Properties

Label 855.2.k.i.406.4
Level $855$
Weight $2$
Character 855.406
Analytic conductor $6.827$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 285)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 406.4
Root \(-0.690702 + 1.19633i\) of defining polynomial
Character \(\chi\) \(=\) 855.406
Dual form 855.2.k.i.676.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.690702 + 1.19633i) q^{2} +(0.0458624 - 0.0794360i) q^{4} +(0.500000 + 0.866025i) q^{5} -4.36264 q^{7} +2.88952 q^{8} +(-0.690702 + 1.19633i) q^{10} +4.31625 q^{11} +(3.18132 - 5.51021i) q^{13} +(-3.01329 - 5.21916i) q^{14} +(1.90407 + 3.29794i) q^{16} +(2.85821 + 4.95056i) q^{17} +(2.97100 + 3.18954i) q^{19} +0.0917248 q^{20} +(2.98124 + 5.16366i) q^{22} +(-0.289678 + 0.501738i) q^{23} +(-0.500000 + 0.866025i) q^{25} +8.78938 q^{26} +(-0.200081 + 0.346551i) q^{28} +(-1.77672 + 3.07737i) q^{29} +1.18345 q^{31} +(0.259229 - 0.448998i) q^{32} +(-3.94834 + 6.83872i) q^{34} +(-2.18132 - 3.77816i) q^{35} -6.54609 q^{37} +(-1.76367 + 5.75732i) q^{38} +(1.44476 + 2.50239i) q^{40} +(-0.381403 - 0.660610i) q^{41} +(3.18132 + 5.51021i) q^{43} +(0.197954 - 0.342866i) q^{44} -0.800326 q^{46} +(-1.36632 + 2.36653i) q^{47} +12.0327 q^{49} -1.38140 q^{50} +(-0.291806 - 0.505423i) q^{52} +(2.56853 - 4.44882i) q^{53} +(2.15812 + 3.73798i) q^{55} -12.6059 q^{56} -4.90874 q^{58} +(1.91484 + 3.31660i) q^{59} +(6.01053 - 10.4105i) q^{61} +(0.817411 + 1.41580i) q^{62} +8.33247 q^{64} +6.36264 q^{65} +(2.00213 - 3.46779i) q^{67} +0.524337 q^{68} +(3.01329 - 5.21916i) q^{70} +(1.53953 + 2.66654i) q^{71} +(-4.04320 - 7.00303i) q^{73} +(-4.52140 - 7.83129i) q^{74} +(0.389622 - 0.0897246i) q^{76} -18.8303 q^{77} +(-5.66836 - 9.81790i) q^{79} +(-1.90407 + 3.29794i) q^{80} +(0.526872 - 0.912569i) q^{82} -7.67889 q^{83} +(-2.85821 + 4.95056i) q^{85} +(-4.39469 + 7.61182i) q^{86} +12.4719 q^{88} +(4.92093 - 8.52330i) q^{89} +(-13.8790 + 24.0391i) q^{91} +(0.0265707 + 0.0460218i) q^{92} -3.77487 q^{94} +(-1.27672 + 4.16773i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(8.31098 + 14.3950i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29}+ \cdots + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.690702 + 1.19633i 0.488400 + 0.845933i 0.999911 0.0133433i \(-0.00424744\pi\)
−0.511511 + 0.859277i \(0.670914\pi\)
\(3\) 0 0
\(4\) 0.0458624 0.0794360i 0.0229312 0.0397180i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −4.36264 −1.64892 −0.824462 0.565917i \(-0.808522\pi\)
−0.824462 + 0.565917i \(0.808522\pi\)
\(8\) 2.88952 1.02160
\(9\) 0 0
\(10\) −0.690702 + 1.19633i −0.218419 + 0.378313i
\(11\) 4.31625 1.30140 0.650699 0.759336i \(-0.274476\pi\)
0.650699 + 0.759336i \(0.274476\pi\)
\(12\) 0 0
\(13\) 3.18132 5.51021i 0.882340 1.52826i 0.0336075 0.999435i \(-0.489300\pi\)
0.848732 0.528823i \(-0.177366\pi\)
\(14\) −3.01329 5.21916i −0.805334 1.39488i
\(15\) 0 0
\(16\) 1.90407 + 3.29794i 0.476017 + 0.824486i
\(17\) 2.85821 + 4.95056i 0.693217 + 1.20069i 0.970778 + 0.239979i \(0.0771405\pi\)
−0.277561 + 0.960708i \(0.589526\pi\)
\(18\) 0 0
\(19\) 2.97100 + 3.18954i 0.681594 + 0.731730i
\(20\) 0.0917248 0.0205103
\(21\) 0 0
\(22\) 2.98124 + 5.16366i 0.635603 + 1.10090i
\(23\) −0.289678 + 0.501738i −0.0604021 + 0.104620i −0.894645 0.446777i \(-0.852572\pi\)
0.834243 + 0.551397i \(0.185905\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 8.78938 1.72374
\(27\) 0 0
\(28\) −0.200081 + 0.346551i −0.0378118 + 0.0654920i
\(29\) −1.77672 + 3.07737i −0.329929 + 0.571454i −0.982497 0.186276i \(-0.940358\pi\)
0.652569 + 0.757730i \(0.273691\pi\)
\(30\) 0 0
\(31\) 1.18345 0.212554 0.106277 0.994337i \(-0.466107\pi\)
0.106277 + 0.994337i \(0.466107\pi\)
\(32\) 0.259229 0.448998i 0.0458257 0.0793724i
\(33\) 0 0
\(34\) −3.94834 + 6.83872i −0.677134 + 1.17283i
\(35\) −2.18132 3.77816i −0.368711 0.638626i
\(36\) 0 0
\(37\) −6.54609 −1.07617 −0.538086 0.842890i \(-0.680852\pi\)
−0.538086 + 0.842890i \(0.680852\pi\)
\(38\) −1.76367 + 5.75732i −0.286105 + 0.933960i
\(39\) 0 0
\(40\) 1.44476 + 2.50239i 0.228436 + 0.395663i
\(41\) −0.381403 0.660610i −0.0595652 0.103170i 0.834705 0.550697i \(-0.185638\pi\)
−0.894270 + 0.447527i \(0.852305\pi\)
\(42\) 0 0
\(43\) 3.18132 + 5.51021i 0.485147 + 0.840299i 0.999854 0.0170666i \(-0.00543274\pi\)
−0.514707 + 0.857366i \(0.672099\pi\)
\(44\) 0.197954 0.342866i 0.0298426 0.0516890i
\(45\) 0 0
\(46\) −0.800326 −0.118002
\(47\) −1.36632 + 2.36653i −0.199298 + 0.345194i −0.948301 0.317372i \(-0.897200\pi\)
0.749003 + 0.662567i \(0.230533\pi\)
\(48\) 0 0
\(49\) 12.0327 1.71895
\(50\) −1.38140 −0.195360
\(51\) 0 0
\(52\) −0.291806 0.505423i −0.0404662 0.0700896i
\(53\) 2.56853 4.44882i 0.352814 0.611092i −0.633927 0.773393i \(-0.718558\pi\)
0.986741 + 0.162300i \(0.0518914\pi\)
\(54\) 0 0
\(55\) 2.15812 + 3.73798i 0.291001 + 0.504029i
\(56\) −12.6059 −1.68454
\(57\) 0 0
\(58\) −4.90874 −0.644549
\(59\) 1.91484 + 3.31660i 0.249291 + 0.431785i 0.963329 0.268322i \(-0.0864691\pi\)
−0.714038 + 0.700107i \(0.753136\pi\)
\(60\) 0 0
\(61\) 6.01053 10.4105i 0.769569 1.33293i −0.168227 0.985748i \(-0.553804\pi\)
0.937797 0.347185i \(-0.112862\pi\)
\(62\) 0.817411 + 1.41580i 0.103811 + 0.179806i
\(63\) 0 0
\(64\) 8.33247 1.04156
\(65\) 6.36264 0.789189
\(66\) 0 0
\(67\) 2.00213 3.46779i 0.244599 0.423658i −0.717420 0.696641i \(-0.754677\pi\)
0.962019 + 0.272983i \(0.0880104\pi\)
\(68\) 0.524337 0.0635852
\(69\) 0 0
\(70\) 3.01329 5.21916i 0.360156 0.623809i
\(71\) 1.53953 + 2.66654i 0.182708 + 0.316460i 0.942802 0.333354i \(-0.108180\pi\)
−0.760094 + 0.649814i \(0.774847\pi\)
\(72\) 0 0
\(73\) −4.04320 7.00303i −0.473221 0.819643i 0.526309 0.850293i \(-0.323575\pi\)
−0.999530 + 0.0306504i \(0.990242\pi\)
\(74\) −4.52140 7.83129i −0.525602 0.910369i
\(75\) 0 0
