Properties

Label 99.3.k.c.73.3
Level $99$
Weight $3$
Character 99.73
Analytic conductor $2.698$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,3,Mod(19,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.k (of order \(10\), degree \(4\), 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: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + 1868 x^{7} - 1619 x^{6} - 16804 x^{5} + 32427 x^{4} + 43316 x^{3} + \cdots + 83521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 73.3
Root \(1.60675 - 1.36085i\) of defining polynomial
Character \(\chi\) \(=\) 99.73
Dual form 99.3.k.c.19.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.184008 - 0.253266i) q^{2} +(1.20578 + 3.71102i) q^{4} +(-5.99919 + 4.35866i) q^{5} +(-9.53633 + 3.09854i) q^{7} +(2.35267 + 0.764430i) q^{8} +O(q^{10})\) \(q+(0.184008 - 0.253266i) q^{2} +(1.20578 + 3.71102i) q^{4} +(-5.99919 + 4.35866i) q^{5} +(-9.53633 + 3.09854i) q^{7} +(2.35267 + 0.764430i) q^{8} +2.32142i q^{10} +(10.2703 - 3.93969i) q^{11} +(2.00157 - 2.75492i) q^{13} +(-0.970009 + 2.98538i) q^{14} +(-12.0006 + 8.71896i) q^{16} +(9.14407 + 12.5857i) q^{17} +(29.1422 + 9.46888i) q^{19} +(-23.4088 - 17.0075i) q^{20} +(0.892031 - 3.32605i) q^{22} -7.67868 q^{23} +(9.26687 - 28.5205i) q^{25} +(-0.329422 - 1.01386i) q^{26} +(-22.9975 - 31.6533i) q^{28} +(-3.21080 + 1.04325i) q^{29} +(3.27045 + 2.37612i) q^{31} +14.5387i q^{32} +4.87012 q^{34} +(43.7047 - 60.1544i) q^{35} +(-0.734229 - 2.25972i) q^{37} +(7.76055 - 5.63837i) q^{38} +(-17.4460 + 5.66856i) q^{40} +(-6.69014 - 2.17376i) q^{41} -3.99630i q^{43} +(27.0040 + 33.3628i) q^{44} +(-1.41294 + 1.94475i) q^{46} +(-15.2775 + 47.0193i) q^{47} +(41.6988 - 30.2959i) q^{49} +(-5.51808 - 7.59498i) q^{50} +(12.6370 + 4.10601i) q^{52} +(-48.3260 - 35.1109i) q^{53} +(-44.4416 + 68.3997i) q^{55} -24.8045 q^{56} +(-0.326594 + 1.00515i) q^{58} +(3.39858 + 10.4597i) q^{59} +(43.6783 + 60.1180i) q^{61} +(1.20358 - 0.391067i) q^{62} +(-44.3203 - 32.2006i) q^{64} +25.2514i q^{65} -3.22579 q^{67} +(-35.6801 + 49.1095i) q^{68} +(-7.19301 - 22.1378i) q^{70} +(94.5613 - 68.7028i) q^{71} +(17.8062 - 5.78557i) q^{73} +(-0.707415 - 0.229853i) q^{74} +119.565i q^{76} +(-85.7336 + 69.3931i) q^{77} +(-2.06629 + 2.84401i) q^{79} +(33.9909 - 104.613i) q^{80} +(-1.78158 + 1.29439i) q^{82} +(86.4628 + 119.006i) q^{83} +(-109.714 - 35.6482i) q^{85} +(-1.01212 - 0.735351i) q^{86} +(27.1743 - 1.41788i) q^{88} +65.8879 q^{89} +(-10.5514 + 32.4737i) q^{91} +(-9.25883 - 28.4957i) q^{92} +(9.09719 + 12.5212i) q^{94} +(-216.101 + 70.2155i) q^{95} +(-52.4543 - 38.1103i) q^{97} -16.1356i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 20 q^{4} + 4 q^{5} - 30 q^{7} + 40 q^{8} + 10 q^{11} + 30 q^{13} + 2 q^{14} + 16 q^{16} + 10 q^{17} - 42 q^{20} + 42 q^{22} - 132 q^{23} - 2 q^{25} - 46 q^{26} - 50 q^{28} - 160 q^{29} + 10 q^{31} - 368 q^{34} + 320 q^{35} - 126 q^{37} + 130 q^{38} + 30 q^{40} + 120 q^{41} + 206 q^{44} + 50 q^{46} + 150 q^{47} + 210 q^{49} - 330 q^{50} + 110 q^{52} - 342 q^{53} + 244 q^{55} - 524 q^{56} + 150 q^{58} - 110 q^{59} - 90 q^{61} - 40 q^{62} - 168 q^{64} + 36 q^{67} - 80 q^{68} + 340 q^{70} + 236 q^{71} - 350 q^{73} + 730 q^{74} + 390 q^{77} + 210 q^{79} + 806 q^{80} + 114 q^{82} + 190 q^{83} + 110 q^{85} - 736 q^{86} + 144 q^{88} - 76 q^{89} + 306 q^{91} + 150 q^{92} - 350 q^{94} - 430 q^{95} - 354 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.184008 0.253266i 0.0920041 0.126633i −0.760533 0.649299i \(-0.775062\pi\)
0.852538 + 0.522666i \(0.175062\pi\)
\(3\) 0 0
\(4\) 1.20578 + 3.71102i 0.301446 + 0.927755i
\(5\) −5.99919 + 4.35866i −1.19984 + 0.871733i −0.994269 0.106910i \(-0.965904\pi\)
−0.205569 + 0.978643i \(0.565904\pi\)
\(6\) 0 0
\(7\) −9.53633 + 3.09854i −1.36233 + 0.442649i −0.896821 0.442393i \(-0.854130\pi\)
−0.465511 + 0.885042i \(0.654130\pi\)
\(8\) 2.35267 + 0.764430i 0.294084 + 0.0955538i
\(9\) 0 0
\(10\) 2.32142i 0.232142i
\(11\) 10.2703 3.93969i 0.933663 0.358153i
\(12\) 0 0
\(13\) 2.00157 2.75492i 0.153967 0.211917i −0.725065 0.688681i \(-0.758190\pi\)
0.879031 + 0.476764i \(0.158190\pi\)
\(14\) −0.970009 + 2.98538i −0.0692864 + 0.213242i
\(15\) 0 0
\(16\) −12.0006 + 8.71896i −0.750038 + 0.544935i
\(17\) 9.14407 + 12.5857i 0.537886 + 0.740337i 0.988307 0.152480i \(-0.0487258\pi\)
−0.450420 + 0.892817i \(0.648726\pi\)
\(18\) 0 0
\(19\) 29.1422 + 9.46888i 1.53380 + 0.498362i 0.949658 0.313289i \(-0.101431\pi\)
0.584142 + 0.811651i \(0.301431\pi\)
\(20\) −23.4088 17.0075i −1.17044 0.850375i
\(21\) 0 0
\(22\) 0.892031 3.32605i 0.0405469 0.151184i
\(23\) −7.67868 −0.333856 −0.166928 0.985969i \(-0.553385\pi\)
−0.166928 + 0.985969i \(0.553385\pi\)
\(24\) 0 0
\(25\) 9.26687 28.5205i 0.370675 1.14082i
\(26\) −0.329422 1.01386i −0.0126701 0.0389944i
\(27\) 0 0
\(28\) −22.9975 31.6533i −0.821339 1.13048i
\(29\) −3.21080 + 1.04325i −0.110717 + 0.0359743i −0.363852 0.931457i \(-0.618539\pi\)
0.253134 + 0.967431i \(0.418539\pi\)
\(30\) 0 0
\(31\) 3.27045 + 2.37612i 0.105498 + 0.0766490i 0.639284 0.768971i \(-0.279231\pi\)
−0.533785 + 0.845620i \(0.679231\pi\)
\(32\) 14.5387i 0.454334i
\(33\) 0 0
\(34\) 4.87012 0.143239
\(35\) 43.7047 60.1544i 1.24871 1.71870i
\(36\) 0 0
\(37\) −0.734229 2.25972i −0.0198440 0.0610736i 0.940644 0.339394i \(-0.110222\pi\)
−0.960488 + 0.278321i \(0.910222\pi\)
\(38\) 7.76055 5.63837i 0.204225 0.148378i
\(39\) 0 0
\(40\) −17.4460 + 5.66856i −0.436151 + 0.141714i
\(41\) −6.69014 2.17376i −0.163174 0.0530185i 0.226291 0.974060i \(-0.427340\pi\)
−0.389465 + 0.921041i \(0.627340\pi\)
\(42\) 0 0
\(43\) 3.99630i 0.0929371i −0.998920 0.0464686i \(-0.985203\pi\)
0.998920 0.0464686i \(-0.0147967\pi\)
\(44\) 27.0040 + 33.3628i 0.613727 + 0.758247i
\(45\) 0 0
\(46\) −1.41294 + 1.94475i −0.0307161 + 0.0422771i
\(47\) −15.2775 + 47.0193i −0.325053 + 1.00041i 0.646363 + 0.763030i \(0.276289\pi\)
−0.971417 + 0.237381i \(0.923711\pi\)
\(48\) 0 0
\(49\) 41.6988 30.2959i 0.850995 0.618284i
\(50\) −5.51808 7.59498i −0.110362 0.151900i
\(51\) 0 0
\(52\) 12.6370 + 4.10601i 0.243020 + 0.0789618i
\(53\) −48.3260 35.1109i −0.911812 0.662470i 0.0296603 0.999560i \(-0.490557\pi\)
−0.941473 + 0.337090i \(0.890557\pi\)
\(54\) 0 0
\(55\) −44.4416 + 68.3997i −0.808030 + 1.24363i
\(56\) −24.8045 −0.442937
\(57\) 0 0
