Properties

Label 1365.2.f.c.274.2
Level $1365$
Weight $2$
Character 1365.274
Analytic conductor $10.900$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1365,2,Mod(274,1365)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1365, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 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("1365.274");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1365 = 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1365.f (of order \(2\), degree \(1\), 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: \(10.8995798759\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 274.2
Root \(0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 1365.274
Dual form 1365.2.f.c.274.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.61803i q^{2} -1.00000i q^{3} -0.618034 q^{4} +(1.90211 + 1.17557i) q^{5} -1.61803 q^{6} +1.00000i q^{7} -2.23607i q^{8} -1.00000 q^{9} +(1.90211 - 3.07768i) q^{10} +2.80423 q^{11} +0.618034i q^{12} -1.00000i q^{13} +1.61803 q^{14} +(1.17557 - 1.90211i) q^{15} -4.85410 q^{16} -2.01062i q^{17} +1.61803i q^{18} +2.34458 q^{19} +(-1.17557 - 0.726543i) q^{20} +1.00000 q^{21} -4.53733i q^{22} +0.939503i q^{23} -2.23607 q^{24} +(2.23607 + 4.47214i) q^{25} -1.61803 q^{26} +1.00000i q^{27} -0.618034i q^{28} +5.69572 q^{29} +(-3.07768 - 1.90211i) q^{30} +0.895549 q^{31} +3.38197i q^{32} -2.80423i q^{33} -3.25325 q^{34} +(-1.17557 + 1.90211i) q^{35} +0.618034 q^{36} -5.52015i q^{37} -3.79360i q^{38} -1.00000 q^{39} +(2.62866 - 4.25325i) q^{40} +3.07768 q^{41} -1.61803i q^{42} -5.12454i q^{43} -1.73311 q^{44} +(-1.90211 - 1.17557i) q^{45} +1.52015 q^{46} -5.96261i q^{47} +4.85410i q^{48} -1.00000 q^{49} +(7.23607 - 3.61803i) q^{50} -2.01062 q^{51} +0.618034i q^{52} +1.30313i q^{53} +1.61803 q^{54} +(5.33395 + 3.29657i) q^{55} +2.23607 q^{56} -2.34458i q^{57} -9.21586i q^{58} +2.47027 q^{59} +(-0.726543 + 1.17557i) q^{60} -4.15838 q^{61} -1.44903i q^{62} -1.00000i q^{63} -4.23607 q^{64} +(1.17557 - 1.90211i) q^{65} -4.53733 q^{66} -15.4797i q^{67} +1.24263i q^{68} +0.939503 q^{69} +(3.07768 + 1.90211i) q^{70} -12.3416 q^{71} +2.23607i q^{72} +2.77455i q^{73} -8.93179 q^{74} +(4.47214 - 2.23607i) q^{75} -1.44903 q^{76} +2.80423i q^{77} +1.61803i q^{78} +6.16495 q^{79} +(-9.23305 - 5.70634i) q^{80} +1.00000 q^{81} -4.97980i q^{82} +15.5861i q^{83} -0.618034 q^{84} +(2.36363 - 3.82443i) q^{85} -8.29168 q^{86} -5.69572i q^{87} -6.27044i q^{88} +0.821412 q^{89} +(-1.90211 + 3.07768i) q^{90} +1.00000 q^{91} -0.580644i q^{92} -0.895549i q^{93} -9.64771 q^{94} +(4.45965 + 2.75621i) q^{95} +3.38197 q^{96} -1.98281i q^{97} +1.61803i q^{98} -2.80423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 4 q^{6} - 8 q^{9} - 8 q^{11} + 4 q^{14} - 12 q^{16} + 4 q^{19} + 8 q^{21} - 4 q^{26} + 12 q^{29} - 4 q^{31} + 8 q^{34} - 4 q^{36} - 8 q^{39} - 4 q^{44} - 12 q^{46} - 8 q^{49} + 40 q^{50}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1365\mathbb{Z}\right)^\times\).

\(n\) \(106\) \(547\) \(911\) \(976\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61803i 1.14412i −0.820211 0.572061i \(-0.806144\pi\)
0.820211 0.572061i \(-0.193856\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −0.618034 −0.309017
\(5\) 1.90211 + 1.17557i 0.850651 + 0.525731i
\(6\) −1.61803 −0.660560
\(7\) 1.00000i 0.377964i
\(8\) 2.23607i 0.790569i
\(9\) −1.00000 −0.333333
\(10\) 1.90211 3.07768i 0.601501 0.973249i
\(11\) 2.80423 0.845506 0.422753 0.906245i \(-0.361064\pi\)
0.422753 + 0.906245i \(0.361064\pi\)
\(12\) 0.618034i 0.178411i
\(13\) 1.00000i 0.277350i
\(14\) 1.61803 0.432438
\(15\) 1.17557 1.90211i 0.303531 0.491123i
\(16\) −4.85410 −1.21353
\(17\) 2.01062i 0.487647i −0.969820 0.243824i \(-0.921598\pi\)
0.969820 0.243824i \(-0.0784018\pi\)
\(18\) 1.61803i 0.381374i
\(19\) 2.34458 0.537883 0.268941 0.963157i \(-0.413326\pi\)
0.268941 + 0.963157i \(0.413326\pi\)
\(20\) −1.17557 0.726543i −0.262866 0.162460i
\(21\) 1.00000 0.218218
\(22\) 4.53733i 0.967363i
\(23\) 0.939503i 0.195900i 0.995191 + 0.0979499i \(0.0312285\pi\)
−0.995191 + 0.0979499i \(0.968772\pi\)
\(24\) −2.23607 −0.456435
\(25\) 2.23607 + 4.47214i 0.447214 + 0.894427i
\(26\) −1.61803 −0.317323
\(27\) 1.00000i 0.192450i
\(28\) 0.618034i 0.116797i
\(29\) 5.69572 1.05767 0.528834 0.848725i \(-0.322629\pi\)
0.528834 + 0.848725i \(0.322629\pi\)
\(30\) −3.07768 1.90211i −0.561906 0.347277i
\(31\) 0.895549 0.160845 0.0804226 0.996761i \(-0.474373\pi\)
0.0804226 + 0.996761i \(0.474373\pi\)
\(32\) 3.38197i 0.597853i
\(33\) 2.80423i 0.488153i
\(34\) −3.25325 −0.557928
\(35\) −1.17557 + 1.90211i −0.198708 + 0.321516i
\(36\) 0.618034 0.103006
\(37\) 5.52015i 0.907507i −0.891127 0.453753i \(-0.850085\pi\)
0.891127 0.453753i \(-0.149915\pi\)
\(38\) 3.79360i 0.615404i
\(39\) −1.00000 −0.160128
\(40\) 2.62866 4.25325i 0.415627 0.672499i
\(41\) 3.07768 0.480653 0.240327 0.970692i \(-0.422745\pi\)
0.240327 + 0.970692i \(0.422745\pi\)
\(42\) 1.61803i 0.249668i
\(43\) 5.12454i 0.781485i −0.920500 0.390743i \(-0.872218\pi\)
0.920500 0.390743i \(-0.127782\pi\)
\(44\) −1.73311 −0.261276
\(45\) −1.90211 1.17557i −0.283550 0.175244i
\(46\) 1.52015 0.224133
\(47\) 5.96261i 0.869736i −0.900494 0.434868i \(-0.856795\pi\)
0.900494 0.434868i \(-0.143205\pi\)
\(48\) 4.85410i 0.700629i
\(49\) −1.00000 −0.142857
\(50\) 7.23607 3.61803i 1.02333 0.511667i
\(51\) −2.01062 −0.281543
\(52\) 0.618034i 0.0857059i
\(53\) 1.30313i 0.178999i 0.995987 + 0.0894993i \(0.0285267\pi\)
−0.995987 + 0.0894993i \(0.971473\pi\)
\(54\) 1.61803 0.220187
\(55\) 5.33395 + 3.29657i 0.719230 + 0.444509i
\(56\) 2.23607 0.298807
\(57\) 2.34458i 0.310547i
\(58\) 9.21586i 1.21010i
\(59\) 2.47027 0.321602 0.160801 0.986987i \(-0.448592\pi\)
0.160801 + 0.986987i \(0.448592\pi\)
\(60\) −0.726543 + 1.17557i −0.0937962 + 0.151765i
