Properties

Label 1035.4.a.k.1.3
Level $1035$
Weight $4$
Character 1035.1
Self dual yes
Analytic conductor $61.067$
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] = [1035,4,Mod(1,1035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1035, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1035.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1035.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: \(61.0669768559\)
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: \(\Z[a_1, \ldots, a_{7}]\)
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 \(\chi\) \(=\) 1035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.404957 q^{2} -7.83601 q^{4} +5.00000 q^{5} +13.7888 q^{7} +6.41290 q^{8} +O(q^{10})\) \(q-0.404957 q^{2} -7.83601 q^{4} +5.00000 q^{5} +13.7888 q^{7} +6.41290 q^{8} -2.02479 q^{10} -24.2317 q^{11} +3.05016 q^{13} -5.58389 q^{14} +60.0911 q^{16} -63.1126 q^{17} -2.07770 q^{19} -39.1800 q^{20} +9.81282 q^{22} +23.0000 q^{23} +25.0000 q^{25} -1.23518 q^{26} -108.049 q^{28} +8.16397 q^{29} -156.989 q^{31} -75.6376 q^{32} +25.5579 q^{34} +68.9442 q^{35} +302.801 q^{37} +0.841380 q^{38} +32.0645 q^{40} +42.7514 q^{41} +215.265 q^{43} +189.880 q^{44} -9.31401 q^{46} -247.096 q^{47} -152.868 q^{49} -10.1239 q^{50} -23.9010 q^{52} -600.400 q^{53} -121.159 q^{55} +88.4265 q^{56} -3.30606 q^{58} -92.2014 q^{59} +532.635 q^{61} +63.5740 q^{62} -450.099 q^{64} +15.2508 q^{65} +30.3010 q^{67} +494.551 q^{68} -27.9194 q^{70} +736.349 q^{71} +349.936 q^{73} -122.622 q^{74} +16.2809 q^{76} -334.127 q^{77} +301.545 q^{79} +300.456 q^{80} -17.3125 q^{82} -139.488 q^{83} -315.563 q^{85} -87.1732 q^{86} -155.396 q^{88} -859.551 q^{89} +42.0581 q^{91} -180.228 q^{92} +100.063 q^{94} -10.3885 q^{95} -927.475 q^{97} +61.9051 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 6 q^{2} + 22 q^{4} + 25 q^{5} - 3 q^{7} - 138 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 6 q^{2} + 22 q^{4} + 25 q^{5} - 3 q^{7} - 138 q^{8} - 30 q^{10} - 23 q^{11} + 132 q^{13} - 93 q^{14} + 282 q^{16} - 23 q^{17} - 161 q^{19} + 110 q^{20} + 193 q^{22} + 115 q^{23} + 125 q^{25} + 257 q^{26} + 17 q^{28} - 401 q^{29} + 32 q^{31} - 670 q^{32} - 663 q^{34} - 15 q^{35} - 38 q^{37} + 875 q^{38} - 690 q^{40} + 12 q^{41} - 566 q^{43} - 47 q^{44} - 138 q^{46} - 919 q^{47} - 738 q^{49} - 150 q^{50} - 305 q^{52} - 1156 q^{53} - 115 q^{55} - 343 q^{56} - 1042 q^{58} - 1324 q^{59} - 1673 q^{61} - 565 q^{62} + 2466 q^{64} + 660 q^{65} + 558 q^{67} + 2267 q^{68} - 465 q^{70} + 108 q^{71} + 1173 q^{73} - 1458 q^{74} - 3477 q^{76} - 2608 q^{77} + 656 q^{79} + 1410 q^{80} + 3505 q^{82} + 82 q^{83} - 115 q^{85} - 112 q^{86} + 2397 q^{88} - 570 q^{89} - 1589 q^{91} + 506 q^{92} - 948 q^{94} - 805 q^{95} + 633 q^{97} + 2555 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.404957 −0.143174 −0.0715870 0.997434i \(-0.522806\pi\)
−0.0715870 + 0.997434i \(0.522806\pi\)
\(3\) 0 0
\(4\) −7.83601 −0.979501
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 13.7888 0.744527 0.372263 0.928127i \(-0.378582\pi\)
0.372263 + 0.928127i \(0.378582\pi\)
\(8\) 6.41290 0.283413
\(9\) 0 0
\(10\) −2.02479 −0.0640293
\(11\) −24.2317 −0.664195 −0.332098 0.943245i \(-0.607756\pi\)
−0.332098 + 0.943245i \(0.607756\pi\)
\(12\) 0 0
\(13\) 3.05016 0.0650739 0.0325370 0.999471i \(-0.489641\pi\)
0.0325370 + 0.999471i \(0.489641\pi\)
\(14\) −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 \(0.648650\pi\)
\(18\) 0 0
\(19\) −2.07770 −0.0250872 −0.0125436 0.999921i \(-0.503993\pi\)
−0.0125436 + 0.999921i \(0.503993\pi\)
\(20\) −39.1800 −0.438046
\(21\) 0 0
\(22\) 9.81282 0.0950955
\(23\) 23.0000 0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) −1.23518 −0.00931689
\(27\) 0 0
\(28\) −108.049 −0.729265
\(29\) 8.16397 0.0522762 0.0261381 0.999658i \(-0.491679\pi\)
0.0261381 + 0.999658i \(0.491679\pi\)
\(30\) 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
\(33\) 0 0
\(34\) 25.5579 0.128916
\(35\) 68.9442 0.332963
\(36\) 0 0
\(37\) 302.801 1.34541 0.672706 0.739910i \(-0.265132\pi\)
0.672706 + 0.739910i \(0.265132\pi\)
\(38\) 0.841380 0.00359184
\(39\) 0 0
\(40\) 32.0645 0.126746
