Properties

Label 354.4.a.a.1.1
Level $354$
Weight $4$
Character 354.1
Self dual yes
Analytic conductor $20.887$
Analytic rank $1$
Dimension $2$
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] = [354,4,Mod(1,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, 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("354.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 354.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: \(20.8866761420\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{21}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.79129\) of defining polynomial
Character \(\chi\) \(=\) 354.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -10.5826 q^{5} -6.00000 q^{6} -18.3739 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -10.5826 q^{5} -6.00000 q^{6} -18.3739 q^{7} -8.00000 q^{8} +9.00000 q^{9} +21.1652 q^{10} +47.3303 q^{11} +12.0000 q^{12} +63.5735 q^{13} +36.7477 q^{14} -31.7477 q^{15} +16.0000 q^{16} +60.7822 q^{17} -18.0000 q^{18} -155.443 q^{19} -42.3303 q^{20} -55.1216 q^{21} -94.6606 q^{22} -120.695 q^{23} -24.0000 q^{24} -13.0091 q^{25} -127.147 q^{26} +27.0000 q^{27} -73.4955 q^{28} -42.8784 q^{29} +63.4955 q^{30} -135.383 q^{31} -32.0000 q^{32} +141.991 q^{33} -121.564 q^{34} +194.443 q^{35} +36.0000 q^{36} -223.025 q^{37} +310.886 q^{38} +190.720 q^{39} +84.6606 q^{40} +75.7133 q^{41} +110.243 q^{42} -354.964 q^{43} +189.321 q^{44} -95.2432 q^{45} +241.390 q^{46} -269.484 q^{47} +48.0000 q^{48} -5.40114 q^{49} +26.0182 q^{50} +182.347 q^{51} +254.294 q^{52} -70.4265 q^{53} -54.0000 q^{54} -500.877 q^{55} +146.991 q^{56} -466.328 q^{57} +85.7568 q^{58} -59.0000 q^{59} -126.991 q^{60} -244.410 q^{61} +270.766 q^{62} -165.365 q^{63} +64.0000 q^{64} -672.771 q^{65} -283.982 q^{66} +340.717 q^{67} +243.129 q^{68} -362.085 q^{69} -388.886 q^{70} +581.951 q^{71} -72.0000 q^{72} -230.181 q^{73} +446.051 q^{74} -39.0273 q^{75} -621.771 q^{76} -869.641 q^{77} -381.441 q^{78} -1016.88 q^{79} -169.321 q^{80} +81.0000 q^{81} -151.427 q^{82} +383.971 q^{83} -220.486 q^{84} -643.232 q^{85} +709.927 q^{86} -128.635 q^{87} -378.642 q^{88} +23.2413 q^{89} +190.486 q^{90} -1168.09 q^{91} -482.780 q^{92} -406.149 q^{93} +538.969 q^{94} +1644.99 q^{95} -96.0000 q^{96} +746.670 q^{97} +10.8023 q^{98} +425.973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} - 23 q^{7} - 16 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} - 23 q^{7} - 16 q^{8} + 18 q^{9} + 24 q^{10} + 58 q^{11} + 24 q^{12} + 8 q^{13} + 46 q^{14} - 36 q^{15} + 32 q^{16} + 7 q^{17} - 36 q^{18} - 123 q^{19} - 48 q^{20} - 69 q^{21} - 116 q^{22} - 81 q^{23} - 48 q^{24} - 136 q^{25} - 16 q^{26} + 54 q^{27} - 92 q^{28} - 127 q^{29} + 72 q^{30} - 367 q^{31} - 64 q^{32} + 174 q^{33} - 14 q^{34} + 201 q^{35} + 72 q^{36} - 249 q^{37} + 246 q^{38} + 24 q^{39} + 96 q^{40} + 211 q^{41} + 138 q^{42} - 270 q^{43} + 232 q^{44} - 108 q^{45} + 162 q^{46} + 153 q^{47} + 96 q^{48} - 327 q^{49} + 272 q^{50} + 21 q^{51} + 32 q^{52} - 260 q^{53} - 108 q^{54} - 516 q^{55} + 184 q^{56} - 369 q^{57} + 254 q^{58} - 118 q^{59} - 144 q^{60} - 915 q^{61} + 734 q^{62} - 207 q^{63} + 128 q^{64} - 594 q^{65} - 348 q^{66} - 730 q^{67} + 28 q^{68} - 243 q^{69} - 402 q^{70} - 440 q^{71} - 144 q^{72} - 135 q^{73} + 498 q^{74} - 408 q^{75} - 492 q^{76} - 919 q^{77} - 48 q^{78} - 1548 q^{79} - 192 q^{80} + 162 q^{81} - 422 q^{82} - 89 q^{83} - 276 q^{84} - 567 q^{85} + 540 q^{86} - 381 q^{87} - 464 q^{88} - 563 q^{89} + 216 q^{90} - 911 q^{91} - 324 q^{92} - 1101 q^{93} - 306 q^{94} + 1599 q^{95} - 192 q^{96} + 1530 q^{97} + 654 q^{98} + 522 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) −10.5826 −0.946534 −0.473267 0.880919i \(-0.656925\pi\)
−0.473267 + 0.880919i \(0.656925\pi\)
\(6\) −6.00000 −0.408248
\(7\) −18.3739 −0.992095 −0.496048 0.868295i \(-0.665216\pi\)
−0.496048 + 0.868295i \(0.665216\pi\)
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) 21.1652 0.669301
\(11\) 47.3303 1.29733 0.648665 0.761074i \(-0.275328\pi\)
0.648665 + 0.761074i \(0.275328\pi\)
\(12\) 12.0000 0.288675
\(13\) 63.5735 1.35632 0.678158 0.734916i \(-0.262778\pi\)
0.678158 + 0.734916i \(0.262778\pi\)
\(14\) 36.7477 0.701517
\(15\) −31.7477 −0.546482
\(16\) 16.0000 0.250000
\(17\) 60.7822 0.867168 0.433584 0.901113i \(-0.357249\pi\)
0.433584 + 0.901113i \(0.357249\pi\)
\(18\) −18.0000 −0.235702
\(19\) −155.443 −1.87690 −0.938448 0.345421i \(-0.887736\pi\)
−0.938448 + 0.345421i \(0.887736\pi\)
\(20\) −42.3303 −0.473267
\(21\) −55.1216 −0.572787
\(22\) −94.6606 −0.917350
\(23\) −120.695 −1.09420 −0.547101 0.837066i \(-0.684269\pi\)
−0.547101 + 0.837066i \(0.684269\pi\)
\(24\) −24.0000 −0.204124
\(25\) −13.0091 −0.104073
\(26\) −127.147 −0.959060
\(27\) 27.0000 0.192450
\(28\) −73.4955 −0.496048
\(29\) −42.8784 −0.274563 −0.137281 0.990532i \(-0.543836\pi\)
−0.137281 + 0.990532i \(0.543836\pi\)
\(30\) 63.4955 0.386421
\(31\) −135.383 −0.784371 −0.392185 0.919886i \(-0.628281\pi\)
−0.392185 + 0.919886i \(0.628281\pi\)
\(32\) −32.0000 −0.176777
\(33\) 141.991 0.749013
\(34\) −121.564 −0.613180
\(35\) 194.443 0.939052
\(36\) 36.0000 0.166667
\(37\) −223.025 −0.990950 −0.495475 0.868622i \(-0.665006\pi\)
−0.495475 + 0.868622i \(0.665006\pi\)
\(38\) 310.886 1.32717
\(39\) 190.720 0.783070