\(61\) −4.15838 −0.532427 −0.266213 0.963914i \(-0.585773\pi\)
−0.266213 + 0.963914i \(0.585773\pi\)
\(62\) 1.44903i 0.184027i
\(63\) 1.00000i 0.125988i
\(64\) −4.23607 −0.529508
\(65\) 1.17557 1.90211i 0.145812 0.235928i
\(66\) −4.53733 −0.558507
\(67\) 15.4797i 1.89115i −0.325402 0.945576i \(-0.605500\pi\)
0.325402 0.945576i \(-0.394500\pi\)
\(68\) 1.24263i 0.150691i
\(69\) 0.939503 0.113103
\(70\) 3.07768 + 1.90211i 0.367854 + 0.227346i
\(71\) −12.3416 −1.46467 −0.732337 0.680943i \(-0.761570\pi\)
−0.732337 + 0.680943i \(0.761570\pi\)
\(72\) 2.23607i 0.263523i
\(73\) 2.77455i 0.324737i 0.986730 + 0.162368i \(0.0519133\pi\)
−0.986730 + 0.162368i \(0.948087\pi\)
\(74\) −8.93179 −1.03830
\(75\) 4.47214 2.23607i 0.516398 0.258199i
\(76\) −1.44903 −0.166215
\(77\) 2.80423i 0.319571i
\(78\) 1.61803i 0.183206i
\(79\) 6.16495 0.693611 0.346805 0.937937i \(-0.387266\pi\)
0.346805 + 0.937937i \(0.387266\pi\)
\(80\) −9.23305 5.70634i −1.03229 0.637988i
\(81\) 1.00000 0.111111
\(82\) 4.97980i 0.549927i
\(83\) 15.5861i 1.71079i 0.517975 + 0.855396i \(0.326686\pi\)
−0.517975 + 0.855396i \(0.673314\pi\)
\(84\) −0.618034 −0.0674330
\(85\) 2.36363 3.82443i 0.256371 0.414818i
\(86\) −8.29168 −0.894115
\(87\) 5.69572i 0.610645i
\(88\) 6.27044i 0.668431i
\(89\) 0.821412 0.0870695 0.0435348 0.999052i \(-0.486138\pi\)
0.0435348 + 0.999052i \(0.486138\pi\)
\(90\) −1.90211 + 3.07768i −0.200500 + 0.324416i
\(91\) 1.00000 0.104828
\(92\) 0.580644i 0.0605364i
\(93\) 0.895549i 0.0928641i
\(94\) −9.64771 −0.995085
\(95\) 4.45965 + 2.75621i 0.457550 + 0.282782i
\(96\) 3.38197 0.345170
\(97\) 1.98281i 0.201324i −0.994921 0.100662i \(-0.967904\pi\)
0.994921 0.100662i \(-0.0320961\pi\)
\(98\) 1.61803i 0.163446i
\(99\) −2.80423 −0.281835
\(100\) −1.38197 2.76393i −0.138197 0.276393i
\(101\) 7.71883 0.768052 0.384026 0.923322i \(-0.374537\pi\)
0.384026 + 0.923322i \(0.374537\pi\)
\(102\) 3.25325i 0.322120i
\(103\) 19.3309i 1.90473i 0.304954 + 0.952367i \(0.401359\pi\)
−0.304954 + 0.952367i \(0.598641\pi\)
\(104\) −2.23607 −0.219265
\(105\) 1.90211 + 1.17557i 0.185627 + 0.114724i
\(106\) 2.10851 0.204796
\(107\) 7.81736i 0.755732i 0.925860 + 0.377866i \(0.123342\pi\)
−0.925860 + 0.377866i \(0.876658\pi\)
\(108\) 0.618034i 0.0594703i
\(109\) −1.33686 −0.128048 −0.0640240 0.997948i \(-0.520393\pi\)
−0.0640240 + 0.997948i \(0.520393\pi\)
\(110\) 5.33395 8.63052i 0.508573 0.822888i
\(111\) −5.52015 −0.523949
\(112\) 4.85410i 0.458670i
\(113\) 6.79766i 0.639470i 0.947507 + 0.319735i \(0.103594\pi\)
−0.947507 + 0.319735i \(0.896406\pi\)
\(114\) −3.79360 −0.355304
\(115\) −1.10445 + 1.78704i −0.102991 + 0.166642i
\(116\) −3.52015 −0.326837
\(117\) 1.00000i 0.0924500i
\(118\) 3.99698i 0.367952i
\(119\) 2.01062 0.184313
\(120\) −4.25325 2.62866i −0.388267 0.239962i
\(121\) −3.13632 −0.285120
\(122\) 6.72841i 0.609161i
\(123\) 3.07768i 0.277505i
\(124\) −0.553479 −0.0497039
\(125\) −1.00406 + 11.1352i −0.0898056 + 0.995959i
\(126\) −1.61803 −0.144146
\(127\) 10.4912i 0.930942i −0.885063 0.465471i \(-0.845885\pi\)
0.885063 0.465471i \(-0.154115\pi\)
\(128\) 13.6180i 1.20368i
\(129\) −5.12454 −0.451191
\(130\) −3.07768 1.90211i −0.269931 0.166826i
\(131\) −2.09319 −0.182883 −0.0914413 0.995810i \(-0.529147\pi\)
−0.0914413 + 0.995810i \(0.529147\pi\)
\(132\) 1.73311i 0.150848i
\(133\) 2.34458i 0.203301i
\(134\) −25.0467 −2.16371
\(135\) −1.17557 + 1.90211i −0.101177 + 0.163708i
\(136\) −4.49589 −0.385519
\(137\) 12.2704i 1.04833i 0.851615 + 0.524167i \(0.175623\pi\)
−0.851615 + 0.524167i \(0.824377\pi\)
\(138\) 1.52015i 0.129404i
\(139\) −13.4538 −1.14114 −0.570568 0.821250i \(-0.693277\pi\)
−0.570568 + 0.821250i \(0.693277\pi\)
\(140\) 0.726543 1.17557i 0.0614041 0.0993538i
\(141\) −5.96261 −0.502142
\(142\) 19.9691i 1.67577i
\(143\) 2.80423i 0.234501i
\(144\) 4.85410 0.404508
\(145\) 10.8339 + 6.69572i 0.899706 + 0.556049i
\(146\) 4.48932 0.371539
\(147\) 1.00000i 0.0824786i
\(148\) 3.41164i 0.280435i
\(149\) −12.6216 −1.03400 −0.517000 0.855985i \(-0.672951\pi\)
−0.517000 + 0.855985i \(0.672951\pi\)
\(150\) −3.61803 7.23607i −0.295411 0.590822i
\(151\) 0.222429 0.0181010 0.00905051 0.999959i \(-0.497119\pi\)
0.00905051 + 0.999959i \(0.497119\pi\)
\(152\) 5.24263i 0.425234i
\(153\) 2.01062i 0.162549i
\(154\) 4.53733 0.365629
\(155\) 1.70343 + 1.05278i 0.136823 + 0.0845614i
\(156\) 0.618034 0.0494823
\(157\) 19.5013i 1.55637i −0.628033 0.778187i \(-0.716140\pi\)
0.628033 0.778187i \(-0.283860\pi\)
\(158\) 9.97510i 0.793576i
\(159\) 1.30313 0.103345
\(160\) −3.97574 + 6.43288i −0.314310 + 0.508564i
\(161\) −0.939503 −0.0740432
\(162\) 1.61803i 0.127125i
\(163\) 1.14712i 0.0898494i −0.998990 0.0449247i \(-0.985695\pi\)
0.998990 0.0449247i \(-0.0143048\pi\)
\(164\) −1.90211 −0.148530
\(165\) 3.29657 5.33395i 0.256637 0.415248i
\(166\) 25.2188 1.95736
\(167\) 17.8232i 1.37920i 0.724191 + 0.689599i \(0.242213\pi\)
−0.724191 + 0.689599i \(0.757787\pi\)
\(168\) 2.23607i 0.172516i
\(169\) −1.00000 −0.0769231
\(170\) −6.18806 3.82443i −0.474602 0.293320i
\(171\) −2.34458 −0.179294
\(172\) 3.16714i 0.241492i
\(173\) 2.11443i 0.160757i 0.996764 + 0.0803786i \(0.0256129\pi\)
−0.996764 + 0.0803786i \(0.974387\pi\)
\(174\) −9.21586 −0.698653
\(175\) −4.47214 + 2.23607i −0.338062 + 0.169031i
\(176\) −13.6120 −1.02604
\(177\) 2.47027i 0.185677i
\(178\) 1.32907i 0.0996182i
\(179\) −18.6737 −1.39574 −0.697870 0.716225i \(-0.745869\pi\)
−0.697870 + 0.716225i \(0.745869\pi\)
\(180\) 1.17557 + 0.726543i 0.0876219 + 0.0541533i
\(181\) 6.07872 0.451828 0.225914 0.974147i \(-0.427463\pi\)
0.225914 + 0.974147i \(0.427463\pi\)
\(182\) 1.61803i 0.119937i
\(183\) 4.15838i 0.307397i
\(184\) 2.10079 0.154872
\(185\) 6.48932 10.4999i 0.477104 0.771971i
\(186\) −1.44903 −0.106248
\(187\) 5.63824i 0.412309i
\(188\) 3.68510i 0.268763i
