Properties

Label 369.2.u.a.289.1
Level $369$
Weight $2$
Character 369.289
Analytic conductor $2.946$
Analytic rank $0$
Dimension $24$
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] = [369,2,Mod(46,369)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(369, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("369.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 369 = 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 369.u (of order \(20\), degree \(8\), 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: \(2.94647983459\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 41)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 289.1
Character \(\chi\) \(=\) 369.289
Dual form 369.2.u.a.226.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.698642 + 0.227002i) q^{2} +(-1.18146 + 0.858384i) q^{4} +(0.422124 + 0.581004i) q^{5} +(-1.42228 - 2.79137i) q^{7} +(1.49413 - 2.05650i) q^{8} +O(q^{10})\) \(q+(-0.698642 + 0.227002i) q^{2} +(-1.18146 + 0.858384i) q^{4} +(0.422124 + 0.581004i) q^{5} +(-1.42228 - 2.79137i) q^{7} +(1.49413 - 2.05650i) q^{8} +(-0.426803 - 0.310091i) q^{10} +(-3.06970 + 0.486193i) q^{11} +(-1.79162 - 0.912875i) q^{13} +(1.62731 + 1.62731i) q^{14} +(0.325524 - 1.00186i) q^{16} +(-0.304435 - 1.92213i) q^{17} +(3.91204 - 1.99329i) q^{19} +(-0.997449 - 0.324091i) q^{20} +(2.03426 - 1.03651i) q^{22} +(-0.275748 - 0.848664i) q^{23} +(1.38571 - 4.26477i) q^{25} +(1.45892 + 0.231071i) q^{26} +(4.07644 + 2.07705i) q^{28} +(1.43151 - 9.03822i) q^{29} +(-5.64731 - 4.10301i) q^{31} +5.85778i q^{32} +(0.649020 + 1.27377i) q^{34} +(1.02142 - 2.00465i) q^{35} +(-3.49299 + 2.53781i) q^{37} +(-2.28064 + 2.28064i) q^{38} +1.82554 q^{40} +(2.53101 - 5.88167i) q^{41} +(-10.3243 + 3.35457i) q^{43} +(3.20940 - 3.20940i) q^{44} +(0.385298 + 0.530317i) q^{46} +(-5.24325 + 10.2905i) q^{47} +(-1.65440 + 2.27709i) q^{49} +3.29411i q^{50} +(2.90033 - 0.459367i) q^{52} +(-0.465724 + 2.94046i) q^{53} +(-1.57828 - 1.57828i) q^{55} +(-7.86552 - 1.24578i) q^{56} +(1.05158 + 6.63944i) q^{58} +(-1.37512 - 4.23218i) q^{59} +(11.3577 + 3.69033i) q^{61} +(4.87684 + 1.58458i) q^{62} +(-0.678682 - 2.08877i) q^{64} +(-0.225901 - 1.42628i) q^{65} +(8.00079 + 1.26720i) q^{67} +(2.00960 + 2.00960i) q^{68} +(-0.258547 + 1.63240i) q^{70} +(0.988102 - 0.156500i) q^{71} -6.49752i q^{73} +(1.86426 - 2.56593i) q^{74} +(-2.91093 + 5.71303i) q^{76} +(5.72311 + 7.87719i) q^{77} +(-4.43337 + 4.43337i) q^{79} +(0.719497 - 0.233779i) q^{80} +(-0.433113 + 4.68372i) q^{82} -7.83744 q^{83} +(0.988256 - 0.988256i) q^{85} +(6.45150 - 4.68729i) q^{86} +(-3.58669 + 7.03928i) q^{88} +(6.40964 + 12.5796i) q^{89} +6.29943i q^{91} +(1.05426 + 0.765968i) q^{92} +(1.32719 - 8.37958i) q^{94} +(2.80948 + 1.43150i) q^{95} +(6.34053 + 1.00424i) q^{97} +(0.638929 - 1.96642i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/369\mathbb{Z}\right)^\times\).

\(n\) \(83\) \(334\)
\(\chi(n)\) \(1\) \(e\left(\frac{13}{20}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.698642 + 0.227002i −0.494014 + 0.160515i −0.545420 0.838163i \(-0.683630\pi\)
0.0514057 + 0.998678i \(0.483630\pi\)
\(3\) 0 0
\(4\) −1.18146 + 0.858384i −0.590732 + 0.429192i
\(5\) 0.422124 + 0.581004i 0.188780 + 0.259833i 0.892907 0.450240i \(-0.148662\pi\)
−0.704128 + 0.710073i \(0.748662\pi\)
\(6\) 0 0
\(7\) −1.42228 2.79137i −0.537570 1.05504i −0.986848 0.161648i \(-0.948319\pi\)
0.449279 0.893392i \(-0.351681\pi\)
\(8\) 1.49413 2.05650i 0.528256 0.727082i
\(9\) 0 0
\(10\) −0.426803 0.310091i −0.134967 0.0980592i
\(11\) −3.06970 + 0.486193i −0.925551 + 0.146593i −0.600976 0.799267i \(-0.705221\pi\)
−0.324575 + 0.945860i \(0.605221\pi\)
\(12\) 0 0
\(13\) −1.79162 0.912875i −0.496905 0.253186i 0.187531 0.982259i \(-0.439952\pi\)
−0.684436 + 0.729073i \(0.739952\pi\)
\(14\) 1.62731 + 1.62731i 0.434917 + 0.434917i
\(15\) 0 0
\(16\) 0.325524 1.00186i 0.0813810 0.250465i
\(17\) −0.304435 1.92213i −0.0738365 0.466185i −0.996708 0.0810768i \(-0.974164\pi\)
0.922871 0.385108i \(-0.125836\pi\)
\(18\) 0 0
\(19\) 3.91204 1.99329i 0.897485 0.457291i 0.0565325 0.998401i \(-0.481996\pi\)
0.840952 + 0.541109i \(0.181996\pi\)
\(20\) −0.997449 0.324091i −0.223036 0.0724689i
\(21\) 0 0
\(22\) 2.03426 1.03651i 0.433705 0.220984i
\(23\) −0.275748 0.848664i −0.0574973 0.176959i 0.918183 0.396156i \(-0.129656\pi\)
−0.975681 + 0.219198i \(0.929656\pi\)
\(24\) 0 0
\(25\) 1.38571 4.26477i 0.277142 0.852954i
\(26\) 1.45892 + 0.231071i 0.286119 + 0.0453167i
\(27\) 0 0
\(28\) 4.07644 + 2.07705i 0.770374 + 0.392525i
\(29\) 1.43151 9.03822i 0.265825 1.67836i −0.387961 0.921676i \(-0.626820\pi\)
0.653786 0.756680i \(-0.273180\pi\)
\(30\) 0 0
\(31\) −5.64731 4.10301i −1.01429 0.736922i −0.0491827 0.998790i \(-0.515662\pi\)
−0.965104 + 0.261868i \(0.915662\pi\)
\(32\) 5.85778i 1.03552i
\(33\) 0 0
\(34\) 0.649020 + 1.27377i 0.111306 + 0.218450i
\(35\) 1.02142 2.00465i 0.172652 0.338848i
\(36\) 0 0
\(37\) −3.49299 + 2.53781i −0.574244 + 0.417213i −0.836644 0.547746i \(-0.815486\pi\)
0.262400 + 0.964959i \(0.415486\pi\)
\(38\) −2.28064 + 2.28064i −0.369968 + 0.369968i
\(39\) 0 0
\(40\) 1.82554 0.288644
\(41\) 2.53101 5.88167i 0.395277 0.918562i
\(42\) 0 0
\(43\) −10.3243 + 3.35457i −1.57444 + 0.511568i −0.960618 0.277874i \(-0.910370\pi\)
−0.613826 + 0.789441i \(0.710370\pi\)
\(44\) 3.20940 3.20940i 0.483836 0.483836i
\(45\) 0 0
\(46\) 0.385298 + 0.530317i 0.0568090 + 0.0781909i
\(47\) −5.24325 + 10.2905i −0.764807 + 1.50102i 0.0978352 + 0.995203i \(0.468808\pi\)
−0.862642 + 0.505815i \(0.831192\pi\)
\(48\) 0 0
\(49\) −1.65440 + 2.27709i −0.236343 + 0.325298i
\(50\) 3.29411i 0.465857i
\(51\) 0 0
\(52\) 2.90033 0.459367i 0.402203 0.0637027i
\(53\) −0.465724 + 2.94046i −0.0639721 + 0.403904i 0.934835 + 0.355081i \(0.115547\pi\)
−0.998807 + 0.0488225i \(0.984453\pi\)
\(54\) 0 0
\(55\) −1.57828 1.57828i −0.212815 0.212815i
\(56\) −7.86552 1.24578i −1.05107 0.166474i
\(57\) 0 0
\(58\) 1.05158 + 6.63944i 0.138080 + 0.871801i
\(59\) −1.37512 4.23218i −0.179025 0.550982i 0.820769 0.571260i \(-0.193545\pi\)
−0.999794 + 0.0202774i \(0.993545\pi\)
\(60\) 0 0
\(61\) 11.3577 + 3.69033i 1.45420 + 0.472499i 0.926294 0.376803i \(-0.122977\pi\)
0.527908 + 0.849301i \(0.322977\pi\)
\(62\) 4.87684 + 1.58458i 0.619359 + 0.201242i
\(63\) 0 0
\(64\) −0.678682 2.08877i −0.0848353 0.261096i
