Properties

Label 2254.4.a.x.1.10
Level $2254$
Weight $4$
Character 2254.1
Self dual yes
Analytic conductor $132.990$
Analytic rank $0$
Dimension $11$
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] = [2254,4,Mod(1,2254)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2254, 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("2254.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2254.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: \(132.990305153\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 5 x^{10} - 165 x^{9} + 798 x^{8} + 8769 x^{7} - 38472 x^{6} - 184213 x^{5} + 644009 x^{4} + \cdots + 2848203 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 322)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-6.47210\) of defining polynomial
Character \(\chi\) \(=\) 2254.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +7.47210 q^{3} +4.00000 q^{4} +5.30939 q^{5} +14.9442 q^{6} +8.00000 q^{8} +28.8323 q^{9} +10.6188 q^{10} +15.0723 q^{11} +29.8884 q^{12} -19.5834 q^{13} +39.6723 q^{15} +16.0000 q^{16} +114.919 q^{17} +57.6646 q^{18} -51.8349 q^{19} +21.2376 q^{20} +30.1447 q^{22} -23.0000 q^{23} +59.7768 q^{24} -96.8104 q^{25} -39.1667 q^{26} +13.6912 q^{27} +227.585 q^{29} +79.3446 q^{30} +178.024 q^{31} +32.0000 q^{32} +112.622 q^{33} +229.838 q^{34} +115.329 q^{36} +20.7398 q^{37} -103.670 q^{38} -146.329 q^{39} +42.4751 q^{40} +107.492 q^{41} +138.795 q^{43} +60.2894 q^{44} +153.082 q^{45} -46.0000 q^{46} -21.4507 q^{47} +119.554 q^{48} -193.621 q^{50} +858.687 q^{51} -78.3334 q^{52} +429.203 q^{53} +27.3825 q^{54} +80.0249 q^{55} -387.316 q^{57} +455.170 q^{58} -128.564 q^{59} +158.689 q^{60} -225.931 q^{61} +356.049 q^{62} +64.0000 q^{64} -103.976 q^{65} +225.244 q^{66} +478.716 q^{67} +459.676 q^{68} -171.858 q^{69} +652.010 q^{71} +230.659 q^{72} +516.418 q^{73} +41.4796 q^{74} -723.377 q^{75} -207.340 q^{76} -292.658 q^{78} -349.397 q^{79} +84.9502 q^{80} -676.170 q^{81} +214.984 q^{82} -373.014 q^{83} +610.150 q^{85} +277.589 q^{86} +1700.54 q^{87} +120.579 q^{88} -896.694 q^{89} +306.164 q^{90} -92.0000 q^{92} +1330.22 q^{93} -42.9014 q^{94} -275.211 q^{95} +239.107 q^{96} +1294.92 q^{97} +434.570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 22 q^{2} + 6 q^{3} + 44 q^{4} + 27 q^{5} + 12 q^{6} + 88 q^{8} + 59 q^{9} + 54 q^{10} + 56 q^{11} + 24 q^{12} + 103 q^{13} + 62 q^{15} + 176 q^{16} + 157 q^{17} + 118 q^{18} + 266 q^{19} + 108 q^{20}+ \cdots + 101 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 7.47210 1.43801 0.719003 0.695007i \(-0.244599\pi\)
0.719003 + 0.695007i \(0.244599\pi\)
\(4\) 4.00000 0.500000
\(5\) 5.30939 0.474886 0.237443 0.971401i \(-0.423691\pi\)
0.237443 + 0.971401i \(0.423691\pi\)
\(6\) 14.9442 1.01682
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 28.8323 1.06786
\(10\) 10.6188 0.335795
\(11\) 15.0723 0.413135 0.206567 0.978432i \(-0.433771\pi\)
0.206567 + 0.978432i \(0.433771\pi\)
\(12\) 29.8884 0.719003
\(13\) −19.5834 −0.417804 −0.208902 0.977937i \(-0.566989\pi\)
−0.208902 + 0.977937i \(0.566989\pi\)
\(14\) 0 0
\(15\) 39.6723 0.682889
\(16\) 16.0000 0.250000
\(17\) 114.919 1.63953 0.819763 0.572702i \(-0.194105\pi\)
0.819763 + 0.572702i \(0.194105\pi\)
\(18\) 57.6646 0.755093
\(19\) −51.8349 −0.625881 −0.312940 0.949773i \(-0.601314\pi\)
−0.312940 + 0.949773i \(0.601314\pi\)
\(20\) 21.2376 0.237443
\(21\) 0 0
\(22\) 30.1447 0.292130
\(23\) −23.0000 −0.208514
\(24\) 59.7768 0.508412
\(25\) −96.8104 −0.774483
\(26\) −39.1667 −0.295432
\(27\) 13.6912 0.0975881
\(28\) 0 0
\(29\) 227.585 1.45729 0.728646 0.684890i \(-0.240150\pi\)
0.728646 + 0.684890i \(0.240150\pi\)
\(30\) 79.3446 0.482876
\(31\) 178.024 1.03142 0.515712 0.856762i \(-0.327528\pi\)
0.515712 + 0.856762i \(0.327528\pi\)
\(32\) 32.0000 0.176777
\(33\) 112.622 0.594090
\(34\) 229.838 1.15932
\(35\) 0 0
\(36\) 115.329 0.533932
\(37\) 20.7398 0.0921513 0.0460756 0.998938i \(-0.485328\pi\)
0.0460756 + 0.998938i \(0.485328\pi\)
\(38\) −103.670 −0.442565
\(39\) −146.329 −0.600804
\(40\) 42.4751 0.167898
\(41\) 107.492 0.409449 0.204724 0.978820i \(-0.434370\pi\)
0.204724 + 0.978820i \(0.434370\pi\)
\(42\) 0 0
\(43\) 138.795 0.492232 0.246116 0.969240i \(-0.420846\pi\)
0.246116 + 0.969240i \(0.420846\pi\)
\(44\) 60.2894 0.206567
\(45\) 153.082 0.507113
\(46\) −46.0000 −0.147442
\(47\) −21.4507 −0.0665725 −0.0332863 0.999446i \(-0.510597\pi\)
−0.0332863 + 0.999446i \(0.510597\pi\)
\(48\) 119.554 0.359502
\(49\) 0 0
\(50\) −193.621 −0.547642
\(51\) 858.687 2.35765
\(52\) −78.3334 −0.208902
\(53\) 429.203 1.11237 0.556185 0.831059i \(-0.312265\pi\)
0.556185 + 0.831059i \(0.312265\pi\)
\(54\) 27.3825 0.0690052
\(55\) 80.0249 0.196192
\(56\) 0 0
\(57\) −387.316 −0.900021
\(58\) 455.170 1.03046
\(59\) −128.564 −0.283689 −0.141844 0.989889i \(-0.545303\pi\)
−0.141844 + 0.989889i \(0.545303\pi\)
\(60\) 158.689 0.341445
