Properties

Label 165.4.a.g.1.3
Level $165$
Weight $4$
Character 165.1
Self dual yes
Analytic conductor $9.735$
Analytic rank $0$
Dimension $3$
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] = [165,4,Mod(1,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("165.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 165.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: \(9.73531515095\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1957.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 9x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.12946\) of defining polynomial
Character \(\chi\) \(=\) 165.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.59486 q^{2} -3.00000 q^{3} +13.1127 q^{4} +5.00000 q^{5} -13.7846 q^{6} +20.6383 q^{7} +23.4921 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.59486 q^{2} -3.00000 q^{3} +13.1127 q^{4} +5.00000 q^{5} -13.7846 q^{6} +20.6383 q^{7} +23.4921 q^{8} +9.00000 q^{9} +22.9743 q^{10} +11.0000 q^{11} -39.3381 q^{12} -15.6584 q^{13} +94.8302 q^{14} -15.0000 q^{15} +3.04132 q^{16} +72.9507 q^{17} +41.3537 q^{18} +61.0513 q^{19} +65.5635 q^{20} -61.9150 q^{21} +50.5434 q^{22} -13.6605 q^{23} -70.4764 q^{24} +25.0000 q^{25} -71.9483 q^{26} -27.0000 q^{27} +270.624 q^{28} -31.4663 q^{29} -68.9228 q^{30} -243.008 q^{31} -173.963 q^{32} -33.0000 q^{33} +335.198 q^{34} +103.192 q^{35} +118.014 q^{36} -65.4018 q^{37} +280.522 q^{38} +46.9753 q^{39} +117.461 q^{40} -109.087 q^{41} -284.491 q^{42} -121.750 q^{43} +144.240 q^{44} +45.0000 q^{45} -62.7678 q^{46} -519.530 q^{47} -9.12396 q^{48} +82.9413 q^{49} +114.871 q^{50} -218.852 q^{51} -205.324 q^{52} -542.673 q^{53} -124.061 q^{54} +55.0000 q^{55} +484.839 q^{56} -183.154 q^{57} -144.583 q^{58} +109.478 q^{59} -196.691 q^{60} -89.6156 q^{61} -1116.59 q^{62} +185.745 q^{63} -823.664 q^{64} -78.2922 q^{65} -151.630 q^{66} +488.446 q^{67} +956.581 q^{68} +40.9814 q^{69} +474.151 q^{70} +837.423 q^{71} +211.429 q^{72} +351.216 q^{73} -300.512 q^{74} -75.0000 q^{75} +800.547 q^{76} +227.022 q^{77} +215.845 q^{78} -831.205 q^{79} +15.2066 q^{80} +81.0000 q^{81} -501.238 q^{82} +1389.13 q^{83} -811.873 q^{84} +364.754 q^{85} -559.423 q^{86} +94.3988 q^{87} +258.413 q^{88} +1523.70 q^{89} +206.769 q^{90} -323.164 q^{91} -179.125 q^{92} +729.025 q^{93} -2387.17 q^{94} +305.256 q^{95} +521.888 q^{96} -426.612 q^{97} +381.103 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} - 9 q^{3} + 17 q^{4} + 15 q^{5} - 3 q^{6} + 6 q^{7} - 3 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} - 9 q^{3} + 17 q^{4} + 15 q^{5} - 3 q^{6} + 6 q^{7} - 3 q^{8} + 27 q^{9} + 5 q^{10} + 33 q^{11} - 51 q^{12} - 20 q^{13} + 144 q^{14} - 45 q^{15} + 25 q^{16} + 32 q^{17} + 9 q^{18} + 116 q^{19} + 85 q^{20} - 18 q^{21} + 11 q^{22} + 240 q^{23} + 9 q^{24} + 75 q^{25} + 302 q^{26} - 81 q^{27} + 160 q^{28} + 238 q^{29} - 15 q^{30} + 92 q^{31} + 197 q^{32} - 99 q^{33} + 354 q^{34} + 30 q^{35} + 153 q^{36} - 90 q^{37} + 324 q^{38} + 60 q^{39} - 15 q^{40} - 46 q^{41} - 432 q^{42} - 134 q^{43} + 187 q^{44} + 135 q^{45} - 240 q^{46} - 220 q^{47} - 75 q^{48} - 457 q^{49} + 25 q^{50} - 96 q^{51} - 1530 q^{52} - 798 q^{53} - 27 q^{54} + 165 q^{55} + 688 q^{56} - 348 q^{57} - 978 q^{58} + 1236 q^{59} - 255 q^{60} + 342 q^{61} - 1792 q^{62} + 54 q^{63} - 1919 q^{64} - 100 q^{65} - 33 q^{66} + 764 q^{67} + 1074 q^{68} - 720 q^{69} + 720 q^{70} + 1816 q^{71} - 27 q^{72} + 100 q^{73} - 1874 q^{74} - 225 q^{75} + 396 q^{76} + 66 q^{77} - 906 q^{78} - 96 q^{79} + 125 q^{80} + 243 q^{81} - 910 q^{82} + 858 q^{83} - 480 q^{84} + 160 q^{85} + 188 q^{86} - 714 q^{87} - 33 q^{88} + 838 q^{89} + 45 q^{90} + 332 q^{91} - 688 q^{92} - 276 q^{93} - 3112 q^{94} + 580 q^{95} - 591 q^{96} - 1322 q^{97} + 1017 q^{98} + 297 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.59486 1.62453 0.812263 0.583291i \(-0.198235\pi\)
0.812263 + 0.583291i \(0.198235\pi\)
\(3\) −3.00000 −0.577350
\(4\) 13.1127 1.63909
\(5\) 5.00000 0.447214
\(6\) −13.7846 −0.937921
\(7\) 20.6383 1.11437 0.557183 0.830390i \(-0.311882\pi\)
0.557183 + 0.830390i \(0.311882\pi\)
\(8\) 23.4921 1.03822
\(9\) 9.00000 0.333333
\(10\) 22.9743 0.726511
\(11\) 11.0000 0.301511
\(12\) −39.3381 −0.946328
\(13\) −15.6584 −0.334067 −0.167033 0.985951i \(-0.553419\pi\)
−0.167033 + 0.985951i \(0.553419\pi\)
\(14\) 94.8302 1.81032
\(15\) −15.0000 −0.258199
\(16\) 3.04132 0.0475206
\(17\) 72.9507 1.04077 0.520387 0.853931i \(-0.325788\pi\)
0.520387 + 0.853931i \(0.325788\pi\)
\(18\) 41.3537 0.541509
\(19\) 61.0513 0.737165 0.368582 0.929595i \(-0.379843\pi\)
0.368582 + 0.929595i \(0.379843\pi\)
\(20\) 65.5635 0.733022
\(21\) −61.9150 −0.643379
\(22\) 50.5434 0.489813
\(23\) −13.6605 −0.123844 −0.0619218 0.998081i \(-0.519723\pi\)
−0.0619218 + 0.998081i \(0.519723\pi\)
\(24\) −70.4764 −0.599414
\(25\) 25.0000 0.200000
\(26\) −71.9483 −0.542701
\(27\) −27.0000 −0.192450
\(28\) 270.624 1.82654
\(29\) −31.4663 −0.201487 −0.100744 0.994912i \(-0.532122\pi\)
−0.100744 + 0.994912i \(0.532122\pi\)
\(30\) −68.9228 −0.419451
\(31\) −243.008 −1.40792 −0.703961 0.710239i \(-0.748587\pi\)
−0.703961 + 0.710239i \(0.748587\pi\)
\(32\) −173.963 −0.961016
\(33\) −33.0000 −0.174078
\(34\) 335.198 1.69076
\(35\) 103.192 0.498360
\(36\) 118.014 0.546363
\(37\) −65.4018 −0.290594 −0.145297 0.989388i \(-0.546414\pi\)