\(41\) 42.7514 0.162845 0.0814225 0.996680i \(-0.474054\pi\)
0.0814225 + 0.996680i \(0.474054\pi\)
\(42\) 0 0
\(43\) 215.265 0.763434 0.381717 0.924279i \(-0.375333\pi\)
0.381717 + 0.924279i \(0.375333\pi\)
\(44\) 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 \(0.625258\pi\)
\(48\) 0 0
\(49\) −152.868 −0.445680
\(50\) −10.1239 −0.0286348
\(51\) 0 0
\(52\) −23.9010 −0.0637400
\(53\) −600.400 −1.55606 −0.778031 0.628225i \(-0.783782\pi\)
−0.778031 + 0.628225i \(0.783782\pi\)
\(54\) 0 0
\(55\) −121.159 −0.297037
\(56\) 88.4265 0.211009
\(57\) 0 0
\(58\) −3.30606 −0.00748460
\(59\) −92.2014 −0.203451 −0.101725 0.994813i \(-0.532436\pi\)
−0.101725 + 0.994813i \(0.532436\pi\)
\(60\) 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
\(63\) 0 0
\(64\) −450.099 −0.879100
\(65\) 15.2508 0.0291019
\(66\) 0 0
\(67\) 30.3010 0.0552515 0.0276258 0.999618i \(-0.491205\pi\)
0.0276258 + 0.999618i \(0.491205\pi\)
\(68\) 494.551 0.881958
\(69\) 0 0
\(70\) −27.9194 −0.0476716
\(71\) 736.349 1.23083 0.615413 0.788205i \(-0.288989\pi\)
0.615413 + 0.788205i \(0.288989\pi\)
\(72\) 0 0
\(73\) 349.936 0.561053 0.280527 0.959846i \(-0.409491\pi\)
0.280527 + 0.959846i \(0.409491\pi\)
\(74\) −122.622 −0.192628
\(75\) 0 0
\(76\) 16.2809 0.0245730
\(77\) −334.127 −0.494511
\(78\) 0 0
\(79\) 301.545 0.429449 0.214725 0.976675i \(-0.431115\pi\)
0.214725 + 0.976675i \(0.431115\pi\)
\(80\) 300.456 0.419900
\(81\) 0 0
\(82\) −17.3125 −0.0233152
\(83\) −139.488 −0.184468 −0.0922340 0.995737i \(-0.529401\pi\)
−0.0922340 + 0.995737i \(0.529401\pi\)
\(84\) 0 0
\(85\) −315.563 −0.402678
\(86\) −87.1732 −0.109304
\(87\) 0 0
\(88\) −155.396 −0.188242
\(89\) −859.551 −1.02373 −0.511866 0.859065i \(-0.671046\pi\)
−0.511866 + 0.859065i \(0.671046\pi\)
\(90\) 0 0
\(91\) 42.0581 0.0484493
\(92\) −180.228 −0.204240
\(93\) 0 0
\(94\) 100.063 0.109795
\(95\) −10.3885 −0.0112193
\(96\) 0 0
\(97\) −927.475 −0.970833 −0.485417 0.874283i \(-0.661332\pi\)
−0.485417 + 0.874283i \(0.661332\pi\)
\(98\) 61.9051 0.0638097
\(99\) 0 0
\(100\) −195.900 −0.195900
\(101\) −1713.34 −1.68796 −0.843979 0.536376i \(-0.819793\pi\)
−0.843979 + 0.536376i \(0.819793\pi\)
\(102\) 0 0
\(103\) −930.516 −0.890160 −0.445080 0.895491i \(-0.646825\pi\)
−0.445080 + 0.895491i \(0.646825\pi\)
\(104\) 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 \(0.739916\pi\)
\(108\) 0 0
\(109\) 1748.76 1.53670 0.768352 0.640027i \(-0.221077\pi\)
0.768352 + 0.640027i \(0.221077\pi\)
\(110\) 49.0641 0.0425280
\(111\) 0 0
\(112\) 828.586 0.699054
\(113\) −2026.23 −1.68683 −0.843416 0.537261i \(-0.819459\pi\)
−0.843416 + 0.537261i \(0.819459\pi\)
\(114\) 0 0
\(115\) 115.000 0.0932505
\(116\) −63.9729 −0.0512046
\(117\) 0 0
\(118\) 37.3376 0.0291289
\(119\) −870.249 −0.670383
\(120\) 0 0
\(121\) −743.822 −0.558845
\(122\) −215.694 −0.160066
\(123\) 0 0
\(124\) 1230.17 0.890908
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −2126.49 −1.48579 −0.742897 0.669406i \(-0.766549\pi\)
−0.742897 + 0.669406i \(0.766549\pi\)
\(128\) 787.371 0.543707
\(129\) 0 0
\(130\) −6.17591 −0.00416664
\(131\) 1494.23 0.996576 0.498288 0.867012i \(-0.333962\pi\)
0.498288 + 0.867012i \(0.333962\pi\)
\(132\) 0 0
\(133\) −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 \(0.749658\pi\)
\(138\) 0 0
\(139\) −2918.66 −1.78099 −0.890496 0.454991i \(-0.849642\pi\)
−0.890496 + 0.454991i \(0.849642\pi\)
\(140\) −540.247 −0.326137
\(141\) 0 0
\(142\) −298.190 −0.176222
\(143\) −73.9106 −0.0432218
\(144\) 0 0
\(145\) 40.8198 0.0233786
\(146\) −141.709 −0.0803282
\(147\) 0 0
\(148\) −2372.75 −1.31783
\(149\) 549.400 0.302071 0.151036 0.988528i \(-0.451739\pi\)
0.151036 + 0.988528i \(0.451739\pi\)
\(150\) 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
\(153\) 0 0
\(154\) 135.307 0.0708011
\(155\) −784.947 −0.406764
\(156\) 0 0
\(157\) −1593.69 −0.810130 −0.405065 0.914288i \(-0.632751\pi\)
−0.405065 + 0.914288i \(0.632751\pi\)
\(158\) −122.113 −0.0614860
\(159\) 0 0
\(160\) −378.188 −0.186865
\(161\) 317.143 0.155245
\(162\) 0 0
\(163\) −2767.63 −1.32992 −0.664962 0.746877i \(-0.731552\pi\)
−0.664962 + 0.746877i \(0.731552\pi\)
