Properties

Label 289.4.a.g.1.2
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 1.2
Root \(-4.62703\) 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)
 
\(f(q)\) \(=\) \(q-4.86166 q^{2} +5.06554 q^{3} +15.6358 q^{4} -18.5634 q^{5} -24.6269 q^{6} +14.0210 q^{7} -37.1225 q^{8} -1.34032 q^{9} +O(q^{10})\) \(q-4.86166 q^{2} +5.06554 q^{3} +15.6358 q^{4} -18.5634 q^{5} -24.6269 q^{6} +14.0210 q^{7} -37.1225 q^{8} -1.34032 q^{9} +90.2489 q^{10} +19.4791 q^{11} +79.2036 q^{12} +29.9060 q^{13} -68.1655 q^{14} -94.0335 q^{15} +55.3912 q^{16} +6.51621 q^{18} -45.7882 q^{19} -290.253 q^{20} +71.0240 q^{21} -94.7006 q^{22} -89.3259 q^{23} -188.046 q^{24} +219.599 q^{25} -145.393 q^{26} -143.559 q^{27} +219.229 q^{28} +57.9077 q^{29} +457.159 q^{30} +161.949 q^{31} +27.6872 q^{32} +98.6719 q^{33} -260.277 q^{35} -20.9570 q^{36} -135.583 q^{37} +222.607 q^{38} +151.490 q^{39} +689.120 q^{40} -56.8918 q^{41} -345.295 q^{42} +52.1442 q^{43} +304.570 q^{44} +24.8809 q^{45} +434.272 q^{46} -482.699 q^{47} +280.586 q^{48} -146.411 q^{49} -1067.62 q^{50} +467.603 q^{52} -529.972 q^{53} +697.935 q^{54} -361.597 q^{55} -520.496 q^{56} -231.942 q^{57} -281.528 q^{58} -280.058 q^{59} -1470.29 q^{60} -586.656 q^{61} -787.341 q^{62} -18.7927 q^{63} -577.735 q^{64} -555.156 q^{65} -479.710 q^{66} +367.471 q^{67} -452.484 q^{69} +1265.38 q^{70} +60.5496 q^{71} +49.7563 q^{72} -368.086 q^{73} +659.161 q^{74} +1112.39 q^{75} -715.933 q^{76} +273.116 q^{77} -736.493 q^{78} +217.721 q^{79} -1028.25 q^{80} -691.015 q^{81} +276.589 q^{82} -594.154 q^{83} +1110.51 q^{84} -253.508 q^{86} +293.334 q^{87} -723.112 q^{88} -887.553 q^{89} -120.963 q^{90} +419.312 q^{91} -1396.68 q^{92} +820.358 q^{93} +2346.72 q^{94} +849.983 q^{95} +140.251 q^{96} -884.682 q^{97} +711.801 q^{98} -26.1083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{2} + 16 q^{4} - 96 q^{8} - 36 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.86166 −1.71886 −0.859429 0.511255i \(-0.829181\pi\)
−0.859429 + 0.511255i \(0.829181\pi\)
\(3\) 5.06554 0.974863 0.487432 0.873161i \(-0.337934\pi\)
0.487432 + 0.873161i \(0.337934\pi\)
\(4\) 15.6358 1.95447
\(5\) −18.5634 −1.66036 −0.830179 0.557497i \(-0.811762\pi\)
−0.830179 + 0.557497i \(0.811762\pi\)
\(6\) −24.6269 −1.67565
\(7\) 14.0210 0.757064 0.378532 0.925588i \(-0.376429\pi\)
0.378532 + 0.925588i \(0.376429\pi\)
\(8\) −37.1225 −1.64060
\(9\) −1.34032 −0.0496417
\(10\) 90.2489 2.85392
\(11\) 19.4791 0.533924 0.266962 0.963707i \(-0.413980\pi\)
0.266962 + 0.963707i \(0.413980\pi\)
\(12\) 79.2036 1.90534
\(13\) 29.9060 0.638033 0.319016 0.947749i \(-0.396648\pi\)
0.319016 + 0.947749i \(0.396648\pi\)
\(14\) −68.1655 −1.30128
\(15\) −94.0335 −1.61862
\(16\) 55.3912 0.865487
\(17\) 0 0
\(18\) 6.51621 0.0853269
\(19\) −45.7882 −0.552870 −0.276435 0.961033i \(-0.589153\pi\)
−0.276435 + 0.961033i \(0.589153\pi\)
\(20\) −290.253 −3.24512
\(21\) 71.0240 0.738034
\(22\) −94.7006 −0.917738
\(23\) −89.3259 −0.809814 −0.404907 0.914358i \(-0.632696\pi\)
−0.404907 + 0.914358i \(0.632696\pi\)
\(24\) −188.046 −1.59936
\(25\) 219.599 1.75679
\(26\) −145.393 −1.09669
\(27\) −143.559 −1.02326
\(28\) 219.229 1.47966
\(29\) 57.9077 0.370800 0.185400 0.982663i \(-0.440642\pi\)
0.185400 + 0.982663i \(0.440642\pi\)
\(30\) 457.159 2.78218
\(31\) 161.949 0.938286 0.469143 0.883122i \(-0.344563\pi\)
0.469143 + 0.883122i \(0.344563\pi\)
\(32\) 27.6872 0.152952
\(33\) 98.6719 0.520502
\(34\) 0 0
\(35\) −260.277 −1.25700
\(36\) −20.9570 −0.0970232
\(37\) −135.583 −0.602426 −0.301213 0.953557i \(-0.597392\pi\)
−0.301213 + 0.953557i \(0.597392\pi\)
\(38\) 222.607 0.950304
\(39\) 151.490 0.621994
\(40\) 689.120 2.72398
\(41\) −56.8918 −0.216708 −0.108354 0.994112i \(-0.534558\pi\)
−0.108354 + 0.994112i \(0.534558\pi\)
\(42\) −345.295 −1.26857
\(43\) 52.1442 0.184928 0.0924642 0.995716i \(-0.470526\pi\)
0.0924642 + 0.995716i \(0.470526\pi\)
\(44\) 304.570 1.04354
\(45\) 24.8809 0.0824229
\(46\) 434.272 1.39196
\(47\) −482.699 −1.49806 −0.749030 0.662536i \(-0.769480\pi\)
−0.749030 + 0.662536i \(0.769480\pi\)
\(48\) 280.586 0.843731
\(49\) −146.411 −0.426855
\(50\) −1067.62 −3.01967
\(51\) 0 0
\(52\) 467.603 1.24702
\(53\) −529.972 −1.37353 −0.686766 0.726879i \(-0.740970\pi\)
−0.686766 + 0.726879i \(0.740970\pi\)
\(54\) 697.935 1.75883
\(55\) −361.597 −0.886504
\(56\) −520.496 −1.24204
\(57\) −231.942 −0.538972
\(58\) −281.528 −0.637352
\(59\) −280.058 −0.617973 −0.308986 0.951066i \(-0.599990\pi\)
−0.308986 + 0.951066i \(0.599990\pi\)
\(60\) −1470.29 −3.16355
\(61\) −586.656 −1.23137 −0.615686 0.787992i \(-0.711121\pi\)
−0.615686 + 0.787992i \(0.711121\pi\)
\(62\) −787.341 −1.61278
\(63\) −18.7927 −0.0375819
\(64\) −577.735 −1.12839
\(65\) −555.156 −1.05936
\(66\) −479.710 −0.894669
\(67\) 367.471 0.670056 0.335028 0.942208i \(-0.391254\pi\)
0.335028 + 0.942208i \(0.391254\pi\)
\(68\) 0 0
\(69\) −452.484 −0.789458
\(70\) 1265.38 2.16060
\(71\) 60.5496 0.101210 0.0506051 0.998719i \(-0.483885\pi\)
