Properties

Label 729.2.c.d.487.6
Level $729$
Weight $2$
Character 729.487
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), 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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 487.6
Root \(0.0878222i\) of defining polynomial
Character \(\chi\) \(=\) 729.487
Dual form 729.2.c.d.244.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35253 - 2.34265i) q^{2} +(-2.65869 - 4.60498i) q^{4} +(-0.836192 - 1.44833i) q^{5} +(-0.250296 + 0.433525i) q^{7} -8.97372 q^{8} +O(q^{10})\) \(q+(1.35253 - 2.34265i) q^{2} +(-2.65869 - 4.60498i) q^{4} +(-0.836192 - 1.44833i) q^{5} +(-0.250296 + 0.433525i) q^{7} -8.97372 q^{8} -4.52391 q^{10} +(-0.958859 + 1.66079i) q^{11} +(-1.55622 - 2.69545i) q^{13} +(0.677066 + 1.17271i) q^{14} +(-6.81987 + 11.8124i) q^{16} -2.66467 q^{17} +5.79664 q^{19} +(-4.44635 + 7.70130i) q^{20} +(2.59378 + 4.49255i) q^{22} +(-2.32293 - 4.02344i) q^{23} +(1.10156 - 1.90797i) q^{25} -8.41934 q^{26} +2.66183 q^{28} +(-1.30754 + 2.26472i) q^{29} +(2.30730 + 3.99636i) q^{31} +(9.47446 + 16.4103i) q^{32} +(-3.60406 + 6.24241i) q^{34} +0.837181 q^{35} -4.85867 q^{37} +(7.84014 - 13.5795i) q^{38} +(7.50375 + 12.9969i) q^{40} +(-5.77408 - 10.0010i) q^{41} +(4.50217 - 7.79798i) q^{43} +10.1972 q^{44} -12.5674 q^{46} +(3.41612 - 5.91689i) q^{47} +(3.37470 + 5.84516i) q^{49} +(-2.97980 - 5.16117i) q^{50} +(-8.27499 + 14.3327i) q^{52} +5.43322 q^{53} +3.20716 q^{55} +(2.24608 - 3.89033i) q^{56} +(3.53697 + 6.12621i) q^{58} +(-1.09566 - 1.89773i) q^{59} +(-3.42017 + 5.92391i) q^{61} +12.4828 q^{62} +23.9786 q^{64} +(-2.60259 + 4.50783i) q^{65} +(-6.24180 - 10.8111i) q^{67} +(7.08453 + 12.2708i) q^{68} +(1.13231 - 1.96123i) q^{70} +2.83568 q^{71} +9.93497 q^{73} +(-6.57151 + 11.3822i) q^{74} +(-15.4114 - 26.6934i) q^{76} +(-0.479996 - 0.831378i) q^{77} +(-2.65561 + 4.59964i) q^{79} +22.8109 q^{80} -31.2385 q^{82} +(-1.36408 + 2.36265i) q^{83} +(2.22818 + 3.85932i) q^{85} +(-12.1787 - 21.0941i) q^{86} +(8.60453 - 14.9035i) q^{88} -11.2189 q^{89} +1.55806 q^{91} +(-12.3519 + 21.3941i) q^{92} +(-9.24082 - 16.0056i) q^{94} +(-4.84710 - 8.39543i) q^{95} +(3.44457 - 5.96617i) q^{97} +18.2576 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28} + 21 q^{29} - 15 q^{31} - 60 q^{35} + 6 q^{37} + 15 q^{38} - 3 q^{40} - 12 q^{41} - 6 q^{43} + 66 q^{44} - 6 q^{46} - 15 q^{47} - 12 q^{49} - 24 q^{50} - 3 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} + 15 q^{58} + 6 q^{59} - 24 q^{61} + 60 q^{62} + 12 q^{64} - 15 q^{65} - 15 q^{67} + 36 q^{68} + 15 q^{70} + 24 q^{73} + 24 q^{74} - 9 q^{76} + 15 q^{77} - 24 q^{79} + 42 q^{80} - 42 q^{82} - 6 q^{83} + 18 q^{85} - 30 q^{86} + 21 q^{88} + 18 q^{89} + 36 q^{91} + 6 q^{92} + 6 q^{94} - 33 q^{95} + 21 q^{97} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35253 2.34265i 0.956385 1.65651i 0.225218 0.974308i \(-0.427691\pi\)
0.731167 0.682199i \(-0.238976\pi\)
\(3\) 0 0
\(4\) −2.65869 4.60498i −1.32934 2.30249i
\(5\) −0.836192 1.44833i −0.373957 0.647712i 0.616214 0.787579i \(-0.288666\pi\)
−0.990170 + 0.139867i \(0.955332\pi\)
\(6\) 0 0
\(7\) −0.250296 + 0.433525i −0.0946028 + 0.163857i −0.909443 0.415829i \(-0.863491\pi\)
0.814840 + 0.579686i \(0.196825\pi\)
\(8\) −8.97372 −3.17269
\(9\) 0 0
\(10\) −4.52391 −1.43059
\(11\) −0.958859 + 1.66079i −0.289107 + 0.500748i −0.973597 0.228275i \(-0.926692\pi\)
0.684490 + 0.729022i \(0.260025\pi\)
\(12\) 0 0
\(13\) −1.55622 2.69545i −0.431617 0.747583i 0.565396 0.824820i \(-0.308723\pi\)
−0.997013 + 0.0772371i \(0.975390\pi\)
\(14\) 0.677066 + 1.17271i 0.180953 + 0.313421i
\(15\) 0 0
\(16\) −6.81987 + 11.8124i −1.70497 + 2.95309i
\(17\) −2.66467 −0.646278 −0.323139 0.946352i \(-0.604738\pi\)
−0.323139 + 0.946352i \(0.604738\pi\)
\(18\) 0 0
\(19\) 5.79664 1.32984 0.664920 0.746915i \(-0.268466\pi\)
0.664920 + 0.746915i \(0.268466\pi\)
\(20\) −4.44635 + 7.70130i −0.994234 + 1.72206i
\(21\) 0 0
\(22\) 2.59378 + 4.49255i 0.552995 + 0.957815i
\(23\) −2.32293 4.02344i −0.484365 0.838945i 0.515473 0.856906i \(-0.327616\pi\)
−0.999839 + 0.0179603i \(0.994283\pi\)
\(24\) 0 0
\(25\) 1.10156 1.90797i 0.220313 0.381593i
\(26\) −8.41934 −1.65117
\(27\) 0 0
\(28\) 2.66183 0.503039
\(29\) −1.30754 + 2.26472i −0.242803 + 0.420547i −0.961512 0.274764i \(-0.911400\pi\)
0.718709 + 0.695312i \(0.244734\pi\)
\(30\) 0 0
\(31\) 2.30730 + 3.99636i 0.414404 + 0.717768i 0.995366 0.0961626i \(-0.0306569\pi\)
−0.580962 + 0.813931i \(0.697324\pi\)
\(32\) 9.47446 + 16.4103i 1.67486 + 2.90095i
\(33\) 0 0
\(34\) −3.60406 + 6.24241i −0.618090 + 1.07056i
\(35\) 0.837181 0.141509
\(36\) 0 0
\(37\) −4.85867 −0.798761 −0.399381 0.916785i \(-0.630775\pi\)
−0.399381 + 0.916785i \(0.630775\pi\)
\(38\) 7.84014 13.5795i 1.27184 2.20289i
\(39\) 0 0
\(40\) 7.50375 + 12.9969i 1.18645 + 2.05499i
\(41\) −5.77408 10.0010i −0.901760 1.56189i −0.825208 0.564828i \(-0.808942\pi\)
−0.0765514 0.997066i \(-0.524391\pi\)
\(42\) 0 0
\(43\) 4.50217 7.79798i 0.686574 1.18918i −0.286365 0.958121i \(-0.592447\pi\)
0.972939 0.231061i \(-0.0742196\pi\)
\(44\) 10.1972 1.53729
\(45\) 0 0
\(46\) −12.5674 −1.85296
\(47\) 3.41612 5.91689i 0.498292 0.863067i −0.501706 0.865038i \(-0.667294\pi\)
0.999998 + 0.00197091i \(0.000627360\pi\)
\(48\) 0 0
\(49\) 3.37470 + 5.84516i 0.482101 + 0.835023i
\(50\) −2.97980 5.16117i −0.421408 0.729900i
\(51\) 0 0
\(52\) −8.27499 + 14.3327i −1.14754 + 1.98759i
\(53\) 5.43322 0.746309 0.373155 0.927769i \(-0.378276\pi\)
0.373155 + 0.927769i \(0.378276\pi\)
\(54\) 0 0
\(55\) 3.20716 0.432454
\(56\) 2.24608 3.89033i 0.300145 0.519867i
\(57\) 0 0
\(58\) 3.53697 + 6.12621i 0.464427 + 0.804410i
\(59\) −1.09566 1.89773i −0.142642 0.247064i 0.785849 0.618419i \(-0.212227\pi\)
−0.928491 + 0.371355i \(0.878893\pi\)
\(60\) 0 0
\(61\) −3.42017 + 5.92391i −0.437908 + 0.758478i −0.997528 0.0702708i \(-0.977614\pi\)
0.559620 + 0.828749i \(0.310947\pi\)
