Properties

Label 441.2.bb.f.46.2
Level $441$
Weight $2$
Character 441.46
Analytic conductor $3.521$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(37,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bb (of order \(21\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(6\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 46.2
Character \(\chi\) \(=\) 441.46
Dual form 441.2.bb.f.163.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.576178 + 1.46808i) q^{2} +(-0.357164 - 0.331400i) q^{4} +(-0.810468 - 0.552568i) q^{5} +(-1.54377 - 2.14867i) q^{7} +(-2.14952 + 1.03515i) q^{8} +O(q^{10})\) \(q+(-0.576178 + 1.46808i) q^{2} +(-0.357164 - 0.331400i) q^{4} +(-0.810468 - 0.552568i) q^{5} +(-1.54377 - 2.14867i) q^{7} +(-2.14952 + 1.03515i) q^{8} +(1.27819 - 0.871452i) q^{10} +(-1.80258 + 0.271695i) q^{11} +(-1.72771 - 2.16648i) q^{13} +(4.04390 - 1.02835i) q^{14} +(-0.354001 - 4.72382i) q^{16} +(-4.65252 - 1.43511i) q^{17} +(0.644188 + 1.11577i) q^{19} +(0.106349 + 0.465946i) q^{20} +(0.639736 - 2.80287i) q^{22} +(-3.68254 + 1.13591i) q^{23} +(-1.47518 - 3.75869i) q^{25} +(4.17602 - 1.28813i) q^{26} +(-0.160692 + 1.27903i) q^{28} +(0.492320 + 2.15699i) q^{29} +(0.292528 - 0.506674i) q^{31} +(2.57932 + 0.795613i) q^{32} +(4.78753 - 6.00338i) q^{34} +(0.0638864 + 2.59446i) q^{35} +(-6.77479 + 6.28609i) q^{37} +(-2.00920 + 0.302837i) q^{38} +(2.31411 + 0.348796i) q^{40} +(10.0896 - 4.85890i) q^{41} +(4.98694 + 2.40158i) q^{43} +(0.733855 + 0.500334i) q^{44} +(0.454190 - 6.06074i) q^{46} +(4.07192 - 10.3751i) q^{47} +(-2.23357 + 6.63409i) q^{49} +6.36801 q^{50} +(-0.100895 + 1.34635i) q^{52} +(-4.99617 - 4.63577i) q^{53} +(1.61106 + 0.775846i) q^{55} +(5.54255 + 3.02057i) q^{56} +(-3.45030 - 0.520049i) q^{58} +(-2.97181 + 2.02615i) q^{59} +(-6.40633 + 5.94420i) q^{61} +(0.575288 + 0.721388i) q^{62} +(3.25286 - 4.07896i) q^{64} +(0.203127 + 2.71054i) q^{65} +(0.712256 - 1.23366i) q^{67} +(1.18612 + 2.05442i) q^{68} +(-3.84568 - 1.40108i) q^{70} +(-2.19834 + 9.63156i) q^{71} +(3.06719 + 7.81508i) q^{73} +(-5.32498 - 13.5678i) q^{74} +(0.139684 - 0.611995i) q^{76} +(3.36654 + 3.45371i) q^{77} +(-1.80317 - 3.12318i) q^{79} +(-2.32332 + 4.02411i) q^{80} +(1.31983 + 17.6119i) q^{82} +(4.89464 - 6.13768i) q^{83} +(2.97772 + 3.73395i) q^{85} +(-6.39907 + 5.93747i) q^{86} +(3.59343 - 2.44996i) q^{88} +(-9.38904 - 1.41517i) q^{89} +(-1.98787 + 7.05681i) q^{91} +(1.69171 + 0.814686i) q^{92} +(12.8853 + 11.9558i) q^{94} +(0.0944427 - 1.26025i) q^{95} -2.17773 q^{97} +(-8.45241 - 7.10147i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{11}{21}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.576178 + 1.46808i −0.407419 + 1.03809i 0.569026 + 0.822320i \(0.307320\pi\)
−0.976445 + 0.215767i \(0.930775\pi\)
\(3\) 0 0
\(4\) −0.357164 0.331400i −0.178582 0.165700i
\(5\) −0.810468 0.552568i −0.362452 0.247116i 0.368376 0.929677i \(-0.379914\pi\)
−0.730829 + 0.682561i \(0.760866\pi\)
\(6\) 0 0
\(7\) −1.54377 2.14867i −0.583489 0.812121i
\(8\) −2.14952 + 1.03515i −0.759969 + 0.365982i
\(9\) 0 0
\(10\) 1.27819 0.871452i 0.404198 0.275577i
\(11\) −1.80258 + 0.271695i −0.543498 + 0.0819191i −0.415052 0.909798i \(-0.636237\pi\)
−0.128445 + 0.991717i \(0.540999\pi\)
\(12\) 0 0
\(13\) −1.72771 2.16648i −0.479180 0.600873i 0.482212 0.876054i \(-0.339833\pi\)
−0.961392 + 0.275182i \(0.911262\pi\)
\(14\) 4.04390 1.02835i 1.08078 0.274838i
\(15\) 0 0
\(16\) −0.354001 4.72382i −0.0885003 1.18095i
\(17\) −4.65252 1.43511i −1.12840 0.348066i −0.326308 0.945263i \(-0.605805\pi\)
−0.802094 + 0.597197i \(0.796281\pi\)
\(18\) 0 0
\(19\) 0.644188 + 1.11577i 0.147787 + 0.255974i 0.930409 0.366523i \(-0.119452\pi\)
−0.782622 + 0.622497i \(0.786118\pi\)
\(20\) 0.106349 + 0.465946i 0.0237804 + 0.104189i
\(21\) 0 0
\(22\) 0.639736 2.80287i 0.136392 0.597573i
\(23\) −3.68254 + 1.13591i −0.767863 + 0.236854i −0.653849 0.756625i \(-0.726847\pi\)
−0.114014 + 0.993479i \(0.536371\pi\)
\(24\) 0 0
\(25\) −1.47518 3.75869i −0.295036 0.751738i
\(26\) 4.17602 1.28813i 0.818985 0.252623i
\(27\) 0 0
\(28\) −0.160692 + 1.27903i −0.0303678 + 0.241714i
\(29\) 0.492320 + 2.15699i 0.0914215 + 0.400544i 0.999847 0.0175034i \(-0.00557179\pi\)
−0.908425 + 0.418047i \(0.862715\pi\)
\(30\) 0 0
\(31\) 0.292528 0.506674i 0.0525397 0.0910014i −0.838559 0.544810i \(-0.816602\pi\)
0.891099 + 0.453809i \(0.149935\pi\)
\(32\) 2.57932 + 0.795613i 0.455963 + 0.140646i
\(33\) 0 0
\(34\) 4.78753 6.00338i 0.821055 1.02957i
\(35\) 0.0638864 + 2.59446i 0.0107988 + 0.438545i
\(36\) 0 0
\(37\) −6.77479 + 6.28609i −1.11377 + 1.03343i −0.114570 + 0.993415i \(0.536549\pi\)
−0.999199 + 0.0400117i \(0.987260\pi\)
\(38\) −2.00920 + 0.302837i −0.325935 + 0.0491267i
\(39\) 0 0
\(40\) 2.31411 + 0.348796i 0.365892 + 0.0551494i
\(41\) 10.0896 4.85890i 1.57573 0.758833i 0.577395 0.816465i \(-0.304069\pi\)
0.998338 + 0.0576326i \(0.0183552\pi\)
\(42\) 0 0
\(43\) 4.98694 + 2.40158i 0.760501 + 0.366238i 0.773598 0.633676i \(-0.218455\pi\)
−0.0130975 + 0.999914i \(0.504169\pi\)
\(44\) 0.733855 + 0.500334i 0.110633 + 0.0754282i
\(45\) 0 0
\(46\) 0.454190 6.06074i 0.0669666 0.893607i
\(47\) 4.07192 10.3751i 0.593950 1.51336i −0.245207 0.969471i \(-0.578856\pi\)
0.839157 0.543889i \(-0.183049\pi\)
\(48\) 0 0
\(49\) −2.23357 + 6.63409i −0.319082 + 0.947727i
\(50\) 6.36801 0.900573
\(51\) 0 0
\(52\) −0.100895 + 1.34635i −0.0139916 + 0.186705i
\(53\) −4.99617 4.63577i −0.686277 0.636772i 0.257915 0.966168i \(-0.416965\pi\)
−0.944192 + 0.329395i \(0.893155\pi\)
\(54\) 0 0
\(55\) 1.61106 + 0.775846i 0.217235 + 0.104615i
\(56\) 5.54255 + 3.02057i 0.740655 + 0.403641i
\(57\) 0 0
\(58\) −3.45030 0.520049i −0.453046 0.0682857i
\(59\) −2.97181 + 2.02615i −0.386897 + 0.263782i −0.741111 0.671382i \(-0.765701\pi\)
0.354214 + 0.935164i \(0.384748\pi\)
\(60\) 0 0
\(61\) −6.40633 + 5.94420i −0.820246 + 0.761077i −0.973883 0.227050i \(-0.927092\pi\)
0.153637 + 0.988127i \(0.450901\pi\)
\(62\) 0.575288 + 0.721388i 0.0730617 + 0.0916164i
\(63\) 0 0
\(64\) 3.25286 4.07896i 0.406607 0.509870i
\(65\) 0.203127 + 2.71054i 0.0251948 + 0.336201i
\(66\) 0 0
\(67\) 0.712256 1.23366i 0.0870160 0.150716i −0.819233 0.573461i \(-0.805600\pi\)
0.906248 + 0.422745i \(0.138934\pi\)
\(68\) 1.18612 + 2.05442i 0.143838 + 0.249134i
\(69\) 0 0
\(70\) −3.84568 1.40108i −0.459647 0.167461i