−0.145297 + 0.989388i \(0.546414\pi\)
\(38\) 280.522 1.19754
\(39\) 46.9753 0.192874
\(40\) 117.461 0.464304
\(41\) −109.087 −0.415524 −0.207762 0.978179i \(-0.566618\pi\)
−0.207762 + 0.978179i \(0.566618\pi\)
\(42\) −284.491 −1.04519
\(43\) −121.750 −0.431783 −0.215891 0.976417i \(-0.569266\pi\)
−0.215891 + 0.976417i \(0.569266\pi\)
\(44\) 144.240 0.494204
\(45\) 45.0000 0.149071
\(46\) −62.7678 −0.201187
\(47\) −519.530 −1.61237 −0.806184 0.591665i \(-0.798471\pi\)
−0.806184 + 0.591665i \(0.798471\pi\)
\(48\) −9.12396 −0.0274361
\(49\) 82.9413 0.241811
\(50\) 114.871 0.324905
\(51\) −218.852 −0.600891
\(52\) −205.324 −0.547565
\(53\) −542.673 −1.40645 −0.703226 0.710967i \(-0.748258\pi\)
−0.703226 + 0.710967i \(0.748258\pi\)
\(54\) −124.061 −0.312640
\(55\) 55.0000 0.134840
\(56\) 484.839 1.15695
\(57\) −183.154 −0.425602
\(58\) −144.583 −0.327322
\(59\) 109.478 0.241574 0.120787 0.992678i \(-0.461458\pi\)
0.120787 + 0.992678i \(0.461458\pi\)
\(60\) −196.691 −0.423211
\(61\) −89.6156 −0.188100 −0.0940501 0.995567i \(-0.529981\pi\)
−0.0940501 + 0.995567i \(0.529981\pi\)
\(62\) −1116.59 −2.28721
\(63\) 185.745 0.371455
\(64\) −823.664 −1.60872
\(65\) −78.2922 −0.149399
\(66\) −151.630 −0.282794
\(67\) 488.446 0.890644 0.445322 0.895371i \(-0.353089\pi\)
0.445322 + 0.895371i \(0.353089\pi\)
\(68\) 956.581 1.70592
\(69\) 40.9814 0.0715011
\(70\) 474.151 0.809599
\(71\) 837.423 1.39977 0.699887 0.714254i \(-0.253234\pi\)
0.699887 + 0.714254i \(0.253234\pi\)
\(72\) 211.429 0.346072
\(73\) 351.216 0.563105 0.281553 0.959546i \(-0.409151\pi\)
0.281553 + 0.959546i \(0.409151\pi\)
\(74\) −300.512 −0.472078
\(75\) −75.0000 −0.115470
\(76\) 800.547 1.20828
\(77\) 227.022 0.335994
\(78\) 215.845 0.313328
\(79\) −831.205 −1.18377 −0.591885 0.806022i \(-0.701616\pi\)
−0.591885 + 0.806022i \(0.701616\pi\)
\(80\) 15.2066 0.0212519
\(81\) 81.0000 0.111111
\(82\) −501.238 −0.675031
\(83\) 1389.13 1.83707 0.918537 0.395335i \(-0.129371\pi\)
0.918537 + 0.395335i \(0.129371\pi\)
\(84\) −811.873 −1.05456
\(85\) 364.754 0.465448
\(86\) −559.423 −0.701443
\(87\) 94.3988 0.116329
\(88\) 258.413 0.313034
\(89\) 1523.70 1.81474 0.907369 0.420335i \(-0.138088\pi\)
0.907369 + 0.420335i \(0.138088\pi\)
\(90\) 206.769 0.242170
\(91\) −323.164 −0.372273
\(92\) −179.125 −0.202990
\(93\) 729.025 0.812864
\(94\) −2387.17 −2.61933
\(95\) 305.256 0.329670
\(96\) 521.888 0.554843
\(97\) −426.612 −0.446555 −0.223278 0.974755i \(-0.571676\pi\)
−0.223278 + 0.974755i \(0.571676\pi\)
\(98\) 381.103 0.392829
\(99\) 99.0000 0.100504
\(100\) 327.818 0.327818
\(101\) 74.1387 0.0730403 0.0365202 0.999333i \(-0.488373\pi\)
0.0365202 + 0.999333i \(0.488373\pi\)
\(102\) −1005.59 −0.976163
\(103\) −69.3916 −0.0663821 −0.0331911 0.999449i \(-0.510567\pi\)
−0.0331911 + 0.999449i \(0.510567\pi\)
\(104\) −367.850 −0.346833
\(105\) −309.575 −0.287728
\(106\) −2493.51 −2.28482
\(107\) 1141.71 1.03152 0.515761 0.856733i \(-0.327509\pi\)
0.515761 + 0.856733i \(0.327509\pi\)
\(108\) −354.043 −0.315443
\(109\) −2226.85 −1.95682 −0.978409 0.206680i \(-0.933734\pi\)
−0.978409 + 0.206680i \(0.933734\pi\)
\(110\) 252.717 0.219051
\(111\) 196.205 0.167775
\(112\) 62.7678 0.0529554
\(113\) −1719.76 −1.43169 −0.715847 0.698257i \(-0.753959\pi\)
−0.715847 + 0.698257i \(0.753959\pi\)
\(114\) −841.566 −0.691402
\(115\) −68.3023 −0.0553845
\(116\) −412.608 −0.330256
\(117\) −140.926 −0.111356
\(118\) 503.038 0.392444
\(119\) 1505.58 1.15980
\(120\) −352.382 −0.268066
\(121\) 121.000 0.0909091
\(122\) −411.771 −0.305574
\(123\) 327.260 0.239903
\(124\) −3186.49 −2.30771
\(125\) 125.000 0.0894427
\(126\) 853.472 0.603439
\(127\) −1601.63 −1.11907 −0.559534 0.828807i \(-0.689020\pi\)
−0.559534 + 0.828807i \(0.689020\pi\)
\(128\) −2392.91 −1.65239
\(129\) 365.249 0.249290
\(130\) −359.741 −0.242703
\(131\) 2004.13 1.33665 0.668327 0.743868i \(-0.267011\pi\)
0.668327 + 0.743868i \(0.267011\pi\)
\(132\) −432.719 −0.285329
\(133\) 1260.00 0.821471
\(134\) 2244.34 1.44687
\(135\) −135.000 −0.0860663
\(136\) 1713.77 1.08055
\(137\) −1672.85 −1.04322 −0.521610 0.853184i \(-0.674669\pi\)
−0.521610 + 0.853184i \(0.674669\pi\)
\(138\) 188.303 0.116155
\(139\) 2540.38 1.55016 0.775080 0.631863i \(-0.217709\pi\)
0.775080 + 0.631863i \(0.217709\pi\)
\(140\) 1353.12 0.816855
\(141\) 1558.59 0.930901
\(142\) 3847.84 2.27397
\(143\) −172.243 −0.100725
\(144\) 27.3719 0.0158402
\(145\) −157.331 −0.0901079
\(146\) 1613.79 0.914780
\(147\) −248.824 −0.139610
\(148\) −857.594 −0.476310
\(149\) 3090.68 1.69932 0.849658 0.527334i \(-0.176808\pi\)
0.849658 + 0.527334i \(0.176808\pi\)
\(150\) −344.614 −0.187584
\(151\) 1358.74 0.732267 0.366134 0.930562i \(-0.380681\pi\)
0.366134 + 0.930562i \(0.380681\pi\)
\(152\) 1434.22 0.765335
\(153\) 656.557 0.346925
\(154\) 1043.13 0.545831
\(155\) −1215.04 −0.629642
\(156\) 615.973 0.316137
\(157\) −1011.95 −0.514411 −0.257205 0.966357i \(-0.582802\pi\)
−0.257205 + 0.966357i \(0.582802\pi\)
\(158\) −3819.27 −1.92307
\(159\) 1628.02 0.812015
\(160\) −869.813 −0.429780
\(161\) −281.929 −0.138007
\(162\) 372.183 0.180503
\(163\) −2816.37 −1.35334 −0.676672 0.736285i \(-0.736578\pi\)
−0.676672 + 0.736285i \(0.736578\pi\)
\(164\) −1430.42 −0.681081
\(165\) −165.000 −0.0778499
\(166\) 6382.87 2.98438
