Properties

Label 99.2.j.a.35.4
Level $99$
Weight $2$
Character 99.35
Analytic conductor $0.791$
Analytic rank $0$
Dimension $16$
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] = [99,2,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 35.4
Root \(-0.556839 - 1.81878i\) of defining polynomial
Character \(\chi\) \(=\) 99.35
Dual form 99.2.j.a.17.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.726437 - 2.23574i) q^{2} +(-2.85280 - 2.07268i) q^{4} +(2.13811 - 0.694712i) q^{5} +(-2.38116 + 3.27739i) q^{7} +(-2.90269 + 2.10893i) q^{8} +O(q^{10})\) \(q+(0.726437 - 2.23574i) q^{2} +(-2.85280 - 2.07268i) q^{4} +(2.13811 - 0.694712i) q^{5} +(-2.38116 + 3.27739i) q^{7} +(-2.90269 + 2.10893i) q^{8} -5.28492i q^{10} +(-3.31656 + 0.0200544i) q^{11} +(4.42495 + 1.43775i) q^{13} +(5.59763 + 7.70448i) q^{14} +(0.427051 + 1.31433i) q^{16} +(-0.0235753 - 0.0725574i) q^{17} +(1.40822 + 1.93825i) q^{19} +(-7.53950 - 2.44973i) q^{20} +(-2.36444 + 7.42955i) q^{22} -3.22717i q^{23} +(0.0437835 - 0.0318106i) q^{25} +(6.42889 - 8.84860i) q^{26} +(13.5860 - 4.41435i) q^{28} +(1.48796 + 1.08107i) q^{29} +(0.517528 - 1.59279i) q^{31} -3.92711 q^{32} -0.179346 q^{34} +(-2.81433 + 8.66162i) q^{35} +(-5.87906 - 4.27138i) q^{37} +(5.35641 - 1.74040i) q^{38} +(-4.74115 + 6.52564i) q^{40} +(-6.82980 + 4.96214i) q^{41} +4.28086i q^{43} +(9.50306 + 6.81697i) q^{44} +(-7.21513 - 2.34434i) q^{46} +(-3.65360 - 5.02874i) q^{47} +(-2.90822 - 8.95058i) q^{49} +(-0.0393143 - 0.120997i) q^{50} +(-9.64348 - 13.2731i) q^{52} +(1.16884 + 0.379779i) q^{53} +(-7.07723 + 2.34694i) q^{55} -14.5349i q^{56} +(3.49789 - 2.54137i) q^{58} +(-0.341086 + 0.469465i) q^{59} +(-3.59710 + 1.16877i) q^{61} +(-3.18511 - 2.31412i) q^{62} +(-3.70690 + 11.4087i) q^{64} +10.4598 q^{65} +12.9984 q^{67} +(-0.0831326 + 0.255856i) q^{68} +(17.3207 + 12.5842i) q^{70} +(1.06563 - 0.346245i) q^{71} +(7.82153 - 10.7654i) q^{73} +(-13.8205 + 10.0412i) q^{74} -8.44824i q^{76} +(7.83155 - 10.9174i) q^{77} +(0.627566 + 0.203908i) q^{79} +(1.82616 + 2.51349i) q^{80} +(6.13265 + 18.8744i) q^{82} +(-3.15542 - 9.71138i) q^{83} +(-0.100813 - 0.138757i) q^{85} +(9.57090 + 3.10977i) q^{86} +(9.58466 - 7.05260i) q^{88} +6.58983i q^{89} +(-15.2486 + 11.0787i) q^{91} +(-6.68890 + 9.20649i) q^{92} +(-13.8971 + 4.51544i) q^{94} +(4.35745 + 3.16587i) q^{95} +(5.08168 - 15.6398i) q^{97} -22.1238 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70} - 20 q^{73} - 12 q^{82} - 100 q^{85} - 12 q^{88} - 72 q^{91} - 80 q^{94} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.726437 2.23574i 0.513668 1.58091i −0.272023 0.962291i \(-0.587693\pi\)
0.785692 0.618618i \(-0.212307\pi\)
\(3\) 0 0
\(4\) −2.85280 2.07268i −1.42640 1.03634i
\(5\) 2.13811 0.694712i 0.956190 0.310685i 0.210962 0.977494i \(-0.432341\pi\)
0.745228 + 0.666809i \(0.232341\pi\)
\(6\) 0 0
\(7\) −2.38116 + 3.27739i −0.899995 + 1.23874i 0.0704753 + 0.997514i \(0.477548\pi\)
−0.970470 + 0.241223i \(0.922452\pi\)
\(8\) −2.90269 + 2.10893i −1.02626 + 0.745618i
\(9\) 0 0
\(10\) 5.28492i 1.67124i
\(11\) −3.31656 + 0.0200544i −0.999982 + 0.00604662i
\(12\) 0 0
\(13\) 4.42495 + 1.43775i 1.22726 + 0.398761i 0.849721 0.527233i \(-0.176771\pi\)
0.377538 + 0.925994i \(0.376771\pi\)
\(14\) 5.59763 + 7.70448i 1.49603 + 2.05911i
\(15\) 0 0
\(16\) 0.427051 + 1.31433i 0.106763 + 0.328582i
\(17\) −0.0235753 0.0725574i −0.00571786 0.0175978i 0.948157 0.317803i \(-0.102945\pi\)
−0.953875 + 0.300205i \(0.902945\pi\)
\(18\) 0 0
\(19\) 1.40822 + 1.93825i 0.323068 + 0.444665i 0.939401 0.342821i \(-0.111382\pi\)
−0.616333 + 0.787486i \(0.711382\pi\)
\(20\) −7.53950 2.44973i −1.68588 0.547777i
\(21\) 0 0
\(22\) −2.36444 + 7.42955i −0.504100 + 1.58399i
\(23\) 3.22717i 0.672912i −0.941699 0.336456i \(-0.890772\pi\)
0.941699 0.336456i \(-0.109228\pi\)
\(24\) 0 0
\(25\) 0.0437835 0.0318106i 0.00875670 0.00636211i
\(26\) 6.42889 8.84860i 1.26081 1.73535i
\(27\) 0 0
\(28\) 13.5860 4.41435i 2.56750 0.834233i
\(29\) 1.48796 + 1.08107i 0.276307 + 0.200749i 0.717305 0.696759i \(-0.245375\pi\)
−0.440998 + 0.897508i \(0.645375\pi\)
\(30\) 0 0
\(31\) 0.517528 1.59279i 0.0929508 0.286073i −0.893763 0.448539i \(-0.851945\pi\)
0.986714 + 0.162466i \(0.0519446\pi\)
\(32\) −3.92711 −0.694222
\(33\) 0 0
\(34\) −0.179346 −0.0307575
\(35\) −2.81433 + 8.66162i −0.475709 + 1.46408i
\(36\) 0 0
\(37\) −5.87906 4.27138i −0.966511 0.702211i −0.0118571 0.999930i \(-0.503774\pi\)
−0.954654 + 0.297718i \(0.903774\pi\)
\(38\) 5.35641 1.74040i 0.868925 0.282331i
\(39\) 0 0
\(40\) −4.74115 + 6.52564i −0.749642 + 1.03179i
\(41\) −6.82980 + 4.96214i −1.06664 + 0.774956i −0.975305 0.220864i \(-0.929112\pi\)
−0.0913313 + 0.995821i \(0.529112\pi\)
\(42\) 0 0
\(43\) 4.28086i 0.652825i 0.945227 + 0.326413i \(0.105840\pi\)
−0.945227 + 0.326413i \(0.894160\pi\)
\(44\) 9.50306 + 6.81697i 1.43264 + 1.02770i
\(45\) 0 0
\(46\) −7.21513 2.34434i −1.06381 0.345654i
\(47\) −3.65360 5.02874i −0.532932 0.733518i 0.454642 0.890674i \(-0.349767\pi\)
−0.987574 + 0.157157i \(0.949767\pi\)
\(48\) 0 0
\(49\) −2.90822 8.95058i −0.415460 1.27865i
\(50\) −0.0393143 0.120997i −0.00555988 0.0171116i
\(51\) 0 0
\(52\) −9.64348 13.2731i −1.33731 1.84065i
\(53\) 1.16884 + 0.379779i 0.160552 + 0.0521666i 0.388190 0.921579i \(-0.373100\pi\)
−0.227638 + 0.973746i \(0.573100\pi\)
\(54\) 0 0
\(55\) −7.07723 + 2.34694i −0.954294 + 0.316461i
\(56\) 14.5349i 1.94231i
\(57\) 0 0
\(58\) 3.49789 2.54137i 0.459296 0.333698i
\(59\) −0.341086 + 0.469465i −0.0444056 + 0.0611191i −0.830642 0.556806i \(-0.812027\pi\)
0.786237 + 0.617925i \(0.212027\pi\)
\(60\) 0 0
\(61\) −3.59710 + 1.16877i −0.460561 + 0.149645i −0.530102 0.847934i \(-0.677847\pi\)
0.0695411 + 0.997579i \(0.477847\pi\)
\(62\) −3.18511 2.31412i −0.404510 0.293893i
\(63\) 0 0
\(64\) −3.70690 + 11.4087i −0.463363 + 1.42608i
\(65\) 10.4598 1.29738
\(66\) 0 0
\(67\) 12.9984 1.58801 0.794003 0.607914i \(-0.207993\pi\)
0.794003 + 0.607914i \(0.207993\pi\)
\(68\) −0.0831326 + 0.255856i −0.0100813 + 0.0310271i
\(69\) 0 0
\(70\) 17.3207 + 12.5842i 2.07022 + 1.50410i
\(71\) 1.06563 0.346245i 0.126467 0.0410917i −0.245100 0.969498i \(-0.578821\pi\)
0.371567 + 0.928406i \(0.378821\pi\)
