Properties

Label 46.4.a.c.1.1
Level $46$
Weight $4$
Character 46.1
Self dual yes
Analytic conductor $2.714$
Analytic rank $0$
Dimension $2$
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] = [46,4,Mod(1,46)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(46, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("46.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 46.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: \(2.71408786026\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.70156\) of defining polynomial
Character \(\chi\) \(=\) 46.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} -10.1047 q^{3} +4.00000 q^{4} +11.4031 q^{5} +20.2094 q^{6} +9.40312 q^{7} -8.00000 q^{8} +75.1047 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -10.1047 q^{3} +4.00000 q^{4} +11.4031 q^{5} +20.2094 q^{6} +9.40312 q^{7} -8.00000 q^{8} +75.1047 q^{9} -22.8062 q^{10} +10.3875 q^{11} -40.4187 q^{12} -33.0891 q^{13} -18.8062 q^{14} -115.225 q^{15} +16.0000 q^{16} +138.837 q^{17} -150.209 q^{18} +68.6281 q^{19} +45.6125 q^{20} -95.0156 q^{21} -20.7750 q^{22} -23.0000 q^{23} +80.8375 q^{24} +5.03124 q^{25} +66.1781 q^{26} -486.083 q^{27} +37.6125 q^{28} +215.602 q^{29} +230.450 q^{30} +87.9266 q^{31} -32.0000 q^{32} -104.962 q^{33} -277.675 q^{34} +107.225 q^{35} +300.419 q^{36} -215.109 q^{37} -137.256 q^{38} +334.355 q^{39} -91.2250 q^{40} +175.267 q^{41} +190.031 q^{42} -40.7125 q^{43} +41.5500 q^{44} +856.428 q^{45} +46.0000 q^{46} +405.245 q^{47} -161.675 q^{48} -254.581 q^{49} -10.0625 q^{50} -1402.91 q^{51} -132.356 q^{52} -276.994 q^{53} +972.166 q^{54} +118.450 q^{55} -75.2250 q^{56} -693.466 q^{57} -431.203 q^{58} +293.550 q^{59} -460.900 q^{60} -450.731 q^{61} -175.853 q^{62} +706.219 q^{63} +64.0000 q^{64} -377.319 q^{65} +209.925 q^{66} +273.675 q^{67} +555.350 q^{68} +232.408 q^{69} -214.450 q^{70} -643.842 q^{71} -600.837 q^{72} +106.345 q^{73} +430.219 q^{74} -50.8391 q^{75} +274.512 q^{76} +97.6750 q^{77} -668.709 q^{78} +60.0844 q^{79} +182.450 q^{80} +2883.89 q^{81} -350.534 q^{82} -372.878 q^{83} -380.062 q^{84} +1583.18 q^{85} +81.4250 q^{86} -2178.59 q^{87} -83.1000 q^{88} -543.947 q^{89} -1712.86 q^{90} -311.141 q^{91} -92.0000 q^{92} -888.470 q^{93} -810.491 q^{94} +782.575 q^{95} +323.350 q^{96} +550.944 q^{97} +509.163 q^{98} +780.150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} - q^{3} + 8 q^{4} + 10 q^{5} + 2 q^{6} + 6 q^{7} - 16 q^{8} + 131 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} - q^{3} + 8 q^{4} + 10 q^{5} + 2 q^{6} + 6 q^{7} - 16 q^{8} + 131 q^{9} - 20 q^{10} + 72 q^{11} - 4 q^{12} - 111 q^{13} - 12 q^{14} - 128 q^{15} + 32 q^{16} + 124 q^{17} - 262 q^{18} + 22 q^{19} + 40 q^{20} - 126 q^{21} - 144 q^{22} - 46 q^{23} + 8 q^{24} - 118 q^{25} + 222 q^{26} - 223 q^{27} + 24 q^{28} + 15 q^{29} + 256 q^{30} + 67 q^{31} - 64 q^{32} + 456 q^{33} - 248 q^{34} + 112 q^{35} + 524 q^{36} + 18 q^{37} - 44 q^{38} - 375 q^{39} - 80 q^{40} + 485 q^{41} + 252 q^{42} - 440 q^{43} + 288 q^{44} + 778 q^{45} + 92 q^{46} + 215 q^{47} - 16 q^{48} - 586 q^{49} + 236 q^{50} - 1538 q^{51} - 444 q^{52} + 240 q^{53} + 446 q^{54} + 32 q^{55} - 48 q^{56} - 1118 q^{57} - 30 q^{58} + 792 q^{59} - 512 q^{60} + 456 q^{61} - 134 q^{62} + 516 q^{63} + 128 q^{64} - 268 q^{65} - 912 q^{66} + 240 q^{67} + 496 q^{68} + 23 q^{69} - 224 q^{70} - 705 q^{71} - 1048 q^{72} + 27 q^{73} - 36 q^{74} - 1171 q^{75} + 88 q^{76} - 112 q^{77} + 750 q^{78} + 594 q^{79} + 160 q^{80} + 3770 q^{81} - 970 q^{82} + 394 q^{83} - 504 q^{84} + 1604 q^{85} + 880 q^{86} - 4005 q^{87} - 576 q^{88} - 486 q^{89} - 1556 q^{90} - 46 q^{91} - 184 q^{92} - 1079 q^{93} - 430 q^{94} + 848 q^{95} + 32 q^{96} + 2152 q^{97} + 1172 q^{98} + 4224 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −10.1047 −1.94465 −0.972324 0.233637i \(-0.924937\pi\)
−0.972324 + 0.233637i \(0.924937\pi\)
\(4\) 4.00000 0.500000
\(5\) 11.4031 1.01993 0.509963 0.860196i \(-0.329659\pi\)
0.509963 + 0.860196i \(0.329659\pi\)
\(6\) 20.2094 1.37507
\(7\) 9.40312 0.507721 0.253860 0.967241i \(-0.418300\pi\)
0.253860 + 0.967241i \(0.418300\pi\)
\(8\) −8.00000 −0.353553
\(9\) 75.1047 2.78166
\(10\) −22.8062 −0.721197
\(11\) 10.3875 0.284723 0.142361 0.989815i \(-0.454530\pi\)
0.142361 + 0.989815i \(0.454530\pi\)
\(12\) −40.4187 −0.972324
\(13\) −33.0891 −0.705943 −0.352971 0.935634i \(-0.614829\pi\)
−0.352971 + 0.935634i \(0.614829\pi\)
\(14\) −18.8062 −0.359013
\(15\) −115.225 −1.98340
\(16\) 16.0000 0.250000
\(17\) 138.837 1.98077 0.990383 0.138350i \(-0.0441797\pi\)
0.990383 + 0.138350i \(0.0441797\pi\)
\(18\) −150.209 −1.96693
\(19\) 68.6281 0.828651 0.414326 0.910129i \(-0.364018\pi\)
0.414326 + 0.910129i \(0.364018\pi\)
\(20\) 45.6125 0.509963
\(21\) −95.0156 −0.987338
\(22\) −20.7750 −0.201329
\(23\) −23.0000 −0.208514
\(24\) 80.8375 0.687537
\(25\) 5.03124 0.0402499
\(26\) 66.1781 0.499177
\(27\) −486.083 −3.46469
\(28\) 37.6125 0.253860
\(29\) 215.602 1.38056 0.690279 0.723543i \(-0.257488\pi\)
0.690279 + 0.723543i \(0.257488\pi\)
\(30\) 230.450 1.40247
\(31\) 87.9266 0.509422 0.254711 0.967017i \(-0.418020\pi\)
0.254711 + 0.967017i \(0.418020\pi\)
\(32\) −32.0000 −0.176777
\(33\) −104.962 −0.553685
\(34\) −277.675 −1.40061
\(35\) 107.225 0.517838
\(36\) 300.419 1.39083
\(37\) −215.109 −0.955777 −0.477889 0.878420i \(-0.658598\pi\)