\(164\) −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 \(0.520876\pi\)
\(168\) 0 0
\(169\) −2187.70 −0.995765
\(170\) 127.790 0.0576530
\(171\) 0 0
\(172\) −1686.82 −0.747784
\(173\) 2331.63 1.02468 0.512342 0.858782i \(-0.328778\pi\)
0.512342 + 0.858782i \(0.328778\pi\)
\(174\) 0 0
\(175\) 344.721 0.148905
\(176\) −1456.11 −0.623629
\(177\) 0 0
\(178\) 348.081 0.146572
\(179\) −109.140 −0.0455726 −0.0227863 0.999740i \(-0.507254\pi\)
−0.0227863 + 0.999740i \(0.507254\pi\)
\(180\) 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
\(183\) 0 0
\(184\) 147.497 0.0590957
\(185\) 1514.01 0.601686
\(186\) 0 0
\(187\) 1529.33 0.598051
\(188\) 1936.25 0.751147
\(189\) 0 0
\(190\) 4.20690 0.00160632
\(191\) −2032.16 −0.769853 −0.384926 0.922947i \(-0.625773\pi\)
−0.384926 + 0.922947i \(0.625773\pi\)
\(192\) 0 0
\(193\) 3883.64 1.44845 0.724224 0.689565i \(-0.242198\pi\)
0.724224 + 0.689565i \(0.242198\pi\)
\(194\) 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 \(0.724180\pi\)
\(198\) 0 0
\(199\) −2831.17 −1.00853 −0.504263 0.863550i \(-0.668236\pi\)
−0.504263 + 0.863550i \(0.668236\pi\)
\(200\) 160.323 0.0566826
\(201\) 0 0
\(202\) 693.830 0.241672
\(203\) 112.572 0.0389211
\(204\) 0 0
\(205\) 213.757 0.0728265
\(206\) 376.819 0.127448
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 613.474 0.195964
\(215\) 1076.33 0.341418
\(216\) 0 0
\(217\) −2164.70 −0.677186
\(218\) −708.173 −0.220016
\(219\) 0 0
\(220\) 949.401 0.290948
\(221\) −192.503 −0.0585935
\(222\) 0 0
\(223\) 454.760 0.136560 0.0682802 0.997666i \(-0.478249\pi\)
0.0682802 + 0.997666i \(0.478249\pi\)
\(224\) −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 \(0.400513\pi\)
\(228\) 0 0
\(229\) −4647.97 −1.34125 −0.670625 0.741796i \(-0.733974\pi\)
−0.670625 + 0.741796i \(0.733974\pi\)
\(230\) −46.5701 −0.0133510
\(231\) 0 0
\(232\) 52.3548 0.0148158
\(233\) −131.118 −0.0368661 −0.0184331 0.999830i \(-0.505868\pi\)
−0.0184331 + 0.999830i \(0.505868\pi\)
\(234\) 0 0
\(235\) −1235.48 −0.342953
\(236\) 722.491 0.199280
\(237\) 0 0
\(238\) 352.414 0.0959814
\(239\) −3467.77 −0.938541 −0.469271 0.883054i \(-0.655483\pi\)
−0.469271 + 0.883054i \(0.655483\pi\)
\(240\) 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
\(243\) 0 0
\(244\) −4173.73 −1.09506
\(245\) −764.341 −0.199314
\(246\) 0 0
\(247\) −6.33731 −0.00163252
\(248\) −1006.76 −0.257779
\(249\) 0 0
\(250\) −50.6196 −0.0128059
\(251\) −4633.30 −1.16515 −0.582573 0.812779i \(-0.697954\pi\)
−0.582573 + 0.812779i \(0.697954\pi\)
\(252\) 0 0
\(253\) −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 \(0.279480\pi\)
\(258\) 0 0
\(259\) 4175.28 1.00170
\(260\) −119.505 −0.0285054
\(261\) 0 0
\(262\) −605.099 −0.142684
\(263\) −1890.26 −0.443189 −0.221594 0.975139i \(-0.571126\pi\)
−0.221594 + 0.975139i \(0.571126\pi\)
\(264\) 0 0
\(265\) −3002.00 −0.695892
\(266\) 11.6016 0.00267422
\(267\) 0 0
\(268\) −237.439 −0.0541189
\(269\) −7472.17 −1.69363 −0.846815 0.531888i \(-0.821483\pi\)
−0.846815 + 0.531888i \(0.821483\pi\)
\(270\) 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
\(273\) 0 0
\(274\) 917.355 0.202261
\(275\) −605.794 −0.132839
\(276\) 0 0
\(277\) −590.262 −0.128034 −0.0640170 0.997949i \(-0.520391\pi\)
−0.0640170 + 0.997949i \(0.520391\pi\)
\(278\) 1181.93 0.254992
\(279\) 0 0
\(280\) 442.132 0.0943659
\(281\) −2501.14 −0.530980 −0.265490 0.964114i \(-0.585534\pi\)
−0.265490 + 0.964114i \(0.585534\pi\)
\(282\) 0 0
\(283\) −803.901 −0.168859 −0.0844293 0.996429i \(-0.526907\pi\)
−0.0844293 + 0.996429i \(0.526907\pi\)
\(284\) −5770.04 −1.20559
\(285\) 0 0
\(286\) 29.9306 0.00618823
\(287\) 589.491 0.121242
\(288\) 0 0
\(289\) −929.797 −0.189252
\(290\) −16.5303 −0.00334721
\(291\) 0 0
\(292\) −2742.10 −0.549552
\(293\) 6332.54 1.26263 0.631316 0.775526i \(-0.282515\pi\)
0.631316 + 0.775526i \(0.282515\pi\)
\(294\) 0 0
\(295\) −461.007 −0.0909860
\(296\) 1941.84 0.381307
\(297\) 0 0
\(298\) −222.483 −0.0432487
\(299\) 70.1536 0.0135688
\(300\) 0 0
\(301\) 2968.26 0.568397
\(302\) −135.952 −0.0259046
\(303\) 0 0
\(304\) −124.851 −0.0235550
\(305\) 2663.17 0.499977
\(306\) 0 0
\(307\) 7317.73 1.36041 0.680203 0.733024i \(-0.261892\pi\)
