Properties

Label 575.4.a.j.1.3
Level $575$
Weight $4$
Character 575.1
Self dual yes
Analytic conductor $33.926$
Analytic rank $1$
Dimension $5$
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] = [575,4,Mod(1,575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(575, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("575.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 575.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: \(33.9260982533\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 27x^{3} + 7x^{2} + 168x + 92 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.595043\) of defining polynomial
Character \(\chi\) \(=\) 575.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.404957 q^{2} +7.11323 q^{3} -7.83601 q^{4} -2.88055 q^{6} -13.7888 q^{7} +6.41290 q^{8} +23.5981 q^{9} +O(q^{10})\) \(q-0.404957 q^{2} +7.11323 q^{3} -7.83601 q^{4} -2.88055 q^{6} -13.7888 q^{7} +6.41290 q^{8} +23.5981 q^{9} +24.2317 q^{11} -55.7394 q^{12} -3.05016 q^{13} +5.58389 q^{14} +60.0911 q^{16} -63.1126 q^{17} -9.55621 q^{18} -2.07770 q^{19} -98.0832 q^{21} -9.81282 q^{22} +23.0000 q^{23} +45.6165 q^{24} +1.23518 q^{26} -24.1987 q^{27} +108.049 q^{28} -8.16397 q^{29} -156.989 q^{31} -75.6376 q^{32} +172.366 q^{33} +25.5579 q^{34} -184.915 q^{36} -302.801 q^{37} +0.841380 q^{38} -21.6965 q^{39} -42.7514 q^{41} +39.7195 q^{42} -215.265 q^{43} -189.880 q^{44} -9.31401 q^{46} -247.096 q^{47} +427.442 q^{48} -152.868 q^{49} -448.935 q^{51} +23.9010 q^{52} -600.400 q^{53} +9.79943 q^{54} -88.4265 q^{56} -14.7792 q^{57} +3.30606 q^{58} +92.2014 q^{59} +532.635 q^{61} +63.5740 q^{62} -325.390 q^{63} -450.099 q^{64} -69.8009 q^{66} -30.3010 q^{67} +494.551 q^{68} +163.604 q^{69} -736.349 q^{71} +151.332 q^{72} -349.936 q^{73} +122.622 q^{74} +16.2809 q^{76} -334.127 q^{77} +8.78614 q^{78} +301.545 q^{79} -809.279 q^{81} +17.3125 q^{82} -139.488 q^{83} +768.581 q^{84} +87.1732 q^{86} -58.0722 q^{87} +155.396 q^{88} +859.551 q^{89} +42.0581 q^{91} -180.228 q^{92} -1116.70 q^{93} +100.063 q^{94} -538.028 q^{96} +927.475 q^{97} +61.9051 q^{98} +571.823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 6 q^{2} - 4 q^{3} + 22 q^{4} + 19 q^{6} + 3 q^{7} - 138 q^{8} + 77 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 6 q^{2} - 4 q^{3} + 22 q^{4} + 19 q^{6} + 3 q^{7} - 138 q^{8} + 77 q^{9} + 23 q^{11} - 47 q^{12} - 132 q^{13} + 93 q^{14} + 282 q^{16} - 23 q^{17} + 15 q^{18} - 161 q^{19} - 60 q^{21} - 193 q^{22} + 115 q^{23} + 105 q^{24} - 257 q^{26} - 577 q^{27} - 17 q^{28} + 401 q^{29} + 32 q^{31} - 670 q^{32} - 189 q^{33} - 663 q^{34} - 659 q^{36} + 38 q^{37} + 875 q^{38} + 335 q^{39} - 12 q^{41} + 798 q^{42} + 566 q^{43} + 47 q^{44} - 138 q^{46} - 919 q^{47} + 773 q^{48} - 738 q^{49} - 993 q^{51} + 305 q^{52} - 1156 q^{53} - 8 q^{54} + 343 q^{56} - 114 q^{57} + 1042 q^{58} + 1324 q^{59} - 1673 q^{61} - 565 q^{62} - 270 q^{63} + 2466 q^{64} - 2781 q^{66} - 558 q^{67} + 2267 q^{68} - 92 q^{69} - 108 q^{71} + 789 q^{72} - 1173 q^{73} + 1458 q^{74} - 3477 q^{76} - 2608 q^{77} - 704 q^{78} + 656 q^{79} - 319 q^{81} - 3505 q^{82} + 82 q^{83} - 718 q^{84} + 112 q^{86} - 2389 q^{87} - 2397 q^{88} + 570 q^{89} - 1589 q^{91} + 506 q^{92} - 911 q^{93} - 948 q^{94} - 5991 q^{96} - 633 q^{97} + 2555 q^{98} + 2021 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.404957 −0.143174 −0.0715870 0.997434i \(-0.522806\pi\)
−0.0715870 + 0.997434i \(0.522806\pi\)
\(3\) 7.11323 1.36894 0.684471 0.729040i \(-0.260033\pi\)
0.684471 + 0.729040i \(0.260033\pi\)
\(4\) −7.83601 −0.979501
\(5\) 0 0
\(6\) −2.88055 −0.195997
\(7\) −13.7888 −0.744527 −0.372263 0.928127i \(-0.621418\pi\)
−0.372263 + 0.928127i \(0.621418\pi\)
\(8\) 6.41290 0.283413
\(9\) 23.5981 0.874003
\(10\) 0 0
\(11\) 24.2317 0.664195 0.332098 0.943245i \(-0.392244\pi\)
0.332098 + 0.943245i \(0.392244\pi\)
\(12\) −55.7394 −1.34088
\(13\) −3.05016 −0.0650739 −0.0325370 0.999471i \(-0.510359\pi\)
−0.0325370 + 0.999471i \(0.510359\pi\)
\(14\) 5.58389 0.106597
\(15\) 0 0
\(16\) 60.0911 0.938924
\(17\) −63.1126 −0.900415 −0.450208 0.892924i \(-0.648650\pi\)
−0.450208 + 0.892924i \(0.648650\pi\)
\(18\) −9.55621 −0.125134
\(19\) −2.07770 −0.0250872 −0.0125436 0.999921i \(-0.503993\pi\)
−0.0125436 + 0.999921i \(0.503993\pi\)
\(20\) 0 0
\(21\) −98.0832 −1.01921
\(22\) −9.81282 −0.0950955
\(23\) 23.0000 0.208514
\(24\) 45.6165 0.387976
\(25\) 0 0
\(26\) 1.23518 0.00931689
\(27\) −24.1987 −0.172483
\(28\) 108.049 0.729265
\(29\) −8.16397 −0.0522762 −0.0261381 0.999658i \(-0.508321\pi\)
−0.0261381 + 0.999658i \(0.508321\pi\)
\(30\) 0 0
\(31\) −156.989 −0.909553 −0.454776 0.890606i \(-0.650281\pi\)
−0.454776 + 0.890606i \(0.650281\pi\)
\(32\) −75.6376 −0.417842
\(33\) 172.366 0.909245
\(34\) 25.5579 0.128916
\(35\) 0 0
\(36\) −184.915 −0.856087
\(37\) −302.801 −1.34541 −0.672706 0.739910i \(-0.734868\pi\)
−0.672706 + 0.739910i \(0.734868\pi\)
\(38\) 0.841380 0.00359184
