2456.74 0.248203 0.124102 0.992270i \(-0.460395\pi\)
0.124102 + 0.992270i \(0.460395\pi\)
\(462\) 326.271 0.0328560
\(463\) 15389.3 1.54471 0.772355 0.635191i \(-0.219079\pi\)
0.772355 + 0.635191i \(0.219079\pi\)
\(464\) 337.124 0.0337297
\(465\) 541.659 0.0540190
\(466\) −4656.74 −0.462917
\(467\) 2300.49 0.227953 0.113976 0.993483i \(-0.463641\pi\)
0.113976 + 0.993483i \(0.463641\pi\)
\(468\) −9059.00 −0.894770
\(469\) −3911.05 −0.385065
\(470\) 134.952 0.0132444
\(471\) 15260.9 1.49297
\(472\) −4412.22 −0.430273
\(473\) −463.487 −0.0450553
\(474\) 5908.64 0.572559
\(475\) −475.000 −0.0458831
\(476\) 3660.17 0.352445
\(477\) −26321.5 −2.52658
\(478\) −615.882 −0.0589326
\(479\) −6297.11 −0.600673 −0.300336 0.953833i \(-0.597099\pi\)
−0.300336 + 0.953833i \(0.597099\pi\)
\(480\) 6071.59 0.577352
\(481\) −4778.13 −0.452940
\(482\) 1157.12 0.109348
\(483\) 8119.77 0.764932
\(484\) −914.328 −0.0858685
\(485\) −3276.80 −0.306787
\(486\) −12713.9 −1.18665
\(487\) −5167.87 −0.480860 −0.240430 0.970667i \(-0.577288\pi\)
−0.240430 + 0.970667i \(0.577288\pi\)
\(488\) 7191.77 0.667123
\(489\) −2449.60 −0.226533
\(490\) 1079.25 0.0995015
\(491\) −5003.25 −0.459865 −0.229932 0.973207i \(-0.573851\pi\)
−0.229932 + 0.973207i \(0.573851\pi\)
\(492\) −22545.4 −2.06590
\(493\) −701.337 −0.0640703
\(494\) −194.696 −0.0177324
\(495\) 4285.51 0.389130
\(496\) 566.367 0.0512715
\(497\) 3241.96 0.292600
\(498\) −8667.65 −0.779933
\(499\) 484.929 0.0435038 0.0217519 0.999763i \(-0.493076\pi\)
0.0217519 + 0.999763i \(0.493076\pi\)
\(500\) 944.554 0.0844835
\(501\) −4038.51 −0.360134
\(502\) 4473.46 0.397730
\(503\) −1005.70 −0.0891487 −0.0445743 0.999006i \(-0.514193\pi\)
−0.0445743 + 0.999006i \(0.514193\pi\)
\(504\) −3510.02 −0.310216
\(505\) 4973.25 0.438231
\(506\) 1335.71 0.117351
\(507\) 20079.0 1.75886
\(508\) 20401.0 1.78179
\(509\) −1588.13 −0.138296 −0.0691482 0.997606i \(-0.522028\pi\)
−0.0691482 + 0.997606i \(0.522028\pi\)
\(510\) −3799.99 −0.329934
\(511\) 452.024 0.0391318
\(512\) 10787.2 0.931115
\(513\) 9909.55 0.852860
\(514\) −256.684 −0.0220269
\(515\) −181.024 −0.0154890
\(516\) 3261.28 0.278236
\(517\) 445.780 0.0379214
\(518\) −899.277 −0.0762779
\(519\) 38514.7 3.25743
\(520\) 797.047 0.0672170
\(521\) −7824.63 −0.657972 −0.328986 0.944335i \(-0.606707\pi\)
−0.328986 + 0.944335i \(0.606707\pi\)
\(522\) 326.694 0.0273928
\(523\) 19970.3 1.66967 0.834837 0.550497i \(-0.185562\pi\)
0.834837 + 0.550497i \(0.185562\pi\)
\(524\) −21038.3 −1.75394
\(525\) −1113.38 −0.0925562
