Properties

Label 460.2.o.a.159.1
Level $460$
Weight $2$
Character 460.159
Analytic conductor $3.673$
Analytic rank $0$
Dimension $40$
CM discriminant -20
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(19,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.o (of order \(22\), degree \(10\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(4\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label 159.1
Character \(\chi\) \(=\) 460.159
Dual form 460.2.o.a.379.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18971 - 0.764582i) q^{2} +(-0.0739958 - 0.514652i) q^{3} +(0.830830 + 1.81926i) q^{4} +(0.629973 - 2.14549i) q^{5} +(-0.305460 + 0.668863i) q^{6} +(-0.858171 - 0.743609i) q^{7} +(0.402527 - 2.79964i) q^{8} +(2.61909 - 0.769034i) q^{9} +O(q^{10})\) \(q+(-1.18971 - 0.764582i) q^{2} +(-0.0739958 - 0.514652i) q^{3} +(0.830830 + 1.81926i) q^{4} +(0.629973 - 2.14549i) q^{5} +(-0.305460 + 0.668863i) q^{6} +(-0.858171 - 0.743609i) q^{7} +(0.402527 - 2.79964i) q^{8} +(2.61909 - 0.769034i) q^{9} +(-2.38989 + 2.07085i) q^{10} +(0.874810 - 0.562206i) q^{12} +(0.452426 + 1.54082i) q^{14} +(-1.15080 - 0.165460i) q^{15} +(-2.61944 + 3.02300i) q^{16} +(-3.70395 - 1.08758i) q^{18} +(4.42662 - 0.636451i) q^{20} +(-0.319199 + 0.496683i) q^{21} +(1.96963 - 4.37271i) q^{23} -1.47062 q^{24} +(-4.20627 - 2.70320i) q^{25} +(-1.23756 - 2.70989i) q^{27} +(0.639827 - 2.17905i) q^{28} +(1.34473 - 2.94454i) q^{29} +(1.24261 + 1.07673i) q^{30} +(5.42771 - 1.59372i) q^{32} +(-2.13603 + 1.37274i) q^{35} +(3.57509 + 4.12588i) q^{36} +(-5.75302 - 2.62732i) q^{40} +(-10.7829 - 3.16615i) q^{41} +(0.759509 - 0.346856i) q^{42} +(-10.1596 + 1.46073i) q^{43} -6.10370i q^{45} +(-5.68658 + 3.69632i) q^{46} +12.1712 q^{47} +(1.74962 + 1.12441i) q^{48} +(-0.812702 - 5.65246i) q^{49} +(2.93743 + 6.43207i) q^{50} +(-0.599585 + 4.17020i) q^{54} +(-2.42727 + 2.10324i) q^{56} +(-3.85118 + 2.47500i) q^{58} +(-0.655102 - 2.23107i) q^{60} +(-1.68634 - 0.242459i) q^{61} +(-2.81948 - 1.28762i) q^{63} +(-7.67594 - 2.25386i) q^{64} +(-1.05385 + 1.63982i) q^{67} +(-2.39617 - 0.690111i) q^{69} +3.59084 q^{70} +(-1.09876 - 7.64205i) q^{72} +(-1.07996 + 2.36479i) q^{75} +(4.83564 + 7.52440i) q^{80} +(5.58593 - 3.58986i) q^{81} +(10.4078 + 12.0112i) q^{82} +(3.95775 + 13.4789i) q^{83} +(-1.16880 - 0.168048i) q^{84} +(13.2038 + 6.02999i) q^{86} +(-1.61492 - 0.474182i) q^{87} +(18.1065 - 2.60331i) q^{89} +(-4.66678 + 7.26165i) q^{90} +(9.59153 - 0.0497018i) q^{92} +(-14.4803 - 9.30591i) q^{94} +(-1.22184 - 2.67545i) q^{96} +(-3.35489 + 7.34618i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{13}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18971 0.764582i −0.841254 0.540641i
\(3\) −0.0739958 0.514652i −0.0427215 0.297134i −0.999969 0.00786458i \(-0.997497\pi\)
0.957248 0.289270i \(-0.0934125\pi\)
\(4\) 0.830830 + 1.81926i 0.415415 + 0.909632i
\(5\) 0.629973 2.14549i 0.281733 0.959493i
\(6\) −0.305460 + 0.668863i −0.124703 + 0.273062i
\(7\) −0.858171 0.743609i −0.324358 0.281058i 0.477426 0.878672i \(-0.341570\pi\)
−0.801784 + 0.597614i \(0.796115\pi\)
\(8\) 0.402527 2.79964i 0.142315 0.989821i
\(9\) 2.61909 0.769034i 0.873029 0.256345i
\(10\) −2.38989 + 2.07085i −0.755750 + 0.654861i
\(11\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(12\) 0.874810 0.562206i 0.252536 0.162295i
\(13\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(14\) 0.452426 + 1.54082i 0.120916 + 0.411802i
\(15\) −1.15080 0.165460i −0.297134 0.0427215i
\(16\) −2.61944 + 3.02300i −0.654861 + 0.755750i
\(17\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(18\) −3.70395 1.08758i −0.873029 0.256345i
\(19\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(20\) 4.42662 0.636451i 0.989821 0.142315i
\(21\) −0.319199 + 0.496683i −0.0696549 + 0.108385i
\(22\) 0 0
\(23\) 1.96963 4.37271i 0.410696 0.911772i
\(24\) −1.47062 −0.300190
\(25\) −4.20627 2.70320i −0.841254 0.540641i
\(26\) 0 0
\(27\) −1.23756 2.70989i −0.238169 0.521518i
\(28\) 0.639827 2.17905i 0.120916 0.411802i
\(29\) 1.34473 2.94454i 0.249709 0.546787i −0.742720 0.669602i \(-0.766465\pi\)
0.992430 + 0.122815i \(0.0391921\pi\)
\(30\) 1.24261 + 1.07673i 0.226868 + 0.196583i
\(31\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(32\) 5.42771 1.59372i 0.959493 0.281733i
\(33\) 0 0
\(34\) 0 0
\(35\) −2.13603 + 1.37274i −0.361055 + 0.232036i
\(36\) 3.57509 + 4.12588i 0.595849 + 0.687646i
\(37\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −5.75302 2.62732i −0.909632 0.415415i
\(41\) −10.7829 3.16615i −1.68401 0.494470i −0.706919 0.707295i \(-0.749915\pi\)
−0.977090 + 0.212825i \(0.931734\pi\)
\(42\) 0.759509 0.346856i 0.117195 0.0535211i
\(43\) −10.1596 + 1.46073i −1.54932 + 0.222759i −0.863251 0.504774i \(-0.831576\pi\)
−0.686072 + 0.727533i \(0.740667\pi\)
\(44\) 0 0
\(45\) 6.10370i 0.909886i
\(46\) −5.68658 + 3.69632i −0.838441 + 0.544993i