\(39\) −21.6965 −0.0890824
\(40\) 0 0
\(41\) −42.7514 −0.162845 −0.0814225 0.996680i \(-0.525946\pi\)
−0.0814225 + 0.996680i \(0.525946\pi\)
\(42\) 39.7195 0.145925
\(43\) −215.265 −0.763434 −0.381717 0.924279i \(-0.624667\pi\)
−0.381717 + 0.924279i \(0.624667\pi\)
\(44\) −189.880 −0.650580
\(45\) 0 0
\(46\) −9.31401 −0.0298538
\(47\) −247.096 −0.766866 −0.383433 0.923569i \(-0.625258\pi\)
−0.383433 + 0.923569i \(0.625258\pi\)
\(48\) 427.442 1.28533
\(49\) −152.868 −0.445680
\(50\) 0 0
\(51\) −448.935 −1.23262
\(52\) 23.9010 0.0637400
\(53\) −600.400 −1.55606 −0.778031 0.628225i \(-0.783782\pi\)
−0.778031 + 0.628225i \(0.783782\pi\)
\(54\) 9.79943 0.0246951
\(55\) 0 0
\(56\) −88.4265 −0.211009
\(57\) −14.7792 −0.0343430
\(58\) 3.30606 0.00748460
\(59\) 92.2014 0.203451 0.101725 0.994813i \(-0.467564\pi\)
0.101725 + 0.994813i \(0.467564\pi\)
\(60\) 0 0
\(61\) 532.635 1.11798 0.558991 0.829174i \(-0.311189\pi\)
0.558991 + 0.829174i \(0.311189\pi\)
\(62\) 63.5740 0.130224
\(63\) −325.390 −0.650719
\(64\) −450.099 −0.879100
\(65\) 0 0
\(66\) −69.8009 −0.130180
\(67\) −30.3010 −0.0552515 −0.0276258 0.999618i \(-0.508795\pi\)
−0.0276258 + 0.999618i \(0.508795\pi\)
\(68\) 494.551 0.881958
\(69\) 163.604 0.285444
\(70\) 0 0
\(71\) −736.349 −1.23083 −0.615413 0.788205i \(-0.711011\pi\)
−0.615413 + 0.788205i \(0.711011\pi\)
\(72\) 151.332 0.247704
\(73\) −349.936 −0.561053 −0.280527 0.959846i \(-0.590509\pi\)
−0.280527 + 0.959846i \(0.590509\pi\)
\(74\) 122.622 0.192628
\(75\) 0 0
\(76\) 16.2809 0.0245730
\(77\) −334.127 −0.494511
\(78\) 8.78614 0.0127543
\(79\) 301.545 0.429449 0.214725 0.976675i \(-0.431115\pi\)
0.214725 + 0.976675i \(0.431115\pi\)
\(80\) 0 0
\(81\) −809.279 −1.11012
\(82\) 17.3125 0.0233152
\(83\) −139.488 −0.184468 −0.0922340 0.995737i \(-0.529401\pi\)
−0.0922340 + 0.995737i \(0.529401\pi\)
\(84\) 768.581 0.998322
\(85\) 0 0
\(86\) 87.1732 0.109304
\(87\) −58.0722 −0.0715631
\(88\) 155.396 0.188242
\(89\) 859.551 1.02373 0.511866 0.859065i \(-0.328954\pi\)
0.511866 + 0.859065i \(0.328954\pi\)
\(90\) 0 0
\(91\) 42.0581 0.0484493
\(92\) −180.228 −0.204240
\(93\) −1116.70 −1.24513
\(94\) 100.063 0.109795
\(95\) 0 0
\(96\) −538.028 −0.572002
\(97\) 927.475 0.970833 0.485417 0.874283i \(-0.338668\pi\)
0.485417 + 0.874283i \(0.338668\pi\)
\(98\) 61.9051 0.0638097
\(99\) 571.823 0.580508
\(100\) 0 0
\(101\) 1713.34 1.68796 0.843979 0.536376i \(-0.180207\pi\)
0.843979 + 0.536376i \(0.180207\pi\)
\(102\) 181.799 0.176479
\(103\) 930.516 0.890160 0.445080 0.895491i \(-0.353175\pi\)
0.445080 + 0.895491i \(0.353175\pi\)
\(104\) −19.5604 −0.0184428
\(105\) 0 0
\(106\) 243.136 0.222788
\(107\) −1514.91 −1.36871 −0.684355 0.729149i \(-0.739916\pi\)
−0.684355 + 0.729149i \(0.739916\pi\)
\(108\) 189.621 0.168947
\(109\) 1748.76 1.53670 0.768352 0.640027i \(-0.221077\pi\)
0.768352 + 0.640027i \(0.221077\pi\)
\(110\) 0 0
\(111\) −2153.90 −1.84179
\(112\) −828.586 −0.699054
\(113\) −2026.23 −1.68683 −0.843416 0.537261i \(-0.819459\pi\)
−0.843416 + 0.537261i \(0.819459\pi\)
\(114\) 5.98493 0.00491702
\(115\) 0 0
\(116\) 63.9729 0.0512046
\(117\) −71.9778 −0.0568748
\(118\) −37.3376 −0.0291289
\(119\) 870.249 0.670383
\(120\) 0 0
\(121\) −743.822 −0.558845
\(122\) −215.694 −0.160066
\(123\) −304.100 −0.222925
\(124\) 1230.17 0.890908
\(125\) 0 0
\(126\) 131.769 0.0931660
\(127\) 2126.49 1.48579 0.742897 0.669406i \(-0.233451\pi\)
0.742897 + 0.669406i \(0.233451\pi\)
\(128\) 787.371 0.543707
\(129\) −1531.23 −1.04510
\(130\) 0 0
\(131\) −1494.23 −0.996576 −0.498288 0.867012i \(-0.666038\pi\)
−0.498288 + 0.867012i \(0.666038\pi\)
\(132\) −1350.66 −0.890606
\(133\) 28.6491 0.0186781
\(134\) 12.2706 0.00791058
\(135\) 0 0
\(136\) −404.735 −0.255189
\(137\) −2265.31 −1.41269 −0.706346 0.707867i \(-0.749658\pi\)
−0.706346 + 0.707867i \(0.749658\pi\)
\(138\) −66.2527 −0.0408682
\(139\) −2918.66 −1.78099 −0.890496 0.454991i \(-0.849642\pi\)
−0.890496 + 0.454991i \(0.849642\pi\)
\(140\) 0 0
\(141\) −1757.65 −1.04980
\(142\) 298.190 0.176222
\(143\) −73.9106 −0.0432218
\(144\) 1418.03 0.820622
\(145\) 0 0
\(146\) 141.709 0.0803282
\(147\) −1087.39 −0.610110
\(148\) 2372.75 1.31783
\(149\) −549.400 −0.302071 −0.151036 0.988528i \(-0.548261\pi\)
−0.151036 + 0.988528i \(0.548261\pi\)
\(150\) 0 0
\(151\) 335.721 0.180931 0.0904654 0.995900i \(-0.471165\pi\)
0.0904654 + 0.995900i \(0.471165\pi\)
\(152\) −13.3241 −0.00711005
\(153\) −1489.34 −0.786965
\(154\) 135.307 0.0708011
\(155\) 0 0
\(156\) 170.014 0.0872563
\(157\) 1593.69 0.810130 0.405065 0.914288i \(-0.367249\pi\)
0.405065 + 0.914288i \(0.367249\pi\)
\(158\) −122.113 −0.0614860
\(159\) −4270.79 −2.13016
\(160\) 0 0
\(161\) −317.143 −0.155245
\(162\) 327.723 0.158941
\(163\) 2767.63 1.32992 0.664962 0.746877i \(-0.268448\pi\)
0.664962 + 0.746877i \(0.268448\pi\)
\(164\) 335.000 0.159507
\(165\) 0 0
\(166\) 56.4868 0.0264110
\(167\) −282.867 −0.131071 −0.0655357 0.997850i \(-0.520876\pi\)
