Properties

Label 608.4.a.j.1.4
Level $608$
Weight $4$
Character 608.1
Self dual yes
Analytic conductor $35.873$
Analytic rank $1$
Dimension $7$
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] = [608,4,Mod(1,608)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(608, 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("608.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 608.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: \(35.8731612835\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 3x^{6} - 121x^{5} + 402x^{4} + 4234x^{3} - 14542x^{2} - 40996x + 141664 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-4.00212\) of defining polynomial
Character \(\chi\) \(=\) 608.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.923414 q^{3} -0.670967 q^{5} +28.6780 q^{7} -26.1473 q^{9} +O(q^{10})\) \(q+0.923414 q^{3} -0.670967 q^{5} +28.6780 q^{7} -26.1473 q^{9} -24.1312 q^{11} -17.5373 q^{13} -0.619580 q^{15} -61.1485 q^{17} +19.0000 q^{19} +26.4817 q^{21} -160.534 q^{23} -124.550 q^{25} -49.0770 q^{27} +287.921 q^{29} +47.5884 q^{31} -22.2831 q^{33} -19.2420 q^{35} -237.442 q^{37} -16.1942 q^{39} +197.712 q^{41} -352.718 q^{43} +17.5440 q^{45} -357.106 q^{47} +479.427 q^{49} -56.4654 q^{51} +381.501 q^{53} +16.1912 q^{55} +17.5449 q^{57} +691.149 q^{59} -827.651 q^{61} -749.852 q^{63} +11.7669 q^{65} -166.560 q^{67} -148.240 q^{69} -296.418 q^{71} -916.657 q^{73} -115.011 q^{75} -692.034 q^{77} -1229.64 q^{79} +660.659 q^{81} -547.516 q^{83} +41.0286 q^{85} +265.870 q^{87} -257.418 q^{89} -502.934 q^{91} +43.9438 q^{93} -12.7484 q^{95} +206.366 q^{97} +630.965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 3 q^{3} - 17 q^{5} - 42 q^{7} + 86 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 3 q^{3} - 17 q^{5} - 42 q^{7} + 86 q^{9} + 33 q^{11} - 35 q^{13} - 120 q^{15} + 66 q^{17} + 133 q^{19} + 33 q^{21} - 389 q^{23} + 44 q^{25} + 39 q^{27} + 233 q^{29} - 158 q^{31} - 206 q^{33} - 123 q^{35} - 436 q^{37} - 807 q^{39} - 94 q^{41} - 645 q^{43} + 103 q^{45} - 1451 q^{47} + 93 q^{49} - 1741 q^{51} + 3 q^{53} - 1971 q^{55} - 57 q^{57} - 297 q^{59} + 93 q^{61} - 2999 q^{63} - 788 q^{65} - 1641 q^{67} + 945 q^{69} - 2392 q^{71} + 324 q^{73} - 1909 q^{75} - 711 q^{77} - 2492 q^{79} + 143 q^{81} - 310 q^{83} + 2353 q^{85} - 4795 q^{87} - 440 q^{89} + 107 q^{91} + 900 q^{93} - 323 q^{95} - 532 q^{97} + 1591 q^{99}+O(q^{100}) \) 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 0
\(3\) 0.923414 0.177711 0.0888556 0.996045i \(-0.471679\pi\)
0.0888556 + 0.996045i \(0.471679\pi\)
\(4\) 0 0
\(5\) −0.670967 −0.0600131 −0.0300066 0.999550i \(-0.509553\pi\)
−0.0300066 + 0.999550i \(0.509553\pi\)
\(6\) 0 0
\(7\) 28.6780 1.54847 0.774233 0.632901i \(-0.218136\pi\)
0.774233 + 0.632901i \(0.218136\pi\)
\(8\) 0 0
\(9\) −26.1473 −0.968419
\(10\) 0 0
\(11\) −24.1312 −0.661439 −0.330719 0.943729i \(-0.607291\pi\)
−0.330719 + 0.943729i \(0.607291\pi\)
\(12\) 0 0
\(13\) −17.5373 −0.374152 −0.187076 0.982345i \(-0.559901\pi\)
−0.187076 + 0.982345i \(0.559901\pi\)
\(14\) 0 0
\(15\) −0.619580 −0.0106650
\(16\) 0 0
\(17\) −61.1485 −0.872393 −0.436197 0.899851i \(-0.643675\pi\)
−0.436197 + 0.899851i \(0.643675\pi\)
\(18\) 0 0
\(19\) 19.0000 0.229416
\(20\) 0 0
\(21\) 26.4817 0.275180
\(22\) 0 0
\(23\) −160.534 −1.45538 −0.727689 0.685907i \(-0.759406\pi\)
−0.727689 + 0.685907i \(0.759406\pi\)
\(24\) 0 0
\(25\) −124.550 −0.996398
\(26\) 0 0
\(27\) −49.0770 −0.349810
\(28\) 0 0
\(29\) 287.921 1.84364 0.921819 0.387620i \(-0.126703\pi\)
0.921819 + 0.387620i \(0.126703\pi\)
\(30\) 0 0
\(31\) 47.5884 0.275714 0.137857 0.990452i \(-0.455979\pi\)
0.137857 + 0.990452i \(0.455979\pi\)
\(32\) 0 0
\(33\) −22.2831 −0.117545
\(34\) 0 0
\(35\) −19.2420 −0.0929283
\(36\) 0 0
\(37\) −237.442 −1.05501 −0.527504 0.849552i \(-0.676872\pi\)
−0.527504 + 0.849552i \(0.676872\pi\)
\(38\) 0 0
\(39\) −16.1942 −0.0664909
\(40\) 0 0
\(41\) 197.712 0.753109 0.376554 0.926395i \(-0.377109\pi\)
0.376554 + 0.926395i \(0.377109\pi\)
\(42\) 0 0
\(43\) −352.718 −1.25091 −0.625454 0.780261i \(-0.715086\pi\)
−0.625454 + 0.780261i \(0.715086\pi\)
\(44\) 0 0
\(45\) 17.5440 0.0581178
\(46\) 0 0
\(47\) −357.106 −1.10828 −0.554141 0.832423i \(-0.686953\pi\)
−0.554141 + 0.832423i \(0.686953\pi\)
