Properties

Label 729.2.e.i.325.1
Level $729$
Weight $2$
Character 729.325
Analytic conductor $5.821$
Analytic rank $0$
Dimension $6$
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] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, 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("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 325.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 729.325
Dual form 729.2.e.i.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.93969 - 1.62760i) q^{2} +(0.766044 - 4.34445i) q^{4} +(-0.439693 + 0.160035i) q^{5} +(-0.560307 - 3.17766i) q^{7} +(-3.05303 - 5.28801i) q^{8} +O(q^{10})\) \(q+(1.93969 - 1.62760i) q^{2} +(0.766044 - 4.34445i) q^{4} +(-0.439693 + 0.160035i) q^{5} +(-0.560307 - 3.17766i) q^{7} +(-3.05303 - 5.28801i) q^{8} +(-0.592396 + 1.02606i) q^{10} +(2.91875 + 1.06234i) q^{11} +(-1.67365 - 1.40436i) q^{13} +(-6.25877 - 5.25173i) q^{14} +(-6.23783 - 2.27038i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-0.0209445 - 0.0362770i) q^{19} +(0.358441 + 2.03282i) q^{20} +(7.39053 - 2.68993i) q^{22} +(1.06031 - 6.01330i) q^{23} +(-3.66250 + 3.07321i) q^{25} -5.53209 q^{26} -14.2344 q^{28} +(5.03596 - 4.22567i) q^{29} +(-1.08125 + 6.13208i) q^{31} +(-4.31908 + 1.57202i) q^{32} +(1.31908 + 7.48086i) q^{34} +(0.754900 + 1.30753i) q^{35} +(-1.79813 + 3.11446i) q^{37} +(-0.0996702 - 0.0362770i) q^{38} +(2.18866 + 1.83651i) q^{40} +(5.90033 + 4.95096i) q^{41} +(0.553033 + 0.201288i) q^{43} +(6.85117 - 11.8666i) q^{44} +(-7.73055 - 13.3897i) q^{46} +(-1.67752 - 9.51368i) q^{47} +(-3.20574 + 1.16679i) q^{49} +(-2.10220 + 11.9221i) q^{50} +(-7.38326 + 6.19529i) q^{52} +4.95811 q^{53} -1.45336 q^{55} +(-15.0929 + 12.6644i) q^{56} +(2.89053 - 16.3930i) q^{58} +(8.01754 - 2.91815i) q^{59} +(-0.220285 - 1.24930i) q^{61} +(7.88326 + 13.6542i) q^{62} +(0.819078 - 1.41868i) q^{64} +(0.960637 + 0.349643i) q^{65} +(7.66637 + 6.43285i) q^{67} +(10.1382 + 8.50692i) q^{68} +(3.59240 + 1.30753i) q^{70} +(-5.91534 + 10.2457i) q^{71} +(4.11721 + 7.13122i) q^{73} +(1.58125 + 8.96773i) q^{74} +(-0.173648 + 0.0632028i) q^{76} +(1.74035 - 9.87003i) q^{77} +(8.46451 - 7.10257i) q^{79} +3.10607 q^{80} +19.5030 q^{82} +(-1.15657 + 0.970481i) q^{83} +(0.243756 - 1.38241i) q^{85} +(1.40033 - 0.509678i) q^{86} +(-3.29339 - 18.6777i) q^{88} +(7.93629 + 13.7461i) q^{89} +(-3.52481 + 6.10516i) q^{91} +(-25.3123 - 9.21291i) q^{92} +(-18.7383 - 15.7233i) q^{94} +(0.0150147 + 0.0125989i) q^{95} +(-17.5214 - 6.37727i) q^{97} +(-4.31908 + 7.48086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31} - 9 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} - 15 q^{38} - 18 q^{40} + 21 q^{41} - 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} - 9 q^{49} - 12 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 21 q^{56} + 3 q^{59} - 27 q^{61} + 12 q^{62} - 12 q^{64} - 3 q^{65} + 27 q^{67} + 27 q^{68} + 18 q^{70} + 9 q^{71} - 6 q^{73} + 12 q^{74} - 24 q^{77} + 18 q^{79} - 6 q^{80} + 36 q^{82} + 15 q^{83} + 9 q^{85} - 6 q^{86} + 27 q^{88} + 6 q^{91} - 51 q^{92} - 27 q^{94} - 30 q^{95} - 36 q^{97} - 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93969 1.62760i 1.37157 1.15088i 0.399354 0.916797i \(-0.369234\pi\)
0.972216 0.234087i \(-0.0752101\pi\)
\(3\) 0 0
\(4\) 0.766044 4.34445i 0.383022 2.17223i
\(5\) −0.439693 + 0.160035i −0.196637 + 0.0715698i −0.438461 0.898750i \(-0.644476\pi\)
0.241825 + 0.970320i \(0.422254\pi\)
\(6\) 0 0
\(7\) −0.560307 3.17766i −0.211776 1.20104i −0.886414 0.462894i \(-0.846811\pi\)
0.674637 0.738149i \(-0.264300\pi\)
\(8\) −3.05303 5.28801i −1.07941 1.86959i
\(9\) 0 0
\(10\) −0.592396 + 1.02606i −0.187332 + 0.324469i
\(11\) 2.91875 + 1.06234i 0.880036 + 0.320307i 0.742224 0.670152i \(-0.233771\pi\)
0.137811 + 0.990458i \(0.455993\pi\)
\(12\) 0 0
\(13\) −1.67365 1.40436i −0.464186 0.389499i 0.380482 0.924788i \(-0.375758\pi\)
−0.844669 + 0.535290i \(0.820202\pi\)
\(14\) −6.25877 5.25173i −1.67273 1.40358i
\(15\) 0 0
\(16\) −6.23783 2.27038i −1.55946 0.567596i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) −0.0209445 0.0362770i −0.00480501 0.00832251i 0.863613 0.504155i \(-0.168196\pi\)
−0.868418 + 0.495833i \(0.834863\pi\)
\(20\) 0.358441 + 2.03282i 0.0801498 + 0.454552i
\(21\) 0 0
\(22\) 7.39053 2.68993i 1.57567 0.573496i
\(23\) 1.06031 6.01330i 0.221089 1.25386i −0.648932 0.760846i \(-0.724784\pi\)
0.870021 0.493014i \(-0.164105\pi\)
\(24\) 0 0
\(25\) −3.66250 + 3.07321i −0.732501 + 0.614641i
\(26\) −5.53209 −1.08493
\(27\) 0 0
\(28\) −14.2344 −2.69005
\(29\) 5.03596 4.22567i 0.935154 0.784688i −0.0415813 0.999135i \(-0.513240\pi\)
0.976735 + 0.214448i \(0.0687951\pi\)
\(30\) 0 0
\(31\) −1.08125 + 6.13208i −0.194199 + 1.10135i 0.719357 + 0.694641i \(0.244437\pi\)
−0.913555 + 0.406714i \(0.866674\pi\)
\(32\) −4.31908 + 1.57202i −0.763512 + 0.277896i
\(33\) 0 0
\(34\) 1.31908 + 7.48086i 0.226220 + 1.28296i
\(35\) 0.754900 + 1.30753i 0.127601 + 0.221012i
\(36\) 0 0
\(37\) −1.79813 + 3.11446i −0.295611 + 0.512014i −0.975127 0.221647i \(-0.928857\pi\)
0.679516 + 0.733661i \(0.262190\pi\)
\(38\) −0.0996702 0.0362770i −0.0161686 0.00588491i
\(39\) 0 0
\(40\) 2.18866 + 1.83651i 0.346058 + 0.290377i
\(41\) 5.90033 + 4.95096i 0.921477 + 0.773211i 0.974268 0.225395i \(-0.0723672\pi\)
−0.0527908 + 0.998606i \(0.516812\pi\)
\(42\) 0 0
\(43\) 0.553033 + 0.201288i 0.0843368 + 0.0306961i 0.383844 0.923398i \(-0.374600\pi\)
−0.299507 + 0.954094i \(0.596822\pi\)
\(44\) 6.85117 11.8666i 1.03285 1.78895i
\(45\) 0 0
\(46\) −7.73055 13.3897i −1.13981 1.97420i
\(47\) −1.67752 9.51368i −0.244691 1.38771i −0.821209 0.570628i \(-0.806700\pi\)
0.576517 0.817085i \(-0.304411\pi\)
\(48\) 0 0
\(49\) −3.20574 + 1.16679i −0.457962 + 0.166685i
\(50\) −2.10220 + 11.9221i −0.297295 + 1.68605i
\(51\) 0 0
\(52\) −7.38326 + 6.19529i −1.02387 + 0.859132i
\(53\) 4.95811 0.681049 0.340524 0.940236i \(-0.389395\pi\)
0.340524 + 0.940236i \(0.389395\pi\)
\(54\) 0 0
\(55\) −1.45336 −0.195971
\(56\) −15.0929 + 12.6644i −2.01687 + 1.69235i
\(57\) 0 0
\(58\) 2.89053 16.3930i 0.379545 2.15251i
\(59\) 8.01754 2.91815i 1.04379 0.379910i 0.237477 0.971393i \(-0.423679\pi\)
0.806318 + 0.591483i \(0.201457\pi\)
\(60\) 0 0
\(61\) −0.220285 1.24930i −0.0282046 0.159956i 0.967452 0.253053i \(-0.0814346\pi\)
−0.995657 + 0.0930965i \(0.970324\pi\)
\(62\) 7.88326 + 13.6542i 1.00117 + 1.73409i
\(63\) 0 0