\(62\) 12.4828 1.58532
\(63\) 0 0
\(64\) 23.9786 2.99733
\(65\) −2.60259 + 4.50783i −0.322812 + 0.559127i
\(66\) 0 0
\(67\) −6.24180 10.8111i −0.762557 1.32079i −0.941529 0.336933i \(-0.890610\pi\)
0.178971 0.983854i \(-0.442723\pi\)
\(68\) 7.08453 + 12.2708i 0.859126 + 1.48805i
\(69\) 0 0
\(70\) 1.13231 1.96123i 0.135337 0.234411i
\(71\) 2.83568 0.336534 0.168267 0.985741i \(-0.446183\pi\)
0.168267 + 0.985741i \(0.446183\pi\)
\(72\) 0 0
\(73\) 9.93497 1.16280 0.581400 0.813618i \(-0.302505\pi\)
0.581400 + 0.813618i \(0.302505\pi\)
\(74\) −6.57151 + 11.3822i −0.763923 + 1.32315i
\(75\) 0 0
\(76\) −15.4114 26.6934i −1.76781 3.06194i
\(77\) −0.479996 0.831378i −0.0547007 0.0947443i
\(78\) 0 0
\(79\) −2.65561 + 4.59964i −0.298779 + 0.517500i −0.975857 0.218411i \(-0.929913\pi\)
0.677078 + 0.735911i \(0.263246\pi\)
\(80\) 22.8109 2.55033
\(81\) 0 0
\(82\) −31.2385 −3.44972
\(83\) −1.36408 + 2.36265i −0.149727 + 0.259334i −0.931126 0.364697i \(-0.881173\pi\)
0.781400 + 0.624031i \(0.214506\pi\)
\(84\) 0 0
\(85\) 2.22818 + 3.85932i 0.241680 + 0.418602i
\(86\) −12.1787 21.0941i −1.31326 2.27463i
\(87\) 0 0
\(88\) 8.60453 14.9035i 0.917246 1.58872i
\(89\) −11.2189 −1.18920 −0.594600 0.804021i \(-0.702690\pi\)
−0.594600 + 0.804021i \(0.702690\pi\)
\(90\) 0 0
\(91\) 1.55806 0.163329
\(92\) −12.3519 + 21.3941i −1.28778 + 2.23049i
\(93\) 0 0
\(94\) −9.24082 16.0056i −0.953118 1.65085i
\(95\) −4.84710 8.39543i −0.497302 0.861353i
\(96\) 0 0
\(97\) 3.44457 5.96617i 0.349743 0.605773i −0.636461 0.771309i \(-0.719602\pi\)
0.986204 + 0.165536i \(0.0529355\pi\)
\(98\) 18.2576 1.84429
\(99\) 0 0
\(100\) −11.7149 −1.17149
\(101\) 1.86482 3.22997i 0.185557 0.321394i −0.758207 0.652014i \(-0.773924\pi\)
0.943764 + 0.330620i \(0.107258\pi\)
\(102\) 0 0
\(103\) −3.84040 6.65177i −0.378406 0.655418i 0.612425 0.790529i \(-0.290194\pi\)
−0.990830 + 0.135111i \(0.956861\pi\)
\(104\) 13.9651 + 24.1882i 1.36939 + 2.37185i
\(105\) 0 0
\(106\) 7.34860 12.7281i 0.713759 1.23627i
\(107\) 10.7658 1.04077 0.520383 0.853933i \(-0.325789\pi\)
0.520383 + 0.853933i \(0.325789\pi\)
\(108\) 0 0
\(109\) 12.2298 1.17141 0.585703 0.810526i \(-0.300819\pi\)
0.585703 + 0.810526i \(0.300819\pi\)
\(110\) 4.33779 7.51328i 0.413592 0.716363i
\(111\) 0 0
\(112\) −3.41396 5.91316i −0.322589 0.558741i
\(113\) −0.971975 1.68351i −0.0914357 0.158371i 0.816680 0.577091i \(-0.195812\pi\)
−0.908115 + 0.418720i \(0.862479\pi\)
\(114\) 0 0
\(115\) −3.88484 + 6.72874i −0.362263 + 0.627458i
\(116\) 13.9053 1.29108
\(117\) 0 0
\(118\) −5.92764 −0.545684
\(119\) 0.666956 1.15520i 0.0611397 0.105897i
\(120\) 0 0
\(121\) 3.66118 + 6.34135i 0.332834 + 0.576486i
\(122\) 9.25178 + 16.0245i 0.837617 + 1.45079i
\(123\) 0 0
\(124\) 12.2688 21.2502i 1.10177 1.90832i
\(125\) −12.0464 −1.07746
\(126\) 0 0
\(127\) 2.34433 0.208026 0.104013 0.994576i \(-0.466832\pi\)
0.104013 + 0.994576i \(0.466832\pi\)
\(128\) 13.4829 23.3531i 1.19173 2.06414i
\(129\) 0 0
\(130\) 7.04019 + 12.1940i 0.617465 + 1.06948i
\(131\) −8.55119 14.8111i −0.747121 1.29405i −0.949197 0.314682i \(-0.898102\pi\)
0.202076 0.979370i \(-0.435231\pi\)
\(132\) 0 0
\(133\) −1.45087 + 2.51298i −0.125807 + 0.217903i
\(134\) −33.7689 −2.91719
\(135\) 0 0
\(136\) 23.9120 2.05044
\(137\) 6.96358 12.0613i 0.594939 1.03046i −0.398617 0.917118i \(-0.630510\pi\)
0.993556 0.113347i \(-0.0361570\pi\)
\(138\) 0 0
\(139\) −3.95832 6.85601i −0.335740 0.581519i 0.647887 0.761737i \(-0.275653\pi\)
−0.983627 + 0.180218i \(0.942320\pi\)
\(140\) −2.22580 3.85520i −0.188115 0.325824i
\(141\) 0 0
\(142\) 3.83536 6.64303i 0.321856 0.557471i
\(143\) 5.96877 0.499134
\(144\) 0 0
\(145\) 4.37340 0.363191
\(146\) 13.4374 23.2742i 1.11208 1.92619i
\(147\) 0 0
\(148\) 12.9177 + 22.3741i 1.06183 + 1.83914i
\(149\) 0.364067 + 0.630583i 0.0298255 + 0.0516594i 0.880553 0.473948i \(-0.157171\pi\)
−0.850727 + 0.525607i \(0.823838\pi\)
\(150\) 0 0
\(151\) −2.17105 + 3.76036i −0.176677 + 0.306014i −0.940740 0.339128i \(-0.889868\pi\)
0.764063 + 0.645141i \(0.223202\pi\)
\(152\) −52.0174 −4.21917
\(153\) 0 0
\(154\) −2.59684 −0.209260
\(155\) 3.85870 6.68346i 0.309938 0.536828i
\(156\) 0 0
\(157\) 7.76163 + 13.4435i 0.619446 + 1.07291i 0.989587 + 0.143936i \(0.0459759\pi\)
−0.370141 + 0.928975i \(0.620691\pi\)
\(158\) 7.18359 + 12.4423i 0.571495 + 0.989859i
\(159\) 0 0
\(160\) 15.8449 27.4443i 1.25265 2.16966i
\(161\) 2.32568 0.183289
\(162\) 0 0
\(163\) 8.49738 0.665566 0.332783 0.943003i \(-0.392012\pi\)
0.332783 + 0.943003i \(0.392012\pi\)
\(164\) −30.7030 + 53.1791i −2.39750 + 4.15259i
\(165\) 0 0
\(166\) 3.68991 + 6.39111i 0.286393 + 0.496047i
\(167\) 11.5710 + 20.0415i 0.895389 + 1.55086i 0.833323 + 0.552787i \(0.186436\pi\)
0.0620658 + 0.998072i \(0.480231\pi\)
\(168\) 0 0
\(169\) 1.65637 2.86892i 0.127413 0.220686i
\(170\) 12.0547 0.924556
\(171\) 0 0
\(172\) −47.8794 −3.65077
\(173\) −1.28924 + 2.23303i −0.0980190 + 0.169774i −0.910865 0.412705i \(-0.864584\pi\)
0.812846 + 0.582479i \(0.197917\pi\)
\(174\) 0 0
\(175\) 0.551433 + 0.955111i 0.0416845 + 0.0721996i
\(176\) −13.0786 22.6528i −0.985835 1.70752i
\(177\) 0 0
\(178\) −15.1739 + 26.2820i −1.13733 + 1.96992i
\(179\) 8.89613 0.664928 0.332464 0.943116i \(-0.392120\pi\)
0.332464 + 0.943116i \(0.392120\pi\)
\(180\) 0 0
\(181\) 7.91183 0.588082 0.294041 0.955793i \(-0.405000\pi\)
0.294041 + 0.955793i \(0.405000\pi\)
\(182\) 2.10732 3.64999i 0.156205 0.270555i
\(183\) 0 0
\(184\) 20.8454 + 36.1052i 1.53674 + 2.66171i
\(185\) 4.06279 + 7.03695i 0.298702 + 0.517367i
\(186\) 0 0
\(187\) 2.55504 4.42547i 0.186843 0.323622i
\(188\) −36.3296 −2.64961
\(189\) 0 0
\(190\) −26.2235 −1.90245
\(191\) −7.94867 + 13.7675i −0.575146 + 0.996182i 0.420880 + 0.907116i \(0.361721\pi\)
−0.996026 + 0.0890656i \(0.971612\pi\)
\(192\) 0 0
\(193\) 2.29239 + 3.97054i 0.165010 + 0.285805i 0.936659 0.350243i \(-0.113901\pi\)