\(72\) 0 0
\(73\) 7.82153 10.7654i 0.915441 1.26000i −0.0498335 0.998758i \(-0.515869\pi\)
0.965274 0.261239i \(-0.0841309\pi\)
\(74\) −13.8205 + 10.0412i −1.60660 + 1.16726i
\(75\) 0 0
\(76\) 8.44824i 0.969079i
\(77\) 7.83155 10.9174i 0.892488 1.24416i
\(78\) 0 0
\(79\) 0.627566 + 0.203908i 0.0706066 + 0.0229415i 0.344107 0.938930i \(-0.388182\pi\)
−0.273501 + 0.961872i \(0.588182\pi\)
\(80\) 1.82616 + 2.51349i 0.204171 + 0.281017i
\(81\) 0 0
\(82\) 6.13265 + 18.8744i 0.677238 + 2.08432i
\(83\) −3.15542 9.71138i −0.346352 1.06596i −0.960856 0.277048i \(-0.910644\pi\)
0.614504 0.788914i \(-0.289356\pi\)
\(84\) 0 0
\(85\) −0.100813 0.138757i −0.0109347 0.0150503i
\(86\) 9.57090 + 3.10977i 1.03206 + 0.335336i
\(87\) 0 0
\(88\) 9.58466 7.05260i 1.02173 0.751810i
\(89\) 6.58983i 0.698520i 0.937026 + 0.349260i \(0.113567\pi\)
−0.937026 + 0.349260i \(0.886433\pi\)
\(90\) 0 0
\(91\) −15.2486 + 11.0787i −1.59849 + 1.16137i
\(92\) −6.68890 + 9.20649i −0.697366 + 0.959843i
\(93\) 0 0
\(94\) −13.8971 + 4.51544i −1.43337 + 0.465732i
\(95\) 4.35745 + 3.16587i 0.447065 + 0.324812i
\(96\) 0 0
\(97\) 5.08168 15.6398i 0.515966 1.58798i −0.265551 0.964097i \(-0.585554\pi\)
0.781517 0.623883i \(-0.214446\pi\)
\(98\) −22.1238 −2.23485
\(99\) 0 0
\(100\) −0.190839 −0.0190839
\(101\) 0.532095 1.63762i 0.0529455 0.162949i −0.921087 0.389356i \(-0.872698\pi\)
0.974033 + 0.226406i \(0.0726977\pi\)
\(102\) 0 0
\(103\) 2.61382 + 1.89905i 0.257548 + 0.187119i 0.709065 0.705143i \(-0.249117\pi\)
−0.451518 + 0.892262i \(0.649117\pi\)
\(104\) −15.8763 + 5.15854i −1.55680 + 0.505836i
\(105\) 0 0
\(106\) 1.69818 2.33734i 0.164941 0.227022i
\(107\) 11.9884 8.71006i 1.15896 0.842034i 0.169314 0.985562i \(-0.445845\pi\)
0.989646 + 0.143529i \(0.0458449\pi\)
\(108\) 0 0
\(109\) 14.9258i 1.42963i 0.699313 + 0.714815i \(0.253489\pi\)
−0.699313 + 0.714815i \(0.746511\pi\)
\(110\) 0.105986 + 17.5278i 0.0101053 + 1.67121i
\(111\) 0 0
\(112\) −5.32444 1.73002i −0.503112 0.163471i
\(113\) 6.61055 + 9.09864i 0.621868 + 0.855928i 0.997487 0.0708461i \(-0.0225699\pi\)
−0.375619 + 0.926774i \(0.622570\pi\)
\(114\) 0 0
\(115\) −2.24196 6.90004i −0.209064 0.643432i
\(116\) −2.00415 6.16813i −0.186080 0.572697i
\(117\) 0 0
\(118\) 0.801825 + 1.10362i 0.0738139 + 0.101596i
\(119\) 0.293935 + 0.0955054i 0.0269450 + 0.00875497i
\(120\) 0 0
\(121\) 10.9992 0.133023i 0.999927 0.0120930i
\(122\) 8.89122i 0.804973i
\(123\) 0 0
\(124\) −4.77775 + 3.47124i −0.429054 + 0.311726i
\(125\) −6.53559 + 8.99547i −0.584561 + 0.804580i
\(126\) 0 0
\(127\) −5.76481 + 1.87310i −0.511544 + 0.166211i −0.553404 0.832913i \(-0.686672\pi\)
0.0418604 + 0.999123i \(0.486672\pi\)
\(128\) 16.4598 + 11.9588i 1.45486 + 1.05701i
\(129\) 0 0
\(130\) 7.59840 23.3855i 0.666424 2.05104i
\(131\) −7.15083 −0.624771 −0.312385 0.949955i \(-0.601128\pi\)
−0.312385 + 0.949955i \(0.601128\pi\)
\(132\) 0 0
\(133\) −9.70560 −0.841582
\(134\) 9.44251 29.0611i 0.815709 2.51049i
\(135\) 0 0
\(136\) 0.221450 + 0.160893i 0.0189892 + 0.0137964i
\(137\) 10.1026 3.28252i 0.863120 0.280445i 0.156189 0.987727i \(-0.450079\pi\)
0.706931 + 0.707283i \(0.250079\pi\)
\(138\) 0 0
\(139\) −0.0311975 + 0.0429397i −0.00264614 + 0.00364210i −0.810338 0.585963i \(-0.800716\pi\)
0.807692 + 0.589605i \(0.200716\pi\)
\(140\) 25.9815 18.8767i 2.19584 1.59537i
\(141\) 0 0
\(142\) 2.63400i 0.221041i
\(143\) −14.7044 4.67966i −1.22965 0.391333i
\(144\) 0 0
\(145\) 3.93244 + 1.27773i 0.326572 + 0.106110i
\(146\) −18.3868 25.3073i −1.52171 2.09445i
\(147\) 0 0
\(148\) 7.91856 + 24.3708i 0.650901 + 2.00327i
\(149\) −6.30238 19.3967i −0.516311 1.58904i −0.780883 0.624677i \(-0.785231\pi\)
0.264572 0.964366i \(-0.414769\pi\)
\(150\) 0 0
\(151\) 0.698980 + 0.962063i 0.0568822 + 0.0782916i 0.836510 0.547951i \(-0.184592\pi\)
−0.779628 + 0.626243i \(0.784592\pi\)
\(152\) −8.17525 2.65630i −0.663101 0.215454i
\(153\) 0 0
\(154\) −18.7194 25.4401i −1.50845 2.05003i
\(155\) 3.76508i 0.302419i
\(156\) 0 0
\(157\) 1.40210 1.01868i 0.111900 0.0812998i −0.530428 0.847730i \(-0.677969\pi\)
0.642328 + 0.766430i \(0.277969\pi\)
\(158\) 0.911773 1.25495i 0.0725368 0.0998383i
\(159\) 0 0
\(160\) −8.39658 + 2.72822i −0.663808 + 0.215684i
\(161\) 10.5767 + 7.68443i 0.833561 + 0.605618i
\(162\) 0 0
\(163\) −0.309821 + 0.953532i −0.0242671 + 0.0746864i −0.962457 0.271435i \(-0.912502\pi\)
0.938190 + 0.346122i \(0.112502\pi\)
\(164\) 29.7690 2.32457
\(165\) 0 0
\(166\) −24.0044 −1.86310
\(167\) −4.17734 + 12.8565i −0.323252 + 0.994868i 0.648971 + 0.760813i \(0.275200\pi\)
−0.972223 + 0.234055i \(0.924800\pi\)
\(168\) 0 0
\(169\) 6.99579 + 5.08274i 0.538138 + 0.390980i
\(170\) −0.383460 + 0.124594i −0.0294100 + 0.00955590i
\(171\) 0 0
\(172\) 8.87286 12.2124i 0.676549 0.931190i
\(173\) −6.08619 + 4.42188i −0.462724 + 0.336189i −0.794599 0.607135i \(-0.792319\pi\)
0.331875 + 0.943324i \(0.392319\pi\)
\(174\) 0 0
\(175\) 0.219242i 0.0165731i
\(176\) −1.44270 4.35049i −0.108748 0.327930i
\(177\) 0 0
\(178\) 14.7332 + 4.78709i 1.10430 + 0.358808i
\(179\) 7.34750 + 10.1130i 0.549178 + 0.755879i 0.989900 0.141765i \(-0.0452777\pi\)
−0.440722 + 0.897643i \(0.645278\pi\)
\(180\) 0 0
\(181\) −5.56261 17.1200i −0.413466 1.27252i −0.913616 0.406578i \(-0.866722\pi\)
0.500150 0.865939i \(-0.333278\pi\)
\(182\) 13.6921 + 42.1399i 1.01492 + 3.12362i
\(183\) 0 0
\(184\) 6.80587 + 9.36748i 0.501736 + 0.690580i
\(185\) −15.5374 5.04842i −1.14233 0.371167i
\(186\) 0 0
\(187\) 0.0796442 + 0.240168i 0.00582416 + 0.0175629i
\(188\) 21.9187i 1.59859i
\(189\) 0 0
\(190\) 10.2435 7.44233i 0.743141 0.539924i
\(191\) −12.7297 + 17.5209i −0.921085 + 1.26777i 0.0421514 + 0.999111i \(0.486579\pi\)
−0.963237 + 0.268654i \(0.913421\pi\)
\(192\) 0 0
\(193\) −4.93306 + 1.60285i −0.355090 + 0.115376i −0.481129 0.876650i \(-0.659773\pi\)
0.126040 + 0.992025i \(0.459773\pi\)
\(194\) −31.2750 22.7226i −2.24542 1.63139i
\(195\) 0 0
\(196\) −10.2551 + 31.5620i −0.732509 + 2.25443i
\(197\) −5.14679 −0.366693 −0.183347 0.983048i \(-0.558693\pi\)
−0.183347 + 0.983048i \(0.558693\pi\)
\(198\) 0 0
\(199\) 24.2595 1.71971 0.859855 0.510539i \(-0.170554\pi\)
0.859855 + 0.510539i \(0.170554\pi\)
