Properties

Label 8032.2.a.h.1.18
Level $8032$
Weight $2$
Character 8032.1
Self dual yes
Analytic conductor $64.136$
Analytic rank $1$
Dimension $30$
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] = [8032,2,Mod(1,8032)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8032, 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("8032.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8032 = 2^{5} \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8032.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: \(64.1358429035\)
Analytic rank: \(1\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 8032.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.513479 q^{3} +3.65851 q^{5} +0.146814 q^{7} -2.73634 q^{9} +O(q^{10})\) \(q+0.513479 q^{3} +3.65851 q^{5} +0.146814 q^{7} -2.73634 q^{9} +1.10614 q^{11} -5.53847 q^{13} +1.87857 q^{15} +4.13916 q^{17} +4.16367 q^{19} +0.0753860 q^{21} -8.90373 q^{23} +8.38472 q^{25} -2.94549 q^{27} -2.49912 q^{29} -10.5175 q^{31} +0.567977 q^{33} +0.537121 q^{35} -3.89054 q^{37} -2.84389 q^{39} -2.80331 q^{41} -7.32039 q^{43} -10.0109 q^{45} +4.06109 q^{47} -6.97845 q^{49} +2.12537 q^{51} -6.79452 q^{53} +4.04681 q^{55} +2.13796 q^{57} -13.3028 q^{59} +3.86321 q^{61} -0.401733 q^{63} -20.2626 q^{65} +12.0938 q^{67} -4.57188 q^{69} +0.607392 q^{71} +1.61197 q^{73} +4.30538 q^{75} +0.162396 q^{77} -0.403251 q^{79} +6.69657 q^{81} -5.41012 q^{83} +15.1432 q^{85} -1.28324 q^{87} +5.27215 q^{89} -0.813126 q^{91} -5.40050 q^{93} +15.2329 q^{95} +12.2094 q^{97} -3.02676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 3 q^{3} - 13 q^{7} + 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 3 q^{3} - 13 q^{7} + 35 q^{9} - 13 q^{11} - 7 q^{13} - 28 q^{15} - 9 q^{17} + 17 q^{19} - 6 q^{21} - 43 q^{23} + 34 q^{25} - 12 q^{27} - q^{29} - 39 q^{31} - 17 q^{35} - q^{37} - 48 q^{39} - 3 q^{41} + 19 q^{43} - 66 q^{47} + 25 q^{49} + 14 q^{51} + 3 q^{53} - 50 q^{55} - 14 q^{57} - 27 q^{59} + 15 q^{61} - 75 q^{63} - 6 q^{65} - 8 q^{67} + 18 q^{69} - 64 q^{71} - 15 q^{73} - 9 q^{75} - 71 q^{79} + 6 q^{81} - 60 q^{83} + 15 q^{85} - 64 q^{87} - 32 q^{89} + 26 q^{91} - 4 q^{93} - 72 q^{95} - 4 q^{97} - 13 q^{99}+O(q^{100}) \) 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
\(3\) 0.513479 0.296457 0.148229 0.988953i \(-0.452643\pi\)
0.148229 + 0.988953i \(0.452643\pi\)
\(4\) 0 0
\(5\) 3.65851 1.63614 0.818068 0.575121i \(-0.195045\pi\)
0.818068 + 0.575121i \(0.195045\pi\)
\(6\) 0 0
\(7\) 0.146814 0.0554905 0.0277453 0.999615i \(-0.491167\pi\)
0.0277453 + 0.999615i \(0.491167\pi\)
\(8\) 0 0
\(9\) −2.73634 −0.912113
\(10\) 0 0
\(11\) 1.10614 0.333512 0.166756 0.985998i \(-0.446671\pi\)
0.166756 + 0.985998i \(0.446671\pi\)
\(12\) 0 0
\(13\) −5.53847 −1.53610 −0.768048 0.640392i \(-0.778772\pi\)
−0.768048 + 0.640392i \(0.778772\pi\)
\(14\) 0 0
\(15\) 1.87857 0.485045
\(16\) 0 0
\(17\) 4.13916 1.00389 0.501947 0.864898i \(-0.332617\pi\)
0.501947 + 0.864898i \(0.332617\pi\)
\(18\) 0 0
\(19\) 4.16367 0.955212 0.477606 0.878574i \(-0.341505\pi\)
0.477606 + 0.878574i \(0.341505\pi\)
\(20\) 0 0
\(21\) 0.0753860 0.0164506
\(22\) 0 0
\(23\) −8.90373 −1.85656 −0.928278 0.371888i \(-0.878710\pi\)
−0.928278 + 0.371888i \(0.878710\pi\)
\(24\) 0 0
\(25\) 8.38472 1.67694
\(26\) 0 0
\(27\) −2.94549 −0.566860
\(28\) 0 0
\(29\) −2.49912 −0.464075 −0.232037 0.972707i \(-0.574539\pi\)
−0.232037 + 0.972707i \(0.574539\pi\)
\(30\) 0 0
\(31\) −10.5175 −1.88899 −0.944497 0.328521i \(-0.893450\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(32\) 0 0
\(33\) 0.567977 0.0988722
\(34\) 0 0
\(35\) 0.537121 0.0907901
\(36\) 0 0
\(37\) −3.89054 −0.639601 −0.319800 0.947485i \(-0.603616\pi\)
−0.319800 + 0.947485i \(0.603616\pi\)
\(38\) 0 0
\(39\) −2.84389 −0.455387
\(40\) 0 0
\(41\) −2.80331 −0.437804 −0.218902 0.975747i \(-0.570247\pi\)
−0.218902 + 0.975747i \(0.570247\pi\)
\(42\) 0 0
\(43\) −7.32039 −1.11635 −0.558175 0.829723i \(-0.688498\pi\)
−0.558175 + 0.829723i \(0.688498\pi\)
\(44\) 0 0
\(45\) −10.0109 −1.49234
\(46\) 0 0
\(47\) 4.06109 0.592371 0.296185 0.955131i \(-0.404285\pi\)
0.296185 + 0.955131i \(0.404285\pi\)
\(48\) 0 0
\(49\) −6.97845 −0.996921
\(50\) 0 0
\(51\) 2.12537 0.297612
\(52\) 0 0
