Properties

Label 1287.2.a.q.1.3
Level $1287$
Weight $2$
Character 1287.1
Self dual yes
Analytic conductor $10.277$
Analytic rank $0$
Dimension $6$
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] = [1287,2,Mod(1,1287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1287, 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("1287.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1287.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: \(10.2767467401\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.194616205.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 10x^{4} - 2x^{3} + 24x^{2} + 7x - 12 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.23127\) of defining polynomial
Character \(\chi\) \(=\) 1287.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.23127 q^{2} -0.483971 q^{4} -1.04428 q^{5} +4.82820 q^{7} +3.05844 q^{8} +O(q^{10})\) \(q-1.23127 q^{2} -0.483971 q^{4} -1.04428 q^{5} +4.82820 q^{7} +3.05844 q^{8} +1.28579 q^{10} +1.00000 q^{11} +1.00000 q^{13} -5.94482 q^{14} -2.79783 q^{16} +2.46254 q^{17} -2.68717 q^{19} +0.505399 q^{20} -1.23127 q^{22} +6.84042 q^{23} -3.90949 q^{25} -1.23127 q^{26} -2.33671 q^{28} -4.25373 q^{29} +9.87743 q^{31} -2.67200 q^{32} -3.03206 q^{34} -5.04197 q^{35} +0.450326 q^{37} +3.30863 q^{38} -3.19386 q^{40} +0.139742 q^{41} -10.8332 q^{43} -0.483971 q^{44} -8.42241 q^{46} -3.74833 q^{47} +16.3115 q^{49} +4.81364 q^{50} -0.483971 q^{52} -13.3115 q^{53} -1.04428 q^{55} +14.7668 q^{56} +5.23749 q^{58} +6.19528 q^{59} +5.87974 q^{61} -12.1618 q^{62} +8.88561 q^{64} -1.04428 q^{65} +6.01222 q^{67} -1.19180 q^{68} +6.20803 q^{70} +8.95234 q^{71} +7.06116 q^{73} -0.554473 q^{74} +1.30051 q^{76} +4.82820 q^{77} +6.25373 q^{79} +2.92171 q^{80} -0.172061 q^{82} +11.6647 q^{83} -2.57157 q^{85} +13.3386 q^{86} +3.05844 q^{88} -1.16116 q^{89} +4.82820 q^{91} -3.31056 q^{92} +4.61521 q^{94} +2.80614 q^{95} -7.16322 q^{97} -20.0839 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 8 q^{4} - q^{5} + 4 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 8 q^{4} - q^{5} + 4 q^{7} + 6 q^{8} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 12 q^{14} + 8 q^{16} - 10 q^{19} - 4 q^{20} - 11 q^{23} + 23 q^{25} + 9 q^{28} - 2 q^{29} - 9 q^{31} + 17 q^{32} - 40 q^{34} + 24 q^{35} + 15 q^{37} + 9 q^{38} + 16 q^{40} + 4 q^{41} - 2 q^{43} + 8 q^{44} - 6 q^{46} - 6 q^{47} + 20 q^{49} + 4 q^{50} + 8 q^{52} - 2 q^{53} - q^{55} + 39 q^{56} + 18 q^{58} - 11 q^{59} + 16 q^{61} - 16 q^{62} + 36 q^{64} - q^{65} + 9 q^{67} - 12 q^{68} + 32 q^{70} + 15 q^{71} + 32 q^{73} - 22 q^{74} - 26 q^{76} + 4 q^{77} + 14 q^{79} - 56 q^{80} - 24 q^{82} + 26 q^{83} - 12 q^{85} + 10 q^{86} + 6 q^{88} + 23 q^{89} + 4 q^{91} - 83 q^{92} + 46 q^{94} + 52 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23127 −0.870640 −0.435320 0.900276i \(-0.643365\pi\)
−0.435320 + 0.900276i \(0.643365\pi\)
\(3\) 0 0
\(4\) −0.483971 −0.241985
\(5\) −1.04428 −0.467014 −0.233507 0.972355i \(-0.575020\pi\)
−0.233507 + 0.972355i \(0.575020\pi\)
\(6\) 0 0
\(7\) 4.82820 1.82489 0.912444 0.409202i \(-0.134193\pi\)
0.912444 + 0.409202i \(0.134193\pi\)
\(8\) 3.05844 1.08132
\(9\) 0 0
\(10\) 1.28579 0.406601
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) −5.94482 −1.58882
\(15\) 0 0
\(16\) −2.79783 −0.699458
\(17\) 2.46254 0.597254 0.298627 0.954370i \(-0.403471\pi\)
0.298627 + 0.954370i \(0.403471\pi\)
\(18\) 0 0
\(19\) −2.68717 −0.616479 −0.308239 0.951309i \(-0.599740\pi\)
−0.308239 + 0.951309i \(0.599740\pi\)
\(20\) 0.505399 0.113011
\(21\) 0 0
\(22\) −1.23127 −0.262508
\(23\) 6.84042 1.42633 0.713163 0.700999i \(-0.247262\pi\)
0.713163 + 0.700999i \(0.247262\pi\)
\(24\) 0 0
\(25\) −3.90949 −0.781898
\(26\) −1.23127 −0.241472
\(27\) 0 0
\(28\) −2.33671 −0.441596
\(29\) −4.25373 −0.789897 −0.394949 0.918703i \(-0.629238\pi\)
−0.394949 + 0.918703i \(0.629238\pi\)
\(30\) 0 0
\(31\) 9.87743 1.77404 0.887019 0.461732i \(-0.152772\pi\)
0.887019 + 0.461732i \(0.152772\pi\)
\(32\) −2.67200 −0.472347
\(33\) 0 0
\(34\) −3.03206 −0.519994
\(35\) −5.04197 −0.852248
\(36\) 0 0
\(37\) 0.450326 0.0740331 0.0370166 0.999315i \(-0.488215\pi\)
0.0370166 + 0.999315i \(0.488215\pi\)
\(38\) 3.30863 0.536731
\(39\) 0 0
\(40\) −3.19386 −0.504993
\(41\) 0.139742 0.0218241 0.0109120 0.999940i \(-0.496527\pi\)
0.0109120 + 0.999940i \(0.496527\pi\)
\(42\) 0 0
\(43\) −10.8332 −1.65204 −0.826020 0.563640i \(-0.809400\pi\)
−0.826020 + 0.563640i \(0.809400\pi\)
\(44\) −0.483971 −0.0729613
\(45\) 0 0
\(46\) −8.42241 −1.24182
\(47\) −3.74833 −0.546750 −0.273375 0.961908i \(-0.588140\pi\)
−0.273375 + 0.961908i \(0.588140\pi\)
\(48\) 0 0