\(200\) −0.0600037 + 0.184672i −0.00424290 + 0.0130583i
\(201\) 0 0
\(202\) −3.27477 2.37926i −0.230412 0.167404i
\(203\) −7.08615 + 2.30243i −0.497350 + 0.161599i
\(204\) 0 0
\(205\) −11.1556 + 15.3543i −0.779139 + 1.07239i
\(206\) 6.14457 4.46429i 0.428113 0.311042i
\(207\) 0 0
\(208\) 6.42982i 0.445828i
\(209\) −4.70933 6.40009i −0.325751 0.442704i
\(210\) 0 0
\(211\) −17.8262 5.79210i −1.22721 0.398744i −0.377506 0.926007i \(-0.623218\pi\)
−0.849702 + 0.527263i \(0.823218\pi\)
\(212\) −2.54730 3.50606i −0.174950 0.240797i
\(213\) 0 0
\(214\) −10.7647 33.1302i −0.735857 2.26474i
\(215\) 2.97397 + 9.15293i 0.202823 + 0.624225i
\(216\) 0 0
\(217\) 3.98787 + 5.48883i 0.270714 + 0.372606i
\(218\) 33.3702 + 10.8426i 2.26012 + 0.734356i
\(219\) 0 0
\(220\) 25.0544 + 7.97350i 1.68917 + 0.537573i
\(221\) 0.354958i 0.0238771i
\(222\) 0 0
\(223\) 4.44037 3.22612i 0.297349 0.216037i −0.429100 0.903257i \(-0.641169\pi\)
0.726449 + 0.687220i \(0.241169\pi\)
\(224\) 9.35109 12.8707i 0.624796 0.859958i
\(225\) 0 0
\(226\) 25.1444 8.16990i 1.67258 0.543454i
\(227\) −11.1352 8.09016i −0.739066 0.536963i 0.153352 0.988172i \(-0.450993\pi\)
−0.892419 + 0.451209i \(0.850993\pi\)
\(228\) 0 0
\(229\) −6.53035 + 20.0983i −0.431538 + 1.32814i 0.465056 + 0.885281i \(0.346034\pi\)
−0.896593 + 0.442855i \(0.853966\pi\)
\(230\) −17.0554 −1.12460
\(231\) 0 0
\(232\) −6.59897 −0.433244
\(233\) −4.62458 + 14.2330i −0.302967 + 0.932435i 0.677462 + 0.735558i \(0.263080\pi\)
−0.980428 + 0.196877i \(0.936920\pi\)
\(234\) 0 0
\(235\) −11.3053 8.21378i −0.737477 0.535808i
\(236\) 1.94610 0.632327i 0.126680 0.0411610i
\(237\) 0 0
\(238\) 0.427051 0.587785i 0.0276816 0.0381005i
\(239\) 4.37274 3.17698i 0.282849 0.205502i −0.437310 0.899311i \(-0.644069\pi\)
0.720159 + 0.693809i \(0.244069\pi\)
\(240\) 0 0
\(241\) 11.7091i 0.754252i 0.926162 + 0.377126i \(0.123088\pi\)
−0.926162 + 0.377126i \(0.876912\pi\)
\(242\) 7.69281 24.6880i 0.494513 1.58700i
\(243\) 0 0
\(244\) 12.6843 + 4.12137i 0.812028 + 0.263844i
\(245\) −12.4362 17.1169i −0.794518 1.09356i
\(246\) 0 0
\(247\) 3.44458 + 10.6013i 0.219173 + 0.674546i
\(248\) 1.85685 + 5.71479i 0.117910 + 0.362890i
\(249\) 0 0
\(250\) 15.3639 + 21.1465i 0.971696 + 1.33743i
\(251\) 21.4920 + 6.98319i 1.35657 + 0.440775i 0.894895 0.446276i \(-0.147250\pi\)
0.461671 + 0.887051i \(0.347250\pi\)
\(252\) 0 0
\(253\) 0.0647190 + 10.7031i 0.00406885 + 0.672900i
\(254\) 14.2493i 0.894081i
\(255\) 0 0
\(256\) 19.2841 14.0107i 1.20526 0.875671i
\(257\) 16.1737 22.2612i 1.00889 1.38862i 0.0891801 0.996016i \(-0.471575\pi\)
0.919709 0.392601i \(-0.128425\pi\)
\(258\) 0 0
\(259\) 27.9980 9.09709i 1.73971 0.565266i
\(260\) −29.8398 21.6799i −1.85059 1.34453i
\(261\) 0 0
\(262\) −5.19462 + 15.9874i −0.320925 + 0.987705i
\(263\) 32.0386 1.97559 0.987793 0.155773i \(-0.0497868\pi\)
0.987793 + 0.155773i \(0.0497868\pi\)
\(264\) 0 0
\(265\) 2.76294 0.169726
\(266\) −7.05051 + 21.6992i −0.432294 + 1.33046i
\(267\) 0 0
\(268\) −37.0818 26.9415i −2.26513 1.64572i
\(269\) −25.7177 + 8.35619i −1.56804 + 0.509486i −0.958940 0.283610i \(-0.908468\pi\)
−0.609097 + 0.793096i \(0.708468\pi\)
\(270\) 0 0
\(271\) 8.74690 12.0391i 0.531336 0.731322i −0.455997 0.889981i \(-0.650717\pi\)
0.987333 + 0.158660i \(0.0507172\pi\)
\(272\) 0.0852963 0.0619714i 0.00517185 0.00375757i
\(273\) 0 0
\(274\) 24.9713i 1.50857i
\(275\) −0.144573 + 0.106380i −0.00871807 + 0.00641495i
\(276\) 0 0
\(277\) −7.49418 2.43501i −0.450282 0.146305i 0.0750927 0.997177i \(-0.476075\pi\)
−0.525374 + 0.850871i \(0.676075\pi\)
\(278\) 0.0733391 + 0.100943i 0.00439859 + 0.00605414i
\(279\) 0 0
\(280\) −10.0976 31.0772i −0.603447 1.85722i
\(281\) 6.56034 + 20.1906i 0.391357 + 1.20447i 0.931763 + 0.363068i \(0.118271\pi\)
−0.540406 + 0.841405i \(0.681729\pi\)
\(282\) 0 0
\(283\) −2.52460 3.47482i −0.150072 0.206556i 0.727362 0.686254i \(-0.240746\pi\)
−0.877434 + 0.479698i \(0.840746\pi\)
\(284\) −3.75769 1.22095i −0.222978 0.0724499i
\(285\) 0 0
\(286\) −21.1444 + 29.4759i −1.25029 + 1.74295i
\(287\) 34.1996i 2.01874i
\(288\) 0 0
\(289\) 13.7486 9.98893i 0.808740 0.587584i
\(290\) 5.71335 7.86374i 0.335499 0.461775i
\(291\) 0 0
\(292\) −44.6265 + 14.5000i −2.61157 + 0.848550i
\(293\) 15.4486 + 11.2241i 0.902518 + 0.655717i 0.939111 0.343613i \(-0.111651\pi\)
−0.0365938 + 0.999330i \(0.511651\pi\)
\(294\) 0 0
\(295\) −0.403135 + 1.24072i −0.0234714 + 0.0722376i
\(296\) 26.0731 1.51547
\(297\) 0 0
\(298\) −47.9444 −2.77735
\(299\) 4.63988 14.2801i 0.268331 0.825838i
\(300\) 0 0
\(301\) −14.0300 10.1934i −0.808678 0.587539i
\(302\) 2.65869 0.863861i 0.152990 0.0497096i
\(303\) 0 0
\(304\) −1.94611 + 2.67860i −0.111617 + 0.153628i
\(305\) −6.87902 + 4.99790i −0.393891 + 0.286179i
\(306\) 0 0
\(307\) 1.86240i 0.106293i 0.998587 + 0.0531463i \(0.0169250\pi\)
−0.998587 + 0.0531463i \(0.983075\pi\)
\(308\) −44.9702 + 14.9129i −2.56241 + 0.849742i
\(309\) 0 0
\(310\) −8.41775 2.73509i −0.478096 0.155343i
\(311\) 5.26339 + 7.24443i 0.298459 + 0.410794i 0.931739 0.363129i \(-0.118292\pi\)
−0.633279 + 0.773923i \(0.718292\pi\)
\(312\) 0 0
\(313\) 5.29558 + 16.2981i 0.299324 + 0.921224i 0.981735 + 0.190255i \(0.0609316\pi\)
−0.682411 + 0.730969i \(0.739068\pi\)
\(314\) −1.25898 3.87474i −0.0710483 0.218664i
\(315\) 0 0
\(316\) −1.36768 1.88245i −0.0769381 0.105896i
\(317\) −25.9678 8.43746i −1.45850 0.473895i −0.530888 0.847442i \(-0.678141\pi\)
−0.927611 + 0.373547i \(0.878141\pi\)
\(318\) 0 0
\(319\) −4.95659 3.55558i −0.277516 0.199075i
\(320\) 26.9682i 1.50757i
\(321\) 0 0
\(322\) 24.8637 18.0645i 1.38560 1.00670i
\(323\) 0.107435 0.147872i 0.00597785 0.00822781i
\(324\) 0 0
\(325\) 0.239475 0.0778102i 0.0132837 0.00431614i
\(326\) 1.90679 + 1.38536i 0.105607 + 0.0767281i
\(327\) 0 0
\(328\) 9.35999 28.8071i 0.516819 1.59061i
\(329\) 25.1809 1.38827
\(330\) 0 0
\(331\) −5.87217 −0.322764 −0.161382 0.986892i \(-0.551595\pi\)
−0.161382 + 0.986892i \(0.551595\pi\)
\(332\) −11.1268 + 34.2448i −0.610663 + 1.87943i
\(333\) 0 0
\(334\) 25.7093 + 18.6789i 1.40675 + 1.02206i
\(335\) 27.7919 9.03014i 1.51844 0.493370i
\(336\) 0 0
\(337\) −9.74004 + 13.4060i −0.530574 + 0.730272i −0.987218 0.159377i \(-0.949051\pi\)
