Properties

Label 162.3.f.a.71.3
Level $162$
Weight $3$
Character 162.71
Analytic conductor $4.414$
Analytic rank $0$
Dimension $36$
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] = [162,3,Mod(17,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\), degree \(6\), 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: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 71.3
Character \(\chi\) \(=\) 162.71
Dual form 162.3.f.a.89.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(3.55779 - 4.24001i) q^{5} +(-10.2625 - 3.73526i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})\) \(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(3.55779 - 4.24001i) q^{5} +(-10.2625 - 3.73526i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(-3.91380 + 6.77890i) q^{10} +(-2.64446 - 3.15155i) q^{11} +(-0.953621 + 5.40825i) q^{13} +(15.2102 + 2.68197i) q^{14} +(3.06418 - 2.57115i) q^{16} +(-4.10708 - 2.37123i) q^{17} +(-17.1665 - 29.7332i) q^{19} +(3.78613 - 10.4023i) q^{20} +(4.45696 + 3.73984i) q^{22} +(-12.6292 - 34.6986i) q^{23} +(-0.978615 - 5.55000i) q^{25} -7.76642i q^{26} -21.8423 q^{28} +(5.18449 - 0.914165i) q^{29} +(34.9235 - 12.7111i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(6.30237 + 2.29387i) q^{34} +(-52.3496 + 30.2240i) q^{35} +(-12.1981 + 21.1278i) q^{37} +(31.2100 + 37.1946i) q^{38} +(-2.71850 + 15.4174i) q^{40} +(22.6189 + 3.98833i) q^{41} +(39.1915 - 32.8855i) q^{43} +(-7.12575 - 4.11406i) q^{44} +(26.1102 + 45.2243i) q^{46} +(-28.3436 + 77.8733i) q^{47} +(53.8315 + 45.1700i) q^{49} +(2.72589 + 7.48932i) q^{50} +(1.90724 + 10.8165i) q^{52} -16.2927i q^{53} -22.7711 q^{55} +(30.4205 - 5.36395i) q^{56} +(-6.99608 + 2.54637i) q^{58} +(45.6558 - 54.4105i) q^{59} +(-74.1675 - 26.9948i) q^{61} +(-45.5174 + 26.2795i) q^{62} +(4.00000 - 6.92820i) q^{64} +(19.5383 + 23.2848i) q^{65} +(-12.1162 + 68.7145i) q^{67} +(-9.34081 - 1.64704i) q^{68} +(65.4865 - 54.9497i) q^{70} +(65.9072 + 38.0516i) q^{71} +(25.5063 + 44.1783i) q^{73} +(11.8002 - 32.4208i) q^{74} +(-52.6012 - 44.1376i) q^{76} +(15.3671 + 42.2207i) q^{77} +(5.51385 + 31.2706i) q^{79} -22.1398i q^{80} -32.4815 q^{82} +(-28.7447 + 5.06847i) q^{83} +(-24.6662 + 8.97776i) q^{85} +(-46.5072 + 55.4251i) q^{86} +(10.9346 + 3.97985i) q^{88} +(69.2878 - 40.0033i) q^{89} +(29.9878 - 51.9404i) q^{91} +(-47.4704 - 56.5731i) q^{92} +(20.3511 - 115.417i) q^{94} +(-187.144 - 32.9986i) q^{95} +(36.3741 - 30.5215i) q^{97} +(-86.0653 - 49.6898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39273 + 0.245576i −0.696364 + 0.122788i
\(3\) 0 0
\(4\) 1.87939 0.684040i 0.469846 0.171010i
\(5\) 3.55779 4.24001i 0.711559 0.848003i −0.282223 0.959349i \(-0.591072\pi\)
0.993782 + 0.111346i \(0.0355162\pi\)
\(6\) 0 0
\(7\) −10.2625 3.73526i −1.46608 0.533609i −0.519045 0.854747i \(-0.673712\pi\)
−0.947032 + 0.321138i \(0.895935\pi\)
\(8\) −2.44949 + 1.41421i −0.306186 + 0.176777i
\(9\) 0 0
\(10\) −3.91380 + 6.77890i −0.391380 + 0.677890i
\(11\) −2.64446 3.15155i −0.240406 0.286505i 0.632328 0.774701i \(-0.282099\pi\)
−0.872734 + 0.488196i \(0.837655\pi\)
\(12\) 0 0
\(13\) −0.953621 + 5.40825i −0.0733555 + 0.416020i 0.925912 + 0.377740i \(0.123299\pi\)
−0.999267 + 0.0382793i \(0.987812\pi\)
\(14\) 15.2102 + 2.68197i 1.08644 + 0.191570i
\(15\) 0 0
\(16\) 3.06418 2.57115i 0.191511 0.160697i
\(17\) −4.10708 2.37123i −0.241593 0.139484i 0.374316 0.927301i \(-0.377878\pi\)
−0.615909 + 0.787817i \(0.711211\pi\)
\(18\) 0 0
\(19\) −17.1665 29.7332i −0.903499 1.56491i −0.822919 0.568158i \(-0.807656\pi\)
−0.0805801 0.996748i \(-0.525677\pi\)
\(20\) 3.78613 10.4023i 0.189306 0.520115i
\(21\) 0 0
\(22\) 4.45696 + 3.73984i 0.202589 + 0.169993i
\(23\) −12.6292 34.6986i −0.549098 1.50863i −0.834931 0.550354i \(-0.814493\pi\)
0.285833 0.958279i \(-0.407730\pi\)
\(24\) 0 0
\(25\) −0.978615 5.55000i −0.0391446 0.222000i
\(26\) 7.76642i 0.298708i
\(27\) 0 0
\(28\) −21.8423 −0.780084
\(29\) 5.18449 0.914165i 0.178775 0.0315229i −0.0835437 0.996504i \(-0.526624\pi\)
0.262319 + 0.964981i \(0.415513\pi\)
\(30\) 0 0
\(31\) 34.9235 12.7111i 1.12656 0.410036i 0.289520 0.957172i \(-0.406504\pi\)
0.837044 + 0.547136i \(0.184282\pi\)
\(32\) −3.63616 + 4.33340i −0.113630 + 0.135419i
\(33\) 0 0
\(34\) 6.30237 + 2.29387i 0.185364 + 0.0674669i
\(35\) −52.3496 + 30.2240i −1.49570 + 0.863544i
\(36\) 0 0
\(37\) −12.1981 + 21.1278i −0.329679 + 0.571021i −0.982448 0.186536i \(-0.940274\pi\)
0.652769 + 0.757557i \(0.273607\pi\)
\(38\) 31.2100 + 37.1946i 0.821316 + 0.978806i
\(39\) 0 0
\(40\) −2.71850 + 15.4174i −0.0679624 + 0.385434i
\(41\) 22.6189 + 3.98833i 0.551681 + 0.0972763i 0.442538 0.896750i \(-0.354078\pi\)
0.109143 + 0.994026i \(0.465189\pi\)
\(42\) 0 0
\(43\) 39.1915 32.8855i 0.911430 0.764780i −0.0609609 0.998140i \(-0.519416\pi\)
0.972390 + 0.233360i \(0.0749720\pi\)
\(44\) −7.12575 4.11406i −0.161949 0.0935013i
\(45\) 0 0
\(46\) 26.1102 + 45.2243i 0.567614 + 0.983136i
\(47\) −28.3436 + 77.8733i −0.603055 + 1.65688i 0.141992 + 0.989868i \(0.454649\pi\)
−0.745047 + 0.667012i \(0.767573\pi\)
\(48\) 0 0
\(49\) 53.8315 + 45.1700i 1.09860 + 0.921836i
\(50\) 2.72589 + 7.48932i 0.0545178 + 0.149786i
\(51\) 0 0
\(52\) 1.90724 + 10.8165i 0.0366777 + 0.208010i
\(53\) 16.2927i 0.307409i −0.988117 0.153704i \(-0.950880\pi\)
0.988117 0.153704i \(-0.0491204\pi\)
\(54\) 0 0
\(55\) −22.7711 −0.414020
\(56\) 30.4205 5.36395i 0.543222 0.0957848i
\(57\) 0 0
\(58\) −6.99608 + 2.54637i −0.120622 + 0.0439029i
\(59\) 45.6558 54.4105i 0.773827 0.922212i −0.224810 0.974403i \(-0.572176\pi\)
0.998637 + 0.0521911i \(0.0166205\pi\)
\(60\) 0 0
\(61\) −74.1675 26.9948i −1.21586 0.442537i −0.347128 0.937818i \(-0.612843\pi\)
−0.868733 + 0.495281i \(0.835065\pi\)
\(62\) −45.5174 + 26.2795i −0.734151 + 0.423862i
\(63\) 0 0
\(64\) 4.00000 6.92820i 0.0625000 0.108253i
\(65\) 19.5383 + 23.2848i 0.300589 + 0.358228i
\(66\) 0 0
\(67\) −12.1162 + 68.7145i −0.180839 + 1.02559i 0.750347 + 0.661045i \(0.229887\pi\)
−0.931186 + 0.364545i \(0.881224\pi\)
\(68\) −9.34081 1.64704i −0.137365 0.0242211i
\(69\) 0 0
\(70\) 65.4865 54.9497i 0.935521 0.784995i
\(71\) 65.9072 + 38.0516i 0.928271 + 0.535937i 0.886264 0.463180i \(-0.153292\pi\)
