Properties

Label 2880.2.t.d.2161.2
Level $2880$
Weight $2$
Character 2880.2161
Analytic conductor $22.997$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2880,2,Mod(721,2880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 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("2880.721");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.t (of order \(4\), degree \(2\), not minimal)

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: no
Analytic conductor: \(22.9969157821\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + 136 x^{10} + 80 x^{9} - 168 x^{8} - 288 x^{7} + 96 x^{6} + 512 x^{5} + 448 x^{4} + \cdots + 1024 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: no (minimal twist has level 240)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2161.2
Root \(1.15787 - 0.811989i\) of defining polynomial
Character \(\chi\) \(=\) 2880.2161
Dual form 2880.2.t.d.721.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{5} -2.18060i q^{7} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{5} -2.18060i q^{7} +(-0.00889637 - 0.00889637i) q^{11} +(1.72965 - 1.72965i) q^{13} +5.54943 q^{17} +(4.94702 - 4.94702i) q^{19} +3.01309i q^{23} +1.00000i q^{25} +(-3.20471 + 3.20471i) q^{29} -3.58009 q^{31} +(-1.54192 + 1.54192i) q^{35} +(4.97761 + 4.97761i) q^{37} +3.76487i q^{41} +(-6.81210 - 6.81210i) q^{43} -10.0800 q^{47} +2.24499 q^{49} +(0.932644 + 0.932644i) q^{53} +0.0125814i q^{55} +(-4.60522 - 4.60522i) q^{59} +(4.17149 - 4.17149i) q^{61} -2.44610 q^{65} +(11.0105 - 11.0105i) q^{67} -12.1092i q^{71} -7.12981i q^{73} +(-0.0193994 + 0.0193994i) q^{77} +3.41789 q^{79} +(5.31631 - 5.31631i) q^{83} +(-3.92404 - 3.92404i) q^{85} +5.06405i q^{89} +(-3.77168 - 3.77168i) q^{91} -6.99615 q^{95} -10.3646 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 8 q^{11} + 24 q^{17} + 4 q^{19} - 16 q^{29} + 16 q^{37} + 8 q^{43} - 52 q^{49} + 16 q^{53} - 16 q^{59} - 4 q^{61} + 8 q^{67} + 40 q^{77} - 56 q^{79} - 48 q^{83} + 4 q^{85} + 8 q^{91} + 56 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(2431\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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 0
\(4\) 0 0
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) 0 0
\(7\) 2.18060i 0.824189i −0.911141 0.412094i \(-0.864797\pi\)
0.911141 0.412094i \(-0.135203\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.00889637 0.00889637i −0.00268236 0.00268236i 0.705764 0.708447i \(-0.250604\pi\)
−0.708447 + 0.705764i \(0.750604\pi\)
\(12\) 0 0
\(13\) 1.72965 1.72965i 0.479719 0.479719i −0.425323 0.905042i \(-0.639839\pi\)
0.905042 + 0.425323i \(0.139839\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.54943 1.34593 0.672967 0.739673i \(-0.265020\pi\)
0.672967 + 0.739673i \(0.265020\pi\)
\(18\) 0 0
\(19\) 4.94702 4.94702i 1.13493 1.13493i 0.145579 0.989347i \(-0.453496\pi\)
0.989347 0.145579i \(-0.0465044\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.01309i 0.628272i 0.949378 + 0.314136i \(0.101715\pi\)
−0.949378 + 0.314136i \(0.898285\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.20471 + 3.20471i −0.595099 + 0.595099i −0.939004 0.343905i \(-0.888250\pi\)
0.343905 + 0.939004i \(0.388250\pi\)
\(30\) 0 0
\(31\) −3.58009 −0.643004 −0.321502 0.946909i \(-0.604188\pi\)
−0.321502 + 0.946909i \(0.604188\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.54192 + 1.54192i −0.260631 + 0.260631i
\(36\) 0 0
\(37\) 4.97761 + 4.97761i 0.818314 + 0.818314i 0.985864 0.167550i \(-0.0535856\pi\)
−0.167550 + 0.985864i \(0.553586\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.76487i 0.587975i 0.955809 + 0.293987i \(0.0949823\pi\)
−0.955809 + 0.293987i \(0.905018\pi\)
\(42\) 0 0
\(43\) −6.81210 6.81210i −1.03884 1.03884i −0.999215 0.0396204i \(-0.987385\pi\)
−0.0396204 0.999215i \(-0.512615\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.0800 −1.47032 −0.735158 0.677896i \(-0.762892\pi\)
−0.735158 + 0.677896i \(0.762892\pi\)
\(48\) 0 0
\(49\) 2.24499 0.320713
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.932644 + 0.932644i 0.128108 + 0.128108i 0.768254 0.640145i \(-0.221126\pi\)
−0.640145 + 0.768254i \(0.721126\pi\)
\(54\) 0 0
\(55\) 0.0125814i 0.00169647i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.60522 4.60522i −0.599548 0.599548i 0.340644 0.940192i \(-0.389355\pi\)
−0.940192 + 0.340644i \(0.889355\pi\)
\(60\) 0 0
\(61\) 4.17149 4.17149i 0.534105 0.534105i −0.387686 0.921791i \(-0.626726\pi\)
0.921791 + 0.387686i \(0.126726\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.44610 −0.303401
\(66\) 0 0
