Properties

Label 289.4.a.h.1.12
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $1$
Dimension $12$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [289,4,Mod(1,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, 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("289.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 289.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: \(17.0515519917\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{3}\cdot 17^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-4.44354\) of defining polynomial
Character \(\chi\) \(=\) 289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.44354 q^{2} -0.537336 q^{3} +11.7450 q^{4} -17.2592 q^{5} -2.38767 q^{6} +6.40763 q^{7} +16.6411 q^{8} -26.7113 q^{9} +O(q^{10})\) \(q+4.44354 q^{2} -0.537336 q^{3} +11.7450 q^{4} -17.2592 q^{5} -2.38767 q^{6} +6.40763 q^{7} +16.6411 q^{8} -26.7113 q^{9} -76.6918 q^{10} -55.3227 q^{11} -6.31102 q^{12} +58.6637 q^{13} +28.4725 q^{14} +9.27398 q^{15} -20.0149 q^{16} -118.692 q^{18} -91.1866 q^{19} -202.709 q^{20} -3.44305 q^{21} -245.829 q^{22} -120.879 q^{23} -8.94185 q^{24} +172.879 q^{25} +260.674 q^{26} +28.8610 q^{27} +75.2576 q^{28} +215.755 q^{29} +41.2093 q^{30} +17.5166 q^{31} -222.065 q^{32} +29.7269 q^{33} -110.590 q^{35} -313.724 q^{36} +8.40485 q^{37} -405.191 q^{38} -31.5221 q^{39} -287.211 q^{40} -99.9530 q^{41} -15.2993 q^{42} -81.5297 q^{43} -649.766 q^{44} +461.015 q^{45} -537.130 q^{46} +195.351 q^{47} +10.7547 q^{48} -301.942 q^{49} +768.195 q^{50} +689.006 q^{52} +260.322 q^{53} +128.245 q^{54} +954.825 q^{55} +106.630 q^{56} +48.9979 q^{57} +958.715 q^{58} -536.401 q^{59} +108.923 q^{60} +265.689 q^{61} +77.8357 q^{62} -171.156 q^{63} -826.636 q^{64} -1012.49 q^{65} +132.093 q^{66} +514.794 q^{67} +64.9526 q^{69} -491.412 q^{70} +704.023 q^{71} -444.504 q^{72} -184.948 q^{73} +37.3473 q^{74} -92.8943 q^{75} -1070.99 q^{76} -354.487 q^{77} -140.070 q^{78} +34.8358 q^{79} +345.440 q^{80} +705.696 q^{81} -444.145 q^{82} -647.682 q^{83} -40.4386 q^{84} -362.280 q^{86} -115.933 q^{87} -920.630 q^{88} -1060.24 q^{89} +2048.53 q^{90} +375.895 q^{91} -1419.72 q^{92} -9.41231 q^{93} +868.051 q^{94} +1573.81 q^{95} +119.324 q^{96} +256.409 q^{97} -1341.69 q^{98} +1477.74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9} - 60 q^{10} - 162 q^{11} - 216 q^{12} - 72 q^{13} - 267 q^{14} - 138 q^{15} + 192 q^{16} + 189 q^{18} - 66 q^{19} - 129 q^{20} + 246 q^{21} - 456 q^{22} - 282 q^{23} - 72 q^{24} + 444 q^{25} + 528 q^{26} - 1092 q^{27} - 120 q^{28} - 648 q^{29} - 1890 q^{30} - 504 q^{31} - 1353 q^{32} + 966 q^{33} - 66 q^{35} - 663 q^{36} + 30 q^{37} - 60 q^{38} - 1758 q^{39} + 450 q^{40} - 318 q^{41} + 804 q^{42} + 486 q^{43} - 2448 q^{44} - 486 q^{45} - 1617 q^{46} - 888 q^{47} - 1257 q^{48} - 570 q^{49} + 435 q^{50} + 225 q^{52} + 1026 q^{53} - 933 q^{54} + 972 q^{55} - 2661 q^{56} + 156 q^{57} - 201 q^{58} - 792 q^{59} + 1458 q^{60} - 1212 q^{61} - 2817 q^{62} - 2112 q^{63} - 1857 q^{64} - 2742 q^{65} - 594 q^{66} + 624 q^{67} - 1506 q^{69} - 1650 q^{70} - 2802 q^{71} + 1455 q^{72} - 726 q^{73} - 270 q^{74} + 264 q^{75} + 675 q^{76} - 1008 q^{77} + 3090 q^{78} + 444 q^{79} + 1143 q^{80} + 2520 q^{81} + 4950 q^{82} + 672 q^{83} - 777 q^{84} + 2778 q^{86} + 726 q^{87} + 3750 q^{88} - 906 q^{89} + 7755 q^{90} - 2280 q^{91} - 87 q^{92} + 132 q^{93} + 735 q^{94} - 966 q^{95} + 5046 q^{96} + 3246 q^{97} + 1911 q^{98} + 282 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.44354 1.57103 0.785514 0.618844i \(-0.212399\pi\)
0.785514 + 0.618844i \(0.212399\pi\)
\(3\) −0.537336 −0.103410 −0.0517052 0.998662i \(-0.516466\pi\)
−0.0517052 + 0.998662i \(0.516466\pi\)
\(4\) 11.7450 1.46813
\(5\) −17.2592 −1.54371 −0.771854 0.635800i \(-0.780670\pi\)
−0.771854 + 0.635800i \(0.780670\pi\)
\(6\) −2.38767 −0.162461
\(7\) 6.40763 0.345979 0.172990 0.984924i \(-0.444657\pi\)
0.172990 + 0.984924i \(0.444657\pi\)
\(8\) 16.6411 0.735439
\(9\) −26.7113 −0.989306
\(10\) −76.6918 −2.42521
\(11\) −55.3227 −1.51640 −0.758201 0.652020i \(-0.773922\pi\)
−0.758201 + 0.652020i \(0.773922\pi\)
\(12\) −6.31102 −0.151819
\(13\) 58.6637 1.25157 0.625784 0.779996i \(-0.284779\pi\)
0.625784 + 0.779996i \(0.284779\pi\)
\(14\) 28.4725 0.543543
\(15\) 9.27398 0.159635
\(16\) −20.0149 −0.312732
\(17\) 0 0
\(18\) −118.692 −1.55423
\(19\) −91.1866 −1.10103 −0.550517 0.834824i \(-0.685569\pi\)
−0.550517 + 0.834824i \(0.685569\pi\)
\(20\) −202.709 −2.26636
\(21\) −3.44305 −0.0357779
\(22\) −245.829 −2.38231
\(23\) −120.879 −1.09587 −0.547935 0.836521i \(-0.684586\pi\)
−0.547935 + 0.836521i \(0.684586\pi\)
\(24\) −8.94185 −0.0760520
\(25\) 172.879 1.38303
\(26\) 260.674 1.96625
\(27\) 28.8610 0.205715
\(28\) 75.2576 0.507941
\(29\) 215.755 1.38154 0.690771 0.723074i \(-0.257271\pi\)
0.690771 + 0.723074i \(0.257271\pi\)
\(30\) 41.2093 0.250792
\(31\) 17.5166 0.101486 0.0507432 0.998712i \(-0.483841\pi\)
0.0507432 + 0.998712i \(0.483841\pi\)
\(32\) −222.065 −1.22675
\(33\) 29.7269 0.156812
\(34\) 0 0
\(35\) −110.590 −0.534091
\(36\) −313.724 −1.45243
\(37\) 8.40485 0.0373446 0.0186723 0.999826i \(-0.494056\pi\)
0.0186723 + 0.999826i \(0.494056\pi\)
