Properties

Label 9200.2.a.co.1.2
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $4$
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] = [9200,2,Mod(1,9200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("9200.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.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: \(73.4623698596\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.53121.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 7x^{2} - x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2300)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.631352\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.631352 q^{3} -3.16780 q^{7} -2.60139 q^{9} +O(q^{10})\) \(q-0.631352 q^{3} -3.16780 q^{7} -2.60139 q^{9} +1.90510 q^{11} +6.76920 q^{13} -0.737296 q^{17} -3.90510 q^{19} +2.00000 q^{21} -1.00000 q^{23} +3.53645 q^{27} -0.935058 q^{29} -1.02996 q^{31} -1.20279 q^{33} -5.94008 q^{37} -4.27375 q^{39} +11.0019 q^{41} -3.90510 q^{43} +5.47151 q^{47} +3.03498 q^{49} +0.465493 q^{51} -3.07290 q^{53} +2.46549 q^{57} -4.90510 q^{59} +11.0729 q^{61} +8.24071 q^{63} -3.20279 q^{67} +0.631352 q^{69} -8.86410 q^{71} +9.40055 q^{73} -6.03498 q^{77} -1.56949 q^{79} +5.57144 q^{81} -2.64240 q^{83} +0.590351 q^{87} -18.6113 q^{89} -21.4435 q^{91} +0.650266 q^{93} +15.3486 q^{97} -4.95592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{7} + 2 q^{9} - q^{11} + q^{13} - 8 q^{17} - 7 q^{19} + 8 q^{21} - 4 q^{23} + 3 q^{27} - 5 q^{29} - 14 q^{31} + 20 q^{33} - 4 q^{37} - 11 q^{39} + 3 q^{41} - 7 q^{43} + 12 q^{47} + q^{49} - 28 q^{51} + 10 q^{53} - 20 q^{57} - 11 q^{59} + 22 q^{61} - 3 q^{63} + 12 q^{67} - 18 q^{71} + 9 q^{73} - 13 q^{77} - 25 q^{79} - 7 q^{83} - 9 q^{87} - 25 q^{91} + 11 q^{93} - 8 q^{97} + 9 q^{99}+O(q^{100}) \) 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
\(3\) −0.631352 −0.364511 −0.182256 0.983251i \(-0.558340\pi\)
−0.182256 + 0.983251i \(0.558340\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.16780 −1.19732 −0.598659 0.801004i \(-0.704299\pi\)
−0.598659 + 0.801004i \(0.704299\pi\)
\(8\) 0 0
\(9\) −2.60139 −0.867132
\(10\) 0 0
\(11\) 1.90510 0.574409 0.287205 0.957869i \(-0.407274\pi\)
0.287205 + 0.957869i \(0.407274\pi\)
\(12\) 0 0
\(13\) 6.76920 1.87744 0.938719 0.344683i \(-0.112014\pi\)
0.938719 + 0.344683i \(0.112014\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.737296 −0.178820 −0.0894102 0.995995i \(-0.528498\pi\)
−0.0894102 + 0.995995i \(0.528498\pi\)
\(18\) 0 0
\(19\) −3.90510 −0.895891 −0.447946 0.894061i \(-0.647844\pi\)
−0.447946 + 0.894061i \(0.647844\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.53645 0.680591
\(28\) 0 0
\(29\) −0.935058 −0.173636 −0.0868179 0.996224i \(-0.527670\pi\)
−0.0868179 + 0.996224i \(0.527670\pi\)
\(30\) 0 0
\(31\) −1.02996 −0.184986 −0.0924929 0.995713i \(-0.529484\pi\)
−0.0924929 + 0.995713i \(0.529484\pi\)
\(32\) 0 0
\(33\) −1.20279 −0.209379
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.94008 −0.976544 −0.488272 0.872692i \(-0.662373\pi\)
−0.488272 + 0.872692i \(0.662373\pi\)
\(38\) 0 0
\(39\) −4.27375 −0.684347
\(40\) 0 0
\(41\) 11.0019 1.71822 0.859108 0.511795i \(-0.171019\pi\)
0.859108 + 0.511795i \(0.171019\pi\)
\(42\) 0 0
\(43\) −3.90510 −0.595522 −0.297761 0.954640i \(-0.596240\pi\)
−0.297761 + 0.954640i \(0.596240\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.47151 0.798102 0.399051 0.916929i \(-0.369340\pi\)
0.399051 + 0.916929i \(0.369340\pi\)
\(48\) 0 0
\(49\) 3.03498 0.433569
\(50\) 0 0
\(51\) 0.465493 0.0651821
\(52\) 0 0
\(53\) −3.07290 −0.422096 −0.211048 0.977476i \(-0.567688\pi\)
−0.211048 + 0.977476i \(0.567688\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.46549 0.326563
\(58\) 0 0
\(59\) −4.90510 −0.638590 −0.319295 0.947655i \(-0.603446\pi\)
−0.319295 + 0.947655i \(0.603446\pi\)
\(60\) 0 0
\(61\) 11.0729 1.41774 0.708870 0.705339i \(-0.249205\pi\)
0.708870 + 0.705339i \(0.249205\pi\)
\(62\) 0 0
\(63\) 8.24071 1.03823
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.20279 −0.391283 −0.195641 0.980675i \(-0.562679\pi\)