\(58\) −0.326594 + 1.00515i −0.00563093 + 0.0173302i
\(59\) 3.39858 + 10.4597i 0.0576030 + 0.177284i 0.975718 0.219030i \(-0.0702892\pi\)
−0.918115 + 0.396314i \(0.870289\pi\)
\(60\) 0 0
\(61\) 43.6783 + 60.1180i 0.716038 + 0.985541i 0.999646 + 0.0266011i \(0.00846840\pi\)
−0.283608 + 0.958940i \(0.591532\pi\)
\(62\) 1.20358 0.391067i 0.0194126 0.00630752i
\(63\) 0 0
\(64\) −44.3203 32.2006i −0.692505 0.503134i
\(65\) 25.2514i 0.388484i
\(66\) 0 0
\(67\) −3.22579 −0.0481461 −0.0240730 0.999710i \(-0.507663\pi\)
−0.0240730 + 0.999710i \(0.507663\pi\)
\(68\) −35.6801 + 49.1095i −0.524708 + 0.722198i
\(69\) 0 0
\(70\) −7.19301 22.1378i −0.102757 0.316254i
\(71\) 94.5613 68.7028i 1.33185 0.967645i 0.332147 0.943228i \(-0.392227\pi\)
0.999702 0.0244174i \(-0.00777307\pi\)
\(72\) 0 0
\(73\) 17.8062 5.78557i 0.243920 0.0792544i −0.184506 0.982831i \(-0.559068\pi\)
0.428426 + 0.903577i \(0.359068\pi\)
\(74\) −0.707415 0.229853i −0.00955966 0.00310612i
\(75\) 0 0
\(76\) 119.565i 1.57322i
\(77\) −85.7336 + 69.3931i −1.11342 + 0.901208i
\(78\) 0 0
\(79\) −2.06629 + 2.84401i −0.0261556 + 0.0360001i −0.821895 0.569640i \(-0.807083\pi\)
0.795739 + 0.605640i \(0.207083\pi\)
\(80\) 33.9909 104.613i 0.424887 1.30767i
\(81\) 0 0
\(82\) −1.78158 + 1.29439i −0.0217266 + 0.0157853i
\(83\) 86.4628 + 119.006i 1.04172 + 1.43380i 0.895773 + 0.444513i \(0.146623\pi\)
0.145948 + 0.989292i \(0.453377\pi\)
\(84\) 0 0
\(85\) −109.714 35.6482i −1.29075 0.419391i
\(86\) −1.01212 0.735351i −0.0117689 0.00855060i
\(87\) 0 0
\(88\) 27.1743 1.41788i 0.308798 0.0161122i
\(89\) 65.8879 0.740313 0.370156 0.928969i \(-0.379304\pi\)
0.370156 + 0.928969i \(0.379304\pi\)
\(90\) 0 0
\(91\) −10.5514 + 32.4737i −0.115949 + 0.356854i
\(92\) −9.25883 28.4957i −0.100639 0.309736i
\(93\) 0 0
\(94\) 9.09719 + 12.5212i 0.0967786 + 0.133204i
\(95\) −216.101 + 70.2155i −2.27475 + 0.739111i
\(96\) 0 0
\(97\) −52.4543 38.1103i −0.540766 0.392890i 0.283603 0.958942i \(-0.408470\pi\)
−0.824369 + 0.566052i \(0.808470\pi\)
\(98\) 16.1356i 0.164649i
\(99\) 0 0
\(100\) 117.014 1.17014
\(101\) 65.7950 90.5591i 0.651436 0.896625i −0.347724 0.937597i \(-0.613046\pi\)
0.999160 + 0.0409723i \(0.0130455\pi\)
\(102\) 0 0
\(103\) −0.871094 2.68095i −0.00845722 0.0260287i 0.946739 0.322002i \(-0.104356\pi\)
−0.955196 + 0.295974i \(0.904356\pi\)
\(104\) 6.81498 4.95137i 0.0655286 0.0476093i
\(105\) 0 0
\(106\) −17.7848 + 5.77863i −0.167781 + 0.0545153i
\(107\) 34.7358 + 11.2863i 0.324634 + 0.105480i 0.466800 0.884363i \(-0.345407\pi\)
−0.142166 + 0.989843i \(0.545407\pi\)
\(108\) 0 0
\(109\) 185.532i 1.70213i −0.525061 0.851064i \(-0.675958\pi\)
0.525061 0.851064i \(-0.324042\pi\)
\(110\) 9.14566 + 23.8416i 0.0831423 + 0.216742i
\(111\) 0 0
\(112\) 87.4258 120.331i 0.780587 1.07439i
\(113\) 56.9948 175.412i 0.504378 1.55232i −0.297435 0.954742i \(-0.596131\pi\)
0.801813 0.597575i \(-0.203869\pi\)
\(114\) 0 0
\(115\) 46.0658 33.4688i 0.400573 0.291033i
\(116\) −7.74307 10.6574i −0.0667506 0.0918743i
\(117\) 0 0
\(118\) 3.27446 + 1.06394i 0.0277497 + 0.00901641i
\(119\) −126.198 91.6884i −1.06049 0.770491i
\(120\) 0 0
\(121\) 89.9578 80.9234i 0.743453 0.668789i
\(122\) 23.2630 0.190680
\(123\) 0 0
\(124\) −4.87438 + 15.0018i −0.0393095 + 0.120982i
\(125\) 11.4304 + 35.1792i 0.0914432 + 0.281433i
\(126\) 0 0
\(127\) 113.643 + 156.417i 0.894830 + 1.23163i 0.972088 + 0.234617i \(0.0753837\pi\)
−0.0772574 + 0.997011i \(0.524616\pi\)
\(128\) −71.6191 + 23.2705i −0.559524 + 0.181800i
\(129\) 0 0
\(130\) 6.39532 + 4.64647i 0.0491948 + 0.0357421i
\(131\) 168.561i 1.28673i 0.765562 + 0.643363i \(0.222461\pi\)
−0.765562 + 0.643363i \(0.777539\pi\)
\(132\) 0 0
\(133\) −307.249 −2.31015
\(134\) −0.593572 + 0.816981i −0.00442964 + 0.00609687i
\(135\) 0 0
\(136\) 11.8921 + 36.6001i 0.0874419 + 0.269119i
\(137\) −0.0117400 + 0.00852964i −8.56938e−5 + 6.22602e-5i −0.587828 0.808986i \(-0.700017\pi\)
0.587742 + 0.809048i \(0.300017\pi\)
\(138\) 0 0
\(139\) −112.600 + 36.5860i −0.810072 + 0.263208i −0.684628 0.728892i \(-0.740035\pi\)
−0.125444 + 0.992101i \(0.540035\pi\)
\(140\) 275.933 + 89.6559i 1.97095 + 0.640399i
\(141\) 0 0
\(142\) 36.5910i 0.257683i
\(143\) 9.70315 36.1794i 0.0678542 0.253003i
\(144\) 0 0
\(145\) 14.7150 20.2535i 0.101483 0.139679i
\(146\) 1.81119 5.57428i 0.0124054 0.0381800i
\(147\) 0 0
\(148\) 7.50056 5.44948i 0.0506795 0.0368208i
\(149\) −107.221 147.577i −0.719604 0.990449i −0.999537 0.0304299i \(-0.990312\pi\)
0.279933 0.960019i \(-0.409688\pi\)
\(150\) 0 0
\(151\) 162.559 + 52.8185i 1.07655 + 0.349791i 0.793034 0.609177i \(-0.208500\pi\)
0.283513 + 0.958968i \(0.408500\pi\)
\(152\) 61.3238 + 44.5544i 0.403446 + 0.293121i
\(153\) 0 0
\(154\) 1.79919 + 34.4823i 0.0116830 + 0.223911i
\(155\) −29.9767 −0.193398
\(156\) 0 0
\(157\) −8.53748 + 26.2757i −0.0543789 + 0.167361i −0.974557 0.224138i \(-0.928043\pi\)
0.920179 + 0.391499i \(0.128043\pi\)
\(158\) 0.340074 + 1.04664i 0.00215237 + 0.00662431i
\(159\) 0 0
\(160\) −63.3693 87.2204i −0.396058 0.545127i
\(161\) 73.2264 23.7927i 0.454823 0.147781i
\(162\) 0 0
\(163\) −167.276 121.533i −1.02623 0.745600i −0.0586796 0.998277i \(-0.518689\pi\)
−0.967551 + 0.252677i \(0.918689\pi\)
\(164\) 27.4483i 0.167368i
\(165\) 0 0
\(166\) 46.0499 0.277409
\(167\) 37.5103 51.6285i 0.224612 0.309153i −0.681806 0.731533i \(-0.738805\pi\)
0.906419 + 0.422380i \(0.138805\pi\)
\(168\) 0 0
\(169\) 48.6406 + 149.700i 0.287814 + 0.885800i
\(170\) −29.2167 + 21.2272i −0.171863 + 0.124866i
\(171\) 0 0
\(172\) 14.8303 4.81867i 0.0862229 0.0280155i
\(173\) −215.709 70.0882i −1.24688 0.405134i −0.390075 0.920783i \(-0.627551\pi\)
−0.856800 + 0.515649i \(0.827551\pi\)
\(174\) 0 0
\(175\) 300.694i 1.71825i
\(176\) −88.8998 + 136.825i −0.505113 + 0.777414i
\(177\) 0 0
\(178\) 12.1239 16.6871i 0.0681119 0.0937479i
\(179\) −87.6693 + 269.818i −0.489773 + 1.50737i 0.335175 + 0.942156i \(0.391205\pi\)
−0.824947 + 0.565209i \(0.808795\pi\)
\(180\) 0 0
\(181\) −109.042 + 79.2238i −0.602443 + 0.437700i −0.846745 0.531999i \(-0.821441\pi\)
0.244302 + 0.969699i \(0.421441\pi\)
\(182\) 6.28295 + 8.64773i 0.0345217 + 0.0475150i
\(183\) 0 0
\(184\) −18.0654 5.86982i −0.0981817 0.0319012i
\(185\) 14.2542 + 10.3563i 0.0770495 + 0.0559797i
\(186\) 0 0
\(187\) 143.496 + 93.2344i 0.767359 + 0.498580i