0.0420065 + 0.999117i \(0.486625\pi\)
\(72\) 0 0
\(73\) 25.5063 + 44.1783i 0.349402 + 0.605182i 0.986143 0.165896i \(-0.0530515\pi\)
−0.636741 + 0.771077i \(0.719718\pi\)
\(74\) 11.8002 32.4208i 0.159462 0.438119i
\(75\) 0 0
\(76\) −52.6012 44.1376i −0.692121 0.580758i
\(77\) 15.3671 + 42.2207i 0.199572 + 0.548321i
\(78\) 0 0
\(79\) 5.51385 + 31.2706i 0.0697956 + 0.395830i 0.999613 + 0.0278099i \(0.00885329\pi\)
−0.929818 + 0.368021i \(0.880036\pi\)
\(80\) 22.1398i 0.276747i
\(81\) 0 0
\(82\) −32.4815 −0.396115
\(83\) −28.7447 + 5.06847i −0.346322 + 0.0610659i −0.344104 0.938932i \(-0.611817\pi\)
−0.00221805 + 0.999998i \(0.500706\pi\)
\(84\) 0 0
\(85\) −24.6662 + 8.97776i −0.290190 + 0.105621i
\(86\) −46.5072 + 55.4251i −0.540781 + 0.644478i
\(87\) 0 0
\(88\) 10.9346 + 3.97985i 0.124256 + 0.0452256i
\(89\) 69.2878 40.0033i 0.778514 0.449475i −0.0573893 0.998352i \(-0.518278\pi\)
0.835903 + 0.548877i \(0.184944\pi\)
\(90\) 0 0
\(91\) 29.9878 51.9404i 0.329536 0.570774i
\(92\) −47.4704 56.5731i −0.515983 0.614925i
\(93\) 0 0
\(94\) 20.3511 115.417i 0.216501 1.22784i
\(95\) −187.144 32.9986i −1.96994 0.347353i
\(96\) 0 0
\(97\) 36.3741 30.5215i 0.374991 0.314655i −0.435741 0.900072i \(-0.643514\pi\)
0.810732 + 0.585417i \(0.199069\pi\)
\(98\) −86.0653 49.6898i −0.878217 0.507039i
\(99\) 0 0
\(100\) −5.63562 9.76118i −0.0563562 0.0976118i
\(101\) 15.6059 42.8769i 0.154514 0.424524i −0.838148 0.545442i \(-0.816362\pi\)
0.992662 + 0.120918i \(0.0385839\pi\)
\(102\) 0 0
\(103\) −10.9188 9.16192i −0.106007 0.0889507i 0.588243 0.808684i \(-0.299820\pi\)
−0.694251 + 0.719733i \(0.744264\pi\)
\(104\) −5.31254 14.5961i −0.0510821 0.140347i
\(105\) 0 0
\(106\) 4.00108 + 22.6913i 0.0377461 + 0.214069i
\(107\) 105.487i 0.985863i −0.870068 0.492931i \(-0.835925\pi\)
0.870068 0.492931i \(-0.164075\pi\)
\(108\) 0 0
\(109\) 57.5260 0.527762 0.263881 0.964555i \(-0.414997\pi\)
0.263881 + 0.964555i \(0.414997\pi\)
\(110\) 31.7139 5.59202i 0.288308 0.0508366i
\(111\) 0 0
\(112\) −41.0502 + 14.9410i −0.366519 + 0.133402i
\(113\) 76.8178 91.5479i 0.679803 0.810158i −0.310279 0.950646i \(-0.600423\pi\)
0.990082 + 0.140487i \(0.0448670\pi\)
\(114\) 0 0
\(115\) −192.055 69.9022i −1.67004 0.607845i
\(116\) 9.11832 5.26446i 0.0786062 0.0453833i
\(117\) 0 0
\(118\) −50.2243 + 86.9910i −0.425629 + 0.737212i
\(119\) 33.2920 + 39.6758i 0.279765 + 0.333410i
\(120\) 0 0
\(121\) 18.0724 102.493i 0.149358 0.847053i
\(122\) 109.924 + 19.3826i 0.901020 + 0.158874i
\(123\) 0 0
\(124\) 56.9397 47.7781i 0.459192 0.385307i
\(125\) 92.8213 + 53.5904i 0.742570 + 0.428723i
\(126\) 0 0
\(127\) −68.8561 119.262i −0.542174 0.939072i −0.998779 0.0494029i \(-0.984268\pi\)
0.456605 0.889669i \(-0.349065\pi\)
\(128\) −3.86952 + 10.6314i −0.0302306 + 0.0830579i
\(129\) 0 0
\(130\) −32.9297 27.6313i −0.253305 0.212549i
\(131\) 21.9189 + 60.2217i 0.167320 + 0.459708i 0.994807 0.101777i \(-0.0324527\pi\)
−0.827487 + 0.561484i \(0.810231\pi\)
\(132\) 0 0
\(133\) 65.1105 + 369.260i 0.489552 + 2.77639i
\(134\) 98.6761i 0.736389i
\(135\) 0 0
\(136\) 13.4137 0.0986300
\(137\) −75.1710 + 13.2547i −0.548694 + 0.0967495i −0.441121 0.897448i \(-0.645419\pi\)
−0.107573 + 0.994197i \(0.534308\pi\)
\(138\) 0 0
\(139\) −100.055 + 36.4171i −0.719821 + 0.261993i −0.675850 0.737039i \(-0.736223\pi\)
−0.0439712 + 0.999033i \(0.514001\pi\)
\(140\) −77.7106 + 92.6118i −0.555075 + 0.661513i
\(141\) 0 0
\(142\) −101.135 36.8103i −0.712221 0.259227i
\(143\) 19.5662 11.2966i 0.136827 0.0789969i
\(144\) 0 0
\(145\) 14.5693 25.2347i 0.100478 0.174032i
\(146\) −46.3725 55.2646i −0.317620 0.378525i
\(147\) 0 0
\(148\) −8.47273 + 48.0512i −0.0572482 + 0.324670i
\(149\) 84.0145 + 14.8140i 0.563856 + 0.0994230i 0.448308 0.893879i \(-0.352027\pi\)
0.115547 + 0.993302i \(0.463138\pi\)
\(150\) 0 0
\(151\) −42.4996 + 35.6614i −0.281454 + 0.236168i −0.772575 0.634923i \(-0.781032\pi\)
0.491121 + 0.871091i \(0.336587\pi\)
\(152\) 84.0983 + 48.5542i 0.553278 + 0.319435i
\(153\) 0 0
\(154\) −31.7705 55.0282i −0.206302 0.357326i
\(155\) 70.3553 193.299i 0.453905 1.24709i
\(156\) 0 0
\(157\) −12.9857 10.8963i −0.0827115 0.0694032i 0.600494 0.799629i \(-0.294970\pi\)
−0.683206 + 0.730226i \(0.739415\pi\)
\(158\) −15.3586 42.1974i −0.0972063 0.267072i
\(159\) 0 0
\(160\) 5.43699 + 30.8347i 0.0339812 + 0.192717i
\(161\) 403.269i 2.50478i
\(162\) 0 0
\(163\) 230.772 1.41578 0.707890 0.706322i \(-0.249647\pi\)
0.707890 + 0.706322i \(0.249647\pi\)
\(164\) 45.2379 7.97666i 0.275841 0.0486382i
\(165\) 0 0
\(166\) 38.7889 14.1180i 0.233668 0.0850481i
\(167\) −103.061 + 122.823i −0.617132 + 0.735469i −0.980574 0.196147i \(-0.937157\pi\)
0.363442 + 0.931617i \(0.381601\pi\)
\(168\) 0 0
\(169\) 130.468 + 47.4866i 0.772001 + 0.280986i
\(170\) 32.1486 18.5610i 0.189109 0.109182i
\(171\) 0 0
\(172\) 51.1608 88.6132i 0.297447 0.515193i
\(173\) −204.014 243.135i −1.17927 1.40540i −0.894653 0.446762i \(-0.852577\pi\)
−0.284620 0.958640i \(-0.591867\pi\)
\(174\) 0 0
\(175\) −10.6876 + 60.6125i −0.0610721 + 0.346357i
\(176\) −16.2062 2.85759i −0.0920808 0.0162363i
\(177\) 0 0
\(178\) −86.6752 + 72.7291i −0.486939 + 0.408591i
\(179\) 38.5365 + 22.2490i 0.215287 + 0.124296i 0.603766 0.797161i \(-0.293666\pi\)
−0.388479 + 0.921458i \(0.626999\pi\)
\(180\) 0 0
\(181\) 19.0288 + 32.9588i 0.105131 + 0.182093i 0.913792 0.406183i \(-0.133140\pi\)
−0.808661 + 0.588276i \(0.799807\pi\)
\(182\) −29.0096 + 79.7032i −0.159393 + 0.437930i
\(183\) 0 0
\(184\) 80.0064 + 67.1333i 0.434817 + 0.364855i
\(185\) 46.1836 + 126.888i 0.249641 + 0.685884i
\(186\) 0 0
\(187\) 3.38800 + 19.2143i 0.0181176 + 0.102750i
\(188\) 165.742i 0.881607i
\(189\) 0 0
\(190\) 268.745 1.41445
\(191\) −201.386 + 35.5097i −1.05438 + 0.185915i −0.673859 0.738860i \(-0.735365\pi\)
−0.380516 + 0.924774i \(0.624254\pi\)
\(192\) 0 0
\(193\) 108.871 39.6259i 0.564100 0.205316i −0.0442003 0.999023i \(-0.514074\pi\)
0.608300 + 0.793707i \(0.291852\pi\)
\(194\) −43.1639 + 51.4408i −0.222495 + 0.265159i
\(195\) 0 0
\(196\) 132.068 + 48.0689i 0.673817 + 0.245249i
\(197\) 76.7079 44.2873i 0.389380 0.224809i −0.292511 0.956262i \(-0.594491\pi\)
0.681892 + 0.731453i \(0.261158\pi\)
\(198\) 0 0