−0.195641 + 0.980675i \(0.562679\pi\)
\(68\) 0 0
\(69\) 0.631352 0.0760059
\(70\) 0 0
\(71\) −8.86410 −1.05197 −0.525987 0.850492i \(-0.676304\pi\)
−0.525987 + 0.850492i \(0.676304\pi\)
\(72\) 0 0
\(73\) 9.40055 1.10025 0.550126 0.835082i \(-0.314580\pi\)
0.550126 + 0.835082i \(0.314580\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.03498 −0.687750
\(78\) 0 0
\(79\) −1.56949 −0.176582 −0.0882908 0.996095i \(-0.528140\pi\)
−0.0882908 + 0.996095i \(0.528140\pi\)
\(80\) 0 0
\(81\) 5.57144 0.619049
\(82\) 0 0
\(83\) −2.64240 −0.290041 −0.145020 0.989429i \(-0.546325\pi\)
−0.145020 + 0.989429i \(0.546325\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.590351 0.0632922
\(88\) 0 0
\(89\) −18.6113 −1.97279 −0.986397 0.164380i \(-0.947438\pi\)
−0.986397 + 0.164380i \(0.947438\pi\)
\(90\) 0 0
\(91\) −21.4435 −2.24789
\(92\) 0 0
\(93\) 0.650266 0.0674294
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 15.3486 1.55841 0.779207 0.626767i \(-0.215622\pi\)
0.779207 + 0.626767i \(0.215622\pi\)
\(98\) 0 0
\(99\) −4.95592 −0.498088
\(100\) 0 0
\(101\) −9.18079 −0.913523 −0.456762 0.889589i \(-0.650991\pi\)
−0.456762 + 0.889589i \(0.650991\pi\)
\(102\) 0 0
\(103\) 7.50341 0.739333 0.369667 0.929164i \(-0.379472\pi\)
0.369667 + 0.929164i \(0.379472\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.5384 1.50215 0.751077 0.660215i \(-0.229535\pi\)
0.751077 + 0.660215i \(0.229535\pi\)
\(108\) 0 0
\(109\) 3.13282 0.300070 0.150035 0.988681i \(-0.452061\pi\)
0.150035 + 0.988681i \(0.452061\pi\)
\(110\) 0 0
\(111\) 3.75029 0.355961
\(112\) 0 0
\(113\) 17.0130 1.60045 0.800224 0.599702i \(-0.204714\pi\)
0.800224 + 0.599702i \(0.204714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −17.6094 −1.62799
\(118\) 0 0
\(119\) 2.33561 0.214105
\(120\) 0 0
\(121\) −7.37059 −0.670054
\(122\) 0 0
\(123\) −6.94610 −0.626309
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2.97004 −0.263549 −0.131774 0.991280i \(-0.542067\pi\)
−0.131774 + 0.991280i \(0.542067\pi\)
\(128\) 0 0
\(129\) 2.46549 0.217075
\(130\) 0 0
\(131\) 4.22967 0.369548 0.184774 0.982781i \(-0.440845\pi\)
0.184774 + 0.982781i \(0.440845\pi\)
\(132\) 0 0
\(133\) 12.3706 1.07267
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.52541 −0.386632 −0.193316 0.981137i \(-0.561924\pi\)
−0.193316 + 0.981137i \(0.561924\pi\)
\(138\) 0 0
\(139\) 7.00991 0.594573 0.297286 0.954788i \(-0.403918\pi\)
0.297286 + 0.954788i \(0.403918\pi\)
\(140\) 0 0
\(141\) −3.45445 −0.290917
\(142\) 0 0
\(143\) 12.8960 1.07842
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.91614 −0.158041
\(148\) 0 0
\(149\) 8.73113 0.715282 0.357641 0.933859i \(-0.383581\pi\)
0.357641 + 0.933859i \(0.383581\pi\)
\(150\) 0 0
\(151\) −19.2697 −1.56814 −0.784072 0.620670i \(-0.786861\pi\)
−0.784072 + 0.620670i \(0.786861\pi\)
\(152\) 0 0
\(153\) 1.91800 0.155061
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −6.65529 −0.531150 −0.265575 0.964090i \(-0.585562\pi\)
−0.265575 + 0.964090i \(0.585562\pi\)
\(158\) 0 0
\(159\) 1.94008 0.153859
\(160\) 0 0
\(161\) 3.16780 0.249658
\(162\) 0 0
\(163\) −9.11585 −0.714009 −0.357004 0.934103i \(-0.616202\pi\)
−0.357004 + 0.934103i \(0.616202\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.6463 1.67504 0.837520 0.546407i \(-0.184005\pi\)
0.837520 + 0.546407i \(0.184005\pi\)
\(168\) 0 0
\(169\) 32.8221 2.52477
\(170\) 0 0
\(171\) 10.1587 0.776856
\(172\) 0 0
\(173\) 12.8102 0.973941 0.486971 0.873418i \(-0.338102\pi\)
0.486971 + 0.873418i \(0.338102\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.09685 0.232773
\(178\) 0 0
\(179\) −25.9769 −1.94160 −0.970801 0.239886i \(-0.922890\pi\)
−0.970801 + 0.239886i \(0.922890\pi\)
\(180\) 0 0
\(181\) −13.1966 −0.980897 −0.490449 0.871470i \(-0.663167\pi\)
−0.490449 + 0.871470i \(0.663167\pi\)
\(182\) 0 0
\(183\) −6.99090 −0.516782
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.40462 −0.102716
\(188\) 0 0
\(189\) −11.2028 −0.814883
\(190\) 0 0
\(191\) −19.3136 −1.39748 −0.698742 0.715374i \(-0.746256\pi\)
−0.698742 + 0.715374i \(0.746256\pi\)
\(192\) 0 0
\(193\) −6.70132 −0.482372 −0.241186 0.970479i \(-0.577536\pi\)
