Properties

Label 1058.4.a.i.1.2
Level $1058$
Weight $4$
Character 1058.1
Self dual yes
Analytic conductor $62.424$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1058,4,Mod(1,1058)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1058, 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("1058.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1058 = 2 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1058.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: \(62.4240207861\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{26}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 26 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(5.09902\) of defining polynomial
Character \(\chi\) \(=\) 1058.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -4.00000 q^{3} +4.00000 q^{4} +10.1980 q^{5} -8.00000 q^{6} +20.3961 q^{7} +8.00000 q^{8} -11.0000 q^{9} +20.3961 q^{10} +71.3863 q^{11} -16.0000 q^{12} -42.0000 q^{13} +40.7922 q^{14} -40.7922 q^{15} +16.0000 q^{16} +20.3961 q^{17} -22.0000 q^{18} +91.7824 q^{19} +40.7922 q^{20} -81.5843 q^{21} +142.773 q^{22} -32.0000 q^{24} -21.0000 q^{25} -84.0000 q^{26} +152.000 q^{27} +81.5843 q^{28} -22.0000 q^{29} -81.5843 q^{30} +296.000 q^{31} +32.0000 q^{32} -285.545 q^{33} +40.7922 q^{34} +208.000 q^{35} -44.0000 q^{36} -275.347 q^{37} +183.565 q^{38} +168.000 q^{39} +81.5843 q^{40} -318.000 q^{41} -163.169 q^{42} +316.139 q^{43} +285.545 q^{44} -112.178 q^{45} -184.000 q^{47} -64.0000 q^{48} +73.0000 q^{49} -42.0000 q^{50} -81.5843 q^{51} -168.000 q^{52} +91.7824 q^{53} +304.000 q^{54} +728.000 q^{55} +163.169 q^{56} -367.129 q^{57} -44.0000 q^{58} -500.000 q^{59} -163.169 q^{60} +30.5941 q^{61} +592.000 q^{62} -224.357 q^{63} +64.0000 q^{64} -428.318 q^{65} -571.090 q^{66} -642.476 q^{67} +81.5843 q^{68} +416.000 q^{70} +224.000 q^{71} -88.0000 q^{72} -210.000 q^{73} -550.694 q^{74} +84.0000 q^{75} +367.129 q^{76} +1456.00 q^{77} +336.000 q^{78} +1080.99 q^{79} +163.169 q^{80} -311.000 q^{81} -636.000 q^{82} +1152.38 q^{83} -326.337 q^{84} +208.000 q^{85} +632.278 q^{86} +88.0000 q^{87} +571.090 q^{88} -815.843 q^{89} -224.357 q^{90} -856.635 q^{91} -1184.00 q^{93} -368.000 q^{94} +936.000 q^{95} -128.000 q^{96} +1244.16 q^{97} +146.000 q^{98} -785.249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} - 8 q^{3} + 8 q^{4} - 16 q^{6} + 16 q^{8} - 22 q^{9} - 32 q^{12} - 84 q^{13} + 32 q^{16} - 44 q^{18} - 64 q^{24} - 42 q^{25} - 168 q^{26} + 304 q^{27} - 44 q^{29} + 592 q^{31} + 64 q^{32}+ \cdots + 292 q^{98}+O(q^{100}) \) 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
\(3\) −4.00000 −0.769800 −0.384900 0.922958i \(-0.625764\pi\)
−0.384900 + 0.922958i \(0.625764\pi\)
\(4\) 4.00000 0.500000
\(5\) 10.1980 0.912140 0.456070 0.889944i \(-0.349257\pi\)
0.456070 + 0.889944i \(0.349257\pi\)
\(6\) −8.00000 −0.544331
\(7\) 20.3961 1.10128 0.550642 0.834741i \(-0.314383\pi\)
0.550642 + 0.834741i \(0.314383\pi\)
\(8\) 8.00000 0.353553
\(9\) −11.0000 −0.407407
\(10\) 20.3961 0.644981
\(11\) 71.3863 1.95671 0.978353 0.206942i \(-0.0663511\pi\)
0.978353 + 0.206942i \(0.0663511\pi\)
\(12\) −16.0000 −0.384900
\(13\) −42.0000 −0.896054 −0.448027 0.894020i \(-0.647873\pi\)
−0.448027 + 0.894020i \(0.647873\pi\)
\(14\) 40.7922 0.778726
\(15\) −40.7922 −0.702166
\(16\) 16.0000 0.250000
\(17\) 20.3961 0.290987 0.145493 0.989359i \(-0.453523\pi\)
0.145493 + 0.989359i \(0.453523\pi\)
\(18\) −22.0000 −0.288081
\(19\) 91.7824 1.10823 0.554114 0.832441i \(-0.313057\pi\)
0.554114 + 0.832441i \(0.313057\pi\)
\(20\) 40.7922 0.456070
\(21\) −81.5843 −0.847769
\(22\) 142.773 1.38360
\(23\) 0 0
\(24\) −32.0000 −0.272166
\(25\) −21.0000 −0.168000
\(26\) −84.0000 −0.633606
\(27\) 152.000 1.08342
\(28\) 81.5843 0.550642
\(29\) −22.0000 −0.140872 −0.0704362 0.997516i \(-0.522439\pi\)
−0.0704362 + 0.997516i \(0.522439\pi\)
\(30\) −81.5843 −0.496506
\(31\) 296.000 1.71494 0.857470 0.514533i \(-0.172035\pi\)
0.857470 + 0.514533i \(0.172035\pi\)
\(32\) 32.0000 0.176777
\(33\) −285.545 −1.50627
\(34\) 40.7922 0.205759
\(35\) 208.000 1.00453
\(36\) −44.0000 −0.203704
\(37\) −275.347 −1.22343 −0.611713 0.791080i \(-0.709519\pi\)
−0.611713 + 0.791080i \(0.709519\pi\)
\(38\) 183.565 0.783635
\(39\) 168.000 0.689783
\(40\) 81.5843 0.322490
\(41\) −318.000 −1.21130 −0.605649 0.795732i \(-0.707087\pi\)
−0.605649 + 0.795732i \(0.707087\pi\)
\(42\) −163.169 −0.599463
\(43\) 316.139 1.12118 0.560590 0.828093i \(-0.310574\pi\)
0.560590 + 0.828093i \(0.310574\pi\)
\(44\) 285.545 0.978353
\(45\) −112.178 −0.371613
\(46\) 0 0
\(47\) −184.000 −0.571046 −0.285523 0.958372i \(-0.592167\pi\)
−0.285523 + 0.958372i \(0.592167\pi\)
\(48\) −64.0000 −0.192450
\(49\) 73.0000 0.212828
\(50\) −42.0000 −0.118794
\(51\) −81.5843 −0.224002
\(52\) −168.000 −0.448027
\(53\) 91.7824 0.237873 0.118937 0.992902i \(-0.462051\pi\)
0.118937 + 0.992902i \(0.462051\pi\)
\(54\) 304.000 0.766096
\(55\) 728.000 1.78479
\(56\) 163.169 0.389363
\(57\) −367.129 −0.853114
\(58\) −44.0000 −0.0996118
\(59\) −500.000 −1.10330 −0.551648 0.834077i \(-0.686001\pi\)
