Properties

Label 243.2.e.d.136.2
Level $243$
Weight $2$
Character 243.136
Analytic conductor $1.940$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 136.2
Root \(0.500000 - 0.0126039i\) of defining polynomial
Character \(\chi\) \(=\) 243.136
Dual form 243.2.e.d.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.28765 + 1.08047i) q^{2} +(0.143341 + 0.812925i) q^{4} +(1.06142 + 0.386327i) q^{5} +(-0.678777 + 3.84954i) q^{7} +(0.987144 - 1.70978i) q^{8} +O(q^{10})\) \(q+(1.28765 + 1.08047i) q^{2} +(0.143341 + 0.812925i) q^{4} +(1.06142 + 0.386327i) q^{5} +(-0.678777 + 3.84954i) q^{7} +(0.987144 - 1.70978i) q^{8} +(0.949332 + 1.64429i) q^{10} +(1.75765 - 0.639734i) q^{11} +(-0.561203 + 0.470905i) q^{13} +(-5.03334 + 4.22347i) q^{14} +(4.66984 - 1.69968i) q^{16} +(-0.944822 - 1.63648i) q^{17} +(-1.37143 + 2.37538i) q^{19} +(-0.161910 + 0.918235i) q^{20} +(2.95446 + 1.07534i) q^{22} +(-1.01197 - 5.73916i) q^{23} +(-2.85285 - 2.39382i) q^{25} -1.23143 q^{26} -3.22668 q^{28} +(-4.07531 - 3.41959i) q^{29} +(0.232793 + 1.32023i) q^{31} +(4.13914 + 1.50652i) q^{32} +(0.551563 - 3.12807i) q^{34} +(-2.20765 + 3.82376i) q^{35} +(-1.69806 - 2.94112i) q^{37} +(-4.33245 + 1.57688i) q^{38} +(1.70831 - 1.43345i) q^{40} +(1.37607 - 1.15466i) q^{41} +(-4.72680 + 1.72041i) q^{43} +(0.771999 + 1.33714i) q^{44} +(4.89793 - 8.48346i) q^{46} +(0.296709 - 1.68272i) q^{47} +(-7.78035 - 2.83182i) q^{49} +(-1.08703 - 6.16483i) q^{50} +(-0.463253 - 0.388716i) q^{52} +2.84494 q^{53} +2.11276 q^{55} +(5.91183 + 4.96061i) q^{56} +(-1.55282 - 8.80649i) q^{58} +(10.5810 + 3.85116i) q^{59} +(0.908335 - 5.15142i) q^{61} +(-1.12672 + 1.95153i) q^{62} +(-1.26751 - 2.19540i) q^{64} +(-0.777597 + 0.283022i) q^{65} +(-1.44708 + 1.21424i) q^{67} +(1.19490 - 1.00264i) q^{68} +(-6.97415 + 2.53838i) q^{70} +(6.09193 + 10.5515i) q^{71} +(-4.94384 + 8.56298i) q^{73} +(0.991282 - 5.62184i) q^{74} +(-2.12759 - 0.774379i) q^{76} +(1.26962 + 7.20039i) q^{77} +(9.46285 + 7.94028i) q^{79} +5.61331 q^{80} +3.01948 q^{82} +(-8.94982 - 7.50979i) q^{83} +(-0.370641 - 2.10201i) q^{85} +(-7.94533 - 2.89186i) q^{86} +(0.641252 - 3.63672i) q^{88} +(2.86437 - 4.96123i) q^{89} +(-1.43183 - 2.48001i) q^{91} +(4.52045 - 1.64531i) q^{92} +(2.20018 - 1.84617i) q^{94} +(-2.37334 + 1.99147i) q^{95} +(0.322670 - 0.117442i) q^{97} +(-6.95870 - 12.0528i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/243\mathbb{Z}\right)^\times\).