\(65\) −0.225901 1.42628i −0.0280196 0.176909i
\(66\) 0 0
\(67\) 8.00079 + 1.26720i 0.977452 + 0.154813i 0.624667 0.780891i \(-0.285235\pi\)
0.352785 + 0.935704i \(0.385235\pi\)
\(68\) 2.00960 + 2.00960i 0.243700 + 0.243700i
\(69\) 0 0
\(70\) −0.258547 + 1.63240i −0.0309023 + 0.195109i
\(71\) 0.988102 0.156500i 0.117266 0.0185731i −0.0975255 0.995233i \(-0.531093\pi\)
0.214792 + 0.976660i \(0.431093\pi\)
\(72\) 0 0
\(73\) 6.49752i 0.760477i −0.924889 0.380238i \(-0.875842\pi\)
0.924889 0.380238i \(-0.124158\pi\)
\(74\) 1.86426 2.56593i 0.216716 0.298284i
\(75\) 0 0
\(76\) −2.91093 + 5.71303i −0.333907 + 0.655330i
\(77\) 5.72311 + 7.87719i 0.652209 + 0.897689i
\(78\) 0 0
\(79\) −4.43337 + 4.43337i −0.498793 + 0.498793i −0.911062 0.412269i \(-0.864736\pi\)
0.412269 + 0.911062i \(0.364736\pi\)
\(80\) 0.719497 0.233779i 0.0804422 0.0261372i
\(81\) 0 0
\(82\) −0.433113 + 4.68372i −0.0478294 + 0.517231i
\(83\) −7.83744 −0.860271 −0.430136 0.902764i \(-0.641534\pi\)
−0.430136 + 0.902764i \(0.641534\pi\)
\(84\) 0 0
\(85\) 0.988256 0.988256i 0.107191 0.107191i
\(86\) 6.45150 4.68729i 0.695683 0.505444i
\(87\) 0 0
\(88\) −3.58669 + 7.03928i −0.382343 + 0.750390i
\(89\) 6.40964 + 12.5796i 0.679420 + 1.33344i 0.930793 + 0.365547i \(0.119118\pi\)
−0.251373 + 0.967890i \(0.580882\pi\)
\(90\) 0 0
\(91\) 6.29943i 0.660360i
\(92\) 1.05426 + 0.765968i 0.109915 + 0.0798577i
\(93\) 0 0
\(94\) 1.32719 8.37958i 0.136890 0.864287i
\(95\) 2.80948 + 1.43150i 0.288246 + 0.146869i
\(96\) 0 0
\(97\) 6.34053 + 1.00424i 0.643783 + 0.101965i 0.469785 0.882781i \(-0.344331\pi\)
0.173998 + 0.984746i \(0.444331\pi\)
\(98\) 0.638929 1.96642i 0.0645415 0.198638i
\(99\) 0 0
\(100\) 2.02365 + 6.22814i 0.202365 + 0.622814i
\(101\) −10.7210 + 5.46262i −1.06678 + 0.543551i −0.897045 0.441938i \(-0.854291\pi\)
−0.169734 + 0.985490i \(0.554291\pi\)
\(102\) 0 0
\(103\) −14.6231 4.75134i −1.44086 0.468163i −0.518694 0.854960i \(-0.673581\pi\)
−0.922165 + 0.386797i \(0.873581\pi\)
\(104\) −4.55424 + 2.32050i −0.446580 + 0.227544i
\(105\) 0 0
\(106\) −0.342119 2.16005i −0.0332295 0.209803i
\(107\) 0.344730 1.06097i 0.0333263 0.102568i −0.933010 0.359851i \(-0.882827\pi\)
0.966336 + 0.257284i \(0.0828274\pi\)
\(108\) 0 0
\(109\) 4.18654 + 4.18654i 0.400998 + 0.400998i 0.878585 0.477587i \(-0.158488\pi\)
−0.477587 + 0.878585i \(0.658488\pi\)
\(110\) 1.46092 + 0.744378i 0.139294 + 0.0709736i
\(111\) 0 0
\(112\) −3.25955 + 0.516262i −0.307999 + 0.0487822i
\(113\) −12.4975 9.07995i −1.17566 0.854170i −0.183988 0.982928i \(-0.558901\pi\)
−0.991676 + 0.128759i \(0.958901\pi\)
\(114\) 0 0
\(115\) 0.376677 0.518452i 0.0351254 0.0483459i
\(116\) 6.06698 + 11.9071i 0.563305 + 1.10555i
\(117\) 0 0
\(118\) 1.92143 + 2.64462i 0.176882 + 0.243457i
\(119\) −4.93239 + 3.58359i −0.452152 + 0.328507i
\(120\) 0 0
\(121\) −1.27492 + 0.414247i −0.115902 + 0.0376588i
\(122\) −8.77266 −0.794240
\(123\) 0 0
\(124\) 10.1940 0.915452
\(125\) 6.47785 2.10478i 0.579396 0.188257i
\(126\) 0 0
\(127\) 3.50780 2.54857i 0.311267 0.226149i −0.421173 0.906980i \(-0.638381\pi\)
0.732440 + 0.680832i \(0.238381\pi\)
\(128\) −5.93792 8.17285i −0.524843 0.722384i
\(129\) 0 0
\(130\) 0.481594 + 0.945182i 0.0422386 + 0.0828979i
\(131\) 9.74217 13.4090i 0.851178 1.17155i −0.132424 0.991193i \(-0.542276\pi\)
0.983602 0.180352i \(-0.0577238\pi\)
\(132\) 0 0
\(133\) −11.1280 8.08497i −0.964921 0.701056i
\(134\) −5.87734 + 0.930880i −0.507725 + 0.0804157i
\(135\) 0 0
\(136\) −4.40772 2.24585i −0.377959 0.192580i
\(137\) 0.166857 + 0.166857i 0.0142555 + 0.0142555i 0.714199 0.699943i \(-0.246791\pi\)
−0.699943 + 0.714199i \(0.746791\pi\)
\(138\) 0 0
\(139\) −0.727856 + 2.24011i −0.0617360 + 0.190004i −0.977168 0.212470i \(-0.931849\pi\)
0.915432 + 0.402473i \(0.131849\pi\)
\(140\) 0.513989 + 3.24520i 0.0434400 + 0.274269i
\(141\) 0 0
\(142\) −0.654803 + 0.333639i −0.0549499 + 0.0279984i
\(143\) 5.94357 + 1.93118i 0.497026 + 0.161494i
\(144\) 0 0
\(145\) 5.85552 2.98354i 0.486275 0.247769i
\(146\) 1.47495 + 4.53944i 0.122068 + 0.375686i
\(147\) 0 0
\(148\) 1.94843 5.99665i 0.160160 0.492922i
\(149\) 8.28803 + 1.31270i 0.678982 + 0.107540i 0.486394 0.873739i \(-0.338312\pi\)
0.192588 + 0.981280i \(0.438312\pi\)
\(150\) 0 0
\(151\) 3.22750 + 1.64449i 0.262650 + 0.133827i 0.580357 0.814362i \(-0.302913\pi\)
−0.317707 + 0.948189i \(0.602913\pi\)
\(152\) 1.74593 11.0233i 0.141613 0.894112i
\(153\) 0 0
\(154\) −5.78655 4.20417i −0.466293 0.338782i
\(155\) 5.01309i 0.402661i
\(156\) 0 0
\(157\) 6.25608 + 12.2783i 0.499290 + 0.979911i 0.993847 + 0.110766i \(0.0353304\pi\)
−0.494557 + 0.869145i \(0.664670\pi\)
\(158\) 2.09095 4.10373i 0.166347 0.326475i
\(159\) 0 0
\(160\) −3.40339 + 2.47271i −0.269062 + 0.195485i
\(161\) −1.97675 + 1.97675i −0.155790 + 0.155790i
\(162\) 0 0
\(163\) −0.923374 −0.0723243 −0.0361621 0.999346i \(-0.511513\pi\)
−0.0361621 + 0.999346i \(0.511513\pi\)
\(164\) 2.05844 + 9.12155i 0.160737 + 0.712273i
\(165\) 0 0
\(166\) 5.47557 1.77912i 0.424986 0.138086i
\(167\) 12.0223 12.0223i 0.930315 0.930315i −0.0674099 0.997725i \(-0.521474\pi\)
0.997725 + 0.0674099i \(0.0214735\pi\)
\(168\) 0 0
\(169\) −5.26465 7.24617i −0.404973 0.557398i
\(170\) −0.466100 + 0.914774i −0.0357483 + 0.0701599i
\(171\) 0 0
\(172\) 9.31829 12.8255i 0.710513 0.977938i
\(173\) 12.1428i 0.923198i 0.887089 + 0.461599i \(0.152724\pi\)
−0.887089 + 0.461599i \(0.847276\pi\)
\(174\) 0 0
\(175\) −13.8754 + 2.19765i −1.04888 + 0.166127i
\(176\) −0.512165 + 3.23368i −0.0386059 + 0.243748i
\(177\) 0 0
\(178\) −7.33365 7.33365i −0.549680 0.549680i
\(179\) 2.11231 + 0.334557i 0.157881 + 0.0250060i 0.234875 0.972026i \(-0.424532\pi\)
−0.0769933 + 0.997032i \(0.524532\pi\)
\(180\) 0 0
\(181\) −0.878821 5.54866i −0.0653222 0.412428i −0.998582 0.0532273i \(-0.983049\pi\)
0.933260 0.359201i \(-0.116951\pi\)
\(182\) −1.42999 4.40105i −0.105998 0.326227i
\(183\) 0 0
\(184\) −2.15728 0.700942i −0.159037 0.0516742i
\(185\) −2.94895 0.958172i −0.216811 0.0704462i
\(186\) 0 0
\(187\) 1.86905 + 5.75236i 0.136679 + 0.420654i
\(188\) −2.63845 16.6585i −0.192429 1.21495i
\(189\) 0 0
\(190\) −2.28777 0.362347i −0.165972 0.0262875i
\(191\) −9.27794 9.27794i −0.671328 0.671328i 0.286694 0.958022i \(-0.407444\pi\)
−0.958022 + 0.286694i \(0.907444\pi\)
\(192\) 0 0