\(199\) 134.773 233.434i 0.677253 1.17304i −0.298551 0.954394i \(-0.596503\pi\)
0.975805 0.218644i \(-0.0701632\pi\)
\(200\) 10.2460 + 12.2107i 0.0512300 + 0.0610535i
\(201\) 0 0
\(202\) −11.2053 + 63.5483i −0.0554717 + 0.314596i
\(203\) −56.6207 9.98375i −0.278920 0.0491810i
\(204\) 0 0
\(205\) 97.3841 81.7149i 0.475044 0.398609i
\(206\) 17.4568 + 10.0787i 0.0847418 + 0.0489257i
\(207\) 0 0
\(208\) 10.9834 + 19.0238i 0.0528047 + 0.0914604i
\(209\) −48.3096 + 132.729i −0.231146 + 0.635069i
\(210\) 0 0
\(211\) −107.762 90.4231i −0.510721 0.428546i 0.350662 0.936502i \(-0.385957\pi\)
−0.861383 + 0.507957i \(0.830401\pi\)
\(212\) −11.1448 30.6202i −0.0525700 0.144435i
\(213\) 0 0
\(214\) 25.9051 + 146.915i 0.121052 + 0.686520i
\(215\) 283.172i 1.31708i
\(216\) 0 0
\(217\) −405.883 −1.87043
\(218\) −80.1181 + 14.1270i −0.367514 + 0.0648027i
\(219\) 0 0
\(220\) −42.7956 + 15.5763i −0.194526 + 0.0708015i
\(221\) 16.7408 19.9509i 0.0757502 0.0902756i
\(222\) 0 0
\(223\) −324.808 118.221i −1.45654 0.530137i −0.512130 0.858908i \(-0.671144\pi\)
−0.944410 + 0.328770i \(0.893366\pi\)
\(224\) 53.5026 30.8897i 0.238851 0.137901i
\(225\) 0 0
\(226\) −84.5044 + 146.366i −0.373913 + 0.647637i
\(227\) 118.546 + 141.278i 0.522230 + 0.622369i 0.961106 0.276178i \(-0.0890680\pi\)
−0.438877 + 0.898547i \(0.644624\pi\)
\(228\) 0 0
\(229\) 38.3747 217.634i 0.167575 0.950365i −0.778794 0.627279i \(-0.784168\pi\)
0.946370 0.323086i \(-0.104720\pi\)
\(230\) 284.646 + 50.1908i 1.23759 + 0.218221i
\(231\) 0 0
\(232\) −11.4065 + 9.57121i −0.0491660 + 0.0412552i
\(233\) −364.370 210.369i −1.56382 0.902872i −0.996865 0.0791236i \(-0.974788\pi\)
−0.566955 0.823748i \(-0.691879\pi\)
\(234\) 0 0
\(235\) 229.343 + 397.234i 0.975929 + 1.69036i
\(236\) 48.5859 133.489i 0.205872 0.565630i
\(237\) 0 0
\(238\) −56.1101 47.0820i −0.235757 0.197823i
\(239\) 27.2416 + 74.8456i 0.113981 + 0.313162i 0.983546 0.180658i \(-0.0578226\pi\)
−0.869565 + 0.493819i \(0.835600\pi\)
\(240\) 0 0
\(241\) −9.36196 53.0943i −0.0388463 0.220308i 0.959205 0.282713i \(-0.0912343\pi\)
−0.998051 + 0.0624044i \(0.980123\pi\)
\(242\) 147.184i 0.608197i
\(243\) 0 0
\(244\) −157.855 −0.646946
\(245\) 383.043 67.5407i 1.56344 0.275677i
\(246\) 0 0
\(247\) 177.175 64.4865i 0.717308 0.261079i
\(248\) −67.5685 + 80.5250i −0.272453 + 0.324697i
\(249\) 0 0
\(250\) −142.435 51.8422i −0.569741 0.207369i
\(251\) 179.256 103.494i 0.714167 0.412325i −0.0984348 0.995144i \(-0.531384\pi\)
0.812602 + 0.582819i \(0.198050\pi\)
\(252\) 0 0
\(253\) −75.9567 + 131.561i −0.300224 + 0.520003i
\(254\) 125.186 + 149.190i 0.492857 + 0.587364i
\(255\) 0 0
\(256\) 2.77837 15.7569i 0.0108530 0.0615505i
\(257\) −201.153 35.4686i −0.782695 0.138010i −0.231999 0.972716i \(-0.574527\pi\)
−0.550696 + 0.834706i \(0.685638\pi\)
\(258\) 0 0
\(259\) 204.102 171.262i 0.788037 0.661241i
\(260\) 52.6477 + 30.3962i 0.202491 + 0.116908i
\(261\) 0 0
\(262\) −45.3161 78.4897i −0.172962 0.299579i
\(263\) −65.2110 + 179.166i −0.247951 + 0.681239i 0.751810 + 0.659379i \(0.229181\pi\)
−0.999761 + 0.0218596i \(0.993041\pi\)
\(264\) 0 0
\(265\) −69.0812 57.9660i −0.260684 0.218740i
\(266\) −181.362 498.289i −0.681814 1.87327i
\(267\) 0 0
\(268\) 24.2324 + 137.429i 0.0904196 + 0.512795i
\(269\) 70.9150i 0.263624i −0.991275 0.131812i \(-0.957920\pi\)
0.991275 0.131812i \(-0.0420796\pi\)
\(270\) 0 0
\(271\) −117.923 −0.435141 −0.217570 0.976045i \(-0.569813\pi\)
−0.217570 + 0.976045i \(0.569813\pi\)
\(272\) −18.6816 + 3.29407i −0.0686824 + 0.0121106i
\(273\) 0 0
\(274\) 101.438 36.9203i 0.370211 0.134746i
\(275\) −14.9032 + 17.7609i −0.0541934 + 0.0645852i
\(276\) 0 0
\(277\) 232.933 + 84.7808i 0.840915 + 0.306068i 0.726331 0.687346i \(-0.241224\pi\)
0.114584 + 0.993414i \(0.463446\pi\)
\(278\) 130.406 75.2902i 0.469088 0.270828i
\(279\) 0 0
\(280\) 85.4865 148.067i 0.305309 0.528811i
\(281\) −46.1416 54.9895i −0.164205 0.195692i 0.677667 0.735369i \(-0.262991\pi\)
−0.841872 + 0.539677i \(0.818547\pi\)
\(282\) 0 0
\(283\) −52.2646 + 296.407i −0.184681 + 1.04738i 0.741685 + 0.670749i \(0.234027\pi\)
−0.926365 + 0.376627i \(0.877084\pi\)
\(284\) 149.894 + 26.4303i 0.527795 + 0.0930646i
\(285\) 0 0
\(286\) −24.4762 + 20.5380i −0.0855813 + 0.0718112i
\(287\) −217.230 125.418i −0.756900 0.436997i
\(288\) 0 0
\(289\) −133.255 230.804i −0.461088 0.798629i
\(290\) −14.0940 + 38.7229i −0.0486000 + 0.133527i
\(291\) 0 0
\(292\) 78.1560 + 65.5806i 0.267657 + 0.224591i
\(293\) 34.3361 + 94.3376i 0.117188 + 0.321971i 0.984394 0.175978i \(-0.0563088\pi\)
−0.867206 + 0.497949i \(0.834087\pi\)
\(294\) 0 0
\(295\) −68.2672 387.163i −0.231414 1.31242i
\(296\) 69.0030i 0.233118i
\(297\) 0 0
\(298\) −120.647 −0.404857
\(299\) 199.702 35.2129i 0.667900 0.117769i
\(300\) 0 0
\(301\) −525.040 + 191.099i −1.74432 + 0.634881i
\(302\) 50.4328 60.1035i 0.166996 0.199018i
\(303\) 0 0
\(304\) −129.050 46.9703i −0.424506 0.154507i
\(305\) −378.331 + 218.429i −1.24043 + 0.716162i
\(306\) 0 0
\(307\) −136.003 + 235.565i −0.443008 + 0.767312i −0.997911 0.0646029i \(-0.979422\pi\)
0.554903 + 0.831915i \(0.312755\pi\)
\(308\) 57.7613 + 68.8372i 0.187537 + 0.223498i
\(309\) 0 0
\(310\) −50.5161 + 286.491i −0.162955 + 0.924165i
\(311\) −402.304 70.9371i −1.29358 0.228094i −0.515845 0.856682i \(-0.672522\pi\)
−0.777738 + 0.628588i \(0.783633\pi\)
\(312\) 0 0
\(313\) 186.473 156.470i 0.595761 0.499903i −0.294319 0.955707i \(-0.595093\pi\)
0.890080 + 0.455805i \(0.150648\pi\)
\(314\) 20.7614 + 11.9866i 0.0661192 + 0.0381739i
\(315\) 0 0
\(316\) 31.7530 + 54.9978i 0.100484 + 0.174044i
\(317\) 92.9426 255.358i 0.293194 0.805545i −0.702400 0.711782i \(-0.747888\pi\)
0.995595 0.0937628i \(-0.0298895\pi\)
\(318\) 0 0
\(319\) −16.5912 13.9217i −0.0520101 0.0436417i
\(320\) −15.1445 41.6092i −0.0473266 0.130029i
\(321\) 0 0
\(322\) −99.0331 561.644i −0.307556 1.74424i
\(323\) 162.822i 0.504094i
\(324\) 0 0
\(325\) 30.9490 0.0952278
\(326\) −321.403 + 56.6720i −0.985899 + 0.173841i
\(327\) 0 0
\(328\) −61.0452 + 22.2186i −0.186113 + 0.0677397i
\(329\) 581.754 693.308i 1.76825 2.10732i
\(330\) 0 0
\(331\) 416.626 + 151.639i 1.25869 + 0.458125i 0.883329 0.468754i \(-0.155297\pi\)
0.375360 + 0.926879i \(0.377519\pi\)
\(332\) −50.5553 + 29.1881i −0.152275 + 0.0879161i