−0.0655357 + 0.997850i \(0.520876\pi\)
\(168\) −628.998 −0.288859
\(169\) −2187.70 −0.995765
\(170\) 0 0
\(171\) −49.0297 −0.0219263
\(172\) 1686.82 0.747784
\(173\) 2331.63 1.02468 0.512342 0.858782i \(-0.328778\pi\)
0.512342 + 0.858782i \(0.328778\pi\)
\(174\) 23.5168 0.0102460
\(175\) 0 0
\(176\) 1456.11 0.623629
\(177\) 655.850 0.278512
\(178\) −348.081 −0.146572
\(179\) 109.140 0.0455726 0.0227863 0.999740i \(-0.492746\pi\)
0.0227863 + 0.999740i \(0.492746\pi\)
\(180\) 0 0
\(181\) 1476.85 0.606483 0.303242 0.952914i \(-0.401931\pi\)
0.303242 + 0.952914i \(0.401931\pi\)
\(182\) −17.0317 −0.00693667
\(183\) 3788.76 1.53045
\(184\) 147.497 0.0590957
\(185\) 0 0
\(186\) 452.217 0.178270
\(187\) −1529.33 −0.598051
\(188\) 1936.25 0.751147
\(189\) 333.672 0.128418
\(190\) 0 0
\(191\) 2032.16 0.769853 0.384926 0.922947i \(-0.374227\pi\)
0.384926 + 0.922947i \(0.374227\pi\)
\(192\) −3201.66 −1.20344
\(193\) −3883.64 −1.44845 −0.724224 0.689565i \(-0.757802\pi\)
−0.724224 + 0.689565i \(0.757802\pi\)
\(194\) −375.588 −0.138998
\(195\) 0 0
\(196\) 1197.88 0.436544
\(197\) −3580.64 −1.29498 −0.647488 0.762076i \(-0.724180\pi\)
−0.647488 + 0.762076i \(0.724180\pi\)
\(198\) −231.564 −0.0831137
\(199\) −2831.17 −1.00853 −0.504263 0.863550i \(-0.668236\pi\)
−0.504263 + 0.863550i \(0.668236\pi\)
\(200\) 0 0
\(201\) −215.538 −0.0756362
\(202\) −693.830 −0.241672
\(203\) 112.572 0.0389211
\(204\) 3517.86 1.20735
\(205\) 0 0
\(206\) −376.819 −0.127448
\(207\) 542.756 0.182242
\(208\) −183.287 −0.0610995
\(209\) −50.3463 −0.0166628
\(210\) 0 0
\(211\) 2903.80 0.947421 0.473711 0.880681i \(-0.342914\pi\)
0.473711 + 0.880681i \(0.342914\pi\)
\(212\) 4704.74 1.52417
\(213\) −5237.82 −1.68493
\(214\) 613.474 0.195964
\(215\) 0 0
\(216\) −155.184 −0.0488839
\(217\) 2164.70 0.677186
\(218\) −708.173 −0.220016
\(219\) −2489.17 −0.768049
\(220\) 0 0
\(221\) 192.503 0.0585935
\(222\) 872.236 0.263697
\(223\) −454.760 −0.136560 −0.0682802 0.997666i \(-0.521751\pi\)
−0.0682802 + 0.997666i \(0.521751\pi\)
\(224\) 1042.95 0.311095
\(225\) 0 0
\(226\) 820.538 0.241510
\(227\) 2103.24 0.614966 0.307483 0.951554i \(-0.400513\pi\)
0.307483 + 0.951554i \(0.400513\pi\)
\(228\) 115.810 0.0336390
\(229\) −4647.97 −1.34125 −0.670625 0.741796i \(-0.733974\pi\)
−0.670625 + 0.741796i \(0.733974\pi\)
\(230\) 0 0
\(231\) −2376.73 −0.676957
\(232\) −52.3548 −0.0148158
\(233\) −131.118 −0.0368661 −0.0184331 0.999830i \(-0.505868\pi\)
−0.0184331 + 0.999830i \(0.505868\pi\)
\(234\) 29.1479 0.00814299
\(235\) 0 0
\(236\) −722.491 −0.199280
\(237\) 2144.96 0.587891
\(238\) −352.414 −0.0959814
\(239\) 3467.77 0.938541 0.469271 0.883054i \(-0.344517\pi\)
0.469271 + 0.883054i \(0.344517\pi\)
\(240\) 0 0
\(241\) 5818.91 1.55531 0.777653 0.628694i \(-0.216410\pi\)
0.777653 + 0.628694i \(0.216410\pi\)
\(242\) 301.216 0.0800120
\(243\) −5103.22 −1.34721
\(244\) −4173.73 −1.09506
\(245\) 0 0
\(246\) 123.148 0.0319171
\(247\) 6.33731 0.00163252
\(248\) −1006.76 −0.257779
\(249\) −992.213 −0.252526
\(250\) 0 0
\(251\) 4633.30 1.16515 0.582573 0.812779i \(-0.302046\pi\)
0.582573 + 0.812779i \(0.302046\pi\)
\(252\) 2549.76 0.637380
\(253\) 557.330 0.138494
\(254\) −861.139 −0.212727
\(255\) 0 0
\(256\) 3281.94 0.801255
\(257\) 5262.78 1.27737 0.638683 0.769470i \(-0.279480\pi\)
0.638683 + 0.769470i \(0.279480\pi\)
\(258\) 620.083 0.149631
\(259\) 4175.28 1.00170
\(260\) 0 0
\(261\) −192.654 −0.0456896
\(262\) 605.099 0.142684
\(263\) −1890.26 −0.443189 −0.221594 0.975139i \(-0.571126\pi\)
−0.221594 + 0.975139i \(0.571126\pi\)
\(264\) 1105.37 0.257692
\(265\) 0 0
\(266\) −11.6016 −0.00267422
\(267\) 6114.18 1.40143
\(268\) 237.439 0.0541189
\(269\) 7472.17 1.69363 0.846815 0.531888i \(-0.178517\pi\)
0.846815 + 0.531888i \(0.178517\pi\)
\(270\) 0 0
\(271\) 1634.38 0.366352 0.183176 0.983080i \(-0.441362\pi\)
0.183176 + 0.983080i \(0.441362\pi\)
\(272\) −3792.51 −0.845421
\(273\) 299.169 0.0663243
\(274\) 917.355 0.202261
\(275\) 0 0
\(276\) −1282.01 −0.279593
\(277\) 590.262 0.128034 0.0640170 0.997949i \(-0.479609\pi\)
0.0640170 + 0.997949i \(0.479609\pi\)
\(278\) 1181.93 0.254992
\(279\) −3704.65 −0.794952
\(280\) 0 0
\(281\) 2501.14 0.530980 0.265490 0.964114i \(-0.414466\pi\)
0.265490 + 0.964114i \(0.414466\pi\)
\(282\) 711.775 0.150303
\(283\) 803.901 0.168859 0.0844293 0.996429i \(-0.473093\pi\)
0.0844293 + 0.996429i \(0.473093\pi\)
\(284\) 5770.04 1.20559
\(285\) 0 0
\(286\) 29.9306 0.00618823
\(287\) 589.491 0.121242
\(288\) −1784.90 −0.365195
\(289\) −929.797 −0.189252
\(290\) 0 0
\(291\) 6597.35 1.32901
\(292\) 2742.10 0.549552
\(293\) 6332.54 1.26263 0.631316 0.775526i \(-0.282515\pi\)
0.631316 + 0.775526i \(0.282515\pi\)
\(294\) 440.345 0.0873518
\(295\) 0 0
\(296\) −1941.84 −0.381307
\(297\) −586.376 −0.114562
\(298\) 222.483 0.0432487
\(299\) −70.1536 −0.0135688
\(300\) 0 0
\(301\) 2968.26 0.568397
\(302\) −135.952 −0.0259046
\(303\) 12187.4 2.31072
\(304\) −124.851 −0.0235550