\(67\) 11.0105 11.0105i 1.34515 1.34515i 0.454293 0.890852i \(-0.349892\pi\)
0.890852 0.454293i \(-0.150108\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.1092i 1.43710i −0.695475 0.718550i \(-0.744806\pi\)
0.695475 0.718550i \(-0.255194\pi\)
\(72\) 0 0
\(73\) 7.12981i 0.834481i −0.908796 0.417240i \(-0.862997\pi\)
0.908796 0.417240i \(-0.137003\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.0193994 + 0.0193994i −0.00221077 + 0.00221077i
\(78\) 0 0
\(79\) 3.41789 0.384543 0.192272 0.981342i \(-0.438415\pi\)
0.192272 + 0.981342i \(0.438415\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.31631 5.31631i 0.583541 0.583541i −0.352333 0.935875i \(-0.614612\pi\)
0.935875 + 0.352333i \(0.114612\pi\)
\(84\) 0 0
\(85\) −3.92404 3.92404i −0.425622 0.425622i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.06405i 0.536788i 0.963309 + 0.268394i \(0.0864929\pi\)
−0.963309 + 0.268394i \(0.913507\pi\)
\(90\) 0 0
\(91\) −3.77168 3.77168i −0.395379 0.395379i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.99615 −0.717790
\(96\) 0 0
\(97\) −10.3646 −1.05237 −0.526184 0.850371i \(-0.676378\pi\)
−0.526184 + 0.850371i \(0.676378\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −9.96414 9.96414i −0.991469 0.991469i 0.00849458 0.999964i \(-0.497296\pi\)
−0.999964 + 0.00849458i \(0.997296\pi\)
\(102\) 0 0
\(103\) 2.25154i 0.221851i 0.993829 + 0.110926i \(0.0353815\pi\)
−0.993829 + 0.110926i \(0.964618\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.51098 + 2.51098i 0.242746 + 0.242746i 0.817985 0.575239i \(-0.195091\pi\)
−0.575239 + 0.817985i \(0.695091\pi\)
\(108\) 0 0
\(109\) 12.0668 12.0668i 1.15579 1.15579i 0.170420 0.985372i \(-0.445488\pi\)
0.985372 0.170420i \(-0.0545124\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 19.7954 1.86219 0.931097 0.364772i \(-0.118853\pi\)
0.931097 + 0.364772i \(0.118853\pi\)
\(114\) 0 0
\(115\) 2.13057 2.13057i 0.198677 0.198677i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 12.1011i 1.10930i
\(120\) 0 0
\(121\) 10.9998i 0.999986i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) 0 0
\(127\) −14.3984 −1.27765 −0.638825 0.769352i \(-0.720579\pi\)
−0.638825 + 0.769352i \(0.720579\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.574754 + 0.574754i −0.0502165 + 0.0502165i −0.731769 0.681553i \(-0.761305\pi\)
0.681553 + 0.731769i \(0.261305\pi\)
\(132\) 0 0
\(133\) −10.7875 10.7875i −0.935393 0.935393i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.0077i 1.36763i 0.729654 + 0.683817i \(0.239681\pi\)
−0.729654 + 0.683817i \(0.760319\pi\)
\(138\) 0 0
\(139\) 1.52424 + 1.52424i 0.129284 + 0.129284i 0.768788 0.639504i \(-0.220860\pi\)
−0.639504 + 0.768788i \(0.720860\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.0307753 −0.00257356
\(144\) 0 0
\(145\) 4.53214 0.376374
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −12.1410 12.1410i −0.994629 0.994629i 0.00535669 0.999986i \(-0.498295\pi\)
−0.999986 + 0.00535669i \(0.998295\pi\)
\(150\) 0 0
\(151\) 12.7940i 1.04116i 0.853813 + 0.520580i \(0.174284\pi\)
−0.853813 + 0.520580i \(0.825716\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.53151 + 2.53151i 0.203336 + 0.203336i
\(156\) 0 0
\(157\) −10.3333 + 10.3333i −0.824686 + 0.824686i −0.986776 0.162090i \(-0.948177\pi\)
0.162090 + 0.986776i \(0.448177\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.57033 0.517814
\(162\) 0 0
\(163\) −13.4362 + 13.4362i −1.05241 + 1.05241i −0.0538580 + 0.998549i \(0.517152\pi\)
−0.998549 + 0.0538580i \(0.982848\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.08389i 0.393403i 0.980463 + 0.196702i \(0.0630230\pi\)
−0.980463 + 0.196702i \(0.936977\pi\)
\(168\) 0 0
\(169\) 7.01660i 0.539739i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.8821 10.8821i 0.827350 0.827350i −0.159799 0.987150i \(-0.551085\pi\)
0.987150 + 0.159799i \(0.0510847\pi\)
\(174\) 0 0
\(175\) 2.18060 0.164838
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.1719 11.1719i 0.835028 0.835028i −0.153172 0.988200i \(-0.548949\pi\)
0.988200 + 0.153172i \(0.0489488\pi\)
\(180\) 0 0
\(181\) −10.1479 10.1479i −0.754290 0.754290i 0.220987 0.975277i \(-0.429072\pi\)
−0.975277 + 0.220987i \(0.929072\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.03940i 0.517547i
\(186\) 0 0
\(187\) −0.0493697 0.0493697i −0.00361027 0.00361027i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 13.3716 0.967532 0.483766 0.875197i \(-0.339269\pi\)
0.483766 + 0.875197i \(0.339269\pi\)
\(192\) 0 0
\(193\) 8.32925 0.599553 0.299776 0.954009i \(-0.403088\pi\)
