Properties

Label 289.4.a.h.1.7
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $1$
Dimension $12$
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] = [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 1.7
Root \(-0.447590\) 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)
 
\(f(q)\) \(=\) \(q+0.447590 q^{2} -9.51519 q^{3} -7.79966 q^{4} +11.7425 q^{5} -4.25890 q^{6} -2.27797 q^{7} -7.07177 q^{8} +63.5388 q^{9} +O(q^{10})\) \(q+0.447590 q^{2} -9.51519 q^{3} -7.79966 q^{4} +11.7425 q^{5} -4.25890 q^{6} -2.27797 q^{7} -7.07177 q^{8} +63.5388 q^{9} +5.25584 q^{10} -22.6868 q^{11} +74.2152 q^{12} +67.4022 q^{13} -1.01960 q^{14} -111.732 q^{15} +59.2321 q^{16} +28.4393 q^{18} +42.9965 q^{19} -91.5878 q^{20} +21.6753 q^{21} -10.1544 q^{22} -117.444 q^{23} +67.2892 q^{24} +12.8870 q^{25} +30.1686 q^{26} -347.673 q^{27} +17.7674 q^{28} -226.336 q^{29} -50.0103 q^{30} +0.673139 q^{31} +83.0858 q^{32} +215.869 q^{33} -26.7491 q^{35} -495.581 q^{36} +99.9003 q^{37} +19.2448 q^{38} -641.345 q^{39} -83.0405 q^{40} +154.092 q^{41} +9.70165 q^{42} -321.792 q^{43} +176.949 q^{44} +746.106 q^{45} -52.5667 q^{46} -30.4214 q^{47} -563.604 q^{48} -337.811 q^{49} +5.76808 q^{50} -525.715 q^{52} -361.595 q^{53} -155.615 q^{54} -266.400 q^{55} +16.1093 q^{56} -409.119 q^{57} -101.306 q^{58} +147.417 q^{59} +871.475 q^{60} -321.075 q^{61} +0.301290 q^{62} -144.739 q^{63} -436.668 q^{64} +791.473 q^{65} +96.6208 q^{66} +612.509 q^{67} +1117.50 q^{69} -11.9726 q^{70} -248.823 q^{71} -449.331 q^{72} +701.031 q^{73} +44.7144 q^{74} -122.622 q^{75} -335.358 q^{76} +51.6798 q^{77} -287.059 q^{78} -773.040 q^{79} +695.534 q^{80} +1592.63 q^{81} +68.9702 q^{82} -1005.91 q^{83} -169.060 q^{84} -144.031 q^{86} +2153.63 q^{87} +160.436 q^{88} +1641.08 q^{89} +333.949 q^{90} -153.540 q^{91} +916.023 q^{92} -6.40505 q^{93} -13.6163 q^{94} +504.887 q^{95} -790.577 q^{96} +479.663 q^{97} -151.201 q^{98} -1441.49 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 18 q^{3} + 48 q^{4} - 30 q^{5} + 9 q^{6} - 24 q^{7} - 51 q^{8} + 108 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.447590 0.158247 0.0791235 0.996865i \(-0.474788\pi\)
0.0791235 + 0.996865i \(0.474788\pi\)
\(3\) −9.51519 −1.83120 −0.915599 0.402092i \(-0.868283\pi\)
−0.915599 + 0.402092i \(0.868283\pi\)
\(4\) −7.79966 −0.974958
\(5\) 11.7425 1.05028 0.525142 0.851015i \(-0.324012\pi\)
0.525142 + 0.851015i \(0.324012\pi\)
\(6\) −4.25890 −0.289782
\(7\) −2.27797 −0.122999 −0.0614994 0.998107i \(-0.519588\pi\)
−0.0614994 + 0.998107i \(0.519588\pi\)
\(8\) −7.07177 −0.312531
\(9\) 63.5388 2.35329
\(10\) 5.25584 0.166204
\(11\) −22.6868 −0.621848 −0.310924 0.950435i \(-0.600638\pi\)
−0.310924 + 0.950435i \(0.600638\pi\)
\(12\) 74.2152 1.78534
\(13\) 67.4022 1.43800 0.719001 0.695009i \(-0.244600\pi\)
0.719001 + 0.695009i \(0.244600\pi\)
\(14\) −1.01960 −0.0194642
\(15\) −111.732 −1.92328
\(16\) 59.2321 0.925501
\(17\) 0 0
\(18\) 28.4393 0.372400
\(19\) 42.9965 0.519161 0.259581 0.965721i \(-0.416416\pi\)
0.259581 + 0.965721i \(0.416416\pi\)
\(20\) −91.5878 −1.02398
\(21\) 21.6753 0.225235
\(22\) −10.1544 −0.0984055
\(23\) −117.444 −1.06473 −0.532364 0.846516i \(-0.678696\pi\)
−0.532364 + 0.846516i \(0.678696\pi\)
\(24\) 67.2892 0.572306
\(25\) 12.8870 0.103096
\(26\) 30.1686 0.227559
\(27\) −347.673 −2.47814
\(28\) 17.7674 0.119919
\(29\) −226.336 −1.44930 −0.724648 0.689120i \(-0.757997\pi\)
−0.724648 + 0.689120i \(0.757997\pi\)
\(30\) −50.0103 −0.304353
\(31\) 0.673139 0.00389998 0.00194999 0.999998i \(-0.499379\pi\)
0.00194999 + 0.999998i \(0.499379\pi\)
\(32\) 83.0858 0.458989
\(33\) 215.869 1.13873
\(34\) 0 0
\(35\) −26.7491 −0.129184
\(36\) −495.581 −2.29436
\(37\) 99.9003 0.443878 0.221939 0.975060i \(-0.428761\pi\)
0.221939 + 0.975060i \(0.428761\pi\)
\(38\) 19.2448 0.0821557
\(39\) −641.345 −2.63327
\(40\) −83.0405 −0.328246
\(41\) 154.092 0.586956 0.293478 0.955966i \(-0.405187\pi\)
0.293478 + 0.955966i \(0.405187\pi\)
\(42\) 9.70165 0.0356428
\(43\) −321.792 −1.14123 −0.570615 0.821218i \(-0.693295\pi\)
−0.570615 + 0.821218i \(0.693295\pi\)
\(44\) 176.949 0.606275
\(45\) 746.106 2.47162
\(46\) −52.5667 −0.168490
\(47\) −30.4214 −0.0944132 −0.0472066 0.998885i \(-0.515032\pi\)
−0.0472066 + 0.998885i \(0.515032\pi\)
\(48\) −563.604 −1.69478
\(49\) −337.811 −0.984871
\(50\) 5.76808 0.0163146
\(51\) 0 0
\(52\) −525.715 −1.40199
\(53\) −361.595 −0.937148 −0.468574 0.883424i \(-0.655232\pi\)
−0.468574 + 0.883424i \(0.655232\pi\)
\(54\) −155.615 −0.392158
\(55\) −266.400 −0.653116
\(56\) 16.1093 0.0384410
\(57\) −409.119 −0.950687
\(58\) −101.306 −0.229347
\(59\) 147.417 0.325289 0.162645 0.986685i \(-0.447998\pi\)
0.162645 + 0.986685i \(0.447998\pi\)
\(60\) 871.475 1.87511
\(61\) −321.075 −0.673925 −0.336963 0.941518i \(-0.609400\pi\)
−0.336963 + 0.941518i \(0.609400\pi\)
\(62\) 0.301290 0.000617160 0
\(63\) −144.739 −0.289452
\(64\) −436.668 −0.852867
\(65\) 791.473 1.51031
\(66\) 96.6208 0.180200
\(67\) 612.509 1.11686 0.558432 0.829550i \(-0.311403\pi\)