\(305\) 0 0
\(306\) 603.117 0.112673
\(307\) −7317.73 −1.36041 −0.680203 0.733024i \(-0.738108\pi\)
−0.680203 + 0.733024i \(0.738108\pi\)
\(308\) 2618.23 0.484374
\(309\) 6618.97 1.21858
\(310\) 0 0
\(311\) 2838.86 0.517611 0.258805 0.965930i \(-0.416671\pi\)
0.258805 + 0.965930i \(0.416671\pi\)
\(312\) −139.137 −0.0252471
\(313\) −160.132 −0.0289175 −0.0144588 0.999895i \(-0.504603\pi\)
−0.0144588 + 0.999895i \(0.504603\pi\)
\(314\) −645.376 −0.115989
\(315\) 0 0
\(316\) −2362.91 −0.420646
\(317\) 3330.78 0.590142 0.295071 0.955475i \(-0.404657\pi\)
0.295071 + 0.955475i \(0.404657\pi\)
\(318\) 1729.49 0.304983
\(319\) −197.827 −0.0347216
\(320\) 0 0
\(321\) −10775.9 −1.87369
\(322\) 128.429 0.0222270
\(323\) 131.129 0.0225889
\(324\) 6341.52 1.08737
\(325\) 0 0
\(326\) −1120.77 −0.190410
\(327\) 12439.3 2.10366
\(328\) −274.161 −0.0461524
\(329\) 3407.17 0.570953
\(330\) 0 0
\(331\) 7337.39 1.21843 0.609214 0.793006i \(-0.291485\pi\)
0.609214 + 0.793006i \(0.291485\pi\)
\(332\) 1093.03 0.180687
\(333\) −7145.53 −1.17589
\(334\) 114.549 0.0187660
\(335\) 0 0
\(336\) −5893.93 −0.956965
\(337\) 7160.54 1.15745 0.578723 0.815524i \(-0.303551\pi\)
0.578723 + 0.815524i \(0.303551\pi\)
\(338\) 885.923 0.142568
\(339\) −14413.1 −2.30918
\(340\) 0 0
\(341\) −3804.13 −0.604121
\(342\) 19.8549 0.00313928
\(343\) 6837.44 1.07635
\(344\) −1380.48 −0.216367
\(345\) 0 0
\(346\) −944.209 −0.146708
\(347\) −6740.51 −1.04279 −0.521397 0.853314i \(-0.674589\pi\)
−0.521397 + 0.853314i \(0.674589\pi\)
\(348\) 455.054 0.0700962
\(349\) −10173.9 −1.56045 −0.780224 0.625501i \(-0.784895\pi\)
−0.780224 + 0.625501i \(0.784895\pi\)
\(350\) 0 0
\(351\) 73.8097 0.0112241
\(352\) −1832.83 −0.277529
\(353\) 2552.87 0.384917 0.192458 0.981305i \(-0.438354\pi\)
0.192458 + 0.981305i \(0.438354\pi\)
\(354\) −265.591 −0.0398757
\(355\) 0 0
\(356\) −6735.45 −1.00275
\(357\) 6190.28 0.917716
\(358\) −44.1970 −0.00652481
\(359\) −6677.47 −0.981681 −0.490841 0.871249i \(-0.663310\pi\)
−0.490841 + 0.871249i \(0.663310\pi\)
\(360\) 0 0
\(361\) −6854.68 −0.999371
\(362\) −598.062 −0.0868326
\(363\) −5290.98 −0.765026
\(364\) −329.567 −0.0474561
\(365\) 0 0
\(366\) −1534.28 −0.219121
\(367\) −11722.8 −1.66738 −0.833688 0.552236i \(-0.813775\pi\)
−0.833688 + 0.552236i \(0.813775\pi\)
\(368\) 1382.10 0.195779
\(369\) −1008.85 −0.142327
\(370\) 0 0
\(371\) 8278.82 1.15853
\(372\) 8750.49 1.21960
\(373\) −8070.71 −1.12034 −0.560168 0.828379i \(-0.689264\pi\)
−0.560168 + 0.828379i \(0.689264\pi\)
\(374\) 619.313 0.0856254
\(375\) 0 0
\(376\) −1584.61 −0.217340
\(377\) 24.9014 0.00340182
\(378\) −135.123 −0.0183861
\(379\) −6693.10 −0.907128 −0.453564 0.891224i \(-0.649848\pi\)
−0.453564 + 0.891224i \(0.649848\pi\)
\(380\) 0 0
\(381\) 15126.2 2.03397
\(382\) −822.937 −0.110223
\(383\) 2502.49 0.333867 0.166934 0.985968i \(-0.446613\pi\)
0.166934 + 0.985968i \(0.446613\pi\)
\(384\) 5600.76 0.744303
\(385\) 0 0
\(386\) 1572.71 0.207380
\(387\) −5079.85 −0.667243
\(388\) −7267.71 −0.950933
\(389\) 5487.69 0.715262 0.357631 0.933863i \(-0.383585\pi\)
0.357631 + 0.933863i \(0.383585\pi\)
\(390\) 0 0
\(391\) −1451.59 −0.187750
\(392\) −980.329 −0.126311
\(393\) −10628.8 −1.36426
\(394\) 1450.01 0.185407
\(395\) 0 0
\(396\) −4480.81 −0.568609
\(397\) −7760.91 −0.981130 −0.490565 0.871405i \(-0.663210\pi\)
−0.490565 + 0.871405i \(0.663210\pi\)
\(398\) 1146.50 0.144395
\(399\) 203.787 0.0255693
\(400\) 0 0
\(401\) 14485.8 1.80395 0.901977 0.431785i \(-0.142116\pi\)
0.901977 + 0.431785i \(0.142116\pi\)
\(402\) 87.2836 0.0108291
\(403\) 478.842 0.0591882
\(404\) −13425.8 −1.65336
\(405\) 0 0
\(406\) −45.5867 −0.00557248
\(407\) −7337.41 −0.893616
\(408\) −2878.98 −0.349340
\(409\) 6664.83 0.805758 0.402879 0.915253i \(-0.368010\pi\)
0.402879 + 0.915253i \(0.368010\pi\)
\(410\) 0 0
\(411\) −16113.7 −1.93389
\(412\) −7291.53 −0.871912
\(413\) −1271.35 −0.151475
\(414\) −219.793 −0.0260923
\(415\) 0 0
\(416\) 230.706 0.0271906
\(417\) −20761.1 −2.43807
\(418\) 20.3881 0.00238568
\(419\) −8437.43 −0.983760 −0.491880 0.870663i \(-0.663690\pi\)
−0.491880 + 0.870663i \(0.663690\pi\)
\(420\) 0 0
\(421\) 13893.2 1.60834 0.804171 0.594397i \(-0.202609\pi\)
0.804171 + 0.594397i \(0.202609\pi\)
\(422\) −1175.91 −0.135646
\(423\) −5831.00 −0.670243
\(424\) −3850.31 −0.441008
\(425\) 0 0
\(426\) 2121.09 0.241238
\(427\) −7344.41 −0.832368
\(428\) 11870.9 1.34065
\(429\) −525.743 −0.0591681
\(430\) 0 0
\(431\) −10611.5 −1.18594 −0.592969 0.805225i \(-0.702044\pi\)
−0.592969 + 0.805225i \(0.702044\pi\)
\(432\) −1454.13 −0.161948
\(433\) 7569.77 0.840139 0.420069 0.907492i \(-0.362006\pi\)
0.420069 + 0.907492i \(0.362006\pi\)
\(434\) −876.611 −0.0969555
\(435\) 0 0
\(436\) −13703.3 −1.50520
\(437\) −47.7871 −0.00523105
\(438\) 1008.01 0.109965
\(439\) −11794.9 −1.28232 −0.641162 0.767406i \(-0.721547\pi\)
−0.641162 + 0.767406i \(0.721547\pi\)
\(440\) 0 0
\(441\) −3607.39 −0.389525
