Properties

Label 289.4.a.g.1.10
Level $289$
Weight $4$
Character 289.1
Self dual yes
Analytic conductor $17.052$
Analytic rank $1$
Dimension $12$
CM no
Inner twists $2$

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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: \( x^{12} - 4 x^{11} - 58 x^{10} + 204 x^{9} + 1191 x^{8} - 3456 x^{7} - 10364 x^{6} + 21448 x^{5} + 38476 x^{4} - 32336 x^{3} - 57024 x^{2} - 15776 x + 1156 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(5.53380\) 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)
 
\(f(q)\) \(=\) \(q+2.68604 q^{2} +4.33137 q^{3} -0.785167 q^{4} -2.08666 q^{5} +11.6343 q^{6} -24.9985 q^{7} -23.5973 q^{8} -8.23920 q^{9} +O(q^{10})\) \(q+2.68604 q^{2} +4.33137 q^{3} -0.785167 q^{4} -2.08666 q^{5} +11.6343 q^{6} -24.9985 q^{7} -23.5973 q^{8} -8.23920 q^{9} -5.60485 q^{10} +3.82158 q^{11} -3.40085 q^{12} +17.6726 q^{13} -67.1470 q^{14} -9.03809 q^{15} -57.1022 q^{16} -22.1309 q^{18} -160.915 q^{19} +1.63837 q^{20} -108.278 q^{21} +10.2649 q^{22} +99.9676 q^{23} -102.209 q^{24} -120.646 q^{25} +47.4693 q^{26} -152.634 q^{27} +19.6280 q^{28} +200.583 q^{29} -24.2767 q^{30} -76.5382 q^{31} +35.3998 q^{32} +16.5527 q^{33} +52.1632 q^{35} +6.46915 q^{36} +244.759 q^{37} -432.224 q^{38} +76.5465 q^{39} +49.2395 q^{40} +54.1132 q^{41} -290.839 q^{42} +142.087 q^{43} -3.00058 q^{44} +17.1924 q^{45} +268.517 q^{46} -468.451 q^{47} -247.331 q^{48} +281.924 q^{49} -324.060 q^{50} -13.8759 q^{52} -96.5673 q^{53} -409.982 q^{54} -7.97432 q^{55} +589.898 q^{56} -696.981 q^{57} +538.776 q^{58} +364.484 q^{59} +7.09641 q^{60} -707.872 q^{61} -205.585 q^{62} +205.967 q^{63} +551.903 q^{64} -36.8766 q^{65} +44.4612 q^{66} -304.454 q^{67} +432.997 q^{69} +140.113 q^{70} +470.003 q^{71} +194.423 q^{72} +142.056 q^{73} +657.432 q^{74} -522.562 q^{75} +126.345 q^{76} -95.5336 q^{77} +205.607 q^{78} -717.865 q^{79} +119.153 q^{80} -438.657 q^{81} +145.350 q^{82} -367.639 q^{83} +85.0162 q^{84} +381.653 q^{86} +868.802 q^{87} -90.1791 q^{88} +1042.28 q^{89} +46.1795 q^{90} -441.788 q^{91} -78.4913 q^{92} -331.516 q^{93} -1258.28 q^{94} +335.773 q^{95} +153.330 q^{96} -903.534 q^{97} +757.260 q^{98} -31.4867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9} - 8 q^{13} - 192 q^{15} - 184 q^{16} - 352 q^{19} - 256 q^{21} - 492 q^{25} - 784 q^{26} + 744 q^{30} + 24 q^{32} - 1400 q^{33} - 632 q^{35} - 856 q^{36} - 624 q^{38} - 1664 q^{42} - 1200 q^{43} - 1512 q^{47} - 1052 q^{49} - 2856 q^{50} + 792 q^{52} - 2504 q^{53} - 1424 q^{55} - 3408 q^{59} - 2808 q^{60} + 272 q^{64} + 272 q^{66} - 1080 q^{67} - 344 q^{69} + 2600 q^{70} + 248 q^{72} + 896 q^{76} + 848 q^{77} - 2404 q^{81} - 2960 q^{83} + 4768 q^{84} - 1200 q^{86} - 160 q^{87} - 2144 q^{89} + 3800 q^{93} + 5984 q^{94} + 3464 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.68604 0.949660 0.474830 0.880078i \(-0.342510\pi\)
0.474830 + 0.880078i \(0.342510\pi\)
\(3\) 4.33137 0.833573 0.416787 0.909004i \(-0.363156\pi\)
0.416787 + 0.909004i \(0.363156\pi\)
\(4\) −0.785167 −0.0981459
\(5\) −2.08666 −0.186636 −0.0933181 0.995636i \(-0.529747\pi\)
−0.0933181 + 0.995636i \(0.529747\pi\)
\(6\) 11.6343 0.791611
\(7\) −24.9985 −1.34979 −0.674895 0.737913i \(-0.735811\pi\)
−0.674895 + 0.737913i \(0.735811\pi\)
\(8\) −23.5973 −1.04287
\(9\) −8.23920 −0.305156
\(10\) −5.60485 −0.177241
\(11\) 3.82158 0.104750 0.0523749 0.998627i \(-0.483321\pi\)
0.0523749 + 0.998627i \(0.483321\pi\)
\(12\) −3.40085 −0.0818118
\(13\) 17.6726 0.377038 0.188519 0.982070i \(-0.439631\pi\)
0.188519 + 0.982070i \(0.439631\pi\)
\(14\) −67.1470 −1.28184
\(15\) −9.03809 −0.155575
\(16\) −57.1022 −0.892221
\(17\) 0 0
\(18\) −22.1309 −0.289794
\(19\) −160.915 −1.94297 −0.971483 0.237111i \(-0.923799\pi\)
−0.971483 + 0.237111i \(0.923799\pi\)
\(20\) 1.63837 0.0183176
\(21\) −108.278 −1.12515
\(22\) 10.2649 0.0994768
\(23\) 99.9676 0.906291 0.453145 0.891437i \(-0.350302\pi\)
0.453145 + 0.891437i \(0.350302\pi\)
\(24\) −102.209 −0.869305
\(25\) −120.646 −0.965167
\(26\) 47.4693 0.358058
\(27\) −152.634 −1.08794
\(28\) 19.6280 0.132476
\(29\) 200.583 1.28439 0.642197 0.766540i \(-0.278023\pi\)
0.642197 + 0.766540i \(0.278023\pi\)
\(30\) −24.2767 −0.147743
\(31\) −76.5382 −0.443441 −0.221720 0.975110i \(-0.571167\pi\)
−0.221720 + 0.975110i \(0.571167\pi\)
\(32\) 35.3998 0.195558
\(33\) 16.5527 0.0873167
\(34\) 0 0
\(35\) 52.1632 0.251920
\(36\) 6.46915 0.0299498
\(37\) 244.759 1.08752 0.543758 0.839242i \(-0.317001\pi\)
0.543758 + 0.839242i \(0.317001\pi\)
\(38\) −432.224 −1.84516
\(39\) 76.5465 0.314289
\(40\) 49.2395 0.194636
\(41\) 54.1132 0.206123 0.103062 0.994675i \(-0.467136\pi\)
0.103062 + 0.994675i \(0.467136\pi\)
\(42\) −290.839 −1.06851
\(43\) 142.087 0.503909 0.251955 0.967739i \(-0.418927\pi\)
0.251955 + 0.967739i \(0.418927\pi\)
\(44\) −3.00058 −0.0102808
\(45\) 17.1924 0.0569531
\(46\) 268.517 0.860668
\(47\) −468.451 −1.45384 −0.726921 0.686721i \(-0.759049\pi\)
−0.726921 + 0.686721i \(0.759049\pi\)
\(48\) −247.331 −0.743732
\(49\) 281.924 0.821935
\(50\) −324.060 −0.916580
\(51\) 0 0
\(52\) −13.8759 −0.0370047