−0.771649 + 0.636049i \(0.780568\pi\)
\(194\) −9.31779 16.1389i −0.668978 1.15870i
\(195\) 0 0
\(196\) 17.9446 31.0809i 1.28176 2.22006i
\(197\) −2.99417 −0.213326 −0.106663 0.994295i \(-0.534017\pi\)
−0.106663 + 0.994295i \(0.534017\pi\)
\(198\) 0 0
\(199\) 14.8885 1.05542 0.527709 0.849425i \(-0.323051\pi\)
0.527709 + 0.849425i \(0.323051\pi\)
\(200\) −9.88513 + 17.1215i −0.698984 + 1.21068i
\(201\) 0 0
\(202\) −5.04447 8.73727i −0.354928 0.614753i
\(203\) −0.654541 1.13370i −0.0459397 0.0795700i
\(204\) 0 0
\(205\) −9.65648 + 16.7255i −0.674438 + 1.16816i
\(206\) −20.7771 −1.44761
\(207\) 0 0
\(208\) 42.4528 2.94357
\(209\) −5.55816 + 9.62701i −0.384466 + 0.665914i
\(210\) 0 0
\(211\) −6.93948 12.0195i −0.477733 0.827459i 0.521941 0.852982i \(-0.325208\pi\)
−0.999674 + 0.0255232i \(0.991875\pi\)
\(212\) −14.4452 25.0199i −0.992102 1.71837i
\(213\) 0 0
\(214\) 14.5610 25.2205i 0.995372 1.72403i
\(215\) −15.0587 −1.02700
\(216\) 0 0
\(217\) −2.31003 −0.156815
\(218\) 16.5412 28.6503i 1.12031 1.94044i
\(219\) 0 0
\(220\) −8.52684 14.7689i −0.574880 0.995721i
\(221\) 4.14681 + 7.18248i 0.278945 + 0.483146i
\(222\) 0 0
\(223\) 3.40599 5.89935i 0.228082 0.395050i −0.729158 0.684346i \(-0.760088\pi\)
0.957240 + 0.289296i \(0.0934213\pi\)
\(224\) −9.48567 −0.633788
\(225\) 0 0
\(226\) −5.25851 −0.349791
\(227\) −4.87042 + 8.43582i −0.323261 + 0.559905i −0.981159 0.193202i \(-0.938113\pi\)
0.657898 + 0.753107i \(0.271446\pi\)
\(228\) 0 0
\(229\) 7.02242 + 12.1632i 0.464055 + 0.803766i 0.999158 0.0410201i \(-0.0130608\pi\)
−0.535104 + 0.844786i \(0.679727\pi\)
\(230\) 10.5087 + 18.2017i 0.692926 + 1.20018i
\(231\) 0 0
\(232\) 11.7334 20.3229i 0.770339 1.33427i
\(233\) −5.32333 −0.348743 −0.174372 0.984680i \(-0.555789\pi\)
−0.174372 + 0.984680i \(0.555789\pi\)
\(234\) 0 0
\(235\) −11.4261 −0.745359
\(236\) −5.82602 + 10.0910i −0.379241 + 0.656865i
\(237\) 0 0
\(238\) −1.80416 3.12489i −0.116946 0.202557i
\(239\) 8.88675 + 15.3923i 0.574836 + 0.995646i 0.996059 + 0.0886886i \(0.0282676\pi\)
−0.421223 + 0.906957i \(0.638399\pi\)
\(240\) 0 0
\(241\) 1.00340 1.73793i 0.0646344 0.111950i −0.831897 0.554930i \(-0.812745\pi\)
0.896532 + 0.442979i \(0.146079\pi\)
\(242\) 19.8075 1.27327
\(243\) 0 0
\(244\) 36.3726 2.32852
\(245\) 5.64380 9.77536i 0.360569 0.624525i
\(246\) 0 0
\(247\) −9.02083 15.6245i −0.573981 0.994165i
\(248\) −20.7051 35.8622i −1.31477 2.27725i
\(249\) 0 0
\(250\) −16.2932 + 28.2206i −1.03047 + 1.78483i
\(251\) −23.5643 −1.48737 −0.743683 0.668533i \(-0.766923\pi\)
−0.743683 + 0.668533i \(0.766923\pi\)
\(252\) 0 0
\(253\) 8.90947 0.560133
\(254\) 3.17079 5.49196i 0.198953 0.344596i
\(255\) 0 0
\(256\) −12.4936 21.6395i −0.780848 1.35247i
\(257\) 2.93728 + 5.08752i 0.183223 + 0.317351i 0.942976 0.332860i \(-0.108014\pi\)
−0.759754 + 0.650211i \(0.774680\pi\)
\(258\) 0 0
\(259\) 1.21610 2.10635i 0.0755651 0.130883i
\(260\) 27.6779 1.71651
\(261\) 0 0
\(262\) −46.2631 −2.85814
\(263\) 10.9891 19.0336i 0.677615 1.17366i −0.298082 0.954540i \(-0.596347\pi\)
0.975697 0.219123i \(-0.0703197\pi\)
\(264\) 0 0
\(265\) −4.54321 7.86908i −0.279087 0.483393i
\(266\) 3.92470 + 6.79779i 0.240639 + 0.416799i
\(267\) 0 0
\(268\) −33.1900 + 57.4867i −2.02740 + 3.51156i
\(269\) 30.6026 1.86587 0.932937 0.360041i \(-0.117237\pi\)
0.932937 + 0.360041i \(0.117237\pi\)
\(270\) 0 0
\(271\) −16.0823 −0.976928 −0.488464 0.872584i \(-0.662443\pi\)
−0.488464 + 0.872584i \(0.662443\pi\)
\(272\) 18.1727 31.4761i 1.10188 1.90852i
\(273\) 0 0
\(274\) −18.8369 32.6265i −1.13798 1.97104i
\(275\) 2.11249 + 3.65894i 0.127388 + 0.220642i
\(276\) 0 0
\(277\) 10.4068 18.0251i 0.625283 1.08302i −0.363203 0.931710i \(-0.618317\pi\)
0.988486 0.151312i \(-0.0483499\pi\)
\(278\) −21.4150 −1.28439
\(279\) 0 0
\(280\) −7.51263 −0.448965
\(281\) 6.13014 10.6177i 0.365693 0.633400i −0.623194 0.782067i \(-0.714165\pi\)
0.988887 + 0.148668i \(0.0474985\pi\)
\(282\) 0 0
\(283\) −2.28629 3.95997i −0.135906 0.235396i 0.790037 0.613059i \(-0.210061\pi\)
−0.925943 + 0.377663i \(0.876728\pi\)
\(284\) −7.53920 13.0583i −0.447369 0.774866i
\(285\) 0 0
\(286\) 8.07296 13.9828i 0.477364 0.826819i
\(287\) 5.78091 0.341236
\(288\) 0 0
\(289\) −9.89952 −0.582325
\(290\) 5.91517 10.2454i 0.347351 0.601629i
\(291\) 0 0
\(292\) −26.4140 45.7504i −1.54576 2.67734i
\(293\) 13.0617 + 22.6235i 0.763073 + 1.32168i 0.941259 + 0.337685i \(0.109644\pi\)
−0.178186 + 0.983997i \(0.557023\pi\)
\(294\) 0 0
\(295\) −1.83236 + 3.17374i −0.106684 + 0.184782i
\(296\) 43.6004 2.53422
\(297\) 0 0
\(298\) 1.96965 0.114099
\(299\) −7.22998 + 12.5227i −0.418121 + 0.724206i
\(300\) 0 0
\(301\) 2.25375 + 3.90360i 0.129904 + 0.225000i
\(302\) 5.87282 + 10.1720i 0.337943 + 0.585334i
\(303\) 0 0
\(304\) −39.5323 + 68.4719i −2.26733 + 3.92713i
\(305\) 11.4397 0.655034
\(306\) 0 0
\(307\) 3.29277 0.187928 0.0939641 0.995576i \(-0.470046\pi\)
0.0939641 + 0.995576i \(0.470046\pi\)
\(308\) −2.55232 + 4.42075i −0.145432 + 0.251896i
\(309\) 0 0
\(310\) −10.4380 18.0792i −0.592840 1.02683i
\(311\) 17.3963 + 30.1313i 0.986455 + 1.70859i 0.635285 + 0.772278i \(0.280883\pi\)
0.351170 + 0.936312i \(0.385784\pi\)
\(312\) 0 0
\(313\) −5.31392 + 9.20398i −0.300360 + 0.520239i −0.976218 0.216793i \(-0.930440\pi\)
0.675857 + 0.737033i \(0.263774\pi\)
\(314\) 41.9914 2.36971
\(315\) 0 0
\(316\) 28.2417 1.58872
\(317\) −7.75011 + 13.4236i −0.435290 + 0.753944i −0.997319 0.0731733i \(-0.976687\pi\)
0.562030 + 0.827117i \(0.310021\pi\)
\(318\) 0 0
\(319\) −2.50748 4.34309i −0.140392 0.243166i
\(320\) −20.0507 34.7289i −1.12087 1.94140i
\(321\) 0 0
\(322\) 3.14556 5.44827i 0.175295 0.303620i
\(323\) −15.4461 −0.859446
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) 11.4930 19.9064i 0.636538 1.10252i
\(327\) 0 0
\(328\) 51.8150 + 89.7461i 2.86100 + 4.95540i
\(329\) 1.71008 + 2.96194i 0.0942797 + 0.163297i
\(330\) 0 0