\(64\) 0.819078 1.41868i 0.102385 0.177336i
\(65\) 0.960637 + 0.349643i 0.119152 + 0.0433679i
\(66\) 0 0
\(67\) 7.66637 + 6.43285i 0.936597 + 0.785898i 0.976990 0.213286i \(-0.0684166\pi\)
−0.0403931 + 0.999184i \(0.512861\pi\)
\(68\) 10.1382 + 8.50692i 1.22943 + 1.03162i
\(69\) 0 0
\(70\) 3.59240 + 1.30753i 0.429373 + 0.156279i
\(71\) −5.91534 + 10.2457i −0.702022 + 1.21594i 0.265733 + 0.964047i \(0.414386\pi\)
−0.967755 + 0.251892i \(0.918947\pi\)
\(72\) 0 0
\(73\) 4.11721 + 7.13122i 0.481883 + 0.834646i 0.999784 0.0207947i \(-0.00661964\pi\)
−0.517901 + 0.855441i \(0.673286\pi\)
\(74\) 1.58125 + 8.96773i 0.183817 + 1.04248i
\(75\) 0 0
\(76\) −0.173648 + 0.0632028i −0.0199188 + 0.00724985i
\(77\) 1.74035 9.87003i 0.198332 1.12479i
\(78\) 0 0
\(79\) 8.46451 7.10257i 0.952332 0.799101i −0.0273571 0.999626i \(-0.508709\pi\)
0.979689 + 0.200525i \(0.0642647\pi\)
\(80\) 3.10607 0.347269
\(81\) 0 0
\(82\) 19.5030 2.15375
\(83\) −1.15657 + 0.970481i −0.126950 + 0.106524i −0.704052 0.710148i \(-0.748628\pi\)
0.577102 + 0.816672i \(0.304184\pi\)
\(84\) 0 0
\(85\) 0.243756 1.38241i 0.0264390 0.149943i
\(86\) 1.40033 0.509678i 0.151001 0.0549600i
\(87\) 0 0
\(88\) −3.29339 18.6777i −0.351076 1.99105i
\(89\) 7.93629 + 13.7461i 0.841245 + 1.45708i 0.888843 + 0.458212i \(0.151510\pi\)
−0.0475978 + 0.998867i \(0.515157\pi\)
\(90\) 0 0
\(91\) −3.52481 + 6.10516i −0.369501 + 0.639995i
\(92\) −25.3123 9.21291i −2.63899 0.960513i
\(93\) 0 0
\(94\) −18.7383 15.7233i −1.93271 1.62173i
\(95\) 0.0150147 + 0.0125989i 0.00154048 + 0.00129262i
\(96\) 0 0
\(97\) −17.5214 6.37727i −1.77903 0.647514i −0.999784 0.0207958i \(-0.993380\pi\)
−0.779246 0.626718i \(-0.784398\pi\)
\(98\) −4.31908 + 7.48086i −0.436293 + 0.755681i
\(99\) 0 0
\(100\) 10.5458 + 18.2658i 1.05458 + 1.82658i
\(101\) 1.57785 + 8.94842i 0.157002 + 0.890401i 0.956933 + 0.290309i \(0.0937582\pi\)
−0.799931 + 0.600092i \(0.795131\pi\)
\(102\) 0 0
\(103\) −0.245100 + 0.0892091i −0.0241504 + 0.00879003i −0.354067 0.935220i \(-0.615202\pi\)
0.329917 + 0.944010i \(0.392979\pi\)
\(104\) −2.31655 + 13.1378i −0.227157 + 1.28827i
\(105\) 0 0
\(106\) 9.61721 8.06980i 0.934106 0.783808i
\(107\) 4.04189 0.390744 0.195372 0.980729i \(-0.437409\pi\)
0.195372 + 0.980729i \(0.437409\pi\)
\(108\) 0 0
\(109\) −5.40373 −0.517584 −0.258792 0.965933i \(-0.583324\pi\)
−0.258792 + 0.965933i \(0.583324\pi\)
\(110\) −2.81908 + 2.36549i −0.268789 + 0.225540i
\(111\) 0 0
\(112\) −3.71941 + 21.0938i −0.351451 + 1.99318i
\(113\) −1.30066 + 0.473401i −0.122356 + 0.0445339i −0.402472 0.915432i \(-0.631849\pi\)
0.280117 + 0.959966i \(0.409627\pi\)
\(114\) 0 0
\(115\) 0.496130 + 2.81369i 0.0462643 + 0.262378i
\(116\) −14.5005 25.1155i −1.34633 2.33192i
\(117\) 0 0
\(118\) 10.8020 18.7096i 0.994405 1.72236i
\(119\) 9.09627 + 3.31077i 0.833853 + 0.303498i
\(120\) 0 0
\(121\) −1.03596 0.869273i −0.0941781 0.0790248i
\(122\) −2.46064 2.06472i −0.222776 0.186931i
\(123\) 0 0
\(124\) 25.8123 + 9.39490i 2.31801 + 0.843687i
\(125\) 2.28833 3.96351i 0.204675 0.354507i
\(126\) 0 0
\(127\) 3.31908 + 5.74881i 0.294521 + 0.510125i 0.974873 0.222760i \(-0.0715067\pi\)
−0.680353 + 0.732885i \(0.738173\pi\)
\(128\) −2.31655 13.1378i −0.204756 1.16123i
\(129\) 0 0
\(130\) 2.43242 0.885328i 0.213337 0.0776484i
\(131\) −2.19506 + 12.4488i −0.191783 + 1.08766i 0.725142 + 0.688599i \(0.241774\pi\)
−0.916926 + 0.399058i \(0.869337\pi\)
\(132\) 0 0
\(133\) −0.103541 + 0.0868809i −0.00897811 + 0.00753353i
\(134\) 25.3405 2.18908
\(135\) 0 0
\(136\) 18.3182 1.57077
\(137\) 8.13223 6.82375i 0.694783 0.582992i −0.225501 0.974243i \(-0.572402\pi\)
0.920284 + 0.391251i \(0.127957\pi\)
\(138\) 0 0
\(139\) −1.29561 + 7.34775i −0.109892 + 0.623228i 0.879261 + 0.476340i \(0.158037\pi\)
−0.989153 + 0.146888i \(0.953074\pi\)
\(140\) 6.25877 2.27801i 0.528963 0.192527i
\(141\) 0 0
\(142\) 5.20187 + 29.5013i 0.436531 + 2.47569i
\(143\) −3.39306 5.87695i −0.283742 0.491455i
\(144\) 0 0
\(145\) −1.53802 + 2.66393i −0.127725 + 0.221227i
\(146\) 19.5929 + 7.13122i 1.62152 + 0.590184i
\(147\) 0 0
\(148\) 12.1532 + 10.1977i 0.998984 + 0.838247i
\(149\) −3.25877 2.73443i −0.266969 0.224013i 0.499469 0.866332i \(-0.333528\pi\)
−0.766438 + 0.642318i \(0.777973\pi\)
\(150\) 0 0
\(151\) −0.127011 0.0462284i −0.0103360 0.00376201i 0.336847 0.941559i \(-0.390640\pi\)
−0.347183 + 0.937797i \(0.612862\pi\)
\(152\) −0.127889 + 0.221510i −0.0103731 + 0.0179668i
\(153\) 0 0
\(154\) −12.6887 21.9774i −1.02248 1.77099i
\(155\) −0.505930 2.86927i −0.0406373 0.230465i
\(156\) 0 0
\(157\) −12.5223 + 4.55774i −0.999387 + 0.363747i −0.789348 0.613946i \(-0.789581\pi\)
−0.210039 + 0.977693i \(0.567359\pi\)
\(158\) 4.85844 27.5536i 0.386517 2.19205i
\(159\) 0 0
\(160\) 1.64749 1.38241i 0.130245 0.109289i
\(161\) −19.7023 −1.55276
\(162\) 0 0
\(163\) −9.76382 −0.764762 −0.382381 0.924005i \(-0.624896\pi\)
−0.382381 + 0.924005i \(0.624896\pi\)
\(164\) 26.0292 21.8411i 2.03254 1.70550i
\(165\) 0 0
\(166\) −0.663848 + 3.76487i −0.0515246 + 0.292211i
\(167\) 3.35844 1.22237i 0.259884 0.0945900i −0.208792 0.977960i \(-0.566953\pi\)
0.468676 + 0.883370i \(0.344731\pi\)
\(168\) 0 0
\(169\) −1.42855 8.10170i −0.109888 0.623208i
\(170\) −1.77719 3.07818i −0.136304 0.236086i
\(171\) 0 0
\(172\) 1.29813 2.24843i 0.0989817 0.171441i
\(173\) −17.6348 6.41852i −1.34075 0.487991i −0.430698 0.902496i \(-0.641733\pi\)
−0.910047 + 0.414505i \(0.863955\pi\)
\(174\) 0 0
\(175\) 11.8177 + 9.91626i 0.893337 + 0.749598i
\(176\) −15.7947 13.2534i −1.19057 0.999009i
\(177\) 0 0
\(178\) 37.7670 + 13.7461i 2.83075 + 1.03031i
\(179\) 2.54189 4.40268i 0.189990 0.329072i −0.755257 0.655429i \(-0.772488\pi\)
0.945247 + 0.326357i \(0.105821\pi\)
\(180\) 0 0
\(181\) −3.57532 6.19264i −0.265752 0.460295i 0.702009 0.712168i \(-0.252287\pi\)
−0.967760 + 0.251873i \(0.918953\pi\)
\(182\) 3.09967 + 17.5791i 0.229763 + 1.30305i
\(183\) 0 0
\(184\) −35.0355 + 12.7519i −2.58285 + 0.940082i
\(185\) 0.292204 1.65717i 0.0214832 0.121837i
\(186\) 0 0
\(187\) −7.13816 + 5.98962i −0.521994 + 0.438005i
\(188\) −42.6168 −3.10815
\(189\) 0 0
\(190\) 0.0496299 0.00360053
\(191\) −8.05097 + 6.75557i −0.582548 + 0.488816i −0.885783 0.464100i \(-0.846378\pi\)
0.303235 + 0.952916i \(0.401933\pi\)
\(192\) 0 0
\(193\) −1.76130 + 9.98881i −0.126781 + 0.719010i 0.853453 + 0.521169i \(0.174504\pi\)
−0.980234 + 0.197841i \(0.936607\pi\)
