Properties

Label 243.2.e.a.109.1
Level $243$
Weight $2$
Character 243.109
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
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] = [243,2,Mod(28,243)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(243, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("243.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 243 = 3^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 243.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.94036476912\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.0126039i\) of defining polynomial
Character \(\chi\) \(=\) 243.109
Dual form 243.2.e.a.136.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28765 + 1.08047i) q^{2} +(0.143341 - 0.812925i) q^{4} +(-1.06142 + 0.386327i) q^{5} +(-0.678777 - 3.84954i) q^{7} +(-0.987144 - 1.70978i) q^{8} +O(q^{10})\) \(q+(-1.28765 + 1.08047i) q^{2} +(0.143341 - 0.812925i) q^{4} +(-1.06142 + 0.386327i) q^{5} +(-0.678777 - 3.84954i) q^{7} +(-0.987144 - 1.70978i) q^{8} +(0.949332 - 1.64429i) q^{10} +(-1.75765 - 0.639734i) q^{11} +(-0.561203 - 0.470905i) q^{13} +(5.03334 + 4.22347i) q^{14} +(4.66984 + 1.69968i) q^{16} +(0.944822 - 1.63648i) q^{17} +(-1.37143 - 2.37538i) q^{19} +(0.161910 + 0.918235i) q^{20} +(2.95446 - 1.07534i) q^{22} +(1.01197 - 5.73916i) q^{23} +(-2.85285 + 2.39382i) q^{25} +1.23143 q^{26} -3.22668 q^{28} +(4.07531 - 3.41959i) q^{29} +(0.232793 - 1.32023i) q^{31} +(-4.13914 + 1.50652i) q^{32} +(0.551563 + 3.12807i) q^{34} +(2.20765 + 3.82376i) q^{35} +(-1.69806 + 2.94112i) q^{37} +(4.33245 + 1.57688i) q^{38} +(1.70831 + 1.43345i) q^{40} +(-1.37607 - 1.15466i) q^{41} +(-4.72680 - 1.72041i) q^{43} +(-0.771999 + 1.33714i) q^{44} +(4.89793 + 8.48346i) q^{46} +(-0.296709 - 1.68272i) q^{47} +(-7.78035 + 2.83182i) q^{49} +(1.08703 - 6.16483i) q^{50} +(-0.463253 + 0.388716i) q^{52} -2.84494 q^{53} +2.11276 q^{55} +(-5.91183 + 4.96061i) q^{56} +(-1.55282 + 8.80649i) q^{58} +(-10.5810 + 3.85116i) q^{59} +(0.908335 + 5.15142i) q^{61} +(1.12672 + 1.95153i) q^{62} +(-1.26751 + 2.19540i) q^{64} +(0.777597 + 0.283022i) q^{65} +(-1.44708 - 1.21424i) q^{67} +(-1.19490 - 1.00264i) q^{68} +(-6.97415 - 2.53838i) q^{70} +(-6.09193 + 10.5515i) q^{71} +(-4.94384 - 8.56298i) q^{73} +(-0.991282 - 5.62184i) q^{74} +(-2.12759 + 0.774379i) q^{76} +(-1.26962 + 7.20039i) q^{77} +(9.46285 - 7.94028i) q^{79} -5.61331 q^{80} +3.01948 q^{82} +(8.94982 - 7.50979i) q^{83} +(-0.370641 + 2.10201i) q^{85} +(7.94533 - 2.89186i) q^{86} +(0.641252 + 3.63672i) q^{88} +(-2.86437 - 4.96123i) q^{89} +(-1.43183 + 2.48001i) q^{91} +(-4.52045 - 1.64531i) q^{92} +(2.20018 + 1.84617i) q^{94} +(2.37334 + 1.99147i) q^{95} +(0.322670 + 0.117442i) q^{97} +(6.95870 - 12.0528i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 3 q^{7} - 6 q^{8} - 3 q^{10} + 6 q^{11} + 3 q^{13} + 21 q^{14} + 9 q^{16} - 9 q^{17} - 3 q^{19} - 24 q^{20} + 12 q^{22} + 12 q^{23} + 12 q^{25} + 30 q^{26} - 12 q^{28} + 24 q^{29} + 12 q^{31} - 27 q^{32} - 12 q^{35} - 3 q^{37} + 30 q^{38} - 15 q^{40} - 6 q^{41} - 15 q^{43} - 3 q^{44} - 3 q^{46} - 12 q^{47} - 33 q^{49} - 21 q^{50} - 45 q^{52} + 18 q^{53} - 12 q^{55} - 30 q^{56} - 51 q^{58} + 3 q^{59} - 33 q^{61} + 12 q^{62} + 12 q^{64} - 21 q^{65} - 6 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} + 21 q^{74} + 6 q^{76} + 12 q^{77} + 21 q^{79} - 42 q^{80} - 12 q^{82} + 6 q^{83} + 36 q^{85} + 21 q^{86} + 42 q^{88} - 9 q^{89} + 6 q^{91} + 3 q^{92} + 48 q^{94} - 3 q^{95} + 39 q^{97} + 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28765 + 1.08047i −0.910508 + 0.764007i −0.972216 0.234087i \(-0.924790\pi\)
0.0617072 + 0.998094i \(0.480346\pi\)
\(3\) 0 0
\(4\) 0.143341 0.812925i 0.0716703 0.406463i
\(5\) −1.06142 + 0.386327i −0.474683 + 0.172771i −0.568273 0.822840i \(-0.692388\pi\)
0.0935894 + 0.995611i \(0.470166\pi\)
\(6\) 0 0
\(7\) −0.678777 3.84954i −0.256554 1.45499i −0.792053 0.610453i \(-0.790988\pi\)
0.535499 0.844536i \(-0.320124\pi\)
\(8\) −0.987144 1.70978i −0.349008 0.604500i
\(9\) 0 0
\(10\) 0.949332 1.64429i 0.300205 0.519971i
\(11\) −1.75765 0.639734i −0.529953 0.192887i 0.0631646 0.998003i \(-0.479881\pi\)
−0.593117 + 0.805116i \(0.702103\pi\)
\(12\) 0 0
\(13\) −0.561203 0.470905i −0.155650 0.130606i 0.561637 0.827384i \(-0.310172\pi\)
−0.717287 + 0.696778i \(0.754616\pi\)
\(14\) 5.03334 + 4.22347i 1.34522 + 1.12877i
\(15\) 0 0
\(16\) 4.66984 + 1.69968i 1.16746 + 0.424921i
\(17\) 0.944822 1.63648i 0.229153 0.396905i −0.728404 0.685147i \(-0.759738\pi\)
0.957557 + 0.288243i \(0.0930711\pi\)
\(18\) 0 0
\(19\) −1.37143 2.37538i −0.314627 0.544950i 0.664731 0.747083i \(-0.268546\pi\)
−0.979358 + 0.202133i \(0.935213\pi\)
\(20\) 0.161910 + 0.918235i 0.0362041 + 0.205324i
\(21\) 0 0
\(22\) 2.95446 1.07534i 0.629893 0.229262i
\(23\) 1.01197 5.73916i 0.211010 1.19670i −0.676687 0.736271i \(-0.736585\pi\)
0.887697 0.460428i \(-0.152304\pi\)
\(24\) 0 0
\(25\) −2.85285 + 2.39382i −0.570570 + 0.478765i
\(26\) 1.23143 0.241504
\(27\) 0 0
\(28\) −3.22668 −0.609786
\(29\) 4.07531 3.41959i 0.756765 0.635002i −0.180517 0.983572i \(-0.557777\pi\)
0.937283 + 0.348570i \(0.113333\pi\)
\(30\) 0 0
\(31\) 0.232793 1.32023i 0.0418108 0.237121i −0.956740 0.290946i \(-0.906030\pi\)
0.998550 + 0.0538247i \(0.0171412\pi\)
\(32\) −4.13914 + 1.50652i −0.731703 + 0.266318i
\(33\) 0 0
\(34\) 0.551563 + 3.12807i 0.0945923 + 0.536459i
\(35\) 2.20765 + 3.82376i 0.373161 + 0.646334i
\(36\) 0 0
\(37\) −1.69806 + 2.94112i −0.279159 + 0.483517i −0.971176 0.238364i \(-0.923389\pi\)
0.692017 + 0.721881i \(0.256722\pi\)
\(38\) 4.33245 + 1.57688i 0.702817 + 0.255804i
\(39\) 0 0
\(40\) 1.70831 + 1.43345i 0.270108 + 0.226648i
\(41\) −1.37607 1.15466i −0.214906 0.180328i 0.528980 0.848635i \(-0.322575\pi\)
−0.743886 + 0.668307i \(0.767019\pi\)
\(42\) 0 0
\(43\) −4.72680 1.72041i −0.720830 0.262361i −0.0445518 0.999007i \(-0.514186\pi\)
−0.676278 + 0.736646i \(0.736408\pi\)
\(44\) −0.771999 + 1.33714i −0.116383 + 0.201582i
\(45\) 0 0
\(46\) 4.89793 + 8.48346i 0.722160 + 1.25082i
\(47\) −0.296709 1.68272i −0.0432794 0.245450i 0.955491 0.295019i \(-0.0953261\pi\)
−0.998771 + 0.0495697i \(0.984215\pi\)
\(48\) 0 0
\(49\) −7.78035 + 2.83182i −1.11148 + 0.404545i
\(50\) 1.08703 6.16483i 0.153729 0.871839i
\(51\) 0 0
\(52\) −0.463253 + 0.388716i −0.0642417 + 0.0539052i
\(53\) −2.84494 −0.390783 −0.195391 0.980725i \(-0.562598\pi\)
−0.195391 + 0.980725i \(0.562598\pi\)
\(54\) 0 0
\(55\) 2.11276 0.284885
\(56\) −5.91183 + 4.96061i −0.790001 + 0.662890i