0.0506051 + 0.998719i \(0.483885\pi\)
\(72\) 49.7563 0.0814421
\(73\) −368.086 −0.590154 −0.295077 0.955473i \(-0.595345\pi\)
−0.295077 + 0.955473i \(0.595345\pi\)
\(74\) 659.161 1.03548
\(75\) 1112.39 1.71263
\(76\) −715.933 −1.08057
\(77\) 273.116 0.404214
\(78\) −736.493 −1.06912
\(79\) 217.721 0.310070 0.155035 0.987909i \(-0.450451\pi\)
0.155035 + 0.987909i \(0.450451\pi\)
\(80\) −1028.25 −1.43702
\(81\) −691.015 −0.947894
\(82\) 276.589 0.372490
\(83\) −594.154 −0.785746 −0.392873 0.919593i \(-0.628519\pi\)
−0.392873 + 0.919593i \(0.628519\pi\)
\(84\) 1110.51 1.44247
\(85\) 0 0
\(86\) −253.508 −0.317866
\(87\) 293.334 0.361479
\(88\) −723.112 −0.875955
\(89\) −887.553 −1.05708 −0.528542 0.848907i \(-0.677261\pi\)
−0.528542 + 0.848907i \(0.677261\pi\)
\(90\) −120.963 −0.141673
\(91\) 419.312 0.483031
\(92\) −1396.68 −1.58276
\(93\) 820.358 0.914701
\(94\) 2346.72 2.57495
\(95\) 849.983 0.917962
\(96\) 140.251 0.149107
\(97\) −884.682 −0.926040 −0.463020 0.886348i \(-0.653234\pi\)
−0.463020 + 0.886348i \(0.653234\pi\)
\(98\) 711.801 0.733702
\(99\) −26.1083 −0.0265048
\(100\) 3433.60 3.43360
\(101\) −1845.31 −1.81798 −0.908988 0.416822i \(-0.863144\pi\)
−0.908988 + 0.416822i \(0.863144\pi\)
\(102\) 0 0
\(103\) −1823.07 −1.74400 −0.872002 0.489502i \(-0.837178\pi\)
−0.872002 + 0.489502i \(0.837178\pi\)
\(104\) −1110.19 −1.04676
\(105\) −1318.44 −1.22540
\(106\) 2576.54 2.36091
\(107\) 1855.35 1.67629 0.838146 0.545445i \(-0.183639\pi\)
0.838146 + 0.545445i \(0.183639\pi\)
\(108\) −2244.66 −1.99993
\(109\) 1387.46 1.21922 0.609610 0.792702i \(-0.291326\pi\)
0.609610 + 0.792702i \(0.291326\pi\)
\(110\) 1757.96 1.52377
\(111\) −686.803 −0.587283
\(112\) 776.640 0.655229
\(113\) −613.115 −0.510416 −0.255208 0.966886i \(-0.582144\pi\)
−0.255208 + 0.966886i \(0.582144\pi\)
\(114\) 1127.62 0.926417
\(115\) 1658.19 1.34458
\(116\) 905.432 0.724717
\(117\) −40.0837 −0.0316730
\(118\) 1361.55 1.06221
\(119\) 0 0
\(120\) 3490.76 2.65551
\(121\) −951.566 −0.714926
\(122\) 2852.13 2.11655
\(123\) −288.188 −0.211260
\(124\) 2532.19 1.83385
\(125\) −1756.07 −1.25654
\(126\) 91.3639 0.0645979
\(127\) 111.688 0.0780368 0.0390184 0.999238i \(-0.487577\pi\)
0.0390184 + 0.999238i \(0.487577\pi\)
\(128\) 2587.26 1.78659
\(129\) 264.139 0.180280
\(130\) 2698.98 1.82089
\(131\) 2132.04 1.42196 0.710981 0.703212i \(-0.248251\pi\)
0.710981 + 0.703212i \(0.248251\pi\)
\(132\) 1542.81 1.01731
\(133\) −641.996 −0.418558
\(134\) −1786.52 −1.15173
\(135\) 2664.94 1.69897
\(136\) 0 0
\(137\) 3087.68 1.92554 0.962769 0.270327i \(-0.0871317\pi\)
0.962769 + 0.270327i \(0.0871317\pi\)
\(138\) 2199.82 1.35697
\(139\) −469.825 −0.286691 −0.143346 0.989673i \(-0.545786\pi\)
−0.143346 + 0.989673i \(0.545786\pi\)
\(140\) −4069.64 −2.45677
\(141\) −2445.13 −1.46040
\(142\) −294.372 −0.173966
\(143\) 582.540 0.340661
\(144\) −74.2421 −0.0429642
\(145\) −1074.96 −0.615660
\(146\) 1789.51 1.01439
\(147\) −741.651 −0.416125
\(148\) −2119.95 −1.17742
\(149\) −2209.36 −1.21475 −0.607374 0.794416i \(-0.707777\pi\)
−0.607374 + 0.794416i \(0.707777\pi\)
\(150\) −5408.05 −2.94377
\(151\) −752.366 −0.405475 −0.202737 0.979233i \(-0.564984\pi\)
−0.202737 + 0.979233i \(0.564984\pi\)
\(152\) 1699.77 0.907038
\(153\) 0 0
\(154\) −1327.80 −0.694787
\(155\) −3006.32 −1.55789
\(156\) 2368.66 1.21567
\(157\) 579.544 0.294603 0.147301 0.989092i \(-0.452941\pi\)
0.147301 + 0.989092i \(0.452941\pi\)
\(158\) −1058.49 −0.532966
\(159\) −2684.59 −1.33901
\(160\) −513.968 −0.253955
\(161\) −1252.44 −0.613081
\(162\) 3359.48 1.62929
\(163\) −1777.74 −0.854253 −0.427126 0.904192i \(-0.640474\pi\)
−0.427126 + 0.904192i \(0.640474\pi\)
\(164\) −889.548 −0.423549
\(165\) −1831.68 −0.864221
\(166\) 2888.58 1.35059
\(167\) 3134.84 1.45258 0.726291 0.687388i \(-0.241243\pi\)
0.726291 + 0.687388i \(0.241243\pi\)
\(168\) −2636.59 −1.21082
\(169\) −1302.63 −0.592914
\(170\) 0 0
\(171\) 61.3710 0.0274454
\(172\) 815.315 0.361437
\(173\) 1169.33 0.513886 0.256943 0.966427i \(-0.417285\pi\)
0.256943 + 0.966427i \(0.417285\pi\)
\(174\) −1426.09 −0.621331
\(175\) 3079.00 1.33000
\(176\) 1078.97 0.462104
\(177\) −1418.64 −0.602439
\(178\) 4314.99 1.81698
\(179\) −1552.54 −0.648281 −0.324140 0.946009i \(-0.605075\pi\)
−0.324140 + 0.946009i \(0.605075\pi\)
\(180\) 389.033 0.161093
\(181\) −1495.92 −0.614313 −0.307156 0.951659i \(-0.599377\pi\)
−0.307156 + 0.951659i \(0.599377\pi\)
\(182\) −2038.55 −0.830262
\(183\) −2971.73 −1.20042
\(184\) 3316.00 1.32858
\(185\) 2516.88 1.00024
\(186\) −3988.30 −1.57224
\(187\) 0 0
\(188\) −7547.37 −2.92792
\(189\) −2012.84 −0.774671
\(190\) −4132.33 −1.57785
\(191\) 3008.79 1.13983 0.569917 0.821702i \(-0.306975\pi\)
0.569917 + 0.821702i \(0.306975\pi\)
\(192\) −2926.54 −1.10002
\(193\) 3893.56 1.45215 0.726074 0.687616i \(-0.241343\pi\)
0.726074 + 0.687616i \(0.241343\pi\)
\(194\) 4301.03 1.59173
\(195\) −2812.16 −1.03273
\(196\) −2289.25 −0.834275
\(197\) 946.676 0.342375 0.171187 0.985238i \(-0.445240\pi\)