\(53\) −6.79452 −0.933299 −0.466649 0.884442i \(-0.654539\pi\)
−0.466649 + 0.884442i \(0.654539\pi\)
\(54\) 0 0
\(55\) 4.04681 0.545672
\(56\) 0 0
\(57\) 2.13796 0.283180
\(58\) 0 0
\(59\) −13.3028 −1.73188 −0.865938 0.500151i \(-0.833278\pi\)
−0.865938 + 0.500151i \(0.833278\pi\)
\(60\) 0 0
\(61\) 3.86321 0.494634 0.247317 0.968935i \(-0.420451\pi\)
0.247317 + 0.968935i \(0.420451\pi\)
\(62\) 0 0
\(63\) −0.401733 −0.0506136
\(64\) 0 0
\(65\) −20.2626 −2.51326
\(66\) 0 0
\(67\) 12.0938 1.47750 0.738748 0.673981i \(-0.235417\pi\)
0.738748 + 0.673981i \(0.235417\pi\)
\(68\) 0 0
\(69\) −4.57188 −0.550389
\(70\) 0 0
\(71\) 0.607392 0.0720842 0.0360421 0.999350i \(-0.488525\pi\)
0.0360421 + 0.999350i \(0.488525\pi\)
\(72\) 0 0
\(73\) 1.61197 0.188667 0.0943335 0.995541i \(-0.469928\pi\)
0.0943335 + 0.995541i \(0.469928\pi\)
\(74\) 0 0
\(75\) 4.30538 0.497142
\(76\) 0 0
\(77\) 0.162396 0.0185068
\(78\) 0 0
\(79\) −0.403251 −0.0453693 −0.0226846 0.999743i \(-0.507221\pi\)
−0.0226846 + 0.999743i \(0.507221\pi\)
\(80\) 0 0
\(81\) 6.69657 0.744063
\(82\) 0 0
\(83\) −5.41012 −0.593838 −0.296919 0.954903i \(-0.595959\pi\)
−0.296919 + 0.954903i \(0.595959\pi\)
\(84\) 0 0
\(85\) 15.1432 1.64251
\(86\) 0 0
\(87\) −1.28324 −0.137578
\(88\) 0 0
\(89\) 5.27215 0.558847 0.279423 0.960168i \(-0.409857\pi\)
0.279423 + 0.960168i \(0.409857\pi\)
\(90\) 0 0
\(91\) −0.813126 −0.0852388
\(92\) 0 0
\(93\) −5.40050 −0.560006
\(94\) 0 0
\(95\) 15.2329 1.56286
\(96\) 0 0
\(97\) 12.2094 1.23968 0.619839 0.784729i \(-0.287198\pi\)
0.619839 + 0.784729i \(0.287198\pi\)
\(98\) 0 0
\(99\) −3.02676 −0.304201
\(100\) 0 0
\(101\) 7.30614 0.726988 0.363494 0.931596i \(-0.381584\pi\)
0.363494 + 0.931596i \(0.381584\pi\)
\(102\) 0 0
\(103\) −9.35535 −0.921810 −0.460905 0.887450i \(-0.652475\pi\)
−0.460905 + 0.887450i \(0.652475\pi\)
\(104\) 0 0
\(105\) 0.275801 0.0269154
\(106\) 0 0
\(107\) 0.651858 0.0630175 0.0315087 0.999503i \(-0.489969\pi\)
0.0315087 + 0.999503i \(0.489969\pi\)
\(108\) 0 0
\(109\) −16.4705 −1.57759 −0.788795 0.614657i \(-0.789294\pi\)
−0.788795 + 0.614657i \(0.789294\pi\)
\(110\) 0 0
\(111\) −1.99771 −0.189614
\(112\) 0 0
\(113\) 2.08521 0.196160 0.0980801 0.995179i \(-0.468730\pi\)
0.0980801 + 0.995179i \(0.468730\pi\)
\(114\) 0 0
\(115\) −32.5744 −3.03758
\(116\) 0 0
\(117\) 15.1551 1.40109
\(118\) 0 0
\(119\) 0.607687 0.0557066
\(120\) 0 0
\(121\) −9.77646 −0.888770
\(122\) 0 0
\(123\) −1.43944 −0.129790
\(124\) 0 0
\(125\) 12.3830 1.10757
\(126\) 0 0
\(127\) 2.77618 0.246346 0.123173 0.992385i \(-0.460693\pi\)
0.123173 + 0.992385i \(0.460693\pi\)
\(128\) 0 0
\(129\) −3.75887 −0.330950
\(130\) 0 0
\(131\) −16.5711 −1.44782 −0.723910 0.689894i \(-0.757657\pi\)
−0.723910 + 0.689894i \(0.757657\pi\)
\(132\) 0 0
\(133\) 0.611286 0.0530052
\(134\) 0 0
\(135\) −10.7761 −0.927460
\(136\) 0 0
\(137\) 12.3014 1.05098 0.525490 0.850800i \(-0.323882\pi\)
0.525490 + 0.850800i \(0.323882\pi\)
\(138\) 0 0
\(139\) −12.1736 −1.03255 −0.516276 0.856422i \(-0.672682\pi\)
−0.516276 + 0.856422i \(0.672682\pi\)
\(140\) 0 0
\(141\) 2.08528 0.175613
\(142\) 0 0
\(143\) −6.12630 −0.512307
\(144\) 0 0
\(145\) −9.14306 −0.759289
\(146\) 0 0
\(147\) −3.58329 −0.295544
\(148\) 0 0
\(149\) 0.332666 0.0272531 0.0136265 0.999907i \(-0.495662\pi\)
0.0136265 + 0.999907i \(0.495662\pi\)
\(150\) 0 0
\(151\) −11.8096 −0.961054 −0.480527 0.876980i \(-0.659555\pi\)
−0.480527 + 0.876980i \(0.659555\pi\)
\(152\) 0 0
\(153\) −11.3261 −0.915665
\(154\) 0 0
\(155\) −38.4783 −3.09065
\(156\) 0 0
\(157\) 10.5185 0.839466 0.419733 0.907648i \(-0.362124\pi\)
0.419733 + 0.907648i \(0.362124\pi\)
\(158\) 0 0
\(159\) −3.48884 −0.276683
\(160\) 0 0
\(161\) −1.30719 −0.103021
\(162\) 0 0
\(163\) 0.925899 0.0725220 0.0362610 0.999342i \(-0.488455\pi\)
0.0362610 + 0.999342i \(0.488455\pi\)
\(164\) 0 0
\(165\) 2.07795 0.161768
\(166\) 0 0
\(167\) 4.06548 0.314596 0.157298 0.987551i \(-0.449722\pi\)
0.157298 + 0.987551i \(0.449722\pi\)
\(168\) 0 0
\(169\) 17.6747 1.35959
\(170\) 0 0
\(171\) −11.3932 −0.871262
\(172\) 0 0
\(173\) 16.9829 1.29118 0.645592 0.763682i \(-0.276611\pi\)
0.645592 + 0.763682i \(0.276611\pi\)
\(174\) 0 0
\(175\) 1.23099 0.0930545
\(176\) 0 0
\(177\) −6.83071 −0.513427
\(178\) 0 0
