Properties

Label 441.2.s.d.362.5
Level $441$
Weight $2$
Character 441.362
Analytic conductor $3.521$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(362,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 362.5
Character \(\chi\) \(=\) 441.362
Dual form 441.2.s.d.374.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61855 + 0.934468i) q^{2} +(-0.710525 + 1.57961i) q^{3} +(0.746462 - 1.29291i) q^{4} +2.50573 q^{5} +(-0.326074 - 3.22063i) q^{6} -0.947692i q^{8} +(-1.99031 - 2.24470i) q^{9} +O(q^{10})\) \(q+(-1.61855 + 0.934468i) q^{2} +(-0.710525 + 1.57961i) q^{3} +(0.746462 - 1.29291i) q^{4} +2.50573 q^{5} +(-0.326074 - 3.22063i) q^{6} -0.947692i q^{8} +(-1.99031 - 2.24470i) q^{9} +(-4.05565 + 2.34153i) q^{10} +5.60957i q^{11} +(1.51191 + 2.09776i) q^{12} +(-0.384312 + 0.221883i) q^{13} +(-1.78039 + 3.95807i) q^{15} +(2.37851 + 4.11970i) q^{16} +(1.53885 + 2.66536i) q^{17} +(5.31901 + 1.77327i) q^{18} +(-2.22932 - 1.28710i) q^{19} +(1.87044 - 3.23969i) q^{20} +(-5.24197 - 9.07935i) q^{22} +7.89210i q^{23} +(1.49698 + 0.673359i) q^{24} +1.27870 q^{25} +(0.414685 - 0.718255i) q^{26} +(4.95990 - 1.54899i) q^{27} +(2.71041 + 1.56485i) q^{29} +(-0.817055 - 8.07004i) q^{30} +(-9.06457 - 5.23343i) q^{31} +(-6.05802 - 3.49760i) q^{32} +(-8.86091 - 3.98574i) q^{33} +(-4.98140 - 2.87601i) q^{34} +(-4.38788 + 0.897709i) q^{36} +(0.708168 - 1.22658i) q^{37} +4.81100 q^{38} +(-0.0774239 - 0.764715i) q^{39} -2.37466i q^{40} +(-1.64665 - 2.85208i) q^{41} +(-4.75676 + 8.23894i) q^{43} +(7.25268 + 4.18733i) q^{44} +(-4.98718 - 5.62462i) q^{45} +(-7.37492 - 12.7737i) q^{46} +(1.07190 + 1.85659i) q^{47} +(-8.19750 + 0.829960i) q^{48} +(-2.06964 + 1.19491i) q^{50} +(-5.30362 + 0.536967i) q^{51} +0.662509i q^{52} +(-4.20379 + 2.42706i) q^{53} +(-6.58035 + 7.14198i) q^{54} +14.0561i q^{55} +(3.61709 - 2.60693i) q^{57} -5.84923 q^{58} +(3.65496 - 6.33057i) q^{59} +(3.78844 + 5.25643i) q^{60} +(7.40950 - 4.27788i) q^{61} +19.5619 q^{62} +3.55953 q^{64} +(-0.962984 + 0.555979i) q^{65} +(18.0664 - 1.82914i) q^{66} +(0.934442 - 1.61850i) q^{67} +4.59477 q^{68} +(-12.4664 - 5.60753i) q^{69} -2.95338i q^{71} +(-2.12728 + 1.88620i) q^{72} +(7.37804 - 4.25971i) q^{73} +2.64704i q^{74} +(-0.908550 + 2.01985i) q^{75} +(-3.32820 + 1.92154i) q^{76} +(0.839916 + 1.16538i) q^{78} +(0.287130 + 0.497324i) q^{79} +(5.95992 + 10.3229i) q^{80} +(-1.07734 + 8.93529i) q^{81} +(5.33036 + 3.07748i) q^{82} +(-4.23521 + 7.33560i) q^{83} +(3.85595 + 6.67870i) q^{85} -17.7802i q^{86} +(-4.39766 + 3.16951i) q^{87} +5.31615 q^{88} +(-3.78929 + 6.56325i) q^{89} +(13.3280 + 4.44334i) q^{90} +(10.2038 + 5.89115i) q^{92} +(14.7074 - 10.6000i) q^{93} +(-3.46984 - 2.00332i) q^{94} +(-5.58607 - 3.22512i) q^{95} +(9.82920 - 7.08415i) q^{96} +(3.22662 + 1.86289i) q^{97} +(12.5918 - 11.1648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 24 q^{4} - 8 q^{9} - 40 q^{15} - 24 q^{16} + 32 q^{18} + 48 q^{25} + 48 q^{30} - 120 q^{32} - 8 q^{36} - 32 q^{39} + 96 q^{44} + 48 q^{50} + 48 q^{53} + 80 q^{57} - 72 q^{60} - 48 q^{64} - 120 q^{65} + 32 q^{72} - 88 q^{78} - 24 q^{79} + 120 q^{81} - 24 q^{85} - 144 q^{92} + 16 q^{93} - 96 q^{95} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61855 + 0.934468i −1.14449 + 0.660769i −0.947537 0.319645i \(-0.896436\pi\)
−0.196948 + 0.980414i \(0.563103\pi\)
\(3\) −0.710525 + 1.57961i −0.410222 + 0.911986i
\(4\) 0.746462 1.29291i 0.373231 0.646455i
\(5\) 2.50573 1.12060 0.560299 0.828290i \(-0.310686\pi\)
0.560299 + 0.828290i \(0.310686\pi\)
\(6\) −0.326074 3.22063i −0.133119 1.31482i
\(7\) 0 0
\(8\) 0.947692i 0.335060i
\(9\) −1.99031 2.24470i −0.663436 0.748233i
\(10\) −4.05565 + 2.34153i −1.28251 + 0.740457i
\(11\) 5.60957i 1.69135i 0.533698 + 0.845675i \(0.320802\pi\)
−0.533698 + 0.845675i \(0.679198\pi\)
\(12\) 1.51191 + 2.09776i 0.436451 + 0.605572i
\(13\) −0.384312 + 0.221883i −0.106589 + 0.0615392i −0.552347 0.833614i \(-0.686268\pi\)
0.445758 + 0.895154i \(0.352934\pi\)
\(14\) 0 0
\(15\) −1.78039 + 3.95807i −0.459694 + 1.02197i
\(16\) 2.37851 + 4.11970i 0.594628 + 1.02993i
\(17\) 1.53885 + 2.66536i 0.373226 + 0.646446i 0.990060 0.140647i \(-0.0449184\pi\)
−0.616834 + 0.787093i \(0.711585\pi\)
\(18\) 5.31901 + 1.77327i 1.25370 + 0.417963i
\(19\) −2.22932 1.28710i −0.511440 0.295280i 0.221985 0.975050i \(-0.428746\pi\)
−0.733425 + 0.679770i \(0.762080\pi\)
\(20\) 1.87044 3.23969i 0.418242 0.724417i
\(21\) 0 0
\(22\) −5.24197 9.07935i −1.11759 1.93572i
\(23\) 7.89210i 1.64562i 0.568319 + 0.822808i \(0.307594\pi\)
−0.568319 + 0.822808i \(0.692406\pi\)
\(24\) 1.49698 + 0.673359i 0.305570 + 0.137449i
\(25\) 1.27870 0.255741
\(26\) 0.414685 0.718255i 0.0813264 0.140861i
\(27\) 4.95990 1.54899i 0.954534 0.298103i
\(28\) 0 0
\(29\) 2.71041 + 1.56485i 0.503310 + 0.290586i 0.730079 0.683362i \(-0.239483\pi\)
−0.226770 + 0.973948i \(0.572816\pi\)
\(30\) −0.817055 8.07004i −0.149173 1.47338i
\(31\) −9.06457 5.23343i −1.62805 0.939952i −0.984675 0.174397i \(-0.944202\pi\)
−0.643370 0.765556i \(-0.722464\pi\)
\(32\) −6.05802 3.49760i −1.07092 0.618294i
\(33\) −8.86091 3.98574i −1.54249 0.693828i
\(34\) −4.98140 2.87601i −0.854303 0.493232i
\(35\) 0 0
\(36\) −4.38788 + 0.897709i −0.731314 + 0.149618i
\(37\) 0.708168 1.22658i 0.116422 0.201649i −0.801925 0.597424i \(-0.796191\pi\)
0.918347 + 0.395775i \(0.129524\pi\)
\(38\) 4.81100 0.780448
\(39\) −0.0774239 0.764715i −0.0123978 0.122452i
\(40\) 2.37466i 0.375467i
\(41\) −1.64665 2.85208i −0.257163 0.445420i 0.708318 0.705894i \(-0.249455\pi\)
−0.965481 + 0.260474i \(0.916121\pi\)
\(42\) 0 0
\(43\) −4.75676 + 8.23894i −0.725398 + 1.25643i 0.233411 + 0.972378i \(0.425011\pi\)
−0.958810 + 0.284049i \(0.908322\pi\)
\(44\) 7.25268 + 4.18733i 1.09338 + 0.631264i
\(45\) −4.98718 5.62462i −0.743446 0.838468i
\(46\) −7.37492 12.7737i −1.08737 1.88338i
\(47\) 1.07190 + 1.85659i 0.156353 + 0.270811i 0.933551 0.358445i \(-0.116693\pi\)
−0.777198 + 0.629256i \(0.783360\pi\)
\(48\) −8.19750 + 0.829960i −1.18321 + 0.119794i
\(49\) 0 0
\(50\) −2.06964 + 1.19491i −0.292691 + 0.168985i
\(51\) −5.30362 + 0.536967i −0.742655 + 0.0751904i
\(52\) 0.662509i 0.0918734i
\(53\) −4.20379 + 2.42706i −0.577435 + 0.333382i −0.760113 0.649791i \(-0.774857\pi\)
0.182678 + 0.983173i \(0.441523\pi\)
\(54\) −6.58035 + 7.14198i −0.895472 + 0.971901i
\(55\) 14.0561i 1.89532i
\(56\) 0 0
\(57\) 3.61709 2.60693i 0.479095 0.345296i
\(58\) −5.84923 −0.768041
\(59\) 3.65496 6.33057i 0.475835 0.824170i −0.523782 0.851852i \(-0.675479\pi\)
0.999617 + 0.0276824i \(0.00881270\pi\)
\(60\) 3.78844 + 5.25643i 0.489086 + 0.678602i
\(61\) 7.40950 4.27788i 0.948690 0.547726i 0.0560160 0.998430i \(-0.482160\pi\)
0.892674 + 0.450704i \(0.148827\pi\)
\(62\) 19.5619 2.48437
\(63\) 0 0
\(64\) 3.55953 0.444941
\(65\) −0.962984 + 0.555979i −0.119443 + 0.0689607i
\(66\) 18.0664 1.82914i 2.22381 0.225151i
\(67\) 0.934442 1.61850i 0.114160 0.197731i −0.803284 0.595597i \(-0.796916\pi\)
