Properties

Label 547.4.a.a.1.20
Level $547$
Weight $4$
Character 547.1
Self dual yes
Analytic conductor $32.274$
Analytic rank $1$
Dimension $65$
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] = [547,4,Mod(1,547)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("547.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 547.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: \(32.2740447731\)
Analytic rank: \(1\)
Dimension: \(65\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 547.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.05184 q^{2} -4.83017 q^{3} +1.31373 q^{4} -18.6497 q^{5} +14.7409 q^{6} +8.22006 q^{7} +20.4054 q^{8} -3.66951 q^{9} +O(q^{10})\) \(q-3.05184 q^{2} -4.83017 q^{3} +1.31373 q^{4} -18.6497 q^{5} +14.7409 q^{6} +8.22006 q^{7} +20.4054 q^{8} -3.66951 q^{9} +56.9157 q^{10} -55.6216 q^{11} -6.34551 q^{12} -5.99977 q^{13} -25.0863 q^{14} +90.0809 q^{15} -72.7839 q^{16} +45.4531 q^{17} +11.1987 q^{18} -100.025 q^{19} -24.5005 q^{20} -39.7042 q^{21} +169.748 q^{22} +148.233 q^{23} -98.5616 q^{24} +222.809 q^{25} +18.3103 q^{26} +148.139 q^{27} +10.7989 q^{28} +147.367 q^{29} -274.912 q^{30} +257.845 q^{31} +58.8814 q^{32} +268.662 q^{33} -138.716 q^{34} -153.301 q^{35} -4.82072 q^{36} +136.398 q^{37} +305.261 q^{38} +28.9799 q^{39} -380.554 q^{40} -137.338 q^{41} +121.171 q^{42} +256.687 q^{43} -73.0715 q^{44} +68.4350 q^{45} -452.385 q^{46} -110.841 q^{47} +351.558 q^{48} -275.431 q^{49} -679.979 q^{50} -219.546 q^{51} -7.88205 q^{52} -45.4094 q^{53} -452.096 q^{54} +1037.32 q^{55} +167.734 q^{56} +483.139 q^{57} -449.741 q^{58} -560.180 q^{59} +118.342 q^{60} -749.990 q^{61} -786.901 q^{62} -30.1635 q^{63} +402.575 q^{64} +111.894 q^{65} -819.912 q^{66} +616.800 q^{67} +59.7129 q^{68} -715.992 q^{69} +467.851 q^{70} -696.830 q^{71} -74.8779 q^{72} +948.852 q^{73} -416.265 q^{74} -1076.21 q^{75} -131.406 q^{76} -457.213 q^{77} -88.4419 q^{78} +818.112 q^{79} +1357.39 q^{80} -616.458 q^{81} +419.134 q^{82} -877.537 q^{83} -52.1605 q^{84} -847.684 q^{85} -783.366 q^{86} -711.808 q^{87} -1134.98 q^{88} -648.168 q^{89} -208.853 q^{90} -49.3184 q^{91} +194.738 q^{92} -1245.43 q^{93} +338.268 q^{94} +1865.44 q^{95} -284.407 q^{96} +1688.84 q^{97} +840.570 q^{98} +204.104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.05184 −1.07899 −0.539494 0.841989i \(-0.681384\pi\)
−0.539494 + 0.841989i \(0.681384\pi\)
\(3\) −4.83017 −0.929566 −0.464783 0.885425i \(-0.653868\pi\)
−0.464783 + 0.885425i \(0.653868\pi\)
\(4\) 1.31373 0.164216
\(5\) −18.6497 −1.66808 −0.834038 0.551707i \(-0.813977\pi\)
−0.834038 + 0.551707i \(0.813977\pi\)
\(6\) 14.7409 1.00299
\(7\) 8.22006 0.443841 0.221921 0.975065i \(-0.428767\pi\)
0.221921 + 0.975065i \(0.428767\pi\)
\(8\) 20.4054 0.901801
\(9\) −3.66951 −0.135908
\(10\) 56.9157 1.79983
\(11\) −55.6216 −1.52459 −0.762297 0.647227i \(-0.775929\pi\)
−0.762297 + 0.647227i \(0.775929\pi\)
\(12\) −6.34551 −0.152649
\(13\) −5.99977 −0.128003 −0.0640014 0.997950i \(-0.520386\pi\)
−0.0640014 + 0.997950i \(0.520386\pi\)
\(14\) −25.0863 −0.478900
\(15\) 90.0809 1.55059
\(16\) −72.7839 −1.13725
\(17\) 45.4531 0.648470 0.324235 0.945977i \(-0.394893\pi\)
0.324235 + 0.945977i \(0.394893\pi\)
\(18\) 11.1987 0.146643
\(19\) −100.025 −1.20776 −0.603878 0.797077i \(-0.706379\pi\)
−0.603878 + 0.797077i \(0.706379\pi\)
\(20\) −24.5005 −0.273924
\(21\) −39.7042 −0.412580
\(22\) 169.748 1.64502
\(23\) 148.233 1.34386 0.671931 0.740614i \(-0.265465\pi\)
0.671931 + 0.740614i \(0.265465\pi\)
\(24\) −98.5616 −0.838284
\(25\) 222.809 1.78248
\(26\) 18.3103 0.138113
\(27\) 148.139 1.05590
\(28\) 10.7989 0.0728857
\(29\) 147.367 0.943635 0.471817 0.881696i \(-0.343598\pi\)
0.471817 + 0.881696i \(0.343598\pi\)
\(30\) −274.912 −1.67306
\(31\) 257.845 1.49388 0.746940 0.664892i \(-0.231522\pi\)
0.746940 + 0.664892i \(0.231522\pi\)
\(32\) 58.8814 0.325277
\(33\) 268.662 1.41721
\(34\) −138.716 −0.699692
\(35\) −153.301 −0.740361
\(36\) −4.82072 −0.0223182
\(37\) 136.398 0.606046 0.303023 0.952983i \(-0.402004\pi\)
0.303023 + 0.952983i \(0.402004\pi\)
\(38\) 305.261 1.30316
\(39\) 28.9799 0.118987
\(40\) −380.554 −1.50427
\(41\) −137.338 −0.523137 −0.261568 0.965185i \(-0.584240\pi\)
−0.261568 + 0.965185i \(0.584240\pi\)
\(42\) 121.171 0.445169
\(43\) 256.687 0.910333 0.455167 0.890406i \(-0.349580\pi\)
0.455167 + 0.890406i \(0.349580\pi\)
\(44\) −73.0715 −0.250362
\(45\) 68.4350 0.226704
\(46\) −452.385 −1.45001
\(47\) −110.841 −0.343995 −0.171998 0.985097i \(-0.555022\pi\)
−0.171998 + 0.985097i \(0.555022\pi\)
\(48\) 351.558 1.05715
\(49\) −275.431 −0.803005
\(50\) −679.979 −1.92327
\(51\) −219.546 −0.602796
\(52\) −7.88205 −0.0210201
\(53\) −45.4094 −0.117688 −0.0588440 0.998267i \(-0.518741\pi\)
−0.0588440 + 0.998267i \(0.518741\pi\)
\(54\) −452.096 −1.13930
\(55\) 1037.32 2.54314
\(56\) 167.734 0.400257
\(57\) 483.139 1.12269
\(58\) −449.741 −1.01817
\(59\) −560.180 −1.23609 −0.618044 0.786144i \(-0.712075\pi\)
−0.618044 + 0.786144i \(0.712075\pi\)
\(60\) 118.342 0.254631
\(61\) −749.990 −1.57420 −0.787102 0.616823i \(-0.788419\pi\)