\(193\) 2.59319 16.3728i 0.186662 1.17854i −0.699317 0.714812i \(-0.746512\pi\)
0.885979 0.463726i \(-0.153488\pi\)
\(194\) −4.65772 + 0.737711i −0.334405 + 0.0529646i
\(195\) 0 0
\(196\) 4.11040i 0.293600i
\(197\) 8.51171 11.7154i 0.606434 0.834685i −0.389844 0.920881i \(-0.627471\pi\)
0.996278 + 0.0861961i \(0.0274711\pi\)
\(198\) 0 0
\(199\) 8.18953 16.0729i 0.580541 1.13938i −0.394820 0.918759i \(-0.629193\pi\)
0.975361 0.220617i \(-0.0708070\pi\)
\(200\) −6.70006 9.22184i −0.473766 0.652083i
\(201\) 0 0
\(202\) 6.25011 6.25011i 0.439756 0.439756i
\(203\) −27.2651 + 8.85895i −1.91363 + 0.621777i
\(204\) 0 0
\(205\) 4.48567 1.01227i 0.313293 0.0707000i
\(206\) 11.2949 0.786952
\(207\) 0 0
\(208\) −1.49779 + 1.49779i −0.103853 + 0.103853i
\(209\) −11.0397 + 8.02081i −0.763632 + 0.554811i
\(210\) 0 0
\(211\) 6.12962 12.0301i 0.421980 0.828183i −0.577946 0.816075i \(-0.696146\pi\)
0.999927 0.0121083i \(-0.00385430\pi\)
\(212\) −1.97381 3.87382i −0.135562 0.266055i
\(213\) 0 0
\(214\) 0.819492i 0.0560193i
\(215\) −6.30717 4.58242i −0.430145 0.312519i
\(216\) 0 0
\(217\) −3.42100 + 21.5994i −0.232233 + 1.46626i
\(218\) −3.87525 1.97454i −0.262465 0.133733i
\(219\) 0 0
\(220\) 3.21944 + 0.509910i 0.217055 + 0.0343781i
\(221\) −1.20923 + 3.72163i −0.0813418 + 0.250344i
\(222\) 0 0
\(223\) −2.34538 7.21835i −0.157059 0.483377i 0.841305 0.540561i \(-0.181788\pi\)
−0.998364 + 0.0571840i \(0.981788\pi\)
\(224\) 16.3512 8.33138i 1.09251 0.556664i
\(225\) 0 0
\(226\) 10.7924 + 3.50667i 0.717902 + 0.233260i
\(227\) 19.3474 9.85797i 1.28413 0.654297i 0.327293 0.944923i \(-0.393864\pi\)
0.956837 + 0.290626i \(0.0938636\pi\)
\(228\) 0 0
\(229\) −0.463354 2.92550i −0.0306193 0.193323i 0.967637 0.252345i \(-0.0812017\pi\)
−0.998257 + 0.0590222i \(0.981202\pi\)
\(230\) −0.145473 + 0.447719i −0.00959219 + 0.0295217i
\(231\) 0 0
\(232\) −16.4482 16.4482i −1.07988 1.07988i
\(233\) 15.5044 + 7.89988i 1.01573 + 0.517538i 0.880886 0.473329i \(-0.156948\pi\)
0.134840 + 0.990867i \(0.456948\pi\)
\(234\) 0 0
\(235\) −8.19210 + 1.29750i −0.534394 + 0.0846397i
\(236\) 5.25748 + 3.81978i 0.342233 + 0.248647i
\(237\) 0 0
\(238\) 2.63249 3.62331i 0.170639 0.234864i
\(239\) 2.69685 + 5.29286i 0.174444 + 0.342366i 0.961630 0.274350i \(-0.0884626\pi\)
−0.787186 + 0.616716i \(0.788463\pi\)
\(240\) 0 0
\(241\) 5.16221 + 7.10518i 0.332527 + 0.457685i 0.942240 0.334938i \(-0.108715\pi\)
−0.609713 + 0.792622i \(0.708715\pi\)
\(242\) 0.796678 0.578820i 0.0512124 0.0372080i
\(243\) 0 0
\(244\) −16.5864 + 5.38925i −1.06184 + 0.345011i
\(245\) −2.02136 −0.129140
\(246\) 0 0
\(247\) −8.82851 −0.561745
\(248\) −16.8757 + 5.48324i −1.07161 + 0.348186i
\(249\) 0 0
\(250\) −4.04790 + 2.94098i −0.256012 + 0.186004i
\(251\) 3.01355 + 4.14780i 0.190214 + 0.261807i 0.893463 0.449137i \(-0.148268\pi\)
−0.703250 + 0.710943i \(0.748268\pi\)
\(252\) 0 0
\(253\) 1.25908 + 2.47108i 0.0791576 + 0.155355i
\(254\) −1.87216 + 2.57681i −0.117470 + 0.161684i
\(255\) 0 0
\(256\) 9.55736 + 6.94383i 0.597335 + 0.433989i
\(257\) 1.08576 0.171967i 0.0677277 0.0107270i −0.122479 0.992471i \(-0.539084\pi\)
0.190206 + 0.981744i \(0.439084\pi\)
\(258\) 0 0
\(259\) 12.0520 + 6.14078i 0.748872 + 0.381569i
\(260\) 1.49119 + 1.49119i 0.0924799 + 0.0924799i
\(261\) 0 0
\(262\) −3.76242 + 11.5796i −0.232443 + 0.715387i
\(263\) 1.99659 + 12.6060i 0.123115 + 0.777317i 0.969562 + 0.244845i \(0.0787369\pi\)
−0.846447 + 0.532472i \(0.821263\pi\)
\(264\) 0 0
\(265\) −1.90502 + 0.970654i −0.117024 + 0.0596268i
\(266\) 9.60980 + 3.12241i 0.589215 + 0.191448i
\(267\) 0 0
\(268\) −10.5404 + 5.37059i −0.643856 + 0.328061i
\(269\) −0.170602 0.525059i −0.0104018 0.0320134i 0.945721 0.324980i \(-0.105358\pi\)
−0.956123 + 0.292967i \(0.905358\pi\)
\(270\) 0 0
\(271\) −0.852971 + 2.62518i −0.0518143 + 0.159468i −0.973615 0.228195i \(-0.926718\pi\)
0.921801 + 0.387663i \(0.126718\pi\)
\(272\) −2.02481 0.320698i −0.122772 0.0194452i
\(273\) 0 0
\(274\) −0.154450 0.0786962i −0.00933067 0.00475421i
\(275\) −2.18021 + 13.7653i −0.131472 + 0.830079i
\(276\) 0 0
\(277\) 17.2011 + 12.4974i 1.03352 + 0.750894i 0.969010 0.247023i \(-0.0794525\pi\)
0.0645072 + 0.997917i \(0.479452\pi\)
\(278\) 1.73026i 0.103774i
\(279\) 0 0
\(280\) −2.59643 5.09578i −0.155166 0.304531i
\(281\) 0.813754 1.59708i 0.0485445 0.0952739i −0.865460 0.500978i \(-0.832974\pi\)
0.914004 + 0.405704i \(0.132974\pi\)
\(282\) 0 0
\(283\) −3.00831 + 2.18566i −0.178825 + 0.129924i −0.673597 0.739099i \(-0.735252\pi\)
0.494772 + 0.869023i \(0.335252\pi\)
\(284\) −1.03307 + 1.03307i −0.0613014 + 0.0613014i
\(285\) 0 0
\(286\) −4.59081 −0.271460
\(287\) −20.0177 + 1.30037i −1.18161 + 0.0767585i
\(288\) 0 0
\(289\) 12.5661 4.08296i 0.739180 0.240174i
\(290\) −3.41364 + 3.41364i −0.200456 + 0.200456i
\(291\) 0 0
\(292\) 5.57736 + 7.67658i 0.326390 + 0.449238i
\(293\) 6.31176 12.3875i 0.368737 0.723687i −0.629856 0.776712i \(-0.716886\pi\)
0.998593 + 0.0530245i \(0.0168861\pi\)
\(294\) 0 0
\(295\) 1.87844 2.58545i 0.109367 0.150531i
\(296\) 10.9751i 0.637917i
\(297\) 0 0
\(298\) −6.08835 + 0.964300i −0.352689 + 0.0558604i
\(299\) −0.280690 + 1.77220i −0.0162327 + 0.102489i
\(300\) 0 0
\(301\) 24.0479 + 24.0479i 1.38610 + 1.38610i
\(302\) −2.62817 0.416261i −0.151234 0.0239532i
\(303\) 0 0
\(304\) −0.723529 4.56818i −0.0414973 0.262003i
\(305\) 2.65025 + 8.15664i 0.151753 + 0.467048i
\(306\) 0 0
\(307\) −20.7993 6.75809i −1.18708 0.385705i −0.352086 0.935968i \(-0.614527\pi\)
−0.834991 + 0.550263i \(0.814527\pi\)
\(308\) −13.5233 4.39399i −0.770562 0.250371i
\(309\) 0 0
\(310\) 1.13798 + 3.50235i 0.0646331 + 0.198920i
\(311\) 2.49509 + 15.7534i 0.141483 + 0.893291i 0.951671 + 0.307120i \(0.0993653\pi\)
−0.810188 + 0.586171i \(0.800635\pi\)
\(312\) 0 0
\(313\) −0.811177 0.128478i −0.0458504 0.00726199i 0.133467 0.991053i \(-0.457389\pi\)
−0.179318 + 0.983791i \(0.557389\pi\)
\(314\) −7.15796 7.15796i −0.403947 0.403947i
\(315\) 0 0
\(316\) 1.43233 9.04340i 0.0805751 0.508731i
\(317\) −27.9438 + 4.42587i −1.56948 + 0.248582i −0.879734 0.475467i \(-0.842279\pi\)
−0.689749 + 0.724048i \(0.742279\pi\)
\(318\) 0 0
\(319\) 28.4407i 1.59237i
\(320\) 0.927096 1.27604i 0.0518262 0.0713327i
\(321\) 0 0
\(322\) 0.932312 1.82977i 0.0519557 0.101969i
\(323\) −5.02232 6.91263i −0.279449 0.384629i
\(324\) 0 0