\(188\) −192.911 −1.02612
\(189\) 0 0
\(190\) −21.9812 + 67.6512i −0.115691 + 0.356059i
\(191\) 30.7925 + 94.7695i 0.161217 + 0.496175i 0.998738 0.0502306i \(-0.0159956\pi\)
−0.837521 + 0.546406i \(0.815996\pi\)
\(192\) 0 0
\(193\) −123.902 170.537i −0.641981 0.883611i 0.356738 0.934204i \(-0.383889\pi\)
−0.998719 + 0.0505933i \(0.983889\pi\)
\(194\) −19.3041 + 6.27227i −0.0995054 + 0.0323313i
\(195\) 0 0
\(196\) 162.709 + 118.215i 0.830145 + 0.603136i
\(197\) 51.1334i 0.259561i 0.991543 + 0.129780i \(0.0414272\pi\)
−0.991543 + 0.129780i \(0.958573\pi\)
\(198\) 0 0
\(199\) 77.3567 0.388727 0.194364 0.980930i \(-0.437736\pi\)
0.194364 + 0.980930i \(0.437736\pi\)
\(200\) 43.6038 60.0155i 0.218019 0.300078i
\(201\) 0 0
\(202\) −10.8287 33.3272i −0.0536073 0.164986i
\(203\) 27.3867 19.8976i 0.134910 0.0980178i
\(204\) 0 0
\(205\) 49.6101 16.1193i 0.242000 0.0786307i
\(206\) −0.839281 0.272699i −0.00407418 0.00132378i
\(207\) 0 0
\(208\) 50.5123i 0.242848i
\(209\) 336.603 17.5630i 1.61054 0.0840335i
\(210\) 0 0
\(211\) −2.82171 + 3.88375i −0.0133730 + 0.0184064i −0.815651 0.578544i \(-0.803621\pi\)
0.802278 + 0.596950i \(0.203621\pi\)
\(212\) 72.0266 221.675i 0.339748 1.04564i
\(213\) 0 0
\(214\) 9.25012 6.72060i 0.0432248 0.0314047i
\(215\) 17.4185 + 23.9745i 0.0810163 + 0.111509i
\(216\) 0 0
\(217\) −38.5506 12.5258i −0.177652 0.0577228i
\(218\) −46.9889 34.1394i −0.215545 0.156603i
\(219\) 0 0
\(220\) −307.420 82.4486i −1.39736 0.374766i
\(221\) 52.9751 0.239706
\(222\) 0 0
\(223\) 77.4813 238.463i 0.347450 1.06934i −0.612810 0.790231i \(-0.709961\pi\)
0.960259 0.279110i \(-0.0900393\pi\)
\(224\) −45.0487 138.646i −0.201110 0.618954i
\(225\) 0 0
\(226\) −33.9383 46.7120i −0.150169 0.206690i
\(227\) 325.217 105.670i 1.43268 0.465504i 0.513070 0.858347i \(-0.328508\pi\)
0.919606 + 0.392842i \(0.128508\pi\)
\(228\) 0 0
\(229\) 187.148 + 135.971i 0.817239 + 0.593759i 0.915920 0.401360i \(-0.131462\pi\)
−0.0986813 + 0.995119i \(0.531462\pi\)
\(230\) 17.8254i 0.0775019i
\(231\) 0 0
\(232\) −8.35147 −0.0359977
\(233\) −50.1968 + 69.0899i −0.215437 + 0.296523i −0.903034 0.429569i \(-0.858665\pi\)
0.687597 + 0.726092i \(0.258665\pi\)
\(234\) 0 0
\(235\) −113.289 348.667i −0.482080 1.48369i
\(236\) −34.7184 + 25.2244i −0.147112 + 0.106883i
\(237\) 0 0
\(238\) −46.4430 + 15.0903i −0.195139 + 0.0634045i
\(239\) −11.2512 3.65574i −0.0470763 0.0152960i 0.285384 0.958413i \(-0.407879\pi\)
−0.332460 + 0.943117i \(0.607879\pi\)
\(240\) 0 0
\(241\) 236.527i 0.981438i −0.871318 0.490719i \(-0.836734\pi\)
0.871318 0.490719i \(-0.163266\pi\)
\(242\) −3.94216 37.6738i −0.0162899 0.155677i
\(243\) 0 0
\(244\) −170.433 + 234.580i −0.698494 + 0.961395i
\(245\) −118.109 + 363.502i −0.482077 + 1.48368i
\(246\) 0 0
\(247\) 84.4160 61.3318i 0.341765 0.248307i
\(248\) 5.87792 + 8.09027i 0.0237013 + 0.0326220i
\(249\) 0 0
\(250\) 11.0130 + 3.57833i 0.0440519 + 0.0143133i
\(251\) −202.797 147.341i −0.807957 0.587015i 0.105281 0.994443i \(-0.466426\pi\)
−0.913238 + 0.407427i \(0.866426\pi\)
\(252\) 0 0
\(253\) −78.8623 + 30.2516i −0.311709 + 0.119572i
\(254\) 60.5263 0.238293
\(255\) 0 0
\(256\) 60.4305 185.986i 0.236057 0.726508i
\(257\) −80.6325 248.161i −0.313745 0.965608i −0.976268 0.216566i \(-0.930514\pi\)
0.662523 0.749042i \(-0.269486\pi\)
\(258\) 0 0
\(259\) 14.0037 + 19.2744i 0.0540683 + 0.0744187i
\(260\) −93.7086 + 30.4478i −0.360418 + 0.117107i
\(261\) 0 0
\(262\) 42.6907 + 31.0166i 0.162942 + 0.118384i
\(263\) 243.396i 0.925459i −0.886499 0.462730i \(-0.846870\pi\)
0.886499 0.462730i \(-0.153130\pi\)
\(264\) 0 0
\(265\) 442.954 1.67152
\(266\) −56.5364 + 77.8157i −0.212543 + 0.292540i
\(267\) 0 0
\(268\) −3.88960 11.9710i −0.0145134 0.0446678i
\(269\) −210.842 + 153.186i −0.783801 + 0.569465i −0.906117 0.423026i \(-0.860968\pi\)
0.122316 + 0.992491i \(0.460968\pi\)
\(270\) 0 0
\(271\) 417.271 135.579i 1.53974 0.500293i 0.588439 0.808542i \(-0.299743\pi\)
0.951306 + 0.308249i \(0.0997428\pi\)
\(272\) −219.469 71.3098i −0.806871 0.262168i
\(273\) 0 0
\(274\) 0.00454288i 1.65798e-5i
\(275\) −17.1883 329.422i −0.0625030 1.19790i
\(276\) 0 0
\(277\) −118.892 + 163.641i −0.429212 + 0.590760i −0.967772 0.251827i \(-0.918969\pi\)
0.538560 + 0.842587i \(0.318969\pi\)
\(278\) −11.4534 + 35.2498i −0.0411992 + 0.126798i
\(279\) 0 0
\(280\) 148.807 108.114i 0.531453 0.386123i
\(281\) 253.750 + 349.257i 0.903026 + 1.24291i 0.969493 + 0.245120i \(0.0788273\pi\)
−0.0664668 + 0.997789i \(0.521173\pi\)
\(282\) 0 0
\(283\) −149.806 48.6750i −0.529350 0.171996i 0.0321343 0.999484i \(-0.489770\pi\)
−0.561485 + 0.827487i \(0.689770\pi\)
\(284\) 368.978 + 268.078i 1.29922 + 0.943937i
\(285\) 0 0
\(286\) −7.37753 9.11477i −0.0257956 0.0318698i
\(287\) 70.5348 0.245766
\(288\) 0 0
\(289\) 14.5193 44.6857i 0.0502397 0.154622i
\(290\) −2.42183 7.45362i −0.00835113 0.0257021i
\(291\) 0 0
\(292\) 42.9408 + 59.1029i 0.147057 + 0.202407i
\(293\) 424.925 138.067i 1.45026 0.471217i 0.525178 0.850992i \(-0.323999\pi\)
0.925079 + 0.379775i \(0.123999\pi\)
\(294\) 0 0
\(295\) −65.9792 47.9367i −0.223658 0.162497i
\(296\) 5.87766i 0.0198570i
\(297\) 0 0
\(298\) −57.1057 −0.191630
\(299\) −15.3694 + 21.1541i −0.0514026 + 0.0707496i
\(300\) 0 0
\(301\) 12.3827 + 38.1100i 0.0411385 + 0.126611i
\(302\) 43.2892 31.4515i 0.143342 0.104144i
\(303\) 0 0
\(304\) −432.283 + 140.457i −1.42198 + 0.462031i
\(305\) −524.069 170.280i −1.71826 0.558296i
\(306\) 0 0
\(307\) 374.322i 1.21929i 0.792674 + 0.609645i \(0.208688\pi\)
−0.792674 + 0.609645i \(0.791312\pi\)
\(308\) −360.895 234.486i −1.17174 0.761318i
\(309\) 0 0
\(310\) −5.51597 + 7.59208i −0.0177934 + 0.0244906i
\(311\) −28.4307 + 87.5008i −0.0914172 + 0.281353i −0.986303 0.164941i \(-0.947257\pi\)
0.894886 + 0.446294i \(0.147257\pi\)
\(312\) 0 0
\(313\) −392.333 + 285.047i −1.25346 + 0.910693i −0.998417 0.0562368i \(-0.982090\pi\)
−0.255044 + 0.966930i \(0.582090\pi\)
\(314\) 5.08376 + 6.99719i 0.0161903 + 0.0222840i
\(315\) 0 0
\(316\) −13.0457 4.23879i −0.0412838 0.0134139i
\(317\) 338.480 + 245.920i 1.06776 + 0.775774i 0.975509 0.219961i \(-0.0705932\pi\)
0.0922530 + 0.995736i \(0.470593\pi\)
\(318\) 0 0
\(319\) −28.8658 + 23.3641i −0.0904884 + 0.0732416i
\(320\) 406.237 1.26949
\(321\) 0 0