−0.241186 + 0.970479i \(0.577536\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.9320 −0.778871 −0.389436 0.921054i \(-0.627330\pi\)
−0.389436 + 0.921054i \(0.627330\pi\)
\(198\) 0 0
\(199\) −8.77228 −0.621850 −0.310925 0.950434i \(-0.600639\pi\)
−0.310925 + 0.950434i \(0.600639\pi\)
\(200\) 0 0
\(201\) 2.02209 0.142627
\(202\) 0 0
\(203\) 2.96208 0.207897
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.60139 0.180809
\(208\) 0 0
\(209\) −7.43961 −0.514608
\(210\) 0 0
\(211\) 6.71530 0.462300 0.231150 0.972918i \(-0.425751\pi\)
0.231150 + 0.972918i \(0.425751\pi\)
\(212\) 0 0
\(213\) 5.59637 0.383457
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.26270 0.221487
\(218\) 0 0
\(219\) −5.93506 −0.401054
\(220\) 0 0
\(221\) −4.99090 −0.335724
\(222\) 0 0
\(223\) 21.7661 1.45757 0.728784 0.684744i \(-0.240086\pi\)
0.728784 + 0.684744i \(0.240086\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.5485 −1.56297 −0.781483 0.623927i \(-0.785536\pi\)
−0.781483 + 0.623927i \(0.785536\pi\)
\(228\) 0 0
\(229\) −11.6204 −0.767898 −0.383949 0.923354i \(-0.625436\pi\)
−0.383949 + 0.923354i \(0.625436\pi\)
\(230\) 0 0
\(231\) 3.81020 0.250693
\(232\) 0 0
\(233\) −12.1178 −0.793863 −0.396932 0.917848i \(-0.629925\pi\)
−0.396932 + 0.917848i \(0.629925\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.990902 0.0643660
\(238\) 0 0
\(239\) 5.63429 0.364452 0.182226 0.983257i \(-0.441670\pi\)
0.182226 + 0.983257i \(0.441670\pi\)
\(240\) 0 0
\(241\) −5.07907 −0.327172 −0.163586 0.986529i \(-0.552306\pi\)
−0.163586 + 0.986529i \(0.552306\pi\)
\(242\) 0 0
\(243\) −14.1269 −0.906241
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −26.4344 −1.68198
\(248\) 0 0
\(249\) 1.66828 0.105723
\(250\) 0 0
\(251\) −19.4186 −1.22569 −0.612845 0.790203i \(-0.709975\pi\)
−0.612845 + 0.790203i \(0.709975\pi\)
\(252\) 0 0
\(253\) −1.90510 −0.119773
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.75507 −0.546126 −0.273063 0.961996i \(-0.588037\pi\)
−0.273063 + 0.961996i \(0.588037\pi\)
\(258\) 0 0
\(259\) 18.8170 1.16923
\(260\) 0 0
\(261\) 2.43245 0.150565
\(262\) 0 0
\(263\) −16.3457 −1.00792 −0.503958 0.863728i \(-0.668124\pi\)
−0.503958 + 0.863728i \(0.668124\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 11.7503 0.719106
\(268\) 0 0
\(269\) −3.14880 −0.191986 −0.0959928 0.995382i \(-0.530603\pi\)
−0.0959928 + 0.995382i \(0.530603\pi\)
\(270\) 0 0
\(271\) −25.1525 −1.52791 −0.763954 0.645271i \(-0.776745\pi\)
−0.763954 + 0.645271i \(0.776745\pi\)
\(272\) 0 0
\(273\) 13.5384 0.819381
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −15.8630 −0.953113 −0.476557 0.879144i \(-0.658115\pi\)
−0.476557 + 0.879144i \(0.658115\pi\)
\(278\) 0 0
\(279\) 2.67933 0.160407
\(280\) 0 0
\(281\) −16.2057 −0.966752 −0.483376 0.875413i \(-0.660590\pi\)
−0.483376 + 0.875413i \(0.660590\pi\)
\(282\) 0 0
\(283\) 30.4814 1.81193 0.905966 0.423350i \(-0.139146\pi\)
0.905966 + 0.423350i \(0.139146\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −34.8520 −2.05725
\(288\) 0 0
\(289\) −16.4564 −0.968023
\(290\) 0 0
\(291\) −9.69037 −0.568060
\(292\) 0 0
\(293\) −15.9339 −0.930870 −0.465435 0.885082i \(-0.654102\pi\)
−0.465435 + 0.885082i \(0.654102\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 6.73730 0.390938
\(298\) 0 0
\(299\) −6.76920 −0.391473
\(300\) 0 0
\(301\) 12.3706 0.713029
\(302\) 0 0
\(303\) 5.79631 0.332990
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −7.93003 −0.452591 −0.226295 0.974059i \(-0.572661\pi\)
−0.226295 + 0.974059i \(0.572661\pi\)
\(308\) 0 0
\(309\) −4.73730 −0.269495
\(310\) 0 0
\(311\) 28.9960 1.64421 0.822107 0.569333i \(-0.192799\pi\)
0.822107 + 0.569333i \(0.192799\pi\)
\(312\) 0 0
\(313\) −21.4564 −1.21279 −0.606394 0.795165i \(-0.707384\pi\)
−0.606394 + 0.795165i \(0.707384\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.70620 0.264327 0.132163 0.991228i \(-0.457808\pi\)
0.132163 + 0.991228i \(0.457808\pi\)
\(318\) 0 0
\(319\) −1.78138 −0.0997381
\(320\) 0 0
\(321\) −9.81020 −0.547552
\(322\) 0 0
\(323\) 2.87921 0.160204
