Properties

Label 580.2.a.c.1.3
Level $580$
Weight $2$
Character 580.1
Self dual yes
Analytic conductor $4.631$
Analytic rank $0$
Dimension $3$
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] = [580,2,Mod(1,580)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(580, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("580.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 580.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: \(4.63132331723\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 5x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.51414\) of defining polynomial
Character \(\chi\) \(=\) 580.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.32088 q^{3} -1.00000 q^{5} +1.32088 q^{7} +8.02827 q^{9} +O(q^{10})\) \(q+3.32088 q^{3} -1.00000 q^{5} +1.32088 q^{7} +8.02827 q^{9} +5.32088 q^{11} -5.02827 q^{13} -3.32088 q^{15} -6.34916 q^{17} -4.34916 q^{19} +4.38650 q^{21} -1.70739 q^{23} +1.00000 q^{25} +16.6983 q^{27} -1.00000 q^{29} +8.34916 q^{31} +17.6700 q^{33} -1.32088 q^{35} -6.93438 q^{37} -16.6983 q^{39} -1.02827 q^{41} +10.7357 q^{43} -8.02827 q^{45} -0.679116 q^{47} -5.25526 q^{49} -21.0848 q^{51} +2.38650 q^{53} -5.32088 q^{55} -14.4431 q^{57} +10.4431 q^{59} -6.38650 q^{61} +10.6044 q^{63} +5.02827 q^{65} -5.70739 q^{67} -5.67004 q^{69} -3.61350 q^{71} -6.73566 q^{73} +3.32088 q^{75} +7.02827 q^{77} -11.3774 q^{79} +31.3684 q^{81} -3.96265 q^{83} +6.34916 q^{85} -3.32088 q^{87} +2.58522 q^{89} -6.64177 q^{91} +27.7266 q^{93} +4.34916 q^{95} -15.3209 q^{97} +42.7175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} - 3 q^{5} - 4 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{3} - 3 q^{5} - 4 q^{7} + 11 q^{9} + 8 q^{11} - 2 q^{13} - 2 q^{15} + 2 q^{17} + 8 q^{19} + 16 q^{21} + 3 q^{25} + 8 q^{27} - 3 q^{29} + 4 q^{31} + 24 q^{33} + 4 q^{35} - 10 q^{37} - 8 q^{39} + 10 q^{41} + 14 q^{43} - 11 q^{45} - 10 q^{47} + 3 q^{49} - 24 q^{51} + 10 q^{53} - 8 q^{55} - 20 q^{57} + 8 q^{59} - 22 q^{61} - 8 q^{63} + 2 q^{65} - 12 q^{67} + 12 q^{69} - 8 q^{71} - 2 q^{73} + 2 q^{75} + 8 q^{77} + 23 q^{81} + 12 q^{83} - 2 q^{85} - 2 q^{87} + 18 q^{89} - 4 q^{91} + 28 q^{93} - 8 q^{95} - 38 q^{97} + 36 q^{99}+O(q^{100}) \) 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
\(3\) 3.32088 1.91731 0.958657 0.284565i \(-0.0918491\pi\)
0.958657 + 0.284565i \(0.0918491\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.32088 0.499247 0.249624 0.968343i \(-0.419693\pi\)
0.249624 + 0.968343i \(0.419693\pi\)
\(8\) 0 0
\(9\) 8.02827 2.67609
\(10\) 0 0
\(11\) 5.32088 1.60431 0.802154 0.597118i \(-0.203688\pi\)
0.802154 + 0.597118i \(0.203688\pi\)
\(12\) 0 0
\(13\) −5.02827 −1.39459 −0.697296 0.716783i \(-0.745614\pi\)
−0.697296 + 0.716783i \(0.745614\pi\)
\(14\) 0 0
\(15\) −3.32088 −0.857449
\(16\) 0 0
\(17\) −6.34916 −1.53990 −0.769949 0.638106i \(-0.779718\pi\)
−0.769949 + 0.638106i \(0.779718\pi\)
\(18\) 0 0
\(19\) −4.34916 −0.997765 −0.498883 0.866670i \(-0.666256\pi\)
−0.498883 + 0.866670i \(0.666256\pi\)
\(20\) 0 0
\(21\) 4.38650 0.957214
\(22\) 0 0
\(23\) −1.70739 −0.356015 −0.178008 0.984029i \(-0.556965\pi\)
−0.178008 + 0.984029i \(0.556965\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 16.6983 3.21359
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 8.34916 1.49955 0.749777 0.661691i \(-0.230161\pi\)
0.749777 + 0.661691i \(0.230161\pi\)
\(32\) 0 0
\(33\) 17.6700 3.07596
\(34\) 0 0
\(35\) −1.32088 −0.223270
\(36\) 0 0
\(37\) −6.93438 −1.14000 −0.570002 0.821643i \(-0.693058\pi\)
−0.570002 + 0.821643i \(0.693058\pi\)
\(38\) 0 0
\(39\) −16.6983 −2.67387
\(40\) 0 0
\(41\) −1.02827 −0.160589 −0.0802947 0.996771i \(-0.525586\pi\)
−0.0802947 + 0.996771i \(0.525586\pi\)
\(42\) 0 0
\(43\) 10.7357 1.63717 0.818587 0.574383i \(-0.194758\pi\)
0.818587 + 0.574383i \(0.194758\pi\)
\(44\) 0 0
\(45\) −8.02827 −1.19678
\(46\) 0 0
\(47\) −0.679116 −0.0990592 −0.0495296 0.998773i \(-0.515772\pi\)
−0.0495296 + 0.998773i \(0.515772\pi\)
\(48\) 0 0
\(49\) −5.25526 −0.750752
\(50\) 0 0
\(51\) −21.0848 −2.95247
\(52\) 0 0
\(53\) 2.38650 0.327812 0.163906 0.986476i \(-0.447591\pi\)
0.163906 + 0.986476i \(0.447591\pi\)
\(54\) 0 0
\(55\) −5.32088 −0.717468
\(56\) 0 0
\(57\) −14.4431 −1.91303
\(58\) 0 0