\(333\) 0 0
\(334\) 113.374 196.369i 0.339442 0.587931i
\(335\) 248.243 + 295.845i 0.741025 + 0.883120i
\(336\) 0 0
\(337\) 26.8736 152.408i 0.0797435 0.452248i −0.918624 0.395133i \(-0.870699\pi\)
0.998368 0.0571153i \(-0.0181903\pi\)
\(338\) −193.368 34.0961i −0.572096 0.100876i
\(339\) 0 0
\(340\) −40.2161 + 33.7453i −0.118283 + 0.0992510i
\(341\) −132.414 76.4490i −0.388310 0.224191i
\(342\) 0 0
\(343\) −116.158 201.191i −0.338652 0.586562i
\(344\) −49.4919 + 135.978i −0.143872 + 0.395285i
\(345\) 0 0
\(346\) 343.844 + 288.520i 0.993770 + 0.833872i
\(347\) 71.9673 + 197.728i 0.207398 + 0.569823i 0.999159 0.0410093i \(-0.0130573\pi\)
−0.791760 + 0.610832i \(0.790835\pi\)
\(348\) 0 0
\(349\) −74.8630 424.569i −0.214507 1.21653i −0.881760 0.471699i \(-0.843641\pi\)
0.667252 0.744832i \(-0.267470\pi\)
\(350\) 87.0414i 0.248690i
\(351\) 0 0
\(352\) 23.2726 0.0661154
\(353\) 269.966 47.6023i 0.764777 0.134851i 0.222365 0.974964i \(-0.428622\pi\)
0.542412 + 0.840113i \(0.317511\pi\)
\(354\) 0 0
\(355\) 395.823 144.068i 1.11500 0.405825i
\(356\) 102.855 122.577i 0.288917 0.344318i
\(357\) 0 0
\(358\) −59.1346 21.5233i −0.165181 0.0601208i
\(359\) 40.2168 23.2192i 0.112025 0.0646774i −0.442941 0.896551i \(-0.646065\pi\)
0.554965 + 0.831873i \(0.312731\pi\)
\(360\) 0 0
\(361\) −408.876 + 708.195i −1.13262 + 1.96176i
\(362\) −34.5958 41.2296i −0.0955685 0.113894i
\(363\) 0 0
\(364\) 20.8293 118.129i 0.0572234 0.324530i
\(365\) 278.063 + 49.0300i 0.761816 + 0.134329i
\(366\) 0 0
\(367\) −490.518 + 411.594i −1.33656 + 1.12151i −0.354067 + 0.935220i \(0.615201\pi\)
−0.982495 + 0.186288i \(0.940354\pi\)
\(368\) −127.914 73.8509i −0.347591 0.200682i
\(369\) 0 0
\(370\) −95.4820 165.380i −0.258059 0.446972i
\(371\) −60.8574 + 167.204i −0.164036 + 0.450686i
\(372\) 0 0
\(373\) −3.55616 2.98397i −0.00953393 0.00799992i 0.638008 0.770030i \(-0.279759\pi\)
−0.647542 + 0.762030i \(0.724203\pi\)
\(374\) −9.43713 25.9283i −0.0252330 0.0693270i
\(375\) 0 0
\(376\) −40.7022 230.834i −0.108251 0.613920i
\(377\) 28.9108i 0.0766864i
\(378\) 0 0
\(379\) 259.991 0.685992 0.342996 0.939337i \(-0.388558\pi\)
0.342996 + 0.939337i \(0.388558\pi\)
\(380\) −374.288 + 65.9971i −0.984969 + 0.173677i
\(381\) 0 0
\(382\) 271.755 98.9108i 0.711401 0.258929i
\(383\) 171.274 204.117i 0.447191 0.532942i −0.494609 0.869116i \(-0.664689\pi\)
0.941800 + 0.336174i \(0.109133\pi\)
\(384\) 0 0
\(385\) 233.689 + 85.0559i 0.606985 + 0.220924i
\(386\) −141.897 + 81.9242i −0.367609 + 0.212239i
\(387\) 0 0
\(388\) 47.4830 82.2430i 0.122379 0.211967i
\(389\) −15.2282 18.1483i −0.0391471 0.0466538i 0.746116 0.665816i \(-0.231917\pi\)
−0.785263 + 0.619163i \(0.787472\pi\)
\(390\) 0 0
\(391\) −30.4088 + 172.457i −0.0777718 + 0.441066i
\(392\) −195.740 34.5142i −0.499336 0.0880464i
\(393\) 0 0
\(394\) −95.9574 + 80.5178i −0.243547 + 0.204360i
\(395\) 152.205 + 87.8756i 0.385329 + 0.222470i
\(396\) 0 0
\(397\) 113.459 + 196.518i 0.285792 + 0.495006i 0.972801 0.231643i \(-0.0744100\pi\)
−0.687009 + 0.726649i \(0.741077\pi\)
\(398\) −130.377 + 358.208i −0.327580 + 0.900020i
\(399\) 0 0
\(400\) −17.2685 14.4900i −0.0431713 0.0362251i
\(401\) 175.968 + 483.469i 0.438824 + 1.20566i 0.940258 + 0.340463i \(0.110584\pi\)
−0.501434 + 0.865196i \(0.667194\pi\)
\(402\) 0 0
\(403\) 35.4411 + 200.997i 0.0879432 + 0.498751i
\(404\) 91.2573i 0.225884i
\(405\) 0 0
\(406\) 81.3090 0.200268
\(407\) 98.8427 17.4286i 0.242857 0.0428222i
\(408\) 0 0
\(409\) 260.800 94.9234i 0.637653 0.232087i −0.00290599 0.999996i \(-0.500925\pi\)
0.640559 + 0.767909i \(0.278703\pi\)
\(410\) −115.562 + 137.722i −0.281859 + 0.335907i
\(411\) 0 0
\(412\) −26.7877 9.74992i −0.0650186 0.0236648i
\(413\) −671.782 + 387.854i −1.62659 + 0.939113i
\(414\) 0 0
\(415\) −80.7773 + 139.910i −0.194644 + 0.337134i
\(416\) −19.9686 23.7977i −0.0480015 0.0572060i
\(417\) 0 0
\(418\) 34.6870 196.720i 0.0829833 0.470622i
\(419\) 316.326 + 55.7768i 0.754955 + 0.133119i 0.537863 0.843032i \(-0.319232\pi\)
0.217092 + 0.976151i \(0.430343\pi\)
\(420\) 0 0
\(421\) −101.935 + 85.5332i −0.242125 + 0.203167i −0.755772 0.654834i \(-0.772738\pi\)
0.513648 + 0.858001i \(0.328294\pi\)
\(422\) 172.289 + 99.4711i 0.408268 + 0.235714i
\(423\) 0 0
\(424\) 23.0413 + 39.9087i 0.0543427 + 0.0941244i
\(425\) −9.14105 + 25.1148i −0.0215084 + 0.0590937i
\(426\) 0 0
\(427\) 660.315 + 554.070i 1.54640 + 1.29759i
\(428\) −72.1576 198.251i −0.168592 0.463204i
\(429\) 0 0
\(430\) 69.5402 + 394.382i 0.161721 + 0.917168i
\(431\) 24.4994i 0.0568432i −0.999596 0.0284216i \(-0.990952\pi\)
0.999596 0.0284216i \(-0.00904810\pi\)
\(432\) 0 0
\(433\) −25.7694 −0.0595137 −0.0297568 0.999557i \(-0.509473\pi\)
−0.0297568 + 0.999557i \(0.509473\pi\)
\(434\) 565.285 99.6750i 1.30250 0.229666i
\(435\) 0 0
\(436\) 108.114 39.3501i 0.247967 0.0902526i
\(437\) −814.901 + 971.161i −1.86476 + 2.22234i
\(438\) 0 0
\(439\) 425.746 + 154.959i 0.969809 + 0.352981i 0.777870 0.628425i \(-0.216300\pi\)
0.191939 + 0.981407i \(0.438522\pi\)
\(440\) 55.7775 32.2032i 0.126767 0.0731890i
\(441\) 0 0
\(442\) −18.4159 + 31.8973i −0.0416650 + 0.0721659i
\(443\) 320.772 + 382.281i 0.724090 + 0.862937i 0.995021 0.0996616i \(-0.0317760\pi\)
−0.270931 + 0.962599i \(0.587332\pi\)
\(444\) 0 0
\(445\) 76.8970 436.105i 0.172802 0.980010i
\(446\) 481.402 + 84.8842i 1.07938 + 0.190323i
\(447\) 0 0
\(448\) −66.9288 + 56.1600i −0.149395 + 0.125357i
\(449\) 172.434 + 99.5548i 0.384040 + 0.221726i 0.679575 0.733606i \(-0.262164\pi\)
−0.295534 + 0.955332i \(0.595498\pi\)
\(450\) 0 0
\(451\) −47.2456 81.8317i −0.104757 0.181445i
\(452\) 81.7478 224.600i 0.180858 0.496903i
\(453\) 0 0
\(454\) −199.797 167.650i −0.440081 0.369272i
\(455\) −113.538 311.942i −0.249533 0.685587i
\(456\) 0 0
\(457\) 1.65470 + 9.38428i 0.00362079 + 0.0205345i 0.986565 0.163371i \(-0.0522369\pi\)
−0.982944 + 0.183906i \(0.941126\pi\)
\(458\) 312.529i 0.682377i
\(459\) 0 0
\(460\) −408.761 −0.888610
\(461\) −746.412 + 131.612i −1.61911 + 0.285493i −0.908436 0.418024i \(-0.862723\pi\)
−0.710678 + 0.703517i \(0.751612\pi\)
\(462\) 0 0
\(463\) −598.493 + 217.833i −1.29264 + 0.470483i −0.894593 0.446882i \(-0.852534\pi\)