\(48\) 0 0
\(49\) 479.427 1.39775
\(50\) 0 0
\(51\) −56.4654 −0.155034
\(52\) 0 0
\(53\) 381.501 0.988739 0.494369 0.869252i \(-0.335399\pi\)
0.494369 + 0.869252i \(0.335399\pi\)
\(54\) 0 0
\(55\) 16.1912 0.0396950
\(56\) 0 0
\(57\) 17.5449 0.0407697
\(58\) 0 0
\(59\) 691.149 1.52508 0.762542 0.646938i \(-0.223951\pi\)
0.762542 + 0.646938i \(0.223951\pi\)
\(60\) 0 0
\(61\) −827.651 −1.73721 −0.868606 0.495504i \(-0.834983\pi\)
−0.868606 + 0.495504i \(0.834983\pi\)
\(62\) 0 0
\(63\) −749.852 −1.49956
\(64\) 0 0
\(65\) 11.7669 0.0224540
\(66\) 0 0
\(67\) −166.560 −0.303710 −0.151855 0.988403i \(-0.548525\pi\)
−0.151855 + 0.988403i \(0.548525\pi\)
\(68\) 0 0
\(69\) −148.240 −0.258637
\(70\) 0 0
\(71\) −296.418 −0.495470 −0.247735 0.968828i \(-0.579686\pi\)
−0.247735 + 0.968828i \(0.579686\pi\)
\(72\) 0 0
\(73\) −916.657 −1.46968 −0.734840 0.678241i \(-0.762743\pi\)
−0.734840 + 0.678241i \(0.762743\pi\)
\(74\) 0 0
\(75\) −115.011 −0.177071
\(76\) 0 0
\(77\) −692.034 −1.02422
\(78\) 0 0
\(79\) −1229.64 −1.75120 −0.875601 0.483036i \(-0.839534\pi\)
−0.875601 + 0.483036i \(0.839534\pi\)
\(80\) 0 0
\(81\) 660.659 0.906254
\(82\) 0 0
\(83\) −547.516 −0.724069 −0.362035 0.932165i \(-0.617918\pi\)
−0.362035 + 0.932165i \(0.617918\pi\)
\(84\) 0 0
\(85\) 41.0286 0.0523550
\(86\) 0 0
\(87\) 265.870 0.327635
\(88\) 0 0
\(89\) −257.418 −0.306587 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(90\) 0 0
\(91\) −502.934 −0.579361
\(92\) 0 0
\(93\) 43.9438 0.0489974
\(94\) 0 0
\(95\) −12.7484 −0.0137679
\(96\) 0 0
\(97\) 206.366 0.216013 0.108007 0.994150i \(-0.465553\pi\)
0.108007 + 0.994150i \(0.465553\pi\)
\(98\) 0 0
\(99\) 630.965 0.640550
\(100\) 0 0
\(101\) 560.665 0.552359 0.276179 0.961106i \(-0.410932\pi\)
0.276179 + 0.961106i \(0.410932\pi\)
\(102\) 0 0
\(103\) −1325.06 −1.26759 −0.633796 0.773500i \(-0.718504\pi\)
−0.633796 + 0.773500i \(0.718504\pi\)
\(104\) 0 0
\(105\) −17.7683 −0.0165144
\(106\) 0 0
\(107\) −1278.56 −1.15517 −0.577583 0.816332i \(-0.696004\pi\)
−0.577583 + 0.816332i \(0.696004\pi\)
\(108\) 0 0
\(109\) 313.965 0.275893 0.137947 0.990440i \(-0.455950\pi\)
0.137947 + 0.990440i \(0.455950\pi\)
\(110\) 0 0
\(111\) −219.258 −0.187487
\(112\) 0 0
\(113\) 2248.70 1.87203 0.936016 0.351958i \(-0.114484\pi\)
0.936016 + 0.351958i \(0.114484\pi\)
\(114\) 0 0
\(115\) 107.713 0.0873418
\(116\) 0 0
\(117\) 458.553 0.362335
\(118\) 0 0
\(119\) −1753.62 −1.35087
\(120\) 0 0
\(121\) −748.686 −0.562499
\(122\) 0 0
\(123\) 182.570 0.133836
\(124\) 0 0
\(125\) 167.440 0.119810
\(126\) 0 0
\(127\) −1045.71 −0.730644 −0.365322 0.930881i \(-0.619041\pi\)
−0.365322 + 0.930881i \(0.619041\pi\)
\(128\) 0 0
\(129\) −325.705 −0.222300
\(130\) 0 0
\(131\) 1723.55 1.14952 0.574761 0.818321i \(-0.305095\pi\)
0.574761 + 0.818321i \(0.305095\pi\)
\(132\) 0 0
\(133\) 544.882 0.355243
\(134\) 0 0
\(135\) 32.9290 0.0209932
\(136\) 0 0
\(137\) −740.069 −0.461521 −0.230761 0.973011i \(-0.574121\pi\)
−0.230761 + 0.973011i \(0.574121\pi\)
\(138\) 0 0
\(139\) −988.103 −0.602948 −0.301474 0.953474i \(-0.597479\pi\)
−0.301474 + 0.953474i \(0.597479\pi\)
\(140\) 0 0
\(141\) −329.756 −0.196954
\(142\) 0 0
\(143\) 423.196 0.247478
\(144\) 0 0
\(145\) −193.185 −0.110642
\(146\) 0 0
\(147\) 442.710 0.248395
\(148\) 0 0
\(149\) 2070.89 1.13862 0.569308 0.822125i \(-0.307211\pi\)
0.569308 + 0.822125i \(0.307211\pi\)
\(150\) 0 0
\(151\) 2702.62 1.45653 0.728267 0.685294i \(-0.240326\pi\)
0.728267 + 0.685294i \(0.240326\pi\)
\(152\) 0 0
\(153\) 1598.87 0.844842
\(154\) 0 0
\(155\) −31.9303 −0.0165465
\(156\) 0 0
\(157\) −190.958 −0.0970706 −0.0485353 0.998821i \(-0.515455\pi\)
−0.0485353 + 0.998821i \(0.515455\pi\)
\(158\) 0 0
\(159\) 352.283 0.175710
\(160\) 0 0
\(161\) −4603.80 −2.25360
\(162\) 0 0
\(163\) 3222.79 1.54864 0.774320 0.632795i \(-0.218092\pi\)
0.774320 + 0.632795i \(0.218092\pi\)
\(164\) 0 0
\(165\) 14.9512 0.00705424
\(166\) 0 0
\(167\) −3334.86 −1.54526 −0.772632 0.634854i \(-0.781060\pi\)
−0.772632 + 0.634854i \(0.781060\pi\)
\(168\) 0 0
\(169\) −1889.44 −0.860011
\(170\) 0 0
\(171\) −496.799 −0.222170
\(172\) 0 0
\(173\) 1037.10 0.455774 0.227887 0.973688i \(-0.426818\pi\)
0.227887 + 0.973688i \(0.426818\pi\)
\(174\) 0 0
\(175\) −3571.84 −1.54289
\(176\) 0 0
\(177\) 638.217 0.271025