\(40\) 84.6606 0.334650
\(41\) 75.7133 0.288401 0.144200 0.989549i \(-0.453939\pi\)
0.144200 + 0.989549i \(0.453939\pi\)
\(42\) 110.243 0.405021
\(43\) −354.964 −1.25887 −0.629435 0.777053i \(-0.716714\pi\)
−0.629435 + 0.777053i \(0.716714\pi\)
\(44\) 189.321 0.648665
\(45\) −95.2432 −0.315511
\(46\) 241.390 0.773718
\(47\) −269.484 −0.836348 −0.418174 0.908367i \(-0.637330\pi\)
−0.418174 + 0.908367i \(0.637330\pi\)
\(48\) 48.0000 0.144338
\(49\) −5.40114 −0.0157468
\(50\) 26.0182 0.0735905
\(51\) 182.347 0.500659
\(52\) 254.294 0.678158
\(53\) −70.4265 −0.182525 −0.0912625 0.995827i \(-0.529090\pi\)
−0.0912625 + 0.995827i \(0.529090\pi\)
\(54\) −54.0000 −0.136083
\(55\) −500.877 −1.22797
\(56\) 146.991 0.350759
\(57\) −466.328 −1.08363
\(58\) 85.7568 0.194145
\(59\) −59.0000 −0.130189
\(60\) −126.991 −0.273241
\(61\) −244.410 −0.513009 −0.256504 0.966543i \(-0.582571\pi\)
−0.256504 + 0.966543i \(0.582571\pi\)
\(62\) 270.766 0.554634
\(63\) −165.365 −0.330698
\(64\) 64.0000 0.125000
\(65\) −672.771 −1.28380
\(66\) −283.982 −0.529633
\(67\) 340.717 0.621271 0.310636 0.950529i \(-0.399458\pi\)
0.310636 + 0.950529i \(0.399458\pi\)
\(68\) 243.129 0.433584
\(69\) −362.085 −0.631738
\(70\) −388.886 −0.664010
\(71\) 581.951 0.972744 0.486372 0.873752i \(-0.338320\pi\)
0.486372 + 0.873752i \(0.338320\pi\)
\(72\) −72.0000 −0.117851
\(73\) −230.181 −0.369051 −0.184525 0.982828i \(-0.559075\pi\)
−0.184525 + 0.982828i \(0.559075\pi\)
\(74\) 446.051 0.700707
\(75\) −39.0273 −0.0600864
\(76\) −621.771 −0.938448
\(77\) −869.641 −1.28707
\(78\) −381.441 −0.553714
\(79\) −1016.88 −1.44820 −0.724098 0.689697i \(-0.757744\pi\)
−0.724098 + 0.689697i \(0.757744\pi\)
\(80\) −169.321 −0.236634
\(81\) 81.0000 0.111111
\(82\) −151.427 −0.203930
\(83\) 383.971 0.507786 0.253893 0.967232i \(-0.418289\pi\)
0.253893 + 0.967232i \(0.418289\pi\)
\(84\) −220.486 −0.286393
\(85\) −643.232 −0.820804
\(86\) 709.927 0.890156
\(87\) −128.635 −0.158519
\(88\) −378.642 −0.458675
\(89\) 23.2413 0.0276806 0.0138403 0.999904i \(-0.495594\pi\)
0.0138403 + 0.999904i \(0.495594\pi\)
\(90\) 190.486 0.223100
\(91\) −1168.09 −1.34560
\(92\) −482.780 −0.547101
\(93\) −406.149 −0.452857
\(94\) 538.969 0.591387
\(95\) 1644.99 1.77655
\(96\) −96.0000 −0.102062
\(97\) 746.670 0.781575 0.390788 0.920481i \(-0.372203\pi\)
0.390788 + 0.920481i \(0.372203\pi\)
\(98\) 10.8023 0.0111346
\(99\) 425.973 0.432443
\(100\) −52.0364 −0.0520364
\(101\) −854.014 −0.841362 −0.420681 0.907209i \(-0.638209\pi\)
−0.420681 + 0.907209i \(0.638209\pi\)
\(102\) −364.693 −0.354020
\(103\) 327.739 0.313525 0.156762 0.987636i \(-0.449894\pi\)
0.156762 + 0.987636i \(0.449894\pi\)
\(104\) −508.588 −0.479530
\(105\) 583.328 0.542162
\(106\) 140.853 0.129065
\(107\) −523.922 −0.473359 −0.236679 0.971588i \(-0.576059\pi\)
−0.236679 + 0.971588i \(0.576059\pi\)
\(108\) 108.000 0.0962250
\(109\) 170.325 0.149671 0.0748355 0.997196i \(-0.476157\pi\)
0.0748355 + 0.997196i \(0.476157\pi\)
\(110\) 1001.75 0.868304
\(111\) −669.076 −0.572125
\(112\) −293.982 −0.248024
\(113\) −1264.30 −1.05252 −0.526261 0.850323i \(-0.676406\pi\)
−0.526261 + 0.850323i \(0.676406\pi\)
\(114\) 932.657 0.766240
\(115\) 1277.26 1.03570
\(116\) −171.514 −0.137281
\(117\) 572.161 0.452105
\(118\) 118.000 0.0920575
\(119\) −1116.80 −0.860313
\(120\) 253.982 0.193211
\(121\) 909.158 0.683064
\(122\) 488.820 0.362752
\(123\) 227.140 0.166508
\(124\) −541.532 −0.392185
\(125\) 1460.49 1.04504
\(126\) 330.730 0.233839
\(127\) −2301.47 −1.60805 −0.804027 0.594593i \(-0.797313\pi\)
−0.804027 + 0.594593i \(0.797313\pi\)
\(128\) −128.000 −0.0883883
\(129\) −1064.89 −0.726809
\(130\) 1345.54 0.907784
\(131\) 244.628 0.163155 0.0815773 0.996667i \(-0.474004\pi\)
0.0815773 + 0.996667i \(0.474004\pi\)
\(132\) 567.964 0.374507
\(133\) 2856.08 1.86206
\(134\) −681.433 −0.439305
\(135\) −285.730 −0.182161
\(136\) −486.258 −0.306590
\(137\) 2176.57 1.35735 0.678676 0.734437i \(-0.262554\pi\)
0.678676 + 0.734437i \(0.262554\pi\)
\(138\) 724.170 0.446706
\(139\) −774.267 −0.472464 −0.236232 0.971697i \(-0.575912\pi\)
−0.236232 + 0.971697i \(0.575912\pi\)
\(140\) 777.771 0.469526
\(141\) −808.453 −0.482866
\(142\) −1163.90 −0.687834
\(143\) 3008.95 1.75959
\(144\) 144.000 0.0833333
\(145\) 453.764 0.259883
\(146\) 460.363 0.260958
\(147\) −16.2034 −0.00909140
\(148\) −892.102 −0.495475
\(149\) −1742.93 −0.958296 −0.479148 0.877734i \(-0.659054\pi\)
−0.479148 + 0.877734i \(0.659054\pi\)
\(150\) 78.0545 0.0424875
\(151\) 1290.03 0.695237 0.347618 0.937636i \(-0.386990\pi\)
0.347618 + 0.937636i \(0.386990\pi\)
\(152\) 1243.54 0.663583
\(153\) 547.040 0.289056
\(154\) 1739.28 0.910099
\(155\) 1432.70 0.742434
\(156\) 762.882 0.391535
\(157\) −165.689 −0.0842258 −0.0421129 0.999113i \(-0.513409\pi\)
−0.0421129 + 0.999113i \(0.513409\pi\)
\(158\) 2033.75 1.02403
\(159\) −211.280 −0.105381
\(160\) 338.642 0.167325
\(161\) 2217.63 1.08555
\(162\) −162.000 −0.0785674
\(163\) 938.091 0.450779 0.225389 0.974269i \(-0.427635\pi\)
0.225389 + 0.974269i \(0.427635\pi\)
\(164\) 302.853 0.144200
\(165\) −1502.63 −0.708967
\(166\) −767.942 −0.359059
\(167\) 2572.71 1.19211 0.596056 0.802943i \(-0.296734\pi\)
0.596056 + 0.802943i \(0.296734\pi\)
\(168\) 440.973 0.202511