\(322\) 7.44839 22.9238i 0.0231317 0.0711919i
\(323\) 147.306 + 453.360i 0.456054 + 1.40359i
\(324\) 0 0
\(325\) −60.0234 82.6151i −0.184687 0.254200i
\(326\) −61.5602 + 20.0021i −0.188835 + 0.0613562i
\(327\) 0 0
\(328\) −14.0780 10.2283i −0.0429208 0.0311838i
\(329\) 495.730i 1.50678i
\(330\) 0 0
\(331\) −232.490 −0.702387 −0.351194 0.936303i \(-0.614224\pi\)
−0.351194 + 0.936303i \(0.614224\pi\)
\(332\) −337.378 + 464.360i −1.01620 + 1.39868i
\(333\) 0 0
\(334\) −6.17352 19.0001i −0.0184836 0.0568866i
\(335\) 19.3521 14.0601i 0.0577675 0.0419705i
\(336\) 0 0
\(337\) 143.609 46.6615i 0.426141 0.138461i −0.0880918 0.996112i \(-0.528077\pi\)
0.514232 + 0.857651i \(0.328077\pi\)
\(338\) 46.8642 + 15.2271i 0.138651 + 0.0450506i
\(339\) 0 0
\(340\) 450.135i 1.32393i
\(341\) 42.9496 + 11.5189i 0.125952 + 0.0337798i
\(342\) 0 0
\(343\) −14.9850 + 20.6251i −0.0436881 + 0.0601315i
\(344\) 3.05489 9.40198i 0.00888049 0.0273313i
\(345\) 0 0
\(346\) −57.4433 + 41.7350i −0.166021 + 0.120621i
\(347\) −154.449 212.581i −0.445099 0.612626i 0.526237 0.850338i \(-0.323603\pi\)
−0.971336 + 0.237712i \(0.923603\pi\)
\(348\) 0 0
\(349\) 418.176 + 135.874i 1.19821 + 0.389323i 0.839103 0.543973i \(-0.183081\pi\)
0.359109 + 0.933295i \(0.383081\pi\)
\(350\) 76.1556 + 55.3303i 0.217587 + 0.158086i
\(351\) 0 0
\(352\) 57.2779 + 149.317i 0.162721 + 0.424195i
\(353\) −479.476 −1.35829 −0.679145 0.734005i \(-0.737649\pi\)
−0.679145 + 0.734005i \(0.737649\pi\)
\(354\) 0 0
\(355\) −267.838 + 824.322i −0.754474 + 2.32203i
\(356\) 79.4465 + 244.511i 0.223164 + 0.686829i
\(357\) 0 0
\(358\) 52.2039 + 71.8524i 0.145821 + 0.200705i
\(359\) −199.027 + 64.6679i −0.554394 + 0.180133i −0.572797 0.819697i \(-0.694142\pi\)
0.0184033 + 0.999831i \(0.494142\pi\)
\(360\) 0 0
\(361\) 467.553 + 339.697i 1.29516 + 0.940990i
\(362\) 42.1945i 0.116559i
\(363\) 0 0
\(364\) −133.233 −0.366026
\(365\) −81.6052 + 112.320i −0.223576 + 0.307726i
\(366\) 0 0
\(367\) 121.788 + 374.824i 0.331846 + 1.02132i 0.968255 + 0.249966i \(0.0804194\pi\)
−0.636408 + 0.771352i \(0.719581\pi\)
\(368\) 92.1489 66.9501i 0.250405 0.181930i
\(369\) 0 0
\(370\) 5.24576 1.70445i 0.0141777 0.00460663i
\(371\) 569.646 + 185.089i 1.53543 + 0.498892i
\(372\) 0 0
\(373\) 497.797i 1.33458i −0.744800 0.667288i \(-0.767455\pi\)
0.744800 0.667288i \(-0.232545\pi\)
\(374\) 50.0175 19.1867i 0.133737 0.0513014i
\(375\) 0 0
\(376\) −71.8860 + 98.9425i −0.191186 + 0.263145i
\(377\) −3.55256 + 10.9336i −0.00942323 + 0.0290017i
\(378\) 0 0
\(379\) 253.529 184.200i 0.668942 0.486015i −0.200729 0.979647i \(-0.564331\pi\)
0.869671 + 0.493632i \(0.164331\pi\)
\(380\) −521.143 717.291i −1.37143 1.88761i
\(381\) 0 0
\(382\) 29.6679 + 9.63969i 0.0776647 + 0.0252348i
\(383\) 218.032 + 158.410i 0.569275 + 0.413603i 0.834842 0.550490i \(-0.185559\pi\)
−0.265567 + 0.964093i \(0.585559\pi\)
\(384\) 0 0
\(385\) 211.871 789.986i 0.550314 2.05191i
\(386\) −65.9902 −0.170959
\(387\) 0 0
\(388\) 78.1795 240.612i 0.201494 0.620133i
\(389\) −71.6009 220.365i −0.184064 0.566491i 0.815867 0.578240i \(-0.196260\pi\)
−0.999931 + 0.0117488i \(0.996260\pi\)
\(390\) 0 0
\(391\) −70.2144 96.6418i −0.179576 0.247166i
\(392\) 121.263 39.4007i 0.309344 0.100512i
\(393\) 0 0
\(394\) 12.9503 + 9.40898i 0.0328689 + 0.0238807i
\(395\) 26.0680i 0.0659950i
\(396\) 0 0
\(397\) −256.488 −0.646065 −0.323033 0.946388i \(-0.604702\pi\)
−0.323033 + 0.946388i \(0.604702\pi\)
\(398\) 14.2343 19.5918i 0.0357645 0.0492256i
\(399\) 0 0
\(400\) 137.461 + 423.061i 0.343652 + 1.05765i
\(401\) −249.122 + 180.998i −0.621252 + 0.451366i −0.853359 0.521324i \(-0.825438\pi\)
0.232106 + 0.972690i \(0.425438\pi\)
\(402\) 0 0
\(403\) 13.0920 4.25386i 0.0324864 0.0105555i
\(404\) 415.401 + 134.972i 1.02822 + 0.334089i
\(405\) 0 0
\(406\) 10.5974i 0.0261021i
\(407\) −16.4433 20.3154i −0.0404013 0.0499150i
\(408\) 0 0
\(409\) 253.972 349.562i 0.620958 0.854676i −0.376464 0.926431i \(-0.622860\pi\)
0.997422 + 0.0717555i \(0.0228601\pi\)
\(410\) 5.04620 15.5306i 0.0123078 0.0378795i
\(411\) 0 0
\(412\) 8.89872 6.46530i 0.0215988 0.0156925i
\(413\) −64.8199 89.2169i −0.156949 0.216022i
\(414\) 0 0
\(415\) −1037.41 337.076i −2.49979 0.812231i
\(416\) 40.0529 + 29.1002i 0.0962811 + 0.0699523i
\(417\) 0 0
\(418\) 57.4897 88.4818i 0.137535 0.211679i
\(419\) −485.955 −1.15980 −0.579898 0.814689i \(-0.696908\pi\)
−0.579898 + 0.814689i \(0.696908\pi\)
\(420\) 0 0
\(421\) −146.062 + 449.532i −0.346940 + 1.06777i 0.613596 + 0.789620i \(0.289722\pi\)
−0.960537 + 0.278153i \(0.910278\pi\)
\(422\) 0.464402 + 1.42928i 0.00110048 + 0.00338693i
\(423\) 0 0
\(424\) −86.8556 119.546i −0.204848 0.281949i
\(425\) 443.688 144.163i 1.04397 0.339207i
\(426\) 0 0
\(427\) −602.809 437.966i −1.41173 1.02568i
\(428\) 142.514i 0.332977i
\(429\) 0 0
\(430\) 9.27708 0.0215746
\(431\) 149.488 205.752i 0.346839 0.477383i −0.599584 0.800312i \(-0.704667\pi\)
0.946423 + 0.322928i \(0.104667\pi\)
\(432\) 0 0
\(433\) −18.7374 57.6679i −0.0432735 0.133182i 0.927086 0.374850i \(-0.122306\pi\)
−0.970359 + 0.241667i \(0.922306\pi\)
\(434\) −10.2660 + 7.45868i −0.0236544 + 0.0171859i
\(435\) 0 0
\(436\) 688.513 223.712i 1.57916 0.513100i
\(437\) −223.774 72.7085i −0.512068 0.166381i
\(438\) 0 0
\(439\) 190.549i 0.434053i −0.976166 0.217026i \(-0.930364\pi\)
0.976166 0.217026i \(-0.0696358\pi\)
\(440\) −156.843 + 126.950i −0.356462 + 0.288522i
\(441\) 0 0
\(442\) 9.74786 13.4168i 0.0220540 0.0303547i
\(443\) 89.7905 276.347i 0.202687 0.623808i −0.797113 0.603830i \(-0.793641\pi\)
0.999800 0.0199775i \(-0.00635945\pi\)
\(444\) 0 0
\(445\) −395.274 + 287.183i −0.888255 + 0.645355i
\(446\) −46.1373 63.5025i −0.103447 0.142382i
\(447\) 0 0
\(448\) 522.428 + 169.747i 1.16613 + 0.378900i
\(449\) 371.736 + 270.082i 0.827920 + 0.601519i 0.918970 0.394327i \(-0.129022\pi\)
−0.0910497 + 0.995846i \(0.529022\pi\)
\(450\) 0 0
\(451\) −77.2736 + 4.03192i −0.171338 + 0.00893995i
\(452\) 719.680 1.59221
\(453\) 0 0
\(454\) 33.0802 101.810i 0.0728639 0.224252i
\(455\) −78.2426 240.806i −0.171962 0.529244i
\(456\) 0 0
\(457\) 7.50425 + 10.3287i 0.0164207 + 0.0226011i 0.817148 0.576427i \(-0.195554\pi\)
−0.800728 + 0.599028i \(0.795554\pi\)
\(458\) 68.8735 22.3783i 0.150379 0.0488610i
\(459\) 0 0
\(460\) 179.749 + 130.595i 0.390758 + 0.283903i