−0.477889 + 0.878420i \(0.658598\pi\)
\(38\) −137.256 −0.585945
\(39\) 334.355 1.37281
\(40\) −91.2250 −0.360598
\(41\) 175.267 0.667613 0.333807 0.942642i \(-0.391667\pi\)
0.333807 + 0.942642i \(0.391667\pi\)
\(42\) 190.031 0.698154
\(43\) −40.7125 −0.144386 −0.0721930 0.997391i \(-0.523000\pi\)
−0.0721930 + 0.997391i \(0.523000\pi\)
\(44\) 41.5500 0.142361
\(45\) 856.428 2.83708
\(46\) 46.0000 0.147442
\(47\) 405.245 1.25768 0.628841 0.777534i \(-0.283529\pi\)
0.628841 + 0.777534i \(0.283529\pi\)
\(48\) −161.675 −0.486162
\(49\) −254.581 −0.742219
\(50\) −10.0625 −0.0284610
\(51\) −1402.91 −3.85189
\(52\) −132.356 −0.352971
\(53\) −276.994 −0.717887 −0.358944 0.933359i \(-0.616863\pi\)
−0.358944 + 0.933359i \(0.616863\pi\)
\(54\) 972.166 2.44991
\(55\) 118.450 0.290396
\(56\) −75.2250 −0.179506
\(57\) −693.466 −1.61143
\(58\) −431.203 −0.976202
\(59\) 293.550 0.647745 0.323873 0.946101i \(-0.395015\pi\)
0.323873 + 0.946101i \(0.395015\pi\)
\(60\) −460.900 −0.991699
\(61\) −450.731 −0.946069 −0.473035 0.881044i \(-0.656841\pi\)
−0.473035 + 0.881044i \(0.656841\pi\)
\(62\) −175.853 −0.360216
\(63\) 706.219 1.41230
\(64\) 64.0000 0.125000
\(65\) −377.319 −0.720010
\(66\) 209.925 0.391515
\(67\) 273.675 0.499026 0.249513 0.968371i \(-0.419730\pi\)
0.249513 + 0.968371i \(0.419730\pi\)
\(68\) 555.350 0.990383
\(69\) 232.408 0.405487
\(70\) −214.450 −0.366167
\(71\) −643.842 −1.07620 −0.538099 0.842882i \(-0.680857\pi\)
−0.538099 + 0.842882i \(0.680857\pi\)
\(72\) −600.837 −0.983464
\(73\) 106.345 0.170504 0.0852519 0.996359i \(-0.472831\pi\)
0.0852519 + 0.996359i \(0.472831\pi\)
\(74\) 430.219 0.675837
\(75\) −50.8391 −0.0782720
\(76\) 274.512 0.414326
\(77\) 97.6750 0.144560
\(78\) −668.709 −0.970723
\(79\) 60.0844 0.0855699 0.0427850 0.999084i \(-0.486377\pi\)
0.0427850 + 0.999084i \(0.486377\pi\)
\(80\) 182.450 0.254982
\(81\) 2883.89 3.95595
\(82\) −350.534 −0.472074
\(83\) −372.878 −0.493117 −0.246558 0.969128i \(-0.579300\pi\)
−0.246558 + 0.969128i \(0.579300\pi\)
\(84\) −380.062 −0.493669
\(85\) 1583.18 2.02024
\(86\) 81.4250 0.102096
\(87\) −2178.59 −2.68470
\(88\) −83.1000 −0.100665
\(89\) −543.947 −0.647846 −0.323923 0.946084i \(-0.605002\pi\)
−0.323923 + 0.946084i \(0.605002\pi\)
\(90\) −1712.86 −2.00612
\(91\) −311.141 −0.358422
\(92\) −92.0000 −0.104257
\(93\) −888.470 −0.990646
\(94\) −810.491 −0.889316
\(95\) 782.575 0.845163
\(96\) 323.350 0.343768
\(97\) 550.944 0.576700 0.288350 0.957525i \(-0.406893\pi\)
0.288350 + 0.957525i \(0.406893\pi\)
\(98\) 509.163 0.524828
\(99\) 780.150 0.792000
\(100\) 20.1250 0.0201250
\(101\) 1084.57 1.06851 0.534254 0.845324i \(-0.320593\pi\)
0.534254 + 0.845324i \(0.320593\pi\)
\(102\) 2805.82 2.72370
\(103\) 1369.19 1.30981 0.654905 0.755712i \(-0.272709\pi\)
0.654905 + 0.755712i \(0.272709\pi\)
\(104\) 264.713 0.249588
\(105\) −1083.47 −1.00701
\(106\) 553.987 0.507623
\(107\) −1193.82 −1.07861 −0.539304 0.842111i \(-0.681313\pi\)
−0.539304 + 0.842111i \(0.681313\pi\)
\(108\) −1944.33 −1.73235
\(109\) −893.309 −0.784986 −0.392493 0.919755i \(-0.628387\pi\)
−0.392493 + 0.919755i \(0.628387\pi\)
\(110\) −236.900 −0.205341
\(111\) 2173.61 1.85865
\(112\) 150.450 0.126930
\(113\) 1842.16 1.53359 0.766797 0.641890i \(-0.221849\pi\)
0.766797 + 0.641890i \(0.221849\pi\)
\(114\) 1386.93 1.13946
\(115\) −262.272 −0.212669
\(116\) 862.406 0.690279
\(117\) −2485.14 −1.96369
\(118\) −587.100 −0.458025
\(119\) 1305.51 1.00568
\(120\) 921.800 0.701237
\(121\) −1223.10 −0.918933
\(122\) 901.462 0.668972
\(123\) −1771.02 −1.29827
\(124\) 351.706 0.254711
\(125\) −1368.02 −0.978874
\(126\) −1412.44 −0.998650
\(127\) 599.361 0.418777 0.209389 0.977833i \(-0.432853\pi\)
0.209389 + 0.977833i \(0.432853\pi\)
\(128\) −128.000 −0.0883883
\(129\) 411.387 0.280780
\(130\) 754.637 0.509124
\(131\) −560.136 −0.373582 −0.186791 0.982400i \(-0.559809\pi\)
−0.186791 + 0.982400i \(0.559809\pi\)
\(132\) −419.850 −0.276843
\(133\) 645.319 0.420724
\(134\) −547.350 −0.352864
\(135\) −5542.86 −3.53373
\(136\) −1110.70 −0.700307
\(137\) −2111.69 −1.31689 −0.658445 0.752629i \(-0.728785\pi\)
−0.658445 + 0.752629i \(0.728785\pi\)
\(138\) −464.816 −0.286723
\(139\) −944.952 −0.576617 −0.288308 0.957538i \(-0.593093\pi\)
−0.288308 + 0.957538i \(0.593093\pi\)
\(140\) 428.900 0.258919
\(141\) −4094.88 −2.44575
\(142\) 1287.68 0.760986
\(143\) −343.713 −0.200998
\(144\) 1201.67 0.695414
\(145\) 2458.53 1.40807
\(146\) −212.691 −0.120564
\(147\) 2572.46 1.44336
\(148\) −860.437 −0.477889
\(149\) −2480.47 −1.36381 −0.681906 0.731440i \(-0.738849\pi\)
−0.681906 + 0.731440i \(0.738849\pi\)
\(150\) 101.678 0.0553466
\(151\) 1164.53 0.627605 0.313802 0.949488i \(-0.398397\pi\)
0.313802 + 0.949488i \(0.398397\pi\)
\(152\) −549.025 −0.292972
\(153\) 10427.3 5.50981
\(154\) −195.350 −0.102219
\(155\) 1002.64 0.519573
\(156\) 1337.42 0.686405
\(157\) −1525.27 −0.775347 −0.387673 0.921797i \(-0.626721\pi\)
−0.387673 + 0.921797i \(0.626721\pi\)
\(158\) −120.169 −0.0605071
\(159\) 2798.93 1.39604
\(160\) −364.900 −0.180299
\(161\) −216.272 −0.105867
\(162\) −5767.77 −2.79728
\(163\) 1944.47 0.934371 0.467185 0.884159i \(-0.345268\pi\)
0.467185 + 0.884159i \(0.345268\pi\)
\(164\) 701.069 0.333807
\(165\) −1196.90 −0.564718
\(166\) 745.756 0.348686
\(167\) −2632.58 −1.21985 −0.609926 0.792458i \(-0.708801\pi\)