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

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 \(-0.0752101\pi\)
−0.0617072 + 0.998094i \(0.519654\pi\)
\(3\) 0 0
\(4\) 0.143341 + 0.812925i 0.0716703 + 0.406463i
\(5\) 1.06142 + 0.386327i 0.474683 + 0.172771i 0.568273 0.822840i \(-0.307612\pi\)
−0.0935894 + 0.995611i \(0.529834\pi\)
\(6\) 0 0
\(7\) −0.678777 + 3.84954i −0.256554 + 1.45499i 0.535499 + 0.844536i \(0.320124\pi\)
−0.792053 + 0.610453i \(0.790988\pi\)
\(8\) 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 \(-0.520119\pi\)
0.593117 + 0.805116i \(0.297897\pi\)
\(12\) 0 0
\(13\) −0.561203 + 0.470905i −0.155650 + 0.130606i −0.717287 0.696778i \(-0.754616\pi\)
0.561637 + 0.827384i \(0.310172\pi\)
\(14\) −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 \(-0.240262\pi\)
−0.957557 + 0.288243i \(0.906929\pi\)
\(18\) 0 0
\(19\) −1.37143 + 2.37538i −0.314627 + 0.544950i −0.979358 0.202133i \(-0.935213\pi\)
0.664731 + 0.747083i \(0.268546\pi\)
\(20\) −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 −0.887697 0.460428i \(-0.847696\pi\)
0.676687 0.736271i \(-0.263415\pi\)
\(24\) 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 \(-0.442223\pi\)
−0.937283 + 0.348570i \(0.886667\pi\)
\(30\) 0 0
\(31\) 0.232793 + 1.32023i 0.0418108 + 0.237121i 0.998550 0.0538247i \(-0.0171412\pi\)
−0.956740 + 0.290946i \(0.906030\pi\)
\(32\) 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 0.692017 0.721881i \(-0.256722\pi\)
−0.971176 + 0.238364i \(0.923389\pi\)
\(38\) −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 \(-0.677425\pi\)
0.743886 + 0.668307i \(0.232981\pi\)
\(42\) 0 0
\(43\) −4.72680 + 1.72041i −0.720830 + 0.262361i −0.676278 0.736646i \(-0.736408\pi\)
−0.0445518 + 0.999007i \(0.514186\pi\)
\(44\) 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 \(-0.904674\pi\)
0.998771 + 0.0495697i \(0.0157850\pi\)
\(48\) 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 \(-0.437402\pi\)
0.195391 + 0.980725i \(0.437402\pi\)
\(54\) 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 \(-0.127024\pi\)
0.456099 + 0.889929i \(0.349246\pi\)
\(60\) 0 0
\(61\) 0.908335 5.15142i 0.116300 0.659572i −0.869798 0.493408i \(-0.835751\pi\)
0.986098 0.166164i \(-0.0531381\pi\)
\(62\) −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 −0.726888 0.686756i \(-0.759034\pi\)
0.550099 + 0.835099i \(0.314590\pi\)
\(68\) 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 0.959800 + 0.280684i \(0.0905613\pi\)
−0.236821 + 0.971553i \(0.576105\pi\)
\(72\) 0 0
\(73\) −4.94384 + 8.56298i −0.578633 + 1.00222i 0.417004 + 0.908905i \(0.363080\pi\)
−0.995637 + 0.0933164i \(0.970253\pi\)
\(74\) 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 0.994557 0.104189i \(-0.0332248\pi\)
0.0700965 + 0.997540i \(0.477669\pi\)
\(80\) 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 \(-0.499340\pi\)
−0.984445 + 0.175691i \(0.943784\pi\)
\(84\) 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 \(-0.735137\pi\)
0.976954 + 0.213452i \(0.0684706\pi\)
\(90\) 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 −0.325587 0.945512i \(-0.605562\pi\)
0.358349 + 0.933588i \(0.383340\pi\)
\(98\) −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 0.342454 + 0.939535i \(0.388742\pi\)
−0.643141 + 0.765748i \(0.722369\pi\)
\(102\) 0 0
\(103\) 14.8594 + 5.40837i 1.46414 + 0.532902i 0.946501 0.322700i \(-0.104590\pi\)
0.517635 + 0.855602i \(0.326813\pi\)
\(104\) 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 \(-0.794637\pi\)
−0.798999 + 0.601332i \(0.794637\pi\)
\(108\) 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 \(-0.776328\pi\)
−0.999990 + 0.00455445i \(0.998550\pi\)
