Properties

Label 1088.4.a.bh.1.1
Level $1088$
Weight $4$
Character 1088.1
Self dual yes
Analytic conductor $64.194$
Analytic rank $0$
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] = [1088,4,Mod(1,1088)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1088, 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("1088.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1088.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: \(64.1940780862\)
Analytic rank: \(0\)
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: \( x^{7} - x^{6} - 67x^{5} - 35x^{4} + 893x^{3} + 595x^{2} - 3064x - 2804 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{11} \)
Twist minimal: no (minimal twist has level 544)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.97069\) of defining polynomial
Character \(\chi\) \(=\) 1088.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-9.82555 q^{3} +4.78233 q^{5} -31.4136 q^{7} +69.5414 q^{9} +O(q^{10})\) \(q-9.82555 q^{3} +4.78233 q^{5} -31.4136 q^{7} +69.5414 q^{9} +25.2655 q^{11} +72.3323 q^{13} -46.9890 q^{15} -17.0000 q^{17} -8.48512 q^{19} +308.656 q^{21} +40.5878 q^{23} -102.129 q^{25} -417.993 q^{27} -222.207 q^{29} -215.443 q^{31} -248.247 q^{33} -150.230 q^{35} +310.596 q^{37} -710.704 q^{39} -387.002 q^{41} +463.310 q^{43} +332.570 q^{45} +74.4547 q^{47} +643.817 q^{49} +167.034 q^{51} -270.732 q^{53} +120.828 q^{55} +83.3710 q^{57} +385.027 q^{59} -724.989 q^{61} -2184.55 q^{63} +345.917 q^{65} -532.662 q^{67} -398.798 q^{69} +341.675 q^{71} -493.586 q^{73} +1003.48 q^{75} -793.680 q^{77} -260.141 q^{79} +2229.39 q^{81} +137.179 q^{83} -81.2996 q^{85} +2183.30 q^{87} +57.3408 q^{89} -2272.22 q^{91} +2116.84 q^{93} -40.5787 q^{95} +484.200 q^{97} +1757.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 2 q^{7} + 67 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 2 q^{7} + 67 q^{9} + 108 q^{11} + 34 q^{13} - 128 q^{15} - 119 q^{17} + 124 q^{19} + 296 q^{21} + 6 q^{23} + 197 q^{25} - 248 q^{29} - 50 q^{31} + 512 q^{33} + 640 q^{35} + 484 q^{37} - 1504 q^{39} - 366 q^{41} + 1412 q^{43} + 80 q^{45} - 1012 q^{47} + 1115 q^{49} + 146 q^{53} - 1024 q^{55} + 48 q^{57} + 2332 q^{59} + 548 q^{61} - 2838 q^{63} - 208 q^{65} + 924 q^{67} + 1672 q^{69} - 1286 q^{71} + 870 q^{73} + 3136 q^{75} + 1344 q^{77} - 1818 q^{79} + 3039 q^{81} + 1772 q^{83} - 384 q^{87} + 1706 q^{89} + 588 q^{91} + 5576 q^{93} - 2048 q^{95} + 1802 q^{97} + 5148 q^{99}+O(q^{100}) \) 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
\(3\) −9.82555 −1.89093 −0.945464 0.325727i \(-0.894391\pi\)
−0.945464 + 0.325727i \(0.894391\pi\)
\(4\) 0 0
\(5\) 4.78233 0.427745 0.213872 0.976862i \(-0.431392\pi\)
0.213872 + 0.976862i \(0.431392\pi\)
\(6\) 0 0
\(7\) −31.4136 −1.69618 −0.848088 0.529855i \(-0.822246\pi\)
−0.848088 + 0.529855i \(0.822246\pi\)
\(8\) 0 0
\(9\) 69.5414 2.57561
\(10\) 0 0
\(11\) 25.2655 0.692529 0.346265 0.938137i \(-0.387450\pi\)
0.346265 + 0.938137i \(0.387450\pi\)
\(12\) 0 0
\(13\) 72.3323 1.54318 0.771591 0.636119i \(-0.219461\pi\)
0.771591 + 0.636119i \(0.219461\pi\)
\(14\) 0 0
\(15\) −46.9890 −0.808835
\(16\) 0 0
\(17\) −17.0000 −0.242536
\(18\) 0 0
\(19\) −8.48512 −0.102454 −0.0512269 0.998687i \(-0.516313\pi\)
−0.0512269 + 0.998687i \(0.516313\pi\)
\(20\) 0 0
\(21\) 308.656 3.20735
\(22\) 0 0
\(23\) 40.5878 0.367963 0.183982 0.982930i \(-0.441101\pi\)
0.183982 + 0.982930i \(0.441101\pi\)
\(24\) 0 0
\(25\) −102.129 −0.817034
\(26\) 0 0
\(27\) −417.993 −2.97936
\(28\) 0 0
\(29\) −222.207 −1.42285 −0.711426 0.702761i \(-0.751951\pi\)
−0.711426 + 0.702761i \(0.751951\pi\)
\(30\) 0 0
\(31\) −215.443 −1.24822 −0.624108 0.781338i \(-0.714537\pi\)
−0.624108 + 0.781338i \(0.714537\pi\)
\(32\) 0 0
\(33\) −248.247 −1.30952
\(34\) 0 0
\(35\) −150.230 −0.725531
\(36\) 0 0
\(37\) 310.596 1.38005 0.690023 0.723787i \(-0.257600\pi\)
0.690023 + 0.723787i \(0.257600\pi\)
\(38\) 0 0
\(39\) −710.704 −2.91805
\(40\) 0 0
\(41\) −387.002 −1.47414 −0.737069 0.675818i \(-0.763791\pi\)
−0.737069 + 0.675818i \(0.763791\pi\)
\(42\) 0 0
\(43\) 463.310 1.64312 0.821560 0.570122i \(-0.193104\pi\)
0.821560 + 0.570122i \(0.193104\pi\)
\(44\) 0 0
\(45\) 332.570 1.10170
\(46\) 0 0
\(47\) 74.4547 0.231071 0.115535 0.993303i \(-0.463142\pi\)
