Properties

Label 289.4.b.f.288.22
Level $289$
Weight $4$
Character 289.288
Analytic conductor $17.052$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [289,4,Mod(288,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("289.288");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.b (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(17.0515519917\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 288.22
Character \(\chi\) \(=\) 289.288
Dual form 289.4.b.f.288.21

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.98104 q^{2} +6.26206i q^{3} +16.8108 q^{4} +15.7477i q^{5} +31.1916i q^{6} -0.789949i q^{7} +43.8870 q^{8} -12.2134 q^{9} +O(q^{10})\) \(q+4.98104 q^{2} +6.26206i q^{3} +16.8108 q^{4} +15.7477i q^{5} +31.1916i q^{6} -0.789949i q^{7} +43.8870 q^{8} -12.2134 q^{9} +78.4401i q^{10} -45.3316i q^{11} +105.270i q^{12} +46.7491 q^{13} -3.93477i q^{14} -98.6131 q^{15} +84.1166 q^{16} -60.8354 q^{18} -100.512 q^{19} +264.732i q^{20} +4.94671 q^{21} -225.798i q^{22} +84.1579i q^{23} +274.823i q^{24} -122.991 q^{25} +232.859 q^{26} +92.5947i q^{27} -13.2797i q^{28} -101.693i q^{29} -491.196 q^{30} +7.36111i q^{31} +67.8926 q^{32} +283.869 q^{33} +12.4399 q^{35} -205.317 q^{36} -251.101i q^{37} -500.657 q^{38} +292.745i q^{39} +691.120i q^{40} -260.918i q^{41} +24.6398 q^{42} +401.442 q^{43} -762.060i q^{44} -192.333i q^{45} +419.194i q^{46} +304.102 q^{47} +526.743i q^{48} +342.376 q^{49} -612.622 q^{50} +785.889 q^{52} -398.236 q^{53} +461.218i q^{54} +713.869 q^{55} -34.6685i q^{56} -629.414i q^{57} -506.536i q^{58} +577.767 q^{59} -1657.77 q^{60} -126.259i q^{61} +36.6660i q^{62} +9.64795i q^{63} -334.757 q^{64} +736.191i q^{65} +1413.96 q^{66} -150.923 q^{67} -527.002 q^{69} +61.9637 q^{70} +434.653i q^{71} -536.008 q^{72} +493.829i q^{73} -1250.74i q^{74} -770.175i q^{75} -1689.69 q^{76} -35.8096 q^{77} +1458.18i q^{78} +72.2153i q^{79} +1324.64i q^{80} -909.595 q^{81} -1299.65i q^{82} -711.089 q^{83} +83.1581 q^{84} +1999.60 q^{86} +636.806 q^{87} -1989.47i q^{88} +1354.30 q^{89} -958.018i q^{90} -36.9294i q^{91} +1414.76i q^{92} -46.0957 q^{93} +1514.75 q^{94} -1582.84i q^{95} +425.147i q^{96} -1402.59i q^{97} +1705.39 q^{98} +553.651i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 96 q^{4} + 102 q^{8} - 216 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 96 q^{4} + 102 q^{8} - 216 q^{9} - 144 q^{13} + 276 q^{15} + 384 q^{16} + 378 q^{18} + 132 q^{19} + 492 q^{21} - 888 q^{25} - 1056 q^{26} - 3780 q^{30} + 2706 q^{32} + 1932 q^{33} - 132 q^{35} + 1326 q^{36} - 120 q^{38} - 1608 q^{42} - 972 q^{43} - 1776 q^{47} + 1140 q^{49} + 870 q^{50} + 450 q^{52} - 2052 q^{53} + 1944 q^{55} + 1584 q^{59} - 2916 q^{60} - 3714 q^{64} + 1188 q^{66} + 1248 q^{67} - 3012 q^{69} + 3300 q^{70} + 2910 q^{72} - 1350 q^{76} + 2016 q^{77} + 5040 q^{81} - 1344 q^{83} - 1554 q^{84} + 5556 q^{86} - 1452 q^{87} - 1812 q^{89} - 264 q^{93} - 1470 q^{94} + 3822 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.98104 1.76107 0.880533 0.473986i \(-0.157185\pi\)
0.880533 + 0.473986i \(0.157185\pi\)
\(3\) 6.26206i 1.20513i 0.798068 + 0.602567i \(0.205855\pi\)
−0.798068 + 0.602567i \(0.794145\pi\)
\(4\) 16.8108 2.10135
\(5\) 15.7477i 1.40852i 0.709943 + 0.704259i \(0.248721\pi\)
−0.709943 + 0.704259i \(0.751279\pi\)
\(6\) 31.1916i 2.12232i
\(7\) − 0.789949i − 0.0426533i −0.999773 0.0213266i \(-0.993211\pi\)
0.999773 0.0213266i \(-0.00678899\pi\)
\(8\) 43.8870 1.93955
\(9\) −12.2134 −0.452347
\(10\) 78.4401i 2.48049i
\(11\) − 45.3316i − 1.24254i −0.783595 0.621272i \(-0.786616\pi\)
0.783595 0.621272i \(-0.213384\pi\)
\(12\) 105.270i 2.53241i
\(13\) 46.7491 0.997374 0.498687 0.866782i \(-0.333816\pi\)
0.498687 + 0.866782i \(0.333816\pi\)
\(14\) − 3.93477i − 0.0751152i
\(15\) −98.6131 −1.69745
\(16\) 84.1166 1.31432
\(17\) 0 0
\(18\) −60.8354 −0.796613
\(19\) −100.512 −1.21364 −0.606819 0.794840i \(-0.707555\pi\)
−0.606819 + 0.794840i \(0.707555\pi\)
\(20\) 264.732i 2.95979i
\(21\) 4.94671 0.0514029
\(22\) − 225.798i − 2.18820i
\(23\) 84.1579i 0.762962i 0.924377 + 0.381481i \(0.124586\pi\)
−0.924377 + 0.381481i \(0.875414\pi\)
\(24\) 274.823i 2.33742i
\(25\) −122.991 −0.983925
\(26\) 232.859 1.75644
\(27\) 92.5947i 0.659995i
\(28\) − 13.2797i − 0.0896294i
\(29\) − 101.693i − 0.651168i −0.945513 0.325584i \(-0.894439\pi\)
0.945513 0.325584i \(-0.105561\pi\)
\(30\) −491.196 −2.98933
\(31\) 7.36111i 0.0426482i 0.999773 + 0.0213241i \(0.00678819\pi\)
−0.999773 + 0.0213241i \(0.993212\pi\)
\(32\) 67.8926 0.375057
\(33\) 283.869 1.49743
\(34\) 0 0
\(35\) 12.4399 0.0600779
\(36\) −205.317 −0.950540
\(37\) − 251.101i − 1.11570i −0.829943 0.557848i \(-0.811627\pi\)
0.829943 0.557848i \(-0.188373\pi\)
\(38\) −500.657 −2.13730
\(39\) 292.745i 1.20197i
\(40\) 691.120i 2.73189i
\(41\) − 260.918i − 0.993868i −0.867788 0.496934i \(-0.834459\pi\)
0.867788 0.496934i \(-0.165541\pi\)
\(42\) 24.6398 0.0905238
\(43\) 401.442 1.42370 0.711852 0.702329i \(-0.247856\pi\)
0.711852 + 0.702329i \(0.247856\pi\)
\(44\) − 762.060i − 2.61102i
\(45\) − 192.333i − 0.637140i
\(46\) 419.194i 1.34363i
\(47\) 304.102 0.943785 0.471892 0.881656i \(-0.343571\pi\)
0.471892 + 0.881656i \(0.343571\pi\)
\(48\) 526.743i 1.58393i
\(49\) 342.376 0.998181
\(50\) −612.622 −1.73276