0.456644 + 0.889650i \(0.349051\pi\)
\(338\) 16.4457 11.9485i 0.894528 0.649912i
\(339\) 0 0
\(340\) 0.604800i 0.0327999i
\(341\) −1.68447 + 5.29296i −0.0912193 + 0.286630i
\(342\) 0 0
\(343\) 9.28988 + 3.01847i 0.501606 + 0.162982i
\(344\) −9.02802 12.4260i −0.486758 0.669965i
\(345\) 0 0
\(346\) 5.46494 + 16.8194i 0.293797 + 0.904215i
\(347\) 0.778158 + 2.39492i 0.0417737 + 0.128566i 0.969768 0.244027i \(-0.0784686\pi\)
−0.927995 + 0.372593i \(0.878469\pi\)
\(348\) 0 0
\(349\) 5.13104 + 7.06228i 0.274658 + 0.378035i 0.923955 0.382500i \(-0.124937\pi\)
−0.649297 + 0.760535i \(0.724937\pi\)
\(350\) 0.490168 + 0.159265i 0.0262006 + 0.00851308i
\(351\) 0 0
\(352\) 13.0245 0.0787558i 0.694210 0.00419770i
\(353\) 0.536500i 0.0285550i −0.999898 0.0142775i \(-0.995455\pi\)
0.999898 0.0142775i \(-0.00454483\pi\)
\(354\) 0 0
\(355\) 2.03789 1.48062i 0.108160 0.0785829i
\(356\) 13.6586 18.7995i 0.723905 0.996370i
\(357\) 0 0
\(358\) 27.9475 9.08069i 1.47707 0.479929i
\(359\) −12.7871 9.29040i −0.674880 0.490329i 0.196775 0.980449i \(-0.436953\pi\)
−0.871655 + 0.490120i \(0.836953\pi\)
\(360\) 0 0
\(361\) 4.09760 12.6111i 0.215663 0.663742i
\(362\) −42.3167 −2.22412
\(363\) 0 0
\(364\) 66.4639 3.48365
\(365\) 9.24439 28.4513i 0.483873 1.48921i
\(366\) 0 0
\(367\) −23.4075 17.0065i −1.22186 0.887734i −0.225608 0.974218i \(-0.572437\pi\)
−0.996253 + 0.0864843i \(0.972437\pi\)
\(368\) 4.24157 1.37817i 0.221107 0.0718420i
\(369\) 0 0
\(370\) −22.5739 + 31.0703i −1.17356 + 1.61527i
\(371\) −4.02788 + 2.92642i −0.209117 + 0.151932i
\(372\) 0 0
\(373\) 6.60935i 0.342219i −0.985252 0.171109i \(-0.945265\pi\)
0.985252 0.171109i \(-0.0547352\pi\)
\(374\) 0.594811 0.00359666i 0.0307570 0.000185979i
\(375\) 0 0
\(376\) 21.2105 + 6.89171i 1.09385 + 0.355413i
\(377\) 5.02984 + 6.92297i 0.259050 + 0.356551i
\(378\) 0 0
\(379\) 0.478524 + 1.47275i 0.0245801 + 0.0756498i 0.962594 0.270948i \(-0.0873370\pi\)
−0.938014 + 0.346597i \(0.887337\pi\)
\(380\) −5.86909 18.0632i −0.301078 0.926623i
\(381\) 0 0
\(382\) 29.9249 + 41.1880i 1.53109 + 2.10736i
\(383\) −12.8467 4.17415i −0.656436 0.213289i −0.0381861 0.999271i \(-0.512158\pi\)
−0.618250 + 0.785982i \(0.712158\pi\)
\(384\) 0 0
\(385\) 9.16021 28.7833i 0.466847 1.46693i
\(386\) 12.1934i 0.620629i
\(387\) 0 0
\(388\) −46.9133 + 34.0845i −2.38166 + 1.73038i
\(389\) −8.80471 + 12.1186i −0.446416 + 0.614440i −0.971623 0.236535i \(-0.923988\pi\)
0.525206 + 0.850975i \(0.323988\pi\)
\(390\) 0 0
\(391\) −0.234155 + 0.0760817i −0.0118417 + 0.00384762i
\(392\) 27.3178 + 19.8475i 1.37976 + 1.00245i
\(393\) 0 0
\(394\) −3.73882 + 11.5069i −0.188359 + 0.579709i
\(395\) 1.48346 0.0746409
\(396\) 0 0
\(397\) −20.7132 −1.03956 −0.519782 0.854299i \(-0.673987\pi\)
−0.519782 + 0.854299i \(0.673987\pi\)
\(398\) 17.6230 54.2380i 0.883360 2.71870i
\(399\) 0 0
\(400\) 0.0605073 + 0.0439611i 0.00302537 + 0.00219806i
\(401\) −25.7211 + 8.35730i −1.28445 + 0.417343i −0.870146 0.492795i \(-0.835975\pi\)
−0.414305 + 0.910138i \(0.635975\pi\)
\(402\) 0 0
\(403\) 4.58007 6.30392i 0.228149 0.314021i
\(404\) −4.91223 + 3.56894i −0.244392 + 0.177561i
\(405\) 0 0
\(406\) 17.5154i 0.869273i
\(407\) 19.5839 + 14.0484i 0.970739 + 0.696354i
\(408\) 0 0
\(409\) −5.80668 1.88670i −0.287122 0.0932915i 0.161915 0.986805i \(-0.448233\pi\)
−0.449037 + 0.893513i \(0.648233\pi\)
\(410\) 26.2245 + 36.0949i 1.29514 + 1.78260i
\(411\) 0 0
\(412\) −3.52058 10.8352i −0.173447 0.533814i
\(413\) −0.726437 2.23574i −0.0357456 0.110014i
\(414\) 0 0
\(415\) −13.4932 18.5718i −0.662357 0.911656i
\(416\) −17.3773 5.64622i −0.851991 0.276829i
\(417\) 0 0
\(418\) −17.7300 + 5.87958i −0.867202 + 0.287580i
\(419\) 35.6619i 1.74220i 0.491110 + 0.871098i \(0.336591\pi\)
−0.491110 + 0.871098i \(0.663409\pi\)
\(420\) 0 0
\(421\) −11.5751 + 8.40982i −0.564137 + 0.409870i −0.832971 0.553317i \(-0.813362\pi\)
0.268834 + 0.963187i \(0.413362\pi\)
\(422\) −25.8993 + 35.6473i −1.26076 + 1.73528i
\(423\) 0 0
\(424\) −4.19370 + 1.36262i −0.203664 + 0.0661745i
\(425\) −0.00334030 0.00242687i −0.000162028 0.000117721i
\(426\) 0 0
\(427\) 4.73477 14.5721i 0.229131 0.705194i
\(428\) −52.2536 −2.52577
\(429\) 0 0
\(430\) 22.6240 1.09103
\(431\) −2.68944 + 8.27725i −0.129546 + 0.398701i −0.994702 0.102802i \(-0.967219\pi\)
0.865156 + 0.501503i \(0.167219\pi\)
\(432\) 0 0
\(433\) 30.3812 + 22.0733i 1.46003 + 1.06077i 0.983355 + 0.181693i \(0.0581576\pi\)
0.476673 + 0.879080i \(0.341842\pi\)
\(434\) 15.1685 4.92856i 0.728113 0.236578i
\(435\) 0 0
\(436\) 30.9364 42.5803i 1.48158 2.03923i
\(437\) 6.25507 4.54458i 0.299221 0.217397i
\(438\) 0 0
\(439\) 32.4669i 1.54956i −0.632232 0.774779i \(-0.717861\pi\)
0.632232 0.774779i \(-0.282139\pi\)
\(440\) 15.5935 21.7378i 0.743390 1.03631i
\(441\) 0 0
\(442\) −0.793595 0.257855i −0.0377474 0.0122649i
\(443\) 11.0630 + 15.2269i 0.525618 + 0.723451i 0.986455 0.164034i \(-0.0524506\pi\)
−0.460837 + 0.887485i \(0.652451\pi\)
\(444\) 0 0
\(445\) 4.57804 + 14.0897i 0.217020 + 0.667918i
\(446\) −3.98712 12.2711i −0.188796 0.581053i
\(447\) 0 0
\(448\) −28.5639 39.3149i −1.34952 1.85745i
\(449\) 6.86840 + 2.23168i 0.324140 + 0.105319i 0.466567 0.884486i \(-0.345491\pi\)
−0.142427 + 0.989805i \(0.545491\pi\)
\(450\) 0 0
\(451\) 22.5520 16.5942i 1.06193 0.781392i
\(452\) 39.6582i 1.86536i
\(453\) 0 0
\(454\) −26.1765 + 19.0183i −1.22852 + 0.892575i
\(455\) −24.9065 + 34.2809i −1.16764 + 1.60711i
\(456\) 0 0
\(457\) 4.01554 1.30473i 0.187839 0.0610326i −0.213587 0.976924i \(-0.568515\pi\)
0.401426 + 0.915891i \(0.368515\pi\)
\(458\) 40.1908 + 29.2004i 1.87799 + 1.36444i
\(459\) 0 0
\(460\) −7.90572 + 24.3313i −0.368606 + 1.13445i
\(461\) −14.1922 −0.660997 −0.330499 0.943806i \(-0.607217\pi\)
−0.330499 + 0.943806i \(0.607217\pi\)
\(462\) 0 0
\(463\) −40.3784 −1.87654 −0.938271 0.345902i \(-0.887573\pi\)
−0.938271 + 0.345902i \(0.887573\pi\)
\(464\) −0.785440 + 2.41734i −0.0364632 + 0.112222i
\(465\) 0 0
\(466\) 28.4619 + 20.6788i 1.31847 + 0.957925i
\(467\) 10.7476 3.49210i 0.497338 0.161595i −0.0495980 0.998769i \(-0.515794\pi\)
0.546936 + 0.837174i \(0.315794\pi\)
\(468\) 0 0
\(469\) −30.9513 + 42.6008i −1.42920 + 1.96712i
\(470\) −26.5765 + 19.3090i −1.22588 + 0.890656i
