Properties

Label 855.2.k.i.676.4
Level $855$
Weight $2$
Character 855.676
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 676.4
Root \(-0.690702 - 1.19633i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.i.406.4

$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.511511 0.859277i \(-0.670914\pi\)
0.999911 + 0.0133433i \(0.00424744\pi\)
\(3\) 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 0.848732 + 0.528823i \(0.177366\pi\)
0.0336075 + 0.999435i \(0.489300\pi\)
\(14\) −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 −0.277561 0.960708i \(-0.589526\pi\)
0.970778 0.239979i \(-0.0771405\pi\)
\(18\) 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 0.834243 0.551397i \(-0.185905\pi\)
−0.894645 + 0.446777i \(0.852572\pi\)
\(24\) 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 0.652569 0.757730i \(-0.273691\pi\)
−0.982497 + 0.186276i \(0.940358\pi\)
\(30\) 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 −0.894270 0.447527i \(-0.852305\pi\)
0.834705 + 0.550697i \(0.185638\pi\)
\(42\) 0 0
\(43\) 3.18132 5.51021i 0.485147 0.840299i −0.514707 0.857366i \(-0.672099\pi\)
0.999854 + 0.0170666i \(0.00543274\pi\)
\(44\) 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 0.749003 0.662567i \(-0.230533\pi\)
−0.948301 + 0.317372i \(0.897200\pi\)
\(48\) 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 0.986741 0.162300i \(-0.0518914\pi\)
−0.633927 + 0.773393i \(0.718558\pi\)
\(54\) 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 −0.714038 0.700107i \(-0.753136\pi\)
0.963329 + 0.268322i \(0.0864691\pi\)
\(60\) 0 0
\(61\) 6.01053 + 10.4105i 0.769569 + 1.33293i 0.937797 + 0.347185i \(0.112862\pi\)
−0.168227 + 0.985748i \(0.553804\pi\)
\(62\) 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 0.962019 0.272983i \(-0.0880104\pi\)
−0.717420 + 0.696641i \(0.754677\pi\)
\(68\) 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 −0.760094 0.649814i \(-0.774847\pi\)
0.942802 + 0.333354i \(0.108180\pi\)
\(72\) 0 0
\(73\) −4.04320 + 7.00303i −0.473221 + 0.819643i −0.999530 0.0306504i \(-0.990242\pi\)
0.526309 + 0.850293i \(0.323575\pi\)
\(74\) −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 0.348187 + 0.937425i \(0.386798\pi\)
−0.985927 + 0.167174i \(0.946536\pi\)
\(80\) −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 0.999684 + 0.0251445i \(0.00800458\pi\)
−0.478066 + 0.878324i \(0.658662\pi\)
\(90\) 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 −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 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 0.732111 0.681185i \(-0.238535\pi\)
−0.955979 + 0.293434i \(0.905202\pi\)
\(102\) 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 −0.567394 0.823447i \(-0.692048\pi\)
0.996823 + 0.0796541i \(0.0253816\pi\)
\(110\) −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 0.969970 0.243225i \(-0.0782052\pi\)
−0.695624 + 0.718406i \(0.744872\pi\)
\(128\) 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 −0.182834 0.983144i \(-0.558527\pi\)
0.942845 0.333233i \(-0.108140\pi\)
\(132\) 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 0.977515 + 0.210865i \(0.0676280\pi\)
−0.306143 + 0.951985i \(0.599039\pi\)
\(138\) 0 0
\(139\) −3.27672 5.67545i −0.277928 0.481385i 0.692942 0.720994i \(-0.256314\pi\)
−0.970870 + 0.239608i \(0.922981\pi\)
\(140\) −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 −0.723862 0.689945i \(-0.757635\pi\)
0.959441 + 0.281911i \(0.0909682\pi\)
\(150\) 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 −0.892225 0.451591i \(-0.850856\pi\)
0.837202 + 0.546894i \(0.184190\pi\)
\(158\) 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 −0.928477 0.371390i \(-0.878881\pi\)
0.142606 0.989780i \(-0.454452\pi\)
\(168\) 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 −0.999233 0.0391527i \(-0.987534\pi\)
0.533524 + 0.845785i \(0.320867\pi\)
\(174\) 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 0.919782 0.392430i \(-0.128366\pi\)