\(461\) 109.347i 0.237195i −0.992942 0.118597i \(-0.962160\pi\)
0.992942 0.118597i \(-0.0378397\pi\)
\(462\) 0 0
\(463\) 419.108 0.905202 0.452601 0.891713i \(-0.350496\pi\)
0.452601 + 0.891713i \(0.350496\pi\)
\(464\) 29.4355 40.5145i 0.0634386 0.0873158i
\(465\) 0 0
\(466\) 8.26148 + 25.4262i 0.0177285 + 0.0545627i
\(467\) −371.163 + 269.666i −0.794782 + 0.577443i −0.909379 0.415969i \(-0.863442\pi\)
0.114597 + 0.993412i \(0.463442\pi\)
\(468\) 0 0
\(469\) 30.7622 9.99524i 0.0655910 0.0213118i
\(470\) −109.151 35.4655i −0.232237 0.0754584i
\(471\) 0 0
\(472\) 27.2063i 0.0576406i
\(473\) −15.7442 41.0431i −0.0332857 0.0867719i
\(474\) 0 0
\(475\) 540.114 743.403i 1.13708 1.56506i
\(476\) 188.090 578.881i 0.395146 1.21614i
\(477\) 0 0
\(478\) −2.99619 + 2.17686i −0.00626819 + 0.00455410i
\(479\) −146.233 201.272i −0.305288 0.420192i 0.628617 0.777715i \(-0.283621\pi\)
−0.933904 + 0.357523i \(0.883621\pi\)
\(480\) 0 0
\(481\) −7.69496 2.50025i −0.0159978 0.00519802i
\(482\) −59.9041 43.5228i −0.124282 0.0902964i
\(483\) 0 0
\(484\) 408.778 + 236.259i 0.844583 + 0.488138i
\(485\) 480.793 0.991326
\(486\) 0 0
\(487\) 42.9047 132.047i 0.0880999 0.271144i −0.897294 0.441433i \(-0.854470\pi\)
0.985394 + 0.170289i \(0.0544703\pi\)
\(488\) 56.8048 + 174.827i 0.116403 + 0.358252i
\(489\) 0 0
\(490\) 70.3295 + 96.8003i 0.143530 + 0.197552i
\(491\) −210.976 + 68.5501i −0.429686 + 0.139613i −0.515872 0.856666i \(-0.672532\pi\)
0.0861863 + 0.996279i \(0.472532\pi\)
\(492\) 0 0
\(493\) −42.4899 30.8707i −0.0861864 0.0626181i
\(494\) 32.6652i 0.0661240i
\(495\) 0 0
\(496\) −59.9647 −0.120897
\(497\) −688.889 + 948.174i −1.38609 + 1.90780i
\(498\) 0 0
\(499\) −232.279 714.883i −0.465490 1.43263i −0.858365 0.513039i \(-0.828520\pi\)
0.392875 0.919592i \(-0.371480\pi\)
\(500\) −116.768 + 84.8369i −0.233536 + 0.169674i
\(501\) 0 0
\(502\) −74.6327 + 24.2496i −0.148671 + 0.0483061i
\(503\) 12.8246 + 4.16698i 0.0254963 + 0.00828425i 0.321737 0.946829i \(-0.395733\pi\)
−0.296241 + 0.955113i \(0.595733\pi\)
\(504\) 0 0
\(505\) 830.059i 1.64368i
\(506\) −6.84962 + 25.5397i −0.0135368 + 0.0504736i
\(507\) 0 0
\(508\) −443.437 + 610.338i −0.872907 + 1.20145i
\(509\) −226.024 + 695.630i −0.444055 + 1.36666i 0.439462 + 0.898261i \(0.355169\pi\)
−0.883517 + 0.468399i \(0.844831\pi\)
\(510\) 0 0
\(511\) −151.879 + 110.346i −0.297218 + 0.215942i
\(512\) −213.036 293.219i −0.416086 0.572694i
\(513\) 0 0
\(514\) −77.6877 25.2423i −0.151143 0.0491095i
\(515\) 16.9112 + 12.2867i 0.0328373 + 0.0238577i
\(516\) 0 0
\(517\) 28.3369 + 543.090i 0.0548103 + 1.05047i
\(518\) 7.45835 0.0143984
\(519\) 0 0
\(520\) −19.3030 + 59.4084i −0.0371211 + 0.114247i
\(521\) −217.426 669.168i −0.417324 1.28439i −0.910156 0.414266i \(-0.864038\pi\)
0.492832 0.870125i \(-0.335962\pi\)
\(522\) 0 0
\(523\) 484.863 + 667.357i 0.927080 + 1.27602i 0.960988 + 0.276591i \(0.0892048\pi\)
−0.0339075 + 0.999425i \(0.510795\pi\)
\(524\) −625.533 + 203.248i −1.19377 + 0.387878i
\(525\) 0 0
\(526\) −61.6438 44.7868i −0.117194 0.0851461i
\(527\) 62.8884i 0.119333i
\(528\) 0 0
\(529\) −470.038 −0.888540
\(530\) 81.5072 112.185i 0.153787 0.211670i
\(531\) 0 0
\(532\) −370.476 1140.21i −0.696384 2.14325i
\(533\) −19.3793 + 14.0799i −0.0363589 + 0.0264163i
\(534\) 0 0
\(535\) −257.580 + 83.6928i −0.481458 + 0.156435i
\(536\) −7.58923 2.46589i −0.0141590 0.00460054i
\(537\) 0 0
\(538\) 81.5866i 0.151648i
\(539\) 308.902 475.428i 0.573102 0.882056i
\(540\) 0 0
\(541\) −579.943 + 798.223i −1.07198 + 1.47546i −0.203931 + 0.978985i \(0.565372\pi\)
−0.868052 + 0.496473i \(0.834628\pi\)
\(542\) 42.4436 130.628i 0.0783093 0.241011i
\(543\) 0 0
\(544\) −182.980 + 132.943i −0.336361 + 0.244380i
\(545\) 808.672 + 1113.04i 1.48380 + 2.04228i
\(546\) 0 0
\(547\) −96.5105 31.3582i −0.176436 0.0573276i 0.219467 0.975620i \(-0.429568\pi\)
−0.395903 + 0.918292i \(0.629568\pi\)
\(548\) −0.0458096 0.0332827i −8.35942e−5 6.07348e-5i
\(549\) 0 0
\(550\) −86.5941 56.2632i −0.157444 0.102297i
\(551\) −103.448 −0.187747
\(552\) 0 0
\(553\) 10.8926 33.5239i 0.0196972 0.0606218i
\(554\) 19.5675 + 60.2224i 0.0353203 + 0.108705i
\(555\) 0 0
\(556\) −271.542 373.746i −0.488386 0.672205i
\(557\) 832.827 270.602i 1.49520 0.485820i 0.556587 0.830789i \(-0.312111\pi\)
0.938614 + 0.344969i \(0.112111\pi\)
\(558\) 0 0
\(559\) −11.0095 7.99885i −0.0196949 0.0143092i
\(560\) 1102.95i 1.96955i
\(561\) 0 0
\(562\) 135.147 0.240475
\(563\) 443.883 610.953i 0.788425 1.08517i −0.205878 0.978578i \(-0.566005\pi\)
0.994302 0.106596i \(-0.0339951\pi\)
\(564\) 0 0
\(565\) 422.639 + 1300.75i 0.748034 + 2.30221i
\(566\) −39.8933 + 28.9841i −0.0704828 + 0.0512087i
\(567\) 0 0
\(568\) 274.990 89.3498i 0.484138 0.157306i
\(569\) 228.284 + 74.1740i 0.401203 + 0.130359i 0.502666 0.864481i \(-0.332353\pi\)
−0.101464 + 0.994839i \(0.532353\pi\)
\(570\) 0 0
\(571\) 343.953i 0.602369i −0.953566 0.301184i \(-0.902618\pi\)
0.953566 0.301184i \(-0.0973820\pi\)
\(572\) 145.962 7.61590i 0.255179 0.0133145i
\(573\) 0 0
\(574\) 12.9790 17.8641i 0.0226115 0.0311220i
\(575\) −71.1573 + 219.000i −0.123752 + 0.380869i
\(576\) 0 0
\(577\) 746.570 542.415i 1.29388 0.940060i 0.294006 0.955804i \(-0.405012\pi\)
0.999876 + 0.0157437i \(0.00501159\pi\)
\(578\) −8.64569 11.8998i −0.0149579 0.0205878i
\(579\) 0 0
\(580\) 92.9042 + 30.1864i 0.160180 + 0.0520455i
\(581\) −1193.28 866.970i −2.05384 1.49220i
\(582\) 0 0
\(583\) −634.649 170.210i −1.08859 0.291955i
\(584\) 46.3148 0.0793061
\(585\) 0 0
\(586\) 43.2222 133.024i 0.0737581 0.227004i
\(587\) 0.794599 + 2.44552i 0.00135366 + 0.00416614i 0.951731 0.306933i \(-0.0993028\pi\)
−0.950377 + 0.311099i \(0.899303\pi\)
\(588\) 0 0
\(589\) 72.8089 + 100.213i 0.123614 + 0.170141i
\(590\) −24.2814 + 7.88952i −0.0411550 + 0.0133721i
\(591\) 0 0
\(592\) 28.5136 + 20.7164i 0.0481649 + 0.0349939i
\(593\) 115.926i 0.195491i −0.995211 0.0977456i \(-0.968837\pi\)
0.995211 0.0977456i \(-0.0311631\pi\)
\(594\) 0 0
\(595\) 1156.73 1.94408
\(596\) 418.376 575.845i 0.701973 0.966183i
\(597\) 0 0
\(598\) 2.52952 + 7.78507i 0.00422997 + 0.0130185i
\(599\) 183.263 133.148i 0.305948 0.222284i −0.424208 0.905565i \(-0.639448\pi\)
0.730156 + 0.683281i \(0.239448\pi\)
\(600\) 0 0
\(601\) −540.904 + 175.750i −0.900006 + 0.292430i −0.722240 0.691643i \(-0.756887\pi\)