\(49\) 16.3115 2.33022
\(50\) 4.81364 0.680752
\(51\) 0 0
\(52\) −0.483971 −0.0671147
\(53\) −13.3115 −1.82848 −0.914238 0.405177i \(-0.867210\pi\)
−0.914238 + 0.405177i \(0.867210\pi\)
\(54\) 0 0
\(55\) −1.04428 −0.140810
\(56\) 14.7668 1.97329
\(57\) 0 0
\(58\) 5.23749 0.687717
\(59\) 6.19528 0.806556 0.403278 0.915077i \(-0.367871\pi\)
0.403278 + 0.915077i \(0.367871\pi\)
\(60\) 0 0
\(61\) 5.87974 0.752823 0.376412 0.926453i \(-0.377158\pi\)
0.376412 + 0.926453i \(0.377158\pi\)
\(62\) −12.1618 −1.54455
\(63\) 0 0
\(64\) 8.88561 1.11070
\(65\) −1.04428 −0.129526
\(66\) 0 0
\(67\) 6.01222 0.734509 0.367255 0.930120i \(-0.380298\pi\)
0.367255 + 0.930120i \(0.380298\pi\)
\(68\) −1.19180 −0.144527
\(69\) 0 0
\(70\) 6.20803 0.742002
\(71\) 8.95234 1.06245 0.531224 0.847231i \(-0.321732\pi\)
0.531224 + 0.847231i \(0.321732\pi\)
\(72\) 0 0
\(73\) 7.06116 0.826446 0.413223 0.910630i \(-0.364403\pi\)
0.413223 + 0.910630i \(0.364403\pi\)
\(74\) −0.554473 −0.0644562
\(75\) 0 0
\(76\) 1.30051 0.149179
\(77\) 4.82820 0.550224
\(78\) 0 0
\(79\) 6.25373 0.703599 0.351800 0.936075i \(-0.385570\pi\)
0.351800 + 0.936075i \(0.385570\pi\)
\(80\) 2.92171 0.326657
\(81\) 0 0
\(82\) −0.172061 −0.0190009
\(83\) 11.6647 1.28037 0.640185 0.768220i \(-0.278858\pi\)
0.640185 + 0.768220i \(0.278858\pi\)
\(84\) 0 0
\(85\) −2.57157 −0.278926
\(86\) 13.3386 1.43833
\(87\) 0 0
\(88\) 3.05844 0.326031
\(89\) −1.16116 −0.123083 −0.0615413 0.998105i \(-0.519602\pi\)
−0.0615413 + 0.998105i \(0.519602\pi\)
\(90\) 0 0
\(91\) 4.82820 0.506133
\(92\) −3.31056 −0.345150
\(93\) 0 0
\(94\) 4.61521 0.476023
\(95\) 2.80614 0.287904
\(96\) 0 0
\(97\) −7.16322 −0.727314 −0.363657 0.931533i \(-0.618472\pi\)
−0.363657 + 0.931533i \(0.618472\pi\)
\(98\) −20.0839 −2.02878
\(99\) 0 0
\(100\) 1.89208 0.189208
\(101\) 6.32776 0.629635 0.314818 0.949152i \(-0.398057\pi\)
0.314818 + 0.949152i \(0.398057\pi\)
\(102\) 0 0
\(103\) 18.6750 1.84010 0.920051 0.391799i \(-0.128147\pi\)
0.920051 + 0.391799i \(0.128147\pi\)
\(104\) 3.05844 0.299905
\(105\) 0 0
\(106\) 16.3901 1.59195
\(107\) 6.67136 0.644944 0.322472 0.946579i \(-0.395486\pi\)
0.322472 + 0.946579i \(0.395486\pi\)
\(108\) 0 0
\(109\) −2.31318 −0.221562 −0.110781 0.993845i \(-0.535335\pi\)
−0.110781 + 0.993845i \(0.535335\pi\)
\(110\) 1.28579 0.122595
\(111\) 0 0
\(112\) −13.5085 −1.27643
\(113\) −3.80601 −0.358040 −0.179020 0.983845i \(-0.557293\pi\)
−0.179020 + 0.983845i \(0.557293\pi\)
\(114\) 0 0
\(115\) −7.14328 −0.666114
\(116\) 2.05868 0.191144
\(117\) 0 0
\(118\) −7.62807 −0.702220
\(119\) 11.8896 1.08992
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −7.23955 −0.655438
\(123\) 0 0
\(124\) −4.78039 −0.429291
\(125\) 9.30396 0.832171
\(126\) 0 0
\(127\) 2.67136 0.237045 0.118522 0.992951i \(-0.462184\pi\)
0.118522 + 0.992951i \(0.462184\pi\)
\(128\) −5.59661 −0.494675
\(129\) 0 0
\(130\) 1.28579 0.112771
\(131\) 9.34193 0.816209 0.408104 0.912935i \(-0.366190\pi\)
0.408104 + 0.912935i \(0.366190\pi\)
\(132\) 0 0
\(133\) −12.9742 −1.12500
\(134\) −7.40267 −0.639493
\(135\) 0 0
\(136\) 7.53154 0.645825
\(137\) −13.5034 −1.15368 −0.576838 0.816858i \(-0.695714\pi\)
−0.576838 + 0.816858i \(0.695714\pi\)
\(138\) 0 0
\(139\) −17.6987 −1.50119 −0.750593 0.660765i \(-0.770232\pi\)
−0.750593 + 0.660765i \(0.770232\pi\)
\(140\) 2.44017 0.206232
\(141\) 0 0
\(142\) −11.0228 −0.925010
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 4.44206 0.368893
\(146\) −8.69420 −0.719538
\(147\) 0 0
\(148\) −0.217945 −0.0179149
\(149\) −5.51666 −0.451942 −0.225971 0.974134i \(-0.572555\pi\)
−0.225971 + 0.974134i \(0.572555\pi\)
\(150\) 0 0
\(151\) −5.01080 −0.407773 −0.203886 0.978995i \(-0.565357\pi\)
−0.203886 + 0.978995i \(0.565357\pi\)
\(152\) −8.21855 −0.666612
\(153\) 0 0
\(154\) −5.94482 −0.479048
\(155\) −10.3148 −0.828501
\(156\) 0 0
\(157\) −4.70901 −0.375820 −0.187910 0.982186i \(-0.560171\pi\)
−0.187910 + 0.982186i \(0.560171\pi\)
\(158\) −7.70004 −0.612582
\(159\) 0 0
\(160\) 2.79030 0.220593
\(161\) 33.0269 2.60288
\(162\) 0 0
\(163\) −9.25284 −0.724739 −0.362369 0.932035i \(-0.618032\pi\)
−0.362369 + 0.932035i \(0.618032\pi\)
\(164\) −0.0676311 −0.00528111
\(165\) 0 0
\(166\) −14.3625 −1.11474
\(167\) 20.5061 1.58681 0.793407 0.608692i \(-0.208305\pi\)
0.793407 + 0.608692i \(0.208305\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 3.16630 0.242844
\(171\) 0 0
\(172\) 5.24293 0.399770
\(173\) 14.0548 1.06857 0.534284 0.845305i \(-0.320581\pi\)
0.534284 + 0.845305i \(0.320581\pi\)
\(174\) 0 0
\(175\) −18.8758 −1.42688
\(176\) −2.79783 −0.210894
\(177\) 0 0
\(178\) 1.42970 0.107161