\(169\) 1844.59 0.839594
\(170\) 1286.46 0.580396
\(171\) −1398.99 −0.625632
\(172\) −1419.85 −0.629435
\(173\) −2338.48 −1.02770 −0.513848 0.857881i \(-0.671781\pi\)
−0.513848 + 0.857881i \(0.671781\pi\)
\(174\) 257.270 0.112090
\(175\) 239.027 0.103250
\(176\) 757.285 0.324332
\(177\) −177.000 −0.0751646
\(178\) −46.4826 −0.0195731
\(179\) −2618.21 −1.09326 −0.546632 0.837373i \(-0.684090\pi\)
−0.546632 + 0.837373i \(0.684090\pi\)
\(180\) −380.973 −0.157756
\(181\) −2858.10 −1.17371 −0.586853 0.809694i \(-0.699633\pi\)
−0.586853 + 0.809694i \(0.699633\pi\)
\(182\) 2336.18 0.951479
\(183\) −733.231 −0.296186
\(184\) 965.561 0.386859
\(185\) 2360.18 0.937968
\(186\) 812.298 0.320218
\(187\) 2876.84 1.12500
\(188\) −1077.94 −0.418174
\(189\) −496.094 −0.190929
\(190\) −3289.97 −1.25621
\(191\) 4461.29 1.69009 0.845047 0.534692i \(-0.179573\pi\)
0.845047 + 0.534692i \(0.179573\pi\)
\(192\) 192.000 0.0721688
\(193\) 3727.85 1.39035 0.695173 0.718842i \(-0.255328\pi\)
0.695173 + 0.718842i \(0.255328\pi\)
\(194\) −1493.34 −0.552657
\(195\) −2018.31 −0.741202
\(196\) −21.6046 −0.00787338
\(197\) 3200.74 1.15758 0.578791 0.815476i \(-0.303525\pi\)
0.578791 + 0.815476i \(0.303525\pi\)
\(198\) −851.945 −0.305783
\(199\) −4664.90 −1.66174 −0.830869 0.556469i \(-0.812156\pi\)
−0.830869 + 0.556469i \(0.812156\pi\)
\(200\) 104.073 0.0367953
\(201\) 1022.15 0.358691
\(202\) 1708.03 0.594933
\(203\) 787.842 0.272392
\(204\) 729.386 0.250330
\(205\) −801.241 −0.272981
\(206\) −655.477 −0.221695
\(207\) −1086.26 −0.364734
\(208\) 1017.18 0.339079
\(209\) −7357.15 −2.43495
\(210\) −1166.66 −0.383367
\(211\) −4340.78 −1.41626 −0.708131 0.706081i \(-0.750462\pi\)
−0.708131 + 0.706081i \(0.750462\pi\)
\(212\) −281.706 −0.0912625
\(213\) 1745.85 0.561614
\(214\) 1047.84 0.334715
\(215\) 3756.43 1.19156
\(216\) −216.000 −0.0680414
\(217\) 2487.51 0.778171
\(218\) −340.649 −0.105833
\(219\) −690.544 −0.213072
\(220\) −2003.51 −0.613983
\(221\) 3864.14 1.17615
\(222\) 1338.15 0.404554
\(223\) 2562.58 0.769521 0.384761 0.923016i \(-0.374284\pi\)
0.384761 + 0.923016i \(0.374284\pi\)
\(224\) 587.964 0.175379
\(225\) −117.082 −0.0346909
\(226\) 2528.59 0.744245
\(227\) −2062.18 −0.602958 −0.301479 0.953473i \(-0.597480\pi\)
−0.301479 + 0.953473i \(0.597480\pi\)
\(228\) −1865.31 −0.541813
\(229\) −5837.14 −1.68441 −0.842203 0.539160i \(-0.818742\pi\)
−0.842203 + 0.539160i \(0.818742\pi\)
\(230\) −2554.53 −0.732351
\(231\) −2608.92 −0.743093
\(232\) 343.027 0.0970726
\(233\) −3673.85 −1.03297 −0.516485 0.856296i \(-0.672760\pi\)
−0.516485 + 0.856296i \(0.672760\pi\)
\(234\) −1144.32 −0.319687
\(235\) 2851.84 0.791632
\(236\) −236.000 −0.0650945
\(237\) −3050.63 −0.836117
\(238\) 2233.61 0.608333
\(239\) −2455.33 −0.664527 −0.332263 0.943187i \(-0.607812\pi\)
−0.332263 + 0.943187i \(0.607812\pi\)
\(240\) −507.964 −0.136620
\(241\) 4882.16 1.30493 0.652463 0.757820i \(-0.273736\pi\)
0.652463 + 0.757820i \(0.273736\pi\)
\(242\) −1818.32 −0.482999
\(243\) 243.000 0.0641500
\(244\) −977.641 −0.256504
\(245\) 57.1580 0.0149048
\(246\) −454.280 −0.117739
\(247\) −9882.04 −2.54566
\(248\) 1083.06 0.277317
\(249\) 1151.91 0.293171
\(250\) −2920.98 −0.738957
\(251\) 6998.75 1.75999 0.879995 0.474984i \(-0.157546\pi\)
0.879995 + 0.474984i \(0.157546\pi\)
\(252\) −661.459 −0.165349
\(253\) −5712.53 −1.41954
\(254\) 4602.95 1.13707
\(255\) −1929.70 −0.473891
\(256\) 256.000 0.0625000
\(257\) 233.205 0.0566027 0.0283014 0.999599i \(-0.490990\pi\)
0.0283014 + 0.999599i \(0.490990\pi\)
\(258\) 2129.78 0.513932
\(259\) 4097.84 0.983117
\(260\) −2691.08 −0.641900
\(261\) −385.906 −0.0915209
\(262\) −489.256 −0.115368
\(263\) −4695.32 −1.10086 −0.550430 0.834881i \(-0.685536\pi\)
−0.550430 + 0.834881i \(0.685536\pi\)
\(264\) −1135.93 −0.264816
\(265\) 745.294 0.172766
\(266\) −5712.17 −1.31668
\(267\) 69.7239 0.0159814
\(268\) 1362.87 0.310636
\(269\) 2959.38 0.670769 0.335384 0.942081i \(-0.391134\pi\)
0.335384 + 0.942081i \(0.391134\pi\)
\(270\) 571.459 0.128807
\(271\) −2964.39 −0.664479 −0.332240 0.943195i \(-0.607804\pi\)
−0.332240 + 0.943195i \(0.607804\pi\)
\(272\) 972.515 0.216792
\(273\) −3504.27 −0.776880
\(274\) −4353.15 −0.959793
\(275\) −615.724 −0.135017
\(276\) −1448.34 −0.315869
\(277\) 5834.05 1.26547 0.632733 0.774370i \(-0.281933\pi\)
0.632733 + 0.774370i \(0.281933\pi\)
\(278\) 1548.53 0.334082
\(279\) −1218.45 −0.261457
\(280\) −1555.54 −0.332005
\(281\) 6519.85 1.38413 0.692067 0.721834i \(-0.256700\pi\)
0.692067 + 0.721834i \(0.256700\pi\)
\(282\) 1616.91 0.341438
\(283\) 5416.05 1.13764 0.568818 0.822463i \(-0.307401\pi\)
0.568818 + 0.822463i \(0.307401\pi\)
\(284\) 2327.80 0.486372
\(285\) 4934.96 1.02569
\(286\) −6017.90 −1.24422
\(287\) −1391.15 −0.286121
\(288\) −288.000 −0.0589256
\(289\) −1218.52 −0.248020
\(290\) −907.528 −0.183765
\(291\) 2240.01 0.451243
\(292\) −920.726 −0.184525
\(293\) −8096.63 −1.61437 −0.807184 0.590300i \(-0.799010\pi\)
−0.807184 + 0.590300i \(0.799010\pi\)
\(294\) 32.4068 0.00642859
\(295\) 624.372 0.123228
\(296\) 1784.20 0.350354
\(297\) 1277.92 0.249671
\(298\) 3485.85 0.677618
\(299\) −7673.01 −1.48409
\(300\) −156.109 −0.0300432
\(301\) 6522.05 1.24892
\(302\) −2580.05 −0.491607
\(303\) −2562.04 −0.485761
\(304\) −2487.08 −0.469224
