Properties

Label 567.2.e.f.487.5
Level $567$
Weight $2$
Character 567.487
Analytic conductor $4.528$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(163,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.e (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 487.5
Root \(1.19343 + 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 567.487
Dual form 567.2.e.f.163.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.19343 + 2.06709i) q^{2} +(-1.84857 + 3.20182i) q^{4} +(1.46043 + 2.52954i) q^{5} +(-2.21886 + 1.44106i) q^{7} -4.05086 q^{8} +O(q^{10})\) \(q+(1.19343 + 2.06709i) q^{2} +(-1.84857 + 3.20182i) q^{4} +(1.46043 + 2.52954i) q^{5} +(-2.21886 + 1.44106i) q^{7} -4.05086 q^{8} +(-3.48586 + 6.03769i) q^{10} +(0.676857 - 1.17235i) q^{11} +1.46600 q^{13} +(-5.62686 - 2.86678i) q^{14} +(-1.13729 - 1.96984i) q^{16} +(1.65514 - 2.86678i) q^{17} +(-1.10329 - 1.91096i) q^{19} -10.7989 q^{20} +3.23114 q^{22} +(-1.31415 - 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +(1.74958 + 3.03036i) q^{26} +(-0.512277 - 9.76830i) q^{28} -1.04344 q^{29} +(-1.63729 + 2.83587i) q^{31} +(-1.33629 + 2.31453i) q^{32} +7.90119 q^{34} +(-6.88572 - 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(2.63342 - 4.56121i) q^{38} +(-5.91601 - 10.2468i) q^{40} +1.80858 q^{41} +4.34257 q^{43} +(2.50244 + 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} +(-1.98957 - 3.44604i) q^{47} +(2.84671 - 6.39502i) q^{49} -8.42913 q^{50} +(-2.71001 + 4.69388i) q^{52} +(-3.22743 + 5.59008i) q^{53} +3.95402 q^{55} +(8.98830 - 5.83752i) q^{56} +(-1.24528 - 2.15688i) q^{58} +(6.10700 - 10.5776i) q^{59} +(-0.279867 - 0.484744i) q^{61} -7.81600 q^{62} -10.9283 q^{64} +(2.14100 + 3.70832i) q^{65} +(-6.40588 + 11.0953i) q^{67} +(6.11928 + 10.5989i) q^{68} +(-0.966003 - 18.4201i) q^{70} +12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-12.9791 + 22.4805i) q^{74} +8.15807 q^{76} +(0.187571 + 3.57668i) q^{77} +(-0.383838 - 0.664827i) q^{79} +(3.32187 - 5.75365i) q^{80} +(2.15842 + 3.73849i) q^{82} +1.96741 q^{83} +9.66887 q^{85} +(5.18258 + 8.97649i) q^{86} +(-2.74185 + 4.74903i) q^{88} +(3.20356 + 5.54872i) q^{89} +(-3.25286 + 2.11259i) q^{91} +9.71719 q^{92} +(4.74884 - 8.22524i) q^{94} +(3.22257 - 5.58166i) q^{95} +8.28285 q^{97} +(16.6164 - 1.74763i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 5 q^{7} - 6 q^{8} - 7 q^{10} + 4 q^{11} + 16 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + q^{19} - 10 q^{20} + 2 q^{22} + 3 q^{23} - q^{25} + 11 q^{26} - 2 q^{28} - 14 q^{29} - 3 q^{31} - 2 q^{32} - 6 q^{34} + 5 q^{35} + 20 q^{38} - 3 q^{40} - 10 q^{41} + 14 q^{43} - 10 q^{44} + 3 q^{46} + 27 q^{47} - 17 q^{49} - 38 q^{50} - 10 q^{52} - 21 q^{53} + 4 q^{55} + 27 q^{56} - 10 q^{58} + 30 q^{59} - 14 q^{61} - 12 q^{62} - 50 q^{64} - 11 q^{65} - 2 q^{67} + 27 q^{68} - 11 q^{70} - 6 q^{71} + 15 q^{73} - 36 q^{74} - 10 q^{76} + 20 q^{77} - 4 q^{79} + 20 q^{80} - 5 q^{82} - 18 q^{83} + 12 q^{85} - 8 q^{86} - 18 q^{88} + 28 q^{89} - 4 q^{91} - 54 q^{92} - 3 q^{94} - 14 q^{95} + 24 q^{97} + 59 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19343 + 2.06709i 0.843886 + 1.46165i 0.886585 + 0.462565i \(0.153071\pi\)
−0.0426999 + 0.999088i \(0.513596\pi\)
\(3\) 0 0
\(4\) −1.84857 + 3.20182i −0.924286 + 1.60091i
\(5\) 1.46043 + 2.52954i 0.653125 + 1.13125i 0.982360 + 0.186998i \(0.0598759\pi\)
−0.329235 + 0.944248i \(0.606791\pi\)
\(6\) 0 0
\(7\) −2.21886 + 1.44106i −0.838652 + 0.544668i
\(8\) −4.05086 −1.43219
\(9\) 0 0
\(10\) −3.48586 + 6.03769i −1.10233 + 1.90929i
\(11\) 0.676857 1.17235i 0.204080 0.353477i −0.745759 0.666216i \(-0.767913\pi\)
0.949839 + 0.312738i \(0.101246\pi\)
\(12\) 0 0
\(13\) 1.46600 0.406596 0.203298 0.979117i \(-0.434834\pi\)
0.203298 + 0.979117i \(0.434834\pi\)
\(14\) −5.62686 2.86678i −1.50384 0.766180i
\(15\) 0 0
\(16\) −1.13729 1.96984i −0.284323 0.492461i
\(17\) 1.65514 2.86678i 0.401430 0.695297i −0.592469 0.805593i \(-0.701847\pi\)
0.993899 + 0.110297i \(0.0351801\pi\)
\(18\) 0 0
\(19\) −1.10329 1.91096i −0.253113 0.438404i 0.711268 0.702921i \(-0.248121\pi\)
−0.964381 + 0.264516i \(0.914788\pi\)
\(20\) −10.7989 −2.41470
\(21\) 0 0
\(22\) 3.23114 0.688881
\(23\) −1.31415 2.27617i −0.274019 0.474614i 0.695868 0.718169i \(-0.255020\pi\)
−0.969887 + 0.243555i \(0.921686\pi\)
\(24\) 0 0
\(25\) −1.76573 + 3.05833i −0.353146 + 0.611666i
\(26\) 1.74958 + 3.03036i 0.343121 + 0.594302i
\(27\) 0 0
\(28\) −0.512277 9.76830i −0.0968112 1.84603i
\(29\) −1.04344 −0.193762 −0.0968810 0.995296i \(-0.530887\pi\)
−0.0968810 + 0.995296i \(0.530887\pi\)
\(30\) 0 0
\(31\) −1.63729 + 2.83587i −0.294066 + 0.509337i −0.974767 0.223224i \(-0.928342\pi\)
0.680701 + 0.732561i \(0.261675\pi\)
\(32\) −1.33629 + 2.31453i −0.236226 + 0.409155i
\(33\) 0 0
\(34\) 7.90119 1.35504
\(35\) −6.88572 3.50815i −1.16390 0.592985i
\(36\) 0 0
\(37\) 5.43773 + 9.41842i 0.893957 + 1.54838i 0.835090 + 0.550113i \(0.185415\pi\)
0.0588664 + 0.998266i \(0.481251\pi\)
\(38\) 2.63342 4.56121i 0.427197 0.739926i
\(39\) 0 0
\(40\) −5.91601 10.2468i −0.935403 1.62017i
\(41\) 1.80858 0.282452 0.141226 0.989977i \(-0.454896\pi\)
0.141226 + 0.989977i \(0.454896\pi\)
\(42\) 0 0
\(43\) 4.34257 0.662236 0.331118 0.943589i \(-0.392574\pi\)
0.331118 + 0.943589i \(0.392574\pi\)
\(44\) 2.50244 + 4.33435i 0.377257 + 0.653428i
\(45\) 0 0
\(46\) 3.13670 5.43292i 0.462481 0.801041i
\(47\) −1.98957 3.44604i −0.290209 0.502656i 0.683650 0.729810i \(-0.260391\pi\)
−0.973859 + 0.227154i \(0.927058\pi\)
\(48\) 0 0
\(49\) 2.84671 6.39502i 0.406673 0.913574i
\(50\) −8.42913 −1.19206
\(51\) 0 0
\(52\) −2.71001 + 4.69388i −0.375811 + 0.650924i
\(53\) −3.22743 + 5.59008i −0.443322 + 0.767856i −0.997934 0.0642533i \(-0.979533\pi\)
0.554612 + 0.832109i \(0.312867\pi\)
\(54\) 0 0
\(55\) 3.95402 0.533160
\(56\) 8.98830 5.83752i 1.20111 0.780071i
\(57\) 0 0
\(58\) −1.24528 2.15688i −0.163513 0.283213i
\(59\) 6.10700 10.5776i 0.795064 1.37709i −0.127735 0.991808i \(-0.540771\pi\)
0.922799 0.385283i \(-0.125896\pi\)
\(60\) 0 0
\(61\) −0.279867 0.484744i −0.0358333 0.0620651i 0.847553 0.530711i \(-0.178075\pi\)
−0.883386 + 0.468646i \(0.844742\pi\)
\(62\) −7.81600 −0.992632
\(63\) 0 0