\(59\) 10.4431 1.35957 0.679785 0.733412i \(-0.262073\pi\)
0.679785 + 0.733412i \(0.262073\pi\)
\(60\) 0 0
\(61\) −6.38650 −0.817708 −0.408854 0.912600i \(-0.634072\pi\)
−0.408854 + 0.912600i \(0.634072\pi\)
\(62\) 0 0
\(63\) 10.6044 1.33603
\(64\) 0 0
\(65\) 5.02827 0.623681
\(66\) 0 0
\(67\) −5.70739 −0.697269 −0.348634 0.937259i \(-0.613354\pi\)
−0.348634 + 0.937259i \(0.613354\pi\)
\(68\) 0 0
\(69\) −5.67004 −0.682593
\(70\) 0 0
\(71\) −3.61350 −0.428843 −0.214421 0.976741i \(-0.568787\pi\)
−0.214421 + 0.976741i \(0.568787\pi\)
\(72\) 0 0
\(73\) −6.73566 −0.788350 −0.394175 0.919035i \(-0.628970\pi\)
−0.394175 + 0.919035i \(0.628970\pi\)
\(74\) 0 0
\(75\) 3.32088 0.383463
\(76\) 0 0
\(77\) 7.02827 0.800946
\(78\) 0 0
\(79\) −11.3774 −1.28006 −0.640031 0.768349i \(-0.721078\pi\)
−0.640031 + 0.768349i \(0.721078\pi\)
\(80\) 0 0
\(81\) 31.3684 3.48537
\(82\) 0 0
\(83\) −3.96265 −0.434958 −0.217479 0.976065i \(-0.569783\pi\)
−0.217479 + 0.976065i \(0.569783\pi\)
\(84\) 0 0
\(85\) 6.34916 0.688663
\(86\) 0 0
\(87\) −3.32088 −0.356036
\(88\) 0 0
\(89\) 2.58522 0.274033 0.137016 0.990569i \(-0.456249\pi\)
0.137016 + 0.990569i \(0.456249\pi\)
\(90\) 0 0
\(91\) −6.64177 −0.696247
\(92\) 0 0
\(93\) 27.7266 2.87511
\(94\) 0 0
\(95\) 4.34916 0.446214
\(96\) 0 0
\(97\) −15.3209 −1.55560 −0.777800 0.628512i \(-0.783664\pi\)
−0.777800 + 0.628512i \(0.783664\pi\)
\(98\) 0 0
\(99\) 42.7175 4.29327
\(100\) 0 0
\(101\) 11.8688 1.18099 0.590493 0.807043i \(-0.298933\pi\)
0.590493 + 0.807043i \(0.298933\pi\)
\(102\) 0 0
\(103\) −3.65084 −0.359728 −0.179864 0.983691i \(-0.557566\pi\)
−0.179864 + 0.983691i \(0.557566\pi\)
\(104\) 0 0
\(105\) −4.38650 −0.428079
\(106\) 0 0
\(107\) −5.32088 −0.514389 −0.257195 0.966360i \(-0.582798\pi\)
−0.257195 + 0.966360i \(0.582798\pi\)
\(108\) 0 0
\(109\) −14.3118 −1.37082 −0.685411 0.728156i \(-0.740378\pi\)
−0.685411 + 0.728156i \(0.740378\pi\)
\(110\) 0 0
\(111\) −23.0283 −2.18575
\(112\) 0 0
\(113\) 2.03735 0.191657 0.0958287 0.995398i \(-0.469450\pi\)
0.0958287 + 0.995398i \(0.469450\pi\)
\(114\) 0 0
\(115\) 1.70739 0.159215
\(116\) 0 0
\(117\) −40.3684 −3.73206
\(118\) 0 0
\(119\) −8.38650 −0.768790
\(120\) 0 0
\(121\) 17.3118 1.57380
\(122\) 0 0
\(123\) −3.41478 −0.307900
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.26434 −0.112192 −0.0560959 0.998425i \(-0.517865\pi\)
−0.0560959 + 0.998425i \(0.517865\pi\)
\(128\) 0 0
\(129\) 35.6519 3.13897
\(130\) 0 0
\(131\) −1.70739 −0.149175 −0.0745877 0.997214i \(-0.523764\pi\)
−0.0745877 + 0.997214i \(0.523764\pi\)
\(132\) 0 0
\(133\) −5.74474 −0.498132
\(134\) 0 0
\(135\) −16.6983 −1.43716
\(136\) 0 0
\(137\) 21.7639 1.85942 0.929709 0.368294i \(-0.120058\pi\)
0.929709 + 0.368294i \(0.120058\pi\)
\(138\) 0 0
\(139\) −16.6983 −1.41633 −0.708166 0.706046i \(-0.750477\pi\)
−0.708166 + 0.706046i \(0.750477\pi\)
\(140\) 0 0
\(141\) −2.25526 −0.189928
\(142\) 0 0
\(143\) −26.7549 −2.23735
\(144\) 0 0
\(145\) 1.00000 0.0830455
\(146\) 0 0
\(147\) −17.4521 −1.43943
\(148\) 0 0
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) 6.44305 0.524328 0.262164 0.965023i \(-0.415564\pi\)
0.262164 + 0.965023i \(0.415564\pi\)
\(152\) 0 0
\(153\) −50.9728 −4.12091
\(154\) 0 0
\(155\) −8.34916 −0.670621
\(156\) 0 0
\(157\) 10.7357 0.856799 0.428400 0.903589i \(-0.359078\pi\)
0.428400 + 0.903589i \(0.359078\pi\)
\(158\) 0 0
\(159\) 7.92531 0.628518
\(160\) 0 0
\(161\) −2.25526 −0.177740
\(162\) 0 0
\(163\) 3.90611 0.305950 0.152975 0.988230i \(-0.451115\pi\)
0.152975 + 0.988230i \(0.451115\pi\)
\(164\) 0 0
\(165\) −17.6700 −1.37561
\(166\) 0 0
\(167\) −5.51960 −0.427120 −0.213560 0.976930i \(-0.568506\pi\)
−0.213560 + 0.976930i \(0.568506\pi\)
\(168\) 0 0
\(169\) 12.2835 0.944888
\(170\) 0 0
\(171\) −34.9162 −2.67011
\(172\) 0 0
\(173\) 5.80128 0.441063 0.220532 0.975380i \(-0.429221\pi\)
0.220532 + 0.975380i \(0.429221\pi\)
\(174\) 0 0
\(175\) 1.32088 0.0998495
\(176\) 0 0
\(177\) 34.6802 2.60672
\(178\) 0 0
\(179\) 14.0565 1.05064 0.525318 0.850906i \(-0.323946\pi\)
0.525318 + 0.850906i \(0.323946\pi\)
\(180\) 0 0
\(181\) −7.08482 −0.526611 −0.263305 0.964713i \(-0.584813\pi\)
−0.263305 + 0.964713i \(0.584813\pi\)
\(182\) 0 0
\(183\) −21.2088 −1.56780
\(184\) 0 0