\(305\) 2586.49 0.485580
\(306\) −1094.08 −0.204393
\(307\) 8252.18 1.53413 0.767063 0.641572i \(-0.221717\pi\)
0.767063 + 0.641572i \(0.221717\pi\)
\(308\) −3478.56 −0.643537
\(309\) 983.216 0.181014
\(310\) −2865.40 −0.524980
\(311\) −3861.70 −0.704107 −0.352053 0.935980i \(-0.614516\pi\)
−0.352053 + 0.935980i \(0.614516\pi\)
\(312\) −1525.76 −0.276857
\(313\) 2319.63 0.418892 0.209446 0.977820i \(-0.432834\pi\)
0.209446 + 0.977820i \(0.432834\pi\)
\(314\) 331.379 0.0595566
\(315\) 1749.99 0.313017
\(316\) −4067.51 −0.724098
\(317\) 453.436 0.0803391 0.0401695 0.999193i \(-0.487210\pi\)
0.0401695 + 0.999193i \(0.487210\pi\)
\(318\) 422.559 0.0745155
\(319\) −2029.45 −0.356198
\(320\) −677.285 −0.118317
\(321\) −1571.76 −0.273294
\(322\) −4435.27 −0.767602
\(323\) −9448.15 −1.62758
\(324\) 324.000 0.0555556
\(325\) −827.033 −0.141156
\(326\) −1876.18 −0.318749
\(327\) 510.974 0.0864126
\(328\) −605.706 −0.101965
\(329\) 4951.47 0.829737
\(330\) 3005.26 0.501315
\(331\) −9235.83 −1.53368 −0.766839 0.641840i \(-0.778171\pi\)
−0.766839 + 0.641840i \(0.778171\pi\)
\(332\) 1535.88 0.253893
\(333\) −2007.23 −0.330317
\(334\) −5145.43 −0.842950
\(335\) −3605.66 −0.588054
\(336\) −881.945 −0.143197
\(337\) 9340.65 1.50984 0.754922 0.655814i \(-0.227675\pi\)
0.754922 + 0.655814i \(0.227675\pi\)
\(338\) −3689.18 −0.593683
\(339\) −3792.89 −0.607673
\(340\) −2572.93 −0.410402
\(341\) −6407.72 −1.01759
\(342\) 2797.97 0.442389
\(343\) 6401.47 1.00772
\(344\) 2839.71 0.445078
\(345\) 3831.79 0.597962
\(346\) 4676.96 0.726691
\(347\) −5432.79 −0.840482 −0.420241 0.907412i \(-0.638054\pi\)
−0.420241 + 0.907412i \(0.638054\pi\)
\(348\) −514.541 −0.0792594
\(349\) 7808.17 1.19760 0.598799 0.800899i \(-0.295645\pi\)
0.598799 + 0.800899i \(0.295645\pi\)
\(350\) −478.055 −0.0730088
\(351\) 1716.48 0.261023
\(352\) −1514.57 −0.229338
\(353\) −177.412 −0.0267499 −0.0133749 0.999911i \(-0.504258\pi\)
−0.0133749 + 0.999911i \(0.504258\pi\)
\(354\) 354.000 0.0531494
\(355\) −6158.54 −0.920736
\(356\) 92.9651 0.0138403
\(357\) −3350.41 −0.496702
\(358\) 5236.42 0.773055
\(359\) −9472.43 −1.39258 −0.696289 0.717761i \(-0.745167\pi\)
−0.696289 + 0.717761i \(0.745167\pi\)
\(360\) 761.945 0.111550
\(361\) 17303.5 2.52274
\(362\) 5716.19 0.829935
\(363\) 2727.47 0.394367
\(364\) −4672.36 −0.672798
\(365\) 2435.91 0.349319
\(366\) 1466.46 0.209435
\(367\) −1628.23 −0.231588 −0.115794 0.993273i \(-0.536941\pi\)
−0.115794 + 0.993273i \(0.536941\pi\)
\(368\) −1931.12 −0.273551
\(369\) 681.419 0.0961335
\(370\) −4720.37 −0.663244
\(371\) 1294.01 0.181082
\(372\) −1624.60 −0.226428
\(373\) 3096.44 0.429833 0.214916 0.976632i \(-0.431052\pi\)
0.214916 + 0.976632i \(0.431052\pi\)
\(374\) −5753.68 −0.795496
\(375\) 4381.47 0.603356
\(376\) 2155.88 0.295694
\(377\) −2725.93 −0.372394
\(378\) 992.189 0.135007
\(379\) 11197.9 1.51767 0.758833 0.651285i \(-0.225770\pi\)
0.758833 + 0.651285i \(0.225770\pi\)
\(380\) 6579.94 0.888273
\(381\) −6904.42 −0.928411
\(382\) −8922.59 −1.19508
\(383\) −6380.04 −0.851188 −0.425594 0.904914i \(-0.639935\pi\)
−0.425594 + 0.904914i \(0.639935\pi\)
\(384\) −384.000 −0.0510310
\(385\) 9203.04 1.21826
\(386\) −7455.71 −0.983123
\(387\) −3194.67 −0.419624
\(388\) 2986.68 0.390788
\(389\) 10070.5 1.31258 0.656291 0.754508i \(-0.272124\pi\)
0.656291 + 0.754508i \(0.272124\pi\)
\(390\) 4036.63 0.524109
\(391\) −7336.11 −0.948857
\(392\) 43.2091 0.00556732
\(393\) 733.884 0.0941973
\(394\) −6401.49 −0.818534
\(395\) 10761.2 1.37077
\(396\) 1703.89 0.216222
\(397\) −1609.08 −0.203419 −0.101709 0.994814i \(-0.532431\pi\)
−0.101709 + 0.994814i \(0.532431\pi\)
\(398\) 9329.79 1.17503
\(399\) 8568.25 1.07506
\(400\) −208.145 −0.0260182
\(401\) 6154.93 0.766490 0.383245 0.923647i \(-0.374806\pi\)
0.383245 + 0.923647i \(0.374806\pi\)
\(402\) −2044.30 −0.253633
\(403\) −8606.77 −1.06385
\(404\) −3416.06 −0.420681
\(405\) −857.189 −0.105170
\(406\) −1575.68 −0.192611
\(407\) −10555.9 −1.28559
\(408\) −1458.77 −0.177010
\(409\) 5914.12 0.714999 0.357499 0.933913i \(-0.383629\pi\)
0.357499 + 0.933913i \(0.383629\pi\)
\(410\) 1602.48 0.193027
\(411\) 6529.72 0.783668
\(412\) 1310.95 0.156762
\(413\) 1084.06 0.129160
\(414\) 2172.51 0.257906
\(415\) −4063.40 −0.480637
\(416\) −2034.35 −0.239765
\(417\) −2322.80 −0.272777
\(418\) 14714.3 1.72177
\(419\) −15412.1 −1.79697 −0.898486 0.439002i \(-0.855332\pi\)
−0.898486 + 0.439002i \(0.855332\pi\)
\(420\) 2333.31 0.271081
\(421\) −7496.68 −0.867852 −0.433926 0.900949i \(-0.642872\pi\)
−0.433926 + 0.900949i \(0.642872\pi\)
\(422\) 8681.56 1.00145
\(423\) −2425.36 −0.278783
\(424\) 563.412 0.0645323
\(425\) −790.721 −0.0902485
\(426\) −3491.70 −0.397121
\(427\) 4490.76 0.508953
\(428\) −2095.69 −0.236679
\(429\) 9026.86 1.01590
\(430\) −7512.86 −0.842563
\(431\) −5517.13 −0.616591 −0.308295 0.951291i \(-0.599759\pi\)
−0.308295 + 0.951291i \(0.599759\pi\)
\(432\) 432.000 0.0481125
\(433\) −9974.48 −1.10703 −0.553514 0.832840i \(-0.686713\pi\)
−0.553514 + 0.832840i \(0.686713\pi\)
\(434\) −4975.02 −0.550250
\(435\) 1361.29 0.150044
\(436\) 681.298 0.0748355
\(437\) 18761.2 2.05370
\(438\) 1381.09 0.150664
\(439\) −7993.13 −0.869000 −0.434500 0.900672i \(-0.643075\pi\)
−0.434500 + 0.900672i \(0.643075\pi\)