\(189\) −1.00000 −0.0727393
\(190\) 4.45965 7.21586i 0.323537 0.523494i
\(191\) 13.9329 1.00815 0.504076 0.863659i \(-0.331833\pi\)
0.504076 + 0.863659i \(0.331833\pi\)
\(192\) 4.23607i 0.305712i
\(193\) 3.14339i 0.226266i 0.993580 + 0.113133i \(0.0360887\pi\)
−0.993580 + 0.113133i \(0.963911\pi\)
\(194\) −3.20826 −0.230340
\(195\) −1.90211 1.17557i −0.136213 0.0841844i
\(196\) 0.618034 0.0441453
\(197\) 5.11141i 0.364173i 0.983283 + 0.182087i \(0.0582851\pi\)
−0.983283 + 0.182087i \(0.941715\pi\)
\(198\) 4.53733i 0.322454i
\(199\) −16.5135 −1.17061 −0.585304 0.810814i \(-0.699025\pi\)
−0.585304 + 0.810814i \(0.699025\pi\)
\(200\) 10.0000 5.00000i 0.707107 0.353553i
\(201\) −15.4797 −1.09186
\(202\) 12.4893i 0.878746i
\(203\) 5.69572i 0.399761i
\(204\) 1.24263 0.0870017
\(205\) 5.85410 + 3.61803i 0.408868 + 0.252694i
\(206\) 31.2781 2.17925
\(207\) 0.939503i 0.0652999i
\(208\) 4.85410i 0.336571i
\(209\) 6.57472 0.454783
\(210\) 1.90211 3.07768i 0.131258 0.212380i
\(211\) −2.47078 −0.170096 −0.0850478 0.996377i \(-0.527104\pi\)
−0.0850478 + 0.996377i \(0.527104\pi\)
\(212\) 0.805379i 0.0553136i
\(213\) 12.3416i 0.845630i
\(214\) 12.6487 0.864650
\(215\) 6.02426 9.74746i 0.410851 0.664771i
\(216\) 2.23607 0.152145
\(217\) 0.895549i 0.0607938i
\(218\) 2.16308i 0.146503i
\(219\) 2.77455 0.187487
\(220\) −3.29657 2.03739i −0.222254 0.137361i
\(221\) −2.01062 −0.135249
\(222\) 8.93179i 0.599462i
\(223\) 9.10445i 0.609679i 0.952404 + 0.304840i \(0.0986029\pi\)
−0.952404 + 0.304840i \(0.901397\pi\)
\(224\) −3.38197 −0.225967
\(225\) −2.23607 4.47214i −0.149071 0.298142i
\(226\) 10.9988 0.731632
\(227\) 7.00779i 0.465123i 0.972582 + 0.232562i \(0.0747107\pi\)
−0.972582 + 0.232562i \(0.925289\pi\)
\(228\) 1.44903i 0.0959642i
\(229\) 20.2385 1.33740 0.668698 0.743534i \(-0.266852\pi\)
0.668698 + 0.743534i \(0.266852\pi\)
\(230\) 2.89149 + 1.78704i 0.190659 + 0.117834i
\(231\) 2.80423 0.184505
\(232\) 12.7360i 0.836160i
\(233\) 14.6750i 0.961391i 0.876887 + 0.480696i \(0.159616\pi\)
−0.876887 + 0.480696i \(0.840384\pi\)
\(234\) 1.61803 0.105774
\(235\) 7.00947 11.3416i 0.457247 0.739842i
\(236\) −1.52671 −0.0993805
\(237\) 6.16495i 0.400456i
\(238\) 3.25325i 0.210877i
\(239\) −23.9963 −1.55219 −0.776097 0.630613i \(-0.782803\pi\)
−0.776097 + 0.630613i \(0.782803\pi\)
\(240\) −5.70634 + 9.23305i −0.368343 + 0.595991i
\(241\) 25.2300 1.62521 0.812605 0.582815i \(-0.198049\pi\)
0.812605 + 0.582815i \(0.198049\pi\)
\(242\) 5.07467i 0.326212i
\(243\) 1.00000i 0.0641500i
\(244\) 2.57002 0.164529
\(245\) −1.90211 1.17557i −0.121522 0.0751044i
\(246\) −4.97980 −0.317500
\(247\) 2.34458i 0.149182i
\(248\) 2.00251i 0.127159i
\(249\) 15.5861 0.987726
\(250\) 18.0171 + 1.62460i 1.13950 + 0.102749i
\(251\) 11.8992 0.751069 0.375534 0.926808i \(-0.377459\pi\)
0.375534 + 0.926808i \(0.377459\pi\)
\(252\) 0.618034i 0.0389325i
\(253\) 2.63458i 0.165634i
\(254\) −16.9751 −1.06511
\(255\) −3.82443 2.36363i −0.239495 0.148016i
\(256\) 13.5623 0.847644
\(257\) 5.49151i 0.342551i 0.985223 + 0.171276i \(0.0547889\pi\)
−0.985223 + 0.171276i \(0.945211\pi\)
\(258\) 8.29168i 0.516218i
\(259\) 5.52015 0.343005
\(260\) −0.726543 + 1.17557i −0.0450583 + 0.0729058i
\(261\) −5.69572 −0.352556
\(262\) 3.38685i 0.209240i
\(263\) 2.38614i 0.147135i 0.997290 + 0.0735677i \(0.0234385\pi\)
−0.997290 + 0.0735677i \(0.976561\pi\)
\(264\) −6.27044 −0.385919
\(265\) −1.53192 + 2.47870i −0.0941052 + 0.152265i
\(266\) 3.79360 0.232601
\(267\) 0.821412i 0.0502696i
\(268\) 9.56701i 0.584398i
\(269\) 18.6149 1.13497 0.567485 0.823383i \(-0.307916\pi\)
0.567485 + 0.823383i \(0.307916\pi\)
\(270\) 3.07768 + 1.90211i 0.187302 + 0.115759i
\(271\) −2.89400 −0.175798 −0.0878990 0.996129i \(-0.528015\pi\)
−0.0878990 + 0.996129i \(0.528015\pi\)
\(272\) 9.75976i 0.591773i
\(273\) 1.00000i 0.0605228i
\(274\) 19.8540 1.19942
\(275\) 6.27044 + 12.5409i 0.378122 + 0.756244i
\(276\) −0.580644 −0.0349507
\(277\) 14.3261i 0.860769i −0.902646 0.430385i \(-0.858378\pi\)
0.902646 0.430385i \(-0.141622\pi\)
\(278\) 21.7687i 1.30560i
\(279\) −0.895549 −0.0536151
\(280\) 4.25325 + 2.62866i 0.254181 + 0.157092i
\(281\) 5.57543 0.332603 0.166301 0.986075i \(-0.446818\pi\)
0.166301 + 0.986075i \(0.446818\pi\)
\(282\) 9.64771i 0.574513i
\(283\) 18.6838i 1.11064i −0.831637 0.555319i \(-0.812596\pi\)
0.831637 0.555319i \(-0.187404\pi\)
\(284\) 7.62750 0.452609
\(285\) 2.75621 4.45965i 0.163264 0.264167i
\(286\) −4.53733 −0.268298
\(287\) 3.07768i 0.181670i
\(288\) 3.38197i 0.199284i
\(289\) 12.9574 0.762200
\(290\) 10.8339 17.5296i 0.636188 1.02937i
\(291\) −1.98281 −0.116235
\(292\) 1.71477i 0.100349i
\(293\) 31.0585i 1.81446i 0.420637 + 0.907229i \(0.361807\pi\)
−0.420637 + 0.907229i \(0.638193\pi\)
\(294\) 1.61803 0.0943657
\(295\) 4.69873 + 2.90398i 0.273571 + 0.169076i
\(296\) −12.3434 −0.717447
\(297\) 2.80423i 0.162718i
\(298\) 20.4221i 1.18302i
\(299\) 0.939503 0.0543328
\(300\) −2.76393 + 1.38197i −0.159576 + 0.0797878i
\(301\) 5.12454 0.295374
\(302\) 0.359898i 0.0207098i
\(303\) 7.71883i 0.443435i
\(304\) −11.3808 −0.652734
\(305\) −7.90972 4.88847i −0.452909 0.279913i
\(306\) 3.25325 0.185976
\(307\) 1.72892i 0.0986745i −0.998782 0.0493373i \(-0.984289\pi\)
0.998782 0.0493373i \(-0.0157109\pi\)
\(308\) 1.73311i 0.0987529i
\(309\) 19.3309 1.09970
\(310\) 1.70343 2.75621i 0.0967486 0.156542i
\(311\) 17.7385 1.00586 0.502930 0.864327i \(-0.332256\pi\)
0.502930 + 0.864327i \(0.332256\pi\)
\(312\) 2.23607i 0.126592i
\(313\) 24.8522i 1.40473i 0.711817 + 0.702365i \(0.247872\pi\)
−0.711817 + 0.702365i \(0.752128\pi\)
\(314\) −31.5538 −1.78068
\(315\) 1.17557 1.90211i 0.0662359 0.107172i
\(316\) −3.81015 −0.214338
\(317\) 2.60626i 0.146382i 0.997318 + 0.0731911i \(0.0233183\pi\)
−0.997318 + 0.0731911i \(0.976682\pi\)
\(318\) 2.10851i 0.118239i
\(319\) 15.9721 0.894265