0.680203 + 0.733024i \(0.261892\pi\)
\(308\) 2618.23 0.484374
\(309\) 0 0
\(310\) 317.870 0.0582381
\(311\) −2838.86 −0.517611 −0.258805 0.965930i \(-0.583329\pi\)
−0.258805 + 0.965930i \(0.583329\pi\)
\(312\) 0 0
\(313\) 160.132 0.0289175 0.0144588 0.999895i \(-0.495397\pi\)
0.0144588 + 0.999895i \(0.495397\pi\)
\(314\) 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 \(0.404657\pi\)
\(318\) 0 0
\(319\) −197.827 −0.0347216
\(320\) −2250.50 −0.393145
\(321\) 0 0
\(322\) −128.429 −0.0222270
\(323\) 131.129 0.0225889
\(324\) 0 0
\(325\) 76.2539 0.0130148
\(326\) 1120.77 0.190410
\(327\) 0 0
\(328\) 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
\(333\) 0 0
\(334\) 114.549 0.0187660
\(335\) 151.505 0.0247092
\(336\) 0 0
\(337\) −7160.54 −1.15745 −0.578723 0.815524i \(-0.696449\pi\)
−0.578723 + 0.815524i \(0.696449\pi\)
\(338\) 885.923 0.142568
\(339\) 0 0
\(340\) 2472.76 0.394424
\(341\) 3804.13 0.604121
\(342\) 0 0
\(343\) −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 \(0.674589\pi\)
\(348\) 0 0
\(349\) −10173.9 −1.56045 −0.780224 0.625501i \(-0.784895\pi\)
−0.780224 + 0.625501i \(0.784895\pi\)
\(350\) −139.597 −0.0213194
\(351\) 0 0
\(352\) 1832.83 0.277529
\(353\) 2552.87 0.384917 0.192458 0.981305i \(-0.438354\pi\)
0.192458 + 0.981305i \(0.438354\pi\)
\(354\) 0 0
\(355\) 3681.75 0.550442
\(356\) 6735.45 1.00275
\(357\) 0 0
\(358\) 44.1970 0.00652481
\(359\) 6677.47 0.981681 0.490841 0.871249i \(-0.336690\pi\)
0.490841 + 0.871249i \(0.336690\pi\)
\(360\) 0 0
\(361\) −6854.68 −0.999371
\(362\) −598.062 −0.0868326
\(363\) 0 0
\(364\) −329.567 −0.0474561
\(365\) 1749.68 0.250911
\(366\) 0 0
\(367\) 11722.8 1.66738 0.833688 0.552236i \(-0.186225\pi\)
0.833688 + 0.552236i \(0.186225\pi\)
\(368\) 1382.10 0.195779
\(369\) 0 0
\(370\) −613.108 −0.0861458
\(371\) −8278.82 −1.15853
\(372\) 0 0
\(373\) 8070.71 1.12034 0.560168 0.828379i \(-0.310736\pi\)
0.560168 + 0.828379i \(0.310736\pi\)
\(374\) −619.313 −0.0856254
\(375\) 0 0
\(376\) −1584.61 −0.217340
\(377\) 24.9014 0.00340182
\(378\) 0 0
\(379\) −6693.10 −0.907128 −0.453564 0.891224i \(-0.649848\pi\)
−0.453564 + 0.891224i \(0.649848\pi\)
\(380\) 81.4044 0.0109894
\(381\) 0 0
\(382\) 822.937 0.110223
\(383\) 2502.49 0.333867 0.166934 0.985968i \(-0.446613\pi\)
0.166934 + 0.985968i \(0.446613\pi\)
\(384\) 0 0
\(385\) −1670.64 −0.221152
\(386\) −1572.71 −0.207380
\(387\) 0 0
\(388\) 7267.71 0.950933
\(389\) −5487.69 −0.715262 −0.357631 0.933863i \(-0.616415\pi\)
−0.357631 + 0.933863i \(0.616415\pi\)
\(390\) 0 0
\(391\) −1451.59 −0.187750
\(392\) −980.329 −0.126311
\(393\) 0 0
\(394\) 1450.01 0.185407
\(395\) 1507.73 0.192056
\(396\) 0 0
\(397\) 7760.91 0.981130 0.490565 0.871405i \(-0.336790\pi\)
0.490565 + 0.871405i \(0.336790\pi\)
\(398\) 1146.50 0.144395
\(399\) 0 0
\(400\) 1502.28 0.187785
\(401\) −14485.8 −1.80395 −0.901977 0.431785i \(-0.857884\pi\)
−0.901977 + 0.431785i \(0.857884\pi\)
\(402\) 0 0
\(403\) −478.842 −0.0591882
\(404\) 13425.8 1.65336
\(405\) 0 0
\(406\) −45.5867 −0.00557248
\(407\) −7337.41 −0.893616
\(408\) 0 0
\(409\) 6664.83 0.805758 0.402879 0.915253i \(-0.368010\pi\)
0.402879 + 0.915253i \(0.368010\pi\)
\(410\) −86.5624 −0.0104269
\(411\) 0 0
\(412\) 7291.53 0.871912
\(413\) −1271.35 −0.151475
\(414\) 0 0
\(415\) −697.442 −0.0824966
\(416\) −230.706 −0.0271906
\(417\) 0 0
\(418\) −20.3881 −0.00238568
\(419\) 8437.43 0.983760 0.491880 0.870663i \(-0.336310\pi\)
0.491880 + 0.870663i \(0.336310\pi\)
\(420\) 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
\(423\) 0 0
\(424\) −3850.31 −0.441008
\(425\) −1577.82 −0.180083
\(426\) 0 0
\(427\) 7344.41 0.832368
\(428\) 11870.9 1.34065
\(429\) 0 0
\(430\) −435.866 −0.0488822
\(431\) 10611.5 1.18594 0.592969 0.805225i \(-0.297956\pi\)
0.592969 + 0.805225i \(0.297956\pi\)
\(432\) 0 0
\(433\) −7569.77 −0.840139 −0.420069 0.907492i \(-0.637994\pi\)
−0.420069 + 0.907492i \(0.637994\pi\)
\(434\) 876.611 0.0969555
\(435\) 0 0
\(436\) −13703.3 −1.50520
\(437\) −47.7871 −0.00523105
\(438\) 0 0
\(439\) −11794.9 −1.28232 −0.641162 0.767406i \(-0.721547\pi\)
−0.641162 + 0.767406i \(0.721547\pi\)