−0.799746 + 0.600339i \(0.795032\pi\)
\(182\) −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 0.118499 + 0.992954i \(0.462192\pi\)
−0.919173 + 0.393854i \(0.871141\pi\)
\(194\) 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 0.978542 0.206048i \(-0.0660602\pi\)
−0.667713 + 0.744418i \(0.732727\pi\)
\(200\) −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 −0.969072 0.246778i \(-0.920628\pi\)
0.698252 + 0.715852i \(0.253962\pi\)
\(212\) −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 0.110232 0.993906i \(-0.464840\pi\)
0.805631 0.592417i \(-0.201826\pi\)
\(224\) −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 −0.576695 0.816960i \(-0.695658\pi\)
0.995855 + 0.0909523i \(0.0289911\pi\)
\(234\) 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 0.883087 0.469209i \(-0.155461\pi\)
−0.847891 + 0.530171i \(0.822128\pi\)
\(242\) 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 0.946034 0.324068i \(-0.105051\pi\)
−0.753668 + 0.657255i \(0.771717\pi\)
\(252\) 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 0.929038 0.369984i \(-0.120637\pi\)
−0.784934 + 0.619579i \(0.787303\pi\)
\(258\) 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 −0.137276 + 0.990533i \(0.543835\pi\)
−0.789189 + 0.614151i \(0.789499\pi\)
\(264\) 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 −0.869228 0.494412i \(-0.835384\pi\)
0.862787 + 0.505568i \(0.168717\pi\)
\(270\) 0 0
\(271\) 3.70364 6.41489i 0.224980 0.389677i −0.731333 0.682020i \(-0.761102\pi\)
0.956313 + 0.292343i \(0.0944350\pi\)
\(272\) −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 0.984859 0.173357i \(-0.0554615\pi\)
−0.642561 + 0.766234i \(0.722128\pi\)
\(282\) 0 0
\(283\) 13.6662 23.6706i 0.812373 1.40707i −0.0988265 0.995105i \(-0.531509\pi\)
0.911199 0.411966i \(-0.135158\pi\)
\(284\) 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 −0.917727 0.397211i \(-0.869978\pi\)
0.802858 + 0.596170i \(0.203312\pi\)
\(308\) −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 −0.989369 0.145424i \(-0.953546\pi\)
0.368744 0.929531i \(-0.379788\pi\)
\(314\) 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 −0.975708 0.219077i \(-0.929695\pi\)
0.298127 0.954526i \(-0.403638\pi\)
\(318\) 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 −0.873674 0.486511i \(-0.838269\pi\)
0.858168 + 0.513368i \(0.171603\pi\)
\(338\) 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 −0.712365 0.701809i \(-0.752376\pi\)
0.963967 + 0.266022i \(0.0857093\pi\)
\(348\) 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 −0.686183 0.727429i \(-0.740715\pi\)
0.973063 + 0.230537i \(0.0740484\pi\)
\(360\) 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 0.999918 0.0128422i \(-0.00408791\pi\)
−0.511080 + 0.859533i \(0.670755\pi\)
\(368\) −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 −0.722794 0.691063i \(-0.757143\pi\)
0.959876 + 0.280426i \(0.0904759\pi\)
\(384\) 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 0.882421 0.470461i \(-0.155912\pi\)
−0.848641 + 0.528969i \(0.822579\pi\)
\(390\) 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 −0.128485 0.991711i \(-0.541011\pi\)
0.923090 0.384584i \(-0.125655\pi\)
\(398\) 12.1143 0.607235
\(399\) 0 0
\(400\) −3.80814 −0.190407
\(401\) −2.44425 + 4.23356i −0.122060 + 0.211414i −0.920580 0.390554i \(-0.872283\pi\)
0.798520 + 0.601968i \(0.205617\pi\)
\(402\) 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 0.997197 + 0.0748266i \(0.0238403\pi\)
−0.433797 + 0.901011i \(0.642826\pi\)
\(410\) 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 0.336007 + 0.941859i \(0.390923\pi\)
−0.983678 + 0.179939i \(0.942410\pi\)
\(422\) 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 0.993325 0.115345i \(-0.0367974\pi\)
−0.596554 + 0.802573i \(0.703464\pi\)
\(432\) 0 0
\(433\) 18.4021 + 31.8733i 0.884346 + 1.53173i 0.846461 + 0.532450i \(0.178729\pi\)
0.0378851 + 0.999282i \(0.487938\pi\)
\(434\) −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 −0.957417 0.288707i \(-0.906775\pi\)