\(64\) −10.9283 −1.36604
\(65\) 2.14100 + 3.70832i 0.265558 + 0.459960i
\(66\) 0 0
\(67\) −6.40588 + 11.0953i −0.782603 + 1.35551i 0.147817 + 0.989015i \(0.452775\pi\)
−0.930420 + 0.366494i \(0.880558\pi\)
\(68\) 6.11928 + 10.5989i 0.742072 + 1.28531i
\(69\) 0 0
\(70\) −0.966003 18.4201i −0.115459 2.20163i
\(71\) 12.9177 1.53305 0.766525 0.642214i \(-0.221984\pi\)
0.766525 + 0.642214i \(0.221984\pi\)
\(72\) 0 0
\(73\) 5.22772 9.05467i 0.611858 1.05977i −0.379069 0.925368i \(-0.623756\pi\)
0.990927 0.134401i \(-0.0429109\pi\)
\(74\) −12.9791 + 22.4805i −1.50879 + 2.61331i
\(75\) 0 0
\(76\) 8.15807 0.935794
\(77\) 0.187571 + 3.57668i 0.0213757 + 0.407600i
\(78\) 0 0
\(79\) −0.383838 0.664827i −0.0431852 0.0747989i 0.843625 0.536933i \(-0.180417\pi\)
−0.886810 + 0.462134i \(0.847084\pi\)
\(80\) 3.32187 5.75365i 0.371397 0.643278i
\(81\) 0 0
\(82\) 2.15842 + 3.73849i 0.238358 + 0.412847i
\(83\) 1.96741 0.215952 0.107976 0.994154i \(-0.465563\pi\)
0.107976 + 0.994154i \(0.465563\pi\)
\(84\) 0 0
\(85\) 9.66887 1.04874
\(86\) 5.18258 + 8.97649i 0.558852 + 0.967960i
\(87\) 0 0
\(88\) −2.74185 + 4.74903i −0.292283 + 0.506248i
\(89\) 3.20356 + 5.54872i 0.339576 + 0.588163i 0.984353 0.176208i \(-0.0563830\pi\)
−0.644777 + 0.764371i \(0.723050\pi\)
\(90\) 0 0
\(91\) −3.25286 + 2.11259i −0.340992 + 0.221460i
\(92\) 9.71719 1.01309
\(93\) 0 0
\(94\) 4.74884 8.22524i 0.489806 0.848369i
\(95\) 3.22257 5.58166i 0.330629 0.572666i
\(96\) 0 0
\(97\) 8.28285 0.840996 0.420498 0.907293i \(-0.361855\pi\)
0.420498 + 0.907293i \(0.361855\pi\)
\(98\) 16.6164 1.74763i 1.67851 0.176537i
\(99\) 0 0
\(100\) −6.52815 11.3071i −0.652815 1.13071i
\(101\) 8.11331 14.0527i 0.807305 1.39829i −0.107419 0.994214i \(-0.534259\pi\)
0.914724 0.404079i \(-0.132408\pi\)
\(102\) 0 0
\(103\) 1.11342 + 1.92849i 0.109708 + 0.190020i 0.915652 0.401972i \(-0.131675\pi\)
−0.805944 + 0.591992i \(0.798342\pi\)
\(104\) −5.93857 −0.582325
\(105\) 0 0
\(106\) −15.4069 −1.49645
\(107\) −8.75403 15.1624i −0.846284 1.46581i −0.884501 0.466537i \(-0.845501\pi\)
0.0382175 0.999269i \(-0.487832\pi\)
\(108\) 0 0
\(109\) −7.79917 + 13.5086i −0.747025 + 1.29388i 0.202218 + 0.979341i \(0.435185\pi\)
−0.949243 + 0.314544i \(0.898148\pi\)
\(110\) 4.71886 + 8.17331i 0.449926 + 0.779295i
\(111\) 0 0
\(112\) 5.36215 + 2.73192i 0.506676 + 0.258142i
\(113\) 1.68911 0.158898 0.0794491 0.996839i \(-0.474684\pi\)
0.0794491 + 0.996839i \(0.474684\pi\)
\(114\) 0 0
\(115\) 3.83845 6.64839i 0.357937 0.619966i
\(116\) 1.92887 3.34091i 0.179092 0.310196i
\(117\) 0 0
\(118\) 29.1532 2.68377
\(119\) 0.458672 + 8.74614i 0.0420464 + 0.801758i
\(120\) 0 0
\(121\) 4.58373 + 7.93925i 0.416703 + 0.721750i
\(122\) 0.668005 1.15702i 0.0604784 0.104752i
\(123\) 0 0
\(124\) −6.05330 10.4846i −0.543602 0.941546i
\(125\) 4.28942 0.383657
\(126\) 0 0
\(127\) −3.96918 −0.352208 −0.176104 0.984372i \(-0.556350\pi\)
−0.176104 + 0.984372i \(0.556350\pi\)
\(128\) −10.3696 17.9607i −0.916552 1.58751i
\(129\) 0 0
\(130\) −5.11028 + 8.85127i −0.448202 + 0.776308i
\(131\) −2.66432 4.61473i −0.232782 0.403191i 0.725844 0.687860i \(-0.241450\pi\)
−0.958626 + 0.284669i \(0.908116\pi\)
\(132\) 0 0
\(133\) 5.20186 + 2.65025i 0.451058 + 0.229806i
\(134\) −30.5800 −2.64171
\(135\) 0 0
\(136\) −6.70473 + 11.6129i −0.574925 + 0.995800i
\(137\) 3.74772 6.49124i 0.320189 0.554584i −0.660338 0.750969i \(-0.729587\pi\)
0.980527 + 0.196385i \(0.0629202\pi\)
\(138\) 0 0
\(139\) −14.0657 −1.19304 −0.596518 0.802600i \(-0.703450\pi\)
−0.596518 + 0.802600i \(0.703450\pi\)
\(140\) 23.9612 15.5618i 2.02509 1.31521i
\(141\) 0 0
\(142\) 15.4164 + 26.7021i 1.29372 + 2.24079i
\(143\) 0.992275 1.71867i 0.0829782 0.143722i
\(144\) 0 0
\(145\) −1.52388 2.63943i −0.126551 0.219193i
\(146\) 24.9557 2.06535
\(147\) 0 0
\(148\) −40.2081 −3.30509
\(149\) −1.08986 1.88769i −0.0892846 0.154645i 0.817924 0.575326i \(-0.195125\pi\)
−0.907209 + 0.420680i \(0.861791\pi\)
\(150\) 0 0
\(151\) −7.01387 + 12.1484i −0.570781 + 0.988621i 0.425705 + 0.904862i \(0.360026\pi\)
−0.996486 + 0.0837595i \(0.973307\pi\)
\(152\) 4.46929 + 7.74103i 0.362507 + 0.627880i
\(153\) 0 0
\(154\) −7.16946 + 4.65626i −0.577731 + 0.375212i
\(155\) −9.56461 −0.768248
\(156\) 0 0
\(157\) −1.48312 + 2.56883i −0.118365 + 0.205015i −0.919120 0.393978i \(-0.871099\pi\)
0.800755 + 0.598993i \(0.204432\pi\)
\(158\) 0.916172 1.58686i 0.0728867 0.126243i
\(159\) 0 0
\(160\) −7.80628 −0.617140
\(161\) 6.19601 + 3.15675i 0.488314 + 0.248787i
\(162\) 0 0
\(163\) −0.194278 0.336499i −0.0152170 0.0263566i 0.858317 0.513120i \(-0.171511\pi\)
−0.873534 + 0.486764i \(0.838177\pi\)
\(164\) −3.34329 + 5.79074i −0.261067 + 0.452181i
\(165\) 0 0
\(166\) 2.34798 + 4.06682i 0.182239 + 0.315646i
\(167\) −7.29778 −0.564719 −0.282360 0.959309i \(-0.591117\pi\)
−0.282360 + 0.959309i \(0.591117\pi\)
\(168\) 0 0
\(169\) −10.8508 −0.834680
\(170\) 11.5392 + 19.9864i 0.885013 + 1.53289i
\(171\) 0 0
\(172\) −8.02756 + 13.9041i −0.612096 + 1.06018i
\(173\) 2.02754 + 3.51181i 0.154151 + 0.266998i 0.932750 0.360525i \(-0.117402\pi\)
−0.778598 + 0.627522i \(0.784069\pi\)
\(174\) 0 0
\(175\) −0.489319 9.33054i −0.0369891 0.705322i
\(176\) −3.07913 −0.232098
\(177\) 0 0
\(178\) −7.64647 + 13.2441i −0.573127 + 0.992685i
\(179\) 5.29243 9.16675i 0.395575 0.685155i −0.597600 0.801795i \(-0.703879\pi\)
0.993174 + 0.116639i \(0.0372121\pi\)
\(180\) 0 0
\(181\) −19.6312 −1.45917 −0.729586 0.683889i \(-0.760287\pi\)
−0.729586 + 0.683889i \(0.760287\pi\)
\(182\) −8.24900 4.20271i −0.611456 0.311526i
\(183\) 0 0
\(184\) 5.32343 + 9.22045i 0.392448 + 0.679740i
\(185\) −15.8829 + 27.5099i −1.16773 + 2.02257i
\(186\) 0 0
\(187\) −2.24058 3.88081i −0.163848 0.283793i
\(188\) 14.7115 1.07294
\(189\) 0 0
\(190\) 15.3837 1.11605
\(191\) −4.14357 7.17688i −0.299818 0.519301i 0.676276 0.736648i \(-0.263593\pi\)
−0.976094 + 0.217348i \(0.930259\pi\)
\(192\) 0 0
\(193\) 9.39242 16.2682i 0.676082 1.17101i −0.300070 0.953917i \(-0.597010\pi\)
0.976152 0.217090i \(-0.0696566\pi\)
\(194\) 9.88504 + 17.1214i 0.709705 + 1.22924i
\(195\) 0 0
\(196\) 15.2133 + 20.9363i 1.08667 + 1.49545i
\(197\) 5.99634 0.427222 0.213611 0.976919i \(-0.431478\pi\)