\(61\) −225.931 −0.474222 −0.237111 0.971483i \(-0.576200\pi\)
−0.237111 + 0.971483i \(0.576200\pi\)
\(62\) 356.049 0.729326
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −103.976 −0.198409
\(66\) 225.244 0.420085
\(67\) 478.716 0.872902 0.436451 0.899728i \(-0.356235\pi\)
0.436451 + 0.899728i \(0.356235\pi\)
\(68\) 459.676 0.819763
\(69\) −171.858 −0.299845
\(70\) 0 0
\(71\) 652.010 1.08985 0.544925 0.838485i \(-0.316558\pi\)
0.544925 + 0.838485i \(0.316558\pi\)
\(72\) 230.659 0.377547
\(73\) 516.418 0.827975 0.413987 0.910283i \(-0.364136\pi\)
0.413987 + 0.910283i \(0.364136\pi\)
\(74\) 41.4796 0.0651608
\(75\) −723.377 −1.11371
\(76\) −207.340 −0.312940
\(77\) 0 0
\(78\) −292.658 −0.424833
\(79\) −349.397 −0.497597 −0.248799 0.968555i \(-0.580036\pi\)
−0.248799 + 0.968555i \(0.580036\pi\)
\(80\) 84.9502 0.118722
\(81\) −676.170 −0.927531
\(82\) 214.984 0.289524
\(83\) −373.014 −0.493297 −0.246649 0.969105i \(-0.579329\pi\)
−0.246649 + 0.969105i \(0.579329\pi\)
\(84\) 0 0
\(85\) 610.150 0.778588
\(86\) 277.589 0.348061
\(87\) 1700.54 2.09560
\(88\) 120.579 0.146065
\(89\) −896.694 −1.06797 −0.533985 0.845494i \(-0.679306\pi\)
−0.533985 + 0.845494i \(0.679306\pi\)
\(90\) 306.164 0.358583
\(91\) 0 0
\(92\) −92.0000 −0.104257
\(93\) 1330.22 1.48319
\(94\) −42.9014 −0.0470739
\(95\) −275.211 −0.297222
\(96\) 239.107 0.254206
\(97\) 1294.92 1.35546 0.677729 0.735312i \(-0.262964\pi\)
0.677729 + 0.735312i \(0.262964\pi\)
\(98\) 0 0
\(99\) 434.570 0.441171
\(100\) −387.242 −0.387242
\(101\) −309.230 −0.304649 −0.152325 0.988331i \(-0.548676\pi\)
−0.152325 + 0.988331i \(0.548676\pi\)
\(102\) 1717.37 1.66711
\(103\) −617.628 −0.590842 −0.295421 0.955367i \(-0.595460\pi\)
−0.295421 + 0.955367i \(0.595460\pi\)
\(104\) −156.667 −0.147716
\(105\) 0 0
\(106\) 858.407 0.786564
\(107\) −1225.20 −1.10696 −0.553481 0.832862i \(-0.686701\pi\)
−0.553481 + 0.832862i \(0.686701\pi\)
\(108\) 54.7649 0.0487941
\(109\) 157.245 0.138177 0.0690886 0.997611i \(-0.477991\pi\)
0.0690886 + 0.997611i \(0.477991\pi\)
\(110\) 160.050 0.138729
\(111\) 154.970 0.132514
\(112\) 0 0
\(113\) −1226.97 −1.02145 −0.510723 0.859745i \(-0.670622\pi\)
−0.510723 + 0.859745i \(0.670622\pi\)
\(114\) −774.631 −0.636411
\(115\) −122.116 −0.0990206
\(116\) 910.340 0.728646
\(117\) −564.634 −0.446157
\(118\) −257.128 −0.200598
\(119\) 0 0
\(120\) 317.378 0.241438
\(121\) −1103.82 −0.829320
\(122\) −451.862 −0.335325
\(123\) 803.190 0.588790
\(124\) 712.097 0.515712
\(125\) −1177.68 −0.842677
\(126\) 0 0
\(127\) 1229.19 0.858840 0.429420 0.903105i \(-0.358718\pi\)
0.429420 + 0.903105i \(0.358718\pi\)
\(128\) 128.000 0.0883883
\(129\) 1037.09 0.707834
\(130\) −207.951 −0.140296
\(131\) 2420.93 1.61464 0.807321 0.590113i \(-0.200917\pi\)
0.807321 + 0.590113i \(0.200917\pi\)
\(132\) 450.488 0.297045
\(133\) 0 0
\(134\) 957.432 0.617235
\(135\) 72.6921 0.0463432
\(136\) 919.352 0.579660
\(137\) 3202.71 1.99727 0.998635 0.0522373i \(-0.0166352\pi\)
0.998635 + 0.0522373i \(0.0166352\pi\)
\(138\) −343.717 −0.212023
\(139\) 1710.35 1.04367 0.521833 0.853048i \(-0.325248\pi\)
0.521833 + 0.853048i \(0.325248\pi\)
\(140\) 0 0
\(141\) −160.282 −0.0957317
\(142\) 1304.02 0.770641
\(143\) −295.167 −0.172609
\(144\) 461.317 0.266966
\(145\) 1208.34 0.692048
\(146\) 1032.84 0.585466
\(147\) 0 0
\(148\) 82.9591 0.0460756
\(149\) −2647.44 −1.45561 −0.727807 0.685782i \(-0.759461\pi\)
−0.727807 + 0.685782i \(0.759461\pi\)
\(150\) −1446.75 −0.787513
\(151\) −1010.81 −0.544761 −0.272381 0.962190i \(-0.587811\pi\)
−0.272381 + 0.962190i \(0.587811\pi\)
\(152\) −414.679 −0.221282
\(153\) 3313.38 1.75079
\(154\) 0 0
\(155\) 945.200 0.489809
\(156\) −585.315 −0.300402
\(157\) −76.7891 −0.0390347 −0.0195173 0.999810i \(-0.506213\pi\)
−0.0195173 + 0.999810i \(0.506213\pi\)
\(158\) −698.793 −0.351854
\(159\) 3207.05 1.59960
\(160\) 169.900 0.0839488
\(161\) 0 0
\(162\) −1352.34 −0.655864
\(163\) 2149.22 1.03276 0.516379 0.856360i \(-0.327280\pi\)
0.516379 + 0.856360i \(0.327280\pi\)
\(164\) 429.967 0.204724
\(165\) 597.954 0.282125
\(166\) −746.029 −0.348814
\(167\) 2071.34 0.959791 0.479896 0.877326i \(-0.340675\pi\)
0.479896 + 0.877326i \(0.340675\pi\)
\(168\) 0 0
\(169\) −1813.49 −0.825440
\(170\) 1220.30 0.550545
\(171\) −1494.52 −0.668355
\(172\) 555.179 0.246116
\(173\) −3121.85 −1.37197 −0.685983 0.727618i \(-0.740627\pi\)
−0.685983 + 0.727618i \(0.740627\pi\)
\(174\) 3401.08 1.48181
\(175\) 0 0
\(176\) 241.157 0.103284
\(177\) −960.645 −0.407946
\(178\) −1793.39 −0.755169
\(179\) −3069.29 −1.28162 −0.640808 0.767701i \(-0.721401\pi\)
−0.640808 + 0.767701i \(0.721401\pi\)
\(180\) 612.328 0.253557
\(181\) −1108.70 −0.455300 −0.227650 0.973743i \(-0.573104\pi\)
−0.227650 + 0.973743i \(0.573104\pi\)
\(182\) 0 0
\(183\) −1688.18 −0.681934
\(184\) −184.000 −0.0737210
\(185\) 110.116 0.0437614
\(186\) 2660.43 1.04878
\(187\) 1732.10 0.677345
