Properties

Label 2151.4.a.g.1.18
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $1$
Dimension $59$
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] = [2151,4,Mod(1,2151)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2151.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.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: \(126.913108422\)
Analytic rank: \(1\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 2151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.94849 q^{2} +0.693582 q^{4} +3.01150 q^{5} -30.9852 q^{7} +21.5429 q^{8} +O(q^{10})\) \(q-2.94849 q^{2} +0.693582 q^{4} +3.01150 q^{5} -30.9852 q^{7} +21.5429 q^{8} -8.87936 q^{10} +60.7325 q^{11} +7.59182 q^{13} +91.3596 q^{14} -69.0676 q^{16} -11.9021 q^{17} +10.6377 q^{19} +2.08872 q^{20} -179.069 q^{22} +110.008 q^{23} -115.931 q^{25} -22.3844 q^{26} -21.4908 q^{28} -158.086 q^{29} -48.9384 q^{31} +31.3019 q^{32} +35.0931 q^{34} -93.3120 q^{35} -266.163 q^{37} -31.3652 q^{38} +64.8763 q^{40} +266.974 q^{41} -494.592 q^{43} +42.1229 q^{44} -324.358 q^{46} -34.2493 q^{47} +617.085 q^{49} +341.821 q^{50} +5.26555 q^{52} +344.258 q^{53} +182.896 q^{55} -667.512 q^{56} +466.116 q^{58} +528.630 q^{59} -39.5050 q^{61} +144.294 q^{62} +460.248 q^{64} +22.8628 q^{65} +541.024 q^{67} -8.25506 q^{68} +275.129 q^{70} -1137.35 q^{71} +1164.62 q^{73} +784.778 q^{74} +7.37813 q^{76} -1881.81 q^{77} -365.495 q^{79} -207.997 q^{80} -787.168 q^{82} +869.830 q^{83} -35.8431 q^{85} +1458.30 q^{86} +1308.35 q^{88} +150.942 q^{89} -235.235 q^{91} +76.2998 q^{92} +100.984 q^{94} +32.0355 q^{95} +70.1786 q^{97} -1819.47 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59 q - 8 q^{2} + 238 q^{4} - 80 q^{5} - 10 q^{7} - 96 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 59 q - 8 q^{2} + 238 q^{4} - 80 q^{5} - 10 q^{7} - 96 q^{8} - 36 q^{10} - 132 q^{11} + 104 q^{13} - 280 q^{14} + 822 q^{16} - 408 q^{17} + 20 q^{19} - 800 q^{20} - 2 q^{22} - 276 q^{23} + 1477 q^{25} - 780 q^{26} + 224 q^{28} - 696 q^{29} - 380 q^{31} - 896 q^{32} - 72 q^{34} - 700 q^{35} + 224 q^{37} - 988 q^{38} - 258 q^{40} - 2706 q^{41} - 156 q^{43} - 1584 q^{44} + 428 q^{46} - 1316 q^{47} + 2135 q^{49} - 1400 q^{50} + 1092 q^{52} - 1484 q^{53} - 992 q^{55} - 3360 q^{56} - 120 q^{58} - 3186 q^{59} - 254 q^{61} - 1240 q^{62} + 3054 q^{64} - 5120 q^{65} + 288 q^{67} - 9420 q^{68} + 1108 q^{70} - 4468 q^{71} - 1770 q^{73} - 6214 q^{74} + 720 q^{76} - 6352 q^{77} - 746 q^{79} - 7040 q^{80} + 276 q^{82} - 5484 q^{83} + 588 q^{85} - 10152 q^{86} + 1186 q^{88} - 11570 q^{89} + 1768 q^{91} - 15366 q^{92} - 2142 q^{94} - 5736 q^{95} + 2390 q^{97} - 6912 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.94849 −1.04245 −0.521224 0.853420i \(-0.674524\pi\)
−0.521224 + 0.853420i \(0.674524\pi\)
\(3\) 0 0
\(4\) 0.693582 0.0866977
\(5\) 3.01150 0.269356 0.134678 0.990889i \(-0.457000\pi\)
0.134678 + 0.990889i \(0.457000\pi\)
\(6\) 0 0
\(7\) −30.9852 −1.67305 −0.836523 0.547932i \(-0.815415\pi\)
−0.836523 + 0.547932i \(0.815415\pi\)
\(8\) 21.5429 0.952070
\(9\) 0 0
\(10\) −8.87936 −0.280790
\(11\) 60.7325 1.66468 0.832342 0.554262i \(-0.186999\pi\)
0.832342 + 0.554262i \(0.186999\pi\)
\(12\) 0 0
\(13\) 7.59182 0.161969 0.0809844 0.996715i \(-0.474194\pi\)
0.0809844 + 0.996715i \(0.474194\pi\)
\(14\) 91.3596 1.74406
\(15\) 0 0
\(16\) −69.0676 −1.07918
\(17\) −11.9021 −0.169804 −0.0849022 0.996389i \(-0.527058\pi\)
−0.0849022 + 0.996389i \(0.527058\pi\)
\(18\) 0 0
\(19\) 10.6377 0.128445 0.0642227 0.997936i \(-0.479543\pi\)
0.0642227 + 0.997936i \(0.479543\pi\)
\(20\) 2.08872 0.0233526
\(21\) 0 0
\(22\) −179.069 −1.73535
\(23\) 110.008 0.997319 0.498659 0.866798i \(-0.333826\pi\)
0.498659 + 0.866798i \(0.333826\pi\)
\(24\) 0 0
\(25\) −115.931 −0.927447
\(26\) −22.3844 −0.168844
\(27\) 0 0
\(28\) −21.4908 −0.145049
\(29\) −158.086 −1.01227 −0.506137 0.862453i \(-0.668927\pi\)
−0.506137 + 0.862453i \(0.668927\pi\)
\(30\) 0 0
\(31\) −48.9384 −0.283535 −0.141768 0.989900i \(-0.545279\pi\)
−0.141768 + 0.989900i \(0.545279\pi\)
\(32\) 31.3019 0.172920
\(33\) 0 0
\(34\) 35.0931 0.177012
\(35\) −93.3120 −0.450646
\(36\) 0 0
\(37\) −266.163 −1.18262 −0.591310 0.806445i \(-0.701389\pi\)
−0.591310 + 0.806445i \(0.701389\pi\)
\(38\) −31.3652 −0.133898
\(39\) 0 0
\(40\) 64.8763 0.256446
\(41\) 266.974 1.01693 0.508467 0.861082i \(-0.330213\pi\)
0.508467 + 0.861082i \(0.330213\pi\)
\(42\) 0 0
\(43\) −494.592 −1.75406 −0.877030 0.480435i \(-0.840479\pi\)
−0.877030 + 0.480435i \(0.840479\pi\)
\(44\) 42.1229 0.144324
\(45\) 0 0
\(46\) −324.358 −1.03965