0.917444 + 0.397865i \(0.130249\pi\)
\(68\) 4.59477 0.557198
\(69\) −12.4664 5.60753i −1.50078 0.675067i
\(70\) 0 0
\(71\) 2.95338i 0.350501i −0.984524 0.175251i \(-0.943926\pi\)
0.984524 0.175251i \(-0.0560736\pi\)
\(72\) −2.12728 + 1.88620i −0.250703 + 0.222291i
\(73\) 7.37804 4.25971i 0.863534 0.498562i −0.00165984 0.999999i \(-0.500528\pi\)
0.865194 + 0.501437i \(0.167195\pi\)
\(74\) 2.64704i 0.307712i
\(75\) −0.908550 + 2.01985i −0.104910 + 0.233232i
\(76\) −3.32820 + 1.92154i −0.381771 + 0.220415i
\(77\) 0 0
\(78\) 0.839916 + 1.16538i 0.0951018 + 0.131953i
\(79\) 0.287130 + 0.497324i 0.0323047 + 0.0559533i 0.881726 0.471762i \(-0.156382\pi\)
−0.849421 + 0.527716i \(0.823049\pi\)
\(80\) 5.95992 + 10.3229i 0.666339 + 1.15413i
\(81\) −1.07734 + 8.93529i −0.119705 + 0.992810i
\(82\) 5.33036 + 3.07748i 0.588639 + 0.339851i
\(83\) −4.23521 + 7.33560i −0.464875 + 0.805186i −0.999196 0.0400951i \(-0.987234\pi\)
0.534321 + 0.845281i \(0.320567\pi\)
\(84\) 0 0
\(85\) 3.85595 + 6.67870i 0.418236 + 0.724406i
\(86\) 17.7802i 1.91728i
\(87\) −4.39766 + 3.16951i −0.471479 + 0.339807i
\(88\) 5.31615 0.566703
\(89\) −3.78929 + 6.56325i −0.401664 + 0.695703i −0.993927 0.110042i \(-0.964901\pi\)
0.592263 + 0.805745i \(0.298235\pi\)
\(90\) 13.3280 + 4.44334i 1.40490 + 0.468369i
\(91\) 0 0
\(92\) 10.2038 + 5.89115i 1.06382 + 0.614195i
\(93\) 14.7074 10.6000i 1.52508 1.09917i
\(94\) −3.46984 2.00332i −0.357887 0.206626i
\(95\) −5.58607 3.22512i −0.573119 0.330890i
\(96\) 9.82920 7.08415i 1.00319 0.723023i
\(97\) 3.22662 + 1.86289i 0.327614 + 0.189148i 0.654781 0.755818i \(-0.272761\pi\)
−0.327167 + 0.944966i \(0.606094\pi\)
\(98\) 0 0
\(99\) 12.5918 11.1648i 1.26552 1.12210i
\(100\) 0.954503 1.65325i 0.0954503 0.165325i
\(101\) −7.53449 −0.749710 −0.374855 0.927083i \(-0.622308\pi\)
−0.374855 + 0.927083i \(0.622308\pi\)
\(102\) 8.08237 5.82517i 0.800274 0.576778i
\(103\) 14.3235i 1.41133i 0.708545 + 0.705666i \(0.249352\pi\)
−0.708545 + 0.705666i \(0.750648\pi\)
\(104\) 0.210276 + 0.364210i 0.0206193 + 0.0357137i
\(105\) 0 0
\(106\) 4.53602 7.85662i 0.440577 0.763102i
\(107\) 11.6798 + 6.74331i 1.12912 + 0.651900i 0.943715 0.330761i \(-0.107305\pi\)
0.185410 + 0.982661i \(0.440639\pi\)
\(108\) 1.69967 7.56897i 0.163551 0.728325i
\(109\) 0.459348 + 0.795613i 0.0439975 + 0.0762059i 0.887186 0.461413i \(-0.152657\pi\)
−0.843188 + 0.537619i \(0.819324\pi\)
\(110\) −13.1350 22.7504i −1.25237 2.16917i
\(111\) 1.43435 + 1.99014i 0.136142 + 0.188896i
\(112\) 0 0
\(113\) 4.10412 2.36952i 0.386083 0.222905i −0.294378 0.955689i \(-0.595113\pi\)
0.680462 + 0.732784i \(0.261779\pi\)
\(114\) −3.41834 + 7.59949i −0.320157 + 0.711757i
\(115\) 19.7755i 1.84407i
\(116\) 4.04643 2.33621i 0.375702 0.216912i
\(117\) 1.26296 + 0.421050i 0.116761 + 0.0389261i
\(118\) 13.6618i 1.25767i
\(119\) 0 0
\(120\) 3.75103 + 1.68726i 0.342421 + 0.154025i
\(121\) −20.4673 −1.86066
\(122\) −7.99508 + 13.8479i −0.723841 + 1.25373i
\(123\) 5.67515 0.574583i 0.511711 0.0518084i
\(124\) −13.5327 + 7.81312i −1.21527 + 0.701639i
\(125\) −9.32458 −0.834016
\(126\) 0 0
\(127\) 7.37245 0.654200 0.327100 0.944990i \(-0.393929\pi\)
0.327100 + 0.944990i \(0.393929\pi\)
\(128\) 6.35477 3.66893i 0.561688 0.324291i
\(129\) −9.63449 13.3678i −0.848269 1.17697i
\(130\) 1.03909 1.79976i 0.0911342 0.157849i
\(131\) 7.86300 0.686993 0.343497 0.939154i \(-0.388389\pi\)
0.343497 + 0.939154i \(0.388389\pi\)
\(132\) −11.7675 + 8.48116i −1.02423 + 0.738191i
\(133\) 0 0
\(134\) 3.49283i 0.301734i
\(135\) 12.4282 3.88136i 1.06965 0.334054i
\(136\) 2.52594 1.45835i 0.216598 0.125053i
\(137\) 11.5698i 0.988477i 0.869326 + 0.494238i \(0.164553\pi\)
−0.869326 + 0.494238i \(0.835447\pi\)
\(138\) 25.4175 2.57341i 2.16368 0.219063i
\(139\) 16.9741 9.79999i 1.43972 0.831224i 0.441893 0.897068i \(-0.354307\pi\)
0.997830 + 0.0658437i \(0.0209739\pi\)
\(140\) 0 0
\(141\) −3.69429 + 0.374030i −0.311115 + 0.0314990i
\(142\) 2.75984 + 4.78018i 0.231600 + 0.401144i
\(143\) −1.24467 2.15583i −0.104084 0.180279i
\(144\) 4.51352 13.5385i 0.376127 1.12821i
\(145\) 6.79156 + 3.92111i 0.564008 + 0.325630i
\(146\) −7.96114 + 13.7891i −0.658868 + 1.14119i
\(147\) 0 0
\(148\) −1.05724 1.83120i −0.0869047 0.150523i
\(149\) 15.7402i 1.28949i −0.764397 0.644746i \(-0.776963\pi\)
0.764397 0.644746i \(-0.223037\pi\)
\(150\) −0.416952 4.11823i −0.0340440 0.336252i
\(151\) −1.98271 −0.161350 −0.0806752 0.996740i \(-0.525708\pi\)
−0.0806752 + 0.996740i \(0.525708\pi\)
\(152\) −1.21977 + 2.11270i −0.0989364 + 0.171363i
\(153\) 2.92015 8.75915i 0.236081 0.708135i
\(154\) 0 0
\(155\) −22.7134 13.1136i −1.82438 1.05331i
\(156\) −1.04650 0.470729i −0.0837872 0.0376885i
\(157\) 7.26790 + 4.19612i 0.580041 + 0.334887i 0.761150 0.648576i \(-0.224635\pi\)
−0.181108 + 0.983463i \(0.557969\pi\)
\(158\) −0.929468 0.536628i −0.0739445 0.0426919i
\(159\) −0.846899 8.36481i −0.0671635 0.663373i
\(160\) −15.1798 8.76405i −1.20007 0.692859i
\(161\) 0 0
\(162\) −6.60602 15.4689i −0.519018 1.21535i
\(163\) 0.537054 0.930204i 0.0420653 0.0728592i −0.844226 0.535987i \(-0.819940\pi\)
0.886291 + 0.463128i \(0.153273\pi\)
\(164\) −4.91665 −0.383926
\(165\) −22.2031 9.98721i −1.72851 0.777503i
\(166\) 15.8307i 1.22870i
\(167\) 3.99731 + 6.92354i 0.309321 + 0.535760i 0.978214 0.207599i \(-0.0665649\pi\)
−0.668893 + 0.743359i \(0.733232\pi\)
\(168\) 0 0
\(169\) −6.40154 + 11.0878i −0.492426 + 0.852907i
\(170\) −12.4821 7.20652i −0.957330 0.552715i
\(171\) 1.54788 + 7.56586i 0.118370 + 0.578576i
\(172\) 7.10148 + 12.3001i 0.541483 + 0.937875i
\(173\) 0.501744 + 0.869046i 0.0381469 + 0.0660723i 0.884468 0.466600i \(-0.154521\pi\)
−0.846322 + 0.532672i \(0.821188\pi\)
\(174\) 4.15602 9.23947i 0.315067 0.700442i
\(175\) 0 0
\(176\) −23.1098 + 13.3424i −1.74197 + 1.00572i
\(177\) 7.40287 + 10.2714i 0.556434 + 0.772047i
\(178\) 14.1639i 1.06163i
\(179\) 1.27773 0.737695i 0.0955017 0.0551379i −0.451489 0.892277i \(-0.649107\pi\)
0.546990 + 0.837139i \(0.315773\pi\)
\(180\) −10.9949 + 2.24942i −0.819509 + 0.167662i
\(181\) 15.0440i 1.11821i −0.829096 0.559106i \(-0.811145\pi\)
0.829096 0.559106i \(-0.188855\pi\)
\(182\) 0 0
\(183\) 1.49273 + 14.7436i 0.110345 + 1.08988i
\(184\) 7.47928 0.551380
\(185\) 1.77448 3.07349i 0.130462 0.225967i
\(186\) −13.8992 + 30.9001i −1.01914 + 2.26571i
\(187\) −14.9516 + 8.63229i −1.09337 + 0.631255i
\(188\) 3.20054 0.233423
\(189\) 0 0
\(190\) 12.0551 0.874568
\(191\) −11.4521 + 6.61187i −0.828644 + 0.478418i −0.853388 0.521276i \(-0.825456\pi\)
0.0247439 + 0.999694i \(0.492123\pi\)
\(192\) −2.52913 + 5.62265i −0.182524 + 0.405780i
\(193\) 0.777855 1.34728i 0.0559912 0.0969796i −0.836671 0.547705i \(-0.815501\pi\)
0.892662 + 0.450726i \(0.148835\pi\)
\(194\) −6.96325 −0.499932
\(195\) −0.194004 1.91617i −0.0138929 0.137220i
\(196\) 0 0
\(197\) 4.96185i 0.353517i −0.984254 0.176759i \(-0.943439\pi\)
0.984254 0.176759i \(-0.0565612\pi\)
\(198\) −9.94728 + 29.8374i −0.706922 + 2.12045i