\(185\) 6.93438 0.509826
\(186\) 0 0
\(187\) −33.7831 −2.47047
\(188\) 0 0
\(189\) 22.0565 1.60438
\(190\) 0 0
\(191\) −0.547875 −0.0396428 −0.0198214 0.999804i \(-0.506310\pi\)
−0.0198214 + 0.999804i \(0.506310\pi\)
\(192\) 0 0
\(193\) 4.40571 0.317130 0.158565 0.987349i \(-0.449313\pi\)
0.158565 + 0.987349i \(0.449313\pi\)
\(194\) 0 0
\(195\) 16.6983 1.19579
\(196\) 0 0
\(197\) −4.64177 −0.330712 −0.165356 0.986234i \(-0.552877\pi\)
−0.165356 + 0.986234i \(0.552877\pi\)
\(198\) 0 0
\(199\) 18.4431 1.30739 0.653697 0.756757i \(-0.273217\pi\)
0.653697 + 0.756757i \(0.273217\pi\)
\(200\) 0 0
\(201\) −18.9536 −1.33688
\(202\) 0 0
\(203\) −1.32088 −0.0927079
\(204\) 0 0
\(205\) 1.02827 0.0718178
\(206\) 0 0
\(207\) −13.7074 −0.952729
\(208\) 0 0
\(209\) −23.1414 −1.60072
\(210\) 0 0
\(211\) −4.54787 −0.313089 −0.156544 0.987671i \(-0.550035\pi\)
−0.156544 + 0.987671i \(0.550035\pi\)
\(212\) 0 0
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) −10.7357 −0.732166
\(216\) 0 0
\(217\) 11.0283 0.748648
\(218\) 0 0
\(219\) −22.3684 −1.51151
\(220\) 0 0
\(221\) 31.9253 2.14753
\(222\) 0 0
\(223\) 1.12217 0.0751459 0.0375730 0.999294i \(-0.488037\pi\)
0.0375730 + 0.999294i \(0.488037\pi\)
\(224\) 0 0
\(225\) 8.02827 0.535218
\(226\) 0 0
\(227\) 9.63270 0.639345 0.319672 0.947528i \(-0.396427\pi\)
0.319672 + 0.947528i \(0.396427\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 23.3401 1.53566
\(232\) 0 0
\(233\) −8.05655 −0.527802 −0.263901 0.964550i \(-0.585009\pi\)
−0.263901 + 0.964550i \(0.585009\pi\)
\(234\) 0 0
\(235\) 0.679116 0.0443006
\(236\) 0 0
\(237\) −37.7831 −2.45428
\(238\) 0 0
\(239\) 15.6135 1.00995 0.504977 0.863133i \(-0.331501\pi\)
0.504977 + 0.863133i \(0.331501\pi\)
\(240\) 0 0
\(241\) 18.5105 1.19237 0.596184 0.802848i \(-0.296683\pi\)
0.596184 + 0.802848i \(0.296683\pi\)
\(242\) 0 0
\(243\) 54.0757 3.46896
\(244\) 0 0
\(245\) 5.25526 0.335747
\(246\) 0 0
\(247\) 21.8688 1.39148
\(248\) 0 0
\(249\) −13.1595 −0.833950
\(250\) 0 0
\(251\) −6.67912 −0.421582 −0.210791 0.977531i \(-0.567604\pi\)
−0.210791 + 0.977531i \(0.567604\pi\)
\(252\) 0 0
\(253\) −9.08482 −0.571158
\(254\) 0 0
\(255\) 21.0848 1.32038
\(256\) 0 0
\(257\) −26.4249 −1.64834 −0.824170 0.566342i \(-0.808358\pi\)
−0.824170 + 0.566342i \(0.808358\pi\)
\(258\) 0 0
\(259\) −9.15951 −0.569145
\(260\) 0 0
\(261\) −8.02827 −0.496938
\(262\) 0 0
\(263\) 27.4340 1.69165 0.845826 0.533459i \(-0.179108\pi\)
0.845826 + 0.533459i \(0.179108\pi\)
\(264\) 0 0
\(265\) −2.38650 −0.146602
\(266\) 0 0
\(267\) 8.58522 0.525407
\(268\) 0 0
\(269\) −10.9717 −0.668958 −0.334479 0.942403i \(-0.608560\pi\)
−0.334479 + 0.942403i \(0.608560\pi\)
\(270\) 0 0
\(271\) 20.1504 1.22405 0.612026 0.790838i \(-0.290355\pi\)
0.612026 + 0.790838i \(0.290355\pi\)
\(272\) 0 0
\(273\) −22.0565 −1.33492
\(274\) 0 0
\(275\) 5.32088 0.320861
\(276\) 0 0
\(277\) 3.15951 0.189837 0.0949184 0.995485i \(-0.469741\pi\)
0.0949184 + 0.995485i \(0.469741\pi\)
\(278\) 0 0
\(279\) 67.0293 4.01294
\(280\) 0 0
\(281\) −10.3118 −0.615151 −0.307576 0.951524i \(-0.599518\pi\)
−0.307576 + 0.951524i \(0.599518\pi\)
\(282\) 0 0
\(283\) 0.423851 0.0251953 0.0125977 0.999921i \(-0.495990\pi\)
0.0125977 + 0.999921i \(0.495990\pi\)
\(284\) 0 0
\(285\) 14.4431 0.855533
\(286\) 0 0
\(287\) −1.35823 −0.0801738
\(288\) 0 0
\(289\) 23.3118 1.37128
\(290\) 0 0
\(291\) −50.8789 −2.98257
\(292\) 0 0
\(293\) 19.2462 1.12437 0.562187 0.827010i \(-0.309960\pi\)
0.562187 + 0.827010i \(0.309960\pi\)
\(294\) 0 0
\(295\) −10.4431 −0.608018
\(296\) 0 0
\(297\) 88.8498 5.15559
\(298\) 0 0
\(299\) 8.58522 0.496496
\(300\) 0 0
\(301\) 14.1806 0.817355
\(302\) 0 0
\(303\) 39.4148 2.26432
\(304\) 0 0
\(305\) 6.38650 0.365690
\(306\) 0 0
\(307\) 22.7357 1.29759 0.648796 0.760962i \(-0.275273\pi\)
0.648796 + 0.760962i \(0.275273\pi\)
\(308\) 0 0
\(309\) −12.1240 −0.689712
\(310\) 0 0
\(311\) 14.8031 0.839409 0.419704 0.907661i \(-0.362134\pi\)
0.419704 + 0.907661i \(0.362134\pi\)
\(312\) 0 0
\(313\) −14.9717 −0.846252 −0.423126 0.906071i \(-0.639067\pi\)
−0.423126 + 0.906071i \(0.639067\pi\)
\(314\) 0 0
\(315\) −10.6044 −0.597492
\(316\) 0 0
\(317\) 23.1222 1.29867 0.649335 0.760502i \(-0.275047\pi\)
0.649335 + 0.760502i \(0.275047\pi\)