\(47\) −34.2493 −0.106293 −0.0531466 0.998587i \(-0.516925\pi\)
−0.0531466 + 0.998587i \(0.516925\pi\)
\(48\) 0 0
\(49\) 617.085 1.79908
\(50\) 341.821 0.966815
\(51\) 0 0
\(52\) 5.26555 0.0140423
\(53\) 344.258 0.892217 0.446109 0.894979i \(-0.352810\pi\)
0.446109 + 0.894979i \(0.352810\pi\)
\(54\) 0 0
\(55\) 182.896 0.448394
\(56\) −667.512 −1.59286
\(57\) 0 0
\(58\) 466.116 1.05524
\(59\) 528.630 1.16647 0.583235 0.812304i \(-0.301787\pi\)
0.583235 + 0.812304i \(0.301787\pi\)
\(60\) 0 0
\(61\) −39.5050 −0.0829197 −0.0414598 0.999140i \(-0.513201\pi\)
−0.0414598 + 0.999140i \(0.513201\pi\)
\(62\) 144.294 0.295571
\(63\) 0 0
\(64\) 460.248 0.898921
\(65\) 22.8628 0.0436273
\(66\) 0 0
\(67\) 541.024 0.986516 0.493258 0.869883i \(-0.335806\pi\)
0.493258 + 0.869883i \(0.335806\pi\)
\(68\) −8.25506 −0.0147217
\(69\) 0 0
\(70\) 275.129 0.469775
\(71\) −1137.35 −1.90111 −0.950556 0.310553i \(-0.899486\pi\)
−0.950556 + 0.310553i \(0.899486\pi\)
\(72\) 0 0
\(73\) 1164.62 1.86724 0.933621 0.358263i \(-0.116631\pi\)
0.933621 + 0.358263i \(0.116631\pi\)
\(74\) 784.778 1.23282
\(75\) 0 0
\(76\) 7.37813 0.0111359
\(77\) −1881.81 −2.78509
\(78\) 0 0
\(79\) −365.495 −0.520524 −0.260262 0.965538i \(-0.583809\pi\)
−0.260262 + 0.965538i \(0.583809\pi\)
\(80\) −207.997 −0.290684
\(81\) 0 0
\(82\) −787.168 −1.06010
\(83\) 869.830 1.15032 0.575158 0.818042i \(-0.304941\pi\)
0.575158 + 0.818042i \(0.304941\pi\)
\(84\) 0 0
\(85\) −35.8431 −0.0457379
\(86\) 1458.30 1.82852
\(87\) 0 0
\(88\) 1308.35 1.58490
\(89\) 150.942 0.179773 0.0898864 0.995952i \(-0.471350\pi\)
0.0898864 + 0.995952i \(0.471350\pi\)
\(90\) 0 0
\(91\) −235.235 −0.270981
\(92\) 76.2998 0.0864652
\(93\) 0 0
\(94\) 100.984 0.110805
\(95\) 32.0355 0.0345976
\(96\) 0 0
\(97\) 70.1786 0.0734594 0.0367297 0.999325i \(-0.488306\pi\)
0.0367297 + 0.999325i \(0.488306\pi\)
\(98\) −1819.47 −1.87545
\(99\) 0 0
\(100\) −80.4075 −0.0804075
\(101\) 658.591 0.648835 0.324417 0.945914i \(-0.394832\pi\)
0.324417 + 0.945914i \(0.394832\pi\)
\(102\) 0 0
\(103\) 1912.26 1.82932 0.914661 0.404221i \(-0.132457\pi\)
0.914661 + 0.404221i \(0.132457\pi\)
\(104\) 163.550 0.154206
\(105\) 0 0
\(106\) −1015.04 −0.930090
\(107\) 601.859 0.543775 0.271887 0.962329i \(-0.412352\pi\)
0.271887 + 0.962329i \(0.412352\pi\)
\(108\) 0 0
\(109\) −201.258 −0.176853 −0.0884266 0.996083i \(-0.528184\pi\)
−0.0884266 + 0.996083i \(0.528184\pi\)
\(110\) −539.266 −0.467427
\(111\) 0 0
\(112\) 2140.08 1.80552
\(113\) −1303.00 −1.08475 −0.542373 0.840138i \(-0.682474\pi\)
−0.542373 + 0.840138i \(0.682474\pi\)
\(114\) 0 0
\(115\) 331.290 0.268634
\(116\) −109.646 −0.0877618
\(117\) 0 0
\(118\) −1558.66 −1.21598
\(119\) 368.789 0.284091
\(120\) 0 0
\(121\) 2357.43 1.77118
\(122\) 116.480 0.0864394
\(123\) 0 0
\(124\) −33.9428 −0.0245819
\(125\) −725.563 −0.519170
\(126\) 0 0
\(127\) 950.566 0.664166 0.332083 0.943250i \(-0.392249\pi\)
0.332083 + 0.943250i \(0.392249\pi\)
\(128\) −1607.45 −1.11000
\(129\) 0 0
\(130\) −67.4106 −0.0454792
\(131\) −1967.89 −1.31248 −0.656241 0.754551i \(-0.727855\pi\)
−0.656241 + 0.754551i \(0.727855\pi\)
\(132\) 0 0
\(133\) −329.612 −0.214895
\(134\) −1595.20 −1.02839
\(135\) 0 0
\(136\) −256.405 −0.161666
\(137\) −1926.79 −1.20158 −0.600790 0.799407i \(-0.705147\pi\)
−0.600790 + 0.799407i \(0.705147\pi\)
\(138\) 0 0
\(139\) −2076.51 −1.26710 −0.633551 0.773701i \(-0.718403\pi\)
−0.633551 + 0.773701i \(0.718403\pi\)
\(140\) −64.7195 −0.0390699
\(141\) 0 0
\(142\) 3353.47 1.98181
\(143\) 461.070 0.269627
\(144\) 0 0
\(145\) −476.077 −0.272662
\(146\) −3433.87 −1.94650
\(147\) 0 0
\(148\) −184.606 −0.102530
\(149\) 1828.22 1.00519 0.502596 0.864522i \(-0.332378\pi\)
0.502596 + 0.864522i \(0.332378\pi\)
\(150\) 0 0
\(151\) −2553.07 −1.37593 −0.687966 0.725743i \(-0.741496\pi\)
−0.687966 + 0.725743i \(0.741496\pi\)
\(152\) 229.167 0.122289
\(153\) 0 0
\(154\) 5548.50 2.90331
\(155\) −147.378 −0.0763721
\(156\) 0 0
\(157\) −1264.56 −0.642819 −0.321409 0.946940i \(-0.604157\pi\)
−0.321409 + 0.946940i \(0.604157\pi\)
\(158\) 1077.66 0.542619
\(159\) 0 0
\(160\) 94.2655 0.0465772
\(161\) −3408.64 −1.66856
\(162\) 0 0
\(163\) −655.491 −0.314982 −0.157491 0.987520i \(-0.550340\pi\)
−0.157491 + 0.987520i \(0.550340\pi\)
\(164\) 185.168 0.0881658
\(165\) 0 0
\(166\) −2564.68 −1.19914
\(167\) −3316.90 −1.53694 −0.768472 0.639883i \(-0.778983\pi\)
−0.768472 + 0.639883i \(0.778983\pi\)
\(168\) 0 0
\(169\) −2139.36 −0.973766
\(170\) 105.683 0.0476794
\(171\) 0 0
\(172\) −343.040 −0.152073
\(173\) 4170.71 1.83291 0.916455 0.400138i \(-0.131038\pi\)