\(114\) 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 −0.888775 0.458344i \(-0.848443\pi\)
0.841325 + 0.540529i \(0.181776\pi\)
\(128\) 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 0.986292 + 0.165007i \(0.0527646\pi\)
−0.870376 + 0.492388i \(0.836124\pi\)
\(132\) 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 \(-0.0446903\pi\)
0.0341275 + 0.999417i \(0.489135\pi\)
\(138\) 0 0
\(139\) 1.50326 + 8.52542i 0.127505 + 0.723116i 0.979788 + 0.200036i \(0.0641060\pi\)
−0.852284 + 0.523080i \(0.824783\pi\)
\(140\) −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 \(-0.754402\pi\)
0.562195 + 0.827005i \(0.309957\pi\)
\(150\) 0 0
\(151\) 9.87937 3.59580i 0.803972 0.292622i 0.0928406 0.995681i \(-0.470405\pi\)
0.711131 + 0.703059i \(0.248183\pi\)
\(152\) 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 0.328488 0.944508i \(-0.393461\pi\)
−0.355482 + 0.934683i \(0.615683\pi\)
\(158\) 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 \(-0.415718\pi\)
−0.419915 + 0.907563i \(0.637940\pi\)
\(168\) 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 \(-0.378348\pi\)
0.882105 + 0.471053i \(0.156126\pi\)
\(174\) 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 \(-0.178618\pi\)
−0.884184 + 0.467138i \(0.845285\pi\)
\(180\) 0 0
\(181\) 10.5866 18.3366i 0.786898 1.36295i −0.140961 0.990015i \(-0.545019\pi\)
0.927859 0.372932i \(-0.121647\pi\)
\(182\) 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 \(-0.393494\pi\)
−0.873168 + 0.487419i \(0.837938\pi\)
\(192\) 0 0
\(193\) −1.93723 10.9866i −0.139445 0.790833i −0.971661 0.236380i \(-0.924039\pi\)
0.832215 0.554452i \(-0.187072\pi\)
\(194\) 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 \(-0.938299\pi\)
0.657456 + 0.753493i \(0.271632\pi\)
\(198\) 0 0
\(199\) 7.34694 + 12.7253i 0.520811 + 0.902071i 0.999707 + 0.0241994i \(0.00770367\pi\)
−0.478896 + 0.877872i \(0.658963\pi\)
\(200\) −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 0.0750892 0.997177i \(-0.476076\pi\)
−0.583451 + 0.812148i \(0.698298\pi\)
\(212\) 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 0.890867 + 0.454265i \(0.150098\pi\)
−0.992509 + 0.122175i \(0.961013\pi\)
\(224\) −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 \(-0.654219\pi\)
0.212016 + 0.977266i \(0.431997\pi\)
\(228\) 0 0
\(229\) 12.3761 10.3848i 0.817837 0.686247i −0.134628 0.990896i \(-0.542984\pi\)
0.952464 + 0.304650i \(0.0985394\pi\)
\(230\) 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 −0.997157 0.0753527i \(-0.975992\pi\)
0.433321 0.901240i \(-0.357342\pi\)
\(234\) 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 \(-0.0713692\pi\)
−0.992216 + 0.124529i \(0.960258\pi\)
\(240\) 0 0
\(241\) −4.22985 3.54926i −0.272468 0.228628i 0.496307 0.868147i \(-0.334689\pi\)
−0.768775 + 0.639519i \(0.779134\pi\)
\(242\) −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 −0.299310 0.954156i \(-0.596756\pi\)
0.975978 0.217868i \(-0.0699102\pi\)
\(252\) 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 \(-0.874795\pi\)
0.217068 + 0.976156i \(0.430351\pi\)
\(258\) 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 \(-0.916904\pi\)
0.996129 + 0.0878987i \(0.0280152\pi\)
\(264\) 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 \(-0.503460\pi\)
−0.0108689 + 0.999941i \(0.503460\pi\)
\(270\) 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 −0.520183 0.854055i \(-0.674136\pi\)
0.780916 0.624636i \(-0.214752\pi\)
\(278\) −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 \(-0.681202\pi\)
0.128511 + 0.991708i \(0.458980\pi\)
\(282\) 0 0
\(283\) −11.0219 + 9.24848i −0.655185 + 0.549765i −0.908639 0.417582i \(-0.862878\pi\)
0.253454 + 0.967347i \(0.418433\pi\)