−0.609926 + 0.792458i \(0.708801\pi\)
\(168\) 760.125 0.349077
\(169\) −1102.11 −0.501645
\(170\) −3166.36 −1.42852
\(171\) 5154.29 2.30502
\(172\) −162.850 −0.0721930
\(173\) 1189.63 0.522806 0.261403 0.965230i \(-0.415815\pi\)
0.261403 + 0.965230i \(0.415815\pi\)
\(174\) 4357.17 1.89837
\(175\) 47.3094 0.0204357
\(176\) 166.200 0.0711807
\(177\) −2966.23 −1.25964
\(178\) 1087.89 0.458096
\(179\) −1548.97 −0.646790 −0.323395 0.946264i \(-0.604824\pi\)
−0.323395 + 0.946264i \(0.604824\pi\)
\(180\) 3425.71 1.41854
\(181\) −1908.38 −0.783697 −0.391848 0.920030i \(-0.628164\pi\)
−0.391848 + 0.920030i \(0.628164\pi\)
\(182\) 622.281 0.253443
\(183\) 4554.50 1.83977
\(184\) 184.000 0.0737210
\(185\) −2452.92 −0.974823
\(186\) 1776.94 0.700492
\(187\) 1442.17 0.563969
\(188\) 1620.98 0.628841
\(189\) −4570.70 −1.75910
\(190\) −1565.15 −0.597621
\(191\) 352.625 0.133587 0.0667933 0.997767i \(-0.478723\pi\)
0.0667933 + 0.997767i \(0.478723\pi\)
\(192\) −646.700 −0.243081
\(193\) −1414.28 −0.527472 −0.263736 0.964595i \(-0.584955\pi\)
−0.263736 + 0.964595i \(0.584955\pi\)
\(194\) −1101.89 −0.407788
\(195\) 3812.69 1.40017
\(196\) −1018.33 −0.371110
\(197\) −432.530 −0.156429 −0.0782144 0.996937i \(-0.524922\pi\)
−0.0782144 + 0.996937i \(0.524922\pi\)
\(198\) −1560.30 −0.560029
\(199\) −108.519 −0.0386567 −0.0193283 0.999813i \(-0.506153\pi\)
−0.0193283 + 0.999813i \(0.506153\pi\)
\(200\) −40.2499 −0.0142305
\(201\) −2765.40 −0.970429
\(202\) −2169.15 −0.755549
\(203\) 2027.33 0.700939
\(204\) −5611.64 −1.92595
\(205\) 1998.59 0.680916
\(206\) −2738.38 −0.926175
\(207\) −1727.41 −0.580015
\(208\) −529.425 −0.176486
\(209\) 712.875 0.235936
\(210\) 2166.95 0.712065
\(211\) −1082.37 −0.353144 −0.176572 0.984288i \(-0.556501\pi\)
−0.176572 + 0.984288i \(0.556501\pi\)
\(212\) −1107.97 −0.358944
\(213\) 6505.82 2.09282
\(214\) 2387.64 0.762691
\(215\) −464.250 −0.147263
\(216\) 3888.66 1.22495
\(217\) 826.784 0.258644
\(218\) 1786.62 0.555069
\(219\) −1074.59 −0.331570
\(220\) 473.800 0.145198
\(221\) −4594.00 −1.39831
\(222\) −4347.22 −1.31426
\(223\) −1619.44 −0.486303 −0.243151 0.969988i \(-0.578181\pi\)
−0.243151 + 0.969988i \(0.578181\pi\)
\(224\) −300.900 −0.0897532
\(225\) 377.870 0.111961
\(226\) −3684.32 −1.08441
\(227\) 6746.10 1.97249 0.986244 0.165299i \(-0.0528589\pi\)
0.986244 + 0.165299i \(0.0528589\pi\)
\(228\) −2773.86 −0.805717
\(229\) 1192.63 0.344155 0.172077 0.985083i \(-0.444952\pi\)
0.172077 + 0.985083i \(0.444952\pi\)
\(230\) 524.544 0.150380
\(231\) −986.975 −0.281118
\(232\) −1724.81 −0.488101
\(233\) −2860.16 −0.804187 −0.402093 0.915599i \(-0.631717\pi\)
−0.402093 + 0.915599i \(0.631717\pi\)
\(234\) 4970.29 1.38854
\(235\) 4621.06 1.28274
\(236\) 1174.20 0.323873
\(237\) −607.134 −0.166403
\(238\) −2611.01 −0.711121
\(239\) −594.373 −0.160865 −0.0804327 0.996760i \(-0.525630\pi\)
−0.0804327 + 0.996760i \(0.525630\pi\)
\(240\) −1843.60 −0.495849
\(241\) 3930.15 1.05047 0.525234 0.850958i \(-0.323978\pi\)
0.525234 + 0.850958i \(0.323978\pi\)
\(242\) 2446.20 0.649784
\(243\) −16016.5 −4.22824
\(244\) −1802.92 −0.473035
\(245\) −2903.02 −0.757009
\(246\) 3542.04 0.918017
\(247\) −2270.84 −0.584980
\(248\) −703.412 −0.180108
\(249\) 3767.82 0.958938
\(250\) 2736.04 0.692169
\(251\) 2122.07 0.533641 0.266821 0.963746i \(-0.414027\pi\)
0.266821 + 0.963746i \(0.414027\pi\)
\(252\) 2824.87 0.706152
\(253\) −238.913 −0.0593688
\(254\) −1198.72 −0.296120
\(255\) −15997.5 −3.92865
\(256\) 256.000 0.0625000
\(257\) 1143.68 0.277591 0.138795 0.990321i \(-0.455677\pi\)
0.138795 + 0.990321i \(0.455677\pi\)
\(258\) −822.775 −0.198541
\(259\) −2022.70 −0.485268
\(260\) −1509.27 −0.360005
\(261\) 16192.7 3.84024
\(262\) 1120.27 0.264163
\(263\) −947.534 −0.222158 −0.111079 0.993812i \(-0.535431\pi\)
−0.111079 + 0.993812i \(0.535431\pi\)
\(264\) 839.700 0.195757
\(265\) −3158.59 −0.732192
\(266\) −1290.64 −0.297496
\(267\) 5496.41 1.25983
\(268\) 1094.70 0.249513
\(269\) 3217.70 0.729317 0.364659 0.931141i \(-0.381186\pi\)
0.364659 + 0.931141i \(0.381186\pi\)
\(270\) 11085.7 2.49872
\(271\) −7284.05 −1.63275 −0.816374 0.577524i \(-0.804019\pi\)
−0.816374 + 0.577524i \(0.804019\pi\)
\(272\) 2221.40 0.495192
\(273\) 3143.98 0.697004
\(274\) 4223.38 0.931182
\(275\) 52.2620 0.0114601
\(276\) 929.631 0.202744
\(277\) 2524.08 0.547498 0.273749 0.961801i \(-0.411736\pi\)
0.273749 + 0.961801i \(0.411736\pi\)
\(278\) 1889.90 0.407730
\(279\) 6603.70 1.41704
\(280\) −857.800 −0.183083
\(281\) −6277.44 −1.33267 −0.666336 0.745652i \(-0.732138\pi\)
−0.666336 + 0.745652i \(0.732138\pi\)
\(282\) 8189.75 1.72941
\(283\) −8.34415 −0.00175268 −0.000876340 1.00000i \(-0.500279\pi\)
−0.000876340 1.00000i \(0.500279\pi\)
\(284\) −2575.37 −0.538099
\(285\) −7907.67 −1.64354
\(286\) 687.426 0.142127
\(287\) 1648.06 0.338961
\(288\) −2403.35 −0.491732
\(289\) 14362.8 2.92344
\(290\) −4917.06 −0.995655
\(291\) −5567.11 −1.12148
\(292\) 425.381 0.0852519
\(293\) 3075.15 0.613147 0.306573 0.951847i \(-0.400818\pi\)
0.306573 + 0.951847i \(0.400818\pi\)
\(294\) −5144.93 −1.02061
\(295\) 3347.39 0.660652
\(296\) 1720.87 0.337918
\(297\) −5049.19 −0.986476
\(298\) 4960.94 0.964360
\(299\) 761.048 0.147199
\(300\) −203.357 −0.0391360
\(301\) −382.825 −0.0733078
\(302\) −2329.07 −0.443784
\(303\) −10959.3 −2.07787