\(194\) −44.3658 + 16.1478i −3.18528 + 1.15935i
\(195\) 0 0
\(196\) 2.61334 + 14.8210i 0.186667 + 1.05864i
\(197\) −7.04189 12.1969i −0.501714 0.868994i −0.999998 0.00198008i \(-0.999370\pi\)
0.498284 0.867014i \(-0.333964\pi\)
\(198\) 0 0
\(199\) −5.13816 + 8.89955i −0.364234 + 0.630872i −0.988653 0.150218i \(-0.952003\pi\)
0.624419 + 0.781090i \(0.285336\pi\)
\(200\) 27.4329 + 9.98475i 1.93980 + 0.706029i
\(201\) 0 0
\(202\) 17.6250 + 14.7891i 1.24009 + 1.04056i
\(203\) −16.2494 13.6349i −1.14049 0.956982i
\(204\) 0 0
\(205\) −3.38666 1.23264i −0.236535 0.0860915i
\(206\) −0.330222 + 0.571962i −0.0230077 + 0.0398505i
\(207\) 0 0
\(208\) 7.25150 + 12.5600i 0.502801 + 0.870877i
\(209\) −0.0225934 0.128134i −0.00156282 0.00886318i
\(210\) 0 0
\(211\) 6.71213 2.44302i 0.462082 0.168184i −0.100480 0.994939i \(-0.532038\pi\)
0.562562 + 0.826755i \(0.309816\pi\)
\(212\) 3.79813 21.5403i 0.260857 1.47939i
\(213\) 0 0
\(214\) 7.84002 6.57856i 0.535933 0.449701i
\(215\) −0.275378 −0.0187806
\(216\) 0 0
\(217\) 20.0915 1.36390
\(218\) −10.4816 + 8.79509i −0.709902 + 0.595679i
\(219\) 0 0
\(220\) −1.11334 + 6.31407i −0.0750614 + 0.425694i
\(221\) 6.15910 2.24173i 0.414306 0.150795i
\(222\) 0 0
\(223\) −1.79473 10.1784i −0.120184 0.681597i −0.984052 0.177880i \(-0.943076\pi\)
0.863868 0.503718i \(-0.168035\pi\)
\(224\) 7.41534 + 12.8438i 0.495459 + 0.858159i
\(225\) 0 0
\(226\) −1.75237 + 3.03520i −0.116566 + 0.201899i
\(227\) 12.2369 + 4.45389i 0.812195 + 0.295615i 0.714530 0.699605i \(-0.246641\pi\)
0.0976647 + 0.995219i \(0.468863\pi\)
\(228\) 0 0
\(229\) −21.5253 18.0619i −1.42243 1.19356i −0.950023 0.312181i \(-0.898940\pi\)
−0.472408 0.881380i \(-0.656615\pi\)
\(230\) 5.54189 + 4.65020i 0.365421 + 0.306625i
\(231\) 0 0
\(232\) −37.7203 13.7291i −2.47646 0.901358i
\(233\) 6.95723 12.0503i 0.455784 0.789440i −0.542949 0.839765i \(-0.682692\pi\)
0.998733 + 0.0503252i \(0.0160258\pi\)
\(234\) 0 0
\(235\) 2.26011 + 3.91463i 0.147434 + 0.255363i
\(236\) −6.53596 37.0673i −0.425455 2.41287i
\(237\) 0 0
\(238\) 23.0326 8.38316i 1.49298 0.543400i
\(239\) −2.60813 + 14.7914i −0.168706 + 0.956777i 0.776455 + 0.630172i \(0.217016\pi\)
−0.945161 + 0.326605i \(0.894095\pi\)
\(240\) 0 0
\(241\) −9.93835 + 8.33926i −0.640185 + 0.537179i −0.904075 0.427374i \(-0.859439\pi\)
0.263890 + 0.964553i \(0.414994\pi\)
\(242\) −3.42427 −0.220120
\(243\) 0 0
\(244\) −5.59627 −0.358264
\(245\) 1.22281 1.02606i 0.0781225 0.0655526i
\(246\) 0 0
\(247\) −0.0158921 + 0.0901285i −0.00101119 + 0.00573474i
\(248\) 35.7276 13.0038i 2.26871 0.825741i
\(249\) 0 0
\(250\) −2.01233 11.4125i −0.127271 0.721788i
\(251\) −0.436289 0.755675i −0.0275383 0.0476978i 0.851928 0.523659i \(-0.175433\pi\)
−0.879466 + 0.475961i \(0.842100\pi\)
\(252\) 0 0
\(253\) 9.48293 16.4249i 0.596186 1.03263i
\(254\) 15.7947 + 5.74881i 0.991049 + 0.360713i
\(255\) 0 0
\(256\) −23.3666 19.6069i −1.46042 1.22543i
\(257\) 3.50593 + 2.94182i 0.218694 + 0.183506i 0.745552 0.666447i \(-0.232186\pi\)
−0.526858 + 0.849953i \(0.676630\pi\)
\(258\) 0 0
\(259\) 10.9042 + 3.96880i 0.677554 + 0.246609i
\(260\) 2.25490 3.90560i 0.139843 0.242215i
\(261\) 0 0
\(262\) 16.0039 + 27.7195i 0.988722 + 1.71252i
\(263\) 0.746282 + 4.23238i 0.0460177 + 0.260979i 0.999133 0.0416273i \(-0.0132542\pi\)
−0.953115 + 0.302607i \(0.902143\pi\)
\(264\) 0 0
\(265\) −2.18004 + 0.793471i −0.133919 + 0.0487426i
\(266\) −0.0594300 + 0.337044i −0.00364389 + 0.0206655i
\(267\) 0 0
\(268\) 33.8200 28.3784i 2.06589 1.73348i
\(269\) 12.1257 0.739315 0.369657 0.929168i \(-0.379475\pi\)
0.369657 + 0.929168i \(0.379475\pi\)
\(270\) 0 0
\(271\) −0.319955 −0.0194359 −0.00971795 0.999953i \(-0.503093\pi\)
−0.00971795 + 0.999953i \(0.503093\pi\)
\(272\) 15.2554 12.8008i 0.924992 0.776161i
\(273\) 0 0
\(274\) 4.66772 26.4719i 0.281987 1.59923i
\(275\) −13.9547 + 5.07910i −0.841501 + 0.306281i
\(276\) 0 0
\(277\) −4.65745 26.4137i −0.279839 1.58705i −0.723158 0.690683i \(-0.757310\pi\)
0.443319 0.896364i \(-0.353801\pi\)
\(278\) 9.44609 + 16.3611i 0.566539 + 0.981274i
\(279\) 0 0
\(280\) 4.60947 7.98384i 0.275469 0.477126i
\(281\) −25.0719 9.12543i −1.49567 0.544378i −0.540731 0.841195i \(-0.681852\pi\)
−0.954934 + 0.296818i \(0.904075\pi\)
\(282\) 0 0
\(283\) −7.11927 5.97378i −0.423197 0.355104i 0.406181 0.913793i \(-0.366860\pi\)
−0.829378 + 0.558689i \(0.811305\pi\)
\(284\) 39.9805 + 33.5476i 2.37240 + 1.99068i
\(285\) 0 0
\(286\) −16.1468 5.87695i −0.954779 0.347511i
\(287\) 12.4265 21.5233i 0.733512 1.27048i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 1.35251 + 7.67047i 0.0794222 + 0.450426i
\(291\) 0 0
\(292\) 34.1352 12.4242i 1.99761 0.727072i
\(293\) −3.41029 + 19.3407i −0.199231 + 1.12990i 0.707031 + 0.707182i \(0.250034\pi\)
−0.906263 + 0.422715i \(0.861077\pi\)
\(294\) 0 0
\(295\) −3.05825 + 2.56617i −0.178058 + 0.149408i
\(296\) 21.9590 1.27634
\(297\) 0 0
\(298\) −10.7716 −0.623980
\(299\) −10.2194 + 8.57510i −0.591004 + 0.495911i
\(300\) 0 0
\(301\) 0.329755 1.87014i 0.0190068 0.107793i
\(302\) −0.321604 + 0.117054i −0.0185062 + 0.00673572i
\(303\) 0 0
\(304\) 0.0482857 + 0.273842i 0.00276937 + 0.0157059i
\(305\) 0.296789 + 0.514054i 0.0169941 + 0.0294346i
\(306\) 0 0
\(307\) −14.1716 + 24.5459i −0.808815 + 1.40091i 0.104870 + 0.994486i \(0.466557\pi\)
−0.913685 + 0.406423i \(0.866776\pi\)
\(308\) −41.5467 15.1218i −2.36734 0.861642i
\(309\) 0 0
\(310\) −5.65136 4.74205i −0.320976 0.269331i
\(311\) −1.56624 1.31423i −0.0888132 0.0745231i 0.597300 0.802018i \(-0.296240\pi\)
−0.686113 + 0.727495i \(0.740685\pi\)
\(312\) 0 0
\(313\) −7.90420 2.87689i −0.446772 0.162612i 0.108830 0.994060i \(-0.465290\pi\)
−0.555601 + 0.831449i \(0.687512\pi\)
\(314\) −16.8712 + 29.2218i −0.952099 + 1.64908i
\(315\) 0 0
\(316\) −24.3726 42.2145i −1.37106 2.37475i
\(317\) 5.40538 + 30.6554i 0.303597 + 1.72178i 0.630038 + 0.776564i \(0.283039\pi\)
−0.326442 + 0.945217i \(0.605850\pi\)
\(318\) 0 0
\(319\) 19.1878 6.98378i 1.07431 0.391017i
\(320\) −0.133103 + 0.754866i −0.00744070 + 0.0421983i
\(321\) 0 0
\(322\) −38.2165 + 32.0674i −2.12972 + 1.78705i
\(323\) 0.125667 0.00699231
\(324\) 0 0
\(325\) 10.4456 0.579419
\(326\) −18.9388 + 15.8916i −1.04892 + 0.880152i
\(327\) 0 0
\(328\) 8.16684 46.3165i 0.450938 2.55740i
\(329\) −29.2913 + 10.6612i −1.61488 + 0.587769i
\(330\) 0 0
\(331\) 5.38847 + 30.5595i 0.296177 + 1.67970i 0.662379 + 0.749169i \(0.269547\pi\)