\(318\) 0 0
\(319\) −5.32088 −0.297912
\(320\) 0 0
\(321\) −17.6700 −0.986246
\(322\) 0 0
\(323\) 27.6135 1.53646
\(324\) 0 0
\(325\) −5.02827 −0.278918
\(326\) 0 0
\(327\) −47.5279 −2.62830
\(328\) 0 0
\(329\) −0.897033 −0.0494550
\(330\) 0 0
\(331\) −9.82048 −0.539783 −0.269891 0.962891i \(-0.586988\pi\)
−0.269891 + 0.962891i \(0.586988\pi\)
\(332\) 0 0
\(333\) −55.6711 −3.05076
\(334\) 0 0
\(335\) 5.70739 0.311828
\(336\) 0 0
\(337\) −8.09389 −0.440903 −0.220451 0.975398i \(-0.570753\pi\)
−0.220451 + 0.975398i \(0.570753\pi\)
\(338\) 0 0
\(339\) 6.76579 0.367467
\(340\) 0 0
\(341\) 44.4249 2.40574
\(342\) 0 0
\(343\) −16.1878 −0.874058
\(344\) 0 0
\(345\) 5.67004 0.305265
\(346\) 0 0
\(347\) −7.37743 −0.396041 −0.198021 0.980198i \(-0.563451\pi\)
−0.198021 + 0.980198i \(0.563451\pi\)
\(348\) 0 0
\(349\) 8.82956 0.472635 0.236318 0.971676i \(-0.424059\pi\)
0.236318 + 0.971676i \(0.424059\pi\)
\(350\) 0 0
\(351\) −83.9637 −4.48165
\(352\) 0 0
\(353\) 13.7266 0.730593 0.365296 0.930891i \(-0.380968\pi\)
0.365296 + 0.930891i \(0.380968\pi\)
\(354\) 0 0
\(355\) 3.61350 0.191784
\(356\) 0 0
\(357\) −27.8506 −1.47401
\(358\) 0 0
\(359\) −1.70739 −0.0901126 −0.0450563 0.998984i \(-0.514347\pi\)
−0.0450563 + 0.998984i \(0.514347\pi\)
\(360\) 0 0
\(361\) −0.0848216 −0.00446429
\(362\) 0 0
\(363\) 57.4905 3.01747
\(364\) 0 0
\(365\) 6.73566 0.352561
\(366\) 0 0
\(367\) −25.9627 −1.35524 −0.677620 0.735412i \(-0.736988\pi\)
−0.677620 + 0.735412i \(0.736988\pi\)
\(368\) 0 0
\(369\) −8.25526 −0.429752
\(370\) 0 0
\(371\) 3.15230 0.163659
\(372\) 0 0
\(373\) 9.92531 0.513913 0.256956 0.966423i \(-0.417280\pi\)
0.256956 + 0.966423i \(0.417280\pi\)
\(374\) 0 0
\(375\) −3.32088 −0.171490
\(376\) 0 0
\(377\) 5.02827 0.258969
\(378\) 0 0
\(379\) 34.2070 1.75710 0.878548 0.477655i \(-0.158513\pi\)
0.878548 + 0.477655i \(0.158513\pi\)
\(380\) 0 0
\(381\) −4.19872 −0.215107
\(382\) 0 0
\(383\) −21.4340 −1.09523 −0.547613 0.836732i \(-0.684463\pi\)
−0.547613 + 0.836732i \(0.684463\pi\)
\(384\) 0 0
\(385\) −7.02827 −0.358194
\(386\) 0 0
\(387\) 86.1888 4.38123
\(388\) 0 0
\(389\) −36.3684 −1.84395 −0.921975 0.387251i \(-0.873425\pi\)
−0.921975 + 0.387251i \(0.873425\pi\)
\(390\) 0 0
\(391\) 10.8405 0.548227
\(392\) 0 0
\(393\) −5.67004 −0.286016
\(394\) 0 0
\(395\) 11.3774 0.572461
\(396\) 0 0
\(397\) −27.4713 −1.37875 −0.689373 0.724406i \(-0.742114\pi\)
−0.689373 + 0.724406i \(0.742114\pi\)
\(398\) 0 0
\(399\) −19.0776 −0.955075
\(400\) 0 0
\(401\) 22.3118 1.11420 0.557099 0.830446i \(-0.311914\pi\)
0.557099 + 0.830446i \(0.311914\pi\)
\(402\) 0 0
\(403\) −41.9819 −2.09127
\(404\) 0 0
\(405\) −31.3684 −1.55871
\(406\) 0 0
\(407\) −36.8970 −1.82892
\(408\) 0 0
\(409\) 4.95358 0.244939 0.122469 0.992472i \(-0.460919\pi\)
0.122469 + 0.992472i \(0.460919\pi\)
\(410\) 0 0
\(411\) 72.2755 3.56509
\(412\) 0 0
\(413\) 13.7941 0.678762
\(414\) 0 0
\(415\) 3.96265 0.194519
\(416\) 0 0
\(417\) −55.4532 −2.71555
\(418\) 0 0
\(419\) −0.198716 −0.00970793 −0.00485397 0.999988i \(-0.501545\pi\)
−0.00485397 + 0.999988i \(0.501545\pi\)
\(420\) 0 0
\(421\) 26.4996 1.29151 0.645756 0.763544i \(-0.276542\pi\)
0.645756 + 0.763544i \(0.276542\pi\)
\(422\) 0 0
\(423\) −5.45213 −0.265091
\(424\) 0 0
\(425\) −6.34916 −0.307979
\(426\) 0 0
\(427\) −8.43584 −0.408239
\(428\) 0 0
\(429\) −88.8498 −4.28971
\(430\) 0 0
\(431\) −21.2835 −1.02519 −0.512596 0.858630i \(-0.671316\pi\)
−0.512596 + 0.858630i \(0.671316\pi\)
\(432\) 0 0
\(433\) −24.8031 −1.19196 −0.595981 0.802998i \(-0.703237\pi\)
−0.595981 + 0.802998i \(0.703237\pi\)
\(434\) 0 0
\(435\) 3.32088 0.159224
\(436\) 0 0
\(437\) 7.42571 0.355220
\(438\) 0 0
\(439\) −32.3118 −1.54216 −0.771079 0.636739i \(-0.780283\pi\)
−0.771079 + 0.636739i \(0.780283\pi\)
\(440\) 0 0
\(441\) −42.1907 −2.00908
\(442\) 0 0
\(443\) 25.3774 1.20572 0.602859 0.797848i \(-0.294028\pi\)
0.602859 + 0.797848i \(0.294028\pi\)
\(444\) 0 0
\(445\) −2.58522 −0.122551
\(446\) 0 0
\(447\) 59.7759 2.82730
\(448\) 0 0
\(449\) 13.7266 0.647798 0.323899 0.946092i \(-0.395006\pi\)
0.323899 + 0.946092i \(0.395006\pi\)
\(450\) 0 0
\(451\) −5.47133 −0.257635
\(452\) 0 0
\(453\) 21.3966 1.00530
\(454\) 0 0
\(455\) 6.64177 0.311371
\(456\) 0 0