0.213611 + 0.976919i \(0.431478\pi\)
\(198\) 0 0
\(199\) 7.20434 12.4783i 0.510702 0.884562i −0.489221 0.872160i \(-0.662719\pi\)
0.999923 0.0124022i \(-0.00394785\pi\)
\(200\) 7.15272 12.3889i 0.505773 0.876025i
\(201\) 0 0
\(202\) 38.7308 2.72509
\(203\) 2.31525 1.50366i 0.162499 0.105536i
\(204\) 0 0
\(205\) 2.64131 + 4.57488i 0.184477 + 0.319523i
\(206\) −2.65758 + 4.60306i −0.185162 + 0.320710i
\(207\) 0 0
\(208\) −1.66727 2.88780i −0.115604 0.200233i
\(209\) −2.98709 −0.206621
\(210\) 0 0
\(211\) 13.8484 0.953360 0.476680 0.879077i \(-0.341840\pi\)
0.476680 + 0.879077i \(0.341840\pi\)
\(212\) −11.9323 20.6673i −0.819512 1.41944i
\(213\) 0 0
\(214\) 20.8947 36.1907i 1.42833 2.47395i
\(215\) 6.34204 + 10.9847i 0.432523 + 0.749153i
\(216\) 0 0
\(217\) −0.453726 8.65184i −0.0308010 0.587325i
\(218\) −37.2312 −2.52161
\(219\) 0 0
\(220\) −7.30929 + 12.6601i −0.492792 + 0.853541i
\(221\) 2.42644 4.20271i 0.163220 0.282705i
\(222\) 0 0
\(223\) −4.67513 −0.313070 −0.156535 0.987672i \(-0.550032\pi\)
−0.156535 + 0.987672i \(0.550032\pi\)
\(224\) −0.370314 7.06130i −0.0247427 0.471803i
\(225\) 0 0
\(226\) 2.01584 + 3.49154i 0.134092 + 0.232254i
\(227\) −9.85631 + 17.0716i −0.654187 + 1.13308i 0.327910 + 0.944709i \(0.393656\pi\)
−0.982097 + 0.188376i \(0.939678\pi\)
\(228\) 0 0
\(229\) −14.0364 24.3118i −0.927552 1.60657i −0.787404 0.616437i \(-0.788575\pi\)
−0.140148 0.990131i \(-0.544758\pi\)
\(230\) 18.3238 1.20823
\(231\) 0 0
\(232\) 4.22683 0.277505
\(233\) −6.90113 11.9531i −0.452108 0.783074i 0.546409 0.837518i \(-0.315994\pi\)
−0.998517 + 0.0544448i \(0.982661\pi\)
\(234\) 0 0
\(235\) 5.81127 10.0654i 0.379085 0.656595i
\(236\) 22.5785 + 39.1070i 1.46973 + 2.54565i
\(237\) 0 0
\(238\) −17.5317 + 11.3861i −1.13641 + 0.738049i
\(239\) −11.0614 −0.715501 −0.357751 0.933817i \(-0.616456\pi\)
−0.357751 + 0.933817i \(0.616456\pi\)
\(240\) 0 0
\(241\) 11.5849 20.0656i 0.746247 1.29254i −0.203362 0.979104i \(-0.565187\pi\)
0.949610 0.313435i \(-0.101480\pi\)
\(242\) −10.9408 + 18.9499i −0.703299 + 1.21815i
\(243\) 0 0
\(244\) 2.06942 0.132481
\(245\) 20.3339 2.13861i 1.29909 0.136631i
\(246\) 0 0
\(247\) −1.61743 2.80147i −0.102915 0.178253i
\(248\) 6.63243 11.4877i 0.421160 0.729470i
\(249\) 0 0
\(250\) 5.11914 + 8.86660i 0.323763 + 0.560773i
\(251\) −7.78402 −0.491323 −0.245662 0.969356i \(-0.579005\pi\)
−0.245662 + 0.969356i \(0.579005\pi\)
\(252\) 0 0
\(253\) −3.55796 −0.223687
\(254\) −4.73696 8.20466i −0.297223 0.514806i
\(255\) 0 0
\(256\) 13.8226 23.9414i 0.863912 1.49634i
\(257\) −5.18798 8.98585i −0.323618 0.560522i 0.657614 0.753355i \(-0.271566\pi\)
−0.981232 + 0.192833i \(0.938232\pi\)
\(258\) 0 0
\(259\) −25.6381 13.0621i −1.59307 0.811640i
\(260\) −15.8312 −0.981807
\(261\) 0 0
\(262\) 6.35937 11.0148i 0.392883 0.680494i
\(263\) 9.56654 16.5697i 0.589898 1.02173i −0.404347 0.914605i \(-0.632501\pi\)
0.994245 0.107128i \(-0.0341653\pi\)
\(264\) 0 0
\(265\) −18.8538 −1.15818
\(266\) 0.729773 + 13.9156i 0.0447453 + 0.853221i
\(267\) 0 0
\(268\) −23.6835 41.0210i −1.44670 2.50576i
\(269\) −4.41840 + 7.65290i −0.269395 + 0.466605i −0.968706 0.248212i \(-0.920157\pi\)
0.699311 + 0.714818i \(0.253490\pi\)
\(270\) 0 0
\(271\) −9.16955 15.8821i −0.557010 0.964770i −0.997744 0.0671321i \(-0.978615\pi\)
0.440734 0.897638i \(-0.354718\pi\)
\(272\) −7.52949 −0.456542
\(273\) 0 0
\(274\) 17.8906 1.08081
\(275\) 2.39029 + 4.14011i 0.144140 + 0.249658i
\(276\) 0 0
\(277\) −2.55241 + 4.42091i −0.153360 + 0.265627i −0.932460 0.361272i \(-0.882343\pi\)
0.779101 + 0.626899i \(0.215676\pi\)
\(278\) −16.7865 29.0750i −1.00679 1.74381i
\(279\) 0 0
\(280\) 27.8931 + 14.2110i 1.66693 + 0.849270i
\(281\) 1.70636 0.101793 0.0508964 0.998704i \(-0.483792\pi\)
0.0508964 + 0.998704i \(0.483792\pi\)
\(282\) 0 0
\(283\) 6.24415 10.8152i 0.371176 0.642896i −0.618571 0.785729i \(-0.712288\pi\)
0.989747 + 0.142833i \(0.0456213\pi\)
\(284\) −23.8793 + 41.3602i −1.41698 + 2.45428i
\(285\) 0 0
\(286\) 4.73686 0.280096
\(287\) −4.01299 + 2.60626i −0.236879 + 0.153843i
\(288\) 0 0
\(289\) 3.02104 + 5.23260i 0.177708 + 0.307800i
\(290\) 3.63729 6.29997i 0.213589 0.369947i
\(291\) 0 0
\(292\) 19.3276 + 33.4764i 1.13106 + 1.95906i
\(293\) 5.20405 0.304024 0.152012 0.988379i \(-0.451425\pi\)
0.152012 + 0.988379i \(0.451425\pi\)
\(294\) 0 0
\(295\) 35.6755 2.07711
\(296\) −22.0275 38.1527i −1.28032 2.21758i
\(297\) 0 0
\(298\) 2.60135 4.50566i 0.150692 0.261006i
\(299\) −1.92654 3.33687i −0.111415 0.192976i
\(300\) 0 0
\(301\) −9.63558 + 6.25790i −0.555386 + 0.360699i
\(302\) −33.4824 −1.92669
\(303\) 0 0
\(304\) −2.50953 + 4.34663i −0.143931 + 0.249297i
\(305\) 0.817453 1.41587i 0.0468072 0.0810725i
\(306\) 0 0
\(307\) 5.00136 0.285442 0.142721 0.989763i \(-0.454415\pi\)
0.142721 + 0.989763i \(0.454415\pi\)
\(308\) −11.7986 6.01118i −0.672289 0.342519i
\(309\) 0 0
\(310\) −11.4147 19.7709i −0.648313 1.12291i
\(311\) 16.1984 28.0565i 0.918528 1.59094i 0.116876 0.993146i \(-0.462712\pi\)
0.801652 0.597791i \(-0.203955\pi\)
\(312\) 0 0
\(313\) −0.759535 1.31555i −0.0429315 0.0743595i 0.843761 0.536719i \(-0.180336\pi\)
−0.886693 + 0.462359i \(0.847003\pi\)
\(314\) −7.08000 −0.399548
\(315\) 0 0
\(316\) 2.83821 0.159662
\(317\) 10.7544 + 18.6272i 0.604029 + 1.04621i 0.992204 + 0.124623i \(0.0397723\pi\)
−0.388175 + 0.921586i \(0.626894\pi\)
\(318\) 0 0
\(319\) −0.706261 + 1.22328i −0.0395430 + 0.0684905i
\(320\) −15.9600 27.6436i −0.892193 1.54532i
\(321\) 0 0
\(322\) 0.869243 + 16.5751i 0.0484410 + 0.923693i
\(323\) −7.30441 −0.406428
\(324\) 0 0
\(325\) −2.58856 + 4.48352i −0.143588 + 0.248701i
\(326\) 0.463715 0.803178i 0.0256828 0.0444839i
\(327\) 0 0
\(328\) −7.32629 −0.404527
\(329\) 9.38052 + 4.77920i 0.517165 + 0.263486i
\(330\) 0 0
\(331\) −9.73902 16.8685i −0.535305 0.927175i −0.999149 0.0412580i \(-0.986863\pi\)
0.463844 0.885917i \(-0.346470\pi\)
\(332\) −3.63691 + 6.29931i −0.199601 + 0.345719i
\(333\) 0 0
\(334\) −8.70942 15.0852i −0.476558 0.825423i
\(335\) −37.4215 −2.04455
\(336\) 0 0
\(337\) −9.69484 −0.528112 −0.264056 0.964507i \(-0.585060\pi\)
−0.264056 + 0.964507i \(0.585060\pi\)
\(338\) −12.9498 22.4296i −0.704374 1.22001i
\(339\) 0 0