\(76\) 0.389622 0.0897246i 0.0446927 0.0102921i
\(77\) −18.8303 −2.14591
\(78\) 0 0
\(79\) −5.66836 9.81790i −0.637741 1.10460i −0.985927 0.167174i \(-0.946536\pi\)
0.348187 0.937425i \(-0.386798\pi\)
\(80\) −1.90407 + 3.29794i −0.212881 + 0.368721i
\(81\) 0 0
\(82\) 0.526872 0.912569i 0.0581833 0.100776i
\(83\) −7.67889 −0.842868 −0.421434 0.906859i \(-0.638473\pi\)
−0.421434 + 0.906859i \(0.638473\pi\)
\(84\) 0 0
\(85\) −2.85821 + 4.95056i −0.310016 + 0.536963i
\(86\) −4.39469 + 7.61182i −0.473891 + 0.820804i
\(87\) 0 0
\(88\) 12.4719 1.32951
\(89\) 4.92093 8.52330i 0.521618 0.903468i −0.478066 0.878324i \(-0.658662\pi\)
0.999684 0.0251445i \(-0.00800458\pi\)
\(90\) 0 0
\(91\) −13.8790 + 24.0391i −1.45491 + 2.51998i
\(92\) 0.0265707 + 0.0460218i 0.00277019 + 0.00479811i
\(93\) 0 0
\(94\) −3.77487 −0.389348
\(95\) −1.27672 + 4.16773i −0.130989 + 0.427600i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 8.31098 + 14.3950i 0.839536 + 1.45412i
\(99\) 0 0
\(100\) 0.0458624 + 0.0794360i 0.00458624 + 0.00794360i
\(101\) −2.24985 + 3.89685i −0.223868 + 0.387751i −0.955979 0.293434i \(-0.905202\pi\)
0.732111 + 0.681185i \(0.238535\pi\)
\(102\) 0 0
\(103\) −16.0717 −1.58359 −0.791796 0.610785i \(-0.790854\pi\)
−0.791796 + 0.610785i \(0.790854\pi\)
\(104\) 9.19248 15.9218i 0.901397 1.56127i
\(105\) 0 0
\(106\) 7.09634 0.689258
\(107\) −13.6789 −1.32239 −0.661194 0.750215i \(-0.729950\pi\)
−0.661194 + 0.750215i \(0.729950\pi\)
\(108\) 0 0
\(109\) 4.48337 + 7.76542i 0.429429 + 0.743792i 0.996823 0.0796541i \(-0.0253816\pi\)
−0.567394 + 0.823447i \(0.692048\pi\)
\(110\) −2.98124 + 5.16366i −0.284250 + 0.492336i
\(111\) 0 0
\(112\) −8.30677 14.3878i −0.784916 1.35951i
\(113\) −6.42952 −0.604838 −0.302419 0.953175i \(-0.597794\pi\)
−0.302419 + 0.953175i \(0.597794\pi\)
\(114\) 0 0
\(115\) −0.579357 −0.0540253
\(116\) 0.162969 + 0.282271i 0.0151313 + 0.0262082i
\(117\) 0 0
\(118\) −2.64517 + 4.58156i −0.243507 + 0.421767i
\(119\) −12.4693 21.5975i −1.14306 1.97984i
\(120\) 0 0
\(121\) 7.63001 0.693637
\(122\) 16.6059 1.50343
\(123\) 0 0
\(124\) 0.0542759 0.0940086i 0.00487412 0.00844222i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 3.09172 5.35502i 0.274346 0.475182i −0.695624 0.718406i \(-0.744872\pi\)
0.969970 + 0.243225i \(0.0782052\pi\)
\(128\) 5.23680 + 9.07040i 0.462872 + 0.801717i
\(129\) 0 0
\(130\) 4.39469 + 7.61182i 0.385440 + 0.667601i
\(131\) 8.69872 + 15.0666i 0.760010 + 1.31638i 0.942845 + 0.333233i \(0.108140\pi\)
−0.182834 + 0.983144i \(0.558527\pi\)
\(132\) 0 0
\(133\) −12.9614 13.9148i −1.12390 1.20657i
\(134\) 5.53149 0.477848
\(135\) 0 0
\(136\) 8.25883 + 14.3047i 0.708189 + 1.22662i
\(137\) 7.85821 13.6108i 0.671372 1.16285i −0.306143 0.951985i \(-0.599039\pi\)
0.977515 0.210865i \(-0.0676280\pi\)
\(138\) 0 0
\(139\) −3.27672 + 5.67545i −0.277928 + 0.481385i −0.970870 0.239608i \(-0.922981\pi\)
0.692942 + 0.720994i \(0.256314\pi\)
\(140\) −0.400163 −0.0338199
\(141\) 0 0
\(142\) −2.12671 + 3.68357i −0.178469 + 0.309118i
\(143\) 13.7314 23.7834i 1.14828 1.98887i
\(144\) 0 0
\(145\) −3.55344 −0.295097
\(146\) 5.58529 9.67401i 0.462242 0.800627i
\(147\) 0 0
\(148\) −0.300220 + 0.519996i −0.0246779 + 0.0427434i
\(149\) 2.87560 + 4.98069i 0.235578 + 0.408034i 0.959441 0.281911i \(-0.0909682\pi\)
−0.723862 + 0.689945i \(0.757635\pi\)
\(150\) 0 0
\(151\) −12.6673 −1.03085 −0.515425 0.856935i \(-0.672366\pi\)
−0.515425 + 0.856935i \(0.672366\pi\)
\(152\) 8.58475 + 9.21622i 0.696315 + 0.747534i
\(153\) 0 0
\(154\) −13.0061 22.5272i −1.04806 1.81529i
\(155\) 0.591725 + 1.02490i 0.0475285 + 0.0823217i
\(156\) 0 0
\(157\) −0.689434 1.19414i −0.0550228 0.0953024i 0.837202 0.546894i \(-0.184190\pi\)
−0.892225 + 0.451591i \(0.850856\pi\)
\(158\) 7.83030 13.5625i 0.622945 1.07897i
\(159\) 0 0
\(160\) 0.518458 0.0409877
\(161\) 1.26376 2.18890i 0.0995986 0.172510i
\(162\) 0 0
\(163\) −11.6120 −0.909523 −0.454762 0.890613i \(-0.650276\pi\)
−0.454762 + 0.890613i \(0.650276\pi\)
\(164\) −0.0699683 −0.00546361
\(165\) 0 0
\(166\) −5.30382 9.18649i −0.411657 0.713010i
\(167\) −10.1557 + 17.5902i −0.785871 + 1.36117i 0.142606 + 0.989780i \(0.454452\pi\)
−0.928477 + 0.371390i \(0.878881\pi\)
\(168\) 0 0
\(169\) −13.7416 23.8012i −1.05705 1.83086i
\(170\) −7.89667 −0.605647
\(171\) 0 0
\(172\) 0.583613 0.0445000
\(173\) −6.12545 10.6096i −0.465709 0.806632i 0.533524 0.845785i \(-0.320867\pi\)
−0.999233 + 0.0391527i \(0.987534\pi\)
\(174\) 0 0
\(175\) 2.18132 3.77816i 0.164892 0.285602i
\(176\) 8.21843 + 14.2347i 0.619488 + 1.07298i
\(177\) 0 0
\(178\) 13.5956 1.01903
\(179\) 19.1840 1.43388 0.716941 0.697134i \(-0.245542\pi\)
0.716941 + 0.697134i \(0.245542\pi\)
\(180\) 0 0
\(181\) 1.61492 2.79713i 0.120036 0.207909i −0.799746 0.600339i \(-0.795032\pi\)
0.919782 + 0.392430i \(0.128366\pi\)
\(182\) −38.3449 −2.84231
\(183\) 0 0
\(184\) −0.837031 + 1.44978i −0.0617067 + 0.106879i
\(185\) −3.27305 5.66908i −0.240639 0.416799i
\(186\) 0 0
\(187\) 12.3367 + 21.3678i 0.902151 + 1.56257i
\(188\) 0.125325 + 0.217070i 0.00914029 + 0.0158314i
\(189\) 0 0
\(190\) −5.86782 + 1.35128i −0.425696 + 0.0980320i
\(191\) −27.5509 −1.99352 −0.996758 0.0804642i \(-0.974360\pi\)
−0.996758 + 0.0804642i \(0.974360\pi\)
\(192\) 0 0
\(193\) −11.1233 19.2662i −0.800674 1.38681i −0.919173 0.393854i \(-0.871141\pi\)
0.118499 0.992954i \(-0.462192\pi\)
\(194\) 1.38140 2.39266i 0.0991790 0.171783i
\(195\) 0 0
\(196\) 0.551847 0.955827i 0.0394176 0.0682734i
\(197\) −12.6627 −0.902178 −0.451089 0.892479i \(-0.648964\pi\)
−0.451089 + 0.892479i \(0.648964\pi\)
\(198\) 0 0
\(199\) 4.38478 7.59466i 0.310829 0.538371i −0.667713 0.744418i \(-0.732727\pi\)
0.978542 + 0.206048i \(0.0660602\pi\)
\(200\) −1.44476 + 2.50239i −0.102160 + 0.176946i
\(201\) 0 0
