Properties

Label 810.2.s.a.557.14
Level $810$
Weight $2$
Character 810.557
Analytic conductor $6.468$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [810,2,Mod(17,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([22, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.s (of order \(36\), degree \(12\), 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: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 557.14
Character \(\chi\) \(=\) 810.557
Dual form 810.2.s.a.413.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-0.160152 + 2.23033i) q^{5} +(1.92341 + 4.12477i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\) \(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-0.160152 + 2.23033i) q^{5} +(1.92341 + 4.12477i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.41045 + 1.73512i) q^{10} +(0.0108394 + 0.0129179i) q^{11} +(-1.70362 - 2.43302i) q^{13} +(-0.790304 + 4.48203i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.126008 - 0.470270i) q^{17} +(2.44011 - 1.40880i) q^{19} +(-2.15060 + 0.612323i) q^{20} +(0.00146971 + 0.0167989i) q^{22} +(-5.98777 - 2.79214i) q^{23} +(-4.94870 - 0.714382i) q^{25} -2.97017i q^{26} +(-3.21817 + 3.21817i) q^{28} +(1.01729 + 5.76933i) q^{29} +(-4.13283 + 1.50423i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(0.166516 - 0.457498i) q^{34} +(-9.50761 + 3.62924i) q^{35} +(9.53706 - 2.55545i) q^{37} +(2.80687 + 0.245569i) q^{38} +(-2.11288 - 0.731946i) q^{40} +(9.02018 + 1.59050i) q^{41} +(0.278251 - 3.18042i) q^{43} +(-0.00843154 + 0.0146039i) q^{44} +(-3.30339 - 5.72164i) q^{46} +(2.19479 - 1.02345i) q^{47} +(-8.81468 + 10.5049i) q^{49} +(-3.64399 - 3.42365i) q^{50} +(1.70362 - 2.43302i) q^{52} +(2.06177 + 2.06177i) q^{53} +(-0.0305470 + 0.0221065i) q^{55} +(-4.48203 + 0.790304i) q^{56} +(-2.47584 + 5.30945i) q^{58} +(10.6270 + 8.91708i) q^{59} +(-5.02715 - 1.82973i) q^{61} +(-4.24821 - 1.13830i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(5.69927 - 3.40998i) q^{65} +(-8.68053 + 6.07817i) q^{67} +(0.398812 - 0.279251i) q^{68} +(-9.86983 - 2.48044i) q^{70} +(12.0016 + 6.92911i) q^{71} +(2.59443 + 0.695176i) q^{73} +(9.27805 + 3.37693i) q^{74} +(2.15840 + 1.81111i) q^{76} +(-0.0324346 + 0.0695563i) q^{77} +(5.13381 - 0.905230i) q^{79} +(-1.31094 - 1.81147i) q^{80} +(6.47662 + 6.47662i) q^{82} +(2.30261 - 3.28847i) q^{83} +(1.06904 - 0.205725i) q^{85} +(2.05214 - 2.44565i) q^{86} +(-0.0152831 + 0.00712665i) q^{88} +(-8.88641 - 15.3917i) q^{89} +(6.75889 - 11.7067i) q^{91} +(0.575818 - 6.58163i) q^{92} +(2.38489 + 0.420520i) q^{94} +(2.75129 + 5.66785i) q^{95} +(-14.2908 - 1.25028i) q^{97} +(-13.2459 + 3.54924i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.819152 + 0.573576i 0.579228 + 0.405580i
\(3\) 0 0
\(4\) 0.342020 + 0.939693i 0.171010 + 0.469846i
\(5\) −0.160152 + 2.23033i −0.0716221 + 0.997432i
\(6\) 0 0
\(7\) 1.92341 + 4.12477i 0.726981 + 1.55902i 0.825834 + 0.563913i \(0.190705\pi\)
−0.0988531 + 0.995102i \(0.531517\pi\)
\(8\) −0.258819 + 0.965926i −0.0915064 + 0.341506i
\(9\) 0 0
\(10\) −1.41045 + 1.73512i −0.446024 + 0.548692i
\(11\) 0.0108394 + 0.0129179i 0.00326820 + 0.00389489i 0.767676 0.640838i \(-0.221413\pi\)
−0.764408 + 0.644733i \(0.776969\pi\)
\(12\) 0 0
\(13\) −1.70362 2.43302i −0.472499 0.674799i 0.510190 0.860062i \(-0.329575\pi\)
−0.982689 + 0.185263i \(0.940686\pi\)
\(14\) −0.790304 + 4.48203i −0.211218 + 1.19787i
\(15\) 0 0
\(16\) −0.766044 + 0.642788i −0.191511 + 0.160697i
\(17\) −0.126008 0.470270i −0.0305615 0.114057i 0.948960 0.315396i \(-0.102137\pi\)
−0.979522 + 0.201339i \(0.935471\pi\)
\(18\) 0 0
\(19\) 2.44011 1.40880i 0.559799 0.323200i −0.193266 0.981146i \(-0.561908\pi\)
0.753065 + 0.657946i \(0.228575\pi\)
\(20\) −2.15060 + 0.612323i −0.480888 + 0.136919i
\(21\) 0 0
\(22\) 0.00146971 + 0.0167989i 0.000313344 + 0.00358154i
\(23\) −5.98777 2.79214i −1.24854 0.582202i −0.317892 0.948127i \(-0.602975\pi\)
−0.930645 + 0.365925i \(0.880753\pi\)
\(24\) 0 0
\(25\) −4.94870 0.714382i −0.989741 0.142876i
\(26\) 2.97017i 0.582499i
\(27\) 0 0
\(28\) −3.21817 + 3.21817i −0.608177 + 0.608177i
\(29\) 1.01729 + 5.76933i 0.188906 + 1.07134i 0.920834 + 0.389956i \(0.127510\pi\)
−0.731928 + 0.681382i \(0.761379\pi\)
\(30\) 0 0
\(31\) −4.13283 + 1.50423i −0.742279 + 0.270167i −0.685353 0.728211i \(-0.740352\pi\)
−0.0569257 + 0.998378i \(0.518130\pi\)
\(32\) −0.996195 + 0.0871557i −0.176104 + 0.0154071i
\(33\) 0 0
\(34\) 0.166516 0.457498i 0.0285572 0.0784602i
\(35\) −9.50761 + 3.62924i −1.60708 + 0.613454i
\(36\) 0 0
\(37\) 9.53706 2.55545i 1.56788 0.420113i 0.632734 0.774369i \(-0.281933\pi\)
0.935148 + 0.354256i \(0.115266\pi\)
\(38\) 2.80687 + 0.245569i 0.455335 + 0.0398366i
\(39\) 0 0
\(40\) −2.11288 0.731946i −0.334075 0.115731i
\(41\) 9.02018 + 1.59050i 1.40871 + 0.248394i 0.825719 0.564081i \(-0.190769\pi\)
0.582995 + 0.812475i \(0.301881\pi\)
\(42\) 0 0
\(43\) 0.278251 3.18042i 0.0424328 0.485010i −0.945011 0.327039i \(-0.893949\pi\)
0.987444 0.157971i \(-0.0504952\pi\)
\(44\) −0.00843154 + 0.0146039i −0.00127110 + 0.00220162i
\(45\) 0 0
\(46\) −3.30339 5.72164i −0.487058 0.843609i
\(47\) 2.19479 1.02345i 0.320143 0.149285i −0.255903 0.966702i \(-0.582373\pi\)
0.576046 + 0.817417i \(0.304595\pi\)
\(48\) 0 0
\(49\) −8.81468 + 10.5049i −1.25924 + 1.50070i
\(50\) −3.64399 3.42365i −0.515338 0.484177i
\(51\) 0 0
\(52\) 1.70362 2.43302i 0.236250 0.337400i
\(53\) 2.06177 + 2.06177i 0.283206 + 0.283206i 0.834386 0.551180i \(-0.185822\pi\)
−0.551180 + 0.834386i \(0.685822\pi\)
\(54\) 0 0
\(55\) −0.0305470 + 0.0221065i −0.00411896 + 0.00298084i
\(56\) −4.48203 + 0.790304i −0.598937 + 0.105609i
\(57\) 0 0
\(58\) −2.47584 + 5.30945i −0.325093 + 0.697165i
\(59\) 10.6270 + 8.91708i 1.38351 + 1.16090i 0.967892 + 0.251366i \(0.0808799\pi\)
0.415620 + 0.909538i \(0.363565\pi\)
\(60\) 0 0
\(61\) −5.02715 1.82973i −0.643660 0.234273i −0.000494160 1.00000i \(-0.500157\pi\)
−0.643166 + 0.765727i \(0.722380\pi\)
\(62\) −4.24821 1.13830i −0.539523 0.144565i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) 5.69927 3.40998i 0.706907 0.422955i
\(66\) 0 0
\(67\) −8.68053 + 6.07817i −1.06050 + 0.742567i −0.967442 0.253094i \(-0.918552\pi\)
−0.0930537 + 0.995661i \(0.529663\pi\)
\(68\) 0.398812 0.279251i 0.0483630 0.0338641i
\(69\) 0 0
\(70\) −9.86983 2.48044i −1.17967 0.296469i
\(71\) 12.0016 + 6.92911i 1.42433 + 0.822335i 0.996665 0.0816050i \(-0.0260046\pi\)