0.916455 + 0.400138i \(0.131038\pi\)
\(174\) 0 0
\(175\) 3592.15 1.55166
\(176\) −4194.65 −1.79650
\(177\) 0 0
\(178\) −445.050 −0.187404
\(179\) −743.541 −0.310474 −0.155237 0.987877i \(-0.549614\pi\)
−0.155237 + 0.987877i \(0.549614\pi\)
\(180\) 0 0
\(181\) 2355.82 0.967439 0.483720 0.875223i \(-0.339285\pi\)
0.483720 + 0.875223i \(0.339285\pi\)
\(182\) 693.586 0.282484
\(183\) 0 0
\(184\) 2369.90 0.949517
\(185\) −801.549 −0.318546
\(186\) 0 0
\(187\) −722.842 −0.282671
\(188\) −23.7547 −0.00921538
\(189\) 0 0
\(190\) −94.4562 −0.0360662
\(191\) 1069.64 0.405217 0.202608 0.979260i \(-0.435058\pi\)
0.202608 + 0.979260i \(0.435058\pi\)
\(192\) 0 0
\(193\) −1458.76 −0.544060 −0.272030 0.962289i \(-0.587695\pi\)
−0.272030 + 0.962289i \(0.587695\pi\)
\(194\) −206.921 −0.0765776
\(195\) 0 0
\(196\) 427.999 0.155976
\(197\) 4612.24 1.66806 0.834032 0.551716i \(-0.186027\pi\)
0.834032 + 0.551716i \(0.186027\pi\)
\(198\) 0 0
\(199\) 3081.14 1.09757 0.548785 0.835964i \(-0.315091\pi\)
0.548785 + 0.835964i \(0.315091\pi\)
\(200\) −2497.49 −0.882995
\(201\) 0 0
\(202\) −1941.85 −0.676376
\(203\) 4898.35 1.69358
\(204\) 0 0
\(205\) 803.990 0.273918
\(206\) −5638.26 −1.90697
\(207\) 0 0
\(208\) −524.349 −0.174794
\(209\) 646.055 0.213821
\(210\) 0 0
\(211\) −4592.03 −1.49824 −0.749120 0.662435i \(-0.769523\pi\)
−0.749120 + 0.662435i \(0.769523\pi\)
\(212\) 238.771 0.0773532
\(213\) 0 0
\(214\) −1774.57 −0.566857
\(215\) −1489.46 −0.472467
\(216\) 0 0
\(217\) 1516.37 0.474368
\(218\) 593.406 0.184360
\(219\) 0 0
\(220\) 126.853 0.0388747
\(221\) −90.3584 −0.0275030
\(222\) 0 0
\(223\) −321.155 −0.0964400 −0.0482200 0.998837i \(-0.515355\pi\)
−0.0482200 + 0.998837i \(0.515355\pi\)
\(224\) −969.897 −0.289303
\(225\) 0 0
\(226\) 3841.89 1.13079
\(227\) 6134.88 1.79377 0.896886 0.442261i \(-0.145824\pi\)
0.896886 + 0.442261i \(0.145824\pi\)
\(228\) 0 0
\(229\) 631.036 0.182096 0.0910480 0.995847i \(-0.470978\pi\)
0.0910480 + 0.995847i \(0.470978\pi\)
\(230\) −976.804 −0.280037
\(231\) 0 0
\(232\) −3405.64 −0.963755
\(233\) −2027.27 −0.570005 −0.285003 0.958527i \(-0.591994\pi\)
−0.285003 + 0.958527i \(0.591994\pi\)
\(234\) 0 0
\(235\) −103.142 −0.0286308
\(236\) 366.648 0.101130
\(237\) 0 0
\(238\) −1087.37 −0.296150
\(239\) 239.000 0.0646846
\(240\) 0 0
\(241\) 6461.36 1.72702 0.863512 0.504329i \(-0.168260\pi\)
0.863512 + 0.504329i \(0.168260\pi\)
\(242\) −6950.87 −1.84636
\(243\) 0 0
\(244\) −27.4000 −0.00718895
\(245\) 1858.35 0.484594
\(246\) 0 0
\(247\) 80.7597 0.0208041
\(248\) −1054.27 −0.269945
\(249\) 0 0
\(250\) 2139.31 0.541208
\(251\) 25.1402 0.00632206 0.00316103 0.999995i \(-0.498994\pi\)
0.00316103 + 0.999995i \(0.498994\pi\)
\(252\) 0 0
\(253\) 6681.08 1.66022
\(254\) −2802.73 −0.692358
\(255\) 0 0
\(256\) 1057.57 0.258195
\(257\) 703.026 0.170636 0.0853182 0.996354i \(-0.472809\pi\)
0.0853182 + 0.996354i \(0.472809\pi\)
\(258\) 0 0
\(259\) 8247.12 1.97858
\(260\) 15.8572 0.00378239
\(261\) 0 0
\(262\) 5802.29 1.36819
\(263\) 1074.16 0.251846 0.125923 0.992040i \(-0.459811\pi\)
0.125923 + 0.992040i \(0.459811\pi\)
\(264\) 0 0
\(265\) 1036.73 0.240324
\(266\) 971.858 0.224017
\(267\) 0 0
\(268\) 375.244 0.0855287
\(269\) −1974.09 −0.447444 −0.223722 0.974653i \(-0.571821\pi\)
−0.223722 + 0.974653i \(0.571821\pi\)
\(270\) 0 0
\(271\) −6933.48 −1.55416 −0.777082 0.629399i \(-0.783301\pi\)
−0.777082 + 0.629399i \(0.783301\pi\)
\(272\) 822.047 0.183250
\(273\) 0 0
\(274\) 5681.11 1.25258
\(275\) −7040.77 −1.54391
\(276\) 0 0
\(277\) −4833.19 −1.04837 −0.524184 0.851605i \(-0.675630\pi\)
−0.524184 + 0.851605i \(0.675630\pi\)
\(278\) 6122.56 1.32089
\(279\) 0 0
\(280\) −2010.21 −0.429046
\(281\) −5582.95 −1.18523 −0.592617 0.805484i \(-0.701905\pi\)
−0.592617 + 0.805484i \(0.701905\pi\)
\(282\) 0 0
\(283\) −5523.03 −1.16011 −0.580053 0.814578i \(-0.696968\pi\)
−0.580053 + 0.814578i \(0.696968\pi\)
\(284\) −788.847 −0.164822
\(285\) 0 0
\(286\) −1359.46 −0.281072
\(287\) −8272.24 −1.70138
\(288\) 0 0
\(289\) −4771.34 −0.971166
\(290\) 1403.71 0.284236
\(291\) 0 0
\(292\) 807.760 0.161886
\(293\) 6073.81 1.21104 0.605522 0.795829i \(-0.292964\pi\)
0.605522 + 0.795829i \(0.292964\pi\)
\(294\) 0 0
\(295\) 1591.97 0.314196
\(296\) −5733.92 −1.12594
\(297\) 0 0
\(298\) −5390.48 −1.04786
\(299\) 835.164 0.161534
\(300\) 0 0
\(301\) 15325.1 2.93462
\(302\) 7527.69 1.43434
\(303\) 0 0
\(304\) −734.722 −0.138616
\(305\) −118.969 −0.0223349
\(306\) 0 0
\(307\) −9068.44 −1.68587 −0.842937 0.538012i \(-0.819176\pi\)
−0.842937 + 0.538012i \(0.819176\pi\)
\(308\) −1305.19 −0.241461