\(202\) −6.21590 −0.437349
\(203\) 7.75120 13.4255i 0.544028 0.942284i
\(204\) 0 0
\(205\) 0.381403 0.660610i 0.0266384 0.0461390i
\(206\) −11.1008 19.2271i −0.773426 1.33961i
\(207\) 0 0
\(208\) 24.2298 1.68004
\(209\) 12.8236 + 13.7668i 0.887025 + 0.952272i
\(210\) 0 0
\(211\) −3.93389 6.81369i −0.270820 0.469074i 0.698252 0.715852i \(-0.253962\pi\)
−0.969072 + 0.246778i \(0.920628\pi\)
\(212\) −0.235598 0.408067i −0.0161809 0.0280262i
\(213\) 0 0
\(214\) −9.44803 16.3645i −0.645854 1.11865i
\(215\) −3.18132 + 5.51021i −0.216964 + 0.375793i
\(216\) 0 0
\(217\) −5.16297 −0.350485
\(218\) −6.19334 + 10.7272i −0.419466 + 0.726536i
\(219\) 0 0
\(220\) 0.395907 0.0266921
\(221\) 36.3715 2.44661
\(222\) 0 0
\(223\) 13.6768 + 23.6889i 0.915864 + 1.58632i 0.805631 + 0.592417i \(0.201826\pi\)
0.110232 + 0.993906i \(0.464840\pi\)
\(224\) −1.13092 + 1.95882i −0.0755631 + 0.130879i
\(225\) 0 0
\(226\) −4.44088 7.69183i −0.295403 0.511653i
\(227\) 25.0922 1.66543 0.832713 0.553704i \(-0.186786\pi\)
0.832713 + 0.553704i \(0.186786\pi\)
\(228\) 0 0
\(229\) 4.98530 0.329438 0.164719 0.986341i \(-0.447328\pi\)
0.164719 + 0.986341i \(0.447328\pi\)
\(230\) −0.400163 0.693102i −0.0263860 0.0457018i
\(231\) 0 0
\(232\) −5.13386 + 8.89211i −0.337055 + 0.583796i
\(233\) 6.39821 + 11.0820i 0.419161 + 0.726007i 0.995855 0.0909523i \(-0.0289911\pi\)
−0.576695 + 0.816960i \(0.695658\pi\)
\(234\) 0 0
\(235\) −2.73264 −0.178258
\(236\) 0.351277 0.0228662
\(237\) 0 0
\(238\) 17.2252 29.8349i 1.11654 1.93391i
\(239\) −12.8049 −0.828283 −0.414142 0.910212i \(-0.635918\pi\)
−0.414142 + 0.910212i \(0.635918\pi\)
\(240\) 0 0
\(241\) 0.546395 0.946383i 0.0351964 0.0609619i −0.847891 0.530171i \(-0.822128\pi\)
0.883087 + 0.469209i \(0.155461\pi\)
\(242\) 5.27006 + 9.12801i 0.338772 + 0.586771i
\(243\) 0 0
\(244\) −0.551315 0.954905i −0.0352943 0.0611315i
\(245\) 6.01633 + 10.4206i 0.384369 + 0.665747i
\(246\) 0 0
\(247\) 27.0267 6.22389i 1.71967 0.396017i
\(248\) 3.41960 0.217145
\(249\) 0 0
\(250\) −0.690702 1.19633i −0.0436838 0.0756626i
\(251\) 3.04764 5.27867i 0.192365 0.333187i −0.753668 0.657255i \(-0.771717\pi\)
0.946034 + 0.324068i \(0.105051\pi\)
\(252\) 0 0
\(253\) −1.25032 + 2.16563i −0.0786072 + 0.136152i
\(254\) 8.54184 0.535963
\(255\) 0 0
\(256\) 1.09835 1.90239i 0.0686467 0.118900i
\(257\) 2.31016 4.00131i 0.144104 0.249595i −0.784934 0.619579i \(-0.787303\pi\)
0.929038 + 0.369984i \(0.120637\pi\)
\(258\) 0 0
\(259\) 28.5583 1.77452
\(260\) 0.291806 0.505423i 0.0180971 0.0313450i
\(261\) 0 0
\(262\) −12.0164 + 20.8131i −0.742378 + 1.28584i
\(263\) −15.0247 26.0236i −0.926465 1.60468i −0.789189 0.614151i \(-0.789499\pi\)
−0.137276 0.990533i \(-0.543835\pi\)
\(264\) 0 0
\(265\) 5.13706 0.315567
\(266\) 7.69425 25.1171i 0.471765 1.54003i
\(267\) 0 0
\(268\) −0.183645 0.318082i −0.0112179 0.0194300i
\(269\) −0.105639 0.182973i −0.00644095 0.0111561i 0.862787 0.505568i \(-0.168717\pi\)
−0.869228 + 0.494412i \(0.835384\pi\)
\(270\) 0 0
\(271\) 3.70364 + 6.41489i 0.224980 + 0.389677i 0.956313 0.292343i \(-0.0944350\pi\)
−0.731333 + 0.682020i \(0.761102\pi\)
\(272\) −10.8844 + 18.8524i −0.659966 + 1.14309i
\(273\) 0 0
\(274\) 21.7107 1.31159
\(275\) −2.15812 + 3.73798i −0.130140 + 0.225409i
\(276\) 0 0
\(277\) −29.0668 −1.74646 −0.873229 0.487310i \(-0.837978\pi\)
−0.873229 + 0.487310i \(0.837978\pi\)
\(278\) −9.05295 −0.542960
\(279\) 0 0
\(280\) −6.30296 10.9171i −0.376674 0.652419i
\(281\) 5.73796 9.93843i 0.342298 0.592877i −0.642561 0.766234i \(-0.722128\pi\)
0.984859 + 0.173357i \(0.0554615\pi\)
\(282\) 0 0
\(283\) 13.6662 + 23.6706i 0.812373 + 1.40707i 0.911199 + 0.411966i \(0.135158\pi\)
−0.0988265 + 0.995105i \(0.531509\pi\)
\(284\) 0.282426 0.0167589
\(285\) 0 0
\(286\) 37.9371 2.24327
\(287\) 1.66393 + 2.88201i 0.0982185 + 0.170119i
\(288\) 0 0
\(289\) −7.83868 + 13.5770i −0.461099 + 0.798647i
\(290\) −2.45437 4.25109i −0.144125 0.249633i
\(291\) 0 0
\(292\) −0.741724 −0.0434061
\(293\) −13.0211 −0.760698 −0.380349 0.924843i \(-0.624196\pi\)
−0.380349 + 0.924843i \(0.624196\pi\)
\(294\) 0 0
\(295\) −1.91484 + 3.31660i −0.111486 + 0.193100i
\(296\) −18.9150 −1.09941
\(297\) 0 0
\(298\) −3.97236 + 6.88034i −0.230113 + 0.398567i
\(299\) 1.84312 + 3.19238i 0.106590 + 0.184620i
\(300\) 0 0
\(301\) −13.8790 24.0391i −0.799971 1.38559i
\(302\) −8.74932 15.1543i −0.503467 0.872030i
\(303\) 0 0
\(304\) −4.86193 + 15.8713i −0.278851 + 0.910281i
\(305\) 12.0211 0.688324
\(306\) 0 0
\(307\) −2.01267 3.48604i −0.114869 0.198959i 0.802858 0.596170i \(-0.203312\pi\)
−0.917727 + 0.397211i \(0.869978\pi\)
\(308\) −0.863601 + 1.49580i −0.0492082 + 0.0852312i
\(309\) 0 0
\(310\) −0.817411 + 1.41580i −0.0464258 + 0.0804119i
\(311\) −15.3578 −0.870860 −0.435430 0.900223i \(-0.643404\pi\)
−0.435430 + 0.900223i \(0.643404\pi\)
\(312\) 0 0
\(313\) −10.9800 + 19.0179i −0.620625 + 1.07495i 0.368744 + 0.929531i \(0.379788\pi\)
−0.989369 + 0.145424i \(0.953546\pi\)
\(314\) 0.952387 1.64958i 0.0537463 0.0930913i
\(315\) 0 0
\(316\) −1.03986 −0.0584967
\(317\) −12.0640 + 20.8954i −0.677580 + 1.17360i 0.298127 + 0.954526i \(0.403638\pi\)
−0.975708 + 0.219077i \(0.929695\pi\)
\(318\) 0 0
\(319\) −7.66877 + 13.2827i −0.429369 + 0.743689i
\(320\) 4.16624 + 7.21613i 0.232900 + 0.403394i
\(321\) 0 0
\(322\) 3.49154 0.194576
\(323\) −7.29826 + 23.8245i −0.406086 + 1.32563i
\(324\) 0 0
\(325\) 3.18132 + 5.51021i 0.176468 + 0.305652i
\(326\) −8.02044 13.8918i −0.444211 0.769396i
\(327\) 0 0
\(328\) −1.10207 1.90884i −0.0608517 0.105398i
\(329\) 5.96076 10.3243i 0.328627 0.569199i
\(330\) 0 0
\(331\) −24.8416 −1.36542 −0.682710 0.730690i \(-0.739199\pi\)
−0.682710 + 0.730690i \(0.739199\pi\)
\(332\) −0.352173 + 0.609981i −0.0193280 + 0.0334771i
\(333\) 0 0
\(334\) −28.0582 −1.53528