\(442\) −77.9556 −0.00838907
\(443\) −11424.0 −1.22521 −0.612606 0.790388i \(-0.709879\pi\)
−0.612606 + 0.790388i \(0.709879\pi\)
\(444\) 16878.0 1.80404
\(445\) 0 0
\(446\) 184.158 0.0195519
\(447\) −3908.01 −0.413518
\(448\) 6206.34 0.654513
\(449\) 8862.74 0.931533 0.465767 0.884908i \(-0.345779\pi\)
0.465767 + 0.884908i \(0.345779\pi\)
\(450\) 0 0
\(451\) −1035.94 −0.108161
\(452\) 15877.6 1.65225
\(453\) 2388.06 0.247684
\(454\) −851.724 −0.0880471
\(455\) 0 0
\(456\) −94.7774 −0.00973324
\(457\) −5187.22 −0.530958 −0.265479 0.964117i \(-0.585530\pi\)
−0.265479 + 0.964117i \(0.585530\pi\)
\(458\) 1882.23 0.192032
\(459\) 1527.24 0.155306
\(460\) 0 0
\(461\) −16816.7 −1.69898 −0.849491 0.527603i \(-0.823091\pi\)
−0.849491 + 0.527603i \(0.823091\pi\)
\(462\) 962.472 0.0969226
\(463\) −6351.26 −0.637512 −0.318756 0.947837i \(-0.603265\pi\)
−0.318756 + 0.947837i \(0.603265\pi\)
\(464\) −490.582 −0.0490834
\(465\) 0 0
\(466\) 53.0970 0.00527827
\(467\) −1057.02 −0.104739 −0.0523693 0.998628i \(-0.516677\pi\)
−0.0523693 + 0.998628i \(0.516677\pi\)
\(468\) 564.019 0.0557089
\(469\) 417.815 0.0411363
\(470\) 0 0
\(471\) 11336.3 1.10902
\(472\) 591.279 0.0576606
\(473\) −5216.25 −0.507069
\(474\) −868.618 −0.0841707
\(475\) 0 0
\(476\) −6819.28 −0.656641
\(477\) −14168.3 −1.36000
\(478\) −1404.30 −0.134375
\(479\) −10138.2 −0.967073 −0.483537 0.875324i \(-0.660648\pi\)
−0.483537 + 0.875324i \(0.660648\pi\)
\(480\) 0 0
\(481\) 923.591 0.0875512
\(482\) −2356.41 −0.222679
\(483\) −2255.91 −0.212521
\(484\) 5828.60 0.547389
\(485\) 0 0
\(486\) 2066.59 0.192885
\(487\) 8874.74 0.825776 0.412888 0.910782i \(-0.364520\pi\)
0.412888 + 0.910782i \(0.364520\pi\)
\(488\) 3415.74 0.316851
\(489\) 19686.8 1.82059
\(490\) 0 0
\(491\) −21452.2 −1.97174 −0.985869 0.167521i \(-0.946424\pi\)
−0.985869 + 0.167521i \(0.946424\pi\)
\(492\) 2382.93 0.218356
\(493\) 515.249 0.0470703
\(494\) −2.56634 −0.000233735 0
\(495\) 0 0
\(496\) −9433.67 −0.854001
\(497\) 10153.4 0.916382
\(498\) 401.804 0.0361551
\(499\) 9696.91 0.869926 0.434963 0.900448i \(-0.356761\pi\)
0.434963 + 0.900448i \(0.356761\pi\)
\(500\) 0 0
\(501\) −2012.10 −0.179429
\(502\) −1876.29 −0.166818
\(503\) 8892.32 0.788249 0.394124 0.919057i \(-0.371048\pi\)
0.394124 + 0.919057i \(0.371048\pi\)
\(504\) −2086.69 −0.184422
\(505\) 0 0
\(506\) −225.695 −0.0198288
\(507\) −15561.6 −1.36315
\(508\) −16663.2 −1.45534
\(509\) −1084.94 −0.0944778 −0.0472389 0.998884i \(-0.515042\pi\)
−0.0472389 + 0.998884i \(0.515042\pi\)
\(510\) 0 0
\(511\) 4825.20 0.417719
\(512\) −7628.02 −0.658426
\(513\) 50.2776 0.00432712
\(514\) −2131.20 −0.182885
\(515\) 0 0
\(516\) 11998.7 1.02367
\(517\) −5987.58 −0.509349
\(518\) −1690.81 −0.143417
\(519\) 16585.4 1.40273
\(520\) 0 0
\(521\) 4578.35 0.384993 0.192496 0.981298i \(-0.438342\pi\)
0.192496 + 0.981298i \(0.438342\pi\)
\(522\) 78.0166 0.00654156
\(523\) −7298.28 −0.610194 −0.305097 0.952321i \(-0.598689\pi\)
−0.305097 + 0.952321i \(0.598689\pi\)
\(524\) 11708.8 0.976148
\(525\) 0 0
\(526\) 765.476 0.0634531
\(527\) 9908.02 0.818975
\(528\) 10357.7 0.853712
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) 2175.77 0.177817
\(532\) −224.494 −0.0182952
\(533\) 130.398 0.0105970
\(534\) −2475.98 −0.200648
\(535\) 0 0
\(536\) −194.317 −0.0156590
\(537\) 776.338 0.0623863
\(538\) −3025.91 −0.242484
\(539\) −3704.26 −0.296018
\(540\) 0 0
\(541\) −14971.5 −1.18979 −0.594895 0.803803i \(-0.702806\pi\)
−0.594895 + 0.803803i \(0.702806\pi\)
\(542\) −661.854 −0.0524521
\(543\) 10505.2 0.830241
\(544\) 4773.69 0.376232
\(545\) 0 0
\(546\) −121.151 −0.00949591
\(547\) 19510.9 1.52509 0.762547 0.646932i \(-0.223948\pi\)
0.762547 + 0.646932i \(0.223948\pi\)
\(548\) 17751.0 1.38373
\(549\) 12569.2 0.977119
\(550\) 0 0
\(551\) 16.9623 0.00131147
\(552\) 1049.18 0.0808986
\(553\) −4157.96 −0.319737
\(554\) −239.031 −0.0183311
\(555\) 0 0
\(556\) 22870.7 1.74448
\(557\) 13098.1 0.996378 0.498189 0.867068i \(-0.333999\pi\)
0.498189 + 0.867068i \(0.333999\pi\)
\(558\) 1500.22 0.113816
\(559\) 656.592 0.0496796
\(560\) 0 0
\(561\) −10878.5 −0.818698
\(562\) −1012.85 −0.0760226
\(563\) 4086.19 0.305883 0.152942 0.988235i \(-0.451125\pi\)
0.152942 + 0.988235i \(0.451125\pi\)
\(564\) 13773.0 1.02828
\(565\) 0 0
\(566\) −325.546 −0.0241762
\(567\) 11159.0 0.826516
\(568\) −4722.14 −0.348832
\(569\) −5021.20 −0.369946 −0.184973 0.982744i \(-0.559220\pi\)
−0.184973 + 0.982744i \(0.559220\pi\)
\(570\) 0 0
\(571\) −8277.56 −0.606664 −0.303332 0.952885i \(-0.598099\pi\)
−0.303332 + 0.952885i \(0.598099\pi\)
\(572\) 579.164 0.0423358
\(573\) 14455.2 1.05388
\(574\) −238.719 −0.0173588
\(575\) 0 0
\(576\) −10621.5 −0.768336
\(577\) 19548.4 1.41042 0.705210 0.708998i \(-0.250853\pi\)
0.705210 + 0.708998i \(0.250853\pi\)
\(578\) 376.528 0.0270960
\(579\) −27625.2 −1.98284
\(580\) 0 0
\(581\) 1923.38 0.137341
\(582\) −2671.64 −0.190280
\(583\) −14548.7 −1.03353