\(57\) 0 0
\(58\) −1.55282 + 8.80649i −0.203895 + 1.15635i
\(59\) −10.5810 + 3.85116i −1.37753 + 0.501379i −0.921427 0.388550i \(-0.872976\pi\)
−0.456099 + 0.889929i \(0.650754\pi\)
\(60\) 0 0
\(61\) 0.908335 + 5.15142i 0.116300 + 0.659572i 0.986098 + 0.166164i \(0.0531381\pi\)
−0.869798 + 0.493408i \(0.835751\pi\)
\(62\) 1.12672 + 1.95153i 0.143093 + 0.247844i
\(63\) 0 0
\(64\) −1.26751 + 2.19540i −0.158439 + 0.274425i
\(65\) 0.777597 + 0.283022i 0.0964491 + 0.0351046i
\(66\) 0 0
\(67\) −1.44708 1.21424i −0.176789 0.148343i 0.550099 0.835099i \(-0.314590\pi\)
−0.726888 + 0.686756i \(0.759034\pi\)
\(68\) −1.19490 1.00264i −0.144903 0.121588i
\(69\) 0 0
\(70\) −6.97415 2.53838i −0.833570 0.303395i
\(71\) −6.09193 + 10.5515i −0.722980 + 1.25224i 0.236821 + 0.971553i \(0.423895\pi\)
−0.959800 + 0.280684i \(0.909439\pi\)
\(72\) 0 0
\(73\) −4.94384 8.56298i −0.578633 1.00222i −0.995637 0.0933164i \(-0.970253\pi\)
0.417004 0.908905i \(-0.363080\pi\)
\(74\) −0.991282 5.62184i −0.115234 0.653526i
\(75\) 0 0
\(76\) −2.12759 + 0.774379i −0.244051 + 0.0888274i
\(77\) −1.26962 + 7.20039i −0.144687 + 0.820561i
\(78\) 0 0
\(79\) 9.46285 7.94028i 1.06465 0.893351i 0.0700965 0.997540i \(-0.477669\pi\)
0.994557 + 0.104189i \(0.0332248\pi\)
\(80\) −5.61331 −0.627587
\(81\) 0 0
\(82\) 3.01948 0.333445
\(83\) 8.94982 7.50979i 0.982371 0.824307i −0.00207468 0.999998i \(-0.500660\pi\)
0.984445 + 0.175691i \(0.0562159\pi\)
\(84\) 0 0
\(85\) −0.370641 + 2.10201i −0.0402016 + 0.227995i
\(86\) 7.94533 2.89186i 0.856767 0.311838i
\(87\) 0 0
\(88\) 0.641252 + 3.63672i 0.0683576 + 0.387675i
\(89\) −2.86437 4.96123i −0.303622 0.525889i 0.673331 0.739341i \(-0.264863\pi\)
−0.976954 + 0.213452i \(0.931529\pi\)
\(90\) 0 0
\(91\) −1.43183 + 2.48001i −0.150097 + 0.259976i
\(92\) −4.52045 1.64531i −0.471290 0.171535i
\(93\) 0 0
\(94\) 2.20018 + 1.84617i 0.226932 + 0.190418i
\(95\) 2.37334 + 1.99147i 0.243500 + 0.204320i
\(96\) 0 0
\(97\) 0.322670 + 0.117442i 0.0327622 + 0.0119245i 0.358349 0.933588i \(-0.383340\pi\)
−0.325587 + 0.945512i \(0.605562\pi\)
\(98\) 6.95870 12.0528i 0.702935 1.21752i
\(99\) 0 0
\(100\) 1.53707 + 2.66228i 0.153707 + 0.266228i
\(101\) 3.02187 + 17.1379i 0.300687 + 1.70528i 0.643141 + 0.765748i \(0.277631\pi\)
−0.342454 + 0.939535i \(0.611258\pi\)
\(102\) 0 0
\(103\) 14.8594 5.40837i 1.46414 0.532902i 0.517635 0.855602i \(-0.326813\pi\)
0.946501 + 0.322700i \(0.104590\pi\)
\(104\) −0.251158 + 1.42439i −0.0246280 + 0.139673i
\(105\) 0 0
\(106\) 3.66330 3.07387i 0.355811 0.298561i
\(107\) 16.5298 1.59800 0.798999 0.601332i \(-0.205363\pi\)
0.798999 + 0.601332i \(0.205363\pi\)
\(108\) 0 0
\(109\) −4.71844 −0.451945 −0.225972 0.974134i \(-0.572556\pi\)
−0.225972 + 0.974134i \(0.572556\pi\)
\(110\) −2.72051 + 2.28278i −0.259390 + 0.217654i
\(111\) 0 0
\(112\) 3.37321 19.1304i 0.318738 1.80765i
\(113\) 18.7420 6.82153i 1.76310 0.641715i 0.763109 0.646270i \(-0.223672\pi\)
0.999990 + 0.00455445i \(0.00144973\pi\)
\(114\) 0 0
\(115\) 1.14306 + 6.48264i 0.106591 + 0.604509i
\(116\) −2.19571 3.80308i −0.203867 0.353108i
\(117\) 0 0
\(118\) 9.46357 16.3914i 0.871193 1.50895i
\(119\) −6.94101 2.52632i −0.636281 0.231588i
\(120\) 0 0
\(121\) −5.74640 4.82180i −0.522400 0.438346i
\(122\) −6.73558 5.65182i −0.609811 0.511692i
\(123\) 0 0
\(124\) −1.03988 0.378486i −0.0933842 0.0339891i
\(125\) 4.92714 8.53407i 0.440697 0.763310i
\(126\) 0 0
\(127\) −0.534728 0.926176i −0.0474495 0.0821849i 0.841325 0.540529i \(-0.181776\pi\)
−0.888775 + 0.458344i \(0.848443\pi\)
\(128\) −2.26971 12.8721i −0.200616 1.13775i
\(129\) 0 0
\(130\) −1.30707 + 0.475736i −0.114638 + 0.0417248i
\(131\) −1.32672 + 7.52422i −0.115916 + 0.657395i 0.870376 + 0.492388i \(0.163876\pi\)
−0.986292 + 0.165007i \(0.947235\pi\)
\(132\) 0 0
\(133\) −8.21323 + 6.89172i −0.712178 + 0.597588i
\(134\) 3.17529 0.274303
\(135\) 0 0
\(136\) −3.73070 −0.319905
\(137\) −11.9890 + 10.0599i −1.02429 + 0.859479i −0.990160 0.139938i \(-0.955310\pi\)
−0.0341275 + 0.999417i \(0.510865\pi\)
\(138\) 0 0
\(139\) 1.50326 8.52542i 0.127505 0.723116i −0.852284 0.523080i \(-0.824783\pi\)
0.979788 0.200036i \(-0.0641060\pi\)
\(140\) 3.42488 1.24655i 0.289455 0.105353i
\(141\) 0 0
\(142\) −3.55632 20.1689i −0.298439 1.69253i
\(143\) 0.685146 + 1.18671i 0.0572948 + 0.0992375i
\(144\) 0 0
\(145\) −3.00455 + 5.20403i −0.249514 + 0.432172i
\(146\) 15.6180 + 5.68448i 1.29255 + 0.470451i
\(147\) 0 0
\(148\) 2.14751 + 1.80197i 0.176524 + 0.148121i
\(149\) 1.88740 + 1.58371i 0.154622 + 0.129743i 0.716817 0.697262i \(-0.245598\pi\)
−0.562195 + 0.827005i \(0.690043\pi\)
\(150\) 0 0
\(151\) 9.87937 + 3.59580i 0.803972 + 0.292622i 0.711131 0.703059i \(-0.248183\pi\)
0.0928406 + 0.995681i \(0.470405\pi\)
\(152\) −2.70760 + 4.68969i −0.219615 + 0.380384i
\(153\) 0 0
\(154\) −6.14497 10.6434i −0.495176 0.857669i
\(155\) 0.262950 + 1.49126i 0.0211206 + 0.119781i
\(156\) 0 0
\(157\) −0.338241 + 0.123110i −0.0269946 + 0.00982522i −0.355482 0.934683i \(-0.615683\pi\)
0.328488 + 0.944508i \(0.393461\pi\)
\(158\) −3.60565 + 20.4486i −0.286850 + 1.62681i
\(159\) 0 0
\(160\) 3.81137 3.19812i 0.301315 0.252834i
\(161\) −22.7800 −1.79532
\(162\) 0 0
\(163\) 14.6186 1.14502 0.572508 0.819899i \(-0.305971\pi\)
0.572508 + 0.819899i \(0.305971\pi\)
\(164\) −1.13590 + 0.953132i −0.0886988 + 0.0744271i
\(165\) 0 0
\(166\) −3.41017 + 19.3400i −0.264680 + 1.50108i
\(167\) 2.04463 0.744184i 0.158218 0.0575867i −0.261697 0.965150i \(-0.584282\pi\)
0.419915 + 0.907563i \(0.362060\pi\)
\(168\) 0 0
\(169\) −2.16423 12.2740i −0.166479 0.944150i
\(170\) −1.79390 3.10712i −0.137586 0.238306i
\(171\) 0 0
\(172\) −2.07611 + 3.59593i −0.158302 + 0.274187i
\(173\) −16.5076 6.00828i −1.25505 0.456801i −0.372945 0.927854i \(-0.621652\pi\)
−0.882105 + 0.471053i \(0.843874\pi\)
\(174\) 0 0
\(175\) 11.1516 + 9.35728i 0.842979 + 0.707344i
\(176\) −7.12061 5.97490i −0.536736 0.450375i
\(177\) 0 0
\(178\) 9.04877 + 3.29348i 0.678234 + 0.246857i
\(179\) 0.502236 0.869898i 0.0375388 0.0650192i −0.846646 0.532157i \(-0.821382\pi\)
0.884184 + 0.467138i \(0.154715\pi\)
\(180\) 0 0
\(181\) 10.5866 + 18.3366i 0.786898 + 1.36295i 0.927859 + 0.372932i \(0.121647\pi\)
−0.140961 + 0.990015i \(0.545019\pi\)
\(182\) −0.835869 4.74045i −0.0619587 0.351385i
\(183\) 0 0
\(184\) −10.8117 + 3.93513i −0.797049 + 0.290102i
\(185\) 0.666125 3.77778i 0.0489745 0.277748i
\(186\) 0 0
\(187\) −2.70758 + 2.27193i −0.197998 + 0.166140i
\(188\) −1.41045 −0.102868
\(189\) 0 0