\(167\) 3448.89 1.59810 0.799052 0.601262i \(-0.205335\pi\)
0.799052 + 0.601262i \(0.205335\pi\)
\(168\) −1454.52 −0.667966
\(169\) −1951.81 −0.888399
\(170\) 1675.99 0.756133
\(171\) 549.462 0.245722
\(172\) −1596.47 −0.707730
\(173\) −2287.85 −1.00545 −0.502723 0.864448i \(-0.667668\pi\)
−0.502723 + 0.864448i \(0.667668\pi\)
\(174\) 433.749 0.188979
\(175\) 515.959 0.222873
\(176\) 33.4545 0.0143280
\(177\) −328.435 −0.139473
\(178\) 7001.17 2.94809
\(179\) 3249.06 1.35668 0.678340 0.734748i \(-0.262700\pi\)
0.678340 + 0.734748i \(0.262700\pi\)
\(180\) 590.072 0.244341
\(181\) 1170.45 0.480655 0.240328 0.970692i \(-0.422745\pi\)
0.240328 + 0.970692i \(0.422745\pi\)
\(182\) −1484.89 −0.604767
\(183\) 268.847 0.108600
\(184\) −320.913 −0.128576
\(185\) −327.009 −0.129958
\(186\) 3349.76 1.32052
\(187\) 802.458 0.313805
\(188\) −6812.44 −2.64281
\(189\) −557.235 −0.214460
\(190\) 1402.61 0.535558
\(191\) −2760.35 −1.04572 −0.522859 0.852419i \(-0.675134\pi\)
−0.522859 + 0.852419i \(0.675134\pi\)
\(192\) 2470.99 0.928794
\(193\) −1250.61 −0.466430 −0.233215 0.972425i \(-0.574925\pi\)
−0.233215 + 0.972425i \(0.574925\pi\)
\(194\) −1960.22 −0.725441
\(195\) 234.877 0.0862557
\(196\) 1087.58 0.396350
\(197\) −143.991 −0.0520756 −0.0260378 0.999661i \(-0.508289\pi\)
−0.0260378 + 0.999661i \(0.508289\pi\)
\(198\) 454.891 0.163271
\(199\) 761.249 0.271174 0.135587 0.990765i \(-0.456708\pi\)
0.135587 + 0.990765i \(0.456708\pi\)
\(200\) 587.303 0.207643
\(201\) −1465.34 −0.514213
\(202\) 340.657 0.118656
\(203\) −649.411 −0.224531
\(204\) −2869.74 −0.984913
\(205\) −545.434 −0.185828
\(206\) −318.844 −0.107840
\(207\) −122.944 −0.0412812
\(208\) −47.6223 −0.0158751
\(209\) 671.564 0.222263
\(210\) −1422.45 −0.467422
\(211\) 3976.58 1.29743 0.648717 0.761029i \(-0.275306\pi\)
0.648717 + 0.761029i \(0.275306\pi\)
\(212\) −7115.91 −2.30530
\(213\) −2512.27 −0.808159
\(214\) 5245.97 1.67573
\(215\) −608.749 −0.193099
\(216\) −634.287 −0.199805
\(217\) −5015.29 −1.56894
\(218\) −10232.0 −3.17890
\(219\) −1053.65 −0.325109
\(220\) 721.199 0.221015
\(221\) −1142.29 −0.347688
\(222\) 901.535 0.272555
\(223\) 908.084 0.272690 0.136345 0.990661i \(-0.456464\pi\)
0.136345 + 0.990661i \(0.456464\pi\)
\(224\) −3590.30 −1.07092
\(225\) 225.000 0.0666667
\(226\) −7902.05 −2.32583
\(227\) −2062.15 −0.602951 −0.301475 0.953474i \(-0.597479\pi\)
−0.301475 + 0.953474i \(0.597479\pi\)
\(228\) −2401.64 −0.697599
\(229\) 4077.47 1.17662 0.588312 0.808634i \(-0.299793\pi\)
0.588312 + 0.808634i \(0.299793\pi\)
\(230\) −313.839 −0.0899737
\(231\) −681.065 −0.193986
\(232\) −739.209 −0.209187
\(233\) 1682.76 0.473138 0.236569 0.971615i \(-0.423977\pi\)
0.236569 + 0.971615i \(0.423977\pi\)
\(234\) −647.534 −0.180900
\(235\) −2597.65 −0.721073
\(236\) 1435.56 0.395961
\(237\) 2493.62 0.683450
\(238\) 6917.93 1.88413
\(239\) 4024.96 1.08934 0.544672 0.838649i \(-0.316654\pi\)
0.544672 + 0.838649i \(0.316654\pi\)
\(240\) −45.6198 −0.0122698
\(241\) −2784.27 −0.744194 −0.372097 0.928194i \(-0.621361\pi\)
−0.372097 + 0.928194i \(0.621361\pi\)
\(242\) 555.978 0.147684
\(243\) −243.000 −0.0641500
\(244\) −1175.10 −0.308313
\(245\) 414.707 0.108141
\(246\) 1503.71 0.389729
\(247\) −955.968 −0.246262
\(248\) −5708.78 −1.46173
\(249\) −4167.40 −1.06064
\(250\) 574.357 0.145302
\(251\) −1827.60 −0.459591 −0.229796 0.973239i \(-0.573806\pi\)
−0.229796 + 0.973239i \(0.573806\pi\)
\(252\) 2435.62 0.608848
\(253\) −150.265 −0.0373402
\(254\) −7359.26 −1.81796
\(255\) −1094.26 −0.268727
\(256\) −4405.79 −1.07563
\(257\) 585.171 0.142031 0.0710155 0.997475i \(-0.477376\pi\)
0.0710155 + 0.997475i \(0.477376\pi\)
\(258\) 1678.27 0.404978
\(259\) −1349.78 −0.323828
\(260\) −1026.62 −0.244878
\(261\) −283.196 −0.0671625
\(262\) 9208.69 2.17143
\(263\) −238.098 −0.0558241 −0.0279120 0.999610i \(-0.508886\pi\)
−0.0279120 + 0.999610i \(0.508886\pi\)
\(264\) −775.240 −0.180730
\(265\) −2713.37 −0.628984
\(266\) 5789.51 1.33450
\(267\) −4571.09 −1.04774
\(268\) 6404.84 1.45984
\(269\) 4618.46 1.04681 0.523406 0.852083i \(-0.324661\pi\)
0.523406 + 0.852083i \(0.324661\pi\)
\(270\) −620.306 −0.139817
\(271\) −143.439 −0.0321525 −0.0160762 0.999871i \(-0.505117\pi\)
−0.0160762 + 0.999871i \(0.505117\pi\)
\(272\) 221.867 0.0494582
\(273\) 969.493 0.214932
\(274\) −7686.51 −1.69474
\(275\) 275.000 0.0603023
\(276\) 537.376 0.117197
\(277\) −8602.51 −1.86597 −0.932987 0.359911i \(-0.882807\pi\)
−0.932987 + 0.359911i \(0.882807\pi\)
\(278\) 11672.7 2.51828
\(279\) −2187.07 −0.469307
\(280\) 2424.19 0.517404
\(281\) −2992.81 −0.635360 −0.317680 0.948198i \(-0.602904\pi\)
−0.317680 + 0.948198i \(0.602904\pi\)
\(282\) 7161.50 1.51227
\(283\) −6858.89 −1.44070 −0.720351 0.693610i \(-0.756019\pi\)
−0.720351 + 0.693610i \(0.756019\pi\)
\(284\) 10980.9 2.29435
\(285\) −915.769 −0.190335
\(286\) −791.431 −0.163630
\(287\) −2251.37 −0.463046
\(288\) −1565.66 −0.320339
\(289\) 408.809 0.0832096
\(290\) −722.915 −0.146383
\(291\) 1279.84 0.257819
\(292\) 4605.39 0.922979
\(293\) 4049.70 0.807461 0.403731 0.914878i \(-0.367713\pi\)
0.403731 + 0.914878i \(0.367713\pi\)
\(294\) −1143.31 −0.226800
\(295\) 547.392 0.108035
\(296\) −1536.43 −0.301699
\(297\) −297.000 −0.0580259
\(298\) 14201.2 2.76059
\(299\) 213.901 0.0413720
\(300\) −983.453 −0.189266
\(301\) −2512.71 −0.481164
