Properties

Label 891.2.u.c.134.1
Level $891$
Weight $2$
Character 891.134
Analytic conductor $7.115$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(107,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.u (of order \(30\), degree \(8\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{30})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 134.1
Character \(\chi\) \(=\) 891.134
Dual form 891.2.u.c.512.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.29943 + 0.488759i) q^{2} +(3.22139 - 1.43426i) q^{4} +(-0.467414 + 2.19901i) q^{5} +(4.02888 + 0.423453i) q^{7} +(-2.90269 + 2.10893i) q^{8} +O(q^{10})\) \(q+(-2.29943 + 0.488759i) q^{2} +(3.22139 - 1.43426i) q^{4} +(-0.467414 + 2.19901i) q^{5} +(4.02888 + 0.423453i) q^{7} +(-2.90269 + 2.10893i) q^{8} -5.28492i q^{10} +(1.67565 + 2.86220i) q^{11} +(-3.45760 + 3.11324i) q^{13} +(-9.47109 + 0.995452i) q^{14} +(0.924716 - 1.02700i) q^{16} +(-0.0235753 - 0.0725574i) q^{17} +(1.40822 + 1.93825i) q^{19} +(1.64822 + 7.75427i) q^{20} +(-5.25196 - 5.76244i) q^{22} +(2.79482 + 1.61359i) q^{23} +(-0.0494405 - 0.0220123i) q^{25} +(6.42889 - 8.84860i) q^{26} +(13.5860 - 4.41435i) q^{28} +(0.192251 - 1.82914i) q^{29} +(1.12063 + 1.24459i) q^{31} +(1.96356 - 3.40098i) q^{32} +(0.0896728 + 0.155318i) q^{34} +(-2.81433 + 8.66162i) q^{35} +(-5.87906 - 4.27138i) q^{37} +(-4.18544 - 3.76859i) q^{38} +(-3.28079 - 7.36878i) q^{40} +(-0.882440 - 8.39585i) q^{41} +(3.70733 - 2.14043i) q^{43} +(9.50306 + 6.81697i) q^{44} +(-7.21513 - 2.34434i) q^{46} +(-2.52822 + 5.67848i) q^{47} +(9.20554 + 1.95670i) q^{49} +(0.124444 + 0.0264513i) q^{50} +(-6.67312 + 14.9881i) q^{52} +(1.16884 + 0.379779i) q^{53} +(-7.07723 + 2.34694i) q^{55} +(-12.5876 + 7.26746i) q^{56} +(0.451943 + 4.29995i) q^{58} +(-0.236025 - 0.530122i) q^{59} +(2.81073 + 2.53079i) q^{61} +(-3.18511 - 2.31412i) q^{62} +(-3.70690 + 11.4087i) q^{64} +(-5.22991 - 9.05847i) q^{65} +(-6.49920 + 11.2569i) q^{67} +(-0.180011 - 0.199923i) q^{68} +(2.23791 - 21.2923i) q^{70} +(1.06563 - 0.346245i) q^{71} +(7.82153 - 10.7654i) q^{73} +(15.6061 + 6.94830i) q^{74} +(7.31639 + 4.22412i) q^{76} +(5.53899 + 12.2410i) q^{77} +(-0.137193 - 0.645442i) q^{79} +(1.82616 + 2.51349i) q^{80} +(6.13265 + 18.8744i) q^{82} +(-6.83259 + 7.58836i) q^{83} +(0.170574 - 0.0179280i) q^{85} +(-7.47859 + 6.73376i) q^{86} +(-10.9001 - 4.77426i) q^{88} +6.58983i q^{89} +(-15.2486 + 11.0787i) q^{91} +(11.3175 + 1.18952i) q^{92} +(3.03806 - 14.2929i) q^{94} +(-4.92045 + 2.19073i) q^{95} +(-16.0853 + 3.41903i) q^{97} -22.1238 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29943 + 0.488759i −1.62594 + 0.345604i −0.928585 0.371120i \(-0.878974\pi\)
−0.697356 + 0.716725i \(0.745641\pi\)
\(3\) 0 0
\(4\) 3.22139 1.43426i 1.61070 0.717129i
\(5\) −0.467414 + 2.19901i −0.209034 + 0.983427i 0.741054 + 0.671445i \(0.234326\pi\)
−0.950088 + 0.311982i \(0.899007\pi\)
\(6\) 0 0
\(7\) 4.02888 + 0.423453i 1.52277 + 0.160050i 0.828634 0.559790i \(-0.189118\pi\)
0.694140 + 0.719840i \(0.255785\pi\)
\(8\) −2.90269 + 2.10893i −1.02626 + 0.745618i
\(9\) 0 0
\(10\) 5.28492i 1.67124i
\(11\) 1.67565 + 2.86220i 0.505227 + 0.862986i
\(12\) 0 0
\(13\) −3.45760 + 3.11324i −0.958966 + 0.863457i −0.990703 0.136039i \(-0.956563\pi\)
0.0317372 + 0.999496i \(0.489896\pi\)
\(14\) −9.47109 + 0.995452i −2.53126 + 0.266046i
\(15\) 0 0
\(16\) 0.924716 1.02700i 0.231179 0.256750i
\(17\) −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 \(0.711382\pi\)
\(20\) 1.64822 + 7.75427i 0.368553 + 1.73391i
\(21\) 0 0
\(22\) −5.25196 5.76244i −1.11972 1.22856i
\(23\) 2.79482 + 1.61359i 0.582759 + 0.336456i 0.762229 0.647307i \(-0.224105\pi\)
−0.179470 + 0.983763i \(0.557438\pi\)
\(24\) 0 0
\(25\) −0.0494405 0.0220123i −0.00988810 0.00440247i
\(26\) 6.42889 8.84860i 1.26081 1.73535i
\(27\) 0 0
\(28\) 13.5860 4.41435i 2.56750 0.834233i
\(29\) 0.192251 1.82914i 0.0357001 0.339664i −0.962064 0.272825i \(-0.912042\pi\)
0.997764 0.0668387i \(-0.0212913\pi\)
\(30\) 0 0
\(31\) 1.12063 + 1.24459i 0.201271 + 0.223534i 0.835328 0.549752i \(-0.185278\pi\)
−0.634056 + 0.773287i \(0.718611\pi\)
\(32\) 1.96356 3.40098i 0.347111 0.601214i
\(33\) 0 0
\(34\) 0.0896728 + 0.155318i 0.0153788 + 0.0266368i
\(35\) −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 \(0.903774\pi\)
\(38\) −4.18544 3.76859i −0.678968 0.611346i
\(39\) 0 0
\(40\) −3.28079 7.36878i −0.518739 1.16511i
\(41\) −0.882440 8.39585i −0.137814 1.31121i −0.816740 0.577006i \(-0.804221\pi\)
0.678926 0.734206i \(-0.262446\pi\)
\(42\) 0 0
\(43\) 3.70733 2.14043i 0.565363 0.326413i −0.189932 0.981797i \(-0.560827\pi\)
0.755295 + 0.655385i \(0.227493\pi\)
\(44\) 9.50306 + 6.81697i 1.43264 + 1.02770i
\(45\) 0 0
\(46\) −7.21513 2.34434i −1.06381 0.345654i
\(47\) −2.52822 + 5.67848i −0.368779 + 0.828291i 0.629889 + 0.776686i \(0.283101\pi\)
−0.998668 + 0.0516056i \(0.983566\pi\)
\(48\) 0 0
\(49\) 9.20554 + 1.95670i 1.31508 + 0.279528i
\(50\) 0.124444 + 0.0264513i 0.0175990 + 0.00374078i
\(51\) 0 0
\(52\) −6.67312 + 14.9881i −0.925395 + 2.07847i
\(53\) 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
\(56\) −12.5876 + 7.26746i −1.68209 + 0.971156i
\(57\) 0 0
\(58\) 0.451943 + 4.29995i 0.0593430 + 0.564611i
\(59\) −0.236025 0.530122i −0.0307279 0.0690159i 0.897530 0.440954i \(-0.145360\pi\)
−0.928257 + 0.371938i \(0.878693\pi\)
\(60\) 0 0
\(61\) 2.81073 + 2.53079i 0.359877 + 0.324035i 0.829158 0.559014i \(-0.188820\pi\)
−0.469281 + 0.883049i \(0.655487\pi\)
\(62\) −3.18511 2.31412i −0.404510 0.293893i
\(63\) 0 0
\(64\) −3.70690 + 11.4087i −0.463363 + 1.42608i
\(65\) −5.22991 9.05847i −0.648691 1.12357i
\(66\) 0 0
\(67\) −6.49920 + 11.2569i −0.794003 + 1.37525i 0.129467 + 0.991584i \(0.458673\pi\)
−0.923470 + 0.383670i \(0.874660\pi\)