0.427660 + 0.903939i \(0.359338\pi\)
\(72\) 0 0
\(73\) 2.59443 + 0.695176i 0.303655 + 0.0813641i 0.407429 0.913237i \(-0.366425\pi\)
−0.103774 + 0.994601i \(0.533092\pi\)
\(74\) 9.27805 + 3.37693i 1.07855 + 0.392560i
\(75\) 0 0
\(76\) 2.15840 + 1.81111i 0.247586 + 0.207749i
\(77\) −0.0324346 + 0.0695563i −0.00369627 + 0.00792668i
\(78\) 0 0
\(79\) 5.13381 0.905230i 0.577599 0.101846i 0.122786 0.992433i \(-0.460817\pi\)
0.454813 + 0.890587i \(0.349706\pi\)
\(80\) −1.31094 1.81147i −0.146568 0.202529i
\(81\) 0 0
\(82\) 6.47662 + 6.47662i 0.715223 + 0.715223i
\(83\) 2.30261 3.28847i 0.252744 0.360956i −0.672651 0.739960i \(-0.734844\pi\)
0.925395 + 0.379004i \(0.123733\pi\)
\(84\) 0 0
\(85\) 1.06904 0.205725i 0.115953 0.0223140i
\(86\) 2.05214 2.44565i 0.221288 0.263721i
\(87\) 0 0
\(88\) −0.0152831 + 0.00712665i −0.00162919 + 0.000759703i
\(89\) −8.88641 15.3917i −0.941957 1.63152i −0.761731 0.647893i \(-0.775650\pi\)
−0.180226 0.983625i \(-0.557683\pi\)
\(90\) 0 0
\(91\) 6.75889 11.7067i 0.708524 1.22720i
\(92\) 0.575818 6.58163i 0.0600332 0.686183i
\(93\) 0 0
\(94\) 2.38489 + 0.420520i 0.245983 + 0.0433734i
\(95\) 2.75129 + 5.66785i 0.282276 + 0.581510i
\(96\) 0 0
\(97\) −14.2908 1.25028i −1.45101 0.126947i −0.665779 0.746149i \(-0.731901\pi\)
−0.785232 + 0.619202i \(0.787456\pi\)
\(98\) −13.2459 + 3.54924i −1.33804 + 0.358527i
\(99\) 0 0
\(100\) −1.02126 4.89459i −0.102126 0.489459i
\(101\) 0.426678 1.17229i 0.0424560 0.116647i −0.916653 0.399684i \(-0.869120\pi\)
0.959109 + 0.283037i \(0.0913420\pi\)
\(102\) 0 0
\(103\) 13.9527 1.22071i 1.37480 0.120280i 0.624321 0.781168i \(-0.285376\pi\)
0.750484 + 0.660888i \(0.229820\pi\)
\(104\) 2.79105 1.01586i 0.273685 0.0996131i
\(105\) 0 0
\(106\) 0.506320 + 2.87149i 0.0491782 + 0.278903i
\(107\) −3.96046 + 3.96046i −0.382872 + 0.382872i −0.872136 0.489264i \(-0.837266\pi\)
0.489264 + 0.872136i \(0.337266\pi\)
\(108\) 0 0
\(109\) 12.5627i 1.20329i −0.798765 0.601643i \(-0.794513\pi\)
0.798765 0.601643i \(-0.205487\pi\)
\(110\) −0.0377024 0.000587563i −0.00359479 5.60219e-5i
\(111\) 0 0
\(112\) −4.12477 1.92341i −0.389754 0.181745i
\(113\) −0.170254 1.94601i −0.0160162 0.183066i −0.999989 0.00474575i \(-0.998489\pi\)
0.983973 0.178320i \(-0.0570662\pi\)
\(114\) 0 0
\(115\) 7.18634 12.9075i 0.670130 1.20363i
\(116\) −5.07346 + 2.92917i −0.471059 + 0.271966i
\(117\) 0 0
\(118\) 3.59047 + 13.3998i 0.330530 + 1.23355i
\(119\) 1.69739 1.42428i 0.155599 0.130563i
\(120\) 0 0
\(121\) 1.91008 10.8326i 0.173644 0.984782i
\(122\) −3.06851 4.38228i −0.277810 0.396753i
\(123\) 0 0
\(124\) −2.82702 3.36912i −0.253874 0.302556i
\(125\) 2.38585 10.9228i 0.213397 0.976966i
\(126\) 0 0
\(127\) 2.78606 10.3977i 0.247223 0.922650i −0.725030 0.688718i \(-0.758174\pi\)
0.972253 0.233932i \(-0.0751593\pi\)
\(128\) −0.422618 0.906308i −0.0373545 0.0801070i
\(129\) 0 0
\(130\) 6.62445 + 0.475679i 0.581003 + 0.0417198i
\(131\) 1.52146 + 4.18019i 0.132931 + 0.365225i 0.988244 0.152887i \(-0.0488572\pi\)
−0.855313 + 0.518112i \(0.826635\pi\)
\(132\) 0 0
\(133\) 10.5043 + 7.35518i 0.910837 + 0.637775i
\(134\) −10.5970 −0.915439
\(135\) 0 0
\(136\) 0.486859 0.0417478
\(137\) −5.44092 3.80978i −0.464849 0.325491i 0.317579 0.948232i \(-0.397130\pi\)
−0.782428 + 0.622741i \(0.786019\pi\)
\(138\) 0 0
\(139\) 5.41440 + 14.8760i 0.459244 + 1.26176i 0.926050 + 0.377402i \(0.123183\pi\)
−0.466806 + 0.884360i \(0.654595\pi\)
\(140\) −6.66217 7.69296i −0.563056 0.650174i
\(141\) 0 0
\(142\) 5.85674 + 12.5598i 0.491487 + 1.05400i
\(143\) 0.0129633 0.0483796i 0.00108404 0.00404571i
\(144\) 0 0
\(145\) −13.0304 + 1.34492i −1.08212 + 0.111689i
\(146\) 1.72650 + 2.05756i 0.142886 + 0.170285i
\(147\) 0 0
\(148\) 5.66320 + 8.08789i 0.465512 + 0.664820i
\(149\) −0.486168 + 2.75720i −0.0398284 + 0.225878i −0.998225 0.0595633i \(-0.981029\pi\)
0.958396 + 0.285442i \(0.0921403\pi\)
\(150\) 0 0
\(151\) 8.42506 7.06946i 0.685621 0.575305i −0.232022 0.972711i \(-0.574534\pi\)
0.917643 + 0.397406i \(0.130090\pi\)
\(152\) 0.729247 + 2.72159i 0.0591497 + 0.220750i
\(153\) 0 0
\(154\) −0.0664648 + 0.0383734i −0.00535588 + 0.00309222i
\(155\) −2.69304 9.45847i −0.216310 0.759722i
\(156\) 0 0
\(157\) 1.07934 + 12.3369i 0.0861406 + 0.984591i 0.909124 + 0.416526i \(0.136752\pi\)
−0.822983 + 0.568065i \(0.807692\pi\)
\(158\) 4.72459 + 2.20311i 0.375868 + 0.175270i
\(159\) 0 0
\(160\) −0.0348431 2.23580i −0.00275459 0.176755i
\(161\) 30.0686i 2.36974i
\(162\) 0 0
\(163\) −4.90931 + 4.90931i −0.384527 + 0.384527i −0.872730 0.488203i \(-0.837653\pi\)
0.488203 + 0.872730i \(0.337653\pi\)
\(164\) 1.59050 + 9.02018i 0.124197 + 0.704357i
\(165\) 0 0
\(166\) 3.77238 1.37303i 0.292793 0.106568i
\(167\) 1.25729 0.109998i 0.0972918 0.00851193i −0.0384059 0.999262i \(-0.512228\pi\)
0.135698 + 0.990750i \(0.456672\pi\)
\(168\) 0 0
\(169\) 1.42899 3.92611i 0.109922 0.302008i
\(170\) 0.993701 + 0.444653i 0.0762134 + 0.0341033i
\(171\) 0 0
\(172\) 3.08378 0.826298i 0.235136 0.0630046i
\(173\) −2.02886 0.177502i −0.154251 0.0134952i 0.00976850 0.999952i \(-0.496891\pi\)
−0.164020 + 0.986457i \(0.552446\pi\)
\(174\) 0 0
\(175\) −6.57173 21.7863i −0.496776 1.64689i
\(176\) −0.0166069 0.00292824i −0.00125179 0.000220725i
\(177\) 0 0
\(178\) 1.54900 17.7052i 0.116103 1.32706i
\(179\) −0.264092 + 0.457421i −0.0197392 + 0.0341892i −0.875726 0.482808i \(-0.839617\pi\)
0.855987 + 0.516997i \(0.172950\pi\)
\(180\) 0 0
\(181\) 8.76525 + 15.1819i 0.651516 + 1.12846i 0.982755 + 0.184911i \(0.0591998\pi\)
−0.331240 + 0.943547i \(0.607467\pi\)
\(182\) 12.2513 5.71286i 0.908124 0.423465i
\(183\) 0 0
\(184\) 4.24675 5.06108i 0.313075 0.373108i
\(185\) 4.17210 + 21.6800i 0.306739 + 1.59395i
\(186\) 0 0
\(187\) 0.00470903 0.00672519i 0.000344359 0.000491795i
\(188\) 1.71239 + 1.71239i 0.124889 + 0.124889i
\(189\) 0 0
\(190\) −0.997226 + 6.22091i −0.0723464 + 0.451312i
\(191\) 16.1961 2.85581i 1.17191 0.206639i 0.446388 0.894840i \(-0.352710\pi\)
0.725520 + 0.688201i \(0.241599\pi\)
\(192\) 0 0
\(193\) 0.754386 1.61779i 0.0543019 0.116451i −0.877285 0.479971i \(-0.840647\pi\)
0.931586 + 0.363520i \(0.118425\pi\)
\(194\) −10.9892 9.22103i −0.788979 0.662032i
\(195\) 0 0
\(196\) −12.8862 4.69019i −0.920443 0.335014i
\(197\) −18.2169 4.88120i −1.29790 0.347771i −0.457243 0.889342i \(-0.651163\pi\)
−0.840655 + 0.541571i \(0.817830\pi\)
\(198\) 0 0
\(199\) 19.5744 + 11.3013i 1.38759 + 0.801126i 0.993043 0.117750i \(-0.0375682\pi\)