\(526\) −4621.08 −0.383058
\(527\) −1178.24 −0.0973912
\(528\) 6033.74 0.497320
\(529\) 21074.3 1.73209
\(530\) 1124.92 0.0921950
\(531\) 33182.3 2.71185
\(532\) 624.237 0.0508723
\(533\) −4481.66 −0.364207
\(534\) 5654.20 0.458204
\(535\) 2059.33 0.166416
\(536\) 9319.76 0.751031
\(537\) −16107.9 −1.29443
\(538\) 3839.05 0.307646
\(539\) 3565.05 0.284894
\(540\) −19705.5 −1.57035
\(541\) −3253.06 −0.258521 −0.129260 0.991611i \(-0.541260\pi\)
−0.129260 + 0.991611i \(0.541260\pi\)
\(542\) −1954.47 −0.154892
\(543\) −16168.0 −1.27778
\(544\) −13207.3 −1.04091
\(545\) 2435.69 0.191437
\(546\) −456.361 −0.0357701
\(547\) 11588.5 0.905828 0.452914 0.891554i \(-0.350384\pi\)
0.452914 + 0.891554i \(0.350384\pi\)
\(548\) 15653.1 1.22020
\(549\) −54086.0 −4.20462
\(550\) −183.153 −0.0141994
\(551\) −119.612 −0.00924799
\(552\) −19348.9 −1.49192
\(553\) −3765.83 −0.289583
\(554\) 497.180 0.0381284
\(555\) −15904.9 −1.21644
\(556\) −3710.43 −0.283017
\(557\) −19300.0 −1.46817 −0.734084 0.679059i \(-0.762388\pi\)
−0.734084 + 0.679059i \(0.762388\pi\)
\(558\) 548.846 0.0416389
\(559\) 648.289 0.0490514
\(560\) −1164.17 −0.0878487
\(561\) −12552.3 −0.944669
\(562\) 3357.65 0.252017
\(563\) 12068.0 0.903387 0.451694 0.892173i \(-0.350820\pi\)
0.451694 + 0.892173i \(0.350820\pi\)
\(564\) −3136.68 −0.234181
\(565\) −6987.63 −0.520304
\(566\) −1547.98 −0.114958
\(567\) 14080.6 1.04291
\(568\) −7725.38 −0.570686
\(569\) 15865.0 1.16889 0.584444 0.811434i \(-0.301313\pi\)
0.584444 + 0.811434i \(0.301313\pi\)
\(570\) −648.082 −0.0476231
\(571\) −14742.2 −1.08046 −0.540230 0.841517i \(-0.681663\pi\)
−0.540230 + 0.841517i \(0.681663\pi\)
\(572\) 1278.89 0.0934844
\(573\) −22812.8 −1.66321
\(574\) −843.480 −0.0613348
\(575\) −4558.05 −0.330580
\(576\) −27228.8 −1.96967
\(577\) 9845.47 0.710351 0.355175 0.934800i \(-0.384421\pi\)
0.355175 + 0.934800i \(0.384421\pi\)
\(578\) 4993.83 0.359370
\(579\) 592.850 0.0425527
\(580\) 237.853 0.0170281
\(581\) 5524.26 0.394466
\(582\) −4470.80 −0.318421
\(583\) 3715.89 0.263974
\(584\) −1077.14 −0.0763228
\(585\) −5994.23 −0.423643
\(586\) 199.313 0.0140504
\(587\) −16055.3 −1.12892 −0.564458 0.825462i \(-0.690915\pi\)
−0.564458 + 0.825462i \(0.690915\pi\)
\(588\) −25085.1 −1.75934
\(589\) −200.948 −0.0140576
\(590\) −1418.13 −0.0989554
\(591\) −25339.6 −1.76367
\(592\) −16630.4 −1.15457
\(593\) −20716.8 −1.43464 −0.717318 0.696746i \(-0.754630\pi\)
−0.717318 + 0.696746i \(0.754630\pi\)
\(594\) 3820.97 0.263933
\(595\) 2421.89 0.166870
\(596\) −1843.16 −0.126676