0.299776 + 0.954009i \(0.403088\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.1995 13.1995i −0.940427 0.940427i 0.0578960 0.998323i \(-0.481561\pi\)
−0.998323 + 0.0578960i \(0.981561\pi\)
\(198\) 0 0
\(199\) 3.66713i 0.259956i −0.991517 0.129978i \(-0.958509\pi\)
0.991517 0.129978i \(-0.0414906\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.98817 + 6.98817i 0.490474 + 0.490474i
\(204\) 0 0
\(205\) 2.66217 2.66217i 0.185934 0.185934i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.0880211 −0.00608855
\(210\) 0 0
\(211\) 12.6423 12.6423i 0.870332 0.870332i −0.122176 0.992508i \(-0.538987\pi\)
0.992508 + 0.122176i \(0.0389873\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.63376i 0.657017i
\(216\) 0 0
\(217\) 7.80675i 0.529956i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.59858 9.59858i 0.645670 0.645670i
\(222\) 0 0
\(223\) 5.37431 0.359891 0.179945 0.983677i \(-0.442408\pi\)
0.179945 + 0.983677i \(0.442408\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.92306 1.92306i 0.127638 0.127638i −0.640402 0.768040i \(-0.721232\pi\)
0.768040 + 0.640402i \(0.221232\pi\)
\(228\) 0 0
\(229\) 5.08104 + 5.08104i 0.335765 + 0.335765i 0.854771 0.519006i \(-0.173698\pi\)
−0.519006 + 0.854771i \(0.673698\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 26.2417i 1.71915i −0.511011 0.859574i \(-0.670729\pi\)
0.511011 0.859574i \(-0.329271\pi\)
\(234\) 0 0
\(235\) 7.12762 + 7.12762i 0.464955 + 0.464955i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7.40931 −0.479268 −0.239634 0.970863i \(-0.577027\pi\)
−0.239634 + 0.970863i \(0.577027\pi\)
\(240\) 0 0
\(241\) −19.6231 −1.26404 −0.632019 0.774953i \(-0.717773\pi\)
−0.632019 + 0.774953i \(0.717773\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.58745 1.58745i −0.101418 0.101418i
\(246\) 0 0
\(247\) 17.1133i 1.08889i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.23610 + 1.23610i 0.0780217 + 0.0780217i 0.745041 0.667019i \(-0.232430\pi\)
−0.667019 + 0.745041i \(0.732430\pi\)
\(252\) 0 0
\(253\) 0.0268055 0.0268055i 0.00168525 0.00168525i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.01050 −0.187790 −0.0938948 0.995582i \(-0.529932\pi\)
−0.0938948 + 0.995582i \(0.529932\pi\)
\(258\) 0 0
\(259\) 10.8542 10.8542i 0.674445 0.674445i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.9000i 0.733788i 0.930263 + 0.366894i \(0.119579\pi\)
−0.930263 + 0.366894i \(0.880421\pi\)
\(264\) 0 0
\(265\) 1.31896i 0.0810229i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.4949 15.4949i 0.944742 0.944742i −0.0538091 0.998551i \(-0.517136\pi\)
0.998551 + 0.0538091i \(0.0171363\pi\)
\(270\) 0 0
\(271\) −7.30492 −0.443742 −0.221871 0.975076i \(-0.571216\pi\)
−0.221871 + 0.975076i \(0.571216\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.00889637 0.00889637i 0.000536471 0.000536471i
\(276\) 0 0
\(277\) 2.23718 + 2.23718i 0.134419 + 0.134419i 0.771115 0.636696i \(-0.219699\pi\)
−0.636696 + 0.771115i \(0.719699\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.85036i 0.289348i 0.989479 + 0.144674i \(0.0462134\pi\)
−0.989479 + 0.144674i \(0.953787\pi\)
\(282\) 0 0
\(283\) −11.4295 11.4295i −0.679414 0.679414i 0.280454 0.959867i \(-0.409515\pi\)
−0.959867 + 0.280454i \(0.909515\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.20968 0.484602
\(288\) 0 0
\(289\) 13.7961 0.811537
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.1686 + 11.1686i 0.652475 + 0.652475i 0.953588 0.301113i \(-0.0973582\pi\)
−0.301113 + 0.953588i \(0.597358\pi\)
\(294\) 0 0
\(295\) 6.51276i 0.379188i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.21159 + 5.21159i 0.301394 + 0.301394i
\(300\) 0 0
\(301\) −14.8544 + 14.8544i −0.856196 + 0.856196i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.89938 −0.337798
\(306\) 0 0
\(307\) −13.5366 + 13.5366i −0.772575 + 0.772575i −0.978556 0.205981i \(-0.933962\pi\)
0.205981 + 0.978556i \(0.433962\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.4956i 0.935378i 0.883893 + 0.467689i \(0.154913\pi\)
−0.883893 + 0.467689i \(0.845087\pi\)
\(312\) 0 0
\(313\) 27.2549i 1.54054i 0.637719 + 0.770269i \(0.279878\pi\)
−0.637719 + 0.770269i \(0.720122\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −23.2962 + 23.2962i −1.30845 + 1.30845i −0.385911 + 0.922536i \(0.626113\pi\)
−0.922536 + 0.385911i \(0.873887\pi\)
\(318\) 0 0
\(319\) 0.0570205 0.00319253
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 27.4531 27.4531i 1.52753 1.52753i
\(324\) 0 0
\(325\) 1.72965 + 1.72965i 0.0959439 + 0.0959439i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 21.9804i 1.21182i
\(330\) 0 0