\(51\) 0 0
\(52\) 785.889 2.09583
\(53\) −398.236 −1.03211 −0.516055 0.856555i \(-0.672600\pi\)
−0.516055 + 0.856555i \(0.672600\pi\)
\(54\) 461.218i 1.16229i
\(55\) 713.869 1.75015
\(56\) − 34.6685i − 0.0827281i
\(57\) − 629.414i − 1.46260i
\(58\) − 506.536i − 1.14675i
\(59\) 577.767 1.27490 0.637448 0.770493i \(-0.279990\pi\)
0.637448 + 0.770493i \(0.279990\pi\)
\(60\) −1657.77 −3.56694
\(61\) − 126.259i − 0.265013i −0.991182 0.132507i \(-0.957697\pi\)
0.991182 0.132507i \(-0.0423026\pi\)
\(62\) 36.6660i 0.0751063i
\(63\) 9.64795i 0.0192941i
\(64\) −334.757 −0.653822
\(65\) 736.191i 1.40482i
\(66\) 1413.96 2.63707
\(67\) −150.923 −0.275198 −0.137599 0.990488i \(-0.543938\pi\)
−0.137599 + 0.990488i \(0.543938\pi\)
\(68\) 0 0
\(69\) −527.002 −0.919471
\(70\) 61.9637 0.105801
\(71\) 434.653i 0.726533i 0.931685 + 0.363267i \(0.118339\pi\)
−0.931685 + 0.363267i \(0.881661\pi\)
\(72\) −536.008 −0.877350
\(73\) 493.829i 0.791757i 0.918303 + 0.395879i \(0.129560\pi\)
−0.918303 + 0.395879i \(0.870440\pi\)
\(74\) − 1250.74i − 1.96481i
\(75\) − 770.175i − 1.18576i
\(76\) −1689.69 −2.55028
\(77\) −35.8096 −0.0529985
\(78\) 1458.18i 2.11674i
\(79\) 72.2153i 0.102846i 0.998677 + 0.0514232i \(0.0163757\pi\)
−0.998677 + 0.0514232i \(0.983624\pi\)
\(80\) 1324.64i 1.85125i
\(81\) −909.595 −1.24773
\(82\) − 1299.65i − 1.75027i
\(83\) −711.089 −0.940388 −0.470194 0.882563i \(-0.655816\pi\)
−0.470194 + 0.882563i \(0.655816\pi\)
\(84\) 83.1581 0.108015
\(85\) 0 0
\(86\) 1999.60 2.50724
\(87\) 636.806 0.784745
\(88\) − 1989.47i − 2.40997i
\(89\) 1354.30 1.61298 0.806489 0.591250i \(-0.201365\pi\)
0.806489 + 0.591250i \(0.201365\pi\)
\(90\) − 958.018i − 1.12204i
\(91\) − 36.9294i − 0.0425412i
\(92\) 1414.76i 1.60325i
\(93\) −46.0957 −0.0513968
\(94\) 1514.75 1.66207
\(95\) − 1582.84i − 1.70943i
\(96\) 425.147i 0.451994i
\(97\) − 1402.59i − 1.46816i −0.679064 0.734079i \(-0.737614\pi\)
0.679064 0.734079i \(-0.262386\pi\)
\(98\) 1705.39 1.75786
\(99\) 553.651i 0.562061i
\(100\) −2067.57 −2.06757
\(101\) 151.252 0.149012 0.0745058 0.997221i \(-0.476262\pi\)
0.0745058 + 0.997221i \(0.476262\pi\)
\(102\) 0 0
\(103\) −687.247 −0.657441 −0.328720 0.944427i \(-0.606617\pi\)
−0.328720 + 0.944427i \(0.606617\pi\)
\(104\) 2051.68 1.93445
\(105\) 77.8994i 0.0724019i
\(106\) −1983.63 −1.81761
\(107\) − 456.959i − 0.412859i −0.978461 0.206430i \(-0.933816\pi\)
0.978461 0.206430i \(-0.0661844\pi\)
\(108\) 1556.59i 1.38688i
\(109\) 1281.43i 1.12605i 0.826441 + 0.563023i \(0.190362\pi\)
−0.826441 + 0.563023i \(0.809638\pi\)
\(110\) 3555.81 3.08212
\(111\) 1572.41 1.34456
\(112\) − 66.4479i − 0.0560601i
\(113\) − 1887.62i − 1.57143i −0.618586 0.785717i \(-0.712294\pi\)
0.618586 0.785717i \(-0.287706\pi\)
\(114\) − 3135.14i − 2.57573i
\(115\) −1325.29 −1.07465
\(116\) − 1709.54i − 1.36833i
\(117\) −570.964 −0.451159
\(118\) 2877.88 2.24518
\(119\) 0 0
\(120\) −4327.83 −3.29229
\(121\) −723.950 −0.543914
\(122\) − 628.902i − 0.466706i
\(123\) 1633.89 1.19774
\(124\) 123.746i 0.0896188i
\(125\) 31.6426i 0.0226416i
\(126\) 48.0569i 0.0339781i
\(127\) −1920.56 −1.34190 −0.670952 0.741501i \(-0.734114\pi\)
−0.670952 + 0.741501i \(0.734114\pi\)
\(128\) −2210.58 −1.52648
\(129\) 2513.85i 1.71575i
\(130\) 3667.00i 2.47398i
\(131\) 1656.13i 1.10456i 0.833660 + 0.552279i \(0.186242\pi\)
−0.833660 + 0.552279i \(0.813758\pi\)
\(132\) 4772.06 3.14663
\(133\) 79.3997i 0.0517656i
\(134\) −751.757 −0.484641
\(135\) −1458.16 −0.929615
\(136\) 0 0
\(137\) −2725.42 −1.69962 −0.849811 0.527088i \(-0.823284\pi\)
−0.849811 + 0.527088i \(0.823284\pi\)
\(138\) −2625.02 −1.61925
\(139\) 1231.94i 0.751739i 0.926673 + 0.375870i \(0.122656\pi\)
−0.926673 + 0.375870i \(0.877344\pi\)
\(140\) 209.125 0.126245
\(141\) 1904.31i 1.13739i
\(142\) 2165.03i 1.27947i
\(143\) − 2119.21i − 1.23928i
\(144\) −1027.35 −0.594530
\(145\) 1601.43 0.917183
\(146\) 2459.78i 1.39434i
\(147\) 2143.98i 1.20294i
\(148\) − 4221.21i − 2.34447i
\(149\) 2317.73 1.27434 0.637169 0.770724i \(-0.280106\pi\)
0.637169 + 0.770724i \(0.280106\pi\)
\(150\) − 3836.27i − 2.08820i
\(151\) −1155.92 −0.622964 −0.311482 0.950252i \(-0.600825\pi\)
−0.311482 + 0.950252i \(0.600825\pi\)
\(152\) −4411.19 −2.35391
\(153\) 0 0
\(154\) −178.369 −0.0933339
\(155\) −115.921 −0.0600708
\(156\) 4921.28i 2.52576i
\(157\) −3226.75 −1.64027 −0.820137 0.572167i \(-0.806103\pi\)
−0.820137 + 0.572167i \(0.806103\pi\)
\(158\) 359.708i 0.181119i
\(159\) − 2493.77i − 1.24383i
\(160\) 1069.15i 0.528275i
\(161\) 66.4805 0.0325428
\(162\) −4530.73 −2.19733
\(163\) − 982.257i − 0.472002i −0.971753 0.236001i \(-0.924163\pi\)
0.971753 0.236001i \(-0.0758369\pi\)
\(164\) − 4386.25i − 2.08847i
\(165\) 4470.29i 2.10916i
\(166\) −3541.97 −1.65608
\(167\) 36.6005i 0.0169595i 0.999964 + 0.00847974i \(0.00269922\pi\)
−0.999964 + 0.00847974i \(0.997301\pi\)
\(168\) 217.096 0.0996984
\(169\) −11.5254 −0.00524596
\(170\) 0 0
\(171\) 1227.60 0.548986
\(172\) 6748.56 2.99170
\(173\) − 2826.57i − 1.24220i −0.783732 0.621099i \(-0.786686\pi\)
0.783732 0.621099i \(-0.213314\pi\)
\(174\) 3171.96 1.38199
\(175\) 97.1564i 0.0419676i
\(176\) − 3813.14i − 1.63310i
\(177\) 3618.01i 1.53642i
\(178\) 6745.80 2.84056
\(179\) 1168.77 0.488032 0.244016 0.969771i \(-0.421535\pi\)
0.244016 + 0.969771i \(0.421535\pi\)