\(325\) −6.37586 + 6.37586i −0.353669 + 0.353669i
\(326\) 0.645108 0.209608i 0.0357292 0.0116091i
\(327\) 0 0
\(328\) −8.31398 13.9930i −0.459063 0.772634i
\(329\) 36.1819 1.99477
\(330\) 0 0
\(331\) 21.7469 21.7469i 1.19532 1.19532i 0.219762 0.975554i \(-0.429472\pi\)
0.975554 0.219762i \(-0.0705281\pi\)
\(332\) 9.25966 6.72753i 0.508190 0.369221i
\(333\) 0 0
\(334\) −5.67020 + 11.1284i −0.310260 + 0.608919i
\(335\) 2.64108 + 5.18341i 0.144297 + 0.283200i
\(336\) 0 0
\(337\) 26.0552i 1.41932i 0.704546 + 0.709658i \(0.251151\pi\)
−0.704546 + 0.709658i \(0.748849\pi\)
\(338\) 5.32301 + 3.86739i 0.289533 + 0.210358i
\(339\) 0 0
\(340\) −0.319286 + 2.01589i −0.0173157 + 0.109327i
\(341\) 19.3304 + 9.84934i 1.04680 + 0.533372i
\(342\) 0 0
\(343\) −12.9506 2.05118i −0.699268 0.110753i
\(344\) −8.52723 + 26.2441i −0.459758 + 1.41499i
\(345\) 0 0
\(346\) −2.75644 8.48345i −0.148187 0.456073i
\(347\) 5.78097 2.94555i 0.310339 0.158126i −0.291884 0.956454i \(-0.594282\pi\)
0.602223 + 0.798328i \(0.294282\pi\)
\(348\) 0 0
\(349\) 7.18918 + 2.33591i 0.384828 + 0.125038i 0.495041 0.868870i \(-0.335153\pi\)
−0.110213 + 0.993908i \(0.535153\pi\)
\(350\) 9.19508 4.68513i 0.491498 0.250431i
\(351\) 0 0
\(352\) −2.84801 17.9817i −0.151800 0.958425i
\(353\) 11.4959 35.3808i 0.611866 1.88313i 0.171899 0.985115i \(-0.445010\pi\)
0.439967 0.898014i \(-0.354990\pi\)
\(354\) 0 0
\(355\) 0.508029 + 0.508029i 0.0269634 + 0.0269634i
\(356\) −18.3709 9.36044i −0.973655 0.496102i
\(357\) 0 0
\(358\) −1.55169 + 0.245764i −0.0820095 + 0.0129890i
\(359\) −17.5992 12.7866i −0.928849 0.674848i 0.0168617 0.999858i \(-0.494633\pi\)
−0.945711 + 0.325009i \(0.894633\pi\)
\(360\) 0 0
\(361\) 0.162984 0.224329i 0.00857813 0.0118068i
\(362\) 1.87354 + 3.67703i 0.0984711 + 0.193260i
\(363\) 0 0
\(364\) −5.40733 7.44255i −0.283421 0.390096i
\(365\) 3.77508 2.74276i 0.197597 0.143563i
\(366\) 0 0
\(367\) −16.6389 + 5.40631i −0.868544 + 0.282207i −0.709193 0.705015i \(-0.750940\pi\)
−0.159352 + 0.987222i \(0.550940\pi\)
\(368\) −0.940005 −0.0490011
\(369\) 0 0
\(370\) 2.27777 0.118416
\(371\) 8.87032 2.88214i 0.460524 0.149633i
\(372\) 0 0
\(373\) 5.79680 4.21162i 0.300147 0.218070i −0.427510 0.904011i \(-0.640609\pi\)
0.727657 + 0.685941i \(0.240609\pi\)
\(374\) −2.61160 3.59456i −0.135043 0.185870i
\(375\) 0 0
\(376\) 13.3282 + 26.1581i 0.687349 + 1.34900i
\(377\) −10.8155 + 14.8862i −0.557026 + 0.766681i
\(378\) 0 0
\(379\) 6.38423 + 4.63842i 0.327936 + 0.238260i 0.739554 0.673097i \(-0.235036\pi\)
−0.411618 + 0.911356i \(0.635036\pi\)
\(380\) −4.54807 + 0.720344i −0.233311 + 0.0369529i
\(381\) 0 0
\(382\) 8.58807 + 4.37584i 0.439404 + 0.223887i
\(383\) 4.35320 + 4.35320i 0.222438 + 0.222438i 0.809524 0.587086i \(-0.199725\pi\)
−0.587086 + 0.809524i \(0.699725\pi\)
\(384\) 0 0
\(385\) −2.16082 + 6.65031i −0.110125 + 0.338931i
\(386\) 1.90495 + 12.0274i 0.0969592 + 0.612177i
\(387\) 0 0
\(388\) −8.35313 + 4.25613i −0.424066 + 0.216072i
\(389\) 21.1299 + 6.86553i 1.07133 + 0.348096i 0.791005 0.611809i \(-0.209558\pi\)
0.280324 + 0.959905i \(0.409558\pi\)
\(390\) 0 0
\(391\) −1.54729 + 0.788386i −0.0782501 + 0.0398704i
\(392\) 2.21093 + 6.80454i 0.111669 + 0.343681i
\(393\) 0 0
\(394\) −3.28722 + 10.1170i −0.165608 + 0.509688i
\(395\) −4.44724 0.704374i −0.223765 0.0354409i
\(396\) 0 0
\(397\) 5.81775 + 2.96429i 0.291984 + 0.148773i 0.593847 0.804578i \(-0.297608\pi\)
−0.301863 + 0.953351i \(0.597608\pi\)
\(398\) −2.07297 + 13.0882i −0.103909 + 0.656053i
\(399\) 0 0
\(400\) −3.82162 2.77657i −0.191081 0.138829i
\(401\) 21.3099i 1.06416i −0.846693 0.532082i \(-0.821410\pi\)
0.846693 0.532082i \(-0.178590\pi\)
\(402\) 0 0
\(403\) 6.37228 + 12.5063i 0.317426 + 0.622984i
\(404\) 7.97745 15.6566i 0.396893 0.778946i
\(405\) 0 0
\(406\) 17.0375 12.3785i 0.845557 0.614333i
\(407\) 9.48858 9.48858i 0.470331 0.470331i
\(408\) 0 0
\(409\) 3.89625 0.192657 0.0963287 0.995350i \(-0.469290\pi\)
0.0963287 + 0.995350i \(0.469290\pi\)
\(410\) −2.90409 + 1.72547i −0.143423 + 0.0852150i
\(411\) 0 0
\(412\) 21.3552 6.93871i 1.05209 0.341846i
\(413\) −9.85779 + 9.85779i −0.485070 + 0.485070i
\(414\) 0 0
\(415\) −3.30838 4.55359i −0.162402 0.223527i
\(416\) 5.34742 10.4949i 0.262179 0.514555i
\(417\) 0 0
\(418\) 5.89205 8.10971i 0.288190 0.396659i
\(419\) 14.8236i 0.724179i 0.932143 + 0.362089i \(0.117937\pi\)
−0.932143 + 0.362089i \(0.882063\pi\)
\(420\) 0 0
\(421\) −10.9908 + 1.74076i −0.535657 + 0.0848397i −0.418402 0.908262i \(-0.637410\pi\)
−0.117255 + 0.993102i \(0.537410\pi\)
\(422\) −1.55156 + 9.79614i −0.0755286 + 0.476869i
\(423\) 0 0
\(424\) 5.35121 + 5.35121i 0.259878 + 0.259878i
\(425\) −8.61930 1.36516i −0.418098 0.0662202i
\(426\) 0 0
\(427\) −5.85265 36.9522i −0.283230 1.78824i
\(428\) 0.503433 + 1.54941i 0.0243343 + 0.0748934i
\(429\) 0 0
\(430\) 5.44667 + 1.76973i 0.262662 + 0.0853440i
\(431\) −25.1750 8.17986i −1.21264 0.394010i −0.368242 0.929730i \(-0.620040\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(432\) 0 0
\(433\) 0.144494 + 0.444707i 0.00694395 + 0.0213713i 0.954468 0.298312i \(-0.0964235\pi\)
−0.947525 + 0.319683i \(0.896424\pi\)
\(434\) −2.51305 15.8668i −0.120630 0.761630i
\(435\) 0 0
\(436\) −8.53990 1.35259i −0.408987 0.0647772i
\(437\) −2.77037 2.77037i −0.132525 0.132525i
\(438\) 0 0
\(439\) −3.05677 + 19.2997i −0.145892 + 0.921123i 0.800788 + 0.598947i \(0.204414\pi\)
−0.946680 + 0.322176i \(0.895586\pi\)
\(440\) −5.60388 + 0.887568i −0.267155 + 0.0423131i
\(441\) 0 0
\(442\) 2.87459i 0.136730i
\(443\) −4.37823 + 6.02611i −0.208016 + 0.286309i −0.900259 0.435355i \(-0.856623\pi\)
0.692243 + 0.721665i \(0.256623\pi\)
\(444\) 0 0
\(445\) −4.60315 + 9.03419i −0.218210 + 0.428262i
\(446\) 3.27717 + 4.51063i 0.155178 + 0.213585i
\(447\) 0 0
\(448\) −4.86526 + 4.86526i −0.229862 + 0.229862i
\(449\) −24.2920 + 7.89296i −1.14641 + 0.372492i −0.819790 0.572664i \(-0.805910\pi\)
−0.326621 + 0.945155i \(0.605910\pi\)
\(450\) 0 0
\(451\) −4.90981 + 19.2855i −0.231194 + 0.908121i
\(452\) 22.5594 1.06110
\(453\) 0 0
\(454\) −11.2791 + 11.2791i −0.529354 + 0.529354i
\(455\) −3.66000 + 2.65914i −0.171583 + 0.124663i
\(456\) 0 0
\(457\) 16.0293 31.4593i 0.749820 1.47161i −0.127571 0.991829i \(-0.540718\pi\)
0.877391 0.479776i \(-0.159282\pi\)
\(458\) 0.987815 + 1.93870i 0.0461576 + 0.0905893i
\(459\) 0 0