\(302\) 6243.20 1.18959
\(303\) −222.416 −0.0421699
\(304\) 185.677 0.0350305
\(305\) −448.078 −0.0841209
\(306\) 3016.78 0.563588
\(307\) −9572.69 −1.77962 −0.889808 0.456335i \(-0.849162\pi\)
−0.889808 + 0.456335i \(0.849162\pi\)
\(308\) 2976.87 0.550724
\(309\) 208.175 0.0383257
\(310\) −5582.94 −1.02287
\(311\) 5396.42 0.983932 0.491966 0.870614i \(-0.336278\pi\)
0.491966 + 0.870614i \(0.336278\pi\)
\(312\) 1103.55 0.200244
\(313\) 9755.04 1.76162 0.880811 0.473469i \(-0.156998\pi\)
0.880811 + 0.473469i \(0.156998\pi\)
\(314\) −4649.77 −0.835674
\(315\) 928.726 0.166120
\(316\) −10899.3 −1.94030
\(317\) −4353.75 −0.771391 −0.385695 0.922626i \(-0.626038\pi\)
−0.385695 + 0.922626i \(0.626038\pi\)
\(318\) 7480.52 1.31914
\(319\) −346.129 −0.0607508
\(320\) −4118.32 −0.719440
\(321\) −3425.12 −0.595549
\(322\) −1295.42 −0.224196
\(323\) 4453.74 0.767221
\(324\) 1062.13 0.182121
\(325\) −391.461 −0.0668134
\(326\) −12940.8 −2.19854
\(327\) 6680.54 1.12977
\(328\) −2562.68 −0.431404
\(329\) −10722.2 −1.79677
\(330\) −758.151 −0.126469
\(331\) 5387.64 0.894656 0.447328 0.894370i \(-0.352376\pi\)
0.447328 + 0.894370i \(0.352376\pi\)
\(332\) 18215.3 3.01113
\(333\) −588.616 −0.0968648
\(334\) 15847.2 2.59616
\(335\) 2442.23 0.398308
\(336\) −188.303 −0.0305738
\(337\) −4500.27 −0.727434 −0.363717 0.931509i \(-0.618492\pi\)
−0.363717 + 0.931509i \(0.618492\pi\)
\(338\) −8968.30 −1.44323
\(339\) 5159.28 0.826589
\(340\) 4782.91 0.762910
\(341\) −2673.09 −0.424504
\(342\) 2524.70 0.399181
\(343\) −5367.18 −0.844899
\(344\) −2860.16 −0.448283
\(345\) 204.907 0.0319763
\(346\) −10512.4 −1.63337
\(347\) 5906.32 0.913740 0.456870 0.889533i \(-0.348970\pi\)
0.456870 + 0.889533i \(0.348970\pi\)
\(348\) 1237.82 0.190673
\(349\) 3636.26 0.557721 0.278860 0.960332i \(-0.410043\pi\)
0.278860 + 0.960332i \(0.410043\pi\)
\(350\) 2370.76 0.362063
\(351\) 422.778 0.0642912
\(352\) −1913.59 −0.289757
\(353\) 210.408 0.0317248 0.0158624 0.999874i \(-0.494951\pi\)
0.0158624 + 0.999874i \(0.494951\pi\)
\(354\) −1509.11 −0.226577
\(355\) 4187.12 0.625998
\(356\) 19979.8 2.97451
\(357\) −4516.75 −0.669612
\(358\) 14928.9 2.20396
\(359\) 2499.68 0.367488 0.183744 0.982974i \(-0.441178\pi\)
0.183744 + 0.982974i \(0.441178\pi\)
\(360\) 1057.15 0.154768
\(361\) −3131.74 −0.456588
\(362\) 5378.03 0.780837
\(363\) −363.000 −0.0524864
\(364\) −4237.56 −0.610188
\(365\) 1756.08 0.251828
\(366\) 1235.31 0.176423
\(367\) 5748.70 0.817656 0.408828 0.912612i \(-0.365938\pi\)
0.408828 + 0.912612i \(0.365938\pi\)
\(368\) −41.5458 −0.00588512
\(369\) −981.781 −0.138508
\(370\) −1502.56 −0.211120
\(371\) −11199.9 −1.56730
\(372\) 9559.48 1.33236
\(373\) 4467.78 0.620196 0.310098 0.950705i \(-0.399638\pi\)
0.310098 + 0.950705i \(0.399638\pi\)
\(374\) 3687.18 0.509785
\(375\) −375.000 −0.0516398
\(376\) −12204.9 −1.67398
\(377\) 492.712 0.0673103
\(378\) −2560.42 −0.348396
\(379\) 7804.08 1.05770 0.528851 0.848715i \(-0.322623\pi\)
0.528851 + 0.848715i \(0.322623\pi\)
\(380\) 4002.74 0.540358
\(381\) 4804.89 0.646094
\(382\) −12683.4 −1.69880
\(383\) −11161.1 −1.48904 −0.744522 0.667597i \(-0.767323\pi\)
−0.744522 + 0.667597i \(0.767323\pi\)
\(384\) 7178.74 0.954007
\(385\) 1135.11 0.150261
\(386\) −5746.38 −0.757728
\(387\) −1095.75 −0.143928
\(388\) −5594.04 −0.731944
\(389\) 8490.24 1.10661 0.553306 0.832978i \(-0.313366\pi\)
0.553306 + 0.832978i \(0.313366\pi\)
\(390\) 1079.22 0.140125
\(391\) −996.540 −0.128893
\(392\) 1948.47 0.251052
\(393\) −6012.39 −0.771717
\(394\) −661.616 −0.0845983
\(395\) −4156.03 −0.529398
\(396\) 1298.16 0.164735
\(397\) 6019.74 0.761013 0.380507 0.924778i \(-0.375750\pi\)
0.380507 + 0.924778i \(0.375750\pi\)
\(398\) 3497.83 0.440529
\(399\) −3779.99 −0.474277
\(400\) 76.0330 0.00950413
\(401\) −10398.8 −1.29499 −0.647495 0.762069i \(-0.724184\pi\)
−0.647495 + 0.762069i \(0.724184\pi\)
\(402\) −6733.01 −0.835354
\(403\) 3805.13 0.470340
\(404\) 972.158 0.119720
\(405\) 405.000 0.0496904
\(406\) −2983.95 −0.364756
\(407\) −719.420 −0.0876175
\(408\) −5141.30 −0.623854
\(409\) −4733.68 −0.572287 −0.286144 0.958187i \(-0.592373\pi\)
−0.286144 + 0.958187i \(0.592373\pi\)
\(410\) −2506.19 −0.301883
\(411\) 5018.55 0.602304
\(412\) −909.911 −0.108806
\(413\) 2259.45 0.269202
\(414\) −564.910 −0.0670624
\(415\) 6945.67 0.821565
\(416\) 2723.98 0.321044
\(417\) −7621.14 −0.894985
\(418\) 3085.74 0.361073
\(419\) −8117.57 −0.946466 −0.473233 0.880937i \(-0.656913\pi\)
−0.473233 + 0.880937i \(0.656913\pi\)
\(420\) −4059.37 −0.471611
\(421\) −9484.27 −1.09795 −0.548973 0.835840i \(-0.684981\pi\)
−0.548973 + 0.835840i \(0.684981\pi\)
\(422\) 18271.8 2.10772
\(423\) −4675.77 −0.537456
\(424\) −12748.5 −1.46020
\(425\) 1823.77 0.208155
\(426\) −11543.5 −1.31288
\(427\) −1849.52 −0.209612
\(428\) 14970.8 1.69075
\(429\) 516.728 0.0581536
\(430\) −2797.11 −0.313695
\(431\) 9335.16 1.04329 0.521646 0.853162i \(-0.325318\pi\)
0.521646 + 0.853162i \(0.325318\pi\)
\(432\) −82.1157 −0.00914535
\(433\) −2983.02 −0.331074 −0.165537 0.986204i \(-0.552936\pi\)
−0.165537 + 0.986204i \(0.552936\pi\)
\(434\) −23044.5 −2.54878
\(435\) 471.994 0.0520238
\(436\) −29200.0 −3.20739
\(437\) −833.988 −0.0912931
\(438\) −4841.36 −0.528148
\(439\) −5232.32 −0.568850 −0.284425 0.958698i \(-0.591803\pi\)
−0.284425 + 0.958698i \(0.591803\pi\)