\(38\) −405.191 −1.72975
\(39\) −31.5221 −0.129425
\(40\) −287.211 −1.13530
\(41\) −99.9530 −0.380733 −0.190366 0.981713i \(-0.560968\pi\)
−0.190366 + 0.981713i \(0.560968\pi\)
\(42\) −15.2993 −0.0562080
\(43\) −81.5297 −0.289143 −0.144572 0.989494i \(-0.546180\pi\)
−0.144572 + 0.989494i \(0.546180\pi\)
\(44\) −649.766 −2.22627
\(45\) 461.015 1.52720
\(46\) −537.130 −1.72164
\(47\) 195.351 0.606275 0.303137 0.952947i \(-0.401966\pi\)
0.303137 + 0.952947i \(0.401966\pi\)
\(48\) 10.7547 0.0323398
\(49\) −301.942 −0.880298
\(50\) 768.195 2.17278
\(51\) 0 0
\(52\) 689.006 1.83746
\(53\) 260.322 0.674678 0.337339 0.941383i \(-0.390473\pi\)
0.337339 + 0.941383i \(0.390473\pi\)
\(54\) 128.245 0.323184
\(55\) 954.825 2.34088
\(56\) 106.630 0.254447
\(57\) 48.9979 0.113858
\(58\) 958.715 2.17044
\(59\) −536.401 −1.18362 −0.591809 0.806078i \(-0.701586\pi\)
−0.591809 + 0.806078i \(0.701586\pi\)
\(60\) 108.923 0.234365
\(61\) 265.689 0.557671 0.278836 0.960339i \(-0.410052\pi\)
0.278836 + 0.960339i \(0.410052\pi\)
\(62\) 77.8357 0.159438
\(63\) −171.156 −0.342280
\(64\) −826.636 −1.61452
\(65\) −1012.49 −1.93206
\(66\) 132.093 0.246356
\(67\) 514.794 0.938687 0.469344 0.883016i \(-0.344491\pi\)
0.469344 + 0.883016i \(0.344491\pi\)
\(68\) 0 0
\(69\) 64.9526 0.113324
\(70\) −491.412 −0.839071
\(71\) 704.023 1.17679 0.588396 0.808573i \(-0.299760\pi\)
0.588396 + 0.808573i \(0.299760\pi\)
\(72\) −444.504 −0.727574
\(73\) −184.948 −0.296528 −0.148264 0.988948i \(-0.547368\pi\)
−0.148264 + 0.988948i \(0.547368\pi\)
\(74\) 37.3473 0.0586693
\(75\) −92.8943 −0.143020
\(76\) −1070.99 −1.61646
\(77\) −354.487 −0.524644
\(78\) −140.070 −0.203330
\(79\) 34.8358 0.0496118 0.0248059 0.999692i \(-0.492103\pi\)
0.0248059 + 0.999692i \(0.492103\pi\)
\(80\) 345.440 0.482767
\(81\) 705.696 0.968033
\(82\) −444.145 −0.598141
\(83\) −647.682 −0.856534 −0.428267 0.903652i \(-0.640876\pi\)
−0.428267 + 0.903652i \(0.640876\pi\)
\(84\) −40.4386 −0.0525264
\(85\) 0 0
\(86\) −362.280 −0.454252
\(87\) −115.933 −0.142866
\(88\) −920.630 −1.11522
\(89\) −1060.24 −1.26275 −0.631377 0.775476i \(-0.717510\pi\)
−0.631377 + 0.775476i \(0.717510\pi\)
\(90\) 2048.53 2.39927
\(91\) 375.895 0.433017
\(92\) −1419.72 −1.60887
\(93\) −9.41231 −0.0104947
\(94\) 868.051 0.952474
\(95\) 1573.81 1.69967
\(96\) 119.324 0.126859
\(97\) 256.409 0.268395 0.134198 0.990955i \(-0.457154\pi\)
0.134198 + 0.990955i \(0.457154\pi\)
\(98\) −1341.69 −1.38297
\(99\) 1477.74 1.50019
\(100\) 2030.47 2.03047
\(101\) −1465.07 −1.44337 −0.721685 0.692222i \(-0.756632\pi\)
−0.721685 + 0.692222i \(0.756632\pi\)
\(102\) 0 0
\(103\) −25.6805 −0.0245668 −0.0122834 0.999925i \(-0.503910\pi\)
−0.0122834 + 0.999925i \(0.503910\pi\)
\(104\) 976.227 0.920452
\(105\) 59.4242 0.0552306
\(106\) 1156.75 1.05994
\(107\) −2030.70 −1.83472 −0.917359 0.398060i \(-0.869683\pi\)
−0.917359 + 0.398060i \(0.869683\pi\)
\(108\) 338.973 0.302015
\(109\) 716.479 0.629598 0.314799 0.949158i \(-0.398063\pi\)
0.314799 + 0.949158i \(0.398063\pi\)
\(110\) 4242.80 3.67759
\(111\) −4.51623 −0.00386182
\(112\) −128.248 −0.108199
\(113\) −16.9632 −0.0141218 −0.00706090 0.999975i \(-0.502248\pi\)
−0.00706090 + 0.999975i \(0.502248\pi\)
\(114\) 217.724 0.178875
\(115\) 2086.27 1.69170
\(116\) 2534.05 2.02828
\(117\) −1566.98 −1.23818
\(118\) −2383.52 −1.85950
\(119\) 0 0
\(120\) 154.329 0.117402
\(121\) 1729.60 1.29948
\(122\) 1180.60 0.876117
\(123\) 53.7084 0.0393717
\(124\) 205.733 0.148995
\(125\) −826.356 −0.591292
\(126\) −760.537 −0.537730
\(127\) −1138.85 −0.795724 −0.397862 0.917445i \(-0.630248\pi\)
−0.397862 + 0.917445i \(0.630248\pi\)
\(128\) −1896.67 −1.30971
\(129\) 43.8089 0.0299004
\(130\) −4499.02 −3.03531
\(131\) 618.036 0.412199 0.206100 0.978531i \(-0.433923\pi\)
0.206100 + 0.978531i \(0.433923\pi\)
\(132\) 349.143 0.230219
\(133\) −584.290 −0.380935
\(134\) 2287.50 1.47470
\(135\) −498.117 −0.317564
\(136\) 0 0
\(137\) −2255.17 −1.40637 −0.703183 0.711009i \(-0.748238\pi\)
−0.703183 + 0.711009i \(0.748238\pi\)
\(138\) 288.619 0.178036
\(139\) −1014.29 −0.618930 −0.309465 0.950911i \(-0.600150\pi\)
−0.309465 + 0.950911i \(0.600150\pi\)
\(140\) −1298.88 −0.784113
\(141\) −104.969 −0.0626951
\(142\) 3128.35 1.84877
\(143\) −3245.44 −1.89788
\(144\) 534.622 0.309388
\(145\) −3723.76 −2.13270
\(146\) −821.822 −0.465853
\(147\) 162.245 0.0910320
\(148\) 98.7150 0.0548265
\(149\) −345.080 −0.189732 −0.0948661 0.995490i \(-0.530242\pi\)
−0.0948661 + 0.995490i \(0.530242\pi\)
\(150\) −412.779 −0.224688
\(151\) 2555.94 1.37748 0.688741 0.725007i \(-0.258164\pi\)
0.688741 + 0.725007i \(0.258164\pi\)
\(152\) −1517.44 −0.809743
\(153\) 0 0
\(154\) −1575.18 −0.824230
\(155\) −302.322 −0.156665
\(156\) −370.228 −0.190012
\(157\) 3651.08 1.85598 0.927988 0.372610i \(-0.121537\pi\)
0.927988 + 0.372610i \(0.121537\pi\)
\(158\) 154.794 0.0779415
\(159\) −139.880 −0.0697688
\(160\) 3832.66 1.89374
\(161\) −774.547 −0.379148
\(162\) 3135.79 1.52081
\(163\) −211.756 −0.101755 −0.0508773 0.998705i \(-0.516202\pi\)
−0.0508773 + 0.998705i \(0.516202\pi\)
\(164\) −1173.95 −0.558963
\(165\) −513.062 −0.242072
\(166\) −2878.00 −1.34564