−0.551648 + 0.834077i \(0.686001\pi\)
\(60\) −163.169 −0.351083
\(61\) 30.5941 0.0642160 0.0321080 0.999484i \(-0.489778\pi\)
0.0321080 + 0.999484i \(0.489778\pi\)
\(62\) 592.000 1.21265
\(63\) −224.357 −0.448672
\(64\) 64.0000 0.125000
\(65\) −428.318 −0.817327
\(66\) −571.090 −1.06510
\(67\) −642.476 −1.17151 −0.585754 0.810489i \(-0.699201\pi\)
−0.585754 + 0.810489i \(0.699201\pi\)
\(68\) 81.5843 0.145493
\(69\) 0 0
\(70\) 416.000 0.710307
\(71\) 224.000 0.374421 0.187211 0.982320i \(-0.440055\pi\)
0.187211 + 0.982320i \(0.440055\pi\)
\(72\) −88.0000 −0.144040
\(73\) −210.000 −0.336694 −0.168347 0.985728i \(-0.553843\pi\)
−0.168347 + 0.985728i \(0.553843\pi\)
\(74\) −550.694 −0.865093
\(75\) 84.0000 0.129326
\(76\) 367.129 0.554114
\(77\) 1456.00 2.15489
\(78\) 336.000 0.487750
\(79\) 1080.99 1.53951 0.769754 0.638341i \(-0.220379\pi\)
0.769754 + 0.638341i \(0.220379\pi\)
\(80\) 163.169 0.228035
\(81\) −311.000 −0.426612
\(82\) −636.000 −0.856518
\(83\) 1152.38 1.52398 0.761988 0.647591i \(-0.224224\pi\)
0.761988 + 0.647591i \(0.224224\pi\)
\(84\) −326.337 −0.423885
\(85\) 208.000 0.265421
\(86\) 632.278 0.792795
\(87\) 88.0000 0.108444
\(88\) 571.090 0.691800
\(89\) −815.843 −0.971676 −0.485838 0.874049i \(-0.661486\pi\)
−0.485838 + 0.874049i \(0.661486\pi\)
\(90\) −224.357 −0.262770
\(91\) −856.635 −0.986811
\(92\) 0 0
\(93\) −1184.00 −1.32016
\(94\) −368.000 −0.403790
\(95\) 936.000 1.01086
\(96\) −128.000 −0.136083
\(97\) 1244.16 1.30232 0.651162 0.758939i \(-0.274282\pi\)
0.651162 + 0.758939i \(0.274282\pi\)
\(98\) 146.000 0.150492
\(99\) −785.249 −0.797177
\(100\) −84.0000 −0.0840000
\(101\) 1934.00 1.90535 0.952674 0.303993i \(-0.0983200\pi\)
0.952674 + 0.303993i \(0.0983200\pi\)
\(102\) −163.169 −0.158393
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −336.000 −0.316803
\(105\) −832.000 −0.773285
\(106\) 183.565 0.168202
\(107\) 132.575 0.119780 0.0598900 0.998205i \(-0.480925\pi\)
0.0598900 + 0.998205i \(0.480925\pi\)
\(108\) 608.000 0.541711
\(109\) −1193.17 −1.04849 −0.524243 0.851569i \(-0.675652\pi\)
−0.524243 + 0.851569i \(0.675652\pi\)
\(110\) 1456.00 1.26204
\(111\) 1101.39 0.941794
\(112\) 326.337 0.275321
\(113\) 2080.40 1.73193 0.865963 0.500109i \(-0.166707\pi\)
0.865963 + 0.500109i \(0.166707\pi\)
\(114\) −734.259 −0.603242
\(115\) 0 0
\(116\) −88.0000 −0.0704362
\(117\) 462.000 0.365059
\(118\) −1000.00 −0.780148
\(119\) 416.000 0.320459
\(120\) −326.337 −0.248253
\(121\) 3765.00 2.82870
\(122\) 61.1882 0.0454076
\(123\) 1272.00 0.932458
\(124\) 1184.00 0.857470
\(125\) −1488.91 −1.06538
\(126\) −448.714 −0.317259
\(127\) −408.000 −0.285072 −0.142536 0.989790i \(-0.545526\pi\)
−0.142536 + 0.989790i \(0.545526\pi\)
\(128\) 128.000 0.0883883
\(129\) −1264.56 −0.863085
\(130\) −856.635 −0.577938
\(131\) 196.000 0.130722 0.0653611 0.997862i \(-0.479180\pi\)
0.0653611 + 0.997862i \(0.479180\pi\)
\(132\) −1142.18 −0.753137
\(133\) 1872.00 1.22047
\(134\) −1284.95 −0.828381
\(135\) 1550.10 0.988234
\(136\) 163.169 0.102879
\(137\) 2467.93 1.53904 0.769522 0.638620i \(-0.220494\pi\)
0.769522 + 0.638620i \(0.220494\pi\)
\(138\) 0 0
\(139\) −2292.00 −1.39860 −0.699298 0.714830i \(-0.746504\pi\)
−0.699298 + 0.714830i \(0.746504\pi\)
\(140\) 832.000 0.502263
\(141\) 736.000 0.439591
\(142\) 448.000 0.264756
\(143\) −2998.22 −1.75331
\(144\) −176.000 −0.101852
\(145\) −224.357 −0.128495
\(146\) −420.000 −0.238078
\(147\) −292.000 −0.163835
\(148\) −1101.39 −0.611713
\(149\) 132.575 0.0728921 0.0364461 0.999336i \(-0.488396\pi\)
0.0364461 + 0.999336i \(0.488396\pi\)
\(150\) 168.000 0.0914476
\(151\) −3072.00 −1.65560 −0.827801 0.561022i \(-0.810408\pi\)
−0.827801 + 0.561022i \(0.810408\pi\)
\(152\) 734.259 0.391817
\(153\) −224.357 −0.118550
\(154\) 2912.00 1.52374
\(155\) 3018.62 1.56427
\(156\) 672.000 0.344891
\(157\) −30.5941 −0.0155521 −0.00777604 0.999970i \(-0.502475\pi\)
−0.00777604 + 0.999970i \(0.502475\pi\)
\(158\) 2161.98 1.08860
\(159\) −367.129 −0.183115
\(160\) 326.337 0.161245
\(161\) 0 0
\(162\) −622.000 −0.301660
\(163\) 3116.00 1.49732 0.748662 0.662951i \(-0.230696\pi\)
0.748662 + 0.662951i \(0.230696\pi\)
\(164\) −1272.00 −0.605649
\(165\) −2912.00 −1.37393
\(166\) 2304.76 1.07761
\(167\) 2112.00 0.978632 0.489316 0.872107i \(-0.337247\pi\)
0.489316 + 0.872107i \(0.337247\pi\)
\(168\) −652.674 −0.299732
\(169\) −433.000 −0.197087
\(170\) 416.000 0.187681
\(171\) −1009.61 −0.451500
\(172\) 1264.56 0.560590
\(173\) 442.000 0.194246 0.0971232 0.995272i \(-0.469036\pi\)
0.0971232 + 0.995272i \(0.469036\pi\)
\(174\) 176.000 0.0766812
\(175\) −428.318 −0.185016
\(176\) 1142.18 0.489177
\(177\) 2000.00 0.849318
\(178\) −1631.69 −0.687079
\(179\) 2764.00 1.15414 0.577070 0.816695i \(-0.304196\pi\)
0.577070 + 0.816695i \(0.304196\pi\)
\(180\) −448.714 −0.185806
\(181\) −4456.54 −1.83012 −0.915061 0.403314i \(-0.867858\pi\)
−0.915061 + 0.403314i \(0.867858\pi\)
\(182\) −1713.27 −0.697781
\(183\) −122.376 −0.0494335
\(184\) 0 0
\(185\) −2808.00 −1.11594
\(186\) −2368.00 −0.933496