\(340\) −17.8736 + 30.9580i −0.969332 + 1.67893i
\(341\) 2.21642 + 3.83896i 0.120026 + 0.207891i
\(342\) 0 0
\(343\) 2.89912 + 18.2919i 0.156538 + 0.987672i
\(344\) −17.5912 −0.948451
\(345\) 0 0
\(346\) −4.83948 + 8.38222i −0.260172 + 0.450631i
\(347\) −1.01302 + 1.75460i −0.0543817 + 0.0941919i −0.891935 0.452164i \(-0.850652\pi\)
0.837553 + 0.546356i \(0.183985\pi\)
\(348\) 0 0
\(349\) −16.2915 −0.872066 −0.436033 0.899931i \(-0.643617\pi\)
−0.436033 + 0.899931i \(0.643617\pi\)
\(350\) 18.7031 12.1469i 0.999722 0.649276i
\(351\) 0 0
\(352\) 1.80896 + 3.13321i 0.0964180 + 0.167001i
\(353\) −8.53072 + 14.7756i −0.454045 + 0.786428i −0.998633 0.0522753i \(-0.983353\pi\)
0.544588 + 0.838704i \(0.316686\pi\)
\(354\) 0 0
\(355\) 18.8655 + 32.6759i 1.00127 + 1.73426i
\(356\) −23.6880 −1.25546
\(357\) 0 0
\(358\) 25.2647 1.33528
\(359\) 1.48363 + 2.56972i 0.0783030 + 0.135625i 0.902518 0.430652i \(-0.141717\pi\)
−0.824215 + 0.566277i \(0.808383\pi\)
\(360\) 0 0
\(361\) 7.06549 12.2378i 0.371868 0.644094i
\(362\) −23.4285 40.5794i −1.23137 2.13280i
\(363\) 0 0
\(364\) −0.750999 14.3204i −0.0393630 0.750590i
\(365\) 30.5389 1.59848
\(366\) 0 0
\(367\) 5.07874 8.79664i 0.265108 0.459181i −0.702484 0.711700i \(-0.747926\pi\)
0.967592 + 0.252519i \(0.0812590\pi\)
\(368\) −2.98914 + 5.17733i −0.155819 + 0.269887i
\(369\) 0 0
\(370\) −75.8207 −3.94173
\(371\) −0.894387 17.0545i −0.0464342 0.885427i
\(372\) 0 0
\(373\) 12.7423 + 22.0703i 0.659771 + 1.14276i 0.980675 + 0.195645i \(0.0626799\pi\)
−0.320904 + 0.947112i \(0.603987\pi\)
\(374\) 5.34798 9.26297i 0.276537 0.478977i
\(375\) 0 0
\(376\) 8.05947 + 13.9594i 0.415635 + 0.719902i
\(377\) −1.52969 −0.0787829
\(378\) 0 0
\(379\) 9.85497 0.506216 0.253108 0.967438i \(-0.418547\pi\)
0.253108 + 0.967438i \(0.418547\pi\)
\(380\) 11.9143 + 20.6362i 0.611191 + 1.05861i
\(381\) 0 0
\(382\) 9.89016 17.1303i 0.506025 0.876460i
\(383\) 13.6563 + 23.6535i 0.697806 + 1.20864i 0.969225 + 0.246175i \(0.0791737\pi\)
−0.271419 + 0.962461i \(0.587493\pi\)
\(384\) 0 0
\(385\) −8.77343 + 5.69797i −0.447135 + 0.290395i
\(386\) 44.8370 2.28214
\(387\) 0 0
\(388\) −15.3114 + 26.5202i −0.777321 + 1.34636i
\(389\) −2.09223 + 3.62385i −0.106080 + 0.183736i −0.914179 0.405311i \(-0.867163\pi\)
0.808099 + 0.589047i \(0.200497\pi\)
\(390\) 0 0
\(391\) −8.70038 −0.439997
\(392\) −11.5316 + 25.9053i −0.582435 + 1.30842i
\(393\) 0 0
\(394\) 7.15624 + 12.3950i 0.360526 + 0.624450i
\(395\) 1.12114 1.94187i 0.0564107 0.0977062i
\(396\) 0 0
\(397\) 15.3354 + 26.5618i 0.769664 + 1.33310i 0.937745 + 0.347323i \(0.112909\pi\)
−0.168082 + 0.985773i \(0.553757\pi\)
\(398\) 34.3916 1.72390
\(399\) 0 0
\(400\) 8.03259 0.401629
\(401\) 3.42402 + 5.93057i 0.170987 + 0.296158i 0.938765 0.344557i \(-0.111971\pi\)
−0.767778 + 0.640716i \(0.778638\pi\)
\(402\) 0 0
\(403\) −2.40027 + 4.15739i −0.119566 + 0.207095i
\(404\) 29.9961 + 51.9547i 1.49236 + 2.58485i
\(405\) 0 0
\(406\) 5.87130 + 2.99132i 0.291388 + 0.148457i
\(407\) 14.7223 0.729756
\(408\) 0 0
\(409\) 9.13490 15.8221i 0.451692 0.782353i −0.546799 0.837264i \(-0.684154\pi\)
0.998491 + 0.0549104i \(0.0174873\pi\)
\(410\) −6.30445 + 10.9196i −0.311355 + 0.539282i
\(411\) 0 0
\(412\) −8.23291 −0.405606
\(413\) 1.69237 + 32.2709i 0.0832763 + 1.58795i
\(414\) 0 0
\(415\) 2.87328 + 4.97666i 0.141044 + 0.244295i
\(416\) −1.95901 + 3.39311i −0.0960485 + 0.166361i
\(417\) 0 0
\(418\) −3.56490 6.17458i −0.174365 0.302009i
\(419\) −22.4619 −1.09734 −0.548669 0.836040i \(-0.684865\pi\)
−0.548669 + 0.836040i \(0.684865\pi\)
\(420\) 0 0
\(421\) −20.8354 −1.01546 −0.507728 0.861517i \(-0.669515\pi\)
−0.507728 + 0.861517i \(0.669515\pi\)
\(422\) 16.5271 + 28.6258i 0.804527 + 1.39348i
\(423\) 0 0
\(424\) 13.0739 22.6446i 0.634923 1.09972i
\(425\) 5.84505 + 10.1239i 0.283526 + 0.491082i
\(426\) 0 0
\(427\) 1.31953 + 0.672276i 0.0638565 + 0.0325337i
\(428\) 64.7298 3.12883
\(429\) 0 0
\(430\) −15.1376 + 26.2191i −0.730001 + 1.26440i
\(431\) −10.1213 + 17.5307i −0.487527 + 0.844422i −0.999897 0.0143427i \(-0.995434\pi\)
0.512370 + 0.858765i \(0.328768\pi\)
\(432\) 0 0
\(433\) −21.6764 −1.04170 −0.520851 0.853648i \(-0.674385\pi\)
−0.520851 + 0.853648i \(0.674385\pi\)
\(434\) 17.3426 11.2633i 0.832473 0.540655i
\(435\) 0 0
\(436\) −28.8346 49.9431i −1.38093 2.39184i
\(437\) −2.89978 + 5.02257i −0.138715 + 0.240262i
\(438\) 0 0
\(439\) 17.7390 + 30.7249i 0.846639 + 1.46642i 0.884191 + 0.467126i \(0.154711\pi\)
−0.0375520 + 0.999295i \(0.511956\pi\)
\(440\) −16.0172 −0.763589
\(441\) 0 0
\(442\) 11.5832 0.550955
\(443\) 9.60313 + 16.6331i 0.456258 + 0.790263i 0.998760 0.0497923i \(-0.0158559\pi\)
−0.542501 + 0.840055i \(0.682523\pi\)
\(444\) 0 0
\(445\) −9.35716 + 16.2071i −0.443572 + 0.768289i
\(446\) −5.57946 9.66391i −0.264195 0.457599i
\(447\) 0 0
\(448\) 24.2484 15.7483i 1.14563 0.744036i
\(449\) −29.6082 −1.39730 −0.698648 0.715465i \(-0.746215\pi\)
−0.698648 + 0.715465i \(0.746215\pi\)
\(450\) 0 0
\(451\) 1.22415 2.12029i 0.0576429 0.0998405i
\(452\) −3.12244 + 5.40823i −0.146867 + 0.254382i
\(453\) 0 0
\(454\) −47.0515 −2.20823
\(455\) −10.0945 5.14295i −0.473237 0.241105i
\(456\) 0 0
\(457\) 4.78098 + 8.28090i 0.223645 + 0.387364i 0.955912 0.293653i \(-0.0948711\pi\)
−0.732267 + 0.681017i \(0.761538\pi\)
\(458\) 33.5031 58.0290i 1.56550 2.71152i
\(459\) 0 0
\(460\) 14.1913 + 24.5800i 0.661673 + 1.14605i
\(461\) −21.8374 −1.01707 −0.508536 0.861041i \(-0.669813\pi\)
−0.508536 + 0.861041i \(0.669813\pi\)
\(462\) 0 0
\(463\) −26.1489 −1.21524 −0.607621 0.794227i \(-0.707876\pi\)
−0.607621 + 0.794227i \(0.707876\pi\)
\(464\) 1.18670 + 2.05542i 0.0550909 + 0.0954203i
\(465\) 0 0
\(466\) 16.4721 28.5305i 0.763054 1.32165i
\(467\) −17.4764 30.2699i −0.808709 1.40073i −0.913758 0.406258i \(-0.866833\pi\)
0.105049 0.994467i \(-0.466500\pi\)
\(468\) 0 0
\(469\) −1.77520 33.8502i −0.0819711 1.56306i
\(470\) 27.7415 1.27962
\(471\) 0 0
\(472\) −24.7386 + 42.8485i −1.13869 + 1.97226i
\(473\) 2.93930 5.09102i 0.135149 0.234086i
\(474\) 0 0
\(475\) 7.79247 0.357543
\(476\) −28.8515 14.6993i −1.32240 0.673741i
\(477\) 0 0
\(478\) −13.2010 22.8649i −0.603801 1.04581i
\(479\) 14.9054 25.8170i 0.681047 1.17961i −0.293615 0.955924i \(-0.594858\pi\)