0.115535 + 0.993303i \(0.463142\pi\)
\(48\) 0 0
\(49\) 643.817 1.87702
\(50\) 0 0
\(51\) 167.034 0.458617
\(52\) 0 0
\(53\) −270.732 −0.701659 −0.350829 0.936439i \(-0.614100\pi\)
−0.350829 + 0.936439i \(0.614100\pi\)
\(54\) 0 0
\(55\) 120.828 0.296226
\(56\) 0 0
\(57\) 83.3710 0.193733
\(58\) 0 0
\(59\) 385.027 0.849598 0.424799 0.905288i \(-0.360345\pi\)
0.424799 + 0.905288i \(0.360345\pi\)
\(60\) 0 0
\(61\) −724.989 −1.52173 −0.760863 0.648913i \(-0.775224\pi\)
−0.760863 + 0.648913i \(0.775224\pi\)
\(62\) 0 0
\(63\) −2184.55 −4.36869
\(64\) 0 0
\(65\) 345.917 0.660088
\(66\) 0 0
\(67\) −532.662 −0.971269 −0.485634 0.874162i \(-0.661411\pi\)
−0.485634 + 0.874162i \(0.661411\pi\)
\(68\) 0 0
\(69\) −398.798 −0.695792
\(70\) 0 0
\(71\) 341.675 0.571118 0.285559 0.958361i \(-0.407821\pi\)
0.285559 + 0.958361i \(0.407821\pi\)
\(72\) 0 0
\(73\) −493.586 −0.791368 −0.395684 0.918387i \(-0.629492\pi\)
−0.395684 + 0.918387i \(0.629492\pi\)
\(74\) 0 0
\(75\) 1003.48 1.54495
\(76\) 0 0
\(77\) −793.680 −1.17465
\(78\) 0 0
\(79\) −260.141 −0.370482 −0.185241 0.982693i \(-0.559307\pi\)
−0.185241 + 0.982693i \(0.559307\pi\)
\(80\) 0 0
\(81\) 2229.39 3.05815
\(82\) 0 0
\(83\) 137.179 0.181414 0.0907068 0.995878i \(-0.471087\pi\)
0.0907068 + 0.995878i \(0.471087\pi\)
\(84\) 0 0
\(85\) −81.2996 −0.103743
\(86\) 0 0
\(87\) 2183.30 2.69051
\(88\) 0 0
\(89\) 57.3408 0.0682934 0.0341467 0.999417i \(-0.489129\pi\)
0.0341467 + 0.999417i \(0.489129\pi\)
\(90\) 0 0
\(91\) −2272.22 −2.61751
\(92\) 0 0
\(93\) 2116.84 2.36029
\(94\) 0 0
\(95\) −40.5787 −0.0438240
\(96\) 0 0
\(97\) 484.200 0.506836 0.253418 0.967357i \(-0.418445\pi\)
0.253418 + 0.967357i \(0.418445\pi\)
\(98\) 0 0
\(99\) 1757.00 1.78368
\(100\) 0 0
\(101\) −576.967 −0.568419 −0.284210 0.958762i \(-0.591731\pi\)
−0.284210 + 0.958762i \(0.591731\pi\)
\(102\) 0 0
\(103\) 343.211 0.328326 0.164163 0.986433i \(-0.447508\pi\)
0.164163 + 0.986433i \(0.447508\pi\)
\(104\) 0 0
\(105\) 1476.10 1.37193
\(106\) 0 0
\(107\) 188.330 0.170154 0.0850772 0.996374i \(-0.472886\pi\)
0.0850772 + 0.996374i \(0.472886\pi\)
\(108\) 0 0
\(109\) 373.234 0.327976 0.163988 0.986462i \(-0.447564\pi\)
0.163988 + 0.986462i \(0.447564\pi\)
\(110\) 0 0
\(111\) −3051.78 −2.60957
\(112\) 0 0
\(113\) 1798.43 1.49719 0.748595 0.663028i \(-0.230729\pi\)
0.748595 + 0.663028i \(0.230729\pi\)
\(114\) 0 0
\(115\) 194.105 0.157394
\(116\) 0 0
\(117\) 5030.09 3.97463
\(118\) 0 0
\(119\) 534.032 0.411383
\(120\) 0 0
\(121\) −692.657 −0.520403
\(122\) 0 0
\(123\) 3802.51 2.78749
\(124\) 0 0
\(125\) −1086.21 −0.777227
\(126\) 0 0
\(127\) −1391.93 −0.972546 −0.486273 0.873807i \(-0.661644\pi\)
−0.486273 + 0.873807i \(0.661644\pi\)
\(128\) 0 0
\(129\) −4552.28 −3.10702
\(130\) 0 0
\(131\) 2323.79 1.54985 0.774927 0.632051i \(-0.217787\pi\)
0.774927 + 0.632051i \(0.217787\pi\)
\(132\) 0 0
\(133\) 266.549 0.173780
\(134\) 0 0
\(135\) −1998.98 −1.27441
\(136\) 0 0
\(137\) 2996.64 1.86876 0.934381 0.356276i \(-0.115954\pi\)
0.934381 + 0.356276i \(0.115954\pi\)
\(138\) 0 0
\(139\) −95.2438 −0.0581185 −0.0290592 0.999578i \(-0.509251\pi\)
−0.0290592 + 0.999578i \(0.509251\pi\)
\(140\) 0 0
\(141\) −731.558 −0.436939
\(142\) 0 0
\(143\) 1827.51 1.06870
\(144\) 0 0
\(145\) −1062.67 −0.608618
\(146\) 0 0
\(147\) −6325.85 −3.54930
\(148\) 0 0
\(149\) 927.943 0.510202 0.255101 0.966914i \(-0.417891\pi\)
0.255101 + 0.966914i \(0.417891\pi\)
\(150\) 0 0
\(151\) −968.271 −0.521833 −0.260916 0.965361i \(-0.584025\pi\)
−0.260916 + 0.965361i \(0.584025\pi\)
\(152\) 0 0
\(153\) −1182.20 −0.624677
\(154\) 0 0
\(155\) −1030.32 −0.533918
\(156\) 0 0
\(157\) −586.667 −0.298224 −0.149112 0.988820i \(-0.547641\pi\)
−0.149112 + 0.988820i \(0.547641\pi\)
\(158\) 0 0
\(159\) 2660.09 1.32679
\(160\) 0 0
\(161\) −1275.01 −0.624131
\(162\) 0 0
\(163\) 1370.56 0.658594 0.329297 0.944226i \(-0.393188\pi\)
0.329297 + 0.944226i \(0.393188\pi\)
\(164\) 0 0
\(165\) −1187.20 −0.560142
\(166\) 0 0
\(167\) 440.160 0.203956 0.101978 0.994787i \(-0.467483\pi\)
0.101978 + 0.994787i \(0.467483\pi\)
\(168\) 0 0
\(169\) 3034.96 1.38141
\(170\) 0 0
\(171\) −590.068 −0.263881
\(172\) 0 0
\(173\) −507.211 −0.222905 −0.111453 0.993770i \(-0.535550\pi\)
−0.111453 + 0.993770i \(0.535550\pi\)
\(174\) 0 0