\(190\) −5.20776 −0.377811
\(191\) 7.52898 6.31756i 0.544778 0.457123i −0.328390 0.944542i \(-0.606506\pi\)
0.873168 + 0.487419i \(0.162062\pi\)
\(192\) 0 0
\(193\) −1.93723 + 10.9866i −0.139445 + 0.790833i 0.832215 + 0.554452i \(0.187072\pi\)
−0.971661 + 0.236380i \(0.924039\pi\)
\(194\) −0.542380 + 0.197410i −0.0389406 + 0.0141732i
\(195\) 0 0
\(196\) 1.18681 + 6.73076i 0.0847724 + 0.480768i
\(197\) 4.54497 + 7.87212i 0.323816 + 0.560865i 0.981272 0.192628i \(-0.0617009\pi\)
−0.657456 + 0.753493i \(0.728368\pi\)
\(198\) 0 0
\(199\) 7.34694 12.7253i 0.520811 0.902071i −0.478896 0.877872i \(-0.658963\pi\)
0.999707 0.0241994i \(-0.00770367\pi\)
\(200\) 6.90910 + 2.51471i 0.488547 + 0.177817i
\(201\) 0 0
\(202\) −22.4081 18.8026i −1.57663 1.32295i
\(203\) −15.9301 13.3669i −1.11807 0.938173i
\(204\) 0 0
\(205\) 1.90667 + 0.693971i 0.133168 + 0.0484691i
\(206\) −13.2901 + 23.0192i −0.925968 + 1.60382i
\(207\) 0 0
\(208\) −1.82034 3.15292i −0.126218 0.218615i
\(209\) 0.890883 + 5.05245i 0.0616237 + 0.349485i
\(210\) 0 0
\(211\) −7.38439 + 2.68770i −0.508362 + 0.185029i −0.583451 0.812148i \(-0.698298\pi\)
0.0750892 + 0.997177i \(0.476076\pi\)
\(212\) −0.407796 + 2.31273i −0.0280075 + 0.158839i
\(213\) 0 0
\(214\) −21.2847 + 17.8600i −1.45499 + 1.22088i
\(215\) 5.68178 0.387494
\(216\) 0 0
\(217\) −5.24030 −0.355735
\(218\) 6.07572 5.09813i 0.411499 0.345289i
\(219\) 0 0
\(220\) 0.302845 1.71752i 0.0204178 0.115795i
\(221\) −1.30086 + 0.473475i −0.0875055 + 0.0318494i
\(222\) 0 0
\(223\) −1.51784 8.60809i −0.101642 0.576440i −0.992509 0.122175i \(-0.961013\pi\)
0.890867 0.454265i \(-0.150098\pi\)
\(224\) 8.60897 + 14.9112i 0.575211 + 0.996295i
\(225\) 0 0
\(226\) −16.7627 + 29.0339i −1.11504 + 1.93131i
\(227\) 3.82306 + 1.39148i 0.253745 + 0.0923558i 0.465761 0.884910i \(-0.345781\pi\)
−0.212016 + 0.977266i \(0.568003\pi\)
\(228\) 0 0
\(229\) 12.3761 + 10.3848i 0.817837 + 0.686247i 0.952464 0.304650i \(-0.0985394\pi\)
−0.134628 + 0.990896i \(0.542984\pi\)
\(230\) −8.47616 7.11235i −0.558902 0.468974i
\(231\) 0 0
\(232\) −9.86968 3.59227i −0.647976 0.235844i
\(233\) 8.60658 14.9070i 0.563836 0.976592i −0.433321 0.901240i \(-0.642658\pi\)
0.997157 0.0753527i \(-0.0240083\pi\)
\(234\) 0 0
\(235\) 0.965013 + 1.67145i 0.0629505 + 0.109034i
\(236\) 1.61402 + 9.15357i 0.105064 + 0.595847i
\(237\) 0 0
\(238\) 11.6672 4.24652i 0.756274 0.275261i
\(239\) 0.266626 1.51211i 0.0172466 0.0978104i −0.974969 0.222339i \(-0.928631\pi\)
0.992216 + 0.124529i \(0.0397419\pi\)
\(240\) 0 0
\(241\) −4.22985 + 3.54926i −0.272468 + 0.228628i −0.768775 0.639519i \(-0.779134\pi\)
0.496307 + 0.868147i \(0.334689\pi\)
\(242\) 12.6092 0.810549
\(243\) 0 0
\(244\) 4.31792 0.276427
\(245\) 7.16425 6.01152i 0.457707 0.384062i
\(246\) 0 0
\(247\) −0.348931 + 1.97888i −0.0222019 + 0.125913i
\(248\) −2.48712 + 0.905236i −0.157932 + 0.0574826i
\(249\) 0 0
\(250\) 2.87634 + 16.3125i 0.181916 + 1.03170i
\(251\) −10.7204 18.5683i −0.676668 1.17202i −0.975978 0.217868i \(-0.930090\pi\)
0.299310 0.954156i \(-0.403244\pi\)
\(252\) 0 0
\(253\) −5.45023 + 9.44007i −0.342653 + 0.593492i
\(254\) 1.68925 + 0.614837i 0.105993 + 0.0385783i
\(255\) 0 0
\(256\) 12.9467 + 10.8635i 0.809167 + 0.678971i
\(257\) 11.3271 + 9.50456i 0.706565 + 0.592878i 0.923633 0.383278i \(-0.125205\pi\)
−0.217068 + 0.976156i \(0.569649\pi\)
\(258\) 0 0
\(259\) 12.4746 + 4.54037i 0.775131 + 0.282125i
\(260\) 0.341537 0.591560i 0.0211812 0.0366870i
\(261\) 0 0
\(262\) −6.42133 11.1221i −0.396711 0.687124i
\(263\) −0.486694 2.76018i −0.0300108 0.170200i 0.966119 0.258099i \(-0.0830959\pi\)
−0.996129 + 0.0878987i \(0.971985\pi\)
\(264\) 0 0
\(265\) 3.01969 1.09908i 0.185498 0.0675158i
\(266\) 3.12950 17.7483i 0.191882 1.08822i
\(267\) 0 0
\(268\) −1.19451 + 1.00232i −0.0729666 + 0.0612262i
\(269\) 0.356528 0.0217379 0.0108689 0.999941i \(-0.496540\pi\)
0.0108689 + 0.999941i \(0.496540\pi\)
\(270\) 0 0
\(271\) −12.1467 −0.737857 −0.368928 0.929458i \(-0.620275\pi\)
−0.368928 + 0.929458i \(0.620275\pi\)
\(272\) 7.19366 6.03620i 0.436180 0.365998i
\(273\) 0 0
\(274\) 4.56818 25.9075i 0.275974 1.56513i
\(275\) 6.54573 2.38245i 0.394722 0.143667i
\(276\) 0 0
\(277\) 4.33946 + 24.6103i 0.260733 + 1.47869i 0.780916 + 0.624636i \(0.214752\pi\)
−0.520183 + 0.854055i \(0.674136\pi\)
\(278\) 7.27577 + 12.6020i 0.436372 + 0.755818i
\(279\) 0 0
\(280\) 4.35854 7.54921i 0.260473 0.451152i
\(281\) 6.88125 + 2.50457i 0.410501 + 0.149410i 0.539012 0.842298i \(-0.318798\pi\)
−0.128511 + 0.991708i \(0.541020\pi\)
\(282\) 0 0
\(283\) −11.0219 9.24848i −0.655185 0.549765i 0.253454 0.967347i \(-0.418433\pi\)
−0.908639 + 0.417582i \(0.862878\pi\)
\(284\) 7.70439 + 6.46475i 0.457171 + 0.383612i
\(285\) 0 0
\(286\) −2.16443 0.787789i −0.127986 0.0465829i
\(287\) −3.51086 + 6.08099i −0.207240 + 0.358950i
\(288\) 0 0
\(289\) 6.71462 + 11.6301i 0.394978 + 0.684122i
\(290\) −1.75398 9.94732i −0.102997 0.584127i
\(291\) 0 0
\(292\) −7.66971 + 2.79155i −0.448836 + 0.163363i
\(293\) 2.50323 14.1965i 0.146240 0.829369i −0.820123 0.572187i \(-0.806095\pi\)
0.966363 0.257182i \(-0.0827938\pi\)
\(294\) 0 0
\(295\) 9.74310 8.17543i 0.567265 0.475992i
\(296\) 6.70491 0.389715
\(297\) 0 0
\(298\) −4.14147 −0.239909
\(299\) −3.27052 + 2.74429i −0.189139 + 0.158707i
\(300\) 0 0
\(301\) −3.41435 + 19.3638i −0.196800 + 1.11611i
\(302\) −16.6064 + 6.04422i −0.955589 + 0.347806i
\(303\) 0 0
\(304\) −2.36695 13.4236i −0.135754 0.769899i
\(305\) −2.95426 5.11693i −0.169161 0.292995i
\(306\) 0 0
\(307\) 15.2163 26.3554i 0.868440 1.50418i 0.00484869 0.999988i \(-0.498457\pi\)
0.863591 0.504193i \(-0.168210\pi\)
\(308\) 5.67139 + 2.06422i 0.323157 + 0.117620i
\(309\) 0 0
\(310\) −1.94985 1.63612i −0.110744 0.0929254i
\(311\) 10.7213 + 8.99620i 0.607947 + 0.510128i 0.893989 0.448089i \(-0.147895\pi\)
−0.286042 + 0.958217i \(0.592340\pi\)
\(312\) 0 0
\(313\) −20.7555 7.55439i −1.17317 0.426999i −0.319386 0.947625i \(-0.603477\pi\)
−0.853785 + 0.520625i \(0.825699\pi\)
\(314\) 0.302521 0.523982i 0.0170722 0.0295700i
\(315\) 0 0
\(316\) −5.09844 8.83075i −0.286810 0.496769i
\(317\) −3.01952 17.1245i −0.169593 0.961810i −0.944201 0.329369i \(-0.893164\pi\)
0.774608 0.632441i \(-0.217947\pi\)
\(318\) 0 0
\(319\) −9.35060 + 3.40334i −0.523533 + 0.190551i
\(320\) 0.497229 2.81993i 0.0277959 0.157639i
\(321\) 0 0
\(322\) 29.3328 24.6131i 1.63465 1.37164i
\(323\) −5.18302 −0.288391
\(324\) 0 0
\(325\) 2.72829 0.151338
\(326\) −18.8237 + 15.7949i −1.04255 + 0.874800i
\(327\) 0 0