\(187\) 1456.00 0.569376
\(188\) −736.000 −0.285523
\(189\) 3100.20 1.19316
\(190\) 1872.00 0.714785
\(191\) 4018.03 1.52217 0.761084 0.648653i \(-0.224667\pi\)
0.761084 + 0.648653i \(0.224667\pi\)
\(192\) −256.000 −0.0962250
\(193\) −1666.00 −0.621354 −0.310677 0.950516i \(-0.600556\pi\)
−0.310677 + 0.950516i \(0.600556\pi\)
\(194\) 2488.32 0.920882
\(195\) 1713.27 0.629179
\(196\) 292.000 0.106414
\(197\) −2190.00 −0.792036 −0.396018 0.918243i \(-0.629608\pi\)
−0.396018 + 0.918243i \(0.629608\pi\)
\(198\) −1570.50 −0.563689
\(199\) 917.824 0.326949 0.163474 0.986548i \(-0.447730\pi\)
0.163474 + 0.986548i \(0.447730\pi\)
\(200\) −168.000 −0.0593970
\(201\) 2569.91 0.901827
\(202\) 3868.00 1.34728
\(203\) −448.714 −0.155141
\(204\) −326.337 −0.112001
\(205\) −3242.98 −1.10487
\(206\) 0 0
\(207\) 0 0
\(208\) −672.000 −0.224014
\(209\) 6552.00 2.16848
\(210\) −1664.00 −0.546795
\(211\) −1324.00 −0.431981 −0.215990 0.976396i \(-0.569298\pi\)
−0.215990 + 0.976396i \(0.569298\pi\)
\(212\) 367.129 0.118937
\(213\) −896.000 −0.288230
\(214\) 265.149 0.0846973
\(215\) 3224.00 1.02267
\(216\) 1216.00 0.383048
\(217\) 6037.24 1.88864
\(218\) −2386.34 −0.741392
\(219\) 840.000 0.259187
\(220\) 2912.00 0.892395
\(221\) −856.635 −0.260740
\(222\) 2202.78 0.665949
\(223\) −1928.00 −0.578962 −0.289481 0.957184i \(-0.593483\pi\)
−0.289481 + 0.957184i \(0.593483\pi\)
\(224\) 652.674 0.194681
\(225\) 231.000 0.0684444
\(226\) 4160.80 1.22466
\(227\) 3905.85 1.14203 0.571014 0.820940i \(-0.306550\pi\)
0.571014 + 0.820940i \(0.306550\pi\)
\(228\) −1468.52 −0.426557
\(229\) −1070.79 −0.308996 −0.154498 0.987993i \(-0.549376\pi\)
−0.154498 + 0.987993i \(0.549376\pi\)
\(230\) 0 0
\(231\) −5824.00 −1.65884
\(232\) −176.000 −0.0498059
\(233\) 762.000 0.214250 0.107125 0.994246i \(-0.465835\pi\)
0.107125 + 0.994246i \(0.465835\pi\)
\(234\) 924.000 0.258136
\(235\) −1876.44 −0.520874
\(236\) −2000.00 −0.551648
\(237\) −4323.97 −1.18511
\(238\) 832.000 0.226599
\(239\) −136.000 −0.0368080 −0.0184040 0.999831i \(-0.505859\pi\)
−0.0184040 + 0.999831i \(0.505859\pi\)
\(240\) −652.674 −0.175541
\(241\) 1448.12 0.387061 0.193531 0.981094i \(-0.438006\pi\)
0.193531 + 0.981094i \(0.438006\pi\)
\(242\) 7530.00 2.00019
\(243\) −2860.00 −0.755017
\(244\) 122.376 0.0321080
\(245\) 744.457 0.194129
\(246\) 2544.00 0.659348
\(247\) −3854.86 −0.993032
\(248\) 2368.00 0.606323
\(249\) −4609.51 −1.17316
\(250\) −2977.83 −0.753337
\(251\) 10.1980 0.00256452 0.00128226 0.999999i \(-0.499592\pi\)
0.00128226 + 0.999999i \(0.499592\pi\)
\(252\) −897.427 −0.224336
\(253\) 0 0
\(254\) −816.000 −0.201576
\(255\) −832.000 −0.204321
\(256\) 256.000 0.0625000
\(257\) −2918.00 −0.708248 −0.354124 0.935198i \(-0.615221\pi\)
−0.354124 + 0.935198i \(0.615221\pi\)
\(258\) −2529.11 −0.610294
\(259\) −5616.00 −1.34734
\(260\) −1713.27 −0.408664
\(261\) 242.000 0.0573924
\(262\) 392.000 0.0924345
\(263\) −5262.19 −1.23377 −0.616883 0.787055i \(-0.711605\pi\)
−0.616883 + 0.787055i \(0.711605\pi\)
\(264\) −2284.36 −0.532548
\(265\) 936.000 0.216974
\(266\) 3744.00 0.863005
\(267\) 3263.37 0.747997
\(268\) −2569.91 −0.585754
\(269\) −5238.00 −1.18724 −0.593618 0.804747i \(-0.702301\pi\)
−0.593618 + 0.804747i \(0.702301\pi\)
\(270\) 3100.20 0.698787
\(271\) 3048.00 0.683221 0.341610 0.939842i \(-0.389028\pi\)
0.341610 + 0.939842i \(0.389028\pi\)
\(272\) 326.337 0.0727467
\(273\) 3426.54 0.759647
\(274\) 4935.85 1.08827
\(275\) −1499.11 −0.328727
\(276\) 0 0
\(277\) 5650.00 1.22554 0.612772 0.790260i \(-0.290054\pi\)
0.612772 + 0.790260i \(0.290054\pi\)
\(278\) −4584.00 −0.988957
\(279\) −3256.00 −0.698680
\(280\) 1664.00 0.355154
\(281\) −4283.18 −0.909299 −0.454649 0.890671i \(-0.650235\pi\)
−0.454649 + 0.890671i \(0.650235\pi\)
\(282\) 1472.00 0.310838
\(283\) 3253.17 0.683326 0.341663 0.939823i \(-0.389010\pi\)
0.341663 + 0.939823i \(0.389010\pi\)
\(284\) 896.000 0.187211
\(285\) −3744.00 −0.778159
\(286\) −5996.45 −1.23978
\(287\) −6485.95 −1.33398
\(288\) −352.000 −0.0720201
\(289\) −4497.00 −0.915327
\(290\) −448.714 −0.0908599
\(291\) −4976.64 −1.00253
\(292\) −840.000 −0.168347
\(293\) −4069.02 −0.811312 −0.405656 0.914026i \(-0.632957\pi\)
−0.405656 + 0.914026i \(0.632957\pi\)
\(294\) −584.000 −0.115849
\(295\) −5099.02 −1.00636
\(296\) −2202.78 −0.432547
\(297\) 10850.7 2.11994
\(298\) 265.149 0.0515425
\(299\) 0 0
\(300\) 336.000 0.0646632
\(301\) 6448.00 1.23474
\(302\) −6144.00 −1.17069
\(303\) −7736.00 −1.46674
\(304\) 1468.52 0.277057
\(305\) 312.000 0.0585740
\(306\) −448.714 −0.0838276
\(307\) 4492.00 0.835088 0.417544 0.908657i \(-0.362891\pi\)
0.417544 + 0.908657i \(0.362891\pi\)
\(308\) 5824.00 1.07745
\(309\) 0 0
\(310\) 6037.24 1.10610
\(311\) −2880.00 −0.525112 −0.262556 0.964917i \(-0.584565\pi\)
−0.262556 + 0.964917i \(0.584565\pi\)
\(312\) 1344.00 0.243875
\(313\) 2263.96 0.408840 0.204420 0.978883i \(-0.434469\pi\)
0.204420 + 0.978883i \(0.434469\pi\)
\(314\) −61.1882 −0.0109970
\(315\) −2288.00 −0.409251
\(316\) 4323.97 0.769754
\(317\) −8454.00 −1.49787 −0.748934 0.662645i \(-0.769434\pi\)