\(320\) −8.05748 4.97980i −0.450427 0.278379i
\(321\) 7.81736 0.436322
\(322\) 1.52015i 0.0847145i
\(323\) 4.71406i 0.262297i
\(324\) −0.618034 −0.0343352
\(325\) 4.47214 2.23607i 0.248069 0.124035i
\(326\) −1.85608 −0.102799
\(327\) 1.33686i 0.0739285i
\(328\) 6.88191i 0.379990i
\(329\) 5.96261 0.328729
\(330\) −8.63052 5.33395i −0.475095 0.293625i
\(331\) −30.7543 −1.69041 −0.845205 0.534443i \(-0.820522\pi\)
−0.845205 + 0.534443i \(0.820522\pi\)
\(332\) 9.63271i 0.528664i
\(333\) 5.52015i 0.302502i
\(334\) 28.8385 1.57797
\(335\) 18.1975 29.4442i 0.994237 1.60871i
\(336\) −4.85410 −0.264813
\(337\) 14.3356i 0.780912i 0.920622 + 0.390456i \(0.127683\pi\)
−0.920622 + 0.390456i \(0.872317\pi\)
\(338\) 1.61803i 0.0880094i
\(339\) 6.79766 0.369198
\(340\) −1.46080 + 2.36363i −0.0792231 + 0.128186i
\(341\) 2.51132 0.135996
\(342\) 3.79360i 0.205135i
\(343\) 1.00000i 0.0539949i
\(344\) −11.4588 −0.617818
\(345\) 1.78704 + 1.10445i 0.0962110 + 0.0594617i
\(346\) 3.42122 0.183926
\(347\) 28.2949i 1.51895i −0.650537 0.759475i \(-0.725456\pi\)
0.650537 0.759475i \(-0.274544\pi\)
\(348\) 3.52015i 0.188700i
\(349\) 7.82174 0.418688 0.209344 0.977842i \(-0.432867\pi\)
0.209344 + 0.977842i \(0.432867\pi\)
\(350\) 3.61803 + 7.23607i 0.193392 + 0.386784i
\(351\) 1.00000 0.0533761
\(352\) 9.48380i 0.505488i
\(353\) 12.6656i 0.674122i −0.941483 0.337061i \(-0.890567\pi\)
0.941483 0.337061i \(-0.109433\pi\)
\(354\) −3.99698 −0.212437
\(355\) −23.4750 14.5084i −1.24593 0.770024i
\(356\) −0.507661 −0.0269060
\(357\) 2.01062i 0.106413i
\(358\) 30.2147i 1.59690i
\(359\) −4.35926 −0.230073 −0.115036 0.993361i \(-0.536698\pi\)
−0.115036 + 0.993361i \(0.536698\pi\)
\(360\) −2.62866 + 4.25325i −0.138542 + 0.224166i
\(361\) −13.5030 −0.710682
\(362\) 9.83558i 0.516947i
\(363\) 3.13632i 0.164614i
\(364\) −0.618034 −0.0323938
\(365\) −3.26168 + 5.27751i −0.170724 + 0.276238i
\(366\) 6.72841 0.351699
\(367\) 23.7244i 1.23840i −0.785233 0.619201i \(-0.787457\pi\)
0.785233 0.619201i \(-0.212543\pi\)
\(368\) 4.56044i 0.237729i
\(369\) −3.07768 −0.160218
\(370\) −16.9893 10.4999i −0.883230 0.545866i
\(371\) −1.30313 −0.0676551
\(372\) 0.553479i 0.0286966i
\(373\) 12.2595i 0.634773i 0.948296 + 0.317387i \(0.102805\pi\)
−0.948296 + 0.317387i \(0.897195\pi\)
\(374\) −9.12286 −0.471732
\(375\) 11.1352 + 1.00406i 0.575017 + 0.0518493i
\(376\) −13.3328 −0.687587
\(377\) 5.69572i 0.293344i
\(378\) 1.61803i 0.0832227i
\(379\) 9.44164 0.484984 0.242492 0.970153i \(-0.422035\pi\)
0.242492 + 0.970153i \(0.422035\pi\)
\(380\) −2.75621 1.70343i −0.141391 0.0873843i
\(381\) −10.4912 −0.537480
\(382\) 22.5440i 1.15345i
\(383\) 1.81922i 0.0929578i −0.998919 0.0464789i \(-0.985200\pi\)
0.998919 0.0464789i \(-0.0148000\pi\)
\(384\) 13.6180 0.694942
\(385\) −3.29657 + 5.33395i −0.168009 + 0.271844i
\(386\) 5.08611 0.258876
\(387\) 5.12454i 0.260495i
\(388\) 1.22545i 0.0622126i
\(389\) 11.2846 0.572152 0.286076 0.958207i \(-0.407649\pi\)
0.286076 + 0.958207i \(0.407649\pi\)
\(390\) −1.90211 + 3.07768i −0.0963172 + 0.155845i
\(391\) 1.88898 0.0955300
\(392\) 2.23607i 0.112938i
\(393\) 2.09319i 0.105587i
\(394\) 8.27044 0.416659
\(395\) 11.7264 + 7.24733i 0.590021 + 0.364653i
\(396\) 1.73311 0.0870919
\(397\) 21.6658i 1.08738i 0.839287 + 0.543688i \(0.182973\pi\)
−0.839287 + 0.543688i \(0.817027\pi\)
\(398\) 26.7194i 1.33932i
\(399\) 2.34458 0.117376
\(400\) −10.8541 21.7082i −0.542705 1.08541i
\(401\) 15.1128 0.754696 0.377348 0.926072i \(-0.376836\pi\)
0.377348 + 0.926072i \(0.376836\pi\)
\(402\) 25.0467i 1.24922i
\(403\) 0.895549i 0.0446105i
\(404\) −4.77050 −0.237341
\(405\) 1.90211 + 1.17557i 0.0945168 + 0.0584146i
\(406\) 9.21586 0.457376
\(407\) 15.4797i 0.767302i
\(408\) 4.49589i 0.222580i
\(409\) −0.0919651 −0.00454738 −0.00227369 0.999997i \(-0.500724\pi\)
−0.00227369 + 0.999997i \(0.500724\pi\)
\(410\) 5.85410 9.47214i 0.289113 0.467795i
\(411\) 12.2704 0.605256
\(412\) 11.9472i 0.588595i
\(413\) 2.47027i 0.121554i
\(414\) −1.52015 −0.0747112
\(415\) −18.3225 + 29.6464i −0.899417 + 1.45529i
\(416\) 3.38197 0.165815
\(417\) 13.4538i 0.658835i
\(418\) 10.6381i 0.520328i
\(419\) −15.8705 −0.775323 −0.387661 0.921802i \(-0.626717\pi\)
−0.387661 + 0.921802i \(0.626717\pi\)
\(420\) −1.17557 0.726543i −0.0573620 0.0354516i
\(421\) −13.6257 −0.664076 −0.332038 0.943266i \(-0.607736\pi\)
−0.332038 + 0.943266i \(0.607736\pi\)
\(422\) 3.99781i 0.194610i
\(423\) 5.96261i 0.289912i
\(424\) 2.91389 0.141511
\(425\) 8.99177 4.49589i 0.436165 0.218083i
\(426\) 19.9691 0.967504
\(427\) 4.15838i 0.201238i
\(428\) 4.83139i 0.233534i
\(429\) −2.80423 −0.135389
\(430\) −15.7717 9.74746i −0.760580 0.470064i
\(431\) −25.4756 −1.22712 −0.613559 0.789649i \(-0.710263\pi\)
−0.613559 + 0.789649i \(0.710263\pi\)
\(432\) 4.85410i 0.233543i
\(433\) 20.3956i 0.980151i 0.871680 + 0.490076i \(0.163031\pi\)
−0.871680 + 0.490076i \(0.836969\pi\)
\(434\) 1.44903 0.0695556
\(435\) 6.69572 10.8339i 0.321035 0.519446i
\(436\) 0.826225 0.0395690
\(437\) 2.20274i 0.105371i
\(438\) 4.48932i 0.214508i
\(439\) −22.8539 −1.09076 −0.545379 0.838190i \(-0.683614\pi\)
−0.545379 + 0.838190i \(0.683614\pi\)
\(440\) 7.37134 11.9271i 0.351415 0.568602i
\(441\) 1.00000 0.0476190
\(442\) 3.25325i 0.154742i
\(443\) 15.9067i 0.755750i −0.925857 0.377875i \(-0.876655\pi\)
0.925857 0.377875i \(-0.123345\pi\)
\(444\) 3.41164 0.161909
\(445\) 1.56242 + 0.965628i 0.0740658 + 0.0457752i
\(446\) 14.7313 0.697548
\(447\) 12.6216i 0.596980i
\(448\) 4.23607i 0.200135i
\(449\) 23.3073 1.09994 0.549969 0.835185i \(-0.314640\pi\)
0.549969 + 0.835185i \(0.314640\pi\)
\(450\) −7.23607 + 3.61803i −0.341112 + 0.170556i
\(451\) 8.63052 0.406395
\(452\) 4.20119i 0.197607i
\(453\) 0.222429i 0.0104506i
\(454\) 11.3388 0.532158
\(455\) 1.90211 + 1.17557i 0.0891724 + 0.0551116i