\(335\) 4.00426 0.218776
\(336\) 0 0
\(337\) −0.284651 0.493031i −0.0155059 0.0268571i 0.858168 0.513368i \(-0.171603\pi\)
−0.873674 + 0.486511i \(0.838269\pi\)
\(338\) 18.9827 32.8790i 1.03252 1.78838i
\(339\) 0 0
\(340\) 0.262168 + 0.454089i 0.0142181 + 0.0246264i
\(341\) 5.10806 0.276617
\(342\) 0 0
\(343\) −21.9557 −1.18550
\(344\) 9.19248 + 15.9218i 0.495625 + 0.858448i
\(345\) 0 0
\(346\) 8.46172 14.6561i 0.454905 0.787918i
\(347\) 4.68682 + 8.11782i 0.251602 + 0.435787i 0.963967 0.266022i \(-0.0857093\pi\)
−0.712365 + 0.701809i \(0.752376\pi\)
\(348\) 0 0
\(349\) 14.8297 0.793815 0.396907 0.917859i \(-0.370083\pi\)
0.396907 + 0.917859i \(0.370083\pi\)
\(350\) 6.02657 0.322134
\(351\) 0 0
\(352\) 1.11890 1.93799i 0.0596375 0.103295i
\(353\) −31.2650 −1.66407 −0.832034 0.554725i \(-0.812824\pi\)
−0.832034 + 0.554725i \(0.812824\pi\)
\(354\) 0 0
\(355\) −1.53953 + 2.66654i −0.0817097 + 0.141525i
\(356\) −0.451372 0.781799i −0.0239226 0.0414352i
\(357\) 0 0
\(358\) 13.2504 + 22.9504i 0.700307 + 1.21297i
\(359\) 5.43561 + 9.41475i 0.286880 + 0.496892i 0.973063 0.230537i \(-0.0740484\pi\)
−0.686183 + 0.727429i \(0.740715\pi\)
\(360\) 0 0
\(361\) −1.34631 + 18.9522i −0.0708586 + 0.997486i
\(362\) 4.46172 0.234503
\(363\) 0 0
\(364\) 1.27305 + 2.20498i 0.0667258 + 0.115572i
\(365\) 4.04320 7.00303i 0.211631 0.366555i
\(366\) 0 0
\(367\) 9.36477 16.2203i 0.488837 0.846691i −0.511080 0.859533i \(-0.670755\pi\)
0.999918 + 0.0128422i \(0.00408791\pi\)
\(368\) −2.20627 −0.115010
\(369\) 0 0
\(370\) 4.52140 7.83129i 0.235056 0.407129i
\(371\) −11.2056 + 19.4086i −0.581764 + 1.00765i
\(372\) 0 0
\(373\) 29.3275 1.51852 0.759259 0.650788i \(-0.225561\pi\)
0.759259 + 0.650788i \(0.225561\pi\)
\(374\) −17.0420 + 29.5176i −0.881221 + 1.52632i
\(375\) 0 0
\(376\) −3.94800 + 6.83813i −0.203602 + 0.352650i
\(377\) 11.3046 + 19.5802i 0.582219 + 1.00843i
\(378\) 0 0
\(379\) −10.6486 −0.546980 −0.273490 0.961875i \(-0.588178\pi\)
−0.273490 + 0.961875i \(0.588178\pi\)
\(380\) 0.272515 + 0.292560i 0.0139797 + 0.0150080i
\(381\) 0 0
\(382\) −19.0295 32.9600i −0.973632 1.68638i
\(383\) 4.63977 + 8.03632i 0.237081 + 0.410637i 0.959876 0.280426i \(-0.0904759\pi\)
−0.722794 + 0.691063i \(0.757143\pi\)
\(384\) 0 0
\(385\) −9.41513 16.3075i −0.479839 0.831106i
\(386\) 15.3658 26.6143i 0.782098 1.35463i
\(387\) 0 0
\(388\) −0.183450 −0.00931325
\(389\) 0.666237 1.15396i 0.0337796 0.0585079i −0.848641 0.528969i \(-0.822579\pi\)
0.882421 + 0.470461i \(0.155912\pi\)
\(390\) 0 0
\(391\) −3.31184 −0.167487
\(392\) 34.7686 1.75608
\(393\) 0 0
\(394\) −8.74613 15.1487i −0.440623 0.763182i
\(395\) 5.66836 9.81790i 0.285206 0.493992i
\(396\) 0 0
\(397\) 15.8324 + 27.4225i 0.794605 + 1.37630i 0.923090 + 0.384584i \(0.125655\pi\)
−0.128485 + 0.991711i \(0.541011\pi\)
\(398\) 12.1143 0.607235
\(399\) 0 0
\(400\) −3.80814 −0.190407
\(401\) −2.44425 4.23356i −0.122060 0.211414i 0.798520 0.601968i \(-0.205617\pi\)
−0.920580 + 0.390554i \(0.872283\pi\)
\(402\) 0 0
\(403\) 3.76493 6.52106i 0.187545 0.324837i
\(404\) 0.206367 + 0.357438i 0.0102671 + 0.0177832i
\(405\) 0 0
\(406\) 21.4151 1.06281
\(407\) −28.2546 −1.40053
\(408\) 0 0
\(409\) 11.3941 19.7351i 0.563400 0.975837i −0.433797 0.901011i \(-0.642826\pi\)
0.997197 0.0748266i \(-0.0238403\pi\)
\(410\) 1.05374 0.0520407
\(411\) 0 0
\(412\) −0.737087 + 1.27667i −0.0363137 + 0.0628972i
\(413\) −8.35377 14.4692i −0.411062 0.711980i
\(414\) 0 0
\(415\) −3.83945 6.65012i −0.188471 0.326441i
\(416\) −1.64938 2.85682i −0.0808677 0.140067i
\(417\) 0 0
\(418\) −7.61243 + 24.8500i −0.372336 + 1.21545i
\(419\) −30.8809 −1.50863 −0.754316 0.656512i \(-0.772031\pi\)
−0.754316 + 0.656512i \(0.772031\pi\)
\(420\) 0 0
\(421\) −13.2891 23.0174i −0.647671 1.12180i −0.983678 0.179939i \(-0.942410\pi\)
0.336007 0.941859i \(-0.390923\pi\)
\(422\) 5.43429 9.41246i 0.264537 0.458191i
\(423\) 0 0
\(424\) 7.42180 12.8549i 0.360434 0.624291i
\(425\) −5.71641 −0.277287
\(426\) 0 0
\(427\) −26.2218 + 45.4175i −1.26896 + 2.19791i
\(428\) −0.627347 + 1.08660i −0.0303240 + 0.0525227i
\(429\) 0 0
\(430\) −8.78938 −0.423861
\(431\) 8.23718 14.2672i 0.396771 0.687228i −0.596554 0.802573i \(-0.703464\pi\)
0.993325 + 0.115345i \(0.0367974\pi\)
\(432\) 0 0
\(433\) 18.4021 31.8733i 0.884346 1.53173i 0.0378851 0.999282i \(-0.487938\pi\)
0.846461 0.532450i \(-0.178729\pi\)
\(434\) −3.56607 6.17662i −0.171177 0.296487i
\(435\) 0 0
\(436\) 0.822473 0.0393893
\(437\) −2.46095 + 0.566723i −0.117723 + 0.0271100i
\(438\) 0 0
\(439\) −4.79140 8.29895i −0.228681 0.396087i 0.728736 0.684794i \(-0.240108\pi\)
−0.957417 + 0.288707i \(0.906775\pi\)
\(440\) 6.23593 + 10.8010i 0.297287 + 0.514915i
\(441\) 0 0
\(442\) 25.1219 + 43.5123i 1.19492 + 2.06967i
\(443\) −11.1218 + 19.2635i −0.528412 + 0.915236i 0.471040 + 0.882112i \(0.343879\pi\)
−0.999451 + 0.0331236i \(0.989454\pi\)
\(444\) 0 0
\(445\) 9.84186 0.466549
\(446\) −18.8931 + 32.7239i −0.894616 + 1.54952i
\(447\) 0 0
\(448\) −36.3516 −1.71745
\(449\) 0.491188 0.0231806 0.0115903 0.999933i \(-0.496311\pi\)
0.0115903 + 0.999933i \(0.496311\pi\)
\(450\) 0 0
\(451\) −1.64623 2.85136i −0.0775180 0.134265i
\(452\) −0.294873 + 0.510736i −0.0138697 + 0.0240230i
\(453\) 0 0
\(454\) 17.3312 + 30.0185i 0.813394 + 1.40884i
\(455\) −27.7579 −1.30131
\(456\) 0 0
\(457\) 13.2607 0.620311 0.310156 0.950686i \(-0.399619\pi\)
0.310156 + 0.950686i \(0.399619\pi\)
\(458\) 3.44336 + 5.96407i 0.160897 + 0.278683i
\(459\) 0 0
\(460\) −0.0265707 + 0.0460218i −0.00123887 + 0.00214578i
\(461\) 11.6867 + 20.2420i 0.544305 + 0.942763i 0.998650 + 0.0519379i \(0.0165398\pi\)
−0.454346 + 0.890825i \(0.650127\pi\)
\(462\) 0 0
\(463\) −0.981649 −0.0456211 −0.0228105 0.999740i \(-0.507261\pi\)
−0.0228105 + 0.999740i \(0.507261\pi\)
\(464\) −13.5320 −0.628207