\(175\) 3208.25 1.38583
\(176\) 0 0
\(177\) −3783.10 −1.60653
\(178\) 0 0
\(179\) 4072.11 1.70036 0.850179 0.526494i \(-0.176494\pi\)
0.850179 + 0.526494i \(0.176494\pi\)
\(180\) 0 0
\(181\) 2942.09 1.20820 0.604098 0.796910i \(-0.293533\pi\)
0.604098 + 0.796910i \(0.293533\pi\)
\(182\) 0 0
\(183\) 7123.41 2.87747
\(184\) 0 0
\(185\) 1485.37 0.590308
\(186\) 0 0
\(187\) −429.513 −0.167963
\(188\) 0 0
\(189\) 13130.7 5.05353
\(190\) 0 0
\(191\) −3537.08 −1.33997 −0.669985 0.742375i \(-0.733699\pi\)
−0.669985 + 0.742375i \(0.733699\pi\)
\(192\) 0 0
\(193\) 3147.89 1.17404 0.587021 0.809572i \(-0.300301\pi\)
0.587021 + 0.809572i \(0.300301\pi\)
\(194\) 0 0
\(195\) −3398.82 −1.24818
\(196\) 0 0
\(197\) −3126.43 −1.13070 −0.565352 0.824850i \(-0.691260\pi\)
−0.565352 + 0.824850i \(0.691260\pi\)
\(198\) 0 0
\(199\) 4072.16 1.45059 0.725296 0.688437i \(-0.241703\pi\)
0.725296 + 0.688437i \(0.241703\pi\)
\(200\) 0 0
\(201\) 5233.69 1.83660
\(202\) 0 0
\(203\) 6980.32 2.41341
\(204\) 0 0
\(205\) −1850.77 −0.630555
\(206\) 0 0
\(207\) 2822.54 0.947729
\(208\) 0 0
\(209\) −214.380 −0.0709522
\(210\) 0 0
\(211\) 666.790 0.217553 0.108777 0.994066i \(-0.465307\pi\)
0.108777 + 0.994066i \(0.465307\pi\)
\(212\) 0 0
\(213\) −3357.15 −1.07994
\(214\) 0 0
\(215\) 2215.70 0.702836
\(216\) 0 0
\(217\) 6767.84 2.11719
\(218\) 0 0
\(219\) 4849.76 1.49642
\(220\) 0 0
\(221\) −1229.65 −0.374277
\(222\) 0 0
\(223\) −2608.78 −0.783395 −0.391697 0.920094i \(-0.628112\pi\)
−0.391697 + 0.920094i \(0.628112\pi\)
\(224\) 0 0
\(225\) −7102.22 −2.10436
\(226\) 0 0
\(227\) −1978.70 −0.578551 −0.289276 0.957246i \(-0.593414\pi\)
−0.289276 + 0.957246i \(0.593414\pi\)
\(228\) 0 0
\(229\) 1969.14 0.568229 0.284115 0.958790i \(-0.408300\pi\)
0.284115 + 0.958790i \(0.408300\pi\)
\(230\) 0 0
\(231\) 7798.34 2.22118
\(232\) 0 0
\(233\) −1037.21 −0.291631 −0.145815 0.989312i \(-0.546581\pi\)
−0.145815 + 0.989312i \(0.546581\pi\)
\(234\) 0 0
\(235\) 356.067 0.0988394
\(236\) 0 0
\(237\) 2556.02 0.700555
\(238\) 0 0
\(239\) −6315.68 −1.70932 −0.854659 0.519189i \(-0.826234\pi\)
−0.854659 + 0.519189i \(0.826234\pi\)
\(240\) 0 0
\(241\) −2715.86 −0.725910 −0.362955 0.931807i \(-0.618232\pi\)
−0.362955 + 0.931807i \(0.618232\pi\)
\(242\) 0 0
\(243\) −10619.2 −2.80338
\(244\) 0 0
\(245\) 3078.94 0.802884
\(246\) 0 0
\(247\) −613.748 −0.158105
\(248\) 0 0
\(249\) −1347.86 −0.343040
\(250\) 0 0
\(251\) 1412.36 0.355168 0.177584 0.984106i \(-0.443172\pi\)
0.177584 + 0.984106i \(0.443172\pi\)
\(252\) 0 0
\(253\) 1025.47 0.254825
\(254\) 0 0
\(255\) 798.814 0.196171
\(256\) 0 0
\(257\) 3979.51 0.965895 0.482947 0.875649i \(-0.339566\pi\)
0.482947 + 0.875649i \(0.339566\pi\)
\(258\) 0 0
\(259\) −9756.96 −2.34080
\(260\) 0 0
\(261\) −15452.6 −3.66471
\(262\) 0 0
\(263\) 2681.54 0.628710 0.314355 0.949305i \(-0.398212\pi\)
0.314355 + 0.949305i \(0.398212\pi\)
\(264\) 0 0
\(265\) −1294.73 −0.300131
\(266\) 0 0
\(267\) −563.405 −0.129138
\(268\) 0 0
\(269\) 3601.95 0.816412 0.408206 0.912890i \(-0.366154\pi\)
0.408206 + 0.912890i \(0.366154\pi\)
\(270\) 0 0
\(271\) −1251.18 −0.280458 −0.140229 0.990119i \(-0.544784\pi\)
−0.140229 + 0.990119i \(0.544784\pi\)
\(272\) 0 0
\(273\) 22325.8 4.94952
\(274\) 0 0
\(275\) −2580.34 −0.565820
\(276\) 0 0
\(277\) 2211.76 0.479754 0.239877 0.970803i \(-0.422893\pi\)
0.239877 + 0.970803i \(0.422893\pi\)
\(278\) 0 0
\(279\) −14982.2 −3.21491
\(280\) 0 0
\(281\) 5455.27 1.15813 0.579064 0.815282i \(-0.303418\pi\)
0.579064 + 0.815282i \(0.303418\pi\)
\(282\) 0 0
\(283\) −1640.92 −0.344674 −0.172337 0.985038i \(-0.555132\pi\)
−0.172337 + 0.985038i \(0.555132\pi\)
\(284\) 0 0
\(285\) 398.708 0.0828681
\(286\) 0 0
\(287\) 12157.2 2.50040
\(288\) 0 0
\(289\) 289.000 0.0588235
\(290\) 0 0
\(291\) −4757.53 −0.958390
\(292\) 0 0
\(293\) 949.282 0.189275 0.0946376 0.995512i \(-0.469831\pi\)
0.0946376 + 0.995512i \(0.469831\pi\)
\(294\) 0 0
\(295\) 1841.33 0.363411
\(296\) 0 0
\(297\) −10560.8 −2.06330
\(298\) 0 0
\(299\) 2935.81 0.567834
\(300\) 0 0
\(301\) −14554.3 −2.78702
\(302\) 0 0
\(303\) 5669.02 1.07484
\(304\) 0 0
\(305\) −3467.14 −0.650910
\(306\) 0 0
\(307\) −3433.54 −0.638314 −0.319157 0.947702i \(-0.603400\pi\)
−0.319157 + 0.947702i \(0.603400\pi\)
\(308\) 0 0