\(304\) 1098.05 0.207163
\(305\) −5139.74 −0.964921
\(306\) −20854.7 −3.89602
\(307\) −1039.90 −0.193323 −0.0966616 0.995317i \(-0.530816\pi\)
−0.0966616 + 0.995317i \(0.530816\pi\)
\(308\) 390.700 0.0722799
\(309\) −13835.2 −2.54712
\(310\) −2005.27 −0.367393
\(311\) 5917.12 1.07887 0.539436 0.842027i \(-0.318638\pi\)
0.539436 + 0.842027i \(0.318638\pi\)
\(312\) −2674.84 −0.485362
\(313\) 2581.67 0.466213 0.233107 0.972451i \(-0.425111\pi\)
0.233107 + 0.972451i \(0.425111\pi\)
\(314\) 3050.53 0.548253
\(315\) 8053.10 1.44045
\(316\) 240.338 0.0427850
\(317\) 7203.26 1.27626 0.638132 0.769927i \(-0.279708\pi\)
0.638132 + 0.769927i \(0.279708\pi\)
\(318\) −5597.87 −0.987147
\(319\) 2239.56 0.393076
\(320\) 729.800 0.127491
\(321\) 12063.2 2.09751
\(322\) 432.544 0.0748594
\(323\) 9528.16 1.64136
\(324\) 11535.5 1.97797
\(325\) −166.479 −0.0284142
\(326\) −3888.93 −0.660700
\(327\) 9026.61 1.52652
\(328\) −1402.14 −0.236037
\(329\) 3810.57 0.638552
\(330\) 2393.80 0.399316
\(331\) −11007.6 −1.82789 −0.913943 0.405843i \(-0.866978\pi\)
−0.913943 + 0.405843i \(0.866978\pi\)
\(332\) −1491.51 −0.246558
\(333\) −16155.7 −2.65864
\(334\) 5265.16 0.862565
\(335\) 3120.75 0.508969
\(336\) −1520.25 −0.246835
\(337\) 1436.15 0.232143 0.116072 0.993241i \(-0.462970\pi\)
0.116072 + 0.993241i \(0.462970\pi\)
\(338\) 2204.23 0.354716
\(339\) −18614.5 −2.98230
\(340\) 6332.72 1.01012
\(341\) 913.337 0.145044
\(342\) −10308.6 −1.62990
\(343\) −5619.13 −0.884561
\(344\) 325.700 0.0510482
\(345\) 2650.17 0.413567
\(346\) −2379.25 −0.369680
\(347\) 4296.61 0.664710 0.332355 0.943154i \(-0.392157\pi\)
0.332355 + 0.943154i \(0.392157\pi\)
\(348\) −8714.34 −1.34235
\(349\) 3496.28 0.536250 0.268125 0.963384i \(-0.413596\pi\)
0.268125 + 0.963384i \(0.413596\pi\)
\(350\) −94.6188 −0.0144502
\(351\) 16084.0 2.44587
\(352\) −332.400 −0.0503323
\(353\) 2884.90 0.434980 0.217490 0.976063i \(-0.430213\pi\)
0.217490 + 0.976063i \(0.430213\pi\)
\(354\) 5932.46 0.890697
\(355\) −7341.81 −1.09764
\(356\) −2175.79 −0.323923
\(357\) −13191.7 −1.95569
\(358\) 3097.94 0.457350
\(359\) −9774.21 −1.43694 −0.718472 0.695556i \(-0.755158\pi\)
−0.718472 + 0.695556i \(0.755158\pi\)
\(360\) −6851.42 −1.00306
\(361\) −2149.18 −0.313337
\(362\) 3816.77 0.554157
\(363\) 12359.0 1.78700
\(364\) −1244.56 −0.179211
\(365\) 1212.67 0.173901
\(366\) −9108.99 −1.30091
\(367\) −5245.42 −0.746073 −0.373036 0.927817i \(-0.621683\pi\)
−0.373036 + 0.927817i \(0.621683\pi\)
\(368\) −368.000 −0.0521286
\(369\) 13163.4 1.85707
\(370\) 4905.84 0.689304
\(371\) −2604.61 −0.364486
\(372\) −3553.88 −0.495323
\(373\) −12320.9 −1.71032 −0.855160 0.518364i \(-0.826541\pi\)
−0.855160 + 0.518364i \(0.826541\pi\)
\(374\) −2884.35 −0.398787
\(375\) 13823.4 1.90357
\(376\) −3241.96 −0.444658
\(377\) −7134.05 −0.974595
\(378\) 9141.39 1.24387
\(379\) −1216.68 −0.164899 −0.0824495 0.996595i \(-0.526274\pi\)
−0.0824495 + 0.996595i \(0.526274\pi\)
\(380\) 3130.30 0.422582
\(381\) −6056.35 −0.814374
\(382\) −705.250 −0.0944600
\(383\) −3989.13 −0.532206 −0.266103 0.963945i \(-0.585736\pi\)
−0.266103 + 0.963945i \(0.585736\pi\)
\(384\) 1293.40 0.171884
\(385\) 1113.80 0.147440
\(386\) 2828.56 0.372979
\(387\) −3057.70 −0.401632
\(388\) 2203.78 0.288350
\(389\) 15077.7 1.96522 0.982608 0.185693i \(-0.0594530\pi\)
0.982608 + 0.185693i \(0.0594530\pi\)
\(390\) −7625.37 −0.990066
\(391\) −3193.26 −0.413018
\(392\) 2036.65 0.262414
\(393\) 5660.00 0.726486
\(394\) 865.060 0.110612
\(395\) 685.150 0.0872750
\(396\) 3120.60 0.396000
\(397\) −12767.4 −1.61405 −0.807026 0.590515i \(-0.798925\pi\)
−0.807026 + 0.590515i \(0.798925\pi\)
\(398\) 217.037 0.0273344
\(399\) −6520.74 −0.818159
\(400\) 80.4999 0.0100625
\(401\) −8846.67 −1.10170 −0.550850 0.834604i \(-0.685696\pi\)
−0.550850 + 0.834604i \(0.685696\pi\)
\(402\) 5530.80 0.686197
\(403\) −2909.41 −0.359623
\(404\) 4338.30 0.534254
\(405\) 32885.3 4.03478
\(406\) −4054.66 −0.495638
\(407\) −2234.45 −0.272132
\(408\) 11223.3 1.36185
\(409\) −3945.27 −0.476970 −0.238485 0.971146i \(-0.576651\pi\)
−0.238485 + 0.971146i \(0.576651\pi\)
\(410\) −3997.19 −0.481481
\(411\) 21338.0 2.56089
\(412\) 5476.76 0.654905
\(413\) 2760.29 0.328874
\(414\) 3454.82 0.410133
\(415\) −4251.97 −0.502943
\(416\) 1058.85 0.124794
\(417\) 9548.44 1.12132
\(418\) −1425.75 −0.166832
\(419\) 13937.2 1.62500 0.812502 0.582958i \(-0.198105\pi\)
0.812502 + 0.582958i \(0.198105\pi\)
\(420\) −4333.90 −0.503506
\(421\) −2471.55 −0.286119 −0.143059 0.989714i \(-0.545694\pi\)
−0.143059 + 0.989714i \(0.545694\pi\)
\(422\) 2164.74 0.249710
\(423\) 30435.8 3.49844
\(424\) 2215.95 0.253811
\(425\) 698.525 0.0797257
\(426\) −13011.6 −1.47985
\(427\) −4238.28 −0.480339
\(428\) −4775.29 −0.539304
\(429\) 3473.11 0.390870
\(430\) 928.500 0.104131
\(431\) 7340.81 0.820404 0.410202 0.911995i \(-0.365458\pi\)
0.410202 + 0.911995i \(0.365458\pi\)
\(432\) −7777.32 −0.866173
\(433\) −8838.13 −0.980909 −0.490455 0.871467i \(-0.663169\pi\)
−0.490455 + 0.871467i \(0.663169\pi\)
\(434\) −1653.57 −0.182889
\(435\) −24842.7 −2.73820
\(436\) −3573.24 −0.392493
\(437\) −1578.45 −0.172786
\(438\) 2149.17 0.234455
\(439\) −10403.7 −1.13107 −0.565534 0.824725i \(-0.691330\pi\)
−0.565534 + 0.824725i \(0.691330\pi\)
\(440\) −947.600 −0.102671
\(441\) −19120.2 −2.06460
\(442\) 9188.01 0.988753