\(180\) − 3233.27i − 1.33885i
\(181\) − 2871.88i − 1.17936i −0.807635 0.589682i \(-0.799253\pi\)
0.807635 0.589682i \(-0.200747\pi\)
\(182\) − 183.947i − 0.0749179i
\(183\) 790.642 0.319377
\(184\) 3693.44i 1.47980i
\(185\) 3954.26 1.57148
\(186\) −229.605 −0.0905131
\(187\) 0 0
\(188\) 5112.20 1.98322
\(189\) 73.1451 0.0281509
\(190\) − 7884.20i − 3.01042i
\(191\) −1626.96 −0.616350 −0.308175 0.951330i \(-0.599718\pi\)
−0.308175 + 0.951330i \(0.599718\pi\)
\(192\) − 2096.27i − 0.787943i
\(193\) − 796.367i − 0.297014i −0.988911 0.148507i \(-0.952553\pi\)
0.988911 0.148507i \(-0.0474468\pi\)
\(194\) − 6986.36i − 2.58552i
\(195\) −4610.07 −1.69300
\(196\) 5755.61 2.09753
\(197\) − 977.275i − 0.353441i −0.984261 0.176721i \(-0.943451\pi\)
0.984261 0.176721i \(-0.0565489\pi\)
\(198\) 2757.76i 0.989826i
\(199\) − 711.695i − 0.253521i −0.991933 0.126761i \(-0.959542\pi\)
0.991933 0.126761i \(-0.0404580\pi\)
\(200\) −5397.69 −1.90837
\(201\) − 945.092i − 0.331650i
\(202\) 753.395 0.262419
\(203\) −80.3322 −0.0277745
\(204\) 0 0
\(205\) 4108.87 1.39988
\(206\) −3423.21 −1.15780
\(207\) − 1027.85i − 0.345124i
\(208\) 3932.37 1.31087
\(209\) 4556.38i 1.50800i
\(210\) 388.020i 0.127504i
\(211\) 3690.17i 1.20399i 0.798501 + 0.601994i \(0.205627\pi\)
−0.798501 + 0.601994i \(0.794373\pi\)
\(212\) −6694.66 −2.16883
\(213\) −2721.82 −0.875570
\(214\) − 2276.13i − 0.727072i
\(215\) 6321.79i 2.00532i
\(216\) 4063.70i 1.28009i
\(217\) 5.81490 0.00181909
\(218\) 6382.87i 1.98304i
\(219\) −3092.38 −0.954173
\(220\) 12000.7 3.67767
\(221\) 0 0
\(222\) 7832.23 2.36786
\(223\) 1726.16 0.518351 0.259176 0.965830i \(-0.416549\pi\)
0.259176 + 0.965830i \(0.416549\pi\)
\(224\) − 53.6317i − 0.0159974i
\(225\) 1502.13 0.445076
\(226\) − 9402.31i − 2.76740i
\(227\) 2144.75i 0.627100i 0.949572 + 0.313550i \(0.101518\pi\)
−0.949572 + 0.313550i \(0.898482\pi\)
\(228\) − 10581.0i − 3.07343i
\(229\) −5082.23 −1.46656 −0.733282 0.679924i \(-0.762013\pi\)
−0.733282 + 0.679924i \(0.762013\pi\)
\(230\) −6601.35 −1.89252
\(231\) − 224.242i − 0.0638703i
\(232\) − 4462.99i − 1.26297i
\(233\) − 3271.12i − 0.919735i −0.887987 0.459868i \(-0.847897\pi\)
0.887987 0.459868i \(-0.152103\pi\)
\(234\) −2844.00 −0.794521
\(235\) 4788.92i 1.32934i
\(236\) 9712.73 2.67900
\(237\) −452.217 −0.123944
\(238\) 0 0
\(239\) −4905.70 −1.32771 −0.663857 0.747860i \(-0.731082\pi\)
−0.663857 + 0.747860i \(0.731082\pi\)
\(240\) −8295.00 −2.23100
\(241\) 494.108i 0.132068i 0.997817 + 0.0660338i \(0.0210345\pi\)
−0.997817 + 0.0660338i \(0.978965\pi\)
\(242\) −3606.03 −0.957869
\(243\) − 3195.88i − 0.843686i
\(244\) − 2122.52i − 0.556886i
\(245\) 5391.64i 1.40596i
\(246\) 8138.46 2.10931
\(247\) −4698.86 −1.21045
\(248\) 323.057i 0.0827183i
\(249\) − 4452.88i − 1.13329i
\(250\) 157.613i 0.0398734i
\(251\) −691.360 −0.173858 −0.0869288 0.996215i \(-0.527705\pi\)
−0.0869288 + 0.996215i \(0.527705\pi\)
\(252\) 162.190i 0.0405436i
\(253\) 3815.01 0.948014
\(254\) −9566.37 −2.36318
\(255\) 0 0
\(256\) −8332.94 −2.03441
\(257\) 2900.44 0.703986 0.351993 0.936003i \(-0.385504\pi\)
0.351993 + 0.936003i \(0.385504\pi\)
\(258\) 12521.6i 3.02156i
\(259\) −198.357 −0.0475880
\(260\) 12376.0i 2.95202i
\(261\) 1242.01i 0.294554i
\(262\) 8249.27i 1.94520i
\(263\) 5458.82 1.27987 0.639934 0.768430i \(-0.278962\pi\)
0.639934 + 0.768430i \(0.278962\pi\)
\(264\) 12458.1 2.90434
\(265\) − 6271.30i − 1.45375i
\(266\) 395.493i 0.0911626i
\(267\) 8480.67i 1.94385i
\(268\) −2537.14 −0.578286
\(269\) − 1028.77i − 0.233179i −0.993180 0.116590i \(-0.962804\pi\)
0.993180 0.116590i \(-0.0371962\pi\)
\(270\) −7263.14 −1.63711
\(271\) −4117.13 −0.922869 −0.461435 0.887174i \(-0.652665\pi\)
−0.461435 + 0.887174i \(0.652665\pi\)
\(272\) 0 0
\(273\) 231.254 0.0512679
\(274\) −13575.4 −2.99314
\(275\) 5575.36i 1.22257i
\(276\) −8859.32 −1.93213
\(277\) − 5787.84i − 1.25544i −0.778438 0.627721i \(-0.783988\pi\)
0.778438 0.627721i \(-0.216012\pi\)
\(278\) 6136.35i 1.32386i
\(279\) − 89.9040i − 0.0192918i
\(280\) 545.950 0.116524
\(281\) −2012.48 −0.427240 −0.213620 0.976917i \(-0.568525\pi\)
−0.213620 + 0.976917i \(0.568525\pi\)
\(282\) 9485.43i 2.00301i
\(283\) 558.874i 0.117391i 0.998276 + 0.0586954i \(0.0186941\pi\)
−0.998276 + 0.0586954i \(0.981306\pi\)
\(284\) 7306.87i 1.52670i
\(285\) 9911.84 2.06009
\(286\) − 10555.9i − 2.18245i
\(287\) −206.112 −0.0423917
\(288\) −829.198 −0.169656
\(289\) 0 0
\(290\) 7976.79 1.61522
\(291\) 8783.10 1.76933
\(292\) 8301.65i 1.66376i
\(293\) 2860.10 0.570268 0.285134 0.958488i \(-0.407962\pi\)
0.285134 + 0.958488i \(0.407962\pi\)
\(294\) 10679.3i 2.11846i
\(295\) 9098.52i 1.79572i
\(296\) − 11020.1i − 2.16395i
\(297\) 4197.46 0.820072
\(298\) 11544.7 2.24419
\(299\) 3934.30i 0.760958i
\(300\) − 12947.3i − 2.49170i
\(301\) − 317.119i − 0.0607257i
\(302\) −5757.70 −1.09708
\(303\) 947.151i 0.179579i
\(304\) −8454.76 −1.59511
\(305\) 1988.29 0.373276
\(306\) 0 0
\(307\) −4297.16 −0.798867 −0.399433 0.916762i \(-0.630793\pi\)
−0.399433 + 0.916762i \(0.630793\pi\)
\(308\) −601.989 −0.111368
\(309\) − 4303.58i − 0.792304i
\(310\) −577.406 −0.105789
\(311\) 2989.87i 0.545145i 0.962135 + 0.272572i \(0.0878744\pi\)
−0.962135 + 0.272572i \(0.912126\pi\)
\(312\) 12847.7i 2.33128i