\(284\) −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 −0.966363 0.257182i \(-0.917206\pi\)
0.820123 0.572187i \(-0.193905\pi\)
\(294\) 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 0.863591 + 0.504193i \(0.168210\pi\)
0.00484869 + 0.999988i \(0.498457\pi\)
\(308\) −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 \(-0.852105\pi\)
0.286042 + 0.958217i \(0.407660\pi\)
\(312\) 0 0
\(313\) −20.7555 + 7.55439i −1.17317 + 0.426999i −0.853785 0.520625i \(-0.825699\pi\)
−0.319386 + 0.947625i \(0.603477\pi\)
\(314\) −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 −0.774608 0.632441i \(-0.782053\pi\)
0.944201 0.329369i \(-0.106836\pi\)
\(318\) 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 −0.980406 0.196987i \(-0.936884\pi\)
0.988654 + 0.150211i \(0.0479953\pi\)
\(332\) 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 −0.634013 0.773322i \(-0.718594\pi\)
0.651478 + 0.758667i \(0.274149\pi\)
\(338\) −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 0.875224 + 0.483718i \(0.160714\pi\)
−0.657000 + 0.753891i \(0.728175\pi\)
\(348\) 0 0
\(349\) 16.2221 + 13.6119i 0.868347 + 0.728630i 0.963749 0.266809i \(-0.0859693\pi\)
−0.0954022 + 0.995439i \(0.530414\pi\)
\(350\) 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 \(-0.0622350\pi\)
−0.0209824 + 0.999780i \(0.506679\pi\)
\(354\) 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 \(-0.744307\pi\)
0.970400 + 0.241502i \(0.0776400\pi\)
\(360\) 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 −0.805923 0.592021i \(-0.798330\pi\)
−0.236829 + 0.971551i \(0.576108\pi\)
\(368\) −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 0.285209 0.958465i \(-0.407937\pi\)
−0.397607 + 0.917556i \(0.630159\pi\)
\(374\) −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 \(-0.221431\pi\)
0.176094 + 0.984373i \(0.443654\pi\)
\(384\) 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 \(-0.452589\pi\)
0.749348 + 0.662177i \(0.230367\pi\)
\(390\) 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 0.495143 + 0.868811i \(0.335116\pi\)
−0.999984 + 0.00559897i \(0.998218\pi\)
\(398\) −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 −0.762889 0.646529i \(-0.776220\pi\)
0.495755 0.868462i \(-0.334891\pi\)
\(402\) 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 0.359849 + 0.933010i \(0.382828\pi\)
−0.0190394 + 0.999819i \(0.506061\pi\)
\(410\) 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 \(-0.599118\pi\)
0.884245 + 0.467023i \(0.154674\pi\)
\(420\) 0 0
\(421\) 17.0025 6.18839i 0.828649 0.301604i 0.107345 0.994222i \(-0.465765\pi\)
0.721304 + 0.692618i \(0.243543\pi\)
\(422\) −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 \(-0.745783\pi\)
−0.697677 + 0.716412i \(0.745783\pi\)
\(432\) 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 −0.912281 0.409564i \(-0.865681\pi\)
0.997343 0.0728458i \(-0.0232081\pi\)
\(440\) 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 \(-0.785348\pi\)
−0.197017 + 0.980400i \(0.563125\pi\)
\(444\) 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 \(-0.242270\pi\)
−0.959356 + 0.282198i \(0.908936\pi\)
\(450\) 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 0.496008 0.868318i \(-0.334799\pi\)
−0.768995 + 0.639254i \(0.779243\pi\)
\(458\) 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 \(-0.455948\pi\)
−0.951436 + 0.307845i \(0.900392\pi\)
\(462\) 0 0
\(463\) −1.52736 8.66211i −0.0709826 0.402562i −0.999510 0.0312986i \(-0.990036\pi\)
0.928527 0.371264i \(-0.121075\pi\)
\(464\) −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 \(-0.751438\pi\)
0.964747 + 0.263180i \(0.0847713\pi\)