\(457\) −15.0101 −0.702144 −0.351072 0.936348i \(-0.614183\pi\)
−0.351072 + 0.936348i \(0.614183\pi\)
\(458\) 0 0
\(459\) −106.020 −4.94860
\(460\) 0 0
\(461\) 32.7549 1.52555 0.762773 0.646666i \(-0.223837\pi\)
0.762773 + 0.646666i \(0.223837\pi\)
\(462\) 0 0
\(463\) −24.5369 −1.14033 −0.570164 0.821531i \(-0.693120\pi\)
−0.570164 + 0.821531i \(0.693120\pi\)
\(464\) 0 0
\(465\) −27.7266 −1.28579
\(466\) 0 0
\(467\) −8.60442 −0.398165 −0.199083 0.979983i \(-0.563796\pi\)
−0.199083 + 0.979983i \(0.563796\pi\)
\(468\) 0 0
\(469\) −7.53880 −0.348110
\(470\) 0 0
\(471\) 35.6519 1.64275
\(472\) 0 0
\(473\) 57.1232 2.62653
\(474\) 0 0
\(475\) −4.34916 −0.199553
\(476\) 0 0
\(477\) 19.1595 0.877254
\(478\) 0 0
\(479\) 3.26434 0.149151 0.0745757 0.997215i \(-0.476240\pi\)
0.0745757 + 0.997215i \(0.476240\pi\)
\(480\) 0 0
\(481\) 34.8680 1.58984
\(482\) 0 0
\(483\) −7.48947 −0.340783
\(484\) 0 0
\(485\) 15.3209 0.695686
\(486\) 0 0
\(487\) 34.2070 1.55007 0.775033 0.631920i \(-0.217733\pi\)
0.775033 + 0.631920i \(0.217733\pi\)
\(488\) 0 0
\(489\) 12.9717 0.586602
\(490\) 0 0
\(491\) −8.93438 −0.403203 −0.201601 0.979468i \(-0.564615\pi\)
−0.201601 + 0.979468i \(0.564615\pi\)
\(492\) 0 0
\(493\) 6.34916 0.285952
\(494\) 0 0
\(495\) −42.7175 −1.92001
\(496\) 0 0
\(497\) −4.77301 −0.214099
\(498\) 0 0
\(499\) 28.6236 1.28137 0.640685 0.767804i \(-0.278651\pi\)
0.640685 + 0.767804i \(0.278651\pi\)
\(500\) 0 0
\(501\) −18.3300 −0.818922
\(502\) 0 0
\(503\) −0.0192012 −0.000856140 0 −0.000428070 1.00000i \(-0.500136\pi\)
−0.000428070 1.00000i \(0.500136\pi\)
\(504\) 0 0
\(505\) −11.8688 −0.528153
\(506\) 0 0
\(507\) 40.7922 1.81165
\(508\) 0 0
\(509\) −8.25526 −0.365908 −0.182954 0.983121i \(-0.558566\pi\)
−0.182954 + 0.983121i \(0.558566\pi\)
\(510\) 0 0
\(511\) −8.89703 −0.393582
\(512\) 0 0
\(513\) −72.6236 −3.20641
\(514\) 0 0
\(515\) 3.65084 0.160875
\(516\) 0 0
\(517\) −3.61350 −0.158921
\(518\) 0 0
\(519\) 19.2654 0.845657
\(520\) 0 0
\(521\) −20.2553 −0.887399 −0.443700 0.896176i \(-0.646334\pi\)
−0.443700 + 0.896176i \(0.646334\pi\)
\(522\) 0 0
\(523\) 1.82048 0.0796042 0.0398021 0.999208i \(-0.487327\pi\)
0.0398021 + 0.999208i \(0.487327\pi\)
\(524\) 0 0
\(525\) 4.38650 0.191443
\(526\) 0 0
\(527\) −53.0101 −2.30916
\(528\) 0 0
\(529\) −20.0848 −0.873253
\(530\) 0 0
\(531\) 83.8397 3.63833
\(532\) 0 0
\(533\) 5.17044 0.223957
\(534\) 0 0
\(535\) 5.32088 0.230042
\(536\) 0 0
\(537\) 46.6802 2.01440
\(538\) 0 0
\(539\) −27.9627 −1.20444
\(540\) 0 0
\(541\) 1.03920 0.0446788 0.0223394 0.999750i \(-0.492889\pi\)
0.0223394 + 0.999750i \(0.492889\pi\)
\(542\) 0 0
\(543\) −23.5279 −1.00968
\(544\) 0 0
\(545\) 14.3118 0.613051
\(546\) 0 0
\(547\) 37.7567 1.61436 0.807180 0.590305i \(-0.200992\pi\)
0.807180 + 0.590305i \(0.200992\pi\)
\(548\) 0 0
\(549\) −51.2726 −2.18826
\(550\) 0 0
\(551\) 4.34916 0.185280
\(552\) 0 0
\(553\) −15.0283 −0.639067
\(554\) 0 0
\(555\) 23.0283 0.977496
\(556\) 0 0
\(557\) 45.8506 1.94275 0.971376 0.237545i \(-0.0763429\pi\)
0.971376 + 0.237545i \(0.0763429\pi\)
\(558\) 0 0
\(559\) −53.9819 −2.28319
\(560\) 0 0
\(561\) −112.190 −4.73666
\(562\) 0 0
\(563\) 33.3027 1.40354 0.701772 0.712402i \(-0.252393\pi\)
0.701772 + 0.712402i \(0.252393\pi\)
\(564\) 0 0
\(565\) −2.03735 −0.0857118
\(566\) 0 0
\(567\) 41.4340 1.74006
\(568\) 0 0
\(569\) −23.6700 −0.992300 −0.496150 0.868237i \(-0.665253\pi\)
−0.496150 + 0.868237i \(0.665253\pi\)
\(570\) 0 0
\(571\) 14.5671 0.609613 0.304807 0.952414i \(-0.401408\pi\)
0.304807 + 0.952414i \(0.401408\pi\)
\(572\) 0 0
\(573\) −1.81943 −0.0760077
\(574\) 0 0
\(575\) −1.70739 −0.0712031
\(576\) 0 0
\(577\) −13.7639 −0.573000 −0.286500 0.958080i \(-0.592492\pi\)
−0.286500 + 0.958080i \(0.592492\pi\)
\(578\) 0 0
\(579\) 14.6308 0.608037
\(580\) 0 0
\(581\) −5.23421 −0.217152
\(582\) 0 0
\(583\) 12.6983 0.525911
\(584\) 0 0
\(585\) 40.3684 1.66903
\(586\) 0 0
\(587\) −1.04748 −0.0432339 −0.0216170 0.999766i \(-0.506881\pi\)
−0.0216170 + 0.999766i \(0.506881\pi\)
\(588\) 0 0
\(589\) −36.3118 −1.49620
\(590\) 0 0
\(591\) −15.4148 −0.634079
\(592\) 0 0
\(593\) 14.3865 0.590783 0.295391 0.955376i \(-0.404550\pi\)
0.295391 + 0.955376i \(0.404550\pi\)
\(594\) 0 0
\(595\) 8.38650 0.343813
\(596\) 0 0
\(597\) 61.2472 2.50668