\(179\) 10.3149 0.770970 0.385485 0.922714i \(-0.374034\pi\)
0.385485 + 0.922714i \(0.374034\pi\)
\(180\) 0 0
\(181\) 5.04859 0.375259 0.187629 0.982240i \(-0.439920\pi\)
0.187629 + 0.982240i \(0.439920\pi\)
\(182\) 0 0
\(183\) 1.98368 0.146638
\(184\) 0 0
\(185\) −14.2336 −1.04647
\(186\) 0 0
\(187\) 4.57847 0.334811
\(188\) 0 0
\(189\) −0.432440 −0.0314553
\(190\) 0 0
\(191\) 10.1335 0.733232 0.366616 0.930372i \(-0.380516\pi\)
0.366616 + 0.930372i \(0.380516\pi\)
\(192\) 0 0
\(193\) 4.97497 0.358106 0.179053 0.983839i \(-0.442697\pi\)
0.179053 + 0.983839i \(0.442697\pi\)
\(194\) 0 0
\(195\) −10.4044 −0.745075
\(196\) 0 0
\(197\) −7.61719 −0.542703 −0.271351 0.962480i \(-0.587471\pi\)
−0.271351 + 0.962480i \(0.587471\pi\)
\(198\) 0 0
\(199\) −15.0875 −1.06952 −0.534761 0.845004i \(-0.679598\pi\)
−0.534761 + 0.845004i \(0.679598\pi\)
\(200\) 0 0
\(201\) 6.20993 0.438015
\(202\) 0 0
\(203\) −0.366906 −0.0257517
\(204\) 0 0
\(205\) −10.2560 −0.716307
\(206\) 0 0
\(207\) 24.3636 1.69339
\(208\) 0 0
\(209\) 4.60559 0.318575
\(210\) 0 0
\(211\) −18.3372 −1.26239 −0.631193 0.775626i \(-0.717434\pi\)
−0.631193 + 0.775626i \(0.717434\pi\)
\(212\) 0 0
\(213\) 0.311883 0.0213699
\(214\) 0 0
\(215\) −26.7818 −1.82650
\(216\) 0 0
\(217\) −1.54411 −0.104821
\(218\) 0 0
\(219\) 0.827714 0.0559317
\(220\) 0 0
\(221\) −22.9246 −1.54208
\(222\) 0 0
\(223\) −25.2459 −1.69059 −0.845295 0.534300i \(-0.820575\pi\)
−0.845295 + 0.534300i \(0.820575\pi\)
\(224\) 0 0
\(225\) −22.9434 −1.52956
\(226\) 0 0
\(227\) 14.7417 0.978440 0.489220 0.872160i \(-0.337282\pi\)
0.489220 + 0.872160i \(0.337282\pi\)
\(228\) 0 0
\(229\) 19.9195 1.31632 0.658158 0.752880i \(-0.271336\pi\)
0.658158 + 0.752880i \(0.271336\pi\)
\(230\) 0 0
\(231\) 0.0833871 0.00548647
\(232\) 0 0
\(233\) −22.1824 −1.45322 −0.726609 0.687051i \(-0.758905\pi\)
−0.726609 + 0.687051i \(0.758905\pi\)
\(234\) 0 0
\(235\) 14.8575 0.969199
\(236\) 0 0
\(237\) −0.207061 −0.0134501
\(238\) 0 0
\(239\) 19.6759 1.27273 0.636364 0.771389i \(-0.280438\pi\)
0.636364 + 0.771389i \(0.280438\pi\)
\(240\) 0 0
\(241\) 24.4588 1.57553 0.787765 0.615975i \(-0.211238\pi\)
0.787765 + 0.615975i \(0.211238\pi\)
\(242\) 0 0
\(243\) 12.2750 0.787443
\(244\) 0 0
\(245\) −25.5307 −1.63110
\(246\) 0 0
\(247\) −23.0604 −1.46730
\(248\) 0 0
\(249\) −2.77798 −0.176048
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) −9.84873 −0.619184
\(254\) 0 0
\(255\) 7.77570 0.486933
\(256\) 0 0
\(257\) 18.4609 1.15156 0.575778 0.817606i \(-0.304699\pi\)
0.575778 + 0.817606i \(0.304699\pi\)
\(258\) 0 0
\(259\) −0.571186 −0.0354918
\(260\) 0 0
\(261\) 6.83844 0.423289
\(262\) 0 0
\(263\) −12.9493 −0.798491 −0.399245 0.916844i \(-0.630728\pi\)
−0.399245 + 0.916844i \(0.630728\pi\)
\(264\) 0 0
\(265\) −24.8578 −1.52700
\(266\) 0 0
\(267\) 2.70714 0.165674
\(268\) 0 0
\(269\) −0.366421 −0.0223411 −0.0111705 0.999938i \(-0.503556\pi\)
−0.0111705 + 0.999938i \(0.503556\pi\)
\(270\) 0 0
\(271\) 10.4672 0.635838 0.317919 0.948118i \(-0.397016\pi\)
0.317919 + 0.948118i \(0.397016\pi\)
\(272\) 0 0
\(273\) −0.417523 −0.0252697
\(274\) 0 0
\(275\) 9.27463 0.559281
\(276\) 0 0
\(277\) −22.3880 −1.34517 −0.672583 0.740022i \(-0.734815\pi\)
−0.672583 + 0.740022i \(0.734815\pi\)
\(278\) 0 0
\(279\) 28.7794 1.72298
\(280\) 0 0
\(281\) 23.1397 1.38040 0.690199 0.723620i \(-0.257523\pi\)
0.690199 + 0.723620i \(0.257523\pi\)
\(282\) 0 0
\(283\) −22.2230 −1.32102 −0.660510 0.750817i \(-0.729660\pi\)
−0.660510 + 0.750817i \(0.729660\pi\)
\(284\) 0 0
\(285\) 7.82175 0.463321
\(286\) 0 0
\(287\) −0.411566 −0.0242940
\(288\) 0 0
\(289\) 0.132645 0.00780262
\(290\) 0 0
\(291\) 6.26928 0.367511
\(292\) 0 0
\(293\) −11.1071 −0.648883 −0.324442 0.945906i \(-0.605176\pi\)
−0.324442 + 0.945906i \(0.605176\pi\)
\(294\) 0 0
\(295\) −48.6684 −2.83359
\(296\) 0 0
\(297\) −3.25811 −0.189055
\(298\) 0 0
\(299\) 49.3131 2.85185
\(300\) 0 0
\(301\) −1.07474 −0.0619468
\(302\) 0 0
\(303\) 3.75155 0.215521
\(304\) 0 0
\(305\) 14.1336 0.809289
\(306\) 0 0
\(307\) −14.7401 −0.841260 −0.420630 0.907232i \(-0.638191\pi\)
−0.420630 + 0.907232i \(0.638191\pi\)
\(308\) 0 0
\(309\) −4.80377 −0.273277
\(310\) 0 0
\(311\) 22.2075 1.25927 0.629636 0.776891i \(-0.283204\pi\)
0.629636 + 0.776891i \(0.283204\pi\)