\(465\) 0 0
\(466\) −8.83851 + 15.3087i −0.409436 + 0.709164i
\(467\) 18.8498 0.872264 0.436132 0.899883i \(-0.356348\pi\)
0.436132 + 0.899883i \(0.356348\pi\)
\(468\) 0 0
\(469\) −8.73457 + 15.1287i −0.403325 + 0.698579i
\(470\) −1.88744 3.26914i −0.0870610 0.150794i
\(471\) 0 0
\(472\) 5.53296 + 9.58337i 0.254675 + 0.441110i
\(473\) 13.7314 + 23.7834i 0.631369 + 1.09356i
\(474\) 0 0
\(475\) −4.24772 + 0.978193i −0.194899 + 0.0448826i
\(476\) −2.28750 −0.104847
\(477\) 0 0
\(478\) −8.84440 15.3189i −0.404533 0.700672i
\(479\) 10.0795 17.4583i 0.460546 0.797688i −0.538443 0.842662i \(-0.680987\pi\)
0.998988 + 0.0449739i \(0.0143205\pi\)
\(480\) 0 0
\(481\) −20.8252 + 36.0704i −0.949549 + 1.64467i
\(482\) 1.50958 0.0687596
\(483\) 0 0
\(484\) 0.349931 0.606098i 0.0159059 0.0275499i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) 2.79159 0.126499 0.0632494 0.997998i \(-0.479854\pi\)
0.0632494 + 0.997998i \(0.479854\pi\)
\(488\) 17.3675 30.0814i 0.786190 1.36172i
\(489\) 0 0
\(490\) −8.31098 + 14.3950i −0.375452 + 0.650302i
\(491\) 2.88904 + 5.00397i 0.130381 + 0.225826i 0.923823 0.382819i \(-0.125047\pi\)
−0.793443 + 0.608645i \(0.791713\pi\)
\(492\) 0 0
\(493\) −20.3129 −0.914849
\(494\) 26.1132 + 28.0341i 1.17489 + 1.26131i
\(495\) 0 0
\(496\) 2.25337 + 3.90295i 0.101179 + 0.175248i
\(497\) −6.71641 11.6332i −0.301272 0.521819i
\(498\) 0 0
\(499\) −6.39792 11.0815i −0.286410 0.496077i 0.686540 0.727092i \(-0.259129\pi\)
−0.972950 + 0.231015i \(0.925795\pi\)
\(500\) −0.0458624 + 0.0794360i −0.00205103 + 0.00355249i
\(501\) 0 0
\(502\) 8.42004 0.375805
\(503\) 15.8339 27.4252i 0.706000 1.22283i −0.260329 0.965520i \(-0.583831\pi\)
0.966329 0.257308i \(-0.0828356\pi\)
\(504\) 0 0
\(505\) −4.49970 −0.200234
\(506\) −3.45440 −0.153567
\(507\) 0 0
\(508\) −0.283588 0.491189i −0.0125822 0.0217930i
\(509\) −2.74405 + 4.75283i −0.121628 + 0.210665i −0.920410 0.390955i \(-0.872145\pi\)
0.798782 + 0.601621i \(0.205478\pi\)
\(510\) 0 0
\(511\) 17.6391 + 30.5517i 0.780306 + 1.35153i
\(512\) 23.9817 1.05985
\(513\) 0 0
\(514\) 6.38252 0.281521
\(515\) −8.03585 13.9185i −0.354102 0.613323i
\(516\) 0 0
\(517\) −5.89737 + 10.2145i −0.259366 + 0.449235i
\(518\) 19.7252 + 34.1651i 0.866678 + 1.50113i
\(519\) 0 0
\(520\) 18.3850 0.806234
\(521\) −8.28086 −0.362791 −0.181396 0.983410i \(-0.558061\pi\)
−0.181396 + 0.983410i \(0.558061\pi\)
\(522\) 0 0
\(523\) −5.77584 + 10.0040i −0.252560 + 0.437446i −0.964230 0.265067i \(-0.914606\pi\)
0.711670 + 0.702514i \(0.247939\pi\)
\(524\) 1.59578 0.0697118
\(525\) 0 0
\(526\) 20.7552 35.9491i 0.904970 1.56745i
\(527\) 3.38254 + 5.85874i 0.147346 + 0.255211i
\(528\) 0 0
\(529\) 11.3322 + 19.6279i 0.492703 + 0.853387i
\(530\) 3.54817 + 6.14561i 0.154123 + 0.266948i
\(531\) 0 0
\(532\) −1.69978 + 0.391436i −0.0736948 + 0.0169709i
\(533\) −4.85347 −0.210227
\(534\) 0 0
\(535\) −6.83945 11.8463i −0.295695 0.512159i
\(536\) 5.78518 10.0202i 0.249882 0.432808i
\(537\) 0 0
\(538\) 0.145931 0.252759i 0.00629152 0.0108972i
\(539\) 51.9360 2.23704
\(540\) 0 0
\(541\) 12.9374 22.4083i 0.556224 0.963409i −0.441583 0.897220i \(-0.645583\pi\)
0.997807 0.0661881i \(-0.0210837\pi\)
\(542\) −5.11622 + 8.86155i −0.219760 + 0.380636i
\(543\) 0 0
\(544\) 2.96372 0.127069
\(545\) −4.48337 + 7.76542i −0.192046 + 0.332634i
\(546\) 0 0
\(547\) −3.20287 + 5.54753i −0.136945 + 0.237195i −0.926339 0.376692i \(-0.877062\pi\)
0.789394 + 0.613887i \(0.210395\pi\)
\(548\) −0.720793 1.24845i −0.0307907 0.0533311i
\(549\) 0 0
\(550\) −5.96248 −0.254241
\(551\) −15.0940 + 3.47595i −0.643028 + 0.148080i
\(552\) 0 0
\(553\) 24.7291 + 42.8320i 1.05159 + 1.82140i
\(554\) −20.0765 34.7736i −0.852970 1.47739i
\(555\) 0 0
\(556\) 0.300557 + 0.520580i 0.0127464 + 0.0220775i
\(557\) −1.76281 + 3.05327i −0.0746925 + 0.129371i −0.900953 0.433918i \(-0.857131\pi\)
0.826260 + 0.563289i \(0.190464\pi\)
\(558\) 0 0
\(559\) 40.4832 1.71226
\(560\) 8.30677 14.3878i 0.351025 0.607993i
\(561\) 0 0
\(562\) 15.8529 0.668713
\(563\) 30.7179 1.29461 0.647303 0.762232i \(-0.275897\pi\)
0.647303 + 0.762232i \(0.275897\pi\)
\(564\) 0 0
\(565\) −3.21476 5.56813i −0.135246 0.234253i
\(566\) −18.8786 + 32.6986i −0.793525 + 1.37443i
\(567\) 0 0
\(568\) 4.44849 + 7.70501i 0.186654 + 0.323295i
\(569\) −9.17896 −0.384802 −0.192401 0.981316i \(-0.561627\pi\)
−0.192401 + 0.981316i \(0.561627\pi\)
\(570\) 0 0
\(571\) −7.49001 −0.313447 −0.156724 0.987643i \(-0.550093\pi\)
−0.156724 + 0.987643i \(0.550093\pi\)
\(572\) −1.25951 2.18153i −0.0526627 0.0912145i
\(573\) 0 0
\(574\) −2.29855 + 3.98121i −0.0959398 + 0.166173i
\(575\) −0.289678 0.501738i −0.0120804 0.0209239i
\(576\) 0 0
\(577\) 32.6093 1.35754 0.678771 0.734350i \(-0.262513\pi\)
0.678771 + 0.734350i \(0.262513\pi\)
\(578\) −21.6568 −0.900803
\(579\) 0 0
\(580\) −0.162969 + 0.282271i −0.00676694 + 0.0117207i
\(581\) 33.5003 1.38983
\(582\) 0 0
\(583\) 11.0864 19.2022i 0.459152 0.795275i
\(584\) −11.6829 20.2354i −0.483442 0.837346i
\(585\) 0 0
\(586\) −8.99367 15.5775i −0.371525 0.643500i
\(587\) −9.19474 15.9258i −0.379508 0.657326i 0.611483 0.791258i \(-0.290573\pi\)
−0.990991 + 0.133931i \(0.957240\pi\)
\(588\) 0 0
\(589\) 3.51603 + 3.77466i 0.144875 + 0.155532i
\(590\) −5.29033 −0.217800
\(591\) 0 0
\(592\) −12.4642 21.5886i −0.512276 0.887288i
\(593\) 0.208669 0.361425i 0.00856900 0.0148419i −0.861709 0.507403i \(-0.830606\pi\)
0.870278 + 0.492561i \(0.163939\pi\)
\(594\) 0 0
\(595\) 12.4693 21.5975i 0.511193 0.885412i
\(596\) 0.527528 0.0216084
\(597\) 0 0
\(598\) −2.54609 + 4.40996i −0.104118 + 0.180337i
\(599\) −19.4828 + 33.7452i −0.796045 + 1.37879i 0.126129 + 0.992014i \(0.459745\pi\)
−0.922174 + 0.386776i \(0.873589\pi\)
\(600\) 0 0
\(601\) 10.0358 0.409367 0.204683 0.978828i \(-0.434383\pi\)