\(47\) 12.1712 1.77536 0.887679 0.460462i \(-0.152316\pi\)
0.887679 + 0.460462i \(0.152316\pi\)
\(48\) 1.74962 + 1.12441i 0.252536 + 0.162295i
\(49\) −0.812702 5.65246i −0.116100 0.807495i
\(50\) 2.93743 + 6.43207i 0.415415 + 0.909632i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(54\) −0.599585 + 4.17020i −0.0815932 + 0.567493i
\(55\) 0 0
\(56\) −2.42727 + 2.10324i −0.324358 + 0.281058i
\(57\) 0 0
\(58\) −3.85118 + 2.47500i −0.505684 + 0.324983i
\(59\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(60\) −0.655102 2.23107i −0.0845733 0.288030i
\(61\) −1.68634 0.242459i −0.215913 0.0310437i 0.0335091 0.999438i \(-0.489332\pi\)
−0.249423 + 0.968395i \(0.580241\pi\)
\(62\) 0 0
\(63\) −2.81948 1.28762i −0.355222 0.162224i
\(64\) −7.67594 2.25386i −0.959493 0.281733i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.05385 + 1.63982i −0.128748 + 0.200336i −0.899643 0.436626i \(-0.856173\pi\)
0.770895 + 0.636963i \(0.219810\pi\)
\(68\) 0 0
\(69\) −2.39617 0.690111i −0.288465 0.0830796i
\(70\) 3.59084 0.429187
\(71\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(72\) −1.09876 7.64205i −0.129490 0.900625i
\(73\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(74\) 0 0
\(75\) −1.07996 + 2.36479i −0.124703 + 0.273062i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(80\) 4.83564 + 7.52440i 0.540641 + 0.841254i
\(81\) 5.58593 3.58986i 0.620659 0.398873i
\(82\) 10.4078 + 12.0112i 1.14935 + 1.32642i
\(83\) 3.95775 + 13.4789i 0.434419 + 1.47950i 0.828274 + 0.560324i \(0.189323\pi\)
−0.393855 + 0.919173i \(0.628859\pi\)
\(84\) −1.16880 0.168048i −0.127526 0.0183355i
\(85\) 0 0
\(86\) 13.2038 + 6.02999i 1.42381 + 0.650231i
\(87\) −1.61492 0.474182i −0.173137 0.0508377i
\(88\) 0 0
\(89\) 18.1065 2.60331i 1.91928 0.275951i 0.924765 0.380540i \(-0.124262\pi\)
0.994516 + 0.104589i \(0.0333526\pi\)
\(90\) −4.66678 + 7.26165i −0.491922 + 0.765445i
\(91\) 0 0
\(92\) 9.59153 0.0497018i 0.999987 0.00518177i
\(93\) 0 0
\(94\) −14.4803 9.30591i −1.49353 0.959831i
\(95\) 0 0
\(96\) −1.22184 2.67545i −0.124703 0.273062i
\(97\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(98\) −3.35489 + 7.34618i −0.338895 + 0.742076i
\(99\) 0 0
\(100\) 1.42315 9.89821i 0.142315 0.989821i
\(101\) −6.03671 + 1.77254i −0.600675 + 0.176374i −0.567912 0.823089i \(-0.692249\pi\)
−0.0327629 + 0.999463i \(0.510431\pi\)
\(102\) 0 0
\(103\) 6.26335 + 9.74596i 0.617146 + 0.960298i 0.999344 + 0.0362175i \(0.0115309\pi\)
−0.382198 + 0.924081i \(0.624833\pi\)
\(104\) 0 0
\(105\) 0.864543 + 0.997735i 0.0843707 + 0.0973690i
\(106\) 0 0
\(107\) 14.1368 + 2.03256i 1.36665 + 0.196495i 0.786287 0.617861i \(-0.212001\pi\)
0.580366 + 0.814356i \(0.302910\pi\)
\(108\) 3.90179 4.50291i 0.375450 0.433293i
\(109\) 18.1352 + 8.28207i 1.73704 + 0.793278i 0.991997 + 0.126258i \(0.0402968\pi\)
0.745040 + 0.667020i \(0.232431\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.49586 0.646407i 0.424819 0.0610797i
\(113\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(114\) 0 0
\(115\) −8.14079 6.98051i −0.759133 0.650936i
\(116\) 6.47413 0.601108
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.926454 + 3.15521i −0.0845733 + 0.288030i
\(121\) −4.56957 + 10.0060i −0.415415 + 0.909632i
\(122\) 1.82088 + 1.57780i 0.164854 + 0.142847i
\(123\) −0.831575 + 5.78373i −0.0749806 + 0.521502i
\(124\) 0 0
\(125\) −8.44954 + 7.32157i −0.755750 + 0.654861i
\(126\) 2.36989 + 3.68762i 0.211126 + 0.328519i
\(127\) 18.9403 12.1722i 1.68068 1.08011i 0.815175 0.579215i \(-0.196641\pi\)
0.865508 0.500894i \(-0.166996\pi\)
\(128\) 7.40890 + 8.55033i 0.654861 + 0.755750i
\(129\) 1.50353 + 5.12057i 0.132379 + 0.450841i
\(130\) 0 0
\(131\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.50756 1.14516i 0.216620 0.0989270i
\(135\) −6.59367 + 0.948027i −0.567493 + 0.0815932i
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 2.32310 + 2.65310i 0.197756 + 0.225847i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −4.27206 2.74549i −0.361055 0.232036i
\(141\) −0.900621 6.26396i −0.0758460 0.527520i
\(142\) 0 0
\(143\) 0 0
\(144\) −4.53576 + 9.93194i −0.377980 + 0.827661i
\(145\) −5.47034 4.74008i −0.454287 0.393642i
\(146\) 0 0
\(147\) −2.84891 + 0.836517i −0.234975 + 0.0689947i
\(148\) 0 0
\(149\) 5.97547 + 9.29801i 0.489529 + 0.761723i 0.994866 0.101200i \(-0.0322681\pi\)
−0.505337 + 0.862922i \(0.668632\pi\)
\(150\) 3.09292 1.98770i 0.252536 0.162295i
\(151\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 12.6491i 1.00000i
\(161\) −4.94186 + 2.28789i −0.389473 + 0.180311i
\(162\) −9.39039 −0.737779
\(163\) −12.4911 8.02754i −0.978378 0.628765i −0.0493527 0.998781i \(-0.515716\pi\)
−0.929025 + 0.370016i \(0.879352\pi\)
\(164\) −3.19871 22.2475i −0.249777 1.73724i
\(165\) 0 0
\(166\) 5.59710 19.0620i 0.434419 1.47950i
\(167\) −0.564020 + 1.23503i −0.0436452 + 0.0955697i −0.930199 0.367057i \(-0.880366\pi\)