\(440\) 1292.07 0.139993
\(441\) 746.472 0.0806038
\(442\) −5248.68 −0.564828
\(443\) 7517.71 0.806269 0.403135 0.915141i \(-0.367921\pi\)
0.403135 + 0.915141i \(0.367921\pi\)
\(444\) 2572.78 0.274997
\(445\) 7618.49 0.811575
\(446\) 4172.52 0.442992
\(447\) −9272.03 −0.981101
\(448\) −16999.1 −1.79270
\(449\) 16070.9 1.68916 0.844581 0.535428i \(-0.179850\pi\)
0.844581 + 0.535428i \(0.179850\pi\)
\(450\) 1033.84 0.108302
\(451\) −1199.96 −0.125285
\(452\) −22550.7 −2.34667
\(453\) −4076.21 −0.422775
\(454\) −9475.29 −0.979510
\(455\) −1615.82 −0.166485
\(456\) −4302.67 −0.441867
\(457\) 9718.51 0.994776 0.497388 0.867528i \(-0.334293\pi\)
0.497388 + 0.867528i \(0.334293\pi\)
\(458\) 18735.4 1.91146
\(459\) −1969.67 −0.200297
\(460\) −895.627 −0.0907801
\(461\) −14538.0 −1.46877 −0.734385 0.678733i \(-0.762529\pi\)
−0.734385 + 0.678733i \(0.762529\pi\)
\(462\) −3129.40 −0.315136
\(463\) −9978.17 −1.00157 −0.500783 0.865573i \(-0.666955\pi\)
−0.500783 + 0.865573i \(0.666955\pi\)
\(464\) −95.6990 −0.00957481
\(465\) 3645.12 0.363524
\(466\) 7732.03 0.768625
\(467\) 15188.2 1.50498 0.752489 0.658605i \(-0.228853\pi\)
0.752489 + 0.658605i \(0.228853\pi\)
\(468\) −1847.92 −0.182522
\(469\) 10080.7 0.992503
\(470\) −11935.8 −1.17140
\(471\) 3035.85 0.296995
\(472\) 2571.88 0.250806
\(473\) −1339.25 −0.130187
\(474\) 11457.8 1.11028
\(475\) 1526.28 0.147433
\(476\) 19742.3 1.90102
\(477\) −4884.06 −0.468817
\(478\) 18494.1 1.76967
\(479\) 11330.8 1.08083 0.540415 0.841399i \(-0.318267\pi\)
0.540415 + 0.841399i \(0.318267\pi\)
\(480\) 2609.44 0.248133
\(481\) 1024.09 0.0970779
\(482\) −12793.3 −1.20896
\(483\) 845.788 0.0796784
\(484\) 1586.64 0.149008
\(485\) −2133.06 −0.199706
\(486\) −1116.55 −0.104213
\(487\) 19086.9 1.77599 0.887997 0.459850i \(-0.152097\pi\)
0.887997 + 0.459850i \(0.152097\pi\)
\(488\) −2105.26 −0.195288
\(489\) 8449.11 0.781353
\(490\) 1905.52 0.175679
\(491\) −8112.85 −0.745677 −0.372839 0.927896i \(-0.621616\pi\)
−0.372839 + 0.927896i \(0.621616\pi\)
\(492\) 4291.27 0.393222
\(493\) −2295.49 −0.209703
\(494\) −4392.53 −0.400060
\(495\) 495.000 0.0449467
\(496\) −739.066 −0.0669053
\(497\) 17283.0 1.55986
\(498\) −19148.6 −1.72303
\(499\) 18329.1 1.64433 0.822167 0.569246i \(-0.192765\pi\)
0.822167 + 0.569246i \(0.192765\pi\)
\(500\) 1639.09 0.146604
\(501\) −10346.7 −0.922666
\(502\) −8397.58 −0.746618
\(503\) 7739.57 0.686064 0.343032 0.939324i \(-0.388546\pi\)
0.343032 + 0.939324i \(0.388546\pi\)
\(504\) 4363.55 0.385651
\(505\) 370.693 0.0326646
\(506\) −690.446 −0.0606602
\(507\) 5855.44 0.512918
\(508\) −21001.7 −1.83425
\(509\) 15914.9 1.38589 0.692943 0.720993i \(-0.256314\pi\)
0.692943 + 0.720993i \(0.256314\pi\)
\(510\) −5027.97 −0.436554
\(511\) 7248.51 0.627505
\(512\) −1100.65 −0.0950048
\(513\) −1648.38 −0.141867
\(514\) 2688.78 0.230733
\(515\) −346.958 −0.0296870
\(516\) 4789.40 0.408608
\(517\) −5714.83 −0.486147
\(518\) −6202.07 −0.526068
\(519\) 6863.56 0.580495
\(520\) −1839.25 −0.155109
\(521\) 2274.50 0.191262 0.0956312 0.995417i \(-0.469513\pi\)
0.0956312 + 0.995417i \(0.469513\pi\)
\(522\) −1301.25 −0.109107
\(523\) 10971.1 0.917274 0.458637 0.888624i \(-0.348338\pi\)
0.458637 + 0.888624i \(0.348338\pi\)
\(524\) 26279.6 2.19089
\(525\) −1547.88 −0.128676
\(526\) −1094.02 −0.0906877
\(527\) −17727.6 −1.46533
\(528\) −100.364 −0.00827228
\(529\) −11980.4 −0.984663
\(530\) −12467.5 −1.02180
\(531\) 985.306 0.0805247
\(532\) 16522.0 1.34646
\(533\) 1708.13 0.138813
\(534\) −21003.5 −1.70208
\(535\) 5708.53 0.461310
\(536\) 11474.6 0.924680
\(537\) −9747.17 −0.783280
\(538\) 21221.2 1.70058
\(539\) 912.355 0.0729089
\(540\) −1770.21 −0.141070
\(541\) 5313.05 0.422229 0.211115 0.977461i \(-0.432291\pi\)
0.211115 + 0.977461i \(0.432291\pi\)
\(542\) −659.084 −0.0522326
\(543\) −3511.34 −0.277506
\(544\) −12690.7 −1.00020
\(545\) −11134.2 −0.875115
\(546\) 4454.68 0.349162
\(547\) 20685.1 1.61688 0.808439 0.588581i \(-0.200313\pi\)
0.808439 + 0.588581i \(0.200313\pi\)
\(548\) −21935.6 −1.70993
\(549\) −806.541 −0.0627000
\(550\) 1263.59 0.0979627
\(551\) −1921.06 −0.148529
\(552\) 962.739 0.0742335
\(553\) −17154.7 −1.31915
\(554\) −39527.3 −3.03132
\(555\) 981.027 0.0750311
\(556\) 33311.2 2.54085
\(557\) −10853.8 −0.825659 −0.412830 0.910808i \(-0.635460\pi\)
−0.412830 + 0.910808i \(0.635460\pi\)
\(558\) −10049.3 −0.762402
\(559\) 1906.41 0.144244
\(560\) 313.839 0.0236824
\(561\) −2407.37 −0.181175
\(562\) −13751.5 −1.03216
\(563\) −15381.2 −1.15141 −0.575704 0.817658i \(-0.695272\pi\)
−0.575704 + 0.817658i \(0.695272\pi\)
\(564\) 20437.3 1.52583
\(565\) −8598.80 −0.640273
\(566\) −31515.6 −2.34046
\(567\) 1671.71 0.123818
\(568\) 19672.9 1.45327
\(569\) −1348.88 −0.0993814 −0.0496907 0.998765i \(-0.515824\pi\)
−0.0496907 + 0.998765i \(0.515824\pi\)
\(570\) −4207.83 −0.309204
\(571\) 3463.51 0.253841 0.126920 0.991913i \(-0.459491\pi\)
0.126920 + 0.991913i \(0.459491\pi\)
\(572\) −2258.57 −0.165097
\(573\) 8281.05 0.603745
\(574\) −10344.7 −0.752231
\(575\) −341.511 −0.0247687
\(576\) −7412.97 −0.536239
\(577\) 12052.6 0.869598 0.434799 0.900528i \(-0.356819\pi\)
0.434799 + 0.900528i \(0.356819\pi\)
\(578\) 1878.42 0.135176
\(579\) 3751.83 0.269293
\(580\) −2063.04 −0.147695
\(581\) 28669.4 2.04717
\(582\) 5880.66 0.418834
\(583\) −5969.41 −0.424061