\(188\) −85.8028 −0.0332863
\(189\) 0 0
\(190\) −550.423 −0.210168
\(191\) −3180.62 −1.20493 −0.602465 0.798146i \(-0.705815\pi\)
−0.602465 + 0.798146i \(0.705815\pi\)
\(192\) 478.215 0.179751
\(193\) −812.325 −0.302966 −0.151483 0.988460i \(-0.548405\pi\)
−0.151483 + 0.988460i \(0.548405\pi\)
\(194\) 2589.84 0.958454
\(195\) −776.917 −0.285314
\(196\) 0 0
\(197\) −3772.40 −1.36433 −0.682164 0.731199i \(-0.738961\pi\)
−0.682164 + 0.731199i \(0.738961\pi\)
\(198\) 869.141 0.311955
\(199\) 1524.28 0.542980 0.271490 0.962441i \(-0.412484\pi\)
0.271490 + 0.962441i \(0.412484\pi\)
\(200\) −774.483 −0.273821
\(201\) 3577.01 1.25524
\(202\) −618.460 −0.215419
\(203\) 0 0
\(204\) 3434.75 1.17883
\(205\) 570.716 0.194441
\(206\) −1235.26 −0.417788
\(207\) −663.143 −0.222665
\(208\) −313.334 −0.104451
\(209\) −781.273 −0.258573
\(210\) 0 0
\(211\) 910.563 0.297089 0.148544 0.988906i \(-0.452541\pi\)
0.148544 + 0.988906i \(0.452541\pi\)
\(212\) 1716.81 0.556185
\(213\) 4871.89 1.56721
\(214\) −2450.41 −0.782740
\(215\) 736.915 0.233754
\(216\) 109.530 0.0345026
\(217\) 0 0
\(218\) 314.489 0.0977060
\(219\) 3858.73 1.19063
\(220\) 320.100 0.0980959
\(221\) −2250.50 −0.685000
\(222\) 309.939 0.0937017
\(223\) −1289.30 −0.387166 −0.193583 0.981084i \(-0.562011\pi\)
−0.193583 + 0.981084i \(0.562011\pi\)
\(224\) 0 0
\(225\) −2791.27 −0.827042
\(226\) −2453.94 −0.722272
\(227\) −1413.94 −0.413419 −0.206710 0.978402i \(-0.566276\pi\)
−0.206710 + 0.978402i \(0.566276\pi\)
\(228\) −1549.26 −0.450010
\(229\) 799.165 0.230613 0.115306 0.993330i \(-0.463215\pi\)
0.115306 + 0.993330i \(0.463215\pi\)
\(230\) −244.232 −0.0700181
\(231\) 0 0
\(232\) 1820.68 0.515231
\(233\) 1554.41 0.437050 0.218525 0.975831i \(-0.429875\pi\)
0.218525 + 0.975831i \(0.429875\pi\)
\(234\) −1129.27 −0.315481
\(235\) −113.890 −0.0316144
\(236\) −514.257 −0.141844
\(237\) −2610.73 −0.715548
\(238\) 0 0
\(239\) −6967.81 −1.88582 −0.942908 0.333052i \(-0.891922\pi\)
−0.942908 + 0.333052i \(0.891922\pi\)
\(240\) 634.757 0.170722
\(241\) 5058.24 1.35199 0.675996 0.736905i \(-0.263714\pi\)
0.675996 + 0.736905i \(0.263714\pi\)
\(242\) −2207.65 −0.586418
\(243\) −5422.08 −1.43138
\(244\) −903.725 −0.237111
\(245\) 0 0
\(246\) 1606.38 0.416337
\(247\) 1015.10 0.261495
\(248\) 1424.19 0.364663
\(249\) −2787.20 −0.709365
\(250\) −2355.35 −0.595863
\(251\) 3363.38 0.845796 0.422898 0.906177i \(-0.361013\pi\)
0.422898 + 0.906177i \(0.361013\pi\)
\(252\) 0 0
\(253\) −346.664 −0.0861445
\(254\) 2458.37 0.607292
\(255\) 4559.10 1.11962
\(256\) 256.000 0.0625000
\(257\) 7020.29 1.70394 0.851972 0.523588i \(-0.175407\pi\)
0.851972 + 0.523588i \(0.175407\pi\)
\(258\) 2074.18 0.500514
\(259\) 0 0
\(260\) −415.903 −0.0992046
\(261\) 6561.80 1.55619
\(262\) 4841.87 1.14172
\(263\) −1118.57 −0.262258 −0.131129 0.991365i \(-0.541860\pi\)
−0.131129 + 0.991365i \(0.541860\pi\)
\(264\) 900.976 0.210043
\(265\) 2278.81 0.528249
\(266\) 0 0
\(267\) −6700.19 −1.53575
\(268\) 1914.86 0.436451
\(269\) 2785.87 0.631439 0.315720 0.948853i \(-0.397754\pi\)
0.315720 + 0.948853i \(0.397754\pi\)
\(270\) 145.384 0.0327696
\(271\) 2689.54 0.602870 0.301435 0.953487i \(-0.402534\pi\)
0.301435 + 0.953487i \(0.402534\pi\)
\(272\) 1838.70 0.409882
\(273\) 0 0
\(274\) 6405.42 1.41228
\(275\) −1459.16 −0.319966
\(276\) −687.433 −0.149923
\(277\) −830.836 −0.180217 −0.0901085 0.995932i \(-0.528721\pi\)
−0.0901085 + 0.995932i \(0.528721\pi\)
\(278\) 3420.69 0.737984
\(279\) 5132.85 1.10142
\(280\) 0 0
\(281\) −8850.37 −1.87889 −0.939447 0.342695i \(-0.888660\pi\)
−0.939447 + 0.342695i \(0.888660\pi\)
\(282\) −320.564 −0.0676925
\(283\) 557.575 0.117118 0.0585590 0.998284i \(-0.481349\pi\)
0.0585590 + 0.998284i \(0.481349\pi\)
\(284\) 2608.04 0.544925
\(285\) −2056.41 −0.427407
\(286\) −590.334 −0.122053
\(287\) 0 0
\(288\) 922.634 0.188773
\(289\) 8293.38 1.68805
\(290\) 2416.67 0.489352
\(291\) 9675.79 1.94916
\(292\) 2065.67 0.413987
\(293\) 263.506 0.0525400 0.0262700 0.999655i \(-0.491637\pi\)
0.0262700 + 0.999655i \(0.491637\pi\)
\(294\) 0 0
\(295\) −682.597 −0.134720
\(296\) 165.918 0.0325804
\(297\) 206.359 0.0403170
\(298\) −5294.88 −1.02928
\(299\) 450.417 0.0871181
\(300\) −2893.51 −0.556856
\(301\) 0 0
\(302\) −2021.63 −0.385204
\(303\) −2310.60 −0.438087
\(304\) −829.358 −0.156470
\(305\) −1199.56 −0.225201
\(306\) 6626.76 1.23800
\(307\) −6200.77 −1.15276 −0.576379 0.817182i \(-0.695535\pi\)
−0.576379 + 0.817182i \(0.695535\pi\)
\(308\) 0 0
\(309\) −4614.98 −0.849635
\(310\) 1890.40 0.346347
\(311\) −8424.24 −1.53600 −0.767999 0.640452i \(-0.778747\pi\)
−0.767999 + 0.640452i \(0.778747\pi\)
\(312\) −1170.63 −0.212416
\(313\) 2421.11 0.437218 0.218609 0.975813i \(-0.429848\pi\)
0.218609 + 0.975813i \(0.429848\pi\)
\(314\) −153.578 −0.0276017
\(315\) 0 0
\(316\) −1397.59 −0.248799
\(317\) −1032.26 −0.182895 −0.0914474 0.995810i \(-0.529149\pi\)
−0.0914474 + 0.995810i \(0.529149\pi\)