\(71\) −2.19834 + 9.63156i −0.260895 + 1.14306i 0.659388 + 0.751803i \(0.270816\pi\)
−0.920283 + 0.391253i \(0.872042\pi\)
\(72\) 0 0
\(73\) 3.06719 + 7.81508i 0.358988 + 0.914686i 0.990273 + 0.139135i \(0.0444323\pi\)
−0.631286 + 0.775550i \(0.717472\pi\)
\(74\) −5.32498 13.5678i −0.619016 1.57723i
\(75\) 0 0
\(76\) 0.139684 0.611995i 0.0160228 0.0702006i
\(77\) 3.36654 + 3.45371i 0.383653 + 0.393587i
\(78\) 0 0
\(79\) −1.80317 3.12318i −0.202872 0.351385i 0.746580 0.665295i \(-0.231694\pi\)
−0.949453 + 0.313910i \(0.898361\pi\)
\(80\) −2.32332 + 4.02411i −0.259756 + 0.449910i
\(81\) 0 0
\(82\) 1.31983 + 17.6119i 0.145751 + 1.94491i
\(83\) 4.89464 6.13768i 0.537256 0.673698i −0.436917 0.899502i \(-0.643929\pi\)
0.974173 + 0.225804i \(0.0725009\pi\)
\(84\) 0 0
\(85\) 2.97772 + 3.73395i 0.322979 + 0.405003i
\(86\) −6.39907 + 5.93747i −0.690029 + 0.640253i
\(87\) 0 0
\(88\) 3.59343 2.44996i 0.383060 0.261166i
\(89\) −9.38904 1.41517i −0.995236 0.150008i −0.368824 0.929499i \(-0.620239\pi\)
−0.626413 + 0.779492i \(0.715477\pi\)
\(90\) 0 0
\(91\) −1.98787 + 7.05681i −0.208386 + 0.739755i
\(92\) 1.69171 + 0.814686i 0.176373 + 0.0849369i
\(93\) 0 0
\(94\) 12.8853 + 11.9558i 1.32901 + 1.23314i
\(95\) 0.0944427 1.26025i 0.00968961 0.129299i
\(96\) 0 0
\(97\) −2.17773 −0.221115 −0.110557 0.993870i \(-0.535264\pi\)
−0.110557 + 0.993870i \(0.535264\pi\)
\(98\) −8.45241 7.10147i −0.853823 0.717357i
\(99\) 0 0
\(100\) −0.718749 + 1.83134i −0.0718749 + 0.183134i
\(101\) −0.137283 + 1.83191i −0.0136602 + 0.182282i 0.986200 + 0.165558i \(0.0529427\pi\)
−0.999860 + 0.0167238i \(0.994676\pi\)
\(102\) 0 0
\(103\) 0.652706 + 0.445007i 0.0643130 + 0.0438479i 0.595050 0.803689i \(-0.297132\pi\)
−0.530737 + 0.847537i \(0.678085\pi\)
\(104\) 5.95637 + 2.86844i 0.584071 + 0.281274i
\(105\) 0 0
\(106\) 9.68435 4.66374i 0.940627 0.452982i
\(107\) −12.6269 1.90320i −1.22069 0.183990i −0.493083 0.869982i \(-0.664130\pi\)
−0.727608 + 0.685993i \(0.759368\pi\)
\(108\) 0 0
\(109\) −16.0702 + 2.42220i −1.53925 + 0.232004i −0.863203 0.504857i \(-0.831545\pi\)
−0.676044 + 0.736861i \(0.736307\pi\)
\(110\) −2.06726 + 1.91814i −0.197105 + 0.182887i
\(111\) 0 0
\(112\) −9.60344 + 8.05310i −0.907440 + 0.760947i
\(113\) −2.79568 + 3.50567i −0.262995 + 0.329786i −0.895743 0.444572i \(-0.853356\pi\)
0.632748 + 0.774358i \(0.281927\pi\)
\(114\) 0 0
\(115\) 3.61225 + 1.11423i 0.336844 + 0.103903i
\(116\) 0.538988 0.933555i 0.0500438 0.0866784i
\(117\) 0 0
\(118\) −1.26225 5.53027i −0.116199 0.509103i
\(119\) 4.09882 + 12.2122i 0.375738 + 1.11949i
\(120\) 0 0
\(121\) −7.33583 + 2.26280i −0.666894 + 0.205710i
\(122\) −5.03536 12.8299i −0.455880 1.16156i
\(123\) 0 0
\(124\) −0.272392 + 0.0840219i −0.0244616 + 0.00754539i
\(125\) −1.97272 + 8.64303i −0.176445 + 0.773056i
\(126\) 0 0
\(127\) 1.72089 + 7.53971i 0.152704 + 0.669041i 0.992093 + 0.125509i \(0.0400563\pi\)
−0.839388 + 0.543532i \(0.817087\pi\)
\(128\) 6.81323 + 11.8009i 0.602210 + 1.04306i
\(129\) 0 0
\(130\) −4.09631 1.26355i −0.359270 0.110820i
\(131\) −0.0177821 0.237286i −0.00155363 0.0207318i 0.996373 0.0850919i \(-0.0271184\pi\)
−0.997927 + 0.0643602i \(0.979499\pi\)
\(132\) 0 0
\(133\) 1.40294 3.10663i 0.121650 0.269379i
\(134\) 1.40073 + 1.75646i 0.121004 + 0.151735i
\(135\) 0 0
\(136\) 11.4862 1.73127i 0.984937 0.148455i
\(137\) −7.11680 + 4.85215i −0.608029 + 0.414547i −0.827815 0.561001i \(-0.810416\pi\)
0.219786 + 0.975548i \(0.429464\pi\)
\(138\) 0 0
\(139\) 16.4947 7.94342i 1.39906 0.673752i 0.426090 0.904681i \(-0.359891\pi\)
0.972971 + 0.230928i \(0.0741763\pi\)
\(140\) 0.836987 0.947821i 0.0707383 0.0801055i
\(141\) 0 0
\(142\) −12.8732 8.77682i −1.08030 0.736535i
\(143\) 3.70295 + 3.43584i 0.309656 + 0.287319i
\(144\) 0 0
\(145\) 0.792876 2.02022i 0.0658448 0.167770i
\(146\) −13.2404 −1.09578
\(147\) 0 0
\(148\) 4.50292 0.370138
\(149\) 7.84938 19.9999i 0.643046 1.63845i −0.120509 0.992712i \(-0.538453\pi\)
0.763555 0.645743i \(-0.223452\pi\)
\(150\) 0 0
\(151\) −1.35911 1.26107i −0.110603 0.102624i 0.622933 0.782275i \(-0.285941\pi\)
−0.733536 + 0.679651i \(0.762131\pi\)
\(152\) −2.53968 1.73152i −0.205995 0.140445i
\(153\) 0 0
\(154\) −7.01004 + 2.95239i −0.564885 + 0.237910i
\(155\) −0.517057 + 0.249001i −0.0415310 + 0.0200003i
\(156\) 0 0
\(157\) −13.0284 + 8.88264i −1.03978 + 0.708912i −0.957716 0.287715i \(-0.907105\pi\)
−0.0820670 + 0.996627i \(0.526152\pi\)
\(158\) 5.62401 0.847683i 0.447422 0.0674380i
\(159\) 0 0
\(160\) −1.65082 2.07007i −0.130509 0.163653i
\(161\) 8.12569 + 6.15899i 0.640394 + 0.485396i
\(162\) 0 0
\(163\) 0.201848 + 2.69348i 0.0158100 + 0.210970i 0.999514 + 0.0311740i \(0.00992461\pi\)
−0.983704 + 0.179796i \(0.942456\pi\)
\(164\) −5.21388 1.60827i −0.407136 0.125585i
\(165\) 0 0
\(166\) 6.19040 + 10.7221i 0.480469 + 0.832196i
\(167\) −3.16201 13.8537i −0.244684 1.07203i −0.936696 0.350144i \(-0.886133\pi\)
0.692012 0.721886i \(-0.256724\pi\)
\(168\) 0 0
\(169\) 1.18412 5.18798i 0.0910863 0.399075i
\(170\) −7.19742 + 2.22011i −0.552017 + 0.170275i
\(171\) 0 0
\(172\) −0.985270 2.51043i −0.0751262 0.191418i
\(173\) 13.1286 4.04964i 0.998149 0.307888i 0.247714 0.968833i \(-0.420321\pi\)
0.750434 + 0.660945i \(0.229844\pi\)
\(174\) 0 0
\(175\) −5.79886 + 8.97221i −0.438353 + 0.678235i
\(176\) 1.92155 + 8.41887i 0.144842 + 0.634596i
\(177\) 0 0
\(178\) 7.48733 12.9684i 0.561199 0.972025i
\(179\) 4.27716 + 1.31933i 0.319690 + 0.0986113i 0.450447 0.892803i \(-0.351265\pi\)
−0.130757 + 0.991414i \(0.541741\pi\)
\(180\) 0 0
\(181\) 4.39373 5.50956i 0.326583 0.409522i −0.591250 0.806488i \(-0.701365\pi\)
0.917833 + 0.396966i \(0.129937\pi\)
\(182\) −9.21457 6.98432i −0.683029 0.517712i
\(183\) 0 0
\(184\) 6.73984 6.25366i 0.496868 0.461026i
\(185\) 8.96425 1.35114i 0.659064 0.0993380i
\(186\) 0 0
\(187\) 8.77644 + 1.32284i 0.641797 + 0.0967354i
\(188\) −4.89264 + 2.35617i −0.356832 + 0.171841i
\(189\) 0 0
\(190\) 1.79573 + 0.864777i 0.130276 + 0.0627375i
\(191\) 15.8564 + 10.8107i 1.14733 + 0.782238i 0.979074 0.203505i \(-0.0652335\pi\)
0.168258 + 0.985743i \(0.446186\pi\)
\(192\) 0 0
\(193\) 1.69283 22.5892i 0.121852 1.62601i −0.516517 0.856277i \(-0.672772\pi\)
0.638369 0.769730i \(-0.279609\pi\)
\(194\) 1.25476 3.19707i 0.0900863 0.229536i
\(195\) 0 0
\(196\) 2.99629 1.62925i 0.214021 0.116375i
\(197\) 3.49854 0.249260 0.124630 0.992203i \(-0.460226\pi\)