\(178\) 0 0
\(179\) −1524.12 −0.636412 −0.318206 0.948022i \(-0.603080\pi\)
−0.318206 + 0.948022i \(0.603080\pi\)
\(180\) 0 0
\(181\) −4005.50 −1.64490 −0.822448 0.568840i \(-0.807392\pi\)
−0.822448 + 0.568840i \(0.807392\pi\)
\(182\) 0 0
\(183\) −764.265 −0.308722
\(184\) 0 0
\(185\) 159.316 0.0633143
\(186\) 0 0
\(187\) 1475.59 0.577035
\(188\) 0 0
\(189\) −1407.43 −0.541669
\(190\) 0 0
\(191\) −3756.82 −1.42322 −0.711608 0.702577i \(-0.752033\pi\)
−0.711608 + 0.702577i \(0.752033\pi\)
\(192\) 0 0
\(193\) −774.721 −0.288941 −0.144471 0.989509i \(-0.546148\pi\)
−0.144471 + 0.989509i \(0.546148\pi\)
\(194\) 0 0
\(195\) 10.8658 0.00399032
\(196\) 0 0
\(197\) 384.941 0.139218 0.0696089 0.997574i \(-0.477825\pi\)
0.0696089 + 0.997574i \(0.477825\pi\)
\(198\) 0 0
\(199\) 620.031 0.220869 0.110434 0.993883i \(-0.464776\pi\)
0.110434 + 0.993883i \(0.464776\pi\)
\(200\) 0 0
\(201\) −153.804 −0.0539726
\(202\) 0 0
\(203\) 8256.98 2.85481
\(204\) 0 0
\(205\) −132.658 −0.0451964
\(206\) 0 0
\(207\) 4197.54 1.40942
\(208\) 0 0
\(209\) −458.492 −0.151744
\(210\) 0 0
\(211\) 2811.84 0.917418 0.458709 0.888586i \(-0.348312\pi\)
0.458709 + 0.888586i \(0.348312\pi\)
\(212\) 0 0
\(213\) −273.716 −0.0880504
\(214\) 0 0
\(215\) 236.662 0.0750709
\(216\) 0 0
\(217\) 1364.74 0.426934
\(218\) 0 0
\(219\) −846.454 −0.261178
\(220\) 0 0
\(221\) 1072.38 0.326407
\(222\) 0 0
\(223\) −5415.68 −1.62628 −0.813141 0.582066i \(-0.802244\pi\)
−0.813141 + 0.582066i \(0.802244\pi\)
\(224\) 0 0
\(225\) 3256.64 0.964931
\(226\) 0 0
\(227\) 3930.45 1.14922 0.574611 0.818427i \(-0.305153\pi\)
0.574611 + 0.818427i \(0.305153\pi\)
\(228\) 0 0
\(229\) 2136.62 0.616558 0.308279 0.951296i \(-0.400247\pi\)
0.308279 + 0.951296i \(0.400247\pi\)
\(230\) 0 0
\(231\) −639.034 −0.182014
\(232\) 0 0
\(233\) 2841.83 0.799031 0.399516 0.916726i \(-0.369178\pi\)
0.399516 + 0.916726i \(0.369178\pi\)
\(234\) 0 0
\(235\) 239.606 0.0665114
\(236\) 0 0
\(237\) −1135.46 −0.311208
\(238\) 0 0
\(239\) 4786.45 1.29544 0.647720 0.761879i \(-0.275723\pi\)
0.647720 + 0.761879i \(0.275723\pi\)
\(240\) 0 0
\(241\) 3583.38 0.957783 0.478891 0.877874i \(-0.341039\pi\)
0.478891 + 0.877874i \(0.341039\pi\)
\(242\) 0 0
\(243\) 1935.14 0.510861
\(244\) 0 0
\(245\) −321.680 −0.0838832
\(246\) 0 0
\(247\) −333.209 −0.0858362
\(248\) 0 0
\(249\) −505.584 −0.128675
\(250\) 0 0
\(251\) 2241.78 0.563744 0.281872 0.959452i \(-0.409045\pi\)
0.281872 + 0.959452i \(0.409045\pi\)
\(252\) 0 0
\(253\) 3873.88 0.962643
\(254\) 0 0
\(255\) 37.8864 0.00930407
\(256\) 0 0
\(257\) −3307.64 −0.802819 −0.401410 0.915899i \(-0.631480\pi\)
−0.401410 + 0.915899i \(0.631480\pi\)
\(258\) 0 0
\(259\) −6809.37 −1.63364
\(260\) 0 0
\(261\) −7528.35 −1.78541
\(262\) 0 0
\(263\) 5733.35 1.34423 0.672117 0.740445i \(-0.265385\pi\)
0.672117 + 0.740445i \(0.265385\pi\)
\(264\) 0 0
\(265\) −255.974 −0.0593373
\(266\) 0 0
\(267\) −237.703 −0.0544839
\(268\) 0 0
\(269\) 4863.10 1.10226 0.551131 0.834419i \(-0.314196\pi\)
0.551131 + 0.834419i \(0.314196\pi\)
\(270\) 0 0
\(271\) 6428.81 1.44104 0.720521 0.693433i \(-0.243903\pi\)
0.720521 + 0.693433i \(0.243903\pi\)
\(272\) 0 0
\(273\) −464.417 −0.102959
\(274\) 0 0
\(275\) 3005.53 0.659056
\(276\) 0 0
\(277\) 6855.48 1.48702 0.743512 0.668722i \(-0.233158\pi\)
0.743512 + 0.668722i \(0.233158\pi\)
\(278\) 0 0
\(279\) −1244.31 −0.267007
\(280\) 0 0
\(281\) 1682.58 0.357203 0.178602 0.983921i \(-0.442843\pi\)
0.178602 + 0.983921i \(0.442843\pi\)
\(282\) 0 0
\(283\) 5894.74 1.23818 0.619091 0.785319i \(-0.287501\pi\)
0.619091 + 0.785319i \(0.287501\pi\)
\(284\) 0 0
\(285\) −11.7720 −0.00244672
\(286\) 0 0
\(287\) 5669.99 1.16616
\(288\) 0 0
\(289\) −1173.86 −0.238930
\(290\) 0 0
\(291\) 190.561 0.0383879
\(292\) 0 0
\(293\) −6625.17 −1.32098 −0.660489 0.750836i \(-0.729651\pi\)
−0.660489 + 0.750836i \(0.729651\pi\)
\(294\) 0 0
\(295\) −463.738 −0.0915251
\(296\) 0 0
\(297\) 1184.29 0.231378
\(298\) 0 0
\(299\) 2815.34 0.544532
\(300\) 0 0
\(301\) −10115.3 −1.93699
\(302\) 0 0
\(303\) 517.726 0.0981603
\(304\) 0 0
\(305\) 555.327 0.104255
\(306\) 0 0
\(307\) 4185.59 0.778125 0.389062 0.921211i \(-0.372799\pi\)
0.389062 + 0.921211i \(0.372799\pi\)
\(308\) 0 0
\(309\) −1223.58 −0.225265
\(310\) 0 0