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.97791 −0.109379
\(328\) 0 0
\(329\) −17.3327 −0.955581
\(330\) 0 0
\(331\) 5.98611 0.329027 0.164513 0.986375i \(-0.447395\pi\)
0.164513 + 0.986375i \(0.447395\pi\)
\(332\) 0 0
\(333\) 15.4525 0.846792
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −6.82319 −0.371683 −0.185841 0.982580i \(-0.559501\pi\)
−0.185841 + 0.982580i \(0.559501\pi\)
\(338\) 0 0
\(339\) −10.7412 −0.583381
\(340\) 0 0
\(341\) −1.96217 −0.106258
\(342\) 0 0
\(343\) 12.5604 0.678197
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.50048 0.187915 0.0939577 0.995576i \(-0.470048\pi\)
0.0939577 + 0.995576i \(0.470048\pi\)
\(348\) 0 0
\(349\) −7.44042 −0.398276 −0.199138 0.979971i \(-0.563814\pi\)
−0.199138 + 0.979971i \(0.563814\pi\)
\(350\) 0 0
\(351\) 23.9389 1.27777
\(352\) 0 0
\(353\) 4.87822 0.259642 0.129821 0.991537i \(-0.458560\pi\)
0.129821 + 0.991537i \(0.458560\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.47459 −0.0780437
\(358\) 0 0
\(359\) −0.0570722 −0.00301216 −0.00150608 0.999999i \(-0.500479\pi\)
−0.00150608 + 0.999999i \(0.500479\pi\)
\(360\) 0 0
\(361\) −3.75019 −0.197379
\(362\) 0 0
\(363\) 4.65344 0.244242
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.11082 0.214583 0.107292 0.994228i \(-0.465782\pi\)
0.107292 + 0.994228i \(0.465782\pi\)
\(368\) 0 0
\(369\) −28.6204 −1.48992
\(370\) 0 0
\(371\) 9.73436 0.505383
\(372\) 0 0
\(373\) −26.2057 −1.35688 −0.678440 0.734655i \(-0.737344\pi\)
−0.678440 + 0.734655i \(0.737344\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.32959 −0.325991
\(378\) 0 0
\(379\) −27.9938 −1.43795 −0.718973 0.695038i \(-0.755388\pi\)
−0.718973 + 0.695038i \(0.755388\pi\)
\(380\) 0 0
\(381\) 1.87514 0.0960665
\(382\) 0 0
\(383\) 4.16487 0.212815 0.106407 0.994323i \(-0.466065\pi\)
0.106407 + 0.994323i \(0.466065\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.1587 0.516396
\(388\) 0 0
\(389\) −26.4593 −1.34154 −0.670771 0.741665i \(-0.734037\pi\)
−0.670771 + 0.741665i \(0.734037\pi\)
\(390\) 0 0
\(391\) 0.737296 0.0372866
\(392\) 0 0
\(393\) −2.67041 −0.134704
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.65036 −0.233395 −0.116697 0.993168i \(-0.537231\pi\)
−0.116697 + 0.993168i \(0.537231\pi\)
\(398\) 0 0
\(399\) −7.81020 −0.390999
\(400\) 0 0
\(401\) −25.1328 −1.25507 −0.627537 0.778587i \(-0.715937\pi\)
−0.627537 + 0.778587i \(0.715937\pi\)
\(402\) 0 0
\(403\) −6.97199 −0.347299
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11.3165 −0.560936
\(408\) 0 0
\(409\) 16.8659 0.833965 0.416982 0.908915i \(-0.363088\pi\)
0.416982 + 0.908915i \(0.363088\pi\)
\(410\) 0 0
\(411\) 2.85713 0.140932
\(412\) 0 0
\(413\) 15.5384 0.764595
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.42572 −0.216728
\(418\) 0 0
\(419\) −19.4594 −0.950655 −0.475328 0.879809i \(-0.657670\pi\)
−0.475328 + 0.879809i \(0.657670\pi\)
\(420\) 0 0
\(421\) −4.41761 −0.215301 −0.107651 0.994189i \(-0.534333\pi\)
−0.107651 + 0.994189i \(0.534333\pi\)
\(422\) 0 0
\(423\) −14.2336 −0.692059
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −35.0768 −1.69749
\(428\) 0 0
\(429\) −8.14192 −0.393096
\(430\) 0 0
\(431\) −1.89220 −0.0911442 −0.0455721 0.998961i \(-0.514511\pi\)
−0.0455721 + 0.998961i \(0.514511\pi\)
\(432\) 0 0
\(433\) −25.4147 −1.22135 −0.610676 0.791881i \(-0.709102\pi\)
−0.610676 + 0.791881i \(0.709102\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.90510 0.186806
\(438\) 0 0
\(439\) 15.8979 0.758768 0.379384 0.925239i \(-0.376136\pi\)
0.379384 + 0.925239i \(0.376136\pi\)
\(440\) 0 0
\(441\) −7.89519 −0.375962
\(442\) 0 0
\(443\) 2.34485 0.111407 0.0557037 0.998447i \(-0.482260\pi\)
0.0557037 + 0.998447i \(0.482260\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −5.51242 −0.260728
\(448\) 0 0
\(449\) −36.3774 −1.71676 −0.858378 0.513017i \(-0.828528\pi\)
−0.858378 + 0.513017i \(0.828528\pi\)
\(450\) 0 0
\(451\) 20.9598 0.986959
\(452\) 0 0
\(453\) 12.1660 0.571606
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.5035 −0.865557 −0.432779 0.901500i \(-0.642467\pi\)
−0.432779 + 0.901500i \(0.642467\pi\)