0.124630 + 0.992203i \(0.460226\pi\)
\(198\) 0 0
\(199\) −0.673086 + 8.98170i −0.0477138 + 0.636696i 0.921167 + 0.389168i \(0.127237\pi\)
−0.968881 + 0.247528i \(0.920382\pi\)
\(200\) 7.06174 + 6.55234i 0.499340 + 0.463320i
\(201\) 0 0
\(202\) −2.61029 1.25705i −0.183659 0.0884457i
\(203\) 3.87465 4.38773i 0.271947 0.307958i
\(204\) 0 0
\(205\) −10.8622 1.63721i −0.758647 0.114348i
\(206\) −1.02938 + 0.701819i −0.0717203 + 0.0488980i
\(207\) 0 0
\(208\) −9.62244 + 8.92832i −0.667196 + 0.619068i
\(209\) −1.46435 1.83623i −0.101291 0.127015i
\(210\) 0 0
\(211\) 5.64473 7.07827i 0.388599 0.487288i −0.548599 0.836086i \(-0.684839\pi\)
0.937198 + 0.348798i \(0.113410\pi\)
\(212\) 0.248160 + 3.31146i 0.0170437 + 0.227432i
\(213\) 0 0
\(214\) 10.0694 17.4407i 0.688330 1.19222i
\(215\) −2.71472 4.70203i −0.185142 0.320676i
\(216\) 0 0
\(217\) −1.54027 + 0.153639i −0.104560 + 0.0104297i
\(218\) 5.70333 24.9879i 0.386278 1.69240i
\(219\) 0 0
\(220\) −0.318298 0.811010i −0.0214596 0.0546783i
\(221\) 4.92906 + 12.5590i 0.331565 + 0.844813i
\(222\) 0 0
\(223\) 6.05723 26.5384i 0.405622 1.77715i −0.198341 0.980133i \(-0.563555\pi\)
0.603963 0.797013i \(-0.293588\pi\)
\(224\) −2.27235 6.77034i −0.151828 0.452362i
\(225\) 0 0
\(226\) −3.53578 6.12416i −0.235197 0.407373i
\(227\) 8.69808 15.0655i 0.577312 0.999934i −0.418474 0.908229i \(-0.637435\pi\)
0.995786 0.0917050i \(-0.0292317\pi\)
\(228\) 0 0
\(229\) −0.918872 12.2615i −0.0607207 0.810262i −0.941560 0.336846i \(-0.890640\pi\)
0.880839 0.473416i \(-0.156979\pi\)
\(230\) −3.71708 + 4.66107i −0.245097 + 0.307342i
\(231\) 0 0
\(232\) −3.29107 4.12687i −0.216069 0.270942i
\(233\) 19.5478 18.1377i 1.28062 1.18824i 0.309168 0.951007i \(-0.399949\pi\)
0.971452 0.237235i \(-0.0762410\pi\)
\(234\) 0 0
\(235\) −9.03309 + 6.15866i −0.589254 + 0.401746i
\(236\) 1.73289 + 0.261191i 0.112801 + 0.0170021i
\(237\) 0 0
\(238\) −20.2901 1.01903i −1.31521 0.0660537i
\(239\) −16.0330 7.72108i −1.03709 0.499435i −0.163725 0.986506i \(-0.552351\pi\)
−0.873362 + 0.487071i \(0.838065\pi\)
\(240\) 0 0
\(241\) −3.94767 3.66290i −0.254292 0.235948i 0.542717 0.839915i \(-0.317395\pi\)
−0.797009 + 0.603967i \(0.793586\pi\)
\(242\) 0.904772 12.0733i 0.0581609 0.776104i
\(243\) 0 0
\(244\) 4.25802 0.272592
\(245\) 5.47603 4.14252i 0.349850 0.264656i
\(246\) 0 0
\(247\) 1.30431 3.32334i 0.0829915 0.211459i
\(248\) −0.104310 + 1.39192i −0.00662367 + 0.0883868i
\(249\) 0 0
\(250\) −11.5520 7.87602i −0.730612 0.498123i
\(251\) 25.6008 + 12.3287i 1.61591 + 0.778180i 0.999954 0.00960250i \(-0.00305662\pi\)
0.615954 + 0.787782i \(0.288771\pi\)
\(252\) 0 0
\(253\) 6.32944 3.04810i 0.397929 0.191632i
\(254\) −12.0604 1.81781i −0.756737 0.114060i
\(255\) 0 0
\(256\) −10.9324 + 1.64779i −0.683273 + 0.102987i
\(257\) −14.1645 + 13.1427i −0.883557 + 0.819821i −0.984557 0.175066i \(-0.943986\pi\)
0.101000 + 0.994886i \(0.467796\pi\)
\(258\) 0 0
\(259\) 23.9654 + 4.85255i 1.48914 + 0.301523i
\(260\) 0.825722 1.03542i 0.0512091 0.0642142i
\(261\) 0 0
\(262\) 0.358600 + 0.110613i 0.0221544 + 0.00683371i
\(263\) −12.1783 + 21.0934i −0.750945 + 1.30067i 0.196421 + 0.980520i \(0.437068\pi\)
−0.947365 + 0.320155i \(0.896265\pi\)
\(264\) 0 0
\(265\) 1.48766 + 6.51787i 0.0913863 + 0.400390i
\(266\) 3.75243 + 3.84959i 0.230076 + 0.236034i
\(267\) 0 0
\(268\) −0.663228 + 0.204579i −0.0405131 + 0.0124966i
\(269\) 9.23847 + 23.5392i 0.563279 + 1.43521i 0.874571 + 0.484898i \(0.161143\pi\)
−0.311291 + 0.950315i \(0.600761\pi\)
\(270\) 0 0
\(271\) −13.7508 + 4.24155i −0.835299 + 0.257656i −0.682761 0.730642i \(-0.739221\pi\)
−0.152538 + 0.988298i \(0.548745\pi\)
\(272\) −5.13222 + 22.4857i −0.311186 + 1.36340i
\(273\) 0 0
\(274\) −3.02279 13.2437i −0.182613 0.800082i
\(275\) 3.68034 + 6.37454i 0.221933 + 0.384399i
\(276\) 0 0
\(277\) −6.48717 2.00103i −0.389776 0.120230i 0.0936717 0.995603i \(-0.470140\pi\)
−0.483448 + 0.875373i \(0.660616\pi\)
\(278\) 2.15768 + 28.7923i 0.129409 + 1.72685i
\(279\) 0 0
\(280\) −2.82299 5.51071i −0.168706 0.329328i
\(281\) −13.3608 16.7539i −0.797038 0.999454i −0.999795 0.0202251i \(-0.993562\pi\)
0.202757 0.979229i \(-0.435010\pi\)
\(282\) 0 0
\(283\) 22.7564 3.42997i 1.35273 0.203891i 0.567639 0.823277i \(-0.307857\pi\)
0.785086 + 0.619387i \(0.212619\pi\)
\(284\) 3.97707 2.71152i 0.235995 0.160899i
\(285\) 0 0
\(286\) −7.17762 + 3.45656i −0.424422 + 0.204391i
\(287\) −26.0162 14.1783i −1.53569 0.836916i
\(288\) 0 0
\(289\) 5.54035 + 3.77735i 0.325903 + 0.222197i
\(290\) 2.50899 + 2.32801i 0.147333 + 0.136705i
\(291\) 0 0
\(292\) 1.49442 3.80773i 0.0874546 0.222831i
\(293\) −30.3611 −1.77371 −0.886857 0.462044i \(-0.847116\pi\)
−0.886857 + 0.462044i \(0.847116\pi\)
\(294\) 0 0
\(295\) 3.52814 0.205416
\(296\) 8.05547 20.5250i 0.468215 1.19299i
\(297\) 0 0
\(298\) 24.8387 + 23.0470i 1.43887 + 1.33508i
\(299\) 8.82329 + 6.01562i 0.510264 + 0.347892i
\(300\) 0 0
\(301\) −2.53845 14.4228i −0.146314 0.831314i
\(302\) 2.63443 1.26868i 0.151595 0.0730041i
\(303\) 0 0
\(304\) 5.04263 3.43801i 0.289215 0.197183i
\(305\) 8.47670 1.27766i 0.485374 0.0731584i
\(306\) 0 0
\(307\) −3.81992 4.79003i −0.218014 0.273381i 0.660783 0.750577i \(-0.270225\pi\)
−0.878797 + 0.477196i \(0.841653\pi\)
\(308\) −0.0578473 2.34921i −0.00329615 0.133859i
\(309\) 0 0
\(310\) −0.0676366 0.902548i −0.00384150 0.0512613i
\(311\) 14.8937 + 4.59411i 0.844547 + 0.260508i 0.686687 0.726953i \(-0.259064\pi\)
0.157860 + 0.987462i \(0.449541\pi\)
\(312\) 0 0
\(313\) 7.45529 + 12.9129i 0.421398 + 0.729883i 0.996077 0.0884963i \(-0.0282062\pi\)
−0.574678 + 0.818379i \(0.694873\pi\)
\(314\) −5.53370 24.2447i −0.312285 1.36821i
\(315\) 0 0
\(316\) −0.390994 + 1.71306i −0.0219951 + 0.0963670i
\(317\) −20.0427 + 6.18235i −1.12571 + 0.347235i −0.801051 0.598596i \(-0.795725\pi\)
−0.324658 + 0.945832i \(0.605249\pi\)
\(318\) 0 0
\(319\) −1.47349 3.75439i −0.0824996 0.210205i
\(320\) −4.89024 + 1.50844i −0.273373 + 0.0843243i
\(321\) 0 0
\(322\) −13.7237 + 8.38046i −0.764792 + 0.467025i
\(323\) −1.39585 6.11561i −0.0776670 0.340281i
\(324\) 0 0
\(325\) −5.59445 + 9.68986i −0.310324 + 0.537497i
\(326\) −4.07054 1.25559i −0.225446 0.0695409i
\(327\) 0 0
\(328\) −16.6581 + 20.8886i −0.919789 + 1.15338i
\(329\) −28.5787 + 7.26747i −1.57559 + 0.400669i
\(330\) 0 0