\(312\) 0 0
\(313\) −1.49330 −0.0844062 −0.0422031 0.999109i \(-0.513438\pi\)
−0.0422031 + 0.999109i \(0.513438\pi\)
\(314\) 0 0
\(315\) −1.46975 −0.0828108
\(316\) 0 0
\(317\) −10.2510 −0.575752 −0.287876 0.957668i \(-0.592949\pi\)
−0.287876 + 0.957668i \(0.592949\pi\)
\(318\) 0 0
\(319\) −2.76436 −0.154775
\(320\) 0 0
\(321\) 0.334715 0.0186820
\(322\) 0 0
\(323\) 17.2341 0.958932
\(324\) 0 0
\(325\) −46.4385 −2.57595
\(326\) 0 0
\(327\) −8.45726 −0.467688
\(328\) 0 0
\(329\) 0.596225 0.0328709
\(330\) 0 0
\(331\) 3.63251 0.199661 0.0998305 0.995004i \(-0.468170\pi\)
0.0998305 + 0.995004i \(0.468170\pi\)
\(332\) 0 0
\(333\) 10.6458 0.583388
\(334\) 0 0
\(335\) 44.2454 2.41739
\(336\) 0 0
\(337\) 23.1260 1.25975 0.629877 0.776695i \(-0.283105\pi\)
0.629877 + 0.776695i \(0.283105\pi\)
\(338\) 0 0
\(339\) 1.07071 0.0581531
\(340\) 0 0
\(341\) −11.6337 −0.630003
\(342\) 0 0
\(343\) −2.05223 −0.110810
\(344\) 0 0
\(345\) −16.7263 −0.900512
\(346\) 0 0
\(347\) 5.28619 0.283778 0.141889 0.989883i \(-0.454682\pi\)
0.141889 + 0.989883i \(0.454682\pi\)
\(348\) 0 0
\(349\) 7.46261 0.399464 0.199732 0.979851i \(-0.435993\pi\)
0.199732 + 0.979851i \(0.435993\pi\)
\(350\) 0 0
\(351\) 16.3135 0.870751
\(352\) 0 0
\(353\) 10.3630 0.551566 0.275783 0.961220i \(-0.411063\pi\)
0.275783 + 0.961220i \(0.411063\pi\)
\(354\) 0 0
\(355\) 2.22215 0.117940
\(356\) 0 0
\(357\) 0.312035 0.0165146
\(358\) 0 0
\(359\) −33.1864 −1.75151 −0.875754 0.482757i \(-0.839635\pi\)
−0.875754 + 0.482757i \(0.839635\pi\)
\(360\) 0 0
\(361\) −1.66382 −0.0875693
\(362\) 0 0
\(363\) −5.02001 −0.263482
\(364\) 0 0
\(365\) 5.89742 0.308685
\(366\) 0 0
\(367\) 17.2801 0.902013 0.451007 0.892521i \(-0.351065\pi\)
0.451007 + 0.892521i \(0.351065\pi\)
\(368\) 0 0
\(369\) 7.67081 0.399326
\(370\) 0 0
\(371\) −0.997531 −0.0517892
\(372\) 0 0
\(373\) 20.8035 1.07716 0.538581 0.842574i \(-0.318960\pi\)
0.538581 + 0.842574i \(0.318960\pi\)
\(374\) 0 0
\(375\) 6.35843 0.328348
\(376\) 0 0
\(377\) 13.8413 0.712863
\(378\) 0 0
\(379\) 19.9226 1.02336 0.511679 0.859177i \(-0.329024\pi\)
0.511679 + 0.859177i \(0.329024\pi\)
\(380\) 0 0
\(381\) 1.42551 0.0730311
\(382\) 0 0
\(383\) 12.2040 0.623595 0.311798 0.950149i \(-0.399069\pi\)
0.311798 + 0.950149i \(0.399069\pi\)
\(384\) 0 0
\(385\) 0.594129 0.0302796
\(386\) 0 0
\(387\) 20.0311 1.01824
\(388\) 0 0
\(389\) 9.64158 0.488848 0.244424 0.969669i \(-0.421401\pi\)
0.244424 + 0.969669i \(0.421401\pi\)
\(390\) 0 0
\(391\) −36.8539 −1.86378
\(392\) 0 0
\(393\) −8.50890 −0.429217
\(394\) 0 0
\(395\) −1.47530 −0.0742304
\(396\) 0 0
\(397\) −13.3447 −0.669754 −0.334877 0.942262i \(-0.608695\pi\)
−0.334877 + 0.942262i \(0.608695\pi\)
\(398\) 0 0
\(399\) 0.313883 0.0157138
\(400\) 0 0
\(401\) 28.5500 1.42572 0.712860 0.701307i \(-0.247400\pi\)
0.712860 + 0.701307i \(0.247400\pi\)
\(402\) 0 0
\(403\) 58.2507 2.90168
\(404\) 0 0
\(405\) 24.4995 1.21739
\(406\) 0 0
\(407\) −4.30346 −0.213315
\(408\) 0 0
\(409\) −10.6542 −0.526818 −0.263409 0.964684i \(-0.584847\pi\)
−0.263409 + 0.964684i \(0.584847\pi\)
\(410\) 0 0
\(411\) 6.31651 0.311570
\(412\) 0 0
\(413\) −1.95304 −0.0961027
\(414\) 0 0
\(415\) −19.7930 −0.971600
\(416\) 0 0
\(417\) −6.25089 −0.306107
\(418\) 0 0
\(419\) −19.3383 −0.944740 −0.472370 0.881400i \(-0.656601\pi\)
−0.472370 + 0.881400i \(0.656601\pi\)
\(420\) 0 0
\(421\) 30.9152 1.50672 0.753358 0.657610i \(-0.228433\pi\)
0.753358 + 0.657610i \(0.228433\pi\)
\(422\) 0 0
\(423\) −11.1125 −0.540309
\(424\) 0 0
\(425\) 34.7057 1.68347
\(426\) 0 0
\(427\) 0.567174 0.0274475
\(428\) 0 0
\(429\) −3.14573 −0.151877
\(430\) 0 0
\(431\) 13.1973 0.635693 0.317847 0.948142i \(-0.397040\pi\)
0.317847 + 0.948142i \(0.397040\pi\)
\(432\) 0 0
\(433\) −3.45262 −0.165922 −0.0829611 0.996553i \(-0.526438\pi\)
−0.0829611 + 0.996553i \(0.526438\pi\)
\(434\) 0 0
\(435\) −4.69477 −0.225097
\(436\) 0 0
\(437\) −37.0722 −1.77340
\(438\) 0 0
\(439\) −21.2950 −1.01636 −0.508178 0.861252i \(-0.669681\pi\)
−0.508178 + 0.861252i \(0.669681\pi\)
\(440\) 0 0
\(441\) 19.0954 0.909304
\(442\) 0 0
\(443\) −27.4198 −1.30275 −0.651377 0.758754i \(-0.725808\pi\)
−0.651377 + 0.758754i \(0.725808\pi\)
\(444\) 0 0
\(445\) 19.2882 0.914350
\(446\) 0 0
\(447\) 0.170817 0.00807937