\(458\) 0 0
\(459\) −2.60741 −0.121704
\(460\) 0 0
\(461\) 34.0296 1.58492 0.792459 0.609925i \(-0.208801\pi\)
0.792459 + 0.609925i \(0.208801\pi\)
\(462\) 0 0
\(463\) −16.7153 −0.776826 −0.388413 0.921485i \(-0.626977\pi\)
−0.388413 + 0.921485i \(0.626977\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −11.0480 −0.511239 −0.255620 0.966777i \(-0.582279\pi\)
−0.255620 + 0.966777i \(0.582279\pi\)
\(468\) 0 0
\(469\) 10.1458 0.468490
\(470\) 0 0
\(471\) 4.20183 0.193610
\(472\) 0 0
\(473\) −7.43961 −0.342073
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 7.99384 0.366013
\(478\) 0 0
\(479\) 30.2508 1.38219 0.691096 0.722763i \(-0.257128\pi\)
0.691096 + 0.722763i \(0.257128\pi\)
\(480\) 0 0
\(481\) −40.2096 −1.83340
\(482\) 0 0
\(483\) −2.00000 −0.0910032
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −17.9211 −0.812082 −0.406041 0.913855i \(-0.633091\pi\)
−0.406041 + 0.913855i \(0.633091\pi\)
\(488\) 0 0
\(489\) 5.75531 0.260264
\(490\) 0 0
\(491\) 34.5861 1.56085 0.780425 0.625249i \(-0.215003\pi\)
0.780425 + 0.625249i \(0.215003\pi\)
\(492\) 0 0
\(493\) 0.689414 0.0310497
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 28.0797 1.25955
\(498\) 0 0
\(499\) 0.653440 0.0292520 0.0146260 0.999893i \(-0.495344\pi\)
0.0146260 + 0.999893i \(0.495344\pi\)
\(500\) 0 0
\(501\) −13.6664 −0.610571
\(502\) 0 0
\(503\) 6.50048 0.289842 0.144921 0.989443i \(-0.453707\pi\)
0.144921 + 0.989443i \(0.453707\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −20.7223 −0.920308
\(508\) 0 0
\(509\) 34.6612 1.53633 0.768166 0.640251i \(-0.221170\pi\)
0.768166 + 0.640251i \(0.221170\pi\)
\(510\) 0 0
\(511\) −29.7791 −1.31735
\(512\) 0 0
\(513\) −13.8102 −0.609735
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.4238 0.458437
\(518\) 0 0
\(519\) −8.08775 −0.355013
\(520\) 0 0
\(521\) −12.8073 −0.561096 −0.280548 0.959840i \(-0.590516\pi\)
−0.280548 + 0.959840i \(0.590516\pi\)
\(522\) 0 0
\(523\) 37.9689 1.66026 0.830132 0.557567i \(-0.188265\pi\)
0.830132 + 0.557567i \(0.188265\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.759383 0.0330793
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 12.7601 0.553741
\(532\) 0 0
\(533\) 74.4744 3.22584
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 16.4006 0.707736
\(538\) 0 0
\(539\) 5.78195 0.249046
\(540\) 0 0
\(541\) 12.3088 0.529198 0.264599 0.964359i \(-0.414760\pi\)
0.264599 + 0.964359i \(0.414760\pi\)
\(542\) 0 0
\(543\) 8.33172 0.357548
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.3009 −0.868002 −0.434001 0.900912i \(-0.642899\pi\)
−0.434001 + 0.900912i \(0.642899\pi\)
\(548\) 0 0
\(549\) −28.8050 −1.22937
\(550\) 0 0
\(551\) 3.65149 0.155559
\(552\) 0 0
\(553\) 4.97184 0.211424
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.59149 −0.279290 −0.139645 0.990202i \(-0.544596\pi\)
−0.139645 + 0.990202i \(0.544596\pi\)
\(558\) 0 0
\(559\) −26.4344 −1.11806
\(560\) 0 0
\(561\) 0.886811 0.0374412
\(562\) 0 0
\(563\) −5.08191 −0.214177 −0.107088 0.994249i \(-0.534153\pi\)
−0.107088 + 0.994249i \(0.534153\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −17.6492 −0.741198
\(568\) 0 0
\(569\) −16.8672 −0.707109 −0.353554 0.935414i \(-0.615027\pi\)
−0.353554 + 0.935414i \(0.615027\pi\)
\(570\) 0 0
\(571\) −38.3174 −1.60353 −0.801767 0.597637i \(-0.796106\pi\)
−0.801767 + 0.597637i \(0.796106\pi\)
\(572\) 0 0
\(573\) 12.1937 0.509399
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 19.0240 0.791981 0.395990 0.918255i \(-0.370401\pi\)
0.395990 + 0.918255i \(0.370401\pi\)
\(578\) 0 0
\(579\) 4.23089 0.175830
\(580\) 0 0
\(581\) 8.37059 0.347271
\(582\) 0 0
\(583\) −5.85419 −0.242456
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.66747 −0.233922 −0.116961 0.993137i \(-0.537315\pi\)
−0.116961 + 0.993137i \(0.537315\pi\)
\(588\) 0 0
\(589\) 4.02209 0.165727
\(590\) 0 0
\(591\) 6.90193 0.283907
\(592\) 0 0
\(593\) −35.7130 −1.46656 −0.733279 0.679928i \(-0.762011\pi\)
−0.733279 + 0.679928i \(0.762011\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.53840 0.226672
\(598\) 0 0