\(331\) −2.80260 + 2.60043i −0.154045 + 0.142933i −0.753430 0.657528i \(-0.771602\pi\)
0.599385 + 0.800461i \(0.295412\pi\)
\(332\) −3.78221 + 0.570077i −0.207576 + 0.0312870i
\(333\) 0 0
\(334\) 22.1601 + 3.34010i 1.21255 + 0.182762i
\(335\) −1.25894 + 0.606276i −0.0687835 + 0.0331244i
\(336\) 0 0
\(337\) −6.99780 3.36996i −0.381195 0.183574i 0.233467 0.972365i \(-0.424993\pi\)
−0.614661 + 0.788791i \(0.710707\pi\)
\(338\) 6.93408 + 4.72758i 0.377164 + 0.257146i
\(339\) 0 0
\(340\) 0.173894 2.32045i 0.00943070 0.125844i
\(341\) −0.389645 + 0.992798i −0.0211004 + 0.0537630i
\(342\) 0 0
\(343\) 17.7026 5.44226i 0.955850 0.293855i
\(344\) −13.2055 −0.711993
\(345\) 0 0
\(346\) −1.61923 + 21.6071i −0.0870502 + 1.16160i
\(347\) 5.68525 + 5.27514i 0.305200 + 0.283185i 0.817872 0.575400i \(-0.195154\pi\)
−0.512672 + 0.858585i \(0.671344\pi\)
\(348\) 0 0
\(349\) −2.92294 1.40762i −0.156462 0.0753479i 0.354014 0.935240i \(-0.384816\pi\)
−0.510476 + 0.859892i \(0.670531\pi\)
\(350\) −9.83072 13.6828i −0.525474 0.731374i
\(351\) 0 0
\(352\) −4.86558 0.733368i −0.259336 0.0390887i
\(353\) 10.9183 7.44395i 0.581121 0.396201i −0.236778 0.971564i \(-0.576091\pi\)
0.817899 + 0.575362i \(0.195139\pi\)
\(354\) 0 0
\(355\) 7.10378 6.59134i 0.377029 0.349832i
\(356\) 2.88444 + 3.61697i 0.152875 + 0.191699i
\(357\) 0 0
\(358\) −4.40128 + 5.51903i −0.232615 + 0.291690i
\(359\) −1.85359 24.7345i −0.0978289 1.30544i −0.802821 0.596221i \(-0.796668\pi\)
0.704992 0.709216i \(-0.250951\pi\)
\(360\) 0 0
\(361\) 8.67004 15.0170i 0.456318 0.790366i
\(362\) 5.55689 + 9.62481i 0.292064 + 0.505869i
\(363\) 0 0
\(364\) 3.04862 1.86166i 0.159791 0.0975774i
\(365\) 1.83250 8.02870i 0.0959174 0.420241i
\(366\) 0 0
\(367\) −6.94109 17.6856i −0.362322 0.923182i −0.989530 0.144329i \(-0.953897\pi\)
0.627208 0.778852i \(-0.284198\pi\)
\(368\) 6.66948 + 16.9935i 0.347670 + 0.885850i
\(369\) 0 0
\(370\) −3.18142 + 13.9387i −0.165394 + 0.724638i
\(371\) −2.24783 + 17.8917i −0.116701 + 0.928890i
\(372\) 0 0
\(373\) 7.37297 + 12.7704i 0.381758 + 0.661224i 0.991314 0.131519i \(-0.0419854\pi\)
−0.609556 + 0.792743i \(0.708652\pi\)
\(374\) −6.99881 + 12.1223i −0.361900 + 0.626829i
\(375\) 0 0
\(376\) 1.98713 + 26.5165i 0.102479 + 1.36748i
\(377\) 3.82250 4.79326i 0.196869 0.246865i
\(378\) 0 0
\(379\) 20.4541 + 25.6487i 1.05066 + 1.31748i 0.946423 + 0.322930i \(0.104668\pi\)
0.104235 + 0.994553i \(0.466761\pi\)
\(380\) −0.451378 + 0.418817i −0.0231552 + 0.0214849i
\(381\) 0 0
\(382\) −25.0071 + 17.0496i −1.27948 + 0.872331i
\(383\) −37.7257 5.68624i −1.92769 0.290553i −0.930556 0.366150i \(-0.880676\pi\)
−0.997138 + 0.0755973i \(0.975914\pi\)
\(384\) 0 0
\(385\) −0.820063 4.65937i −0.0417943 0.237463i
\(386\) 32.1873 + 15.5006i 1.63829 + 0.788960i
\(387\) 0 0
\(388\) 0.777805 + 0.721698i 0.0394871 + 0.0366387i
\(389\) −1.85242 + 24.7188i −0.0939212 + 1.25329i 0.728752 + 0.684777i \(0.240101\pi\)
−0.822673 + 0.568514i \(0.807518\pi\)
\(390\) 0 0
\(391\) 18.7633 0.948899
\(392\) −2.06619 16.5722i −0.104358 0.837022i
\(393\) 0 0
\(394\) −2.01578 + 5.13612i −0.101553 + 0.258754i
\(395\) −0.264358 + 3.52761i −0.0133013 + 0.177493i
\(396\) 0 0
\(397\) −28.8606 19.6768i −1.44847 0.987551i −0.995373 0.0960904i \(-0.969366\pi\)
−0.453099 0.891460i \(-0.649681\pi\)
\(398\) −12.7980 6.16320i −0.641506 0.308933i
\(399\) 0 0
\(400\) −17.2332 + 8.29906i −0.861658 + 0.414953i
\(401\) −9.06529 1.36637i −0.452699 0.0682334i −0.0812645 0.996693i \(-0.525896\pi\)
−0.371434 + 0.928459i \(0.621134\pi\)
\(402\) 0 0
\(403\) −1.60310 + 0.241629i −0.0798562 + 0.0120364i
\(404\) 0.656129 0.608798i 0.0326436 0.0302888i
\(405\) 0 0
\(406\) 4.20904 + 8.21639i 0.208891 + 0.407772i
\(407\) 10.5042 13.1718i 0.520674 0.652904i
\(408\) 0 0
\(409\) −36.0305 11.1139i −1.78159 0.549548i −0.784119 0.620610i \(-0.786885\pi\)
−0.997472 + 0.0710621i \(0.977361\pi\)
\(410\) 8.66209 15.0032i 0.427790 0.740954i
\(411\) 0 0
\(412\) −0.0856477 0.375247i −0.00421956 0.0184871i
\(413\) 8.94131 + 3.25755i 0.439973 + 0.160294i
\(414\) 0 0
\(415\) −7.35843 + 2.26978i −0.361211 + 0.111419i
\(416\) −2.73263 6.96262i −0.133978 0.341370i
\(417\) 0 0
\(418\) 3.53945 1.09178i 0.173120 0.0534005i
\(419\) −3.06592 + 13.4327i −0.149780 + 0.656230i 0.843165 + 0.537655i \(0.180690\pi\)
−0.992945 + 0.118575i \(0.962167\pi\)
\(420\) 0 0
\(421\) 4.90355 + 21.4839i 0.238984 + 1.04706i 0.941928 + 0.335814i \(0.109011\pi\)
−0.702944 + 0.711245i \(0.748132\pi\)
\(422\) 7.13907 + 12.3652i 0.347525 + 0.601930i
\(423\) 0 0
\(424\) 15.5381 + 4.79287i 0.754597 + 0.232762i
\(425\) 1.46915 + 19.6044i 0.0712642 + 0.950955i
\(426\) 0 0
\(427\) 22.6620 + 4.58863i 1.09669 + 0.222060i
\(428\) 3.87916 + 4.86432i 0.187506 + 0.235126i
\(429\) 0 0
\(430\) 8.46709 1.27621i 0.408319 0.0615442i
\(431\) 11.2152 7.64637i 0.540216 0.368313i −0.262260 0.964997i \(-0.584468\pi\)
0.802476 + 0.596684i \(0.203516\pi\)
\(432\) 0 0
\(433\) −12.6117 + 6.07346i −0.606078 + 0.291872i −0.711644 0.702540i \(-0.752049\pi\)
0.105566 + 0.994412i \(0.466335\pi\)
\(434\) 0.661916 2.34976i 0.0317730 0.112792i
\(435\) 0 0
\(436\) 6.54242 + 4.46054i 0.313325 + 0.213621i
\(437\) −3.63966 3.37711i −0.174109 0.161549i
\(438\) 0 0
\(439\) 14.9350 38.0538i 0.712809 1.81621i 0.151778 0.988415i \(-0.451500\pi\)
0.561032 0.827794i \(-0.310405\pi\)
\(440\) −4.26612 −0.203379
\(441\) 0 0
\(442\) −21.2776 −1.01207
\(443\) 12.0541 30.7134i 0.572709 1.45924i −0.291729 0.956501i \(-0.594231\pi\)
0.864439 0.502738i \(-0.167674\pi\)
\(444\) 0 0
\(445\) 6.82754 + 6.33503i 0.323656 + 0.300309i
\(446\) 35.4704 + 24.1833i 1.67957 + 1.14511i
\(447\) 0 0
\(448\) −13.7860 0.692372i −0.651327 0.0327115i
\(449\) −7.94141 + 3.82438i −0.374778 + 0.180484i −0.611785 0.791024i \(-0.709548\pi\)
0.237006 + 0.971508i \(0.423834\pi\)
\(450\) 0 0
\(451\) −16.8672 + 11.4998i −0.794244 + 0.541506i
\(452\) 2.16029 0.325612i 0.101612 0.0153155i
\(453\) 0 0
\(454\) 17.1057 + 21.4499i 0.802810 + 1.00669i
\(455\) 5.51047 4.62089i 0.258335 0.216631i
\(456\) 0 0
\(457\) 1.71516 + 22.8873i 0.0802320 + 1.07062i 0.881459 + 0.472261i \(0.156562\pi\)
−0.801227 + 0.598361i \(0.795819\pi\)
\(458\) 18.5302 + 5.71582i 0.865861 + 0.267083i
\(459\) 0 0
\(460\) −0.920910 1.59506i −0.0429376 0.0743702i
\(461\) −4.73476 20.7443i −0.220520 0.966160i −0.957088 0.289797i \(-0.906412\pi\)
0.736568 0.676363i \(-0.236445\pi\)