\(448\) 0 0
\(449\) −41.4545 −1.95636 −0.978180 0.207757i \(-0.933384\pi\)
−0.978180 + 0.207757i \(0.933384\pi\)
\(450\) 0 0
\(451\) −3.10084 −0.146013
\(452\) 0 0
\(453\) −6.06400 −0.284911
\(454\) 0 0
\(455\) −2.97483 −0.139462
\(456\) 0 0
\(457\) −35.6703 −1.66859 −0.834293 0.551321i \(-0.814124\pi\)
−0.834293 + 0.551321i \(0.814124\pi\)
\(458\) 0 0
\(459\) −12.1919 −0.569067
\(460\) 0 0
\(461\) 10.7995 0.502982 0.251491 0.967860i \(-0.419079\pi\)
0.251491 + 0.967860i \(0.419079\pi\)
\(462\) 0 0
\(463\) −37.6864 −1.75144 −0.875718 0.482824i \(-0.839611\pi\)
−0.875718 + 0.482824i \(0.839611\pi\)
\(464\) 0 0
\(465\) −19.7578 −0.916246
\(466\) 0 0
\(467\) 27.7099 1.28226 0.641131 0.767432i \(-0.278466\pi\)
0.641131 + 0.767432i \(0.278466\pi\)
\(468\) 0 0
\(469\) 1.77555 0.0819871
\(470\) 0 0
\(471\) 5.40102 0.248866
\(472\) 0 0
\(473\) −8.09735 −0.372316
\(474\) 0 0
\(475\) 34.9112 1.60184
\(476\) 0 0
\(477\) 18.5921 0.851274
\(478\) 0 0
\(479\) −12.3872 −0.565984 −0.282992 0.959122i \(-0.591327\pi\)
−0.282992 + 0.959122i \(0.591327\pi\)
\(480\) 0 0
\(481\) 21.5477 0.982488
\(482\) 0 0
\(483\) −0.671216 −0.0305414
\(484\) 0 0
\(485\) 44.6683 2.02828
\(486\) 0 0
\(487\) −38.5896 −1.74866 −0.874331 0.485331i \(-0.838699\pi\)
−0.874331 + 0.485331i \(0.838699\pi\)
\(488\) 0 0
\(489\) 0.475430 0.0214997
\(490\) 0 0
\(491\) 10.5864 0.477756 0.238878 0.971050i \(-0.423220\pi\)
0.238878 + 0.971050i \(0.423220\pi\)
\(492\) 0 0
\(493\) −10.3442 −0.465882
\(494\) 0 0
\(495\) −11.0734 −0.497714
\(496\) 0 0
\(497\) 0.0891737 0.00399999
\(498\) 0 0
\(499\) −3.40586 −0.152467 −0.0762336 0.997090i \(-0.524289\pi\)
−0.0762336 + 0.997090i \(0.524289\pi\)
\(500\) 0 0
\(501\) 2.08754 0.0932644
\(502\) 0 0
\(503\) −27.0841 −1.20762 −0.603809 0.797129i \(-0.706351\pi\)
−0.603809 + 0.797129i \(0.706351\pi\)
\(504\) 0 0
\(505\) 26.7296 1.18945
\(506\) 0 0
\(507\) 9.07559 0.403061
\(508\) 0 0
\(509\) −6.13933 −0.272121 −0.136060 0.990701i \(-0.543444\pi\)
−0.136060 + 0.990701i \(0.543444\pi\)
\(510\) 0 0
\(511\) 0.236660 0.0104692
\(512\) 0 0
\(513\) −12.2641 −0.541472
\(514\) 0 0
\(515\) −34.2267 −1.50821
\(516\) 0 0
\(517\) 4.49211 0.197563
\(518\) 0 0
\(519\) 8.72035 0.382781
\(520\) 0 0
\(521\) 0.900655 0.0394584 0.0197292 0.999805i \(-0.493720\pi\)
0.0197292 + 0.999805i \(0.493720\pi\)
\(522\) 0 0
\(523\) 25.7590 1.12636 0.563182 0.826333i \(-0.309577\pi\)
0.563182 + 0.826333i \(0.309577\pi\)
\(524\) 0 0
\(525\) 0.632090 0.0275867
\(526\) 0 0
\(527\) −43.5335 −1.89635
\(528\) 0 0
\(529\) 56.2763 2.44680
\(530\) 0 0
\(531\) 36.4010 1.57967
\(532\) 0 0
\(533\) 15.5261 0.672509
\(534\) 0 0
\(535\) 2.38483 0.103105
\(536\) 0 0
\(537\) 5.29647 0.228560
\(538\) 0 0
\(539\) −7.71911 −0.332485
\(540\) 0 0
\(541\) −0.555268 −0.0238728 −0.0119364 0.999929i \(-0.503800\pi\)
−0.0119364 + 0.999929i \(0.503800\pi\)
\(542\) 0 0
\(543\) 2.59234 0.111248
\(544\) 0 0
\(545\) −60.2576 −2.58115
\(546\) 0 0
\(547\) 30.3057 1.29578 0.647890 0.761734i \(-0.275652\pi\)
0.647890 + 0.761734i \(0.275652\pi\)
\(548\) 0 0
\(549\) −10.5711 −0.451162
\(550\) 0 0
\(551\) −10.4055 −0.443290
\(552\) 0 0
\(553\) −0.0592030 −0.00251757
\(554\) 0 0
\(555\) −7.30865 −0.310235
\(556\) 0 0
\(557\) 7.66320 0.324700 0.162350 0.986733i \(-0.448093\pi\)
0.162350 + 0.986733i \(0.448093\pi\)
\(558\) 0 0
\(559\) 40.5438 1.71482
\(560\) 0 0
\(561\) 2.35095 0.0992572
\(562\) 0 0
\(563\) 16.4275 0.692337 0.346169 0.938172i \(-0.387482\pi\)
0.346169 + 0.938172i \(0.387482\pi\)
\(564\) 0 0
\(565\) 7.62877 0.320945
\(566\) 0 0
\(567\) 0.983151 0.0412885
\(568\) 0 0
\(569\) 13.7236 0.575325 0.287663 0.957732i \(-0.407122\pi\)
0.287663 + 0.957732i \(0.407122\pi\)
\(570\) 0 0
\(571\) 14.6548 0.613285 0.306643 0.951825i \(-0.400794\pi\)
0.306643 + 0.951825i \(0.400794\pi\)
\(572\) 0 0
\(573\) 5.20332 0.217372
\(574\) 0 0
\(575\) −74.6552 −3.11334
\(576\) 0 0
\(577\) −33.3647 −1.38899 −0.694495 0.719498i \(-0.744372\pi\)
−0.694495 + 0.719498i \(0.744372\pi\)
\(578\) 0 0
\(579\) 2.55454 0.106163
\(580\) 0 0
\(581\) −0.794282 −0.0329524
\(582\) 0 0
\(583\) −7.51565 −0.311267
\(584\) 0 0
\(585\) 55.4453 2.29238
\(586\) 0 0
\(587\) 34.6944 1.43199 0.715996 0.698104i \(-0.245973\pi\)
0.715996 + 0.698104i \(0.245973\pi\)