0.558432 + 0.829550i \(0.311403\pi\)
\(68\) 0 0
\(69\) 1117.50 1.94973
\(70\) −11.9726 −0.0204429
\(71\) −248.823 −0.415913 −0.207956 0.978138i \(-0.566681\pi\)
−0.207956 + 0.978138i \(0.566681\pi\)
\(72\) −449.331 −0.735475
\(73\) 701.031 1.12397 0.561983 0.827149i \(-0.310039\pi\)
0.561983 + 0.827149i \(0.310039\pi\)
\(74\) 44.7144 0.0702424
\(75\) −122.622 −0.188789
\(76\) −335.358 −0.506160
\(77\) 51.6798 0.0764865
\(78\) −287.059 −0.416706
\(79\) −773.040 −1.10093 −0.550467 0.834857i \(-0.685550\pi\)
−0.550467 + 0.834857i \(0.685550\pi\)
\(80\) 695.534 0.972038
\(81\) 1592.63 2.18467
\(82\) 68.9702 0.0928840
\(83\) −1005.91 −1.33028 −0.665139 0.746720i \(-0.731628\pi\)
−0.665139 + 0.746720i \(0.731628\pi\)
\(84\) −169.060 −0.219595
\(85\) 0 0
\(86\) −144.031 −0.180596
\(87\) 2153.63 2.65395
\(88\) 160.436 0.194347
\(89\) 1641.08 1.95454 0.977271 0.211994i \(-0.0679958\pi\)
0.977271 + 0.211994i \(0.0679958\pi\)
\(90\) 333.949 0.391126
\(91\) −153.540 −0.176872
\(92\) 916.023 1.03806
\(93\) −6.40505 −0.00714164
\(94\) −13.6163 −0.0149406
\(95\) 504.887 0.545267
\(96\) −790.577 −0.840499
\(97\) 479.663 0.502087 0.251043 0.967976i \(-0.419226\pi\)
0.251043 + 0.967976i \(0.419226\pi\)
\(98\) −151.201 −0.155853
\(99\) −1441.49 −1.46339
\(100\) −100.514 −0.100514
\(101\) −814.043 −0.801984 −0.400992 0.916082i \(-0.631334\pi\)
−0.400992 + 0.916082i \(0.631334\pi\)
\(102\) 0 0
\(103\) −543.806 −0.520222 −0.260111 0.965579i \(-0.583759\pi\)
−0.260111 + 0.965579i \(0.583759\pi\)
\(104\) −476.653 −0.449420
\(105\) 254.523 0.236561
\(106\) −161.846 −0.148301
\(107\) 171.706 0.155135 0.0775673 0.996987i \(-0.475285\pi\)
0.0775673 + 0.996987i \(0.475285\pi\)
\(108\) 2711.73 2.41608
\(109\) −1310.16 −1.15129 −0.575644 0.817700i \(-0.695249\pi\)
−0.575644 + 0.817700i \(0.695249\pi\)
\(110\) −119.238 −0.103354
\(111\) −950.570 −0.812830
\(112\) −134.929 −0.113836
\(113\) −879.939 −0.732546 −0.366273 0.930507i \(-0.619366\pi\)
−0.366273 + 0.930507i \(0.619366\pi\)
\(114\) −183.118 −0.150443
\(115\) −1379.09 −1.11827
\(116\) 1765.35 1.41300
\(117\) 4282.65 3.38403
\(118\) 65.9824 0.0514760
\(119\) 0 0
\(120\) 790.145 0.601084
\(121\) −816.310 −0.613306
\(122\) −143.710 −0.106647
\(123\) −1466.22 −1.07483
\(124\) −5.25026 −0.00380232
\(125\) −1316.49 −0.942004
\(126\) −64.7839 −0.0458048
\(127\) −1303.39 −0.910684 −0.455342 0.890317i \(-0.650483\pi\)
−0.455342 + 0.890317i \(0.650483\pi\)
\(128\) −860.135 −0.593952
\(129\) 3061.91 2.08982
\(130\) 354.255 0.239002
\(131\) −1523.87 −1.01634 −0.508171 0.861256i \(-0.669678\pi\)
−0.508171 + 0.861256i \(0.669678\pi\)
\(132\) −1683.71 −1.11021
\(133\) −97.9447 −0.0638562
\(134\) 274.153 0.176740
\(135\) −4082.56 −2.60275
\(136\) 0 0
\(137\) −2617.59 −1.63238 −0.816189 0.577785i \(-0.803917\pi\)
−0.816189 + 0.577785i \(0.803917\pi\)
\(138\) 500.182 0.308538
\(139\) 232.950 0.142148 0.0710741 0.997471i \(-0.477357\pi\)
0.0710741 + 0.997471i \(0.477357\pi\)
\(140\) 208.634 0.125949
\(141\) 289.466 0.172889
\(142\) −111.370 −0.0658169
\(143\) −1529.14 −0.894218
\(144\) 3763.53 2.17797
\(145\) −2657.76 −1.52217
\(146\) 313.774 0.177864
\(147\) 3214.33 1.80349
\(148\) −779.189 −0.432763
\(149\) 429.754 0.236287 0.118144 0.992997i \(-0.462306\pi\)
0.118144 + 0.992997i \(0.462306\pi\)
\(150\) −54.8844 −0.0298753
\(151\) −1373.00 −0.739953 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(152\) −304.061 −0.162254
\(153\) 0 0
\(154\) 23.1314 0.0121038
\(155\) 7.90436 0.00409609
\(156\) 5002.27 2.56732
\(157\) 616.059 0.313165 0.156582 0.987665i \(-0.449952\pi\)
0.156582 + 0.987665i \(0.449952\pi\)
\(158\) −346.005 −0.174220
\(159\) 3440.64 1.71610
\(160\) 975.638 0.482068
\(161\) 267.534 0.130960
\(162\) 712.844 0.345718
\(163\) 3460.81 1.66301 0.831507 0.555515i \(-0.187479\pi\)
0.831507 + 0.555515i \(0.187479\pi\)
\(164\) −1201.87 −0.572257
\(165\) 2534.85 1.19599
\(166\) −450.235 −0.210512
\(167\) 2424.76 1.12355 0.561777 0.827288i \(-0.310118\pi\)
0.561777 + 0.827288i \(0.310118\pi\)
\(168\) −153.283 −0.0703930
\(169\) 2346.06 1.06785
\(170\) 0 0
\(171\) 2731.94 1.22174
\(172\) 2509.87 1.11265
\(173\) −2853.14 −1.25388 −0.626938 0.779069i \(-0.715692\pi\)
−0.626938 + 0.779069i \(0.715692\pi\)
\(174\) 963.943 0.419979
\(175\) −29.3562 −0.0126807
\(176\) −1343.79 −0.575521
\(177\) −1402.70 −0.595669
\(178\) 734.531 0.309300
\(179\) 1195.13 0.499040 0.249520 0.968370i \(-0.419727\pi\)
0.249520 + 0.968370i \(0.419727\pi\)
\(180\) −5819.37 −2.40972
\(181\) −2669.80 −1.09638 −0.548190 0.836354i \(-0.684683\pi\)
−0.548190 + 0.836354i \(0.684683\pi\)
\(182\) −68.7231 −0.0279895
\(183\) 3055.09 1.23409
\(184\) 830.536 0.332760
\(185\) 1173.08 0.466198
\(186\) −2.86683 −0.00113014
\(187\) 0 0
\(188\) 237.277 0.0920489
\(189\) 791.989 0.304808
\(190\) 225.982 0.0862868
\(191\) −3394.56 −1.28598 −0.642988 0.765876i \(-0.722306\pi\)
−0.642988 + 0.765876i \(0.722306\pi\)
\(192\) 4154.98 1.56177
\(193\) −3003.88 −1.12033 −0.560165 0.828381i \(-0.689262\pi\)