\(440\) −776.980 −0.0841842
\(441\) 0 0
\(442\) 77.9556 0.00838907
\(443\) −11424.0 −1.22521 −0.612606 0.790388i \(-0.709879\pi\)
−0.612606 + 0.790388i \(0.709879\pi\)
\(444\) 0 0
\(445\) −4297.75 −0.457827
\(446\) −184.158 −0.0195519
\(447\) 0 0
\(448\) −6206.34 −0.654513
\(449\) −8862.74 −0.931533 −0.465767 0.884908i \(-0.654221\pi\)
−0.465767 + 0.884908i \(0.654221\pi\)
\(450\) 0 0
\(451\) −1035.94 −0.108161
\(452\) 15877.6 1.65225
\(453\) 0 0
\(454\) −851.724 −0.0880471
\(455\) 210.290 0.0216672
\(456\) 0 0
\(457\) 5187.22 0.530958 0.265479 0.964117i \(-0.414470\pi\)
0.265479 + 0.964117i \(0.414470\pi\)
\(458\) 1882.23 0.192032
\(459\) 0 0
\(460\) −901.141 −0.0913390
\(461\) 16816.7 1.69898 0.849491 0.527603i \(-0.176909\pi\)
0.849491 + 0.527603i \(0.176909\pi\)
\(462\) 0 0
\(463\) 6351.26 0.637512 0.318756 0.947837i \(-0.396735\pi\)
0.318756 + 0.947837i \(0.396735\pi\)
\(464\) 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 \(0.516677\pi\)
\(468\) 0 0
\(469\) 417.815 0.0411363
\(470\) 500.317 0.0491020
\(471\) 0 0
\(472\) −591.279 −0.0576606
\(473\) −5216.25 −0.507069
\(474\) 0 0
\(475\) −51.9425 −0.00501745
\(476\) 6819.28 0.656641
\(477\) 0 0
\(478\) 1404.30 0.134375
\(479\) 10138.2 0.967073 0.483537 0.875324i \(-0.339352\pi\)
0.483537 + 0.875324i \(0.339352\pi\)
\(480\) 0 0
\(481\) 923.591 0.0875512
\(482\) −2356.41 −0.222679
\(483\) 0 0
\(484\) 5828.60 0.547389
\(485\) −4637.38 −0.434170
\(486\) 0 0
\(487\) −8874.74 −0.825776 −0.412888 0.910782i \(-0.635480\pi\)
−0.412888 + 0.910782i \(0.635480\pi\)
\(488\) 3415.74 0.316851
\(489\) 0 0
\(490\) 309.525 0.0285366
\(491\) 21452.2 1.97174 0.985869 0.167521i \(-0.0535761\pi\)
0.985869 + 0.167521i \(0.0535761\pi\)
\(492\) 0 0
\(493\) −515.249 −0.0470703
\(494\) 2.56634 0.000233735 0
\(495\) 0 0
\(496\) −9433.67 −0.854001
\(497\) 10153.4 0.916382
\(498\) 0 0
\(499\) 9696.91 0.869926 0.434963 0.900448i \(-0.356761\pi\)
0.434963 + 0.900448i \(0.356761\pi\)
\(500\) −979.501 −0.0876093
\(501\) 0 0
\(502\) 1876.29 0.166818
\(503\) 8892.32 0.788249 0.394124 0.919057i \(-0.371048\pi\)
0.394124 + 0.919057i \(0.371048\pi\)
\(504\) 0 0
\(505\) −8566.71 −0.754878
\(506\) 225.695 0.0198288
\(507\) 0 0
\(508\) 16663.2 1.45534
\(509\) 1084.94 0.0944778 0.0472389 0.998884i \(-0.484958\pi\)
0.0472389 + 0.998884i \(0.484958\pi\)
\(510\) 0 0
\(511\) 4825.20 0.417719
\(512\) −7628.02 −0.658426
\(513\) 0 0
\(514\) −2131.20 −0.182885
\(515\) −4652.58 −0.398091
\(516\) 0 0
\(517\) 5987.58 0.509349
\(518\) −1690.81 −0.143417
\(519\) 0 0
\(520\) 97.8018 0.00824787
\(521\) −4578.35 −0.384993 −0.192496 0.981298i \(-0.561658\pi\)
−0.192496 + 0.981298i \(0.561658\pi\)
\(522\) 0 0
\(523\) 7298.28 0.610194 0.305097 0.952321i \(-0.401311\pi\)
0.305097 + 0.952321i \(0.401311\pi\)
\(524\) −11708.8 −0.976148
\(525\) 0 0
\(526\) 765.476 0.0634531
\(527\) 9908.02 0.818975
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) 1215.68 0.0996337
\(531\) 0 0
\(532\) 224.494 0.0182952
\(533\) 130.398 0.0105970
\(534\) 0 0
\(535\) −7574.56 −0.612106
\(536\) 194.317 0.0156590
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) 4773.69 0.376232
\(545\) 8743.80 0.687235
\(546\) 0 0
\(547\) −19510.9 −1.52509 −0.762547 0.646932i \(-0.776052\pi\)
−0.762547 + 0.646932i \(0.776052\pi\)
\(548\) 17751.0 1.38373
\(549\) 0 0
\(550\) 245.320 0.0190191
\(551\) −16.9623 −0.00131147
\(552\) 0 0
\(553\) 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 \(0.333999\pi\)
\(558\) 0 0
\(559\) 656.592 0.0496796
\(560\) 4142.93 0.312626
\(561\) 0 0
\(562\) 1012.85 0.0760226
\(563\) 4086.19 0.305883 0.152942 0.988235i \(-0.451125\pi\)
0.152942 + 0.988235i \(0.451125\pi\)
\(564\) 0 0
\(565\) −10131.2 −0.754374
\(566\) 325.546 0.0241762
\(567\) 0 0
\(568\) 4722.14 0.348832
\(569\) 5021.20 0.369946 0.184973 0.982744i \(-0.440780\pi\)
0.184973 + 0.982744i \(0.440780\pi\)
\(570\) 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
\(573\) 0 0
\(574\) −238.719 −0.0173588
\(575\) 575.000 0.0417029
\(576\) 0 0
\(577\) −19548.4 −1.41042 −0.705210 0.708998i \(-0.749147\pi\)
−0.705210 + 0.708998i \(0.749147\pi\)
\(578\) 376.528 0.0270960
\(579\) 0 0