\(53\) −96.5673 −0.250274 −0.125137 0.992139i \(-0.539937\pi\)
−0.125137 + 0.992139i \(0.539937\pi\)
\(54\) −409.982 −1.03318
\(55\) −7.97432 −0.0195501
\(56\) 589.898 1.40765
\(57\) −696.981 −1.61960
\(58\) 538.776 1.21974
\(59\) 364.484 0.804268 0.402134 0.915581i \(-0.368269\pi\)
0.402134 + 0.915581i \(0.368269\pi\)
\(60\) 7.09641 0.0152690
\(61\) −707.872 −1.48580 −0.742899 0.669404i \(-0.766550\pi\)
−0.742899 + 0.669404i \(0.766550\pi\)
\(62\) −205.585 −0.421118
\(63\) 205.967 0.411896
\(64\) 551.903 1.07794
\(65\) −36.8766 −0.0703689
\(66\) 44.4612 0.0829212
\(67\) −304.454 −0.555150 −0.277575 0.960704i \(-0.589531\pi\)
−0.277575 + 0.960704i \(0.589531\pi\)
\(68\) 0 0
\(69\) 432.997 0.755460
\(70\) 140.113 0.239238
\(71\) 470.003 0.785621 0.392810 0.919619i \(-0.371503\pi\)
0.392810 + 0.919619i \(0.371503\pi\)
\(72\) 194.423 0.318236
\(73\) 142.056 0.227759 0.113880 0.993495i \(-0.463672\pi\)
0.113880 + 0.993495i \(0.463672\pi\)
\(74\) 657.432 1.03277
\(75\) −522.562 −0.804537
\(76\) 126.345 0.190694
\(77\) −95.5336 −0.141390
\(78\) 205.607 0.298467
\(79\) −717.865 −1.02236 −0.511178 0.859475i \(-0.670791\pi\)
−0.511178 + 0.859475i \(0.670791\pi\)
\(80\) 119.153 0.166521
\(81\) −438.657 −0.601725
\(82\) 145.350 0.195747
\(83\) −367.639 −0.486188 −0.243094 0.970003i \(-0.578162\pi\)
−0.243094 + 0.970003i \(0.578162\pi\)
\(84\) 85.0162 0.110429
\(85\) 0 0
\(86\) 381.653 0.478542
\(87\) 868.802 1.07064
\(88\) −90.1791 −0.109240
\(89\) 1042.28 1.24137 0.620684 0.784061i \(-0.286855\pi\)
0.620684 + 0.784061i \(0.286855\pi\)
\(90\) 46.1795 0.0540861
\(91\) −441.788 −0.508922
\(92\) −78.4913 −0.0889488
\(93\) −331.516 −0.369640
\(94\) −1258.28 −1.38066
\(95\) 335.773 0.362628
\(96\) 153.330 0.163012
\(97\) −903.534 −0.945773 −0.472887 0.881123i \(-0.656788\pi\)
−0.472887 + 0.881123i \(0.656788\pi\)
\(98\) 757.260 0.780559
\(99\) −31.4867 −0.0319650
\(100\) 94.7272 0.0947272
\(101\) 443.233 0.436667 0.218333 0.975874i \(-0.429938\pi\)
0.218333 + 0.975874i \(0.429938\pi\)
\(102\) 0 0
\(103\) −1396.36 −1.33580 −0.667901 0.744250i \(-0.732807\pi\)
−0.667901 + 0.744250i \(0.732807\pi\)
\(104\) −417.026 −0.393200
\(105\) 225.938 0.209994
\(106\) −259.384 −0.237676
\(107\) −1843.89 −1.66594 −0.832972 0.553315i \(-0.813363\pi\)
−0.832972 + 0.553315i \(0.813363\pi\)
\(108\) 119.843 0.106777
\(109\) −372.960 −0.327735 −0.163867 0.986482i \(-0.552397\pi\)
−0.163867 + 0.986482i \(0.552397\pi\)
\(110\) −21.4194 −0.0185660
\(111\) 1060.14 0.906524
\(112\) 1427.47 1.20431
\(113\) 1779.13 1.48112 0.740560 0.671990i \(-0.234560\pi\)
0.740560 + 0.671990i \(0.234560\pi\)
\(114\) −1872.12 −1.53807
\(115\) −208.598 −0.169147
\(116\) −157.492 −0.126058
\(117\) −145.608 −0.115055
\(118\) 979.020 0.763781
\(119\) 0 0
\(120\) 213.275 0.162244
\(121\) −1316.40 −0.989027
\(122\) −1901.37 −1.41100
\(123\) 234.384 0.171819
\(124\) 60.0953 0.0435219
\(125\) 512.578 0.366771
\(126\) 553.238 0.391161
\(127\) 1735.00 1.21225 0.606126 0.795368i \(-0.292723\pi\)
0.606126 + 0.795368i \(0.292723\pi\)
\(128\) 1199.24 0.828114
\(129\) 615.433 0.420045
\(130\) −99.0522 −0.0668265
\(131\) 565.413 0.377102 0.188551 0.982063i \(-0.439621\pi\)
0.188551 + 0.982063i \(0.439621\pi\)
\(132\) −12.9966 −0.00856978
\(133\) 4022.62 2.62260
\(134\) −817.778 −0.527203
\(135\) 318.495 0.203050
\(136\) 0 0
\(137\) −1150.24 −0.717314 −0.358657 0.933469i \(-0.616765\pi\)
−0.358657 + 0.933469i \(0.616765\pi\)
\(138\) 1163.05 0.717430
\(139\) 984.663 0.600849 0.300425 0.953806i \(-0.402872\pi\)
0.300425 + 0.953806i \(0.402872\pi\)
\(140\) −40.9569 −0.0247249
\(141\) −2029.04 −1.21188
\(142\) 1262.45 0.746073
\(143\) 67.5371 0.0394947
\(144\) 470.476 0.272266
\(145\) −418.549 −0.239714
\(146\) 381.569 0.216294
\(147\) 1221.12 0.685143
\(148\) −192.176 −0.106735
\(149\) 1772.18 0.974382 0.487191 0.873295i \(-0.338021\pi\)
0.487191 + 0.873295i \(0.338021\pi\)
\(150\) −1403.63 −0.764037
\(151\) −1892.09 −1.01971 −0.509855 0.860260i \(-0.670301\pi\)
−0.509855 + 0.860260i \(0.670301\pi\)
\(152\) 3797.16 2.02625
\(153\) 0 0
\(154\) −256.607 −0.134273
\(155\) 159.709 0.0827621
\(156\) −60.1019 −0.0308462
\(157\) 289.955 0.147395 0.0736973 0.997281i \(-0.476520\pi\)
0.0736973 + 0.997281i \(0.476520\pi\)
\(158\) −1928.22 −0.970891
\(159\) −418.269 −0.208622
\(160\) −73.8673 −0.0364982
\(161\) −2499.04 −1.22330
\(162\) −1178.25 −0.571434
\(163\) 1691.93 0.813022 0.406511 0.913646i \(-0.366745\pi\)
0.406511 + 0.913646i \(0.366745\pi\)
\(164\) −42.4879 −0.0202302
\(165\) −34.5397 −0.0162965
\(166\) −987.495 −0.461714
\(167\) 1255.82 0.581907 0.290953 0.956737i \(-0.406028\pi\)
0.290953 + 0.956737i \(0.406028\pi\)
\(168\) 2555.07 1.17338
\(169\) −1884.68 −0.857842
\(170\) 0 0
\(171\) 1325.81 0.592907
\(172\) −111.562 −0.0494566
\(173\) −401.192 −0.176313 −0.0881564 0.996107i \(-0.528098\pi\)
−0.0881564 + 0.996107i \(0.528098\pi\)
\(174\) 2333.64 1.01674
\(175\) 3015.96 1.30277
\(176\) −218.220 −0.0934601
\(177\) 1578.72 0.670416
\(178\) 2799.62 1.17888
\(179\) −769.231 −0.321201 −0.160601 0.987019i \(-0.551343\pi\)
−0.160601 + 0.987019i \(0.551343\pi\)
\(180\) −13.4989 −0.00558971