0.974662 0.223684i \(-0.0718083\pi\)
\(480\) 0 0
\(481\) 7.97172 + 13.8074i 0.363479 + 0.629565i
\(482\) 55.3031 2.51899
\(483\) 0 0
\(484\) −33.8934 −1.54061
\(485\) 12.0965 + 20.9518i 0.549276 + 0.951374i
\(486\) 0 0
\(487\) −11.2253 + 19.4428i −0.508667 + 0.881037i 0.491283 + 0.871000i \(0.336528\pi\)
−0.999950 + 0.0100365i \(0.996805\pi\)
\(488\) 1.13370 + 1.96363i 0.0513202 + 0.0888892i
\(489\) 0 0
\(490\) 28.6879 + 39.4797i 1.29599 + 1.78351i
\(491\) −35.0444 −1.58153 −0.790767 0.612118i \(-0.790318\pi\)
−0.790767 + 0.612118i \(0.790318\pi\)
\(492\) 0 0
\(493\) −1.72704 + 2.99132i −0.0777819 + 0.134722i
\(494\) 3.86060 6.68675i 0.173696 0.300851i
\(495\) 0 0
\(496\) 7.44830 0.334438
\(497\) −28.6626 + 18.6152i −1.28570 + 0.835004i
\(498\) 0 0
\(499\) 4.46760 + 7.73811i 0.199997 + 0.346405i 0.948527 0.316696i \(-0.102573\pi\)
−0.748530 + 0.663101i \(0.769240\pi\)
\(500\) −7.92929 + 13.7339i −0.354609 + 0.614200i
\(501\) 0 0
\(502\) −9.28972 16.0903i −0.414621 0.718144i
\(503\) −12.6403 −0.563603 −0.281802 0.959473i \(-0.590932\pi\)
−0.281802 + 0.959473i \(0.590932\pi\)
\(504\) 0 0
\(505\) 47.3958 2.10909
\(506\) −4.24620 7.35463i −0.188766 0.326953i
\(507\) 0 0
\(508\) 7.33732 12.7086i 0.325541 0.563854i
\(509\) 14.0555 + 24.3449i 0.623000 + 1.07907i 0.988924 + 0.148423i \(0.0474196\pi\)
−0.365924 + 0.930645i \(0.619247\pi\)
\(510\) 0 0
\(511\) 1.44871 + 27.6245i 0.0640870 + 1.22204i
\(512\) 24.5070 1.08307
\(513\) 0 0
\(514\) 12.3830 21.4480i 0.546192 0.946033i
\(515\) −3.25214 + 5.63287i −0.143306 + 0.248214i
\(516\) 0 0
\(517\) −5.38662 −0.236903
\(518\) −3.59678 68.5849i −0.158034 3.01345i
\(519\) 0 0
\(520\) −8.67288 15.0219i −0.380331 0.658753i
\(521\) 4.23768 7.33988i 0.185656 0.321566i −0.758141 0.652090i \(-0.773892\pi\)
0.943797 + 0.330524i \(0.107226\pi\)
\(522\) 0 0
\(523\) 16.7236 + 28.9662i 0.731273 + 1.26660i 0.956339 + 0.292259i \(0.0944069\pi\)
−0.225066 + 0.974344i \(0.572260\pi\)
\(524\) 19.7007 0.860630
\(525\) 0 0
\(526\) 45.6681 1.99123
\(527\) 5.41988 + 9.38751i 0.236094 + 0.408926i
\(528\) 0 0
\(529\) 8.04603 13.9361i 0.349827 0.605919i
\(530\) −22.5008 38.9725i −0.977371 1.69286i
\(531\) 0 0
\(532\) −18.1016 + 11.7562i −0.784806 + 0.509698i
\(533\) 2.65138 0.114844
\(534\) 0 0
\(535\) 25.5693 44.2874i 1.10546 1.91471i
\(536\) 25.9493 44.9456i 1.12084 1.94135i
\(537\) 0 0
\(538\) −21.0923 −0.909354
\(539\) −5.57039 7.66586i −0.239934 0.330192i
\(540\) 0 0
\(541\) −9.12929 15.8124i −0.392499 0.679828i 0.600280 0.799790i \(-0.295056\pi\)
−0.992778 + 0.119962i \(0.961723\pi\)
\(542\) 21.8865 37.9085i 0.940106 1.62831i
\(543\) 0 0
\(544\) 4.42350 + 7.66173i 0.189656 + 0.328494i
\(545\) −45.5606 −1.95160
\(546\) 0 0
\(547\) 5.77199 0.246792 0.123396 0.992357i \(-0.460621\pi\)
0.123396 + 0.992357i \(0.460621\pi\)
\(548\) 13.8558 + 23.9990i 0.591892 + 1.02519i
\(549\) 0 0
\(550\) −5.70532 + 9.88190i −0.243276 + 0.421366i
\(551\) 1.15122 + 1.99397i 0.0490437 + 0.0849461i
\(552\) 0 0
\(553\) 1.80974 + 0.922028i 0.0769579 + 0.0392086i
\(554\) −12.1845 −0.517672
\(555\) 0 0
\(556\) 26.0014 45.0358i 1.10271 1.90994i
\(557\) 16.6911 28.9098i 0.707223 1.22495i −0.258661 0.965968i \(-0.583281\pi\)
0.965883 0.258977i \(-0.0833855\pi\)
\(558\) 0 0
\(559\) 6.36623 0.269263
\(560\) 0.920558 + 17.5536i 0.0389007 + 0.741774i
\(561\) 0 0
\(562\) 2.03643 + 3.52720i 0.0859015 + 0.148786i
\(563\) −1.09566 + 1.89773i −0.0461764 + 0.0799799i −0.888190 0.459477i \(-0.848037\pi\)
0.842013 + 0.539457i \(0.181370\pi\)
\(564\) 0 0
\(565\) 2.46683 + 4.27268i 0.103780 + 0.179753i
\(566\) 29.8079 1.25292
\(567\) 0 0
\(568\) −52.3278 −2.19563
\(569\) −9.49302 16.4424i −0.397968 0.689301i 0.595507 0.803350i \(-0.296951\pi\)
−0.993475 + 0.114049i \(0.963618\pi\)
\(570\) 0 0
\(571\) 10.8690 18.8257i 0.454854 0.787831i −0.543825 0.839198i \(-0.683025\pi\)
0.998680 + 0.0513674i \(0.0163580\pi\)
\(572\) 3.66858 + 6.35417i 0.153391 + 0.265681i
\(573\) 0 0
\(574\) −10.1766 5.18480i −0.424764 0.216409i
\(575\) 9.28172 0.387074
\(576\) 0 0
\(577\) −15.4516 + 26.7629i −0.643258 + 1.11416i 0.341443 + 0.939903i \(0.389084\pi\)
−0.984701 + 0.174253i \(0.944249\pi\)
\(578\) −7.21083 + 12.4895i −0.299931 + 0.519496i
\(579\) 0 0
\(580\) 11.2680 0.467877
\(581\) −4.36542 + 2.83516i −0.181108 + 0.117622i
\(582\) 0 0
\(583\) 4.36902 + 7.56737i 0.180946 + 0.313408i
\(584\) −21.1767 + 36.6792i −0.876299 + 1.51780i
\(585\) 0 0
\(586\) 6.21069 + 10.7572i 0.256561 + 0.444377i
\(587\) 18.3666 0.758072 0.379036 0.925382i \(-0.376256\pi\)
0.379036 + 0.925382i \(0.376256\pi\)
\(588\) 0 0
\(589\) 7.22565 0.297728
\(590\) 42.5763 + 73.7444i 1.75284 + 3.03601i
\(591\) 0 0
\(592\) 12.3685 21.4230i 0.508344 0.880478i
\(593\) 13.8775 + 24.0365i 0.569880 + 0.987061i 0.996577 + 0.0826662i \(0.0263435\pi\)
−0.426698 + 0.904394i \(0.640323\pi\)
\(594\) 0 0
\(595\) −21.4539 + 13.9334i −0.879524 + 0.571213i
\(596\) 8.05871 0.330098
\(597\) 0 0
\(598\) 4.59841 7.96468i 0.188043 0.325700i
\(599\) −0.201412 + 0.348855i −0.00822945 + 0.0142538i −0.870111 0.492856i \(-0.835953\pi\)
0.861881 + 0.507110i \(0.169286\pi\)
\(600\) 0 0
\(601\) −24.7466 −1.00943 −0.504717 0.863285i \(-0.668403\pi\)
−0.504717 + 0.863285i \(0.668403\pi\)
\(602\) −24.4351 12.4492i −0.995899 0.507392i
\(603\) 0 0
\(604\) −25.9313 44.9143i −1.05513 1.82754i
\(605\) −13.3885 + 23.1895i −0.544318 + 0.942787i
\(606\) 0 0
\(607\) −12.0348 20.8449i −0.488479 0.846070i 0.511434 0.859323i \(-0.329115\pi\)
−0.999912 + 0.0132531i \(0.995781\pi\)
\(608\) 5.89730 0.239167
\(609\) 0 0
\(610\) 3.90231 0.158000
\(611\) −2.91672 5.05190i −0.117998 0.204378i
\(612\) 0 0
\(613\) 10.1907 17.6509i 0.411600 0.712912i −0.583465 0.812138i \(-0.698303\pi\)
0.995065 + 0.0992261i \(0.0316367\pi\)
\(614\) 5.96879 + 10.3382i 0.240881 + 0.417218i
\(615\) 0 0
\(616\) −0.759823 14.4886i −0.0306141 0.583763i
\(617\) 41.8629 1.68534 0.842669 0.538431i \(-0.180983\pi\)
0.842669 + 0.538431i \(0.180983\pi\)
\(618\) 0 0
\(619\) −7.41095 + 12.8361i −0.297871 + 0.515928i −0.975649 0.219339i \(-0.929610\pi\)
0.677777 + 0.735267i \(0.262943\pi\)
\(620\) 17.6809 30.6242i 0.710081 1.22990i
\(621\) 0 0
\(622\) 77.3270 3.10053