\(328\) −0.615840 + 3.49260i −0.0340041 + 0.192847i
\(329\) −6.27629 + 2.28438i −0.346023 + 0.125942i
\(330\) 0 0
\(331\) 0.150058 + 0.851019i 0.00824791 + 0.0467762i 0.988654 0.150211i \(-0.0479953\pi\)
−0.980406 + 0.196987i \(0.936884\pi\)
\(332\) −4.82203 8.35199i −0.264643 0.458375i
\(333\) 0 0
\(334\) −1.82870 + 3.16741i −0.100062 + 0.173313i
\(335\) 2.00506 + 0.729782i 0.109548 + 0.0398723i
\(336\) 0 0
\(337\) 0.320612 + 0.269025i 0.0174648 + 0.0146547i 0.651478 0.758667i \(-0.274149\pi\)
−0.634013 + 0.773322i \(0.718594\pi\)
\(338\) 16.0484 + 13.4662i 0.872918 + 0.732466i
\(339\) 0 0
\(340\) 1.65565 + 0.602606i 0.0897901 + 0.0326809i
\(341\) −1.25377 + 2.17159i −0.0678953 + 0.117598i
\(342\) 0 0
\(343\) 2.50108 + 4.33199i 0.135046 + 0.233906i
\(344\) 1.72450 + 9.78010i 0.0929786 + 0.527308i
\(345\) 0 0
\(346\) 27.7478 10.0994i 1.49173 0.542946i
\(347\) −4.06506 + 23.0541i −0.218224 + 1.23761i 0.657000 + 0.753891i \(0.271825\pi\)
−0.875224 + 0.483718i \(0.839286\pi\)
\(348\) 0 0
\(349\) 16.2221 13.6119i 0.868347 0.728630i −0.0954022 0.995439i \(-0.530414\pi\)
0.963749 + 0.266809i \(0.0859693\pi\)
\(350\) −24.4696 −1.30796
\(351\) 0 0
\(352\) 8.23894 0.439137
\(353\) −18.0361 + 15.1341i −0.959965 + 0.805506i −0.980947 0.194274i \(-0.937765\pi\)
0.0209824 + 0.999780i \(0.493321\pi\)
\(354\) 0 0
\(355\) 2.38978 13.5531i 0.126837 0.719326i
\(356\) −4.44369 + 1.61737i −0.235515 + 0.0857204i
\(357\) 0 0
\(358\) 0.293192 + 1.66278i 0.0154957 + 0.0878805i
\(359\) −5.23047 9.05943i −0.276053 0.478139i 0.694347 0.719640i \(-0.255693\pi\)
−0.970400 + 0.241502i \(0.922360\pi\)
\(360\) 0 0
\(361\) 5.73837 9.93915i 0.302019 0.523113i
\(362\) −33.4440 12.1726i −1.75778 0.639779i
\(363\) 0 0
\(364\) 1.81082 + 1.51946i 0.0949129 + 0.0796414i
\(365\) 8.55562 + 7.17902i 0.447822 + 0.375767i
\(366\) 0 0
\(367\) −19.9762 7.27076i −1.04275 0.379530i −0.236829 0.971551i \(-0.576108\pi\)
−0.805923 + 0.592021i \(0.798330\pi\)
\(368\) 14.4805 25.0809i 0.754848 1.30743i
\(369\) 0 0
\(370\) 3.22404 + 5.58420i 0.167610 + 0.290309i
\(371\) 1.93108 + 10.9517i 0.100257 + 0.568585i
\(372\) 0 0
\(373\) −2.17077 + 0.790096i −0.112398 + 0.0409096i −0.397607 0.917556i \(-0.630159\pi\)
0.285209 + 0.958465i \(0.407937\pi\)
\(374\) 1.03167 5.85092i 0.0533466 0.302544i
\(375\) 0 0
\(376\) −2.58419 + 2.16839i −0.133270 + 0.111826i
\(377\) −3.89737 −0.200725
\(378\) 0 0
\(379\) 12.5539 0.644850 0.322425 0.946595i \(-0.395502\pi\)
0.322425 + 0.946595i \(0.395502\pi\)
\(380\) 1.95911 1.64389i 0.100500 0.0843298i
\(381\) 0 0
\(382\) −2.86878 + 16.2697i −0.146780 + 0.832428i
\(383\) −18.4692 + 6.72225i −0.943733 + 0.343491i −0.767639 0.640883i \(-0.778569\pi\)
−0.176094 + 0.984373i \(0.556346\pi\)
\(384\) 0 0
\(385\) −1.43410 8.13316i −0.0730883 0.414504i
\(386\) −9.37620 16.2401i −0.477236 0.826597i
\(387\) 0 0
\(388\) 0.141724 0.245472i 0.00719492 0.0124620i
\(389\) −17.7062 6.44454i −0.897742 0.326751i −0.148394 0.988928i \(-0.547411\pi\)
−0.749348 + 0.662177i \(0.769633\pi\)
\(390\) 0 0
\(391\) −8.43589 7.07855i −0.426621 0.357978i
\(392\) 12.5221 + 10.5073i 0.632463 + 0.530699i
\(393\) 0 0
\(394\) −14.3579 5.22586i −0.723342 0.263275i
\(395\) −6.97656 + 12.0838i −0.351029 + 0.608000i
\(396\) 0 0
\(397\) −10.0589 17.4225i −0.504841 0.874410i −0.999984 0.00559897i \(-0.998218\pi\)
0.495143 0.868811i \(-0.335116\pi\)
\(398\) 4.28896 + 24.3239i 0.214986 + 1.21925i
\(399\) 0 0
\(400\) −17.3911 + 6.32984i −0.869554 + 0.316492i
\(401\) 5.34935 30.3377i 0.267134 1.51499i −0.495755 0.868462i \(-0.665109\pi\)
0.762889 0.646529i \(-0.223780\pi\)
\(402\) 0 0
\(403\) −0.752349 + 0.631295i −0.0374772 + 0.0314471i
\(404\) 14.3650 0.714684
\(405\) 0 0
\(406\) 34.9549 1.73478
\(407\) 4.86613 4.08317i 0.241205 0.202395i
\(408\) 0 0
\(409\) 6.89245 39.0891i 0.340810 1.93283i −0.0190394 0.999819i \(-0.506061\pi\)
0.359849 0.933010i \(-0.382828\pi\)
\(410\) −3.20495 + 1.16650i −0.158281 + 0.0576096i
\(411\) 0 0
\(412\) −2.26665 12.8548i −0.111670 0.633310i
\(413\) 22.0073 + 38.1178i 1.08291 + 1.87565i
\(414\) 0 0
\(415\) −6.59832 + 11.4286i −0.323899 + 0.561010i
\(416\) 3.03232 + 1.10368i 0.148672 + 0.0541122i
\(417\) 0 0
\(418\) −6.60617 5.54323i −0.323118 0.271128i
\(419\) −11.8286 9.92537i −0.577865 0.484886i 0.306380 0.951909i \(-0.400882\pi\)
−0.884245 + 0.467023i \(0.845326\pi\)
\(420\) 0 0
\(421\) 17.0025 + 6.18839i 0.828649 + 0.301604i 0.721304 0.692618i \(-0.243543\pi\)
0.107345 + 0.994222i \(0.465765\pi\)
\(422\) 6.60456 11.4394i 0.321505 0.556863i
\(423\) 0 0
\(424\) 2.80837 + 4.86424i 0.136386 + 0.236228i
\(425\) 1.22201 + 6.93037i 0.0592762 + 0.336172i
\(426\) 0 0
\(427\) 19.2140 6.99334i 0.929833 0.338431i
\(428\) 2.36939 13.4375i 0.114529 0.649526i
\(429\) 0 0
\(430\) −7.31616 + 6.13899i −0.352817 + 0.296048i
\(431\) 28.9683 1.39535 0.697677 0.716412i \(-0.254217\pi\)
0.697677 + 0.716412i \(0.254217\pi\)
\(432\) 0 0
\(433\) −37.5902 −1.80647 −0.903235 0.429146i \(-0.858815\pi\)
−0.903235 + 0.429146i \(0.858815\pi\)
\(434\) 6.74770 5.66199i 0.323900 0.271784i
\(435\) 0 0
\(436\) −0.676344 + 3.83574i −0.0323910 + 0.183699i
\(437\) −15.0206 + 5.46704i −0.718531 + 0.261524i
\(438\) 0 0
\(439\) 1.78224 + 10.1076i 0.0850619 + 0.482410i 0.997343 + 0.0728458i \(0.0232081\pi\)
−0.912281 + 0.409564i \(0.865681\pi\)
\(440\) −2.08560 3.61237i −0.0994272 0.172213i
\(441\) 0 0
\(442\) 1.16348 2.01521i 0.0553413 0.0958540i
\(443\) 20.5873 + 7.49315i 0.978130 + 0.356010i 0.781113 0.624390i \(-0.214652\pi\)
0.197017 + 0.980400i \(0.436875\pi\)
\(444\) 0 0
\(445\) 4.95696 + 4.15939i 0.234983 + 0.197174i
\(446\) 11.2552 + 9.44426i 0.532951 + 0.447199i
\(447\) 0 0
\(448\) 9.31164 + 3.38916i 0.439933 + 0.160123i
\(449\) 4.98565 8.63540i 0.235287 0.407530i −0.724069 0.689728i \(-0.757730\pi\)
0.959356 + 0.282198i \(0.0910635\pi\)
\(450\) 0 0
\(451\) 1.67998 + 2.90981i 0.0791072 + 0.137018i
\(452\) −2.85890 16.2136i −0.134471 0.762625i
\(453\) 0 0
\(454\) −6.42623 + 2.33896i −0.301598 + 0.109773i
\(455\) 0.561689 3.18550i 0.0263324 0.149338i
\(456\) 0 0
\(457\) −5.83580 + 4.89682i −0.272987 + 0.229064i −0.768995 0.639254i \(-0.779243\pi\)
0.496008 + 0.868318i \(0.334799\pi\)
\(458\) −27.1566 −1.26894
\(459\) 0 0
\(460\) 5.43375 0.253350
\(461\) 17.4662 14.6559i 0.813483 0.682593i −0.137953 0.990439i \(-0.544052\pi\)
0.951436 + 0.307845i \(0.0996080\pi\)
\(462\) 0 0
\(463\) −1.52736 + 8.66211i −0.0709826 + 0.402562i 0.928527 + 0.371264i \(0.121075\pi\)
−0.999510 + 0.0312986i \(0.990036\pi\)