\(181\) −2627.89 −1.07917 −0.539585 0.841931i \(-0.681419\pi\)
−0.539585 + 0.841931i \(0.681419\pi\)
\(182\) −1186.66 −0.483303
\(183\) −3066.06 −1.23852
\(184\) −2358.97 −0.945139
\(185\) −510.727 −0.202970
\(186\) −890.465 −0.351033
\(187\) 0 0
\(188\) 367.812 0.142689
\(189\) 3815.62 1.46850
\(190\) 901.902 0.344373
\(191\) 207.856 0.0787430 0.0393715 0.999225i \(-0.487464\pi\)
0.0393715 + 0.999225i \(0.487464\pi\)
\(192\) 2390.50 0.898538
\(193\) −4577.63 −1.70728 −0.853640 0.520864i \(-0.825610\pi\)
−0.853640 + 0.520864i \(0.825610\pi\)
\(194\) −2426.93 −0.898163
\(195\) −159.726 −0.0586576
\(196\) −221.357 −0.0806696
\(197\) −2640.99 −0.955140 −0.477570 0.878594i \(-0.658482\pi\)
−0.477570 + 0.878594i \(0.658482\pi\)
\(198\) −84.5748 −0.0303559
\(199\) −1650.96 −0.588106 −0.294053 0.955789i \(-0.595004\pi\)
−0.294053 + 0.955789i \(0.595004\pi\)
\(200\) 2846.92 1.00654
\(201\) −1318.71 −0.462758
\(202\) 1190.54 0.414685
\(203\) −5014.28 −1.73366
\(204\) 0 0
\(205\) −112.916 −0.0384701
\(206\) −3750.69 −1.26856
\(207\) −823.653 −0.276560
\(208\) −1009.14 −0.336401
\(209\) −614.947 −0.203525
\(210\) 606.881 0.199423
\(211\) 1104.55 0.360381 0.180191 0.983632i \(-0.442328\pi\)
0.180191 + 0.983632i \(0.442328\pi\)
\(212\) 75.8215 0.0245634
\(213\) 2035.76 0.654873
\(214\) −4952.78 −1.58208
\(215\) −296.487 −0.0940477
\(216\) 3601.76 1.13458
\(217\) 1913.34 0.598552
\(218\) −1001.79 −0.311237
\(219\) 615.299 0.189854
\(220\) 6.26117 0.00191876
\(221\) 0 0
\(222\) 2847.59 0.860889
\(223\) 2164.79 0.650067 0.325033 0.945703i \(-0.394624\pi\)
0.325033 + 0.945703i \(0.394624\pi\)
\(224\) −884.942 −0.263963
\(225\) 994.025 0.294526
\(226\) 4778.83 1.40656
\(227\) 2605.70 0.761879 0.380940 0.924600i \(-0.375601\pi\)
0.380940 + 0.924600i \(0.375601\pi\)
\(228\) 547.247 0.158958
\(229\) −1128.94 −0.325774 −0.162887 0.986645i \(-0.552081\pi\)
−0.162887 + 0.986645i \(0.552081\pi\)
\(230\) −560.304 −0.160632
\(231\) −413.792 −0.117859
\(232\) −4733.24 −1.33945
\(233\) 4315.97 1.21351 0.606756 0.794888i \(-0.292470\pi\)
0.606756 + 0.794888i \(0.292470\pi\)
\(234\) −391.109 −0.109263
\(235\) 977.496 0.271340
\(236\) −286.181 −0.0789356
\(237\) −3109.34 −0.852209
\(238\) 0 0
\(239\) 788.197 0.213323 0.106662 0.994295i \(-0.465984\pi\)
0.106662 + 0.994295i \(0.465984\pi\)
\(240\) 516.094 0.138807
\(241\) 3622.86 0.968335 0.484167 0.874975i \(-0.339123\pi\)
0.484167 + 0.874975i \(0.339123\pi\)
\(242\) −3535.90 −0.939240
\(243\) 2221.13 0.586361
\(244\) 555.798 0.145825
\(245\) −588.278 −0.153403
\(246\) 629.567 0.163170
\(247\) −2843.78 −0.732571
\(248\) 1806.10 0.462449
\(249\) −1592.38 −0.405274
\(250\) 1376.81 0.348308
\(251\) −5974.99 −1.50254 −0.751271 0.659994i \(-0.770559\pi\)
−0.751271 + 0.659994i \(0.770559\pi\)
\(252\) −161.719 −0.0404259
\(253\) 382.034 0.0949339
\(254\) 4660.28 1.15123
\(255\) 0 0
\(256\) −1194.02 −0.291509
\(257\) −3750.91 −0.910411 −0.455205 0.890386i \(-0.650434\pi\)
−0.455205 + 0.890386i \(0.650434\pi\)
\(258\) 1653.08 0.398900
\(259\) −6118.59 −1.46792
\(260\) 28.9543 0.00690642
\(261\) −1652.65 −0.391940
\(262\) 1518.73 0.358119
\(263\) −7566.43 −1.77401 −0.887007 0.461755i \(-0.847220\pi\)
−0.887007 + 0.461755i \(0.847220\pi\)
\(264\) −390.599 −0.0910596
\(265\) 201.503 0.0467103
\(266\) 10804.9 2.49057
\(267\) 4514.52 1.03477
\(268\) 239.048 0.0544857
\(269\) −6990.63 −1.58449 −0.792243 0.610206i \(-0.791087\pi\)
−0.792243 + 0.610206i \(0.791087\pi\)
\(270\) 855.492 0.192828
\(271\) −1356.64 −0.304097 −0.152049 0.988373i \(-0.548587\pi\)
−0.152049 + 0.988373i \(0.548587\pi\)
\(272\) 0 0
\(273\) −1913.55 −0.424224
\(274\) −3089.61 −0.681204
\(275\) −461.057 −0.101101
\(276\) −339.975 −0.0741453
\(277\) −7174.85 −1.55630 −0.778150 0.628078i \(-0.783842\pi\)
−0.778150 + 0.628078i \(0.783842\pi\)
\(278\) 2644.85 0.570603
\(279\) 630.613 0.135318
\(280\) −1230.91 −0.262718
\(281\) 6611.42 1.40357 0.701787 0.712387i \(-0.252386\pi\)
0.701787 + 0.712387i \(0.252386\pi\)
\(282\) −5450.08 −1.15088
\(283\) −2310.88 −0.485398 −0.242699 0.970102i \(-0.578033\pi\)
−0.242699 + 0.970102i \(0.578033\pi\)
\(284\) −369.031 −0.0771055
\(285\) 1454.36 0.302277
\(286\) 181.408 0.0375065
\(287\) −1352.75 −0.278223
\(288\) −291.666 −0.0596757
\(289\) 0 0
\(290\) −1124.24 −0.227647
\(291\) −3913.55 −0.788371
\(292\) −111.538 −0.0223537
\(293\) −6445.85 −1.28522 −0.642612 0.766192i \(-0.722149\pi\)
−0.642612 + 0.766192i \(0.722149\pi\)
\(294\) 3279.98 0.650653
\(295\) −760.553 −0.150105
\(296\) −5775.65 −1.13413
\(297\) −583.303 −0.113962
\(298\) 4760.16 0.925332
\(299\) 1766.69 0.341706
\(300\) 410.299 0.0789621
\(301\) −3551.96 −0.680172
\(302\) −5082.24 −0.968378
\(303\) 1919.81 0.363994
\(304\) 9188.57 1.73356
\(305\) 1477.08 0.277304
\(306\) 0 0
\(307\) 221.421 0.0411634 0.0205817 0.999788i \(-0.493448\pi\)
0.0205817 + 0.999788i \(0.493448\pi\)
\(308\) 75.0099 0.0138769
\(309\) −6048.17 −1.11349
\(310\) 428.985 0.0785959
\(311\) −1293.87 −0.235912 −0.117956 0.993019i \(-0.537634\pi\)
−0.117956 + 0.993019i \(0.537634\pi\)
\(312\) −1806.30 −0.327761
\(313\) 385.448 0.0696064 0.0348032 0.999394i \(-0.488920\pi\)
0.0348032 + 0.999394i \(0.488920\pi\)