−0.366202 + 0.930535i \(0.619342\pi\)
\(332\) 3.33022 + 5.76811i 0.182770 + 0.316566i
\(333\) 0 0
\(334\) 4.52481 7.83721i 0.247587 0.428833i
\(335\) −4.40033 1.60159i −0.240416 0.0875042i
\(336\) 0 0
\(337\) 18.1780 + 15.2531i 0.990218 + 0.830892i 0.985599 0.169098i \(-0.0540854\pi\)
0.00461869 + 0.999989i \(0.498530\pi\)
\(338\) −15.9572 13.3897i −0.867959 0.728304i
\(339\) 0 0
\(340\) −5.81908 2.11797i −0.315584 0.114863i
\(341\) −9.67024 + 16.7494i −0.523673 + 0.907028i
\(342\) 0 0
\(343\) −5.78952 10.0277i −0.312604 0.541447i
\(344\) −0.624018 3.53898i −0.0336448 0.190809i
\(345\) 0 0
\(346\) −44.6528 + 16.2523i −2.40055 + 0.873728i
\(347\) −0.314025 + 1.78093i −0.0168578 + 0.0956052i −0.992076 0.125641i \(-0.959901\pi\)
0.975218 + 0.221246i \(0.0710124\pi\)
\(348\) 0 0
\(349\) 11.6905 9.80947i 0.625777 0.525089i −0.273837 0.961776i \(-0.588293\pi\)
0.899613 + 0.436687i \(0.143848\pi\)
\(350\) 39.0624 2.08797
\(351\) 0 0
\(352\) −14.2763 −0.760930
\(353\) −24.8063 + 20.8150i −1.32031 + 1.10787i −0.334069 + 0.942549i \(0.608422\pi\)
−0.986240 + 0.165321i \(0.947134\pi\)
\(354\) 0 0
\(355\) 0.961266 5.45161i 0.0510187 0.289341i
\(356\) 65.7987 23.9488i 3.48732 1.26928i
\(357\) 0 0
\(358\) −2.23530 12.6770i −0.118139 0.670001i
\(359\) 0.957234 + 1.65798i 0.0505209 + 0.0875047i 0.890180 0.455609i \(-0.150579\pi\)
−0.839659 + 0.543114i \(0.817245\pi\)
\(360\) 0 0
\(361\) 9.49912 16.4530i 0.499954 0.865945i
\(362\) −17.0141 6.19264i −0.894243 0.325478i
\(363\) 0 0
\(364\) 23.8234 + 19.9902i 1.24869 + 1.04777i
\(365\) −2.95155 2.47665i −0.154491 0.129634i
\(366\) 0 0
\(367\) 25.2447 + 9.18832i 1.31776 + 0.479626i 0.902741 0.430185i \(-0.141552\pi\)
0.415022 + 0.909812i \(0.363774\pi\)
\(368\) −20.2665 + 35.1026i −1.05646 + 1.82985i
\(369\) 0 0
\(370\) −2.13041 3.68999i −0.110755 0.191833i
\(371\) −2.77807 15.7552i −0.144230 0.817969i
\(372\) 0 0
\(373\) −13.9452 + 5.07564i −0.722056 + 0.262807i −0.676798 0.736169i \(-0.736633\pi\)
−0.0452575 + 0.998975i \(0.514411\pi\)
\(374\) −4.09714 + 23.2361i −0.211858 + 1.20151i
\(375\) 0 0
\(376\) −45.1869 + 37.9163i −2.33034 + 1.95538i
\(377\) −14.3628 −0.739721
\(378\) 0 0
\(379\) −33.7870 −1.73552 −0.867762 0.496980i \(-0.834442\pi\)
−0.867762 + 0.496980i \(0.834442\pi\)
\(380\) 0.0662372 0.0555796i 0.00339789 0.00285117i
\(381\) 0 0
\(382\) −4.62108 + 26.2075i −0.236435 + 1.34089i
\(383\) 8.71941 3.17360i 0.445541 0.162164i −0.109500 0.993987i \(-0.534925\pi\)
0.555041 + 0.831823i \(0.312703\pi\)
\(384\) 0 0
\(385\) 0.814330 + 4.61830i 0.0415021 + 0.235370i
\(386\) 12.8414 + 22.2419i 0.653608 + 1.13208i
\(387\) 0 0
\(388\) −41.1279 + 71.2357i −2.08796 + 3.61644i
\(389\) 15.0150 + 5.46502i 0.761291 + 0.277087i 0.693349 0.720602i \(-0.256134\pi\)
0.0679423 + 0.997689i \(0.478357\pi\)
\(390\) 0 0
\(391\) 14.0326 + 11.7747i 0.709657 + 0.595473i
\(392\) 15.9572 + 13.3897i 0.805962 + 0.676282i
\(393\) 0 0
\(394\) −33.5107 12.1969i −1.68825 0.614471i
\(395\) −2.58512 + 4.47756i −0.130072 + 0.225291i
\(396\) 0 0
\(397\) −9.85251 17.0650i −0.494483 0.856470i 0.505496 0.862829i \(-0.331309\pi\)
−0.999980 + 0.00635841i \(0.997976\pi\)
\(398\) 4.51842 + 25.6252i 0.226488 + 1.28448i
\(399\) 0 0
\(400\) 29.8234 10.8548i 1.49117 0.542742i
\(401\) 0.199340 1.13052i 0.00995459 0.0564553i −0.979426 0.201804i \(-0.935319\pi\)
0.989380 + 0.145349i \(0.0464306\pi\)
\(402\) 0 0
\(403\) 10.4213 8.74449i 0.519121 0.435594i
\(404\) 40.0847 1.99429
\(405\) 0 0
\(406\) −53.7110 −2.66563
\(407\) −8.55690 + 7.18009i −0.424150 + 0.355904i
\(408\) 0 0
\(409\) −0.538485 + 3.05390i −0.0266264 + 0.151006i −0.995222 0.0976342i \(-0.968872\pi\)
0.968596 + 0.248640i \(0.0799836\pi\)
\(410\) −8.57532 + 3.12116i −0.423505 + 0.154143i
\(411\) 0 0
\(412\) 0.199807 + 1.13316i 0.00984380 + 0.0558270i
\(413\) −13.7652 23.8420i −0.677340 1.17319i
\(414\) 0 0
\(415\) 0.353226 0.611806i 0.0173392 0.0300324i
\(416\) 9.43629 + 3.43453i 0.462652 + 0.168392i
\(417\) 0 0
\(418\) −0.252374 0.211767i −0.0123440 0.0103579i
\(419\) 27.1557 + 22.7863i 1.32664 + 1.11319i 0.984850 + 0.173410i \(0.0554786\pi\)
0.341793 + 0.939775i \(0.388966\pi\)
\(420\) 0 0
\(421\) −8.66132 3.15246i −0.422127 0.153642i 0.122218 0.992503i \(-0.460999\pi\)
−0.544345 + 0.838862i \(0.683222\pi\)
\(422\) 9.04323 15.6633i 0.440218 0.762479i
\(423\) 0 0
\(424\) −15.1373 26.2185i −0.735131 1.27328i
\(425\) −2.49067 14.1253i −0.120815 0.685176i
\(426\) 0 0
\(427\) −3.84642 + 1.39998i −0.186141 + 0.0677499i
\(428\) 3.09627 17.5598i 0.149664 0.848785i
\(429\) 0 0
\(430\) −0.534148 + 0.448204i −0.0257589 + 0.0216143i
\(431\) 11.5794 0.557758 0.278879 0.960326i \(-0.410037\pi\)
0.278879 + 0.960326i \(0.410037\pi\)
\(432\) 0 0
\(433\) 6.06511 0.291471 0.145735 0.989324i \(-0.453445\pi\)
0.145735 + 0.989324i \(0.453445\pi\)
\(434\) 38.9714 32.7009i 1.87069 1.56969i
\(435\) 0 0
\(436\) −4.13950 + 23.4763i −0.198246 + 1.12431i
\(437\) −0.240352 + 0.0874810i −0.0114976 + 0.00418479i
\(438\) 0 0
\(439\) 5.03684 + 28.5653i 0.240395 + 1.36335i 0.830948 + 0.556350i \(0.187798\pi\)
−0.590553 + 0.806999i \(0.701090\pi\)
\(440\) 4.43717 + 7.68540i 0.211534 + 0.366387i
\(441\) 0 0
\(442\) 8.29813 14.3728i 0.394702 0.683644i
\(443\) −29.0292 10.5657i −1.37922 0.501994i −0.457276 0.889325i \(-0.651175\pi\)
−0.921941 + 0.387331i \(0.873397\pi\)
\(444\) 0 0
\(445\) −5.68938 4.77396i −0.269702 0.226307i
\(446\) −20.0476 16.8219i −0.949280 0.796540i
\(447\) 0 0
\(448\) −4.96703 1.80785i −0.234670 0.0854130i
\(449\) 19.5410 33.8460i 0.922197 1.59729i 0.126190 0.992006i \(-0.459725\pi\)
0.796008 0.605287i \(-0.206941\pi\)
\(450\) 0 0
\(451\) 11.9620 + 20.7188i 0.563268 + 0.975608i
\(452\) 1.06031 + 6.01330i 0.0498727 + 0.282842i
\(453\) 0 0
\(454\) 30.9850 11.2776i 1.45420 0.529286i
\(455\) 0.572796 3.24849i 0.0268531 0.152291i
\(456\) 0 0
\(457\) −1.15270 + 0.967233i −0.0539212 + 0.0452453i −0.669350 0.742947i \(-0.733427\pi\)
0.615429 + 0.788192i \(0.288983\pi\)
\(458\) −71.1498 −3.32461
\(459\) 0 0
\(460\) 12.6040 0.587665
\(461\) 20.0988 16.8649i 0.936094 0.785476i −0.0408072 0.999167i \(-0.512993\pi\)
0.976901 + 0.213691i \(0.0685485\pi\)
\(462\) 0 0
\(463\) 1.17324 6.65376i 0.0545250 0.309227i −0.945333 0.326108i \(-0.894263\pi\)
0.999857 + 0.0168815i \(0.00537380\pi\)
\(464\) −41.0073 + 14.9254i −1.90372 + 0.692897i
\(465\) 0 0