\(598\) 0 0
\(599\) −5.98080 −0.244369 −0.122184 0.992507i \(-0.538990\pi\)
−0.122184 + 0.992507i \(0.538990\pi\)
\(600\) 0 0
\(601\) −7.08482 −0.288996 −0.144498 0.989505i \(-0.546157\pi\)
−0.144498 + 0.989505i \(0.546157\pi\)
\(602\) 0 0
\(603\) −45.8205 −1.86595
\(604\) 0 0
\(605\) −17.3118 −0.703825
\(606\) 0 0
\(607\) 32.7175 1.32796 0.663982 0.747749i \(-0.268865\pi\)
0.663982 + 0.747749i \(0.268865\pi\)
\(608\) 0 0
\(609\) −4.38650 −0.177750
\(610\) 0 0
\(611\) 3.41478 0.138147
\(612\) 0 0
\(613\) 9.22699 0.372675 0.186337 0.982486i \(-0.440338\pi\)
0.186337 + 0.982486i \(0.440338\pi\)
\(614\) 0 0
\(615\) 3.41478 0.137697
\(616\) 0 0
\(617\) 0.281683 0.0113401 0.00567006 0.999984i \(-0.498195\pi\)
0.00567006 + 0.999984i \(0.498195\pi\)
\(618\) 0 0
\(619\) 21.2462 0.853957 0.426978 0.904262i \(-0.359578\pi\)
0.426978 + 0.904262i \(0.359578\pi\)
\(620\) 0 0
\(621\) −28.5105 −1.14409
\(622\) 0 0
\(623\) 3.41478 0.136810
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −76.8498 −3.06909
\(628\) 0 0
\(629\) 44.0275 1.75549
\(630\) 0 0
\(631\) 37.8688 1.50753 0.753766 0.657143i \(-0.228235\pi\)
0.753766 + 0.657143i \(0.228235\pi\)
\(632\) 0 0
\(633\) −15.1030 −0.600289
\(634\) 0 0
\(635\) 1.26434 0.0501737
\(636\) 0 0
\(637\) 26.4249 1.04699
\(638\) 0 0
\(639\) −29.0101 −1.14762
\(640\) 0 0
\(641\) −36.7658 −1.45216 −0.726081 0.687609i \(-0.758660\pi\)
−0.726081 + 0.687609i \(0.758660\pi\)
\(642\) 0 0
\(643\) −24.9728 −0.984830 −0.492415 0.870360i \(-0.663886\pi\)
−0.492415 + 0.870360i \(0.663886\pi\)
\(644\) 0 0
\(645\) −35.6519 −1.40379
\(646\) 0 0
\(647\) −3.56522 −0.140163 −0.0700816 0.997541i \(-0.522326\pi\)
−0.0700816 + 0.997541i \(0.522326\pi\)
\(648\) 0 0
\(649\) 55.5663 2.18117
\(650\) 0 0
\(651\) 36.6236 1.43539
\(652\) 0 0
\(653\) −21.5652 −0.843912 −0.421956 0.906616i \(-0.638656\pi\)
−0.421956 + 0.906616i \(0.638656\pi\)
\(654\) 0 0
\(655\) 1.70739 0.0667132
\(656\) 0 0
\(657\) −54.0757 −2.10970
\(658\) 0 0
\(659\) −40.4623 −1.57619 −0.788093 0.615556i \(-0.788931\pi\)
−0.788093 + 0.615556i \(0.788931\pi\)
\(660\) 0 0
\(661\) 26.1987 1.01901 0.509506 0.860467i \(-0.329828\pi\)
0.509506 + 0.860467i \(0.329828\pi\)
\(662\) 0 0
\(663\) 106.020 4.11749
\(664\) 0 0
\(665\) 5.74474 0.222771
\(666\) 0 0
\(667\) 1.70739 0.0661104
\(668\) 0 0
\(669\) 3.72659 0.144078
\(670\) 0 0
\(671\) −33.9819 −1.31185
\(672\) 0 0
\(673\) 3.35823 0.129450 0.0647251 0.997903i \(-0.479383\pi\)
0.0647251 + 0.997903i \(0.479383\pi\)
\(674\) 0 0
\(675\) 16.6983 0.642719
\(676\) 0 0
\(677\) −15.6965 −0.603264 −0.301632 0.953424i \(-0.597531\pi\)
−0.301632 + 0.953424i \(0.597531\pi\)
\(678\) 0 0
\(679\) −20.2371 −0.776629
\(680\) 0 0
\(681\) 31.9891 1.22582
\(682\) 0 0
\(683\) −40.1998 −1.53820 −0.769101 0.639128i \(-0.779296\pi\)
−0.769101 + 0.639128i \(0.779296\pi\)
\(684\) 0 0
\(685\) −21.7639 −0.831557
\(686\) 0 0
\(687\) 6.64177 0.253399
\(688\) 0 0
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) 25.7084 0.977995 0.488998 0.872285i \(-0.337363\pi\)
0.488998 + 0.872285i \(0.337363\pi\)
\(692\) 0 0
\(693\) 56.4249 2.14340
\(694\) 0 0
\(695\) 16.6983 0.633403
\(696\) 0 0
\(697\) 6.52867 0.247291
\(698\) 0 0
\(699\) −26.7549 −1.01196
\(700\) 0 0
\(701\) −8.51775 −0.321711 −0.160855 0.986978i \(-0.551425\pi\)
−0.160855 + 0.986978i \(0.551425\pi\)
\(702\) 0 0
\(703\) 30.1587 1.13746
\(704\) 0 0
\(705\) 2.25526 0.0849382
\(706\) 0 0
\(707\) 15.6773 0.589604
\(708\) 0 0
\(709\) 35.0848 1.31764 0.658819 0.752301i \(-0.271056\pi\)
0.658819 + 0.752301i \(0.271056\pi\)
\(710\) 0 0
\(711\) −91.3411 −3.42556
\(712\) 0 0
\(713\) −14.2553 −0.533864
\(714\) 0 0
\(715\) 26.7549 1.00058
\(716\) 0 0
\(717\) 51.8506 1.93640
\(718\) 0 0
\(719\) 31.3292 1.16838 0.584190 0.811617i \(-0.301412\pi\)
0.584190 + 0.811617i \(0.301412\pi\)
\(720\) 0 0
\(721\) −4.82234 −0.179593
\(722\) 0 0
\(723\) 61.4713 2.28614
\(724\) 0 0
\(725\) −1.00000 −0.0371391
\(726\) 0 0
\(727\) −13.9627 −0.517846 −0.258923 0.965898i \(-0.583368\pi\)
−0.258923 + 0.965898i \(0.583368\pi\)
\(728\) 0 0
\(729\) 85.4742 3.16571
\(730\) 0 0
\(731\) −68.1624 −2.52108
\(732\) 0 0
\(733\) −29.5761 −1.09242 −0.546210 0.837648i \(-0.683930\pi\)
−0.546210 + 0.837648i \(0.683930\pi\)