\(309\) −3372.23 −0.620840
\(310\) 0 0
\(311\) −4219.73 −0.769386 −0.384693 0.923044i \(-0.625693\pi\)
−0.384693 + 0.923044i \(0.625693\pi\)
\(312\) 0 0
\(313\) 10302.4 1.86047 0.930233 0.366969i \(-0.119605\pi\)
0.930233 + 0.366969i \(0.119605\pi\)
\(314\) 0 0
\(315\) −10447.2 −1.86868
\(316\) 0 0
\(317\) 11088.2 1.96459 0.982295 0.187338i \(-0.0599861\pi\)
0.982295 + 0.187338i \(0.0599861\pi\)
\(318\) 0 0
\(319\) −5614.15 −0.985367
\(320\) 0 0
\(321\) −1850.44 −0.321750
\(322\) 0 0
\(323\) 144.247 0.0248487
\(324\) 0 0
\(325\) −7387.24 −1.26083
\(326\) 0 0
\(327\) −3667.23 −0.620178
\(328\) 0 0
\(329\) −2338.89 −0.391937
\(330\) 0 0
\(331\) 4136.16 0.686839 0.343419 0.939182i \(-0.388415\pi\)
0.343419 + 0.939182i \(0.388415\pi\)
\(332\) 0 0
\(333\) 21599.3 3.55446
\(334\) 0 0
\(335\) −2547.37 −0.415455
\(336\) 0 0
\(337\) −10177.9 −1.64518 −0.822589 0.568636i \(-0.807471\pi\)
−0.822589 + 0.568636i \(0.807471\pi\)
\(338\) 0 0
\(339\) −17670.6 −2.83108
\(340\) 0 0
\(341\) −5443.26 −0.864426
\(342\) 0 0
\(343\) −9449.74 −1.48757
\(344\) 0 0
\(345\) −1907.18 −0.297621
\(346\) 0 0
\(347\) −7857.54 −1.21560 −0.607802 0.794088i \(-0.707949\pi\)
−0.607802 + 0.794088i \(0.707949\pi\)
\(348\) 0 0
\(349\) −9125.05 −1.39958 −0.699789 0.714349i \(-0.746723\pi\)
−0.699789 + 0.714349i \(0.746723\pi\)
\(350\) 0 0
\(351\) −30234.4 −4.59770
\(352\) 0 0
\(353\) 6800.32 1.02534 0.512669 0.858586i \(-0.328657\pi\)
0.512669 + 0.858586i \(0.328657\pi\)
\(354\) 0 0
\(355\) 1634.00 0.244293
\(356\) 0 0
\(357\) −5247.16 −0.777896
\(358\) 0 0
\(359\) −5094.04 −0.748894 −0.374447 0.927248i \(-0.622168\pi\)
−0.374447 + 0.927248i \(0.622168\pi\)
\(360\) 0 0
\(361\) −6787.00 −0.989503
\(362\) 0 0
\(363\) 6805.73 0.984045
\(364\) 0 0
\(365\) −2360.49 −0.338504
\(366\) 0 0
\(367\) 12242.5 1.74129 0.870646 0.491909i \(-0.163701\pi\)
0.870646 + 0.491909i \(0.163701\pi\)
\(368\) 0 0
\(369\) −26912.7 −3.79680
\(370\) 0 0
\(371\) 8504.68 1.19014
\(372\) 0 0
\(373\) 2538.51 0.352384 0.176192 0.984356i \(-0.443622\pi\)
0.176192 + 0.984356i \(0.443622\pi\)
\(374\) 0 0
\(375\) 10672.6 1.46968
\(376\) 0 0
\(377\) −16072.7 −2.19572
\(378\) 0 0
\(379\) 10337.5 1.40106 0.700528 0.713625i \(-0.252948\pi\)
0.700528 + 0.713625i \(0.252948\pi\)
\(380\) 0 0
\(381\) 13676.4 1.83902
\(382\) 0 0
\(383\) 6184.48 0.825097 0.412549 0.910936i \(-0.364639\pi\)
0.412549 + 0.910936i \(0.364639\pi\)
\(384\) 0 0
\(385\) −3795.64 −0.502451
\(386\) 0 0
\(387\) 32219.3 4.23203
\(388\) 0 0
\(389\) 1150.38 0.149940 0.0749699 0.997186i \(-0.476114\pi\)
0.0749699 + 0.997186i \(0.476114\pi\)
\(390\) 0 0
\(391\) −689.993 −0.0892442
\(392\) 0 0
\(393\) −22832.6 −2.93066
\(394\) 0 0
\(395\) −1244.08 −0.158472
\(396\) 0 0
\(397\) −5511.93 −0.696816 −0.348408 0.937343i \(-0.613278\pi\)
−0.348408 + 0.937343i \(0.613278\pi\)
\(398\) 0 0
\(399\) −2618.99 −0.328605
\(400\) 0 0
\(401\) −1138.27 −0.141752 −0.0708761 0.997485i \(-0.522580\pi\)
−0.0708761 + 0.997485i \(0.522580\pi\)
\(402\) 0 0
\(403\) −15583.5 −1.92622
\(404\) 0 0
\(405\) 10661.7 1.30811
\(406\) 0 0
\(407\) 7847.36 0.955722
\(408\) 0 0
\(409\) 1848.76 0.223510 0.111755 0.993736i \(-0.464353\pi\)
0.111755 + 0.993736i \(0.464353\pi\)
\(410\) 0 0
\(411\) −29443.6 −3.53369
\(412\) 0 0
\(413\) −12095.1 −1.44107
\(414\) 0 0
\(415\) 656.035 0.0775987
\(416\) 0 0
\(417\) 935.822 0.109898
\(418\) 0 0
\(419\) −2951.99 −0.344187 −0.172093 0.985081i \(-0.555053\pi\)
−0.172093 + 0.985081i \(0.555053\pi\)
\(420\) 0 0
\(421\) −2836.80 −0.328402 −0.164201 0.986427i \(-0.552504\pi\)
−0.164201 + 0.986427i \(0.552504\pi\)
\(422\) 0 0
\(423\) 5177.69 0.595148
\(424\) 0 0
\(425\) 1736.20 0.198160
\(426\) 0 0
\(427\) 22774.5 2.58112
\(428\) 0 0
\(429\) −17956.3 −2.02083
\(430\) 0 0
\(431\) −2330.19 −0.260420 −0.130210 0.991486i \(-0.541565\pi\)
−0.130210 + 0.991486i \(0.541565\pi\)
\(432\) 0 0
\(433\) −6900.15 −0.765820 −0.382910 0.923786i \(-0.625078\pi\)
−0.382910 + 0.923786i \(0.625078\pi\)
\(434\) 0 0
\(435\) 10441.3 1.15085
\(436\) 0 0
\(437\) −344.393 −0.0376992
\(438\) 0 0
\(439\) 11428.6 1.24250 0.621248 0.783614i \(-0.286626\pi\)
0.621248 + 0.783614i \(0.286626\pi\)
\(440\) 0 0
\(441\) 44771.9 4.83446
\(442\) 0 0
\(443\) 13566.6 1.45501 0.727503 0.686105i \(-0.240681\pi\)