−0.398048 + 0.917365i \(0.630312\pi\)
\(464\) 13.5357 16.1313i 0.0291718 0.0347656i
\(465\) 0 0
\(466\) 559.130 + 203.507i 1.19985 + 0.436710i
\(467\) 632.615 365.241i 1.35464 0.782100i 0.365742 0.930716i \(-0.380815\pi\)
0.988895 + 0.148617i \(0.0474821\pi\)
\(468\) 0 0
\(469\) 381.010 659.929i 0.812388 1.40710i
\(470\) −416.964 496.919i −0.887158 1.05727i
\(471\) 0 0
\(472\) −34.8854 + 197.845i −0.0739098 + 0.419163i
\(473\) −207.281 36.5492i −0.438226 0.0772711i
\(474\) 0 0
\(475\) −148.220 + 124.371i −0.312042 + 0.261834i
\(476\) 89.7083 + 51.7931i 0.188463 + 0.108809i
\(477\) 0 0
\(478\) −56.3204 97.5497i −0.117825 0.204079i
\(479\) 119.189 327.468i 0.248828 0.683650i −0.750902 0.660414i \(-0.770381\pi\)
0.999730 0.0232359i \(-0.00739687\pi\)
\(480\) 0 0
\(481\) −102.632 86.1184i −0.213372 0.179040i
\(482\) 26.0773 + 71.6469i 0.0541023 + 0.148645i
\(483\) 0 0
\(484\) −36.1447 204.987i −0.0746791 0.423527i
\(485\) 262.816i 0.541889i
\(486\) 0 0
\(487\) −24.8144 −0.0509535 −0.0254768 0.999675i \(-0.508110\pi\)
−0.0254768 + 0.999675i \(0.508110\pi\)
\(488\) 219.849 38.7653i 0.450510 0.0794371i
\(489\) 0 0
\(490\) −516.888 + 188.132i −1.05487 + 0.383943i
\(491\) 357.910 426.541i 0.728941 0.868719i −0.266525 0.963828i \(-0.585876\pi\)
0.995467 + 0.0951093i \(0.0303200\pi\)
\(492\) 0 0
\(493\) −23.4608 8.53904i −0.0475879 0.0173206i
\(494\) −230.921 + 133.322i −0.467451 + 0.269883i
\(495\) 0 0
\(496\) 74.3296 128.743i 0.149858 0.259562i
\(497\) −534.243 636.686i −1.07494 1.28106i
\(498\) 0 0
\(499\) −71.2311 + 403.972i −0.142748 + 0.809562i 0.826400 + 0.563083i \(0.190385\pi\)
−0.969148 + 0.246479i \(0.920726\pi\)
\(500\) 211.105 + 37.2235i 0.422210 + 0.0744470i
\(501\) 0 0
\(502\) −224.239 + 188.159i −0.446692 + 0.374819i
\(503\) 435.156 + 251.237i 0.865121 + 0.499478i 0.865724 0.500522i \(-0.166859\pi\)
−0.000603145 1.00000i \(0.500192\pi\)
\(504\) 0 0
\(505\) −126.276 218.717i −0.250052 0.433102i
\(506\) 73.4789 201.882i 0.145215 0.398976i
\(507\) 0 0
\(508\) −210.987 177.039i −0.415329 0.348503i
\(509\) −40.2964 110.713i −0.0791678 0.217512i 0.893794 0.448478i \(-0.148034\pi\)
−0.972962 + 0.230966i \(0.925811\pi\)
\(510\) 0 0
\(511\) −96.7426 548.654i −0.189320 1.07369i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 288.861 0.561987
\(515\) −77.6934 + 13.6994i −0.150861 + 0.0266008i
\(516\) 0 0
\(517\) 320.375 116.607i 0.619681 0.225546i
\(518\) −242.200 + 288.643i −0.467568 + 0.557226i
\(519\) 0 0
\(520\) −80.7885 29.4046i −0.155363 0.0565474i
\(521\) −0.627494 + 0.362284i −0.00120440 + 0.000695363i −0.500602 0.865678i \(-0.666888\pi\)
0.499398 + 0.866373i \(0.333555\pi\)
\(522\) 0 0
\(523\) 290.424 503.029i 0.555304 0.961814i −0.442576 0.896731i \(-0.645935\pi\)
0.997880 0.0650834i \(-0.0207313\pi\)
\(524\) 82.3881 + 98.1863i 0.157229 + 0.187379i
\(525\) 0 0
\(526\) 46.8225 265.544i 0.0890162 0.504836i
\(527\) −173.575 30.6059i −0.329363 0.0580757i
\(528\) 0 0
\(529\) −639.256 + 536.399i −1.20842 + 1.01399i
\(530\) 110.446 + 63.7662i 0.208389 + 0.120314i
\(531\) 0 0
\(532\) 374.956 + 649.443i 0.704805 + 1.22076i
\(533\) −43.1398 + 118.526i −0.0809377 + 0.222374i
\(534\) 0 0
\(535\) −447.268 375.302i −0.836014 0.701499i
\(536\) −67.4984 185.450i −0.125930 0.345990i
\(537\) 0 0
\(538\) 17.4150 + 98.7653i 0.0323699 + 0.183579i
\(539\) 289.103i 0.536369i
\(540\) 0 0
\(541\) 15.2361 0.0281629 0.0140815 0.999901i \(-0.495518\pi\)
0.0140815 + 0.999901i \(0.495518\pi\)
\(542\) 164.235 28.9590i 0.303016 0.0534300i
\(543\) 0 0
\(544\) 25.2095 9.17550i 0.0463409 0.0168667i
\(545\) 204.666 243.911i 0.375534 0.447543i
\(546\) 0 0
\(547\) −539.917 196.514i −0.987051 0.359257i −0.202473 0.979288i \(-0.564898\pi\)
−0.784578 + 0.620031i \(0.787120\pi\)
\(548\) −132.209 + 76.3307i −0.241257 + 0.139290i
\(549\) 0 0
\(550\) 16.3944 28.3960i 0.0298081 0.0516291i
\(551\) −116.180 138.458i −0.210854 0.251286i
\(552\) 0 0
\(553\) 60.2177 341.512i 0.108893 0.617562i
\(554\) −345.233 60.8739i −0.623164 0.109881i
\(555\) 0 0
\(556\) −163.131 + 136.883i −0.293402 + 0.246193i
\(557\) 276.094 + 159.403i 0.495680 + 0.286181i 0.726928 0.686714i \(-0.240948\pi\)
−0.231248 + 0.972895i \(0.574281\pi\)
\(558\) 0 0
\(559\) 140.480 + 243.318i 0.251305 + 0.435273i
\(560\) −82.6979 + 227.210i −0.147675 + 0.405733i
\(561\) 0 0
\(562\) 77.7668 + 65.2541i 0.138375 + 0.116111i
\(563\) −84.4286 231.966i −0.149962 0.412017i 0.841852 0.539708i \(-0.181466\pi\)
−0.991814 + 0.127691i \(0.959243\pi\)
\(564\) 0 0
\(565\) −114.862 651.417i −0.203296 1.15295i
\(566\) 425.650i 0.752031i
\(567\) 0 0
\(568\) −215.252 −0.378965
\(569\) −165.837 + 29.2415i −0.291454 + 0.0513911i −0.317463 0.948271i \(-0.602831\pi\)
0.0260097 + 0.999662i \(0.491720\pi\)
\(570\) 0 0
\(571\) −605.483 + 220.378i −1.06039 + 0.385951i −0.812575 0.582856i \(-0.801935\pi\)
−0.247816 + 0.968807i \(0.579713\pi\)
\(572\) 29.0451 34.6146i 0.0507782 0.0605151i
\(573\) 0 0
\(574\) 333.343 + 121.327i 0.580736 + 0.211371i
\(575\) −180.218 + 104.049i −0.313422 + 0.180955i
\(576\) 0 0
\(577\) 63.2482 109.549i 0.109616 0.189860i −0.805999 0.591917i \(-0.798371\pi\)
0.915615 + 0.402057i \(0.131705\pi\)
\(578\) 242.267 + 288.723i 0.419147 + 0.499520i
\(579\) 0 0
\(580\) 10.1197 57.3917i 0.0174478 0.0989512i
\(581\) 313.926 + 55.3536i 0.540320 + 0.0952730i
\(582\) 0 0
\(583\) −51.3472 + 43.0854i −0.0880741 + 0.0739029i
\(584\) −124.955 72.1428i −0.213964 0.123532i
\(585\) 0 0
\(586\) −70.9878 122.955i −0.121140 0.209820i
\(587\) 327.703 900.357i 0.558268 1.53383i −0.263881 0.964555i \(-0.585003\pi\)
0.822149 0.569273i \(-0.192775\pi\)
\(588\) 0 0
\(589\) −977.455 820.182i −1.65952 1.39250i
\(590\) 190.155 + 522.448i 0.322297 + 0.885504i
\(591\) 0 0
\(592\) 16.9455 + 96.1025i 0.0286241 + 0.162335i
\(593\) 733.805i 1.23745i −0.785609 0.618723i \(-0.787650\pi\)
0.785609 0.618723i \(-0.212350\pi\)
\(594\) 0 0
\(595\) 286.672 0.481802
\(596\) 168.029 29.6280i 0.281928 0.0497115i
\(597\) 0 0
\(598\) −269.484 + 98.0840i −0.450641 + 0.164020i
\(599\) −727.241 + 866.692i −1.21409 + 1.44690i −0.355162 + 0.934805i \(0.615574\pi\)
−0.858930 + 0.512094i \(0.828870\pi\)
\(600\) 0 0
\(601\) 713.313 + 259.625i 1.18688 + 0.431988i 0.858626 0.512602i \(-0.171318\pi\)