\(331\) 15.9057 + 15.9057i 0.874257 + 0.874257i 0.992933 0.118676i \(-0.0378649\pi\)
−0.118676 + 0.992933i \(0.537865\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −15.5712 −0.850745
\(336\) 0 0
\(337\) 7.15503 0.389759 0.194880 0.980827i \(-0.437568\pi\)
0.194880 + 0.980827i \(0.437568\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.0318498 + 0.0318498i 0.00172477 + 0.00172477i
\(342\) 0 0
\(343\) 20.1596i 1.08852i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9.64716 9.64716i −0.517887 0.517887i 0.399045 0.916931i \(-0.369342\pi\)
−0.916931 + 0.399045i \(0.869342\pi\)
\(348\) 0 0
\(349\) 20.3332 20.3332i 1.08841 1.08841i 0.0927209 0.995692i \(-0.470444\pi\)
0.995692 0.0927209i \(-0.0295564\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −32.1660 −1.71202 −0.856010 0.516958i \(-0.827064\pi\)
−0.856010 + 0.516958i \(0.827064\pi\)
\(354\) 0 0
\(355\) −8.56251 + 8.56251i −0.454451 + 0.454451i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.8239i 0.835155i 0.908641 + 0.417578i \(0.137121\pi\)
−0.908641 + 0.417578i \(0.862879\pi\)
\(360\) 0 0
\(361\) 29.9461i 1.57611i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.04154 + 5.04154i −0.263886 + 0.263886i
\(366\) 0 0
\(367\) −4.34838 −0.226984 −0.113492 0.993539i \(-0.536204\pi\)
−0.113492 + 0.993539i \(0.536204\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.03372 2.03372i 0.105586 0.105586i
\(372\) 0 0
\(373\) −17.3659 17.3659i −0.899171 0.899171i 0.0961919 0.995363i \(-0.469334\pi\)
−0.995363 + 0.0961919i \(0.969334\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.0861i 0.570961i
\(378\) 0 0
\(379\) 15.3936 + 15.3936i 0.790717 + 0.790717i 0.981611 0.190893i \(-0.0611385\pi\)
−0.190893 + 0.981611i \(0.561138\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.6393 −0.799129 −0.399564 0.916705i \(-0.630839\pi\)
−0.399564 + 0.916705i \(0.630839\pi\)
\(384\) 0 0
\(385\) 0.0274349 0.00139821
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −17.0067 17.0067i −0.862276 0.862276i 0.129326 0.991602i \(-0.458719\pi\)
−0.991602 + 0.129326i \(0.958719\pi\)
\(390\) 0 0
\(391\) 16.7209i 0.845612i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.41682 2.41682i −0.121603 0.121603i
\(396\) 0 0
\(397\) −12.5043 + 12.5043i −0.627572 + 0.627572i −0.947457 0.319884i \(-0.896356\pi\)
0.319884 + 0.947457i \(0.396356\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.6398 0.731079 0.365539 0.930796i \(-0.380885\pi\)
0.365539 + 0.930796i \(0.380885\pi\)
\(402\) 0 0
\(403\) −6.19232 + 6.19232i −0.308461 + 0.308461i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.0885653i 0.00439002i
\(408\) 0 0
\(409\) 33.5504i 1.65896i 0.558537 + 0.829479i \(0.311363\pi\)
−0.558537 + 0.829479i \(0.688637\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.0421 + 10.0421i −0.494141 + 0.494141i
\(414\) 0 0
\(415\) −7.51840 −0.369064
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16.5641 16.5641i 0.809211 0.809211i −0.175303 0.984514i \(-0.556091\pi\)
0.984514 + 0.175303i \(0.0560906\pi\)
\(420\) 0 0
\(421\) 14.1472 + 14.1472i 0.689492 + 0.689492i 0.962120 0.272628i \(-0.0878928\pi\)
−0.272628 + 0.962120i \(0.587893\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 5.54943i 0.269187i
\(426\) 0 0
\(427\) −9.09635 9.09635i −0.440203 0.440203i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13.1169 0.631819 0.315909 0.948789i \(-0.397690\pi\)
0.315909 + 0.948789i \(0.397690\pi\)
\(432\) 0 0
\(433\) 0.300976 0.0144640 0.00723199 0.999974i \(-0.497698\pi\)
0.00723199 + 0.999974i \(0.497698\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 14.9058 + 14.9058i 0.713041 + 0.713041i
\(438\) 0 0
\(439\) 30.3358i 1.44785i −0.689879 0.723925i \(-0.742336\pi\)
0.689879 0.723925i \(-0.257664\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.99367 3.99367i −0.189745 0.189745i 0.605841 0.795586i \(-0.292837\pi\)
−0.795586 + 0.605841i \(0.792837\pi\)
\(444\) 0 0
\(445\) 3.58082 3.58082i 0.169747 0.169747i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.4806 0.494610 0.247305 0.968938i \(-0.420455\pi\)
0.247305 + 0.968938i \(0.420455\pi\)
\(450\) 0 0
\(451\) 0.0334937 0.0334937i 0.00157716 0.00157716i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.33396i 0.250060i
\(456\) 0 0
\(457\) 5.70188i 0.266723i −0.991067 0.133361i \(-0.957423\pi\)
0.991067 0.133361i \(-0.0425771\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.78282 + 1.78282i −0.0830341 + 0.0830341i −0.747404 0.664370i \(-0.768700\pi\)
0.664370 + 0.747404i \(0.268700\pi\)
\(462\) 0 0
\(463\) 37.2015 1.72890 0.864451 0.502717i \(-0.167666\pi\)