\(179\) −14.7568 −1.10298 −0.551488 0.834183i \(-0.685940\pi\)
−0.551488 + 0.834183i \(0.685940\pi\)
\(180\) 0 0
\(181\) 3.23728 0.240625 0.120313 0.992736i \(-0.461610\pi\)
0.120313 + 0.992736i \(0.461610\pi\)
\(182\) −5.94482 −0.440660
\(183\) 0 0
\(184\) 20.9210 1.54232
\(185\) −0.470264 −0.0345745
\(186\) 0 0
\(187\) 2.46254 0.180079
\(188\) 1.81408 0.132306
\(189\) 0 0
\(190\) −3.45512 −0.250661
\(191\) 9.09575 0.658146 0.329073 0.944305i \(-0.393264\pi\)
0.329073 + 0.944305i \(0.393264\pi\)
\(192\) 0 0
\(193\) 7.87478 0.566839 0.283420 0.958996i \(-0.408531\pi\)
0.283420 + 0.958996i \(0.408531\pi\)
\(194\) 8.81986 0.633229
\(195\) 0 0
\(196\) −7.89429 −0.563878
\(197\) −9.71126 −0.691898 −0.345949 0.938253i \(-0.612443\pi\)
−0.345949 + 0.938253i \(0.612443\pi\)
\(198\) 0 0
\(199\) 13.1240 0.930332 0.465166 0.885223i \(-0.345995\pi\)
0.465166 + 0.885223i \(0.345995\pi\)
\(200\) −11.9569 −0.845484
\(201\) 0 0
\(202\) −7.79119 −0.548186
\(203\) −20.5378 −1.44147
\(204\) 0 0
\(205\) −0.145929 −0.0101921
\(206\) −22.9940 −1.60207
\(207\) 0 0
\(208\) −2.79783 −0.193995
\(209\) −2.68717 −0.185875
\(210\) 0 0
\(211\) 7.85926 0.541054 0.270527 0.962712i \(-0.412802\pi\)
0.270527 + 0.962712i \(0.412802\pi\)
\(212\) 6.44238 0.442465
\(213\) 0 0
\(214\) −8.21425 −0.561515
\(215\) 11.3128 0.771526
\(216\) 0 0
\(217\) 47.6902 3.23742
\(218\) 2.84815 0.192901
\(219\) 0 0
\(220\) 0.505399 0.0340740
\(221\) 2.46254 0.165649
\(222\) 0 0
\(223\) −7.07805 −0.473981 −0.236991 0.971512i \(-0.576161\pi\)
−0.236991 + 0.971512i \(0.576161\pi\)
\(224\) −12.9009 −0.861979
\(225\) 0 0
\(226\) 4.68624 0.311724
\(227\) −20.6501 −1.37059 −0.685296 0.728264i \(-0.740327\pi\)
−0.685296 + 0.728264i \(0.740327\pi\)
\(228\) 0 0
\(229\) −1.44402 −0.0954238 −0.0477119 0.998861i \(-0.515193\pi\)
−0.0477119 + 0.998861i \(0.515193\pi\)
\(230\) 8.79531 0.579946
\(231\) 0 0
\(232\) −13.0098 −0.854134
\(233\) 0.537803 0.0352326 0.0176163 0.999845i \(-0.494392\pi\)
0.0176163 + 0.999845i \(0.494392\pi\)
\(234\) 0 0
\(235\) 3.91429 0.255340
\(236\) −2.99833 −0.195175
\(237\) 0 0
\(238\) −14.6394 −0.948930
\(239\) 5.48993 0.355114 0.177557 0.984110i \(-0.443181\pi\)
0.177557 + 0.984110i \(0.443181\pi\)
\(240\) 0 0
\(241\) −19.6463 −1.26553 −0.632765 0.774344i \(-0.718080\pi\)
−0.632765 + 0.774344i \(0.718080\pi\)
\(242\) −1.23127 −0.0791491
\(243\) 0 0
\(244\) −2.84562 −0.182172
\(245\) −17.0337 −1.08824
\(246\) 0 0
\(247\) −2.68717 −0.170980
\(248\) 30.2095 1.91831
\(249\) 0 0
\(250\) −11.4557 −0.724522
\(251\) 7.10538 0.448487 0.224244 0.974533i \(-0.428009\pi\)
0.224244 + 0.974533i \(0.428009\pi\)
\(252\) 0 0
\(253\) 6.84042 0.430053
\(254\) −3.28917 −0.206381
\(255\) 0 0
\(256\) −10.8803 −0.680017
\(257\) −4.33990 −0.270716 −0.135358 0.990797i \(-0.543218\pi\)
−0.135358 + 0.990797i \(0.543218\pi\)
\(258\) 0 0
\(259\) 2.17426 0.135102
\(260\) 0.505399 0.0313435
\(261\) 0 0
\(262\) −11.5025 −0.710624
\(263\) 5.36105 0.330576 0.165288 0.986245i \(-0.447145\pi\)
0.165288 + 0.986245i \(0.447145\pi\)
\(264\) 0 0
\(265\) 13.9009 0.853924
\(266\) 15.9747 0.979474
\(267\) 0 0
\(268\) −2.90974 −0.177740
\(269\) −0.305701 −0.0186389 −0.00931946 0.999957i \(-0.502967\pi\)
−0.00931946 + 0.999957i \(0.502967\pi\)
\(270\) 0 0
\(271\) 6.89804 0.419026 0.209513 0.977806i \(-0.432812\pi\)
0.209513 + 0.977806i \(0.432812\pi\)
\(272\) −6.88978 −0.417754
\(273\) 0 0
\(274\) 16.6264 1.00444
\(275\) −3.90949 −0.235751
\(276\) 0 0
\(277\) 31.6001 1.89867 0.949334 0.314269i \(-0.101759\pi\)
0.949334 + 0.314269i \(0.101759\pi\)
\(278\) 21.7919 1.30699
\(279\) 0 0
\(280\) −15.4206 −0.921555
\(281\) −26.8160 −1.59971 −0.799855 0.600193i \(-0.795090\pi\)
−0.799855 + 0.600193i \(0.795090\pi\)
\(282\) 0 0
\(283\) −27.8032 −1.65273 −0.826363 0.563138i \(-0.809594\pi\)
−0.826363 + 0.563138i \(0.809594\pi\)
\(284\) −4.33267 −0.257097
\(285\) 0 0
\(286\) −1.23127 −0.0728066
\(287\) 0.674703 0.0398265
\(288\) 0 0
\(289\) −10.9359 −0.643287
\(290\) −5.46939 −0.321173
\(291\) 0 0
\(292\) −3.41740 −0.199988
\(293\) 2.83370 0.165546 0.0827731 0.996568i \(-0.473622\pi\)
0.0827731 + 0.996568i \(0.473622\pi\)
\(294\) 0 0
\(295\) −6.46957 −0.376673
\(296\) 1.37730 0.0800537
\(297\) 0 0
\(298\) 6.79250 0.393479
\(299\) 6.84042 0.395591
\(300\) 0 0
\(301\) −52.3046 −3.01479
\(302\) 6.16965 0.355024
\(303\) 0 0
\(304\) 7.51824 0.431201
\(305\) −6.14006 −0.351579
\(306\) 0 0
\(307\) −0.417630 −0.0238354 −0.0119177 0.999929i \(-0.503794\pi\)
−0.0119177 + 0.999929i \(0.503794\pi\)
\(308\) −2.33671 −0.133146
\(309\) 0 0
\(310\) 12.7003 0.721327
\(311\) −14.5524 −0.825190 −0.412595 0.910915i \(-0.635377\pi\)
−0.412595 + 0.910915i \(0.635377\pi\)