\(584\) −2244.10 −0.159010
\(585\) 0 0
\(586\) −2564.41 −0.180776
\(587\) 17479.7 1.22907 0.614536 0.788889i \(-0.289343\pi\)
0.614536 + 0.788889i \(0.289343\pi\)
\(588\) 8520.77 0.597603
\(589\) 326.177 0.0228182
\(590\) 0 0
\(591\) −25469.9 −1.77275
\(592\) −18195.7 −1.26324
\(593\) −513.405 −0.0355531 −0.0177766 0.999842i \(-0.505659\pi\)
−0.0177766 + 0.999842i \(0.505659\pi\)
\(594\) 237.457 0.0164023
\(595\) 0 0
\(596\) 4305.10 0.295879
\(597\) −20138.8 −1.38061
\(598\) 28.4092 0.00194271
\(599\) 13706.8 0.934964 0.467482 0.884003i \(-0.345161\pi\)
0.467482 + 0.884003i \(0.345161\pi\)
\(600\) 0 0
\(601\) −24403.7 −1.65632 −0.828159 0.560493i \(-0.810612\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(602\) −1202.02 −0.0813796
\(603\) −715.045 −0.0482900
\(604\) −2630.71 −0.177222
\(605\) 0 0
\(606\) −4935.37 −0.330835
\(607\) −16304.7 −1.09026 −0.545129 0.838352i \(-0.683519\pi\)
−0.545129 + 0.838352i \(0.683519\pi\)
\(608\) 157.152 0.0104825
\(609\) 800.748 0.0532807
\(610\) 0 0
\(611\) 753.683 0.0499030
\(612\) 11670.5 0.770834
\(613\) −7754.74 −0.510948 −0.255474 0.966816i \(-0.582231\pi\)
−0.255474 + 0.966816i \(0.582231\pi\)
\(614\) 2963.36 0.194775
\(615\) 0 0
\(616\) −2142.73 −0.140151
\(617\) 1574.90 0.102760 0.0513801 0.998679i \(-0.483638\pi\)
0.0513801 + 0.998679i \(0.483638\pi\)
\(618\) −2680.40 −0.174468
\(619\) −9160.25 −0.594800 −0.297400 0.954753i \(-0.596120\pi\)
−0.297400 + 0.954753i \(0.596120\pi\)
\(620\) 0 0
\(621\) −556.570 −0.0359652
\(622\) −1149.62 −0.0741083
\(623\) −11852.2 −0.762196
\(624\) −1303.76 −0.0836416
\(625\) 0 0
\(626\) 64.8465 0.00414024
\(627\) −358.125 −0.0228104
\(628\) −12488.2 −0.793523
\(629\) 19110.6 1.21143
\(630\) 0 0
\(631\) 11663.9 0.735871 0.367935 0.929851i \(-0.380065\pi\)
0.367935 + 0.929851i \(0.380065\pi\)
\(632\) 1933.78 0.121712
\(633\) 20655.4 1.29697
\(634\) −1348.82 −0.0844930
\(635\) 0 0
\(636\) 33465.9 2.08649
\(637\) 466.272 0.0290021
\(638\) 80.1115 0.00497123
\(639\) −17376.4 −1.07574
\(640\) 0 0
\(641\) −27074.5 −1.66830 −0.834148 0.551541i \(-0.814040\pi\)
−0.834148 + 0.551541i \(0.814040\pi\)
\(642\) 4363.78 0.268263
\(643\) 4463.82 0.273773 0.136886 0.990587i \(-0.456290\pi\)
0.136886 + 0.990587i \(0.456290\pi\)
\(644\) 2485.14 0.152062
\(645\) 0 0
\(646\) −53.1017 −0.00323415
\(647\) 11755.0 0.714277 0.357139 0.934051i \(-0.383752\pi\)
0.357139 + 0.934051i \(0.383752\pi\)
\(648\) −5189.83 −0.314623
\(649\) 2234.20 0.135131
\(650\) 0 0
\(651\) 15398.0 0.927029
\(652\) −21687.2 −1.30266
\(653\) 1236.64 0.0741094 0.0370547 0.999313i \(-0.488202\pi\)
0.0370547 + 0.999313i \(0.488202\pi\)
\(654\) −5037.40 −0.301189
\(655\) 0 0
\(656\) −2568.98 −0.152899
\(657\) −8257.81 −0.490362
\(658\) −1379.76 −0.0817456
\(659\) 23646.9 1.39780 0.698901 0.715218i \(-0.253673\pi\)
0.698901 + 0.715218i \(0.253673\pi\)
\(660\) 0 0
\(661\) 10150.5 0.597290 0.298645 0.954364i \(-0.403465\pi\)
0.298645 + 0.954364i \(0.403465\pi\)
\(662\) −2971.33 −0.174447
\(663\) 1369.32 0.0802112
\(664\) −894.526 −0.0522806
\(665\) 0 0
\(666\) 2893.63 0.168357
\(667\) −187.771 −0.0109003
\(668\) 2216.55 0.128385
\(669\) −3234.81 −0.186943
\(670\) 0 0
\(671\) 12906.7 0.742558
\(672\) 7418.77 0.425871
\(673\) −13941.8 −0.798540 −0.399270 0.916833i \(-0.630736\pi\)
−0.399270 + 0.916833i \(0.630736\pi\)
\(674\) −2899.71 −0.165716
\(675\) 0 0
\(676\) 17142.8 0.975353
\(677\) 13370.4 0.759035 0.379518 0.925185i \(-0.376090\pi\)
0.379518 + 0.925185i \(0.376090\pi\)
\(678\) 5836.68 0.330614
\(679\) −12788.8 −0.722812
\(680\) 0 0
\(681\) 14960.9 0.841852
\(682\) 1540.51 0.0864943
\(683\) −15659.3 −0.877288 −0.438644 0.898661i \(-0.644541\pi\)
−0.438644 + 0.898661i \(0.644541\pi\)
\(684\) 384.198 0.0214768
\(685\) 0 0
\(686\) −2768.87 −0.154105
\(687\) −33062.1 −1.83609
\(688\) −12935.5 −0.716806
\(689\) 1831.31 0.101259
\(690\) 0 0
\(691\) −9631.82 −0.530263 −0.265131 0.964212i \(-0.585415\pi\)
−0.265131 + 0.964212i \(0.585415\pi\)
\(692\) −18270.7 −1.00368
\(693\) −7884.77 −0.432204
\(694\) 2729.62 0.149301
\(695\) 0 0
\(696\) −372.412 −0.0202819
\(697\) 2698.15 0.146628
\(698\) 4119.99 0.223415
\(699\) −932.671 −0.0504676
\(700\) 0 0
\(701\) 21140.9 1.13906 0.569530 0.821971i \(-0.307125\pi\)
0.569530 + 0.821971i \(0.307125\pi\)
\(702\) −29.8898 −0.00160700
\(703\) 629.131 0.0337527
\(704\) −10906.7 −0.583894
\(705\) 0 0
\(706\) −1033.80 −0.0551101
\(707\) −23625.0 −1.25673
\(708\) −5139.25 −0.272803
\(709\) −15917.4 −0.843144 −0.421572 0.906795i \(-0.638522\pi\)
−0.421572 + 0.906795i \(0.638522\pi\)
\(710\) 0 0
\(711\) 7115.89 0.375340
\(712\) 5512.22 0.290139
\(713\) −3610.76 −0.189655
\(714\) −2506.80 −0.131393
\(715\) 0 0
\(716\) −855.221 −0.0446384
\(717\) 24667.1 1.28481
\(718\) 2704.09 0.140551
\(719\) 3323.34 0.172378 0.0861889 0.996279i \(-0.472531\pi\)
0.0861889 + 0.996279i \(0.472531\pi\)
\(720\) 0 0
\(721\) −12830.7 −0.662748
\(722\) 2775.85 0.143084
\(723\) 41391.2 2.12912