\(588\) 0 0
\(589\) −43.7913 −1.80439
\(590\) 0 0
\(591\) −3.91127 −0.160888
\(592\) 0 0
\(593\) −37.1688 −1.52634 −0.763171 0.646197i \(-0.776358\pi\)
−0.763171 + 0.646197i \(0.776358\pi\)
\(594\) 0 0
\(595\) 2.22323 0.0911436
\(596\) 0 0
\(597\) −7.74709 −0.317067
\(598\) 0 0
\(599\) 27.4568 1.12185 0.560927 0.827865i \(-0.310445\pi\)
0.560927 + 0.827865i \(0.310445\pi\)
\(600\) 0 0
\(601\) −10.6136 −0.432936 −0.216468 0.976290i \(-0.569454\pi\)
−0.216468 + 0.976290i \(0.569454\pi\)
\(602\) 0 0
\(603\) −33.0928 −1.34764
\(604\) 0 0
\(605\) −35.7673 −1.45415
\(606\) 0 0
\(607\) −42.6277 −1.73021 −0.865103 0.501594i \(-0.832747\pi\)
−0.865103 + 0.501594i \(0.832747\pi\)
\(608\) 0 0
\(609\) −0.188398 −0.00763429
\(610\) 0 0
\(611\) −22.4922 −0.909938
\(612\) 0 0
\(613\) 34.6046 1.39767 0.698834 0.715284i \(-0.253703\pi\)
0.698834 + 0.715284i \(0.253703\pi\)
\(614\) 0 0
\(615\) −5.26622 −0.212354
\(616\) 0 0
\(617\) 3.90255 0.157111 0.0785554 0.996910i \(-0.474969\pi\)
0.0785554 + 0.996910i \(0.474969\pi\)
\(618\) 0 0
\(619\) −8.70819 −0.350012 −0.175006 0.984567i \(-0.555994\pi\)
−0.175006 + 0.984567i \(0.555994\pi\)
\(620\) 0 0
\(621\) 26.2258 1.05241
\(622\) 0 0
\(623\) 0.774026 0.0310107
\(624\) 0 0
\(625\) 3.37988 0.135195
\(626\) 0 0
\(627\) 2.36487 0.0944439
\(628\) 0 0
\(629\) −16.1036 −0.642091
\(630\) 0 0
\(631\) 7.90155 0.314556 0.157278 0.987554i \(-0.449728\pi\)
0.157278 + 0.987554i \(0.449728\pi\)
\(632\) 0 0
\(633\) −9.41578 −0.374244
\(634\) 0 0
\(635\) 10.1567 0.403056
\(636\) 0 0
\(637\) 38.6499 1.53137
\(638\) 0 0
\(639\) −1.66203 −0.0657489
\(640\) 0 0
\(641\) −40.2276 −1.58889 −0.794447 0.607333i \(-0.792239\pi\)
−0.794447 + 0.607333i \(0.792239\pi\)
\(642\) 0 0
\(643\) −43.3566 −1.70982 −0.854909 0.518778i \(-0.826387\pi\)
−0.854909 + 0.518778i \(0.826387\pi\)
\(644\) 0 0
\(645\) −13.7519 −0.541479
\(646\) 0 0
\(647\) −19.8168 −0.779078 −0.389539 0.921010i \(-0.627366\pi\)
−0.389539 + 0.921010i \(0.627366\pi\)
\(648\) 0 0
\(649\) −14.7147 −0.577602
\(650\) 0 0
\(651\) −0.792870 −0.0310750
\(652\) 0 0
\(653\) −6.18807 −0.242158 −0.121079 0.992643i \(-0.538635\pi\)
−0.121079 + 0.992643i \(0.538635\pi\)
\(654\) 0 0
\(655\) −60.6255 −2.36883
\(656\) 0 0
\(657\) −4.41090 −0.172086
\(658\) 0 0
\(659\) −16.5381 −0.644233 −0.322116 0.946700i \(-0.604394\pi\)
−0.322116 + 0.946700i \(0.604394\pi\)
\(660\) 0 0
\(661\) −15.3680 −0.597747 −0.298874 0.954293i \(-0.596611\pi\)
−0.298874 + 0.954293i \(0.596611\pi\)
\(662\) 0 0
\(663\) −11.7713 −0.457160
\(664\) 0 0
\(665\) 2.23640 0.0867238
\(666\) 0 0
\(667\) 22.2515 0.861580
\(668\) 0 0
\(669\) −12.9632 −0.501188
\(670\) 0 0
\(671\) 4.27324 0.164967
\(672\) 0 0
\(673\) −14.1903 −0.546995 −0.273498 0.961873i \(-0.588181\pi\)
−0.273498 + 0.961873i \(0.588181\pi\)
\(674\) 0 0
\(675\) −24.6971 −0.950592
\(676\) 0 0
\(677\) −12.6816 −0.487394 −0.243697 0.969851i \(-0.578360\pi\)
−0.243697 + 0.969851i \(0.578360\pi\)
\(678\) 0 0
\(679\) 1.79251 0.0687904
\(680\) 0 0
\(681\) 7.56955 0.290066
\(682\) 0 0
\(683\) 21.9509 0.839927 0.419964 0.907541i \(-0.362043\pi\)
0.419964 + 0.907541i \(0.362043\pi\)
\(684\) 0 0
\(685\) 45.0048 1.71955
\(686\) 0 0
\(687\) 10.2282 0.390231
\(688\) 0 0
\(689\) 37.6313 1.43364
\(690\) 0 0
\(691\) −8.23221 −0.313168 −0.156584 0.987665i \(-0.550048\pi\)
−0.156584 + 0.987665i \(0.550048\pi\)
\(692\) 0 0
\(693\) −0.444371 −0.0168803
\(694\) 0 0
\(695\) −44.5373 −1.68940
\(696\) 0 0
\(697\) −11.6034 −0.439508
\(698\) 0 0
\(699\) −11.3902 −0.430817
\(700\) 0 0
\(701\) −5.72402 −0.216193 −0.108097 0.994140i \(-0.534476\pi\)
−0.108097 + 0.994140i \(0.534476\pi\)
\(702\) 0 0
\(703\) −16.1989 −0.610955
\(704\) 0 0
\(705\) 7.62904 0.287326
\(706\) 0 0
\(707\) 1.07264 0.0403410
\(708\) 0 0
\(709\) 0.810559 0.0304412 0.0152206 0.999884i \(-0.495155\pi\)
0.0152206 + 0.999884i \(0.495155\pi\)
\(710\) 0 0
\(711\) 1.10343 0.0413819
\(712\) 0 0
\(713\) 93.6447 3.50702
\(714\) 0 0
\(715\) −22.4132 −0.838204
\(716\) 0 0
\(717\) 10.1032 0.377310
\(718\) 0 0
\(719\) −12.4465 −0.464176 −0.232088 0.972695i \(-0.574556\pi\)
−0.232088 + 0.972695i \(0.574556\pi\)
\(720\) 0 0
\(721\) −1.37350 −0.0511517
\(722\) 0 0
\(723\) 12.5591 0.467078
\(724\) 0 0
\(725\) −20.9544 −0.778227