\(311\) −507.256 −0.0924882 −0.0462441 0.998930i \(-0.514725\pi\)
−0.0462441 + 0.998930i \(0.514725\pi\)
\(312\) 0 0
\(313\) 10307.5 1.86139 0.930696 0.365793i \(-0.119202\pi\)
0.930696 + 0.365793i \(0.119202\pi\)
\(314\) 0 0
\(315\) 503.126 0.0899935
\(316\) 0 0
\(317\) 9.58898 0.00169896 0.000849481 1.00000i \(-0.499730\pi\)
0.000849481 1.00000i \(0.499730\pi\)
\(318\) 0 0
\(319\) −6947.86 −1.21945
\(320\) 0 0
\(321\) −1180.64 −0.205286
\(322\) 0 0
\(323\) −1161.82 −0.200141
\(324\) 0 0
\(325\) 2184.27 0.372804
\(326\) 0 0
\(327\) 289.919 0.0490293
\(328\) 0 0
\(329\) −10241.1 −1.71614
\(330\) 0 0
\(331\) −1770.81 −0.294055 −0.147028 0.989132i \(-0.546971\pi\)
−0.147028 + 0.989132i \(0.546971\pi\)
\(332\) 0 0
\(333\) 6208.48 1.02169
\(334\) 0 0
\(335\) 111.756 0.0182266
\(336\) 0 0
\(337\) 1494.60 0.241590 0.120795 0.992677i \(-0.461456\pi\)
0.120795 + 0.992677i \(0.461456\pi\)
\(338\) 0 0
\(339\) 2076.48 0.332681
\(340\) 0 0
\(341\) −1148.36 −0.182368
\(342\) 0 0
\(343\) 3912.46 0.615898
\(344\) 0 0
\(345\) 99.4638 0.0155216
\(346\) 0 0
\(347\) −12738.1 −1.97065 −0.985326 0.170685i \(-0.945402\pi\)
−0.985326 + 0.170685i \(0.945402\pi\)
\(348\) 0 0
\(349\) 2634.06 0.404006 0.202003 0.979385i \(-0.435255\pi\)
0.202003 + 0.979385i \(0.435255\pi\)
\(350\) 0 0
\(351\) 860.677 0.130882
\(352\) 0 0
\(353\) −8694.21 −1.31090 −0.655448 0.755241i \(-0.727520\pi\)
−0.655448 + 0.755241i \(0.727520\pi\)
\(354\) 0 0
\(355\) 198.887 0.0297347
\(356\) 0 0
\(357\) −1619.31 −0.240065
\(358\) 0 0
\(359\) 4297.38 0.631774 0.315887 0.948797i \(-0.397698\pi\)
0.315887 + 0.948797i \(0.397698\pi\)
\(360\) 0 0
\(361\) 361.000 0.0526316
\(362\) 0 0
\(363\) −691.347 −0.0999623
\(364\) 0 0
\(365\) 615.047 0.0882000
\(366\) 0 0
\(367\) −7786.34 −1.10748 −0.553738 0.832691i \(-0.686799\pi\)
−0.553738 + 0.832691i \(0.686799\pi\)
\(368\) 0 0
\(369\) −5169.64 −0.729324
\(370\) 0 0
\(371\) 10940.7 1.53103
\(372\) 0 0
\(373\) 3268.99 0.453785 0.226893 0.973920i \(-0.427143\pi\)
0.226893 + 0.973920i \(0.427143\pi\)
\(374\) 0 0
\(375\) 154.616 0.0212916
\(376\) 0 0
\(377\) −5049.35 −0.689800
\(378\) 0 0
\(379\) −2284.10 −0.309569 −0.154784 0.987948i \(-0.549468\pi\)
−0.154784 + 0.987948i \(0.549468\pi\)
\(380\) 0 0
\(381\) −965.624 −0.129844
\(382\) 0 0
\(383\) −9724.98 −1.29745 −0.648725 0.761023i \(-0.724697\pi\)
−0.648725 + 0.761023i \(0.724697\pi\)
\(384\) 0 0
\(385\) 464.332 0.0614663
\(386\) 0 0
\(387\) 9222.64 1.21140
\(388\) 0 0
\(389\) −4135.23 −0.538984 −0.269492 0.963003i \(-0.586856\pi\)
−0.269492 + 0.963003i \(0.586856\pi\)
\(390\) 0 0
\(391\) 9816.43 1.26966
\(392\) 0 0
\(393\) 1591.55 0.204283
\(394\) 0 0
\(395\) 825.045 0.105095
\(396\) 0 0
\(397\) 1908.00 0.241208 0.120604 0.992701i \(-0.461517\pi\)
0.120604 + 0.992701i \(0.461517\pi\)
\(398\) 0 0
\(399\) 503.152 0.0631305
\(400\) 0 0
\(401\) 7253.91 0.903349 0.451675 0.892183i \(-0.350827\pi\)
0.451675 + 0.892183i \(0.350827\pi\)
\(402\) 0 0
\(403\) −834.572 −0.103159
\(404\) 0 0
\(405\) −443.280 −0.0543871
\(406\) 0 0
\(407\) 5729.77 0.697823
\(408\) 0 0
\(409\) −3288.67 −0.397589 −0.198795 0.980041i \(-0.563703\pi\)
−0.198795 + 0.980041i \(0.563703\pi\)
\(410\) 0 0
\(411\) −683.390 −0.0820174
\(412\) 0 0
\(413\) 19820.8 2.36154
\(414\) 0 0
\(415\) 367.365 0.0434536
\(416\) 0 0
\(417\) −912.429 −0.107151
\(418\) 0 0
\(419\) 2946.70 0.343570 0.171785 0.985134i \(-0.445047\pi\)
0.171785 + 0.985134i \(0.445047\pi\)
\(420\) 0 0
\(421\) −3705.67 −0.428987 −0.214493 0.976725i \(-0.568810\pi\)
−0.214493 + 0.976725i \(0.568810\pi\)
\(422\) 0 0
\(423\) 9337.35 1.07328
\(424\) 0 0
\(425\) 7616.03 0.869251
\(426\) 0 0
\(427\) −23735.4 −2.69001
\(428\) 0 0
\(429\) 390.785 0.0439796
\(430\) 0 0
\(431\) −7988.10 −0.892746 −0.446373 0.894847i \(-0.647284\pi\)
−0.446373 + 0.894847i \(0.647284\pi\)
\(432\) 0 0
\(433\) 8406.05 0.932954 0.466477 0.884533i \(-0.345523\pi\)
0.466477 + 0.884533i \(0.345523\pi\)
\(434\) 0 0
\(435\) −178.390 −0.0196624
\(436\) 0 0
\(437\) −3050.15 −0.333887
\(438\) 0 0
\(439\) −984.085 −0.106988 −0.0534941 0.998568i \(-0.517036\pi\)
−0.0534941 + 0.998568i \(0.517036\pi\)
\(440\) 0 0
\(441\) −12535.7 −1.35360
\(442\) 0 0
\(443\) −7540.20 −0.808681 −0.404341 0.914608i \(-0.632499\pi\)
−0.404341 + 0.914608i \(0.632499\pi\)
\(444\) 0 0