\(167\) −977.319 −0.452858 −0.226429 0.974028i \(-0.572705\pi\)
−0.226429 + 0.974028i \(0.572705\pi\)
\(168\) −57.2960 −0.0263124
\(169\) 1244.43 0.566424
\(170\) 0 0
\(171\) 2435.71 1.08926
\(172\) −957.567 −0.424499
\(173\) −3607.58 −1.58543 −0.792714 0.609594i \(-0.791333\pi\)
−0.792714 + 0.609594i \(0.791333\pi\)
\(174\) −515.152 −0.224446
\(175\) 1107.75 0.478501
\(176\) 1107.28 0.474228
\(177\) 288.228 0.122398
\(178\) −4711.21 −1.98382
\(179\) 3180.10 1.32789 0.663943 0.747783i \(-0.268882\pi\)
0.663943 + 0.747783i \(0.268882\pi\)
\(180\) 5414.62 2.24212
\(181\) 1094.34 0.449401 0.224701 0.974428i \(-0.427860\pi\)
0.224701 + 0.974428i \(0.427860\pi\)
\(182\) 1670.30 0.680281
\(183\) −142.764 −0.0576690
\(184\) −2011.56 −0.805945
\(185\) −145.061 −0.0576491
\(186\) −41.8239 −0.0164875
\(187\) 0 0
\(188\) 2294.40 0.890088
\(189\) 184.931 0.0711731
\(190\) 6993.26 2.67023
\(191\) −2323.98 −0.880406 −0.440203 0.897898i \(-0.645094\pi\)
−0.440203 + 0.897898i \(0.645094\pi\)
\(192\) 444.182 0.166959
\(193\) −2521.70 −0.940498 −0.470249 0.882534i \(-0.655836\pi\)
−0.470249 + 0.882534i \(0.655836\pi\)
\(194\) 1139.36 0.421656
\(195\) 544.046 0.199795
\(196\) −3546.31 −1.29239
\(197\) 2196.87 0.794521 0.397260 0.917706i \(-0.369961\pi\)
0.397260 + 0.917706i \(0.369961\pi\)
\(198\) 6566.39 2.35683
\(199\) −3596.88 −1.28129 −0.640643 0.767839i \(-0.721332\pi\)
−0.640643 + 0.767839i \(0.721332\pi\)
\(200\) 2876.90 1.01714
\(201\) −276.617 −0.0970700
\(202\) −6510.11 −2.26757
\(203\) 1382.48 0.477985
\(204\) 0 0
\(205\) 1725.11 0.587740
\(206\) −114.112 −0.0385951
\(207\) 3228.83 1.08415
\(208\) −1174.15 −0.391406
\(209\) 5044.69 1.66961
\(210\) 264.054 0.0867687
\(211\) −3677.29 −1.19979 −0.599893 0.800080i \(-0.704790\pi\)
−0.599893 + 0.800080i \(0.704790\pi\)
\(212\) 3057.48 0.990513
\(213\) −378.297 −0.121692
\(214\) −9023.47 −2.88239
\(215\) 1407.14 0.446353
\(216\) 480.278 0.151291
\(217\) 112.240 0.0351122
\(218\) 3183.70 0.989116
\(219\) 99.3792 0.0306640
\(220\) 11214.4 3.43671
\(221\) 0 0
\(222\) −20.0680 −0.00606702
\(223\) 972.699 0.292093 0.146047 0.989278i \(-0.453345\pi\)
0.146047 + 0.989278i \(0.453345\pi\)
\(224\) −1422.91 −0.424430
\(225\) −4617.82 −1.36824
\(226\) −75.3766 −0.0221857
\(227\) −4696.68 −1.37326 −0.686629 0.727008i \(-0.740910\pi\)
−0.686629 + 0.727008i \(0.740910\pi\)
\(228\) 575.480 0.167158
\(229\) −2105.80 −0.607664 −0.303832 0.952726i \(-0.598266\pi\)
−0.303832 + 0.952726i \(0.598266\pi\)
\(230\) 9270.42 2.65771
\(231\) 190.479 0.0542537
\(232\) 3590.40 1.01604
\(233\) −641.400 −0.180341 −0.0901706 0.995926i \(-0.528741\pi\)
−0.0901706 + 0.995926i \(0.528741\pi\)
\(234\) −6962.94 −1.94522
\(235\) −3371.60 −0.935911
\(236\) −6300.03 −1.73770
\(237\) −18.7185 −0.00513038
\(238\) 0 0
\(239\) 4322.85 1.16997 0.584984 0.811045i \(-0.301101\pi\)
0.584984 + 0.811045i \(0.301101\pi\)
\(240\) −185.617 −0.0499231
\(241\) −2462.38 −0.658156 −0.329078 0.944303i \(-0.606738\pi\)
−0.329078 + 0.944303i \(0.606738\pi\)
\(242\) 7685.56 2.04151
\(243\) −1158.44 −0.305820
\(244\) 3120.52 0.818732
\(245\) 5211.28 1.35892
\(246\) 238.655 0.0618540
\(247\) −5349.35 −1.37802
\(248\) 291.495 0.0746370
\(249\) 348.023 0.0885746
\(250\) −3671.94 −0.928936
\(251\) 2631.96 0.661865 0.330932 0.943654i \(-0.392637\pi\)
0.330932 + 0.943654i \(0.392637\pi\)
\(252\) −2010.23 −0.502509
\(253\) 6687.35 1.66178
\(254\) −5060.54 −1.25010
\(255\) 0 0
\(256\) −1814.81 −0.443068
\(257\) −3375.79 −0.819361 −0.409680 0.912229i \(-0.634360\pi\)
−0.409680 + 0.912229i \(0.634360\pi\)
\(258\) 194.666 0.0469744
\(259\) 53.8552 0.0129204
\(260\) −11891.7 −2.83650
\(261\) −5763.09 −1.36677
\(262\) 2746.27 0.647576
\(263\) −1603.60 −0.375977 −0.187989 0.982171i \(-0.560197\pi\)
−0.187989 + 0.982171i \(0.560197\pi\)
\(264\) 494.688 0.115325
\(265\) −4492.94 −1.04151
\(266\) −2596.31 −0.598459
\(267\) 569.705 0.130582
\(268\) 6046.26 1.37811
\(269\) 6543.59 1.48316 0.741580 0.670864i \(-0.234077\pi\)
0.741580 + 0.670864i \(0.234077\pi\)
\(270\) −2213.40 −0.498901
\(271\) −356.005 −0.0797998 −0.0398999 0.999204i \(-0.512704\pi\)
−0.0398999 + 0.999204i \(0.512704\pi\)
\(272\) 0 0
\(273\) −201.982 −0.0447784
\(274\) −10020.9 −2.20944
\(275\) −9564.15 −2.09724
\(276\) 762.869 0.166374
\(277\) −3175.91 −0.688887 −0.344444 0.938807i \(-0.611932\pi\)
−0.344444 + 0.938807i \(0.611932\pi\)
\(278\) −4507.05 −0.972356
\(279\) −467.891 −0.100401
\(280\) −1840.34 −0.392791
\(281\) 1667.30 0.353960 0.176980 0.984214i \(-0.443367\pi\)
0.176980 + 0.984214i \(0.443367\pi\)
\(282\) −466.435 −0.0984957
\(283\) −7800.28 −1.63844 −0.819220 0.573479i \(-0.805593\pi\)
−0.819220 + 0.573479i \(0.805593\pi\)
\(284\) 8268.76 1.72768
\(285\) −845.663 −0.175764
\(286\) −14421.2 −2.98162
\(287\) −640.461 −0.131726
\(288\) 5931.65 1.21363
\(289\) 0 0
\(290\) −16546.6 −3.35052
\(291\) −137.778 −0.0277549
\(292\) −2172.21 −0.435340
\(293\) −2403.16 −0.479161 −0.239580 0.970877i \(-0.577010\pi\)
−0.239580 + 0.970877i \(0.577010\pi\)
\(294\) 720.939 0.143014
\(295\) 9257.84 1.82716
\(296\) 139.866 0.0274646
\(297\) −1596.67 −0.311947
\(298\) −1533.38 −0.298074
\(299\) −7091.21 −1.37156
\(300\) −1091.04 −0.209971