\(314\) 778.833 0.139975
\(315\) −429.783 −0.0768747
\(316\) 563.644 0.100340
\(317\) 649.047 0.114997 0.0574986 0.998346i \(-0.481688\pi\)
0.0574986 + 0.998346i \(0.481688\pi\)
\(318\) −1123.49 −0.198120
\(319\) 766.545 0.134540
\(320\) −1151.63 −0.201182
\(321\) −7986.60 −1.38869
\(322\) −6712.53 −1.16172
\(323\) 0 0
\(324\) 344.419 0.0590568
\(325\) −2132.12 −0.363904
\(326\) 4544.61 0.772094
\(327\) −1615.43 −0.273191
\(328\) −1276.93 −0.214959
\(329\) 11710.6 1.96238
\(330\) −92.7753 −0.0154761
\(331\) 1429.71 0.237415 0.118707 0.992929i \(-0.462125\pi\)
0.118707 + 0.992929i \(0.462125\pi\)
\(332\) 288.658 0.0477174
\(333\) −2016.61 −0.331861
\(334\) 3373.19 0.552614
\(335\) 635.292 0.103611
\(336\) 6182.89 1.00388
\(337\) 565.364 0.0913867 0.0456934 0.998956i \(-0.485450\pi\)
0.0456934 + 0.998956i \(0.485450\pi\)
\(338\) −5062.33 −0.814659
\(339\) 7706.08 1.23462
\(340\) 0 0
\(341\) −292.497 −0.0464504
\(342\) 3561.18 0.563060
\(343\) 1526.81 0.240350
\(344\) −3352.88 −0.525509
\(345\) −903.516 −0.140996
\(346\) −1077.62 −0.167437
\(347\) −3788.72 −0.586135 −0.293068 0.956092i \(-0.594676\pi\)
−0.293068 + 0.956092i \(0.594676\pi\)
\(348\) −682.155 −0.105079
\(349\) −6387.30 −0.979669 −0.489834 0.871816i \(-0.662943\pi\)
−0.489834 + 0.871816i \(0.662943\pi\)
\(350\) 8101.01 1.23719
\(351\) −2697.44 −0.410196
\(352\) 135.283 0.0204847
\(353\) 6291.34 0.948595 0.474298 0.880365i \(-0.342702\pi\)
0.474298 + 0.880365i \(0.342702\pi\)
\(354\) 4240.50 0.636667
\(355\) −980.735 −0.146625
\(356\) −818.367 −0.121835
\(357\) 0 0
\(358\) −2066.19 −0.305032
\(359\) −3369.51 −0.495364 −0.247682 0.968841i \(-0.579669\pi\)
−0.247682 + 0.968841i \(0.579669\pi\)
\(360\) −405.694 −0.0593944
\(361\) 19034.5 2.77511
\(362\) −7058.63 −1.02484
\(363\) −5701.80 −0.824427
\(364\) 346.877 0.0499486
\(365\) −296.423 −0.0425081
\(366\) −8235.56 −1.17617
\(367\) −997.517 −0.141880 −0.0709400 0.997481i \(-0.522600\pi\)
−0.0709400 + 0.997481i \(0.522600\pi\)
\(368\) −5708.37 −0.808612
\(369\) −445.849 −0.0628997
\(370\) −1371.84 −0.192752
\(371\) 2414.04 0.337818
\(372\) 260.295 0.0362787
\(373\) 3180.59 0.441514 0.220757 0.975329i \(-0.429147\pi\)
0.220757 + 0.975329i \(0.429147\pi\)
\(374\) 0 0
\(375\) 2220.17 0.305731
\(376\) 11054.2 1.51616
\(377\) 3544.83 0.484265
\(378\) 10248.9 1.39457
\(379\) 10833.9 1.46834 0.734170 0.678965i \(-0.237571\pi\)
0.734170 + 0.678965i \(0.237571\pi\)
\(380\) −263.638 −0.0355904
\(381\) 7514.92 1.01050
\(382\) 558.310 0.0747791
\(383\) −7567.93 −1.00967 −0.504834 0.863216i \(-0.668446\pi\)
−0.504834 + 0.863216i \(0.668446\pi\)
\(384\) 5194.34 0.690294
\(385\) 199.346 0.0263886
\(386\) −12295.7 −1.62134
\(387\) −1170.69 −0.153771
\(388\) 709.426 0.0928238
\(389\) 9599.36 1.25117 0.625587 0.780154i \(-0.284859\pi\)
0.625587 + 0.780154i \(0.284859\pi\)
\(390\) −429.032 −0.0557048
\(391\) 0 0
\(392\) −6652.65 −0.857168
\(393\) 2449.02 0.314342
\(394\) −7093.81 −0.907058
\(395\) 1497.94 0.190809
\(396\) 24.7224 0.00313724
\(397\) −5272.03 −0.666487 −0.333244 0.942841i \(-0.608143\pi\)
−0.333244 + 0.942841i \(0.608143\pi\)
\(398\) −4434.54 −0.558501
\(399\) 17423.5 2.18613
\(400\) 6889.14 0.861143
\(401\) 3600.34 0.448360 0.224180 0.974548i \(-0.428030\pi\)
0.224180 + 0.974548i \(0.428030\pi\)
\(402\) −3542.10 −0.439463
\(403\) −1352.63 −0.167194
\(404\) −348.012 −0.0428571
\(405\) 915.327 0.112304
\(406\) −13468.6 −1.64639
\(407\) 935.364 0.113917
\(408\) 0 0
\(409\) 9516.13 1.15047 0.575235 0.817988i \(-0.304911\pi\)
0.575235 + 0.817988i \(0.304911\pi\)
\(410\) −303.296 −0.0365335
\(411\) −4982.14 −0.597933
\(412\) 1096.38 0.131104
\(413\) −9111.55 −1.08559
\(414\) −2212.37 −0.262638
\(415\) 767.137 0.0907404
\(416\) 625.606 0.0737329
\(417\) 4264.95 0.500852
\(418\) −1651.78 −0.193280
\(419\) 6310.52 0.735774 0.367887 0.929871i \(-0.380081\pi\)
0.367887 + 0.929871i \(0.380081\pi\)
\(420\) −177.400 −0.0206100
\(421\) −1544.81 −0.178835 −0.0894177 0.995994i \(-0.528501\pi\)
−0.0894177 + 0.995994i \(0.528501\pi\)
\(422\) 2966.88 0.342240
\(423\) 3859.66 0.443648
\(424\) 2278.73 0.261002
\(425\) 0 0
\(426\) 5468.14 0.621906
\(427\) 17695.7 2.00552
\(428\) 1447.77 0.163506
\(429\) 292.528 0.0329217
\(430\) −796.378 −0.0893134
\(431\) −897.334 −0.100286 −0.0501428 0.998742i \(-0.515968\pi\)
−0.0501428 + 0.998742i \(0.515968\pi\)
\(432\) 8715.74 0.970686
\(433\) 4896.47 0.543440 0.271720 0.962376i \(-0.412408\pi\)
0.271720 + 0.962376i \(0.412408\pi\)
\(434\) 5139.31 0.568421
\(435\) −1812.89 −0.199819
\(436\) 292.836 0.0321659
\(437\) −16086.2 −1.76089
\(438\) 1652.72 0.180297
\(439\) 1404.01 0.152642 0.0763210 0.997083i \(-0.475683\pi\)
0.0763210 + 0.997083i \(0.475683\pi\)
\(440\) 188.173 0.0203881
\(441\) −2322.83 −0.250818
\(442\) 0 0
\(443\) −6453.57 −0.692141 −0.346070 0.938209i \(-0.612484\pi\)
−0.346070 + 0.938209i \(0.612484\pi\)
\(444\) −832.388 −0.0889716
\(445\) −2174.89 −0.231684
\(446\) 5814.71 0.617342
\(447\) 7675.99 0.812219
\(448\) −13796.7 −1.45499
\(449\) 4409.11 0.463427 0.231714 0.972784i \(-0.425567\pi\)
0.231714 + 0.972784i \(0.425567\pi\)
\(450\) 2670.00 0.279700
\(451\) 206.798 0.0215914