\(309\) 0 0
\(310\) 434.542 0.0796139
\(311\) 5169.60 0.942577 0.471288 0.881979i \(-0.343789\pi\)
0.471288 + 0.881979i \(0.343789\pi\)
\(312\) 0 0
\(313\) −8108.59 −1.46430 −0.732148 0.681145i \(-0.761482\pi\)
−0.732148 + 0.681145i \(0.761482\pi\)
\(314\) 3728.53 0.670105
\(315\) 0 0
\(316\) −253.501 −0.0451282
\(317\) −752.282 −0.133288 −0.0666441 0.997777i \(-0.521229\pi\)
−0.0666441 + 0.997777i \(0.521229\pi\)
\(318\) 0 0
\(319\) −9600.98 −1.68512
\(320\) 1386.03 0.242130
\(321\) 0 0
\(322\) 10050.3 1.73939
\(323\) −126.611 −0.0218106
\(324\) 0 0
\(325\) −880.127 −0.150217
\(326\) 1932.71 0.328352
\(327\) 0 0
\(328\) 5751.38 0.968192
\(329\) 1061.22 0.177833
\(330\) 0 0
\(331\) −4543.36 −0.754459 −0.377229 0.926120i \(-0.623123\pi\)
−0.377229 + 0.926120i \(0.623123\pi\)
\(332\) 603.298 0.0997298
\(333\) 0 0
\(334\) 9779.85 1.60219
\(335\) 1629.29 0.265725
\(336\) 0 0
\(337\) 635.014 0.102645 0.0513226 0.998682i \(-0.483656\pi\)
0.0513226 + 0.998682i \(0.483656\pi\)
\(338\) 6307.89 1.01510
\(339\) 0 0
\(340\) −24.8601 −0.00396537
\(341\) −2972.15 −0.471997
\(342\) 0 0
\(343\) −8492.59 −1.33690
\(344\) −10654.9 −1.66999
\(345\) 0 0
\(346\) −12297.3 −1.91071
\(347\) −6898.85 −1.06729 −0.533645 0.845709i \(-0.679178\pi\)
−0.533645 + 0.845709i \(0.679178\pi\)
\(348\) 0 0
\(349\) 3737.75 0.573287 0.286644 0.958037i \(-0.407460\pi\)
0.286644 + 0.958037i \(0.407460\pi\)
\(350\) −10591.4 −1.61753
\(351\) 0 0
\(352\) 1901.04 0.287858
\(353\) −3933.96 −0.593155 −0.296578 0.955009i \(-0.595845\pi\)
−0.296578 + 0.955009i \(0.595845\pi\)
\(354\) 0 0
\(355\) −3425.13 −0.512077
\(356\) 104.690 0.0155859
\(357\) 0 0
\(358\) 2192.32 0.323653
\(359\) −1651.18 −0.242746 −0.121373 0.992607i \(-0.538730\pi\)
−0.121373 + 0.992607i \(0.538730\pi\)
\(360\) 0 0
\(361\) −6745.84 −0.983502
\(362\) −6946.10 −1.00850
\(363\) 0 0
\(364\) −163.154 −0.0234934
\(365\) 3507.25 0.502953
\(366\) 0 0
\(367\) 304.439 0.0433013 0.0216506 0.999766i \(-0.493108\pi\)
0.0216506 + 0.999766i \(0.493108\pi\)
\(368\) −7598.01 −1.07629
\(369\) 0 0
\(370\) 2363.36 0.332068
\(371\) −10666.9 −1.49272
\(372\) 0 0
\(373\) 6639.18 0.921618 0.460809 0.887499i \(-0.347559\pi\)
0.460809 + 0.887499i \(0.347559\pi\)
\(374\) 2131.29 0.294670
\(375\) 0 0
\(376\) −737.830 −0.101199
\(377\) −1200.16 −0.163957
\(378\) 0 0
\(379\) −12535.4 −1.69894 −0.849470 0.527637i \(-0.823078\pi\)
−0.849470 + 0.527637i \(0.823078\pi\)
\(380\) 22.2192 0.00299953
\(381\) 0 0
\(382\) −3153.82 −0.422417
\(383\) 9432.96 1.25849 0.629245 0.777207i \(-0.283364\pi\)
0.629245 + 0.777207i \(0.283364\pi\)
\(384\) 0 0
\(385\) −5667.07 −0.750183
\(386\) 4301.12 0.567154
\(387\) 0 0
\(388\) 48.6746 0.00636876
\(389\) −13408.0 −1.74759 −0.873793 0.486298i \(-0.838347\pi\)
−0.873793 + 0.486298i \(0.838347\pi\)
\(390\) 0 0
\(391\) −1309.33 −0.169349
\(392\) 13293.8 1.71285
\(393\) 0 0
\(394\) −13599.1 −1.73887
\(395\) −1100.69 −0.140207
\(396\) 0 0
\(397\) 4323.18 0.546535 0.273267 0.961938i \(-0.411896\pi\)
0.273267 + 0.961938i \(0.411896\pi\)
\(398\) −9084.70 −1.14416
\(399\) 0 0
\(400\) 8007.07 1.00088
\(401\) −9306.73 −1.15899 −0.579496 0.814975i \(-0.696751\pi\)
−0.579496 + 0.814975i \(0.696751\pi\)
\(402\) 0 0
\(403\) −371.532 −0.0459239
\(404\) 456.787 0.0562525
\(405\) 0 0
\(406\) −14442.7 −1.76547
\(407\) −16164.7 −1.96869
\(408\) 0 0
\(409\) −15210.7 −1.83892 −0.919460 0.393184i \(-0.871374\pi\)
−0.919460 + 0.393184i \(0.871374\pi\)
\(410\) −2370.55 −0.285545
\(411\) 0 0
\(412\) 1326.31 0.158598
\(413\) −16379.7 −1.95156
\(414\) 0 0
\(415\) 2619.49 0.309845
\(416\) 237.638 0.0280077
\(417\) 0 0
\(418\) −1904.89 −0.222897
\(419\) 8083.79 0.942528 0.471264 0.881992i \(-0.343798\pi\)
0.471264 + 0.881992i \(0.343798\pi\)
\(420\) 0 0
\(421\) 13087.0 1.51501 0.757506 0.652829i \(-0.226418\pi\)
0.757506 + 0.652829i \(0.226418\pi\)
\(422\) 13539.6 1.56184
\(423\) 0 0
\(424\) 7416.32 0.849453
\(425\) 1379.82 0.157485
\(426\) 0 0
\(427\) 1224.07 0.138728
\(428\) 417.438 0.0471440
\(429\) 0 0
\(430\) 4391.66 0.492523
\(431\) −656.182 −0.0733345 −0.0366673 0.999328i \(-0.511674\pi\)
−0.0366673 + 0.999328i \(0.511674\pi\)
\(432\) 0 0
\(433\) −1520.21 −0.168722 −0.0843611 0.996435i \(-0.526885\pi\)
−0.0843611 + 0.996435i \(0.526885\pi\)
\(434\) −4470.99 −0.494503
\(435\) 0 0
\(436\) −139.589 −0.0153328
\(437\) 1170.24 0.128101
\(438\) 0 0
\(439\) 7687.24 0.835745 0.417872 0.908506i \(-0.362776\pi\)
0.417872 + 0.908506i \(0.362776\pi\)
\(440\) 3940.10 0.426902
\(441\) 0 0
\(442\) 266.421 0.0286705
\(443\) −8124.34 −0.871330 −0.435665 0.900109i \(-0.643487\pi\)