\(462\) 0 0
\(463\) −0.343768 + 1.50615i −0.0159762 + 0.0699965i −0.982288 0.187379i \(-0.940001\pi\)
0.966311 + 0.257376i \(0.0828578\pi\)
\(464\) 10.0150 3.08921i 0.464933 0.143413i
\(465\) 0 0
\(466\) 15.3646 + 39.1482i 0.711749 + 1.81351i
\(467\) 1.27752 0.394062i 0.0591164 0.0182350i −0.265056 0.964233i \(-0.585390\pi\)
0.324172 + 0.945998i \(0.394914\pi\)
\(468\) 0 0
\(469\) −3.75030 + 0.374084i −0.173173 + 0.0172736i
\(470\) −3.83671 16.8097i −0.176974 0.775376i
\(471\) 0 0
\(472\) 4.29059 7.43152i 0.197490 0.342063i
\(473\) −9.64184 2.97411i −0.443332 0.136750i
\(474\) 0 0
\(475\) 3.24353 4.06725i 0.148823 0.186618i
\(476\) 2.58318 5.72011i 0.118400 0.262181i
\(477\) 0 0
\(478\) 20.5730 19.0889i 0.940986 0.873107i
\(479\) 11.7812 1.77573i 0.538297 0.0811352i 0.125733 0.992064i \(-0.459872\pi\)
0.412563 + 0.910929i \(0.364634\pi\)
\(480\) 0 0
\(481\) 25.3235 + 3.81691i 1.15465 + 0.174036i
\(482\) 7.65198 3.68500i 0.348538 0.167847i
\(483\) 0 0
\(484\) 3.36999 + 1.62290i 0.153181 + 0.0737682i
\(485\) 1.76498 + 1.20334i 0.0801435 + 0.0546409i
\(486\) 0 0
\(487\) 0.265737 3.54601i 0.0120417 0.160685i −0.987941 0.154830i \(-0.950517\pi\)
0.999983 0.00585546i \(-0.00186386\pi\)
\(488\) 7.61735 19.4087i 0.344821 0.878591i
\(489\) 0 0
\(490\) 2.92637 + 10.4260i 0.132200 + 0.471001i
\(491\) −3.71083 −0.167467 −0.0837336 0.996488i \(-0.526684\pi\)
−0.0837336 + 0.996488i \(0.526684\pi\)
\(492\) 0 0
\(493\) 0.805002 10.7420i 0.0362554 0.483795i
\(494\) 4.12739 + 3.82966i 0.185700 + 0.172305i
\(495\) 0 0
\(496\) −2.49699 1.20249i −0.112118 0.0539933i
\(497\) 24.0888 10.1454i 1.08053 0.455082i
\(498\) 0 0
\(499\) 30.6734 + 4.62327i 1.37313 + 0.206966i 0.793825 0.608146i \(-0.208086\pi\)
0.579304 + 0.815112i \(0.303325\pi\)
\(500\) 3.56888 2.43322i 0.159605 0.108817i
\(501\) 0 0
\(502\) −32.8501 + 30.4804i −1.46617 + 1.36041i
\(503\) 13.0212 + 16.3281i 0.580587 + 0.728033i 0.982213 0.187771i \(-0.0601262\pi\)
−0.401626 + 0.915804i \(0.631555\pi\)
\(504\) 0 0
\(505\) 1.12352 1.40885i 0.0499960 0.0626930i
\(506\) 0.827960 + 11.0484i 0.0368073 + 0.491159i
\(507\) 0 0
\(508\) 1.88402 3.26321i 0.0835898 0.144782i
\(509\) −16.4615 28.5122i −0.729643 1.26378i −0.957034 0.289976i \(-0.906353\pi\)
0.227390 0.973804i \(-0.426981\pi\)
\(510\) 0 0
\(511\) 12.0570 18.6550i 0.533370 0.825250i
\(512\) −2.18444 + 9.57065i −0.0965395 + 0.422967i
\(513\) 0 0
\(514\) −11.1333 28.3671i −0.491067 1.25122i
\(515\) −0.283101 0.721329i −0.0124749 0.0317855i
\(516\) 0 0
\(517\) −4.52109 + 19.8082i −0.198837 + 0.871163i
\(518\) −20.9323 + 32.3872i −0.919711 + 1.42301i
\(519\) 0 0
\(520\) −3.24244 5.61608i −0.142191 0.246281i
\(521\) 3.86730 6.69836i 0.169430 0.293461i −0.768790 0.639501i \(-0.779141\pi\)
0.938219 + 0.346041i \(0.112474\pi\)
\(522\) 0 0
\(523\) 0.145534 + 1.94202i 0.00636376 + 0.0849184i 0.999481 0.0322031i \(-0.0102523\pi\)
−0.993118 + 0.117122i \(0.962633\pi\)
\(524\) −0.0722854 + 0.0906430i −0.00315780 + 0.00395976i
\(525\) 0 0
\(526\) −23.9499 30.0322i −1.04426 1.30947i
\(527\) −2.08813 + 1.93750i −0.0909604 + 0.0843989i
\(528\) 0 0
\(529\) −6.73268 + 4.59026i −0.292725 + 0.199577i
\(530\) −10.4259 1.57145i −0.452872 0.0682594i
\(531\) 0 0
\(532\) −1.53061 + 0.644642i −0.0663606 + 0.0279488i
\(533\) −27.9586 13.4642i −1.21102 0.583197i
\(534\) 0 0
\(535\) 9.18207 + 8.51972i 0.396976 + 0.368340i
\(536\) −0.253976 + 3.38908i −0.0109701 + 0.146386i
\(537\) 0 0
\(538\) −39.8804 −1.71937
\(539\) 2.22374 12.5653i 0.0957835 0.541226i
\(540\) 0 0
\(541\) −1.46372 + 3.72949i −0.0629301 + 0.160343i −0.958880 0.283812i \(-0.908401\pi\)
0.895950 + 0.444155i \(0.146496\pi\)
\(542\) 1.69596 22.6310i 0.0728478 0.972087i
\(543\) 0 0
\(544\) −10.8585 7.40322i −0.465555 0.317410i
\(545\) 14.3628 + 6.91677i 0.615236 + 0.296282i
\(546\) 0 0
\(547\) −20.6693 + 9.95381i −0.883756 + 0.425594i −0.819995 0.572371i \(-0.806024\pi\)
−0.0637608 + 0.997965i \(0.520309\pi\)
\(548\) 4.14987 + 0.625492i 0.177274 + 0.0267197i
\(549\) 0 0
\(550\) −11.4788 + 1.73016i −0.489459 + 0.0737741i
\(551\) −2.08955 + 1.93882i −0.0890180 + 0.0825966i
\(552\) 0 0
\(553\) −3.92701 + 8.69587i −0.166994 + 0.369786i
\(554\) 6.67542 8.37072i 0.283612 0.355638i
\(555\) 0 0
\(556\) −8.52376 2.62923i −0.361488 0.111504i
\(557\) 15.7311 27.2471i 0.666548 1.15449i −0.312315 0.949978i \(-0.601105\pi\)
0.978863 0.204516i \(-0.0655621\pi\)
\(558\) 0 0
\(559\) −3.41300 14.9533i −0.144354 0.632458i
\(560\) 12.2332 1.22023i 0.516946 0.0515642i
\(561\) 0 0
\(562\) 32.2942 9.96144i 1.36225 0.420198i
\(563\) −0.895432 2.28152i −0.0377379 0.0961547i 0.910762 0.412931i \(-0.135495\pi\)
−0.948500 + 0.316776i \(0.897400\pi\)
\(564\) 0 0
\(565\) 4.20293 1.29643i 0.176818 0.0545413i
\(566\) −8.07625 + 35.3844i −0.339470 + 1.48732i
\(567\) 0 0
\(568\) −5.24477 22.9788i −0.220066 0.964170i
\(569\) 20.8347 + 36.0867i 0.873436 + 1.51283i 0.858420 + 0.512948i \(0.171447\pi\)
0.0150158 + 0.999887i \(0.495220\pi\)
\(570\) 0 0
\(571\) 6.80024 + 2.09760i 0.284581 + 0.0877817i 0.433760 0.901029i \(-0.357187\pi\)
−0.149178 + 0.988810i \(0.547663\pi\)
\(572\) −0.183925 2.45431i −0.00769030 0.102620i
\(573\) 0 0
\(574\) 35.8047 30.0245i 1.49446 1.25320i
\(575\) 9.70195 + 12.1659i 0.404599 + 0.507352i
\(576\) 0 0
\(577\) −13.7617 + 2.07425i −0.572908 + 0.0863520i −0.429106 0.903254i \(-0.641171\pi\)
−0.143803 + 0.989606i \(0.545933\pi\)
\(578\) −8.73766 + 5.95723i −0.363439 + 0.247788i
\(579\) 0 0
\(580\) −0.952686 + 0.458789i −0.0395581 + 0.0190502i
\(581\) −20.7440 1.04182i −0.860607 0.0432222i
\(582\) 0 0
\(583\) 10.2655 + 6.99891i 0.425154 + 0.289865i
\(584\) −14.6828 13.6236i −0.607578 0.563750i
\(585\) 0 0
\(586\) 17.4934 44.5724i 0.722645 1.84127i
\(587\) −45.9865 −1.89807 −0.949034 0.315174i \(-0.897937\pi\)
−0.949034 + 0.315174i \(0.897937\pi\)
\(588\) 0 0
\(589\) 0.753773 0.0310587
\(590\) −2.03284 + 5.17958i −0.0836906 + 0.213240i
\(591\) 0 0
\(592\) 32.0926 + 29.7776i 1.31900 + 1.22385i
\(593\) −4.05079 2.76178i −0.166346 0.113413i 0.477286 0.878748i \(-0.341621\pi\)
−0.643632 + 0.765335i \(0.722573\pi\)
\(594\) 0 0
\(595\) 3.42612 12.1625i 0.140457 0.498613i
\(596\) −9.43147 + 4.54196i −0.386328 + 0.186046i
\(597\) 0 0
\(598\) −13.9152 + 9.48720i −0.569033 + 0.387960i
\(599\) −33.1327 + 4.99396i −1.35377 + 0.204047i −0.785533 0.618820i \(-0.787611\pi\)