\(199\) 9.69273 5.59610i 0.687100 0.396697i −0.115425 0.993316i \(-0.536823\pi\)
0.802525 + 0.596619i \(0.203490\pi\)
\(200\) 1.21182i 0.0856883i
\(201\) 1.89265 + 2.62604i 0.133497 + 0.185226i
\(202\) 12.1949 7.04074i 0.858032 0.495385i
\(203\) 0 0
\(204\) −3.26470 + 7.25793i −0.228575 + 0.508157i
\(205\) −4.12606 7.14655i −0.288177 0.499137i
\(206\) −13.3848 23.1832i −0.932565 1.61525i
\(207\) 17.7154 15.7077i 1.23130 1.09176i
\(208\) −1.82818 1.05550i −0.126762 0.0731859i
\(209\) 7.22006 12.5055i 0.499422 0.865024i
\(210\) 0 0
\(211\) 7.68026 + 13.3026i 0.528731 + 0.915789i 0.999439 + 0.0334999i \(0.0106654\pi\)
−0.470708 + 0.882289i \(0.656001\pi\)
\(212\) 7.24683i 0.497714i
\(213\) 4.66517 + 2.09845i 0.319652 + 0.143783i
\(214\) −25.2056 −1.72302
\(215\) −11.9192 + 20.6446i −0.812880 + 1.40795i
\(216\) −1.46796 4.70046i −0.0998824 0.319826i
\(217\) 0 0
\(218\) −1.48695 0.858492i −0.100709 0.0581444i
\(219\) 1.48639 + 14.6810i 0.100441 + 0.992052i
\(220\) 18.1733 + 10.4923i 1.22524 + 0.707394i
\(221\) −1.18280 0.682888i −0.0795635 0.0459360i
\(222\) −4.18128 1.88079i −0.280629 0.126230i
\(223\) −2.76845 1.59837i −0.185389 0.107034i 0.404433 0.914568i \(-0.367469\pi\)
−0.589822 + 0.807533i \(0.700802\pi\)
\(224\) 0 0
\(225\) −2.54501 2.87030i −0.169668 0.191353i
\(226\) −4.42848 + 7.67035i −0.294578 + 0.510224i
\(227\) 14.6699 0.973675 0.486837 0.873493i \(-0.338150\pi\)
0.486837 + 0.873493i \(0.338150\pi\)
\(228\) −0.670502 6.62254i −0.0444051 0.438589i
\(229\) 3.37807i 0.223229i 0.993752 + 0.111615i \(0.0356022\pi\)
−0.993752 + 0.111615i \(0.964398\pi\)
\(230\) −18.4796 32.0076i −1.21851 2.11052i
\(231\) 0 0
\(232\) 1.48300 2.56863i 0.0973637 0.168639i
\(233\) 4.22628 + 2.44005i 0.276873 + 0.159853i 0.632007 0.774963i \(-0.282231\pi\)
−0.355134 + 0.934815i \(0.615565\pi\)
\(234\) −2.43762 + 0.498707i −0.159352 + 0.0326015i
\(235\) 2.68590 + 4.65211i 0.175209 + 0.303470i
\(236\) −5.45657 9.45106i −0.355193 0.615212i
\(237\) −0.989589 + 0.100191i −0.0642807 + 0.00650813i
\(238\) 0 0
\(239\) 13.6253 7.86657i 0.881347 0.508846i 0.0102448 0.999948i \(-0.496739\pi\)
0.871102 + 0.491101i \(0.163406\pi\)
\(240\) −20.5408 + 2.07966i −1.32590 + 0.134241i
\(241\) 0.769383i 0.0495603i 0.999693 + 0.0247801i \(0.00788857\pi\)
−0.999693 + 0.0247801i \(0.992111\pi\)
\(242\) 33.1273 19.1260i 2.12950 1.22947i
\(243\) −13.3488 8.05052i −0.856323 0.516441i
\(244\) 12.7731i 0.817714i
\(245\) 0 0
\(246\) −8.64856 + 6.23323i −0.551412 + 0.397416i
\(247\) 1.14234 0.0726852
\(248\) −4.95968 + 8.59042i −0.314940 + 0.545492i
\(249\) −8.57813 11.9021i −0.543617 0.754264i
\(250\) 15.0923 8.71353i 0.954519 0.551092i
\(251\) 1.14544 0.0722996 0.0361498 0.999346i \(-0.488491\pi\)
0.0361498 + 0.999346i \(0.488491\pi\)
\(252\) 0 0
\(253\) −44.2713 −2.78331
\(254\) −11.9327 + 6.88933i −0.748722 + 0.432275i
\(255\) −13.2895 + 1.34550i −0.832218 + 0.0842583i
\(256\) −10.4165 + 18.0420i −0.651033 + 1.12762i
\(257\) 28.9835 1.80794 0.903969 0.427598i \(-0.140640\pi\)
0.903969 + 0.427598i \(0.140640\pi\)
\(258\) 28.0856 + 12.6332i 1.74853 + 0.786511i
\(259\) 0 0
\(260\) 1.66007i 0.102953i
\(261\) −1.88192 9.19859i −0.116488 0.569378i
\(262\) −12.7266 + 7.34772i −0.786254 + 0.453944i
\(263\) 13.6998i 0.844763i −0.906418 0.422381i \(-0.861194\pi\)
0.906418 0.422381i \(-0.138806\pi\)
\(264\) −3.77725 + 8.39742i −0.232474 + 0.516825i
\(265\) −10.5336 + 6.08156i −0.647072 + 0.373587i
\(266\) 0 0
\(267\) −7.67496 10.6489i −0.469700 0.651704i
\(268\) −1.39505 2.41630i −0.0852163 0.147599i
\(269\) −5.23973 9.07548i −0.319472 0.553342i 0.660906 0.750469i \(-0.270172\pi\)
−0.980378 + 0.197127i \(0.936839\pi\)
\(270\) −16.4886 + 17.8959i −1.00346 + 1.08911i
\(271\) −5.66907 3.27304i −0.344371 0.198823i 0.317832 0.948147i \(-0.397045\pi\)
−0.662203 + 0.749324i \(0.730379\pi\)
\(272\) −7.32034 + 12.6792i −0.443861 + 0.768790i
\(273\) 0 0
\(274\) −10.8116 18.7263i −0.653155 1.13130i
\(275\) 7.17298i 0.432547i
\(276\) −16.5557 + 11.9321i −0.996538 + 0.718230i
\(277\) 22.4313 1.34777 0.673883 0.738838i \(-0.264625\pi\)
0.673883 + 0.738838i \(0.264625\pi\)
\(278\) −18.3156 + 31.7235i −1.09849 + 1.90265i
\(279\) 6.29382 + 30.7634i 0.376801 + 1.84176i
\(280\) 0 0
\(281\) 19.3552 + 11.1747i 1.15463 + 0.666627i 0.950012 0.312214i \(-0.101071\pi\)
0.204621 + 0.978841i \(0.434404\pi\)
\(282\) 5.62986 4.05758i 0.335253 0.241625i
\(283\) −16.4296 9.48563i −0.976638 0.563862i −0.0753848 0.997155i \(-0.524019\pi\)
−0.901254 + 0.433292i \(0.857352\pi\)
\(284\) −3.81845 2.20459i −0.226584 0.130818i
\(285\) 9.06346 6.53226i 0.536873 0.386938i
\(286\) 4.02910 + 2.32620i 0.238246 + 0.137551i
\(287\) 0 0
\(288\) 4.20627 + 20.5597i 0.247857 + 1.21149i
\(289\) 3.76389 6.51924i 0.221405 0.383485i
\(290\) −14.6566 −0.860665
\(291\) −5.23523 + 3.77316i −0.306895 + 0.221187i
\(292\) 12.7189i 0.744315i
\(293\) −4.41136 7.64069i −0.257714 0.446374i 0.707915 0.706298i \(-0.249636\pi\)
−0.965629 + 0.259924i \(0.916303\pi\)
\(294\) 0 0
\(295\) 9.15835 15.8627i 0.533220 0.923563i
\(296\) −1.16242 0.671125i −0.0675644 0.0390083i
\(297\) 8.68917 + 27.8229i 0.504197 + 1.61445i
\(298\) 14.7088 + 25.4763i 0.852056 + 1.47580i
\(299\) −1.75112 3.03303i −0.101270 0.175405i
\(300\) 1.93328 + 2.68241i 0.111618 + 0.154869i
\(301\) 0 0
\(302\) 3.20910 1.85278i 0.184663 0.106615i
\(303\) 5.35344 11.9015i 0.307547 0.683725i
\(304\) 12.2455i 0.702327i
\(305\) 18.5662 10.7192i 1.06310 0.613781i
\(306\) 3.45874 + 16.9059i 0.197723 + 0.966445i
\(307\) 28.7533i 1.64104i −0.571620 0.820519i \(-0.693685\pi\)
0.571620 0.820519i \(-0.306315\pi\)
\(308\) 0 0
\(309\) −22.6254 10.1772i −1.28712 0.578959i
\(310\) 49.0169 2.78398
\(311\) 6.64294 11.5059i 0.376687 0.652441i −0.613891 0.789391i \(-0.710397\pi\)
0.990578 + 0.136950i \(0.0437300\pi\)
\(312\) −0.724714 + 0.0733740i −0.0410289 + 0.00415399i
\(313\) 27.3227 15.7748i 1.54437 0.891643i 0.545815 0.837905i \(-0.316220\pi\)
0.998555 0.0537372i \(-0.0171133\pi\)
\(314\) −15.6846 −0.885132
\(315\) 0 0
\(316\) 0.857328 0.0482285
\(317\) −17.3819 + 10.0354i −0.976264 + 0.563646i −0.901140 0.433528i \(-0.857268\pi\)
−0.0751236 + 0.997174i \(0.523935\pi\)
\(318\) 9.18740 + 12.7474i 0.515204 + 0.714841i
\(319\) −8.77816 + 15.2042i −0.491483 + 0.851273i
\(320\) 8.91923 0.498600
\(321\) −18.9505 + 13.6581i −1.05772 + 0.762322i
\(322\) 0 0
\(323\) 7.92259i 0.440824i
\(324\) 10.7483 + 8.06276i 0.597130 + 0.447931i
\(325\) −0.491421 + 0.283722i −0.0272591 + 0.0157381i
\(326\) 2.00744i 0.111182i
\(327\) −1.58313 + 0.160285i −0.0875475 + 0.00886378i
\(328\) −2.70289 + 1.56052i −0.149242 + 0.0861651i
\(329\) 0 0
\(330\) 45.2695 4.58333i 2.49200 0.252304i
\(331\) −0.623957 1.08073i −0.0342958 0.0594020i 0.848368 0.529407i \(-0.177585\pi\)
−0.882664 + 0.470005i \(0.844252\pi\)
\(332\) 6.32285 + 10.9515i 0.347011 + 0.601041i
\(333\) −4.16278 + 0.851655i −0.228119 + 0.0466704i
\(334\) −12.9397 7.47072i −0.708027 0.408780i
\(335\) 2.34146 4.05553i 0.127928 0.221577i