\(460\) 0.935866i 0.0436350i
\(461\) −23.0488 16.7459i −1.07349 0.779936i −0.0969530 0.995289i \(-0.530910\pi\)
−0.976536 + 0.215353i \(0.930910\pi\)
\(462\) 0 0
\(463\) −2.00832 + 12.6801i −0.0933348 + 0.589293i 0.896048 + 0.443958i \(0.146426\pi\)
−0.989383 + 0.145335i \(0.953574\pi\)
\(464\) −8.58904 4.37633i −0.398736 0.203166i
\(465\) 0 0
\(466\) −12.6253 1.99965i −0.584856 0.0926321i
\(467\) −9.10432 + 28.0202i −0.421297 + 1.29662i 0.485198 + 0.874404i \(0.338748\pi\)
−0.906495 + 0.422216i \(0.861252\pi\)
\(468\) 0 0
\(469\) −7.84210 24.1355i −0.362114 1.11447i
\(470\) 5.42881 2.76612i 0.250412 0.127591i
\(471\) 0 0
\(472\) −10.7581 3.49551i −0.495180 0.160894i
\(473\) 30.0616 15.3172i 1.38224 0.704284i
\(474\) 0 0
\(475\) −3.07996 19.4461i −0.141318 0.892248i
\(476\) 2.75134 8.46777i 0.126108 0.388120i
\(477\) 0 0
\(478\) −3.08562 3.08562i −0.141133 0.141133i
\(479\) 23.8053 + 12.1294i 1.08769 + 0.554207i 0.903459 0.428675i \(-0.141020\pi\)
0.184234 + 0.982882i \(0.441020\pi\)
\(480\) 0 0
\(481\) 8.57480 1.35812i 0.390977 0.0619247i
\(482\) −5.21943 3.79214i −0.237739 0.172727i
\(483\) 0 0
\(484\) 1.15069 1.58379i 0.0523041 0.0719904i
\(485\) 2.09302 + 4.10779i 0.0950393 + 0.186525i
\(486\) 0 0
\(487\) 6.82210 + 9.38981i 0.309139 + 0.425493i 0.935112 0.354351i \(-0.115298\pi\)
−0.625974 + 0.779844i \(0.715298\pi\)
\(488\) 24.5591 17.8432i 1.11174 0.807724i
\(489\) 0 0
\(490\) 1.41221 0.458853i 0.0637969 0.0207289i
\(491\) 26.8852 1.21331 0.606656 0.794964i \(-0.292511\pi\)
0.606656 + 0.794964i \(0.292511\pi\)
\(492\) 0 0
\(493\) −17.8084 −0.802052
\(494\) 6.16797 2.00409i 0.277510 0.0901685i
\(495\) 0 0
\(496\) −5.94898 + 4.32218i −0.267117 + 0.194072i
\(497\) −1.84220 2.53557i −0.0826341 0.113736i
\(498\) 0 0
\(499\) 5.83710 + 11.4559i 0.261304 + 0.512839i 0.983964 0.178365i \(-0.0570808\pi\)
−0.722660 + 0.691204i \(0.757081\pi\)
\(500\) −5.84663 + 8.04720i −0.261469 + 0.359882i
\(501\) 0 0
\(502\) −3.04695 2.21374i −0.135992 0.0988041i
\(503\) −11.9300 + 1.88953i −0.531934 + 0.0842501i −0.416623 0.909079i \(-0.636786\pi\)
−0.115311 + 0.993329i \(0.536786\pi\)
\(504\) 0 0
\(505\) −7.69940 3.92304i −0.342619 0.174573i
\(506\) −1.44059 1.44059i −0.0640419 0.0640419i
\(507\) 0 0
\(508\) −1.95669 + 6.02208i −0.0868141 + 0.267186i
\(509\) −4.55017 28.7287i −0.201683 1.27338i −0.855929 0.517094i \(-0.827014\pi\)
0.654246 0.756282i \(-0.272986\pi\)
\(510\) 0 0
\(511\) −18.1370 + 9.24126i −0.802333 + 0.408809i
\(512\) 10.9621 + 3.56179i 0.484460 + 0.157411i
\(513\) 0 0
\(514\) −0.719519 + 0.366613i −0.0317366 + 0.0161706i
\(515\) −3.41223 10.5017i −0.150361 0.462762i
\(516\) 0 0
\(517\) 11.0921 34.1379i 0.487829 1.50138i
\(518\) −9.81397 1.55438i −0.431201 0.0682956i
\(519\) 0 0
\(520\) −3.27068 1.66649i −0.143429 0.0730806i
\(521\) −3.39562 + 21.4391i −0.148765 + 0.939264i 0.794510 + 0.607251i \(0.207728\pi\)
−0.943275 + 0.332013i \(0.892272\pi\)
\(522\) 0 0
\(523\) −12.7639 9.27355i −0.558128 0.405504i 0.272645 0.962115i \(-0.412102\pi\)
−0.830773 + 0.556611i \(0.812102\pi\)
\(524\) 24.2047i 1.05739i
\(525\) 0 0
\(526\) −4.25648 8.35382i −0.185592 0.364244i
\(527\) −6.16728 + 12.1040i −0.268651 + 0.527257i
\(528\) 0 0
\(529\) 17.9632 13.0510i 0.781009 0.567436i
\(530\) 1.11058 1.11058i 0.0482406 0.0482406i
\(531\) 0 0
\(532\) 20.0874 0.870897
\(533\) −9.90382 + 8.22721i −0.428982 + 0.356360i
\(534\) 0 0
\(535\) 0.761946 0.247571i 0.0329418 0.0107034i
\(536\) 14.5602 14.5602i 0.628907 0.628907i
\(537\) 0 0
\(538\) 0.238379 + 0.328101i 0.0102773 + 0.0141454i
\(539\) 3.97141 7.79434i 0.171061 0.335726i
\(540\) 0 0
\(541\) 2.48515 3.42051i 0.106845 0.147059i −0.752246 0.658882i \(-0.771030\pi\)
0.859091 + 0.511823i \(0.171030\pi\)
\(542\) 2.02768i 0.0870965i
\(543\) 0 0
\(544\) 11.2594 1.78332i 0.482743 0.0764590i
\(545\) −0.665157 + 4.19964i −0.0284922 + 0.179893i
\(546\) 0 0
\(547\) −1.68661 1.68661i −0.0721143 0.0721143i 0.670130 0.742244i \(-0.266238\pi\)
−0.742244 + 0.670130i \(0.766238\pi\)
\(548\) −0.340362 0.0539081i −0.0145396 0.00230284i
\(549\) 0 0
\(550\) −1.60157 10.1119i −0.0682913 0.431174i
\(551\) −12.4156 38.2113i −0.528923 1.62786i
\(552\) 0 0
\(553\) 18.6807 + 6.06972i 0.794383 + 0.258111i
\(554\) −14.8544 4.82648i −0.631102 0.205057i
\(555\) 0 0
\(556\) −1.06294 3.27139i −0.0450787 0.138738i
\(557\) −1.20951 7.63657i −0.0512487 0.323572i −0.999972 0.00746438i \(-0.997624\pi\)
0.948723 0.316107i \(-0.102376\pi\)
\(558\) 0 0
\(559\) 21.5595 + 3.41470i 0.911871 + 0.144426i
\(560\) −1.67589 1.67589i −0.0708191 0.0708191i
\(561\) 0 0
\(562\) −0.205981 + 1.30051i −0.00868878 + 0.0548588i
\(563\) −29.4356 + 4.66214i −1.24056 + 0.196486i −0.742019 0.670379i \(-0.766131\pi\)
−0.498543 + 0.866865i \(0.666131\pi\)
\(564\) 0 0
\(565\) 11.0940i 0.466726i
\(566\) 1.60558 2.20989i 0.0674875 0.0928885i
\(567\) 0 0
\(568\) 1.15451 2.26586i 0.0484423 0.0950734i
\(569\) 5.19710 + 7.15320i 0.217874 + 0.299878i 0.903938 0.427663i \(-0.140663\pi\)
−0.686064 + 0.727541i \(0.740663\pi\)
\(570\) 0 0
\(571\) 15.7965 15.7965i 0.661063 0.661063i −0.294567 0.955631i \(-0.595176\pi\)
0.955631 + 0.294567i \(0.0951756\pi\)
\(572\) −8.67981 + 2.82024i −0.362921 + 0.117920i
\(573\) 0 0
\(574\) 13.6900 5.45256i 0.571411 0.227586i
\(575\) −4.00146 −0.166872
\(576\) 0 0
\(577\) 8.51989 8.51989i 0.354688 0.354688i −0.507163 0.861850i \(-0.669306\pi\)
0.861850 + 0.507163i \(0.169306\pi\)
\(578\) −7.85233 + 5.70505i −0.326614 + 0.237299i
\(579\) 0 0
\(580\) −4.35707 + 8.55122i −0.180917 + 0.355070i
\(581\) 11.1470 + 21.8772i 0.462456 + 0.907621i
\(582\) 0 0
\(583\) 9.25279i 0.383211i
\(584\) −13.3621 9.70816i −0.552929 0.401726i
\(585\) 0 0
\(586\) −1.59766 + 10.0872i −0.0659988 + 0.416700i
\(587\) 22.9909 + 11.7145i 0.948936 + 0.483507i 0.858737 0.512417i \(-0.171250\pi\)
0.0901991 + 0.995924i \(0.471250\pi\)
\(588\) 0 0
\(589\) −30.2710 4.79445i −1.24729 0.197552i
\(590\) −0.725454 + 2.23272i −0.0298664 + 0.0919195i
\(591\) 0 0
\(592\) 1.40547 + 4.32560i 0.0577646 + 0.177781i
\(593\) −18.5585 + 9.45605i −0.762108 + 0.388313i −0.791432 0.611257i \(-0.790664\pi\)
0.0293248 + 0.999570i \(0.490664\pi\)
\(594\) 0 0
\(595\) −4.16416 1.35302i −0.170714 0.0554684i
\(596\) −10.9188 + 5.56341i −0.447252 + 0.227886i
\(597\) 0 0
\(598\) −0.206193 1.30185i −0.00843187 0.0532367i