\(68\) −0.180011 0.199923i −0.0218296 0.0242442i
\(69\) 0 0
\(70\) 2.23791 21.2923i 0.267482 2.54492i
\(71\) 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 \(-0.0841309\pi\)
\(74\) 15.6061 + 6.94830i 1.81418 + 0.807724i
\(75\) 0 0
\(76\) 7.31639 + 4.22412i 0.839247 + 0.484540i
\(77\) 5.53899 + 12.2410i 0.631226 + 1.39499i
\(78\) 0 0
\(79\) −0.137193 0.645442i −0.0154354 0.0726179i 0.969756 0.244077i \(-0.0784851\pi\)
−0.985191 + 0.171459i \(0.945152\pi\)
\(80\) 1.82616 + 2.51349i 0.204171 + 0.281017i
\(81\) 0 0
\(82\) 6.13265 + 18.8744i 0.677238 + 2.08432i
\(83\) −6.83259 + 7.58836i −0.749974 + 0.832931i −0.990471 0.137719i \(-0.956023\pi\)
0.240497 + 0.970650i \(0.422690\pi\)
\(84\) 0 0
\(85\) 0.170574 0.0179280i 0.0185013 0.00194457i
\(86\) −7.47859 + 6.73376i −0.806438 + 0.726120i
\(87\) 0 0
\(88\) −10.9001 4.77426i −1.16195 0.508937i
\(89\) 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
\(92\) 11.3175 + 1.18952i 1.17993 + 0.124016i
\(93\) 0 0
\(94\) 3.03806 14.2929i 0.313352 1.47420i
\(95\) −4.92045 + 2.19073i −0.504828 + 0.224764i
\(96\) 0 0
\(97\) −16.0853 + 3.41903i −1.63321 + 0.347150i −0.931058 0.364872i \(-0.881113\pi\)
−0.702157 + 0.712023i \(0.747779\pi\)
\(98\) −22.1238 −2.23485
\(99\) 0 0
\(100\) −0.190839 −0.0190839
\(101\) −1.68427 + 0.358002i −0.167591 + 0.0356226i −0.290943 0.956740i \(-0.593969\pi\)
0.123352 + 0.992363i \(0.460636\pi\)
\(102\) 0 0
\(103\) −2.95154 + 1.31411i −0.290824 + 0.129483i −0.546963 0.837157i \(-0.684216\pi\)
0.256139 + 0.966640i \(0.417549\pi\)
\(104\) 3.47075 16.3286i 0.340335 1.60115i
\(105\) 0 0
\(106\) −2.87328 0.301994i −0.279078 0.0293323i
\(107\) 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 \(0.746511\pi\)
\(110\) 15.1265 8.85567i 1.44226 0.844355i
\(111\) 0 0
\(112\) 4.16046 3.74609i 0.393126 0.353972i
\(113\) −11.1849 + 1.17558i −1.05219 + 0.110590i −0.614800 0.788683i \(-0.710763\pi\)
−0.437389 + 0.899272i \(0.644097\pi\)
\(114\) 0 0
\(115\) −4.85463 + 5.39161i −0.452697 + 0.502771i
\(116\) −2.00415 6.16813i −0.186080 0.572697i
\(117\) 0 0
\(118\) 0.801825 + 1.10362i 0.0738139 + 0.101596i
\(119\) −0.0642576 0.302308i −0.00589048 0.0277125i
\(120\) 0 0
\(121\) −5.38440 + 9.59209i −0.489491 + 0.872009i
\(122\) −7.70002 4.44561i −0.697127 0.402487i
\(123\) 0 0
\(124\) 5.39505 + 2.40203i 0.484490 + 0.215709i
\(125\) −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 \(0.486672\pi\)
\(128\) 2.12668 20.2340i 0.187974 1.78845i
\(129\) 0 0
\(130\) 16.4532 + 18.2731i 1.44304 + 1.60266i
\(131\) 3.57541 6.19280i 0.312385 0.541067i −0.666493 0.745511i \(-0.732205\pi\)
0.978878 + 0.204444i \(0.0655387\pi\)
\(132\) 0 0
\(133\) 4.85280 + 8.40530i 0.420791 + 0.728832i
\(134\) 9.44251 29.0611i 0.815709 2.51049i
\(135\) 0 0
\(136\) 0.221450 + 0.160893i 0.0189892 + 0.0137964i
\(137\) −7.89402 7.10781i −0.674432 0.607261i 0.259059 0.965861i \(-0.416587\pi\)
−0.933491 + 0.358600i \(0.883254\pi\)
\(138\) 0 0
\(139\) −0.0215881 0.0484877i −0.00183108 0.00411267i 0.912628 0.408792i \(-0.134050\pi\)
−0.914459 + 0.404679i \(0.867383\pi\)
\(140\) 3.35692 + 31.9390i 0.283712 + 2.69934i
\(141\) 0 0
\(142\) −2.28111 + 1.31700i −0.191427 + 0.110520i
\(143\) −14.7044 4.67966i −1.22965 0.391333i
\(144\) 0 0
\(145\) 3.93244 + 1.27773i 0.326572 + 0.106110i
\(146\) −12.7234 + 28.5771i −1.05299 + 2.36506i
\(147\) 0 0
\(148\) −25.0650 5.32773i −2.06033 0.437937i
\(149\) 19.9493 + 4.24035i 1.63431 + 0.347383i 0.931428 0.363926i \(-0.118564\pi\)
0.702880 + 0.711309i \(0.251897\pi\)
\(150\) 0 0
\(151\) 0.483681 1.08637i 0.0393614 0.0884072i −0.892795 0.450464i \(-0.851259\pi\)
0.932156 + 0.362057i \(0.117925\pi\)
\(152\) −8.17525 2.65630i −0.663101 0.215454i
\(153\) 0 0
\(154\) −18.7194 25.4401i −1.50845 2.05003i
\(155\) −3.26066 + 1.88254i −0.261902 + 0.151209i
\(156\) 0 0
\(157\) 0.181157 + 1.72359i 0.0144579 + 0.137558i 0.999370 0.0354993i \(-0.0113022\pi\)
−0.984912 + 0.173057i \(0.944635\pi\)
\(158\) 0.630930 + 1.41709i 0.0501941 + 0.112738i
\(159\) 0 0
\(160\) 6.56100 + 5.90755i 0.518692 + 0.467033i
\(161\) 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 \(0.112502\pi\)
\(164\) −14.8845 25.7807i −1.16228 2.01314i
\(165\) 0 0
\(166\) 12.0022 20.7884i 0.931550 1.61349i
\(167\) −9.04541 10.0459i −0.699955 0.777379i 0.283414 0.958998i \(-0.408533\pi\)
−0.983369 + 0.181619i \(0.941866\pi\)
\(168\) 0 0
\(169\) 0.903886 8.59990i 0.0695297 0.661531i
\(170\) −0.383460 + 0.124594i −0.0294100 + 0.00955590i
\(171\) 0 0
\(172\) 8.87286 12.2124i 0.676549 0.931190i
\(173\) 6.87255 + 3.05986i 0.522510 + 0.232637i 0.651005 0.759074i \(-0.274348\pi\)
−0.128494 + 0.991710i \(0.541014\pi\)
\(174\) 0 0
\(175\) −0.189869 0.109621i −0.0143527 0.00828655i
\(176\) 4.48898 + 0.925829i 0.338370 + 0.0697870i
\(177\) 0 0
\(178\) −3.22083 15.1528i −0.241412 1.13575i
\(179\) 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 \(-0.333278\pi\)
\(182\) 29.6482 32.9276i 2.19767 2.44076i
\(183\) 0 0
\(184\) −11.5154 + 1.21032i −0.848928 + 0.0892259i
\(185\) 12.1408 10.9316i 0.892607 0.803707i
\(186\) 0 0
\(187\) 0.168170 0.189058i 0.0122978 0.0138253i
\(188\) 21.9187i 1.59859i
\(189\) 0 0
\(190\) 10.2435 7.44233i 0.743141 0.539924i
\(191\) 21.5383 + 2.26377i 1.55846 + 0.163801i 0.844180 0.536060i \(-0.180088\pi\)
0.714280 + 0.699861i \(0.246755\pi\)
\(192\) 0 0
\(193\) 1.07842 5.07358i 0.0776266 0.365204i −0.922139 0.386859i \(-0.873560\pi\)
0.999766 + 0.0216545i \(0.00689339\pi\)
\(194\) 35.3159 15.7237i 2.53553 1.12889i
\(195\) 0 0
\(196\) 32.4611 6.89982i 2.31865 0.492844i
\(197\) −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 \(0.170554\pi\)
\(200\) 0.189933 0.0403715i 0.0134303 0.00285469i
\(201\) 0 0
\(202\) 3.69788 1.64640i 0.260182 0.115840i