−0.560165 + 0.828381i \(0.689262\pi\)
\(194\) 214.692 0.0794537
\(195\) −7531.01 −2.76568
\(196\) 2634.81 0.960208
\(197\) −1636.63 −0.591902 −0.295951 0.955203i \(-0.595637\pi\)
−0.295951 + 0.955203i \(0.595637\pi\)
\(198\) −645.197 −0.231576
\(199\) −1600.54 −0.570146 −0.285073 0.958506i \(-0.592018\pi\)
−0.285073 + 0.958506i \(0.592018\pi\)
\(200\) −91.1337 −0.0322206
\(201\) −5828.14 −2.04520
\(202\) −364.358 −0.126911
\(203\) 515.587 0.178262
\(204\) 0 0
\(205\) 1809.44 0.616470
\(206\) −243.402 −0.0823235
\(207\) −7462.24 −2.50561
\(208\) 3992.37 1.33087
\(209\) −975.452 −0.322839
\(210\) 113.922 0.0374350
\(211\) 4282.36 1.39720 0.698602 0.715510i \(-0.253806\pi\)
0.698602 + 0.715510i \(0.253806\pi\)
\(212\) 2820.32 0.913680
\(213\) 2367.59 0.761619
\(214\) 76.8537 0.0245496
\(215\) −3778.65 −1.19861
\(216\) 2458.66 0.774495
\(217\) −1.53339 −0.000479693 0
\(218\) −586.414 −0.182188
\(219\) −6670.44 −2.05820
\(220\) 2077.83 0.636761
\(221\) 0 0
\(222\) −425.465 −0.128628
\(223\) −1396.84 −0.419460 −0.209730 0.977759i \(-0.567258\pi\)
−0.209730 + 0.977759i \(0.567258\pi\)
\(224\) −189.267 −0.0564551
\(225\) 818.822 0.242614
\(226\) −393.852 −0.115923
\(227\) 1612.43 0.471458 0.235729 0.971819i \(-0.424252\pi\)
0.235729 + 0.971819i \(0.424252\pi\)
\(228\) 3190.99 0.926880
\(229\) −2530.45 −0.730204 −0.365102 0.930968i \(-0.618966\pi\)
−0.365102 + 0.930968i \(0.618966\pi\)
\(230\) −617.266 −0.176962
\(231\) −491.743 −0.140062
\(232\) 1600.60 0.452950
\(233\) 4689.59 1.31856 0.659282 0.751896i \(-0.270860\pi\)
0.659282 + 0.751896i \(0.270860\pi\)
\(234\) 1916.87 0.535512
\(235\) −357.225 −0.0991607
\(236\) −1149.80 −0.317143
\(237\) 7355.62 2.01603
\(238\) 0 0
\(239\) −6332.33 −1.71383 −0.856913 0.515462i \(-0.827620\pi\)
−0.856913 + 0.515462i \(0.827620\pi\)
\(240\) −6618.14 −1.78000
\(241\) 4438.39 1.18631 0.593157 0.805087i \(-0.297881\pi\)
0.593157 + 0.805087i \(0.297881\pi\)
\(242\) −365.372 −0.0970537
\(243\) −5766.97 −1.52243
\(244\) 2504.28 0.657049
\(245\) −3966.75 −1.03439
\(246\) −656.265 −0.170089
\(247\) 2898.06 0.746555
\(248\) −4.76029 −0.00121886
\(249\) 9571.43 2.43600
\(250\) −589.248 −0.149069
\(251\) 2085.26 0.524385 0.262193 0.965016i \(-0.415554\pi\)
0.262193 + 0.965016i \(0.415554\pi\)
\(252\) 1128.92 0.282203
\(253\) 2664.42 0.662098
\(254\) −583.383 −0.144113
\(255\) 0 0
\(256\) 3108.36 0.758876
\(257\) −537.124 −0.130369 −0.0651846 0.997873i \(-0.520764\pi\)
−0.0651846 + 0.997873i \(0.520764\pi\)
\(258\) 1370.48 0.330707
\(259\) −227.570 −0.0545965
\(260\) −6173.22 −1.47249
\(261\) −14381.1 −3.41061
\(262\) −682.068 −0.160833
\(263\) 6617.18 1.55146 0.775728 0.631068i \(-0.217383\pi\)
0.775728 + 0.631068i \(0.217383\pi\)
\(264\) −1526.58 −0.355887
\(265\) −4246.03 −0.984271
\(266\) −43.8390 −0.0101051
\(267\) −15615.2 −3.57915
\(268\) −4777.36 −1.08890
\(269\) 617.429 0.139945 0.0699726 0.997549i \(-0.477709\pi\)
0.0699726 + 0.997549i \(0.477709\pi\)
\(270\) −1827.31 −0.411877
\(271\) −5332.00 −1.19519 −0.597594 0.801799i \(-0.703877\pi\)
−0.597594 + 0.801799i \(0.703877\pi\)
\(272\) 0 0
\(273\) 1460.96 0.323889
\(274\) −1171.61 −0.258319
\(275\) −292.364 −0.0641099
\(276\) −8716.12 −1.90090
\(277\) 2486.63 0.539376 0.269688 0.962948i \(-0.413079\pi\)
0.269688 + 0.962948i \(0.413079\pi\)
\(278\) 104.266 0.0224945
\(279\) 42.7704 0.00917777
\(280\) 189.164 0.0403739
\(281\) −4951.96 −1.05128 −0.525639 0.850708i \(-0.676174\pi\)
−0.525639 + 0.850708i \(0.676174\pi\)
\(282\) 129.562 0.0273592
\(283\) 8216.86 1.72594 0.862971 0.505253i \(-0.168601\pi\)
0.862971 + 0.505253i \(0.168601\pi\)
\(284\) 1940.73 0.405498
\(285\) −4804.10 −0.998491
\(286\) −684.428 −0.141507
\(287\) −351.018 −0.0721949
\(288\) 5279.17 1.08013
\(289\) 0 0
\(290\) −1189.59 −0.240879
\(291\) −4564.08 −0.919420
\(292\) −5467.81 −1.09582
\(293\) −737.775 −0.147103 −0.0735516 0.997291i \(-0.523433\pi\)
−0.0735516 + 0.997291i \(0.523433\pi\)
\(294\) 1438.70 0.285397
\(295\) 1731.05 0.341646
\(296\) −706.472 −0.138726
\(297\) 7887.59 1.54102
\(298\) 192.354 0.0373917
\(299\) −7915.98 −1.53108
\(300\) 956.410 0.184061
\(301\) 733.033 0.140370
\(302\) −614.539 −0.117095
\(303\) 7745.77 1.46859
\(304\) 2546.77 0.480484
\(305\) −3770.23 −0.707813
\(306\) 0 0
\(307\) 5994.47 1.11441 0.557203 0.830377i \(-0.311875\pi\)
0.557203 + 0.830377i \(0.311875\pi\)
\(308\) −403.085 −0.0745712
\(309\) 5174.42 0.952629
\(310\) 3.53791 0.000648193 0
\(311\) −9460.76 −1.72498 −0.862492 0.506070i \(-0.831098\pi\)
−0.862492 + 0.506070i \(0.831098\pi\)
\(312\) 4535.44 0.822977
\(313\) 4674.92 0.844225 0.422112 0.906544i \(-0.361289\pi\)
0.422112 + 0.906544i \(0.361289\pi\)
\(314\) 275.742 0.0495574
\(315\) −1699.61 −0.304006
\(316\) 6029.45 1.07336
\(317\) −692.929 −0.122772 −0.0613861 0.998114i \(-0.519552\pi\)
−0.0613861 + 0.998114i \(0.519552\pi\)
\(318\) 1540.00 0.271568
\(319\) 5134.84 0.901241
\(320\) −5127.59 −0.895753
\(321\) −1633.81 −0.284082
\(322\) 119.745 0.0207241
\(323\) 0 0
\(324\) −12422.0 −2.12997