\(584\) 8250.80 0.584624
\(585\) −704.630 −0.0497997
\(586\) 18607.8 1.31174
\(587\) −11133.1 −0.782813 −0.391407 0.920218i \(-0.628011\pi\)
−0.391407 + 0.920218i \(0.628011\pi\)
\(588\) −3262.75 −0.228833
\(589\) −14836.0 −1.03787
\(590\) 2515.19 0.175506
\(591\) 431.972 0.0300659
\(592\) −198.908 −0.0138092
\(593\) −7939.69 −0.549821 −0.274911 0.961470i \(-0.588648\pi\)
−0.274911 + 0.961470i \(0.588648\pi\)
\(594\) −1364.67 −0.0942646
\(595\) 7527.91 0.518680
\(596\) 40527.1 2.78533
\(597\) −2283.75 −0.156562
\(598\) 982.846 0.0672100
\(599\) −19474.7 −1.32840 −0.664202 0.747553i \(-0.731229\pi\)
−0.664202 + 0.747553i \(0.731229\pi\)
\(600\) −1761.91 −0.119883
\(601\) −19946.1 −1.35377 −0.676887 0.736087i \(-0.736671\pi\)
−0.676887 + 0.736087i \(0.736671\pi\)
\(602\) −11545.6 −0.781664
\(603\) 4396.01 0.296881
\(604\) 17816.7 1.20025
\(605\) 605.000 0.0406558
\(606\) −1021.97 −0.0685061
\(607\) 1427.44 0.0954496 0.0477248 0.998861i \(-0.484803\pi\)
0.0477248 + 0.998861i \(0.484803\pi\)
\(608\) −10620.6 −0.708427
\(609\) 1948.23 0.129633
\(610\) −2058.85 −0.136657
\(611\) 8135.03 0.538638
\(612\) 8609.23 0.568640
\(613\) −8029.40 −0.529045 −0.264522 0.964380i \(-0.585214\pi\)
−0.264522 + 0.964380i \(0.585214\pi\)
\(614\) −43985.1 −2.89103
\(615\) 1636.30 0.107288
\(616\) 5333.22 0.348834
\(617\) 20795.5 1.35688 0.678440 0.734655i \(-0.262656\pi\)
0.678440 + 0.734655i \(0.262656\pi\)
\(618\) 956.533 0.0622612
\(619\) 1677.43 0.108920 0.0544602 0.998516i \(-0.482656\pi\)
0.0544602 + 0.998516i \(0.482656\pi\)
\(620\) −15932.5 −1.03204
\(621\) 368.832 0.0238337
\(622\) 24795.8 1.59842
\(623\) 31446.6 2.02228
\(624\) 142.867 0.00916547
\(625\) 625.000 0.0400000
\(626\) 44823.0 2.86180
\(627\) −2014.69 −0.128324
\(628\) −13269.4 −0.843165
\(629\) −4771.11 −0.302443
\(630\) 4267.36 0.269866
\(631\) −25225.2 −1.59144 −0.795719 0.605666i \(-0.792907\pi\)
−0.795719 + 0.605666i \(0.792907\pi\)
\(632\) −19526.8 −1.22901
\(633\) −11929.7 −0.749074
\(634\) −20004.8 −1.25315
\(635\) −8008.15 −0.500462
\(636\) 21347.7 1.33096
\(637\) −1298.73 −0.0807812
\(638\) −1590.41 −0.0986912
\(639\) 7536.81 0.466591
\(640\) −11964.6 −0.738971
\(641\) 15165.3 0.934468 0.467234 0.884134i \(-0.345251\pi\)
0.467234 + 0.884134i \(0.345251\pi\)
\(642\) −15737.9 −0.967486
\(643\) 27156.1 1.66553 0.832763 0.553630i \(-0.186758\pi\)
0.832763 + 0.553630i \(0.186758\pi\)
\(644\) −3696.85 −0.226206
\(645\) 1826.25 0.111486
\(646\) 20464.3 1.24637
\(647\) 29154.9 1.77156 0.885778 0.464110i \(-0.153626\pi\)
0.885778 + 0.464110i \(0.153626\pi\)
\(648\) 1902.86 0.115357
\(649\) 1204.26 0.0728374
\(650\) −1798.71 −0.108540
\(651\) 15045.9 0.905828
\(652\) −36930.2 −2.21825
\(653\) −19141.7 −1.14713 −0.573564 0.819161i \(-0.694440\pi\)
−0.573564 + 0.819161i \(0.694440\pi\)
\(654\) 30696.1 1.83534
\(655\) 10020.7 0.597770
\(656\) −331.768 −0.0197460
\(657\) 3160.94 0.187702
\(658\) −49267.2 −2.91890
\(659\) −24939.6 −1.47422 −0.737110 0.675773i \(-0.763810\pi\)
−0.737110 + 0.675773i \(0.763810\pi\)
\(660\) −2163.60 −0.127603
\(661\) 22617.7 1.33090 0.665452 0.746440i \(-0.268239\pi\)
0.665452 + 0.746440i \(0.268239\pi\)
\(662\) 24755.4 1.45339
\(663\) 3426.88 0.200738
\(664\) 32633.7 1.90728
\(665\) 6299.99 0.367373
\(666\) −2704.61 −0.157359
\(667\) 429.843 0.0249529
\(668\) 45224.3 2.61943
\(669\) −2724.25 −0.157438
\(670\) 11221.7 0.647062
\(671\) −985.772 −0.0567143
\(672\) 10770.9 0.618298
\(673\) −13855.8 −0.793615 −0.396807 0.917902i \(-0.629882\pi\)
−0.396807 + 0.917902i \(0.629882\pi\)
\(674\) −20678.1 −1.18174
\(675\) −675.000 −0.0384900
\(676\) −25593.5 −1.45616
\(677\) −24992.8 −1.41884 −0.709419 0.704787i \(-0.751043\pi\)
−0.709419 + 0.704787i \(0.751043\pi\)
\(678\) 23706.1 1.34282
\(679\) −8804.57 −0.497626
\(680\) 8568.84 0.483235
\(681\) 6186.46 0.348114
\(682\) −12282.5 −0.689619
\(683\) −14420.5 −0.807887 −0.403943 0.914784i \(-0.632361\pi\)
−0.403943 + 0.914784i \(0.632361\pi\)
\(684\) 7204.93 0.402759
\(685\) −8364.25 −0.466543
\(686\) −24661.4 −1.37256
\(687\) −12232.4 −0.679324
\(688\) −370.280 −0.0205186
\(689\) 8497.42 0.469849
\(690\) 941.517 0.0519463
\(691\) 30552.4 1.68201 0.841005 0.541027i \(-0.181964\pi\)
0.841005 + 0.541027i \(0.181964\pi\)
\(692\) −29999.9 −1.64801
\(693\) 2043.20 0.111998
\(694\) 27138.7 1.48440
\(695\) 12701.9 0.693253
\(696\) 2217.63 0.120774
\(697\) −7957.96 −0.432467
\(698\) 16708.1 0.906032
\(699\) −5048.27 −0.273166
\(700\) 6765.61 0.365309
\(701\) −9151.47 −0.493076 −0.246538 0.969133i \(-0.579293\pi\)
−0.246538 + 0.969133i \(0.579293\pi\)
\(702\) 1942.60 0.104443
\(703\) −3992.86 −0.214216
\(704\) −9060.30 −0.485047
\(705\) 7792.95 0.416311
\(706\) 966.793 0.0515378
\(707\) 1530.10 0.0813937
\(708\) −4306.67 −0.228608
\(709\) −6261.96 −0.331697 −0.165848 0.986151i \(-0.553036\pi\)
−0.165848 + 0.986151i \(0.553036\pi\)
\(710\) 19239.2 1.01695
\(711\) −7480.85 −0.394590
\(712\) 35794.9 1.88409
\(713\) 3319.60 0.174362
\(714\) −20753.8 −1.08780
\(715\) −861.214 −0.0450456
\(716\) 42603.9 2.22372
\(717\) −12074.9 −0.628933
\(718\) 11485.7 0.596995
\(719\) −18228.7 −0.945500 −0.472750 0.881197i \(-0.656739\pi\)
−0.472750 + 0.881197i \(0.656739\pi\)
\(720\) 136.859 0.00708396
\(721\) −1432.13 −0.0739740
\(722\) −14389.9 −0.741740
\(723\) 8352.81 0.429660
\(724\) 15347.7 0.787836