\(599\) −20.1717 −0.824193 −0.412097 0.911140i \(-0.635203\pi\)
−0.412097 + 0.911140i \(0.635203\pi\)
\(600\) 0 0
\(601\) −41.9069 −1.70942 −0.854709 0.519107i \(-0.826264\pi\)
−0.854709 + 0.519107i \(0.826264\pi\)
\(602\) 0 0
\(603\) 8.33172 0.339294
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 35.8678 1.45583 0.727915 0.685667i \(-0.240489\pi\)
0.727915 + 0.685667i \(0.240489\pi\)
\(608\) 0 0
\(609\) −1.87012 −0.0757809
\(610\) 0 0
\(611\) 37.0377 1.49839
\(612\) 0 0
\(613\) −21.7819 −0.879765 −0.439882 0.898055i \(-0.644980\pi\)
−0.439882 + 0.898055i \(0.644980\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.8480 −0.557501 −0.278750 0.960364i \(-0.589920\pi\)
−0.278750 + 0.960364i \(0.589920\pi\)
\(618\) 0 0
\(619\) −38.6113 −1.55192 −0.775960 0.630783i \(-0.782734\pi\)
−0.775960 + 0.630783i \(0.782734\pi\)
\(620\) 0 0
\(621\) −3.53645 −0.141913
\(622\) 0 0
\(623\) 58.9570 2.36206
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 4.69701 0.187581
\(628\) 0 0
\(629\) 4.37960 0.174626
\(630\) 0 0
\(631\) 0.598221 0.0238148 0.0119074 0.999929i \(-0.496210\pi\)
0.0119074 + 0.999929i \(0.496210\pi\)
\(632\) 0 0
\(633\) −4.23972 −0.168514
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 20.5444 0.813999
\(638\) 0 0
\(639\) 23.0590 0.912201
\(640\) 0 0
\(641\) −22.5254 −0.889700 −0.444850 0.895605i \(-0.646743\pi\)
−0.444850 + 0.895605i \(0.646743\pi\)
\(642\) 0 0
\(643\) 36.1908 1.42723 0.713614 0.700539i \(-0.247057\pi\)
0.713614 + 0.700539i \(0.247057\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.33067 0.248884 0.124442 0.992227i \(-0.460286\pi\)
0.124442 + 0.992227i \(0.460286\pi\)
\(648\) 0 0
\(649\) −9.34471 −0.366812
\(650\) 0 0
\(651\) −2.05992 −0.0807344
\(652\) 0 0
\(653\) −14.3057 −0.559827 −0.279914 0.960025i \(-0.590306\pi\)
−0.279914 + 0.960025i \(0.590306\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −24.4545 −0.954063
\(658\) 0 0
\(659\) 38.6563 1.50584 0.752919 0.658114i \(-0.228645\pi\)
0.752919 + 0.658114i \(0.228645\pi\)
\(660\) 0 0
\(661\) 12.5954 0.489903 0.244952 0.969535i \(-0.421228\pi\)
0.244952 + 0.969535i \(0.421228\pi\)
\(662\) 0 0
\(663\) 3.15102 0.122375
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.935058 0.0362056
\(668\) 0 0
\(669\) −13.7421 −0.531300
\(670\) 0 0
\(671\) 21.0950 0.814363
\(672\) 0 0
\(673\) 0.356707 0.0137500 0.00687501 0.999976i \(-0.497812\pi\)
0.00687501 + 0.999976i \(0.497812\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.8831 −0.725737 −0.362868 0.931840i \(-0.618203\pi\)
−0.362868 + 0.931840i \(0.618203\pi\)
\(678\) 0 0
\(679\) −48.6214 −1.86592
\(680\) 0 0
\(681\) 14.8674 0.569719
\(682\) 0 0
\(683\) 18.7520 0.717525 0.358763 0.933429i \(-0.383199\pi\)
0.358763 + 0.933429i \(0.383199\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.33656 0.279907
\(688\) 0 0
\(689\) −20.8011 −0.792459
\(690\) 0 0
\(691\) 18.3175 0.696831 0.348415 0.937340i \(-0.386720\pi\)
0.348415 + 0.937340i \(0.386720\pi\)
\(692\) 0 0
\(693\) 15.6994 0.596370
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −8.11169 −0.307252
\(698\) 0 0
\(699\) 7.65060 0.289372
\(700\) 0 0
\(701\) 27.0007 1.01980 0.509900 0.860233i \(-0.329682\pi\)
0.509900 + 0.860233i \(0.329682\pi\)
\(702\) 0 0
\(703\) 23.1966 0.874877
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 29.0830 1.09378
\(708\) 0 0
\(709\) 16.1875 0.607935 0.303968 0.952682i \(-0.401689\pi\)
0.303968 + 0.952682i \(0.401689\pi\)
\(710\) 0 0
\(711\) 4.08287 0.153119
\(712\) 0 0
\(713\) 1.02996 0.0385722
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3.55722 −0.132847
\(718\) 0 0
\(719\) 49.2926 1.83830 0.919151 0.393904i \(-0.128876\pi\)
0.919151 + 0.393904i \(0.128876\pi\)
\(720\) 0 0
\(721\) −23.7693 −0.885217
\(722\) 0 0
\(723\) 3.20668 0.119258
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 23.2447 0.862098 0.431049 0.902329i \(-0.358144\pi\)
0.431049 + 0.902329i \(0.358144\pi\)
\(728\) 0 0
\(729\) −7.79527 −0.288714
\(730\) 0 0
\(731\) 2.87921 0.106492
\(732\) 0 0
\(733\) 25.8203 0.953693 0.476846 0.878987i \(-0.341780\pi\)