0.886553 + 0.462626i \(0.153093\pi\)
\(168\) 1.26205 + 1.09357i 0.0973690 + 0.0843707i
\(169\) −1.85009 + 12.8677i −0.142315 + 0.989821i
\(170\) 0 0
\(171\) 0 0
\(172\) −11.0983 17.2694i −0.846241 1.31678i
\(173\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(174\) 1.55873 + 1.79888i 0.118167 + 0.136372i
\(175\) 1.59957 + 5.44763i 0.120916 + 0.411802i
\(176\) 0 0
\(177\) 0 0
\(178\) −23.5319 10.7467i −1.76379 0.805497i
\(179\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(180\) 11.1042 5.07114i 0.827661 0.377980i
\(181\) −5.73933 + 0.825191i −0.426601 + 0.0613360i −0.352272 0.935898i \(-0.614591\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 0.885818i 0.0654815i
\(184\) −11.4492 7.27438i −0.844044 0.536274i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 10.1122 + 22.1427i 0.737511 + 1.61492i
\(189\) −0.953056 + 3.24581i −0.0693246 + 0.236098i
\(190\) 0 0
\(191\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(192\) −0.591966 + 4.11722i −0.0427215 + 0.297134i
\(193\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 9.60811 6.17475i 0.686293 0.441054i
\(197\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(198\) 0 0
\(199\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(200\) −9.26113 + 10.6879i −0.654861 + 0.755750i
\(201\) 0.921919 + 0.421026i 0.0650271 + 0.0296969i
\(202\) 8.53720 + 2.50675i 0.600675 + 0.176374i
\(203\) −3.34359 + 1.52697i −0.234674 + 0.107172i
\(204\) 0 0
\(205\) −13.5859 + 21.1401i −0.948880 + 1.47649i
\(206\) 16.3837i 1.14151i
\(207\) 1.79587 12.9672i 0.124822 0.901284i
\(208\) 0 0
\(209\) 0 0
\(210\) −0.265707 1.84803i −0.0183355 0.127526i
\(211\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −15.2646 13.2269i −1.04347 0.904171i
\(215\) −3.26629 + 22.7175i −0.222759 + 1.54932i
\(216\) −8.08486 + 2.37393i −0.550105 + 0.161525i
\(217\) 0 0
\(218\) −15.2434 23.7191i −1.03241 1.60646i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 6.19543 7.14991i 0.414877 0.478793i −0.509393 0.860534i \(-0.670130\pi\)
0.924269 + 0.381741i \(0.124675\pi\)
\(224\) −5.84301 2.66841i −0.390402 0.178291i
\(225\) −13.0954 3.84517i −0.873029 0.256345i
\(226\) 0 0
\(227\) −24.2691 + 3.48937i −1.61080 + 0.231597i −0.888127 0.459598i \(-0.847994\pi\)
−0.722668 + 0.691195i \(0.757084\pi\)
\(228\) 0 0
\(229\) 15.0042i 0.991507i 0.868463 + 0.495754i \(0.165108\pi\)
−0.868463 + 0.495754i \(0.834892\pi\)
\(230\) 4.34803 + 14.5291i 0.286701 + 0.958020i
\(231\) 0 0
\(232\) −7.70235 4.95000i −0.505684 0.324983i
\(233\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(234\) 0 0
\(235\) 7.66756 26.1133i 0.500176 1.70344i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(240\) 3.51463 3.04544i 0.226868 0.196583i
\(241\) 16.1905 + 25.1929i 1.04292 + 1.62282i 0.743549 + 0.668682i \(0.233141\pi\)
0.299373 + 0.954136i \(0.403223\pi\)
\(242\) 13.0868 8.41040i 0.841254 0.540641i
\(243\) −8.11355 9.36354i −0.520485 0.600671i
\(244\) −0.959964 3.26934i −0.0614554 0.209298i
\(245\) −12.6393 1.81726i −0.807495 0.116100i
\(246\) 5.41147 6.24517i 0.345023 0.398177i
\(247\) 0 0
\(248\) 0 0
\(249\) 6.64406 3.03424i 0.421050 0.192287i
\(250\) 15.6505 2.25020i 0.989821 0.142315i
\(251\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(252\) 6.19918i 0.390511i
\(253\) 0 0
\(254\) −31.8402 −1.99783
\(255\) 0 0
\(256\) −2.27704 15.8371i −0.142315 0.989821i
\(257\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(258\) 2.12632 7.24158i 0.132379 0.450841i
\(259\) 0 0
\(260\) 0 0
\(261\) 1.25751 8.74614i 0.0778376 0.541373i
\(262\) 0 0
\(263\) 19.6294 17.0090i 1.21040 1.04882i 0.212981 0.977056i \(-0.431683\pi\)
0.997422 0.0717640i \(-0.0228629\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.67960 9.12589i −0.163989 0.558495i
\(268\) −3.85884 0.554818i −0.235716 0.0338909i
\(269\) 16.7308 19.3084i 1.02009 1.17725i 0.0360466 0.999350i \(-0.488524\pi\)
0.984048 0.177902i \(-0.0569310\pi\)
\(270\) 8.56942 + 3.91352i 0.521518 + 0.238169i
\(271\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.735312 4.93262i −0.0442606 0.296909i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 2.98338 + 6.53268i 0.178291 + 0.390402i
\(281\) 6.73908 22.9512i 0.402020 1.36915i −0.471286 0.881981i \(-0.656210\pi\)
0.873305 0.487173i \(-0.161972\pi\)
\(282\) −3.71783 + 8.14090i −0.221393 + 0.484784i
\(283\) −22.1870 19.2251i −1.31888 1.14282i −0.979339 0.202225i \(-0.935183\pi\)
−0.339541 0.940591i \(-0.610272\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.89921 + 10.7354i 0.407247 + 0.633689i
\(288\) 12.9900 8.34818i 0.765445 0.491922i
\(289\) 11.1326 + 12.8477i 0.654861 + 0.755750i
\(290\) 2.88396 + 9.82185i 0.169352 + 0.576759i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(294\) 4.02897 + 1.18301i 0.234975 + 0.0689947i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 15.6307i 0.905461i
\(299\) 0 0
\(300\) −5.19944 −0.300190