−0.435665 + 0.900109i \(0.643487\pi\)
\(444\) 0 0
\(445\) 454.560 0.0484230
\(446\) 946.922 0.100534
\(447\) 0 0
\(448\) −14260.9 −1.50394
\(449\) −18128.8 −1.90545 −0.952727 0.303828i \(-0.901735\pi\)
−0.952727 + 0.303828i \(0.901735\pi\)
\(450\) 0 0
\(451\) 16214.0 1.69287
\(452\) −903.740 −0.0940450
\(453\) 0 0
\(454\) −18088.6 −1.86991
\(455\) −708.408 −0.0729905
\(456\) 0 0
\(457\) 11175.2 1.14389 0.571943 0.820294i \(-0.306190\pi\)
0.571943 + 0.820294i \(0.306190\pi\)
\(458\) −1860.60 −0.189826
\(459\) 0 0
\(460\) 229.777 0.0232900
\(461\) 3955.48 0.399620 0.199810 0.979835i \(-0.435967\pi\)
0.199810 + 0.979835i \(0.435967\pi\)
\(462\) 0 0
\(463\) 7668.34 0.769715 0.384857 0.922976i \(-0.374251\pi\)
0.384857 + 0.922976i \(0.374251\pi\)
\(464\) 10918.7 1.09243
\(465\) 0 0
\(466\) 5977.40 0.594201
\(467\) −7427.44 −0.735976 −0.367988 0.929831i \(-0.619953\pi\)
−0.367988 + 0.929831i \(0.619953\pi\)
\(468\) 0 0
\(469\) −16763.8 −1.65049
\(470\) 304.112 0.0298461
\(471\) 0 0
\(472\) 11388.2 1.11056
\(473\) −30037.8 −2.91996
\(474\) 0 0
\(475\) −1233.24 −0.119126
\(476\) 255.785 0.0246300
\(477\) 0 0
\(478\) −704.689 −0.0674304
\(479\) 14201.1 1.35463 0.677314 0.735694i \(-0.263144\pi\)
0.677314 + 0.735694i \(0.263144\pi\)
\(480\) 0 0
\(481\) −2020.66 −0.191547
\(482\) −19051.2 −1.80033
\(483\) 0 0
\(484\) 1635.07 0.153557
\(485\) 211.343 0.0197868
\(486\) 0 0
\(487\) 14212.8 1.32247 0.661236 0.750178i \(-0.270032\pi\)
0.661236 + 0.750178i \(0.270032\pi\)
\(488\) −851.052 −0.0789453
\(489\) 0 0
\(490\) −5479.32 −0.505164
\(491\) −15438.9 −1.41904 −0.709521 0.704684i \(-0.751089\pi\)
−0.709521 + 0.704684i \(0.751089\pi\)
\(492\) 0 0
\(493\) 1881.56 0.171889
\(494\) −238.119 −0.0216872
\(495\) 0 0
\(496\) 3380.06 0.305986
\(497\) 35241.2 3.18065
\(498\) 0 0
\(499\) −21095.9 −1.89255 −0.946276 0.323361i \(-0.895187\pi\)
−0.946276 + 0.323361i \(0.895187\pi\)
\(500\) −503.237 −0.0450109
\(501\) 0 0
\(502\) −74.1257 −0.00659042
\(503\) 4997.19 0.442970 0.221485 0.975164i \(-0.428910\pi\)
0.221485 + 0.975164i \(0.428910\pi\)
\(504\) 0 0
\(505\) 1983.35 0.174768
\(506\) −19699.1 −1.73069
\(507\) 0 0
\(508\) 659.295 0.0575817
\(509\) 66.7780 0.00581509 0.00290755 0.999996i \(-0.499074\pi\)
0.00290755 + 0.999996i \(0.499074\pi\)
\(510\) 0 0
\(511\) −36086.1 −3.12398
\(512\) 9741.38 0.840844
\(513\) 0 0
\(514\) −2072.86 −0.177879
\(515\) 5758.75 0.492740
\(516\) 0 0
\(517\) −2080.05 −0.176945
\(518\) −24316.5 −2.06256
\(519\) 0 0
\(520\) 492.530 0.0415363
\(521\) −18888.9 −1.58837 −0.794184 0.607678i \(-0.792101\pi\)
−0.794184 + 0.607678i \(0.792101\pi\)
\(522\) 0 0
\(523\) −12882.2 −1.07706 −0.538529 0.842607i \(-0.681020\pi\)
−0.538529 + 0.842607i \(0.681020\pi\)
\(524\) −1364.89 −0.113789
\(525\) 0 0
\(526\) −3167.14 −0.262536
\(527\) 582.468 0.0481456
\(528\) 0 0
\(529\) −65.1627 −0.00535569
\(530\) −3056.79 −0.250526
\(531\) 0 0
\(532\) −228.613 −0.0186309
\(533\) 2026.82 0.164711
\(534\) 0 0
\(535\) 1812.50 0.146469
\(536\) 11655.2 0.939233
\(537\) 0 0
\(538\) 5820.58 0.466437
\(539\) 37477.1 2.99490
\(540\) 0 0
\(541\) −8225.78 −0.653704 −0.326852 0.945076i \(-0.605988\pi\)
−0.326852 + 0.945076i \(0.605988\pi\)
\(542\) 20443.3 1.62014
\(543\) 0 0
\(544\) −372.557 −0.0293626
\(545\) −606.087 −0.0476366
\(546\) 0 0
\(547\) −11783.2 −0.921049 −0.460524 0.887647i \(-0.652339\pi\)
−0.460524 + 0.887647i \(0.652339\pi\)
\(548\) −1336.38 −0.104174
\(549\) 0 0
\(550\) 20759.6 1.60944
\(551\) −1681.68 −0.130022
\(552\) 0 0
\(553\) 11324.9 0.870860
\(554\) 14250.6 1.09287
\(555\) 0 0
\(556\) −1440.23 −0.109855
\(557\) −8763.38 −0.666636 −0.333318 0.942814i \(-0.608168\pi\)
−0.333318 + 0.942814i \(0.608168\pi\)
\(558\) 0 0
\(559\) −3754.86 −0.284103
\(560\) 6444.83 0.486328
\(561\) 0 0
\(562\) 16461.3 1.23555
\(563\) 17285.5 1.29396 0.646978 0.762509i \(-0.276033\pi\)
0.646978 + 0.762509i \(0.276033\pi\)
\(564\) 0 0
\(565\) −3923.99 −0.292183
\(566\) 16284.6 1.20935
\(567\) 0 0
\(568\) −24501.9 −1.80999
\(569\) −16391.4 −1.20767 −0.603835 0.797110i \(-0.706361\pi\)
−0.603835 + 0.797110i \(0.706361\pi\)
\(570\) 0 0
\(571\) −2412.70 −0.176827 −0.0884134 0.996084i \(-0.528180\pi\)
−0.0884134 + 0.996084i \(0.528180\pi\)
\(572\) 319.790 0.0233760
\(573\) 0 0
\(574\) 24390.6 1.77360
\(575\) −12753.4 −0.924960
\(576\) 0 0
\(577\) −22394.9 −1.61579 −0.807897 0.589324i \(-0.799394\pi\)
−0.807897 + 0.589324i \(0.799394\pi\)
\(578\) 14068.2 1.01239
\(579\) 0 0
\(580\) −330.198 −0.0236392
\(581\) −26951.9 −1.92453
\(582\) 0 0
\(583\) 20907.7 1.48526
\(584\) 25089.3 1.77774
\(585\) 0 0