\(203\) 1.54911 7.28800i 0.108726 0.511517i
\(204\) 0 0
\(205\) 18.8750 + 1.98385i 1.31829 + 0.138558i
\(206\) 6.14457 4.46429i 0.428113 0.311042i
\(207\) 0 0
\(208\) 6.42982i 0.445828i
\(209\) −3.18798 + 7.27844i −0.220517 + 0.503460i
\(210\) 0 0
\(211\) 13.9292 12.5419i 0.958927 0.863422i −0.0317716 0.999495i \(-0.510115\pi\)
0.990699 + 0.136073i \(0.0434483\pi\)
\(212\) 4.30999 0.452998i 0.296011 0.0311121i
\(213\) 0 0
\(214\) −23.3093 + 25.8876i −1.59339 + 1.76964i
\(215\) 2.97397 + 9.15293i 0.202823 + 0.624225i
\(216\) 0 0
\(217\) 3.98787 + 5.48883i 0.270714 + 0.372606i
\(218\) −7.29511 34.3208i −0.494087 2.32450i
\(219\) 0 0
\(220\) −19.4324 + 17.7110i −1.31013 + 1.19407i
\(221\) 0.307403 + 0.177479i 0.0206781 + 0.0119385i
\(222\) 0 0
\(223\) −5.01408 2.23241i −0.335768 0.149493i 0.231926 0.972734i \(-0.425497\pi\)
−0.567693 + 0.823240i \(0.692164\pi\)
\(224\) 9.35109 12.8707i 0.624796 0.859958i
\(225\) 0 0
\(226\) 25.1444 8.16990i 1.67258 0.543454i
\(227\) −1.43871 + 13.6884i −0.0954905 + 0.908531i 0.836967 + 0.547253i \(0.184326\pi\)
−0.932458 + 0.361279i \(0.882340\pi\)
\(228\) 0 0
\(229\) −14.1405 15.7046i −0.934431 1.03779i −0.999204 0.0398904i \(-0.987299\pi\)
0.0647734 0.997900i \(-0.479368\pi\)
\(230\) 8.52768 14.7704i 0.562298 0.973929i
\(231\) 0 0
\(232\) 3.29949 + 5.71488i 0.216622 + 0.375200i
\(233\) −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
\(236\) −1.52066 1.36921i −0.0989866 0.0891280i
\(237\) 0 0
\(238\) 0.295511 + 0.663730i 0.0191552 + 0.0430232i
\(239\) 0.564976 + 5.37539i 0.0365453 + 0.347705i 0.997481 + 0.0709336i \(0.0225978\pi\)
−0.960936 + 0.276772i \(0.910735\pi\)
\(240\) 0 0
\(241\) 10.1404 5.85457i 0.653202 0.377126i −0.136480 0.990643i \(-0.543579\pi\)
0.789682 + 0.613517i \(0.210246\pi\)
\(242\) 7.69281 24.6880i 0.494513 1.58700i
\(243\) 0 0
\(244\) 12.6843 + 4.12137i 0.812028 + 0.263844i
\(245\) −8.60560 + 19.3285i −0.549792 + 1.23485i
\(246\) 0 0
\(247\) −10.9033 2.31757i −0.693761 0.147463i
\(248\) −5.87758 1.24932i −0.373227 0.0793318i
\(249\) 0 0
\(250\) 10.6315 23.8788i 0.672396 1.51023i
\(251\) 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
\(254\) 12.3403 7.12466i 0.774297 0.447041i
\(255\) 0 0
\(256\) 2.49159 + 23.7059i 0.155725 + 1.48162i
\(257\) 11.1919 + 25.1375i 0.698133 + 1.56803i 0.817985 + 0.575240i \(0.195091\pi\)
−0.119852 + 0.992792i \(0.538242\pi\)
\(258\) 0 0
\(259\) −21.8773 19.6984i −1.35939 1.22400i
\(260\) −29.8398 21.6799i −1.85059 1.34453i
\(261\) 0 0
\(262\) −5.19462 + 15.9874i −0.320925 + 0.987705i
\(263\) −16.0193 27.7463i −0.987793 1.71091i −0.628800 0.777567i \(-0.716453\pi\)
−0.358993 0.933340i \(-0.616880\pi\)
\(264\) 0 0
\(265\) −1.38147 + 2.39277i −0.0848630 + 0.146987i
\(266\) −15.2668 16.9555i −0.936069 1.03961i
\(267\) 0 0
\(268\) −4.79113 + 45.5846i −0.292665 + 2.78452i
\(269\) −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 \(0.0507172\pi\)
\(272\) −0.0963170 0.0428831i −0.00584008 0.00260017i
\(273\) 0 0
\(274\) 21.6257 + 12.4856i 1.30646 + 0.754284i
\(275\) −0.0198412 0.178394i −0.00119647 0.0107575i
\(276\) 0 0
\(277\) 1.63831 + 7.70765i 0.0984366 + 0.463108i 0.999563 + 0.0295520i \(0.00940805\pi\)
−0.901127 + 0.433556i \(0.857259\pi\)
\(278\) 0.0733391 + 0.100943i 0.00439859 + 0.00605414i
\(279\) 0 0
\(280\) −10.0976 31.0772i −0.603447 1.85722i
\(281\) 14.2054 15.7767i 0.847426 0.941161i −0.151455 0.988464i \(-0.548396\pi\)
0.998881 + 0.0473027i \(0.0150625\pi\)
\(282\) 0 0
\(283\) 4.27158 0.448961i 0.253919 0.0266880i 0.0232863 0.999729i \(-0.492587\pi\)
0.230633 + 0.973041i \(0.425920\pi\)
\(284\) 2.93622 2.64378i 0.174232 0.156880i
\(285\) 0 0
\(286\) 36.0990 + 3.57361i 2.13458 + 0.211312i
\(287\) 34.1996i 2.01874i
\(288\) 0 0
\(289\) 13.7486 9.98893i 0.808740 0.587584i
\(290\) −9.66688 1.01603i −0.567658 0.0596633i
\(291\) 0 0
\(292\) 9.75586 45.8977i 0.570919 2.68596i
\(293\) −17.4446 + 7.76685i −1.01913 + 0.453744i −0.847148 0.531356i \(-0.821683\pi\)
−0.171978 + 0.985101i \(0.555016\pi\)
\(294\) 0 0
\(295\) 1.27606 0.271236i 0.0742953 0.0157920i
\(296\) 26.0731 1.51547
\(297\) 0 0
\(298\) −47.9444 −2.77735
\(299\) −14.6868 + 3.12178i −0.849362 + 0.180537i
\(300\) 0 0
\(301\) 15.8428 7.05366i 0.913163 0.406566i
\(302\) −0.581220 + 2.73442i −0.0334454 + 0.157348i
\(303\) 0 0
\(304\) 3.29279 + 0.346086i 0.188854 + 0.0198494i
\(305\) −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 \(0.983075\pi\)
\(308\) 35.4001 + 31.4889i 2.01711 + 1.79424i
\(309\) 0 0
\(310\) 6.57754 5.92244i 0.373579 0.336372i
\(311\) −8.90556 + 0.936012i −0.504988 + 0.0530763i −0.353597 0.935398i \(-0.615042\pi\)
−0.151390 + 0.988474i \(0.548375\pi\)
\(312\) 0 0
\(313\) 11.4668 12.7352i 0.648142 0.719834i −0.326101 0.945335i \(-0.605735\pi\)
0.974243 + 0.225501i \(0.0724017\pi\)
\(314\) −1.25898 3.87474i −0.0710483 0.218664i
\(315\) 0 0
\(316\) −1.36768 1.88245i −0.0769381 0.105896i
\(317\) 5.67686 + 26.7075i 0.318844 + 1.50004i 0.787307 + 0.616561i \(0.211475\pi\)
−0.468463 + 0.883483i \(0.655192\pi\)
\(318\) 0 0
\(319\) 5.55752 2.51474i 0.311162 0.140799i
\(320\) −23.3551 13.4841i −1.30559 0.753783i
\(321\) 0 0
\(322\) −28.0762 12.5003i −1.56463 0.696616i
\(323\) 0.107435 0.147872i 0.00597785 0.00822781i
\(324\) 0 0
\(325\) 0.239475 0.0778102i 0.0132837 0.00431614i
\(326\) 0.246365 2.34401i 0.0136449 0.129823i
\(327\) 0 0
\(328\) 20.2677 + 22.5095i 1.11910 + 1.24288i
\(329\) −12.5905 + 21.8073i −0.694135 + 1.20228i
\(330\) 0 0
\(331\) 2.93609 + 5.08545i 0.161382 + 0.279522i 0.935365 0.353685i \(-0.115072\pi\)
−0.773983 + 0.633207i \(0.781738\pi\)
\(332\) −11.1268 + 34.2448i −0.610663 + 1.87943i
\(333\) 0 0
\(334\) 25.7093 + 18.6789i 1.40675 + 1.02206i
\(335\) −21.7163 19.5534i −1.18649 1.06832i
\(336\) 0 0