\(452\) −1396.92 −0.145366
\(453\) −8195.36 −0.850003
\(454\) 6999.03 0.723526
\(455\) 921.859 0.0949833
\(456\) 16446.9 1.68903
\(457\) 12571.6 1.28681 0.643406 0.765525i \(-0.277521\pi\)
0.643406 + 0.765525i \(0.277521\pi\)
\(458\) −3032.37 −0.309374
\(459\) 0 0
\(460\) 163.784 0.0166011
\(461\) −5115.00 −0.516767 −0.258383 0.966042i \(-0.583190\pi\)
−0.258383 + 0.966042i \(0.583190\pi\)
\(462\) −1111.46 −0.111926
\(463\) 5280.96 0.530080 0.265040 0.964237i \(-0.414615\pi\)
0.265040 + 0.964237i \(0.414615\pi\)
\(464\) −11453.8 −1.14596
\(465\) 691.759 0.0689883
\(466\) 11592.9 1.15242
\(467\) −4430.45 −0.439008 −0.219504 0.975612i \(-0.570444\pi\)
−0.219504 + 0.975612i \(0.570444\pi\)
\(468\) 114.327 0.0112922
\(469\) 7610.90 0.749336
\(470\) 2625.60 0.257680
\(471\) 1255.91 0.122864
\(472\) −8600.86 −0.838743
\(473\) 542.997 0.0527844
\(474\) −8351.83 −0.809308
\(475\) 19413.7 1.87529
\(476\) 0 0
\(477\) 795.637 0.0763726
\(478\) 2117.13 0.202584
\(479\) −8697.09 −0.829604 −0.414802 0.909912i \(-0.636149\pi\)
−0.414802 + 0.909912i \(0.636149\pi\)
\(480\) −319.947 −0.0304240
\(481\) 4325.52 0.410034
\(482\) 9731.15 0.919589
\(483\) −10824.3 −1.01971
\(484\) 1033.59 0.0970690
\(485\) 1885.37 0.176516
\(486\) 5966.06 0.556844
\(487\) 13031.1 1.21252 0.606258 0.795268i \(-0.292670\pi\)
0.606258 + 0.795268i \(0.292670\pi\)
\(488\) 16703.9 1.54949
\(489\) 7328.40 0.677713
\(490\) −1580.14 −0.145681
\(491\) −11760.3 −1.08093 −0.540464 0.841367i \(-0.681751\pi\)
−0.540464 + 0.841367i \(0.681751\pi\)
\(492\) −184.031 −0.0168633
\(493\) 0 0
\(494\) −7638.51 −0.695694
\(495\) 65.7020 0.00596583
\(496\) 4370.50 0.395647
\(497\) −11749.4 −1.06042
\(498\) −4277.21 −0.384872
\(499\) 10724.6 0.962118 0.481059 0.876688i \(-0.340252\pi\)
0.481059 + 0.876688i \(0.340252\pi\)
\(500\) −402.460 −0.0359971
\(501\) 5439.43 0.485062
\(502\) −16049.1 −1.42690
\(503\) 3904.96 0.346150 0.173075 0.984909i \(-0.444630\pi\)
0.173075 + 0.984909i \(0.444630\pi\)
\(504\) −4860.29 −0.429552
\(505\) −924.875 −0.0814978
\(506\) 1026.16 0.0901549
\(507\) −8163.25 −0.715075
\(508\) −1362.26 −0.118978
\(509\) 15132.3 1.31774 0.658870 0.752257i \(-0.271035\pi\)
0.658870 + 0.752257i \(0.271035\pi\)
\(510\) 0 0
\(511\) −3551.19 −0.307427
\(512\) −12801.1 −1.10495
\(513\) 24561.1 2.11383
\(514\) −10075.1 −0.864581
\(515\) 2913.73 0.249309
\(516\) −483.218 −0.0412257
\(517\) −1790.22 −0.152290
\(518\) −16434.8 −1.39402
\(519\) −1737.71 −0.146970
\(520\) 870.190 0.0733853
\(521\) 16534.9 1.39041 0.695207 0.718810i \(-0.255313\pi\)
0.695207 + 0.718810i \(0.255313\pi\)
\(522\) −4439.08 −0.372210
\(523\) −8724.36 −0.729426 −0.364713 0.931120i \(-0.618833\pi\)
−0.364713 + 0.931120i \(0.618833\pi\)
\(524\) −443.944 −0.0370111
\(525\) 13063.3 1.08596
\(526\) −20323.8 −1.68471
\(527\) 0 0
\(528\) −945.194 −0.0779058
\(529\) −2173.47 −0.178637
\(530\) 541.245 0.0443589
\(531\) −3003.06 −0.245427
\(532\) −3158.43 −0.257397
\(533\) 956.319 0.0777163
\(534\) 12126.2 0.982681
\(535\) 3847.57 0.310925
\(536\) 7184.32 0.578946
\(537\) −3331.83 −0.267745
\(538\) −18777.2 −1.50472
\(539\) 1077.39 0.0860976
\(540\) −250.072 −0.0199285
\(541\) −8246.12 −0.655320 −0.327660 0.944796i \(-0.606260\pi\)
−0.327660 + 0.944796i \(0.606260\pi\)
\(542\) −3644.01 −0.288789
\(543\) −11382.4 −0.899567
\(544\) 0 0
\(545\) 778.240 0.0611672
\(546\) −5139.87 −0.402868
\(547\) −23842.2 −1.86366 −0.931829 0.362898i \(-0.881787\pi\)
−0.931829 + 0.362898i \(0.881787\pi\)
\(548\) 903.134 0.0704014
\(549\) 5832.30 0.453399
\(550\) −1238.42 −0.0960117
\(551\) −32276.8 −2.49553
\(552\) −10217.6 −0.787843
\(553\) 17945.5 1.37997
\(554\) −19272.0 −1.47796
\(555\) −2212.15 −0.169190
\(556\) −773.126 −0.0589709
\(557\) 19341.5 1.47132 0.735661 0.677350i \(-0.236872\pi\)
0.735661 + 0.677350i \(0.236872\pi\)
\(558\) 1693.86 0.128506
\(559\) 2511.05 0.189993
\(560\) −2978.63 −0.224768
\(561\) 0 0
\(562\) 17758.6 1.33292
\(563\) −14210.3 −1.06376 −0.531878 0.846821i \(-0.678513\pi\)
−0.531878 + 0.846821i \(0.678513\pi\)
\(564\) 1593.13 0.118942
\(565\) −3712.44 −0.276431
\(566\) −6207.12 −0.460963
\(567\) 10965.8 0.812202
\(568\) −11090.8 −0.819297
\(569\) −9576.15 −0.705542 −0.352771 0.935710i \(-0.614761\pi\)
−0.352771 + 0.935710i \(0.614761\pi\)
\(570\) 3906.48 0.287060
\(571\) −14785.0 −1.08359 −0.541796 0.840510i \(-0.682255\pi\)
−0.541796 + 0.840510i \(0.682255\pi\)
\(572\) −53.0279 −0.00387624
\(573\) 900.301 0.0656381
\(574\) −3633.54 −0.264218
\(575\) −12060.7 −0.874722
\(576\) −4547.24 −0.328938
\(577\) −11438.5 −0.825284 −0.412642 0.910893i \(-0.635394\pi\)
−0.412642 + 0.910893i \(0.635394\pi\)
\(578\) 0 0
\(579\) −19827.4 −1.42314
\(580\) 328.631 0.0235270
\(581\) 9190.42 0.656253
\(582\) −10512.0 −0.748685
\(583\) −369.039 −0.0262162
\(584\) −3352.15 −0.237522
\(585\) 303.834 0.0214735
\(586\) −17313.8 −1.22053
\(587\) −7892.09 −0.554925 −0.277463 0.960736i \(-0.589493\pi\)
−0.277463 + 0.960736i \(0.589493\pi\)
\(588\) −958.782 −0.0672440
\(589\) 12316.1 0.861590
\(590\) −2042.88 −0.142549
\(591\) −11439.1 −0.796179
\(592\) −13976.2 −0.970304
\(593\) 7829.44 0.542186 0.271093 0.962553i \(-0.412615\pi\)