\(726\) 0 0
\(727\) −24.7123 −0.916529 −0.458264 0.888816i \(-0.651529\pi\)
−0.458264 + 0.888816i \(0.651529\pi\)
\(728\) 0 0
\(729\) −13.7867 −0.510620
\(730\) 0 0
\(731\) −30.3003 −1.12070
\(732\) 0 0
\(733\) 2.98022 0.110077 0.0550386 0.998484i \(-0.482472\pi\)
0.0550386 + 0.998484i \(0.482472\pi\)
\(734\) 0 0
\(735\) −13.1095 −0.483551
\(736\) 0 0
\(737\) 13.3774 0.492763
\(738\) 0 0
\(739\) 15.3734 0.565520 0.282760 0.959191i \(-0.408750\pi\)
0.282760 + 0.959191i \(0.408750\pi\)
\(740\) 0 0
\(741\) −11.8410 −0.434991
\(742\) 0 0
\(743\) 35.6367 1.30738 0.653691 0.756762i \(-0.273220\pi\)
0.653691 + 0.756762i \(0.273220\pi\)
\(744\) 0 0
\(745\) 1.21706 0.0445898
\(746\) 0 0
\(747\) 14.8039 0.541647
\(748\) 0 0
\(749\) 0.0957019 0.00349687
\(750\) 0 0
\(751\) −30.4970 −1.11285 −0.556426 0.830897i \(-0.687828\pi\)
−0.556426 + 0.830897i \(0.687828\pi\)
\(752\) 0 0
\(753\) −0.513479 −0.0187122
\(754\) 0 0
\(755\) −43.2057 −1.57242
\(756\) 0 0
\(757\) −12.1242 −0.440661 −0.220331 0.975425i \(-0.570714\pi\)
−0.220331 + 0.975425i \(0.570714\pi\)
\(758\) 0 0
\(759\) −5.05711 −0.183562
\(760\) 0 0
\(761\) −22.4881 −0.815194 −0.407597 0.913162i \(-0.633633\pi\)
−0.407597 + 0.913162i \(0.633633\pi\)
\(762\) 0 0
\(763\) −2.41810 −0.0875412
\(764\) 0 0
\(765\) −41.4368 −1.49815
\(766\) 0 0
\(767\) 73.6772 2.66033
\(768\) 0 0
\(769\) −32.1763 −1.16031 −0.580153 0.814507i \(-0.697007\pi\)
−0.580153 + 0.814507i \(0.697007\pi\)
\(770\) 0 0
\(771\) 9.47926 0.341387
\(772\) 0 0
\(773\) 35.3506 1.27147 0.635737 0.771906i \(-0.280696\pi\)
0.635737 + 0.771906i \(0.280696\pi\)
\(774\) 0 0
\(775\) −88.1860 −3.16773
\(776\) 0 0
\(777\) −0.293292 −0.0105218
\(778\) 0 0
\(779\) −11.6721 −0.418196
\(780\) 0 0
\(781\) 0.671858 0.0240410
\(782\) 0 0
\(783\) 7.36113 0.263065
\(784\) 0 0
\(785\) 38.4820 1.37348
\(786\) 0 0
\(787\) 54.3310 1.93669 0.968346 0.249613i \(-0.0803035\pi\)
0.968346 + 0.249613i \(0.0803035\pi\)
\(788\) 0 0
\(789\) −6.64922 −0.236718
\(790\) 0 0
\(791\) 0.306138 0.0108850
\(792\) 0 0
\(793\) −21.3963 −0.759805
\(794\) 0 0
\(795\) −12.7640 −0.452691
\(796\) 0 0
\(797\) −19.5327 −0.691884 −0.345942 0.938256i \(-0.612441\pi\)
−0.345942 + 0.938256i \(0.612441\pi\)
\(798\) 0 0
\(799\) 16.8095 0.594677
\(800\) 0 0
\(801\) −14.4264 −0.509731
\(802\) 0 0
\(803\) 1.78306 0.0629228
\(804\) 0 0
\(805\) −4.78238 −0.168557
\(806\) 0 0
\(807\) −0.188150 −0.00662318
\(808\) 0 0
\(809\) −8.62037 −0.303076 −0.151538 0.988451i \(-0.548423\pi\)
−0.151538 + 0.988451i \(0.548423\pi\)
\(810\) 0 0
\(811\) 32.8093 1.15209 0.576045 0.817418i \(-0.304595\pi\)
0.576045 + 0.817418i \(0.304595\pi\)
\(812\) 0 0
\(813\) 5.37470 0.188499
\(814\) 0 0
\(815\) 3.38741 0.118656
\(816\) 0 0
\(817\) −30.4797 −1.06635
\(818\) 0 0
\(819\) 2.22499 0.0777474
\(820\) 0 0
\(821\) −10.7721 −0.375949 −0.187975 0.982174i \(-0.560192\pi\)
−0.187975 + 0.982174i \(0.560192\pi\)
\(822\) 0 0
\(823\) 0.811789 0.0282972 0.0141486 0.999900i \(-0.495496\pi\)
0.0141486 + 0.999900i \(0.495496\pi\)
\(824\) 0 0
\(825\) 4.76233 0.165803
\(826\) 0 0
\(827\) 11.5287 0.400891 0.200446 0.979705i \(-0.435761\pi\)
0.200446 + 0.979705i \(0.435761\pi\)
\(828\) 0 0
\(829\) 18.1809 0.631450 0.315725 0.948851i \(-0.397752\pi\)
0.315725 + 0.948851i \(0.397752\pi\)
\(830\) 0 0
\(831\) −11.4958 −0.398784
\(832\) 0 0
\(833\) −28.8849 −1.00080
\(834\) 0 0
\(835\) 14.8736 0.514723
\(836\) 0 0
\(837\) 30.9791 1.07079
\(838\) 0 0
\(839\) −11.8944 −0.410640 −0.205320 0.978695i \(-0.565824\pi\)
−0.205320 + 0.978695i \(0.565824\pi\)
\(840\) 0 0
\(841\) −22.7544 −0.784635
\(842\) 0 0
\(843\) 11.8817 0.409229
\(844\) 0 0
\(845\) 64.6631 2.22448
\(846\) 0 0
\(847\) −1.43532 −0.0493183
\(848\) 0 0
\(849\) −11.4110 −0.391626
\(850\) 0 0
\(851\) 34.6403 1.18745
\(852\) 0 0
\(853\) −4.98122 −0.170554 −0.0852769 0.996357i \(-0.527177\pi\)
−0.0852769 + 0.996357i \(0.527177\pi\)
\(854\) 0 0
\(855\) −41.6823 −1.42550
\(856\) 0 0
\(857\) −28.0481 −0.958104 −0.479052 0.877787i \(-0.659019\pi\)
−0.479052 + 0.877787i \(0.659019\pi\)
\(858\) 0 0
\(859\) −53.7436 −1.83371 −0.916855 0.399221i \(-0.869281\pi\)
−0.916855 + 0.399221i \(0.869281\pi\)
\(860\) 0 0
\(861\) −0.211330 −0.00720212
\(862\) 0 0
\(863\) 5.84177 0.198856 0.0994281 0.995045i \(-0.468299\pi\)