\(599\) 5.67622 17.4696i 0.231924 0.713789i −0.765591 0.643328i \(-0.777553\pi\)
0.997515 0.0704605i \(-0.0224469\pi\)
\(600\) 0 0
\(601\) −7.61945 7.61945i −0.310804 0.310804i 0.534417 0.845221i \(-0.320531\pi\)
−0.845221 + 0.534417i \(0.820531\pi\)
\(602\) −22.2598 11.3419i −0.907241 0.462263i
\(603\) 0 0
\(604\) −5.22478 + 0.827524i −0.212593 + 0.0336715i
\(605\) −0.778854 0.565870i −0.0316649 0.0230059i
\(606\) 0 0
\(607\) −8.17357 + 11.2500i −0.331755 + 0.456622i −0.942011 0.335583i \(-0.891067\pi\)
0.610256 + 0.792205i \(0.291067\pi\)
\(608\) 11.6762 + 22.9159i 0.473534 + 0.929362i
\(609\) 0 0
\(610\) −3.70315 5.09695i −0.149936 0.206370i
\(611\) 18.7878 13.6501i 0.760073 0.552226i
\(612\) 0 0
\(613\) −14.1988 + 4.61346i −0.573482 + 0.186336i −0.581379 0.813633i \(-0.697487\pi\)
0.00789628 + 0.999969i \(0.497487\pi\)
\(614\) 16.0653 0.648344
\(615\) 0 0
\(616\) 24.7505 0.997227
\(617\) −7.99439 + 2.59753i −0.321842 + 0.104573i −0.465482 0.885057i \(-0.654119\pi\)
0.143640 + 0.989630i \(0.454119\pi\)
\(618\) 0 0
\(619\) −22.0401 + 16.0131i −0.885866 + 0.643619i −0.934797 0.355183i \(-0.884418\pi\)
0.0489312 + 0.998802i \(0.484418\pi\)
\(620\) 4.30315 + 5.92278i 0.172819 + 0.237865i
\(621\) 0 0
\(622\) −5.31922 10.4396i −0.213281 0.418588i
\(623\) 25.9981 35.7834i 1.04159 1.43363i
\(624\) 0 0
\(625\) −14.1818 10.3037i −0.567272 0.412148i
\(626\) 0.595887 0.0943792i 0.0238164 0.00377215i
\(627\) 0 0
\(628\) −17.9308 9.13619i −0.715516 0.364574i
\(629\) 5.94138 + 5.94138i 0.236898 + 0.236898i
\(630\) 0 0
\(631\) 0.989181 3.04439i 0.0393787 0.121195i −0.929435 0.368987i \(-0.879705\pi\)
0.968813 + 0.247792i \(0.0797048\pi\)
\(632\) 2.49317 + 15.7413i 0.0991731 + 0.626154i
\(633\) 0 0
\(634\) 18.5181 9.43542i 0.735446 0.374728i
\(635\) 2.96145 + 0.962235i 0.117522 + 0.0381851i
\(636\) 0 0
\(637\) 5.04275 2.56941i 0.199801 0.101804i
\(638\) −6.45610 19.8698i −0.255599 0.786654i
\(639\) 0 0
\(640\) 2.24192 6.89991i 0.0886196 0.272743i
\(641\) 42.6511 + 6.75528i 1.68462 + 0.266817i 0.924003 0.382385i \(-0.124897\pi\)
0.760615 + 0.649203i \(0.224897\pi\)
\(642\) 0 0
\(643\) −3.56855 1.81827i −0.140730 0.0717054i 0.382208 0.924076i \(-0.375164\pi\)
−0.522937 + 0.852371i \(0.675164\pi\)
\(644\) 0.638648 4.03226i 0.0251663 0.158893i
\(645\) 0 0
\(646\) 5.07799 + 3.68937i 0.199791 + 0.145156i
\(647\) 16.9523i 0.666465i −0.942845 0.333232i \(-0.891861\pi\)
0.942845 0.333232i \(-0.108139\pi\)
\(648\) 0 0
\(649\) 6.27886 + 12.3230i 0.246467 + 0.483718i
\(650\) 3.00711 5.90178i 0.117948 0.231487i
\(651\) 0 0
\(652\) 1.09093 0.792609i 0.0427242 0.0310410i
\(653\) −12.3449 + 12.3449i −0.483092 + 0.483092i −0.906118 0.423026i \(-0.860968\pi\)
0.423026 + 0.906118i \(0.360968\pi\)
\(654\) 0 0
\(655\) 11.9031 0.465091
\(656\) −5.06870 4.45034i −0.197900 0.173757i
\(657\) 0 0
\(658\) −25.2782 + 8.21337i −0.985445 + 0.320191i
\(659\) 19.4232 19.4232i 0.756620 0.756620i −0.219086 0.975706i \(-0.570308\pi\)
0.975706 + 0.219086i \(0.0703075\pi\)
\(660\) 0 0
\(661\) −4.42412 6.08928i −0.172078 0.236846i 0.714264 0.699877i \(-0.246762\pi\)
−0.886342 + 0.463031i \(0.846762\pi\)
\(662\) −10.2567 + 20.1299i −0.398637 + 0.782369i
\(663\) 0 0
\(664\) −11.7102 + 16.1177i −0.454443 + 0.625488i
\(665\) 9.87829i 0.383063i
\(666\) 0 0
\(667\) −8.06515 + 1.27739i −0.312284 + 0.0494609i
\(668\) −3.88417 + 24.5237i −0.150283 + 0.948851i
\(669\) 0 0
\(670\) −3.02181 3.02181i −0.116743 0.116743i
\(671\) −36.6589 5.80620i −1.41520 0.224146i
\(672\) 0 0
\(673\) 6.65260 + 42.0029i 0.256439 + 1.61909i 0.694049 + 0.719927i \(0.255825\pi\)
−0.437610 + 0.899165i \(0.644175\pi\)
\(674\) −5.91459 18.2032i −0.227822 0.701163i
\(675\) 0 0
\(676\) 12.4400 + 4.04200i 0.478461 + 0.155462i
\(677\) 44.0320 + 14.3069i 1.69229 + 0.549857i 0.987231 0.159294i \(-0.0509219\pi\)
0.705056 + 0.709152i \(0.250922\pi\)
\(678\) 0 0
\(679\) −6.21477 19.1271i −0.238501 0.734030i
\(680\) −0.555760 3.50893i −0.0213124 0.134561i
\(681\) 0 0
\(682\) −15.7409 2.49311i −0.602749 0.0954661i
\(683\) −10.8884 10.8884i −0.416633 0.416633i 0.467409 0.884041i \(-0.345188\pi\)
−0.884041 + 0.467409i \(0.845188\pi\)
\(684\) 0 0
\(685\) −0.0265102 + 0.167379i −0.00101290 + 0.00639522i
\(686\) 9.51347 1.50679i 0.363226 0.0575293i
\(687\) 0 0
\(688\) 11.4355i 0.435975i
\(689\) 3.51868 4.84304i 0.134051 0.184505i
\(690\) 0 0
\(691\) 19.4697 38.2115i 0.740664 1.45363i −0.145060 0.989423i \(-0.546338\pi\)
0.885724 0.464212i \(-0.153662\pi\)
\(692\) −10.4232 14.3462i −0.396229 0.545363i
\(693\) 0 0
\(694\) −3.37018 + 3.37018i −0.127930 + 0.127930i
\(695\) −1.60876 + 0.522718i −0.0610237 + 0.0198278i
\(696\) 0 0
\(697\) −12.0759 3.07433i −0.457406 0.116449i
\(698\) −5.55292 −0.210181
\(699\) 0 0
\(700\) 14.5069 14.5069i 0.548309 0.548309i
\(701\) −23.6599 + 17.1899i −0.893623 + 0.649255i −0.936820 0.349812i \(-0.886246\pi\)
0.0431974 + 0.999067i \(0.486246\pi\)
\(702\) 0 0
\(703\) −8.60616 + 16.8905i −0.324587 + 0.637039i
\(704\) 3.09890 + 6.08193i 0.116794 + 0.229222i
\(705\) 0 0
\(706\) 27.3281i 1.02851i
\(707\) 30.4964 + 22.1570i 1.14694 + 0.833298i
\(708\) 0 0
\(709\) 1.32698 8.37821i 0.0498357 0.314650i −0.950160 0.311762i \(-0.899081\pi\)
0.999996 0.00288796i \(-0.000919268\pi\)
\(710\) −0.470254 0.239606i −0.0176483 0.00899227i
\(711\) 0 0
\(712\) 35.4468 + 5.61423i 1.32843 + 0.210402i
\(713\) −1.92484 + 5.92406i −0.0720860 + 0.221858i
\(714\) 0 0
\(715\) 1.38690 + 4.26844i 0.0518671 + 0.159631i
\(716\) −2.78279 + 1.41790i −0.103998 + 0.0529896i
\(717\) 0 0
\(718\) 15.1981 + 4.93816i 0.567188 + 0.184291i
\(719\) −34.3184 + 17.4861i −1.27986 + 0.652121i −0.955828 0.293926i \(-0.905038\pi\)
−0.324031 + 0.946046i \(0.605038\pi\)
\(720\) 0 0
\(721\) 7.53535 + 47.5763i 0.280631 + 1.77183i
\(722\) −0.0629445 + 0.193723i −0.00234255 + 0.00720964i
\(723\) 0 0
\(724\) 5.80117 + 5.80117i 0.215599 + 0.215599i
\(725\) −36.5623 18.6294i −1.35789 0.691879i
\(726\) 0 0
\(727\) −51.1019 + 8.09374i −1.89526 + 0.300180i −0.991730 0.128338i \(-0.959036\pi\)
−0.903533 + 0.428518i \(0.859036\pi\)
\(728\) 12.9548 + 9.41220i 0.480136 + 0.348839i
\(729\) 0 0
\(730\) −2.01482 + 2.77316i −0.0745718 + 0.102639i
\(731\) 9.59102 + 18.8234i 0.354737 + 0.696210i
\(732\) 0 0
\(733\) 0.369332 + 0.508342i 0.0136416 + 0.0187760i 0.815783 0.578358i \(-0.196306\pi\)