0.328251 + 0.944590i \(0.393541\pi\)
\(602\) 684.309 395.086i 1.13673 0.656289i
\(603\) 0 0
\(604\) −55.4793 + 96.0929i −0.0918531 + 0.159094i
\(605\) −370.276 441.278i −0.612026 0.729384i
\(606\) 0 0
\(607\) 79.5776 451.307i 0.131100 0.743504i −0.846397 0.532553i \(-0.821233\pi\)
0.977497 0.210951i \(-0.0676561\pi\)
\(608\) 191.266 + 33.7254i 0.314582 + 0.0554693i
\(609\) 0 0
\(610\) 473.271 397.122i 0.775855 0.651019i
\(611\) −394.130 227.551i −0.645057 0.372424i
\(612\) 0 0
\(613\) 44.6060 + 77.2599i 0.0727667 + 0.126036i 0.900113 0.435657i \(-0.143484\pi\)
−0.827346 + 0.561692i \(0.810150\pi\)
\(614\) 131.567 361.477i 0.214278 0.588725i
\(615\) 0 0
\(616\) −97.3506 81.6868i −0.158037 0.132608i
\(617\) −185.560 509.821i −0.300745 0.826290i −0.994371 0.105955i \(-0.966210\pi\)
0.693626 0.720335i \(-0.256012\pi\)
\(618\) 0 0
\(619\) 89.2899 + 506.388i 0.144249 + 0.818075i 0.967967 + 0.251076i \(0.0807844\pi\)
−0.823719 + 0.566999i \(0.808104\pi\)
\(620\) 411.410i 0.663565i
\(621\) 0 0
\(622\) 577.721 0.928812
\(623\) −860.491 + 151.728i −1.38121 + 0.243544i
\(624\) 0 0
\(625\) 689.857 251.087i 1.10377 0.401740i
\(626\) −221.281 + 263.713i −0.353485 + 0.421266i
\(627\) 0 0
\(628\) −31.8587 11.5956i −0.0507304 0.0184643i
\(629\) 100.197 57.8490i 0.159296 0.0919698i
\(630\) 0 0
\(631\) 317.732 550.327i 0.503537 0.872151i −0.496455 0.868062i \(-0.665365\pi\)
0.999992 0.00408856i \(-0.00130143\pi\)
\(632\) −57.7294 68.7993i −0.0913440 0.108860i
\(633\) 0 0
\(634\) −66.7342 + 378.469i −0.105259 + 0.596954i
\(635\) −750.649 132.360i −1.18212 0.208440i
\(636\) 0 0
\(637\) −295.625 + 248.059i −0.464090 + 0.389418i
\(638\) 26.5259 + 15.3147i 0.0415766 + 0.0240043i
\(639\) 0 0
\(640\) 31.3104 + 54.2312i 0.0489225 + 0.0847362i
\(641\) −219.882 + 604.121i −0.343030 + 0.942466i 0.641481 + 0.767139i \(0.278320\pi\)
−0.984510 + 0.175327i \(0.943902\pi\)
\(642\) 0 0
\(643\) 499.083 + 418.781i 0.776179 + 0.651292i 0.942283 0.334816i \(-0.108674\pi\)
−0.166104 + 0.986108i \(0.553119\pi\)
\(644\) 275.852 + 757.898i 0.428342 + 1.17686i
\(645\) 0 0
\(646\) −39.9852 226.768i −0.0618966 0.351033i
\(647\) 736.107i 1.13772i 0.822433 + 0.568862i \(0.192616\pi\)
−0.822433 + 0.568862i \(0.807384\pi\)
\(648\) 0 0
\(649\) −292.213 −0.450250
\(650\) −43.1036 + 7.60033i −0.0663132 + 0.0116928i
\(651\) 0 0
\(652\) 433.710 157.858i 0.665199 0.242113i
\(653\) −102.032 + 121.597i −0.156251 + 0.186213i −0.838491 0.544916i \(-0.816562\pi\)
0.682240 + 0.731129i \(0.261006\pi\)
\(654\) 0 0
\(655\) 333.324 + 121.320i 0.508891 + 0.185221i
\(656\) 79.5630 45.9357i 0.121285 0.0700240i
\(657\) 0 0
\(658\) −639.966 + 1108.45i −0.972593 + 1.68458i
\(659\) 813.429 + 969.407i 1.23434 + 1.47103i 0.831281 + 0.555852i \(0.187608\pi\)
0.403057 + 0.915175i \(0.367948\pi\)
\(660\) 0 0
\(661\) −155.505 + 881.911i −0.235257 + 1.33421i 0.606816 + 0.794842i \(0.292447\pi\)
−0.842073 + 0.539364i \(0.818665\pi\)
\(662\) −617.486 108.879i −0.932758 0.164470i
\(663\) 0 0
\(664\) 63.2419 53.0663i 0.0952439 0.0799191i
\(665\) 1797.32 + 1037.68i 2.70273 + 1.56042i
\(666\) 0 0
\(667\) −97.1964 168.349i −0.145722 0.252397i
\(668\) −109.675 + 301.330i −0.164185 + 0.451093i
\(669\) 0 0
\(670\) −418.388 351.069i −0.624460 0.523984i
\(671\) 111.058 + 305.129i 0.165511 + 0.454738i
\(672\) 0 0
\(673\) 198.279 + 1124.50i 0.294620 + 1.67087i 0.668742 + 0.743495i \(0.266833\pi\)
−0.374122 + 0.927380i \(0.622056\pi\)
\(674\) 218.862i 0.324721i
\(675\) 0 0
\(676\) 277.683 0.410773
\(677\) 1228.42 216.603i 1.81450 0.319945i 0.839703 0.543046i \(-0.182729\pi\)
0.974795 + 0.223101i \(0.0716180\pi\)
\(678\) 0 0
\(679\) −487.297 + 177.362i −0.717668 + 0.261210i
\(680\) 47.7231 56.8742i 0.0701811 0.0836385i
\(681\) 0 0
\(682\) 203.190 + 73.9552i 0.297933 + 0.108439i
\(683\) 779.418 449.997i 1.14117 0.658854i 0.194449 0.980913i \(-0.437708\pi\)
0.946720 + 0.322059i \(0.104375\pi\)
\(684\) 0 0
\(685\) −211.243 + 365.884i −0.308384 + 0.534137i
\(686\) 211.184 + 251.679i 0.307848 + 0.366879i
\(687\) 0 0
\(688\) 35.5359 201.534i 0.0516511 0.292928i
\(689\) 88.1149 + 15.5370i 0.127888 + 0.0225501i
\(690\) 0 0
\(691\) −286.646 + 240.525i −0.414828 + 0.348082i −0.826192 0.563389i \(-0.809497\pi\)
0.411363 + 0.911471i \(0.365053\pi\)
\(692\) −549.735 317.390i −0.794415 0.458656i
\(693\) 0 0
\(694\) −148.788 257.709i −0.214392 0.371338i
\(695\) −201.567 + 553.800i −0.290024 + 0.796834i
\(696\) 0 0
\(697\) −83.4406 70.0150i −0.119714 0.100452i
\(698\) 208.528 + 572.925i 0.298750 + 0.820810i
\(699\) 0 0
\(700\) 21.3752 + 121.225i 0.0305361 + 0.173179i
\(701\) 574.292i 0.819247i 0.912255 + 0.409624i \(0.134340\pi\)
−0.912255 + 0.409624i \(0.865660\pi\)
\(702\) 0 0
\(703\) 837.596 1.19146
\(704\) −32.4124 + 5.71519i −0.0460404 + 0.00811816i
\(705\) 0 0
\(706\) −364.300 + 132.594i −0.516005 + 0.187811i
\(707\) −320.313 + 381.734i −0.453059 + 0.539935i
\(708\) 0 0
\(709\) −98.2153 35.7475i −0.138527 0.0504195i 0.271827 0.962346i \(-0.412372\pi\)
−0.410353 + 0.911927i \(0.634595\pi\)
\(710\) −515.895 + 297.852i −0.726613 + 0.419510i
\(711\) 0 0
\(712\) −113.146 + 195.975i −0.158914 + 0.275246i
\(713\) −882.114 1051.26i −1.23719 1.47442i
\(714\) 0 0
\(715\) 21.7150 123.152i 0.0303706 0.172240i
\(716\) 87.6441 + 15.4540i 0.122408 + 0.0215838i
\(717\) 0 0
\(718\) −50.3091 + 42.2143i −0.0700683 + 0.0587943i
\(719\) −960.194 554.368i −1.33546 0.771027i −0.349328 0.937001i \(-0.613590\pi\)
−0.986130 + 0.165974i \(0.946923\pi\)
\(720\) 0 0
\(721\) 77.8320 + 134.809i 0.107950 + 0.186975i
\(722\) 395.539 1086.73i 0.547837 1.50517i
\(723\) 0 0
\(724\) 58.3075 + 48.9258i 0.0805353 + 0.0675771i
\(725\) −10.1472 27.8793i −0.0139962 0.0384542i
\(726\) 0 0
\(727\) −178.676 1013.32i −0.245772 1.39384i −0.818693 0.574232i \(-0.805301\pi\)
0.572921 0.819611i \(-0.305810\pi\)
\(728\) 169.637i 0.233017i
\(729\) 0 0
\(730\) −399.307 −0.546995
\(731\) −238.942 + 42.1319i −0.326870 + 0.0576359i
\(732\) 0 0
\(733\) 315.178 114.715i 0.429984 0.156501i −0.117956 0.993019i \(-0.537634\pi\)
0.547940 + 0.836517i \(0.315412\pi\)
\(734\) 582.081 693.697i 0.793026 0.945092i
\(735\) 0 0
\(736\) 196.285 + 71.4418i 0.266691 + 0.0970677i
\(737\) 248.598 143.528i 0.337311 0.194747i