\(623\) −15.1043 7.69535i −0.605140 0.308308i
\(624\) 0 0
\(625\) 15.0930 + 26.1419i 0.603722 + 1.04568i
\(626\) 1.81291 3.14005i 0.0724585 0.125502i
\(627\) 0 0
\(628\) −5.48329 9.49734i −0.218807 0.378985i
\(629\) 36.0007 1.43544
\(630\) 0 0
\(631\) −21.0294 −0.837169 −0.418585 0.908178i \(-0.637474\pi\)
−0.418585 + 0.908178i \(0.637474\pi\)
\(632\) 1.55487 + 2.69312i 0.0618496 + 0.107127i
\(633\) 0 0
\(634\) −25.6694 + 44.4607i −1.01946 + 1.76576i
\(635\) −5.79673 10.0402i −0.230036 0.398434i
\(636\) 0 0
\(637\) 4.17329 9.37511i 0.165352 0.371456i
\(638\) −3.37150 −0.133479
\(639\) 0 0
\(640\) 30.2882 52.4607i 1.19725 2.07369i
\(641\) −5.96592 + 10.3333i −0.235640 + 0.408140i −0.959458 0.281850i \(-0.909052\pi\)
0.723819 + 0.689990i \(0.242385\pi\)
\(642\) 0 0
\(643\) 39.9355 1.57490 0.787452 0.616377i \(-0.211400\pi\)
0.787452 + 0.616377i \(0.211400\pi\)
\(644\) −21.5611 + 14.0030i −0.849627 + 0.551796i
\(645\) 0 0
\(646\) −8.71733 15.0989i −0.342979 0.594057i
\(647\) 0.494477 0.856459i 0.0194399 0.0336709i −0.856142 0.516741i \(-0.827145\pi\)
0.875582 + 0.483070i \(0.160478\pi\)
\(648\) 0 0
\(649\) −8.26714 14.3191i −0.324514 0.562074i
\(650\) −12.3571 −0.484686
\(651\) 0 0
\(652\) 1.43654 0.0562594
\(653\) −11.3573 19.6715i −0.444447 0.769804i 0.553567 0.832805i \(-0.313266\pi\)
−0.998014 + 0.0630004i \(0.979933\pi\)
\(654\) 0 0
\(655\) 7.78211 13.4790i 0.304072 0.526668i
\(656\) −2.05688 3.56262i −0.0803076 0.139097i
\(657\) 0 0
\(658\) 1.31600 + 25.0940i 0.0513031 + 0.978267i
\(659\) 38.3885 1.49540 0.747702 0.664035i \(-0.231157\pi\)
0.747702 + 0.664035i \(0.231157\pi\)
\(660\) 0 0
\(661\) −16.9629 + 29.3806i −0.659780 + 1.14277i 0.320892 + 0.947116i \(0.396017\pi\)
−0.980672 + 0.195657i \(0.937316\pi\)
\(662\) 23.2458 40.2628i 0.903472 1.56486i
\(663\) 0 0
\(664\) −7.96972 −0.309285
\(665\) 0.893040 + 17.0288i 0.0346306 + 0.660350i
\(666\) 0 0
\(667\) 1.37124 + 2.37505i 0.0530944 + 0.0919623i
\(668\) 13.4905 23.3662i 0.521962 0.904064i
\(669\) 0 0
\(670\) −44.6601 77.3535i −1.72537 2.98843i
\(671\) −0.757720 −0.0292514
\(672\) 0 0
\(673\) 32.2060 1.24145 0.620725 0.784028i \(-0.286838\pi\)
0.620725 + 0.784028i \(0.286838\pi\)
\(674\) −11.5702 20.0401i −0.445666 0.771916i
\(675\) 0 0
\(676\) 20.0585 34.7424i 0.771483 1.33625i
\(677\) 18.9842 + 32.8816i 0.729622 + 1.26374i 0.957043 + 0.289946i \(0.0936375\pi\)
−0.227421 + 0.973797i \(0.573029\pi\)
\(678\) 0 0
\(679\) −18.3785 + 11.9361i −0.705303 + 0.458064i
\(680\) −39.1672 −1.50199
\(681\) 0 0
\(682\) −5.29031 + 9.16309i −0.202577 + 0.350873i
\(683\) 7.59357 13.1525i 0.290560 0.503265i −0.683382 0.730061i \(-0.739492\pi\)
0.973942 + 0.226796i \(0.0728251\pi\)
\(684\) 0 0
\(685\) 21.8932 0.836495
\(686\) −34.3512 + 27.8230i −1.31153 + 1.06229i
\(687\) 0 0
\(688\) −4.93877 8.55420i −0.188289 0.326126i
\(689\) −4.73142 + 8.19507i −0.180253 + 0.312207i
\(690\) 0 0
\(691\) −1.34574 2.33089i −0.0511943 0.0886711i 0.839293 0.543680i \(-0.182969\pi\)
−0.890487 + 0.455009i \(0.849636\pi\)
\(692\) −14.9922 −0.569919
\(693\) 0 0
\(694\) −4.83589 −0.183568
\(695\) −20.5420 35.5798i −0.779203 1.34962i
\(696\) 0 0
\(697\) 2.99344 5.18480i 0.113385 0.196388i
\(698\) −19.4429 33.6761i −0.735924 1.27466i
\(699\) 0 0
\(700\) 30.7792 + 15.6815i 1.16335 + 0.592703i
\(701\) −11.8515 −0.447625 −0.223813 0.974632i \(-0.571850\pi\)
−0.223813 + 0.974632i \(0.571850\pi\)
\(702\) 0 0
\(703\) 11.9988 20.7826i 0.452544 0.783829i
\(704\) −7.39689 + 12.8118i −0.278781 + 0.482862i
\(705\) 0 0
\(706\) −40.7234 −1.53265
\(707\) 2.24836 + 42.8727i 0.0845584 + 1.61239i
\(708\) 0 0
\(709\) 20.5167 + 35.5359i 0.770520 + 1.33458i 0.937278 + 0.348582i \(0.113337\pi\)
−0.166759 + 0.985998i \(0.553330\pi\)
\(710\) −45.0294 + 77.9931i −1.68992 + 2.92703i
\(711\) 0 0
\(712\) −12.9772 22.4771i −0.486339 0.842364i
\(713\) 8.60657 0.322318
\(714\) 0 0
\(715\) 5.79660 0.216781
\(716\) 19.5669 + 33.8908i 0.731248 + 1.26656i
\(717\) 0 0
\(718\) −3.54123 + 6.13359i −0.132158 + 0.228904i
\(719\) 10.4555 + 18.1094i 0.389923 + 0.675366i 0.992439 0.122741i \(-0.0391685\pi\)
−0.602516 + 0.798107i \(0.705835\pi\)
\(720\) 0 0
\(721\) −5.24958 2.67457i −0.195505 0.0996060i
\(722\) 33.7288 1.25526
\(723\) 0 0
\(724\) 36.2896 62.8554i 1.34869 2.33600i
\(725\) 1.84243 3.19119i 0.0684263 0.118518i
\(726\) 0 0
\(727\) −2.64330 −0.0980347 −0.0490173 0.998798i \(-0.515609\pi\)
−0.0490173 + 0.998798i \(0.515609\pi\)
\(728\) 13.1769 8.55782i 0.488368 0.317174i
\(729\) 0 0
\(730\) 36.4462 + 63.1267i 1.34893 + 2.33642i
\(731\) 7.18756 12.4492i 0.265841 0.460451i
\(732\) 0 0
\(733\) −7.07446 12.2533i −0.261301 0.452587i 0.705287 0.708922i \(-0.250818\pi\)
−0.966588 + 0.256335i \(0.917485\pi\)
\(734\) 24.2446 0.894884
\(735\) 0 0
\(736\) 7.02436 0.258921
\(737\) 8.67174 + 15.0199i 0.319428 + 0.553265i
\(738\) 0 0
\(739\) −7.85905 + 13.6123i −0.289100 + 0.500736i −0.973595 0.228282i \(-0.926689\pi\)
0.684495 + 0.729017i \(0.260023\pi\)
\(740\) −58.7212 101.708i −2.15864 3.73887i
\(741\) 0 0
\(742\) 34.1858 22.2022i 1.25500 0.815070i
\(743\) −21.0991 −0.774051 −0.387026 0.922069i \(-0.626497\pi\)
−0.387026 + 0.922069i \(0.626497\pi\)
\(744\) 0 0
\(745\) 3.18333 5.51368i 0.116628 0.202006i
\(746\) −30.4142 + 52.6789i −1.11354 + 1.92871i
\(747\) 0 0
\(748\) 16.5675 0.605768
\(749\) 41.2739 + 21.0283i 1.50812 + 0.768357i
\(750\) 0 0
\(751\) −6.51848 11.2903i −0.237863 0.411990i 0.722238 0.691644i \(-0.243113\pi\)
−0.960101 + 0.279654i \(0.909780\pi\)
\(752\) −4.52544 + 7.83829i −0.165026 + 0.285833i
\(753\) 0 0
\(754\) −1.82558 3.16200i −0.0664838 0.115153i
\(755\) −40.9732 −1.49117
\(756\) 0 0
\(757\) −12.6856 −0.461065 −0.230532 0.973065i \(-0.574047\pi\)
−0.230532 + 0.973065i \(0.574047\pi\)
\(758\) 11.7613 + 20.3711i 0.427188 + 0.739912i
\(759\) 0 0
\(760\) −13.0542 + 22.6105i −0.473525 + 0.820169i
\(761\) 3.02038 + 5.23146i 0.109489 + 0.189640i 0.915563 0.402174i \(-0.131745\pi\)
−0.806074 + 0.591814i \(0.798412\pi\)
\(762\) 0 0
\(763\) −2.16131 41.2127i −0.0782446 1.49200i
\(764\) 30.6388 1.10847
\(765\) 0 0
\(766\) −32.5959 + 56.4577i −1.17774 + 2.03990i
\(767\) 8.95288 15.5068i 0.323270 0.559920i
\(768\) 0 0