0.864451 + 0.502717i \(0.167666\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −14.3669 + 14.3669i −0.664822 + 0.664822i −0.956513 0.291691i \(-0.905782\pi\)
0.291691 + 0.956513i \(0.405782\pi\)
\(468\) 0 0
\(469\) −24.0094 24.0094i −1.10865 1.10865i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.121206i 0.00557305i
\(474\) 0 0
\(475\) 4.94702 + 4.94702i 0.226985 + 0.226985i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −36.6561 −1.67486 −0.837431 0.546544i \(-0.815943\pi\)
−0.837431 + 0.546544i \(0.815943\pi\)
\(480\) 0 0
\(481\) 17.2191 0.785122
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.32890 + 7.32890i 0.332788 + 0.332788i
\(486\) 0 0
\(487\) 34.3322i 1.55574i 0.628425 + 0.777870i \(0.283700\pi\)
−0.628425 + 0.777870i \(0.716300\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.6224 + 17.6224i 0.795287 + 0.795287i 0.982348 0.187061i \(-0.0598963\pi\)
−0.187061 + 0.982348i \(0.559896\pi\)
\(492\) 0 0
\(493\) −17.7843 + 17.7843i −0.800963 + 0.800963i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −26.4053 −1.18444
\(498\) 0 0
\(499\) 14.6801 14.6801i 0.657173 0.657173i −0.297537 0.954710i \(-0.596165\pi\)
0.954710 + 0.297537i \(0.0961652\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 13.0618i 0.582398i 0.956663 + 0.291199i \(0.0940541\pi\)
−0.956663 + 0.291199i \(0.905946\pi\)
\(504\) 0 0
\(505\) 14.0914i 0.627060i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 22.0202 22.0202i 0.976027 0.976027i −0.0236921 0.999719i \(-0.507542\pi\)
0.999719 + 0.0236921i \(0.00754213\pi\)
\(510\) 0 0
\(511\) −15.5472 −0.687770
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.59208 1.59208i 0.0701555 0.0701555i
\(516\) 0 0
\(517\) 0.0896752 + 0.0896752i 0.00394391 + 0.00394391i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 22.0123i 0.964375i 0.876068 + 0.482188i \(0.160158\pi\)
−0.876068 + 0.482188i \(0.839842\pi\)
\(522\) 0 0
\(523\) 14.7575 + 14.7575i 0.645299 + 0.645299i 0.951853 0.306554i \(-0.0991760\pi\)
−0.306554 + 0.951853i \(0.599176\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.8675 −0.865441
\(528\) 0 0
\(529\) 13.9213 0.605275
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.51192 + 6.51192i 0.282063 + 0.282063i
\(534\) 0 0
\(535\) 3.55106i 0.153526i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.0199723 0.0199723i −0.000860267 0.000860267i
\(540\) 0 0
\(541\) 8.39925 8.39925i 0.361112 0.361112i −0.503110 0.864222i \(-0.667811\pi\)
0.864222 + 0.503110i \(0.167811\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −17.0651 −0.730987
\(546\) 0 0
\(547\) 8.81903 8.81903i 0.377074 0.377074i −0.492971 0.870046i \(-0.664089\pi\)
0.870046 + 0.492971i \(0.164089\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 31.7075i 1.35079i
\(552\) 0 0
\(553\) 7.45305i 0.316936i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.98592 + 6.98592i −0.296003 + 0.296003i −0.839446 0.543443i \(-0.817120\pi\)
0.543443 + 0.839446i \(0.317120\pi\)
\(558\) 0 0
\(559\) −23.5651 −0.996699
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.94396 3.94396i 0.166218 0.166218i −0.619097 0.785315i \(-0.712501\pi\)
0.785315 + 0.619097i \(0.212501\pi\)
\(564\) 0 0
\(565\) −13.9975 13.9975i −0.588877 0.588877i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 31.6307i 1.32603i −0.748607 0.663014i \(-0.769277\pi\)
0.748607 0.663014i \(-0.230723\pi\)
\(570\) 0 0
\(571\) −5.70590 5.70590i −0.238785 0.238785i 0.577562 0.816347i \(-0.304004\pi\)
−0.816347 + 0.577562i \(0.804004\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.01309 −0.125654
\(576\) 0 0
\(577\) 21.9772 0.914921 0.457461 0.889230i \(-0.348759\pi\)
0.457461 + 0.889230i \(0.348759\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.5927 11.5927i −0.480948 0.480948i
\(582\) 0 0
\(583\) 0.0165943i 0.000687265i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.3747 15.3747i −0.634583 0.634583i 0.314631 0.949214i \(-0.398119\pi\)
−0.949214 + 0.314631i \(0.898119\pi\)
\(588\) 0 0
\(589\) −17.7108 + 17.7108i −0.729761 + 0.729761i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.9206 0.694846 0.347423 0.937708i \(-0.387057\pi\)
0.347423 + 0.937708i \(0.387057\pi\)
\(594\) 0 0
\(595\) −8.55675 + 8.55675i −0.350792 + 0.350792i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.1715i 0.783327i −0.920109 0.391663i \(-0.871900\pi\)
0.920109 0.391663i \(-0.128100\pi\)
\(600\) 0 0
\(601\) 10.1428i 0.413735i −0.978369 0.206867i \(-0.933673\pi\)
0.978369 0.206867i \(-0.0663269\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.77806 + 7.77806i −0.316223 + 0.316223i