\(724\) −11572.6 −0.594051
\(725\) 0 0
\(726\) 2142.62 0.109532
\(727\) 9877.52 0.503902 0.251951 0.967740i \(-0.418928\pi\)
0.251951 + 0.967740i \(0.418928\pi\)
\(728\) 269.714 0.0137312
\(729\) −14449.9 −0.734130
\(730\) 0 0
\(731\) 13586.0 0.687407
\(732\) −29688.7 −1.49908
\(733\) −28951.5 −1.45886 −0.729432 0.684053i \(-0.760216\pi\)
−0.729432 + 0.684053i \(0.760216\pi\)
\(734\) 4747.24 0.238725
\(735\) 0 0
\(736\) −1739.66 −0.0871262
\(737\) −734.246 −0.0366978
\(738\) 408.541 0.0203775
\(739\) −31009.5 −1.54358 −0.771788 0.635880i \(-0.780637\pi\)
−0.771788 + 0.635880i \(0.780637\pi\)
\(740\) 0 0
\(741\) 45.0788 0.00223483
\(742\) −3352.57 −0.165871
\(743\) 13761.0 0.679465 0.339733 0.940522i \(-0.389663\pi\)
0.339733 + 0.940522i \(0.389663\pi\)
\(744\) −7161.31 −0.352885
\(745\) 0 0
\(746\) 3268.29 0.160403
\(747\) −3291.66 −0.161226
\(748\) 11983.8 0.585792
\(749\) 20888.9 1.01904
\(750\) 0 0
\(751\) 32197.4 1.56445 0.782223 0.622998i \(-0.214086\pi\)
0.782223 + 0.622998i \(0.214086\pi\)
\(752\) −14848.3 −0.720029
\(753\) 32957.8 1.59502
\(754\) −10.0840 −0.000487052 0
\(755\) 0 0
\(756\) −2614.65 −0.125786
\(757\) −26139.9 −1.25505 −0.627524 0.778597i \(-0.715932\pi\)
−0.627524 + 0.778597i \(0.715932\pi\)
\(758\) 2710.42 0.129877
\(759\) 3964.42 0.189591
\(760\) 0 0
\(761\) −24004.0 −1.14342 −0.571712 0.820454i \(-0.693721\pi\)
−0.571712 + 0.820454i \(0.693721\pi\)
\(762\) −6125.48 −0.291211
\(763\) −24113.3 −1.14412
\(764\) −15924.0 −0.754072
\(765\) 0 0
\(766\) −1013.40 −0.0478011
\(767\) −281.229 −0.0132393
\(768\) 23345.2 1.09687
\(769\) −33733.4 −1.58187 −0.790934 0.611902i \(-0.790405\pi\)
−0.790934 + 0.611902i \(0.790405\pi\)
\(770\) 0 0
\(771\) 37435.3 1.74864
\(772\) 30432.2 1.41876
\(773\) −40247.1 −1.87269 −0.936344 0.351083i \(-0.885814\pi\)
−0.936344 + 0.351083i \(0.885814\pi\)
\(774\) 2057.12 0.0955318
\(775\) 0 0
\(776\) 5947.81 0.275147
\(777\) 29699.7 1.37126
\(778\) −2222.28 −0.102407
\(779\) 88.8246 0.00408533
\(780\) 0 0
\(781\) −17843.0 −0.817508
\(782\) 587.832 0.0268808
\(783\) 197.557 0.00901676
\(784\) −9186.02 −0.418459
\(785\) 0 0
\(786\) 4304.21 0.195326
\(787\) 16327.3 0.739522 0.369761 0.929127i \(-0.379440\pi\)
0.369761 + 0.929127i \(0.379440\pi\)
\(788\) 28057.9 1.26843
\(789\) −13445.9 −0.606700
\(790\) 0 0
\(791\) 27939.4 1.25589
\(792\) 3667.04 0.164524
\(793\) −1624.62 −0.0727515
\(794\) 3142.83 0.140472
\(795\) 0 0
\(796\) 22185.1 0.987852
\(797\) 29358.8 1.30482 0.652410 0.757866i \(-0.273758\pi\)
0.652410 + 0.757866i \(0.273758\pi\)
\(798\) −82.5252 −0.00366085
\(799\) 15594.9 0.690498
\(800\) 0 0
\(801\) 20283.7 0.894745
\(802\) −5866.12 −0.258279
\(803\) −8479.56 −0.372649
\(804\) 1688.96 0.0740857
\(805\) 0 0
\(806\) −193.911 −0.00847420
\(807\) 53151.3 2.31848
\(808\) 10987.5 0.478389
\(809\) −2426.36 −0.105447 −0.0527234 0.998609i \(-0.516790\pi\)
−0.0527234 + 0.998609i \(0.516790\pi\)
\(810\) 0 0
\(811\) −31170.9 −1.34964 −0.674819 0.737983i \(-0.735778\pi\)
−0.674819 + 0.737983i \(0.735778\pi\)
\(812\) −882.112 −0.0381232
\(813\) 11625.7 0.501515
\(814\) 2971.34 0.127943
\(815\) 0 0
\(816\) −26977.0 −1.15733
\(817\) 447.257 0.0191524
\(818\) −2698.97 −0.115363
\(819\) 992.490 0.0423448
\(820\) 0 0
\(821\) −6679.93 −0.283960 −0.141980 0.989870i \(-0.545347\pi\)
−0.141980 + 0.989870i \(0.545347\pi\)
\(822\) 6525.36 0.276883
\(823\) −29299.3 −1.24096 −0.620480 0.784222i \(-0.713062\pi\)
−0.620480 + 0.784222i \(0.713062\pi\)
\(824\) 5967.31 0.252283
\(825\) 0 0
\(826\) 514.842 0.0216872
\(827\) −39806.7 −1.67378 −0.836889 0.547372i \(-0.815628\pi\)
−0.836889 + 0.547372i \(0.815628\pi\)
\(828\) −4253.04 −0.178506
\(829\) −17854.1 −0.748007 −0.374004 0.927427i \(-0.622015\pi\)
−0.374004 + 0.927427i \(0.622015\pi\)
\(830\) 0 0
\(831\) 4198.67 0.175271
\(832\) 1372.87 0.0572065
\(833\) 9647.91 0.401297
\(834\) 8407.37 0.349069
\(835\) 0 0
\(836\) 394.514 0.0163212
\(837\) 3798.94 0.156882
\(838\) 3416.80 0.140849
\(839\) −6656.92 −0.273924 −0.136962 0.990576i \(-0.543734\pi\)
−0.136962 + 0.990576i \(0.543734\pi\)
\(840\) 0 0
\(841\) −24322.3 −0.997267
\(842\) −5626.14 −0.230273
\(843\) 17791.2 0.726881
\(844\) −22754.2 −0.928000
\(845\) 0 0
\(846\) 2361.31 0.0959614
\(847\) 10256.4 0.416075
\(848\) −36078.7 −1.46102
\(849\) 5718.34 0.231158
\(850\) 0 0
\(851\) −6964.43 −0.280538
\(852\) 41043.6 1.65039
\(853\) 30008.7 1.20455 0.602273 0.798290i \(-0.294262\pi\)
0.602273 + 0.798290i \(0.294262\pi\)
\(854\) 2974.17 0.119173
\(855\) 0 0
\(856\) −9714.98 −0.387910
\(857\) −24281.5 −0.967843 −0.483922 0.875111i \(-0.660788\pi\)
−0.483922 + 0.875111i \(0.660788\pi\)
\(858\) 212.903 0.00847133
\(859\) 30635.5 1.21685 0.608423 0.793613i \(-0.291802\pi\)
0.608423 + 0.793613i \(0.291802\pi\)
\(860\) 0 0
\(861\) 4193.19 0.165974
\(862\) 4297.22 0.169796
\(863\) 26572.1 1.04812 0.524058 0.851683i \(-0.324418\pi\)
0.524058 + 0.851683i \(0.324418\pi\)
\(864\) 1830.33 0.0720707