0.171187 + 0.985238i \(0.445240\pi\)
\(198\) 126.930 0.0455581
\(199\) −1765.84 −0.629031 −0.314515 0.949252i \(-0.601842\pi\)
−0.314515 + 0.949252i \(0.601842\pi\)
\(200\) −8152.07 −2.88219
\(201\) 1861.44 0.653213
\(202\) 8971.29 3.12484
\(203\) 811.925 0.280719
\(204\) 0 0
\(205\) 1056.10 0.359812
\(206\) 8863.15 2.99769
\(207\) 119.726 0.0402005
\(208\) 1656.53 0.552209
\(209\) −891.910 −0.295190
\(210\) 6409.83 2.10629
\(211\) −371.398 −0.121176 −0.0605879 0.998163i \(-0.519298\pi\)
−0.0605879 + 0.998163i \(0.519298\pi\)
\(212\) −8286.52 −2.68453
\(213\) 306.716 0.0986660
\(214\) −9020.08 −2.88131
\(215\) −967.973 −0.307047
\(216\) 5329.28 1.67876
\(217\) 2270.69 0.710342
\(218\) −6745.38 −2.09566
\(219\) −1864.56 −0.575319
\(220\) −5653.85 −1.73265
\(221\) 0 0
\(222\) 3339.00 1.00946
\(223\) 2573.90 0.772919 0.386459 0.922306i \(-0.373698\pi\)
0.386459 + 0.922306i \(0.373698\pi\)
\(224\) 388.203 0.115794
\(225\) −294.334 −0.0872100
\(226\) 2980.76 0.877332
\(227\) 5204.65 1.52178 0.760892 0.648879i \(-0.224762\pi\)
0.760892 + 0.648879i \(0.224762\pi\)
\(228\) −3626.59 −1.05341
\(229\) 3198.73 0.923048 0.461524 0.887128i \(-0.347303\pi\)
0.461524 + 0.887128i \(0.347303\pi\)
\(230\) −8061.56 −2.31115
\(231\) 1383.48 0.394053
\(232\) −2149.68 −0.608334
\(233\) −853.101 −0.239865 −0.119932 0.992782i \(-0.538268\pi\)
−0.119932 + 0.992782i \(0.538268\pi\)
\(234\) 194.873 0.0544414
\(235\) 8960.51 2.48732
\(236\) −4378.92 −1.20781
\(237\) 1102.87 0.302276
\(238\) 0 0
\(239\) 1892.67 0.512246 0.256123 0.966644i \(-0.417555\pi\)
0.256123 + 0.966644i \(0.417555\pi\)
\(240\) −5208.62 −1.40090
\(241\) −1849.42 −0.494322 −0.247161 0.968974i \(-0.579498\pi\)
−0.247161 + 0.968974i \(0.579498\pi\)
\(242\) 4626.19 1.22886
\(243\) 375.731 0.0991900
\(244\) −9172.83 −2.40668
\(245\) 2717.88 0.708732
\(246\) 1401.07 0.363126
\(247\) −1369.34 −0.352749
\(248\) −6011.95 −1.53935
\(249\) −3009.71 −0.765995
\(250\) 8537.43 2.15982
\(251\) 1026.39 0.258109 0.129055 0.991637i \(-0.458806\pi\)
0.129055 + 0.991637i \(0.458806\pi\)
\(252\) −293.839 −0.0734527
\(253\) −1739.98 −0.432379
\(254\) −542.987 −0.134134
\(255\) 0 0
\(256\) −7956.49 −1.94250
\(257\) 2615.84 0.634910 0.317455 0.948273i \(-0.397172\pi\)
0.317455 + 0.948273i \(0.397172\pi\)
\(258\) −1284.15 −0.309875
\(259\) −1901.02 −0.456075
\(260\) −8680.29 −2.07049
\(261\) −77.6151 −0.0184071
\(262\) −10365.2 −2.44415
\(263\) −4992.16 −1.17045 −0.585227 0.810869i \(-0.698995\pi\)
−0.585227 + 0.810869i \(0.698995\pi\)
\(264\) −3662.95 −0.853936
\(265\) 9838.06 2.28056
\(266\) 3121.17 0.719441
\(267\) −4495.94 −1.03051
\(268\) 5745.70 1.30961
\(269\) −3410.52 −0.773023 −0.386512 0.922284i \(-0.626320\pi\)
−0.386512 + 0.922284i \(0.626320\pi\)
\(270\) −12956.0 −2.92029
\(271\) 75.0911 0.0168319 0.00841597 0.999965i \(-0.497321\pi\)
0.00841597 + 0.999965i \(0.497321\pi\)
\(272\) 0 0
\(273\) 2124.04 0.470889
\(274\) −15011.3 −3.30972
\(275\) 4277.58 0.937992
\(276\) −7074.93 −1.54297
\(277\) −3441.88 −0.746580 −0.373290 0.927715i \(-0.621770\pi\)
−0.373290 + 0.927715i \(0.621770\pi\)
\(278\) 2284.13 0.492781
\(279\) −217.064 −0.0465781
\(280\) 9662.16 2.06223
\(281\) 1673.05 0.355181 0.177591 0.984104i \(-0.443170\pi\)
0.177591 + 0.984104i \(0.443170\pi\)
\(282\) 11887.4 2.51023
\(283\) 6792.22 1.42670 0.713349 0.700809i \(-0.247178\pi\)
0.713349 + 0.700809i \(0.247178\pi\)
\(284\) 946.740 0.197812
\(285\) 4305.62 0.894887
\(286\) −2832.11 −0.585547
\(287\) −797.682 −0.164062
\(288\) −37.1098 −0.00759277
\(289\) 0 0
\(290\) 5226.11 1.05823
\(291\) −4481.39 −0.902762
\(292\) −5755.31 −1.15344
\(293\) −6436.90 −1.28344 −0.641720 0.766939i \(-0.721779\pi\)
−0.641720 + 0.766939i \(0.721779\pi\)
\(294\) 3605.66 0.715259
\(295\) 5198.81 1.02606
\(296\) 5033.20 0.988340
\(297\) −2796.39 −0.546341
\(298\) 10741.2 2.08798
\(299\) −2671.38 −0.516688
\(300\) 17393.0 3.34729
\(301\) 731.115 0.140003
\(302\) 3657.75 0.696953
\(303\) −9347.51 −1.77228
\(304\) −2536.26 −0.478501
\(305\) 10890.3 2.04452
\(306\) 0 0
\(307\) 5129.87 0.953672 0.476836 0.878992i \(-0.341784\pi\)
0.476836 + 0.878992i \(0.341784\pi\)
\(308\) 4270.38 0.790025
\(309\) −9234.83 −1.70017
\(310\) 14615.7 2.67779
\(311\) −3422.67 −0.624058 −0.312029 0.950073i \(-0.601009\pi\)
−0.312029 + 0.950073i \(0.601009\pi\)
\(312\) −5623.69 −1.02044
\(313\) −4283.53 −0.773544 −0.386772 0.922175i \(-0.626410\pi\)
−0.386772 + 0.922175i \(0.626410\pi\)
\(314\) −2817.55 −0.506380
\(315\) 348.856 0.0623994
\(316\) 3404.23 0.606022
\(317\) 390.350 0.0691617 0.0345808 0.999402i \(-0.488990\pi\)
0.0345808 + 0.999402i \(0.488990\pi\)
\(318\) 13051.6 2.30156
\(319\) 1127.99 0.197979
\(320\) 10724.7 1.87353
\(321\) 9398.34 1.63416
\(322\) 6088.94 1.05380
\(323\) 0 0
\(324\) −10804.5 −1.85263
\(325\) 6567.31 1.12089
\(326\) 8642.77 1.46834
\(327\) 7028.25 1.18857
\(328\) 2111.97 0.355531
\(329\) −6767.93 −1.13413
\(330\) 8905.03 1.48547
\(331\) 3824.89 0.635151 0.317575 0.948233i \(-0.397131\pi\)