\(443\) −4415.27 −0.473535 −0.236767 0.971566i \(-0.576088\pi\)
−0.236767 + 0.971566i \(0.576088\pi\)
\(444\) 8694.45 0.929325
\(445\) −6202.69 −0.660755
\(446\) 3238.88 0.343868
\(447\) 25064.4 2.65213
\(448\) 601.800 0.0634651
\(449\) 3711.34 0.390087 0.195044 0.980795i \(-0.437515\pi\)
0.195044 + 0.980795i \(0.437515\pi\)
\(450\) −755.740 −0.0791687
\(451\) 1820.59 0.190085
\(452\) 7368.65 0.766797
\(453\) −11767.2 −1.22047
\(454\) −13492.2 −1.39476
\(455\) −3547.97 −0.365564
\(456\) 5547.72 0.569728
\(457\) 15711.9 1.60825 0.804124 0.594461i \(-0.202635\pi\)
0.804124 + 0.594461i \(0.202635\pi\)
\(458\) −2385.27 −0.243354
\(459\) −67486.5 −6.86275
\(460\) −1049.09 −0.106335
\(461\) 3177.04 0.320975 0.160488 0.987038i \(-0.448693\pi\)
0.160488 + 0.987038i \(0.448693\pi\)
\(462\) 1973.95 0.198780
\(463\) −14774.8 −1.48303 −0.741516 0.670935i \(-0.765893\pi\)
−0.741516 + 0.670935i \(0.765893\pi\)
\(464\) 3449.62 0.345140
\(465\) −10131.3 −1.01039
\(466\) 5720.33 0.568646
\(467\) −2408.12 −0.238618 −0.119309 0.992857i \(-0.538068\pi\)
−0.119309 + 0.992857i \(0.538068\pi\)
\(468\) −9940.58 −0.981845
\(469\) 2573.40 0.253366
\(470\) −9242.12 −0.907037
\(471\) 15412.3 1.50778
\(472\) −2348.40 −0.229012
\(473\) −422.901 −0.0411100
\(474\) 1214.27 0.117665
\(475\) 345.285 0.0333532
\(476\) 5222.02 0.502838
\(477\) −20803.5 −1.99691
\(478\) 1188.75 0.113749
\(479\) −12528.3 −1.19506 −0.597528 0.801848i \(-0.703850\pi\)
−0.597528 + 0.801848i \(0.703850\pi\)
\(480\) 3687.20 0.350618
\(481\) 7117.77 0.674724
\(482\) −7860.29 −0.742794
\(483\) 2185.36 0.205874
\(484\) −4892.40 −0.459466
\(485\) 6282.48 0.588191
\(486\) 32033.1 2.98982
\(487\) 16798.6 1.56307 0.781537 0.623858i \(-0.214436\pi\)
0.781537 + 0.623858i \(0.214436\pi\)
\(488\) 3605.85 0.334486
\(489\) −19648.2 −1.81702
\(490\) 5806.04 0.535286
\(491\) −18007.7 −1.65514 −0.827571 0.561361i \(-0.810278\pi\)
−0.827571 + 0.561361i \(0.810278\pi\)
\(492\) −7084.08 −0.649136
\(493\) 29933.6 2.73456
\(494\) 4541.68 0.413643
\(495\) 8896.15 0.807782
\(496\) 1406.82 0.127355
\(497\) −6054.13 −0.546408
\(498\) −7535.63 −0.678072
\(499\) 696.627 0.0624956 0.0312478 0.999512i \(-0.490052\pi\)
0.0312478 + 0.999512i \(0.490052\pi\)
\(500\) −5472.07 −0.489437
\(501\) 26601.4 2.37218
\(502\) −4244.14 −0.377341
\(503\) −20469.0 −1.81444 −0.907222 0.420652i \(-0.861801\pi\)
−0.907222 + 0.420652i \(0.861801\pi\)
\(504\) −5649.75 −0.499325
\(505\) 12367.5 1.08980
\(506\) 477.825 0.0419801
\(507\) 11136.5 0.975523
\(508\) 2397.44 0.209389
\(509\) 13437.5 1.17015 0.585073 0.810980i \(-0.301066\pi\)
0.585073 + 0.810980i \(0.301066\pi\)
\(510\) 31995.1 2.77797
\(511\) 999.978 0.0865683
\(512\) −512.000 −0.0441942
\(513\) −33358.9 −2.87102
\(514\) −2287.36 −0.196286
\(515\) 15613.0 1.33591
\(516\) 1645.55 0.140390
\(517\) 4209.49 0.358091
\(518\) 4045.40 0.343136
\(519\) −12020.8 −1.01667
\(520\) 3018.55 0.254562
\(521\) −4917.10 −0.413478 −0.206739 0.978396i \(-0.566285\pi\)
−0.206739 + 0.978396i \(0.566285\pi\)
\(522\) −32385.4 −2.71546
\(523\) 15959.4 1.33434 0.667168 0.744908i \(-0.267507\pi\)
0.667168 + 0.744908i \(0.267507\pi\)
\(524\) −2240.54 −0.186791
\(525\) −478.047 −0.0397403
\(526\) 1895.07 0.157089
\(527\) 12207.5 1.00905
\(528\) −1679.40 −0.138421
\(529\) 529.000 0.0434783
\(530\) 6317.19 0.517738
\(531\) 22047.0 1.80180
\(532\) 2581.27 0.210362
\(533\) −5799.43 −0.471297
\(534\) −10992.8 −0.890835
\(535\) −13613.3 −1.10010
\(536\) −2189.40 −0.176432
\(537\) 15651.9 1.25778
\(538\) −6435.39 −0.515705
\(539\) −2644.46 −0.211327
\(540\) −22171.4 −1.76687
\(541\) −8018.32 −0.637217 −0.318608 0.947886i \(-0.603216\pi\)
−0.318608 + 0.947886i \(0.603216\pi\)
\(542\) 14568.1 1.15453
\(543\) 19283.6 1.52401
\(544\) −4442.80 −0.350153
\(545\) −10186.5 −0.800628
\(546\) −6287.96 −0.492857
\(547\) 13255.0 1.03609 0.518047 0.855352i \(-0.326659\pi\)
0.518047 + 0.855352i \(0.326659\pi\)
\(548\) −8446.76 −0.658445
\(549\) −33852.0 −2.63164
\(550\) −104.524 −0.00810349
\(551\) 14796.3 1.14400
\(552\) −1859.26 −0.143361
\(553\) 564.981 0.0434456
\(554\) −5048.15 −0.387140
\(555\) 24786.0 1.89569
\(556\) −3779.81 −0.288308
\(557\) −10410.3 −0.791918 −0.395959 0.918268i \(-0.629588\pi\)
−0.395959 + 0.918268i \(0.629588\pi\)
\(558\) −13207.4 −1.00200
\(559\) 1347.14 0.101928
\(560\) 1715.60 0.129460
\(561\) −14572.7 −1.09672
\(562\) 12554.9 0.942341
\(563\) 19009.9 1.42304 0.711520 0.702666i \(-0.248007\pi\)
0.711520 + 0.702666i \(0.248007\pi\)
\(564\) −16379.5 −1.22288
\(565\) 21006.4 1.56415
\(566\) 16.6883 0.00123933
\(567\) 27117.6 2.00852
\(568\) 5150.74 0.380493
\(569\) 11671.7 0.859934 0.429967 0.902845i \(-0.358525\pi\)
0.429967 + 0.902845i \(0.358525\pi\)
\(570\) 15815.3 1.16216
\(571\) −21359.8 −1.56546 −0.782732 0.622359i \(-0.786174\pi\)
−0.782732 + 0.622359i \(0.786174\pi\)
\(572\) −1374.85 −0.100499
\(573\) −3563.16 −0.259779
\(574\) −3296.12 −0.239682
\(575\) −115.719 −0.00839269
\(576\) 4806.70 0.347707
\(577\) 13416.4 0.967996 0.483998 0.875069i \(-0.339184\pi\)
0.483998 + 0.875069i \(0.339184\pi\)
\(578\) −28725.7 −2.06718
\(579\) 14290.9 1.02575
\(580\) 9834.12 0.704034
\(581\) −3506.22 −0.250366
\(582\) 11134.2 0.793005
\(583\) −2877.27 −0.204399
\(584\) −850.762 −0.0602822
\(585\) −28338.4 −2.00282
\(586\) −6150.29 −0.433560
\(587\) −11542.3 −0.811586 −0.405793 0.913965i \(-0.633005\pi\)