\(456\) −5.24263 −0.245509
\(457\) 18.1531i 0.849164i 0.905389 + 0.424582i \(0.139579\pi\)
−0.905389 + 0.424582i \(0.860421\pi\)
\(458\) 32.7465i 1.53014i
\(459\) 2.01062 0.0938478
\(460\) 0.682589 1.10445i 0.0318259 0.0514953i
\(461\) 30.5416 1.42246 0.711232 0.702957i \(-0.248138\pi\)
0.711232 + 0.702957i \(0.248138\pi\)
\(462\) 4.53733i 0.211096i
\(463\) 18.8199i 0.874636i 0.899307 + 0.437318i \(0.144072\pi\)
−0.899307 + 0.437318i \(0.855928\pi\)
\(464\) −27.6476 −1.28351
\(465\) 1.05278 1.70343i 0.0488215 0.0789949i
\(466\) 23.7447 1.09995
\(467\) 14.3948i 0.666114i −0.942907 0.333057i \(-0.891920\pi\)
0.942907 0.333057i \(-0.108080\pi\)
\(468\) 0.618034i 0.0285686i
\(469\) 15.4797 0.714788
\(470\) −18.3510 11.3416i −0.846470 0.523147i
\(471\) −19.5013 −0.898572
\(472\) 5.52369i 0.254249i
\(473\) 14.3704i 0.660751i
\(474\) −9.97510 −0.458171
\(475\) 5.24263 + 10.4853i 0.240548 + 0.481097i
\(476\) −1.24263 −0.0569560
\(477\) 1.30313i 0.0596662i
\(478\) 38.8269i 1.77590i
\(479\) 25.3568 1.15858 0.579292 0.815120i \(-0.303329\pi\)
0.579292 + 0.815120i \(0.303329\pi\)
\(480\) 6.43288 + 3.97574i 0.293620 + 0.181467i
\(481\) −5.52015 −0.251697
\(482\) 40.8231i 1.85944i
\(483\) 0.939503i 0.0427488i
\(484\) 1.93835 0.0881068
\(485\) 2.33094 3.77154i 0.105842 0.171257i
\(486\) −1.61803 −0.0733955
\(487\) 6.55671i 0.297113i −0.988904 0.148556i \(-0.952537\pi\)
0.988904 0.148556i \(-0.0474627\pi\)
\(488\) 9.29843i 0.420920i
\(489\) −1.14712 −0.0518746
\(490\) −1.90211 + 3.07768i −0.0859287 + 0.139036i
\(491\) −36.7728 −1.65954 −0.829768 0.558109i \(-0.811527\pi\)
−0.829768 + 0.558109i \(0.811527\pi\)
\(492\) 1.90211i 0.0857539i
\(493\) 11.4519i 0.515769i
\(494\) −3.79360 −0.170682
\(495\) −5.33395 3.29657i −0.239743 0.148170i
\(496\) −4.34708 −0.195190
\(497\) 12.3416i 0.553595i
\(498\) 25.2188i 1.13008i
\(499\) −33.8073 −1.51342 −0.756712 0.653748i \(-0.773196\pi\)
−0.756712 + 0.653748i \(0.773196\pi\)
\(500\) 0.620541 6.88191i 0.0277515 0.307768i
\(501\) 17.8232 0.796280
\(502\) 19.2533i 0.859315i
\(503\) 2.57397i 0.114768i −0.998352 0.0573838i \(-0.981724\pi\)
0.998352 0.0573838i \(-0.0182759\pi\)
\(504\) −2.23607 −0.0996024
\(505\) 14.6821 + 9.07402i 0.653344 + 0.403789i
\(506\) 4.26284 0.189506
\(507\) 1.00000i 0.0444116i
\(508\) 6.48391i 0.287677i
\(509\) −14.2906 −0.633422 −0.316711 0.948522i \(-0.602578\pi\)
−0.316711 + 0.948522i \(0.602578\pi\)
\(510\) −3.82443 + 6.18806i −0.169349 + 0.274012i
\(511\) −2.77455 −0.122739
\(512\) 5.29180i 0.233867i
\(513\) 2.34458i 0.103516i
\(514\) 8.88546 0.391921
\(515\) −22.7249 + 36.7696i −1.00138 + 1.62026i
\(516\) 3.16714 0.139426
\(517\) 16.7205i 0.735367i
\(518\) 8.93179i 0.392440i
\(519\) 2.11443 0.0928132
\(520\) −4.25325 2.62866i −0.186518 0.115274i
\(521\) 15.9346 0.698108 0.349054 0.937103i \(-0.386503\pi\)
0.349054 + 0.937103i \(0.386503\pi\)
\(522\) 9.21586i 0.403367i
\(523\) 42.2459i 1.84729i 0.383254 + 0.923643i \(0.374803\pi\)
−0.383254 + 0.923643i \(0.625197\pi\)
\(524\) 1.29366 0.0565138
\(525\) 2.23607 + 4.47214i 0.0975900 + 0.195180i
\(526\) 3.86085 0.168341
\(527\) 1.80061i 0.0784358i
\(528\) 13.6120i 0.592386i
\(529\) 22.1173 0.961623
\(530\) 4.01062 + 2.47870i 0.174210 + 0.107668i
\(531\) −2.47027 −0.107201
\(532\) 1.44903i 0.0628233i
\(533\) 3.07768i 0.133309i
\(534\) −1.32907 −0.0575146
\(535\) −9.18985 + 14.8695i −0.397312 + 0.642864i
\(536\) −34.6138 −1.49509
\(537\) 18.6737i 0.805830i
\(538\) 30.1195i 1.29855i
\(539\) −2.80423 −0.120787
\(540\) 0.726543 1.17557i 0.0312654 0.0505885i
\(541\) −32.0729 −1.37892 −0.689460 0.724324i \(-0.742152\pi\)
−0.689460 + 0.724324i \(0.742152\pi\)
\(542\) 4.68259i 0.201134i
\(543\) 6.07872i 0.260863i
\(544\) 6.79985 0.291541
\(545\) −2.54286 1.57157i −0.108924 0.0673188i
\(546\) −1.61803 −0.0692455
\(547\) 19.6201i 0.838895i 0.907779 + 0.419448i \(0.137776\pi\)
−0.907779 + 0.419448i \(0.862224\pi\)
\(548\) 7.58355i 0.323953i
\(549\) 4.15838 0.177476
\(550\) 20.2916 10.1458i 0.865235 0.432618i
\(551\) 13.3540 0.568901
\(552\) 2.10079i 0.0894156i
\(553\) 6.16495i 0.262160i
\(554\) −23.1800 −0.984826
\(555\) −10.4999 6.48932i −0.445698 0.275456i
\(556\) 8.31490 0.352630
\(557\) 0.768499i 0.0325624i 0.999867 + 0.0162812i \(0.00518269\pi\)
−0.999867 + 0.0162812i \(0.994817\pi\)
\(558\) 1.44903i 0.0613422i
\(559\) −5.12454 −0.216745
\(560\) 5.70634 9.23305i 0.241137 0.390168i
\(561\) −5.63824 −0.238047
\(562\) 9.02124i 0.380538i
\(563\) 35.0266i 1.47620i −0.674694 0.738098i \(-0.735724\pi\)
0.674694 0.738098i \(-0.264276\pi\)
\(564\) 3.68510 0.155171
\(565\) −7.99113 + 12.9299i −0.336189 + 0.543966i
\(566\) −30.2311 −1.27071
\(567\) 1.00000i 0.0419961i
\(568\) 27.5966i 1.15793i
\(569\) −26.3124 −1.10307 −0.551537 0.834150i \(-0.685958\pi\)
−0.551537 + 0.834150i \(0.685958\pi\)
\(570\) −7.21586 4.45965i −0.302239 0.186794i
\(571\) −40.3772 −1.68973 −0.844866 0.534978i \(-0.820320\pi\)
−0.844866 + 0.534978i \(0.820320\pi\)
\(572\) 1.73311i 0.0724648i
\(573\) 13.9329i 0.582057i
\(574\) 4.97980 0.207853
\(575\) −4.20158 + 2.10079i −0.175218 + 0.0876091i
\(576\) 4.23607 0.176503
\(577\) 33.7497i 1.40502i 0.711675 + 0.702509i \(0.247937\pi\)
−0.711675 + 0.702509i \(0.752063\pi\)
\(578\) 20.9655i 0.872050i
\(579\) 3.14339 0.130635
\(580\) −6.69572 4.13818i −0.278025 0.171829i
\(581\) −15.5861 −0.646619
\(582\) 3.20826i 0.132987i
\(583\) 3.65427i 0.151344i
\(584\) 6.20409 0.256727
\(585\) −1.17557 + 1.90211i −0.0486039 + 0.0786427i
\(586\) 50.2537 2.07596
\(587\) 35.8502i 1.47970i 0.672774 + 0.739848i \(0.265103\pi\)
−0.672774 + 0.739848i \(0.734897\pi\)
\(588\) 0.618034i 0.0254873i
\(589\) 2.09968 0.0865159
\(590\) 4.69873 7.60271i 0.193444 0.312999i
\(591\) 5.11141 0.210255
\(592\) 26.7954i 1.10128i
\(593\) 28.7642i 1.18120i 0.806963 + 0.590602i \(0.201110\pi\)