0.394547 + 0.918876i \(0.370902\pi\)
\(200\) 1.97086 4.59518i 0.139361 0.324929i
\(201\) 0 0
\(202\) 1.02191 0.715549i 0.0719014 0.0503459i
\(203\) −21.8405 + 15.2929i −1.53290 + 1.07335i
\(204\) 0 0
\(205\) −4.99193 + 19.8632i −0.348652 + 1.38731i
\(206\) 12.1296 + 7.00302i 0.845108 + 0.487924i
\(207\) 0 0
\(208\) 2.86897 + 0.768737i 0.198927 + 0.0533023i
\(209\) 0.0446479 + 0.0162505i 0.00308836 + 0.00112407i
\(210\) 0 0
\(211\) −1.02102 0.856741i −0.0702902 0.0589805i 0.606966 0.794728i \(-0.292387\pi\)
−0.677256 + 0.735748i \(0.736831\pi\)
\(212\) −1.23226 + 2.64260i −0.0846322 + 0.181494i
\(213\) 0 0
\(214\) −5.51585 + 0.972593i −0.377056 + 0.0664851i
\(215\) 7.04881 + 1.12994i 0.480725 + 0.0770613i
\(216\) 0 0
\(217\) −14.1537 14.1537i −0.960817 0.960817i
\(218\) 7.20565 10.2907i 0.488029 0.696977i
\(219\) 0 0
\(220\) −0.0312210 0.0211439i −0.00210492 0.00142552i
\(221\) −0.929506 + 1.10774i −0.0625254 + 0.0745148i
\(222\) 0 0
\(223\) 3.08091 1.43665i 0.206313 0.0962052i −0.316715 0.948521i \(-0.602580\pi\)
0.523028 + 0.852315i \(0.324802\pi\)
\(224\) −2.27559 3.94143i −0.152044 0.263348i
\(225\) 0 0
\(226\) 0.976724 1.69174i 0.0649707 0.112533i
\(227\) −0.671589 + 7.67630i −0.0445749 + 0.509494i 0.940785 + 0.339005i \(0.110090\pi\)
−0.985360 + 0.170489i \(0.945465\pi\)
\(228\) 0 0
\(229\) 3.17958 + 0.560647i 0.210113 + 0.0370486i 0.277714 0.960664i \(-0.410423\pi\)
−0.0676009 + 0.997712i \(0.521534\pi\)
\(230\) 13.2902 6.45130i 0.876327 0.425386i
\(231\) 0 0
\(232\) −5.83604 0.510587i −0.383155 0.0335217i
\(233\) 20.7700 5.56531i 1.36069 0.364595i 0.496619 0.867968i \(-0.334574\pi\)
0.864069 + 0.503373i \(0.167908\pi\)
\(234\) 0 0
\(235\) 1.93112 + 5.05900i 0.125972 + 0.330013i
\(236\) −4.74468 + 13.0359i −0.308852 + 0.848564i
\(237\) 0 0
\(238\) 2.20735 0.193118i 0.143081 0.0125180i
\(239\) −13.1835 + 4.79841i −0.852771 + 0.310383i −0.731169 0.682196i \(-0.761025\pi\)
−0.121601 + 0.992579i \(0.538803\pi\)
\(240\) 0 0
\(241\) −1.17662 6.67294i −0.0757928 0.429842i −0.998966 0.0454585i \(-0.985525\pi\)
0.923173 0.384384i \(-0.125586\pi\)
\(242\) 7.77797 7.77797i 0.499987 0.499987i
\(243\) 0 0
\(244\) 5.34978i 0.342484i
\(245\) −22.0177 21.3420i −1.40666 1.36349i
\(246\) 0 0
\(247\) −7.58465 3.53678i −0.482600 0.225040i
\(248\) −0.383317 4.38133i −0.0243407 0.278215i
\(249\) 0 0
\(250\) 8.21944 7.57897i 0.519843 0.479336i
\(251\) −0.317436 + 0.183272i −0.0200364 + 0.0115680i −0.509985 0.860183i \(-0.670349\pi\)
0.489948 + 0.871751i \(0.337016\pi\)
\(252\) 0 0
\(253\) −0.0288352 0.107614i −0.00181285 0.00676566i
\(254\) 8.24610 6.91930i 0.517407 0.434156i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −6.69084 9.55551i −0.417363 0.596056i 0.554332 0.832296i \(-0.312974\pi\)
−0.971695 + 0.236240i \(0.924085\pi\)
\(258\) 0 0
\(259\) 28.8843 + 34.4230i 1.79478 + 2.13894i
\(260\) 5.15359 + 4.18928i 0.319612 + 0.259808i
\(261\) 0 0
\(262\) −1.15135 + 4.29689i −0.0711304 + 0.265462i
\(263\) −2.74490 5.88645i −0.169258 0.362974i 0.803322 0.595545i \(-0.203064\pi\)
−0.972579 + 0.232571i \(0.925286\pi\)
\(264\) 0 0
\(265\) −4.92861 + 4.26822i −0.302762 + 0.262195i
\(266\) 4.38585 + 12.0500i 0.268914 + 0.738834i
\(267\) 0 0
\(268\) −8.68053 6.07817i −0.530248 0.371283i
\(269\) 13.3876 0.816257 0.408129 0.912924i \(-0.366182\pi\)
0.408129 + 0.912924i \(0.366182\pi\)
\(270\) 0 0
\(271\) 27.6092 1.67714 0.838569 0.544796i \(-0.183393\pi\)
0.838569 + 0.544796i \(0.183393\pi\)
\(272\) 0.398812 + 0.279251i 0.0241815 + 0.0169321i
\(273\) 0 0
\(274\) −2.27175 6.24157i −0.137241 0.377067i
\(275\) −0.0444126 0.0716702i −0.00267818 0.00432187i
\(276\) 0 0
\(277\) −9.94504 21.3272i −0.597539 1.28143i −0.939769 0.341811i \(-0.888960\pi\)
0.342230 0.939616i \(-0.388818\pi\)
\(278\) −4.09728 + 15.2912i −0.245738 + 0.917108i
\(279\) 0 0
\(280\) −1.04483 10.1230i −0.0624404 0.604963i
\(281\) −8.73492 10.4099i −0.521082 0.621001i 0.439755 0.898118i \(-0.355065\pi\)
−0.960836 + 0.277117i \(0.910621\pi\)
\(282\) 0 0
\(283\) −2.40016 3.42778i −0.142675 0.203760i 0.741454 0.671003i \(-0.234136\pi\)
−0.884129 + 0.467243i \(0.845247\pi\)
\(284\) −2.40646 + 13.6477i −0.142797 + 0.809841i
\(285\) 0 0
\(286\) 0.0383683 0.0321948i 0.00226877 0.00190372i
\(287\) 10.7891 + 40.2653i 0.636858 + 2.37679i
\(288\) 0 0
\(289\) 14.5172 8.38148i 0.853950 0.493028i
\(290\) −11.4453 6.37224i −0.672091 0.374191i
\(291\) 0 0
\(292\) 0.234096 + 2.67573i 0.0136994 + 0.156585i
\(293\) −0.782306 0.364795i −0.0457028 0.0213116i 0.399633 0.916675i \(-0.369138\pi\)
−0.445335 + 0.895364i \(0.646916\pi\)
\(294\) 0 0
\(295\) −21.5899 + 22.2735i −1.25701 + 1.29681i
\(296\) 9.87349i 0.573885i
\(297\) 0 0
\(298\) −1.97971 + 1.97971i −0.114681 + 0.114681i
\(299\) 3.40754 + 19.3251i 0.197063 + 1.11760i
\(300\) 0 0
\(301\) 13.6537 4.96953i 0.786985 0.286439i
\(302\) 10.9563 0.958550i 0.630463 0.0551584i
\(303\) 0 0
\(304\) −0.963674 + 2.64767i −0.0552705 + 0.151854i
\(305\) 4.88601 10.9191i 0.279772 0.625228i
\(306\) 0 0
\(307\) −26.2129 + 7.02373i −1.49605 + 0.400865i −0.911775 0.410690i \(-0.865288\pi\)
−0.584275 + 0.811556i \(0.698621\pi\)
\(308\) −0.0764548 0.00668893i −0.00435642 0.000381137i
\(309\) 0 0
\(310\) 3.21915 9.29258i 0.182835 0.527783i
\(311\) −6.73289 1.18719i −0.381787 0.0673193i −0.0205388 0.999789i \(-0.506538\pi\)
−0.361248 + 0.932470i \(0.617649\pi\)
\(312\) 0 0
\(313\) 0.180127 2.05887i 0.0101814 0.116374i −0.989403 0.145194i \(-0.953619\pi\)
0.999585 + 0.0288199i \(0.00917495\pi\)
\(314\) −6.19201 + 10.7249i −0.349435 + 0.605240i
\(315\) 0 0
\(316\) 2.60651 + 4.51460i 0.146627 + 0.253966i
\(317\) −3.70798 + 1.72906i −0.208261 + 0.0971136i −0.523950 0.851749i \(-0.675542\pi\)
0.315689 + 0.948863i \(0.397764\pi\)
\(318\) 0 0
\(319\) −0.0635007 + 0.0756772i −0.00355536 + 0.00423711i
\(320\) 1.25386 1.85144i 0.0700928 0.103499i
\(321\) 0 0
\(322\) 17.2466 24.6308i 0.961118 1.37262i
\(323\) −0.969988 0.969988i −0.0539716 0.0539716i
\(324\) 0 0
\(325\) 6.69261 + 13.2573i 0.371239 + 0.735385i
\(326\) −6.83734 + 1.20561i −0.378685 + 0.0667724i
\(327\) 0 0
\(328\) −3.87090 + 8.30117i −0.213735 + 0.458355i
\(329\) 8.44296 + 7.08448i 0.465475 + 0.390580i
\(330\) 0 0
\(331\) −22.6746 8.25289i −1.24631 0.453620i −0.367157 0.930159i \(-0.619669\pi\)
−0.879153 + 0.476539i \(0.841891\pi\)
\(332\) 3.87769 + 1.03902i 0.212816 + 0.0570238i
\(333\) 0 0