\(331\) 7.28514 12.6182i 0.400427 0.693561i −0.593350 0.804945i \(-0.702195\pi\)
0.993777 + 0.111384i \(0.0355283\pi\)
\(332\) 14.5066 0.796153
\(333\) 0 0
\(334\) 62.6005 3.42534
\(335\) −10.4387 + 18.0803i −0.570327 + 0.987834i
\(336\) 0 0
\(337\) 10.3074 + 17.8529i 0.561479 + 0.972511i 0.997368 + 0.0725099i \(0.0231009\pi\)
−0.435888 + 0.900001i \(0.643566\pi\)
\(338\) −4.48060 7.76062i −0.243712 0.422122i
\(339\) 0 0
\(340\) 11.8481 20.5214i 0.642551 1.11293i
\(341\) −8.84951 −0.479228
\(342\) 0 0
\(343\) −6.88283 −0.371638
\(344\) −40.4012 + 69.9769i −2.17829 + 3.77290i
\(345\) 0 0
\(346\) 3.48748 + 6.04048i 0.187488 + 0.324738i
\(347\) −10.5918 18.3455i −0.568596 0.984838i −0.996705 0.0811104i \(-0.974153\pi\)
0.428109 0.903727i \(-0.359180\pi\)
\(348\) 0 0
\(349\) 2.31299 4.00621i 0.123811 0.214447i −0.797456 0.603377i \(-0.793822\pi\)
0.921268 + 0.388929i \(0.127155\pi\)
\(350\) 2.98333 0.159466
\(351\) 0 0
\(352\) −36.3387 −1.93686
\(353\) −6.82171 + 11.8155i −0.363083 + 0.628878i −0.988467 0.151440i \(-0.951609\pi\)
0.625384 + 0.780317i \(0.284942\pi\)
\(354\) 0 0
\(355\) −2.37118 4.10700i −0.125849 0.217977i
\(356\) 29.8275 + 51.6628i 1.58086 + 2.73812i
\(357\) 0 0
\(358\) 12.0323 20.8406i 0.635927 1.10146i
\(359\) 28.2447 1.49070 0.745349 0.666675i \(-0.232283\pi\)
0.745349 + 0.666675i \(0.232283\pi\)
\(360\) 0 0
\(361\) 14.6010 0.768473
\(362\) 10.7010 18.5347i 0.562432 0.974162i
\(363\) 0 0
\(364\) −4.14239 7.17483i −0.217120 0.376063i
\(365\) −8.30755 14.3891i −0.434837 0.753160i
\(366\) 0 0
\(367\) −17.4401 + 30.2071i −0.910366 + 1.57680i −0.0968183 + 0.995302i \(0.530867\pi\)
−0.813548 + 0.581498i \(0.802467\pi\)
\(368\) 63.3684 3.30331
\(369\) 0 0
\(370\) 21.9802 1.14270
\(371\) −1.35991 + 2.35543i −0.0706030 + 0.122288i
\(372\) 0 0
\(373\) −1.52972 2.64955i −0.0792059 0.137189i 0.823702 0.567023i \(-0.191905\pi\)
−0.902908 + 0.429835i \(0.858572\pi\)
\(374\) −6.91156 11.9712i −0.357388 0.619015i
\(375\) 0 0
\(376\) −30.6553 + 53.0965i −1.58093 + 2.73824i
\(377\) 8.13924 0.419192
\(378\) 0 0
\(379\) −7.67705 −0.394344 −0.197172 0.980369i \(-0.563176\pi\)
−0.197172 + 0.980369i \(0.563176\pi\)
\(380\) −25.7739 + 44.6417i −1.32217 + 2.29007i
\(381\) 0 0
\(382\) 21.5017 + 37.2420i 1.10012 + 1.90547i
\(383\) 5.18097 + 8.97370i 0.264735 + 0.458535i 0.967494 0.252893i \(-0.0813821\pi\)
−0.702759 + 0.711428i \(0.748049\pi\)
\(384\) 0 0
\(385\) −0.802739 + 1.39038i −0.0409113 + 0.0708605i
\(386\) 12.4021 0.631252
\(387\) 0 0
\(388\) −36.6322 −1.85972
\(389\) −0.213476 + 0.369751i −0.0108236 + 0.0187471i −0.871386 0.490597i \(-0.836779\pi\)
0.860563 + 0.509344i \(0.170112\pi\)
\(390\) 0 0
\(391\) 6.18986 + 10.7211i 0.313035 + 0.542192i
\(392\) −30.2836 52.4528i −1.52955 2.64927i
\(393\) 0 0
\(394\) −4.04971 + 7.01430i −0.204021 + 0.353376i
\(395\) 8.88239 0.446922
\(396\) 0 0
\(397\) −27.0891 −1.35956 −0.679781 0.733416i \(-0.737925\pi\)
−0.679781 + 0.733416i \(0.737925\pi\)
\(398\) 20.1372 34.8786i 1.00939 1.74831i
\(399\) 0 0
\(400\) 15.0250 + 26.0241i 0.751252 + 1.30121i
\(401\) 14.6802 + 25.4269i 0.733096 + 1.26976i 0.955554 + 0.294817i \(0.0952588\pi\)
−0.222458 + 0.974942i \(0.571408\pi\)
\(402\) 0 0
\(403\) 7.18133 12.4384i 0.357727 0.619602i
\(404\) −19.8319 −0.986675
\(405\) 0 0
\(406\) −3.54115 −0.175744
\(407\) 4.65878 8.06925i 0.230927 0.399978i
\(408\) 0 0
\(409\) 10.0920 + 17.4798i 0.499015 + 0.864320i 0.999999 0.00113651i \(-0.000361762\pi\)
−0.500984 + 0.865457i \(0.667028\pi\)
\(410\) 26.1214 + 45.2436i 1.29004 + 2.23442i
\(411\) 0 0
\(412\) −20.4208 + 35.3699i −1.00606 + 1.74255i
\(413\) 1.09695 0.0539775
\(414\) 0 0
\(415\) 4.56252 0.223965
\(416\) 29.4887 51.0758i 1.44580 2.50420i
\(417\) 0 0
\(418\) 15.0352 + 26.0417i 0.735395 + 1.27374i
\(419\) 12.1852 + 21.1053i 0.595284 + 1.03106i 0.993507 + 0.113774i \(0.0362938\pi\)
−0.398223 + 0.917289i \(0.630373\pi\)
\(420\) 0 0
\(421\) 13.0873 22.6678i 0.637835 1.10476i −0.348072 0.937468i \(-0.613164\pi\)
0.985907 0.167294i \(-0.0535030\pi\)
\(422\) −37.5435 −1.82759
\(423\) 0 0
\(424\) −48.7561 −2.36781
\(425\) −2.93531 + 5.08410i −0.142383 + 0.246615i
\(426\) 0 0
\(427\) −1.71211 2.96545i −0.0828546 0.143508i
\(428\) −28.6228 49.5761i −1.38353 2.39635i
\(429\) 0 0
\(430\) −20.3674 + 35.2774i −0.982203 + 1.70123i
\(431\) −31.9185 −1.53746 −0.768731 0.639572i \(-0.779111\pi\)
−0.768731 + 0.639572i \(0.779111\pi\)
\(432\) 0 0
\(433\) 0.0123080 0.000591484 0.000295742 1.00000i \(-0.499906\pi\)
0.000295742 1.00000i \(0.499906\pi\)
\(434\) −3.12439 + 5.41160i −0.149976 + 0.259765i
\(435\) 0 0
\(436\) −32.5153 56.3182i −1.55720 2.69715i
\(437\) −13.4652 23.3224i −0.644128 1.11566i
\(438\) 0 0
\(439\) −2.65240 + 4.59410i −0.126592 + 0.219264i −0.922354 0.386345i \(-0.873737\pi\)
0.795762 + 0.605610i \(0.207071\pi\)
\(440\) −28.7802 −1.37204
\(441\) 0 0
\(442\) 22.4348 1.06711
\(443\) 20.3482 35.2441i 0.966771 1.67450i 0.261990 0.965071i \(-0.415621\pi\)
0.704781 0.709425i \(-0.251045\pi\)
\(444\) 0 0
\(445\) 9.38116 + 16.2486i 0.444709 + 0.770259i
\(446\) −9.21342 15.9581i −0.436268 0.755639i
\(447\) 0 0
\(448\) −6.00174 + 10.3953i −0.283556 + 0.491133i
\(449\) −15.4280 −0.728093 −0.364047 0.931381i \(-0.618605\pi\)
−0.364047 + 0.931381i \(0.618605\pi\)
\(450\) 0 0
\(451\) 22.1461 1.04282
\(452\) −5.16835 + 8.95185i −0.243099 + 0.421060i
\(453\) 0 0
\(454\) 13.1748 + 22.8194i 0.618324 + 1.07097i
\(455\) −1.30284 2.25658i −0.0610779 0.105790i
\(456\) 0 0
\(457\) −1.19437 + 2.06872i −0.0558704 + 0.0967704i −0.892608 0.450834i \(-0.851127\pi\)
0.836737 + 0.547604i \(0.184460\pi\)
\(458\) 37.9922 1.77526
\(459\) 0 0
\(460\) 41.3143 1.92629
\(461\) 16.2419 28.1319i 0.756462 1.31023i −0.188182 0.982134i \(-0.560259\pi\)
0.944644 0.328097i \(-0.106407\pi\)
\(462\) 0 0
\(463\) −16.9393 29.3397i −0.787234 1.36353i −0.927655 0.373438i \(-0.878179\pi\)
0.140421 0.990092i \(-0.455155\pi\)