\(606\) 0 0
\(607\) −6.80048 −0.276023 −0.138011 0.990431i \(-0.544071\pi\)
−0.138011 + 0.990431i \(0.544071\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17.4349 + 17.4349i −0.705339 + 0.705339i
\(612\) 0 0
\(613\) 18.1431 + 18.1431i 0.732793 + 0.732793i 0.971172 0.238379i \(-0.0766161\pi\)
−0.238379 + 0.971172i \(0.576616\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 30.4488i 1.22582i 0.790151 + 0.612912i \(0.210002\pi\)
−0.790151 + 0.612912i \(0.789998\pi\)
\(618\) 0 0
\(619\) 12.1946 + 12.1946i 0.490143 + 0.490143i 0.908351 0.418208i \(-0.137342\pi\)
−0.418208 + 0.908351i \(0.637342\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.0427 0.442415
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 27.6229 + 27.6229i 1.10140 + 1.10140i
\(630\) 0 0
\(631\) 27.9943i 1.11444i 0.830366 + 0.557218i \(0.188131\pi\)
−0.830366 + 0.557218i \(0.811869\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.1812 + 10.1812i 0.404028 + 0.404028i
\(636\) 0 0
\(637\) 3.88306 3.88306i 0.153852 0.153852i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5.01913 −0.198244 −0.0991219 0.995075i \(-0.531603\pi\)
−0.0991219 + 0.995075i \(0.531603\pi\)
\(642\) 0 0
\(643\) −1.55218 + 1.55218i −0.0612118 + 0.0612118i −0.737050 0.675838i \(-0.763782\pi\)
0.675838 + 0.737050i \(0.263782\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24.6915i 0.970722i 0.874314 + 0.485361i \(0.161312\pi\)
−0.874314 + 0.485361i \(0.838688\pi\)
\(648\) 0 0
\(649\) 0.0819394i 0.00321640i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.4301 10.4301i 0.408161 0.408161i −0.472936 0.881097i \(-0.656806\pi\)
0.881097 + 0.472936i \(0.156806\pi\)
\(654\) 0 0
\(655\) 0.812825 0.0317597
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −15.4151 + 15.4151i −0.600487 + 0.600487i −0.940442 0.339955i \(-0.889588\pi\)
0.339955 + 0.940442i \(0.389588\pi\)
\(660\) 0 0
\(661\) 17.9150 + 17.9150i 0.696813 + 0.696813i 0.963722 0.266909i \(-0.0860022\pi\)
−0.266909 + 0.963722i \(0.586002\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 15.2558i 0.591594i
\(666\) 0 0
\(667\) −9.65605 9.65605i −0.373884 0.373884i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.0742223 −0.00286532
\(672\) 0 0
\(673\) 28.8891 1.11359 0.556796 0.830649i \(-0.312030\pi\)
0.556796 + 0.830649i \(0.312030\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.8421 10.8421i −0.416695 0.416695i 0.467368 0.884063i \(-0.345202\pi\)
−0.884063 + 0.467368i \(0.845202\pi\)
\(678\) 0 0
\(679\) 22.6011i 0.867350i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −2.04256 2.04256i −0.0781564 0.0781564i 0.666948 0.745104i \(-0.267600\pi\)
−0.745104 + 0.666948i \(0.767600\pi\)
\(684\) 0 0
\(685\) 11.3192 11.3192i 0.432484 0.432484i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.22630 0.122912
\(690\) 0 0
\(691\) −33.4347 + 33.4347i −1.27192 + 1.27192i −0.326837 + 0.945081i \(0.605983\pi\)
−0.945081 + 0.326837i \(0.894017\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.15559i 0.0817664i
\(696\) 0 0
\(697\) 20.8929i 0.791375i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.02037 + 4.02037i −0.151847 + 0.151847i −0.778943 0.627095i \(-0.784244\pi\)
0.627095 + 0.778943i \(0.284244\pi\)
\(702\) 0 0
\(703\) 49.2487 1.85745
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21.7278 + 21.7278i −0.817158 + 0.817158i
\(708\) 0 0
\(709\) 18.0101 + 18.0101i 0.676385 + 0.676385i 0.959180 0.282795i \(-0.0912617\pi\)
−0.282795 + 0.959180i \(0.591262\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10.7871i 0.403981i
\(714\) 0 0
\(715\) 0.0217614 + 0.0217614i 0.000813830 + 0.000813830i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 50.2917 1.87556 0.937782 0.347224i \(-0.112876\pi\)
0.937782 + 0.347224i \(0.112876\pi\)
\(720\) 0 0
\(721\) 4.90971 0.182847
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.20471 3.20471i −0.119020 0.119020i
\(726\) 0 0
\(727\) 15.1799i 0.562991i 0.959562 + 0.281496i \(0.0908305\pi\)
−0.959562 + 0.281496i \(0.909169\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −37.8032 37.8032i −1.39820 1.39820i
\(732\) 0 0
\(733\) −12.1524 + 12.1524i −0.448859 + 0.448859i −0.894975 0.446116i \(-0.852807\pi\)
0.446116 + 0.894975i \(0.352807\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.195907 −0.00721632
\(738\) 0 0
\(739\) 17.9947 17.9947i 0.661947 0.661947i −0.293892 0.955839i \(-0.594950\pi\)
0.955839 + 0.293892i \(0.0949505\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 19.2456i 0.706051i −0.935614 0.353026i \(-0.885153\pi\)