−0.787102 + 0.616823i \(0.788419\pi\)
\(62\) −786.901 −1.61188
\(63\) −30.1635 −0.0603214
\(64\) 402.575 0.786279
\(65\) 111.894 0.213518
\(66\) −819.912 −1.52915
\(67\) 616.800 1.12469 0.562344 0.826903i \(-0.309900\pi\)
0.562344 + 0.826903i \(0.309900\pi\)
\(68\) 59.7129 0.106489
\(69\) −715.992 −1.24921
\(70\) 467.851 0.798841
\(71\) −696.830 −1.16477 −0.582384 0.812914i \(-0.697880\pi\)
−0.582384 + 0.812914i \(0.697880\pi\)
\(72\) −74.8779 −0.122562
\(73\) 948.852 1.52130 0.760649 0.649164i \(-0.224881\pi\)
0.760649 + 0.649164i \(0.224881\pi\)
\(74\) −416.265 −0.653917
\(75\) −1076.21 −1.65693
\(76\) −131.406 −0.198333
\(77\) −457.213 −0.676678
\(78\) −88.4419 −0.128386
\(79\) 818.112 1.16512 0.582562 0.812786i \(-0.302050\pi\)
0.582562 + 0.812786i \(0.302050\pi\)
\(80\) 1357.39 1.89702
\(81\) −616.458 −0.845622
\(82\) 419.134 0.564459
\(83\) −877.537 −1.16051 −0.580254 0.814435i \(-0.697047\pi\)
−0.580254 + 0.814435i \(0.697047\pi\)
\(84\) −52.1605 −0.0677520
\(85\) −847.684 −1.08170
\(86\) −783.366 −0.982239
\(87\) −711.808 −0.877171
\(88\) −1134.98 −1.37488
\(89\) −648.168 −0.771973 −0.385987 0.922504i \(-0.626139\pi\)
−0.385987 + 0.922504i \(0.626139\pi\)
\(90\) −208.853 −0.244611
\(91\) −49.3184 −0.0568129
\(92\) 194.738 0.220683
\(93\) −1245.43 −1.38866
\(94\) 338.268 0.371167
\(95\) 1865.44 2.01463
\(96\) −284.407 −0.302366
\(97\) 1688.84 1.76779 0.883893 0.467689i \(-0.154913\pi\)
0.883893 + 0.467689i \(0.154913\pi\)
\(98\) 840.570 0.866433
\(99\) 204.104 0.207204
\(100\) 292.711 0.292711
\(101\) 944.290 0.930300 0.465150 0.885232i \(-0.346000\pi\)
0.465150 + 0.885232i \(0.346000\pi\)
\(102\) 670.019 0.650409
\(103\) 170.504 0.163109 0.0815546 0.996669i \(-0.474011\pi\)
0.0815546 + 0.996669i \(0.474011\pi\)
\(104\) −122.428 −0.115433
\(105\) 740.470 0.688214
\(106\) 138.582 0.126984
\(107\) −672.500 −0.607598 −0.303799 0.952736i \(-0.598255\pi\)
−0.303799 + 0.952736i \(0.598255\pi\)
\(108\) 194.614 0.173395
\(109\) 501.855 0.441000 0.220500 0.975387i \(-0.429231\pi\)
0.220500 + 0.975387i \(0.429231\pi\)
\(110\) −3165.74 −2.74402
\(111\) −658.826 −0.563360
\(112\) −598.288 −0.504758
\(113\) −192.702 −0.160424 −0.0802119 0.996778i \(-0.525560\pi\)
−0.0802119 + 0.996778i \(0.525560\pi\)
\(114\) −1474.46 −1.21137
\(115\) −2764.50 −2.24166
\(116\) 193.600 0.154960
\(117\) 22.0162 0.0173965
\(118\) 1709.58 1.33372
\(119\) 373.627 0.287818
\(120\) 1838.14 1.39832
\(121\) 1762.76 1.32439
\(122\) 2288.85 1.69855
\(123\) 663.366 0.486290
\(124\) 338.737 0.245318
\(125\) −1824.11 −1.30523
\(126\) 92.0543 0.0650861
\(127\) −1496.60 −1.04569 −0.522843 0.852429i \(-0.675129\pi\)
−0.522843 + 0.852429i \(0.675129\pi\)
\(128\) −1699.65 −1.17366
\(129\) −1239.84 −0.846215
\(130\) −341.481 −0.230384
\(131\) −1312.54 −0.875395 −0.437698 0.899122i \(-0.644206\pi\)
−0.437698 + 0.899122i \(0.644206\pi\)
\(132\) 352.948 0.232728
\(133\) −822.213 −0.536052
\(134\) −1882.38 −1.21353
\(135\) −2762.74 −1.76132
\(136\) 927.490 0.584791
\(137\) −1937.32 −1.20815 −0.604075 0.796927i \(-0.706457\pi\)
−0.604075 + 0.796927i \(0.706457\pi\)
\(138\) 2185.09 1.34788
\(139\) −1823.83 −1.11292 −0.556459 0.830875i \(-0.687840\pi\)
−0.556459 + 0.830875i \(0.687840\pi\)
\(140\) −201.396 −0.121579
\(141\) 535.379 0.319766
\(142\) 2126.61 1.25677
\(143\) 333.717 0.195152
\(144\) 267.081 0.154561
\(145\) −2748.35 −1.57405
\(146\) −2895.74 −1.64146
\(147\) 1330.38 0.746446
\(148\) 179.190 0.0995223
\(149\) 1524.19 0.838029 0.419014 0.907980i \(-0.362376\pi\)
0.419014 + 0.907980i \(0.362376\pi\)
\(150\) 3284.41 1.78781
\(151\) 1475.07 0.794963 0.397481 0.917610i \(-0.369884\pi\)
0.397481 + 0.917610i \(0.369884\pi\)
\(152\) −2041.06 −1.08916
\(153\) −166.790 −0.0881320
\(154\) 1395.34 0.730128
\(155\) −4808.71 −2.49190
\(156\) 38.0716 0.0195395
\(157\) 515.159 0.261874 0.130937 0.991391i \(-0.458201\pi\)
0.130937 + 0.991391i \(0.458201\pi\)
\(158\) −2496.75 −1.25716
\(159\) 219.335 0.109399
\(160\) −1098.12 −0.542586
\(161\) 1218.49 0.596461
\(162\) 1881.33 0.912416
\(163\) 1038.96 0.499248 0.249624 0.968343i \(-0.419693\pi\)
0.249624 + 0.968343i \(0.419693\pi\)
\(164\) −180.425 −0.0859073
\(165\) −5010.44 −2.36402
\(166\) 2678.10 1.25217
\(167\) 2025.31 0.938461 0.469230 0.883076i \(-0.344531\pi\)
0.469230 + 0.883076i \(0.344531\pi\)
\(168\) −810.182 −0.372065
\(169\) −2161.00 −0.983615
\(170\) 2587.00 1.16714
\(171\) 367.043 0.164143
\(172\) 337.216 0.149491
\(173\) −804.840 −0.353704 −0.176852 0.984237i \(-0.556591\pi\)
−0.176852 + 0.984237i \(0.556591\pi\)
\(174\) 2172.32 0.946457
\(175\) 1831.51 0.791136
\(176\) 4048.36 1.73384
\(177\) 2705.76 1.14902
\(178\) 1978.10 0.832950
\(179\) 227.764 0.0951056 0.0475528 0.998869i \(-0.484858\pi\)
0.0475528 + 0.998869i \(0.484858\pi\)
\(180\) 89.9048 0.0372284
\(181\) 2185.27 0.897403 0.448702 0.893682i \(-0.351887\pi\)
0.448702 + 0.893682i \(0.351887\pi\)
\(182\) 150.512 0.0613005
\(183\) 3622.58 1.46333
\(184\) 3024.77 1.21190
\(185\) −2543.78 −1.01093
\(186\) 3800.86 1.49835
\(187\) −2528.17 −0.988654
\(188\) −145.614 −0.0564895
\(189\) 1217.71 0.468652