0.476846 + 0.878987i \(0.341780\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.10163 −0.224757
\(738\) 0 0
\(739\) −21.6853 −0.797705 −0.398852 0.917015i \(-0.630591\pi\)
−0.398852 + 0.917015i \(0.630591\pi\)
\(740\) 0 0
\(741\) 16.6894 0.613101
\(742\) 0 0
\(743\) −27.5932 −1.01230 −0.506148 0.862447i \(-0.668931\pi\)
−0.506148 + 0.862447i \(0.668931\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6.87391 0.251503
\(748\) 0 0
\(749\) −49.2226 −1.79855
\(750\) 0 0
\(751\) 48.2644 1.76119 0.880597 0.473866i \(-0.157142\pi\)
0.880597 + 0.473866i \(0.157142\pi\)
\(752\) 0 0
\(753\) 12.2600 0.446778
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −5.87012 −0.213353 −0.106676 0.994294i \(-0.534021\pi\)
−0.106676 + 0.994294i \(0.534021\pi\)
\(758\) 0 0
\(759\) 1.20279 0.0436585
\(760\) 0 0
\(761\) −5.67624 −0.205764 −0.102882 0.994694i \(-0.532806\pi\)
−0.102882 + 0.994694i \(0.532806\pi\)
\(762\) 0 0
\(763\) −9.92416 −0.359279
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −33.2036 −1.19891
\(768\) 0 0
\(769\) 17.3226 0.624670 0.312335 0.949972i \(-0.398889\pi\)
0.312335 + 0.949972i \(0.398889\pi\)
\(770\) 0 0
\(771\) 5.52753 0.199069
\(772\) 0 0
\(773\) −28.3773 −1.02066 −0.510331 0.859978i \(-0.670477\pi\)
−0.510331 + 0.859978i \(0.670477\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −11.8802 −0.426199
\(778\) 0 0
\(779\) −42.9637 −1.53933
\(780\) 0 0
\(781\) −16.8870 −0.604264
\(782\) 0 0
\(783\) −3.30679 −0.118175
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 31.3995 1.11927 0.559636 0.828739i \(-0.310941\pi\)
0.559636 + 0.828739i \(0.310941\pi\)
\(788\) 0 0
\(789\) 10.3199 0.367397
\(790\) 0 0
\(791\) −53.8938 −1.91624
\(792\) 0 0
\(793\) 74.9547 2.66172
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21.0169 0.744456 0.372228 0.928141i \(-0.378594\pi\)
0.372228 + 0.928141i \(0.378594\pi\)
\(798\) 0 0
\(799\) −4.03412 −0.142717
\(800\) 0 0
\(801\) 48.4153 1.71067
\(802\) 0 0
\(803\) 17.9090 0.631995
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.98800 0.0699809
\(808\) 0 0
\(809\) 25.6712 0.902552 0.451276 0.892384i \(-0.350969\pi\)
0.451276 + 0.892384i \(0.350969\pi\)
\(810\) 0 0
\(811\) −40.3647 −1.41740 −0.708698 0.705512i \(-0.750717\pi\)
−0.708698 + 0.705512i \(0.750717\pi\)
\(812\) 0 0
\(813\) 15.8801 0.556940
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 15.2498 0.533523
\(818\) 0 0
\(819\) 55.7830 1.94922
\(820\) 0 0
\(821\) 25.6396 0.894827 0.447413 0.894327i \(-0.352345\pi\)
0.447413 + 0.894327i \(0.352345\pi\)
\(822\) 0 0
\(823\) 15.6726 0.546312 0.273156 0.961970i \(-0.411932\pi\)
0.273156 + 0.961970i \(0.411932\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 45.8429 1.59411 0.797057 0.603904i \(-0.206389\pi\)
0.797057 + 0.603904i \(0.206389\pi\)
\(828\) 0 0
\(829\) −15.6214 −0.542552 −0.271276 0.962502i \(-0.587446\pi\)
−0.271276 + 0.962502i \(0.587446\pi\)
\(830\) 0 0
\(831\) 10.0151 0.347420
\(832\) 0 0
\(833\) −2.23768 −0.0775311
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −3.64240 −0.125900
\(838\) 0 0
\(839\) −35.7853 −1.23544 −0.617722 0.786396i \(-0.711944\pi\)
−0.617722 + 0.786396i \(0.711944\pi\)
\(840\) 0 0
\(841\) −28.1257 −0.969851
\(842\) 0 0
\(843\) 10.2315 0.352392
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 23.3486 0.802267
\(848\) 0 0
\(849\) −19.2445 −0.660470
\(850\) 0 0
\(851\) 5.94008 0.203623
\(852\) 0 0
\(853\) −28.0350 −0.959900 −0.479950 0.877296i \(-0.659345\pi\)
−0.479950 + 0.877296i \(0.659345\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 9.37562 0.320265 0.160133 0.987096i \(-0.448808\pi\)
0.160133 + 0.987096i \(0.448808\pi\)
\(858\) 0 0
\(859\) 9.85704 0.336318 0.168159 0.985760i \(-0.446218\pi\)
0.168159 + 0.985760i \(0.446218\pi\)
\(860\) 0 0
\(861\) 22.0039 0.749891
\(862\) 0 0
\(863\) −53.1607 −1.80961 −0.904805 0.425827i \(-0.859983\pi\)
−0.904805 + 0.425827i \(0.859983\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 10.3898 0.352855
\(868\) 0 0
\(869\) −2.99004 −0.101430
\(870\) 0 0
\(871\) −21.6803 −0.734609
\(872\) 0 0
\(873\) −39.9278 −1.35135
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 55.8780 1.88687 0.943433 0.331564i \(-0.107576\pi\)