\(597\) 37841.5 2.59422
\(598\) −1868.28 −0.127759
\(599\) −10546.3 −0.719380 −0.359690 0.933072i \(-0.617118\pi\)
−0.359690 + 0.933072i \(0.617118\pi\)
\(600\) 2653.12 0.180522
\(601\) −14403.3 −0.977574 −0.488787 0.872403i \(-0.662561\pi\)
−0.488787 + 0.872403i \(0.662561\pi\)
\(602\) 122.013 0.00826057
\(603\) −70089.7 −4.73346
\(604\) 20276.2 1.36594
\(605\) −605.000 −0.0406558
\(606\) 6785.42 0.454849
\(607\) 489.614 0.0327394 0.0163697 0.999866i \(-0.494789\pi\)
0.0163697 + 0.999866i \(0.494789\pi\)
\(608\) −2252.48 −0.150247
\(609\) −280.366 −0.0186552
\(610\) 2311.51 0.153427
\(611\) −623.521 −0.0412847
\(612\) 65593.7 4.33247
\(613\) 4970.44 0.327495 0.163747 0.986502i \(-0.447642\pi\)
0.163747 + 0.986502i \(0.447642\pi\)
\(614\) 4836.32 0.317880
\(615\) −14918.0 −0.978134
\(616\) 495.521 0.0324109
\(617\) −25969.2 −1.69446 −0.847229 0.531228i \(-0.821731\pi\)
−0.847229 + 0.531228i \(0.821731\pi\)
\(618\) −246.986 −0.0160764
\(619\) 683.267 0.0443665 0.0221832 0.999754i \(-0.492938\pi\)
0.0221832 + 0.999754i \(0.492938\pi\)
\(620\) 399.592 0.0258839
\(621\) 95091.0 6.14472
\(622\) −4135.06 −0.266561
\(623\) −3603.66 −0.231746
\(624\) −8439.52 −0.541428
\(625\) 625.000 0.0400000
\(626\) −750.859 −0.0479399
\(627\) −2140.78 −0.136355
\(628\) 11258.3 0.715373
\(629\) 34597.1 2.19313
\(630\) −1128.16 −0.0713442
\(631\) −12579.4 −0.793626 −0.396813 0.917900i \(-0.629884\pi\)
−0.396813 + 0.917900i \(0.629884\pi\)
\(632\) 8973.71 0.564802
\(633\) −27432.7 −1.72252
\(634\) −4830.87 −0.302616
\(635\) 13499.1 0.843617
\(636\) −26146.5 −1.63015
\(637\) −4986.51 −0.310161
\(638\) −46.1205 −0.00286196
\(639\) 58099.1 3.59681
\(640\) 5905.75 0.364758
\(641\) 26965.5 1.66158 0.830792 0.556583i \(-0.187888\pi\)
0.830792 + 0.556583i \(0.187888\pi\)
\(642\) 2809.71 0.172727
\(643\) 3846.15 0.235890 0.117945 0.993020i \(-0.462369\pi\)
0.117945 + 0.993020i \(0.462369\pi\)
\(644\) 5990.11 0.366527
\(645\) 2157.95 0.131735
\(646\) 1409.74 0.0858600
\(647\) −15946.5 −0.968966 −0.484483 0.874801i \(-0.660992\pi\)
−0.484483 + 0.874801i \(0.660992\pi\)
\(648\) −33553.0 −2.03408
\(649\) −4684.46 −0.283330
\(650\) 256.179 0.0154587
\(651\) −471.015 −0.0283572
\(652\) −1807.12 −0.108546
\(653\) 18804.9 1.12694 0.563471 0.826136i \(-0.309466\pi\)
0.563471 + 0.826136i \(0.309466\pi\)
\(654\) 3323.21 0.198697
\(655\) −13920.8 −0.830428
\(656\) −15598.5 −0.928384
\(657\) 8100.70 0.481033
\(658\) −117.351 −0.00695262
\(659\) −15615.7 −0.923065 −0.461533 0.887123i \(-0.652700\pi\)