−0.405793 + 0.913965i \(0.633005\pi\)
\(588\) 10289.9 0.721678
\(589\) 6034.23 0.422133
\(590\) −6694.77 −0.467152
\(591\) 4370.58 0.304199
\(592\) −3441.75 −0.238944
\(593\) 3151.02 0.218207 0.109104 0.994030i \(-0.465202\pi\)
0.109104 + 0.994030i \(0.465202\pi\)
\(594\) 10098.4 0.697544
\(595\) 14886.8 1.02572
\(596\) −9921.87 −0.681906
\(597\) 1096.55 0.0751736
\(598\) −1522.10 −0.104086
\(599\) −293.676 −0.0200322 −0.0100161 0.999950i \(-0.503188\pi\)
−0.0100161 + 0.999950i \(0.503188\pi\)
\(600\) 406.713 0.0276733
\(601\) −19297.6 −1.30976 −0.654881 0.755732i \(-0.727281\pi\)
−0.654881 + 0.755732i \(0.727281\pi\)
\(602\) 765.650 0.0518365
\(603\) 20554.3 1.38812
\(604\) 4658.13 0.313802
\(605\) −13947.2 −0.937244
\(606\) 21918.6 1.46928
\(607\) −24573.1 −1.64315 −0.821573 0.570103i \(-0.806903\pi\)
−0.821573 + 0.570103i \(0.806903\pi\)
\(608\) −2196.10 −0.146486
\(609\) −20485.5 −1.36308
\(610\) 10279.5 0.682302
\(611\) −13409.2 −0.887852
\(612\) 41709.4 2.75491
\(613\) 14171.5 0.933738 0.466869 0.884326i \(-0.345382\pi\)
0.466869 + 0.884326i \(0.345382\pi\)
\(614\) 2079.80 0.136700
\(615\) −20195.2 −1.32414
\(616\) −781.400 −0.0511096
\(617\) −3693.48 −0.240995 −0.120498 0.992714i \(-0.538449\pi\)
−0.120498 + 0.992714i \(0.538449\pi\)
\(618\) 27670.5 1.80108
\(619\) 29215.7 1.89705 0.948527 0.316697i \(-0.102574\pi\)
0.948527 + 0.316697i \(0.102574\pi\)
\(620\) 4010.55 0.259786
\(621\) 11179.9 0.722438
\(622\) −11834.2 −0.762878
\(623\) −5114.80 −0.328925
\(624\) 5349.67 0.343202
\(625\) −16228.6 −1.03863
\(626\) −5163.34 −0.329663
\(627\) −7203.38 −0.458812
\(628\) −6101.06 −0.387673
\(629\) −29865.2 −1.89317
\(630\) −16106.2 −1.01855
\(631\) −10216.8 −0.644571 −0.322286 0.946643i \(-0.604451\pi\)
−0.322286 + 0.946643i \(0.604451\pi\)
\(632\) −480.675 −0.0302535
\(633\) 10937.0 0.686740
\(634\) −14406.5 −0.902454
\(635\) 6834.59 0.427122
\(636\) 11195.7 0.698019
\(637\) 8423.86 0.523964
\(638\) −4479.12 −0.277947
\(639\) −48355.6 −2.99361
\(640\) −1459.60 −0.0901496
\(641\) 11330.1 0.698148 0.349074 0.937095i \(-0.386496\pi\)
0.349074 + 0.937095i \(0.386496\pi\)
\(642\) −24126.4 −1.48317
\(643\) −18572.6 −1.13908 −0.569542 0.821962i \(-0.692879\pi\)
−0.569542 + 0.821962i \(0.692879\pi\)
\(644\) −865.087 −0.0529336
\(645\) 4691.10 0.286375
\(646\) −19056.3 −1.16062
\(647\) −13995.8 −0.850436 −0.425218 0.905091i \(-0.639802\pi\)
−0.425218 + 0.905091i \(0.639802\pi\)
\(648\) −23071.1 −1.39864
\(649\) 3049.25 0.184428
\(650\) 332.958 0.0200918
\(651\) −8354.40 −0.502972
\(652\) 7777.87 0.467185
\(653\) 20473.1 1.22691 0.613456 0.789729i \(-0.289779\pi\)
0.613456 + 0.789729i \(0.289779\pi\)
\(654\) −18053.2 −1.07941
\(655\) −6387.30 −0.381027
\(656\) 2804.28 0.166903
\(657\) 7987.03 0.474283
\(658\) −7621.14 −0.451524
\(659\) −27951.8 −1.65227 −0.826135 0.563473i \(-0.809465\pi\)
−0.826135 + 0.563473i \(0.809465\pi\)
\(660\) −4787.60 −0.282359
\(661\) 20698.3 1.21796 0.608980 0.793185i \(-0.291579\pi\)
0.608980 + 0.793185i \(0.291579\pi\)
\(662\) 22015.1 1.29251
\(663\) 46421.0 2.71922
\(664\) 2983.02 0.174343
\(665\) 7358.65 0.429107
\(666\) 32311.4 1.87994
\(667\) −4958.84 −0.287866
\(668\) −10530.3 −0.609926
\(669\) 16363.9 0.945688
\(670\) −6241.50 −0.359896
\(671\) −4681.97 −0.269367
\(672\) 3040.50 0.174538
\(673\) 28428.7 1.62830 0.814150 0.580654i \(-0.197203\pi\)
0.814150 + 0.580654i \(0.197203\pi\)
\(674\) −2872.31 −0.164150
\(675\) −2445.60 −0.139454
\(676\) −4408.46 −0.250822
\(677\) −7179.44 −0.407575 −0.203787 0.979015i \(-0.565325\pi\)
−0.203787 + 0.979015i \(0.565325\pi\)
\(678\) 37228.9 2.10880
\(679\) 5180.59 0.292803
\(680\) −12665.4 −0.714261
\(681\) −68167.3 −3.83579
\(682\) −1826.67 −0.102562
\(683\) 5146.87 0.288345 0.144172 0.989553i \(-0.453948\pi\)
0.144172 + 0.989553i \(0.453948\pi\)
\(684\) 20617.2 1.15251
\(685\) −24079.9 −1.34313
\(686\) 11238.3 0.625479
\(687\) −12051.2 −0.669260
\(688\) −651.400 −0.0360965
\(689\) 9165.46 0.506787
\(690\) −5300.35 −0.292436
\(691\) 29679.6 1.63396 0.816978 0.576669i \(-0.195648\pi\)
0.816978 + 0.576669i \(0.195648\pi\)
\(692\) 4758.50 0.261403
\(693\) 7335.85 0.402115
\(694\) −8593.23 −0.470021
\(695\) −10775.4 −0.588107
\(696\) 17428.7 0.949185
\(697\) 24333.7 1.32239
\(698\) −6992.55 −0.379186
\(699\) 28901.1 1.56386
\(700\) 189.238 0.0102179
\(701\) 9627.78 0.518739 0.259370 0.965778i \(-0.416485\pi\)
0.259370 + 0.965778i \(0.416485\pi\)
\(702\) −32168.0 −1.72949
\(703\) −14762.5 −0.792006
\(704\) 664.800 0.0355903
\(705\) −46694.4 −2.49449
\(706\) −5769.80 −0.307577
\(707\) 10198.4 0.542504
\(708\) −11864.9 −0.629818
\(709\) 11527.4 0.610606 0.305303 0.952255i \(-0.401242\pi\)
0.305303 + 0.952255i \(0.401242\pi\)
\(710\) 14683.6 0.776150
\(711\) 4512.62 0.238026
\(712\) 4351.57 0.229048
\(713\) −2022.31 −0.106222
\(714\) 26383.5 1.38288
\(715\) −3919.40 −0.205003
\(716\) −6195.88 −0.323395
\(717\) 6005.96 0.312826
\(718\) 19548.4 1.01607
\(719\) −7837.87 −0.406542 −0.203271 0.979123i \(-0.565157\pi\)
−0.203271 + 0.979123i \(0.565157\pi\)
\(720\) 13702.8 0.709271
\(721\) 12874.7 0.665018
\(722\) 4298.36 0.221563
\(723\) −39712.9 −2.04279
\(724\) −7633.54 −0.391848
\(725\) 1084.74 0.0555674
\(726\) −24718.1 −1.26360
\(727\) 726.845 0.0370800 0.0185400 0.999828i \(-0.494098\pi\)
0.0185400 + 0.999828i \(0.494098\pi\)