\(440\) 4007.01 0.434152
\(441\) −48.6102 −0.00524892
\(442\) −7728.27 −0.831666
\(443\) 18221.4 1.95423 0.977114 0.212716i \(-0.0682309\pi\)
0.977114 + 0.212716i \(0.0682309\pi\)
\(444\) −2676.30 −0.286063
\(445\) −245.953 −0.0262006
\(446\) −5125.17 −0.544134
\(447\) −5228.78 −0.553273
\(448\) −1175.93 −0.124012
\(449\) −11013.4 −1.15758 −0.578790 0.815477i \(-0.696475\pi\)
−0.578790 + 0.815477i \(0.696475\pi\)
\(450\) 234.164 0.0245302
\(451\) 3583.53 0.374151
\(452\) −5057.18 −0.526261
\(453\) 3870.08 0.401395
\(454\) 4124.35 0.426355
\(455\) 12361.4 1.27365
\(456\) 3730.63 0.383120
\(457\) 5504.77 0.563462 0.281731 0.959493i \(-0.409091\pi\)
0.281731 + 0.959493i \(0.409091\pi\)
\(458\) 11674.3 1.19105
\(459\) 1641.12 0.166886
\(460\) 5109.06 0.517850
\(461\) 17623.4 1.78049 0.890244 0.455484i \(-0.150534\pi\)
0.890244 + 0.455484i \(0.150534\pi\)
\(462\) 5217.84 0.525446
\(463\) 18820.0 1.88907 0.944537 0.328404i \(-0.106511\pi\)
0.944537 + 0.328404i \(0.106511\pi\)
\(464\) −686.055 −0.0686407
\(465\) 4298.10 0.428644
\(466\) 7347.71 0.730421
\(467\) 2558.84 0.253552 0.126776 0.991931i \(-0.459537\pi\)
0.126776 + 0.991931i \(0.459537\pi\)
\(468\) 2288.65 0.226053
\(469\) −6260.28 −0.616360
\(470\) −5703.68 −0.559768
\(471\) −497.068 −0.0486278
\(472\) 472.000 0.0460287
\(473\) −16800.5 −1.63317
\(474\) 6101.26 0.591224
\(475\) 2022.17 0.195334
\(476\) −4467.22 −0.430156
\(477\) −633.839 −0.0608417
\(478\) 4910.65 0.469891
\(479\) 8222.33 0.784317 0.392158 0.919898i \(-0.371729\pi\)
0.392158 + 0.919898i \(0.371729\pi\)
\(480\) 1015.93 0.0966053
\(481\) −14178.5 −1.34404
\(482\) −9764.31 −0.922722
\(483\) 6652.90 0.626745
\(484\) 3636.63 0.341532
\(485\) −7901.69 −0.739788
\(486\) −486.000 −0.0453609
\(487\) −13014.7 −1.21099 −0.605495 0.795849i \(-0.707025\pi\)
−0.605495 + 0.795849i \(0.707025\pi\)
\(488\) 1955.28 0.181376
\(489\) 2814.27 0.260257
\(490\) −114.316 −0.0105393
\(491\) 2376.25 0.218408 0.109204 0.994019i \(-0.465170\pi\)
0.109204 + 0.994019i \(0.465170\pi\)
\(492\) 908.559 0.0832541
\(493\) −2606.24 −0.238092
\(494\) 19764.1 1.80006
\(495\) −4507.89 −0.409322
\(496\) −2166.13 −0.196093
\(497\) −10692.7 −0.965055
\(498\) −2303.82 −0.207303
\(499\) −22141.4 −1.98634 −0.993172 0.116662i \(-0.962781\pi\)
−0.993172 + 0.116662i \(0.962781\pi\)
\(500\) 5841.97 0.522521
\(501\) 7718.14 0.688266
\(502\) −13997.5 −1.24450
\(503\) −15148.8 −1.34285 −0.671424 0.741073i \(-0.734317\pi\)
−0.671424 + 0.741073i \(0.734317\pi\)
\(504\) 1322.92 0.116920
\(505\) 9037.67 0.796378
\(506\) 11425.1 1.00377
\(507\) 5533.76 0.484740
\(508\) −9205.90 −0.804027
\(509\) −11338.3 −0.987348 −0.493674 0.869647i \(-0.664346\pi\)
−0.493674 + 0.869647i \(0.664346\pi\)
\(510\) 3859.39 0.335092
\(511\) 4229.32 0.366133
\(512\) −512.000 −0.0441942
\(513\) −4196.96 −0.361209
\(514\) −466.409 −0.0400242
\(515\) −3468.32 −0.296762
\(516\) −4259.56 −0.363405
\(517\) −12754.8 −1.08502
\(518\) −8195.68 −0.695169
\(519\) −7015.45 −0.593341
\(520\) 5382.17 0.453892
\(521\) −14243.1 −1.19770 −0.598849 0.800862i \(-0.704375\pi\)
−0.598849 + 0.800862i \(0.704375\pi\)
\(522\) 771.811 0.0647151
\(523\) −15660.8 −1.30937 −0.654684 0.755903i \(-0.727198\pi\)
−0.654684 + 0.755903i \(0.727198\pi\)
\(524\) 978.512 0.0815773
\(525\) 717.082 0.0596115
\(526\) 9390.65 0.778425
\(527\) −8228.87 −0.680181
\(528\) 2271.85 0.187253
\(529\) 2400.30 0.197280
\(530\) −1490.59 −0.122164
\(531\) −531.000 −0.0433963
\(532\) 11424.3 0.931030
\(533\) 4813.36 0.391162
\(534\) −139.448 −0.0113005
\(535\) 5544.44 0.448051
\(536\) −2725.73 −0.219653
\(537\) −7854.63 −0.631196
\(538\) −5918.77 −0.474305
\(539\) −255.638 −0.0204287
\(540\) −1142.92 −0.0910803
\(541\) 16850.4 1.33910 0.669551 0.742766i \(-0.266487\pi\)
0.669551 + 0.742766i \(0.266487\pi\)
\(542\) 5928.78 0.469858
\(543\) −8574.29 −0.677639
\(544\) −1945.03 −0.153295
\(545\) −1802.47 −0.141669
\(546\) 7008.54 0.549337
\(547\) 23374.5 1.82709 0.913547 0.406733i \(-0.133332\pi\)
0.913547 + 0.406733i \(0.133332\pi\)
\(548\) 8706.30 0.678676
\(549\) −2199.69 −0.171003
\(550\) 1231.45 0.0954712
\(551\) 6665.14 0.515326
\(552\) 2896.68 0.223353
\(553\) 18684.0 1.43675
\(554\) −11668.1 −0.894819
\(555\) 7080.55 0.541536
\(556\) −3097.07 −0.236232
\(557\) −10403.4 −0.791396 −0.395698 0.918381i \(-0.629497\pi\)
−0.395698 + 0.918381i \(0.629497\pi\)
\(558\) 2436.89 0.184878
\(559\) −22566.3 −1.70743
\(560\) 3111.08 0.234763
\(561\) 8630.52 0.649520
\(562\) −13039.7 −0.978730
\(563\) 1918.38 0.143606 0.0718029 0.997419i \(-0.477125\pi\)
0.0718029 + 0.997419i \(0.477125\pi\)
\(564\) −3233.81 −0.241433
\(565\) 13379.5 0.996248
\(566\) −10832.1 −0.804430
\(567\) −1488.28 −0.110233
\(568\) −4655.61 −0.343917
\(569\) 20752.9 1.52901 0.764506 0.644617i \(-0.222983\pi\)
0.764506 + 0.644617i \(0.222983\pi\)
\(570\) −9869.91 −0.725272
\(571\) 19619.5 1.43791 0.718957 0.695054i \(-0.244620\pi\)
0.718957 + 0.695054i \(0.244620\pi\)
\(572\) 12035.8 0.879795
\(573\) 13383.9 0.975776
\(574\) 2782.29 0.202318
\(575\) 1570.13 0.113877
\(576\) 576.000 0.0416667
\(577\) −16614.2 −1.19872 −0.599358 0.800481i \(-0.704577\pi\)
−0.599358 + 0.800481i \(0.704577\pi\)
\(578\) 2437.05 0.175377
\(579\) 11183.6 0.802717
\(580\) 1815.06 0.129942
\(581\) −7055.03 −0.503773