\(301\) 9.80488 + 6.30121i 0.565144 + 0.363196i
\(302\) 0 0
\(303\) 1.35893 + 2.97565i 0.0780686 + 0.170946i
\(304\) 0 0
\(305\) −1.58254 + 3.46528i −0.0906160 + 0.198421i
\(306\) 0 0
\(307\) −3.34589 + 23.2711i −0.190960 + 1.32815i 0.638515 + 0.769610i \(0.279549\pi\)
−0.829474 + 0.558545i \(0.811360\pi\)
\(308\) 0 0
\(309\) 4.55232 3.94460i 0.258972 0.224401i
\(310\) 0 0
\(311\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(312\) 0 0
\(313\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(314\) 0 0
\(315\) −4.53877 + 5.23802i −0.255731 + 0.295129i
\(316\) 0 0
\(317\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −9.67128 + 15.0488i −0.540641 + 0.841254i
\(321\) 7.42592i 0.414474i
\(322\) 7.62867 + 1.05652i 0.425129 + 0.0588776i
\(323\) 0 0
\(324\) 11.1719 + 7.17972i 0.620659 + 0.398873i
\(325\) 0 0
\(326\) 8.72310 + 19.1009i 0.483128 + 1.05790i
\(327\) 2.92045 9.94615i 0.161501 0.550024i
\(328\) −13.2045 + 28.9138i −0.729096 + 1.59650i
\(329\) −10.4450 9.05065i −0.575852 0.498978i
\(330\) 0 0
\(331\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(332\) −21.2334 + 18.3988i −1.16533 + 1.00977i
\(333\) 0 0
\(334\) 1.61530 1.03809i 0.0883855 0.0568019i
\(335\) 2.85433 + 3.29407i 0.155949 + 0.179974i
\(336\) −0.665349 2.26597i −0.0362978 0.123619i
\(337\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(338\) 12.0395 13.8943i 0.654861 0.755750i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −7.80315 + 12.1419i −0.421331 + 0.655603i
\(344\) 29.0312i 1.56526i
\(345\) −2.99015 + 4.70620i −0.160984 + 0.253373i
\(346\) 0 0
\(347\) −26.5771 17.0801i −1.42673 0.916907i −0.999921 0.0125674i \(-0.996000\pi\)
−0.426814 0.904339i \(-0.640364\pi\)
\(348\) −0.479058 3.33192i −0.0256802 0.178610i
\(349\) 15.4972 + 33.9341i 0.829544 + 1.81645i 0.465356 + 0.885124i \(0.345926\pi\)
0.364188 + 0.931325i \(0.381346\pi\)
\(350\) 2.26213 7.70411i 0.120916 0.411802i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 19.7795 + 30.7775i 1.04831 + 1.63120i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(360\) −17.0882 2.45691i −0.900625 0.129490i
\(361\) 12.4424 14.3592i 0.654861 0.755750i
\(362\) 7.45908 + 3.40645i 0.392040 + 0.179039i
\(363\) 5.48771 + 1.61134i 0.288030 + 0.0845733i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.677280 1.05387i 0.0354020 0.0550866i
\(367\) 38.2451i 1.99638i 0.0601346 + 0.998190i \(0.480847\pi\)
−0.0601346 + 0.998190i \(0.519153\pi\)
\(368\) 8.05936 + 17.4082i 0.420123 + 0.907467i
\(369\) −30.6763 −1.59694
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(374\) 0 0
\(375\) 4.39329 + 3.80681i 0.226868 + 0.196583i
\(376\) 4.89926 34.0751i 0.252660 1.75729i
\(377\) 0 0
\(378\) 3.61555 3.13289i 0.185964 0.161138i
\(379\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(380\) 0 0
\(381\) −7.66596 8.84699i −0.392739 0.453245i
\(382\) 0 0
\(383\) 38.5483 + 5.54241i 1.96973 + 0.283204i 0.999090 + 0.0426504i \(0.0135802\pi\)
0.970636 + 0.240553i \(0.0773289\pi\)
\(384\) 3.85222 4.44569i 0.196583 0.226868i
\(385\) 0 0
\(386\) 0 0
\(387\) −25.4855 + 11.6388i −1.29550 + 0.591636i
\(388\) 0 0
\(389\) 7.22297 11.2392i 0.366219 0.569848i −0.608424 0.793612i \(-0.708198\pi\)
0.974643 + 0.223764i \(0.0718344\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −16.1520 −0.815798
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 19.1899 5.63465i 0.959493 0.281733i
\(401\) −17.3130 + 15.0018i −0.864571 + 0.749155i −0.969439 0.245331i \(-0.921103\pi\)
0.104869 + 0.994486i \(0.466558\pi\)
\(402\) −0.774909 1.20578i −0.0386489 0.0601389i
\(403\) 0 0
\(404\) −8.24020 9.50970i −0.409965 0.473125i
\(405\) −4.18303 14.2461i −0.207856 0.707893i
\(406\) 5.14540 + 0.739797i 0.255362 + 0.0367155i
\(407\) 0 0
\(408\) 0 0
\(409\) 7.19768 + 2.11343i 0.355902 + 0.104502i 0.454796 0.890596i \(-0.349712\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 32.3266 14.7631i 1.59650 0.729096i
\(411\) 0 0
\(412\) −12.5267 + 19.4919i −0.617146 + 0.960298i
\(413\) 0 0
\(414\) −12.0511 + 14.0542i −0.592277 + 0.690724i
\(415\) 31.4120 1.54196
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(420\) −1.09686 + 2.40178i −0.0535211 + 0.117195i
\(421\) −15.3505 13.3013i −0.748138 0.648265i 0.194948 0.980814i \(-0.437546\pi\)
−0.943086 + 0.332548i \(0.892092\pi\)
\(422\) 0 0
\(423\) 31.8776 9.36010i 1.54994 0.455103i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.26687 + 1.46205i 0.0613082 + 0.0707534i
\(428\) 8.04749 + 27.4072i 0.388990 + 1.32478i
\(429\) 0 0
\(430\) 21.2554 24.5300i 1.02502 1.18294i
\(431\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(432\) 11.4337 + 3.35724i 0.550105 + 0.161525i
\(433\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(434\) 0 0
\(435\) −2.03471 + 3.16607i −0.0975568 + 0.151801i
\(436\) 39.8737i 1.90960i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(440\) 0 0
\(441\) −6.47547 14.1793i −0.308356 0.675205i