\(728\) 2489.12 0.126721
\(729\) 83977.2 4.26648
\(730\) −2425.34 −0.122967
\(731\) −5652.42 −0.285995
\(732\) 18218.0 0.919886
\(733\) −378.674 −0.0190814 −0.00954069 0.999954i \(-0.503037\pi\)
−0.00954069 + 0.999954i \(0.503037\pi\)
\(734\) 10490.8 0.527553
\(735\) 29334.1 1.47212
\(736\) 736.000 0.0368605
\(737\) 2842.80 0.142084
\(738\) −26326.8 −1.31315
\(739\) 18952.9 0.943428 0.471714 0.881752i \(-0.343636\pi\)
0.471714 + 0.881752i \(0.343636\pi\)
\(740\) −9811.67 −0.487411
\(741\) 22946.1 1.13758
\(742\) 5209.21 0.257731
\(743\) −19317.8 −0.953838 −0.476919 0.878947i \(-0.658246\pi\)
−0.476919 + 0.878947i \(0.658246\pi\)
\(744\) 7107.76 0.350246
\(745\) −28285.1 −1.39099
\(746\) 24641.7 1.20938
\(747\) −28004.9 −1.37168
\(748\) 5768.70 0.281985
\(749\) −11225.7 −0.547632
\(750\) −27646.8 −1.34602
\(751\) −25592.6 −1.24353 −0.621763 0.783206i \(-0.713583\pi\)
−0.621763 + 0.783206i \(0.713583\pi\)
\(752\) 6483.92 0.314421
\(753\) −21442.9 −1.03774
\(754\) 14268.1 0.689143
\(755\) 13279.3 0.640111
\(756\) −18282.8 −0.879548
\(757\) −36790.6 −1.76642 −0.883208 0.468981i \(-0.844621\pi\)
−0.883208 + 0.468981i \(0.844621\pi\)
\(758\) 2433.36 0.116601
\(759\) 2414.14 0.115451
\(760\) −6260.60 −0.298810
\(761\) 2257.71 0.107545 0.0537726 0.998553i \(-0.482875\pi\)
0.0537726 + 0.998553i \(0.482875\pi\)
\(762\) 12112.7 0.575849
\(763\) −8399.90 −0.398554
\(764\) 1410.50 0.0667933
\(765\) 118904. 5.61960
\(766\) 7978.26 0.376327
\(767\) −9713.30 −0.457271
\(768\) −2586.80 −0.121540
\(769\) 6903.74 0.323739 0.161869 0.986812i \(-0.448248\pi\)
0.161869 + 0.986812i \(0.448248\pi\)
\(770\) −2227.60 −0.104256
\(771\) −11556.5 −0.539816
\(772\) −5657.12 −0.263736
\(773\) −30096.1 −1.40036 −0.700182 0.713965i \(-0.746898\pi\)
−0.700182 + 0.713965i \(0.746898\pi\)
\(774\) 6115.40 0.283997
\(775\) 442.380 0.0205042
\(776\) −4407.55 −0.203894
\(777\) 20438.7 0.943676
\(778\) −30155.4 −1.38962
\(779\) 12028.3 0.553218
\(780\) 15250.7 0.700083
\(781\) −6687.91 −0.306418
\(782\) 6386.52 0.292048
\(783\) −104800. −4.78321
\(784\) −4073.30 −0.185555
\(785\) −17392.8 −0.790797
\(786\) −11320.0 −0.513703
\(787\) −6753.37 −0.305885 −0.152943 0.988235i \(-0.548875\pi\)
−0.152943 + 0.988235i \(0.548875\pi\)
\(788\) −1730.12 −0.0782144
\(789\) 9574.54 0.432018
\(790\) −1370.30 −0.0617128
\(791\) 17322.1 0.778638
\(792\) −6241.20 −0.280014
\(793\) 14914.3 0.667871
\(794\) 25534.9 1.14131
\(795\) 31916.6 1.42386
\(796\) −434.074 −0.0193283
\(797\) 26666.0 1.18514 0.592570 0.805519i \(-0.298113\pi\)
0.592570 + 0.805519i \(0.298113\pi\)
\(798\) 13041.5 0.578526
\(799\) 56263.2 2.49118
\(800\) −161.000 −0.00711525
\(801\) −40853.0 −1.80208
\(802\) 17693.3 0.779019
\(803\) 1104.66 0.0485463
\(804\) −11061.6 −0.485215
\(805\) −2466.17 −0.107977
\(806\) 5818.82 0.254292
\(807\) −32513.8 −1.41827
\(808\) −8676.60 −0.377774
\(809\) −16430.2 −0.714035 −0.357018 0.934098i \(-0.616206\pi\)
−0.357018 + 0.934098i \(0.616206\pi\)
\(810\) −65770.7 −2.85302
\(811\) −23394.6 −1.01294 −0.506470 0.862257i \(-0.669050\pi\)
−0.506470 + 0.862257i \(0.669050\pi\)
\(812\) 8109.31 0.350469
\(813\) 73603.0 3.17512
\(814\) 4468.90 0.192426
\(815\) 22173.0 0.952989
\(816\) −22446.5 −0.962974
\(817\) −2794.02 −0.119646
\(818\) 7890.54 0.337269
\(819\) −23368.1 −0.997006
\(820\) 7994.37 0.340458
\(821\) 30615.7 1.30145 0.650727 0.759312i \(-0.274464\pi\)
0.650727 + 0.759312i \(0.274464\pi\)
\(822\) −42675.9 −1.81082
\(823\) −959.744 −0.0406496 −0.0203248 0.999793i \(-0.506470\pi\)
−0.0203248 + 0.999793i \(0.506470\pi\)
\(824\) −10953.5 −0.463087
\(825\) −528.092 −0.0222858
\(826\) −5520.57 −0.232549
\(827\) 37507.5 1.57710 0.788551 0.614970i \(-0.210832\pi\)
0.788551 + 0.614970i \(0.210832\pi\)
\(828\) −6909.63 −0.290008
\(829\) −27029.9 −1.13243 −0.566217 0.824256i \(-0.691594\pi\)
−0.566217 + 0.824256i \(0.691594\pi\)
\(830\) 8503.95 0.355634
\(831\) −25505.0 −1.06469
\(832\) −2117.70 −0.0882428
\(833\) −35345.4 −1.47016
\(834\) −19096.9 −0.792891
\(835\) −30019.6 −1.24416
\(836\) 2851.50 0.117968
\(837\) −42739.6 −1.76499
\(838\) −27874.4 −1.14905
\(839\) 38982.8 1.60409 0.802047 0.597261i \(-0.203744\pi\)
0.802047 + 0.597261i \(0.203744\pi\)
\(840\) 8667.80 0.356033
\(841\) 22095.0 0.905942
\(842\) 4943.10 0.202316
\(843\) 63431.6 2.59158
\(844\) −4329.48 −0.176572
\(845\) −12567.5 −0.511641
\(846\) −60871.6 −2.47377
\(847\) −11501.0 −0.466562
\(848\) −4431.90 −0.179472
\(849\) 84.3151 0.00340835
\(850\) −1397.05 −0.0563746
\(851\) 4947.52 0.199293
\(852\) 26023.3 1.04641
\(853\) −16634.7 −0.667715 −0.333858 0.942624i \(-0.608350\pi\)
−0.333858 + 0.942624i \(0.608350\pi\)
\(854\) 8476.56 0.339651
\(855\) 58775.0 2.35095
\(856\) 9550.57 0.381346
\(857\) −15234.4 −0.607230 −0.303615 0.952795i \(-0.598194\pi\)
−0.303615 + 0.952795i \(0.598194\pi\)
\(858\) −6946.22 −0.276387
\(859\) 31925.2 1.26807 0.634036 0.773303i \(-0.281397\pi\)
0.634036 + 0.773303i \(0.281397\pi\)
\(860\) −1857.00 −0.0736316
\(861\) −16653.1 −0.659160
\(862\) −14681.6 −0.580113
\(863\) −19518.9 −0.769910 −0.384955 0.922935i \(-0.625783\pi\)
−0.384955 + 0.922935i \(0.625783\pi\)
\(864\) 15554.6 0.612477
\(865\) 13565.4 0.533224
\(866\) 17676.3 0.693607
\(867\) −145132. −5.68506
\(868\) 3307.14 0.129322
\(869\) 624.127 0.0243637
\(870\) 49685.4 1.93620
\(871\) −9055.65 −0.352284
