Properties

Label 1859.4.a.q.1.16
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $0$
Dimension $51$
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] = [1859,4,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, 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("1859.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(109.684550701\)
Analytic rank: \(0\)
Dimension: \(51\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.92218 q^{2} -6.70384 q^{3} +0.539146 q^{4} +12.5727 q^{5} +19.5898 q^{6} -15.7135 q^{7} +21.8020 q^{8} +17.9414 q^{9} +O(q^{10})\) \(q-2.92218 q^{2} -6.70384 q^{3} +0.539146 q^{4} +12.5727 q^{5} +19.5898 q^{6} -15.7135 q^{7} +21.8020 q^{8} +17.9414 q^{9} -36.7396 q^{10} +11.0000 q^{11} -3.61435 q^{12} +45.9177 q^{14} -84.2851 q^{15} -68.0225 q^{16} +88.6878 q^{17} -52.4281 q^{18} +129.741 q^{19} +6.77851 q^{20} +105.341 q^{21} -32.1440 q^{22} -172.749 q^{23} -146.157 q^{24} +33.0721 q^{25} +60.7273 q^{27} -8.47187 q^{28} +5.46969 q^{29} +246.296 q^{30} +222.253 q^{31} +24.3583 q^{32} -73.7422 q^{33} -259.162 q^{34} -197.561 q^{35} +9.67305 q^{36} +351.233 q^{37} -379.128 q^{38} +274.109 q^{40} +424.792 q^{41} -307.825 q^{42} -155.625 q^{43} +5.93061 q^{44} +225.571 q^{45} +504.804 q^{46} +406.439 q^{47} +456.012 q^{48} -96.0862 q^{49} -96.6427 q^{50} -594.548 q^{51} +280.727 q^{53} -177.456 q^{54} +138.299 q^{55} -342.585 q^{56} -869.765 q^{57} -15.9834 q^{58} -108.495 q^{59} -45.4420 q^{60} +388.485 q^{61} -649.464 q^{62} -281.922 q^{63} +473.000 q^{64} +215.488 q^{66} -651.390 q^{67} +47.8157 q^{68} +1158.08 q^{69} +577.308 q^{70} +382.632 q^{71} +391.158 q^{72} -211.476 q^{73} -1026.37 q^{74} -221.710 q^{75} +69.9496 q^{76} -172.848 q^{77} +313.752 q^{79} -855.225 q^{80} -891.524 q^{81} -1241.32 q^{82} +1127.22 q^{83} +56.7940 q^{84} +1115.04 q^{85} +454.764 q^{86} -36.6679 q^{87} +239.822 q^{88} -591.138 q^{89} -659.161 q^{90} -93.1370 q^{92} -1489.95 q^{93} -1187.69 q^{94} +1631.20 q^{95} -163.294 q^{96} -490.807 q^{97} +280.781 q^{98} +197.356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.92218 −1.03315 −0.516574 0.856243i \(-0.672793\pi\)
−0.516574 + 0.856243i \(0.672793\pi\)
\(3\) −6.70384 −1.29015 −0.645077 0.764118i \(-0.723175\pi\)
−0.645077 + 0.764118i \(0.723175\pi\)
\(4\) 0.539146 0.0673933
\(5\) 12.5727 1.12453 0.562267 0.826956i \(-0.309929\pi\)
0.562267 + 0.826956i \(0.309929\pi\)
\(6\) 19.5898 1.33292
\(7\) −15.7135 −0.848449 −0.424224 0.905557i \(-0.639453\pi\)
−0.424224 + 0.905557i \(0.639453\pi\)
\(8\) 21.8020 0.963520
\(9\) 17.9414 0.664497
\(10\) −36.7396 −1.16181
\(11\) 11.0000 0.301511
\(12\) −3.61435 −0.0869477
\(13\) 0 0
\(14\) 45.9177 0.876572
\(15\) −84.2851 −1.45082
\(16\) −68.0225 −1.06285
\(17\) 88.6878 1.26529 0.632646 0.774441i \(-0.281969\pi\)
0.632646 + 0.774441i \(0.281969\pi\)
\(18\) −52.4281 −0.686523
\(19\) 129.741 1.56656 0.783282 0.621666i \(-0.213544\pi\)
0.783282 + 0.621666i \(0.213544\pi\)
\(20\) 6.77851 0.0757861
\(21\) 105.341 1.09463
\(22\) −32.1440 −0.311506
\(23\) −172.749 −1.56611 −0.783057 0.621949i \(-0.786341\pi\)
−0.783057 + 0.621949i \(0.786341\pi\)
\(24\) −146.157 −1.24309
\(25\) 33.0721 0.264577
\(26\) 0 0
\(27\) 60.7273 0.432851
\(28\) −8.47187 −0.0571798
\(29\) 5.46969 0.0350240 0.0175120 0.999847i \(-0.494425\pi\)
0.0175120 + 0.999847i \(0.494425\pi\)
\(30\) 246.296 1.49891
\(31\) 222.253 1.28767 0.643836 0.765164i \(-0.277342\pi\)
0.643836 + 0.765164i \(0.277342\pi\)
\(32\) 24.3583 0.134562
\(33\) −73.7422 −0.388996
\(34\) −259.162 −1.30723
\(35\) −197.561 −0.954109
\(36\) 9.67305 0.0447826
\(37\) 351.233 1.56060 0.780302 0.625403i \(-0.215066\pi\)
0.780302 + 0.625403i \(0.215066\pi\)
\(38\) −379.128 −1.61849
\(39\) 0 0
\(40\) 274.109 1.08351
\(41\) 424.792 1.61808 0.809042 0.587751i \(-0.199987\pi\)
0.809042 + 0.587751i \(0.199987\pi\)
\(42\) −307.825 −1.13091
\(43\) −155.625 −0.551920 −0.275960 0.961169i \(-0.588996\pi\)
−0.275960 + 0.961169i \(0.588996\pi\)
\(44\) 5.93061 0.0203198
\(45\) 225.571 0.747249
\(46\) 504.804 1.61803
\(47\) 406.439 1.26139 0.630694 0.776031i \(-0.282770\pi\)
0.630694 + 0.776031i \(0.282770\pi\)
\(48\) 456.012 1.37124
\(49\) −96.0862 −0.280135
\(50\) −96.6427 −0.273347
\(51\) −594.548 −1.63242
\(52\) 0 0
\(53\) 280.727 0.727562 0.363781 0.931485i \(-0.381486\pi\)
0.363781 + 0.931485i \(0.381486\pi\)
\(54\) −177.456 −0.447199
\(55\) 138.299 0.339060
\(56\) −342.585 −0.817497
\(57\) −869.765 −2.02111
\(58\) −15.9834 −0.0361849
\(59\) −108.495 −0.239405 −0.119702 0.992810i \(-0.538194\pi\)
−0.119702 + 0.992810i \(0.538194\pi\)
\(60\) −45.4420 −0.0977757
\(61\) 388.485 0.815416 0.407708 0.913112i \(-0.366328\pi\)
0.407708 + 0.913112i \(0.366328\pi\)
\(62\) −649.464 −1.33035
\(63\) −281.922 −0.563791
\(64\) 473.000 0.923829
\(65\) 0 0
\(66\) 215.488 0.401890
\(67\) −651.390 −1.18776 −0.593881 0.804553i \(-0.702405\pi\)
−0.593881 + 0.804553i \(0.702405\pi\)
\(68\) 47.8157 0.0852722