\(464\) −17.8344 30.8901i −0.827943 1.43404i
\(465\) 0 0
\(466\) −7.19998 + 12.4707i −0.333533 + 0.577696i
\(467\) 13.8027 0.638711 0.319356 0.947635i \(-0.396534\pi\)
0.319356 + 0.947635i \(0.396534\pi\)
\(468\) 0 0
\(469\) 6.24918 0.288560
\(470\) −15.4542 + 26.7675i −0.712850 + 1.23469i
\(471\) 0 0
\(472\) 9.83211 + 17.0297i 0.452559 + 0.783856i
\(473\) 8.63389 + 14.9543i 0.396987 + 0.687601i
\(474\) 0 0
\(475\) 6.38537 11.0598i 0.292981 0.507458i
\(476\) −7.09291 −0.325103
\(477\) 0 0
\(478\) 48.0785 2.19906
\(479\) 2.94556 5.10186i 0.134586 0.233110i −0.790853 0.612006i \(-0.790363\pi\)
0.925439 + 0.378896i \(0.123696\pi\)
\(480\) 0 0
\(481\) 7.56115 + 13.0963i 0.344759 + 0.597140i
\(482\) −2.71425 4.70122i −0.123631 0.214135i
\(483\) 0 0
\(484\) 19.4679 33.7193i 0.884903 1.53270i
\(485\) −11.5213 −0.523155
\(486\) 0 0
\(487\) 29.0299 1.31547 0.657736 0.753249i \(-0.271514\pi\)
0.657736 + 0.753249i \(0.271514\pi\)
\(488\) 30.6916 53.1594i 1.38934 2.40642i
\(489\) 0 0
\(490\) −15.2669 26.4430i −0.689686 1.19457i
\(491\) 2.19175 + 3.79623i 0.0989125 + 0.171321i 0.911235 0.411887i \(-0.135130\pi\)
−0.812322 + 0.583209i \(0.801797\pi\)
\(492\) 0 0
\(493\) 3.48415 6.03473i 0.156918 0.271791i
\(494\) −48.8038 −2.19579
\(495\) 0 0
\(496\) −62.9420 −2.82618
\(497\) −0.709759 + 1.22934i −0.0318371 + 0.0551434i
\(498\) 0 0
\(499\) −17.6718 30.6084i −0.791096 1.37022i −0.925289 0.379264i \(-0.876177\pi\)
0.134192 0.990955i \(-0.457156\pi\)
\(500\) 32.0276 + 55.4735i 1.43232 + 2.48085i
\(501\) 0 0
\(502\) −31.8715 + 55.2030i −1.42249 + 2.46383i
\(503\) 8.37659 0.373494 0.186747 0.982408i \(-0.440206\pi\)
0.186747 + 0.982408i \(0.440206\pi\)
\(504\) 0 0
\(505\) −6.23740 −0.277561
\(506\) 12.0503 20.8718i 0.535703 0.927865i
\(507\) 0 0
\(508\) −6.23285 10.7956i −0.276538 0.478978i
\(509\) −1.92148 3.32811i −0.0851683 0.147516i 0.820295 0.571941i \(-0.193809\pi\)
−0.905463 + 0.424425i \(0.860476\pi\)
\(510\) 0 0
\(511\) −2.48668 + 4.30706i −0.110004 + 0.190533i
\(512\) −13.6601 −0.603699
\(513\) 0 0
\(514\) 15.8911 0.700925
\(515\) −6.42262 + 11.1243i −0.283015 + 0.490196i
\(516\) 0 0
\(517\) 6.55115 + 11.3469i 0.288119 + 0.499037i
\(518\) −3.28964 5.69783i −0.144539 0.250348i
\(519\) 0 0
\(520\) 23.3549 40.4520i 1.02418 1.77394i
\(521\) −19.6523 −0.860983 −0.430491 0.902595i \(-0.641660\pi\)
−0.430491 + 0.902595i \(0.641660\pi\)
\(522\) 0 0
\(523\) −39.6103 −1.73204 −0.866018 0.500012i \(-0.833329\pi\)
−0.866018 + 0.500012i \(0.833329\pi\)
\(524\) −45.4699 + 78.7562i −1.98636 + 3.44048i
\(525\) 0 0
\(526\) −29.7261 51.4872i −1.29612 2.24495i
\(527\) −6.14820 10.6490i −0.267820 0.463878i
\(528\) 0 0
\(529\) 0.707953 1.22621i 0.0307806 0.0533135i
\(530\) −24.5794 −1.06766
\(531\) 0 0
\(532\) 15.4297 0.668961
\(533\) −17.9715 + 31.1275i −0.778430 + 1.34828i
\(534\) 0 0
\(535\) −9.00224 15.5923i −0.389201 0.674116i
\(536\) 56.0121 + 97.0159i 2.41936 + 4.19045i
\(537\) 0 0
\(538\) 41.3910 71.6913i 1.78449 3.09083i
\(539\) −12.9435 −0.557514
\(540\) 0 0
\(541\) −41.8257 −1.79823 −0.899115 0.437713i \(-0.855788\pi\)
−0.899115 + 0.437713i \(0.855788\pi\)
\(542\) −21.7518 + 37.6752i −0.934319 + 1.61829i
\(543\) 0 0
\(544\) −25.2463 43.7279i −1.08243 1.87482i
\(545\) −10.2265 17.7128i −0.438055 0.758733i
\(546\) 0 0
\(547\) 8.51716 14.7522i 0.364168 0.630757i −0.624475 0.781045i \(-0.714687\pi\)
0.988642 + 0.150288i \(0.0480202\pi\)
\(548\) −74.0559 −3.16351
\(549\) 0 0
\(550\) 11.4288 0.487328
\(551\) −7.57931 + 13.1277i −0.322889 + 0.559261i
\(552\) 0 0
\(553\) −1.32937 2.30254i −0.0565307 0.0979140i
\(554\) −28.1510 48.7590i −1.19602 2.07157i
\(555\) 0 0
\(556\) −21.0479 + 36.4560i −0.892628 + 1.54608i
\(557\) 33.7680 1.43080 0.715398 0.698717i \(-0.246245\pi\)
0.715398 + 0.698717i \(0.246245\pi\)
\(558\) 0 0
\(559\) −28.0254 −1.18535
\(560\) −5.70946 + 9.88908i −0.241269 + 0.417890i
\(561\) 0 0
\(562\) −16.5824 28.7216i −0.699487 1.21155i
\(563\) −11.3556 19.6685i −0.478583 0.828930i 0.521115 0.853486i \(-0.325516\pi\)
−0.999698 + 0.0245561i \(0.992183\pi\)
\(564\) 0 0
\(565\) −1.62552 + 2.81548i −0.0683860 + 0.118448i
\(566\) −12.3691 −0.519913
\(567\) 0 0
\(568\) −25.4466 −1.06772
\(569\) 5.43572 9.41495i 0.227877 0.394695i −0.729301 0.684193i \(-0.760155\pi\)
0.957179 + 0.289497i \(0.0934881\pi\)
\(570\) 0 0
\(571\) −7.44185 12.8897i −0.311432 0.539416i 0.667241 0.744842i \(-0.267475\pi\)
−0.978673 + 0.205426i \(0.934142\pi\)
\(572\) −15.8691 27.4861i −0.663521 1.14925i
\(573\) 0 0
\(574\) 7.81886 13.5427i 0.326353 0.565260i
\(575\) −10.2354 −0.426848
\(576\) 0 0
\(577\) −37.1163 −1.54517 −0.772586 0.634910i \(-0.781037\pi\)
−0.772586 + 0.634910i \(0.781037\pi\)
\(578\) −13.3894 + 23.1912i −0.556927 + 0.964625i
\(579\) 0 0
\(580\) −11.6275 20.1394i −0.482806 0.836245i
\(581\) −0.682844 1.18272i −0.0283291 0.0490675i
\(582\) 0 0
\(583\) −5.20969 + 9.02344i −0.215763 + 0.373713i
\(584\) −89.1536 −3.68920
\(585\) 0 0
\(586\) 70.6655 2.91917
\(587\) 7.32161 12.6814i 0.302195 0.523417i −0.674438 0.738332i \(-0.735614\pi\)
0.976633 + 0.214914i \(0.0689472\pi\)
\(588\) 0 0
\(589\) 13.3746 + 23.1655i 0.551090 + 0.954516i
\(590\) 4.95665 + 8.58517i 0.204062 + 0.353446i
\(591\) 0 0
\(592\) 33.1355 57.3924i 1.36186 2.35881i
\(593\) 36.4392 1.49638 0.748189 0.663485i \(-0.230924\pi\)
0.748189 + 0.663485i \(0.230924\pi\)
\(594\) 0 0
\(595\) −2.23081 −0.0914544
\(596\) 1.93588 3.35305i 0.0792968 0.137346i
\(597\) 0 0
\(598\) 19.5576 + 33.8747i 0.799769 + 1.38524i
\(599\) −13.7474 23.8113i −0.561705 0.972902i −0.997348 0.0727826i \(-0.976812\pi\)
0.435642 0.900120i \(-0.356521\pi\)
\(600\) 0 0
\(601\) −22.5885 + 39.1244i −0.921404 + 1.59592i −0.124159 + 0.992262i \(0.539623\pi\)
−0.797245 + 0.603656i \(0.793710\pi\)
\(602\) 12.1931 0.496952
\(603\) 0 0
\(604\) 23.0885 0.939459
\(605\) 6.12290 10.6052i 0.248931 0.431162i
\(606\) 0 0