\(872\) 7146.48 0.277535
\(873\) 41378.5 1.60418
\(874\) 3156.89 0.122178
\(875\) −12863.6 −0.496995
\(876\) −4298.34 −0.165785
\(877\) 16853.3 0.648913 0.324456 0.945901i \(-0.394819\pi\)
0.324456 + 0.945901i \(0.394819\pi\)
\(878\) 20807.3 0.799786
\(879\) −31073.4 −1.19235
\(880\) 1895.20 0.0725991
\(881\) 10834.3 0.414320 0.207160 0.978307i \(-0.433578\pi\)
0.207160 + 0.978307i \(0.433578\pi\)
\(882\) 38240.5 1.45989
\(883\) −23506.2 −0.895863 −0.447931 0.894068i \(-0.647839\pi\)
−0.447931 + 0.894068i \(0.647839\pi\)
\(884\) −18376.0 −0.699154
\(885\) −33824.3 −1.28474
\(886\) 8830.54 0.334840
\(887\) 34287.2 1.29792 0.648958 0.760824i \(-0.275205\pi\)
0.648958 + 0.760824i \(0.275205\pi\)
\(888\) −17388.9 −0.657132
\(889\) 5635.87 0.212622
\(890\) 12405.4 0.467224
\(891\) 29956.4 1.12635
\(892\) −6477.75 −0.243151
\(893\) 27811.2 1.04218
\(894\) −50128.7 −1.87534
\(895\) −17663.1 −0.659679
\(896\) −1203.60 −0.0448766
\(897\) −7690.16 −0.286251
\(898\) −7422.69 −0.275833
\(899\) 18957.1 0.703287
\(900\) 1511.48 0.0559807
\(901\) −38457.1 −1.42197
\(902\) −3641.18 −0.134410
\(903\) 3868.33 0.142558
\(904\) −14737.3 −0.542207
\(905\) −21761.5 −0.799313
\(906\) 23534.5 0.863003
\(907\) 47930.9 1.75471 0.877354 0.479844i \(-0.159307\pi\)
0.877354 + 0.479844i \(0.159307\pi\)
\(908\) 26984.4 0.986244
\(909\) 81456.7 2.97222
\(910\) 7095.95 0.258493
\(911\) 9787.98 0.355972 0.177986 0.984033i \(-0.443042\pi\)
0.177986 + 0.984033i \(0.443042\pi\)
\(912\) −11095.4 −0.402859
\(913\) −3873.27 −0.140402
\(914\) −31423.7 −1.13720
\(915\) 51935.5 1.87643
\(916\) 4770.54 0.172077
\(917\) −5267.03 −0.189676
\(918\) 134973. 4.85269
\(919\) 25226.6 0.905495 0.452748 0.891639i \(-0.350444\pi\)
0.452748 + 0.891639i \(0.350444\pi\)
\(920\) 2098.17 0.0751900
\(921\) 10507.9 0.375946
\(922\) −6354.08 −0.226964
\(923\) 21304.1 0.759734
\(924\) −3947.90 −0.140559
\(925\) −1082.27 −0.0384700
\(926\) 29549.6 1.04866
\(927\) 102833. 3.64344
\(928\) −6899.25 −0.244051
\(929\) 38214.5 1.34960 0.674800 0.738001i \(-0.264230\pi\)
0.674800 + 0.738001i \(0.264230\pi\)
\(930\) 20262.7 0.714451
\(931\) −17471.4 −0.615041
\(932\) −11440.7 −0.402093
\(933\) −59790.6 −2.09803
\(934\) 4816.25 0.168728
\(935\) 16445.3 0.575207
\(936\) 19881.2 0.694269
\(937\) −19742.9 −0.688338 −0.344169 0.938908i \(-0.611839\pi\)
−0.344169 + 0.938908i \(0.611839\pi\)
\(938\) −5146.80 −0.179157
\(939\) −26087.0 −0.906621
\(940\) 18484.2 0.641372
\(941\) −39767.5 −1.37767 −0.688833 0.724920i \(-0.741877\pi\)
−0.688833 + 0.724920i \(0.741877\pi\)
\(942\) −30824.7 −1.06616
\(943\) −4031.15 −0.139207
\(944\) 4696.80 0.161936
\(945\) −52120.2 −1.79415
\(946\) 845.803 0.0290692
\(947\) 32884.3 1.12840 0.564200 0.825638i \(-0.309185\pi\)
0.564200 + 0.825638i \(0.309185\pi\)
\(948\) −2428.54 −0.0832017
\(949\) −3518.87 −0.120366
\(950\) −690.569 −0.0235842
\(951\) −72786.7 −2.48188
\(952\) −10444.0 −0.355560
\(953\) 4674.79 0.158899 0.0794497 0.996839i \(-0.474684\pi\)
0.0794497 + 0.996839i \(0.474684\pi\)
\(954\) 41607.1 1.41203
\(955\) 4021.02 0.136248
\(956\) −2377.49 −0.0804327
\(957\) −22630.1 −0.764395
\(958\) 25056.6 0.845032
\(959\) −19856.5 −0.668613
\(960\) −7374.40 −0.247925
\(961\) −22059.9 −0.740489
\(962\) −14235.5 −0.477102
\(963\) −89661.6 −3.00032
\(964\) 15720.6 0.525234
\(965\) −16127.2 −0.537982
\(966\) −4370.72 −0.145575
\(967\) −27165.3 −0.903390 −0.451695 0.892173i \(-0.649180\pi\)
−0.451695 + 0.892173i \(0.649180\pi\)
\(968\) 9784.80 0.324892
\(969\) −96279.0 −3.19188
\(970\) −12565.0 −0.415914
\(971\) 14597.4 0.482443 0.241221 0.970470i \(-0.422452\pi\)
0.241221 + 0.970470i \(0.422452\pi\)
\(972\) −64066.2 −2.11412
\(973\) −8885.50 −0.292760
\(974\) −33597.2 −1.10526
\(975\) 1682.22 0.0552555
\(976\) −7211.70 −0.236517
\(977\) 33327.5 1.09134 0.545670 0.838000i \(-0.316275\pi\)
0.545670 + 0.838000i \(0.316275\pi\)
\(978\) 39296.5 1.28483
\(979\) −5650.25 −0.184456
\(980\) −11612.1 −0.378505
\(981\) −67091.7 −2.18356
\(982\) 36015.4 1.17036
\(983\) −21834.8 −0.708465 −0.354232 0.935157i \(-0.615258\pi\)
−0.354232 + 0.935157i \(0.615258\pi\)
\(984\) 14168.2 0.459009
\(985\) −4932.19 −0.159546
\(986\) −59867.2 −1.93363
\(987\) −38504.6 −1.24176
\(988\) −9083.36 −0.292490
\(989\) 936.388 0.0301066
\(990\) −17792.3 −0.571188
\(991\) 45191.9 1.44861 0.724303 0.689482i \(-0.242162\pi\)
0.724303 + 0.689482i \(0.242162\pi\)
\(992\) −2813.65 −0.0900539
\(993\) 111228. 3.55459
\(994\) 12108.3 0.386369
\(995\) −1237.45 −0.0394269
\(996\) 15071.3 0.479469
\(997\) 18760.0 0.595924 0.297962 0.954578i \(-0.403693\pi\)
0.297962 + 0.954578i \(0.403693\pi\)
\(998\) −1393.25 −0.0441911
\(999\) 104561. 3.31147
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 46.4.a.c.1.1 2
3.2 odd 2 414.4.a.j.1.1 2
4.3 odd 2 368.4.a.g.1.2 2
5.2 odd 4 1150.4.b.i.599.2 4
5.3 odd 4 1150.4.b.i.599.3 4
5.4 even 2 1150.4.a.k.1.2 2
7.6 odd 2 2254.4.a.d.1.2 2
8.3 odd 2 1472.4.a.l.1.1 2
8.5 even 2 1472.4.a.m.1.2 2
23.22 odd 2 1058.4.a.f.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
46.4.a.c.1.1 2 1.1 even 1 trivial
368.4.a.g.1.2 2 4.3 odd 2
414.4.a.j.1.1 2 3.2 odd 2
1058.4.a.f.1.1 2 23.22 odd 2
1150.4.a.k.1.2 2 5.4 even 2
1150.4.b.i.599.2 4 5.2 odd 4
1150.4.b.i.599.3 4 5.3 odd 4
1472.4.a.l.1.1 2 8.3 odd 2
1472.4.a.m.1.2 2 8.5 even 2
2254.4.a.d.1.2 2 7.6 odd 2