\(69\) 1158.08 2.02053
\(70\) 577.308 0.985736
\(71\) 382.632 0.639578 0.319789 0.947489i \(-0.396388\pi\)
0.319789 + 0.947489i \(0.396388\pi\)
\(72\) 391.158 0.640256
\(73\) −211.476 −0.339060 −0.169530 0.985525i \(-0.554225\pi\)
−0.169530 + 0.985525i \(0.554225\pi\)
\(74\) −1026.37 −1.61233
\(75\) −221.710 −0.341345
\(76\) 69.9496 0.105576
\(77\) −172.848 −0.255817
\(78\) 0 0
\(79\) 313.752 0.446834 0.223417 0.974723i \(-0.428279\pi\)
0.223417 + 0.974723i \(0.428279\pi\)
\(80\) −855.225 −1.19521
\(81\) −891.524 −1.22294
\(82\) −1241.32 −1.67172
\(83\) 1127.22 1.49070 0.745351 0.666673i \(-0.232282\pi\)
0.745351 + 0.666673i \(0.232282\pi\)
\(84\) 56.7940 0.0737707
\(85\) 1115.04 1.42286
\(86\) 454.764 0.570214
\(87\) −36.6679 −0.0451863
\(88\) 239.822 0.290512
\(89\) −591.138 −0.704051 −0.352025 0.935990i \(-0.614507\pi\)
−0.352025 + 0.935990i \(0.614507\pi\)
\(90\) −659.161 −0.772018
\(91\) 0 0
\(92\) −93.1370 −0.105546
\(93\) −1489.95 −1.66129
\(94\) −1187.69 −1.30320
\(95\) 1631.20 1.76165
\(96\) −163.294 −0.173606
\(97\) −490.807 −0.513751 −0.256876 0.966444i \(-0.582693\pi\)
−0.256876 + 0.966444i \(0.582693\pi\)
\(98\) 280.781 0.289421
\(99\) 197.356 0.200353
\(100\) 17.8307 0.0178307
\(101\) 1763.94 1.73781 0.868904 0.494980i \(-0.164825\pi\)
0.868904 + 0.494980i \(0.164825\pi\)
\(102\) 1737.38 1.68653
\(103\) −1850.35 −1.77010 −0.885049 0.465497i \(-0.845876\pi\)
−0.885049 + 0.465497i \(0.845876\pi\)
\(104\) 0 0
\(105\) 1324.41 1.23095
\(106\) −820.335 −0.751679
\(107\) −1214.07 −1.09690 −0.548452 0.836182i \(-0.684783\pi\)
−0.548452 + 0.836182i \(0.684783\pi\)
\(108\) 32.7409 0.0291712
\(109\) −890.434 −0.782460 −0.391230 0.920293i \(-0.627950\pi\)
−0.391230 + 0.920293i \(0.627950\pi\)
\(110\) −404.136 −0.350299
\(111\) −2354.61 −2.01342
\(112\) 1068.87 0.901775
\(113\) 511.933 0.426183 0.213091 0.977032i \(-0.431647\pi\)
0.213091 + 0.977032i \(0.431647\pi\)
\(114\) 2541.61 2.08810
\(115\) −2171.92 −1.76115
\(116\) 2.94896 0.00236038
\(117\) 0 0
\(118\) 317.043 0.247340
\(119\) −1393.59 −1.07353
\(120\) −1837.58 −1.39790
\(121\) 121.000 0.0909091
\(122\) −1135.22 −0.842445
\(123\) −2847.74 −2.08758
\(124\) 119.827 0.0867804
\(125\) −1155.78 −0.827008
\(126\) 823.828 0.582480
\(127\) 770.909 0.538639 0.269319 0.963051i \(-0.413201\pi\)
0.269319 + 0.963051i \(0.413201\pi\)
\(128\) −1577.06 −1.08901
\(129\) 1043.28 0.712061
\(130\) 0 0
\(131\) −910.833 −0.607480 −0.303740 0.952755i \(-0.598235\pi\)
−0.303740 + 0.952755i \(0.598235\pi\)
\(132\) −39.7578 −0.0262157
\(133\) −2038.69 −1.32915
\(134\) 1903.48 1.22713
\(135\) 763.504 0.486755
\(136\) 1933.57 1.21913
\(137\) 639.809 0.398997 0.199498 0.979898i \(-0.436069\pi\)
0.199498 + 0.979898i \(0.436069\pi\)
\(138\) −3384.12 −2.08750
\(139\) −1313.92 −0.801765 −0.400882 0.916130i \(-0.631296\pi\)
−0.400882 + 0.916130i \(0.631296\pi\)
\(140\) −106.514 −0.0643006
\(141\) −2724.70 −1.62739
\(142\) −1118.12 −0.660778
\(143\) 0 0
\(144\) −1220.42 −0.706261
\(145\) 68.7686 0.0393857
\(146\) 617.971 0.350299
\(147\) 644.146 0.361417
\(148\) 189.366 0.105174
\(149\) −179.585 −0.0987394 −0.0493697 0.998781i \(-0.515721\pi\)
−0.0493697 + 0.998781i \(0.515721\pi\)
\(150\) 647.876 0.352659
\(151\) −113.223 −0.0610193 −0.0305097 0.999534i \(-0.509713\pi\)
−0.0305097 + 0.999534i \(0.509713\pi\)
\(152\) 2828.62 1.50942
\(153\) 1591.18 0.840782
\(154\) 505.094 0.264297
\(155\) 2794.31 1.44803
\(156\) 0 0
\(157\) −704.857 −0.358304 −0.179152 0.983821i \(-0.557335\pi\)
−0.179152 + 0.983821i \(0.557335\pi\)
\(158\) −916.841 −0.461645
\(159\) −1881.95 −0.938667
\(160\) 306.249 0.151320
\(161\) 2714.49 1.32877
\(162\) 2605.19 1.26348
\(163\) −2260.35 −1.08616 −0.543080 0.839681i \(-0.682742\pi\)
−0.543080 + 0.839681i \(0.682742\pi\)
\(164\) 229.025 0.109048
\(165\) −927.136 −0.437439
\(166\) −3293.93 −1.54011
\(167\) −923.890 −0.428100 −0.214050 0.976823i \(-0.568666\pi\)
−0.214050 + 0.976823i \(0.568666\pi\)
\(168\) 2296.63 1.05470
\(169\) 0 0
\(170\) −3258.36 −1.47003
\(171\) 2327.74 1.04098
\(172\) −83.9045 −0.0371957
\(173\) 1403.82 0.616939 0.308469 0.951234i \(-0.400183\pi\)
0.308469 + 0.951234i \(0.400183\pi\)
\(174\) 107.150 0.0466841
\(175\) −519.678 −0.224480
\(176\) −748.247 −0.320462
\(177\) 727.334 0.308869
\(178\) 1727.41 0.727388
\(179\) 1096.26 0.457754 0.228877 0.973455i \(-0.426495\pi\)
0.228877 + 0.973455i \(0.426495\pi\)
\(180\) 121.616 0.0503596
\(181\) −2728.67 −1.12055 −0.560277 0.828305i \(-0.689305\pi\)
−0.560277 + 0.828305i \(0.689305\pi\)
\(182\) 0 0
\(183\) −2604.34 −1.05201
\(184\) −3766.27 −1.50898
\(185\) 4415.94 1.75495
\(186\) 4353.90 1.71636
\(187\) 975.566 0.381500
\(188\) 219.130 0.0850092
\(189\) −954.238 −0.367252
\(190\) −4766.65 −1.82005
\(191\) −4359.38 −1.65149 −0.825743 0.564046i \(-0.809244\pi\)
−0.825743 + 0.564046i \(0.809244\pi\)
\(192\) −3170.92 −1.19188
\(193\) −3799.30 −1.41699 −0.708496 0.705715i \(-0.750626\pi\)