0.728736 + 0.684794i \(0.240108\pi\)
\(440\) 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 −0.999451 0.0331236i \(-0.989454\pi\)
0.471040 0.882112i \(-0.343879\pi\)
\(444\) 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 −0.454346 0.890825i \(-0.650127\pi\)
0.998650 0.0519379i \(-0.0165398\pi\)
\(462\) 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 0.998988 0.0449739i \(-0.0143205\pi\)
−0.538443 + 0.842662i \(0.680987\pi\)
\(480\) 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 −0.793443 0.608645i \(-0.791713\pi\)
0.923823 + 0.382819i \(0.125047\pi\)
\(492\) 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 −0.972950 0.231015i \(-0.925795\pi\)
0.686540 + 0.727092i \(0.259129\pi\)
\(500\) −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 0.966329 + 0.257308i \(0.0828356\pi\)
−0.260329 + 0.965520i \(0.583831\pi\)
\(504\) 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 0.798782 0.601621i \(-0.205478\pi\)
−0.920410 + 0.390955i \(0.872145\pi\)
\(510\) 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 0.711670 0.702514i \(-0.247939\pi\)
−0.964230 + 0.265067i \(0.914606\pi\)
\(524\) 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 0.997807 + 0.0661881i \(0.0210837\pi\)
−0.441583 + 0.897220i \(0.645583\pi\)
\(542\) −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 0.789394 0.613887i \(-0.210395\pi\)
−0.926339 + 0.376692i \(0.877062\pi\)
\(548\) −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 0.826260 0.563289i \(-0.190464\pi\)
−0.900953 + 0.433918i \(0.857131\pi\)
\(558\) 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 −0.990991 0.133931i \(-0.957240\pi\)
0.611483 + 0.791258i \(0.290573\pi\)
\(588\) 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 0.870278 0.492561i \(-0.163939\pi\)
−0.861709 + 0.507403i \(0.830606\pi\)
\(594\) 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 −0.922174 0.386776i \(-0.873589\pi\)
0.126129 0.992014i \(-0.459745\pi\)
\(600\) 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 0.389011 + 0.921233i \(0.372817\pi\)
−0.992317 + 0.123723i \(0.960517\pi\)
\(614\) 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 −0.990075 0.140540i \(-0.955116\pi\)
0.373326 0.927700i \(-0.378217\pi\)
\(618\) 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 0.999781 + 0.0209274i \(0.00666189\pi\)
−0.481767 + 0.876299i \(0.660005\pi\)
\(632\) −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 −0.990942 0.134292i \(-0.957124\pi\)
0.611771 + 0.791035i \(0.290457\pi\)
\(642\) 0 0
\(643\) −4.27305 + 7.40113i −0.168513 + 0.291872i −0.937897 0.346914i \(-0.887230\pi\)
0.769385 + 0.638786i \(0.220563\pi\)
\(644\) −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 0.679975 0.733235i \(-0.261991\pi\)
−0.974988 + 0.222258i \(0.928657\pi\)
\(660\) 0 0
\(661\) −3.65794 6.33574i −0.142277 0.246432i 0.786076 0.618129i \(-0.212109\pi\)
−0.928354 + 0.371698i \(0.878776\pi\)
\(662\) −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 −0.181136 0.983458i \(-0.557978\pi\)
0.942268 0.334860i \(-0.108689\pi\)
\(702\) 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 0.911286 0.411774i \(-0.135091\pi\)
−0.812249 + 0.583310i \(0.801757\pi\)
\(710\) −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 −0.554747 0.832019i \(-0.687185\pi\)
0.997923 + 0.0644151i \(0.0205182\pi\)
\(720\) 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 −0.360408 0.932795i \(-0.617363\pi\)
0.988028 0.154275i \(-0.0493040\pi\)
\(728\) −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 −0.984342 0.176268i \(-0.943597\pi\)
0.644824 + 0.764331i \(0.276931\pi\)
\(740\) −0.600439 −0.0220726
\(741\) 0 0
\(742\) −30.9588 −1.13653
\(743\) −4.47864 + 7.75723i −0.164305 + 0.284585i −0.936408 0.350912i \(-0.885872\pi\)
0.772103 + 0.635497i \(0.219205\pi\)
\(744\) 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 0.999247 + 0.0388032i \(0.0123545\pi\)
−0.466019 + 0.884775i \(0.654312\pi\)