−0.806963 + 0.590602i \(0.798890\pi\)
\(594\) 4.53733 0.186169
\(595\) 3.82443 + 2.36363i 0.156786 + 0.0968993i
\(596\) 7.80057 0.319524
\(597\) 16.5135i 0.675851i
\(598\) 1.52015i 0.0621634i
\(599\) 16.1612 0.660327 0.330163 0.943924i \(-0.392896\pi\)
0.330163 + 0.943924i \(0.392896\pi\)
\(600\) −5.00000 10.0000i −0.204124 0.408248i
\(601\) −40.3491 −1.64587 −0.822936 0.568134i \(-0.807666\pi\)
−0.822936 + 0.568134i \(0.807666\pi\)
\(602\) 8.29168i 0.337944i
\(603\) 15.4797i 0.630384i
\(604\) −0.137469 −0.00559352
\(605\) −5.96563 3.68696i −0.242537 0.149896i
\(606\) −12.4893 −0.507344
\(607\) 34.9319i 1.41784i −0.705289 0.708920i \(-0.749183\pi\)
0.705289 0.708920i \(-0.250817\pi\)
\(608\) 7.92928i 0.321575i
\(609\) 5.69572 0.230802
\(610\) −7.90972 + 12.7982i −0.320255 + 0.518184i
\(611\) −5.96261 −0.241221
\(612\) 1.24263i 0.0502304i
\(613\) 36.1928i 1.46181i −0.682477 0.730907i \(-0.739097\pi\)
0.682477 0.730907i \(-0.260903\pi\)
\(614\) −2.79745 −0.112896
\(615\) 3.61803 5.85410i 0.145893 0.236060i
\(616\) 6.27044 0.252643
\(617\) 27.8387i 1.12074i 0.828242 + 0.560371i \(0.189342\pi\)
−0.828242 + 0.560371i \(0.810658\pi\)
\(618\) 31.2781i 1.25819i
\(619\) −14.9807 −0.602126 −0.301063 0.953604i \(-0.597341\pi\)
−0.301063 + 0.953604i \(0.597341\pi\)
\(620\) −1.05278 0.650654i −0.0422807 0.0261309i
\(621\) −0.939503 −0.0377009
\(622\) 28.7015i 1.15083i
\(623\) 0.821412i 0.0329092i
\(624\) 4.85410 0.194320
\(625\) −15.0000 + 20.0000i −0.600000 + 0.800000i
\(626\) 40.2117 1.60718
\(627\) 6.57472i 0.262569i
\(628\) 12.0525i 0.480946i
\(629\) −11.0989 −0.442543
\(630\) −3.07768 1.90211i −0.122618 0.0757820i
\(631\) 10.7583 0.428281 0.214140 0.976803i \(-0.431305\pi\)
0.214140 + 0.976803i \(0.431305\pi\)
\(632\) 13.7852i 0.548348i
\(633\) 2.47078i 0.0982047i
\(634\) 4.21702 0.167479
\(635\) 12.3331 19.9554i 0.489425 0.791907i
\(636\) −0.805379 −0.0319353
\(637\) 1.00000i 0.0396214i
\(638\) 25.8434i 1.02315i
\(639\) 12.3416 0.488225
\(640\) −16.0090 + 25.9030i −0.632810 + 1.02391i
\(641\) −12.9112 −0.509961 −0.254981 0.966946i \(-0.582069\pi\)
−0.254981 + 0.966946i \(0.582069\pi\)
\(642\) 12.6487i 0.499206i
\(643\) 20.8057i 0.820495i −0.911974 0.410248i \(-0.865442\pi\)
0.911974 0.410248i \(-0.134558\pi\)
\(644\) 0.580644 0.0228806
\(645\) −9.74746 6.02426i −0.383806 0.237205i
\(646\) −7.62750 −0.300100
\(647\) 25.7610i 1.01277i 0.862308 + 0.506384i \(0.169018\pi\)
−0.862308 + 0.506384i \(0.830982\pi\)
\(648\) 2.23607i 0.0878410i
\(649\) 6.92720 0.271916
\(650\) −3.61803 7.23607i −0.141911 0.283822i
\(651\) 0.895549 0.0350993
\(652\) 0.708959i 0.0277650i
\(653\) 33.0209i 1.29221i −0.763250 0.646103i \(-0.776398\pi\)
0.763250 0.646103i \(-0.223602\pi\)
\(654\) 2.16308 0.0845833
\(655\) −3.98148 2.46069i −0.155569 0.0961471i
\(656\) −14.9394 −0.583285
\(657\) 2.77455i 0.108246i
\(658\) 9.64771i 0.376107i
\(659\) 36.4979 1.42176 0.710879 0.703315i \(-0.248298\pi\)
0.710879 + 0.703315i \(0.248298\pi\)
\(660\) −2.03739 + 3.29657i −0.0793053 + 0.128319i
\(661\) 35.1393 1.36676 0.683380 0.730063i \(-0.260509\pi\)
0.683380 + 0.730063i \(0.260509\pi\)
\(662\) 49.7615i 1.93404i
\(663\) 2.01062i 0.0780861i
\(664\) 34.8515 1.35250
\(665\) −2.75621 + 4.45965i −0.106881 + 0.172938i
\(666\) 8.93179 0.346100
\(667\) 5.35114i 0.207197i
\(668\) 11.0153i 0.426196i
\(669\) 9.10445 0.351998
\(670\) −47.6417 29.4442i −1.84056 1.13753i
\(671\) −11.6611 −0.450170
\(672\) 3.38197i 0.130462i
\(673\) 10.0652i 0.387985i −0.981003 0.193992i \(-0.937856\pi\)
0.981003 0.193992i \(-0.0621437\pi\)
\(674\) 23.1955 0.893459
\(675\) −4.47214 + 2.23607i −0.172133 + 0.0860663i
\(676\) 0.618034 0.0237705
\(677\) 34.4229i 1.32298i −0.749955 0.661489i \(-0.769925\pi\)
0.749955 0.661489i \(-0.230075\pi\)
\(678\) 10.9988i 0.422408i
\(679\) 1.98281 0.0760934
\(680\) −8.55168 5.28523i −0.327942 0.202679i
\(681\) 7.00779 0.268539
\(682\) 4.06340i 0.155596i
\(683\) 7.19340i 0.275248i −0.990485 0.137624i \(-0.956053\pi\)
0.990485 0.137624i \(-0.0439465\pi\)
\(684\) 1.44903 0.0554050
\(685\) −14.4248 + 23.3398i −0.551142 + 0.891767i
\(686\) −1.61803 −0.0617768
\(687\) 20.2385i 0.772146i
\(688\) 24.8750i 0.948352i
\(689\) 1.30313 0.0496453
\(690\) 1.78704 2.89149i 0.0680315 0.110077i
\(691\) 2.19402 0.0834645 0.0417323 0.999129i \(-0.486712\pi\)
0.0417323 + 0.999129i \(0.486712\pi\)
\(692\) 1.30679i 0.0496767i
\(693\) 2.80423i 0.106524i
\(694\) −45.7821 −1.73787
\(695\) −25.5906 15.8159i −0.970708 0.599931i
\(696\) −12.7360 −0.482757
\(697\) 6.18806i 0.234389i
\(698\) 12.6558i 0.479031i
\(699\) 14.6750 0.555060
\(700\) 2.76393 1.38197i 0.104467 0.0522334i
\(701\) 9.08651 0.343193 0.171596 0.985167i \(-0.445108\pi\)
0.171596 + 0.985167i \(0.445108\pi\)
\(702\) 1.61803i 0.0610688i
\(703\) 12.9424i 0.488132i
\(704\) −11.8789 −0.447703
\(705\) −11.3416 7.00947i −0.427148 0.263992i
\(706\) −20.4934 −0.771278
\(707\) 7.71883i 0.290296i
\(708\) 1.52671i 0.0573773i
\(709\) 17.0828 0.641557 0.320778 0.947154i \(-0.396056\pi\)
0.320778 + 0.947154i \(0.396056\pi\)
\(710\) −23.4750 + 37.9834i −0.881003 + 1.42549i
\(711\) −6.16495 −0.231204
\(712\) 1.83673i 0.0688345i
\(713\) 0.841370i 0.0315096i
\(714\) −3.25325 −0.121750
\(715\) 3.29657 5.33395i 0.123285 0.199479i
\(716\) 11.5410 0.431307
\(717\) 23.9963i 0.896160i
\(718\) 7.05342i 0.263231i
\(719\) 46.0179 1.71618 0.858088 0.513502i \(-0.171652\pi\)
0.858088 + 0.513502i \(0.171652\pi\)
\(720\) 9.23305 + 5.70634i 0.344095 + 0.212663i
\(721\) −19.3309 −0.719922
\(722\) 21.8482i 0.813108i
\(723\) 25.2300i 0.938315i
\(724\) −3.75686 −0.139623
\(725\) 12.7360 + 25.4720i 0.473004 + 0.946007i
\(726\) 5.07467 0.188339
\(727\) 41.4822i 1.53849i −0.638954 0.769245i \(-0.720632\pi\)
0.638954 0.769245i \(-0.279368\pi\)
\(728\) 2.23607i 0.0828742i
\(729\) −1.00000 −0.0370370
\(730\) 8.53920 + 5.27751i 0.316050 + 0.195330i