\(318\) 6414.10 1.13108
\(319\) 3430.24 0.602058
\(320\) 339.801 0.0593608
\(321\) −9154.85 −1.59182
\(322\) 0 0
\(323\) −5956.81 −1.02615
\(324\) −2704.68 −0.463766
\(325\) 1895.87 0.323582
\(326\) 4298.43 0.730270
\(327\) 1174.95 0.198700
\(328\) 859.934 0.144762
\(329\) 0 0
\(330\) 1195.91 0.199493
\(331\) 1815.35 0.301453 0.150726 0.988576i \(-0.451839\pi\)
0.150726 + 0.988576i \(0.451839\pi\)
\(332\) −1492.06 −0.246649
\(333\) 597.976 0.0984050
\(334\) 4142.68 0.678675
\(335\) 2541.69 0.414529
\(336\) 0 0
\(337\) −8160.36 −1.31906 −0.659530 0.751678i \(-0.729245\pi\)
−0.659530 + 0.751678i \(0.729245\pi\)
\(338\) −3626.98 −0.583674
\(339\) −9168.03 −1.46885
\(340\) 2440.60 0.389294
\(341\) 2683.24 0.426117
\(342\) −2989.04 −0.472599
\(343\) 0 0
\(344\) 1110.36 0.174030
\(345\) −912.463 −0.142392
\(346\) −6243.70 −0.970126
\(347\) −5693.79 −0.880861 −0.440431 0.897787i \(-0.645174\pi\)
−0.440431 + 0.897787i \(0.645174\pi\)
\(348\) 6802.15 1.04780
\(349\) −4560.60 −0.699494 −0.349747 0.936844i \(-0.613733\pi\)
−0.349747 + 0.936844i \(0.613733\pi\)
\(350\) 0 0
\(351\) −268.120 −0.0407727
\(352\) 482.315 0.0730326
\(353\) −8580.49 −1.29375 −0.646874 0.762597i \(-0.723924\pi\)
−0.646874 + 0.762597i \(0.723924\pi\)
\(354\) −1921.29 −0.288462
\(355\) 3461.78 0.517555
\(356\) −3586.78 −0.533985
\(357\) 0 0
\(358\) −6138.58 −0.906240
\(359\) 1989.15 0.292433 0.146217 0.989253i \(-0.453290\pi\)
0.146217 + 0.989253i \(0.453290\pi\)
\(360\) 1224.66 0.179292
\(361\) −4172.15 −0.608273
\(362\) −2217.41 −0.321945
\(363\) −8247.89 −1.19257
\(364\) 0 0
\(365\) 2741.86 0.393194
\(366\) −3376.36 −0.482200
\(367\) 114.888 0.0163409 0.00817046 0.999967i \(-0.497399\pi\)
0.00817046 + 0.999967i \(0.497399\pi\)
\(368\) −368.000 −0.0521286
\(369\) 3099.24 0.437235
\(370\) 220.231 0.0309440
\(371\) 0 0
\(372\) 5320.87 0.741597
\(373\) 12568.7 1.74473 0.872363 0.488858i \(-0.162586\pi\)
0.872363 + 0.488858i \(0.162586\pi\)
\(374\) 3464.20 0.478956
\(375\) −8799.73 −1.21178
\(376\) −171.606 −0.0235369
\(377\) −4456.88 −0.608862
\(378\) 0 0
\(379\) −12075.5 −1.63662 −0.818308 0.574781i \(-0.805087\pi\)
−0.818308 + 0.574781i \(0.805087\pi\)
\(380\) −1100.85 −0.148611
\(381\) 9184.61 1.23502
\(382\) −6361.24 −0.852014
\(383\) 12228.0 1.63139 0.815695 0.578482i \(-0.196355\pi\)
0.815695 + 0.578482i \(0.196355\pi\)
\(384\) 956.429 0.127103
\(385\) 0 0
\(386\) −1624.65 −0.214229
\(387\) 4001.77 0.525637
\(388\) 5179.69 0.677729
\(389\) 3137.56 0.408948 0.204474 0.978872i \(-0.434452\pi\)
0.204474 + 0.978872i \(0.434452\pi\)
\(390\) −1553.83 −0.201747
\(391\) −2643.14 −0.341865
\(392\) 0 0
\(393\) 18089.5 2.32187
\(394\) −7544.81 −0.964725
\(395\) −1855.08 −0.236302
\(396\) 1738.28 0.220586
\(397\) −15489.8 −1.95821 −0.979106 0.203352i \(-0.934816\pi\)
−0.979106 + 0.203352i \(0.934816\pi\)
\(398\) 3048.55 0.383945
\(399\) 0 0
\(400\) −1548.97 −0.193621
\(401\) −6052.52 −0.753737 −0.376869 0.926267i \(-0.622999\pi\)
−0.376869 + 0.926267i \(0.622999\pi\)
\(402\) 7154.03 0.887588
\(403\) −3486.32 −0.430932
\(404\) −1236.92 −0.152325
\(405\) −3590.05 −0.440472
\(406\) 0 0
\(407\) 312.597 0.0380709
\(408\) 6869.49 0.833555
\(409\) −11921.8 −1.44130 −0.720652 0.693297i \(-0.756157\pi\)
−0.720652 + 0.693297i \(0.756157\pi\)
\(410\) 1141.43 0.137491
\(411\) 23931.0 2.87209
\(412\) −2470.51 −0.295421
\(413\) 0 0
\(414\) −1326.29 −0.157448
\(415\) −1980.48 −0.234260
\(416\) −626.668 −0.0738579
\(417\) 12779.9 1.50080
\(418\) −1562.55 −0.182839
\(419\) 7468.53 0.870792 0.435396 0.900239i \(-0.356608\pi\)
0.435396 + 0.900239i \(0.356608\pi\)
\(420\) 0 0
\(421\) 6039.59 0.699172 0.349586 0.936904i \(-0.386322\pi\)
0.349586 + 0.936904i \(0.386322\pi\)
\(422\) 1821.13 0.210073
\(423\) −618.474 −0.0710903
\(424\) 3433.63 0.393282
\(425\) −11125.4 −1.26979
\(426\) 9743.78 1.10819
\(427\) 0 0
\(428\) −4900.81 −0.553481
\(429\) −2205.52 −0.248213
\(430\) 1473.83 0.165289
\(431\) 13552.1 1.51458 0.757289 0.653079i \(-0.226523\pi\)
0.757289 + 0.653079i \(0.226523\pi\)
\(432\) 219.060 0.0243970
\(433\) −2807.93 −0.311641 −0.155821 0.987785i \(-0.549802\pi\)
−0.155821 + 0.987785i \(0.549802\pi\)
\(434\) 0 0
\(435\) 9028.82 0.995169
\(436\) 628.979 0.0690886
\(437\) 1192.20 0.130505
\(438\) 7717.45 0.841905
\(439\) 15898.7 1.72849 0.864243 0.503075i \(-0.167798\pi\)
0.864243 + 0.503075i \(0.167798\pi\)
\(440\) 640.199 0.0693643
\(441\) 0 0
\(442\) −4501.00 −0.484368
\(443\) −9194.64 −0.986118 −0.493059 0.869996i \(-0.664121\pi\)
−0.493059 + 0.869996i \(0.664121\pi\)
\(444\) 619.879 0.0662571
\(445\) −4760.90 −0.507164
\(446\) −2578.61 −0.273768
\(447\) −19781.9 −2.09318
\(448\) 0 0
\(449\) −11231.7 −1.18053 −0.590265 0.807209i \(-0.700977\pi\)
−0.590265 + 0.807209i \(0.700977\pi\)
\(450\) −5582.54 −0.584807
\(451\) 1620.15 0.169157
\(452\) −4907.87 −0.510723
\(453\) −7552.91 −0.783370
\(454\) −2827.87 −0.292332