\(312\) 0 0
\(313\) 10.8588 0.613778 0.306889 0.951745i \(-0.400712\pi\)
0.306889 + 0.951745i \(0.400712\pi\)
\(314\) 5.79807 0.327204
\(315\) 0 0
\(316\) −3.02662 −0.170261
\(317\) 30.8428 1.73230 0.866151 0.499782i \(-0.166586\pi\)
0.866151 + 0.499782i \(0.166586\pi\)
\(318\) 0 0
\(319\) −4.25373 −0.238163
\(320\) −9.27903 −0.518713
\(321\) 0 0
\(322\) −40.6651 −2.26618
\(323\) −6.61727 −0.368195
\(324\) 0 0
\(325\) −3.90949 −0.216859
\(326\) 11.3928 0.630987
\(327\) 0 0
\(328\) 0.427393 0.0235989
\(329\) −18.0977 −0.997757
\(330\) 0 0
\(331\) 14.4885 0.796359 0.398179 0.917308i \(-0.369642\pi\)
0.398179 + 0.917308i \(0.369642\pi\)
\(332\) −5.64539 −0.309831
\(333\) 0 0
\(334\) −25.2486 −1.38154
\(335\) −6.27841 −0.343026
\(336\) 0 0
\(337\) 13.3856 0.729159 0.364579 0.931172i \(-0.381213\pi\)
0.364579 + 0.931172i \(0.381213\pi\)
\(338\) −1.23127 −0.0669723
\(339\) 0 0
\(340\) 1.24457 0.0674961
\(341\) 9.87743 0.534893
\(342\) 0 0
\(343\) 44.9578 2.42749
\(344\) −33.1326 −1.78639
\(345\) 0 0
\(346\) −17.3053 −0.930339
\(347\) 12.0449 0.646605 0.323302 0.946296i \(-0.395207\pi\)
0.323302 + 0.946296i \(0.395207\pi\)
\(348\) 0 0
\(349\) −12.9479 −0.693086 −0.346543 0.938034i \(-0.612645\pi\)
−0.346543 + 0.938034i \(0.612645\pi\)
\(350\) 23.2412 1.24230
\(351\) 0 0
\(352\) −2.67200 −0.142418
\(353\) −32.4161 −1.72533 −0.862666 0.505773i \(-0.831207\pi\)
−0.862666 + 0.505773i \(0.831207\pi\)
\(354\) 0 0
\(355\) −9.34871 −0.496178
\(356\) 0.561967 0.0297842
\(357\) 0 0
\(358\) 18.1697 0.960296
\(359\) 12.0843 0.637787 0.318893 0.947791i \(-0.396689\pi\)
0.318893 + 0.947791i \(0.396689\pi\)
\(360\) 0 0
\(361\) −11.7791 −0.619954
\(362\) −3.98597 −0.209498
\(363\) 0 0
\(364\) −2.33671 −0.122477
\(365\) −7.37380 −0.385962
\(366\) 0 0
\(367\) −7.69698 −0.401779 −0.200890 0.979614i \(-0.564383\pi\)
−0.200890 + 0.979614i \(0.564383\pi\)
\(368\) −19.1383 −0.997654
\(369\) 0 0
\(370\) 0.579023 0.0301020
\(371\) −64.2706 −3.33676
\(372\) 0 0
\(373\) 6.53373 0.338304 0.169152 0.985590i \(-0.445897\pi\)
0.169152 + 0.985590i \(0.445897\pi\)
\(374\) −3.03206 −0.156784
\(375\) 0 0
\(376\) −11.4640 −0.591213
\(377\) −4.25373 −0.219078
\(378\) 0 0
\(379\) −17.7605 −0.912298 −0.456149 0.889903i \(-0.650772\pi\)
−0.456149 + 0.889903i \(0.650772\pi\)
\(380\) −1.35809 −0.0696686
\(381\) 0 0
\(382\) −11.1993 −0.573008
\(383\) −27.8411 −1.42261 −0.711307 0.702881i \(-0.751896\pi\)
−0.711307 + 0.702881i \(0.751896\pi\)
\(384\) 0 0
\(385\) −5.04197 −0.256963
\(386\) −9.69599 −0.493513
\(387\) 0 0
\(388\) 3.46679 0.175999
\(389\) 18.0202 0.913658 0.456829 0.889555i \(-0.348985\pi\)
0.456829 + 0.889555i \(0.348985\pi\)
\(390\) 0 0
\(391\) 16.8448 0.851879
\(392\) 49.8878 2.51971
\(393\) 0 0
\(394\) 11.9572 0.602395
\(395\) −6.53061 −0.328591
\(396\) 0 0
\(397\) −3.40061 −0.170672 −0.0853360 0.996352i \(-0.527196\pi\)
−0.0853360 + 0.996352i \(0.527196\pi\)
\(398\) −16.1592 −0.809985
\(399\) 0 0
\(400\) 10.9381 0.546904
\(401\) 12.4817 0.623306 0.311653 0.950196i \(-0.399117\pi\)
0.311653 + 0.950196i \(0.399117\pi\)
\(402\) 0 0
\(403\) 9.87743 0.492030
\(404\) −3.06245 −0.152363
\(405\) 0 0
\(406\) 25.2877 1.25501
\(407\) 0.450326 0.0223218
\(408\) 0 0
\(409\) −31.2077 −1.54312 −0.771561 0.636155i \(-0.780524\pi\)
−0.771561 + 0.636155i \(0.780524\pi\)
\(410\) 0.179679 0.00887370
\(411\) 0 0
\(412\) −9.03815 −0.445278
\(413\) 29.9120 1.47187
\(414\) 0 0
\(415\) −12.1812 −0.597951
\(416\) −2.67200 −0.131005
\(417\) 0 0
\(418\) 3.30863 0.161831
\(419\) 22.6750 1.10775 0.553873 0.832601i \(-0.313149\pi\)
0.553873 + 0.832601i \(0.313149\pi\)
\(420\) 0 0
\(421\) −28.9661 −1.41172 −0.705860 0.708351i \(-0.749439\pi\)
−0.705860 + 0.708351i \(0.749439\pi\)
\(422\) −9.67688 −0.471063
\(423\) 0 0
\(424\) −40.7125 −1.97717
\(425\) −9.62728 −0.466992
\(426\) 0 0
\(427\) 28.3885 1.37382
\(428\) −3.22874 −0.156067
\(429\) 0 0
\(430\) −13.9291 −0.671722
\(431\) −12.8485 −0.618891 −0.309446 0.950917i \(-0.600143\pi\)
−0.309446 + 0.950917i \(0.600143\pi\)
\(432\) 0 0
\(433\) 12.4007 0.595942 0.297971 0.954575i \(-0.403690\pi\)
0.297971 + 0.954575i \(0.403690\pi\)
\(434\) −58.7196 −2.81863
\(435\) 0 0
\(436\) 1.11951 0.0536148
\(437\) −18.3814 −0.879299
\(438\) 0 0
\(439\) −14.8848 −0.710414 −0.355207 0.934788i \(-0.615590\pi\)
−0.355207 + 0.934788i \(0.615590\pi\)
\(440\) −3.19386 −0.152261
\(441\) 0 0
\(442\) −3.03206 −0.144220
\(443\) 12.4823 0.593052 0.296526 0.955025i \(-0.404172\pi\)
0.296526 + 0.955025i \(0.404172\pi\)
\(444\) 0 0
\(445\) 1.21257 0.0574814
\(446\) 8.71500 0.412667
\(447\) 0 0
\(448\) 42.9015 2.02691
\(449\) 14.4224 0.680636 0.340318 0.940310i \(-0.389465\pi\)