\(337\) −6.73993 15.1381i −0.367147 0.824627i −0.998781 0.0493597i \(-0.984282\pi\)
0.631634 0.775267i \(-0.282385\pi\)
\(338\) 2.12485 + 20.2166i 0.115577 + 1.09964i
\(339\) 0 0
\(340\) 0.523772 0.302400i 0.0284055 0.0163999i
\(341\) −1.68447 + 5.29296i −0.0912193 + 0.286630i
\(342\) 0 0
\(343\) 9.28988 + 3.01847i 0.501606 + 0.162982i
\(344\) −6.24722 + 14.0315i −0.336828 + 0.756527i
\(345\) 0 0
\(346\) −17.2985 3.67690i −0.929972 0.197672i
\(347\) −2.46314 0.523557i −0.132228 0.0281060i 0.141322 0.989964i \(-0.454865\pi\)
−0.273550 + 0.961858i \(0.588198\pi\)
\(348\) 0 0
\(349\) 3.55059 7.97475i 0.190059 0.426879i −0.793232 0.608919i \(-0.791603\pi\)
0.983291 + 0.182040i \(0.0582701\pi\)
\(350\) 0.490168 + 0.159265i 0.0262006 + 0.00851308i
\(351\) 0 0
\(352\) 13.0245 0.0787558i 0.694210 0.00419770i
\(353\) −0.464623 + 0.268250i −0.0247294 + 0.0142775i −0.512314 0.858798i \(-0.671211\pi\)
0.487584 + 0.873076i \(0.337878\pi\)
\(354\) 0 0
\(355\) 0.263304 + 2.50517i 0.0139748 + 0.132961i
\(356\) 9.45151 + 21.2284i 0.500929 + 1.12510i
\(357\) 0 0
\(358\) −21.8379 19.6629i −1.15417 1.03922i
\(359\) −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
\(362\) 21.1584 + 36.6474i 1.11206 + 1.92614i
\(363\) 0 0
\(364\) −33.2319 + 57.5594i −1.74183 + 3.01693i
\(365\) 20.0174 + 22.2315i 1.04776 + 1.16365i
\(366\) 0 0
\(367\) −3.02435 + 28.7747i −0.157870 + 1.50203i 0.573024 + 0.819538i \(0.305770\pi\)
−0.730894 + 0.682491i \(0.760897\pi\)
\(368\) 4.24157 1.37817i 0.221107 0.0718420i
\(369\) 0 0
\(370\) −22.5739 + 31.0703i −1.17356 + 1.61527i
\(371\) 4.54830 + 2.02503i 0.236136 + 0.105134i
\(372\) 0 0
\(373\) 5.72386 + 3.30467i 0.296370 + 0.171109i 0.640811 0.767699i \(-0.278598\pi\)
−0.344441 + 0.938808i \(0.611931\pi\)
\(374\) −0.294291 + 0.516920i −0.0152174 + 0.0267293i
\(375\) 0 0
\(376\) −4.63685 21.8147i −0.239127 1.12501i
\(377\) 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 \(0.887337\pi\)
\(380\) −12.7087 + 14.1144i −0.651940 + 0.724053i
\(381\) 0 0
\(382\) −50.6323 + 5.32167i −2.59057 + 0.272280i
\(383\) 10.0383 9.03850i 0.512932 0.461846i −0.371555 0.928411i \(-0.621175\pi\)
0.884487 + 0.466565i \(0.154509\pi\)
\(384\) 0 0
\(385\) −29.5071 + 6.45866i −1.50382 + 0.329164i
\(386\) 12.1934i 0.620629i
\(387\) 0 0
\(388\) −46.9133 + 34.0845i −2.38166 + 1.73038i
\(389\) 14.8974 + 1.56578i 0.755329 + 0.0793882i 0.474363 0.880330i \(-0.342679\pi\)
0.280966 + 0.959718i \(0.409345\pi\)
\(390\) 0 0
\(391\) 0.0511890 0.240825i 0.00258874 0.0121791i
\(392\) −30.8474 + 13.7341i −1.55803 + 0.693678i
\(393\) 0 0
\(394\) 11.8347 2.51554i 0.596222 0.126731i
\(395\) 1.48346 0.0746409
\(396\) 0 0
\(397\) −20.7132 −1.03956 −0.519782 0.854299i \(-0.673987\pi\)
−0.519782 + 0.854299i \(0.673987\pi\)
\(398\) −55.7829 + 11.8570i −2.79615 + 0.594339i
\(399\) 0 0
\(400\) −0.0683251 + 0.0304203i −0.00341626 + 0.00152101i
\(401\) 5.62292 26.4538i 0.280795 1.32104i −0.581050 0.813868i \(-0.697358\pi\)
0.861845 0.507171i \(-0.169309\pi\)
\(402\) 0 0
\(403\) −7.74939 0.814494i −0.386025 0.0405728i
\(404\) −4.91223 + 3.56894i −0.244392 + 0.177561i
\(405\) 0 0
\(406\) 17.5154i 0.869273i
\(407\) 2.37432 23.9844i 0.117691 1.18886i
\(408\) 0 0
\(409\) 4.53727 4.08538i 0.224354 0.202009i −0.549287 0.835634i \(-0.685100\pi\)
0.773640 + 0.633625i \(0.218434\pi\)
\(410\) −44.3714 + 4.66362i −2.19135 + 0.230320i
\(411\) 0 0
\(412\) −7.62330 + 8.46653i −0.375573 + 0.417116i
\(413\) −0.726437 2.23574i −0.0357456 0.110014i
\(414\) 0 0
\(415\) −13.4932 18.5718i −0.662357 0.911656i
\(416\) 3.79887 + 17.8723i 0.186255 + 0.876260i
\(417\) 0 0
\(418\) 3.77313 18.2944i 0.184550 0.894809i
\(419\) −30.8841 17.8309i −1.50879 0.871098i −0.999948 0.0102354i \(-0.996742\pi\)
−0.508838 0.860862i \(-0.669925\pi\)
\(420\) 0 0
\(421\) 13.0707 + 5.81944i 0.637026 + 0.283622i 0.699727 0.714410i \(-0.253305\pi\)
−0.0627012 + 0.998032i \(0.519972\pi\)
\(422\) −25.8993 + 35.6473i −1.26076 + 1.73528i
\(423\) 0 0
\(424\) −4.19370 + 1.36262i −0.203664 + 0.0661745i
\(425\) −0.000431581 0.00410622i −2.09348e−5 0.000199181i
\(426\) 0 0
\(427\) 10.2524 + 11.3865i 0.496150 + 0.551031i
\(428\) 26.1268 45.2530i 1.26289 2.18738i
\(429\) 0 0
\(430\) −11.3120 19.5930i −0.545513 0.944856i
\(431\) −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 \(0.341842\pi\)
\(434\) −11.8525 10.6721i −0.568939 0.512275i
\(435\) 0 0
\(436\) 21.4074 + 48.0818i 1.02523 + 2.30270i
\(437\) 0.808182 + 7.68934i 0.0386606 + 0.367831i
\(438\) 0 0
\(439\) −28.1171 + 16.2334i −1.34196 + 0.774779i −0.987094 0.160139i \(-0.948806\pi\)
−0.354863 + 0.934918i \(0.615472\pi\)
\(440\) 15.5935 21.7378i 0.743390 1.03631i
\(441\) 0 0
\(442\) −0.793595 0.257855i −0.0377474 0.0122649i
\(443\) 7.65538 17.1943i 0.363718 0.816924i −0.635285 0.772278i \(-0.719117\pi\)
0.999003 0.0446461i \(-0.0142160\pi\)
\(444\) 0 0
\(445\) −14.4911 3.08018i −0.686944 0.146014i
\(446\) 12.6206 + 2.68260i 0.597604 + 0.127025i
\(447\) 0 0
\(448\) −19.7657 + 44.3945i −0.933842 + 2.09744i
\(449\) 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
\(452\) −34.3450 + 19.8291i −1.61545 + 0.932681i
\(453\) 0 0
\(454\) −3.38212 32.1787i −0.158731 1.51022i
\(455\) −17.2349 38.7101i −0.807983 1.81476i
\(456\) 0 0
\(457\) −3.13770 2.82520i −0.146775 0.132157i 0.592472 0.805591i \(-0.298152\pi\)
−0.739248 + 0.673434i \(0.764819\pi\)
\(458\) 40.1908 + 29.2004i 1.87799 + 1.36444i
\(459\) 0 0
\(460\) −7.90572 + 24.3313i −0.368606 + 1.13445i
\(461\) 7.09611 + 12.2908i 0.330499 + 0.572441i 0.982610 0.185683i \(-0.0594497\pi\)
−0.652111 + 0.758123i \(0.726116\pi\)
\(462\) 0 0
\(463\) 20.1892 34.9687i 0.938271 1.62513i 0.169576 0.985517i \(-0.445760\pi\)
0.768695 0.639616i \(-0.220906\pi\)
\(464\) −1.70076 1.88888i −0.0789556 0.0876891i
\(465\) 0 0