\(334\) 1.09300 + 0.631045i 0.0598064 + 0.0345292i
\(335\) −12.1661 20.3338i −0.664705 1.11096i
\(336\) 0 0
\(337\) −24.3789 + 17.0703i −1.32800 + 0.929876i −0.999891 0.0147629i \(-0.995301\pi\)
−0.328110 + 0.944639i \(0.606412\pi\)
\(338\) 3.42248 2.39645i 0.186158 0.130350i
\(339\) 0 0
\(340\) 0.558950 + 0.934202i 0.0303133 + 0.0506642i
\(341\) −0.0642288 0.0370825i −0.00347818 0.00200813i
\(342\) 0 0
\(343\) −29.5119 7.90770i −1.59350 0.426976i
\(344\) 3.00003 + 1.09192i 0.161751 + 0.0588725i
\(345\) 0 0
\(346\) −1.56013 1.30911i −0.0838733 0.0703780i
\(347\) 15.0129 32.1952i 0.805934 1.72833i 0.129816 0.991538i \(-0.458561\pi\)
0.676118 0.736793i \(-0.263661\pi\)
\(348\) 0 0
\(349\) −33.1408 + 5.84362i −1.77399 + 0.312802i −0.962442 0.271486i \(-0.912485\pi\)
−0.811546 + 0.584288i \(0.801374\pi\)
\(350\) 7.11286 21.6157i 0.380198 1.15541i
\(351\) 0 0
\(352\) −0.0119240 0.0119240i −0.000635552 0.000635552i
\(353\) −6.95485 + 9.93256i −0.370169 + 0.528657i −0.960417 0.278565i \(-0.910141\pi\)
0.590248 + 0.807222i \(0.299030\pi\)
\(354\) 0 0
\(355\) −17.3763 + 25.6577i −0.922236 + 1.36177i
\(356\) 11.4241 13.6148i 0.605479 0.721581i
\(357\) 0 0
\(358\) −0.478697 + 0.223220i −0.0252999 + 0.0117976i
\(359\) 1.47918 + 2.56202i 0.0780682 + 0.135218i 0.902416 0.430865i \(-0.141791\pi\)
−0.824348 + 0.566083i \(0.808458\pi\)
\(360\) 0 0
\(361\) −5.53058 + 9.57925i −0.291083 + 0.504171i
\(362\) −1.52788 + 17.4638i −0.0803037 + 0.917876i
\(363\) 0 0
\(364\) 13.3124 + 2.34734i 0.697760 + 0.123034i
\(365\) −1.96597 + 5.67509i −0.102904 + 0.297048i
\(366\) 0 0
\(367\) 20.0177 + 1.75132i 1.04492 + 0.0914183i 0.596666 0.802490i \(-0.296492\pi\)
0.448250 + 0.893908i \(0.352047\pi\)
\(368\) 6.38166 1.70996i 0.332667 0.0891378i
\(369\) 0 0
\(370\) −9.01756 + 20.1522i −0.468800 + 1.04767i
\(371\) −4.53869 + 12.4699i −0.235637 + 0.647407i
\(372\) 0 0
\(373\) 7.77776 0.680465i 0.402717 0.0352332i 0.116002 0.993249i \(-0.462992\pi\)
0.286715 + 0.958016i \(0.407437\pi\)
\(374\) 0.00771483 0.00280797i 0.000398924 0.000145197i
\(375\) 0 0
\(376\) 0.420520 + 2.38489i 0.0216867 + 0.122991i
\(377\) 12.3038 12.3038i 0.633680 0.633680i
\(378\) 0 0
\(379\) 8.70072i 0.446926i −0.974712 0.223463i \(-0.928264\pi\)
0.974712 0.223463i \(-0.0717362\pi\)
\(380\) −4.38505 + 4.52388i −0.224948 + 0.232070i
\(381\) 0 0
\(382\) 14.9051 + 6.95036i 0.762611 + 0.355611i
\(383\) −0.341882 3.90773i −0.0174694 0.199676i −0.999914 0.0131209i \(-0.995823\pi\)
0.982445 0.186555i \(-0.0597322\pi\)
\(384\) 0 0
\(385\) −0.149939 0.0834794i −0.00764158 0.00425450i
\(386\) 1.54588 0.892515i 0.0786833 0.0454278i
\(387\) 0 0
\(388\) −3.71286 13.8566i −0.188492 0.703461i
\(389\) −5.04731 + 4.23519i −0.255909 + 0.214733i −0.761712 0.647916i \(-0.775641\pi\)
0.505803 + 0.862649i \(0.331196\pi\)
\(390\) 0 0
\(391\) −0.558551 + 3.16770i −0.0282472 + 0.160198i
\(392\) −7.86557 11.2332i −0.397272 0.567363i
\(393\) 0 0
\(394\) −12.1227 14.4472i −0.610730 0.727840i
\(395\) 1.19677 + 11.5951i 0.0602159 + 0.583410i
\(396\) 0 0
\(397\) −0.745079 + 2.78067i −0.0373944 + 0.139558i −0.982099 0.188364i \(-0.939682\pi\)
0.944705 + 0.327922i \(0.106348\pi\)
\(398\) 9.55224 + 20.4849i 0.478811 + 1.02681i
\(399\) 0 0
\(400\) 4.25012 2.63372i 0.212506 0.131686i
\(401\) −7.66206 21.0513i −0.382625 1.05125i −0.970247 0.242118i \(-0.922158\pi\)
0.587622 0.809136i \(-0.300064\pi\)
\(402\) 0 0
\(403\) 10.7006 + 7.49264i 0.533035 + 0.373235i
\(404\) 1.24752 0.0620666
\(405\) 0 0
\(406\) −26.6623 −1.32323
\(407\) 0.136387 + 0.0954991i 0.00676044 + 0.00473371i
\(408\) 0 0
\(409\) −12.6634 34.7925i −0.626167 1.72038i −0.691363 0.722507i \(-0.742990\pi\)
0.0651964 0.997872i \(-0.479233\pi\)
\(410\) −15.4822 + 13.4077i −0.764612 + 0.662161i
\(411\) 0 0
\(412\) 5.91921 + 12.6938i 0.291618 + 0.625378i
\(413\) −16.3409 + 60.9849i −0.804081 + 3.00087i
\(414\) 0 0
\(415\) 6.96559 + 5.66223i 0.341927 + 0.277948i
\(416\) 1.90919 + 2.27528i 0.0936057 + 0.111555i
\(417\) 0 0
\(418\) 0.0272525 + 0.0389206i 0.00133296 + 0.00190367i
\(419\) 5.70006 32.3266i 0.278466 1.57926i −0.449266 0.893398i \(-0.648315\pi\)
0.727732 0.685861i \(-0.240574\pi\)
\(420\) 0 0
\(421\) 19.0796 16.0097i 0.929884 0.780266i −0.0459123 0.998945i \(-0.514619\pi\)
0.975797 + 0.218680i \(0.0701750\pi\)
\(422\) −0.344968 1.28744i −0.0167928 0.0626714i
\(423\) 0 0
\(424\) −2.52514 + 1.45789i −0.122632 + 0.0708015i
\(425\) 0.287626 + 2.41724i 0.0139519 + 0.117254i
\(426\) 0 0
\(427\) −2.12205 24.2551i −0.102693 1.17379i
\(428\) −5.07618 2.36706i −0.245366 0.114416i
\(429\) 0 0
\(430\) 5.12594 + 4.96862i 0.247195 + 0.239608i
\(431\) 18.2671i 0.879894i −0.898024 0.439947i \(-0.854997\pi\)
0.898024 0.439947i \(-0.145003\pi\)
\(432\) 0 0
\(433\) −10.2353 + 10.2353i −0.491877 + 0.491877i −0.908897 0.417020i \(-0.863074\pi\)
0.417020 + 0.908897i \(0.363074\pi\)
\(434\) −3.47581 19.7123i −0.166844 0.946220i
\(435\) 0 0
\(436\) 11.8051 4.29669i 0.565360 0.205774i
\(437\) −18.5444 + 1.62242i −0.887098 + 0.0776110i
\(438\) 0 0
\(439\) −6.65902 + 18.2955i −0.317818 + 0.873197i 0.673199 + 0.739461i \(0.264920\pi\)
−0.991017 + 0.133736i \(0.957303\pi\)
\(440\) −0.0134471 0.0352277i −0.000641066 0.00167942i
\(441\) 0 0
\(442\) −1.39678 + 0.374267i −0.0664382 + 0.0178020i
\(443\) −34.1642 2.98898i −1.62319 0.142011i −0.761055 0.648687i \(-0.775318\pi\)
−0.862136 + 0.506676i \(0.830874\pi\)
\(444\) 0 0
\(445\) 35.7517 17.3546i 1.69479 0.822686i
\(446\) 3.34776 + 0.590300i 0.158521 + 0.0279515i
\(447\) 0 0
\(448\) 0.396661 4.53386i 0.0187405 0.214205i
\(449\) −9.51605 + 16.4823i −0.449090 + 0.777847i −0.998327 0.0578197i \(-0.981585\pi\)
0.549237 + 0.835667i \(0.314918\pi\)
\(450\) 0 0
\(451\) 0.0772273 + 0.133762i 0.00363649 + 0.00629859i
\(452\) 1.77042 0.825563i 0.0832738 0.0388312i
\(453\) 0 0
\(454\) −4.95308 + 5.90285i −0.232459 + 0.277034i
\(455\) 25.0274 + 16.9494i 1.17330 + 0.794599i
\(456\) 0 0
\(457\) 11.4432 16.3425i 0.535289 0.764472i −0.456859 0.889539i \(-0.651026\pi\)
0.992148 + 0.125067i \(0.0399147\pi\)
\(458\) 2.28299 + 2.28299i 0.106677 + 0.106677i
\(459\) 0 0
\(460\) 14.5870 + 2.33832i 0.680121 + 0.109025i
\(461\) 5.44016 0.959247i 0.253374 0.0446766i −0.0455186 0.998963i \(-0.514494\pi\)
0.298892 + 0.954287i \(0.403383\pi\)
\(462\) 0 0
\(463\) −9.73650 + 20.8800i −0.452494 + 0.970376i 0.539251 + 0.842145i \(0.318708\pi\)
−0.991744 + 0.128231i \(0.959070\pi\)