−0.708496 + 0.705715i \(0.750626\pi\)
\(194\) 1434.23 0.530781
\(195\) 0 0
\(196\) −51.8046 −0.0188792
\(197\) 3685.29 1.33282 0.666411 0.745585i \(-0.267830\pi\)
0.666411 + 0.745585i \(0.267830\pi\)
\(198\) −576.709 −0.206994
\(199\) −1531.37 −0.545506 −0.272753 0.962084i \(-0.587934\pi\)
−0.272753 + 0.962084i \(0.587934\pi\)
\(200\) 721.037 0.254925
\(201\) 4366.81 1.53239
\(202\) −5154.56 −1.79541
\(203\) −85.9479 −0.0297160
\(204\) −320.549 −0.110014
\(205\) 5340.77 1.81959
\(206\) 5407.05 1.82877
\(207\) −3099.36 −1.04068
\(208\) 0 0
\(209\) 1427.16 0.472337
\(210\) −3870.18 −1.27175
\(211\) 2857.26 0.932237 0.466118 0.884722i \(-0.345652\pi\)
0.466118 + 0.884722i \(0.345652\pi\)
\(212\) 151.353 0.0490328
\(213\) −2565.10 −0.825154
\(214\) 3547.74 1.13326
\(215\) −1956.62 −0.620653
\(216\) 1323.97 0.417060
\(217\) −3492.37 −1.09252
\(218\) 2602.01 0.808396
\(219\) 1417.70 0.437439
\(220\) 74.5636 0.0228504
\(221\) 0 0
\(222\) 6880.59 2.08016
\(223\) −1800.43 −0.540654 −0.270327 0.962769i \(-0.587132\pi\)
−0.270327 + 0.962769i \(0.587132\pi\)
\(224\) −382.754 −0.114169
\(225\) 593.360 0.175810
\(226\) −1495.96 −0.440309
\(227\) −967.195 −0.282797 −0.141399 0.989953i \(-0.545160\pi\)
−0.141399 + 0.989953i \(0.545160\pi\)
\(228\) −468.931 −0.136209
\(229\) 6011.19 1.73463 0.867316 0.497758i \(-0.165843\pi\)
0.867316 + 0.497758i \(0.165843\pi\)
\(230\) 6346.73 1.81953
\(231\) 1158.75 0.330043
\(232\) 119.250 0.0337463
\(233\) 3591.35 1.00977 0.504887 0.863185i \(-0.331534\pi\)
0.504887 + 0.863185i \(0.331534\pi\)
\(234\) 0 0
\(235\) 5110.03 1.41847
\(236\) −58.4948 −0.0161343
\(237\) −2103.34 −0.576484
\(238\) 4072.34 1.10912
\(239\) −344.523 −0.0932441 −0.0466221 0.998913i \(-0.514846\pi\)
−0.0466221 + 0.998913i \(0.514846\pi\)
\(240\) 5733.28 1.54201
\(241\) 6225.31 1.66393 0.831965 0.554828i \(-0.187216\pi\)
0.831965 + 0.554828i \(0.187216\pi\)
\(242\) −353.584 −0.0939225
\(243\) 4336.99 1.14493
\(244\) 209.450 0.0549536
\(245\) −1208.06 −0.315021
\(246\) 8321.61 2.15677
\(247\) 0 0
\(248\) 4845.55 1.24070
\(249\) −7556.68 −1.92323
\(250\) 3377.40 0.854422
\(251\) 2041.80 0.513456 0.256728 0.966484i \(-0.417355\pi\)
0.256728 + 0.966484i \(0.417355\pi\)
\(252\) −151.997 −0.0379958
\(253\) −1900.24 −0.472201
\(254\) −2252.74 −0.556493
\(255\) −7475.06 −1.83571
\(256\) 824.452 0.201282
\(257\) 4146.55 1.00644 0.503219 0.864159i \(-0.332149\pi\)
0.503219 + 0.864159i \(0.332149\pi\)
\(258\) −3048.66 −0.735664
\(259\) −5519.09 −1.32409
\(260\) 0 0
\(261\) 98.1339 0.0232733
\(262\) 2661.62 0.627616
\(263\) 5697.94 1.33593 0.667966 0.744192i \(-0.267165\pi\)
0.667966 + 0.744192i \(0.267165\pi\)
\(264\) −1607.73 −0.374805
\(265\) 3529.49 0.818168
\(266\) 5957.42 1.37321
\(267\) 3962.89 0.908334
\(268\) −351.195 −0.0800471
\(269\) −407.309 −0.0923200 −0.0461600 0.998934i \(-0.514698\pi\)
−0.0461600 + 0.998934i \(0.514698\pi\)
\(270\) −2231.10 −0.502890
\(271\) −1527.40 −0.342373 −0.171187 0.985239i \(-0.554760\pi\)
−0.171187 + 0.985239i \(0.554760\pi\)
\(272\) −6032.77 −1.34482
\(273\) 0 0
\(274\) −1869.64 −0.412222
\(275\) 363.793 0.0797729
\(276\) 624.375 0.136170
\(277\) 2903.33 0.629762 0.314881 0.949131i \(-0.398035\pi\)
0.314881 + 0.949131i \(0.398035\pi\)
\(278\) 3839.51 0.828341
\(279\) 3987.53 0.855654
\(280\) −4307.21 −0.919304
\(281\) −1930.54 −0.409844 −0.204922 0.978778i \(-0.565694\pi\)
−0.204922 + 0.978778i \(0.565694\pi\)
\(282\) 7962.08 1.68133
\(283\) 4950.15 1.03977 0.519887 0.854235i \(-0.325974\pi\)
0.519887 + 0.854235i \(0.325974\pi\)
\(284\) 206.294 0.0431033
\(285\) −10935.3 −2.27281
\(286\) 0 0
\(287\) −6674.97 −1.37286
\(288\) 437.023 0.0894160
\(289\) 2952.53 0.600962
\(290\) −200.954 −0.0406912
\(291\) 3290.29 0.662818
\(292\) −114.016 −0.0228504
\(293\) −4052.66 −0.808051 −0.404025 0.914748i \(-0.632389\pi\)
−0.404025 + 0.914748i \(0.632389\pi\)
\(294\) −1882.31 −0.373397
\(295\) −1364.07 −0.269219
\(296\) 7657.57 1.50367
\(297\) 668.000 0.130509
\(298\) 524.780 0.102012
\(299\) 0 0
\(300\) −119.534 −0.0230043
\(301\) 2445.41 0.468276
\(302\) 330.857 0.0630420
\(303\) −11825.2 −2.24204
\(304\) −8825.33 −1.66503
\(305\) 4884.29 0.916963
\(306\) −4649.73 −0.868651
\(307\) −8180.84 −1.52086 −0.760432 0.649418i \(-0.775013\pi\)
−0.760432 + 0.649418i \(0.775013\pi\)
\(308\) −93.1906 −0.0172403
\(309\) 12404.4 2.28370
\(310\) −8165.49 −1.49603
\(311\) 4985.56 0.909019 0.454509 0.890742i \(-0.349815\pi\)
0.454509 + 0.890742i \(0.349815\pi\)
\(312\) 0 0
\(313\) −102.182 −0.0184527 −0.00922633 0.999957i \(-0.502937\pi\)
−0.00922633 + 0.999957i \(0.502937\pi\)
\(314\) 2059.72 0.370181
\(315\) −3544.52 −0.634003
\(316\) 169.158 0.0301136
\(317\) 749.307 0.132761 0.0663806 0.997794i \(-0.478855\pi\)
0.0663806 + 0.997794i \(0.478855\pi\)
\(318\) 5499.39 0.969781
\(319\) 60.1666 0.0105601
\(320\) 5946.88 1.03888
\(321\) 8138.94 1.41518
\(322\) −7932.23 −1.37281
\(323\) 11506.5 1.98216
\(324\) −480.662 −0.0824180