0.204683 + 0.978828i \(0.434383\pi\)
\(602\) 19.1725 33.2077i 0.781411 1.35344i
\(603\) 0 0
\(604\) −0.580953 + 1.00624i −0.0236386 + 0.0409433i
\(605\) 3.81500 + 6.60778i 0.155102 + 0.268644i
\(606\) 0 0
\(607\) −6.25423 −0.253851 −0.126926 0.991912i \(-0.540511\pi\)
−0.126926 + 0.991912i \(0.540511\pi\)
\(608\) 2.20227 0.507152i 0.0893137 0.0205677i
\(609\) 0 0
\(610\) 8.30296 + 14.3812i 0.336177 + 0.582276i
\(611\) 8.69340 + 15.0574i 0.351697 + 0.609157i
\(612\) 0 0
\(613\) −14.9371 25.8719i −0.603306 1.04496i −0.992317 0.123723i \(-0.960517\pi\)
0.389011 0.921233i \(-0.372817\pi\)
\(614\) 2.78031 4.81563i 0.112204 0.194343i
\(615\) 0 0
\(616\) −54.4103 −2.19225
\(617\) −15.3197 + 26.5346i −0.616749 + 1.06824i 0.373326 + 0.927700i \(0.378217\pi\)
−0.990075 + 0.140540i \(0.955116\pi\)
\(618\) 0 0
\(619\) 21.1480 0.850011 0.425006 0.905191i \(-0.360272\pi\)
0.425006 + 0.905191i \(0.360272\pi\)
\(620\) 0.108552 0.00435954
\(621\) 0 0
\(622\) −10.6076 18.3730i −0.425328 0.736690i
\(623\) −21.4683 + 37.1841i −0.860108 + 1.48975i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −30.3356 −1.21245
\(627\) 0 0
\(628\) −0.126476 −0.00504696
\(629\) −18.7101 32.4068i −0.746020 1.29214i
\(630\) 0 0
\(631\) 13.0124 22.5381i 0.518014 0.897227i −0.481767 0.876299i \(-0.660005\pi\)
0.999781 0.0209274i \(-0.00666189\pi\)
\(632\) −16.3788 28.3690i −0.651515 1.12846i
\(633\) 0 0
\(634\) −33.3304 −1.32372
\(635\) 6.18345 0.245383
\(636\) 0 0
\(637\) 38.2798 66.3025i 1.51670 2.62700i
\(638\) −21.1873 −0.838815
\(639\) 0 0
\(640\) −5.23680 + 9.07040i −0.207003 + 0.358539i
\(641\) −9.59982 16.6274i −0.379170 0.656742i 0.611771 0.791035i \(-0.290457\pi\)
−0.990942 + 0.134292i \(0.957124\pi\)
\(642\) 0 0
\(643\) −4.27305 7.40113i −0.168513 0.291872i 0.769385 0.638786i \(-0.220563\pi\)
−0.937897 + 0.346914i \(0.887230\pi\)
\(644\) −0.115919 0.200777i −0.00456783 0.00791172i
\(645\) 0 0
\(646\) −33.5429 + 7.72446i −1.31973 + 0.303915i
\(647\) 21.6966 0.852983 0.426492 0.904492i \(-0.359749\pi\)
0.426492 + 0.904492i \(0.359749\pi\)
\(648\) 0 0
\(649\) 8.26493 + 14.3153i 0.324427 + 0.561924i
\(650\) −4.39469 + 7.61182i −0.172374 + 0.298560i
\(651\) 0 0
\(652\) −0.532555 + 0.922413i −0.0208565 + 0.0361245i
\(653\) 4.39011 0.171798 0.0858991 0.996304i \(-0.472624\pi\)
0.0858991 + 0.996304i \(0.472624\pi\)
\(654\) 0 0
\(655\) −8.69872 + 15.0666i −0.339887 + 0.588702i
\(656\) 1.45244 2.51569i 0.0567081 0.0982213i
\(657\) 0 0
\(658\) 16.4684 0.642006
\(659\) −7.57327 + 13.1173i −0.295013 + 0.510977i −0.974988 0.222258i \(-0.928657\pi\)
0.679975 + 0.733235i \(0.261991\pi\)
\(660\) 0 0
\(661\) −3.65794 + 6.33574i −0.142277 + 0.246432i −0.928354 0.371698i \(-0.878776\pi\)
0.786076 + 0.618129i \(0.212109\pi\)
\(662\) −17.1582 29.7188i −0.666871 1.15505i
\(663\) 0 0
\(664\) −22.1883 −0.861072
\(665\) 5.56988 18.1823i 0.215991 0.705080i
\(666\) 0 0
\(667\) −1.02936 1.78290i −0.0398568 0.0690340i
\(668\) 0.931530 + 1.61346i 0.0360420 + 0.0624265i
\(669\) 0 0
\(670\) 2.76575 + 4.79041i 0.106850 + 0.185070i
\(671\) 25.9429 44.9345i 1.00152 1.73468i
\(672\) 0 0
\(673\) 39.7027 1.53043 0.765213 0.643777i \(-0.222634\pi\)
0.765213 + 0.643777i \(0.222634\pi\)
\(674\) 0.393218 0.681074i 0.0151462 0.0262340i
\(675\) 0 0
\(676\) −2.52090 −0.0969575
\(677\) 9.45197 0.363269 0.181634 0.983366i \(-0.441861\pi\)
0.181634 + 0.983366i \(0.441861\pi\)
\(678\) 0 0
\(679\) 4.36264 + 7.55632i 0.167423 + 0.289985i
\(680\) −8.25883 + 14.3047i −0.316712 + 0.548561i
\(681\) 0 0
\(682\) 3.52815 + 6.11093i 0.135100 + 0.234000i
\(683\) 6.27600 0.240145 0.120072 0.992765i \(-0.461687\pi\)
0.120072 + 0.992765i \(0.461687\pi\)
\(684\) 0 0
\(685\) 15.7164 0.600493
\(686\) −15.1648 26.2663i −0.578996 1.00285i
\(687\) 0 0
\(688\) −12.1149 + 20.9836i −0.461877 + 0.799994i
\(689\) −16.3426 28.3063i −0.622604 1.07838i
\(690\) 0 0
\(691\) −33.8913 −1.28929 −0.644643 0.764483i \(-0.722994\pi\)
−0.644643 + 0.764483i \(0.722994\pi\)
\(692\) −1.12371 −0.0427171
\(693\) 0 0
\(694\) −6.47439 + 11.2140i −0.245765 + 0.425677i
\(695\) −6.55344 −0.248586
\(696\) 0 0
\(697\) 2.18026 3.77632i 0.0825832 0.143038i
\(698\) 10.2429 + 17.7412i 0.387699 + 0.671514i
\(699\) 0 0
\(700\) −0.200081 0.346551i −0.00756237 0.0130984i
\(701\) 20.1520 + 34.9043i 0.761131 + 1.31832i 0.942268 + 0.334860i \(0.108689\pi\)
−0.181136 + 0.983458i \(0.557978\pi\)
\(702\) 0 0
\(703\) −19.4484 20.8790i −0.733512 0.787467i
\(704\) 35.9650 1.35548
\(705\) 0 0
\(706\) −21.5948 37.4033i −0.812730 1.40769i
\(707\) 9.81529 17.0006i 0.369142 0.639373i
\(708\) 0 0
\(709\) 2.63706 4.56751i 0.0990367 0.171537i −0.812249 0.583310i \(-0.801757\pi\)
0.911286 + 0.411774i \(0.135091\pi\)
\(710\) −4.25342 −0.159628
\(711\) 0 0
\(712\) 14.2191 24.6282i 0.532884 0.922981i
\(713\) −0.342820 + 0.593782i −0.0128387 + 0.0222373i
\(714\) 0 0
\(715\) 27.4628 1.02705
\(716\) 0.879826 1.52390i 0.0328806 0.0569509i
\(717\) 0 0
\(718\) −7.50877 + 13.0056i −0.280225 + 0.485364i
\(719\) 11.8834 + 20.5827i 0.443176 + 0.767604i 0.997923 0.0644151i \(-0.0205182\pi\)
−0.554747 + 0.832019i \(0.687185\pi\)
\(720\) 0 0
\(721\) 70.1151 2.61122
\(722\) −23.6030 + 11.4797i −0.878414 + 0.427231i
\(723\) 0 0
\(724\) −0.148128 0.256566i −0.00550515 0.00953520i
\(725\) −1.77672 3.07737i −0.0659858 0.114291i
\(726\) 0 0
\(727\) 16.9225 + 29.3106i 0.627620 + 1.08707i 0.988028 + 0.154275i \(0.0493040\pi\)
−0.360408 + 0.932795i \(0.617363\pi\)
\(728\) −40.1035 + 69.4613i −1.48634 + 2.57441i
\(729\) 0 0
\(730\) 11.1706 0.413442
\(731\) −18.1857 + 31.4986i −0.672624 + 1.16502i
\(732\) 0 0
\(733\) 24.6249 0.909542 0.454771 0.890608i \(-0.349721\pi\)
0.454771 + 0.890608i \(0.349721\pi\)
\(734\) 25.8731 0.954992
\(735\) 0 0
\(736\) 0.150186 + 0.260130i 0.00553594 + 0.00958853i