\(190\) −5693.01 −2.17376
\(191\) −3805.29 −1.44158 −0.720788 0.693155i \(-0.756220\pi\)
−0.720788 + 0.693155i \(0.756220\pi\)
\(192\) −1944.50 −0.730898
\(193\) 1405.60 0.524235 0.262118 0.965036i \(-0.415579\pi\)
0.262118 + 0.965036i \(0.415579\pi\)
\(194\) −5154.06 −1.90742
\(195\) −540.464 −0.198479
\(196\) −361.840 −0.131866
\(197\) 4167.91 1.50737 0.753684 0.657237i \(-0.228275\pi\)
0.753684 + 0.657237i \(0.228275\pi\)
\(198\) −622.892 −0.223571
\(199\) 253.726 0.0903829 0.0451914 0.998978i \(-0.485610\pi\)
0.0451914 + 0.998978i \(0.485610\pi\)
\(200\) 4546.52 1.60744
\(201\) −2979.25 −1.04547
\(202\) −2881.82 −1.00378
\(203\) 1211.37 0.418824
\(204\) −288.423 −0.0989885
\(205\) 2561.31 0.872632
\(206\) −520.351 −0.175993
\(207\) −543.943 −0.182641
\(208\) 436.687 0.145571
\(209\) 5563.57 1.84134
\(210\) −2259.80 −0.742575
\(211\) 252.781 0.0824746 0.0412373 0.999149i \(-0.486870\pi\)
0.0412373 + 0.999149i \(0.486870\pi\)
\(212\) −59.6555 −0.0193262
\(213\) 3365.80 1.08273
\(214\) 2052.36 0.655592
\(215\) −4787.12 −1.51850
\(216\) 3022.84 0.952213
\(217\) 2119.50 0.663045
\(218\) −1531.58 −0.475834
\(219\) −4583.11 −1.41415
\(220\) 1362.76 0.417623
\(221\) −272.708 −0.0830060
\(222\) 2010.63 0.607859
\(223\) 5253.04 1.57744 0.788721 0.614752i \(-0.210744\pi\)
0.788721 + 0.614752i \(0.210744\pi\)
\(224\) 484.008 0.144371
\(225\) −817.601 −0.242252
\(226\) 588.096 0.173095
\(227\) 3921.94 1.14673 0.573367 0.819299i \(-0.305637\pi\)
0.573367 + 0.819299i \(0.305637\pi\)
\(228\) 634.712 0.184363
\(229\) −3640.54 −1.05054 −0.525270 0.850935i \(-0.676036\pi\)
−0.525270 + 0.850935i \(0.676036\pi\)
\(230\) 8436.82 2.41873
\(231\) 2208.41 0.629017
\(232\) 3007.09 0.850971
\(233\) 4500.26 1.26533 0.632665 0.774426i \(-0.281961\pi\)
0.632665 + 0.774426i \(0.281961\pi\)
\(234\) −67.1898 −0.0187707
\(235\) 2067.14 0.573810
\(236\) −735.922 −0.202985
\(237\) −3951.62 −1.08306
\(238\) −1140.25 −0.310552
\(239\) 1935.90 0.523945 0.261973 0.965075i \(-0.415627\pi\)
0.261973 + 0.965075i \(0.415627\pi\)
\(240\) −6556.44 −1.76340
\(241\) −4055.79 −1.08405 −0.542025 0.840362i \(-0.682342\pi\)
−0.542025 + 0.840362i \(0.682342\pi\)
\(242\) −5379.67 −1.42900
\(243\) −1022.15 −0.269840
\(244\) −985.282 −0.258509
\(245\) 5136.69 1.33947
\(246\) −2024.49 −0.524701
\(247\) 600.129 0.154596
\(248\) 5261.43 1.34718
\(249\) 4238.65 1.07877
\(250\) 5566.90 1.40833
\(251\) −1701.68 −0.427924 −0.213962 0.976842i \(-0.568637\pi\)
−0.213962 + 0.976842i \(0.568637\pi\)
\(252\) −39.6266 −0.00990572
\(253\) −8244.98 −2.04884
\(254\) 4567.40 1.12828
\(255\) 4094.45 1.00551
\(256\) 1966.45 0.480089
\(257\) −6075.54 −1.47464 −0.737318 0.675546i \(-0.763908\pi\)
−0.737318 + 0.675546i \(0.763908\pi\)
\(258\) 3783.79 0.913056
\(259\) 1121.20 0.268988
\(260\) 146.997 0.0350631
\(261\) −540.765 −0.128247
\(262\) 4005.65 0.944541
\(263\) 1342.71 0.314810 0.157405 0.987534i \(-0.449687\pi\)
0.157405 + 0.987534i \(0.449687\pi\)
\(264\) 5482.16 1.27804
\(265\) 846.870 0.196312
\(266\) 2509.26 0.578394
\(267\) 3130.76 0.717600
\(268\) 810.306 0.184692
\(269\) 2680.07 0.607460 0.303730 0.952758i \(-0.401768\pi\)
0.303730 + 0.952758i \(0.401768\pi\)
\(270\) 8431.43 1.90045
\(271\) 4103.49 0.919814 0.459907 0.887967i \(-0.347883\pi\)
0.459907 + 0.887967i \(0.347883\pi\)
\(272\) −3308.25 −0.737472
\(273\) 238.216 0.0528113
\(274\) 5912.40 1.30358
\(275\) −12393.0 −2.71755
\(276\) −940.617 −0.205139
\(277\) 3269.10 0.709103 0.354551 0.935037i \(-0.384634\pi\)
0.354551 + 0.935037i \(0.384634\pi\)
\(278\) 5566.05 1.20082
\(279\) −946.162 −0.203030
\(280\) −3128.18 −0.667658
\(281\) −67.5547 −0.0143415 −0.00717077 0.999974i \(-0.502283\pi\)
−0.00717077 + 0.999974i \(0.502283\pi\)
\(282\) −1633.89 −0.345024
\(283\) −5255.14 −1.10384 −0.551918 0.833898i \(-0.686104\pi\)
−0.551918 + 0.833898i \(0.686104\pi\)
\(284\) −915.443 −0.191273
\(285\) −9010.37 −1.87273
\(286\) −1018.45 −0.210567
\(287\) −1128.93 −0.232190
\(288\) −216.066 −0.0442076
\(289\) −2847.02 −0.579487
\(290\) 8387.52 1.69839
\(291\) −8157.35 −1.64327
\(292\) 1246.53 0.249821
\(293\) −9962.56 −1.98641 −0.993207 0.116362i \(-0.962877\pi\)
−0.993207 + 0.116362i \(0.962877\pi\)
\(294\) −4060.09 −0.805406
\(295\) 10447.2 2.06189
\(296\) 2783.26 0.546534
\(297\) −8239.72 −1.60982
\(298\) −4651.57 −0.904223
\(299\) −889.366 −0.172018
\(300\) −1413.84 −0.272094
\(301\) 2109.98 0.404044
\(302\) −4501.67 −0.857756
\(303\) −4561.07 −0.864775
\(304\) 7280.23 1.37352
\(305\) 13987.1 2.62589
\(306\) 509.017 0.0950934
\(307\) −7118.59 −1.32339 −0.661693 0.749775i \(-0.730162\pi\)
−0.661693 + 0.749775i \(0.730162\pi\)
\(308\) −600.652 −0.111121
\(309\) −823.562 −0.151621
\(310\) 14675.4 2.68874
\(311\) 4458.54 0.812927 0.406464 0.913667i \(-0.366762\pi\)
0.406464 + 0.913667i \(0.366762\pi\)
\(312\) 591.347 0.107303
\(313\) −8251.00 −1.49001 −0.745006 0.667057i \(-0.767554\pi\)
−0.745006 + 0.667057i \(0.767554\pi\)
\(314\) −1572.18 −0.282559
\(315\) 562.539 0.100621
\(316\) 1074.77 0.191332
\(317\) 5399.17 0.956618 0.478309 0.878192i \(-0.341250\pi\)