0.317575 + 0.948233i \(0.397131\pi\)
\(332\) −9290.06 −1.53572
\(333\) 181.726 0.0299054
\(334\) −15240.5 −2.49678
\(335\) −6821.51 −1.11253
\(336\) 3934.10 0.638758
\(337\) 2376.90 0.384208 0.192104 0.981375i \(-0.438469\pi\)
0.192104 + 0.981375i \(0.438469\pi\)
\(338\) 6332.96 1.01914
\(339\) −3105.76 −0.497586
\(340\) 0 0
\(341\) 3154.61 0.500973
\(342\) −298.365 −0.0471747
\(343\) −6862.04 −1.08022
\(344\) −1935.73 −0.303394
\(345\) 8399.62 1.31078
\(346\) −5684.87 −0.883296
\(347\) −11923.2 −1.84459 −0.922293 0.386491i \(-0.873687\pi\)
−0.922293 + 0.386491i \(0.873687\pi\)
\(348\) 4586.50 0.706500
\(349\) −7389.94 −1.13345 −0.566726 0.823906i \(-0.691790\pi\)
−0.566726 + 0.823906i \(0.691790\pi\)
\(350\) −14969.1 −2.28608
\(351\) −4293.27 −0.652871
\(352\) 539.321 0.0816645
\(353\) 2966.18 0.447235 0.223617 0.974677i \(-0.428213\pi\)
0.223617 + 0.974677i \(0.428213\pi\)
\(354\) 6896.96 1.03551
\(355\) −1124.01 −0.168045
\(356\) −13877.6 −2.06604
\(357\) 0 0
\(358\) 7547.93 1.11430
\(359\) −6526.33 −0.959460 −0.479730 0.877416i \(-0.659265\pi\)
−0.479730 + 0.877416i \(0.659265\pi\)
\(360\) −923.644 −0.135223
\(361\) −4762.44 −0.694335
\(362\) 7272.64 1.05592
\(363\) −4820.19 −0.696955
\(364\) 6556.27 0.944071
\(365\) 6832.92 0.979867
\(366\) 14447.6 2.06335
\(367\) −5896.51 −0.838679 −0.419340 0.907829i \(-0.637738\pi\)
−0.419340 + 0.907829i \(0.637738\pi\)
\(368\) −4947.86 −0.700884
\(369\) 76.2536 0.0107577
\(370\) −12236.2 −1.71928
\(371\) −7430.74 −1.03985
\(372\) 12826.9 1.78776
\(373\) −9234.98 −1.28195 −0.640977 0.767560i \(-0.721471\pi\)
−0.640977 + 0.767560i \(0.721471\pi\)
\(374\) 0 0
\(375\) −8895.45 −1.22496
\(376\) 17919.0 2.45772
\(377\) 1731.79 0.236582
\(378\) 9785.77 1.33155
\(379\) −1449.66 −0.196475 −0.0982373 0.995163i \(-0.531320\pi\)
−0.0982373 + 0.995163i \(0.531320\pi\)
\(380\) 13290.1 1.79413
\(381\) 565.758 0.0760752
\(382\) −14627.7 −1.95921
\(383\) 8159.07 1.08854 0.544268 0.838911i \(-0.316808\pi\)
0.544268 + 0.838911i \(0.316808\pi\)
\(384\) 13105.8 1.74168
\(385\) −5069.96 −0.671140
\(386\) −18929.2 −2.49604
\(387\) −69.8902 −0.00918015
\(388\) −13832.7 −1.80992
\(389\) −1467.86 −0.191320 −0.0956598 0.995414i \(-0.530496\pi\)
−0.0956598 + 0.995414i \(0.530496\pi\)
\(390\) 13671.8 1.77512
\(391\) 0 0
\(392\) 5435.15 0.700298
\(393\) 10799.9 1.38622
\(394\) −4602.42 −0.588494
\(395\) −4041.63 −0.514827
\(396\) −408.223 −0.0518030
\(397\) 6018.22 0.760821 0.380411 0.924818i \(-0.375783\pi\)
0.380411 + 0.924818i \(0.375783\pi\)
\(398\) 8584.92 1.08121
\(399\) −3252.06 −0.408036
\(400\) 12163.8 1.52048
\(401\) −5899.13 −0.734634 −0.367317 0.930096i \(-0.619724\pi\)
−0.367317 + 0.930096i \(0.619724\pi\)
\(402\) −9049.70 −1.12278
\(403\) 4843.24 0.598657
\(404\) −28852.9 −3.55318
\(405\) 12827.6 1.57384
\(406\) −3947.31 −0.482516
\(407\) −2641.04 −0.321649
\(408\) 0 0
\(409\) −9261.09 −1.11964 −0.559818 0.828616i \(-0.689129\pi\)
−0.559818 + 0.828616i \(0.689129\pi\)
\(410\) −5134.42 −0.618466
\(411\) 15640.8 1.87714
\(412\) −28505.1 −3.40861
\(413\) −3926.69 −0.467845
\(414\) −582.066 −0.0690990
\(415\) 11029.5 1.30462
\(416\) 828.013 0.0975881
\(417\) −2379.92 −0.279485
\(418\) 4336.17 0.507390
\(419\) 8538.07 0.995494 0.497747 0.867322i \(-0.334161\pi\)
0.497747 + 0.867322i \(0.334161\pi\)
\(420\) −20614.9 −2.39501
\(421\) −1617.31 −0.187228 −0.0936140 0.995609i \(-0.529842\pi\)
−0.0936140 + 0.995609i \(0.529842\pi\)
\(422\) 1805.61 0.208284
\(423\) 646.973 0.0743662
\(424\) 19673.9 2.25342
\(425\) 0 0
\(426\) −1491.15 −0.169593
\(427\) −8225.52 −0.932227
\(428\) 29009.8 3.27627
\(429\) 2950.88 0.332097
\(430\) 4705.96 0.527771
\(431\) −2537.10 −0.283544 −0.141772 0.989899i \(-0.545280\pi\)
−0.141772 + 0.989899i \(0.545280\pi\)
\(432\) −7951.90 −0.885616
\(433\) 1833.33 0.203474 0.101737 0.994811i \(-0.467560\pi\)
0.101737 + 0.994811i \(0.467560\pi\)
\(434\) −11039.3 −1.22098
\(435\) −5445.26 −0.600185
\(436\) 21694.1 2.38293
\(437\) 4090.07 0.447722
\(438\) 9064.84 0.988892
\(439\) −10398.5 −1.13051 −0.565257 0.824915i \(-0.691223\pi\)
−0.565257 + 0.824915i \(0.691223\pi\)
\(440\) 13423.4 1.45440
\(441\) 196.238 0.0211898
\(442\) 0 0
\(443\) −3984.14 −0.427296 −0.213648 0.976911i \(-0.568535\pi\)
−0.213648 + 0.976911i \(0.568535\pi\)
\(444\) −10738.7 −1.14783
\(445\) 16476.0 1.75514
\(446\) −12513.4 −1.32854
\(447\) −11191.6 −1.18421
\(448\) −8100.43 −0.854262
\(449\) 13184.1 1.38574 0.692868 0.721064i \(-0.256347\pi\)
0.692868 + 0.721064i \(0.256347\pi\)
\(450\) 1430.95 0.149902
\(451\) −1108.20 −0.115705
\(452\) −9586.52 −0.997593
\(453\) −3811.14 −0.395282
\(454\) −25303.3 −2.61573
\(455\) −7783.85 −0.802005
\(456\) 8610.26 0.884238
\(457\) −16241.9 −1.66250 −0.831252 0.555896i \(-0.812375\pi\)
−0.831252 + 0.555896i \(0.812375\pi\)
\(458\) −15551.2 −1.58659
\(459\) 0 0
\(460\) 25927.1 2.62795
\(461\) 11054.7 1.11685 0.558425 0.829555i \(-0.311406\pi\)
0.558425 + 0.829555i \(0.311406\pi\)
\(462\) −6726.02 −0.677322