−0.461533 + 0.887123i \(0.652700\pi\)
\(660\) 4257.02 0.251067
\(661\) 21958.6 1.29212 0.646058 0.763288i \(-0.276416\pi\)
0.646058 + 0.763288i \(0.276416\pi\)
\(662\) −3757.31 −0.220592
\(663\) 17557.2 1.02845
\(664\) −13163.9 −0.769367
\(665\) 413.050 0.0240863
\(666\) −16115.9 −0.937656
\(667\) −1147.78 −0.0666302
\(668\) −2979.29 −0.172563
\(669\) −30038.4 −1.73595
\(670\) 2995.47 0.172724
\(671\) 7635.51 0.439293
\(672\) −5279.73 −0.303080
\(673\) −10989.6 −0.629447 −0.314723 0.949183i \(-0.601912\pi\)
−0.314723 + 0.949183i \(0.601912\pi\)
\(674\) −1306.04 −0.0746394
\(675\) −13038.9 −0.743507
\(676\) 14812.7 0.842778
\(677\) −18922.0 −1.07420 −0.537099 0.843519i \(-0.680480\pi\)
−0.537099 + 0.843519i \(0.680480\pi\)
\(678\) −9533.81 −0.540035
\(679\) 2849.43 0.161047
\(680\) −5771.20 −0.325464
\(681\) −66461.8 −3.73983
\(682\) −77.4824 −0.00435037
\(683\) −6913.53 −0.387319 −0.193660 0.981069i \(-0.562036\pi\)
−0.193660 + 0.981069i \(0.562036\pi\)
\(684\) 11186.9 0.625354
\(685\) 10357.5 0.577722
\(686\) −1931.74 −0.107513
\(687\) 20809.2 1.15564
\(688\) 2256.39 0.125035
\(689\) −5197.50 −0.287386
\(690\) −6218.92 −0.343116
\(691\) 9389.56 0.516926 0.258463 0.966021i \(-0.416784\pi\)
0.258463 + 0.966021i \(0.416784\pi\)
\(692\) 28413.0 1.56084
\(693\) −3726.59 −0.204273
\(694\) −1336.68 −0.0731119
\(695\) −2455.15 −0.133999
\(696\) 668.094 0.0363851
\(697\) 32450.5 1.76348
\(698\) 2036.02 0.110407
\(699\) 71618.8 3.87535
\(700\) −821.364 −0.0443495
\(701\) 32662.0 1.75981 0.879905 0.475149i \(-0.157606\pi\)
0.879905 + 0.475149i \(0.157606\pi\)
\(702\) −5344.47 −0.287342
\(703\) 5900.49 0.316559
\(704\) 3843.98 0.205789
\(705\) −2075.50 −0.110877
\(706\) 6129.53 0.326753
\(707\) −4324.63 −0.230049
\(708\) 32961.7 1.74968
\(709\) −27679.7 −1.46620 −0.733098 0.680123i \(-0.761926\pi\)
−0.733098 + 0.680123i \(0.761926\pi\)
\(710\) −2483.02 −0.131248
\(711\) −67487.2 −3.55973
\(712\) 8587.27 0.451996
\(713\) −1928.27 −0.101283
\(714\) 3304.39 0.173198
\(715\) 846.226 0.0442616
\(716\) −11883.1 −0.620241
\(717\) 9472.03 0.493360
\(718\) 7034.13 0.365615
\(719\) 7449.56 0.386400 0.193200 0.981159i \(-0.438113\pi\)
0.193200 + 0.981159i \(0.438113\pi\)
\(720\) −20863.1 −1.07989
\(721\) 157.414 0.00813095
\(722\) 240.429 0.0123932
\(723\) −17796.1 −0.915415
\(724\) −11927.4 −0.612265
\(725\) 157.384 0.00806221
\(726\) −825.452 −0.0421975
\(727\) −3546.51 −0.180926 −0.0904628 0.995900i \(-0.528835\pi\)
−0.0904628 + 0.995900i \(0.528835\pi\)
\(728\) −693.095 −0.0352855
\(729\) 108096. 5.49183