\(731\) −10.3035 −0.381089
\(732\) 2.57002i 0.0949908i
\(733\) 8.95740i 0.330849i 0.986222 + 0.165425i \(0.0528994\pi\)
−0.986222 + 0.165425i \(0.947101\pi\)
\(734\) −38.3868 −1.41688
\(735\) −1.17557 + 1.90211i −0.0433616 + 0.0701605i
\(736\) −3.17737 −0.117119
\(737\) 43.4087i 1.59898i
\(738\) 4.97980i 0.183309i
\(739\) −41.1448 −1.51354 −0.756769 0.653683i \(-0.773223\pi\)
−0.756769 + 0.653683i \(0.773223\pi\)
\(740\) −4.01062 + 6.48932i −0.147433 + 0.238552i
\(741\) −2.34458 −0.0861302
\(742\) 2.10851i 0.0774058i
\(743\) 51.2608i 1.88058i 0.340379 + 0.940288i \(0.389445\pi\)
−0.340379 + 0.940288i \(0.610555\pi\)
\(744\) −2.00251 −0.0734155
\(745\) −24.0077 14.8376i −0.879573 0.543606i
\(746\) 19.8363 0.726258
\(747\) 15.5861i 0.570264i
\(748\) 3.48462i 0.127410i
\(749\) −7.81736 −0.285640
\(750\) 1.62460 18.0171i 0.0593219 0.657890i
\(751\) −9.69851 −0.353904 −0.176952 0.984220i \(-0.556624\pi\)
−0.176952 + 0.984220i \(0.556624\pi\)
\(752\) 28.9431i 1.05545i
\(753\) 11.8992i 0.433630i
\(754\) −9.21586 −0.335622
\(755\) 0.423085 + 0.261481i 0.0153976 + 0.00951627i
\(756\) 0.618034 0.0224777
\(757\) 42.0784i 1.52936i −0.644408 0.764682i \(-0.722896\pi\)
0.644408 0.764682i \(-0.277104\pi\)
\(758\) 15.2769i 0.554882i
\(759\) 2.63458 0.0956291
\(760\) 6.16308 9.97208i 0.223559 0.361725i
\(761\) −20.1288 −0.729668 −0.364834 0.931072i \(-0.618874\pi\)
−0.364834 + 0.931072i \(0.618874\pi\)
\(762\) 16.9751i 0.614943i
\(763\) 1.33686i 0.0483976i
\(764\) −8.61103 −0.311536
\(765\) −2.36363 + 3.82443i −0.0854571 + 0.138273i
\(766\) −2.94356 −0.106355
\(767\) 2.47027i 0.0891963i
\(768\) 13.5623i 0.489388i
\(769\) −23.5408 −0.848902 −0.424451 0.905451i \(-0.639533\pi\)
−0.424451 + 0.905451i \(0.639533\pi\)
\(770\) 8.63052 + 5.33395i 0.311022 + 0.192222i
\(771\) 5.49151 0.197772
\(772\) 1.94272i 0.0699201i
\(773\) 9.93937i 0.357494i −0.983895 0.178747i \(-0.942796\pi\)
0.983895 0.178747i \(-0.0572044\pi\)
\(774\) 8.29168 0.298038
\(775\) 2.00251 + 4.00501i 0.0719322 + 0.143864i
\(776\) −4.43371 −0.159161
\(777\) 5.52015i 0.198034i
\(778\) 18.2589i 0.654613i
\(779\) 7.21586 0.258535
\(780\) 1.17557 + 0.726543i 0.0420922 + 0.0260144i
\(781\) −34.6085 −1.23839
\(782\) 3.05644i 0.109298i
\(783\) 5.69572i 0.203548i
\(784\) 4.85410 0.173361
\(785\) 22.9252 37.0937i 0.818234 1.32393i
\(786\) 3.38685 0.120805
\(787\) 37.9659i 1.35334i 0.736287 + 0.676670i \(0.236577\pi\)
−0.736287 + 0.676670i \(0.763423\pi\)
\(788\) 3.15903i 0.112536i
\(789\) 2.38614 0.0849487
\(790\) 11.7264 18.9738i 0.417208 0.675056i
\(791\) −6.79766 −0.241697
\(792\) 6.27044i 0.222810i
\(793\) 4.15838i 0.147669i
\(794\) 35.0560 1.24409
\(795\) 2.47870 + 1.53192i 0.0879104 + 0.0543316i
\(796\) 10.2059 0.361738
\(797\) 42.9372i 1.52091i 0.649389 + 0.760456i \(0.275025\pi\)
−0.649389 + 0.760456i \(0.724975\pi\)
\(798\) 3.79360i 0.134292i
\(799\) −11.9886 −0.424125
\(800\) −15.1246 + 7.56231i −0.534736 + 0.267368i
\(801\) −0.821412 −0.0290232
\(802\) 24.4530i 0.863464i
\(803\) 7.78048i 0.274567i
\(804\) 9.56701 0.337402
\(805\) −1.78704 1.10445i −0.0629849 0.0389268i
\(806\) −1.44903 −0.0510398
\(807\) 18.6149i 0.655276i
\(808\) 17.2598i 0.607198i
\(809\) −47.5910 −1.67321 −0.836605 0.547807i \(-0.815463\pi\)
−0.836605 + 0.547807i \(0.815463\pi\)
\(810\) 1.90211 3.07768i 0.0668334 0.108139i
\(811\) −40.0579 −1.40662 −0.703312 0.710882i \(-0.748296\pi\)
−0.703312 + 0.710882i \(0.748296\pi\)
\(812\) 3.52015i 0.123533i
\(813\) 2.89400i 0.101497i
\(814\) −25.0467 −0.877888
\(815\) 1.34852 2.18195i 0.0472366 0.0764305i
\(816\) 9.75976 0.341660
\(817\) 12.0149i 0.420347i
\(818\) 0.148803i 0.00520276i
\(819\) −1.00000 −0.0349428
\(820\) −3.61803 2.23607i −0.126347 0.0780869i
\(821\) −2.41652 −0.0843372 −0.0421686 0.999111i \(-0.513427\pi\)
−0.0421686 + 0.999111i \(0.513427\pi\)
\(822\) 19.8540i 0.692487i
\(823\) 57.1896i 1.99350i −0.0805350 0.996752i \(-0.525663\pi\)
0.0805350 0.996752i \(-0.474337\pi\)
\(824\) 43.2253 1.50582
\(825\) 12.5409 6.27044i 0.436617 0.218309i
\(826\) 3.99698 0.139073
\(827\) 5.71058i 0.198576i −0.995059 0.0992881i \(-0.968343\pi\)
0.995059 0.0992881i \(-0.0316566\pi\)
\(828\) 0.580644i 0.0201788i
\(829\) 32.2179 1.11898 0.559488 0.828839i \(-0.310998\pi\)
0.559488 + 0.828839i \(0.310998\pi\)
\(830\) 47.9689 + 29.6464i 1.66503 + 1.02904i
\(831\) −14.3261 −0.496965
\(832\) 4.23607i 0.146859i
\(833\) 2.01062i 0.0696639i
\(834\) 21.7687 0.753788
\(835\) −20.9524 + 33.9017i −0.725087 + 1.17322i
\(836\) −4.06340 −0.140536
\(837\) 0.895549i 0.0309547i
\(838\) 25.6789i 0.887065i
\(839\) −39.2649 −1.35557 −0.677787 0.735258i \(-0.737061\pi\)
−0.677787 + 0.735258i \(0.737061\pi\)
\(840\) 2.62866 4.25325i 0.0906972 0.146751i
\(841\) 3.44120 0.118662
\(842\) 22.0469i 0.759785i
\(843\) 5.57543i 0.192028i
\(844\) 1.52703 0.0525624
\(845\) −1.90211 1.17557i −0.0654347 0.0404409i
\(846\) 9.64771 0.331695
\(847\) 3.13632i 0.107765i
\(848\) 6.32553i 0.217219i
\(849\) −18.6838 −0.641227
\(850\) −7.27450 14.5490i −0.249513 0.499026i
\(851\) 5.18619 0.177780
\(852\) 7.62750i 0.261314i
\(853\) 13.4267i 0.459722i 0.973224 + 0.229861i \(0.0738271\pi\)
−0.973224 + 0.229861i \(0.926173\pi\)
\(854\) −6.72841 −0.230241
\(855\) −4.45965 2.75621i −0.152517 0.0942606i
\(856\) 17.4801 0.597459
\(857\) 48.4140i 1.65379i −0.562356 0.826895i \(-0.690105\pi\)
0.562356 0.826895i \(-0.309895\pi\)
\(858\) 4.53733i 0.154902i
\(859\) 16.8574 0.575168 0.287584 0.957755i \(-0.407148\pi\)
0.287584 + 0.957755i \(0.407148\pi\)
\(860\) −3.72320 + 6.02426i −0.126960 + 0.205426i
\(861\) 3.07768 0.104887
\(862\) 41.2205i 1.40397i
\(863\) 47.6860i 1.62325i 0.584178 + 0.811625i \(0.301417\pi\)
−0.584178 + 0.811625i \(0.698583\pi\)
\(864\) −3.38197 −0.115057
\(865\) −2.48566 + 4.02189i −0.0845150 + 0.136748i
\(866\) 33.0008 1.12141