\(325\) 868.611 0.148252
\(326\) 1549.02 0.263167
\(327\) 12466.4 2.10824
\(328\) −1089.71 −0.183442
\(329\) 69.2991 0.0116127
\(330\) 1134.57 0.189261
\(331\) −7067.34 −1.17358 −0.586792 0.809738i \(-0.699609\pi\)
−0.586792 + 0.809738i \(0.699609\pi\)
\(332\) 7845.76 1.29696
\(333\) 6347.54 1.04457
\(334\) 1085.30 0.177799
\(335\) 7192.40 1.17302
\(336\) 1283.87 0.208455
\(337\) −5897.11 −0.953223 −0.476611 0.879114i \(-0.658135\pi\)
−0.476611 + 0.879114i \(0.658135\pi\)
\(338\) 1050.07 0.168984
\(339\) 8372.78 1.34144
\(340\) 0 0
\(341\) −15.2714 −0.00242519
\(342\) 1222.79 0.193336
\(343\) 1550.87 0.244137
\(344\) 2275.64 0.356669
\(345\) 13122.3 2.04777
\(346\) −1277.04 −0.198422
\(347\) −9529.27 −1.47423 −0.737115 0.675767i \(-0.763812\pi\)
−0.737115 + 0.675767i \(0.763812\pi\)
\(348\) −16797.6 −2.58749
\(349\) −2516.87 −0.386031 −0.193016 0.981196i \(-0.561827\pi\)
−0.193016 + 0.981196i \(0.561827\pi\)
\(350\) −13.1395 −0.00200668
\(351\) −23433.9 −3.56356
\(352\) −1884.95 −0.285421
\(353\) 9296.21 1.40166 0.700832 0.713327i \(-0.252812\pi\)
0.700832 + 0.713327i \(0.252812\pi\)
\(354\) −627.834 −0.0942628
\(355\) −2921.81 −0.436826
\(356\) −12799.9 −1.90560
\(357\) 0 0
\(358\) 534.928 0.0789716
\(359\) 10477.8 1.54038 0.770192 0.637812i \(-0.220160\pi\)
0.770192 + 0.637812i \(0.220160\pi\)
\(360\) −5276.29 −0.772458
\(361\) −5010.30 −0.730472
\(362\) −1194.98 −0.173499
\(363\) 7767.34 1.12308
\(364\) 1197.56 0.172443
\(365\) 8231.88 1.18048
\(366\) 1367.43 0.195291
\(367\) −2779.47 −0.395332 −0.197666 0.980269i \(-0.563336\pi\)
−0.197666 + 0.980269i \(0.563336\pi\)
\(368\) −6956.44 −0.985406
\(369\) 9790.84 1.38128
\(370\) 525.060 0.0737745
\(371\) 823.702 0.115268
\(372\) 49.9572 0.00696280
\(373\) 2548.58 0.353782 0.176891 0.984230i \(-0.443396\pi\)
0.176891 + 0.984230i \(0.443396\pi\)
\(374\) 0 0
\(375\) 12526.7 1.72500
\(376\) 215.133 0.0295071
\(377\) −15255.6 −2.08409
\(378\) 354.486 0.0482349
\(379\) 11378.4 1.54213 0.771067 0.636754i \(-0.219723\pi\)
0.771067 + 0.636754i \(0.219723\pi\)
\(380\) −3937.95 −0.531612
\(381\) 12402.0 1.66764
\(382\) −1519.37 −0.203502
\(383\) −633.266 −0.0844867 −0.0422433 0.999107i \(-0.513450\pi\)
−0.0422433 + 0.999107i \(0.513450\pi\)
\(384\) 8184.34 1.08764
\(385\) 606.852 0.0803326
\(386\) −1344.50 −0.177289
\(387\) −20446.3 −2.68564
\(388\) −3741.21 −0.489513
\(389\) 12163.4 1.58537 0.792685 0.609632i \(-0.208683\pi\)
0.792685 + 0.609632i \(0.208683\pi\)
\(390\) −3370.80 −0.437660
\(391\) 0 0
\(392\) 2388.92 0.307803
\(393\) 14499.9 1.86113
\(394\) −732.537 −0.0936667
\(395\) −9077.45 −1.15629
\(396\) 11243.1 1.42674
\(397\) 11911.8 1.50589 0.752944 0.658084i \(-0.228633\pi\)
0.752944 + 0.658084i \(0.228633\pi\)
\(398\) −716.384 −0.0902239
\(399\) 931.962 0.116933
\(400\) 763.322 0.0954153
\(401\) −7875.79 −0.980793 −0.490396 0.871499i \(-0.663148\pi\)
−0.490396 + 0.871499i \(0.663148\pi\)
\(402\) −2608.62 −0.323647
\(403\) 45.3711 0.00560818
\(404\) 6349.26 0.781900
\(405\) 18701.5 2.29453
\(406\) 230.772 0.0282094
\(407\) −2266.42 −0.276025
\(408\) 0 0
\(409\) −4351.34 −0.526064 −0.263032 0.964787i \(-0.584722\pi\)
−0.263032 + 0.964787i \(0.584722\pi\)
\(410\) 809.885 0.0975545
\(411\) 24906.9 2.98921
\(412\) 4241.51 0.507194
\(413\) −335.812 −0.0400102
\(414\) −3340.02 −0.396505
\(415\) −11811.9 −1.39717
\(416\) 5600.17 0.660026
\(417\) −2216.57 −0.260301
\(418\) −436.602 −0.0510883
\(419\) 2066.20 0.240908 0.120454 0.992719i \(-0.461565\pi\)
0.120454 + 0.992719i \(0.461565\pi\)
\(420\) −1985.19 −0.230637
\(421\) 10563.5 1.22289 0.611443 0.791289i \(-0.290589\pi\)
0.611443 + 0.791289i \(0.290589\pi\)
\(422\) 1916.74 0.221103
\(423\) −1932.94 −0.222181
\(424\) 2557.11 0.292888
\(425\) 0 0
\(426\) 1059.71 0.120524
\(427\) 731.399 0.0828920
\(428\) −1339.25 −0.151250
\(429\) 14550.1 1.63749
\(430\) −1691.29 −0.189677
\(431\) 4347.98 0.485928 0.242964 0.970035i \(-0.421880\pi\)
0.242964 + 0.970035i \(0.421880\pi\)
\(432\) −20593.4 −2.29352
\(433\) 949.003 0.105326 0.0526630 0.998612i \(-0.483229\pi\)
0.0526630 + 0.998612i \(0.483229\pi\)
\(434\) −0.686331 −7.59100e−5 0
\(435\) 25289.1 2.78740
\(436\) 10218.8 1.12246
\(437\) −5049.67 −0.552765
\(438\) −2985.62 −0.325704
\(439\) −7256.78 −0.788946 −0.394473 0.918908i \(-0.629073\pi\)
−0.394473 + 0.918908i \(0.629073\pi\)
\(440\) 1883.92 0.204119
\(441\) −21464.1 −2.31769
\(442\) 0 0
\(443\) −3674.08 −0.394043 −0.197021 0.980399i \(-0.563127\pi\)
−0.197021 + 0.980399i \(0.563127\pi\)
\(444\) 7414.12 0.792475
\(445\) 19270.4 2.05282
\(446\) −625.213 −0.0663782
\(447\) −4089.19 −0.432689
\(448\) 994.717 0.104902
\(449\) 13012.3 1.36769 0.683843 0.729630i \(-0.260307\pi\)
0.683843 + 0.729630i \(0.260307\pi\)
\(450\) 366.497 0.0383929
\(451\) −3495.86 −0.364997
\(452\) 6863.23 0.714201
\(453\) 13064.3 1.35500
\(454\) 721.708 0.0746067
\(455\) −1802.95 −0.185766
\(456\) 2893.20 0.297119
\(457\) −13.1283 −0.00134380 −0.000671900 1.00000i \(-0.500214\pi\)
−0.000671900 1.00000i \(0.500214\pi\)