\(325\) 0 0
\(326\) 6605.15 1.12216
\(327\) 5969.32 1.00949
\(328\) 9261.31 1.55906
\(329\) −6386.58 −1.07022
\(330\) 2709.26 0.451939
\(331\) 10513.1 1.74577 0.872886 0.487924i \(-0.162246\pi\)
0.872886 + 0.487924i \(0.162246\pi\)
\(332\) 607.735 0.100463
\(333\) 6301.61 1.03702
\(334\) 2699.77 0.442291
\(335\) −8189.72 −1.33568
\(336\) −7165.53 −1.16343
\(337\) −3157.75 −0.510426 −0.255213 0.966885i \(-0.582146\pi\)
−0.255213 + 0.966885i \(0.582146\pi\)
\(338\) 0 0
\(339\) −3431.92 −0.549841
\(340\) 601.171 0.0958914
\(341\) 2444.78 0.388248
\(342\) −6802.09 −1.07548
\(343\) 6899.58 1.08613
\(344\) −3392.93 −0.531786
\(345\) 14560.2 2.27215
\(346\) −4102.22 −0.637389
\(347\) 8642.04 1.33697 0.668486 0.743725i \(-0.266943\pi\)
0.668486 + 0.743725i \(0.266943\pi\)
\(348\) −19.7694 −0.00304526
\(349\) −8480.84 −1.30077 −0.650385 0.759604i \(-0.725393\pi\)
−0.650385 + 0.759604i \(0.725393\pi\)
\(350\) 1518.59 0.231921
\(351\) 0 0
\(352\) 267.942 0.0405720
\(353\) 12797.4 1.92957 0.964784 0.263044i \(-0.0847264\pi\)
0.964784 + 0.263044i \(0.0847264\pi\)
\(354\) −2125.40 −0.319107
\(355\) 4810.70 0.719227
\(356\) −318.710 −0.0474483
\(357\) 9342.43 1.38502
\(358\) −3203.46 −0.472927
\(359\) 11231.4 1.65118 0.825589 0.564272i \(-0.190843\pi\)
0.825589 + 0.564272i \(0.190843\pi\)
\(360\) 4917.90 0.719990
\(361\) 9973.84 1.45412
\(362\) 7973.66 1.15770
\(363\) −811.164 −0.117287
\(364\) 0 0
\(365\) −2658.82 −0.381284
\(366\) 7610.35 1.08688
\(367\) 3920.84 0.557673 0.278836 0.960339i \(-0.410051\pi\)
0.278836 + 0.960339i \(0.410051\pi\)
\(368\) 11750.8 1.66455
\(369\) 7621.37 1.07521
\(370\) −12904.2 −1.81312
\(371\) −4411.20 −0.617299
\(372\) −803.300 −0.111960
\(373\) −9140.22 −1.26880 −0.634401 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(374\) −2850.78 −0.394145
\(375\) 7748.16 1.06697
\(376\) 8861.18 1.21537
\(377\) 0 0
\(378\) 2788.46 0.379425
\(379\) −2568.60 −0.348127 −0.174063 0.984734i \(-0.555690\pi\)
−0.174063 + 0.984734i \(0.555690\pi\)
\(380\) 879.454 0.118724
\(381\) −5168.05 −0.694927
\(382\) 12738.9 1.70623
\(383\) −8400.48 −1.12074 −0.560372 0.828241i \(-0.689342\pi\)
−0.560372 + 0.828241i \(0.689342\pi\)
\(384\) 10572.4 1.40499
\(385\) −2173.17 −0.287675
\(386\) 11102.2 1.46396
\(387\) −2792.13 −0.366749
\(388\) −264.617 −0.0346234
\(389\) −1411.45 −0.183968 −0.0919839 0.995760i \(-0.529321\pi\)
−0.0919839 + 0.995760i \(0.529321\pi\)
\(390\) 0 0
\(391\) −15320.7 −1.98159
\(392\) −2094.87 −0.269916
\(393\) 6106.07 0.783742
\(394\) −10769.1 −1.37700
\(395\) 3944.70 0.502480
\(396\) 106.404 0.0135025
\(397\) −10352.7 −1.30878 −0.654391 0.756156i \(-0.727075\pi\)
−0.654391 + 0.756156i \(0.727075\pi\)
\(398\) 4474.93 0.563588
\(399\) 13667.0 1.71481
\(400\) −2249.65 −0.281206
\(401\) 11410.4 1.42097 0.710484 0.703714i \(-0.248476\pi\)
0.710484 + 0.703714i \(0.248476\pi\)
\(402\) −12760.6 −1.58319
\(403\) 0 0
\(404\) 951.022 0.117117
\(405\) −11208.8 −1.37524
\(406\) 251.155 0.0307011
\(407\) 3863.56 0.470540
\(408\) −12962.3 −1.57287
\(409\) 2454.14 0.296698 0.148349 0.988935i \(-0.452604\pi\)
0.148349 + 0.988935i \(0.452604\pi\)
\(410\) −15606.7 −1.87990
\(411\) −4289.17 −0.514767
\(412\) −997.608 −0.119293
\(413\) 1704.84 0.203122
\(414\) 9056.89 1.07517
\(415\) 14172.1 1.67634
\(416\) 0 0
\(417\) 8808.31 1.03440
\(418\) −4170.41 −0.487994
\(419\) −13489.0 −1.57274 −0.786372 0.617753i \(-0.788043\pi\)
−0.786372 + 0.617753i \(0.788043\pi\)
\(420\) 714.053 0.0829576
\(421\) 11358.3 1.31489 0.657446 0.753502i \(-0.271637\pi\)
0.657446 + 0.753502i \(0.271637\pi\)
\(422\) −8349.44 −0.963138
\(423\) 7292.10 0.838189
\(424\) 6120.40 0.701021
\(425\) 2933.09 0.334767
\(426\) 7495.69 0.852505
\(427\) −6104.45 −0.691839
\(428\) −654.563 −0.0739240
\(429\) 0 0
\(430\) 5717.60 0.641225
\(431\) 12014.1 1.34269 0.671344 0.741146i \(-0.265718\pi\)
0.671344 + 0.741146i \(0.265718\pi\)
\(432\) −4130.82 −0.460056
\(433\) 9197.86 1.02083 0.510417 0.859927i \(-0.329491\pi\)
0.510417 + 0.859927i \(0.329491\pi\)
\(434\) 10205.3 1.12874
\(435\) −461.013 −0.0508135
\(436\) −480.074 −0.0527325
\(437\) −22412.7 −2.45342
\(438\) −4142.77 −0.451939
\(439\) 6367.85 0.692302 0.346151 0.938179i \(-0.387488\pi\)
0.346151 + 0.938179i \(0.387488\pi\)
\(440\) 3015.20 0.326691
\(441\) −1723.92 −0.186149
\(442\) 0 0
\(443\) −11022.3 −1.18214 −0.591068 0.806622i \(-0.701293\pi\)
−0.591068 + 0.806622i \(0.701293\pi\)
\(444\) −1269.48 −0.135691
\(445\) −7432.19 −0.791729
\(446\) 5261.19 0.558575
\(447\) 1203.91 0.127389
\(448\) −7432.49 −0.783822
\(449\) 1296.75 0.136298 0.0681488 0.997675i \(-0.478291\pi\)
0.0681488 + 0.997675i \(0.478291\pi\)
\(450\) −1733.91 −0.181638
\(451\) 4672.72 0.487870
\(452\) 276.007 0.0287219
\(453\) 759.025 0.0787243
\(454\) 2826.32 0.292171
\(455\) 0 0
\(456\) −18962.6 −1.94738
\(457\) 12474.9 1.27692 0.638458 0.769656i \(-0.279572\pi\)
0.638458 + 0.769656i \(0.279572\pi\)
\(458\) −17565.8 −1.79213