\(737\) 8.64168 14.9678i 0.318320 0.551347i
\(738\) 0 0
\(739\) −9.22966 15.9862i −0.339518 0.588063i 0.644824 0.764331i \(-0.276931\pi\)
−0.984342 + 0.176268i \(0.943597\pi\)
\(740\) −0.600439 −0.0220726
\(741\) 0 0
\(742\) −30.9588 −1.13653
\(743\) −4.47864 7.75723i −0.164305 0.284585i 0.772103 0.635497i \(-0.219205\pi\)
−0.936408 + 0.350912i \(0.885872\pi\)
\(744\) 0 0
\(745\) −2.87560 + 4.98069i −0.105354 + 0.182478i
\(746\) 20.2565 + 35.0853i 0.741644 + 1.28457i
\(747\) 0 0
\(748\) 2.26317 0.0827497
\(749\) 59.6761 2.18052
\(750\) 0 0
\(751\) 14.6128 25.3101i 0.533228 0.923578i −0.466019 0.884775i \(-0.654312\pi\)
0.999247 0.0388032i \(-0.0123545\pi\)
\(752\) −10.4063 −0.379477
\(753\) 0 0
\(754\) −15.6163 + 27.0482i −0.568711 + 0.985037i
\(755\) −6.33364 10.9702i −0.230505 0.399246i
\(756\) 0 0
\(757\) −9.33886 16.1754i −0.339427 0.587904i 0.644898 0.764268i \(-0.276900\pi\)
−0.984325 + 0.176364i \(0.943566\pi\)
\(758\) −7.35499 12.7392i −0.267145 0.462709i
\(759\) 0 0
\(760\) −3.68911 + 12.0427i −0.133818 + 0.436836i
\(761\) −41.5952 −1.50782 −0.753912 0.656975i \(-0.771836\pi\)
−0.753912 + 0.656975i \(0.771836\pi\)
\(762\) 0 0
\(763\) −19.5593 33.8778i −0.708096 1.22646i
\(764\) −1.26355 + 2.18854i −0.0457137 + 0.0791785i
\(765\) 0 0
\(766\) −6.40940 + 11.1014i −0.231581 + 0.401110i
\(767\) 24.3669 0.879838
\(768\) 0 0
\(769\) −17.6255 + 30.5282i −0.635590 + 1.10087i 0.350800 + 0.936450i \(0.385910\pi\)
−0.986390 + 0.164424i \(0.947424\pi\)
\(770\) 13.0061 22.5272i 0.468707 0.811824i
\(771\) 0 0
\(772\) −2.04057 −0.0734417
\(773\) 23.9762 41.5280i 0.862364 1.49366i −0.00727780 0.999974i \(-0.502317\pi\)
0.869641 0.493684i \(-0.164350\pi\)
\(774\) 0 0
\(775\) −0.591725 + 1.02490i −0.0212554 + 0.0368154i
\(776\) −2.88952 5.00479i −0.103728 0.179661i
\(777\) 0 0
\(778\) 1.84068 0.0659917
\(779\) 0.973891 3.17917i 0.0348933 0.113906i
\(780\) 0 0
\(781\) 6.64499 + 11.5095i 0.237776 + 0.411841i
\(782\) −2.28750 3.96206i −0.0818007 0.141683i
\(783\) 0 0
\(784\) 22.9110 + 39.6830i 0.818250 + 1.41725i
\(785\) 0.689434 1.19414i 0.0246070 0.0426205i
\(786\) 0 0
\(787\) −5.26074 −0.187525 −0.0937626 0.995595i \(-0.529889\pi\)
−0.0937626 + 0.995595i \(0.529889\pi\)
\(788\) −0.580741 + 1.00587i −0.0206880 + 0.0358327i
\(789\) 0 0
\(790\) 15.6606 0.557179
\(791\) 28.0497 0.997333
\(792\) 0 0
\(793\) −38.2429 66.2386i −1.35804 2.35220i
\(794\) −21.8709 + 37.8815i −0.776170 + 1.34437i
\(795\) 0 0
\(796\) −0.402193 0.696619i −0.0142554 0.0246910i
\(797\) 21.0174 0.744474 0.372237 0.928138i \(-0.378591\pi\)
0.372237 + 0.928138i \(0.378591\pi\)
\(798\) 0 0
\(799\) −15.6209 −0.552627
\(800\) 0.259229 + 0.448998i 0.00916514 + 0.0158745i
\(801\) 0 0
\(802\) 3.37649 5.84825i 0.119228 0.206509i
\(803\) −17.4515 30.2268i −0.615849 1.06668i
\(804\) 0 0
\(805\) 2.52753 0.0890837
\(806\) 10.4018 0.366387
\(807\) 0 0
\(808\) −6.50098 + 11.2600i −0.228704 + 0.396126i
\(809\) −35.3856 −1.24409 −0.622046 0.782981i \(-0.713698\pi\)
−0.622046 + 0.782981i \(0.713698\pi\)
\(810\) 0 0
\(811\) −2.67523 + 4.63364i −0.0939401 + 0.162709i −0.909166 0.416434i \(-0.863280\pi\)
0.815226 + 0.579143i \(0.196613\pi\)
\(812\) −0.710978 1.23145i −0.0249504 0.0432154i
\(813\) 0 0
\(814\) −19.5155 33.8018i −0.684017 1.18475i
\(815\) −5.80601 10.0563i −0.203376 0.352257i
\(816\) 0 0
\(817\) −8.12332 + 26.5178i −0.284199 + 0.927740i
\(818\) 31.4796 1.10066
\(819\) 0 0
\(820\) −0.0349842 0.0605943i −0.00122170 0.00211605i
\(821\) 3.81886 6.61446i 0.133279 0.230846i −0.791660 0.610962i \(-0.790783\pi\)
0.924939 + 0.380116i \(0.124116\pi\)
\(822\) 0 0
\(823\) −13.7866 + 23.8791i −0.480570 + 0.832372i −0.999752 0.0222919i \(-0.992904\pi\)
0.519181 + 0.854664i \(0.326237\pi\)
\(824\) −46.4394 −1.61779
\(825\) 0 0
\(826\) 11.5399 19.9877i 0.401525 0.695462i
\(827\) −9.51585 + 16.4819i −0.330898 + 0.573133i −0.982688 0.185267i \(-0.940685\pi\)
0.651790 + 0.758400i \(0.274018\pi\)
\(828\) 0 0
\(829\) −13.7455 −0.477402 −0.238701 0.971093i \(-0.576722\pi\)
−0.238701 + 0.971093i \(0.576722\pi\)
\(830\) 5.30382 9.18649i 0.184098 0.318868i
\(831\) 0 0
\(832\) 26.5083 45.9137i 0.919009 1.59177i
\(833\) 34.3918 + 59.5684i 1.19161 + 2.06392i
\(834\) 0 0
\(835\) −20.3114 −0.702905
\(836\) 1.68170 0.387274i 0.0581629 0.0133941i
\(837\) 0 0
\(838\) −21.3295 36.9438i −0.736815 1.27620i
\(839\) 17.1800 + 29.7566i 0.593118 + 1.02731i 0.993809 + 0.111098i \(0.0354367\pi\)
−0.400691 + 0.916213i \(0.631230\pi\)
\(840\) 0 0
\(841\) 8.18652 + 14.1795i 0.282294 + 0.488947i
\(842\) 18.3576 31.7963i 0.632644 1.09577i
\(843\) 0 0
\(844\) −0.721671 −0.0248409
\(845\) 13.7416 23.8012i 0.472726 0.818786i
\(846\) 0 0
\(847\) −33.2870 −1.14375
\(848\) 19.5626 0.671783
\(849\) 0 0
\(850\) −3.94834 6.83872i −0.135427 0.234566i
\(851\) 1.89626 3.28442i 0.0650030 0.112589i
\(852\) 0 0
\(853\) −22.7147 39.3431i −0.777738 1.34708i −0.933243 0.359247i \(-0.883034\pi\)
0.155505 0.987835i \(-0.450300\pi\)
\(854\) −72.4457 −2.47904
\(855\) 0 0
\(856\) −39.5254 −1.35095
\(857\) 6.94674 + 12.0321i 0.237296 + 0.411009i 0.959937 0.280214i \(-0.0904055\pi\)
−0.722641 + 0.691223i \(0.757072\pi\)
\(858\) 0 0
\(859\) 1.60333 2.77705i 0.0547049 0.0947517i −0.837376 0.546627i \(-0.815912\pi\)
0.892081 + 0.451875i \(0.149245\pi\)
\(860\) 0.291806 + 0.505423i 0.00995051 + 0.0172348i
\(861\) 0 0
\(862\) 22.7577 0.775132
\(863\) −51.7277 −1.76083 −0.880416 0.474201i \(-0.842737\pi\)
−0.880416 + 0.474201i \(0.842737\pi\)
\(864\) 0 0
\(865\) 6.12545 10.6096i 0.208272 0.360737i
\(866\) 50.8413 1.72766
\(867\) 0 0
\(868\) −0.236786 + 0.410126i −0.00803705 + 0.0139206i
\(869\) −24.4661 42.3765i −0.829955 1.43752i
\(870\) 0 0
\(871\) −12.7388 22.0643i −0.431639 0.747620i
\(872\) 12.9548 + 22.4383i 0.438704 + 0.759857i