\(301\) −522.412 −0.100038
\(302\) 11357.4 2.16406
\(303\) 787.238 0.149259
\(304\) 1825.09 0.344329
\(305\) −4585.57 −0.860881
\(306\) 0 0
\(307\) −4027.80 −0.748791 −0.374395 0.927269i \(-0.622150\pi\)
−0.374395 + 0.927269i \(0.622150\pi\)
\(308\) −4163.46 −0.770244
\(309\) 13.7991 0.00254046
\(310\) −1343.38 −0.246125
\(311\) −3944.44 −0.719192 −0.359596 0.933108i \(-0.617085\pi\)
−0.359596 + 0.933108i \(0.617085\pi\)
\(312\) −524.562 −0.0951843
\(313\) −6540.41 −1.18111 −0.590553 0.806999i \(-0.701090\pi\)
−0.590553 + 0.806999i \(0.701090\pi\)
\(314\) 16223.7 2.91579
\(315\) 2954.01 0.528380
\(316\) 409.147 0.0728364
\(317\) 3711.41 0.657582 0.328791 0.944403i \(-0.393359\pi\)
0.328791 + 0.944403i \(0.393359\pi\)
\(318\) −621.563 −0.109609
\(319\) −11936.2 −2.09497
\(320\) 14267.1 2.49235
\(321\) 1091.17 0.189729
\(322\) −3441.73 −0.595652
\(323\) 0 0
\(324\) 8288.41 1.42119
\(325\) 10141.7 1.73096
\(326\) −940.945 −0.159859
\(327\) −384.990 −0.0651070
\(328\) −1663.33 −0.280005
\(329\) 1251.74 0.209759
\(330\) −2279.81 −0.380301
\(331\) 3510.10 0.582877 0.291439 0.956590i \(-0.405866\pi\)
0.291439 + 0.956590i \(0.405866\pi\)
\(332\) −7607.03 −1.25750
\(333\) −224.504 −0.0369452
\(334\) −4342.75 −0.711451
\(335\) −8884.92 −1.44906
\(336\) 68.9121 0.0111889
\(337\) 5718.46 0.924346 0.462173 0.886790i \(-0.347070\pi\)
0.462173 + 0.886790i \(0.347070\pi\)
\(338\) 5529.68 0.889867
\(339\) 9.11494 0.00146034
\(340\) 0 0
\(341\) −969.067 −0.153894
\(342\) 10823.2 1.71126
\(343\) −4132.55 −0.650544
\(344\) −1356.74 −0.212647
\(345\) −1121.03 −0.174940
\(346\) −16030.4 −2.49075
\(347\) −677.787 −0.104857 −0.0524287 0.998625i \(-0.516696\pi\)
−0.0524287 + 0.998625i \(0.516696\pi\)
\(348\) −1361.63 −0.209745
\(349\) 12161.8 1.86534 0.932670 0.360731i \(-0.117473\pi\)
0.932670 + 0.360731i \(0.117473\pi\)
\(350\) 4922.31 0.751738
\(351\) 1693.09 0.257466
\(352\) 12285.3 1.86025
\(353\) 5681.58 0.856657 0.428328 0.903623i \(-0.359103\pi\)
0.428328 + 0.903623i \(0.359103\pi\)
\(354\) 1280.75 0.192291
\(355\) −12150.9 −1.81662
\(356\) −12452.5 −1.85388
\(357\) 0 0
\(358\) 14130.9 2.08614
\(359\) −5883.91 −0.865017 −0.432508 0.901630i \(-0.642371\pi\)
−0.432508 + 0.901630i \(0.642371\pi\)
\(360\) 7671.78 1.12316
\(361\) 1456.00 0.212276
\(362\) 4862.74 0.706022
\(363\) −929.379 −0.134380
\(364\) 4414.89 0.635723
\(365\) 3192.05 0.457752
\(366\) −634.377 −0.0905996
\(367\) 11526.1 1.63939 0.819695 0.572801i \(-0.194143\pi\)
0.819695 + 0.572801i \(0.194143\pi\)
\(368\) 2419.37 0.342714
\(369\) 2669.87 0.376661
\(370\) −644.583 −0.0905683
\(371\) 1668.05 0.233425
\(372\) −110.548 −0.0154076
\(373\) 3533.27 0.490471 0.245236 0.969464i \(-0.421135\pi\)
0.245236 + 0.969464i \(0.421135\pi\)
\(374\) 0 0
\(375\) 444.031 0.0611458
\(376\) 3250.86 0.445878
\(377\) 12657.0 1.72909
\(378\) 821.746 0.111815
\(379\) 13568.8 1.83901 0.919503 0.393082i \(-0.128591\pi\)
0.919503 + 0.393082i \(0.128591\pi\)
\(380\) 18484.4 2.49534
\(381\) 611.947 0.0822861
\(382\) −10326.7 −1.38314
\(383\) −12948.4 −1.72750 −0.863748 0.503923i \(-0.831889\pi\)
−0.863748 + 0.503923i \(0.831889\pi\)
\(384\) 1019.15 0.135438
\(385\) 6118.16 0.809897
\(386\) −11205.3 −1.47755
\(387\) 2177.76 0.286051
\(388\) 3011.52 0.394038
\(389\) 8901.44 1.16021 0.580104 0.814542i \(-0.303012\pi\)
0.580104 + 0.814542i \(0.303012\pi\)
\(390\) 2417.49 0.313883
\(391\) 0 0
\(392\) −5024.64 −0.647405
\(393\) −332.093 −0.0426257
\(394\) 9761.88 1.24821
\(395\) −601.237 −0.0765862
\(396\) 17356.1 2.20246
\(397\) 7180.09 0.907703 0.453852 0.891077i \(-0.350050\pi\)
0.453852 + 0.891077i \(0.350050\pi\)
\(398\) −15982.9 −2.01293
\(399\) 313.960 0.0393926
\(400\) −3460.15 −0.432519
\(401\) −5087.50 −0.633560 −0.316780 0.948499i \(-0.602602\pi\)
−0.316780 + 0.948499i \(0.602602\pi\)
\(402\) −1229.16 −0.152500
\(403\) 1027.59 0.127017
\(404\) −17207.3 −2.11905
\(405\) −12179.7 −1.49436
\(406\) 6143.09 0.750927
\(407\) −464.979 −0.0566294
\(408\) 0 0
\(409\) −5287.62 −0.639256 −0.319628 0.947543i \(-0.603558\pi\)
−0.319628 + 0.947543i \(0.603558\pi\)
\(410\) 7665.57 0.923355
\(411\) 1211.78 0.145433
\(412\) −301.618 −0.0360671
\(413\) −3437.06 −0.409507
\(414\) 14347.4 1.70323
\(415\) 11178.5 1.32224
\(416\) −13027.2 −1.53536
\(417\) 545.017 0.0640038
\(418\) 22416.3 2.62300
\(419\) −15292.9 −1.78307 −0.891533 0.452956i \(-0.850370\pi\)
−0.891533 + 0.452956i \(0.850370\pi\)
\(420\) 697.938 0.0810854
\(421\) −1484.20 −0.171818 −0.0859089 0.996303i \(-0.527379\pi\)
−0.0859089 + 0.996303i \(0.527379\pi\)
\(422\) −16340.2 −1.88490
\(423\) −5218.08 −0.599792
\(424\) 4332.04 0.496185
\(425\) 0 0
\(426\) −1680.98 −0.191182
\(427\) 1702.43 0.192943
\(428\) −23850.6 −2.69360
\(429\) 1743.89 0.196261
\(430\) 6252.66 0.701232
\(431\) −2361.94 −0.263969 −0.131984 0.991252i \(-0.542135\pi\)
−0.131984 + 0.991252i \(0.542135\pi\)
\(432\) −577.649 −0.0643337
\(433\) −12384.3 −1.37449 −0.687244 0.726426i \(-0.741180\pi\)
−0.687244 + 0.726426i \(0.741180\pi\)
\(434\) 498.742 0.0551622
\(435\) 2000.91 0.220543
\(436\) 8415.05 0.924330
\(437\) 11022.5 1.20659
\(438\) 441.595 0.0481740
\(439\) −7612.65 −0.827636 −0.413818 0.910360i \(-0.635805\pi\)