\(313\) 3932.78i 0.710204i 0.934828 + 0.355102i \(0.115554\pi\)
−0.934828 + 0.355102i \(0.884446\pi\)
\(314\) −16072.6 −2.88863
\(315\) −151.933 −0.0271761
\(316\) 1214.00i 0.216116i
\(317\) 10623.2i 1.88221i 0.338120 + 0.941103i \(0.390209\pi\)
−0.338120 + 0.941103i \(0.609791\pi\)
\(318\) − 12421.6i − 2.19047i
\(319\) −4609.89 −0.809105
\(320\) − 5271.65i − 0.920920i
\(321\) 2861.51 0.497550
\(322\) 331.142 0.0573100
\(323\) 0 0
\(324\) −15291.0 −2.62192
\(325\) −5749.70 −0.981341
\(326\) − 4892.67i − 0.831226i
\(327\) −8024.41 −1.35704
\(328\) − 11450.9i − 1.92766i
\(329\) − 240.225i − 0.0402555i
\(330\) 22266.7i 3.71437i
\(331\) 7246.73 1.20337 0.601687 0.798732i \(-0.294496\pi\)
0.601687 + 0.798732i \(0.294496\pi\)
\(332\) −11954.0 −1.97608
\(333\) 3066.79i 0.504682i
\(334\) 182.309i 0.0298667i
\(335\) − 2376.70i − 0.387621i
\(336\) 416.100 0.0675599
\(337\) 4128.94i 0.667411i 0.942677 + 0.333706i \(0.108299\pi\)
−0.942677 + 0.333706i \(0.891701\pi\)
\(338\) −57.4084 −0.00923847
\(339\) 11820.4 1.89379
\(340\) 0 0
\(341\) 333.691 0.0529923
\(342\) 6114.71 0.966800
\(343\) − 541.412i − 0.0852289i
\(344\) 17618.1 2.76135
\(345\) − 8299.07i − 1.29509i
\(346\) − 14079.3i − 2.18759i
\(347\) − 6293.09i − 0.973575i −0.873520 0.486788i \(-0.838169\pi\)
0.873520 0.486788i \(-0.161831\pi\)
\(348\) 10705.2 1.64902
\(349\) 6188.65 0.949201 0.474600 0.880201i \(-0.342593\pi\)
0.474600 + 0.880201i \(0.342593\pi\)
\(350\) 483.940i 0.0739077i
\(351\) 4328.72i 0.658261i
\(352\) − 3077.68i − 0.466025i
\(353\) −1116.16 −0.168292 −0.0841460 0.996453i \(-0.526816\pi\)
−0.0841460 + 0.996453i \(0.526816\pi\)
\(354\) 18021.5i 2.70574i
\(355\) −6844.80 −1.02334
\(356\) 22766.8 3.38943
\(357\) 0 0
\(358\) 5821.68 0.859457
\(359\) −78.6313 −0.0115599 −0.00577995 0.999983i \(-0.501840\pi\)
−0.00577995 + 0.999983i \(0.501840\pi\)
\(360\) − 8440.91i − 1.23576i
\(361\) 3243.74 0.472917
\(362\) − 14304.9i − 2.07694i
\(363\) − 4533.42i − 0.655490i
\(364\) − 620.813i − 0.0893940i
\(365\) −7776.68 −1.11520
\(366\) 3938.22 0.562443
\(367\) − 6974.49i − 0.992004i −0.868321 0.496002i \(-0.834801\pi\)
0.868321 0.496002i \(-0.165199\pi\)
\(368\) 7079.07i 1.00278i
\(369\) 3186.69i 0.449574i
\(370\) 19696.4 2.76747
\(371\) 314.586i 0.0440229i
\(372\) −774.906 −0.108003
\(373\) 32.5559 0.00451925 0.00225963 0.999997i \(-0.499281\pi\)
0.00225963 + 0.999997i \(0.499281\pi\)
\(374\) 0 0
\(375\) −198.148 −0.0272862
\(376\) 13346.1 1.83052
\(377\) − 4754.04i − 0.649458i
\(378\) 364.339 0.0495756
\(379\) 5407.85i 0.732935i 0.930431 + 0.366468i \(0.119433\pi\)
−0.930431 + 0.366468i \(0.880567\pi\)
\(380\) − 26608.8i − 3.59212i
\(381\) − 12026.6i − 1.61717i
\(382\) −8103.97 −1.08543
\(383\) −2705.02 −0.360889 −0.180444 0.983585i \(-0.557754\pi\)
−0.180444 + 0.983585i \(0.557754\pi\)
\(384\) − 13842.8i − 1.83961i
\(385\) − 563.920i − 0.0746494i
\(386\) − 3966.74i − 0.523061i
\(387\) −4902.96 −0.644009
\(388\) − 23578.6i − 3.08511i
\(389\) 392.912 0.0512119 0.0256059 0.999672i \(-0.491848\pi\)
0.0256059 + 0.999672i \(0.491848\pi\)
\(390\) −22963.0 −2.98147
\(391\) 0 0
\(392\) 15025.8 1.93602
\(393\) −10370.8 −1.33114
\(394\) − 4867.85i − 0.622433i
\(395\) −1137.23 −0.144861
\(396\) 9307.32i 1.18109i
\(397\) 11750.1i 1.48544i 0.669601 + 0.742721i \(0.266465\pi\)
−0.669601 + 0.742721i \(0.733535\pi\)
\(398\) − 3544.98i − 0.446467i
\(399\) −497.206 −0.0623845
\(400\) −10345.6 −1.29319
\(401\) 2918.07i 0.363395i 0.983354 + 0.181697i \(0.0581591\pi\)
−0.983354 + 0.181697i \(0.941841\pi\)
\(402\) − 4707.54i − 0.584057i
\(403\) 344.125i 0.0425362i
\(404\) 2542.67 0.313125
\(405\) − 14324.0i − 1.75745i
\(406\) −400.138 −0.0489126
\(407\) −11382.8 −1.38630
\(408\) 0 0
\(409\) 5650.88 0.683174 0.341587 0.939850i \(-0.389036\pi\)
0.341587 + 0.939850i \(0.389036\pi\)
\(410\) 20466.5 2.46528
\(411\) − 17066.7i − 2.04827i
\(412\) −11553.2 −1.38151
\(413\) − 456.407i − 0.0543785i
\(414\) − 5119.78i − 0.607786i
\(415\) − 11198.0i − 1.32455i
\(416\) 3173.92 0.374072
\(417\) −7714.48 −0.905947
\(418\) 22695.5i 2.65568i
\(419\) − 14806.3i − 1.72633i −0.504920 0.863166i \(-0.668478\pi\)
0.504920 0.863166i \(-0.331522\pi\)
\(420\) 1309.55i 0.152142i
\(421\) 3314.27 0.383676 0.191838 0.981427i \(-0.438555\pi\)
0.191838 + 0.981427i \(0.438555\pi\)
\(422\) 18380.9i 2.12030i
\(423\) −3714.12 −0.426918
\(424\) −17477.4 −2.00183
\(425\) 0 0
\(426\) −13557.5 −1.54193
\(427\) −99.7383 −0.0113037
\(428\) − 7681.85i − 0.867561i
\(429\) 13270.6 1.49350
\(430\) 31489.1i 3.53149i
\(431\) − 12204.2i − 1.36394i −0.731381 0.681969i \(-0.761124\pi\)
0.731381 0.681969i \(-0.238876\pi\)
\(432\) 7788.75i 0.867446i
\(433\) −423.908 −0.0470479 −0.0235239 0.999723i \(-0.507489\pi\)
−0.0235239 + 0.999723i \(0.507489\pi\)
\(434\) 28.9643 0.00320353
\(435\) 10028.2i 1.10533i
\(436\) 21541.9i 2.36622i
\(437\) − 8458.91i − 0.925960i
\(438\) −15403.3 −1.68036
\(439\) 14528.7i 1.57953i 0.613407 + 0.789767i \(0.289799\pi\)
−0.613407 + 0.789767i \(0.710201\pi\)
\(440\) 31329.5 3.39449
\(441\) −4181.57 −0.451524
\(442\) 0 0
\(443\) 15763.6 1.69063 0.845317 0.534265i \(-0.179411\pi\)
0.845317 + 0.534265i \(0.179411\pi\)
\(444\) 26433.4 2.82539
\(445\) 21327.1i 2.27191i
\(446\) 8598.09 0.912850
\(447\) 14513.8i 1.53575i
\(448\) 264.441i 0.0278876i