0.478309 + 0.878192i \(0.341250\pi\)
\(318\) −669.375 −0.118040
\(319\) −8196.80 −1.43866
\(320\) −7507.88 −1.31157
\(321\) 3248.29 0.564803
\(322\) −3718.63 −0.643574
\(323\) −4546.46 −0.783194
\(324\) −809.857 −0.138864
\(325\) −1336.81 −0.228162
\(326\) −3170.73 −0.538683
\(327\) −2424.04 −0.409939
\(328\) −2802.44 −0.471766
\(329\) −911.117 −0.152679
\(330\) 15291.1 2.55074
\(331\) 5255.10 0.872649 0.436324 0.899789i \(-0.356280\pi\)
0.436324 + 0.899789i \(0.356280\pi\)
\(332\) −1152.84 −0.190574
\(333\) −500.514 −0.0823663
\(334\) −6180.91 −1.01259
\(335\) −11503.1 −1.87607
\(336\) 2889.83 0.469206
\(337\) −4542.20 −0.734212 −0.367106 0.930179i \(-0.619651\pi\)
−0.367106 + 0.930179i \(0.619651\pi\)
\(338\) 6595.03 1.06131
\(339\) 930.782 0.149124
\(340\) −1113.62 −0.177632
\(341\) −14341.7 −2.27756
\(342\) −1120.16 −0.177109
\(343\) −5083.53 −0.800248
\(344\) 5237.80 0.820940
\(345\) 13353.0 2.08377
\(346\) 2456.24 0.381643
\(347\) −12025.9 −1.86048 −0.930239 0.366954i \(-0.880401\pi\)
−0.930239 + 0.366954i \(0.880401\pi\)
\(348\) −935.121 −0.144045
\(349\) 5004.17 0.767527 0.383763 0.923431i \(-0.374628\pi\)
0.383763 + 0.923431i \(0.374628\pi\)
\(350\) −5589.46 −0.853627
\(351\) −888.798 −0.135158
\(352\) −3275.08 −0.495915
\(353\) 8368.90 1.26185 0.630923 0.775846i \(-0.282676\pi\)
0.630923 + 0.775846i \(0.282676\pi\)
\(354\) −8257.55 −1.23978
\(355\) 12995.6 1.94292
\(356\) −851.514 −0.126770
\(357\) −1804.68 −0.267546
\(358\) −695.100 −0.102618
\(359\) 7835.14 1.15187 0.575937 0.817494i \(-0.304637\pi\)
0.575937 + 0.817494i \(0.304637\pi\)
\(360\) 1396.45 0.204442
\(361\) 3146.06 0.458676
\(362\) −6669.10 −0.968288
\(363\) −8514.43 −1.23111
\(364\) −64.7909 −0.00932957
\(365\) −17695.8 −2.53764
\(366\) −11055.5 −1.57891
\(367\) −4026.77 −0.572741 −0.286370 0.958119i \(-0.592449\pi\)
−0.286370 + 0.958119i \(0.592449\pi\)
\(368\) −10789.0 −1.52830
\(369\) 503.963 0.0710983
\(370\) 7763.20 1.09078
\(371\) −373.268 −0.0522348
\(372\) −1636.16 −0.228040
\(373\) −2266.98 −0.314691 −0.157345 0.987544i \(-0.550294\pi\)
−0.157345 + 0.987544i \(0.550294\pi\)
\(374\) 7715.58 1.06675
\(375\) 8810.76 1.21330
\(376\) −2261.75 −0.310216
\(377\) −884.169 −0.120788
\(378\) −3716.25 −0.505670
\(379\) 5290.45 0.717024 0.358512 0.933525i \(-0.383284\pi\)
0.358512 + 0.933525i \(0.383284\pi\)
\(380\) 2450.67 0.330834
\(381\) 7228.85 0.972035
\(382\) 11613.1 1.55544
\(383\) 12087.6 1.61265 0.806327 0.591470i \(-0.201452\pi\)
0.806327 + 0.591470i \(0.201452\pi\)
\(384\) 8209.57 1.09100
\(385\) 8526.86 1.12875
\(386\) −4289.67 −0.565644
\(387\) −941.913 −0.123721
\(388\) 2218.67 0.290298
\(389\) −4255.95 −0.554717 −0.277359 0.960766i \(-0.589459\pi\)
−0.277359 + 0.960766i \(0.589459\pi\)
\(390\) 1649.41 0.214157
\(391\) 6737.67 0.871454
\(392\) −5620.28 −0.724151
\(393\) 6339.77 0.813738
\(394\) −12719.8 −1.62643
\(395\) −15257.5 −1.94352
\(396\) 268.136 0.0340262
\(397\) 13084.9 1.65418 0.827092 0.562066i \(-0.189994\pi\)
0.827092 + 0.562066i \(0.189994\pi\)
\(398\) −774.333 −0.0975221
\(399\) 3971.43 0.498296
\(400\) −16216.9 −2.02712
\(401\) −11455.7 −1.42661 −0.713305 0.700853i \(-0.752803\pi\)
−0.713305 + 0.700853i \(0.752803\pi\)
\(402\) 9092.18 1.12805
\(403\) −1547.01 −0.191221
\(404\) 1240.54 0.152770
\(405\) 11496.7 1.41056
\(406\) −3696.90 −0.451906
\(407\) −7586.68 −0.923975
\(408\) −4479.93 −0.543602
\(409\) 4971.40 0.601026 0.300513 0.953778i \(-0.402842\pi\)
0.300513 + 0.953778i \(0.402842\pi\)
\(410\) −7816.70 −0.941559
\(411\) 9357.58 1.12306
\(412\) 223.995 0.0267851
\(413\) −4604.71 −0.548627
\(414\) 1660.03 0.197067
\(415\) 16365.8 1.93582
\(416\) −353.275 −0.0416363
\(417\) 8809.41 1.03453
\(418\) −16979.1 −1.98678
\(419\) −1264.56 −0.147441 −0.0737205 0.997279i \(-0.523487\pi\)
−0.0737205 + 0.997279i \(0.523487\pi\)
\(420\) 972.774 0.113016
\(421\) 1666.53 0.192926 0.0964628 0.995337i \(-0.469247\pi\)
0.0964628 + 0.995337i \(0.469247\pi\)
\(422\) −771.446 −0.0889891
\(423\) 406.731 0.0467516
\(424\) −926.599 −0.106131
\(425\) 10127.4 1.15588
\(426\) −10271.9 −1.16825
\(427\) −6164.96 −0.698697
\(428\) −883.481 −0.0997772
\(429\) −1611.91 −0.181407
\(430\) 14609.5 1.63845
\(431\) −136.825 −0.0152915 −0.00764574 0.999971i \(-0.502434\pi\)
−0.00764574 + 0.999971i \(0.502434\pi\)
\(432\) −10782.1 −1.20082
\(433\) −13058.9 −1.44935 −0.724677 0.689089i \(-0.758011\pi\)
−0.724677 + 0.689089i \(0.758011\pi\)
\(434\) −6468.37 −0.715418
\(435\) 13275.0 1.46319
\(436\) 659.300 0.0724191
\(437\) −14827.1 −1.62306
\(438\) 13986.9 1.52585
\(439\) 17310.5 1.88197 0.940986 0.338447i \(-0.109901\pi\)
0.940986 + 0.338447i \(0.109901\pi\)
\(440\) 21167.0 2.29341
\(441\) 1010.69 0.109134
\(442\) 832.261 0.0895625
\(443\) −12017.3 −1.28885 −0.644425 0.764667i \(-0.722903\pi\)
−0.644425 + 0.764667i \(0.722903\pi\)
\(444\) −865.516 −0.0925126
\(445\) 12088.1 1.28771
\(446\) −16031.4 −1.70204
\(447\) −7362.07 −0.779003
\(448\) 3309.19 0.348983
\(449\) 6756.72 0.710177 0.355088 0.934833i \(-0.384451\pi\)
0.355088 + 0.934833i \(0.384451\pi\)
\(450\) 2495.19 0.261387
\(451\) 7638.97 0.797572