\(445\) 172.719 0.0183992
\(446\) 0 0
\(447\) 1912.29 0.202345
\(448\) 0 0
\(449\) −2931.72 −0.308143 −0.154072 0.988060i \(-0.549239\pi\)
−0.154072 + 0.988060i \(0.549239\pi\)
\(450\) 0 0
\(451\) −4771.03 −0.498135
\(452\) 0 0
\(453\) 2495.64 0.258842
\(454\) 0 0
\(455\) 337.452 0.0347692
\(456\) 0 0
\(457\) 6833.35 0.699455 0.349727 0.936852i \(-0.386274\pi\)
0.349727 + 0.936852i \(0.386274\pi\)
\(458\) 0 0
\(459\) 3000.98 0.305172
\(460\) 0 0
\(461\) 4006.80 0.404805 0.202402 0.979302i \(-0.435125\pi\)
0.202402 + 0.979302i \(0.435125\pi\)
\(462\) 0 0
\(463\) 1786.36 0.179307 0.0896536 0.995973i \(-0.471424\pi\)
0.0896536 + 0.995973i \(0.471424\pi\)
\(464\) 0 0
\(465\) −29.4848 −0.00294049
\(466\) 0 0
\(467\) −10194.6 −1.01017 −0.505085 0.863070i \(-0.668539\pi\)
−0.505085 + 0.863070i \(0.668539\pi\)
\(468\) 0 0
\(469\) −4776.61 −0.470284
\(470\) 0 0
\(471\) −176.333 −0.0172505
\(472\) 0 0
\(473\) 8511.51 0.827399
\(474\) 0 0
\(475\) −2366.45 −0.228589
\(476\) 0 0
\(477\) −9975.21 −0.957513
\(478\) 0 0
\(479\) −153.262 −0.0146195 −0.00730973 0.999973i \(-0.502327\pi\)
−0.00730973 + 0.999973i \(0.502327\pi\)
\(480\) 0 0
\(481\) 4164.10 0.394733
\(482\) 0 0
\(483\) −4251.21 −0.400491
\(484\) 0 0
\(485\) −138.465 −0.0129636
\(486\) 0 0
\(487\) 3387.94 0.315241 0.157620 0.987500i \(-0.449618\pi\)
0.157620 + 0.987500i \(0.449618\pi\)
\(488\) 0 0
\(489\) 2975.97 0.275210
\(490\) 0 0
\(491\) −8555.18 −0.786334 −0.393167 0.919467i \(-0.628621\pi\)
−0.393167 + 0.919467i \(0.628621\pi\)
\(492\) 0 0
\(493\) −17605.9 −1.60838
\(494\) 0 0
\(495\) −423.357 −0.0384414
\(496\) 0 0
\(497\) −8500.67 −0.767218
\(498\) 0 0
\(499\) −12148.2 −1.08984 −0.544919 0.838489i \(-0.683440\pi\)
−0.544919 + 0.838489i \(0.683440\pi\)
\(500\) 0 0
\(501\) −3079.46 −0.274611
\(502\) 0 0
\(503\) 4758.81 0.421839 0.210919 0.977503i \(-0.432354\pi\)
0.210919 + 0.977503i \(0.432354\pi\)
\(504\) 0 0
\(505\) −376.188 −0.0331488
\(506\) 0 0
\(507\) −1744.74 −0.152833
\(508\) 0 0
\(509\) −11419.1 −0.994386 −0.497193 0.867640i \(-0.665636\pi\)
−0.497193 + 0.867640i \(0.665636\pi\)
\(510\) 0 0
\(511\) −26287.9 −2.27575
\(512\) 0 0
\(513\) −932.462 −0.0802519
\(514\) 0 0
\(515\) 889.071 0.0760722
\(516\) 0 0
\(517\) 8617.38 0.733060
\(518\) 0 0
\(519\) 957.669 0.0809962
\(520\) 0 0
\(521\) 8619.66 0.724826 0.362413 0.932018i \(-0.381953\pi\)
0.362413 + 0.932018i \(0.381953\pi\)
\(522\) 0 0
\(523\) −20411.3 −1.70654 −0.853271 0.521467i \(-0.825385\pi\)
−0.853271 + 0.521467i \(0.825385\pi\)
\(524\) 0 0
\(525\) −3298.29 −0.274189
\(526\) 0 0
\(527\) −2909.96 −0.240531
\(528\) 0 0
\(529\) 13604.2 1.11813
\(530\) 0 0
\(531\) −18071.7 −1.47692
\(532\) 0 0
\(533\) −3467.34 −0.281777
\(534\) 0 0
\(535\) 857.869 0.0693250
\(536\) 0 0
\(537\) −1407.39 −0.113097
\(538\) 0 0
\(539\) −11569.1 −0.924524
\(540\) 0 0
\(541\) −4553.14 −0.361838 −0.180919 0.983498i \(-0.557907\pi\)
−0.180919 + 0.983498i \(0.557907\pi\)
\(542\) 0 0
\(543\) −3698.73 −0.292316
\(544\) 0 0
\(545\) −210.660 −0.0165572
\(546\) 0 0
\(547\) 16216.8 1.26761 0.633804 0.773494i \(-0.281493\pi\)
0.633804 + 0.773494i \(0.281493\pi\)
\(548\) 0 0
\(549\) 21640.9 1.68235
\(550\) 0 0
\(551\) 5470.49 0.422960
\(552\) 0 0
\(553\) −35263.5 −2.71168
\(554\) 0 0
\(555\) 147.115 0.0112517
\(556\) 0 0
\(557\) 175.385 0.0133417 0.00667084 0.999978i \(-0.497877\pi\)
0.00667084 + 0.999978i \(0.497877\pi\)
\(558\) 0 0
\(559\) 6185.73 0.468029
\(560\) 0 0
\(561\) 1362.58 0.102545
\(562\) 0 0
\(563\) 6323.70 0.473378 0.236689 0.971585i \(-0.423938\pi\)
0.236689 + 0.971585i \(0.423938\pi\)
\(564\) 0 0
\(565\) −1508.80 −0.112346
\(566\) 0 0
\(567\) 18946.4 1.40330
\(568\) 0 0
\(569\) 12606.5 0.928811 0.464406 0.885623i \(-0.346268\pi\)
0.464406 + 0.885623i \(0.346268\pi\)
\(570\) 0 0
\(571\) −8389.93 −0.614899 −0.307450 0.951564i \(-0.599476\pi\)
−0.307450 + 0.951564i \(0.599476\pi\)
\(572\) 0 0
\(573\) −3469.10 −0.252921
\(574\) 0 0
\(575\) 19994.5 1.45014
\(576\) 0 0
\(577\) −22630.3 −1.63278 −0.816389 0.577502i \(-0.804027\pi\)
−0.816389 + 0.577502i \(0.804027\pi\)
\(578\) 0 0
\(579\) −715.388 −0.0513480
\(580\) 0 0
\(581\) −15701.7 −1.12120
\(582\) 0 0
\(583\) −9206.06 −0.653990
\(584\) 0 0
\(585\) −307.674 −0.0217449
\(586\) 0 0
\(587\) −5085.58 −0.357589 −0.178794 0.983886i \(-0.557220\pi\)