\(466\) 3.67740 34.9881i 0.170352 1.62079i
\(467\) 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
\(470\) 30.0103 + 13.3614i 1.38427 + 0.616317i
\(471\) 0 0
\(472\) 1.80309 + 1.04102i 0.0829942 + 0.0479167i
\(473\) 12.3385 + 7.02453i 0.567326 + 0.322988i
\(474\) 0 0
\(475\) −0.0269578 0.126826i −0.00123691 0.00581919i
\(476\) −0.640587 0.881692i −0.0293612 0.0404123i
\(477\) 0 0
\(478\) −3.92639 12.0842i −0.179589 0.552718i
\(479\) −15.3220 + 17.0168i −0.700079 + 0.777516i −0.983389 0.181512i \(-0.941901\pi\)
0.283310 + 0.959028i \(0.408567\pi\)
\(480\) 0 0
\(481\) 33.6253 3.53416i 1.53318 0.161144i
\(482\) −20.4557 + 18.4184i −0.931731 + 0.838935i
\(483\) 0 0
\(484\) −3.58773 + 38.6225i −0.163079 + 1.75557i
\(485\) 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 \(0.245338\pi\)
\(488\) −13.4959 1.41848i −0.610932 0.0642116i
\(489\) 0 0
\(490\) 10.3410 48.6505i 0.467158 2.19781i
\(491\) 34.8885 15.5333i 1.57449 0.701010i 0.580896 0.813978i \(-0.302702\pi\)
0.993599 + 0.112967i \(0.0360356\pi\)
\(492\) 0 0
\(493\) −0.137250 + 0.0291735i −0.00618144 + 0.00131391i
\(494\) 26.2041 1.17898
\(495\) 0 0
\(496\) 2.31446 0.103922
\(497\) 4.43992 0.943735i 0.199158 0.0423323i
\(498\) 0 0
\(499\) −7.36234 + 3.27793i −0.329584 + 0.146740i −0.564856 0.825189i \(-0.691068\pi\)
0.235273 + 0.971929i \(0.424402\pi\)
\(500\) −8.15190 + 38.3517i −0.364564 + 1.71514i
\(501\) 0 0
\(502\) −52.8325 5.55292i −2.35803 0.247839i
\(503\) 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
\(506\) −5.38006 24.5795i −0.239173 1.09269i
\(507\) 0 0
\(508\) −15.8842 + 14.3022i −0.704748 + 0.634558i
\(509\) 27.8101 2.92296i 1.23266 0.129558i 0.534295 0.845298i \(-0.320577\pi\)
0.698367 + 0.715740i \(0.253911\pi\)
\(510\) 0 0
\(511\) 36.0707 40.0605i 1.59567 1.77217i
\(512\) −4.74153 14.5929i −0.209548 0.644922i
\(513\) 0 0
\(514\) −38.0212 52.3316i −1.67704 2.30825i
\(515\) −1.51015 7.10470i −0.0665452 0.313070i
\(516\) 0 0
\(517\) −20.4894 + 2.27886i −0.901121 + 0.100224i
\(518\) 59.9330 + 34.6024i 2.63331 + 1.52034i
\(519\) 0 0
\(520\) 34.2844 + 15.2644i 1.50347 + 0.669389i
\(521\) 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 \(0.276079\pi\)
\(524\) 2.63575 25.0775i 0.115143 1.09552i
\(525\) 0 0
\(526\) 50.3965 + 55.9710i 2.19739 + 2.44045i
\(527\) 0.0638847 0.110652i 0.00278286 0.00482006i
\(528\) 0 0
\(529\) −6.29267 10.8992i −0.273594 0.473879i
\(530\) 2.00710 6.17722i 0.0871828 0.268321i
\(531\) 0 0
\(532\) 27.6881 + 20.1166i 1.20043 + 0.872166i
\(533\) 29.1894 + 26.2823i 1.26433 + 1.13841i
\(534\) 0 0
\(535\) 13.5500 + 30.4338i 0.585817 + 1.31577i
\(536\) −4.87491 46.3817i −0.210564 2.00338i
\(537\) 0 0
\(538\) 55.0519 31.7842i 2.37345 1.37031i
\(539\) 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 \(0.669499\pi\)
\(542\) −14.2287 + 31.9581i −0.611174 + 1.37272i
\(543\) 0 0
\(544\) −0.293058 0.0622914i −0.0125648 0.00267072i
\(545\) −32.8219 6.97652i −1.40594 0.298841i
\(546\) 0 0
\(547\) 9.70462 21.7969i 0.414939 0.931969i −0.578293 0.815829i \(-0.696281\pi\)
0.993233 0.116140i \(-0.0370522\pi\)
\(548\) −35.6242 11.5750i −1.52179 0.494460i
\(549\) 0 0
\(550\) 0.132815 + 0.400506i 0.00566325 + 0.0170776i
\(551\) 3.81607 2.20321i 0.162570 0.0938599i
\(552\) 0 0
\(553\) −0.279420 2.65850i −0.0118821 0.113051i
\(554\) −7.53436 16.9225i −0.320104 0.718966i
\(555\) 0 0
\(556\) −0.139088 0.125235i −0.00589863 0.00531115i
\(557\) 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
\(560\) 6.29304 + 10.8999i 0.265929 + 0.460603i
\(561\) 0 0
\(562\) −24.9534 + 43.2205i −1.05259 + 1.82315i
\(563\) −3.35948 3.73108i −0.141585 0.157246i 0.668181 0.743998i \(-0.267073\pi\)
−0.809767 + 0.586752i \(0.800406\pi\)
\(564\) 0 0
\(565\) 2.64287 25.1452i 0.111186 1.05787i
\(566\) −9.60276 + 3.12012i −0.403634 + 0.131149i
\(567\) 0 0
\(568\) −2.36299 + 3.25238i −0.0991489 + 0.136467i
\(569\) 8.68706 + 3.86773i 0.364181 + 0.162144i 0.580665 0.814142i \(-0.302792\pi\)
−0.216485 + 0.976286i \(0.569459\pi\)
\(570\) 0 0
\(571\) −34.4930 19.9146i −1.44349 0.833398i −0.445408 0.895328i \(-0.646941\pi\)
−0.998081 + 0.0619297i \(0.980275\pi\)
\(572\) −54.0807 + 6.01494i −2.26123 + 0.251497i
\(573\) 0 0
\(574\) 16.7153 + 78.6395i 0.697685 + 3.28235i
\(575\) −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 \(0.987619\pi\)
\(578\) −26.7317 + 29.6886i −1.11189 + 1.23488i
\(579\) 0 0
\(580\) 14.5005 1.52407i 0.602102 0.0632835i
\(581\) −30.7410 + 27.6793i −1.27535 + 1.14833i
\(582\) 0 0
\(583\) 0.871561 + 3.98183i 0.0360964 + 0.164911i
\(584\) 47.7437i 1.97565i
\(585\) 0 0
\(586\) 36.3166 26.3855i 1.50022 1.08998i
\(587\) −23.6214 2.48270i −0.974958 0.102472i −0.396369 0.918091i \(-0.629730\pi\)
−0.578589 + 0.815619i \(0.696396\pi\)
\(588\) 0 0
\(589\) −0.834224 + 3.92472i −0.0343736 + 0.161715i
\(590\) −2.80165 + 1.24737i −0.115342 + 0.0513536i
\(591\) 0 0
\(592\) −9.82317 + 2.08798i −0.403730 + 0.0858154i
\(593\) −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
\(596\) 70.3462 14.9525i 2.88149 0.612480i
\(597\) 0 0
\(598\) 32.2455 14.3566i 1.31862 0.587087i
\(599\) 0.496033 2.33365i 0.0202673 0.0953503i −0.966851 0.255340i \(-0.917813\pi\)
0.987119 + 0.159989i \(0.0511460\pi\)
\(600\) 0 0
\(601\) −6.75664 0.710152i −0.275609 0.0289677i −0.0342844 0.999412i \(-0.510915\pi\)
−0.241325 + 0.970444i \(0.577582\pi\)
\(602\) −32.9818 + 23.9627i −1.34424 + 0.976646i
\(603\) 0 0
\(604\) 4.19334i 0.170624i
\(605\) −18.5764 16.3238i −0.755237 0.663658i
\(606\) 0 0
\(607\) 30.0946 27.0973i 1.22150 1.09985i 0.229544 0.973298i \(-0.426277\pi\)
0.991960 0.126549i \(-0.0403900\pi\)
\(608\) 9.35708 0.983468i 0.379480 0.0398849i
\(609\) 0 0
\(610\) 13.3750 14.8545i 0.541540 0.601441i