\(607\) −8.56858 14.8412i −0.347788 0.602387i 0.638068 0.769980i \(-0.279734\pi\)
−0.985856 + 0.167593i \(0.946400\pi\)
\(608\) 54.9200 + 95.1243i 2.22730 + 3.85780i
\(609\) 0 0
\(610\) 15.4725 26.7992i 0.626464 1.08507i
\(611\) −21.2649 −0.860286
\(612\) 0 0
\(613\) −0.468761 −0.0189331 −0.00946653 0.999955i \(-0.503013\pi\)
−0.00946653 + 0.999955i \(0.503013\pi\)
\(614\) 4.45358 7.71382i 0.179732 0.311304i
\(615\) 0 0
\(616\) 4.30735 + 7.46055i 0.173548 + 0.300594i
\(617\) 1.06742 + 1.84883i 0.0429729 + 0.0744312i 0.886712 0.462323i \(-0.152984\pi\)
−0.843739 + 0.536754i \(0.819650\pi\)
\(618\) 0 0
\(619\) −4.26880 + 7.39378i −0.171578 + 0.297181i −0.938972 0.343995i \(-0.888220\pi\)
0.767394 + 0.641176i \(0.221553\pi\)
\(620\) −41.0363 −1.64806
\(621\) 0 0
\(622\) 94.1163 3.77372
\(623\) 2.80804 4.86367i 0.112502 0.194859i
\(624\) 0 0
\(625\) 4.56529 + 7.90731i 0.182612 + 0.316292i
\(626\) 14.3745 + 24.8974i 0.574520 + 0.995098i
\(627\) 0 0
\(628\) 41.2715 71.4844i 1.64691 2.85254i
\(629\) 12.9468 0.516222
\(630\) 0 0
\(631\) −11.8708 −0.472569 −0.236284 0.971684i \(-0.575930\pi\)
−0.236284 + 0.971684i \(0.575930\pi\)
\(632\) 23.8307 41.2759i 0.947933 1.64187i
\(633\) 0 0
\(634\) 20.9646 + 36.3117i 0.832609 + 1.44212i
\(635\) −1.96031 3.39536i −0.0777926 0.134741i
\(636\) 0 0
\(637\) 10.5035 18.1927i 0.416166 0.720820i
\(638\) −13.5658 −0.537076
\(639\) 0 0
\(640\) −45.0973 −1.78263
\(641\) −2.65183 + 4.59310i −0.104741 + 0.181417i −0.913632 0.406541i \(-0.866735\pi\)
0.808891 + 0.587958i \(0.200068\pi\)
\(642\) 0 0
\(643\) 0.411934 + 0.713491i 0.0162451 + 0.0281374i 0.874034 0.485865i \(-0.161495\pi\)
−0.857789 + 0.514003i \(0.828162\pi\)
\(644\) −6.18326 10.7097i −0.243655 0.422022i
\(645\) 0 0
\(646\) −20.8914 + 36.1850i −0.821961 + 1.42368i
\(647\) −40.8373 −1.60548 −0.802740 0.596329i \(-0.796626\pi\)
−0.802740 + 0.596329i \(0.796626\pi\)
\(648\) 0 0
\(649\) 4.20232 0.164955
\(650\) −9.27445 + 16.0638i −0.363774 + 0.630074i
\(651\) 0 0
\(652\) −22.5919 39.1303i −0.884767 1.53246i
\(653\) −0.534678 0.926090i −0.0209236 0.0362407i 0.855374 0.518011i \(-0.173327\pi\)
−0.876298 + 0.481770i \(0.839994\pi\)
\(654\) 0 0
\(655\) −14.3009 + 24.7699i −0.558782 + 0.967838i
\(656\) 157.514 6.14988
\(657\) 0 0
\(658\) 9.25175 0.360671
\(659\) 14.3321 24.8240i 0.558301 0.967006i −0.439337 0.898322i \(-0.644787\pi\)
0.997638 0.0686837i \(-0.0218799\pi\)
\(660\) 0 0
\(661\) 2.24786 + 3.89341i 0.0874316 + 0.151436i 0.906425 0.422367i \(-0.138801\pi\)
−0.818993 + 0.573803i \(0.805467\pi\)
\(662\) −19.7068 34.1331i −0.765925 1.32662i
\(663\) 0 0
\(664\) 12.2408 21.2017i 0.475036 0.822787i
\(665\) 4.85283 0.188185
\(666\) 0 0
\(667\) 12.1493 0.470422
\(668\) 61.5272 106.568i 2.38056 4.12325i
\(669\) 0 0
\(670\) 28.2373 + 48.9085i 1.09090 + 1.88950i
\(671\) −6.55892 11.3604i −0.253204 0.438563i
\(672\) 0 0
\(673\) −9.02929 + 15.6392i −0.348054 + 0.602846i −0.985904 0.167314i \(-0.946491\pi\)
0.637850 + 0.770161i \(0.279824\pi\)
\(674\) 55.7643 2.14796
\(675\) 0 0
\(676\) −17.6151 −0.677505
\(677\) −7.86959 + 13.6305i −0.302453 + 0.523864i −0.976691 0.214650i \(-0.931139\pi\)
0.674238 + 0.738514i \(0.264472\pi\)
\(678\) 0 0
\(679\) 1.72432 + 2.98661i 0.0661734 + 0.114616i
\(680\) −19.9950 34.6324i −0.766775 1.32809i
\(681\) 0 0
\(682\) −11.9692 + 20.7313i −0.458326 + 0.793844i
\(683\) −2.76118 −0.105654 −0.0528268 0.998604i \(-0.516823\pi\)
−0.0528268 + 0.998604i \(0.516823\pi\)
\(684\) 0 0
\(685\) −23.2916 −0.889925
\(686\) −9.30925 + 16.1241i −0.355429 + 0.615621i
\(687\) 0 0
\(688\) 61.4084 + 106.362i 2.34117 + 4.05503i
\(689\) −8.45526 14.6449i −0.322120 0.557928i
\(690\) 0 0
\(691\) 17.2628 29.9000i 0.656707 1.13745i −0.324756 0.945798i \(-0.605282\pi\)
0.981463 0.191652i \(-0.0613844\pi\)
\(692\) 13.7107 0.521204
\(693\) 0 0
\(694\) −57.3029 −2.17519
\(695\) −6.61983 + 11.4659i −0.251104 + 0.434926i
\(696\) 0 0
\(697\) 15.3860 + 26.6494i 0.582787 + 1.00942i
\(698\) −6.25678 10.8371i −0.236822 0.410189i
\(699\) 0 0
\(700\) 2.93218 5.07868i 0.110826 0.191956i
\(701\) −20.7410 −0.783378 −0.391689 0.920098i \(-0.628109\pi\)
−0.391689 + 0.920098i \(0.628109\pi\)
\(702\) 0 0
\(703\) −28.1640 −1.06222
\(704\) −22.9921 + 39.8235i −0.866548 + 1.50090i
\(705\) 0 0
\(706\) 18.4532 + 31.9618i 0.694494 + 1.20290i
\(707\) 0.933514 + 1.61689i 0.0351084 + 0.0608095i
\(708\) 0 0
\(709\) −13.8536 + 23.9951i −0.520281 + 0.901154i 0.479441 + 0.877574i \(0.340840\pi\)
−0.999722 + 0.0235795i \(0.992494\pi\)
\(710\) −12.8284 −0.481441
\(711\) 0 0
\(712\) 100.675 3.77296
\(713\) 10.7194 18.5666i 0.401445 0.695324i
\(714\) 0 0
\(715\) −4.99104 8.64474i −0.186654 0.323295i
\(716\) −23.6520 40.9665i −0.883918 1.53099i
\(717\) 0 0
\(718\) 38.2018 66.1675i 1.42568 2.46935i
\(719\) 33.1314 1.23559 0.617797 0.786337i \(-0.288025\pi\)
0.617797 + 0.786337i \(0.288025\pi\)
\(720\) 0 0
\(721\) 3.84494 0.143193
\(722\) 19.7483 34.2051i 0.734956 1.27298i
\(723\) 0 0
\(724\) −21.0351 36.4338i −0.781763 1.35405i
\(725\) 2.88067 + 4.98946i 0.106985 + 0.185304i
\(726\) 0 0
\(727\) 0.0413027 0.0715384i 0.00153183 0.00265321i −0.865258 0.501326i \(-0.832846\pi\)
0.866790 + 0.498673i \(0.166179\pi\)
\(728\) −13.9816 −0.518191
\(729\) 0 0
\(730\) −44.9449 −1.66349
\(731\) −11.9968 + 20.7791i −0.443718 + 0.768542i
\(732\) 0 0
\(733\) 15.9587 + 27.6414i 0.589450 + 1.02096i 0.994305 + 0.106576i \(0.0339887\pi\)
−0.404855 + 0.914381i \(0.632678\pi\)
\(734\) 47.1766 + 81.7123i 1.74132 + 3.01606i
\(735\) 0 0
\(736\) 44.0171 76.2399i 1.62249 2.81024i
\(737\) 23.9400 0.881842
\(738\) 0 0
\(739\) −35.7919 −1.31663 −0.658314 0.752744i \(-0.728730\pi\)
−0.658314 + 0.752744i \(0.728730\pi\)
\(740\) 21.6034 37.4181i 0.794155 1.37552i
\(741\) 0 0
\(742\) 3.67864 + 6.37160i 0.135047 + 0.233909i
\(743\) −9.88944 17.1290i −0.362808 0.628402i 0.625614 0.780133i \(-0.284849\pi\)
−0.988422 + 0.151731i \(0.951515\pi\)