\(463\) 14185.7 1.42390 0.711952 0.702228i \(-0.247811\pi\)
0.711952 + 0.702228i \(0.247811\pi\)
\(464\) 3207.58 0.320922
\(465\) −15228.6 −1.51873
\(466\) 4147.49 0.412293
\(467\) 9689.39 0.960110 0.480055 0.877238i \(-0.340617\pi\)
0.480055 + 0.877238i \(0.340617\pi\)
\(468\) −626.740 −0.0619040
\(469\) 5152.32 0.507275
\(470\) −43563.0 −4.27534
\(471\) 2935.70 0.287197
\(472\) 10396.5 1.01385
\(473\) 1015.72 0.0987376
\(474\) −5361.80 −0.519569
\(475\) −10055.0 −0.971276
\(476\) 0 0
\(477\) 710.334 0.0681844
\(478\) −9201.54 −0.880478
\(479\) −13237.0 −1.26266 −0.631330 0.775514i \(-0.717491\pi\)
−0.631330 + 0.775514i \(0.717491\pi\)
\(480\) −2603.52 −0.247571
\(481\) −4054.75 −0.384367
\(482\) 8991.25 0.849669
\(483\) −6344.28 −0.597670
\(484\) −14878.5 −1.39730
\(485\) 16422.7 1.53756
\(486\) −1826.68 −0.170493
\(487\) 19300.3 1.79585 0.897924 0.440150i \(-0.145075\pi\)
0.897924 + 0.440150i \(0.145075\pi\)
\(488\) 21778.2 2.02019
\(489\) −9005.20 −0.832780
\(490\) −13213.4 −1.21821
\(491\) −72.2707 −0.00664263 −0.00332131 0.999994i \(-0.501057\pi\)
−0.00332131 + 0.999994i \(0.501057\pi\)
\(492\) −4506.04 −0.412902
\(493\) 0 0
\(494\) 6657.27 0.606325
\(495\) 484.658 0.0440075
\(496\) 8970.53 0.812074
\(497\) 848.967 0.0766225
\(498\) 14632.2 1.31664
\(499\) 14805.5 1.32823 0.664116 0.747630i \(-0.268808\pi\)
0.664116 + 0.747630i \(0.268808\pi\)
\(500\) −27457.6 −2.45588
\(501\) 15879.6 1.41607
\(502\) −4989.98 −0.443653
\(503\) −6693.90 −0.593372 −0.296686 0.954975i \(-0.595882\pi\)
−0.296686 + 0.954975i \(0.595882\pi\)
\(504\) 697.633 0.0616569
\(505\) 34255.2 3.01849
\(506\) 8459.22 0.743198
\(507\) −6598.54 −0.578011
\(508\) 1746.32 0.152521
\(509\) 4414.17 0.384390 0.192195 0.981357i \(-0.438439\pi\)
0.192195 + 0.981357i \(0.438439\pi\)
\(510\) 0 0
\(511\) −5160.94 −0.446784
\(512\) 17983.7 1.55230
\(513\) 6573.30 0.565728
\(514\) −12717.4 −1.09132
\(515\) 33842.3 2.89567
\(516\) 4130.01 0.352352
\(517\) −9402.52 −0.799850
\(518\) 9242.10 0.783928
\(519\) 5923.27 0.500968
\(520\) 20608.8 1.73799
\(521\) −1152.08 −0.0968781 −0.0484391 0.998826i \(-0.515425\pi\)
−0.0484391 + 0.998826i \(0.515425\pi\)
\(522\) 377.339 0.0316392
\(523\) 8548.79 0.714747 0.357373 0.933962i \(-0.383672\pi\)
0.357373 + 0.933962i \(0.383672\pi\)
\(524\) 33336.0 2.77918
\(525\) 15596.8 1.29657
\(526\) 24270.2 2.01185
\(527\) 0 0
\(528\) 5465.55 0.450488
\(529\) −4187.89 −0.344201
\(530\) −47829.3 −3.91995
\(531\) 375.368 0.0306772
\(532\) −10038.1 −0.818059
\(533\) −1701.41 −0.138267
\(534\) 21857.7 1.77130
\(535\) −34441.5 −2.78325
\(536\) −13641.5 −1.09929
\(537\) −7864.45 −0.631985
\(538\) 16580.8 1.32872
\(539\) −2851.95 −0.227908
\(540\) 41668.4 3.32060
\(541\) −1820.54 −0.144679 −0.0723393 0.997380i \(-0.523046\pi\)
−0.0723393 + 0.997380i \(0.523046\pi\)
\(542\) −365.067 −0.0289317
\(543\) −7577.62 −0.598871
\(544\) 0 0
\(545\) −25756.0 −2.02434
\(546\) −10326.4 −0.809392
\(547\) 82.7848 0.00647097 0.00323549 0.999995i \(-0.498970\pi\)
0.00323549 + 0.999995i \(0.498970\pi\)
\(548\) 48278.3 3.76341
\(549\) 786.310 0.0611273
\(550\) −20796.1 −1.61227
\(551\) −2651.49 −0.205004
\(552\) 16797.3 1.29519
\(553\) 3052.67 0.234743
\(554\) 16733.3 1.28326
\(555\) 12749.4 0.975100
\(556\) −7346.08 −0.560329
\(557\) −12671.9 −0.963963 −0.481981 0.876181i \(-0.660083\pi\)
−0.481981 + 0.876181i \(0.660083\pi\)
\(558\) 1055.29 0.0800611
\(559\) 1559.42 0.117990
\(560\) −14417.1 −1.08791
\(561\) 0 0
\(562\) −8133.82 −0.610506
\(563\) 4708.47 0.352466 0.176233 0.984348i \(-0.443609\pi\)
0.176233 + 0.984348i \(0.443609\pi\)
\(564\) −38231.5 −2.85432
\(565\) 11381.5 0.847473
\(566\) −33021.5 −2.45229
\(567\) −9688.73 −0.717616
\(568\) −2247.76 −0.166045
\(569\) 8492.74 0.625719 0.312860 0.949799i \(-0.398713\pi\)
0.312860 + 0.949799i \(0.398713\pi\)
\(570\) −20932.5 −1.53818
\(571\) −1128.62 −0.0827166 −0.0413583 0.999144i \(-0.513169\pi\)
−0.0413583 + 0.999144i \(0.513169\pi\)
\(572\) 9108.47 0.665811
\(573\) 15241.1 1.11118
\(574\) 3878.06 0.281998
\(575\) −19615.9 −1.42267
\(576\) 774.353 0.0560151
\(577\) 18288.9 1.31955 0.659773 0.751465i \(-0.270652\pi\)
0.659773 + 0.751465i \(0.270652\pi\)
\(578\) 0 0
\(579\) 19723.0 1.41565
\(580\) −16807.9 −1.20329
\(581\) −8330.65 −0.594860
\(582\) 21787.0 1.55172
\(583\) −10323.4 −0.733361
\(584\) 13664.3 0.968207
\(585\) 744.089 0.0525885
\(586\) 31294.1 2.20605
\(587\) 11310.2 0.795265 0.397633 0.917545i \(-0.369832\pi\)
0.397633 + 0.917545i \(0.369832\pi\)
\(588\) −11596.3 −0.813304
\(589\) −7415.34 −0.518750
\(590\) −25274.9 −1.76364
\(591\) 4795.42 0.333769
\(592\) −7510.12 −0.521392
\(593\) 5283.47 0.365879 0.182939 0.983124i \(-0.441439\pi\)
0.182939 + 0.983124i \(0.441439\pi\)
\(594\) 13595.1 0.939082
\(595\) 0 0
\(596\) −34545.0 −2.37419
\(597\) −8944.93 −0.613219
\(598\) 12987.3 0.888113
\(599\) −22287.6 −1.52028 −0.760138 0.649762i \(-0.774869\pi\)
−0.760138 + 0.649762i \(0.774869\pi\)
\(600\) −41294.6 −2.80974