\(471\) 0 0
\(472\) 2.08203i 0.0958334i
\(473\) −0.0858500 14.1977i −0.00394739 0.652813i
\(474\) 0 0
\(475\) 0.123314 + 0.0400671i 0.00565802 + 0.00183840i
\(476\) −0.640587 0.881692i −0.0293612 0.0404123i
\(477\) 0 0
\(478\) −3.92639 12.0842i −0.179589 0.552718i
\(479\) −7.07597 21.7776i −0.323309 0.995044i −0.972198 0.234161i \(-0.924766\pi\)
0.648889 0.760883i \(-0.275234\pi\)
\(480\) 0 0
\(481\) −19.8733 27.3533i −0.906145 1.24720i
\(482\) 26.1786 + 8.50595i 1.19240 + 0.387436i
\(483\) 0 0
\(484\) −31.6542 22.4183i −1.43883 1.01902i
\(485\) 36.9698i 1.67871i
\(486\) 0 0
\(487\) 6.10169 4.43314i 0.276494 0.200885i −0.440893 0.897560i \(-0.645338\pi\)
0.717387 + 0.696675i \(0.245338\pi\)
\(488\) 7.97641 10.9786i 0.361075 0.496977i
\(489\) 0 0
\(490\) −47.3031 + 15.3697i −2.13694 + 0.694333i
\(491\) −30.8965 22.4476i −1.39434 1.01305i −0.995373 0.0960820i \(-0.969369\pi\)
−0.398967 0.916965i \(-0.630631\pi\)
\(492\) 0 0
\(493\) 0.0433602 0.133449i 0.00195285 0.00601024i
\(494\) 26.2041 1.17898
\(495\) 0 0
\(496\) 2.31446 0.103922
\(497\) −1.40266 + 4.31695i −0.0629181 + 0.193642i
\(498\) 0 0
\(499\) 6.51994 + 4.73701i 0.291873 + 0.212058i 0.724079 0.689717i \(-0.242265\pi\)
−0.432207 + 0.901775i \(0.642265\pi\)
\(500\) 37.2895 12.1161i 1.66764 0.541848i
\(501\) 0 0
\(502\) 31.2252 42.9778i 1.39365 1.91820i
\(503\) 21.0846 15.3188i 0.940115 0.683033i −0.00833362 0.999965i \(-0.502653\pi\)
0.948448 + 0.316932i \(0.102653\pi\)
\(504\) 0 0
\(505\) 3.87106i 0.172260i
\(506\) 23.9765 + 7.63045i 1.06588 + 0.339215i
\(507\) 0 0
\(508\) 20.3282 + 6.60503i 0.901917 + 0.293051i
\(509\) −16.4364 22.6228i −0.728531 1.00274i −0.999197 0.0400639i \(-0.987244\pi\)
0.270666 0.962673i \(-0.412756\pi\)
\(510\) 0 0
\(511\) 16.6581 + 51.2684i 0.736911 + 2.26798i
\(512\) −4.74153 14.5929i −0.209548 0.644922i
\(513\) 0 0
\(514\) −38.0212 52.3316i −1.67704 2.30825i
\(515\) 6.90792 + 2.24452i 0.304399 + 0.0989054i
\(516\) 0 0
\(517\) 12.2182 + 16.6049i 0.537357 + 0.730282i
\(518\) 69.2047i 3.04068i
\(519\) 0 0
\(520\) −30.3616 + 22.0590i −1.33144 + 0.967351i
\(521\) 18.9804 26.1242i 0.831545 1.14452i −0.156088 0.987743i \(-0.549888\pi\)
0.987633 0.156781i \(-0.0501117\pi\)
\(522\) 0 0
\(523\) 16.5104 5.36454i 0.721948 0.234575i 0.0750804 0.997177i \(-0.476079\pi\)
0.646868 + 0.762602i \(0.276079\pi\)
\(524\) 20.3999 + 14.8214i 0.891173 + 0.647475i
\(525\) 0 0
\(526\) 23.2740 71.6301i 1.01480 3.12322i
\(527\) −0.127769 −0.00556572
\(528\) 0 0
\(529\) 12.5853 0.547189
\(530\) 2.00710 6.17722i 0.0871828 0.268321i
\(531\) 0 0
\(532\) 27.6881 + 20.1166i 1.20043 + 0.872166i
\(533\) −37.3558 + 12.1376i −1.61806 + 0.525740i
\(534\) 0 0
\(535\) 19.5814 26.9515i 0.846578 1.16522i
\(536\) −37.7303 + 27.4126i −1.62970 + 1.18405i
\(537\) 0 0
\(538\) 63.5684i 2.74063i
\(539\) 9.82480 + 29.6269i 0.423184 + 1.27612i
\(540\) 0 0
\(541\) −9.58312 3.11375i −0.412011 0.133870i 0.0956753 0.995413i \(-0.469499\pi\)
−0.507686 + 0.861542i \(0.669499\pi\)
\(542\) −20.5622 28.3014i −0.883222 1.21565i
\(543\) 0 0
\(544\) 0.0925830 + 0.284941i 0.00396946 + 0.0122168i
\(545\) 10.3691 + 31.9129i 0.444165 + 1.36700i
\(546\) 0 0
\(547\) 14.0244 + 19.3029i 0.599639 + 0.825333i 0.995675 0.0929023i \(-0.0296144\pi\)
−0.396036 + 0.918235i \(0.629614\pi\)
\(548\) −35.6242 11.5750i −1.52179 0.494460i
\(549\) 0 0
\(550\) 0.132815 + 0.400506i 0.00566325 + 0.0170776i
\(551\) 4.40642i 0.187720i
\(552\) 0 0
\(553\) −2.16262 + 1.57124i −0.0919640 + 0.0668158i
\(554\) −10.8881 + 14.9862i −0.462591 + 0.636702i
\(555\) 0 0
\(556\) 0.178001 0.0578359i 0.00754891 0.00245279i
\(557\) 31.6776 + 23.0151i 1.34222 + 0.975181i 0.999359 + 0.0357950i \(0.0113963\pi\)
0.342862 + 0.939386i \(0.388604\pi\)
\(558\) 0 0
\(559\) −6.15482 + 18.9426i −0.260321 + 0.801185i
\(560\) −12.5861 −0.531859
\(561\) 0 0
\(562\) 49.9068 2.10519
\(563\) −1.55147 + 4.77494i −0.0653868 + 0.201240i −0.978412 0.206663i \(-0.933740\pi\)
0.913025 + 0.407903i \(0.133740\pi\)
\(564\) 0 0
\(565\) 20.4550 + 14.8614i 0.860548 + 0.625225i
\(566\) −9.60276 + 3.12012i −0.403634 + 0.131149i
\(567\) 0 0
\(568\) −2.36299 + 3.25238i −0.0991489 + 0.136467i
\(569\) −7.69308 + 5.58935i −0.322511 + 0.234318i −0.737246 0.675624i \(-0.763874\pi\)
0.414735 + 0.909942i \(0.363874\pi\)
\(570\) 0 0
\(571\) 39.8291i 1.66680i 0.552673 + 0.833398i \(0.313608\pi\)
−0.552673 + 0.833398i \(0.686392\pi\)
\(572\) 32.2494 + 43.8278i 1.34842 + 1.83253i
\(573\) 0 0
\(574\) −76.4614 24.8438i −3.19144 1.03696i
\(575\) −0.102658 0.141297i −0.00428115 0.00589249i
\(576\) 0 0
\(577\) −4.03506 12.4186i −0.167982 0.516994i 0.831262 0.555881i \(-0.187619\pi\)
−0.999244 + 0.0388866i \(0.987619\pi\)
\(578\) −12.3452 37.9946i −0.513493 1.58037i
\(579\) 0 0
\(580\) −8.57016 11.7958i −0.355856 0.489794i
\(581\) 39.3415 + 12.7828i 1.63216 + 0.530321i
\(582\) 0 0
\(583\) −3.88415 1.23612i −0.160865 0.0511949i
\(584\) 47.7437i 1.97565i
\(585\) 0 0
\(586\) 36.3166 26.3855i 1.50022 1.08998i
\(587\) 13.9608 19.2153i 0.576222 0.793102i −0.417053 0.908882i \(-0.636937\pi\)
0.993275 + 0.115780i \(0.0369369\pi\)
\(588\) 0 0
\(589\) 3.81602 1.23990i 0.157236 0.0510891i
\(590\) 2.48108 + 1.80261i 0.102145 + 0.0742123i
\(591\) 0 0
\(592\) 3.10334 9.55111i 0.127547 0.392548i
\(593\) −37.1489 −1.52552 −0.762761 0.646680i \(-0.776157\pi\)
−0.762761 + 0.646680i \(0.776157\pi\)
\(594\) 0 0
\(595\) 0.694814 0.0284846
\(596\) −22.2238 + 68.3979i −0.910323 + 2.80169i
\(597\) 0 0
\(598\) −28.5560 20.7471i −1.16774 0.848414i
\(599\) −2.26902 + 0.737248i −0.0927095 + 0.0301231i −0.355004 0.934865i \(-0.615521\pi\)
0.262295 + 0.964988i \(0.415521\pi\)
\(600\) 0 0
\(601\) 3.99333 5.49635i 0.162891 0.224201i −0.719767 0.694216i \(-0.755751\pi\)
0.882658 + 0.470015i \(0.155751\pi\)
\(602\) −32.9818 + 23.9627i −1.34424 + 0.976646i
\(603\) 0 0
\(604\) 4.19334i 0.170624i
\(605\) 23.4250 7.92570i 0.952363 0.322225i
\(606\) 0 0
\(607\) −38.5143 12.5141i −1.56325 0.507930i −0.605575 0.795788i \(-0.707057\pi\)
−0.957673 + 0.287859i \(0.907057\pi\)
\(608\) −5.53025 7.61173i −0.224281 0.308696i
\(609\) 0 0
\(610\) 6.17684 + 19.0104i 0.250093 + 0.769707i
\(611\) −8.93688 27.5049i −0.361547 1.11273i