\(455\) 0 0
\(456\) −3098.52 −0.318205
\(457\) −9751.96 −0.998200 −0.499100 0.866544i \(-0.666336\pi\)
−0.499100 + 0.866544i \(0.666336\pi\)
\(458\) 1598.33 0.163068
\(459\) 1573.38 0.159998
\(460\) −488.464 −0.0495103
\(461\) 6728.85 0.679813 0.339906 0.940459i \(-0.389605\pi\)
0.339906 + 0.940459i \(0.389605\pi\)
\(462\) 0 0
\(463\) −7665.18 −0.769398 −0.384699 0.923042i \(-0.625695\pi\)
−0.384699 + 0.923042i \(0.625695\pi\)
\(464\) 3641.36 0.364323
\(465\) 7062.63 0.704348
\(466\) 3108.82 0.309041
\(467\) 16755.9 1.66033 0.830163 0.557521i \(-0.188248\pi\)
0.830163 + 0.557521i \(0.188248\pi\)
\(468\) −2258.53 −0.223079
\(469\) 0 0
\(470\) −227.780 −0.0223547
\(471\) −573.776 −0.0561321
\(472\) −1028.51 −0.100299
\(473\) 2091.96 0.203358
\(474\) −5221.45 −0.505969
\(475\) 5018.16 0.484734
\(476\) 0 0
\(477\) 12374.9 1.18786
\(478\) −13935.6 −1.33347
\(479\) −5518.57 −0.526409 −0.263205 0.964740i \(-0.584779\pi\)
−0.263205 + 0.964740i \(0.584779\pi\)
\(480\) 1269.51 0.120719
\(481\) −406.154 −0.0385011
\(482\) 10116.5 0.956003
\(483\) 0 0
\(484\) −4415.30 −0.414660
\(485\) 6875.24 0.643688
\(486\) −10844.2 −1.01214
\(487\) 3953.92 0.367904 0.183952 0.982935i \(-0.441111\pi\)
0.183952 + 0.982935i \(0.441111\pi\)
\(488\) −1807.45 −0.167663
\(489\) 16059.2 1.48511
\(490\) 0 0
\(491\) 12730.6 1.17011 0.585053 0.810995i \(-0.301074\pi\)
0.585053 + 0.810995i \(0.301074\pi\)
\(492\) 3212.76 0.294395
\(493\) 26153.8 2.38927
\(494\) 2030.20 0.184905
\(495\) 2307.30 0.209506
\(496\) 2848.39 0.257856
\(497\) 0 0
\(498\) −5574.40 −0.501596
\(499\) −18019.9 −1.61659 −0.808297 0.588775i \(-0.799611\pi\)
−0.808297 + 0.588775i \(0.799611\pi\)
\(500\) −4710.71 −0.421339
\(501\) 15477.3 1.38019
\(502\) 6726.77 0.598068
\(503\) 10200.1 0.904175 0.452087 0.891974i \(-0.350680\pi\)
0.452087 + 0.891974i \(0.350680\pi\)
\(504\) 0 0
\(505\) −1641.82 −0.144674
\(506\) −693.328 −0.0609134
\(507\) −13550.6 −1.18699
\(508\) 4916.75 0.429420
\(509\) −12372.6 −1.07741 −0.538707 0.842493i \(-0.681087\pi\)
−0.538707 + 0.842493i \(0.681087\pi\)
\(510\) 9118.20 0.791688
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −709.683 −0.0610785
\(514\) 14040.6 1.20487
\(515\) −3279.23 −0.280583
\(516\) 4148.35 0.353917
\(517\) −323.312 −0.0275034
\(518\) 0 0
\(519\) −23326.8 −1.97290
\(520\) −831.805 −0.0701482
\(521\) −11660.6 −0.980538 −0.490269 0.871571i \(-0.663101\pi\)
−0.490269 + 0.871571i \(0.663101\pi\)
\(522\) 13123.6 1.10039
\(523\) 3985.38 0.333210 0.166605 0.986024i \(-0.446720\pi\)
0.166605 + 0.986024i \(0.446720\pi\)
\(524\) 9683.74 0.807321
\(525\) 0 0
\(526\) −2237.13 −0.185444
\(527\) 20458.4 1.69105
\(528\) 1801.95 0.148523
\(529\) 529.000 0.0434783
\(530\) 4557.61 0.373528
\(531\) −3706.80 −0.302941
\(532\) 0 0
\(533\) −2105.05 −0.171069
\(534\) −13400.4 −1.08594
\(535\) −6505.08 −0.525681
\(536\) 3829.73 0.308618
\(537\) −22934.0 −1.84297
\(538\) 5571.73 0.446495
\(539\) 0 0
\(540\) 290.768 0.0231716
\(541\) 8567.19 0.680836 0.340418 0.940274i \(-0.389431\pi\)
0.340418 + 0.940274i \(0.389431\pi\)
\(542\) 5379.07 0.426293
\(543\) −8284.34 −0.654724
\(544\) 3677.41 0.289830
\(545\) 834.873 0.0656184
\(546\) 0 0
\(547\) −14381.3 −1.12413 −0.562067 0.827091i \(-0.689994\pi\)
−0.562067 + 0.827091i \(0.689994\pi\)
\(548\) 12810.8 0.998635
\(549\) −6514.12 −0.506404
\(550\) −2918.32 −0.226250
\(551\) −11796.8 −0.912091
\(552\) −1374.87 −0.106011
\(553\) 0 0
\(554\) −1661.67 −0.127433
\(555\) 822.794 0.0629291
\(556\) 6841.38 0.521833
\(557\) −1759.65 −0.133857 −0.0669287 0.997758i \(-0.521320\pi\)
−0.0669287 + 0.997758i \(0.521320\pi\)
\(558\) 10265.7 0.778821
\(559\) −2718.07 −0.205656
\(560\) 0 0
\(561\) 12942.4 0.974027
\(562\) −17700.7 −1.32858
\(563\) 12597.1 0.942989 0.471495 0.881869i \(-0.343715\pi\)
0.471495 + 0.881869i \(0.343715\pi\)
\(564\) −641.128 −0.0478659
\(565\) −6514.45 −0.485071
\(566\) 1115.15 0.0828149
\(567\) 0 0
\(568\) 5216.08 0.385320
\(569\) −6429.70 −0.473721 −0.236860 0.971544i \(-0.576118\pi\)
−0.236860 + 0.971544i \(0.576118\pi\)
\(570\) −4112.82 −0.302223
\(571\) −5090.14 −0.373057 −0.186529 0.982450i \(-0.559724\pi\)
−0.186529 + 0.982450i \(0.559724\pi\)
\(572\) −1180.67 −0.0863046
\(573\) −23765.9 −1.73270
\(574\) 0 0
\(575\) 2226.64 0.161491
\(576\) 1845.27 0.133483
\(577\) 12748.9 0.919834 0.459917 0.887962i \(-0.347879\pi\)
0.459917 + 0.887962i \(0.347879\pi\)
\(578\) 16586.8 1.19363
\(579\) −6069.78 −0.435667
\(580\) 4833.35 0.346024
\(581\) 0 0
\(582\) 19351.6 1.37826
\(583\) 6469.10 0.459559
\(584\) 4131.34 0.292733
\(585\) −2997.86 −0.211874
\(586\) 527.013 0.0371514
\(587\) −7455.98 −0.524261 −0.262131 0.965032i \(-0.584425\pi\)
−0.262131 + 0.965032i \(0.584425\pi\)
\(588\) 0 0
\(589\) −9227.87 −0.645548
\(590\) −1365.19 −0.0952613
\(591\) −28187.8 −1.96191
\(592\) 331.836 0.0230378
\(593\) −9005.60 −0.623635 −0.311817 0.950142i \(-0.600938\pi\)