−0.748934 + 0.662645i \(0.769434\pi\)
\(318\) −734.259 −0.129482
\(319\) −1570.50 −0.275646
\(320\) 652.674 0.114018
\(321\) −530.298 −0.0922067
\(322\) 0 0
\(323\) 1872.00 0.322479
\(324\) −1244.00 −0.213306
\(325\) 882.000 0.150537
\(326\) 6232.00 1.05877
\(327\) 4772.68 0.807125
\(328\) −2544.00 −0.428259
\(329\) −3752.88 −0.628884
\(330\) −5824.00 −0.971517
\(331\) −10052.0 −1.66921 −0.834604 0.550850i \(-0.814304\pi\)
−0.834604 + 0.550850i \(0.814304\pi\)
\(332\) 4609.51 0.761988
\(333\) 3028.82 0.498433
\(334\) 4224.00 0.691997
\(335\) −6552.00 −1.06858
\(336\) −1305.35 −0.211942
\(337\) −489.506 −0.0791249 −0.0395624 0.999217i \(-0.512596\pi\)
−0.0395624 + 0.999217i \(0.512596\pi\)
\(338\) −866.000 −0.139362
\(339\) −8321.60 −1.33324
\(340\) 832.000 0.132710
\(341\) 21130.3 3.35564
\(342\) −2019.21 −0.319259
\(343\) −5506.94 −0.866900
\(344\) 2529.11 0.396397
\(345\) 0 0
\(346\) 884.000 0.137353
\(347\) −8604.00 −1.33109 −0.665543 0.746359i \(-0.731800\pi\)
−0.665543 + 0.746359i \(0.731800\pi\)
\(348\) 352.000 0.0542218
\(349\) −1174.00 −0.180065 −0.0900326 0.995939i \(-0.528697\pi\)
−0.0900326 + 0.995939i \(0.528697\pi\)
\(350\) −856.635 −0.130826
\(351\) −6384.00 −0.970805
\(352\) 2284.36 0.345900
\(353\) −2818.00 −0.424892 −0.212446 0.977173i \(-0.568143\pi\)
−0.212446 + 0.977173i \(0.568143\pi\)
\(354\) 4000.00 0.600558
\(355\) 2284.36 0.341525
\(356\) −3263.37 −0.485838
\(357\) −1664.00 −0.246690
\(358\) 5528.00 0.816100
\(359\) 1366.54 0.200900 0.100450 0.994942i \(-0.467972\pi\)
0.100450 + 0.994942i \(0.467972\pi\)
\(360\) −897.427 −0.131385
\(361\) 1565.00 0.228167
\(362\) −8913.09 −1.29409
\(363\) −15060.0 −2.17753
\(364\) −3426.54 −0.493405
\(365\) −2141.59 −0.307112
\(366\) −244.753 −0.0349548
\(367\) 3079.81 0.438051 0.219025 0.975719i \(-0.429712\pi\)
0.219025 + 0.975719i \(0.429712\pi\)
\(368\) 0 0
\(369\) 3498.00 0.493492
\(370\) −5616.00 −0.789086
\(371\) 1872.00 0.261966
\(372\) −4736.00 −0.660081
\(373\) 4415.75 0.612973 0.306486 0.951875i \(-0.400847\pi\)
0.306486 + 0.951875i \(0.400847\pi\)
\(374\) 2912.00 0.402609
\(375\) 5955.65 0.820130
\(376\) −1472.00 −0.201895
\(377\) 924.000 0.126229
\(378\) 6200.41 0.843689
\(379\) 10.1980 0.00138216 0.000691079 1.00000i \(-0.499780\pi\)
0.000691079 1.00000i \(0.499780\pi\)
\(380\) 3744.00 0.505429
\(381\) 1632.00 0.219449
\(382\) 8036.05 1.07634
\(383\) −40.7922 −0.00544225 −0.00272113 0.999996i \(-0.500866\pi\)
−0.00272113 + 0.999996i \(0.500866\pi\)
\(384\) −512.000 −0.0680414
\(385\) 14848.3 1.96556
\(386\) −3332.00 −0.439364
\(387\) −3477.53 −0.456777
\(388\) 4976.64 0.651162
\(389\) −14328.2 −1.86753 −0.933767 0.357881i \(-0.883499\pi\)
−0.933767 + 0.357881i \(0.883499\pi\)
\(390\) 3426.54 0.444897
\(391\) 0 0
\(392\) 584.000 0.0752461
\(393\) −784.000 −0.100630
\(394\) −4380.00 −0.560054
\(395\) 11024.0 1.40425
\(396\) −3141.00 −0.398588
\(397\) 11046.0 1.39643 0.698215 0.715888i \(-0.253978\pi\)
0.698215 + 0.715888i \(0.253978\pi\)
\(398\) 1835.65 0.231188
\(399\) −7488.00 −0.939521
\(400\) −336.000 −0.0420000
\(401\) −4425.95 −0.551175 −0.275588 0.961276i \(-0.588872\pi\)
−0.275588 + 0.961276i \(0.588872\pi\)
\(402\) 5139.81 0.637688
\(403\) −12432.0 −1.53668
\(404\) 7736.00 0.952674
\(405\) −3171.59 −0.389130
\(406\) −897.427 −0.109701
\(407\) −19656.0 −2.39389
\(408\) −652.674 −0.0791966
\(409\) −5194.00 −0.627938 −0.313969 0.949433i \(-0.601659\pi\)
−0.313969 + 0.949433i \(0.601659\pi\)
\(410\) −6485.95 −0.781264
\(411\) −9871.70 −1.18476
\(412\) 0 0
\(413\) −10198.0 −1.21504
\(414\) 0 0
\(415\) 11752.0 1.39008
\(416\) −1344.00 −0.158401
\(417\) 9168.00 1.07664
\(418\) 13104.0 1.53334
\(419\) 5272.39 0.614733 0.307366 0.951591i \(-0.400552\pi\)
0.307366 + 0.951591i \(0.400552\pi\)
\(420\) −3328.00 −0.386642
\(421\) −9616.75 −1.11328 −0.556641 0.830753i \(-0.687910\pi\)
−0.556641 + 0.830753i \(0.687910\pi\)
\(422\) −2648.00 −0.305456
\(423\) 2024.00 0.232648
\(424\) 734.259 0.0841008
\(425\) −428.318 −0.0488858
\(426\) −1792.00 −0.203809
\(427\) 624.000 0.0707201
\(428\) 530.298 0.0598900
\(429\) 11992.9 1.34970
\(430\) 6448.00 0.723140
\(431\) 7607.74 0.850236 0.425118 0.905138i \(-0.360233\pi\)
0.425118 + 0.905138i \(0.360233\pi\)
\(432\) 2432.00 0.270856
\(433\) −9932.89 −1.10241 −0.551206 0.834369i \(-0.685832\pi\)
−0.551206 + 0.834369i \(0.685832\pi\)
\(434\) 12074.5 1.33547
\(435\) 897.427 0.0989158
\(436\) −4772.68 −0.524243
\(437\) 0 0
\(438\) 1680.00 0.183273
\(439\) −6768.00 −0.735806 −0.367903 0.929864i \(-0.619924\pi\)
−0.367903 + 0.929864i \(0.619924\pi\)
\(440\) 5824.00 0.631019
\(441\) −803.000 −0.0867077
\(442\) −1713.27 −0.184371
\(443\) −7292.00 −0.782062 −0.391031 0.920378i \(-0.627881\pi\)
−0.391031 + 0.920378i \(0.627881\pi\)
\(444\) 4405.55 0.470897
\(445\) −8320.00 −0.886305
\(446\) −3856.00 −0.409388
\(447\) −530.298 −0.0561124
\(448\) 1305.35 0.137661
\(449\) −10198.0 −1.07188 −0.535939 0.844257i \(-0.680042\pi\)
−0.535939 + 0.844257i \(0.680042\pi\)
\(450\) 462.000 0.0483975
\(451\) −22700.8 −2.37016