\(464\) 24.8432 9.04220i 1.15332 0.419774i
\(465\) 0 0
\(466\) 5.02430 + 28.4942i 0.232746 + 1.31997i
\(467\) −5.49878 9.52416i −0.254453 0.440726i 0.710294 0.703905i \(-0.248562\pi\)
−0.964747 + 0.263180i \(0.915229\pi\)
\(468\) 0 0
\(469\) −3.69203 + 6.39479i −0.170482 + 0.295284i
\(470\) −3.04856 1.10958i −0.140619 0.0511813i
\(471\) 0 0
\(472\) 17.0296 + 14.2895i 0.783852 + 0.657730i
\(473\) 7.20747 + 6.04778i 0.331400 + 0.278077i
\(474\) 0 0
\(475\) 9.59873 + 3.49365i 0.440420 + 0.160300i
\(476\) −3.04864 + 5.28040i −0.139734 + 0.242027i
\(477\) 0 0
\(478\) 1.29047 + 2.23516i 0.0590247 + 0.102234i
\(479\) −4.46146 25.3022i −0.203849 1.15609i −0.899240 0.437455i \(-0.855880\pi\)
0.695391 0.718632i \(-0.255231\pi\)
\(480\) 0 0
\(481\) 2.33794 0.850941i 0.106601 0.0387996i
\(482\) 1.61171 9.14044i 0.0734112 0.416336i
\(483\) 0 0
\(484\) −4.74346 + 3.98023i −0.215612 + 0.180920i
\(485\) −0.387861 −0.0176119
\(486\) 0 0
\(487\) −30.3800 −1.37665 −0.688325 0.725402i \(-0.741654\pi\)
−0.688325 + 0.725402i \(0.741654\pi\)
\(488\) 7.91117 6.63826i 0.358122 0.300500i
\(489\) 0 0
\(490\) −2.72981 + 15.4815i −0.123320 + 0.699383i
\(491\) 8.18310 2.97840i 0.369298 0.134414i −0.150703 0.988579i \(-0.548154\pi\)
0.520001 + 0.854166i \(0.325932\pi\)
\(492\) 0 0
\(493\) −1.74565 9.90006i −0.0786200 0.445876i
\(494\) −1.68882 2.92512i −0.0759837 0.131608i
\(495\) 0 0
\(496\) 3.33108 5.76961i 0.149570 0.259063i
\(497\) 44.7536 + 16.2890i 2.00747 + 0.730661i
\(498\) 0 0
\(499\) 8.91329 + 7.47914i 0.399014 + 0.334812i 0.820112 0.572203i \(-0.193911\pi\)
−0.421099 + 0.907015i \(0.638355\pi\)
\(500\) −6.23130 5.22868i −0.278672 0.233834i
\(501\) 0 0
\(502\) 33.8667 + 12.3265i 1.51155 + 0.550158i
\(503\) −18.8996 + 32.7350i −0.842689 + 1.45958i 0.0449234 + 0.998990i \(0.485696\pi\)
−0.887613 + 0.460590i \(0.847638\pi\)
\(504\) 0 0
\(505\) −9.82831 17.0231i −0.437354 0.757519i
\(506\) −3.18170 18.0443i −0.141444 0.802169i
\(507\) 0 0
\(508\) −0.829560 + 0.301935i −0.0368058 + 0.0133962i
\(509\) −4.09352 + 23.2155i −0.181442 + 1.02901i 0.749000 + 0.662570i \(0.230534\pi\)
−0.930442 + 0.366439i \(0.880577\pi\)
\(510\) 0 0
\(511\) −29.6078 + 24.8439i −1.30977 + 1.09903i
\(512\) −2.26711 −0.100193
\(513\) 0 0
\(514\) −24.8548 −1.09630
\(515\) −13.6827 + 11.4811i −0.602931 + 0.505919i
\(516\) 0 0
\(517\) −0.554981 + 3.14745i −0.0244080 + 0.138425i
\(518\) −20.9686 + 7.63196i −0.921309 + 0.335329i
\(519\) 0 0
\(520\) −0.283694 1.60891i −0.0124408 0.0705553i
\(521\) 3.93474 + 6.81517i 0.172384 + 0.298578i 0.939253 0.343226i \(-0.111520\pi\)
−0.766869 + 0.641804i \(0.778186\pi\)
\(522\) 0 0
\(523\) −16.6467 + 28.8330i −0.727911 + 1.26078i 0.229854 + 0.973225i \(0.426175\pi\)
−0.957765 + 0.287554i \(0.907158\pi\)
\(524\) 5.92646 + 2.15705i 0.258898 + 0.0942313i
\(525\) 0 0
\(526\) 3.60898 + 3.02829i 0.157359 + 0.132040i
\(527\) −1.94059 1.62835i −0.0845333 0.0709319i
\(528\) 0 0
\(529\) −10.3010 3.74925i −0.447869 0.163011i
\(530\) −2.70080 + 4.67792i −0.117315 + 0.203196i
\(531\) 0 0
\(532\) 4.42516 + 7.66461i 0.191855 + 0.332303i
\(533\) 0.228519 + 1.29600i 0.00989826 + 0.0561358i
\(534\) 0 0
\(535\) −17.5452 + 6.38591i −0.758543 + 0.276087i
\(536\) −0.647619 + 3.67283i −0.0279729 + 0.158642i
\(537\) 0 0
\(538\) −0.459084 + 0.385217i −0.0197925 + 0.0166079i
\(539\) 15.4868 0.667062
\(540\) 0 0
\(541\) 22.4283 0.964266 0.482133 0.876098i \(-0.339862\pi\)
0.482133 + 0.876098i \(0.339862\pi\)
\(542\) 15.6407 13.1241i 0.671825 0.563728i
\(543\) 0 0
\(544\) −1.44535 + 8.19701i −0.0619690 + 0.351444i
\(545\) 5.00827 1.82286i 0.214531 0.0780827i
\(546\) 0 0
\(547\) −3.62771 20.5738i −0.155110 0.879671i −0.958685 0.284468i \(-0.908183\pi\)
0.803576 0.595202i \(-0.202928\pi\)
\(548\) 6.45948 + 11.1881i 0.275935 + 0.477934i
\(549\) 0 0
\(550\) −5.85447 + 10.1402i −0.249635 + 0.432381i
\(551\) −13.7118 4.99070i −0.584143 0.212611i
\(552\) 0 0
\(553\) −36.9896 31.0379i −1.57296 1.31987i
\(554\) −32.1784 27.0009i −1.36713 1.14716i
\(555\) 0 0
\(556\) −6.71505 2.44408i −0.284781 0.103652i
\(557\) 4.28920 7.42911i 0.181739 0.314782i −0.760734 0.649064i \(-0.775161\pi\)
0.942473 + 0.334283i \(0.108494\pi\)
\(558\) 0 0
\(559\) 1.84254 + 3.19137i 0.0779311 + 0.134981i
\(560\) 3.81019 + 21.6087i 0.161010 + 0.913132i
\(561\) 0 0
\(562\) −11.5668 + 4.20996i −0.487915 + 0.177586i
\(563\) 2.72886 15.4761i 0.115008 0.652241i −0.871739 0.489971i \(-0.837007\pi\)
0.986746 0.162270i \(-0.0518816\pi\)
\(564\) 0 0
\(565\) −17.2579 + 14.4811i −0.726044 + 0.609223i
\(566\) 24.1851 1.01658
\(567\) 0 0
\(568\) 24.0545 1.00930
\(569\) −9.70792 + 8.14591i −0.406977 + 0.341494i −0.823183 0.567776i \(-0.807804\pi\)
0.416206 + 0.909270i \(0.363360\pi\)
\(570\) 0 0
\(571\) −4.57089 + 25.9228i −0.191286 + 1.08483i 0.726324 + 0.687352i \(0.241227\pi\)
−0.917610 + 0.397483i \(0.869884\pi\)
\(572\) 1.06291 0.386869i 0.0444427 0.0161758i
\(573\) 0 0
\(574\) −2.04955 11.6236i −0.0855467 0.485159i
\(575\) 10.8516 + 18.7954i 0.452541 + 0.783824i
\(576\) 0 0
\(577\) 11.0577 19.1525i 0.460338 0.797329i −0.538640 0.842536i \(-0.681062\pi\)
0.998978 + 0.0452074i \(0.0143949\pi\)
\(578\) −21.2120 7.72055i −0.882305 0.321133i
\(579\) 0 0
\(580\) 3.79982 + 3.18842i 0.157779 + 0.132392i
\(581\) −34.9842 29.3552i −1.45139 1.21786i
\(582\) 0 0
\(583\) 5.00042 + 1.82001i 0.207096 + 0.0753769i
\(584\) −9.76057 + 16.9058i −0.403895 + 0.699567i
\(585\) 0 0
\(586\) 12.1156 + 20.9848i 0.500491 + 0.866876i
\(587\) −2.48371 14.0858i −0.102514 0.581385i −0.992184 0.124781i \(-0.960177\pi\)
0.889670 0.456603i \(-0.150934\pi\)
\(588\) 0 0
\(589\) −3.45532 + 1.25763i −0.142374 + 0.0518199i
\(590\) −3.71243 + 21.0543i −0.152838 + 0.866790i
\(591\) 0 0
\(592\) −12.9286 + 10.8484i −0.531363 + 0.445866i
\(593\) −47.7300 −1.96004 −0.980018 0.198908i \(-0.936260\pi\)
−0.980018 + 0.198908i \(0.936260\pi\)
\(594\) 0 0
\(595\) 8.34334 0.342044
\(596\) 1.55798 1.30730i 0.0638174 0.0535492i
\(597\) 0 0
\(598\) 1.24617 7.06739i 0.0509598 0.289007i
\(599\) −0.469442 + 0.170863i −0.0191809 + 0.00698127i −0.351593 0.936153i \(-0.614360\pi\)
0.332412 + 0.943134i \(0.392138\pi\)
\(600\) 0 0
\(601\) −2.93936 16.6699i −0.119899 0.679980i −0.984208 0.177019i \(-0.943355\pi\)
0.864309 0.502962i \(-0.167756\pi\)
\(602\) −16.5254 28.6229i −0.673527 1.16658i
\(603\) 0 0
\(604\) 4.33923 7.51577i 0.176561 0.305812i
\(605\) 7.96216 + 2.89799i 0.323708 + 0.117820i
\(606\) 0 0
\(607\) 0.532119 + 0.446501i 0.0215981 + 0.0181229i 0.653523 0.756907i \(-0.273290\pi\)