\(611\) −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 \(0.798698\pi\)
\(614\) −0.910262 4.28245i −0.0367352 0.172825i
\(615\) 0 0
\(616\) −41.8934 23.8506i −1.68793 0.960967i
\(617\) −7.00117 4.04213i −0.281857 0.162730i 0.352407 0.935847i \(-0.385363\pi\)
−0.634264 + 0.773117i \(0.718697\pi\)
\(618\) 0 0
\(619\) 19.1722 + 8.53602i 0.770597 + 0.343092i 0.754089 0.656772i \(-0.228079\pi\)
0.0165075 + 0.999864i \(0.494745\pi\)
\(620\) −7.80381 + 10.7410i −0.313409 + 0.431370i
\(621\) 0 0
\(622\) 20.0202 6.50496i 0.802737 0.260825i
\(623\) −2.79048 + 26.5496i −0.111798 + 1.06369i
\(624\) 0 0
\(625\) −16.9074 18.7775i −0.676295 0.751101i
\(626\) −20.1427 + 34.8881i −0.805062 + 1.39441i
\(627\) 0 0
\(628\) 3.05565 + 5.29255i 0.121934 + 0.211196i
\(629\) −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 \(0.539587\pi\)
\(632\) 1.75942 + 1.58419i 0.0699859 + 0.0630156i
\(633\) 0 0
\(634\) −26.1071 58.6374i −1.03684 2.32879i
\(635\) −1.42441 13.5524i −0.0565261 0.537810i
\(636\) 0 0
\(637\) −37.9208 + 21.8936i −1.50248 + 0.867455i
\(638\) −11.5500 + 8.49876i −0.457270 + 0.336469i
\(639\) 0 0
\(640\) 43.5007 + 14.1342i 1.71952 + 0.558705i
\(641\) 6.56437 14.7438i 0.259277 0.582346i −0.736262 0.676697i \(-0.763411\pi\)
0.995539 + 0.0943509i \(0.0300776\pi\)
\(642\) 0 0
\(643\) −12.3090 2.61635i −0.485419 0.103179i −0.0412999 0.999147i \(-0.513150\pi\)
−0.444119 + 0.895968i \(0.646483\pi\)
\(644\) 45.0932 + 9.58485i 1.77692 + 0.377696i
\(645\) 0 0
\(646\) −0.174766 + 0.392530i −0.00687607 + 0.0154439i
\(647\) −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
\(650\) −0.512626 + 0.295965i −0.0201068 + 0.0116087i
\(651\) 0 0
\(652\) 0.369553 + 3.51607i 0.0144728 + 0.137700i
\(653\) 7.96901 + 17.8987i 0.311851 + 0.700430i 0.999676 0.0254470i \(-0.00810090\pi\)
−0.687825 + 0.725877i \(0.741434\pi\)
\(654\) 0 0
\(655\) 11.9468 + 10.7570i 0.466801 + 0.420310i
\(656\) −9.43855 6.85751i −0.368514 0.267741i
\(657\) 0 0
\(658\) 18.2924 56.2981i 0.713111 2.19473i
\(659\) 0.674716 + 1.16864i 0.0262832 + 0.0455238i 0.878868 0.477065i \(-0.158300\pi\)
−0.852585 + 0.522589i \(0.824966\pi\)
\(660\) 0 0
\(661\) −14.3929 + 24.9293i −0.559821 + 0.969638i 0.437690 + 0.899126i \(0.355797\pi\)
−0.997511 + 0.0705120i \(0.977537\pi\)
\(662\) −9.23687 10.2586i −0.359001 0.398711i
\(663\) 0 0
\(664\) 3.82959 36.4361i 0.148617 1.41399i
\(665\) −20.7516 + 6.74260i −0.804712 + 0.261467i
\(666\) 0 0
\(667\) 3.48879 4.80191i 0.135086 0.185931i
\(668\) −43.5473 19.3885i −1.68490 0.750164i
\(669\) 0 0
\(670\) 59.4920 + 34.3477i 2.29838 + 1.32697i
\(671\) −2.53384 + 12.2856i −0.0978179 + 0.474281i
\(672\) 0 0
\(673\) −4.52227 21.2756i −0.174321 0.820114i −0.975206 0.221297i \(-0.928971\pi\)
0.800886 0.598817i \(-0.204362\pi\)
\(674\) 22.8969 + 31.5149i 0.881955 + 1.21391i
\(675\) 0 0
\(676\) −9.42270 29.0001i −0.362411 1.11539i
\(677\) 12.6502 14.0494i 0.486185 0.539963i −0.449276 0.893393i \(-0.648318\pi\)
0.935461 + 0.353430i \(0.114985\pi\)
\(678\) 0 0
\(679\) −66.2536 + 6.96353i −2.54258 + 0.267236i
\(680\) −0.457314 + 0.411767i −0.0175372 + 0.0157905i
\(681\) 0 0
\(682\) 1.28634 12.9941i 0.0492567 0.497569i
\(683\) 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
\(686\) −22.8367 2.40024i −0.871910 0.0916414i
\(687\) 0 0
\(688\) 1.23001 5.78672i 0.0468936 0.220617i
\(689\) −5.22372 + 2.32575i −0.199008 + 0.0886041i
\(690\) 0 0
\(691\) 26.9313 5.72442i 1.02451 0.217767i 0.335136 0.942170i \(-0.391218\pi\)
0.689377 + 0.724403i \(0.257884\pi\)
\(692\) 26.5278 1.00844
\(693\) 0 0
\(694\) 5.91971 0.224709
\(695\) 0.116716 0.0248087i 0.00442727 0.000941046i
\(696\) 0 0
\(697\) −0.588377 + 0.261963i −0.0222864 + 0.00992254i
\(698\) −4.26659 + 20.0727i −0.161493 + 0.759765i
\(699\) 0 0
\(700\) −0.768867 0.0808112i −0.0290604 0.00305437i
\(701\) 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
\(704\) −38.8654 + 8.50704i −1.46479 + 0.320621i
\(705\) 0 0
\(706\) 0.937258 0.843911i 0.0352742 0.0317610i
\(707\) −6.93732 + 0.729141i −0.260905 + 0.0274222i
\(708\) 0 0
\(709\) −13.4139 + 14.8976i −0.503768 + 0.559491i −0.940365 0.340166i \(-0.889517\pi\)
0.436598 + 0.899657i \(0.356183\pi\)
\(710\) −1.82988 5.63178i −0.0686740 0.211357i
\(711\) 0 0
\(712\) −13.8975 19.1282i −0.520829 0.716860i
\(713\) 1.12371 + 5.28663i 0.0420832 + 0.197986i
\(714\) 0 0
\(715\) 17.1637 30.1479i 0.641885 1.12747i
\(716\) 38.1738 + 22.0397i 1.42662 + 0.823660i
\(717\) 0 0
\(718\) 33.9439 + 15.1128i 1.26677 + 0.564004i
\(719\) 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
\(722\) −3.25834 + 31.0011i −0.121263 + 1.15374i
\(723\) 0 0
\(724\) −42.4738 47.1719i −1.57853 1.75313i
\(725\) −0.0497687 + 0.0862019i −0.00184836 + 0.00320146i
\(726\) 0 0
\(727\) 7.22282 + 12.5103i 0.267880 + 0.463981i 0.968314 0.249736i \(-0.0803437\pi\)
−0.700434 + 0.713717i \(0.747010\pi\)
\(728\) 20.8976 64.3163i 0.774517 2.38372i
\(729\) 0 0
\(730\) −56.8943 41.3361i −2.10575 1.52992i
\(731\) −0.242706 0.218533i −0.00897679 0.00808274i
\(732\) 0 0
\(733\) 2.97291 + 6.67726i 0.109807 + 0.246630i 0.960088 0.279699i \(-0.0902347\pi\)
−0.850281 + 0.526329i \(0.823568\pi\)
\(734\) −7.10963 67.6436i −0.262421 2.49677i
\(735\) 0 0
\(736\) 10.9756 6.33674i 0.404565 0.233575i
\(737\) −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 \(0.677661\pi\)
\(740\) 23.4315 52.6280i 0.861358 1.93464i
\(741\) 0 0
\(742\) −11.4482 2.43340i −0.420278 0.0893328i
\(743\) −34.5995 7.35434i −1.26933 0.269805i −0.476461 0.879196i \(-0.658081\pi\)
−0.792870 + 0.609391i \(0.791414\pi\)
\(744\) 0 0
\(745\) −18.6491 + 41.8866i −0.683251 + 1.53461i
\(746\) −14.7768 4.80127i −0.541017 0.175787i
\(747\) 0 0
\(748\) 0.270584 0.850230i 0.00989352 0.0310875i
\(749\) 51.9880 30.0153i 1.89960 1.09674i
\(750\) 0 0