\(452\) 8321.60 0.865963
\(453\) 12288.0 1.27448
\(454\) 7811.70 0.807536
\(455\) −8736.00 −0.900110
\(456\) −2937.04 −0.301621
\(457\) 10707.9 1.09605 0.548027 0.836461i \(-0.315379\pi\)
0.548027 + 0.836461i \(0.315379\pi\)
\(458\) −2141.59 −0.218493
\(459\) 3100.20 0.315262
\(460\) 0 0
\(461\) 4794.00 0.484336 0.242168 0.970234i \(-0.422142\pi\)
0.242168 + 0.970234i \(0.422142\pi\)
\(462\) −11648.0 −1.17297
\(463\) 9848.00 0.988500 0.494250 0.869320i \(-0.335443\pi\)
0.494250 + 0.869320i \(0.335443\pi\)
\(464\) −352.000 −0.0352181
\(465\) −12074.5 −1.20417
\(466\) 1524.00 0.151498
\(467\) −5986.25 −0.593170 −0.296585 0.955006i \(-0.595848\pi\)
−0.296585 + 0.955006i \(0.595848\pi\)
\(468\) 1848.00 0.182530
\(469\) −13104.0 −1.29016
\(470\) −3752.88 −0.368314
\(471\) 122.376 0.0119720
\(472\) −4000.00 −0.390074
\(473\) 22568.0 2.19382
\(474\) −8647.94 −0.838002
\(475\) −1927.43 −0.186182
\(476\) 1664.00 0.160230
\(477\) −1009.61 −0.0969113
\(478\) −272.000 −0.0260272
\(479\) 2651.49 0.252922 0.126461 0.991972i \(-0.459638\pi\)
0.126461 + 0.991972i \(0.459638\pi\)
\(480\) −1305.35 −0.124127
\(481\) 11564.6 1.09626
\(482\) 2896.24 0.273693
\(483\) 0 0
\(484\) 15060.0 1.41435
\(485\) 12688.0 1.18790
\(486\) −5720.00 −0.533878
\(487\) 9328.00 0.867951 0.433975 0.900925i \(-0.357110\pi\)
0.433975 + 0.900925i \(0.357110\pi\)
\(488\) 244.753 0.0227038
\(489\) −12464.0 −1.15264
\(490\) 1488.91 0.137270
\(491\) 1332.00 0.122428 0.0612142 0.998125i \(-0.480503\pi\)
0.0612142 + 0.998125i \(0.480503\pi\)
\(492\) 5088.00 0.466229
\(493\) −448.714 −0.0409920
\(494\) −7709.72 −0.702179
\(495\) −8008.00 −0.727137
\(496\) 4736.00 0.428735
\(497\) 4568.72 0.412344
\(498\) −9219.03 −0.829547
\(499\) −6308.00 −0.565902 −0.282951 0.959134i \(-0.591313\pi\)
−0.282951 + 0.959134i \(0.591313\pi\)
\(500\) −5955.65 −0.532690
\(501\) −8448.00 −0.753351
\(502\) 20.3961 0.00181339
\(503\) 1325.75 0.117519 0.0587595 0.998272i \(-0.481285\pi\)
0.0587595 + 0.998272i \(0.481285\pi\)
\(504\) −1794.85 −0.158629
\(505\) 19723.0 1.73795
\(506\) 0 0
\(507\) 1732.00 0.151718
\(508\) −1632.00 −0.142536
\(509\) 5034.00 0.438366 0.219183 0.975684i \(-0.429661\pi\)
0.219183 + 0.975684i \(0.429661\pi\)
\(510\) −1664.00 −0.144477
\(511\) −4283.18 −0.370796
\(512\) 512.000 0.0441942
\(513\) 13950.9 1.20068
\(514\) −5836.00 −0.500807
\(515\) 0 0
\(516\) −5058.23 −0.431543
\(517\) −13135.1 −1.11737
\(518\) −11232.0 −0.952714
\(519\) −1768.00 −0.149531
\(520\) −3426.54 −0.288969
\(521\) 7077.44 0.595141 0.297570 0.954700i \(-0.403824\pi\)
0.297570 + 0.954700i \(0.403824\pi\)
\(522\) 484.000 0.0405826
\(523\) −13573.6 −1.13486 −0.567430 0.823422i \(-0.692062\pi\)
−0.567430 + 0.823422i \(0.692062\pi\)
\(524\) 784.000 0.0653611
\(525\) 1713.27 0.142425
\(526\) −10524.4 −0.872404
\(527\) 6037.24 0.499025
\(528\) −4568.72 −0.376568
\(529\) 0 0
\(530\) 1872.00 0.153424
\(531\) 5500.00 0.449491
\(532\) 7488.00 0.610237
\(533\) 13356.0 1.08539
\(534\) 6526.74 0.528914
\(535\) 1352.00 0.109256
\(536\) −5139.81 −0.414190
\(537\) −11056.0 −0.888457
\(538\) −10476.0 −0.839503
\(539\) 5211.20 0.416442
\(540\) 6200.41 0.494117
\(541\) −13334.0 −1.05966 −0.529828 0.848105i \(-0.677743\pi\)
−0.529828 + 0.848105i \(0.677743\pi\)
\(542\) 6096.00 0.483110
\(543\) 17826.2 1.40883
\(544\) 652.674 0.0514397
\(545\) −12168.0 −0.956367
\(546\) 6853.08 0.537152
\(547\) −1468.00 −0.114748 −0.0573740 0.998353i \(-0.518273\pi\)
−0.0573740 + 0.998353i \(0.518273\pi\)
\(548\) 9871.70 0.769522
\(549\) −336.535 −0.0261621
\(550\) −2998.22 −0.232445
\(551\) −2019.21 −0.156119
\(552\) 0 0
\(553\) 22048.0 1.69544
\(554\) 11300.0 0.866590
\(555\) 11232.0 0.859048
\(556\) −9168.00 −0.699298
\(557\) 18427.9 1.40182 0.700910 0.713250i \(-0.252778\pi\)
0.700910 + 0.713250i \(0.252778\pi\)
\(558\) −6512.00 −0.494041
\(559\) −13277.8 −1.00464
\(560\) 3328.00 0.251132
\(561\) −5824.00 −0.438306
\(562\) −8566.35 −0.642971
\(563\) 22507.1 1.68483 0.842416 0.538828i \(-0.181133\pi\)
0.842416 + 0.538828i \(0.181133\pi\)
\(564\) 2944.00 0.219796
\(565\) 21216.0 1.57976
\(566\) 6506.35 0.483184
\(567\) −6343.18 −0.469821
\(568\) 1792.00 0.132378
\(569\) −8382.79 −0.617618 −0.308809 0.951124i \(-0.599930\pi\)
−0.308809 + 0.951124i \(0.599930\pi\)
\(570\) −7488.00 −0.550242
\(571\) 4089.41 0.299714 0.149857 0.988708i \(-0.452119\pi\)
0.149857 + 0.988708i \(0.452119\pi\)
\(572\) −11992.9 −0.876657
\(573\) −16072.1 −1.17177
\(574\) −12971.9 −0.943270
\(575\) 0 0
\(576\) −704.000 −0.0509259
\(577\) −8378.00 −0.604473 −0.302236 0.953233i \(-0.597733\pi\)
−0.302236 + 0.953233i \(0.597733\pi\)
\(578\) −8994.00 −0.647234
\(579\) 6664.00 0.478318
\(580\) −897.427 −0.0642477
\(581\) 23504.0 1.67833
\(582\) −9953.29 −0.708895
\(583\) 6552.00 0.465448
\(584\) −1680.00 −0.119039
\(585\) 4711.49 0.332985
\(586\) −8138.04 −0.573685
\(587\) 27228.0 1.91451 0.957257 0.289238i \(-0.0934020\pi\)
0.957257 + 0.289238i \(0.0934020\pi\)
\(588\) −1168.00 −0.0819175
\(589\) 27167.6 1.90054
\(590\) −10198.0 −0.711604
\(591\) 8760.00 0.609709