\(580\) −319.865 −0.0228994
\(581\) −1923.38 −0.137341
\(582\) 0 0
\(583\) 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 \(0.289343\pi\)
\(588\) 0 0
\(589\) 326.177 0.0228182
\(590\) 186.688 0.0130268
\(591\) 0 0
\(592\) 18195.7 1.26324
\(593\) −513.405 −0.0355531 −0.0177766 0.999842i \(-0.505659\pi\)
−0.0177766 + 0.999842i \(0.505659\pi\)
\(594\) 0 0
\(595\) −4351.25 −0.299805
\(596\) −4305.10 −0.295879
\(597\) 0 0
\(598\) −28.4092 −0.00194271
\(599\) −13706.8 −0.934964 −0.467482 0.884003i \(-0.654839\pi\)
−0.467482 + 0.884003i \(0.654839\pi\)
\(600\) 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
\(603\) 0 0
\(604\) −2630.71 −0.177222
\(605\) −3719.11 −0.249923
\(606\) 0 0
\(607\) 16304.7 1.09026 0.545129 0.838352i \(-0.316481\pi\)
0.545129 + 0.838352i \(0.316481\pi\)
\(608\) 157.152 0.0104825
\(609\) 0 0
\(610\) −1078.47 −0.0715837
\(611\) −753.683 −0.0499030
\(612\) 0 0
\(613\) 7754.74 0.510948 0.255474 0.966816i \(-0.417769\pi\)
0.255474 + 0.966816i \(0.417769\pi\)
\(614\) −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 \(0.483638\pi\)
\(618\) 0 0
\(619\) −9160.25 −0.594800 −0.297400 0.954753i \(-0.596120\pi\)
−0.297400 + 0.954753i \(0.596120\pi\)
\(620\) 6150.85 0.398426
\(621\) 0 0
\(622\) 1149.62 0.0741083
\(623\) −11852.2 −0.762196
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −64.8465 −0.00414024
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) −1348.82 −0.0844930
\(635\) −10632.5 −0.664467
\(636\) 0 0
\(637\) −466.272 −0.0290021
\(638\) 80.1115 0.00497123
\(639\) 0 0
\(640\) 3936.86 0.243153
\(641\) 27074.5 1.66830 0.834148 0.551541i \(-0.185960\pi\)
0.834148 + 0.551541i \(0.185960\pi\)
\(642\) 0 0
\(643\) −4463.82 −0.273773 −0.136886 0.990587i \(-0.543710\pi\)
−0.136886 + 0.990587i \(0.543710\pi\)
\(644\) −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 \(0.383752\pi\)
\(648\) 0 0
\(649\) 2234.20 0.135131
\(650\) −30.8796 −0.00186338
\(651\) 0 0
\(652\) 21687.2 1.30266
\(653\) 1236.64 0.0741094 0.0370547 0.999313i \(-0.488202\pi\)
0.0370547 + 0.999313i \(0.488202\pi\)
\(654\) 0 0
\(655\) 7471.15 0.445682
\(656\) 2568.98 0.152899
\(657\) 0 0
\(658\) 1379.76 0.0817456
\(659\) −23646.9 −1.39780 −0.698901 0.715218i \(-0.746327\pi\)
−0.698901 + 0.715218i \(0.746327\pi\)
\(660\) 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
\(663\) 0 0
\(664\) −894.526 −0.0522806
\(665\) −143.245 −0.00835311
\(666\) 0 0
\(667\) 187.771 0.0109003
\(668\) 2216.55 0.128385
\(669\) 0 0
\(670\) −61.3530 −0.00353772
\(671\) −12906.7 −0.742558
\(672\) 0 0
\(673\) 13941.8 0.798540 0.399270 0.916833i \(-0.369264\pi\)
0.399270 + 0.916833i \(0.369264\pi\)
\(674\) 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 \(0.376090\pi\)
\(678\) 0 0
\(679\) −12788.8 −0.722812
\(680\) −2023.68 −0.114124
\(681\) 0 0
\(682\) −1540.51 −0.0864943
\(683\) −15659.3 −0.877288 −0.438644 0.898661i \(-0.644541\pi\)
−0.438644 + 0.898661i \(0.644541\pi\)
\(684\) 0 0
\(685\) −11326.6 −0.631775
\(686\) 2768.87 0.154105
\(687\) 0 0
\(688\) 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
\(693\) 0 0
\(694\) 2729.62 0.149301
\(695\) −14593.3 −0.796484
\(696\) 0 0
\(697\) −2698.15 −0.146628
\(698\) 4119.99 0.223415
\(699\) 0 0
\(700\) −2701.24 −0.145853
\(701\) −21140.9 −1.13906 −0.569530 0.821971i \(-0.692875\pi\)
−0.569530 + 0.821971i \(0.692875\pi\)
\(702\) 0 0
\(703\) −629.131 −0.0337527
\(704\) 10906.7 0.583894
\(705\) 0 0
\(706\) −1033.80 −0.0551101
\(707\) −23625.0 −1.25673
\(708\) 0 0
\(709\) −15917.4 −0.843144 −0.421572 0.906795i \(-0.638522\pi\)
−0.421572 + 0.906795i \(0.638522\pi\)
\(710\) −1490.95 −0.0788089
\(711\) 0 0
\(712\) −5512.22 −0.290139
\(713\) −3610.76 −0.189655
\(714\) 0 0
\(715\) −369.553 −0.0193294
\(716\) 855.221 0.0446384
\(717\) 0 0
\(718\) −2704.09 −0.140551
\(719\) −3323.34 −0.172378 −0.0861889 0.996279i \(-0.527469\pi\)
−0.0861889 + 0.996279i \(0.527469\pi\)
\(720\) 0 0
\(721\) −12830.7 −0.662748
\(722\) 2775.85 0.143084
\(723\) 0 0
\(724\) −11572.6 −0.594051
\(725\) 204.099 0.0104552
\(726\) 0 0
\(727\) −9877.52 −0.503902 −0.251951 0.967740i \(-0.581072\pi\)
−0.251951 + 0.967740i \(0.581072\pi\)