\(442\) 0 0
\(443\) 10.6623 23.3472i 0.506581 1.10926i −0.467693 0.883891i \(-0.654915\pi\)
0.974274 0.225367i \(-0.0723580\pi\)
\(444\) 0 0
\(445\) 5.82119 40.4873i 0.275951 1.91928i
\(446\) −12.8375 + 3.76942i −0.607872 + 0.178487i
\(447\) 4.34308 3.76330i 0.205421 0.177998i
\(448\) 4.91128 + 7.64210i 0.232036 + 0.361055i
\(449\) 35.6475 22.9092i 1.68231 1.08115i 0.832835 0.553521i \(-0.186716\pi\)
0.849473 0.527633i \(-0.176920\pi\)
\(450\) 12.6399 + 14.5872i 0.595849 + 0.687646i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 31.5411 + 14.4043i 1.48030 + 0.676029i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(458\) 11.4720 17.8507i 0.536049 0.834109i
\(459\) 0 0
\(460\) 5.93577 20.6099i 0.276757 0.960940i
\(461\) −40.1683 −1.87082 −0.935412 0.353560i \(-0.884971\pi\)
−0.935412 + 0.353560i \(0.884971\pi\)
\(462\) 0 0
\(463\) 5.60772 + 39.0025i 0.260613 + 1.81260i 0.528259 + 0.849083i \(0.322845\pi\)
−0.267646 + 0.963517i \(0.586246\pi\)
\(464\) 5.37890 + 11.7782i 0.249709 + 0.546787i
\(465\) 0 0
\(466\) 0 0
\(467\) 21.5090 + 18.6377i 0.995318 + 0.862448i 0.990496 0.137540i \(-0.0439196\pi\)
0.00482209 + 0.999988i \(0.498465\pi\)
\(468\) 0 0
\(469\) 2.12377 0.623595i 0.0980666 0.0287950i
\(470\) −29.0879 + 25.2048i −1.34173 + 1.16261i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(480\) −6.50989 + 0.935981i −0.297134 + 0.0427215i
\(481\) 0 0
\(482\) 42.3513i 1.92905i
\(483\) 1.54315 + 2.37404i 0.0702156 + 0.108023i
\(484\) −22.0000 −1.00000
\(485\) 0 0
\(486\) 2.49360 + 17.3434i 0.113112 + 0.786712i
\(487\) −3.43790 7.52795i −0.155786 0.341124i 0.815605 0.578609i \(-0.196404\pi\)
−0.971391 + 0.237485i \(0.923677\pi\)
\(488\) −1.35759 + 4.62354i −0.0614554 + 0.209298i
\(489\) −3.20710 + 7.02257i −0.145030 + 0.317572i
\(490\) 13.6477 + 11.8258i 0.616539 + 0.534234i
\(491\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(492\) −11.2130 + 3.29244i −0.505523 + 0.148435i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −10.2244 1.47005i −0.458168 0.0658747i
\(499\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(500\) −20.3400 9.28896i −0.909632 0.415415i
\(501\) 0.677347 + 0.198887i 0.0302616 + 0.00888562i
\(502\) 0 0
\(503\) −31.3604 + 4.50894i −1.39829 + 0.201044i −0.799887 0.600151i \(-0.795107\pi\)
−0.598403 + 0.801195i \(0.704198\pi\)
\(504\) −4.73978 + 7.37523i −0.211126 + 0.328519i
\(505\) 14.0684i 0.626034i
\(506\) 0 0
\(507\) 6.75927 0.300190
\(508\) 37.8807 + 24.3444i 1.68068 + 1.08011i
\(509\) −5.43465 37.7988i −0.240886 1.67540i −0.647703 0.761893i \(-0.724270\pi\)
0.406817 0.913510i \(-0.366639\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −9.39977 + 20.5826i −0.415415 + 0.909632i
\(513\) 0 0
\(514\) 0 0
\(515\) 24.8556 7.29827i 1.09527 0.321600i
\(516\) −8.06648 + 6.98965i −0.355107 + 0.307702i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.27690 0.758704i −0.231185 0.0332394i 0.0257485 0.999668i \(-0.491803\pi\)
−0.256934 + 0.966429i \(0.582712\pi\)
\(522\) −8.18321 + 9.44393i −0.358169 + 0.413349i
\(523\) −31.2428 14.2681i −1.36615 0.623901i −0.408746 0.912648i \(-0.634034\pi\)
−0.957405 + 0.288747i \(0.906761\pi\)
\(524\) 0 0
\(525\) 2.68527 1.22632i 0.117195 0.0535211i
\(526\) −36.3582 + 5.22751i −1.58529 + 0.227930i
\(527\) 0 0
\(528\) 0 0
\(529\) −15.2411 17.2252i −0.662658 0.748922i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −3.78953 + 12.9060i −0.163989 + 0.558495i
\(535\) 13.2666 29.0499i 0.573566 1.25593i
\(536\) 4.16671 + 3.61047i 0.179974 + 0.155949i
\(537\) 0 0
\(538\) −34.6677 + 10.1793i −1.49463 + 0.438863i
\(539\) 0 0
\(540\) −7.20293 11.2080i −0.309965 0.482315i
\(541\) 26.8929 17.2830i 1.15622 0.743055i 0.185349 0.982673i \(-0.440658\pi\)
0.970867 + 0.239618i \(0.0770221\pi\)
\(542\) 0 0
\(543\) 0.849373 + 2.89270i 0.0364501 + 0.124138i
\(544\) 0 0
\(545\) 29.1938 33.6914i 1.25052 1.44318i
\(546\) 0 0
\(547\) −43.8196 12.8666i −1.87359 0.550136i −0.997712 0.0676046i \(-0.978464\pi\)
−0.875879 0.482531i \(-0.839717\pi\)
\(548\) 0 0
\(549\) −4.60313 + 0.661829i −0.196457 + 0.0282462i
\(550\) 0 0
\(551\) 0 0
\(552\) −2.89658 + 6.43061i −0.123287 + 0.273705i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.44541 10.0530i 0.0610797 0.424819i
\(561\) 0 0
\(562\) −25.5656 + 22.1527i −1.07842 + 0.934457i
\(563\) 17.3716 + 27.0308i 0.732127 + 1.13921i 0.985141 + 0.171749i \(0.0549419\pi\)
−0.253014 + 0.967463i \(0.581422\pi\)
\(564\) 10.6475 6.84275i 0.448342 0.288132i
\(565\) 0 0
\(566\) 11.6969 + 39.8361i 0.491659 + 1.67444i
\(567\) −7.46313 1.07304i −0.313422 0.0450633i
\(568\) 0 0
\(569\) −28.3609 12.9520i −1.18895 0.542975i −0.280048 0.959986i \(-0.590351\pi\)
−0.908902 + 0.417011i \(0.863078\pi\)
\(570\) 0 0
\(571\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 18.0470i 0.753268i
\(575\) −20.1051 + 13.0685i −0.838441 + 0.544993i
\(576\) −21.8373 −0.909886