\(865\) 0 0
\(866\) −3065.43 −0.120286
\(867\) −6613.87 −0.259076
\(868\) −16962.6 −0.663305
\(869\) 7306.97 0.285238
\(870\) 0 0
\(871\) 92.4227 0.00359543
\(872\) 11214.6 0.435522
\(873\) 21886.6 0.848511
\(874\) 19.3517 0.000748950 0
\(875\) 0 0
\(876\) 19505.2 0.752305
\(877\) 37158.4 1.43073 0.715366 0.698750i \(-0.246260\pi\)
0.715366 + 0.698750i \(0.246260\pi\)
\(878\) 4776.43 0.183595
\(879\) 45044.9 1.72847
\(880\) 0 0
\(881\) −3353.12 −0.128229 −0.0641143 0.997943i \(-0.520422\pi\)
−0.0641143 + 0.997943i \(0.520422\pi\)
\(882\) 1460.84 0.0557699
\(883\) −16292.5 −0.620936 −0.310468 0.950584i \(-0.600486\pi\)
−0.310468 + 0.950584i \(0.600486\pi\)
\(884\) −1508.46 −0.0573924
\(885\) 0 0
\(886\) 4626.22 0.175418
\(887\) 5949.82 0.225226 0.112613 0.993639i \(-0.464078\pi\)
0.112613 + 0.993639i \(0.464078\pi\)
\(888\) −13812.7 −0.521988
\(889\) −29321.9 −1.10621
\(890\) 0 0
\(891\) −19610.2 −0.737338
\(892\) 3563.50 0.133761
\(893\) 513.393 0.0192386
\(894\) 1582.58 0.0592050
\(895\) 0 0
\(896\) −10856.9 −0.404804
\(897\) −499.019 −0.0185750
\(898\) −3589.03 −0.133371
\(899\) 1281.66 0.0475480
\(900\) 0 0
\(901\) 37892.8 1.40110
\(902\) 419.512 0.0154858
\(903\) 21113.9 0.778102
\(904\) −12994.0 −0.478070
\(905\) 0 0
\(906\) −967.062 −0.0354619
\(907\) 44105.2 1.61465 0.807326 0.590106i \(-0.200914\pi\)
0.807326 + 0.590106i \(0.200914\pi\)
\(908\) −16481.0 −0.602360
\(909\) 40431.6 1.47528
\(910\) 0 0
\(911\) 4385.18 0.159481 0.0797407 0.996816i \(-0.474591\pi\)
0.0797407 + 0.996816i \(0.474591\pi\)
\(912\) −888.097 −0.0322454
\(913\) −3380.05 −0.122523
\(914\) 2100.60 0.0760194
\(915\) 0 0
\(916\) 36421.5 1.31376
\(917\) 20603.7 0.741978
\(918\) −618.468 −0.0222358
\(919\) 30027.0 1.07780 0.538901 0.842369i \(-0.318840\pi\)
0.538901 + 0.842369i \(0.318840\pi\)
\(920\) 0 0
\(921\) −52052.7 −1.86232
\(922\) 6810.03 0.243250
\(923\) 2245.98 0.0800946
\(924\) 18624.1 0.663080
\(925\) 0 0
\(926\) 2571.99 0.0912751
\(927\) 21958.4 0.778002
\(928\) 617.503 0.0218432
\(929\) −5457.52 −0.192740 −0.0963700 0.995346i \(-0.530723\pi\)
−0.0963700 + 0.995346i \(0.530723\pi\)
\(930\) 0 0
\(931\) 317.614 0.0111809
\(932\) 1027.44 0.0361104
\(933\) 20193.5 0.708579
\(934\) 428.046 0.0149958
\(935\) 0 0
\(936\) −461.587 −0.0161191
\(937\) −3039.15 −0.105960 −0.0529802 0.998596i \(-0.516872\pi\)
−0.0529802 + 0.998596i \(0.516872\pi\)
\(938\) −169.197 −0.00588964
\(939\) −1139.05 −0.0395864
\(940\) 0 0
\(941\) 25791.0 0.893479 0.446740 0.894664i \(-0.352585\pi\)
0.446740 + 0.894664i \(0.352585\pi\)
\(942\) −4590.71 −0.158783
\(943\) −983.282 −0.0339555
\(944\) 5540.48 0.191025
\(945\) 0 0
\(946\) 2112.36 0.0725991
\(947\) −18339.3 −0.629299 −0.314650 0.949208i \(-0.601887\pi\)
−0.314650 + 0.949208i \(0.601887\pi\)
\(948\) −16807.9 −0.575840
\(949\) 1067.36 0.0365099
\(950\) 0 0
\(951\) 23692.6 0.807871
\(952\) 5580.83 0.189995
\(953\) −12658.7 −0.430278 −0.215139 0.976583i \(-0.569021\pi\)
−0.215139 + 0.976583i \(0.569021\pi\)
\(954\) 5737.55 0.194717
\(955\) 0 0
\(956\) −27173.5 −0.919302
\(957\) −1407.19 −0.0475319
\(958\) 4105.55 0.138460
\(959\) 31236.0 1.05179
\(960\) 0 0
\(961\) −5145.31 −0.172714
\(962\) −374.015 −0.0125351
\(963\) −35749.0 −1.19626
\(964\) −45597.0 −1.52342
\(965\) 0 0
\(966\) 913.548 0.0304275
\(967\) −50470.3 −1.67840 −0.839201 0.543822i \(-0.816977\pi\)
−0.839201 + 0.543822i \(0.816977\pi\)
\(968\) −4770.06 −0.158384
\(969\) 932.752 0.0309229
\(970\) 0 0
\(971\) 30778.2 1.01722 0.508610 0.860997i \(-0.330160\pi\)
0.508610 + 0.860997i \(0.330160\pi\)
\(972\) 39988.9 1.31959
\(973\) 40245.0 1.32600
\(974\) −3593.89 −0.118230
\(975\) 0 0
\(976\) 32006.6 1.04970
\(977\) 23575.5 0.772004 0.386002 0.922498i \(-0.373856\pi\)
0.386002 + 0.922498i \(0.373856\pi\)
\(978\) −7972.31 −0.260661
\(979\) 20828.4 0.679958
\(980\) 0 0
\(981\) 41267.4 1.34308
\(982\) 8687.21 0.282301
\(983\) 44798.3 1.45355 0.726777 0.686874i \(-0.241018\pi\)
0.726777 + 0.686874i \(0.241018\pi\)
\(984\) −1950.17 −0.0631799
\(985\) 0 0
\(986\) −208.654 −0.00673924
\(987\) 24236.0 0.781601
\(988\) −49.6592 −0.00159906
\(989\) −4951.10 −0.159187
\(990\) 0 0
\(991\) −12153.5 −0.389574 −0.194787 0.980846i \(-0.562402\pi\)
−0.194787 + 0.980846i \(0.562402\pi\)
\(992\) 11874.3 0.380050
\(993\) 52192.6 1.66796
\(994\) −4111.69 −0.131202
\(995\) 0 0
\(996\) 7774.99 0.247350
\(997\) −36538.1 −1.16065 −0.580327 0.814383i \(-0.697075\pi\)
−0.580327 + 0.814383i \(0.697075\pi\)
\(998\) −3926.83 −0.124551
\(999\) 7327.40 0.232061
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 575.4.a.j.1.3 5
5.2 odd 4 575.4.b.i.24.5 10
5.3 odd 4 575.4.b.i.24.6 10
5.4 even 2 115.4.a.e.1.3 5
15.14 odd 2 1035.4.a.k.1.3 5
20.19 odd 2 1840.4.a.n.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.a.e.1.3 5 5.4 even 2
575.4.a.j.1.3 5 1.1 even 1 trivial
575.4.b.i.24.5 10 5.2 odd 4
575.4.b.i.24.6 10 5.3 odd 4
1035.4.a.k.1.3 5 15.14 odd 2
1840.4.a.n.1.5 5 20.19 odd 2