\(582\) −4480.02 −0.319077
\(583\) −3333.31 −0.236795
\(584\) 1841.45 0.130479
\(585\) −6054.94 −0.427933
\(586\) 16193.3 1.14153
\(587\) −4898.71 −0.344449 −0.172224 0.985058i \(-0.555095\pi\)
−0.172224 + 0.985058i \(0.555095\pi\)
\(588\) −64.8137 −0.00454570
\(589\) 21044.3 1.47218
\(590\) −1248.74 −0.0871355
\(591\) 9602.23 0.668330
\(592\) −3568.41 −0.247737
\(593\) 9958.75 0.689641 0.344820 0.938669i \(-0.387940\pi\)
0.344820 + 0.938669i \(0.387940\pi\)
\(594\) −2555.84 −0.176544
\(595\) 11818.7 0.814316
\(596\) −6971.71 −0.479148
\(597\) −13994.7 −0.959404
\(598\) 15346.0 1.04941
\(599\) 3477.65 0.237217 0.118609 0.992941i \(-0.462157\pi\)
0.118609 + 0.992941i \(0.462157\pi\)
\(600\) 312.218 0.0212438
\(601\) 251.900 0.0170969 0.00854844 0.999963i \(-0.497279\pi\)
0.00854844 + 0.999963i \(0.497279\pi\)
\(602\) −13044.1 −0.883120
\(603\) 3066.45 0.207090
\(604\) 5160.10 0.347618
\(605\) −9621.23 −0.646543
\(606\) 5124.09 0.343485
\(607\) 27085.9 1.81117 0.905587 0.424161i \(-0.139431\pi\)
0.905587 + 0.424161i \(0.139431\pi\)
\(608\) 4974.17 0.331791
\(609\) 2363.53 0.157266
\(610\) −5172.98 −0.343357
\(611\) −17132.1 −1.13435
\(612\) 2188.16 0.144528
\(613\) 21711.2 1.43052 0.715258 0.698861i \(-0.246309\pi\)
0.715258 + 0.698861i \(0.246309\pi\)
\(614\) −16504.4 −1.08479
\(615\) −2403.72 −0.157606
\(616\) 6957.12 0.455050
\(617\) −2582.21 −0.168486 −0.0842431 0.996445i \(-0.526847\pi\)
−0.0842431 + 0.996445i \(0.526847\pi\)
\(618\) −1966.43 −0.127996
\(619\) −10035.8 −0.651654 −0.325827 0.945429i \(-0.605643\pi\)
−0.325827 + 0.945429i \(0.605643\pi\)
\(620\) 5730.80 0.371217
\(621\) −3258.77 −0.210579
\(622\) 7723.41 0.497879
\(623\) −427.032 −0.0274618
\(624\) 3051.53 0.195767
\(625\) −13829.6 −0.885096
\(626\) −4639.26 −0.296201
\(627\) −22071.5 −1.40582
\(628\) −662.758 −0.0421129
\(629\) −13556.0 −0.859320
\(630\) −3499.97 −0.221337
\(631\) −8839.40 −0.557672 −0.278836 0.960339i \(-0.589949\pi\)
−0.278836 + 0.960339i \(0.589949\pi\)
\(632\) 8135.01 0.512015
\(633\) −13022.3 −0.817680
\(634\) −906.871 −0.0568083
\(635\) 24355.5 1.52208
\(636\) −845.118 −0.0526904
\(637\) −343.369 −0.0213576
\(638\) 4058.90 0.251870
\(639\) 5237.56 0.324248
\(640\) 1354.57 0.0836626
\(641\) −11130.3 −0.685836 −0.342918 0.939365i \(-0.611415\pi\)
−0.342918 + 0.939365i \(0.611415\pi\)
\(642\) 3143.53 0.193248
\(643\) −15678.6 −0.961593 −0.480797 0.876832i \(-0.659653\pi\)
−0.480797 + 0.876832i \(0.659653\pi\)
\(644\) 8870.54 0.542777
\(645\) 11269.3 0.687950
\(646\) 18896.3 1.15088
\(647\) −7444.89 −0.452379 −0.226189 0.974083i \(-0.572627\pi\)
−0.226189 + 0.974083i \(0.572627\pi\)
\(648\) −648.000 −0.0392837
\(649\) −2792.49 −0.168898
\(650\) 1654.07 0.0998120
\(651\) 7462.52 0.449277
\(652\) 3752.36 0.225389
\(653\) 21982.0 1.31734 0.658670 0.752432i \(-0.271119\pi\)
0.658670 + 0.752432i \(0.271119\pi\)
\(654\) −1021.95 −0.0611029
\(655\) −2588.79 −0.154431
\(656\) 1211.41 0.0721001
\(657\) −2071.63 −0.123017
\(658\) −9902.94 −0.586713
\(659\) 727.025 0.0429755 0.0214878 0.999769i \(-0.493160\pi\)
0.0214878 + 0.999769i \(0.493160\pi\)
\(660\) −6010.52 −0.354483
\(661\) −12708.7 −0.747821 −0.373911 0.927465i \(-0.621983\pi\)
−0.373911 + 0.927465i \(0.621983\pi\)
\(662\) 18471.7 1.08447
\(663\) 11592.4 0.679053
\(664\) −3071.77 −0.179530
\(665\) −30224.7 −1.76250
\(666\) 4014.46 0.233569
\(667\) 5175.21 0.300427
\(668\) 10290.9 0.596056
\(669\) 7687.75 0.444283
\(670\) 7211.32 0.415817
\(671\) −11568.0 −0.665541
\(672\) 1763.89 0.101255
\(673\) −5174.21 −0.296361 −0.148181 0.988960i \(-0.547342\pi\)
−0.148181 + 0.988960i \(0.547342\pi\)
\(674\) −18681.3 −1.06762
\(675\) −351.245 −0.0200288
\(676\) 7378.35 0.419797
\(677\) 13165.1 0.747377 0.373689 0.927554i \(-0.378093\pi\)
0.373689 + 0.927554i \(0.378093\pi\)
\(678\) 7585.77 0.429690
\(679\) −13719.2 −0.775397
\(680\) 5145.86 0.290198
\(681\) −6186.53 −0.348118
\(682\) 12815.4 0.719543
\(683\) 19713.4 1.10441 0.552206 0.833708i \(-0.313786\pi\)
0.552206 + 0.833708i \(0.313786\pi\)
\(684\) −5595.94 −0.312816
\(685\) −23033.8 −1.28478
\(686\) −12802.9 −0.712564
\(687\) −17511.4 −0.972492
\(688\) −5679.42 −0.314718
\(689\) −4477.26 −0.247562
\(690\) −7663.59 −0.422823
\(691\) −11628.0 −0.640158 −0.320079 0.947391i \(-0.603709\pi\)
−0.320079 + 0.947391i \(0.603709\pi\)
\(692\) −9353.93 −0.513848
\(693\) −7826.76 −0.429025
\(694\) 10865.6 0.594311
\(695\) 8193.74 0.447203
\(696\) 1029.08 0.0560449
\(697\) 4602.02 0.250092
\(698\) −15616.3 −0.846830
\(699\) −11021.6 −0.596386
\(700\) 956.109 0.0516250
\(701\) −1961.03 −0.105659 −0.0528295 0.998604i \(-0.516824\pi\)
−0.0528295 + 0.998604i \(0.516824\pi\)
\(702\) −3432.97 −0.184571
\(703\) 34667.7 1.85991
\(704\) 3029.14 0.162166
\(705\) 8555.52 0.457049
\(706\) 354.825 0.0189150
\(707\) 15691.5 0.834712
\(708\) −708.000 −0.0375823
\(709\) 4838.42 0.256292 0.128146 0.991755i \(-0.459097\pi\)
0.128146 + 0.991755i \(0.459097\pi\)
\(710\) 12317.1 0.651059
\(711\) −9151.89 −0.482732
\(712\) −185.930 −0.00978656
\(713\) 16340.1 0.858261
\(714\) 6700.82 0.351221
\(715\) −31842.5 −1.66551
\(716\) −10472.8 −0.546632
\(717\) −7365.98 −0.383665
\(718\) 18944.9 0.984702
\(719\) −23993.5 −1.24452 −0.622259 0.782812i \(-0.713785\pi\)
−0.622259 + 0.782812i \(0.713785\pi\)