\(612\) 0 0
\(613\) 0.119072 + 0.163888i 0.00480926 + 0.00661938i 0.811415 0.584471i \(-0.198698\pi\)
−0.806606 + 0.591090i \(0.798698\pi\)
\(614\) 4.16384 + 1.35291i 0.168039 + 0.0545991i
\(615\) 0 0
\(616\) 0.291489 + 48.2060i 0.0117444 + 1.94228i
\(617\) 8.08426i 0.325460i 0.986671 + 0.162730i \(0.0520299\pi\)
−0.986671 + 0.162730i \(0.947970\pi\)
\(618\) 0 0
\(619\) −16.9785 + 12.3356i −0.682424 + 0.495810i −0.874161 0.485636i \(-0.838588\pi\)
0.191737 + 0.981446i \(0.438588\pi\)
\(620\) −7.80381 + 10.7410i −0.313409 + 0.431370i
\(621\) 0 0
\(622\) 20.0202 6.50496i 0.802737 0.260825i
\(623\) −21.5974 15.6914i −0.865282 0.628664i
\(624\) 0 0
\(625\) −7.80814 + 24.0310i −0.312326 + 0.961239i
\(626\) 40.2853 1.61012
\(627\) 0 0
\(628\) −6.11131 −0.243868
\(629\) −0.171320 + 0.527268i −0.00683097 + 0.0210236i
\(630\) 0 0
\(631\) 19.6268 + 14.2597i 0.781332 + 0.567671i 0.905378 0.424606i \(-0.139587\pi\)
−0.124047 + 0.992276i \(0.539587\pi\)
\(632\) −2.25165 + 0.731607i −0.0895660 + 0.0291018i
\(633\) 0 0
\(634\) −37.7280 + 51.9281i −1.49837 + 2.06233i
\(635\) −11.0245 + 8.00977i −0.437494 + 0.317858i
\(636\) 0 0
\(637\) 43.7871i 1.73491i
\(638\) −11.5500 + 8.49876i −0.457270 + 0.336469i
\(639\) 0 0
\(640\) 43.5007 + 14.1342i 1.71952 + 0.558705i
\(641\) 9.48633 + 13.0568i 0.374688 + 0.515713i 0.954167 0.299273i \(-0.0967442\pi\)
−0.579480 + 0.814987i \(0.696744\pi\)
\(642\) 0 0
\(643\) 3.88866 + 11.9681i 0.153354 + 0.471975i 0.997990 0.0633656i \(-0.0201834\pi\)
−0.844637 + 0.535340i \(0.820183\pi\)
\(644\) −14.2459 43.8443i −0.561366 1.72771i
\(645\) 0 0
\(646\) −0.252558 0.347617i −0.00993678 0.0136768i
\(647\) −28.7701 9.34797i −1.13107 0.367507i −0.317087 0.948396i \(-0.602705\pi\)
−0.813982 + 0.580890i \(0.802705\pi\)
\(648\) 0 0
\(649\) 1.12182 1.56385i 0.0440352 0.0613865i
\(650\) 0.591929i 0.0232174i
\(651\) 0 0
\(652\) 2.86023 2.07808i 0.112015 0.0813837i
\(653\) 11.5162 15.8507i 0.450664 0.620286i −0.521876 0.853021i \(-0.674768\pi\)
0.972540 + 0.232735i \(0.0747676\pi\)
\(654\) 0 0
\(655\) −15.2892 + 4.96777i −0.597399 + 0.194107i
\(656\) −9.43855 6.85751i −0.368514 0.267741i
\(657\) 0 0
\(658\) 18.2924 56.2981i 0.713111 2.19473i
\(659\) −1.34943 −0.0525664 −0.0262832 0.999655i \(-0.508367\pi\)
−0.0262832 + 0.999655i \(0.508367\pi\)
\(660\) 0 0
\(661\) 28.7859 1.11964 0.559821 0.828614i \(-0.310870\pi\)
0.559821 + 0.828614i \(0.310870\pi\)
\(662\) −4.26576 + 13.1287i −0.165794 + 0.510260i
\(663\) 0 0
\(664\) 29.6398 + 21.5346i 1.15025 + 0.835703i
\(665\) −20.7516 + 6.74260i −0.804712 + 0.261467i
\(666\) 0 0
\(667\) 3.48879 4.80191i 0.135086 0.185931i
\(668\) 38.5646 28.0188i 1.49211 1.08408i
\(669\) 0 0
\(670\) 68.6954i 2.65394i
\(671\) 11.9066 3.94843i 0.459648 0.152428i
\(672\) 0 0
\(673\) 20.6864 + 6.72140i 0.797400 + 0.259091i 0.679252 0.733905i \(-0.262304\pi\)
0.118148 + 0.992996i \(0.462304\pi\)
\(674\) 22.8969 + 31.5149i 0.881955 + 1.21391i
\(675\) 0 0
\(676\) −9.42270 29.0001i −0.362411 1.11539i
\(677\) 5.84208 + 17.9801i 0.224529 + 0.691030i 0.998339 + 0.0576121i \(0.0183487\pi\)
−0.773810 + 0.633418i \(0.781651\pi\)
\(678\) 0 0
\(679\) 39.1574 + 53.8955i 1.50272 + 2.06832i
\(680\) 0.585258 + 0.190162i 0.0224436 + 0.00729237i
\(681\) 0 0
\(682\) 10.6100 + 7.61105i 0.406279 + 0.291442i
\(683\) 33.7466i 1.29128i −0.763642 0.645640i \(-0.776591\pi\)
0.763642 0.645640i \(-0.223409\pi\)
\(684\) 0 0
\(685\) 19.3199 14.0367i 0.738176 0.536316i
\(686\) 13.4970 18.5771i 0.515319 0.709275i
\(687\) 0 0
\(688\) −5.62645 + 1.82815i −0.214507 + 0.0696974i
\(689\) 4.62602 + 3.36100i 0.176237 + 0.128044i
\(690\) 0 0
\(691\) −8.50814 + 26.1854i −0.323665 + 0.996138i 0.648375 + 0.761321i \(0.275449\pi\)
−0.972040 + 0.234817i \(0.924551\pi\)
\(692\) 26.5278 1.00844
\(693\) 0 0
\(694\) 5.91971 0.224709
\(695\) −0.0368728 + 0.113483i −0.00139867 + 0.00430465i
\(696\) 0 0
\(697\) 0.521055 + 0.378569i 0.0197364 + 0.0143393i
\(698\) 19.5168 6.34140i 0.738722 0.240025i
\(699\) 0 0
\(700\) 0.454418 0.625453i 0.0171754 0.0236399i
\(701\) 8.43699 6.12983i 0.318661 0.231521i −0.416943 0.908933i \(-0.636899\pi\)
0.735604 + 0.677412i \(0.236899\pi\)
\(702\) 0 0
\(703\) 17.4101i 0.656636i
\(704\) 12.0654 37.9119i 0.454731 1.42886i
\(705\) 0 0
\(706\) −1.19948 0.389734i −0.0451429 0.0146678i
\(707\) 4.10011 + 5.64332i 0.154201 + 0.212239i
\(708\) 0 0
\(709\) −6.19477 19.0655i −0.232649 0.716021i −0.997425 0.0717239i \(-0.977150\pi\)
0.764775 0.644297i \(-0.222850\pi\)
\(710\) −1.82988 5.63178i −0.0686740 0.211357i
\(711\) 0 0
\(712\) −13.8975 19.1282i −0.520829 0.716860i
\(713\) −5.14021 1.67015i −0.192502 0.0625478i
\(714\) 0 0
\(715\) −34.6907 + 0.209765i −1.29736 + 0.00784477i
\(716\) 44.0793i 1.64732i
\(717\) 0 0
\(718\) −30.0600 + 21.8399i −1.12183 + 0.815057i
\(719\) 6.01752 8.28241i 0.224416 0.308882i −0.681931 0.731417i \(-0.738860\pi\)
0.906347 + 0.422535i \(0.138860\pi\)
\(720\) 0 0
\(721\) −12.4479 + 4.04456i −0.463583 + 0.150627i
\(722\) −25.2185 18.3223i −0.938537 0.681887i
\(723\) 0 0
\(724\) −19.6152 + 60.3694i −0.728993 + 2.24361i
\(725\) 0.0995374 0.00369673
\(726\) 0 0
\(727\) −14.4456 −0.535759 −0.267880 0.963452i \(-0.586323\pi\)
−0.267880 + 0.963452i \(0.586323\pi\)
\(728\) 20.8976 64.3163i 0.774517 2.38372i
\(729\) 0 0
\(730\) −56.8943 41.3361i −2.10575 1.52992i
\(731\) 0.310608 0.100923i 0.0114883 0.00373276i
\(732\) 0 0
\(733\) 4.29622 5.91324i 0.158685 0.218411i −0.722270 0.691611i \(-0.756901\pi\)
0.880955 + 0.473200i \(0.156901\pi\)
\(734\) −55.0263 + 39.9789i −2.03106 + 1.47565i
\(735\) 0 0
\(736\) 12.6735i 0.467151i
\(737\) −43.1100 + 0.260675i −1.58798 + 0.00960207i
\(738\) 0 0
\(739\) −12.4909 4.05854i −0.459485 0.149296i 0.0701229 0.997538i \(-0.477661\pi\)
−0.529608 + 0.848243i \(0.677661\pi\)
\(740\) 33.8614 + 46.6062i 1.24477 + 1.71328i
\(741\) 0 0
\(742\) 3.61673 + 11.1312i 0.132774 + 0.408638i
\(743\) 10.9307 + 33.6412i 0.401008 + 1.23418i 0.924183 + 0.381950i \(0.124747\pi\)
−0.523175 + 0.852225i \(0.675253\pi\)
\(744\) 0 0
\(745\) −26.9503 37.0939i −0.987383 1.35902i
\(746\) −14.7768 4.80127i −0.541017 0.175787i
\(747\) 0 0
\(748\) 0.270584 0.850230i 0.00989352 0.0310875i
\(749\) 60.0306i 2.19347i
\(750\) 0 0