\(458\) −1132.60 −0.115553
\(459\) 0 0
\(460\) 10756.4 1.09026
\(461\) −14382.6 −1.45307 −0.726537 0.687128i \(-0.758871\pi\)
−0.726537 + 0.687128i \(0.758871\pi\)
\(462\) −220.099 −0.0221644
\(463\) −13264.3 −1.33141 −0.665705 0.746215i \(-0.731869\pi\)
−0.665705 + 0.746215i \(0.731869\pi\)
\(464\) −13406.4 −1.34132
\(465\) −75.2114 −0.00750075
\(466\) 2099.01 0.208659
\(467\) 12992.0 1.28736 0.643681 0.765294i \(-0.277406\pi\)
0.643681 + 0.765294i \(0.277406\pi\)
\(468\) −33403.3 −3.29929
\(469\) −1395.28 −0.137373
\(470\) −159.890 −0.0156919
\(471\) −5861.92 −0.573467
\(472\) −1042.50 −0.101663
\(473\) 7300.43 0.709671
\(474\) 3292.30 0.319030
\(475\) 554.094 0.0535234
\(476\) 0 0
\(477\) −22975.3 −2.20538
\(478\) −2834.29 −0.271208
\(479\) −8697.74 −0.829665 −0.414833 0.909898i \(-0.636160\pi\)
−0.414833 + 0.909898i \(0.636160\pi\)
\(480\) −9283.37 −0.882763
\(481\) 6733.50 0.638298
\(482\) 1986.58 0.187730
\(483\) −2545.63 −0.239814
\(484\) 6366.94 0.597947
\(485\) 5632.46 0.527333
\(486\) −2581.24 −0.240920
\(487\) −1219.66 −0.113487 −0.0567435 0.998389i \(-0.518072\pi\)
−0.0567435 + 0.998389i \(0.518072\pi\)
\(488\) 2270.57 0.210623
\(489\) −32930.2 −3.04531
\(490\) −1775.48 −0.163690
\(491\) 11340.1 1.04231 0.521154 0.853463i \(-0.325502\pi\)
0.521154 + 0.853463i \(0.325502\pi\)
\(492\) 11436.0 1.04792
\(493\) 0 0
\(494\) 1297.14 0.118140
\(495\) −16926.7 −1.53697
\(496\) 39.8714 0.00360944
\(497\) 566.811 0.0511568
\(498\) 4284.07 0.385490
\(499\) 7357.73 0.660074 0.330037 0.943968i \(-0.392939\pi\)
0.330037 + 0.943968i \(0.392939\pi\)
\(500\) 10268.2 0.918414
\(501\) −23072.1 −2.05745
\(502\) 933.343 0.0829824
\(503\) −4549.92 −0.403321 −0.201661 0.979455i \(-0.564634\pi\)
−0.201661 + 0.979455i \(0.564634\pi\)
\(504\) 1023.56 0.0904626
\(505\) −9558.93 −0.842310
\(506\) 1192.57 0.104775
\(507\) −22323.2 −1.95544
\(508\) 10166.0 0.887879
\(509\) −13630.1 −1.18692 −0.593461 0.804863i \(-0.702239\pi\)
−0.593461 + 0.804863i \(0.702239\pi\)
\(510\) 0 0
\(511\) −1596.93 −0.138246
\(512\) 8272.35 0.714042
\(513\) −14948.7 −1.28655
\(514\) −240.411 −0.0206305
\(515\) −6385.66 −0.546380
\(516\) −23881.9 −2.03748
\(517\) 690.165 0.0587106
\(518\) −101.858 −0.00863974
\(519\) 27148.2 2.29609
\(520\) −5597.11 −0.472018
\(521\) −14004.2 −1.17761 −0.588805 0.808275i \(-0.700402\pi\)
−0.588805 + 0.808275i \(0.700402\pi\)
\(522\) −6436.84 −0.539718
\(523\) −5652.21 −0.472570 −0.236285 0.971684i \(-0.575930\pi\)
−0.236285 + 0.971684i \(0.575930\pi\)
\(524\) 11885.7 0.990891
\(525\) 279.329 0.0232208
\(526\) 2961.78 0.245513
\(527\) 0 0
\(528\) 12786.4 1.05389
\(529\) 1626.06 0.133645
\(530\) −1900.48 −0.155758
\(531\) 9366.69 0.765499
\(532\) 763.935 0.0622571
\(533\) 10386.2 0.844044
\(534\) −6989.20 −0.566390
\(535\) 2016.26 0.162935
\(536\) −4331.52 −0.349055
\(537\) −11371.9 −0.913842
\(538\) 276.355 0.0221459
\(539\) 7663.84 0.612440
\(540\) 31842.6 2.53757
\(541\) −8809.75 −0.700112 −0.350056 0.936729i \(-0.613837\pi\)
−0.350056 + 0.936729i \(0.613837\pi\)
\(542\) −2386.55 −0.189135
\(543\) 25403.7 2.00769
\(544\) 0 0
\(545\) −15384.6 −1.20918
\(546\) 653.913 0.0512544
\(547\) −2198.83 −0.171874 −0.0859372 0.996301i \(-0.527388\pi\)
−0.0859372 + 0.996301i \(0.527388\pi\)
\(548\) 20416.3 1.59150
\(549\) −20400.7 −1.58594
\(550\) −130.859 −0.0101452
\(551\) −9731.65 −0.752418
\(552\) −7902.70 −0.609350
\(553\) 1760.96 0.135414
\(554\) 1112.99 0.0853546
\(555\) −11162.1 −0.853702
\(556\) −1816.93 −0.138588
\(557\) 19799.3 1.50614 0.753072 0.657938i \(-0.228571\pi\)
0.753072 + 0.657938i \(0.228571\pi\)
\(558\) 19.1436 0.00145235
\(559\) −21689.5 −1.64109
\(560\) −1584.41 −0.119560
\(561\) 0 0
\(562\) −2216.45 −0.166362
\(563\) −20671.9 −1.54745 −0.773726 0.633521i \(-0.781609\pi\)
−0.773726 + 0.633521i \(0.781609\pi\)
\(564\) −2257.73 −0.168560
\(565\) −10332.7 −0.769381
\(566\) 3677.78 0.273125
\(567\) −3627.96 −0.268712
\(568\) 1759.62 0.129986
\(569\) −10735.1 −0.790928 −0.395464 0.918481i \(-0.629416\pi\)
−0.395464 + 0.918481i \(0.629416\pi\)
\(570\) −2150.26 −0.158008
\(571\) −1413.36 −0.103586 −0.0517929 0.998658i \(-0.516494\pi\)
−0.0517929 + 0.998658i \(0.516494\pi\)
\(572\) 11926.8 0.871825
\(573\) 32299.8 2.35488
\(574\) −157.112 −0.0114246
\(575\) −1513.50 −0.109769
\(576\) −27745.3 −2.00704
\(577\) 13903.6 1.00314 0.501572 0.865116i \(-0.332755\pi\)
0.501572 + 0.865116i \(0.332755\pi\)
\(578\) 0 0
\(579\) 28582.4 2.05155
\(580\) 20729.6 1.48405
\(581\) 2291.43 0.163623
\(582\) −2042.84 −0.145495
\(583\) 8203.42 0.582763
\(584\) −4957.53 −0.351274
\(585\) 50289.2 3.55419
\(586\) −330.220 −0.0232786
\(587\) 7153.64 0.503002 0.251501 0.967857i \(-0.419076\pi\)
0.251501 + 0.967857i \(0.419076\pi\)
\(588\) −25070.7 −1.75833
\(589\) 28.9426 0.00202472
\(590\) 774.800 0.0540644
\(591\) 15572.8 1.08389
\(592\) 5917.30 0.410810
\(593\) −22686.9 −1.57106 −0.785530 0.618824i \(-0.787610\pi\)
−0.785530 + 0.618824i \(0.787610\pi\)
\(594\) 3530.40 0.243862
\(595\) 0 0
\(596\) −3351.94 −0.230370