\(720\) −1523.89 −0.0788779
\(721\) −6021.82 −0.311046
\(722\) −34606.9 −1.78385
\(723\) 14646.5 0.753400
\(724\) −11432.4 −0.586853
\(725\) 557.809 0.0285745
\(726\) −5454.95 −0.278860
\(727\) −20017.6 −1.02120 −0.510600 0.859819i \(-0.670577\pi\)
−0.510600 + 0.859819i \(0.670577\pi\)
\(728\) 9344.72 0.475740
\(729\) 729.000 0.0370370
\(730\) −4871.82 −0.247006
\(731\) −21575.5 −1.09165
\(732\) −2932.92 −0.148093
\(733\) −26043.8 −1.31235 −0.656173 0.754610i \(-0.727826\pi\)
−0.656173 + 0.754610i \(0.727826\pi\)
\(734\) 3256.46 0.163758
\(735\) 171.474 0.00860532
\(736\) 3862.24 0.193430
\(737\) 16126.2 0.805993
\(738\) −1362.84 −0.0679767
\(739\) −17133.2 −0.852847 −0.426423 0.904524i \(-0.640227\pi\)
−0.426423 + 0.904524i \(0.640227\pi\)
\(740\) 9440.73 0.468984
\(741\) −29646.1 −1.46974
\(742\) −2588.01 −0.128044
\(743\) 8594.93 0.424384 0.212192 0.977228i \(-0.431940\pi\)
0.212192 + 0.977228i \(0.431940\pi\)
\(744\) 3249.19 0.160109
\(745\) 18444.7 0.907060
\(746\) −6192.88 −0.303938
\(747\) 3455.74 0.169262
\(748\) 11507.4 0.562501
\(749\) 9626.46 0.469617
\(750\) −8762.95 −0.426637
\(751\) −27804.9 −1.35102 −0.675510 0.737351i \(-0.736076\pi\)
−0.675510 + 0.737351i \(0.736076\pi\)
\(752\) −4311.75 −0.209087
\(753\) 20996.3 1.01613
\(754\) 5451.86 0.263322
\(755\) −13651.8 −0.658066
\(756\) −1984.38 −0.0954644
\(757\) −4208.30 −0.202052 −0.101026 0.994884i \(-0.532213\pi\)
−0.101026 + 0.994884i \(0.532213\pi\)
\(758\) −22395.7 −1.07315
\(759\) −17137.6 −0.819573
\(760\) −13159.9 −0.628104
\(761\) −1448.37 −0.0689927 −0.0344964 0.999405i \(-0.510983\pi\)
−0.0344964 + 0.999405i \(0.510983\pi\)
\(762\) 13808.8 0.656485
\(763\) −3129.52 −0.148488
\(764\) 17845.2 0.845047
\(765\) −5789.09 −0.273601
\(766\) 12760.1 0.601881
\(767\) −3750.84 −0.176577
\(768\) 768.000 0.0360844
\(769\) −14538.5 −0.681758 −0.340879 0.940107i \(-0.610725\pi\)
−0.340879 + 0.940107i \(0.610725\pi\)
\(770\) −18406.1 −0.861440
\(771\) 699.614 0.0326796
\(772\) 14911.4 0.695173
\(773\) 12173.4 0.566423 0.283212 0.959057i \(-0.408600\pi\)
0.283212 + 0.959057i \(0.408600\pi\)
\(774\) 6389.35 0.296719
\(775\) 1761.21 0.0816316
\(776\) −5973.36 −0.276329
\(777\) 12293.5 0.567603
\(778\) −20141.0 −0.928136
\(779\) −11769.1 −0.541298
\(780\) −8073.25 −0.370601
\(781\) 27543.9 1.26197
\(782\) 14672.2 0.670943
\(783\) −1157.72 −0.0528396
\(784\) −86.4182 −0.00393669
\(785\) 1753.42 0.0797226
\(786\) −1467.77 −0.0666076
\(787\) −31829.2 −1.44166 −0.720832 0.693110i \(-0.756240\pi\)
−0.720832 + 0.693110i \(0.756240\pi\)
\(788\) 12803.0 0.578791
\(789\) −14086.0 −0.635582
\(790\) −21522.3 −0.969279
\(791\) 23230.0 1.04420
\(792\) −3407.78 −0.152892
\(793\) −15538.0 −0.695802
\(794\) 3218.15 0.143839
\(795\) 2235.88 0.0997466
\(796\) −18659.6 −0.830869
\(797\) 26250.6 1.16668 0.583339 0.812229i \(-0.301746\pi\)
0.583339 + 0.812229i \(0.301746\pi\)
\(798\) −17136.5 −0.760183
\(799\) −16379.9 −0.725254
\(800\) 416.291 0.0183976
\(801\) 209.172 0.00922686
\(802\) −12309.9 −0.541990
\(803\) −10894.6 −0.478780
\(804\) 4088.60 0.179346
\(805\) −23468.3 −1.02751
\(806\) 17213.5 0.752259
\(807\) 8878.15 0.387268
\(808\) 6832.12 0.297467
\(809\) 20265.6 0.880716 0.440358 0.897822i \(-0.354851\pi\)
0.440358 + 0.897822i \(0.354851\pi\)
\(810\) 1714.38 0.0743668
\(811\) −6139.57 −0.265832 −0.132916 0.991127i \(-0.542434\pi\)
−0.132916 + 0.991127i \(0.542434\pi\)
\(812\) 3151.37 0.136196
\(813\) −8893.17 −0.383637
\(814\) 21111.7 0.909048
\(815\) −9927.41 −0.426677
\(816\) 2917.55 0.125165
\(817\) 55176.5 2.36277
\(818\) −11828.2 −0.505581
\(819\) −10512.8 −0.448532
\(820\) −3204.97 −0.136491
\(821\) −44128.0 −1.87585 −0.937927 0.346832i \(-0.887257\pi\)
−0.937927 + 0.346832i \(0.887257\pi\)
\(822\) −13059.4 −0.554137
\(823\) 14143.6 0.599044 0.299522 0.954089i \(-0.403173\pi\)
0.299522 + 0.954089i \(0.403173\pi\)
\(824\) −2621.91 −0.110848
\(825\) −1847.17 −0.0779519
\(826\) −2168.12 −0.0913298
\(827\) −32831.8 −1.38050 −0.690251 0.723570i \(-0.742500\pi\)
−0.690251 + 0.723570i \(0.742500\pi\)
\(828\) −4345.02 −0.182367
\(829\) 1172.52 0.0491234 0.0245617 0.999698i \(-0.492181\pi\)
0.0245617 + 0.999698i \(0.492181\pi\)
\(830\) 8126.80 0.339862
\(831\) 17502.1 0.730617
\(832\) 4068.70 0.169540
\(833\) −328.293 −0.0136551
\(834\) 4645.60 0.192882
\(835\) −27225.9 −1.12837
\(836\) −29428.6 −1.21748
\(837\) −3655.34 −0.150952
\(838\) 30824.2 1.27065
\(839\) −696.702 −0.0286684 −0.0143342 0.999897i \(-0.504563\pi\)
−0.0143342 + 0.999897i \(0.504563\pi\)
\(840\) −4666.63 −0.191683
\(841\) −22550.4 −0.924615
\(842\) 14993.4 0.613664
\(843\) 19559.5 0.799130
\(844\) −17363.1 −0.708131
\(845\) −19520.5 −0.794704
\(846\) 4850.72 0.197129
\(847\) −16704.7 −0.677664
\(848\) −1126.82 −0.0456313
\(849\) 16248.2 0.656815
\(850\) 1581.44 0.0638153
\(851\) 26918.1 1.08430
\(852\) 6983.41 0.280807
\(853\) 23022.2 0.924110 0.462055 0.886851i \(-0.347112\pi\)
0.462055 + 0.886851i \(0.347112\pi\)
\(854\) −8981.52 −0.359884
\(855\) 14804.9 0.592182
\(856\) 4191.37 0.167358
\(857\) 40458.2 1.61263 0.806315 0.591486i \(-0.201458\pi\)
0.806315 + 0.591486i \(0.201458\pi\)
\(858\) −18053.7 −0.718349
\(859\) 25380.9 1.00813 0.504066 0.863665i \(-0.331837\pi\)
0.504066 + 0.863665i \(0.331837\pi\)