\(751\) 18.6629 13.5594i 0.681018 0.494789i −0.192677 0.981262i \(-0.561717\pi\)
0.873695 + 0.486473i \(0.161717\pi\)
\(752\) 5.04914 6.94955i 0.184123 0.253424i
\(753\) 0 0
\(754\) 19.1318 6.21631i 0.696741 0.226385i
\(755\) 2.16285 + 1.57140i 0.0787141 + 0.0571892i
\(756\) 0 0
\(757\) 3.02640 9.31430i 0.109996 0.338534i −0.880874 0.473350i \(-0.843044\pi\)
0.990871 + 0.134816i \(0.0430445\pi\)
\(758\) 3.64030 0.132222
\(759\) 0 0
\(760\) −19.3249 −0.700988
\(761\) 14.9642 46.0550i 0.542452 1.66949i −0.184522 0.982828i \(-0.559074\pi\)
0.726973 0.686666i \(-0.240926\pi\)
\(762\) 0 0
\(763\) −48.9176 35.5407i −1.77094 1.28666i
\(764\) 72.6303 23.5990i 2.62767 0.853783i
\(765\) 0 0
\(766\) −18.6646 + 25.6897i −0.674381 + 0.928205i
\(767\) −2.18426 + 1.58696i −0.0788691 + 0.0573017i
\(768\) 0 0
\(769\) 33.4223i 1.20524i −0.798029 0.602619i \(-0.794124\pi\)
0.798029 0.602619i \(-0.205876\pi\)
\(770\) −57.6977 41.3891i −2.07928 1.49156i
\(771\) 0 0
\(772\) 17.3952 + 5.65205i 0.626068 + 0.203422i
\(773\) −3.82924 5.27050i −0.137728 0.189567i 0.734581 0.678521i \(-0.237379\pi\)
−0.872310 + 0.488954i \(0.837379\pi\)
\(774\) 0 0
\(775\) −0.0280083 0.0862007i −0.00100609 0.00309642i
\(776\) 18.2326 + 56.1143i 0.654514 + 2.01439i
\(777\) 0 0
\(778\) 20.6981 + 28.4885i 0.742063 + 1.02136i
\(779\) −19.2357 6.25007i −0.689192 0.223932i
\(780\) 0 0
\(781\) −3.52729 + 1.16971i −0.126216 + 0.0418556i
\(782\) 0.578780i 0.0206971i
\(783\) 0 0
\(784\) 10.5220 7.64471i 0.375787 0.273025i
\(785\) 2.29014 3.15211i 0.0817386 0.112503i
\(786\) 0 0
\(787\) 27.5749 8.95962i 0.982939 0.319376i 0.226911 0.973916i \(-0.427137\pi\)
0.756028 + 0.654539i \(0.227137\pi\)
\(788\) 14.6828 + 10.6676i 0.523052 + 0.380019i
\(789\) 0 0
\(790\) 1.07764 3.31663i 0.0383407 0.118000i
\(791\) −45.5606 −1.61995
\(792\) 0 0
\(793\) −17.5974 −0.624901
\(794\) −15.0468 + 46.3093i −0.533991 + 1.64346i
\(795\) 0 0
\(796\) −69.2075 50.2822i −2.45299 1.78220i
\(797\) 25.7264 8.35900i 0.911274 0.296091i 0.184392 0.982853i \(-0.440968\pi\)
0.726882 + 0.686762i \(0.240968\pi\)
\(798\) 0 0
\(799\) −0.278738 + 0.383650i −0.00986103 + 0.0135725i
\(800\) −0.171943 + 0.124924i −0.00607910 + 0.00441672i
\(801\) 0 0
\(802\) 63.5768i 2.24498i
\(803\) −25.7247 + 35.8610i −0.907805 + 1.26551i
\(804\) 0 0
\(805\) 27.9526 + 9.08234i 0.985199 + 0.320110i
\(806\) −10.7668 14.8193i −0.379245 0.521986i
\(807\) 0 0
\(808\) 1.90911 + 5.87565i 0.0671624 + 0.206705i
\(809\) 12.9385 + 39.8205i 0.454892 + 1.40001i 0.871262 + 0.490818i \(0.163302\pi\)
−0.416370 + 0.909195i \(0.636698\pi\)
\(810\) 0 0
\(811\) −7.51871 10.3486i −0.264018 0.363389i 0.656341 0.754464i \(-0.272103\pi\)
−0.920359 + 0.391075i \(0.872103\pi\)
\(812\) 24.9876 + 8.11895i 0.876891 + 0.284919i
\(813\) 0 0
\(814\) 45.6351 33.5793i 1.59951 1.17695i
\(815\) 2.25399i 0.0789538i
\(816\) 0 0
\(817\) −8.29738 + 6.02840i −0.290289 + 0.210907i
\(818\) −8.43637 + 11.6117i −0.294971 + 0.405992i
\(819\) 0 0
\(820\) 63.6493 20.6809i 2.22273 0.722208i
\(821\) 9.59682 + 6.97250i 0.334931 + 0.243342i 0.742520 0.669824i \(-0.233630\pi\)
−0.407589 + 0.913166i \(0.633630\pi\)
\(822\) 0 0
\(823\) 8.11976 24.9900i 0.283037 0.871098i −0.703943 0.710256i \(-0.748579\pi\)
0.986980 0.160842i \(-0.0514210\pi\)
\(824\) −11.5921 −0.403829
\(825\) 0 0
\(826\) −5.52626 −0.192283
\(827\) 7.99992 24.6212i 0.278184 0.856163i −0.710175 0.704025i \(-0.751384\pi\)
0.988359 0.152138i \(-0.0486159\pi\)
\(828\) 0 0
\(829\) −14.0195 10.1858i −0.486918 0.353766i 0.317080 0.948399i \(-0.397298\pi\)
−0.803998 + 0.594632i \(0.797298\pi\)
\(830\) −51.3238 + 16.6761i −1.78148 + 0.578837i
\(831\) 0 0
\(832\) −32.8057 + 45.1531i −1.13733 + 1.56540i
\(833\) −0.580869 + 0.422026i −0.0201259 + 0.0146223i
\(834\) 0 0
\(835\) 30.3907i 1.05171i
\(836\) 0.169424 + 28.0191i 0.00585965 + 0.969061i
\(837\) 0 0
\(838\) 79.7307 + 25.9061i 2.75425 + 0.894911i
\(839\) 18.2513 + 25.1207i 0.630104 + 0.867264i 0.998039 0.0625873i \(-0.0199352\pi\)
−0.367935 + 0.929851i \(0.619935\pi\)
\(840\) 0 0
\(841\) −7.91617 24.3635i −0.272971 0.840120i
\(842\) 10.3936 + 31.9882i 0.358187 + 1.10239i
\(843\) 0 0
\(844\) 38.8495 + 53.4718i 1.33726 + 1.84058i
\(845\) 18.4888 + 6.00737i 0.636033 + 0.206660i
\(846\) 0 0
\(847\) −25.7549 + 36.3654i −0.884949 + 1.24953i
\(848\) 1.69842i 0.0583241i
\(849\) 0 0
\(850\) −0.00785238 + 0.00570509i −0.000269334 + 0.000195683i
\(851\) −13.7845 + 18.9727i −0.472527 + 0.650377i
\(852\) 0 0
\(853\) 0.303737 0.0986902i 0.0103998 0.00337909i −0.303812 0.952732i \(-0.598260\pi\)
0.314212 + 0.949353i \(0.398260\pi\)
\(854\) −29.1400 21.1714i −0.997150 0.724472i
\(855\) 0 0
\(856\) −16.4296 + 50.5652i −0.561553 + 1.72828i
\(857\) 13.2476 0.452528 0.226264 0.974066i \(-0.427349\pi\)
0.226264 + 0.974066i \(0.427349\pi\)
\(858\) 0 0
\(859\) −8.58152 −0.292798 −0.146399 0.989226i \(-0.546768\pi\)
−0.146399 + 0.989226i \(0.546768\pi\)
\(860\) 10.4870 32.2756i 0.357603 1.10059i
\(861\) 0 0
\(862\) 16.5521 + 12.0258i 0.563766 + 0.409600i
\(863\) 51.0889 16.5998i 1.73909 0.565063i 0.744374 0.667763i \(-0.232748\pi\)
0.994712 + 0.102700i \(0.0327482\pi\)
\(864\) 0 0
\(865\) −9.94098 + 13.6826i −0.338004 + 0.465222i
\(866\) 71.4202 51.8898i 2.42696 1.76329i
\(867\) 0 0
\(868\) 23.9241i 0.812037i
\(869\) −2.08545 0.663690i −0.0707441 0.0225141i
\(870\) 0 0
\(871\) 57.5172 + 18.6885i 1.94889 + 0.633234i
\(872\) −31.4774 43.3249i −1.06596 1.46717i
\(873\) 0 0
\(874\) −5.61659 17.2861i −0.189984 0.584710i
\(875\) −13.9193 42.8394i −0.470560 1.44823i
\(876\) 0 0
\(877\) −25.8716 35.6092i −0.873623 1.20244i −0.978147 0.207916i \(-0.933332\pi\)
0.104524 0.994522i \(-0.466668\pi\)
\(878\) −72.5876 23.5851i −2.44971 0.795959i
\(879\) 0 0
\(880\) −6.10698 8.29954i −0.205866 0.279777i
\(881\) 7.44194i 0.250725i −0.992111 0.125363i \(-0.959991\pi\)
0.992111 0.125363i \(-0.0400095\pi\)
\(882\) 0 0
\(883\) 7.59369 5.51714i 0.255548 0.185667i −0.452634 0.891696i \(-0.649516\pi\)
0.708182 + 0.706030i \(0.249516\pi\)
\(884\) −0.735715 + 1.01262i −0.0247448 + 0.0340582i
\(885\) 0 0
\(886\) 42.0799 13.6726i 1.41370 0.459340i
\(887\) −19.5658 14.2154i −0.656957 0.477307i 0.208677 0.977985i \(-0.433084\pi\)