0.943433 + 0.331564i \(0.107576\pi\)
\(878\) 0 0
\(879\) 10.0599 0.339313
\(880\) 0 0
\(881\) 35.8961 1.20937 0.604685 0.796465i \(-0.293299\pi\)
0.604685 + 0.796465i \(0.293299\pi\)
\(882\) 0 0
\(883\) −31.2225 −1.05072 −0.525361 0.850880i \(-0.676070\pi\)
−0.525361 + 0.850880i \(0.676070\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −44.3094 −1.48776 −0.743882 0.668311i \(-0.767018\pi\)
−0.743882 + 0.668311i \(0.767018\pi\)
\(888\) 0 0
\(889\) 9.40851 0.315551
\(890\) 0 0
\(891\) 10.6141 0.355587
\(892\) 0 0
\(893\) −21.3668 −0.715013
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.27375 0.142696
\(898\) 0 0
\(899\) 0.963070 0.0321202
\(900\) 0 0
\(901\) 2.26564 0.0754794
\(902\) 0 0
\(903\) −7.81020 −0.259907
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −50.5424 −1.67823 −0.839116 0.543952i \(-0.816927\pi\)
−0.839116 + 0.543952i \(0.816927\pi\)
\(908\) 0 0
\(909\) 23.8829 0.792145
\(910\) 0 0
\(911\) −0.446726 −0.0148007 −0.00740034 0.999973i \(-0.502356\pi\)
−0.00740034 + 0.999973i \(0.502356\pi\)
\(912\) 0 0
\(913\) −5.03403 −0.166602
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −13.3988 −0.442466
\(918\) 0 0
\(919\) −36.6373 −1.20855 −0.604276 0.796775i \(-0.706538\pi\)
−0.604276 + 0.796775i \(0.706538\pi\)
\(920\) 0 0
\(921\) 5.00664 0.164974
\(922\) 0 0
\(923\) −60.0028 −1.97502
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −19.5193 −0.641099
\(928\) 0 0
\(929\) −17.8243 −0.584797 −0.292399 0.956297i \(-0.594453\pi\)
−0.292399 + 0.956297i \(0.594453\pi\)
\(930\) 0 0
\(931\) −11.8519 −0.388431
\(932\) 0 0
\(933\) −18.3067 −0.599334
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −0.503505 −0.0164488 −0.00822440 0.999966i \(-0.502618\pi\)
−0.00822440 + 0.999966i \(0.502618\pi\)
\(938\) 0 0
\(939\) 13.5465 0.442075
\(940\) 0 0
\(941\) −42.3593 −1.38087 −0.690437 0.723392i \(-0.742582\pi\)
−0.690437 + 0.723392i \(0.742582\pi\)
\(942\) 0 0
\(943\) −11.0019 −0.358273
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.89002 −0.158904 −0.0794521 0.996839i \(-0.525317\pi\)
−0.0794521 + 0.996839i \(0.525317\pi\)
\(948\) 0 0
\(949\) 63.6342 2.06565
\(950\) 0 0
\(951\) −2.97127 −0.0963501
\(952\) 0 0
\(953\) 8.04399 0.260570 0.130285 0.991477i \(-0.458411\pi\)
0.130285 + 0.991477i \(0.458411\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.12468 0.0363557
\(958\) 0 0
\(959\) 14.3356 0.462921
\(960\) 0 0
\(961\) −29.9392 −0.965780
\(962\) 0 0
\(963\) −40.4215 −1.30256
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 21.1938 0.681548 0.340774 0.940145i \(-0.389311\pi\)
0.340774 + 0.940145i \(0.389311\pi\)
\(968\) 0 0
\(969\) −1.81780 −0.0583961
\(970\) 0 0
\(971\) −61.5773 −1.97611 −0.988054 0.154106i \(-0.950750\pi\)
−0.988054 + 0.154106i \(0.950750\pi\)
\(972\) 0 0
\(973\) −22.2060 −0.711892
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −43.8339 −1.40237 −0.701185 0.712979i \(-0.747346\pi\)
−0.701185 + 0.712979i \(0.747346\pi\)
\(978\) 0 0
\(979\) −35.4564 −1.13319
\(980\) 0 0
\(981\) −8.14970 −0.260200
\(982\) 0 0
\(983\) −37.6752 −1.20165 −0.600826 0.799380i \(-0.705162\pi\)
−0.600826 + 0.799380i \(0.705162\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 10.9430 0.348320
\(988\) 0 0
\(989\) 3.90510 0.124175
\(990\) 0 0
\(991\) −17.1831 −0.545838 −0.272919 0.962037i \(-0.587989\pi\)
−0.272919 + 0.962037i \(0.587989\pi\)
\(992\) 0 0
\(993\) −3.77935 −0.119934
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 13.3297 0.422157 0.211079 0.977469i \(-0.432302\pi\)
0.211079 + 0.977469i \(0.432302\pi\)
\(998\) 0 0
\(999\) −21.0068 −0.664627
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 9200.2.a.co.1.2 4
4.3 odd 2 2300.2.a.l.1.3 4
5.4 even 2 9200.2.a.cm.1.3 4
20.3 even 4 2300.2.c.j.1749.6 8
20.7 even 4 2300.2.c.j.1749.3 8
20.19 odd 2 2300.2.a.m.1.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2300.2.a.l.1.3 4 4.3 odd 2
2300.2.a.m.1.2 yes 4 20.19 odd 2
2300.2.c.j.1749.3 8 20.7 even 4
2300.2.c.j.1749.6 8 20.3 even 4
9200.2.a.cm.1.3 4 5.4 even 2
9200.2.a.co.1.2 4 1.1 even 1 trivial