0.727503 + 0.686105i \(0.240681\pi\)
\(444\) 0 0
\(445\) 274.223 0.0292121
\(446\) 0 0
\(447\) −9117.55 −0.964755
\(448\) 0 0
\(449\) −7070.48 −0.743154 −0.371577 0.928402i \(-0.621183\pi\)
−0.371577 + 0.928402i \(0.621183\pi\)
\(450\) 0 0
\(451\) −9777.79 −1.02088
\(452\) 0 0
\(453\) 9513.80 0.986749
\(454\) 0 0
\(455\) −10866.5 −1.11963
\(456\) 0 0
\(457\) 11888.1 1.21686 0.608429 0.793608i \(-0.291800\pi\)
0.608429 + 0.793608i \(0.291800\pi\)
\(458\) 0 0
\(459\) 7105.88 0.722602
\(460\) 0 0
\(461\) 15019.0 1.51737 0.758683 0.651460i \(-0.225843\pi\)
0.758683 + 0.651460i \(0.225843\pi\)
\(462\) 0 0
\(463\) 8898.99 0.893242 0.446621 0.894723i \(-0.352627\pi\)
0.446621 + 0.894723i \(0.352627\pi\)
\(464\) 0 0
\(465\) 10123.5 1.00960
\(466\) 0 0
\(467\) 16088.7 1.59421 0.797105 0.603841i \(-0.206364\pi\)
0.797105 + 0.603841i \(0.206364\pi\)
\(468\) 0 0
\(469\) 16732.8 1.64744
\(470\) 0 0
\(471\) 5764.32 0.563919
\(472\) 0 0
\(473\) 11705.7 1.13791
\(474\) 0 0
\(475\) 866.580 0.0837082
\(476\) 0 0
\(477\) −18827.1 −1.80720
\(478\) 0 0
\(479\) −20715.7 −1.97604 −0.988020 0.154329i \(-0.950679\pi\)
−0.988020 + 0.154329i \(0.950679\pi\)
\(480\) 0 0
\(481\) 22466.1 2.12966
\(482\) 0 0
\(483\) 12527.7 1.18019
\(484\) 0 0
\(485\) 2315.61 0.216796
\(486\) 0 0
\(487\) 8182.89 0.761401 0.380700 0.924698i \(-0.375683\pi\)
0.380700 + 0.924698i \(0.375683\pi\)
\(488\) 0 0
\(489\) −13466.5 −1.24535
\(490\) 0 0
\(491\) −2500.68 −0.229845 −0.114922 0.993374i \(-0.536662\pi\)
−0.114922 + 0.993374i \(0.536662\pi\)
\(492\) 0 0
\(493\) 3777.51 0.345093
\(494\) 0 0
\(495\) 8402.54 0.762962
\(496\) 0 0
\(497\) −10733.3 −0.968718
\(498\) 0 0
\(499\) 17638.8 1.58241 0.791203 0.611553i \(-0.209455\pi\)
0.791203 + 0.611553i \(0.209455\pi\)
\(500\) 0 0
\(501\) −4324.82 −0.385666
\(502\) 0 0
\(503\) −5199.12 −0.460870 −0.230435 0.973088i \(-0.574015\pi\)
−0.230435 + 0.973088i \(0.574015\pi\)
\(504\) 0 0
\(505\) −2759.25 −0.243138
\(506\) 0 0
\(507\) −29820.1 −2.61215
\(508\) 0 0
\(509\) −14573.8 −1.26910 −0.634549 0.772883i \(-0.718814\pi\)
−0.634549 + 0.772883i \(0.718814\pi\)
\(510\) 0 0
\(511\) 15505.3 1.34230
\(512\) 0 0
\(513\) 3546.72 0.305247
\(514\) 0 0
\(515\) 1641.35 0.140440
\(516\) 0 0
\(517\) 1881.13 0.160023
\(518\) 0 0
\(519\) 4983.63 0.421497
\(520\) 0 0
\(521\) 6274.38 0.527612 0.263806 0.964576i \(-0.415022\pi\)
0.263806 + 0.964576i \(0.415022\pi\)
\(522\) 0 0
\(523\) 12818.6 1.07174 0.535868 0.844302i \(-0.319985\pi\)
0.535868 + 0.844302i \(0.319985\pi\)
\(524\) 0 0
\(525\) −31522.8 −2.62051
\(526\) 0 0
\(527\) 3662.53 0.302737
\(528\) 0 0
\(529\) −10519.6 −0.864603
\(530\) 0 0
\(531\) 26775.3 2.18823
\(532\) 0 0
\(533\) −27992.8 −2.27486
\(534\) 0 0
\(535\) 900.656 0.0727827
\(536\) 0 0
\(537\) −40010.8 −3.21525
\(538\) 0 0
\(539\) 16266.3 1.29989
\(540\) 0 0
\(541\) 6380.97 0.507097 0.253549 0.967323i \(-0.418402\pi\)
0.253549 + 0.967323i \(0.418402\pi\)
\(542\) 0 0
\(543\) −28907.6 −2.28461
\(544\) 0 0
\(545\) 1784.93 0.140290
\(546\) 0 0
\(547\) 19317.0 1.50994 0.754968 0.655761i \(-0.227652\pi\)
0.754968 + 0.655761i \(0.227652\pi\)
\(548\) 0 0
\(549\) −50416.8 −3.91937
\(550\) 0 0
\(551\) 1885.45 0.145777
\(552\) 0 0
\(553\) 8171.96 0.628403
\(554\) 0 0
\(555\) −14594.6 −1.11623
\(556\) 0 0
\(557\) 15712.8 1.19528 0.597642 0.801763i \(-0.296104\pi\)
0.597642 + 0.801763i \(0.296104\pi\)
\(558\) 0 0
\(559\) 33512.3 2.53563
\(560\) 0 0
\(561\) 4220.20 0.317606
\(562\) 0 0
\(563\) 24974.0 1.86950 0.934751 0.355304i \(-0.115623\pi\)
0.934751 + 0.355304i \(0.115623\pi\)
\(564\) 0 0
\(565\) 8600.71 0.640415
\(566\) 0 0
\(567\) −70033.3 −5.18717
\(568\) 0 0
\(569\) −5049.16 −0.372007 −0.186003 0.982549i \(-0.559554\pi\)
−0.186003 + 0.982549i \(0.559554\pi\)
\(570\) 0 0
\(571\) 17697.6 1.29706 0.648530 0.761189i \(-0.275384\pi\)
0.648530 + 0.761189i \(0.275384\pi\)
\(572\) 0 0
\(573\) 34753.8 2.53379
\(574\) 0 0
\(575\) −4145.21 −0.300639
\(576\) 0 0
\(577\) −19390.5 −1.39903 −0.699513 0.714620i \(-0.746600\pi\)
−0.699513 + 0.714620i \(0.746600\pi\)
\(578\) 0 0
\(579\) −30929.7 −2.22003
\(580\) 0 0
\(581\) −4309.29 −0.307710
\(582\) 0 0
\(583\) −6840.17 −0.485919
\(584\) 0 0
\(585\) 24055.6 1.70013
\(586\) 0 0
\(587\) 15898.5 1.11789 0.558946 0.829204i \(-0.311206\pi\)