\(734\) 0 0
\(735\) 17.4521 0.643731
\(736\) 0 0
\(737\) −30.3684 −1.11863
\(738\) 0 0
\(739\) −6.66819 −0.245293 −0.122647 0.992450i \(-0.539138\pi\)
−0.122647 + 0.992450i \(0.539138\pi\)
\(740\) 0 0
\(741\) 72.6236 2.66790
\(742\) 0 0
\(743\) −33.7002 −1.23634 −0.618170 0.786045i \(-0.712126\pi\)
−0.618170 + 0.786045i \(0.712126\pi\)
\(744\) 0 0
\(745\) −18.0000 −0.659469
\(746\) 0 0
\(747\) −31.8133 −1.16399
\(748\) 0 0
\(749\) −7.02827 −0.256808
\(750\) 0 0
\(751\) −48.3129 −1.76296 −0.881481 0.472220i \(-0.843453\pi\)
−0.881481 + 0.472220i \(0.843453\pi\)
\(752\) 0 0
\(753\) −22.1806 −0.808305
\(754\) 0 0
\(755\) −6.44305 −0.234487
\(756\) 0 0
\(757\) 42.3985 1.54100 0.770500 0.637440i \(-0.220007\pi\)
0.770500 + 0.637440i \(0.220007\pi\)
\(758\) 0 0
\(759\) −30.1696 −1.09509
\(760\) 0 0
\(761\) −44.7933 −1.62375 −0.811877 0.583828i \(-0.801554\pi\)
−0.811877 + 0.583828i \(0.801554\pi\)
\(762\) 0 0
\(763\) −18.9043 −0.684380
\(764\) 0 0
\(765\) 50.9728 1.84292
\(766\) 0 0
\(767\) −52.5105 −1.89605
\(768\) 0 0
\(769\) −52.2080 −1.88267 −0.941335 0.337473i \(-0.890428\pi\)
−0.941335 + 0.337473i \(0.890428\pi\)
\(770\) 0 0
\(771\) −87.7541 −3.16039
\(772\) 0 0
\(773\) −24.2179 −0.871058 −0.435529 0.900175i \(-0.643439\pi\)
−0.435529 + 0.900175i \(0.643439\pi\)
\(774\) 0 0
\(775\) 8.34916 0.299911
\(776\) 0 0
\(777\) −30.4177 −1.09123
\(778\) 0 0
\(779\) 4.47213 0.160231
\(780\) 0 0
\(781\) −19.2270 −0.687996
\(782\) 0 0
\(783\) −16.6983 −0.596749
\(784\) 0 0
\(785\) −10.7357 −0.383172
\(786\) 0 0
\(787\) −1.43398 −0.0511159 −0.0255579 0.999673i \(-0.508136\pi\)
−0.0255579 + 0.999673i \(0.508136\pi\)
\(788\) 0 0
\(789\) 91.1051 3.24343
\(790\) 0 0
\(791\) 2.69110 0.0956845
\(792\) 0 0
\(793\) 32.1131 1.14037
\(794\) 0 0
\(795\) −7.92531 −0.281082
\(796\) 0 0
\(797\) −14.4732 −0.512666 −0.256333 0.966588i \(-0.582514\pi\)
−0.256333 + 0.966588i \(0.582514\pi\)
\(798\) 0 0
\(799\) 4.31181 0.152541
\(800\) 0 0
\(801\) 20.7549 0.733337
\(802\) 0 0
\(803\) −35.8397 −1.26476
\(804\) 0 0
\(805\) 2.25526 0.0794876
\(806\) 0 0
\(807\) −36.4358 −1.28260
\(808\) 0 0
\(809\) 49.2654 1.73208 0.866039 0.499976i \(-0.166658\pi\)
0.866039 + 0.499976i \(0.166658\pi\)
\(810\) 0 0
\(811\) −4.69832 −0.164980 −0.0824901 0.996592i \(-0.526287\pi\)
−0.0824901 + 0.996592i \(0.526287\pi\)
\(812\) 0 0
\(813\) 66.9173 2.34689
\(814\) 0 0
\(815\) −3.90611 −0.136825
\(816\) 0 0
\(817\) −46.6911 −1.63351
\(818\) 0 0
\(819\) −53.3219 −1.86322
\(820\) 0 0
\(821\) 34.7730 1.21359 0.606793 0.794860i \(-0.292456\pi\)
0.606793 + 0.794860i \(0.292456\pi\)
\(822\) 0 0
\(823\) −44.1323 −1.53836 −0.769178 0.639035i \(-0.779334\pi\)
−0.769178 + 0.639035i \(0.779334\pi\)
\(824\) 0 0
\(825\) 17.6700 0.615192
\(826\) 0 0
\(827\) 22.6610 0.787999 0.394000 0.919111i \(-0.371091\pi\)
0.394000 + 0.919111i \(0.371091\pi\)
\(828\) 0 0
\(829\) −37.9144 −1.31682 −0.658410 0.752659i \(-0.728771\pi\)
−0.658410 + 0.752659i \(0.728771\pi\)
\(830\) 0 0
\(831\) 10.4924 0.363977
\(832\) 0 0
\(833\) 33.3665 1.15608
\(834\) 0 0
\(835\) 5.51960 0.191014
\(836\) 0 0
\(837\) 139.417 4.81895
\(838\) 0 0
\(839\) 30.7175 1.06049 0.530243 0.847846i \(-0.322101\pi\)
0.530243 + 0.847846i \(0.322101\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −34.2443 −1.17944
\(844\) 0 0
\(845\) −12.2835 −0.422567
\(846\) 0 0
\(847\) 22.8669 0.785716
\(848\) 0 0
\(849\) 1.40756 0.0483074
\(850\) 0 0
\(851\) 11.8397 0.405859
\(852\) 0 0
\(853\) 1.25341 0.0429159 0.0214579 0.999770i \(-0.493169\pi\)
0.0214579 + 0.999770i \(0.493169\pi\)
\(854\) 0 0
\(855\) 34.9162 1.19411
\(856\) 0 0
\(857\) −7.85783 −0.268418 −0.134209 0.990953i \(-0.542849\pi\)
−0.134209 + 0.990953i \(0.542849\pi\)
\(858\) 0 0
\(859\) −14.4913 −0.494438 −0.247219 0.968960i \(-0.579517\pi\)
−0.247219 + 0.968960i \(0.579517\pi\)
\(860\) 0 0
\(861\) −4.51053 −0.153718
\(862\) 0 0
\(863\) −9.69646 −0.330071 −0.165036 0.986288i \(-0.552774\pi\)
−0.165036 + 0.986288i \(0.552774\pi\)
\(864\) 0 0
\(865\) −5.80128 −0.197250
\(866\) 0 0
\(867\) 77.4158 2.62918
\(868\) 0 0
\(869\) −60.5380 −2.05361
\(870\) 0 0
\(871\) 28.6983 0.972405
\(872\) 0 0
\(873\) −123.000 −4.16293
\(874\) 0 0
\(875\) −1.32088 −0.0446540
\(876\) 0 0