\(459\) 5385.77 0.547682
\(460\) −1170.98 −0.118690
\(461\) −11524.1 −1.16427 −0.582136 0.813091i \(-0.697783\pi\)
−0.582136 + 0.813091i \(0.697783\pi\)
\(462\) −3386.07 −0.340983
\(463\) −11186.2 −1.12282 −0.561412 0.827537i \(-0.689742\pi\)
−0.561412 + 0.827537i \(0.689742\pi\)
\(464\) −372.062 −0.0372253
\(465\) −18732.6 −1.86818
\(466\) −10494.6 −1.04325
\(467\) −2751.87 −0.272680 −0.136340 0.990662i \(-0.543534\pi\)
−0.136340 + 0.990662i \(0.543534\pi\)
\(468\) 0 0
\(469\) 10235.6 1.00775
\(470\) −14932.4 −1.46549
\(471\) 4725.24 0.462267
\(472\) −2365.41 −0.230671
\(473\) −1711.87 −0.166410
\(474\) 6146.35 0.595593
\(475\) 4290.82 0.414476
\(476\) −751.352 −0.0723490
\(477\) 5036.63 0.483463
\(478\) 1006.76 0.0963349
\(479\) −14990.4 −1.42991 −0.714955 0.699170i \(-0.753553\pi\)
−0.714955 + 0.699170i \(0.753553\pi\)
\(480\) −2053.04 −0.195225
\(481\) 0 0
\(482\) −18191.5 −1.71909
\(483\) −18197.5 −1.71432
\(484\) 65.2367 0.00612666
\(485\) −6170.75 −0.577731
\(486\) −12673.5 −1.18288
\(487\) −14043.7 −1.30674 −0.653369 0.757040i \(-0.726645\pi\)
−0.653369 + 0.757040i \(0.726645\pi\)
\(488\) 8469.74 0.785670
\(489\) 15153.0 1.40131
\(490\) 3530.17 0.325463
\(491\) −11747.4 −1.07974 −0.539871 0.841748i \(-0.681527\pi\)
−0.539871 + 0.841748i \(0.681527\pi\)
\(492\) −1535.35 −0.140689
\(493\) 485.095 0.0443155
\(494\) 0 0
\(495\) 2481.29 0.225304
\(496\) −15118.2 −1.36860
\(497\) −6012.48 −0.542649
\(498\) 22082.0 1.98698
\(499\) 894.096 0.0802109 0.0401055 0.999195i \(-0.487231\pi\)
0.0401055 + 0.999195i \(0.487231\pi\)
\(500\) −623.134 −0.0557348
\(501\) 6193.61 0.552315
\(502\) −5966.52 −0.530476
\(503\) −18061.6 −1.60105 −0.800525 0.599300i \(-0.795446\pi\)
−0.800525 + 0.599300i \(0.795446\pi\)
\(504\) −6146.46 −0.543224
\(505\) 22177.4 1.95422
\(506\) 5552.84 0.487854
\(507\) 0 0
\(508\) 415.633 0.0363006
\(509\) 17066.9 1.48621 0.743103 0.669177i \(-0.233353\pi\)
0.743103 + 0.669177i \(0.233353\pi\)
\(510\) 21843.5 1.89656
\(511\) 3323.02 0.287675
\(512\) 10207.3 0.881059
\(513\) 7878.84 0.678089
\(514\) −12117.0 −1.03980
\(515\) −23263.8 −1.99054
\(516\) 562.482 0.0479882
\(517\) 4470.83 0.380323
\(518\) 16127.8 1.36798
\(519\) −9410.98 −0.795946
\(520\) 0 0
\(521\) −6638.80 −0.558256 −0.279128 0.960254i \(-0.590045\pi\)
−0.279128 + 0.960254i \(0.590045\pi\)
\(522\) −286.765 −0.0240448
\(523\) 3961.57 0.331219 0.165609 0.986191i \(-0.447041\pi\)
0.165609 + 0.986191i \(0.447041\pi\)
\(524\) −491.072 −0.0409401
\(525\) 3483.84 0.289613
\(526\) −16650.4 −1.38021
\(527\) 19711.1 1.62928
\(528\) 5016.13 0.413445
\(529\) 17675.2 1.45272
\(530\) −10313.8 −0.845288
\(531\) −1946.56 −0.159084
\(532\) −1099.15 −0.0895758
\(533\) 0 0
\(534\) −11580.3 −0.938442
\(535\) −15264.1 −1.23351
\(536\) −14201.6 −1.14443
\(537\) −7349.11 −0.590573
\(538\) 1190.23 0.0953801
\(539\) −1056.95 −0.0844638
\(540\) 411.641 0.0328041
\(541\) 3050.55 0.242428 0.121214 0.992626i \(-0.461321\pi\)
0.121214 + 0.992626i \(0.461321\pi\)
\(542\) 4463.35 0.353722
\(543\) 18292.5 1.44569
\(544\) 2160.29 0.170260
\(545\) −11195.1 −0.879902
\(546\) 0 0
\(547\) 1239.50 0.0968870 0.0484435 0.998826i \(-0.484574\pi\)
0.0484435 + 0.998826i \(0.484574\pi\)
\(548\) 344.951 0.0268897
\(549\) 6969.97 0.541841
\(550\) −1063.07 −0.0824171
\(551\) 709.645 0.0548673
\(552\) 25248.4 1.94682
\(553\) −4930.14 −0.379116
\(554\) −8484.05 −0.650636
\(555\) −29603.7 −2.26416
\(556\) −708.396 −0.0540336
\(557\) 11458.5 0.871659 0.435830 0.900029i \(-0.356455\pi\)
0.435830 + 0.900029i \(0.356455\pi\)
\(558\) −11652.3 −0.884016
\(559\) 0 0
\(560\) 13438.6 1.01408
\(561\) −6540.03 −0.492193
\(562\) 5641.38 0.423429
\(563\) −4582.32 −0.343022 −0.171511 0.985182i \(-0.554865\pi\)
−0.171511 + 0.985182i \(0.554865\pi\)
\(564\) −1469.01 −0.109675
\(565\) 6436.37 0.479257
\(566\) −14465.2 −1.07424
\(567\) 14009.0 1.03760
\(568\) 8342.12 0.616246
\(569\) 2749.09 0.202544 0.101272 0.994859i \(-0.467709\pi\)
0.101272 + 0.994859i \(0.467709\pi\)
\(570\) 31954.9 2.34814
\(571\) 1449.90 0.106264 0.0531318 0.998588i \(-0.483080\pi\)
0.0531318 + 0.998588i \(0.483080\pi\)
\(572\) 0 0
\(573\) 29224.6 2.13067
\(574\) 19505.5 1.41837
\(575\) −5713.17 −0.414358
\(576\) 8486.30 0.613881
\(577\) 11347.4 0.818713 0.409357 0.912375i \(-0.365753\pi\)
0.409357 + 0.912375i \(0.365753\pi\)
\(578\) −8627.82 −0.620882
\(579\) 25469.9 1.82814
\(580\) 37.0763 0.00265433
\(581\) −17712.5 −1.26478
\(582\) −9614.82 −0.684789
\(583\) 3087.99 0.219368
\(584\) −4610.59 −0.326691
\(585\) 0 0
\(586\) 11842.6 0.834836
\(587\) −16081.3 −1.13075 −0.565373 0.824835i \(-0.691268\pi\)
−0.565373 + 0.824835i \(0.691268\pi\)
\(588\) 347.289 0.0243571
\(589\) 28835.4 2.01722
\(590\) 3986.07 0.278142
\(591\) −24705.6 −1.71955
\(592\) −23891.7 −1.65869
\(593\) −26318.9 −1.82257 −0.911287 0.411771i \(-0.864910\pi\)
−0.911287 + 0.411771i \(0.864910\pi\)
\(594\) −1952.02 −0.134835
\(595\) −17521.2 −1.20723