−0.413818 + 0.910360i \(0.635805\pi\)
\(440\) 15889.3 1.72158
\(441\) 8065.26 0.870885
\(442\) 0 0
\(443\) 11492.3 1.23254 0.616272 0.787533i \(-0.288642\pi\)
0.616272 + 0.787533i \(0.288642\pi\)
\(444\) −53.0432 −0.00566963
\(445\) 18298.9 1.94932
\(446\) 4322.22 0.458886
\(447\) 185.424 0.0196203
\(448\) −5296.78 −0.558592
\(449\) 13654.4 1.43517 0.717584 0.696472i \(-0.245248\pi\)
0.717584 + 0.696472i \(0.245248\pi\)
\(450\) −20519.5 −2.14955
\(451\) 5529.67 0.577344
\(452\) −199.233 −0.0207326
\(453\) −1373.40 −0.142446
\(454\) −20869.9 −2.15743
\(455\) −6487.64 −0.668451
\(456\) 815.377 0.0837358
\(457\) 12274.9 1.25645 0.628223 0.778034i \(-0.283783\pi\)
0.628223 + 0.778034i \(0.283783\pi\)
\(458\) −9357.20 −0.954657
\(459\) 0 0
\(460\) 24503.3 2.48363
\(461\) −932.142 −0.0941739 −0.0470869 0.998891i \(-0.514994\pi\)
−0.0470869 + 0.998891i \(0.514994\pi\)
\(462\) 846.400 0.0852340
\(463\) 5569.01 0.558993 0.279496 0.960147i \(-0.409832\pi\)
0.279496 + 0.960147i \(0.409832\pi\)
\(464\) −4318.31 −0.432053
\(465\) 162.449 0.0162008
\(466\) −2850.08 −0.283321
\(467\) 14662.2 1.45286 0.726428 0.687243i \(-0.241179\pi\)
0.726428 + 0.687243i \(0.241179\pi\)
\(468\) −18404.2 −1.81781
\(469\) 3298.61 0.324766
\(470\) −14981.8 −1.47034
\(471\) −1961.86 −0.191927
\(472\) −8926.29 −0.870478
\(473\) 4510.45 0.438458
\(474\) −83.1765 −0.00805996
\(475\) −15764.3 −1.52277
\(476\) 0 0
\(477\) −6953.53 −0.667464
\(478\) 19208.8 1.83805
\(479\) 12651.6 1.20682 0.603409 0.797432i \(-0.293809\pi\)
0.603409 + 0.797432i \(0.293809\pi\)
\(480\) −2059.43 −0.195833
\(481\) 493.060 0.0467393
\(482\) −10941.7 −1.03398
\(483\) 416.192 0.0392079
\(484\) 20314.2 1.90780
\(485\) −4425.40 −0.414324
\(486\) −5147.58 −0.480451
\(487\) 13319.7 1.23937 0.619683 0.784852i \(-0.287261\pi\)
0.619683 + 0.784852i \(0.287261\pi\)
\(488\) 4421.34 0.410133
\(489\) 113.784 0.0105225
\(490\) 23156.5 2.13491
\(491\) −19380.9 −1.78136 −0.890679 0.454633i \(-0.849771\pi\)
−0.890679 + 0.454633i \(0.849771\pi\)
\(492\) 630.805 0.0578026
\(493\) 0 0
\(494\) −23770.0 −2.16491
\(495\) −25504.6 −2.31585
\(496\) −350.593 −0.0317381
\(497\) 4511.12 0.407146
\(498\) 1546.45 0.139153
\(499\) 20101.1 1.80330 0.901650 0.432466i \(-0.142356\pi\)
0.901650 + 0.432466i \(0.142356\pi\)
\(500\) −9705.56 −0.868091
\(501\) 525.149 0.0468302
\(502\) 11695.2 1.03981
\(503\) −6166.84 −0.546652 −0.273326 0.961921i \(-0.588124\pi\)
−0.273326 + 0.961921i \(0.588124\pi\)
\(504\) −2848.22 −0.251726
\(505\) 25286.0 2.22814
\(506\) 29715.5 2.61070
\(507\) −668.679 −0.0585741
\(508\) −13375.8 −1.16822
\(509\) 14496.0 1.26233 0.631165 0.775649i \(-0.282577\pi\)
0.631165 + 0.775649i \(0.282577\pi\)
\(510\) 0 0
\(511\) −1185.08 −0.102592
\(512\) 7109.16 0.613639
\(513\) −2631.74 −0.226499
\(514\) −15000.4 −1.28724
\(515\) 443.225 0.0379239
\(516\) 514.535 0.0438976
\(517\) −10807.4 −0.919357
\(518\) 239.307 0.0202984
\(519\) 1938.48 0.163950
\(520\) −16848.9 −1.42091
\(521\) −2642.20 −0.222182 −0.111091 0.993810i \(-0.535435\pi\)
−0.111091 + 0.993810i \(0.535435\pi\)
\(522\) −25608.5 −2.14723
\(523\) 12574.5 1.05133 0.525665 0.850692i \(-0.323817\pi\)
0.525665 + 0.850692i \(0.323817\pi\)
\(524\) 7258.84 0.605160
\(525\) −595.232 −0.0494820
\(526\) −7125.63 −0.590670
\(527\) 0 0
\(528\) −594.980 −0.0490401
\(529\) 2444.72 0.200930
\(530\) −19964.5 −1.63623
\(531\) 14328.0 1.17096
\(532\) −6862.49 −0.559261
\(533\) −5863.61 −0.476513
\(534\) 2531.50 0.205148
\(535\) 35048.2 2.83227
\(536\) 8566.72 0.690347
\(537\) −1708.78 −0.137317
\(538\) 29076.7 2.33008
\(539\) 16704.3 1.33489
\(540\) −5850.39 −0.466224
\(541\) 18289.3 1.45345 0.726726 0.686927i \(-0.241041\pi\)
0.726726 + 0.686927i \(0.241041\pi\)
\(542\) −1581.92 −0.125368
\(543\) −588.028 −0.0464728
\(544\) 0 0
\(545\) −12365.8 −0.971916
\(546\) −897.515 −0.0703481
\(547\) −9989.86 −0.780869 −0.390435 0.920631i \(-0.627675\pi\)
−0.390435 + 0.920631i \(0.627675\pi\)
\(548\) −26487.0 −2.06472
\(549\) −7096.88 −0.551708
\(550\) −42498.6 −3.29482
\(551\) −19674.0 −1.52112
\(552\) 1080.88 0.0833431
\(553\) 223.215 0.0171647
\(554\) −14112.3 −1.08226
\(555\) 77.9464 0.00596152
\(556\) −11912.9 −0.908668
\(557\) −4181.95 −0.318124 −0.159062 0.987269i \(-0.550847\pi\)
−0.159062 + 0.987269i \(0.550847\pi\)
\(558\) −2079.09 −0.157733
\(559\) −4782.84 −0.361883
\(560\) 2213.45 0.167027
\(561\) 0 0
\(562\) 7408.70 0.556080
\(563\) 10429.1 0.780697 0.390348 0.920667i \(-0.372355\pi\)
0.390348 + 0.920667i \(0.372355\pi\)
\(564\) −1232.87 −0.0920443
\(565\) 292.771 0.0217999
\(566\) −34660.8 −2.57403
\(567\) 4521.84 0.334920
\(568\) 11715.7 0.865458
\(569\) 8440.98 0.621906 0.310953 0.950425i \(-0.399352\pi\)
0.310953 + 0.950425i \(0.399352\pi\)
\(570\) −3757.73 −0.276130
\(571\) 27092.6 1.98562 0.992811 0.119694i \(-0.0381913\pi\)
0.992811 + 0.119694i \(0.0381913\pi\)
\(572\) −38117.7 −2.78633
\(573\) 1248.76 0.0910431
\(574\) −2845.91 −0.206944
\(575\) −20897.5 −1.51562
\(576\) 22080.5 1.59726
\(577\) −10864.3 −0.783857 −0.391929 0.919996i \(-0.628192\pi\)
−0.391929 + 0.919996i \(0.628192\pi\)
\(578\) 0 0
\(579\) 1355.00 0.0972572
\(580\) −43735.5 −3.13107
\(581\) −4150.11 −0.296343