−0.311817 + 0.950142i \(0.600938\pi\)
\(594\) 412.718 0.0285084
\(595\) 0 0
\(596\) −10589.8 −0.727807
\(597\) 11389.5 0.780809
\(598\) 900.835 0.0616018
\(599\) −14196.3 −0.968359 −0.484179 0.874969i \(-0.660882\pi\)
−0.484179 + 0.874969i \(0.660882\pi\)
\(600\) −5787.02 −0.393757
\(601\) −4208.80 −0.285658 −0.142829 0.989747i \(-0.545620\pi\)
−0.142829 + 0.989747i \(0.545620\pi\)
\(602\) 0 0
\(603\) 13802.5 0.932140
\(604\) −4043.26 −0.272381
\(605\) −5860.63 −0.393832
\(606\) −4621.20 −0.309775
\(607\) 13431.8 0.898155 0.449078 0.893493i \(-0.351753\pi\)
0.449078 + 0.893493i \(0.351753\pi\)
\(608\) −1658.72 −0.110641
\(609\) 0 0
\(610\) −2399.11 −0.159241
\(611\) 420.077 0.0278142
\(612\) 13253.5 0.875395
\(613\) 27774.2 1.83000 0.914999 0.403456i \(-0.132191\pi\)
0.914999 + 0.403456i \(0.132191\pi\)
\(614\) −12401.5 −0.815123
\(615\) 4264.44 0.279608
\(616\) 0 0
\(617\) 10560.5 0.689061 0.344530 0.938775i \(-0.388038\pi\)
0.344530 + 0.938775i \(0.388038\pi\)
\(618\) −9229.96 −0.600782
\(619\) 20438.9 1.32715 0.663577 0.748108i \(-0.269038\pi\)
0.663577 + 0.748108i \(0.269038\pi\)
\(620\) 3780.80 0.244904
\(621\) −314.898 −0.0203485
\(622\) −16848.5 −1.08611
\(623\) 0 0
\(624\) −2341.26 −0.150201
\(625\) 5848.55 0.374308
\(626\) 4842.22 0.309160
\(627\) −5837.75 −0.371830
\(628\) −307.157 −0.0195173
\(629\) 2383.39 0.151085
\(630\) 0 0
\(631\) −15693.6 −0.990099 −0.495049 0.868865i \(-0.664850\pi\)
−0.495049 + 0.868865i \(0.664850\pi\)
\(632\) −2795.17 −0.175927
\(633\) 6803.82 0.427216
\(634\) −2064.53 −0.129326
\(635\) 6526.23 0.407851
\(636\) 12828.2 0.799798
\(637\) 0 0
\(638\) 6860.48 0.425719
\(639\) 18799.0 1.16381
\(640\) 679.602 0.0419744
\(641\) −13898.9 −0.856434 −0.428217 0.903676i \(-0.640858\pi\)
−0.428217 + 0.903676i \(0.640858\pi\)
\(642\) −18309.7 −1.12559
\(643\) −18032.4 −1.10595 −0.552977 0.833196i \(-0.686508\pi\)
−0.552977 + 0.833196i \(0.686508\pi\)
\(644\) 0 0
\(645\) 5506.30 0.336140
\(646\) −11913.6 −0.725597
\(647\) 2023.00 0.122925 0.0614624 0.998109i \(-0.480424\pi\)
0.0614624 + 0.998109i \(0.480424\pi\)
\(648\) −5409.36 −0.327932
\(649\) −1937.76 −0.117202
\(650\) 3791.75 0.228807
\(651\) 0 0
\(652\) 8596.86 0.516379
\(653\) −153.043 −0.00917154 −0.00458577 0.999989i \(-0.501460\pi\)
−0.00458577 + 0.999989i \(0.501460\pi\)
\(654\) 2349.90 0.140502
\(655\) 12853.7 0.766771
\(656\) 1719.87 0.102362
\(657\) 14889.5 0.884164
\(658\) 0 0
\(659\) −5171.29 −0.305683 −0.152841 0.988251i \(-0.548842\pi\)
−0.152841 + 0.988251i \(0.548842\pi\)
\(660\) 2391.82 0.141063
\(661\) 4426.43 0.260466 0.130233 0.991483i \(-0.458427\pi\)
0.130233 + 0.991483i \(0.458427\pi\)
\(662\) 3630.71 0.213159
\(663\) −16816.0 −0.985035
\(664\) −2984.12 −0.174407
\(665\) 0 0
\(666\) 1195.95 0.0695828
\(667\) −5234.46 −0.303866
\(668\) 8285.36 0.479896
\(669\) −9633.80 −0.556748
\(670\) 5083.38 0.293116
\(671\) −3405.31 −0.195917
\(672\) 0 0
\(673\) 19846.7 1.13675 0.568377 0.822768i \(-0.307571\pi\)
0.568377 + 0.822768i \(0.307571\pi\)
\(674\) −16320.7 −0.932717
\(675\) −1325.45 −0.0755804
\(676\) −7253.97 −0.412720
\(677\) 23737.7 1.34758 0.673792 0.738921i \(-0.264664\pi\)
0.673792 + 0.738921i \(0.264664\pi\)
\(678\) −18336.1 −1.03863
\(679\) 0 0
\(680\) 4881.20 0.275273
\(681\) −10565.1 −0.594500
\(682\) 5366.49 0.301310
\(683\) −4733.62 −0.265193 −0.132597 0.991170i \(-0.542332\pi\)
−0.132597 + 0.991170i \(0.542332\pi\)
\(684\) −5978.08 −0.334178
\(685\) 17004.4 0.948475
\(686\) 0 0
\(687\) 5971.45 0.331623
\(688\) 2220.72 0.123058
\(689\) −8405.24 −0.464752
\(690\) −1824.93 −0.100687
\(691\) 275.544 0.0151696 0.00758480 0.999971i \(-0.497586\pi\)
0.00758480 + 0.999971i \(0.497586\pi\)
\(692\) −12487.4 −0.685983
\(693\) 0 0
\(694\) −11387.6 −0.622863
\(695\) 9080.89 0.495623
\(696\) 13604.3 0.740905
\(697\) 12352.9 0.671302
\(698\) −9121.21 −0.494617
\(699\) 11614.7 0.628481
\(700\) 0 0
\(701\) 15236.5 0.820933 0.410467 0.911876i \(-0.365366\pi\)
0.410467 + 0.911876i \(0.365366\pi\)
\(702\) −536.241 −0.0288306
\(703\) −1075.04 −0.0576757
\(704\) 964.630 0.0516418
\(705\) −850.999 −0.0454617
\(706\) −17161.0 −0.914819
\(707\) 0 0
\(708\) −3842.58 −0.203973
\(709\) 20262.7 1.07332 0.536659 0.843799i \(-0.319686\pi\)
0.536659 + 0.843799i \(0.319686\pi\)
\(710\) 6923.55 0.365967
\(711\) −10073.9 −0.531366
\(712\) −7173.55 −0.377585
\(713\) −4094.56 −0.215067
\(714\) 0 0
\(715\) −1567.16 −0.0819697
\(716\) −12277.2 −0.640808
\(717\) −52064.2 −2.71182
\(718\) 3978.30 0.206781
\(719\) −4018.57 −0.208439 −0.104219 0.994554i \(-0.533234\pi\)
−0.104219 + 0.994554i \(0.533234\pi\)
\(720\) 2449.31 0.126778
\(721\) 0 0
\(722\) −8344.29 −0.430114
\(723\) 37795.7 1.94417
\(724\) −4434.81 −0.227650
\(725\) −22032.6 −1.12865
\(726\) −16495.8 −0.843273
\(727\) −31658.7 −1.61507 −0.807536 0.589819i \(-0.799199\pi\)
−0.807536 + 0.589819i \(0.799199\pi\)
\(728\) 0 0
\(729\) −22257.7 −1.13081