0.340318 + 0.940310i \(0.389465\pi\)
\(450\) 0 0
\(451\) 0.139742 0.00658020
\(452\) 1.84200 0.0866404
\(453\) 0 0
\(454\) 25.4258 1.19329
\(455\) −5.04197 −0.236371
\(456\) 0 0
\(457\) −16.7181 −0.782041 −0.391021 0.920382i \(-0.627878\pi\)
−0.391021 + 0.920382i \(0.627878\pi\)
\(458\) 1.77799 0.0830798
\(459\) 0 0
\(460\) 3.45714 0.161190
\(461\) 4.25625 0.198233 0.0991166 0.995076i \(-0.468398\pi\)
0.0991166 + 0.995076i \(0.468398\pi\)
\(462\) 0 0
\(463\) 28.0962 1.30574 0.652870 0.757470i \(-0.273565\pi\)
0.652870 + 0.757470i \(0.273565\pi\)
\(464\) 11.9012 0.552500
\(465\) 0 0
\(466\) −0.662181 −0.0306749
\(467\) 5.37530 0.248739 0.124370 0.992236i \(-0.460309\pi\)
0.124370 + 0.992236i \(0.460309\pi\)
\(468\) 0 0
\(469\) 29.0282 1.34040
\(470\) −4.81955 −0.222309
\(471\) 0 0
\(472\) 18.9479 0.872147
\(473\) −10.8332 −0.498109
\(474\) 0 0
\(475\) 10.5055 0.482023
\(476\) −5.75424 −0.263745
\(477\) 0 0
\(478\) −6.75960 −0.309177
\(479\) −28.8326 −1.31740 −0.658698 0.752408i \(-0.728892\pi\)
−0.658698 + 0.752408i \(0.728892\pi\)
\(480\) 0 0
\(481\) 0.450326 0.0205331
\(482\) 24.1899 1.10182
\(483\) 0 0
\(484\) −0.483971 −0.0219987
\(485\) 7.48037 0.339666
\(486\) 0 0
\(487\) −28.0821 −1.27252 −0.636260 0.771474i \(-0.719520\pi\)
−0.636260 + 0.771474i \(0.719520\pi\)
\(488\) 17.9828 0.814045
\(489\) 0 0
\(490\) 20.9731 0.947469
\(491\) 33.8170 1.52614 0.763069 0.646317i \(-0.223692\pi\)
0.763069 + 0.646317i \(0.223692\pi\)
\(492\) 0 0
\(493\) −10.4750 −0.471770
\(494\) 3.30863 0.148862
\(495\) 0 0
\(496\) −27.6354 −1.24087
\(497\) 43.2237 1.93885
\(498\) 0 0
\(499\) −2.05872 −0.0921611 −0.0460806 0.998938i \(-0.514673\pi\)
−0.0460806 + 0.998938i \(0.514673\pi\)
\(500\) −4.50284 −0.201373
\(501\) 0 0
\(502\) −8.74865 −0.390471
\(503\) −30.1771 −1.34553 −0.672766 0.739855i \(-0.734894\pi\)
−0.672766 + 0.739855i \(0.734894\pi\)
\(504\) 0 0
\(505\) −6.60792 −0.294049
\(506\) −8.42241 −0.374422
\(507\) 0 0
\(508\) −1.29286 −0.0573613
\(509\) 13.0536 0.578591 0.289296 0.957240i \(-0.406579\pi\)
0.289296 + 0.957240i \(0.406579\pi\)
\(510\) 0 0
\(511\) 34.0927 1.50817
\(512\) 24.5898 1.08673
\(513\) 0 0
\(514\) 5.34359 0.235696
\(515\) −19.5018 −0.859353
\(516\) 0 0
\(517\) −3.74833 −0.164851
\(518\) −2.67711 −0.117625
\(519\) 0 0
\(520\) −3.19386 −0.140060
\(521\) 0.881997 0.0386410 0.0193205 0.999813i \(-0.493850\pi\)
0.0193205 + 0.999813i \(0.493850\pi\)
\(522\) 0 0
\(523\) −22.7936 −0.996694 −0.498347 0.866978i \(-0.666059\pi\)
−0.498347 + 0.866978i \(0.666059\pi\)
\(524\) −4.52122 −0.197511
\(525\) 0 0
\(526\) −6.60090 −0.287813
\(527\) 24.3236 1.05955
\(528\) 0 0
\(529\) 23.7913 1.03440
\(530\) −17.1158 −0.743461
\(531\) 0 0
\(532\) 6.27913 0.272235
\(533\) 0.139742 0.00605291
\(534\) 0 0
\(535\) −6.96673 −0.301198
\(536\) 18.3880 0.794241
\(537\) 0 0
\(538\) 0.376401 0.0162278
\(539\) 16.3115 0.702586
\(540\) 0 0
\(541\) 38.0273 1.63492 0.817460 0.575986i \(-0.195382\pi\)
0.817460 + 0.575986i \(0.195382\pi\)
\(542\) −8.49336 −0.364821
\(543\) 0 0
\(544\) −6.57990 −0.282111
\(545\) 2.41559 0.103473
\(546\) 0 0
\(547\) 10.9245 0.467100 0.233550 0.972345i \(-0.424966\pi\)
0.233550 + 0.972345i \(0.424966\pi\)
\(548\) 6.53527 0.279173
\(549\) 0 0
\(550\) 4.81364 0.205254
\(551\) 11.4305 0.486955
\(552\) 0 0
\(553\) 30.1942 1.28399
\(554\) −38.9083 −1.65306
\(555\) 0 0
\(556\) 8.56566 0.363265
\(557\) −4.24090 −0.179693 −0.0898463 0.995956i \(-0.528638\pi\)
−0.0898463 + 0.995956i \(0.528638\pi\)
\(558\) 0 0
\(559\) −10.8332 −0.458194
\(560\) 14.1066 0.596112
\(561\) 0 0
\(562\) 33.0178 1.39277
\(563\) 35.4686 1.49482 0.747412 0.664361i \(-0.231296\pi\)
0.747412 + 0.664361i \(0.231296\pi\)
\(564\) 0 0
\(565\) 3.97453 0.167210
\(566\) 34.2332 1.43893
\(567\) 0 0
\(568\) 27.3802 1.14885
\(569\) 32.8755 1.37821 0.689106 0.724661i \(-0.258004\pi\)
0.689106 + 0.724661i \(0.258004\pi\)
\(570\) 0 0
\(571\) 13.5303 0.566227 0.283114 0.959086i \(-0.408633\pi\)
0.283114 + 0.959086i \(0.408633\pi\)
\(572\) −0.483971 −0.0202358
\(573\) 0 0
\(574\) −0.830743 −0.0346745
\(575\) −26.7425 −1.11524
\(576\) 0 0
\(577\) 38.1270 1.58725 0.793624 0.608409i \(-0.208192\pi\)
0.793624 + 0.608409i \(0.208192\pi\)
\(578\) 13.4650 0.560072
\(579\) 0 0
\(580\) −2.14983 −0.0892668
\(581\) 56.3197 2.33653
\(582\) 0 0
\(583\) −13.3115 −0.551306
\(584\) 21.5962 0.893655
\(585\) 0 0
\(586\) −3.48905 −0.144131
\(587\) 0.611402 0.0252353 0.0126176 0.999920i \(-0.495984\pi\)
0.0126176 + 0.999920i \(0.495984\pi\)
\(588\) 0 0
\(589\) −26.5423 −1.09366
\(590\) 7.96580 0.327947
\(591\) 0 0
\(592\) −1.25994 −0.0517830