\(586\) −17908.6 −1.26245
\(587\) 5624.16 0.395458 0.197729 0.980257i \(-0.436643\pi\)
0.197729 + 0.980257i \(0.436643\pi\)
\(588\) 0 0
\(589\) −520.593 −0.0364188
\(590\) −4693.89 −0.327533
\(591\) 0 0
\(592\) 18383.2 1.27626
\(593\) −17933.9 −1.24192 −0.620960 0.783843i \(-0.713257\pi\)
−0.620960 + 0.783843i \(0.713257\pi\)
\(594\) 0 0
\(595\) 1110.61 0.0765217
\(596\) 1268.02 0.0871478
\(597\) 0 0
\(598\) −2462.47 −0.168391
\(599\) 20410.3 1.39223 0.696113 0.717932i \(-0.254911\pi\)
0.696113 + 0.717932i \(0.254911\pi\)
\(600\) 0 0
\(601\) −26687.9 −1.81135 −0.905675 0.423973i \(-0.860635\pi\)
−0.905675 + 0.423973i \(0.860635\pi\)
\(602\) −45185.7 −3.05919
\(603\) 0 0
\(604\) −1770.76 −0.119290
\(605\) 7099.41 0.477077
\(606\) 0 0
\(607\) −9563.73 −0.639505 −0.319753 0.947501i \(-0.603600\pi\)
−0.319753 + 0.947501i \(0.603600\pi\)
\(608\) 332.981 0.0222108
\(609\) 0 0
\(610\) 350.779 0.0232830
\(611\) −260.015 −0.0172162
\(612\) 0 0
\(613\) −18801.5 −1.23880 −0.619400 0.785075i \(-0.712624\pi\)
−0.619400 + 0.785075i \(0.712624\pi\)
\(614\) 26738.2 1.75744
\(615\) 0 0
\(616\) −40539.6 −2.65160
\(617\) 9903.34 0.646181 0.323090 0.946368i \(-0.395278\pi\)
0.323090 + 0.946368i \(0.395278\pi\)
\(618\) 0 0
\(619\) 6474.65 0.420417 0.210208 0.977657i \(-0.432586\pi\)
0.210208 + 0.977657i \(0.432586\pi\)
\(620\) −102.219 −0.00662128
\(621\) 0 0
\(622\) −15242.5 −0.982587
\(623\) −4676.96 −0.300768
\(624\) 0 0
\(625\) 12306.3 0.787605
\(626\) 23908.1 1.52645
\(627\) 0 0
\(628\) −877.073 −0.0557309
\(629\) 3167.89 0.200814
\(630\) 0 0
\(631\) 17350.1 1.09461 0.547304 0.836934i \(-0.315654\pi\)
0.547304 + 0.836934i \(0.315654\pi\)
\(632\) −7873.82 −0.495575
\(633\) 0 0
\(634\) 2218.10 0.138946
\(635\) 2862.63 0.178897
\(636\) 0 0
\(637\) 4684.80 0.291395
\(638\) 28308.4 1.75665
\(639\) 0 0
\(640\) −4840.83 −0.298985
\(641\) −22564.0 −1.39037 −0.695183 0.718833i \(-0.744677\pi\)
−0.695183 + 0.718833i \(0.744677\pi\)
\(642\) 0 0
\(643\) 4977.44 0.305274 0.152637 0.988282i \(-0.451224\pi\)
0.152637 + 0.988282i \(0.451224\pi\)
\(644\) −2364.17 −0.144660
\(645\) 0 0
\(646\) 373.311 0.0227364
\(647\) 13751.2 0.835571 0.417785 0.908546i \(-0.362806\pi\)
0.417785 + 0.908546i \(0.362806\pi\)
\(648\) 0 0
\(649\) 32105.0 1.94180
\(650\) 2595.04 0.156594
\(651\) 0 0
\(652\) −454.636 −0.0273082
\(653\) −11758.0 −0.704635 −0.352317 0.935881i \(-0.614606\pi\)
−0.352317 + 0.935881i \(0.614606\pi\)
\(654\) 0 0
\(655\) −5926.29 −0.353526
\(656\) −18439.2 −1.09746
\(657\) 0 0
\(658\) −3129.01 −0.185382
\(659\) −9970.21 −0.589354 −0.294677 0.955597i \(-0.595212\pi\)
−0.294677 + 0.955597i \(0.595212\pi\)
\(660\) 0 0
\(661\) −3802.25 −0.223737 −0.111869 0.993723i \(-0.535684\pi\)
−0.111869 + 0.993723i \(0.535684\pi\)
\(662\) 13396.1 0.786484
\(663\) 0 0
\(664\) 18738.6 1.09518
\(665\) −992.627 −0.0578833
\(666\) 0 0
\(667\) −17390.8 −1.00956
\(668\) −2300.54 −0.133250
\(669\) 0 0
\(670\) −4803.95 −0.277004
\(671\) −2399.24 −0.138035
\(672\) 0 0
\(673\) −2812.14 −0.161070 −0.0805350 0.996752i \(-0.525663\pi\)
−0.0805350 + 0.996752i \(0.525663\pi\)
\(674\) −1872.33 −0.107002
\(675\) 0 0
\(676\) −1483.82 −0.0844233
\(677\) 10291.8 0.584261 0.292131 0.956378i \(-0.405636\pi\)
0.292131 + 0.956378i \(0.405636\pi\)
\(678\) 0 0
\(679\) −2174.50 −0.122901
\(680\) −772.163 −0.0435457
\(681\) 0 0
\(682\) 8763.35 0.492032
\(683\) −617.671 −0.0346040 −0.0173020 0.999850i \(-0.505508\pi\)
−0.0173020 + 0.999850i \(0.505508\pi\)
\(684\) 0 0
\(685\) −5802.51 −0.323653
\(686\) 25040.3 1.39365
\(687\) 0 0
\(688\) 34160.3 1.89295
\(689\) 2613.55 0.144511
\(690\) 0 0
\(691\) 23997.5 1.32114 0.660569 0.750766i \(-0.270315\pi\)
0.660569 + 0.750766i \(0.270315\pi\)
\(692\) 2892.73 0.158909
\(693\) 0 0
\(694\) 20341.2 1.11259
\(695\) −6253.40 −0.341302
\(696\) 0 0
\(697\) −3177.54 −0.172680
\(698\) −11020.7 −0.597622
\(699\) 0 0
\(700\) 2491.45 0.134525
\(701\) −24153.2 −1.30136 −0.650682 0.759351i \(-0.725517\pi\)
−0.650682 + 0.759351i \(0.725517\pi\)
\(702\) 0 0
\(703\) −2831.37 −0.151902
\(704\) 27952.0 1.49642
\(705\) 0 0
\(706\) 11599.2 0.618333
\(707\) −20406.6 −1.08553
\(708\) 0 0
\(709\) −2210.49 −0.117090 −0.0585450 0.998285i \(-0.518646\pi\)
−0.0585450 + 0.998285i \(0.518646\pi\)
\(710\) 10099.0 0.533813
\(711\) 0 0
\(712\) 3251.72 0.171156
\(713\) −5383.63 −0.282775
\(714\) 0 0
\(715\) 1388.51 0.0726257
\(716\) −515.706 −0.0269174
\(717\) 0 0
\(718\) 4868.48 0.253050
\(719\) −33927.5 −1.75978 −0.879891 0.475175i \(-0.842385\pi\)
−0.879891 + 0.475175i \(0.842385\pi\)
\(720\) 0 0
\(721\) −59251.7 −3.06054