0.558946 + 0.829204i \(0.311206\pi\)
\(588\) 0 0
\(589\) 1828.06 0.127884
\(590\) 0 0
\(591\) 30718.9 2.13808
\(592\) 0 0
\(593\) 5849.37 0.405067 0.202533 0.979275i \(-0.435082\pi\)
0.202533 + 0.979275i \(0.435082\pi\)
\(594\) 0 0
\(595\) 2553.92 0.175967
\(596\) 0 0
\(597\) −40011.2 −2.74297
\(598\) 0 0
\(599\) 2126.73 0.145068 0.0725340 0.997366i \(-0.476891\pi\)
0.0725340 + 0.997366i \(0.476891\pi\)
\(600\) 0 0
\(601\) −5400.05 −0.366510 −0.183255 0.983065i \(-0.558663\pi\)
−0.183255 + 0.983065i \(0.558663\pi\)
\(602\) 0 0
\(603\) −37042.1 −2.50161
\(604\) 0 0
\(605\) −3312.51 −0.222600
\(606\) 0 0
\(607\) 8805.60 0.588811 0.294406 0.955681i \(-0.404878\pi\)
0.294406 + 0.955681i \(0.404878\pi\)
\(608\) 0 0
\(609\) −68585.5 −4.56359
\(610\) 0 0
\(611\) 5385.48 0.356584
\(612\) 0 0
\(613\) 6701.54 0.441554 0.220777 0.975324i \(-0.429141\pi\)
0.220777 + 0.975324i \(0.429141\pi\)
\(614\) 0 0
\(615\) 18184.9 1.19233
\(616\) 0 0
\(617\) 372.923 0.0243328 0.0121664 0.999926i \(-0.496127\pi\)
0.0121664 + 0.999926i \(0.496127\pi\)
\(618\) 0 0
\(619\) −24575.2 −1.59573 −0.797867 0.602834i \(-0.794038\pi\)
−0.797867 + 0.602834i \(0.794038\pi\)
\(620\) 0 0
\(621\) −16965.4 −1.09630
\(622\) 0 0
\(623\) −1801.28 −0.115838
\(624\) 0 0
\(625\) 7571.56 0.484580
\(626\) 0 0
\(627\) 2106.41 0.134165
\(628\) 0 0
\(629\) −5280.14 −0.334710
\(630\) 0 0
\(631\) 1434.70 0.0905144 0.0452572 0.998975i \(-0.485589\pi\)
0.0452572 + 0.998975i \(0.485589\pi\)
\(632\) 0 0
\(633\) −6551.58 −0.411377
\(634\) 0 0
\(635\) −6656.65 −0.416002
\(636\) 0 0
\(637\) 46568.7 2.89658
\(638\) 0 0
\(639\) 23760.6 1.47098
\(640\) 0 0
\(641\) 15095.1 0.930138 0.465069 0.885274i \(-0.346029\pi\)
0.465069 + 0.885274i \(0.346029\pi\)
\(642\) 0 0
\(643\) −24785.5 −1.52013 −0.760067 0.649845i \(-0.774834\pi\)
−0.760067 + 0.649845i \(0.774834\pi\)
\(644\) 0 0
\(645\) −21770.5 −1.32901
\(646\) 0 0
\(647\) −5515.74 −0.335157 −0.167578 0.985859i \(-0.553595\pi\)
−0.167578 + 0.985859i \(0.553595\pi\)
\(648\) 0 0
\(649\) 9727.89 0.588371
\(650\) 0 0
\(651\) −66497.8 −4.00346
\(652\) 0 0
\(653\) 2126.79 0.127455 0.0637273 0.997967i \(-0.479701\pi\)
0.0637273 + 0.997967i \(0.479701\pi\)
\(654\) 0 0
\(655\) 11113.2 0.662942
\(656\) 0 0
\(657\) −34324.7 −2.03826
\(658\) 0 0
\(659\) −5366.36 −0.317213 −0.158607 0.987342i \(-0.550700\pi\)
−0.158607 + 0.987342i \(0.550700\pi\)
\(660\) 0 0
\(661\) 295.485 0.0173873 0.00869367 0.999962i \(-0.497233\pi\)
0.00869367 + 0.999962i \(0.497233\pi\)
\(662\) 0 0
\(663\) 12082.0 0.707730
\(664\) 0 0
\(665\) 1274.72 0.0743333
\(666\) 0 0
\(667\) −9018.89 −0.523557
\(668\) 0 0
\(669\) 25632.7 1.48134
\(670\) 0 0
\(671\) −18317.2 −1.05384
\(672\) 0 0
\(673\) 12772.8 0.731585 0.365792 0.930696i \(-0.380798\pi\)
0.365792 + 0.930696i \(0.380798\pi\)
\(674\) 0 0
\(675\) 42689.3 2.43424
\(676\) 0 0
\(677\) −325.253 −0.0184645 −0.00923226 0.999957i \(-0.502939\pi\)
−0.00923226 + 0.999957i \(0.502939\pi\)
\(678\) 0 0
\(679\) −15210.5 −0.859683
\(680\) 0 0
\(681\) 19441.8 1.09400
\(682\) 0 0
\(683\) −17438.3 −0.976954 −0.488477 0.872577i \(-0.662447\pi\)
−0.488477 + 0.872577i \(0.662447\pi\)
\(684\) 0 0
\(685\) 14330.9 0.799353
\(686\) 0 0
\(687\) −19347.9 −1.07448
\(688\) 0 0
\(689\) −19582.7 −1.08279
\(690\) 0 0
\(691\) −20220.1 −1.11318 −0.556592 0.830786i \(-0.687891\pi\)
−0.556592 + 0.830786i \(0.687891\pi\)
\(692\) 0 0
\(693\) −55193.6 −3.02544
\(694\) 0 0
\(695\) −455.487 −0.0248599
\(696\) 0 0
\(697\) 6579.04 0.357531
\(698\) 0 0
\(699\) 10191.2 0.551453
\(700\) 0 0
\(701\) −10335.5 −0.556869 −0.278435 0.960455i \(-0.589816\pi\)
−0.278435 + 0.960455i \(0.589816\pi\)
\(702\) 0 0
\(703\) −2635.45 −0.141391
\(704\) 0 0
\(705\) −3498.56 −0.186898
\(706\) 0 0
\(707\) 18124.6 0.964140
\(708\) 0 0
\(709\) 36807.0 1.94967 0.974835 0.222927i \(-0.0715611\pi\)
0.974835 + 0.222927i \(0.0715611\pi\)
\(710\) 0 0
\(711\) −18090.5 −0.954217
\(712\) 0 0
\(713\) −8744.36 −0.459297
\(714\) 0 0
\(715\) 8739.75 0.457130
\(716\) 0 0
\(717\) 62055.0 3.23220
\(718\) 0 0
\(719\) −6204.20 −0.321805 −0.160902 0.986970i \(-0.551440\pi\)
−0.160902 + 0.986970i \(0.551440\pi\)
\(720\) 0 0
\(721\) −10781.5 −0.556899
\(722\) 0 0
\(723\) 26684.9 1.37264
\(724\) 0 0
\(725\) 22693.8 1.16252
\(726\) 0 0