\(593\) 23.7963 0.977198 0.488599 0.872508i \(-0.337508\pi\)
0.488599 + 0.872508i \(0.337508\pi\)
\(594\) 0 0
\(595\) −12.4161 −0.509009
\(596\) 2.66990 0.109363
\(597\) 0 0
\(598\) −8.42241 −0.344418
\(599\) 6.35281 0.259569 0.129784 0.991542i \(-0.458571\pi\)
0.129784 + 0.991542i \(0.458571\pi\)
\(600\) 0 0
\(601\) 42.0793 1.71645 0.858224 0.513275i \(-0.171568\pi\)
0.858224 + 0.513275i \(0.171568\pi\)
\(602\) 64.4012 2.62480
\(603\) 0 0
\(604\) 2.42508 0.0986751
\(605\) −1.04428 −0.0424558
\(606\) 0 0
\(607\) −44.2945 −1.79786 −0.898929 0.438093i \(-0.855654\pi\)
−0.898929 + 0.438093i \(0.855654\pi\)
\(608\) 7.18010 0.291192
\(609\) 0 0
\(610\) 7.56008 0.306099
\(611\) −3.74833 −0.151641
\(612\) 0 0
\(613\) 4.69112 0.189473 0.0947363 0.995502i \(-0.469799\pi\)
0.0947363 + 0.995502i \(0.469799\pi\)
\(614\) 0.514215 0.0207520
\(615\) 0 0
\(616\) 14.7668 0.594970
\(617\) −2.55837 −0.102996 −0.0514981 0.998673i \(-0.516400\pi\)
−0.0514981 + 0.998673i \(0.516400\pi\)
\(618\) 0 0
\(619\) −21.9375 −0.881742 −0.440871 0.897571i \(-0.645330\pi\)
−0.440871 + 0.897571i \(0.645330\pi\)
\(620\) 4.99204 0.200485
\(621\) 0 0
\(622\) 17.9179 0.718444
\(623\) −5.60631 −0.224612
\(624\) 0 0
\(625\) 9.83155 0.393262
\(626\) −13.3702 −0.534380
\(627\) 0 0
\(628\) 2.27902 0.0909429
\(629\) 1.10895 0.0442166
\(630\) 0 0
\(631\) 17.9394 0.714158 0.357079 0.934074i \(-0.383773\pi\)
0.357079 + 0.934074i \(0.383773\pi\)
\(632\) 19.1267 0.760818
\(633\) 0 0
\(634\) −37.9758 −1.50821
\(635\) −2.78963 −0.110703
\(636\) 0 0
\(637\) 16.3115 0.646286
\(638\) 5.23749 0.207354
\(639\) 0 0
\(640\) 5.84440 0.231020
\(641\) −29.1930 −1.15306 −0.576528 0.817078i \(-0.695593\pi\)
−0.576528 + 0.817078i \(0.695593\pi\)
\(642\) 0 0
\(643\) −49.1335 −1.93764 −0.968819 0.247770i \(-0.920302\pi\)
−0.968819 + 0.247770i \(0.920302\pi\)
\(644\) −15.9841 −0.629860
\(645\) 0 0
\(646\) 8.14765 0.320565
\(647\) −44.0511 −1.73183 −0.865914 0.500193i \(-0.833262\pi\)
−0.865914 + 0.500193i \(0.833262\pi\)
\(648\) 0 0
\(649\) 6.19528 0.243186
\(650\) 4.81364 0.188807
\(651\) 0 0
\(652\) 4.47811 0.175376
\(653\) −31.6536 −1.23870 −0.619350 0.785115i \(-0.712604\pi\)
−0.619350 + 0.785115i \(0.712604\pi\)
\(654\) 0 0
\(655\) −9.75555 −0.381181
\(656\) −0.390975 −0.0152650
\(657\) 0 0
\(658\) 22.2832 0.868688
\(659\) −41.1367 −1.60246 −0.801229 0.598358i \(-0.795820\pi\)
−0.801229 + 0.598358i \(0.795820\pi\)
\(660\) 0 0
\(661\) −24.3438 −0.946863 −0.473432 0.880831i \(-0.656985\pi\)
−0.473432 + 0.880831i \(0.656985\pi\)
\(662\) −17.8393 −0.693342
\(663\) 0 0
\(664\) 35.6759 1.38449
\(665\) 13.5486 0.525393
\(666\) 0 0
\(667\) −29.0973 −1.12665
\(668\) −9.92438 −0.383986
\(669\) 0 0
\(670\) 7.73043 0.298652
\(671\) 5.87974 0.226985
\(672\) 0 0
\(673\) −15.7516 −0.607178 −0.303589 0.952803i \(-0.598185\pi\)
−0.303589 + 0.952803i \(0.598185\pi\)
\(674\) −16.4813 −0.634835
\(675\) 0 0
\(676\) −0.483971 −0.0186143
\(677\) 11.9285 0.458451 0.229226 0.973373i \(-0.426381\pi\)
0.229226 + 0.973373i \(0.426381\pi\)
\(678\) 0 0
\(679\) −34.5854 −1.32727
\(680\) −7.86501 −0.301609
\(681\) 0 0
\(682\) −12.1618 −0.465699
\(683\) −45.8727 −1.75527 −0.877636 0.479328i \(-0.840880\pi\)
−0.877636 + 0.479328i \(0.840880\pi\)
\(684\) 0 0
\(685\) 14.1013 0.538783
\(686\) −55.3553 −2.11347
\(687\) 0 0
\(688\) 30.3093 1.15553
\(689\) −13.3115 −0.507128
\(690\) 0 0
\(691\) 10.3374 0.393253 0.196627 0.980478i \(-0.437001\pi\)
0.196627 + 0.980478i \(0.437001\pi\)
\(692\) −6.80212 −0.258578
\(693\) 0 0
\(694\) −14.8306 −0.562960
\(695\) 18.4823 0.701075
\(696\) 0 0
\(697\) 0.344121 0.0130345
\(698\) 15.9424 0.603429
\(699\) 0 0
\(700\) 9.13533 0.345283
\(701\) −22.9944 −0.868487 −0.434243 0.900796i \(-0.642984\pi\)
−0.434243 + 0.900796i \(0.642984\pi\)
\(702\) 0 0
\(703\) −1.21010 −0.0456398
\(704\) 8.88561 0.334889
\(705\) 0 0
\(706\) 39.9130 1.50214
\(707\) 30.5517 1.14901
\(708\) 0 0
\(709\) −34.6028 −1.29954 −0.649768 0.760132i \(-0.725134\pi\)
−0.649768 + 0.760132i \(0.725134\pi\)
\(710\) 11.5108 0.431993
\(711\) 0 0
\(712\) −3.55134 −0.133092
\(713\) 67.5657 2.53036
\(714\) 0 0
\(715\) −1.04428 −0.0390537
\(716\) 7.14187 0.266904
\(717\) 0 0
\(718\) −14.8791 −0.555283
\(719\) −37.2446 −1.38899 −0.694495 0.719497i \(-0.744372\pi\)
−0.694495 + 0.719497i \(0.744372\pi\)
\(720\) 0 0
\(721\) 90.1666 3.35798
\(722\) 14.5033 0.539757
\(723\) 0 0
\(724\) −1.56675 −0.0582277
\(725\) 16.6299 0.617619
\(726\) 0 0
\(727\) −20.0501 −0.743619 −0.371809 0.928309i \(-0.621262\pi\)
−0.371809 + 0.928309i \(0.621262\pi\)
\(728\) 14.7668 0.547293
\(729\) 0 0
\(730\) 9.07914 0.336034
\(731\) −26.6771 −0.986688
\(732\) 0 0