\(582\) −612.220 −0.0436037
\(583\) −14401.7 −1.02308
\(584\) −3077.73 −0.218078
\(585\) 27044.8 1.91140
\(586\) −10678.5 −0.752774
\(587\) 25173.8 1.77008 0.885038 0.465518i \(-0.154132\pi\)
0.885038 + 0.465518i \(0.154132\pi\)
\(588\) 1905.56 0.133646
\(589\) −1597.28 −0.111740
\(590\) 41137.5 2.87052
\(591\) −1180.46 −0.0821617
\(592\) −168.222 −0.0116788
\(593\) 777.712 0.0538563 0.0269282 0.999637i \(-0.491427\pi\)
0.0269282 + 0.999637i \(0.491427\pi\)
\(594\) −7094.86 −0.490077
\(595\) 0 0
\(596\) −4052.97 −0.278551
\(597\) 1932.73 0.132498
\(598\) −31510.0 −2.15475
\(599\) 6690.40 0.456365 0.228182 0.973618i \(-0.426722\pi\)
0.228182 + 0.973618i \(0.426722\pi\)
\(600\) −1545.86 −0.105182
\(601\) −1574.80 −0.106884 −0.0534421 0.998571i \(-0.517019\pi\)
−0.0534421 + 0.998571i \(0.517019\pi\)
\(602\) −2321.36 −0.157162
\(603\) −13750.8 −0.928649
\(604\) 30019.6 2.02232
\(605\) −29851.6 −2.00601
\(606\) 3498.12 0.234491
\(607\) −24567.4 −1.64276 −0.821382 0.570378i \(-0.806797\pi\)
−0.821382 + 0.570378i \(0.806797\pi\)
\(608\) 20249.4 1.35069
\(609\) −742.856 −0.0494286
\(610\) −20376.1 −1.35247
\(611\) 11460.0 0.758795
\(612\) 0 0
\(613\) −27992.8 −1.84440 −0.922201 0.386710i \(-0.873611\pi\)
−0.922201 + 0.386710i \(0.873611\pi\)
\(614\) −17897.7 −1.17637
\(615\) −926.962 −0.0607784
\(616\) −5899.05 −0.385843
\(617\) −3787.41 −0.247124 −0.123562 0.992337i \(-0.539432\pi\)
−0.123562 + 0.992337i \(0.539432\pi\)
\(618\) 61.3167 0.00399113
\(619\) 4066.72 0.264063 0.132032 0.991246i \(-0.457850\pi\)
0.132032 + 0.991246i \(0.457850\pi\)
\(620\) −3550.78 −0.230004
\(621\) −3488.69 −0.225437
\(622\) −17527.3 −1.12987
\(623\) −6793.62 −0.436887
\(624\) 630.911 0.0404754
\(625\) −7347.68 −0.470251
\(626\) −29062.6 −1.85555
\(627\) −2710.70 −0.172655
\(628\) 42882.0 2.72481
\(629\) 0 0
\(630\) 13126.2 0.830099
\(631\) −11686.8 −0.737309 −0.368655 0.929566i \(-0.620182\pi\)
−0.368655 + 0.929566i \(0.620182\pi\)
\(632\) 579.705 0.0364864
\(633\) 1975.94 0.124070
\(634\) 16491.8 1.03308
\(635\) 19655.7 1.22836
\(636\) −1642.90 −0.102429
\(637\) −17713.1 −1.10175
\(638\) −53038.8 −3.29126
\(639\) −18805.4 −1.16421
\(640\) 32734.9 2.02181
\(641\) −23652.6 −1.45744 −0.728721 0.684810i \(-0.759885\pi\)
−0.728721 + 0.684810i \(0.759885\pi\)
\(642\) 4848.64 0.298069
\(643\) 2712.61 0.166368 0.0831841 0.996534i \(-0.473491\pi\)
0.0831841 + 0.996534i \(0.473491\pi\)
\(644\) −9097.06 −0.556637
\(645\) −756.105 −0.0461575
\(646\) 0 0
\(647\) 3672.97 0.223183 0.111592 0.993754i \(-0.464405\pi\)
0.111592 + 0.993754i \(0.464405\pi\)
\(648\) 11743.5 0.711929
\(649\) 29675.2 1.79484
\(650\) 45065.2 2.71939
\(651\) −60.3106 −0.00363097
\(652\) −2487.08 −0.149389
\(653\) 26090.8 1.56357 0.781785 0.623548i \(-0.214309\pi\)
0.781785 + 0.623548i \(0.214309\pi\)
\(654\) −1710.72 −0.102285
\(655\) −10666.8 −0.636315
\(656\) 2000.54 0.119067
\(657\) 4940.19 0.293357
\(658\) 5562.14 0.329536
\(659\) −14303.7 −0.845515 −0.422758 0.906243i \(-0.638938\pi\)
−0.422758 + 0.906243i \(0.638938\pi\)
\(660\) −6025.92 −0.355392
\(661\) −9780.49 −0.575517 −0.287759 0.957703i \(-0.592910\pi\)
−0.287759 + 0.957703i \(0.592910\pi\)
\(662\) 15597.2 0.915716
\(663\) 0 0
\(664\) −10778.1 −0.629928
\(665\) 10084.4 0.588052
\(666\) −997.593 −0.0580419
\(667\) −26080.2 −1.51399
\(668\) −11478.6 −0.664852
\(669\) −522.667 −0.0302055
\(670\) −39480.4 −2.27651
\(671\) −14698.6 −0.845654
\(672\) 764.582 0.0438905
\(673\) 21380.1 1.22458 0.612289 0.790634i \(-0.290249\pi\)
0.612289 + 0.790634i \(0.290249\pi\)
\(674\) 25410.2 1.45217
\(675\) 4989.47 0.284511
\(676\) 14615.9 0.831581
\(677\) 7244.51 0.411269 0.205635 0.978629i \(-0.434074\pi\)
0.205635 + 0.978629i \(0.434074\pi\)
\(678\) 40.5026 0.00229424
\(679\) 1642.97 0.0928593
\(680\) 0 0
\(681\) 2523.70 0.142009
\(682\) −4306.08 −0.241772
\(683\) 4140.24 0.231950 0.115975 0.993252i \(-0.463001\pi\)
0.115975 + 0.993252i \(0.463001\pi\)
\(684\) 28607.4 1.59917
\(685\) 38922.4 2.17102
\(686\) −18363.1 −1.02202
\(687\) 1131.52 0.0628388
\(688\) 1631.81 0.0904244
\(689\) 15271.4 0.844406
\(690\) −4981.33 −0.274835
\(691\) −30750.3 −1.69290 −0.846451 0.532466i \(-0.821265\pi\)
−0.846451 + 0.532466i \(0.821265\pi\)
\(692\) −42371.0 −2.32761
\(693\) 9468.81 0.519034
\(694\) −3011.77 −0.164734
\(695\) 17505.9 0.955448
\(696\) −1929.25 −0.105069
\(697\) 0 0
\(698\) 54041.2 2.93050
\(699\) 344.647 0.0186492
\(700\) 13010.5 0.702500
\(701\) −20466.3 −1.10271 −0.551356 0.834270i \(-0.685890\pi\)
−0.551356 + 0.834270i \(0.685890\pi\)
\(702\) 7523.32 0.404487
\(703\) −766.410 −0.0411176
\(704\) 45731.8 2.44827
\(705\) 1811.68 0.0967830
\(706\) 25246.3 1.34583
\(707\) −9387.65 −0.499376
\(708\) 3385.24 0.179696
\(709\) 24814.8 1.31444 0.657222 0.753697i \(-0.271731\pi\)
0.657222 + 0.753697i \(0.271731\pi\)
\(710\) −53992.8 −2.85396
\(711\) −930.509 −0.0490813
\(712\) −17643.5 −0.928678
\(713\) −2117.39 −0.111216
\(714\) 0 0
\(715\) 56013.6 2.92978
\(716\) 37350.3 1.94950
\(717\) −2322.83 −0.120987
\(718\) −26145.4 −1.35897
\(719\) −24507.8 −1.27119 −0.635597 0.772021i \(-0.719246\pi\)
−0.635597 + 0.772021i \(0.719246\pi\)
\(720\) −9227.14 −0.477604
\(721\) −164.551 −0.00849960