\(730\) −346.205 −0.0175529
\(731\) −4694.09 −0.237506
\(732\) −53726.4 −2.71282
\(733\) −3983.00 −0.200703 −0.100351 0.994952i \(-0.531997\pi\)
−0.100351 + 0.994952i \(0.531997\pi\)
\(734\) −4135.92 −0.207983
\(735\) −16598.5 −0.832987
\(736\) −21614.5 −1.08250
\(737\) 9894.80 0.494545
\(738\) −15116.0 −0.753965
\(739\) −8915.23 −0.443778 −0.221889 0.975072i \(-0.571222\pi\)
−0.221889 + 0.975072i \(0.571222\pi\)
\(740\) −11733.3 −0.582872
\(741\) 2994.35 0.148448
\(742\) −978.205 −0.0483976
\(743\) −13972.3 −0.689898 −0.344949 0.938622i \(-0.612104\pi\)
−0.344949 + 0.938622i \(0.612104\pi\)
\(744\) 1122.40 0.0553078
\(745\) −1219.60 −0.0599765
\(746\) 55.2817 0.00271314
\(747\) 98999.9 4.84902
\(748\) −9260.09 −0.452650
\(749\) −1790.75 −0.0873599
\(750\) 852.739 0.0415169
\(751\) −37400.2 −1.81725 −0.908624 0.417614i \(-0.862866\pi\)
−0.908624 + 0.417614i \(0.862866\pi\)
\(752\) −2170.18 −0.105237
\(753\) −68800.1 −3.32964
\(754\) 64.5097 0.00311579
\(755\) 13416.5 0.646725
\(756\) 17135.5 0.824353
\(757\) −4311.96 −0.207029 −0.103515 0.994628i \(-0.533009\pi\)
−0.103515 + 0.994628i \(0.533009\pi\)
\(758\) −2828.08 −0.135515
\(759\) −20542.7 −0.982414
\(760\) −984.270 −0.0469779
\(761\) 25152.1 1.19811 0.599056 0.800707i \(-0.295543\pi\)
0.599056 + 0.800707i \(0.295543\pi\)
\(762\) 18418.0 0.875608
\(763\) −2118.02 −0.100495
\(764\) −16829.4 −0.796946
\(765\) 43402.6 2.05127
\(766\) 3238.19 0.152742
\(767\) 6552.25 0.308459
\(768\) −20577.7 −0.966842
\(769\) −39413.4 −1.84822 −0.924112 0.382122i \(-0.875194\pi\)
−0.924112 + 0.382122i \(0.875194\pi\)
\(770\) 159.266 0.00745394
\(771\) 3947.70 0.184401
\(772\) 437.357 0.0203897
\(773\) −22805.4 −1.06113 −0.530565 0.847644i \(-0.678020\pi\)
−0.530565 + 0.847644i \(0.678020\pi\)
\(774\) 2186.58 0.101544
\(775\) 264.405 0.0122551
\(776\) −6790.00 −0.314107
\(777\) 13830.5 0.638568
\(778\) 4878.99 0.224833
\(779\) 5534.38 0.254544
\(780\) −5954.37 −0.273334
\(781\) −8202.04 −0.375790
\(782\) 13527.7 0.618607
\(783\) −3283.38 −0.149858
\(784\) −17355.7 −0.790620
\(785\) 7449.47 0.338704
\(786\) −18993.3 −0.861919
\(787\) 6818.43 0.308832 0.154416 0.988006i \(-0.450650\pi\)
0.154416 + 0.988006i \(0.450650\pi\)
\(788\) −18693.5 −0.845087
\(789\) 71070.3 3.20681
\(790\) 2884.24 0.129895
\(791\) 6076.30 0.273133
\(792\) 8880.21 0.398415
\(793\) −10679.9 −0.478254
\(794\) −411.517 −0.0183932
\(795\) −17300.8 −0.771820
\(796\) 27916.4 1.24305
\(797\) 15742.9 0.699675 0.349838 0.936810i \(-0.386237\pi\)
0.349838 + 0.936810i \(0.386237\pi\)