\(769\) −0.216258 −0.00779848 −0.00389924 0.999992i \(-0.501241\pi\)
−0.00389924 + 0.999992i \(0.501241\pi\)
\(770\) −22.2487 11.3353i −0.801788 0.408496i
\(771\) 0 0
\(772\) 34.7251 + 60.1457i 1.24979 + 2.16469i
\(773\) 18.8132 32.5854i 0.676663 1.17202i −0.299316 0.954154i \(-0.596759\pi\)
0.975980 0.217861i \(-0.0699081\pi\)
\(774\) 0 0
\(775\) −5.78202 10.0148i −0.207696 0.359741i
\(776\) −33.5527 −1.20447
\(777\) 0 0
\(778\) −9.98776 −0.358078
\(779\) −1.99539 3.45612i −0.0714923 0.123828i
\(780\) 0 0
\(781\) 8.74345 15.1441i 0.312865 0.541898i
\(782\) −10.3833 17.9845i −0.371307 0.643123i
\(783\) 0 0
\(784\) −15.8347 + 1.66541i −0.565526 + 0.0594791i
\(785\) −8.66396 −0.309230
\(786\) 0 0
\(787\) −15.4067 + 26.6853i −0.549191 + 0.951226i 0.449139 + 0.893462i \(0.351731\pi\)
−0.998330 + 0.0577648i \(0.981603\pi\)
\(788\) −11.0847 + 19.1992i −0.394875 + 0.683943i
\(789\) 0 0
\(790\) 5.35203 0.190417
\(791\) −3.74791 + 2.43410i −0.133260 + 0.0865468i
\(792\) 0 0
\(793\) −0.410286 0.710636i −0.0145697 0.0252354i
\(794\) −36.6037 + 63.3994i −1.29902 + 2.24996i
\(795\) 0 0
\(796\) 26.6355 + 46.1340i 0.944070 + 1.63518i
\(797\) 35.9583 1.27371 0.636855 0.770984i \(-0.280235\pi\)
0.636855 + 0.770984i \(0.280235\pi\)
\(798\) 0 0
\(799\) −13.1720 −0.465994
\(800\) −4.71907 8.17367i −0.166844 0.288983i
\(801\) 0 0
\(802\) −8.17268 + 14.1555i −0.288587 + 0.499848i
\(803\) −7.07684 12.2574i −0.249736 0.432556i
\(804\) 0 0
\(805\) 1.06371 + 20.2833i 0.0374909 + 0.714892i
\(806\) −11.4583 −0.403600
\(807\) 0 0
\(808\) −32.8659 + 56.9254i −1.15622 + 2.00263i
\(809\) −19.4818 + 33.7435i −0.684943 + 1.18636i 0.288511 + 0.957477i \(0.406840\pi\)
−0.973455 + 0.228880i \(0.926494\pi\)
\(810\) 0 0
\(811\) −28.2811 −0.993082 −0.496541 0.868013i \(-0.665397\pi\)
−0.496541 + 0.868013i \(0.665397\pi\)
\(812\) 0.534530 + 10.1926i 0.0187583 + 0.357692i
\(813\) 0 0
\(814\) 17.5701 + 30.4322i 0.615830 + 1.06665i
\(815\) 0.567459 0.982867i 0.0198772 0.0344283i
\(816\) 0 0
\(817\) −4.79113 8.29849i −0.167621 0.290327i
\(818\) 43.6076 1.52471
\(819\) 0 0
\(820\) −19.5306 −0.682037
\(821\) −20.7917 36.0123i −0.725635 1.25684i −0.958712 0.284378i \(-0.908213\pi\)
0.233077 0.972458i \(-0.425121\pi\)
\(822\) 0 0
\(823\) −4.22999 + 7.32656i −0.147448 + 0.255388i −0.930284 0.366841i \(-0.880439\pi\)
0.782835 + 0.622229i \(0.213773\pi\)
\(824\) −4.51029 7.81205i −0.157123 0.272146i
\(825\) 0 0
\(826\) −64.6870 + 42.0115i −2.25075 + 1.46177i
\(827\) 44.2823 1.53985 0.769923 0.638137i \(-0.220294\pi\)
0.769923 + 0.638137i \(0.220294\pi\)
\(828\) 0 0
\(829\) −8.31637 + 14.4044i −0.288839 + 0.500284i −0.973533 0.228547i \(-0.926603\pi\)
0.684694 + 0.728831i \(0.259936\pi\)
\(830\) −6.85813 + 11.8786i −0.238049 + 0.412314i
\(831\) 0 0
\(832\) −16.0209 −0.555425
\(833\) −13.6214 18.7455i −0.471954 0.649494i
\(834\) 0 0
\(835\) −10.6579 18.4601i −0.368832 0.638836i
\(836\) 5.52185 9.56412i 0.190977 0.330782i
\(837\) 0 0
\(838\) −26.8068 46.4308i −0.926027 1.60393i
\(839\) −29.6012 −1.02195 −0.510974 0.859596i \(-0.670715\pi\)
−0.510974 + 0.859596i \(0.670715\pi\)
\(840\) 0 0
\(841\) −27.9112 −0.962456
\(842\) −24.8657 43.0687i −0.856929 1.48424i
\(843\) 0 0
\(844\) −25.5997 + 44.3400i −0.881178 + 1.52624i
\(845\) −15.8469 27.4477i −0.545151 0.944228i
\(846\) 0 0
\(847\) −21.6116 11.0107i −0.742583 0.378332i
\(848\) 14.6821 0.504186
\(849\) 0 0
\(850\) −13.9514 + 24.1645i −0.478528 + 0.828834i
\(851\) 14.2920 24.7544i 0.489922 0.848570i
\(852\) 0 0
\(853\) 30.1238 1.03142 0.515710 0.856763i \(-0.327528\pi\)
0.515710 + 0.856763i \(0.327528\pi\)
\(854\) 0.185118 + 3.52990i 0.00633460 + 0.120791i
\(855\) 0 0
\(856\) 35.4613 + 61.4208i 1.21204 + 2.09932i
\(857\) −18.5447 + 32.1204i −0.633475 + 1.09721i 0.353361 + 0.935487i \(0.385039\pi\)
−0.986836 + 0.161724i \(0.948295\pi\)
\(858\) 0 0
\(859\) 1.89166 + 3.27646i 0.0645427 + 0.111791i 0.896491 0.443062i \(-0.146108\pi\)
−0.831948 + 0.554853i \(0.812774\pi\)
\(860\) −46.8949 −1.59910
\(861\) 0 0
\(862\) −48.3166 −1.64567
\(863\) 0.213559 + 0.369895i 0.00726963 + 0.0125914i 0.869637 0.493691i \(-0.164353\pi\)
−0.862368 + 0.506282i \(0.831019\pi\)
\(864\) 0 0
\(865\) −5.92218 + 10.2575i −0.201360 + 0.348766i
\(866\) −25.8694 44.8071i −0.879077 1.52261i
\(867\) 0 0
\(868\) 28.5404 + 14.5408i 0.968723 + 0.493547i
\(869\) −1.03922 −0.0352530
\(870\) 0 0
\(871\) −9.39105 + 16.2658i −0.318203 + 0.551145i
\(872\) 31.5933 54.7212i 1.06988 1.85309i
\(873\) 0 0
\(874\) −13.8428 −0.468240
\(875\) −9.51763 + 6.18129i −0.321755 + 0.208966i
\(876\) 0 0
\(877\) −5.63038 9.75210i −0.190124 0.329305i 0.755167 0.655532i \(-0.227556\pi\)
−0.945291 + 0.326228i \(0.894222\pi\)
\(878\) −42.3408 + 73.3364i −1.42893 + 2.47498i
\(879\) 0 0
\(880\) −4.49687 7.78881i −0.151589 0.262561i
\(881\) −35.4810 −1.19538 −0.597692 0.801726i \(-0.703916\pi\)
−0.597692 + 0.801726i \(0.703916\pi\)
\(882\) 0 0
\(883\) −5.30092 −0.178390 −0.0891952 0.996014i \(-0.528429\pi\)
−0.0891952 + 0.996014i \(0.528429\pi\)
\(884\) 8.97088 + 15.5380i 0.301723 + 0.522600i
\(885\) 0 0
\(886\) −22.9214 + 39.7010i −0.770060 + 1.33378i
\(887\) −28.7832 49.8540i −0.966446 1.67393i −0.705679 0.708532i \(-0.749358\pi\)
−0.260767 0.965402i \(-0.583975\pi\)
\(888\) 0 0
\(889\) 8.80708 5.71982i 0.295380 0.191837i
\(890\) −44.6686 −1.49730
\(891\) 0 0
\(892\) 8.64231 14.9689i 0.289366 0.501197i
\(893\) −4.39016 + 7.60398i −0.146911 + 0.254458i
\(894\) 0 0
\(895\) 30.9169 1.03344
\(896\) 48.8911 + 24.9091i 1.63334 + 0.832155i
\(897\) 0 0
\(898\) −35.3354 61.2027i −1.17916 2.04236i
\(899\) 1.70842 2.95906i 0.0569788 0.0986903i
\(900\) 0 0
\(901\) 10.6837 + 18.5047i 0.355925 + 0.616480i
\(902\) 5.84377 0.194576
\(903\) 0 0
\(904\) −6.84235 −0.227573
\(905\) −28.6700 49.6579i −0.953023 1.65068i
\(906\) 0 0
\(907\) −10.4486 + 18.0975i −0.346939 + 0.600917i −0.985704 0.168485i \(-0.946112\pi\)
0.638765 + 0.769402i \(0.279446\pi\)
\(908\) −36.4402 63.1163i −1.20931 2.09459i
\(909\) 0 0
\(910\) −1.41616 27.0040i −0.0469454 0.895173i
\(911\) −22.7639 −0.754201 −0.377101 0.926172i \(-0.623079\pi\)
−0.377101 + 0.926172i \(0.623079\pi\)
\(912\) 0 0
\(913\) 1.33166 2.30650i 0.0440715 0.0763340i
\(914\) −11.4116 + 19.7654i −0.377461 + 0.653782i