\(733\) 22.8983 0.845769 0.422885 0.906184i \(-0.361018\pi\)
0.422885 + 0.906184i \(0.361018\pi\)
\(734\) 9.47708 0.349805
\(735\) 0 0
\(736\) −18.2776 −0.673720
\(737\) 6.01222 0.221463
\(738\) 0 0
\(739\) −15.0535 −0.553751 −0.276876 0.960906i \(-0.589299\pi\)
−0.276876 + 0.960906i \(0.589299\pi\)
\(740\) 0.227594 0.00836653
\(741\) 0 0
\(742\) 79.1346 2.90512
\(743\) −39.0967 −1.43432 −0.717159 0.696909i \(-0.754558\pi\)
−0.717159 + 0.696909i \(0.754558\pi\)
\(744\) 0 0
\(745\) 5.76091 0.211063
\(746\) −8.04480 −0.294541
\(747\) 0 0
\(748\) −1.19180 −0.0435765
\(749\) 32.2106 1.17695
\(750\) 0 0
\(751\) 20.3300 0.741853 0.370927 0.928662i \(-0.379040\pi\)
0.370927 + 0.928662i \(0.379040\pi\)
\(752\) 10.4872 0.382428
\(753\) 0 0
\(754\) 5.23749 0.190738
\(755\) 5.23265 0.190436
\(756\) 0 0
\(757\) 36.5436 1.32820 0.664100 0.747644i \(-0.268815\pi\)
0.664100 + 0.747644i \(0.268815\pi\)
\(758\) 21.8681 0.794283
\(759\) 0 0
\(760\) 8.58243 0.311317
\(761\) −2.77210 −0.100488 −0.0502442 0.998737i \(-0.516000\pi\)
−0.0502442 + 0.998737i \(0.516000\pi\)
\(762\) 0 0
\(763\) −11.1685 −0.404326
\(764\) −4.40208 −0.159262
\(765\) 0 0
\(766\) 34.2800 1.23859
\(767\) 6.19528 0.223698
\(768\) 0 0
\(769\) 4.26336 0.153741 0.0768704 0.997041i \(-0.475507\pi\)
0.0768704 + 0.997041i \(0.475507\pi\)
\(770\) 6.20803 0.223722
\(771\) 0 0
\(772\) −3.81116 −0.137167
\(773\) −41.2964 −1.48533 −0.742665 0.669663i \(-0.766438\pi\)
−0.742665 + 0.669663i \(0.766438\pi\)
\(774\) 0 0
\(775\) −38.6157 −1.38712
\(776\) −21.9083 −0.786462
\(777\) 0 0
\(778\) −22.1877 −0.795468
\(779\) −0.375511 −0.0134541
\(780\) 0 0
\(781\) 8.95234 0.320340
\(782\) −20.7405 −0.741680
\(783\) 0 0
\(784\) −45.6368 −1.62989
\(785\) 4.91750 0.175513
\(786\) 0 0
\(787\) −0.706140 −0.0251712 −0.0125856 0.999921i \(-0.504006\pi\)
−0.0125856 + 0.999921i \(0.504006\pi\)
\(788\) 4.69996 0.167429
\(789\) 0 0
\(790\) 8.04096 0.286084
\(791\) −18.3762 −0.653382
\(792\) 0 0
\(793\) 5.87974 0.208796
\(794\) 4.18708 0.148594
\(795\) 0 0
\(796\) −6.35161 −0.225127
\(797\) −49.8834 −1.76696 −0.883481 0.468467i \(-0.844807\pi\)
−0.883481 + 0.468467i \(0.844807\pi\)
\(798\) 0 0
\(799\) −9.23042 −0.326549
\(800\) 10.4461 0.369327
\(801\) 0 0
\(802\) −15.3684 −0.542676
\(803\) 7.06116 0.249183
\(804\) 0 0
\(805\) −34.4892 −1.21558
\(806\) −12.1618 −0.428381
\(807\) 0 0
\(808\) 19.3531 0.680839
\(809\) −3.29718 −0.115923 −0.0579613 0.998319i \(-0.518460\pi\)
−0.0579613 + 0.998319i \(0.518460\pi\)
\(810\) 0 0
\(811\) −19.9951 −0.702123 −0.351061 0.936352i \(-0.614179\pi\)
−0.351061 + 0.936352i \(0.614179\pi\)
\(812\) 9.93972 0.348816
\(813\) 0 0
\(814\) −0.554473 −0.0194343
\(815\) 9.66252 0.338463
\(816\) 0 0
\(817\) 29.1105 1.01845
\(818\) 38.4252 1.34350
\(819\) 0 0
\(820\) 0.0706255 0.00246635
\(821\) −12.4547 −0.434671 −0.217335 0.976097i \(-0.569737\pi\)
−0.217335 + 0.976097i \(0.569737\pi\)
\(822\) 0 0
\(823\) 22.1636 0.772575 0.386288 0.922378i \(-0.373757\pi\)
0.386288 + 0.922378i \(0.373757\pi\)
\(824\) 57.1164 1.98974
\(825\) 0 0
\(826\) −36.8298 −1.28147
\(827\) 46.4124 1.61392 0.806958 0.590609i \(-0.201112\pi\)
0.806958 + 0.590609i \(0.201112\pi\)
\(828\) 0 0
\(829\) 23.9506 0.831839 0.415920 0.909401i \(-0.363460\pi\)
0.415920 + 0.909401i \(0.363460\pi\)
\(830\) 14.9984 0.520601
\(831\) 0 0
\(832\) 8.88561 0.308053
\(833\) 40.1678 1.39173
\(834\) 0 0
\(835\) −21.4141 −0.741064
\(836\) 1.30051 0.0449791
\(837\) 0 0
\(838\) −27.9191 −0.964448
\(839\) −20.7000 −0.714645 −0.357322 0.933981i \(-0.616310\pi\)
−0.357322 + 0.933981i \(0.616310\pi\)
\(840\) 0 0
\(841\) −10.9058 −0.376062
\(842\) 35.6651 1.22910
\(843\) 0 0
\(844\) −3.80365 −0.130927
\(845\) −1.04428 −0.0359242
\(846\) 0 0
\(847\) 4.82820 0.165899
\(848\) 37.2433 1.27894
\(849\) 0 0
\(850\) 11.8538 0.406582
\(851\) 3.08042 0.105595
\(852\) 0 0
\(853\) −27.3776 −0.937390 −0.468695 0.883360i \(-0.655276\pi\)
−0.468695 + 0.883360i \(0.655276\pi\)
\(854\) −34.9540 −1.19610
\(855\) 0 0
\(856\) 20.4040 0.697393
\(857\) −1.98167 −0.0676925 −0.0338463 0.999427i \(-0.510776\pi\)
−0.0338463 + 0.999427i \(0.510776\pi\)
\(858\) 0 0
\(859\) −37.7870 −1.28928 −0.644638 0.764488i \(-0.722992\pi\)
−0.644638 + 0.764488i \(0.722992\pi\)
\(860\) −5.47506 −0.186698
\(861\) 0 0
\(862\) 15.8200 0.538832
\(863\) −21.4243 −0.729290 −0.364645 0.931147i \(-0.618810\pi\)
−0.364645 + 0.931147i \(0.618810\pi\)
\(864\) 0 0
\(865\) −14.6771 −0.499037
\(866\) −15.2687 −0.518851
\(867\) 0 0
\(868\) −23.0807 −0.783409
\(869\) 6.25373 0.212143
\(870\) 0 0
\(871\) 6.01222 0.203716
\(872\) −7.07472 −0.239580
\(873\) 0 0
\(874\) 22.6324 0.765553
\(875\) 44.9214 1.51862