\(449\) 5204.32i 0.547009i 0.961871 + 0.273504i \(0.0881828\pi\)
−0.961871 + 0.273504i \(0.911817\pi\)
\(450\) 7482.18 0.783808
\(451\) −11827.8 −1.23492
\(452\) − 31732.4i − 3.30213i
\(453\) − 7238.45i − 0.750755i
\(454\) 10683.1i 1.10436i
\(455\) 581.554 0.0599201
\(456\) − 27623.1i − 2.83678i
\(457\) 4156.78 0.425484 0.212742 0.977108i \(-0.431761\pi\)
0.212742 + 0.977108i \(0.431761\pi\)
\(458\) −25314.8 −2.58272
\(459\) 0 0
\(460\) −22279.3 −2.25821
\(461\) −6715.13 −0.678427 −0.339214 0.940709i \(-0.610161\pi\)
−0.339214 + 0.940709i \(0.610161\pi\)
\(462\) − 1116.96i − 0.112480i
\(463\) −14587.2 −1.46420 −0.732098 0.681199i \(-0.761459\pi\)
−0.732098 + 0.681199i \(0.761459\pi\)
\(464\) − 8554.05i − 0.855845i
\(465\) − 725.902i − 0.0723933i
\(466\) − 16293.6i − 1.61971i
\(467\) 7011.17 0.694729 0.347364 0.937730i \(-0.387077\pi\)
0.347364 + 0.937730i \(0.387077\pi\)
\(468\) −9598.36 −0.948043
\(469\) 119.222i 0.0117381i
\(470\) 23853.8i 2.34105i
\(471\) − 20206.1i − 1.97675i
\(472\) 25356.5 2.47272
\(473\) − 18198.0i − 1.76902i
\(474\) −2252.51 −0.218273
\(475\) 12362.1 1.19413
\(476\) 0 0
\(477\) 4863.80 0.466872
\(478\) −24435.5 −2.33819
\(479\) 10914.1i 1.04108i 0.853837 + 0.520540i \(0.174269\pi\)
−0.853837 + 0.520540i \(0.825731\pi\)
\(480\) −6695.10 −0.636642
\(481\) − 11738.7i − 1.11276i
\(482\) 2461.18i 0.232580i
\(483\) 416.305i 0.0392185i
\(484\) −12170.2 −1.14295
\(485\) 22087.6 2.06793
\(486\) − 15918.8i − 1.48579i
\(487\) − 8144.98i − 0.757873i −0.925423 0.378937i \(-0.876290\pi\)
0.925423 0.378937i \(-0.123710\pi\)
\(488\) − 5541.13i − 0.514007i
\(489\) 6150.95 0.568826
\(490\) 26856.0i 2.47598i
\(491\) −3767.66 −0.346297 −0.173149 0.984896i \(-0.555394\pi\)
−0.173149 + 0.984896i \(0.555394\pi\)
\(492\) 27466.9 2.51688
\(493\) 0 0
\(494\) −23405.2 −2.13168
\(495\) −8718.75 −0.791674
\(496\) 619.192i 0.0560535i
\(497\) 343.354 0.0309890
\(498\) − 22180.0i − 1.99580i
\(499\) − 12922.1i − 1.15926i −0.814879 0.579631i \(-0.803197\pi\)
0.814879 0.579631i \(-0.196803\pi\)
\(500\) 531.938i 0.0475780i
\(501\) −229.194 −0.0204384
\(502\) −3443.70 −0.306175
\(503\) − 2856.34i − 0.253196i −0.991954 0.126598i \(-0.959594\pi\)
0.991954 0.126598i \(-0.0404059\pi\)
\(504\) 423.419i 0.0374218i
\(505\) 2381.88i 0.209886i
\(506\) 19002.7 1.66951
\(507\) − 72.1726i − 0.00632208i
\(508\) −32286.1 −2.81981
\(509\) −1841.34 −0.160346 −0.0801729 0.996781i \(-0.525547\pi\)
−0.0801729 + 0.996781i \(0.525547\pi\)
\(510\) 0 0
\(511\) 390.100 0.0337710
\(512\) −23822.1 −2.05625
\(513\) − 9306.92i − 0.800995i
\(514\) 14447.2 1.23976
\(515\) − 10822.6i − 0.926018i
\(516\) 42259.9i 3.60540i
\(517\) − 13785.4i − 1.17269i
\(518\) −988.025 −0.0838056
\(519\) 17700.2 1.49702
\(520\) 32309.2i 2.72472i
\(521\) − 15200.3i − 1.27819i −0.769127 0.639096i \(-0.779309\pi\)
0.769127 0.639096i \(-0.220691\pi\)
\(522\) 6186.52i 0.518729i
\(523\) −20391.5 −1.70489 −0.852444 0.522818i \(-0.824881\pi\)
−0.852444 + 0.522818i \(0.824881\pi\)
\(524\) 27840.9i 2.32106i
\(525\) −608.399 −0.0505766
\(526\) 27190.6 2.25393
\(527\) 0 0
\(528\) 23878.1 1.96811
\(529\) 5084.45 0.417889
\(530\) − 31237.6i − 2.56014i
\(531\) −7056.49 −0.576696
\(532\) 1334.77i 0.108778i
\(533\) − 12197.7i − 0.991258i
\(534\) 42242.6i 3.42325i
\(535\) 7196.07 0.581520
\(536\) −6623.58 −0.533759
\(537\) 7318.89i 0.588144i
\(538\) − 5124.35i − 0.410644i
\(539\) − 15520.4i − 1.24028i
\(540\) −24512.8 −1.95345
\(541\) − 14367.0i − 1.14175i −0.821038 0.570874i \(-0.806604\pi\)
0.821038 0.570874i \(-0.193396\pi\)
\(542\) −20507.6 −1.62523
\(543\) 17983.9 1.42129
\(544\) 0 0
\(545\) −20179.6 −1.58606
\(546\) 1151.89 0.0902861
\(547\) 18943.7i 1.48076i 0.672190 + 0.740378i \(0.265354\pi\)
−0.672190 + 0.740378i \(0.734646\pi\)
\(548\) −45816.4 −3.57150
\(549\) 1542.05i 0.119878i
\(550\) 27771.1i 2.15303i
\(551\) 10221.4i 0.790283i
\(552\) −23128.5 −1.78336
\(553\) 57.0465 0.00438673
\(554\) − 28829.5i − 2.21092i
\(555\) 24761.8i 1.89384i
\(556\) 20709.9i 1.57967i
\(557\) −23122.6 −1.75895 −0.879477 0.475941i \(-0.842108\pi\)
−0.879477 + 0.475941i \(0.842108\pi\)
\(558\) − 447.816i − 0.0339741i
\(559\) 18767.0 1.41997
\(560\) 1046.40 0.0789617
\(561\) 0 0
\(562\) −10024.3 −0.752398
\(563\) 13150.5 0.984416 0.492208 0.870478i \(-0.336190\pi\)
0.492208 + 0.870478i \(0.336190\pi\)
\(564\) 32012.9i 2.39005i
\(565\) 29725.7 2.21340
\(566\) 2783.77i 0.206733i
\(567\) 718.534i 0.0532197i
\(568\) 19075.6i 1.40915i
\(569\) 15690.7 1.15605 0.578023 0.816021i \(-0.303824\pi\)
0.578023 + 0.816021i \(0.303824\pi\)
\(570\) 49371.3 3.62796
\(571\) 18135.9i 1.32918i 0.747207 + 0.664592i \(0.231394\pi\)
−0.747207 + 0.664592i \(0.768606\pi\)
\(572\) − 35625.6i − 2.60416i
\(573\) − 10188.1i − 0.742785i
\(574\) −1026.65 −0.0746546
\(575\) − 10350.6i − 0.750698i
\(576\) 4088.51 0.295754
\(577\) −15740.7 −1.13569 −0.567847 0.823134i \(-0.692223\pi\)
−0.567847 + 0.823134i \(0.692223\pi\)
\(578\) 0 0
\(579\) 4986.89 0.357942
\(580\) 26921.3 1.92732
\(581\) 561.724i 0.0401106i
\(582\) 43749.0 3.11590
\(583\) 18052.6i 1.28244i
\(584\) 21672.7i 1.53565i
\(585\) − 8991.38i − 0.635466i
\(586\) 14246.3 1.00428
\(587\) 9153.33 0.643609 0.321804 0.946806i \(-0.395711\pi\)
0.321804 + 0.946806i \(0.395711\pi\)
\(588\) 36042.0i 2.52780i