\(336\) 0 0
\(337\) 6.58745 + 11.4098i 0.358842 + 0.621532i 0.987768 0.155933i \(-0.0498385\pi\)
−0.628926 + 0.777465i \(0.716505\pi\)
\(338\) 23.9281i 1.30152i
\(339\) 0.826821 + 8.16650i 0.0449067 + 0.443543i
\(340\) 11.5133 0.624395
\(341\) 29.3573 50.8484i 1.58979 2.75359i
\(342\) −9.57538 10.7992i −0.517777 0.583956i
\(343\) 0 0
\(344\) 7.80798 + 4.50794i 0.420978 + 0.243052i
\(345\) −31.2375 14.0510i −1.68177 0.756479i
\(346\) −1.62419 0.937727i −0.0873171 0.0504125i
\(347\) 23.4411 + 13.5337i 1.25838 + 0.726529i 0.972760 0.231813i \(-0.0744658\pi\)
0.285624 + 0.958342i \(0.407799\pi\)
\(348\) 0.815198 + 8.05170i 0.0436992 + 0.431616i
\(349\) 30.3413 + 17.5176i 1.62413 + 0.937694i 0.985798 + 0.167936i \(0.0537101\pi\)
0.638336 + 0.769758i \(0.279623\pi\)
\(350\) 0 0
\(351\) −1.56246 + 1.69581i −0.0833978 + 0.0905158i
\(352\) 19.6200 33.9829i 1.04575 1.81129i
\(353\) −2.52512 −0.134398 −0.0671992 0.997740i \(-0.521406\pi\)
−0.0671992 + 0.997740i \(0.521406\pi\)
\(354\) −21.5802 9.70702i −1.14697 0.515922i
\(355\) 7.40038i 0.392771i
\(356\) 5.65713 + 9.79843i 0.299827 + 0.519316i
\(357\) 0 0
\(358\) −1.37871 + 2.38799i −0.0728669 + 0.126209i
\(359\) 6.29395 + 3.63381i 0.332182 + 0.191785i 0.656809 0.754057i \(-0.271906\pi\)
−0.324628 + 0.945842i \(0.605239\pi\)
\(360\) −5.33040 + 4.72631i −0.280937 + 0.249099i
\(361\) −6.18677 10.7158i −0.325619 0.563989i
\(362\) 14.0581 + 24.3494i 0.738880 + 1.27978i
\(363\) 14.5425 32.3303i 0.763285 1.69690i
\(364\) 0 0
\(365\) 18.4874 10.6737i 0.967675 0.558688i
\(366\) −16.1935 22.4684i −0.846448 1.17444i
\(367\) 13.4770i 0.703492i 0.936095 + 0.351746i \(0.114412\pi\)
−0.936095 + 0.351746i \(0.885588\pi\)
\(368\) −32.5131 + 18.7715i −1.69486 + 0.978530i
\(369\) −3.12472 + 9.37275i −0.162666 + 0.487926i
\(370\) 6.63278i 0.344822i
\(371\) 0 0
\(372\) −2.72632 26.9278i −0.141353 1.39614i
\(373\) 23.7639 1.23045 0.615224 0.788352i \(-0.289065\pi\)
0.615224 + 0.788352i \(0.289065\pi\)
\(374\) 16.1332 27.9435i 0.834228 1.44492i
\(375\) 6.62535 14.7292i 0.342131 0.760611i
\(376\) 1.75947 1.01583i 0.0907379 0.0523875i
\(377\) −1.38886 −0.0715297
\(378\) 0 0
\(379\) 21.2283 1.09042 0.545211 0.838299i \(-0.316449\pi\)
0.545211 + 0.838299i \(0.316449\pi\)
\(380\) −8.33958 + 4.81486i −0.427812 + 0.246997i
\(381\) −5.23831 + 11.6456i −0.268367 + 0.596621i
\(382\) 12.3572 21.4032i 0.632248 1.09509i
\(383\) −12.9586 −0.662154 −0.331077 0.943604i \(-0.607412\pi\)
−0.331077 + 0.943604i \(0.607412\pi\)
\(384\) 1.28024 + 12.6449i 0.0653319 + 0.645282i
\(385\) 0 0
\(386\) 2.90752i 0.147989i
\(387\) 27.9614 5.72056i 1.42136 0.290792i
\(388\) 4.81710 2.78116i 0.244551 0.141192i
\(389\) 10.9470i 0.555035i −0.960721 0.277517i \(-0.910488\pi\)
0.960721 0.277517i \(-0.0895116\pi\)
\(390\) 2.10461 + 2.92012i 0.106571 + 0.147866i
\(391\) −21.0353 + 12.1447i −1.06380 + 0.614186i
\(392\) 0 0
\(393\) −5.58685 + 12.4204i −0.281819 + 0.626528i
\(394\) 4.63669 + 8.03098i 0.233593 + 0.404595i
\(395\) 0.719472 + 1.24616i 0.0362006 + 0.0627012i
\(396\) −5.03576 24.6142i −0.253057 1.23691i
\(397\) −25.8856 14.9451i −1.29916 0.750071i −0.318901 0.947788i \(-0.603314\pi\)
−0.980259 + 0.197717i \(0.936647\pi\)
\(398\) −10.4588 + 18.1151i −0.524250 + 0.908028i
\(399\) 0 0
\(400\) 3.04141 + 5.26788i 0.152071 + 0.263394i
\(401\) 19.1949i 0.958547i 0.877666 + 0.479273i \(0.159100\pi\)
−0.877666 + 0.479273i \(0.840900\pi\)
\(402\) −5.51729 2.48174i −0.275177 0.123778i
\(403\) 4.64483 0.231376
\(404\) −5.62421 + 9.74142i −0.279815 + 0.484654i
\(405\) −2.69953 + 22.3894i −0.134141 + 1.11254i
\(406\) 0 0
\(407\) 6.88060 + 3.97252i 0.341059 + 0.196910i
\(408\) 0.508879 + 5.02619i 0.0251933 + 0.248834i
\(409\) 24.9737 + 14.4186i 1.23487 + 0.712953i 0.968041 0.250790i \(-0.0806905\pi\)
0.266830 + 0.963744i \(0.414024\pi\)
\(410\) 13.3565 + 7.71135i 0.659628 + 0.380837i
\(411\) −18.2758 8.22065i −0.901477 0.405495i
\(412\) 18.5190 + 10.6919i 0.912363 + 0.526753i
\(413\) 0 0
\(414\) −13.9948 + 41.9781i −0.687807 + 2.06311i
\(415\) −10.6123 + 18.3811i −0.520938 + 0.902290i
\(416\) 3.10423 0.152197
\(417\) 3.41961 + 33.7755i 0.167459 + 1.65399i
\(418\) 26.9877i 1.32001i
\(419\) 5.06390 + 8.77094i 0.247388 + 0.428488i 0.962800 0.270214i \(-0.0870945\pi\)
−0.715412 + 0.698702i \(0.753761\pi\)
\(420\) 0 0
\(421\) 12.7094 22.0134i 0.619419 1.07287i −0.370173 0.928963i \(-0.620702\pi\)
0.989592 0.143902i \(-0.0459651\pi\)
\(422\) −24.8617 14.3539i −1.21025 0.698738i
\(423\) 2.03406 6.10128i 0.0988996 0.296654i
\(424\) 2.30010 + 3.98390i 0.111703 + 0.193475i
\(425\) 1.96773 + 3.40821i 0.0954490 + 0.165322i
\(426\) −9.51173 + 0.963020i −0.460845 + 0.0466585i
\(427\) 0 0
\(428\) 17.4370 10.0673i 0.842849 0.486619i
\(429\) 4.28972 0.434315i 0.207110 0.0209689i
\(430\) 44.5523i 2.14850i
\(431\) 9.39066 5.42170i 0.452332 0.261154i −0.256482 0.966549i \(-0.582564\pi\)
0.708815 + 0.705395i \(0.249230\pi\)
\(432\) 18.1786 + 16.7490i 0.874617 + 0.805839i
\(433\) 13.0519i 0.627233i 0.949550 + 0.313616i \(0.101541\pi\)
−0.949550 + 0.313616i \(0.898459\pi\)
\(434\) 0 0
\(435\) −11.0194 + 7.94194i −0.528338 + 0.380787i
\(436\) 1.37154 0.0656850
\(437\) 10.1579 17.5940i 0.485918 0.841634i
\(438\) −16.1247 22.3730i −0.770470 1.06902i
\(439\) −27.6736 + 15.9773i −1.32079 + 0.762557i −0.983854 0.178972i \(-0.942723\pi\)
−0.336933 + 0.941529i \(0.609389\pi\)
\(440\) 13.3208 0.635046
\(441\) 0 0
\(442\) 2.55255 0.121412
\(443\) −21.4748 + 12.3985i −1.02030 + 0.589068i −0.914190 0.405286i \(-0.867172\pi\)
−0.106107 + 0.994355i \(0.533838\pi\)
\(444\) 3.64376 0.368914i 0.172925 0.0175079i
\(445\) −9.49496 + 16.4458i −0.450104 + 0.779603i
\(446\) 5.97449 0.282900
\(447\) 24.8634 + 11.1838i 1.17600 + 0.528977i
\(448\) 0 0
\(449\) 13.7710i 0.649892i 0.945733 + 0.324946i \(0.105346\pi\)
−0.945733 + 0.324946i \(0.894654\pi\)
\(450\) 6.80143 + 2.26748i 0.320622 + 0.106890i
\(451\) 15.9989 9.23700i 0.753361 0.434953i
\(452\) 7.07502i 0.332781i
\(453\) 1.40876 3.13189i 0.0661894 0.147149i
\(454\) −23.7439 + 13.7085i −1.11436 + 0.643374i
\(455\) 0 0
\(456\) −2.47056 3.42789i −0.115695 0.160525i
\(457\) −13.6554 23.6518i −0.638771 1.10638i −0.985703 0.168494i \(-0.946110\pi\)
0.346931 0.937890i \(-0.387224\pi\)
\(458\) −3.15670 5.46757i −0.147503 0.255483i
\(459\) 11.7612 + 10.8363i 0.548964 + 0.505795i
\(460\) 25.5680 + 14.7617i 1.19211 + 0.688266i
\(461\) −5.51822 + 9.55784i −0.257009 + 0.445153i −0.965439 0.260628i \(-0.916070\pi\)
0.708430 + 0.705781i \(0.249404\pi\)
\(462\) 0 0
\(463\) −12.2346 21.1910i −0.568591 0.984829i −0.996706 0.0811042i \(-0.974155\pi\)
0.428115 0.903724i \(-0.359178\pi\)
\(464\) 14.8881i 0.691163i
\(465\) 36.8527 26.5607i 1.70901 1.23172i
\(466\) −9.12059 −0.422503
\(467\) −7.95241 + 13.7740i −0.367994 + 0.637384i −0.989252 0.146222i \(-0.953289\pi\)
0.621258 + 0.783606i \(0.286622\pi\)
\(468\) 1.48713 1.31860i 0.0687427 0.0609521i
\(469\) 0 0
\(470\) −8.69451 5.01978i −0.401048 0.231545i