\(738\) 0 0
\(739\) 130.983 226.869i 0.177244 0.306995i −0.763692 0.645581i \(-0.776615\pi\)
0.940935 + 0.338586i \(0.109949\pi\)
\(740\) 173.594 + 206.881i 0.234586 + 0.279569i
\(741\) 0 0
\(742\) 43.6965 247.815i 0.0588902 0.333983i
\(743\) 477.341 + 84.1680i 0.642450 + 0.113281i 0.485376 0.874305i \(-0.338683\pi\)
0.157074 + 0.987587i \(0.449794\pi\)
\(744\) 0 0
\(745\) 361.718 303.517i 0.485527 0.407406i
\(746\) 5.68555 + 3.28255i 0.00762138 + 0.00440021i
\(747\) 0 0
\(748\) 19.5107 + 33.7936i 0.0260838 + 0.0451785i
\(749\) −394.023 + 1082.57i −0.526065 + 1.44535i
\(750\) 0 0
\(751\) 668.630 + 561.047i 0.890320 + 0.747067i 0.968274 0.249890i \(-0.0803944\pi\)
−0.0779544 + 0.996957i \(0.524839\pi\)
\(752\) 113.374 + 311.493i 0.150764 + 0.414220i
\(753\) 0 0
\(754\) −7.09978 40.2649i −0.00941616 0.0534017i
\(755\) 307.075i 0.406722i
\(756\) 0 0
\(757\) 599.418 0.791834 0.395917 0.918286i \(-0.370427\pi\)
0.395917 + 0.918286i \(0.370427\pi\)
\(758\) −362.097 + 63.8474i −0.477700 + 0.0842314i
\(759\) 0 0
\(760\) 505.075 183.832i 0.664572 0.241884i
\(761\) 754.984 899.755i 0.992094 1.18233i 0.00886470 0.999961i \(-0.497178\pi\)
0.983230 0.182371i \(-0.0583773\pi\)
\(762\) 0 0
\(763\) −590.364 214.875i −0.773740 0.281618i
\(764\) −354.191 + 204.492i −0.463601 + 0.267660i
\(765\) 0 0
\(766\) −188.412 + 326.340i −0.245969 + 0.426031i
\(767\) 250.727 + 298.805i 0.326894 + 0.389577i
\(768\) 0 0
\(769\) −74.9660 + 425.153i −0.0974850 + 0.552865i 0.896473 + 0.443099i \(0.146121\pi\)
−0.993958 + 0.109766i \(0.964990\pi\)
\(770\) −346.353 61.0714i −0.449809 0.0793135i
\(771\) 0 0
\(772\) 177.505 148.945i 0.229929 0.192933i
\(773\) −1315.06 759.248i −1.70124 0.982209i −0.944513 0.328473i \(-0.893466\pi\)
−0.756723 0.653736i \(-0.773201\pi\)
\(774\) 0 0
\(775\) −104.723 181.386i −0.135127 0.234046i
\(776\) −45.9341 + 126.203i −0.0591934 + 0.162633i
\(777\) 0 0
\(778\) 25.6656 + 21.5360i 0.0329892 + 0.0276812i
\(779\) −269.702 740.999i −0.346215 0.951219i
\(780\) 0 0
\(781\) −54.3679 308.336i −0.0696132 0.394796i
\(782\) 247.653i 0.316692i
\(783\) 0 0
\(784\) 281.088 0.358531
\(785\) −92.4010 + 16.2928i −0.117708 + 0.0207551i
\(786\) 0 0
\(787\) 1107.17 402.976i 1.40682 0.512040i 0.476624 0.879107i \(-0.341860\pi\)
0.930195 + 0.367067i \(0.119638\pi\)
\(788\) 113.869 135.704i 0.144504 0.172214i
\(789\) 0 0
\(790\) −233.560 85.0090i −0.295646 0.107606i
\(791\) −1130.30 + 652.580i −1.42895 + 0.825006i
\(792\) 0 0
\(793\) 216.722 375.374i 0.273294 0.473359i
\(794\) −206.278 245.833i −0.259796 0.309613i
\(795\) 0 0
\(796\) 93.6126 530.904i 0.117604 0.666964i
\(797\) 351.259 + 61.9364i 0.440726 + 0.0777119i 0.389608 0.920981i \(-0.372610\pi\)
0.0511179 + 0.998693i \(0.483722\pi\)
\(798\) 0 0
\(799\) 301.065 252.623i 0.376802 0.316174i
\(800\) 27.6088 + 15.9399i 0.0345110 + 0.0199249i
\(801\) 0 0
\(802\) −363.804 630.128i −0.453622 0.785696i
\(803\) 71.7794 197.212i 0.0893891 0.245595i
\(804\) 0 0
\(805\) 1709.87 + 1434.75i 2.12406 + 1.78230i
\(806\) −98.7197 271.230i −0.122481 0.336514i
\(807\) 0 0
\(808\) 22.4106 + 127.097i 0.0277359 + 0.157298i
\(809\) 1097.22i 1.35627i 0.734937 + 0.678135i \(0.237212\pi\)
−0.734937 + 0.678135i \(0.762788\pi\)
\(810\) 0 0
\(811\) −1027.37 −1.26680 −0.633398 0.773826i \(-0.718341\pi\)
−0.633398 + 0.773826i \(0.718341\pi\)
\(812\) −113.241 + 19.9675i −0.139460 + 0.0245905i
\(813\) 0 0
\(814\) −133.381 + 48.5467i −0.163859 + 0.0596397i
\(815\) 821.040 978.478i 1.00741 1.20059i
\(816\) 0 0
\(817\) −1650.57 600.760i −2.02029 0.735324i
\(818\) −339.913 + 196.249i −0.415541 + 0.239913i
\(819\) 0 0
\(820\) 127.126 220.189i 0.155032 0.268523i
\(821\) 595.875 + 710.137i 0.725792 + 0.864966i 0.995180 0.0980663i \(-0.0312657\pi\)
−0.269388 + 0.963032i \(0.586821\pi\)
\(822\) 0 0
\(823\) −47.2612 + 268.032i −0.0574255 + 0.325676i −0.999965 0.00841973i \(-0.997320\pi\)
0.942539 + 0.334096i \(0.108431\pi\)
\(824\) 39.7023 + 7.00059i 0.0481824 + 0.00849586i
\(825\) 0 0
\(826\) 840.363 705.148i 1.01739 0.853690i
\(827\) 623.416 + 359.929i 0.753828 + 0.435223i 0.827075 0.562091i \(-0.190003\pi\)
−0.0732475 + 0.997314i \(0.523336\pi\)
\(828\) 0 0
\(829\) −67.8015 117.436i −0.0817871 0.141659i 0.822231 0.569155i \(-0.192729\pi\)
−0.904018 + 0.427495i \(0.859396\pi\)
\(830\) 78.1423 214.694i 0.0941474 0.258668i
\(831\) 0 0
\(832\) 33.6550 + 28.2399i 0.0404507 + 0.0339422i
\(833\) −113.982 313.163i −0.136833 0.375947i
\(834\) 0 0
\(835\) 154.103 + 873.961i 0.184554 + 1.04666i
\(836\) 282.496i 0.337913i
\(837\) 0 0
\(838\) −454.254 −0.542069
\(839\) −672.509 + 118.582i −0.801561 + 0.141337i −0.559398 0.828899i \(-0.688968\pi\)
−0.242162 + 0.970236i \(0.577857\pi\)
\(840\) 0 0
\(841\) −764.238 + 278.160i −0.908726 + 0.330749i
\(842\) 120.962 144.157i 0.143661 0.171208i
\(843\) 0 0
\(844\) −264.380 96.2263i −0.313246 0.114012i
\(845\) 665.523 384.240i 0.787601 0.454722i
\(846\) 0 0
\(847\) −568.308 + 984.338i −0.670966 + 1.16215i
\(848\) −41.8909 49.9237i −0.0493997 0.0588722i
\(849\) 0 0
\(850\) 6.56341 37.2230i 0.00772166 0.0437917i
\(851\) 887.157 + 156.430i 1.04249 + 0.183819i
\(852\) 0 0
\(853\) 515.666 432.695i 0.604533 0.507263i −0.288366 0.957520i \(-0.593112\pi\)
0.892899 + 0.450257i \(0.148668\pi\)
\(854\) −1055.71 609.512i −1.23619 0.713714i
\(855\) 0 0
\(856\) 149.182 + 258.390i 0.174278 + 0.301858i
\(857\) −266.513 + 732.238i −0.310983 + 0.854420i 0.681476 + 0.731841i \(0.261339\pi\)
−0.992459 + 0.122579i \(0.960884\pi\)
\(858\) 0 0
\(859\) −661.624 555.168i −0.770226 0.646296i 0.170541 0.985351i \(-0.445448\pi\)
−0.940767 + 0.339054i \(0.889893\pi\)
\(860\) −193.701 532.190i −0.225234 0.618826i
\(861\) 0 0
\(862\) 6.01646 + 34.1211i 0.00697966 + 0.0395836i
\(863\) 538.992i 0.624556i −0.949991 0.312278i \(-0.898908\pi\)
0.949991 0.312278i \(-0.101092\pi\)
\(864\) 0 0
\(865\) −1756.73 −2.03091
\(866\) 35.8898 6.32834i 0.0414432 0.00730755i
\(867\) 0 0
\(868\) −762.810 + 277.640i −0.878814 + 0.319862i
\(869\) 83.9697 100.071i 0.0966279 0.115157i
\(870\) 0 0
\(871\) −360.071 131.055i −0.413400 0.150465i
\(872\) −140.909 + 81.3541i −0.161593 + 0.0932960i
\(873\) 0 0
\(874\) 896.442 1552.68i 1.02568 1.77653i
\(875\) −752.409 896.686i −0.859895 1.02478i