\(468\) 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 −0.695391 0.718632i \(-0.744769\pi\)
0.899240 0.437455i \(-0.144120\pi\)
\(480\) 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 \(-0.451846\pi\)
−0.520001 + 0.854166i \(0.674068\pi\)
\(492\) 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 −0.421099 0.907015i \(-0.638355\pi\)
0.820112 + 0.572203i \(0.193911\pi\)
\(500\) 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 0.887613 + 0.460590i \(0.152362\pi\)
−0.0449234 + 0.998990i \(0.514304\pi\)
\(504\) 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 0.930442 + 0.366439i \(0.119423\pi\)
−0.749000 + 0.662570i \(0.769466\pi\)
\(510\) 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 \(-0.888480\pi\)
0.766869 + 0.641804i \(0.221814\pi\)
\(522\) 0 0
\(523\) −16.6467 28.8330i −0.727911 1.26078i −0.957765 0.287554i \(-0.907158\pi\)
0.229854 0.973225i \(-0.426175\pi\)
\(524\) −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 0.803576 + 0.595202i \(0.202928\pi\)
−0.958685 + 0.284468i \(0.908183\pi\)
\(548\) −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 \(-0.224839\pi\)
−0.942473 + 0.334283i \(0.891506\pi\)
\(558\) 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 −0.986746 0.162270i \(-0.948118\pi\)
0.871739 0.489971i \(-0.162993\pi\)
\(564\) 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 \(-0.192196\pi\)
−0.416206 + 0.909270i \(0.636640\pi\)
\(570\) 0 0
\(571\) −4.57089 25.9228i −0.191286 1.08483i −0.917610 0.397483i \(-0.869884\pi\)
0.726324 0.687352i \(-0.241227\pi\)
\(572\) −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 0.998978 0.0452074i \(-0.0143949\pi\)
−0.538640 + 0.842536i \(0.681062\pi\)
\(578\) 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 −0.889670 0.456603i \(-0.849066\pi\)
0.992184 0.124781i \(-0.0398230\pi\)
\(588\) 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 \(-0.0637397\pi\)
0.980018 + 0.198908i \(0.0637397\pi\)
\(594\) 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 \(-0.385640\pi\)
−0.332412 + 0.943134i \(0.607862\pi\)
\(600\) 0 0
\(601\) −2.93936 + 16.6699i −0.119899 + 0.679980i 0.864309 + 0.502962i \(0.167756\pi\)
−0.984208 + 0.177019i \(0.943355\pi\)
\(602\) 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 −0.631925 0.775030i \(-0.717735\pi\)
0.653523 + 0.756907i \(0.273290\pi\)
\(608\) −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 −0.321081 0.947052i \(-0.604046\pi\)
0.980711 0.195461i \(-0.0626204\pi\)
\(614\) −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 0.954090 + 0.299521i \(0.0968267\pi\)
−0.794109 + 0.607775i \(0.792062\pi\)
\(618\) 0 0
\(619\) 6.50045 + 5.45453i 0.261275 + 0.219236i 0.764009 0.645205i \(-0.223228\pi\)
−0.502734 + 0.864441i \(0.667673\pi\)
\(620\) −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 0.849749 0.527187i \(-0.176753\pi\)
−0.881432 + 0.472311i \(0.843420\pi\)
\(632\) 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 −0.815696 0.578481i \(-0.803646\pi\)
0.964355 0.264610i \(-0.0852433\pi\)
\(642\) 0 0
\(643\) 6.48582 + 2.36064i 0.255776 + 0.0930947i 0.466726 0.884402i \(-0.345434\pi\)
−0.210950 + 0.977497i \(0.567656\pi\)
\(644\) 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 \(-0.538825\pi\)
−0.121671 + 0.992570i \(0.538825\pi\)
\(648\) 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 \(-0.210144\pi\)
0.210881 + 0.977512i \(0.432367\pi\)
\(654\) 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 \(-0.643916\pi\)
0.243531 + 0.969893i \(0.421694\pi\)
\(660\) 0 0
\(661\) 8.93594 7.49814i 0.347568 0.291644i −0.452245 0.891894i \(-0.649377\pi\)
0.799813 + 0.600250i \(0.204932\pi\)
\(662\) 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 0.932626 + 0.360845i \(0.117512\pi\)