\(464\) −4.48774 3.76566i −0.208338 0.174817i
\(465\) 0 0
\(466\) 20.2059 + 7.35436i 0.936021 + 0.340684i
\(467\) −34.5186 9.24923i −1.59733 0.428003i −0.653095 0.757276i \(-0.726530\pi\)
−0.944235 + 0.329273i \(0.893197\pi\)
\(468\) 0 0
\(469\) −41.7673 24.1143i −1.92863 1.11350i
\(470\) −1.31984 + 5.25173i −0.0608798 + 0.242244i
\(471\) 0 0
\(472\) −11.3637 + 7.95694i −0.523056 + 0.366248i
\(473\) 0.0441003 0.0308794i 0.00202774 0.00141984i
\(474\) 0 0
\(475\) −13.0818 + 5.22855i −0.600233 + 0.239902i
\(476\) 1.91892 + 1.10789i 0.0879537 + 0.0507801i
\(477\) 0 0
\(478\) −13.5516 3.63113i −0.619834 0.166084i
\(479\) 16.3049 + 5.93451i 0.744991 + 0.271155i 0.686497 0.727133i \(-0.259148\pi\)
0.0584947 + 0.998288i \(0.481370\pi\)
\(480\) 0 0
\(481\) −22.4650 18.8504i −1.02432 0.859503i
\(482\) 2.86361 6.14104i 0.130434 0.279717i
\(483\) 0 0
\(484\) 10.8326 1.91008i 0.492391 0.0868218i
\(485\) 5.07724 31.6729i 0.230545 1.43819i
\(486\) 0 0
\(487\) 9.51142 + 9.51142i 0.431004 + 0.431004i 0.888970 0.457966i \(-0.151422\pi\)
−0.457966 + 0.888970i \(0.651422\pi\)
\(488\) 3.06851 4.38228i 0.138905 0.198377i
\(489\) 0 0
\(490\) −5.79460 30.1112i −0.261773 1.36028i
\(491\) −22.1705 + 26.4218i −1.00054 + 1.19240i −0.0192602 + 0.999815i \(0.506131\pi\)
−0.981281 + 0.192584i \(0.938313\pi\)
\(492\) 0 0
\(493\) 2.58495 1.20538i 0.116421 0.0542878i
\(494\) −4.18437 7.24754i −0.188264 0.326082i
\(495\) 0 0
\(496\) 2.19903 3.80884i 0.0987396 0.171022i
\(497\) −5.49702 + 62.8312i −0.246575 + 2.81837i
\(498\) 0 0
\(499\) 2.97985 + 0.525427i 0.133396 + 0.0235213i 0.239948 0.970786i \(-0.422870\pi\)
−0.106551 + 0.994307i \(0.533981\pi\)
\(500\) 11.0801 1.49386i 0.495517 0.0668073i
\(501\) 0 0
\(502\) −0.365149 0.0319464i −0.0162974 0.00142584i
\(503\) 4.78545 1.28226i 0.213373 0.0571731i −0.150549 0.988603i \(-0.548104\pi\)
0.363922 + 0.931429i \(0.381437\pi\)
\(504\) 0 0
\(505\) 2.54625 + 1.13937i 0.113307 + 0.0507015i
\(506\) 0.0381047 0.104692i 0.00169396 0.00465412i
\(507\) 0 0
\(508\) 10.7236 0.938190i 0.475781 0.0416255i
\(509\) 3.58837 1.30606i 0.159052 0.0578901i −0.261267 0.965267i \(-0.584140\pi\)
0.420319 + 0.907376i \(0.361918\pi\)
\(510\) 0 0
\(511\) 2.12272 + 12.0385i 0.0939035 + 0.532553i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 11.6651i 0.514526i
\(515\) 0.488014 + 31.3147i 0.0215045 + 1.37989i
\(516\) 0 0
\(517\) 0.0370109 + 0.0172585i 0.00162774 + 0.000759026i
\(518\) 3.91643 + 44.7650i 0.172078 + 1.96686i
\(519\) 0 0
\(520\) 1.81870 + 6.38764i 0.0797554 + 0.280117i
\(521\) 11.1024 6.40996i 0.486404 0.280825i −0.236677 0.971588i \(-0.576058\pi\)
0.723081 + 0.690763i \(0.242725\pi\)
\(522\) 0 0
\(523\) 1.78222 + 6.65134i 0.0779311 + 0.290843i 0.993882 0.110448i \(-0.0352285\pi\)
−0.915951 + 0.401290i \(0.868562\pi\)
\(524\) −3.40772 + 2.85942i −0.148867 + 0.124914i
\(525\) 0 0
\(526\) 1.12784 6.39631i 0.0491762 0.278892i
\(527\) 1.22816 + 1.75400i 0.0534997 + 0.0764055i
\(528\) 0 0
\(529\) 13.2732 + 15.8184i 0.577097 + 0.687757i
\(530\) −6.48543 + 0.669385i −0.281709 + 0.0290762i
\(531\) 0 0
\(532\) −3.31893 + 12.3864i −0.143894 + 0.537019i
\(533\) −11.4972 24.6559i −0.498001 1.06797i
\(534\) 0 0
\(535\) −8.19885 9.46740i −0.354467 0.409311i
\(536\) −3.62438 9.95789i −0.156549 0.430115i
\(537\) 0 0
\(538\) 10.9665 + 7.67882i 0.472799 + 0.331057i
\(539\) −0.231247 −0.00996052
\(540\) 0 0
\(541\) −11.8481 −0.509388 −0.254694 0.967022i \(-0.581975\pi\)
−0.254694 + 0.967022i \(0.581975\pi\)
\(542\) 22.6161 + 15.8360i 0.971445 + 0.680213i
\(543\) 0 0
\(544\) 0.166516 + 0.457498i 0.00713930 + 0.0196151i
\(545\) 28.0189 + 2.01194i 1.20020 + 0.0861819i
\(546\) 0 0
\(547\) 14.1538 + 30.3529i 0.605173 + 1.29780i 0.935298 + 0.353860i \(0.115131\pi\)
−0.330126 + 0.943937i \(0.607091\pi\)
\(548\) 1.71911 6.41582i 0.0734369 0.274070i
\(549\) 0 0
\(550\) 0.00472766 0.0841828i 0.000201588 0.00358957i
\(551\) 10.6101 + 12.6446i 0.452006 + 0.538679i
\(552\) 0 0
\(553\) 13.6083 + 19.4347i 0.578684 + 0.826446i
\(554\) 4.08628 23.1745i 0.173609 0.984588i
\(555\) 0 0
\(556\) −12.1270 + 10.1758i −0.514299 + 0.431548i
\(557\) −2.88256 10.7579i −0.122138 0.455825i 0.877584 0.479424i \(-0.159154\pi\)
−0.999722 + 0.0235987i \(0.992488\pi\)
\(558\) 0 0
\(559\) −8.21207 + 4.74124i −0.347333 + 0.200533i
\(560\) 4.95042 8.89153i 0.209193 0.375736i
\(561\) 0 0
\(562\) −1.18437 13.5374i −0.0499596 0.571041i
\(563\) −14.1413 6.59418i −0.595983 0.277911i 0.101129 0.994873i \(-0.467754\pi\)
−0.697112 + 0.716962i \(0.745532\pi\)
\(564\) 0 0
\(565\) 4.36751 0.0680642i 0.183743 0.00286348i
\(566\) 4.18455i 0.175890i
\(567\) 0 0
\(568\) −9.79925 + 9.79925i −0.411167 + 0.411167i
\(569\) 0.939874 + 5.33029i 0.0394016 + 0.223458i 0.998150 0.0607983i \(-0.0193646\pi\)
−0.958748 + 0.284256i \(0.908254\pi\)
\(570\) 0 0
\(571\) 4.93193 1.79508i 0.206395 0.0751217i −0.236754 0.971570i \(-0.576084\pi\)
0.443149 + 0.896448i \(0.353861\pi\)
\(572\) 0.0498957 0.00436531i 0.00208624 0.000182523i
\(573\) 0 0
\(574\) −14.2574 + 39.1718i −0.595090 + 1.63500i
\(575\) 27.6370 + 18.0950i 1.15254 + 0.754616i
\(576\) 0 0
\(577\) −25.9887 + 6.96365i −1.08192 + 0.289901i −0.755384 0.655283i \(-0.772550\pi\)
−0.326540 + 0.945183i \(0.605883\pi\)
\(578\) 16.6992 + 1.46099i 0.694594 + 0.0607691i
\(579\) 0 0
\(580\) −5.72047 11.7846i −0.237530 0.489328i
\(581\) 17.9930 + 3.17266i 0.746477 + 0.131624i
\(582\) 0 0
\(583\) −0.00428537 + 0.0489820i −0.000177482 + 0.00202863i
\(584\) −1.34298 + 2.32610i −0.0555727 + 0.0962548i
\(585\) 0 0
\(586\) −0.431590 0.747535i −0.0178288 0.0308804i
\(587\) −4.20831 + 1.96237i −0.173695 + 0.0809955i −0.507521 0.861639i \(-0.669438\pi\)
0.333826 + 0.942635i \(0.391660\pi\)
\(588\) 0 0
\(589\) −7.96540 + 9.49280i −0.328209 + 0.391144i
\(590\) −30.4610 + 5.86191i −1.25406 + 0.241331i
\(591\) 0 0
\(592\) −5.66320 + 8.08789i −0.232756 + 0.332410i
\(593\) 20.1984 + 20.1984i 0.829450 + 0.829450i 0.987441 0.157991i \(-0.0505017\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(594\) 0 0
\(595\) 2.90476 + 4.01383i 0.119084 + 0.164551i
\(596\) −2.75720 + 0.486168i −0.112939 + 0.0199142i
\(597\) 0 0
\(598\) −8.29315 + 17.7847i −0.339132 + 0.727271i
\(599\) −20.5738 17.2635i −0.840622 0.705366i 0.117081 0.993122i \(-0.462646\pi\)
−0.957704 + 0.287756i \(0.907091\pi\)
\(600\) 0 0
\(601\) 4.32986 + 1.57594i 0.176619 + 0.0642839i 0.428816 0.903392i \(-0.358931\pi\)