\(592\) −4405.55 −0.305857
\(593\) −13462.0 −0.932240 −0.466120 0.884722i \(-0.654348\pi\)
−0.466120 + 0.884722i \(0.654348\pi\)
\(594\) 21701.4 1.49902
\(595\) 4242.38 0.292304
\(596\) 530.298 0.0364461
\(597\) −3671.29 −0.251685
\(598\) 0 0
\(599\) −16224.0 −1.10667 −0.553334 0.832959i \(-0.686645\pi\)
−0.553334 + 0.832959i \(0.686645\pi\)
\(600\) 672.000 0.0457238
\(601\) 13118.0 0.890340 0.445170 0.895446i \(-0.353143\pi\)
0.445170 + 0.895446i \(0.353143\pi\)
\(602\) 12896.0 0.873093
\(603\) 7067.24 0.477281
\(604\) −12288.0 −0.827801
\(605\) 38395.6 2.58017
\(606\) −15472.0 −1.03714
\(607\) 1144.00 0.0764968 0.0382484 0.999268i \(-0.487822\pi\)
0.0382484 + 0.999268i \(0.487822\pi\)
\(608\) 2937.04 0.195909
\(609\) 1794.85 0.119427
\(610\) 624.000 0.0414181
\(611\) 7728.00 0.511688
\(612\) −897.427 −0.0592751
\(613\) −27259.4 −1.79608 −0.898038 0.439917i \(-0.855008\pi\)
−0.898038 + 0.439917i \(0.855008\pi\)
\(614\) 8984.00 0.590496
\(615\) 12971.9 0.850533
\(616\) 11648.0 0.761869
\(617\) −21334.3 −1.39204 −0.696018 0.718024i \(-0.745047\pi\)
−0.696018 + 0.718024i \(0.745047\pi\)
\(618\) 0 0
\(619\) 19692.4 1.27868 0.639342 0.768923i \(-0.279207\pi\)
0.639342 + 0.768923i \(0.279207\pi\)
\(620\) 12074.5 0.782133
\(621\) 0 0
\(622\) −5760.00 −0.371310
\(623\) −16640.0 −1.07009
\(624\) 2688.00 0.172446
\(625\) −12559.0 −0.803776
\(626\) 4527.93 0.289093
\(627\) −26208.0 −1.66929
\(628\) −122.376 −0.00777604
\(629\) −5616.00 −0.356001
\(630\) −4576.00 −0.289384
\(631\) 5384.56 0.339709 0.169854 0.985469i \(-0.445670\pi\)
0.169854 + 0.985469i \(0.445670\pi\)
\(632\) 8647.94 0.544298
\(633\) 5296.00 0.332539
\(634\) −16908.0 −1.05915
\(635\) −4160.80 −0.260026
\(636\) −1468.52 −0.0915574
\(637\) −3066.00 −0.190705
\(638\) −3141.00 −0.194911
\(639\) −2464.00 −0.152542
\(640\) 1305.35 0.0806226
\(641\) −10422.4 −0.642215 −0.321108 0.947043i \(-0.604055\pi\)
−0.321108 + 0.947043i \(0.604055\pi\)
\(642\) −1060.60 −0.0652000
\(643\) −18162.7 −1.11395 −0.556973 0.830531i \(-0.688037\pi\)
−0.556973 + 0.830531i \(0.688037\pi\)
\(644\) 0 0
\(645\) −12896.0 −0.787255
\(646\) 3744.00 0.228027
\(647\) −23824.0 −1.44763 −0.723816 0.689993i \(-0.757614\pi\)
−0.723816 + 0.689993i \(0.757614\pi\)
\(648\) −2488.00 −0.150830
\(649\) −35693.1 −2.15883
\(650\) 1764.00 0.106446
\(651\) −24149.0 −1.45387
\(652\) 12464.0 0.748662
\(653\) −5690.00 −0.340991 −0.170495 0.985358i \(-0.554537\pi\)
−0.170495 + 0.985358i \(0.554537\pi\)
\(654\) 9545.36 0.570724
\(655\) 1998.82 0.119237
\(656\) −5088.00 −0.302825
\(657\) 2310.00 0.137172
\(658\) −7505.76 −0.444688
\(659\) −4109.81 −0.242937 −0.121468 0.992595i \(-0.538760\pi\)
−0.121468 + 0.992595i \(0.538760\pi\)
\(660\) −11648.0 −0.686966
\(661\) −20936.6 −1.23198 −0.615990 0.787754i \(-0.711244\pi\)
−0.615990 + 0.787754i \(0.711244\pi\)
\(662\) −20104.0 −1.18031
\(663\) 3426.54 0.200718
\(664\) 9219.03 0.538807
\(665\) 19090.7 1.11324
\(666\) 6057.64 0.352445
\(667\) 0 0
\(668\) 8448.00 0.489316
\(669\) 7712.00 0.445685
\(670\) −13104.0 −0.755600
\(671\) 2184.00 0.125652
\(672\) −2610.70 −0.149866
\(673\) 18986.0 1.08745 0.543727 0.839262i \(-0.317013\pi\)
0.543727 + 0.839262i \(0.317013\pi\)
\(674\) −979.012 −0.0559497
\(675\) −3192.00 −0.182015
\(676\) −1732.00 −0.0985435
\(677\) −1091.19 −0.0619466 −0.0309733 0.999520i \(-0.509861\pi\)
−0.0309733 + 0.999520i \(0.509861\pi\)
\(678\) −16643.2 −0.942741
\(679\) 25376.0 1.43423
\(680\) 1664.00 0.0938404
\(681\) −15623.4 −0.879133
\(682\) 42260.7 2.37279
\(683\) −21396.0 −1.19868 −0.599338 0.800496i \(-0.704569\pi\)
−0.599338 + 0.800496i \(0.704569\pi\)
\(684\) −4038.42 −0.225750
\(685\) 25168.0 1.40382
\(686\) −11013.9 −0.612991
\(687\) 4283.18 0.237865
\(688\) 5058.23 0.280295
\(689\) −3854.86 −0.213147
\(690\) 0 0
\(691\) 15700.0 0.864336 0.432168 0.901793i \(-0.357749\pi\)
0.432168 + 0.901793i \(0.357749\pi\)
\(692\) 1768.00 0.0971232
\(693\) −16016.0 −0.877919
\(694\) −17208.0 −0.941220
\(695\) −23373.9 −1.27572
\(696\) 704.000 0.0383406
\(697\) −6485.95 −0.352472
\(698\) −2348.00 −0.127325
\(699\) −3048.00 −0.164930
\(700\) −1713.27 −0.0925079
\(701\) −10657.0 −0.574190 −0.287095 0.957902i \(-0.592690\pi\)
−0.287095 + 0.957902i \(0.592690\pi\)
\(702\) −12768.0 −0.686463
\(703\) −25272.0 −1.35583
\(704\) 4568.72 0.244588
\(705\) 7505.76 0.400969
\(706\) −5636.00 −0.300444
\(707\) 39446.0 2.09833
\(708\) 8000.00 0.424659
\(709\) 9188.43 0.486712 0.243356 0.969937i \(-0.421752\pi\)
0.243356 + 0.969937i \(0.421752\pi\)
\(710\) 4568.72 0.241494
\(711\) −11890.9 −0.627207
\(712\) −6526.74 −0.343539
\(713\) 0 0
\(714\) −3328.00 −0.174436
\(715\) −30576.0 −1.59927
\(716\) 11056.0 0.577070
\(717\) 544.000 0.0283348
\(718\) 2733.07 0.142058
\(719\) −18600.0 −0.964761 −0.482380 0.875962i \(-0.660228\pi\)
−0.482380 + 0.875962i \(0.660228\pi\)
\(720\) −1794.85 −0.0929032
\(721\) 0 0
\(722\) 3130.00 0.161339
\(723\) −5792.49 −0.297960
\(724\) −17826.2 −0.915061
\(725\) 462.000 0.0236666
\(726\) −30120.0 −1.53975
\(727\) −16786.0 −0.856337 −0.428169 0.903699i \(-0.640841\pi\)