\(589\) − 739.883i − 0.0517595i
\(590\) 45320.1i 3.16237i
\(591\) 6119.75 0.425944
\(592\) − 21121.7i − 1.46638i
\(593\) 3898.87 0.269995 0.134998 0.990846i \(-0.456897\pi\)
0.134998 + 0.990846i \(0.456897\pi\)
\(594\) 20907.7 1.44420
\(595\) 0 0
\(596\) 38963.0 2.67783
\(597\) 4456.68 0.305527
\(598\) 19596.9i 1.34010i
\(599\) −11841.6 −0.807740 −0.403870 0.914816i \(-0.632335\pi\)
−0.403870 + 0.914816i \(0.632335\pi\)
\(600\) − 33800.6i − 2.29984i
\(601\) 17152.8i 1.16419i 0.813122 + 0.582093i \(0.197766\pi\)
−0.813122 + 0.582093i \(0.802234\pi\)
\(602\) − 1579.58i − 0.106942i
\(603\) 1843.29 0.124485
\(604\) −19432.0 −1.30907
\(605\) − 11400.6i − 0.766114i
\(606\) 4717.80i 0.316250i
\(607\) 10576.6i 0.707234i 0.935390 + 0.353617i \(0.115048\pi\)
−0.935390 + 0.353617i \(0.884952\pi\)
\(608\) −6824.05 −0.455184
\(609\) − 503.045i − 0.0334719i
\(610\) 9903.77 0.657364
\(611\) 14216.5 0.941306
\(612\) 0 0
\(613\) 16518.7 1.08839 0.544196 0.838958i \(-0.316835\pi\)
0.544196 + 0.838958i \(0.316835\pi\)
\(614\) −21404.4 −1.40686
\(615\) 25730.0i 1.68705i
\(616\) −1571.58 −0.102793
\(617\) − 14629.4i − 0.954547i −0.878755 0.477274i \(-0.841625\pi\)
0.878755 0.477274i \(-0.158375\pi\)
\(618\) − 21436.3i − 1.39530i
\(619\) 19584.0i 1.27164i 0.771836 + 0.635822i \(0.219339\pi\)
−0.771836 + 0.635822i \(0.780661\pi\)
\(620\) −1948.72 −0.126230
\(621\) −7792.57 −0.503551
\(622\) 14892.7i 0.960035i
\(623\) − 1069.82i − 0.0687987i
\(624\) 24624.7i 1.57977i
\(625\) −15872.1 −1.01582
\(626\) 19589.3i 1.25072i
\(627\) −28532.3 −1.81734
\(628\) −54244.3 −3.44679
\(629\) 0 0
\(630\) −756.786 −0.0478588
\(631\) −28856.7 −1.82055 −0.910276 0.414002i \(-0.864131\pi\)
−0.910276 + 0.414002i \(0.864131\pi\)
\(632\) 3169.31i 0.199476i
\(633\) −23108.0 −1.45097
\(634\) 52914.7i 3.31469i
\(635\) − 30244.4i − 1.89010i
\(636\) − 41922.3i − 2.61372i
\(637\) 16005.8 0.995559
\(638\) −22962.1 −1.42489
\(639\) − 5308.58i − 0.328645i
\(640\) − 34811.6i − 2.15008i
\(641\) 9419.79i 0.580436i 0.956961 + 0.290218i \(0.0937278\pi\)
−0.956961 + 0.290218i \(0.906272\pi\)
\(642\) 14253.3 0.876218
\(643\) − 2848.83i − 0.174723i −0.996177 0.0873615i \(-0.972156\pi\)
0.996177 0.0873615i \(-0.0278435\pi\)
\(644\) 1117.59 0.0683839
\(645\) −39587.4 −2.41667
\(646\) 0 0
\(647\) −6881.30 −0.418132 −0.209066 0.977901i \(-0.567042\pi\)
−0.209066 + 0.977901i \(0.567042\pi\)
\(648\) −39919.4 −2.42003
\(649\) − 26191.1i − 1.58411i
\(650\) −28639.5 −1.72821
\(651\) 36.4133i 0.00219224i
\(652\) − 16512.5i − 0.991841i
\(653\) − 10521.5i − 0.630534i −0.949003 0.315267i \(-0.897906\pi\)
0.949003 0.315267i \(-0.102094\pi\)
\(654\) −39969.9 −2.38983
\(655\) −26080.3 −1.55579
\(656\) − 21947.6i − 1.30626i
\(657\) − 6031.32i − 0.358149i
\(658\) − 1196.57i − 0.0708925i
\(659\) 26606.5 1.57275 0.786374 0.617751i \(-0.211956\pi\)
0.786374 + 0.617751i \(0.211956\pi\)
\(660\) 75149.1i 4.43208i
\(661\) 15511.7 0.912758 0.456379 0.889785i \(-0.349146\pi\)
0.456379 + 0.889785i \(0.349146\pi\)
\(662\) 36096.3 2.11922
\(663\) 0 0
\(664\) −31207.6 −1.82393
\(665\) −1250.36 −0.0729128
\(666\) 15275.8i 0.888777i
\(667\) 8558.25 0.496817
\(668\) 615.284i 0.0356378i
\(669\) 10809.3i 0.624683i
\(670\) − 11838.5i − 0.682626i
\(671\) −5723.52 −0.329291
\(672\) 335.845 0.0192790
\(673\) 5711.21i 0.327119i 0.986533 + 0.163559i \(0.0522975\pi\)
−0.986533 + 0.163559i \(0.947702\pi\)
\(674\) 20566.4i 1.17535i
\(675\) − 11388.3i − 0.649386i
\(676\) −193.751 −0.0110236
\(677\) 398.222i 0.0226070i 0.999936 + 0.0113035i \(0.00359809\pi\)
−0.999936 + 0.0113035i \(0.996402\pi\)
\(678\) 58877.8 3.33509
\(679\) −1107.97 −0.0626217
\(680\) 0 0
\(681\) −13430.5 −0.755740
\(682\) 1662.13 0.0933228
\(683\) − 6504.72i − 0.364416i −0.983260 0.182208i \(-0.941676\pi\)
0.983260 0.182208i \(-0.0583244\pi\)
\(684\) 20636.9 1.15361
\(685\) − 42919.1i − 2.39395i
\(686\) − 2696.80i − 0.150094i
\(687\) − 31825.2i − 1.76741i
\(688\) 33767.9 1.87121
\(689\) −18617.1 −1.02940
\(690\) − 41338.0i − 2.28074i
\(691\) − 7641.66i − 0.420698i −0.977626 0.210349i \(-0.932540\pi\)
0.977626 0.210349i \(-0.0674601\pi\)
\(692\) − 47516.9i − 2.61029i
\(693\) 437.357 0.0239737
\(694\) − 31346.1i − 1.71453i
\(695\) −19400.2 −1.05884
\(696\) 27947.5 1.52205
\(697\) 0 0
\(698\) 30826.0 1.67160
\(699\) 20484.0 1.10840
\(700\) 1633.28i 0.0881887i
\(701\) 27948.0 1.50582 0.752912 0.658122i \(-0.228649\pi\)
0.752912 + 0.658122i \(0.228649\pi\)
\(702\) 21561.5i 1.15924i
\(703\) 25238.7i 1.35405i
\(704\) 15175.0i 0.812402i
\(705\) −29988.5 −1.60203
\(706\) −5559.63 −0.296373
\(707\) − 119.482i − 0.00635583i
\(708\) 60821.7i 3.22856i
\(709\) 28431.5i 1.50602i 0.658009 + 0.753010i \(0.271399\pi\)
−0.658009 + 0.753010i \(0.728601\pi\)
\(710\) −34094.2 −1.80216
\(711\) − 881.993i − 0.0465223i
\(712\) 59435.9 3.12845
\(713\) −619.495 −0.0325390
\(714\) 0 0
\(715\) 33372.7 1.74555
\(716\) 19647.9 1.02553
\(717\) − 30719.8i − 1.60007i
\(718\) −391.666 −0.0203577
\(719\) 21104.4i 1.09466i 0.836917 + 0.547330i \(0.184356\pi\)
−0.836917 + 0.547330i \(0.815644\pi\)
\(720\) − 16178.4i − 0.837406i
\(721\) 542.890i 0.0280420i
\(722\) 16157.2 0.832838
\(723\) −3094.13 −0.159159
\(724\) − 48278.5i − 2.47826i
\(725\) 12507.3i 0.640701i
\(726\) − 22581.2i − 1.15436i
\(727\) −7655.66 −0.390554 −0.195277 0.980748i \(-0.562561\pi\)