\(601\) −15046.8 −1.02125 −0.510625 0.859804i \(-0.670586\pi\)
−0.510625 + 0.859804i \(0.670586\pi\)
\(602\) −3554.44 −0.240644
\(603\) −492.531 −0.0332627
\(604\) −11763.8 −0.792489
\(605\) 17664.3 1.18703
\(606\) 45444.4 3.04629
\(607\) 11288.7 0.754848 0.377424 0.926041i \(-0.376810\pi\)
0.377424 + 0.926041i \(0.376810\pi\)
\(608\) −1267.75 −0.0845623
\(609\) 4112.84 0.273663
\(610\) −52945.1 −3.51424
\(611\) −14435.6 −0.955811
\(612\) 0 0
\(613\) 14753.0 0.972054 0.486027 0.873944i \(-0.338446\pi\)
0.486027 + 0.873944i \(0.338446\pi\)
\(614\) −24939.7 −1.63923
\(615\) 5349.74 0.350768
\(616\) −10138.8 −0.663154
\(617\) 6693.56 0.436747 0.218373 0.975865i \(-0.429925\pi\)
0.218373 + 0.975865i \(0.429925\pi\)
\(618\) 44896.6 2.92234
\(619\) 1285.36 0.0834617 0.0417308 0.999129i \(-0.486713\pi\)
0.0417308 + 0.999129i \(0.486713\pi\)
\(620\) −47006.1 −3.04485
\(621\) 12823.5 0.828648
\(622\) 16639.9 1.07267
\(623\) −12444.4 −0.800280
\(624\) 8391.20 0.538328
\(625\) 5148.78 0.329522
\(626\) 20825.1 1.32961
\(627\) −4518.01 −0.287770
\(628\) 9061.61 0.575792
\(629\) 0 0
\(630\) −1696.02 −0.107256
\(631\) 27186.8 1.71520 0.857598 0.514320i \(-0.171956\pi\)
0.857598 + 0.514320i \(0.171956\pi\)
\(632\) −8082.35 −0.508700
\(633\) −1881.33 −0.118130
\(634\) −1897.75 −0.118879
\(635\) −2073.30 −0.129569
\(636\) −41975.7 −2.61705
\(637\) −4378.57 −0.272347
\(638\) −5483.90 −0.340297
\(639\) −81.1562 −0.00502424
\(640\) −48028.2 −2.96638
\(641\) 12321.5 0.759236 0.379618 0.925143i \(-0.376055\pi\)
0.379618 + 0.925143i \(0.376055\pi\)
\(642\) −45691.6 −2.80888
\(643\) −25577.1 −1.56868 −0.784341 0.620330i \(-0.786999\pi\)
−0.784341 + 0.620330i \(0.786999\pi\)
\(644\) −19582.9 −1.19825
\(645\) −4903.30 −0.299329
\(646\) 0 0
\(647\) −28275.5 −1.71812 −0.859062 0.511872i \(-0.828952\pi\)
−0.859062 + 0.511872i \(0.828952\pi\)
\(648\) 25652.2 1.55512
\(649\) −5455.26 −0.329950
\(650\) −31928.1 −1.92665
\(651\) 11502.3 0.692487
\(652\) −27796.3 −1.66961
\(653\) 2354.19 0.141082 0.0705411 0.997509i \(-0.477527\pi\)
0.0705411 + 0.997509i \(0.477527\pi\)
\(654\) −34169.0 −2.04299
\(655\) −39577.8 −2.36097
\(656\) −3151.31 −0.187558
\(657\) 493.355 0.0292962
\(658\) 32903.4 1.94940
\(659\) 21272.6 1.25745 0.628727 0.777626i \(-0.283576\pi\)
0.628727 + 0.777626i \(0.283576\pi\)
\(660\) −28639.8 −1.68909
\(661\) −16621.3 −0.978051 −0.489026 0.872269i \(-0.662648\pi\)
−0.489026 + 0.872269i \(0.662648\pi\)
\(662\) −18595.3 −1.09173
\(663\) 0 0
\(664\) 22056.5 1.28910
\(665\) 11917.6 0.694956
\(666\) −883.489 −0.0514032
\(667\) −5172.66 −0.300279
\(668\) 49015.6 2.83903
\(669\) 13038.2 0.753490
\(670\) 33163.9 1.91229
\(671\) −11427.5 −0.657458
\(672\) 1966.46 0.112883
\(673\) 228.679 0.0130979 0.00654897 0.999979i \(-0.497915\pi\)
0.00654897 + 0.999979i \(0.497915\pi\)
\(674\) −11555.7 −0.660399
\(675\) −31525.4 −1.79765
\(676\) −20367.7 −1.15883
\(677\) 9975.67 0.566316 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(678\) 15099.1 0.855279
\(679\) −12404.1 −0.701071
\(680\) 0 0
\(681\) 26364.4 1.48353
\(682\) −15336.7 −0.861101
\(683\) 31110.8 1.74293 0.871464 0.490459i \(-0.163171\pi\)
0.871464 + 0.490459i \(0.163171\pi\)
\(684\) 959.583 0.0536412
\(685\) −57317.8 −3.19708
\(686\) 33360.9 1.85674
\(687\) 16203.3 0.899846
\(688\) 2888.33 0.160053
\(689\) −15849.3 −0.876358
\(690\) −40836.1 −2.25305
\(691\) −5108.91 −0.281262 −0.140631 0.990062i \(-0.544913\pi\)
−0.140631 + 0.990062i \(0.544913\pi\)
\(692\) 18283.3 1.00437
\(693\) −366.064 −0.0200659
\(694\) 57966.6 3.17058
\(695\) 8721.54 0.476010
\(696\) −10889.3 −0.593043
\(697\) 0 0
\(698\) 35927.4 1.94824
\(699\) −4321.41 −0.233835
\(700\) 48142.5 2.59945
\(701\) 11204.5 0.603691 0.301846 0.953357i \(-0.402397\pi\)
0.301846 + 0.953357i \(0.402397\pi\)
\(702\) 20872.4 1.12219
\(703\) 6208.11 0.333063
\(704\) −11253.7 −0.602473
\(705\) 45389.8 2.42479
\(706\) −14420.6 −0.768733
\(707\) −25873.2 −1.37632
\(708\) −22181.6 −1.17745
\(709\) −33950.0 −1.79833 −0.899167 0.437605i \(-0.855827\pi\)
−0.899167 + 0.437605i \(0.855827\pi\)
\(710\) 5464.54 0.288846
\(711\) −291.817 −0.0153924
\(712\) 32948.2 1.73425
\(713\) −14466.2 −0.759838
\(714\) 0 0
\(715\) −10813.9 −0.565619
\(716\) −24275.2 −1.26705
\(717\) 9587.41 0.499370
\(718\) 31728.8 1.64918
\(719\) 6231.07 0.323198 0.161599 0.986856i \(-0.448335\pi\)
0.161599 + 0.986856i \(0.448335\pi\)
\(720\) 1378.18 0.0713360
\(721\) −25561.3 −1.32032
\(722\) 23153.4 1.19346
\(723\) −9368.30 −0.481896
\(724\) −23389.8 −1.20066
\(725\) 12716.5 0.651417
\(726\) 23434.2 1.19797
\(727\) −5206.88 −0.265629 −0.132815 0.991141i \(-0.542402\pi\)
−0.132815 + 0.991141i \(0.542402\pi\)
\(728\) −15565.9 −0.792461
\(729\) 20560.7 1.04459
\(730\) −33219.4 −1.68425
\(731\) 0 0
\(732\) −46465.3 −2.34618
\(733\) 3817.57 0.192367 0.0961835 0.995364i \(-0.469336\pi\)
0.0961835 + 0.995364i \(0.469336\pi\)
\(734\) 28666.8 1.44157
\(735\) 13767.5 0.690916
\(736\) −2473.18 −0.123862
\(737\) 7158.00 0.357759
\(738\) −370.719 −0.0184910