\(727\) 16362.3 0.834726 0.417363 0.908740i \(-0.362954\pi\)
0.417363 + 0.908740i \(0.362954\pi\)
\(728\) 0 0
\(729\) 44145.9 2.24284
\(730\) 0 0
\(731\) −7876.27 −0.398515
\(732\) 0 0
\(733\) 15333.2 0.772640 0.386320 0.922365i \(-0.373746\pi\)
0.386320 + 0.922365i \(0.373746\pi\)
\(734\) 0 0
\(735\) −30252.3 −1.51820
\(736\) 0 0
\(737\) −13457.9 −0.672632
\(738\) 0 0
\(739\) 1454.83 0.0724178 0.0362089 0.999344i \(-0.488472\pi\)
0.0362089 + 0.999344i \(0.488472\pi\)
\(740\) 0 0
\(741\) 6030.41 0.298965
\(742\) 0 0
\(743\) 21843.5 1.07855 0.539274 0.842130i \(-0.318699\pi\)
0.539274 + 0.842130i \(0.318699\pi\)
\(744\) 0 0
\(745\) 4437.73 0.218236
\(746\) 0 0
\(747\) 9539.61 0.467251
\(748\) 0 0
\(749\) −5916.12 −0.288612
\(750\) 0 0
\(751\) −248.492 −0.0120741 −0.00603703 0.999982i \(-0.501922\pi\)
−0.00603703 + 0.999982i \(0.501922\pi\)
\(752\) 0 0
\(753\) −13877.2 −0.671597
\(754\) 0 0
\(755\) −4630.59 −0.223211
\(756\) 0 0
\(757\) 13766.8 0.660980 0.330490 0.943810i \(-0.392786\pi\)
0.330490 + 0.943810i \(0.392786\pi\)
\(758\) 0 0
\(759\) −10075.8 −0.481856
\(760\) 0 0
\(761\) −10363.2 −0.493646 −0.246823 0.969061i \(-0.579387\pi\)
−0.246823 + 0.969061i \(0.579387\pi\)
\(762\) 0 0
\(763\) −11724.6 −0.556305
\(764\) 0 0
\(765\) −5653.69 −0.267202
\(766\) 0 0
\(767\) 27849.9 1.31108
\(768\) 0 0
\(769\) 36605.3 1.71654 0.858271 0.513197i \(-0.171539\pi\)
0.858271 + 0.513197i \(0.171539\pi\)
\(770\) 0 0
\(771\) −39100.9 −1.82644
\(772\) 0 0
\(773\) 5876.31 0.273423 0.136712 0.990611i \(-0.456347\pi\)
0.136712 + 0.990611i \(0.456347\pi\)
\(774\) 0 0
\(775\) 22003.0 1.01983
\(776\) 0 0
\(777\) 95867.5 4.42629
\(778\) 0 0
\(779\) 3283.76 0.151031
\(780\) 0 0
\(781\) 8632.58 0.395516
\(782\) 0 0
\(783\) 92880.8 4.23920
\(784\) 0 0
\(785\) −2805.63 −0.127564
\(786\) 0 0
\(787\) 8932.04 0.404565 0.202283 0.979327i \(-0.435164\pi\)
0.202283 + 0.979327i \(0.435164\pi\)
\(788\) 0 0
\(789\) −26347.6 −1.18885
\(790\) 0 0
\(791\) −56495.4 −2.53950
\(792\) 0 0
\(793\) −52440.1 −2.34830
\(794\) 0 0
\(795\) 12721.4 0.567526
\(796\) 0 0
\(797\) 3732.65 0.165894 0.0829468 0.996554i \(-0.473567\pi\)
0.0829468 + 0.996554i \(0.473567\pi\)
\(798\) 0 0
\(799\) −1265.73 −0.0560429
\(800\) 0 0
\(801\) 3987.56 0.175897
\(802\) 0 0
\(803\) −12470.7 −0.548046
\(804\) 0 0
\(805\) −6097.53 −0.266969
\(806\) 0 0
\(807\) −35391.2 −1.54378
\(808\) 0 0
\(809\) −23045.5 −1.00153 −0.500764 0.865584i \(-0.666948\pi\)
−0.500764 + 0.865584i \(0.666948\pi\)
\(810\) 0 0
\(811\) 36697.8 1.58894 0.794471 0.607301i \(-0.207748\pi\)
0.794471 + 0.607301i \(0.207748\pi\)
\(812\) 0 0
\(813\) 12293.6 0.530325
\(814\) 0 0
\(815\) 6554.49 0.281710
\(816\) 0 0
\(817\) −3931.24 −0.168344
\(818\) 0 0
\(819\) −158013. −6.74168
\(820\) 0 0
\(821\) 13102.3 0.556970 0.278485 0.960441i \(-0.410168\pi\)
0.278485 + 0.960441i \(0.410168\pi\)
\(822\) 0 0
\(823\) 3392.07 0.143670 0.0718348 0.997417i \(-0.477115\pi\)
0.0718348 + 0.997417i \(0.477115\pi\)
\(824\) 0 0
\(825\) 25353.3 1.06993
\(826\) 0 0
\(827\) −18548.1 −0.779904 −0.389952 0.920835i \(-0.627508\pi\)
−0.389952 + 0.920835i \(0.627508\pi\)
\(828\) 0 0
\(829\) 31374.4 1.31445 0.657224 0.753695i \(-0.271730\pi\)
0.657224 + 0.753695i \(0.271730\pi\)
\(830\) 0 0
\(831\) −21731.8 −0.907181
\(832\) 0 0
\(833\) −10944.9 −0.455243
\(834\) 0 0
\(835\) 2104.99 0.0872410
\(836\) 0 0
\(837\) 90053.6 3.71889
\(838\) 0 0
\(839\) 30785.1 1.26677 0.633386 0.773836i \(-0.281665\pi\)
0.633386 + 0.773836i \(0.281665\pi\)
\(840\) 0 0
\(841\) 24986.8 1.02451
\(842\) 0 0
\(843\) −53601.0 −2.18994
\(844\) 0 0
\(845\) 14514.2 0.590891
\(846\) 0 0
\(847\) 21758.9 0.882696
\(848\) 0 0
\(849\) 16123.0 0.651754
\(850\) 0 0
\(851\) 12606.4 0.507806
\(852\) 0 0
\(853\) −41137.6 −1.65126 −0.825630 0.564212i \(-0.809180\pi\)
−0.825630 + 0.564212i \(0.809180\pi\)
\(854\) 0 0
\(855\) −2821.90 −0.112874
\(856\) 0 0
\(857\) −19075.8 −0.760345 −0.380172 0.924916i \(-0.624135\pi\)
−0.380172 + 0.924916i \(0.624135\pi\)
\(858\) 0 0
\(859\) −8716.76 −0.346231 −0.173115 0.984902i \(-0.555383\pi\)
−0.173115 + 0.984902i \(0.555383\pi\)
\(860\) 0 0
\(861\) −119451. −4.72807
\(862\) 0 0
\(863\) −35845.2 −1.41389 −0.706943 0.707270i \(-0.749926\pi\)
−0.706943 + 0.707270i \(0.749926\pi\)