\(597\) 15229.4 1.04405
\(598\) −3543.11 −0.242289
\(599\) 9190.22 0.626882 0.313441 0.949608i \(-0.398518\pi\)
0.313441 + 0.949608i \(0.398518\pi\)
\(600\) 867.154 0.0590024
\(601\) −12350.7 −0.838260 −0.419130 0.907926i \(-0.637665\pi\)
−0.419130 + 0.907926i \(0.637665\pi\)
\(602\) 328.098 0.0222131
\(603\) 38918.1 2.62830
\(604\) 10708.9 0.721423
\(605\) −9585.54 −0.644145
\(606\) 3466.93 0.232400
\(607\) 22662.6 1.51540 0.757698 0.652606i \(-0.226324\pi\)
0.757698 + 0.652606i \(0.226324\pi\)
\(608\) 3572.40 0.238289
\(609\) −4905.91 −0.326432
\(610\) −1687.52 −0.112009
\(611\) −2050.47 −0.135766
\(612\) 0 0
\(613\) 5314.94 0.350193 0.175097 0.984551i \(-0.443976\pi\)
0.175097 + 0.984551i \(0.443976\pi\)
\(614\) 2683.06 0.176351
\(615\) −17217.1 −1.12888
\(616\) −365.468 −0.0239044
\(617\) 7956.05 0.519122 0.259561 0.965727i \(-0.416422\pi\)
0.259561 + 0.965727i \(0.416422\pi\)
\(618\) 2316.02 0.150751
\(619\) −13874.9 −0.900933 −0.450467 0.892793i \(-0.648742\pi\)
−0.450467 + 0.892793i \(0.648742\pi\)
\(620\) −61.6513 −0.00399351
\(621\) 40832.1 2.63854
\(622\) −4234.54 −0.272974
\(623\) −3738.33 −0.240406
\(624\) −37988.2 −2.43709
\(625\) −17069.8 −1.09247
\(626\) 2092.45 0.133596
\(627\) 9281.60 0.591183
\(628\) −4805.06 −0.305323
\(629\) 0 0
\(630\) −760.727 −0.0481081
\(631\) −23668.0 −1.49320 −0.746598 0.665276i \(-0.768314\pi\)
−0.746598 + 0.665276i \(0.768314\pi\)
\(632\) 5466.76 0.344076
\(633\) −40747.5 −2.55856
\(634\) −310.148 −0.0194283
\(635\) −15305.1 −0.956477
\(636\) −26835.8 −1.67313
\(637\) −22769.2 −1.41625
\(638\) 2298.30 0.142619
\(639\) −15809.9 −0.978762
\(640\) −10100.2 −0.623818
\(641\) −18274.3 −1.12604 −0.563021 0.826442i \(-0.690361\pi\)
−0.563021 + 0.826442i \(0.690361\pi\)
\(642\) −731.277 −0.0449552
\(643\) 19527.2 1.19763 0.598815 0.800887i \(-0.295639\pi\)
0.598815 + 0.800887i \(0.295639\pi\)
\(644\) −2086.67 −0.127681
\(645\) 35954.6 2.19490
\(646\) 0 0
\(647\) −4471.27 −0.271690 −0.135845 0.990730i \(-0.543375\pi\)
−0.135845 + 0.990730i \(0.543375\pi\)
\(648\) −11262.7 −0.682778
\(649\) −3344.42 −0.202280
\(650\) 388.781 0.0234604
\(651\) 14.5905 0.000878413 0
\(652\) −26993.1 −1.62137
\(653\) −10869.7 −0.651399 −0.325699 0.945473i \(-0.605600\pi\)
−0.325699 + 0.945473i \(0.605600\pi\)
\(654\) 5579.84 0.333622
\(655\) −17894.1 −1.06745
\(656\) 9127.21 0.543228
\(657\) 44542.6 2.64501
\(658\) 31.0176 0.00183768
\(659\) −3827.54 −0.226252 −0.113126 0.993581i \(-0.536086\pi\)
−0.113126 + 0.993581i \(0.536086\pi\)
\(660\) −19771.0 −1.16604
\(661\) 15347.3 0.903087 0.451543 0.892249i \(-0.350874\pi\)
0.451543 + 0.892249i \(0.350874\pi\)
\(662\) −3163.27 −0.185716
\(663\) 0 0
\(664\) 7113.57 0.415753
\(665\) −1150.12 −0.0670672
\(666\) 2841.09 0.165301
\(667\) 26581.8 1.54310
\(668\) −18912.3 −1.09542
\(669\) 13291.2 0.768114
\(670\) 3219.25 0.185627
\(671\) 7284.16 0.419079
\(672\) 1800.91 0.103380
\(673\) 26133.5 1.49684 0.748418 0.663227i \(-0.230814\pi\)
0.748418 + 0.663227i \(0.230814\pi\)
\(674\) −2639.49 −0.150845
\(675\) −4480.45 −0.255486
\(676\) −18298.5 −1.04111
\(677\) 19539.0 1.10922 0.554612 0.832109i \(-0.312867\pi\)
0.554612 + 0.832109i \(0.312867\pi\)
\(678\) 3747.57 0.212278
\(679\) −1092.66 −0.0617561
\(680\) 0 0
\(681\) −15342.6 −0.863332
\(682\) −6.83531 −0.000383779 0
\(683\) −16057.8 −0.899612 −0.449806 0.893126i \(-0.648507\pi\)
−0.449806 + 0.893126i \(0.648507\pi\)
\(684\) −21308.2 −1.19114
\(685\) −30737.1 −1.71446
\(686\) 694.152 0.0386339
\(687\) 24077.7 1.33715
\(688\) −19060.4 −1.05621
\(689\) −24372.3 −1.34762
\(690\) 5873.40 0.324053
\(691\) 14698.6 0.809206 0.404603 0.914493i \(-0.367410\pi\)
0.404603 + 0.914493i \(0.367410\pi\)
\(692\) 22253.6 1.22248
\(693\) 3283.67 0.179995
\(694\) −4265.20 −0.233292
\(695\) 2735.43 0.149296
\(696\) −15230.0 −0.829441
\(697\) 0 0
\(698\) −1126.53 −0.0610883
\(699\) −44622.3 −2.41455
\(700\) 228.968 0.0123631
\(701\) −7042.75 −0.379459 −0.189730 0.981836i \(-0.560761\pi\)
−0.189730 + 0.981836i \(0.560761\pi\)
\(702\) −10488.8 −0.563923
\(703\) 4295.36 0.230445
\(704\) 9906.60 0.530354
\(705\) 3399.06 0.181583
\(706\) 4160.89 0.221809
\(707\) 1854.37 0.0986431
\(708\) 10940.6 0.580752
\(709\) −5951.66 −0.315260 −0.157630 0.987498i \(-0.550385\pi\)
−0.157630 + 0.987498i \(0.550385\pi\)
\(710\) −1307.77 −0.0691265
\(711\) −49118.0 −2.59082
\(712\) −11605.3 −0.610855
\(713\) −79.0561 −0.00415242
\(714\) 0 0
\(715\) −17956.0 −0.939182
\(716\) −9321.61 −0.486543
\(717\) 60253.3 3.13835
\(718\) 4689.76 0.243761
\(719\) 34823.3 1.80625 0.903123 0.429381i \(-0.141268\pi\)
0.903123 + 0.429381i \(0.141268\pi\)
\(720\) 44193.4 2.28749
\(721\) 1238.77 0.0639866
\(722\) −2242.56 −0.115595
\(723\) −42232.1 −2.17238
\(724\) 20823.6 1.06892
\(725\) −2916.79 −0.149416
\(726\) 3476.58 0.177725
\(727\) −3241.15 −0.165348 −0.0826738 0.996577i \(-0.526346\pi\)
−0.0826738 + 0.996577i \(0.526346\pi\)
\(728\) 1085.80 0.0552781
\(729\) 11872.9 0.603204
\(730\) 3684.51 0.186808
\(731\) 0 0
\(732\) −23828.7 −1.20319