−0.631925 + 0.775030i \(0.717735\pi\)
\(608\) 9.25510 + 7.76595i 0.375344 + 0.314951i
\(609\) 0 0
\(610\) 9.33276 + 3.39685i 0.377872 + 0.137534i
\(611\) −0.625887 + 1.08407i −0.0253207 + 0.0438567i
\(612\) 0 0
\(613\) 16.3317 + 28.2873i 0.659630 + 1.14251i 0.980711 + 0.195461i \(0.0626204\pi\)
−0.321081 + 0.947052i \(0.604046\pi\)
\(614\) 8.88288 + 50.3773i 0.358484 + 2.03306i
\(615\) 0 0
\(616\) 13.5644 4.93704i 0.546526 0.198919i
\(617\) −3.97384 + 22.5368i −0.159981 + 0.907296i 0.794109 + 0.607775i \(0.207938\pi\)
−0.954090 + 0.299521i \(0.903173\pi\)
\(618\) 0 0
\(619\) 6.50045 5.45453i 0.261275 0.219236i −0.502734 0.864441i \(-0.667673\pi\)
0.764009 + 0.645205i \(0.223228\pi\)
\(620\) 1.24998 0.0502002
\(621\) 0 0
\(622\) −23.5254 −0.943282
\(623\) −17.1542 + 14.3941i −0.687267 + 0.576686i
\(624\) 0 0
\(625\) 1.30059 7.37601i 0.0520236 0.295040i
\(626\) 34.8882 12.6983i 1.39441 0.507525i
\(627\) 0 0
\(628\) 0.0515953 + 0.292611i 0.00205887 + 0.0116765i
\(629\) 3.20872 + 5.55767i 0.127940 + 0.221599i
\(630\) 0 0
\(631\) −0.795865 + 1.37848i −0.0316829 + 0.0548763i −0.881432 0.472311i \(-0.843420\pi\)
0.849749 + 0.527187i \(0.176753\pi\)
\(632\) −22.9174 8.34124i −0.911604 0.331797i
\(633\) 0 0
\(634\) 22.3906 + 18.7880i 0.889246 + 0.746166i
\(635\) 0.925380 + 0.776486i 0.0367226 + 0.0308139i
\(636\) 0 0
\(637\) 5.69987 + 2.07458i 0.225837 + 0.0821980i
\(638\) 8.36313 14.4854i 0.331099 0.573481i
\(639\) 0 0
\(640\) 7.38198 + 12.7860i 0.291798 + 0.505409i
\(641\) −3.76377 21.3454i −0.148660 0.843092i −0.964355 0.264610i \(-0.914757\pi\)
0.815696 0.578481i \(-0.196354\pi\)
\(642\) 0 0
\(643\) 6.48582 2.36064i 0.255776 0.0930947i −0.210950 0.977497i \(-0.567656\pi\)
0.466726 + 0.884402i \(0.345434\pi\)
\(644\) −3.26530 + 18.5185i −0.128671 + 0.729729i
\(645\) 0 0
\(646\) 6.67393 5.60010i 0.262582 0.220333i
\(647\) 6.18972 0.243343 0.121671 0.992570i \(-0.461175\pi\)
0.121671 + 0.992570i \(0.461175\pi\)
\(648\) 0 0
\(649\) 21.0614 0.826733
\(650\) −3.51309 + 2.94783i −0.137795 + 0.115624i
\(651\) 0 0
\(652\) 2.09544 11.8838i 0.0820636 0.465406i
\(653\) −25.5732 + 9.30790i −1.00076 + 0.364246i −0.789877 0.613265i \(-0.789856\pi\)
−0.210881 + 0.977512i \(0.567633\pi\)
\(654\) 0 0
\(655\) −1.49859 8.49894i −0.0585549 0.332081i
\(656\) −4.46347 7.73096i −0.174269 0.301843i
\(657\) 0 0
\(658\) 5.61348 9.72283i 0.218836 0.379035i
\(659\) 4.96345 + 1.80655i 0.193349 + 0.0703732i 0.436880 0.899520i \(-0.356084\pi\)
−0.243531 + 0.969893i \(0.578306\pi\)
\(660\) 0 0
\(661\) 8.93594 + 7.49814i 0.347568 + 0.291644i 0.799813 0.600250i \(-0.204932\pi\)
−0.452245 + 0.891894i \(0.649377\pi\)
\(662\) −1.11272 0.933685i −0.0432472 0.0362887i
\(663\) 0 0
\(664\) −21.6749 7.88902i −0.841149 0.306153i
\(665\) 6.05527 10.4880i 0.234813 0.406708i
\(666\) 0 0
\(667\) −15.5015 26.8494i −0.600220 1.03961i
\(668\) −0.311887 1.76880i −0.0120673 0.0684370i
\(669\) 0 0
\(670\) −3.37033 + 1.22670i −0.130207 + 0.0473915i
\(671\) 1.69900 9.63551i 0.0655892 0.371975i
\(672\) 0 0
\(673\) 37.6146 31.5624i 1.44994 1.21664i 0.517312 0.855797i \(-0.326933\pi\)
0.932626 0.360845i \(-0.117512\pi\)
\(674\) −0.703510 −0.0270982
\(675\) 0 0
\(676\) −10.2880 −0.395693
\(677\) 17.3272 14.5392i 0.665938 0.558789i −0.245922 0.969290i \(-0.579091\pi\)
0.911860 + 0.410501i \(0.134646\pi\)
\(678\) 0 0
\(679\) 0.233077 1.32185i 0.00894469 0.0507279i
\(680\) 3.95986 1.44127i 0.151854 0.0552702i
\(681\) 0 0
\(682\) −0.731918 4.15091i −0.0280266 0.158947i
\(683\) −8.56931 14.8425i −0.327896 0.567932i 0.654198 0.756323i \(-0.273006\pi\)
−0.982094 + 0.188391i \(0.939673\pi\)
\(684\) 0 0
\(685\) 8.83897 15.3095i 0.337720 0.584947i
\(686\) −7.90111 2.87577i −0.301666 0.109797i
\(687\) 0 0
\(688\) −19.1492 16.0681i −0.730057 0.612591i
\(689\) 1.59659 + 1.33970i 0.0608252 + 0.0510384i
\(690\) 0 0
\(691\) −17.1549 6.24389i −0.652605 0.237529i −0.00556457 0.999985i \(-0.501771\pi\)
−0.647040 + 0.762456i \(0.723993\pi\)
\(692\) −7.25049 + 12.5582i −0.275622 + 0.477392i
\(693\) 0 0
\(694\) −19.6749 34.0779i −0.746848 1.29358i
\(695\) 1.69800 + 9.62983i 0.0644088 + 0.365280i
\(696\) 0 0
\(697\) −3.18972 + 1.16096i −0.120819 + 0.0439746i
\(698\) −6.18112 + 35.0549i −0.233959 + 1.32685i
\(699\) 0 0
\(700\) 9.20524 7.72411i 0.347925 0.291944i
\(701\) 2.92075 0.110315 0.0551575 0.998478i \(-0.482434\pi\)
0.0551575 + 0.998478i \(0.482434\pi\)
\(702\) 0 0
\(703\) 9.31505 0.351324
\(704\) 3.63232 3.04788i 0.136898 0.114871i
\(705\) 0 0
\(706\) 6.87233 38.9749i 0.258644 1.46684i
\(707\) 63.9217 23.2656i 2.40402 0.874993i
\(708\) 0 0
\(709\) 5.21419 + 29.5711i 0.195823 + 1.11057i 0.911242 + 0.411872i \(0.135125\pi\)
−0.715419 + 0.698696i \(0.753764\pi\)
\(710\) 11.5665 + 20.0338i 0.434084 + 0.751856i
\(711\) 0 0
\(712\) −5.65509 + 9.79490i −0.211933 + 0.367079i
\(713\) −7.34146 2.67207i −0.274940 0.100070i
\(714\) 0 0
\(715\) −1.18569 0.994910i −0.0443422 0.0372075i
\(716\) −0.635171 0.532971i −0.0237374 0.0199181i
\(717\) 0 0
\(718\) 16.5235 + 6.01405i 0.616650 + 0.224442i
\(719\) 20.0285 34.6903i 0.746936 1.29373i −0.202349 0.979314i \(-0.564857\pi\)
0.949285 0.314418i \(-0.101809\pi\)
\(720\) 0 0
\(721\) −30.9059 53.5306i −1.15100 1.99358i
\(722\) 3.34992 + 18.9983i 0.124671 + 0.707044i
\(723\) 0 0
\(724\) 16.4238 5.97776i 0.610384 0.222162i
\(725\) −3.44034 + 19.5111i −0.127771 + 0.724626i
\(726\) 0 0
\(727\) −1.17877 + 0.989109i −0.0437183 + 0.0366840i −0.664385 0.747390i \(-0.731306\pi\)
0.620667 + 0.784075i \(0.286862\pi\)
\(728\) 5.65371 0.209540
\(729\) 0 0
\(730\) −18.7734 −0.694834
\(731\) −7.28140 + 6.10982i −0.269312 + 0.225980i
\(732\) 0 0
\(733\) −0.262538 + 1.48893i −0.00969705 + 0.0549947i −0.989272 0.146083i \(-0.953333\pi\)
0.979575 + 0.201078i \(0.0644444\pi\)
\(734\) 33.5783 12.2215i 1.23940 0.451104i
\(735\) 0 0
\(736\) 4.45750 + 25.2797i 0.164306 + 0.931824i
\(737\) 1.76667 + 3.05997i 0.0650762 + 0.112715i
\(738\) 0 0
\(739\) −10.6779 + 18.4946i −0.392792 + 0.680336i −0.992817 0.119646i \(-0.961824\pi\)
0.600024 + 0.799982i \(0.295157\pi\)
\(740\) −2.97557 1.08302i −0.109384 0.0398126i
\(741\) 0 0
\(742\) −14.3196 12.0155i −0.525687 0.441104i
\(743\) 15.5727 + 13.0671i 0.571308 + 0.479384i 0.882080 0.471101i \(-0.156143\pi\)
−0.310772 + 0.950485i \(0.600588\pi\)
\(744\) 0 0
\(745\) −2.61516 0.951841i −0.0958121 0.0348728i
\(746\) 1.94153 3.36282i 0.0710843 0.123122i
\(747\) 0 0
\(748\) 1.45880 + 2.52672i 0.0533391 + 0.0923860i
\(749\) −11.2201 63.6322i −0.409972 2.32507i