\(728\) 269.714 0.0137312
\(729\) 0 0
\(730\) −708.545 −0.0359239
\(731\) −13586.0 −0.687407
\(732\) 0 0
\(733\) 28951.5 1.45886 0.729432 0.684053i \(-0.239784\pi\)
0.729432 + 0.684053i \(0.239784\pi\)
\(734\) −4747.24 −0.238725
\(735\) 0 0
\(736\) −1739.66 −0.0871262
\(737\) −734.246 −0.0366978
\(738\) 0 0
\(739\) −31009.5 −1.54358 −0.771788 0.635880i \(-0.780637\pi\)
−0.771788 + 0.635880i \(0.780637\pi\)
\(740\) −11863.8 −0.589353
\(741\) 0 0
\(742\) 3352.57 0.165871
\(743\) 13761.0 0.679465 0.339733 0.940522i \(-0.389663\pi\)
0.339733 + 0.940522i \(0.389663\pi\)
\(744\) 0 0
\(745\) 2747.00 0.135090
\(746\) −3268.29 −0.160403
\(747\) 0 0
\(748\) −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
\(753\) 0 0
\(754\) −10.0840 −0.000487052 0
\(755\) 1678.60 0.0809148
\(756\) 0 0
\(757\) 26139.9 1.25505 0.627524 0.778597i \(-0.284068\pi\)
0.627524 + 0.778597i \(0.284068\pi\)
\(758\) 2710.42 0.129877
\(759\) 0 0
\(760\) −66.6205 −0.00317971
\(761\) 24004.0 1.14342 0.571712 0.820454i \(-0.306279\pi\)
0.571712 + 0.820454i \(0.306279\pi\)
\(762\) 0 0
\(763\) 24113.3 1.14412
\(764\) 15924.0 0.754072
\(765\) 0 0
\(766\) −1013.40 −0.0478011
\(767\) −281.229 −0.0132393
\(768\) 0 0
\(769\) −33733.4 −1.58187 −0.790934 0.611902i \(-0.790405\pi\)
−0.790934 + 0.611902i \(0.790405\pi\)
\(770\) 676.537 0.0316632
\(771\) 0 0
\(772\) −30432.2 −1.41876
\(773\) −40247.1 −1.87269 −0.936344 0.351083i \(-0.885814\pi\)
−0.936344 + 0.351083i \(0.885814\pi\)
\(774\) 0 0
\(775\) −3924.74 −0.181911
\(776\) −5947.81 −0.275147
\(777\) 0 0
\(778\) 2222.28 0.102407
\(779\) −88.8246 −0.00408533
\(780\) 0 0
\(781\) −17843.0 −0.817508
\(782\) 587.832 0.0268808
\(783\) 0 0
\(784\) −9186.02 −0.418459
\(785\) −7968.45 −0.362301
\(786\) 0 0
\(787\) −16327.3 −0.739522 −0.369761 0.929127i \(-0.620560\pi\)
−0.369761 + 0.929127i \(0.620560\pi\)
\(788\) 28057.9 1.26843
\(789\) 0 0
\(790\) −610.565 −0.0274974
\(791\) −27939.4 −1.25589
\(792\) 0 0
\(793\) 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 \(0.273758\pi\)
\(798\) 0 0
\(799\) 15594.9 0.690498
\(800\) −1890.94 −0.0835685
\(801\) 0 0
\(802\) 5866.12 0.258279
\(803\) −8479.56 −0.372649
\(804\) 0 0
\(805\) 1585.72 0.0694275
\(806\) 193.911 0.00847420
\(807\) 0 0
\(808\) −10987.5 −0.478389
\(809\) 2426.36 0.105447 0.0527234 0.998609i \(-0.483210\pi\)
0.0527234 + 0.998609i \(0.483210\pi\)
\(810\) 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
\(813\) 0 0
\(814\) 2971.34 0.127943
\(815\) −13838.2 −0.594760
\(816\) 0 0
\(817\) −447.257 −0.0191524
\(818\) −2698.97 −0.115363
\(819\) 0 0
\(820\) −1675.00 −0.0713336
\(821\) 6679.93 0.283960 0.141980 0.989870i \(-0.454653\pi\)
0.141980 + 0.989870i \(0.454653\pi\)
\(822\) 0 0
\(823\) 29299.3 1.24096 0.620480 0.784222i \(-0.286938\pi\)
0.620480 + 0.784222i \(0.286938\pi\)
\(824\) −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 \(0.815628\pi\)
\(828\) 0 0
\(829\) −17854.1 −0.748007 −0.374004 0.927427i \(-0.622015\pi\)
−0.374004 + 0.927427i \(0.622015\pi\)
\(830\) 282.434 0.0118114
\(831\) 0 0
\(832\) −1372.87 −0.0572065
\(833\) 9647.91 0.401297
\(834\) 0 0
\(835\) −1414.34 −0.0586169
\(836\) −394.514 −0.0163212
\(837\) 0 0
\(838\) −3416.80 −0.140849
\(839\) 6656.92 0.273924 0.136962 0.990576i \(-0.456266\pi\)
0.136962 + 0.990576i \(0.456266\pi\)
\(840\) 0 0
\(841\) −24322.3 −0.997267
\(842\) −5626.14 −0.230273
\(843\) 0 0
\(844\) −22754.2 −0.928000
\(845\) −10938.5 −0.445320
\(846\) 0 0
\(847\) −10256.4 −0.416075
\(848\) −36078.7 −1.46102
\(849\) 0 0
\(850\) 638.948 0.0257832
\(851\) 6964.43 0.280538
\(852\) 0 0
\(853\) −30008.7 −1.20455 −0.602273 0.798290i \(-0.705738\pi\)
−0.602273 + 0.798290i \(0.705738\pi\)
\(854\) −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 \(0.660788\pi\)
\(858\) 0 0
\(859\) 30635.5 1.21685 0.608423 0.793613i \(-0.291802\pi\)
0.608423 + 0.793613i \(0.291802\pi\)
\(860\) −8434.10 −0.334419
\(861\) 0 0
\(862\) −4297.22 −0.169796
\(863\) 26572.1 1.04812 0.524058 0.851683i \(-0.324418\pi\)
0.524058 + 0.851683i \(0.324418\pi\)
\(864\) 0 0
\(865\) 11658.1 0.458253
\(866\) 3065.43 0.120286
\(867\) 0 0
\(868\) 16962.6 0.663305
\(869\) −7306.97 −0.285238