0.517312 + 0.855797i \(0.326933\pi\)
\(674\) 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 \(-0.420909\pi\)
−0.911860 + 0.410501i \(0.865354\pi\)
\(678\) 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 \(-0.726994\pi\)
0.982094 + 0.188391i \(0.0603272\pi\)
\(684\) 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 −0.647040 0.762456i \(-0.723993\pi\)
−0.00556457 + 0.999985i \(0.501771\pi\)
\(692\) 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 \(-0.517566\pi\)
−0.0551575 + 0.998478i \(0.517566\pi\)
\(702\) 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 −0.715419 0.698696i \(-0.753764\pi\)
0.911242 0.411872i \(-0.135125\pi\)
\(710\) −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 −0.949285 0.314418i \(-0.898191\pi\)
0.202349 0.979314i \(-0.435143\pi\)
\(720\) 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 0.620667 0.784075i \(-0.286862\pi\)
−0.664385 + 0.747390i \(0.731306\pi\)
\(728\) −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 0.979575 0.201078i \(-0.0644444\pi\)
−0.989272 + 0.146083i \(0.953333\pi\)
\(734\) −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 0.600024 0.799982i \(-0.295157\pi\)
−0.992817 + 0.119646i \(0.961824\pi\)
\(740\) 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 \(-0.843857\pi\)
0.310772 + 0.950485i \(0.399412\pi\)
\(744\) 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 0.267892 0.963449i \(-0.413673\pi\)
−0.414075 + 0.910243i \(0.635895\pi\)
\(752\) −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 \(-0.495658\pi\)
−0.632278 + 0.774741i \(0.717880\pi\)
\(762\) 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 −0.231331 0.972875i \(-0.574308\pi\)
0.917925 + 0.396755i \(0.129864\pi\)
\(770\) −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 −0.971158 0.238437i \(-0.923365\pi\)
0.279087 0.960266i \(-0.409968\pi\)
\(774\) 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 0.981309 0.192441i \(-0.0616404\pi\)
−0.987947 + 0.154792i \(0.950529\pi\)
\(788\) −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 \(-0.574661\pi\)
0.917484 + 0.397772i \(0.130216\pi\)
\(798\) 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 \(-0.566132\pi\)
−0.206268 + 0.978495i \(0.566132\pi\)
\(810\) 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 \(-0.765588\pi\)
−0.135817 + 0.990734i \(0.543366\pi\)
\(822\) 0 0
\(823\) 3.34322 2.80529i 0.116537 0.0977864i −0.582657 0.812718i \(-0.697987\pi\)
0.699194 + 0.714932i \(0.253542\pi\)
\(824\) 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 0.974795 + 0.223102i \(0.0716184\pi\)
−0.294185 + 0.955748i \(0.595048\pi\)
\(828\) 0 0
\(829\) 16.4433 28.4807i 0.571101 0.989176i −0.425352 0.905028i \(-0.639850\pi\)
0.996453 0.0841481i \(-0.0268169\pi\)
\(830\) 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 \(-0.0938620\pi\)
−0.120053 + 0.992767i \(0.538306\pi\)
\(840\) 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 −0.249396 0.968402i \(-0.580232\pi\)
0.431428 + 0.902147i \(0.358010\pi\)
\(854\) 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 0.577324 + 0.816515i \(0.304097\pi\)
−0.821772 + 0.569817i \(0.807014\pi\)
\(858\) 0 0
\(859\) −33.6921 12.2629i −1.14956 0.418406i −0.304203 0.952607i \(-0.598390\pi\)
−0.845357 + 0.534201i \(0.820612\pi\)
\(860\) −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 \(-0.383833\pi\)
0.356903 + 0.934142i \(0.383833\pi\)
\(864\) 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 −0.337739 0.941240i \(-0.609662\pi\)
0.868292 + 0.496053i \(0.165218\pi\)
\(878\) 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 0.984308 + 0.176459i \(0.0564644\pi\)