\(750\) 0 0
\(751\) −4.00606 + 1.45808i −0.146183 + 0.0532063i −0.414075 0.910243i \(-0.635895\pi\)
0.267892 + 0.963449i \(0.413673\pi\)
\(752\) 1.47451 8.36233i 0.0537697 0.304943i
\(753\) 0 0
\(754\) 5.01847 4.21099i 0.182762 0.153355i
\(755\) −11.8754 −0.432189
\(756\) 0 0
\(757\) 54.3419 1.97509 0.987546 0.157332i \(-0.0502892\pi\)
0.987546 + 0.157332i \(0.0502892\pi\)
\(758\) −16.1651 + 13.5641i −0.587141 + 0.492670i
\(759\) 0 0
\(760\) 1.06215 6.02377i 0.0385283 0.218505i
\(761\) 17.0659 6.21147i 0.618637 0.225165i −0.0136411 0.999907i \(-0.504342\pi\)
0.632278 + 0.774741i \(0.282120\pi\)
\(762\) 0 0
\(763\) 3.20277 + 18.1638i 0.115948 + 0.657574i
\(764\) −4.05650 7.02606i −0.146759 0.254194i
\(765\) 0 0
\(766\) 16.5188 28.6113i 0.596847 1.03377i
\(767\) 7.75161 + 2.82135i 0.279894 + 0.101873i
\(768\) 0 0
\(769\) 19.0398 + 15.9763i 0.686594 + 0.576121i 0.917925 0.396755i \(-0.129864\pi\)
−0.231331 + 0.972875i \(0.574308\pi\)
\(770\) 10.6342 + 8.92319i 0.383232 + 0.321570i
\(771\) 0 0
\(772\) 8.65360 + 3.14965i 0.311450 + 0.113358i
\(773\) 19.2416 33.3274i 0.692071 1.19870i −0.279087 0.960266i \(-0.590032\pi\)
0.971158 0.238437i \(-0.0766350\pi\)
\(774\) 0 0
\(775\) 2.49629 + 4.32369i 0.0896692 + 0.155312i
\(776\) −0.117721 0.667629i −0.00422594 0.0239665i
\(777\) 0 0
\(778\) 29.7626 10.8327i 1.06704 0.388372i
\(779\) −0.855579 + 4.85223i −0.0306543 + 0.173849i
\(780\) 0 0
\(781\) 17.4577 14.6487i 0.624685 0.524173i
\(782\) 18.5107 0.661940
\(783\) 0 0
\(784\) −41.1462 −1.46951
\(785\) 0.311457 0.261343i 0.0111164 0.00932774i
\(786\) 0 0
\(787\) −0.186234 + 1.05619i −0.00663852 + 0.0376489i −0.987947 0.154792i \(-0.950529\pi\)
0.981309 + 0.192441i \(0.0616404\pi\)
\(788\) 7.05092 2.56633i 0.251179 0.0914215i
\(789\) 0 0
\(790\) −4.07274 23.0976i −0.144902 0.821777i
\(791\) −38.9814 67.5177i −1.38602 2.40065i
\(792\) 0 0
\(793\) 1.91607 3.31873i 0.0680417 0.117852i
\(794\) 31.7768 + 11.5658i 1.12772 + 0.410456i
\(795\) 0 0
\(796\) −9.29158 7.79656i −0.329331 0.276342i
\(797\) −19.3405 16.2286i −0.685075 0.574846i 0.232409 0.972618i \(-0.425339\pi\)
−0.917484 + 0.397772i \(0.869784\pi\)
\(798\) 0 0
\(799\) −3.03407 1.10431i −0.107338 0.0390677i
\(800\) 8.20198 14.2063i 0.289984 0.502267i
\(801\) 0 0
\(802\) 25.8908 + 44.8442i 0.914237 + 1.58350i
\(803\) 3.21153 + 18.2135i 0.113332 + 0.642740i
\(804\) 0 0
\(805\) 24.1793 8.80054i 0.852207 0.310178i
\(806\) 0.286669 1.62578i 0.0100975 0.0572656i
\(807\) 0 0
\(808\) 26.3190 22.0843i 0.925901 0.776923i
\(809\) 11.7337 0.412536 0.206268 0.978495i \(-0.433868\pi\)
0.206268 + 0.978495i \(0.433868\pi\)
\(810\) 0 0
\(811\) −38.4085 −1.34871 −0.674353 0.738409i \(-0.735577\pi\)
−0.674353 + 0.738409i \(0.735577\pi\)
\(812\) −13.1497 + 11.0339i −0.461465 + 0.387215i
\(813\) 0 0
\(814\) −1.85415 + 10.5154i −0.0649879 + 0.368565i
\(815\) −15.5165 + 5.64755i −0.543520 + 0.197825i
\(816\) 0 0
\(817\) 2.39582 + 13.5874i 0.0838192 + 0.475362i
\(818\) 33.3594 + 57.7802i 1.16639 + 2.02024i
\(819\) 0 0
\(820\) 0.837450 1.45051i 0.0292450 0.0506539i
\(821\) 25.1199 + 9.14290i 0.876691 + 0.319089i 0.740874 0.671644i \(-0.234412\pi\)
0.135817 + 0.990734i \(0.456634\pi\)
\(822\) 0 0
\(823\) 3.34322 + 2.80529i 0.116537 + 0.0977864i 0.699194 0.714932i \(-0.253542\pi\)
−0.582657 + 0.812718i \(0.697987\pi\)
\(824\) −23.9155 20.0675i −0.833135 0.699083i
\(825\) 0 0
\(826\) −69.5229 25.3043i −2.41901 0.880448i
\(827\) −19.5727 + 33.9009i −0.680610 + 1.17885i 0.294185 + 0.955748i \(0.404952\pi\)
−0.974795 + 0.223102i \(0.928382\pi\)
\(828\) 0 0
\(829\) 16.4433 + 28.4807i 0.571101 + 0.989176i 0.996453 + 0.0841481i \(0.0268169\pi\)
−0.425352 + 0.905028i \(0.639850\pi\)
\(830\) −3.85193 21.8454i −0.133703 0.758265i
\(831\) 0 0
\(832\) 1.74516 0.635185i 0.0605024 0.0220211i
\(833\) −2.71684 + 15.4079i −0.0941328 + 0.533854i
\(834\) 0 0
\(835\) −1.88272 + 1.57979i −0.0651542 + 0.0546709i
\(836\) 4.23496 0.146469
\(837\) 0 0
\(838\) 25.9552 0.896607
\(839\) −24.2379 + 20.3380i −0.836785 + 0.702146i −0.956838 0.290621i \(-0.906138\pi\)
0.120053 + 0.992767i \(0.461694\pi\)
\(840\) 0 0
\(841\) −0.121257 + 0.687680i −0.00418126 + 0.0237131i
\(842\) −28.5796 + 10.4021i −0.984920 + 0.358481i
\(843\) 0 0
\(844\) 1.12641 + 6.38821i 0.0387728 + 0.219891i
\(845\) 7.03892 + 12.1918i 0.242146 + 0.419410i
\(846\) 0 0
\(847\) −14.6612 + 25.3939i −0.503764 + 0.872545i
\(848\) −13.2854 4.83550i −0.456223 0.166052i
\(849\) 0 0
\(850\) −9.06158 7.60356i −0.310809 0.260800i
\(851\) 15.1612 + 12.7217i 0.519719 + 0.436096i
\(852\) 0 0
\(853\) 5.31645 + 1.93503i 0.182032 + 0.0662541i 0.431428 0.902147i \(-0.358010\pi\)
−0.249396 + 0.968402i \(0.580232\pi\)
\(854\) −17.1849 + 29.7652i −0.588057 + 1.01854i
\(855\) 0 0
\(856\) −16.3173 28.2624i −0.557715 0.965990i
\(857\) 7.15610 + 40.5843i 0.244448 + 1.38633i 0.821772 + 0.569817i \(0.192986\pi\)
−0.577324 + 0.816515i \(0.695903\pi\)
\(858\) 0 0
\(859\) −33.6921 + 12.2629i −1.14956 + 0.418406i −0.845357 0.534201i \(-0.820612\pi\)
−0.304203 + 0.952607i \(0.598390\pi\)
\(860\) 0.814430 4.61886i 0.0277718 0.157502i
\(861\) 0 0
\(862\) −37.3012 + 31.2994i −1.27048 + 1.06606i
\(863\) −20.9694 −0.713806 −0.356903 0.934142i \(-0.616167\pi\)
−0.356903 + 0.934142i \(0.616167\pi\)
\(864\) 0 0
\(865\) 19.8427 0.674673
\(866\) 48.4032 40.6151i 1.64481 1.38016i
\(867\) 0 0
\(868\) −0.751149 + 4.25997i −0.0254956 + 0.144593i
\(869\) −21.7121 + 7.90255i −0.736532 + 0.268076i
\(870\) 0 0
\(871\) 0.240311 + 1.36287i 0.00814264 + 0.0461792i
\(872\) 4.65778 + 8.06751i 0.157732 + 0.273201i
\(873\) 0 0
\(874\) 13.4343 23.2689i 0.454422 0.787082i
\(875\) −36.1966 13.1745i −1.22367 0.445379i
\(876\) 0 0
\(877\) 15.7119 + 13.1838i 0.530553 + 0.445187i 0.868292 0.496053i \(-0.165218\pi\)
−0.337739 + 0.941240i \(0.609662\pi\)
\(878\) −13.2159 11.0894i −0.446014 0.374250i
\(879\) 0 0
\(880\) 9.86626 + 3.59102i 0.332591 + 0.121053i
\(881\) −19.1438 + 33.1581i −0.644972 + 1.11712i 0.339336 + 0.940665i \(0.389798\pi\)
−0.984308 + 0.176459i \(0.943536\pi\)
\(882\) 0 0
\(883\) 8.72326 + 15.1091i 0.293561 + 0.508463i 0.974649 0.223739i \(-0.0718263\pi\)
−0.681088 + 0.732201i \(0.738493\pi\)
\(884\) 0.198433 + 1.12537i 0.00667404 + 0.0378504i
\(885\) 0 0
\(886\) −34.6054 + 12.5953i −1.16259 + 0.423148i
\(887\) 9.41466 53.3932i 0.316113 1.79277i −0.249793 0.968299i \(-0.580363\pi\)
0.565906 0.824469i \(-0.308526\pi\)
\(888\) 0 0
\(889\) −3.20239 + 2.68712i −0.107405 + 0.0901232i
\(890\) −10.8769 −0.364596
\(891\) 0 0