\(739\) −9211.40 −0.458521 −0.229260 0.973365i \(-0.573631\pi\)
−0.229260 + 0.973365i \(0.573631\pi\)
\(740\) 39353.4 1.95495
\(741\) −6936.44 −0.343882
\(742\) 36125.8 1.78736
\(743\) −23138.9 −1.14251 −0.571255 0.820773i \(-0.693543\pi\)
−0.571255 + 0.820773i \(0.693543\pi\)
\(744\) −30453.8 −1.50066
\(745\) 41013.1 2.01692
\(746\) 44897.4 2.20350
\(747\) 796.360 0.0390057
\(748\) 0 0
\(749\) 26013.9 1.26906
\(750\) 43246.7 2.10553
\(751\) −31141.4 −1.51314 −0.756569 0.653914i \(-0.773126\pi\)
−0.756569 + 0.653914i \(0.773126\pi\)
\(752\) −26737.2 −1.29655
\(753\) 5199.24 0.251621
\(754\) −8419.36 −0.406651
\(755\) 13966.4 0.673233
\(756\) −31472.4 −1.51407
\(757\) 30991.3 1.48798 0.743988 0.668193i \(-0.232932\pi\)
0.743988 + 0.668193i \(0.232932\pi\)
\(758\) 7047.74 0.337712
\(759\) −8813.96 −0.421510
\(760\) −31553.5 −1.50601
\(761\) −14150.5 −0.674053 −0.337026 0.941495i \(-0.609421\pi\)
−0.337026 + 0.941495i \(0.609421\pi\)
\(762\) −2750.52 −0.130762
\(763\) 19453.7 0.923027
\(764\) 47044.7 2.22777
\(765\) 0 0
\(766\) −39666.7 −1.87104
\(767\) −8375.39 −0.394287
\(768\) −40303.9 −1.89367
\(769\) −619.823 −0.0290655 −0.0145328 0.999894i \(-0.504626\pi\)
−0.0145328 + 0.999894i \(0.504626\pi\)
\(770\) 24648.4 1.15359
\(771\) 13250.7 0.618950
\(772\) 60878.8 2.83818
\(773\) 10196.4 0.474436 0.237218 0.971456i \(-0.423764\pi\)
0.237218 + 0.971456i \(0.423764\pi\)
\(774\) 339.783 0.0157794
\(775\) 35563.8 1.64837
\(776\) 32841.7 1.51926
\(777\) −9629.67 −0.444611
\(778\) 7136.23 0.328851
\(779\) 2604.97 0.119811
\(780\) −43970.3 −2.01845
\(781\) 1179.45 0.0540385
\(782\) 0 0
\(783\) −8313.17 −0.379423
\(784\) −8109.88 −0.369437
\(785\) −10758.3 −0.489146
\(786\) −52505.5 −2.38271
\(787\) 33206.7 1.50405 0.752027 0.659132i \(-0.229076\pi\)
0.752027 + 0.659132i \(0.229076\pi\)
\(788\) 14802.0 0.669162
\(789\) −25288.0 −1.14103
\(790\) 19649.1 0.884914
\(791\) −8596.49 −0.386417
\(792\) 969.205 0.0434839
\(793\) −17544.5 −0.785655
\(794\) −29258.6 −1.30774
\(795\) 49835.1 2.22323
\(796\) −27610.3 −1.22942
\(797\) −4351.64 −0.193404 −0.0967020 0.995313i \(-0.530829\pi\)
−0.0967020 + 0.995313i \(0.530829\pi\)
\(798\) 15810.4 0.701356
\(799\) 0 0
\(800\) 6080.08 0.268704
\(801\) 1189.61 0.0524754
\(802\) 28679.6 1.26273
\(803\) −7169.98 −0.315097
\(804\) 29105.1 1.27669
\(805\) 23249.5 1.01793
\(806\) −23546.2 −1.02901
\(807\) −17276.1 −0.753592
\(808\) 68502.7 2.98257
\(809\) 13515.2 0.587355 0.293678 0.955905i \(-0.405121\pi\)
0.293678 + 0.955905i \(0.405121\pi\)
\(810\) −62363.3 −2.70521
\(811\) 5758.39 0.249327 0.124664 0.992199i \(-0.460215\pi\)
0.124664 + 0.992199i \(0.460215\pi\)
\(812\) 12695.1 0.548657
\(813\) 380.377 0.0164088
\(814\) 12839.8 0.552870
\(815\) 33000.8 1.41837
\(816\) 0 0
\(817\) −2387.59 −0.102241
\(818\) 45024.3 1.92450
\(819\) −562.014 −0.0239785
\(820\) 16513.0 0.703243
\(821\) −27956.3 −1.18841 −0.594203 0.804315i \(-0.702532\pi\)
−0.594203 + 0.804315i \(0.702532\pi\)
\(822\) −76040.2 −3.22653
\(823\) −38040.6 −1.61119 −0.805596 0.592465i \(-0.798155\pi\)
−0.805596 + 0.592465i \(0.798155\pi\)
\(824\) 67677.0 2.86121
\(825\) 21668.2 0.914414
\(826\) 19090.3 0.804159
\(827\) 14467.5 0.608324 0.304162 0.952620i \(-0.401624\pi\)
0.304162 + 0.952620i \(0.401624\pi\)
\(828\) 1872.00 0.0785708
\(829\) −24519.4 −1.02726 −0.513628 0.858013i \(-0.671699\pi\)
−0.513628 + 0.858013i \(0.671699\pi\)
\(830\) −53621.8 −2.24246
\(831\) −17435.0 −0.727813
\(832\) −17277.7 −0.719949
\(833\) 0 0
\(834\) 11570.4 0.480394
\(835\) −58193.2 −2.41181
\(836\) −13945.7 −0.576941
\(837\) −23249.2 −0.960108
\(838\) −41509.2 −1.71111
\(839\) −38066.2 −1.56638 −0.783188 0.621785i \(-0.786408\pi\)
−0.783188 + 0.621785i \(0.786408\pi\)
\(840\) 48944.0 2.01039
\(841\) −21035.7 −0.862508
\(842\) 7862.83 0.321818
\(843\) 8474.91 0.346253
\(844\) −5807.09 −0.236835
\(845\) 24181.3 0.984451
\(846\) −3145.36 −0.127825
\(847\) −13341.9 −0.541244
\(848\) −29355.7 −1.18877
\(849\) 34406.2 1.39083
\(850\) 0 0
\(851\) 12111.1 0.487853
\(852\) 4795.75 0.192840
\(853\) −37413.0 −1.50175 −0.750877 0.660442i \(-0.770369\pi\)
−0.750877 + 0.660442i \(0.770369\pi\)
\(854\) 39989.7 1.60237
\(855\) −1139.25 −0.0455691
\(856\) −68875.3 −2.75013
\(857\) 29090.0 1.15951 0.579753 0.814793i \(-0.303149\pi\)
0.579753 + 0.814793i \(0.303149\pi\)
\(858\) −14346.2 −0.570828
\(859\) −43523.6 −1.72876 −0.864381 0.502837i \(-0.832290\pi\)
−0.864381 + 0.502837i \(0.832290\pi\)
\(860\) −15135.0 −0.600115
\(861\) −4040.69 −0.159938
\(862\) 12334.5 0.487373
\(863\) 15659.4 0.617672 0.308836 0.951115i \(-0.400061\pi\)
0.308836 + 0.951115i \(0.400061\pi\)
\(864\) −3974.75 −0.156509
\(865\) −21706.6 −0.853234
\(866\) −8913.05 −0.349743
\(867\) 0 0
\(868\) 35503.9 1.38834
\(869\) 4241.00 0.165553
\(870\) 26473.0 1.03163
\(871\) 10989.6 0.427518
\(872\) −51506.2 −2.00025
\(873\) 1185.76 0.0459702
\(874\) −19884.5 −0.769570
\(875\) −24621.9 −0.951283
\(876\) −29153.8 −1.12445