0.935614 0.353026i \(-0.114847\pi\)
\(744\) 0 0
\(745\) 17.1700i 0.629059i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.47544 5.47544i 0.200068 0.200068i
\(750\) 0 0
\(751\) 53.5813 1.95521 0.977604 0.210451i \(-0.0674933\pi\)
0.977604 + 0.210451i \(0.0674933\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.04671 9.04671i 0.329244 0.329244i
\(756\) 0 0
\(757\) 10.4133 + 10.4133i 0.378477 + 0.378477i 0.870552 0.492076i \(-0.163762\pi\)
−0.492076 + 0.870552i \(0.663762\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 38.1651i 1.38348i −0.722145 0.691742i \(-0.756844\pi\)
0.722145 0.691742i \(-0.243156\pi\)
\(762\) 0 0
\(763\) −26.3129 26.3129i −0.952590 0.952590i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15.9309 −0.575230
\(768\) 0 0
\(769\) −38.1071 −1.37418 −0.687089 0.726573i \(-0.741112\pi\)
−0.687089 + 0.726573i \(0.741112\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 32.9401 + 32.9401i 1.18477 + 1.18477i 0.978493 + 0.206280i \(0.0661358\pi\)
0.206280 + 0.978493i \(0.433864\pi\)
\(774\) 0 0
\(775\) 3.58009i 0.128601i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18.6249 + 18.6249i 0.667307 + 0.667307i
\(780\) 0 0
\(781\) −0.107728 + 0.107728i −0.00385481 + 0.00385481i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14.6135 0.521577
\(786\) 0 0
\(787\) −21.5631 + 21.5631i −0.768642 + 0.768642i −0.977867 0.209225i \(-0.932906\pi\)
0.209225 + 0.977867i \(0.432906\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 43.1658i 1.53480i
\(792\) 0 0
\(793\) 14.4305i 0.512441i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.81695 + 7.81695i −0.276891 + 0.276891i −0.831866 0.554976i \(-0.812727\pi\)
0.554976 + 0.831866i \(0.312727\pi\)
\(798\) 0 0
\(799\) −55.9381 −1.97895
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −0.0634294 + 0.0634294i −0.00223837 + 0.00223837i
\(804\) 0 0
\(805\) −4.64592 4.64592i −0.163747 0.163747i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8.21009i 0.288651i 0.989530 + 0.144326i \(0.0461013\pi\)
−0.989530 + 0.144326i \(0.953899\pi\)
\(810\) 0 0
\(811\) 0.466318 + 0.466318i 0.0163746 + 0.0163746i 0.715247 0.698872i \(-0.246314\pi\)
−0.698872 + 0.715247i \(0.746314\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 19.0017 0.665600
\(816\) 0 0
\(817\) −67.3992 −2.35800
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −22.1688 22.1688i −0.773696 0.773696i 0.205054 0.978751i \(-0.434263\pi\)
−0.978751 + 0.205054i \(0.934263\pi\)
\(822\) 0 0
\(823\) 14.7926i 0.515636i −0.966193 0.257818i \(-0.916996\pi\)
0.966193 0.257818i \(-0.0830035\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 27.9227 + 27.9227i 0.970967 + 0.970967i 0.999590 0.0286237i \(-0.00911246\pi\)
−0.0286237 + 0.999590i \(0.509112\pi\)
\(828\) 0 0
\(829\) −0.798074 + 0.798074i −0.0277182 + 0.0277182i −0.720830 0.693112i \(-0.756239\pi\)
0.693112 + 0.720830i \(0.256239\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 12.4584 0.431659
\(834\) 0 0
\(835\) 3.59485 3.59485i 0.124405 0.124405i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 29.3983i 1.01494i −0.861669 0.507470i \(-0.830581\pi\)
0.861669 0.507470i \(-0.169419\pi\)
\(840\) 0 0
\(841\) 8.45973i 0.291715i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 4.96149 4.96149i 0.170680 0.170680i
\(846\) 0 0
\(847\) −23.9862 −0.824177
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −14.9980 + 14.9980i −0.514123 + 0.514123i
\(852\) 0 0
\(853\) 24.2137 + 24.2137i 0.829060 + 0.829060i 0.987387 0.158326i \(-0.0506098\pi\)
−0.158326 + 0.987387i \(0.550610\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16.2011i 0.553419i 0.960954 + 0.276709i \(0.0892440\pi\)
−0.960954 + 0.276709i \(0.910756\pi\)
\(858\) 0 0
\(859\) −0.266646 0.266646i −0.00909783 0.00909783i 0.702543 0.711641i \(-0.252048\pi\)
−0.711641 + 0.702543i \(0.752048\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 10.2561 0.349121 0.174560 0.984646i \(-0.444150\pi\)
0.174560 + 0.984646i \(0.444150\pi\)
\(864\) 0 0
\(865\) −15.3896 −0.523262
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −0.0304068 0.0304068i −0.00103148 0.00103148i
\(870\) 0 0
\(871\) 38.0886i 1.29058i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.54192 1.54192i −0.0521263 0.0521263i
\(876\) 0 0
\(877\) −20.4974 + 20.4974i −0.692149 + 0.692149i −0.962704 0.270555i \(-0.912793\pi\)
0.270555 + 0.962704i \(0.412793\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 56.8144 1.91413 0.957063 0.289881i \(-0.0936159\pi\)
0.957063 + 0.289881i \(0.0936159\pi\)
\(882\) 0 0
\(883\) −26.2082 + 26.2082i −0.881978 + 0.881978i −0.993735 0.111758i \(-0.964352\pi\)