\(452\) −253.158 −0.0263441
\(453\) −7124.83 −0.738970
\(454\) −11969.1 −1.23731
\(455\) 919.771 0.0947682
\(456\) 9858.66 1.01244
\(457\) −7989.53 −0.817800 −0.408900 0.912579i \(-0.634088\pi\)
−0.408900 + 0.912579i \(0.634088\pi\)
\(458\) 11110.3 1.13352
\(459\) 6733.36 0.684720
\(460\) −3631.80 −0.368116
\(461\) −6899.96 −0.697100 −0.348550 0.937290i \(-0.613326\pi\)
−0.348550 + 0.937290i \(0.613326\pi\)
\(462\) −6739.72 −0.678702
\(463\) 1447.67 0.145311 0.0726557 0.997357i \(-0.476853\pi\)
0.0726557 + 0.997357i \(0.476853\pi\)
\(464\) −10726.0 −1.07315
\(465\) 23226.9 2.31639
\(466\) −13734.1 −1.36528
\(467\) 1188.56 0.117773 0.0588864 0.998265i \(-0.481245\pi\)
0.0588864 + 0.998265i \(0.481245\pi\)
\(468\) 28.9232 0.00285679
\(469\) 5070.13 0.499183
\(470\) −6308.58 −0.619135
\(471\) −2488.30 −0.243429
\(472\) −11430.7 −1.11471
\(473\) −14277.3 −1.38789
\(474\) 12059.7 1.16861
\(475\) −22286.6 −2.15280
\(476\) 490.843 0.0472642
\(477\) 166.630 0.0159947
\(478\) −5908.05 −0.565331
\(479\) 16089.0 1.53470 0.767352 0.641226i \(-0.221574\pi\)
0.767352 + 0.641226i \(0.221574\pi\)
\(480\) 5304.09 0.504370
\(481\) −818.357 −0.0775756
\(482\) 12377.6 1.16968
\(483\) −5885.49 −0.554450
\(484\) 2315.79 0.217486
\(485\) −31496.2 −2.94880
\(486\) 3119.45 0.291154
\(487\) 2465.14 0.229376 0.114688 0.993402i \(-0.463413\pi\)
0.114688 + 0.993402i \(0.463413\pi\)
\(488\) −15303.9 −1.41962
\(489\) −5018.34 −0.464084
\(490\) −15676.3 −1.44528
\(491\) 2884.85 0.265156 0.132578 0.991173i \(-0.457675\pi\)
0.132578 + 0.991173i \(0.457675\pi\)
\(492\) 871.481 0.0798565
\(493\) 6698.30 0.611919
\(494\) −1831.50 −0.166807
\(495\) −3806.46 −0.345632
\(496\) −18766.9 −1.69891
\(497\) −5727.98 −0.516972
\(498\) −12935.7 −1.16398
\(499\) −9012.81 −0.808555 −0.404277 0.914636i \(-0.632477\pi\)
−0.404277 + 0.914636i \(0.632477\pi\)
\(500\) −2396.38 −0.214339
\(501\) −9782.57 −0.872361
\(502\) 5193.25 0.461725
\(503\) 5366.33 0.475692 0.237846 0.971303i \(-0.423559\pi\)
0.237846 + 0.971303i \(0.423559\pi\)
\(504\) −615.500 −0.0543979
\(505\) −17610.7 −1.55181
\(506\) 25162.4 2.21068
\(507\) 10438.0 0.914335
\(508\) −1966.13 −0.171718
\(509\) −16598.5 −1.44541 −0.722705 0.691156i \(-0.757102\pi\)
−0.722705 + 0.691156i \(0.757102\pi\)
\(510\) −12495.6 −1.08493
\(511\) 7799.61 0.675214
\(512\) 7595.88 0.655652
\(513\) −14817.6 −1.27527
\(514\) 18541.6 1.59112
\(515\) −3179.84 −0.272078
\(516\) −1628.81 −0.138962
\(517\) 6165.14 0.524454
\(518\) −3421.72 −0.290235
\(519\) 3887.51 0.328791
\(520\) 2283.24 0.192551
\(521\) −10111.6 −0.850278 −0.425139 0.905128i \(-0.639775\pi\)
−0.425139 + 0.905128i \(0.639775\pi\)
\(522\) 1650.33 0.138377
\(523\) −14827.7 −1.23972 −0.619858 0.784714i \(-0.712810\pi\)
−0.619858 + 0.784714i \(0.712810\pi\)
\(524\) −1724.31 −0.143754
\(525\) −8846.48 −0.735413
\(526\) −4097.74 −0.339676
\(527\) 11719.8 0.968736
\(528\) −19554.2 −1.61172
\(529\) 9806.15 0.805963
\(530\) −2584.51 −0.211819
\(531\) 2055.58 0.167994
\(532\) −1080.16 −0.0880282
\(533\) 823.997 0.0669630
\(534\) −9554.57 −0.774282
\(535\) 12541.9 1.01352
\(536\) 12586.1 1.01425
\(537\) −1100.14 −0.0884069
\(538\) −8179.15 −0.655443
\(539\) 15319.9 1.22426
\(540\) −3629.48 −0.289237
\(541\) −12737.4 −1.01224 −0.506121 0.862463i \(-0.668921\pi\)
−0.506121 + 0.862463i \(0.668921\pi\)
\(542\) −12523.2 −0.992468
\(543\) −10555.2 −0.834195
\(544\) 2676.34 0.210932
\(545\) −9359.43 −0.735622
\(546\) −726.997 −0.0569828
\(547\) 547.000 0.0427569
\(548\) −2545.11 −0.198397
\(549\) 2752.09 0.213946
\(550\) 37821.5 2.93221
\(551\) −14740.5 −1.13968
\(552\) −14610.1 −1.12654
\(553\) 6724.93 0.517130
\(554\) −9976.78 −0.765113
\(555\) 12286.9 0.939727
\(556\) −2396.02 −0.182758
\(557\) 19395.6 1.47543 0.737716 0.675111i \(-0.235904\pi\)
0.737716 + 0.675111i \(0.235904\pi\)
\(558\) 2887.54 0.219067
\(559\) −1540.06 −0.116525
\(560\) 11157.9 0.841974
\(561\) 12211.5 0.919019
\(562\) 206.166 0.0154744
\(563\) −18180.4 −1.36094 −0.680472 0.732774i \(-0.738225\pi\)
−0.680472 + 0.732774i \(0.738225\pi\)
\(564\) 703.341 0.0525107
\(565\) 3593.82 0.267599
\(566\) 16037.9 1.19103
\(567\) −5067.32 −0.375322
\(568\) −14219.1 −1.05039
\(569\) −22011.7 −1.62176 −0.810878 0.585215i \(-0.801010\pi\)
−0.810878 + 0.585215i \(0.801010\pi\)
\(570\) 27498.2 2.02065
\(571\) −10392.7 −0.761683 −0.380841 0.924640i \(-0.624366\pi\)
−0.380841 + 0.924640i \(0.624366\pi\)
\(572\) 438.412 0.0320471
\(573\) 18380.2 1.34004
\(574\) 3445.30 0.250530
\(575\) 33027.8 2.39540
\(576\) −1477.25 −0.106861
\(577\) 7966.26 0.574766 0.287383 0.957816i \(-0.407215\pi\)
0.287383 + 0.957816i \(0.407215\pi\)
\(578\) 8688.64 0.625259
\(579\) −6789.29 −0.487311
\(580\) −3610.57 −0.258484
\(581\) −7213.40 −0.515081
\(582\) 24894.9 1.77307
\(583\) 2525.74 0.179427
\(584\) 19361.7 1.37191
\(585\) −410.594 −0.0290188
\(586\) 30404.2 2.14332
\(587\) 21271.0 1.49565 0.747826 0.663895i \(-0.231098\pi\)
0.747826 + 0.663895i \(0.231098\pi\)
\(588\) 1747.75 0.122578
\(589\) −25791.0 −1.80424
\(590\) −31883.0 −2.22475
\(591\) −20131.7 −1.40120
\(592\) −9927.59 −0.689226