\(915\) 0 0
\(916\) 103.789 3.42929
\(917\) 12.5618 + 6.40002i 0.414828 + 0.211347i
\(918\) 0 0
\(919\) 18.6515 + 32.3054i 0.615257 + 1.06566i 0.990339 + 0.138664i \(0.0442809\pi\)
−0.375083 + 0.926991i \(0.622386\pi\)
\(920\) −15.5490 + 26.9317i −0.512636 + 0.887911i
\(921\) 0 0
\(922\) −26.0616 45.1399i −0.858292 1.48660i
\(923\) 18.9374 0.623332
\(924\) 0 0
\(925\) −38.4062 −1.26279
\(926\) −31.2070 54.0521i −1.02553 1.77626i
\(927\) 0 0
\(928\) 1.39434 2.41508i 0.0457716 0.0792787i
\(929\) −2.83363 4.90799i −0.0929683 0.161026i 0.815791 0.578347i \(-0.196302\pi\)
−0.908759 + 0.417322i \(0.862969\pi\)
\(930\) 0 0
\(931\) −15.3614 + 1.61563i −0.503449 + 0.0529501i
\(932\) 51.0289 1.67151
\(933\) 0 0
\(934\) 41.7138 72.2503i 1.36492 2.36410i
\(935\) 6.54444 11.3353i 0.214026 0.370704i
\(936\) 0 0
\(937\) −7.64754 −0.249834 −0.124917 0.992167i \(-0.539866\pi\)
−0.124917 + 0.992167i \(0.539866\pi\)
\(938\) 67.8529 44.0675i 2.21547 1.43886i
\(939\) 0 0
\(940\) 21.4851 + 37.2133i 0.700766 + 1.21376i
\(941\) −10.2276 + 17.7147i −0.333410 + 0.577483i −0.983178 0.182650i \(-0.941533\pi\)
0.649768 + 0.760132i \(0.274866\pi\)
\(942\) 0 0
\(943\) −2.37674 4.11663i −0.0773973 0.134056i
\(944\) −27.7817 −0.904219
\(945\) 0 0
\(946\) 14.0315 0.456202
\(947\) 2.38343 + 4.12823i 0.0774512 + 0.134149i 0.902150 0.431423i \(-0.141988\pi\)
−0.824698 + 0.565573i \(0.808655\pi\)
\(948\) 0 0
\(949\) 7.66385 13.2742i 0.248779 0.430898i
\(950\) 9.29980 + 16.1077i 0.301725 + 0.522604i
\(951\) 0 0
\(952\) −1.85802 35.4294i −0.0602186 1.14827i
\(953\) −48.9412 −1.58536 −0.792680 0.609638i \(-0.791315\pi\)
−0.792680 + 0.609638i \(0.791315\pi\)
\(954\) 0 0
\(955\) 12.1028 20.9627i 0.391638 0.678337i
\(956\) 20.4478 35.4166i 0.661328 1.14545i
\(957\) 0 0
\(958\) 71.1546 2.29890
\(959\) 1.03857 + 19.8038i 0.0335371 + 0.639499i
\(960\) 0 0
\(961\) 10.1386 + 17.5605i 0.327050 + 0.566468i
\(962\) −19.0275 + 32.9565i −0.613470 + 1.06256i
\(963\) 0 0
\(964\) 42.8309 + 74.1854i 1.37949 + 2.38935i
\(965\) 54.8680 1.76626
\(966\) 0 0
\(967\) 5.91712 0.190282 0.0951409 0.995464i \(-0.469670\pi\)
0.0951409 + 0.995464i \(0.469670\pi\)
\(968\) −18.5680 32.1608i −0.596799 1.03369i
\(969\) 0 0
\(970\) −28.8729 + 50.0093i −0.927052 + 1.60570i
\(971\) 14.4888 + 25.0953i 0.464966 + 0.805345i 0.999200 0.0399914i \(-0.0127331\pi\)
−0.534234 + 0.845337i \(0.679400\pi\)
\(972\) 0 0
\(973\) 31.2099 20.2695i 1.00054 0.649809i
\(974\) −53.5866 −1.71703
\(975\) 0 0
\(976\) −0.636580 + 1.10259i −0.0203764 + 0.0352930i
\(977\) −11.4228 + 19.7848i −0.365447 + 0.632972i −0.988848 0.148930i \(-0.952417\pi\)
0.623401 + 0.781902i \(0.285750\pi\)
\(978\) 0 0
\(979\) 8.67340 0.277203
\(980\) −30.7412 + 69.0589i −0.981992 + 2.20601i
\(981\) 0 0
\(982\) −41.8232 72.4400i −1.33463 2.31165i
\(983\) 15.6351 27.0809i 0.498684 0.863745i −0.501315 0.865265i \(-0.667150\pi\)
0.999999 + 0.00151933i \(0.000483619\pi\)
\(984\) 0 0
\(985\) 8.75726 + 15.1680i 0.279029 + 0.483293i
\(986\) −8.24442 −0.262556
\(987\) 0 0
\(988\) 11.9598 0.380490
\(989\) −5.70679 9.88444i −0.181465 0.314307i
\(990\) 0 0
\(991\) 3.50732 6.07485i 0.111414 0.192974i −0.804927 0.593374i \(-0.797796\pi\)
0.916340 + 0.400400i \(0.131129\pi\)
\(992\) −4.37581 7.57912i −0.138932 0.240637i
\(993\) 0 0
\(994\) −72.6862 37.0323i −2.30547 1.17459i
\(995\) 42.0858 1.33421
\(996\) 0 0
\(997\) 10.6439 18.4358i 0.337095 0.583866i −0.646790 0.762668i \(-0.723889\pi\)
0.983885 + 0.178802i \(0.0572222\pi\)
\(998\) −10.6636 + 18.4698i −0.337549 + 0.584653i
\(999\) 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 567.2.e.f.487.5 10
3.2 odd 2 567.2.e.e.487.1 10
7.2 even 3 inner 567.2.e.f.163.5 10
7.3 odd 6 3969.2.a.ba.1.1 5
7.4 even 3 3969.2.a.z.1.1 5
9.2 odd 6 189.2.g.b.172.1 10
9.4 even 3 63.2.h.b.25.1 yes 10
9.5 odd 6 189.2.h.b.46.5 10
9.7 even 3 63.2.g.b.4.5 10
21.2 odd 6 567.2.e.e.163.1 10
21.11 odd 6 3969.2.a.bc.1.5 5
21.17 even 6 3969.2.a.bb.1.5 5
36.7 odd 6 1008.2.t.i.193.3 10
36.11 even 6 3024.2.t.i.1873.4 10
36.23 even 6 3024.2.q.i.2881.2 10
36.31 odd 6 1008.2.q.i.529.4 10
63.2 odd 6 189.2.h.b.37.5 10
63.4 even 3 441.2.f.e.295.5 10
63.5 even 6 1323.2.g.f.667.1 10
63.11 odd 6 1323.2.f.e.442.1 10
63.13 odd 6 441.2.h.f.214.1 10
63.16 even 3 63.2.h.b.58.1 yes 10
63.20 even 6 1323.2.g.f.361.1 10
63.23 odd 6 189.2.g.b.100.1 10
63.25 even 3 441.2.f.e.148.5 10
63.31 odd 6 441.2.f.f.295.5 10
63.32 odd 6 1323.2.f.e.883.1 10
63.34 odd 6 441.2.g.f.67.5 10
63.38 even 6 1323.2.f.f.442.1 10
63.40 odd 6 441.2.g.f.79.5 10
63.41 even 6 1323.2.h.f.802.5 10
63.47 even 6 1323.2.h.f.226.5 10
63.52 odd 6 441.2.f.f.148.5 10
63.58 even 3 63.2.g.b.16.5 yes 10
63.59 even 6 1323.2.f.f.883.1 10
63.61 odd 6 441.2.h.f.373.1 10
252.23 even 6 3024.2.t.i.289.4 10
252.79 odd 6 1008.2.q.i.625.4 10
252.191 even 6 3024.2.q.i.2305.2 10
252.247 odd 6 1008.2.t.i.961.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.5 10 9.7 even 3
63.2.g.b.16.5 yes 10 63.58 even 3
63.2.h.b.25.1 yes 10 9.4 even 3
63.2.h.b.58.1 yes 10 63.16 even 3
189.2.g.b.100.1 10 63.23 odd 6
189.2.g.b.172.1 10 9.2 odd 6
189.2.h.b.37.5 10 63.2 odd 6
189.2.h.b.46.5 10 9.5 odd 6
441.2.f.e.148.5 10 63.25 even 3
441.2.f.e.295.5 10 63.4 even 3
441.2.f.f.148.5 10 63.52 odd 6
441.2.f.f.295.5 10 63.31 odd 6
441.2.g.f.67.5 10 63.34 odd 6
441.2.g.f.79.5 10 63.40 odd 6
441.2.h.f.214.1 10 63.13 odd 6
441.2.h.f.373.1 10 63.61 odd 6
567.2.e.e.163.1 10 21.2 odd 6
567.2.e.e.487.1 10 3.2 odd 2
567.2.e.f.163.5 10 7.2 even 3 inner
567.2.e.f.487.5 10 1.1 even 1 trivial
1008.2.q.i.529.4 10 36.31 odd 6
1008.2.q.i.625.4 10 252.79 odd 6
1008.2.t.i.193.3 10 36.7 odd 6
1008.2.t.i.961.3 10 252.247 odd 6
1323.2.f.e.442.1 10 63.11 odd 6
1323.2.f.e.883.1 10 63.32 odd 6
1323.2.f.f.442.1 10 63.38 even 6
1323.2.f.f.883.1 10 63.59 even 6
1323.2.g.f.361.1 10 63.20 even 6
1323.2.g.f.667.1 10 63.5 even 6
1323.2.h.f.226.5 10 63.47 even 6
1323.2.h.f.802.5 10 63.41 even 6
3024.2.q.i.2305.2 10 252.191 even 6
3024.2.q.i.2881.2 10 36.23 even 6
3024.2.t.i.289.4 10 252.23 even 6
3024.2.t.i.1873.4 10 36.11 even 6
3969.2.a.z.1.1 5 7.4 even 3
3969.2.a.ba.1.1 5 7.3 odd 6
3969.2.a.bb.1.5 5 21.17 even 6
3969.2.a.bc.1.5 5 21.11 odd 6