\(722\) 19890.0 1.02525
\(723\) 0 0
\(724\) 1633.95 0.0838747
\(725\) 18327.1 0.938830
\(726\) 0 0
\(727\) −19140.6 −0.976461 −0.488231 0.872715i \(-0.662358\pi\)
−0.488231 + 0.872715i \(0.662358\pi\)
\(728\) −5067.63 −0.257993
\(729\) 0 0
\(730\) −10341.1 −0.524303
\(731\) 5886.67 0.297847
\(732\) 0 0
\(733\) 28268.3 1.42444 0.712219 0.701957i \(-0.247690\pi\)
0.712219 + 0.701957i \(0.247690\pi\)
\(734\) −897.634 −0.0451393
\(735\) 0 0
\(736\) 3443.47 0.172456
\(737\) 32857.7 1.64224
\(738\) 0 0
\(739\) 36066.3 1.79529 0.897645 0.440719i \(-0.145277\pi\)
0.897645 + 0.440719i \(0.145277\pi\)
\(740\) −555.940 −0.0276172
\(741\) 0 0
\(742\) 31451.3 1.55608
\(743\) 19646.9 0.970088 0.485044 0.874490i \(-0.338804\pi\)
0.485044 + 0.874490i \(0.338804\pi\)
\(744\) 0 0
\(745\) 5505.67 0.270755
\(746\) −19575.5 −0.960739
\(747\) 0 0
\(748\) −501.350 −0.0245069
\(749\) −18648.7 −0.909760
\(750\) 0 0
\(751\) −14286.8 −0.694183 −0.347092 0.937831i \(-0.612831\pi\)
−0.347092 + 0.937831i \(0.612831\pi\)
\(752\) 2365.52 0.114710
\(753\) 0 0
\(754\) 3538.67 0.170916
\(755\) −7688.56 −0.370616
\(756\) 0 0
\(757\) −6082.28 −0.292027 −0.146013 0.989283i \(-0.546644\pi\)
−0.146013 + 0.989283i \(0.546644\pi\)
\(758\) 36960.4 1.77106
\(759\) 0 0
\(760\) 690.137 0.0329393
\(761\) 14570.0 0.694038 0.347019 0.937858i \(-0.387194\pi\)
0.347019 + 0.937858i \(0.387194\pi\)
\(762\) 0 0
\(763\) 6236.02 0.295884
\(764\) 741.882 0.0351314
\(765\) 0 0
\(766\) −27813.0 −1.31191
\(767\) 4013.26 0.188932
\(768\) 0 0
\(769\) 40710.2 1.90904 0.954518 0.298153i \(-0.0963705\pi\)
0.954518 + 0.298153i \(0.0963705\pi\)
\(770\) 16709.3 0.782027
\(771\) 0 0
\(772\) −1011.77 −0.0471687
\(773\) −22309.4 −1.03805 −0.519026 0.854758i \(-0.673705\pi\)
−0.519026 + 0.854758i \(0.673705\pi\)
\(774\) 0 0
\(775\) 5673.47 0.262964
\(776\) 1511.85 0.0699385
\(777\) 0 0
\(778\) 39533.2 1.82177
\(779\) 2839.99 0.130620
\(780\) 0 0
\(781\) −69074.3 −3.16475
\(782\) 3860.54 0.176538
\(783\) 0 0
\(784\) −42620.6 −1.94154
\(785\) −3808.21 −0.173147
\(786\) 0 0
\(787\) 29959.9 1.35700 0.678499 0.734602i \(-0.262631\pi\)
0.678499 + 0.734602i \(0.262631\pi\)
\(788\) 3198.97 0.144617
\(789\) 0 0
\(790\) 3245.36 0.146158
\(791\) 40373.9 1.81483
\(792\) 0 0
\(793\) −299.915 −0.0134304
\(794\) −12746.8 −0.569734
\(795\) 0 0
\(796\) 2137.02 0.0951567
\(797\) −33708.9 −1.49815 −0.749077 0.662483i \(-0.769503\pi\)
−0.749077 + 0.662483i \(0.769503\pi\)
\(798\) 0 0
\(799\) 407.638 0.0180491
\(800\) −3628.86 −0.160374
\(801\) 0 0
\(802\) 27440.8 1.20819
\(803\) 70730.3 3.10837
\(804\) 0 0
\(805\) −10265.1 −0.449437
\(806\) 1095.46 0.0478732
\(807\) 0 0
\(808\) 14188.0 0.617736
\(809\) 33454.7 1.45390 0.726951 0.686690i \(-0.240937\pi\)
0.726951 + 0.686690i \(0.240937\pi\)
\(810\) 0 0
\(811\) 10656.8 0.461418 0.230709 0.973023i \(-0.425895\pi\)
0.230709 + 0.973023i \(0.425895\pi\)
\(812\) 3397.40 0.146829
\(813\) 0 0
\(814\) 47661.5 2.05225
\(815\) −1974.01 −0.0848423
\(816\) 0 0
\(817\) −5261.33 −0.225301
\(818\) 44848.4 1.91698
\(819\) 0 0
\(820\) 557.633 0.0237480
\(821\) −12361.9 −0.525497 −0.262749 0.964864i \(-0.584629\pi\)
−0.262749 + 0.964864i \(0.584629\pi\)
\(822\) 0 0
\(823\) −4611.71 −0.195327 −0.0976634 0.995220i \(-0.531137\pi\)
−0.0976634 + 0.995220i \(0.531137\pi\)
\(824\) 41195.5 1.74164
\(825\) 0 0
\(826\) 48295.4 2.03440
\(827\) 12793.3 0.537927 0.268964 0.963150i \(-0.413319\pi\)
0.268964 + 0.963150i \(0.413319\pi\)
\(828\) 0 0
\(829\) −8373.92 −0.350830 −0.175415 0.984495i \(-0.556127\pi\)
−0.175415 + 0.984495i \(0.556127\pi\)
\(830\) −7723.54 −0.322997
\(831\) 0 0
\(832\) 3494.12 0.145597
\(833\) −7344.59 −0.305492
\(834\) 0 0
\(835\) −9988.85 −0.413986
\(836\) 448.092 0.0185378
\(837\) 0 0
\(838\) −23835.0 −0.982536
\(839\) 18047.5 0.742633 0.371316 0.928506i \(-0.378906\pi\)
0.371316 + 0.928506i \(0.378906\pi\)
\(840\) 0 0
\(841\) 602.340 0.0246972
\(842\) −38586.8 −1.57932
\(843\) 0 0
\(844\) −3184.95 −0.129894
\(845\) −6442.69 −0.262290
\(846\) 0 0
\(847\) −73045.7 −2.96326
\(848\) −23777.1 −0.962864
\(849\) 0 0
\(850\) −4068.38 −0.164170
\(851\) −29280.1 −1.17945
\(852\) 0 0
\(853\) −31063.1 −1.24687 −0.623436 0.781875i \(-0.714264\pi\)
−0.623436 + 0.781875i \(0.714264\pi\)
\(854\) −3609.16 −0.144617
\(855\) 0 0
\(856\) 12965.8 0.517712
\(857\) −653.734 −0.0260573 −0.0130287 0.999915i \(-0.504147\pi\)
−0.0130287 + 0.999915i \(0.504147\pi\)
\(858\) 0 0
\(859\) 227.597 0.00904018 0.00452009 0.999990i \(-0.498561\pi\)
0.00452009 + 0.999990i \(0.498561\pi\)
\(860\) −1033.06 −0.0409618
\(861\) 0 0
\(862\) 1934.75 0.0764474