−0.252197 + 0.967676i \(0.581153\pi\)
\(602\) 14.0348 + 3.76063i 0.572018 + 0.153272i
\(603\) 0 0
\(604\) 9.52466 + 5.49906i 0.387553 + 0.223754i
\(605\) 23.8543 + 5.99496i 0.969816 + 0.243730i
\(606\) 0 0
\(607\) 6.29189 4.40563i 0.255380 0.178819i −0.438875 0.898548i \(-0.644623\pi\)
0.694255 + 0.719729i \(0.255734\pi\)
\(608\) −2.30804 + 1.61611i −0.0936033 + 0.0655417i
\(609\) 0 0
\(610\) 10.2653 6.14194i 0.415632 0.248680i
\(611\) −6.22915 3.59640i −0.252005 0.145495i
\(612\) 0 0
\(613\) −41.4873 11.1165i −1.67565 0.448990i −0.709028 0.705180i \(-0.750866\pi\)
−0.966626 + 0.256190i \(0.917533\pi\)
\(614\) −25.5010 9.28161i −1.02914 0.374575i
\(615\) 0 0
\(616\) −0.0587915 0.0493320i −0.00236878 0.00198764i
\(617\) 1.21970 2.61566i 0.0491033 0.105302i −0.880225 0.474556i \(-0.842609\pi\)
0.929329 + 0.369253i \(0.120387\pi\)
\(618\) 0 0
\(619\) 5.65266 0.996717i 0.227200 0.0400614i −0.0588892 0.998265i \(-0.518756\pi\)
0.286089 + 0.958203i \(0.407645\pi\)
\(620\) 7.96698 5.76561i 0.319962 0.231553i
\(621\) 0 0
\(622\) −4.83431 4.83431i −0.193838 0.193838i
\(623\) 46.3950 66.2589i 1.85878 2.65461i
\(624\) 0 0
\(625\) 23.9793 + 7.07053i 0.959173 + 0.282821i
\(626\) 1.32847 1.58321i 0.0530963 0.0632777i
\(627\) 0 0
\(628\) −11.2237 + 5.23371i −0.447876 + 0.208848i
\(629\) −2.40350 4.16298i −0.0958338 0.165989i
\(630\) 0 0
\(631\) 9.87500 17.1040i 0.393118 0.680900i −0.599741 0.800194i \(-0.704730\pi\)
0.992859 + 0.119294i \(0.0380632\pi\)
\(632\) −0.454344 + 5.19317i −0.0180728 + 0.206573i
\(633\) 0 0
\(634\) −4.02914 0.710447i −0.160018 0.0282155i
\(635\) 22.7441 + 7.87905i 0.902573 + 0.312670i
\(636\) 0 0
\(637\) 40.5756 + 3.54991i 1.60766 + 0.140652i
\(638\) −0.0954234 + 0.0255686i −0.00377785 + 0.00101227i
\(639\) 0 0
\(640\) 2.08904 0.797429i 0.0825767 0.0315212i
\(641\) −7.62318 + 20.9445i −0.301098 + 0.827259i 0.693212 + 0.720733i \(0.256195\pi\)
−0.994310 + 0.106525i \(0.966027\pi\)
\(642\) 0 0
\(643\) 15.1249 1.32326i 0.596470 0.0521843i 0.215076 0.976597i \(-0.431000\pi\)
0.381393 + 0.924413i \(0.375444\pi\)
\(644\) 28.2552 10.2841i 1.11341 0.405249i
\(645\) 0 0
\(646\) −0.238206 1.35093i −0.00937207 0.0531517i
\(647\) 0.132123 0.132123i 0.00519428 0.00519428i −0.704505 0.709699i \(-0.748831\pi\)
0.709699 + 0.704505i \(0.248831\pi\)
\(648\) 0 0
\(649\) 0.233933i 0.00918269i
\(650\) −2.12184 + 14.6985i −0.0832253 + 0.576523i
\(651\) 0 0
\(652\) −6.29233 2.93416i −0.246427 0.114911i
\(653\) −2.75084 31.4422i −0.107649 1.23043i −0.837352 0.546665i \(-0.815897\pi\)
0.729703 0.683764i \(-0.239658\pi\)
\(654\) 0 0
\(655\) −9.56684 + 2.72389i −0.373808 + 0.106431i
\(656\) −7.93221 + 4.57966i −0.309701 + 0.178806i
\(657\) 0 0
\(658\) 2.85257 + 10.6459i 0.111205 + 0.415022i
\(659\) −17.5238 + 14.7042i −0.682630 + 0.572794i −0.916773 0.399408i \(-0.869216\pi\)
0.234144 + 0.972202i \(0.424771\pi\)
\(660\) 0 0
\(661\) −8.41643 + 47.7319i −0.327361 + 1.85656i 0.165174 + 0.986264i \(0.447181\pi\)
−0.492535 + 0.870292i \(0.663930\pi\)
\(662\) −13.8403 19.7660i −0.537919 0.768228i
\(663\) 0 0
\(664\) 2.58046 + 3.07527i 0.100141 + 0.119344i
\(665\) −18.0867 + 22.2500i −0.701373 + 0.862819i
\(666\) 0 0
\(667\) 10.0175 37.3859i 0.387880 1.44759i
\(668\) 0.533382 + 1.14384i 0.0206372 + 0.0442566i
\(669\) 0 0
\(670\) 1.69713 23.6347i 0.0655657 0.913088i
\(671\) −0.0308549 0.0847732i −0.00119114 0.00327263i
\(672\) 0 0
\(673\) −25.5908 17.9189i −0.986452 0.690721i −0.0352782 0.999378i \(-0.511232\pi\)
−0.951174 + 0.308657i \(0.900121\pi\)
\(674\) −29.7611 −1.14635
\(675\) 0 0
\(676\) 4.17808 0.160695
\(677\) −32.3349 22.6411i −1.24273 0.870169i −0.247612 0.968859i \(-0.579646\pi\)
−0.995118 + 0.0986900i \(0.968535\pi\)
\(678\) 0 0
\(679\) −22.3299 61.3510i −0.856944 2.35444i
\(680\) −0.0779714 + 1.08585i −0.00299007 + 0.0416406i
\(681\) 0 0
\(682\) −0.0313435 0.0672163i −0.00120020 0.00257385i
\(683\) 1.75572 6.55243i 0.0671807 0.250722i −0.924166 0.381991i \(-0.875239\pi\)
0.991347 + 0.131269i \(0.0419052\pi\)
\(684\) 0 0
\(685\) 9.36841 11.5249i 0.357949 0.440343i
\(686\) −19.6391 23.4050i −0.749824 0.893606i
\(687\) 0 0
\(688\) 1.83118 + 2.61520i 0.0698132 + 0.0997035i
\(689\) 1.50386 8.52881i 0.0572925 0.324922i
\(690\) 0 0
\(691\) −15.9693 + 13.3998i −0.607501 + 0.509754i −0.893847 0.448373i \(-0.852004\pi\)
0.286346 + 0.958126i \(0.407559\pi\)
\(692\) −0.527113 1.96721i −0.0200378 0.0747822i
\(693\) 0 0
\(694\) 30.7643 17.7618i 1.16780 0.674227i
\(695\) −34.0453 + 9.69347i −1.29141 + 0.367694i
\(696\) 0 0
\(697\) −0.388654 4.44233i −0.0147213 0.168265i
\(698\) −30.4992 14.2220i −1.15441 0.538310i
\(699\) 0 0
\(700\) 18.2248 13.6268i 0.688831 0.515043i
\(701\) 8.08020i 0.305185i 0.988289 + 0.152593i \(0.0487622\pi\)
−0.988289 + 0.152593i \(0.951238\pi\)
\(702\) 0 0
\(703\) 19.6713 19.6713i 0.741919 0.741919i
\(704\) −0.00292824 0.0166069i −0.000110362 0.000625896i
\(705\) 0 0
\(706\) −11.3942 + 4.14714i −0.428825 + 0.156080i
\(707\) 5.65609 0.494844i 0.212719 0.0186105i
\(708\) 0 0
\(709\) 11.3633 31.2204i 0.426757 1.17251i −0.521012 0.853549i \(-0.674445\pi\)
0.947769 0.318957i \(-0.103332\pi\)
\(710\) −28.9505 + 11.0510i −1.08649 + 0.414735i
\(711\) 0 0
\(712\) 17.1672 4.59994i 0.643369 0.172390i
\(713\) 28.9465 + 2.53249i 1.08405 + 0.0948425i
\(714\) 0 0
\(715\) 0.105826 + 0.0366604i 0.00395768 + 0.00137102i
\(716\) −0.520160 0.0917182i −0.0194393 0.00342767i
\(717\) 0 0
\(718\) −0.257838 + 2.94710i −0.00962243 + 0.109985i
\(719\) 21.0211 36.4096i 0.783954 1.35785i −0.145667 0.989334i \(-0.546533\pi\)
0.929622 0.368515i \(-0.120134\pi\)
\(720\) 0 0
\(721\) 31.8720 + 55.2039i 1.18697 + 2.05590i
\(722\) −10.0248 + 4.67465i −0.373085 + 0.173973i
\(723\) 0 0
\(724\) −11.2684 + 13.4291i −0.418786 + 0.499090i
\(725\) −0.912753 29.2774i −0.0338988 1.08734i
\(726\) 0 0
\(727\) −12.7185 + 18.1639i −0.471704 + 0.673662i −0.982548 0.186011i \(-0.940444\pi\)
0.510844 + 0.859673i \(0.329333\pi\)
\(728\) 9.55851 + 9.55851i 0.354262 + 0.354262i
\(729\) 0 0
\(730\) −4.86553 + 3.52113i −0.180081 + 0.130323i
\(731\) −1.53072 + 0.269907i −0.0566156 + 0.00998286i
\(732\) 0 0
\(733\) 12.7711 27.3878i 0.471712 1.01159i −0.516185 0.856477i \(-0.672648\pi\)
0.987897 0.155113i \(-0.0495741\pi\)
\(734\) 15.3930 + 12.9163i 0.568167 + 0.476749i
\(735\) 0 0
\(736\) 6.20834 + 2.25965i 0.228842 + 0.0832918i
\(737\) −0.172609 0.0462503i −0.00635812 0.00170365i
\(738\) 0 0