−0.865634 + 0.500678i \(0.833084\pi\)
\(888\) 0 0
\(889\) 7.58806 23.3537i 0.254496 0.783257i
\(890\) 34.8267 1.16739
\(891\) 0 0
\(892\) −19.3542 −0.648026
\(893\) 4.60189 14.1632i 0.153996 0.473952i
\(894\) 0 0
\(895\) 22.7353 + 16.5182i 0.759958 + 0.552142i
\(896\) −78.3870 + 25.4695i −2.61873 + 0.850875i
\(897\) 0 0
\(898\) 9.97892 13.7348i 0.333001 0.458336i
\(899\) 2.49197 1.81052i 0.0831119 0.0603843i
\(900\) 0 0
\(901\) 0.0937613i 0.00312364i
\(902\) −20.7178 62.4750i −0.689829 2.08019i
\(903\) 0 0
\(904\) −38.3767 12.4693i −1.27639 0.414724i
\(905\) −23.7869 32.7399i −0.790703 1.08831i
\(906\) 0 0
\(907\) −11.0734 34.0803i −0.367685 1.13162i −0.948282 0.317428i \(-0.897181\pi\)
0.580597 0.814191i \(-0.302819\pi\)
\(908\) 14.9980 + 46.1592i 0.497728 + 1.53185i
\(909\) 0 0
\(910\) 58.5502 + 80.5875i 1.94092 + 2.67145i
\(911\) 8.33061 + 2.70678i 0.276005 + 0.0896796i 0.443749 0.896151i \(-0.353648\pi\)
−0.167744 + 0.985831i \(0.553648\pi\)
\(912\) 0 0
\(913\) 10.6599 + 32.1451i 0.352791 + 1.06385i
\(914\) 9.92552i 0.328307i
\(915\) 0 0
\(916\) 60.2872 43.8012i 1.99195 1.44723i
\(917\) 17.0273 23.4360i 0.562290 0.773926i
\(918\) 0 0
\(919\) −39.4876 + 12.8303i −1.30258 + 0.423233i −0.876477 0.481443i \(-0.840113\pi\)
−0.426100 + 0.904676i \(0.640113\pi\)
\(920\) 21.0594 + 15.3005i 0.694307 + 0.504444i
\(921\) 0 0
\(922\) −10.3097 + 31.7301i −0.339533 + 1.04498i
\(923\) 5.21318 0.171594
\(924\) 0 0
\(925\) −0.393281 −0.0129310
\(926\) −29.3323 + 90.2756i −0.963920 + 2.96664i
\(927\) 0 0
\(928\) −5.84339 4.24547i −0.191819 0.139364i
\(929\) 51.5363 16.7451i 1.69085 0.549390i 0.703883 0.710316i \(-0.251448\pi\)
0.986967 + 0.160925i \(0.0514478\pi\)
\(930\) 0 0
\(931\) 13.2531 18.2413i 0.434351 0.597833i
\(932\) 42.6935 31.0186i 1.39847 1.01605i
\(933\) 0 0
\(934\) 26.5656i 0.869253i
\(935\) 0.337136 + 0.458176i 0.0110255 + 0.0149839i
\(936\) 0 0
\(937\) −16.5444 5.37559i −0.540480 0.175613i 0.0260393 0.999661i \(-0.491710\pi\)
−0.566520 + 0.824048i \(0.691710\pi\)
\(938\) 72.7602 + 100.146i 2.37571 + 3.26988i
\(939\) 0 0
\(940\) 15.2272 + 46.8646i 0.496657 + 1.52855i
\(941\) −6.64708 20.4576i −0.216689 0.666899i −0.999029 0.0440486i \(-0.985974\pi\)
0.782341 0.622851i \(-0.214026\pi\)
\(942\) 0 0
\(943\) 16.0137 + 22.0410i 0.521478 + 0.717753i
\(944\) −0.762692 0.247814i −0.0248235 0.00806564i
\(945\) 0 0
\(946\) −31.8049 10.1218i −1.03407 0.329089i
\(947\) 44.7887i 1.45544i 0.685875 + 0.727719i \(0.259420\pi\)
−0.685875 + 0.727719i \(0.740580\pi\)
\(948\) 0 0
\(949\) 50.0878 36.3909i 1.62592 1.18130i
\(950\) 0.179159 0.246592i 0.00581269 0.00800049i
\(951\) 0 0
\(952\) −1.05462 + 0.342666i −0.0341803 + 0.0111059i
\(953\) 8.11741 + 5.89765i 0.262949 + 0.191043i 0.711446 0.702741i \(-0.248041\pi\)
−0.448497 + 0.893784i \(0.648041\pi\)
\(954\) 0 0
\(955\) −15.0454 + 46.3049i −0.486857 + 1.49839i
\(956\) −19.0594 −0.616425
\(957\) 0 0
\(958\) −53.8294 −1.73915
\(959\) −13.2977 + 40.9262i −0.429406 + 1.32158i
\(960\) 0 0
\(961\) 22.8104 + 16.5727i 0.735819 + 0.534604i
\(962\) −75.5916 + 24.5612i −2.43717 + 0.791884i
\(963\) 0 0
\(964\) 24.2693 33.4039i 0.781662 1.07587i
\(965\) −9.43388 + 6.85412i −0.303688 + 0.220642i
\(966\) 0 0
\(967\) 4.32167i 0.138976i −0.997583 0.0694878i \(-0.977863\pi\)
0.997583 0.0694878i \(-0.0221365\pi\)
\(968\) −31.6467 + 23.5826i −1.01716 + 0.757974i
\(969\) 0 0
\(970\) −82.6550 26.8562i −2.65389 0.862302i
\(971\) −33.7344 46.4314i −1.08259 1.49005i −0.856640 0.515914i \(-0.827452\pi\)
−0.225947 0.974140i \(-0.572548\pi\)
\(972\) 0 0
\(973\) −0.0664437 0.204493i −0.00213009 0.00655574i
\(974\) −5.47886 16.8622i −0.175554 0.540300i
\(975\) 0 0
\(976\) −3.07229 4.22864i −0.0983416 0.135356i
\(977\) −3.28130 1.06616i −0.104978 0.0341095i 0.256057 0.966662i \(-0.417577\pi\)
−0.361035 + 0.932552i \(0.617577\pi\)
\(978\) 0 0
\(979\) −0.132155 21.8556i −0.00422369 0.698508i
\(980\) 74.6073i 2.38324i
\(981\) 0 0
\(982\) −72.6315 + 52.7699i −2.31776 + 1.68395i
\(983\) −0.608167 + 0.837070i −0.0193975 + 0.0266984i −0.818606 0.574356i \(-0.805253\pi\)
0.799208 + 0.601054i \(0.205253\pi\)
\(984\) 0 0
\(985\) −11.0044 + 3.57554i −0.350628 + 0.113926i
\(986\) −0.266859 0.193884i −0.00849853 0.00617454i
\(987\) 0 0
\(988\) 12.1465 37.3830i 0.386431 1.18931i
\(989\) 13.8151 0.439294
\(990\) 0 0
\(991\) 9.78910 0.310961 0.155481 0.987839i \(-0.450307\pi\)
0.155481 + 0.987839i \(0.450307\pi\)
\(992\) −2.03239 + 6.25506i −0.0645285 + 0.198598i
\(993\) 0 0
\(994\) 8.63265 + 6.27199i 0.273811 + 0.198935i
\(995\) 51.8693 16.8534i 1.64437 0.534288i
\(996\) 0 0
\(997\) −6.82690 + 9.39642i −0.216210 + 0.297588i −0.903321 0.428965i \(-0.858878\pi\)
0.687111 + 0.726552i \(0.258878\pi\)
\(998\) 15.3271 11.1358i 0.485170 0.352496i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 99.2.j.a.35.4 yes 16
3.2 odd 2 inner 99.2.j.a.35.1 yes 16
4.3 odd 2 1584.2.cd.c.1025.4 16
9.2 odd 6 891.2.u.c.134.4 32
9.4 even 3 891.2.u.c.431.4 32
9.5 odd 6 891.2.u.c.431.1 32
9.7 even 3 891.2.u.c.134.1 32
11.4 even 5 1089.2.d.g.1088.13 16
11.6 odd 10 inner 99.2.j.a.17.1 16
11.7 odd 10 1089.2.d.g.1088.3 16
12.11 even 2 1584.2.cd.c.1025.1 16
33.17 even 10 inner 99.2.j.a.17.4 yes 16
33.26 odd 10 1089.2.d.g.1088.4 16
33.29 even 10 1089.2.d.g.1088.14 16
44.39 even 10 1584.2.cd.c.17.1 16
99.50 even 30 891.2.u.c.512.1 32
99.61 odd 30 891.2.u.c.215.1 32
99.83 even 30 891.2.u.c.215.4 32
99.94 odd 30 891.2.u.c.512.4 32
132.83 odd 10 1584.2.cd.c.17.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.j.a.17.1 16 11.6 odd 10 inner
99.2.j.a.17.4 yes 16 33.17 even 10 inner
99.2.j.a.35.1 yes 16 3.2 odd 2 inner
99.2.j.a.35.4 yes 16 1.1 even 1 trivial
891.2.u.c.134.1 32 9.7 even 3
891.2.u.c.134.4 32 9.2 odd 6
891.2.u.c.215.1 32 99.61 odd 30
891.2.u.c.215.4 32 99.83 even 30
891.2.u.c.431.1 32 9.5 odd 6
891.2.u.c.431.4 32 9.4 even 3
891.2.u.c.512.1 32 99.50 even 30
891.2.u.c.512.4 32 99.94 odd 30
1089.2.d.g.1088.3 16 11.7 odd 10
1089.2.d.g.1088.4 16 33.26 odd 10
1089.2.d.g.1088.13 16 11.4 even 5
1089.2.d.g.1088.14 16 33.29 even 10
1584.2.cd.c.17.1 16 44.39 even 10
1584.2.cd.c.17.4 16 132.83 odd 10
1584.2.cd.c.1025.1 16 12.11 even 2
1584.2.cd.c.1025.4 16 4.3 odd 2