\(577\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(578\) −3.42148 23.7969i −0.142315 0.989821i
\(579\) 0 0
\(580\) 4.07853 13.8902i 0.169352 0.576759i
\(581\) 6.62657 14.5102i 0.274917 0.601983i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −39.7577 + 25.5507i −1.64097 + 1.05459i −0.701104 + 0.713059i \(0.747309\pi\)
−0.939870 + 0.341532i \(0.889054\pi\)
\(588\) −3.88881 4.48792i −0.160372 0.185079i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −11.9509 + 18.5960i −0.489529 + 0.761723i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 6.18584 + 3.97540i 0.252536 + 0.162295i
\(601\) 6.44906 + 44.8542i 0.263063 + 1.82964i 0.509485 + 0.860479i \(0.329836\pi\)
−0.246422 + 0.969163i \(0.579255\pi\)
\(602\) −6.84719 14.9933i −0.279071 0.611079i
\(603\) −1.49905 + 5.10529i −0.0610459 + 0.207903i
\(604\) 0 0
\(605\) 18.5890 + 16.1074i 0.755750 + 0.654861i
\(606\) 0.658386 4.57918i 0.0267451 0.186016i
\(607\) 32.4017 9.51399i 1.31514 0.386161i 0.452405 0.891812i \(-0.350566\pi\)
0.862738 + 0.505652i \(0.168748\pi\)
\(608\) 0 0
\(609\) 1.03327 + 1.60780i 0.0418701 + 0.0651512i
\(610\) 4.53226 2.91271i 0.183506 0.117932i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(614\) 21.7733 25.1278i 0.878700 1.01407i
\(615\) 11.8851 + 5.42773i 0.479253 + 0.218867i
\(616\) 0 0
\(617\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(618\) −8.43192 + 1.21233i −0.339181 + 0.0487669i
\(619\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(620\) 0 0
\(621\) −14.2871 + 0.0740334i −0.573321 + 0.00297086i
\(622\) 0 0
\(623\) −17.4743 11.2300i −0.700092 0.449922i
\(624\) 0 0
\(625\) 10.3854 + 22.7408i 0.415415 + 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 9.40472 2.76147i 0.374693 0.110020i
\(631\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −14.1835 48.3045i −0.562854 1.91691i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 23.0121 10.5093i 0.909632 0.415415i
\(641\) −43.3740 + 6.23624i −1.71317 + 0.246317i −0.927898 0.372834i \(-0.878386\pi\)
−0.785272 + 0.619151i \(0.787477\pi\)
\(642\) −5.67772 + 8.83470i −0.224082 + 0.348678i
\(643\) 44.0922i 1.73883i 0.494084 + 0.869414i \(0.335503\pi\)
−0.494084 + 0.869414i \(0.664497\pi\)
\(644\) −8.26813 7.08970i −0.325810 0.279373i
\(645\) 11.9333 0.469874
\(646\) 0 0
\(647\) −7.05423 49.0633i −0.277330 1.92888i −0.361390 0.932415i \(-0.617698\pi\)
0.0840596 0.996461i \(-0.473211\pi\)
\(648\) −7.80182 17.0836i −0.306484 0.671107i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 4.22624 29.3941i 0.165512 1.15116i
\(653\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(654\) −11.0791 + 9.60013i −0.433229 + 0.375395i
\(655\) 0 0
\(656\) 37.8165 24.3032i 1.47649 0.948880i
\(657\) 0 0
\(658\) 5.50659 + 18.7537i 0.214669 + 0.731096i
\(659\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(660\) 0 0
\(661\) 43.3297 + 19.7880i 1.68533 + 0.769664i 0.999106 + 0.0422726i \(0.0134598\pi\)
0.686223 + 0.727391i \(0.259267\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 39.3290 5.65466i 1.52626 0.219443i
\(665\) 0 0
\(666\) 0 0
\(667\) −10.2270 11.6797i −0.395991 0.452241i
\(668\) −2.71545 −0.105064
\(669\) −4.13815 2.65943i −0.159990 0.102819i
\(670\) −0.877244 6.10136i −0.0338909 0.235716i
\(671\) 0 0
\(672\) −0.940946 + 3.20457i −0.0362978 + 0.123619i
\(673\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(674\) 0 0
\(675\) −2.11985 + 14.7439i −0.0815932 + 0.567493i
\(676\) −24.9468 + 7.32505i −0.959493 + 0.281733i
\(677\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 3.59162 + 12.2319i 0.137631 + 0.468728i
\(682\) 0 0
\(683\) 32.8861 37.9526i 1.25835 1.45222i 0.419595 0.907711i \(-0.362172\pi\)
0.838757 0.544505i \(-0.183283\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 18.5670 8.47927i 0.708892 0.323740i
\(687\) 7.72196 1.11025i 0.294611 0.0423587i
\(688\) 22.1967 34.5387i 0.846241 1.31678i
\(689\) 0 0
\(690\) 7.15569 3.31281i 0.272413 0.126117i
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 18.5600 + 40.6408i 0.704529 + 1.54270i
\(695\) 0 0
\(696\) −1.97759 + 4.33031i −0.0749602 + 0.164140i
\(697\) 0 0
\(698\) 7.50819 52.2206i 0.284189 1.97658i
\(699\) 0 0
\(700\) −8.58171 + 7.43609i −0.324358 + 0.281058i
\(701\) 28.6276 + 44.5455i 1.08125 + 1.68246i 0.546981 + 0.837145i \(0.315777\pi\)
0.534270 + 0.845314i \(0.320587\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −14.0066 2.01385i −0.527520 0.0758460i
\(706\) 0 0
\(707\) 6.49860 + 2.96781i 0.244405 + 0.111616i
\(708\) 0 0
\(709\) −24.4080 + 11.1468i −0.916661 + 0.418625i −0.817159 0.576412i \(-0.804452\pi\)
−0.0995021 + 0.995037i \(0.531725\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 51.7394i 1.93902i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(720\) 18.4515 + 15.9883i 0.687646 + 0.595849i
\(721\) 1.87216 13.0212i 0.0697230 0.484934i
\(722\) −25.7816 + 7.57017i −0.959493 + 0.281733i
\(723\) 11.7676 10.1966i 0.437640 0.379217i