0.111758 + 0.993735i \(0.464352\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 26.0161i 0.873537i −0.899574 0.436768i \(-0.856123\pi\)
0.899574 0.436768i \(-0.143877\pi\)
\(888\) 0 0
\(889\) 31.3971i 1.05302i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −49.8659 + 49.8659i −1.66870 + 1.66870i
\(894\) 0 0
\(895\) −15.7995 −0.528118
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 11.4731 11.4731i 0.382651 0.382651i
\(900\) 0 0
\(901\) 5.17564 + 5.17564i 0.172425 + 0.172425i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.3513i 0.477055i
\(906\) 0 0
\(907\) 27.6233 + 27.6233i 0.917218 + 0.917218i 0.996826 0.0796085i \(-0.0253670\pi\)
−0.0796085 + 0.996826i \(0.525367\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −5.83194 −0.193221 −0.0966104 0.995322i \(-0.530800\pi\)
−0.0966104 + 0.995322i \(0.530800\pi\)
\(912\) 0 0
\(913\) −0.0945918 −0.00313053
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.25331 + 1.25331i 0.0413879 + 0.0413879i
\(918\) 0 0
\(919\) 11.8292i 0.390208i 0.980783 + 0.195104i \(0.0625045\pi\)
−0.980783 + 0.195104i \(0.937496\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −20.9447 20.9447i −0.689405 0.689405i
\(924\) 0 0
\(925\) −4.97761 + 4.97761i −0.163663 + 0.163663i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 45.8141 1.50311 0.751556 0.659669i \(-0.229304\pi\)
0.751556 + 0.659669i \(0.229304\pi\)
\(930\) 0 0
\(931\) 11.1060 11.1060i 0.363986 0.363986i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.0698194i 0.00228334i
\(936\) 0 0
\(937\) 6.21014i 0.202876i 0.994842 + 0.101438i \(0.0323444\pi\)
−0.994842 + 0.101438i \(0.967656\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.43886 2.43886i 0.0795045 0.0795045i −0.666236 0.745741i \(-0.732096\pi\)
0.745741 + 0.666236i \(0.232096\pi\)
\(942\) 0 0
\(943\) −11.3439 −0.369408
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −33.4856 + 33.4856i −1.08814 + 1.08814i −0.0924159 + 0.995720i \(0.529459\pi\)
−0.995720 + 0.0924159i \(0.970541\pi\)
\(948\) 0 0
\(949\) −12.3321 12.3321i −0.400317 0.400317i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 14.3013i 0.463266i −0.972803 0.231633i \(-0.925593\pi\)
0.972803 0.231633i \(-0.0744068\pi\)
\(954\) 0 0
\(955\) −9.45512 9.45512i −0.305961 0.305961i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 34.9064 1.12719
\(960\) 0 0
\(961\) −18.1829 −0.586546
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5.88967 5.88967i −0.189595 0.189595i
\(966\) 0 0
\(967\) 53.0546i 1.70612i 0.521812 + 0.853060i \(0.325256\pi\)
−0.521812 + 0.853060i \(0.674744\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.58090 + 4.58090i 0.147008 + 0.147008i 0.776780 0.629772i \(-0.216852\pi\)
−0.629772 + 0.776780i \(0.716852\pi\)
\(972\) 0 0
\(973\) 3.32375 3.32375i 0.106554 0.106554i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −11.2092 −0.358614 −0.179307 0.983793i \(-0.557385\pi\)
−0.179307 + 0.983793i \(0.557385\pi\)
\(978\) 0 0
\(979\) 0.0450516 0.0450516i 0.00143986 0.00143986i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 20.1018i 0.641147i −0.947224 0.320573i \(-0.896124\pi\)
0.947224 0.320573i \(-0.103876\pi\)
\(984\) 0 0
\(985\) 18.6669i 0.594778i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 20.5254 20.5254i 0.652671 0.652671i
\(990\) 0 0
\(991\) −20.7088 −0.657835 −0.328918 0.944359i \(-0.606684\pi\)
−0.328918 + 0.944359i \(0.606684\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.59305 + 2.59305i −0.0822052 + 0.0822052i
\(996\) 0 0
\(997\) 0.704128 + 0.704128i 0.0223000 + 0.0223000i 0.718169 0.695869i \(-0.244981\pi\)
−0.695869 + 0.718169i \(0.744981\pi\)
\(998\) 0 0
\(999\) 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 2880.2.t.d.2161.2 20
3.2 odd 2 960.2.s.c.241.2 20
4.3 odd 2 720.2.t.d.181.4 20
12.11 even 2 240.2.s.c.181.7 yes 20
16.3 odd 4 720.2.t.d.541.4 20
16.13 even 4 inner 2880.2.t.d.721.4 20
24.5 odd 2 1920.2.s.f.481.7 20
24.11 even 2 1920.2.s.e.481.4 20
48.5 odd 4 1920.2.s.f.1441.9 20
48.11 even 4 1920.2.s.e.1441.2 20
48.29 odd 4 960.2.s.c.721.4 20
48.35 even 4 240.2.s.c.61.7 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.2.s.c.61.7 20 48.35 even 4
240.2.s.c.181.7 yes 20 12.11 even 2
720.2.t.d.181.4 20 4.3 odd 2
720.2.t.d.541.4 20 16.3 odd 4
960.2.s.c.241.2 20 3.2 odd 2
960.2.s.c.721.4 20 48.29 odd 4
1920.2.s.e.481.4 20 24.11 even 2
1920.2.s.e.1441.2 20 48.11 even 4
1920.2.s.f.481.7 20 24.5 odd 2
1920.2.s.f.1441.9 20 48.5 odd 4
2880.2.t.d.721.4 20 16.13 even 4 inner
2880.2.t.d.2161.2 20 1.1 even 1 trivial