\(751\) 2.41132 + 22.9422i 0.0879905 + 0.837174i 0.946137 + 0.323768i \(0.104950\pi\)
−0.858146 + 0.513406i \(0.828384\pi\)
\(752\) 3.49392 + 7.84746i 0.127410 + 0.286168i
\(753\) 0 0
\(754\) −14.9494 13.4605i −0.544425 0.490203i
\(755\) 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 \(0.0430445\pi\)
\(758\) −1.82015 3.15259i −0.0661108 0.114507i
\(759\) 0 0
\(760\) 9.66246 16.7359i 0.350494 0.607074i
\(761\) 32.4027 + 35.9869i 1.17460 + 1.30452i 0.943415 + 0.331614i \(0.107593\pi\)
0.231183 + 0.972910i \(0.425740\pi\)
\(762\) 0 0
\(763\) −6.32036 + 60.1342i −0.228812 + 2.17701i
\(764\) 72.6303 23.5990i 2.62767 0.853783i
\(765\) 0 0
\(766\) −18.6646 + 25.6897i −0.674381 + 0.928205i
\(767\) 2.46648 + 1.09815i 0.0890593 + 0.0396518i
\(768\) 0 0
\(769\) 28.9445 + 16.7111i 1.04377 + 0.602619i 0.920898 0.389804i \(-0.127457\pi\)
0.122869 + 0.992423i \(0.460791\pi\)
\(770\) 64.6928 29.2731i 2.33137 1.05493i
\(771\) 0 0
\(772\) −3.80279 17.8907i −0.136866 0.643902i
\(773\) −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
\(776\) 39.4801 43.8471i 1.41725 1.57402i
\(777\) 0 0
\(778\) −35.0208 + 3.68084i −1.25556 + 0.131964i
\(779\) 15.0306 13.5336i 0.538527 0.484892i
\(780\) 0 0
\(781\) 2.77665 + 2.46987i 0.0993563 + 0.0883788i
\(782\) 0.578780i 0.0206971i
\(783\) 0 0
\(784\) 10.5220 7.64471i 0.375787 0.273025i
\(785\) −3.87487 0.407266i −0.138300 0.0145359i
\(786\) 0 0
\(787\) −6.02818 + 28.3604i −0.214881 + 1.01094i 0.729980 + 0.683468i \(0.239529\pi\)
−0.944862 + 0.327470i \(0.893804\pi\)
\(788\) −16.5798 + 7.38182i −0.590632 + 0.262966i
\(789\) 0 0
\(790\) −3.41111 + 0.725053i −0.121362 + 0.0257962i
\(791\) −45.5606 −1.61995
\(792\) 0 0
\(793\) −17.5974 −0.624901
\(794\) 47.6285 10.1237i 1.69027 0.359278i
\(795\) 0 0
\(796\) 78.1494 34.7943i 2.76993 1.23325i
\(797\) −5.62407 + 26.4592i −0.199215 + 0.937232i 0.758980 + 0.651114i \(0.225698\pi\)
−0.958194 + 0.286118i \(0.907635\pi\)
\(798\) 0 0
\(799\) 0.471619 + 0.0495692i 0.0166847 + 0.00175363i
\(800\) −0.171943 + 0.124924i −0.00607910 + 0.00441672i
\(801\) 0 0
\(802\) 63.5768i 2.24498i
\(803\) 43.9189 + 4.34774i 1.54987 + 0.153428i
\(804\) 0 0
\(805\) −21.8418 + 19.6665i −0.769823 + 0.693152i
\(806\) 18.2173 1.91471i 0.641676 0.0674428i
\(807\) 0 0
\(808\) 4.13391 4.59117i 0.145430 0.161517i
\(809\) 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 \(0.872103\pi\)
\(812\) −5.46256 25.6993i −0.191698 0.901870i
\(813\) 0 0
\(814\) 6.26299 + 56.3108i 0.219518 + 1.97369i
\(815\) −1.95201 1.12699i −0.0683760 0.0394769i
\(816\) 0 0
\(817\) 9.36944 + 4.17154i 0.327795 + 0.145944i
\(818\) −8.43637 + 11.6117i −0.294971 + 0.405992i
\(819\) 0 0
\(820\) 63.6493 20.6809i 2.22273 0.722208i
\(821\) 1.23995 11.7973i 0.0432746 0.411730i −0.951344 0.308130i \(-0.900297\pi\)
0.994619 0.103601i \(-0.0330364\pi\)
\(822\) 0 0
\(823\) 17.5821 + 19.5269i 0.612875 + 0.680666i 0.967072 0.254505i \(-0.0819124\pi\)
−0.354197 + 0.935171i \(0.615246\pi\)
\(824\) 5.79604 10.0390i 0.201914 0.349726i
\(825\) 0 0
\(826\) 2.76313 + 4.78588i 0.0961415 + 0.166522i
\(827\) 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 \(0.797298\pi\)
\(830\) 40.1039 + 36.1097i 1.39203 + 1.25339i
\(831\) 0 0
\(832\) −22.7009 50.9871i −0.787013 1.76766i
\(833\) −0.0750507 0.714060i −0.00260035 0.0247407i
\(834\) 0 0
\(835\) 26.3191 15.1953i 0.910809 0.525856i
\(836\) 0.169424 + 28.0191i 0.00585965 + 0.969061i
\(837\) 0 0
\(838\) 79.7307 + 25.9061i 2.75425 + 0.894911i
\(839\) 12.6296 28.3664i 0.436021 0.979318i −0.553222 0.833034i \(-0.686602\pi\)
0.989243 0.146284i \(-0.0467315\pi\)
\(840\) 0 0
\(841\) 25.0575 + 5.32613i 0.864051 + 0.183660i
\(842\) −32.8994 6.99298i −1.13379 0.240994i
\(843\) 0 0
\(844\) 26.8832 60.3806i 0.925357 2.07839i
\(845\) 18.4888 + 6.00737i 0.636033 + 0.206660i
\(846\) 0 0
\(847\) −25.7549 + 36.3654i −0.884949 + 1.24953i
\(848\) 1.47088 0.849211i 0.0505101 0.0291620i
\(849\) 0 0
\(850\) −0.00101456 0.00965290i −3.47992e−5 0.000331092i
\(851\) −9.53862 21.4241i −0.326980 0.734409i
\(852\) 0 0
\(853\) −0.237337 0.213699i −0.00812626 0.00731692i 0.665057 0.746792i \(-0.268407\pi\)
−0.673184 + 0.739475i \(0.735074\pi\)
\(854\) −29.1400 21.1714i −0.997150 0.724472i
\(855\) 0 0
\(856\) −16.4296 + 50.5652i −0.561553 + 1.72828i
\(857\) −6.62378 11.4727i −0.226264 0.391901i 0.730434 0.682983i \(-0.239318\pi\)
−0.956698 + 0.291083i \(0.905985\pi\)
\(858\) 0 0
\(859\) 4.29076 7.43181i 0.146399 0.253570i −0.783495 0.621398i \(-0.786565\pi\)
0.929894 + 0.367828i \(0.119898\pi\)
\(860\) 22.7080 + 25.2198i 0.774336 + 0.859987i
\(861\) 0 0
\(862\) 2.13860 20.3474i 0.0728410 0.693036i
\(863\) 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
\(866\) −80.6480 35.9068i −2.74053 1.22016i
\(867\) 0 0
\(868\) 20.7189 + 11.9620i 0.703245 + 0.406018i
\(869\) 1.61750 1.47421i 0.0548698 0.0500091i
\(870\) 0 0
\(871\) −12.5739 59.1556i −0.426050 2.00441i
\(872\) −31.4774 43.3249i −1.06596 1.46717i
\(873\) 0 0
\(874\) −5.61659 17.2861i −0.189984 0.584710i
\(875\) −30.1403 + 33.4742i −1.01893 + 1.13163i
\(876\) 0 0
\(877\) 43.7743 4.60087i 1.47815 0.155360i 0.669134 0.743142i \(-0.266665\pi\)
0.809020 + 0.587782i \(0.199999\pi\)
\(878\) 56.7191 51.0701i 1.91418 1.72353i
\(879\) 0 0
\(880\) −4.13412 + 9.43857i −0.139361 + 0.318174i
\(881\) 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 \(0.249516\pi\)
\(884\) 1.24482 + 0.130835i 0.0418677 + 0.00440047i
\(885\) 0 0
\(886\) −9.19915 + 43.2786i −0.309052 + 1.45397i
\(887\) 22.0938 9.83681i 0.741838 0.330288i −0.000782633 1.00000i \(-0.500249\pi\)
0.742621 + 0.669712i \(0.233582\pi\)
\(888\) 0 0
\(889\) −24.0189 + 5.10537i −0.805568 + 0.171229i
\(890\) 34.8267 1.16739
\(891\) 0 0
\(892\) −19.3542 −0.648026
\(893\) −14.5666 + 3.09623i −0.487453 + 0.103611i