0.271093 + 0.962553i \(0.412615\pi\)
\(594\) −1566.78 −0.108225
\(595\) 0 0
\(596\) −1391.46 −0.0956317
\(597\) −7150.91 −0.490230
\(598\) 4745.40 0.324504
\(599\) −18939.7 −1.29191 −0.645956 0.763375i \(-0.723541\pi\)
−0.645956 + 0.763375i \(0.723541\pi\)
\(600\) 12331.1 0.839024
\(601\) 17777.4 1.20658 0.603290 0.797522i \(-0.293856\pi\)
0.603290 + 0.797522i \(0.293856\pi\)
\(602\) −9540.73 −0.645932
\(603\) 2508.46 0.169407
\(604\) 1485.61 0.100080
\(605\) 2746.86 0.184588
\(606\) 5156.69 0.345670
\(607\) 17713.3 1.18445 0.592223 0.805774i \(-0.298250\pi\)
0.592223 + 0.805774i \(0.298250\pi\)
\(608\) −5696.35 −0.379963
\(609\) −21718.7 −1.44513
\(610\) 3967.51 0.263344
\(611\) −8278.74 −0.548154
\(612\) 0 0
\(613\) 25427.3 1.67537 0.837683 0.546156i \(-0.183910\pi\)
0.837683 + 0.546156i \(0.183910\pi\)
\(614\) 594.746 0.0390912
\(615\) −489.080 −0.0320676
\(616\) 2254.34 0.147451
\(617\) 10028.4 0.654343 0.327172 0.944965i \(-0.393904\pi\)
0.327172 + 0.944965i \(0.393904\pi\)
\(618\) −16245.6 −1.05744
\(619\) 4460.94 0.289661 0.144831 0.989456i \(-0.453736\pi\)
0.144831 + 0.989456i \(0.453736\pi\)
\(620\) −125.398 −0.00812276
\(621\) −15258.5 −0.985993
\(622\) −3475.39 −0.224036
\(623\) −26055.5 −1.67559
\(624\) −4370.97 −0.280415
\(625\) 14011.2 0.896714
\(626\) 1035.33 0.0661024
\(627\) −2663.57 −0.169653
\(628\) −227.664 −0.0144662
\(629\) 0 0
\(630\) −1154.42 −0.0730049
\(631\) −1098.49 −0.0693032 −0.0346516 0.999399i \(-0.511032\pi\)
−0.0346516 + 0.999399i \(0.511032\pi\)
\(632\) 16939.7 1.06618
\(633\) 4784.23 0.300404
\(634\) 1743.37 0.109208
\(635\) −3620.34 −0.226250
\(636\) 328.411 0.0204754
\(637\) 4982.32 0.309901
\(638\) 2058.97 0.127767
\(639\) −3872.45 −0.239737
\(640\) −2502.39 −0.154556
\(641\) 1063.17 0.0655115 0.0327557 0.999463i \(-0.489572\pi\)
0.0327557 + 0.999463i \(0.489572\pi\)
\(642\) −21452.4 −1.31878
\(643\) 6571.26 0.403025 0.201513 0.979486i \(-0.435414\pi\)
0.201513 + 0.979486i \(0.435414\pi\)
\(644\) 1962.16 0.120062
\(645\) −1284.20 −0.0783957
\(646\) 0 0
\(647\) −14783.1 −0.898273 −0.449137 0.893463i \(-0.648268\pi\)
−0.449137 + 0.893463i \(0.648268\pi\)
\(648\) 10351.1 0.627518
\(649\) 1392.90 0.0842469
\(650\) −5726.98 −0.345585
\(651\) 8287.38 0.498937
\(652\) −1328.45 −0.0797948
\(653\) 25912.0 1.55285 0.776427 0.630208i \(-0.217030\pi\)
0.776427 + 0.630208i \(0.217030\pi\)
\(654\) −4339.12 −0.259439
\(655\) −1179.82 −0.0703809
\(656\) −3089.98 −0.183908
\(657\) −1170.43 −0.0695020
\(658\) 31455.1 1.86360
\(659\) 4302.30 0.254315 0.127158 0.991883i \(-0.459415\pi\)
0.127158 + 0.991883i \(0.459415\pi\)
\(660\) 27.1195 0.00159943
\(661\) −7467.66 −0.439423 −0.219711 0.975565i \(-0.570512\pi\)
−0.219711 + 0.975565i \(0.570512\pi\)
\(662\) 3840.28 0.225463
\(663\) 0 0
\(664\) 8675.31 0.507029
\(665\) −8393.82 −0.489471
\(666\) −5416.72 −0.315155
\(667\) 20051.9 1.16403
\(668\) −986.031 −0.0571118
\(669\) 9376.50 0.541878
\(670\) 1706.42 0.0983953
\(671\) −2705.19 −0.155637
\(672\) −3833.01 −0.220032
\(673\) 4236.79 0.242669 0.121335 0.992612i \(-0.461283\pi\)
0.121335 + 0.992612i \(0.461283\pi\)
\(674\) 1518.59 0.0867863
\(675\) 18414.7 1.05005
\(676\) 1479.79 0.0841938
\(677\) 23130.5 1.31311 0.656555 0.754278i \(-0.272013\pi\)
0.656555 + 0.754278i \(0.272013\pi\)
\(678\) 20698.9 1.17247
\(679\) 22587.0 1.27660
\(680\) 0 0
\(681\) 11286.3 0.635082
\(682\) −785.659 −0.0441121
\(683\) −11474.5 −0.642839 −0.321419 0.946937i \(-0.604160\pi\)
−0.321419 + 0.946937i \(0.604160\pi\)
\(684\) −1040.98 −0.0581914
\(685\) 2400.16 0.133877
\(686\) 4101.08 0.228251
\(687\) −4889.84 −0.271556
\(688\) −8113.49 −0.449599
\(689\) −1706.59 −0.0943629
\(690\) −2426.88 −0.133898
\(691\) 15221.6 0.837997 0.418999 0.907987i \(-0.362381\pi\)
0.418999 + 0.907987i \(0.362381\pi\)
\(692\) 315.003 0.0173044
\(693\) 787.120 0.0431461
\(694\) −10176.7 −0.556629
\(695\) −2054.65 −0.112140
\(696\) −20501.4 −1.11653
\(697\) 0 0
\(698\) −17156.6 −0.930352
\(699\) 18694.1 1.01155
\(700\) −2368.04 −0.127862
\(701\) −23996.1 −1.29289 −0.646447 0.762959i \(-0.723746\pi\)
−0.646447 + 0.762959i \(0.723746\pi\)
\(702\) −7245.44 −0.389546
\(703\) −39385.2 −2.11300
\(704\) 2109.14 0.112914
\(705\) 4233.90 0.226181
\(706\) 16898.8 0.900843
\(707\) −11080.2 −0.589409
\(708\) −1239.56 −0.0657986
\(709\) −22346.8 −1.18371 −0.591856 0.806044i \(-0.701605\pi\)
−0.591856 + 0.806044i \(0.701605\pi\)
\(710\) −2634.30 −0.139244
\(711\) 5914.63 0.311978
\(712\) −24595.1 −1.29458
\(713\) −7651.34 −0.401886
\(714\) 0 0
\(715\) −140.927 −0.00737113
\(716\) 603.975 0.0315246
\(717\) 3413.98 0.177820
\(718\) −9050.64 −0.470427
\(719\) 32468.2 1.68409 0.842045 0.539408i \(-0.181352\pi\)
0.842045 + 0.539408i \(0.181352\pi\)
\(720\) −981.722 −0.0508148
\(721\) 34906.9 1.80305
\(722\) 51127.5 2.63541
\(723\) 15691.9 0.807178
\(724\) 2063.34 0.105916
\(725\) −24199.6 −1.23965
\(726\) −15315.3 −0.782925
\(727\) −2899.33 −0.147909 −0.0739547 0.997262i \(-0.523562\pi\)
−0.0739547 + 0.997262i \(0.523562\pi\)
\(728\) 10425.0 0.530737
\(729\) 21464.3 1.09050
\(730\) −796.204 −0.0403683
\(731\) 0 0
\(732\) 2407.37 0.121556