\(877\) −28891.8 −1.11244 −0.556219 0.831036i \(-0.687748\pi\)
−0.556219 + 0.831036i \(0.687748\pi\)
\(878\) 50554.2 1.94319
\(879\) −32606.4 −1.25118
\(880\) −20029.3 −0.767258
\(881\) 22094.9 0.844943 0.422471 0.906376i \(-0.361163\pi\)
0.422471 + 0.906376i \(0.361163\pi\)
\(882\) −954.045 −0.0364222
\(883\) 40158.3 1.53050 0.765252 0.643731i \(-0.222615\pi\)
0.765252 + 0.643731i \(0.222615\pi\)
\(884\) 0 0
\(885\) 26334.8 1.00026
\(886\) 19369.6 0.734462
\(887\) 27801.7 1.05241 0.526207 0.850357i \(-0.323614\pi\)
0.526207 + 0.850357i \(0.323614\pi\)
\(888\) 25495.9 0.963497
\(889\) 1565.97 0.0590788
\(890\) −80100.7 −3.01683
\(891\) −13460.3 −0.506103
\(892\) 40244.9 1.51065
\(893\) 22101.9 0.828232
\(894\) 54409.7 2.03550
\(895\) 28820.4 1.07638
\(896\) 36276.0 1.35256
\(897\) −13532.0 −0.503700
\(898\) −64096.6 −2.38188
\(899\) 9378.09 0.347916
\(900\) −4602.13 −0.170449
\(901\) 0 0
\(902\) 5387.70 0.198881
\(903\) 3703.49 0.136483
\(904\) 22760.4 0.837388
\(905\) 27769.3 1.01998
\(906\) 18528.5 0.679434
\(907\) 18413.3 0.674095 0.337048 0.941488i \(-0.390572\pi\)
0.337048 + 0.941488i \(0.390572\pi\)
\(908\) 81378.8 2.97428
\(909\) 2473.32 0.0902473
\(910\) 37842.4 1.37853
\(911\) 32271.8 1.17367 0.586834 0.809708i \(-0.300374\pi\)
0.586834 + 0.809708i \(0.300374\pi\)
\(912\) −12847.5 −0.466473
\(913\) −11573.6 −0.419528
\(914\) 78962.7 2.85761
\(915\) 55165.3 1.99313
\(916\) 50014.6 1.80407
\(917\) 29893.3 1.07652
\(918\) 0 0
\(919\) 19185.3 0.688643 0.344322 0.938852i \(-0.388109\pi\)
0.344322 + 0.938852i \(0.388109\pi\)
\(920\) −61556.2 −2.20592
\(921\) 25985.6 0.929700
\(922\) −53744.2 −1.91971
\(923\) 1810.80 0.0645754
\(924\) 21631.8 0.770166
\(925\) −29773.9 −1.05834
\(926\) −68966.3 −2.44749
\(927\) 2443.51 0.0865752
\(928\) 1603.30 0.0567144
\(929\) −20823.7 −0.735419 −0.367709 0.929941i \(-0.619858\pi\)
−0.367709 + 0.929941i \(0.619858\pi\)
\(930\) 74036.4 2.61048
\(931\) 6703.89 0.235995
\(932\) −13338.9 −0.468809
\(933\) −17337.7 −0.608371
\(934\) −47106.5 −1.65029
\(935\) 0 0
\(936\) 1488.01 0.0519627
\(937\) 21072.0 0.734677 0.367338 0.930087i \(-0.380269\pi\)
0.367338 + 0.930087i \(0.380269\pi\)
\(938\) −25048.9 −0.871934
\(939\) −21698.4 −0.754100
\(940\) 140105. 4.86139
\(941\) 11156.4 0.386491 0.193245 0.981150i \(-0.438099\pi\)
0.193245 + 0.981150i \(0.438099\pi\)
\(942\) −14272.4 −0.493651
\(943\) 5081.91 0.175493
\(944\) −15512.7 −0.534847
\(945\) 37365.2 1.28623
\(946\) −4938.09 −0.169716
\(947\) 3045.57 0.104506 0.0522532 0.998634i \(-0.483360\pi\)
0.0522532 + 0.998634i \(0.483360\pi\)
\(948\) 17244.3 0.590789
\(949\) −11008.0 −0.376537
\(950\) 48884.1 1.66949
\(951\) 1977.33 0.0674232
\(952\) 0 0
\(953\) 6037.53 0.205220 0.102610 0.994722i \(-0.467281\pi\)
0.102610 + 0.994722i \(0.467281\pi\)
\(954\) −3453.41 −0.117199
\(955\) −55853.2 −1.89253
\(956\) 29593.4 1.00117
\(957\) 5713.87 0.193002
\(958\) 64353.9 2.17033
\(959\) 43292.5 1.45775
\(960\) 54326.4 1.82644
\(961\) −3563.58 −0.119619
\(962\) 19712.8 0.660673
\(963\) −2486.77 −0.0832140
\(964\) −28917.1 −0.966138
\(965\) −72277.6 −2.41109
\(966\) 30843.8 1.02731
\(967\) −11151.0 −0.370829 −0.185414 0.982660i \(-0.559363\pi\)
−0.185414 + 0.982660i \(0.559363\pi\)
\(968\) 35324.6 1.17291
\(969\) 0 0
\(970\) −79841.6 −2.64284
\(971\) 29051.5 0.960152 0.480076 0.877227i \(-0.340609\pi\)
0.480076 + 0.877227i \(0.340609\pi\)
\(972\) 5874.85 0.193864
\(973\) −6587.43 −0.217043
\(974\) −93831.4 −3.08681
\(975\) 33267.0 1.09271
\(976\) −32495.6 −1.06574
\(977\) 2430.15 0.0795778 0.0397889 0.999208i \(-0.487331\pi\)
0.0397889 + 0.999208i \(0.487331\pi\)
\(978\) 43780.3 1.43143
\(979\) −17288.7 −0.564402
\(980\) 42496.2 1.38520
\(981\) −1859.65 −0.0605241
\(982\) 351.356 0.0114177
\(983\) −2167.32 −0.0703222 −0.0351611 0.999382i \(-0.511194\pi\)
−0.0351611 + 0.999382i \(0.511194\pi\)
\(984\) 10698.3 0.346594
\(985\) −17573.5 −0.568465
\(986\) 0 0
\(987\) −34283.2 −1.10562
\(988\) −21410.7 −0.689437
\(989\) −4657.83 −0.149758
\(990\) −2356.24 −0.0756427
\(991\) 19533.1 0.626124 0.313062 0.949733i \(-0.398645\pi\)
0.313062 + 0.949733i \(0.398645\pi\)
\(992\) 4483.91 0.143512
\(993\) 19375.1 0.619185
\(994\) −4127.39 −0.131703
\(995\) 32780.0 1.04442
\(996\) −47059.2 −1.49712
\(997\) −8892.06 −0.282462 −0.141231 0.989977i \(-0.545106\pi\)
−0.141231 + 0.989977i \(0.545106\pi\)
\(998\) −71979.6 −2.28304
\(999\) 19464.2 0.616437
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.1.2 12
17.4 even 4 289.4.b.e.288.11 12
17.11 odd 16 17.4.d.a.2.1 12
17.13 even 4 289.4.b.e.288.12 12
17.14 odd 16 17.4.d.a.9.1 yes 12
17.16 even 2 inner 289.4.a.g.1.1 12
51.11 even 16 153.4.l.a.19.3 12
51.14 even 16 153.4.l.a.145.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.d.a.2.1 12 17.11 odd 16
17.4.d.a.9.1 yes 12 17.14 odd 16
153.4.l.a.19.3 12 51.11 even 16
153.4.l.a.145.3 12 51.14 even 16
289.4.a.g.1.1 12 17.16 even 2 inner
289.4.a.g.1.2 12 1.1 even 1 trivial
289.4.b.e.288.11 12 17.4 even 4
289.4.b.e.288.12 12 17.13 even 4