\(870\) 0 0
\(871\) 92.4227 0.00359543
\(872\) 11214.6 0.435522
\(873\) 0 0
\(874\) 19.3517 0.000748950 0
\(875\) 1723.60 0.0665925
\(876\) 0 0
\(877\) −37158.4 −1.43073 −0.715366 0.698750i \(-0.753740\pi\)
−0.715366 + 0.698750i \(0.753740\pi\)
\(878\) 4776.43 0.183595
\(879\) 0 0
\(880\) −7280.57 −0.278895
\(881\) 3353.12 0.128229 0.0641143 0.997943i \(-0.479578\pi\)
0.0641143 + 0.997943i \(0.479578\pi\)
\(882\) 0 0
\(883\) 16292.5 0.620936 0.310468 0.950584i \(-0.399514\pi\)
0.310468 + 0.950584i \(0.399514\pi\)
\(884\) 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 \(0.464078\pi\)
\(888\) 0 0
\(889\) −29321.9 −1.10621
\(890\) 1740.41 0.0655489
\(891\) 0 0
\(892\) −3563.50 −0.133761
\(893\) 513.393 0.0192386
\(894\) 0 0
\(895\) −545.700 −0.0203807
\(896\) 10856.9 0.404804
\(897\) 0 0
\(898\) 3589.03 0.133371
\(899\) −1281.66 −0.0475480
\(900\) 0 0
\(901\) 37892.8 1.40110
\(902\) 419.512 0.0154858
\(903\) 0 0
\(904\) −12994.0 −0.478070
\(905\) 7384.26 0.271228
\(906\) 0 0
\(907\) −44105.2 −1.61465 −0.807326 0.590106i \(-0.799086\pi\)
−0.807326 + 0.590106i \(0.799086\pi\)
\(908\) −16481.0 −0.602360
\(909\) 0 0
\(910\) −85.1586 −0.00310218
\(911\) −4385.18 −0.159481 −0.0797407 0.996816i \(-0.525409\pi\)
−0.0797407 + 0.996816i \(0.525409\pi\)
\(912\) 0 0
\(913\) 3380.05 0.122523
\(914\) −2100.60 −0.0760194
\(915\) 0 0
\(916\) 36421.5 1.31376
\(917\) 20603.7 0.741978
\(918\) 0 0
\(919\) 30027.0 1.07780 0.538901 0.842369i \(-0.318840\pi\)
0.538901 + 0.842369i \(0.318840\pi\)
\(920\) 737.484 0.0264284
\(921\) 0 0
\(922\) −6810.03 −0.243250
\(923\) 2245.98 0.0800946
\(924\) 0 0
\(925\) 7570.03 0.269082
\(926\) −2571.99 −0.0912751
\(927\) 0 0
\(928\) −617.503 −0.0218432
\(929\) 5457.52 0.192740 0.0963700 0.995346i \(-0.469277\pi\)
0.0963700 + 0.995346i \(0.469277\pi\)
\(930\) 0 0
\(931\) 317.614 0.0111809
\(932\) 1027.44 0.0361104
\(933\) 0 0
\(934\) 428.046 0.0149958
\(935\) 7646.65 0.267457
\(936\) 0 0
\(937\) 3039.15 0.105960 0.0529802 0.998596i \(-0.483128\pi\)
0.0529802 + 0.998596i \(0.483128\pi\)
\(938\) −169.197 −0.00588964
\(939\) 0 0
\(940\) 9681.25 0.335923
\(941\) −25791.0 −0.893479 −0.446740 0.894664i \(-0.647415\pi\)
−0.446740 + 0.894664i \(0.647415\pi\)
\(942\) 0 0
\(943\) 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 \(0.601887\pi\)
\(948\) 0 0
\(949\) 1067.36 0.0365099
\(950\) 21.0345 0.000718368 0
\(951\) 0 0
\(952\) −5580.83 −0.189995
\(953\) −12658.7 −0.430278 −0.215139 0.976583i \(-0.569021\pi\)
−0.215139 + 0.976583i \(0.569021\pi\)
\(954\) 0 0
\(955\) −10160.8 −0.344289
\(956\) 27173.5 0.919302
\(957\) 0 0
\(958\) −4105.55 −0.138460
\(959\) −31236.0 −1.05179
\(960\) 0 0
\(961\) −5145.31 −0.172714
\(962\) −374.015 −0.0125351
\(963\) 0 0
\(964\) −45597.0 −1.52342
\(965\) 19418.2 0.647765
\(966\) 0 0
\(967\) 50470.3 1.67840 0.839201 0.543822i \(-0.183023\pi\)
0.839201 + 0.543822i \(0.183023\pi\)
\(968\) −4770.06 −0.158384
\(969\) 0 0
\(970\) 1877.94 0.0621618
\(971\) −30778.2 −1.01722 −0.508610 0.860997i \(-0.669840\pi\)
−0.508610 + 0.860997i \(0.669840\pi\)
\(972\) 0 0
\(973\) −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 \(0.373856\pi\)
\(978\) 0 0
\(979\) 20828.4 0.679958
\(980\) 5989.38 0.195228
\(981\) 0 0
\(982\) −8687.21 −0.282301
\(983\) 44798.3 1.45355 0.726777 0.686874i \(-0.241018\pi\)
0.726777 + 0.686874i \(0.241018\pi\)
\(984\) 0 0
\(985\) −17903.2 −0.579131
\(986\) 208.654 0.00673924
\(987\) 0 0
\(988\) 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
\(993\) 0 0
\(994\) −4111.69 −0.131202
\(995\) −14155.9 −0.451026
\(996\) 0 0
\(997\) 36538.1 1.16065 0.580327 0.814383i \(-0.302925\pi\)
0.580327 + 0.814383i \(0.302925\pi\)
\(998\) −3926.83 −0.124551
\(999\) 0 0
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 1035.4.a.k.1.3 5
3.2 odd 2 115.4.a.e.1.3 5
12.11 even 2 1840.4.a.n.1.5 5
15.2 even 4 575.4.b.i.24.6 10
15.8 even 4 575.4.b.i.24.5 10
15.14 odd 2 575.4.a.j.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.a.e.1.3 5 3.2 odd 2
575.4.a.j.1.3 5 15.14 odd 2
575.4.b.i.24.5 10 15.8 even 4
575.4.b.i.24.6 10 15.2 even 4
1035.4.a.k.1.3 5 1.1 even 1 trivial
1840.4.a.n.1.5 5 12.11 even 2