\(733\) 16399.9 0.826390 0.413195 0.910643i \(-0.364413\pi\)
0.413195 + 0.910643i \(0.364413\pi\)
\(734\) −2679.37 −0.134738
\(735\) −2548.05 −0.127873
\(736\) 3538.84 0.177233
\(737\) −1163.50 −0.0581519
\(738\) −1197.57 −0.0597333
\(739\) 6470.65 0.322093 0.161047 0.986947i \(-0.448513\pi\)
0.161047 + 0.986947i \(0.448513\pi\)
\(740\) 401.006 0.0199207
\(741\) −12317.5 −0.610652
\(742\) 6484.21 0.320812
\(743\) 7520.20 0.371318 0.185659 0.982614i \(-0.440558\pi\)
0.185659 + 0.982614i \(0.440558\pi\)
\(744\) 7822.89 0.385485
\(745\) −3697.94 −0.181855
\(746\) 8543.20 0.419288
\(747\) 3029.05 0.148363
\(748\) 0 0
\(749\) 46094.6 2.24868
\(750\) 5963.47 0.290340
\(751\) −10921.9 −0.530685 −0.265342 0.964154i \(-0.585485\pi\)
−0.265342 + 0.964154i \(0.585485\pi\)
\(752\) 26749.6 1.29715
\(753\) −25879.9 −1.25248
\(754\) 9521.56 0.459887
\(755\) 3948.14 0.190315
\(756\) −2995.90 −0.144127
\(757\) 17112.9 0.821636 0.410818 0.911717i \(-0.365243\pi\)
0.410818 + 0.911717i \(0.365243\pi\)
\(758\) 29100.4 1.39442
\(759\) 1654.73 0.0791343
\(760\) −7923.36 −0.378172
\(761\) −35934.3 −1.71172 −0.855860 0.517207i \(-0.826972\pi\)
−0.855860 + 0.517207i \(0.826972\pi\)
\(762\) 20185.4 0.959633
\(763\) 9323.44 0.442374
\(764\) −163.202 −0.00772831
\(765\) 0 0
\(766\) −20327.8 −0.958842
\(767\) 6441.37 0.303239
\(768\) −5171.75 −0.242994
\(769\) 29085.3 1.36390 0.681952 0.731397i \(-0.261131\pi\)
0.681952 + 0.731397i \(0.261131\pi\)
\(770\) 535.451 0.0250602
\(771\) −16246.6 −0.758894
\(772\) 3594.21 0.167563
\(773\) −16502.8 −0.767873 −0.383936 0.923360i \(-0.625432\pi\)
−0.383936 + 0.923360i \(0.625432\pi\)
\(774\) −3144.51 −0.146030
\(775\) 9234.02 0.427994
\(776\) 21321.0 0.986314
\(777\) −26501.9 −1.22362
\(778\) 25784.3 1.18819
\(779\) −8707.60 −0.400491
\(780\) 125.412 0.00575701
\(781\) 1796.15 0.0822937
\(782\) 0 0
\(783\) −30615.9 −1.39735
\(784\) −16098.5 −0.733348
\(785\) −605.037 −0.0275092
\(786\) 6578.17 0.298518
\(787\) −27374.1 −1.23987 −0.619937 0.784651i \(-0.712842\pi\)
−0.619937 + 0.784651i \(0.712842\pi\)
\(788\) 2073.62 0.0937431
\(789\) −32773.0 −1.47877
\(790\) 4023.53 0.181203
\(791\) −44475.6 −1.99920
\(792\) 743.003 0.0333352
\(793\) −12509.9 −0.560202
\(794\) −14160.9 −0.632936
\(795\) 872.784 0.0389364
\(796\) 1296.28 0.0577202
\(797\) −31776.1 −1.41226 −0.706128 0.708084i \(-0.749560\pi\)
−0.706128 + 0.708084i \(0.749560\pi\)
\(798\) 46800.2 2.07608
\(799\) 0 0
\(800\) −4270.84 −0.188746
\(801\) −8587.58 −0.378810
\(802\) 9670.68 0.425790
\(803\) 542.879 0.0238578
\(804\) 1035.41 0.0454178
\(805\) 5214.63 0.228313
\(806\) −3633.22 −0.158777
\(807\) −30279.0 −1.32078
\(808\) −10459.1 −0.455385
\(809\) 34367.2 1.49355 0.746777 0.665074i \(-0.231600\pi\)
0.746777 + 0.665074i \(0.231600\pi\)
\(810\) 2458.61 0.106650
\(811\) 1316.99 0.0570232 0.0285116 0.999593i \(-0.490923\pi\)
0.0285116 + 0.999593i \(0.490923\pi\)
\(812\) 3937.05 0.170152
\(813\) −5876.14 −0.253487
\(814\) 2512.43 0.108182
\(815\) −3530.49 −0.151739
\(816\) 0 0
\(817\) −22863.9 −0.979078
\(818\) 25560.7 1.09256
\(819\) 3639.98 0.155300
\(820\) 88.6577 0.00377568
\(821\) −33481.1 −1.42326 −0.711632 0.702552i \(-0.752044\pi\)
−0.711632 + 0.702552i \(0.752044\pi\)
\(822\) −13382.2 −0.567833
\(823\) −11746.8 −0.497529 −0.248765 0.968564i \(-0.580025\pi\)
−0.248765 + 0.968564i \(0.580025\pi\)
\(824\) 32950.5 1.39306
\(825\) −1997.01 −0.0842752
\(826\) −24474.0 −1.03094
\(827\) 4367.84 0.183658 0.0918288 0.995775i \(-0.470729\pi\)
0.0918288 + 0.995775i \(0.470729\pi\)
\(828\) 646.706 0.0271432
\(829\) 19994.7 0.837689 0.418844 0.908058i \(-0.362435\pi\)
0.418844 + 0.908058i \(0.362435\pi\)
\(830\) 2060.56 0.0861725
\(831\) −31077.0 −1.29729
\(832\) 9753.55 0.406422
\(833\) 0 0
\(834\) 11455.8 0.475639
\(835\) −2620.47 −0.108605
\(836\) 482.837 0.0199752
\(837\) 11682.3 0.482438
\(838\) 16950.3 0.698735
\(839\) 25672.1 1.05638 0.528189 0.849127i \(-0.322871\pi\)
0.528189 + 0.849127i \(0.322871\pi\)
\(840\) −5331.55 −0.218995
\(841\) 15844.7 0.649667
\(842\) −4149.44 −0.169833
\(843\) 28636.5 1.16998
\(844\) −867.258 −0.0353700
\(845\) 3932.68 0.160104
\(846\) 10367.2 0.421315
\(847\) 32907.9 1.33498
\(848\) 5514.20 0.223300
\(849\) −10009.3 −0.404614
\(850\) 0 0
\(851\) 24467.9 0.985605
\(852\) −1598.41 −0.0642731
\(853\) 15504.6 0.622355 0.311178 0.950352i \(-0.399277\pi\)
0.311178 + 0.950352i \(0.399277\pi\)
\(854\) 47531.5 1.90456
\(855\) −2766.50 −0.110658
\(856\) 43511.0 1.73736
\(857\) 35915.1 1.43155 0.715774 0.698332i \(-0.246074\pi\)
0.715774 + 0.698332i \(0.246074\pi\)
\(858\) 785.744 0.0312644
\(859\) −36575.0 −1.45276 −0.726382 0.687292i \(-0.758799\pi\)
−0.726382 + 0.687292i \(0.758799\pi\)
\(860\) 232.792 0.00923040
\(861\) −5859.25 −0.231920
\(862\) −2410.28 −0.0952372
\(863\) 11402.6 0.449768 0.224884 0.974386i \(-0.427800\pi\)
0.224884 + 0.974386i \(0.427800\pi\)
\(864\) −5403.22 −0.212756
\(865\) 837.151 0.0329063
\(866\) 13152.1 0.516083
\(867\) 0 0
\(868\) −1502.29 −0.0587455
\(869\) −2743.38 −0.107092
\(870\) −4869.51 −0.189761
\(871\) −5380.50 −0.209312
\(872\) 8800.87 0.341783
\(873\) 7444.40 0.288608
\(874\) −43208.4 −1.67225