\(471\) −11.7922 + 8.49896i −0.543358 + 0.391612i
\(472\) −5.99943 3.46377i −0.276146 0.159433i
\(473\) −46.2169 26.6834i −2.12506 1.22690i
\(474\) 1.50807 1.08690i 0.0692680 0.0499232i
\(475\) −2.85063 1.64581i −0.130796 0.0755151i
\(476\) 0 0
\(477\) 13.8149 + 4.60564i 0.632539 + 0.210878i
\(478\) −14.7021 + 25.4648i −0.672459 + 1.16473i
\(479\) 13.8537 0.632991 0.316496 0.948594i \(-0.397494\pi\)
0.316496 + 0.948594i \(0.397494\pi\)
\(480\) 24.6294 17.7510i 1.12417 0.810218i
\(481\) 0.628521i 0.0286581i
\(482\) −0.718964 1.24528i −0.0327479 0.0567210i
\(483\) 0 0
\(484\) −15.2781 + 26.4624i −0.694458 + 1.20284i
\(485\) 8.08506 + 4.66791i 0.367123 + 0.211959i
\(486\) 29.1285 + 0.556150i 1.32130 + 0.0252275i
\(487\) −14.3993 24.9404i −0.652496 1.13016i −0.982515 0.186182i \(-0.940389\pi\)
0.330020 0.943974i \(-0.392945\pi\)
\(488\) −4.05411 7.02193i −0.183521 0.317868i
\(489\) 1.08777 + 1.50927i 0.0491905 + 0.0682514i
\(490\) 0 0
\(491\) −33.5627 + 19.3774i −1.51466 + 0.874492i −0.514812 + 0.857303i \(0.672138\pi\)
−0.999852 + 0.0171884i \(0.994528\pi\)
\(492\) 3.49340 7.76636i 0.157495 0.350135i
\(493\) 9.63230i 0.433817i
\(494\) −1.84893 + 1.06748i −0.0831872 + 0.0480281i
\(495\) 31.5517 27.9760i 1.41814 1.25743i
\(496\) 49.7911i 2.23569i
\(497\) 0 0
\(498\) 25.0062 + 11.2481i 1.12056 + 0.504039i
\(499\) −3.46667 −0.155189 −0.0775946 0.996985i \(-0.524724\pi\)
−0.0775946 + 0.996985i \(0.524724\pi\)
\(500\) −6.96045 + 12.0558i −0.311281 + 0.539154i
\(501\) −13.7767 + 1.39482i −0.615496 + 0.0623161i
\(502\) −1.85395 + 1.07038i −0.0827458 + 0.0477733i
\(503\) −28.2202 −1.25828 −0.629138 0.777293i \(-0.716592\pi\)
−0.629138 + 0.777293i \(0.716592\pi\)
\(504\) 0 0
\(505\) −18.8794 −0.840124
\(506\) 71.6552 41.3701i 3.18546 1.83913i
\(507\) −12.9659 17.9901i −0.575835 0.798966i
\(508\) 5.50326 9.53193i 0.244168 0.422911i
\(509\) −35.8124 −1.58736 −0.793678 0.608338i \(-0.791836\pi\)
−0.793678 + 0.608338i \(0.791836\pi\)
\(510\) 20.2523 14.5963i 0.896786 0.646336i
\(511\) 0 0
\(512\) 24.2599i 1.07215i
\(513\) −13.0509 2.93068i −0.576211 0.129393i
\(514\) −46.9111 + 27.0841i −2.06916 + 1.19463i
\(515\) 35.8908i 1.58154i
\(516\) −24.4751 + 2.47799i −1.07746 + 0.109088i
\(517\) −10.4147 + 6.01291i −0.458036 + 0.264447i
\(518\) 0 0
\(519\) −1.72925 + 0.175079i −0.0759057 + 0.00768511i
\(520\) 0.526897 + 0.912612i 0.0231060 + 0.0400207i
\(521\) 13.4608 + 23.3148i 0.589729 + 1.02144i 0.994268 + 0.106920i \(0.0340989\pi\)
−0.404538 + 0.914521i \(0.632568\pi\)
\(522\) 11.6418 + 13.1297i 0.509546 + 0.574673i
\(523\) −7.82181 4.51593i −0.342024 0.197468i 0.319143 0.947707i \(-0.396605\pi\)
−0.661167 + 0.750239i \(0.729938\pi\)
\(524\) 5.86943 10.1662i 0.256407 0.444110i
\(525\) 0 0
\(526\) 12.8020 + 22.1737i 0.558193 + 0.966819i
\(527\) 32.2139i 1.40326i
\(528\) −4.65572 45.9845i −0.202614 2.00122i
\(529\) −39.2852 −1.70805
\(530\) 11.3661 19.6866i 0.493710 0.855131i
\(531\) −21.4847 + 4.39552i −0.932357 + 0.190749i
\(532\) 0 0
\(533\) 1.26565 + 0.730726i 0.0548216 + 0.0316513i
\(534\) 22.3734 + 10.0638i 0.968190 + 0.435503i
\(535\) 29.2664 + 16.8969i 1.26530 + 0.730518i
\(536\) −1.53384 0.885563i −0.0662518 0.0382505i
\(537\) 0.257412 + 2.54245i 0.0111081 + 0.109715i
\(538\) 16.9615 + 9.79273i 0.731262 + 0.422195i
\(539\) 0 0
\(540\) 4.25893 18.9658i 0.183275 0.816159i
\(541\) −5.66792 + 9.81713i −0.243683 + 0.422071i −0.961760 0.273892i \(-0.911689\pi\)
0.718078 + 0.695963i \(0.245022\pi\)
\(542\) 12.2342 0.525504
\(543\) 23.7636 + 10.6891i 1.01979 + 0.458715i
\(544\) 21.5291i 0.923053i
\(545\) 1.15100 + 1.99360i 0.0493035 + 0.0853962i
\(546\) 0 0
\(547\) 19.4246 33.6444i 0.830537 1.43853i −0.0670762 0.997748i \(-0.521367\pi\)
0.897613 0.440784i \(-0.145300\pi\)
\(548\) 14.9587 + 8.63644i 0.639006 + 0.368930i
\(549\) −24.3497 8.11780i −1.03922 0.346459i
\(550\) −6.70292 11.6098i −0.285813 0.495043i
\(551\) −4.02823 6.97711i −0.171609 0.297235i
\(552\) −5.31421 + 11.8143i −0.226188 + 0.502850i
\(553\) 0 0
\(554\) −36.3061 + 20.9613i −1.54250 + 0.890562i
\(555\) 3.59409 + 4.98677i 0.152561 + 0.211677i
\(556\) 29.2613i 1.24096i
\(557\) 6.29167 3.63249i 0.266586 0.153914i −0.360749 0.932663i \(-0.617479\pi\)
0.627335 + 0.778749i \(0.284146\pi\)
\(558\) −38.9342 43.9106i −1.64822 1.85888i
\(559\) 4.22177i 0.178562i
\(560\) 0 0
\(561\) −3.01216 29.7510i −0.127173 1.25609i
\(562\) −41.7697 −1.76195
\(563\) −11.5409 + 19.9894i −0.486390 + 0.842453i −0.999878 0.0156446i \(-0.995020\pi\)
0.513487 + 0.858097i \(0.328353\pi\)
\(564\) −2.27406 + 5.05558i −0.0957552 + 0.212879i
\(565\) 10.2838 5.93738i 0.432644 0.249787i
\(566\) 35.4561 1.49033
\(567\) 0 0
\(568\) −2.79889 −0.117439
\(569\) 15.5482 8.97677i 0.651815 0.376326i −0.137336 0.990525i \(-0.543854\pi\)
0.789151 + 0.614199i \(0.210521\pi\)
\(570\) −8.56544 + 19.0423i −0.358767 + 0.797594i
\(571\) 7.04234 12.1977i 0.294713 0.510457i −0.680205 0.733022i \(-0.738109\pi\)
0.974918 + 0.222564i \(0.0714427\pi\)
\(572\) −3.71639 −0.155390
\(573\) −2.30715 22.7877i −0.0963826 0.951969i
\(574\) 0 0
\(575\) 10.0916i 0.420851i
\(576\) −7.08456 7.99007i −0.295190 0.332919i
\(577\) −26.0392 + 15.0337i −1.08403 + 0.625862i −0.931979 0.362511i \(-0.881919\pi\)
−0.152046 + 0.988373i \(0.548586\pi\)
\(578\) 14.0689i 0.585190i
\(579\) 1.57549 + 2.18598i 0.0654752 + 0.0908463i
\(580\) 10.1393 5.85392i 0.421011 0.243071i
\(581\) 0 0
\(582\) 4.94756 10.9992i 0.205083 0.455931i
\(583\) −13.6148 23.5815i −0.563866 0.976644i
\(584\) −4.03690 6.99211i −0.167048 0.289336i
\(585\) 3.16464 + 1.05504i 0.130842 + 0.0436205i
\(586\) 14.2800 + 8.24455i 0.589900 + 0.340579i
\(587\) 18.0979 31.3465i 0.746981 1.29381i −0.202283 0.979327i \(-0.564836\pi\)
0.949264 0.314481i \(-0.101831\pi\)
\(588\) 0 0
\(589\) 13.4719 + 23.3339i 0.555098 + 0.961459i
\(590\) 34.2327i 1.40934i
\(591\) 7.83776 + 3.52552i 0.322403 + 0.145020i
\(592\) 6.73755 0.276911
\(593\) 1.02158 1.76943i 0.0419514 0.0726620i −0.844287 0.535891i \(-0.819976\pi\)
0.886239 + 0.463229i \(0.153309\pi\)
\(594\) −40.0635 36.9130i −1.64382 1.51456i
\(595\) 0 0
\(596\) −20.3507 11.7495i −0.833598 0.481278i
\(597\) 1.95271 + 19.2869i 0.0799190 + 0.789359i
\(598\) 5.66854 + 3.27273i 0.231804 + 0.133832i
\(599\) 15.7873 + 9.11478i 0.645050 + 0.372420i 0.786557 0.617517i \(-0.211861\pi\)
−0.141507 + 0.989937i \(0.545195\pi\)
\(600\) 1.91419 + 0.861025i 0.0781466 + 0.0351512i
\(601\) −32.1713 18.5741i −1.31230 0.757654i −0.329820 0.944044i \(-0.606988\pi\)
−0.982476 + 0.186390i \(0.940321\pi\)
\(602\) 0 0
\(603\) −5.49287 + 1.12378i −0.223687 + 0.0457637i
\(604\) −1.48002 + 2.56346i −0.0602210 + 0.104306i
\(605\) −51.2856 −2.08506
\(606\) 2.45680 + 24.2658i 0.0998008 + 0.985731i
\(607\) 19.8296i 0.804860i 0.915451 + 0.402430i \(0.131834\pi\)
−0.915451 + 0.402430i \(0.868166\pi\)
\(608\) 9.00349 + 15.5945i 0.365140 + 0.632440i
\(609\) 0 0
\(610\) −20.0336 + 34.6991i −0.811135 + 1.40493i
\(611\) −0.823890 0.475673i −0.0333310 0.0192437i