−0.177767 + 0.984073i \(0.556887\pi\)
\(602\) 11.9305 + 3.87644i 0.0198181 + 0.00643928i
\(603\) 0 0
\(604\) 666.946i 1.10422i
\(605\) −186.955 + 877.571i −0.309017 + 1.45053i
\(606\) 0 0
\(607\) −182.276 + 250.882i −0.300291 + 0.413315i −0.932323 0.361628i \(-0.882221\pi\)
0.632032 + 0.774942i \(0.282221\pi\)
\(608\) −137.665 + 423.690i −0.226423 + 0.696858i
\(609\) 0 0
\(610\) −139.559 + 101.396i −0.228785 + 0.166222i
\(611\) 98.9555 + 136.200i 0.161957 + 0.222914i
\(612\) 0 0
\(613\) −213.251 69.2895i −0.347881 0.113033i 0.129864 0.991532i \(-0.458546\pi\)
−0.477745 + 0.878498i \(0.658546\pi\)
\(614\) 94.8029 + 68.8784i 0.154402 + 0.112180i
\(615\) 0 0
\(616\) −254.749 + 97.7219i −0.413554 + 0.158639i
\(617\) −693.508 −1.12400 −0.562000 0.827137i \(-0.689968\pi\)
−0.562000 + 0.827137i \(0.689968\pi\)
\(618\) 0 0
\(619\) 115.272 354.771i 0.186223 0.573135i −0.813744 0.581223i \(-0.802574\pi\)
0.999967 + 0.00808783i \(0.00257446\pi\)
\(620\) −36.1455 111.244i −0.0582991 0.179426i
\(621\) 0 0
\(622\) 16.9295 + 23.3014i 0.0272178 + 0.0374621i
\(623\) −628.328 + 204.156i −1.00855 + 0.327699i
\(624\) 0 0
\(625\) 384.617 + 279.441i 0.615387 + 0.447105i
\(626\) 151.816i 0.242517i
\(627\) 0 0
\(628\) −107.804 −0.171662
\(629\) 21.7264 29.9039i 0.0345412 0.0475419i
\(630\) 0 0
\(631\) −214.459 660.038i −0.339872 1.04602i −0.964272 0.264914i \(-0.914656\pi\)
0.624400 0.781105i \(-0.285344\pi\)
\(632\) −7.03536 + 5.11149i −0.0111319 + 0.00808780i
\(633\) 0 0
\(634\) 124.566 40.4741i 0.196477 0.0638392i
\(635\) −1363.54 443.040i −2.14730 0.697701i
\(636\) 0 0
\(637\) 175.516i 0.275535i
\(638\) 0.605772 + 11.6099i 0.000949485 + 0.0181973i
\(639\) 0 0
\(640\) 328.228 451.767i 0.512857 0.705887i
\(641\) 272.173 837.663i 0.424607 1.30681i −0.478762 0.877945i \(-0.658914\pi\)
0.903370 0.428863i \(-0.141086\pi\)
\(642\) 0 0
\(643\) 835.085 606.725i 1.29873 0.943584i 0.298790 0.954319i \(-0.403417\pi\)
0.999942 + 0.0107345i \(0.00341696\pi\)
\(644\) 176.590 + 243.056i 0.274209 + 0.377416i
\(645\) 0 0
\(646\) 141.926 + 46.1145i 0.219700 + 0.0713847i
\(647\) −287.108 208.596i −0.443752 0.322405i 0.343372 0.939199i \(-0.388431\pi\)
−0.787124 + 0.616795i \(0.788431\pi\)
\(648\) 0 0
\(649\) 76.1125 + 94.0353i 0.117277 + 0.144893i
\(650\) −31.9684 −0.0491821
\(651\) 0 0
\(652\) 249.313 767.305i 0.382381 1.17685i
\(653\) 222.565 + 684.985i 0.340835 + 1.04898i 0.963776 + 0.266713i \(0.0859376\pi\)
−0.622941 + 0.782269i \(0.714062\pi\)
\(654\) 0 0
\(655\) −734.701 1011.23i −1.12168 1.54386i
\(656\) 99.2387 32.2446i 0.151278 0.0491534i
\(657\) 0 0
\(658\) −125.551 91.2183i −0.190807 0.138630i
\(659\) 745.955i 1.13195i −0.824423 0.565975i \(-0.808500\pi\)
0.824423 0.565975i \(-0.191500\pi\)
\(660\) 0 0
\(661\) −655.463 −0.991623 −0.495811 0.868430i \(-0.665129\pi\)
−0.495811 + 0.868430i \(0.665129\pi\)
\(662\) −42.7801 + 58.8818i −0.0646225 + 0.0889453i
\(663\) 0 0
\(664\) 112.447 + 346.077i 0.169348 + 0.521200i
\(665\) 1843.25 1339.20i 2.77180 2.01383i
\(666\) 0 0
\(667\) 24.6547 8.01081i 0.0369636 0.0120102i
\(668\) 236.824 + 76.9486i 0.354526 + 0.115193i
\(669\) 0 0
\(670\) 7.48840i 0.0111767i
\(671\) 685.435 + 445.351i 1.02151 + 0.663712i
\(672\) 0 0
\(673\) 668.255 919.774i 0.992950 1.36668i 0.0633970 0.997988i \(-0.479807\pi\)
0.929553 0.368690i \(-0.120193\pi\)
\(674\) 14.6076 44.9574i 0.0216729 0.0667024i
\(675\) 0 0
\(676\) −496.891 + 361.012i −0.735045 + 0.534042i
\(677\) 282.199 + 388.414i 0.416838 + 0.573728i 0.964869 0.262730i \(-0.0846227\pi\)
−0.548032 + 0.836457i \(0.684623\pi\)
\(678\) 0 0
\(679\) 618.308 + 200.900i 0.910615 + 0.295877i
\(680\) −230.871 167.737i −0.339516 0.246673i
\(681\) 0 0
\(682\) 10.8204 8.75809i 0.0158657 0.0128418i
\(683\) 110.003 0.161059 0.0805294 0.996752i \(-0.474339\pi\)
0.0805294 + 0.996752i \(0.474339\pi\)
\(684\) 0 0
\(685\) 0.0332529 0.102342i 4.85444e−5 0.000149404i
\(686\) 2.46627 + 7.59038i 0.00359514 + 0.0110647i
\(687\) 0 0
\(688\) 34.8435 + 47.9580i 0.0506447 + 0.0697064i
\(689\) −193.456 + 62.8575i −0.280777 + 0.0912301i
\(690\) 0 0
\(691\) 436.497 + 317.134i 0.631689 + 0.458949i 0.856985 0.515341i \(-0.172335\pi\)
−0.225296 + 0.974290i \(0.572335\pi\)
\(692\) 885.013i 1.27892i
\(693\) 0 0
\(694\) −82.2595 −0.118530
\(695\) 516.043 710.272i 0.742507 1.02197i
\(696\) 0 0
\(697\) −33.8168 104.077i −0.0485176 0.149322i
\(698\) 111.360 80.9078i 0.159542 0.115914i
\(699\) 0 0
\(700\) −1115.88 + 362.572i −1.59412 + 0.517961i
\(701\) 396.564 + 128.852i 0.565712 + 0.183811i 0.577890 0.816115i \(-0.303876\pi\)
−0.0121775 + 0.999926i \(0.503876\pi\)
\(702\) 0 0
\(703\) 72.8057i 0.103564i
\(704\) −582.043 156.101i −0.826765 0.221735i
\(705\) 0 0
\(706\) −88.2276 + 121.435i −0.124968 + 0.172004i
\(707\) −346.842 + 1067.47i −0.490583 + 1.50986i
\(708\) 0 0
\(709\) 73.0353 53.0633i 0.103012 0.0748424i −0.535087 0.844797i \(-0.679721\pi\)
0.638099 + 0.769955i \(0.279721\pi\)
\(710\) 159.488 + 219.516i 0.224631 + 0.309178i
\(711\) 0 0
\(712\) 155.013 + 50.3667i 0.217714 + 0.0707397i
\(713\) −25.1127 18.2455i −0.0352212 0.0255897i
\(714\) 0 0
\(715\) 99.4827 + 259.340i 0.139137 + 0.362713i
\(716\) −1107.01 −1.54611
\(717\) 0 0
\(718\) −20.2445 + 62.3062i −0.0281957 + 0.0867775i
\(719\) 412.231 + 1268.72i 0.573339 + 1.76456i 0.641766 + 0.766901i \(0.278202\pi\)
−0.0684266 + 0.997656i \(0.521798\pi\)
\(720\) 0 0
\(721\) 16.6141 + 22.8673i 0.0230431 + 0.0317161i
\(722\) 172.067 55.9081i 0.238320 0.0774350i
\(723\) 0 0
\(724\) −425.482 309.131i −0.587683 0.426976i
\(725\) 101.241i 0.139643i
\(726\) 0 0
\(727\) −68.6829 −0.0944744 −0.0472372 0.998884i \(-0.515042\pi\)
−0.0472372 + 0.998884i \(0.515042\pi\)
\(728\) −49.6478 + 68.3344i −0.0681976 + 0.0938659i
\(729\) 0 0
\(730\) 13.4307 + 41.3356i 0.0183983 + 0.0566241i
\(731\) 50.2963 36.5424i 0.0688048 0.0499896i
\(732\) 0 0
\(733\) −629.447 + 204.520i −0.858727 + 0.279017i −0.705097 0.709111i \(-0.749096\pi\)
−0.153630 + 0.988128i \(0.549096\pi\)
\(734\) 117.340 + 38.1261i 0.159864 + 0.0519428i
\(735\) 0 0
\(736\) 111.638i 0.151682i
\(737\) −33.1298 + 12.7086i −0.0449522 + 0.0172437i
\(738\) 0 0
\(739\) −106.053 + 145.970i −0.143509 + 0.197524i −0.874721 0.484627i \(-0.838955\pi\)
0.731211 + 0.682151i \(0.238955\pi\)