\(744\) 0 0
\(745\) 0.608860 1.05458i 0.0223069 0.0386367i
\(746\) −8.27598 −0.303005
\(747\) 0 0
\(748\) −27.1723 −0.993517
\(749\) −2.69462 + 4.66722i −0.0984593 + 0.170537i
\(750\) 0 0
\(751\) −15.2903 26.4835i −0.557950 0.966398i −0.997667 0.0682617i \(-0.978255\pi\)
0.439717 0.898136i \(-0.355079\pi\)
\(752\) 46.5950 + 80.7048i 1.69914 + 2.94300i
\(753\) 0 0
\(754\) 11.0086 19.0674i 0.400909 0.694395i
\(755\) 7.26165 0.264278
\(756\) 0 0
\(757\) 25.4129 0.923647 0.461824 0.886972i \(-0.347195\pi\)
0.461824 + 0.886972i \(0.347195\pi\)
\(758\) −10.3835 + 17.9847i −0.377144 + 0.653233i
\(759\) 0 0
\(760\) 43.4965 + 75.3382i 1.57778 + 2.73280i
\(761\) −23.4090 40.5456i −0.848575 1.46978i −0.882480 0.470350i \(-0.844128\pi\)
0.0339049 0.999425i \(-0.489206\pi\)
\(762\) 0 0
\(763\) −3.06107 + 5.30194i −0.110818 + 0.191943i
\(764\) 84.5322 3.05827
\(765\) 0 0
\(766\) 28.0297 1.01275
\(767\) −3.41016 + 5.90657i −0.123134 + 0.213274i
\(768\) 0 0
\(769\) −7.28271 12.6140i −0.262621 0.454873i 0.704316 0.709886i \(-0.251254\pi\)
−0.966938 + 0.255013i \(0.917920\pi\)
\(770\) 2.17146 + 3.76108i 0.0782540 + 0.135540i
\(771\) 0 0
\(772\) 12.1895 21.1128i 0.438710 0.759867i
\(773\) −24.3533 −0.875929 −0.437964 0.898992i \(-0.644300\pi\)
−0.437964 + 0.898992i \(0.644300\pi\)
\(774\) 0 0
\(775\) 10.1666 0.365194
\(776\) −30.9106 + 53.5387i −1.10963 + 1.92193i
\(777\) 0 0
\(778\) 0.577465 + 1.00020i 0.0207031 + 0.0358589i
\(779\) −33.4702 57.9722i −1.19920 2.07707i
\(780\) 0 0
\(781\) −2.71902 + 4.70948i −0.0972943 + 0.168519i
\(782\) 33.4879 1.19753
\(783\) 0 0
\(784\) −92.0601 −3.28786
\(785\) 12.9804 22.4828i 0.463292 0.802445i
\(786\) 0 0
\(787\) 13.7836 + 23.8739i 0.491332 + 0.851012i 0.999950 0.00998024i \(-0.00317686\pi\)
−0.508618 + 0.860992i \(0.669844\pi\)
\(788\) 7.96056 + 13.7881i 0.283583 + 0.491181i
\(789\) 0 0
\(790\) 12.0137 20.8084i 0.427429 0.740329i
\(791\) 0.973124 0.0346003
\(792\) 0 0
\(793\) 21.2901 0.756034
\(794\) −36.6388 + 63.4603i −1.30026 + 2.25212i
\(795\) 0 0
\(796\) −39.5839 68.5613i −1.40301 2.43009i
\(797\) −3.30846 5.73042i −0.117192 0.202982i 0.801462 0.598046i \(-0.204056\pi\)
−0.918654 + 0.395064i \(0.870722\pi\)
\(798\) 0 0
\(799\) −9.10284 + 15.7666i −0.322035 + 0.557781i
\(800\) 41.7469 1.47598
\(801\) 0 0
\(802\) 79.4220 2.80449
\(803\) −9.52624 + 16.4999i −0.336174 + 0.582270i
\(804\) 0 0
\(805\) −1.94472 3.36835i −0.0685422 0.118719i
\(806\) −19.4260 33.6467i −0.684250 1.18516i
\(807\) 0 0
\(808\) −16.7344 + 28.9848i −0.588714 + 1.01968i
\(809\) 8.61362 0.302839 0.151419 0.988470i \(-0.451616\pi\)
0.151419 + 0.988470i \(0.451616\pi\)
\(810\) 0 0
\(811\) −9.58716 −0.336651 −0.168325 0.985732i \(-0.553836\pi\)
−0.168325 + 0.985732i \(0.553836\pi\)
\(812\) −3.48044 + 6.02830i −0.122139 + 0.211552i
\(813\) 0 0
\(814\) −12.6023 21.8278i −0.441711 0.765065i
\(815\) −7.10545 12.3070i −0.248893 0.431095i
\(816\) 0 0
\(817\) 26.0974 45.2021i 0.913034 1.58142i
\(818\) 54.5988 1.90900
\(819\) 0 0
\(820\) 102.694 3.58624
\(821\) −6.93174 + 12.0061i −0.241919 + 0.419016i −0.961261 0.275640i \(-0.911110\pi\)
0.719342 + 0.694656i \(0.244444\pi\)
\(822\) 0 0
\(823\) −23.9129 41.4183i −0.833550 1.44375i −0.895205 0.445654i \(-0.852971\pi\)
0.0616554 0.998097i \(-0.480362\pi\)
\(824\) 34.4626 + 59.6911i 1.20056 + 2.07944i
\(825\) 0 0
\(826\) 1.48366 2.56978i 0.0516232 0.0894141i
\(827\) 42.4417 1.47584 0.737921 0.674887i \(-0.235808\pi\)
0.737921 + 0.674887i \(0.235808\pi\)
\(828\) 0 0
\(829\) 26.0037 0.903146 0.451573 0.892234i \(-0.350863\pi\)
0.451573 + 0.892234i \(0.350863\pi\)
\(830\) 6.17095 10.6884i 0.214197 0.371000i
\(831\) 0 0
\(832\) −37.3159 64.6331i −1.29370 2.24075i
\(833\) −8.99248 15.5754i −0.311571 0.539657i
\(834\) 0 0
\(835\) 19.3511 33.5171i 0.669673 1.15991i
\(836\) 59.1096 2.04435
\(837\) 0 0
\(838\) 65.9233 2.27728
\(839\) 0.628138 1.08797i 0.0216857 0.0375608i −0.854979 0.518663i \(-0.826430\pi\)
0.876665 + 0.481102i \(0.159763\pi\)
\(840\) 0 0
\(841\) 11.0807 + 19.1923i 0.382093 + 0.661805i
\(842\) −35.4019 61.3179i −1.22003 2.11315i
\(843\) 0 0
\(844\) −36.8998 + 63.9124i −1.27014 + 2.19995i
\(845\) −5.54019 −0.190588
\(846\) 0 0
\(847\) −3.66551 −0.125948
\(848\) −37.0538 + 64.1791i −1.27243 + 2.20392i
\(849\) 0 0
\(850\) 7.94020 + 13.7528i 0.272347 + 0.471718i
\(851\) 11.2864 + 19.5486i 0.386892 + 0.670117i
\(852\) 0 0
\(853\) −0.727173 + 1.25950i −0.0248979 + 0.0431245i −0.878206 0.478283i \(-0.841259\pi\)
0.853308 + 0.521407i \(0.174593\pi\)
\(854\) −9.26272 −0.316964
\(855\) 0 0
\(856\) −96.6089 −3.30202
\(857\) −26.1548 + 45.3015i −0.893432 + 1.54747i −0.0576998 + 0.998334i \(0.518377\pi\)
−0.835733 + 0.549136i \(0.814957\pi\)
\(858\) 0 0
\(859\) 10.5022 + 18.1903i 0.358329 + 0.620645i 0.987682 0.156475i \(-0.0500132\pi\)
−0.629353 + 0.777120i \(0.716680\pi\)
\(860\) 40.0364 + 69.3451i 1.36523 + 2.36465i
\(861\) 0 0
\(862\) −43.1708 + 74.7741i −1.47040 + 2.54682i
\(863\) −12.9813 −0.441890 −0.220945 0.975286i \(-0.570914\pi\)
−0.220945 + 0.975286i \(0.570914\pi\)
\(864\) 0 0
\(865\) 4.31221 0.146619
\(866\) 0.0166469 0.0288334i 0.000565686 0.000979797i
\(867\) 0 0
\(868\) 6.14165 + 10.6376i 0.208461 + 0.361065i
\(869\) −5.09270 8.82082i −0.172758 0.299226i
\(870\) 0 0
\(871\) −19.4272 + 33.6489i −0.658265 + 1.14015i
\(872\) −109.747 −3.71650
\(873\) 0 0
\(874\) −72.8485 −2.46414
\(875\) 3.01516 5.22241i 0.101931 0.176550i
\(876\) 0 0
\(877\) −15.5228 26.8863i −0.524169 0.907887i −0.999604 0.0281364i \(-0.991043\pi\)
0.475435 0.879751i \(-0.342291\pi\)
\(878\) 7.17492 + 12.4273i 0.242142 + 0.419402i
\(879\) 0 0
\(880\) −21.8724 + 37.8841i −0.737319 + 1.27707i
\(881\) −19.2957 −0.650087 −0.325044 0.945699i \(-0.605379\pi\)
−0.325044 + 0.945699i \(0.605379\pi\)
\(882\) 0 0
\(883\) −9.82388 −0.330600 −0.165300 0.986243i \(-0.552859\pi\)
−0.165300 + 0.986243i \(0.552859\pi\)