−0.195277 + 0.980748i \(0.562561\pi\)
\(728\) − 1620.72i − 0.0825108i
\(729\) −4546.28 −0.230975
\(730\) −38736.0 −1.96395
\(731\) 0 0
\(732\) 13291.3 0.671122
\(733\) −1921.12 −0.0968052 −0.0484026 0.998828i \(-0.515413\pi\)
−0.0484026 + 0.998828i \(0.515413\pi\)
\(734\) − 34740.2i − 1.74698i
\(735\) −33762.8 −1.69437
\(736\) 5713.70i 0.286154i
\(737\) 6841.60i 0.341945i
\(738\) 15873.1i 0.791728i
\(739\) −24081.6 −1.19872 −0.599362 0.800478i \(-0.704579\pi\)
−0.599362 + 0.800478i \(0.704579\pi\)
\(740\) 66474.4 3.30222
\(741\) − 29424.5i − 1.45875i
\(742\) 1566.97i 0.0775271i
\(743\) − 17540.0i − 0.866058i −0.901380 0.433029i \(-0.857445\pi\)
0.901380 0.433029i \(-0.142555\pi\)
\(744\) −2023.00 −0.0996866
\(745\) 36499.0i 1.79493i
\(746\) 162.163 0.00795870
\(747\) 8684.80 0.425382
\(748\) 0 0
\(749\) −360.975 −0.0176098
\(750\) −986.984 −0.0480528
\(751\) 21239.6i 1.03202i 0.856583 + 0.516009i \(0.172583\pi\)
−0.856583 + 0.516009i \(0.827417\pi\)
\(752\) 25580.0 1.24044
\(753\) − 4329.34i − 0.209522i
\(754\) − 23680.1i − 1.14374i
\(755\) − 18203.1i − 0.877457i
\(756\) 1229.63 0.0591550
\(757\) 22831.4 1.09620 0.548098 0.836414i \(-0.315352\pi\)
0.548098 + 0.836414i \(0.315352\pi\)
\(758\) 26936.7i 1.29075i
\(759\) 23889.8i 1.14248i
\(760\) − 69466.1i − 3.31553i
\(761\) −12398.1 −0.590579 −0.295289 0.955408i \(-0.595416\pi\)
−0.295289 + 0.955408i \(0.595416\pi\)
\(762\) − 59905.2i − 2.84795i
\(763\) 1012.27 0.0480295
\(764\) −27350.6 −1.29517
\(765\) 0 0
\(766\) −13473.8 −0.635548
\(767\) 27010.1 1.27155
\(768\) − 52181.3i − 2.45173i
\(769\) −40338.4 −1.89160 −0.945800 0.324751i \(-0.894720\pi\)
−0.945800 + 0.324751i \(0.894720\pi\)
\(770\) − 2808.91i − 0.131462i
\(771\) 18162.7i 0.848397i
\(772\) − 13387.6i − 0.624131i
\(773\) 6385.94 0.297136 0.148568 0.988902i \(-0.452534\pi\)
0.148568 + 0.988902i \(0.452534\pi\)
\(774\) −24421.9 −1.13414
\(775\) − 905.348i − 0.0419626i
\(776\) − 61555.4i − 2.84756i
\(777\) − 1242.12i − 0.0573499i
\(778\) 1957.11 0.0901874
\(779\) 26225.5i 1.20620i
\(780\) −77499.0 −3.55758
\(781\) 19703.5 0.902749
\(782\) 0 0
\(783\) 9416.22 0.429768
\(784\) 28799.5 1.31193
\(785\) − 50814.0i − 2.31036i
\(786\) −51657.4 −2.34422
\(787\) 26132.8i 1.18365i 0.806066 + 0.591826i \(0.201593\pi\)
−0.806066 + 0.591826i \(0.798407\pi\)
\(788\) − 16428.8i − 0.742704i
\(789\) 34183.4i 1.54241i
\(790\) −5664.58 −0.255110
\(791\) −1491.12 −0.0670268
\(792\) 24298.1i 1.09015i
\(793\) − 5902.49i − 0.264317i
\(794\) 58527.8i 2.61596i
\(795\) 39271.3 1.75196
\(796\) − 11964.2i − 0.532737i
\(797\) −8629.21 −0.383516 −0.191758 0.981442i \(-0.561419\pi\)
−0.191758 + 0.981442i \(0.561419\pi\)
\(798\) −2476.60 −0.109863
\(799\) 0 0
\(800\) −8350.16 −0.369028
\(801\) −16540.5 −0.729626
\(802\) 14535.0i 0.639962i
\(803\) 22386.0 0.983793
\(804\) − 15887.7i − 0.696913i
\(805\) 1046.92i 0.0458372i
\(806\) 1714.10i 0.0749090i
\(807\) 6442.22 0.281012
\(808\) 6638.01 0.289015
\(809\) 42653.7i 1.85368i 0.375460 + 0.926839i \(0.377485\pi\)
−0.375460 + 0.926839i \(0.622515\pi\)
\(810\) − 71348.7i − 3.09498i
\(811\) 45388.0i 1.96521i 0.185700 + 0.982607i \(0.440545\pi\)
−0.185700 + 0.982607i \(0.559455\pi\)
\(812\) −1350.45 −0.0583639
\(813\) − 25781.7i − 1.11218i
\(814\) −56698.2 −2.44136
\(815\) 15468.3 0.664824
\(816\) 0 0
\(817\) −40349.9 −1.72786
\(818\) 28147.3 1.20311
\(819\) 451.033i 0.0192434i
\(820\) 69073.4 2.94164
\(821\) − 16898.6i − 0.718349i −0.933270 0.359175i \(-0.883058\pi\)
0.933270 0.359175i \(-0.116942\pi\)
\(822\) − 85010.1i − 3.60714i
\(823\) 38258.3i 1.62042i 0.586143 + 0.810208i \(0.300646\pi\)
−0.586143 + 0.810208i \(0.699354\pi\)
\(824\) −30161.2 −1.27514
\(825\) −34913.2 −1.47336
\(826\) − 2273.38i − 0.0957641i
\(827\) 30489.3i 1.28200i 0.767540 + 0.641001i \(0.221480\pi\)
−0.767540 + 0.641001i \(0.778520\pi\)
\(828\) − 17279.0i − 0.725226i
\(829\) 44358.5 1.85843 0.929213 0.369545i \(-0.120486\pi\)
0.929213 + 0.369545i \(0.120486\pi\)
\(830\) − 55777.9i − 2.33263i
\(831\) 36243.8 1.51298
\(832\) −15649.6 −0.652104
\(833\) 0 0
\(834\) −38426.2 −1.59543
\(835\) −576.374 −0.0238877
\(836\) 76596.4i 3.16883i
\(837\) −681.600 −0.0281476
\(838\) − 73750.6i − 3.04018i
\(839\) 20819.6i 0.856702i 0.903612 + 0.428351i \(0.140905\pi\)
−0.903612 + 0.428351i \(0.859095\pi\)
\(840\) 3418.77i 0.140427i
\(841\) 14047.6 0.575980
\(842\) 16508.5 0.675678
\(843\) − 12602.3i − 0.514882i
\(844\) 62034.6i 2.53000i
\(845\) − 181.498i − 0.00738903i
\(846\) −18500.2 −0.751831
\(847\) 571.884i 0.0231997i
\(848\) −33498.2 −1.35653
\(849\) −3499.70 −0.141472
\(850\) 0 0
\(851\) 21132.1 0.851233
\(852\) −45756.0 −1.83988
\(853\) 43406.9i 1.74235i 0.490973 + 0.871175i \(0.336641\pi\)
−0.490973 + 0.871175i \(0.663359\pi\)
\(854\) −496.801 −0.0199065
\(855\) 19331.8i 0.773257i
\(856\) − 20054.6i − 0.800760i
\(857\) − 7893.90i − 0.314645i −0.987547 0.157322i \(-0.949714\pi\)
0.987547 0.157322i \(-0.0502862\pi\)
\(858\) 66101.5 2.63015
\(859\) 10441.9 0.414751 0.207376 0.978261i \(-0.433508\pi\)
0.207376 + 0.978261i \(0.433508\pi\)
\(860\) 106274.i 4.21387i
\(861\) − 1290.69i − 0.0510877i
\(862\) − 60789.9i − 2.40198i
\(863\) 39784.6 1.56928 0.784638 0.619954i \(-0.212849\pi\)
0.784638 + 0.619954i \(0.212849\pi\)