\(722\) 6469.79 0.333491
\(723\) 1323.12 0.0680601
\(724\) 12853.0 0.659778
\(725\) 37299.6 1.91072
\(726\) −4129.73 −0.211114
\(727\) −7468.67 −0.381015 −0.190507 0.981686i \(-0.561013\pi\)
−0.190507 + 0.981686i \(0.561013\pi\)
\(728\) 6255.30 0.318457
\(729\) −18431.3 −0.936408
\(730\) 14184.0 0.719140
\(731\) 0 0
\(732\) −1676.77 −0.0846654
\(733\) 2801.95 0.141190 0.0705952 0.997505i \(-0.477510\pi\)
0.0705952 + 0.997505i \(0.477510\pi\)
\(734\) 51216.5 2.57552
\(735\) −2800.21 −0.140527
\(736\) 26843.0 1.34436
\(737\) −28479.8 −1.42343
\(738\) 11863.7 0.591745
\(739\) 5867.20 0.292055 0.146027 0.989281i \(-0.453351\pi\)
0.146027 + 0.989281i \(0.453351\pi\)
\(740\) −1703.74 −0.0846361
\(741\) 2874.40 0.142502
\(742\) 7412.02 0.366717
\(743\) −23585.7 −1.16457 −0.582286 0.812984i \(-0.697841\pi\)
−0.582286 + 0.812984i \(0.697841\pi\)
\(744\) −156.631 −0.00771824
\(745\) 5955.80 0.292891
\(746\) 15700.2 0.770543
\(747\) 17300.4 0.847375
\(748\) 0 0
\(749\) −13011.9 −0.634775
\(750\) 1973.07 0.0960616
\(751\) 15142.8 0.735775 0.367887 0.929870i \(-0.380081\pi\)
0.367887 + 0.929870i \(0.380081\pi\)
\(752\) −3909.93 −0.189602
\(753\) −1414.25 −0.0684437
\(754\) 56241.8 2.71645
\(755\) −44113.5 −2.12643
\(756\) 2172.01 0.104491
\(757\) −13149.7 −0.631353 −0.315676 0.948867i \(-0.602231\pi\)
−0.315676 + 0.948867i \(0.602231\pi\)
\(758\) 60293.5 2.88913
\(759\) −3593.36 −0.171845
\(760\) 26189.8 1.25001
\(761\) −12831.3 −0.611213 −0.305607 0.952158i \(-0.598859\pi\)
−0.305607 + 0.952158i \(0.598859\pi\)
\(762\) 2719.21 0.129274
\(763\) 4590.93 0.217828
\(764\) −27295.2 −1.29255
\(765\) 0 0
\(766\) −57536.6 −2.71394
\(767\) −31467.3 −1.48138
\(768\) 975.162 0.0458179
\(769\) −11365.1 −0.532949 −0.266474 0.963842i \(-0.585859\pi\)
−0.266474 + 0.963842i \(0.585859\pi\)
\(770\) 27186.3 1.27237
\(771\) 1813.93 0.0847304
\(772\) −29617.4 −1.38077
\(773\) −16551.8 −0.770150 −0.385075 0.922885i \(-0.625824\pi\)
−0.385075 + 0.922885i \(0.625824\pi\)
\(774\) 9676.96 0.449394
\(775\) 3028.26 0.140359
\(776\) 4266.91 0.197388
\(777\) −28.9383 −0.00133611
\(778\) 39553.9 1.82272
\(779\) 9114.37 0.419199
\(780\) 6389.83 0.293324
\(781\) −38948.5 −1.78449
\(782\) 0 0
\(783\) 6226.91 0.284204
\(784\) 6043.33 0.275298
\(785\) −63014.7 −2.86509
\(786\) −1475.67 −0.0669661
\(787\) 32051.7 1.45174 0.725870 0.687832i \(-0.241438\pi\)
0.725870 + 0.687832i \(0.241438\pi\)
\(788\) 25802.3 1.16646
\(789\) 861.670 0.0388799
\(790\) −2671.62 −0.120319
\(791\) −108.694 −0.00488585
\(792\) 24591.2 1.10330
\(793\) 15586.3 0.697964
\(794\) 31905.0 1.42603
\(795\) 2414.22 0.107703
\(796\) −42245.4 −1.88109
\(797\) 27679.0 1.23016 0.615082 0.788463i \(-0.289123\pi\)
0.615082 + 0.788463i \(0.289123\pi\)
\(798\) 1395.09 0.0618869
\(799\) 0 0
\(800\) −38390.5 −1.69664
\(801\) 28320.3 1.24925
\(802\) −22606.5 −0.995340
\(803\) 10231.8 0.449655
\(804\) −3248.87 −0.142511
\(805\) 13368.0 0.585294
\(806\) 4566.13 0.199547
\(807\) −3516.11 −0.153374
\(808\) −24380.4 −1.06151
\(809\) −7438.60 −0.323272 −0.161636 0.986850i \(-0.551677\pi\)
−0.161636 + 0.986850i \(0.551677\pi\)
\(810\) −54121.1 −2.34768
\(811\) −10261.1 −0.444288 −0.222144 0.975014i \(-0.571306\pi\)
−0.222144 + 0.975014i \(0.571306\pi\)
\(812\) 16237.2 0.701742
\(813\) 191.294 0.00825213
\(814\) −2066.15 −0.0889663
\(815\) 3654.73 0.157079
\(816\) 0 0
\(817\) 7434.42 0.318357
\(818\) −23495.7 −1.00429
\(819\) −10040.6 −0.428386
\(820\) 20261.4 0.862876
\(821\) 21739.5 0.924134 0.462067 0.886845i \(-0.347108\pi\)
0.462067 + 0.886845i \(0.347108\pi\)
\(822\) 5384.60 0.228479
\(823\) −23728.9 −1.00503 −0.502514 0.864569i \(-0.667592\pi\)
−0.502514 + 0.864569i \(0.667592\pi\)
\(824\) −427.352 −0.0180674
\(825\) 5139.16 0.216876
\(826\) −15272.7 −0.643347
\(827\) −21101.5 −0.887270 −0.443635 0.896207i \(-0.646311\pi\)
−0.443635 + 0.896207i \(0.646311\pi\)
\(828\) 37922.6 1.59167
\(829\) −1621.77 −0.0679448 −0.0339724 0.999423i \(-0.510816\pi\)
−0.0339724 + 0.999423i \(0.510816\pi\)
\(830\) 49671.9 2.07727
\(831\) 1706.53 0.0712381
\(832\) −48493.6 −2.02069
\(833\) 0 0
\(834\) 2421.80 0.100552
\(835\) 16867.7 0.699080
\(836\) 59250.0 2.45120
\(837\) 505.547 0.0208773
\(838\) −67954.3 −2.80124
\(839\) 1287.05 0.0529607 0.0264803 0.999649i \(-0.491570\pi\)
0.0264803 + 0.999649i \(0.491570\pi\)
\(840\) 988.883 0.0406187
\(841\) 22161.3 0.908658
\(842\) −6595.08 −0.269930
\(843\) −895.900 −0.0366031
\(844\) −43189.8 −1.76144
\(845\) −21477.9 −0.874392
\(846\) −23186.7 −0.942289
\(847\) 11082.7 0.449592
\(848\) −5210.30 −0.210994
\(849\) 4191.37 0.169432
\(850\) 0 0
\(851\) −1015.97 −0.0409248
\(852\) −4443.10 −0.178660
\(853\) −18173.4 −0.729479 −0.364740 0.931110i \(-0.618842\pi\)
−0.364740 + 0.931110i \(0.618842\pi\)
\(854\) 7564.83 0.303118
\(855\) −42038.4 −1.68150
\(856\) −33793.0 −1.34932
\(857\) 39590.2 1.57803 0.789017 0.614371i \(-0.210590\pi\)
0.789017 + 0.614371i \(0.210590\pi\)
\(858\) 7749.04 0.308331
\(859\) −17747.9 −0.704948 −0.352474 0.935822i \(-0.614659\pi\)
−0.352474 + 0.935822i \(0.614659\pi\)
\(860\) 16526.8 0.655302
\(861\) 344.143 0.0136218
\(862\) −10495.3 −0.414702
\(863\) −8155.37 −0.321683 −0.160841 0.986980i \(-0.551421\pi\)