−0.802142 + 0.597134i \(0.796306\pi\)
\(734\) 10.3974 7.55415i 0.383775 0.278829i
\(735\) 0 0
\(736\) 4.97128 1.61527i 0.183244 0.0595396i
\(737\) −25.1762 −0.927376
\(738\) 0 0
\(739\) 40.6971 1.49707 0.748533 0.663097i \(-0.230758\pi\)
0.748533 + 0.663097i \(0.230758\pi\)
\(740\) 4.30656 1.39929i 0.158312 0.0514388i
\(741\) 0 0
\(742\) −5.54292 + 4.02717i −0.203487 + 0.147842i
\(743\) −9.43650 12.9882i −0.346192 0.476492i 0.600045 0.799966i \(-0.295149\pi\)
−0.946237 + 0.323474i \(0.895149\pi\)
\(744\) 0 0
\(745\) 2.73590 + 5.36950i 0.100236 + 0.196723i
\(746\) −3.09384 + 4.25830i −0.113273 + 0.155908i
\(747\) 0 0
\(748\) −7.14595 5.19184i −0.261282 0.189832i
\(749\) −3.45186 + 0.546721i −0.126128 + 0.0199768i
\(750\) 0 0
\(751\) 26.2079 + 13.3536i 0.956339 + 0.487279i 0.861245 0.508189i \(-0.169685\pi\)
0.0950935 + 0.995468i \(0.469685\pi\)
\(752\) 8.60280 + 8.60280i 0.313712 + 0.313712i
\(753\) 0 0
\(754\) 4.17694 12.8553i 0.152115 0.468162i
\(755\) 0.406949 + 2.56937i 0.0148104 + 0.0935090i
\(756\) 0 0
\(757\) 32.6350 16.6284i 1.18614 0.604369i 0.254260 0.967136i \(-0.418168\pi\)
0.931880 + 0.362767i \(0.118168\pi\)
\(758\) −5.51323 1.79136i −0.200249 0.0650650i
\(759\) 0 0
\(760\) 7.14161 3.63883i 0.259053 0.131994i
\(761\) 8.21482 + 25.2826i 0.297787 + 0.916494i 0.982271 + 0.187466i \(0.0600276\pi\)
−0.684484 + 0.729028i \(0.739972\pi\)
\(762\) 0 0
\(763\) 5.73178 17.6406i 0.207504 0.638633i
\(764\) 18.9256 + 2.99752i 0.684703 + 0.108446i
\(765\) 0 0
\(766\) −4.02951 2.05314i −0.145592 0.0741830i
\(767\) −1.39976 + 8.83775i −0.0505425 + 0.319113i
\(768\) 0 0
\(769\) −17.8728 12.9853i −0.644509 0.468263i 0.216887 0.976197i \(-0.430410\pi\)
−0.861396 + 0.507933i \(0.830410\pi\)
\(770\) 5.13669i 0.185114i
\(771\) 0 0
\(772\) 10.9904 + 21.5698i 0.395552 + 0.776314i
\(773\) 15.6700 30.7541i 0.563610 1.10615i −0.416767 0.909014i \(-0.636837\pi\)
0.980377 0.197133i \(-0.0631632\pi\)
\(774\) 0 0
\(775\) −25.3239 + 18.3989i −0.909662 + 0.660908i
\(776\) 11.5388 11.5388i 0.414219 0.414219i
\(777\) 0 0
\(778\) −16.3207 −0.585127
\(779\) −1.82244 28.0544i −0.0652957 1.00515i
\(780\) 0 0
\(781\) −2.95709 + 0.960817i −0.105813 + 0.0343807i
\(782\) 0.902039 0.902039i 0.0322569 0.0322569i
\(783\) 0 0
\(784\) 1.74277 + 2.39872i 0.0622419 + 0.0856687i
\(785\) −4.49287 + 8.81776i −0.160358 + 0.314719i
\(786\) 0 0
\(787\) 4.79695 6.60244i 0.170993 0.235351i −0.714917 0.699210i \(-0.753535\pi\)
0.885909 + 0.463858i \(0.153535\pi\)
\(788\) 21.1476i 0.753351i
\(789\) 0 0
\(790\) 3.26692 0.517430i 0.116232 0.0184093i
\(791\) −7.57067 + 47.7993i −0.269182 + 1.69955i
\(792\) 0 0
\(793\) −16.9798 16.9798i −0.602971 0.602971i
\(794\) −4.73742 0.750334i −0.168125 0.0266284i
\(795\) 0 0
\(796\) 4.12105 + 26.0193i 0.146067 + 0.922229i
\(797\) −14.2797 43.9483i −0.505812 1.55673i −0.799402 0.600797i \(-0.794850\pi\)
0.293590 0.955931i \(-0.405150\pi\)
\(798\) 0 0
\(799\) 21.3758 + 6.94543i 0.756223 + 0.245712i
\(800\) 24.9821 + 8.11717i 0.883250 + 0.286985i
\(801\) 0 0
\(802\) 4.83739 + 14.8880i 0.170814 + 0.525712i
\(803\) 3.15905 + 19.9455i 0.111480 + 0.703860i
\(804\) 0 0
\(805\) −1.98293 0.314066i −0.0698892 0.0110694i
\(806\) −7.29091 7.29091i −0.256811 0.256811i
\(807\) 0 0
\(808\) −4.78473 + 30.2096i −0.168326 + 1.06277i
\(809\) −0.358629 + 0.0568012i −0.0126087 + 0.00199703i −0.162736 0.986670i \(-0.552032\pi\)
0.150127 + 0.988667i \(0.452032\pi\)
\(810\) 0 0
\(811\) 22.6805i 0.796419i −0.917295 0.398209i \(-0.869632\pi\)
0.917295 0.398209i \(-0.130368\pi\)
\(812\) 24.6083 33.8704i 0.863582 1.18862i
\(813\) 0 0
\(814\) −4.47519 + 8.78305i −0.156855 + 0.307846i
\(815\) −0.389779 0.536484i −0.0136534 0.0187922i
\(816\) 0 0
\(817\) −33.7026 + 33.7026i −1.17910 + 1.17910i
\(818\) −2.72209 + 0.884459i −0.0951755 + 0.0309244i
\(819\) 0 0
\(820\) −4.43074 + 5.04639i −0.154728 + 0.176227i
\(821\) 12.5246 0.437111 0.218556 0.975824i \(-0.429865\pi\)
0.218556 + 0.975824i \(0.429865\pi\)
\(822\) 0 0
\(823\) −21.7847 + 21.7847i −0.759365 + 0.759365i −0.976207 0.216842i \(-0.930425\pi\)
0.216842 + 0.976207i \(0.430425\pi\)
\(824\) −31.6200 + 22.9733i −1.10154 + 0.800312i
\(825\) 0 0
\(826\) 4.64932 9.12480i 0.161771 0.317493i
\(827\) 5.75807 + 11.3008i 0.200228 + 0.392969i 0.969186 0.246330i \(-0.0792247\pi\)
−0.768958 + 0.639299i \(0.779225\pi\)
\(828\) 0 0
\(829\) 47.8117i 1.66057i −0.557341 0.830284i \(-0.688178\pi\)
0.557341 0.830284i \(-0.311822\pi\)
\(830\) 3.34505 + 2.43032i 0.116108 + 0.0843576i
\(831\) 0 0
\(832\) −0.690846 + 4.36183i −0.0239508 + 0.151219i
\(833\) 4.88051 + 2.48675i 0.169100 + 0.0861606i
\(834\) 0 0
\(835\) 12.0599 + 1.91011i 0.417351 + 0.0661020i
\(836\) 6.15807 18.9526i 0.212981 0.655489i
\(837\) 0 0
\(838\) −3.36499 10.3564i −0.116242 0.357755i
\(839\) 5.31936 2.71035i 0.183645 0.0935717i −0.359751 0.933048i \(-0.617138\pi\)
0.543396 + 0.839477i \(0.317138\pi\)
\(840\) 0 0
\(841\) −52.0596 16.9152i −1.79516 0.583282i
\(842\) 7.28344 3.71110i 0.251004 0.127893i
\(843\) 0 0
\(844\) 3.08448 + 19.4746i 0.106172 + 0.670345i
\(845\) 1.98772 6.11757i 0.0683796 0.210451i
\(846\) 0 0
\(847\) 2.96961 + 2.96961i 0.102037 + 0.102037i
\(848\) 2.79433 + 1.42378i 0.0959577 + 0.0488929i
\(849\) 0 0
\(850\) 6.33170 1.00284i 0.217176 0.0343972i
\(851\) 3.11693 + 2.26458i 0.106847 + 0.0776288i
\(852\) 0 0
\(853\) −3.50643 + 4.82618i −0.120058 + 0.165245i −0.864816 0.502089i \(-0.832565\pi\)
0.744758 + 0.667335i \(0.232565\pi\)
\(854\) 12.4771 + 24.4878i 0.426959 + 0.837955i
\(855\) 0 0
\(856\) −1.66681 2.29417i −0.0569704 0.0784130i
\(857\) −6.99504 + 5.08219i −0.238946 + 0.173604i −0.700814 0.713344i \(-0.747180\pi\)
0.461868 + 0.886949i \(0.347180\pi\)
\(858\) 0 0
\(859\) 34.4964 11.2086i 1.17700 0.382432i 0.345751 0.938326i \(-0.387624\pi\)
0.831253 + 0.555895i \(0.187624\pi\)
\(860\) 11.3852 0.388231
\(861\) 0 0
\(862\) 19.4452 0.662305
\(863\) 32.6565 10.6107i 1.11164 0.361193i 0.305068 0.952331i \(-0.401321\pi\)
0.806571 + 0.591137i \(0.201321\pi\)
\(864\) 0 0
\(865\) −7.05500 + 5.12576i −0.239877 + 0.174281i
\(866\) −0.201899 0.277891i −0.00686082 0.00944311i
\(867\) 0 0
\(868\) −14.4987 28.4554i −0.492119 0.965839i
\(869\) 11.4537 15.7646i 0.388539 0.534778i
\(870\) 0 0
\(871\) −13.1776 9.57406i −0.446505 0.324405i
\(872\) 14.8649 2.35436i 0.503388 0.0797288i
\(873\) 0 0