\(798\) 563.558 0.0249997
\(799\) 4514.75 0.199900
\(800\) 2963.79 0.130982
\(801\) −64581.0 −2.84876
\(802\) 4752.57 0.209251
\(803\) −1143.60 −0.0502577
\(804\) −69623.7 −3.05403
\(805\) 3963.58 0.173538
\(806\) 108.376 0.00473621
\(807\) −59043.1 −2.57549
\(808\) 10305.3 0.448687
\(809\) −12949.3 −0.562761 −0.281381 0.959596i \(-0.590792\pi\)
−0.281381 + 0.959596i \(0.590792\pi\)
\(810\) −10784.3 −0.467804
\(811\) 20025.2 0.867052 0.433526 0.901141i \(-0.357269\pi\)
0.433526 + 0.901141i \(0.357269\pi\)
\(812\) −206.832 −0.00893887
\(813\) 30059.0 1.29670
\(814\) 2275.14 0.0979650
\(815\) −1195.75 −0.0513929
\(816\) 61108.3 2.62159
\(817\) −800.569 −0.0342820
\(818\) 5821.50 0.248831
\(819\) 5212.46 0.222391
\(820\) −11005.3 −0.468685
\(821\) −32269.7 −1.37177 −0.685884 0.727711i \(-0.740584\pi\)
−0.685884 + 0.727711i \(0.740584\pi\)
\(822\) 14131.6 0.599630
\(823\) 35677.7 1.51111 0.755556 0.655084i \(-0.227367\pi\)
0.755556 + 0.655084i \(0.227367\pi\)
\(824\) −375.108 −0.0158586
\(825\) 2816.82 0.118871
\(826\) 1233.18 0.0519465
\(827\) 39059.3 1.64235 0.821176 0.570675i \(-0.193318\pi\)
0.821176 + 0.570675i \(0.193318\pi\)
\(828\) 107348. 4.50557
\(829\) −4550.98 −0.190666 −0.0953330 0.995445i \(-0.530392\pi\)
−0.0953330 + 0.995445i \(0.530392\pi\)
\(830\) −4231.02 −0.176941
\(831\) −7646.43 −0.319196
\(832\) −5376.65 −0.224041
\(833\) 36106.0 1.50180
\(834\) −3349.76 −0.139080
\(835\) −1971.36 −0.0817026
\(836\) −1579.29 −0.0653362
\(837\) −5516.08 −0.227794
\(838\) −5331.11 −0.219761
\(839\) −47860.9 −1.96942 −0.984709 0.174205i \(-0.944265\pi\)
−0.984709 + 0.174205i \(0.944265\pi\)
\(840\) −2307.09 −0.0947646
\(841\) −24349.4 −0.998375
\(842\) −55.8638 −0.00228645
\(843\) −51639.3 −2.10979
\(844\) −20237.6 −0.825365
\(845\) 9801.37 0.399026
\(846\) −2103.04 −0.0854659
\(847\) 526.095 0.0213422
\(848\) −18090.0 −0.732563
\(849\) 23807.3 0.962383
\(850\) −1854.92 −0.0748510
\(851\) 56620.4 2.28076
\(852\) 57712.8 2.32067
\(853\) −21752.8 −0.873155 −0.436578 0.899667i \(-0.643810\pi\)
−0.436578 + 0.899667i \(0.643810\pi\)
\(854\) −2010.04 −0.0805411
\(855\) 7402.25 0.296084
\(856\) 4267.23 0.170387
\(857\) 24128.7 0.961752 0.480876 0.876789i \(-0.340319\pi\)
0.480876 + 0.876789i \(0.340319\pi\)
\(858\) 1154.58 0.0459401
\(859\) 36459.9 1.44819 0.724095 0.689700i \(-0.242258\pi\)
0.724095 + 0.689700i \(0.242258\pi\)
\(860\) 1591.96 0.0631225
\(861\) 12972.4 0.513470
\(862\) 9144.63 0.361331
\(863\) 6415.63 0.253060 0.126530 0.991963i \(-0.459616\pi\)