\(466\) −6.11809 34.6974i −0.283415 1.60733i
\(467\) −16.8735 29.2257i −0.780810 1.35240i −0.931470 0.363818i \(-0.881473\pi\)
0.150660 0.988586i \(-0.451860\pi\)
\(468\) 0 0
\(469\) 16.1459 27.9655i 0.745548 1.29133i
\(470\) 10.7554 + 3.91463i 0.496108 + 0.180569i
\(471\) 0 0
\(472\) −39.9090 33.4876i −1.83696 1.54139i
\(473\) 1.40033 + 1.17502i 0.0643872 + 0.0540273i
\(474\) 0 0
\(475\) 0.188196 + 0.0684978i 0.00863503 + 0.00314289i
\(476\) 21.3516 36.9821i 0.978651 1.69507i
\(477\) 0 0
\(478\) 19.0155 + 32.9358i 0.869748 + 1.50645i
\(479\) 1.93211 + 10.9576i 0.0882805 + 0.500664i 0.996600 + 0.0823875i \(0.0262545\pi\)
−0.908320 + 0.418276i \(0.862634\pi\)
\(480\) 0 0
\(481\) 7.38326 2.68729i 0.336647 0.122530i
\(482\) −5.70439 + 32.3512i −0.259828 + 1.47356i
\(483\) 0 0
\(484\) −4.57011 + 3.83478i −0.207732 + 0.174308i
\(485\) 8.72462 0.396165
\(486\) 0 0
\(487\) −4.74691 −0.215103 −0.107552 0.994200i \(-0.534301\pi\)
−0.107552 + 0.994200i \(0.534301\pi\)
\(488\) −5.93376 + 4.97902i −0.268609 + 0.225390i
\(489\) 0 0
\(490\) 0.701867 3.98048i 0.0317071 0.179820i
\(491\) −20.9932 + 7.64090i −0.947410 + 0.344829i −0.769088 0.639143i \(-0.779289\pi\)
−0.178322 + 0.983972i \(0.557067\pi\)
\(492\) 0 0
\(493\) 3.42468 + 19.4223i 0.154240 + 0.874737i
\(494\) 0.115867 + 0.200688i 0.00521310 + 0.00902936i
\(495\) 0 0
\(496\) 20.6668 35.7960i 0.927969 1.60729i
\(497\) 35.8717 + 13.0562i 1.60907 + 0.585652i
\(498\) 0 0
\(499\) −8.01367 6.72427i −0.358741 0.301020i 0.445548 0.895258i \(-0.353009\pi\)
−0.804289 + 0.594239i \(0.797453\pi\)
\(500\) −15.4663 12.9778i −0.691675 0.580384i
\(501\) 0 0
\(502\) −2.07620 0.755675i −0.0926653 0.0337274i
\(503\) −12.5209 + 21.6869i −0.558281 + 0.966972i 0.439359 + 0.898312i \(0.355206\pi\)
−0.997640 + 0.0686600i \(0.978128\pi\)
\(504\) 0 0
\(505\) −2.12583 3.68204i −0.0945982 0.163849i
\(506\) −8.33915 47.2936i −0.370720 2.10246i
\(507\) 0 0
\(508\) 27.5180 10.0157i 1.22091 0.444376i
\(509\) 3.13651 17.7880i 0.139023 0.788440i −0.832950 0.553348i \(-0.813350\pi\)
0.971973 0.235092i \(-0.0755390\pi\)
\(510\) 0 0
\(511\) 20.3537 17.0788i 0.900394 0.755521i
\(512\) −50.5553 −2.23425
\(513\) 0 0
\(514\) 11.5885 0.511148
\(515\) 0.0934920 0.0784491i 0.00411975 0.00345688i
\(516\) 0 0
\(517\) 5.21048 29.5501i 0.229157 1.29961i
\(518\) 27.6104 10.0494i 1.21313 0.441544i
\(519\) 0 0
\(520\) −1.08394 6.14733i −0.0475339 0.269578i
\(521\) 12.9791 + 22.4804i 0.568623 + 0.984883i 0.996703 + 0.0811425i \(0.0258569\pi\)
−0.428080 + 0.903741i \(0.640810\pi\)
\(522\) 0 0
\(523\) −12.7973 + 22.1655i −0.559585 + 0.969230i 0.437946 + 0.899001i \(0.355706\pi\)
−0.997531 + 0.0702283i \(0.977627\pi\)
\(524\) 52.4017 + 19.0727i 2.28918 + 0.833193i
\(525\) 0 0
\(526\) 8.33615 + 6.99486i 0.363473 + 0.304990i
\(527\) −14.3097 12.0073i −0.623342 0.523046i
\(528\) 0 0
\(529\) −13.4226 4.88543i −0.583592 0.212410i
\(530\) −2.93717 + 5.08732i −0.127582 + 0.220979i
\(531\) 0 0
\(532\) 0.298133 + 0.516382i 0.0129257 + 0.0223880i
\(533\) −2.92215 16.5723i −0.126572 0.717828i
\(534\) 0 0
\(535\) −1.77719 + 0.646844i −0.0768346 + 0.0279655i
\(536\) 10.6113 60.1796i 0.458338 2.59936i
\(537\) 0 0
\(538\) 23.5201 19.7357i 1.01402 0.850866i
\(539\) −10.5963 −0.456414
\(540\) 0 0
\(541\) 27.8476 1.19726 0.598631 0.801025i \(-0.295712\pi\)
0.598631 + 0.801025i \(0.295712\pi\)
\(542\) −0.620615 + 0.520758i −0.0266577 + 0.0223685i
\(543\) 0 0
\(544\) 2.39440 13.5793i 0.102659 0.582208i
\(545\) 2.37598 0.864787i 0.101776 0.0370434i
\(546\) 0 0
\(547\) −1.02600 5.81872i −0.0438685 0.248790i 0.954985 0.296653i \(-0.0958703\pi\)
−0.998854 + 0.0478621i \(0.984759\pi\)
\(548\) −23.4158 40.5574i −1.00027 1.73253i
\(549\) 0 0
\(550\) −18.8011 + 32.5645i −0.801683 + 1.38856i
\(551\) −0.258770 0.0941848i −0.0110240 0.00401241i
\(552\) 0 0
\(553\) −27.3123 22.9177i −1.16144 0.974560i
\(554\) −52.0249 43.6541i −2.21032 1.85468i
\(555\) 0 0
\(556\) 30.9295 + 11.2574i 1.31170 + 0.477421i
\(557\) −13.3525 + 23.1272i −0.565764 + 0.979932i 0.431214 + 0.902250i \(0.358085\pi\)
−0.996978 + 0.0776824i \(0.975248\pi\)
\(558\) 0 0
\(559\) −0.642903 1.11354i −0.0271919 0.0470978i
\(560\) −1.74035 9.87003i −0.0735433 0.417085i
\(561\) 0 0
\(562\) −63.4843 + 23.1064i −2.67792 + 0.974685i
\(563\) 6.26217 35.5146i 0.263919 1.49676i −0.508176 0.861253i \(-0.669680\pi\)
0.772095 0.635507i \(-0.219209\pi\)
\(564\) 0 0
\(565\) 0.496130 0.416302i 0.0208723 0.0175140i
\(566\) −23.5321 −0.989127
\(567\) 0 0
\(568\) 72.2390 3.03108
\(569\) −6.93061 + 5.81547i −0.290546 + 0.243797i −0.776396 0.630245i \(-0.782954\pi\)
0.485850 + 0.874042i \(0.338510\pi\)
\(570\) 0 0
\(571\) 5.30999 30.1145i 0.222216 1.26025i −0.645719 0.763575i \(-0.723442\pi\)
0.867936 0.496676i \(-0.165446\pi\)
\(572\) −28.1313 + 10.2390i −1.17623 + 0.428113i
\(573\) 0 0
\(574\) −10.9277 61.9739i −0.456112 2.58674i
\(575\) 14.5967 + 25.2823i 0.608726 + 1.05434i
\(576\) 0 0
\(577\) 12.5744 21.7796i 0.523481 0.906696i −0.476146 0.879367i \(-0.657966\pi\)
0.999626 0.0273292i \(-0.00870022\pi\)
\(578\) 19.0351 + 6.92820i 0.791755 + 0.288175i
\(579\) 0 0
\(580\) 10.3951 + 8.72254i 0.431634 + 0.362184i
\(581\) 3.73190 + 3.13143i 0.154825 + 0.129914i
\(582\) 0 0
\(583\) 14.4715 + 5.26719i 0.599347 + 0.218145i
\(584\) 25.1400 43.5437i 1.04030 1.80185i
\(585\) 0 0
\(586\) 24.8640 + 43.0656i 1.02712 + 1.77903i
\(587\) 3.62465 + 20.5564i 0.149605 + 0.848453i 0.963553 + 0.267516i \(0.0862028\pi\)
−0.813948 + 0.580937i \(0.802686\pi\)
\(588\) 0 0
\(589\) 0.245100 0.0892091i 0.0100992 0.00367580i
\(590\) −1.75537 + 9.95518i −0.0722673 + 0.409848i
\(591\) 0 0
\(592\) 18.2875 15.3450i 0.751610 0.630676i
\(593\) 15.6212 0.641488 0.320744 0.947166i \(-0.396067\pi\)
0.320744 + 0.947166i \(0.396067\pi\)
\(594\) 0 0
\(595\) −4.52940 −0.185687
\(596\) −14.3760 + 12.0629i −0.588863 + 0.494115i
\(597\) 0 0
\(598\) −5.86571 + 33.2661i −0.239867 + 1.36035i
\(599\) 0.421274 0.153331i 0.0172128 0.00626495i −0.333399 0.942786i \(-0.608196\pi\)
0.350612 + 0.936521i \(0.385974\pi\)
\(600\) 0 0
\(601\) −3.06876 17.4038i −0.125177 0.709917i −0.981202 0.192982i \(-0.938184\pi\)
0.856025 0.516935i \(-0.172927\pi\)
\(602\) −2.40420 4.16420i −0.0979879 0.169720i
\(603\) 0 0
\(604\) −0.298133 + 0.516382i −0.0121309 + 0.0210113i
\(605\) 0.594618 + 0.216423i 0.0241747 + 0.00879885i
\(606\) 0 0
\(607\) 20.0692 + 16.8401i 0.814585 + 0.683518i 0.951697 0.307038i \(-0.0993377\pi\)