\(596\) −96.8225 −0.00665437
\(597\) 10266.0 0.703786
\(598\) 0 0
\(599\) −25996.4 −1.77327 −0.886633 0.462474i \(-0.846962\pi\)
−0.886633 + 0.462474i \(0.846962\pi\)
\(600\) −4833.71 −0.328892
\(601\) 19672.9 1.33523 0.667617 0.744505i \(-0.267314\pi\)
0.667617 + 0.744505i \(0.267314\pi\)
\(602\) −7145.93 −0.483798
\(603\) −11686.9 −0.789263
\(604\) −61.0435 −0.00411230
\(605\) 1521.29 0.102230
\(606\) 34555.3 2.31636
\(607\) −19916.4 −1.33177 −0.665883 0.746057i \(-0.731945\pi\)
−0.665883 + 0.746057i \(0.731945\pi\)
\(608\) 3160.28 0.210800
\(609\) 576.180 0.0383383
\(610\) −14272.8 −0.947358
\(611\) 0 0
\(612\) 857.881 0.0566631
\(613\) −630.454 −0.0415396 −0.0207698 0.999784i \(-0.506612\pi\)
−0.0207698 + 0.999784i \(0.506612\pi\)
\(614\) 23905.9 1.57128
\(615\) −35803.7 −2.34755
\(616\) −3768.44 −0.246485
\(617\) −2499.88 −0.163114 −0.0815569 0.996669i \(-0.525989\pi\)
−0.0815569 + 0.996669i \(0.525989\pi\)
\(618\) −36248.0 −2.35940
\(619\) 26887.2 1.74586 0.872930 0.487846i \(-0.162217\pi\)
0.872930 + 0.487846i \(0.162217\pi\)
\(620\) 1506.54 0.0975876
\(621\) −10490.6 −0.677894
\(622\) −14568.7 −0.939150
\(623\) 9288.84 0.597351
\(624\) 0 0
\(625\) −18665.2 −1.19458
\(626\) 298.595 0.0190643
\(627\) −9567.42 −0.609387
\(628\) −380.021 −0.0241473
\(629\) 31150.1 1.97462
\(630\) 10357.7 0.655018
\(631\) 20589.6 1.29898 0.649492 0.760369i \(-0.274982\pi\)
0.649492 + 0.760369i \(0.274982\pi\)
\(632\) 6840.42 0.430533
\(633\) −19154.6 −1.20273
\(634\) −2189.61 −0.137162
\(635\) 9692.39 0.605718
\(636\) −1014.64 −0.0632599
\(637\) 0 0
\(638\) −175.818 −0.0109102
\(639\) 6864.95 0.424997
\(640\) −19827.9 −1.22463
\(641\) −15597.9 −0.961126 −0.480563 0.876960i \(-0.659568\pi\)
−0.480563 + 0.876960i \(0.659568\pi\)
\(642\) −23783.5 −1.46208
\(643\) −17616.1 −1.08042 −0.540209 0.841531i \(-0.681655\pi\)
−0.540209 + 0.841531i \(0.681655\pi\)
\(644\) 1463.51 0.0895501
\(645\) 13116.9 0.800737
\(646\) −33624.0 −2.04786
\(647\) 23071.4 1.40190 0.700951 0.713210i \(-0.252759\pi\)
0.700951 + 0.713210i \(0.252759\pi\)
\(648\) −19437.0 −1.17833
\(649\) −1193.45 −0.0721832
\(650\) 0 0
\(651\) 23412.3 1.40952
\(652\) −1218.66 −0.0731999
\(653\) 28718.7 1.72105 0.860527 0.509405i \(-0.170135\pi\)
0.860527 + 0.509405i \(0.170135\pi\)
\(654\) −17443.4 −1.04296
\(655\) −11451.6 −0.683131
\(656\) −28895.4 −1.71978
\(657\) −3794.17 −0.225304
\(658\) 18662.7 1.10570
\(659\) 12960.6 0.766118 0.383059 0.923724i \(-0.374871\pi\)
0.383059 + 0.923724i \(0.374871\pi\)
\(660\) −499.862 −0.0294805
\(661\) −10384.9 −0.611081 −0.305541 0.952179i \(-0.598837\pi\)
−0.305541 + 0.952179i \(0.598837\pi\)
\(662\) −30721.1 −1.80364
\(663\) 0 0
\(664\) 24575.6 1.43632
\(665\) −25631.8 −1.49467
\(666\) −18414.5 −1.07139
\(667\) −944.883 −0.0548516
\(668\) −498.112 −0.0288511
\(669\) 12069.8 0.697527
\(670\) 23931.8 1.37995
\(671\) 4273.33 0.245857
\(672\) 2565.92 0.147296
\(673\) −23524.6 −1.34741 −0.673706 0.739000i \(-0.735298\pi\)
−0.673706 + 0.739000i \(0.735298\pi\)
\(674\) 9227.52 0.527345
\(675\) 2008.38 0.114522
\(676\) 0 0
\(677\) 349.546 0.0198436 0.00992182 0.999951i \(-0.496842\pi\)
0.00992182 + 0.999951i \(0.496842\pi\)
\(678\) 10028.7 0.568067
\(679\) 7712.29 0.435892
\(680\) 24310.1 1.37096
\(681\) 6483.92 0.364852
\(682\) −7144.10 −0.401117
\(683\) 29509.5 1.65322 0.826611 0.562774i \(-0.190266\pi\)
0.826611 + 0.562774i \(0.190266\pi\)
\(684\) 1254.99 0.0701549
\(685\) 8044.10 0.448685
\(686\) −20161.8 −1.12213
\(687\) −40298.0 −2.23794
\(688\) 10586.0 0.586609
\(689\) 0 0
\(690\) −42547.5 −2.34747
\(691\) −13847.6 −0.762358 −0.381179 0.924501i \(-0.624482\pi\)
−0.381179 + 0.924501i \(0.624482\pi\)
\(692\) 756.864 0.0415775
\(693\) −3101.14 −0.169989
\(694\) −25253.6 −1.38129
\(695\) −16519.5 −0.901612
\(696\) −799.432 −0.0435379
\(697\) 37673.9 2.04735
\(698\) 24782.6 1.34389
\(699\) −24075.9 −1.30276
\(700\) −280.182 −0.0151284
\(701\) 11463.4 0.617639 0.308819 0.951121i \(-0.400066\pi\)
0.308819 + 0.951121i \(0.400066\pi\)
\(702\) 0 0
\(703\) 45569.4 2.44479
\(704\) 5203.01 0.278545
\(705\) −34256.8 −1.83005
\(706\) −37396.4 −1.99353
\(707\) −27717.7 −1.47444
\(708\) 392.139 0.0208157
\(709\) −23414.0 −1.24024 −0.620121 0.784507i \(-0.712916\pi\)
−0.620121 + 0.784507i \(0.712916\pi\)
\(710\) −14057.7 −0.743067
\(711\) 5629.16 0.296920
\(712\) −12888.0 −0.678367
\(713\) −38394.0 −2.01664
\(714\) −27300.3 −1.43093
\(715\) 0 0
\(716\) 591.042 0.0308496
\(717\) 2309.63 0.120299
\(718\) −32820.3 −1.70591
\(719\) 12468.3 0.646718 0.323359 0.946276i \(-0.395188\pi\)
0.323359 + 0.946276i \(0.395188\pi\)
\(720\) −15343.9 −0.794215
\(721\) 29075.4 1.50184
\(722\) −29145.4 −1.50232
\(723\) −41733.4 −2.14673
\(724\) −1471.15 −0.0755178
\(725\) 180.894 0.00926653
\(726\) 2370.37 0.121174
\(727\) 33013.9 1.68421 0.842103 0.539317i \(-0.181318\pi\)
0.842103 + 0.539317i \(0.181318\pi\)
\(728\) 0 0
\(729\) −5003.34 −0.254196
\(730\) 7769.54 0.393923