0.126530 + 0.991963i \(0.459616\pi\)
\(864\) −61831.1 −2.43465
\(865\) 18800.5 0.739003
\(866\) 491.454 0.0192844
\(867\) −76803.1 −3.00850
\(868\) −347.477 −0.0135877
\(869\) 9527.40 0.371916
\(870\) 214.732 0.00836794
\(871\) −13840.1 −0.538407
\(872\) 5047.10 0.196005
\(873\) 51064.5 1.97969
\(874\) 2307.13 0.0892906
\(875\) −543.487 −0.0209979
\(876\) 8046.84 0.310362
\(877\) 2230.38 0.0858775 0.0429388 0.999078i \(-0.486328\pi\)
0.0429388 + 0.999078i \(0.486328\pi\)
\(878\) 5564.66 0.213893
\(879\) −3065.36 −0.117624
\(880\) 2945.31 0.112825
\(881\) −1477.52 −0.0565028 −0.0282514 0.999601i \(-0.508994\pi\)
−0.0282514 + 0.999601i \(0.508994\pi\)
\(882\) −16818.8 −0.642083
\(883\) −22570.9 −0.860217 −0.430109 0.902777i \(-0.641525\pi\)
−0.430109 + 0.902777i \(0.641525\pi\)
\(884\) 12952.3 0.492796
\(885\) 21810.4 0.828415
\(886\) 7857.60 0.297947
\(887\) 40168.8 1.52056 0.760280 0.649595i \(-0.225061\pi\)
0.760280 + 0.649595i \(0.225061\pi\)
\(888\) −32957.2 −1.24546
\(889\) −11738.6 −0.442855
\(890\) 2760.04 0.103951
\(891\) −35623.3 −1.33942
\(892\) −22159.9 −0.831802
\(893\) 769.983 0.0288539
\(894\) −1664.00 −0.0622509
\(895\) −7862.91 −0.293663
\(896\) −5135.51 −0.191479
\(897\) 28733.5 1.06955
\(898\) 1188.64 0.0441710
\(899\) 66.5811 0.00247008
\(900\) −14719.6 −0.545171
\(901\) 37633.6 1.39152
\(902\) 2133.97 0.0787732
\(903\) −1876.51 −0.0691542
\(904\) −14479.4 −0.532719
\(905\) −7892.25 −0.289886
\(906\) 18305.3 0.671250
\(907\) −9829.85 −0.359862 −0.179931 0.983679i \(-0.557587\pi\)
−0.179931 + 0.983679i \(0.557587\pi\)
\(908\) −49030.1 −1.79199
\(909\) −77501.5 −2.82790
\(910\) −222.768 −0.00811504
\(911\) 2662.85 0.0968434 0.0484217 0.998827i \(-0.484581\pi\)
0.0484217 + 0.998827i \(0.484581\pi\)
\(912\) 10421.9 0.378404
\(913\) −13976.2 −0.506619
\(914\) −10208.0 −0.369421
\(915\) −35550.1 −1.28443
\(916\) 15351.4 0.553738
\(917\) 12105.2 0.435932
\(918\) 38697.8 1.39131
\(919\) 35978.4 1.29142 0.645711 0.763582i \(-0.276561\pi\)
0.645711 + 0.763582i \(0.276561\pi\)
\(920\) −9444.94 −0.338468
\(921\) −74380.7 −2.66116
\(922\) 1636.21 0.0584444
\(923\) 11472.4 0.409120
\(924\) −3701.81 −0.131797
\(925\) −7763.80 −0.275970
\(926\) 10249.4 0.363733
\(927\) 2821.01 0.0999507
\(928\) 746.325 0.0264001
\(929\) −35971.3 −1.27038 −0.635189 0.772357i \(-0.719078\pi\)
−0.635189 + 0.772357i \(0.719078\pi\)
\(930\) 360.750 0.0127198
\(931\) 6157.82 0.216772
\(932\) 52834.5 1.85692
\(933\) 63595.5 2.23154
\(934\) 1532.15 0.0536760
\(935\) −6127.29 −0.214314
\(936\) −12420.9 −0.433751