\(593\) 13778.7 0.954169 0.477084 0.878857i \(-0.341694\pi\)
0.477084 + 0.878857i \(0.341694\pi\)
\(594\) 25146.3 1.73698
\(595\) −6968.01 −0.480102
\(596\) 2002.36 0.137617
\(597\) −1225.54 −0.0840168
\(598\) 2714.20 0.185605
\(599\) −19900.1 −1.35742 −0.678710 0.734406i \(-0.737461\pi\)
−0.678710 + 0.734406i \(0.737461\pi\)
\(600\) −21960.5 −1.49422
\(601\) 7290.25 0.494801 0.247401 0.968913i \(-0.420424\pi\)
0.247401 + 0.968913i \(0.420424\pi\)
\(602\) −6439.31 −0.435958
\(603\) −2263.35 −0.152854
\(604\) 1937.84 0.130545
\(605\) −32874.9 −2.20918
\(606\) 13919.7 0.933082
\(607\) −13667.6 −0.913920 −0.456960 0.889487i \(-0.651062\pi\)
−0.456960 + 0.889487i \(0.651062\pi\)
\(608\) −5889.63 −0.392855
\(609\) −5851.10 −0.389325
\(610\) −42686.3 −2.83331
\(611\) 665.019 0.0440324
\(612\) −219.117 −0.0144727
\(613\) −1155.72 −0.0761483 −0.0380742 0.999275i \(-0.512122\pi\)
−0.0380742 + 0.999275i \(0.512122\pi\)
\(614\) 21724.8 1.42792
\(615\) −12371.5 −0.811169
\(616\) −9329.62 −0.610229
\(617\) −15683.6 −1.02333 −0.511666 0.859184i \(-0.670972\pi\)
−0.511666 + 0.859184i \(0.670972\pi\)
\(618\) 2513.38 0.163597
\(619\) 17762.6 1.15337 0.576686 0.816966i \(-0.304345\pi\)
0.576686 + 0.816966i \(0.304345\pi\)
\(620\) −6317.33 −0.409210
\(621\) 21959.1 1.41898
\(622\) −13606.7 −0.877139
\(623\) −5327.97 −0.342634
\(624\) −2109.27 −0.135318
\(625\) 6167.88 0.394744
\(626\) 25180.7 1.60771
\(627\) −26872.9 −1.71165
\(628\) 676.778 0.0430038
\(629\) 6199.72 0.393003
\(630\) −1716.78 −0.108568
\(631\) −4371.92 −0.275821 −0.137911 0.990445i \(-0.544039\pi\)
−0.137911 + 0.990445i \(0.544039\pi\)
\(632\) 16693.9 1.05071
\(633\) −1220.97 −0.0766655
\(634\) −16477.4 −1.03218
\(635\) 27911.2 1.74428
\(636\) 288.146 0.0179650
\(637\) 1652.52 0.102787
\(638\) 25015.3 1.55230
\(639\) 2557.02 0.158301
\(640\) 31697.8 1.95776
\(641\) −31519.2 −1.94217 −0.971086 0.238730i \(-0.923269\pi\)
−0.971086 + 0.238730i \(0.923269\pi\)
\(642\) −9913.25 −0.609415
\(643\) 27118.7 1.66323 0.831616 0.555351i \(-0.187416\pi\)
0.831616 + 0.555351i \(0.187416\pi\)
\(644\) 1600.76 0.0979483
\(645\) 23122.6 1.41155
\(646\) 13875.1 0.845057
\(647\) 16554.6 1.00592 0.502958 0.864311i \(-0.332245\pi\)
0.502958 + 0.864311i \(0.332245\pi\)
\(648\) −12579.1 −0.762583
\(649\) 31158.1 1.88453
\(650\) 4079.71 0.246184
\(651\) −10237.5 −0.616344
\(652\) 1364.91 0.0819844
\(653\) 7929.54 0.475202 0.237601 0.971363i \(-0.423639\pi\)
0.237601 + 0.971363i \(0.423639\pi\)
\(654\) 7397.79 0.442319
\(655\) 24478.3 1.46023
\(656\) 9996.01 0.594937
\(657\) −3481.82 −0.206756
\(658\) 2780.58 0.164739
\(659\) 26012.3 1.53762 0.768812 0.639475i \(-0.220848\pi\)
0.768812 + 0.639475i \(0.220848\pi\)
\(660\) −6582.35 −0.388208
\(661\) −16667.3 −0.980763 −0.490381 0.871508i \(-0.663143\pi\)
−0.490381 + 0.871508i \(0.663143\pi\)
\(662\) −16037.7 −0.941578
\(663\) 1317.22 0.0771595
\(664\) −17906.5 −1.04655
\(665\) 15334.0 0.894176
\(666\) 1527.49 0.0888723
\(667\) 21844.8 1.26811
\(668\) 2660.70 0.154110
\(669\) −25373.0 −1.46634
\(670\) 35105.6 2.02425
\(671\) 41715.7 2.40002
\(672\) −2337.84 −0.134203
\(673\) −30293.2 −1.73509 −0.867545 0.497359i \(-0.834303\pi\)
−0.867545 + 0.497359i \(0.834303\pi\)
\(674\) 13862.1 0.792206
\(675\) 33006.7 1.88212
\(676\) −2838.96 −0.161525
\(677\) −19076.2 −1.08295 −0.541475 0.840717i \(-0.682134\pi\)
−0.541475 + 0.840717i \(0.682134\pi\)
\(678\) −2840.60 −0.160903
\(679\) 13882.3 0.784616
\(680\) −17297.4 −0.975476
\(681\) −18943.6 −1.06596
\(682\) 43768.7 2.45746
\(683\) 23158.5 1.29742 0.648709 0.761037i \(-0.275309\pi\)
0.648709 + 0.761037i \(0.275309\pi\)
\(684\) 482.194 0.0269549
\(685\) 36130.4 2.01529
\(686\) 15514.1 0.863458
\(687\) 17584.4 0.976546
\(688\) −18682.7 −1.03528
\(689\) 272.446 0.0150644
\(690\) −40751.2 −2.24837
\(691\) −29264.2 −1.61109 −0.805544 0.592536i \(-0.798127\pi\)
−0.805544 + 0.592536i \(0.798127\pi\)
\(692\) −1057.34 −0.0580838
\(693\) 1677.74 0.0919657
\(694\) 36701.2 2.00743
\(695\) 34013.8 1.85643
\(696\) −14524.8 −0.791034
\(697\) −6242.44 −0.339239
\(698\) −15271.9 −0.828152
\(699\) −21737.0 −1.17621
\(700\) 2406.10 0.129917
\(701\) 5862.34 0.315859 0.157930 0.987450i \(-0.449518\pi\)
0.157930 + 0.987450i \(0.449518\pi\)
\(702\) 2712.47 0.145834
\(703\) −13643.3 −0.731957
\(704\) −22391.9 −1.19876
\(705\) −9984.64 −0.533394
\(706\) −25540.5 −1.36152
\(707\) 7762.11 0.412906
\(708\) 3554.63 0.188688
\(709\) −5084.08 −0.269304 −0.134652 0.990893i \(-0.542992\pi\)
−0.134652 + 0.990893i \(0.542992\pi\)
\(710\) −39660.6 −2.09639
\(711\) −3002.07 −0.158349
\(712\) −13226.1 −0.696167
\(713\) 38221.2 2.00757
\(714\) 5507.59 0.288678
\(715\) −6223.70 −0.325529
\(716\) 299.220 0.0156178
\(717\) −9350.71 −0.487041
\(718\) −23911.6 −1.24286
\(719\) −18272.7 −0.947785 −0.473892 0.880583i \(-0.657151\pi\)
−0.473892 + 0.880583i \(0.657151\pi\)
\(720\) −4980.97 −0.257819
\(721\) 1401.55 0.0723946
\(722\) −9601.27 −0.494906
\(723\) 19590.1 1.00770
\(724\) 2870.85 0.147368
\(725\) 32834.8 1.68201
\(726\) 25984.7 1.32835