\(863\) −41470.6 −1.63578 −0.817889 0.575377i \(-0.804855\pi\)
−0.817889 + 0.575377i \(0.804855\pi\)
\(864\) 0 0
\(865\) 12560.1 0.493706
\(866\) 4482.33 0.175884
\(867\) 0 0
\(868\) 1051.72 0.0411266
\(869\) −22197.4 −0.866508
\(870\) 0 0
\(871\) 4107.36 0.159785
\(872\) −4335.67 −0.168377
\(873\) 0 0
\(874\) −3450.43 −0.133539
\(875\) 22481.7 0.868596
\(876\) 0 0
\(877\) 8502.68 0.327383 0.163692 0.986512i \(-0.447660\pi\)
0.163692 + 0.986512i \(0.447660\pi\)
\(878\) −22665.7 −0.871221
\(879\) 0 0
\(880\) −12632.2 −0.483898
\(881\) 8892.91 0.340079 0.170040 0.985437i \(-0.445610\pi\)
0.170040 + 0.985437i \(0.445610\pi\)
\(882\) 0 0
\(883\) −20622.6 −0.785964 −0.392982 0.919546i \(-0.628557\pi\)
−0.392982 + 0.919546i \(0.628557\pi\)
\(884\) −62.6710 −0.00238445
\(885\) 0 0
\(886\) 23954.5 0.908316
\(887\) −67.3701 −0.00255024 −0.00127512 0.999999i \(-0.500406\pi\)
−0.00127512 + 0.999999i \(0.500406\pi\)
\(888\) 0 0
\(889\) −29453.5 −1.11118
\(890\) −1340.27 −0.0504784
\(891\) 0 0
\(892\) −222.747 −0.00836113
\(893\) −364.335 −0.0136529
\(894\) 0 0
\(895\) −2239.17 −0.0836282
\(896\) 49807.2 1.85708
\(897\) 0 0
\(898\) 53452.4 1.98634
\(899\) 7736.50 0.287015
\(900\) 0 0
\(901\) −4097.39 −0.151502
\(902\) −47806.7 −1.76473
\(903\) 0 0
\(904\) −28070.5 −1.03275
\(905\) 7094.53 0.260586
\(906\) 0 0
\(907\) 19833.4 0.726082 0.363041 0.931773i \(-0.381738\pi\)
0.363041 + 0.931773i \(0.381738\pi\)
\(908\) 4255.04 0.155516
\(909\) 0 0
\(910\) 2088.73 0.0760888
\(911\) 27914.0 1.01518 0.507591 0.861598i \(-0.330536\pi\)
0.507591 + 0.861598i \(0.330536\pi\)
\(912\) 0 0
\(913\) 52826.9 1.91491
\(914\) −32950.1 −1.19244
\(915\) 0 0
\(916\) 437.675 0.0157873
\(917\) 60975.5 2.19584
\(918\) 0 0
\(919\) −7309.96 −0.262387 −0.131193 0.991357i \(-0.541881\pi\)
−0.131193 + 0.991357i \(0.541881\pi\)
\(920\) 7136.94 0.255759
\(921\) 0 0
\(922\) −11662.7 −0.416583
\(923\) −8634.58 −0.307921
\(924\) 0 0
\(925\) 30856.5 1.09682
\(926\) −22610.0 −0.802387
\(927\) 0 0
\(928\) −4948.41 −0.175042
\(929\) 11015.8 0.389037 0.194518 0.980899i \(-0.437686\pi\)
0.194518 + 0.980899i \(0.437686\pi\)
\(930\) 0 0
\(931\) 6564.38 0.231084
\(932\) −1406.08 −0.0494181
\(933\) 0 0
\(934\) 21899.7 0.767217
\(935\) −2176.84 −0.0761392
\(936\) 0 0
\(937\) 24322.9 0.848018 0.424009 0.905658i \(-0.360622\pi\)
0.424009 + 0.905658i \(0.360622\pi\)
\(938\) 49427.7 1.72055
\(939\) 0 0
\(940\) −71.5373 −0.00248222
\(941\) −33881.0 −1.17374 −0.586869 0.809682i \(-0.699640\pi\)
−0.586869 + 0.809682i \(0.699640\pi\)
\(942\) 0 0
\(943\) 29369.3 1.01421
\(944\) −36511.2 −1.25883
\(945\) 0 0
\(946\) 88566.1 3.04390
\(947\) 7065.40 0.242444 0.121222 0.992625i \(-0.461319\pi\)
0.121222 + 0.992625i \(0.461319\pi\)
\(948\) 0 0
\(949\) 8841.60 0.302435
\(950\) 3636.20 0.124183
\(951\) 0 0
\(952\) 7944.77 0.270474
\(953\) −21167.4 −0.719495 −0.359747 0.933050i \(-0.617137\pi\)
−0.359747 + 0.933050i \(0.617137\pi\)
\(954\) 0 0
\(955\) 3221.22 0.109148
\(956\) 165.766 0.00560801
\(957\) 0 0
\(958\) −41871.9 −1.41213
\(959\) 59701.9 2.01030
\(960\) 0 0
\(961\) −27396.0 −0.919608
\(962\) 5957.90 0.199678
\(963\) 0 0
\(964\) 4481.48 0.149729
\(965\) −4393.04 −0.146546
\(966\) 0 0
\(967\) −10137.8 −0.337134 −0.168567 0.985690i \(-0.553914\pi\)
−0.168567 + 0.985690i \(0.553914\pi\)
\(968\) 50785.9 1.68628
\(969\) 0 0
\(970\) −623.141 −0.0206267
\(971\) 13500.9 0.446203 0.223101 0.974795i \(-0.428382\pi\)
0.223101 + 0.974795i \(0.428382\pi\)
\(972\) 0 0
\(973\) 64341.1 2.11992
\(974\) −41906.3 −1.37861
\(975\) 0 0
\(976\) 2728.52 0.0894853
\(977\) −25825.9 −0.845695 −0.422848 0.906201i \(-0.638969\pi\)
−0.422848 + 0.906201i \(0.638969\pi\)
\(978\) 0 0
\(979\) 9167.06 0.299265
\(980\) 1288.92 0.0420132
\(981\) 0 0
\(982\) 45521.5 1.47928
\(983\) −21515.7 −0.698113 −0.349056 0.937102i \(-0.613498\pi\)
−0.349056 + 0.937102i \(0.613498\pi\)
\(984\) 0 0
\(985\) 13889.8 0.449304
\(986\) −5547.75 −0.179185
\(987\) 0 0
\(988\) 56.0135 0.00180367
\(989\) −54409.3 −1.74936
\(990\) 0 0
\(991\) 1578.43 0.0505957 0.0252979 0.999680i \(-0.491947\pi\)
0.0252979 + 0.999680i \(0.491947\pi\)
\(992\) −1531.86 −0.0490290
\(993\) 0 0
\(994\) −103908. −3.31566
\(995\) 9278.84 0.295637
\(996\) 0 0
\(997\) −42702.0 −1.35645 −0.678227 0.734852i \(-0.737252\pi\)
−0.678227 + 0.734852i \(0.737252\pi\)
\(998\) 62201.1 1.97289
\(999\) 0 0
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 2151.4.a.g.1.18 59
3.2 odd 2 2151.4.a.h.1.42 yes 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.18 59 1.1 even 1 trivial
2151.4.a.h.1.42 yes 59 3.2 odd 2