\(724\) −6.26965 9.75577i −0.233010 0.362570i
\(725\) −13.6160 + 8.75045i −0.505684 + 0.324983i
\(726\) −5.29680 6.11283i −0.196583 0.226868i
\(727\) −14.1953 48.3448i −0.526476 1.79301i −0.605151 0.796111i \(-0.706887\pi\)
0.0786754 0.996900i \(-0.474931\pi\)
\(728\) 0 0
\(729\) 8.82624 10.1860i 0.326898 0.377260i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.61154 + 0.735964i −0.0595641 + 0.0272020i
\(733\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(734\) 29.2415 45.5007i 1.07932 1.67946i
\(735\) 6.63931i 0.244894i
\(736\) 3.72171 26.8728i 0.137184 0.990546i
\(737\) 0 0
\(738\) 36.4960 + 23.4545i 1.34343 + 0.863373i
\(739\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −40.1174 34.7619i −1.47176 1.27529i −0.885049 0.465498i \(-0.845875\pi\)
−0.586715 0.809793i \(-0.699579\pi\)
\(744\) 0 0
\(745\) 23.7132 6.96282i 0.868784 0.255098i
\(746\) 0 0
\(747\) 20.7314 + 32.2587i 0.758521 + 1.18028i
\(748\) 0 0
\(749\) −10.6203 12.2565i −0.388058 0.447843i
\(750\) −2.31613 7.88803i −0.0845733 0.288030i
\(751\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(752\) −31.8819 + 36.7937i −1.16261 + 1.34173i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −6.69681 + 0.962856i −0.243561 + 0.0350187i
\(757\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.391715 0.251740i −0.0141996 0.00912556i 0.533522 0.845786i \(-0.320868\pi\)
−0.547721 + 0.836661i \(0.684505\pi\)
\(762\) 2.35604 + 16.3866i 0.0853503 + 0.593625i
\(763\) −9.40447 20.5929i −0.340465 0.745514i
\(764\) 0 0
\(765\) 0 0
\(766\) −41.6238 36.0672i −1.50393 1.30316i
\(767\) 0 0
\(768\) −7.98213 + 2.34376i −0.288030 + 0.0845733i
\(769\) −26.4727 + 22.9387i −0.954629 + 0.827191i −0.985036 0.172347i \(-0.944865\pi\)
0.0304075 + 0.999538i \(0.490319\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(774\) 39.2193 + 5.63888i 1.40971 + 0.202685i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −17.1865 + 7.84882i −0.616167 + 0.281394i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −9.64355 −0.344632
\(784\) 19.2162 + 12.3495i 0.686293 + 0.441054i
\(785\) 0 0
\(786\) 0 0
\(787\) −15.5593 + 52.9902i −0.554630 + 1.88890i −0.108071 + 0.994143i \(0.534467\pi\)
−0.446560 + 0.894754i \(0.647351\pi\)
\(788\) 0 0
\(789\) −10.2062 8.84373i −0.363351 0.314845i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −27.1386 7.96860i −0.959493 0.281733i
\(801\) 45.4204 20.7428i 1.60485 0.732910i
\(802\) 32.0676 4.61063i 1.13235 0.162807i
\(803\) 0 0
\(804\) 2.02701i 0.0714873i
\(805\) 1.79542 + 12.0440i 0.0632802 + 0.424496i
\(806\) 0 0
\(807\) −11.1751 7.18180i −0.393382 0.252811i
\(808\) 2.53253 + 17.6141i 0.0890939 + 0.619662i
\(809\) 14.8538 + 32.5252i 0.522230 + 1.14352i 0.968588 + 0.248670i \(0.0799935\pi\)
−0.446358 + 0.894854i \(0.647279\pi\)
\(810\) −5.91569 + 20.1470i −0.207856 + 0.707893i
\(811\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(812\) −5.55591 4.81422i −0.194974 0.168946i
\(813\) 0 0
\(814\) 0 0
\(815\) −25.0921 + 21.7424i −0.878937 + 0.761603i
\(816\) 0 0
\(817\) 0 0
\(818\) −6.94728 8.01759i −0.242906 0.280328i
\(819\) 0 0
\(820\) −49.7469 7.15253i −1.73724 0.249777i
\(821\) −35.9357 + 41.4720i −1.25416 + 1.44738i −0.409300 + 0.912400i \(0.634227\pi\)
−0.844863 + 0.534982i \(0.820318\pi\)
\(822\) 0 0
\(823\) 23.1899 + 6.80918i 0.808351 + 0.237353i 0.659693 0.751536i \(-0.270686\pi\)
0.148658 + 0.988889i \(0.452505\pi\)
\(824\) 29.8063 13.6121i 1.03835 0.474200i
\(825\) 0 0
\(826\) 0 0
\(827\) 47.4342i 1.64945i 0.565536 + 0.824724i \(0.308669\pi\)
−0.565536 + 0.824724i \(0.691331\pi\)
\(828\) 25.0828 7.50638i 0.871689 0.260865i
\(829\) −26.5328 −0.921521 −0.460760 0.887525i \(-0.652423\pi\)
−0.460760 + 0.887525i \(0.652423\pi\)
\(830\) −37.3713 24.0171i −1.29718 0.833645i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 2.29443 + 1.98814i 0.0794022 + 0.0688024i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(840\) 3.14130 2.01879i 0.108385 0.0696549i
\(841\) 12.1289 + 13.9975i 0.418239 + 0.482674i
\(842\) 8.09277 + 27.5614i 0.278895 + 0.949830i
\(843\) −12.3105 1.76999i −0.423998 0.0609616i
\(844\) 0 0
\(845\) 26.4420 + 12.0757i 0.909632 + 0.415415i
\(846\) −45.0817 13.2372i −1.54994 0.455103i
\(847\) 11.3620 5.18884i 0.390402 0.178291i
\(848\) 0 0
\(849\) −8.25251 + 12.8412i −0.283225 + 0.440707i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(854\) −0.389358 2.70804i −0.0133235 0.0926673i
\(855\) 0 0
\(856\) 11.3809 38.7597i 0.388990 1.32478i
\(857\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(858\) 0 0
\(859\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(860\) −44.0429 + 12.9322i −1.50185 + 0.440983i
\(861\) 5.01447 4.34506i 0.170893 0.148079i
\(862\) 0 0
\(863\) −37.9744 + 24.4047i −1.29266 + 0.830745i −0.992393 0.123108i \(-0.960714\pi\)
−0.300272 + 0.953854i \(0.597077\pi\)
\(864\) −11.0359 12.7362i −0.375450 0.433293i