\(725\) −786.656 −0.0402975
\(726\) −1667.93 −0.0852655
\(727\) −7233.66 −0.369026 −0.184513 0.982830i \(-0.559071\pi\)
−0.184513 + 0.982830i \(0.559071\pi\)
\(728\) −7591.81 −0.386499
\(729\) 729.000 0.0370370
\(730\) 8068.93 0.409102
\(731\) −8881.73 −0.449388
\(732\) 3525.31 0.178004
\(733\) −13444.8 −0.677485 −0.338743 0.940879i \(-0.610002\pi\)
−0.338743 + 0.940879i \(0.610002\pi\)
\(734\) 26414.4 1.32830
\(735\) −1244.12 −0.0624355
\(736\) 2376.41 0.119016
\(737\) 5372.90 0.268539
\(738\) −4511.14 −0.225010
\(739\) 18490.9 0.920432 0.460216 0.887807i \(-0.347772\pi\)
0.460216 + 0.887807i \(0.347772\pi\)
\(740\) −4287.97 −0.213012
\(741\) 2867.90 0.142180
\(742\) −51461.8 −2.54612
\(743\) −25160.9 −1.24235 −0.621173 0.783674i \(-0.713343\pi\)
−0.621173 + 0.783674i \(0.713343\pi\)
\(744\) 17126.3 0.843927
\(745\) 15453.4 0.759957
\(746\) 20528.8 1.00752
\(747\) 12502.2 0.612358
\(748\) 10522.4 0.514354
\(749\) 23562.9 1.14949
\(750\) −1723.07 −0.0838902
\(751\) −13419.5 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(752\) −1580.06 −0.0766207
\(753\) 5482.81 0.265345
\(754\) 2263.94 0.109347
\(755\) 6793.68 0.327480
\(756\) −7306.86 −0.351518
\(757\) −7014.90 −0.336804 −0.168402 0.985718i \(-0.553861\pi\)
−0.168402 + 0.985718i \(0.553861\pi\)
\(758\) 35858.6 1.71826
\(759\) 450.795 0.0215584
\(760\) 7171.12 0.342268
\(761\) −30156.9 −1.43651 −0.718256 0.695779i \(-0.755059\pi\)
−0.718256 + 0.695779i \(0.755059\pi\)
\(762\) 22077.8 1.04960
\(763\) −45958.4 −2.18061
\(764\) −36195.7 −1.71402
\(765\) 3282.78 0.155149
\(766\) −51283.5 −2.41899
\(767\) −1714.26 −0.0807019
\(768\) 13217.4 0.621017
\(769\) 11292.2 0.529530 0.264765 0.964313i \(-0.414706\pi\)
0.264765 + 0.964313i \(0.414706\pi\)
\(770\) 5215.66 0.244103
\(771\) −1755.51 −0.0820016
\(772\) −16398.9 −0.764519
\(773\) 8524.10 0.396624 0.198312 0.980139i \(-0.436454\pi\)
0.198312 + 0.980139i \(0.436454\pi\)
\(774\) −5034.80 −0.233814
\(775\) −6075.21 −0.281584
\(776\) −10022.0 −0.463621
\(777\) 4049.35 0.186962
\(778\) 39011.4 1.79772
\(779\) −6659.89 −0.306310
\(780\) 3079.87 0.141381
\(781\) 9211.66 0.422047
\(782\) −4578.96 −0.209390
\(783\) 849.589 0.0387763
\(784\) 252.251 0.0114910
\(785\) −5059.76 −0.230052
\(786\) −27626.1 −1.25368
\(787\) −14983.9 −0.678676 −0.339338 0.940665i \(-0.610203\pi\)
−0.339338 + 0.940665i \(0.610203\pi\)
\(788\) −1888.10 −0.0853565
\(789\) 714.293 0.0322300
\(790\) −19096.3 −0.860022
\(791\) −35493.0 −1.59543
\(792\) 2325.72 0.104345
\(793\) 1403.24 0.0628380
\(794\) 27659.9 1.23629
\(795\) 8140.10 0.363144
\(796\) 9982.04 0.444477
\(797\) 37172.3 1.65208 0.826041 0.563610i \(-0.190588\pi\)
0.826041 + 0.563610i \(0.190588\pi\)
\(798\) −17368.5 −0.770475
\(799\) −37900.1 −1.67811
\(800\) −4349.06 −0.192203
\(801\) 13713.3 0.604913
\(802\) −47781.0 −2.10375
\(803\) 3863.37 0.169783
\(804\) −19214.5 −0.842841
\(805\) −1409.65 −0.0617186
\(806\) 17484.0 0.764080
\(807\) −13855.4 −0.604378
\(808\) 1741.68 0.0758316
\(809\) 23797.1 1.03419 0.517096 0.855928i \(-0.327013\pi\)
0.517096 + 0.855928i \(0.327013\pi\)
\(810\) 1860.92 0.0807234
\(811\) 8988.35 0.389178 0.194589 0.980885i \(-0.437663\pi\)
0.194589 + 0.980885i \(0.437663\pi\)
\(812\) −8515.54 −0.368026
\(813\) 430.318 0.0185633
\(814\) −3305.63 −0.142337
\(815\) −14081.8 −0.605234
\(816\) −665.600 −0.0285547
\(817\) −7432.98 −0.318295
\(818\) −21750.6 −0.929696
\(819\) −2908.48 −0.124091
\(820\) −7152.11 −0.304589
\(821\) −25156.8 −1.06940 −0.534702 0.845041i \(-0.679576\pi\)
−0.534702 + 0.845041i \(0.679576\pi\)
\(822\) 23059.5 0.978459
\(823\) 1318.51 0.0558447 0.0279224 0.999610i \(-0.491111\pi\)
0.0279224 + 0.999610i \(0.491111\pi\)
\(824\) −1630.16 −0.0689189
\(825\) −825.000 −0.0348155
\(826\) 10381.9 0.437326
\(827\) 124.982 0.00525519 0.00262760 0.999997i \(-0.499164\pi\)
0.00262760 + 0.999997i \(0.499164\pi\)
\(828\) −1612.13 −0.0676635
\(829\) −8886.80 −0.372318 −0.186159 0.982520i \(-0.559604\pi\)
−0.186159 + 0.982520i \(0.559604\pi\)
\(830\) 31914.3 1.33465
\(831\) 25807.5 1.07732
\(832\) 12897.3 0.537419
\(833\) 6050.63 0.251671
\(834\) −35018.0 −1.45393
\(835\) 17244.5 0.714694
\(836\) 8806.02 0.364309
\(837\) 6561.22 0.270955
\(838\) −37299.1 −1.53756
\(839\) 2995.21 0.123249 0.0616247 0.998099i \(-0.480372\pi\)
0.0616247 + 0.998099i \(0.480372\pi\)
\(840\) −7272.58 −0.298724
\(841\) −23398.9 −0.959403
\(842\) −43578.8 −1.78364
\(843\) 8978.43 0.366825
\(844\) 52143.6 2.12661
\(845\) −9759.07 −0.397304
\(846\) −21484.5 −0.873111
\(847\) 2497.24 0.101306
\(848\) −1650.44 −0.0668355
\(849\) 20576.7 0.831789
\(850\) 8379.95 0.338153
\(851\) 893.418 0.0359882
\(852\) −32942.7 −1.32464
\(853\) 18130.5 0.727757 0.363878 0.931446i \(-0.381452\pi\)
0.363878 + 0.931446i \(0.381452\pi\)
\(854\) −8498.27 −0.340521
\(855\) 2747.31 0.109890
\(856\) 26821.1 1.07094
\(857\) 26394.1 1.05205 0.526024 0.850470i \(-0.323682\pi\)
0.526024 + 0.850470i \(0.323682\pi\)
\(858\) 2374.29 0.0944720
\(859\) −29456.2 −1.17000 −0.585002 0.811032i \(-0.698906\pi\)
−0.585002 + 0.811032i \(0.698906\pi\)
\(860\) −7982.34 −0.316506
\(861\) 6754.12 0.267340
\(862\) 42893.7 1.69486
\(863\) −762.616 −0.0300808 −0.0150404 0.999887i \(-0.504788\pi\)
−0.0150404 + 0.999887i \(0.504788\pi\)
\(864\) 4696.99 0.184948
\(865\) −11439.3 −0.449649