\(937\) 38333.1 1.33649 0.668244 0.743942i \(-0.267046\pi\)
0.668244 + 0.743942i \(0.267046\pi\)
\(938\) −2604.80 −0.0906712
\(939\) 11547.9 0.401333
\(940\) −1531.14 −0.0531279
\(941\) −20686.8 −0.716653 −0.358326 0.933596i \(-0.616653\pi\)
−0.358326 + 0.933596i \(0.616653\pi\)
\(942\) 10163.9 0.351549
\(943\) 53107.3 1.83395
\(944\) 22805.3 0.786280
\(945\) 11338.3 0.390303
\(946\) −308.687 −0.0106092
\(947\) −54586.6 −1.87310 −0.936550 0.350533i \(-0.886000\pi\)
−0.936550 + 0.350533i \(0.886000\pi\)
\(948\) −67038.5 −2.29674
\(949\) 1599.58 0.0547151
\(950\) −316.355 −0.0108041
\(951\) 74296.9 2.53338
\(952\) 5018.51 0.170852
\(953\) 39163.8 1.33121 0.665604 0.746305i \(-0.268174\pi\)
0.665604 + 0.746305i \(0.268174\pi\)
\(954\) −17530.4 −0.594934
\(955\) −11135.8 −0.377326
\(956\) 6987.69 0.236400
\(957\) 709.316 0.0239592
\(958\) −4193.94 −0.141440
\(959\) −9006.65 −0.303274
\(960\) −17897.1 −0.601696
\(961\) −29679.1 −0.996245
\(962\) −3182.28 −0.106654
\(963\) −32091.9 −1.07388
\(964\) −13128.5 −0.438632
\(965\) 289.394 0.00965379
\(966\) 5407.84 0.180119
\(967\) 23663.7 0.786943 0.393471 0.919337i \(-0.371274\pi\)
0.393471 + 0.919337i \(0.371274\pi\)
\(968\) −1253.65 −0.0416258
\(969\) −21681.3 −0.718786
\(970\) −2182.38 −0.0722391
\(971\) 33344.5 1.10204 0.551018 0.834493i \(-0.314240\pi\)
0.551018 + 0.834493i \(0.314240\pi\)
\(972\) 144250. 4.76009
\(973\) 2134.94 0.0703424
\(974\) −3441.85 −0.113228
\(975\) −3939.94 −0.129414
\(976\) −37171.8 −1.21910
\(977\) 8943.73 0.292871 0.146436 0.989220i \(-0.453220\pi\)
0.146436 + 0.989220i \(0.453220\pi\)
\(978\) −1631.46 −0.0533418
\(979\) 9117.11 0.297634
\(980\) −12245.0 −0.399136
\(981\) −37956.9 −1.23534
\(982\) −3332.22 −0.108284
\(983\) 17462.5 0.566599 0.283300 0.959031i \(-0.408571\pi\)
0.283300 + 0.959031i \(0.408571\pi\)
\(984\) −30912.3 −1.00147
\(985\) −12369.3 −0.400119
\(986\) −467.097 −0.0150866
\(987\) 1804.81 0.0582045
\(988\) 2208.99 0.0711309
\(989\) −7682.18 −0.246996
\(990\) 2854.19 0.0916285
\(991\) 9370.69 0.300373 0.150186 0.988658i \(-0.452013\pi\)
0.150186 + 0.988658i \(0.452013\pi\)
\(992\) 1253.82 0.0401300
\(993\) 57786.0 1.84671
\(994\) 2159.18 0.0688984
\(995\) 18471.9 0.588542
\(996\) 98341.6 3.12859
\(997\) 10592.9 0.336489 0.168244 0.985745i \(-0.446190\pi\)
0.168244 + 0.985745i \(0.446190\pi\)
\(998\) 322.968 0.0102438
\(999\) 161970. 5.12963
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.g.1.12 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.4.a.g.1.12 23 1.1 even 1 trivial