−0.178794 + 0.983886i \(0.557220\pi\)
\(588\) 0 0
\(589\) 904.180 0.0632531
\(590\) 0 0
\(591\) 355.460 0.0247405
\(592\) 0 0
\(593\) 11917.6 0.825293 0.412647 0.910891i \(-0.364604\pi\)
0.412647 + 0.910891i \(0.364604\pi\)
\(594\) 0 0
\(595\) 1176.62 0.0810700
\(596\) 0 0
\(597\) 572.545 0.0392508
\(598\) 0 0
\(599\) −3541.30 −0.241559 −0.120779 0.992679i \(-0.538539\pi\)
−0.120779 + 0.992679i \(0.538539\pi\)
\(600\) 0 0
\(601\) 8131.45 0.551895 0.275947 0.961173i \(-0.411008\pi\)
0.275947 + 0.961173i \(0.411008\pi\)
\(602\) 0 0
\(603\) 4355.10 0.294118
\(604\) 0 0
\(605\) 502.344 0.0337573
\(606\) 0 0
\(607\) −18658.0 −1.24762 −0.623809 0.781577i \(-0.714416\pi\)
−0.623809 + 0.781577i \(0.714416\pi\)
\(608\) 0 0
\(609\) 7624.62 0.507332
\(610\) 0 0
\(611\) 6262.67 0.414665
\(612\) 0 0
\(613\) 23985.1 1.58034 0.790172 0.612885i \(-0.209991\pi\)
0.790172 + 0.612885i \(0.209991\pi\)
\(614\) 0 0
\(615\) −122.499 −0.00803190
\(616\) 0 0
\(617\) −12011.0 −0.783706 −0.391853 0.920028i \(-0.628166\pi\)
−0.391853 + 0.920028i \(0.628166\pi\)
\(618\) 0 0
\(619\) −21339.0 −1.38560 −0.692800 0.721129i \(-0.743623\pi\)
−0.692800 + 0.721129i \(0.743623\pi\)
\(620\) 0 0
\(621\) 7878.53 0.509106
\(622\) 0 0
\(623\) −7382.22 −0.474739
\(624\) 0 0
\(625\) 15456.4 0.989208
\(626\) 0 0
\(627\) −423.378 −0.0269667
\(628\) 0 0
\(629\) 14519.3 0.920382
\(630\) 0 0
\(631\) 595.619 0.0375772 0.0187886 0.999823i \(-0.494019\pi\)
0.0187886 + 0.999823i \(0.494019\pi\)
\(632\) 0 0
\(633\) 2596.50 0.163035
\(634\) 0 0
\(635\) 701.637 0.0438482
\(636\) 0 0
\(637\) −8407.86 −0.522969
\(638\) 0 0
\(639\) 7750.53 0.479822
\(640\) 0 0
\(641\) 7385.91 0.455111 0.227555 0.973765i \(-0.426927\pi\)
0.227555 + 0.973765i \(0.426927\pi\)
\(642\) 0 0
\(643\) −29627.4 −1.81710 −0.908548 0.417781i \(-0.862808\pi\)
−0.908548 + 0.417781i \(0.862808\pi\)
\(644\) 0 0
\(645\) 218.537 0.0133409
\(646\) 0 0
\(647\) −8698.54 −0.528555 −0.264277 0.964447i \(-0.585133\pi\)
−0.264277 + 0.964447i \(0.585133\pi\)
\(648\) 0 0
\(649\) −16678.3 −1.00875
\(650\) 0 0
\(651\) 1260.22 0.0758709
\(652\) 0 0
\(653\) −3594.96 −0.215439 −0.107719 0.994181i \(-0.534355\pi\)
−0.107719 + 0.994181i \(0.534355\pi\)
\(654\) 0 0
\(655\) −1156.45 −0.0689864
\(656\) 0 0
\(657\) 23968.1 1.42327
\(658\) 0 0
\(659\) 25031.1 1.47962 0.739811 0.672814i \(-0.234915\pi\)
0.739811 + 0.672814i \(0.234915\pi\)
\(660\) 0 0
\(661\) 22574.8 1.32838 0.664191 0.747563i \(-0.268776\pi\)
0.664191 + 0.747563i \(0.268776\pi\)
\(662\) 0 0
\(663\) 990.250 0.0580062
\(664\) 0 0
\(665\) −365.598 −0.0213192
\(666\) 0 0
\(667\) −46221.1 −2.68319
\(668\) 0 0
\(669\) −5000.92 −0.289009
\(670\) 0 0
\(671\) 19972.2 1.14906
\(672\) 0 0
\(673\) −19302.8 −1.10560 −0.552799 0.833315i \(-0.686440\pi\)
−0.552799 + 0.833315i \(0.686440\pi\)
\(674\) 0 0
\(675\) 6112.53 0.348550
\(676\) 0 0
\(677\) 23517.4 1.33508 0.667538 0.744576i \(-0.267348\pi\)
0.667538 + 0.744576i \(0.267348\pi\)
\(678\) 0 0
\(679\) 5918.16 0.334489
\(680\) 0 0
\(681\) 3629.44 0.204230
\(682\) 0 0
\(683\) 14773.7 0.827671 0.413835 0.910352i \(-0.364189\pi\)
0.413835 + 0.910352i \(0.364189\pi\)
\(684\) 0 0
\(685\) 496.562 0.0276973
\(686\) 0 0
\(687\) 1972.98 0.109569
\(688\) 0 0
\(689\) −6690.49 −0.369938
\(690\) 0 0
\(691\) −4165.18 −0.229306 −0.114653 0.993406i \(-0.536576\pi\)
−0.114653 + 0.993406i \(0.536576\pi\)
\(692\) 0 0
\(693\) 18094.8 0.991869
\(694\) 0 0
\(695\) 662.985 0.0361848
\(696\) 0 0
\(697\) −12089.8 −0.657007
\(698\) 0 0
\(699\) 2624.18 0.141997
\(700\) 0 0
\(701\) 19303.8 1.04008 0.520039 0.854143i \(-0.325917\pi\)
0.520039 + 0.854143i \(0.325917\pi\)
\(702\) 0 0
\(703\) −4511.41 −0.242035
\(704\) 0 0
\(705\) 221.256 0.0118198
\(706\) 0 0
\(707\) 16078.7 0.855309
\(708\) 0 0
\(709\) −7913.04 −0.419155 −0.209577 0.977792i \(-0.567209\pi\)
−0.209577 + 0.977792i \(0.567209\pi\)
\(710\) 0 0
\(711\) 32151.7 1.69590
\(712\) 0 0
\(713\) −7639.57 −0.401268
\(714\) 0 0
\(715\) −283.950 −0.0148519
\(716\) 0 0
\(717\) 4419.88 0.230214
\(718\) 0 0
\(719\) −35512.6 −1.84200 −0.921000 0.389563i \(-0.872626\pi\)
−0.921000 + 0.389563i \(0.872626\pi\)
\(720\) 0 0
\(721\) −38000.1 −1.96282
\(722\) 0 0
\(723\) 3308.94 0.170209
\(724\) 0 0
\(725\) −35860.4 −1.83700
\(726\) 0 0