\(866\) −13706.6 −0.537838
\(867\) −1226.43 −0.0480411
\(868\) −65764.0 −2.57163
\(869\) −9143.26 −0.356920
\(870\) 2168.74 0.0845141
\(871\) −7648.29 −0.297535
\(872\) −52313.3 −2.03160
\(873\) −3839.51 −0.148852
\(874\) −3832.06 −0.148308
\(875\) 2579.79 0.0996719
\(876\) −13816.2 −0.532882
\(877\) 44767.2 1.72369 0.861847 0.507168i \(-0.169308\pi\)
0.861847 + 0.507168i \(0.169308\pi\)
\(878\) −24041.8 −0.924112
\(879\) −12149.1 −0.466188
\(880\) 167.273 0.00640768
\(881\) −32057.9 −1.22595 −0.612973 0.790104i \(-0.710027\pi\)
−0.612973 + 0.790104i \(0.710027\pi\)
\(882\) 3429.93 0.130943
\(883\) 7078.95 0.269791 0.134896 0.990860i \(-0.456930\pi\)
0.134896 + 0.990860i \(0.456930\pi\)
\(884\) −14978.6 −0.569891
\(885\) −1642.18 −0.0623742
\(886\) 34542.8 1.30981
\(887\) −25148.1 −0.951964 −0.475982 0.879455i \(-0.657907\pi\)
−0.475982 + 0.879455i \(0.657907\pi\)
\(888\) 4609.28 0.174186
\(889\) −33055.0 −1.24705
\(890\) 35005.9 1.31843
\(891\) 891.000 0.0335013
\(892\) 11907.4 0.446963
\(893\) −31718.0 −1.18858
\(894\) −42603.6 −1.59382
\(895\) 16245.3 0.606726
\(896\) −49385.8 −1.84137
\(897\) −641.704 −0.0238862
\(898\) 73843.6 2.74409
\(899\) 7646.56 0.283679
\(900\) 2950.36 0.109273
\(901\) −39588.4 −1.46380
\(902\) −5513.62 −0.203529
\(903\) 7538.14 0.277800
\(904\) −40400.8 −1.48641
\(905\) 5852.23 0.214955
\(906\) −18729.6 −0.686809
\(907\) 1269.76 0.0464848 0.0232424 0.999730i \(-0.492601\pi\)
0.0232424 + 0.999730i \(0.492601\pi\)
\(908\) −27040.4 −0.988289
\(909\) 667.248 0.0243468
\(910\) −7424.47 −0.270460
\(911\) −33783.1 −1.22863 −0.614316 0.789060i \(-0.710568\pi\)
−0.614316 + 0.789060i \(0.710568\pi\)
\(912\) −557.030 −0.0202249
\(913\) 15280.5 0.553899
\(914\) 44655.1 1.61604
\(915\) 1344.23 0.0485672
\(916\) 53466.6 1.92859
\(917\) 41361.9 1.48952
\(918\) −9050.35 −0.325388
\(919\) 39262.5 1.40930 0.704652 0.709553i \(-0.251103\pi\)
0.704652 + 0.709553i \(0.251103\pi\)
\(920\) −1604.57 −0.0575010
\(921\) 28718.1 1.02746
\(922\) −66800.1 −2.38606
\(923\) −13112.7 −0.467618
\(924\) −8930.61 −0.317960
\(925\) −1635.04 −0.0581189
\(926\) −45848.3 −1.62707
\(927\) −624.525 −0.0221274
\(928\) 5473.95 0.193633
\(929\) −21175.0 −0.747825 −0.373913 0.927464i \(-0.621984\pi\)
−0.373913 + 0.927464i \(0.621984\pi\)
\(930\) 16748.8 0.590554
\(931\) 5063.68 0.178255
\(932\) 22065.5 0.775515
\(933\) −16189.3 −0.568073
\(934\) 69787.5 2.44488
\(935\) 4012.29 0.140338
\(936\) −3310.65 −0.115611
\(937\) −5135.11 −0.179036 −0.0895180 0.995985i \(-0.528533\pi\)
−0.0895180 + 0.995985i \(0.528533\pi\)
\(938\) 46319.4 1.61235
\(939\) −29265.1 −1.01707
\(940\) −34062.2 −1.18190
\(941\) −9702.77 −0.336133 −0.168067 0.985776i \(-0.553752\pi\)
−0.168067 + 0.985776i \(0.553752\pi\)
\(942\) 13949.3 0.482477
\(943\) 1490.18 0.0514600
\(944\) 332.959 0.0114798
\(945\) −2786.18 −0.0959094
\(946\) −6153.65 −0.211493
\(947\) −699.579 −0.0240055 −0.0120028 0.999928i \(-0.503821\pi\)
−0.0120028 + 0.999928i \(0.503821\pi\)
\(948\) 32698.0 1.12024
\(949\) −5499.49 −0.188115
\(950\) 7013.05 0.239509
\(951\) 13061.2 0.445363
\(952\) 35369.3 1.20412
\(953\) 42039.3 1.42895 0.714473 0.699663i \(-0.246667\pi\)
0.714473 + 0.699663i \(0.246667\pi\)
\(954\) −22441.6 −0.761606
\(955\) −13801.8 −0.467659
\(956\) 52778.1 1.78553
\(957\) 1038.39 0.0350745
\(958\) 52063.4 1.75584
\(959\) −34524.9 −1.16253
\(960\) 12355.0 0.415369
\(961\) 29262.0 0.982243
\(962\) 4705.55 0.157706
\(963\) 10275.3 0.343841
\(964\) −36509.3 −1.21980
\(965\) −6253.05 −0.208594
\(966\) 3886.27 0.129440
\(967\) −32794.8 −1.09060 −0.545299 0.838242i \(-0.683584\pi\)
−0.545299 + 0.838242i \(0.683584\pi\)
\(968\) 2842.55 0.0943832
\(969\) −13361.2 −0.442955
\(970\) −9801.10 −0.324427
\(971\) −3322.53 −0.109810 −0.0549048 0.998492i \(-0.517486\pi\)
−0.0549048 + 0.998492i \(0.517486\pi\)
\(972\) −3186.39 −0.105148
\(973\) 52429.3 1.72745
\(974\) 87701.4 2.88515
\(975\) 1174.38 0.0385747
\(976\) −272.550 −0.00893864
\(977\) 22192.5 0.726716 0.363358 0.931650i \(-0.381630\pi\)
0.363358 + 0.931650i \(0.381630\pi\)
\(978\) 38822.4 1.26933
\(979\) 16760.7 0.547164
\(980\) 5437.92 0.177253
\(981\) −20041.6 −0.652272
\(982\) −37277.4 −1.21137
\(983\) 7383.09 0.239556 0.119778 0.992801i \(-0.461782\pi\)
0.119778 + 0.992801i \(0.461782\pi\)
\(984\) 7688.04 0.249071
\(985\) −719.953 −0.0232889
\(986\) −10547.4 −0.340668
\(987\) 32166.7 1.03736
\(988\) −12535.3 −0.403645
\(989\) 1663.16 0.0534735
\(990\) 2274.45 0.0730171
\(991\) 46260.8 1.48287 0.741434 0.671026i \(-0.234146\pi\)
0.741434 + 0.671026i \(0.234146\pi\)
\(992\) 42274.3 1.35304
\(993\) −16162.9 −0.516530
\(994\) 79413.1 2.53403
\(995\) 3806.25 0.121273
\(996\) −54645.9 −1.73847
\(997\) 41196.8 1.30864 0.654320 0.756217i \(-0.272955\pi\)
0.654320 + 0.756217i \(0.272955\pi\)
\(998\) 84219.5 2.67127
\(999\) 1765.85 0.0559249
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 165.4.a.g.1.3 3
3.2 odd 2 495.4.a.i.1.1 3
5.2 odd 4 825.4.c.m.199.6 6
5.3 odd 4 825.4.c.m.199.1 6
5.4 even 2 825.4.a.p.1.1 3
11.10 odd 2 1815.4.a.q.1.1 3
15.14 odd 2 2475.4.a.z.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.4.a.g.1.3 3 1.1 even 1 trivial
495.4.a.i.1.1 3 3.2 odd 2
825.4.a.p.1.1 3 5.4 even 2
825.4.c.m.199.1 6 5.3 odd 4
825.4.c.m.199.6 6 5.2 odd 4
1815.4.a.q.1.1 3 11.10 odd 2
2475.4.a.z.1.3 3 15.14 odd 2