\(877\) 6.27341 0.211838 0.105919 0.994375i \(-0.466222\pi\)
0.105919 + 0.994375i \(0.466222\pi\)
\(878\) 0 0
\(879\) 63.9144 2.15578
\(880\) 0 0
\(881\) 19.5953 0.660184 0.330092 0.943949i \(-0.392920\pi\)
0.330092 + 0.943949i \(0.392920\pi\)
\(882\) 0 0
\(883\) −5.24619 −0.176548 −0.0882742 0.996096i \(-0.528135\pi\)
−0.0882742 + 0.996096i \(0.528135\pi\)
\(884\) 0 0
\(885\) −34.6802 −1.16576
\(886\) 0 0
\(887\) −32.6044 −1.09475 −0.547375 0.836888i \(-0.684373\pi\)
−0.547375 + 0.836888i \(0.684373\pi\)
\(888\) 0 0
\(889\) −1.67004 −0.0560114
\(890\) 0 0
\(891\) 166.907 5.59161
\(892\) 0 0
\(893\) 2.95358 0.0988378
\(894\) 0 0
\(895\) −14.0565 −0.469859
\(896\) 0 0
\(897\) 28.5105 0.951939
\(898\) 0 0
\(899\) −8.34916 −0.278460
\(900\) 0 0
\(901\) −15.1523 −0.504796
\(902\) 0 0
\(903\) 47.0920 1.56712
\(904\) 0 0
\(905\) 7.08482 0.235507
\(906\) 0 0
\(907\) −1.96265 −0.0651688 −0.0325844 0.999469i \(-0.510374\pi\)
−0.0325844 + 0.999469i \(0.510374\pi\)
\(908\) 0 0
\(909\) 95.2856 3.16043
\(910\) 0 0
\(911\) 50.7066 1.67998 0.839992 0.542599i \(-0.182560\pi\)
0.839992 + 0.542599i \(0.182560\pi\)
\(912\) 0 0
\(913\) −21.0848 −0.697806
\(914\) 0 0
\(915\) 21.2088 0.701143
\(916\) 0 0
\(917\) −2.25526 −0.0744754
\(918\) 0 0
\(919\) 56.2371 1.85509 0.927546 0.373710i \(-0.121914\pi\)
0.927546 + 0.373710i \(0.121914\pi\)
\(920\) 0 0
\(921\) 75.5025 2.48789
\(922\) 0 0
\(923\) 18.1696 0.598061
\(924\) 0 0
\(925\) −6.93438 −0.228001
\(926\) 0 0
\(927\) −29.3100 −0.962665
\(928\) 0 0
\(929\) −5.34009 −0.175203 −0.0876013 0.996156i \(-0.527920\pi\)
−0.0876013 + 0.996156i \(0.527920\pi\)
\(930\) 0 0
\(931\) 22.8560 0.749074
\(932\) 0 0
\(933\) 49.1595 1.60941
\(934\) 0 0
\(935\) 33.7831 1.10483
\(936\) 0 0
\(937\) −3.01013 −0.0983366 −0.0491683 0.998791i \(-0.515657\pi\)
−0.0491683 + 0.998791i \(0.515657\pi\)
\(938\) 0 0
\(939\) −49.7194 −1.62253
\(940\) 0 0
\(941\) −0.829557 −0.0270428 −0.0135214 0.999909i \(-0.504304\pi\)
−0.0135214 + 0.999909i \(0.504304\pi\)
\(942\) 0 0
\(943\) 1.75566 0.0571723
\(944\) 0 0
\(945\) −22.0565 −0.717500
\(946\) 0 0
\(947\) 21.3027 0.692246 0.346123 0.938189i \(-0.387498\pi\)
0.346123 + 0.938189i \(0.387498\pi\)
\(948\) 0 0
\(949\) 33.8688 1.09943
\(950\) 0 0
\(951\) 76.7860 2.48996
\(952\) 0 0
\(953\) −40.0203 −1.29638 −0.648192 0.761477i \(-0.724474\pi\)
−0.648192 + 0.761477i \(0.724474\pi\)
\(954\) 0 0
\(955\) 0.547875 0.0177288
\(956\) 0 0
\(957\) −17.6700 −0.571191
\(958\) 0 0
\(959\) 28.7476 0.928310
\(960\) 0 0
\(961\) 38.7084 1.24866
\(962\) 0 0
\(963\) −42.7175 −1.37655
\(964\) 0 0
\(965\) −4.40571 −0.141825
\(966\) 0 0
\(967\) −31.0365 −0.998068 −0.499034 0.866582i \(-0.666312\pi\)
−0.499034 + 0.866582i \(0.666312\pi\)
\(968\) 0 0
\(969\) 91.7012 2.94587
\(970\) 0 0
\(971\) −2.66819 −0.0856262 −0.0428131 0.999083i \(-0.513632\pi\)
−0.0428131 + 0.999083i \(0.513632\pi\)
\(972\) 0 0
\(973\) −22.0565 −0.707100
\(974\) 0 0
\(975\) −16.6983 −0.534774
\(976\) 0 0
\(977\) 45.6519 1.46053 0.730267 0.683162i \(-0.239396\pi\)
0.730267 + 0.683162i \(0.239396\pi\)
\(978\) 0 0
\(979\) 13.7557 0.439633
\(980\) 0 0
\(981\) −114.899 −3.66845
\(982\) 0 0
\(983\) −17.4521 −0.556636 −0.278318 0.960489i \(-0.589777\pi\)
−0.278318 + 0.960489i \(0.589777\pi\)
\(984\) 0 0
\(985\) 4.64177 0.147899
\(986\) 0 0
\(987\) −2.97894 −0.0948208
\(988\) 0 0
\(989\) −18.3300 −0.582859
\(990\) 0 0
\(991\) −4.49960 −0.142935 −0.0714673 0.997443i \(-0.522768\pi\)
−0.0714673 + 0.997443i \(0.522768\pi\)
\(992\) 0 0
\(993\) −32.6127 −1.03493
\(994\) 0 0
\(995\) −18.4431 −0.584684
\(996\) 0 0
\(997\) −21.1896 −0.671083 −0.335541 0.942025i \(-0.608919\pi\)
−0.335541 + 0.942025i \(0.608919\pi\)
\(998\) 0 0
\(999\) −115.792 −3.66351
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 580.2.a.c.1.3 3
3.2 odd 2 5220.2.a.x.1.3 3
4.3 odd 2 2320.2.a.m.1.1 3
5.2 odd 4 2900.2.c.f.349.1 6
5.3 odd 4 2900.2.c.f.349.6 6
5.4 even 2 2900.2.a.g.1.1 3
8.3 odd 2 9280.2.a.bw.1.3 3
8.5 even 2 9280.2.a.bk.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.2.a.c.1.3 3 1.1 even 1 trivial
2320.2.a.m.1.1 3 4.3 odd 2
2900.2.a.g.1.1 3 5.4 even 2
2900.2.c.f.349.1 6 5.2 odd 4
2900.2.c.f.349.6 6 5.3 odd 4
5220.2.a.x.1.3 3 3.2 odd 2
9280.2.a.bk.1.1 3 8.5 even 2
9280.2.a.bw.1.3 3 8.3 odd 2