\(739\) 3.55947 + 2.05506i 0.130937 + 0.0755966i 0.564038 0.825749i \(-0.309247\pi\)
−0.433101 + 0.901346i \(0.642581\pi\)
\(740\) −18.9456 + 11.3355i −0.696454 + 0.416701i
\(741\) 0 0
\(742\) −10.8703 + 7.61150i −0.399063 + 0.279427i
\(743\) 14.2538 9.98062i 0.522921 0.366153i −0.282113 0.959381i \(-0.591035\pi\)
0.805035 + 0.593228i \(0.202147\pi\)
\(744\) 0 0
\(745\) −6.07158 1.52588i −0.222446 0.0559040i
\(746\) 6.76146 + 3.90373i 0.247555 + 0.142926i
\(747\) 0 0
\(748\) 0.00793020 + 0.00212489i 0.000289957 + 7.76937e-5i
\(749\) −23.9536 8.71839i −0.875245 0.318563i
\(750\) 0 0
\(751\) −18.5689 15.5811i −0.677588 0.568564i 0.237713 0.971336i \(-0.423602\pi\)
−0.915300 + 0.402772i \(0.868047\pi\)
\(752\) −1.02345 + 2.19479i −0.0373213 + 0.0800357i
\(753\) 0 0
\(754\) 17.1359 3.02152i 0.624053 0.110037i
\(755\) 14.4179 + 19.9228i 0.524721 + 0.725065i
\(756\) 0 0
\(757\) −8.09867 8.09867i −0.294351 0.294351i 0.544445 0.838796i \(-0.316740\pi\)
−0.838796 + 0.544445i \(0.816740\pi\)
\(758\) 4.99053 7.12722i 0.181264 0.258872i
\(759\) 0 0
\(760\) −6.18681 + 1.19059i −0.224419 + 0.0431872i
\(761\) 8.63831 10.2947i 0.313139 0.373184i −0.586403 0.810020i \(-0.699456\pi\)
0.899541 + 0.436836i \(0.143901\pi\)
\(762\) 0 0
\(763\) 51.8181 24.1632i 1.87594 0.874766i
\(764\) 8.22297 + 14.2426i 0.297497 + 0.515279i
\(765\) 0 0
\(766\) 1.96133 3.39712i 0.0708657 0.122743i
\(767\) 3.59114 41.0469i 0.129669 1.48212i
\(768\) 0 0
\(769\) 10.9734 + 1.93491i 0.395712 + 0.0697747i 0.367963 0.929840i \(-0.380055\pi\)
0.0277484 + 0.999615i \(0.491166\pi\)
\(770\) −0.0749408 0.154384i −0.00270068 0.00556360i
\(771\) 0 0
\(772\) 1.77824 + 0.155576i 0.0640002 + 0.00559929i
\(773\) 21.6373 5.79770i 0.778240 0.208529i 0.152231 0.988345i \(-0.451354\pi\)
0.626009 + 0.779816i \(0.284687\pi\)
\(774\) 0 0
\(775\) 21.5268 4.49156i 0.773264 0.161341i
\(776\) 4.90641 13.4803i 0.176130 0.483913i
\(777\) 0 0
\(778\) −6.56372 + 0.574251i −0.235321 + 0.0205879i
\(779\) 24.2509 8.82660i 0.868878 0.316246i
\(780\) 0 0
\(781\) 0.0405803 + 0.230142i 0.00145208 + 0.00823513i
\(782\) −2.27446 + 2.27446i −0.0813344 + 0.0813344i
\(783\) 0 0
\(784\) 13.7132i 0.489758i
\(785\) −27.6881 + 0.431498i −0.988232 + 0.0154008i
\(786\) 0 0
\(787\) 30.8512 + 14.3862i 1.09973 + 0.512811i 0.885814 0.464041i \(-0.153601\pi\)
0.213914 + 0.976853i \(0.431379\pi\)
\(788\) −1.64371 18.7877i −0.0585549 0.669285i
\(789\) 0 0
\(790\) −5.67031 + 10.1845i −0.201741 + 0.362350i
\(791\) 7.69939 4.44524i 0.273759 0.158055i
\(792\) 0 0
\(793\) 4.11257 + 15.3483i 0.146042 + 0.545035i
\(794\) −2.20526 + 1.85043i −0.0782618 + 0.0656694i
\(795\) 0 0
\(796\) −3.92489 + 22.2592i −0.139114 + 0.788955i
\(797\) 11.6005 + 16.5672i 0.410910 + 0.586840i 0.970252 0.242097i \(-0.0778352\pi\)
−0.559342 + 0.828937i \(0.688946\pi\)
\(798\) 0 0
\(799\) −0.757858 0.903180i −0.0268111 0.0319522i
\(800\) 4.99213 + 0.280356i 0.176499 + 0.00991207i
\(801\) 0 0
\(802\) 5.79816 21.6390i 0.204740 0.764101i
\(803\) 0.0191418 + 0.0410498i 0.000675501 + 0.00144862i
\(804\) 0 0
\(805\) 67.0628 + 4.81555i 2.36365 + 0.169726i
\(806\) 4.46782 + 12.2752i 0.157372 + 0.432376i
\(807\) 0 0
\(808\) 1.02191 + 0.715549i 0.0359507 + 0.0251729i
\(809\) −14.3424 −0.504253 −0.252126 0.967694i \(-0.581130\pi\)
−0.252126 + 0.967694i \(0.581130\pi\)
\(810\) 0 0
\(811\) 18.2253 0.639976 0.319988 0.947422i \(-0.396321\pi\)
0.319988 + 0.947422i \(0.396321\pi\)
\(812\) −21.8405 15.2929i −0.766451 0.536675i
\(813\) 0 0
\(814\) 0.0569455 + 0.156456i 0.00199594 + 0.00548380i
\(815\) −10.1631 11.7356i −0.355999 0.411080i
\(816\) 0 0
\(817\) −3.80160 8.15256i −0.133001 0.285222i
\(818\) 9.58289 35.7638i 0.335058 1.25045i
\(819\) 0 0
\(820\) −20.3726 + 2.10273i −0.711444 + 0.0734307i
\(821\) −8.94276 10.6576i −0.312104 0.371951i 0.587074 0.809533i \(-0.300280\pi\)
−0.899179 + 0.437582i \(0.855835\pi\)
\(822\) 0 0
\(823\) −3.60500 5.14847i −0.125662 0.179464i 0.751391 0.659857i \(-0.229383\pi\)
−0.877054 + 0.480393i \(0.840494\pi\)
\(824\) −2.43212 + 13.7933i −0.0847270 + 0.480511i
\(825\) 0 0
\(826\) −48.3652 + 40.5832i −1.68284 + 1.41207i
\(827\) 6.66511 + 24.8745i 0.231769 + 0.864972i 0.979579 + 0.201060i \(0.0644386\pi\)
−0.747810 + 0.663912i \(0.768895\pi\)
\(828\) 0 0
\(829\) −18.2474 + 10.5352i −0.633759 + 0.365901i −0.782206 0.623019i \(-0.785906\pi\)
0.148447 + 0.988920i \(0.452572\pi\)
\(830\) 2.45816 + 8.63352i 0.0853238 + 0.299674i
\(831\) 0 0
\(832\) 0.258868 + 2.95887i 0.00897462 + 0.102580i
\(833\) 6.05087 + 2.82157i 0.209650 + 0.0977616i
\(834\) 0 0
\(835\) 0.0439752 + 2.82178i 0.00152182 + 0.0976516i
\(836\) 0.0475133i 0.00164328i
\(837\) 0 0
\(838\) 23.2110 23.2110i 0.801811 0.801811i
\(839\) 9.27233 + 52.5860i 0.320116 + 1.81547i 0.541979 + 0.840392i \(0.317675\pi\)
−0.221862 + 0.975078i \(0.571214\pi\)
\(840\) 0 0
\(841\) −4.99921 + 1.81957i −0.172387 + 0.0627436i
\(842\) 24.8119 2.17076i 0.855075 0.0748094i
\(843\) 0 0
\(844\) 0.455862 1.25247i 0.0156914 0.0431119i
\(845\) 8.52764 + 3.81588i 0.293360 + 0.131270i
\(846\) 0 0
\(847\) 48.3558 12.9569i 1.66153 0.445205i
\(848\) −2.90469 0.254127i −0.0997474 0.00872676i
\(849\) 0 0
\(850\) −1.15086 + 2.14507i −0.0394743 + 0.0735751i
\(851\) −64.2409 11.3274i −2.20215 0.388298i
\(852\) 0 0
\(853\) 3.92268 44.8364i 0.134310 1.53517i −0.567839 0.823140i \(-0.692220\pi\)
0.702149 0.712030i \(-0.252224\pi\)
\(854\) 12.1739 21.0858i 0.416582 0.721541i
\(855\) 0 0
\(856\) −2.80047 4.85056i −0.0957181 0.165789i
\(857\) 27.0397 12.6088i 0.923658 0.430709i 0.0981964 0.995167i \(-0.468693\pi\)
0.825462 + 0.564458i \(0.190915\pi\)
\(858\) 0 0
\(859\) −11.3187 + 13.4891i −0.386190 + 0.460244i −0.923758 0.382977i \(-0.874899\pi\)
0.537567 + 0.843221i \(0.319343\pi\)
\(860\) 1.34904 + 7.01018i 0.0460018 + 0.239045i
\(861\) 0 0
\(862\) 10.4776 14.9635i 0.356867 0.509659i
\(863\) −8.79886 8.79886i −0.299517 0.299517i 0.541308 0.840824i \(-0.317929\pi\)
−0.840824 + 0.541308i \(0.817929\pi\)
\(864\) 0 0
\(865\) 0.720813 4.49659i 0.0245084 0.152889i
\(866\) −14.2550 + 2.51354i −0.484404 + 0.0854136i
\(867\) 0 0
\(868\) 8.45929 18.1410i 0.287127 0.615746i
\(869\) 0.0673410 + 0.0565058i 0.00228439 + 0.00191683i
\(870\) 0 0
\(871\) 29.5767 + 10.7650i 1.00217 + 0.364759i
\(872\) 12.1346 + 3.25146i 0.410930 + 0.110108i
\(873\) 0 0
\(874\) −16.1212 9.30760i −0.545309 0.314834i
\(875\) 49.6430 11.1680i 1.67824 0.377546i
\(876\) 0 0