\(740\) −21.2448 + 65.3849i −0.0287092 + 0.0883579i
\(741\) 0 0
\(742\) 151.696 110.214i 0.204442 0.148536i
\(743\) 253.792 + 349.314i 0.341577 + 0.470141i 0.944901 0.327356i \(-0.106157\pi\)
−0.603324 + 0.797496i \(0.706157\pi\)
\(744\) 0 0
\(745\) 1286.48 + 418.002i 1.72681 + 0.561076i
\(746\) −126.075 91.5987i −0.169001 0.122787i
\(747\) 0 0
\(748\) −172.969 + 644.937i −0.231243 + 0.862216i
\(749\) −366.223 −0.488949
\(750\) 0 0
\(751\) 204.687 629.961i 0.272552 0.838830i −0.717304 0.696760i \(-0.754624\pi\)
0.989857 0.142070i \(-0.0453757\pi\)
\(752\) −226.620 697.464i −0.301356 0.927479i
\(753\) 0 0
\(754\) 2.11542 + 2.91162i 0.00280559 + 0.00386157i
\(755\) −1205.44 + 391.671i −1.59661 + 0.518769i
\(756\) 0 0
\(757\) −1013.22 736.147i −1.33847 0.972453i −0.999499 0.0316551i \(-0.989922\pi\)
−0.338968 0.940798i \(-0.610078\pi\)
\(758\) 98.1044i 0.129425i
\(759\) 0 0
\(760\) −562.091 −0.739593
\(761\) 366.101 503.895i 0.481079 0.662148i −0.497633 0.867388i \(-0.665797\pi\)
0.978712 + 0.205239i \(0.0657973\pi\)
\(762\) 0 0
\(763\) 574.879 + 1769.29i 0.753445 + 2.31887i
\(764\) −314.562 + 228.543i −0.411731 + 0.299140i
\(765\) 0 0
\(766\) 80.2395 26.0714i 0.104751 0.0340358i
\(767\) 35.6182 + 11.5731i 0.0464384 + 0.0150887i
\(768\) 0 0
\(769\) 39.8312i 0.0517960i 0.999665 + 0.0258980i \(0.00824452\pi\)
−0.999665 + 0.0258980i \(0.991755\pi\)
\(770\) −161.090 199.024i −0.209208 0.258472i
\(771\) 0 0
\(772\) 483.467 665.435i 0.626252 0.861962i
\(773\) 174.658 537.543i 0.225949 0.695398i −0.772245 0.635325i \(-0.780866\pi\)
0.998194 0.0600740i \(-0.0191337\pi\)
\(774\) 0 0
\(775\) 98.0749 71.2556i 0.126548 0.0919427i
\(776\) −94.2753 129.759i −0.121489 0.167215i
\(777\) 0 0
\(778\) −68.9860 22.4149i −0.0886710 0.0288110i
\(779\) −174.382 126.696i −0.223854 0.162640i
\(780\) 0 0
\(781\) 700.504 1078.14i 0.896933 1.38046i
\(782\) −37.3961 −0.0478211
\(783\) 0 0
\(784\) −236.262 + 727.140i −0.301355 + 0.927474i
\(785\) −63.3089 194.845i −0.0806482 0.248210i
\(786\) 0 0
\(787\) 597.189 + 821.960i 0.758817 + 1.04442i 0.997312 + 0.0732781i \(0.0233461\pi\)
−0.238495 + 0.971144i \(0.576654\pi\)
\(788\) −189.757 + 61.6559i −0.240809 + 0.0782435i
\(789\) 0 0
\(790\) −6.60213 4.79673i −0.00835713 0.00607181i
\(791\) 1849.39i 2.33803i
\(792\) 0 0
\(793\) 253.045 0.319099
\(794\) −47.1959 + 64.9596i −0.0594407 + 0.0818131i
\(795\) 0 0
\(796\) 93.2754 + 287.072i 0.117180 + 0.360643i
\(797\) −285.961 + 207.763i −0.358796 + 0.260681i −0.752550 0.658535i \(-0.771176\pi\)
0.393753 + 0.919216i \(0.371176\pi\)
\(798\) 0 0
\(799\) −731.471 + 237.669i −0.915483 + 0.297458i
\(800\) 414.651 + 134.728i 0.518313 + 0.168410i
\(801\) 0 0
\(802\) 96.3992i 0.120199i
\(803\) 160.081 129.570i 0.199354 0.161358i
\(804\) 0 0
\(805\) −335.595 + 461.906i −0.416888 + 0.573797i
\(806\) 1.33169 4.09851i 0.00165222 0.00508500i
\(807\) 0 0
\(808\) 224.020 162.760i 0.277253 0.201436i
\(809\) −269.354 370.734i −0.332947 0.458263i 0.609418 0.792849i \(-0.291403\pi\)
−0.942365 + 0.334587i \(0.891403\pi\)
\(810\) 0 0
\(811\) −1413.55 459.292i −1.74298 0.566328i −0.747756 0.663973i \(-0.768869\pi\)
−0.995221 + 0.0976457i \(0.968869\pi\)
\(812\) 106.863 + 77.6404i 0.131605 + 0.0956163i
\(813\) 0 0
\(814\) −8.17090 + 0.426335i −0.0100380 + 0.000523753i
\(815\) 1533.24 1.88127
\(816\) 0 0
\(817\) 37.8404 116.461i 0.0463163 0.142547i
\(818\) −41.7992 128.645i −0.0510993 0.157267i
\(819\) 0 0
\(820\) 119.638 + 164.668i 0.145900 + 0.200814i
\(821\) −1272.74 + 413.539i −1.55023 + 0.503702i −0.954178 0.299241i \(-0.903267\pi\)
−0.596057 + 0.802942i \(0.703267\pi\)
\(822\) 0 0
\(823\) 837.396 + 608.404i 1.01749 + 0.739252i 0.965767 0.259410i \(-0.0835280\pi\)
0.0517251 + 0.998661i \(0.483528\pi\)
\(824\) 6.97330i 0.00846274i
\(825\) 0 0
\(826\) −34.5230 −0.0417954
\(827\) 530.876 730.689i 0.641930 0.883541i −0.356786 0.934186i \(-0.616128\pi\)
0.998717 + 0.0506448i \(0.0161276\pi\)
\(828\) 0 0
\(829\) −156.886 482.844i −0.189247 0.582442i 0.810749 0.585394i \(-0.199060\pi\)
−0.999996 + 0.00295239i \(0.999060\pi\)
\(830\) −276.262 + 200.716i −0.332846 + 0.241827i
\(831\) 0 0
\(832\) −177.420 + 57.6473i −0.213245 + 0.0692876i
\(833\) 762.593 + 247.781i 0.915478 + 0.297457i
\(834\) 0 0
\(835\) 473.224i 0.566735i
\(836\) 471.047 + 1227.96i 0.563454 + 1.46886i
\(837\) 0 0
\(838\) −89.4197 + 123.076i −0.106706 + 0.146868i
\(839\) 368.755 1134.91i 0.439518 1.35270i −0.448868 0.893598i \(-0.648173\pi\)
0.888386 0.459098i \(-0.151827\pi\)
\(840\) 0 0
\(841\) −671.162 + 487.628i −0.798053 + 0.579819i
\(842\) 86.9745 + 119.710i 0.103295 + 0.142174i
\(843\) 0 0
\(844\) −17.8150 5.78846i −0.0211079 0.00685836i
\(845\) −944.297 686.072i −1.11751 0.811919i
\(846\) 0 0
\(847\) −607.122 + 1050.45i −0.716791 + 1.24020i
\(848\) 886.073 1.04490
\(849\) 0 0
\(850\) 45.1307 138.898i 0.0530950 0.163410i
\(851\) 5.63791 + 17.3517i 0.00662504 + 0.0203898i
\(852\) 0 0
\(853\) 690.939 + 950.997i 0.810011 + 1.11488i 0.991322 + 0.131459i \(0.0419661\pi\)
−0.181311 + 0.983426i \(0.558034\pi\)
\(854\) −221.844 + 72.0813i −0.259770 + 0.0844044i
\(855\) 0 0
\(856\) 73.0944 + 53.1062i 0.0853906 + 0.0620399i
\(857\) 921.178i 1.07489i 0.843300 + 0.537444i \(0.180610\pi\)
−0.843300 + 0.537444i \(0.819390\pi\)
\(858\) 0 0
\(859\) −674.852 −0.785625 −0.392813 0.919619i \(-0.628498\pi\)
−0.392813 + 0.919619i \(0.628498\pi\)
\(860\) −67.9670 + 93.5486i −0.0790314 + 0.108777i
\(861\) 0 0
\(862\) −24.6030 75.7202i −0.0285418 0.0878425i
\(863\) −533.760 + 387.799i −0.618494 + 0.449362i −0.852395 0.522898i \(-0.824851\pi\)
0.233901 + 0.972260i \(0.424851\pi\)
\(864\) 0 0
\(865\) 1599.57 519.733i 1.84922 0.600847i
\(866\) −18.0531 5.86582i −0.0208466 0.00677347i
\(867\) 0 0
\(868\) 158.165i 0.182218i
\(869\) −10.0169 + 37.3493i −0.0115270 + 0.0429797i
\(870\) 0 0
\(871\) −6.45663 + 8.88678i −0.00741289 + 0.0102030i
\(872\) 141.826 436.497i 0.162645 0.500569i
\(873\) 0 0
\(874\) −59.5908 + 43.2952i −0.0681817 + 0.0495369i
\(875\) −218.008 300.063i −0.249152 0.342929i
\(876\) 0 0
\(877\) −132.496 43.0505i −0.151078 0.0490883i 0.232502 0.972596i \(-0.425309\pi\)
−0.383580 + 0.923508i \(0.625309\pi\)
\(878\) −48.2596 35.0626i −0.0549653 0.0399346i
\(879\) 0 0
\(880\) −63.0469 1208.32i −0.0716442 1.37309i
\(881\) 28.6079 0.0324721 0.0162360 0.999868i \(-0.494832\pi\)