−0.137112 + 0.990555i \(0.543782\pi\)
\(608\) 0.147489 + 0.123758i 0.00598147 + 0.00501905i
\(609\) 0 0
\(610\) 1.41235 + 0.514054i 0.0571844 + 0.0208134i
\(611\) −10.5530 + 18.2784i −0.426930 + 0.739465i
\(612\) 0 0
\(613\) −7.27719 12.6045i −0.293923 0.509089i 0.680811 0.732459i \(-0.261628\pi\)
−0.974734 + 0.223370i \(0.928294\pi\)
\(614\) 12.4623 + 70.6771i 0.502937 + 2.85230i
\(615\) 0 0
\(616\) −57.5061 + 20.9305i −2.31699 + 0.843315i
\(617\) 2.43464 13.8075i 0.0980149 0.555870i −0.895767 0.444524i \(-0.853373\pi\)
0.993782 0.111346i \(-0.0355162\pi\)
\(618\) 0 0
\(619\) −24.2931 + 20.3844i −0.976424 + 0.819317i −0.983546 0.180658i \(-0.942177\pi\)
0.00712236 + 0.999975i \(0.497733\pi\)
\(620\) −12.8530 −0.516188
\(621\) 0 0
\(622\) −5.17705 −0.207581
\(623\) 39.2335 32.9209i 1.57186 1.31895i
\(624\) 0 0
\(625\) 3.77925 21.4332i 0.151170 0.857327i
\(626\) −20.0141 + 7.28455i −0.799926 + 0.291149i
\(627\) 0 0
\(628\) 10.2083 + 57.8939i 0.407354 + 2.31022i
\(629\) −5.39440 9.34337i −0.215089 0.372545i
\(630\) 0 0
\(631\) 19.2879 33.4077i 0.767840 1.32994i −0.170892 0.985290i \(-0.554665\pi\)
0.938732 0.344648i \(-0.112002\pi\)
\(632\) −63.4009 23.0760i −2.52195 0.917915i
\(633\) 0 0
\(634\) 60.3794 + 50.6644i 2.39797 + 2.01214i
\(635\) −2.37939 1.99654i −0.0944230 0.0792303i
\(636\) 0 0
\(637\) 7.00387 + 2.54920i 0.277503 + 0.101003i
\(638\) 25.8516 44.7763i 1.02348 1.77271i
\(639\) 0 0
\(640\) 3.12108 + 5.40587i 0.123372 + 0.213686i
\(641\) −5.31655 30.1517i −0.209991 1.19092i −0.889390 0.457150i \(-0.848870\pi\)
0.679399 0.733769i \(-0.262241\pi\)
\(642\) 0 0
\(643\) 32.1609 11.7056i 1.26830 0.461624i 0.381756 0.924263i \(-0.375320\pi\)
0.886547 + 0.462639i \(0.153097\pi\)
\(644\) −15.0929 + 85.5959i −0.594742 + 3.37295i
\(645\) 0 0
\(646\) 0.243756 0.204535i 0.00959044 0.00804734i
\(647\) −12.8726 −0.506073 −0.253037 0.967457i \(-0.581429\pi\)
−0.253037 + 0.967457i \(0.581429\pi\)
\(648\) 0 0
\(649\) 26.5012 1.04026
\(650\) 20.2613 17.0012i 0.794713 0.666844i
\(651\) 0 0
\(652\) −7.47952 + 42.4185i −0.292921 + 1.66124i
\(653\) 10.6365 3.87137i 0.416239 0.151498i −0.125407 0.992105i \(-0.540024\pi\)
0.541646 + 0.840607i \(0.317801\pi\)
\(654\) 0 0
\(655\) −1.02709 5.82493i −0.0401318 0.227599i
\(656\) −25.5646 44.2793i −0.998132 1.72881i
\(657\) 0 0
\(658\) −39.4641 + 68.3538i −1.53847 + 2.66471i
\(659\) 12.9388 + 4.70934i 0.504025 + 0.183450i 0.581503 0.813544i \(-0.302465\pi\)
−0.0774786 + 0.996994i \(0.524687\pi\)
\(660\) 0 0
\(661\) −15.5253 13.0273i −0.603863 0.506702i 0.288821 0.957383i \(-0.406737\pi\)
−0.892685 + 0.450681i \(0.851181\pi\)
\(662\) 60.1905 + 50.5059i 2.33937 + 1.96297i
\(663\) 0 0
\(664\) 8.66297 + 3.15306i 0.336188 + 0.122363i
\(665\) 0.0316221 0.0547710i 0.00122625 0.00212393i
\(666\) 0 0
\(667\) −20.0706 34.7633i −0.777136 1.34604i
\(668\) −2.73783 15.5270i −0.105930 0.600757i
\(669\) 0 0
\(670\) −11.1420 + 4.05537i −0.430454 + 0.156672i
\(671\) 0.684220 3.88040i 0.0264140 0.149801i
\(672\) 0 0
\(673\) −23.3987 + 19.6339i −0.901955 + 0.756830i −0.970572 0.240813i \(-0.922586\pi\)
0.0686165 + 0.997643i \(0.478142\pi\)
\(674\) 60.0856 2.31441
\(675\) 0 0
\(676\) −36.2918 −1.39584
\(677\) −2.84911 + 2.39068i −0.109500 + 0.0918815i −0.695894 0.718145i \(-0.744992\pi\)
0.586394 + 0.810026i \(0.300547\pi\)
\(678\) 0 0
\(679\) −10.4474 + 59.2503i −0.400936 + 2.27382i
\(680\) −8.05438 + 2.93155i −0.308871 + 0.112420i
\(681\) 0 0
\(682\) 8.50387 + 48.2278i 0.325630 + 1.84674i
\(683\) 10.8735 + 18.8334i 0.416061 + 0.720639i 0.995539 0.0943487i \(-0.0300769\pi\)
−0.579478 + 0.814988i \(0.696744\pi\)
\(684\) 0 0
\(685\) −2.48364 + 4.30179i −0.0948950 + 0.164363i
\(686\) −27.5510 10.0277i −1.05190 0.382861i
\(687\) 0 0
\(688\) −2.99273 2.51120i −0.114097 0.0957384i
\(689\) −8.29813 6.96296i −0.316134 0.265268i
\(690\) 0 0
\(691\) 35.3276 + 12.8582i 1.34392 + 0.489149i 0.911046 0.412304i \(-0.135276\pi\)
0.432878 + 0.901452i \(0.357498\pi\)
\(692\) −41.3940 + 71.6965i −1.57356 + 2.72549i
\(693\) 0 0
\(694\) 2.28952 + 3.96556i 0.0869088 + 0.150530i
\(695\) −0.606229 3.43810i −0.0229956 0.130414i
\(696\) 0 0
\(697\) −21.7135 + 7.90306i −0.822457 + 0.299350i
\(698\) 6.71007 38.0547i 0.253980 1.44039i
\(699\) 0 0
\(700\) 52.1336 43.7453i 1.97047 1.65342i
\(701\) 23.3351 0.881355 0.440678 0.897665i \(-0.354738\pi\)
0.440678 + 0.897665i \(0.354738\pi\)
\(702\) 0 0
\(703\) 0.150644 0.00568166
\(704\) 3.89780 3.27065i 0.146904 0.123267i
\(705\) 0 0
\(706\) −14.2383 + 80.7494i −0.535865 + 3.03904i
\(707\) 27.5510 10.0277i 1.03616 0.377132i
\(708\) 0 0
\(709\) 1.14244 + 6.47908i 0.0429051 + 0.243327i 0.998716 0.0506545i \(-0.0161307\pi\)
−0.955811 + 0.293981i \(0.905020\pi\)
\(710\) −7.00846 12.1390i −0.263023 0.455569i
\(711\) 0 0
\(712\) 48.4595 83.9343i 1.81610 3.14557i
\(713\) 35.7276 + 13.0038i 1.33801 + 0.486996i
\(714\) 0 0
\(715\) 2.43242 + 2.04104i 0.0909673 + 0.0763306i
\(716\) −17.1800 14.4158i −0.642048 0.538743i
\(717\) 0 0
\(718\) 4.55525 + 1.65798i 0.170001 + 0.0618752i
\(719\) 8.41622 14.5773i 0.313872 0.543642i −0.665325 0.746554i \(-0.731707\pi\)
0.979197 + 0.202911i \(0.0650403\pi\)
\(720\) 0 0
\(721\) 0.420807 + 0.728860i 0.0156717 + 0.0271442i
\(722\) −8.35339 47.3744i −0.310881 1.76309i
\(723\) 0 0
\(724\) −29.6425 + 10.7890i −1.10165 + 0.400969i
\(725\) −5.45786 + 30.9531i −0.202700 + 1.14957i
\(726\) 0 0
\(727\) 19.5817 16.4310i 0.726246 0.609393i −0.202860 0.979208i \(-0.565023\pi\)
0.929105 + 0.369815i \(0.120579\pi\)
\(728\) 43.0455 1.59537
\(729\) 0 0
\(730\) −9.75608 −0.361089
\(731\) −1.35251 + 1.13489i −0.0500244 + 0.0419755i
\(732\) 0 0
\(733\) −2.56964 + 14.5732i −0.0949118 + 0.538272i 0.899862 + 0.436174i \(0.143667\pi\)
−0.994774 + 0.102098i \(0.967444\pi\)
\(734\) 63.9218 23.2656i 2.35940 0.858750i
\(735\) 0 0
\(736\) 4.87346 + 27.6387i 0.179638 + 1.01878i
\(737\) 15.5424 + 26.9202i 0.572510 + 0.991616i
\(738\) 0 0
\(739\) −4.59539 + 7.95945i −0.169044 + 0.292793i −0.938084 0.346408i \(-0.887401\pi\)
0.769040 + 0.639201i \(0.220735\pi\)
\(740\) −6.97565 2.53893i −0.256430 0.0933329i
\(741\) 0 0
\(742\) −31.0317 26.0387i −1.13921 0.955910i
\(743\) 34.0501 + 28.5714i 1.24918 + 1.04818i 0.996749 + 0.0805681i \(0.0256735\pi\)
0.252428 + 0.967616i \(0.418771\pi\)
\(744\) 0 0
\(745\) 1.87046 + 0.680793i 0.0685284 + 0.0249423i
\(746\) −18.7883 + 32.5423i −0.687890 + 1.19146i