\(727\) 2510.77 0.128087 0.0640435 0.997947i \(-0.479600\pi\)
0.0640435 + 0.997947i \(0.479600\pi\)
\(728\) 0 0
\(729\) −16050.9 −0.815468
\(730\) 0 0
\(731\) 21568.2 1.09128
\(732\) 0 0
\(733\) −5261.38 −0.265121 −0.132560 0.991175i \(-0.542320\pi\)
−0.132560 + 0.991175i \(0.542320\pi\)
\(734\) 0 0
\(735\) −297.044 −0.0149070
\(736\) 0 0
\(737\) 4019.29 0.200885
\(738\) 0 0
\(739\) −10267.1 −0.511071 −0.255535 0.966800i \(-0.582252\pi\)
−0.255535 + 0.966800i \(0.582252\pi\)
\(740\) 0 0
\(741\) −307.689 −0.0152541
\(742\) 0 0
\(743\) −19722.5 −0.973819 −0.486910 0.873452i \(-0.661876\pi\)
−0.486910 + 0.873452i \(0.661876\pi\)
\(744\) 0 0
\(745\) −1389.50 −0.0683318
\(746\) 0 0
\(747\) 14316.1 0.701202
\(748\) 0 0
\(749\) −36666.4 −1.78873
\(750\) 0 0
\(751\) 27422.3 1.33243 0.666214 0.745760i \(-0.267914\pi\)
0.666214 + 0.745760i \(0.267914\pi\)
\(752\) 0 0
\(753\) 2070.09 0.100184
\(754\) 0 0
\(755\) −1813.37 −0.0874111
\(756\) 0 0
\(757\) −6549.67 −0.314467 −0.157234 0.987561i \(-0.550258\pi\)
−0.157234 + 0.987561i \(0.550258\pi\)
\(758\) 0 0
\(759\) 3577.20 0.171072
\(760\) 0 0
\(761\) 24815.5 1.18208 0.591038 0.806644i \(-0.298718\pi\)
0.591038 + 0.806644i \(0.298718\pi\)
\(762\) 0 0
\(763\) 9003.87 0.427211
\(764\) 0 0
\(765\) −1072.79 −0.0507016
\(766\) 0 0
\(767\) −12120.9 −0.570613
\(768\) 0 0
\(769\) 1759.56 0.0825116 0.0412558 0.999149i \(-0.486864\pi\)
0.0412558 + 0.999149i \(0.486864\pi\)
\(770\) 0 0
\(771\) −3054.32 −0.142670
\(772\) 0 0
\(773\) −20707.5 −0.963517 −0.481758 0.876304i \(-0.660002\pi\)
−0.481758 + 0.876304i \(0.660002\pi\)
\(774\) 0 0
\(775\) −5927.13 −0.274721
\(776\) 0 0
\(777\) −6287.87 −0.290317
\(778\) 0 0
\(779\) 3756.53 0.172775
\(780\) 0 0
\(781\) 7152.91 0.327723
\(782\) 0 0
\(783\) −14130.3 −0.644923
\(784\) 0 0
\(785\) 128.126 0.00582551
\(786\) 0 0
\(787\) 16060.1 0.727422 0.363711 0.931512i \(-0.381510\pi\)
0.363711 + 0.931512i \(0.381510\pi\)
\(788\) 0 0
\(789\) 5294.26 0.238885
\(790\) 0 0
\(791\) 64488.1 2.89878
\(792\) 0 0
\(793\) 14514.8 0.649980
\(794\) 0 0
\(795\) −236.370 −0.0105449
\(796\) 0 0
\(797\) −6369.68 −0.283094 −0.141547 0.989932i \(-0.545208\pi\)
−0.141547 + 0.989932i \(0.545208\pi\)
\(798\) 0 0
\(799\) 21836.5 0.966857
\(800\) 0 0
\(801\) 6730.78 0.296904
\(802\) 0 0
\(803\) 22120.0 0.972103
\(804\) 0 0
\(805\) 3089.00 0.135246
\(806\) 0 0
\(807\) 4490.66 0.195884
\(808\) 0 0
\(809\) 18129.0 0.787863 0.393932 0.919140i \(-0.371115\pi\)
0.393932 + 0.919140i \(0.371115\pi\)
\(810\) 0 0
\(811\) −29297.4 −1.26852 −0.634260 0.773120i \(-0.718695\pi\)
−0.634260 + 0.773120i \(0.718695\pi\)
\(812\) 0 0
\(813\) 5936.45 0.256089
\(814\) 0 0
\(815\) −2162.38 −0.0929386
\(816\) 0 0
\(817\) −6701.65 −0.286978
\(818\) 0 0
\(819\) 13150.4 0.561064
\(820\) 0 0
\(821\) −42698.9 −1.81510 −0.907552 0.419939i \(-0.862051\pi\)
−0.907552 + 0.419939i \(0.862051\pi\)
\(822\) 0 0
\(823\) 27961.5 1.18430 0.592149 0.805829i \(-0.298280\pi\)
0.592149 + 0.805829i \(0.298280\pi\)
\(824\) 0 0
\(825\) 2775.35 0.117122
\(826\) 0 0
\(827\) −22115.7 −0.929912 −0.464956 0.885334i \(-0.653930\pi\)
−0.464956 + 0.885334i \(0.653930\pi\)
\(828\) 0 0
\(829\) −7144.36 −0.299317 −0.149659 0.988738i \(-0.547817\pi\)
−0.149659 + 0.988738i \(0.547817\pi\)
\(830\) 0 0
\(831\) 6330.45 0.264261
\(832\) 0 0
\(833\) −29316.3 −1.21939
\(834\) 0 0
\(835\) 2237.58 0.0927361
\(836\) 0 0
\(837\) −2335.50 −0.0964475
\(838\) 0 0
\(839\) 9019.32 0.371134 0.185567 0.982632i \(-0.440588\pi\)
0.185567 + 0.982632i \(0.440588\pi\)
\(840\) 0 0
\(841\) 58509.2 2.39900
\(842\) 0 0
\(843\) 1553.72 0.0634790
\(844\) 0 0
\(845\) 1267.75 0.0516119
\(846\) 0 0
\(847\) −21470.8 −0.871011
\(848\) 0 0
\(849\) 5443.28 0.220039
\(850\) 0 0
\(851\) 38117.6 1.53544
\(852\) 0 0
\(853\) −37503.6 −1.50539 −0.752695 0.658369i \(-0.771246\pi\)
−0.752695 + 0.658369i \(0.771246\pi\)
\(854\) 0 0
\(855\) 333.336 0.0133331
\(856\) 0 0
\(857\) 19556.1 0.779490 0.389745 0.920923i \(-0.372563\pi\)
0.389745 + 0.920923i \(0.372563\pi\)
\(858\) 0 0
\(859\) 38405.1 1.52545 0.762727 0.646720i \(-0.223860\pi\)
0.762727 + 0.646720i \(0.223860\pi\)
\(860\) 0 0
\(861\) 5235.75 0.207240
\(862\) 0 0
\(863\) −22495.9 −0.887334 −0.443667 0.896192i \(-0.646323\pi\)
−0.443667 + 0.896192i \(0.646323\pi\)
\(864\) 0 0