\(727\) −2173.44 −0.110878 −0.0554391 0.998462i \(-0.517656\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(728\) −1006.36 −0.0512340
\(729\) 21581.5 1.09646
\(730\) 54004.6 2.73808
\(731\) 11667.2 0.590324
\(732\) 4759.07 0.240301
\(733\) 2179.93 0.109846 0.0549232 0.998491i \(-0.482509\pi\)
0.0549232 + 0.998491i \(0.482509\pi\)
\(734\) 12289.1 0.617981
\(735\) −24811.0 −1.24513
\(736\) 8728.19 0.437127
\(737\) −34307.4 −1.71469
\(738\) −1538.01 −0.0767142
\(739\) 9515.50 0.473658 0.236829 0.971551i \(-0.423892\pi\)
0.236829 + 0.971551i \(0.423892\pi\)
\(740\) −3341.83 −0.166011
\(741\) −2898.72 −0.143707
\(742\) 1139.15 0.0563607
\(743\) 29655.3 1.46426 0.732131 0.681164i \(-0.238526\pi\)
0.732131 + 0.681164i \(0.238526\pi\)
\(744\) −25413.6 −1.25230
\(745\) −28425.6 −1.39789
\(746\) 6918.46 0.339548
\(747\) 3220.13 0.157722
\(748\) −3321.33 −0.162353
\(749\) −5527.99 −0.269677
\(750\) −26889.0 −1.30913
\(751\) −2484.36 −0.120713 −0.0603565 0.998177i \(-0.519224\pi\)
−0.0603565 + 0.998177i \(0.519224\pi\)
\(752\) 8067.43 0.391208
\(753\) 8219.39 0.397784
\(754\) 2698.34 0.130329
\(755\) −27509.5 −1.32606
\(756\) 1599.74 0.0769601
\(757\) 511.317 0.0245497 0.0122749 0.999925i \(-0.496093\pi\)
0.0122749 + 0.999925i \(0.496093\pi\)
\(758\) −16145.6 −0.773660
\(759\) 39824.6 1.90453
\(760\) 38065.1 1.81680
\(761\) −2959.68 −0.140984 −0.0704918 0.997512i \(-0.522457\pi\)
−0.0704918 + 0.997512i \(0.522457\pi\)
\(762\) −22061.3 −1.04881
\(763\) 4125.28 0.195734
\(764\) −4999.11 −0.236730
\(765\) 3110.58 0.147011
\(766\) −36889.4 −1.74004
\(767\) 3360.95 0.158223
\(768\) −9498.26 −0.446274
\(769\) −16105.0 −0.755217 −0.377609 0.925965i \(-0.623254\pi\)
−0.377609 + 0.925965i \(0.623254\pi\)
\(770\) −26022.6 −1.21791
\(771\) 29345.8 1.37077
\(772\) 1846.57 0.0860877
\(773\) −1944.13 −0.0904598 −0.0452299 0.998977i \(-0.514402\pi\)
−0.0452299 + 0.998977i \(0.514402\pi\)
\(774\) 2874.57 0.133494
\(775\) 57450.2 2.66280
\(776\) 34461.4 1.59419
\(777\) −5415.58 −0.250042
\(778\) 12988.5 0.598533
\(779\) 13737.3 0.631822
\(780\) −710.022 −0.0325934
\(781\) 38758.8 1.77580
\(782\) −20562.3 −0.940288
\(783\) 21830.8 0.996385
\(784\) 20046.9 0.913216
\(785\) −9607.54 −0.436825
\(786\) −19347.9 −0.878013
\(787\) −26798.1 −1.21378 −0.606892 0.794784i \(-0.707584\pi\)
−0.606892 + 0.794784i \(0.707584\pi\)
\(788\) 5475.49 0.247533
\(789\) −6485.51 −0.292637
\(790\) 46563.5 2.09703
\(791\) −1584.02 −0.0712027
\(792\) 4164.83 0.186857
\(793\) 4499.77 0.201502
\(794\) −39932.9 −1.78485
\(795\) −4090.52 −0.182485
\(796\) 333.327 0.0148423
\(797\) −39080.3 −1.73688 −0.868440 0.495794i \(-0.834877\pi\)
−0.868440 + 0.495794i \(0.834877\pi\)
\(798\) −12120.2 −0.537655
\(799\) −5038.05 −0.223071
\(800\) 13119.3 0.579798
\(801\) 2378.45 0.104917
\(802\) 34961.0 1.53930
\(803\) −52776.6 −2.31936
\(804\) −3913.91 −0.171683
\(805\) −22724.4 −0.994942
\(806\) 4721.22 0.206325
\(807\) −12945.2 −0.564674
\(808\) 19268.6 0.838946
\(809\) −18829.3 −0.818299 −0.409149 0.912467i \(-0.634175\pi\)
−0.409149 + 0.912467i \(0.634175\pi\)
\(810\) −35086.2 −1.52198
\(811\) −43802.1 −1.89655 −0.948274 0.317454i \(-0.897172\pi\)
−0.948274 + 0.317454i \(0.897172\pi\)
\(812\) 1591.40 0.0687775
\(813\) −19820.6 −0.855027
\(814\) 23153.3 0.996959
\(815\) −19376.2 −0.832784
\(816\) 15979.4 0.685529
\(817\) −25675.2 −1.09946
\(818\) −15171.9 −0.648500
\(819\) 180.974 0.00772131
\(820\) 3364.86 0.143300
\(821\) −22524.8 −0.957516 −0.478758 0.877947i \(-0.658913\pi\)
−0.478758 + 0.877947i \(0.658913\pi\)
\(822\) −28557.8 −1.21176
\(823\) 3043.19 0.128893 0.0644466 0.997921i \(-0.479472\pi\)
0.0644466 + 0.997921i \(0.479472\pi\)
\(824\) 3479.21 0.147092
\(825\) 59860.3 2.52614
\(826\) 14052.8 0.591962
\(827\) 28785.8 1.21037 0.605187 0.796083i \(-0.293098\pi\)
0.605187 + 0.796083i \(0.293098\pi\)
\(828\) −714.592 −0.0299925
\(829\) −18463.9 −0.773557 −0.386778 0.922173i \(-0.626412\pi\)
−0.386778 + 0.922173i \(0.626412\pi\)
\(830\) −49945.7 −2.08872
\(831\) −15790.3 −0.659157
\(832\) −2415.36 −0.100646
\(833\) −12519.2 −0.520725
\(834\) −26884.9 −1.11625
\(835\) −37771.3 −1.56542
\(836\) 7309.00 0.302377
\(837\) 38196.8 1.57739
\(838\) 3859.23 0.159087
\(839\) −38615.0 −1.58896 −0.794479 0.607291i \(-0.792256\pi\)
−0.794479 + 0.607291i \(0.792256\pi\)
\(840\) 15109.6 0.620632
\(841\) −2671.89 −0.109553
\(842\) −5085.98 −0.208165
\(843\) 326.300 0.0133314
\(844\) 332.084 0.0135436
\(845\) 40301.9 1.64074
\(846\) −1241.28 −0.0504444
\(847\) 14490.0 0.587819
\(848\) 3305.08 0.133841
\(849\) 25383.2 1.02609
\(850\) −30907.1 −1.24718
\(851\) 20218.8 0.814442
\(852\) 4421.74 0.177801
\(853\) −7435.50 −0.298460 −0.149230 0.988803i \(-0.547680\pi\)
−0.149230 + 0.988803i \(0.547680\pi\)
\(854\) 18814.5 0.753885
\(855\) −6845.23 −0.273803
\(856\) −13722.7 −0.547933
\(857\) −43195.0 −1.72172 −0.860859 0.508843i \(-0.830073\pi\)
−0.860859 + 0.508843i \(0.830073\pi\)
\(858\) 4919.28 0.195736
\(859\) 32407.2 1.28722 0.643609 0.765354i \(-0.277436\pi\)
0.643609 + 0.765354i \(0.277436\pi\)
\(860\) −6288.96 −0.249362
\(861\) 5452.90 0.215836
\(862\) 417.568 0.0164993