−0.568234 + 0.822867i \(0.692373\pi\)
\(600\) 0 0
\(601\) −10.2815 12.8926i −0.419390 0.525898i 0.526592 0.850118i \(-0.323470\pi\)
−0.945982 + 0.324220i \(0.894898\pi\)
\(602\) 22.6363 + 4.58343i 0.922588 + 0.186807i
\(603\) 0 0
\(604\) 0.0675068 + 0.900816i 0.00274681 + 0.0366537i
\(605\) 7.19581 + 2.21961i 0.292551 + 0.0902401i
\(606\) 0 0
\(607\) −20.1768 34.9473i −0.818952 1.41847i −0.906455 0.422301i \(-0.861222\pi\)
0.0875039 0.996164i \(-0.472111\pi\)
\(608\) 0.773845 + 3.39044i 0.0313835 + 0.137500i
\(609\) 0 0
\(610\) −3.00839 + 13.1806i −0.121806 + 0.533667i
\(611\) −29.5124 + 9.10338i −1.19395 + 0.368284i
\(612\) 0 0
\(613\) 4.29486 + 10.9431i 0.173468 + 0.441989i 0.990995 0.133902i \(-0.0427506\pi\)
−0.817527 + 0.575891i \(0.804655\pi\)
\(614\) 9.23308 2.84803i 0.372617 0.114937i
\(615\) 0 0
\(616\) −10.8116 3.93893i −0.435610 0.158704i
\(617\) 6.39881 + 28.0350i 0.257606 + 1.12865i 0.923802 + 0.382870i \(0.125064\pi\)
−0.666196 + 0.745777i \(0.732078\pi\)
\(618\) 0 0
\(619\) 9.15775 15.8617i 0.368081 0.637535i −0.621185 0.783664i \(-0.713348\pi\)
0.989265 + 0.146129i \(0.0466816\pi\)
\(620\) 0.267193 + 0.0824181i 0.0107307 + 0.00330999i
\(621\) 0 0
\(622\) −15.3259 + 19.2181i −0.614515 + 0.770577i
\(623\) 11.4537 + 22.3586i 0.458884 + 0.895780i
\(624\) 0 0
\(625\) −8.42494 + 7.81720i −0.336998 + 0.312688i
\(626\) −23.2528 + 3.50479i −0.929368 + 0.140080i
\(627\) 0 0
\(628\) 7.59700 + 1.14506i 0.303153 + 0.0456930i
\(629\) 40.5411 19.5236i 1.61648 0.778456i
\(630\) 0 0
\(631\) −14.2211 6.84854i −0.566134 0.272636i 0.128846 0.991665i \(-0.458873\pi\)
−0.694980 + 0.719029i \(0.744587\pi\)
\(632\) 7.10891 + 4.84677i 0.282777 + 0.192794i
\(633\) 0 0
\(634\) 2.47198 32.9863i 0.0981749 1.31005i
\(635\) 2.77147 7.06160i 0.109983 0.280231i
\(636\) 0 0
\(637\) 18.2316 6.62278i 0.722361 0.262404i
\(638\) 6.36072 0.251823
\(639\) 0 0
\(640\) 0.998870 13.3290i 0.0394838 0.526875i
\(641\) −19.2939 17.9021i −0.762062 0.707090i 0.200038 0.979788i \(-0.435894\pi\)
−0.962100 + 0.272698i \(0.912084\pi\)
\(642\) 0 0
\(643\) 36.3534 + 17.5069i 1.43364 + 0.690404i 0.979671 0.200613i \(-0.0642935\pi\)
0.453969 + 0.891018i \(0.350008\pi\)
\(644\) −0.861116 4.89262i −0.0339327 0.192796i
\(645\) 0 0
\(646\) 9.78243 + 1.47446i 0.384885 + 0.0580120i
\(647\) −30.9391 + 21.0939i −1.21634 + 0.829287i −0.989484 0.144641i \(-0.953797\pi\)
−0.226856 + 0.973928i \(0.572845\pi\)
\(648\) 0 0
\(649\) 4.80643 4.45971i 0.188669 0.175059i
\(650\) −11.0021 13.7962i −0.431537 0.541130i
\(651\) 0 0
\(652\) 0.820526 1.02891i 0.0321343 0.0402951i
\(653\) −0.228595 3.05039i −0.00894563 0.119371i 0.990943 0.134282i \(-0.0428727\pi\)
−0.999889 + 0.0149106i \(0.995254\pi\)
\(654\) 0 0
\(655\) −0.116705 + 0.202139i −0.00456003 + 0.00789820i
\(656\) −26.5243 45.9414i −1.03560 1.79371i
\(657\) 0 0
\(658\) 5.79720 46.1431i 0.225998 1.79884i
\(659\) −5.70915 + 25.0134i −0.222397 + 0.974384i 0.733271 + 0.679937i \(0.237993\pi\)
−0.955668 + 0.294448i \(0.904864\pi\)
\(660\) 0 0
\(661\) −6.83253 17.4090i −0.265755 0.677132i 0.734244 0.678886i \(-0.237537\pi\)
−0.999998 + 0.00175402i \(0.999442\pi\)
\(662\) −2.20284 5.61274i −0.0856158 0.218145i
\(663\) 0 0
\(664\) −4.16767 + 18.2597i −0.161737 + 0.708616i
\(665\) −2.85366 + 1.74260i −0.110660 + 0.0675753i
\(666\) 0 0
\(667\) −4.26315 7.38399i −0.165070 0.285909i
\(668\) −3.46175 + 5.99592i −0.133939 + 0.231989i
\(669\) 0 0
\(670\) −0.164684 2.19755i −0.00636228 0.0848987i
\(671\) 9.93290 12.4555i 0.383455 0.480838i
\(672\) 0 0
\(673\) −1.18995 1.49214i −0.0458690 0.0575179i 0.758368 0.651827i \(-0.225997\pi\)
−0.804237 + 0.594309i \(0.797426\pi\)
\(674\) 8.97934 8.33161i 0.345871 0.320922i
\(675\) 0 0
\(676\) −2.14222 + 1.46054i −0.0823931 + 0.0561747i
\(677\) 31.7283 + 4.78227i 1.21942 + 0.183797i 0.727046 0.686588i \(-0.240893\pi\)
0.492370 + 0.870386i \(0.336131\pi\)
\(678\) 0 0
\(679\) 3.36190 + 4.67922i 0.129018 + 0.179572i
\(680\) −10.2659 4.94378i −0.393678 0.189585i
\(681\) 0 0
\(682\) −1.23300 1.14406i −0.0472140 0.0438082i
\(683\) 0.394922 5.26986i 0.0151113 0.201646i −0.984538 0.175170i \(-0.943952\pi\)
0.999649 0.0264757i \(-0.00842847\pi\)
\(684\) 0 0
\(685\) 8.44908 0.322823
\(686\) −2.21018 + 29.1245i −0.0843851 + 1.11198i
\(687\) 0 0
\(688\) 9.57926 24.4076i 0.365206 0.930529i
\(689\) −1.41137 + 18.8334i −0.0537688 + 0.717494i
\(690\) 0 0
\(691\) −37.9438 25.8697i −1.44345 0.984128i −0.995956 0.0898421i \(-0.971364\pi\)
−0.447495 0.894286i \(-0.647684\pi\)
\(692\) −6.03111 2.90443i −0.229268 0.110410i
\(693\) 0 0
\(694\) −11.0200 + 5.30697i −0.418315 + 0.201450i
\(695\) −17.7577 2.67654i −0.673588 0.101527i
\(696\) 0 0
\(697\) −53.9152 + 8.12641i −2.04218 + 0.307810i
\(698\) 3.75062 3.48007i 0.141963 0.131723i
\(699\) 0 0
\(700\) 5.04453 1.28281i 0.190665 0.0484856i
\(701\) −13.2240 + 16.5824i −0.499465 + 0.626310i −0.966109 0.258136i \(-0.916892\pi\)
0.466643 + 0.884446i \(0.345463\pi\)
\(702\) 0 0
\(703\) −11.3780 3.50966i −0.429131 0.132369i
\(704\) −4.75530 + 8.23642i −0.179222 + 0.310422i
\(705\) 0 0
\(706\) 4.63743 + 20.3179i 0.174532 + 0.764674i
\(707\) 4.14811 2.53307i 0.156006 0.0952659i
\(708\) 0 0
\(709\) −13.0499 + 4.02535i −0.490098 + 0.151175i −0.529947 0.848031i \(-0.677788\pi\)
0.0398497 + 0.999206i \(0.487312\pi\)
\(710\) 5.58356 + 14.2267i 0.209547 + 0.533917i
\(711\) 0 0
\(712\) 21.6468 6.67716i 0.811249 0.250237i
\(713\) −0.501710 + 2.19814i −0.0187892 + 0.0823208i
\(714\) 0 0
\(715\) −1.10259 4.83077i −0.0412346 0.180660i
\(716\) −1.09042 1.88867i −0.0407510 0.0705828i
\(717\) 0 0
\(718\) 37.3801 + 11.5302i 1.39501 + 0.430305i
\(719\) −0.184875 2.46699i −0.00689468 0.0920032i 0.992695 0.120652i \(-0.0384986\pi\)
−0.999590 + 0.0286490i \(0.990880\pi\)
\(720\) 0 0
\(721\) −0.0514506 2.08944i −0.00191612 0.0778147i
\(722\) 17.0506 + 21.3807i 0.634556 + 0.795708i
\(723\) 0 0
\(724\) −3.39515 + 0.511736i −0.126180 + 0.0190185i
\(725\) 7.38122 5.03243i 0.274132 0.186900i
\(726\) 0 0
\(727\) −22.8931 + 11.0247i −0.849059 + 0.408885i −0.807228 0.590239i \(-0.799033\pi\)
−0.0418307 + 0.999125i \(0.513319\pi\)
\(728\) −3.03192 17.2265i −0.112370 0.638456i
\(729\) 0 0
\(730\) 10.7309 + 7.31621i 0.397169 + 0.270785i
\(731\) −19.7553 18.3302i −0.730676 0.677968i
\(732\) 0 0
\(733\) 17.5793 44.7914i 0.649308 1.65441i −0.102264 0.994757i \(-0.532609\pi\)