\(747\) 0 0
\(748\) 20.5535 + 35.5997i 0.751510 + 1.30165i
\(749\) −2.26470 12.8438i −0.0827503 0.469301i
\(750\) 0 0
\(751\) 33.6467 12.2464i 1.22778 0.446877i 0.354946 0.934887i \(-0.384499\pi\)
0.872838 + 0.488010i \(0.162277\pi\)
\(752\) −11.1356 + 63.1533i −0.406075 + 2.30296i
\(753\) 0 0
\(754\) −27.8594 + 23.3768i −1.01458 + 0.851333i
\(755\) 0.0632441 0.00230169
\(756\) 0 0
\(757\) −45.8976 −1.66818 −0.834088 0.551632i \(-0.814005\pi\)
−0.834088 + 0.551632i \(0.814005\pi\)
\(758\) −65.5365 + 54.9916i −2.38039 + 1.99739i
\(759\) 0 0
\(760\) 0.0207824 0.117863i 0.000753857 0.00427534i
\(761\) 34.9521 12.7215i 1.26701 0.461155i 0.380896 0.924618i \(-0.375616\pi\)
0.886116 + 0.463463i \(0.153393\pi\)
\(762\) 0 0
\(763\) 3.02775 + 17.1712i 0.109612 + 0.621640i
\(764\) 23.1819 + 40.1522i 0.838690 + 1.45265i
\(765\) 0 0
\(766\) 11.7476 20.3475i 0.424459 0.735185i
\(767\) −17.5167 6.37554i −0.632490 0.230208i
\(768\) 0 0
\(769\) −29.3653 24.6404i −1.05894 0.888556i −0.0649348 0.997890i \(-0.520684\pi\)
−0.994005 + 0.109333i \(0.965128\pi\)
\(770\) 9.09627 + 7.63267i 0.327807 + 0.275062i
\(771\) 0 0
\(772\) 42.0467 + 15.3037i 1.51329 + 0.550794i
\(773\) −26.4136 + 45.7497i −0.950031 + 1.64550i −0.204680 + 0.978829i \(0.565615\pi\)
−0.745351 + 0.666673i \(0.767718\pi\)
\(774\) 0 0
\(775\) −14.8851 25.7817i −0.534687 0.926106i
\(776\) 19.7704 + 112.123i 0.709715 + 4.02500i
\(777\) 0 0
\(778\) 38.0194 13.8379i 1.36306 0.496113i
\(779\) 0.0560265 0.317742i 0.00200736 0.0113843i
\(780\) 0 0
\(781\) −28.1498 + 23.6205i −1.00728 + 0.845206i
\(782\) 46.3833 1.65866
\(783\) 0 0
\(784\) 22.6459 0.808782
\(785\) 4.77656 4.00801i 0.170483 0.143052i
\(786\) 0 0
\(787\) 7.85591 44.5531i 0.280033 1.58815i −0.442473 0.896782i \(-0.645899\pi\)
0.722506 0.691365i \(-0.242990\pi\)
\(788\) −58.3833 + 21.2498i −2.07982 + 0.756992i
\(789\) 0 0
\(790\) 2.27332 + 12.8926i 0.0808810 + 0.458699i
\(791\) 2.23308 + 3.86780i 0.0793991 + 0.137523i
\(792\) 0 0
\(793\) −1.38578 + 2.40024i −0.0492106 + 0.0852352i
\(794\) −46.8858 17.0650i −1.66392 0.605616i
\(795\) 0 0
\(796\) 34.7276 + 29.1399i 1.23089 + 1.03284i
\(797\) −12.9606 10.8753i −0.459089 0.385222i 0.383706 0.923455i \(-0.374647\pi\)
−0.842796 + 0.538233i \(0.819092\pi\)
\(798\) 0 0
\(799\) 27.2335 + 9.91220i 0.963454 + 0.350668i
\(800\) 10.9875 19.0309i 0.388467 0.672845i
\(801\) 0 0
\(802\) −1.45336 2.51730i −0.0513200 0.0888889i
\(803\) 4.44134 + 25.1881i 0.156732 + 0.888869i
\(804\) 0 0
\(805\) 8.66297 3.15306i 0.305330 0.111131i
\(806\) 5.98158 33.9232i 0.210692 1.19490i
\(807\) 0 0
\(808\) 42.5021 35.6635i 1.49522 1.25464i
\(809\) −34.9145 −1.22753 −0.613764 0.789490i \(-0.710345\pi\)
−0.613764 + 0.789490i \(0.710345\pi\)
\(810\) 0 0
\(811\) 18.0419 0.633536 0.316768 0.948503i \(-0.397402\pi\)
0.316768 + 0.948503i \(0.397402\pi\)
\(812\) −71.6840 + 60.1500i −2.51561 + 2.11085i
\(813\) 0 0
\(814\) −4.91147 + 27.8544i −0.172147 + 0.976295i
\(815\) 4.29308 1.56255i 0.150380 0.0547339i
\(816\) 0 0
\(817\) −0.00428091 0.0242783i −0.000149770 0.000849389i
\(818\) 3.92602 + 6.80007i 0.137270 + 0.237759i
\(819\) 0 0
\(820\) −7.94949 + 13.7689i −0.277608 + 0.480832i
\(821\) −38.1883 13.8994i −1.33278 0.485092i −0.425248 0.905077i \(-0.639813\pi\)
−0.907531 + 0.419985i \(0.862035\pi\)
\(822\) 0 0
\(823\) 19.9552 + 16.7444i 0.695594 + 0.583672i 0.920516 0.390704i \(-0.127768\pi\)
−0.224923 + 0.974377i \(0.572213\pi\)
\(824\) 1.22004 + 1.02373i 0.0425020 + 0.0356634i
\(825\) 0 0
\(826\) −65.5053 23.8420i −2.27922 0.829568i
\(827\) 18.8097 32.5794i 0.654079 1.13290i −0.328045 0.944662i \(-0.606390\pi\)
0.982124 0.188236i \(-0.0602769\pi\)
\(828\) 0 0
\(829\) 17.5107 + 30.3295i 0.608173 + 1.05339i 0.991541 + 0.129791i \(0.0414306\pi\)
−0.383368 + 0.923595i \(0.625236\pi\)
\(830\) −0.310622 1.76162i −0.0107818 0.0611469i
\(831\) 0 0
\(832\) −3.36319 + 1.22410i −0.116598 + 0.0424380i
\(833\) 1.77719 10.0789i 0.0615759 0.349215i
\(834\) 0 0
\(835\) −1.28106 + 1.07494i −0.0443329 + 0.0371997i
\(836\) −0.573978 −0.0198514
\(837\) 0 0
\(838\) 89.7606 3.10073
\(839\) 20.3876 17.1072i 0.703858 0.590607i −0.219010 0.975723i \(-0.570283\pi\)
0.922868 + 0.385116i \(0.125838\pi\)
\(840\) 0 0
\(841\) 2.46879 14.0012i 0.0851306 0.482800i
\(842\) −21.9312 + 7.98232i −0.755800 + 0.275089i
\(843\) 0 0
\(844\) −5.47178 31.0320i −0.188346 1.06817i
\(845\) 1.92468 + 3.33364i 0.0662109 + 0.114681i
\(846\) 0 0
\(847\) −2.18180 + 3.77899i −0.0749675 + 0.129848i
\(848\) −30.9278 11.2568i −1.06207 0.386560i
\(849\) 0 0
\(850\) −27.8214 23.3449i −0.954265 0.800723i
\(851\) 16.8216 + 14.1150i 0.576637 + 0.483856i
\(852\) 0 0
\(853\) −2.30706 0.839700i −0.0789921 0.0287508i 0.302222 0.953238i \(-0.402272\pi\)
−0.381214 + 0.924487i \(0.624494\pi\)
\(854\) −5.18227 + 8.97595i −0.177334 + 0.307151i
\(855\) 0 0
\(856\) −12.3400 21.3735i −0.421773 0.730533i
\(857\) −1.70692 9.68042i −0.0583072 0.330677i 0.941676 0.336522i \(-0.109251\pi\)
−0.999983 + 0.00584499i \(0.998139\pi\)
\(858\) 0 0
\(859\) −8.28523 + 3.01558i −0.282689 + 0.102890i −0.479473 0.877557i \(-0.659172\pi\)
0.196785 + 0.980447i \(0.436950\pi\)
\(860\) −0.210952 + 1.19637i −0.00719339 + 0.0407957i
\(861\) 0 0
\(862\) 22.4604 18.8465i 0.765004 0.641914i
\(863\) −6.62124 −0.225390 −0.112695 0.993630i \(-0.535948\pi\)
−0.112695 + 0.993630i \(0.535948\pi\)
\(864\) 0 0
\(865\) 8.78106 0.298565
\(866\) 11.7645 9.87155i 0.399772 0.335449i
\(867\) 0 0
\(868\) 15.3910 87.2867i 0.522404 2.96270i
\(869\) 32.2511 11.7384i 1.09404 0.398199i
\(870\) 0 0
\(871\) −3.79679 21.5327i −0.128649 0.729606i
\(872\) 16.4978 + 28.5750i 0.558685 + 0.967671i
\(873\) 0 0
\(874\) −0.323826 + 0.560882i −0.0109536 + 0.0189721i
\(875\) −13.8769 5.05076i −0.469123 0.170747i
\(876\) 0 0
\(877\) −3.12243 2.62003i −0.105437 0.0884720i 0.588545 0.808464i \(-0.299701\pi\)
−0.693982 + 0.719992i \(0.744145\pi\)
\(878\) 56.2627 + 47.2100i 1.89877 + 1.59326i
\(879\) 0 0
\(880\) 9.06583 + 3.29969i 0.305609 + 0.111233i
\(881\) −4.62567 + 8.01189i −0.155843 + 0.269927i −0.933366 0.358927i \(-0.883143\pi\)
0.777523 + 0.628855i \(0.216476\pi\)
\(882\) 0 0
\(883\) 18.8851 + 32.7099i 0.635533 + 1.10078i 0.986402 + 0.164351i \(0.0525530\pi\)
−0.350869 + 0.936425i \(0.614114\pi\)
\(884\) −5.02094 28.4752i −0.168873 0.957724i
\(885\) 0 0
\(886\) −73.5044 + 26.7534i −2.46943 + 0.898798i