\(884\) 22.0501 38.1920i 0.741627 1.28453i
\(885\) 0 0
\(886\) −55.0431 95.3375i −1.84921 3.20293i
\(887\) 22.0566 + 38.2032i 0.740590 + 1.28274i 0.952227 + 0.305391i \(0.0987870\pi\)
−0.211638 + 0.977348i \(0.567880\pi\)
\(888\) 0 0
\(889\) −0.586776 + 1.01633i −0.0196798 + 0.0340865i
\(890\) 50.7533 1.70125
\(891\) 0 0
\(892\) −36.2219 −1.21280
\(893\) 19.8020 34.2981i 0.662649 1.14774i
\(894\) 0 0
\(895\) −7.43888 12.8845i −0.248654 0.430682i
\(896\) 6.74943 + 11.6904i 0.225483 + 0.390548i
\(897\) 0 0
\(898\) −20.8669 + 36.1425i −0.696338 + 1.20609i
\(899\) −12.0675 −0.402474
\(900\) 0 0
\(901\) −14.4777 −0.482323
\(902\) 29.9533 51.8807i 0.997337 1.72744i
\(903\) 0 0
\(904\) 8.72222 + 15.1073i 0.290097 + 0.502463i
\(905\) −6.61581 11.4589i −0.219917 0.380908i
\(906\) 0 0
\(907\) 21.2062 36.7302i 0.704140 1.21961i −0.262861 0.964834i \(-0.584666\pi\)
0.967001 0.254773i \(-0.0820006\pi\)
\(908\) 51.7957 1.71890
\(909\) 0 0
\(910\) −7.04851 −0.233656
\(911\) 18.3552 31.7921i 0.608134 1.05332i −0.383414 0.923577i \(-0.625252\pi\)
0.991548 0.129743i \(-0.0414151\pi\)
\(912\) 0 0
\(913\) −2.61591 4.53089i −0.0865740 0.149951i
\(914\) 3.23086 + 5.59601i 0.106867 + 0.185100i
\(915\) 0 0
\(916\) 37.3409 64.6763i 1.23378 2.13696i
\(917\) 8.56130 0.282719
\(918\) 0 0
\(919\) −14.0589 −0.463761 −0.231881 0.972744i \(-0.574488\pi\)
−0.231881 + 0.972744i \(0.574488\pi\)
\(920\) 34.8615 60.3818i 1.14935 1.99073i
\(921\) 0 0
\(922\) −43.9355 76.0985i −1.44694 2.50617i
\(923\) −4.41294 7.64344i −0.145254 0.251587i
\(924\) 0 0
\(925\) −5.35214 + 9.27018i −0.175977 + 0.304802i
\(926\) −91.6436 −3.01160
\(927\) 0 0
\(928\) −49.5528 −1.62665
\(929\) −9.25875 + 16.0366i −0.303770 + 0.526144i −0.976987 0.213301i \(-0.931579\pi\)
0.673217 + 0.739445i \(0.264912\pi\)
\(930\) 0 0
\(931\) 19.5619 + 33.8823i 0.641116 + 1.11045i
\(932\) 14.1531 + 24.5139i 0.463600 + 0.802978i
\(933\) 0 0
\(934\) 18.6686 32.3349i 0.610854 1.05803i
\(935\) −8.54604 −0.279485
\(936\) 0 0
\(937\) 4.46818 0.145969 0.0729845 0.997333i \(-0.476748\pi\)
0.0729845 + 0.997333i \(0.476748\pi\)
\(938\) 8.45222 14.6397i 0.275975 0.478002i
\(939\) 0 0
\(940\) 30.3785 + 52.6171i 0.990838 + 1.71618i
\(941\) −1.00193 1.73539i −0.0326620 0.0565722i 0.849232 0.528019i \(-0.177065\pi\)
−0.881894 + 0.471447i \(0.843732\pi\)
\(942\) 0 0
\(943\) −26.8256 + 46.4633i −0.873562 + 1.51305i
\(944\) 29.8889 0.972801
\(945\) 0 0
\(946\) 46.7105 1.51869
\(947\) −6.29191 + 10.8979i −0.204460 + 0.354134i −0.949960 0.312370i \(-0.898877\pi\)
0.745501 + 0.666505i \(0.232210\pi\)
\(948\) 0 0
\(949\) −15.4610 26.7792i −0.501885 0.869290i
\(950\) −17.2728 29.9174i −0.560405 0.970650i
\(951\) 0 0
\(952\) −5.98507 + 10.3664i −0.193977 + 0.335978i
\(953\) 19.9641 0.646700 0.323350 0.946279i \(-0.395191\pi\)
0.323350 + 0.946279i \(0.395191\pi\)
\(954\) 0 0
\(955\) 26.5865 0.860318
\(956\) 47.2542 81.8467i 1.52831 2.64711i
\(957\) 0 0
\(958\) −7.96793 13.8009i −0.257432 0.445885i
\(959\) 3.48591 + 6.03777i 0.112566 + 0.194970i
\(960\) 0 0
\(961\) 4.85272 8.40515i 0.156539 0.271134i
\(962\) 40.9068 1.31889
\(963\) 0 0
\(964\) −10.6709 −0.343686
\(965\) 3.83376 6.64026i 0.123413 0.213758i
\(966\) 0 0
\(967\) 16.1043 + 27.8934i 0.517879 + 0.896993i 0.999784 + 0.0207695i \(0.00661162\pi\)
−0.481905 + 0.876223i \(0.660055\pi\)
\(968\) −32.8544 56.9055i −1.05598 1.82901i
\(969\) 0 0
\(970\) −15.5829 + 26.9904i −0.500338 + 0.866610i
\(971\) 6.62934 0.212746 0.106373 0.994326i \(-0.466076\pi\)
0.106373 + 0.994326i \(0.466076\pi\)
\(972\) 0 0
\(973\) 3.96300 0.127048
\(974\) 39.2639 68.0071i 1.25810 2.17909i
\(975\) 0 0
\(976\) −46.6502 80.8005i −1.49324 2.58636i
\(977\) 5.92832 + 10.2682i 0.189664 + 0.328507i 0.945138 0.326671i \(-0.105927\pi\)
−0.755474 + 0.655178i \(0.772594\pi\)
\(978\) 0 0
\(979\) 10.7573 18.6323i 0.343806 0.595490i
\(980\) −60.0205 −1.91728
\(981\) 0 0
\(982\) 11.8577 0.378394
\(983\) −26.0325 + 45.0896i −0.830308 + 1.43814i 0.0674866 + 0.997720i \(0.478502\pi\)
−0.897794 + 0.440415i \(0.854831\pi\)
\(984\) 0 0
\(985\) 2.50370 + 4.33654i 0.0797746 + 0.138174i
\(986\) −9.42486 16.3243i −0.300149 0.519873i
\(987\) 0 0
\(988\) −47.9671 + 83.0815i −1.52604 + 2.64317i
\(989\) −41.8330 −1.33021
\(990\) 0 0
\(991\) 1.47115 0.0467326 0.0233663 0.999727i \(-0.492562\pi\)
0.0233663 + 0.999727i \(0.492562\pi\)
\(992\) −43.7209 + 75.7268i −1.38814 + 2.40433i
\(993\) 0 0
\(994\) 1.91995 + 3.32544i 0.0608970 + 0.105477i
\(995\) −12.4496 21.5634i −0.394680 0.683606i
\(996\) 0 0
\(997\) 13.2106 22.8815i 0.418385 0.724665i −0.577392 0.816467i \(-0.695930\pi\)
0.995777 + 0.0918025i \(0.0292628\pi\)
\(998\) −95.6065 −3.02637
\(999\) 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.c.d.487.6 12
3.2 odd 2 729.2.c.a.487.1 12
9.2 odd 6 729.2.a.e.1.6 yes 6
9.4 even 3 inner 729.2.c.d.244.6 12
9.5 odd 6 729.2.c.a.244.1 12
9.7 even 3 729.2.a.b.1.1 6
27.2 odd 18 729.2.e.u.325.2 12
27.4 even 9 729.2.e.t.163.2 12
27.5 odd 18 729.2.e.u.406.2 12
27.7 even 9 729.2.e.s.82.1 12
27.11 odd 18 729.2.e.k.568.1 12
27.13 even 9 729.2.e.s.649.1 12
27.14 odd 18 729.2.e.l.649.2 12
27.16 even 9 729.2.e.t.568.2 12
27.20 odd 18 729.2.e.l.82.2 12
27.22 even 9 729.2.e.j.406.1 12
27.23 odd 18 729.2.e.k.163.1 12
27.25 even 9 729.2.e.j.325.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.1 6 9.7 even 3
729.2.a.e.1.6 yes 6 9.2 odd 6
729.2.c.a.244.1 12 9.5 odd 6
729.2.c.a.487.1 12 3.2 odd 2
729.2.c.d.244.6 12 9.4 even 3 inner
729.2.c.d.487.6 12 1.1 even 1 trivial
729.2.e.j.325.1 12 27.25 even 9
729.2.e.j.406.1 12 27.22 even 9
729.2.e.k.163.1 12 27.23 odd 18
729.2.e.k.568.1 12 27.11 odd 18
729.2.e.l.82.2 12 27.20 odd 18
729.2.e.l.649.2 12 27.14 odd 18
729.2.e.s.82.1 12 27.7 even 9
729.2.e.s.649.1 12 27.13 even 9
729.2.e.t.163.2 12 27.4 even 9
729.2.e.t.568.2 12 27.16 even 9
729.2.e.u.325.2 12 27.2 odd 18
729.2.e.u.406.2 12 27.5 odd 18