\(730\) 5483.73 0.278030
\(731\) 15950.2 0.807028
\(732\) −6752.72 −0.340967
\(733\) −35997.8 −1.81393 −0.906963 0.421210i \(-0.861605\pi\)
−0.906963 + 0.421210i \(0.861605\pi\)
\(734\) 229.776 0.0115548
\(735\) 0 0
\(736\) −736.000 −0.0368605
\(737\) 7215.37 0.360626
\(738\) 6198.47 0.309172
\(739\) 8160.48 0.406209 0.203104 0.979157i \(-0.434897\pi\)
0.203104 + 0.979157i \(0.434897\pi\)
\(740\) 440.462 0.0218807
\(741\) 7584.94 0.376032
\(742\) 0 0
\(743\) −2264.67 −0.111821 −0.0559104 0.998436i \(-0.517806\pi\)
−0.0559104 + 0.998436i \(0.517806\pi\)
\(744\) 10641.7 0.524388
\(745\) −14056.3 −0.691251
\(746\) 25137.4 1.23371
\(747\) −10754.9 −0.526774
\(748\) 6928.39 0.338673
\(749\) 0 0
\(750\) −17599.5 −0.856855
\(751\) −20177.1 −0.980391 −0.490195 0.871613i \(-0.663075\pi\)
−0.490195 + 0.871613i \(0.663075\pi\)
\(752\) −343.211 −0.0166431
\(753\) 25131.5 1.21626
\(754\) −8913.76 −0.430530
\(755\) −5366.81 −0.258700
\(756\) 0 0
\(757\) 2404.49 0.115446 0.0577231 0.998333i \(-0.481616\pi\)
0.0577231 + 0.998333i \(0.481616\pi\)
\(758\) −24151.0 −1.15726
\(759\) −2590.31 −0.123876
\(760\) −2201.69 −0.105084
\(761\) −36396.7 −1.73374 −0.866871 0.498532i \(-0.833873\pi\)
−0.866871 + 0.498532i \(0.833873\pi\)
\(762\) 18369.2 0.873290
\(763\) 0 0
\(764\) −12722.5 −0.602465
\(765\) 17592.0 0.831426
\(766\) 24456.0 1.15357
\(767\) 2517.72 0.118526
\(768\) 1912.86 0.0898754
\(769\) 29050.2 1.36226 0.681129 0.732163i \(-0.261489\pi\)
0.681129 + 0.732163i \(0.261489\pi\)
\(770\) 0 0
\(771\) 52456.3 2.45028
\(772\) −3249.30 −0.151483
\(773\) 30769.4 1.43169 0.715847 0.698257i \(-0.246041\pi\)
0.715847 + 0.698257i \(0.246041\pi\)
\(774\) 8003.54 0.371681
\(775\) −17234.6 −0.798820
\(776\) 10359.4 0.479227
\(777\) 0 0
\(778\) 6275.12 0.289170
\(779\) −5571.82 −0.256266
\(780\) −3107.67 −0.142657
\(781\) 9827.32 0.450255
\(782\) −5286.27 −0.241735
\(783\) 3115.92 0.142214
\(784\) 0 0
\(785\) −407.703 −0.0185370
\(786\) 36178.9 1.64181
\(787\) −11172.5 −0.506043 −0.253022 0.967461i \(-0.581424\pi\)
−0.253022 + 0.967461i \(0.581424\pi\)
\(788\) −15089.6 −0.682164
\(789\) −8358.04 −0.377128
\(790\) −3710.16 −0.167091
\(791\) 0 0
\(792\) 3476.56 0.155978
\(793\) 4424.49 0.198132
\(794\) −30979.6 −1.38466
\(795\) 17027.5 0.759626
\(796\) 6097.10 0.271490
\(797\) 7065.60 0.314023 0.157012 0.987597i \(-0.449814\pi\)
0.157012 + 0.987597i \(0.449814\pi\)
\(798\) 0 0
\(799\) −2465.09 −0.109147
\(800\) −3097.93 −0.136911
\(801\) −25853.8 −1.14045
\(802\) −12105.0 −0.532973
\(803\) 7783.63 0.342065
\(804\) 14308.1 0.627620
\(805\) 0 0
\(806\) −6972.63 −0.304715
\(807\) 20816.3 0.908014
\(808\) −2473.84 −0.107710
\(809\) 37869.3 1.64575 0.822875 0.568222i \(-0.192368\pi\)
0.822875 + 0.568222i \(0.192368\pi\)
\(810\) −7180.10 −0.311460
\(811\) −33563.4 −1.45323 −0.726616 0.687044i \(-0.758908\pi\)
−0.726616 + 0.687044i \(0.758908\pi\)
\(812\) 0 0
\(813\) 20096.5 0.866931
\(814\) 625.194 0.0269202
\(815\) 11411.0 0.490442
\(816\) 13739.0 0.589413
\(817\) −7194.41 −0.308079
\(818\) −23843.5 −1.01916
\(819\) 0 0
\(820\) 2282.86 0.0972207
\(821\) −17903.5 −0.761069 −0.380534 0.924767i \(-0.624260\pi\)
−0.380534 + 0.924767i \(0.624260\pi\)
\(822\) 47861.9 2.03087
\(823\) 6635.99 0.281064 0.140532 0.990076i \(-0.455119\pi\)
0.140532 + 0.990076i \(0.455119\pi\)
\(824\) −4941.02 −0.208894
\(825\) −10903.0 −0.460113
\(826\) 0 0
\(827\) 30086.7 1.26508 0.632538 0.774529i \(-0.282013\pi\)
0.632538 + 0.774529i \(0.282013\pi\)
\(828\) −2652.57 −0.111332
\(829\) −18965.3 −0.794562 −0.397281 0.917697i \(-0.630046\pi\)
−0.397281 + 0.917697i \(0.630046\pi\)
\(830\) −3960.96 −0.165647
\(831\) −6208.09 −0.259153
\(832\) −1253.34 −0.0522254
\(833\) 0 0
\(834\) 25559.8 1.06123
\(835\) 10997.5 0.455791
\(836\) −3125.09 −0.129287
\(837\) 2437.37 0.100655
\(838\) 14937.1 0.615743
\(839\) 5909.42 0.243166 0.121583 0.992581i \(-0.461203\pi\)
0.121583 + 0.992581i \(0.461203\pi\)
\(840\) 0 0
\(841\) 27405.9 1.12370
\(842\) 12079.2 0.494389
\(843\) −66130.9 −2.70186
\(844\) 3642.25 0.148544
\(845\) −9628.53 −0.391990
\(846\) −1236.95 −0.0502685
\(847\) 0 0
\(848\) 6867.25 0.278092
\(849\) 4166.26 0.168416
\(850\) −22250.7 −0.897874
\(851\) −477.015 −0.0192149
\(852\) 19487.6 0.783606
\(853\) 4235.96 0.170031 0.0850156 0.996380i \(-0.472906\pi\)
0.0850156 + 0.996380i \(0.472906\pi\)
\(854\) 0 0
\(855\) −7934.98 −0.317393
\(856\) −9801.63 −0.391370
\(857\) −22565.0 −0.899424 −0.449712 0.893174i \(-0.648473\pi\)
−0.449712 + 0.893174i \(0.648473\pi\)
\(858\) −4411.04 −0.175513
\(859\) 3340.91 0.132701 0.0663505 0.997796i \(-0.478864\pi\)
0.0663505 + 0.997796i \(0.478864\pi\)
\(860\) 2947.66 0.116877
\(861\) 0 0
\(862\) 27104.3 1.07097
\(863\) −49888.4 −1.96781 −0.983905 0.178691i \(-0.942814\pi\)
−0.983905 + 0.178691i \(0.942814\pi\)
\(864\) 438.119 0.0172513
\(865\) −16575.1 −0.651527
\(866\) −5615.86 −0.220364