\(887\) 3.29561 18.6903i 0.110656 0.627559i −0.878154 0.478378i \(-0.841225\pi\)
0.988810 0.149182i \(-0.0476639\pi\)
\(888\) 0 0
\(889\) 16.4081 13.7680i 0.550309 0.461764i
\(890\) −18.8057 −0.630369
\(891\) 0 0
\(892\) −45.5945 −1.52662
\(893\) −0.309993 + 0.260115i −0.0103735 + 0.00870441i
\(894\) 0 0
\(895\) −0.413067 + 2.34262i −0.0138073 + 0.0783051i
\(896\) −40.4495 + 14.7224i −1.35132 + 0.491842i
\(897\) 0 0
\(898\) −17.1841 97.4557i −0.573440 3.25214i
\(899\) 20.4670 + 35.4499i 0.682614 + 1.18232i
\(900\) 0 0
\(901\) −7.43717 + 12.8816i −0.247768 + 0.429147i
\(902\) 56.9243 + 20.7188i 1.89537 + 0.689859i
\(903\) 0 0
\(904\) 6.47431 + 5.43259i 0.215332 + 0.180685i
\(905\) 2.56308 + 2.15068i 0.0851997 + 0.0714911i
\(906\) 0 0
\(907\) −9.06418 3.29909i −0.300971 0.109545i 0.187120 0.982337i \(-0.440085\pi\)
−0.488091 + 0.872792i \(0.662307\pi\)
\(908\) 28.7237 49.7510i 0.953231 1.65104i
\(909\) 0 0
\(910\) −4.17617 7.23335i −0.138439 0.239783i
\(911\) −1.13475 6.43550i −0.0375960 0.213218i 0.960222 0.279237i \(-0.0900813\pi\)
−0.997818 + 0.0660189i \(0.978970\pi\)
\(912\) 0 0
\(913\) −4.40673 + 1.60392i −0.145841 + 0.0530819i
\(914\) −0.661626 + 3.75227i −0.0218847 + 0.124114i
\(915\) 0 0
\(916\) −94.9582 + 79.6794i −3.13751 + 2.63268i
\(917\) 40.7880 1.34694
\(918\) 0 0
\(919\) 3.89124 0.128360 0.0641802 0.997938i \(-0.479557\pi\)
0.0641802 + 0.997938i \(0.479557\pi\)
\(920\) 13.3641 11.2138i 0.440602 0.369709i
\(921\) 0 0
\(922\) 11.5363 65.4254i 0.379927 2.15467i
\(923\) 24.2888 8.84040i 0.799476 0.290985i
\(924\) 0 0
\(925\) −2.98570 16.9327i −0.0981692 0.556745i
\(926\) −8.55391 14.8158i −0.281099 0.486878i
\(927\) 0 0
\(928\) −15.1079 + 26.1676i −0.495940 + 0.858994i
\(929\) 37.4495 + 13.6305i 1.22868 + 0.447203i 0.873145 0.487460i \(-0.162077\pi\)
0.355535 + 0.934663i \(0.384299\pi\)
\(930\) 0 0
\(931\) 0.109470 + 0.0918566i 0.00358775 + 0.00301048i
\(932\) −47.0223 39.4564i −1.54027 1.29244i
\(933\) 0 0
\(934\) −80.2969 29.2257i −2.62739 0.956294i
\(935\) 2.18004 3.77595i 0.0712951 0.123487i
\(936\) 0 0
\(937\) −16.5326 28.6352i −0.540095 0.935472i −0.998898 0.0469340i \(-0.985055\pi\)
0.458803 0.888538i \(-0.348278\pi\)
\(938\) −14.1985 80.5235i −0.463596 2.62919i
\(939\) 0 0
\(940\) 18.7383 6.82018i 0.611176 0.222450i
\(941\) −9.34343 + 52.9892i −0.304587 + 1.72740i 0.320855 + 0.947128i \(0.396030\pi\)
−0.625442 + 0.780270i \(0.715081\pi\)
\(942\) 0 0
\(943\) 36.0278 30.2309i 1.17323 0.984454i
\(944\) −56.6373 −1.84339
\(945\) 0 0
\(946\) 4.62866 0.150491
\(947\) 32.3542 27.1484i 1.05137 0.882203i 0.0581321 0.998309i \(-0.481486\pi\)
0.993237 + 0.116106i \(0.0370411\pi\)
\(948\) 0 0
\(949\) 3.12402 17.7172i 0.101410 0.575124i
\(950\) 0.476529 0.173442i 0.0154607 0.00562722i
\(951\) 0 0
\(952\) −10.2638 58.2090i −0.332652 1.88657i
\(953\) −12.2888 21.2848i −0.398073 0.689483i 0.595415 0.803418i \(-0.296988\pi\)
−0.993488 + 0.113935i \(0.963654\pi\)
\(954\) 0 0
\(955\) 2.45883 4.25881i 0.0795657 0.137812i
\(956\) 62.2627 + 22.6618i 2.01372 + 0.732934i
\(957\) 0 0
\(958\) 21.5822 + 18.1096i 0.697289 + 0.585095i
\(959\) −26.2401 22.0181i −0.847337 0.711000i
\(960\) 0 0
\(961\) −7.30288 2.65803i −0.235577 0.0857429i
\(962\) 9.94743 17.2295i 0.320718 0.555500i
\(963\) 0 0
\(964\) 28.6163 + 49.5649i 0.921670 + 1.59638i
\(965\) −0.824130 4.67388i −0.0265297 0.150457i
\(966\) 0 0
\(967\) −4.20233 + 1.52952i −0.135138 + 0.0491862i −0.408704 0.912667i \(-0.634019\pi\)
0.273566 + 0.961853i \(0.411797\pi\)
\(968\) −1.43391 + 8.13208i −0.0460875 + 0.261375i
\(969\) 0 0
\(970\) 16.9231 14.2002i 0.543368 0.455939i
\(971\) −4.61949 −0.148246 −0.0741232 0.997249i \(-0.523616\pi\)
−0.0741232 + 0.997249i \(0.523616\pi\)
\(972\) 0 0
\(973\) 24.0746 0.771796
\(974\) −9.20755 + 7.72605i −0.295029 + 0.247559i
\(975\) 0 0
\(976\) −1.46229 + 8.29304i −0.0468066 + 0.265454i
\(977\) 10.6004 3.85825i 0.339138 0.123436i −0.166836 0.985985i \(-0.553355\pi\)
0.505975 + 0.862548i \(0.331133\pi\)
\(978\) 0 0
\(979\) 8.56108 + 48.5523i 0.273613 + 1.55174i
\(980\) −3.52094 6.09845i −0.112472 0.194808i
\(981\) 0 0
\(982\) −28.2841 + 48.9894i −0.902580 + 1.56332i
\(983\) 16.0351 + 5.83629i 0.511440 + 0.186149i 0.584832 0.811154i \(-0.301160\pi\)
−0.0733925 + 0.997303i \(0.523383\pi\)
\(984\) 0 0
\(985\) 5.04820 + 4.23594i 0.160849 + 0.134968i
\(986\) 38.2545 + 32.0993i 1.21827 + 1.02225i
\(987\) 0 0
\(988\) 0.379385 + 0.138085i 0.0120699 + 0.00439307i
\(989\) 1.79679 3.11213i 0.0571346 0.0989600i
\(990\) 0 0
\(991\) −1.00000 1.73205i −0.0317660 0.0550204i 0.849705 0.527258i \(-0.176780\pi\)
−0.881471 + 0.472237i \(0.843446\pi\)
\(992\) −4.96972 28.1847i −0.157789 0.894865i
\(993\) 0 0
\(994\) 90.8303 33.0595i 2.88096 1.04858i
\(995\) 0.834970 4.73535i 0.0264703 0.150121i
\(996\) 0 0
\(997\) 17.1477 14.3886i 0.543073 0.455693i −0.329514 0.944151i \(-0.606885\pi\)
0.872587 + 0.488458i \(0.162440\pi\)
\(998\) −26.4884 −0.838477
\(999\) 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 729.2.e.i.325.1 6
3.2 odd 2 729.2.e.a.325.1 6
9.2 odd 6 729.2.e.h.568.1 6
9.4 even 3 729.2.e.b.82.1 6
9.5 odd 6 729.2.e.g.82.1 6
9.7 even 3 729.2.e.c.568.1 6
27.2 odd 18 729.2.e.h.163.1 6
27.4 even 9 243.2.a.f.1.3 yes 3
27.5 odd 18 243.2.c.f.82.3 6
27.7 even 9 729.2.e.b.649.1 6
27.11 odd 18 729.2.e.a.406.1 6
27.13 even 9 243.2.c.e.163.1 6
27.14 odd 18 243.2.c.f.163.3 6
27.16 even 9 inner 729.2.e.i.406.1 6
27.20 odd 18 729.2.e.g.649.1 6
27.22 even 9 243.2.c.e.82.1 6
27.23 odd 18 243.2.a.e.1.1 3
27.25 even 9 729.2.e.c.163.1 6
108.23 even 18 3888.2.a.bd.1.3 3
108.31 odd 18 3888.2.a.bk.1.1 3
135.4 even 18 6075.2.a.bq.1.1 3
135.104 odd 18 6075.2.a.bv.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
243.2.a.e.1.1 3 27.23 odd 18
243.2.a.f.1.3 yes 3 27.4 even 9
243.2.c.e.82.1 6 27.22 even 9
243.2.c.e.163.1 6 27.13 even 9
243.2.c.f.82.3 6 27.5 odd 18
243.2.c.f.163.3 6 27.14 odd 18
729.2.e.a.325.1 6 3.2 odd 2
729.2.e.a.406.1 6 27.11 odd 18
729.2.e.b.82.1 6 9.4 even 3
729.2.e.b.649.1 6 27.7 even 9
729.2.e.c.163.1 6 27.25 even 9
729.2.e.c.568.1 6 9.7 even 3
729.2.e.g.82.1 6 9.5 odd 6
729.2.e.g.649.1 6 27.20 odd 18
729.2.e.h.163.1 6 27.2 odd 18
729.2.e.h.568.1 6 9.2 odd 6
729.2.e.i.325.1 6 1.1 even 1 trivial
729.2.e.i.406.1 6 27.16 even 9 inner
3888.2.a.bd.1.3 3 108.23 even 18
3888.2.a.bk.1.1 3 108.31 odd 18
6075.2.a.bq.1.1 3 135.4 even 18
6075.2.a.bv.1.3 3 135.104 odd 18