\(864\) 0 0
\(865\) −2425.65 −0.0953465
\(866\) 0 0
\(867\) −2839.58 −0.111231
\(868\) 0 0
\(869\) −6572.57 −0.256570
\(870\) 0 0
\(871\) −38528.6 −1.49884
\(872\) 0 0
\(873\) 33672.0 1.30541
\(874\) 0 0
\(875\) 34121.7 1.31831
\(876\) 0 0
\(877\) −20973.5 −0.807556 −0.403778 0.914857i \(-0.632303\pi\)
−0.403778 + 0.914857i \(0.632303\pi\)
\(878\) 0 0
\(879\) −9327.21 −0.357906
\(880\) 0 0
\(881\) −26246.8 −1.00372 −0.501861 0.864948i \(-0.667351\pi\)
−0.501861 + 0.864948i \(0.667351\pi\)
\(882\) 0 0
\(883\) −36750.5 −1.40063 −0.700313 0.713836i \(-0.746956\pi\)
−0.700313 + 0.713836i \(0.746956\pi\)
\(884\) 0 0
\(885\) −18092.1 −0.687184
\(886\) 0 0
\(887\) −11807.1 −0.446950 −0.223475 0.974710i \(-0.571740\pi\)
−0.223475 + 0.974710i \(0.571740\pi\)
\(888\) 0 0
\(889\) 43725.4 1.64961
\(890\) 0 0
\(891\) 56326.6 2.11786
\(892\) 0 0
\(893\) −631.757 −0.0236741
\(894\) 0 0
\(895\) 19474.2 0.727319
\(896\) 0 0
\(897\) −28846.0 −1.07373
\(898\) 0 0
\(899\) 47872.8 1.77603
\(900\) 0 0
\(901\) 4602.45 0.170177
\(902\) 0 0
\(903\) 143004. 5.27006
\(904\) 0 0
\(905\) 14070.0 0.516800
\(906\) 0 0
\(907\) 21549.1 0.788894 0.394447 0.918919i \(-0.370936\pi\)
0.394447 + 0.918919i \(0.370936\pi\)
\(908\) 0 0
\(909\) −40123.1 −1.46403
\(910\) 0 0
\(911\) 8561.19 0.311356 0.155678 0.987808i \(-0.450244\pi\)
0.155678 + 0.987808i \(0.450244\pi\)
\(912\) 0 0
\(913\) 3465.89 0.125634
\(914\) 0 0
\(915\) 34066.5 1.23082
\(916\) 0 0
\(917\) −72998.8 −2.62883
\(918\) 0 0
\(919\) −18999.2 −0.681965 −0.340983 0.940070i \(-0.610760\pi\)
−0.340983 + 0.940070i \(0.610760\pi\)
\(920\) 0 0
\(921\) 33736.4 1.20701
\(922\) 0 0
\(923\) 24714.2 0.881339
\(924\) 0 0
\(925\) −31721.0 −1.12755
\(926\) 0 0
\(927\) 23867.4 0.845639
\(928\) 0 0
\(929\) 34845.6 1.23062 0.615311 0.788284i \(-0.289030\pi\)
0.615311 + 0.788284i \(0.289030\pi\)
\(930\) 0 0
\(931\) −5462.86 −0.192307
\(932\) 0 0
\(933\) 41461.2 1.45485
\(934\) 0 0
\(935\) −2054.07 −0.0718453
\(936\) 0 0
\(937\) −34508.0 −1.20313 −0.601563 0.798825i \(-0.705455\pi\)
−0.601563 + 0.798825i \(0.705455\pi\)
\(938\) 0 0
\(939\) −101227. −3.51801
\(940\) 0 0
\(941\) 485.186 0.0168083 0.00840416 0.999965i \(-0.497325\pi\)
0.00840416 + 0.999965i \(0.497325\pi\)
\(942\) 0 0
\(943\) −15707.6 −0.542428
\(944\) 0 0
\(945\) 62795.3 2.16162
\(946\) 0 0
\(947\) 28153.8 0.966077 0.483038 0.875599i \(-0.339533\pi\)
0.483038 + 0.875599i \(0.339533\pi\)
\(948\) 0 0
\(949\) −35702.2 −1.22123
\(950\) 0 0
\(951\) −108948. −3.71490
\(952\) 0 0
\(953\) −47163.6 −1.60313 −0.801563 0.597910i \(-0.795998\pi\)
−0.801563 + 0.597910i \(0.795998\pi\)
\(954\) 0 0
\(955\) −16915.5 −0.573165
\(956\) 0 0
\(957\) 55162.1 1.86326
\(958\) 0 0
\(959\) −94135.4 −3.16975
\(960\) 0 0
\(961\) 16624.6 0.558041
\(962\) 0 0
\(963\) 13096.7 0.438251
\(964\) 0 0
\(965\) 15054.3 0.502190
\(966\) 0 0
\(967\) 33489.3 1.11370 0.556848 0.830615i \(-0.312011\pi\)
0.556848 + 0.830615i \(0.312011\pi\)
\(968\) 0 0
\(969\) −1417.31 −0.0469871
\(970\) 0 0
\(971\) −18478.6 −0.610717 −0.305358 0.952238i \(-0.598776\pi\)
−0.305358 + 0.952238i \(0.598776\pi\)
\(972\) 0 0
\(973\) 2991.95 0.0985792
\(974\) 0 0
\(975\) 72583.7 2.38414
\(976\) 0 0
\(977\) 38784.3 1.27003 0.635015 0.772500i \(-0.280994\pi\)
0.635015 + 0.772500i \(0.280994\pi\)
\(978\) 0 0
\(979\) 1448.74 0.0472952
\(980\) 0 0
\(981\) 25955.2 0.844737
\(982\) 0 0
\(983\) −11294.6 −0.366473 −0.183237 0.983069i \(-0.558657\pi\)
−0.183237 + 0.983069i \(0.558657\pi\)
\(984\) 0 0
\(985\) −14951.6 −0.483653
\(986\) 0 0
\(987\) 22980.9 0.741125
\(988\) 0 0
\(989\) 18804.8 0.604607
\(990\) 0 0
\(991\) −25813.5 −0.827439 −0.413719 0.910404i \(-0.635771\pi\)
−0.413719 + 0.910404i \(0.635771\pi\)
\(992\) 0 0
\(993\) −40640.0 −1.29876
\(994\) 0 0
\(995\) 19474.4 0.620483
\(996\) 0 0
\(997\) 8447.32 0.268334 0.134167 0.990959i \(-0.457164\pi\)
0.134167 + 0.990959i \(0.457164\pi\)
\(998\) 0 0
\(999\) −129827. −4.11166
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 1088.4.a.bh.1.1 7
4.3 odd 2 1088.4.a.bg.1.7 7
8.3 odd 2 544.4.a.k.1.1 7
8.5 even 2 544.4.a.l.1.7 yes 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
544.4.a.k.1.1 7 8.3 odd 2
544.4.a.l.1.7 yes 7 8.5 even 2
1088.4.a.bg.1.7 7 4.3 odd 2
1088.4.a.bh.1.1 7 1.1 even 1 trivial