\(733\) 18578.8 0.936185 0.468093 0.883679i \(-0.344941\pi\)
0.468093 + 0.883679i \(0.344941\pi\)
\(734\) −1244.06 −0.0625601
\(735\) 37744.4 1.89418
\(736\) −9757.92 −0.488698
\(737\) −13895.9 −0.694519
\(738\) 4382.28 0.218583
\(739\) 30393.0 1.51289 0.756444 0.654058i \(-0.226935\pi\)
0.756444 + 0.654058i \(0.226935\pi\)
\(740\) −9149.64 −0.454524
\(741\) −27575.6 −1.36709
\(742\) 368.681 0.0182408
\(743\) −37449.0 −1.84908 −0.924542 0.381081i \(-0.875552\pi\)
−0.924542 + 0.381081i \(0.875552\pi\)
\(744\) 45.2950 0.00223198
\(745\) 5046.40 0.248169
\(746\) 1140.72 0.0559849
\(747\) −63914.3 −3.13052
\(748\) 0 0
\(749\) −391.140 −0.0190814
\(750\) 5606.80 0.272975
\(751\) 5541.28 0.269247 0.134623 0.990897i \(-0.457018\pi\)
0.134623 + 0.990897i \(0.457018\pi\)
\(752\) −1801.92 −0.0873795
\(753\) −19841.7 −0.960253
\(754\) −6828.23 −0.329801
\(755\) −16122.5 −0.777160
\(756\) −6177.25 −0.297175
\(757\) 13531.4 0.649680 0.324840 0.945769i \(-0.394690\pi\)
0.324840 + 0.945769i \(0.394690\pi\)
\(758\) 5092.85 0.244038
\(759\) −25352.5 −1.21243
\(760\) −3570.45 −0.170413
\(761\) −37110.8 −1.76776 −0.883879 0.467715i \(-0.845077\pi\)
−0.883879 + 0.467715i \(0.845077\pi\)
\(762\) 5551.00 0.263899
\(763\) 2984.50 0.141607
\(764\) 26476.4 1.25377
\(765\) 0 0
\(766\) −283.444 −0.0133698
\(767\) 9936.24 0.467766
\(768\) −29576.6 −1.38965
\(769\) −820.351 −0.0384689 −0.0192345 0.999815i \(-0.506123\pi\)
−0.0192345 + 0.999815i \(0.506123\pi\)
\(770\) 271.621 0.0127124
\(771\) 5110.84 0.238732
\(772\) 23429.2 1.09227
\(773\) −25113.2 −1.16851 −0.584255 0.811570i \(-0.698613\pi\)
−0.584255 + 0.811570i \(0.698613\pi\)
\(774\) −9151.55 −0.424994
\(775\) 8.67473 0.000402072 0
\(776\) −3392.07 −0.156918
\(777\) 2165.37 0.0999771
\(778\) 5444.21 0.250880
\(779\) 6625.43 0.304725
\(780\) 58739.3 2.69642
\(781\) 5644.99 0.258634
\(782\) 0 0
\(783\) 78691.0 3.59155
\(784\) −20009.2 −0.911499
\(785\) 7234.10 0.328912
\(786\) 6490.00 0.294517
\(787\) 20784.0 0.941384 0.470692 0.882298i \(-0.344004\pi\)
0.470692 + 0.882298i \(0.344004\pi\)
\(788\) 12765.1 0.577080
\(789\) −62963.7 −2.84102
\(790\) −4062.97 −0.182980
\(791\) 2004.47 0.0901023
\(792\) 10193.9 0.457354
\(793\) −21641.2 −0.969105
\(794\) 5331.62 0.238302
\(795\) 40401.8 1.80240
\(796\) 12483.7 0.555868
\(797\) 4974.23 0.221074 0.110537 0.993872i \(-0.464743\pi\)
0.110537 + 0.993872i \(0.464743\pi\)
\(798\) 417.137 0.0185044
\(799\) 0 0
\(800\) 1070.73 0.0473198
\(801\) 104272. 4.59960
\(802\) −3525.12 −0.155207
\(803\) −15904.1 −0.698935
\(804\) 45457.5 1.99398
\(805\) 3141.52 0.137545
\(806\) 20.3076 0.000887477 0
\(807\) −5874.95 −0.256268
\(808\) 5756.73 0.250645
\(809\) −27460.1 −1.19338 −0.596692 0.802471i \(-0.703519\pi\)
−0.596692 + 0.802471i \(0.703519\pi\)
\(810\) 8370.59 0.363102
\(811\) −14356.6 −0.621612 −0.310806 0.950473i \(-0.600599\pi\)
−0.310806 + 0.950473i \(0.600599\pi\)
\(812\) −4021.40 −0.173798
\(813\) 50735.0 2.18863
\(814\) −1014.43 −0.0436801
\(815\) 40638.6 1.74664
\(816\) 0 0
\(817\) −13835.9 −0.592482
\(818\) −1947.62 −0.0832480
\(819\) −9755.76 −0.416232
\(820\) −14113.0 −0.601033
\(821\) 15953.0 0.678155 0.339077 0.940758i \(-0.389885\pi\)
0.339077 + 0.940758i \(0.389885\pi\)
\(822\) 11148.1 0.473033
\(823\) 17581.1 0.744641 0.372321 0.928104i \(-0.378562\pi\)
0.372321 + 0.928104i \(0.378562\pi\)
\(824\) 3845.67 0.162585
\(825\) 2781.90 0.117398
\(826\) −150.306 −0.00633149
\(827\) −39492.2 −1.66056 −0.830278 0.557349i \(-0.811818\pi\)
−0.830278 + 0.557349i \(0.811818\pi\)
\(828\) 58202.9 2.44286
\(829\) 15789.1 0.661494 0.330747 0.943720i \(-0.392699\pi\)
0.330747 + 0.943720i \(0.392699\pi\)
\(830\) −5286.90 −0.221098
\(831\) −23660.7 −0.987704
\(832\) −29432.4 −1.22642
\(833\) 0 0
\(834\) −992.112 −0.0411919
\(835\) 28472.8 1.18005
\(836\) 7608.19 0.314755
\(837\) −234.032 −0.00966469
\(838\) 924.812 0.0381230
\(839\) −9439.37 −0.388419 −0.194209 0.980960i \(-0.562214\pi\)
−0.194209 + 0.980960i \(0.562214\pi\)
\(840\) −1799.93 −0.0739326
\(841\) 26839.0 1.10046
\(842\) 4728.13 0.193518
\(843\) 47118.8 1.92510
\(844\) −33401.0 −1.36222
\(845\) 27548.7 1.12154
\(846\) −865.164 −0.0351595
\(847\) 1859.53 0.0754359
\(848\) −21418.0 −0.867331
\(849\) −78185.0 −3.16054
\(850\) 0 0
\(851\) −11732.7 −0.472610
\(852\) −18466.4 −0.742546
\(853\) −2324.12 −0.0932898 −0.0466449 0.998912i \(-0.514853\pi\)
−0.0466449 + 0.998912i \(0.514853\pi\)
\(854\) 327.367 0.0131174
\(855\) 32079.9 1.28317
\(856\) −1214.26 −0.0484844
\(857\) 22464.0 0.895399 0.447699 0.894184i \(-0.352244\pi\)
0.447699 + 0.894184i \(0.352244\pi\)
\(858\) 6512.46 0.259128
\(859\) −1314.36 −0.0522064 −0.0261032 0.999659i \(-0.508310\pi\)
−0.0261032 + 0.999659i \(0.508310\pi\)
\(860\) 29472.2 1.16860
\(861\) 3340.00 0.132203
\(862\) 1946.11 0.0768966
\(863\) −15380.5 −0.606674 −0.303337 0.952883i \(-0.598101\pi\)
−0.303337 + 0.952883i \(0.598101\pi\)
\(864\) −28886.7 −1.13744
\(865\) −33503.1 −1.31693
\(866\) 424.764 0.0166675
\(867\) 0 0
\(868\) 11.9599 0.000467681 0