\(752\) −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 −0.984325 0.176364i \(-0.943566\pi\)
0.644898 + 0.764268i \(0.276900\pi\)
\(758\) −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 −0.986390 0.164424i \(-0.947424\pi\)
0.350800 0.936450i \(-0.385910\pi\)
\(770\) 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 0.869641 + 0.493684i \(0.164350\pi\)
−0.00727780 + 0.999974i \(0.502317\pi\)
\(774\) 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 0.815226 0.579143i \(-0.196613\pi\)
−0.909166 + 0.416434i \(0.863280\pi\)
\(812\) −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 0.924939 0.380116i \(-0.124116\pi\)
−0.791660 + 0.610962i \(0.790783\pi\)
\(822\) 0 0
\(823\) −13.7866 23.8791i −0.480570 0.832372i 0.519181 0.854664i \(-0.326237\pi\)
−0.999752 + 0.0222919i \(0.992904\pi\)
\(824\) −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 0.651790 0.758400i \(-0.274018\pi\)
−0.982688 + 0.185267i \(0.940685\pi\)
\(828\) 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 −0.400691 0.916213i \(-0.631230\pi\)
0.993809 0.111098i \(-0.0354367\pi\)
\(840\) 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 0.155505 + 0.987835i \(0.450300\pi\)
−0.933243 + 0.359247i \(0.883034\pi\)
\(854\) −72.4457 −2.47904
\(855\) 0 0
\(856\) −39.5254 −1.35095
\(857\) 6.94674 12.0321i 0.237296 0.411009i −0.722641 0.691223i \(-0.757072\pi\)
0.959937 + 0.280214i \(0.0904055\pi\)
\(858\) 0 0
\(859\) 1.60333 + 2.77705i 0.0547049 + 0.0947517i 0.892081 0.451875i \(-0.149245\pi\)
−0.837376 + 0.546627i \(0.815912\pi\)
\(860\) 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 −0.973208 0.229926i \(-0.926151\pi\)
0.685726 + 0.727860i \(0.259485\pi\)
\(878\) 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 0.575035 0.818129i \(-0.304989\pi\)
−0.996038 + 0.0889302i \(0.971655\pi\)
\(884\) 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 0.938105 0.346351i \(-0.112579\pi\)
−0.769001 + 0.639247i \(0.779246\pi\)
\(888\) 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 −0.793326 0.608797i \(-0.791653\pi\)
0.923897 + 0.382642i \(0.124986\pi\)
\(908\) 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 0.265642 + 0.964072i \(0.414416\pi\)
−0.967732 + 0.251983i \(0.918917\pi\)
\(930\) 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 0.758254 0.651960i \(-0.226053\pi\)
−0.943740 + 0.330687i \(0.892719\pi\)
\(938\) −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 0.961199 + 0.275856i \(0.0889613\pi\)
−0.241701 + 0.970351i \(0.577705\pi\)
\(942\) 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 0.387007 + 0.922077i \(0.373509\pi\)
−0.992045 + 0.125880i \(0.959825\pi\)
\(948\) 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 0.349926 + 0.936777i \(0.386207\pi\)
−0.986236 + 0.165344i \(0.947127\pi\)
\(954\) 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 −0.984252 0.176772i \(-0.943434\pi\)
0.645215 + 0.764001i \(0.276768\pi\)
\(968\) 22.0470 0.708618
\(969\) 0 0
\(970\) 2.76281 0.0887084
\(971\) −12.1226 + 20.9969i −0.389031 + 0.673822i −0.992319 0.123701i \(-0.960523\pi\)
0.603288 + 0.797523i \(0.293857\pi\)
\(972\) 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 −0.783947 0.620828i \(-0.786797\pi\)
0.929626 + 0.368504i \(0.120130\pi\)
\(984\) 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 −0.689884 0.723920i \(-0.742338\pi\)
0.971875 + 0.235497i \(0.0756717\pi\)
\(992\) 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 0.839131 + 0.543929i \(0.183064\pi\)
0.0514903 + 0.998673i \(0.483603\pi\)
\(998\) 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.676.4 10
3.2 odd 2 285.2.i.f.106.2 10
19.7 even 3 inner 855.2.k.i.406.4 10
57.8 even 6 5415.2.a.z.1.2 5
57.11 odd 6 5415.2.a.y.1.4 5
57.26 odd 6 285.2.i.f.121.2 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.2.i.f.106.2 10 3.2 odd 2
285.2.i.f.121.2 yes 10 57.26 odd 6
855.2.k.i.406.4 10 19.7 even 3 inner
855.2.k.i.676.4 10 1.1 even 1 trivial
5415.2.a.y.1.4 5 57.11 odd 6
5415.2.a.z.1.2 5 57.8 even 6