\(892\) −7.21530 −0.241586
\(893\) −3.59019 + 3.01252i −0.120141 + 0.100810i
\(894\) 0 0
\(895\) −0.197020 + 1.11736i −0.00658566 + 0.0373491i
\(896\) −48.0112 + 17.4746i −1.60394 + 0.583787i
\(897\) 0 0
\(898\) 2.91050 + 16.5062i 0.0971245 + 0.550821i
\(899\) −3.56595 6.17641i −0.118931 0.205995i
\(900\) 0 0
\(901\) −2.68796 + 4.65569i −0.0895491 + 0.155104i
\(902\) −5.30719 1.93166i −0.176710 0.0643173i
\(903\) 0 0
\(904\) −30.1644 25.3109i −1.00325 0.841829i
\(905\) −18.3208 15.3730i −0.609004 0.511015i
\(906\) 0 0
\(907\) −26.9533 9.81022i −0.894971 0.325743i −0.146735 0.989176i \(-0.546877\pi\)
−0.748236 + 0.663433i \(0.769099\pi\)
\(908\) 1.67917 2.90841i 0.0557252 0.0965188i
\(909\) 0 0
\(910\) 2.71857 + 4.70871i 0.0901198 + 0.156092i
\(911\) 4.92841 + 27.9504i 0.163286 + 0.926039i 0.950815 + 0.309761i \(0.100249\pi\)
−0.787529 + 0.616278i \(0.788640\pi\)
\(912\) 0 0
\(913\) −20.5350 + 7.47411i −0.679608 + 0.247357i
\(914\) 2.22363 12.6108i 0.0735510 0.417129i
\(915\) 0 0
\(916\) 10.2161 8.57229i 0.337548 0.283236i
\(917\) 29.8653 0.986240
\(918\) 0 0
\(919\) 37.7786 1.24620 0.623101 0.782141i \(-0.285873\pi\)
0.623101 + 0.782141i \(0.285873\pi\)
\(920\) 9.95554 8.35369i 0.328225 0.275413i
\(921\) 0 0
\(922\) −6.65519 + 37.7434i −0.219177 + 1.24301i
\(923\) 8.38758 3.05283i 0.276081 0.100485i
\(924\) 0 0
\(925\) −2.19623 12.4554i −0.0722115 0.409532i
\(926\) −7.39243 12.8041i −0.242930 0.420768i
\(927\) 0 0
\(928\) −11.7166 + 20.2937i −0.384615 + 0.666173i
\(929\) −32.4916 11.8260i −1.06602 0.387998i −0.251330 0.967901i \(-0.580868\pi\)
−0.814685 + 0.579903i \(0.803090\pi\)
\(930\) 0 0
\(931\) 17.3968 + 14.5977i 0.570158 + 0.478420i
\(932\) −10.8846 9.13329i −0.356538 0.299171i
\(933\) 0 0
\(934\) 17.3711 + 6.32256i 0.568399 + 0.206880i
\(935\) 1.99618 3.45749i 0.0652822 0.113072i
\(936\) 0 0
\(937\) 9.71839 + 16.8328i 0.317486 + 0.549902i 0.979963 0.199180i \(-0.0638280\pi\)
−0.662477 + 0.749082i \(0.730495\pi\)
\(938\) −2.15531 12.2234i −0.0703735 0.399108i
\(939\) 0 0
\(940\) 1.49709 0.544896i 0.0488297 0.0177726i
\(941\) −1.72580 + 9.78747i −0.0562593 + 0.319062i −0.999930 0.0118234i \(-0.996236\pi\)
0.943671 + 0.330886i \(0.107348\pi\)
\(942\) 0 0
\(943\) −8.01932 + 6.72901i −0.261145 + 0.219127i
\(944\) −55.9572 −1.82125
\(945\) 0 0
\(946\) −15.8152 −0.514195
\(947\) −12.9544 + 10.8700i −0.420960 + 0.353227i −0.828528 0.559947i \(-0.810821\pi\)
0.407568 + 0.913175i \(0.366377\pi\)
\(948\) 0 0
\(949\) −1.25785 + 7.13365i −0.0408317 + 0.231568i
\(950\) −16.1346 + 5.87252i −0.523476 + 0.190530i
\(951\) 0 0
\(952\) 2.53232 + 14.3615i 0.0820728 + 0.465458i
\(953\) 8.67866 + 15.0319i 0.281129 + 0.486930i 0.971663 0.236370i \(-0.0759577\pi\)
−0.690534 + 0.723300i \(0.742624\pi\)
\(954\) 0 0
\(955\) −5.55079 + 9.61426i −0.179620 + 0.311110i
\(956\) −1.19102 0.433494i −0.0385202 0.0140202i
\(957\) 0 0
\(958\) 33.0831 + 27.7600i 1.06887 + 0.896884i
\(959\) 46.8640 + 39.3236i 1.51332 + 1.26982i
\(960\) 0 0
\(961\) 27.4416 + 9.98794i 0.885214 + 0.322192i
\(962\) −2.09104 + 3.62179i −0.0674179 + 0.116771i
\(963\) 0 0
\(964\) 2.27898 + 3.94730i 0.0734009 + 0.127134i
\(965\) −2.18819 12.4098i −0.0704404 0.399487i
\(966\) 0 0
\(967\) 15.7712 5.74024i 0.507167 0.184594i −0.0757476 0.997127i \(-0.524134\pi\)
0.582915 + 0.812533i \(0.301912\pi\)
\(968\) −2.57172 + 14.5849i −0.0826581 + 0.468777i
\(969\) 0 0
\(970\) 0.499431 0.419072i 0.0160357 0.0134556i
\(971\) 33.4811 1.07446 0.537230 0.843436i \(-0.319471\pi\)
0.537230 + 0.843436i \(0.319471\pi\)
\(972\) 0 0
\(973\) −33.8393 −1.08484
\(974\) 39.1190 32.8247i 1.25345 1.05177i
\(975\) 0 0
\(976\) −4.51401 + 25.6002i −0.144490 + 0.819442i
\(977\) 21.3638 7.77577i 0.683487 0.248769i 0.0231430 0.999732i \(-0.492633\pi\)
0.660344 + 0.750963i \(0.270410\pi\)
\(978\) 0 0
\(979\) 1.86070 + 10.5526i 0.0594682 + 0.337261i
\(980\) −3.85998 6.68569i −0.123303 0.213567i
\(981\) 0 0
\(982\) −7.31892 + 12.6767i −0.233556 + 0.404531i
\(983\) 44.3155 + 16.1295i 1.41344 + 0.514452i 0.932139 0.362101i \(-0.117940\pi\)
0.481306 + 0.876553i \(0.340163\pi\)
\(984\) 0 0
\(985\) −7.86535 6.59981i −0.250611 0.210288i
\(986\) 12.9445 + 10.8617i 0.412237 + 0.345908i
\(987\) 0 0
\(988\) 1.55867 + 0.567309i 0.0495878 + 0.0180485i
\(989\) −14.6571 + 25.3869i −0.466069 + 0.807255i
\(990\) 0 0
\(991\) 2.18837 + 3.79036i 0.0695158 + 0.120405i 0.898688 0.438588i \(-0.144521\pi\)
−0.829172 + 0.558993i \(0.811188\pi\)
\(992\) 1.02540 + 5.81534i 0.0325565 + 0.184637i
\(993\) 0 0
\(994\) −75.2269 + 27.3803i −2.38605 + 0.868452i
\(995\) −2.88211 + 16.3452i −0.0913689 + 0.518179i
\(996\) 0 0
\(997\) −1.64278 + 1.37846i −0.0520275 + 0.0436562i −0.668431 0.743775i \(-0.733034\pi\)
0.616403 + 0.787431i \(0.288589\pi\)
\(998\) −19.5582 −0.619104
\(999\) 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 243.2.e.a.109.1 12
3.2 odd 2 243.2.e.d.109.2 12
9.2 odd 6 27.2.e.a.4.1 12
9.4 even 3 243.2.e.b.28.1 12
9.5 odd 6 243.2.e.c.28.2 12
9.7 even 3 81.2.e.a.64.2 12
27.2 odd 18 27.2.e.a.7.1 yes 12
27.4 even 9 729.2.a.d.1.1 6
27.5 odd 18 729.2.c.e.244.1 12
27.7 even 9 243.2.e.b.217.1 12
27.11 odd 18 243.2.e.d.136.2 12
27.13 even 9 729.2.c.b.487.6 12
27.14 odd 18 729.2.c.e.487.1 12
27.16 even 9 inner 243.2.e.a.136.1 12
27.20 odd 18 243.2.e.c.217.2 12
27.22 even 9 729.2.c.b.244.6 12
27.23 odd 18 729.2.a.a.1.6 6
27.25 even 9 81.2.e.a.19.2 12
36.11 even 6 432.2.u.c.193.1 12
45.2 even 12 675.2.u.b.274.4 24
45.29 odd 6 675.2.l.c.301.2 12
45.38 even 12 675.2.u.b.274.1 24
108.83 even 18 432.2.u.c.385.1 12
135.2 even 36 675.2.u.b.574.1 24
135.29 odd 18 675.2.l.c.601.2 12
135.83 even 36 675.2.u.b.574.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.4.1 12 9.2 odd 6
27.2.e.a.7.1 yes 12 27.2 odd 18
81.2.e.a.19.2 12 27.25 even 9
81.2.e.a.64.2 12 9.7 even 3
243.2.e.a.109.1 12 1.1 even 1 trivial
243.2.e.a.136.1 12 27.16 even 9 inner
243.2.e.b.28.1 12 9.4 even 3
243.2.e.b.217.1 12 27.7 even 9
243.2.e.c.28.2 12 9.5 odd 6
243.2.e.c.217.2 12 27.20 odd 18
243.2.e.d.109.2 12 3.2 odd 2
243.2.e.d.136.2 12 27.11 odd 18
432.2.u.c.193.1 12 36.11 even 6
432.2.u.c.385.1 12 108.83 even 18
675.2.l.c.301.2 12 45.29 odd 6
675.2.l.c.601.2 12 135.29 odd 18
675.2.u.b.274.1 24 45.38 even 12
675.2.u.b.274.4 24 45.2 even 12
675.2.u.b.574.1 24 135.2 even 36
675.2.u.b.574.4 24 135.83 even 36
729.2.a.a.1.6 6 27.23 odd 18
729.2.a.d.1.1 6 27.4 even 9
729.2.c.b.244.6 12 27.22 even 9
729.2.c.b.487.6 12 27.13 even 9
729.2.c.e.244.1 12 27.5 odd 18
729.2.c.e.487.1 12 27.14 odd 18