\(867\) 61969.0 2.42742
\(868\) 0 0
\(869\) −5266.22 −0.205575
\(870\) 18057.6 0.703691
\(871\) −9374.86 −0.364702
\(872\) 1257.96 0.0488530
\(873\) 37335.6 1.44744
\(874\) 2384.40 0.0922811
\(875\) 0 0
\(876\) 15434.9 0.595316
\(877\) 41188.0 1.58588 0.792942 0.609297i \(-0.208548\pi\)
0.792942 + 0.609297i \(0.208548\pi\)
\(878\) 31797.5 1.22222
\(879\) 1968.95 0.0755528
\(880\) 1280.40 0.0490480
\(881\) −19351.1 −0.740018 −0.370009 0.929028i \(-0.620645\pi\)
−0.370009 + 0.929028i \(0.620645\pi\)
\(882\) 0 0
\(883\) −31330.1 −1.19404 −0.597022 0.802225i \(-0.703649\pi\)
−0.597022 + 0.802225i \(0.703649\pi\)
\(884\) −9002.00 −0.342500
\(885\) −5100.44 −0.193728
\(886\) −18389.3 −0.697291
\(887\) 18838.7 0.713124 0.356562 0.934272i \(-0.383949\pi\)
0.356562 + 0.934272i \(0.383949\pi\)
\(888\) 1239.76 0.0468508
\(889\) 0 0
\(890\) −9521.79 −0.358619
\(891\) −10191.5 −0.383195
\(892\) −5157.21 −0.193583
\(893\) 1111.90 0.0416665
\(894\) −39563.9 −1.48010
\(895\) −16296.0 −0.608622
\(896\) 0 0
\(897\) 3365.56 0.125276
\(898\) −22463.5 −0.834761
\(899\) 40515.7 1.50309
\(900\) −11165.1 −0.413521
\(901\) 49323.6 1.82376
\(902\) 3240.31 0.119612
\(903\) 0 0
\(904\) −9815.75 −0.361136
\(905\) −5886.53 −0.216215
\(906\) −15105.8 −0.553926
\(907\) −28754.5 −1.05268 −0.526339 0.850275i \(-0.676436\pi\)
−0.526339 + 0.850275i \(0.676436\pi\)
\(908\) −5655.74 −0.206710
\(909\) −8915.82 −0.325324
\(910\) 0 0
\(911\) 7679.37 0.279285 0.139643 0.990202i \(-0.455405\pi\)
0.139643 + 0.990202i \(0.455405\pi\)
\(912\) −6197.05 −0.225005
\(913\) −5622.20 −0.203798
\(914\) −19503.9 −0.705834
\(915\) −8963.21 −0.323841
\(916\) 3196.66 0.115306
\(917\) 0 0
\(918\) 3146.77 0.113136
\(919\) 45937.0 1.64888 0.824440 0.565950i \(-0.191490\pi\)
0.824440 + 0.565950i \(0.191490\pi\)
\(920\) −976.927 −0.0350091
\(921\) −46332.8 −1.65767
\(922\) 13457.7 0.480700
\(923\) −12768.6 −0.455344
\(924\) 0 0
\(925\) −2007.83 −0.0713696
\(926\) −15330.4 −0.544046
\(927\) −17807.6 −0.630938
\(928\) 7282.72 0.257615
\(929\) 35684.8 1.26026 0.630129 0.776490i \(-0.283002\pi\)
0.630129 + 0.776490i \(0.283002\pi\)
\(930\) 14125.3 0.498049
\(931\) 0 0
\(932\) 6217.64 0.218525
\(933\) −62946.8 −2.20877
\(934\) 33511.9 1.17403
\(935\) 9196.38 0.321662
\(936\) −4517.07 −0.157740
\(937\) −4161.99 −0.145108 −0.0725540 0.997364i \(-0.523115\pi\)
−0.0725540 + 0.997364i \(0.523115\pi\)
\(938\) 0 0
\(939\) 18090.8 0.628722
\(940\) −455.561 −0.0158072
\(941\) 30661.7 1.06221 0.531106 0.847305i \(-0.321776\pi\)
0.531106 + 0.847305i \(0.321776\pi\)
\(942\) −1147.55 −0.0396914
\(943\) −2472.31 −0.0853760
\(944\) −2057.03 −0.0709222
\(945\) 0 0
\(946\) 4183.92 0.143796
\(947\) 9165.36 0.314503 0.157251 0.987559i \(-0.449737\pi\)
0.157251 + 0.987559i \(0.449737\pi\)
\(948\) −10442.9 −0.357774
\(949\) −10113.2 −0.345931
\(950\) 10036.3 0.342759
\(951\) −7713.18 −0.263004
\(952\) 0 0
\(953\) −27150.4 −0.922862 −0.461431 0.887176i \(-0.652664\pi\)
−0.461431 + 0.887176i \(0.652664\pi\)
\(954\) 24749.8 0.839943
\(955\) −16887.1 −0.572204
\(956\) −27871.2 −0.942908
\(957\) 25631.1 0.865763
\(958\) −11037.1 −0.372227
\(959\) 0 0
\(960\) 2539.03 0.0853612
\(961\) 1901.68 0.0638340
\(962\) −812.309 −0.0272244
\(963\) −35325.5 −1.18208
\(964\) 20233.0 0.675996
\(965\) −4312.95 −0.143874
\(966\) 0 0
\(967\) −34024.7 −1.13150 −0.565750 0.824577i \(-0.691413\pi\)
−0.565750 + 0.824577i \(0.691413\pi\)
\(968\) −8830.60 −0.293209
\(969\) −44509.9 −1.47561
\(970\) 13750.5 0.455156
\(971\) −18794.4 −0.621154 −0.310577 0.950548i \(-0.600522\pi\)
−0.310577 + 0.950548i \(0.600522\pi\)
\(972\) −21688.3 −0.715692
\(973\) 0 0
\(974\) 7907.83 0.260147
\(975\) 14166.2 0.465313
\(976\) −3614.90 −0.118555
\(977\) −60427.0 −1.97874 −0.989371 0.145411i \(-0.953549\pi\)
−0.989371 + 0.145411i \(0.953549\pi\)
\(978\) 32118.3 1.05013
\(979\) −13515.3 −0.441216
\(980\) 0 0
\(981\) 4533.73 0.147554
\(982\) 25461.1 0.827390
\(983\) −38938.6 −1.26343 −0.631713 0.775203i \(-0.717648\pi\)
−0.631713 + 0.775203i \(0.717648\pi\)
\(984\) 6425.52 0.208169
\(985\) −20029.1 −0.647900
\(986\) 52307.7 1.68947
\(987\) 0 0
\(988\) 4060.40 0.130748
\(989\) −3192.28 −0.102638
\(990\) 4614.61 0.148143
\(991\) −31599.6 −1.01291 −0.506455 0.862267i \(-0.669044\pi\)
−0.506455 + 0.862267i \(0.669044\pi\)
\(992\) 5696.78 0.182332
\(993\) 13564.5 0.433491
\(994\) 0 0
\(995\) 8092.97 0.257854
\(996\) −11148.8 −0.354682
\(997\) −38706.6 −1.22954 −0.614770 0.788707i \(-0.710751\pi\)
−0.614770 + 0.788707i \(0.710751\pi\)
\(998\) −36039.8 −1.14310
\(999\) 283.953 0.00899287
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 2254.4.a.x.1.10 11
7.3 odd 6 322.4.e.b.93.10 22
7.5 odd 6 322.4.e.b.277.10 yes 22
7.6 odd 2 2254.4.a.w.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.4.e.b.93.10 22 7.3 odd 6
322.4.e.b.277.10 yes 22 7.5 odd 6
2254.4.a.w.1.2 11 7.6 odd 2
2254.4.a.x.1.10 11 1.1 even 1 trivial