\(731\) −13802.0 −0.698339
\(732\) −1404.12 −0.0708986
\(733\) −17188.8 −0.866142 −0.433071 0.901360i \(-0.642570\pi\)
−0.433071 + 0.901360i \(0.642570\pi\)
\(734\) −11457.4 −0.576158
\(735\) 8098.64 0.406426
\(736\) −4207.87 −0.210740
\(737\) −7165.29 −0.358123
\(738\) −22271.0 −1.11085
\(739\) 9120.36 0.453989 0.226995 0.973896i \(-0.427110\pi\)
0.226995 + 0.973896i \(0.427110\pi\)
\(740\) 2380.84 0.118272
\(741\) 0 0
\(742\) 12890.3 0.637761
\(743\) 38627.2 1.90726 0.953629 0.300984i \(-0.0973152\pi\)
0.953629 + 0.300984i \(0.0973152\pi\)
\(744\) −32483.8 −1.60069
\(745\) −2257.86 −0.111036
\(746\) 26709.4 1.31086
\(747\) 20223.9 0.990566
\(748\) 525.973 0.0257105
\(749\) 19077.3 0.930667
\(750\) −22641.5 −1.10234
\(751\) 28140.4 1.36732 0.683661 0.729799i \(-0.260387\pi\)
0.683661 + 0.729799i \(0.260387\pi\)
\(752\) −27647.0 −1.34067
\(753\) −13687.9 −0.662438
\(754\) 0 0
\(755\) −1423.51 −0.0686183
\(756\) −514.474 −0.0247503
\(757\) −8906.12 −0.427607 −0.213803 0.976877i \(-0.568585\pi\)
−0.213803 + 0.976877i \(0.568585\pi\)
\(758\) 7505.91 0.359666
\(759\) 12738.9 0.609212
\(760\) 35563.3 1.69739
\(761\) 31956.1 1.52222 0.761108 0.648625i \(-0.224656\pi\)
0.761108 + 0.648625i \(0.224656\pi\)
\(762\) 15102.0 0.717962
\(763\) 13991.8 0.663877
\(764\) −2350.35 −0.111299
\(765\) 20005.4 0.945488
\(766\) 24547.7 1.15789
\(767\) 0 0
\(768\) −5526.99 −0.259685
\(769\) 21225.7 0.995342 0.497671 0.867366i \(-0.334189\pi\)
0.497671 + 0.867366i \(0.334189\pi\)
\(770\) 6350.39 0.297210
\(771\) −27797.8 −1.29846
\(772\) −2048.38 −0.0954958
\(773\) −1379.06 −0.0641672 −0.0320836 0.999485i \(-0.510214\pi\)
−0.0320836 + 0.999485i \(0.510214\pi\)
\(774\) 8159.10 0.378906
\(775\) 7350.37 0.340688
\(776\) −10700.6 −0.495010
\(777\) 36999.1 1.70828
\(778\) 4124.52 0.190066
\(779\) 55113.2 2.53483
\(780\) 0 0
\(781\) 4208.95 0.192840
\(782\) 44769.9 2.04728
\(783\) 332.159 0.0151602
\(784\) 6536.03 0.297742
\(785\) −8861.93 −0.402925
\(786\) −17843.1 −0.809721
\(787\) 32672.8 1.47987 0.739935 0.672678i \(-0.234856\pi\)
0.739935 + 0.672678i \(0.234856\pi\)
\(788\) 1986.91 0.0898233
\(789\) −38198.0 −1.72356
\(790\) −11527.1 −0.519136
\(791\) −8044.26 −0.361594
\(792\) 4302.74 0.193044
\(793\) 0 0
\(794\) 30252.4 1.35216
\(795\) −23661.1 −1.05556
\(796\) −825.630 −0.0367634
\(797\) 7048.81 0.313277 0.156639 0.987656i \(-0.449934\pi\)
0.156639 + 0.987656i \(0.449934\pi\)
\(798\) −39937.6 −1.77165
\(799\) 36046.2 1.59602
\(800\) 805.581 0.0356020
\(801\) −10605.9 −0.467839
\(802\) −33343.2 −1.46807
\(803\) −2326.23 −0.102230
\(804\) 2354.35 0.103273
\(805\) 34128.4 1.49424
\(806\) 0 0
\(807\) 2730.53 0.119107
\(808\) 38457.4 1.67441
\(809\) 23849.5 1.03647 0.518234 0.855239i \(-0.326590\pi\)
0.518234 + 0.855239i \(0.326590\pi\)
\(810\) 32754.3 1.42082
\(811\) −13844.2 −0.599426 −0.299713 0.954029i \(-0.596891\pi\)
−0.299713 + 0.954029i \(0.596891\pi\)
\(812\) −46.3385 −0.00200266
\(813\) 10239.5 0.441714
\(814\) −11290.0 −0.486137
\(815\) −28418.6 −1.22142
\(816\) 40442.7 1.73502
\(817\) −20191.0 −0.864618
\(818\) −7171.44 −0.306532
\(819\) 0 0
\(820\) 2879.46 0.122628
\(821\) −8548.53 −0.363393 −0.181697 0.983355i \(-0.558159\pi\)
−0.181697 + 0.983355i \(0.558159\pi\)
\(822\) 12533.7 0.531830
\(823\) 26379.4 1.11729 0.558644 0.829407i \(-0.311322\pi\)
0.558644 + 0.829407i \(0.311322\pi\)
\(824\) −40341.2 −1.70553
\(825\) −2438.81 −0.102919
\(826\) −4981.85 −0.209855
\(827\) −9853.94 −0.414335 −0.207167 0.978305i \(-0.566425\pi\)
−0.207167 + 0.978305i \(0.566425\pi\)
\(828\) −1671.01 −0.0701347
\(829\) 32349.2 1.35529 0.677645 0.735390i \(-0.263001\pi\)
0.677645 + 0.735390i \(0.263001\pi\)
\(830\) −41413.6 −1.73191
\(831\) −19463.4 −0.812489
\(832\) 0 0
\(833\) −8521.68 −0.354452
\(834\) −25739.5 −1.06869
\(835\) −11615.8 −0.481413
\(836\) 769.446 0.0318323
\(837\) 13496.8 0.557370
\(838\) 39417.2 1.62488
\(839\) 9431.30 0.388087 0.194043 0.980993i \(-0.437840\pi\)
0.194043 + 0.980993i \(0.437840\pi\)
\(840\) 28874.8 1.18604
\(841\) −24359.1 −0.998773
\(842\) −33191.0 −1.35848
\(843\) 12942.0 0.528762
\(844\) 1540.48 0.0628265
\(845\) 0 0
\(846\) −21308.8 −0.865972
\(847\) −1901.33 −0.0771317
\(848\) −19095.7 −0.773290
\(849\) −33185.0 −1.34147
\(850\) −8571.02 −0.345863
\(851\) −60675.1 −2.44408
\(852\) −1382.96 −0.0556098
\(853\) −34267.5 −1.37550 −0.687748 0.725950i \(-0.741401\pi\)
−0.687748 + 0.725950i \(0.741401\pi\)
\(854\) 17838.3 0.714771
\(855\) 29266.0 1.17061
\(856\) −26469.2 −1.05689
\(857\) −14640.9 −0.583577 −0.291788 0.956483i \(-0.594250\pi\)
−0.291788 + 0.956483i \(0.594250\pi\)
\(858\) 0 0
\(859\) 20542.6 0.815952 0.407976 0.912993i \(-0.366235\pi\)
0.407976 + 0.912993i \(0.366235\pi\)
\(860\) −1054.90 −0.0418278
\(861\) 44747.9 1.77120
\(862\) −35107.3 −1.38719
\(863\) −12466.2 −0.491721 −0.245861 0.969305i \(-0.579071\pi\)
−0.245861 + 0.969305i \(0.579071\pi\)
\(864\) 1479.22 0.0582453
\(865\) 17649.8 0.693769