\(876\) 0 0
\(877\) −0.165496 −0.00558840 −0.00279420 0.999996i \(-0.500889\pi\)
−0.00279420 + 0.999996i \(0.500889\pi\)
\(878\) 18.3273 0.618515
\(879\) 0 0
\(880\) 2.92171 0.0984907
\(881\) −30.7459 −1.03586 −0.517928 0.855424i \(-0.673297\pi\)
−0.517928 + 0.855424i \(0.673297\pi\)
\(882\) 0 0
\(883\) 24.5890 0.827485 0.413743 0.910394i \(-0.364221\pi\)
0.413743 + 0.910394i \(0.364221\pi\)
\(884\) −1.19180 −0.0400845
\(885\) 0 0
\(886\) −15.3691 −0.516335
\(887\) 13.5461 0.454833 0.227417 0.973798i \(-0.426972\pi\)
0.227417 + 0.973798i \(0.426972\pi\)
\(888\) 0 0
\(889\) 12.8978 0.432580
\(890\) −1.49300 −0.0500456
\(891\) 0 0
\(892\) 3.42557 0.114696
\(893\) 10.0724 0.337060
\(894\) 0 0
\(895\) 15.4102 0.515106
\(896\) −27.0215 −0.902727
\(897\) 0 0
\(898\) −17.7579 −0.592589
\(899\) −42.0159 −1.40131
\(900\) 0 0
\(901\) −32.7802 −1.09207
\(902\) −0.172061 −0.00572899
\(903\) 0 0
\(904\) −11.6405 −0.387156
\(905\) −3.38061 −0.112375
\(906\) 0 0
\(907\) 8.57868 0.284850 0.142425 0.989806i \(-0.454510\pi\)
0.142425 + 0.989806i \(0.454510\pi\)
\(908\) 9.99403 0.331663
\(909\) 0 0
\(910\) 6.20803 0.205794
\(911\) −38.6360 −1.28007 −0.640034 0.768346i \(-0.721080\pi\)
−0.640034 + 0.768346i \(0.721080\pi\)
\(912\) 0 0
\(913\) 11.6647 0.386046
\(914\) 20.5846 0.680877
\(915\) 0 0
\(916\) 0.698865 0.0230912
\(917\) 45.1047 1.48949
\(918\) 0 0
\(919\) 2.45847 0.0810975 0.0405488 0.999178i \(-0.487089\pi\)
0.0405488 + 0.999178i \(0.487089\pi\)
\(920\) −21.8473 −0.720284
\(921\) 0 0
\(922\) −5.24060 −0.172590
\(923\) 8.95234 0.294670
\(924\) 0 0
\(925\) −1.76054 −0.0578863
\(926\) −34.5940 −1.13683
\(927\) 0 0
\(928\) 11.3659 0.373105
\(929\) 18.0463 0.592079 0.296039 0.955176i \(-0.404334\pi\)
0.296039 + 0.955176i \(0.404334\pi\)
\(930\) 0 0
\(931\) −43.8318 −1.43653
\(932\) −0.260281 −0.00852578
\(933\) 0 0
\(934\) −6.61845 −0.216562
\(935\) −2.57157 −0.0840994
\(936\) 0 0
\(937\) −36.3652 −1.18800 −0.594000 0.804465i \(-0.702452\pi\)
−0.594000 + 0.804465i \(0.702452\pi\)
\(938\) −35.7416 −1.16700
\(939\) 0 0
\(940\) −1.89440 −0.0617885
\(941\) 40.0377 1.30519 0.652596 0.757706i \(-0.273680\pi\)
0.652596 + 0.757706i \(0.273680\pi\)
\(942\) 0 0
\(943\) 0.955895 0.0311282
\(944\) −17.3333 −0.564152
\(945\) 0 0
\(946\) 13.3386 0.433674
\(947\) −22.2749 −0.723836 −0.361918 0.932210i \(-0.617878\pi\)
−0.361918 + 0.932210i \(0.617878\pi\)
\(948\) 0 0
\(949\) 7.06116 0.229215
\(950\) −12.9351 −0.419669
\(951\) 0 0
\(952\) 36.3638 1.17856
\(953\) −14.5545 −0.471468 −0.235734 0.971818i \(-0.575749\pi\)
−0.235734 + 0.971818i \(0.575749\pi\)
\(954\) 0 0
\(955\) −9.49847 −0.307363
\(956\) −2.65697 −0.0859325
\(957\) 0 0
\(958\) 35.5008 1.14698
\(959\) −65.1973 −2.10533
\(960\) 0 0
\(961\) 66.5636 2.14721
\(962\) −0.554473 −0.0178769
\(963\) 0 0
\(964\) 9.50824 0.306240
\(965\) −8.22344 −0.264722
\(966\) 0 0
\(967\) 25.7075 0.826697 0.413349 0.910573i \(-0.364359\pi\)
0.413349 + 0.910573i \(0.364359\pi\)
\(968\) 3.05844 0.0983021
\(969\) 0 0
\(970\) −9.21037 −0.295727
\(971\) −24.2273 −0.777492 −0.388746 0.921345i \(-0.627092\pi\)
−0.388746 + 0.921345i \(0.627092\pi\)
\(972\) 0 0
\(973\) −85.4529 −2.73949
\(974\) 34.5767 1.10791
\(975\) 0 0
\(976\) −16.4505 −0.526568
\(977\) −8.34241 −0.266897 −0.133449 0.991056i \(-0.542605\pi\)
−0.133449 + 0.991056i \(0.542605\pi\)
\(978\) 0 0
\(979\) −1.16116 −0.0371108
\(980\) 8.24382 0.263339
\(981\) 0 0
\(982\) −41.6379 −1.32872
\(983\) 14.6977 0.468784 0.234392 0.972142i \(-0.424690\pi\)
0.234392 + 0.972142i \(0.424690\pi\)
\(984\) 0 0
\(985\) 10.1412 0.323126
\(986\) 12.8976 0.410742
\(987\) 0 0
\(988\) 1.30051 0.0413748
\(989\) −74.1033 −2.35635
\(990\) 0 0
\(991\) −25.4700 −0.809082 −0.404541 0.914520i \(-0.632569\pi\)
−0.404541 + 0.914520i \(0.632569\pi\)
\(992\) −26.3924 −0.837961
\(993\) 0 0
\(994\) −53.2201 −1.68804
\(995\) −13.7050 −0.434478
\(996\) 0 0
\(997\) 22.8048 0.722236 0.361118 0.932520i \(-0.382395\pi\)
0.361118 + 0.932520i \(0.382395\pi\)
\(998\) 2.53485 0.0802392
\(999\) 0 0
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 1287.2.a.q.1.3 6
3.2 odd 2 143.2.a.c.1.4 6
12.11 even 2 2288.2.a.z.1.4 6
15.14 odd 2 3575.2.a.p.1.3 6
21.20 even 2 7007.2.a.r.1.4 6
24.5 odd 2 9152.2.a.cm.1.4 6
24.11 even 2 9152.2.a.cs.1.3 6
33.32 even 2 1573.2.a.m.1.3 6
39.38 odd 2 1859.2.a.m.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.a.c.1.4 6 3.2 odd 2
1287.2.a.q.1.3 6 1.1 even 1 trivial
1573.2.a.m.1.3 6 33.32 even 2
1859.2.a.m.1.3 6 39.38 odd 2
2288.2.a.z.1.4 6 12.11 even 2
3575.2.a.p.1.3 6 15.14 odd 2
7007.2.a.r.1.4 6 21.20 even 2
9152.2.a.cm.1.4 6 24.5 odd 2
9152.2.a.cs.1.3 6 24.11 even 2