−0.339336 + 0.940665i \(0.610202\pi\)
\(882\) 0 0
\(883\) 8.72326 15.1091i 0.293561 0.508463i −0.681088 0.732201i \(-0.738493\pi\)
0.974649 + 0.223739i \(0.0718263\pi\)
\(884\) −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 −0.565906 0.824469i \(-0.691474\pi\)
0.249793 0.968299i \(-0.419637\pi\)
\(888\) 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 −0.748236 0.663433i \(-0.769099\pi\)
−0.146735 + 0.989176i \(0.546877\pi\)
\(908\) −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 0.787529 + 0.616278i \(0.211360\pi\)
−0.950815 + 0.309761i \(0.899751\pi\)
\(912\) 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 \(-0.419132\pi\)
0.814685 + 0.579903i \(0.196910\pi\)
\(930\) 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 −0.662477 0.749082i \(-0.730495\pi\)
0.979963 + 0.199180i \(0.0638280\pi\)
\(938\) 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 \(-0.00376360\pi\)
−0.943671 + 0.330886i \(0.892652\pi\)
\(942\) 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 \(-0.189179\pi\)
−0.407568 + 0.913175i \(0.633623\pi\)
\(948\) 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 \(-0.924042\pi\)
0.690534 + 0.723300i \(0.257376\pi\)
\(954\) 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 0.582915 0.812533i \(-0.301912\pi\)
−0.0757476 + 0.997127i \(0.524134\pi\)
\(968\) 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 \(-0.680529\pi\)
−0.537230 + 0.843436i \(0.680529\pi\)
\(972\) 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 \(-0.507367\pi\)
−0.660344 + 0.750963i \(0.729590\pi\)
\(978\) 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 \(-0.882060\pi\)
−0.481306 + 0.876553i \(0.659837\pi\)
\(984\) 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 −0.829172 0.558993i \(-0.811188\pi\)
0.898688 + 0.438588i \(0.144521\pi\)
\(992\) −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 0.616403 0.787431i \(-0.288589\pi\)
−0.668431 + 0.743775i \(0.733034\pi\)
\(998\) 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.d.136.2 12
3.2 odd 2 243.2.e.a.136.1 12
9.2 odd 6 243.2.e.b.217.1 12
9.4 even 3 27.2.e.a.7.1 yes 12
9.5 odd 6 81.2.e.a.19.2 12
9.7 even 3 243.2.e.c.217.2 12
27.2 odd 18 729.2.c.b.244.6 12
27.4 even 9 243.2.e.c.28.2 12
27.5 odd 18 243.2.e.a.109.1 12
27.7 even 9 729.2.a.a.1.6 6
27.11 odd 18 729.2.c.b.487.6 12
27.13 even 9 27.2.e.a.4.1 12
27.14 odd 18 81.2.e.a.64.2 12
27.16 even 9 729.2.c.e.487.1 12
27.20 odd 18 729.2.a.d.1.1 6
27.22 even 9 inner 243.2.e.d.109.2 12
27.23 odd 18 243.2.e.b.28.1 12
27.25 even 9 729.2.c.e.244.1 12
36.31 odd 6 432.2.u.c.385.1 12
45.4 even 6 675.2.l.c.601.2 12
45.13 odd 12 675.2.u.b.574.4 24
45.22 odd 12 675.2.u.b.574.1 24
108.67 odd 18 432.2.u.c.193.1 12
135.13 odd 36 675.2.u.b.274.1 24
135.67 odd 36 675.2.u.b.274.4 24
135.94 even 18 675.2.l.c.301.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.4.1 12 27.13 even 9
27.2.e.a.7.1 yes 12 9.4 even 3
81.2.e.a.19.2 12 9.5 odd 6
81.2.e.a.64.2 12 27.14 odd 18
243.2.e.a.109.1 12 27.5 odd 18
243.2.e.a.136.1 12 3.2 odd 2
243.2.e.b.28.1 12 27.23 odd 18
243.2.e.b.217.1 12 9.2 odd 6
243.2.e.c.28.2 12 27.4 even 9
243.2.e.c.217.2 12 9.7 even 3
243.2.e.d.109.2 12 27.22 even 9 inner
243.2.e.d.136.2 12 1.1 even 1 trivial
432.2.u.c.193.1 12 108.67 odd 18
432.2.u.c.385.1 12 36.31 odd 6
675.2.l.c.301.2 12 135.94 even 18
675.2.l.c.601.2 12 45.4 even 6
675.2.u.b.274.1 24 135.13 odd 36
675.2.u.b.274.4 24 135.67 odd 36
675.2.u.b.574.1 24 45.22 odd 12
675.2.u.b.574.4 24 45.13 odd 12
729.2.a.a.1.6 6 27.7 even 9
729.2.a.d.1.1 6 27.20 odd 18
729.2.c.b.244.6 12 27.2 odd 18
729.2.c.b.487.6 12 27.11 odd 18
729.2.c.e.244.1 12 27.25 even 9
729.2.c.e.487.1 12 27.16 even 9