\(612\) −9.14501 10.3139i −0.369665 0.416914i
\(613\) 6.34412 + 10.9883i 0.256237 + 0.443815i 0.965231 0.261400i \(-0.0841840\pi\)
−0.708994 + 0.705214i \(0.750851\pi\)
\(614\) 26.8690 + 46.5385i 1.08435 + 1.87814i
\(615\) 14.2204 1.43975i 0.573422 0.0580564i
\(616\) 0 0
\(617\) 4.37247 2.52445i 0.176029 0.101630i −0.409397 0.912357i \(-0.634261\pi\)
0.585426 + 0.810726i \(0.300927\pi\)
\(618\) 46.1305 4.67051i 1.85564 0.187875i
\(619\) 0.267890i 0.0107674i −0.999986 0.00538370i \(-0.998286\pi\)
0.999986 0.00538370i \(-0.00171369\pi\)
\(620\) −33.9094 + 19.5776i −1.36183 + 0.786255i
\(621\) 12.2248 + 39.1440i 0.490563 + 1.57080i
\(622\) 24.8305i 0.995611i
\(623\) 0 0
\(624\) 2.96625 2.13785i 0.118745 0.0855824i
\(625\) −29.7584 −1.19034
\(626\) −29.4820 + 51.0644i −1.17834 + 2.04094i
\(627\) 14.6237 + 20.2903i 0.584016 + 0.810317i
\(628\) 10.8504 6.26449i 0.432979 0.249981i
\(629\) 4.35905 0.173807
\(630\) 0 0
\(631\) 37.7899 1.50439 0.752197 0.658938i \(-0.228994\pi\)
0.752197 + 0.658938i \(0.228994\pi\)
\(632\) 0.471310 0.272111i 0.0187477 0.0108240i
\(633\) −26.4699 + 2.67996i −1.05208 + 0.106519i
\(634\) 18.7556 32.4856i 0.744880 1.29017i
\(635\) 18.4734 0.733095
\(636\) −11.4471 5.14905i −0.453908 0.204173i
\(637\) 0 0
\(638\) 32.8117i 1.29903i
\(639\) −6.62944 + 5.87813i −0.262257 + 0.232535i
\(640\) 15.9234 9.19336i 0.629426 0.363400i
\(641\) 34.4090i 1.35907i −0.733641 0.679537i \(-0.762181\pi\)
0.733641 0.679537i \(-0.237819\pi\)
\(642\) 17.9092 39.8150i 0.706821 1.57137i
\(643\) 0.676278 0.390449i 0.0266698 0.0153978i −0.486606 0.873622i \(-0.661765\pi\)
0.513276 + 0.858224i \(0.328432\pi\)
\(644\) 0 0
\(645\) −24.1415 33.4961i −0.950569 1.31891i
\(646\) 7.40341 + 12.8231i 0.291283 + 0.504517i
\(647\) 9.82182 + 17.0119i 0.386136 + 0.668807i 0.991926 0.126818i \(-0.0404763\pi\)
−0.605790 + 0.795624i \(0.707143\pi\)
\(648\) 8.46790 + 1.02099i 0.332650 + 0.0401082i
\(649\) 35.5118 + 20.5027i 1.39396 + 0.804803i
\(650\) 0.530259 0.918435i 0.0207985 0.0360240i
\(651\) 0 0
\(652\) −0.801781 1.38872i −0.0314001 0.0543867i
\(653\) 3.20545i 0.125439i 0.998031 + 0.0627194i \(0.0199773\pi\)
−0.998031 + 0.0627194i \(0.980023\pi\)
\(654\) 2.41259 1.73882i 0.0943399 0.0679931i
\(655\) 19.7026 0.769843
\(656\) 7.83315 13.5674i 0.305833 0.529719i
\(657\) −24.2464 8.08333i −0.945940 0.315361i
\(658\) 0 0
\(659\) −24.2959 14.0273i −0.946435 0.546425i −0.0544636 0.998516i \(-0.517345\pi\)
−0.891972 + 0.452091i \(0.850678\pi\)
\(660\) −29.4863 + 21.2515i −1.14775 + 0.827215i
\(661\) −28.0490 16.1941i −1.09098 0.629878i −0.157143 0.987576i \(-0.550228\pi\)
−0.933837 + 0.357698i \(0.883562\pi\)
\(662\) 2.01981 + 1.16614i 0.0785020 + 0.0453232i
\(663\) 1.91910 1.38314i 0.0745317 0.0537169i
\(664\) 6.95189 + 4.01367i 0.269785 + 0.155761i
\(665\) 0 0
\(666\) 5.94181 5.26843i 0.230240 0.204148i
\(667\) −12.3500 + 21.3908i −0.478193 + 0.828255i
\(668\) 11.9354 0.461793
\(669\) 4.49184 3.23738i 0.173665 0.125164i
\(670\) 8.75209i 0.338123i
\(671\) 23.9971 + 41.5641i 0.926397 + 1.60457i
\(672\) 0 0
\(673\) −10.3088 + 17.8554i −0.397375 + 0.688273i −0.993401 0.114692i \(-0.963412\pi\)
0.596026 + 0.802965i \(0.296745\pi\)
\(674\) −21.3242 12.3115i −0.821378 0.474223i
\(675\) 6.34224 1.98070i 0.244113 0.0762371i
\(676\) 9.55701 + 16.5532i 0.367577 + 0.636663i
\(677\) −25.1655 43.5880i −0.967190 1.67522i −0.703612 0.710585i \(-0.748431\pi\)
−0.263578 0.964638i \(-0.584903\pi\)
\(678\) −8.96958 12.4452i −0.344475 0.477956i
\(679\) 0 0
\(680\) 6.32935 3.65425i 0.242719 0.140134i
\(681\) −10.4233 + 23.1726i −0.399422 + 0.887977i
\(682\) 109.734i 4.20193i
\(683\) −11.9031 + 6.87227i −0.455460 + 0.262960i −0.710133 0.704067i \(-0.751365\pi\)
0.254673 + 0.967027i \(0.418032\pi\)
\(684\) 10.9374 + 3.64635i 0.418203 + 0.139422i
\(685\) 28.9909i 1.10769i
\(686\) 0 0
\(687\) −5.33602 2.40020i −0.203582 0.0915735i
\(688\) −45.2560 −1.72537
\(689\) 1.07705 1.86550i 0.0410321 0.0710698i
\(690\) 63.6895 6.44828i 2.42462 0.245482i
\(691\) −25.4328 + 14.6837i −0.967511 + 0.558593i −0.898476 0.439022i \(-0.855325\pi\)
−0.0690343 + 0.997614i \(0.521992\pi\)
\(692\) 1.49813 0.0569504
\(693\) 0 0
\(694\) −50.5874 −1.92027
\(695\) 42.5325 24.5562i 1.61335 0.931468i
\(696\) 3.00371 + 4.16763i 0.113856 + 0.157974i
\(697\) 5.06789 8.77784i 0.191960 0.332484i
\(698\) −65.4785 −2.47840
\(699\) −6.85719 + 4.94215i −0.259363 + 0.186929i
\(700\) 0 0
\(701\) 44.2011i 1.66945i 0.550666 + 0.834726i \(0.314374\pi\)
−0.550666 + 0.834726i \(0.685626\pi\)
\(702\) 0.944227 4.20482i 0.0356375 0.158701i
\(703\) −3.15746 + 1.82296i −0.119086 + 0.0687542i
\(704\) 19.9674i 0.752551i
\(705\) −9.25691 + 0.937220i −0.348635 + 0.0352977i
\(706\) 4.08702 2.35964i 0.153817 0.0888063i
\(707\) 0 0
\(708\) 18.8060 1.90402i 0.706772 0.0715575i
\(709\) 5.66629 + 9.81430i 0.212802 + 0.368584i 0.952590 0.304256i \(-0.0984077\pi\)
−0.739788 + 0.672840i \(0.765074\pi\)
\(710\) 6.91542 + 11.9779i 0.259531 + 0.449521i
\(711\) 0.544865 1.63435i 0.0204340 0.0612929i
\(712\) 6.21994 + 3.59108i 0.233102 + 0.134581i
\(713\) 41.3028 71.5385i 1.54680 2.67914i
\(714\) 0 0
\(715\) −3.11881 5.40193i −0.116637 0.202021i
\(716\) 2.20265i 0.0823168i
\(717\) 2.74497 + 27.1120i 0.102513 + 1.01252i
\(718\) −13.5827 −0.506903
\(719\) 18.0647 31.2890i 0.673700 1.16688i −0.303147 0.952944i \(-0.598037\pi\)
0.976847 0.213939i \(-0.0686294\pi\)
\(720\) 11.3097 33.9240i 0.421487 1.26427i
\(721\) 0 0
\(722\) 20.0271 + 11.5627i 0.745333 + 0.430318i
\(723\) −1.21532 0.546665i −0.0451983 0.0203307i
\(724\) −19.4505 11.2298i −0.722874 0.417351i
\(725\) 3.46580 + 2.00098i 0.128717 + 0.0743146i
\(726\) 6.67386 + 65.9176i 0.247690 + 2.44643i
\(727\) −6.20547 3.58273i −0.230148 0.132876i 0.380492 0.924784i \(-0.375755\pi\)
−0.610640 + 0.791908i \(0.709088\pi\)
\(728\) 0 0
\(729\) 22.2013 15.3657i 0.822269 0.569099i
\(730\) −19.9485 + 34.5518i −0.738327 + 1.27882i
\(731\) −29.2797 −1.08295
\(732\) 20.1765 + 9.07560i 0.745744 + 0.335444i
\(733\) 47.8498i 1.76737i 0.468081 + 0.883685i \(0.344945\pi\)
−0.468081 + 0.883685i \(0.655055\pi\)
\(734\) −12.5938 21.8131i −0.464846 0.805136i
\(735\) 0 0
\(736\) 27.6034 47.8105i 1.01747 1.76232i
\(737\) 9.07910 + 5.24182i 0.334433 + 0.193085i
\(738\) −3.70104 18.0902i −0.136237 0.665909i
\(739\) −7.67416 13.2920i −0.282299 0.488956i 0.689652 0.724141i \(-0.257764\pi\)
−0.971951 + 0.235185i \(0.924430\pi\)
\(740\) −2.64917 4.58849i −0.0973853 0.168676i
\(741\) −0.811659 + 1.80444i −0.0298170 + 0.0662879i
\(742\) 0 0
\(743\) 34.9422 20.1739i 1.28191 0.740109i 0.304709 0.952445i \(-0.401441\pi\)
0.977197 + 0.212337i \(0.0681073\pi\)
\(744\) −10.0455 13.9380i −0.368286 0.510994i
\(745\) 39.4409i 1.44500i
\(746\) −38.4630 + 22.2066i −1.40823 + 0.813042i
\(747\) 24.8956 5.09334i 0.910882 0.186355i
\(748\) 25.7747i 0.942417i
\(749\) 0 0
\(750\) 3.04050 + 30.0310i 0.111023 + 1.09658i
\(751\) 33.8898 1.23665 0.618327 0.785921i \(-0.287811\pi\)