\(874\) 2.56437 + 1.30661i 0.0867412 + 0.0441969i
\(875\) −15.0885 15.0885i −0.510085 0.510085i
\(876\) 0 0
\(877\) −13.8957 + 42.7666i −0.469225 + 1.44413i 0.384366 + 0.923181i \(0.374420\pi\)
−0.853591 + 0.520944i \(0.825580\pi\)
\(878\) −2.24549 14.1775i −0.0757815 0.478466i
\(879\) 0 0
\(880\) −2.09498 + 1.06745i −0.0706218 + 0.0359836i
\(881\) −26.6642 8.66372i −0.898339 0.291888i −0.176788 0.984249i \(-0.556571\pi\)
−0.721551 + 0.692361i \(0.756571\pi\)
\(882\) 0 0
\(883\) 34.0612 17.3551i 1.14625 0.584044i 0.225519 0.974239i \(-0.427592\pi\)
0.920733 + 0.390194i \(0.127592\pi\)
\(884\) −1.76593 5.43496i −0.0593945 0.182798i
\(885\) 0 0
\(886\) 1.69087 5.20396i 0.0568059 0.174830i
\(887\) −15.7052 2.48746i −0.527329 0.0835207i −0.112907 0.993606i \(-0.536016\pi\)
−0.414422 + 0.910085i \(0.636016\pi\)
\(888\) 0 0
\(889\) −12.1031 6.16682i −0.405923 0.206828i
\(890\) 1.16517 7.35659i 0.0390566 0.246593i
\(891\) 0 0
\(892\) 8.96710 + 6.51498i 0.300241 + 0.218138i
\(893\) 50.7080i 1.69688i
\(894\) 0 0
\(895\) 0.697278 + 1.36849i 0.0233074 + 0.0457434i
\(896\) −14.3681 + 28.1990i −0.480005 + 0.942062i
\(897\) 0 0
\(898\) 15.1797 11.0287i 0.506553 0.368032i
\(899\) −45.1681 + 45.1681i −1.50644 + 1.50644i
\(900\) 0 0
\(901\) 5.79374 0.193017
\(902\) −0.947666 14.5882i −0.0315538 0.485735i
\(903\) 0 0
\(904\) −37.3458 + 12.1344i −1.24210 + 0.403584i
\(905\) 2.85282 2.85282i 0.0948310 0.0948310i
\(906\) 0 0
\(907\) 25.3442 + 34.8834i 0.841542 + 1.15828i 0.985664 + 0.168723i \(0.0539643\pi\)
−0.144122 + 0.989560i \(0.546036\pi\)
\(908\) −14.3963 + 28.2543i −0.477757 + 0.937652i
\(909\) 0 0
\(910\) 1.95340 2.68862i 0.0647544 0.0891268i
\(911\) 26.3499i 0.873010i 0.899702 + 0.436505i \(0.143784\pi\)
−0.899702 + 0.436505i \(0.856216\pi\)
\(912\) 0 0
\(913\) 24.0586 3.81051i 0.796225 0.126110i
\(914\) −4.05741 + 25.6175i −0.134207 + 0.847352i
\(915\) 0 0
\(916\) 3.05864 + 3.05864i 0.101060 + 0.101060i
\(917\) −51.2854 8.12282i −1.69359 0.268239i
\(918\) 0 0
\(919\) 4.74106 + 29.9339i 0.156393 + 0.987427i 0.933635 + 0.358226i \(0.116618\pi\)
−0.777242 + 0.629202i \(0.783382\pi\)
\(920\) −0.503389 1.54927i −0.0165963 0.0510780i
\(921\) 0 0
\(922\) 19.9042 + 6.46727i 0.655510 + 0.212988i
\(923\) −1.91317 0.621625i −0.0629726 0.0204610i
\(924\) 0 0
\(925\) 5.98289 + 18.4135i 0.196716 + 0.605431i
\(926\) −1.47531 9.31472i −0.0484816 0.306101i
\(927\) 0 0
\(928\) 52.9439 + 8.38549i 1.73797 + 0.275267i
\(929\) 14.3945 + 14.3945i 0.472267 + 0.472267i 0.902647 0.430381i \(-0.141621\pi\)
−0.430381 + 0.902647i \(0.641621\pi\)
\(930\) 0 0
\(931\) −1.93320 + 12.2058i −0.0633581 + 0.400027i
\(932\) −25.0990 + 3.97529i −0.822145 + 0.130215i
\(933\) 0 0
\(934\) 21.6428i 0.708174i
\(935\) −2.55317 + 3.51414i −0.0834976 + 0.114925i
\(936\) 0 0
\(937\) −16.9622 + 33.2901i −0.554130 + 1.08754i 0.428772 + 0.903413i \(0.358946\pi\)
−0.982902 + 0.184129i \(0.941054\pi\)
\(938\) 10.9576 + 15.0819i 0.357779 + 0.492441i
\(939\) 0 0
\(940\) 8.56492 8.56492i 0.279357 0.279357i
\(941\) 23.3267 7.57929i 0.760427 0.247078i 0.0969652 0.995288i \(-0.469086\pi\)
0.663462 + 0.748210i \(0.269086\pi\)
\(942\) 0 0
\(943\) −5.68948 0.526117i −0.185275 0.0171327i
\(944\) −4.68768 −0.152571
\(945\) 0 0
\(946\) −17.5253 + 17.5253i −0.569796 + 0.569796i
\(947\) 46.3059 33.6432i 1.50474 1.09326i 0.536292 0.844032i \(-0.319825\pi\)
0.968446 0.249224i \(-0.0801755\pi\)
\(948\) 0 0
\(949\) −5.93142 + 11.6411i −0.192542 + 0.377885i
\(950\) 6.56610 + 12.8867i 0.213032 + 0.418099i
\(951\) 0 0
\(952\) 15.4978i 0.502287i
\(953\) −20.8828 15.1723i −0.676461 0.491478i 0.195721 0.980660i \(-0.437295\pi\)
−0.872182 + 0.489182i \(0.837295\pi\)
\(954\) 0 0
\(955\) 1.47408 9.30696i 0.0477000 0.301166i
\(956\) −7.72953 3.93839i −0.249991 0.127377i
\(957\) 0 0
\(958\) −19.3848 3.07025i −0.626294 0.0991953i
\(959\) 0.228443 0.703076i 0.00737682 0.0227035i
\(960\) 0 0
\(961\) 5.47787 + 16.8592i 0.176706 + 0.543844i
\(962\) −5.68242 + 2.89534i −0.183209 + 0.0933494i
\(963\) 0 0
\(964\) −12.1979 3.96335i −0.392869 0.127651i
\(965\) 10.6073 5.40469i 0.341461 0.173983i
\(966\) 0 0
\(967\) −7.85597 49.6006i −0.252631 1.59505i −0.708967 0.705241i \(-0.750839\pi\)
0.456336 0.889807i \(-0.349161\pi\)
\(968\) −1.05300 + 3.24081i −0.0338448 + 0.104164i
\(969\) 0 0
\(970\) −2.39475 2.39475i −0.0768908 0.0768908i
\(971\) 21.9048 + 11.1611i 0.702960 + 0.358176i 0.768655 0.639664i \(-0.220926\pi\)
−0.0656949 + 0.997840i \(0.520926\pi\)
\(972\) 0 0
\(973\) 7.28820 1.15434i 0.233649 0.0370064i
\(974\) −6.89771 5.01148i −0.221017 0.160578i
\(975\) 0 0
\(976\) 7.39440 10.1775i 0.236689 0.325774i
\(977\) 16.7259 + 32.8265i 0.535110 + 1.05021i 0.987386 + 0.158334i \(0.0506124\pi\)
−0.452275 + 0.891878i \(0.649388\pi\)
\(978\) 0 0
\(979\) −25.7918 35.4994i −0.824310 1.13457i
\(980\) 2.38816 1.73510i 0.0762870 0.0554258i
\(981\) 0 0
\(982\) −18.7831 + 6.10301i −0.599394 + 0.194755i
\(983\) −24.1327 −0.769713 −0.384857 0.922976i \(-0.625749\pi\)
−0.384857 + 0.922976i \(0.625749\pi\)
\(984\) 0 0
\(985\) 10.3997 0.331361
\(986\) 12.4417 4.04256i 0.396225 0.128741i
\(987\) 0 0
\(988\) 10.4306 7.57825i 0.331841 0.241096i
\(989\) 5.69381 + 7.83686i 0.181053 + 0.249198i
\(990\) 0 0
\(991\) −3.15702 6.19601i −0.100286 0.196823i 0.835412 0.549624i \(-0.185229\pi\)
−0.935698 + 0.352802i \(0.885229\pi\)
\(992\) 24.0345 33.0807i 0.763097 1.05031i
\(993\) 0 0
\(994\) 1.86262 + 1.35327i 0.0590788 + 0.0429232i
\(995\) 12.7954 2.02659i 0.405642 0.0642473i
\(996\) 0 0
\(997\) −29.1900 14.8731i −0.924458 0.471035i −0.0741065 0.997250i \(-0.523610\pi\)
−0.850351 + 0.526216i \(0.823610\pi\)
\(998\) −6.67857 6.67857i −0.211406 0.211406i
\(999\) 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 369.2.u.a.289.1 24
3.2 odd 2 41.2.g.a.2.3 24
12.11 even 2 656.2.bs.d.289.2 24
41.21 even 20 inner 369.2.u.a.226.1 24
123.29 even 40 1681.2.a.m.1.9 24
123.53 even 40 1681.2.a.m.1.10 24
123.62 odd 20 41.2.g.a.21.3 yes 24
492.431 even 20 656.2.bs.d.513.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
41.2.g.a.2.3 24 3.2 odd 2
41.2.g.a.21.3 yes 24 123.62 odd 20
369.2.u.a.226.1 24 41.21 even 20 inner
369.2.u.a.289.1 24 1.1 even 1 trivial
656.2.bs.d.289.2 24 12.11 even 2
656.2.bs.d.513.2 24 492.431 even 20
1681.2.a.m.1.9 24 123.29 even 40
1681.2.a.m.1.10 24 123.53 even 40