\(877\) 7.03938 4.92903i 0.237703 0.166441i −0.448656 0.893705i \(-0.648097\pi\)
0.686359 + 0.727263i \(0.259208\pi\)
\(878\) −15.9486 + 11.1673i −0.538240 + 0.376880i
\(879\) 0 0
\(880\) 0.00919057 0.0365698i 0.000309814 0.00123277i
\(881\) −37.0508 21.3913i −1.24827 0.720690i −0.277507 0.960723i \(-0.589508\pi\)
−0.970765 + 0.240033i \(0.922842\pi\)
\(882\) 0 0
\(883\) 9.31280 + 2.49536i 0.313401 + 0.0839754i 0.412091 0.911143i \(-0.364799\pi\)
−0.0986903 + 0.995118i \(0.531465\pi\)
\(884\) −1.35885 0.494580i −0.0457030 0.0166345i
\(885\) 0 0
\(886\) −26.2713 22.0442i −0.882601 0.740590i
\(887\) −2.47227 + 5.30181i −0.0830108 + 0.178017i −0.943432 0.331567i \(-0.892423\pi\)
0.860421 + 0.509584i \(0.170201\pi\)
\(888\) 0 0
\(889\) 48.2470 8.50724i 1.61815 0.285324i
\(890\) 39.2403 + 6.29030i 1.31534 + 0.210851i
\(891\) 0 0
\(892\) 2.40374 + 2.40374i 0.0804832 + 0.0804832i
\(893\) 3.91369 5.58933i 0.130967 0.187040i
\(894\) 0 0
\(895\) −0.977902 0.662268i −0.0326877 0.0221372i
\(896\) 2.92544 3.48640i 0.0977321 0.116473i
\(897\) 0 0
\(898\) −17.2489 + 8.04331i −0.575605 + 0.268409i
\(899\) −12.8827 22.3134i −0.429661 0.744195i
\(900\) 0 0
\(901\) 0.709788 1.22939i 0.0236465 0.0409569i
\(902\) −0.0134616 + 0.153867i −0.000448222 + 0.00512320i
\(903\) 0 0
\(904\) 1.92377 + 0.339213i 0.0639837 + 0.0112820i
\(905\) −35.2642 + 17.1179i −1.17222 + 0.569020i
\(906\) 0 0
\(907\) 5.83355 + 0.510370i 0.193700 + 0.0169466i 0.183593 0.983002i \(-0.441227\pi\)
0.0101071 + 0.999949i \(0.496783\pi\)
\(908\) −7.44306 + 1.99436i −0.247007 + 0.0661852i
\(909\) 0 0
\(910\) 10.7795 + 28.2392i 0.357336 + 0.936122i
\(911\) 0.418240 1.14910i 0.0138569 0.0380715i −0.932571 0.360986i \(-0.882440\pi\)
0.946428 + 0.322914i \(0.104663\pi\)
\(912\) 0 0
\(913\) 0.0674389 0.00590014i 0.00223190 0.000195266i
\(914\) 18.7474 6.82349i 0.620108 0.225701i
\(915\) 0 0
\(916\) 0.560647 + 3.17958i 0.0185243 + 0.105056i
\(917\) −14.3159 + 14.3159i −0.472753 + 0.472753i
\(918\) 0 0
\(919\) 6.99440i 0.230724i −0.993324 0.115362i \(-0.963197\pi\)
0.993324 0.115362i \(-0.0368028\pi\)
\(920\) 10.6077 + 10.2822i 0.349727 + 0.338994i
\(921\) 0 0
\(922\) 5.00652 + 2.33458i 0.164881 + 0.0768853i
\(923\) −3.58745 41.0047i −0.118082 1.34969i
\(924\) 0 0
\(925\) −49.0216 + 5.83305i −1.61182 + 0.191789i
\(926\) −19.9520 + 11.5193i −0.655662 + 0.378547i
\(927\) 0 0
\(928\) −1.51625 5.65871i −0.0497733 0.185756i
\(929\) 27.6437 23.1958i 0.906961 0.761030i −0.0645776 0.997913i \(-0.520570\pi\)
0.971538 + 0.236882i \(0.0761256\pi\)
\(930\) 0 0
\(931\) −6.70946 + 38.0512i −0.219894 + 1.24708i
\(932\) 12.3334 + 17.6140i 0.403995 + 0.576965i
\(933\) 0 0
\(934\) −22.9708 27.3756i −0.751629 0.895756i
\(935\) 0.0142452 + 0.0115797i 0.000465868 + 0.000378698i
\(936\) 0 0
\(937\) −6.45571 + 24.0931i −0.210899 + 0.787086i 0.776671 + 0.629906i \(0.216907\pi\)
−0.987570 + 0.157179i \(0.949760\pi\)
\(938\) −20.3823 43.7100i −0.665506 1.42718i
\(939\) 0 0
\(940\) −4.09342 + 3.54494i −0.133513 + 0.115623i
\(941\) 18.0347 + 49.5498i 0.587913 + 1.61528i 0.774313 + 0.632803i \(0.218096\pi\)
−0.186400 + 0.982474i \(0.559682\pi\)
\(942\) 0 0
\(943\) −49.5699 34.7092i −1.61422 1.13029i
\(944\) −13.8725 −0.451512
\(945\) 0 0
\(946\) 0.0538366 0.00175038
\(947\) 29.0385 + 20.3330i 0.943624 + 0.660732i 0.940691 0.339263i \(-0.110178\pi\)
0.00293227 + 0.999996i \(0.499067\pi\)
\(948\) 0 0
\(949\) −2.72855 7.49662i −0.0885724 0.243351i
\(950\) −13.7149 3.22043i −0.444971 0.104484i
\(951\) 0 0
\(952\) 0.936430 + 2.00818i 0.0303499 + 0.0650855i
\(953\) 7.42681 27.7172i 0.240578 0.897850i −0.734977 0.678093i \(-0.762807\pi\)
0.975555 0.219757i \(-0.0705265\pi\)
\(954\) 0 0
\(955\) 3.77555 + 36.5799i 0.122174 + 1.18370i
\(956\) −9.01806 10.7473i −0.291665 0.347593i
\(957\) 0 0
\(958\) 9.95232 + 14.2134i 0.321545 + 0.459214i
\(959\) 5.24931 29.7703i 0.169509 0.961333i
\(960\) 0 0
\(961\) −8.92977 + 7.49297i −0.288057 + 0.241709i
\(962\) −7.59012 28.3267i −0.244715 0.913290i
\(963\) 0 0
\(964\) 5.86809 3.38794i 0.188998 0.109118i
\(965\) 3.48737 + 1.94162i 0.112263 + 0.0625029i
\(966\) 0 0
\(967\) −2.66829 30.4986i −0.0858063 0.980770i −0.910040 0.414520i \(-0.863949\pi\)
0.824234 0.566250i \(-0.191606\pi\)
\(968\) 9.96913 + 4.64868i 0.320420 + 0.149414i
\(969\) 0 0
\(970\) 22.3258 23.0327i 0.716840 0.739536i
\(971\) 2.72736i 0.0875251i −0.999042 0.0437626i \(-0.986065\pi\)
0.999042 0.0437626i \(-0.0139345\pi\)
\(972\) 0 0
\(973\) −50.9457 + 50.9457i −1.63324 + 1.63324i
\(974\) 2.33577 + 13.2468i 0.0748430 + 0.424456i
\(975\) 0 0
\(976\) 5.02715 1.82973i 0.160915 0.0585683i
\(977\) −16.0934 + 1.40799i −0.514873 + 0.0450456i −0.341632 0.939834i \(-0.610980\pi\)
−0.173241 + 0.984879i \(0.555424\pi\)
\(978\) 0 0
\(979\) 0.102505 0.281630i 0.00327607 0.00900094i
\(980\) 12.5244 27.9893i 0.400078 0.894085i
\(981\) 0 0
\(982\) −33.3159 + 8.92697i −1.06315 + 0.284871i
\(983\) 9.44671 + 0.826480i 0.301303 + 0.0263606i 0.236805 0.971557i \(-0.423900\pi\)
0.0644982 + 0.997918i \(0.479455\pi\)
\(984\) 0 0
\(985\) 13.8041 39.8478i 0.439836 1.26966i
\(986\) 2.80885 + 0.495276i 0.0894520 + 0.0157728i
\(987\) 0 0
\(988\) 0.729384 8.33689i 0.0232048 0.265232i
\(989\) −10.5463 + 18.2667i −0.335353 + 0.580848i
\(990\) 0 0
\(991\) −27.6207 47.8405i −0.877400 1.51970i −0.854184 0.519972i \(-0.825943\pi\)
−0.0232168 0.999730i \(-0.507391\pi\)
\(992\) 3.98600 1.85870i 0.126556 0.0590139i
\(993\) 0 0
\(994\) −40.5414 + 48.3154i −1.28590 + 1.53247i
\(995\) −28.3404 + 41.8473i −0.898450 + 1.32665i
\(996\) 0 0
\(997\) −22.8056 + 32.5697i −0.722259 + 1.03149i 0.275279 + 0.961364i \(0.411230\pi\)
−0.997538 + 0.0701285i \(0.977659\pi\)
\(998\) 2.13957 + 2.13957i 0.0677270 + 0.0677270i
\(999\) 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 810.2.s.a.557.14 216
3.2 odd 2 270.2.r.a.257.8 yes 216
5.3 odd 4 inner 810.2.s.a.233.10 216
15.8 even 4 270.2.r.a.203.4 yes 216
27.2 odd 18 inner 810.2.s.a.737.10 216
27.25 even 9 270.2.r.a.137.4 yes 216
135.83 even 36 inner 810.2.s.a.413.14 216
135.133 odd 36 270.2.r.a.83.8 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.2.r.a.83.8 216 135.133 odd 36
270.2.r.a.137.4 yes 216 27.25 even 9
270.2.r.a.203.4 yes 216 15.8 even 4
270.2.r.a.257.8 yes 216 3.2 odd 2
810.2.s.a.233.10 216 5.3 odd 4 inner
810.2.s.a.413.14 216 135.83 even 36 inner
810.2.s.a.557.14 216 1.1 even 1 trivial
810.2.s.a.737.10 216 27.2 odd 18 inner