\(876\) 0 0
\(877\) −273.081 + 1548.72i −0.311381 + 1.76593i 0.280451 + 0.959868i \(0.409516\pi\)
−0.591832 + 0.806061i \(0.701595\pi\)
\(878\) −631.003 111.263i −0.718682 0.126723i
\(879\) 0 0
\(880\) −69.7746 + 58.5479i −0.0792893 + 0.0665317i
\(881\) −399.139 230.443i −0.453052 0.261570i 0.256066 0.966659i \(-0.417573\pi\)
−0.709118 + 0.705090i \(0.750907\pi\)
\(882\) 0 0
\(883\) −225.254 390.151i −0.255101 0.441848i 0.709822 0.704381i \(-0.248775\pi\)
−0.964923 + 0.262533i \(0.915442\pi\)
\(884\) 17.8152 48.9468i 0.0201529 0.0553697i
\(885\) 0 0
\(886\) −540.627 453.640i −0.610189 0.512009i
\(887\) 183.324 + 503.678i 0.206679 + 0.567845i 0.999113 0.0421126i \(-0.0134088\pi\)
−0.792434 + 0.609957i \(0.791187\pi\)
\(888\) 0 0
\(889\) 261.163 + 1481.13i 0.293772 + 1.66606i
\(890\) 626.259i 0.703662i
\(891\) 0 0
\(892\) −691.308 −0.775009
\(893\) 2801.98 494.066i 3.13772 0.553265i
\(894\) 0 0
\(895\) 231.441 84.2376i 0.258593 0.0941203i
\(896\) 79.4222 94.6517i 0.0886408 0.105638i
\(897\) 0 0
\(898\) −264.602 96.3073i −0.294657 0.107246i
\(899\) 169.440 97.8263i 0.188476 0.108817i
\(900\) 0 0
\(901\) −38.6336 + 66.9154i −0.0428786 + 0.0742679i
\(902\) 85.8961 + 102.367i 0.0952285 + 0.113489i
\(903\) 0 0
\(904\) −58.6961 + 332.882i −0.0649293 + 0.368233i
\(905\) 207.446 + 36.5784i 0.229222 + 0.0404181i
\(906\) 0 0
\(907\) 1035.69 869.048i 1.14189 0.958157i 0.142388 0.989811i \(-0.454522\pi\)
0.999499 + 0.0316538i \(0.0100774\pi\)
\(908\) 319.434 + 184.425i 0.351799 + 0.203111i
\(909\) 0 0
\(910\) 234.732 + 406.569i 0.257948 + 0.446779i
\(911\) 589.249 1618.95i 0.646816 1.77711i 0.0176469 0.999844i \(-0.494383\pi\)
0.629169 0.777268i \(-0.283395\pi\)
\(912\) 0 0
\(913\) 91.9879 + 77.1870i 0.100753 + 0.0845421i
\(914\) −4.60910 12.6634i −0.00504278 0.0138549i
\(915\) 0 0
\(916\) −76.7494 435.267i −0.0837875 0.475183i
\(917\) 699.901i 0.763250i
\(918\) 0 0
\(919\) −1327.65 −1.44467 −0.722336 0.691542i \(-0.756932\pi\)
−0.722336 + 0.691542i \(0.756932\pi\)
\(920\) 569.293 100.382i 0.618796 0.109110i
\(921\) 0 0
\(922\) 1007.23 366.601i 1.09244 0.397615i
\(923\) −268.643 + 320.156i −0.291054 + 0.346865i
\(924\) 0 0
\(925\) 129.196 + 47.0236i 0.139672 + 0.0508364i
\(926\) 780.043 450.358i 0.842379 0.486348i
\(927\) 0 0
\(928\) −14.8902 + 25.7905i −0.0160454 + 0.0277915i
\(929\) 1056.80 + 1259.44i 1.13757 + 1.35570i 0.925636 + 0.378414i \(0.123531\pi\)
0.211930 + 0.977285i \(0.432025\pi\)
\(930\) 0 0
\(931\) 418.952 2375.99i 0.450002 2.55209i
\(932\) −828.693 146.121i −0.889155 0.156782i
\(933\) 0 0
\(934\) −791.367 + 664.036i −0.847288 + 0.710959i
\(935\) 93.5227 + 53.9954i 0.100024 + 0.0577491i
\(936\) 0 0
\(937\) 269.132 + 466.150i 0.287227 + 0.497492i 0.973147 0.230185i \(-0.0739332\pi\)
−0.685920 + 0.727677i \(0.740600\pi\)
\(938\) −368.581 + 1012.67i −0.392944 + 1.07960i
\(939\) 0 0
\(940\) 702.749 + 589.676i 0.747605 + 0.627315i
\(941\) −408.125 1121.31i −0.433714 1.19162i −0.943516 0.331327i \(-0.892504\pi\)
0.509802 0.860292i \(-0.329719\pi\)
\(942\) 0 0
\(943\) −147.271 835.214i −0.156173 0.885699i
\(944\) 284.111i 0.300965i
\(945\) 0 0
\(946\) 297.662 0.314653
\(947\) −1715.44 + 302.478i −1.81145 + 0.319407i −0.973903 0.226965i \(-0.927120\pi\)
−0.837543 + 0.546372i \(0.816009\pi\)
\(948\) 0 0
\(949\) −263.251 + 95.8154i −0.277398 + 0.100965i
\(950\) 175.888 209.615i 0.185145 0.220647i
\(951\) 0 0
\(952\) −137.659 50.1036i −0.144599 0.0526298i
\(953\) −264.703 + 152.826i −0.277758 + 0.160364i −0.632408 0.774636i \(-0.717933\pi\)
0.354650 + 0.934999i \(0.384600\pi\)
\(954\) 0 0
\(955\) −565.927 + 980.214i −0.592594 + 1.02640i
\(956\) 102.395 + 122.029i 0.107108 + 0.127646i
\(957\) 0 0
\(958\) −85.5793 + 485.344i −0.0893312 + 0.506622i
\(959\) 820.956 + 144.757i 0.856054 + 0.150945i
\(960\) 0 0
\(961\) 321.908 270.113i 0.334972 0.281075i
\(962\) 164.087 + 94.7357i 0.170569 + 0.0984779i
\(963\) 0 0
\(964\) −53.9134 93.3807i −0.0559267 0.0968679i
\(965\) 219.327 602.596i 0.227282 0.624452i
\(966\) 0 0
\(967\) −340.677 285.862i −0.352303 0.295617i 0.449411 0.893325i \(-0.351634\pi\)
−0.801714 + 0.597708i \(0.796078\pi\)
\(968\) 100.680 + 276.615i 0.104008 + 0.285759i
\(969\) 0 0
\(970\) 64.5412 + 366.031i 0.0665373 + 0.377352i
\(971\) 455.670i 0.469279i 0.972083 + 0.234639i \(0.0753909\pi\)
−0.972083 + 0.234639i \(0.924609\pi\)
\(972\) 0 0
\(973\) 1162.85 1.19512
\(974\) 34.5597 6.09381i 0.0354822 0.00625647i
\(975\) 0 0
\(976\) −296.670 + 107.979i −0.303965 + 0.110634i
\(977\) −1075.29 + 1281.49i −1.10061 + 1.31165i −0.154432 + 0.988003i \(0.549355\pi\)
−0.946176 + 0.323651i \(0.895090\pi\)
\(978\) 0 0
\(979\) −309.301 112.577i −0.315936 0.114991i
\(980\) 673.684 388.952i 0.687433 0.396889i
\(981\) 0 0
\(982\) −393.724 + 681.950i −0.400941 + 0.694450i
\(983\) −145.881 173.854i −0.148403 0.176860i 0.686722 0.726921i \(-0.259049\pi\)
−0.835125 + 0.550060i \(0.814605\pi\)
\(984\) 0 0
\(985\) 85.1321 482.808i 0.0864285 0.490160i
\(986\) 34.7715 + 6.13116i 0.0352652 + 0.00621821i
\(987\) 0 0
\(988\) 288.869 242.390i 0.292378 0.245334i
\(989\) −1636.04 944.568i −1.65424 0.955074i
\(990\) 0 0
\(991\) 76.9538 + 133.288i 0.0776527 + 0.134498i 0.902237 0.431241i \(-0.141924\pi\)
−0.824584 + 0.565739i \(0.808591\pi\)
\(992\) −71.9049 + 197.557i −0.0724847 + 0.199150i
\(993\) 0 0
\(994\) 900.411 + 755.534i 0.905846 + 0.760095i
\(995\) −510.269 1401.95i −0.512833 1.40900i
\(996\) 0 0
\(997\) −183.930 1043.12i −0.184483 1.04626i −0.926617 0.376005i \(-0.877297\pi\)
0.742134 0.670251i \(-0.233814\pi\)
\(998\) 580.115i 0.581278i
\(999\) 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 162.3.f.a.71.3 36
3.2 odd 2 54.3.f.a.41.6 yes 36
12.11 even 2 432.3.bc.c.257.1 36
27.2 odd 18 inner 162.3.f.a.89.3 36
27.5 odd 18 1458.3.b.c.1457.15 36
27.22 even 9 1458.3.b.c.1457.22 36
27.25 even 9 54.3.f.a.29.6 36
108.79 odd 18 432.3.bc.c.353.1 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.29.6 36 27.25 even 9
54.3.f.a.41.6 yes 36 3.2 odd 2
162.3.f.a.71.3 36 1.1 even 1 trivial
162.3.f.a.89.3 36 27.2 odd 18 inner
432.3.bc.c.257.1 36 12.11 even 2
432.3.bc.c.353.1 36 108.79 odd 18
1458.3.b.c.1457.15 36 27.5 odd 18
1458.3.b.c.1457.22 36 27.22 even 9