\(873\) 0 0
\(874\) −2.37777 2.55267i −0.0804292 0.0863453i
\(875\) 4.36264 0.147484
\(876\) 0 0
\(877\) −8.51355 14.7459i −0.287482 0.497933i 0.685726 0.727860i \(-0.259485\pi\)
−0.973208 + 0.229926i \(0.926151\pi\)
\(878\) 6.61885 11.4642i 0.223376 0.386898i
\(879\) 0 0
\(880\) −8.21843 + 14.2347i −0.277043 + 0.479853i
\(881\) −12.9112 −0.434990 −0.217495 0.976061i \(-0.569789\pi\)
−0.217495 + 0.976061i \(0.569789\pi\)
\(882\) 0 0
\(883\) −12.5102 + 21.6684i −0.421003 + 0.729199i −0.996038 0.0889302i \(-0.971655\pi\)
0.575035 + 0.818129i \(0.304989\pi\)
\(884\) 1.66808 2.88921i 0.0561038 0.0971746i
\(885\) 0 0
\(886\) −30.7273 −1.03230
\(887\) 5.03634 8.72319i 0.169104 0.292896i −0.769001 0.639247i \(-0.779246\pi\)
0.938105 + 0.346351i \(0.112579\pi\)
\(888\) 0 0
\(889\) −13.4881 + 23.3621i −0.452376 + 0.783539i
\(890\) 6.79779 + 11.7741i 0.227862 + 0.394669i
\(891\) 0 0
\(892\) 2.50900 0.0840075
\(893\) −11.6075 + 2.67304i −0.388430 + 0.0894500i
\(894\) 0 0
\(895\) 9.59201 + 16.6139i 0.320626 + 0.555340i
\(896\) −22.8463 39.5709i −0.763240 1.32197i
\(897\) 0 0
\(898\) 0.339264 + 0.587623i 0.0113214 + 0.0196092i
\(899\) −2.10266 + 3.64191i −0.0701276 + 0.121465i
\(900\) 0 0
\(901\) 29.3655 0.978307
\(902\) 2.27411 3.93887i 0.0757196 0.131150i
\(903\) 0 0
\(904\) −18.5782 −0.617902
\(905\) 3.22984 0.107364
\(906\) 0 0
\(907\) 3.93231 + 6.81096i 0.130570 + 0.226154i 0.923897 0.382642i \(-0.124986\pi\)
−0.793326 + 0.608797i \(0.791653\pi\)
\(908\) 1.15079 1.99322i 0.0381903 0.0661475i
\(909\) 0 0
\(910\) −19.1725 33.2077i −0.635561 1.10082i
\(911\) 52.2665 1.73167 0.865833 0.500333i \(-0.166789\pi\)
0.865833 + 0.500333i \(0.166789\pi\)
\(912\) 0 0
\(913\) −33.1440 −1.09691
\(914\) 9.15922 + 15.8642i 0.302960 + 0.524742i
\(915\) 0 0
\(916\) 0.228638 0.396013i 0.00755441 0.0130846i
\(917\) −37.9494 65.7303i −1.25320 2.17061i
\(918\) 0 0
\(919\) 24.2225 0.799026 0.399513 0.916728i \(-0.369179\pi\)
0.399513 + 0.916728i \(0.369179\pi\)
\(920\) −1.67406 −0.0551922
\(921\) 0 0
\(922\) −16.1441 + 27.9623i −0.531677 + 0.920891i
\(923\) 19.5909 0.644844
\(924\) 0 0
\(925\) 3.27305 5.66908i 0.107617 0.186398i
\(926\) −0.678026 1.17438i −0.0222813 0.0385924i
\(927\) 0 0
\(928\) 0.921156 + 1.59549i 0.0302384 + 0.0523745i
\(929\) −21.3993 37.0647i −0.702089 1.21605i −0.967732 0.251983i \(-0.918917\pi\)
0.265642 0.964072i \(-0.414416\pi\)
\(930\) 0 0
\(931\) 35.7490 + 38.3786i 1.17163 + 1.25781i
\(932\) 1.17375 0.0384474
\(933\) 0 0
\(934\) 13.0196 + 22.5506i 0.426014 + 0.737877i
\(935\) −12.3367 + 21.3678i −0.403454 + 0.698803i
\(936\) 0 0
\(937\) −5.67783 + 9.83429i −0.185487 + 0.321272i −0.943740 0.330687i \(-0.892719\pi\)
0.758254 + 0.651960i \(0.226053\pi\)
\(938\) −24.1319 −0.787935
\(939\) 0 0
\(940\) −0.125325 + 0.217070i −0.00408766 + 0.00708004i
\(941\) 22.0711 38.2283i 0.719498 1.24621i −0.241701 0.970351i \(-0.577705\pi\)
0.961199 0.275856i \(-0.0889613\pi\)
\(942\) 0 0
\(943\) 0.441937 0.0143915
\(944\) −7.29198 + 12.6301i −0.237334 + 0.411074i
\(945\) 0 0
\(946\) −18.9686 + 32.8545i −0.616721 + 1.06819i
\(947\) −18.6191 32.2492i −0.605038 1.04796i −0.992045 0.125880i \(-0.959825\pi\)
0.387007 0.922077i \(-0.373509\pi\)
\(948\) 0 0
\(949\) −51.4509 −1.67017
\(950\) −4.10415 4.40604i −0.133156 0.142951i
\(951\) 0 0
\(952\) −36.0303 62.4064i −1.16775 2.02260i
\(953\) −19.6433 34.0232i −0.636310 1.10212i −0.986236 0.165344i \(-0.947127\pi\)
0.349926 0.936777i \(-0.386207\pi\)
\(954\) 0 0
\(955\) −13.7755 23.8598i −0.445764 0.772085i
\(956\) −0.587266 + 1.01717i −0.0189935 + 0.0328978i
\(957\) 0 0
\(958\) 27.8478 0.899721
\(959\) −34.2826 + 59.3791i −1.10704 + 1.91745i
\(960\) 0 0
\(961\) −29.5994 −0.954821
\(962\) −57.5361 −1.85504
\(963\) 0 0
\(964\) −0.0501180 0.0868069i −0.00161419 0.00279586i
\(965\) 11.1233 19.2662i 0.358072 0.620200i
\(966\) 0 0
\(967\) −10.5429 18.2608i −0.339037 0.587229i 0.645215 0.764001i \(-0.276768\pi\)
−0.984252 + 0.176772i \(0.943434\pi\)
\(968\) 22.0470 0.708618
\(969\) 0 0
\(970\) 2.76281 0.0887084
\(971\) −12.1226 20.9969i −0.389031 0.673822i 0.603288 0.797523i \(-0.293857\pi\)
−0.992319 + 0.123701i \(0.960523\pi\)
\(972\) 0 0
\(973\) 14.2952 24.7600i 0.458282 0.793768i
\(974\) 1.92815 + 3.33966i 0.0617820 + 0.107010i
\(975\) 0 0
\(976\) 45.7778 1.46531
\(977\) 51.4540 1.64616 0.823080 0.567926i \(-0.192254\pi\)
0.823080 + 0.567926i \(0.192254\pi\)
\(978\) 0 0
\(979\) 21.2400 36.7887i 0.678832 1.17577i
\(980\) 1.10369 0.0352562
\(981\) 0 0
\(982\) −3.99093 + 6.91249i −0.127356 + 0.220587i
\(983\) 4.56746 + 7.91108i 0.145679 + 0.252324i 0.929626 0.368504i \(-0.120130\pi\)
−0.783947 + 0.620828i \(0.786797\pi\)
\(984\) 0 0
\(985\) −6.33133 10.9662i −0.201733 0.349412i
\(986\) −14.0302 24.3010i −0.446812 0.773901i
\(987\) 0 0
\(988\) 0.745111 2.43234i 0.0237051 0.0773830i
\(989\) −3.68624 −0.117216
\(990\) 0 0
\(991\) 8.87713 + 15.3756i 0.281991 + 0.488424i 0.971875 0.235497i \(-0.0756717\pi\)
−0.689884 + 0.723920i \(0.742338\pi\)
\(992\) 0.306785 0.531367i 0.00974042 0.0168709i
\(993\) 0 0
\(994\) 9.27807 16.0701i 0.294283 0.509712i
\(995\) 8.76955 0.278014
\(996\) 0 0
\(997\) 28.1217 48.7081i 0.890622 1.54260i 0.0514903 0.998673i \(-0.483603\pi\)
0.839131 0.543929i \(-0.183064\pi\)
\(998\) 8.83810 15.3080i 0.279765 0.484568i
\(999\) 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 855.2.k.i.406.4 10
3.2 odd 2 285.2.i.f.121.2 yes 10
19.11 even 3 inner 855.2.k.i.676.4 10
57.11 odd 6 285.2.i.f.106.2 10
57.26 odd 6 5415.2.a.y.1.4 5
57.50 even 6 5415.2.a.z.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.2.i.f.106.2 10 57.11 odd 6
285.2.i.f.121.2 yes 10 3.2 odd 2
855.2.k.i.406.4 10 1.1 even 1 trivial
855.2.k.i.676.4 10 19.11 even 3 inner
5415.2.a.y.1.4 5 57.26 odd 6
5415.2.a.z.1.2 5 57.50 even 6