\(866\) −26877.8 −1.05467
\(867\) −19793.2 −0.775333
\(868\) −1882.90 −0.0736288
\(869\) 3451.27 0.134726
\(870\) 1347.16 0.0524979
\(871\) 0 0
\(872\) −19413.2 −0.753916
\(873\) −8805.76 −0.341386
\(874\) 65494.0 2.53474
\(875\) 18161.3 0.701674
\(876\) 764.347 0.0294805
\(877\) −11451.9 −0.440939 −0.220470 0.975394i \(-0.570759\pi\)
−0.220470 + 0.975394i \(0.570759\pi\)
\(878\) −18608.0 −0.715250
\(879\) 27168.4 1.04251
\(880\) −9407.47 −0.360370
\(881\) 12598.4 0.481784 0.240892 0.970552i \(-0.422560\pi\)
0.240892 + 0.970552i \(0.422560\pi\)
\(882\) 5037.62 0.192319
\(883\) −2803.60 −0.106850 −0.0534251 0.998572i \(-0.517014\pi\)
−0.0534251 + 0.998572i \(0.517014\pi\)
\(884\) 0 0
\(885\) 9144.53 0.347333
\(886\) 32209.2 1.22132
\(887\) −12962.9 −0.490700 −0.245350 0.969435i \(-0.578903\pi\)
−0.245350 + 0.969435i \(0.578903\pi\)
\(888\) −51335.1 −1.93997
\(889\) −12113.7 −0.457007
\(890\) 21718.2 0.817973
\(891\) −9806.76 −0.368731
\(892\) −970.697 −0.0364365
\(893\) 52732.0 1.97605
\(894\) −3518.04 −0.131612
\(895\) 13782.9 0.514760
\(896\) 24781.1 0.923972
\(897\) 0 0
\(898\) −3789.35 −0.140815
\(899\) 1215.65 0.0450994
\(900\) 319.908 0.0118484
\(901\) 24897.0 0.920578
\(902\) −13654.5 −0.504042
\(903\) −16393.6 −0.604148
\(904\) 11161.2 0.410636
\(905\) −34306.6 −1.26010
\(906\) −2218.01 −0.0813338
\(907\) −15508.9 −0.567766 −0.283883 0.958859i \(-0.591623\pi\)
−0.283883 + 0.958859i \(0.591623\pi\)
\(908\) −521.460 −0.0190586
\(909\) 31647.6 1.15477
\(910\) 0 0
\(911\) 11245.1 0.408963 0.204482 0.978870i \(-0.434449\pi\)
0.204482 + 0.978870i \(0.434449\pi\)
\(912\) 59163.6 2.14814
\(913\) 12399.4 0.449463
\(914\) −36453.9 −1.31924
\(915\) −32743.5 −1.18302
\(916\) 3240.91 0.116903
\(917\) 14312.4 0.515415
\(918\) −15738.2 −0.565837
\(919\) 5457.33 0.195887 0.0979437 0.995192i \(-0.468773\pi\)
0.0979437 + 0.995192i \(0.468773\pi\)
\(920\) −47352.0 −1.69690
\(921\) 54843.0 1.96215
\(922\) 33675.4 1.20287
\(923\) 0 0
\(924\) 624.734 0.0222427
\(925\) 11616.0 0.412899
\(926\) 32688.1 1.16004
\(927\) −33197.8 −1.17622
\(928\) 133.232 0.00471290
\(929\) −5746.40 −0.202942 −0.101471 0.994838i \(-0.532355\pi\)
−0.101471 + 0.994838i \(0.532355\pi\)
\(930\) 54740.1 1.93011
\(931\) −12466.4 −0.438849
\(932\) 1936.27 0.0680520
\(933\) −33422.3 −1.17277
\(934\) 8041.47 0.281718
\(935\) 12265.5 0.429009
\(936\) 0 0
\(937\) 26289.8 0.916595 0.458297 0.888799i \(-0.348459\pi\)
0.458297 + 0.888799i \(0.348459\pi\)
\(938\) −29910.3 −1.04116
\(939\) 685.013 0.0238068
\(940\) 2755.05 0.0955957
\(941\) 9889.52 0.342603 0.171301 0.985219i \(-0.445203\pi\)
0.171301 + 0.985219i \(0.445203\pi\)
\(942\) −13808.0 −0.477590
\(943\) −73382.4 −2.53410
\(944\) 7380.11 0.254451
\(945\) −11997.3 −0.412987
\(946\) 5002.40 0.171926
\(947\) 9671.32 0.331865 0.165932 0.986137i \(-0.446937\pi\)
0.165932 + 0.986137i \(0.446937\pi\)
\(948\) −1134.01 −0.0388512
\(949\) 0 0
\(950\) −12538.6 −0.428215
\(951\) −5023.23 −0.171282
\(952\) −30383.1 −1.03437
\(953\) 10982.2 0.373294 0.186647 0.982427i \(-0.440238\pi\)
0.186647 + 0.982427i \(0.440238\pi\)
\(954\) −14718.0 −0.499488
\(955\) −54809.1 −1.85715
\(956\) −185.748 −0.00628403
\(957\) −403.347 −0.0136242
\(958\) 43804.6 1.47731
\(959\) −10053.6 −0.338528
\(960\) −39866.9 −1.34031
\(961\) 19605.4 0.658098
\(962\) 0 0
\(963\) −21782.2 −0.728889
\(964\) 3356.35 0.112138
\(965\) −47767.3 −1.59346
\(966\) 53176.4 1.77114
\(967\) −53005.8 −1.76272 −0.881361 0.472443i \(-0.843372\pi\)
−0.881361 + 0.472443i \(0.843372\pi\)
\(968\) 2638.04 0.0875927
\(969\) −77137.6 −2.55729
\(970\) 18032.1 0.596881
\(971\) −15906.8 −0.525720 −0.262860 0.964834i \(-0.584666\pi\)
−0.262860 + 0.964834i \(0.584666\pi\)
\(972\) 2338.27 0.0771607
\(973\) 20646.3 0.680256
\(974\) 41038.3 1.35005
\(975\) 0 0
\(976\) −26425.7 −0.866666
\(977\) 5306.33 0.173761 0.0868805 0.996219i \(-0.472310\pi\)
0.0868805 + 0.996219i \(0.472310\pi\)
\(978\) −44279.8 −1.44776
\(979\) −6502.52 −0.212279
\(980\) −651.322 −0.0212303
\(981\) −15975.6 −0.519942
\(982\) 34328.0 1.11553
\(983\) 27448.6 0.890613 0.445307 0.895378i \(-0.353095\pi\)
0.445307 + 0.895378i \(0.353095\pi\)
\(984\) −62086.3 −2.01142
\(985\) 46333.9 1.49880
\(986\) −1417.53 −0.0457845
\(987\) 42814.6 1.38075
\(988\) 0 0
\(989\) 26884.0 0.864370
\(990\) −7250.77 −0.232772
\(991\) −26958.2 −0.864132 −0.432066 0.901842i \(-0.642215\pi\)
−0.432066 + 0.901842i \(0.642215\pi\)
\(992\) 5413.71 0.173272
\(993\) −70477.9 −2.25231
\(994\) 17569.6 0.560636
\(995\) −19253.4 −0.613440
\(996\) −4074.16 −0.129613
\(997\) −3569.84 −0.113398 −0.0566991 0.998391i \(-0.518058\pi\)
−0.0566991 + 0.998391i \(0.518058\pi\)
\(998\) −2612.71 −0.0828697
\(999\) 21329.4 0.675508
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 1859.4.a.q.1.16 yes 51
13.12 even 2 1859.4.a.p.1.36 51
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.4.a.p.1.36 51 13.12 even 2
1859.4.a.q.1.16 yes 51 1.1 even 1 trivial