\(875\) −12813.7 −0.495065
\(876\) −483.113 −0.0186334
\(877\) 23424.6 0.901932 0.450966 0.892541i \(-0.351080\pi\)
0.450966 + 0.892541i \(0.351080\pi\)
\(878\) 3771.24 0.144958
\(879\) −27919.4 −1.07133
\(880\) 455.351 0.0174430
\(881\) −2452.52 −0.0937882 −0.0468941 0.998900i \(-0.514932\pi\)
−0.0468941 + 0.998900i \(0.514932\pi\)
\(882\) −6239.21 −0.238192
\(883\) 3832.99 0.146082 0.0730409 0.997329i \(-0.476730\pi\)
0.0730409 + 0.997329i \(0.476730\pi\)
\(884\) 0 0
\(885\) −3294.24 −0.125124
\(886\) −17334.6 −0.657298
\(887\) −13334.4 −0.504762 −0.252381 0.967628i \(-0.581214\pi\)
−0.252381 + 0.967628i \(0.581214\pi\)
\(888\) −25016.5 −0.945382
\(889\) −43372.3 −1.63629
\(890\) −5841.84 −0.220021
\(891\) −1676.36 −0.0630306
\(892\) −1699.72 −0.0638014
\(893\) 75380.6 2.82477
\(894\) 20618.1 0.771332
\(895\) 1605.12 0.0599478
\(896\) −29979.1 −1.11778
\(897\) 7652.18 0.284837
\(898\) 11843.1 0.440098
\(899\) −15352.3 −0.569553
\(900\) −780.476 −0.0289065
\(901\) 0 0
\(902\) 555.468 0.0205045
\(903\) −15384.9 −0.566973
\(904\) −41982.8 −1.54461
\(905\) 5483.51 0.201412
\(906\) −22013.1 −0.807214
\(907\) 14432.7 0.528368 0.264184 0.964472i \(-0.414897\pi\)
0.264184 + 0.964472i \(0.414897\pi\)
\(908\) −2045.91 −0.0747753
\(909\) −3651.89 −0.133251
\(910\) 2476.15 0.0902018
\(911\) −50465.5 −1.83534 −0.917670 0.397343i \(-0.869932\pi\)
−0.917670 + 0.397343i \(0.869932\pi\)
\(912\) 39799.1 1.44505
\(913\) −1404.96 −0.0509282
\(914\) 33767.8 1.22203
\(915\) 6397.81 0.231153
\(916\) 886.404 0.0319734
\(917\) −14134.5 −0.509009
\(918\) 0 0
\(919\) −33955.2 −1.21880 −0.609401 0.792862i \(-0.708590\pi\)
−0.609401 + 0.792862i \(0.708590\pi\)
\(920\) 4922.36 0.176397
\(921\) 959.057 0.0343127
\(922\) −13739.1 −0.490753
\(923\) 8306.16 0.296209
\(924\) 324.896 0.0115674
\(925\) −29529.1 −1.04963
\(926\) 14184.9 0.503396
\(927\) 11504.9 0.407628
\(928\) 7100.62 0.251174
\(929\) −14807.7 −0.522954 −0.261477 0.965210i \(-0.584210\pi\)
−0.261477 + 0.965210i \(0.584210\pi\)
\(930\) 1858.09 0.0655154
\(931\) −45365.6 −1.59699
\(932\) −3388.76 −0.119101
\(933\) −5604.23 −0.196650
\(934\) −11900.4 −0.416908
\(935\) 0 0
\(936\) 3435.96 0.119987
\(937\) −5141.33 −0.179253 −0.0896265 0.995975i \(-0.528567\pi\)
−0.0896265 + 0.995975i \(0.528567\pi\)
\(938\) 20443.2 0.711614
\(939\) 1669.52 0.0580220
\(940\) −767.498 −0.0266309
\(941\) −38958.4 −1.34964 −0.674819 0.737984i \(-0.735778\pi\)
−0.674819 + 0.737984i \(0.735778\pi\)
\(942\) 3373.42 0.116679
\(943\) 5409.57 0.186808
\(944\) −20812.8 −0.717585
\(945\) −7961.89 −0.274074
\(946\) 1458.51 0.0501273
\(947\) 14191.6 0.486974 0.243487 0.969904i \(-0.421709\pi\)
0.243487 + 0.969904i \(0.421709\pi\)
\(948\) 2441.35 0.0836408
\(949\) 2510.50 0.0858739
\(950\) 52146.0 1.78088
\(951\) 2811.27 0.0958586
\(952\) 0 0
\(953\) −32646.8 −1.10969 −0.554844 0.831955i \(-0.687222\pi\)
−0.554844 + 0.831955i \(0.687222\pi\)
\(954\) 2137.12 0.0725280
\(955\) −433.724 −0.0146963
\(956\) −618.867 −0.0209368
\(957\) 3320.19 0.112149
\(958\) −23360.8 −0.787842
\(959\) 28754.3 0.968223
\(960\) −4988.15 −0.167700
\(961\) −23932.9 −0.803360
\(962\) 11618.5 0.389393
\(963\) 15192.2 0.508372
\(964\) −2844.55 −0.0950381
\(965\) 9551.94 0.318640
\(966\) −29074.5 −0.968381
\(967\) −16183.8 −0.538196 −0.269098 0.963113i \(-0.586726\pi\)
−0.269098 + 0.963113i \(0.586726\pi\)
\(968\) 31063.4 1.03142
\(969\) 0 0
\(970\) 5064.18 0.167630
\(971\) 28807.7 0.952095 0.476048 0.879420i \(-0.342069\pi\)
0.476048 + 0.879420i \(0.342069\pi\)
\(972\) −1743.96 −0.0575490
\(973\) −24615.1 −0.811021
\(974\) 35002.1 1.15148
\(975\) −9235.02 −0.303341
\(976\) 40421.0 1.32566
\(977\) 3155.66 0.103335 0.0516675 0.998664i \(-0.483546\pi\)
0.0516675 + 0.998664i \(0.483546\pi\)
\(978\) 19684.4 0.643597
\(979\) 3983.16 0.130033
\(980\) 461.897 0.0150559
\(981\) 3072.89 0.100010
\(982\) −31588.8 −1.02651
\(983\) 14818.7 0.480816 0.240408 0.970672i \(-0.422719\pi\)
0.240408 + 0.970672i \(0.422719\pi\)
\(984\) −5530.85 −0.179184
\(985\) 5510.83 0.178264
\(986\) 0 0
\(987\) 50722.8 1.63579
\(988\) 2232.84 0.0718989
\(989\) 14204.1 0.456688
\(990\) 176.478 0.00566551
\(991\) −888.414 −0.0284777 −0.0142389 0.999899i \(-0.504533\pi\)
−0.0142389 + 0.999899i \(0.504533\pi\)
\(992\) −2709.44 −0.0867185
\(993\) 6192.63 0.197902
\(994\) −31559.3 −1.00704
\(995\) 3444.98 0.109762
\(996\) 1250.29 0.0397760
\(997\) 5116.97 0.162544 0.0812718 0.996692i \(-0.474102\pi\)
0.0812718 + 0.996692i \(0.474102\pi\)
\(998\) 28806.6 0.913685
\(999\) −37358.5 −1.18315
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.g.1.10 12
17.4 even 4 289.4.b.e.288.3 12
17.5 odd 16 17.4.d.a.8.1 12
17.7 odd 16 17.4.d.a.15.1 yes 12
17.13 even 4 289.4.b.e.288.4 12
17.16 even 2 inner 289.4.a.g.1.9 12
51.5 even 16 153.4.l.a.127.3 12
51.41 even 16 153.4.l.a.100.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.d.a.8.1 12 17.5 odd 16
17.4.d.a.15.1 yes 12 17.7 odd 16
153.4.l.a.100.3 12 51.41 even 16
153.4.l.a.127.3 12 51.5 even 16
289.4.a.g.1.9 12 17.16 even 2 inner
289.4.a.g.1.10 12 1.1 even 1 trivial
289.4.b.e.288.3 12 17.4 even 4
289.4.b.e.288.4 12 17.13 even 4