\(863\) 15662.3 0.617788 0.308894 0.951096i \(-0.400041\pi\)
0.308894 + 0.951096i \(0.400041\pi\)
\(864\) 8722.62 0.343460
\(865\) 15010.0 0.590006
\(866\) 39853.6 1.56384
\(867\) 13751.6 0.538671
\(868\) 2784.44 0.108882
\(869\) −45504.7 −1.77634
\(870\) −40513.1 −1.57876
\(871\) −3700.66 −0.143963
\(872\) 10240.6 0.397695
\(873\) −6197.19 −0.240256
\(874\) 45249.9 1.75126
\(875\) −14994.3 −0.579314
\(876\) −6020.95 −0.232225
\(877\) −12540.9 −0.482870 −0.241435 0.970417i \(-0.577618\pi\)
−0.241435 + 0.970417i \(0.577618\pi\)
\(878\) −52828.9 −2.03062
\(879\) 48120.8 1.84650
\(880\) −75500.5 −2.89218
\(881\) 20257.0 0.774660 0.387330 0.921941i \(-0.373397\pi\)
0.387330 + 0.921941i \(0.373397\pi\)
\(882\) −3084.48 −0.117755
\(883\) 11721.6 0.446730 0.223365 0.974735i \(-0.428296\pi\)
0.223365 + 0.974735i \(0.428296\pi\)
\(884\) −358.263 −0.0136309
\(885\) −50461.5 −1.91666
\(886\) 36675.0 1.39065
\(887\) −26633.4 −1.00819 −0.504094 0.863649i \(-0.668173\pi\)
−0.504094 + 0.863649i \(0.668173\pi\)
\(888\) −13443.6 −0.508039
\(889\) −12302.2 −0.464119
\(890\) −36890.9 −1.38942
\(891\) 34288.4 1.28923
\(892\) 6901.05 0.259041
\(893\) 11086.9 0.415463
\(894\) 22467.9 0.840535
\(895\) −4247.73 −0.158643
\(896\) −13971.2 −0.520920
\(897\) 4295.78 0.159902
\(898\) −20620.4 −0.766272
\(899\) 37997.9 1.40968
\(900\) −1074.10 −0.0397816
\(901\) −2064.00 −0.0763171
\(902\) −23312.9 −0.860571
\(903\) −10191.5 −0.375585
\(904\) −3932.17 −0.144670
\(905\) −40754.6 −1.49694
\(906\) 21743.8 0.797340
\(907\) 52864.8 1.93533 0.967666 0.252236i \(-0.0811658\pi\)
0.967666 + 0.252236i \(0.0811658\pi\)
\(908\) 5152.36 0.188312
\(909\) −3465.08 −0.126435
\(910\) −2806.99 −0.102254
\(911\) −24823.0 −0.902770 −0.451385 0.892329i \(-0.649070\pi\)
−0.451385 + 0.892329i \(0.649070\pi\)
\(912\) −35164.7 −1.27678
\(913\) 48810.0 1.76930
\(914\) 24382.8 0.882397
\(915\) −67559.8 −2.44094
\(916\) −4782.67 −0.172515
\(917\) −10789.1 −0.388537
\(918\) −20549.1 −0.738805
\(919\) 10573.4 0.379525 0.189763 0.981830i \(-0.439228\pi\)
0.189763 + 0.981830i \(0.439228\pi\)
\(920\) −56410.9 −2.02153
\(921\) 34384.0 1.23017
\(922\) 21057.6 0.752163
\(923\) 4180.82 0.149093
\(924\) 2901.25 0.103294
\(925\) 30390.8 1.08026
\(926\) −4418.07 −0.156789
\(927\) −625.665 −0.0221678
\(928\) 8677.19 0.306943
\(929\) 27281.3 0.963477 0.481738 0.876315i \(-0.340006\pi\)
0.481738 + 0.876315i \(0.340006\pi\)
\(930\) −70884.7 −2.49936
\(931\) 27550.0 0.969835
\(932\) 5912.10 0.207787
\(933\) −21535.5 −0.755669
\(934\) −3627.29 −0.127075
\(935\) 47149.5 1.64915
\(936\) 449.250 0.0156882
\(937\) −31556.2 −1.10021 −0.550104 0.835096i \(-0.685412\pi\)
−0.550104 + 0.835096i \(0.685412\pi\)
\(938\) −15473.2 −0.538613
\(939\) 39853.7 1.38506
\(940\) 2715.66 0.0942287
\(941\) −44188.2 −1.53081 −0.765405 0.643548i \(-0.777461\pi\)
−0.765405 + 0.643548i \(0.777461\pi\)
\(942\) 7593.90 0.262657
\(943\) −20358.1 −0.703023
\(944\) 40772.1 1.40574
\(945\) −22709.8 −0.781747
\(946\) 43572.1 1.49752
\(947\) 3137.42 0.107658 0.0538292 0.998550i \(-0.482857\pi\)
0.0538292 + 0.998550i \(0.482857\pi\)
\(948\) −5191.34 −0.177855
\(949\) −5692.89 −0.194730
\(950\) 68015.1 2.32284
\(951\) −26078.9 −0.889239
\(952\) 7624.02 0.259554
\(953\) 11820.9 0.401800 0.200900 0.979612i \(-0.435613\pi\)
0.200900 + 0.979612i \(0.435613\pi\)
\(954\) −508.528 −0.0172581
\(955\) 70967.3 2.40466
\(956\) 2543.24 0.0860400
\(957\) 39591.9 1.33733
\(958\) −49100.9 −1.65593
\(959\) −15924.9 −0.536227
\(960\) 36264.3 1.21919
\(961\) 36692.9 1.23168
\(962\) 2497.50 0.0837032
\(963\) 2467.74 0.0825772
\(964\) −5328.19 −0.178018
\(965\) −26214.0 −0.874464
\(966\) 17961.6 0.598245
\(967\) 37853.2 1.25882 0.629409 0.777074i \(-0.283297\pi\)
0.629409 + 0.777074i \(0.283297\pi\)
\(968\) 35969.9 1.19434
\(969\) 21960.1 0.728030
\(970\) 96121.3 3.18172
\(971\) 20469.5 0.676515 0.338258 0.941054i \(-0.390162\pi\)
0.338258 + 0.941054i \(0.390162\pi\)
\(972\) −1342.83 −0.0443120
\(973\) −14992.0 −0.493959
\(974\) −7523.21 −0.247494
\(975\) 6456.99 0.212091
\(976\) 54587.2 1.79026
\(977\) 40696.2 1.33264 0.666318 0.745667i \(-0.267869\pi\)
0.666318 + 0.745667i \(0.267869\pi\)
\(978\) 15315.2 0.500741
\(979\) 36052.1 1.17695
\(980\) 6748.20 0.219962
\(981\) −1841.56 −0.0599353
\(982\) −8804.10 −0.286100
\(983\) −44630.9 −1.44812 −0.724062 0.689735i \(-0.757727\pi\)
−0.724062 + 0.689735i \(0.757727\pi\)
\(984\) 13536.3 0.438537
\(985\) −77730.1 −2.51440
\(986\) −20442.1 −0.660253
\(987\) 4400.85 0.141926
\(988\) 788.404 0.0253871
\(989\) 38049.5 1.22336
\(990\) 11616.7 0.372933
\(991\) 31116.3 0.997417 0.498709 0.866770i \(-0.333808\pi\)
0.498709 + 0.866770i \(0.333808\pi\)
\(992\) 15182.3 0.485924
\(993\) −25383.0 −0.811184
\(994\) 17480.9 0.557806
\(995\) −4731.91 −0.150765
\(996\) 5568.42 0.177151
\(997\) −16605.9 −0.527497 −0.263748 0.964592i \(-0.584959\pi\)
−0.263748 + 0.964592i \(0.584959\pi\)
\(998\) 27505.7 0.872421
\(999\) 20205.9 0.639925
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 547.4.a.a.1.20 65
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.4.a.a.1.20 65 1.1 even 1 trivial