−0.428169 + 0.903699i \(0.640841\pi\)
\(728\) −6853.08 −0.348890
\(729\) 19837.0 1.00782
\(730\) −4283.18 −0.217161
\(731\) 6448.00 0.326249
\(732\) −489.506 −0.0247167
\(733\) 7108.03 0.358174 0.179087 0.983833i \(-0.442686\pi\)
0.179087 + 0.983833i \(0.442686\pi\)
\(734\) 6159.62 0.309749
\(735\) −2977.83 −0.149441
\(736\) 0 0
\(737\) −45864.0 −2.29230
\(738\) 6996.00 0.348952
\(739\) −35364.0 −1.76033 −0.880166 0.474665i \(-0.842569\pi\)
−0.880166 + 0.474665i \(0.842569\pi\)
\(740\) −11232.0 −0.557968
\(741\) 15419.4 0.764436
\(742\) 3744.00 0.185238
\(743\) −7505.76 −0.370605 −0.185302 0.982682i \(-0.559326\pi\)
−0.185302 + 0.982682i \(0.559326\pi\)
\(744\) −9472.00 −0.466748
\(745\) 1352.00 0.0664878
\(746\) 8831.50 0.433437
\(747\) −12676.2 −0.620879
\(748\) 5824.00 0.284688
\(749\) 2704.00 0.131912
\(750\) 11911.3 0.579919
\(751\) 37936.7 1.84332 0.921658 0.388004i \(-0.126835\pi\)
0.921658 + 0.388004i \(0.126835\pi\)
\(752\) −2944.00 −0.142761
\(753\) −40.7922 −0.00197417
\(754\) 1848.00 0.0892575
\(755\) −31328.4 −1.51014
\(756\) 12400.8 0.596578
\(757\) −32440.0 −1.55753 −0.778765 0.627316i \(-0.784154\pi\)
−0.778765 + 0.627316i \(0.784154\pi\)
\(758\) 20.3961 0.000977334 0
\(759\) 0 0
\(760\) 7488.00 0.357393
\(761\) 9046.00 0.430903 0.215452 0.976515i \(-0.430878\pi\)
0.215452 + 0.976515i \(0.430878\pi\)
\(762\) 3264.00 0.155174
\(763\) −24336.0 −1.15468
\(764\) 16072.1 0.761084
\(765\) −2288.00 −0.108134
\(766\) −81.5843 −0.00384825
\(767\) 21000.0 0.988613
\(768\) −1024.00 −0.0481125
\(769\) −40690.2 −1.90810 −0.954048 0.299655i \(-0.903128\pi\)
−0.954048 + 0.299655i \(0.903128\pi\)
\(770\) 29696.7 1.38986
\(771\) 11672.0 0.545210
\(772\) −6664.00 −0.310677
\(773\) −26076.4 −1.21333 −0.606664 0.794958i \(-0.707493\pi\)
−0.606664 + 0.794958i \(0.707493\pi\)
\(774\) −6955.06 −0.322990
\(775\) −6216.00 −0.288110
\(776\) 9953.29 0.460441
\(777\) 22464.0 1.03718
\(778\) −28656.5 −1.32055
\(779\) −29186.8 −1.34239
\(780\) 6853.08 0.314589
\(781\) 15990.5 0.732632
\(782\) 0 0
\(783\) −3344.00 −0.152624
\(784\) 1168.00 0.0532070
\(785\) −312.000 −0.0141857
\(786\) −1568.00 −0.0711561
\(787\) 28870.6 1.30766 0.653829 0.756642i \(-0.273161\pi\)
0.653829 + 0.756642i \(0.273161\pi\)
\(788\) −8760.00 −0.396018
\(789\) 21048.8 0.949753
\(790\) 22048.0 0.992953
\(791\) 42432.0 1.90734
\(792\) −6281.99 −0.281845
\(793\) −1284.95 −0.0575410
\(794\) 22092.0 0.987425
\(795\) −3744.00 −0.167026
\(796\) 3671.29 0.163474
\(797\) −24607.9 −1.09367 −0.546835 0.837240i \(-0.684168\pi\)
−0.546835 + 0.837240i \(0.684168\pi\)
\(798\) −14976.0 −0.664342
\(799\) −3752.88 −0.166167
\(800\) −672.000 −0.0296985
\(801\) 8974.27 0.395868
\(802\) −8851.90 −0.389740
\(803\) −14991.1 −0.658811
\(804\) 10279.6 0.450913
\(805\) 0 0
\(806\) −24864.0 −1.08660
\(807\) 20952.0 0.913935
\(808\) 15472.0 0.673642
\(809\) −9594.00 −0.416943 −0.208472 0.978028i \(-0.566849\pi\)
−0.208472 + 0.978028i \(0.566849\pi\)
\(810\) −6343.18 −0.275156
\(811\) 14060.0 0.608771 0.304386 0.952549i \(-0.401549\pi\)
0.304386 + 0.952549i \(0.401549\pi\)
\(812\) −1794.85 −0.0775703
\(813\) −12192.0 −0.525944
\(814\) −39312.0 −1.69273
\(815\) 31777.1 1.36577
\(816\) −1305.35 −0.0560004
\(817\) 29016.0 1.24252
\(818\) −10388.0 −0.444019
\(819\) 9422.99 0.402034
\(820\) −12971.9 −0.552437
\(821\) −14850.0 −0.631265 −0.315633 0.948882i \(-0.602217\pi\)
−0.315633 + 0.948882i \(0.602217\pi\)
\(822\) −19743.4 −0.837750
\(823\) 944.000 0.0399827 0.0199914 0.999800i \(-0.493636\pi\)
0.0199914 + 0.999800i \(0.493636\pi\)
\(824\) 0 0
\(825\) 5996.45 0.253054
\(826\) −20396.1 −0.859165
\(827\) 15959.9 0.671078 0.335539 0.942026i \(-0.391082\pi\)
0.335539 + 0.942026i \(0.391082\pi\)
\(828\) 0 0
\(829\) 27482.0 1.15137 0.575687 0.817670i \(-0.304735\pi\)
0.575687 + 0.817670i \(0.304735\pi\)
\(830\) 23504.0 0.982935
\(831\) −22600.0 −0.943424
\(832\) −2688.00 −0.112007
\(833\) 1488.91 0.0619301
\(834\) 18336.0 0.761299
\(835\) 21538.3 0.892649
\(836\) 26208.0 1.08424
\(837\) 44992.0 1.85801
\(838\) 10544.8 0.434682
\(839\) 11748.1 0.483422 0.241711 0.970348i \(-0.422291\pi\)
0.241711 + 0.970348i \(0.422291\pi\)
\(840\) −6656.00 −0.273397
\(841\) −23905.0 −0.980155
\(842\) −19233.5 −0.787209
\(843\) 17132.7 0.699978
\(844\) −5296.00 −0.215990
\(845\) −4415.75 −0.179771
\(846\) 4048.00 0.164507
\(847\) 76791.2 3.11520
\(848\) 1468.52 0.0594683
\(849\) −13012.7 −0.526024
\(850\) −856.635 −0.0345675
\(851\) 0 0
\(852\) −3584.00 −0.144115
\(853\) −12850.0 −0.515798 −0.257899 0.966172i \(-0.583030\pi\)
−0.257899 + 0.966172i \(0.583030\pi\)
\(854\) 1248.00 0.0500067
\(855\) −10296.0 −0.411831
\(856\) 1060.60 0.0423486
\(857\) 25098.0 1.00039 0.500193 0.865914i \(-0.333262\pi\)
0.500193 + 0.865914i \(0.333262\pi\)
\(858\) 23985.8 0.954384
\(859\) 40052.0 1.59087 0.795435 0.606039i \(-0.207243\pi\)
0.795435 + 0.606039i \(0.207243\pi\)
\(860\) 12896.0 0.511337
\(861\) 25943.8 1.02690
\(862\) 15215.5 0.601208
\(863\) 11928.0 0.470491 0.235246 0.971936i \(-0.424411\pi\)