0.618327 + 0.785921i \(0.287811\pi\)
\(752\) −5.09906 + 8.83183i −0.185944 + 0.322064i
\(753\) −0.813864 + 1.80935i −0.0296589 + 0.0659362i
\(754\) 2.24793 1.29784i 0.0818647 0.0472646i
\(755\) −4.96814 −0.180809
\(756\) 0 0
\(757\) −5.73237 −0.208346 −0.104173 0.994559i \(-0.533220\pi\)
−0.104173 + 0.994559i \(0.533220\pi\)
\(758\) −34.3589 + 19.8371i −1.24797 + 0.720517i
\(759\) 31.4559 69.9312i 1.14178 2.53834i
\(760\) −3.05642 + 5.29387i −0.110868 + 0.192029i
\(761\) −26.5332 −0.961828 −0.480914 0.876768i \(-0.659695\pi\)
−0.480914 + 0.876768i \(0.659695\pi\)
\(762\) −2.40397 23.7439i −0.0870865 0.860152i
\(763\) 0 0
\(764\) 19.7420i 0.714242i
\(765\) 7.31713 21.9481i 0.264551 0.793535i
\(766\) 20.9741 12.1094i 0.757825 0.437531i
\(767\) 3.24389i 0.117130i
\(768\) −21.0980 29.2733i −0.761307 1.05631i
\(769\) 23.3944 13.5068i 0.843623 0.487066i −0.0148711 0.999889i \(-0.504734\pi\)
0.858494 + 0.512823i \(0.171400\pi\)
\(770\) 0 0
\(771\) −20.5935 + 45.7824i −0.741655 + 1.64881i
\(772\) −1.16128 2.01139i −0.0417953 0.0723916i
\(773\) 11.3009 + 19.5737i 0.406464 + 0.704016i 0.994491 0.104826i \(-0.0334284\pi\)
−0.588027 + 0.808841i \(0.700095\pi\)
\(774\) −39.9111 + 35.3880i −1.43457 + 1.27200i
\(775\) −11.5909 6.69201i −0.416357 0.240384i
\(776\) 1.76545 3.05784i 0.0633758 0.109770i
\(777\) 0 0
\(778\) 10.2296 + 17.7182i 0.366750 + 0.635229i
\(779\) 8.47758i 0.303741i
\(780\) −2.62226 1.17952i −0.0938918 0.0422336i
\(781\) 16.5672 0.592821
\(782\) 22.6978 39.3137i 0.811670 1.40585i
\(783\) 15.8673 + 3.56313i 0.567051 + 0.127336i
\(784\) 0 0
\(785\) 18.2114 + 10.5144i 0.649993 + 0.375274i
\(786\) −2.56392 25.3238i −0.0914519 0.903270i
\(787\) −22.6864 13.0980i −0.808683 0.466893i 0.0378153 0.999285i \(-0.487960\pi\)
−0.846498 + 0.532391i \(0.821293\pi\)
\(788\) −6.41523 3.70383i −0.228533 0.131944i
\(789\) 21.6402 + 9.73401i 0.770412 + 0.346540i
\(790\) −2.32900 1.34465i −0.0828620 0.0478404i
\(791\) 0 0
\(792\) −10.5808 11.9331i −0.375971 0.424026i
\(793\) −1.89838 + 3.28808i −0.0674133 + 0.116763i
\(794\) 55.8627 1.98249
\(795\) −2.12210 20.9600i −0.0752633 0.743375i
\(796\) 16.7091i 0.592239i
\(797\) −5.96560 10.3327i −0.211312 0.366004i 0.740813 0.671711i \(-0.234440\pi\)
−0.952126 + 0.305707i \(0.901107\pi\)
\(798\) 0 0
\(799\) −3.29899 + 5.71402i −0.116710 + 0.202147i
\(800\) −7.74640 4.47239i −0.273877 0.158123i
\(801\) 22.2744 4.55707i 0.787026 0.161016i
\(802\) −17.9370 31.0678i −0.633378 1.09704i
\(803\) 23.8952 + 41.3877i 0.843242 + 1.46054i
\(804\) 4.80802 0.486790i 0.169566 0.0171678i
\(805\) 0 0
\(806\) −7.51788 + 4.34045i −0.264806 + 0.152886i
\(807\) 18.0586 1.82836i 0.635694 0.0643612i
\(808\) 7.14038i 0.251198i
\(809\) −22.9399 + 13.2443i −0.806522 + 0.465646i −0.845747 0.533585i \(-0.820845\pi\)
0.0392244 + 0.999230i \(0.487511\pi\)
\(810\) −16.5529 38.7610i −0.581610 1.36192i
\(811\) 13.7419i 0.482544i −0.970458 0.241272i \(-0.922435\pi\)
0.970458 0.241272i \(-0.0775646\pi\)
\(812\) 0 0
\(813\) 9.19812 6.62932i 0.322592 0.232500i
\(814\) −14.8488 −0.520449
\(815\) 1.34571 2.33084i 0.0471383 0.0816459i
\(816\) −14.8269 20.5722i −0.519044 0.720169i
\(817\) 21.2086 12.2448i 0.741996 0.428391i
\(818\) −53.8949 −1.88439
\(819\) 0 0
\(820\) −12.3198 −0.430226
\(821\) 11.7493 6.78346i 0.410053 0.236744i −0.280759 0.959778i \(-0.590586\pi\)
0.690813 + 0.723034i \(0.257253\pi\)
\(822\) 37.2621 3.77262i 1.29967 0.131585i
\(823\) −7.34857 + 12.7281i −0.256155 + 0.443674i −0.965209 0.261481i \(-0.915789\pi\)
0.709053 + 0.705155i \(0.249122\pi\)
\(824\) 13.5742 0.472881
\(825\) −11.3305 5.09658i −0.394476 0.177440i
\(826\) 0 0
\(827\) 40.8787i 1.42149i 0.703449 + 0.710746i \(0.251642\pi\)
−0.703449 + 0.710746i \(0.748358\pi\)
\(828\) −7.08481 34.6296i −0.246214 1.20346i
\(829\) 17.7189 10.2300i 0.615402 0.355302i −0.159675 0.987170i \(-0.551045\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(830\) 39.6675i 1.37688i
\(831\) −15.9380 + 35.4326i −0.552883 + 1.22914i
\(832\) −1.36797 + 0.789798i −0.0474258 + 0.0273813i
\(833\) 0 0
\(834\) −37.0969 51.4717i −1.28456 1.78232i
\(835\) 10.0162 + 17.3486i 0.346625 + 0.600372i
\(836\) −10.7790 18.6698i −0.372800 0.645708i
\(837\) −53.0659 11.9164i −1.83423 0.411891i
\(838\) −16.3923 9.46412i −0.566264 0.326932i
\(839\) −27.3475 + 47.3673i −0.944141 + 1.63530i −0.186680 + 0.982421i \(0.559773\pi\)
−0.757462 + 0.652880i \(0.773561\pi\)
\(840\) 0 0
\(841\) −9.60247 16.6320i −0.331120 0.573516i
\(842\) 47.5062i 1.63717i
\(843\) −31.4040 + 22.6336i −1.08161 + 0.779544i
\(844\) 22.9321 0.789356
\(845\) −16.0405 + 27.7830i −0.551812 + 0.955766i
\(846\) 2.40922 + 11.7760i 0.0828308 + 0.404866i
\(847\) 0 0
\(848\) −19.9975 11.5456i −0.686718 0.396477i
\(849\) 26.6572 19.2125i 0.914873 0.659372i
\(850\) −6.36973 3.67756i −0.218480 0.126139i
\(851\) 9.68031 + 5.58893i 0.331837 + 0.191586i
\(852\) 6.19548 4.46524i 0.212254 0.152977i
\(853\) −11.0684 6.39037i −0.378976 0.218802i 0.298396 0.954442i \(-0.403548\pi\)
−0.677373 + 0.735640i \(0.736882\pi\)
\(854\) 0 0
\(855\) 3.87859 + 18.9580i 0.132645 + 0.648351i
\(856\) 6.39058 11.0688i 0.218426 0.378324i
\(857\) 18.3240 0.625936 0.312968 0.949764i \(-0.398677\pi\)
0.312968 + 0.949764i \(0.398677\pi\)
\(858\) −6.53727 + 4.71157i −0.223179 + 0.160850i
\(859\) 38.6339i 1.31817i −0.752068 0.659085i \(-0.770944\pi\)
0.752068 0.659085i \(-0.229056\pi\)
\(860\) 17.7944 + 30.8208i 0.606784 + 1.05098i
\(861\) 0 0
\(862\) −10.1328 + 17.5505i −0.345125 + 0.597774i
\(863\) 14.4626 + 8.35001i 0.492314 + 0.284238i 0.725534 0.688186i \(-0.241593\pi\)
−0.233220 + 0.972424i \(0.574926\pi\)
\(864\) −35.4649 7.96394i −1.20654 0.270939i
\(865\) 1.25724 + 2.17760i 0.0427473 + 0.0740405i
\(866\) −12.1966 21.1251i −0.414456 0.717859i
\(867\) 7.62350 + 10.5775i 0.258908 + 0.359232i
\(868\) 0 0
\(869\) −2.78978 + 1.61068i −0.0946367 + 0.0546385i
\(870\) 10.4139 23.1517i 0.353064 0.784915i
\(871\) 0.829346i 0.0281013i
\(872\) 0.753996 0.435320i 0.0255335 0.0147418i
\(873\) −2.24035 10.9505i −0.0758242 0.370619i
\(874\) 37.9689i 1.28432i
\(875\) 0 0
\(876\) 20.0908 + 9.03707i 0.678805 + 0.305334i
\(877\) 33.5234 1.13200 0.566002 0.824404i \(-0.308489\pi\)
0.566002 + 0.824404i \(0.308489\pi\)
\(878\) 29.8606 51.7201i 1.00775 1.74547i
\(879\) 15.2037 1.53930i 0.512807 0.0519194i
\(880\) −57.9070 + 33.4326i −1.95204 + 1.12701i
\(881\) 28.6657 0.965771 0.482885 0.875684i \(-0.339589\pi\)
0.482885 + 0.875684i \(0.339589\pi\)
\(882\) 0 0
\(883\) −38.2091 −1.28584 −0.642919 0.765935i \(-0.722277\pi\)
−0.642919 + 0.765935i \(0.722277\pi\)
\(884\) −1.76583 + 1.01950i −0.0593912 + 0.0342895i
\(885\) 18.5496 + 25.7374i 0.623539 + 0.865154i
\(886\) 23.1719 40.1350i 0.778476 1.34836i
\(887\) 35.1828 1.18132 0.590662 0.806919i \(-0.298867\pi\)
0.590662 + 0.806919i \(0.298867\pi\)
\(888\) 1.88604 1.35932i 0.0632915 0.0456157i
\(889\) 0 0
\(890\) 35.4910i 1.18966i
\(891\) −50.1231 6.04342i −1.67919 0.202462i