\(860\) 15025.7 0.595782
\(861\) −4173.44 −0.165192
\(862\) 11034.3 0.435996
\(863\) 21524.6 0.849023 0.424512 0.905422i \(-0.360446\pi\)
0.424512 + 0.905422i \(0.360446\pi\)
\(864\) −864.000 −0.0340207
\(865\) 24747.2 0.972750
\(866\) 19949.0 0.782786
\(867\) −3655.57 −0.143195
\(868\) 9950.03 0.389085
\(869\) −48129.1 −1.87879
\(870\) −2722.58 −0.106097
\(871\) 21660.5 0.842640
\(872\) −1362.60 −0.0529167
\(873\) 6720.03 0.260525
\(874\) −37522.4 −1.45219
\(875\) −26834.9 −1.03678
\(876\) −2762.18 −0.106536
\(877\) −43051.6 −1.65764 −0.828820 0.559515i \(-0.810987\pi\)
−0.828820 + 0.559515i \(0.810987\pi\)
\(878\) 15986.3 0.614476
\(879\) −24289.9 −0.932056
\(880\) −8014.02 −0.306992
\(881\) −40233.2 −1.53858 −0.769292 0.638898i \(-0.779391\pi\)
−0.769292 + 0.638898i \(0.779391\pi\)
\(882\) 97.2205 0.00371155
\(883\) 42342.7 1.61375 0.806877 0.590720i \(-0.201156\pi\)
0.806877 + 0.590720i \(0.201156\pi\)
\(884\) 15456.5 0.588077
\(885\) 1873.12 0.0711459
\(886\) −36442.7 −1.38185
\(887\) 2936.80 0.111170 0.0555852 0.998454i \(-0.482298\pi\)
0.0555852 + 0.998454i \(0.482298\pi\)
\(888\) 5352.61 0.202277
\(889\) 42287.0 1.59534
\(890\) 491.905 0.0185266
\(891\) 3833.75 0.144148
\(892\) 10250.3 0.384761
\(893\) 41889.4 1.56974
\(894\) 10457.6 0.391223
\(895\) 27707.4 1.03481
\(896\) 2351.85 0.0876897
\(897\) −23019.0 −0.856837
\(898\) 22026.8 0.818533
\(899\) 5805.01 0.215359
\(900\) −468.327 −0.0173455
\(901\) −4280.68 −0.158280
\(902\) −7167.06 −0.264564
\(903\) 19566.2 0.721064
\(904\) 10114.4 0.372122
\(905\) 30246.0 1.11095
\(906\) −7740.15 −0.283829
\(907\) −10543.4 −0.385985 −0.192993 0.981200i \(-0.561819\pi\)
−0.192993 + 0.981200i \(0.561819\pi\)
\(908\) −8248.70 −0.301479
\(909\) −7686.13 −0.280454
\(910\) −24722.8 −0.900608
\(911\) 14443.2 0.525273 0.262637 0.964895i \(-0.415408\pi\)
0.262637 + 0.964895i \(0.415408\pi\)
\(912\) −7461.25 −0.270907
\(913\) 18173.5 0.658766
\(914\) −11009.5 −0.398428
\(915\) 7759.47 0.280350
\(916\) −23348.6 −0.842203
\(917\) −4494.76 −0.161865
\(918\) −3282.24 −0.118007
\(919\) 32863.3 1.17961 0.589804 0.807546i \(-0.299205\pi\)
0.589804 + 0.807546i \(0.299205\pi\)
\(920\) −10218.1 −0.366175
\(921\) 24756.5 0.885728
\(922\) −35246.9 −1.25900
\(923\) 36996.6 1.31935
\(924\) −10435.7 −0.371546
\(925\) 2901.36 0.103131
\(926\) −37640.1 −1.33578
\(927\) 2949.65 0.104508
\(928\) 1372.11 0.0485363
\(929\) 25233.0 0.891140 0.445570 0.895247i \(-0.353001\pi\)
0.445570 + 0.895247i \(0.353001\pi\)
\(930\) −8596.20 −0.303097
\(931\) 839.568 0.0295550
\(932\) −14695.4 −0.516485
\(933\) −11585.1 −0.406516
\(934\) −5117.67 −0.179288
\(935\) −30444.4 −1.06485
\(936\) −4577.29 −0.159843
\(937\) −35290.6 −1.23041 −0.615205 0.788367i \(-0.710927\pi\)
−0.615205 + 0.788367i \(0.710927\pi\)
\(938\) 12520.6 0.435832
\(939\) 6958.89 0.241847
\(940\) 11407.4 0.395816
\(941\) 27389.9 0.948868 0.474434 0.880291i \(-0.342653\pi\)
0.474434 + 0.880291i \(0.342653\pi\)
\(942\) 994.136 0.0343850
\(943\) −9138.22 −0.315569
\(944\) −944.000 −0.0325472
\(945\) 5249.96 0.180721
\(946\) 33601.1 1.15483
\(947\) 57562.9 1.97523 0.987615 0.156896i \(-0.0501487\pi\)
0.987615 + 0.156896i \(0.0501487\pi\)
\(948\) −12202.5 −0.418058
\(949\) −14633.4 −0.500549
\(950\) −4044.34 −0.138122
\(951\) 1360.31 0.0463838
\(952\) 8934.43 0.304167
\(953\) 31567.6 1.07301 0.536504 0.843898i \(-0.319745\pi\)
0.536504 + 0.843898i \(0.319745\pi\)
\(954\) 1267.68 0.0430216
\(955\) −47212.0 −1.59973
\(956\) −9821.31 −0.332263
\(957\) −6088.34 −0.205651
\(958\) −16444.7 −0.554596
\(959\) −39992.1 −1.34662
\(960\) −2031.85 −0.0683102
\(961\) −11462.5 −0.384762
\(962\) 28357.0 0.950381
\(963\) −4715.29 −0.157786
\(964\) 19528.6 0.652463
\(965\) −39450.3 −1.31601
\(966\) −13305.8 −0.443175
\(967\) 4311.95 0.143395 0.0716975 0.997426i \(-0.477158\pi\)
0.0716975 + 0.997426i \(0.477158\pi\)
\(968\) −7273.26 −0.241499
\(969\) −28344.5 −0.939686
\(970\) 15803.4 0.523109
\(971\) 50749.1 1.67726 0.838628 0.544705i \(-0.183358\pi\)
0.838628 + 0.544705i \(0.183358\pi\)
\(972\) 972.000 0.0320750
\(973\) 14226.3 0.468729
\(974\) 26029.4 0.856300
\(975\) −2481.10 −0.0814962
\(976\) −3910.56 −0.128252
\(977\) −52342.5 −1.71401 −0.857003 0.515312i \(-0.827676\pi\)
−0.857003 + 0.515312i \(0.827676\pi\)
\(978\) −5628.54 −0.184030
\(979\) 1100.02 0.0359108
\(980\) 228.632 0.00745242
\(981\) 1532.92 0.0498903
\(982\) −4752.49 −0.154438
\(983\) 50740.8 1.64637 0.823184 0.567775i \(-0.192196\pi\)
0.823184 + 0.567775i \(0.192196\pi\)
\(984\) −1817.12 −0.0588695
\(985\) −33872.1 −1.09569
\(986\) 5212.49 0.168356
\(987\) 14854.4 0.479049
\(988\) −39528.2 −1.27283
\(989\) 42842.4 1.37746
\(990\) 9015.78 0.289435
\(991\) −14693.4 −0.470989 −0.235494 0.971876i \(-0.575671\pi\)
−0.235494 + 0.971876i \(0.575671\pi\)
\(992\) 4332.25 0.138658
\(993\) −27707.5 −0.885469
\(994\) 21385.4 0.682397
\(995\) 49366.6 1.57289
\(996\) 4607.65 0.146585
\(997\) 46107.5 1.46463 0.732317 0.680964i \(-0.238439\pi\)
0.732317 + 0.680964i \(0.238439\pi\)
\(998\) 44282.8 1.40456
\(999\) −6021.69 −0.190708
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 354.4.a.a.1.1 2
3.2 odd 2 1062.4.a.h.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.4.a.a.1.1 2 1.1 even 1 trivial
1062.4.a.h.1.2 2 3.2 odd 2