\(869\) 17537.8 0.684614
\(870\) 11319.1 0.441097
\(871\) 41284.5 1.60605
\(872\) 9265.14 0.359813
\(873\) 30477.2 1.18155
\(874\) −2260.18 −0.0874734
\(875\) 2998.93 0.115865
\(876\) 52027.2 2.00666
\(877\) 14688.9 0.565574 0.282787 0.959183i \(-0.408741\pi\)
0.282787 + 0.959183i \(0.408741\pi\)
\(878\) −3248.06 −0.124848
\(879\) 7020.06 0.269375
\(880\) −15779.4 −0.604460
\(881\) −9512.25 −0.363764 −0.181882 0.983320i \(-0.558219\pi\)
−0.181882 + 0.983320i \(0.558219\pi\)
\(882\) −9607.11 −0.366767
\(883\) 14662.1 0.558798 0.279399 0.960175i \(-0.409865\pi\)
0.279399 + 0.960175i \(0.409865\pi\)
\(884\) 0 0
\(885\) −16471.2 −0.625621
\(886\) −1644.48 −0.0623561
\(887\) 27847.1 1.05413 0.527065 0.849825i \(-0.323292\pi\)
0.527065 + 0.849825i \(0.323292\pi\)
\(888\) 6722.21 0.254034
\(889\) 2969.08 0.112013
\(890\) 8625.25 0.324853
\(891\) −36131.6 −1.35853
\(892\) 10894.9 0.408956
\(893\) −1308.01 −0.0490157
\(894\) −1830.28 −0.0684717
\(895\) 14033.8 0.524134
\(896\) 1959.36 0.0730554
\(897\) 75322.0 2.80371
\(898\) 5824.20 0.216432
\(899\) −152.356 −0.00565222
\(900\) −6386.54 −0.236538
\(901\) 0 0
\(902\) −1564.71 −0.0577597
\(903\) −6974.95 −0.257045
\(904\) 6222.72 0.228943
\(905\) −31350.2 −1.15151
\(906\) 5847.46 0.214425
\(907\) 141.986 0.00519799 0.00259899 0.999997i \(-0.499173\pi\)
0.00259899 + 0.999997i \(0.499173\pi\)
\(908\) −12576.4 −0.459651
\(909\) −51723.3 −1.88730
\(910\) −806.983 −0.0293969
\(911\) 32439.3 1.17976 0.589881 0.807490i \(-0.299175\pi\)
0.589881 + 0.807490i \(0.299175\pi\)
\(912\) −24233.0 −0.879862
\(913\) 22820.9 0.827230
\(914\) −5.87610 −0.000212652 0
\(915\) 35874.5 1.29615
\(916\) 19736.6 0.711918
\(917\) 3471.32 0.125009
\(918\) 0 0
\(919\) 11802.3 0.423638 0.211819 0.977309i \(-0.432061\pi\)
0.211819 + 0.977309i \(0.432061\pi\)
\(920\) 9752.59 0.349493
\(921\) −57038.5 −2.04070
\(922\) −6437.53 −0.229944
\(923\) −16771.2 −0.598083
\(924\) 3835.43 0.136555
\(925\) 1287.41 0.0457620
\(926\) −5936.95 −0.210691
\(927\) −34552.8 −1.22423
\(928\) −18805.3 −0.665210
\(929\) 30089.9 1.06267 0.531334 0.847163i \(-0.321691\pi\)
0.531334 + 0.847163i \(0.321691\pi\)
\(930\) −33.6639 −0.00118697
\(931\) −14524.7 −0.511307
\(932\) −36577.2 −1.28554
\(933\) 90020.9 3.15879
\(934\) 5815.09 0.203721
\(935\) 0 0
\(936\) −30285.9 −1.05761
\(937\) −34961.5 −1.21894 −0.609468 0.792810i \(-0.708617\pi\)
−0.609468 + 0.792810i \(0.708617\pi\)
\(938\) −624.512 −0.0217389
\(939\) −44482.8 −1.54594
\(940\) 2786.23 0.0966775
\(941\) −8933.80 −0.309494 −0.154747 0.987954i \(-0.549456\pi\)
−0.154747 + 0.987954i \(0.549456\pi\)
\(942\) −2623.74 −0.0907494
\(943\) −18097.2 −0.624948
\(944\) 8731.81 0.301055
\(945\) 9299.95 0.320135
\(946\) 3267.60 0.112303
\(947\) −17816.2 −0.611350 −0.305675 0.952136i \(-0.598882\pi\)
−0.305675 + 0.952136i \(0.598882\pi\)
\(948\) −57371.4 −1.96554
\(949\) 47251.1 1.61626
\(950\) 248.007 0.00846991
\(951\) 6593.35 0.224820
\(952\) 0 0
\(953\) 36249.3 1.23214 0.616070 0.787691i \(-0.288724\pi\)
0.616070 + 0.787691i \(0.288724\pi\)
\(954\) −10283.5 −0.348994
\(955\) −39860.7 −1.35064
\(956\) 49390.0 1.67091
\(957\) −48858.9 −1.65035
\(958\) −3893.02 −0.131292
\(959\) 5962.79 0.200781
\(960\) 48789.9 1.64030
\(961\) −29790.5 −0.999985
\(962\) 3013.85 0.101009
\(963\) 10910.0 0.365076
\(964\) −34617.9 −1.15661
\(965\) −35273.1 −1.17666
\(966\) −1139.40 −0.0379499
\(967\) 10020.3 0.333227 0.166613 0.986022i \(-0.446717\pi\)
0.166613 + 0.986022i \(0.446717\pi\)
\(968\) 5772.75 0.191677
\(969\) 0 0
\(970\) 2521.03 0.0834489
\(971\) 24562.5 0.811789 0.405894 0.913920i \(-0.366960\pi\)
0.405894 + 0.913920i \(0.366960\pi\)
\(972\) 44980.4 1.48431
\(973\) −530.654 −0.0174841
\(974\) −545.908 −0.0179590
\(975\) −8264.99 −0.271479
\(976\) −19017.9 −0.623718
\(977\) −17102.8 −0.560048 −0.280024 0.959993i \(-0.590342\pi\)
−0.280024 + 0.959993i \(0.590342\pi\)
\(978\) −14739.2 −0.481911
\(979\) −37230.9 −1.21543
\(980\) 30939.3 1.00849
\(981\) −83245.8 −2.70931
\(982\) 5075.73 0.164942
\(983\) −51204.2 −1.66140 −0.830702 0.556718i \(-0.812061\pi\)
−0.830702 + 0.556718i \(0.812061\pi\)
\(984\) 10368.8 0.335919
\(985\) −19218.1 −0.621665
\(986\) 0 0
\(987\) −659.394 −0.0212652
\(988\) −22603.9 −0.727859
\(989\) 37792.5 1.21510
\(990\) −7576.24 −0.243221
\(991\) −19176.3 −0.614686 −0.307343 0.951599i \(-0.599440\pi\)
−0.307343 + 0.951599i \(0.599440\pi\)
\(992\) 55.9283 0.00179005
\(993\) 67247.0 2.14906
\(994\) 253.699 0.00809541
\(995\) −18794.4 −0.598815
\(996\) −74653.9 −2.37500
\(997\) −18251.7 −0.579775 −0.289888 0.957061i \(-0.593618\pi\)
−0.289888 + 0.957061i \(0.593618\pi\)
\(998\) 3293.24 0.104455
\(999\) −34732.6 −1.09999
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.1.7 12
17.4 even 4 289.4.b.f.288.11 24
17.13 even 4 289.4.b.f.288.12 24
17.16 even 2 289.4.a.i.1.7 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.4.a.h.1.7 12 1.1 even 1 trivial
289.4.a.i.1.7 yes 12 17.16 even 2
289.4.b.f.288.11 24 17.4 even 4
289.4.b.f.288.12 24 17.13 even 4