\(865\) −695.857 −0.0273524
\(866\) 0 0
\(867\) −1083.96 −0.0424604
\(868\) 0 0
\(869\) 29672.6 1.15831
\(870\) 0 0
\(871\) 2921.01 0.113633
\(872\) 0 0
\(873\) −5395.91 −0.209191
\(874\) 0 0
\(875\) 4801.83 0.185522
\(876\) 0 0
\(877\) 44597.3 1.71716 0.858578 0.512683i \(-0.171349\pi\)
0.858578 + 0.512683i \(0.171349\pi\)
\(878\) 0 0
\(879\) −6117.78 −0.234753
\(880\) 0 0
\(881\) 36144.0 1.38220 0.691102 0.722758i \(-0.257126\pi\)
0.691102 + 0.722758i \(0.257126\pi\)
\(882\) 0 0
\(883\) 14216.5 0.541815 0.270908 0.962605i \(-0.412676\pi\)
0.270908 + 0.962605i \(0.412676\pi\)
\(884\) 0 0
\(885\) −428.223 −0.0162650
\(886\) 0 0
\(887\) 22404.0 0.848088 0.424044 0.905642i \(-0.360610\pi\)
0.424044 + 0.905642i \(0.360610\pi\)
\(888\) 0 0
\(889\) −29988.9 −1.13138
\(890\) 0 0
\(891\) −15942.5 −0.599431
\(892\) 0 0
\(893\) −6785.01 −0.254257
\(894\) 0 0
\(895\) 1022.63 0.0381930
\(896\) 0 0
\(897\) 2599.72 0.0967694
\(898\) 0 0
\(899\) 13701.7 0.508317
\(900\) 0 0
\(901\) −23328.2 −0.862569
\(902\) 0 0
\(903\) −9340.57 −0.344224
\(904\) 0 0
\(905\) 2687.56 0.0987153
\(906\) 0 0
\(907\) 16211.5 0.593489 0.296745 0.954957i \(-0.404099\pi\)
0.296745 + 0.954957i \(0.404099\pi\)
\(908\) 0 0
\(909\) −14659.9 −0.534915
\(910\) 0 0
\(911\) 8529.11 0.310189 0.155094 0.987900i \(-0.450432\pi\)
0.155094 + 0.987900i \(0.450432\pi\)
\(912\) 0 0
\(913\) 13212.2 0.478927
\(914\) 0 0
\(915\) 512.796 0.0185274
\(916\) 0 0
\(917\) 49428.0 1.78000
\(918\) 0 0
\(919\) −18155.1 −0.651666 −0.325833 0.945427i \(-0.605645\pi\)
−0.325833 + 0.945427i \(0.605645\pi\)
\(920\) 0 0
\(921\) 3865.03 0.138281
\(922\) 0 0
\(923\) 5198.37 0.185381
\(924\) 0 0
\(925\) 29573.4 1.05121
\(926\) 0 0
\(927\) 34646.8 1.22756
\(928\) 0 0
\(929\) 26472.1 0.934898 0.467449 0.884020i \(-0.345173\pi\)
0.467449 + 0.884020i \(0.345173\pi\)
\(930\) 0 0
\(931\) 9109.12 0.320665
\(932\) 0 0
\(933\) −468.407 −0.0164362
\(934\) 0 0
\(935\) −990.069 −0.0346296
\(936\) 0 0
\(937\) −3891.08 −0.135663 −0.0678313 0.997697i \(-0.521608\pi\)
−0.0678313 + 0.997697i \(0.521608\pi\)
\(938\) 0 0
\(939\) 9518.12 0.330790
\(940\) 0 0
\(941\) −5700.50 −0.197483 −0.0987413 0.995113i \(-0.531482\pi\)
−0.0987413 + 0.995113i \(0.531482\pi\)
\(942\) 0 0
\(943\) −31739.6 −1.09606
\(944\) 0 0
\(945\) 944.338 0.0325072
\(946\) 0 0
\(947\) −16631.9 −0.570712 −0.285356 0.958422i \(-0.592112\pi\)
−0.285356 + 0.958422i \(0.592112\pi\)
\(948\) 0 0
\(949\) 16075.7 0.549883
\(950\) 0 0
\(951\) 8.85460 0.000301924 0
\(952\) 0 0
\(953\) −12213.3 −0.415140 −0.207570 0.978220i \(-0.566556\pi\)
−0.207570 + 0.978220i \(0.566556\pi\)
\(954\) 0 0
\(955\) 2520.70 0.0854116
\(956\) 0 0
\(957\) −6415.75 −0.216710
\(958\) 0 0
\(959\) −21223.7 −0.714650
\(960\) 0 0
\(961\) −27526.3 −0.923982
\(962\) 0 0
\(963\) 33430.8 1.11868
\(964\) 0 0
\(965\) 519.812 0.0173402
\(966\) 0 0
\(967\) −34551.6 −1.14902 −0.574512 0.818496i \(-0.694808\pi\)
−0.574512 + 0.818496i \(0.694808\pi\)
\(968\) 0 0
\(969\) −1072.84 −0.0355672
\(970\) 0 0
\(971\) 55055.9 1.81959 0.909797 0.415053i \(-0.136237\pi\)
0.909797 + 0.415053i \(0.136237\pi\)
\(972\) 0 0
\(973\) −28336.8 −0.933645
\(974\) 0 0
\(975\) 2016.98 0.0662514
\(976\) 0 0
\(977\) −23388.2 −0.765871 −0.382935 0.923775i \(-0.625087\pi\)
−0.382935 + 0.923775i \(0.625087\pi\)
\(978\) 0 0
\(979\) 6211.79 0.202788
\(980\) 0 0
\(981\) −8209.33 −0.267180
\(982\) 0 0
\(983\) 9127.57 0.296159 0.148079 0.988975i \(-0.452691\pi\)
0.148079 + 0.988975i \(0.452691\pi\)
\(984\) 0 0
\(985\) −258.282 −0.00835489
\(986\) 0 0
\(987\) −9456.75 −0.304976
\(988\) 0 0
\(989\) 56623.4 1.82054
\(990\) 0 0
\(991\) −39058.6 −1.25201 −0.626003 0.779820i \(-0.715310\pi\)
−0.626003 + 0.779820i \(0.715310\pi\)
\(992\) 0 0
\(993\) −1635.19 −0.0522569
\(994\) 0 0
\(995\) −416.020 −0.0132550
\(996\) 0 0
\(997\) −9990.46 −0.317353 −0.158677 0.987331i \(-0.550723\pi\)
−0.158677 + 0.987331i \(0.550723\pi\)
\(998\) 0 0
\(999\) 11653.0 0.369052
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 608.4.a.j.1.4 7
4.3 odd 2 608.4.a.k.1.4 yes 7
8.3 odd 2 1216.4.a.bf.1.4 7
8.5 even 2 1216.4.a.bg.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
608.4.a.j.1.4 7 1.1 even 1 trivial
608.4.a.k.1.4 yes 7 4.3 odd 2
1216.4.a.bf.1.4 7 8.3 odd 2
1216.4.a.bg.1.4 7 8.5 even 2