0.751572 0.659652i \(-0.229296\pi\)
\(734\) 29.9631 1.10596
\(735\) 0 0
\(736\) −10.4022 −0.383430
\(737\) −0.948717 + 2.41729i −0.0349464 + 0.0890421i
\(738\) 0 0
\(739\) 15.1924 + 14.0965i 0.558862 + 0.518548i 0.908249 0.418431i \(-0.137420\pi\)
−0.349387 + 0.936978i \(0.613610\pi\)
\(740\) −3.64947 2.48817i −0.134157 0.0914669i
\(741\) 0 0
\(742\) −24.9712 13.6088i −0.916722 0.499594i
\(743\) 24.6672 11.8791i 0.904952 0.435802i 0.0772768 0.997010i \(-0.475377\pi\)
0.827675 + 0.561208i \(0.189663\pi\)
\(744\) 0 0
\(745\) −17.4130 + 11.8720i −0.637962 + 0.434955i
\(746\) −22.9960 + 3.46609i −0.841944 + 0.126903i
\(747\) 0 0
\(748\) −2.69624 3.38098i −0.0985844 0.123621i
\(749\) 15.4037 + 30.0692i 0.562837 + 1.09871i
\(750\) 0 0
\(751\) −2.82950 37.7570i −0.103250 1.37777i −0.772631 0.634855i \(-0.781060\pi\)
0.669382 0.742919i \(-0.266559\pi\)
\(752\) −50.4514 15.5622i −1.83977 0.567495i
\(753\) 0 0
\(754\) 4.83443 + 8.37348i 0.176060 + 0.304944i
\(755\) 0.404688 + 1.77305i 0.0147281 + 0.0645281i
\(756\) 0 0
\(757\) −1.71911 + 7.53191i −0.0624821 + 0.273752i −0.996513 0.0834410i \(-0.973409\pi\)
0.934031 + 0.357193i \(0.116266\pi\)
\(758\) −49.4394 + 15.2500i −1.79572 + 0.553906i
\(759\) 0 0
\(760\) 1.10154 + 2.80669i 0.0399572 + 0.101809i
\(761\) 25.4811 7.85989i 0.923691 0.284921i 0.203804 0.979012i \(-0.434670\pi\)
0.719887 + 0.694091i \(0.244193\pi\)
\(762\) 0 0
\(763\) 30.0131 + 30.7903i 1.08655 + 1.11468i
\(764\) −2.08067 9.11603i −0.0752761 0.329806i
\(765\) 0 0
\(766\) 30.0845 52.1080i 1.08700 1.88274i
\(767\) 9.52403 + 2.93777i 0.343893 + 0.106077i
\(768\) 0 0
\(769\) 13.1660 16.5096i 0.474777 0.595352i −0.485557 0.874205i \(-0.661383\pi\)
0.960334 + 0.278854i \(0.0899545\pi\)
\(770\) 7.31281 + 1.48071i 0.263535 + 0.0533610i
\(771\) 0 0
\(772\) −8.09068 + 7.50705i −0.291190 + 0.270185i
\(773\) −19.4909 + 2.93778i −0.701038 + 0.105665i −0.489883 0.871788i \(-0.662961\pi\)
−0.211155 + 0.977453i \(0.567722\pi\)
\(774\) 0 0
\(775\) −2.33596 0.352090i −0.0839103 0.0126474i
\(776\) 4.68106 2.25428i 0.168040 0.0809239i
\(777\) 0 0
\(778\) −35.2217 16.9619i −1.26276 0.608113i
\(779\) 11.9210 + 8.12760i 0.427114 + 0.291201i
\(780\) 0 0
\(781\) 1.34584 17.9589i 0.0481578 0.642621i
\(782\) −10.8110 + 27.5459i −0.386600 + 0.985040i
\(783\) 0 0
\(784\) 32.1289 + 8.20253i 1.14746 + 0.292947i
\(785\) 15.4674 0.552055
\(786\) 0 0
\(787\) −2.80339 + 37.4086i −0.0999301 + 1.33347i 0.691572 + 0.722308i \(0.256918\pi\)
−0.791502 + 0.611166i \(0.790701\pi\)
\(788\) −1.24955 1.15941i −0.0445134 0.0413024i
\(789\) 0 0
\(790\) −5.02648 2.42063i −0.178834 0.0861220i
\(791\) 11.8484 + 0.595060i 0.421281 + 0.0211579i
\(792\) 0 0
\(793\) 23.9463 + 3.60932i 0.850356 + 0.128171i
\(794\) 45.5159 31.0322i 1.61530 1.10129i
\(795\) 0 0
\(796\) 3.21694 2.98488i 0.114021 0.105796i
\(797\) −1.63719 2.05297i −0.0579921 0.0727198i 0.751989 0.659175i \(-0.229094\pi\)
−0.809982 + 0.586455i \(0.800523\pi\)
\(798\) 0 0
\(799\) −33.8341 + 42.4266i −1.19696 + 1.50094i
\(800\) −0.814483 10.8685i −0.0287963 0.384260i
\(801\) 0 0
\(802\) 7.22915 12.5213i 0.255270 0.442141i
\(803\) −7.65217 13.2539i −0.270039 0.467722i
\(804\) 0 0
\(805\) −3.18235 9.48165i −0.112163 0.334184i
\(806\) 0.568942 2.49270i 0.0200401 0.0878015i
\(807\) 0 0
\(808\) −1.60122 4.07984i −0.0563307 0.143528i
\(809\) −8.21399 20.9289i −0.288789 0.735821i −0.999478 0.0323151i \(-0.989712\pi\)
0.710689 0.703506i \(-0.248383\pi\)
\(810\) 0 0
\(811\) −0.265942 + 1.16517i −0.00933848 + 0.0409146i −0.979382 0.202015i \(-0.935251\pi\)
0.970044 + 0.242929i \(0.0781083\pi\)
\(812\) −2.83798 + 0.283082i −0.0995934 + 0.00993423i
\(813\) 0 0
\(814\) 13.2850 + 23.0103i 0.465639 + 0.806510i
\(815\) 1.32474 2.29452i 0.0464036 0.0803734i
\(816\) 0 0
\(817\) 0.532920 + 7.11132i 0.0186445 + 0.248794i
\(818\) 37.0760 46.4919i 1.29633 1.62555i
\(819\) 0 0
\(820\) 3.33701 + 4.18448i 0.116533 + 0.146128i
\(821\) −9.54245 + 8.85410i −0.333034 + 0.309010i −0.828909 0.559384i \(-0.811038\pi\)
0.495875 + 0.868394i \(0.334847\pi\)
\(822\) 0 0
\(823\) −31.6425 + 21.5735i −1.10299 + 0.752005i −0.970960 0.239241i \(-0.923101\pi\)
−0.132028 + 0.991246i \(0.542149\pi\)
\(824\) −1.86365 0.280901i −0.0649234 0.00978563i
\(825\) 0 0
\(826\) −9.93411 + 11.2496i −0.345652 + 0.391423i
\(827\) 31.6793 + 15.2559i 1.10160 + 0.530501i 0.894160 0.447747i \(-0.147774\pi\)
0.207437 + 0.978248i \(0.433488\pi\)
\(828\) 0 0
\(829\) −6.30110 5.84657i −0.218846 0.203060i 0.563129 0.826369i \(-0.309597\pi\)
−0.781976 + 0.623309i \(0.785788\pi\)
\(830\) 0.907559 12.1105i 0.0315018 0.420363i
\(831\) 0 0
\(832\) −14.4570 −0.501205
\(833\) 19.9124 27.6598i 0.689925 0.958356i
\(834\) 0 0
\(835\) −5.09238 + 12.9752i −0.176229 + 0.449025i
\(836\) −0.0855151 + 1.14112i −0.00295760 + 0.0394664i
\(837\) 0 0
\(838\) −17.9537 12.2406i −0.620200 0.422845i
\(839\) 39.0723 + 18.8162i 1.34893 + 0.649608i 0.962139 0.272561i \(-0.0878706\pi\)
0.386787 + 0.922169i \(0.373585\pi\)
\(840\) 0 0
\(841\) 21.7179 10.4588i 0.748891 0.360647i
\(842\) −34.3653 5.17973i −1.18431 0.178505i
\(843\) 0 0
\(844\) −4.36183 + 0.657440i −0.150140 + 0.0226300i
\(845\) −3.82640 + 3.55038i −0.131632 + 0.122137i
\(846\) 0 0
\(847\) 16.1868 + 12.2691i 0.556186 + 0.421570i
\(848\) −20.1299 + 25.2421i −0.691264 + 0.866817i
\(849\) 0 0
\(850\) −29.6273 9.13881i −1.01621 0.313459i
\(851\) 17.8080 30.8444i 0.610450 1.05733i
\(852\) 0 0
\(853\) 9.41102 + 41.2324i 0.322227 + 1.41177i 0.833580 + 0.552399i \(0.186287\pi\)
−0.511353 + 0.859371i \(0.670855\pi\)
\(854\) −19.7938 + 30.6257i −0.677330 + 1.04799i
\(855\) 0 0
\(856\) 29.1119 8.97983i 0.995024 0.306924i
\(857\) −3.36529 8.57462i −0.114956 0.292903i 0.861803 0.507243i \(-0.169335\pi\)
−0.976759 + 0.214340i \(0.931240\pi\)
\(858\) 0 0
\(859\) −6.03607 + 1.86188i −0.205948 + 0.0635266i −0.396013 0.918245i \(-0.629606\pi\)
0.190065 + 0.981772i \(0.439130\pi\)
\(860\) −0.588651 + 2.57905i −0.0200728 + 0.0879449i
\(861\) 0 0
\(862\) 4.76353 + 20.8704i 0.162246 + 0.710848i
\(863\) 6.05094 + 10.4805i 0.205976 + 0.356761i 0.950443 0.310898i \(-0.100630\pi\)
−0.744467 + 0.667659i \(0.767296\pi\)
\(864\) 0 0
\(865\) −12.8780 3.97234i −0.437865 0.135064i
\(866\) −1.64974 22.0143i −0.0560605 0.748076i
\(867\) 0 0
\(868\) 0.601045 + 0.455571i 0.0204008 + 0.0154631i
\(869\) 4.09890 + 5.13986i 0.139046 + 0.174358i