0.0162360 + 0.999868i \(0.494832\pi\)
\(882\) 0 0
\(883\) −234.024 + 720.250i −0.265032 + 0.815686i 0.726654 + 0.687004i \(0.241075\pi\)
−0.991686 + 0.128682i \(0.958925\pi\)
\(884\) 63.8765 + 196.592i 0.0722585 + 0.222389i
\(885\) 0 0
\(886\) −53.4669 73.5909i −0.0603464 0.0830597i
\(887\) 953.563 309.831i 1.07504 0.349303i 0.282593 0.959240i \(-0.408805\pi\)
0.792450 + 0.609937i \(0.208805\pi\)
\(888\) 0 0
\(889\) −1568.41 1139.51i −1.76424 1.28179i
\(890\) 152.953i 0.171858i
\(891\) 0 0
\(892\) 978.366 1.09682
\(893\) −890.440 + 1225.59i −0.997133 + 1.37244i
\(894\) 0 0
\(895\) −650.103 2000.81i −0.726372 2.23554i
\(896\) 610.879 443.829i 0.681784 0.495345i
\(897\) 0 0
\(898\) 136.805 44.4507i 0.152344 0.0494996i
\(899\) −12.9797 4.21735i −0.0144379 0.00469115i
\(900\) 0 0
\(901\) 929.275i 1.03138i
\(902\) −13.1978 + 20.3127i −0.0146317 + 0.0225196i
\(903\) 0 0
\(904\) 268.180 369.118i 0.296660 0.408317i
\(905\) 308.855 950.557i 0.341276 1.05034i
\(906\) 0 0
\(907\) −1050.71 + 763.387i −1.15845 + 0.841661i −0.989581 0.143977i \(-0.954011\pi\)
−0.168867 + 0.985639i \(0.554011\pi\)
\(908\) 784.283 + 1079.47i 0.863748 + 1.18885i
\(909\) 0 0
\(910\) −75.3851 24.4941i −0.0828408 0.0269166i
\(911\) −627.031 455.565i −0.688288 0.500071i 0.187809 0.982206i \(-0.439862\pi\)
−0.876097 + 0.482135i \(0.839862\pi\)
\(912\) 0 0
\(913\) 1356.84 + 881.588i 1.48614 + 0.965595i
\(914\) 3.99675 0.00437281
\(915\) 0 0
\(916\) −278.931 + 858.460i −0.304509 + 0.937184i
\(917\) −522.293 1607.45i −0.569567 1.75295i
\(918\) 0 0
\(919\) −63.8375 87.8648i −0.0694641 0.0956091i 0.772871 0.634563i \(-0.218820\pi\)
−0.842335 + 0.538954i \(0.818820\pi\)
\(920\) 133.963 43.5271i 0.145611 0.0473120i
\(921\) 0 0
\(922\) −27.6938 20.1207i −0.0300366 0.0218229i
\(923\) 398.022i 0.431226i
\(924\) 0 0
\(925\) −71.2524 −0.0770296
\(926\) 77.1194 106.146i 0.0832823 0.114628i
\(927\) 0 0
\(928\) −15.1675 46.6809i −0.0163443 0.0503027i
\(929\) 245.254 178.187i 0.263997 0.191805i −0.447910 0.894079i \(-0.647832\pi\)
0.711907 + 0.702273i \(0.247832\pi\)
\(930\) 0 0
\(931\) 1502.06 488.050i 1.61339 0.524221i
\(932\) −316.920 102.974i −0.340043 0.110487i
\(933\) 0 0
\(934\) 143.624i 0.153773i
\(935\) −1267.24 + 66.1209i −1.35533 + 0.0707175i
\(936\) 0 0
\(937\) 209.048 287.730i 0.223104 0.307076i −0.682762 0.730641i \(-0.739221\pi\)
0.905866 + 0.423565i \(0.139221\pi\)
\(938\) 3.12904 9.63021i 0.00333587 0.0102667i
\(939\) 0 0
\(940\) 1157.31 840.834i 1.23118 0.894504i
\(941\) −735.016 1011.66i −0.781101 1.07509i −0.995160 0.0982724i \(-0.968668\pi\)
0.214059 0.976821i \(-0.431332\pi\)
\(942\) 0 0
\(943\) 51.3714 + 16.6916i 0.0544766 + 0.0177005i
\(944\) −131.983 95.8913i −0.139813 0.101580i
\(945\) 0 0
\(946\) −13.2919 3.56482i −0.0140506 0.00376831i
\(947\) 373.371 0.394267 0.197134 0.980377i \(-0.436837\pi\)
0.197134 + 0.980377i \(0.436837\pi\)
\(948\) 0 0
\(949\) 19.7014 60.6348i 0.0207602 0.0638933i
\(950\) −88.8930 273.585i −0.0935716 0.287984i
\(951\) 0 0
\(952\) −226.814 312.183i −0.238250 0.327923i
\(953\) −626.818 + 203.666i −0.657732 + 0.213710i −0.618820 0.785533i \(-0.712389\pi\)
−0.0389116 + 0.999243i \(0.512389\pi\)
\(954\) 0 0
\(955\) −597.798 434.326i −0.625967 0.454791i
\(956\) 46.1616i 0.0482862i
\(957\) 0 0
\(958\) −77.8833 −0.0812979
\(959\) 0.0855275 0.117719i 8.91841e−5 0.000122751i
\(960\) 0 0
\(961\) −291.915 898.423i −0.303762 0.934884i
\(962\) −2.04916 + 1.48880i −0.00213011 + 0.00154761i
\(963\) 0 0
\(964\) 877.755 285.200i 0.910534 0.295850i
\(965\) 1486.63 + 483.034i 1.54055 + 0.500554i
\(966\) 0 0
\(967\) 1521.95i 1.57389i 0.617021 + 0.786947i \(0.288339\pi\)
−0.617021 + 0.786947i \(0.711661\pi\)
\(968\) 273.502 121.620i 0.282543 0.125641i
\(969\) 0 0
\(970\) 88.4699 121.768i 0.0912061 0.125534i
\(971\) −308.318 + 948.907i −0.317527 + 0.977247i 0.657175 + 0.753738i \(0.271751\pi\)
−0.974702 + 0.223509i \(0.928249\pi\)
\(972\) 0 0
\(973\) 960.428 697.792i 0.987079 0.717155i
\(974\) −25.5481 35.1640i −0.0262301 0.0361027i
\(975\) 0 0
\(976\) −1048.33 340.624i −1.07411 0.349000i
\(977\) 1399.82 + 1017.03i 1.43278 + 1.04097i 0.989491 + 0.144593i \(0.0461873\pi\)
0.443286 + 0.896380i \(0.353813\pi\)
\(978\) 0 0
\(979\) 676.687 259.577i 0.691203 0.265145i
\(980\) −1491.38 −1.52181
\(981\) 0 0
\(982\) −21.4599 + 66.0467i −0.0218532 + 0.0672573i
\(983\) −57.9189 178.256i −0.0589206 0.181339i 0.917264 0.398279i \(-0.130392\pi\)
−0.976185 + 0.216940i \(0.930392\pi\)
\(984\) 0 0
\(985\) −222.874 306.759i −0.226268 0.311431i
\(986\) −15.6370 + 5.08077i −0.0158590 + 0.00515291i
\(987\) 0 0
\(988\) 329.391 + 239.317i 0.333392 + 0.242223i
\(989\) 30.6863i 0.0310276i
\(990\) 0 0
\(991\) 1229.91 1.24108 0.620540 0.784175i \(-0.286913\pi\)
0.620540 + 0.784175i \(0.286913\pi\)
\(992\) −34.5457 + 47.5481i −0.0348243 + 0.0479315i
\(993\) 0 0
\(994\) 113.379 + 348.944i 0.114063 + 0.351050i
\(995\) −464.077 + 337.172i −0.466409 + 0.338866i
\(996\) 0 0
\(997\) −1782.23 + 579.083i −1.78760 + 0.580826i −0.999401 0.0345987i \(-0.988985\pi\)
−0.788196 + 0.615424i \(0.788985\pi\)
\(998\) −223.797 72.7159i −0.224245 0.0728616i
\(999\) 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 99.3.k.c.73.3 16
3.2 odd 2 33.3.g.a.7.2 16
11.5 even 5 1089.3.c.m.604.9 16
11.6 odd 10 1089.3.c.m.604.8 16
11.8 odd 10 inner 99.3.k.c.19.3 16
12.11 even 2 528.3.bf.b.337.2 16
33.2 even 10 363.3.g.g.94.2 16
33.5 odd 10 363.3.c.e.241.8 16
33.8 even 10 33.3.g.a.19.2 yes 16
33.14 odd 10 363.3.g.f.118.3 16
33.17 even 10 363.3.c.e.241.9 16
33.20 odd 10 363.3.g.a.94.3 16
33.26 odd 10 363.3.g.g.112.2 16
33.29 even 10 363.3.g.a.112.3 16
33.32 even 2 363.3.g.f.40.3 16
132.107 odd 10 528.3.bf.b.481.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.3.g.a.7.2 16 3.2 odd 2
33.3.g.a.19.2 yes 16 33.8 even 10
99.3.k.c.19.3 16 11.8 odd 10 inner
99.3.k.c.73.3 16 1.1 even 1 trivial
363.3.c.e.241.8 16 33.5 odd 10
363.3.c.e.241.9 16 33.17 even 10
363.3.g.a.94.3 16 33.20 odd 10
363.3.g.a.112.3 16 33.29 even 10
363.3.g.f.40.3 16 33.32 even 2
363.3.g.f.118.3 16 33.14 odd 10
363.3.g.g.94.2 16 33.2 even 10
363.3.g.g.112.2 16 33.26 odd 10
528.3.bf.b.337.2 16 12.11 even 2
528.3.bf.b.481.2 16 132.107 odd 10
1089.3.c.m.604.8 16 11.6 odd 10
1089.3.c.m.604.9 16 11.5 even 5