0.0994281 + 0.995045i \(0.468299\pi\)
\(864\) 0 0
\(865\) 62.1321 2.11255
\(866\) 0 0
\(867\) 0.0681102 0.00231314
\(868\) 0 0
\(869\) −0.446050 −0.0151312
\(870\) 0 0
\(871\) −66.9814 −2.26958
\(872\) 0 0
\(873\) −33.4091 −1.13073
\(874\) 0 0
\(875\) 1.81800 0.0614597
\(876\) 0 0
\(877\) −25.6192 −0.865097 −0.432549 0.901611i \(-0.642386\pi\)
−0.432549 + 0.901611i \(0.642386\pi\)
\(878\) 0 0
\(879\) −5.70326 −0.192366
\(880\) 0 0
\(881\) 9.46664 0.318939 0.159470 0.987203i \(-0.449022\pi\)
0.159470 + 0.987203i \(0.449022\pi\)
\(882\) 0 0
\(883\) −20.2535 −0.681586 −0.340793 0.940138i \(-0.610695\pi\)
−0.340793 + 0.940138i \(0.610695\pi\)
\(884\) 0 0
\(885\) −24.9902 −0.840037
\(886\) 0 0
\(887\) −21.7078 −0.728875 −0.364438 0.931228i \(-0.618739\pi\)
−0.364438 + 0.931228i \(0.618739\pi\)
\(888\) 0 0
\(889\) 0.407582 0.0136699
\(890\) 0 0
\(891\) 7.40731 0.248154
\(892\) 0 0
\(893\) 16.9090 0.565840
\(894\) 0 0
\(895\) 37.7371 1.26141
\(896\) 0 0
\(897\) 25.3212 0.845451
\(898\) 0 0
\(899\) 26.2844 0.876634
\(900\) 0 0
\(901\) −28.1236 −0.936933
\(902\) 0 0
\(903\) −0.551855 −0.0183646
\(904\) 0 0
\(905\) 18.4703 0.613974
\(906\) 0 0
\(907\) 50.1616 1.66559 0.832794 0.553583i \(-0.186740\pi\)
0.832794 + 0.553583i \(0.186740\pi\)
\(908\) 0 0
\(909\) −19.9921 −0.663096
\(910\) 0 0
\(911\) 15.8879 0.526390 0.263195 0.964743i \(-0.415224\pi\)
0.263195 + 0.964743i \(0.415224\pi\)
\(912\) 0 0
\(913\) −5.98432 −0.198052
\(914\) 0 0
\(915\) 7.25732 0.239920
\(916\) 0 0
\(917\) −2.43287 −0.0803403
\(918\) 0 0
\(919\) −8.65979 −0.285660 −0.142830 0.989747i \(-0.545620\pi\)
−0.142830 + 0.989747i \(0.545620\pi\)
\(920\) 0 0
\(921\) −7.56872 −0.249398
\(922\) 0 0
\(923\) −3.36403 −0.110728
\(924\) 0 0
\(925\) −32.6211 −1.07257
\(926\) 0 0
\(927\) 25.5994 0.840795
\(928\) 0 0
\(929\) 49.5223 1.62477 0.812387 0.583118i \(-0.198168\pi\)
0.812387 + 0.583118i \(0.198168\pi\)
\(930\) 0 0
\(931\) −29.0560 −0.952271
\(932\) 0 0
\(933\) 11.4031 0.373320
\(934\) 0 0
\(935\) 16.7504 0.547797
\(936\) 0 0
\(937\) −21.8046 −0.712325 −0.356163 0.934424i \(-0.615915\pi\)
−0.356163 + 0.934424i \(0.615915\pi\)
\(938\) 0 0
\(939\) −0.766778 −0.0250228
\(940\) 0 0
\(941\) 39.4317 1.28544 0.642718 0.766103i \(-0.277807\pi\)
0.642718 + 0.766103i \(0.277807\pi\)
\(942\) 0 0
\(943\) 24.9599 0.812807
\(944\) 0 0
\(945\) −1.58209 −0.0514653
\(946\) 0 0
\(947\) −15.4145 −0.500904 −0.250452 0.968129i \(-0.580579\pi\)
−0.250452 + 0.968129i \(0.580579\pi\)
\(948\) 0 0
\(949\) −8.92786 −0.289811
\(950\) 0 0
\(951\) −5.26366 −0.170686
\(952\) 0 0
\(953\) 16.2434 0.526175 0.263087 0.964772i \(-0.415259\pi\)
0.263087 + 0.964772i \(0.415259\pi\)
\(954\) 0 0
\(955\) 37.0734 1.19967
\(956\) 0 0
\(957\) −1.41944 −0.0458841
\(958\) 0 0
\(959\) 1.80602 0.0583194
\(960\) 0 0
\(961\) 79.6172 2.56830
\(962\) 0 0
\(963\) −1.78370 −0.0574790
\(964\) 0 0
\(965\) 18.2010 0.585910
\(966\) 0 0
\(967\) 37.8299 1.21653 0.608264 0.793735i \(-0.291866\pi\)
0.608264 + 0.793735i \(0.291866\pi\)
\(968\) 0 0
\(969\) 8.84936 0.284282
\(970\) 0 0
\(971\) −35.4728 −1.13838 −0.569189 0.822207i \(-0.692743\pi\)
−0.569189 + 0.822207i \(0.692743\pi\)
\(972\) 0 0
\(973\) −1.78726 −0.0572968
\(974\) 0 0
\(975\) −23.8452 −0.763658
\(976\) 0 0
\(977\) −52.9898 −1.69529 −0.847647 0.530561i \(-0.821981\pi\)
−0.847647 + 0.530561i \(0.821981\pi\)
\(978\) 0 0
\(979\) 5.83171 0.186382
\(980\) 0 0
\(981\) 45.0689 1.43894
\(982\) 0 0
\(983\) −20.2492 −0.645850 −0.322925 0.946425i \(-0.604666\pi\)
−0.322925 + 0.946425i \(0.604666\pi\)
\(984\) 0 0
\(985\) −27.8676 −0.887936
\(986\) 0 0
\(987\) 0.306149 0.00974483
\(988\) 0 0
\(989\) 65.1788 2.07256
\(990\) 0 0
\(991\) 53.5315 1.70049 0.850243 0.526391i \(-0.176455\pi\)
0.850243 + 0.526391i \(0.176455\pi\)
\(992\) 0 0
\(993\) 1.86522 0.0591910
\(994\) 0 0
\(995\) −55.1976 −1.74988
\(996\) 0 0
\(997\) −46.0483 −1.45837 −0.729183 0.684319i \(-0.760099\pi\)
−0.729183 + 0.684319i \(0.760099\pi\)
\(998\) 0 0
\(999\) 11.4595 0.362564
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 8032.2.a.h.1.18 30
4.3 odd 2 8032.2.a.i.1.13 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8032.2.a.h.1.18 30 1.1 even 1 trivial
8032.2.a.i.1.13 yes 30 4.3 odd 2