\(892\) −4.13309 + 2.38624i −0.138386 + 0.0798972i
\(893\) 5.51856i 0.184672i
\(894\) −50.6935 + 5.13249i −1.69544 + 0.171656i
\(895\) 3.20164 1.84847i 0.107019 0.0617875i
\(896\) 0 0
\(897\) 6.03521 0.611037i 0.201510 0.0204019i
\(898\) −12.8685 22.2890i −0.429429 0.743792i
\(899\) −16.3791 28.3695i −0.546274 0.946174i
\(900\) −5.61080 + 1.14790i −0.187027 + 0.0382634i
\(901\) −12.9380 7.46975i −0.431027 0.248854i
\(902\) −17.2634 + 29.9010i −0.574807 + 0.995595i
\(903\) 0 0
\(904\) −2.24557 3.88944i −0.0746866 0.129361i
\(905\) 37.6963i 1.25307i
\(906\) 0.646509 + 6.38556i 0.0214788 + 0.212146i
\(907\) −42.5954 −1.41436 −0.707179 0.707034i \(-0.750033\pi\)
−0.707179 + 0.707034i \(0.750033\pi\)
\(908\) 10.9505 18.9669i 0.363406 0.629437i
\(909\) 14.9960 + 16.9127i 0.497385 + 0.560958i
\(910\) 0 0
\(911\) −43.5221 25.1275i −1.44195 0.832510i −0.443970 0.896042i \(-0.646430\pi\)
−0.997980 + 0.0635313i \(0.979764\pi\)
\(912\) 19.3431 + 8.70073i 0.640513 + 0.288110i
\(913\) −41.1496 23.7577i −1.36185 0.786265i
\(914\) 44.2037 + 25.5210i 1.46213 + 0.844160i
\(915\) 3.74037 + 36.9436i 0.123653 + 1.22132i
\(916\) 4.36754 + 2.52160i 0.144308 + 0.0833161i
\(917\) 0 0
\(918\) −29.1622 6.54860i −0.962495 0.216136i
\(919\) 29.3486 50.8333i 0.968121 1.67684i 0.267137 0.963658i \(-0.413922\pi\)
0.700984 0.713177i \(-0.252744\pi\)
\(920\) 18.7411 0.617875
\(921\) 45.4189 + 20.4299i 1.49660 + 0.673189i
\(922\) 20.6264i 0.679295i
\(923\) 0.655304 + 1.13502i 0.0215696 + 0.0373596i
\(924\) 0 0
\(925\) 0.905536 1.56843i 0.0297738 0.0515698i
\(926\) 39.6046 + 22.8657i 1.30149 + 0.751415i
\(927\) 32.1518 28.5081i 1.05601 0.936329i
\(928\) −10.9465 18.9598i −0.359335 0.622387i
\(929\) 7.19115 + 12.4554i 0.235934 + 0.408650i 0.959544 0.281560i \(-0.0908518\pi\)
−0.723610 + 0.690209i \(0.757518\pi\)
\(930\) −34.8278 + 77.4275i −1.14205 + 2.53895i
\(931\) 0 0
\(932\) 6.30952 3.64281i 0.206675 0.119324i
\(933\) 13.4548 + 18.6685i 0.440491 + 0.611178i
\(934\) 29.7251i 0.972636i
\(935\) −37.4646 + 21.6302i −1.22522 + 0.707384i
\(936\) 0.399025 1.19690i 0.0130426 0.0391218i
\(937\) 44.2981i 1.44716i 0.690243 + 0.723578i \(0.257504\pi\)
−0.690243 + 0.723578i \(0.742496\pi\)
\(938\) 0 0
\(939\) 5.50446 + 54.3675i 0.179631 + 1.77422i
\(940\) 8.01969 0.261573
\(941\) 7.44400 12.8934i 0.242667 0.420312i −0.718806 0.695211i \(-0.755311\pi\)
0.961473 + 0.274899i \(0.0886443\pi\)
\(942\) 11.1443 24.7754i 0.363100 0.807228i
\(943\) 22.5089 12.9955i 0.732990 0.423192i
\(944\) 34.7734 1.13178
\(945\) 0 0
\(946\) 99.7390 3.24280
\(947\) −36.3343 + 20.9776i −1.18071 + 0.681681i −0.956178 0.292787i \(-0.905417\pi\)
−0.224528 + 0.974468i \(0.572084\pi\)
\(948\) −0.609153 + 1.35424i −0.0197844 + 0.0439837i
\(949\) −1.89031 + 3.27412i −0.0613622 + 0.106282i
\(950\) 6.15184 0.199592
\(951\) −3.50177 34.5869i −0.113553 1.12156i
\(952\) 0 0
\(953\) 13.9821i 0.452926i −0.974020 0.226463i \(-0.927284\pi\)
0.974020 0.226463i \(-0.0727162\pi\)
\(954\) −26.6638 + 5.45510i −0.863273 + 0.176615i
\(955\) −28.6959 + 16.5676i −0.928578 + 0.536115i
\(956\) 23.4884i 0.759669i
\(957\) −17.7796 24.6690i −0.574732 0.797436i
\(958\) −22.4228 + 12.9458i −0.724449 + 0.418261i
\(959\) 0 0
\(960\) −6.33733 + 14.0889i −0.204537 + 0.454716i
\(961\) 39.2776 + 68.0309i 1.26702 + 2.19454i
\(962\) −0.587333 1.01729i −0.0189364 0.0327988i
\(963\) −8.10963 39.6388i −0.261329 1.27734i
\(964\) 0.994743 + 0.574315i 0.0320385 + 0.0184974i
\(965\) 1.94910 3.37593i 0.0627436 0.108675i
\(966\) 0 0
\(967\) −11.5757 20.0497i −0.372249 0.644754i 0.617662 0.786443i \(-0.288080\pi\)
−0.989911 + 0.141690i \(0.954746\pi\)
\(968\) 19.3967i 0.623433i
\(969\) 12.5146 + 5.62919i 0.402026 + 0.180836i
\(970\) −17.4481 −0.560223
\(971\) −21.6869 + 37.5628i −0.695965 + 1.20545i 0.273890 + 0.961761i \(0.411690\pi\)
−0.969854 + 0.243685i \(0.921644\pi\)
\(972\) −20.3729 + 11.2493i −0.653462 + 0.360823i
\(973\) 0 0
\(974\) 46.6120 + 26.9114i 1.49354 + 0.862298i
\(975\) −0.0990022 0.977843i −0.00317061 0.0313160i
\(976\) 35.2472 + 20.3500i 1.12824 + 0.651387i
\(977\) 10.4210 + 6.01657i 0.333397 + 0.192487i 0.657348 0.753587i \(-0.271678\pi\)
−0.323951 + 0.946074i \(0.605011\pi\)
\(978\) −3.17096 1.42633i −0.101396 0.0456092i
\(979\) −36.8170 21.2563i −1.17668 0.679355i
\(980\) 0 0
\(981\) 0.871668 2.61461i 0.0278302 0.0834782i
\(982\) 36.2152 62.7266i 1.15567 2.00169i
\(983\) 6.29658 0.200830 0.100415 0.994946i \(-0.467983\pi\)
0.100415 + 0.994946i \(0.467983\pi\)
\(984\) −0.544527 5.37829i −0.0173589 0.171454i
\(985\) 12.4331i 0.396151i
\(986\) −9.00108 15.5903i −0.286653 0.496497i
\(987\) 0 0
\(988\) 0.852712 1.47694i 0.0271284 0.0469877i
\(989\) −65.0225 37.5408i −2.06760 1.19373i
\(990\) −24.9252 + 74.7645i −0.792176 + 2.37617i
\(991\) −16.7814 29.0662i −0.533078 0.923317i −0.999254 0.0386256i \(-0.987702\pi\)
0.466176 0.884692i \(-0.345631\pi\)
\(992\) 36.6089 + 63.4085i 1.16233 + 2.01322i
\(993\) 2.15046 0.217724i 0.0682427 0.00690926i
\(994\) 0 0
\(995\) 24.2874 14.0223i 0.769963 0.444538i
\(996\) −21.7916 + 2.20630i −0.690493 + 0.0699092i
\(997\) 11.2565i 0.356495i −0.983986 0.178248i \(-0.942957\pi\)
0.983986 0.178248i \(-0.0570428\pi\)
\(998\) 5.61096 3.23949i 0.177612 0.102544i
\(999\) 1.61248 7.18068i 0.0510166 0.227187i
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 441.2.s.d.362.5 48
3.2 odd 2 1323.2.s.d.656.19 48
7.2 even 3 441.2.o.e.146.19 48
7.3 odd 6 441.2.i.d.227.5 48
7.4 even 3 441.2.i.d.227.6 48
7.5 odd 6 441.2.o.e.146.20 yes 48
7.6 odd 2 inner 441.2.s.d.362.6 48
9.4 even 3 1323.2.i.d.1097.22 48
9.5 odd 6 441.2.i.d.68.19 48
21.2 odd 6 1323.2.o.e.440.6 48
21.5 even 6 1323.2.o.e.440.5 48
21.11 odd 6 1323.2.i.d.521.7 48
21.17 even 6 1323.2.i.d.521.22 48
21.20 even 2 1323.2.s.d.656.20 48
63.4 even 3 1323.2.s.d.962.20 48
63.5 even 6 441.2.o.e.293.19 yes 48
63.13 odd 6 1323.2.i.d.1097.7 48
63.23 odd 6 441.2.o.e.293.20 yes 48
63.31 odd 6 1323.2.s.d.962.19 48
63.32 odd 6 inner 441.2.s.d.374.6 48
63.40 odd 6 1323.2.o.e.881.6 48
63.41 even 6 441.2.i.d.68.20 48
63.58 even 3 1323.2.o.e.881.5 48
63.59 even 6 inner 441.2.s.d.374.5 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.i.d.68.19 48 9.5 odd 6
441.2.i.d.68.20 48 63.41 even 6
441.2.i.d.227.5 48 7.3 odd 6
441.2.i.d.227.6 48 7.4 even 3
441.2.o.e.146.19 48 7.2 even 3
441.2.o.e.146.20 yes 48 7.5 odd 6
441.2.o.e.293.19 yes 48 63.5 even 6
441.2.o.e.293.20 yes 48 63.23 odd 6
441.2.s.d.362.5 48 1.1 even 1 trivial
441.2.s.d.362.6 48 7.6 odd 2 inner
441.2.s.d.374.5 48 63.59 even 6 inner
441.2.s.d.374.6 48 63.32 odd 6 inner
1323.2.i.d.521.7 48 21.11 odd 6
1323.2.i.d.521.22 48 21.17 even 6
1323.2.i.d.1097.7 48 63.13 odd 6
1323.2.i.d.1097.22 48 9.4 even 3
1323.2.o.e.440.5 48 21.5 even 6
1323.2.o.e.440.6 48 21.2 odd 6
1323.2.o.e.881.5 48 63.58 even 3
1323.2.o.e.881.6 48 63.40 odd 6
1323.2.s.d.656.19 48 3.2 odd 2
1323.2.s.d.656.20 48 21.20 even 2
1323.2.s.d.962.19 48 63.31 odd 6
1323.2.s.d.962.20 48 63.4 even 3