0.235246 + 0.971936i \(0.424411\pi\)
\(864\) 4864.00 0.191524
\(865\) 4507.53 0.177180
\(866\) −19865.8 −0.779523
\(867\) 17988.0 0.704619
\(868\) 24149.0 0.944319
\(869\) 77168.0 3.01236
\(870\) 1794.85 0.0699440
\(871\) 26984.0 1.04973
\(872\) −9545.36 −0.370696
\(873\) −13685.8 −0.530576
\(874\) 0 0
\(875\) −30368.0 −1.17329
\(876\) 3360.00 0.129593
\(877\) 3306.00 0.127293 0.0636463 0.997973i \(-0.479727\pi\)
0.0636463 + 0.997973i \(0.479727\pi\)
\(878\) −13536.0 −0.520294
\(879\) 16276.1 0.624549
\(880\) 11648.0 0.446198
\(881\) −28065.0 −1.07325 −0.536625 0.843821i \(-0.680301\pi\)
−0.536625 + 0.843821i \(0.680301\pi\)
\(882\) −1606.00 −0.0613116
\(883\) −6812.00 −0.259617 −0.129809 0.991539i \(-0.541436\pi\)
−0.129809 + 0.991539i \(0.541436\pi\)
\(884\) −3426.54 −0.130370
\(885\) 20396.1 0.774697
\(886\) −14584.0 −0.553001
\(887\) 25440.0 0.963012 0.481506 0.876443i \(-0.340090\pi\)
0.481506 + 0.876443i \(0.340090\pi\)
\(888\) 8811.11 0.332974
\(889\) −8321.60 −0.313945
\(890\) −16640.0 −0.626712
\(891\) −22201.1 −0.834754
\(892\) −7712.00 −0.289481
\(893\) −16888.0 −0.632849
\(894\) −1060.60 −0.0396774
\(895\) 28187.4 1.05274
\(896\) 2610.70 0.0973407
\(897\) 0 0
\(898\) −20396.0 −0.757932
\(899\) −6512.00 −0.241588
\(900\) 924.000 0.0342222
\(901\) 1872.00 0.0692179
\(902\) −45401.7 −1.67595
\(903\) −25792.0 −0.950503
\(904\) 16643.2 0.612328
\(905\) −45448.0 −1.66933
\(906\) 24576.0 0.901195
\(907\) −9514.77 −0.348327 −0.174164 0.984717i \(-0.555722\pi\)
−0.174164 + 0.984717i \(0.555722\pi\)
\(908\) 15623.4 0.571014
\(909\) −21274.0 −0.776253
\(910\) −17472.0 −0.636474
\(911\) 41628.4 1.51395 0.756976 0.653443i \(-0.226676\pi\)
0.756976 + 0.653443i \(0.226676\pi\)
\(912\) −5874.07 −0.213278
\(913\) 82264.0 2.98197
\(914\) 21415.9 0.775027
\(915\) −1248.00 −0.0450903
\(916\) −4283.18 −0.154498
\(917\) 3997.63 0.143962
\(918\) 6200.41 0.222924
\(919\) 30043.4 1.07839 0.539195 0.842181i \(-0.318728\pi\)
0.539195 + 0.842181i \(0.318728\pi\)
\(920\) 0 0
\(921\) −17968.0 −0.642851
\(922\) 9588.00 0.342477
\(923\) −9408.00 −0.335502
\(924\) −23296.0 −0.829418
\(925\) 5782.29 0.205536
\(926\) 19696.0 0.698975
\(927\) 0 0
\(928\) −704.000 −0.0249029
\(929\) 16266.0 0.574457 0.287228 0.957862i \(-0.407266\pi\)
0.287228 + 0.957862i \(0.407266\pi\)
\(930\) −24149.0 −0.851479
\(931\) 6700.11 0.235862
\(932\) 3048.00 0.107125
\(933\) 11520.0 0.404231
\(934\) −11972.5 −0.419435
\(935\) 14848.3 0.519351
\(936\) 3696.00 0.129068
\(937\) 11013.9 0.384000 0.192000 0.981395i \(-0.438503\pi\)
0.192000 + 0.981395i \(0.438503\pi\)
\(938\) −26208.0 −0.912283
\(939\) −9055.86 −0.314725
\(940\) −7505.76 −0.260437
\(941\) 42393.2 1.46863 0.734315 0.678809i \(-0.237504\pi\)
0.734315 + 0.678809i \(0.237504\pi\)
\(942\) 244.753 0.00846548
\(943\) 0 0
\(944\) −8000.00 −0.275824
\(945\) 31616.0 1.08833
\(946\) 45136.0 1.55127
\(947\) −3428.00 −0.117629 −0.0588147 0.998269i \(-0.518732\pi\)
−0.0588147 + 0.998269i \(0.518732\pi\)
\(948\) −17295.9 −0.592557
\(949\) 8820.00 0.301696
\(950\) −3854.86 −0.131651
\(951\) 33816.0 1.15306
\(952\) 3328.00 0.113299
\(953\) −21191.5 −0.720316 −0.360158 0.932891i \(-0.617277\pi\)
−0.360158 + 0.932891i \(0.617277\pi\)
\(954\) −2019.21 −0.0685266
\(955\) 40976.0 1.38843
\(956\) −544.000 −0.0184040
\(957\) 6281.99 0.212192
\(958\) 5302.98 0.178843
\(959\) 50336.0 1.69493
\(960\) −2610.70 −0.0877707
\(961\) 57825.0 1.94102
\(962\) 23129.2 0.775170
\(963\) −1458.32 −0.0487993
\(964\) 5792.49 0.193531
\(965\) −16989.9 −0.566762
\(966\) 0 0
\(967\) −3568.00 −0.118655 −0.0593274 0.998239i \(-0.518896\pi\)
−0.0593274 + 0.998239i \(0.518896\pi\)
\(968\) 30120.0 1.00010
\(969\) −7488.00 −0.248245
\(970\) 25376.0 0.839973
\(971\) 31195.8 1.03102 0.515510 0.856883i \(-0.327602\pi\)
0.515510 + 0.856883i \(0.327602\pi\)
\(972\) −11440.0 −0.377508
\(973\) −46747.8 −1.54025
\(974\) 18656.0 0.613734
\(975\) −3528.00 −0.115884
\(976\) 489.506 0.0160540
\(977\) −11401.4 −0.373350 −0.186675 0.982422i \(-0.559771\pi\)
−0.186675 + 0.982422i \(0.559771\pi\)
\(978\) −24928.0 −0.815040
\(979\) −58240.0 −1.90129
\(980\) 2977.83 0.0970645
\(981\) 13124.9 0.427161
\(982\) 2664.00 0.0865699
\(983\) −34326.6 −1.11378 −0.556891 0.830585i \(-0.688006\pi\)
−0.556891 + 0.830585i \(0.688006\pi\)
\(984\) 10176.0 0.329674
\(985\) −22333.7 −0.722448
\(986\) −897.427 −0.0289857
\(987\) 15011.5 0.484115
\(988\) −15419.4 −0.496516
\(989\) 0 0
\(990\) −16016.0 −0.514164
\(991\) −10376.0 −0.332598 −0.166299 0.986075i \(-0.553182\pi\)
−0.166299 + 0.986075i \(0.553182\pi\)
\(992\) 9472.00 0.303162
\(993\) 40208.0 1.28496
\(994\) 9137.44 0.291572
\(995\) 9360.00 0.298223
\(996\) −18438.1 −0.586578
\(997\) 25922.0 0.823428 0.411714 0.911313i \(-0.364930\pi\)
0.411714 + 0.911313i \(0.364930\pi\)
\(998\) −12616.0 −0.400153
\(999\) −41852.8 −1.32549
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 1058.4.a.i.1.2 yes 2
23.22 odd 2 inner 1058.4.a.i.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1058.4.a.i.1.1 2 23.22 odd 2 inner
1058.4.a.i.1.2 yes 2 1.1 even 1 trivial