\(867\) 12.9574i 0.440056i
\(868\) 0.553479i 0.0187863i
\(869\) 17.2879 0.586452
\(870\) −17.5296 10.8339i −0.594310 0.367304i
\(871\) −15.4797 −0.524511
\(872\) 2.98931i 0.101231i
\(873\) 1.98281i 0.0671081i
\(874\) 3.56410 0.120558
\(875\) −11.1352 1.00406i −0.376437 0.0339433i
\(876\) −1.71477 −0.0579367
\(877\) 5.74990i 0.194160i 0.995277 + 0.0970801i \(0.0309503\pi\)
−0.995277 + 0.0970801i \(0.969050\pi\)
\(878\) 36.9784i 1.24796i
\(879\) 31.0585 1.04758
\(880\) −25.8916 16.0019i −0.872804 0.539423i
\(881\) −16.9157 −0.569905 −0.284952 0.958542i \(-0.591978\pi\)
−0.284952 + 0.958542i \(0.591978\pi\)
\(882\) 1.61803i 0.0544820i
\(883\) 8.09873i 0.272544i 0.990671 + 0.136272i \(0.0435121\pi\)
−0.990671 + 0.136272i \(0.956488\pi\)
\(884\) 1.24263 0.0417943
\(885\) 2.90398 4.69873i 0.0976161 0.157946i
\(886\) −25.7376 −0.864671
\(887\) 44.5786i 1.49680i −0.663247 0.748401i \(-0.730822\pi\)
0.663247 0.748401i \(-0.269178\pi\)
\(888\) 12.3434i 0.414218i
\(889\) 10.4912 0.351863
\(890\) 1.56242 2.52805i 0.0523724 0.0847403i
\(891\) 2.80423 0.0939451
\(892\) 5.62686i 0.188401i
\(893\) 13.9798i 0.467816i
\(894\) 20.4221 0.683019
\(895\) −35.5195 21.9523i −1.18729 0.733784i
\(896\) −13.6180 −0.454947
\(897\) 0.939503i 0.0313691i
\(898\) 37.7119i 1.25846i
\(899\) 5.10079 0.170121
\(900\) 1.38197 + 2.76393i 0.0460655 + 0.0921311i
\(901\) 2.62010 0.0872882
\(902\) 13.9645i 0.464966i
\(903\) 5.12454i 0.170534i
\(904\) 15.2000 0.505546
\(905\) 11.5624 + 7.14597i 0.384348 + 0.237540i
\(906\) −0.359898 −0.0119568
\(907\) 24.1868i 0.803110i −0.915835 0.401555i \(-0.868470\pi\)
0.915835 0.401555i \(-0.131530\pi\)
\(908\) 4.33105i 0.143731i
\(909\) −7.71883 −0.256017
\(910\) 1.90211 3.07768i 0.0630544 0.102024i
\(911\) 9.27522 0.307302 0.153651 0.988125i \(-0.450897\pi\)
0.153651 + 0.988125i \(0.450897\pi\)
\(912\) 11.3808i 0.376856i
\(913\) 43.7068i 1.44648i
\(914\) 29.3723 0.971548
\(915\) −4.88847 + 7.90972i −0.161608 + 0.261487i
\(916\) −12.5081 −0.413278
\(917\) 2.09319i 0.0691231i
\(918\) 3.25325i 0.107373i
\(919\) 2.91209 0.0960611 0.0480305 0.998846i \(-0.484706\pi\)
0.0480305 + 0.998846i \(0.484706\pi\)
\(920\) 3.99594 + 2.46963i 0.131742 + 0.0814212i
\(921\) −1.72892 −0.0569698
\(922\) 49.4173i 1.62747i
\(923\) 12.3416i 0.406227i
\(924\) −1.73311 −0.0570150
\(925\) 24.6868 12.3434i 0.811699 0.405849i
\(926\) 30.4513 1.00069
\(927\) 19.3309i 0.634911i
\(928\) 19.2627i 0.632330i
\(929\) −35.9359 −1.17902 −0.589510 0.807761i \(-0.700679\pi\)
−0.589510 + 0.807761i \(0.700679\pi\)
\(930\) −2.75621 1.70343i −0.0903799 0.0558578i
\(931\) −2.34458 −0.0768404
\(932\) 9.06965i 0.297086i
\(933\) 17.7385i 0.580733i
\(934\) −23.2914 −0.762116
\(935\) 6.62815 10.7246i 0.216764 0.350731i
\(936\) 2.23607 0.0730882
\(937\) 25.0249i 0.817527i 0.912640 + 0.408763i \(0.134040\pi\)
−0.912640 + 0.408763i \(0.865960\pi\)
\(938\) 25.0467i 0.817805i
\(939\) 24.8522 0.811021
\(940\) −4.33209 + 7.00947i −0.141297 + 0.228624i
\(941\) 12.7170 0.414562 0.207281 0.978281i \(-0.433538\pi\)
0.207281 + 0.978281i \(0.433538\pi\)
\(942\) 31.5538i 1.02808i
\(943\) 2.89149i 0.0941599i
\(944\) −11.9909 −0.390272
\(945\) −1.90211 1.17557i −0.0618757 0.0382413i
\(946\) −23.2518 −0.755980
\(947\) 42.4461i 1.37931i −0.724137 0.689656i \(-0.757762\pi\)
0.724137 0.689656i \(-0.242238\pi\)
\(948\) 3.81015i 0.123748i
\(949\) 2.77455 0.0900658
\(950\) 16.9655 8.48276i 0.550434 0.275217i
\(951\) 2.60626 0.0845138
\(952\) 4.49589i 0.145713i
\(953\) 44.1291i 1.42948i 0.699389 + 0.714741i \(0.253456\pi\)
−0.699389 + 0.714741i \(0.746544\pi\)
\(954\) −2.10851 −0.0682655
\(955\) 26.5020 + 16.3792i 0.857585 + 0.530017i
\(956\) 14.8306 0.479654
\(957\) 15.9721i 0.516304i
\(958\) 41.0282i 1.32556i
\(959\) −12.2704 −0.396233
\(960\) −4.97980 + 8.05748i −0.160722 + 0.260054i
\(961\) −30.1980 −0.974129
\(962\) 8.93179i 0.287972i
\(963\) 7.81736i 0.251911i
\(964\) −15.5930 −0.502217
\(965\) −3.69528 + 5.97908i −0.118955 + 0.192474i
\(966\) 1.52015 0.0489099
\(967\) 5.88712i 0.189317i −0.995510 0.0946585i \(-0.969824\pi\)
0.995510 0.0946585i \(-0.0301759\pi\)
\(968\) 7.01302i 0.225407i
\(969\) −4.71406 −0.151437
\(970\) −6.10247 3.77154i −0.195939 0.121097i
\(971\) 44.7978 1.43763 0.718814 0.695202i \(-0.244685\pi\)
0.718814 + 0.695202i \(0.244685\pi\)
\(972\) 0.618034i 0.0198234i
\(973\) 13.4538i 0.431309i
\(974\) −10.6090 −0.339934
\(975\) −2.23607 4.47214i −0.0716115 0.143223i
\(976\) 20.1852 0.646113
\(977\) 7.32375i 0.234308i 0.993114 + 0.117154i \(0.0373770\pi\)
−0.993114 + 0.117154i \(0.962623\pi\)
\(978\) 1.85608i 0.0593509i
\(979\) 2.30343 0.0736178
\(980\) 1.17557 + 0.726543i 0.0375522 + 0.0232085i
\(981\) 1.33686 0.0426826
\(982\) 59.4997i 1.89871i
\(983\) 15.2176i 0.485367i 0.970106 + 0.242683i \(0.0780276\pi\)
−0.970106 + 0.242683i \(0.921972\pi\)
\(984\) −6.88191 −0.219387
\(985\) −6.00883 + 9.72249i −0.191457 + 0.309784i
\(986\) −18.5296 −0.590103
\(987\) 5.96261i 0.189792i
\(988\) 1.44903i 0.0460997i
\(989\) 4.81452 0.153093
\(990\) −5.33395 + 8.63052i −0.169524 + 0.274296i
\(991\) 1.65833 0.0526785 0.0263393 0.999653i \(-0.491615\pi\)
0.0263393 + 0.999653i \(0.491615\pi\)
\(992\) 3.02871i 0.0961618i
\(993\) 30.7543i 0.975958i
\(994\) −19.9691 −0.633380
\(995\) −31.4105 19.4127i −0.995779 0.615425i
\(996\) −9.63271 −0.305224
\(997\) 2.49409i 0.0789887i −0.999220 0.0394943i \(-0.987425\pi\)
0.999220 0.0394943i \(-0.0125747\pi\)
\(998\) 54.7014i 1.73154i
\(999\) 5.52015 0.174650
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 1365.2.f.c.274.2 8
5.2 odd 4 6825.2.a.bm.1.4 4
5.3 odd 4 6825.2.a.be.1.2 4
5.4 even 2 inner 1365.2.f.c.274.8 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1365.2.f.c.274.2 8 1.1 even 1 trivial
1365.2.f.c.274.8 yes 8 5.4 even 2 inner
6825.2.a.be.1.2 4 5.3 odd 4
6825.2.a.bm.1.4 4 5.2 odd 4