\(894\) 0 0
\(895\) −25.6728 + 11.4303i −0.858148 + 0.382072i
\(896\) 17.1363 80.6199i 0.572483 2.69332i
\(897\) 0 0
\(898\) −16.8842 1.77460i −0.563431 0.0592190i
\(899\) 2.49197 1.81052i 0.0831119 0.0603843i
\(900\) 0 0
\(901\) 0.0937613i 0.00312364i
\(902\) −43.7461 + 49.1797i −1.45658 + 1.63751i
\(903\) 0 0
\(904\) 29.9871 27.0005i 0.997357 0.898024i
\(905\) 40.2470 4.23013i 1.33786 0.140614i
\(906\) 0 0
\(907\) −23.9778 + 26.6300i −0.796168 + 0.884234i −0.995409 0.0957163i \(-0.969486\pi\)
0.199241 + 0.979951i \(0.436152\pi\)
\(908\) 14.9980 + 46.1592i 0.497728 + 1.53185i
\(909\) 0 0
\(910\) 58.5502 + 80.5875i 1.94092 + 2.67145i
\(911\) −1.82117 8.56791i −0.0603379 0.283868i 0.937626 0.347645i \(-0.113019\pi\)
−0.997964 + 0.0637775i \(0.979685\pi\)
\(912\) 0 0
\(913\) −33.1684 6.84082i −1.09772 0.226398i
\(914\) 8.59575 + 4.96276i 0.284322 + 0.164154i
\(915\) 0 0
\(916\) −68.0766 30.3097i −2.24931 1.00146i
\(917\) 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 \(0.640113\pi\)
\(920\) 2.72096 25.8882i 0.0897075 0.853510i
\(921\) 0 0
\(922\) −22.3242 24.7936i −0.735209 0.816533i
\(923\) −2.60659 + 4.51474i −0.0857969 + 0.148605i
\(924\) 0 0
\(925\) 0.196640 + 0.340591i 0.00646550 + 0.0111986i
\(926\) −29.3323 + 90.2756i −0.963920 + 2.96664i
\(927\) 0 0
\(928\) −5.84339 4.24547i −0.191819 0.139364i
\(929\) −40.2699 36.2591i −1.32121 1.18962i −0.967093 0.254423i \(-0.918114\pi\)
−0.354118 0.935201i \(-0.615219\pi\)
\(930\) 0 0
\(931\) 9.17087 + 20.5981i 0.300563 + 0.675076i
\(932\) 5.51618 + 52.4830i 0.180689 + 1.71914i
\(933\) 0 0
\(934\) −23.0065 + 13.2828i −0.752795 + 0.434626i
\(935\) 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 \(0.691710\pi\)
\(938\) 50.3487 113.085i 1.64394 3.69236i
\(939\) 0 0
\(940\) −48.1995 10.2451i −1.57209 0.334159i
\(941\) 21.0404 + 4.47227i 0.685896 + 0.145792i 0.537662 0.843161i \(-0.319308\pi\)
0.148234 + 0.988952i \(0.452641\pi\)
\(942\) 0 0
\(943\) 11.0812 24.8888i 0.360853 0.810489i
\(944\) −0.762692 0.247814i −0.0248235 0.00806564i
\(945\) 0 0
\(946\) −31.8049 10.1218i −1.03407 0.329089i
\(947\) 38.7882 22.3944i 1.26045 0.727719i 0.287286 0.957845i \(-0.407247\pi\)
0.973161 + 0.230126i \(0.0739137\pi\)
\(948\) 0 0
\(949\) 6.47156 + 61.5728i 0.210076 + 1.99874i
\(950\) 0.123975 + 0.278452i 0.00402228 + 0.00903418i
\(951\) 0 0
\(952\) 0.824065 + 0.741992i 0.0267081 + 0.0240481i
\(953\) 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
\(956\) 9.52970 + 16.5059i 0.308213 + 0.533840i
\(957\) 0 0
\(958\) 26.9147 46.6176i 0.869574 1.50615i
\(959\) −28.7943 31.9793i −0.929815 1.03266i
\(960\) 0 0
\(961\) 2.94720 28.0407i 0.0950710 0.904540i
\(962\) −75.5916 + 24.5612i −2.43717 + 0.791884i
\(963\) 0 0
\(964\) 24.2693 33.4039i 0.781662 1.07587i
\(965\) 10.6528 + 4.74292i 0.342925 + 0.152680i
\(966\) 0 0
\(967\) 3.74268 + 2.16084i 0.120356 + 0.0694878i 0.558970 0.829188i \(-0.311197\pi\)
−0.438613 + 0.898676i \(0.644530\pi\)
\(968\) −4.59980 39.1981i −0.147843 1.25988i
\(969\) 0 0
\(970\) 18.0693 + 85.0095i 0.580171 + 2.72949i
\(971\) −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
\(974\) −11.8637 + 13.1759i −0.380136 + 0.422184i
\(975\) 0 0
\(976\) 5.19826 0.546359i 0.166392 0.0174885i
\(977\) 2.56397 2.30861i 0.0820288 0.0738591i −0.627096 0.778942i \(-0.715757\pi\)
0.709125 + 0.705083i \(0.249090\pi\)
\(978\) 0 0
\(979\) −18.8614 + 11.0422i −0.602813 + 0.352912i
\(980\) 74.6073i 2.38324i
\(981\) 0 0
\(982\) −72.6315 + 52.7699i −2.31776 + 1.68395i
\(983\) 1.02901 + 0.108153i 0.0328203 + 0.00344955i 0.120924 0.992662i \(-0.461414\pi\)
−0.0881041 + 0.996111i \(0.528081\pi\)
\(984\) 0 0
\(985\) 2.40568 11.3178i 0.0766513 0.360616i
\(986\) 0.301338 0.134165i 0.00959657 0.00427267i
\(987\) 0 0
\(988\) −38.4478 + 8.17234i −1.22319 + 0.259997i
\(989\) 13.8151 0.439294
\(990\) 0 0
\(991\) 9.78910 0.310961 0.155481 0.987839i \(-0.450307\pi\)
0.155481 + 0.987839i \(0.450307\pi\)
\(992\) 6.43324 1.36743i 0.204255 0.0434158i
\(993\) 0 0
\(994\) −9.74803 + 4.34010i −0.309189 + 0.137660i
\(995\) −11.3392 + 53.3468i −0.359477 + 1.69121i
\(996\) 0 0
\(997\) 11.5510 + 1.21406i 0.365823 + 0.0384496i 0.285657 0.958332i \(-0.407788\pi\)
0.0801664 + 0.996781i \(0.474455\pi\)
\(998\) 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 891.2.u.c.134.1 32
3.2 odd 2 inner 891.2.u.c.134.4 32
9.2 odd 6 inner 891.2.u.c.431.1 32
9.4 even 3 99.2.j.a.35.4 yes 16
9.5 odd 6 99.2.j.a.35.1 yes 16
9.7 even 3 inner 891.2.u.c.431.4 32
11.6 odd 10 inner 891.2.u.c.215.1 32
33.17 even 10 inner 891.2.u.c.215.4 32
36.23 even 6 1584.2.cd.c.1025.1 16
36.31 odd 6 1584.2.cd.c.1025.4 16
99.4 even 15 1089.2.d.g.1088.13 16
99.40 odd 30 1089.2.d.g.1088.3 16
99.50 even 30 99.2.j.a.17.4 yes 16
99.59 odd 30 1089.2.d.g.1088.4 16
99.61 odd 30 inner 891.2.u.c.512.4 32
99.83 even 30 inner 891.2.u.c.512.1 32
99.94 odd 30 99.2.j.a.17.1 16
99.95 even 30 1089.2.d.g.1088.14 16
396.347 odd 30 1584.2.cd.c.17.4 16
396.391 even 30 1584.2.cd.c.17.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.j.a.17.1 16 99.94 odd 30
99.2.j.a.17.4 yes 16 99.50 even 30
99.2.j.a.35.1 yes 16 9.5 odd 6
99.2.j.a.35.4 yes 16 9.4 even 3
891.2.u.c.134.1 32 1.1 even 1 trivial
891.2.u.c.134.4 32 3.2 odd 2 inner
891.2.u.c.215.1 32 11.6 odd 10 inner
891.2.u.c.215.4 32 33.17 even 10 inner
891.2.u.c.431.1 32 9.2 odd 6 inner
891.2.u.c.431.4 32 9.7 even 3 inner
891.2.u.c.512.1 32 99.83 even 30 inner
891.2.u.c.512.4 32 99.61 odd 30 inner
1089.2.d.g.1088.3 16 99.40 odd 30
1089.2.d.g.1088.4 16 99.59 odd 30
1089.2.d.g.1088.13 16 99.4 even 15
1089.2.d.g.1088.14 16 99.95 even 30
1584.2.cd.c.17.1 16 396.391 even 30
1584.2.cd.c.17.4 16 396.347 odd 30
1584.2.cd.c.1025.1 16 36.23 even 6
1584.2.cd.c.1025.4 16 36.31 odd 6