\(870\) 0 0
\(871\) −3.90328 + 0.588324i −0.132258 + 0.0199346i
\(872\) 32.0359 21.8417i 1.08487 0.739653i
\(873\) 0 0
\(874\) 7.05495 3.39748i 0.238637 0.114922i
\(875\) 21.6164 9.10410i 0.730769 0.307775i
\(876\) 0 0
\(877\) 33.4776 + 22.8246i 1.13046 + 0.770733i 0.976109 0.217284i \(-0.0697196\pi\)
0.154349 + 0.988016i \(0.450672\pi\)
\(878\) 47.2607 + 43.8515i 1.59497 + 1.47992i
\(879\) 0 0
\(880\) 3.09464 7.88502i 0.104320 0.265804i
\(881\) −7.37500 −0.248470 −0.124235 0.992253i \(-0.539648\pi\)
−0.124235 + 0.992253i \(0.539648\pi\)
\(882\) 0 0
\(883\) −6.83587 −0.230045 −0.115023 0.993363i \(-0.536694\pi\)
−0.115023 + 0.993363i \(0.536694\pi\)
\(884\) 2.40158 6.11913i 0.0807739 0.205809i
\(885\) 0 0
\(886\) 38.1443 + 35.3928i 1.28148 + 1.18904i
\(887\) 36.0312 + 24.5657i 1.20981 + 0.824835i 0.988626 0.150397i \(-0.0480553\pi\)
0.221185 + 0.975232i \(0.429008\pi\)
\(888\) 0 0
\(889\) 13.5437 15.3372i 0.454241 0.514392i
\(890\) −13.2342 + 6.37325i −0.443611 + 0.213632i
\(891\) 0 0
\(892\) −10.9583 + 7.47121i −0.366910 + 0.250155i
\(893\) 14.1992 2.14019i 0.475159 0.0716187i
\(894\) 0 0
\(895\) −2.73748 3.43270i −0.0915040 0.114742i
\(896\) 14.8381 32.8572i 0.495707 1.09768i
\(897\) 0 0
\(898\) −1.03882 13.8621i −0.0346659 0.462585i
\(899\) 1.23691 + 0.381537i 0.0412533 + 0.0127250i
\(900\) 0 0
\(901\) 16.5920 + 28.7381i 0.552758 + 0.957405i
\(902\) −7.16416 31.3882i −0.238540 1.04511i
\(903\) 0 0
\(904\) 2.38045 10.4295i 0.0791727 0.346878i
\(905\) −6.60538 + 2.03749i −0.219570 + 0.0677285i
\(906\) 0 0
\(907\) 19.9294 + 50.7793i 0.661745 + 1.68610i 0.725579 + 0.688139i \(0.241572\pi\)
−0.0638339 + 0.997961i \(0.520333\pi\)
\(908\) −8.09935 + 2.49832i −0.268786 + 0.0829096i
\(909\) 0 0
\(910\) 3.60880 + 10.7522i 0.119631 + 0.356433i
\(911\) −3.81557 16.7171i −0.126415 0.553862i −0.997977 0.0635761i \(-0.979749\pi\)
0.871562 0.490286i \(-0.163108\pi\)
\(912\) 0 0
\(913\) −7.15539 + 12.3935i −0.236809 + 0.410165i
\(914\) −34.5885 10.6691i −1.14409 0.352904i
\(915\) 0 0
\(916\) −3.73527 + 4.68388i −0.123417 + 0.154760i
\(917\) −0.482398 + 0.404522i −0.0159302 + 0.0133585i
\(918\) 0 0
\(919\) −36.6523 + 34.0083i −1.20905 + 1.12183i −0.219804 + 0.975544i \(0.570542\pi\)
−0.989242 + 0.146287i \(0.953268\pi\)
\(920\) −8.91800 + 1.34417i −0.294018 + 0.0443160i
\(921\) 0 0
\(922\) 33.1823 + 5.00143i 1.09280 + 0.164713i
\(923\) 24.6647 11.8779i 0.811847 0.390965i
\(924\) 0 0
\(925\) 33.6215 + 16.1913i 1.10547 + 0.532365i
\(926\) −2.01307 1.37248i −0.0661534 0.0451026i
\(927\) 0 0
\(928\) −0.446285 + 5.95527i −0.0146500 + 0.195491i
\(929\) 8.86963 22.5994i 0.291003 0.741464i −0.708363 0.705849i \(-0.750566\pi\)
0.999366 0.0356149i \(-0.0113390\pi\)
\(930\) 0 0
\(931\) −8.84093 + 1.78145i −0.289750 + 0.0583847i
\(932\) −12.9926 −0.425587
\(933\) 0 0
\(934\) −0.157564 + 2.10254i −0.00515564 + 0.0687972i
\(935\) −6.38207 5.92170i −0.208716 0.193660i
\(936\) 0 0
\(937\) −22.6593 10.9121i −0.740246 0.356484i 0.0254587 0.999676i \(-0.491895\pi\)
−0.765705 + 0.643192i \(0.777610\pi\)
\(938\) 1.61165 5.72126i 0.0526223 0.186806i
\(939\) 0 0
\(940\) 5.26727 + 0.793913i 0.171799 + 0.0258946i
\(941\) −23.2468 + 15.8494i −0.757823 + 0.516675i −0.879502 0.475895i \(-0.842124\pi\)
0.121680 + 0.992569i \(0.461172\pi\)
\(942\) 0 0
\(943\) −31.6361 + 29.3540i −1.03021 + 0.955899i
\(944\) 10.6232 + 13.3210i 0.345755 + 0.433563i
\(945\) 0 0
\(946\) 9.92164 12.4413i 0.322580 0.404503i
\(947\) 3.95065 + 52.7177i 0.128379 + 1.71310i 0.574817 + 0.818282i \(0.305073\pi\)
−0.446438 + 0.894815i \(0.647308\pi\)
\(948\) 0 0
\(949\) 11.6320 20.1472i 0.377590 0.654005i
\(950\) 4.10219 + 7.10521i 0.133093 + 0.230523i
\(951\) 0 0
\(952\) −21.4520 22.0075i −0.695263 0.713266i
\(953\) −7.34553 + 32.1829i −0.237945 + 1.04251i 0.704909 + 0.709298i \(0.250988\pi\)
−0.942854 + 0.333207i \(0.891869\pi\)
\(954\) 0 0
\(955\) −6.87747 17.5235i −0.222550 0.567048i
\(956\) 3.16764 + 8.07102i 0.102449 + 0.261035i
\(957\) 0 0
\(958\) −4.18116 + 18.3188i −0.135087 + 0.591855i
\(959\) 21.4124 + 7.80108i 0.691441 + 0.251910i
\(960\) 0 0
\(961\) 15.3289 + 26.5504i 0.494479 + 0.856463i
\(962\) −20.1944 + 34.9777i −0.651093 + 1.12773i
\(963\) 0 0
\(964\) 0.196081 + 2.61651i 0.00631533 + 0.0842723i
\(965\) −13.8541 + 17.3724i −0.445978 + 0.559239i
\(966\) 0 0
\(967\) −29.1688 36.5766i −0.938007 1.17622i −0.984159 0.177289i \(-0.943267\pi\)
0.0461521 0.998934i \(-0.485304\pi\)
\(968\) 13.4261 12.4576i 0.431533 0.400404i
\(969\) 0 0
\(970\) −2.78354 + 1.89778i −0.0893740 + 0.0609342i
\(971\) −7.62194 1.14882i −0.244600 0.0368675i 0.0255981 0.999672i \(-0.491851\pi\)
−0.270198 + 0.962805i \(0.587089\pi\)
\(972\) 0 0
\(973\) −42.5317 23.1789i −1.36350 0.743081i
\(974\) 5.05271 + 2.43326i 0.161899 + 0.0779665i
\(975\) 0 0
\(976\) 30.3472 + 28.1581i 0.971390 + 0.901318i
\(977\) 0.569471 7.59906i 0.0182190 0.243116i −0.980658 0.195731i \(-0.937292\pi\)
0.998877 0.0473850i \(-0.0150888\pi\)
\(978\) 0 0
\(979\) 17.3090 0.553197
\(980\) −3.32867 0.335196i −0.106330 0.0107074i
\(981\) 0 0
\(982\) 2.13809 5.44778i 0.0682293 0.173846i
\(983\) 1.78661 23.8407i 0.0569841 0.760399i −0.893388 0.449285i \(-0.851679\pi\)
0.950372 0.311114i \(-0.100702\pi\)
\(984\) 0 0
\(985\) −2.83545 1.93318i −0.0903450 0.0615962i
\(986\) 15.3063 + 7.37110i 0.487450 + 0.234744i
\(987\) 0 0
\(988\) −1.56721 + 0.754727i −0.0498595 + 0.0240111i
\(989\) −21.0926 3.17920i −0.670705 0.101093i
\(990\) 0 0
\(991\) −29.2692 + 4.41162i −0.929766 + 0.140140i −0.596427 0.802667i \(-0.703414\pi\)
−0.333339 + 0.942807i \(0.608175\pi\)
\(992\) 1.15764 1.07413i 0.0367551 0.0341038i
\(993\) 0 0
\(994\) 1.01475 + 41.2097i 0.0321860 + 1.30709i
\(995\) 5.50851 6.90746i 0.174632 0.218981i
\(996\) 0 0
\(997\) −33.1407 10.2225i −1.04958 0.323751i −0.278461 0.960447i \(-0.589824\pi\)
−0.771115 + 0.636696i \(0.780301\pi\)
\(998\) −24.4606 + 42.3670i −0.774287 + 1.34111i
\(999\) 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 441.2.bb.f.46.2 72
3.2 odd 2 inner 441.2.bb.f.46.5 yes 72
49.16 even 21 inner 441.2.bb.f.163.2 yes 72
147.65 odd 42 inner 441.2.bb.f.163.5 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bb.f.46.2 72 1.1 even 1 trivial
441.2.bb.f.46.5 yes 72 3.2 odd 2 inner
441.2.bb.f.163.2 yes 72 49.16 even 21 inner
441.2.bb.f.163.5 yes 72 147.65 odd 42 inner