\(864\) 6286.50i 0.247536i
\(865\) 44512.1 1.74966
\(866\) −2111.51 −0.0828544
\(867\) 0 0
\(868\) 97.7532 0.00382253
\(869\) 3273.63 0.127791
\(870\) 49951.1i 1.94655i
\(871\) −7055.53 −0.274475
\(872\) 56238.2i 2.18402i
\(873\) 17130.3i 0.664117i
\(874\) − 42134.2i − 1.63068i
\(875\) 24.9961 0.000965739 0
\(876\) −51985.4 −2.00505
\(877\) − 11135.4i − 0.428752i −0.976751 0.214376i \(-0.931228\pi\)
0.976751 0.214376i \(-0.0687717\pi\)
\(878\) 72367.9i 2.78166i
\(879\) 17910.1i 0.687250i
\(880\) 60048.2 2.30025
\(881\) − 18890.9i − 0.722416i −0.932485 0.361208i \(-0.882364\pi\)
0.932485 0.361208i \(-0.117636\pi\)
\(882\) −20828.6 −0.795164
\(883\) 36453.6 1.38931 0.694656 0.719342i \(-0.255557\pi\)
0.694656 + 0.719342i \(0.255557\pi\)
\(884\) 0 0
\(885\) −56975.5 −2.16408
\(886\) 78519.2 2.97732
\(887\) 23100.3i 0.874446i 0.899353 + 0.437223i \(0.144038\pi\)
−0.899353 + 0.437223i \(0.855962\pi\)
\(888\) 69008.2 2.60784
\(889\) 1517.14i 0.0572366i
\(890\) 106231.i 4.00098i
\(891\) 41233.3i 1.55036i
\(892\) 29018.2 1.08924
\(893\) −30566.0 −1.14541
\(894\) 72293.8i 2.70455i
\(895\) 18405.4i 0.687403i
\(896\) 1746.25i 0.0651093i
\(897\) −24636.8 −0.917057
\(898\) 25922.9i 0.963318i
\(899\) 748.572 0.0277712
\(900\) 25252.0 0.935260
\(901\) 0 0
\(902\) −58915.0 −2.17478
\(903\) 1985.82 0.0731825
\(904\) − 82841.8i − 3.04787i
\(905\) 45225.5 1.66116
\(906\) − 36055.1i − 1.32213i
\(907\) − 25240.6i − 0.924036i −0.886871 0.462018i \(-0.847126\pi\)
0.886871 0.462018i \(-0.152874\pi\)
\(908\) 36054.9i 1.31776i
\(909\) −1847.30 −0.0674050
\(910\) 2896.74 0.105523
\(911\) − 12331.2i − 0.448465i −0.974536 0.224232i \(-0.928013\pi\)
0.974536 0.224232i \(-0.0719874\pi\)
\(912\) − 52944.2i − 1.92232i
\(913\) 32234.8i 1.16847i
\(914\) 20705.1 0.749304
\(915\) 12450.8i 0.449848i
\(916\) −85436.4 −3.08177
\(917\) 1308.26 0.0471130
\(918\) 0 0
\(919\) 40235.8 1.44424 0.722121 0.691767i \(-0.243168\pi\)
0.722121 + 0.691767i \(0.243168\pi\)
\(920\) −58163.2 −2.08433
\(921\) − 26909.1i − 0.962741i
\(922\) −33448.4 −1.19475
\(923\) 20319.6i 0.724625i
\(924\) − 3769.69i − 0.134214i
\(925\) 30883.1i 1.09776i
\(926\) −72659.3 −2.57855
\(927\) 8393.60 0.297392
\(928\) − 6904.19i − 0.244225i
\(929\) − 45692.0i − 1.61368i −0.590772 0.806838i \(-0.701177\pi\)
0.590772 0.806838i \(-0.298823\pi\)
\(930\) − 3615.75i − 0.127489i
\(931\) −34413.0 −1.21143
\(932\) − 54990.2i − 1.93269i
\(933\) −18722.7 −0.656972
\(934\) 34923.0 1.22346
\(935\) 0 0
\(936\) −25057.9 −0.875045
\(937\) 3141.20 0.109518 0.0547590 0.998500i \(-0.482561\pi\)
0.0547590 + 0.998500i \(0.482561\pi\)
\(938\) 593.850i 0.0206715i
\(939\) −24627.3 −0.855891
\(940\) 80505.5i 2.79341i
\(941\) 24333.2i 0.842975i 0.906834 + 0.421487i \(0.138492\pi\)
−0.906834 + 0.421487i \(0.861508\pi\)
\(942\) − 100648.i − 3.48119i
\(943\) 21958.3 0.758284
\(944\) 48599.8 1.67562
\(945\) 1151.87i 0.0396511i
\(946\) − 90645.0i − 3.11535i
\(947\) − 39879.6i − 1.36844i −0.729276 0.684220i \(-0.760143\pi\)
0.729276 0.684220i \(-0.239857\pi\)
\(948\) −7602.12 −0.260449
\(949\) 23086.0i 0.789678i
\(950\) 61576.1 2.10294
\(951\) −66523.2 −2.26831
\(952\) 0 0
\(953\) −26021.7 −0.884496 −0.442248 0.896893i \(-0.645819\pi\)
−0.442248 + 0.896893i \(0.645819\pi\)
\(954\) 24226.8 0.822193
\(955\) − 25621.0i − 0.868141i
\(956\) −82468.8 −2.78999
\(957\) − 28867.4i − 0.975080i
\(958\) 54363.6i 1.83341i
\(959\) 2152.94i 0.0724944i
\(960\) 33011.4 1.10983
\(961\) 29736.8 0.998181
\(962\) − 58471.1i − 1.95965i
\(963\) 5581.01i 0.186756i
\(964\) 8306.36i 0.277520i
\(965\) 12541.0 0.418350
\(966\) 2073.63i 0.0690662i
\(967\) −42806.0 −1.42352 −0.711762 0.702420i \(-0.752103\pi\)
−0.711762 + 0.702420i \(0.752103\pi\)
\(968\) −31772.0 −1.05495
\(969\) 0 0
\(970\) 110019. 3.64176
\(971\) 19147.5 0.632825 0.316413 0.948622i \(-0.397522\pi\)
0.316413 + 0.948622i \(0.397522\pi\)
\(972\) − 53725.3i − 1.77288i
\(973\) 973.170 0.0320641
\(974\) − 40570.5i − 1.33466i
\(975\) − 36004.9i − 1.18265i
\(976\) − 10620.5i − 0.348313i
\(977\) −8209.83 −0.268839 −0.134420 0.990925i \(-0.542917\pi\)
−0.134420 + 0.990925i \(0.542917\pi\)
\(978\) 30638.2 1.00174
\(979\) − 61392.3i − 2.00419i
\(980\) 90637.8i 2.95441i
\(981\) − 15650.6i − 0.509364i
\(982\) −18766.9 −0.609852
\(983\) 35203.4i 1.14223i 0.820870 + 0.571116i \(0.193489\pi\)
−0.820870 + 0.571116i \(0.806511\pi\)
\(984\) 71706.3 2.32308
\(985\) 15389.9 0.497829
\(986\) 0 0
\(987\) 1504.31 0.0485132
\(988\) −78991.6 −2.54358
\(989\) 33784.5i 1.08623i
\(990\) −43428.5 −1.39419
\(991\) − 5669.58i − 0.181736i −0.995863 0.0908678i \(-0.971036\pi\)
0.995863 0.0908678i \(-0.0289641\pi\)
\(992\) 499.765i 0.0159955i
\(993\) 45379.5i 1.45023i
\(994\) 1710.26 0.0545737
\(995\) 11207.6 0.357089
\(996\) − 74856.5i − 2.38144i
\(997\) 27125.7i 0.861666i 0.902432 + 0.430833i \(0.141780\pi\)
−0.902432 + 0.430833i \(0.858220\pi\)
\(998\) − 64365.4i − 2.04153i
\(999\) 23250.6 0.736353
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 289.4.b.f.288.22 24
17.4 even 4 289.4.a.i.1.2 yes 12
17.13 even 4 289.4.a.h.1.2 12
17.16 even 2 inner 289.4.b.f.288.21 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.2 12 17.13 even 4
289.4.a.i.1.2 yes 12 17.4 even 4
289.4.b.f.288.21 24 17.16 even 2 inner
289.4.b.f.288.22 24 1.1 even 1 trivial