\(865\) 0 0
\(866\) 0 0
\(867\) 5.78835 6.68011i 0.196583 0.226868i
\(868\) 0 0
\(869\) 0 0
\(870\) 4.84143 2.21101i 0.164140 0.0749602i
\(871\) 0 0
\(872\) 30.4867 47.4382i 1.03241 1.60646i
\(873\) 0 0
\(874\) 0 0
\(875\) 12.6955 0.429187
\(876\) 0 0
\(877\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 15.2297 + 13.1966i 0.513100 + 0.444604i 0.872524 0.488570i \(-0.162481\pi\)
−0.359424 + 0.933174i \(0.617027\pi\)
\(882\) −3.13729 + 21.8203i −0.105638 + 0.734728i
\(883\) 56.0021 16.4437i 1.88462 0.553375i 0.889232 0.457456i \(-0.151239\pi\)
0.995389 0.0959188i \(-0.0305789\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −30.5359 + 19.6242i −1.02587 + 0.659288i
\(887\) −38.9028 44.8963i −1.30623 1.50747i −0.708269 0.705943i \(-0.750523\pi\)
−0.597960 0.801526i \(-0.704022\pi\)
\(888\) 0 0
\(889\) −25.3054 3.63837i −0.848716 0.122027i
\(890\) −37.8814 + 43.7174i −1.26979 + 1.46541i
\(891\) 0 0
\(892\) 18.1549 + 5.33077i 0.607872 + 0.178487i
\(893\) 0 0
\(894\) −8.04436 + 1.15660i −0.269044 + 0.0386827i
\(895\) 0 0
\(896\) 12.8470i 0.429187i
\(897\) 0 0
\(898\) −59.9262 −1.99976
\(899\) 0 0
\(900\) −3.88471 27.0187i −0.129490 0.900625i
\(901\) 0 0
\(902\) 0 0
\(903\) 2.51741 5.51236i 0.0837742 0.183440i
\(904\) 0 0
\(905\) −1.84518 + 12.8335i −0.0613360 + 0.426601i
\(906\) 0 0
\(907\) 36.4661 31.5980i 1.21084 1.04920i 0.213449 0.976954i \(-0.431530\pi\)
0.997387 0.0722410i \(-0.0230151\pi\)
\(908\) −26.5116 41.2528i −0.879817 1.36902i
\(909\) −14.4475 + 9.28487i −0.479195 + 0.307960i
\(910\) 0 0
\(911\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 1.90051 + 0.558041i 0.0628291 + 0.0184483i
\(916\) −27.2967 + 12.4660i −0.901907 + 0.411887i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) −22.8198 + 19.9814i −0.752346 + 0.658768i
\(921\) 12.2241 0.402799
\(922\) 47.7887 + 30.7119i 1.57384 + 1.01144i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 23.1490 50.6893i 0.760725 1.66575i
\(927\) 23.8992 + 20.7088i 0.784954 + 0.680166i
\(928\) 2.60601 18.1252i 0.0855466 0.594990i
\(929\) −46.4406 + 13.6362i −1.52367 + 0.447389i −0.933105 0.359605i \(-0.882912\pi\)
−0.590561 + 0.806993i \(0.701093\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −11.3395 38.6188i −0.371040 1.26365i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(938\) −3.00347 0.881897i −0.0980666 0.0287950i
\(939\) 0 0
\(940\) 53.8774 7.74641i 1.75729 0.252660i
\(941\) 10.6110 16.5110i 0.345907 0.538242i −0.624092 0.781351i \(-0.714531\pi\)
0.969999 + 0.243109i \(0.0781673\pi\)
\(942\) 0 0
\(943\) −35.0830 + 40.9144i −1.14246 + 1.33236i
\(944\) 0 0
\(945\) 6.36346 + 4.08955i 0.207003 + 0.133033i
\(946\) 0 0
\(947\) 23.3823 + 51.2001i 0.759823 + 1.66378i 0.747865 + 0.663851i \(0.231079\pi\)
0.0119574 + 0.999929i \(0.496194\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 8.46053 + 3.86379i 0.273062 + 0.124703i
\(961\) −29.7443 8.73371i −0.959493 0.281733i
\(962\) 0 0
\(963\) 38.5885 5.54819i 1.24350 0.178788i
\(964\) −32.3810 + 50.3858i −1.04292 + 1.62282i
\(965\) 0 0
\(966\) −0.0207496 4.00429i −0.000667607 0.128836i
\(967\) 61.4860 1.97726 0.988629 0.150377i \(-0.0480486\pi\)
0.988629 + 0.150377i \(0.0480486\pi\)
\(968\) 26.1737 + 16.8208i 0.841254 + 0.540641i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(972\) 10.2938 22.5402i 0.330173 0.722978i
\(973\) 0 0
\(974\) −1.66562 + 11.5846i −0.0533699 + 0.371196i
\(975\) 0 0
\(976\) 5.15022 4.46269i 0.164854 0.142847i
\(977\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(978\) 9.18485 5.90275i 0.293699 0.188749i
\(979\) 0 0
\(980\) −7.19504 24.5040i −0.229837 0.782753i
\(981\) 53.8669 + 7.74489i 1.71984 + 0.247275i
\(982\) 0 0
\(983\) 16.1290 + 7.36585i 0.514434 + 0.234934i 0.655678 0.755041i \(-0.272383\pi\)
−0.141244 + 0.989975i \(0.545110\pi\)
\(984\) 15.8576 + 4.65622i 0.505523 + 0.148435i
\(985\) 0 0
\(986\) 0 0
\(987\) −3.88505 + 6.04525i −0.123662 + 0.192422i
\(988\) 0 0
\(989\) −13.6233 + 47.3020i −0.433195 + 1.50412i
\(990\) 0 0
\(991\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 11.0402 + 9.56636i 0.349821 + 0.303122i
\(997\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(998\) 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 460.2.o.a.159.1 40
4.3 odd 2 inner 460.2.o.a.159.4 yes 40
5.4 even 2 inner 460.2.o.a.159.4 yes 40
20.19 odd 2 CM 460.2.o.a.159.1 40
23.11 odd 22 inner 460.2.o.a.379.1 yes 40
92.11 even 22 inner 460.2.o.a.379.4 yes 40
115.34 odd 22 inner 460.2.o.a.379.4 yes 40
460.379 even 22 inner 460.2.o.a.379.1 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.o.a.159.1 40 1.1 even 1 trivial
460.2.o.a.159.1 40 20.19 odd 2 CM
460.2.o.a.159.4 yes 40 4.3 odd 2 inner
460.2.o.a.159.4 yes 40 5.4 even 2 inner
460.2.o.a.379.1 yes 40 23.11 odd 22 inner
460.2.o.a.379.1 yes 40 460.379 even 22 inner
460.2.o.a.379.4 yes 40 92.11 even 22 inner
460.2.o.a.379.4 yes 40 115.34 odd 22 inner