−0.160841 + 0.986980i \(0.551421\pi\)
\(864\) −6409.03 −0.252361
\(865\) 62263.8 2.44744
\(866\) −55030.3 −2.15936
\(867\) 0 0
\(868\) 1318.26 0.0515491
\(869\) −1927.21 −0.0752315
\(870\) 8891.11 0.346479
\(871\) 30199.7 1.17483
\(872\) 11923.0 0.463031
\(873\) −6849.00 −0.265525
\(874\) 48979.1 1.89559
\(875\) −5294.98 −0.204575
\(876\) 1167.21 0.0450187
\(877\) −37979.1 −1.46233 −0.731164 0.682202i \(-0.761023\pi\)
−0.731164 + 0.682202i \(0.761023\pi\)
\(878\) −33827.1 −1.30024
\(879\) 1291.30 0.0495502
\(880\) −19110.7 −0.732069
\(881\) −18289.7 −0.699427 −0.349714 0.936857i \(-0.613721\pi\)
−0.349714 + 0.936857i \(0.613721\pi\)
\(882\) 35838.3 1.36818
\(883\) 18414.9 0.701825 0.350912 0.936408i \(-0.385871\pi\)
0.350912 + 0.936408i \(0.385871\pi\)
\(884\) 0 0
\(885\) −4974.57 −0.188947
\(886\) 51066.6 1.93636
\(887\) −50689.5 −1.91881 −0.959406 0.282028i \(-0.908993\pi\)
−0.959406 + 0.282028i \(0.908993\pi\)
\(888\) −75.1549 −0.00284013
\(889\) −7297.35 −0.275304
\(890\) 81311.6 3.06244
\(891\) −39041.0 −1.46793
\(892\) 11424.4 0.428830
\(893\) −17813.4 −0.667529
\(894\) 823.939 0.0308240
\(895\) −54885.8 −2.04987
\(896\) −12153.1 −0.453133
\(897\) 3810.36 0.141833
\(898\) 60673.8 2.25469
\(899\) 3779.30 0.140208
\(900\) −54236.4 −2.00875
\(901\) 0 0
\(902\) 24571.3 0.907023
\(903\) 280.711 0.0103449
\(904\) −282.286 −0.0103857
\(905\) −18887.4 −0.693744
\(906\) −6102.76 −0.223786
\(907\) −44568.0 −1.63160 −0.815798 0.578338i \(-0.803702\pi\)
−0.815798 + 0.578338i \(0.803702\pi\)
\(908\) −55162.5 −2.01612
\(909\) 39134.0 1.42794
\(910\) −28828.1 −1.05016
\(911\) 7809.03 0.284001 0.142000 0.989867i \(-0.454647\pi\)
0.142000 + 0.989867i \(0.454647\pi\)
\(912\) −980.685 −0.0356072
\(913\) 35831.5 1.29885
\(914\) 54543.9 1.97391
\(915\) 2463.99 0.0890241
\(916\) −24732.6 −0.892128
\(917\) 3960.15 0.142612
\(918\) 0 0
\(919\) −36710.8 −1.31771 −0.658856 0.752269i \(-0.728959\pi\)
−0.658856 + 0.752269i \(0.728959\pi\)
\(920\) 34717.8 1.24414
\(921\) 2164.28 0.0774328
\(922\) −4142.00 −0.147950
\(923\) 41300.6 1.47284
\(924\) 2237.18 0.0796512
\(925\) 1453.02 0.0516488
\(926\) 24746.1 0.878193
\(927\) 685.960 0.0243041
\(928\) −47911.7 −1.69481
\(929\) 15068.9 0.532180 0.266090 0.963948i \(-0.414268\pi\)
0.266090 + 0.963948i \(0.414268\pi\)
\(930\) 721.847 0.0254519
\(931\) 27533.1 0.969238
\(932\) −7533.25 −0.264764
\(933\) 2119.49 0.0743719
\(934\) 65151.8 2.28248
\(935\) 0 0
\(936\) −26076.3 −0.910609
\(937\) 38416.7 1.33940 0.669700 0.742632i \(-0.266423\pi\)
0.669700 + 0.742632i \(0.266423\pi\)
\(938\) 14657.5 0.510217
\(939\) 3514.40 0.122139
\(940\) −39599.5 −1.37404
\(941\) −34621.7 −1.19940 −0.599701 0.800224i \(-0.704714\pi\)
−0.599701 + 0.800224i \(0.704714\pi\)
\(942\) −8717.59 −0.301523
\(943\) 12082.2 0.417233
\(944\) 10736.0 0.370155
\(945\) −3191.75 −0.109871
\(946\) 20042.3 0.688829
\(947\) −20331.6 −0.697665 −0.348832 0.937185i \(-0.613422\pi\)
−0.348832 + 0.937185i \(0.613422\pi\)
\(948\) −219.849 −0.00753204
\(949\) −10849.7 −0.371124
\(950\) −70049.1 −2.39231
\(951\) −1994.28 −0.0680009
\(952\) 0 0
\(953\) 17934.5 0.609607 0.304803 0.952415i \(-0.401409\pi\)
0.304803 + 0.952415i \(0.401409\pi\)
\(954\) −30898.2 −1.04860
\(955\) 40110.0 1.35909
\(956\) 50771.9 1.71766
\(957\) 6413.73 0.216642
\(958\) 56217.8 1.89594
\(959\) −14450.3 −0.486573
\(960\) −7666.21 −0.257735
\(961\) −29484.2 −0.989701
\(962\) 2190.93 0.0734287
\(963\) 54242.5 1.81510
\(964\) −28920.6 −0.966256
\(965\) 43522.5 1.45185
\(966\) 1849.37 0.0615966
\(967\) 8758.07 0.291252 0.145626 0.989340i \(-0.453480\pi\)
0.145626 + 0.989340i \(0.453480\pi\)
\(968\) 28782.5 0.955686
\(969\) 0 0
\(970\) −19664.4 −0.650914
\(971\) −52844.2 −1.74650 −0.873250 0.487273i \(-0.837992\pi\)
−0.873250 + 0.487273i \(0.837992\pi\)
\(972\) −13605.9 −0.448982
\(973\) −6499.22 −0.214137
\(974\) 59186.4 1.94708
\(975\) −5449.52 −0.178999
\(976\) −5317.72 −0.174402
\(977\) −45377.7 −1.48594 −0.742970 0.669325i \(-0.766583\pi\)
−0.742970 + 0.669325i \(0.766583\pi\)
\(978\) 505.604 0.0165311
\(979\) 58655.3 1.91484
\(980\) 61206.5 1.99507
\(981\) −19138.1 −0.622866
\(982\) −86119.6 −2.79856
\(983\) 20092.8 0.651944 0.325972 0.945379i \(-0.394309\pi\)
0.325972 + 0.945379i \(0.394309\pi\)
\(984\) 893.765 0.0289555
\(985\) −37916.2 −1.22651
\(986\) 0 0
\(987\) −672.604 −0.0216912
\(988\) −62828.1 −2.02311
\(989\) 9855.23 0.316863
\(990\) −113331. −3.63826
\(991\) −8915.20 −0.285773 −0.142886 0.989739i \(-0.545638\pi\)
−0.142886 + 0.989739i \(0.545638\pi\)
\(992\) −3889.83 −0.124498
\(993\) −1886.10 −0.0602756
\(994\) 20045.3 0.639637
\(995\) 62079.1 1.97793
\(996\) 4087.53 0.130039
\(997\) −12587.1 −0.399837 −0.199919 0.979812i \(-0.564068\pi\)
−0.199919 + 0.979812i \(0.564068\pi\)
\(998\) 89319.8 2.83303
\(999\) 242.572 0.00768234
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 289.4.a.h.1.12 12
17.4 even 4 289.4.b.f.288.2 24
17.13 even 4 289.4.b.f.288.1 24
17.16 even 2 289.4.a.i.1.12 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.12 12 1.1 even 1 trivial
289.4.a.i.1.12 yes 12 17.16 even 2
289.4.b.f.288.1 24 17.13 even 4
289.4.b.f.288.2 24 17.4 even 4